From 7ca589a654e8f09e8b263f9398db7a8053eb12f9 Mon Sep 17 00:00:00 2001 From: Morten Hjorth-Jensen Date: Wed, 8 Dec 2021 06:59:22 +0100 Subject: [PATCH] buidl --- .../_build/.doctrees/chapter10.doctree | Bin 433265 -> 432674 bytes .../_build/.doctrees/chapter11.doctree | Bin 293180 -> 578260 bytes .../_build/.doctrees/chapter12.doctree | Bin 0 -> 193999 bytes .../_build/.doctrees/chapter13.doctree | Bin 0 -> 200762 bytes .../.doctrees/chapteroptimization.doctree | Bin 578606 -> 597011 bytes .../_build/.doctrees/clustering.doctree | Bin 0 -> 381090 bytes .../_build/.doctrees/environment.pickle | Bin 184041 -> 200875 bytes .../_build/.doctrees/intro.doctree | Bin 50592 -> 50655 bytes .../_build/html/_images/chapter10_39_1.png | Bin 0 -> 2976 bytes .../_build/html/_images/chapter10_59_1.png | Bin 0 -> 22294 bytes .../_build/html/_images/chapter10_59_2.png | Bin 0 -> 28628 bytes .../_build/html/_images/chapter10_63_0.png | Bin 0 -> 26114 bytes .../_build/html/_images/chapter10_63_1.png | Bin 0 -> 28453 bytes .../_build/html/_images/chapter11_50_2.png | Bin 0 -> 23393 bytes .../_build/html/_images/chapter11_52_3.png | Bin 0 -> 23850 bytes .../_build/html/_images/chapter11_58_3.png | Bin 0 -> 29238 bytes .../_build/html/_images/chapter11_66_3.png | Bin 0 -> 29238 bytes .../_build/html/_images/chapter11_66_4.png | Bin 0 -> 34711 bytes .../_build/html/_images/chapter11_79_3.png | Bin 0 -> 27834 bytes .../_build/html/_images/chapter11_91_3.png | Bin 0 -> 27834 bytes .../_build/html/_images/chapter11_91_4.png | Bin 0 -> 27519 bytes .../_build/html/_images/chapter12_35_0.png | Bin 0 -> 7811 bytes .../_build/html/_images/chapter12_51_0.png | Bin 0 -> 9850 bytes .../_build/html/_images/chapter12_67_1.png | Bin 0 -> 2976 bytes .../_build/html/_images/chapter13_3_0.png | Bin 0 -> 19939 bytes .../_build/html/_images/chapter13_3_192.png | Bin 0 -> 3541 bytes .../_images/chapteroptimization_123_1.png | Bin 0 -> 11310 bytes .../_images/chapteroptimization_132_1.png | Bin 0 -> 10420 bytes .../_images/chapteroptimization_148_1.png | Bin 0 -> 11347 bytes .../_images/chapteroptimization_188_0.png | Bin 0 -> 17433 bytes .../html/_images/chapteroptimization_61_2.png | Bin 0 -> 48442 bytes .../html/_images/chapteroptimization_63_0.png | Bin 0 -> 27781 bytes .../html/_images/chapteroptimization_69_1.png | Bin 0 -> 101313 bytes .../_build/html/_images/clustering_17_0.png | Bin 0 -> 79050 bytes .../_build/html/_images/clustering_20_0.png | Bin 0 -> 82072 bytes .../_build/html/_images/clustering_24_0.png | Bin 0 -> 79456 bytes .../_build/html/_sources/chapter10.ipynb | 583 ++- .../_build/html/_sources/chapter11.ipynb | 704 +++- .../_build/html/_sources/chapter12.ipynb | 1577 ++++++++ .../_build/html/_sources/chapter13.ipynb | 1873 ++++++++++ .../html/_sources/chapteroptimization.ipynb | 1501 ++++++-- .../_build/html/_sources/clustering.ipynb | 649 ++++ doc/LectureNotes/_build/html/chapter10.html | 303 +- doc/LectureNotes/_build/html/chapter11.html | 454 ++- doc/LectureNotes/_build/html/chapter12.html | 1509 ++++++++ doc/LectureNotes/_build/html/chapter13.html | 2386 ++++++++++++ doc/LectureNotes/_build/html/chapter9.html | 91 +- .../_build/html/chapteroptimization.html | 500 ++- doc/LectureNotes/_build/html/clustering.html | 828 +++++ doc/LectureNotes/_build/html/genindex.html | 21 +- doc/LectureNotes/_build/html/intro.html | 21 +- doc/LectureNotes/_build/html/objects.inv | Bin 786 -> 849 bytes doc/LectureNotes/_build/html/search.html | 21 +- doc/LectureNotes/_build/html/searchindex.js | 2 +- .../_build/jupyter_execute/chapter10.ipynb | 691 ++-- .../_build/jupyter_execute/chapter10.py | 113 +- .../_build/jupyter_execute/chapter10_39_1.png | Bin 0 -> 2976 bytes .../_build/jupyter_execute/chapter10_59_1.png | Bin 0 -> 22294 bytes .../_build/jupyter_execute/chapter10_59_2.png | Bin 0 -> 28628 bytes .../_build/jupyter_execute/chapter10_63_0.png | Bin 0 -> 26114 bytes .../_build/jupyter_execute/chapter10_63_1.png | Bin 0 -> 28453 bytes .../_build/jupyter_execute/chapter11.ipynb | 991 ++++- .../_build/jupyter_execute/chapter11.py | 70 +- .../_build/jupyter_execute/chapter11_50_2.png | Bin 0 -> 23393 bytes .../_build/jupyter_execute/chapter11_52_3.png | Bin 0 -> 23850 bytes .../_build/jupyter_execute/chapter11_58_3.png | Bin 0 -> 29238 bytes .../_build/jupyter_execute/chapter11_66_3.png | Bin 0 -> 29238 bytes .../_build/jupyter_execute/chapter11_66_4.png | Bin 0 -> 34711 bytes .../_build/jupyter_execute/chapter11_79_3.png | Bin 0 -> 27834 bytes .../_build/jupyter_execute/chapter11_91_3.png | Bin 0 -> 27834 bytes .../_build/jupyter_execute/chapter11_91_4.png | Bin 0 -> 27519 bytes .../_build/jupyter_execute/chapter12.ipynb | 1942 ++++++++++ .../_build/jupyter_execute/chapter12.py | 921 +++++ .../_build/jupyter_execute/chapter12_35_0.png | Bin 0 -> 7811 bytes .../_build/jupyter_execute/chapter12_51_0.png | Bin 0 -> 9850 bytes .../_build/jupyter_execute/chapter12_67_1.png | Bin 0 -> 2976 bytes .../_build/jupyter_execute/chapter13.ipynb | 3294 +++++++++++++++++ .../_build/jupyter_execute/chapter13.py | 1306 +++++++ .../_build/jupyter_execute/chapter13_3_0.png | Bin 0 -> 19939 bytes .../jupyter_execute/chapter13_3_192.png | Bin 0 -> 3541 bytes .../jupyter_execute/chapteroptimization.ipynb | 1607 ++++++-- .../jupyter_execute/chapteroptimization.py | 424 ++- .../chapteroptimization_123_1.png | Bin 0 -> 11310 bytes .../chapteroptimization_132_1.png | Bin 0 -> 10420 bytes .../chapteroptimization_148_1.png | Bin 0 -> 11347 bytes .../chapteroptimization_188_0.png | Bin 0 -> 17433 bytes .../chapteroptimization_61_2.png | Bin 0 -> 48442 bytes .../chapteroptimization_63_0.png | Bin 0 -> 27781 bytes .../chapteroptimization_69_1.png | Bin 0 -> 101313 bytes .../_build/jupyter_execute/clustering.ipynb | 718 ++++ .../_build/jupyter_execute/clustering.py | 443 +++ .../jupyter_execute/clustering_17_0.png | Bin 0 -> 79050 bytes .../jupyter_execute/clustering_20_0.png | Bin 0 -> 82072 bytes .../jupyter_execute/clustering_24_0.png | Bin 0 -> 79456 bytes 94 files changed, 23333 insertions(+), 2210 deletions(-) create mode 100644 doc/LectureNotes/_build/.doctrees/chapter12.doctree create mode 100644 doc/LectureNotes/_build/.doctrees/chapter13.doctree create mode 100644 doc/LectureNotes/_build/.doctrees/clustering.doctree create mode 100644 doc/LectureNotes/_build/html/_images/chapter10_39_1.png create mode 100644 doc/LectureNotes/_build/html/_images/chapter10_59_1.png create mode 100644 doc/LectureNotes/_build/html/_images/chapter10_59_2.png create mode 100644 doc/LectureNotes/_build/html/_images/chapter10_63_0.png create mode 100644 doc/LectureNotes/_build/html/_images/chapter10_63_1.png create mode 100644 doc/LectureNotes/_build/html/_images/chapter11_50_2.png create mode 100644 doc/LectureNotes/_build/html/_images/chapter11_52_3.png create mode 100644 doc/LectureNotes/_build/html/_images/chapter11_58_3.png create mode 100644 doc/LectureNotes/_build/html/_images/chapter11_66_3.png create mode 100644 doc/LectureNotes/_build/html/_images/chapter11_66_4.png create mode 100644 doc/LectureNotes/_build/html/_images/chapter11_79_3.png create mode 100644 doc/LectureNotes/_build/html/_images/chapter11_91_3.png create mode 100644 doc/LectureNotes/_build/html/_images/chapter11_91_4.png create mode 100644 doc/LectureNotes/_build/html/_images/chapter12_35_0.png create mode 100644 doc/LectureNotes/_build/html/_images/chapter12_51_0.png create mode 100644 doc/LectureNotes/_build/html/_images/chapter12_67_1.png create mode 100644 doc/LectureNotes/_build/html/_images/chapter13_3_0.png create mode 100644 doc/LectureNotes/_build/html/_images/chapter13_3_192.png create mode 100644 doc/LectureNotes/_build/html/_images/chapteroptimization_123_1.png create mode 100644 doc/LectureNotes/_build/html/_images/chapteroptimization_132_1.png create mode 100644 doc/LectureNotes/_build/html/_images/chapteroptimization_148_1.png create mode 100644 doc/LectureNotes/_build/html/_images/chapteroptimization_188_0.png create mode 100644 doc/LectureNotes/_build/html/_images/chapteroptimization_61_2.png create mode 100644 doc/LectureNotes/_build/html/_images/chapteroptimization_63_0.png create mode 100644 doc/LectureNotes/_build/html/_images/chapteroptimization_69_1.png create mode 100644 doc/LectureNotes/_build/html/_images/clustering_17_0.png create mode 100644 doc/LectureNotes/_build/html/_images/clustering_20_0.png create mode 100644 doc/LectureNotes/_build/html/_images/clustering_24_0.png create mode 100644 doc/LectureNotes/_build/html/_sources/chapter12.ipynb create mode 100644 doc/LectureNotes/_build/html/_sources/chapter13.ipynb create mode 100644 doc/LectureNotes/_build/html/_sources/clustering.ipynb create mode 100644 doc/LectureNotes/_build/html/chapter12.html create mode 100644 doc/LectureNotes/_build/html/chapter13.html create mode 100644 doc/LectureNotes/_build/html/clustering.html create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter10_39_1.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter10_59_1.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter10_59_2.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter10_63_0.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter10_63_1.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter11_50_2.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter11_52_3.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter11_58_3.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter11_66_3.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter11_66_4.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter11_79_3.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter11_91_3.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter11_91_4.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter12.ipynb create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter12.py create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter12_35_0.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter12_51_0.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter12_67_1.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter13.ipynb create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter13.py create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter13_3_0.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapter13_3_192.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapteroptimization_123_1.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapteroptimization_132_1.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapteroptimization_148_1.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapteroptimization_188_0.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapteroptimization_61_2.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapteroptimization_63_0.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/chapteroptimization_69_1.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/clustering.ipynb create mode 100644 doc/LectureNotes/_build/jupyter_execute/clustering.py create mode 100644 doc/LectureNotes/_build/jupyter_execute/clustering_17_0.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/clustering_20_0.png create mode 100644 doc/LectureNotes/_build/jupyter_execute/clustering_24_0.png diff --git a/doc/LectureNotes/_build/.doctrees/chapter10.doctree b/doc/LectureNotes/_build/.doctrees/chapter10.doctree index 29cd6c4a62c47bcba0ccf3311b87a2d7e1e436b7..89cd2d5cdbc0b8b923d5933a494f114458671ef4 100644 GIT binary patch delta 90692 zcmd6Q2YeL8{tJWs3t6fu@bO|8a7m+Y3y zofUE zyl+1!$N+GzjzpGGz_J+l-x>aQf&X0>)mFQDxYAuIQ{r=6Nv>q5oqF^Ml!H)&+SU&BdKJsY-^ zU84k43;i-`BrqyLXOzb8tfLRf_Y;PdG%aZ1a8>IJQ{QizFh9aAC#Cm_>ys?7ZLMAn z`08IgR|3=&29e=|-RtaD#Ufd3BD!S695|)F~ zW*u$UI*pi0cAJz4hwDe9BwRJ>nl`aewyRBN0QIM_EUyo z^$`Tl{)o=Y97+VbwnCjfRVDh7bnH4?CC(cRT?(Y-S*s51`k>79Ye;T3tcX2?NFN949Ke0afwi}D=u=HLuqF$2^6F$5u|p? z#2a&Un5<`_lI~9Gh1gDNT-Ow^0#?9uKxvC}m!ghE5fILoRaSE6rhNxV^=M37n&I!4 zqV}Vk#VxHa&95pdE3E|xB2pHizC|5%NqkpzZhTJ*s=&6l$M*zo?v9UD&&9W>aVVoh zp~3}WuTOTOGy|95ixmOQnfAMz49%;E!{7Bq%>bPvYaMeP%G{t)(I;oF1WmtO;a=bj zqgZJ|iCUPja&V~ZG<4zUK5LS>c|dPq zGBF{?pt`?Xu9@R%z+>z?}HVLc{c_hA&S4(~C^8uYC_q5E%(Nx7&-{Vr*qJ;FU6|51WwgDyW13dU5IcXCc0(Hc|N5Ee&GKJzBufzxKb=>8TB(&aOVH>L9F5gKOEz61p9 z+1lFyW-g);*vt*=)^(7m;P<^h?-}8?PgrUsmwp9mM+$hu=(cD;6!@>$K9PXM1fe*v z+TF(0j`dCb=DI#{AawQT$IHGAW2DsIf`<* zsZo#tKN+Fs^mD*W!z2@nnTENJx~pF=OM$BI^^2;Ba5r1%a#mfjdQGl~|KUc#AJBJO z#BCa$&3Tf!IsULO>Ik;w3Duqo8oG~AjdQ{fXSEwJz?v7jSx<2&Zw3vTq|wP};=`=n zZE#w96r=t;pq+m;x|%@L)JW9nFB=6Lsz%2Lrr_SgAv$|vU<$Y|&Y>Vv9!5I36NMRD z|IDKxxRIH+tL{N9VAf^}^Ebt`nzjA&T73q^dj|LX-$9$8=jR6xQ=c3>4n)@$dN$57 zU4q)g2<5(AvJbW401Rq#WXNz3ATQF^MfBK2`JMzIngGS%q<7FLF?G7{fX)mCvziKU z#n24!1MD|_n6U5z<~r)TL(@U%VnN`M(|`>Z4G4YCunG{3b6B3*b2t(Dw17hIAxzbu zd`+j5_w33_R)>t3E>Ui(dxuX@2aT8sh%X6=jU?=RxgNP(AHERQxn23{?(xK{B~Q2+bni6fk1q8AZ+_uy;1g@RRMnM55IE84@)ygq-Y_b~8{Q=aI>?ft)r|rUNN0pm*OXQ7akD z=x5O@DEU)UHiSjEThCIT7#pR!a@xX>)rp{PNQ}ZH;)a|UfW1E_8vI&!q1cxuc#Mlg z8+n)Nuvy=96483Aw-+6RConoi>J;R2Qhd$q5E&`}%w=(D%2 zjuTo2rmuk0=K+KM;GZXmfp)`_H$O@m2MaP?OPiSq`ehc4dil(Fkld{^y8_i~8wVbMYc?x3bf&9~ z2L8iYN$Oj(GOQ_%ogJAU;cmJT=BCOT5WF|f?`$+AcFu>NtW4@)5gnTAsI_yFKv~3sz|O;9tlW8kdu=jz0;u5hxnsb+z6%8Vcdz0| zQ2{e~enhXQ}wMa^jW8t#zSp|mVtfjKY!M7 z@_=QVT=p!eXb>vh8;;6M&D|T*2Fmjup_+JPq1_gBx~q52@2)mm*f$Vu!zMGWvKPa% zH=9Q`oHoYh6ANR(+(b+Ro0~yyUgnmvs1$T*=OP6(bUvWz-`qqEy)QP*%G}h##rvSw zmbtTlZAAj{#t5Lw5CM>9Z?;tkEdy)klVfyzJYX5yKFzK5kBa03_p8fL`{s?#H4Q_j zg~9zMs%IDXPx=m|s2TFyRKwcS2$ciL1}67H}BRYL9|m65VsE&MQbAXxMey6Pg-khlY8-c@C;R zR*(Rk_^_aB_H!OIpY_WQKL5PqOTv#^9g?G>x@~Nf!Ae?z!Al#tV zRx#uULiND9{2z`AgGHnDHm>$+6BqFU?C0Pkc0-?pJT})<%Uvg7_VGZt`j;zS-Q!Yw zd29a9loh^EwwmVHU>2#3!yFLsGFM3l!E9Ahr!{Lr^`{B>W0>Ul0^$)7(Vw=>By-m= z*0x+e4Z2>ud@^W%2k134PZpnU(JLU_qIekeIKJnXz{Q74X95>nmTdqo&K3Az;G(@~n4%A(D_h6TvU!ihOnD>Itx(&1mh;d{^HFP$2Vcs#GO|e%u#wr%QRKhqT7Njh|Ae93b^l zCK_7qr!Aw1ekcdwnT600CzFhFmfEvA74R&7Ev4oKQq`fHqAmDw2mk6wsCRKhpVb-% ziKwCF{#d=KHKK8sWx(c$znrK$o|=ckYd-Rz`(eoFDjeMpbeMjrWPCNW42W)*m0f_Z zBUW~*`L74jUqVK-m?QdQXownG20|2{=xG}Wn5M7lR};~cYCvo9C#1ovlw;aLYaFBo z7+MCxR7I;N0ish@!+9+aqKP3RTFw#e78;_4miy=E(qOL5a&S`aBK5q?k@y@>c;d2% z@4S2lEH8`#6a(;)99x=L@q_NvM$#s5#-P&`Yiz)+o7WtM{hc$6j8f-c39bpBIAkZe zn?=T=Ks$AmOG$0ms>%Vfu1OH*lD$VZR>mSZ({{=Z;BU;8)KxX9YFW)d6XFll^dN{g zwUKP+Il$;4OXR!=#*}7=hPldhf))&CGPL8+F z1965roHq64^-n{(($w6@*ZB_RM9^4=!qzcE>QzWC}s-??L0FGrQlFn9hXI0I)R3* zX+*T$?0hL(erCr@4VvTe_Zmahu&o^cljyCnfXTMT#RSfX8+08ugA;+7MXTvYSGF;i zX8)Px&_oS8SKVw|(v90PVDRFlz6UQ}M^~{LwRl@!pmxu;450SDP^k55*;Yw?4&H;J z;QLa9gX?4pW-u);=Xb@8Es68nsQv=Z@05VGm35ixs1Mgp1Why*7)Nb5OY)x3xo>CZ zV^HD%bf&|`;_ZssVS5z}2)x*mDHc4riaS%z6G#iaww-L$I=ekjy&IE!&`*H5?2$E64wtukyn1?52etIpernFGv%y;H+mYIP_XIU@_soWLA>B4X{k>sbY`pD8@D}wY z!ri2(#JQ}n(s;~E{|UUI*stIxJSGvPUvNRxOEoBgdUVeKq#XTn&(mSB5$({w++l$0 zO22vq(_A>K>uy@?EL~O&sKLb?MdhojTxF$w$sHO>HBlOeQlaY(6Ro%6yTkJfi;HtT zafOp##F601VwIETDHGR6%Pb>aqIC$99!33le|JDT{GRS8{1*5fW?@ zynA zqV}^((z0XL*M+Fg$2-*YP*f9^TXif2a+_0f%c`qL9A%)_L+%Zv861?>TJvGcTb}MP z(u>wyqIp+5-HAGOgM-ta9+;Oi_n`JW)=f*=EkWVf|El{5xCKW2 z@(FU5>QA9pLxx_;OpjaGoz3;MZ{D-KCe1^^iL7&M=Q#ZtuEC~DU8heZsL!4t+sOQ( zl;MSv=bJZ5(T#`Fl~1P3Go$0JfZR?!f+haMKqC<><2%br%v%QgJ=GOY=N`>{sx=8j z%AS4+TykFlajUV#qE4i`f;eTmwBQ*TRQkgs9TR!`S03AY~KOH+f2JVECttdXrqZs7YC&bp#{B z76Yapf|OeQCk4afA{YQXzrctA4{o`#s-nTIB&6j@@8@_hh}63~-Xwc6*-sn^b>W*)%i+ANtEix$u+%WSWxoIqK5k4z z&b>(vx>+C+_ZG<@41TKgR87nPWyJ@PKCMlxUY{K=V4bpnm^OEZZ^k{W~cz7wZnF`_^2meIyTZ z-7!K@*St&af!XzLH1yg(J=ib$oGDMUg7c?5Y8BZ%|_uY)rGTE5KfNJDzI=K z;kYo6^gy|K@coJY(XhjoHHHX%_SO?;!%<K#cJkxvZTR_gALpaM#S9&81z@?F9n0%@KL5( z^HFxBLwQNS+%w|c_;GtJ8FlfacyRS^3bp(iF&pKMaXV&E$S8-y+MooWiT%cmC$NJx zbjWFf1lO657XnRbpO8Dlz6VT0bEr>nGdj5P3u(!iz}Q7x9Qt9x{;}04LI&s6KizQGM}0 z{n9Kj;CmvPEvzhBR^m)rm8{vM+WSWmbi5QaQp^xv=FDLTd0gdSZsTq=m@N0Pa^@*T z&L_iE*02GUB%}`<->`8YoY8t}d*oWd4&166D}VAqeOBJGmAd}d?lo4sO?CLv1jC*JxAu)gPx3%dB!5E6 z13#^!QKNLzT3g_6M4xT$ZJ-|e{!31-9QyAPwfZ*&jAf)& z%JkW{1ruW-I`NE7kHWiFxoy*Uf|v z4rNEs>|o0HB1iBht+5a3!!6F9TlJZ78Jgbczp36*lfI!P=ZY(LCz0nhM{8I zI}BY0LDYQ$NmfCWxek6m44ndri6!27!!Vb#Lce?1^F?PVys>~5I+Ujc41DVtFqK7y zF9ToO(L^gpf=;r|$Y={bDWjdecmeYr0(O;UOW77JytxS?SGT@ZUtBCuagW9;?Pv@h z+!RfRX`jd{HcDA;gQkv*(5Ut6CB`?JqErxL-3Luk95So~{)Zs%P%ef-0|oSo4?tHo zM`1)?I<-Vwal4l2X7Cu7v<4uC@da)*Jkb)tR1lwSiO5-`WX zRwxCRw?h3u(O3Z!rE$um9~463F`-V4gA1ARMB|(mC>m$AMoAW2fSY*Nv_^0(Dc;c< zk!0dI34vI^oG3BO8mZ=>Kr(#m*xN0bKUZ9+sydmalK zqK~kM1K?p1-V%v&@wJhtCR1RL@2 zifGhB@HSrq75=?Vx^Oi8eQw?y20xna-b6yn61+bK!Le`rat!(sVw~RvW?98J<~sQM zPG~&jGQ^U=Zue{eB;Up>Vv!Sn*BR9Sl4Y^z71-j?zKt-jTC8JO)LDrybVjT24_(mJ zAT+T;U|i2z<68G*92y4xdwV=O2OR7b1ajs&`0Z}!A$+G=RIDdT{2KRg0dn9G z;1f;}gIQfe9IvgH@sJSt2GJ6$V&Qu2dAiGU(`P++g$X2FRu}?iHJ*g36>0=CNZsgt zE9X4P5D~G!qBQi*ZNsw;i(4n6{;*>;5$}mcUGUOG)E<&LE}+1_`H351Kj*yVAY57a zy+rg3sPYp%P}?n^-*lljA;6m%Zp)oF;lV&SM?U4Ti7uWd<(br!Lq%v)}LwQI2k+4yKcxK!eUR(&dJiwhF^qypdlLwCT#-tGdCUm1oo5D2a$szU+63~ukVay`A0OC`wXh9 z7ll^dVi0!Z(23W_91{l8bA$aieNc7)JjUyIj2G~bBD@E(2Hmw2 z#*XMKSp~Gx5;~FTfS06#zmMyHTHw$7BeJx?Q5Q8=DI>RUY12IMLX>HZf|S$OP%2^- z*xedvCN|2pG~sgt&_uA)o&(WX7(bT*+M>7Oc4jqM{)}53?-%U<)q!Xf^!x5WGyqS@ zMB&p`6OO>qf{++Pvfp1=L4Y89UnWWe2ybK}vi<6sfSC6Y0`IS^`ZWaJWpnY_bkq%R z9fW4U?t!`dYhV0wH<;><8;ll!hTJ4j#KQu=Vc>3|SzxE~4M&*4^dthh4MBq;RAxUi zrxI8x3_Wt;0c-CXg5bU({Ob@zE*yF=AZx{->N}1p?-!I}-%wNvFpR-PJA%Oje7Aof_wq*$Kh+Ei7+LOCetupNk=lmeJNfy5-r3}k49t{ z8Ltv-D#L&z*Cx=?m18LJhsGds=lc{OJ~aRT8`lipFPQr1vFH;}(kVD+ESjQT@q0MF zY8)a*3Kt3dwNevv9o%9(a)E}JN(2ol6MFaU5PWC|2f&$+J550Q;j$54CdLA8X~E(v zT>A9y!UWVFROzaqkzuOz2j?aOMyG#P(`iYXXwIW&zqXF$-^>gzkjS4^Ku4-ZvRlffVl%7~{1_yTGB`FO-KYMGk;V z(cNq%U%!Gcz!OmMN61vPuz~}DMPp%cgZ-xS zK#1f>AZJl03zy}iEWCRenrcl8a?$sF!FzXM&HdiSM7+j@5<*7Y!2d2qXb^T3p;6X| zmlVO?jR<^05lR8fpKDCaWd&8h&>*tY+f0pW#RfQo42e>+ki_dvupbGS3U7k_S}69d z%Ld(P#&w5vPjp8W-UQ3am<|DGB)DO(?2+nW@ zjQa8)D-pTj6I0 z!`&bMw*qFwQ&!S3kE6?G|6cFCeZ8^3;;yR@c`2a?FR%d`=r9^!-L6&W9TLZ_yd0f| z49vFzrdAmka~)iB1)2xOVk+T6vE}z*YiQ)rd*S(#4k3(YR4nbe)iR)AV77u9whFpm zA8N?@<^en`PJR0inhfM+Oy-0vUi2B#zYY{md zz%gawRQE=8g7X8%qGEuB`Hcb)#!;NL4&6E33@@+=8`OZCFl&Z0*P~?p?)>)?;?V2)22+g`3u8Ly^IV9L1o zD)c#VHD|AZP3v!5gLX#3x|G0H&!%bgDr30gwlGNN$2sgTV7b@;_oNL-)%x2 zz@9z|8XMgU`jFz(>rpXu$g%U-FEb2CocVYwh(Rrgj(TQ*Fny8T2;LomLH1dAr<*1R ze}{74YHzjn9m%ofokPIeWHUMkPQ`QAMhl1cxM$#6*h0=Tx95xZnAt&S>(>(Km>JDc zB7pg3t?O?<*0jf67j&Kjf!#1O#_^vI8TplXI z7L|8s(4c)NF9%>y-kZ0gw?K7xS+J^OAj&A+y2rPn$B2u2T!j(teie-d7dJ;hU2}2M zYf)D%T|b}}k<-_?LPft4W$f+Dg~|XC-{y7tntTD@&B}G}X1G>hDE_)HY5|JrxmTbv zXjFW#o5M1&`U46h;xGFma-!11(>sDjB@~{H*nv`jP7|wmsSB7`9SDx;1iLCqkGB{TejcXnc!Yaj+`>|4Ua=F8IEwn<$9JQDK!$S=;2v5OlE6m?4h5o+TW*83 z1h}JT4=S8KiEzZBObCfFWQn+kb?3>r^uav@pn6rvsP^KhuGQiBwJ(OMq2M!$2<4j=COwkd$n}$_j;gMg0=^hC~@0?m_Car;0*C;&fF4Rq*k#{P?XV#-m<{7zR zrtE)4e*7*3cmLrJ?m{uyFA|nGl;`130R5wz@ZNS9sCr~SBJVwU zTVS$P;?Gc$y(%L)DKi<%3(xaXqhAs;(g&jlgSyWrDYW* zEa=m}>k)uk{|QvNkIMi@Hej8KZ} z+TDk`gSFJf-iJCMoO3_T3QPi=eVdiqtq1TGTr~E8>5cR}M9z^|tsUl*5 z{iNQlLorfackV&d%m(g$6#nKxu)p39qv>FOYXr2dJds76;kZv78jgQ?7)=hj6Yfy( zm5-n~V8kW>HTd&KP$J0a!XqdOCq0T<04sI~s0QY6U&dh$f-<<~QIyyKw6{NoBJt0U z(mbFA>Zy-`_D0~DkI^d`?{74$pL`4rZ2;Cd^Kp6t%#5+_cx*lO6N}{0Tft8^1|ekG z2rm6N1__&X$I$48khAR=&1H$?zyR>wF%%C1XnP!y+X2501#dP2_|lvkj-$*5Aiezw zbOQ{)BF_Gej@t{IG>EtZIq7UhQrL%dXuM6vI7wd!+bV=|-|oc6B%K2=NN6a$FA}4(aGgt8CnVwHPon}j zu*|D!5f{&8cn&OA>1*dx|4lF9$O#%dmMrSWIl{nEV>|qBGyuFO`z`p<+0Y?jv7WK- z^9;?{4}AtQ_S$ydWl-*0YF1=@wFXeWn*?-WCynD2B5zENJq2$} zEVb$aIufWf>M z&}`5(Ucsa8+{5@<9Wv16r4GNmK-6LTi)f(XGO8B|0Wcp6nhwG}q7oxH_c#<#iI-kP zi$OH0FQEmX5^qDlp(%5=RllGTU%W(5B7FZ6q-BP^49fhK2lFpN#(cCD1i&1>j5Y)2 z-A|*9fceiMV?NfZUzo49IRh)H`pQ|8Xu*|o_tk7^k0fUhUs1NEJ3h8);07<%OvOU~cS zdJ|=73woEn3EQD(yopAE=gA8Nb?Or)TUh{D*10!P4zQ&6TWBI!)(Yr1G@p>;qu+Pm zLbIUX^taJ8=yzSfe#LVz)2#aq_8d&JchJqvU}}BGM`(L9Px0owTke2h8}pYG_01_TlnA?J1~npN_XhmPPiO;v@xN%h1#F1rSN?|J?Zdd{H3LZ2K z=!^WtzoS%jaZWhSg$HXi_CN`s@zU?87r62zjRo3kI}2N|5hcJ(6ov@0V zJi2z>{s+n?>D^ENgaxV&V2!H;%$2q`-ED*2pf^2ZBX3GsClm*zRr9%4vF@o>Ek?F3 zcs8;n!!isjU|MArIGXF=2cdPdn>lFRs^q04W>^1q~MVnK1FJ*ITO4s__B@ zL5D1sN(|k5snET48(mL(T(aGWFaKEz$H(9aC_g2D5Vy9yDwO-yB_Dp61K@rbk8ENa zfd@9RO@Q~^@e10C)as^u1>G%OR#Z?}rp+brfhM--zHlW;&`2p8p)+?Uyd})msT+OA z?<)8KoajQX?hFB{?#r9nl5t*BTVKdRu>z*Ku0rxwce==dPc*efrosJ`As~jE zG_#H4i@`n+vQ!KavA}v^=-sFn$#pLR5@h6B+uW9iS2nj5gPA+X@|7_YXt6WNT&FIk zh3z2(hAkEa#x9o&gJV~p8})u~SvRAVEey7`)lF?>v$ewWQ*7i$y?#KEzwpIp)ZRyD z1=C({1MnNQ=MAI55WP_^P3uU+LW~xL_gFG^Sj36bdfHf=xB?!

)Aq{zAPIJ#FO0 z?CGoeWiKKa!U9?VR*~EgxjL_+K#%n1(I$`uDeGn1LRh7k2LPo&$(jxhF{FAm)tG*BPzmjf_xXjq2rAnuo8d&q)Kd?nZQ2)iRr zT-rJqG*(1g$U!w9Y*=jR-Z;*|#^r|Yi86X3CrC;>*Vjfi%g6MyO@ZXWzoAI9Kdxj} zS@%_3dc0ql(wypNbL!c?*9C5H4!Y3iDL<>w^%+2wv5wi5q$>wr*+0KeehN(Up|exw12)$)taW~U*sfhF_EOy>OUzM z9^nF{V4d3Z>9&q|$q9QKJb9L_JFb}w6VA{Q?s&vWJME$^{&uo0_*}o{RT%*=B|{&xdfx524T*%R=bskV-xGLg~H20u2_ zmViH<8afTY$s~^yS5FHa0gz%2ZUNd5D&_#TAk;QMZ8UCk#@-4ypJ5vkYHJXd)_T_r z+u-`PZjDoC+6IN%nql4-e>l_T2(|U%xgeq`vuvrMHtaRq))QZtY>OY5**`qIwt7vi z5~7tt4|76=N*P`A8aRhmGi+V)Z?i+!j;`fkSkqp%hvBuafw*^*em2c%NIxTI*;*3O z#p5V2+E7UX3Cs?)4X`0E)Ha|e`JuJ}IEi@D8}>weY+mTPMLFI2yuCHP=bXJeet&*F zx>#VF**7%3g3-o32lts~>wsIIv$w##X4<;puNH(Z7$Cj}?s5i(fXgop!S`9M7>COD zZ3{z?Z({%i<%q(2&I7x?o(v)%w)pQSxI0m_?s#|Z-wc{+>F)C$&!2$*T+%@J^;OsQ z9{zW#gu!-kUI^-HCI5OLF`n2AMM86CyQ^&BK`X8m5O zJcc@=@_&X$t#Db1ZP@>3_J9gG8ySUqn9>})ZoRD?Ui-PdB?fyAKAg0&qI$p|ufuQU ziA(BZ%8jhJAeruX^XD)b`5(|(YDFVA*xLNh*fpJW0!FRz6JJ1RN&@TuB}P%Sy8ka= zL|rmv6in3qCzJ^^I}*440s@Ho*m~oe8AYZwp0*)`ndtw`U`1uM_A7foJhIZ(k!7kI zdDkOkK3hNlQC?k@n_pI4T2(t~EF>Eh73Kkugx4}w^zQM`^o*5|^75CdW@#>SsyV1k zHB0=No8ua{t+SS?-V2X2ge{Cbh3qF&tuOPooKsX;?JQ>Jv$WkBZ8qDYYs$OO)O9KR z@s}}Vsq6bLX~uRoE~icEwIcJr{gO+%#a#wS)!n_>_P!lbm%BIHKCy9&A0y zZBbBESq|?L%q?(MIct@D&^ybcD)+z_$hsWB=YF#1#|+BtlU823thTb!kcl}=>#Gq5 zy5T)*!{X}}-E2#$nijdjvq6nl^qsv41%Zsf2<&KWPrS*g(Q1I&$UZ^X39X5pNPW95 z^$>gjQx&rjTl)aRPUz+OJ0poPc`GhoL2$Pumcq?fe**zIOKC3D7A?r(N^Y&LRNVVc zyQ8heKIgf2+IzxsR_>klSllWJ_Qc%-Pw@80vw%`CF5#6N-6gz7o4^(rd7phX>K5UW zz1Lm7)v44rqb$UG5826z_=!XIB-pe0qfo(H48{d5;>9oZY+`$jBftRA%_W(4+f(42 z5Bp7DM6=k(Wl?7+?z7K66u))1ePYO+u*DNtOk23$UJGY;EdZc!zNAI>Lhw4gy?YEk zvd=ySueirPv)*XHKF&Yyp=^%5m$Er2j%k}m4*uC3K`u{EndpnnFW+m=z|Y)kC#TFg z3EFa@UtTjZ0l%RK?BwkOiw@Yy+XqHACVsCUu&;t`?jma3zI>f7G!RS_TU+wW!aEMy zKQ-(20s&`5)NQ9w!9UYA-F}zrHUmI)`|`u~!FceGV69ic6YN%GrT(8-~|mas&0g=ZJk%L)w?!XU~KIpZD$2o4~>`Fop}KUcpFBUE)#u2C{s5=mGmS z8(^~wB<0WZ`3ygH>LO+=@)ok+<$OaqfagE<_kg8SZCGH|)^{V1{XJl5&VhoZYr=0F|9imFIT(PQ6tq$_ zK%xv7U3LyR?NuKg;t=U7b*q2dgI|Da0HL5mN%-FLurT)0Gxp#YT^j%qjHU4J5Ft=D z1y4Tp_plLcg0H$K;P4mz9aGva-F@Eds=pt=BYGLAbN!XTmrZJ>rz@Zt|cZwL?* zam+b;$Q$FRVAy_+A@x|7;@dK`eK&{C+B?>xp97}t9Ut0DgEmBAwRvJa5ICf-mAAm| z*X%uT-beP5P!ag!Bl`oPwmJ8)JvY=gC7;;$*Mr6*`XXXW&sy`=PwnNQ!cP0l{$M>| zAJAcI3z)DMpdBvx+`cgMyBFrof@~-0uPg5Sh5cPT?_-Gk`2te)m-cq}wv+bY7xuaS z@MWI_d|R%qKB|1kgW1##u;Jm-uk7XjS64%H{n~gngfn?9;E%s-09zWlxJ%E2+Gvw{ zWh2hhrIE7os-n8i-`dZ^(#V4s?f)U0x}yT%;WI1YAavAsQN;E%rD_?`hIU#<^~_2H zyIPRfX+YoH^uWsnxBqN!v0>VS+JXAUT(6)Q_+2rngB6n{wg2~P6{_=b!=){nFo-Nt zbyC-hjQN9z`<~lezS}MVD(b7uDftriWIaFSUB?uvhdL~+W1rpS}EZ7`qdvCf} zf_mS#F%lu|yH3&tAZ>RLq?zmBj>`~3 zs?NkoBk{>NiLA;T4}vs{I-~KQU8K=?YgcJT$ekD{>=Z9;0t!U{+!}l>EOfG_u1HB0cY;K&dp{Qhb>=#FVRvaOkYz403y#+@kd>Gy?Py5*UlOJ5u;Ru0_H9wT4u=mn zO}9*tM&Uho+MDCZBx!6z`s$0PCrJJ9OG(m5kQ4_OtS-j+kktHSX)u!LMHu+`6p7tu zRF@*9!TlF;-I#~;!14Cb##Kys8A7|BQtx>EWe7buz)o5(WWC4T8}CV$dSkVxGz?_J ziu^71Sk%eKr<0|8T+&Ng0XL3_6}+#8mzGsH%U$eZkLIaTG=w0-gC>kD&uZ(2zDP2y ze{zHj+AyH1EUu!kyrQrYf0`<#;nH5P=Jj5xGzie)4Lp4Irl3h>VPz$`j#xY7tbfYFqq5DEiZgHP3i|4Ct?`bHyAo3V-@r1b-jB_w<9?-Lc<29^_Mbn_x@7$Y;z}prPhxdBo){KNn$25jR2p_*?WWY|fO!O37?i1!h0Tik}-O4QrOse^9@E>4W+X#H}->PUr{RD^r@$ z8ZOuD(>sHgZO)WZaQQH)b9l_9=_T|d4!@ZxjbqzLosD~WrgV_LBDGI~8yXMIM-l!!Nn3k9|fmqvnO>>Muj0N3qV(nX;2rz~k`Bxr+VMiGt#^@lq7-K3?hu5f>|9x*2#3HT25m4_AC^FG+U~#2<{8V)3KnC9<#Zz46jy zApbLgFxaCvbb=IF1Q#e#)cJ-?_5--P3qm8`+%QB^Rh(!BloI{;1Sx%{8Ii#B8alM1 z7q6Ho^^~=Z{qWqsrbTz^>BGq%!!3q>v3C(qe;G%eLkiNkhgq%votssp){%&XrCE*gGr9)LjJnCQrH{zrhV=Q;S(3sZ zSzjIuYX}c+?ADxwXVkR}{@ZyFy;wSFYZ5WycMq zp5!)!C;yztd9v_t=gEBq(mJx?^zi~|g?Jy?)%E4ax_a`%6A#_Df-;1}cUS)H{CG@} zFtL+o73n(t5YV0VWyJ0EWCV>1pWML}V^1iI;7gaxYw~cMxp(|Zg)~rGx@=V`4HWMm z;|mpjmM-z?N@)O$Y3nMbWFAW^FB4=P%8LQGM&fyLap^0^b$OqnO@ei5hS+J|&2{st zq}w7}U2=)%%#dgNshd+J?TO^5(J=qR0C@Ry{~r*#>alw1QS0-c>SVsFbrh8Q=h7tH z@rJKUbJv|xFHM>+-YKPu(&Q}mC(X2dkV=lgx9yWs$!&7scn>_m@tdZJ{>Muu$crso zuoHO_Z32s1;de|j3ZCfGKMICUYVVcEA)5NOhg4(I-H>YBe}JYM>)p*VTz0p#4DUTC zRX2p1X@{ik5DbWDFtze5#Tr8+HV6NYx2TCUVGiB}%#Ve=+8q3#>FwKw$avcPvg$Y- zeMHL9=AgNUrJ1<-5or-1l_zLP;BfJGj#RGJShO&K7WNKnL(7G<hZB(W=y9L)9_anlqf#~=dsL!t85Jn9Qo1$fI&kFbK1eG^+)vZW78OkMYhK5o zx!>Innf6cbmu3KOd4*snxqouraxyIh9^l>Tu^@3=_kh$DSo8J+QqP(@3B3;G4uNdH ztfzAWTPxk!?A00vlGp+AdX|)lhL*cy^`_SER^R)ev=307P$%_+N!z0WmhcMlZFO|Q zzQ0b2E^{bP3l)5m;hC;Rk?AVTR?8~$ofT>MkcclRtX!VvEb^MRhH+9E26P6u_aUhe z?|4Wm1BtSN;HRyIULVrA;2U8wqtqB^Xt|rVq}JlsX)tRs@Sdv?3=_{hEUhQ&%@ZD# zUVsteD}j$zmSV1hr#vP-1MbjVVjdxQ9fOHXd0ZkdN9AR{2M1oq(Ej-2(m5C$cv)!e z-TiTkN2LKc;<%IzD|TWxei=+{LgtF%#ogVzj#^ zyPu`|l|Fn{>X*HY$R4ts@F#$~q_MfJzwTx8XcMs2xhJJ!qD@afCv68&RtBL>7Intr zyG}wN^v)?72w7AxjcUA(L6lkeyOUBDzUO&qDrf|+;#(tl9YZ%`aG&R3jJ@IoI>z!U zp>>1jzX)UOv=^lrV7_7}Otij(sxWV6vrwY$n-`^}gyDC+EKS0|9dH;e-l5xH zSjSAn{v}`_f5$u04lu>~ws*(j?_QU>;?3_$so=N7Zj72{t!M`3cqy9np45sc+GyPR zJ=o;9;C*QZDB5I!|5jw0>)-(&fTE>-Ko!kgY*sX0$H1vaK9JlXE?(wa(Rdw0`?Y7K zDqs;W^Ry4lqA0FEUMw1MPI`*CcKdlL4K(;Nfj2P07;|1)3l;u4FQwz3&P#&<{TiW` z6$dTq499EFLlWlhkEBWP$}X{jZyG#Pl{9?noRsGE%C1;W6hoXE#j1~`L=ZIl&7VG- z>)@uJNXhuGkEOmqskzuJXkN!4sNzrP&QD(EThP1?Zx45!lz#~Ez*V18edAR^>jt;^ zOsa*^p}y_iwmycTfPRD6P3+CL374r^VVYB(u{`SG6ui(1!&*$@1&Ux>82l!{Zi_WdtZ>Uz-fsj1yCE%nnZ5j zURv|$1?d!VT5nziT3@>1*`~xiD$3Ljn)w`2*f70E{^=%I< z+5Ic9WXoR-LgS_w`NjsY;-=5!T2MEUh`{PL(1*G`gXF11-5g;u$uc|=gt}SO8H1ll zms4;XNiGGOw5VY6FT9RHUB==?HhJuJS)LU#D!dnbgIo_%4DAm$ktg7NO=PmWoTKSm zWqBP#C+nKZqw%Vya!vy}+1^Yh=W=-eA>xn_4ur&nH;jKRe%@T}o*kP)Gj5&WPcRv`whQ%)TNG^qYe`dE z$S0t?h?ep$V0#Mb(6EonYN)lSla2SZkh5`eD|uSTof!1zlU8yvey^3>7pz@`!kFkg z#ns-MIz1<`ptXD_2`Ny7d^2D-DF_lR>Wsz*T7z~+wUxYv*+gB>vP^9*@6i zU?;2FQ5)d^eA@`GV?g58_FyBm?Wv9M3L$pVwS#;)$VqG;SWc1Fa>Ac>ke`GZ{djz# z1Muhvhdc*Df$M^hmbngI*O87m<`Q!#!0Q+|R1*oB_}fz0r?3{DfJ|P?!=}JwcCjK8 zUQ_y?NO>J-<6n{TieBD(#P6au=__Ys^~%!ttGo=FsXU$?E&mKKro_nGfrk$T!9#N$ z9MefACoIh+W*+i71|CLqmb>Amo#j-RrSb}zmg#RQbxRAYoTcmt9{c9am{$b?e6eT| z*^o=$W0$dCXUsz>;U1qx^9RQ|%adWWHsND&gD0=UiE_tabU}*7OJZem?3Y&wRx1pM z5f{uPR`+_WypcGm+&DP_ME0XVv6UY-*TIj*$%lbDbBS4Gyp9)jBf7{j_{pwvaznZq zi!bdWkHsbN@+^=&hveJC@H#p+TtnoA&f;>Hlbvv6U%hptb5HM)OVg2>DC+@(yr*~| zR}u!F=E%e1%9a|>rFp(Xc7)Z^vrZhxu=KR_J`6+87mDAE+9Y@btqhIRtq}|zKOB)D zXIt@A$Hw>De@8VI5;k`Se7cL=0e_JocLOhBVvU7C@jAMYBk;EF5IAh;E|X0xyh2Et z5`kMK$`xRaV*9{O+MohPbHvXl%GF?vSv};6X=Q|G4y7a{){#Y$5nR8#I=3guDs98&>E;t$b=DZAgj}ZPjMcxZ6|0_kV#i_mI z@S4LOmLCj-PPz|b3@7p)t#N?Rn{90|w7e@;Z)&|a=(S$*T)?+iDtORmJ*fUWWK_p- zRG-x0`In@&3&+s%u1R`Rzvjet;TWjof?_T4#5B2!HUlb!M{zGHpP=}g0i8&by8&}X zrpsMMDPMcI^CkQVAP2hXAp49S7<@*Xz!Yd)Z}}Hbe*<9X{Y9f!ck&jV%v=W_OqbsP z7iKOo552sO!4DqmBYz7njF$x)QH=JcNRKFf&X9MJB!@geF2aBGmn(s`s9xTKq*Yj9 zu7kS_luNN=pu7qQG#8r*WRvJsMM%6D4yfMervWi=6R`ZjnoA z6W9iH!!UU;iH3)a0Nu?PL3MX!5V~uwgWn$^mjkm+C3>*rM&&GSgD0H~8nbN_VET2Q zbmB3KQ^P=3=hX9;$TZ=#AJT+GC3g+|mSUEQPE5b;J@&)_}#vJpyv}6Y@KBY}y zfSf!|{sb~J1$fRlxd87NFOzMSKMMk~(h7?@1^7|Y$z2ob(TPDEvnI+3aKcms!1?Oy zR;mJT`j`o@qXqb{iECH!ld* znd{&Q)9H$dxx^gL@Hz$!Trxu*j_1yh$Ac~K3cf=LUdPbM+cO%5#BVbplY4O{&E#?b zAtF&Ti>8z7-G2IPc^8ao^=+H28LG$?!xEf0;+oBCBYHd8hTmAE!G65;n3 z$WH)S7cK?U{_Ij}+J6WXS&a@Bb;jbfOCb;Y$U>RiJ!VnCv}VQYa3|&NijORX{Lq#~ zayTwtB&R{>$?F9h23^frY^1jClSQ%%4n^Y}r`!)bX>6MJFl$ArMIBgxbjc1JmnWy< zznt>akbC0f;thFp-NOQkiCw&oq5a-`;Q5Yxx)jPQ`1Z-Xj-iv%0(lfJERd%(gp#id zWU_CK0|*TX*ta$<7q%uWrCSr~+Y7#7DIMeL-Tu%rSPr~%nM}65)wdJablG)@JO;0J zQG2RyH+WtV80FNWhINvv06_@~T}ZAsCWjSyQ$rZiUR_by4sTp8cOxf^1grDwzi1kC zgOxe6X84cga=I2eW)#cmVw#T!b$&ueyuDZ+1CC*Lv79+spO!0!2&xX{0Q?Cs1k!xp z`VxKk+fSQ7{J5k<-b1nrsEj6)9udn!SY|)6tVm#X8+we; zFbZIfEW$IiY(-l}(ewRQhxzLktd>t(ykK>>zyn~?lq=*(VQ{PHOnjmWVwGR6kmK-c zSIA?4V`GHcL2+y==NN-VIkxN{vV+`l#C{B(V}>4wgvK#L%YYo~uokv+nbpcA@BldW z>pH4dvFoW?l?fGsV$zMANelpG((d(;;Q%JFAA@I-p~u3|m}F=fkV*fzR(=}wFfB~p zDDXf#n|Er1oS|hf&TN1UpC>oS{XngD3bljcSS{xmgGM=4vq|oS>Mq+P4?u8KhZQlt z!JA{BxL&3gxUH-xgBM)u!=YR9{6I#;knquNt@eQr&T`AgYoJqx$xVw|Uqb&elmdGQ zL)Tk0)PnR7TFZ&#mL`uZiHGnDky3Y!txHZI+)0A9`l9d~Au%JmqzQmqU3q z6wcA;XFC@o2g4A=N4LmBo3ZoN{qd11IaU$VWE)T&HSx$DvH6^ zZIyeV&iD{~8|U44N_-AoLwC6B9zt1D^C;<-E6b`Y@(XKS$*@HVciSeQ{=#Rs%Z?5lOJxdF zBRE#)VJDW`+msv}hvg0_5pG+?K%vWA>n?M#9NEsIOS}ooXHJ{FP>2W$^h+L4csVYOQM zkbLArK3-YUixhuE9?y}FQII%LMv{+xU=GS1CK_E<|wN`NFL&HC}BC2s2nA? z2C&Vc)Z|b~awru!lz<$Hd=5oCha#O*?TT7cn?!}{O7%$gZMc%lBiUVH@I)p1G!ZnF z?1m=rL?t`2DLhfho+W~&l6|l_5f&9~OCo71+Bb=$sc4-<(p0op6G=xC`JN<_rjm^# zU#Vn2CxWJuoks*sB&$>sLBCF($SdzXA|>y7QkKDO_w?N|RJaT2EyEt^k{h@@(k1t6 zc%(~?MtP)5_ELa!;e%{j@CcVICwYWRR%$%LCAk&lBO>AbxYaH4kEk0C+a;I$KV=DDT_E%p(g-0y8c7JD1*C=^Aan>dTnbz^Aqgo|F`$BoN8P~K5xZhR zQKO<1yJADJ7wlr8=_~qT`<|KG+1cCOyW6|u_5bnvaoM|_nWsPV%rot_Mh z*cG`WWL#TUtHSbvn(E@xs=0*^v&DgO zdk#Wj@}ZE;8BxwOCvw`I$vMuXoSJ-Rm0- zIaAykT*ZsQR(!gNbEFQ{B4;#VTg-wwXDs}Wga6&(fBb^F8fT(2#hEmzLxM9Ium(mE z&H(1A2bMH_lrSthw6H~#)1fjDLtL|5$Jd^?&dGu+KSgWsClBB4W3#HdNn*e7(Bhqymv7@1+xh zD`TNm`J)!Cec{ks#i6$jhdUaKLt_Bu2@OPo;y}BK z&a59IeTBjpjguJ>)?LmFOY?>0Y8A`XIxL4a2A0jzVrLi0--Jb9s^aJF?EEXes);S+ z!JR5V&mQQM8yh9f0kpjPco}7d)w-IkTv|G)s=`rFROf11QCU<~RJpu}^fA(GLR8YE zxEy^qqq<(ZqpXnegg&dXla`XoQBsK?#*i*e*R5sLc*2u%n6`;ovHG75lc}RPTzu}YonxVbeKB1wX|9lJHNOrcK(|5l-S<$*D{Lr zKdZz$LBph-y7qj!lSn7&YNtKtMp4Cux|GnU=niJ+;iz>ex+u)mV!qQ+y~b_OYjt{g zXCO%Uz~Nxjj7$?8j6s-+IuF$3vC(O>jg|c?HDiYw-!x~62MmTDKhfDnel0o~G~>7E zgyF9dQlq3-;g5HfcLz_cf!DJcuV11SKpPfyo&ilcJCBwB>>Qf&k-NDM$RADI=~Id{ zDx0Him{hIF2MwMT^C~pnwabg3!Qc8skyvH2sRrl&pr{8y+1)aPd?RB=BYT*uk31!| zk9?@>h}Kck1ufEYtGIa3@>`dn@SG?K*#e+P`iC@>lwH{tU7~YLn4jP1l z(j@?cNeZI+@~SGuV&vA{2o4<^6Nj2^aiEzDEv|Kj9@3e0l1qQ5iWkR6vYBl^)UT2RYQoD zsdBsIyk=@YCm&0mKpiU#fsZB620(WOf;?6IRh(nDDU~V5mi7#X_SjF1S^g2%wC92N zTRrEZ61iteZqqQ=xK*)3VtdQ$lM`@x8R{&*nbHEx_PKy@zl`I4SjF9^o)Cwht*NG> zXotbLydZT4nC{tB2*joLb=YX43pA1i6!4^KHjN=Z*VXck3~@cRoCXH6Cf^1EeK9Sz zr%yD*k%WtEEG@U~)e!{tOXDB_@R#-4?2`>n*~=ha672zWSyTy4nc#$2Hzc;YTp)M8HRe$;bPJLHK6izsbPDSVr#BKgC>l zdHo}5!(7eiz-ZOlJU#w<8wG!&%O(+>f@do=RV|GHCn`UDRVQ~GR}dvVY8k#7$4RrG z5z{D+^M!|C^3?;psI_X+pw%y1MuTLWN$=vtq~)BY8wCxbO*;oJ z1hP0oEM`x%WO1JfgSLAI9srpw81xVf+I|5ny^kx&pe@ByJnrmC_7$1x*on6d!GZJA z&CvG1!9(Qq!DBl`N%j!WUe2gBEp#QkdteJ%!@+5^rp=I{AV&U5iTl+6QTmdE1Bw{+ zu}Z9E^q4m7%u`vzVAfEl@YawFa0=`prPrY1o{{LJ5CKYTu`6{j}5H^ zK^+;IFK-^!0u*5c(CJ$dQcV@%wv8&aynX1H<+|Zh1&Q} zpY)4*t*NcsmYKBe4#LSyxXVZ0{JfiOiqJXtfk;q0@Y`i$Zt-Lg4aJzjs%YurhDy8DcnSn zh$G`$6)0<)<`bq&c^TScKQVCr6;{)p2N4BRKLaeYrjh8pmkvvfnc7!EFsbx_^x4xy zGj%on)7O{N=LXx9&g6%=I?C&(c9dI8@8%mJVRc^d!cvBk^34;e2@OLkl$kX|>rYJY z?;9PYq5@BzXe?|P8Vm~9FcjmPYztDj zs$uA8rEq@cTyygCW`!5P_anDAd6#0vQyTIv4g ziOqct!)69Y$7~R0&<&H=(O5=)cXlFZj{b#zucEPH?o~)%k~<#saeD4R`B*M-y{`e$ zzGFx8{v@lV-OTl>{0>=BTaoC5Cs?EHKKR*4G3qkah2zp+MHD zIfH32hy3x}9`euyef-fj zWFpfmdnr77vblG|X=7}@upkCZPmig8)6>Y!!}RhNmVq9R6!F(P~YwK%PCBSD>ruUq^SorQ+iT%b3^EQRf>K!2u3g zm89~`6P@J^L#KttA;-(D7A45@^80{9_5ATKQ4N)x>)>@h%!kz)^4Nl6km$A`C3@R$ zDhGMnAkh|uE1~TTg*CJG5;nk4C?IZ-@x&uBAx0m~sFkM_r3iExr@X!>HA}PNB^0V^ z29BE4fXP6W&3bm2A@3+@AIdD#{Z)=#+&t?kH~LTbr_2; zLGl=ekZ&r4w9FuxX!}w{n70p1e5-sqv|m~=OfIMx4~!hAV}*v1_TnKDGi&Kx2mT^+Dv z73$Cne$hEajcejgk+m%UxvXobV)3rXLiu8JWM6#?>Jl$s>&I49P6g4_R*sTeR)uC= zPS_hIUFK8%+?gb&di<0q8L7BP-)mZ&Pd8)dH;<1G%90RkJbqK5|O z6K;osccbSH8pRXt)PqESi1mLoQ~9TORlU<0kOBe+fLF%IoenLb{t6)N$I5QL=KcS zP13$jQS~b{reN>Xh(tg5?FgR7SV-QnE>+&NZh!&tH`XPL41*<;MU_Q7dQrYZOC=Ub zku%r#9-k-``=rGzZKX$5Hwg^fTyGJD1$7oCfjKxn2@IR}oJHF8LGJIAk8M0{7nV9M zx+1(d%q2|989#l7hGWVPP-&NCe92OMWxcT%>C0bSacGd4JdJC8%_x(HU9~{&f7KG0 zZ0E1tQ`|Z}!&2KvEaM$4pZm&Bt?et9ZpcbE;-d)&n`dOsuP$C%R27?%sRV}dXB)_5 z%8Qm!Wb=XE__}Ok581h~mw(2<+LaG2Lk*HKa{ARzKzds*B3O?0=hYE~u&RggBaQxBwE^8nd{_R;3+U}=Nc%+r#{ zN+R8ER+BRFC)Xy)?_AplxMOIbM2>W&g@n0ca`BGQsJ)!$>ICSA>)`n8Ht7nVUfl6A z7<9hvs4E6ckNxD;--5;SGTf=i5nKA2U=0q$u_YY1vU*D-ES2sX2)4{uctg13)?~TG z*1iovde7EqdH2?MbHv};3X8nuAGeY<-cuVB@!D-&wJRDCBCPX; zedgRfDBnGl(}Sg5*?t1*NX&RD|GFbl{%J=>@cL9D=kDwS*-tB>q?#oI& zLJBrPz^QSQ3@)s{?~Ucz8k_R)VN2weWUEoNyiBf^f2_L#JlR1V?q;6MSVn$hSFHTP zu4L$O^e=T?G4wdE>p*ySVitNF4vyQ4{Ksxd{&{ybI86RpWtJaa4d4!w^9piG4`Z@y z>}i~z;u*4j2h?~EyS--^FExV$BknWTB>|iv*GJ2Jua5@`ezVLi(hHJt_DHjqNmlH7 z7`(~*uTRiXK+>|oP%zpI4h$wrZ#YbP#*~|OgFb~Rc|Kn~jIoS-@upkBGL0{c-6}7m zQGmo-CdgfGnc09QcJ3K3|8~pt2DBi*2Ti=br$J53y>(|pFo@q90~ssMA*(hpRwG&Y zs=fWuyaNaKJ|6rlpRuB{hyEWH)kg#j0v&d08L28+kF& zj3}u6jtleN6963d*G(dee!yzRg^8M ztEyRBC+&h7o2v3%Axen@pFHqp>lVtdw18ayOfquGUp~{lR{0suM{)1H@^k1*wXzIt~uK7ZzZi&)-cLU4`8XJ)RIn+(f*+v)0+iIc*>T|Z*Y=h5yhP?i8 z0))GrX2?fh2%E&adg)y^8t=d#?@o%Ra5HABitrY#0xq@nk+tBDwj5bK?F@!-R@bs-;3s6J$IkD;<^q&&o_)#hy4s!+*B==} zmecj;c%2PZYSZ|>?Ad94(8=&X$NkL{o#xF0VUtgE#y^(~eVLv+o~o#)kMw04`iM9g z-wzymZVl;U2EFhG^fBFac$&p5#xnBo7l%W zyz-@DaP|DPM?C8h&hj#vCZb;cxgph;z0y^7zS0w9#9O!8TV!$_L;G@^t+IPqY zsd>&SNJ|a~uXZJ!Nt;*OhRB(3lg*t@;IS|B=Bsk0<o#w+CvAtfF8Edm?zv9d zDR+KnH0u`}(!KCfx{rM9BOhuL55Tu;qzB=1lcv)NxF129ek6-iR&<$4nvORI0iuC7 zO83F|Vf6m)EVlHlXJuXI!SumcU0!!0rWu>?>m(m}q0=DfgmhDe8fWgi^I+3d6IBN$ z-A~AklJ0{)z7&fD%_J*6?M_t(?xs~BkcD|KGCUe2?|FBSeD=L@Fz9_kVIm7>bs3MN zy4RkZ);Tzq@tDCuv*xJ_f9?H@G&6{>XNOsoOLP_&78aGUL}JPZ(U87)w=uEU{XvR< zER-n3y^vZyN3r<6F|kK)hmqhd7@L?BG`%cZ#d=tHQni5&%l`@lAv!EK zl?*IcJ`nLy2L!%SkB9&MOw%G!Gk1RmW3!bXr$Kji_s7YwS|JRUUU^qp?<2}tT#r23 zPW^-&R5kIFNN77g$hLFM+J?~T*-w6lnIYxGo&L(2F*C6&R>iVdCzfHlT0U)tie)ZG zhJkeNiC_O&ti19wa>fVy-2@doES+P>&}UCAnbvT0*ebrMC%fVwy219ZX(zk-#L4I8 z+@gjf1heIIAKtGg$$mfsZ%mTaCS^k4Y$%U;B>Ej(tf8#BztCl0q2V=o-Z0A}lv&p( zw82E8obpAK-0h1VX5^{p_++!(D5#_WE*@Ds^2LNl#whbn%kV8knOr0+9s(A9^5sJL zoiCl>xA<$TF`mZcxNiab-}u!$=pp;b+rR23M|?dJddR~%I-rNF_&ORK(3Y>`robL$ z-D{uL&U(m&+~8UBq=$5c;jtac(-B;w!^_OVnASTp0AZ(Jbw+iLjKySgD>Uo!h_Hoets54>I;5p zih#)5bR-yw+@~wiAR;+94Uy@;CdmoEk~wq!+D#;^C@A~YeNISK@sg#E#Fa@plRRu0 zJ7$vQoGlET+lvn3O}o$_(#0$9v()9(T)n($m!@^jbm)J^T_B6JH(nSB{m%!0b1?l+ zCC8k%4Lx?$Z-=1mkA6Ei>j%OOSRx+~Q;1Pin>Ed-m4E!byP6g5TqsXo-r1NH){M4& z5A4hT8#V=|wkJAP6;*1cwk3NjiaUZo-kHO*!pk|vf47w1{cn$2v(>KZs9G3LXB(7# z!OAyvm>@;Cfp;Q*0?Hzi#1!5a!J{mntv;zCZnZP`Qk;g z|K|7~i*VFIAyl^iu?XC7?|_L~tr8{i_N6w^4&$eLBE)n>DJ$Y?F%A+Lt&7THVNRx~ zQt4FXBY#HJjw2XFNn-*=>@tqnNTsqxW@~B=A8oO!!fj1e&JAGp&3~N&W}p8%UmpBJ zsQmNa`QT0$=}0oV(_&qT2DwuXPUB8b|Fae?*j0iyfb4kztG&kMoW-2lfMqXEhKVp- zj!;uLZmN_98|so z4^GJi8^j0SxfGu64~oqoo9=Ii{!dPDx8kOHofS)cva349$05)V1bQ z*iI=DEM^l&mf=D~jh|_Sl4&XnAA%>}m?Cw*6Fhlh)Uq`&(Q=PThD4?a!H@`VYmGYN zjjd4v7y?6;Dn16tp4fpoi^W-!$!Vg^+S_eH(-U<;iW4 z3}N3OK-s&q@}30V%q7TM2lq3y9hy(n?Z);f1LT*j;|SL@sWo|}oC&5E;B;LzKPm+R z+`{o;FljClPws#g2aiZmqaY%HZoA^~mUbu}=XFGV!I?26nJ#h0xSG)82OVpfGdtW7 zg@MOe(I}`8Dd7?+mzf?7?bDNNI;bMj)oD`4xfnd|)Q4-!1kI2^bIe>pKrgt;v zF9!prcP<{i2q5YcPzFR!#X9adOYmO_s8fEJ(%I$f?;okuRq!w9Jsc4RjfRv@CZa)j zep}YayPR0FM5XBvfL8lz-7`NaZ}2 z7QhM_mgZ10A!duBG^KJsLG>>tqp!*6V_yn7L(c8E!>1l-SKOK|klL$qiFIq9lJmJh zDnA3xxuQ#WqNH1thV(jVx)7*VT}8_HVO$7AHa60nPZg~HVGDxzFS->$nna$@#G#wv zxNSP>%1|p{?dB?-&S;NiR20Ab_;|dKMpXvhx!-xBz1c=r2*cfBSD9eB?#Eu*sGcpKc zm-R(&`(}*Kj@2@LY{tTjF?5{M5$_m?I^cyJQ49QCKNRj8sYT>8GG!E~Klx=uqafw* z)~9kdT8(HmG!tWGtE%wH{wNy^HhBOV16^q@psjaX+~B+qsaJ3V72D3&{(W7sJil$Bm70tYq4s2Ng=GgrA!kX5( zxPYTKUW(vYCH&K+h@7i*caR*d<+$_KfunVUQ5kSF8Q(G(Qf0k{piJOsy^b{&IeJ7_ z%|A!ibF3IlH%HSk<>)^{(A-%@eEc(0(=aF39jz*7m+c;g*d;^oI2%~|L6EGyk`uvU zLF($jFw}{x!;Qm7hM_oob~s9h(Djs#Nih3swqyFdu9$ybUd_>9FlfN~(FimV27~N3 zrjTZXL6b5Oxa)8ffmdbGj!9p@*fF(iXSGMP&@pjvYR6Q92acq}{beH&IRiM_GCbDN zc;S-^rSK?&d;zz};VYq%ZpC3ZxnGeNQjrY9Lr0+(Verh~S?v-u*l}e7FEDvDrF!mY zlz<-`O@~-Rf%IVd1s7Ko4gy?3*ckK;sOuygI|fa{6UL%>FhI}I@z+dkjAig=W04aA z8T}ihzAVzU?_JL==nDs@5yi=I=sr*s{>~8g3Ue2(akBKNOZnzGTC28qoKE0la2b}AG4{Rxcur#f4)rx&{ytT&ECl=;2<=I z$M3@B6VVd<`~*7qUpf&2C?6y8<7wDWw7~89M}vJFc|lqjCv}=zZR3x6d>bG%lsnxM*_6#%^C+X z?w*X`ENFawG8zqi-e*Cgexq6I1oh2R(PawiJEo#)dW{I)2~R-8nShD7*$fO2F?AY( zlMM0vX=o%qHH~WdUw$b`G1c-trXYOm0;^v!9d#5S#jzz9wH3g#v~Tar5Bp7Vw1MjG z$wj8Up2pxa#c{==NRg#DS}F}S?jErE6$_CI{h#atyMohJl%Nu)Xk=V`= zstQb_RUr24osVuOvFA)YG#|~B&t-+;{)K1`_~rtIkt_~0`sPwy2~URek*B4jy*N0g z-H=;YUxcRMl|^VSOkDB;ZU^o6*4}lN(Ib7Ca*|ga=Me))gX3!#qZoX}Vw4D>4tv2k zV;1Td%ivy1&?p?g1m&19mngQVC6FS@t z*YbXu zc>Pi|QMr_tJd-UZ%{%yVP~H<$H*&UVq2YdIu+}3C4=+O#$=$gCA<8cV^U(DcGYFc{ zwMagn+D+b^I-(iua)NAOA_&cWKW^G)2JO$%2y&!i?qaXmvi-#{mWnh_l1pF(Jh9WLj7+3yx8F~lA`g$cI$8Y875QY4Q z#}%he-FyF>yq$BBHBNndMHM3FezM<;oRoas2DzqD@Sv%E<&sk$i1@nXbW7tQ@?JIS z551Hg5n~9j$1+R{qjC;T)APJugSz17YfzG@N?^1c!EIf*^KwK^m^@$^9WweM>+ihj z#BQGceh1R0#o32D3k(CsaSEB+vW;I$0 z(aT94x@OUfu?+rkHOd7eF}zXNPq=Ia32Y*cJbLCu&g-E1x7NG3wKAYhV8r5iH!U1| z`j6$7EvO)a#3OlNPkX#~C2EfsU53amXI@0__-xwe%#KUXRZ4f^iAnNj*B+bdoXsr0N%V9CZyO-0&5WIk%fj<3gR-+I@ z{p^jksMMT)QR`4NtS@gtS3=H*s{pEDIi#m1&uA1pNC$e$I&{}mEyJvuyT&xQxwC#3 z?^=(N)D22;1#JzWp94=e<&URafx57;4xW>;Rueu%Nh{%xmBHr&+?;D@ z6&QRTyaJsf?rHD_v<>&!fUXCjY}BzA0`Si_pl&ckZG#`&h@x=Uji@~gGPdc;`7|ds zx_gKt!QfE!et9FTH$1!%jRhTNFVrx=M8{3aY{h%8L|gG2SEHNEsknR-qDN1cmKQiQ z6V5Kd{R6P_{>CKfpG{~Ybm4kTb^a6l*%8Z7E%;9kjvK$L^=L3~D%iYm3s z-*#_C?EnW}P45z1qT32t&%(ZX+T;n#G_ZbOqX{h-bgBwBZ$_oi2eaRp7BK7bzRg0@ zB2jR4j(*0q2yX1adDo&5x^(bqDCXUCybp^Ga4qJLAby_gLZ1U9a##td;9okPz|yxx zTTq8Q*gZ3!+}!KQK`|`Q-sv%p1p`GHcn*Nz@3x>A6CA*pBev31!Jw@)RS*#fSZ2lE zAYa^yhT-#D(Rk2%h7yyXQSVbNgSMde9Gph)3uicst72;^;84Y)*aAmcY<^K}Wl=>D ze8p$Cp{GI3cs;AWUqifB`1KdIqo;{4y|5E{+S5DHsPHIhtd2x?$_#Iok+MAn+oy z$r}a5T}CEVc{hLM`m5Ti+}&jvlVG_!7t=jddY))f6DWr{ba?XgME6=okNI*_F4-W! z8hRZ{$NjEDgMk0OkeQ?+qdAz9u4a6?@sK%p9m+Pt!>6_}S%O8`!IyAWxxYft;DauE zPA`=*`n;jm<8Y!68izQYwMzx0SuJ9W2x*L+WVs){s*|dVKUhW~SY3SP29#ySc0O*k zXXUAfoX}@aef--pieB|mIWLRue=_kE&@(@NBkdL6zY%qTUZHKLKs#eo695YsaTDD* zqE{0C(Tt`+-p#;->WQ1sQ{dFL-HaZGv}-aT8cYOpnD-jIb%ElQX6;Hhz$Hek6LYVAPxO5dK>ql$YJB)s zR0M=R1%L47y(qLc&rR)ufU$akV>MT)>|G)r*Q9A`&W=&5nj(*T--b2-z5{QA{XV^J z2Yi>i@vROR-=xqA{?65$g(iM_*cvi|#^mVV{64a(my%PYByc=~>CZkK>u~s)3tr?! z23L=~suKz6l=K(Wn3Ne=U5>lni^A~(_rR8<*X~18As{p<=c6swyMed8bsrjz@jjH@ zkVc~JM|BOU|NZ@FJNUO?iEuToEGn!ifa{wy!3O^gq^ED$b0WTZ`SPMl{QCo_B^Z|Y zAlgx}_(lk$0OPwD6;6bz+Fu(C37)$Pa z2#tsSIzop&#P(+&qTBC7_akzhPMofQcYmOX?ce3}F#vS@ynH{(g&2VSW=4`ZMVbaV zMN)2k#KWiu*=aTG5!4kyr#%?3_1;BzPdmKN5$5efr~UK+Fi6-3@+j($osXj7pnMZ` z4ADgXP3D(6mgW~an6ps7t6qWz-ZOPA_+%-a$@!R}*NVfZ3@v^P^~8%FL;ZlOdc^#@ zRJGYCNlSJ8=Z~RgHgH2D@#)84aape?sOu=xp>5`dOv((!y&p$I@$XO271$;P4E~3g z(fFUspG31jU->(hO~a?2MDZY_b5Fu>Kk+Hl0$6d44psjg{)};$gP;tqeG0{c$1;F5 zalyO{M|<}{@V~!3h2qRnPdy0g8-}MJMBM@FI~xt_XAh#m4Zs>_K23MYaf%qTSv2Uf z^;9=@l1EPkKiU|CxTk}npMjK5`)AOohLE%48I)}z0OISOL2*sOT&?pR1tl`7>WEVh z(G2{jfl$D_x;Gu#dI)7U0R7#E(N>5848pLef@JGOJ?e%}A4a{ved(L=?DwAmo3ng$7n)ro?*7wAMm>I-ND zTdSN4@4XAndsls$WN$OXv-Nq|AG4)KLK0l|No4S7zh1S5R+|*fw1O z@7l>!;1>>d*K*W+a z&=w%#*Ei5L5N4kW68}HVT8DA(M{lBVGQmUC9C8r9>(JJO*v%FvBs%h7r&1DgenXDa zy{0JA({p>*K&JVBb7UAms` zmZ;3bxlW)cC9$;P1WJd2mKjHs_^Ld&`9t$(*r@B`T|>)x*dT-05iJpJ(L4_{@?ddHkeU9v>S{Y2=UVTp7+rV zX#KwTA$OGd0o@T)86*hN6ojuGK`(uPZfFKW@%%5*?q;C+n|wm{yCZ0W%5$cLo)+zM zN6>AHohtvYP#UthBPfyI=|t}u^mZ*27?&#pM}7_~I4}H!!qb$S1O3)6s;q=drSRa> zXoNkZPak~za@$gQt& zh5sabJLJTPB{Od>j1}D3kV>0J=1a~pv zmA|8S=+2TG5h`ByUvw>A@n5vd1Tw_j@zg)iQ~df5N`htT z>;)swEVMM1*|o*iBZLHqyEfT+LI-Oo!DCB%nPznadG?Gew*^8NRUHFWY}!8)*^*O@ zxOmQ+2t^g;1x^;QZ$mb658Q2mAi>PmfCt=;rC*Z8lt|AX=JH{NA=b;piKclEC7Nlo z)et2*X1Ar0yEG2!a5wtm=XE8#>y8Cq%)x1V@kfGf7(Oo8$Se*opakI(P7`h6j*oaHapbr?&| zI4`O!(jevj4mh0-1gE`CY-9QCvlpC9{R=~y8K71*%qO5Ut!p(SseVaQ+gQ?rJ=Dxb zuCr|t?b(BwnYOV^{bQlFC&)>G`d9uDJHkc55ew$r!arNq|J1@3(hAi4e59>aE5N1) z5aTO`;b#e$o?95F@`9)TJWP}K_WAW08 z%JSvKWlK^aqF7vBxztfsP^3A=kQa#cETD@Jc>w2*5Ice;7(+z4?J9CU@0Mg+->e)$ z4$Rm2;V#Kjkc9$of2uNKJgou=6MIkFX5x^xrr7A^K64cgF@-idqyk+DPf-LI9CC0> zvJf2hO0%s5U&Py1tjEN>*JHeU208q!@B(|!cys{`w<4n|_ zfXA$?%9jw&JysAkUuzj13!a+8e0S%^9B7a^A&`>(fuA?XipLw9y@BL1trEhK+0m*pXqI1euM;;g#N6xsG{H?tj3=%v*;M(V#vy z2eeM|gTTlabxh%mbfNJqqXti&QO}#YTHY;yvGOC14Fl;uz0=Xx)&=MGwI%sP#=BI% zY#daaVY~a;$bMpm9aD1{Go}QJsB>&S`09`_??kZ8`2QW4x7VeR95nO{U zGX+oANu^0=&ki$4seu2<>2HgN!Koe#|0=B!Ggmracc9mQ+ut_RMmoy=w$V1-$fySp z$q{3xSxelcgCu*CvcC*z!cM~JqBLYN?`1LVMABaABMJ&?Djfx@ z+`bnNn_+8FRe{#+14G|8OP|z)h9>K^U&cvUTu{jXi@SL!UiyxwE0TI1w9c zHyde71`ns_jDHWOp^m74(rNq3=HEHeCfdQn?H_5oV8dlggciVr=b^4Ijq@`eII41j ziQH3zjIK@N*=&yKsu~~SG^_)M^6At)Ao3Lae}Rr^<xLsI1x^ENq79xn(-w#C3!(|2p&(GYfpvvJNo?f9Q0Cpm-co}&9OAxhz+D`cMDYo{wbuKXMswsgZ06eEnObC=~v|`0n zTfh|w(z~bGCI-Rs37E1xW`?a5oS}0NO#?-EsQ70J?-mLxL*Jkp;GPxMF?)ENnFRlnDUe zy4p1wXi(f9xL2NSuw}(*G|-^45qQyj@Y7W7A6e8u(PswXDpKI5>Z{`*V- z{>S6t1%aC$T5cP~R(I^C4__>|-9R6Dt+m}`nGz+i0~HL%C!MyIxNN0uh~?UfGBh$W zV2>1;fbF4?@t{ok=WBaLP=2YAkpWHVgtvb4{|7Q)yPfc7PUxiHx-x)n*35SVZ?D~Ob2+~U0|>PwY|EY7z0Pf5Ca90-AP|HA22wqc&(B&-^C$CaiJb31v7w((JH zYaf0cw8~PV(oOIM79ZaNf8@Le@}m0=%}2}7?cMf7Sc&=qFYO&wge3#iu zEn^wn`yTr+oOq9YJZup%zBV4r!OJiY1M^(_?y=XwmR|l&nc_0pjl;|E`mWKt@3N1^ zNA9&x4;l+t?KTj=x~-i6njdP zG)-5)H`5ixzLYCA13=e84Z!FD`v83SLHlUXZ}!TUejCf+!4KK50-+h-7*(5>;i`!* zK4jnAkot%A+cQBjyluDA_?L`^D_k-@V+rTO_FZHZ$KMC+J8Te3Yyn~T@@#%$iOs4k z89O|s>2rEB%W+n9mscwdHF7M0*B`h4V|g5-o0ja4zk0%MeMV9lFB6DCWZjjy)XSc- z54DW12BPIUIvVNJYryHXV7Lln+ytC519IwJ4%w|w6*quJnl0nAyPq8Xcfl$%!WX~& zx52{1NjE(Ex!_bc2t}HN!(IpuSWtGNo561LT5zy~Ae7E}2Rtzmq_Jox$)~^i@6ZSq zL&5gN{}xv%M3|B9i(h~J-=Puw5ShyFk6mxt!z?R71KbeI+b58j|M&p|f=mhrqd}10 zj3QI^Fo#R#G0%SZ?+{D4OICN#1Tp*K7zI16xg;(yf2|v=vV9Uqo$WF2;BoNrKm z5*1CLx@SIFCzv&%mt5k|XH}IQCi$a>sQ8B{4F!>?urM#suTNgO|9OG$f3>&RlsHV; z*53%z5dhZb1c-Y&qG@f&&^l&X|GVi3SV`a7ZToy5^EOf&3Wo1l&Ml&&=b97Hn zl$PdI!!aCnE}Wh(H0Aqki8_1g70=qioeqV)`R-aWJ0ZOa2~>wuGbO=I!)<%gYfxeW zGTl(i7X7L5ghgt;_dJI+z(8Kiu|pD1Y&{IO!Cm4&L7FQ8TU#i_Z2 z(IuDQDV>CJ{C7v;1Z1dlIti8XgSDY}GCV-)wM>zPuhgrt3@#5Bmg2?X!U}TQXFyG` zgd@yhIIt8Z| z3!;T{kRdj{F=m)~8BQU-y0bub!SHuhGsG*+NyC437LEgHZ^Q_jfvWu$s4|wp+q($Y z0aeB~Myhxj4ORPMh2i+NSRoro;{~jew$_}q`T<>q8;IE6juWl}+KyYG%~%GX=_ZWC z-*giu0fENXMgn;m4S}WIDTDYs@3TR?jHdq39>VU1z;6}bu==0H3(G+^95<`7S?@(Q zdlG~}NKo!!ND?BIgXjKA6w=b*o|JCPnY!V4dUb8*45xFXSAfGw3)=)~te zNkSPY0sGCDcQTg2ImyC%aMFwZjqaqEC6$f}^`w`nJq2>oOE1f$kiJcsS@c4LQQ0^` zTv=TGtINrCWR*o#I3-0$!{I3cx!#?Zbu$$v8Ou|INHCDiDFQj|erzM6iZ7%HeL-XN zK>hn*4eg}!VLrINCRMndSaV4)VLZ<7B}@ltI&>JDO=BC&;GyZlINUE?m`W*VFEFEbZ6I<3sqFl7La?E;iWx9kWtdjI(d4xdorLP=g!Jz zkd;A2cs_*k3q-PFHAJ_-a86-rbpYZZQ!nD?K++y!u z8T{S*gM?(fzMs&kS=7ArrJ>{lCtfOyWnsOeaZgn=#_~uL%WJ4FdO;;$$3I`OJmZl$`GqACCbK>MxD1B9V?{QzMcI0^Q`SLbC?CK2!ND+9bYpdw?hUfLXsGTv@bcuh z54%gszAfWJmF*EqLwX-zdeBm5pSpvu9xMz8GPeyD`rtnX3!$|`NaIn`r7E&+-SI?K zryA73J#tAimN97n^YK+fgwcS|t3w2GSK(wpLr1DlOc)#B8P}yT!F5gn@YZ2w@}~KB0eYJbYq{Wh5;e)5O6s>A|ABTe4u3 zvnxxO1lqw1xOwN_LufeB03`(v(Y^pXMhf8|$Au$>FuZ*v^$-sL`Fa%zKwa-sxyK0h z6tYhb@nuGhD&@PChV-}uqpoX43FJ_xPe%!v(5JkjqR7-0Cyf@mLxG&pLI$Ym+qwdt z6nHRWHGXik5D}-U>CZQ*1TZjEO~dfvQ9`HPV}x!Hr?WRqMg7ZM(=3-coUT$fMi>Wp ze=$bria!`5^n_v4X&v&?By#^A>lK8OqDluGX4?ePZg9%gSRs=1p}H#G>DBb1|KXG} zkhBlIZmf_#-H3*N8Z`}SX=JG5iQ|NxqJlU)_p5E!gSz=Pv-2o51vU=!BF=X>3iF_=F?p#^{AB3Na;V<-7T~#uIFdSRP z^Qzv(C=KaxF*Tf#KDt(`9I5X*UHFPj9i&Vb-m&8k=2Aa0reW+D*${TL%lJ`c$MAoh z9pBFrUbZy}%YDRl$t9t9#6Vk2efWH#&W0ri<&3jooGEGuXW}y2g|ZMQ|6k|KntWkB zSqJ-9p|F;$gWcRPPF&p(PGn>ZR5@|gzs`wTr-1GDu-x_ai+-}tMD=A$g~5a)_cx3q z_cnwhSs9B|j@%UpNBC?gbEkZ4$NWCtRv`>fW>;B4tJWz()!$$X1evFhkFgRtBi>N{2nd&1kJOTeMSKX=EJdjnkO zhEGlsV(R->3TwkTk~Hh_ogWPS3bOyACY$)kq*nH}PD%oEs4O!|UxO54(JmIU- zoqmUqqDc3uJA~AJx}$43%Y8^U2~WOL=!cJ7fP?YFaO|BzA#4I_74N%OWkRidSEa5w ztpb~Xj@~JB0(XPE-Xjdd;r9sRA&c1=UTUKSvn-~u48Hyz;W|kA8Q&Nan7j<@$N|O# zJmoH70)FCNVGiULcoBC5>Kh5(44!bGK(_M)TOabEi)vv4^Wt4XPwd!7lcB-3h0pF2 zK5GarBk|U|g;99Y0|L28T#p9REcf)VHjW|^C)vnqPl*$uLZ+lmD<17CX~;c>%f&Sb zrzvyFYhrQqgTgdWl=26K{eX*8rz8F&%F8$|MM`D8ZRtpml>4|fHS=lB;e-sI5T({Y zBQQWym8iU%0Wc`|>>=S3Am-qHVJj&7l{#X~bj?@>uYXv$0iPimwZk4A#t1&@pYTgl}RyDr}KKD`KZWOlrF`+LE*pBLubYGaR4%jAF6*wx{fX(rk z5D5d+S9MjqBM5nvdmj_J@+rFwoInPc4%>csOgI6m&wjH$G}SbCNG01lLZm}dR9{o` z4qB6{zE8tvs;^--*ADRbYwLw8VBTu?lfrAD`sa0QGE;qH8C>#|un^}zB{;!T8($ms zpO@kKk3$X$8KDR- zJt|ZIvv?8j9Oq?tGkChb3$c9P`Up(;pM4DQhb^QbzfV| zM8>M&7oHb-D?!>H@Ms9Z)yh7CG`#2qVL;O`SHf&(ae-6r{dGtD=nF!4)>5JXkj{iZ ze!4FjgI}k@lAN>(7;mc=g;JtdYhI%3CstWdDU&i|aNdj1@$7h+MmHt}3>jlyMxzZ~ zUJ-VJ2>Cnj+QiFf>JNSuri%N#N~gVffdCt6a|{}3a*TGN`bL;ky$47)c=DLV2laOx z6BZLb=e-UQ>8#gY~44B>X4PgdYjY$Cmvw0cLELR^q;x(AOIrD}v zB4Av2GkE`-FnxFTn{@h)!|~2@UPjZ1<1O%Nxo-&r=Lb)a{@4Ky$c+r_&OZH?KyK5G zJuc)xxBIz{{l5E8WfpTUmoEe0o)XdAQNgY#Vg=0lbuU*GX__Y{s;W=q+rj~&KD|x| zxj6oWkPq(vzdHQQdRk){eB^|16A0Y+#_0KZ8I7!VzbnLp-tl+dWzEa*`mR`f{B0pt zj`+Gc?)IM04dw=TF;!A?-=lHm{`a7JxcfbUoD$JF(X+R+B(8h7xEK@~d3AnY=-v<} zy!JjgiRa#@o`yBd#OzxRoD+ER2XxI`(Dl21C`^GMLto#&lhSa-L(882P-sQ8?AS+i zJ>fJR$IS>cmcge#hV@Hde=LyGD~zv=TE@$0c(d#i!3A2z-+9+EUWV6)%R6^`1m3Om zQ(+jeh!=4;FVaQSo==G%#5BRa)d?~N7 z3_kp&kR-1bL-7%K067_p80E~%Xyi0P|FuftoWZ|VJ zg)H3s8=4*A_#;8ZU zj7D-Fo~OMaf9G9tyo{#)zMtvHg})21{^4JQOY!5s2%|xZgKfk$62E*F)|agQk1(|% z%_QL#=U~-h?_Y)f&}-?j@vi{K%oU*ikza)>8{9EF93TD_HX=BG7ji)0#TEo^EQ8Pd zP8n`|V-z?qqY>Dl|5AbTcisiY%V_F;=f}-}UAWN{T)XvsGLce(Rf*!n2f{iVl@8BCX!|CCZ!DHUS39{K1c21c>IK2B#{Cy z;9Y%q8QzF%1MNzv+x4m&6$_cG?L!7VMxqq2Zq#Y7YfBQ;RzfIhY}bju6}q;E3rRr z(_SRA5c+2P%j}%F%<#?a#b?2pFX|xP3JSHwf~-u+jKJsGizD!wjv|TpO$r$NI4`5& zcKR2N1Ni)K2H z#c=UAX#MYSaX0AtAq)I7mcg$@h$P@PzA@@LFQZ}H?nrS;vPpe@!MrfP+EJ$N^J^0& zb^tB zs^m3TX=PKtFn@xHLxG50-0uV-yZA!)bFx;d9ZD5UJ`S zlC%mh;@tu8GMZ+_;1->s--wA7XF#T#7YV2tt`OpUM`?xA!M3-tuj>ALy3ndyPtV>- zQIOgg^S*&-2<95XaHQGvkl6CYv3&QO%l#d?R8~sW8IEH}dRlsKhN1fl#cvwfnL`om zZ;oK#_~B=}idklSRk87YIq>+#Lc-?ih}U-(JK`JS#BN|t2G*DyH_Xd$UBSP_iCY^| z|8O_45-gFoZPgMr($`udzO1`g1BQ52chQOG_7Fp-)DWJ*Y48EDjx1N&%k|3x!lOMz z86Z5}L)?hphzAH)x*@C&7{cvdAS5P;$;K0dx9Qr4IjNciF%eK%mmr4YUX!8kKLSsn zTf22deY#t=$L>y!4Fg5&Nk28l-WgYnDyEtY;j%U+CcMj1a0;HgjFf(Mv+5lD@go$v3Sl2-&}mu)MmxW!h`+nr>knP;-wN@nlQ;2X z#xgiBO?(ghnDLFV>*ZxMez3fkcn16!e`nQ?J>W?Zi}vd8Nf&P-xsUojVljTOk5~n? zbxHB;B+bGKV;THbU$G3o)K^>y1R7r(3FKuo1g`2Q{?L&6H}@A^4XOYB0I>wWF+e2C zt2lz*LlRy_L&Vxl@!N*fzj>gz9Na5!+p3fwHj^^5F~}~o&v#T8I8)2YE0>yF*r2?Q zrLTu+E_BctBexD8#)yv(5sw3M>g4 zcBwds1j0WJ2DSZaFjd>N7Sz^Q25%iARsgdNZ`3%+g(_Ic22Uy(G+f)JgXzzKCDo^J=ap zg^CTScdKZB^03Z?q-<_4zRYvYD6uOT(9NU7n5^@Jl~K}J_+!N&pW}S|iB^H$@vl+h zH;^bR#7#zvg?RiJk*st4OD7^Ty)Y?Lh)YQ$bH)bIh(;X3II%lyIMoB-eDx-d7d+`> zMxf?W_m30PSS}TwGpEF+QvSt|Kbq91Z;d4J>MQ1uaOQY%3<#%oyqE?3af+^8Gd3E_ z;MiZBD_~ zhdF|klOWfVJzXU0L4$5)1U@_o(y~!A#K{e5CIX`zF%ln{A;v>5smF#Xxp_*6nC;u1 zisyC^K8KmPGevTX)uNeV4Bz@EJwwzoN;;_1PXB)6Q;xtBN@YI=!^WDQc1u(fo{yDeebUO1J{bVg&e7e2BV1Zrdd14wE5-(>p-295OSW9jF z?s=jU4i3QoEEM~K@9b`YQj;=ScDf+=DZBY1>c-6?raDxV=!6(8uV}hT@%1T z1c=74LfWwfU4Ky#bnvr_=zM6gk$9{mk~6g?OJe3kb$}>6Mkt7q4!|Ej9V5;6{l?MXPpd#A*|tQy zm82N{EQN^Umr`*8F!rd9F=j5;q|9i%pahl=JhPOlh)Ds158-7rc6(D9IDfgUVU5I= z)0tTgz`ND*G8!a$S3pdgSV3c2ULe3m&Qyq(;%_R%(E;;RgGu2sI=<5*!L-hM`1W5< zX|q079p4S96z8+?9Xv0d(zF-VCXxIJXncpdtHBo0D+_^QWR-ZkG>r(Rqu9yQ@qnT`j*srzcFI=xv-)u~2Tz!H<1aV9YU zlu476^q9RG+X(?2lmU4tvE|2B$?YyGA4@^KHIHBqy{T2ne=vu(cQ1 zc-Cfd9-g#WEUew-Y)ucZA$_PG2mf9`)BY|6KZ{;KshQmq;JW2Tyns)LY~ZAEAl%hL zVsiDh;xXXY7?=3+td9vcuu3QprqS@GC6^X&oS}saw}^wAvGAtf?n*IIex|M&er=1` zG07u2o0QE14Hna=t%PnBQ&B9=+$tuZIJ^kHjrFWNsa*n{43Bc!-5rT{MRSQ&=MJs!~PH36==!awyw!D9dsvyK*S2awwZ}D2s9^ zdvYjiawuDJC`)pH9RNRv@*;<_A&0UchmxN|Nzaik2MM}qg+_tI97BH<3FP^xs78RM0OIxl=(;BXXyLt|4-7PNe-Lkvo-hTk@64x%NXMcPi-d zMD9e;QX!H1i{xoO`EW~^JmtbU`x3dp#w}}dVwzjlzY7PW%-m;m58Qm;OI?tzZ2B diff --git a/doc/LectureNotes/_build/.doctrees/chapter11.doctree b/doc/LectureNotes/_build/.doctrees/chapter11.doctree index 8037b99f94879ae05d7cfaeec385379314438d41..1c46f61973c5d095a606d0c366363b79440c42cf 100644 GIT binary patch literal 578260 zcmeFaX|OEUc^F0z3xP|3AV3fl!EFFs68F7%@6EnZ1f|*c<<34A54`D~>6z(Sdgk^r z8~p5ul4Z*t%L?@*+bKJem`Jgz64_B?m83ti#klM^QtU`nDzT!9q9rQ3%6}x4U5@EW zzH@pz-P5z&_vQhV0#}b{q+Z+MZ3?AIy}SOe;ZzY1hp60 zk#I-p;BjcJecOL>{a3#9>h0UMR5hQob=eVPqa<-MrbM<)jYdmbkKq`e5}A&z%TLC( z*rZ+L+Kf#e&UV%p#i{T`hoi@eeTlx)o{SwZ-UOOx|K2!Jp4hq*9y+%5#qr42?o(5d z;a#pfoyi?>A=+%WZ-4oI|3h!z??1DCqRK1~e&1HG{l)v3+WjZ{PpzMtQb1qve*amC zrq(BvDDo^Vi7-ECJ|1T~0?>Z_q4tOp1b7I4Kgm&J`LCxt(p3LJQ|%$oba9)fWCGn^ zKY>VefBnp2Jo=(ArO>=SJ>?mJ;b+W!Y5gIQ>Y*O)_fOVOsS}@d)Zo3~$WM5Y;nHKO z?Wi&oumaa}*6zw=G=uSMF}B-f5W!e#WQ$)(z+Dqg zu-WFoHMSVTOl>M?G6%fyK%eRpF`0q3D-{;`JSKq!b_21|_ z`#1Bi75ZoW8_@bT#_t)JR;tHS(>{sD&sF=3t;Vr4ATPilo=*A6f<+=S;cW13!ZTx= zAcBwxHn9&3PT4p{;-M+Wi1P_Qw6!Vjgwj3(5#yG&uEb$l+VBSgkO^e3&vrTtXB$yV zhPP3p3D6GHXu>fzmYYiA3B`466G?ech>{(I2$lYn-u`AJD8AX{TJ4;V?cjj zqwSIU1CmD&TlLQh{hI|K{tN5JPV`ZLt2P@XjzdCyl=ZQCv;cM+Ho$E+vmd|+pB+4x zI`t3##taj)Qy9J*gyB>Z21Ve*vV8#?aT(@p6TZW86u-1}NNHviX||meWAPg{Rse3a zX%AU$rlcvaCB8w3ib zImJ|tZXpWnA=YRz849)$I|Ln$Ox_FY2k$^fNdT0tu7}c1GfE%U=G>0`0##dswxO93 z%&ws01~vk)0K0vnVsWi+bik3c|Ak%pdaatq{%Qa7{VyQ(eS+uWX5KBq$G4RU(V_qN zmpbgs#&+I(4cw;JzWgNz{M6yx^418^4?ZA79ulHw)+b;o`j_-*(jJml<@-+V(oB!# z-cg0+p6xEC@jC!8{0%n#9oM~+?%fg770(v8Y)#_q6nVRdK}gnk0)eKAl>Ea;nqMM&*sZsI0f-U# z+X^x8$k_ILb~oY#;QLx`AoPox2078mr(#1sGUD`W4~^5)DozCS`m-HyKE|ow!CywG ze&?Z~dU2Cm^fA^}Z+AetmoxtOq2Yb(4gntgFhjH7kI>jn)ykS5(R}HHANT_&>*@#xg}$vD5e=Tl4KRbo!)|05HpV< zGy|@ymEQk~kVlq4rQ9KG4z>3=xH70)!uG^iHupVv@;NF5ze+&^z zr^BM2A*g}qUj7?Afi8wYQ=W=Wh1l38E~jb+0YxS!5ZdCl!ej*52t>Gvjb>~T$6iT_ z|A(TLClGN629$sIUmiRQ2@#UF`?{L>^20HcD*F%HjX`k?K5l|{zm|?ET3SODE9x(! z*?VwSCrJ6QJ?)-^#}+Cb;V&a8&W=QiC$R+Tov)P#y8-*MtY98g$W^Q!wi_c!zVk>V zv0p<45rn(eXIA8W26B!_qcD)@BR!YLTq?cbFAe22di?UBbTHEEr=WLcjHTb@k7EtUD6jU{&rEj!AVf|W; z5wX7r3oGDrYF^`M?-G(B5VzBE<_!6apV-otAl=p`0QYa1rjMBVr{vL8o2LHM$b!<; zgWorOzu(i#sGgoWH1_l!M>uI+uklX{@b;5c?Or3Ro)x=ReonDB*ZM|-ACu-k0%>+< zag-IW&9q+m8xVM^0i=$=cW7z7OSDeu+Q{r}Z(s!NS%^d*5VQ&j+JB)b$<{_f@8lVo ze<1VLzjOiH+U)R$8glW|d!e(rnQvUHDd1S4@iwU;=%vv0L;Y|Fki ze+O7XNx;c8!Ld9=B;e2r+L#(bh^q;^0EsrCyM(Y+Ugi=Q@dRQ|JrccTJC#WafxUV0 z4KJY08I%J>ixV9i%~G%^djhNJZCJI1n3!JLPD@HkK%O6)GC`-Z1!AnS2oP|e7}xpk z*wAvIji10u-bQF_>i8B;R!vSAPJmTdP<4Pc^r)`w;l*|hCkO#o3=c_;KCJO+RAGe^ z2Bin^>b&wfP8Z<793?qqLZfbFy6FV7jZyZ5W=>?%vP?$-UXSI~=@I%9Y1F~1kqn*~ z9Rg)uPS6N?--o3^2XTA73`nTs zU9CV%??UDfBa%E4GB4RIWQ9P(`n?qb7CyuVk}s^EH;ExJ)W$2TQ8bTx{gf4nu8IyoOJsg#7jj70nkMP~V#zyA)-yex8uOHxv5!f8m+zP8hsrt#S zULOI)jz(5vYZP4{8;vjX(c zIey;klxr4sz46Looc(DA)tlC$bUk}>8iDe}IWC2yp;!?IHfk-T8q|Cjw)`l6^Qj%J z39{^L1{kDGQ$pr(4)HC^rtkN2B0FYRa&79E5&M%4L}n;{LyN6~yZ{Uf$fyyDIvE=(d4+~h+lpdV zbM&k%M$-%`<7FX$-VCHs6MiD~`ZiR{Jg4{$l%YjPded zcrE@w^@3xCKP)D(nNZflmAQ~7OkNZ3Fi?TSKnc>Efn0_>Wl%H;i|{a&5VdO|I>h{a zl+b|B)G5`-{pbeJ3GB@ zYD|pt)IVgxW54RZQdPf70<8K!vy-_9a_(tpLE7sq$o-cGqqAi}&Kf(*MRpZ`VgcP; z`o75~FRUw%K)ML}K9cS&W<_WCopHoJJa|IX6+-J7AZzmmPoluZLIy1yM17KoJky&G zrHBY(KV(N%IOxH|V_jAJ;V+}q{>vj#^%+g0>I1BahgJX{O5_)-8>*Zb#OkfpXgWDQ zW})C!0$IK@lI-6eiDaL}rg6JX(ME+l+8*n($-(=*V^umd$4Xy?8=pjV6R20d-=*2! z+3`#g>h8u@+*}eZKo`(g}QFx z+TL4*(_6~Q5$WmB3~VBWosuXggQCO70RTc|@K2DD&jHd~R*xPls1gBx8A)|!`f9JC z&wMqg5=R>nn|dgV-$fC9T#$g>Eq5dH5hH0;%*>CCXnyC>(0txBl>}ZJuXZEyI52?< zJ^tGWa^YwoKZ!Yw091Lf8@%TXoT&n8dTIojIvU82-6Ft+A6B4RSey+Rcwzm?&Co#= zC=K{sjVwmqtBwg7(G;>?v2m^Pk%uoi`Cgcm2dnGId=0A8EQ?NF){0J0w6#%kvhB4- zaIB@j_TYg1un{ob*!{*v$%(p$3<0XtlX&i(Jfqk|qb|8+D-i~=%TsOGaQ03CJ`<$z zj4bgJ zds$+);rjxsw3H3XaZv6Mxd|dqL2?li8Ui(*j!+E`vi)*a3R!c&=yrpj)4REWJf|+mjdjR@0Y94^L8q`E9tksEa%J2{ZjIrJ^ zWW6PH_=OFQ-RQ6oF5tBd_*c$?YEO}V*<;0UB_T?fLowS4Bs0gT>NQ)8Nr0d=?~cUr6;$BUZ2}DMXD~@ z+s@4j&90-lsoB@x$Vu%XiJOROShrDox8(gT)3^H_hM&_3rVgwu>F%U~K5?HxT4@KdHWAv-g9K1$7E!(% zfO^kzYd?!QX*(^qpVE~1m2aZl+Q1Tv&uZy4*ycB5E`c{ea5mCx`;v1j!RrzAZluh=*h`t+S*L%D z$b+*^^bb zx^mg*zOerEu5Ss7?`{X=e(5P=Bx{NwyehpP^Af$n5BT&mrcbxCkQ_ifXTXO{fqheF zEfpTjT2Ek{wOL-vzb&BNKN-Xj#ALi@b|eV2+vUXUup__w+6TAV5!2RR_l5=8-aw-= zwjId_hwt|`;L~l#f3jgakaLx=;Ag4`ifQ zeJ{OsTa-UQMB8CeelR5;846{LRvJSogN1!XxNdYhf%CrLP*EkJhMwZ$%`rN&+18)T zq4sh#f&fxq9Knb5q9_u@mHRZ2o}pX4cW@E<=)Hsjv{Bcj2oKSrgU_RnULH(L-#)k! z{iC$TLMlL5iCWeysx1z;W<>Xd0@bbA9b}Q9>K(GiW2l$__JUOICW`?dVymXwmFs?{ ziQV9@$^`s@g9(Tn8K_Cm{E1E|0+aX56#NZ9-~mm+2d}o9f>(?oh1C(TyP9Zp#^&Is z9vsHUH(=DwL2<(zsEhZQNAy!*{r67r@rVZo5l8RWNR5B6mm0g3{ga3!JCuD)IUPdx z=aq7@Q#pWA&S}7Lg}g0=^uFcu4|El+9=odHuvVXd`uWEu>CsmW*JSLVtR9k&wC*s2 z{LiL-wyQBUoOtnXYD7?h!0PHLx!j7-?&_1>;65eOM%63oPa~NB*U`Xy66|n?tjbd! z>;`gA1oJ0H1Md~s}Twk zbjDVJz>K|vW7Kx4H70<48l)VPLj_fTUX9a=`maOpSVQm+m{*C1w zcJ4v>z~(tuA}lg1=d>tne8(16kC``rfy!&)JUMpz5&Z%zKFd1+F*#A{*0v80g4Oo7 z1szHXv4r}$vZZJPsvZVv;t7tpF680!3fT+bnC>zVcnTDp58PQgFBy{qQd3+NZItLg|Xav9I?mM>9 ze5ok+fN&Wc*PKpO&s_UEO&qaO`j!cz{Z5EicS2NjuoGexD5?!KPs5_} z%A(D421X^O!t`P{MPJl7PLT}TJ(XxyuZ(p0#M8!%!GqJ~^#g>8K=GjFyAgk3Lqt`) zE#4T>zIimXpOT9b3Cz?dyMcFZ&f0D@qT+V_4~?k5c{J2NyIZjlB-z(;H>p0VkxJ2! zDk(N!7*Q=94b@MZncJX~wNcl*+gYHw-_jC#$kNi%XqN@purABPc4~+?r7Ms^RKh^)t-vQf0MiJC_Y_rO9(t&U>qO||GKBZULn9UW@nG)c&9hFh`j z7KWP)X0d-k;;lIa844UvnFOFY~qV%MMh|Fi&q-E zVavvw`rWU=1G;5Xfx?#U$G*+kgP`)aJ*ZX_Zs8QD^d}q#lkL|gdu@7QHG*Cir(1rF z*Hx`)^-3EBv(yhBjiolMyoJCL(|SmMR(SOKCS zZr-U1+?uV^=53#jQqg;mPc`uHy#L(M(0^KS4anP>^k)_%*l!03tz~5g*J2usn!yN~ z%o8?tkSirk6Fx-`3?ba)t?XZx4Jf)e&tNH4+Xj^!#P_mUfc2F3W^irx2LBw*+{=Ss zyVeAvvXC$8w!n(2&F4@Yzi})du||IfUwvR&#lnkMU1`)s6)||}Q@bSq)nvg*bQC@- z63)~!R$ckk`cL`FL|FCGs=Ac>9?8?5@r?*hWoZKy1}H~N!^MoE?KE*FpZ@x!yrpa}8@Hc&7*p5Kk1K%brmeGWU}?&f^;v=)Q=h4K1NroQ$WEAFOI-xdt7vaL*O(Ej_Gh2DZk)dj z-DgQ5BQP^Q-;Km8+htS5XIB#=YM(nAYCDP*RH@M%HQm)Z(e;Q5Jo(57tovxd-n@p+ z(qLF$=PQdj+;64{wjm74dsb(d1$ysZnMP+5P~!cKo2W98=N{i$a{dXe&JbI^jf(TF z@3oo0QhD*<&_y?()7Shr?~76^3^BAy9eDuC3(=)&y8VRgHEAee0dd=grAIh|kwWZV z3hk~eh$AwYs}6N8UVl=l$+}H!jJz#x-=zAVdi#F=GjHEtzoIny;^y|r`&9pP(CXE< z(aw&(-LM1mko}{dEThAD$I=K27jQKLE+>X6_OYr@s*eem1R;lvUYBfw$_+{LFJHBKBlgPfO0C*t{nx_a{cE!#9}NQ0n6?4-7Hm{9 zI;ywinj^fZ10UkEmOD^vaqC2ops)i|61F3#yF_Id6UxTXJOk}a1V#sE;!{P=Ud&=__!~7>*-0sY;-^ ztCaIkx#G9GK-JSm!-FxCMg1vx*2(RT+faSZz!}8IrWgAWunYlJW%aFVVqhHuZbQOyyOBDhs$$tM zutfKk0{bEo4`Z%HoiwXgnhF|x#|hThFQb31Wh>v(8I*uXcQs!>z=u>pJgBV(Gj@D-e#_wKY-m8P4+~&41N9!tb^%@Nz+O`$o}oHR*%-@4ThC*W8{O~N8pv6a zvxtHkAft_iMm>osfs#jGeDHAz33-@aK%BfLZqT*d^|ryhY3gUc+T*{fO^XTyR(qe? zK}Z7coy~S4wo`qVj)upHuD%Jd$)^@j?pF^4*$82L&tmKTUg1Pev}J7l)t?3ifKzQ0 zr3{m=W1+{+90%tG?ue~T?~STs{@~Dk?*??b!fR~Zy@#PuV(TD|t>IK$CAhwAQ})_u z5%;#p`jPc-q|W#6rOs}}`WF$2&AV3Cop8^ghYTsmnLJ}6fwZAJ~ZpmKy0VWkav z#3d@QVxwDJ6ht6!00vL^I+XnR$H-6-5}KJyLFZLia&|_3kj#XtXq569rYJN;zvAZV|_|Cff0I(7!q) zTrxGssS&is1;-Xl(UoYhf+WHf+6;xR{6<$Jpe-BdKmv4s6vx0VZWu13V~3WD@tzkr zBXkOzNKn27oz)DVA|#A-*Ja6$T*L#XoDj2XeFpOIOD1_R#S%eP&>jmCgTN2?^c$v6 zw~LY*OJJ@fV~P8^V5xv$!Ro(ToJ%0}?u}_dcHL#$>Dl~m2a{Y4Ot(?k`yc{KQ0u|I zx5C^alcVy2szbrimfjOxK_L7d0dQ@K5f?;#@3(=bBPjT70ge?twI#rvviGf{$=)Zn z>3-dJ+1kVc{{8U=p#-cvjCFcz(S%_gz;Y2m0;8@ax#g+~5Z5F2s1xOgodOwO`tWsg zD1TG8RsyKN4 ztGYm2-Wmz~B~$O)og&pj|LkXKX_!Xv z@U5qmz-4#4otUgYq;Q5hVcKuw6j4V*>aiOH*VOyL<13&B72|>-#Mx<4->#8uwsp^#d@~ z4`Z!}u4r}`x;$`VLfzu$?- zPA2`$qe1?ZJoyBy>XSXt?YI!?503`j(<(<2@afNXLb&hpr+-yw#|VU535BwZo86` zObnnKIpIjJ4UbTHZu0cD+_m}b3Z8Lp8hhtv_gdv2pb6TsR{6&{M#R;(8`oLmjY`U0 z*LW?)bhR};RLtt$EOcavc@|mQ_2=&tk{sLw7LQPrW=N{ZD^NJU!LH=2iCR#KBW5CQ zlUMU_vh5Zugc+~dep*GIP^kJdkhq>n4H5>yd>OT}amoDHIGa;bfBRjSKZ0vHmHAVF z!7j|Fv)OJ0_uR(#y+=c3$IcTKWebCR_ffK*Y9Sx(AV%K!(W4Qx`N#xE zgLwVu#<1YZ{kEPE6T;T(w&-)3nXy^%jg~;(+fJhZww!+t=4`i3->scL_`8~P6JYDX z_61svQgc`vr!t{4A+Q$SOqk%n4;Ino!%wLZoFxVN9QJv@g1UfP&&3_^7n zpTn&DvWY61AO$CeeY{wwWJ}UdlgoE~T#eLN z&i~{g<@_a`VF|M8a{j9cRJp^#?cr=2ZlZ(SHQsizJ-aV?Jk zH=O$k${NlMfl^U)zBOLE*G|R3L*64!0=s2HxS+kWES&$MD0eg>aZHO09AiN0jtw7N z0#^moa0&_32OvssITBQc2b@QXvp*tO3M83HX;MjPsX>#mZT$v!>Zz*2UErp5_wiJIut6cu};&6hd-?kuH zP3=w=B1#6aERpKKEWrc;_P4cyL}#)WHk5&C4lLdn8SSqfjnO1kU%adOhoItn1itX>%>=f{sWIad2CR5fw9r6zQYm8D*P9l7=>FMGHL!Yit!9oP{x^?? z{t5Q6FdGm^l27-bV#PZeDwZ#esQls4Q2FFmjwLYL(P%fKj}26;;4dQz|Ig7-com8B zZo$%qULVld0;T?04CNPo?#WrPWa(GzTMqbLh<-_i*7VRj*#kP%Z5r~tyGAm7P2ia-RJ{cX=J;5>)Kxz5QH~i!QE1o zSps5vFl7dxx!^w;QuH_0Zs-x9ut7<{1U4%y$MDZPQ$%pUTVxjEJBkN= z?<-YXQ~pw$Bt<*EKZ6EB*?`&>7R^X?mEj3<1fRY8GpMNotomaQsrn;u)Z(rRm!C&E zS*epSBn7u{+$m1JiL3~FzagoHE~n#RyE1GCuv&nFgykwSv4tk-5#u8KS0h@r{kcu#tD4eH1d9v zQvOM8%2cqiN%`bf(i4d9XtbLQ`eN>8fWEmRsgH=cbb2%-3&&*{9nST!d$u6wA&U`% z9P&S29(?b?B-^qYv5ieES0hwLIy}cgbWivQy3hEtVeBaOsTs~aOeA!o5h+Sre1ub6 zsL#w89+qe2^oZg@qIFo%BO)jy#c@*B9MBW3lnc`T;AaZxs07dnXr;F;vNO5Ntt)Zx z1CC`pr7qbsBQQ6Jbo|FGU?(`m@-&D-jiJ ztVBLcke@)=@OUSxJN@ThJQ|#JBG5h}V-P4msu6ZlZ~ZX~&Qux0@|}?p{->i6*eVmM za?0Uaf?zXCEipvpQ)ux|yWkuNv%vPo6Bbq~Re3d^c?OaVLXMhRNjGvFu;*cjue3dg z@9LP^^sL|2VS&kh?^>*Y5B=120x?-y*tdT5qEg= z#9^eZfph(YiCm%s>4D>Rsu5)H#Piq#_#pb{T1PJOf4rLtr7GZ~Y|}N^;>Ep<1q7&$ z#0v&kkStR=6XzL{G>bET1Gy`_N#?E7;?1hELo)0IXY z;$}ThVKK3`d!SLe_}~h(%|UOw#r47aQ%+QFcvRhM#FC?In45=DPcxmP2qNj~siF%e z>|rH|U`;TnTt>%Npv|eOr;Ah-xdUG>Bz%_aoZtfEbC~?9i34@UU7Kq7HnasyqBC3L0JQw17J=P!-V(|G%`HigRq6rY6x4sGa~$VkB0E`CQU)0v+>FbC5vJ-OOnNoqJcCj ztdG;51xEWV5WzcE7HIubNIl}(+728oipp5^N+G226}_P3-k@a2vPuc!DAd@Ps8f=3 zN)NK`1?>zwG}sXZ;ntSeO1H{*LV+xmtc@BZN>D230I3FeeAasr4F^I-eNBkb3wUkhurRl&phwDKtEr2)HsB;8w(c)#``2w6CX( z^H^0-m{gIb&Qw(d-d$-3s>p!kvh)mksSQ z>yjJr1d*BE!sXkBl;5`g!G%V?HuMM8Fp6`n<$CZjo4U8We9uTln2h%j2+*G2WilUx zfik2ht;wz0szaI@1tDb`cfZ;C*}tx_z6vxpTVHw@mLlfi;re+GN%_{%ND0yF0n(#Q z}m%HZoV`~3K|+2_}Pdp9M*DY(e! zmaWHA9Tru^p)?!%7awbaohL!0;5XJb0#X#FY8wstBlM)>`}bvhf9Bfwe$xtHUG1(v zN!-B9^&tPm+*X7fZroPy0d~d~LqaiSa+m#P}!h z&n}@*FX8^(CqAU+5dH`J32_Pc_amK$?x8~QKOnz3@zkg{fo(Ybv0_`KDIBX{uqiBe zLctYPJlq|HswL-8Bx7MdkWqqLE(KVs>!Cv%K+q^z)TFWQiN=ot58=%msY5V0ziHw< zt3^1AHsAfww9zJh{qTKR;GqkH%J1guoqylRKpU5v{xWFK9>XzEcQ5bBRCokf3NQN- z{)ZuSxeIH;Jqk*PwE?D|2JknB9;s-FjE!6$E@CItbwiMzcux|KbH7I zeP&g#a4hkhVM+*GO)sp_u~#pJXmcaqeEw+Yy=Wm^+E{C=w-)H{S4afgB8#RdB;5!8OIDJvo}$Mw zb2!%rImATun4%rvnB%)6YD{-1+g*;LM-+Ut+3KFvL3^9cZfMT(w+%enTws0iWtjI} z4#fJY-6v}Pk=@`}Y}kb#L#5S}O)tn{AqK^MGZfYEHVN`@Bikv=1Kay^`2Vb?#58R% zL7S8&x;TZ{7BX?*Ux_CkhT=Ju zPdbBh(c~!gbeA%NlPcvkM5F(Y13u+S*b}92Lp{^Qu z)WlSTkbFp?t;*fnZ;d0cB3qhz*w2Y_(mf%PG+tw^zx@d6?^?by68cw< zM(EvasnTG-4I{Lhl?_|}pAhGwdmH2$aaiw!eYcRZ*_HaV2(RH<5c#;{6XND@ltY5m zMObWw^-Hj4YRR`=U5Zi!a27JGu&7)1<)!))x%AI!<3C>YR9h=+nda6?HNpv`6LiPU z^8knvy!1ey1F!wQi6aP$_R>Z`2V_*m+xn%E+y0HI@BOy!8Qs>YfMHwrBu?rQ=qeAa z5U>zVwJ*Xd#gD=W1Vl&b@Y)!uq6Rs>r({MWfKs1W^{OkChdKe_#TT!eaM(7p(Nb|{&1cwd)mHio1$lG? zBj`LiHHwm&m`vzWh|R-qbxbzj0bXA=k&RFTv>Cj(k17SBhY3g^sYWaw+ zT2!DE)q?arF(b-t5r+b=(QFfV{gn~;i=zSm5z{ld2zPph|oxu+wiGO+UgL??1E`z@I6B;4@D*j~s+;}O7 zmmGbE1BitC>!+j4XjFi|@Bi?9^%_T*132C9Z1A_?ll60`L7IayKg(AAXV%Y+aE^0y zNslJ&A<<9sCm>P%c_=2Fjwa%Wr6Gkfg4L~)6S#oQ(B@{x6}jZ=d8e7q9@k<+<`=A2R3Em?s&OB5(atf=@J2j8cj#y$qB5xsb^}y z0S;e0vBCd%MwEEY=5m~&Lmas29mpA>QygxboV;!eqb-S zquo)u!w{lHX$U;z(U6X(Y$N5|e`19aF(y960Q-Gv2Z(Q#y{XDxYN)J)%M;Xjz<}V- zZyK!EHaiI3U~&x|P!VMXTFtU9_QlV*M?TW?sukOz3n`8FP6eyJd?y>Pv) zQd34>kmts>fYhr@M>Ju#JM5T&3lJu#P80)=y8|}7RH|a%MDvYGJ2SQ3K%%}@9YeIqp!}+T(<}mZU8GP z5Wt_*0$Alun^VDTrB48S4Z<{*MrZ1*Xdfzs(%UMB)SRiGt8{wZR+L0gC?>?xnA>F> zWC>j8eO&_!g;}i7(Ab4ULw<F84Hk0Q?Q40(0;p_O&eUWE@nLxcmJv3B= z$UDH%BzG97Q8ZRPe-Ud0xS1M#bGEpph>fl11fsi~M*Ra1?Y6~DYyAP-3CgGn!|-gc z4<$;d1`_xJ4GiW*83=~3DWkz3)Obw6IBw%GxAF6vN;9=rLrtLE8+vr9u4JE;3@R*+ z#0Qnipz&pjs4eAcD)hW9@jNQ8A{0;w^DK-FaOq?zsSKm5MkrUqN0mY9W`2jiBZ6Qn z*cvH}`|BWWi>3*BRaA{;JI;*syydz9s32;}lC0_C?E@OoQwEe#*ceQ~>6Y^bOofit z)_KFdA<7|oD6^-)#_;^5aK*!mv(6eMw-hr42=)6hxp3WOK?13lF;du znq>rDMS2N6g~J&XnUtR)KjW5dG^Q2SeH{R0M2Ih8L>5D+noeYTWZR|9DA+i}eTsI# zmJSnaiiD1v^4M?S&aB3E+jPcIx>1w^(T&T{jbb2-Sb!kAY&XDA*j*s0Xx{}sl^%4h zqQ5&bv?b{3t*H~PzfkSjl!yD%&fZ8XXrkHsqV4m&H$HD6jVi1_9FYPy3o44R4}q}9 zg`6;xDxG9CrMkna%d62$^+-xfDEZ{H?I1u%a4L8P-S!BqA+PpnohSl{Ak)6Ulzv^2 zSp6s2FvO@2w1EfT*9650Sm8mo8T&25cVfWgPY~2<##kF!R+A;wk^;>R{X!;SVO`8mvs@gG?WlJE_6oFF$Ck-f%|GAB1)^=0JM|I%jhAz1w{Il86Bmkh7fqM}s z``BO6b0yig?_E;x;ZkJVSevRQ5UioK$-N1>6TADeRg}%Ft`y~}3Z-cFgzefcFFDw5 zaCvEa^G(|umzQITH^`Bct+-4>HKMIdPc%M7j}$fhc8*l$E{)M-SEAy_NpDKEg}xt#b< zi#RTfDpbw)cVbqzbh;`$RyFkJuYhG2c>)mUDh6aTH;SUhQfCGBR z>2#@bT7%>0&=5)pg_|KwxzCaq$2D6Lwf7Rzu(O- zh&g+s#PGmm5T}8W0;VxpdPH(1oI>6J+6D;09S}u6>_Wv4&{Zk)hU`@%5K!Qaq|ith z%lB_NZ+-D?{mqDhlH1PNTW{zCym9Ldj(dY>vlvk{Gdg=?L5#Rmo`EZMgLn)ZgXU-I zLe%@oiuaQhNMJP6tQ7RWpR7=XT24>ApRAA-?EA@zEuPc+$%+GV2S#&>ZT9=giuaQh zg6h5{-cMG5DSkg$p&YgSezF3^G&|E9?V-ei? zqzxq?^5QTQ!+ZuVe*7H#_v+iYldq$%Z)V*8RI4=kF{M9=mMcg;f+|Rgc*WPUghX!j zlHMu;HzAD}L)-P!%5tl4A1YJUALnSCof4spMP%s7WXPcsmi4m*<){Af+4{q>ZMYPd zQ)u#(Ai|dX@%{A^C}WF%cc20MMi<`QUw_=V#^Uh@?m!CizI5;Y`k71ET{oFS4ch&` zEYO2r13aN*=4|lK;Sa6f!T+NC!o3cD1N{n-X=})7`u+Z(GjOss-3Lv)o`5$L!s8D9 zSLkDNz-K$GFopG}OE{Z=f~kdLIVk+62H5(e93+H=OPXpAdpx>d>i+skxX`u_XgfJ7@VIPy@U!*J;_)pk@-aR%i39C`dNlVd0z6>vB@ zleQxVXCOdI5m8=nT+$Ld>No}x@EOBjG7F{+*W5Ya;GHS_cDXKn&P(?lG>!liRWVyX zVFLUF&4mN7W4Zh5SHG0NNlREVgQGVBZs!92lk?*)TX?|;Up64n{NI-!_yAjv6w7mG zHrbnm;eUlntsk%T;IEMv{x8#xhFj?Q#7|un&>zKSInhX!tF-&V*>NY97w3^et684Y z$&iyyj@WeSV$|jeQ`+ra8b^ zntAw3sKWo{;`4ZTJe>mo5o$FY#n0Sd#0HX+hf zPxN$nzIip4Bq_jOxg}4lSLk23Ta|E@?M>2btjzXel_t&i7hTSg_ZCC`QD6|~s)bd+ zF>{qlOk`XwEsE6ySDF<&`BlEpvgu*vB2x?TIX1>dGQ&~1+{n$*v&y2F9#t-~wRFEV zgMWvKT*6zqNDrs2L89VI53{wJ&}4^|^Kq|sKI<*}xv;mNia0zej!g`+ljJbtEqN>R ze7ZVk#D&krHsbA6E8S|u+QsTcBAQL`(PZK(*$Jf_i&)f7HN2jfx8DzsM&nv@%F|VP zIi`X$=dj;T7b=}*kZ!q3?))+tAF;`Jrjm>Y;-0)v;F?Q+ORxu>uBM$!dih#$dF~oB z&0JzNpY%%+F?y9tmJ6PCKObf$iCVKS1o^P+>5)?66;S_yz}6Bzh4OZ`;llO zp31SSX(n4MmqVz1hf8tUwDWvEjraRe_%B=Q_j3SOrW1|k-MMNt80aUWEl<2HL@TM_ zSX`9o#7xLv&6+`9y3$>C6M0v6nroHk)ST_RmKSYDV0b>4+;rYm^k?fMxXWqa&$X`D zc8eb#;fGM6G@vqrwg$Hd~12es4R@XTxtrtx6ucV8nt37tjyHRhd*^Bat=_r(H^`#ESuR_s6-w*5CgGrzpi1Y30 zP@1t)KgV6nlY?HR&NTwWy;H$E8k>dE#J&hX!4HIPz+09&KvQ~Q)1W& zte%!4l~yvdbj*SYI$RG%m#Ct~RnPKqfgWB-UMCl(+I7i4AN1_@s%zSddiZgYE_ogC z!fY`L&K9d-P_&n3;fyoOw>szEYV zN^X11wMckpiFUb|TZrju-0Lp6io)o^wQ9v((d2?=TBDW29&XKq@NnYji|vIc119A7ro

=2$addf}T?7HFKrn32HCuslDAKxW)4h^Ad{K+R{B|8Hd)XCphKjte z*mjKj%hYrdaaSq~9hGKu00bd7Yx}~bLFOu4X~$#BIUVT;=ba4isR{N_bH#Xi%el`J zo)jz2TqGTs<$@gT5p#gVvcIfwBiE|Y>~bLZlk&3J@Jpj8b6(6uxbsFk5}hZ;Y=z_6 z9zPrERF~amZ2;E9y^Q-D6hCCfex{keD21==H7V&U3LP;3Vl}pRgACB8GFnvV(3B~7 zQa*cgPKR^t*t|fwJ-$-8SxGLMjas)D6z&u}Y>g3<;deK8R(U(_%X{O?Ycp ze8S;%6hoEL!k+CHyc5pOM{+suz>#r>u1bp-kcuuDjBuLc*O}#T~hMtX^p> zx*mYj!*$YhUvz{6zD$$%+Sy8%_xeh!pszdZQVucN^))KeoUTMFt_AS_ARtw;VQ-3; zn*Nn5B?RmCEKSWrY$a=tct@dCoy#m;9cF2FcVl8Xx02efOpY#PfgNbKC*7S~#FrPt z;zguR_XR0jW*gmch;k0-lpDMbrX5*k7OqSo&N{}P<;Y!hc$z}pZ;!NnX$K!nI%AyA z;dWPpp2R%J`=yH8n;X@p;~YJb8l|GWmGG>@4lTA)o?L0_vA25m^A+dF3>sh!$}LBc z=Au`=bgR;27mH-g;q8Vz)XbHcv1zHmdxnu&d(}>{3#Ydo9(t$ZAUpGVm(sG~P1+YV zZ+FyQHn{4dlMjp|G@ooR&0$K)w{Y%_REGh3cd<%vY!o5I3>jwblQOQ^i*IojaQDs^}|?s`b3IU|UkwC-$7>{wiu;3@Yj*$p>^#yB=FN;wbh?@G}~OOV)bw$A|T&b%4Q zmCLtNy^_5#&ICo)>2a{h^uV>Oy3;{1ol0cp87?TKys0>qkfv;($t0X?;ymwSeIaM2 zlw%tHl_NEt%$jbVS}dGnI~5(eyXU!#Fv@1>#vIhWbL0>8XFN1by9T-LgpPY1j-Ia+ zoP`}%H5k{Gn3i31t-wpAP^Z`B64hC!yYTS7p-{;UW|Ps14<`Hx7wf472lj?HJ@${h zd?Ofe7b2sSoq@Kj*mSffEKj8;SN(b--e{IbNhg=D7Jc9{%_q5fcUgA3;_hs-;mCsS z@?={>&MBhdLv*fU&rbTa5kDyM?vlM3_7qvi$}wrDxTR+?38!1t*m;kI{|2k!Y*@@V zl2;Vn@Hxx&67RZd%#yxP{3 z!#X}q2)-cCkc^{WaKZ8)ze>YPbPE+*}#YUT3|H(lCC`SQ7ad{uCPyFFVvx)-s8 zmlZ1flH)VJYJ+mJ?wNCZ9^&KGMi%0dY9n9puh{Hl8cGLZQ7K)DyPe~7rRdA&D)gLc zj$Ffnn+}X?4z`iG;Lhj$0AF#<6Y<(=vV<@zeZ@|NNMfD@+GRb>cE-*J936*iJX~J5 zgB9AzFcm4+TIOq`oU5J9JK12B7AZCWo_(a~vHQ~FVT1)sp6BRki4J<=LywT5!77FM z70q_9+TjlHX2TD5yl-!GA=WBR#-71|cIWFgjwwrgqGL}sS$ZLk8@X(HdKGp$=Ch!* zu*X{Nej6E*h9~HsmJ=ygtkw6}XQD3}O($G@yld}-q)v65y>LaBNEivk@o8|4-~;LC2DEjcn^*J_=s=pvRF_(Ps#VVrh2=d(#-n3QOHzRmN8i&v@pTC78%8-8xT#e)4D1 zzNTAZOSMeroNbpENzW(@!D2sOjFhJIhz<6*Rgwuiz&ekYU5?H>#zT=!tx6Yzc+bA{ zgA7X1Y@BE5PO2I545gYB9MSCwJmQE+KIgLGoAJVEYHySokk#cP*G$$TtZy~%G4#~Ic8c?1 zM=T}c%}}ocvX;+@0!8Qgkw`I{yD0j6g;rrw8&-s+JKZW*&*wc~x|?uCV^XCUk9ewe z@3>uF<)}92puH<*9)nmu0KU$F>#;VIsOcaYx(R3(|C_1^J1hz@=8wgj@JJ8MpwqGxR!AMQpIk=i6d+ zo^NJqG$^^N9&Sfq!^3FhjEGZ zWSv8y?aL;Gq(2mdknk#4@SF!KBcaZxm*<{d(mV8sfo$3l&wBkK!ClG*x%N3%j#CwT zy2=KNW#4#N>bCmnfEe-)xk0~_>87qkx*}B@w0|I!=?KSEiwTN%mGYf(Cw>*5hMdLL zDxNJ&2bpwWk)%V5wxf}9FTKMWlW}Ld@knnq9CG~#4-xG$JsFjnac{K5HWwYy?We~< zfn^Ha8T_6X>=z)%nQ^cf%VZ!-fq7n3&WmgzIACZ;u96D)3tg^pZij5mId$%iC+yM% zT@}I{U0swD-P$N!_f(<27Z3j~qo>d~tx!vtrI)#a=nYyToU|B^+n_`&~E)5esrsRuzJ>zMi1X$*}p|p4GmJ%1$CEY0& zJo#Xd3oP18x_uE?Ru_|TBoZyAD4_dn0MRbnD7mg68^`t9k(94JWg~aN zx9W)Z)2VpFA1`Ix4o^0c>COY?s~F8JkiLb91$|4!#7M1@v(Jawt{ZZOtzM8SGsPA} z-u5tLbkcEY)CQ3kmX)hut>X37LY3Si40I3GUCg*0FXx;ioD-~;K!3$1!}6%fh@Q%H z7MJXFvpsSaN|ie8Yt5pSk>nNAvs^Qj_l^b?)}JXrf8sPfkmh2#o6fm=^+Alvl~#Q1 zA~U=?ueICd+>kw=mOD9#4K~453xw>W6u6#X4%tLz$d{S9w^bM~3W-`P@2a+?v{!8S zI}Irr>pQ8=d;$GbT~QW-vP`4oaf}+1WjRxuOaY!U;!vFN$34iY|;@*>2U-rKab@t5&8ZG}4I>!`B5*S&XppxL<7WVlX-AFHoL3 zeHD+-nm#@c3NpuLYU9c%nr`Hr@NX)~Fm|sm$Ik>|R%b3|ywgwHyQP^U7+eek9ciBQ zxVjF<%;^gXy+Ogz_fziNV#t;=zIrYLv{_v^LvBwhl}bhm7l;Nx3s)fI?*P60LZMJB zhLVHwJQ$|L%4FVldOXf0^y`^;a>JG2rVC*y7J~nAgO$hK%5^&(so3ky1Aa$$RZp-X zrka6P?LlcZ@ARBhCLtyRow3;Ic75*txwo@)kH;Luldu4g3EG=kKlJUlJA>!l*=n%} zlxH5F&mHJY7v6L{6&^%}%ShDUDRNPopNZvZTWVhP=B;*S%y}3`b(pP8!~8^?byN8i z?VkuP{}`a;+cn2PoK9yKoq%sT;;s^sCnreF9Aq9nkob{`#bV3ORi@3Vf%|C_jTsX@x_b>x=zQgrF}_M&!&Ba?R1oynXI zd4u5`-37?(j#4JqhIEI$xLmCQgXwfCdV@iyr(hSB0@nwAuGAQb?e{%{K!9#X#<9#O z+DB|yu1srJj+C=opVaax`-~Q&%Zi<`FNZ^?k6ldW7kuK%MNK^2akFW+Go96H1=E{z z1v)-oC^Q-~jC3{abOH{*Ip$7vyWOVU!P8Thf1aJUi;3uJ!1K8%@N~SF_I5jEG4IJB z`Kk5lwed7L6~w5c>j~QJ_W5cy^SB%SY5mGcH~Eq40`a^=k9{*wFm&#@a2I;DMC3fu z?#{STGv#r)%8O8_kaB{AcN=b?eKRDr{qXNNSDD6#`6O88xsZvv`3q4Bdh@k%MGR6x zkLI~iVg|JHIGFBC6f;9NRW2}6v)X}d(`=cHhLC(Oql>mQjRPx9{~Gc30?iH0EDKAOM+ShGoA^y{J|wVFk)D$Rn9tjEJm zAV^uv!!wZQxx?iTb-I3gy;!t6oj$?dT`k8jelEZ?m~OY)YBoKqMPS}-@*%2seqQj0 zii3#IZZnmD=nhnYS2FpqRD^Zez+kcH&n_sSUp6`yJo$59lg^))>&XjGDK>WH5(99u zUDHK)Sn1@FNr+=pF@PanYUkU0Jn6Ov=QMDw09mMjzvY~X9p@@tNS{NTdo>u0*}yDc z_g6B}@u1lZKoWB0bk@2~e<#lc*a3ghO;$4T;YEN+rob`>&aXzkL8d*d)U(-9f?Gt{ zcrfnFwo)}Po6IsOK`cLm|Je4(;rCVRj+#`-WE-^5UoDuP*DL1BzQQ~fg7qaTBC*X< z#@UF@GR;NV6&bRXdfQ!Z%(Cf;y`OE>?Ky!KVplnP!kd!%Ont_H?@t9C)$l41VlRBP znIjYs>>1GCg=wdjvX|;vi0P8&u}pUXYN?fm^*a$fKJW$Okh7fSvV}yoFcoK&QijjO z?2h2nxtf(>{jlCxOc_rk1nM5ac9o3R%ZqudkepVhUB*3MER%VjpYyQT8yxqWxm2kE zbb*5?Ld^u_g1F**6b_1xi!2>*h;9Cg>6KiKe6K`1f}Q}&!lF%`hN!a8nzTXBMx)WC zuQ&C%+}>fxVegl6qotjrLcr@O2gpnH%9S38V#wX#0|7{c_$L>YT-{?Yxl&xX(N1)i z9`L`qr4X!$7n%Mlb;Y_o7mSpv@`-^v;Ro%p7XWO>47MMBNE7!N`C!ARr)FdPJ3+)7AfjwV(Gpr?ETRuy8Wx2sNq- z02AJR`=FfF{$?Vw{tF-WGXzId};)`X2^4+2^Vdlm>+e3Nrhr0~9w9^#pcgCtp zr6HT-D2=2|PO<|2Tg-xE4SK$PTFB9zk52+YnIGzVRW*L-6XdoPIN9pkM&C<2^PgKZ z-=_*QLeiPF;T4jU;q7z|eNG$J6@qD`1b`o64Hu z%B+${0QL;{?bw?QVe7j-TX2}2eLyfN?0!AnoX zZyUcordQ6YDhK%Fjf5ZiDC5|vk8nKFtaIT^?Nm$KS_LVq4dDN$1(RVGKaa0*fVEH4 zJaURp{D@F=EvACyW)=>*A`y@Xw}cq1?oMXU+enboloe>erjlYD4~~@0yL{be@83PL znkUTCvj+e&G@Jx`)LX58BH7KE4Y(%t4K>ic|GxNqE}l*H@uNZ}bNA#1#10&uy}l2( z-B07%|4uM>YfvhJ+Ye{h{tgONd8#~&$*wmOTeln2JQYtxRO11)+OreHo`$0|=m0%u zxc(UGr!fdHRQbQxqgBU9lcTmegm_|D1ungpL;H7aiT+-M@ZvRZ|A$6YRfd+_Khaz` z{(rB>FZPpUP$!JB-*78{PDa)O=ixzop5AaFye4F&55~LL4-gZMzdMjFtTQ&Bd*kl3 zX?oR)afrTD4nd)W^P#IpCJ}emSVy|an7WLu_!%Oo1Ru4}dNEqz^%9TtjE{Nrt7@DV z{OuD(O5j1*p|~dl;7jOz(Qiz&#b5JZ+-rsqm7}Y?aE$LrA%W{lb~o=Z0AbD=e2R6r zS4z^Td!3r!ezaShOJRPB%W&%}((<()Sys)n5SjB2p-L4HkO0qXqR` zObrJGx%2Gy{rA}?d^Vf}8q+1P>cZ*Ao82Ku#n(H9tqZkK zt%-Ei-g~IKSm++Kve(n&-@d52byhrUc{5DC)>x*nwvWJOAaQQ1B#*w;068Oi>LxVZa8pe=@-L^RIft5 z`S+R$uUVa^qNc-lFwv2@eOYnr{4L#Mcu<{p3*Hpc;CyQ>Veq#;)ywkZ&F-ZLSIgtg ze$|Ku{CHyc{C9?$d!;_#Q}AnC8fmqAuV?>#&H=8{W)E_VtL>5VHGD2d)k@;C-+9d8 za}W5OV7_4{q98@s+RJdr|NYJv{LUx%l(g&cg?kdyeTBUB{tJD|c~4XozWayuLHy0v zNVnxaXR{*cpl-1){y=|6H+uGOHlu$=G~~6+P(uDIe)`!L0};wEvEjH5`yfHUJg=r9-6`-=A-k=_|p@0R-U8>x)H zljnX?0GZvg$ahS(%U7SbUtY-3XIyfds^r|Z5VFOk&B>>Eo!j1MDFoaC8yIpD^u^?_ zsuNZYp1s@O?!#ZaQ=0_HWxxXq@u*NaJgzZcV6w%Kmw$1`nk;bd)pff=Xe7KB-uk!4 zWKE(vU#cg2+R_{RJ>`cuMO~Pm&;R{B_}<=SQtyNJzDSQBr@ zks_BZ(yooN4pROv*I3izF$LeLo(RNOTpKaZdPxOLZ4tDmS7Pux1&e{-iC%z+(_q=Z zYkghMYmKyY_KwTZkLImF*{(nP9;>;-J-tpf>wj)s+>{KQdj0)e7)bW|1NOEJy?xco zaXQpjf4T&RiFN@g{>9eLkJlZSV_iDb&k7mG7o6npeitg>x3j>e+H|W!**|V*!TjZ> z>e5cZb(#^&HjrNCdd+(4Z?3+h&A(jDKwjIM3!Acw`u}~`0^jx9?;#o(wCmrfZ0DcJ z_21rUhPQd|uY8;3mItqrb)Nm&6EkCy-gsu41UD8h2n>gnIcsHq`f_&L zq;u~}rXL~P9fer@gIwmH`Nn}M@%(9crlaq_)f0S^byn?PeXGa70I{DeT(y^Z_la(f z_HRvr)k{^rG3j$Jg(!?UN}pS^12r-rSNz3t^~_069_oL~JKCzvm>tgZ7wCwJd&~rx z78)Hl_u_!4`9_ivBEeZ3HKMN_YU>jwdYO)v9?HL(%2OgZ&)#bzh$x|&$wf*e-WES^ zG|1Rzovheav?O&OKNwmq7bGh;OCc381tj2%LGRsb^-aMdl-SJQqD`zJ~!t2g<1Xhk&X|IJ7xbX2qMOS zI|F!m{-lFJX*uIO#6Qc6WQoVakKkRfFMScbk5O*4U63&A!3^ivB#P3=VU>RH%(*kK zL%-m0^TUG~21W_&M<*`QDBRSx00b2cu#0e?iW>VYjI#IjAp-0O2Y{4Sm#&oFUPB&Gq(C( zWd(08bmH1#y*E(oJWTn%QV0n5vgh|L6VorDSuNmf(-3LHFWf^Ey$gSRgt|a_{00d? z8~Lu@MlvdZl|_to!A*a8PVoS)Gk?GCX zKHlVy8t27>(p|rh3)>i>dfR-tV#jQeV{r? zb3DyZ6b8`4jSd&nW-kWaj?$2#waIo7^X;cU;XzwwCv~W z#1ITm2{V19@KX`9mH-L=_9K+-u*QD>}P)rqbRN7!;Z)GIjn$tGhs_i z$m00>*I%m<)SHi5w&vbir*VP6k%Y3BB5v9y?^!Mtt_Cfc2(f6O_IX_uX1C!?kgDVk^lAKjcQ-t zOXUqL#h?vNuf%kv8E9R700aK|3n|Heou_I0Sc@xyG|%Aq=2A`ni}kmr@Uzw(b*I>}|Fj>vlUk_K=)*w>RTc5zihSx5<=bHhdXRknfo^^&=7LvSSp9pSJqF`ji zekbVU3hgu4In1bZ#U0Onxh_~)a6NbLryIc*S}jM8-u%V?-hRGK+1|!R?WTSc@LPU; zZ#3dYKY%pZGp~Sn<=4GQKQU*%)`d~J&~HQl%-fvKqPw)+j)mFFRQ9+zhgs#Pen&1T zQ}yhl_}52tN2XQ|j4#K7J!bxR4%3}7n+0FvzdY;WQ2!FOJps?}K{CU%i41CvKPn&* z?Qg&PjYjpJUeTV|SkJ62>G%3W7SjD%IP6i{b zIv#vpjG1hgb$ z?lua+0EHDV`O2l%Dz1C6Z>o7l`m9h)imq!eY=E4e{dWz_LQe~CZ%I;s+CIfM_0#gp zJG%pA(2C2--p)PW4Uae;vs?O2cTcx-oCmVP-*0rpeO9aIlz)C2vbCa8@EuNx+_Rw* z_is-U;t%SDcke~{UIxGmPT%g*EK~ex)gPjqeWk74Hpq5$4>(>i@OPxq`cVX0x^z|k zV*I<7H@EKZFB5ZQ#!^*P@I90-iI0L>;%s}S_+FIP-lnv#853r>nKY0MK6&(C&8KF7 z=aqd&e1Ox)Jo+R1z>I?D^tx03yVu>1PHhziXm~v22OowQ+H7Pzg;U>tVB?=Nfam6d zK8!W_cd{*sbp@hsUe_;9{=;@)7B&W-PHcPweQ~rO3my+868hZ!7e6XZWK@gBebJzC z{hd}qB$Fz~Tb^N?5%lzXfoK(>I8!!3H@ow?pFeZT39cyT{>w9c0x@jcqv~1sCSud` z=qCqFi!9(MWti@YQjWa~xnR3hW4;>d1kf(W+=whQ7dU-T-&Z!gmr;X+DA@fz7*xXN z!!E}pll|*IHMMwp8W$~Tp$mBSVGVg?_3X+2a2xf;R&0>OwqH#Lmp(Gn zBx&NWR#sdE&anMK!`XYG^hbXUKLyvw6d-EXA@}ZGO@h?Kt_b-+mAhH3wM96GG*)CMGz~2PcsSdjH)@ zjVjN+QK{d#XlHd#U(u3nIN&4%I7PJ>0)s<;3(wyJGN?tgiLvE*k-yKWOD8-lm?kv% z|M~}P2aL|HKmgia~XPus~h= zJ5LS(DQ+`pdmru-irSCc{$byU$>j~@|Mwj&^rMx@fOzrNqF$Xe`SYv;@kcTR2y8W2 z`)6p1wl#hb=E}KV#Oky?W;7$h7yXw@&c9Pft=Hwr3uP6yD$(bh4>bK*6H-ookPC?V z;%kI&1TNPsNCWfh;sEFx;a|82+NQ?@z43Vd9sxYk#}CgG{J2^Vqc$m^SMM>@c+ht} zh#%~?Itmo6wG5gBN@SgJWR?i@j}E2ae2)S^uv!(@r-582(aWYI&qRmRy(a$4y-CJbU0mG^*%ToM6K- zBl+o`ly~7fnRJimNK-G-K~2|V(R9O?XBU-1RxwU#Pw)#DpwLZm;T-( zpYN%UGzL=A-0QOwu#rzA(Q1o1OekPhsr&Kn63}ZY=DZqwxjB-i*%7+A8logN%xnO4 z(L`3wg)x1xPK8ce!Z-nwn|Cq5_P6}EE}9ScYjs?c8x?+lTVUf#K@8?|1FAo(;U?tC z5?a<&L!tldaYpmVGiO!IIvOxmB^)>A?mPZv zo1t+f7|NC{TR}X%+~IpX8P7(`X@1#vx+m<2(`7kjG6+M&yxKazPC&0$C4DCKtvRap6g>4=T&)4pBMmAA0UX5qf81AqHS43L<6 z44&+XTS!B5)Z(0C=yUE<`pmBVK7FZ|1dVk!lI0lK+By0nu+f+7#HjL?(IgGUrO16E1prIlC5}6^gn0{|GrOy_jL`8=wBXv(j}U9I&d&h zsHh{2Pdw16-l2Yi8c`-MqMjn=S1r+vd>7wEILe9rIA`yAc>t}bkCMF+ZVB$d8I8rd z<#(DKfq*WnpWzGd)7066UU7vp2f9=Vczzu4RulMVW+u#?``M|N+tWqC^wKj)k*P#F zLv-b!Z9Er&vjmVSE9#jB0-x&!9M$-O5SPS}EBEe`q%W;F?O__ayC4i;lJw+1etNF? zEO4GfTRvy}vI`VFvH5^Dp+2<df`~BXj zdqx^=W7FSM<`U44eGJpWB}`&3?ySn?7cPtWiXxEA077VqNWXk=tMaha8XcjSBWtJ} zME*)Yex>b2sN?XHrF(Z?qjNpPXm3{?cyMddI5B-`-<8Tu({5s>TMJ{c9IPnjaf5Z4 zG-|is^KTzp8xY_nwXHw(^XA`25fpwG<2pu-@rX#vobn6)$+rnP8dWJ6Gfq*;NKURo z?BIJI4Qm21?*6=LZ_tbu-S@C%!mC#2&hIKrkwpfV=OBIgI*p)n_ZMFj*BLE)0iL*| zJkXr@0p>B&F#9FU2bE#g6b$RDF-JE*VtMfM?j4icpnR2DqcDhL0JWe-2!wk)N^g$@ zy>ZNt@6wNaqI7re@gMgn(7!z{0EAjj5e$6%b>+oG%3*Z59LtAzgtX|8gK zTmID-&aX~;^BI3I2L-GVw#NB4lkNlkOcz80h?I@2BZup&8NBS>v*tEvr3i&$2&0zH z{zAOAk-`bTfdF{W4&mVg6u94I$Eoa?4^chqUAIwR&?oke6E$lyIkP-^5o)KSyJ`(e zXX}4;F}&}oy7Q?mG2mYV7>^G`E=}5d|E^vh2-WEN51P;sStBdY5iJ9OAiS@Kd7bS0 z5%9n@Pq+y{gTBA7AL`P4Quab$g&PBB5cQsxTeccJVpjOs{HykS&RbHY`LgSSMxM1* zK^TJ>OV#AN4(a-8eHy^Ergr{8TV9GZ972P-&8_=7e#=pbDidj!NjBZj5N0~nQ4C97 zCw2pzK}x%SF|quGIOeqbhsl68{{6^;4mQkcN=`6K=6L9E@+osP)*wLdm3cwKVgu3o zzmjEZh|z)tf_($GTe|;Rpx#^yR8^*j`*~CJg>L6BQ1+YyWT+*|#VKhmOVtCu!rKFI z03P!9E1Y`t=zA5SvM92ic!zYS**->BhH5=Zw}PYRzLHwk++{x-{g4CpAs+ zT{~6|%KSDv&`%mKhq{6N+&rD)A9Ma!H@Ka^pyLh1IoJ00jXe2}P73`0A6|a)*xtN& zu){UD^Sy@FqPWcnC~T0Ly9RfV|2Z(TvI}#N&^x2G4iNl{FAIC`0o>GcKO?Z8j}P`; zE?@2`rxo{L4OvRY(N+ zb(KD9aQR}_kWwGs7U+{y3Zl=;-LV2u-9HQm-+t&0E+0-N=l4nb%aQg=f_rojpWL!U z91E@VLcZ?)=fYm*Byi)fdmdi-yFACKF__VnYP#?{>v1X zZ?eihOjoDt_MX$qu`};VW7GG`JgGNV9;w=3_bn%-F|wDC*s|X$ zzn_YJE8wp`+FwZxE4kTWKiLw{f}0juBX%`p5;HVjCF{=)NFNDO>~zEjj1_S*{z1K=*vE|v%1Zr0@3Zb)ndmtu z&XXUl3ZKg*n}KH5tW;aw=10}RK1>V?1+4`^6I9j#AISHPZC?@~g~m{S>~?hr&hrio zo648(G}m-c6ve!U{$?HlX$BA6)W4jnz5xQL9zbFE7)8UtHZ@R)3cid2A`Vn0gADz@ zcw&PV2(B~E@&dFx2jS$Pq^Fms0-nzl|KX;+`pcK9e}P_JU3Zau>1H}hP4!|e@F_X( z8>6C6m2!dKvv=SjLUn>uyAuk}$EJb)`BVuSM0r7&X+1kqii>69Hv9k%sG7OD}) z<*%6!*hLUWwdZ+#5B_rJ6Zoa&tYZIaD<12c#(oVqispaS zjW<7hZMwG#y?Y5VDXaGls5cMw=oN4Y)xumB%fQ_t0i9OOx$IG)4Kkrkg85*aarOY= zeBInhwRVhI6B+GH89R{Q#{0Jn0jC)j)N5vTHWh#!n39cEL1Pn=+#X*Fsf`4$Uy{zQ zP{<>-_V_@X0$ekwaXR_sT^ft6VD+v!`dlbv>VN1dE|dPa=fimp9z;2Mnq8+}G#ZLV z-}wB>@Y1nqFy5!othqX%WH$^*TRjYb|NcJVfLXvV(u z1SAdj%Oy{*9kz6d^bV093ye?Lls`}lj0OO@wiifE2`$nW8m+x}eb<{vt_Is+goBmj z&M?@eK5$Z!T+R$<3F2~b_ALIIJ*qHzyeRF;wmA__*8;y?(M4}RdAO7HAZ79>S=B2A zXPbL9yn$!@tUO=*9`r+dv0n%Hd-F{Y#%HMeFsD3NR!%10kEv1xyA@c#Cj=jnv>0(3 zvkmNY*bH{L{Qyq;n2FlD6;=R{wE_Fc_Ra-=R8$@*V~4ebyDI3%3t2z-TnKyu=ag$DE(_~`1gZASS=?s)Pds(+D&Y0 ztRgd`4C3ul9$PI0NR-BfHkAOHB#nzri1DF9gHpq0`j)9FC1i2gtH5!JVVNsB zlK#^Ym-o4RYBDP@UmB_kN`Zb{h8Ro>meKfE>%SA4N>|{^A8+m~{XOH3`y+$|r0LksYxivc!VPT>f$;xDaa zt9J<-Iq*6`Lk@AY1NK!a6*PK&%IPwnuOk*!BAGT|IsuaSZWM|}Rn zPIu^EAJD%l3=7JhKu9p&c_1{6I2PUT!$CKYlkPA?+NpD$txAS-(wRZrJ7dD_HuyrJ zUlj2C(WfW>G5!w+(?yhdYe@VH7nQ+!WiI$Q2$3}iQSo8r+}ol)MnVX|JHdM zu9R)}eBeSF-xv^1t=C*<`z&DI%`*onG7lqshc&6TwLv@#`%!1?{pfA z=J!Q_%%_kdn2ap1D)a$bOW`)A=RJ2~GfzP#4wQR9J`j>XoL3%v$$qw=C|k&>wf?T1 zf*DC!g!)YuE*iWaY)Q~8EV3bZ(n)@?yeF&BU=WwGR}Mh1?YxgQph<@L1(fh>b{q)A zBz1_NEQM6J-W!MCK&2zhH5l7%RY)Uvv5|Mu8t7^d4&9_TD>p0w`CY7@u|o{m$2}0MQlAZXY5G*kp&bhIePs z&kRY4fq)6Wwa}>Ksmse^hig)T8kA!}`vtRy9eRNSrT|*+rP%Fgez7a_F$)eDHN()< z0lcf`FqoP*a`nO_|&& zz(_;sbtKu?-ijNyN^og>gYW_U**`e!R0DNy3U#l&NDv=2GgClRdPnFtD&%t{)F2XI zvQ_u_oVbd>^@aUpbt9`#_PYb4lyJ=p^j0m?w)Y2{Y0w~&$BO!v!4}ek01on|;6_Huz$KYfrU`U>6ypMM9U5IaLXMvm3j?i7cVfFR zHz8Cm$ADP=8)IRh^rD%g`Ljse-Jg8EMi?nIGDC@Tp10hgeA%F<2U|ZN&|I0VkUBAK&13V7X zRxamwy>D*O^mxJ~-H6ic)&r`y$C^oIs<31?8l{8LoI4n1drG$49}jC)!3X3MO+Bkw z9w^uV$0#bO(fs4oih@G`7y$8rsnX4|&J=taO}q_=>estez)=6^^2pBZqTIX|6$VRB z@J1BLD+YcWHh1gR*X8&1)|FNy|Hg_dFc~T6OGMzP9+HlFGbHZ9FnjBhuWRW3yN@5n z=D_sHN+pm*!i-s!TD`e!oD6z==ERomMwkT7Ip#{xy?6(PDw;?F)JRZ+DKVLM0BxUJ zuJF+fn{2u+teee_V3Q!QadqGx2_baihi0oJGewP7`aNKbSW^&l#C#RNo&{Om zImz}lWv3B6j3Aby?Ig=OhK}};{ za$K@&Iu{`EFu3}7Lmd*m)B|E0jM940DkRtg8HX2G0D(e!>i5Qg9XvolPQg5JhkE!8 z^)O&lK?ON{|IO=hxQU-%x){&UAGzenX|A??H8@16P4#C#Z6jgi39lTHU79Lt0xaF^ z0eK-(ZUV9g(pmWp-1ujfI@Lpbqmu0j@|a$Z?{Y^vFUI;9&v_B`ki4A=8HJ`VFaqEt zJYgPp;xcaHIGJR#twTlwq&~2QBocgyWEBL?mnWh}AEU>LI7wkQTr0uX7!f{WK^q4~?UH-%V87R@o zuhI`+fQIq)C=;x|cGQ6M6KD)DX-+tP!?cQogB#iV*?W509cQr{H42DV&n!R~ZWcay zr66TsC!(9pGxk}dt1WOHJD`FckT_njE}tj}2UIZW7-kf;$=A>W3TL07y9dBj%BB2t z2h3WWOOk(4HZ;jg1Z`e|%;1A7+`t+QaNeksVQ>sQi5{|Xb6dYq{4dA;o2UVOOu0!T z8p;yKuh`A(n*k>CfjSI&fMIdsUu)uS94Ew4WlVuLiJ902a^BaZmUHdjuJ_#g`yHVirbYP{+RctfXRdgu3RAet*Ck%?FM?<*ATA035i zEd{ppIX{Q5Zq!pV&TNkxD`OrNzeqxjZByfZ7{Iw>nSDns&P+AALt8+(i6#>7Y#q+iE@ zi}^E%AN$$hJX`1V0VXWPi@u7Ue-~n=IXk)J8%|Gtf^Y@vC`EVX68!An+%i^wBZxsc zaJSh(dSEml;1j3xUIIGDlf}(p&1UG9)yYitGoaB14$V} zBkTNPcDY08c{2h9kJHx^Y)EFaz?`!;bvp-+EA$~p!~=PuOQA-NoglAFyfwia1_+2| zOkXdM8;J8-Upr`wzE#5VN!aR7 zJ@-!a8b`jD0VBE$=PQMWv6Nw`x0x0qD^S8A%ijy)R)=<1`aHbFIPJ$oc_u2Q1bFB#!4a9l-r|tB8#huBjBqrb$3=8-tWbUYOVO^cU!4D;R7B zcSs^yD;;LUviItlF!}g7P^F0c9qIr<{m$No_yA`LYgBMrjnQ`P_3Ed>$jwj3} zUCCc-t>`Wm3j-rM^<4K5a4tPc>TPIIehRd8P>A4?lI`q-~t>{Z=_NgdAr`Sn8pfdo+Z<`_!QC zr^S;%D#PxmVYXEVv_a6VsjE2XgCx@iJ>=1XxH0Zv(pS^AM z%0eTxS#YJ@V-}0RdSi5g2JkL@J3T?iG#5x2v$3`~_q$qVyF}13wJ&VR=0HPwnRmWm zF-E5l=&Jw#Spn>_6yP}nhizB(S-XDH%;^I_X^jtAGl{;W-)^DF92^!v@(uUMexLWh z4-a*i=7{c6bTd`~ya9)mBt`${84oCcx46J~T)sDMh2bjjf42Mu zRtpDXX8B0}!fH!N{nYqD&ES3lZ#FRtH_-tUnWU+}_;J8tk&RSJg~oH?sRY7_ot~PV zeXvWMFbz%#zbL9#qT%K5IQiZMU}j$>$7nzwsH@#sGdxOZMmQ5AW|U$qFo3+!yPvyA zvmKv}n;6h@Liv2g73Ctm;IQ>Gz0oqM8(`xtR#w0AXdXOGaDAi8E%r2MdMz;Af>@ga zuscm8SeW9U?T4^lFpl-Q;z5VK(_1WT4*+o7)JZzPT6qOq&SM}C{v#r{mteV zky7aHlqOFsp!u`_#I5-!Lr}?AUjft7h2)Z<*lt=2kib!18*aG3;}g zn?aof`oS2;gkHaIWUz2`z+RbOv`_*wY=^-Z+1$xsGzn5C+i&!jK2^{YQ~GObNlsc-5IfsXic)N&9p@v)9l#Sg;Xc>J8)KW!+RuIEcGVC_oK_44_?_=ua{J^U9n`u8)b2?KdKT%s;Wfy0 zM*3Wb{fwXYvcs4#yi=gn`H6^u;<4E;R*}Yz`MYrBePD;IC28=1hmP2)&Q;bbEME0}|vRIM|G6TO&aQhU40`7!U&WCqnlJa$IBdQw_Hko(#c& zmx%>7i&^|&`y8O|;fl)h)MQ(3xV_ZSm|U4N8Jcv9VzyVi#CZ->oAmmsSK>a+UM(>! z2#83E%pS>?pQaSmfE^ZSh_w6*6zpT`KxGB%4O|*up5RU#?1vcV=GDeW&OKQ-DAYi@ zt@*(*raT6kG@ra{Yx(n4+dscanu4OfFAGR4X-F0g|1Gh)AYRQaV>#J0ll}MR@g)J@ zIU59Fz#Z4XDimahD7F-b@aM>w&;I0gn_LSIH&AA32#eh;?(_DH38zpW_S<<1jeb zsbVjEeAb759xs5MJ}3n2Ziz*{Ut%`ozaVAM{enW$;5j!VNq?Y~-1)Bu85-*LGU-!^ zwsylnsi#z-tOiEssE}&j3`UD6e$)Y-i*)p4APXDpe!HQzuKHpvnO$$#1rK zKd6shE|=CHmMfNY%Ve=RjJ@CC@hD&N;bP{zy?dO3kXa}%;EBG0cbejdqn|hvXi|L` zcu+2#8Zy9?61lHDJwD$x$U&RmWef6U1IuI-^)w$mNzWR_et~}0cPuu$2t;N`=Hg_$ z(@3Hgl~kIM&jp2j0*dx45c_~H(2gybyn@a&@!WwvgdccBzT;&u=d6k?zGV6Vnj{h$ zASWd#QGDTy^r<|Mg1sbe1O6<`!Qc77g}KFoQaM!)^r}~l<11eWqzk~K_nphmh|-4y zdkUYQuKd*ClC&p0fCo+PLk_cR~$Jo$-`qjH{XT4JbU@QXhAQw#VjRMq& ze#{)t{H)|#1SM5eGtLMj2GZm2Yw%fciS(W6)`9cv%U>_k<;`3k%vBVzw>iup`GQ>N z9=})*M*HR9@Ysa}?Bv^W8`Rg1;ce!`x-c-x4p#wN&`>*X*`m(_`$bBd0bZ&UmnUBF76o^2wsc__Ff~=bd4G0J$zYSO8fT-7bmpUn*6c2l3+4c($BYE|Z z=^a3L$&Z_Xn7C)Bar%qR(EflFFM2|Uj^!n?((Fz~mR6Tx9)G1^I(oDESjnreDJz9g z+r}?2`v8CP@fN)F@sGw=!_!QXn|Rsj_hevuW(o~{fxtzSmcxDD;D!4PB9lCR$N>_p z(5n1;nkRDywBa>_F?a%Hvg8)vh3eh<%l&yVDe#8{sW01)4;*sAeJ69#{RU`^Rt8uq z*G}$vyscW!o*)?C#{o(^&YO0G2OJ%Jr)EsW;aNrE@wp&32Ygx)SP9K%Vb8;q70%5Q z41ljvj%8qXLc^5q1CJn*;&S#`vd!Wb#T3ZJOo)v8@7`X_3;O&44%|;lvYj=i-J9LW zhpTxr8_?}Rp55<|#J{gEpeJYovBMAHNR za^QGDOa!!3>^~|ZFBfZ0Io=Kd#H63z;}?Q+6oT_C3`oF`Nw~@9UX33rq2iEAPp?k3 z1uoq8gU7%1FhQ+Nf|KTpC)V!`WZ2#hT4@k(0pK5s{wy}>y?X!EXr&gjYD>aBbd&dCJbL)**N!0`Y;xpR8sCfj!M@t^rpqXD=gH_uxD;XZQa; z^I*#(Tx16NBA6YUz|NDR1SUMkjpkkWEjc`$LmFPt7*b;RcgD&Dc=-7boc@}hMyhw7 z(Z2o7tSr4Yd%1K{h%2BWWLfY$UDgw00bKT2Fe?4n=bAmpEJW-Fv3|bXz$OA@tK8;C z0X7&jiE;)q$l$EA?5iU#?Dvp(xqj*ef?Bd(Kf8%>r0#f5W13hs&KwYja7H{iP>NdL zRQuDupH8zRWr}(F*$t{$sY!~rp{%7DWFdo&s@`4@7Uc9`ITl#&mm zm8$pFO`0)C8~OlfIJ>m;99P@6PvluIDUVuAh;xe|#bmN{X!Xvvt`YZ~{f^a&dzf0_ zh6>7L!;}8JST$_s)LVXs7zgvxmF(9QeATtb*uxXk<`zN-5b6kmtjJG=s&iTX^=#1_ zN}R2^H%~6>41!y#mx1KFi-$vZypa##(9Nj3gu%U1Z3hV()PGpfPIWO0KiC5{Jm-WY zK+KRmui$IOn?XInd_`aS-0CYouCID6v`~+L&VGt3fG7oe$5|IaUEcqC&$hULo^YEs z3bcrI6c11yF8A7*Z$^D;wxA}7Kmvj09O@3_V9{D)M&gQW{0qohPjH+3SSsMQ!2c@WG%LIN)PI9v+QGyC`e#sYf)Cq!5AzGF zU6-sr;$vanJL2w&RNVTb6kRgI@5W4Q0`CtMK#cp4!rlia{-X!2ov?$`ro%m-@g!2% z_qwa~^@E4x&VQIDW&9VDroU7jnlMR{@&31O9&XKOV&<+HA}C*8nK9^pgbVyCEw4M^ zYr0S|mBtXnwcA2@AvL6Y)_veJV`J`N&bs>2a|Om({$b@N%-dAq!o^R1ab5`Ya+w2e zjE+8AWk|l2znt9L7&zbh1$MB2$Mt9qd{{5$t%h-r>;~j_J(BMXJS8u;-|^&!Qd*HS z2$lypOQ6B~{S+`3S(HiTGk7e4$>P!ibD{wZUXWuRF3taA?`?Ws*S0mGLR3N3p&B5> zMWv$g!d9`@KHhuVj_o);#X;o5j`QI-ah$~Q(bbYa6Fau!_$#&rO(YOUbl6>xfCl^n zXwU#8kZ2%;=p%%XXz~|$oa9{}`|Nvf-I6HL*lX!sZ6#f$e_kIy|=VSd#j#x3H6 zXVgBp`DS2T0i{#}#zOMQECmVsQSL6lcy(*q`>GKROVf3M|JZNGJ)55K{O)$_*8kWa z?VZwHF8fOD+&yx011=n`aEClrZew<`AcP5d!VbeNS)L9^y`IoSo`(-PY_0^(6P*CC z4Je%?mg*$(FO)K>>Lbk-#f_lWHY-GY%hT5b0^Rny+uwjJ8Q8hM5)#9cD=MB=)FJfT zo~GB!AON98ifoHD}A_B55GUJKrw zs|;m81JhCv%sRtTe;F%X{sE3Y9@7g6f|ZGJlkVK8+8OOly9cNHVs+E56^%Tm!6a-l zy`(t<=bTcCDGyk`FE%*yOiz-_C=4&7^duzL{ltiEnK}>}(?3HHM5l{$Y&B!j&p92e zW+Z!j;OT9rN$c->HaWiSARDvkV_k-G?+>35=S#Im+khE`^Qt&MJKvtCU7QmB^`GKu zck2@D1Hgd8Z~P}##tjJrSaywI-C1FRxjrI zqA-^?oVA(WYM^u5*QV-Qjw05k4!SrrBtdAGs zL$5~L0PzU`7OczR>WZA-?r$wzrZO3wmG z2G%A8#BX&<&+-IZN0_?Ge9|Cu3FmJB2z|x`)PlqWMEl6;uKC^hn%bNK=O_Uz6S$UK z8hkF@@u`d&%SQ~mK)q9)s^G9Ke+D=J&rm$yC3^*kkZPtLe?KiV+wK{^s&GAN{j&Rbuw1*pz$M{gd|D*r_ ze&~ijkDv@Rak3J{*%0C6t8qF2YY|2ch0c#jRAC6#u4@!34uQ?jTYjzYumfm&=coXm zU%yho#kEZ(^H2)?<{(nTJ3C5F!5O53c`+O8v!m3%ZZ-&fZO+{puS;!~*ITwys|f6r z@^Ny#kF!$~+!g_?==veod&Zp5gRlUSxVQokGfoPCb5*o#y&oGc&VTwKLjd4bqi;7? z#z?v0@|@2 z;!JBcnDp-R$qpx&(CH>lgvg#%-PPXM5-I%bz_bRE9E9@>Z-~+M%f(sYhxgz%GjAKt zI$1RX^32WQG_QsSpKU@qqJfNzMZ!&__F5mh;BZ=j;nB6qJl$Eo>GSs`4}O*gd|3O_ z1m|J5iF$CSJ2PXzojKcGaL{cA0vvYkA*`v*kw9bY`=EMfa(HS)VRVxYDE< zHJ|MpCt0&1a)J_h!wkLt{G!CoB$SfD!N% zf=5ByiSACaPD2_ABG`kTFVrsA!_uQZU z{XhO~&kYL8j=Z1#y)Vi;|1I#V|Fd8@|Cj%rpFW)b9zOhi{Cq)u{>Q(IWcjo#K04sl zE`D14(;cDu{{W)yues3w`|b+3)l2(loa+DFgH!!k#-Ea^|F_*^e-^$osh>Z*GqZbN zHRz9jvn%E6$N%_u9wk4?&i|&<(V}-v`;VU`{s*u2{8EX3{8x&z_e1x@4irgt6t z>g5k-`u)Nmk2=apyyAY%E>Dv0YvR2H3HtgCZ0BC~{ac=TPJlqE`<9fk?PYIQ|Lu$* ztd~6R$iIKH68Eip?%Bc5%RfB^^k4Y@vW9>6r`LOhfB#>6jNsqHub+?omtusWIaBDP z(f{+_N8z769yt#`^~irTE8c?q&5H8tTYAm&0K)oKT;IGJ{OsbeGf1j5HVM)*;}dynH@6b90@RkG@#o|5Z(%$pUysL2Y(I~Q`;gL4(wBH; zh9P*!D|*heoby*5_J)&^Z>OMwgjyKMwKP5l6M%u8gj@>{%WT zqNmZdhywe)#I)%ybT_3@@tfbkti0vH32g1|hxWVQ{pJmSGOsAJ8uztgTZjIfOok)IUn;y6&&~^Ud>Nujpn-r^KS@(Y$A4 z{~E_+}JTumO&e`yqce7@8-Z^JwYPeS!Okl z%F#_9D=RAT)aSmazk7UF<5K-&=H+KA^*;PSf8TZL>u!if_v-I;qD@xuXxNt`;a*W} zaxKme4SoIM`}$eI$LHOs=DoN{`LGKyJf9$ijrdAsfBy#Q4WP)ax5~wox$roWrIEb|;p3okeoXDCx#w*$=3t`hXt ztCf!z=}Nx8%l7Zl0hkd_dHh54=g+1+D<8Tp`X#&GAI395&!amazEKG$rz`zaai88B zvJaVdfL)Q`=fem5A7(QD@PYpRi;?~g)9l$(_+-^+-S6M1*Z6l;x1U>w0-%5}cpu)I z{Qm4yqPpAb&$oZlL$6C;6#C8EE_KnU_p0*}=I9}0$Z&XhQEv`J8_MF*<*(s>DAix+ z!cXt~Uj3)RRv$j_yIj14XX-trxf`J~X8d0^Lidlay1yQsAL!TceDgN@VibNRdVkF! z_|p++KiB?c??0RLb??`oZ+(C2*$XfI|Ni~E)-N!{qRuxiA3j+LW%zWoIw6EH_|hi) z?xC+wA0N+r>~8o_fB&wfPZUIkroOf|xJbO!zkLYw&s6;TbI?OC1C({c0BsCWeobg~ zBEITGMQ^W)@xh8?3$^vWuIz`$_20g3doMM&Vh>s!evDrxPsbCJ5Ev2gGrxZrE(iKL ze@?ou+lZN!7alD7~w4=&YgC6_UrrYPvh8KcS@**r1;We ztRK&#*?6U&b?*9;3YOmW3YLyRWfkzz-tIqUKXxYI)mvW=)}v6jv#6a!py;3b8&7Na z^&5XrfA?YieK#cCEdJ*0AEDN-U-VV$^JV^|#xLLQd+Iw3>gN~K(K){;0gocPj_kVU zB?qqtdRg`{zh(I1gZr_o^M}VEfA`zp_8w0?h79HsH(=i2!-v-sujgNL;?r&9Cr{z? zec!xovA}!|DqJS$&ZOw3jO#g8^9BipcIxKL*S-Jq6=A1ay4A@`i#!*IUph{I@^;OtkxPW*UoNhEfKlKuXPs@jg>HLL?i!+RO=D}j;=;fy|`{ps7K9}{C zv+&6)`Xs1-!HrLi{BF=+^3b`2T`OKM^)B@oaae{j#q zQq{fv>4-0dPw_h%jq{r&qZf8oQd;Z*#Eg+(ari$3{71QYkEsb979;cmR^iHA?~vzB)%Wc`Qk z`EL5XxBTT{zWV&}b=L)tu6XywAAS;~@a5UK&rV1)EJHth`|9(DPXFE8KRA8+5B?&} z{KbG47FK9Jbm+TzyQT#gfTM?d)*1ijB<|K>L8qQw54i;imQp{{gX^X^BXsdeuRpw% z&l3BPf=`9K^m5m{PfxrGe5&qluqgzt@S>eFZ)GRA_Ne`bA5ai{ZFE6*%b&_09(a87 znhX!^@`a1@S^2#;^r;}amSHfuUmyOo)1Z;x-*@?PjmoEgW_xdLr@cDC=rqV1`VNzz z>zhvCg04AFm-+pUFU0Mex33K2r`~z3CEg9fw$C1a@5x_Sd=T^(ec9djn!b-;KXj`6?YGY=K2`c@(eRovP>zuFu3`U3^W|j~ z*Uvb@>7#|Gn<8)?w)frjf*1D74&QHKX&<45r#JR=?>?K*XK)GeBdqJ<-vs{K$Bzj- zw2vR(e*gQoZ$EyF5z+hj@!O}~?6gMidF}_Adl$`b-X;jD!bR*R28IAjAPoNd%z3Pb zx^LdQyHl+XEBP4U6@;Ir9v{1PFIpPG#Y-*6`#^pF2F7C%^yjc%?34)D_a*Py|Kf zefW0mWzYk$)x}Y|(Reu1Klg~bH|w-7)^nZLpo&0^>@?ZS^57hU+dv$yFWQ4$F;(qwUx1THc_WN($B>DD>o0`Z%DD%U&@Grmn zqSpL;y?^-b6+`|t)(6+|OP3Ww{Y#q~zsCBy+3{EW`R26)^lPjSPT8-qzDK0{liBWM z2SL|gV}0<6e~tA$Bdx#2`kpS~%Q^iu*7s##_Ti8H8tW@Q{u=B1HP)B^8tZ%ZK<7sM z8tcRQ{nuFEpKM+I8tZ%b*uTd5o>@V^#`?Pbo?l~qzsCALWfvj?@Xx{-()<3hG|clq zIRES6e}#m=@V~}CUHCU#BOA|Kq1i;s1n>fBw^l@PB?@`Vjsv`0&Sn2HCcr75^0eudn~P zSV#U8{%_s?{_N|GG^WS?*kk)&C9eOKrD2==S(@=5{!@SBZ;(6eOy{J6Y)DYI$KbR@ z%oW=-uEmf@RwUEM<{9(jfXuOr^aJAV7whEZBm#+PLxQ!$BR^XCBYgg2+Wc<7{O)ZZ zJkp3K-JURVn2_0au(AYUu&2d|8%AM^!6(BnJxR~2L2-n4S7jk^2q4IEsw0Z z{JXA9_tiwt{qb$)zcttL4VV+y%tL(J?Q+%vY{5USme>w_Zud8D-@07_{O_-Jh+MI6 z-|lB*-a79u*6E{HBe24It$d%m3l`Gkx+lL!96fD*FCpm~pRXCRLw^7G_q)H|Kz@ixIg{z zZ$(|6&rjk1i5qc7;{WPo5eLG4E;@RboQ&ZmmB(*y={*OYbgvFrejH@8f;FIk_ zAacpDgnW6~N3ZsrvhYX;8IAZqO@HKiADJK1zbTM%M&dn!t(a`SpRG{o>6wG8Z za*|bQ_t-c90n1vzE zx}gChC!!*8v)9-JNBCUeV3^KYVqK!W9XFm=lG~u(;4s(xw4sN2Fbl>bpcZ6&kD*C3 z043mXxRZt(ZJLfRSydU%ta9CQy=LBraJHW1z?S zVd9-#)??}Vbidc7S5~=LDSK5>wp44#-0jF*26sL!vWXlwmzKFOvfvU~r3eFZMgl&1 z8inC1swdE>O?_&WX3!D<&}gm=>g&_)EnQyxg;=${>NFNSEX<6)RyhB*GWYfD?I zz1i?~pMrI~7~G~r5K2XS9o`y-zFB>FyV*<+>oKGBHwgV-gD$yOi&xe=ed{c8bPN9k93S9YwOfnq7Uf(C6q!hDlUTkDxG}w%Iec|}0 z!Ld&=q~?rrb{O0z(?Dm9R6p77eSaO#@1x;qv^!11)4Di~gVU0qED6Cef;EsQPvF^M zPKVx5QAQCv(UP!Q)Ev%lU%kPkxr65o(5JieU0{aOQlM9NWo<6QoL*C8-)0KC>_E>Q zV>n@l#c3{|%xHKr0o7C6de-Nd!}&hipJc-u2qdHD#V%`gR$y~G$w!Lf@;#JmQj?3N z@tGcz-f1viPCW;h{pFBjM=K^T$YDHdnTeHn{zX+*1Ae(PlWN+FCzEJJH{r=Y4DB3b ziHm$iRhtq3MhUT$COScaMPTj^J#{Fy;hd7~p{N4boa_rxIi>eJ!Ax|1m9Ou+Txk21 z%;LoE++~Jyv!4!dHfJs~q#_N~oNIioW=H3fxK?AKnk^XzP=Cpdoy)_8B9NMJ7wyWk z2O~~b1cm}Uk~2Om7v^Yz^S;%jS#q_y8VFamuk;4PaTr!sGZ1)D^)!;NP7UMTsUurq z3>PCKtqONkfKAkIS$P!5gZgHVz?$JK%dG24%g-fc$N(d^H&E3c=!6+(#4|c)PZ(!M z^@MhJoX$y!*bl}OMKHD;7-zmWocBS>b?37toSa5xYaB4X<3)HuTOt=n!37^w3&lF? zQ$5G@?x5a1UWa}&%;|eIT%>V)w$`lG>XUMuUnmj)Za6u-r=}Cg43N=c)91`&Y7q0$ zMD6cMo(5(2QtKz6*X~(SG8b0&CHU7oDr43x4vj0RU#Nic5DuH|1&3OBQ*xH^imsLy zmEG1^!ErH}wo4%x8T~pw;lwKVt`%bJH;a7WBy4Nmb=8c*l~QeLfd`WI5t!G@oVl)` zU8M0*6M5mM*T`t}q9w0o z>*$wRq4?%a0&&)!y4?rqWlDoWfErEBd8099IT$*3X?s#5N8$(MfVwO6Vni}gayZG= zJ>7|his2xL(NaG}Gf>iiDm$XsG8)C>VZ#o^>okrDV3~PB)noE<=`|$DtaE2kjt5gI z?K@oC^A5YR=AiL>V&iv`R$AC+rQ7&E{)8c=JH zmE<&ELpaKEf%3`G)#R3gYE`Z7^OZ6J)j{7eJkHTq9-$6*Ku!xlIW2LZWHMa#xChAW zNsLJqjGN)g2fe^`+frV$^NxEqj`u+2W2dv?$om>e8O3pDHhX|1`h-A^ymgaJY+WU0 zb}WN84UlC0maXpfy?4O45SZ8Aq_^5Y-}BPper(n&u-t@qNx85SFf0)&Ga9Yn^A0_d z3fEF>U#<2~6Am0e1K@dw(FzI;^GO~q-P1lcqgx(MP2h7^Q9WKb)Y)6*+|1>dK*&Qg z*~TbLn``zCV@rKrUzWg3tAVw8QlR`-?!^ISQZt3-*f(n4o35J!Z$j?*woll!(W=Ki z!>yFQeRnaBfg^_gx=A;Ho|ci|M?E2>ii;=HMJ+{!wAmkqL{T$Q;2iS7s+nwx6!WCu zLGKy%gh((%&!?xXRf8yQB`6KkZW;N&ZHyUV@5oWlb;T=S<*rF0EJ#5%6SZNEZZa?m z0M_{#N$SgkA~}0@?E(bfVzah)0}`^|^BdASP3-6hfS`oxOM1hS%pfp^trmMNSDL_5 ztx2Lvmvc~l_4W)qt}!1^k+~s3n|gDAh$O(7oUR5--t8w$m8`8b*qK&l!Cjchb(UEY znML87HfW1l!k79xzzVKaa;ma@Ah8mQyc$;Eu;{pa<9>Bl1m#vM3=l^&6L1+*YTSz* z*4KBN2oRg|^?EHHL&)~U)DxdFPZfwm_}tKfh3T(g-}Zfz4@nK!2c9hUiV?ucm#6K? zF-=Bs0hR87WtRl>`Drk9So>W0E>%X}a+O^C`hEmINR$yHcV>W4o7B{bR+i-XHki^` z)i-7=05|UjK&ISwWc2 zm8rE?s*?p^sU(3T$w3tB#|;=%uFFAjhf6Bm?zU6pVYgP}=E^t?D^+Vt}`+nbT})MikijgyH-;%NRkb zhHl?8WfDHm>gXNRN&wi(Nx$05iNZ~lyn@%SKJ3K)9I51eGl&Lsu^WJdO`R$sWHe7@ z7(7YW$MhYLIN*`b9)404-(kz?`=+)N=AI}m1JY1+Tmn+2lF(nmNxaV-U@PX6t-e|Z z;KWSiyG^uXQ=j)n^E5Vy1lMwgDOhgX2mJ8qoR?E4wxxwo(Ei9`Di$fFwA*XwlW`QS zxX%n$)jV68UTrwQ6>C(h=Q~lnKB_IC43~f;?5pD)zsT3Ex~E5tF*BRMo*eDgUWlAu zt@vSYS7?d=y?*HVWZt)08wciz#h&7ifJRe*CQpu>Yi-Qo&MAkYkPcOG7i>$Lx8bF| z+DEqU5c%4i>}Tbj04g~%2K$NFo8MeuxN%IAaGAXat02*?25UiNXJdL5z)LZPJ@b49 zfU7YD(8p9>FJp@(TfJ&_ClVBLv=ez#!4_jjs>boMT}B*pj(vtPGaKB(9DM@YRRu_G zIR+~7sA5V*0d`l>t|L-#!$eQdncf=>1}uFfIBlvgs=IqRMuQ}B23K~;`$08X&zF~? zNAbH|8;6tYsaY$6#QQNX9JxzVN9}cOfRYS#EEK-HsWtG0_iHIkM)B5Mo9Q)<;F=Gr z3u6&foD6A7{U!<))qX z4ktK1cCO?$r8uVOjmY-0-1XM^iiTgIR<2`?gf?D#c`uQsQ+~Q(NPSj?wVAlo;^1U) zZj$aX)~Hh-@2{G*dpvq=GmuH0TTL+E`NC&;!F8%wC=Ro-ptaJb!7&ILVyy9dz=!r@ zI3~a_Iyv21sE4%%QQ=tJADz1XDqW0-36%uEh^&g z7LcP-wT&g-S=d>;lZU)>Jf3K^?*k|>$y@Y44Z)rr2mMWLUKwWCtYk+tWrtTw?=B>! zny-(8I>t{6X#2J07t}eKTa#?z3b7L&z$UcM?68v7i&C6{q>mO>gB1-}c_!af@X1#T z(-VN=MhnIDUhnjPuUEXRI{j!0?9!mrUF%xWua&0TIqk*38fVVMdz@D)>?e9cL zD=Is!#eVFv$zpj>?UR`Rf+`-i>zS4BE%;=|AXKxwSkT}FRTryOX(qDj#_FKY(rmk( z=k8H$nxm|$z;a6K@WPmVodGmjxrX~DDGiUI3MQ(r+*p08(G2M4bgc1eURl};dX>8t zVc&YinO|kqY|RV|EPfp8ct6LbpJkCV3OBTopS;u5VfJZag}!RX%n%TutGZa3>UX4P2pQ-@PrI%f*K`?)UP8z ze)hceeX(QD0P1d&bG-!gOT`_}$3YXR3sofvM!j#%3huCBG&QJavINPY&oc! zepY}ITkaLaK;B)cng-NA7$;!jN_L3bfXl|xp?l2{5r>=fF@8G%;dNHwBk^Ljc~ z?&~?g+4PC(=u5;DB>E&1#cnb?0{8P?XPc(J=)q(xB*wZ=0FVWGXfqm!d^_bE$m$V` z#i#$G)=V-2TVSY4QEg5TJ zJKV7g{x+b70!yt6m9Ed>_?(82#f?$f;FcqHl)gPl1Fl|qlYEn0cP1MW^m1d3i?;BO zoTiQye$a1dM^7%j&4C(eY+HwoLu;ttbnIh&wKzcqW$I+%m^T_Q>gqB-V@j(%(HH`B zSh$3aYi{lS$l+?s3vEN?=z1frLVfIqzMPf7<1_<**uV64phg@_mPhcX)lqmv-=Fb0 zB*4fx1tHE=s;gMNOXTndzHf6~`ovu(RtjLT8|n`5a4ag+h)Y5_cH@;&P7t0M@FkH+ ziQwHGy)MGwT!c_4&YA>g9NCUN*;`Ek49AY{tvkug3Wwy1eK|Ti6QB&9XDBmE)_cRP zj^p|9UTeDQxQ(3=OM0kzWPj26Qx-_=D&Rcn`#IEyMX0Z+9K0Ea9#pzQGi!fFwwt52 zvwF-l8-z0}>uEa!82D4nN1NwQ#wcvZ#qi?Z#nr&1pnG=0lIK*g&ZmvKQiPn~Y^?-K z7sq)X07;2)k(@bT_<}0$-ZJ30r|0lKLH!%Ir;1m1?5GBrblNv0G6@`==LYp!&8~*+ zxc!=2nL2a1FCF>FlS9ZL6O;+>(W`UJ%Gv2)@_I7vkNLu|i|Jv@%APl@nQl#&(FSDU z#teZ@zp9zr#p6+5GQ+CP)ZaEn+e}*%x z!kk@jvk;0gsZ@7$r=w94q@Kda-rNKNt!?ylViYB^@0Ym7m^`>NTs@5`mh%eC)posH zaA0WnhBC;8BfVLXG{L#fj+0`5=|xUf0qHm~b+EQ#*5x8s%Ei?NpuVFGV9P9*C@1;$ z){_S`f^n(4%u=5=CT(w&wyt@k>oA0_bMJ~V?V%ha?O!~^;@rDYR>jHT5502G0IyOZ zJfHDq%!0d#WGw*|Eg!=VAOl~V1T%%dvYf(F#0+u26*EnH1*HeREtQKMgT;`^lZeTT z0DK0ATWHF#n%9Slbkmlu;au;k417FXwshF3o2?mlKlK#4l1bKRS&I@7e*=#L&B(@J z-vT3E8ua^pcPr=iqR(eh4i;T%tt&@vu$rA()g>Ex)3$}+=S<*67q~S6P~h4jv7G=F z>@Fzb#ch(+VrkZNKbbnmdr9UnF>7;O>>B>i>K7qnTAK!RA+7kbwpkpM!|~Q$r#9&_ z>g+1dp+H*qG;y=#KFJ9%7b0vc#o%8QEheYJLl>`gWYb)c2SU__{umUV%X+F&K)J7i zEM}~Izn=z0x#eZ3cInIxr3El8sR<}qC>-@apObxWcWD#AwEA=45nnIXC<@sG#DTKb ztf=Hl-MHy9tW0Xz<@g9N%lCL@906C(S=8Pt4ldYA5R9H}XDmR$Q|d0=Y|eD65vA8a z(x(?E;NB;ozr5luF;K&aY?9a8*bNVh?l}U1?1=3?1%TNN=8tRQc_^z&)LrBnHku!I z9n$$Gn(G%g-JZk|1?G(dSasuBpoFx&-wwLQZSt)u>p9^6Pxr2EwI8`w7}<1mRpqdq zg=dPtN%-Q%RVm$Db>*Ys>Ed|V&Ud$~tL{d}`#svG8?J`y1`~gTrc-=(qjkO!dKRTjVz| zTW|5`MNA!1zI7@^@Up$rPPJ#5A$wT3YH|R?>nNf7f}dbfK@6?Y=DJ%92z9YsO?fAt zufm8q>v$Nj-TT&inQ81%Az24)j39q2L;!HYw<-|nK>P?ha`Djl+YY>2@K zsGZAT1IE8TSWo6+J<~-HP^UQq(mIiKJYbxKX0a{T)9{ekML-R~WWG*&#u7ACBw59j zy^6Q4R~vLaolzOag9g`>&a(*&JJP?=fh@G@Kv##-uFI@6Fv5PUs+ti;x+6o;Q`cn&qf$e zsg~ez3ar(knx;S&9;zNfZm0$UTgC>Q=7m=WVcB}1D%qOoRWID#G-Wb6H75fNOBrTR z8fZa=cj3uu(H?u!bsTCexxG@(dIes?6ZS8FLQ7Q({UJ}{b>1lLVlVf>*6w7N##BwE z=ctM<*2Of@&$sPm-t8Mz;EKIk_k1$i?q~%;IbGA3BnY-1OIBGH>nXjs5rRUuH zuA5~9==!d^Bc>+UUi4v&dBR0}(QxX%Pj-Sm9Nw+fIJCk1RWWI=gxPHb0rWTwz@?pq z6dVbNwo5O0o;}{oRXnhuZ}K5o@cS6#3!@W6R>{lkD<%N$m&v_oQV$eqw+a{#vcmvZand8!SShE zy1N-Hmljp2#&O&WopK_%VEq`e^C(G5nFC8-0h*xW#qd|9D9YlVOZyrVKJ>>) zE~uU3o6bTUAMYTX;fuv2g2tLbXHADf8G|dssj8)BWV3T7dp*#mt!^j=yDN}k&&fkC0@AU-!}}2FxtkQ@PM*$7 zuzb?&;ZP<+)@c$07Di2%>hL&9{AD(9NRgDLe(w3$$KQHbA2EKXLucVd+7En|Hh{96 z+xK-*^}VLFW(~*GK}(H-77i*w`WNe#Ot?d|r94pI^jV)H!V?NuHhLd&dd6NVNf147 zW!3Ruon`*PkJZ9H^b336zwH;%z_&mNLG!ETc8cj$c3cxtEnhVD4lwGxT|oM;)K zKy#Mo+Zul8X{1g_*AZ5$6(g@!uDiL>$0A7}le!ls?aKFA(y%FT6-Z1~^;ZJ94$WIa z)`is^sq5C7@@%y5L{d{gH5HayboLCp=66}G&5P|b2m5$7)>Ua)1ej1o0Qe95HU+Z) zbzT9Q917=%b{>_}N(a88y-omPJn&W=NUw}ouQ}y3g6ia=#+*f(2$pde0~@3!f+XJd z)@@fHDm|YNq#nlpjv444IW$R5F<=iY`{&gw$94-}~fN3aB!YBxr^DRjp;f=<|;w-6;pZrgTW_xl$3 zX~SDIeXHce2+ z4fw9C!%aCHwuNo-djWji(Q!YGcr5|laCiebht4d6vF(T5SZwE`&A_>hm7~3*b76DI z)tp@Pu)zeZPjPeEF3zm!tp|G~a;$-`9JxLP{-61khGTY~Il~e@5H+e-#cEq`bGtr+ zaSJ%@f{O@&xEJT^k%U2O2kK}9=EK2p!9?KYnP{RbCxQ&NRlpH%rjh04>T+Ib0MXB? zMx<}Lf2KBu8wQ(TmMjm8$jX};SZ#!W^m)?W9p__L-cZuEIII_I8~&jSrxFBabDi&j z3LH$FR26YWqjtWBQ$Vkb!GCfi%w9Mj$M91*3qCT4R;5*6-}Y|;NIRv6GIUPdu9D}7 zcuAM0@1)0$-LY(v=lD;x;ld80O||MFX(6x1)4deZ(&3VH(dSu%PCZEr^o6k=ag!Z5 zpBB>#0##WK?I5F5waaE4vFU!f1T)xuxwxNG%_j7H+8m>@u5pJc4pVip-`0J^$mD3p zVb;*YZd9n?7W3hU^cWmw|h109qn#`W^cGu$ zb7?QML**g}+kn(>5Bm{bl51uhHmCK3SYOXO0S)E?=BTfkBO9Veg5eH467UA>RXI;h zz8^_hU)4?NAxFVtt6))<*BejHEp5ymmIlVYt9S5G~h`wCJmQiSRe1sn-M{*;f+MMR&hW!qetv}u*; z#$BNBu1kqpbXc*(cWoldPt&Jwvolyn#bNuy- z4c$gqqv3uM@Nu<`wbgZ0T=>IN22N~O_SP&i6#`>_v^AhEB}Q zQ$k2EecY$K!=<=F-ovI(3K7T%rll7?Y_OoJZ%aDGL1Yy>DdzJH{ z@?}#3opFxHTfkMu{?Q&WnC(b;VX}u{CWICusB{krJeBb3LlK@@$lbw7SuWKb7+Bh3 z+)w5&9j`_GGfV6y=OM&nWq^7-PM}smHw7aPaTXV6s0cm@%7D$U^-ti3&C}iUqn#~&pH9thf+0^pZxOG0C7^i4ZlOGiEx+*l`yb5=f*SOcci1e?i zwp%Pg4l(ax*EoqSdQOa+m3PG&dA8YNEo(^Q!LGJ%&pK0AP~&-ZF?Zb$+7@Z4j@LU4>Kw)d3F-`UvayF{^XWxkbVg8=*7YDj0J-2t zd9|?=btQxtmM#V`)4Dnrgg0!LR#*@1HQ3bimP54VS!a$l$+}j0L{*t`1V)raf=)u7 z-saMSo+r%9qCOynaZQbm>56d-y*$3Z>!^FzIo`GCYkV(8Pb1C)9lsq1YF(Mr z7B_(goerS;IjnU$y##9VtGA9*Yzi~o&v8M9CWwyf{_U{Hw}Yl~byC$-w#3R_+1xy z5K^h1%;fRQR*rY4n{k?6bjL3<5ieWKcAv%-dIwRn#E_(TzYL7y<-%{J6V<+C$+^OI z43~dE)KRGkF>!i9Zt5_!;#8NkMD&>zJ`yaKzbKks?PS;HR}oPqK060e#oTW7DMbT zf&YwLFrr%5Ds@@9)A#Z=DDRZnC8$28jYgZ^TE;6qNr%XfNaeQG6ZaB`-JEZ=H1 zqn04>c#ba^y7w89Ub5+R?g!-lghzYG$RR+d<2-ET#)hpNu_=;CpejcrChK$_n_=$E zmg30WFBLfB6ZRU}<2~2g1Ptg+p%hPt{jwQ1Kl49*46cBdVJ0ue|=@lV64m+GgA;J9^v72bH+(uTiI8MXl;D1L?5E zo>RMHk`jZtW$@yNQ!XDi^%RY>!)<2*mR}75EuZfX;iIyI!x-f=?76Xn<&8hgS6-kg z&#_RnsvC=&YbVjcq;ehk?cmp=)m`}RS9RYbw@1Mm);_fcdOk$zZ};+ZV&m+xV0lP) ztgUGtaS9;&o&P}2W?Ajz*jg5_zE8te#Lr|D>dTF-9v7~1JRXpje6kI^U0|n&aTh|J zGK5{T(}Qvw&IY5_>d})UXgDUwawZc5aXvRHlM@?)bGm0e@P1tG?!5C)o@*Fw9Gy#kdd(-R`(%Gw&xf1C zT9M7TGW(2BN14q?nO#ZSbO)Dox<|X*TIf@hvh5X1Zm}ftsVDWgZat)pFI`zhK008Z zhv@g{g)^)+2$wq7?M{sk%UmVKX&dF^dPz2fx=Bi|Hy=SKo0CwhWQ5V{OE|mK^%=Rf z_GEh2?q`mjW-+;`3wC%;D3U{YWCAFUC&Uy)M$2;}XjkBFBfx}rkGclWA@`}3|#?0@n_k=8N zY$xn|@6m+XXQ0#b)BTYvOzz}_JGKVnTz~o039|*rdc0ZLFLaMJx$L$+_R8tS-dCrG z4`EJEX*t`o*KDedCN_CCdcDKU0guQvU3i?li@JBYLTAl+6Fkib^N*USwueZ4CpEX| zq_B#ldY9kpWa8RjyH$l zH!4*_F5kXt;6~`FZj!@1L4t4doFCz4=TEm4wU^J5T%_1lwsr;1D`?eLEa=yGKJM{* zXR~N$`T|tqdu297o&bkn!NZT(>f-5CBAp(;#gjW zRKNGSUa;QtuZN&WKGmj#j~a=UwE2 zFJI#}#JEK%y}K^bmbwX~)SGO3$fRArViMyRqsA>ldgS!X-STeJzPn;esQJTleLdd8 zZl|;GcyCuWL+n+lJVZ-rz46ldGahgf=c8TKfZ#qotjwNwmYSQLA62!&ZnLX(KGGPp zt72RlE|X4TOEjoficA7KT15Naj<9Qoged+D5ZW#qGTN;-F)HV|HkrX#!>hT3;po&e z_sE7oG|HMOV2ZyCJUGkbG z=&P7o-zb|vtmiTA!yU$Tz%BayqBws~)%T-~PNIrO)1 z5~_)N>@&y9({_RR_23l;?5Z5335{?baz`u6(uw|K&OdB>I9Kfskla7oV+1T#*)kCu z^`-y&Dj#zUl0I@WE>O#5R!p*yYFfi(q$}PODsqH9Ljs+82o=*gWMxd(X0OmO zzmJ^5U0xO^K9NC4oaK)(s~1>%i?MfO44G)Q$6g-I+Wi<6S>i5zZ^vE`LJH* zwlTl7+QPu$qTT+zFFTulo>$;pL%yYjd{aMNBS5F-#C&Y9;N(q!WX*0?IXA&yr%gVE;FzY@uIm#Wy4 zeXPxHSm)0rLBfQdlc&PJN^<{zG;m@mKlQ8Bz~wZ!tTgu%ei3bCs_d--qjd|W96iTt z1#NMu1_K#K;|8Zh(kE?pZhLa!+J)A|CU4wkpe_7`)JHB}d1K&H&IfkG(S-h7Qy~rs z*L+~c781zM>)ZWm9xNzYIo!VH@<6}rm!xRw6e43FRgR7(5*viG{FhIR#)=G=7>LhGn@H0)KHV4o}(NTo}lHfS?yNLy^?;@N&5v$!00* zL@F0u9Cg|40LR%Z&ko#SGD#9`mJF6NgRg^<@M`EaV>tB%0FjqYBK=AqXVD`GzX$E~Xn^5Y+(hbg2n? zaYuSD+B)FEu|&4W+j;mha}I~z7UW)CfG$o%BC?aRlYixuJ6LNMRR6MBh*y;5d49LYsn zfr!2Op=S|8hA!WYkhK_+_tSFR_gB%0WRcVAJ@sgS*ejZ{t)(VbN}uC;$6dv;oHLq_ zw@I1Ok021;=^%A17EE&l5oR(toSSvGhucRUR=4hx=PUSMW1U9q#-xbrZN_cZ+d*|} zZIKXqvo4;Ev_|+7Lmd3u&xy*rSM>Qvo~c^Yw-mVx;hP3*g}BaGJ8AYFCw&%SX&8RZ z)<bhVY(5RJK7f*`NocZ|7Vv8CF_ZHBWliZ*kHR1o5*VKDglYdwVdICp`_pAHh=g+9#mDNd1B_8dG+8QbiHlBaWOcrBC!FpKv(iOH z;wD87(S6J0!_y$yIGd@)Of;@ftS2113S2eKZtfO#dy{Uv`$%kF%u4WQuG~a5b`HUT z@ILCP1&#^rA&~pYS0gdgvMIZaY-ac9gYy=1d6T11KK*)6V2 zLSLmF65rPIgqgAf)wnE+QS3)-jHoN{VN=qs$);^BQ-40jdKJaYD4ltJxtcBka zU9IYJ6f#&#J!wXL>3t#2+XEXRb$sFhIa)PA@cZI}S$`HUsPHIH|GtrhFVP9Ykb=mrAQ_ zX{>ONW3}aWH_j^&xz84>eB|JOXu)F@6t0O;%5YYCCUxmN)z%8pq$YU}{@{*@~r1W3Tsnd13 z+TCLeP*wQPFYzZg_hs$1)?VvdYjwBR%M6F~(+Ye}(+L{k4|DaRjc@>7HM>MKZO-zF zKX#TwKyiVkbSX$-K!FW@ug?4YsdweDTc|);=yE{RonvpczfLb)V{o6#cGesMjji!*0)Ocu)F2~hiw`J@8TEsc4p%aU=Zg+T_k|ut#0YB|o3vIl?JI{(iBh+xa zjamH2Dbw$c`tj+|9Hay@AGEe9BLirA+3kRbStqC_UeP=)ucrJ`+9N*Znn;dp08u?w z)kNo6%=?|5Cpe!CJ?)xoE_2hrqLyn*%z=Iyh)$7^=_ntTepbjS1n8x3L5oMLvG3d6 zq06{!U6ckZ$y!X)@OB@RukG?!A8jW4WUe3nDT;Gb zazpl2Om@jP+e|d?7q-130d=$IU^;>~!Y!2&=Gj_u9X_{Q=}1xJY+N744zub} zd`s^Xu4=f8XgH@Qie}oq7%4nT9y=cuO{0H`06X4xBNg#Gz7rpnZ8I)o3J7m|4HhQ3 zarV+8(tk2` z=M1qlFQZl1A`G_TQ*y3F(034g*xaE+tYBNRJZL56G9WD4r!VXAX(DNpV6ZxiE`6!D zo4j3+9s^rnsZzm!ZWi@snxDd|Z1YfP(T&_%9cctp38U_57w7DTJv9K}qDDAi9rgOQ zmltQBnQUQ0h(lFXcBE^KFjsR*!wy*BB?@hYGb_~p$-;wH3W3;+XHy5B>j)D#QDWVF%>2qQL z#+B|3EU_;bX`2rOVqV5=tYiS31Ym-8s!JM833!7J z-Rv6NjG{N4`ec^wOTND1z`ama*t38*YK{>Pcx<$*NQ1sU`JmB$GYiF3>HhBBCwHWGWhVM2ag(2i1qFwbe zqUBMGq-M+j$2==YSOVLKuuyJ&s3B;j(T`X=Qku53ZEmlu*UL`van;XSgx>Qui@GZ} z$L2{^CW=og5mYqDcQ{5_I@pqWI3RfsqHM!QtR`{Y&U(4&MOzzCqEL}KGeEcjHqF?KrytpDOvmq(22@mq!ruVYRv-EJ=`^hW)5V)JGK#{G!Nf?=&FBMvn8A z%CkbNK2y?7CFfvE*+{tF+0{E&3nkyP#9z#Eg^F5T*QLkq{M?_ad^Mi@X$DSr#%zbqY}$EV}XaHcwp+}OzKpg(VI2OL2phrNfWII+}M#L)t_tfALBYb(#YBKBDu zWXsDgnlVw|Uh?*JdY8wQUmJP?c?rX_h+Hl$vk^9;V&Ml3uhJ!t|)Dkf;_arr& z-d3B9{M(vnM;Ghn5b=E1lIO7VS^Z1E)=xc|)d{h4Zf|zyf>!`i9koky$))AZ#R08D zQjRhr*LeR@-@=|7s1wS7aS-%S%z?9Ur21LD!d}u~H{Ay35vD}MYjsB&*ZnlHD_Jlp zL1Dcmw=t(Iy&g;{dDYnUwKXMlU82Z53CUt^d$YZQ{-5``y#O|p$2esHKDq*_P!lsD zjD10aBPI;w%fv1fiY2$z7q)=|5bi;I=1#NZolz`}84<~J!|ue%1?Qa`?hA#F*~w*V zWesiJT&41*709DHBgoSx;c@jmY%eLGDuzWH2ZzNFuBT>e9$l2NN|KUDY{bdnpsWqr zKxPqBGZffbgtZApb+IfbA9%4TM|FUO&DrkJYl^MzDL{Sp@KEvJ!9wW+VPGAP>b})o zQgCKyNk*Jqc1F!8an`M8yO{P4Q33z#vQrYgFdj|dIM!9*U$x!4*&Rp1*$VTxABfO3Cd9H!jTqxXB=@1!iG%;o9<<^ zzLfHFSj@`%^%>%ApmT1dx^}o42yoL$@`{jHJ4gP9x|pmYZ`oM&eBg|n`LgQ_99msE zUg0QOU)D|PeCF+C-B(j-b-5l|{u;usJAyrRID*R|*W@Hy4YwX8vHWz?ij#c<{GIZ> zx>xFyaJY|*a<62|<#{5`RcCoxxlD^y(!t1!5*QQmLpyHHv}?M@!Owy{XK4z-+PWr0 zzF!7F+_OquMEU20;Z=Rp9U(c5L6*9zU7mqQZMUEIBnk-_97ge5^yGrvAb6bS57~hS zwDGL3pg)FXC+5p&e%{*kW_{VM1DRjFza(+HE#eY zVcwjsJ7Y7o)RA&lA@U8sw%KmBzUGv9P4(eClGFnFuoaZ1H}C6G!NbDerkh0{>@NiSJ0Gff7Rq@xhWl9){+X_$oL1^|I3MvQf4ruS+bLa_WZJFcX%GAQlpqWyk0q;-VFw0 z89aQv9PrU*+!-^yeAiAOmZyjMkv;5z1z8!hQjTf|6)EbhNZGMY;2z8U;LH|=(O%%- zQG~j4)RRkrh@~~f)hPtzUy1yBuJ(IdfUhj?F_XO44`$$JleN^6uH;m21(&^oc(SV# zvs@E>pWN_8&Zro9k^}-&tDH84MM3_Jq%1Pb9tTiJ8FTLi9H<3|A;T+cv~8)rPIi<+;q(E=U>GQ-G))5BDs;UwQ7S&NOB)bUD*fevB6yLY2z4 zy9-zryTV zs9ga&JprfGY3LvQ#10!o)|9PXeWld5#X8m*M0PlPkEWq3-tL8tI`qAW6#comTEhP@ z<$RMK^tpo(%uK4oz`VNeR{Kq<_QZ&Z8abcJQzbjn#tvzgR*PV}G`gu^PWN%z%&I+6 z`3cuf{V+v%z6~dF&*$A<+&VSS{RZsc*vebgzn*XWQUmtwG`x6z!-7t@G&^pS@)>%> zkK0g;M!4CNd4!x*^pW-?Kw($KhTm*8q+VOJStA<|efd1zjTlj_bEL}=tg9k|8~Qp^ z?H`3Bo7^~|@+paA0`8Jx5cn2=2}bgcNbRq{hK zXiHJk<1T4H!;F_tuzv7o85CwMwVsJEQ%rAIBLmsYqGC?|rkKD2?EfBChR>ycx5G=$j*Q z+7bIzyO-0rq)|!~ZGneAwT}9(vAt{^$blKRn^GKn)>e1Km(H>AQiX42F`4tx0`QEO zU#W2n_*+aMuV21YR;`_VxK8T`KUuGjvr<35#&Qb8z?PqO`6l6W zlR-VI)*F`UlCP!krygXjm58lDc232Kss;v`tMV>W77*t!)@_gb^Op7Z9mF#r15K1q zZn-74h=U)b;ikQii{3=(_K^xl(&^P@tL=Pljf_LdWZjNiGrHbtV-Dw+oz(*`6fa1* zcOY}lY{Sx*k*ST~A4Eo<2&*A;YgtmXE5el#tj0JeKev|0L)ThfU=Kdcdyyr#QbMG` zFU7(&+I85xnmeSox>#Z8F4e0(=pCt5%WUs3FOFqE1gisp|KxSwM?`_FxZSVVfEWA8 zLe7Oim*%^y(9BHRoG4=K4ubBvAN3lZER-oSdv(1zgZz){>Xr7k$nMyUV;*7wmSfm} z&Fvsnx6M>N72&2h!uJT=pWQRt$oz?50?yrE~N%MG9qXPnX5^1e2XW(FGZ@c8kBluq&LEUZ0XRCG=pRK2w+Ll1s=)$XK_d z%Wy#DJ_Q&#_M>(r&0Sq_gyo>;ZY`!jc7R-ATWd!3KR(mc^^ZQ{F#8KDGTmds(th~aF#-SmkanP48)}E2fiVu99YJh zvQHG8+s&qh%rbh+aLk3F#K0C>aQ=$~aJHvmFo@>vj5dq2r}rDJ2#mM0CcT(iu|u5X z%#IrI^)u*5%;oYRVM{w$totdqZ__Pyt(fs%YsNFnm?Ilx=uG`O?B6g`fKE)ZoA*Ld zfPy{s)mHD!x19R)fGmwltnLFuOSgC{SBtB;nBK=QsKy}ZZZKG1QnAqkKV%2+hjgXp z8Hr~SZksUsbWyC%2M;!^InI;dt;^18Og6P?-Sh;hZw#Q%6U*qr3>OXsHHhGuGTIfs zs0RA)l)`!>JL^bT^8|-{9b9wc@r<{O$UK@d`LP|>JplG)&4d$2LjVR$9(c!^MhwKD z(Nm^{gyg}*Zor--+8)igXsRGGv*880-r*efRE^t01XB0R*Es=-6_{MZ}%}`I1gM)bhr^zLpz)`y*S`BwRUyI88GK^Yo z$(w^if7z*<(&l*C(icXT0NUn{d3~#nyU~U6V(fy#D91d!jah{MZO&6GPH0?)+wGR+ zEgd0(&NM+vvlaxLw2988FJXqG26TJ`&5aI2ftt?cW<(C^i^j_9BL`_qiG?l8XcoQN z)Jv>p6F#z1wqRPdy>KRYfvoq|GwHBVxRJ@o!Lmu6vSKi-6UwaHMS>FGFYaTwG^a|} z^yx*vUsrXctfRwvxRgVu;U{eObfdjd|3-U%uGzd9;UrXXZ91tq_v z>>^?~CygleIRqkJ>Zch}eG>8}&K*jbo0@ZUOFPe^H}OIQ9w8&i*=h8$tKBx}INmX$ zjj*Di;YZ6gQQeO~q1*lEgzF(Bt-r3122q|Ns;(X(ABjuw+O;J^MeppQp`0#^RSc;< zas~(%?QLnJ7<;CpwOE9~E;lfs%}h9CS9QZZux?SFsTl;?!S74kL){rcvD>w^i6W8H zfVIriiK?4DBBeBLdW=sVO(5v5h4>wz6qmy@PE^vO4iA&M3}IXY4u)@sQ@MQ!xyxEx zIE0QEG~9p8s{5nUg1Me)J(ujG-iPiLj9q5GTh0i3Nde+dt-)LvuuTek2A)MOLJqjp z-{D|4AJ>svX%^5P&rP;#zDqPSr#Nfk}~Y1ogs-A zeT=*awkl~uVU^c&k=k8`twSa6wX-S=4>FEMGh0H~5z>{(g{lo@)mRR$O~fqCVEZc1 zCP*j?yTf9(LAE?vO)vRir3bkgkS%+q+eM1(swa}$vcPzH(2vIz4fU^UbG=MO?z{sI zog>-8q`WX6aU6%ZJH+v4CwE@$d+z|1Y3FF?<`~JKS#zSSTMe1q$rPPV>3O@st64Vd z^u?*(=8N&t+F_M@w&8SOWS#46udau>Z*?YI!ex^(FM@w6_){!1D+?SE`dew^8#+h@ z>RKyR&JNA)c)!iyrtK>&b9Y>98g)P0c3{*5Z=69U2qiyV_FIvDrL=mcLj&whx(YHT zaZ_J|GcBDL>Lnv1T`zF{he-tUQ_T4j@DB$zz1uu04jHP>3W#E{4Nni~vUBc-``8WK_-*o^}L#)8-|^hu=0F1?(Y z2eG>#=dC1IhV6ap1Y>?EcQ+1=410*}mtaz8l3h+AwmYR6NEa@pg+JL$5H0W|e=r2313^?cYtrZVCK ztWmW`&B<{$lQ>oG4$XB-;}vAry%NPz&BuhHGJ{KF(XmRMduRbZYP7eR*;d!ctY!`- z9kISokWGylZ5JGSLJBcpMjK>f)*1{Mp){uUfJxsnUAwinoBqL~=@GIy67@+!Pmjdu zY}I{^pLATMHEOrx>V70ZP;}&VGNu~cv5g^sj9Efh$I#_3gj=X743)d7wy2&FZqFda zD%oFUjSd;`^L=`hnUlgG?V-BxWpcqIU7^;mCwum|?UeR1hdy#n=h$I4R}m`AMsRi^ zC(648)leu#o0%am@+slRZ@}Bi!0NA>2p4)Ny_-6SD>Ly}fU_^<=kDWO=a} z0hem+F&EakdaA89}Z9l|_cb*5%;?Dc^?>Fwbs6EdW@M8b3M?`C3VHqsGY8VBw= zYA-JLzRyNiOFx#hy~ex_7W4iX=h*qa+iwom9R&_Q3=T((ylaDr`;e!Xo^u$B}h}++54EN^joT?D~!-H~q!{snd30Z&F+f zX$3?)qpNZl30-2=JX{dsCe*9(wx#eKt$Om6?n{P0yYBN~m4&=hN0O&>1~#_Mh;WL| zD0Qb?ub!1Tow&16o87cdCr-FTI?V0DWD)5zK`vQQYtGXR+}6B__$Z4gF`eMwNC*i8 zN*H6ITdrc-MIHdRXbz$3jzogRDZT8{%~;$XIaz0WX^0%rj&}f*hDW|9Q_;m7AzJ&w z_UP^@$7Wb+`vKP19>%~@3;fiDZ6H|EX`q_f7U%&rXK@@eNv~?Wv#$78rd?gj*i&@< zNcyykEc5+N-fbJr=~klrCV`+rtglb|l!b$N4q^EVAIBYCuq7fog2Bv@Oey(H}wEsEZXhBzyBll`FNBYx+` ztLiI5Zd23tsu&u8eff27jSPbR1Q^m5N38rg?>UWS{f6m899wglpyq|enw(@1ZITQE zB4gve=$Y-4>P0T~ z%WxnB)!dZ!yD5S!FYL}BXj>WgA;@6y3mD{VnF5?7fpAX9OH{>Tb<;o2ETh zsRqBkI?L2YP%I&*UR3s7L1_GvXx1M`Lnb>M*uZ2 zi%7}lB-K7&9g!k#EG^xGaYb^wD=U>))|TWS_da`RFv?}b(avP$!vSGACX#=)2!dsh zn+Y{LkYMT>=oVsxSDqeRW15#!wvWJnw>y^t4iK2xxCra+{OlYTJLH&>T4Hw~$-`|D za|M@FvTD@h^rm*GYg=xSHhaiar*^%G9gW54)L<70WjV+Q>%hsqGW`QXx0X$~J=|lo z9dE`ul^nRCvE`QSmaAtwE}*voj2m^Uj-1d`zB!j?S-QlWqmzZb^O8ldHmJtadO?Y%qnTYa{?*KH07#9E7DeYT}e!kKDg9H>d({~Y3$O@;> z9w_Y<)z*&Ybg;@BeSHM5g{Qm4LLNhj$G$L;F+F2;4P%QS`D?@#sXCmw3!P$27qvx% zbJ)KeeYUWtmmClEO8p4=*EVU~xG)5wzY+CEt@#*-$r-UnV2-iU4G-}eD?Zi&N#)kS zLzlW_iIYVP<#iM4SMzvT4f?Hf(TDa0ho!Mdx)HDXb;K~Ch{vde--g+yVrg*hh(X=f zRajR<49K3TC9sy4Mr-d9A8a1hca|n(+FT!-jM(qq`AI5K!+63gQ`zpP0XJpHMOWpI z%VscI#yo8yxzT}h?Sak<2lzmG>rJr$M7NZYi&zXggBDj;4rkeIcEx7MBTG)v+eJiu zwGiv>3bul*eH^I>+FdRhh-EGJsnwpU<6)RmM$6%6GSrni(*(FizzeAWW`A`h5g;y(8Z06DjVPO9QG`5l{~YCoF|Rt1$F9i1J@e>DA?N)WO1FXFZ1yl z1W%(jL%WeLFB;h_V`*317L~1##$r!rfftRhBCGNgGa9-9b&3npLFR0Fc|Or&$pDbc z(qd^MCFk}SXg>(S-n`%x3nq&7IVTmos9mf#&D7_Y#yOV;0L3=t;;8Gn(OmaW6Cm~G ziGYKs(QYcj(P}2^0K9BzA;4>PJi}&Y}smc1MJ0>U}~}#MaIgjMa#0HpXLL#?is# zC%3qI|7cB@O}*G&niId>6uW6N0^l|8^9_fw2bsEb*W>Xv&eKBMXu%rAn$8F>t9S-% z;fb%xlevm|H7E+RPnn_DNW1w~o2Sk7RChB0ti(Tv%ms)uN00M-zNv3iVBq#!0I7N8X3bn!u;eVeENnPOWs$Y7q#Gtca(B4#Xi*n}5O@TgnkU_O zEzM5N&E(WIPaX$e(6!(lIx6Qo_fFm=qsY?mlBMbf(q6ZIS< zu|T%LRc9EIs7Mkubcx<8BtPnzT`ux1bbBnsTK7UGfvmB}=2NmdVTn||sSLQ)Y;%NZ z?TBh5V~Ps_K97zp3= zp@W=fN4i4`n}{{tSUt;?9L|;jjGwTNWxc_5$GAmw=BG03;v;`ISk2kVf|QMDR2Q#9 zp}tY_nSIkEdlr)ay4N-|l_r$t=5<^T^qIqLZ3c@p+vWNMXHb#WWUc~Y=@hL)Uj<{SF>dX^US zipauQL=DYm1xEwc3Sl9;Lgiw+#NN<^zA*}S(%I9O3q4oY4#M50)|Obcj!va3V@(rx z2G%)KW0!$DTs!s(rFTl`a4M|FNQ>u0Vz{0q<9)uEzzZGrs&i;5NriBeM)~^COLzywR92 zt$29^RPyL5TEpx^T5ecQ27I~FsTVzI4eZzmy6I(H0^1GQ0;E25y40{yZ2Wc8ylf}e zks%|Lu3N^1mLXuLd_>BtfuwWOZ0hGM@-&kD@uH;^TDaXP;>MBsJrRkQi7xL2ohwqu zr(5-4uVN8-YD&GgGwa6osVIoK0~*nC6E3TDBB6N5=_Fs9F40;|T$jrZOT%Ww(+r1m zB=QY6nwu0^zqG+2hD;&$dQpt9*CL{4)Ne?UF<#~}0zg#Coaso)#*>|s z!w-s1%aPKyK;P_T&Hxs?)mHB;6Kc|w?5?-J%#NLwz1f{yVmf38W2BoShs?A`cZT)B zEYX1NgsD&&4m*^_CJ7HCNU4+ewdR5+01=1naq88#^fqr(oo$>>LuG%(nVBKGal=!= z3CT{Dh?C4rC+S)`EKuD{dZ_VtO<)6Tc#|zVKx~g* zGS-Eb5*aktPwl02qINiW-f53Pbqm-~g|uC^GL513H^svQam)GAKotgKuwT|=tH^p? zvS4!k2)ixxx$@s?ZI)$b1(`$KpL*HH*Frg5P2jE0euC3bGyvRr?5`a=9{~q9N5o1) zwweHm?hBcOHL+47;S)?q1G&9ZDpM+bE>7DtneCF0MxY0AJf2tKVyq742;iksxvd71 zf`_}cmEUZ>$l#1Pn=J~4lspq_qo{io`Cw;SxS`i6lR#k|IO{YUOjp4+?;gaZy5{Cc zhuvefsEi-Qnk)w9%v_(M?Mz{}s^*-UM-eA&ci%@%KUq-5XG0mrqvh8_9j_rsdoU`CL<1MFZqm_?&4OlyaYYhlMYu3K3Yc3+J_J_Y@IJpcDOyW zqG{axBG}eS;{-BA$~dSl3JQ0$4sdWN;#ii#UI_&}*(j_MAr5?R50Zx1-L~4+61gIM z`(}IS;mosKp2Afhzzr}-o$aHL&^cX(#3)+yu4iqsjRa5JdW{^Y^Ns-v|3X@+nldZ# zdL?IRBgqJJS`i96kSFnpLayoh4uy35@Y3C%W;^S!@AtXxlJ4m;Jw4lvqh1E2m3SUJ z4crqd2lbbS3pMePRUWX~m7xu;8IpY#O-twF=7oMmya0)+ zL37vx$A@F1NdUpo-oNX) z4W4tWwL%QUVt|C7ph?(0V8|_9WB9+`Q{)mWgR%_$laD&5fh!(UhfAjuW4B`KI9;#$ zNI+-pm;Nwcu_427n*vFs;<5zElo}7b@QMm$YLu+HgAnxskW}e(Id#?^3fon+Q~RfL znXK9!A?}k#4x_di#beZ!fy=@hC`MfwQv+n3bXKA_YswSZlP86jrFxTB)mCHbtvIVY zwR#&tbCB6fxU8?rVa}rO2llOY;d;Xi{3b><%5YSrKZ&3x&&m_rM<{H!-SfNaZbz!sf94u!s8Nj3sVAuRH%BhuRrh4JvxYs>=oRjZ@nf@`$IN?cbB}Tj zsp2IN>KKkFoBzO~j9xlZ~gH z2%nvbqpPSL*>ukuIbx!<9r_6H-DuQd>!_k;3HCdw(%~fY$^%cR2T%p5wT1Y%bya&|pJ zTH>rjn)7Dv&O3EWM(XKUt~<6mo?PHsJkGkZv5mr!04E7D3oFeH!yUWbCZi~v9#0R3 z(4%*|)~@T$dz%P*(j!hNbka%nIh{5=2YIYfQP@z~(Rp;t)D229xyj*_31n9S=wB|A z0aJpC8nH2RnTrTN%;{7pbCn?sX69MLLKzr?0dl6XoS@gwddd+;tVNvY+c?=^^KZ6o z;I43p1yB(Q#Uox6Le!?x2GdDb6zq7SinH}}TCNFFc`TNw^|9Y|582>ghT&?WOfOpm zJ`7Ln8iCFz8AMn*!%PCItgD6^K}arRAotZQWaWd9r|tGAr^X@RCN6@xkf#`R2 zFQZ*bNNsM6>t;UGi%A20+yY0on6;U;fZfMq9bpt%ZZ3>GCJ}^hAv>hk*61|y%J@cI z>*S3NVy3%RcP}iFW38LEH$y?vC>~W|=qVUK!m2teea|`u~io_3^}81uX-_dEE*;dz7Q^Z!Np{P*3?{h_LjPsYEHs>YiS|MJ@pfAKxdIGtXX z#q7WQ;up0*H@+;}`&+m6zW>{lQEl`qSY-G}+oCLb<*@#lK^!3$5u4{CA{rpUwY z1bz*5=d;BAvYL`V{k6CJ-k0~5zxFPS^4~$P-kz4XCd6)FHr3A`XY=2#9{p{C(B)wsRV&}(W@&CE;tPk-^3f8IU%@@ay9{_nyv{k=!xncAOB zQx#+U&Woo`V4J-2o{xUgiF+E(PyEO`-uUJQd7F&>HIR}1CK=r}rTx!8l2ZLQf9=yx zYrS)NBly!nHBK=or-pP_j*l3(+R5>caqZJjf9u7=KKMq@JPx#)vj6fu)c?hI%^>m) z$(Qzr_HWpK5xd!bapMQ0NXLfwzFTgFuZ-eXe^YlZHAnya*Rd~t{kMLTz}Kh#{+PeM z*|Y!tr|(((m7e|W$N62q_-)m&9RGK)y{akx-P&(gll(jADL%s~{ySvjcVB$Z`siiy zaqaWkZy(?_Jk%_FdnwdDtv-DG;w9O$53=YGe)(6w_^zLN zsu6uTeOSD|1rkil>AA^;XN&j5&Hga6jmW5dSPuEanp5(tH<*uZ__31|H88Qn@o;1E z;j7w*_j&rQTI0j&fjf(eP_zczOs{qpU-)5yCAq)h8H2U4LCRjnC^%kryiu;4^}2zMJq!k4%CW=&daT(2QvB7x zb>jrFhMzsM&F|jse&Q=%JX`^#|KXj|?U#2J^q)Uc)i0KF^{^dpU*24^|L?75-xR}d zGm1aJD*fw!?QxYJUR-g#4}O9bdDj1*==QH4+;_11OC1CpH+gEgVjus)zjWLD4^#5f z59?37sy(&+MfvUPJN4p;-X41Q{L-7VU;CML^H<+V+s}IbV{Z8R!TeISHy*}u|Mun( zsGr#om|6eeB~EkbJIJ9@qVrD8MA(uNLBtLoC$}eT!RFHOR+rHyn?Vo zb^Ak9^Nl16qGPG#LD{MZ2v!aF8~wyNoN77>vlcZJp!cnskS2i@9rRi$@KggbERCV~ zCjsQz>0;cTy(>1K)x;n(aIApfyh%r=d~YdGZ@Q)DSawp2Q`0n}ni&ON&G^i!K?)m@ zqv6F)DIHOC2(tb~DZy>rkKP+vTAjrz+5fT{(ygWHBm%|Z5Qc{cZ+VpDw*i;3_jD;o zA$NQ6$FE-8hID{Jt424)_Gr{5Osf>QFXKD|RJf0(UjN_p)q%i34T=5Y{Ty#L;J^yB?I=Gk&S+cE#l zY-#^5mg(y($zNkj`x}4%$J^3=3A?NzkWJje8sl*6W;x}HWh*W;;;VHJ^weq z((@-Ftl^WpB>gue^8OzTOh|H_OTU8cW=-JQ%N@3|ddh z>4RnJu}jZwRUe>drB(KE!#?rV=O@LxUFZ3w$L1=^c=c90@8_|9=YM$|(?ch2*7|p_ zo`)MAdink>|E%?ATmH#*`LBLOW5;pfWWaEEw-A1ccvj;7_;&zc`T z&F;Va;~IKmpkMs>d%(`RZ_S+jYz3bB^1$;SY**;s(+jEne$dHm&{S?9icTZ^Z`fAMhT>*w-&kBj%v(PvlQ>}>oq z>+HM4=-U(dep-IEPVc1U-`g5ErG1Koo&CSz_KfCyjPQQOWpS|qadOj&sf8mAwn!LFsOSV_9CAHty z^dPBCUnZ~Qk00HT@4fG_%aw@v$C#C`S6shdjrn^|bM&m+PeM7XOm!dLI{6{U>4EBQ z*p-{@v7|!ZNFy+`2ZLz!SZ0)L4-5<@Jroa*fsrV!q(*7xI~@vG?KB)%4K2a;#3`<9 zCNAZ@{7jhtQq|HkI=o-NBK=QqQN%O(_uX5EALPoz*Ei?xpS<<_`zh)_d77<J z{?Sa#vsw6~dgIqlv-?;61XR_#e^GwwT}7FH_%oZ`cZuwW>3`6D-oHVgt=&5*{m-pH zeh2?>DgXs~CYoW&ejuZ-yXBFz+!x=k&gQ>d{(7dye?4`T_>%whiMpQk@QH=ApzGgo z4XD4a{f+=W^1HutV#*2RG@*_JKW4}NGhOJ9+Vp=3eup(rg4HHDrU+biKpH*Fhw*UI6^_TY!-cU$59#-A0 zPG;37>wa{7K8otzS2f{P&1&3+s~bl6`X*iRt8zEKlwZ~Id*dI}rmt;B2e9V>8*s;-ni>&aFk26;KE6cr9 z&f^=+*Mw=ex_Va(s+Yc~Uiv{zxT7Z>A9&YVewUV*WlZ6xI)F%cQvlYBqfT@vs)sO& z*O$X7h0gHQ*Zkw^Z#gdIpG8J&A422hr{t^B^Lf7;t6mbt!#i(_TK4w#?wi`72WYme zOefx&jJT%u$K?On0OHarH1fBei!M}p1*K|NRhuQ_6%0sENM@Dth zL#0=!>D4Rl9lK8u)~6!I$hbH`3OXtkq8ml$uR~ld2YKtqy$>JM#M?sO7W4N=^-xPcKYgq%73YbuEPho>LiI#m7v)2{;wTLb2|q#rCZoDu3=(a3`4owBmAo-d3pJwJzD~`@73E`INjb$_KUKv$=nZ%)a5oe|6rkPw#v_=eLf$ zIp_J)tq)J##(rnx4}X7g<9=EYC$G&r6MtRu!UyJepPF9DB+8X3=jV1%ez^Un0916H zg05k7dE(7Axq9AuU1EyxZ)uIWHJ_KKv3ukFhmD~FS8;*j0GvklS@c=S!|wa{%~w{> z>923izAXn|K7Y@v#>X$8ziNfkZ5gB@~jeb((&O_oDKM@>9Z_V(UEBZ^+f=Lmmz zd3)!lwerS~Kl$V)YO2WtZXGvZS@7ZI{fYbY_bGq8jd&CaPxpOLIe^~TvmaD4@1alS z3_cfluPPZ<&hA@6u^Q0*)s?vWl(d1$FeK&;=sI8b6<)lQyz@7M>` zEjM=faA&Dhz=8l){vbNg3}DG6f!-Udwi)D4b*z6b7QeEKo*sRETYQ_A2f=kG)>1Wj z*5fhv8!+Nw6wN7%tQYUOnal}w|AA#m%QPj=XXu&zObeAsHUKr ziU;kmY`Ub1yDZmluL&c^PhNg>pK~Y@aq@%OZ&)Aw#*bs*&lWT};OJ25Adj}C5CFAj zYkPynlt&4t<@x-tx9chN5#fW!-7KG=6<$>c2WG)kz79 zQFidEfz!Mz1yDgDs-L=9b+BTORWCoURfPJceo-yNP06^;csahew(i4t z>g2PzEbqH--|E+=C2OsHa(l(&OCQzb`;LK%0ZK1B_7m-wyWEstyl~9g>(@RGvaes) zKL5P-(d*aV!SP?e{^-Wm%1s?3sP`pJGRy<*;IwOKrFv0LH0B7ziq&}_?Mg*2|MI9n zL1nMp{nZLgOI3+%RG(Mn$Ldpg5i$vpO)-E;#>>X5)vMa{K|^`s*JZm8Jo||SS51_3 z`IgiHOC}qQS2YGdP3A|Bw^amQ_M&m?M>)gzYJ5uF)~aOYRgZtHAWUv7^v(CZEe~&v zS+8~9e|@mf<{K(SWv?$++j{*V+_8k^O%Goo>mPROqYC)|**~b2F7xEl!--qPxxPdM zmy=Ze6*Bs^jHTc2)`d#3&dWm)T7W8f?;E0;9$yOu>?Ub$wDs#NG>6yLexg@au0|&= zsqoi-?qDTFY*3&Uaa5N-p_ego3E})>>8>*}t`xJ+n~WRM>B=Wp}U9x7IRvnqJ-% zm~X9Rr9Z4xvA@Qa_^q|<(Z2U^`uNsb_GI(?)>;M?1P<|Ut!3X@%f7XieQPZPH~7|C zb~EQxzKd_IWzQ^OKPPM1Bf_nM68_*lP(mA7tK5G8P@4M(_@~T9_wVC35UK1VF76?K z`b}`9`wwy7S5o8so$}#NMt}bozV{HgMc>;=Rrep^k8eWc-2dwFlKWrdV+or3Z*G@f zy8kUceDU2liHw8yrTgFAzvjw6Y4wePH zHh?)LY&%9SE(5mSxb`x$QQo@r4BmXjp9ayVNm@dsUA{JXnaFyJjS;m z;>)kFN4TZJcf}u15hQTs?Q z^BH~~s4h@VAC>u}kU8pMV5PDB-U+aQha*-w(3b}Qy2>YC!9pDtpZ5=^7@v{G&4@m) z{smtDn=IrLU7%v!lfS3&8T=SD$?{aQ$`bg^ZS`dfH0pXZ_^<2GpVFN;gtP25AWVlZ z-G2fCeWblF{zV^NqWHB6azWlNL?3rf;vw`vBP7f?90t=M0SUfVkq=QP+!QowM6Yj&NDKnt$`Id4@-@S~ralXO>&y80 zwEiD&bo506s1<>6IR2Mk{Mv8!D~AL?Tk!9*%|?!&8!3@BAvfaR`tpnK!HH}cMA@t| z{I>vS-Lz+mtT7%~L7Dt>x?J16wS`X}jeka32L%oVp)Cv?hr|bArY!nfaj{aH`-a}^ z7yEg8x}+W(i?h(1qV9kmUiKQrD)d#mj+>#k z)DRJD2(v{O{ zHJWjqWq1WO483J@(%f&+bkpnm^in^}TioTepRz19I$w5U**XPUXUt#ALQB`Cb~UE# zWI4JzOr{CjV7$1pXGW8{)3q|U*TN)dF$A(E?=tf`E(YG}cy)*ld%9eYzI@SV8`EU3 zVUfjo%hQjI37g)UyOGcex(=U>_>ry6C1Q6*W@H~(d`)}5m`@3Hm@fy0mPvbmXLEv|^-jXGH52p9GTc*eD=b5GhlL$pMupXGdx}lPSL;w6a0! z=`_M6MSKf@rNs+@(3$@Pa(WUD;`L7MVO_ z1TWh0x&7?(BAZBeNMsnib!b1H-&$iF0a6u_slq^lVOt;w*L)6Zr*`sQm zt!uK_iN4iUgq0^O*YaY=F;u_KYZ-^yQ$l;!xyO!fW&O*+Cky?6@l|>m4EM zW@&qB`-gEhbFI$8>MQNYj`nsYa>cb-_ZTHGCjxPCu2v^)^ShqnBnz#}p!%uV?p?=w zn~4O0-gU;;ezSFH?S^VI7OpGGKJP-_7Mgq{XoS`?kM#61GZLZR=n83bDg^aQTcsz2 z*yLIb!sF}RZ6;m^`)gm;cf!cpZizOksLaV&+=*vPT}5-G4R4vKGoRR`aLn>VQykMa zrM)z)vjUf(8kMl`jhZ&GX>q!;=*k- z8q_<|YG#iYS)H6oa=X40Ta-vfo~5dhHB*FX+KvL0{+U{)*6C!@RpwUn0g2i}f~4|I zsQ{mm+wEO`PTR$GI%$!)rKfGCMYqM6bp43yt9GFc>=UOOvpOYQIe}bFxG*!a8S+Rg z+(x~$*y%1|SS?*PcPOQBB`yleY8%~Cpz{oFv^ zI6tL3`}x>(nB+Lwta6)+a`VM7Q-uvF_?mNYO4U{8p zNhk;sh*+jO;a`MXsFMWGa(!$~S!bqM={MMEdlb{tQxX^!b*u@O3n4>b8(LJkb5)Qd z@x+&NnZzs0zX}nl3{<#K5+O>5C6XJXbclpkf+S|Ru-`lNXp(zqZs*|*DML!?)gxBCGMGv^@ll$3Q36m%A4LMdwhpixv(15 zW_zF@PpARzeAF>g+JRn}Q3VrZB= zf?NdZu@yOw7JL&mc}HEVrR8{Ydm+m7A({lK%6-nLvqV;#$Tx|-QSTQX-1Yg6@;;4< zZnFhL4PYgg%#v zpzv(_@uQ8pbx7>K>Ati|l}nMyoz^^dL~`Oj@H?FAM66RB$^$lyHpS(2&yr4+AG zP}2bXkCqH~7DN zvqz`(I=?p78>8oPwa@FQW)jKZL|J$>!pgGc7TfiU2?&C|C0~%^5cG{{Lpm)J*(}8* z$673QrT<}QGzaM*RD6)P!l*Yy$Au)fgx$OGvQ81^s%$Eu zMisJ7lu?5Mz=E6NwqRz;y>CsPG1w_th&*G){g8xNASI4St0XNZ20Z?4vrz$r#)NrT z6;w!$;tZAyPm_x7j0rhgzGtPP1hwDPSjhmHFjCcdf^<^t1+Y%$fo+dqI)(ttuo40&#lo-0#r@$Cv*(lJ1wHU)-)EvYC%WbX3oY1jCka7qkl2fXawGE_DUA$j9 z(j;q?bMs(wMTNYmT5@opK-_1$q;~ zt?vUR=!rXFEd}Hsw2ee#Qe!-tS0m+COFmm{glUM$T_4Dy*3#679(+gZKtIi5?FBHF+_+2)8=qdj|bbT5Nm&?e4 zL5}^2KxU*FOV^ds6~BiTzxLW*Ld9t)Byf*|RIw21v&YlPyc8>LWb8c`rA zn_j530)e0Lc@rtrk2=?nFV_Q^qLpMLdGqn`78u_XM9L-q;|`7gNh|~pIeZOwko+SV zwqHE`nV(E}tyeNy-PPm1&i6skIod^C2D*{~c^%2VC<~W_I{C;9I0?d+K?tQ!yd6?gfEOkhVCDqwNWov(IuJN3} zhY`p=-Q^Cg(N~t3tAOY($P(h271tO8cl|iW9*^{!(FeB9dLcO@_e_`&Wl8#DIVr6%8MQet<1_I%_Z{ z@gS&GK0?ukdyS-T7ZPOCEgaR%TQ-fE;k-^#!4XGe9ZFErli851W10F>;?u50oP62s z8RXxBUFt6xeapY#?_tpNvo) z3PFRU55?~LWt;@&yr{?PF=ngDt&oLh!CT=x+YhFVG7tTH-x6QU(ffwI$eej-B!!)z z9*HwN)Rj9c6zMTp8ClUHd(HwrgN*Y z%Q~u%EGP&o7vVwF@y;a2Q*|XD1kJA}fGyWeD3+X+&ZrG3Ljlp9k$l#d92pRmb1f*e zvGSzJfynK`YbcUoaH-L2i#eGSAr0Le?_JbC)K9-zX?TfusMUgb=jt5ZgIR$-@-4c^ z8HH|RUwOHtZr3>3Y<;<2Dt)V$<_Y^RJ(4oXwq6iu`$V14>m@EtX;U~D<+81z{+;(z z+tI4?X(dNEH#Kyp2nqd{9&sN302UE@VhCut^4}wp6;)7?6kiuz^ zsn0D=ezQ`~CMf^1ij=ObaDN)P!B`(hl!huOtSj;EgKj_1x1ad0g=G~COEw)fM*9Y9 z;vdrnLg*Bz4M!dRMm7#H{b{9odXP*9wg`$k6vZV~pW4*xCMMXnuMCSSpnHr^6Z(XU znG)Ymk>>y=LP5+4HSu0tNdbR*<^6qHd$ronN+qe$LafwfMTWO3DU`i3HdshbnA*tV z>IN0Wc&>&nM5KDp@$eE#CnQ6xaM|xCPeP17^Dn5@`Eu6;HDCZzZU81LHAV4%+armH z+RhgRZ$SjD&@ekCHYaSGmNGK1Y<(Law^Xi{*R6o{H$P;}CLm+V+6;4cJySAIQy|vH zC{Wg*UI!|(7Lr>6}QOQE7&X^JT108G-f1*ecYzXB5S6a;MX+qMkj|^m3oFY{iRx?}Ax8#j` zs~7LMHF$;gih+_Zocmb;sA;}iz)!vqcU16XNlH^M_%jAo!SqF?#2O3F=_J2 zv;sLoe)b6Tv{&qccUfsgZW$|W6s9=kn}C{qgk{nR8{FWyY>=M5mTN{bV+4A9 zJI~Z(2>wxPe82KGp<4>TiTu>|;KN!40ZnUFMMnGDnzy&zk>xW6Usf!_7E~R(dP6N| z-{u2?%h|Y@`4!SaUwEVd6_*P|uUGrj!1lgLFA#)!W!tDc(Yv*ZOBkRoeluF!YMt*- z5%2oeupRpkBjq32PN>x9bx`S-y48;XX^$&>3X(#}?9cgp_xDx*esM?8)7bPsTgZmS z%1+J?Jhj~LJcuLcps(}Pe$snCU{%?*njUwpBy_TJf&i zP&TK3U;O({TOh=Y^izF5gbjVLviZYi)3;OI!&}%16{xDdg|28buc^*+lyMpl-D{DQZ}3E2VGJV?_#Bi8;%U7+wxZ&@-Fc3P#Vth?q#whJP<|b&p2s z$hEL7>wJ81qgLM4AK>|_8Xm@EOMrjz1Y@c_BtuJa2LAoHx4A6|!llnwsh=+l*ddab z{C&$TDuTa`kEwg3d4>S1ph$Z2%r3S2w&kq% z!&xs3$JsbdK^jNP)LIk;hK#Q-{vpPVil}`TO353VOYMMi?0h?;rX(|K6q+Ma)1Jt1 z;rP8V9VF~;yNGvK_{tY=G#^xSXVaFcLy{qgeqFDRDFIA?Lr(Z@*&@mNUBBovp(8{x zBZaC`X!H9Vm0zGVjjL*>-yxe@p4uFOXV-mD=F=ul8vm2faYxaF549c}5 z2sxwrFi_mFInMyoIkdpxgPxxkMHF4e$B?q#s2Fc&n`ex9X1#;A>DCzB+kWQP)-&CIb?N4~k0z&F1KwUS9Lu`oDu+8B)kj~fT zcV-bV9_2L==xp9mbP3)DYpdrImmNMC`&M3P7W%m~hcG5$D|KFYj|a-`XJ%R!Nq{M& zXPDlvAQ|h%rq&!Uc}xwey+nbsq9~Vu{5;LZq2Zh18hr2|nJ;$UQ|I&Smp}5a^&Mo- zPxTULEog2}{(TC@Bh+42rzke7wf>iv1QxM{X$RQocrQ>+s``?Dzh9IDJjU=g1a=18 z6Z7r*e)?X;2f(ZT=e3!L;?_`3{q`f|6>G0*e|tL*@i8H}{cKGyenry-WPLdl8fXN= zHED)&vZBy0SSSj%sH>(+phe!AQ&Co&D?9+xV_37IN*zJ;5O0#u9~}EsE7p^DusK?m zXfB_X-#%Q5`VD%TB*#%8`2NK+8w-+Rm*+$o8 zANtaEF4Wb_FW6mVa#VXRx+OY4f|jcsaKD{?pRS#b=A`79wDNs%awf@EmKr&K55-RC z$W(yn)ADyjaE)`uLPlcB7m}ugF9aJjuP`wva?gIs0f;nLHG+{TLF zGW6vsfnplZ46l<=Lgl(?yc|zHd4NE!N?(2IIUF1aZNV zZ1M9o__D>iuIQY_0|QAg3$V&`tND0I4RSs+9#dlI8r8nQrF^^Hd}00~LYYclnQ;a6 zLcu(X_o%I*ZB5bk%@OIF6^xQnzemgSg+VTghnhzgO+Lh$#M}3Mz9ec}3*}ypV6(%b z>*Mzh$l;BT#JHQjSezN5c_GvKBrdm~4^!*~uhJ_!-kC;F_(&5G09V3`_v*~aGph1& z%OB-OWOguD+erABPY?372tCOcrGB%z)ZZ)eoK0Rj%|uw8yUml@^XY3Kz3cPBr|1m( zD?D?Qj4!`iPZ#xr$D9UnapL_kTh1Ip;ii0W8ZB%xe3?oImWELo((IQnE05EqOCIM| zqq8OObl(rxQOINAu@w0>(*bb-41(pn58K`$AA+}~sMgts1{DSG${ARQw`8tV1;_H} zEN!eUY|nE3nD_+=sNHE)XMu)!3a#VMyyE@b;VBdRUFYY-e-_I>w3=Ae`;NW(lPPBe zn)$HTA((aS*-zDg-|8EeUyH9w>=rvS%G;&#V?kWFnX3pokEZ|qg{5kN`~u!g203XD z(d-b4Ff|c;KQ{Bx`*f`;b7WeSxnjTP0QJ|#6Lg2gVh+h3`PKZ|b&xY}tnAxk_^qbp z02ZCXHjcnhekwsPe~%IOMZ7>nT- zZY@`%t?Dy(5b0OZ7Xgz<%nRM-^@p}hx_?vFA=-~etcK6R(3bB`L$YwHxQ54mj=DR@ z*n7>u7Rs)QPSe0Hr<8OMo+_3}-VXm=;U1ejpXZa(kK|$p?(K4-i1Ym8PQ{>mG?DTg z<=$h?yJkMH@A)*_kev>VCgG_I@R+1|pxE;GBRj68C9rJ1L;^0&@%Hbq_Gr$?0xY=G z?qWv)dH(-KIH2h24T$JV_?KW< zSXeQ72GIL#spOrV&7ar)fn1XPz=FrN%ta5|yXaA}13(wjzc+H#c%K0LcNwp9=%?^hqeYJ6_A?xD1(FoI>j#IYQe7^|Q@ud4DR>`Ap|?JPNh-^?pRY&g*9fcks!e zG%u$RnENpmGA}Wsh7+BY)0+%#+!gz~mYkOnTh&)1W4*ZC3iyAo|NVbE_@A_2_h5EX z)(oG0Hgn^Y{#i30zT8~P1>kI1yvc2b3=U4h4=ZZ_QIo4xJ6!7_(v6d<^jSF5fc&$u zy9NTtr6+FWp6M~&x8|yLt0DnMM)}!7IRM{~JyCPC z2ZH6$1N&pA>Qy!m@u@48x!ViYmK@XkkFAuSh4(87imcSWvP$&y?a!{5=lIW7R3HMC zt#HkSH{-XIEhf3b0oceU|E>Gux9+#Ek7oI)yzqB4BJ$Vmk=I{47x=3@A3$0uYS^EcXR?Y?F1w%l}*- zxt{R+^~>@n5KP}6X3wC#`Pc75YX4i?^nH#mL<>UeUt|u+UM- z^@}@5WC_G08SY;5e}%kmXhrZw66Lox5h|{Ok0<}urn&#_?`C$p;v&t<3HDD|fF|<4 zYb(ENf9+{Fi)J4Ma|a|`M3;X)N~a#MwgQxam455-ho~*Q(bNIz0dWgUm!+A=%Pi} zGuV`8iT=;Mm&}=xXK2t$_vAW)A5-zXIRFGwAxYt%-yePqWnfm7#)sLrFW8@XP=vdY z*$~e16ra9x{kBP`5T}8%e|?m9I1wqENRdADeQR5s`Sj*u4Z_hHUCPJ%c76$!DLz`+ zP<_DaE+>vtkG>CUaej_$5bips=$T#$x2T$N=!+R*bJLa&DJWNO<>P!oat@;%Q~Y z4eF6jf0K)jt@x|Jz&9)4n?2n_K0q3To6>mwvhcT_CyaEWX1n%y=nX|yRCN7yQiw8% zkv7U2>5T`Sk7(RiKR%6@hEV#re|;p|@|(b9`VqJxZfxHus7QN|S~*_icho+kIpNWd0<67hE!44AYs$Xf!~ z0rrD-hkS(pKJq=%S*1_+r~oL}l3e9qE~RMEpYPK(bC+Vu=uVV={_~Y`IxGV4%pTvT z+OD4oskb3S(`fDf<*1jiy}h# zg$hjbZ$E3WpKmjN|60;5E5P5~(@Q^fw)j7BPzQgf(UL`T@uSDF1U4%wZ3Tg}e`5i~ z|9=1e)xY80y-emH*Rj4vCd$@p+JHrfPN3=KD+EU4C7LKYc~X|uzT7KH{C$^K%5~r= zU$u0619HuFxix9DojsZSx5ii6{jCvBdyMS5WV)Q><8_gK!LpJ*@cY{0lD1X|MAi{% z5&<{w{1=P7Mg^ZH2l6|7CW!~UE{k1<12hxrDARzuBVJJuDA8y^Y1D-$J-@&&|Do%|y zxJJ}=bNO_8=6F$;T11b(xt;g11pjS&pA_(UY*{>ZD#rhfDeBQfycUOR_j-QzPY$3S zB(3)w@xcG9Gk}huZt=y51Lmg2yEU@nLf{Ox?0?c;$}5MZO1G$X$1@6?;^>Y(izZl1%(6 z?}uo|&~A^O5d!(+ef*a{S`gA+&nm;L@U>#~>_jHnPYS~P%eAEUo0MPL%iXg!jxWMP z3s#C1F+h&~?lDE>|J(!DaROz#x51{VeSxM3^d^2bW;uWhZQAsRUhZjC%=P)SDd7(0 zy#I^aJ1v#3>5W?>h8~Ujaa!`KuW-sM)KPzG{X1W$#pde68RfN-Y{@Viy`gr6s0G}T>kmP z@}niFMWhDC^fTji!xhNDxaR)zCTd6-$|h;TgVS$5w-IE_WYA5G`0Dubv%(GP z7cWsUH_E#DI9TAij zW3M=~^D4BNzx9CIU|>Ma<;b32!&oVodRy?HZ0{+RlKYm^gb91m8IsdxG-z2!N zJ@Gntj>!MR8fvJg&+ZG5=!;tI`&xO)>U{meg4F$&w}1Tjx5ls6<9f4ieUQ2bCw`kk znb1G^Irgh@HPB>*wKk2G@z-;aahp;}_&oCbyI;zu54M&zNBhQt$56~vq3Us6c$KJ4CY-K#e z>3%uG;={n+fj)ui(lA5dhI9snTKWwM2qQ(%+iszdRz`yjyHH0CGW6k8yJkCa-RmPR z%FFPL`;AEci#4tG(ezq{)B4@zU2zMMluKxHp?xJ-GbR50Rt&#&1UF{vjk$R56z{HL zyht|!Om2aA@b|Z*{};}?0tn-I@yTBzAfm(<9AGqpJ-g2A49PI-Gv9gxpL|5dI;dX* z=K4~q)pVFklFkM9z3AAZSTFY9+@O4leMjvVEW~U`B{L|fNVx~H&q@vZNJjhEToeez z{0iKEdJ_?0M>NUU2mfuG)Z|t7SL-;D!$=DfrJxuwDx;5WCigfxpOxlLW1W^u-z~nD;(fo*2a{~V)R&wWK<=+X&DJ>g*#~}P z{OhexQnX$14qsbRMa1-meA5{C41a)Ms$gX3BAJ9gZp`NPQJG$#?~lIwaGjF1`T1l1 zJAL?lfwIIbGeq5lH)NZ_Fj4J`FKgCY-QKCY#+RL|ght<8y)XhL#!|mC@>%y8{s-%k zpED2p$rzI^+$$8w)um$vQBRv54>)25NaxCqIDc5sY*PL4`JGaoeiQ;ba3$%#|Keh9 z=luWUt6r>8L&Wz$AC-l&S5;o{MHjGgc_@{_S^)RO&PyDNO6OuyUOG9SGY8a=(N)~>t+KT9H8dE&cs9V3mJL8x%O*FylM?F1hCbpIe*6|w zj@JL~#k&J7rzQG&3$|`S_IcgaASsBiv2@}3j9`pOiAK_n>4FR*?bpB-pw91>IBGJ{ zBRK!$(QLKD3;J+drbxbx0={1d45rzj7v11H?!+?*pyGJ&h9WeI8?H5s>2UfLaz)MK zpM>}bs_+@rXtr!~!E}uFIjv?R3rL=~FXStLGrEoQbCvk%n>y>aNes-RJk(uhvCEEI zUL5zwU&CC9;1&AS_6t7(9hiNp)L>)2y9saPe`3C?t znqH}ERbhTfd|MF}8ts8B;=NsUCd1}m4fy+<`}cDnz#tI&!S0_k!>8v8sQoRAtZHrw z$lLs1{o+Du))1#R`6P9Al-oor5>Kw6eKVQ}?a3`%M*r>Y=-1azD0-5CGO6F5yAn9; zfFL#neTtutzqrCOKCsw!E5EDs>xuCb*<*`2ISV|D&TB0k|)qkEB-WWVDAo!A1RKbTJHKc)-R*cF-Je5vsLk;uiIexMC ziX$nO@GOy!N?M>sv+OGz$Il|}FaaZx@PF~Mfe$`$*gYW∪Smtm?l@LYS1@I?R?Qn~0m+WuWj^T%DWi|*0cP}>^J@_6?1_)yXhQT8&ikxB;d z=f@XuUyuN*V*MQVTH0iDWK9K=;{Ait52Bx!)kBBB*ZdQQtuhT3dl{TrnV#H}9Lr0) znHWclTmpU6Kkw%O@wiekv5b_om0<4QM(JH(A$+eJYAbKC=1uf$b z_HA8PWvJv>>HK8v9MYKf2O-R91$BtZb9%}Y|AT?XwpOl0n!RNJo-hHlV5 zJ*VO~U)kJdFT}$WsLEA*^k6e~5JFM|a4tcmJdz?J z+3BQ#0Bz~#!<~lsJ%7fJ!KuX;W(`QLkYQ@tCCX3CeM0qQ#Y_9k{UASRzJQTJALvi+ z#|`@qvzZ0m<4rPu<5M<4=Y!;{9)J_XawIMi@tNv><1u{odiyV z`}tt+s6*J%_ua~Jg9Ol74pw}&@^uXO;RQonq6Y2Mp$(7gAc463a15 zo0^o~=$lupU*g1n7);$r09lG|zenM)hg?b*(v02-box5)o+yvgCiPeI@0u`zwp{!B zEjuWAe!br)^ewkpr31%qHPQ+%h=TI~6dzF74_g0wHb8xUdEPc+;pB2akF+`!vu5g| ze~jYSwEFMaTBvU-%{gxa4C4kYVlQ{0((-I|GBmc z*LJav8DAe?S7U)e;J)64 z*Q2+8*RJ8(^1cv&nA|S8;MfJ@L;d^BK1R^8Rys~fR}u7I8xhMVp?Lx@Yk>7NkY=a9 zE&|LTk7RnHoBbGkX@X*(F~^2p^o1pRkm0~oGegb5{eF*7Tw|Mm31 zMta?a4>u0q=mrpTFzPoeg>LMG>L0V0pSq!=_7*bc2m@q)a?<_*b)-1#9UJ=;r9QsE zYwF`6?3nesysjl9nrJ~0*`M~XiUoq_e4Cu5zaH7Vuii;>Pc= zY> zNuE9A;2nQ-QPn}cG+`Q0RT6|>K24k9?j&E_&;RLTRr&z<9(|Y38nx-HnRPCi*k3Q7 z-1R5Lyd&Sal&Z($8v;yof6qx-0KqYX&7f#HJ?JMqfg=;N*|&7}--|3^vXUg*6-J~U z*esoKR+0i8ns8l+OTX)C*p?Co%y`$OxnwCbi6w9y;u1!1?gXE54M&^}flGa`L(^XU zVfJ5CZ(YG(I|rKy9|&QHennfH^`lQAF)$JhBV7(U`Bp~cKijAqzlGlLDFTCbUKN-P zc~oQwv*qxI(_mhy=P#I$te5W-leCY6;oqOrpP=4wuasF4RxUga7z@jP@$}DnD11l% zX4-+tq@$Lf<|pO(^wW@lH9w8}`{lal_g-!a?9onoB^;_OgZy%adce>}I-w5CLd@gJ z{_#WiMrS7J=E#Pyd=o#^q5x*29KiiuP2`~6-tr1C`?lbwIbABWo6xJ^!gti}%oeEU zlalfFa%d|(u@$~o6Z(editq@g9Z8p zmU%sUciZ?jUg#?&6H5R2fvFH>!QTMX`d?0rNA37lq$6HS_rAl}K{6>%xz?NfPd(7W z@>+eBhQTnCWaGS5Eue)D;4iJro1h8i*>3>l|MWE)_vfSD@Vtne*U!rG zauX#EVi(3RlSFK(w$|Qot_Dgp0K`rsLJsl-GVS}l3Uh>i4S(?Y+71%lI4wJ)7!oS9 zr%|%*&lkW~ybjXA=^2A3`eL>W=_HKPK@vXSv&S`&_6H|Kl0tHl4%H8_UVr_5o9;+4 zmi_e#esCv~#_&fImEX5^T*GUt5i3l4rZi&RW9SV4tFHXj(mbTS0|#OL%eupyjt8#4 zQCJ5O5bAJ@h~S<>7Z?$P9mVD!(L%jK-RXQd1B#nBHF?UTx0*ZGO-sgq=fcS=Sb)cf zI2-Ur>;5P!_%Kkz`Tno1#r{ zXwQsXqNUeHlYyRm&H-Kel8}WdKo8&@li2&-sw8|#jc!7R$|xGO&gzp#Vh_DZwJ`GC zSg+SCG0_X^QuHJn9cE=d)%_C(r8=nU4|h&B{BtHW(AZ9rg^BE;On@^zve&Lcuh`DP zOcu)AkjD@2gQ}N&`)-v0qq-lv4fa)#Sim7W_0)+Kg~Y{Egh@f+@C;7lcv$wKg%|bE zbs!tJ?YOjIbCJ<;iAO76xH7*!Fog|w+2zlJR)`2F9xt$M{sRFre|(r4Wq2UuJQN*` z?QSA!56)mIr`MZ|c&A}V_wmA{FCQSfEZiPWW5d^+&wa9`+zyWRN7p)~W~2JaEvfYR z`tD-!;FK&fs~lapB)k9a(fr-xovw=OhK)FpzdzoLFu$%%?ry2xmx|lwN&^QEoNIu{piFo#fB5ixmxdih+5b@oujYgWqYzZyn9wIxfF;ByoPyK6gSGoww@w+3iH)BUGNI##Up^ zV1P#^Q9pC5aG~7<_<%sIdG@?#J!zb50M5GxFz~u;4O`swdQ35kPiY%YT@Ww@34v(ZC-7e!m8n|34!6mi}pcduxc1=ylj(#&>xuM(C zCU_+MBXZyuWnIRRxbIN0fCVvPR z9Psu+1f!5m4F#AmKWE_i^e+``*_uyX(d9?0;^;HN3|S<`eCZam~^Sn;dpS=$4SH`5~IbN^)Wc)Pk>r zkZA|zdwDENKEBERd?781SGpnwpzZwpfNMY{?GHe~n1N;3JYQXME6~s7^MagjJ`wtH z`pJwFUtXqHM9*4p zm&nN7x^vxLkjB1tKev|HMDn3*wC_8su@(-*0`=x(F^MJ|oL%#|DkVqXijkB8b_}s5 z6TH#icHqx9Lcq7OdA5n%7|~|CHC-HRXojn)d9YELLUr<6(;UY zQ?NE6pY(Rgz5K}vA$pK4^Y7jC{s+4IrD6&7Q$R^YDZx`(tQMW)Xr4*`&0k03mdyu9 zLAuGu;CAZy<{+rn8GFynu%vgF)Obl zFUJsv^g_d|;p*V@L(|}hj(Ka*ajv!WWdE)yw0byEnS4Gg0^T0tf_%YL5+GSt&q45( zoK4W6xy7G%IPT-iCVoOt4L;nNHzfA5`ee2mXE{)9B#hH7ds1d`JCn|Wu~J-Za=<<(*XBS|q#0!H&l z-jN`*q1>N;`%bIwaUsAM&1QgCkTns8-$@iQ*WkO~hwwgJD;TaU&FK0Fot@IGh>?~M z^aghr=x`XQIO#44Efa>5e|B!wt*KYs@9>`qD-1?}cXJW1-Q%gq%PY!U*yn2CK7t@ZJIq}NoqY&=)0lA>7lZ%!Z1 zE?CaZrgvj_Ug_~k(#-iiZJaO&!-9W@Y2pqZG1guNSXLpC8Yb(U_KT@^HGv6hl7yMo z8}s$H9|!8ulD_)V93m52v&P~V%n~Ok_ePdsuJ+|S-}N*2=&zNvU?isvKJa=44NHOe z|2Q6a6{c`H()sMyW`Dr=DJg$CrYTthJmU2-vsbA7u9pW&y`Tm8=AAz&ghIJSy?Cbf z8(KQMS9c|v3V zZ@aW%Vp$8{g%t8xhhD~K_)B@0Uy5TdqxUJl5ToI!i)T09q?y=YABUs79WZi7lubR7 z5c-nOk3$P7n1fkb-#MM z-oHMWn+C&upXS)L8$-r$+!S|#1Ml<<#$xLYM#ED70-Mdfci2^71Bs9B9f?;;}Ns$4rF)PHoxrlAM&c%iN?+~0Hu2jykN=WAMM zcJ6FR4RD-+c&qTGu?ZMDdbFoB2+7}lUZ`3CRJ|MTU2JS5VIg1e50f{xNr9t=ETMvC z5A;Mom~{SM{q5r}2g?c^z&H6iVBRx2?_UOdJ)`a5ogM0`lT;vw$QKUL`o%q+fgb(; zN58wiIn=lHm-3;yfW zBtqjTlYVBIh%bJ0vOh>xjZ>Md+vyd`m)pK|Lg?@i!C_>^fwj7%#MLvB)!tpym}H_QUdC6%Z)|lYeQqtP@kdc0`v? z5eg2Ho8b5YLF1RUgTZy@kUHXE_dnxG+eaZFqf+2>Q&tK$I5=hD=ck0O+EAz_00|?O zr(80V)@_w%7;$X6Uv4{_Q7tSfCtxkRMdkZB0@Qy)hxiMAh~lZUiY4!?e{+XrWI)*r z2RGiqF(TX{a>3ACH?vBtN=W&ls85PTI?4`RzXTsna@jC~hLzaT`O4k|>E1seS3wC~#jykrG#lMkC2Z5D!oo zBtQko1n~rz36KCmZUO|E0p=nxW(E@=L68NxNiY}2AcG*mINN>lQ2Mv3u0G{)4#o0@E8a2#EuOkUuP$TF(TY^<+prJ3mdsIW#9W?w%2f z<)4Z^gchj2(1*qKr0@jzs!2V4Rlgz$%?l;;&3?Odw<+O< zM~l&O2vBTPWVgD`Qq)!Kv`#BPau41#N*!4_C zF6nDMk^ioeg9hX6mWah&LLatgmXeE2TkZCiW2H#Pr(<&zw_4K7IC2qu>JWy??&aXl zz4e40&l%T?Nm{st+XA(1x?F7&(LH zeB&Y3E$$B%jXs?58qX38Vv2TMa|sH~(R9&(JAJmR?BhiSdD}Mkx}?LK%-lb&WlIL5mDH?)ajs> z2|T!@4qC5SfP;uiwx@&uLFdUPHUwBQd-`SXIktb)+X3H_rOkvtt*{%2EYO$Z<8iEX zK!OJWWF#M|)+L?So4#q$Bd+fF(7)@b0byQ~TKhk5J-VB%>6J)*k$*UO_3Gjym;Vy9#Qv zoC=?TxwJJqt9CKM8+R=_s*W(sbxB2|M|+Sf^6CYi7EzO`7%VzO^SIj2_j_Pqx@;Xbfz7?P=|x_04cDse*H$xu(urRA*sT&8uDY z04F)o&$gx*Q$uXJo5(1v!_`jFaS^t4?y|>2EpN}ybPQ*|)jJr47Y|))-eedvULTEI zJ6Dvlv0Du*Td)JdgFMxf#ajQE56Uq|svzjx6+lP~frLf4OS(TEOdz?YY)LHx;P7;= z>CbbpV)ZqCVjwECY)u0IdO=L9s#c@+jV9rh zLpn%PV7#z_iLebSGrmKb8W_MDE*pWekVHInB-02P*1)4F0HAs8+wE{r_iYds#3Wp? z#7Q|UdIvT{&_2Y@!nLNstQ9QeIoIe&+rk_0xvS1BoKL4gsE8v4^eEzm{>>YWmefZmoVy-9Becf$Vad2vrY^0`)CPAF#=&dZB?U`H_CzTCCZWm?UZ%0 z&*~xwFCOeDWxOe-<^V1N*H@Kb6E(3vi1C#lTLlN-=VL0kis9?f%)?PcZ{-Q#gYLtwvE`cLxNyUL{x4IEz zN`1NqeQyj~aUEc=*ssp#U9OG_gn3SuDaF~w1vu7=vu+$PMEo|#iFqo)WGq+`uzk)b zTmUP!to6S6h+$)@+w($hcQ~wvHU|>9d6?3>@i9`?ygaTUp#~v!)WVy<5P6kX=9eRE z)Pv-3(%~H{q`Z{$oZ{5YJZsrgIKLKlKNY%T7Pu%xRFJUNt@p>VoOouU&u80#-S^ zCSFCb-2jnTyFB1WeASQ>ik;i-@hwE)EDx702PB8v@B8IjSu}Q~`j4`nZNDvye zwC%LEcLPh(6XY4u@sRBc0r?Ja6HpS=pT5?*volV%4r3sa)a-( zSOzP|bTvu@>#m{q`s8FNfJc!L+T@7csqT_IR1*vPcv3VvK?EOwW_h&K92wY$0h>Vo z^ms&1HF|iCWLP|>vW-#mm`qOdfpOWDGl->(Wo)&?s4*U$1CR3+82bU@@DE2bpUs`k z#I{{%mw>dbcfIYNTSTTVZiOfYdV=pP$woi&&Kn!L=%v=N_ce2KZ#aa)xQU_#AjW<+ zss%hPE8}wn8!5&VeqW~@Hk_s6Ent6}j_Y}Fp4GUIsATit9AZnD;;~)WIS7$fs#%+t zi;9=QXb1C4bGkoVIq5w(dlz&WX5Cztj}!^MlfJxROuZaS0o`7^tk~J|(o7>NPJpd% z-hp&x_?myR!g8p289&-D{W1Z3dcIHB3Q?JTnD~bkJr3qDwQ+*fJhz%43#*@Xu`T0S zxc(y8f(&LgILfn)w4+FM8*)-mKdWl+8SRdyDDi{{B7VL_s_^j>*EQDb#H(bBz(qD+ zv_gNssz5tCJ0t?x$Rz~SK}hbzAheuN-GxjmMZKrUmn)ynRG&az?l$C235fDK$W_JC z%^J8ymRs8GZZt8U0J28Ixs9L~5}0QAK7pUYSS}I9miwskfz>wM64gJ`{cN({P0z)C zBY6!H0iLv#fX754=GhXqk2;3a??%&8=qQ~vznV9vXWlrU7AvY05Slb=&n!Wd*R4_r zjP00-U}rfEjtYF!=kBoMtw!x=;)8qHp9_m{l=m053PL>ix|+}A^l@rzEgViI)Fm^# zy)#*i&d_&~4T2nW#-1Fh;hY`U&#k>>)}Ib2b*%1MYe^bi`$wx|PVzxpSs}g-oLW(v z)6+E!60x=`Fi0tELMyq)C<sn(6{_9-&j#$C*js@c92-ZYmnwp`kowhVB+`4Wmok+tQhQO^g3M-v zcUn9%0l6s&r~slZbLGOW(Wg@ea1eQ1RHrPN=d0L&&4r$LKjgsCFSbC>)DEAuidOaV`2b#O16{erKXA{VNn*wjkg_b&JrxkmUG^jXP?ds4DgQpeixRao1n&Gw-fbx5nHb8Kl8V0X0WvTz9C zkDFMB>+T{P+ScB>h@LwRB``TC@Hxa)pBf&f(kn5Dlt3B-bMajMQPWhLmg1XM-k5w0Q&+HkO9%(R3Im z^pSLdwSk3_t&KE0*qbA@Q}-(n@cpHVU0Pr0LJn+@cyd+*=d$vGJU7`UXkHLPM{;2R zwvB$vIcN~bGIeq8G^U1)9b|P#|r@a?2^(1s*c|b!Jptj9wT@jRG>Ce zddMJ9-oj@i*R~24rh|1M@Q9s(w0K%EmB&I1<#}(@sr+d_@S1&ZKOw-*o4ABXcVQCZ zS|vvTUg?cz{LaR4fm9yDmC|c~9i>TxhnOMz3zn5;wxI3~UCzn*S)j$XCxDZM*;j)$ zUBzN{AQszQu@bB(`W1919rE5vFi!o9QIoTn<5Y@5eGMSF+?y@jeIeg*soFRr3_#N1h;3djRv+_N;t~$&`=xtbjj?kO# z5gCST$ieYyZuO_kf>`NV1`($DSW&};;NWek9=tHPB)VViY=x#_Cu+?-h#S2A)bGVJ(LV#@Dfdijfh*gpc za}Zp>cV@w_lSBo);)9lrcm}alwWg;$v) zW&{GK*tRO6v8pJ!d6C$oBZjNm0kI?4^1LOs2%*^?2O=UKhd9T?#%k14`_f6s&aHEZ zb+k-eqg4=Qe{__{X)#5{gECzP%vfur9mGPF`D!^GjbR_HZF(J-uV5dY1&!V&o3D;l z2~0*c0)TozRa2f)NUbn6K`>#{)d4||Qxth8Gk7Vuabo(L}v zOvFAy;V)*buF3LUZzo8m1}RGutQaQ%#&0%W_TdAY);1Aa7lA?@Q~SJFU5s;W zt7yq$wb2H{VTWpGd_$~lWJ^(Ijt;J6C%J8&6jo%}`fu*ligtapLvGT1(yG zLSiRY6XAR_)vxy*JnL_nG203oi%sM)xiMY{!BCwOLU+yVd=(SG&w`z%P}v()Q0b zja(VRp=z_|)vi@IB@n(R8)5?A*`$=sIm2~O^tfu+8xBAt1-?qQ)2+5miGzi%6;Cyf zF?T%>vK|U&bI$ufD(1m_td;yV_M?8Trk|>x8>qm&Zy1Crs#ZUPE#4;9=6pgo1fM)_ zoGE=a`f?Ko=xLt>?rOgVJ{G$7Wo|=ZT3&=fvex9bD#GlQ4I`VoocBw|!2tz7lU(+T z#MQBNV?FDGwp827`ZK3LJJeXoLz9;?>V7>}Ypc3|+XtBfmMfQ`f~=YQ&g|MoFgw+C zZK$1PKk4x{l}3xxes-a$phrveIUBRhKEE}3iA&FS34a*@(+as`w7~jR{5?Gg{XpVd ziDAOiW6e@QWt6kC4Uu{6Jcr>0;m{=bBLp680#y@i@Li`j124dN#t1D*X`FzFpybga zx=d)$D|fr+i7qaPL?TB$#2vVJXmQKF%C zy$*8gptkqd_(fl_bA3#W5;JT@VDR-pI4#aIf^W2%sob{_0}V9?F+|uA+^oj=6&J|y z)@g<)Em?z$mzISU*BJr~ku@7K$aOn{1gZgGgJr~l_*=JovX7x(X(tbOO!CC&63-k< z9%LOtxJuwo6~KquL;|w}ImKpec?erJ_OD@Ek>X3FHEf!l!+saF-Ml%=dhW%QRg|jU7s6xakrt2iZit$(Y9Vg%GoU$ZyYoewis{H-%M*8)CTz2GGF4n zz1jm{dmHtZ={~LFd6870if0>xS#t}+J}(_`ABtHYX{?-8LFU)-cJ10$2a)F-%ukyg zVrh%yM|n@-Ie-A#wVY2M~>ps0ai7wwRkK>Z=a9GM2}IdL?i zwR~Cwmr{@0yo2~Rthv!tI<4Zsi>X4#+z3g!$FgF0NdnJ8k}A>&R;kz zuzydLP9-7d<$T#FxKvAE-Go9NrqeC6XEfBNx(p%G- z*$Y+{yKil~7ubam50w%{d#iGqUSsCjtK3`b&;Vi}MB$W2%wCug3O{g_k>T(ic4QmN zVm^qL24XHx*Ksz*=as7(m=dLfs*^8mbYJai!S+Hdf0 z)$$zS6r^|QFAi;E5v{Z}G`tZ(ul!bgK3?OZQVTvM5+qKYVM5Ml%LdVK_v@%w&iIC_ z>wyZIke=ymaS9c;_&T=6_CnqrOzimVtH5=0qL3k!4g8AQ{s>rLLuXFFKpwTwI>fH& z)wZXu>-AsE{|J=7O46 zZR^miW0nkX?t+)rJ{X%3vgGJj?x&izmhHU<=Q4ob?sQ(OE+LIs!siiENgT+=KwDCU zo3ZeA?9JLQJVX|q#OZBguJ$d$OohAJZcf0<6P!OH=Ij4Fr;EM zk||MQ&rv6o^r{nETZk&I+HV((DS<1ub@ibd@r7K=(~Oq-Wd+W}t$a+kLb*Ux6RmC7 zjdmiyqu6WF;Iz|wgV>fMfL>RwyxhqMU-#TDAR=aU0GF|gR3uB7oU?P+<&})LJaCZm zJ@ChBXJ4I(^q*|EKSoMhFJS3|rOI8LMh9{StDL)|cqgYOIt7?hrY4RU z1~4zQ&BfLMd_!*xsjVT@XOkP9kifWcKAT9CS~}av%+;9=XTaqkC!tSh;sKr+$8Ku7 z6XGx6QHS%=)VZ-KjGvI`Bfg8Wg9N^p{f#Q*A|D&@XR&&a%{IZ#U+~vWp4vNNqAVfS)rUWv8{E6W`i4+(n1k^wXLUZa7hal zcW^gTQJOyEl$g}9zC(Th@CGt?M6Ot#w5>yIl|u2ofh|nd`&Dx%d94Qg^aO}dvXGkIh`#DB61Pn~0aohmZr4;VxS7R*02 z%i4rpAq!gwT((l{KClC5c7JASCkX;DEl&K>Z1}r|$Pj2id);glC2cB`NN%N#39Ivi zQ62x^ATQ}$^$umt89>o#YgZTh3ZZvju&j4lH;A z8XIcY$o9*dIR|mmfequO;*c$gFeiSapK+&|wpv95px|qgF-XyQtwl8Xuviq#PCDU zU1PBKv8Shu3q>4w#4d!r6uiD9MGsg^9Tr9%zT&5=-Fc^TPK7KuD*{-ZvCyAwR~3$$ zWCOD79%*^ka;`Dt_wwev5w{!Ka@f!&P;OJBku)c(RoqUc^I2++5h4VfxVGM_Fnc8J zp_FIy!xr+a=9$?(fE;;WPLq$3{BSu*`(|Y+d(a|rxi#Md_jqAp|2ic0XmMH>JG<&k zz>FC5C!=tZLyOE6%jw$tEjU?k@>gg>@0TXD(5&(|+4jKqX(s4md0% z8w`Qz2KEBDgB7sUD9Msd$!-sJyd?v9e~IX$dfs%_oLX86wrCqM@7d)fH~W#c1Rnvx z2$x_uLZGS^sO@+**`(MkokJq`Y^PPh(Lr&8(Q+oA=w%EBtXoq-$Wq6dAqm-d5ye}{ zZb_4sC6VIXYc$%e=(LWI$Rsb36$}1JX$CU^@HWw8G9wf7aNzXgYzmLaT!fzt2Q-%X zd|j+EkLZm{rlJNTw+Gzt1o=Ky5bp^xHp?@Vl{M{M2shm)89BJ9@gP~W=yp7roR(eI z@|WQ8tp}oR?~)o~cFS!_>M7^8K~)*QJ`oY!unBoFjOZz6%Lj6qhU z)52I?PH_VHSAdLll^tNlN32pyL_aKRY<3-E4fq+q<)*9oCId)uID!tPFQ{V+cu$~a zE*OVZ4B>t$H9;l}&gA>~It|$^h&fs^kH9>3NKae)Bo@5R($@<4Gz9X*(QL$^@|wIv zoOWy9Ob|c?mo2F(%k^Qi3ZZvsh{~&{8@LYxy3)72cpf{TpY)q@l(%H7I|vw-4v~%x z@$3M^0R2FK=$zuDP~-`3PER`I73)5qnVW40%8~myHxHT2ud3V?c8!2qo^07tPgy&m z8zxciaLSH?oxeoFlHmxxU26vM;ylB-G&7>Cb?of7K}i6o%hti{*Yz+RB{_6^k=Lf# z5bo4wAZTT=>Yr>DX!jP9n)VLWzMAfnwbE|%8Y>|4K*-7-ulf`?>Sow@m^mnuAIbxD z$nqd9O%S@yRd%79ZpS1JjlpRrg{?8ef+?*LF2EbA+VJP)Lx0P;er+nXPt8NR=$&Ao zyV-+lc{T7-nU@z@NgTA(+TvN`SmhqFU`_iwI$Jj2HdQ+rV&LHT7lS>rSO|UIf@xCC zbkEMB0I^@xywb`rIJv8Eg7eIkH663o*wLeu z+b!nVdCDRO8}_;cz5@^!-qu5Vrj9PiWo-!A#+6nJ2M}T6C||Qp@wM}E_d*FwfaChsEuT1UFL{S zj+PnMWc4d{uma}|zrOAzC$8Uu{g^-2CiGhNP7fTTIUv7J5@5{R$eSiEsYd@a(m>Xc zvcqljoC?_cFh^DgdN=1WM~p)b&qFKIj~xpX4c#M%+Y#1(Eibk}SOy~|VQfh7Tp@^< zZ||GAswS+_Xp=)nkw999fT(Vd2Z>hKvliYc(@uO8a(XsfhVZ}E`XE*q2vTQNZ>PCA zLA1di3g%yX9)R zw^kzq;rXM}Je^$@uszjhC=87K~ zxw>P!>m&(Sj;9biGH#Ez#e6;`X$!vKebmafm&js@QP|17zECJz_@l0RbA*-U8?~XL zO$@>G=8jB$>NbmNA)_oSMM6qsL`L+D6jOG-3jvYhrB0v&*V{5No7&Rw2#_ zgBmLbH%3afTbnxw5}7)+{U@JJsFgUNThjrEV3wB&kagxdIR=;XgyibrSkWLaCNg|w z$!Z&e(UM%QP{;9+Om?x*SkK`zeJJ)aO=W>cI4;+0Fq7c|yTPQX?hy>ivgJ`T?Mr8c z^Dsv*rh;=hZ{0#I=b$~wIt9iiLcmh@q>oy~YS(^TzfpK3;iyH@ifY!B&Z-m$w9vkY zgSka(;i*qMIm;J2q<XZl1@nB< z1H${ftf7I|b9^5*OqW>&%&6x5vGh8IS0x%5A}P(o<~&*lF;db@&vpb)JP1_Tep^=y z&{0j$evo)(2)Rbuxme5ZC(_m%IQwEJkrTKL8;&PTrKZZZIO0NYlRhhW15RjdN`R{; z!LUU}NBE~an5O0{^ z{Ryo$X<%buOnODpy9?{>I@^m~>{{?&rbpS^s92K;l6kCp78Yu5O}E`R~=?mIfv{N zAw4`DoWd~y0&Suz!!~(cQ{Etz@=LqDBE+gMW6GB}%a0sb$<4OYk686+=jwbpky#yf z@flL9ZgUW|VXsp`nW&h}K2p)lPOD?IWkU2_c$(Y5_g?GWnQo1pD}m6A27E!tMQ1dD z3&1ndcttoJalSwjLL*Tv1Y8e*D+DDmts-G#RS6J|aUyoj*?ibMwMh6u@6Vl7PLb{j zS%gVmt_;9jjn2eIx}9mdp)b3Qzz^DlvO4!_4ju||jgXbO1uM4T{)i@aItE$YO7B6J zP)_S~R`bnC%c4kRVB6N}F?$ zgcmgQ3&P5l9^VHX8If2wfdWFY?t=c+XZHuK+c1W)yf>FB$E=ek-2DQKA&WidGdvk^1K<5k+jWPJI@8u6SW!SaEE8ww|JIx(uH^AxQ z*!jFq>oSvc*>R*Od-Rd*?KYX|_i6Lcr3|2HV&FNK@q%+&>^j_zmWJh@k-PSO35=GP zxdpiA-r}tOVq0|7OE0h5sBWcbax@g=g&Yk)-_mP%5NB5wJ2GC=*bwJB{~8hS6zqwd%05 z9gyGMqpk*sWd(;aI8_^KRv9!?q&ObA>orp?`s_TadCCy*d79Jny^*B7hj}rGO$Lmg zRncL4y||);bht9|DD&3YWiW#Y$u`4!9#=3fAhqR8BX{Xwu}AO(BH(Mxk!LcKODkU@ zIns6TU>}Dd1AI3>h{S@{;G=L)?pB8htV8!#hul&+=KiQJaX{`iXHeEL)~4&j&X9?% zcHWo`iA|%nT_HHj&1OgLaSi*_W~_EkJI*7!n;X$DobJ5V!&6w)0DQ5`A52R&r{MU2vIYuxXu9r$OAPUQs7GH8uB zafAJ@IQLfR;nV=^^Dw=51Tr)R$Z!iFXr|^nv7;jtf7o(1N|Rf)?Oh^+D~wP2ZHrNn zmZZ*Y!L;q^Xo#4<{hFJCsvFiiP8|1PA3Yo(v@oIyNmW!Od7~Dy8B?7!(OS0WVEEI3 z&+E$oIiilhc*+6WMm}>Sq8=H;GEmG-vOgvqHR=zGrhAIqM%d68y@3>bVLrd~!4t(E z>ZGto=`d1eLO9zxxJzUZ$8I#Hqk~(t5Z2!cH%kH z?~8}##ALIJJEb+`&Hyesf_PC2yt6LXDGroeF)L;5BHFAzr?8#0XB&c_tsR9nQk4(7 zyH&a^Fn9PRaMy}K5BlA{qUWoIla0uwzM9A2rM;*~UKo?qN-);@CA!J+?|;iv}RuDY?R1rktqtBfAaVLS^Ko!bV&heFj;jjAT~UOEh{0MVKZr`t;pf~IxTVSDA19A?+9{{4I^<8JvfgmmLE(I zH_uJuZq}4Vf{ejn z`q9{3(>CnrW1v&!rMPfAb^i9TR9<3nU5c_c=+Sd+bJ_}P4>9_+)t5a>;Z_w6+@UYC z3xVq))U(@znr0czX%8_P7f@Jl)@A08ea93K$(@aM`P$&<2Iilg@ELVXn+8!ZavRYE zn?}C{w4jwqU>8|;Hl;+U9n&UQ=EzbtwSCPM(=bJ_Wfw>f-X|fvBT$3p3zwx6DHb9I zk*OonDfmf?HH$UBZ(G)QFDMJxQ3Ij}5(lt-89jbPWQ(Tn&bv!prVbkdjG&u|WjIyT zkS0j;)e(>i9#jYjn^ChVX&Ok2K&d)-4QS*nk1f@8)JkPU5D-R65WmMUZ$~IC%IoW(apW!rMm#P8X{h z+$sYe%S~>TOjpdv24=ZDMat`GYn`}uilo|?X%BX)nm=wZT(89}+f0Sgyrg8e;E6j=d}TqvrdOhJg16!lgHh9d%I( z(ng2gX3ULMcu^;ACW{*K6oM243AxYxH83RWTszK>2PC};;kLT%MeY)S7O&d_L2E0d z*$qa#@BE&tUtsFAx5L_t4^Ik z?{=p*t#Nm__<+&D>e-8&0wU3`w&|p5iYYP+heWOwACFLMbrlF9FZ{z zV!lmtZl)nriCw#6W+6gqcC(R5^qBl9-}m$S4h_zWPFC3ma`Fe?#Ybzlg&5+xyXro? z?YXG-TYckN!%9o^^-ih!7xn;dnVFIAC^K*4Fg=jzNmJc?A$Kl|OQ|W_BLIWz@K8Ba zj8lyzBV{{jUrg+)Kap_F?jI@B(E5w z>Ba6|*2v-q-vKEC88RfQLp}q4K~oFBJ;@Bf#-u>iPWRy7k`{>KkqqRV+O~#-W6idd z>ReJ#SRBX6gDa?9ZxMPuy?W0A}93A(vhPLR1K_2yrVmM@*WR#Y~k! z`^mEVtDAgYgqGgvUEn|UBMqrN3=^gpanv0W+64Nb3IwV+DLVlSCp@PzQy;;-jp=2p z%#ibd63r&3AYMA$DSKuBJ};?L=gXSlUI(D@CCEhO!ZBN*Y$wRhfs>ErsZ>%e@Wyp| zKvD*q<+;d+jW{7feYxzYD;I{XZBK0r%=k-=d;#3djbMl0`*i=i3pA+o5Zlui3i zFsf+C53naPlk{Lev~yVY<3rv%YZI23j!iDe=kV*$&Mw;`m$AuE)q$Sugwu$}IER%k z4*C8xOj#%o)tug_4#-D(vu#7Q$cC}0Wu*;u$ii-n7)55dqs?S!Cho|#LS${@3nZY0 zi+bpcNg$orqYVNG~4vH#a6}v@bunA!UWhM zM?`Zgt*Aho8W2sR;TgPYP5dvx?Ijj)p01Fo38}YX7i%IlGZ_A*aRSaeiAa+OYtE?0 zB-?o0bkVOm`?j#{uNy1>uxmIwE2+r*47@~09S@Vn#1dzwTBx>J^W#oSB{NDTaAj4j zS-1=2Tp11sgbMF@WHak+Tq32HA;>;9=Tie|0tb!)zR=m?sKaN^6k{R{JP!#hwURe|q?@eJUW0h}pyUIyUbq8gJl4$k)Z6dPbsfpeY! zt`$jdW6d(fWDtSMYgG360h${}P6m4(qYs21cJ6?=(V7k_XLh|$!}*51RT#Q812WJ4 zrH!RoJ8<^?8GMD;wjm83aGF2%d1WhvXorBpkj1Q{@5K6FH|#C;^L%>fbUu2MfB#MJ z-~aMgzVZjD@$91={0XiF|6Bdzf3JW1m-zANzx?J!@PFdNUk?5+{QQGw_j_OSe$M;) z_uhEF`u#UAykEzMzli_;EdKxV`2U;Vd-M7iW6<^F*(($IEVDPGpUu5bg1?JWyl)Nv zqp$qJSG*VAr`|V$$v1H2tKQG#hW=Jj!B>CfD__x{7g#_4pVrTRBVg_yx|Z>+(N}VW z#yqb_@bm9J{Q4J6I}BfCm!tjW_0O8IWxuJ*`@>s#e-*dam3UuyuYVnhV-HAL@bVZR z^H9&Q*}im>xXipa`a`2%|Hl1I-@bdg>+bQc`!2y7y#|_ZeCOvMn*WXaH$QK|>viVY zFC!a4rpf+g>1W={II>^DLYikUL*(E}UZzLe^c~-}UPk!=RNpUS=cVUcmL1)0NMGua zb$#kK2)C=x>bu1&?(Sc4SHI#8ueiIu;_mv2&+Z=Iad&&iUF_W5-f_Dl{p=1exjuJ$ z$?Y;;@=kNxfAaPF=6Wx0L+yQrnN`o5`$_b|BOflj{&<=Ck$dOFNvS8+T{lO9mb)yz zOXIMx@9JtJar&F<)cd7B<<0-foBOu~|4uz|z7hN(e!V;4-kEA%69e@}pFGaff9v{) zCqCA5BHpE0qWi9wJ=C?-FLfu?HLaVVM|D-}-UA^X@;rr?&+h!RZcCopw}yR^-W}}B zi>=QeTBQ9Xiv8n%>90N&{M7pY@YeeOp#F88?Gx`?lMnU7UqV0powxhpeh{DfVt*Z_ z$Hvs{OYau?1;J`}DH@Nz&}#j7OaKr)=-F)?3q8#3J3YJ8@0>g`>xFgqvGeim3fz6i zyN|yBolvIVoj<;FlK61<@%iI#UpwlB_e-xw*OxwP>W}f-H;A>B3{LT`T?H{lqH$bGPAsR^Nv!Us~1RTVH+Z((}{P*V_G~ zpIGg_`t7HpU*nJW)amWx=-u(Em(;WIs<)Q=CH2=HX2)ydBj?5Wu5tI!`Jdi>aa%uk zxc=$0FYcUAaN(ne!TFJ&dwUH3Z`9?>c7)eI7sX|wAK(0Ce7YVzZzkSvd%sg3ZGVVn z{r#tD_^eq^JB2fd?&3VTGxgN|3=6j2C*N6cKXj+S*7~vgzU?7<*dFlV;@hE>K5i0! z>4&}V`M&XGZ+te?zxTt+dfNEDv?R=vzwoPXZ@o|3!RxQO4?~DgZx70^z4O$EcZ2`p zX&4?}`J?Ox56^fnZYRXEYCbIf?4h<#7v8RP<0n?>hqeD${_BS;U)rO=U-+kBoqqK6_J?tLe(CL=ir*>c z!yC*W=Z}5!P>JgX^VQFvS`d7#K8}B|mLFaM&q{x`1fEWjKT>S;Z}!SZ_xg8Vm{y!U z9F#Z$O3zO0N7*sMJzqG9ZvOt_`@cVVmAxdt|9H#d2)isN8kX zzkc84&sy<#>B}4P8~5VPdj{#DF<*Ae+YR~~|1UNu`0I7y&j$t8i>u|~*|2ErKe*D>8Y2SJJ)ik8vreb}}{%n2M zvo5{;jUN5EUqi<{Gk!clAMVR%uYJ~+PoiY-1EOSous|^MANOU5iun754?&Rp^zrJWUW!$7y&-$` z`#w(AXF})?5f=ZyeC1uSj=p{I?G}sgl=b0x`se=6V;dhT za-FANt9Re%S)K1Myr;q+o|VsD@~k8O{G;ik@w>nI^5tFklwWP_uqqpNnBM8>U7T1D z(~`?w=tukX?&Zthdo+9eNYA|8OS=!w3rKM=TE6i6Pq@wJ=epw$toaAc@|pH|yXVWa%=#@CeUtDL`@85>#`*&Yty8HVi_5Fu=_0wL0Q6Am$!+PoMnR@= z;XhqZ*PC1L*^+wNVTpTn>i+1z>0?l@Yb6_-?M>T$pVIxa^@GoLuiM{PxqtA^4*6`i zeLDQ_jr30!-fs23{!SSm-erI5mp^)F=R*bVciGyZ_N<;?yEd^lFhAV)AV)o`=&%3K z9(Xt-zT}R#oAU4e#G3LxS@7L9eE6hz)=}@B5dY%iA@Sn7B=x-)-@L8kPd|k%CJ(JU z11`W_~D^ZNS5H-f+W&eK19 zngy>=?(47LcgEGvJ;4=N=Rba$cn_7iPQ1^4ln#4VwIA)d_jCayqOX4RRNz%kd#Kst zRR5*d|H6+mMo&HYV-@qB+JATgKkM+P2^{=2pbj3!9ZiN0@I~-9e&Aa0??1b=S$zE~ zU-{;pn5OV1-zFy<%1?e%3!HY*)%XZIRP8FQXYD;E;qGBhzdd_D`sSSuJ6RZ;aL8JB zwbAVJk3NF@`s!7rAM97J?!NP#yH8%dI_Q4%>eVOThHP+m7afz&Q`@#)FeJ-<`qA~; zH@|r&0ghljdUfIMg|9|Wz*CQfclG_&)p>OC!b@^Buw9>?)V3e8dHuYoKVCo87o+3n z5cJZcZrU%JpDkcI%bwmiht(`UUYmJsIIMR^9ShgakmTxG1Z1vPH@w2D$j*V;Nm1r^ z$!7C2w)q*we(&)nBsov6b!gsd5gv^CPx~c(YoCU{uJwI|?d6qa+sA8xdWc_FjK+)X zv)ar5&f9L+>cT&}Ly`AYcVAgi^h$S8ru!;Oe3Vj`h$6I4uQhUCfi@t#WHn;odeg(7 zu+`u9_g&A&IZ=1%L5Dv*KiuhvZVPkx)h*v~Fp!aHWAn>O+rDji*Kg4Sw?V9Lx>W&P zj3Qp(7fN{XST`8`pVi{iTg8rvA7w9oYjJz+pYD~A9#Yt=zJ2%G?r;6}{cG=AaSXH1 z!Jw2U_6z(<{mTB%3$pnc*~IIv9Z}zq`B`Yc_(VhMhFS)%n}wNG4<|b30lrd?%`?1( ziL|1a*yy16+D8xlhbOMxfI5A0-y*!>7{*yWes4AS@%>NV-bM{}-EV*I>EY0Jadf=+ z?k7+0_~f%sqUe)n_nfb?(~D2CXD_|nU#tBuxO{ybR?&4>ff{)NO4N{u`(|METzw0- zMU3uvg2&tnxVmjVyA#ott3+gHubx)Ki(93wdR;Au7g%()KL0SE?)&!xpqu;YXsQ}xey^Ul&0FEM{yj4RjUzp5|1& zd_K7@9}HRDZMUWP!6NI8<=w?nOPKE~nR=QGSP^%Lo#tV7+erUZEA@V*+z-{$5_!D- z^wRfy`K%Y8t^UX5bsZP1tfw;Y2cCJ~I$P8}oDVIwx=E=QmoGlOm$`m=zW(%l{ptDo z)AKdD$0Ysqe65e8@BZ|B{W8h=r{`;Zj=oQreRjS+s^3@T{!d`V_%bI{E&-dlzM)05E%eU3= z;O{+N3jT9^tQGUeIEeoW7heAyFyFR*coY2B_kUTyzP}0n+xo9x9n=~))C@CDvv1!u zKc^_AakZOJ|+HZ*@|7;7Cl zpd$C%cO5h>yVs=fiu$RWF(J`i7YbEm1C?z7(S6Em4KuxaQG#{Us{si*d@^bFGEQD* zISg*KmR4U#AFtG(?(PdsZ@Kt;H}h%-&t2;2M?3wrF4MZNqHTSCH*oGQ zaSjnA8?xM)hkTr8WM52`^2h)JiZeffo*1=)X0?R&U|QCtux$u#`W|HutPjU(!pzh-}A4gqOUs^h|#f z`~$3-$9{bMPe!mSrLPRkVFb?Pk@e>F*MM;Ju)O{lHzI23AJ(hP{=qe|sP#L{TVj0u zZ7cR|MiW+S5(=gPj0}@F!@787ZtrTuxT`G~cO2C`t8_3gKHCY zv75oa`IWEutF}5TnU0t4m4}aWJE<*PFUgaQMb{AqC z?H5{Ic4yNbtT$tPN*DN{bjz-IIF_hD`y4mJ?sPR{B9*o*+Fi0v(&z2QV&?l^yE~X5 zh!lx92diFt*WQmmPf0tV8?%u@ZrY7vP!wMXjnZe` z_IR-G&!|0-RU6|lM@9ikI3jY`+H*^RIkV@o4vzLgXwg9|o><4pffo0g@8R9}=_`K- z_yf8l`4&rFhjU+Zc-&&f*Nj`HC1M;id2Ah#6OHCJOofm>#650#GCd+Y02i6U3>;1_ zViWh7Kt?rp0lo)a2v`!d2{(z&VB!p`p|Ri1n{!$owUT_{w^~gqZE&oB)b`9_PK~ME z8bwowUc}5TecIxSa5v#NdUz_fBh7`$6)EbgMmacD6xe+x+;~2$d=?~I>v%M)xD#tC z(qy@rdP{K}w^$zo%A5AV16`C@Frz?8=efj6R7*b6=M}^44Nw48*=#FEu7o5Q2XVgCW?P=6 zdkw)X`5u>w?QN%+YLZ;$eD88-3k_9Qh8#DN#CfA5mQtCwCtjqFkRR0T%-r6lop{O4 zD`oytQH=w;iJh@XAbFJAK~(*=yYaIbGNAU&t<&ySqn*blqR4DJqpC->iq>{uP^nlg zXz#Q=3Z6&_iD(jL*V!`@#Q0`nqbZ3wH4)=R(KeVdAtOt1lQ;+sXQ1Yby@H zutc;SH=U9xauuIk@PNHI znS^}n>S?G=_#p6v1-Gy|mr_x=$wVs0Yf(hXvl%H8Zokn{7OFRzl}HAwXzj*UZqYKC z99+XlToobdc{_>aQGen(W(N#h$WpzS_DOe~h>9Ul$_4w3)^2alr@VcsCSbKcyH?(2 zTTEL{$skJjp5a~0z8CVAtu|<};zbhq?vABhs!E&R@GGNeaY(+&a%MiKw(C~EB8rXc zKxPUrbw*J7&_NQ6^`y!N94Y1om{lx7Oer;u&UPm$qnzpNrXwey`dp|>sZ@wtK5T^K zxg609P1#6k(pb<%sd)`K+(+G}we@1Lvh(A9+1Hp!-`KX>5+_mSnO;-v{#IdVkryIe zO|8SkwA}T+S!oNFi(07xz9{xm7=qp2a&)sK9M7J1<;KNWbXHR;?R0r@<#fP7PP8dj zqC3(>{eS3sk8M|#Y+d((C;-A2F+zBdK*H4U2q%OWPk%deuDSO)?cQ5hnJsgTp@D*k z9^L+*NN$YM0m8N_SCDh*rc_0w<^Zui;7P%C;RvAbw|yIaMI|7LO}Dlj8uE7Vv%>-l zdvk<$i1whXQXZbOXY1#J^YVo+Fmd!afpr`wPw&bS-JN+XgYLtByt;Tbft^KcM2xFi zn#IWHylzX_rshNOmAGdv)*t2|DkLHLD{pz5?C~95<-%%Kn*-X;0igxB{{c0uoV&b= z4Pd#U+~)5$;46znSMQ+iU@_(ME6mL`wV5}kyej)B6fra{9ziYw_1KCWP|A0qmB{=-HCjY*c}?8=JwA*Vz3GDenXtJ;>=tk;^D8tu0oGbmuk-t0#*4=ex%bti|xs`yCpNiM@j#y>)z%S2Fkj&txYP%cG@?;Fji zWUoSNC&AGD%mB2eekdbu&XIx&+05_;;Kse!T6lTQiX8`NYi=raef#AOxtTr6rsK_? zSrz2WnSDM|iAS#fuPaFY17e=ef{Olu)HM@i_Q1@NOsSVryhcIkaNG4|_AC)4zTFfU z{Sso33quZBwFwh+<0T95c9hqeRY$6;K!`DjP}m$@7X9b6fBEK&_txwD+FWmp0jkUU zypCEXkql0hg;yi2EQ40tcKu=kf}n577vwnn5CaHG9kzvRwqlVZVC;9L|6VzE`!al8 z_8Vd!rR57Nv%b+Z4_OZtALOkt>kTn*A<1oF_inswP=vKAn?`6+g{%{0)_g-QxFv22 zNQ!aqTLW-5?2v2(aM`B%lZ06SJ{6HxNm@({Sp3`OpaNlEgn3vMR7idxTC`-K^i)=$^4vHDPE=> zHzk*xgHu-FS&bpBh(6ip72UJJVV4o88-I=Yt?<*=o^QlkFn@t(k7|u!sAOnV0ATd> zjz<8HAWBe}15Gc_A0A&}-$>GUI*ezFh@>I~k25AK(+xj8k6C4}C@@PAw0yHyy+h*e z^#O@VbJ+kZwAdgx$Y{By*ChbY$DA;*LXdK}Mx=YGP4+gBLUr*@ccxKh4F2kZZlDYfS?B4d%U7j*t9yY@*n|HNv-*SK;N17)M;(&yrj;fJ0=o%fdqIqO zC5Z67DrH^S#3?P%g5i@q7)+`xWIJ-Op#};K4IFvGr0c_6xLigS41DZQ)MkB(k4isg zqm~RKCOpi`+=DFdzP_cKVn6YTSW&%qnyDVY6!K|sP+^_R2NE%_<;9Noe!#xDnjPl* z6I`?~Mb>6~BiTzxKuLy)dMrq;2!f;+(k6D`qahSW-6(}h(}*H+8W`kj#b)UEyonSF zykyspFV`P3MJvfh^5)~=Eik`Fe?cYx;|`7gNo)iUIeZQG4?BgqYU!F9vsvNPr4nt}q3Aj28Fh0s*Lh(hJ z^YlwzU1sT(i3Ty%{15f=p#vYH1n+ej{2J407jHsC~FCY+ljR6f@O2oDd{p**jxWo{PLq)^Kq#v*sJcBhEi+B*!D*r&88J;zg zzFkO=O}B7VGjG{6X6F5MkP436b@omPN_sFGvUMy|e@YN&)FV#5?9RMKQ?N_@1>|`0 zFWCFIx;)bAU<4Zh%9+;&Vh_{`hIVdQzGp$*UoTO5kN~AdnX6Amr~!eXNzy;X>HB4z z1m?H^NaitStHrJ0g=fKA;XKC=rj4?G#_NhP}v~dFUjC9T~fW&?&@~J1Z3F zZ?ZG8qDA(Y1$iw|7 zuwrKdjzGoD>xUwodliEY6oT+2d4O!KIa-@Zg6<=QOvuedScZRWSF4jdAgmPe9<_YI7{Uv3RfgY|vI|q6Xywb`7|&I zI5#zodl3MWOFiC)xZ31=%f*z8kf#T5aMCDIws5r@-{z73G!GphUp)s;4*;u)74lEA z?yv(5=nISnp0mUNOEQ#-@ z$h$*Mgn~OK)J3(pk^=trO7(r%d$l^xN+YS!M(osOMTWO4DU`i3Hd$~^nA!xu(+whs z@mNhmh)7M%@$eE#2RK8laM{&^C*h7h@-H3rz+7qq066nfZbG71YKr3j-j5_A>N{T) zybU*Kg@)N70UOeBXelED+X345=A*@Pku)?t{V>zR^yS^}{G2?}LR z>h(iq)<#mBZ1EwJ;C>oGb~2@QACzuWBDl_$v)w!1Sb6ZWA-MiTp9i%DsFO5VMc4Oa|eA861}l+|$=`%}8d9Lxlh%?(qov zGREIMc&Oy=HH5>NO~$<+Xi{fgiW>nb6U;okVIOY^h&{6#_%ctoW}WDb-^0bu6l&u@ zMt#Ruk4=rn+X&|bFD$QO$yW+}+sk z&(vcG{!#0Ezw!=Y*b1Z*`Kj%}hP4VJXQiegqjPPo+uJ!A<1yH>ViC5W>e$r-1XA{G zKKzts<7VYoa0`6_I9~RnTqt_II)@H>@0;`jL1_3f3{*mp3MtxpCD*aL*!#e zMSv+W&sqM9;pLEkpJ8(cNU(D-A{G*~z!W+c3eZ(P zWtu<4xKRb(ufB37XVPpe)MC=I^>F#NstHR@h zB`w`Ae;A_Y2Bva92rh})NmqW97ozT9|5VqPTm(e!yR**}9XtoZk3iP=(Fk%=FCYxB zZlS46$aXNztZXJwok@p(wV(Cz*Cfr z_Dx8K!{l!&PyW^?yk@aq%>k*do5Udw+|+Q);d>yRZ^-Y=CgL{tnn(m(If^d9+hiT> zc;fP%PsYBL7n+44GtD84g*Zx`7vAH6vip%)woMYS71AS2)hjj|E`Xz&-%B1-6XYJF zKv_|gOPB$t**G+PD_nyQ9whSx2t3pQf|7sq2(Ptz0dRnJ3G`N%!^u~tVEl#p%kC7# zVfEJk^1v=e9AVlaZS;FD5Kd|aFtom3l!SbY>21I$U*MUTZ`b$J_bNUhz3P8nn+0;{ zHH1^=c?7>=?KSAL(958zhYb-v1kxu5k+dP%E zZC?dzycH!==|2*aF1-E;5xQtWB0tt6BYk&hpdQ^`kVxj3U6*}m;Gen>S1;#fcah0a z>$wQHvOFkFQ*ywaCtaPcoq^`0bhl{b`{F<_R0bVe&_7i}u@gEn72x)1c@+^{^O&)a zk(ly@q$%MG!3M=EOauNV8~#}XPz;Y)1+pqB;HBaxS0h=M7z1iQ<_P~N z|PDA+QNmPWx)^k3!y;~DbH_^l!<{w5btIn_s^fUbM6P+d%w!^YWo^QYPS@I-12h? z-#RKB=`ZGU7RUmi>A8Wd*&JBm~oVW_q23 zA|mXWa}D)G@JF1oHZlYOT$-jYb-GA0z-5{a0a){JS%Y!j34*v_Nw)a;8hqJeT~~Al zJS788Fbipw=~naclA7dvWIXm)U)C46lyA42FU(&=C{xKRGp?XsC~VK-4FH|cv8QPJ z=7{vo3Pwq(^Q-0g!XOvLLqR$}ntZrx5^vx4`I2aDEtGpX!k!%#!x+B+IJ9m&kbk@B zi^Z84S{E{{58`q=ZJ6RLc$Hq+QDquI;Uir{Ah{A=yce)|J+mqwxBO9lL}rKW>X->1 z^Pm;{T7;hDi_*B+UFz=@dCV3s9U!H<-c^Su_2<*qC*AOQ;Zt;`^A(;sO2(J-(bGly z;4!Dey*Tmym@Uwr{`zjp2dB}(A;XuYbgE|7y@Iq$=^D)>Y2wiM7v2b>)h1#h7BuyEg!xl$Dz%cHZju@0cK%lTvB z7bKwedjnGDP%uxSbo`lDyq`NfWrDx!{G9mDV*5ZzBvwt`u@~qAmooyzd;s~tW!AAr zKUD*Mt8ZL>ExsDD+w9CJZL6#{SlPF~;apAo4!P(Qj&TJ0 z_R6&xaFl~uj0ieV!DoO}N@^o?a(gxx(3$66ie#uX;V4&Lr0!jT3}Z2z+UB;a({}Zl zJGkjr(H9{nkysbH&Fc?sTXg@X?4Rg79f`D)16wG& zCf=I{PB{fgK;fxjndI&8|0~>M1Eluxq>Nv3aRT>tIZ)*O{9{fRB{j~$td9u9y+qGX2zT}YpAcJGKA15l(|$oGY{JrVng;`+T?xxTG_&`!HBD4}xTO3zDIDEeO=hq*mVhJ2n%D&f+fR`5rzyj`h-JKfx3kYa4$!ynGZsngZ zxkq^SAj*I1a%%M#0`Eu5KBW*#VGK;Rtx#ke()wJOQ-}U=)9hFdC;dW}7E&D#SaMBG zpMVnesx5?paKtHN(Gyo;)j-5nHuaBV)a|+zR-2umAmbJJ_GJU-w|Xr!0U; z`wXyBQ~GDkeE8+&S}u^zmc^UgX2@{IN%+Hx)_=6*YS(wJ^$_XCNmcqR?$dz$+hZzl zwB*t|#o99?ru)`fwQf};=#f#*y-*IW=u^@Mw=Gs~Z{F8#*Sqqi3B*6&q~#jz&cOx;^sxyUzvwD$hS?S~^@kN}kGf z$bUVcp`Z%ED1U4~BZ3VOMhl~Otlg*#!tnS1@q9M#@A}u**}hrS1^U<~`xh_&^ZCdX zxH2j5ef&vX@cm)+4BA_N?LN5n=h~+4V|*cc5ZW&<;Y4S+aKOF)V*_gPJf}aci8OC4 z-ii%jEL3D=3LJ?$M7q4ezaSo4jDWRl)kniYv(ewOZ|A<+-=UU>P<)pz76B!Wfm-7| zE{^2iIdWPV_Jsnzde$u6tm5Xc0+`A7@7fw~e)EZ|eEY_tXT&AeSl!dJFS*73x2NH< z5dEzlzz^YH-&YV?2(V3f>fgRCz%~NT?F&BE7IBCCvc5;d+atQVf7do`Pc~jPEOb|tfd0+@ zeYSFb_Scz!;L_|Ppo1Y3E~3jn8)Z-rSX%+Yz{KX?yx%<{WeX|Nhp}&MivxV#TI@miwPu&{@xC2jLSu@L zUN%%8u!hTt8%{bJ>OtHEcM&x8ybDyWE2H))(f$MGL zucZSK`&W&K&T^fASe}jol|%mLkG=GMzQy0H!#4Q-10|I-gchOu?Q*gy+#eGLzU>uH zJ1cGwk95YHTnuc*Uj+uXSpnPZ86NV1ra^cpoi{EEf9rX|Oebn~YLAE7P-I6%*Iy@v zD3cgzqpXqMc+mNX&V7yFr}5GdLLc|9jbvLM_(+-Y3)~Pl0SgjTq%%mZ94|637arf) zyf-b@bOgn2IrlsNuEqmXBS=e?1p0x39WKB|V(=c`T4RaHBd`qfN?w`rlk%i?x8^yQ8A$C)Pw0UXTP&c8 z3vVvjPsc(8M(F+W(OdU=Cv$wxJkB$FuB4&DtoQ4(5kDV7%t}?ty1Ub_pJGCQKlBCG z&TiyHOrsgo-}9`y(7}+3pZ8CLF1^)>c=!8QA{H?{bo=WIIXVx%kbo`zB;xNd7%*vN zkhcVB2RIM93jPTHedK#&uu7lqQ30u3TXL0uzLcUze}12?8C8lYvpZ1w`Oj9$>97dU zXZH9$wRZhXNWBdqngWaYpU**wsyuJT?NIC4(kgB&E6t%>DX1X+4z=qRW4!&%G8GD+ zHbsQ;3l*5=-+9*IJl|$s{o2wkE5P2V>7}1KNBp0A&;Wa<(~?bd@dJRe2^>~b+6n?` z|K0@@fBt zQZDeggjX&7z5%&ryWCnd+RmO#{#)ZK?Vf9d(;g$cE(u^S^6|Pz=Ve(*ANc$F;*ySD z2t?KqS`tBT-tq4)@)`|nnjFaQ@Cigr=u5slAo8Ek7?N-2@5A$BI)r@?9~#ggXb@kh zLqz0%v0nNC1`z)hKCMzQHx4&aMi|%I`tSSqB7gq=JK-`9$!J`?jEg`B<;=nG0X*N2 z2bQHcHTvM1QQOVs)9snxi@MYz`upqKc^_Nw-wr^_AU}^Si^opI_`i1wFfri17Kdy1 zdVcm#4oN+5TGboz!2gRgpdCTm;>$e_n41>w_Q;A0fiu{$|8aY%6Ovb@TU5K_Nl64G z`Y#bLaNqv-4i!Fy@1S;$`GfGJeAzezv&(ex#nT&+W!OV^dR`W#6fc_|Jc|;Yxcws|>Tl*NWBiJ+jDtQV`~!uO+?Tr2Nuf z0RL>`_#!;?V5L|QgUr$2Gp1<#pJ(7YPM{q3HaIl3FHjVL+QhlX?E4AK)~84Gat}b4 zU7t^f5>(jE`@eg8r={{W0kCnzP(Trnld}*qFkSxLy8xNqbObO$vL2b)jnk7?eFcsL z#8H1@{){kTJ=CjS4fm=dnx?!zdJxXfp=RO%yccf(1JiQRS{0p@$U>I;17wO za&La_Wg$PJ5!rC>|NDN1UIDwE=WNt{*UF%TEdV0>iO7e){@$Rs!oK8nbH?LedhpRCDM zkwYov?4>l1KD-G6(uYCenEpxljv676k)9JQ-WMh6(^Ke4h}p7D|D4B>D~zmlvv zF{LiQ;%nf40FT?r(MmMTjk2!3jsSde-{2;L2l4luiTtoMAL1K@%Q2WCzqQ*}e>wR- zzw2a@){vv3BZ9JH>=kEDUWE?xHy&^s3^q`6`DM?qX|9w@z3ul?IoAg|0sr{iA0H6p zbMs?2az3lZ-y~4io_PIuj>!MZHPjGKAKe#HqAzN7)V1=G_5Sq>8(jC(Z~yr5xyG;8 z<9Y)|Wstf*PW(27GNFI`bL@<9b-9IisaR&q0C9Pdafi}K_<7{{_q>!(ANE?>{Mt7b zJceSX3eAY?!qY|;9v9YAgLC_Q!w+3MTeA0iNy+Wl*@})SG|prq%nTJ;2xTbYPKzDw zs+3Ye>DU|gi=&J`aZ)cwSbP{bJ5VRkTpAc`Zb)YksHNYKfNP`(ddDpk(#~ku!!E>; zgA8>z&8gW=T=)7H7v*L6#{EVl|J^mM{?UzE1H}$^c~{&*B;^u1T=U0Y}l4 zOshWftvB(>M`Wyn_%&dzFQrGGek0}`wB6YpC zs4`3cVvNI%22-9Ns-F4_bfn+VYO|p2yW(xXae6Kf;a9m%#vYNcOi3jAbf0ObMHV1q z*Dp?23aFLnaU`YW1~vh>W)@E>1;vO_8GRfpQRC=%R=PWlby_ZcxA=OB_x(Qqm}C>C zzT~_Be18pMw&t$RKJ-V%XKj4~g4h-B@U*@CI*F7$yLd^JUF?tJ~k}uJPsjRYIfh z4(w`y5@V^~8TqLD4F8ks0n{=N=gAzCF5D{=nybsZ9Yj5Cd4R@pGRSnU?1=L}8;VVu zKR&-xYS52DUZ27@%71L;ZI zfkao!CO4y#66(cxhRDTuGRbm97pV2nut z2DTH^1sOy-(d2!qydku3Xf>#(<$1nT{`fzPEd@1+$2sS_U{yP(z z4UXTn%XQgg-{b0h!I)cP*5^ zC%n5ho}}>dgL^$k{=_o(K^Hs3r4W`|N_A1GZvfR9DG}G212Ev9brYYBo(x70Q;{Y$ zh6fF80^N6*MvF|e5#!(CnG2iG1Yn~Zm9|zD=9j=67Ez(mAIKuA?P@R?HlH!z`E%~y zpZh=#0&yPf{y8#ydajVQzh#kK%}oJ*n}5bHF1Th5ad?wYQb$L*O|&BMu->*8qM3T$?2^(th9vufXfnEH=Z5-fvyQNE0Y8k2UaMr368)CAvaf{pb6_8-wo)8GOku zs^CMAI?_N%D@J7^p2~acKn(Nedz^Rg6-QDm;aMUdm9#+3X4%*D4Q&AKFhNHm;h*34kRF6Zud&0| zW5kLkcittC!_;o@gKD=XHO)!GOMe8=4kvv{|6520i3($R-e1sDQR(O9etog<$bG#L zYB&+bI~fsU1(@#>v8fzM))E?7gD(xJKFwTOY7`i zaf1)3%x|FxFPY8p7mAw=V6!cLW8Vi|Dq{ z+7Q%`bUiYtr1p62^LY*A=3iFr_!n$5Fkg#X2L8~skCT0XL5}wJF+1jWYkjQXw;!@T z7C^pE*l7TQUq`wxk*4T_Zp9K>R&10>1svH^Xg9d}MgHI4hd%LCvrAc?{@9e!%pp=q zenE0Wo_a$Su)7!wt+LA>UkiB#qW4i=P%{2t-_~_ChDv@bogb`|gFDm0@W-EX&W0DU z+uWIzB)Gt6>yng5mqGar6B*T$YUfqL&<*;h=2V>XmCbGTLOeX6Rk@0<-iy(@%LBhp z4a|ly>3{30XxRqq3aH>L0Mh#e>0E*WiX@PZ$<8261lpEP8-8zy^ZRG~7#wWBI~>w@HUB;nM$ndPuimmBCC{(-8-=>%HfwZncUqma!waI| zJS2*L5ZDiTe||T}`ksE?He%uAa?l=WcN%8T)W!Ii#aXoa@4K}S-&FejxDB8lfMR5@ z?$j-8UUs81QcAoS)@7+nW5pHVK9UFKM$W&ALrDjy0ia@Q)4AT^e#(n(g6n8*AM7 zf*dhhw4=!RSK^b2g{f@KSgbx{op;9T*FsEM9qdkmMfS3H-m?qLrO;B{zeGT(r;uv= z6F)iU{=|Q0j37g|m1@2yD(;_1H~KGuER_#;*QQ{@ydJ&%`|KJ%TizD}GA6f6F5I1h z@ge^GW*;+XSvwskrK31 zVhQfaue}@H_VUQ(I|TiAVFMVhUW5rH4KcGSsy}Obut$2sg&%J2d}ElOlB9K-919OSBXbj5^g&?R-qJyWyONK>No8sV7nGE#7 zpRC&X^7`bE3&ml!yEi4r4%*jBy2y_kUQk7EoAu~BESTI4J(5q3!)PVTwa8yv4Go8R z(kscMzO&GEav_DJ^wUFn!qjeW*w)>PVLTK1ZeZxh1(q%TxfWB>Mw9GLs;k^W6pz#2 ztxr1^ohSWkg}D!i*(bD+Nx^w1!AOtolGLk(2|>Uw^K*Ymo;~>B9sdK|bqDd%gz3<# zk|6x@Y1#~TC;8%j{!bgL(LYGvqwn%rqYj-lv%w`3d)D&F-FQ;WJM!|46~`65f0tR%^Hg%PO-HcLmGm83w27JM$;OXuh6 z*p?C|%y`$OwPYzXi6!(p#3hX2s05#K4M!XeflGa`L(yJ4bM{}%wbjk-hL-_=D9%Iz($Kxf|;-1K{w3hgHJ8kq1Mbvmns*7HfpcxUwg`~qOA#GA z!Mn6Yk9-@3D}DYBk^re^x1&|Ii;zX{8o;VQB( zEZnk8#%xi*^oPdw1V+e3 zhQTn4WaGTmY-kG~z+T#!H$f51bKa1Y|5Mj!+|x$A;rk+TUOy|_%Po}n5xX#knIvLM zwYAQMb2YR?LxT9;h~R@fp_%smUWGZrzotLA(q})$DOir2WAOk))8EWI*&otk<*N@6a77#rbz+5S&y+@NHHO*%bk&t-EX{-4J8*E#e_3~!)A5HJZxq&ngbZ~!Mns_I zPz6TBU`Mg}Y_!m>5O>}`oC(3ro0>f3(c6v6b<>jZ-?_Nw6)eDGL~=oa1{}G6|H;ci zxq2)4_W5~1+mhjr>My>dMB&|>^}@!`3{8vPt2?PvLAoq z?-?}-cA=YB#_(^*W6>Z?A(u-LloT_gRdQYm@(seGw;D+{mA)z30)zI<$R%2OeY6;; z$>$ujOJ5SQumq?9ykio3tF1=DFKN+D=ujC&qxQb~IG3JO2Zro#5A=?OKP_Y*atFC6zv3-(4&ooRURW zm7@!nWa{~h*7=MoT@}|28*w6kf4muCpsQLwTx^40iz7t9xaOi~D_ij(iWq;KH9QDt zhz6kSkouk^ib)!c^^-idL>C-(>OiiRH$b5g_ffkqHeZL_O!cw(u4&+y&u*Eaj_x=` zeSL?s$nApaZmH3iireN&1HuEx8X)o;{EPC;56`MJG?9m+_tqHOkg0JDwlBdbMf|H` z=)BK(x7Ucl@ATqaM_{8vo7}mMB+gIzMM_M^KBXN{T@Wwt@VcBF7&jNK9rzVRZPC)y+=yh{neQ?5pkzKe+WwIF1oCIUjx(cbk~YK?76fA_raM z`frcTkey|iE7}-ZdOqKwY&c~cNCTHkC78r^fviROyj@cZyrXjlEH@2@+61qJ4#{RR z6Vs{lBU#(WaD8ujyS&94YsN54HkMAxEnT`%#L<2+OJ+y~@;T*iha!InIXLLs3lWS$ zHZ2rj!u*(_&!>MuG5!TZg-;nR3(QO)Rv&l0fdN1eT^^s!`H7>Q$taEy~ExUU%g_tUVKe? zio-q^#tp3T+UBwtx)6#ppC6UcY_Zc;YIF%SvqCfb{IRP&e{Q7TlQF%c0`zIS*OJD+ ziVH6I`OF*pRSXaX+uC(MtmbLv4@}4#KX#01JV~ysDr_Lcd&y)PF@-}QG!xH~Vpd*9UXI}& zG725DhwB}uAG!__9rM`8AEXda)M2pV<9Tl) z`;INzQ}*k=Ki@lX_c1=#`2*Z=2coIL6iCY0ZecM=89HTdr85URtqg5k>2ims3FzEip#G13wOy?uv) zjynSpC*38XZNYHzxzFvowTy~8#eXKOFc|^f%|*O+kEbFpuPAfjoNIym2zq#?aPlBO zao&FlLZ{YG)gkf9zo$SPV80V@;(Xzd1HD2!JIoUl=`|HD8_$)Rq$sv?&gp}8!E$U4 zy_>`HN{>&HW{&US;Dkw-HvD&(Chp)7W9?;-%PJ&N$7F-k&pTDs5}2?iNtkK9F<);x zd!QaI>1!|jPGn+h)mZ$3S>goc-pDe{)xLaZ)i{EW@mg6MMsnKV1Fu)mu@oBrAHN4) zg(;{b9nXGk_6LlglJcixnvx~JB3>^udxhBVdU>GK3rdi0{{F{>P$<`|7thkqp{1jH zbq5l8&mpdc6(Z#_h3t%wAT%#Pty`{cj}3Af59I($qiOv}mwIOT3E~XQ9u`UYc1i~( zmi6#mNFkqf=w*C{r^~yXE{?N|-lzP+9Su?!&u+X)GqJ%r4o7+W!N?s^HuXrt)t7wE z9$Ik0bR>s*ST(vs@JW~lh$Yc^0tw9tVv`#(vNruK#4KrHl<&Wvf0G}TWWcAyujk!d zDJ<1wgnkU-1#-C_>0Y`fXppcgvNMKP_I~THxS*QKh(>_lU+2vN4NFv`VaxLH)U9}T> zbYb{t291%_T+|CFx^?cY+%sP(8ml7rEzFO(fk%LW6}>}lNdgQuQD3&c9cw0m z70QbgMu_^nMThIdycg&Dy@M|3F!S1U2^FmKJMmDOsr1= z@o)n(Mddl36fg4-HLIBzT|`7&mFvF<^&j1D)6pODc%iN#sBgLhp}dUvd@UQzj-4&3 z0ptwCTZJ!;L%`6{qdlZSNdBJlLem3i)w}WD#lc1r7V-uEVe#fRDIhgu3l$W5peFjk zq~rgpZ~s&|SXSr(e3P#q%zH+M`ene@Gx`qJ`A%I8k_zMy`GSbndG8qv)ad^|>fN=9 z&v)Oqk<7PYJc1usvAAn<5lU5=Aj&!OH2W|SD#c|H1a^XVvP{4{$H#45uwRER5jsa% z^fSvueDR}$JyWt;oXTX~POnhD-1e;#!aEN)IE>8PVXZDHarMk3xrN7Z+yA6^vahXG zpj}9wt;O^UsUFpW5cdmx_Skb<_)33JdC))+ZKrRpx3XUjW_=aSWUnD1{){lqIDC8^ z$+tSj&nf?hr-8gJtr)ylT6>VmMt!8$K!+s6X_S^W-y4jD8ZXj8wu>^RRdqNq^i<&yN|N@4cB%^-({P2yNy5ov_6hUaEF5^=ZrQ9(W)`yz-(1qH<7 z4!QTJRwB;!iMa_OO2BR^?>S|GN`c>R5c7%;=V5!V3K}T{i+}02tP@kdzKbrOA`}S8 zO(0(&=={=lFt~pINgeTH_dnxG+eab5qf$WKl$F8_gi{uNeoE-74~1qyB4NbxluKsP zzOC{MBaTgX`nIzb)xwf;0@kuyRKA}hr222@5P!iAQ9N~2vE&`~Id@n_CWOr(+^B+K zM7W>G1w(V)tSYf9EphB&BWcnC6^rp9#L|{w-F07h>oe*T76Eer|hO=f<}t3!=k8h7kLG+eL92MUK`>FgGOEqvaNJq_Z-h zEy$o1#LSTO_8>nrs4y&B9zB=N$@M{XlGA>)b#kKm-5cKK8vRz#17;B%DVrpW#DRj) zTieJp&V+u}Zz9S0^1Zh%L{8M_y2B{e`@7!2X@Sre;$hym){28#H6HhH8KyU=xi@#c za~X_;p_#lsZU>G!RV%^TG~u%hC$wybjEom>ps0SG|32$uf@kGL`ul>G+^)L!Q=u50 z(SgVh{9bg+kGvTnb-Y%aC}IiqJbejaBmO)mFmn#2M#w69!Yu9+;^F*}84Hi)_EmnG z#yXkb0n7k|$&d_%Kb){SR7NrsfR6~wp`w$>3YQPs(-KrNV<^~nax_xe{huokT@30g~!c0+gO`jm4soy;W%IS~j z$cLW-;%(tlUGaiVN%uYY3LmTQ5yY!<36v^8%nAC3beD&GpZa<6ky3^Rj>b*PSUM=< zr6A~76vwY1Dd@I~7la?)F>CfMD}D*oMxPKD+3rWSDEXYUW@{l`VNRrwq1}yIr*?G? zW9kw6Wo%R6G_O`~>>l6D_?Pqr4SEWLI-hHFf8XDZdO$PBAgp-w${o5NyaUBJwPt9N ze~PL-u3LQOPwO9Y%`({UFYvjcsS|3;O~W^ii8AZ9L@6#pGL+z;Bg;gMwe53t0r^r# zxqtc}YhC3=lDz%`w#&Y&r%zBpNvd;XYy}OX%NTw~6a+fIIU1m#k}1c(rYiFH5DPU+ zD^g&w-xpW|o`UX6a~MoR1Q9%NKwdof46Nl}TaN&F9_SeGY0xim?v^YzGBn;m?~B9z zd1fAZm|(pO_b_u^bFSN&V7)>McCufrN=89rX83<7dzYPO*)?0QI%#AnjVMP@=_Nu6 zW)D&n34?8Hu))S`>`uw-jRD*2K}sXNG^#ldC8x2JUYcn{k#ZUt`1@zAs+Enjru5JG z{oj1;*Jkr@KleSxH6HyUK9$S~EOa@f4bZ$i9P8itjpt*&Nz8|MrZlgagd^#aC|uWg zcHD+F*~F6WqA>SFmkvph5(%s~RuMLg}CR)qrc;-|GIHAXPr zc7q6jAhtw@#p6~LKW{nsl_C=nvwV%vccu3auj3LDM#x;(TIN9Y4-7*=ViS!U^%NQa zh%>x&J8ZZeSZW1RQDp*3>U$E?yMk8x7=a^HCzBcsQoz5!N6mWL5FYqUTlB8-r7dS- zW)M2D6}R*K4SVCAXR7&w#@vQ7EJl9;t|*!lCM~k1&Tmk3$koSv*{>HgFdJ^uFg{l2 zc&XdCWR5C1xRWQSCgxc09aR?qwLM_!jV&cFFdv7#yh3Q>9Ter2du`{p7;XSM`OwVE zZME6rD!eY-eA$~!cJz<{Z@cSqi$!m5eO?B%&#IAS`8CSxw&V(! z_EC2BX>`sne16qzfl$<2pY6piH7^mKPv3oE$hraWiu~ew+7S(EhIFxnnnrt*Ue!#O zImUAdXPwq^-%6o;%!VD8@TlK)2ZLf5VKd8JRLZ_lGTYj41YoD4Z#a=%((eURV#-*pHE-|5?LmYLCgD*%G{5KWfG-C#l^f0x+3&fKCEW&xMw zwboy+UFH-Q=r*O2x;~d@YUAZFlVkPdoQN3M*mR&H;MKkq*8HYIP5C&#fbV^ySG*Vu zt}k~S@13dluz8-Gh8E&rf{t}cJfg%Y5^o)znBM^;V<}Rh?Mw9H3ayy4?E7pG(BAZB zn-#*nEWJZ403v4>4Rb$!D#H`C<01(SNL4ZW?1V<-uU@gI4|>%5y8J#c9qQF?P#+yF zn7-Ze@fpLfYrJcu&5?sH3XTd2-8%2}`SaQtCh40j-;Pc02=Yu?Y#86p(WW$+J#gy2No7+ z)0Z`s`uK)uYLsx#iJ8UYnF)$#DMrCd>)JtUW(<`Hal_#@a8c7ODiPdw#ACaoP6r7b zMOIo&E1F)iuQCE6^br`Y<9G|TS_Y|?k>nN7P>r9T&SD*Uy zwfDhvA1)|M*(kVKb+BkWlv2d=6&m|JeE8)j>@IfVpW-;h?h=wV@4mgggliQ(4k!( z8M9C5r*JME*x0%!K61%f{${|(ADLZy^6uxcfB9-gP%wBhQ4NlXO4_Z1-pAtMd~T}q zw@3`d6J2|C9>rk%UR`>SU`@KLFOei`9zRHVa67UU`Yhl5$G~iQ+#Hn5)z{VO3HI{S zmac`~?XIy2ARcC2tAACeADiG7;o&r3yA&3GerJ8vN9=cMA0~$f8=pS(!RC(3>%7cq zcjrBA9?d)NsjB`vKGxzn>Go^Gg})9=t!gbi8V?PLw{`Dvk{a}cTy4u52Cyg}VW&CK zZ1v%v*B;gtmir@vs&j3eg3X2&z$P^~5Uz4FfF`Du8>=p*GE`NNhs>EipSm1683HhD zE_OZgDccrp9xl1@?6k!B7N*LpbTWy&aYBDHe>PUJ=eLh|%p~JBlNG_WI%YF&A#~vd z;wp7S)mF$%s9HBuKFLc{77`Ezh!=&IDYVRQFJg=K^Z1QK{xq?@ab2)z8 zaC6RAzE5`*Ire4F zo~^jCVoZLlE7q;GRdD~NmvSj0`91GX=3EXCB1mAcUbP#X>lTK9fjUDdcd*^!#C`YK z;c2h#TQSt!pez6luvhs#KheTFP;)Oh6Q1z4hJl{n9&=@r%^0BXiM18F!DH|Vwv8cK zS9Le*y3D++ZNtv7OuuB~2AGYH-x-PQ32;*iQUSOvJ7eNJ9MdxkIf!=b=Wkovo%;^Z zb74*{V|m()qfMT&m74A8GucaT+3m^C6`yo(^vAhV9N7iiK2O65qn{%k$_*#Y$$i@V zNBSByz%$oDquhjM;G!Bm4;ij&92>yOs0=>v&9XNP2F53G>wTMpwk6)4XCLgnmEIYH z-PP$BLfIeF;I>SRswkh>=CA9|2a}ySjWI4gxY%67{)PRln!LAa?HElG`QltG{poOB z_PRnv+lRmnK@YlP#0-5xLVvu%edukj#UYMf(IjW-u~0#BFfem?&pY~1o(Db8<&!5j z{V08es5E!n|Bv^!-+y=6V|!)=j4sY(yxaQu6WXwlJQmHO1=QAjwp^=bYCM?p`s%+U z3xZX(BUd#($m?)O>$SCtTCci}4ShR?R)2g!lgfLQ$p%FKF-U^m94JpWK%_2e4^?h# zU-m1CT#GOi5>60j3{$*o=0l~>+Mq+pElrv``puQ8EXNfJ_?=^7m3~|wQU`62{7qa^ zNIC6FjVo>i%nK}Zlu+cLZS45udm~5G(u-#kOWnu8`O}+@X_?0}N*tV$_N!Hx)_)Rd zJ)0qg-UUFe^9DNcf$XcH+4l*!@)z^+(_`5C&2@`M1V~w*k*6z)215no^n_el?(^E3 z*HIzPL5vl|EgP+p35|gpJ%A=3m=-L2#XenzBoW8mD>8&V*eLxF&)L$k;axITP}Pb4 z0sMpn^%yCNK!L`H^w0oMzF}sgExig3tpl%@M0jUVEq+~g&N!5zqL}&0{5E&rs&m0PQZMb=N}%cA)RR{HrMb;5(!?3qvlyOU`8(w63_ zu5mB?23ogN9&Zq1ov@4YpU+^lpdsbmkRpl7E$Wu(PLNn{9t^)}kVZq&Xb&K!={b7P z)b#76o`Wu#eODCK*LmhH{SI96C8%}iS7g=xsOPcv@cFfPCNn6$=kZnY*Mn_vSM=$y zAGzN99g4$;cdcx6g#-;qrwu3+$6FP_Sa@;Ljh37{lMqjqDq2q4z2E^c&-Jo@dfAhs zXTgD{Vwx)?AU_l>gJ)de+=FrY4$6|fkz((LxPY7W04ZMT2_X^u2M>enasc;F`YO+L zC)og8V0IQ^u2WY%rs8`(hMz$mOly^yme_h~=rY~Q^eFhLme2d*IHXM}vhb`e>hL{&{10Su!m(1RI2=5~{ z{QZUBgq*m^?vff>U@6l9{Ihswz3~LV`MVsQ9cEzXr6&?UWT;S&^sDRLDHxYt1+U4o zZ|x5Ug^Y!@7_QhqRPlAHnLMvd*7yZojw94i|!mm2a3c`~=lqiryMWf9!7AS!-C$3k-O@_sAKhwWhxjMTo|bINAEtyBRWI{tmOGB&(#0c0)v#2>pI zl!{$$AFVSBb$b)Kcb|n#(TsL2dhs#oh4zUdq$f4{$(b30owmXQ^!uvw z)O~r-$71h2*)cXu&Lr(?&(hYWjJ8*MsA6FnUrv(X0fjk}HthO3ePHRv{ruRk)umUq zyCl0yxo9QJm8iA!U-$FuMe_u<50U~LH)ZL(U3Jgo^81b;J1w7;FcoK4Z^f8ys_XZ4 znHW0XGAc8+M{czfZ^5=s8T(#~lMYQQ>JI&i``38Bn0@igRgtfQ5R;zh(nuz2jLEG) z^4e&l@d7(E1%8Ai;yVG=gdY4R*SzxXub?s25` zIxJQd2)<7Mr)9e(MS@>7+Af9%8rvLrh_E80?V|JRC)DxL_X3xeW?{t3Xp$=^2Z$ls z6`=vHt4JzP1JDL*@PRyU>E;`Misx*7Gw3m?FZ)nM_A`ipbx4Ip_>YoHtv6{|)z?epbKkJI~&9 z|G>3TP|TL&sfyhbkP8 z_p5uCJv4+Euqb@HihW5J(h&Elp$CbmaC#g#y}hrT0G`Y5@3|zu2Y9WHpTgq^gU|Av zK%COh{A8*?`vvIrQm1C)9^5z)dm!_7+%Vr->Nzs$schO^%XM(AT+71_PbV4o$-l?X z&llB1m?=?!I4OskvM&xn66wpUdgme%>En@`z=UkWKje01MKDl>esG4BMUa{qE*OQH)a~3+4boAWW zPiR-56<4xj==S9+dmyynwzD=@5~%A;ZDVkb$i9F`Jw?_a(lCF_4P0UDyF4E1xk?C4 zhlDDAiI6vHq$*70nU#uU2lQMz@X0eh|5<{rglJoenpB8K_xBY+7x$H5w z`;MNOlIoEopCT-kWJwWw%c1+U^VE~S|(8YMuYwY z(bcYaQu)}Lp#RaiH2Xm9bzP%nl^ZLiP#?4Mj&3MbQggTN*-!;5m;cRBgZD&v+PP)a z-7tfhc+)=3O&YFnH8GaY`PP>NM{&zDVA?&l`**BW5WTvo=G-;d*Rym3iAXq?U>T=~ zB5}}iZpTe38m$;*V33Mi@MEpx{dq=1z@3(nc;<|Nt>f9n3sU*W-x~~8*e1+_k2YaE+KCF&rM)u=@n$H|H2WUM7 zvGHVIe0c>+ztONXi`tH?3_Ci&9iqWb z_4i$CLL3xmPT2(OF^(aEQitSLg`IhMU>Go! zT3tLzOD-{)N#d1t|H6k^#V$1Hc7+n+L8$t0@(SU$i@@$U-HRZcQGd+(0QUG}*dI^x zdJ!U}h~kRiqhPcB*}z6=9~>MDq^B20w0M0F;vV7+BzRP*JbbNNLf(wtcxL-pI(aX5byqV+ zdgNMa1ukL)d*mzTNLD6A?W1l{>K{(Hw%L zplKNYotxHSnyEdgssBVDCqJ9iXILR5WtlmfV(q40iyTFP8QS4OS;Es$fzxaF0Gk1{ zU`seUBD8-N%G!x@k-}C$mu)P2AM^pNcy|e{uZjYgkx$PdB%XIdW=VX3wYMVrfeDRM zrST1M;vV8&U;O_BH8r-G!AF0*yducPFRNpDzMc%^Jdvy9qB8At=i4Evzxk0*Jfmr^ z%tV(QI01xD---6+{AuUFH=W05UK$C-t7Le361!ITUM$zGNJzmwiVY|^SUgUy0Hoxi zTYOcDR8ctJ@cmbpF~xj}GpJ~Xk@}9-iU7U&19>5e`21{wL3mue9?sHZy6yz3+dcB! z`S?%JV4+VSb+5KFANAc;EI8I&y!vSAj8cOOEAzh+ja^B<5{Y>A92+LN=;iZu9>n(g z#vIyCgZ=A?HN9a|Y{a2Q+@RQN!1bkQX3yc$;n36(XYuUb$NNJ_W~AV_B(yq5X?MA~ zGafay4_Nk=in8DP{5<4;)tff)UK5scAgmKMw@pCQtCQ=#*Nr-k>gouK5Om^}_cGD; zsMiOzYwhxede+Lq_LZZK{Of&I;v3>KWIH2>HD7(b3PC2_fK)8ZC)Equ1kl@5r_+V1!?F|}pUW8&5nINb43z_JbKC3P zHY2ykft~5So^GKVJ|XYZ1b9!^s3FpCm zqquj}6=1?(CjWK4o(t{HRJs#6?R;Y`GQaJ*W{8j+?s&@T z`Tgl2u;id)wi{hgUW^w!mo7oo@*m}O%LfuVU2ZY6|L%vgUU%5r%c6B|4;ZJea>*Kc zclV7ssNH#lnr_SaHJ@L#XRL`W;X;`QAS?Iz?We$~yI|pAZ6K5X{(eA*IHl@@0J_>H zcYTDZ5|Smc|K8PtKe8N1X+&`aH`I(V&+87)n~*-2R%!fQmCbegMT727KX|EE^Q_TC z?P?8VX??v&(?hScT;rsvG0>1^t-^u>B%A~CyeiQXB&~NsADRtD?%;UwJ18AYqP|3v4S#aww8Dye{Ir8Jm^Y&L zTT8yejz|Ak{46c>rS@)0fwdCA@9P>G^EGnQWQQhpU)=(%qu~y>)!0Z_`*4l8C3Ck$ zTq8l*Ve-JYkB<@o(Xjad+zwm+@BQ8pfMsZ6l7UZwa|IKzxPGlV)2z9GSW}0@Pywxj zA!@S~0nyrI(KXXs>nm1;@Mteif%)sQAH*F7KV;X<$V9O z;l>H`;kn3hyQW+t8UeYIXtRhf8<>~fIVOT+RbIUqW82sL(ve` z%B~u$1T3E5?f_gaX~W}NLk1F^m;)aUxAp_*Wg%^WfKVj`inMYU>D7sLR^R2lkPY=O z@8x&Z=V(HeVmc#jFqe+hSFrxYaP#AUtiQX0H2p>jHq>JZn>N-z=jPlJo*O(<_c~L0 z1BphwvR7a={l2Vu*=W&VB*L)4KSxt1dk9XM^I>C~cW&d=b7do?(PL7QlhHl59oS{+S569+HsNhsnG}eJ-ar~4u<*2B&C)-Prz)>CP0ecO1mpB z>PyGh7+OE6n)R6qPG9%B8CPqAhS%t!xCNdQ0ev*e^o>ZiKi^q_N#vX?{h#i9qFs5< z@aH{1FwS&>vM%)MPd+tYgsX$GVxeBFHO$It_x1+Sl5$*p#^Z;o?{A6lY|Kpm{ESNSmCG27gcy9M-a@m{P!zdARWhU9q{$w6t#VeghN%!yXU31O3x7l$DrPyMa6 zo3+8m9lOP|5>utu+367)`^FK_bG!4mPb$?w*w``xh`nyVlVk+@B&^QvntRHe_6yxldenS8h|>-+9b0n~#?HCho}^ zVIJ-_!VSFXZUG(#3-|1IFC7sCF(yiDL>bvd10YOJ0NxW!5c88q*1J0jWpY`KB$mlB zo#Ppj@V1BX()_pz>&{8pek;VoGx@hTk^pFv8x6h5-#wM>8?~F(YnPPgorX((z_a`# zfJz>&lU>D`pSUw^=cI8D^u;fTR=srqwPCF@flM^Q)eccKm#_P&Zft>LSA6Xl`rhB? zR?fHJo~i(vF_14vot)?=i~zErdAnqy$o3T>gh6daFkJ7UD+H35F%j4}&k~AbJP|kH z#XhXQJcT*vU(cOJYY_K@6k$r#<^VF+Ksm*T+c`HrGu?ej+^>J&Fe!0Oz`7JCWf>ou2!SO2@lHqSQ=yXQR(s6qETq{G0!PwbvH;eT!3D?iuM zhq&Bf45$%O*f60jQ<#Dl&z_80Clhy&Bg2XHr=UPl{78X+eR8kT+7Q9vt-V6W6j-lb zVcajF8FGCISx3U`tYQZDfQB^H&V2!+fm?6!5V=0V4dAJJ00`J`8CX0Vg>NDE@_83T zOLT5KDMV;0ls0cVCx73&K6P|HNfo~L3VR*|!0JAKOwqUkNDsFGo0kCPy`GWYwH7ic zK43ILS-m|c`wro7;iB_fkx0WDd-<^liD!NYvr8Nr#-!~vhj z2q=)Ny|_;e27u@$PJ^aft88*b7k4eU=%~0 z7{F2_trh0C?$X>W_^3M|8k93aaoey(te5A;nQgEFaL#~e9KpZ-tNutEmh)860LM~O zR(ByLz;sFC&fYN(jjcD_u`-Moj!~T5{Wg5=n6TW?0n{{a=sBJDRY-WwD{i_IM9&e~ zwSV0Lx-;1kH-^Uvvb~#b7p!>AOGdOZ&QeP&spU}qY&PSUORhX?;%dNL@!uGe)|u)F^j@g>*stV1g!0GWXIP0#Pwhh-lO z<+=)YxkLHA`8>=VURE%a!BizY&e*RSL>%j>=dts3$Jy1wDTCqjYcuvMsGIHIuZ#UV zWI_C#dxhI>-!m;W2RG=dHuKtPe?bc=4vXbFp3z)DwB^O3?#=%Cf_VZC_(gM+h3skK zI|t!NzmtdlI0_l)yTyGa_l$)ZMfy!|546A(X6Ke&WGLb5^KkHhy!#`Nb!_Bsp6D~Q zGQaMK%YpQXrFR8$R@z=Z!oS?ZPuf44o9|u7sEwb$1Lv+wDzi|^;}byydw+iRYU3M* zzg)Y=oIN4(5=9Fuo2XP}Q`LO4zg*b)Ysrzbwn6x_pwHWB z5IN#ALgT6B+!}f22%^@5!;l-HU%x)JKMVN)&{}J_tnc6`eipz=`6@B^36f zmb!6~c7>mf7&wG(iM}|A`?tDnqydR*Ya^P|Z9jmUFR+SV`D!zNhl``UZFaYl%hf65 z+9^FV7P2#-ORi8}ECugnBPe}IYcuN_UJAF_@|?nQvcCAFc<~a02^v$(H+Q$W^|*FK z2fAw`VD`Js&Ukb#k+eGHJY4$?F70F@yzosmV=bSg*QOO>Sp;8rbJH}NRlo-ZojD8y zr9#$A5-*r~ER|2I+5@&T2z}->f^6-oc#XY<$!bo*h06Ww37@Cm?5(7DUPl^-q(?Pa zyUGNx;kV$UnoJI>dfo6;37V&3Kg>-k25FkPw>qP=l7;vX|hqu zyYLW!mw+XGUfp)`cwRz65hd@{#}ZvK@G9-9kw5_I?h=nBzyRh2qU3M99-YUT8ep&u z6L^-^jWv-7ksYIXkDBQ^dOURSD+0!3P^zgorlFpr$)axnV+hz?bxb`bMj!nMb&5U6 z*Hl^Z+mGrny=8BZHEX|RY|H=NBrk(Uf9d*iqgvcdsT9hc#$6?03#;d5i)~sItj=3_ zG$tUdeQ#)=$7d2saB{c$z4HQrA#nZ0wb;_1W)+YxEd*W*yMaP$9 zT+v6($t@rbpnU~fQ77B$>Y3Ub=b_Q1Pl5>QpQ0d{D?&XX=1Y+f1rHPgY%^wirosTR z2(~9k{PG&v)8*dwwcf zZGDw6zOlILE_fPnju~KY|G92yDvv}DI*F%OTP~0K^x8x7MUm-Bzw-t#MTFn66i?Ll zE0q1)b{cj;y0K+@K=#ue1!#Y+SEJdOoKjZ|JjMKwi@4o1eqc9pOA)xrwKF2G&%9Ts zaf49p>AXdsYT?K251uEtt$&tud!V-++7A_b5L9;M`DQh}Po6pG6s`rp`;U5rG65{M zo|7>C%;4TMw)--5BntEFCKSKP>@&XnC4M!B?R_TIzcdI$c)kvp3^29DiCUgraEWTM zI6SCX8kqhAcJF%9_Z4X!1Q~N{E&WVzHIqrKJvk%+0f>*O2M>?OpG`3|s<4`4B2L_< ztS(UxtaCNU)HTr@?IIL369k5Ce5h=_)!GE@rs&qAO-vdQBZ{D?h*bc>DGW8E@?ISm zUhf56c)fV`#f%s{&)IKWkCyK+uwHwg9y91;ce(M*D7p@KCE%#c2Qvytib}9Yr3oQZC&km^}T_ z$}Ih}yL>BHgr@B>+6s z`6HcMe#v>+pZ@tcf9^~C5@ngM|M?}0He`9n^By2V&UeiCC>&q6%_{C!19#granIhc zc+ozqpNh?ATKRk3DqaPaLb7n$6}ROg_snnhL0_$*JBKr-hUYsB?XW4ZmAJ2!uq|Mz zxnJ~<+_K$&$ou}+pZ5?5S@n&E9h8&*&)+3h9>>E&j1T=ghJV)F|M=LX(P6gghj%yT z-Ncn(%Upu)PKVtZ57UxrzLuGGS529&(_k654+Mi=QO*hd##4=>D&ufGv7h_r4!C6k zzyrN?99-A;f;t6A&#Z&#UNr>|9D#9!VBTU7uXLH$_t%OL zf=Hkhn%Q9Iq^75M-MrUZgf^i^kzXIQqejCKT>L#H8i9VE;?3kC#SgOsN`^AzK+a`% z0l#2n;d(fB+Y_*#g_*?1~E*>>N=G2WpkV$m8(PlC=jC^h|aiZ43Tba4y?i#G; z_32S&-ti}*8G(6kTf(|-i@dA0{ijl!eInPZ>3T6WU_UwT^&6AheGxsB?S%R1v$7EF z5rk;P$ol3$S|{uWO(;<1)1c&NoQQ(So}V!H66fh=T#$J{%i&5e;Fm7$#*5v9=cOu3 zUe*aen?N+~04A#SNyr1)PEtxKXrJLb7>$)@$0Z(+(m=Bu`sU8v+NR&WQYPO;MK#Fx)T)#K`K(eRVp3w|w0|L> zhr)1fn|i}+Fdt68hW3@=tXw*w0FRNqbmKS=f=IYlVUj;cFihzc z6!Ol-T!%^S?G0JRAxqCCbGl1kUBr1V=7)R`cjuzvuz8qm#y1ndN4A$6VMY`Y_)D$i z(`8$1-tZ{0hdUG2hpu19Gx|@~PTDt8#!hM!^BDqKPOm!pl5(WJ! zPsAybFQM6+ak%ht&x6qhgOR72DK8Z69+@kLJqfGuOGKL4)=$ZXaSFgb{P9a5CUBn^ z;DuhUp9g04Y=0yhz-r@{On`qY7>)YcPQV7D%PS(VVr(o-(Yn41LkiwC;SEgb@e*&7 zp~%e{s>lnBP$J0#7W4qnU|BKWXA|@B-*Wq(xTbU0^6t^i*hxlXLf?z#85a6IhAB%f z1N3jzqDeaDV?2J}0VpaM&Xdr!BJ}ocMWI~pE1CIeqMye;_R{~?a|h(c z=)9kk%kSqbJl~L8g;VFTfO+nwHEzvifb)8e;1&M98)ERF(_9`U|B2u2-#)KmgOuX} zQW&bgD380m{AW{auP?hhmx}W5{?`4Ef6M>3|LPz9;eT#|fAz=w-{Y_T+yCir|4shC z;t&7)Uw}*UDIU{5MUVFJxBP#{-~G!^{PTZV#c|a96S7fWX^phX=x_i0pB2wEYyX!2 zANWDM|NptXM@%{mh(qM@jSIipmyeLV#*Z+2Rw;S>{cmi<5BLx9@6kIXjW}$(I!5ks z+>rkibk8Cp^A6QmT>n!%A`-cc$uN6-@b47$Pdxum?0@&E(!VwT`dj>8|K@}KJEWVn zB)-S9`rAMM*Z=+Ynd1Hbv3bt%KMM3}#6SNyJlpIasehEmxcMLc_Rs(MvwWm6LgUlF z`TzcZ`G&%p4EO*FLPm?t*}brpIY)Qq;!>f$WqnX_A#L84Z{>Zv z#!A32AC!Vu=+n2xIu!`#sTYBq)~mIi?!SA~EtrbEGNjro(<)1C8}ciP1O^Tax>v;^ zxP2be4NQo02Y8#LmHur7)CjMN`uNM+ce}Bwho9ACu zP+k7@N4U-qmG)QlX8=(toHy*-{Z2Pjst>*!Zp&Nmix_(;hF@{_V(n6hD`MXP99i$B zGQ(>!C{3P6Xal{Y>C@;{d=^y{)F!+>oiGx4ex1}~c!Mm3$CL5pp=KZPrFTxv ziGS6&u+HdzIhM~AI3v~_cKrSLt0FH`;SoUK-tn%VOG|T6mWl~hyYi4a#x|cw zQVf%Xz7FhBBh3;i>pivNBXC{P)njEG3Y!U9I`w7txKrbJ8b>-0+9zdMB(=KsR8A`4 z(!Rjq)VZ( zfD{_ASn}&IMb}=-$1f!a4BDFYcH&++ClT146`$`T?uE*#m}Rs3k;gxU`Q$jwL>uUD z>_oD!>n*)X;KK}wJ08`cyMtW90}#kX*Q>nVV=;Jdlyy8kR@C;-8<;ll$IPMB%~c=~ zv6fT3Xg>3t(#2RqoFaWX*qdj1*}rT73ZB>WaliSxrk=A%Cad0jis^o@PG|?r!yu9? zJ+icEHf~Ml8Ik>Q#PCCoGg+K(3n6H4BaE{5Ka^jg3wr%f{Oj7%i^9g(vilXo zV4hOa{L{xNER>JSBYEfgc}*F})Z}5$NAc(UUfoXjhKQ@s`UKoG8b?gnP}zbT5-tG6 zP`e$MowvVR2qTn(oa7UI)uv+8OXlqFY9nlPa}V`U^LfylheS`RcTpf1znu+DR}ANCOfgK^d3o^s|{sCKc;OoE|6a5yF7vboa^ z+i~<5Wk&ZS*!U$lG)*_n<(2HR_kQltc?(pl`3`DPdW9UBves5YoGMr7z+?3^eg$bJ zUH|joTgO^bp*Fz_X_xwmrc~tMOqe^aHA71MGFYA7`%B^3u*>$iBeJ(|#!AH7)(78N zotsAzRX30cH<#}GxE@~2b2x`dZ@$No6%&gj1uIFyfrT897X<&+`9|k0=av`xBlu9& zcE04;IkaO;e*5b^WCi10m9w=|Rcm)yXZilC=YYbz*ury-Lf^hPerGUPqQBaoog0dp znK0<_0&k~5!CBXZte=@cI_=66Fs3WnnuNo%$sN?F)Wm%TA66sWUx|fqDLt;_ zQBJg#^nNHQ-a}TGW2>$Q(7ti6a9}iUz!EDN7K%TDweH^hAGBimijJF)`?26d41G6jc)Q1H!Wu*@9VdS7%@n385wh`z)ujIEm zCFmP;4Muz&8w%GmR$&A2Z*gFsxFNbMsY)AC;J;n(84@zAmg@-LyYDyS(LR@lZ2tn# znKniaBJ4*S8#q3q_TG5L_B&!?`#tUE#P0FjVXC^WZ(Ya5WPjyA`M;+^G_mrEzn{S5 z>Y4ufS+U6=fdinu&zRWG$VyR=(fKCaPH)S=*pb zPYQapvewu822v3E9*J_FCp%U4aD%PFB7rL?o+pbz8~84LGWtH1r1PW`>9{=W;iE+G471#?Tob zCpm@3GAqK73LUx3CmCp~FJ`lGXLZ zZPGXb znR#pR(OmUn^>Fgj#>c)$j5G>(q%&l5REWKyxnNz=fE!tZrP zj%DSIiO2VzNDSm+(Wj4tW1c0^Ljo8)A+w4QzLm;=0TqCB8yL` zCdM#m>L?ta>rFnV5;ADpv$Ix`B)Q#tzoyn-Zp$wqaV&4*gR`_&^xU|*5xAaZ$>QDL_aStX$U&E-~vk?Y!-OP%2#y$wK?H{gmA z{EQFIDr$hkh?%K*4caTg4U8pT+r6S)8U$kfY7>ixGxR1`UgyBQnkj72Wf|e~eEBQ4 z>3yu1gT=$-Axk+wWbU)K@51Zqv>4#bY_al;!CNQYnJb}W{4 z;Iu;cC3?d}I;35+mi6zYIC>R%r4ay%?$rTw;8z!m(&=CT3nEbMYYgAh@_VU(n&Nk^ zxwI!v@Z(*fi!=8N(XB4S=ciE_7bV&)|K0o*Z?c1bsT{Z(^GMDHTx{BeSUo;g-lc|BoK0B+7-E%_F>3Xw|@Nm3!1 z`Gpgro`$_0R}bQlebnH0s}cpQhjFxtR$Z&OptYY)kB^YJNAh>YnF zJ(%y+pnAOKt@en#@Ah`oRN{fh7i=n%iFp)Blri=UbF;WF-%n6`_-)y%$M}t`Dkp6w zlUY&6A>YEU0BC7gx_le=SJVpRBMaII=8qXGi z+ExB>e{q#F^{G1H&;qAoZ{89IsKatUyc+DIP49fbcER~_Zy7p}RmeJ#%x z#m4HZ8GDcGvRZ)16YW~nrB+XxFcG?l#%O5rpbVk}2|v8<4Z?Rd$u~wF-|UG$-loU( z0w)Kg-oNXU=k`heW-L7+3#5fm7pWGH3=Qxa)0e|R^_V=F&lkdUK8%`{bH}HDP&OhZR3(Sj#;ED0q3t^iBKHR*4 z&N=dX4|3r1{A`;qv-0fpA_4rrrI(b`jla$Gk~1j-o&mGGZ?k6Z+P$bgZlUjF-}@KO z9`@IQFdUS-?^?D=l-e$r!y<}Z%iar2kDd^q@s#Q0w`OlHalv-?*K$vWiVXSzac13% zG1FID_@WWwRwnY=aJB9`8_e_cQCG(olijzUli!<0<1OJ< z-9d3r*oY$P_<&tl;bHI9S#0J%$_sb1LRw!$!{gLeNY%NZ9p$|{13{B1rP`bPbUX3% zOB&sHOc8iJRrg>ysi4KN-vHT`PM_w*b97SzPOd_4$U+vNreFO!%6uF%D&vt3D;<^hv6h~}+B=S+gb301?>a~g|`%It@gm z8F8fhtEaih@4@A^w2#*2r!!t@G)HPhB08ZXPKW+*+_Y4Xe-G>>y(jghuZ7*8YvZEe z$G;ydR>8)_{tSC&%%G1FY_7-_I}6v6nt~kExyyFkWe&3)-H_fB-p$d(jka@U5YMd_ z9e-YH59i!_I0s}p?Vxe3xAV;h%QjcUAa#n4K8-nK0L*Gi+=7j=7}szdYQNr{9iDNI zWWM)y-vFrw)2;7s?;W;eaUbQ4g^WM1|LY4L%(saQ#~R>$Gmk(l*_tcyQr*}36nvP~ zb9K6ZsM{2kPJ>$KN3YEboLy!sombZ0#>BOG>}*YC?wVR8&vWo3s+z%Cv7}pqSckQO z?drl9Q``eaXsjY99*uoBeBKzAJ-rAfzvJF^@-eE=>%^W`jz690D8IG9S|h}*vBtN~ zSSw3!71LAAdjkbs^H}bMkFMf;PN@e0V5jv$xWoI0>;IdwH(6Gd>$(Onhz25cQ$#>1 zRix@sim0g6aP|LSpZEPEzAqy(BO9mpJX@-@)|_LGVy}{{1HlTCCIv|NB0qZB?gI%) zfNm%BCBQtEmwR~6}GuGCu8e8^l!YV(F_xrqm zH_gpLGS%QmmK3~kIM=^ez7{@ep#1M)?Ih6AklwS%lqR;hWk!JA7|$0Gd>_rP0A9ho zJYE*$Xr>^Z$Ib_$33GWP=2^Z1Dp|4cXt}p-V5zpLfW0B4rUoZG1QaUtU6SQ~-=~f# zLWpw<+#+eS#O4d9IS$Ebi&;WkH5E%ZPB zDWW)-MFVroTKHAM$+R_WY57>%%Wcq0EsoK)N0de%XMb<>d-AYhU{PJs9)cXOaBg{u zFR#1oAh<<1*E-Xkew0XO71HLhUQH$Kle@!A+wK}}=I@^7yS+Efllsl6M!f9p>}rzb zYaXAweV4O!#C^*b@t{i8Q|tg@#lOA#Sbax3+QVfD((3B?+)Ve8nm*%*0P-XKBCo1s zo}67QJT=NZJ0an4yUKLT;ziSjYB-*1m`c3EYW!6~^Y{sYdiY7Dch3j#?7LCy<00n# zO9@aRo_Pj3|FtJtb|aXd-D7H?gx=QUb#L(Iu)mhvBd6%?Bg^==Z+-$&Za;I>u{NyM zjz^tP97Ne(GV8;>FM@3#L=3!&o49X2{ORAGw}b2R4~f;E6=9w9;I@^~JI z;>enXRWB`#dC&17gD3ZDdrzP5*0gP2a7Hel<<;CyM$ma5;yPPT%3-4}qrYmF$Nopa zmT;M4>PBn&m%P(P`Ut=E?Z&tFB9p$CcWPgQSo)0ZO5~AU> z!*V=4(pveefjT!$2N(~YH3kvYIMB$N|59=BF;A|ElI~*P7#nw7J+14v@4f1KZn#ZT zE(aM3G2ky4U`x@@rD%WWMKAhsOFSjPBo}cp;D#P*#lX=59&&pkEY~+eI!Baq$UnOA z<}lGV1g1tM%YF0rShHWSK2|uI#%Xx>#dp$dc`<)UK3x5_L>v~{ce%`#L;sX^1E+PU zd)9iMbzzB=Ji4rHs&R7?z3LU&`~T{(%O#D>l$f?xUyxy{)a5 zEi72*w6LyzEhq*^@!lsGydHg9OeQVUP z8xAfDqs;X^_mniv^IFF@WqKH|zmZgHOY}cE+`|!G8DY+G5n?}jifX_2lovzyfaedxL zxU$=uXMiyOxJCX2XU2a0#*g&1g`+!BBi?xWs$OkkQrVJnH?exjZ)&T|35zw6$U?@YEuTSXQ=JNu; zzL}QK@b`gO<9U5fm|AP_`-bPZVY9uRUP%gv?}_FU#&i)3mj_{xBf2*APy6+K5V3ee zmv%3(?w;Q(ti49iOUazG+0(%OWFe*XaL_@FW{kh<8i)uVV(uAY3u?ZuY~8s3Kp(#o zTl=)+*Bp)(yn1~y&$^D_?}#5EAFT&R7Z96mvV175qv<|3rK4HhK#WgIUi$nQX$<|yM;dv?JFMpK zbvy!;xP4%AVNSR1xR4@q@sDA7zEP*PGT1O1g8%*wwV@T`Og1#uVZ=IDKfze;5F|f7 z65hY$GzZvW(f*m8*{3{okT7{sOStpsQ#8f;L2*#W;Le|fiaQE99(|l z{_)x@He75}TNriBxT~YJ7FGx+fh5)N4#ywHPxkPB@E9^DJ;Z1&OaqUn{$W*km+PG? zOv@#WwL!b2HIAFy5*MC+|TgXuB$MiN;-dpKHjM4*w=apwuU@^$9C5Mc?Z z)fRE%R!FwJsO$;c0OEFKKX>orHHXh;w(Te85zf8wm4}Ba*9o_<#vy zR^Gbb9ZBqW^=@N*U!Jr*_H=m&7kz(SZg1KgUOk7f^>SrmMrw1bHSpw`KtI43e?z>< z+I&fvDm=LCQ?p2LwP^QxfW+~6`@}4d99t_%9Gp4X*V=eNyx{&$`cQd!fqeJ1Zh{gi^cmg>deYl^U7N#}x>C+=MyRhoqnxcg)B%-OdE3*3=09w1 z?&jZj|5~5#dGrM*d4NUrBItVFm!}H}8uXjF1#~~8u+`C|$wBKo=YJbu;k{;i zIKtB?B8`Qe404-?Hz)F?hx+Rt9e;o=Tl$~hdHns(jrQdIOQpV!@Cw-Cao9YH*5aAS zzhS1_-Pc~P-;L}0(Eqy+RUb@}NsTFpjT6JI9(}~smt+Ve3r7oJJ+YoY#j{?&`9{rA z`;=_&DB@({eT<{Ye)wzSqL1sumRNIs)?V0rAf%ysg-jp}b{V(Wr>zYLF<+i-$PH+# zqTSKhDXlyG;Hw+N0nfGGc%J+9eJpEFbT|>$v6#9O@*`X7(n-TBIAt}Wjv9OIr2nl& z&`{9)#*~gz+}DXp>uw+Ob~hWV<|O4-o!sszJS>FNm*R>)RL64NBdRBDZJa`oBws_$ z7h~6lViM2mzT!&C!-V3f=!#9f6aLmBi&lLfY+}iF`sn*0_)?dZ<6MT=ui_JTTaIT$ zalQ|~|Mt?mTG`Rl$K!8|!*R|DZdDvb@-74#$N}JXX=ySLwtaYC{ri8=p7v;qu&Jw{ z8KnBN+g=Ka|1xQS{0^Iik%+Ivsc*tomF7=GxF!PXEBzU8_J1(E?W-{s>UdA~wzvoD zyu&g{W=gzM4;XYT)^A-{kCjVg{TIU{e9N)S!a2RjS#|OrnGW;&cD`<=6N4mL%oqRF zX`Zz_2LpJhe~A#z$jyhgI7p>AT_OjLrjbcboS@|X<;ok|ziTtt8u)!JWmin8{4n*y zp=Un6_YTxhKC>E}LXka%VHT5T-e-X!1d`d$>jmOu)d3$oSG=YAQWo2a;&&FsJFXki=8J_PF9prc~Sww{9;|Lsr*L}m+MUDPT|?tKuFuRl?hklgOL*+zVg z@e|2*7nHDRt!YkuNG`^iJvV&FsM_670~kyC?QiDLqbUI|cmIo9!9%1yeyKtXCA{22 zZT8o;O|#&u+(L}Sb}Bkdj3R>9A84oPJHWWVC17=w}-Qn6jQXl8Xv(}d!#$9BVH!y=aUy)&kypwjTNYrjq4+XryH&CU6rAW zx~@1ILJK^m16=uAxU*8+k>F+i2&8w*%KI%J-eY-3{fw01f;hnL1T~S?RvY$7=7;6A zkjLe+1uq@ZUmNBcS_>||Ara8!Jp;2`xnV;24h)s^qYLejRja>ux6RzK)LfSC{vq@H zrf(tgA=IxJy-N5udl7R}_UF&+)V5oAFkg_8k$4CG`@DNf<8Cw>I`tRKVdvvE)Mx^p zIPdiDoL~$Vo_*6SR%P6@*$qtmc0ZbWa$#UE-Lsad7aSCWJTqS(zP{ZH&XaIk zre}5Quw-V$LL51-1;hpiha#y2dc9(d&RGBd>6Ld1@|1wqw9_lx3ka}RJ3@R1#ZLaj zun*pAiA5@7@dcIt@N&*rAh6o&5sepq?{>rQ_v}FvKrT}a>L;FjvieWmIGNT(fn(R- zZ2l`8?hj(pC+?H7xa5z#wOH0}p8o&9gZtPz;oB_&HQk-uNWd5lu@NW&%kP_yItApr z+`d?NTjys@!`hb%9yT~2vUlY_EqMvKSqIKSM@ak z_ED7I&7xj6i#`-jJ&DGOGSWo+MGSHs^l$>KZ!g^QZ%wS6$`^b(asKYFKz1y4gV47d z*&ChAQbkC~&*b-Ir3G`B3lRGsIltjNyv|)7;V%i0A1plm&wSsk#hbhidGQ2!cVX>n))6q!3isP_s+Fx)r z*&|>`Bv7gs2e`5u^N~qyAr|GLsVJ4zt+|w9hq;*H_eT6Y!~1cLAH~ff{l)a)mVIunn1d+dRwg_? zSn>P=aku!Mw)ihV#JXorR}1?y?5^L+=C`g@kOZdNwue!wrV8SwNt67iS!TsQ)NcY> z^M^Zx@F^GDonOdsaK<3rQfl9d&cym1+c#2i3l0gBp1#>XHhWuWw@+(7SDw%kNeRab z_4Zh{=0Si;lv95@N*K@}PGgFT*G^~3O<7r(5Rrt0up0yOU<-wGSZp`7=ie>MC#s1{ zBA8D3C0+P~;GCwDjUf;&{;O-K$xa0o^1ZaDsRwN-LhFD|*;+TQM^>3Rfzm~yRSzRg z(YdbZ6Fi4?#`J@9t18~}mGyQ|LX0`v*n&!)j0<1)J9!2j&r|yK{Kq#9d0n+H*L6g% z>!`|~?p`U%Cj2biY)#_*3fIxteS;LnUO!X1w;alDu3C`$POCG2gKCF*fHWS$@OAf4|LhkUT@3udas7@ORAGxI5Z*-F7nrl z^7-LQS?2^3YQxJYWH|hKkwBij%Tg}j<65CZ;zfkiWkeH2J4Ykb=@Ltkx zb$qDxz6&)@>Wic)^RO< z{-sNwPAV;h)4WCJ@)7Y0~e z*n5>y=xKj8f1-~?^?tRFu6b@w>%3fNq4G$!$IVpsIp%HVxg)1EEP);`we)eXWCbg#Z255)fwMs`3Lyy18&3WLoI+*Xv3E zms)wf|E?V$Yhs&Mu}Qz~vE3&gkzkTIG%6e*n&6g{M*I{kozC^dCjC(yqT3h4RL1(@ z*5Tg17RYk1VeWl!>-aYkaE~ZDb|$T_ZMNa|24M9W!+7Q=dFj4IHFlPs=l7+$ZyG$i z>vcVLQiLIwqA7YuX^=hA0u`PjE8Rq(xTUq{mVENT9rkD64wnDd-zLkquM=<;@YKHG z{mZ@cj_OC5FTPzP+l%?Y>z`&HzZs3g@p>J2T0df-*AC4gM&4gdY{z;n@3B#Vp98JE zrB69XTQ1Ue;mh^b>@P*fS8vol2vI!nF_PoF3MTg??0yG;`0gC1NM*qug`w{cPi$Q1 zYj=5_xD$8?LyI+cR(}Ya8JDIKg>ziR9h?H6;oJb}po7C-O_tsdo<*w+a6|(ds>x5- zBxf$-?F_f`?{Pwoi8Y(Q``CV+UMKD1Itl|;X*DeW`Sy;zi*qnVQWKxTGM;v85oQCB z0T0i@I19Cg;MqY!&H8}{iyl(3b99*wb2w?O2?InXyou}a18g{trR)^&iIVzykrmTQ zxGy>Bc!9f;BRHR_72M}!$i%Uls(TAC#CVLDd7sSGOv*@q-*jS-;pfF-%|G75cN8~} z!#qUz`B7V=|J6)jl8GGxugpTm(t$NGA8-ryu107N4%Z(1`cc4)-;}d-`XSO&e95Bs zf(yeifU;g39OfE$4STpgV}0aTJnF$5F)y9H15M4WLPLLADckYQA@)dZ$u=Dt#*QUk zFdzYHAhLX1Qw%4qntb;9`u(rG0X)C&c`D0n_&uZB`SB|Zw;NF)sV{7N;D+XiTemAt z3H&`l&;vt(h_$u%T)X~(2k`9Yv;-ezy!3DbK^+0VQt3u&zQDgnVfXn4B}Ei$qs7O$ zf*uk$3HA@%8a(zFTtjUeUjr@sVjM#_6VqLUkN#d~_z2S58N)>(LC`WR=7|x+ zc%tBq$9?^I!rB_tvP*~!bLinYNv7BRIfH|uG{tVWmm+t(kau@=$E>GiL)wpj z&v6fo|G=g3*0`r^*m{iNvAux&lOt0{_lIZUv2nV zx3k(s^_$ZxR~z|9%e#U>}dn zj6!j%k(&qtERQK()VdnWned!J{aDpxDCf>E?9laGh^0O*%(i|8n^D&+q9x~_~P5hS~tPE#Opxq0looK={cv2 z%8s8!u;1V8*~b){)Di9mJFV&wgkx!i=@^l)FDa*liT3IGDwnl(d2pawDFy$gqI-s^ zZR32wWoaDo5OOkO-+H6$*fb2@Df2n2Zc81BJDh|4AXc%qt^ zwB4sK1GGWEjcLAm*kez7^cx5SieEOY@oD){Ddp_)HVpDI zf~nQBk<&+P;!4B9IYRQYJq;saVq3JBL|_L~D0~$AGip)X5B($Z<#xSwCzj-k#!x0j z-@u6miS{y7=a6)N#oef&jh*8a*=x*MyI9~2B2{jAw7vAIhRT3`<5hJp!~|1bwd|pl z(LWRWc^cgZq$HZ5p_kcA?~w-5DU1mhRI;X3vYNDmxJjuCktW>lbawu*_Jj&CP?5iI z;6N;&U)^BC%T{Q5LSpYAN(G(cA=zp%|9;x@UtN84|DPC;Ms81xDb26QaMLtMQ6^F-igGt-Q_ zwQF~HLoKmAaL@1 zf=FYxz&S)bK$5UFaRjsD%ukpjL7SSQ<%tFr3QA48d2wu8t#b_Us~AxRx$6s+m&A?i z$FQ*TR^9tbJ|1*itH5^&7KShCb>~9bRi_&GY=IBL*`OYhmD+8x=iWd4G;Sfyxi=f4 zsNoFBoc_+v=dSnvVJs5h1o)Q)O0)$j1ma3+=h-_O3(f)Wd@~=+YxqF^M!X3$b#J=u9-HF+#mWpa1j!a(SEQg{9jWF=KMrpj@`U@^lS$Zn8H|U7 z^x|)SQ3yWD(hyreing<{AKdmgwv1-qH@V-3UhPNFP_A&2asixVy9}Jo5qF4?Kp$#h zi;D-QzlnC6su_IRuca>qtauo5(>sK;x}mOlc^VpxmQ7#5S#?e);MVU&Q+J90qcLzF z2Eu`?x+lOYOwH%z#~L)aSyA1Kew|yB9xN_FQk8DYz zm8 zbS6PU5$eZ{>4(NfiWo}K*r|Z+q4&7Sou|V(8EwT#yy!3N%Ccdf1l)*(J;pf`B{Hk8 zKMxLgLcy^W%7Hu2fAvSsMDSS&LOScdA*Mz9zj~r!9Pim<@MN}$| zyj{<5niSg6wP<@#5aHNq3mDw&l5vtp3%tJc0q;K!^1mwcn#P zp4kU$3vYpbLPH_g<#?4s(pA$fd=ocM`m1FzypP&<+gIbUO%de`3~dFNgtv#bDa{ki zI)gZK;VCBG@_~d?!G%$rqqEGadU**xN;B@6d8eU9m~&pc8j0yK>cjFVBZLDUAWaS` z8U<_6hjB1Ob|1cLMLdzMcMq9i1X;Azo;32n~W8txa} zI$tUfY=Uda(a(})b#|f@yg__r6_03U{=zDEAWJgRmO;wd?X6$MNlUC2YBP~e+m^5F z$+W0>U#QL24n~S9B8>GDJ?5h}CdY9aBwe8LkN-RW+?nDZ zHC2n%^9{z_an`(Z8kxc|lY{3b$hZk3WvQcenUXcH~$jk@)dH_Y88kiG|A@ zkF0A328ySv$vtaBSz>%c&%CdIsj?GznKN}Pe>)-qTH?L_q-+o41l2|-IC9|Y%n(8{HBgQzf1RUen4>>`Yu$kU8?GfMJ;0EPB-5KD ztvzTopAJ0ZM$pu4(MW4tB_7_yZaWzD*7d?H*ajN4ZgX9x0?UAF#rL)AUr{rTF1dz( zW{)RH$CpRHy^ouIEG}^iN4lLwII7Cg`A3`X`GqGL`e08J4x%l30i6D;W;o9f0~W(1 z?H&zAad)1iL4329jBcAYB*x08RKA(}1+gEoi=5)zk?+YUTdt!CvysP7oW;)OM#ZW8z9r<7c1c{gp|U^VbYOOBJNtd`!?Ab*Qap z8#DL=E-96hyO8qUI}sVz5&E8f7Q6_4{GLg!dP)NY=OG10jttFaJZQihdjK8AaN%0i zT%35tkFMz3@U1sDRI-X^z;cCamhQBqmB3H=541j{6pws_VLu~?Ls2b48vVSa4I6ME zad6gD_Pk^Lo#q@h`xEB*AZ=i)i>(i@!62QUrDrZ#_2wK8zC=@;G=#`y*5n0q2}lyH z)I611K@+!-$nEV_rPe*+8^5uZp+N(lx6W%#)Yt*qq3=M``{^lLu!lYQ!@knB8U~Js ze0Li^+2&yWM)QJKa`jK#=etED6ZB>)USH@6%Xa}oO+TrJ74}f5M(@5Pa{InxBB}jm zygBI;?#s$YG|p%}Wyf%UM}z3jOa6*wBVFr*=T6+fXM^2y{OSXgzA2_dbU!^>z?3P8&S$BgiIdT3+gZ=UL-k~oS>D|{rQ|q05;yLd(bXQXM>ezlZFpRh|_+PNg_nGOU zTTPKsPt%cs%X|7Gp1(2tw@$1s|EUv44fa3a6%*A)?-x#rV9^*vUyhZ1$7=4k3mW}) zU;AJuEIft2%q?!UiqGpcl`&kLU);W8i~cl!%E@JdBsdln)LR1_K4{2+lL<}pvZFoz z5y_x?Ay5_Q?6er*L(fs(gGd~OP#J(s8-_FfQ7&_`GXDGSyjumfi;6^@8?O@(WJ{0! z_PcKup7&8c-!Rd*+*%ZC@~^Q3S|ApI3+p0gAx=87a9=c38MAu{GiyhE>+~+}B^OtA zZ)NQ*Z7p-lj%c`#M4|(~&gn~t6C~&E{DR@1UBH2V_uF*)xp}-jAO!!>@sAhgK$K-A)j#2Me#paV zB$nM@zrU?U-nrizWp@%!UH_K&*S$R)CwhA_V?c4eb;f1a;vqZE$yUxh>|^V*^R2O+ ziSNhHLVD$T59yWIoBgaol+0~kvBOiNmND{KOWubJ{&Twjn6~viB4rtFF_ga_}eUmB;q%GaR%Ye3TsX z`gV|)HcoglQx%R=gMZo7Rl{8&cEPk9_3T)!vzGko+EX_g4_}seJ~?aO_iNbn^!pxC z#xo=9yPUNfxLCZlH`vm~LwG&J=_6O^E}p*M6_0$;KIL)fn!2rY*z5{M4eqyicNLDW zmmhE1nQH2F{n&9i?*s5}A;rrO)+X5T&=V8QB!a55*FK@USKcajq&YWqyPV%o2m2wc z0j&*11w5@F&D^p5--b~Tw0cwbyZv?t=9|N4?pg6*1hUn>C3?FOd=bRzVHimej(HdO zIBzWwT>{Jp`FuNYsfBr8xXbq?aVIaQ=58e%>T4>{Jh2{DqZwEez=QZ#$>HvD-oM%n zvom+%XIJAH)-_BSC9TdID35cP7GR?7Y^Qf1o>_w0FzpV2@ujgf;rvWx zj&Le2Wf5$QKj8*)QKkbm&fKt5c(!$}6zU(Nm!kWw?oPc_I{2hI;Ib|Q%|; z7v>PXo&5&*ZuFKJfQgIy*-8z1vgK$cNBCls8}YE$g-E^+7LEV~ger5-!U2-*k?j2F zvk!&B$!K4U#NPvZS8KaU8(1%-10C)?}}AJ$>^)u4NCZ6aUifB-L=!;<2g{uM)H?0euw7xz9x zoZqAY*rKo+FBdFjv}5x zQc^DZ8ShPrB&VvGQ=}ZyyR9B=FZ6cv99hm4;Q1-N=%O?>MrZ>F#=eKK=9rk?6ZiT(@T7L=8z+w$Ze9{VUDo8 zcWCQR%{4h6V{c6FujA%ry1Y9Sz+-UEuQL=D1_spLPS&rU&FvSVycsf11XOfHdpI$o zuWB{nZOePCnu)vhciYqv%w>**$ILsA4W{ac^uF;d78ryk&>ptubia2Bo`}vI%m8+- zi3XS}fWk?Msp;&<4qO*;eh6?#I=xCZn?G0Ufc@id4Y`=jA6#NLiI`0@u`faUB-qCU z7AEy6`VLI1y-X%=wB0SjcIO9T0WtfpqpbuG7ZdhvKx)QaAqNay)@!@{U7L>ap+=BY zBYCxTv*L>6=`ufYuxH8wGoVbm@N1vj0Ia=AzJTl!;ayokY4cJ!DXBd!vPVGE3 zY7$|ysKr|py_&OgC3&^^|MJJ8#NETBOvEzhm@f}+ zy5Q?Ys@n6sIGrIj3ShjN4=@wi%jZzm2m-mob)7+Bqaw!of7jkoPOd(ItolQ3x|pXV z%0$5a$eaEjn7rI5ho)u1aqemAcj12L9a4GY(+8-W*ihhwrT1QfnT<@O+nOa>KIf6m z08*W>YsOtp43JhnP)+v#zPVF^XjaJA&kvq)E_bFLKwbxzR1f8L;LJXoG^4FJ6yn3m zHHD$p?p|WZ+;*!2h_Ndqz?SQtx>oQpJev@uv} z(9sFCd_$h0q1JnkL|)Kvjz#=kb~Gj~khhER5a+WNt*x2r!xS&&{W9Ihvrr-BXcuKZ8fg;~{SUS%@cllgs zi8lEK>I`1l*Y}C(2C6=6XNExitI!y$?A}Oll5C@; zq{e%Bwn=i^k7rNgug$ZZ$|~345gz|;f?bsHr9U|; zjNk%j*vFteBVCr@WeN{8iObFd@;v>*V)Ew8=vrfB$&6|1=E*o%p z9-Ca1b?J3nc=^s6n|*-&48mDl+r>(ZuJO9fw;-XVfY~3}y+&7rRVu3h_{Ub#X!ErD zES=93)-!;wq+{A>S%gM7=)=b=iPo1DV7H#l%RfD?fE~8dSr~4?(?z|~t@TQ+OBhzb zr<>YJx(_c2)e^tj2F5=UBfj^_jg)2P*sA&{Bgg!?y;Nzkq)nyMug`n~9<95fNCH&o zk0Uhv4|g~{zw-wcWBUWb3*xzDTmfEc_)O$peF~a0%F2i2D1a7WvI%K_-251BxWQ-^ z*97hxt_dnb^i!uD@o_nOI6YJ{IIww|bV5SG$XV?e1GM-Ze8YqoKuUY!%%qBA>YDjL za!=P2u%e#g3)K9ri-(RsxkoFHx;^1&2kfYmLmDzbU1!fgMa!W4ZfpN!B5o8dLSdzY4Tj6C-$6!&;HNn%iZph0&l?t zNmqz#hs_f4-bj`D_VflwJ=`MQ61{iQGvn{lrZfpUC;vr~7vErHScl?8u-*w-ZA0c5Dqa|tf*>2(oD{of=95H!PD-D{?HWkFNr$NB zp|{e)`u89M``;{OeYZEw0eXV^N!~lMg>M|((ySt-=j}IITN382cR~+q&8ez@$zY*M zC>Cm~PXRC8e|{_A(CzDfY71K7iXE`r%0b)&ob@u80V(rtMD|47DLeLU9W@c&tkkSz z=VlnAUrTQ#OR?2Wsgj}|e-vYO#fu|7MnJobfC-NpI?vv~;UFR!HCkGv}|2BVOB z>%A{w2^AuZsC_%z;k^8`tdBeIO<>Et_?O4z|GnF5xUPo)wZ;Ax@yOWnSbsxeLMLbl zNOE`2pll$y>q}lRcjv83lEE=T3qmSejxXTy{^3XP#!s_m?P762UHkm4o29a(!xf2s zx~E<}p3E+2{n|6bK4PNGW!v}m5ND0CTpnDKh9MVy%+##o47s!Ut$g^D;7$IWEtp02 z#sf94faSG~!U1QDe5-Ci9q89ggJq*ISIOBRtYDChBQJ9dEo7U9O>-gMs>q&yOB*v- zt|?($;KKl&5yqgm8XzPRZ&ykhdqm97VK~8)c(7pR8Rx}1b9r#*LHurH51~SY$xAJ7 z06FnMQO%tg@z*tffTt;SVGombx?;X@Y+eV%91w%G8dAZ3q%eFuCc9@<%_6UnY+#=M zJq2*@3>Zm}k0NFzX~9sv6J>rFj8h0-I0h4Pg#||Xbfg>o^p@uuzu4=5)?BtIkaOT~ z1crYmz1GPKMyDh)ZxFTJ=LD6pG1YI4oY>@H0q^Z_NlqHJ;Sy0t;Li!K7ue2u9eiJV zNV;Wqh%|!U{oFdGZS9S4=V`B0;xpg!9XA_+sBZUuErZOSM>!D<8BShIgz>#xB+T;H zzXu2*CDif`+Mh^6cnYTD6&_@1wpi82Y?FZLQ4hGXaXeI97 zH|Xxr^C{_1x!#S*R4LUWMfr{1xc1D*S;+PVUfE9HHk%#Nn&fI@-jBrgai-P;3ms=Z zF_8p}AYU&=-e%APd@xvr77N?->3cFP=+P@AEO?+@{}=BN+^iL^7jRmr?efvS*+%B3 z%)WNJ2_Ob0VZF24o*jfw?DFMzP19g}zOU(Jnln5dP%eVIv@cC(wCUqHx8Zg zKo6tEDS|>3SEFN?0%RkvLBjn&+n18Q*`9SV&(iu3)9OGYDw7%N+c!ubfy6~E<3JQ( z7KPauGtK}<94k(KAcfgdIUTGnxqi{0%Me9lW*A9rqXu)x@F0VfEJvVTTi{ZCHQz;4Kh$<`G{n3w<*_?fnEQz}DSDy#ML$xaZ7@DOJ~IfURQ>`(RI zJ2-x#CtsyLKVybl?3s_k-rjpTj5a*C-Dhbf*pU zFMyz~)$FAr?pK311jrfbJwLE`rbhL7nQOg5U_!}T-U!#Kn8dL4o7cjjM+)? zfs`v!%1Kzs<+NAlJnOU`P*)>7-gFf~C88YDArw zN0%l}N=?-tV)G%83C= zxtZhv6B?f8e-tX$7q>~~Y{(H+_`-p8NADOup3S<=)Xy928Jkqv4~S&xw+R!z>gMsip(!W|#;EPhrCq2NsMikzTxv#rj(XC@~h(ZSdL07v%Qy z>#HdAMhx1*Iv`&+qd|U2YQ|AJL5mko1r`gRdQs~|kefe_gSBDz#buFCPZG3`!weSx z3BCAdt&<#tHUDlh?px3=Y@fjGGm~yf#V)5FjqQ#Cua1o!B%Gf*@O0jn7a7gnPu~)- z%&F4>BTtylrAzVx&*Gn6;i8wfVZS3QwbYNUFd(b(A;-gZBHVNdw~{yza`qtiR4;ZZ zPrXQ)j=P|_aP@NG&X7EOPc3@|oB&@q;UTO?m2?E?uPuZb9~yWPfy&f8d>T|_xH}C^ z#O;`KG+qjUlv48^PO~kO)z_f4o+8$!z>jJB|*Ct`r{IGa~f} ziXvZzyIE>TiD+S4_DEG<-}mbC2QQ9O@nZ4z3U?VmO3Ozje==e{7J9Fh8#K2 z4fQAgl}2uud;RJEghNmpm^ohi0_Q`vm^OP~-tbHc4%aoOqldf0iq9d|rO;{*QAP2d zh7_Zi3SYW7V3$J%Uddy=l*@h}QFs19o(LU-|N9)kM&bD!n={rF_z!4`SAXR{u-uKsp{&oX2CwsjMaxfPc?Qx1?-GK}r2X8c(>Ko&JLvekN29?s zeNd9w5_D zFtbaE9Fe+5F|BJGb^2v~o3{SmdeO|tp*}5Fth~5=JuLiSmkbY*42^ z?FS5eZ#j37RoF3BxnISX?l`B-UUUD=AcSzd*iE$erMVV~4 zTa_Nu_-RLWcXx^R03?sSl{>$a_%d2|&j8gP_n~`&QReuA%n>_|s9M=u+dIEXmA7Q~ zGy`{k+X(Oa?~H+SoSoRr<$Np^a?D{}Pck5vkGlk(emt@vrHFa}*RSC3Cw%tKJ&l8$ zf4trvOb%Xt4}Jnz>C!ofZR4TS76Luin(k0*jJ$)~(R8A(GztCd#!yc3ToU4tL>O%* z1So6Xo7Nt8B+v_V@$FWB>#&v6T|S%J=(TL2{m{%u1T5T6m14_T$M^XJKj%x{H;cV1 z`0-7qDLh%X(v^Y#Yow-|*y>f-mH8(ko1mp3#np~rHFUkj@m|HZ!w;TJ~K+k?SfW}TAJ$2{Z%v*Ta!lB>);h$=%ks{7;PTCne zWZ>8fF$)ZZ(e&P2glQYVx-4p~G-`L*XJ0L!-@ugVd&5xI!FVy+&YlnH z;eE)OMatqv@A8vJ^}^#vXo-L#8^D{4eN4m}Ej{s9Lr{B=RDQn`y0Js>#;t^vfeVq- z5EkySWVd{O*gg`LqbcA5tX?m<_%m=WF4=IY-S9qx*Y{ZIV1b!e!8w{tn8GXs-uWN* z{N}dbcMNK1=)@3S-viV<{>flrkkRw+#O5y|^@3q*Z`>bbcs4KUOs{+|{=u^y^~ZC9 z#hu0#qERdn?g0xE9NBEucRx;B#Y^^U4PtTj9UKI@;5oGe?r81M>{FMIj1_)1UT?u{ zp>=Swr-azZx@ewOWO8n(z#6V7+p!qGz?|sgwr1dK?g2lTR9>eBn68RA2(82aVed_1 zrAgQHpxe0J;A(r(wsmpavPgGzyZ*XaRgp1Abh|7fGBPuAj+`Uo-plWpGa@r0BV*3A zdI1t(i&|M_$wIOv%)%@XLLg)#Az>^)@`4Qr_JD+hSeU^}BzPk8ob#W*#=h+adr>9* zbo5kG^47;`?(AtP zD1Hw-j;e9AZNaelF5HL(k(#ZsxfX>Zm82)>#wf5RUk+tItL? za>|GB__h__E`y`o*l86qIgzVqYPRfC8H~QP;2fm#D>#N0v#WN2yR3`6+u>;##v>Z> ztYuLf(9?vLjCQI!uz=1~Caot7g38Qj2RSKtEME9;%ULRH*QiC? zDH1I~H>#P>-sa;#yDAM$9IG5crAxTmA*E6$9R?Eo2FZmwTB|82lzZbXYT*N_AEln$ z$vvN|xy2qRXqS$AQe$Mqtuo+1O^x|L@UPdgK3};Z&OlUSyV;AR*^|i&7>q!Ke079u zw2ZGjKnOdd4%KZc*vd7hs0XoYNK1j15p-P`677!2$T7r0rnW1PoKXz&G(&4NcZdj< z2G0BY0Ms9Xv)KaXbrUr)w0#!#oYg8aLO%`=4FZm`)!}Wxa>zLx=D7j9J%D=1o8zsR zCPyTkoGYvBF#0L1r6@8?n;(r=6E-@-G*$o)vZ2RQi!D`W4?2n6d?Er^p}p<_<)wcS z#^QfQV}ndU)9tL2Gu?V!w-U9OPhtM-u0;jIefqw6B!MB|XzBC|g`r|_4>b7i~g4E@?s zhSZ>P&nWmU=RLJpa7VzBw5iD4FSfuasI{7pnNG($QXAIXtuoX*S&g58iHGKCMRXm) zrq~m5)N%CQ*}A)_@N9RTNFw63Deo<&C~zPzF-5n7Xdu*OkqW?>+mu73C&xsu2a2V| zc7y_yIZ$?krtlQta$MrXz)1JSH1PEfp~LmSaBMZl8GF~3dv@XPh=oH8xlWE7ys)z>xwy}FOYoRCTq9$- z8ZX+0lCiyou-XcpMQ@$4ggje#w}qE!^UkHB49Z?|^)w+n&oEE2-Lf)>6BUX(Fz_}W6DMXz! zmU6ZT0Sw?{2R8wmEJ}77lgvgyJ@QUFCz8LjVt2V^2U{de4mGa7QH=vT5$d)-Oxhza zf?M3%j7d)Glcs<~PS6P~qxtUC@8Xm%QtxU2L(4DK2r65(WpQ)cSBO5>M#sH& z!BOwi96-2`J`|vedz}FRl<BpvSHVU0NEaZX6^v+e*^y(;+tg84mJoscrH)2kp_D1A=jsL z>*LLVIdxKO8mTw5#mw5iw?L61JjfPks5m{%Z;P_SR<$Wu6;~ws9ruzpR){wPr=~`( zop-fWFH9Yd95}0v+9w3pPkLt)?K9~gn?G;K*2y&GJ%_Tq8FB8ZlO8!$v8|ype&=r>sp`>dnCZ{{Eebuzk zLMZ}LEc#@b!+~kI$7XMG_ZRO}IiZ_dLBN+?Ky-toX+QFAqom%bI+$sYNUnOhsF2n= ztmfAp!Dl-pgLnwTK$l+x?}pMA4Olo0f5@iE-D>PewkLpBkL+bNk;r=EvpFS(2%k+D z%#nt^Nh;?m?DwWpO(9s_bq$<3aG>w{b0Bz>b}azEsIcySmU$lapW1x5w|Q%#F3a&0 zRQz3U*s`@mQjjmB+gzZU;8Jk&GI7gprnLR#k(lz-9BI}-fDUb=c9@&nj)@g5QuVy9 zoa1n5uNw}L@hYi7!;To=c+!R=R2@k&Q4s4(*Fe(GXm!jhF)I7Gr)Kk0Mke`f z9nIIBwVH@PgVH=vRE@-(DE;cZSyBUH!6H#@l+|7?^q1R7$PbkK6HaYs)A(RXFXK=tvI`gw))v z>m?5o@i{TH96&P44R|8B+0J{PIRd`~KKlvIS@64ceYMcQ*rcj~j#_%lwPT=5*l>oF z;J8r)jX>Z5xvI)aA)>Plfj?4Of)OWl>L&VGmG#+^jp9b+9^ap90UU-S7equdjIX@sxrugU24eJm2Pl9BA?bt20P|D22Km@8uBJb+h>m zYaC>BPvm8B7=&cET33@&(P0 zBh7EmUY$)--wdov5YQQn;ejN~DUi=bY^JDl#IgG#bYkbW@P%V_McKmsmb$6Jm-Df3 z3|LbIU1IHI?UTCDL2wFOBMv#L1yLJnNdPx-wB9EGeF1(zgSE4qFRn!nkc|CE-Q~S1 zmvGjatdJyVsJ3>o0c$7eTyLiIMeNCJIi1HxbIFauoz_6iBHQ$|^FrcU@Y*`q`wG|J zB@G`m;5LnWZi?bX@NG*qiX1I2S16c60{M0J05J#8kkSYF|$RD%#>UK&W34aI9|5hGxaHVN5S1v~JC z-UcZQAnJ--oFh3Bro?zZYSUh0k6wEX&OVm%F!ZEBPxFAuI(0e!)YQN^Gt0#9%lwO}p+P5xWT6E%hzG~nY z-5ZpuI`vUlFmp!}Z-sgdq+U8h#4+P!edMD_?{Eyyhl3u_I*Bx|Yw7d-KzHU7ySrs= zqARCNX)VS9V0($`(i4{_Wbd8%;@-{`Vor#?E&yXKYIV8G!D>bWI%~mgR$R%qZF5&> z#gyd|FfVQ`X%iDVaEOQtEm#uoNBtfa8P2ptA9% zCcWB-2#RJl&S@+5>Je|#(oNZ&^kY)FX0NGv*^=-<>YW>Q@RjZ!#0__IEfA$mZgYEV zAT5sv#h+?#`5`l*v*=i^XTT}XhtmZ}=!_m>*pnj&Q%63O4$UbqagWArtc99YhPByKoZu2Oo3NdIl1}VfxWT49j^99Lj6&umPaQBvSsa` z*Vx1GkCJrtG?6l{TB1yV=-Vg*4?y&rkI7Xm?X-N1qvuLS4pgx&c-FjfG1JGMUtAW0 z(ehj&Bw&bR-j0xiUIUNke2w^SvXkH;IiRXzadF#291^=z28OJ?qDq2~jTl@;MH0F! z&G{(zCH1XGj}C`A@rNi^>^bVX6S|8H*2BKR{A+vHLO$P;oiQH*S-9iHwjqG~#8%A) zcFEuEW#FrLH85Yaz|O~e5TZ+oK$gaQT8y=7iI9i06ppdFq}HRJa5KP9vm6c!7wNon ziSe-?dPK*O?W#M7HlE$Slq44$UI)BF#dv4vWVG9wOoKtQ*bD&F282{;nQ?4qZuPJ8 zV$mkyjH*;5RnxYNT0l@VIvX-+%jdpx9Y+=rD|&NQf%~DoaFt7L#rye;-=iup&)xWn zs)-`X+Vkal#2auN&i4|ERW%fXb?ZKggze#eBVYn6(MRpAb2d@mlTv`66f_Dsx4XI?&w-X24YpGb zobx;AeN+sDjHwMWZK_WU;k1wJc_etVfim5i(sUzr82MbunuHoV4Y9SsTv9ARy`m)L zfOu6OJXn{#T8`yHlD&Zgj&N|D)%$+wdt>S7N?Kx^bbX6bF(mZ_WA)>{eyND zch{>1EG^OfSYc%B63e0jgNljG1$n;T7jb9HQ6A zw}dz8bgTo~t_1K(E!Q0}l6xG3`1O(-$1LCoOl6w(fE@4jz*8U!DlL>A!RxHr?uggp zsJt<=18XP(ATmhK-tNMTN1(3ZwSzT5wREGB6`bmFdWC= z2qS<&G1U{E5a<(C7dU&LFSMYpm862!kt!7Z0d0tk-*f&g!T3j=X- z5j8X5>(s#jC7z^=-6QdB8>-j5whOq)t;98lIe@rBZQa(_lZ3v4v7s2ZmsW^GB-FaB z&MK1XE5*oH2;Me0tGloo(EiR*w_a}qP9&UuMk|>;g2rItbROpiR2CQuZ41n@+csHT z@^R%H27CzUGh<-2cPyaW!;MxQ;2q1lS$j0=HM^)CXAV%wj ze^OA;1wzV;f`A-$asqi>a&TBl#AMKh8J}PhUBMxG3KL?~$IS^7CV3;Ty z6g!&if_p7+iteN|6Qv)Dz$^AqFm;8@O=5)Gfu{FxlF%ksX)U!+o;g59o|y z99&rND-okh#VN=&q$a3$wE$0>43+dI4QSK>u9g?UTyI9EZ@&Gk=1-s5%H}8csOJgSZ*gmOKWv_ zCYICr3P?@@;8QOBFQ;V*7pcl4%|8pg_w zm?1v}KA`EK@9B}Sp|-_kI~_Rny>H@}?Eom+sye0#zxIqfB;dxKE){Xf1>0#KRiW(- z%CUHlF}J)huSLt05rHcGjin&bSQh-nLne*EWH++@)>gaITm8eQXp!Y-7C13NhDRpjy5Z(=eSQq&Cu;MK~Ah87Qa zQx1FQj{=1Kjuno@);yTgOffnOWe>DI$6l(aUvjRh31FV}Z3nzP^DtSn2<6DOIH>p- zZqM8CSa-(Ag~+7?&Xnf03nHE-a0Pt=td5a_gB^2B6=G6%O5~slly8U~1n)2PH0bwZ zji^iH^&sY9*D0XbZ~oq4m8w_tgr3LrX8UvtbV1qNM3uR?WbFe4X1MO2EknPk+fwF$ zL1?fJt6t8mSZm- z))U5}J+T~tRsi(n4mdTaO~1i!Re{)h;|h--C~+s_Ytk}HV3nyP8SLsMplI4%cUO8o zPwz$}i^(86g>P)u`K;(oS{&3fbwv%8Pb8-v^Cw7!lUb$(tiFEm%Jgi6kV+$pz#k(H_x z@bSg~84iIsrF8=CNV~guM#TDJxF1l9sbQfQM~-`!hYo|&35@i&8~95`))2(Xs8?E# zZYTW=`s7}x?E+ZjIzgq$ZVC`VRq`6&0pY5Y+g00Lc&f=sEUtEk5x}N-=uV!JFON!wU@D(k}T&JePXZIx|yzu-e`$EDjZ%5aD^i* zR16{oHQs@_P1`1ev|90SJuEVth}Ky+%7HkSd$JIa6gaN5L%Lk-XU3>&pP%d~CX|e* zc^_=mhEs#xEro7GU1Y6)WUpy+COduM?Z7!a@&$5j6_*fW zi6PMRqSKQGSyOP**d)tAJl7F2)&~>uj@vQaAPR%r*gZ(f^W-wqVt-mfJi4*BCO~nq z*MQ49I&boGzvc?!rpQFr*R|U*MI{Mgmf4&yd{gMg9kC+~z=k)!U0E#EC-pd+<@4H7 zsVb)g!G)9H+;5li@Nknk%|cPgh16;-u&x;JI&uOW6Sx$BF2JWHLssh#?&U-jM3ZZ1lb^ zH?O&mqrS)aqf5Is5TE;nc+`P6&sF=LK$@G&4HUwTevzq~;-hB1$OE}QYz{=w6R1L7 z&XaX+&nW=H?iLI(wmMEBb?YVfKtxjFZ3wG6YoHgg`u z$^4j}3=zR1?P?MY?Y6*!2bW#w2Joh&C2(~UyWP=OM+%6gTLbQK=+dohbSDC|^A1PP z5>XO(ke5%UkKyjX1vd&M3J*Vt2e}h7rFye3j!HWdo4)vVz8`}F2;0jE3WG?Y*!4b5`bE^w8q!{v|Z-@h&H-ge>hq7Q(NBh)u4S?R$C-lBoEyCM4BvCg9D4(PF z#dJ>`M!YmZ0ZPA!7DCmgxbyV1E-g7+^_;~}vjk6&IspLKALqbhQQ{0@-^>mcBi9kD zgk7^pWETr%=SDjQ$o4QbcHA`?ZI#1#+XqNsbYqWX&KhkMv3~vrWRyhb_ifW#p0!Dq^)xqNRC1gNd1O;NM&~9H5cyZXBN@m0$OZ5r)W}_Pg!G?ZDTtvn*5GjW%M# zRMq(SM;YoeR_&b{^n&(|F7^$6WCL6P2E73yU+3+}TI|D!_M!tYp~oPWtKo_Ox{g^t&?QLqW^%n?Bbc?Kib99va2ij5399G-NkS~(hANfov_k*o`Szo9GS*R|9 zide4%p&=sScl&>Fq;ENegy00`4C2&CR6UGV<7MnGkO?&Omg%5($5~bB5TPD+#>#EG z_B^LEJ31u-XJEhFA9w)Xkx3RMM(GJXNqZ zGWnjC)?hig3AX^WccAC;sP43+mh)M3Rw=TV-`t{m&8zdMa)22yqb8_d1sFieH9iT# z5WvxZ%ts&kb`bA@GF6fZ0RHAT!2rRgjzaF@N-r3<_65L=US?vMlD#yq9FpY_n__`! zidKve(>tld(`a9SZBHntyAyf zE!cFOuCP{d&Lnn`qsyr_Cyh%`O~MODYC!y%9bhC0gOZ!ImBD#vnWwJOMSWM}`|26J zbOjq?Ukv6)`bx9DpNfL#Gdt_N9Z!2Gjn&Uo)IX;_+wPuhqc=QiZJH0ZF>f?{^}P+! z7ANot1WFwB02nUr>6D?boj@Th!hj<&kA2$!kPsuzMOm@+F0W=pv3oW;M%Qq`_F_uA zAfkEqqh_5rImm!g?R2r9+;+oJ5Xei4@2YjQ4fbhxK`v8{IY6jXxi$DLXFWv$(G?&t zjlL<7txX(2?u&hfh-!EzJYNyI-A=j9Ws{98(2mj*o<34QP`^(AQb?}H6O3k@`MZUA!aTHb9sq|m@)_oYt$0~*+r?z6!34kU^aI${BcSju(hb14k@k829oq?sa^C%3W_Y+8V=Szkx5Ax%C>p!DN?@Js-1XM};^o zLw>GuX1IhU3LJOmYTOh7Cp7KMF8o=STgJO137^Xm5ChZ%UF{FXMQvGX0cS_nHpWKx zxVTW#3HbsrS4>Uh+0*n%At0%5?jSEJK>9zn%|jivi9Un%ZWrcm&aX~3@5)^z6^Vws zsaqj8V{XCx0OjSms|uz}t_Jx-2HZF*CIy7B9gX!t1(P$cWg4|;U4IQM(88y?a}bEo zE7Zc@?bLofg|DBIM_>;<(*^;2#e90ZY&X$ymRYCv4&*hP1StdzFAV2+mY?t)Vyc&f z1rp7D5TlxAWQ|2~eB-HCp0k(#alIDP)_KdOUO4n6G*p31mvZ^i)N?$>OcxeZS z0HHpz+5S;4KWg%Bn;KTwx3@#T4X3%3519=6p}=jsII6VINN+Iffx@{8@KxM>5B0E| z9g8=5IUfRr{a!2d>p#CwLb=5({79S{WtyTEAcbB^x%1(eNVonH=SY)d^=Tg1vN zjZ5w@Pb2F@gS7y)M7?m#Ou2=wpBrw0#s&vHbjKD0QCc5(aW1T!wxq3knKY|}p}8BT zcGLsG;&P^eEc3Z7dM~*w12Yvfw{qup(l6RWCc-(sV2eX3Uk~mHZCN>@PlpsJej z{?tFT=~B4e<1YinUI4SHf05xs;5$l@&q8xZstT8P!C=>$#EtPwP0q#|IH^{bwWcU- zL+aHs>+)P*g(b9n-nZaT%Yy49wY^|BS%>{$PQ`Yt=q-x5*dxGwV)rd67p?-LN{u#`@_nSck1S^e zRC&!m#DZoAhizZH*>+%RN90c3)i_ex?A0O)HXDA;0~oLq@6>go7>Usj7IHa1t!^hP zi2D0707nnOw}-3F0o1;3x4g|N9ss*F1!N6@8!5%&F*fe>RMEX^elo480`b<$g5-iB zQ|4GwCK88{f1PYEwYpqZRlf!_(GaN!oxMOq5wzKOkMH1@`_GBT$nw${x1}F5EqTNky&QcwRQ|1I3D~1n_=o?Zl;wS*2 z*)ZYeBwUUcif>QMZ4ej7?vB3KofXhYfSzJx8+{xO1<;9XNx!r%Ck6%CC}a!|ZCzX1 za~UeK1U(o6L5n?Nf~gBY9?(W33C2e3h>@CjyIFdq%nFsy}_Y9 zg<$}4x&aD-1sZn3wAWr(#;A02ax`D~a+jxFmm5v>u5WHp=DZgj%wM@#^) z1Jz`WE#p}+)nI#5?M<5$s4MblXueM#-RlTQY}=!;@9G*%cfxa0axbskfvItI#Nb198P{wZ8z*g=i_F4hU1Zuxw=jLMys6U{e-W9r{ zRW>piN@;|nDyMs};Xotj@Kt74wI@`CPyx8fii8?4_oR1@kN`rw{kYZpm4 z?+1rG8tVIQPLCFsjjdgWTf69TGm6@njiS^JCxl$&1l2DSehZvVxaDJ&O%H?gl%ld@ zsv&ZXz`31YDP&ALNoRVHQ(&Zr;6jYaKH*isCslzey<@E{L7myVFm+eNRk&V}Y}8St z;-+&)H|R0FbI(eAZF)-MbJC_e`ibR?TR!NW>+5tbgmQa0wL>L8kLhhKci>|0XyOY?gUhkbQpsm}~ zVA@`QE4B?d?N#4zD}p*D!KKugK+~`fKqPNYhz>p6hXyZYAdne~^mPP)xpsHN7h)`| zj3%dH1rCnmP30|gelMyHA51Ea=X;! z^L)2D`a@Sst(z#WSH-T6fT#`AO+TPK2_>*yCY=WZxH|HA>O~=a>i>wPk;0d7e6S{RJ>`I*LRB(D7c(|>!=bH5 zJ&T#hh<`Vr5i}n%6kj5r3XxOQi5W61fN(inFanmju{bWS(J1bUXD#=Sv)v`mWVWOh z?R>K}QffmKDU$NcF^WCNv_I+~7Gqw{i+E*jH9jd4Krb}RTGMc_Q?JvbyaDLMf=r^o zI)rl#Iaz!z5?DeVAfxTP3XUDiy)nlXVL3~lqj`?vT{H|SeyHkoFF8f*b)T$!BvTJK zmOJGJzXu%}cp+BXkvF>RA~zj%bg?Ept*4&|dFiP3psgCkC8K-%jGigC_9Y^d6$*~d z0&0PkG@HeT+leKLwOz=&+P~0gp0UnARZq($JVxf0o^>*MR!*V<0AgA-AjC<0IXjC1 zvic0VyBzJ(l|i}d1w6!>Mz>cr=mldNLx)DN4tu_!?)!P7=-^Nv4p41FMweMVF)D2i$~hX)jXXg&be^A3r?flkgE9V%XuWEu=(49?fU;1}N>Iu;JvSNL81`xct%{z6D=r5jZgD`3 z)dKW>InLflQUYtu=y+OHpbrKg>3YJ_QLt+}j4K05keQ^(#uj-8JFrwlZ ztjOCTUjs?GEqXh4s5!)$n%gm#7MEPn3(6`wb7%;|_6n7CR#y?g-8?9j4G zdTwTj(R$&T&M3aO^yiTQK48{9PsB>x_+ooGF^DiWct!z?sW~aF&Pnw7&NOcf;e1Az zAaS3uy4I~!B@9Q$XtfK@w}F1jv+x|w&_ZVJ?<>l^?C5dMpHdLL8To$DX6u&c^h%_cxjs4d&f2M$ zJ7h{FWU(p7%)qFQ$a(BcStp*G##Y!f(|&y*I`Cm}z{!QHgIv)wuz88#*1d|3azT7y zM4ZXAi+w$Y3-2y>;r3+47Ys$UXWNKRd9<=e^egog&QLeAyePOWxl?qQedS_$aw67P z3+|Zl7bp!a<+U+J+G?6v+5~AmAd!^7ZUz;kcKbuYQ{lNu;=qB~t)~O|d?sxGx&bKP1an66wAPNGyt4<g;cw&}`eloz?{ z{;{6j761=EfKI5d?Va`Ah|NgxH($uZ$~T><_*T$2C@mca2e=|rn!IIJ2S zJ(735YD29?<0Dd2@AvihI>xDYymW{6v0g0zHVc_sb+ZZd0Q9;n4QBr|p8+_|Ox%z& zz+=UdF&Ge46){Mx)|u(VV8xxzXIF1@M5Qr`6oDb?|A*(~ECTVIN%a|u~$Cpvc@$_uU@BnDU zWa}%P2Pm3Z;oAOwakFsmYOy`oeW;;{9}iC)Ov&j|*h8#jVJU1~5~gXdmfGYQMX{Ts zqj?v47hG`->UrrIH=gI^jP#N#>WdEWP>%wwuy$L4zg+AX*`7M;dgsC124D9nBE?|N z#lFS?xnP3ym5krDv6XBc%UlPle;yv$eyw;eNCkGD1Mj4~KMcbQN_utF+wJAD9xe;u z9~3nhTs(`61jUoIa&#J)HK(%XnJ$tlqY*ApGBzb=i`)^S=hyk(9zc?R*)5c zO2}>{sps}^bklCuaF%w&JOww9SnWt~#%oqu25i_)h{Z5-&fFG|a#N>=GRzyGij2ZY z*GMgho9A^@|F})gRJFwRJ&y1$FFK75Z7!x8LPsNE)Z5YPk&J3d`-C8dx*%EK ziWV|N>;=4PnnV-`_)EJEKhfL;x0@ghodL|*zy!+<5l$*@Qq^Gm^e$Vn76K5l42*Uz zMzEj;sR*3%+@E{i;2fvx#MJWT&>Q4RmqMpv}O1!j?g_YZl!2tj5a+0eXg*_B7vS+?Gg*JS`U3*FOTe? zR-FsYV&jr*OHh5H5TpT!r$Mjsn^}yO0f$vY8kL8+F)%= z8k`FrSmSB#g3e<(@B#*@8ceW6aTyzE!7WgHv$q%f%f5p{GB-p5E;aW`z})l31F1ES8;@tn?^eQwL!N?VpImFQ}fDn@KXOUP4GO`z_kjLJ`GoSkI_)V^NZ z&mbPi;FvE70ElBdx$V5WlP6#m2;GSyFP5T;L{A|D_)_|NZWl;s5Z*fApij zl3B&OU)}H@;j{36Z~pgxH2?c=@V}4$)i2+K{}+DwtKmP!|NqLX>kohU@GFOZ{^wsF z{>9(@^3CDb@ynmVzdwtA{}TTFxu1Xe#UDKvc~azW?Q;?5UylE9arh|wuke(^PezpZ z!H*7a4j&(W9R8tS$0xsZ_(O$dzW1o`m;S_$eq_FWU~~W9Z|?tb_`m+C$4&QV{ABzi zI9%Vq`Cs_z&0qWx9PCeT^K0UM`Nc2WXUF}rdEVcAJn!HB@wY$ki{C7=Aof4?&S_<) z&ZlmH(AB5;`P1xtD&0@>gZpXoH1oOtPuI7eu5aD1Z{_FK{rVQJZ#}Mm8YeX4(8iej zgOC2m)0iASeGJIq6O4Z|x=%y>=0HAw@Wm%9ydBMYJTG=zP5=PsEI7yJsimEREIY?7 z_kvV4eDvjgqJHfcyy;*6^6Bm2Pn$XVak$5iuTIlfCg{*XPvpP!GP~RREeGkP-Sis$ z|7!c1v1*5S`Li{pdGDjzNXO^DTx z!*A@xum1%nC|iN^`EMi-+5e5d_!kI#^sdd{amD*B{2Raj7OuY5!oT%0&f^b$X1RV4 z|K;aJ`Ma&3-3R+GKeZTt=cfOcN&0s`Xth4|Kl%vL*!sNX;l~F*b7SY-jW6@?2l~wS zN8#^$?^99%JT&~P345gns)L)lt>0|AheZ#G zYxzOx#x1Xi?M7!kbVA+w85F{s&L`x@zxmmV9{82V&94^y^CysxzxyQR-?YM;w>=B- zFW>)ozt?~NEBAi8oHl~ltZ?f;cb7kzg}e)ZM3Joo3l&))CW zfAD8cpqi`^dp104j6Eu>LVUIKOm;E7Y*@rVoS(`1@ zD^6Z;I(^bIQ};zW{^U2^{jS+xeDn9{$p7}0Vfsb(hJXB(d%s_DoOhD*{NlUh{OLw= zzNL#V)B44CUG)uJ`TjY1)tpyz@=kvV&-%+e1%CXKMoIZ^Iv=t{c^|4Ban ze5kAE>z?KF_y2&GUf*|+KlZ1;+X{g``cBQ1{`W5{_Ekq;G?V^0q#F2F*^Bkmvdy?< zxexozX+hh$X<(bD)3tTC3|mQh_ER&;S`W44e&)BNB5yu(T4wCD)-cS@Y5#Pt8ac&H zuJhRkjgY2pR=^$H^3rp3H{@a$36Cju+vb%ym_wTP+UF?2eNH3r_zaIUPuIL@LDQt7 zSt6f(FpOKK^H?vRw1ONr6(^^;JBV{A+AP1@iZDW5w{>V5(t;^`e@5iyhqH56x39a_ zSgXxFncFPH#u{+b)?DeKZIAX~Sw7km13?#Ud2ahVHEsQWKa8)I_5UAl!^--z5WmKV zdf8rn?TcUf;9WEBBKi&2%>H2K``rt__=A4(FWg5QtPzJRkp= z-+fvCe=rYwzu*7i_xAg{t>^!w>HK$`>-(?(^1Jn1n^AJYo>bkBa#_&WkIl9NKts2& zl;g+YAA|CSu3PO^{jX3T{|xj&jYHs_4cYz$p7(06`h{+Tp#A-?sEk+Y=1(>1=9^mi ze6acU3*I04fB2Pme7{=y2Y=&bu%8=vS4-b?3V*)f*)IKlZSm^que8O>LFkKd9|psH zE}JQX)@vo_EDOM!)ymW0)#;;^!ONU^*JpS1J6->B40#@_KhS5s3~%^9H$(g5@PGV; zM!4~g{+I7Y_|+J^ThG7sf&Vst%s+N$+d1d0H{_>~hsW=;H`*s~&pr3<_jvV7yYHIl zAED9T3{jAKD?WTKLs^`Q$A44Cn9U+W6k%@P763iKEZ4~p7UXA_Vy4s4m3Z!E6rB$a2&VJUhC=elX-R1?Eco5Yd>#Z ziIO|_^;18F6p*bCTc46>Zfv`)$IGB^5ChBd=8^YLTsS}OjtaPI?yr3BMJ;Kj+&_Ip zDiQp^>p!@^{==4(W$^T5aG)TF3H#h~8~p~q48l{NzK*t;X=+~YH=#doOTgpfu6M15 zerQIq#z*yM@WdR<#C`KA`AO6Jr>ilN%_Yz8M3dm}YzFA@?t8OZ4&W(U@fj-?&3JOX zJhkodg13*q@S5kxDFsyZxfQ|56ksoYf0RFIVX^~++RRpILZ3H!J#{^tBV+sBE1nwm zG(Z^ErddhqmH_}t9|QK7-TH0wY17F^JD%F`VM~2X`D1E-`|)veLOV4vFvzIyzImSO zCqa3PMgQ3;cKZ5+YQNJ$)8P?AW9)O9x^@mbBk=PB0txus3LwzUOYZvZF|Ey0oByh3 zA^aQz0MUI&&QDK2e>APR1QX%Fb=OMaC_|Sq;ddE=pq&cGy+8dvF3q(s{f3l6`fL+G zhxqsA4gPL!eDj9<vsDg0*ESO_o*pXR@L-0fZK@Bpk=Ox~O4CO_Z%kf_Jo zp9K2zcgyza39ladVQYg7s@#2kbynET;S53+yLJAU#kJPFUheMoaNLnuQ1&KauSKE3<>+4+=wnw}3^!&kHL718?zr{L=| zaC`Um*Q5Vv()*)dzq|DLuE!`msmtf@pLA-IEASR^|F_?yF6)OfXp|`Q*W-@>n(LF+ zDY9O)XCpMzeO@ED2BEk{XrCT-KZs+YxhAIkweowKvR40j9lg8t z^<~*(h@V&JE4|h<=jkQS`s>5i3R7JqSlNi&z(V}$nsl@0*A5?7K&{^e?z#Q%l=kDj z8eaI*8P?IyfAXRwunFNT^N4?jU>Uz++}OB?OV`ztMPR<`!j=Kf|I zd2adBmhm*^_ph5FxDUniHh5Qjkcy{4aUQQpQbYmXeDpNt(3n~N+pXX7Kl-iax3|v@ z!@Fq0pv8v$YC>}p7D}URpRN0Ik_XYNxqZYy8ao78Z#i^oX5;5e|DMH5yCTf+D!hAF zKdFmN1F<|Pg=YF*9`dx$G|hVn2tO&4>a+B-hdSwe3K!F3&ofcD-a1nrUAia0N zXjXI!V~0i1yrmJi0PTO;0~^t4u6QMGAGUgpHPJlhz0r9x4(tLOANu^wozy@8`3;NQu^F8%(SN5+*7;&|y zPGN_IUG=V+_i??e$9pS3|JI3k$mm1Do=5Tzh}43r}zy=mC*X}vtDe(i$~K73Jy&4@G)c#-2)mbiA{1qkT9SSVjjh=Q5)m^5%i z9dc~#usWXB1VV6kE4}ebJapvKTi?(>xw}z*@)PRgpJ4ZTxKbY5&(}rvF@{g(*jEJY zak_t23$I+cPXhN&Nw>87^y7@&ERMJL8y{+<{zQ9LBJZ{sxPSr_7a`B1^$@B0xmWMM z^8QeVdi!|pSC2byzV^ZEH)Ab+{N~-;?*sVuK7dcTH1~(QY5F$1q-gbj*WCvW=YYE+{tUmodAjqdb5CRcd>MgpzaLfJUGjPu%$qZA(xGSV?{%?LPDPv@!ei-zIl? zi0s^dZ+=BvkY$!7rtLPlKA*H^I5pkBeSaZ6+ZFF5@P1LFJ0Du-*&@L+e@b=ms7~kS zFPGdEaP!{IsYoM}-JtXj=D>f0OR%J&tP49s|%D$CV%6%p5Ob_4|omY+ZoLTc>u`THy>$k3auCc%;T={8e<2;^W;~!&(6~+9C{FX z^?NfTK6>gB-q1KYu+HA^@uS1Q^sC4H^teAqV5lb1K>oz92{%*6`EG0^c55Ff- zsj0OL|1NTf!oP?AHKpu-2S1Sm*J^UG?)53pbs6vH8HWEEuKQYD{oihG{>kW{V_(vn z{_N9p3M>3C@a6mIP2qq2@=^E?@oSUt^nw@g|8n*wyRy4aw$KP95CcYx|BUWM=9c^J zii>2Yoo>=yy2-RXDY?ybn@;!kGn5d6dM|{SGeAf@12ZDeuj;BwNFdnKK0Eh5*|>=> zzK9hoV*O9>hky7_r+F-r?jP&_`Ja9R?0@{n`hS7n!v6s}tk7TrW)5ls|EcJ;F3C^; z)_%mnghYX!gbshoh2-CHD2%Kv{v9C0P4X%x6kwv^K!Nj7pnsoCf2vh~Hyr<-Bme#1 z9@QUmqV%gN0u2KY$!9Y502luIzg^&1{&YYAeFr|`N7(tR>1s?~FDS$SPh*B36ZGZ+ z`vsuvf4jXaD40VT@vqwYzxzPT|MKI|0Lc9-R!{%&FTY3s{HD+X_T#<(GdK&>ilYBR zN`a^RA^uGN&F?+)e>z0y1N)m+{_XfIf9r|_N_pTY^Iua{1tfq!e_fz(^jE#;_}jn9 zf71*8!zZnQ?(%Q`qR?jld}2TF_n*!T;?{o(KK`8OzfFMY^Lyog3&HGg{D*7O{@9#< z8oK_&pMQbC_%8-K{J-8vsOJ53Bmd#Q`qvd@ie~?gpqc-_?-u>bY8&=<7)Ih4j+1{n z<^I3p(7!jpD2Bo~?*Hk4{)@bt2H*?)J(O#cf2{vku+RT^0si5??4jy0{e23?_Zne} zMgEWf@Si~U;~UQZe}gB&@QnZcXWhmB-I)C!-vUezHUIo9jN&g-MDtIE8gTyr47WZr z81&z#OV#FRy@16ROlYV8F)M> zoJZCF<3Ie@|K0Tu*bZewU{|mNw!`;dhKc`8*o*1E|Hps$&!B|=D$w8ChX3dP2u#F> zXuBJBQ(m9n>=4Tf-g5AQN1Y7+=-EYx;OAwRLz99Bf*rcor|SAC0s3jg^@#7H6@~7W zg6d+bw3VjDZPr@@OqD*38fK&%+bdCB4CK=pTM8BA>YBHFchxf^^q22;UmkQUCHEkxe=zIF!RVV z?f9I=aa@)sxfjH^AYbOoFcpkv%5erp*1oXmCHlkaW$#uLG%Y1^a_7!Pk`+(Zx|kc; z!leqccR+xdi3_B(VYU^_>QtZ421bO+UXw;oT7sEtTBUha>tB9}YrVd{T9xWdH+$y*TGia4g(>94TUEgKe(?cAq(67dwVzqf5)VI*iw z)n*oFadgt8`m`e$qY9(%P0&K$S^8bqMn_yq6P~umEH_Qmj3l6Hfl&*HuY5LoNpK{@ zrtBb7MX{V*xmr~%H0b_1=CwU+I&D`NC*G#Gf9a-*1V17P9iH%Q*j3(+^wC(Xe)Ytb= zdmn6nXGug;+pd()E+n4jw|p!b_BGAN!h^Cf0&11?tnY@h9xzsssJRYRI%6@-j4ME} zs5GaPTkGIN;zilBIOzy`_EYJJkE03G?=E~O37M4^8f|1ERJECR}tPi&H2a@dXg0<=ySc4h>*gwd5=ZKuvQV&q#}{N zi!dQlpNljFWk(UjryOx@Vi*$t5k8+SwcqtCMa0ErQ53T(CoRhQb{El2CIk>m=C>5wMCspoV+Be z7!H(|_?OHIP9corvm+9b-OO~2P&CJcHInFit(191j2mdgWeatXLR>x%z zIr$uzqobA~m*F#;&sJ!baFpr$`9ymmuJrg|2cy}pmRI`qWDvZNVOOYkF zc-c^k87Jo~s!`<74>ikMRgZUD$XW`YunUWZYoKuH%gOLkuR($#j#!n1b5dER!Qjr% zFf{BW%|sFzbZtHak#;aN4Ceh7DoDHWOpcx}Q$9vcxnUg1Vg|3qAg8sFcrI-z{jj+f zw|S0ZMHn5N!01EE8EAMGgz zLHTk+qvwJmCwDmo9~9yPAvSM@h?XF`%dh^L+wg6cT+Jx?Maa&5UU^F{a?1JX4YC@{ zQImy-$)zxLc7Cv%zq4<db|Ylt~Js z?pCwLK>-|9xeeyx9hB^Su#>R`A}(tY8XVk?_uzI`8#;I(A>} zJb6=#KkI@i`%OXun?pb^uCQU&BPo!0E-U+4vK=6<;15mJLSz zf=3-y3e*!qyUQK)1KK-WjF~D(-XL;}5~iIG#P{q|#Xqk4&S_sX%i5QcD=bA?X<}z3 z%yI@15p`h0pt`|PoaI-|&H+AW6oYlYU*puJWns;NfMbUC4HgUN{6ElsC79 zm)cm?d)N7?$}Ug7kj2?pYrlXdDS4kMl(}_@7fu`b4JYb)upD2%;!WXD&MX{lJIP0F zpdgq55^Tn1cLj+c6$~eyoB{PcN;XylS@oDn_gJ`|JNgaEJ9uGM?5mONh!sQ-v2bQ> zbQ`W2UzA5C*p322CpTxVQ7P)V*cZU>hbl);h9u_T+P=tl=BXUwzg}qj@htCGkRbEh z>;XY0nh7;r@A73(0gDf--(D`ybtq<3W4)LzG2Ya8YZ0UfRu0(0&WsAP)$W}{q-Wja zExEA*{u#v@xv*7FE`iLl-+)Q+=@s?(P;p|}8Y?%F0*QS1>-i8$gB;-8Q3vi6B9$-n zl{f=Y@C>ZVl;Vhf!8HZ6d!#S>>ab9ztj55ZyZ2rSXLx*Gpy`H}+pVytbM6@f=H4b$ zUK}MDmhkm+-pSbt`?xraVl7yZCLQ^}&dl{NBQzl{vCZ-u=d<3X}f-NVAQ>L*CMEjGOB4I_>p zxa87xQ8}kNF^jmi)oKx(FGH0G z0Y}!H#Xp=vgTQ8t8LCp4Ugn%QzZ;wE*8U|aR<}3SpT3)e>)UGWXN*kq9o*%$UUtV) zmRyJ?{u6OLDWN8Wjcl>U5_XM1|~z|Qo)j_ z#l}kxD#>Uld0eLt%;B|g13M)C!aY37B4>rKev-hC*#t%!BO4AC~!k0y# z4%{GY9mA4l)KXhu&bDdZ;kpVIRdt~AfH{1e%TjTZiejXk^ZW+>$7&OaTpPKBeJTxM z!JQdQB*z!f!$u@+BtnT^0bgx+u*Cd{dd4t)fqkc;eo0Jk%n)t`igQ{s$OTAx^q{OEnkBjOv zyJ~dzO(v1bd3GgqZ?5)(d!8;+BVrwbR5s|5tWNadchwoF5Ixj<%`==Y6E%(weeZ1! zWHolyplzW`Yr=aK=Y!%F(q%3GHs2zYZB)=&M|0y6fruptdSRn_+e^nyPz(r;a4A{R z_fU08Ypxk%6+*m`=Ho=(QHh)LUPQ=a{&cg>b_*fxNVRhyvwC$LmtEP1 z2|labSKFoGzSrM?Bh(9`&y`LyPIhNMc{;^4%sfw@AHGjHj9kZl3}e*UP;)0~B@@W= z`I?dR!rY^X2I0Cgu|WDel0nshVxF+#5^pW@-E(l9Q5z1F7>S98Da;V&5a8d@Fqp0| zFF8lUki*|2>u=nFN-!iffq}L=ghIxg`&oICwnu;r+^&?f#QcY6FzqB2jln?(#$be}JLJ1$dxZ-2JS2Xb&z!07pS5j-dY zID!KyIXf_*KTEOuoMk&pwxC1|qP$6T+$=M8_EPg1s+Lh3V!kqiwWxCuZ0pJfdGHHz z#}C+83&E;FSl+5GL0YdjGz;sZltV#$*Dx^uyb=Ix3O@BBGpSZ{+DCKy#!2TCsE#-m zaYf{kljm#^Fw((G7e31qdn>4`i55$$Sm)C=?G!D{nQ&;f8}^6wK_C}5YE^MTM&RZq z2j`w3yj%D1lgz$7Nz*Yz7BwgdI)WnFDox6T|5-zXO1OepmklmZi0Jvr--I1(IU^tF z#?KVanN!4VD5st#2Xax6Lga5TLD?YemXProBBJX58}B^1yw01 zTw}S&)@v75wtP1n>Q1tw5j+5k*b7iTZT#(mnps!fz^8=C8evhpx~oA^?QX3-N%6wF%v> zqtHeh1<46_3P8Kw0WFrjw5&#q>DBJpc1_@tze&*0y0S`!q|D_(q2FQt)(h9U=^J^} z@3aOCsSfGvF^^wVW>L~NDjAgEAV&y^f7j~8S znOiR?9fD0v0EsfFv0PFB3kdGw_Eu14QVQFH1dnhb{5 zDTBoa&bNZgQe*FfyC02k6?#r}Kooa^bdhEJo4Z6jzCIDEB>1-t3gp(hkBT*N;s#om zDho)DJ|V|>A2zyzgxD77^?8N2I8Y@c_q#JN&K#n17;z~K!G94jOTAbuZAnS`x;S(+ z+ft!3jt}eQBt{b<>nDB3Dd+VaK?9&1(-@*q3siWmWx zx6RMuMO&bcs?@PLM^6vpmL-#ZD z`Fm`5_V+t}x!yP!yZTHz-fBW9@0R2?kd?D{^bo+s?xIiSa=bF2o=L+JUOo~hjtDL@F#_H}KJ*or3QBD(LoaL#>ad-z%?o(EAImRWbG66g(5 zoVPum=+_=?(YmgnVnO4ix)f!3QjSyJ?nqM0l1&9N+i3{&sXm zx%QaA+i2Ni9E!$pLc$9{9Z@P*_UuvT`(+S$wO8KB&g(CA|;N4WR)gmWJ_VG zwQG-S8RFR^t6hq1UK@u9(%D<-x^1r&$6RKHvW`o(9B9KtvC=GLyW<`KdLu3OyIj2ut5ZSS4#yIf(bca9~QXBbW+f|d)7*f-E@WEU7Xw@{xbP1l+M z2u%uF%kTX5)ED^7gN8f9w%co3MO(6M1a0CIWfj-#{jW#NYZR$O579H61?&Ph#!~9^ zrmhqA`uRH}%?bALQ6#Z`*$qrBMV@fZHTV@ML=0_DtUk!M#hlXF&!;l0mJb`^s{xm+ zxF1zDjI`X?5!P(K5~-EDb@OTe_-oBj9F*N9K6AU~RNvaq)4ssv{(11Pe6L-_u#)Z^ zvwUB}dru!h`~XeJHufGtD-zA;d&u8a^S;wyd=u*PVUy!+jkf@<%mFfGw@>*sL2AWL z63FVLB%Ac{wpHVoi7Q+HWQqLh3!A!hCotNOIg43MDuKZNC6;D!vMuyc}X4n&=%+Z@hW4n!lmGW2j%R zPkju(D(T}9=hfHj_QyBPqt>;aDZ_j56}tj@&{b*{GbI*=AVTH6XHk48fs8>mklZrm z^3^`DYrTi>rYqwmVk)b?$&2<*M?lU&0Yv!LtMn<%TTOky5WMWG53JUyRYmPLt!}WF zRY88{yovn+LKaZE^&@T9C0`3zebrIu0+$bmXZUx-eI{hRm)JBopQe7nMfT-qE6tt2 z4-rzj!G0CIP!2E(yZUf&9UpV+nbp0<1RYZYoay3Pss>_KFh^@NsS+L1+k9O1cTg&_ zn+2{qSi(czvL=;v*9;YTx6`}4PmZJPW(G1rv~X7gs9y*b<9;$dgcc zjA5Mm^&WHB{qL4AWV@7}J#!m7zSx~_Odcx2uZY)K;?~nWRfjox8RzG`(ERWslqBR3 zs@hVEV4Js_7u26U%f4I=_Ju$4QcNx|rzp8z_UtIocq&&rB~j`92BrG6j?h1Aa0VHl zI_B>ad0ufVYB-Qt+R^HY0JPn{qexFidU|EqeE{)x=DI-{Hs)EWJyqrnsys@fkm}l% zu+XOW3rodG0v#6B-LTQ2c6bop?La3c~ z2Ph$l)i>9%9rSa`8(s6_uFT=YXiGysd&fi{*pbMwAcJD=b$wdxU{~40F)j6kT4wHU z?#c+Tmw}}HmZ7LH?<|knR}%2gaJ4;pM?=uey7NLLwj^oWYvrC6z3nKC8blagGB3;M zD8cbQ(PQ_6rSTs9)I%Xg?R5%o4GeF1{keX$3EAZUqJ-W71j59H*KPE)KFuAv3z!z4 z?A3a_KSaSugXdirh_5h7eC?a+Ss%;!*S?tl{0`ac2!K3RQpmkvDk(2G+b0`3-{}I< zQ$Z=}I!P`*lmjEIi}Q1dAc4SDxxXrUu*-w-2p+7o9?`6kt8k#(7i}z=bSCBw3gAnC zc6mPFpdP&L-r;)Qf}J#OZ#h7s-bJ^++Mi=ks!qGbG=24E3IGoGRG(#r^f{9^ps$w= zD_AP~{@jL|zny@Wq$;2^*s9%d`g(bMg}hz7^|@-?_jgX>F*YxQaKi1&meE8#(Yc(C zc19U-cA|Z39eU07-Q-^wQWxgfvLHUr=XVSgA&XhlysXnd>1AuQ$Mm$CF@YpjzeJs# z@NEAqOi^(oLLyTp{{Va?w+p}yG!6oFWJosetd)}4&qMUQ&hZ1ViQ8i-DGNu@=r-Ue zw(Bzbrh-9nUol;TO>h-Gs{YAXbvh`+)mmc3^Lz{L^0Rv{Gd|uzP-HW2;MzN&_kh~y z@@QQx9R(@{7~QAWWQSr#KG-|jtqh7$mVZLMF26k?W^WR&jlwW)3N_Yh!5KW_>Q14@b74rhiRU?G&a@SZ9zE;@F%P5}(@mn(8*%E* zYJovK#W*)5(2JGw<^=#(jq0gZ{zj1F_*d{{4PTLC z_qf8x9RrJA3NOQow?5hTbT+s6Ue3%p7)nT0*%~RRE98aif>PJdc4?)WVt|@U#>n3% z+L`BKew(=fkx&hw0>p;ZDTpXEx_pX!2*f)0WJP&j(59RD(2U)k<(WA?qshev2r#;im{gzd0r1aal zpqTyx>;|OmQFp>k7H2^2{Zug&Vd_-*ko9bnC>4@qe}V+=&3$}>KMOH11Cg(H&VG|8 zjf$UbEn+S*RZm`SzvHm9huWwiRBb_NGYjRBWaTSFLI6;^-feb&_x77*1u2u_iz)7_ z!qGM9b4px7pk3YHfg9m`D*rAd) z?jl?6g^{69Z(C8kuJ6uQCj@YBM$KJa-LfC@8fHF$S_IfglbLh?r5xo|EZJA8X-@7y z#*gd}l1FHCT*G94RSscd~aD0E^Gs*P97jb zmc$>DyYhKf-V{YEbw3P}!pj+%1VD+erl$jN`RzM=Lpk#j{|^UDPmp#HFk2 z&L^3|B>*{i-L6KJad6bmASQoKp(*{lwbK?`ok06B4|#RB#|Nw#S=NVH}7if87a%# zcx)~GLf6_;f{a2Z`6k99sJ2<9qqZ%e;P4*CpZCxh#s)FGTwL;&KaGWes(M<#ulE=x zPPDe3WiM@%Yc}Ee7kb%DN$)~V{rZnNb9a3(2e_a2#+vi6ame5r<`KVpvy1I5!fY$% zH8ar%LvjZUCnP>=0VvQ!AxV626{x%+KfCHCuh%ock@)~>cT_ZSz{BIs`jpB9_;F+H zbhZH+!*JmsRC7=)bOyN6#L2}_k8V)lh+%_Nhu`G>7|J_aL%|FEIAW?ufE-SAa2*GG zFtniTrZ-5tZy!Z{DXn1jmmO*kEM&GhL~HB!*eZD(CM0AJl^zsgVVy!UXpuhI7dmUz zhbPov<~}CGgxo7fe6z#B!1N6*!KD7$qnffgPW&BFqJ__&8NR=i{CNFpqvZX@U6yl? z+{nE^G6FS{h(imXc~n^QExnQ>T8k&zD5@@@#+@wT8uSFlqY|;Tqb!sZzp7$XE4jzp zd=p9a8*=O!mKhc`8}qnj5|2B^Iz zu^(=BsXCc?rRk%NqW7iIT6?feE5)_A$*S#S=o%fh$5`2VsZFcLzp9VM?fNuD^7hC? zV}F!e3@~kiTeFpPTgM6gSw7bVEXmeA5y}$?6zK;FeV;g9B}dMK`;sd`X=r{t`$i^F1jXw9=pJoOF&UL5WHsPrSf_#EFsXnKvyKW=?@BnIjoX=)m69Z`&U~-v~I~&LPSih90e^>xaM2vnBboHDcC?pK7 z&2-Bcn($tCzz~3id&P1)1K8fk9wk!nhwgj|ZW(zS^0P4ba!@!w(MclMrP%I)+An^q zBWP%6zHG;Td<|zk9#e^K-qP_%U6<9_Ig^AlFOR%c4DMGfb-Z_=FX%Tk&kV*#Fc?%( zVCeX^^y&(vUs@5OYKB0R-EwtoR&F-DJU^HYJH3Fto3ih@qUsJ7x+zfk`H8s#Z<%w@ z?8K?2dH;arpccNDHFqIQ@!^_h61CsWj!H&g zXo|P$hbQS5F}Nc5i|3IZyS0r9#couB+<)Z^DKHzuO&-JmL^2%drlYBl;b9QzTiW*A zAb9f$K@JyA&jrXaysd?DHIOER^Q1A>mHxsd-OQ#>o>AV!aysS2uEoGERFWXW88)6T z|B3Oh9J?skK>L=Xr3dpiIj~5XCfPRFc2WN#;92T*0n66$=+o360S&n8NlwPOx} z7%hIVww?}dj=Y%qy}_ahx=Z+YQA%DQo6g8(zeB;0hmtBD|Loxc+;17=WwTxi^;UyK zUKxFfuhz3j?;*}E5!HM=?b}Zv-x^%oSTt0FWpoLN$6hgZ^(zj$tQs4O ztpP;#ou(I4flFwqu17v0;OhRlLM(-K_uz-wrTl%a3)N^*r2dBQ7yagrm{=$bi10vK zH($BEeo&~l`8frtRB%1t_Mpky@3=$NdG@zr{am*v=E%HI=v4%HT~Nu=U_(Y(Zp2xg zeB~4+a<`A~fJyar2t9~j79$%zNcri}{YoAQgm{2i?xY%&O+o-o4tpRFf!VV8TuTQ^d@OpjVvxv_~5L0a>x72gbv5rv~|ru`3QIyR5eHGm7IU44fxiPlDQJNyv-KsFlTqI4jn=xekj@+Wtq+-s_SI0nhh?%@t{L>2% zpD~ZTH3|57!hpjTxYpVwVe3lVi&WC`5gg8>y*~TIp#6t?j^Qo$w43mYmF(+v&qQAD zA<3#CiUbeFk-uY3%$vtG4e}X*9o_^OqU1M#1T&Te`!`;{wZ3bO<@5Y4m@%zp+MZe>P>fCqgjEY>jH-Xf*80mAe24~J+U>f;_4-lp;pWsu^S7o?2V4&sm1Xa)lnetnI_Z~#^{@stnhiU}+ zy?;t@rDT7zqYW+|9AedB~e1#7-sYhDZDDBhI{x1GR6o0Uz5ngl=V~ zt8Rep*fLYS?!s>^*iR_j_ReQT4``A_NrK@?Kb?3gV_6*9F4j7A$sXRY?YLW`>Jgp3MArnn0w+{APvGIW%E|^p13?wSo7*` zqw-Kb-at$N%Ja^E=zVlNl|S}1F*t(svB&!CMBF)uO3BgwFj~lb;#^Sp;|W_i356@z zS_c=_*hCzhZjyGv3ee5rEZQ9|7{9?@C8y{!E2Z|~UN2n~osIch%Qs)IUQ~cR!=*1g zHGirbT^5iuI~C3ub--7irC;B!iySC%iJ7ym-q5f0dtJMdtUrGDiW`O!+QRhdimRdm za01E%tzii%%g|~V1{okFzw4}<6H?qz^;%NqG_gJAJb}^;5Wq`*D|8*>;v|21xNa%H zvao0S-Ip3Puc=W^E7yxXOK7$J)}ySe5VO*1x=V_U86iS4r(eat5)F8k{;{tVW^e(I0ZhSH>K!5%P6zrAh26t?)>Z>~{o;?5_1+9+g zSas?8NzdX$sXHpqCW6D2X`;)+&H}c!)ZS;o>Grhzi<6Y`F)^NQ6OK#)YplbF^#Gz~ z4S6887-H1v#7jlK*x&}Pv!0Gd9V-$WS(Fw&VLZ#9ZQK*Q{@KQ5;cw!G*H;G&ws9|z zkXX+hfaZw@Hh3!lBj|@q+MXkv?@2Gr{aq~7_mP07@GH~)t&6uIeTjM?pdzciWw&YvrYFwMyWk(zA zqmqHMq+Cy^Q7Tsh)9(50Xh~JR|EXzTPCWurMh9fT67)2V7mvbmfp64r_gsN{@;$p1 z_)?Yhg*_qi?nFHrM31Rm9DCYh1C*{8vC+`El9{;F4p~r;s?dp>Zau@ULk2>DP@?O;p_e|bZ4bTY~@vX@h zY#p+tcObksGzIOI*-(1$6%qmi^6cd-m+? z&leN^I{kBCD-(#fh=0W+QS3t0wZT*4x~qRbJ6{i~bkW`0&JYlZC-=Xu@qQhRl17k@ zhr?SvncOc$Yg0_~d0{Uii#|+e-d5zY>ID1CPgF1&d21?_1b$?08fq1+#r?>CtzkcZ zfxT|Ij^lcLYr8&*_Dlcyb1y%u2<_mon4`BAU}ZA+4sIr{_Od@%BpNhTv=~%Rm3zSb zI=!`19T&k%z_XZs3AKS8tOfjgGepOGvT_V+L{l^o%$%@*86w~*8u=9<&(Xe3eaQ7I zk3pe_=e|EX?r)~~&AIjz>jP3!65`E&e$8^b9k*^Qm&k(Pp#KgLFFuX>S1&zk(eRN` z81hosw@H_g; zm_?_B4C=HFbgCC%=o8TA)G+l2+Kgrz!Zio$!Ir7&cV9H|J62Wqu~xF_j+>{_)X>~j zcz*MH{>oVq>H&LQz6HO!!%O|PZc)-2Fd*H#y~fI?R)F(BRhqc;+&`b8bb$Fj!vrvi3*D(y z6FT>gi$PrksBRAIQJ?vnTk#WOV>O*H*sHf7f_v!;r!%e#y{C}0vm(Av%W+ z+K1%dK1A$b^!JOWUa!`(Gf+&|pBFtJR#f@b{FA#4xdkaHx5rd8@KXrlpP>j2ls6b| ztDZros@S+2F5nfpOnkJRwE?$eAil>dGK5@4bnTyy6s9tNi76hE0q+)a!Sw23{IT6n zWJ^yQyF*+my3aq)h#5Am5U3lwY4}$7#r~Eg_D14k(5Y#N0|_xLRCnS|CdYKd0XufLT`u zpabnU=%qN|yMo6JdBpDF-$#>-&%(`pR;VLin%^|r{`{b=M|k;)R7koxJXj#deU03; z(M>Lqg^d$2N}MP~uYEO<2%oyV;ppF+T8b`9K3v8Hepbbo>nB=MxQb`_I{&ie=!mMW z!}9@Pk5pvo1^pAhtB0Pm+Y|{MbKp<-eqMb-(zASQ*$Ogj;4{GxQ1} zc?ms#6VUb3FF8xxCX{m-sgHJy@nLlFc66C%H;nP(y=8P(q=yI{t)>2$`+(}^Df|3c zOFB=zPdRyvi^oGee!EHZ^zmCEhbGbts5vi=1h^9@@|Vy|lKNNsKqNpo)44~ZHVOcu z&i0jGFsP8XXII6PQ`epeZG~riZ&T5^?|TOg=*&&1s0+zVJS2SWT-*64A{_H_5pFlf zed})p%EG0aeUrzES@u4+^5BP@@maKs;g8H4{K{oTp<5DzJyPJ>Mu#~TPeIBgcC(;> zQp|I*Sf-yv5y5U}9~G1NiKgvztfN_H=PNuhJxXJuWi=Cxw4)_Xh@o6ug}O*IgugxO zY0!Yh0=yJZ*~HF#YKvV&E;i#9HCjsfIUn0ry$WAC5y-6Pr%F2s(%zu0T#GENFb@0>gFV74LudP8TG(b^z^ReXPMD38CfZFLvPWPWwoM z=1h@P23}o#{uN_GZlr~a-Dl7~qqV@3k-oQC`*Gx7(7TA{7X5BoRzwk*fF0|H+1;Bv zP-7D#Cc13groNwu(Mcg{9Q0qUH!E%jvwr6FzFxIwiz(zc{apvx<{1ARyiPYQm^V_) zur8FQ`(Y3JNdvyoLeP*xD-QzG8tOlvv#Gw`H!f00quv1)6eK^tXzgD|eAy-VTqurK z7pC#qzWDj|OW;EuS@!n*7{jbnq@V5T7l`2-%7Pc{Ttg7di>JKoE<*!W{ej&}r~UC2 zf&D12A9j{KeW(qaCJC&dg}I%K1c1vAGrD-fT&!LPKI_Hx+2^U4!Uw1~+N%!PlhGvH zau&HqxAC(5V)Pg$5YR0z_@o}8kQ^s~ONl@HtDzi|1)Wal=VGV-fFW-AlB&Ri( zkFMW5H$xyk)2#uxv($8f5)W`DkEWp_@L~1OhrI!$f7_mN1+UPU#9I8>!{rNnM2AD0 zf6Uc0%3Ic&)X+Cg{cP^fYnnX2H@PpVVAsEx4?HShU!FLp2s-Au~WhRR#+Lf?SK ziy!oLXx`<4(#-<#@$3EzLFUBi6eBoebibuGwsjNKk^b19`KI1AWHzvE2p_;@s6Ov?4fRv&W2VfurH6|dii zh&5d`iHyim&vN6TOA1pOkGP9DpjedNgiQ4am_tW8gKR`#WO>B9g< z%Ez9-HT`%8InXR1sCYre9^)&@pq$$;&w>sOJve3e057xD6diNJrCET92(4Qh#1fVK z+3Ur`fIexr#MQxn{zY+X0t#_*#dhDD>u{p1|8l%Tdw)%of-V@h9)-v6-u>oGRAnt} zC7jw&<{r?L<5PDQm-m7Vz5&+`9RMgs=+#zUn9}B(XPGbnihPF zMqu0v4HzJBOts5&%eiZ07ClNPP*51aFs#9a0vOQbfk9G4->?wPzx=(>SRQU6bN!x$ z8m4+#5sc;d1%Ln;5&iuMzD1UwyRBeE|9SkuA3TK01;~k~=NSSPoc`ihX!Oj65NL;L zfSs&KBJ28u?XoYKzOUjRR`!3f_inMSqvdGcDa1i4-f`rPz#}G=P@G`fJfOwRZ3BK4(tPKu~XKujN&)`s%y?Z@>TV8+62iMOHga zcX)xTgxf$UcZcKae1N`qak|5X8ng99BdiS#ieAVK!NT5A?Wf%y4eVOGw3{Qv0Gr~q z>@x$DO|5QG@j|TaF0hGUK)`Rf*>;2-AJr_W>mU)6_$@PkPOm@fr0fRMea>_nv)N!# zjWfT2Ip{gaLML|p`Qnq*=)5aqxG<)*Q`D08;cSMp5+SpP!eFd#VWZc9n3|*C#eL@Y zsnc4WlNQ4Zdl2i5k+}q%sF~gGTiwo#b;T|{#4(TXf$Yf|1J<&7^ddzlf#;;Z5Q_~o zfQP&=;3^g-MWqWKOi3tJOrF$0tv1MIEHJ_Ntj}(l^UY zW6|syLSw#musPanpTvsg&30BU*<}v7+HLRB;KfZ!BYw$mI~H%Phhz-O9q1H^14kkc z-+`Ef{h>N6R@_-SY?n=N1d+WI_tWvdW(_)9A}80x=3ow{D%I*|+nYo>{Kee^lBasDg;SjXMry`Pr+7AtwKdP2 z6Ux~%ge~!JAr6F$R3sv8%S}+%Y$B)EhOl#pjR_kf3Epsb~eRc9N(fREF~wl`)sa^_FeS+Ov*H%*zB2(^oDyPhgT~`9UNwpS{q7NsXQq`eM}psWG*z0F23Kh*>7|i&(?y>sP26Nj$KqmALYk_t z&tNUXjKCghc4qzwp|))>^_fz4RZWfN0=?B7SmoLY?j|RmB^ztk>K~`Xzl&J1AN7qs zvUh4Wol>bw+JG0B-IE6~A3CLmpYY5`x_E?Pjf9Q| zq7GY2X|3FvnN*VfbZqVVo+^y%1D5#VQ{X|UGaM@RxuhD&X0#56d}oB1Pm6X`_yO0` zt<@0x2Gt=k5^}#nd9`*+zHH5tvxV2xOXgU=+yGQa!-myNi|jPA1kk^oyKbfj9f#|U z8;l20xP;Sh;=r%hY(ds=&LE&mEbuf3V>rKPMMRH~J5??Q@@(D(`ycQsyDD_cjWI~; zC!^7=t)YMx&oh5~0COSyn6UA}O&K0>>=yM7Rh>@iYtlDt7f!65#xHGGwkE}F^9LW~ zc(c?ZuG61|uA~fFaG3Ev|P9$T~i}?-8|`@6ytCH9a_?j6Kt4TW2L+t*usEv>I!_oOXSY zDrIYnvxnVAv0bl3s57{2viZ{1lWJNGup}Fo(~$!N*R@(lEv<#)A!T_K#2(_Ef-J{rDU#7iWhvWTjwLQ=~^W#A}SJFju zpbq*xY`@wD9A5onb2#KU@U>OD45$XV#!kMJ&gwD{I!;JcmdA0pa@!F&GQ7iNtY>=y zjB2s#_b>6dYw?{F&@%+@dLTIAzz?!WdOe8=MpYhuv3{jD0=Gf~Irycz!xy0nhJkDw z?EY9w=Z(<@SkXAw$3?2Qaknu#om)$im*=1x;#3-UPe?^kH?b~ksADh?I^n=6*6Yb$ ztcG&3sh`yl*BpW`B9;DX|02(nA8W(@o_(jZFdU zti#kk)J8RCvQt}f+o#z}qY0~OtP2Besd5yO{N2OUPQ;mSusWQ{=WVzF<{&z6jaI@T z6>lR}g-vbbS#!;cI}KKEsho2MIX*vt04xyT<*R(Y3%k$}n5A$zM=wKbu%X=-{4 zq?ecWo@y3du5mGUiwzZPM`UibF8ray8B~3UL@QYbo6Qgb^%92wb~y>`f1TNdnyeAfuX zRfIfUrk}LKy;x5YM)iR^@>2QI6T4$jNcLw4ZDGr_tHX7<%YkCSn%AbggeG&Rd*E#j zoDZgf;8iTZ*99DEvlxt~9VA;*vua>#+iqN4z`1nD_Bmrf;S}B(SVy``Rth1yXc%?M zp;uJF=b%>FRGm%cHD$bmldmJjp0Vx} ztk#3AU$h<)y~O#M?SpJhBz^A$frh@XfopS(ahYS5!{6FuT0GpVQ@O~@^iGExx?Fuf zkYhX-E?^CN9Vh0|baT}|PuJ<*tk}_3+bD|-Ko0c2$DXUHKai6eG9ylVYdueB zf7f>V`$jf&r#ZS10^oZMEUl z>n%d^d*&vgHW-Y34%84d*lh+wb~HXzbgLIHX~Gu>i1Az%o0mz_VB_VA-Y>ecYwbJ7 zKwO_%$hR+XwMwtU@jbl>mh)YarhOoH(-OT|R0U-1Y1+I_3zK#Y`8UY-0RCIBh4PXJ znGkuQRUh)9iNhglN!XS~QRfm`oN%f&LlCn8JaSyKvg3|-J}`xuEz=T?TCu|LgHD&- z&j+RE2K5BdZ8h2Kc}!Nw`c)!Fc4bbN<{c~)k)~^HS>~l_It|I5D(MhY!?~$@qwXjS zS6jIZ#dsZdNz4yJ>3M@zx_6HN;0SU|Y#9#>m4n%9HsqO}PJ zUcBmvOV}P_)C1QD_Sq$50eH*L2h5upL)*mwecxQGT4_2SFDH$|Qf(|+)Xtu(U3Ls7fN2PQfIRKP7^#tSDeiXo)b>279 zirBG*(*kOn+1p;UWmt*eq;Jd{es_CW9E5h_grF@5hX59UztBT0#v{B6baeJ~q@%_j z7+S!PHKmQRVALy~gyBKKqco+5Jup-=hCf_vpj&e6I1(LQp@Q(( z*?qf9kqqFlh&KaAynvtPL;YQIHzoT%Tq-9QGS^xE8&zJifF+mAY|yygJjONf!UM zk-rUgzKH7`Le_Goyo1j`*ri^k4@)K@NN;YJ+^L!aHEQA%5Y(1inc){@iHGXle&rCFgC2 zhnczR2*{;C{==fw^$wSgAz5?>I$LLX0EeOGvT_m8C!=3!wBW6bkkhp7R*F!07ag_h zu7_;4uHyc<3|>xeFL#$arxB@<$1UO3m|eP<$ExpYlL18e+Eyw;f05~Oln!jq1`(mz zT=!O7kG-fX(YGof%wbDvVi;1#1+QXepT&IBC{ox5I>u}*F$$4GK%|dLUv4bH2spv^;<8Rl&rw8~mA^CyGu(x2AOJ!z>UWnh4CqT8cp z&T=8LOfp%DbCZvdb9NZ@P4zq|mZ=cB-=KweeirVd;B5s(}{^A3ij(0@lA}8 z{nfZMD=g-!3{Ycv9Wt4(0sh7LUV;0E_oR`=?S)av2QK{*oEvqzW&)Jt`;D4U`%5%y7F7fXIATKH)n z+o21%Gw?9|cr--X*%W=W0@53#PXhQ!eUmzFLHATSO%=1`Y|2#*T!tiGA;{9o=fFqH zo`K97gZr|IK*a%)E0#oL1Zq33HrkHGWj&A43O&jSf$%UZR*!`)(yK#2Zj|9+6*bs{ z0LBCrMuJ;zCE>biZgjqX9!rAFj%ODS$;BJxESLQCsx4dLioa;}-LzrxmwAyqKI}-^fFI3IAA-1+-CMx#~wIqVy#Qk z)|F;Q&SK(^+3mSDl;;hg$*XBLk9+4x6PtX}-kccZ3#5x8;iX~h#q^*r$3v&YAC6F* z!3S2&{FYWl8mq?{^45UUQKptv+9O7WsP*#X?%}hSC0#<)#UhL;Ce?(_V;19?&-Uri zpH)aMR2{}1)7XIf3js)QhL22JnG!!|+BbLd+*Ib4BIC@3ZnkF@9RBnDnFt3vnr#u1xSJz+<7pbBNPJj(h7+%zx?*mhJo zm4jisem)Xjtzrzo1h(L2dkYMe3Y>m6XL?Max)B_2d~JowdA>&c<8Eq)Wg9dk17*Xz zID0_z03wG!j-T(Drd`rU3o(XCT_k>^S$7))s=i1^4py>FVmJMu8wBxWK0YQ#c!Z<9 zQSQ{p9iCWg7Kv%QU&-}z0Xft)YtHN2(z1T0Tm)1gPsd`wY)W%o90g$C zMg7SBZY?#X$#dg?8M(v#c?Rq;e*hoS(f3c&;27#->-Cc-r9Bjv+19Rp~up5|Ln%O^`42G>J%m7Z+7MWYbMIFjGB%lUtlA_j{Tns!1!ETUygS~~ldfRK5!Z{NmTG|zTeQ&d) z#_?<>_3~1}0VD7T)fxnUPp~E{e@@xs%dnv=a5hUYtr)-D@*7>F48h>X1fDCrZYZ- z7f{OBIKhNBvYbrfauDNES?55Kv8lApfr^|7%DPC1p_RDxpbxwyHKZAr@TqZ=Da}&c zl=n^mKg}+y{m_toxo-nwt`|+qC^UaIrx&H!!4D5 zLl6dz90xQu%V4-9bw7xmQjOVdj8m^Nnt+0b%;9-UnrKmL&MkM^1zwUNbdI5ojxUGI zR;N~}q_nFudLk?{pC0ftzPu}Mtx`M&g)iCrhL8s`as-qj@}zX5>S_R>lNdB`o`)Tm z><=@|k43+{FA>ORJE^=Xx;8}6CQx-#n!&lda(|OSm4%BRr%#jOsF|ogI zd$HzD)C)L}f*pxBVtrsb;W#n->IbhwX735Mv|sf+SI49o6_Lzywh_D9jM|yr31DR! znMfBLC5|$x8v$~LgxUhB1;>F8pv6$}Mu0>?m)SevBCb{WHWDQ`1x`YQ9ID9W9WHwY z0`pGKmizM5opPCO(j2(;;*6zmY6S9=Hi+|fkirzZGb%xPjW9iNAWX^aWpUd=JVTy> zXJ6w^@L4UlII?Ox=`vd{SUTEt3#uFr(on1H@;ZBS5shp|y)yW&V1y$EYg2MuD(e0; z)?!bxDvOQSk;Nh*m!wXID%hhn*I~{|6?3+WajzpTtwS(Y?xz zX6RC8kb4>-D23!WRw4Lzh`u@Y6S~=?{Ed^_SPaQ!^%1NfSfJz8 zVz+Pkm-+FeYp@G9>TIW_JrM_PAwDd(5VGnsmE#mVfNtNP@`;ZJAxyRuG~(Rs*d4cHCC)~r5-QoKZNV!7S( z`;2oEBX@TM4i@}c7H{lYVEtpk15-@5!#xnf_!d{dCF~hRA#OypOmv&F~Fw^Qu9i-K3n{1px4a^Y0Pl9 zAm-SmTkw4?rRB-Su|8)p2i<7c3U`aJ)NFT5S(`8A^(4m^@F!4< zF_dX87E4yH%u1kagc;ef5%8?FMibfxbPbsf0#Poyz9f-YY2x9`4pBSLwo<}(I=lV0 zJ>H3>%XW`EAic6DIbZPL^}WWh+Ne(Z&2jG2tuL~1I+tR)WZU|78x1D8o~Gkm9~&IZ z>Y;aLMl0k3R$Syf$Xz}3<>g9inA??60?k1gcDqdEZ9fg;>0qwL3gXxoz~?-FMk=ni z80|!z<(i0GpfHed2*Yv&LLtqpGH1j%aj?;Dm1t#g6|WL|$hq2HSJwhqkms4*-ao;v zSjUML^9QUSY5W%KdkKdX)ZsIBz~?dr?tQRY#Ou?TJ&C>)?RLE_p|B)^9{TFunJZLn z?DYq30w))Atghd}VN211KlFNff6A@<9PkpG1{|Y7)t@w?Vx_ayjR3KfQPAk&tc|b_ z&Z&W$<;asW5L0br!5m{NgTT6+Eu4E}yE`sT(p6A9ul!wem-H9IdP%RX7z_XTRXa}3 zi4l~o_4X8=fJp81_Laj3%&D18wdD^%QKy_P?A(hnkH-zVGbo*b@g6mi)VJP)d|S30kdLBc5F6p>)6rEEfSBOruNS19m;DScL1RI|1SB zI6jJ#u(mvhKv9P^8GJ=b$G49`+IK_e1i$otuPwqxoy+tMUX*?9h@`{Ta>u#qxTw{h zVc6Yr1q`ZcV+X{V5Ar&5r{wxGFkYbYVEU5c8&g4L;bb}XF9g4DR=6V0Hi&Q@09?Mk z#6iZLTebj%_Nw9fAhIgo21L3zxULcDAh;!*apMeGC>ay54DS$AS<=ZE5UYAqu5?#7 z|1M$&5ofhKKFY6G`WiPvTmc8>Bcw@`Q5mR)|VJjV6nA;vB*(-%{Ip9p{jiQ42#5l-{ z?=-#BK<}^1X_*m>#1N_t^#XYSIR^NnJZaQMT$2qdBx4nTo@K`b8mVW>)7G&$fiIZo zxuQ*L^9}M)Eh(h(FjM&q?7JAOsIXHQ%CS=8|V$`#`PBV$Pm#7 zl1~q%W)nvX^%lVSw?uENS(p1bt`m3DhH`W6Iq{mk_`?7=+*WxZ@!`zlcd~f#jRoB3 z3c_o=k5g=VOFnIaXDg0b8p%Hn-hgUT$$(2+~5t08(w?*%>|`f{!nDaOQ-bY{kX#(y5&N&ayR+=T#80 z>m4(Y+e$~RXEsB{M_{#CZ>jyZm+2%Nh@e*6*15VmNZ<|8(^>PJ*-@~O*ZfWcAZjZE za-~g|RWShWZ60&g3tP2ymYK1Vb*dH@Q3Wwq@bX&~Lnkp;z!Xn=1CtAQy{6!Y;>t>g zgBV$aTO3cL&|L%6or~?lZG&P4>|(H6*T+pwgoC)nML0@oH}lrvbXD%LI9I?Ha{C^R zh>Gh?Ja4nCmzj7;=C2JhMZW2~mt(o%gv@1Dx2Cs!(pezq68<25y>r0f&ATCd`J+C! z+BwKUDw@lXGK)I6Sz4J53*MICaFXWzU|^I|2eOlD`BK7-Mpk(ZPNG4Nno?8O7r<$( zG%fH^!T-#TQm>~^+lDp}&zv)@?b1!F#fV71VAoWmTh09*Z9||Ad~#TAf{!~eA!?x?k~o4dQ|K1EL4 z^nkpEQ*A0WqWBO+J!(5y*j19_359CfUAL0R9MzVkAX#8dpOXuWwG!9}i`}vqUZk~~ zbR!S}X(o>`9jf(;F|FdLtvT4b`wF|YytPuEt#H0UyDZ}X8f$U7V#7eF+)vN`WRnoaa&ETo`5v0#kssc)KA<=EuN<{Q)|k_RDJQ0Dg*eiJ;8RH1)5a1faSV-^9xRc}h%u8FD7#Is*3P7P zDORG$GU!>km>RcwyL%+mC+)tZN$}atV;@lvqaoKP?2K``?QXf4WIk21QyO-sb9Opv zP}LM_;K~PguzslXoAklTg0Y-R|ICx*Vg?&l{X`5eI))#WD@v>hV#ML zYEfM7j%_{at@%LC)+l6}REvZNF+3zMDibDV)WPzzo!2t_j zvpFe_MC5NzYRPWDS%!fB`#k(2vsw=!FoZ@bH7Zy%sLXzC33_KV--#ojiWL*c00lhz zlyl)4OOSBri((}l^(!^YVH?pkKG6~kdc9E>bBnL-FOX01Ac9;hZpP&Z88yA(s@E$M zeHHT#Yu{SkSd4`%9zh2 z=H740Yv6#^;)&s#h;)~+J1{1X#dq-nwlSplIQd0&&hU&~<%Gy{2x(|@WS9vtBLSCa zO~{%91Zq~Y<+CMC=lMh#i5mk)gU=`Wr3P{6k166)@8h(|iG_F`;ycrb(gzE-lk2!$ zj+V<>YwX9Jw#4e|RdRx=&~L&aqUD@xTx@SR;!4T9O6EkbLn z?d`H2*$4);iN0vv^hF&p!v^7g6#`P2J+*@cBr$DokSl>B0!mGHMAfSn+%Wc4-){lH z2!CWdVoIV@0j-sH9!Wxogn$&M;7xjA11z)zqXhre5NC&0qd|jD$PsRk=i+M7V(g|* z0ey`#oCm8SJ?)2dZ;|7Yc-@CShI~EWsw-wPvxpBXYRho+Y)a;EDk{$8c=e0g!2tRh z52&tj8Hyg>d9ee?7A>g4PjosSwzRHJHK`~}V!stonh)?OX4$aev}cQ`-Zm3e?jbz{M=~6@BibKTXn7Kii}u(p^_AQwA+``7 zJkAuO-7>m0BKTof2EcAnd!<(cCHq$B)No?Q(6DRMEM{kFDd7uk z2gr%t!WKtNZGyZ|JFt+ifgCjWi>k90Xk1U1Cdof1lW@Ql8>|JIFT)4mBdCb9u8%uY zuv#@}M)K{%ir3R>u6y=d+b+)2RS4eHwcOkNa8}Ov78S_5i+q!BJlI@_-PCuz`TCOC zOOMRV7^}0J;$)*Ch?FNZ z9AiYcDe<*+1u3TUQ-vv=Pc5=Cx;X4)>I~Mief1Ev(k?Q%7ulW<3{ii$o=v$X6Z+-T zbbKg7NmcZV1RqhY43ZWGr)GlHO$IYQ^n*!>>b6@$oX0X)>{%1KXHnRfjqb!?;kE2_ z`m&}0@G~TOO+4(UnICe^_>Bo9 zf%5X$uce?wG)B9HtCu1_YIJP3D&^u0v=0%eo@o~8{AXU>^2V%i z_d}+Z>KX0TLQtG$@hBB9qfw;=`)%AnLLOp;;3FH>`#OowmHRlr-~?O~ndiPQU3#W8 zKs%?$#wv>|;@kwYauk}|&i3TVK}sR7h2T3TOSoU*wU&`9s;zac=~Wtp2aL>HSq5tk zxRoaH+74$^tzMCQqrGkipzWogt~cxJb{J~|iTMAyL7(xs0SBjP9gGF_#?r=tI%ZnY zw&GIlLJ=0T^@H&T$LJR9Qy`Pxxg_RCKr*x~K)jus%5gc2Pjc18nGe@|EAR+8W2vdL zlveg|5D)YZ12`53lNMK&MchSkG0SH{mJgK<>h5(Hqp0a4*JbC4(p=;Co`Fl4Nve74VeL?sEY$CC)2Gb zDq5}wVF@8&n7hy}j!CGTwQ{qFwP4gb=Ty|FkY?KpzaF9&#)!28n*slp-5L62Sk!jN z*I-I`z+Ci}poil2UhMMY=?OgTB<=`bPe-N4UB0#EPXK3^juhd8_iVKd!=V*Ta26+$oUPL+*t5hB zXtjGr!q2!#i`yM1IB&H<>+!+idc|U?S^?jJ>Cg5IB5Fcinm0&d<~*~}Fg3TE2Sl`Au>{O$pHwW-39uW_rR@{D8>(1t(rEJPa zmZ!oHXCK2agO+Qd7Vvn}+Hpar zYn?2qF+tAA)bGi<6b*1@yt7Q9FPi;hLo1dlZFcsQ>%FPLQz3w70`I9WR+lqAMIHB8Mhf|t;B2ExZ=vI)I=Bev zurwr(^^47^hU3`|;g*^BjI}xy3I9i9H}5KK(q? zb@D;aIOWKPx1Ngz*9p1n%GpLfm<0cT4q z^Qf{F{jeg1_CV_5#N4?*ZXPT2*%oQgan9@KdD56$2tt?F29pf9`kVYl^KP9=dTzK; zTNMuH9jEJ9ugD<3sji19T}OziSfkdRgxlhXS`fS9q?-8vhdXmYG~CBYMM``#U5l0W z8u1O51Ll1soHRM|(rDQ-$NLS}+Cwx9aZY1pBOzbLRdEJ!QtmNpqcnV)Pq1F&P)cRD zDnpcak4?o*WzkCkRiMZL7PUldo(?T{HBsd<)!gFT?ll=ljOR+Fq+K`%L!DDMxr7_* zy_Md_*~B|3UQ#%X@$A-0OJS#VMx}w^v!kHP7Gp2Pxo^mbt-DR&8*pA+V(wU^I#JuL zTW@P{obGl~JyDA|I_)qT?E4#}UGoMwn=rpdqqej=HKAm*S59}8c0+D_;6@Z@A$a4S z5209Q_KOWW>uRTl+}Xp{doC;IhM6oE*{-7NeQe3AaM*kn)yk z3+Av?=c-(=-))#6ilrhY?niTAYLL0k;;d|Ej?8hk)6|DSf58gQR7#aK=YrmIFkp6w zC+&2t2KQErPn^tdajT54S3!qcRU{=m5d|q@{K0oy$~}Bb~1C2(RF*cEjr1?Xy0B z-`a48U6AHQZWDeF5rw&4vzUN^c_G@fY55qp6}z}WKX<#m@x=u{01n8T0SB|jIUYwG zf?R42bR0^{MqCsoC2ncWVyqRdA9~y@iFz7*bqt8S;IkcfkLEr`PPnmfydw>kwKHqc zdJ|ajS+^SRG$AayqXv zPk0t#_aokCfjLPhXQpqk?&>&CgU0`PmBv{!r!y5f8`x%U_b{oq$7{WN+*dF3sW#Zd zQUC=Fkpp5qyjUgVqYRlZ0B0@GA$C`qshm^c zfx17^aR5jLPNNXGIWSTHsv1xd^-yp6VND}vtv7WX7;`YgHM41GTN1~Sml4YI~^FK$N8bv zdgt}=)7RF2`)l9&)?bZwPd=*F|B7qY|3-fN@8rjSfgd0I3$Gun{{tU>&-y3$`B$IZ zZ~VOR3&t=0@U`*Jefs*r_;dL17x4er@&7O5|8M;8^=H5A9b-UWU+ul48^0d@+|hX7 z`Ufb*_;B#Y*kAsZ@nC#leA}x11zhG zb;7SVJL8RRFevoluYGdw!zg>i;O;ftFATLX^UNsn+=3b$<=DgrGb;FA6q!3mEyP|S z@|=@eI7Xx$3psVXun?gYYDB)2eVj^gHV<-)dr=sUhVWda0BS|^gwjsxN4GZqk-Y1% zm;U9vm;NR43)9AUm>3^UzN)|edGyym`@FyMIrpT`etY@(o_O*0wiouYTiB@u_3VRs z8rks$Il6VnPg~4mOJCIc1Z8&@4x?W{-E%2;S(*C_dn7f&V^#( zleX%_ask(078qRm0N3#A<^B4nKe~PV9p+Pf$-lZ^_!PIlbL)aXwDRwLgRSS=*1wL9 z`Lcok>=#@Q(%OIhd-!yOzaV@)F}`bj59{9e8<-G(_O0FYxQOP7p@wSVy<4N-BMV3_ zL~q(jH}F6I+8X%nFBq%)`#$@kJKoZ;=VIv1ekR+{lYS=K_UE=C zVdQx>nL8lKNef!&9p0ElQ9;M{i<#&?*`&$#j$Qk$JN5T(UHXSn^kXmmVU&&@{-1xM zfhIltmmX*GlOFzO?u)4STfg!0Wr4p*MMvJL4!Sccc%fpta+nqz)3u|*%a^}>-_m}f zXYPHHEyaI=27LK8rFkLb>}%t_+wSyEu7?c1^H(6^ziqv>6@T`(6!TOtm5;xZi|X(E z_HUJN<*~|Ne8cnl{p?@-1K01}&(-fy$o!ReKG~_d>Hg@ZetcT^B3tI=@8uFq&+di1e`S8~UIA0G@E&=Xe({Oo#Zh7M>P*yv z_i~N*J^cAp#^vI*;Aw@EOc2lc^XK*wwRMq1?}Y@w&rgM*W1e z`@_K(t;t_{+=U+B`{d$VD*x4L-IJF+*^eK^;lFtkhq7bpVA#G&J#4mx?|n}2VJm*z zpKsAo{aE+j zt8e`sGTpyz{p}xn))O0+=(@uH^|m@cPP^{srrpb{?T>k)5gR|BG7n|q0XY8-^T8)@ zY7k>SQ>8vPF}}9)?rqP8?(hGUL$~|Of8tBEq2HAqkFY3J)?~pq*&jHg1vBPqY-p%E6B;FoaTAB&7|CtE}ADQPIGe=vdJrNJedyk$$ zC(Z3JqV)XvFRsp$t?dqfNJ2`MK-QN8x{Xqr|UPd&17W-*45) z)SjPt@z@S4`nha!-)^{h?1)r)=kc~|9=zoq{%aYH$M<~pH5K^fBk*%%^l#ms|M9%9 z|Ie?jum8mJId*@|XK#G*mI{BhSbH+SPxi$B*KFxu`Sq{b;<5DJZcG1*2Tawkw51Uj zh|=gwZ0R>|xOaCpfB(`SyncV>bM<@N#sAT57r)!m?-UAG^ZLF;7oZh1P5t3!KmR!5 zzd)XV29n7FqF_K8pd6wp5Y?fWs}3&scrzP+havI<&ycDRv-@6==SKL=>d!mw zX7yJ;y&LEM|7_gzdGYcq=f#(+CcjH2$Cp_9|4JrtawDve8SF2fSnRnQTYp6nG56|6 zxhap~CDJZ8{_~N<1?T~pu85y^T>xVYLq0KZEFSR%6Yry&8Tdr`iF|dByx#py3wrc% z|6FD_-uvOR{BJD5kI@-lVB7zhw>IInkAA_o_g7>~u=7UgUoFJ`+UtAg-l~=fv0p@+ zNdVx9?6_b0ie|jEukX!x`?t@VvH9AX@g**ZTXXLs`7zRPUEE(hC2pKmUo%=y|H z_Tf)3Derao>?e8ZEu;L^BJ;^~dLl9(%?Nfufy~@*WQ&G{f)dCl zCj0dG5_0YSn)_Y%H(kxSTVYuRcb=m}=>flf#C`h7lfU#&Gdcg{iuUP?x7&l?j3Ci` zZruvs%RfaUc;6B-vH2Q{`=@c9{LTOHE<~R!^~YV0%k_tYY$G~g#%}?l5OsmrdM9-s zljy_qDf!-`VgZs?qKf?ZMLiMVKl!uR`2N-#8{ZR4`%gZvf_=(CK>)uTo%j}{ zhHm&K4(ie4l4HRhoo22YCthe@;YS=8sP#}*?qcqb@|E|&`RtGKtr)3)@Dt4gB2fSK z<2-mADeLzEV!L_Pv6$h3e6aqF&t0?r?I)MkfBnyV>s#i*_rka!UpxOJjGmv8K)CC_ zlK~HI-xRKQk|BCgP~q%U-8eBL^%c4D&Rfg*Cdbt(4_|&2C3_RL>!baFCTo6->#^t|H@U5 z;Kj$UY*IaB*Dy=vL-Yc8ro5bYVG$Xoq7WSm5I5{JkMWo5bw^IsFv{L~zxQMEN&@tG zS}O6$(}j15Y5>p}oWl9bh+h$h$HycPnq5%=`^n*SfDDmWK6_Dto3yj5*Ts>&{+;ag z?-sZy0;mvsr3(yY;d~7n!Q<$;>PyAM2t@E-%1%KBaafu?g!a6;#$O+64OcGd#WOVd z^G8^)hU}{kFXajs!IZ9z?VnXNg3{x#1R#GbYm)s`d$LIh|-F)W!!1-Zb zHF66ELVwt;5A+Re|W&(t?GpJc9jj`RM>1Pq+(*#JKk7MO5vcHzCv=j*%fgFVd<$G3TLojhGNpUq^1 z3>XDpHbTj(>${(i&P)0_Jnt6zPe$R5srM5O!RJTd^7!_ry`NXjWONj18?wx8cY@SEi2xB5SB+WC8Dc;OEwSVuqn@V-kx2*D0}m;54u zpxde>#a!o3zTmUjH~Rtg!>rO_CJ)_*C)LJRFA7W{UrldpN%V_blb>u#Gwc#ySeS#t zo)+$4&fcr~tfpjly7fcns&qfAIa%4WACTusci(D$6&cq)&%P#IkafjP3}zc2X2rEr zl>9Y5pz`s<``13ljv2+@FML;j|GVVVEA8m+Nz^Qxnh!G~u%8TQEJH&f!M02$kUsWf zpwb`5Hpj0MJ;a1kf;~0b7Z`N~vp1U_s&&0*n{zzwE69goPCtNg}mwA!UBDfRhyJ?SCYuqfu6oi^lU+8%1rc|Ss&eB z_}J&4f7g?@pe>}+pYAgGX8*K@qk?*E6eKM4s>f<(70kBBtd<`a@+#kEOuloHuktyX z&#+rhzD1iT(og!5+;?5R*{_#mYb|`3zvBMVyB2U=G1we2(@DjCto3r;`e*OF^X`2s zBt1e3xX+rU=xee9%H7F(KNabzIlPw9RK)Ivh^d=3U?VQ2sE35PbL{ z^TCJMq^~f7?B=X%pLJy3hgWs%jfn=wCt7{G{n3QHO}NKRx-iRzUw;*o#qlb8FyBVb zFJ`w*iH|PLKWs!UhbRb&co*}Jbg3P;s+0pZ_hgLRn~zy-Xfni z$O(8A1tDtv@bdbimxafBKR_pDmB=~{c0jffe}oSY*C(%yyY~IFKHim&W8S_S zKH>Y>pggU0R^wdc-SmeKALy6o4?cXGzA$?MqvAS4WX#YsM*Qbi_-|edzkTuMJUL$r zelkT&t?=rVD<9NXuL>W3TzLQ0tAlL1uU@^M*NBLqNL7`G3eB>&QGK`2M&Jqal1y-{ zXl$*Rp|_1V)0fFN_gMr?g4o*+P1j~-y+vAa zjPu;QT#X@Z!EAb#OPD{ZWK*{EfT;`D!>zoV!b_gJMvS=ZO&o?4v-+Zj9!$W=`6cs$ z{J8Zyhel?KX}-;nKQnFbC7r+R4dnpZ==o*&i8$kaV7>s1oG6HRge(;DFS|;v<)z*) z6>m4@Rr^8KhB8@YXiMcuA>8w?%6VCN*FA0O)kUmj-)OJ!Ctj+Yv1>x4LNfh;{yr-A z*hyKUBk7}C*e!cde+A_)?n+@^fI*INJC9{PND)dn$D+r706}gYj>w-Ut@s6eTa9_j(f$=#1Fp8uCx96C* zJV(0ZtqXWa~1c;+J3H^LpGX^tNwoVu>;=n<+BYVZ#K4@`;PHu<*{!(7KcCZ z_|sh^GQ8yBgV%rkPyH4g`S_PZNx$*bVpP$SSHHqD?LO=ByZ!L!8_1NF+_CnJr#4#_ z-*{@j@zmyy@NYb|xw!mEoaNtmYT?BB##5VX07N%_;_mszQwwd6n91LGYDqZn>O0K* zgr9eNedDPmlZAMliLU-km&?qGZ#=c%cxuVa_{LM4XOey6sr|-N`^@!|d75rcgl{~x z-*{@j@zkpOZ#=aSnYT^hNeJW{Pwm}}`-kGGy#t3c1pR;i6$pAl?qvN3z~EYc7e5I3 zMC5ujD9$i+tp#->;XyUs#zLwPl-tdVqsO3{a9o7g59S7g}gpe2pLC z6$CMxL(xN7*MWopP%_4^2=O7nPZ1S*xTibj;I@}u_%c2c5G!Jn1T7ZbuaHlLYoSq& zR=7odfNfOW3>Au7GURRa0Rhb^*D9*YM+NX7rQWe{P-PM_@_^TYZDaz4mt8%=9>`NH z)57}-VK4pI+gZSyzE6@9fyTczjA+f*O28|A4dQ1FeUJgQB~QLU*wjxy?#NDr&mcQf z!;iC{U~YUu?D~}h`8X~9%clSp>LZFO(-cjY-&vqChzEU5(IrwaRjF2}di|#^`OT2b z_Y0(SrdqAD^)Ks%U&bltK5%`nfMb{faG+0TRJ z#lY(M$G8!6yZ;keMC#|~{DQ;+F)vHw?6*2n^BG%GynSheVMgeD;>DQvuXab%QA*Yk z3quWGsW{K{7^^sKN%rwKO}}c;ugV|!uKqfDI+p*-vx>eG18-YGJ52ZWXTR}Voh&pD zcn?sJHHJFle?EWd0(VxU-+uksF9B+&t0hwG`v3mdkTI}oPKAUTc6E=?3QxqP!7p`u zI`H^0*tfV1ez(s2dR)N=Zn_paQV)mXFuO^VvK-HOJTFd7z8oBf%$Ng}by%x9A!zr*@OYHUXO#($ z#h@Bgt7cGT6}nmldova3&4qsw_lDEt`u!cFl+X3cvCVfyzJJ)(!TxxNa;A$X6G7fSk~ykw6rm9 zJ8x_CD5}Io8Aq>Dm1AkQ^%C|d)5SFv?b9+y#3wVQ+nJaaXP3@;8lRkW%I=&~xYwK= z2&WH`S*!a(ZB-d5Ah~v}1wR<=(pt6BYRuc{*iAzQ0k>Y%{~xx#tLIT|+4cwVKu(Wf zFgX~o4ZIO;qD>CJ{*=F7=SoMqEwy@WZQH=4W`$9s=3sA10pbw>S?1m=1OelCf4|3C zYqvhR&(G(CPJBvaG*KJTw#PpO1P}`GKiK{T;a(cffLF?A7ZOivC_&-{8{m-og(s*E z0kHvk)^}4`4;HhCn(I(FT^pMjIWBxC zgND2Lbd@|#c1Msiki-#7I8#{NFM`bo$~;{-=B_Z_iq(W5frOs&&EBuor_m_B721JB z+DS{Rz;S|flf9Sr5R6hG9G~GZhGZ8z5s*yMZ;}ts@!H2Mj!jZ3!rMyc9D2OD09is` zf|LHy=Xxm-A%#!#K8uQBts7*Wn|4K3fVZH?I^C z7mr0z%&y$DC~M;;qMJ+zcTV89D{AFzxD{f17fVVh1+@}F$9xp;VFBG3nw~c)#Oaw} zTpFcKat;=0C}z8Ug^S2$f=H>>i|;CTq18U6By#azmj|3BUoa?Imjykz5u)-L22P88 z>4o@Z2{#Jv+c2}(I9^!NG&N!&U5e| zywq#ey~Po$lJHC_%QP6g`8lfCle7{^WYD$w5JcLc6(x;Rp*jT3GdX&`EcqBY#lSd{ z#Y|p}FAfcQ^trU9^uys=+~GNn6(>?oDkrnu(eT;=AvZzeQf&AZSC(3tg^cD%$Pt^q zQ7b-n!edkV-=~rQ?I{;Qc@U6`o(qbc+~pL4RJh!Q*fLBJEzxJeufdu-@YgE2no;tL zke&Oy^0r*$l-rxL$!cpu%fiFrQffoy2MZ!P?As|3%&~YfUf%&HTv+zDx#EI`WWO#) zQP}($thSZ9a}gkAlA^V_S~Y$*CsgG&%@qzx_CNAMc5RrIH=qB$N#{mh@5rVUMp@D= z=_s%VxU2el-x9J;-eie!l8c&%E4tt=R+xkVw}z+;hdxfwd+-rs*y$q4(U(#1{>Q2W z84^+6-BS0xzE9WbtDPqewfNf?OxbS|a(6f+-OR$_%mX$DkGAf%>S{^p7y&oqsX{GN zd3#eqY-|oIJ|zVdO$k(I77w0EoX~OvMHi)Si~}Jh6BG#3{?SrC{BO|A(8*=#sY`2V z>}m2IPhDt{TtNC)oSzPg5IC~cF2h)SUzfbGPuvyFX%?Ae*O|GM90QSDL5Jf?k-gX3 z>Wd3DcQ5Q@Rl;|{ZVtzA(fU&1eFtk*6fRP)tQ^14IA=IBSXVOFHg-{p2oNi!xpaD3CMliv^@0?E}Q@+G48 z1?7)*?Yng=-Eg2bmi6Ct{u4js$rrM?8*A^EVJ6AjOrea?C4M+<#c2xi}EO?}sW!Po^a1;MxXcn0YFP{I3_< zemu+DHOr!)%^r|sqM1;`dY3N~WNh*88nlQh*}d=QZUtUT#L= zOy}G)<}QOoXI>m77?v;uIq&9dg?&6cmC%CqA1a|xIY{1^j>T}teg+j4E+(h%KsYRQy?q*U_0>&Z{hF%9q!3;8eiMV!lX zDHO<)bY-3;Vx4)0!0GTsm=1{VP#*`)oD(Z(pCuF8gRnjJb@33;m>tQb5%e*=KP3V= z7M`@|$u1F=lCIf;q991CbP5Q#2q6fmkVR>fHS%1CMmE{AaQ0(7NH(f_*tmB6^p<0B z;9KuwOdq)9(RER|r#dllAt6WF z#qu&$i4bsP%~|}zDYPlYF=nbtVfmSR;{0xcidr39l4A9Gb9Eg&c5!`M?fs0AX}*EG zyw=O^+RBm(AawPKIG&VH3(`im*yHlE%gSOY&&6V*YY*X{kwdnpVg?=i9hC0LJrC~| zL*i1wlBmtbOU^VT8cIGF?#;dBRhCT~%tY`yKNf|R+~>HU&9es^VCLC>P<#`FAoZE1 z73_t9MV~IbAZ#7Ol4jIWTV@QgtQ)MWU{h6BN;u~7aV|@RAr-|)x#v0DgOA-N61g^V z32`b7VZ)u-D1vHJJo$*Ejl5jiFo=~qPC7EhsyuBZ)^>Obyvui`z=@Ejk$58*vP-)X zfr0x~;aRjN`eZv#&gp!s3S7li28(zymXXE5s2d65kWzw56aV;vc23*WQXdo~DeVByZJ=A>7Gn_9IHI5E_ z?;Q@mqC0ESjsT+Qg#Rke2gNO<$J&808xhJj>hbE(+`NE3?v7d^Hmb&6x?X}}Fo*z4 z$&!JOs#98X%^0hY;*B&PC-RPhs94^M2zkt(u6G}}a|GRT197xup=_lc6%Y<|iaLX7 zafu$B&%579E$>Ifm*_BQhYdwgIYUsRv7Tu~-E`3KhFXQ?`?0``5Xz2JJ3*noUR~E? zSN36n&noxT@o0GO^>F71^@8YgrPGX?-Pli_PH`PN9Ec6_ead0vI`(52qwa=UJ4q{< zK%URnjHDOl7Dcp{bY)`GJQv9zXG}3q*l~%!mig|xIL@dIrxG|Z@d+V9nnQqpN5lJc z<g2F1C>VlnOK&$Ln>s>d61PS>G;G2L8!l5p4?69a57gk6fYI~uBKVZ1 zUBQKt93=Eqo~PJ-&a#~)Tk>6GDipW}h_A)&UTOhD)iUZp&R1rz7j-Uzu&!)S2fv_p z{D6(MkgS53m%pmZJ*|I=+hJXlawv%JdYsbpN&x;T1k{Vnq*~4C0L>kPlg{a`y5d;G z6_HDBp0l9!E*-pd;j@(Su|p~aFa_W5)yCq)ZuCS02BzWc-eAW(~&wW@ex?HXQk zaNd~_bltm^ zXA0-6DdIMiQ%{TgPERNy@#1mvK-o%xVk0ad|%x-)}b-0hn_i03vHRHdM> z#&VIZSI|0iyq^HrUT7oM1fZ*DZIQK00$>>hyvxsKQ5O-O=Ul_3O{>Sg za*%c0$VTly()k7nlPu+YAPKGU2SS0>`yyz!t!=2M<_RM{WL=?Vi+yU`7xbH(Bg*p!u0xQQ-<&}K;Go^wXj zL7!q3Fg@WKu3m)E+S}ovKs*8w!L8{BJ*=KZY^T1Z5lC92KGi{Ogj|RRWUNi-bsdE^ z+9*hFxKjYy^)6eWduiK^7}KlMv+bI|lD|oLVy>)`At`ftQ0VZThkD^UFMT7A`kmH* zA=M$BJwQVo6}gCrl77TT39)Fsd*{c_K5T?xuMP56sI)(}mW4W*p4ZahUPqA<^dg{) zNgoamLan6&zjtsDc6T|doh2`!0?uc$JZx9l?4BGGHS8ceN^m`6Sn{)AlXpd z4sxBdYhis)hY&FE_w5bJlIhKH=l+J^XpJnDo$M9h5Fwk$B(*tSEi?u#ywD|wN3qHG zxr7(PkJ7S3r9cG@Co-S1=y60vD}WtH{u;AAZ(gQ3L2Kg9aEY{)8ADz;epDBd$s}}( zPpEO;hl8#!>apEHO!EpqaiB^@?lpA{U?j#-fIr?yxb%=OSlId905+B~TB)3e}q z-d{WX{)znk#Prx(|Gxrz>pAa4e#Kb3_Tnz?mJjv*$;D=^XSUTDCk)7lKlfw>tTZS;p!c|f4)Z=Z=BnYPw|#%#1EpHHr{DkklK!7S?JLNv=TEHG^qpZC2d*~{ z#;HD&j<=c+f-1V?HIdT93V`X1?SJ8;@bP0>P3@HTCOfS_+xBs>WK)^ucl5l{PS`f_ z^MM!ejl$Ms5FD4U5AS|gROyZ1H;wVED00-`gB27~{rkf^N9hW{6%junBQ zy&xdf^Mu%)1A2_Q$7+^xh`xN;%WNi5uTp7(~$ zt5bS!Xiw|5i>@Pc+o-~o-_OSzlKuQHT*WMG=q^4&6ybL6Y2vK)jiD+U#rJl+R+A_X z+GDk5>d;=X<$ew5R<caX-^8>BdmJ)S_UH`=0gU0)SV zgTnn%l;ugeZh5b?LgPYGfe_D!pt`Lc`k$>$7?54V5D)0BCH+)W5&7L{49O9XKLy}W1ly(sm@s6GSi z5(^&XE+Oih$^($124{W{BnPs^==XA-CzCp%+hukRy&`gStK8|Wib(S%asZy3(uqt3UT%S+soCi$&!e@ouG;q^F!kd zpX`yPTs|CNXc!^eZ<`S1x^)UOP*M$hN!xN1#+{hRGX zrk@ApEUt#E=s3VV4BxnBmhV4-)If&e`QVG|!5w6JwYy8vK93&hd#B(J3f);U3u&50 z-7L#M54~{I8^@B&GYqE@K|z%paSU^1*<~1(h5CSy^I9_ip-K1F4!WQ{^#!hZ(C}v1 zc6&{$=tz!(piO+Dtm0XHF!;p0Mv+SNkUhgwKol?-Td7k+T_^1IbA4u-6YS%oNMikR z8aPf4dBQW-;8&m#@ojrz4M=;9Ii+)+AYQB50R+U?Po!G$KB{V(X}Pf@?Ad-LQaktR z=JQVwRWlVAWp|0syskObxAyb2|9^3Cr;1@G-8g0$Uf=hgKJM|u^ZPdTANN)yn$K{^ z!>aki^fiZs`h3{rc-y0Khm|>oYBWCOU^P4LBneb?Qj$&jXl&IuFmZ(ofGm-N&R_t3 zkNKYu6q@TSJ^b(%K4~86dza3G@NqRBVWYRjv&FCe^M1uWzr$N442!AvJ}#_z(7tW4 zP;mMl+#hezdtldl=s&#qqea6@*luP(lK8cL-W|G16hAS>%V%f^>*1?AE#4LiB{%|Y z2LL#gKz%>19AX`s=pWE;H2hi3-_YMN)xq!60K>0J`gp{7HCWyL7}7jyJ^Pt5ydPh& zE1(BmrDicxVqu6NjQ^fR@uA#h461>|$dt>VeIRPRzr&_0<0WD$yEf!Sd#58H=M_~6 zL%m9$!ZK>=1BT#dgZ^c;POU0xH?+FJUUmibnfoU8%e|4IbsI$5u1kS-XZ2M_;j|X{ zaCwG*N8D#Z)?0~9U-#40FIeP2ezwxw3H&!gO7Fg31wWMU7=>K}xVesxx%JHIUSsYZ zQv;mo;TmZ5idn%Nt=XhXbVzUOaoOMZQu!&Qd+OH~9`cqosjPcesK~pM-sF99U1hg2 zPxWZwrrx1{Ayka_$pY0=3;n~LT5>nzN5T0Zg8ki9oce^*vdT49f5|jjQhN4`F@jwC?hY|| zs0hCzerJnYPxn+E=ICXdpYuZV-xr}IA%{@amf8f{yuG}j{$iGMxg6{Zf8?c@T;M#x zWrdByFh;iU1kqtz7wXuEw!k)Dk7 z^vbf^cjQs#xb?r*nXw&Dhoyo8ehFd7@ih@e z_0%f&9nsN;yr}E^1OV_GTv1fsmoE4qk()1b<_mWgH36YbJ5ySOfM$3JpbnQSwKAjx zF827gru{y^P?oyLZ>m6{wLpA|McOz>wbSmfa#^f~T*r2K*Ghw~d2t7^?TOKrhJN<0 zg+8z&kz+xQv*o%z?e^0Pw!|b zywMvkL}E*lj(G)He~{n}9xEy2{(UMb|9-YlHgt#S@@V*bDe5{&E&;RyBdm+_bBUmUz*V`wDnH@w zulcw?SZO_?StD2BK(_&HY?*W?=9a=~6L+-B^DoZc)php|&-WMXq;Y4<0TT5ux-)2h z_n=grX2djo^=AqI4)0W-Wrp-QlQ&WR+fbhIu6vV#-) zb-D3`oV`i>HV#{-Nj1n=FP?F`CcXB&*X;SY48zd3$aZl7wG3OM6XvTIE9<@#@qM*4 znT}wSBPdxt8SGZ2cRiKh+2i4xp@)nIG_RdQ<50To@8w z;`?ryGi`;UM-QDf|p8-umR+(%IVLTRAi5*Hl8P z%GO9hJs~eVPu>4)msYAN2B^7Y%=~?#opmnO(98v$`yTo@`b+!$0u&OsXp6kzgpWAG zP?IURX@<;9RLZ*mu`1~NrH1{}e^lePBIgAlE~^hwt%MSLfpgk{g;T}l`ANl`6gm2_ zAqY^ypxXSp*T^rgKMv8&`LapkLgVYk<&PS*4@7LN#g*xI@40!54Y7OUd7yLoDCd0l zg5QjzN0%E@H`VxG%(U{LWz`xfgLW<`rvCuD0cm^Gn{bQ8nf6khDuyCVohl!)o*fdU zLXzxHC-)8SG2H();@!H7e7$qdn>=Y${A_CxbCIR`@?!k%!`2>ZqlVD6eZ_qi$|K3j zSIC3_p!R%Y_I~en$g+ZzN%6%Lw^iZjnhZE4E}>Dd_|%|h`}X}(sX8-i&3Cx3?7TX@ z5ah@fJc0czKR=JZ+WNr*KvwL~$s2c(E%(CAQ0TXN_KtLrWxnZoCg;@c@2dOf=#DE6V?@%}m@=E5OJ?GCv> z?U#oD<+bKdpU-n`q&rl)?*Y&-4)4~Vaa0La`<{!h%X_i=J5z_25u;|8ZSayS7Yf1e zTYDQm-?NA1;2jCT9zkW&m1XrKu~djJ&FRTcZ$MWRTn=})s4}gbiw{uL?`9T7Zs<|i@x?fmn;^boJM>i;N#IUbaheL9E ze9IeKL&FRGxMHeEfE-Tr{W^Y~uc_V3ZhDJty?qq*rL=02~kFPWxd%OSocoY21?pNu? zG}o){zVE=oxU4;r`LZ6H6-q2Iu*OHi9)wpezJY#cs6Bl{4)b~UX@q4I2H|-<7`=<3 z(%CfMJE!k~WTA6?`O^6)p%Cii--*N9iNk#p=lJ}5GWR{bh)5gaMUlcu&sO% z*iCSuKhq)7C8z|SZeB!rN1Zi^gK%?7)y=FcO&@g>y)TW{I$zteQ(TLitlCb7uF+9@ zjFqF8+O+!otNLi%u1`}WZ;wng_eZ(K0MjP8J=;mQb)3+j<#S!Yk{sO^p*?{>lm1Jg z?-R$XNtI8Fj!sP70-9ZD-f}gYVd=Wzt8bL#OfF0EX7gAd z>p+S6hXuey#ON16SI_x@Lc!oUOt*}o1;2Fz4B>WpT(R8A0Jb-?M~M{tp}U`gTSnf2 z`YgN;95l{Pbdm^mDYn~P?U$g{5j1qNKz8CkU&Gmt$5f)5zjQoO*JX8f?j+&N%O{PB z!GnsWj`t4q1>HdN%wz%tgClDS3?1LLUR^C+rWGNoW=KTYEmy~8&iS-L1y- zk_YhxA{mZ!)6rDO_hAz0TiW*ABzWryNe&lI&jrXayrYG3^(8Gx=Sg#{EB%E_x|L0z zJfr-H<#fu8J)40jRFba%?8Oh{za0O{v5SIz>A-fi^kCi=2No&QB-`G%UDO8zJWIV! zKz1~PVNYR?p{v&W$9sg|@c;dWjV3b@IrPw+gYkl9R*lC=lINfF_pI{rJ&7A+XrTp# zM1tETRQUptQIo(a3bK$ty0yUi?c6IrHUP2X!$NP1dJtM3#)n`io zew`-?eLm(*SJ>re6Q#^LF^52o7C%@=PrqJ{yqNmE!KS%)m+~TLUBARfb0mrdx~x|jI$*M!LmLRPURiXX>kAqU?5;%Z>p|uSTTS5z-9JZ{!5E=d zLoHzJqqN@B=C#zXI7C@BHWx<&h-{dq7gK>tXsND8J|W=h!MQ>%g>|?453@`8+gul_ z*`i22gzp#q=8l+HC=7`3Kw7t6xwC#y=(hzq1*O#edcK{nCTqX@4psNr8^!v$ZcogW zd7;p&2Uj4=~G} zRPSYz5I~c|9tdQ)*<+1>bwv^nVjOelVGk!;m z=(MPqbMn9(ijL@b!c*4k2)@wM)X*mADtFq~#+xoJo6q_K89J z5BD5HBlk5!_~lB@^}1&wulG=7)sRJk2jj@!Jtvmob4`PMMqr0GcMMT-10cbSWx@W< z*Ke=yT4M)1Z`@~0tQx>_w|1X?*Ofdy*HG^P%%sD+oLyx0Ba=HK0?+sW+oWY;CPI%DoAsHjc~s ziwWvielmS{lcFp+7}oAXxqx=xuVJLm$$CF?{sOAI7ygbgZTSSBdcG>tGk}4X&l7Y( z7i7wf{^mc3=KXsgNdVmlbhv#=aHV8#IMD`+2e)|l9ls!77o@GTwxc409Sza=TaT}d z-yihNM>1w+CI2g#Y!%M=?rAi1)0Oak$DqnxfCYnJg|GLkJFp6Ry=Zh;%Ny!?H1C_Q z9fSZBI?wcd@yMvD50AQK$k)73xO&fkSNvyd89zggq~3a^q&_qGttIyB+HkGw*WQ47 z!6?4*bWL4hpmiyT{?AT&28xA2TKIU4V%q$a++7-BOU}lKVYx*oqMyX;n_b+&}wSejSy`vWw$;i)s@HlY#qP#<2<}3Yc6UELQL0SX%;nu?RVO;+UR4mgHZgXtbPygC&8 z6AE@e__in($V_V2f{zlWj{xG4`#PUbr*Ac|Gv^OgVFT1s;in`X_wgyMjZOk-19(~< z6WF)_!$K01eATs$aoQ8BBt~g^o9Q2Ry)@UdM(=vHRB$^dM~k(ugs6MlQac|zm1cRwq7xTCgOfI`zQ344yTQ) zmtOlbs9FD>JjyIRU^e20J&Vt8p8}0A&-dpJ+B0~Myo54nj=w#cDi=3cVVv!?*iDJW zO8}sF1ow4YONp?sI3lNODk)a~hE1dU+8iZ(kMRb9&BsIT*J-1mKlIC;5h1S)XUC<= z9)9+6dSEY^@BaJVG$D)7?%$GYk!SqiExusR-!&(d7`lA)!jkmZ~1rwF$E~kJL7RybUc+m`A9Au^B=zJJ0 zWIk~&DE#q+P)FkkGW5vbOQwN zlHUql$GAAjpB~mN1y~khcF+yfSM!@1<+O6WIJ1OS>u*2Gx(Ycft){!AIG7nCBy$E; z{JSs5|6FU5&&V+ewXci#tH)*kuF;x7JyyZ&xcL1{9Y=NQ zFE(Aa;rgz{2#AUves$&Gw;#C*hu%C^-w>Et?AJ?}`R(_Yi|yLI_|lv5c*u8?rJniE zypRtpmS!`1Hb-WiK|*>%^a%L^Rl1lct&wYOkfn~cIx7u6H|lHr{PCY(m9WPnctFIa zfZtikZ{Qk`+UD>E z#(5Xpq^Y1QBx@KGi#zO2VBLPAop`CpfPKBY=dP!#QOAnJW)`JIK$y?+XB)Q!uYb02 zS$IR-@cQb4!8YCn3KILd1JFG2zy@yxUwZDsn8XgIFilDNb-@bU8 z(m>Q-0$M^Kdy!v;gVIf?+YWuaZ=7`I#S@E$ljI2y&k`|IRE#%LfV7JN7pp8IT0wu8}MT-6U~=>gRt>N2t?z}7pNo>kpC+YRB>`{@o*z@^b4`k08@WU5T@j$w~{XhT8sEy=5{>hJTS9Xy_KgmAdcbp2`ZLbhSiuV2tXW?Z9_BkAb-an?t*ROB znY^nSpc61+qsbR+{boz=LV9m%?9!fW^NUrg`~>F(1HaU^Uj%Cj@s^^(SBDE|>#r(ZbkEos0y6RB z_HT{%>u8oVf^$TB#eH87N{`2=PKdT7i;INsaw|2+Myw8T)*-dGq# zWXQiVPyu*H|BP95Td1H;`#`690fs&Sb50FYe_+gLrXgK(u^w!hs($Z96Nj;?x{tk* zO?Mc+N>ktFro!i&-{)7(j!+-i>#}kG^&MX7(0WBlYruf?Zq6DjpIQOV1664f=R3>S zcjy;@-s}mp5+h_Ga0%h^!*|RtLGl(k*VfW<_`pM_R`yh`$>_aT4E6X6Cf?sQlnyZ8 zXP5vcaiKevYC`w+@i6F%R8i$ZjQY$&ZpTl^jn#C*AXabp2;OBNobI?T^qxY|&WiYc z&7Fw)?c?407l-6u93plw`rE};`$M=so{F%VkP>o{~Qr`GCDKn8~01y|WOAkt5I}!8W+_Y25?y z*N@W$w`cvmBRCIU^L^+sR1LwO*V>D|OTkh0i@&FioZ-0Az^M{)b@PQKfsyvtV1V5fXU(ts)uE;lTrXQXK+2#|7XjaIwALMYD`%|6bU;b)Ub#rUKqp&BQ0T>9c zWpVfOZ_3Y3OBnl0P!5{!TNQ)Gk!&R4D8D|{j?++I+d>@k98e4)i7`s^d$qaPva@7@ zf2ZF$0JE-sfey4AFiUa3-wOV_A&=NQg4<}3@mY9zzzTH~Nb{R!+n*nF^aw9skqSjO zhu;^dabF{MZFGxEWMSh(j1nhG(d$4>BqE?LZ@BySrk0||k`IsZfS*jyL#w3yG@bMF$eyHzmM!Fh>KBI!sD(sf4`m z+eI&+eqCtV<4@WMT#bQZ0+I=^d6&Kt?vQA{y@m0D%3_BV5f3HNNKVa68Oy!Tnx z*G>%t^W>Q=Jyj)iN`6uG{dQNxfHMq4v_~^ui&dWh?l6a1LjK-SIRxiR>wftSu`&=N z1S2!C8D@o$yo8y*3F!LiK+Y1k3FTZy>Z2WF{5yJhJ9^Bs`;PJAzh!h*q=yI-t)>2$ z`#aUmQ}+4WOFB=zPdRyvi_b$oZWt0heS%iVVTd#XYR-!z0qz8f{3W!Kr2h3j5D5^@ zbnelpjqU(ZXZy-87<9OwLT4+UR4*G~S4 z2-mt?1jBH>xBgb3EnIrpkUUn*cJ{fIzd^{EpGCWv!N|P9uUu9XrX?|mkpkB?I-Fzi z6r@aIHyau##XKjAZ3S5r5$tyMQ88JcXxdKKKALrQ2jPk7Q5q91t66BI9W8M}4&~u0 z^hKg?_={OjlLjmn;H5j2P3+94j@U)y;xJxOqotIe^RaE!s|chMfy#P*sjPT_G^D-?CCNlP>E#^b}9Xg zwkai=y~0?`hHbTbx2p#GR}N5=qy&sv(D=*+hU>;F-v8d6E=Y3i0@}j{Sc5|mLd(xz z?!evL_L1J3GeuGvcy;ypFUN-3NDCLI&tQB;Yk?;t4aThfIPx!;T|{%6em5;EqKHgD z#QI@&x8?@a*u;#9E*rP0?>`mfiU6~@7=pLxBlSMAwi3OS^|b$~F(1n1Z9 zbjybGMv58sh0=6C>|sA?z&Bb*8d4bLLEyB8`tLfM8t8rFA%!&R9biHC zQ-aTh=4f?cnt<(#pI^V+1E?d*-nkuPn01Quvt9iHIebIe@P(ag2!eU>l%L&X7{IDO z5WRFd7+(?CkMjCqXW27=-mqnnzzSLz<76ZNTz;6*#TVvc^*iucFRsr%PsI{GK)umk zb;zEKCgHZb$UVA^m+hCM$8Z7x-SR>}>JbXXaRRuM_`|;%YEtn~^Xx-CEYke0_j~cr z_udl8ZLQ^_>xS=T2;^tF{RQ40HC>>^1DwgDX{ZQ%SpD;1Zvg4vj;~z7D>N3d7Jo5Z zzQ83q9LD@(uAWiew%4SFxoPTWbAR7y^8D81fuw?6|8hR?sDOR>;+!JrnCDV(&Gi~O zZ@C9^0~#-W(AS~)mj_BW3*^VI+b;!~6Sq^$`x&FVkviDcP0&aBvp?%iy=$m!AZ!R9 zz-8rEdi4ERAAWQhhm6~xJb;DvRg8!FU4=SDBjK!qD)l|jpPv~wiZ)+o^zE#ySMrym z-V)#=HXiXd${fJCuSc0Z&7nkKsO)E-o!Ck@m|{|{23vi|5r@+s zG^}|2E+W=+xoA~z@H{kG(N)&T1S6q#xV6U<2qEuUH4yanoiVkkeprtR_}c_5?m{jH zDSXE|c_zQy>~fQ52ZbIm34VAV5@gPHT9y9xTB^`JN4|GsfXTyzhdiqphrc}l(>xo} zA3K~h@`8gDU?mq_!eL~>Q%S(E#tXH)aJ2m8PB1TG>*TTg#gQiiL^<@wv$lNIUD=oF zrw1H8;qQ*_LIFUL>S%D zAeX4*&t5MU2J}g%C9W?1^Dl~56VQm0E4CX9&*gv&^Q-X=?LAm11ye9yJqnNCyZfCp zQI)l@mGEfaGWUU|9G|+oz-b^VeC_T>RW;z>?+J&Gh%|eFAvnl0>>tK~SeFb2TVI;K zd^`2kd$JFUWPx*m371FarO7u&c=;TGz4V7W4fq5s9(W-ofJIP>7cT;`^uKq$8xQt< zUX35FQ#M%}K<-?YZ1O^Hhr@~i`Xi_O?Mq;;Y&$!3G1#e^d|+k})nFgXuaRimXxCnI zO$z}=BXHac4HzJBOts5oa4@y75V;k_Ds2csQ|iUW5|Lem?J7=Tm!@3(gXST-zIV{_oM=?OIv6cB(LM)B24 z<%zAIN(+OSKiu*U&rvn^de9M=`;Aa|*VO}N{=*F_U2S0s{a4rT=l3@n{ckB}fG`|( zoi0f>x-MuML(Dcj-Fn4PqjSKRy1}~p*&pu1;Uy@k zE4Tr2%z%MpzdZ(AOJ?~@xrf3zCtBbmJUoC5@!}0ov1c#d0KI0U%-&P8|2d*SfU3HT za1;1bni9%(6E!8+r6+gQonCL~_@T<1hH$y`berZ^GfDOX=Oeg6QyPIeGvNwT_`iIi z!hAUdw${5587O^V^?#Q*%ivo;Z8CJ!wV={GxV~Y0@`qh{$=62iKXO9j0akCvc&lI9 zpG`>O<6$SadHocZ=?bH*D)U#HXcbBDfvCJa{uZ|292;8u^@@`yc1g4$1(?;AJ|{2x z(Sbw%QjV{+T!+T*9gtVZDYh1XL>aIHe;YNUFc7MD4?`j=I3wuiOX2hQoUyfjjel`6 z{M8&pR~1i=yTK73Log!rE)+0@=75vm!Rc91vnFta(B_R0Y`2E~`~CESE?O}0H^h_q z{~_(&d7f3*b+Of?$X1FdzhI?HgcME&j1)xz8)IW*Fkpk-EOEwwF(-pTN|7$blG4n- z6{Sm=B8rs1kqduguFRcm?G%~P7{l|`Yrhzt!~I4k?Ptm{=n|BZ`g#PNo6y))W8(Y%)dpniDfG=(Jj57Hy&dW}aE^pL;!Q!?p9E)y{v<%lXZk1xtkU4yN`gQ7Tfc;fSJ?A3#@VYtzwiwI zE|E(gI&Ft3_CD1LQ6mAjJsFX_5~bB9nr3lQC+DyfP15;F_qKB;AychW6Q^YyBd~@( zcV<1H)%IwNnjzI2KV`CmyCrKmD-3{}%HACBd9XQrj0N9CFS+gx*#YVup`a&fs+RA7 zKk!tCH@5k4o$kA-~MyL!Mw#k*2iS z!RT-0WXJVQKNR(bUc-Hm@9u*?1%#xZsBqy;+u?BJK&mLPiA4`P#aS!b+$!NYuEx;N z^WgA~Eq$$V3l2Yl4?=wbs1#o^&c^%6YmdtAgr3iaE@R+;p7F>NHi4*DFud)4S#*IohoolD?)@&#NddPnibdF?IthEoAz1&MMkDnCCHzr`PZkox_abkgo%wv`)c8vtfXd0+yK zGh_Y4GIGh+ui}x?(^8v!4dPahd}c9}@eOagw$YV6Fx-t@ae+AP#)rmL?-c;DT@CcT zqwberA|E&7Rkl9X%!1o|qyFaQo1Vx;uVyE;wkh&Ax1{2zio|xk>Tu2Qw)u^hZ94K3 z-(X6L^YEd;Z@?5$KrPZ)2$c-WpaCq`M+!$#d^RLRYL#z3$t1M;k;>l`wmtMatyDWe z_X>7Q#)Np|b$mK+Jf@nAC3e5r$bt!1uHU)ql>I)wY92#`|^F)8CqaL$$5ehq>3)T-i;ao}qcShrx*ie-LNf?_H)j z@d|LU!)kwmw}J=_KDjOx0;OQv_(jHrA7Q$Pr#rZ!{hxZ=ruO&h(c`8|p6kBXi zihQ`f_EBHLv-CB>?DW3+8vWCPJL_>OUcyOW&OyBKw>8bpqKs3Oo?2RRjU@^q|LSEF zqixn1mjX=wKH57t2i^CPZAJ-Fyt~a?cj5HTFG(F#k!`|r;B`V*5EzCfX|cH4=S|>3 zU-W0}!GrLwOYmlR0Ly_F-!0Y3QO9?#X!DkQZQCuhMUDJD_;2Yl-IL?~x9(kRV>&Edx_&y`v3e_8oZPy3s@I;s4~%!7A z>xg>g+!k9GjYD1Z+7mJS9OBiMT65z?i1Yv;-$uJgWNOVEz$ZSQ$4bGPsMJ$nx| zYMuFq=dnLI2R=t(?AjN%tuB#fr=j55@CoQ44c^0nGu--DiRy%ZwjBQqI)Fw$hm{$K!w~40dwFGMj8tyjQkvr+HRhsYnE4}yyf?|A$ZFxSABG+GUbm*vlm4~}e zV|&8}dV5k5R{Nc#>{A(L=m9~~HJG~-N#7mbf@&{GE^FF4Zw2UYp!Wd(+bS&fx@6O z9oGq?TYkKU3I;3o`rGJt#p*(nmmMaGP1C~G_Z8QejCNU5-4xr@@$yXHC-u~}w};Q7 zF!ow?>G|PNzTetr3abwYIF{cpXPGw&M!Nv+BVK0Zh@qFN_Aq`!>p2gQS-dyOa#_~2K+#PyEbX~WO zyVO?2L%J@t6}r;bZ-9~OXyvKR8S6X0# zATIL4!_iGkb#~yAEVaZ_8Cvv34#gNT^t}&dsyvvlDcevRBFpk_84IDj8+QZ!04*ni zP*IxT6!;QG=y>W;-@`+s%4gZrm_ zWO22F_eR+YF1)fNHsuNLdS6{iUBo_r`i`J1nH!F~T{Lbt0aXq{`fmO6FQGdJ;XgfuSRKb|svDcH8WbBnKQ63W~b|VtR z(o%Ag#5bX_vw)AQO4Xp3vK5*q*0`})A7Mm5lSj67lT~^b?}c~&2u@A?upQ;%^Tr(< zHK7IbC1D;?RoAszjfD577+BRU`?=2odI=UFc(hmLQ!dVOW(jCZvij>M%e{| z(h<&ue~{L%hPEUwkJbn2Q~Mum)cNX&vv@@MYhbt5Znx!_*LmAq;GLm?SliC}shKi( zt{cA^4(m;P^z3)b>hl&>srPcP#Aec+fBo+Q`fa%Lb<+OTa(QVeC3=V5WoW&&m7?0R zhc7ygIJ01+S>jFvfxc;vyY4eCdpv*BO+_fJTPdDrDxe?g);E)<{MTpu(7aJ&cABS% zIY76B+J6U9&D!bOM@}C#@{wu3GiGxDkKDS%8or}Dj4)p}idI^%>Veh*)Cqo5m)#cT zQ!Ax}+s%RtYiD4S0RF1(!6fkxOQrOF9AD=1wzHt6fd0WD)%R=OWo}OIP_yl>FL)Rx z73UM^K4piMxB*((LDTe5R|HC4XBVrLcjSKasz2x~d^z8tuU>;v?Beb%T>)#Dvx;#X z*Hv=Xu$6m7w6YG)ua=`yaC`3P2$`4keUtXw9N+9ZU%@bkBjYj4++77<#ozg?SLBSK zunz1p({q_<*@wVL*Gc{KdOX%svp>`?wubHqw7K7!bONC{XtCMq8?Ow`cgwo+7zelY z8_b~?btu}N{K7x{jj{KI6ThQ6`W$7D(>`gx@O-K(crQb`eaAVwqCdM)$A8h|fe!U*t>@^(*&6j~>;1}}YX zzT%n|o**UFwJ6lfeu+}q&d=QT7?>7quq)`suLBQkrQqP{5;y^jk`wugzBj-9{yD!q zTl>---lv}O=)5~P2()vk#9T)k^U5tsy$aC+$Wb^WJDYwfAL1;gXH%J&>< zk^LGQ>_!AfA*ridFV{X?z5P*VRjKSNxv?Su*CV{Hi??O zWZbT;O$R$ttTC^WqAQ(qt#gmBaP%)C*yQ~58^`-^m)Np0ZtnvFy};xUi!TjRIL0fz z>c^5)ULO?B@B`z2xMjX__4s2#w+5b0WaK#+qDO|V^>wI1VD`S7y6C#(i(|@@l2P+K ziQcTa1Krl0KH1anzQCIX z#{zEKtp>I^Zr9(>;;TjUAWUEhmbVXZsABN+e`99PG;!4dcvFNMF790?3qD>=Mavej zAUuDmmp`6`bu!xSqM1XFEnStpAxd7E zdH1wI@gzJWaKY=d+Y@nC!+5J-!QbUIrYCxOgOYV>qGwbTG!L%ir^h*(uwvpuwN0ma zf|W8Ot=`AA2yKdw+T$ycSNPWC`pWB=N0tBXA>8F|t(Sq2qhUaAyx~DFg}|RaB=*)l zJ9L*VN@ZrZj71CUwOf0l0D>D;!{LG!VD5_VYN9EWn)|EUop;gVw<0`mziY=FC+}a< zu7UFHs}jeV@50@{*h-#<*N`#XDq=K%s+(nOEf96tt@ zYfpbAwvDsW96CPEeWY?i?PlL=x3m)U2Gir|KE)T)wW;6!_c>M9p~u`463{G(<=HNK zv5Sx%V|Sc8@%pPeety>u$-~&f#It`~JC}{FsDmoVG7IJrfF85cU+oM_nF0wW zO7_!aE|7!WlWZ!%B;&r?KD8K{2`Zmm^w3Dj(+=QUQb(Gp7C$xVY|tDf8OnPA`N^Db z;jwUo`{z}#CZEy}e00#YgFn7t8Q{?9?mpubhdmG;qH+FyEq-0?^&w`)>98h=0Xz-t z9f+%V^FItc?QYzHfzSBr&&RoJMSefP&92=v1n*Kd1;!k(WYloi=pb5_R{DKIW3gQ)atemN`qcWslZ6a&c znlL#EsS(g8-O=aWLBiBmCN)A{V;O@4!<0YgW&5!~Kf^cRv!6%i$ta2pmhRG`UbItFIjW49M}9t)#cfF7qNY}XmrteolAMahFft8HMg z+Z#I=Vs@LsiyjwdsW(|}!;u#KDcfX#F(&I)A@8Udle=vIxYN4fC z7w37BKLD}tmS*7;tb+t68~Th2B4gkX+P z*Jmz6O@XP7fFt#sM~`BkHiI|Nf9es;Ae=z;n-headcJ&yG{L#>9-Bcj?QH~Zp+D?z z(6Tx(tB(O6!0J#N%2;EK5H58YNS7PU@D;}e9wW>1#)em9g&H5dN-Qf$%*^~v{Z>eF zq_)M%o37pW$Rr}p4abeSHc%8_p-p7B`})9?gWXlZ2RvB#YvoE7Y~cFG!3Tzz9>)W~ z{1{k63IH+l^Ho z9d&;1IsT($ev5oC$aTAKL#?8(#<8e9nB}@x&m(x{*e9UzC2rv3^)kwIc|#MCS=s&& zedARIKUJ8TuYU7$qujJ~{p=uP2Hb+4qe^dpeO=w_P$1UlTl%~Xw;3$uB`)V8q5pBW z1K_!8lIvKT8Svj+DL;D2Xs~|AbbMuEw^XfPPZRq@v4IzqE+2O}S;soe4)pRQS+``+ zyr?g(R!!3b<`ypg=~2UQeq^?~GS4n?;O)A+tx9XD;@ zw4}Vmg_*@$E0u0X?6*qqLE4eA<{4%Sj!sI}`Z zz0&cG%nm#Gnh$qWcDo>aZ1un<=SK(~P`U~i%@+{7!&^M^B5xdI{ST(Qc7D(4OZGHb z6zSv9Y3Dz6T8dns0v^oqYyV|VH)sJ@6*LdNnzprny(QxFamz^99I!aI`^$cNnA+aZ zE^!~Bk3EAv_pZ(5!qW|t4Aj>bY-oYn#zhFj^#ntqQ?aKR}}5);?qorsx1fL(qWi5t+;`WYNASa~o9H>xwkiaCHRpToTH_n#|?K(;}L zJODtx`>}-Lu3~c#q2GM#y=*R4wxCE8+Fx_TeOVQWjGOYvp~yJHWjH`jX1k$^c9e!dyhc4+il*=jD^^#t~)_S?dB@H;iKOw*>4^@ zihYVvorRUL6%Po#tB)!Aq=0yt3-f_uGM)t_MPYSs!<#?i20i5&3wlCh@2Qvh={~0~ z{mt*&6EI57w87K%!dnx~b(%c(epe}`IaRlAhGPD8%npCA96`q2pJd4X!@= z#b5h6l-T#;QJ>=>E`6`R>c!cc+t}RL|if@y2dlo(|h`KpMgkw8Y^mc+;)ifkVGS8|{2(&(lG0>HfC| zH@8lbZ=t`Dk`|_g=mAWL^Dch;d~AFQu|wuWIzDXYGw)X4dUxGi`U?+3_H_4b{B5+0 z*S|Bvszzf~UT@;V_Wi3#Bp5;69-A+Jd%5rpNheeO{?1W2BYR4afDrZYLAgqdD{nX8 zyP8gn1Q<(&aK|(F4zEwH&TZvsla@Dt#M=b9C8H;>(BWfK*XwgpWpBMb)iPJI$1il#NJ75YIl@Qr=0cRNu=#5gEFexf~RpL=kTKf{>+`G_dYeY zS)$orsWgOOx^Fg&4fzGoH6y+< ze|nU5_>5QISCKiBaHlsodl@byjTbe=8A+cv6!^SZvz7FHzIc1!O#Rhf9|q2?$MgG6 z;C#}oE;}55AaD2<+fri10h%z>-oU?Z$AI#(;8F!fI6)ITz}o ze$jZMpfXf%Gj`9Da3!13!JPh%GY)Gc+z1JkwcFYCs!{D=1e81#Jkw*mUS$T4sI3d! zx(^Ze$lqSXnm6PdY*`-xG`TbU#SMd@@?rYc=g(=^d9dHZ90GOt^!l=Z1ocVko^Ho` z(6f4=t1ajHWpv#q;IPu0&E`AH$=6MC&Oahg=JO$#?-G1rp(9@Ar%Eh-wi-QXHivCVfvqD*^CLzw-FUb9Le!n%KXeDDSi2lTZ@WS%Q2pjwkGE@Y$x_-cuU?H%GCjxk6`k=;1+#!Q|iM z@)4M%fr;tC$w8;-TlB~N-0MDWjgiXo(|8p^^zeKOdiO0c-4PuDORDa{GA7b}&QA}= z-DM0O*QJ=;fewke=z#xmt5q$WOu=MRv#7hRWSUgE=axF%63^mln>DS!Tf2-DSI4!@ zJwrn{bE??#CUFE2!nYW~fCntF=I5C>+0bvFg)s>4*B12uS^+L%3VXD`&>C3@RO5)$ z@BF&4(%tD2*e9@xqbHaF5q$Qka+bs^OgK`9Shc6aO2|u2?EdOcY^;p-?y+;p6(O9l zKlNINeUZ59YzIZn{&?H(*#%F;wZM!_;~mOPcXTTeAm`xB_+@~LJy_4w_sv>TbUe^M zJuN_KHOeIQSa*huWeEKo>V=-{o$p^{XM1taTpb4(-NH#*?t7|~#`A6fmwfcQj|Y>O z-@PgGRXGxtHAUzR`WVkk&;20#9(X{WJur%lPB)9yfq5#JeDk~E#3LOd`6VvDK*s*s zCu~JROCz~JVP^G=3tnP=UgjJqP$pUU-`q7We+J6QzGsLAzns%qz;;;c)PkuWkT!YF z(a%GF$LOe3bE@5+8dsHQpG`J;-S4(8mwLBxK&fyL`xkp3cGMnWL)gcD7mWkMw0SZX z>AuK>Tl%pSjEnBl_gX>~4`b>2q!cSSq=)368tSrP-}~Z{*l(t=&e3DxwK6Z|6G*SJ zFbi;|LK_i8zkUj|?ow{5iW)YyRgLq40oA(ZPiH#1T`AU!z|wu__gsEY@gE%x-eL@} zuUUf>bm>BkDVDm0=|7l56msXMGztTh?!Tsoc7!#@nQJy@oP!V5VZkC#et{8*bb`Bg zdXMYgI(f$*UaTzvT&ozg{K@0M4FBs|#&dA1cqL$-$Z*zf1Z^Bzdhh(@7*d11B0juLqsR#(nNUhWqJ-aXpRh(5m9@(Yz6k zaC!6_jNLmA>mL9!eZ6U@qy~8uqwFY_Thr;*+vgbjd&ol&$?$oc==!vx{d1=ig{;+le5<8ArAsD}&-7}eBKYBr00SbEH zDa38du~KrkrqdSWE$A$P(LZ3VfU}nh2V0T?*;1wu*geN?Lo;zPz-$091fO; z=v};4+?PRQakJ}9=ksS>c`7B!RI1N1BU{MF73NS}C?C|*qQGIR1h%|FB5V4@leczk z0LL4-<$rr2cfkC)!MM~d1dlTw5U%jfu-g97h+{=8c%YHd5!gjeK_(J%C*(}sT2QF% zq=pGFy5IuVIP|1oHm<`gFZ%Ok5NZ-3aye|ivKoYsW@Xc9s_zWA zT8T8{*2S3jp27dAJrA3QiagzD;hR=@_4nTgSZOL7s_}!_|NH)?z|CbjHyx_?#hZWU zCKdkX(R*r+UHcvq3a-VzUb{$A{iBsS*jr{NU;!Q6qv(D4u>ERGz6%T_8y#V!e5L`6 zEwv4)2;K@3)61}8$nUUOW`>He6Qk5TGvr_0W>TTxc7AIO{#sRh5?+$*Ffber% z>YDy|n0`2<$JFOPIAnq!y3$ZWm||Z5|8>rOR+?je|7#D2EBf2cYS{ZWXBa47KL=rg zC1Q38oGK-|x)XOr#k+sDH`qROuzG@N@o}BsKhYP$YV=0kMjme?w-pD*<1E(HPURLB zdy9Td;iQxot|X|=)mO&1}^L$45iWXJU(UHWtE0RaXBcumVVuWNVSKV1#q)A)$DUtbZq z3D4EXk{`Rr@b;UDg05xZcbu<)Ux8Zt(26Ern#k{!xcGoAO7}a^02S5ibB}_%^y5} zc#J;aJ_R%Bpjvu<3rU79ENpLIIr?0W{owNzG9UiZTfs-D)Ll8{sDynZhzIpY1|Ca^ zL5rVUi8^=p3lsRS`E%&6XYIQ=(=B)%*23%9G?Gm}FFQlHkF}BIx5|#40q*gOZWzPH zhT>3^vvYkcONM(7`1&&XZ9Yz&9Wlb4{v$XEas`&H9A=ys8VAN#Vw}!RgR__oci)3;U=`Y&#e;x?H>Pcu^#&Z-6c_8#Ghd5vklX7>Iytk;-*zy8BxCq25;hLQI{ zMXmOr{umN^KKt9QcP?zrbK*0IFB0)y6DY)f&&GhQN^?a-cHIN^g_AM8yN++J_=e$7 zs2qEpgQtvpyNtnF_7K)bfll^hTCN>{4;>i|yJ&@g%Cqr!+fnkT4#E_IU|5>z3NZ<* zZ^Ft1=0YayzLT9$EzND6dfnnK=;*bBn*n^Q*d1#YC+ebA1RN#a;9Tslu!oYucV8*G zF~FyN={o}J*~PT3DjQE3K+YyV)ZzzUBd?Us`uv=gdD6Fs2+d>yQWUh(z|G7O?)7Rs zrwG*D8wZ73G(T17{Z4<*G5zs)%)2wPI3aS*hf@=B3l5lX_t~hJ(s?5VpEL4SMLO+Y zrL-pql3&4Z;aQs@gN~ZDb}!;0%)I>0Xc(H0dxty>!~RsCkjf^K%?^}&F3YxuM@h4i zyfiM(TwNfCof3DctN~N}pdUirq|g*p^U~(go&9hM)wak!1}=kdo*cJ}1qSZrEdWdV z46h4tX3>6aKOrYDpHFg5^HXK0C-bhJjMe+NN$I=k_UsV2?{=%a3evKpYWXlAu6+Tw zf>VA7_*WBgpe(OECa@ZQK0VSsvVisbCXkw)nh&`vo}n2r>b;-3orcW#@;aejd>%ex zLXfL1Xa1wtyPN>2u;4R+zq593N!iM~3z9D!?T#$hX0_Qr+tK+B5;TFsbmg{rmbMXF zkJPw)<}>Mb)rWG?AQt}*F}SGF zcKOc5W0UKIk02pn3k$bzdGYz<3%tDi>DQMR>CaPcd4VWOcu(SI|G`X3%q?)NfNMM# z{sUf|@B*5{`bVhPk*xKmPjyJfS?tR{t_dQ;-s;( z=hb*f^*~+ z%G^~|4fHaDPKW1_f%*0zNcwOa{y*n>|Ednk*-^OQa5MBB@}M1zz&54**#9Ua?B_yu zy%z#4{lYD;_+UO4EASu!XuK{4^3A)|!>-$v+ZLLuA~E+;>+)wse+!$29p`2Jy^P`| zM-!U$GG^4I_5ah~=%TKvabLCfc(am_cRYE0y7FOu!+XbxUZcfC2$Z)Qr3WHvVeE>e znu~^TXQ}CqVLz_iv3^dTz1n){Z*USg?pd3bHA+d1}GN`4@>+gqL^ zp64y5+@QU{p{`s%rBTw;{VhEpn>cX$D}^-1ZzYgdD@b-HQnPCA)TkWMzbE9rK@q#I zWbhl17dJiw4pJxT@u=3@1i)z!xa%<{5S{iqY2o1x*|n0vvkBwtblSSXAfw3G-b(d0 zsjZ~Hq!T6OXx>!cS8KCO=-fF|O$O25g*a$Jgf*j-D!)P%vEX}aDeC_6k|z^Q?9okLc3d4Y1A+sWy%IXIkE8txQ% zQU!ZYO=AM|lY%r6z+dvUm_2HM(}nPCZftdeT17ZeP6a$hN2rZ^T$oHTkmEg_Pdl86tq{6)t=>t zV*5=s;MQ4nRAHLeRWfi78y{A^WnzQ_vtt*g!G8K}R1kOEXI0(na|M3@1mv0E!Fb5= z_#gzCl(iJ0v|J~3?MO=3-0U$|l0*BJ%(2@i!0H$nc>%N4)z35Rp$X5N^8KOVvi9Y2 zI+ei{H&wn5600SuQwJiTPgv|&Zg(&3!JDJUJ+Vi$r~T!i>;5`5;-HbCE%Pd=UF{B` zDaI|Mo|cuzlE(vg|7#u7U<31S>)35s(7<~Hmblct7D^-N-G48B83K5@7$Lx?7DchL z_$=bwkA7bc=cIJWOuu8^t&yie= zXqJ7zUbk~jLXUDpZHqP7{{lCGW%c`)r+iIiGI*o<1uy>fKLf3+F8%3WBER?lmj7?~ z*}wh9zy9Y{jOF@Y0zWL$_Wh}%zy0ffQi62W|1JOD@r(HU|6}=#n7npz+mZUa?c?h3 z@EpWl7lk^d5Wo@GSlpL*)!_FrN&a6f$v zc*%#Yc1zR$BGUh|`futg{ag2s-{SxL_b&9`_3^hS@jaf^-~RQ#{BL*96rcak9niXe z78vM{8S0Tyf_wj6B zGv%7%RjK1&2XZ6b@n6}A=vl)H$?&Y5yGIv*c~B9vn;sYWeD|yonG;k1yN1L5QHIsI z4w%(^$}b;%8dHC7!7f1OPm|dHwW{aLDp>x=Upj#W`Y3pZZ0ciw-A^8RBsN3&aGH3+Rxq~vErz+t zZb4RX06u2|?C6(@>SQ_U`MCVBmJU??r`l*P|Iwdm>o(_*@zm0R_h9;_Gf!Y}97^r8 zBqK9e$^vimre_d*MEDjVpwo#3npKoEf6HGeLYl zrSQA2hP6*Sv{tFuco@zBVsz*IK7O2~D2DaS*&ST!#ECI7D1_~Sk3RE(I_|bd7`IC9 zR!X5tb+YZFbM?LXok4&ZktQwkqM9KQnWDl=lS~G-W?4b(CLdAe-}^ead@5j;Et1<)Jvs^VD78x%wuXOm2%<)?v2x6w zJ^kp6HC&+B^^$DgEzi2%Avs;!IXUtNk>lD%N!z1Bn_DRF^PV90xj>qx=`x?*glt+N zm?eq6>!Zhq6@=*gB4c)kT_if2P{{`U>suqXeinj9&oE!#g?5P3cKa4d)m}x4*jy5% zkApN6_yx7%Cz}iU?(3ss)K$mqMkIQ}6~T4tbQ}>mIXw#o*lZl{MbBdydU>C|M%4Ct z8_27({9%x12em@)^sLZ2u3Pq@r;Y+_v)>Uh-|s%&Q&k|b1On_TVMlA8E4T%0vlU{R zw?jmbaj^UjTt>VhIG;s=!rTdvj*iIW<|xQflBj!!>Q6{R_E3?f*ADFpn9@PF$kRy+ zFSk$Sd>H}XgU0t@PbWN?lhD53>6tvuNfc=Y4Fx~eEiyU3D*LMney_h={24z#jQWQ$ z_kgh8l&uMT^Qv5YW&lO3*fee1o=kHXx|tNvg$BD^FcDidB9U^efYO32O@zHB?_T7g z6+N24BUks7fDJ1TIKwHZ)2+RYTlkh}FhCB@N<>0rs%&lO$QG?_88v8rnLZ5GWzdx8 z2Z3dWin6;67E1v)cQgNjko0Pgb2n}Yb3d=+Rs_?EOavm1lePGrA*M=2uc_gH#6Z1D z5F2?IlB+8jxM57ftv_y2^I_68XbgS*&TU=9kdQnqk(cMI@15qFz7L!8O9&_9RaK+V zfuLFKNvEOjgFd5e{;7g~s^7HFXHGq?kYxW&Cr!%66Np(?#y@YX@tm*Mr!(Xm3?|?Q zf$WItb6YE2*6qYZ>N|3g^i>?2UWf2K&Avcuw!M=pk$o3x`9mbE<7T;3iHxCpmPT?W zypb4jL>qO42AO2qle?8EA;Jm&-AF$2tj`(W+x5sMN#Z4koPN!Zj-Et{S=L0;Bw?b8 z!22r_+P4>E)9<(U`fI;kA^fl`Ntzb2%D13j!Hp6lgg=6xo{;N-9YB^Rxl}(q>GF+r zcGg5vTl_Zg`%O%`gz7w^?l%7;2&F{0uiuKgjSax*LXHK!)3Pf90xTDq z5U}V+;;Ox({PXQOJ){EPcU%c3T(q!GKM|Fi%al;o_ugesS!TtEPk5-0*Zma;aI0+2 z`<(Z?)|f_iZC?A=vSyIUJYYHz6`n02Uk-9PaRK@yCd`4(ays6>evfdWCGlF^jQ1-t zvZH!;xhgXLIC~P4fc$ErBrIK;^!iEms*3!B;+nh}0Y>r;D~?F}8#<6#XHLV1NBsGT z02kP$tXCFG__F*J(&t1#p@g*$iE~^4b@uhBZoi_T%PHvLvBxk3iQr?zd6P`y&f!N> zWN8d8kbHZmb{@y{>}4EBl2s8WrYxhTnlTXB6X@fCS?xqly}$IlZ3WVpp_6vB@Z-g~ z-^U+0SltKgR2V5+Z}HZRjO?WKe(rqfyVMs5=#l>#@Bg1ai+jxgi~X($peDbK zvXma63{&mh>`1O0zi~FO++=4sUh{nfDEO1&n*m2IiU_ z;0Jg}Pi_qhf-e|&3A-=g%s+2U5D*63CoHY(IuY{+(!}`EkBpbJ`|>;_tD&x+AxXTf z{FFetk5&lPFbw?)^&orfFJa)=FCe_l)d38;l>sXpaJ|+^Oo@cV8S2Pyr~pw^(2mun zBd<2kLfh>W|9HF?Jtpeg!F96SaU6HYK$C6IIoQpTFqXVOx!@L%_o&5T%)TB(*Hw-l zDL0R+mR!H=KEu$BUR6o1ZU<|hzg}+grjM1AI(zynpG{-KA5U5Bp#I$Z$^aK34hDcH zP7AuXXhk+mP|{7z3sb2hbciBjbGl}4N;Qk-%vZA3%&HZY9EqCVm z!g%mb${A~rx>u|=)~cX#MyrjmP>#oT4781NJJ@Jd7=hwW*Rs|&G3=$ZutZJCJTDcE z=V(@V8f<|kQqz=a70rZvDzrXZ+qD{}Sre8#nD6@F6*d$XNo9y0;fB(#HTI6o|- z7UGhUHrm@0Xfm+^MllTLO|!3P3RYf(`;l73^f<2?)O+1&5IF-HOz^yy$iFKw9w38< zQ60}SEX+N2&5j_=8gI?8POXIk#pzJPCn3XS?X)Gzpz^`jU^|+IzFsBV2j+bZ%+qT(RJ{pnpE!^ZH&lX=fXI!lQ2G#q&Km zDlfan0!e#4AVK5a*8!-%8=3jqE;$hF@$ykWP)<}Zqg^xXntu;10*mO#eX{_h&dFNe ztk0GM^1k0;_8~NeG{oj!!uYF9~?bdj^IBMlI5BG;f8>i{gx%0 zozvF|JnpD{?q4pMf0Y3$Y<9TRYzW|epKQ6Lo$HOYY93yPio?#iTJv6Sgjr?2#+AP9 ztQg^0Wdesd0Rxm9vVy(ehl_gcVeW-jJvnZ>BP|%ozt=Iy%<7Hc0>S*&boM~lQC zfYhkD7WJBf9fLdO|s5QHF{LqnEWNTN;=YS_?_B&4E{Mhwx;Z(T1%qdMZ_>P93T zc1NmrB>%3UpxYpidLBfJlZYGqC0c|ekfw@Wrs`a6-*T@FlWct{kvr1#YKRyZAE9(4 z!bOD>iP}SBpO1LILO>A#PApDgda`4kV4^jyew;YM=#jJQ@m$+Jc7vydfQ*kZnZO7H z$DrPRUcZ?_R(rvTQ}8*q1Qm#QE_nu3Wc9h$|d^Ab<>z zs+t5j&o})8)jXZv6K**tLcL>(A2p?7YW;5rO!OQG`VaL$^Xb!_fozX(SZ-~l%@e}-#@ z@A~<~(Znze8zuo9mcwGhcx`w2=8$a9>U=L0oNJ){ z3fe{kBK%tGsHJPeaq^}P2SK`qU)X|NNcVPl#Dnv`yNQW5WN}}84*LUD!QIOwFSs}6 z)7C#iiwY0KsM)k<6H1K0M8nl*=%1DATp(@vt zG`t-;@5Cd?l=MG3-zq#$kaLc52)+~ZOb*8L_T0xUab5>{7X^%QcKQ{eBUJ)!BEi;O zzlpkMaq4)6kLzt#VLwXD2Y4?JCwt!CLNk!cBnxXlD zg~RZgcGRInoxCOM}Pj785|5!Ltk&k=& zL_Fv*)^6Jmz)962Jvajx&aEm7I087dgIGU*e7^(f^CC@90)l-M0Nf6v(M) zM2Sk48VIN)k)-hJUuUj;?=8L4+H9w?=h6vZ7^9CKoUbNjW`(4`BB4(H3)D(Q(zD-a zFZpWz+Cr}Mo@}?y-ljCT4#|uKSUHdeP9# zZedJLyuFE3kpr5=zkg_`EG)`t|BKBSG7Zr<-RtP%(*m8bC=uPumhuSgCB7aoPkG$~ zvg*d*PLk0(ZIkg9=%(A+G+6yhL(7}5crC*YHiiO~v`K3f$7efVODXq{U<-ykBxoh{ zH{e`)IfBe_$X&WH&X3I=Yh1mEVmDpV+wK17WA9}+bmk){slDOm76`b6DWWpbtLyMpUvb)( zKe==xZd+SU9qogF=qxD+OQ%hFrubgBbRJIhyeNbx?*lJZ{4t+FAyyql!;8n+{_ZvC z;C@ng8s4w;Hjv=oGnFl(-WLVnWa15Sh#4sF7y@8?d^bpunW}odv+W3|P4o~_=kpcm zS7-zm#W*e8{rF*%o<@ztmIhpu*LR9gJRvjdB)qUknA!MMel(sm`3tQoA}yw9qa|pa z3cSjvx;RccGyzrAuvis|%aR3M6(zw0TtRsdB;vTbY>8xHc@G-=J%F14e-ok+*q}7V zNwNT2{J_%k+ba)gzFQIA2_if%sG5s!nnB44c;lpLn9c*okiw>^j%hrFgoG?<@!fL) ziaI)+SmHhs@NqXmxBrq9ff6Dd;;l&lyDhbxpO)uv=DGKDH74)zHD845hJ!{J_hv@+ z1J4Fhz;3{{roN9`Q^2LXO&er4-rYPRg;Y((z_&UvIcC$z&Dn9PzXM;c&$EF*P%r}s zYm|LCtA|rqr1i3WY@|t_v0UrrriA++GIvd2WMAZ0dBzEr*{MTEf&U4ZSt8rHbn39YMs73UTU?BPS!R zQ!A@$z{T?Z3PEza&(Qq)~#725_wVcaulcM15HH)icSY&&u>5_hC0mpX0; zMS_|kOZUK$S_w+6AB6;&4-1ET^4|BT4>rcOh0lPkhT%y$;vT?_#YC{vy&b=g(|BQu znXL%X%kHqd1-SbFVWi3+qe$dQ|5_X)a1YA|$koyT&`fT9#_D=q_ZJEn#8l|6L9?zxuJi+mEz;JayWLNN>7h1fR%>Im?Q!kP$rR6`6+nr!(L?eybbDJu+_1O-Z z$swSeykiLd8j>ZY-~l&%q~Er==uVxch5^rbcQxw0FT{be6Eu0r zhOba*e2RlK_NW|1J}Rk4a-Yp(_>x0c6f%SiLPdbPOf7&%7GQgO;*q^<8Q~IflHA;; z?$;R~;mHhH;O#J$|44U$b;{>fp^z{FA*GS|Fu{QX7K9;f?V8G{Kvuf^7^)}_J24jA zqA$UVc6EhI5y3mIcaD)+qMOQKq7BXMdO`RoMZYjO%cVXQXTJ9IQMsH_RcAhpsz0sb zG=?%mZnq&5LsQD@cI|`dJssvBJ1rcb5c${Sw*qFOs%Xx<#~GicdUi}wEh>!EZStOn z;U~j=t?qncB3pxb72jPpzoHXj*V#A3Wa(nnStj9#P`ouk;>@mY&Mravh*b>1#sE#ti~a6UvK(DtpmM$9V1^EL*eEh&vM$9I}o_OFtYT_nu^Kf^8Q_&X?!Dxv<=Ri}_M- zU5hvQZ9{30<)odFujXRiAC?juBLKz6=@IWK)jSfwa8Z#D$hvg~oxhkor@TSv6zSID zMWiwcS#g@TtJM%lIt8b;A(*~$u5~kfj`>MumcSkPy_69*`gndXSR+q(oAyJ&^0dm{ zhwS`yN$*7Dqh5p;WbOp3wSq_DWjymJI*=;4&{!yRCMOpY~uftBLki-Q2?B(YN)_xkze$9`MT#Puh?UE(4~NGc`t*Lg2=YH%j8JO_4}38Lx1kbE7#GmoF%OvT-dS{X;QIV7 z`-qW6?+XEi#ps7tSU9*lY3a?$Zw*ABGB z!wqipRfoY?Xp#!6 z-ua~*dPR=8*6&39(6B0TuouHTHVspkbb#p-k`lJ$Z7Xgl&<`O$ZoN3nC z_$@b#DL-;WS~*izO6a?pWqqd3?mc6m-=%|y1ma`^34i0VuwK6#8V1wdbYYTzuC#k0 zMEFB+$fd%)=Zzv&jesCwLu`P|ylD{jpz5j6?9jA(Iud|CQnuDcLuvuwo4p7I)3fxR-Ur4J1}bWfXo$4#ENecn8kex&@X%q* ziX1Dw)_0?!vLB5Evznx())GPho}2xE~RW~=BXNc z>E&Pse&M9?X*6J;9|pq@DMNMZ-?Z>Z<&fmz{`VeLyhl9h+dX}WQ$d`Q_kqiAgv;t% zbxS5YspZ5`&GuGvolimb(>8~W%T5c_vm>Az{RrYSOlcf{Uigw?7PeW-*Mqg5C2<8V zO-B%ygP&y@0biCo? zF;f|0ob`OzJ;2gn+rjJ|5Tfz7mOa=ZB2!(gSOVcCyC+1M4P`P}2@;ujo`T#*aU{5w zso|1-yE;*9g%1o){ED#(%gHaG7`fJO>%(#fKAZpkP1qu3!C1^(6&nV%_hsV>LM+KI zNrT8s2Tm30Mx>MWWaU9h-SXtaNx-%xIdSqm_ko>BNL&Rs(2Vt*^VRnyT39&xqlTVh zitBxlzN%k*gwKkx1?Gk%S0T9@pK}_{aFO;Gu%uJzmn^VRdz_!Zw4Cc=*IUhYx7Qr86^3!4CgKmexLiqj6yu4&C5IU zT-qxi!NXR~$^LfYBWRZv7iqyE(oxulJY7Gv@)73QhCm?uQmBgs*rnqx3md}>OX)RX zPXUN#LDEHWkicihpJ4L&&<=k1lI3F!k=Nt#?QByyD z($%|_;zYCLi~`cV1Gy_|-h z{?&<^Af)E9C@_>5 z;3lN{=P|ouzTIylHhPKi6}gOikrSI!=-B#k#j<&L;7P`zO7_uH0&mW2!+T@Fvp*;Ft z{Us&l+kDO-ZfvKwq3!f)X!bmTt1if`lNd;4Tw1P|3lph|<6@1LQ%jz;JPi3^)> z)9JfN-&1JW+TXKlj}Xbg7M8F&^0S3gx1RI6;Z3_^5SR2vT%NGcKtKRuBHavhwrjC% zMWny-)WiEbBSIDYII9aRBuU)P>9_A7)%c3tV^lHN)XMaMsJxyjuJ0K1g%+-!`o+BS zhdQKce|sqE;wZq0JVD_7_Kj*PO!%9|N&PiQ4HBkPU=tt$JL$WjRCZpr=gH68<#?!# zU8Hs1-tjKCL_sQ3=NqL>Ff&bRs6I@%8$7#mc)76tOYs*_r_EPzAc;iV>Xx5%zrvbt zA}umRzS0)r8bUXQ>8rB^n)^}`JL~YNs2gd`NWEZH*Klu0x2t%ic<&K+*2!-;=1*Br zB=ql_e~=tAQ)IpN_k!B`KQ;&)HGG#q}n6w#S?vppjg`0R52J)cVIGN8_#OLg?7AKB_5wnSxubKM^I*~Gf+q9@hq=n(ry zAl8j>$ts3E?{`;5=25eKRveMDArDyuMTWKbF?Jjt^&7FKb8o^^?nn#`!2+e$oKXU8*>EzruMr)-mIwnJ19_np(4Ah?*o8tYyVilKNl(M`t*7D#qp9 zHSAd{o083c)w&t-_M}v6*9T7RQ9Px{DbMapY*J(QCHPAM%Ut~PuVP$+BS?10`2{x; zC?kfxHc+;oYHLl@u*+GKlwmO*SiwdTvEb-1Wc!q;uj z6cK;{&ynsCtZS3sUdr|4$Udy{{wmN5IomlRO#awiu8}fkm-7eqVO^FoJto-Y)BBs@ zT|4bLuAiCIWXvzBp`veX4zD=OCu!%Z0j?zmo}2t6N(g9a;?=r0XKka~W3Am`33J%z zU+me4aBEXjH{8J?A*Uo}vSe;%C@{ive@czwAI^sZ&W=3v6`zJjTN4IwyofTFq@cNY zT|xV9?!Om!LV^3b*RRqXGxVUzx4Cz2Yf|L^xgr8|nyR(?Mru4Qi- z?qL1wS>Yg}gF3yfvM;qaJJRjgm*utQ9df@d+Z1j=2MWEw3-04ceI<+wb5RxRh6IF{ z-T1>i?5x74o0sPdrOzbaLA(S0)?rQ{*t2%{!9s9ac z5&@bmr(6%KcIQ=2L3p=vk7bPSa+JkGoR=7DaqS#qE!nT{uvyn)%R+jzXrSI%>3O@J z|8L}#urjB*rgZb)p)6gxSc-FdM9mOELDTB**1s@HdewpyTuuJeoz8Hs#}Q)$NrEgA zK9$p+d8Z#K4F!)Z;9ew@G}WTW_7ESEFtZk^*T5p)kP;w!F;fSAJ!B4tZU5#`m9mFo zqa5RYOoTNupX6$_fRv%?;5q4K znTNtht@rYSuqQ{eil(v;XfP)C?dfD{>)t!QuW&6O?RZywGa8&F=!`AbE}}MuBM)X& z^rwAlujE%;*wehM4l|%>0w;j!1wzvZHn$!+RBNU7JtcKF(a3&14>pwcZf-hHNQY1N z)~xpbeh;|)E7W;~0X2&Pxe!yBpP6<)65i8GcQtlwlt$4x+`k6ED@Ojjr~2>mcgDP{ z@;&b*VrsQCe2|IRin^0A@xA%55cv3b1;ykepxd5Cixz9v@uu<4+4h3F2P{z8kSE@w zC&i|9i#|J|vCZ9)=$~YI_+YdoKIwPZy2_IjhV2;x8F0v9xQgFZJqbK|@^nfw#yKE= znvq{W0PEhq2&Rs68CxjgckY=OdEQbTlBU0VTDsz*t?hVwwWMr!s>G8j%tw-<>pQdm z?4_`dy3cUnDikJd4!%N;H(CNhg23(_))*`mKf!wiDiZpW8K7M0*wodIM zFl!jS*(pN8uwCO1oD>iNFn70!yTQdwK5dBh1@qtEXbGO|W@GucmV#cc2QVaHpt7zZ z6x;53IFu(8U-B$J-J5oyUU1*mj=oyw%yLpw)kXohKNvzYYybN@)v=`fl;nO5Lw%Iq z!u&oP3+%JQ+4w}FS~t8NH5C|u75}d`#x}zHx3z5u4^jYb3$3H`smkS%5;?1i##s3G zh-=O{*eWsncrQ=0+aukI&JPeY+v^<_qZ4tb*DTe~lexo}nZk%7Fa6I$6AdZC+_A}f(2;hJ`_*F91q!J6G+l!;qe>rXn@ zG)T@^pDQR0w*I^}Qz&uS@j%tT(-`;leUJFX(e^#*B64_T#o7-*5_0-Fof5*Wj>61Q z!g+Rm)exggmT+7S6U@zrAGjS!6e2p9h{q4*mT(`Sg~OA%+3y@AhpTRONO#XZk2~(T zjh&dt$0UIrmT5|0O>$Ord$h{TNw&@le?E;C?zPwHr)%Ff{CnPQ0Ei2d0Z_u%yB)S_bWvSV zJk_>yRHT*+2%TU!e?v~Vm*tYR5^mR=S&(cN9reH9{MG;Vc_;5=^3}c3vu;@bHnEI{ z?>aqt45LL1VJjStrD`hG{7q1U*s;8x`=9rN2)L1h&0&~{h|6~AOlNT6_FEd5jNMi% zCiAvew?c3*Hfeo`PvnCYz*kk)+BDN|G^S?UK$m;8i4ya4CyW4Pg~Xbz4%%=~0h?cS zt2yZ(B8)-30yd7%-LE+6{^|83cYwv)aDG>Y9w&jtrRw(VCy=M%g}i9iU3&m$i#QNI-BVbPt`?uaBdxD>ftsSm zY;abk4k;bpv$+%B_IVW8tUsP&hJ!o$Js(QC)TZ5t`;i}LZ1|oE(g{lXI%hd79&~~hBEc$>7AY6} zJwH{s>U?xZIhbP_xn>!x_nHpqKK$nmaMNIix`StHD!D3it!SMT{4f1h!%p2Q?Y3k) z2tAw(Q@V<){`5X{uzYw?Zj$P}duOaXhSAl={RX2e*Vdf4FaQgUv$Hj!|02xl_HNeR zgx-yE^y4nc^t#FQc^?**Yn&=@a3}|)BzB^=&-{we>BI7c^Fk(}pK8^$pBh3q6v*UH z)(_h=?%q*hukyzgOpAQHFsej031XCt9T27&?JT)oPV+~-w3hCxmyP@hr3?x!Wvbne zKOn6gCab44G5rk4m9<~lvhzW1Pv+=0nI`s^v%9~Mv?2Z0_-hB5oEmM1)lls(*lVZP9R+k`1z<*jk*JKawow{fe^AKsgtPZbFF?|eCG%+m?lOP{@s z8?6gZVZPe;yW7a=P8P#PEFj>cPJ!j0^*L0V54?Q8aQ&a@>9ei4qrH{M4YaLq@pf#^ z8uE+G<_s`&p2s`eOKb!BSzx4Js@t=Qputja|4mrj{l!^b*ZB2sjc2HRBfoJKZzFs$ zyuKwe;*ji{w5+c5)%P;>Blxp0_IQ5!QaYs1LsXXO2$KXyB?4hxCx-LGLF0g!_Td=+ zWuGvI)=tC$_5?mJfW|FHu?#4RJCG;1R4U;GCR;>Xcl63tE_TmAb%taHAVl6cGMxGM z5V3o=KgHvVx|UZU#MYXx(Hmkd{M9*cpXYwV^}rDZ0>R%$b7E~o;8Nauh5sh*85X%6 z4AVXs#$uIN+CQp0)HM2h_RzDpOAW!`>IA6s)RG3Up0d8nSoKPptBJ7#?Y?SGGv(0I zdu{^{V*zTm4CiKBn}L&w4Qxxy7@IWTDxe%(xpFhLyvtP+J?RIUC2FkyAX!FGkzy+K zsq*|(O7s*ntPJvvurH!myNlF=?aiA~xTkQlmG)G(!)@i!n9H**>S8ouPe%mWYVu!WG zZ%1EfUPza{V$NP5JFmr0H?b43*d&7gpi|Df#7n!xUw>q*+uRS36lGlXC;O!6hQ8hC z*TT^_Z)IIcBjpTn?DJ%gwq#s>#$>K%7+k2W$BTBh15y@X(vri)Kn$8~P!RudZP&!h z_^G_#B*w>?t(eKr7>)+wn#%qW%9qO`pJ)5_1#OXM_w@JpZyh|K9HgRC|E{itHVnpF zaaiH^<+m$t+4}vAe0NDXyl9L99>}0fHJ|9fUv%J>@(n+%bI#^`T;{BO5E6y9FFYIT zIjyx8S)cF0MC}Gc`F2)2=#b=p!}WXK#lpxO8up;5ae@@b0f!pr53lsz4eIQ2@%XdU zTFaRu-mb-4K?jxr^pORuhC(-pwr5c&%kw#%aUadclLL&tRrLt>Up65qIzC^C{nuscrNcCg-KUO?c;smZo`q&>dyN8` zAOnZ$*Xog4XQrR4^W3Zj(Oy}o$0h3zOI4Ucv}O4Mu3Y;xzFS=K_;>#8t_u7oGE4)eA0tdpqFzpomY$KgV_*ncs6w7^Mse~v zCfPQaNw4H6syG*?9k-k)q1yvXu32AP2Ozn24NQ&S7Qi9BmM+GrqJJb-m!ph&h4@fY4iO-tRY;e$YLn>G5i9raDhqQ zh6U@1ZlycUppWtpeha@{wQD1W9A-ok#wK}NCv-T=-Q-9rDAzg#&jd+(G`B0?)e;bU z)F~g-)^IdlajOh6xXa!q&qdJR!i$~xKjHcoJDlU{hAIgirf_Th#g}1do4isI~+XuQ#Ne()X4}q(tv&2TKj&%+(}KuiS2XXcj9qDEuIor z;FbJ-18+)j3Q)*>y9Bzo=xnnf9Xow-28lBW-zIde3OC(vWRWk8z%Tp`v?}jZ9=WSF zkQfs5CAFWP=Z~uZd<2w?YYe!0ADCimUXr!;U5~4BTh`C#v8Ox*+y_Y_Z3=< zx3$3UhnE;cj8K3)mHpalhUas~(#)A3pht)%q*UP?$p4)K&l77;cj;l@s$DWSn1Q_3 zxyyWzyo6@YzcXf~JEFb9PT-Kc223;YS%_`jfg zHmZ1ugj!41wZB{8oV*xGO{^zwaG&?^gY34Q&oqt!0_~*mBMeQ~{n>%6*b8d5eo((t?3i2tCNvo%!@o0s zJH!PH0KDr1_>5khg2i6r$jbOQ8*jUHc*S&Q2QlDIr zLOUfBQa-)zPVp~i)WKsJOham&>j)wfwh!~JL=#5r>Z)%|PnZM}VA|1q%@Lgnal)&{ zd;aO^w?2`VJlc3We$>@wkJ)>Tn$$kbA3rGHgt8BD>FwNWt!kV(5y_TpjH94Gy9Syu zXLkw8lE6$HuAm+>!X_+e6E0K8%N6(z$D^k;oXI;4+=yzb5VbA%*n2@{*=P`^qckTdM`hhmvkCF40Fn) z#q9O;80Q+E`2o?;6Azcf?x)}!xN-$@Xj2LVoJ@UfXZM~k0(H?hlB@IUb12v6pm~!z zKy~`C_tcbR?EXa=i!hOucLlQSy)pmN;NxXgqH+$YW0^c$Z4k`|(Zf6A1fOZLhV%WK zHlK8f_}ypjTGOqF&-W=o^#KE@N?#vDx`-UPjRLiKsL2mt+}#kk>2UjdeothQLWp#M zRyh|ks}ibl{T=_S9Rs%F1o}G9>|C~>g5|^{bgcF?Lz z!ofdaQl(R2VmJFmy4-GWn6@B@4&3$oeI#YBj=^h_t|{;tBx44mkKwD>VQM?On6Met z%Ar{ANceP7-=(MDkjDZS60Y^{E(rka^%Xnxe;hPW?0sW_44N`j@*5e<9j)vPF5X9Z zmxNN}aV{>#X-h!~OHu9XI`RsUF0^r+nI~c|VNK`>)yk9mdls!f!oPjL4p`OkDyXoA zb`KT&p%R4B7i>0wQ0aczy@CYhG6hYg11sxj#myn4!ExCAasv82i^a^N1gq~RQ&jkR zrZzF|tjA)Vyl#=zwa%~)AO?gtrobar*Sf*TWuA72WnJ$#S#rF9JS1N(N>Qf|Z*#3R z@H=pV30u1LeMc{(oh#)FKq^7W&PVQ2y)}bem>ZUQ$rX`VHw}y%kZHfl~8ls1#ELkz4lJ2FQ?Z1&(|5H z_&c51mQ}a+oNa^u+3&i~P4>vR*A9vcZ`Z@z`QFlQzqqxk-=ZCLftEB>H+}NLy$l^F z-@OM!0k!5szLvtrG1kk9Uh(8wcfPfh^R$WF?^=Yn&GDg%o_o>we}7N1&p4)e*(69H zFJIshmb@Hb*m1w}{b_=2S3K)_ntvPcWw8y>PdU1W9F4=Tz+{_1jP`B1z~_WtZf&=& z+j{`6D3)LT+T28o1?r`6C6TOmKc0ISEpo73icrqCn`ZJ*(uvXy4laDKL_76~5fnA@D+ zzncg(jdNc(={zJsc3TMjmM;{$w;0X%s}n}`PG(oDI=!XtxFCOf^y(EybPrD?w42NSjG zvqdxC8d@I#!$bW)^t z+9v+ez|r&2nu+;*oWFOd0}4=g)*j2&Xz*9ySQ(%FVTTZ`+h%NKm?7Pg|DK(*h|sO> z-+t7eM)m(bXH;i&qVWR`-z_MPTz)nsU2YHfo~7xb-w z^fQaJP!Uh^@s&4HKy_rqo`$A1gX&)Oy7tqd$zn9CD`7&V?}9CplcnffqhNwroH)|3 z;xCcJOJBC!-m1#}bwWytEEd^#uUBsq|5yNlgOgk9+I>8l6JjoQ68i8D*>T003ZD1& z3tK`ymId)q4&$pUz3UP1#qX;xC-BZFaj%31l+@3^I#GF30&IP*djlDF>D{Y(DtbAe z{T3mRtO2w6cfYej1#R1x=zo9rr>0tqoIrVt{&QE|){A=8(K{G1ZAnTRFAiyL+D&go z)gCuGxWEo#)4aHPi}fw42LGv^{i3s8X&s~G{#~ZL+7n+I%Z*{D-$*E_;YDE!9HM|u z>Is_~oI!M!zIa4Xc8&VNhk3T{KZE&Tc4~X7Ou_XgzJPzckC_kfnZcWd$=lsDA=@Fz zVf`HYG&L`JxbaJX)s})nwzIkh^?;^kv=}#Brvz4pX$sCQ12bAx0YH#}^y<+$rR$zU zCBZgy(POo6BM|=43WU=7GJgYwhFerB)fvkJcFn% z65*k(8Xa&3@XQdkGyI4xO?PzyRx~#2fA6Py5e3srrS5bs51|DTE&hFmi;}(#LhdqC zJv){H{4P*SR>$5lzAk*ii~D`=d|(AOD8K8>uIr${*BGq#NqFe5UW(G^6`lm(AK`9! zKW0K6RsFJ45YP_tOqRAP`9RDaQcM{qs4fru{R9iDE#3^a^ZPYF4TM72qj3QJ#hKJ4 zhUGMB8&!#5_rYx+YNL}x#$ix^FV-9aeR-#G9C?Mx4utc0L`b$rV&G4ABpJaByJ{rB z^9#`PG(=F$uBL46S z5u^nVwtIZsI@O?EwtUb{;sN!HxAJ~?F#_%9E=JMNRx}Yx6s$^bGW6a^H__Vthx={u z{_k?v6y><`;X~`U z*7SW}rmy<_8%*g8@Gq9(2TI4jOf79$y#fpqz+A)k(&RMM>x*&6{KUim@9?AFQjSdE zS`DL~oT3&yh?YEp&=ku=W)H{HLpl<%!S_rS{H?3x2 z%+I3O+MHrPHt9pROv9#$dw21_=O$pP<*`Wn!~76@=4iqR=F&jXt`oxf@O*M?@%*S` zwfUSYJ%yoo?*K!uJ_{gUU!!;31;MG=cLRS?*yne)j1PIz(uRS5DLhP*i6z;aQXXr5 zC4OKQH19zMhKJas+_l4HsQ+qQuF?~}G&Z%~ymr#PqT*h<&F_71BCq0-_qkk7-^+MxC50*Zzy~f zH?Q@MKhhYRxW{^cE4MtsGpU9>%q98JY_?F)(~9mVo5>HmauCl?jSY&(I15Jqih^hO z*JedLh9(MU?WeuL9WXSZaJSq-U;sDOq0=#YvaJFKb&Ve089kKQe*0jo)=yuL4Rg#+ zx{tzH&|^9dskj&rdkk#-gm5(?8q@yQ3I!^sR<{zh)j=7u?aBAP$C6BGZ{^_Gh4%v-ThUp&-g zV5=x?xF_`F!^)dW@la>FXWPuWAHj*Op%sgdYVhEZzD6w?buWtXmpoI}(=RQFY9z$*tZO6$E z*%HKa%FChb4jkYaXQ;?qCbnoc1>wP?pqq$Ph5~R>;c#Jvesmw z64LOEpvQ(1#2ccjPK^g0+mHg+fMxn2zEm%|Ro)vP!$;7iuK;T5)@Us>tmye6)v@^f zk`)lo0T(-CsakWewciKIZ(9s5BJ|cPmUR9cuAKn;mGp0|4uC2s7XehX-#4({0ObBWK~iuxFP|ByLkf z^{sbVFnJ&4Lj4fkHncU&C)XK`Z9vQ`UDQki6Qz%$^;~)a3-a}MbpOds@1_URXVMXH zc<|TPsPj>8tB5~6P2u}yfV--}+Pl|P28CWJUoXf|$?sRzq#*NI>+CW%uV?vqdc*P0 zZ=QM|D_4P^-z$Hp3c4)^@5I<^-vek9DB?a`fnMVPDEnqXwQY+R_+VQGO*_^4%v4Rz z3rJ87@vb#JnRyH5VI_dzIrrJa&J1^RdDap_ha5rM1LODV%16Atqf_u+7L{h#I`9!-#aJz-imvzD_uB$?VJq$9;N;J5{7jFDuz5Rs01^DblfhH#juL&D zz8h^TT}mS{r|aK7KHAqe?=Z(xk6yTwpXh~Okh`jOz`!vIGnV1z) zo6a?+aD;BYHyQqVrG)|!@6miBPnpYATi8#`*FaJhD5vY+e*M57&AL)ZmH9<|Lr4H? zb<_yE>iTZ=bUN)8tmaVFH?I>9mn`$sz|ZV=J~Ku3ae^!=+AvGdGoD*PmLNEt@~}MN zhEjrMXZ-ON|7vl^fht3JcDL<^rJkFKd%-K;b}{=ZD!82)I;1yh_E@eD>9l+T6uc|9dxE zoad&#GlR@p5K7oXeCYO=_3~O_hSLU2d73bqnB@{}d-~VYpO5$UJkS1nzZruZ$?IyM zwysgx*k>amf6ONg$e;%OuinS{uY&iL8=g4-7q8DX61mzMAYzA(h~M5uLk>=-|7FH= z-mU3?5pGJD3nKbsc^k<{+FddBA5!_%bcP!z)nB+J}L?@c>oC{aY{C_k5mE>-`c* ziVGedzhvXzd<42;Cy0?-i}FDSw-U7g1{^Qv4s-cn+Ti+r0 zbB@5{*|o;aU^jP^Fn@KA2Q3g?;%<#M%4dFlff?DRmXt3zC`d)DT{e+xwP(ArSIyUI z%Y26e!T8he$~PtNAK(fo1WaxJ8KHICHv<}UPgG7fxO6{PPZ()Lo}E)flP|yntm82D zbY|@`Va|O^VA~my=*hkE7%c}z{~CYKb%b!Aj2ry-4ePomH9DT4Eh0R3|K^37KH)B< zO-+re(YxqW_vd;Daa0a15V$M35>6gv__ysON{IebNi1V_tO08A`>!bOtrFcMqm zX(v+!{316aTqVkdO6zdDQ~qIP&L%v^@*{fuK014f(gTtSTC`jzev!9dW_ROPMI`$f zROsJ;tvQ?gEHv-r6u{og0RIbGr4=8_i2#&hX|CXMmLiH$dPC*CuJxC_O?!SsIM1%v zk8Fc_;uRm@;jnxOfhNl59e^zR#&_~N@Sl-_dpMVwyHLgRR?}ey0U;*>$HXyZ%r~MB z_Ty2@4)S18Ug}Vk|e*5AsvkVy}1NmRaKAy}QgyVn+eubRXYr<)2|;y{HppZ4z|sSEL_6f1w8Y zd%j&tczV|C=D6`j^@wIDpjoh>`Moa_$NHUcVA7A!PQ(qkWF{h znY)vlHNynIqCIoi+!uG94y*?D``i)y$UjU2USvm|Ay0|432`;49n{f(_d9f@s^*zC z4!nOH=QOHQ8Z z`;%_EeQLg4C?Le);{4t32ggo_dcTQY%*tg(Fr5_y*iPngi8hFZF$lSgT9ue?JWi8# z0t(bnE*{*YvVNI>@N#SYojkcbruoa{Z8xEsJ7Tc-uimVbI*yn)QUU%I9}1YjYL?;N zv+g%uW%u%Xy|Nf74M|$R$G;jyHNcft2IWj&D`d98k21S+09cS?6OW|&iiYI7X?QUGTwqq&_x8-(!VJ^GQ^c+pj=V}Ikow53q+!&Y*{~s zG=Ks*25;bh?#sh)aUI0wO5b>dSIVCe274?8f%B(hCOvD=iQOkV8~=KHb#tSPl8*i` zX$Cc92CaQ{y=QrXnB?tdxx0&?s;eFqJzQ~Ep*8mUfc9)Yitr>@y(+X)#L#uo6t+j6 z4fQSa<9>ngY3*T*Sk(o3#STmX7$fGMPR;eUjx4N(QLOjT#*Ci_GWYlQ+6w&4uQvNe z_`9~_QCc>pazhbUk)?`R>?iHYKq)CgI3l5R<&S}DVh@ojMVGeg&yj>u#KM_&d?Xn` z6sCAlw}J6~L0>d-fBV!f+}RwB{k4W6_!NvKk51M2{80YD-6JFB)8I&FLx2gv=}nBz z8~fDqKYk%y9*P9rwZ;85jQOz(mU444I!_oO5?@oWgedvfw<@MnutB+5j+D5B@EXFp z18o%PJ%9qY0g|b*SRE{kSrmXLk7kX*f zcHHhcW8>L=T2}GT@D3SD5s&-eH^X9C>$yP*+xg+`*y!96sB?zNm` z$NXJi7Ti&V|Ht0j0JoB5=V3Fu`$k$y+TEF5jrK>{?Va~_AKwG{@Jj%knYUViAPEu# z2$CQPaNZ1spTbI(2J+;i2#9cF_8 zOzm1RT4npl^;Qe}$m|6i4H?7;wt6u&8Sd_P*IEN4^mepyJ{kM_{oM^*J?!3w!F_nP z>un>Pz7an>#W6akf3JQ4*>{Lc4!bH z#}iHuj?~sx7fD`5-c|^435igF8Q?r7aUjzgYr4Z0itHiD2c$H;1$YNrqDJI%wkYq(a0p42=E z^tYlH2s*?;9M~v)xQ+^DyQ)0GeMLPP{@BBd=4kUI6uj7I<%WI#fjX=Vy^(Ou6M^%Q z?X?Fngc%;e^O8(&L;!N3+vo%C=eU^mfN&*6p@CEZ=~G8}Ingm4{p za3d4X9Vr7(`Xq$0A1NNsUeVdAZuSu+x1U%87wEQ`P$x1-XR-)@@{i6E`3=aO6OtoG zupsZRAxmI$V_#lVhX^;6869pO>}Rogt-!k%-aPwz7JM&@4 z-|l4dxZW|2@V(;z)XC#m#?y)=5y`$&>%cy|ySML!Yr&Oew1Io=+WTkjE)GAHTh+Z? z7;Y|*cVN4Q8y)wf+w~Z1rD6Po>n2!id2kaY#rZ=O9pV63uoc=wJ|SPGUc%`DS@l#x zKKB-Gj;s_;A@-V)vx{LCxd&^N!@(eh^D77(#jUH|QivURC?Yz_;o4}I(%lQ^;ReK- ze9>G#%j~pTH5@u~dD|EMa0%;EE!ZpIzOtIHKiX+;Y!ScL4%gb%kvmj7(^3aIy+|Fn z(JXn^ag(zfH!!=l!m*3eaVFG2%;{eHWFr%)lkOkeP@2RO(Vg1bUUN6Kf6zxdPUPi5 zM#^IxrEcH~+JvL$i8^unYBrY`4(c1Y%*}xl+-sdt*m}Z`(br zowSsJ;;%)DjqQCT-HV@PhCVM=EYF}bl6#8FG3s_(kvJ059_NDxoBjw6rRCztHA8fI zw1>Mr_8quX@vIeGUmG+|aJEv}uO~|3Gx$y&o9ks4oT%iBwVYEJICr|f>RK7$M)K$c zr{Up-!R^By_;4BhG}mKD8cyq|*Q>&mby36Z!>QxFEDoFuQ&Cvsb{ipi9m-QK=z{^S z=-oG^VB_TZDig)87XDjl5F(ug+Cw{UXO+X}0htPgau4cj^rLIlYt zaIra9>$Gv}jq@0J$}{y4IzNSPI(ZTbdsMZkp5jvIwNfk|-rFAemF5URrQ6YTw}UwW zEoMtKIWj=-|HWW87TqWu*H8ENW0??c3@(Pk&fprZB#rh`${3Qo<39fVYM%^aaL*Fa^h{6OP-_pr&r9onbE2-DCP9?6`Z_ z<{&e0Qciof1M7qI){cAFJMQB;9Ooe5T-&9<^MuRq&FrQRgUr5q>|e+6m&2N4IB1hl zLdaDUSt+BZxiwsOTrIZ4>OFH0jWs}ygR&2+6(x}Ax1Lxs!jciOqZ18Zs zO{xuz$~SBy!&$ZB%VYnww_dMg-Df++WIvcg3@Bt}`T*`kWGY|Z@+2$e>``s4yi?C7 zqOyyvcdf0ME2r*6OEG67<=xF6L(a7-d-0*$DIaAT2+&O^$sO-emF+nzJ109xh36Y> zWN{O=8XR~UCwsV&seBX;)i<4c!{FJ$MPWD`D2F|7Oxv$ia2HeE7dxvt`h!*_5DY7{ zkJ{O%yw~|aZ#Rr=5&Mqpsh9aTcUtM~?agEgX6#dk>tf)`McNHSEyWLy%b#VKDDI%N-t`#xD-4!@T1l?1qZFAMkGHG?{_(=`m+6OJ~jedurZ|A#YqH zE)FXFvmP{n_C^$^6t)}Dvpm9{$i7fHIf^N1#gla)1xn-;zTOiAhQ%_K{(b_BVsx_; zJJ}oJ-stsx+%^Mw?@6RLTS#o&KMwk~82vX~HC#lO%$y=UZn?TuaP1wB5bCi70|xe* zhzV>V0#%I_&wQtdp3AT2TQ%$_hV5u0*~aP6rlU-kxL$0zlzy7_ALX5ze33~)-1>1N zXudW$l3_oLCU>GojhZs(4~7*-H10do`6!EfCcOu1b(!V%*(aY1azEfqU$U3l>!#Bu zYfW4!y@?byux^01DIX#3@k^ZIj^@B-y+`);3+P$Vy-ggg9mUpzRS%Nnx)TwkKp~#r zZY8SjWj#g(K#l3!cI~f9EPw(4g}m$+}1>G<5CXX*%Zg=^Mh8l z)H(>XycBbd*xsXdCXkFGKgIE`Qj^zYTy$JLhHku{+8qqHTn$7Oc#->DNyA&9kbd7& z4{_l5a1BS~+=XVbUE91UBTZhSfUA5E9~3U64|?r*Iukn9=L-qtJdwk4E)zrS1I{C@ z9UzTg<>IWfj;M7c4M%7Matb3Bz@x3_yIAqmE{wNZ!MG#14jUlWnXMD$xV?Uu8?MX! zwL)ct-1)@;eBrRWRQC4Q_Kpjo{06S5NaCubgAFBHyI6+}zZZx^vq&791dZa}6yAQz z4Iy60?3PcunO=U)jZJ&h|JYR;Wh6>*bC-Ci)CNgmfxzO-|YD4eEGs|S(2eI(sZ zw`-yHVLjHWc)W7&EV|o_d+S?js*ddFIG0QJ+?Auq%d%As*Dr={_;f)J2hhJR)_au( zPS$TA$8w+%I_f#wtu4~;+{#gT|EzNqiKyN-_V4-5$mNDQUpq_Hg5E$lxz{}1^+rxR zI3UjWck?LkZo2)UR0Ij{^I*q*fVH38Nf(E?V%AZ~@3%lAp_C5KcB6pkh|mW4vJ!(~ zE;>R;@6L$~m2xZZEmlYE%x+~gP`$|00)2Ml0J@lRTCQZmLr1&6jkSB=8l+nn?H!~* zkk2y7q)Uy$9oSh%j3Sc{hmpPQY8Y0StjCLNC$TurG+$Kqk_cVchVStp<0}ST>C+g= zlEb*Vlk04H8oqp@J^;TcRagiUCz(WGsH`ctbLC|3^tkI^s~<5R9(1`T3^gw3dI*|x z1R|;0HY>j$bIE=Lj4S)DH3wqhu>XP|7Ac^m%ZHJK_=sF-J%3 zHPf}D=2qq;a;wV z<8JOfToqnm=c`DbT=Y`C{c^0R9*xf8g#y&dXsRA-Rs%Q#U5dLL2>o&If}}k9T%By! zj`xtJyjWUqht^=59Q2V4uoeq;_KuwEJJn6x5>a))zs_hmc2ZYc{&q5ZvUvb|EbzI7 zy}^+Z4!GdeTJJSl+x7BZeTY0mnk?UJ;ih>Hf@u+7g@gQvuR1PlW&F*fWHOpa`l}}! z%Kp&1rq5Rl3Zx@L_Q-)_BN^R2E<`i_3*5;HS=}FwDuLlq8Rwxda+)o@nk~Bz+Bm5g zYT;Cp2T{xI+C{RAOJt7%ha-O=dJu;VsT3LDu95vJ{PH_%Cyg`QqY)1Dk^M%+R%O3( zu@*l$4wr-JjAK3PsGfQ^V@+4kH_-9p-d1BFccu{z!FyU8Hfp=Q?UT?k(%nQ6VAP2Z zM#qk=wRPM|O;No&C+^fx-GK=<;*Fm=!4gO9S}SxoR5FQ3vbBYHzkqLZge3D>_+C*S zwz;j`g?|(Jb$d{OejP++-TmrWFO{pqH4fZ^DO6N-=KF;MSRarK0{MVy zh!Lqrn%lT9SWfqj{VBNPMv4=DeZBpocrBi3)SXCm=0Seh<6tY1aWpeHO5@$=bdE~B z0~{3HQF=IOKz5EQj&M@UTmtsjVHNpmWAbq&m^+TA%l>ujaLf5veBS}ppho-A!%C{z z^>+`B;u%Uo1bwEq)7y4$;Q(#gSC0qW0sl!9CvW{wpvm4u6&mnj_Cq+la#CIQY}a;S zoZZ^aI^xI0;K5#`yY56h0L4%oAkkX8sH|f>jCEqQc56R&C?_tm`-nscDQV={t=7Pv zj%YN(eIBj&5sq=XHikzdMP*~%!dT&X8{yCx{I|V8VsAZ)7SRjFk1qq5tp?bA1o>gw^Rci1UqT8$C(`tI@0dMp#WkkiRP zHy2H@mj&56tsCtRSxTC8}U)5z8%dW@k!plmJ7kpu~r(&7l_M? zw_CBivobn68|mxfV8?qJNq0i=?UU|VG??mka>tv;qhJuxnx|obUHRq>aLFt3~h)5-pN zSBz}N;>-KIAUk3-G+aw=&0kYQVr*B;Uh&1 z4ucM~Q5nHPS#Ci3cP@*8P4>Lpiy7z!X_8E09B73WbsaQF4aR- zCD6dxUBHgpVTS$o2~2I??Q&+9| z_3Wodo#?2LPUKrpYKBYSG3T1&Tjnf6{Dp`^}WrQ15F<~J{#9UU)g8yjaT%v#0m z(@i9GM%=MOiRaQdI*5Ci%divsa5hnmXuMk9uAk;Tp0#KPS5|Z!gLFDJf>~#Eru~R>sMVY$Aj^3gf|3 zjNiHGETmg?N2}MD?EYj`{8_vygUV$IIKFIXFIXUGEHnXk`MBuaiD$I=; zBz-u@hjDN5niKY7=N6T3fS2lt%}A&o@WKE|y3qc?j-zoPBgcBbzI%c^kF9;j8LneH z$hk_LSfLoMWm8JQxlt*)lkpQKlPcjsIA7Ztjt+Kq+uO*#vvyFd6gur=T)PvDI$_s# zVaogt_(}+kt=4dm+*yZb8uyp)rJ>tY!+GVRb`Xn4oWZsON9S>f9a@gI&)7YJ-tNwW zlp>h>6qn`ix z@M46N+H{5t_-V>fw_GpDN0`?x<~2G2Vju%Jgt%GMuT5=;D<% zuQL>?7rl;@GaaLKsS%6Ijl6F=6It{7Grm2w+Q>onw%hJpJ>I(Lwu;yw6&oeaN8z#? zmj|biXQ7|~>J&Ga$SS^1Pi4QP8upzMdL5>*(JMwTR8c8K^ zL?)j?M0aoGKRpBe$RNU9Z?zTH_bfGpRMk)1t*y<{D2Z&SfP1LObtMvwD5)*nce2@5 zBHP|5uERsD%*dAvq(`IVb|K~ry0?=f2d*5vI6Q{Gy^h>tEvAQ5k1vk5vhA(?sw3?8 z^%Z4ULjZWew;e8p3!%tuQd$Pii#7F{IF;G&;p@xRyyACUZ(WCdc9M>hCu* zzCr7_gPQ;y-m_R5ajwt_D31_sMJC$}E&;*bZWM7l0&=0yI<)4^K>~IUG|W+|cNz?w zctay^%+)EY-hx`w>xYZD3?%G{3~F^pp4AU~FAyi*L7tv%s7TSi;c>Z7PHnop>R zC*2QkWH#3Kl|!GWfJ+2+5`lEwgUffetGkuV$?kFSunJxaBN-OZh+F{2{$Lx&>Nec* zqa2LM@tsB}9Ym7tdcn83x87SnPLn-8aN@}iPrXs)823^F9M~fc1O4Gy)|G&hp&Ls1 zwtMk#%B@~(!MD&}4>%piawtO4{Na;OJiT@39ujX=Vuuia(I~FQOnM^4Or-5Q!zI+~ zkmKFG))05vpz(uB8rKYk0*qgFP7267Nj#sevV87j6WUObN8wM&vy9*E4*Iqeo&$fU zoyjCm5Yc^n;3^&lTS@HdsxD+`t*4Kihv7hBcWt}1-}R^0a8FOTSs?Gi;N--EbbtG* z3X4u5s5o0V@gMA#92FdcO2g+FXeD>nk}ZcTj{_Vec*~T7g!V$ah>hCpBi|~nr9grP z^dqN_iiaCHMBi*7M{li)T$s*5a^$6ZSx7du(iI;i^QXEvm0d}}m0K>WO0C>dPLO9J zr!+SGxGM%{S=ZZZ>o{!O=r)z4T-#4L_R~eDGZjs4N0P|1l-xQz%?I}jyX$#1qROa$ zfO7}=LK1MM#9w#bRDUZhZ5w5!twZ;yWk%=k=Wmf6BMDt1oo-YOZ$OY$#W;Wa>y#j*V+6b+Tg-;Ow5rU&7=jv}=jPj!%?xkx5 zBE5jKjsrnzHriK}SSgVyu19(a$H3_+MCHRuJMAhWCv!07aQb5h7mehmBY2Rh_P6s9 zWsp@)yo0tfa<Q|6OQ+z$gzG}?sjqY%UU>( zTdjND3!g86z3To>&55%ngVbJr&}|{{l4E~V)Xuf+w{ZUNQzUEbK(&Xv2wQ z$hesdIp|JWZLi;tTOG>BUO0F6v1WiC4&$epm!J2dR|~3iGjDf0Ay5X zrlWOShPoHeX3l~eXZ>E!x7T$y^TCvV;O@dV8UXJ@mG%cWdWje;@lhoA2)H7RZNyd| z)|6~15)Ea#?QUuxe3*Bf=4D6Bcbv%#n&Dh#>%@K1Y$YA(PS)!^#*Ml|cPX2Q7xJNK zAc;eD8#2z;;2_OezFTy0qtk35p1at>{v;H_p~h4dS&`}+8%tN+zqt9~7hjCdm@&!Zo?T2}rTUw%ya6a4*}P`-Sx{8ITl-o7e- z-+Ncf<D=kV_b@b3%w_ri-hee^vRWUWv8wIQBv}CtE9j=XmAI zkLKlC?OYwUg70xZ0qgnAO{NkTnIuO|uh#=r{y(2@>T zc~zUC@(Kuordyx;<+7VUxcq!F+g2;tniQ!Ni*j3TupgT`RGlkED=*J2_Ghm29+brA z*;Mc0W1Kd|sG{rw62IXxNNR^wDTfT${$WVM1TugMB6NK0(sDAg`A8~fJD4vZyGw|a z$`}PhU9sE9)03r2M=Hq0N<%J4xuI0=*3?R?CQCgKM>dD7HBTfd1ymc&*0V#Y(&%CK zWGP##N!3cD&{=90B~VnZ(qQw|k?^};uH?&RJCeYl=Mdw6WOKrK+lJlyhHlHx$ zE|*`v+*-^)uZ&q(Sc_oVGn!CvdU-ifew^s$0Pl-SW>*j=wq-UKf_1Z>%LO%P5ABQ* zLEJG>Mf0>68W0Axs1|QCs_zm>(j+0vW1IF(NynuqUqVPgeigj^O)GEf!pP)rb*CYf zq5Ezm;IS0-jv@pgF zSTL(eG-A3pZqd6igSTo1X#F?F+3Ob#`S*$OF>+}<`NEhs#*Y8iSew=*dRz>D9aHr` znN!69Vx0bxhE-v_{K-tvmB$}}&>%Gf!XjbTX3+h$g+cfEIa6(5<#Jw0o6*dtZvknv zcIou}UB>)5-u&X~s>Ih)sg}*jH7r$FI@$#+BkiG7t2C+|X?680OMGf?RL2+}!|T@p z!>lFu@+I(4J*!@oAC$jT{xWgtlBPNB{`M(W;a3&gQGD;4g-TDV6rR3@)%LZoyy?VG z6W%Frt&sh<&kxz}OhERN9KY#3=*3IVa&oECc$Y8U?@7-Xp5Fzq_^xJ4@45r;ElE=G zSq&FgGNB^Bv^Qd%S@gR!mUE8}(#BG&uKA zW!^D^+}hMTkfvio(F%6rod!_Su9V8^Bk8H+T6!io3MS?_4c_5((Rj6T!*9;zhDNjB z&bF?8?D8e-LXe&2D#01{Cm^eTmsmpEg$WF6E~~%ZXDaZ6;seq_vkkudk#el5wb+!H ziY+O!t!AfFfhsK3D+8>O1#FXgP;=pxptm+_ZMOvlmfD6WliSjR#)Bsk)>G{lE!DJl zF;sFC#VXuwR4%&m3Le*?R~HHuQqHmS$TtxaL*F~l%{wX}>#*`A^xrU*Z11?$G(`H}YtX^fr(EKI(eIh^uubG4&kHp1rmQwsw({l3wu(b8^0u++JJGx6LQvf`!*dR1}aW0o32dJ9<&KJ*_N zoVdcO2$q8u?dMxs&r-A7mKwOcwArp|0*34|vIHr$LQLDK)Dc4tiPdC6Yd^9n<+C06 z$4r2()2a|L0fLU7mGVLEouLQwXASlVW+R3*oInBKK zAPK36cMq;Ly*4Upw?pbFF^T4gkc#bQo&6pIvC`1S)6Wh~`O9@eW5Pr&@z0JiK-rW) zuS_DE6Pw*Dqj^RTe}1gp`SR(tKQSnP1I6Ui_cJwe%H#^-c6K@NI&XDSA-;TNl17Z7 z+Ptz3^`{m#)GyAZOJTg%C~P-q8&mZJVqU)dqz(NGecQga>rJ4hN$xRFZ1c*B;{R%4 zDE`v5I93?yH7m>S18rT$<%bHD394bf%;_0_*W#EWg@YofgaEdr*+|5{V` zfa&zm<+T+NO<;8t785dOOmZMwhDLI`374MSuwO;7Rginx8r-$yN6;Fj-@1*&;*Eea z!f->5FSpvJ0=gbwmJ3gq`%xU|xVD5fyv$TYBs(r=>|R-i{pp1b`(vbGn4~TYas17k;n=7O`o!8P7}nu97B-wO&~Rq(r7*s^ zMQ0EAdn_Ezr*7=2b(mjS*f8I`jX)7_aJzP9Bgjrq<`iM0U0YFgurO48(neMa7_fak zXJEG>^}@mi_Gx{^n3V1YDley(u^Hn01zV7v=7McjyZkr>X00}htGcaCh+<-|L<3+} z3=g3ADZzkuJ)7dE61o+y4R2qijR>xWYD6g6zcetT{F^inuPR@|$E>Y8w=Q}<_i^rI z`7^AFX6=BSQ5&$Km!Peb+r2&)TNDD&BH(^0EmiA(^R%`b4{q0gG3r9$$ zAXEI3xQpig6K;xJk#b#Cf=NMh#@CxHz=@nM4SC6kVj=@3mi!JHZ0iwC_?eems)W-T z2x9`mvamui7^&+wB*a8Pm61BKO3_X5ed4Jqw_!%WCce`}Y?Glr=^+&4Lt>7lhP3>a zJMi}MeG0*P#CENnrF^Z~!LXa!`hqcWzmlndFoWhT5hrl-LYf0v{G~B2wX=`fl!+{2 z3Web;ro9`FM+|XV3_S^B+FDSHw;9#PtmG{~H~z-17h_*Pb8GuI$4F?tX6iF#45uxo znSORU?+K94Dm8l)vpk~z{lZ3Z4<>JESpZmnU;~@74~fddIxaut4sh*?z8WH2d-1CB zTh|6rIY+yfA0ZjV!iE$0iG^nx-oHbaV?vk4BO9n^%Lsv|K08A$nxmUl%BFX76`mG; zCk&I8uyHH%Q19PdNy|Q)Df`UyC>oQiH4g!PQ*#FAyHmjLcm*^cA=*(ZH zBCrW-0AB{R-L17r-Yu`EHkWvDEG2CADMSy^_6vYen9c`i#HyVK;YjcPM%58md7^j&nMy6O$jNGu;G77Z-JqgHpIv-77wb0bS2GDC#}R? z5Evmw3W^Fv?`3%Eh%Z6k^nty!<=MiM7 zCacneXSrsr&>7b8@$TR~g!(Gn+$*AK>OKfr#1on%0iR&A(xwXH%vk5xQ&nGDjfD zH}NTCh<9A>8p_$_%1wsNHH@28vQFunW3bHE_zo+^B=UhUjql+#Cqcl=wX4iV+Q-MH zmE&dNxpnCK3mbZLVRU3bc)7SXZICyA)e>gecGU{KXs%jTnq85EMN5xZMnE$KE`wV| zrXH742>rDdcw~+Jof)z`v!-p#^2{3Un+7e&Uwbjm#WTKHr|d_@YRzAZ+P`2-67Q0&MW3HN z6K21c^GePh%)|<#`wAwWTL*fzuz@a_G$ag4d^&poK`WGF~)#*%3N*cyz>0| z%tYO5XfzXbZmH8uv}do?JTdm+cZi*K!fjmYjuFOG#2ReFRGfbd-o1^A^P|6Itez%g znEZ74Dc!WWYVlQ?2`Bh_?0y7a=7f(_a6_6tQlXpA>jxH*Tf$7=U?i332>w`J(p=r? zI0HX6NhQbfNSK)!u9HXN3!8&%9a$A#XR%BK4dTk+EaV+%S1BAo?YQ6CBCR#j#RvYbAB$1_=M@Q&v_E`}D} zs(}Z_gI}IAdGkzSKeb|+)CrT=BP|FInFaXq#(cS1$+OTxGdK>GFPT&44Qd!eQG(i( z`fog?KYL^czd5BpJbt>OwCuu^N?*p=U1{an1$;3DNtK?J6cmlp9h2>z8Mrw zP4Gw#GoaxfD{pFsm-+)Rd1{Ozgq_?+sC`a#+7Ih6-yW+wTR>0>hj0A*#=v;TY(Muo zT|u@Th0*Ed%wjf!F&Cj}{zm~IlDQM?>E2>4L~P;dyxj^}ulv~sWyaA0Q|Q<+$XSR) zVF)9~;1}jp6{cfuQH-rOhHPP?UebWzQ^kK8cw;pAua4E9KUv>2CyRH^CTq!b{R?9d zpW1*se=3CTgsJ$JWvciqz}IZ$i(CfwnJRt_RQ{@BJBsf&GF6cNfh8R)`9#8s*@dk0 z`qR%3=kH9wY0C9K$K^U#E$H0bB3Ex~UI(5L!$b;Cj1e>!`fn?kth4a*b7x`pX}jO0 zsnGHz2xMbQ{14-}8s~5J-RNHVHDc^nm0zWg8)<8Q^!s*wnk4Y8UQ=~j+qW7F1Jg{5 ze)EH);2js*}bw3`}fA$ zoxgg#@)cvC94NMWy!gaiG?aTV&46}!0e)a&{$e4tZp$zKVyn{bs4L9X+{Kwvc$_JH z1Hym`vfLUwNU9w!wRwS9R>Y)gZeUiKg;I9Zb~mr$C@YJIt#tBTmbMEDDzz_bdrUgV zTBFR0>>)yzI!~5#m`I19c5BUMmD%B?GQwsS?S$8QJ7+OW1M?Iz(Ztofb zYoSm#S@SGG08Y5F=tb2$htx4?W%WjgFsJ77h7~c3_wHLIkX^WuO&K|5KP!txzA&;6 zsKXm$LpO)dFgf!Y zBBh6r01n(tnLc+1;9k|er0mSSYW##0%eK({paMNwJBnbWW6G+g4ExIM zW>jGP+qMLn{qi-WoK2ZcKIgY0D`6-LYVgJ*5~Nh<)aw6E`F|r6bCxE?}_HHwx&(9XR0<7~&+CgD(!{t3Dz4-<} z|7B((1m4+>5GO zR09`bvrV=Zv8}xyXb3ykegSRzZ|KN9!lL#<@8iA{)$pN>`*rOxDX}%$e79)}vCI*n z&p9FbzO==2KGh~io74}k(s1>?0(=LRl3F&iQt8KrFb~?8sa5)~&u8eVMui&1y;XZ# z1C5FRGX**oi|{`}Ggd)NW)tw{Yu$p(a$d19Q`y0}K5mc{9kzw4jq3sA<`SMyp{%`F8TQTw_I=I z|GFk{CoY-Hy%U$56Ys?3ow(Em@SV7%JEwGUY3RXhtMtoI#Ai8+DK)zC3s6gyuj3B_ zzLcNFCluqqjf$Grj@wnNrU&J3q1?n(RX;_QAMd^<8!nc=rMEKvU13L(?|L*5^tEt_AG}c^i-TGPA+ISAVEXY z6=~hX$l4;s6BbEJ0#LG|P(NdtYM~BrJ0@j8gBqiiYp|G&4m%CLo6R?o8Wi?eErpx4 z3DfrY=559-Z24~24k+cf3`&`P#gR>!SMAX*KsK#}U7zN*bk+v?55_>XlC<5`E}lz+ zlKB{zHEl)$MP82k3{6kxOiSN~9&m=!(D?kYy)sF!0#@zb&cx_-EHa;381Nr8cuIg- zcxVTzjg7^e1TMZ{+}vCUmkMw#sKMKe={|{>c{0OT6E3e++yPqsF5&V1Y@&@c|!Hxs)@wHMEO!LBe*KLPkPQ$NiVH_dNN2W(N z3Ri=%%%56x08ATNMr7T0oZ3=G$w3(wceB7ITq)D-7|GL zzRQK}fXp4t#iyB8SR=@d3~uMmqji>5(!&F_2F$oaW2Jq+yRk}>zlT}5%>o@V=SV=BNwY4^W$}P;@|0nO z?A-cZbTU#>SPEa#Y6>&VpI~|R-c|Hzkay4RWpyqz2yhk8CE39Z}Ggi3pTL&=8~fkj~EU-8@F(y@~EZmh-r|xS|fpm_|3+ox;CZ-sBcio4zlZUWo2wY^SN@z!xlq4v{Mjjp9;#YSa3Bu_lm? ztyudf2;kffQ zo<8C?SH>hcmagCvwpv?+o{eKq*nwb+@A5YhL3*=jW~O(-*?wm&~sZNAhxGNl&pbDq@VW3>y;gxoJ@VXA!O4cr1pndHFK32(}Q$vzYd7GotUc^A z^7v0f+h$JEw--jXc2aqq7UxT4fniOl{5)p@9)0+Q7w$_(=Am%SOvQEb*VzdGG6GwU z3LxN?%;NZHRUQxYa{_P!(w*zeOm~N4S`YYLQDIJI&sb2f9&*cU>yMdr8Fu)`%qss_ zeavF&$IcogS6FTIa-W^~Y}1X#uv{Rz8`?a{dYmcO04-{rTY+^w;WaG@&$Sx#=$wys zIf=MoND;k0dxxldGKXvN!WiPYqK8YdT6o2OFYDvi0=}taSzDiYLH(y$j^Tq=y1_Zc z*AFy=QK&du{@6p+d`K@CCeSG`&(2aTzcn~tQP1BN0?4TtdPgB0AY(#|IC#B?F%+$= z@sj~Oy_P->y^=Ucv(7|U1sx!xleZ8hPH^!52w?>e9qkZMr$rcQxaS3FvQUaowe=+~ zIyvuLwDEpfB1E5~-&NKk+NM()RQu86#~w@H#zZ@w(p4$cf+aqjzto zcyk{ABW)gkhCXhTPLLd0qx*ZaU(MgBQK*`)eb&@ z*KjCUJ7|D}QzQ=10?Xur0TJ8c)+5<8sl*pLYGFIL;D#YPzd1&;cIJ4SGND_~gfOZF zG>WS2FxLI2rEn)!+D#heXhzIZ*NeFra z>F{Lf7(%clr4Vl2Y;O@ve8~hbSwslHbgDDEJdpEj$z)6myDM&ptf*gPLZ8yP{?%{i zaSELB?F}bL@c+1mII$@cy8Tp|e71nbY(_GlnSRKQnQSar%X8CO{OD(1cmc~~vke!s zo;mOdPVrN^32HuD6D4+_n?)>>O@4z|@+t*O>3 zIo@EtKJ86wNJXi7tETFOTD5bv*{oF|1)g9%Y^q-5H`K>4kUQQ2OjZ`NoUUGL89D9} zc#tvZE`i70iS)Y@>31j6k-Es5z=O%ohzzf^mLX-H3F6Mjap&XU-UWOL{s-O0`~N2& zhvZx~Gj2V4%shQa1OuxIIpC1$3H~bG^wyz0iS?p|#Zj7}`=lqSuJqJ?_@H^od zM32mPqd6BJdmgJg6r#V;RE~s`q|9s97VbmlMpk1h#7e-(#WVRc@YpWtyj76T?Yxh4 zyp*L9BkK#ZY*2XgtN0JT;FPwWl|(yYa5o8uMULiY3+` z5~Q&?m`uQ>IS`XT^;-#qX}IL{!WV}&8m%_d zhcOu@*m$)fd00Eto<~oDCgwzC(+sna!_pPfPH1SMi4l^FxmRq`j3trxYbpdaKp;X? zLl!Dye3O0Z$RlE&7%qu|b>heQ< zqL}sjb?M;>b1F`Fo^=YaygaA934o!GWy>4Nh^G%_Pfy&{)v|{n6EX|RC76j=*;d}f zb%jh2T0%EoLZ@VcnDwD|s{P<_GEkVC9LXtFy>qHEHi3Nl9B!dmDyL5(`&cCgk{+Ag z8HwF=lxEQFxRo3I?ZZO z)!q|a>cDEwVjo=+uo+ zY}}>uLZfk>EulLMel zAYc|^VHV+mA5?_?vyHYuEreTW1+>2$?zbu{3JDD;5SBm~ZP>hqI0m!E*b2$H8XTZS zR@SpE<0?SpmxQIRFC*0u(EzUslxRkGI(AGakB|W!)5a`$3|@-iH_)5Sbr2w-BYag7 zq0&aD^I$wXkWiM|fk@G>Eu0Pk@6Z56C&$;NFO?pC3Da874wiL5D8VRU1tgs$3keN| z*JoEbQ^t7XdOs{4%zdHV_zdx7q=RRpMue!=T52V&kwzT}LQ8GrIaOCEM2UJTR*1M@ zhIxW-xVB;$ACz14>9QLas=0J3!-x@IQYk$t<+IChdMU_G3j6HShu*?N4L8{VWQ2OI zR@9oj{P0LevNSW}MBgcWsi0+BeE6lBtSz8ce$o4!+13xo9X!<3#^-#VV5 z{x&Hj+JE@yjivV!d7(*9tq#;QG>D}7!K32+Bcq7HTyqehv(L9?>|oYZwn~hOY_y#k z?q_7HA@Qy^0@iB6uc36|;HOm(?tCj#!~KXQ3yyi5&k=PJh`E6qWUnni^vi=^q&Fp0 zr$-}Udg{f~gu1FPOe$4T-(r=u)l8*o+7pldgsNyyyhdKqBZ8ZO#+@Jr>qZg@CMxiP zTIW3X*6S-mH+V@MjlI-+#7pXP?4@1jg5=iW;9U#r96=$H`~)OISpv$YtO=Md=g6tHP{A+HM`TA~WIrzohBZ@4PYG zFm!j~#5nx{6_DI4JPPA3cz#Oo{GB(3rMWilow@VIXttO;Z_J%HrrEgj#@u;hY%b?A zgrwEFeCLg6uzcCf=tPDm`p;qkGyFH)lBCBgXfhYE4=@2TtKpqD=FS_#?Ykem8J-dF z`{T;G^Tu$e-kmq*&KtuR&1xOL^Tv$f!}Kv+&s#9d@qQ!kk>FPmyhoEyt?&x(KVWzT zzls3wL(x0KDavd(ETS+@wqSM%Dwo?3+(o+SC#M4+v(<% z{~9-T@ni7-jxMhKRpXKJck%V@t7YZawMWa!|9~%-FLl(moULCezoGv^p6T|L@;~BN z`rpRY-%dnywL8u@PWH%+oq9I!ga${c$g*B1&geK>EYqa-NzjShyz(kyuBzFR+;PG> z-5NS^E2-=}&vsZwl_#y?>p}19(n+OL!D;6RWu3%Dp@{!D&9)mjLif6~0a(~semb>Y zV70W+k9M|HLeLFv5@oSBh%%LN8Ei*dHZqfCB?{17ZMIj{E{?%c92q_67*FUMZxs1~ z=@dP=`{gzz&P3D*yEYX?*xk3CM-**X&_Tq3U1^7<)|Bcp!a~RcU!coiD^S*ua1&?z z;Fj;S5X)8^N)HR_uq8ij<|w-5q12~~%kq3+YI2~1D^T0z z$>-j3z2SA&R~PpmTC86g4NpKrueBYB&EFIUPFk*0t^`mZO+T_3)Zj1ZsE@AF!w^>(S}_5^!gU#Zb35Bk;hMmz7qf2Ec)<*c-ZRk_`e zYv;az&lhwCyn!{(y4wZPXJ8?=iZ$)8zgceQxmg7o z0)0W?Ap4C!Z+Lz6r{)iTox%y}xBhPO>sZSkv$EDP{YK|#*@Jodisbfr*)O+-M|z#4 zKN{>p?{&nK_2g**-c*IP)X|1_gtbRP znaQsV1pru>10R**qtBXB04)|al*sSke;005_len0MA#sA->(=f(bvXanBl=U}--xa&4gRang0txt{;_fD z-|IwiW27XK%ZFctC+15GYeQT4Fype4W&x>s2;F-q=UWZcf z_;D5aK}sD4p~xbVz#B3ky>P$%zdNZht zpcbCLrGMAB2|s8)-lm6qPOrmqXcWvPG%L=W@L2yU@Di4zNnX;&MtrSlP#m6mm(4~K z*^IIf!a~c&__Pu%>INly}!1U(N$FO8HLD+dbQCgz~q04IwAJ7?WCh45W z=N2v5jNKqaJ}{v}4!?yI1?HX6q75?b8oo;ZgIn;Ip@}2n`keRJnPfIPI>TTEtHJq? zq>_^y<{|CHR9!GtEIB@-YEHCSlg1&Vjq$kaKcs)Jqjj6dG{44V*K=JaURiyO5RFdi zQ1lrX^oO9POGk_cIGv)(Y$SZHo*3^^LPZ|mKriu+^ott;Yt%IK4aBo&al;!H+*UxruXGDNNQT z?d6tV+oof0%?7emWm~OU1siGXXt6~_PB-m#8-61qa(dDRz4JtR4Z7)X-h#u)6fnup z!o1RqPvvPzQ!E)KJ$0On`n{XnM4K=41(Z5=kO1DMrq#}soK4&Tag{mgQ(OY|%nV4Z) zd7&Z)YizVAVU>$F#k3di+vk&+#qF9qn*j32HluMW6YSb3fm6Q zrl#KgO~_|Vt_VXPlL@mxpDo+1Xfwg)GGB+9kYxQzmZ-mQi`9O{e%aiBG5WVr;N4yV zi11EoAOoqs`!xuGL889|uGyNx01?$Z>z3K%(@{m#a}AzB zC)VAtS!0@zzY%j=^lfpV4Dg9Pvpr|i!26M9)%hrQg6h#R_$7VbDFhBSr3Cyyhml7b=zY7(czlKPCqB??}{Vog+qP^fD=w z7AH=4%-gWSX6or2J}M{1$kT6IAgxjKLQe**EeKrTfLt%wEC($b{5ZsVx}@mym55d0W zY|GX_U|(U}tZbl#T%V%dM}*%*(j*n>Xb_7}8LnkF<=3`KdTqVN*i35%GQG(2t$2U& zzx!)1u>aEk=oWe#>{tl%Wq;4f=7+$GNjCt;EMrO*>xu}O>;MVWXmpm{deAigu+br& zjc#N1ze1%@O>7x&y&y@K<1{ZEm5T(ouy-YI>oH}*&|3^8-B+sE3l#tFZV z_@i?f2uv-Ux3V2kr?H(BQ@J4z}SPY@%Xtr7W)g}`2;vkkVdSl*r zcfvbyhHkQQvv^z6{Yot&9E`MJ`l`Vt?k4n?A~_jac&jNY=LWQVkZ6$bB|<6;K>uph z%2+6@p_Oq*0#1){EqxNevEB^etQ2PeCk$4Hk1KZMb6{$X{#;bPt}zCSnlJ3H1^q~* z1f+A-V@CDvOrFq&OZc%NlPO;3X;{#@5od3_AMu?y%o`DvmqANI<^RzG8`|N>raNe@ z<7eoeoZf7qaBkDi_|Fzv~e4Rr>9Pug-7Qvh`dcYiOJ{ zOSIpVy&U=c^ECt}(pkxO-;?@u%^M3%kX-CeMSZvR+7nPEu4SX(%qRQ;03_5F7e&9h zZ{sZ!T67MZoHM+z8j+3Jvc}9BxF+mA)-jF!mF0|rwUANjd14W0>17MEpZ13qF+<~G z&&F3Ss-w*T!AE5*stw~3jsatsQ)JIHorn#Q^?ogBX^}L3t9M=>gIqH=e)T;LIicAa zg3PQDde1juc)z*Ii4>s`*tsZ0jp?I#g(>0O;!ZZL(%M^*jR|TUH2o{B@y%PXm}t+y z6xp0Wn9puL;j{*U6*_Mq)joaWR3MDW-WJ6x=z}w;CZrGZIZPz&Mnx~yhz z1QAszWVK4;P=#*<6}U<}X6j=HH4GkOtv)YrAq-rtcWdX_f#Q~2dNK$)dsKP$|%!OWCuVGPOeeBGHCQBfNrwEIzJ@II$5CAbj z*Rh25rf{H8fN`M?IA;^cFg0+5Zz zK88@2?qqR1#Tk7vJW-!Mh{cBPw;1UfSq-5PF8V8A+$ThC2^#Qnr|$$Aa~ zwyAXn#f_ItpAeDES`e+Ike(GdgXFx>{tXsJ-=w|dd9cwz1`Js{I;4-$K!=H2{f#-l zQ&2l?xtTzrEh*iEDz4IBxrLyZcFv%v`yPy=fpbscvJ4029#_}xbOnTQ86T>-R?qT^ zLxd4I2s)y;lhZU8fnLlRIoGSPsj?hXN9?v-7(Zw_PY?@>zT_j@lFb;W9kLU#$Qg$d z)wudS77A^Qhm~852JW*BW2PbTo$TZk(VKH*r$JJiZhp!E;3*r7y4~=NaS>%q8*_bP zqhYBA(h$YA`EGLKJ%4sdq8W;W{Q{e#GZ3S(x!TauG)cZ zg1D2Wm;bhLXnH4^P&gprBZZx5H-=|VIz6k(av!^iXhHYC$7@} z^DXwc_8dTa0-c=onO!!h8#2Pm01Q|Q9R{Y;p{}PC=@7zU6@C8CKsBenw8(-{fiEM!@9SaV%@EPYd8W>Zr><8xl_8gdHjj}%*GPy?4 zljpIbSvIo9%!-?Ok+V$UVW5^%yG|e$+nrcd{4Nj^uV&?jiTxf8@5bv~?G{{q?M*dD z1Y7qQr(;(gp5Snw?iOO`vif(Y7!8ccn8Ie-7MQgsrfryJO`0bZg;nv}#sX(%k12Ox5U+KYMiMc9@%0Rnpni#`i@x#?yEYW6!l1n zL9OVsj(}R^#l^MW?GyG2W9#A!pNVKa7U_6C!x?Le+czGdYD3TG_CA8CvC-4uG8LyO zEl#r`K6itf8S|V{OzC)Mlgj7dx!bLDC_u9&50IeuCJhT^ISil!i$TWi(*!pjPbHT% zEiP6s^4t`7b@_SLgu8B=0QYt2N)~bj%gXN~X|VDK^yd%hkC6oWkMZlrlt01WuLQ`W=3n4;QDdwg>Fu^R{qZM%9kI_%e5LKm8;8- zD6v)6>gqY{ZjSSZigQ7{EzHav0JOH;?inT!7Psb z^7A+iNR-Q&n-NkX}{( zEIyE=!$J;YR8)2WlkH_AKl;DUs+2eT82e4FLPLv-f z=0WsTK%`nB(oy`A22`n~XGJVQ?>>WNkt|2=c%%{%@T!mAGagCmJD&G&ysJy06O~FvH2_iqA?LK<~i2z&8W+U z_+O0GnoWma$Dn?^XAFvW3C4Q)QkpvmqvvaswHc5p;kcaQlAG{N1Sx<K-`(z9@- zB>gMr@2cQJ*L&1@54D$`A^6tln&ai$3MOL?7#;sMCSaD#n#Za?g@skWeL|QHlU08X zS01!w>A{UL`hZ=ppq+e2&izUc>l)S;1Y11Ngy92id4Xz(yB63r3=h-?bW;Pne;`YD zL*TH`12#VoV6w)gVh?D7A821`wz&K#q2-2g^uA+?jh8g&P2RucPe8kWG)B9E;Ben~ zxSUj;qo#F2|L-xV<_o5u{X51K@*y$7^qHwMAmC$0q1h;UNt;DJZvN9cn2#;rWNjrW zJ8dv8Pf&|62%DEPfmc5MDZr)4ycbooA;wW(Tp-Nj)NFQj`SJv*U(JO1@*d*^j&J>! z72V#2f&P-la00yi$!s7$LLACr)P7h&+*%lj_m~_IAk-hs0g&W|0U-Nf1u(NP0KZRH z3?`(L(c$IPA~u7VuLcObV=K#Fo79#mDvs{`kPzas0*d6AxlU1I7>Y_bdsS)Q2z8_k z{G2Je1c<-OP~aSIesOhG+SE5ih}+A-??OqcafeQYa)IDpphmSLA={RrAm6BtF$Tu^ z{~87`dok6b=da2SxVpQf?QC~{`JX}vzpB`d;?*|`m7Y{7JbjH++txZ| z@#_Fl~3}~^FDP=W!hi` z@&1{q7@>uex5sz!81suuW^KmaHf0<)L8ghk8&$J`ZoVuRP-QDqZY1UO8N5*)W3UW$ ze{U|`PnC?ny^cwrA{jqxNJiR_+DgY+MXWIXFV7F-?@YjGO2}_mHl%Xly(M8ox*~m9 zm7bO43vF*IY)vQLh?`Wr96YNu-g2$D-=+<#RbJZdSM9f})Q*IPB-WC!c?FnUW^&Bx zvfSe`ZAt$!4$Vpv|L0tqm@Th=mk48qygu5|vzO>b+7)ECz@{}1qk>!Cs4}C(Q|TFu z(96$S72I+n>|jxD6%WOi=I-@-Z5ua*+U1l2;I@|@SvOv$NWZ+tfa8ju{>zHBkB`-! zFWLX-hYURNu9;+?p``P2hQv1QcCSq0jKgd9$_o5z?;G&S7pZ9xxmd`VQ$s-StF)(> zoK_D1wAa=#_!c&X7oV8)qTItJpceQwi}(E1NSIz>H8RzfKR(htFXMg_Eb9eI^a2Uh zLE@iUwk;vR2siwZ4zFn}a5re45HbzXUW6NjCp{fcnCio>I)SFsDBfJ-^cDWpo7rqE)$S(ldI^0?k! zzR$(xqepC?NvaqnQZ}qiCYu&Nn8BO#c={qf zB@D$}@b57@1qW0AWq_dkCp0;)D*y3~=7|!g zU~Yav16qc#U%Vy4{)H{zCc=IcXM`XJNdsY4nlXtuRV86-Xa!EQ?lOFw z6a9^`-sa1V4`+?N4F{FUjq4%Z=>76~msd|wPRtFsk61;__CAxwg z78N}nPm`KB0mg2!e0>SW^du7huP;$hvv$w{V|+q0jgMC4F_r{YiWUb;sa5U0ZQ-(e znOz2>*8q)y#Ml$DpJg}bOMU#<^XM^Of*!Lqh;@jip0=P`Ls-+b&ZjhGbV%C3W2O!~ zrj{QUWVvQ37b&1MJ zLTeL^4>r+k3Okijy;&(NkF3<|c7pmG)QCK2Ew7HK5n={AdSTBHikPLt&72GFO9L{M zKnrBsBIMa&W{#}nj!3$+pya%7z+O{@DuK7yhSj?DhJFBqX%8{x0-OZ+BzZr?$L9JYqA8I>!A0-}Fv z*`eI-us)5lCOiTTXjO1a_oY?0zS-1JL%U4mJV#>UBAp1wjmR)lvAcA$i1Q`>vUDVc z5)t-Pi=EcG*Jl2{6zYJn3~i4zF@#rZMPLsDqHsom3|M5hqL#Jy0}Wv~z5f5TcWpg# z991}RSjX$jdhH~JkOUfUtQ|XZ-Am#Ni?HlCu^l%n#|{yzsMRywGt=Xqp3QXk?rc!P zMT%rZO9*8oF5-z79(h3u0)!Na|AE8{FZ=)`Uii+bs_yEUU3;9^7D8jmwbOMyb?Tf` zms95yJ2`Ut5-S9OI17;lD z>N5JEI-nURgN$Ho`Tf{&x%RZW0Sq{}-=J{}O#>Ig0{kx!7g50iZUJUgbNVz$Ta>^r z@<$Ggfdtd)KFFX$1;Wa)pg>k-1<6up23hu$17(y}>4I^46OOc8)pT~s7`Ov9;0>Hu z#8{3KP9?GM6wGV$JPOl3tLD?e{tn;J7Z{ggyi%i@*=V#`t~lT7IV zPG35l!8ZiBTuShIa+e%g2`nsy(55Rj)+YRy>?V(Ck54j|=XD4j@!>(-Kzr1!OJ>a$ zKGOfd7$drSN;|D`Nv#vr#>_&5p!^-|AtnTMtb@Zg=qcv+&ZL3{QxZ0$3-pI%n__H@ z^aa6lOY0ay)DdjK{kBGuraTj5@ z4(YTf1U?|pA@ad1Y5&ICl*qfn*Dz8}&-iO)hg+)0~kknyx-dHU1T0wEx1e+s!2nzv12vfR&G+=UD<&`p*7>C)aWy4RRJ803g+W-wI+y*WC!=>{z5X})~KwMw2Dn4)}#WP!q!j_ zCVrzObe!K)FBHrHP!eIWOg%wjIyrzQ_RL3E@QPx?LZ`gxWD+7g09a|C?t87&@@I~vvRKLnAnjkoDoNAps1$=kyL4jJNeF=dJ5?iP3 zKT(q^L{g2tFv6p%i?ugTg?vIPtb&jVeGOZwaAPEIL~XZ%QMZS<+7 zCd@jpS@)wde#L#afIqY)Su50V+omeV9=%(mtmRh2F5t|ogOx4-SX*3n76l&c0eCjD zA}{jY!s6RXkt~;PkcHTpk8IeC?TT^A5sS3NQ@$%^v^)XJ_K7Uf0-bqSVcc&L$D&t7 zj7t$L>~4Eb)LyF=?SNem;W*b>yMiaH-C_f#_G^u9dCNn;@$3$FS^_)Zo12BjTfh`7 zCtl8XWk;s2E2O?WK#mIsA0^%{j-NS7pzeVIji~>xkZ~Cd0YxMfocF;2an9rKx#ZJZ zwBZk-pC$EdLrhG>w#%2nRXxm2otV6*VnT9-z|Hs>$_>mOIAV_Jrbo6uz?O1Q1I3HU zfWDUSMQa!{sw@c-rr2e~no&tk5)l=NHn^~uS|TbYVwPkK6%jGZa-)g4fZ%3P19pOI zQd~7rd)~{Y$qa)8svUne&KI>75J7EZ@v!>gC{S++&(7LtlXf}NCP`0`y(9L5Ft?+ zA{QLc6V}FK5vjqcrTcCRHh6`NMJEUri;Edj7uAvBLxoq8-w3?pv3Yp4^v4YE@~-$D zkIloYrB4QL*zRo?l%dR2r+_6*w#}dF6x6;X-DHZ54sW}rItA^-lSJWEr!dtiOmzyp z9-HbENL7Wi52e+c>J%na>r8bDQ=LNY(4DrVQl&N3DWoctsZL?4Q{b6)s#6%hIF%}1 z^GC8%odWGrYz#KZ&DU1m2QLTn{);`rKOmzxS z;AuJ=O*^3JY{p~rG^V9LkWL|QH*xgLz3nE*(NgDA7&vtPhyb>Ho!{Xv>`4xzpzzzO ztnl-uJe|KF-dNZb`fCmz!l<3Au2h{est}sH zylHy-adk#f!{ci(C7|T-wFxr4DMg2JVUia>x-)BG%x^y2LDoG2JezTXDWMt_XgWN~ zbFfzI`eemAS1I3_Yg)-GY01tt{LFKk#!kQ4FoiF1d7n_Y08u=&H@jRc8*jn_pl$av zHenY6kUZ@eoKm*E%7_Fl;Z9yj30=MFRPctSroFUWwHvE$b)~Tz!+iUTf~y$ei&vBp z_!qAWgd58do0M?hRfPMn(XNy5iHwBbPbq3|mQp0F6$>USrbt*TIVlN$w(+)fQKQq8 zHZ_Wu0!HTw$ow1S8^)!!N0voByb{Sb8gG=1>z*69lCB~B8{yK@xpElU0qEB$yG~r8 z+lfon+HyrJElQOnESI&3=5^`)FT9QW3N1mvrgYuE*Tiu9k@QIs|0AkB2M_s@Hzr&jTo+Fx z7&`5yj$T6p3YbUeUN&HolA7g75{CO#s{5+vSihE4SP}jC8t{IIPrry*rh2 zubo|9U8ycDt*+v}JyT(R9rVUSf<+PdL#r<%>4#P&i1^PBNW^6&>nFpoPKsa6Nb%Fj zXo^WuEB1%UiYZdmN@k>ZPj?BO%hW<{`9eDf@nk|)GFio5SL}mIc$P&M_SymhtNjw~ zgG%W>D0@mKs{nS6d+h~iyO7^VjcwnuEsom0X;9Ygv%=xMx5;4XbW9?ocY4n*m(?ondmk z+3Q6x=ykQk>rW;}LYNegEzAHjd3T7IIlN@%Qil!@&ys&ikG89i?C@md^-#Q zGFp@c(ul)-m;5?dzPsi6!|VH!gKgVSKWCC-?f?&8qc>3;s!TJB8+c8gw*$LmqaJ~tR9&%l-$D=HXdZh|n-4BY<#CHrAo4DAkn&3X=*yEeVSu)RN- zBL^8)7M1MtKut%SxVvek6bFoQ1g0jp4?_p4@F>UN1-c-lanGVQLpOGM)}TwYG!LtN zyu$*E?yMw}Mh z!0G|SmrhkzfR?#_voX>P#bnLAsG1>fA7R;Zqb4`gj=DaYn2qc@Xdf0Y!|Ml-`vf8=~Yh{4G8$zXu;V0)sEnuG4N{lmtIv#7OYK{;z*0ruUELAawX{ zyyWwrfJk}`56kzA@sE=z2;+J_-@FSC1`c>}2W_=oH$rXCHT<4^$HM84=UcYpU=kux za5s6%4Yr1OoGLjWL;zS1R0OSuM>hIa1j|7;;xRvlhCme&`@IB(G{Yg@eM^qw@h*oS zcq`E_IJuimzC4vxB4aw>pA=y`3RS?k6eES=FwZBWXdq5B;$8(qn;QV0^taaW*bGt(P zJ%WRVr>Tl3`$?Pt)gKO%rzukWE_D8d1xM$f6nr#`;QJJOHjm)16x_uLb?0LWp26FA zop}m=aRR}Rf}c^4Q1JHi2-YdM@-+mPDEJly7btiNkIr?Tpy0;_f*(-upKl=eHw8b0 z-0yry!GMC8f+_)2qTnAC{2f7@%o5!6Y$M}?AvYOnlOZ-4T9Y9)8A_8OG#NURAu|~& zlOZx08j~S0848mjFu8S;TQ=kN^PpHpP`f0s^U(|-V(k2gkj2>f8zGCa^HV|=W9I}R zi?Q=7`o-A!H6e?!^9~`4u@k<4UyPlrge=BR@$2}-*!h@{#n_>z`vi9A;X#2NI_GEX zboj_QIiiay9_%9x4^uFSCJ=y#q3J~B6Ktx-hS>c^6xkCz>vOr9I9OQt-L9K>YD@_}acL-6(DL$II^Sm``{i5`YT{3jsgkB2vD wVzK*}L%=2>=2_8TI_Kr052ev8vfv&8)3BVeXgQe7H@mQa%tRL9E3TLS3*+tQasU7T literal 293180 zcmeFa39u~LRUoFX-k;R!megwKZXrtDPwMx({{OXaLM>7IzP#G&^=~~gtFkJymaKZY z)Yg0$z$~7qVLwI_Zo_JJE8K>u4kCr((7pWmT69e&(l z#QUqKJL9%IVtDEPSMJ~Zp8NOipRJw|sF^sHg*J14^#N$nX1QTUVEFrQ-(P(MHJ7-d zct`#IDUoSQ+?dxtXP;o7WS@Hb{u%qs>IsRHh79p)<*tl}Q;zT1VqCY&K&KK%4Q=r& znL?e2HrtGoSX+!?Cbk?y2|P5tk9vd79W0eX2dAL=hgs-%s$=NcrpOjyy4b&{TUMFkRF}UOgpIJ@o26 z``qgBA;&ZK^B;SC^`u70tfM9}g6PPP1&QI)BdYDFG8E93?>X}LUq-{&0YrA>fUdH@ z6vhCUqs>wii4k0`JKSW!)A!j|*bmDz5ak)bh3W~^ge9r`i&d7f)p%|S0|I%&lZh~% zb0bV+8@w9}%*ZB66m)HqSW2={HlC3MXv#CvY%C0HZHhmk^v@U@#V>4Kna5LY!ykwM z_>i%&T&KhEwjs4(1RFIR!_?v_9P^Bg<0rCoLh&8jSeD>VwUso+-Sq%G-Zl}KHYdW| z-@)^I#=f|U9RvFN`ivi`KOp%X_6GYH`$mDiSped{xVmv-i~>x**&uNo5*nkdj@6?D zu-mX@D_Y{)N}s zHvl{k1~fAO;%!BRu}`cn!@O-QbU2<87PbzlY#3G9*v^Wv_)Qxp0yo<9ha5juHI&Bg zqK&1n%0etXr38+mhm69lzyptb9G#NvIUrgjS&-UGpqI82D46DLJ%(pM>Te+m>><{0 zJRXR)AvXa1hV=1^s|WAEKTy;Y4ezg>nU98_6DJh1u1|yZ z1EVlyFh>tCGvCa=S|B)jsB`ouKHuS{Hm>vLt6;fb{le!R@Y8^Q%iDEGzxyCa+3#fU zvEPMcOoQk(5~62TCx8!oNe{>E0ZI1%=;SWV^f>+t z9Wq_%Y<|mj_m-`9HovL-@w)Ms{^#A!SQ1e)rOB7xIpc5MgLZcXuE$C@ZExC~CwCdX zV~nWJ=Qjp0>*W8D-Q?%TGce@$|Krt@ygZ^A;eJ7zhaU!A_nE?0U3W2K!IiR|B4VB* zg(iXd*VLB{%x#zBJ4nbo&_*Ys-tv?`y$w!RhY`3bxCm3mHtwpO8Aka@Wema;X-|Mz ze~J`gHvKZ#>%p=M7#15B^$*>YqL|R3F>q7GsQ+)!QAA?&XYs z_0aI%xI=&kKg`hV_cL^M+we1*FMRL=A3*-ouY+b&v{>(Tr-R`on7cyAs4w z@8D1F*$iM#ZO|)H9!NvmM6QEX0eXN``jC?r@UVvlww=A@di(4(Q0zBv-Z?=8U_m7_ z06+K<5D9<=G4#nT1q)R%O{t-*s2KkA7PNx6W(3g^Xst0GTkk*{7e$837@A>0q=2}K z5d@}#J_FNE*;F;Ad=9SNos+N;ju7D9vWepnL^PcahkAyfr#rHKrCP)1VY^u;#;s!z!+s5gLy+uRpKTBpvL;x0Fg*C+ zTGk6f#v3k;Qt+3KEPnh-KYTE{t0$p%S>V9qNBR-D_WduSuW#lpWa5K2N$Z4uZNO`h zXjs=BFRuI#rhy48AGC)JXmv%#{xdaDG`k@E?>Ly2n!jg3xHk^B9R!-!`Dz2T?Gr)d zNIs3GVyB@Zz&W7t1{4Pn_?=@A_#?>8Gps2AwfW5khzAks!=!m8dS8ET?z{i(fSc}* zTZ?Qzjqrb^|F;e%L%#$~50ckA;M!foe<1L>?w4lF2^V3X)7=00gE8MBVK3M$+#UiU z>-QUAAH)ow+T%?b>UdvE^Z5I{dtJF~c=xMUbBu(YJXj(CM^Sh6PJ5S-!GK_!R?=a} z(fg(?Z3&8PZ34{t+omZaru#`{G|f6`KXsa*+;ji;OyBSK&_1tvX!_9DNqY?8q<6i- zKP|x9PgbpaJvnQnvaXeEQ?1CgzR}^wr1>{Mn%$`vHAlCZ`HK7<;3thQ3+nZ^Ikwv<`(e+Rm&Su=$uH~^=JtQlGs8&Ly@ zOLbuvAv-2^7Z7VIYgZy8oj|~7gpapurwU0S8aJ<~;Z?C2gA$i$#i3)PISQ5+Phb_c z4eO5($kGejX-SRamHDx$6LhMW9L6g2hbZ}Eeev#&4XyFngfT47ZN#&tj&I=%)A)qp zMObVERR>r@kJ^G=R~U~BoFIBzG6G~KSXj8zsltgT42tPtHL-)12GQp@#>de#%1kJP zM$Z+x83eP9P|Aa5P88B|Oh*OY2*9=J5!takgaII?XYj-r5UBHVf<`dO*6_`!de&STZ1?j(4>JExikwLySo9NXWck zvyc@64eR$-2yA)}n@GO6dd?(<#84ZrtVYp&>eZ8q$mw&g{#>8)>XFEF^I$bWAasq7 ztWe!aP$G_bc1pNjeQpqHwXdZW^$(rlHx4%&1Vq>Q$_l!NoPwV`(iA+UT0R0Z{gD;ehZ6OZyDTX& z*zR^#5Ez6zNJsthkqGq>WS0!HPoQ9avj^xy?9V?r63~wU&;+FTrxkdI&gv^WJRD-2 zoz1Mq*XOkV3JTwp!itT&^B*6HDz6>ji4oWw)Z7ZIL#g`GR`AFbDt@&#N%*Hb-Ko6bc=gdyIZc$eouPnyd zpJvd!X+26eYQRn-P;)rL^^G)CAmYeGD{#~TwJ&1JkMcLK>}XApWoI+M;B%%aA>)Zd ze9Nfm`~4jGmKINFL*sbj#uo{o;fDoi`-!V{Z9&|>9~NQpR*PL>O?t|WWpTJripeGt zH{zB`!Rd&R*l`CUGZep}6;e@IwS`q*)CfhLj1ASXLPIE6MKP;6dRAAEX$F-Ja}Ypp z2GXdBFqV6)4OQjND4_$jrQ-?J!$2s(Ak6Y#Hn4SZ>3<0^#w-21*WwRUCHWh`eN@&1m+LY?#eslvE zgc&M?>0g^L^j5+&M_`WA5^{Z%lm$+V5H%hTTe=1r9VMRu@_=hA5cRN^Wv;DgKu!b7 zGu!NVEP|+vQHBFmW+=r6BL?1yP@I7(A)p=trW1-G6rD@X5lXK^OI(p{gPhErlL`mR zpJ;ATk{?xfBGH1W)C;$fK%smJ*^Rb-f7%5Elu?z+jP+)xZN0{?WYa5L5E{@Wtd2tc zIZ^~_J`1IdL|qMkbc5`K9ysXLNOH46q^|S^;<{kv~@5(Bs4)R&T9FGsy9A3+=8E$nxDf$^P|`NcJgg7q=S} zeN;%I?J+%@CS<>Btciy1RT)cgqm!s%|BPDoyENB3JDxp4-QE0>Td#P3mq*pfi%r)D z9)Gx{I{J^dE!C}NX{bgo!1^58O$JM6;5#Tj8Ls-A!ZtbZZBFmf<6%c!jNqSl=J#OD ziG%7DX2_tejj)6_zvNDB$O$^-U>VeP3)kY_DxBU@7mY|Khi2MPAZmCdj{yLLz~G-C zA})N7hNJ zVP<~3j^?eSq4}I?Dha$cUhPKYF<=4>di?h~$X`4f$WLHSBLGz&>;~`IHO|xkH9cJi zxqLK`Z`>llg&$U+TG$(nAqki2rOl{86DS?{)s99MBkxtlgpBCw*eKSxR^`aUSDQ#M zDZ8r{Ko6lEVH?#ZnePpPs9V*Wyr|ckpg?P*+GN{no#0qUf8T=x_I>Ms8K&-^ZB(0R zd%h5$YAK25-pMnnMO@b@5#$Jwg0+^Cs4`lnp9zP}&f=36elT zUJ-H`A~l)}QTYzC{YpX#rFk9Kgo@CM*ZvfA*-x8PG!d!^Xjw;H@-Z)t|AOhW{cggS zFSV)A$HZ>JK{O?hJgmJHW)}8g1AAz5Mhpf&EP65}89bUTyx}1~g~zY-f9qg6DLIBG zFy9b0`I&8Wd(OmL#LyeBEN~#^`4t4CI?rZz@P9rSel;ZD3h&1@IiCR8>g`UbS9`pr zuOAKYjckIMY4)3cV-9umudf0%-+)wZb!?k308xeDWpt8-4bIT$a1bltH4XSz z$$sijk#gB%!f*v4N|Zwp+X*BwN2t^fGUJm8=sOYZZG-G8+KG!3tvsY-so_FGTgtRV zDB45@10e@$ec-bVvk9fgxHfN17xowkb)+$*;bDUyEW~se7#a@;9nV;<&6?7=DAx;X zI2>#!M44q+m@)KZ>=-m7IPf_A0na}1#MZd$TlY+nrbza-Tep%QF^#xi8UMJUj5Tnv zGX4-+QBZk=pv~H2D-TD}L#$T+pCGmQO8?D+f!t=cwsBbECY<8)dB+RqsPA#e{kMSqO$xMkb9JgeK zQYrd?6=i@NP8m?Q-GiVRB_^;v0!f&*wG!in0=m}@=#Sw4gPH@X-(zND!$$4he)rc+ z-|lx9e##)2Hn6&syORdS#C;3WN;`l=<)WQf7C`>1PmmaLS3CPCeXP`LU@5 z1>!{KL-j75%DNBUvkOHuA_QZQAHv5@DkqV^MkXhbA9@0RPbdua0kF?MRfRxzxeb+Y zVvMILT=LO63H~QjKigSa3;MtMpX*3#Kw$Oot=OO0jvIl--ln?|d<>|hVTS)+N9pTF zLun%&pdqYLeZSr!s72^4gGJm`up>nHt#9iEXYTARFC-U9X@Vpp6q73!_r=vGcYRBc zdv`ma^%GC7hq0#c!K)GbhL`9Se!!<6F@3t7f0XFq*)@E~0;OaPKAKWg9(Vd z7$`)~{Bwg)1Sap9Dfl5k-~mm+AHMp*t?|Um>+yuuVXeEG=yb;B;Kv^v#(%j1qhSt; z8|FY;w#PhToY(5VcY+TxJTQVddcW(`_}RVG*sbjU2$5umvX7}pLKx1xT1a-PL{IAB z3^=Gz_M(ukw{qx#p`x_|Qgs|w+7nPeUo%OMv0k_$0|#~8kbIPqva^ zd09P~Mdjf;wy<_uy!i`MRSU<&?Ko*)gk@)C?;oZmO4{1?!9noZ{f5s^-ZclD@7upr}pjw8rGaGc?4eD(xyWQI~d z6l*Gbvh@R~@Bv5g=B8f7erR)@8dzCWVfJ>ra=RUa4_@gukw8LMpUoONE{cPS@>2zY zQyV_!0V#TAXP~lK8#cwkTB6uRYmbU&V4N(BPhU5V-9ktsy-U`9Y@X+g7Ch9uQ*gNl z`fUmwwT;Y*^*$}x(4lk+U}*Q=aH!nRqZO8HZk)v_M0694ay`o(TLJ_c$fd=!a0?DB zWOfup6#&#bV$eoJwBQP9Gkw>f(#b9SfV>+X}FeZV>-ln?| zQxDKVJKYhBYsS<3cpcHN91YQzwu%&i;*Lf;k=wbs?q`pN!x{E)4-kCIX3;n5oj*Y=TJ{oxc*6 zy<0ZpnPSxLL3;ci?5&3lV<5gT3>xaRVEWJo+tZK{NB7;qZhs``>y{Fp!1;u^x>X*+X)XQdB^5xI8{`SKKa`Jj-Avka`@Q$N^%j-ZHPuoK6jt|7atWAzC9 z^sh`RfN&Wc*PKpG&s_UET^zAe`nn0C{Z7b>h7+QpgPo9#C{cT>yBQV*R~BuaUE@+> z9!xKGlk;ObyQyMfyQfji>eV_?o__keG5$89ymo*@5hxzid^h4B-H=ZWZ;LnUXuona zw4YRJ5edw+C%b`nZqC|n9iriO{SVhszjHLyKebz{5hU5yayO}-*GZ+SM~xJlFV;~F z9}U${nwfh|A?u^AcDJ)YbHAA-P<7}C>@2P*&Q9~u{24@ZB|<~?G{#>jAXHM zLE^1@1RG{s@6cN0bUmsYZo}xlU`1yy1Qy|5a=sD?8vzs~EL*0g%1 zkAhk1yN||F8&=*zV2NoxsQDhmb%D{vUq{^H)jHx|J{sbh6QK7GVKuD%P!KflR0VF` z*6H)MPe*C!J;5f&hxC^}a>qb{WF$1|M7Ut68~9F{h;er9nHo<1K|FJXFq+cZ6d3qY0^ z?5#NXJySpXP5!5hY1V+iCO?1F=_54xkvp~^o~hEzuc^TsegX{m0iXV#2h&Tb)_q2) z)?L3kF0+k>pT3EfW_R%^0nh=BEpR0m0I(4hQ z_xem=smwk&bgykdXDs+{UJs?!7Gh}C3i1FH7NR@U4EqVGYtm4{>fyG1N{?`abqZbV zrO@uOg3ll_nd=P=E?&K)R%6{J_CwxQc5PCu?d|*Qt8d?5y{tC++~%&y`xJW$tv>rU z+S9?FtZlqJWZURVWpozrNFGAf0xo61g~U+5KGJl_jutwp`ZJ_fUg^twsD)ren?v3I zhfWm%e?n{y&A@@IGfrf|Z$oDh%TS2`D_C;!%dABo!d|vN5_Ud*-z0_p&H^Sik>$9Sq2m;ZVzVG!GY*AWw zRBtH-M|edCKEy{Wcc9YZ)`=)XRR^XdY(&sDhbk^66pW*J2HKejjE>60MZhREXJnpU z-47OFjt^-K9P^_l>K)=$_5UB_OuW+n3DdXRDZk6D@*A_E0fSxBm*H$N97k+Yl|XY> zD+~0%Z{OGnuZ^lP5VVOLVcK*?JxXsDxENYYQ&glXLX1w37K!-=qyG@fWtx~z3Ef~b z3{DWMr+R78FAA5HOY`tOc?OkWj?6`gkb*vYD**8vwmGnc&nV0?i;uzM-}Vp?5nS<5 z-2kcop^38%|GU5I$gtlseYRa7G$%V`Fuyh?X8u=gdudCcdq`^wtW2^V&@9f40MR%6 zfKPw_V9XRze^Qxsa--umRG(er3}R%{i~R^#hJc!~`ua67u#N$@Az``ENSjejvFsOE zqI*k${TLFD^<0ZKX;!av71V#`1Z(W4&_CC*mEUGCC;^e-YQA=W52=B8P+J{l>>z&v z0N(As?{@zp&pxKPe+2l3spnZ(0HYZw_E0wp7-9$Zni>iW)mbRUSTWj09*f-He#h28 z&XSTv6tw^uZ7E#Wlb8}HdGxslAD57jhv@~x=`$v7FtptDHo)95^|N2?mA(43Xh2}K z_sR}J5_s=ywiB_P>N|WiJWdStO@K{4wSaQJdLYO~aPxZ>TetQKCvu`KV{7^?U;sGG zMpeo%`34q7?9B6UOyG{#+Vp;1b+8W(U3&vML*X^H?%TuAsIher$JTHXt{Pn5wyC>p z^oV;~Wc|qcU#HG&FLib+RtAwsiK~f8G!*M=kWE(?0Py89wl`=7$`e4_YKhV}46pBb zb7MkiHs1l?{Gdrv*=JTyGouM8RX8W&EBEz7nVvTfs+pqA7dm-Xo9|%6FPlc(spI-T zf?D6q2;Zv{NrM=xxsCcU?d{>70@1Y<{hR-nS`{*6y6W9f=*A*k$04YvVuEqP&tOUH z?5!X;>X?DSQP=k!jYn|aKTMy!_!nS#xYtUUsz%A&~C1jAn=%NoP8ZRTk&IVXeQm5fbZkHw4LEg_j3TIU!@$`V55O7fixn3M7J>l-&ptgTN2?^cPK^ zZkHo1kic9?1`@I%RT>~zs@Qjna|xv0y)iAwZuo0E-J1X5V3KQ5={5>`A4FgYYCYKZ zR+w9)aWr1gbSQY)@_V8y2!!7w0Ip3j;y$SF`v%Z-1O>k#z_FsIzW%pU_P%~J+54t# zy5DeIwl=YVe}Aw+C;=-EW0l@oF|oD?V7Y=IgHhKr+)7CWi0cu1G>CG4!I8Ym)>R`Y*waJ$d~jzbc#3dn zI`WJ3Gz)eI7aRk(P+>0#pD{0wkl>uE9i1xMAyEqEBkQ9QI>-D5=Ka((?}q7JeZmr4 z%>~->cAdbtO}%e-iZl!T<^NG9sRkPMfuPXd@QgR9L?F4Zb!418aAJVX#@}7 zdP)ggcDLJ!$?7SUGqefQf3Htb`DjSpxJf_`KPGS*mx7J&iWl)M&0#w%xmX@21Vd5M1l~EhghHKO#E!U~9F6seTx1 z_0#`eSFOav8`kQZAgPI>du8K_dVnol=ZqByGAtjrXh4X(tJ4`3oC^s0djSxG74{k3x+uT;PIg zDU`FDu)2b4vmpef;B@lBsrG#1Vo95Fv!o5KmPBrVlJ!o>c(X@-o6T|J|ttC=6-$vRvASEgR}&-2%edDcL{^ZbGpWeKFL-|s|Z zCx`yl(I9_PnS26P?a3bKc3l7T`$vQBX^kTZ_>5;eA>4P>(;puV$Q>7BYD}VuJHe;V zap)W_Floq>aj;ig z)(StN*Wp^N6mEH|Qyu#Yp$CWTH#Q(M{KLPsb)66(RaXf^aE9|*@PBvP1)OA70NuX{ zCwXnSgX(jWo44g=&2Loj*5@X*cW!pCQvN2IpdG7}f0|v}<9h!98~`N=HLw$DR`nWebCR_ffK*W+5N#AnUyGgGVE1^N|UT4)N;IjbXu+ z`)xfTCWNgwY|*#sX2xd4H+uGXZ#$g=*mC|9%-L?6zFRy0;a7C&Ccri#?F+ONr6sU7 z4r4;6L0~PsnJvMAAFQA&XP#0+I6?~aIqdL&)pQY;qhJ56xH_q^od3~7%K5)F z7?vQbA?LrHKxI1|+!fBX;p#a^T;mPr8>gNs88=`OR9hnmC=IlJD=+w7aQD0sr_L`6 zaDt0+YAhs-G#BoUP1(_|6c52o4U;jaortquS)*N;t}ihe^-2JvTHgkTzP%NK@+t7h zZr(J~fT0J*icmuj(FsVvzcYy^p|f7yPdQBu9MW{1VgAB2?tY#2{~0Wz0gZK@}i$_UB+NU>kJb{;(`X%=E+ewVNWl_N}~jG>UvPQPH<1Aq1w| z+gM;=DlH3XOnDn5JO*NCc-?|XpTdBe3--nXT z1Uke^3GhssNZFSKcblU`_>2;i{aIKgikn4|CdDWkhsjSstwJaI?Yr7ShI-m2r7Z{I z-`K&T)|Lg810#r2yYMn2Hr=>1vNMJ>J_N3i<4425t?$CP4Q>~XV>^^YL7xjyodU$Q z0s@>-S5lM#@$ETKCyI`>#tZlQc{q5;d&C)Fw`>R(v}=}wlV4Qjjz%O7XiS)f?7SdZcmik`T&lN=ej1xt_5v^e7~jmGs9A7C}B(S<9gZhHx`Ez zH2sDJ(Q0aUvJg=(h-HaX2WAN-2(Z7c6(k0eeRM+^Xy(A;%{rrf*U=bF*7U`@s(%P7 zzDEG;o*Ls&IX$Y;=EmyP`sDoR(I#hOXN9IC4mZ<;g0V8wtDi=GJxa=+a;LZ9J_=N2 zV^q;-Rt#P!B{#Oy*(LX-^>eGW)CE3~?3A{8ulN8;7s$lv=VhMu@u-T;vN$jsb`BV4 zR6VW1O0bXd3}*D_Oq3@ggd3bTf$-P*e0|mQ)qbu0fnU~h7TS4Ix3bg*HQWXqoMNBR*oew+tFw@qBr^) zR`Az43jg=fQ1~QZ0 z^xrPjKMZ4T#_*kYbX2rS{;Q3o&P3P+e*7a3mqq{JAL^==U>GC2_BIN!An`2^Vf$ql z^69E!(vBNaLP*V$s76h#2~~vw9Y_N)&`jVY3F@g}(;Q_}*4_+LbNgDu7&5%N=7%6u zF95~JQw$8F)&E7L44#4mnZSKDTdi*~eYW3fee9VhwB=)MOl-AoBSmpIiS+qiUGqZ= zT=y#w0%(FCbOqA<8l)LCDc1#$jNX>_K%rQw6SUdj>^e%tWkbcVRw~3&3)$wEZu9{z zGqT;ib?vVU2*R7N+HR@JECI1Sm@(XJRE7x0YW4M& zZN_rYMBUY`Wcajw29Tu0VG*(*#MyCV;Vso}<4Y^y0>82K63T}N_z8=#_84?z+@#nI zd$4-#06Ei~j)U5+Phi0`@_v)zZs=2{fsIYdOIt}#Aikr~ZZa4vxtr1X=5nMlBIZ)+ zXh;^0%Q6O>t7G?ULC!-~BKmJ4|KpXubTG-bEJbW%6U(Itjgbz|aS+{GDvqy)v7^XR zQ=EGk%jh5@Qk1s%2&cG8pP4cOtj#Lv5!Ho6i?9}%5+!KV>$sF$yNC`+0G)uAdD{{< zRchS2G7mrCG{#fvk~>=m<|dJg|F{M01gBWOhAI1D)0AyfB3m%GR3h8jt}BrrH;ues ziFgeqqJfQ-$cG5>6DY4e-ihi?|M};S24|fJw2#Ob1j>(Ugq_q|ecXaGHO8=fx6TOv z?a>Ilkp|V+?zQ*;AM|M`1Y)xEm~ZvzlkV9P-GiW)CZlT#??Oe~ zJ7>3-H}4r6$PZ|#69#(+{}Oo%W6vl3)uH3 ziU?v6l4mH5It0x|lEPwQZTCQ(Dgil(4Gu^aBBpmRdqGntfg^JZ-2M!Gf;Ne`!iQ0vstclazw$vkuO8FHz_zBsk zn&<}`i1Z!etTiJj<8mo+Jc4AtdiOH9Jgszl@80PNf>k@{n@Hd44WNWpb^kDKCs6B$ z>T*Ru_6&bUjoq#woe#rZ&Qr7S`cHQ8@H*B0;S2u%`7a-|3nL8sg`4xA{83RsOYA*AtDy`U!EpkBzb zL(HB1PFC7KVCj8YzPG>c2#s3Y+#>0ey^l$IZ z(ahq?22-?Ta=L{#ApA3mXDqK9Mc15esC2bP$I_`cN^m|z06^%PwZ|YDe__%QhLT); z(-yEbHre`qozhP|zn(1GuTOqQ$#>%-{9?|u16txAqyT|GtC{4}sGnJoZ!6>?w90E!4v=?KTm=nQ;;;(OScRgZgv zOa+{*4^2_N44yaP9V5%5Pi$;6fu`8~TG%7}Y)3b3OQUO~YGWyl12$ zOvZZ%1ZYpE$$St7YAr=+O>WIr9ny4N5JIML_nWORhjrH1fW~I)^AE#P#5_D)Kkp$a zb4Md3M6U-(k3NyB!`fSrX1|RlX4^{9t@(oDH$crTfZy^e*H?ggqd4&sGaJhkY)D>LxqZWE!?;`^XS;0cQHWoi_iG>j< ze(A*OlpS*Qy#NQmL8|=nK@J8xx&LGF4}wXB|EUCc)Z^(S!|uZO0KFc@UHEBM*O`_) zPyho6b)m4j4=JkcB7n@VZ9I{XgeV1KAXeiw`ux&XXun@EdCz5h)5&wT+Ja5qdK4{ksajKY49@ zf6)qGL+!3!B5qygdys!(ZmZG`w`^;7aj!R0bgFWZ^5#|C#x>W6T*du-(nM%Y!EC-T zi17~;V*C>Pvr8zni?_dKkl??@pAZ*s{{T{c==v!X{{!-y6Hg6$W7vbkj#S$sPvAg> zHJifmCluUFCBT(Ys8n(WMKTuV0~sZ_*;0h1x*j^N0R)XwL`@zkJcEwLiXR0Y!kal# zhhTYr%fx$Di*OcgzWt$Tqfh+m;rp_{!w?3I-_2J#|I#`GZCvU6tDrr549`H(y;57N z@(8dLUiKyYkG0U{F02XnC@39L?r}%jMU+monkrxz2wuQLq0wciO4w&~{4#euo-Dhe3`qy+{l9&cP3Ag%5R9a2hjDj2vVo>ZiLs5-jlOYc`w4K5{ zaJ}!u|7SHNrfGu-+N3nm#VN$Lkck5aLma`Kn#iMvKvyv!ikXqd@RWi?pW$_!9s(#K zw}-U{*8ZYNvWTowfdJYHr)%P^vD&e_UFVpT37`EI=6C*AokuicU<+fv&OGTrtgiK$ z#RTlvEd;<;Ox=80t;JI=VF4HCRMi;h@NATJ5pmuHN*5rtjG`nZlVrHj_)s;88ZalE za*B)LI-}l>p?FS}GtS^dG$l$s-KEUnj7nt(v;G$Lfj^aAFHGBFh)Bu}Zd)wo;#t#brcWPMW)``Pk$4Yt&V$871m?j#bJUH@Av z1=(Pf8c1-ys=lwg2WqTb4DAY8WFRz zE@;FIm|pBA{U>(`s7BJ=jn+x^caKJ@SNE$20_#IsTajWX*AwLaxP>MnhPQleHJ-us zmT{Gu!IY`2AE&90=UMPLnA zfhb2DpAc7tqwEo^E5b6XQj@L~dmDA7C^-Plhzd35q3=sYDUiqe^wOeovEdEl*q$>ux2%V8oLp%eD^2K+}%^Q4cnGQY7vXFrb- zG$VM-NL&5cMzyc`oRnM2c}*yVh0oeEzrSaZz}jeImA-LM?(;;Fxbco;7L zZ!UBi%Zi6Abbb=$1KMM#NjGNzPpi5o&NVAiGQX4-Fpb6Er9-s zT_?nM;!jr3juxVH$C%Ecbdt*~uqE@%GL+59l$Xuc)*8SXp6lVvvW8&@vr9Tn|W$eiU0fib( zhSJFithi~XX~5A9pF6R^{{%*o1>WXzoT1|z_{kl}7NPSSZl0XHW(%XumuMo<22@-y zeoNi_sZ=T|DnQv#iF;Qn9xr(YS0J9@l|i`Na}I;y(O$D9IItgxFSPjK42m*`at9Y- z>N`YlnnDQd>yV?}QMIZ`EC?>Mm-i zse}s?w0XdQ;LnunVIVQ1Vx>ZW>>-Jd){DT5C>~)&X4R}Zx}%V0cBxozSh-LJc+2@V z9%6Q>BCfx1y{%DGL0?qn#x{qft3pRKVYfTnh=EHF#;8IR1CP4{HoR2pVc$gajfyO_;OWu3IR%ueJt;K>VUIg-UXSIOYp=Q>}JW1Dwl*k6<(2&y@i# zmDVtf+TClm6xV@k36&0XHVJn+FpKDTF zUlKTACQ$EC2@SO%%HD4@$sGo&6W8mVKZi8}+(wPQIh)^7#m3fi0?}R0b^QYm?Y8+F z*7^gu6O>UEh7q_P3&lyO`Vsg74GiW*9SDZ7siVOk)M!M(IPUdfZsX@~sLixq*UAEw z-q52sgdh}Kf6qe9QyvLK+sDnbF3Fwer+0GC0QlEyHGYJ@^H zd_ozdZf19cI}!-CitRduaep18ZP7GAud1riZO7Rg0xF1_iX`j0c>93s=&1uL zC~OR-;&jV-6Q;sIYwNt>-Vo&wJ=ED#VPgd0QoIu2#aZVP4R;&Y=ihwe4LAM@PY>88 zXaGzOf1IgbsNbvXt2cA#n$BqVnymtEiZY8}^gvy}f+cV_Ec3vADc~!Wz1L~3%rG=Q z$R6TrQZK>rfJs7!R_c}!copd-^c0R|P-RkihWw0Mw&93YS@$&nl#w95gb_Imp=LUf z=}~N#KBHjc5cjFt0b4puun7`6ej;GMfj_ev+if!#L+wUY4n#MuwQf`cv5o}@vdeZ8 z429hVl8Sa*;KS%a*Q)xvqd;4NuHKqB;mQlmo=pU}Gwtm4w2CI0z0cV`(|i3h7SgD} z3dE5paI>J62>TESdtAZ^GpW%@QB#^bthu~8%`}gsw18qyUf&1;gaoHTV9*VZz#7Ur zpWcZokO(sU3ry+PRGCG9IHBNBwU4k~2geZ?D*VILFN^%K^hE=apv-Aoc)?Drfi2m(gco6afXQ-($Acg@4^p4Z%(&V%T2hpJ+)DQ|cLz;4*C0QTWY)Q1J%8 z?*KMAcS!L_f(%s-s=J3_0c8l#thq0Uzu~dYe89V?g~5v|4OR7?r{*?_#+`x^;<{a^ zCk88_usU{G=g57BCTD1{+ory6qRx8j<|CaOC=iWBn3>hf4?VP>!x-r1(w_fM@*NHasAw@I8v)AXu zhzs=@xKcNX$FL=6cBU;vy`QXjKUskUMmNoBDgXP)3RS3;^u+tg3Pr)bpRCy8IlZ5( zI3RbhZceeyem`09ezHQ;+_%L0$qF#V?fR-l+>XL{rPWCg5EzMrhH!Ggg1 z$%?g=sP~fOaNK^cq0(BtudMZ!?4=J|cQd&%)$&;c4oAF2YSC6BNE&kns2Jjo*b9aCBiS;!Wk3Vn+QjquM zd-qq*T*AJ(@eFFv?*EWT_kRWOgp!%F{;$CwdcXZ&SAXGN`~L|23Xy4R$Z7ih{-85( zvNhcYO}w6fHx$C-_Wyh6V{^a{cQ|nZ>ra<(Dggyk3kPyg_)i_M)$=?ggvCpmY7cq> zx>oA`>It~VmIXAQ>2gCT2!NH1`v@~Q?5oE(CVcPyig7@qRS+F{DA8f~^oVLZs;D>v z@_mjx{+G!ylz<929G!97k%Q9@Af<>XFFG!1nHzQ-eHr+S5iXfI(}vsa9B|~$1b(|* zm)^jo`wkjM1d3{ytsXZ4euC!00oZZ;{ne*GpTJ2=STch{Hv(?w9R5@C<1Slx&WK-F zL!kLD79aQkSC16SGiNs08;9Y4g-VT$*Lv{R&

UX-C5?^nC26t_tXnVzZoRq{>y= zec|l56N`)UNTJm%&*)^xNhgO~I(0E@^MwiR_AYb%b2-15^{7O0zuq#MmV{3TZ5|8ntJJUp7r0DuU!91P><^|F^QdO97Nt#z1OD%kCM zBCMyW zj=Z-R@(%<3IA1L+1CFVyRAM5dYH41qCiv2{*vT*REXSn>m5WR*B;>dl7s(8U<#Ho8 zL(eMnVtQD)$kx(qYYP7k61jx8a*-ZPTKz=DmmXwmHL=MJD(9nK?R?r>u(`08O+_4@ z6wf6F*>Q4^@s_-mSw3BzG1A=U;u`UGs+DdvV(nt}A`#6dglIBxmF$F4j(IFQ z%*(Rj;c!%IP6WD2FGf^w>Kw3ax=`sfgLKPPa_1Mx_>fD+GnHgK5clN80^eNtTcSPa zbT#dK(ks-8i*whAY335k*_bUwr07*HSuS|mY(C746SZc!a3Rhwu3G-os26voWzL_j zcxSi7QPBfZ#=c?6U zfK5bOo_Je~R#L%{G%wMKshGc-HiN!&rMu`R@~-YA*DBAb8OOR77i~via6XgWblz3; zXX`__#i{SlwXV42FkVZvsSC=bzWd9Bf!2h!)~{T{O#oJ|6o%nix$BpF=k``4GOq`}j&Y>K@Kt6J z><&AN zkz96N%wl{ZBQXiO*BymtfKw}4@3cK0x76zP#lbLGi?+h^S*Mf>x_!A^x^MTD@;-Xz zsZS%#aV)o}@~!jbx!CDDCt{R7j|65}Pb48W_)?f=ntUNx@jL4NR+9j~u0o zQf?YAEbKC$@mIxB)fX&HGo_%zdm)z=jpnS}%-9+vq!vuuwBTEuF-V1m7pFPg6Q$TjOmy{Tp|DkLVuP^!hs9bQ<5q6O9u z>)ZWtpc{w_?dm|Dax$CaFJ{SpuW6U5kQgrYVoWxdEci0z#nhE=GO?C#>L@e?M`<91 z;zU%%aKYenOQid!2}(y2crvAQRAv-g}6u$u4J#14^!>B?4R{}c6-$| z=|w%lC`p&Rj(A}@9|ouMzN5NmHKSCnmrR9AtUU89 zgnGAk;Z5W?$GqgW$6WJ-cbaIIi@CX!uExFYlB*~VFI>x3+!amEX{I$?I_%-rR16Qs z4pwTYXH92%86VjDY$ip=Ba2R{u;ARmt}p3j>xUqlV5QtB(8IED9xhfofl+jEo}C8)tUxeq&ox_tawyWeYSX=vJA6@#!Tfd| zOMBTBbB2n7uh@2s*hOkGj<_oohK|ZpIsk%@o3?%7Qa^JQuC(K^#f*-0#Pd!@@YF+> zsSM{8Iy7Mlo|MntoYCQ2J2op&ZjY~2ZdQ`>W}_Caw~CH|y;;u$vddCB7ccOWbg)S| zS{*)Q4^ADWa49HvCXyr4_c3$FxHT9q?VZ{n$kgp^KGhm?-K-ZTyfDxEe9d-UP~?JH zcDot7`)ba*N6tZ6;2ZMDeV&abmo9-~T!B*8ei4c1DXzNA4ZFeVELO=>1|gAm+554K zb5d-lCJArtN=P`oj$)`%n%lE%!8_*dLL`^-_8l2_=&Cf2QH~~^niLm6<+>|fDkR*w zW!#aQ#p;#Dyz2otJ$xrkvyvkm@MW5U*UnYCg4b7C27TQ@mvTtauCGy%XLKb}am|7M z`vJL<4SQ39-1IM9DKS{LXK88{;wo8t#5)Wv>wIS6>M#qtyBm|rxux88WpZ>W3+zC< zJ?ZZFBEGm76fYumnib`6nQL@MAzdh3S zr5!>r>5TC{hud8ZdJ?ms;Fl|IZ*EwdjB@l)Zj_4lR>HHCI<(YEd2*$R$KLAM&zHO- z({F$^D7PF%nvY)j(ydC9o6nOqhqoK@P*YcC%BAIk;2A`w?PWW~&7IzMc;KB#{p{51 zUC4`uH))^Oyxn1Y(cr7|PChV-&_c4oGzTd;mum$o4!-Ynctz(Ze=({JCxJRWbGyYh z$N--UmbkL3QWsLoCYSOpCVVA9IZE8b!^G=gqe?+$mJAMae6SxZ&Z*(FL8YW6FO0gK z{w(UxbVH7UEKY$C-NLyyQXK^B-T5-Xb5Vp8GhmpRPtLef(+HGD$xJM;ph_|Kg<}yc zCj&yL6K;$KO^!>Q_iIg&0UsyIg<`d7yX(D}Wx^Go$C=|3E>U)cI@7Q>3ZA-KrtFb? zh?$oL-f3q#X1r;B;P3?_0dD4|8`DM&uJ2IIOCld_Ah6$H5y>h!vNqB`w#=N`c~5G%R?Rm+Z~3r^q>$j&VE1FFf;cINhqo&U+mE z*Iy2%gJQ;!yrSra&snyY1lLt#n)HR@SHV$t=!^NJT)yK-`9|{$_<6|;(^$Ac7UgAo zRciA|OpH4-<7zQece|(ICiu@TuAI!(T7z7mJ$DC#jZDFxm8-?IlW~@#GZ(>W;=G%1JHxD3lqQ~1 zIuI`us1mriv&zyd2<~OD;qq1E`QfmgmgQt1F7-SuN11X8V$~(g=D}_?;7q4ofD`zd zjsfis&x^%{J(sxv>m!^y+RLRc-)dG$zJOOAj)HC%?aZ@mat!f6Cl<{VV$rme9%ctp zWeSm9w~+29{e{>f5llGK-aJ3FFBtcN%UAuLPRu1P{X_S8paC;n<-i7coijGy%~ZS5 z4po8}K=w{LnW0dkYcoFBigblWb1^Msn6BRyjb`eZR4L?4c}J|j;tqo%bF)Qp$p*`_ zK>b1(B`C^X_en)5%-P$?sH=WeVWJJ^6-Avh3E9P@{Zy@d-r*+;`!HWVw~ww0E^xP} z3rF`Nmhf_7MOg4c##e1nPR>1bj?P0uyxPb@TvBc13;rdS9Zy2(KrAY!OL4bzl&%zg z`CNsbQO%)iP;k?MQO&_MG8g>$j134C*DMjQEyoK8v(i`GM2sY6NuXWU(`;w#Lcq~+ zxJHA;g*#ZGoeWcvbFD?bHq5!&*}RhrR%wai0^r$4iXOW!JsLzfu;h83o|NdICqD3q z85*ooSXk0r_o^N40B<(@V8>Z|qYJTCaXj+$`?Nb>uklP-77`tMvdPhNY1GJN)03;P z(=nR{<+(l9avmG@4Ghgm~B93CW%6D0|_GF3O#TXE~)( zfh9K>cpygR1s4T6WID{vd%&07I9GCHz^>IgSJ8Pa(f5Zu$-*e@aL%UV#2_;++tZRK z1^#_~+AL*#LNYK;y2F81+Iz({#HjtsUX*g4AcUaBel~WMm>1)P&a5!a!YM=R&<~0bpk0@mwYrP1K`aUapL;9G=nCF-(QI7c=uWB`@(kpf930Z^G2{V4mDH@;fOvo0aHd<`?jRINg}o57%i^d! z2H@MCX}wZi_JXrWG+JcNfk*wt>MY`j$v)?z;hPHLaAI$i8IaY*Jl9OtBAjnI>oN4i z!F7tWK}RYj;>}R61G1LSNg_q(*hr+9&0Q3IzCx=ot_>>U!kuoFtLL+xFWpVJqA|Hr zj7L1xx_8trFLP9zchKG?GmAki9|74a)YHpim!eB$chi+w)QcBXT%3AcMX&>Ge_UbG zt*fcMF^&5cMfa?F&U3AKLL5tOPu$V=_JTCsX+eIXDDtVLJm%-VP6n>N?F_t*RM8uY zz+@KOWA>t1bi3p6?C>HR_YTDKdC3>{c9IDOO>M`eij+;kHL8@QROydnYVz0#GC10_{i{t*ehgv!T*i17Xaj{IK z;LA@XdEp)ke7owQYjI~K?F;74d#np$$XdQHLhb}~VAx$*&f~eksNEd!Ts{R!kzy87qEx*}H_w7)Nw=?KqMiwR0_mGYf(Cw>*5 zgq+3JGM+6=`k8cKo}@$bwxf}9FT8^qlW}Ld@knnu81QUFfQWXH9uG^+xHnqjn)8n2 z_S2)F$T5ZP6n@VN_6v~X%qUolWik+^z&y_@=S8j%>@&0@S4jo@g)ZMXw?nq(oH}>M z6L$H6u8LuvuFlJeZfzK}%k~h=d#X^M4?6D14CXYGpUU-Gxf)6in&oCBQ(8(O3+bs) zlw;{^T4>mF7c}Ss<# zattzDaxUe7A4<~;aEOIk2;%OmcxzN?hNmrLXKIzY+#aO7UPs5g9>5t8G3EJx% zw0oY5dVUae#KmrP3K_RVav*q%l>%Q4R?>ccS!vA%(|DC@l}hz~FqG>xA?+0!IR-As zB+u&!XGa`_*y5Chd1+(|nNsN@L$g61jz%uKlYV!r<1PuI<`D9!=~lD9aQGpNEcke& zuZ5Dm>`4cjzT~hsx0n0=iOc1y1x87yz|EYa(jd`eO1`+)Gny1ifMu>5N_$6cIdM^4 z(4AtzlMe>@z`VVn+ZTaFbv_C|%xNN7J?V+n=!1V-k$R#oZq0G#@t-@$tNYq++SG6st zy;8&9X~@YK>!dofIrLL?ML7t{GL4eQF>H(%(G=?jXze!;=|DR*u@;K~_aJ(mI6EH9iPw!4}WGj=fFqWp> zR6a%f$D+$W0w{%c&C!=8lj%h#;F}EjtAy;yiE=XsnMV&Ke&k}Y*s}ALNwX?@GD8Ot ztlLZhF4d*Wl_&)RjgX^dw}(P*`g|Nu#^c5Qg}8ukQ~46$?r_-co;u8Gm7cf*?W*)sqbUQMN zWrk4}v0=F~sa-iz&Tf5N%cty9T8b_zcE-LK44gi0KAv3&i7OX1_H;+hrrpkTmdhnf zZ_X9y_ljKB{qK>X7Xt&#E%jwkPZulqlD<|C)hOP_5^D;g1O+CTTx#z-N=+zRD z^GLfp<%i9b$K@)|L!m;-2@>9IxPkV~klgmezoT4b5+CG~V3}uPCh8V0Bsu8K*UA+s zNQpgK;D?DR(9Yvvx>HHY4BS+?z{t&N2eM7mMKT&f^1X=8+wvq1tTe0$^|5E}4Yrq5 zA=(Q;9;g9x8ICO-j#5FGb`}>GzCb2RG3{BO=lN18z*OskYgCh&qP@FZj9~m+fN3z@Znf2HdY1FRtlJbqRPX$} z;13o15wYE7DgntIr~#~9Ve9lfUD4<_9Iukwlb6=CrpO@>&3r{IFa^(_z zaI#&Kd3aFiP*!Owa3;@?~FP77M}p5*3lT zW+~%rM5meNyzGh$xJte4t~aLH^w`d3TXlO*q{Y}(&Ytk5WR|H<8Swq7praaI214A0 zuQqjr0-`+w`nxdc)Kd0RJqs~i@;sL5&Ot4;(y)FffyW2FU>tIm(_FTYs1_#Dv{K3l znV8)XoH&=$GOQog8}kX{iG)DiBiOEz@p^eaYZa1{>ZHrKXY)leF90y~|?(%p{K z@#m@+Gw+}dTftim5R9vA+!+iGs-Pz##V{=2M%mu%;(QXccj>+)fg=*gl}d$?-CjsU zA^Pvmqtmb?LNcM%7^l6}S%qa_)h(ZidyBDwpFS_kLtm*>Zq0zeDeu?|Gn@6fsEb0< zLw7p$b{GU_Jj;UJo`t<3iT(eXdXGg_xvpvSf@qLaQ$;{PK(h3RDmkaC{|9S7?{`jP zceX4g%sE1hs-i%VjN|(FX$|{N6}n0bpN6I`EGfQNHYndM3KM2-%(Fd|7k{|RkV`vF zv3_T)s#F@XNsiJ;+TP_R#iE`CvPNN=%b8dr#`~*NVCp`J+)IUZEF>ztTurEpB7ApS^PY{ z#sThqn&y#HeBwuhqH8e~EH|^T(G`h+M7SlyV0Cvgd)`KZl%}je12&Zu<9KkSY~JPT zK70S3k<~n5mYzKTkfC8G*rVQR{S(P<&TPOrsc)!(?)~@0=X3FFvX37XGMT$4Hz0Ok z^X&C~xb1!#*Zy~cxm$x$5j=j_!}fPjsLE62VN7sMVgGAoetD zr9lViIm7kGP(O`9fT7C&eIBhkMw%S8)gi7v&K5oO~%w^Y{kzIK_&Q8`>YqE6+SQVNYD6~ zN587ZdBNX0QKST3fgOr_G624W-WUDGL|gnd|HZv#2vIq@$_vN%juaBOzGQdv4g(P8 ztih*Phi9cEjk?#V`Rzx$#kmybr??D{zB1lRpiDziiqEiNT`zsVQCj^4@GK&Qg3sVa z?{>7Ho{OpBpdfdi-M;_+_6dI*P6CbT#`~^?Ax@BOYx+0~mX63eWUR}dUW*+|cj4@aP z(P2XJ5gf#kur>`z;VAmErbpWxJ~R48Sp;4V15CA6<7={}1&|uV;7WRr0aUO}nI-!h z`Ra}<8OZr;HDrfpS9^hR_;L@Uyw@aOqWi(4=1fs%zf^cXZZB`agQLqwPqfeMgSz7D zox;+ETBz1Ux@zw|)Lkre4_evl>G5w}RNXo&p0&Igre15T)B2)0W67)h;YrwgkFMgX zNn`YG^(=&4_#2!o21%0I7-3B%~JJi0etjL-*uhpjKx++M*}8XAsRVpG2n@BPOK zLA$aA+}~fNsCYl3^q6**z{oaeH0zPgyuxIHP z!--U{LcaO;nF*g+ou{Iv!*?*zk-2?YaqPU7?lC;5&btL~3Tbe@wU#jWyFb;-^5f0! zr3hEcwR^8;|NWft@ng=TgdUqPondnBIv}#z`Bb6 zt*>e~9?(}LXJM;lG{`z=eC8AEiP?NKF#ag_C`w~;1*cG zkdvSo( zQ3c;y>QQr_wGhx8o-^cs_rH!mi8~Y-nXw7~{2~3pi@Ll(TvtEb7}WJ>y`Ph$ADk?< zqr}ZzX`$j@JtJYi^ScR_WWxluEB~*KP!q_Zx|00XFn(%9=*QOEXy0OcFp2?>)K1&G z*mF-zmD$kUO=ge*B>nH+ej>;<{>A%{16LBxNc^@`a1M*)qQ6)**cMRs!ghRa)$!!} zakh(%gt+|bT)gINF<^OVxH9a0v@SW<3Kzzlu5%a8#e`J`i?gLay0{aZEr4Y$}Z~v_gxEo*KfavXkgH; zf1|RUenQao>SiB%G9PZ3n zEBn)zv)d+}dtWmB2;uH1#Nr?1GXKms4or#XPs1}EegCbV;G3+oYX9n6Jq8Ad{bb>+ zz0A8$baS+S_Y_#YROK6!KKD|H!kDABpD$RoV8IS`r4tkK4GGl>1gSp{Hv)vC4&9zy*7e~5~`V8 zq(tIv@$*K5jD6P0ifu(pQupzLq18ej=$o5DU873SCnQ8euvN3!%xXsmN=Q}sl>S?9 zaBqfSDu$oN?ON0cGzN!?5iH~ zA#feRiu5;cVE^h8wYmLfW7>-DqB9pAyV|W>KBy&gsi`@k839ZTf zqRNfj!m>1{-RMY|Im99fdlB%}PAIadSRaVstL?D1zeT-H)Mb8VcI%3R2b3UF_L;(- z?{+uf^ou|9OWl{o1DFNewSoC8?miwD=kt=TsZe}|W`3GL0iM00ca(!A`Rr3EW&L;o zr3N63JNYr>OE1}y+&6}6iQX~RH66?7;|#+25onb0TZhkCgSc(t?0o_}uZ6OJGe7{= zg%^?57Pp`3jgi&vT0hA5HI#fdyJX&K3=R{R_Wx!YGFW$nu=tt)* zR+lC+z4_Y5o1Ak-86Bj*`yc~n?dM*M?m#pqgkOc`P3nIaAcT6IT8_1_-9J~InY@Zs zDS){TR3~YUrx}XE0D8F5;bPkCh2oGBljz3(&`d4)bO|-?nb$Jk*xVWDQ0KTOCJ`uM z@1YKj1o)+=`e#9Y1BH=Bqnq7|!G=rY~?2lm-rB!^`@wh&R z6>x7RY>5e39Do1%Yc+!0uUSTAPe8D)uPOh;Y5;mGl>3(x3pLu@Wx#`Yd2E%>>_X&_ zb+$W*Q3z*!TZTKLR&HJKd&7q!3`|fY^sKx0uU@>B1=Q893f#3xayZ~sZVcCb1%o~E zzdpQC?dyA~yn&?{w880>n65Mft*Z}Uz+ZnMCHb%OG;JSiaYc~k89d)ys_B2R{?-(} zwqvif$6$V)Ghg%?40;|WtNHrt;VRo2L@Ijg6S&y$+J*OgGeGq06^PHX&QQxjk~i!V z!9z+EjEvat1f5)=eFi&+8I`WMIJe;A{MsXI&iXU!t}r;Q2jBW|%gS zLCx_;1tg;Vt#`lCsNT~n+7lb=nYAVTUVq3!x?ih&<&jORu>0Q<nl}TBX|o6Dx4& zFL@+90^b08ssd;ym|#p$9GlRECCMd^N_@|70QZVy!Cv{7y3@sRl*G83sXX00#fM_O zONcocjI@p$p0I$(N~fgRe8|7Jqq;i871c8J0v+ogDfgJ1i)P-{`18CGa2Z$ljlGOP z@L&mONygl56oLT?D_-)IORZI0_hR2v^NjRap_mk1*Id{DIX(OD8kmKi7T(^HqyV*j zif`(t<(GGM2g;xomzBMpYrY#EaXeVof?DEid#3nal-J&-w67TxX1JL&kPSY0 z^k2=VW`O6FeMfwN)5tvfBm2ONg6H(QQ~!I`-H%Rf6$WT{Jmd!-h8WsxWITma-+o}> zpEH2x=7K(qHTie4Es1pnqHbQ-FHZi$c3>7Z2A@uBd;@)Pv>yu|43^m~D56`?p&HbFPL^SYlubIJ*>DChpmGkpRvY}=#i zS@zU5OZNZZM^dAfVS?j zH56Jr$3TIp;CVlacMN;Tc0jXv!>cUCvRQ3@(iiPG`LEx85E3;9SjiJY<+COxIL`+s zkq3JJ-Aaur&%RNq-??aKbx&W>l5IHPBm_7`wHN|}Lw^g;>j4?mBHF~*^1R63=hUSW zo)t_J8vK9#1GWQ3XICJCp`oc2P#~fbJ{J%WEUf7^*0e;(tO3B zIzd>VuKn#N2Y?i}8MM6*_X$Pq$8G#dFgMQbgCCV>)JXB?R&0{x>yDL9W&00>sA;`%g@>m+*FbmW=nkh<5z zf4LXx4~T=$67h)nl^``w9C;tISDtxhzhM5mFE*fMTeg=w+koWkx3fuYjy=yFxDbsh zdKD*FaLh=4x+mpb_)aF><2lmQOLS1v^;q=YxBv>7{+`{cLr;5acrpP9#|&{jTAa$2 zgwCbEW90Lg`bc9SCC$A)I{_Q{G!m`0n8SnuW|g`h?=AtomSWDU!IzsOX__6Oo2wy8 zV#CY^P!~;P)m#|U7wc5$v?YuaFu8db18jfGfA>Z60e`KIYjUH)4{!@?Tq%gbd~QJX zXEoe}JXu1^nrbNYpIxpNVJ!=wl!cK%BOdMxW*I<2tzJGz>q;}!eI`5Fu^5quT=4ZWND%&(8n_d*tq%&Y#X@;h@@#jK+NV^zX& zWA47=U$z+`*cG1Odr;WjSCz5G73@-=>t z@@&Yk>~?$Fo&Sz=&f}^zj_&P7mtRWRf-9a;p^~k5P4qu#3je-OgX6k}M)WU_KIsxo zI~_O}C{)yu#wQ-=RPRtfL5(Pr7g0|U^Q)HVM!t*hA{^z!ew?#+y*z+c)JMtQ2)6`x zV2{RP-SRt4jzB<{)z9#S<1}^lpjTXB&w(yg0-hfSywwE$nVAW5=YDqT<@R(@Fun9l zQe-NT&JbNWXdBN(;4A@T%8GiXfxzdw0Y^2yAjBncBGL zJk-0cMNo~mEV&)P?_GfR%D>javvKO=YkB?+t~CsmAM4;V;{q`a0!#xi#w}w`GwPBzM=>uGk_3UBGNA(+^Re*wMIuM z=Exc<2a&(hk6&qf5$ZVnWa-|W=jdDyG1}Wz2Oiv-G)_!k+IOXL)3lqI>DIznEC(x! zdE8)KCXL$d_xxMO)&>N4Np0&-{k-}2Q3QqG#kh`9V>}|#GN=54fAVcYjz(1q#*9;x zGLn<45IgvuN5h&xjJrRt+8Z>ZMfW{yneeLBx%0aUQ)H3Bz*G|YYp^Fd{pH3h@^YRu6MkXRo4ynDywHYi`E)+h|(7(gwk5dz^J zkJ8&CL2n#0(Qv?Gae_eSok#ZPaF2^!wj9%uwh;HG`MEd)C|rtrVe9 z3}MvL*^PMj^C7Bdz3VpW3;M*~aiV5zCTEsMFGB5f zbXToG>1_S4E{5Ztsym23D%=>@gQ)kk+_Kf+<+8%h=3lkvbKa6F&6iyt zH1e#i3c?u7SgI!9bx7A&>(c1~nS*jlJ z72Y0z1MrZ)U*XiFN8hUul|_;D#5<%r&Gs?6GK@P7v*IJu$hjof6}_ez>eK4qdHeP3 zJ>B8gE6%C>cHK)(0c-fzQ`1gdZK7Wssih%zh1!PdZ`8@DjhzZfsBj4MuurRQ(5yxG zDIvJj+|6BY$L9lR=^_L`fhG)UC5%ZGs$;)IsV{MBwY;MP*rfd|LcKjHZj|zUenlt+ z_W6$z_|K!cq=fI=V_RO)HT9eLTg_hu#2pB{Pa=~r(JGUaJ!iBYQEMIpv1Mtm)}In)j8=jQ1Y|CsZ?y20%P1|4r8&bhX~Z{*2;bW-5||M2pY z$M)vMgB`BHo$ocY7R7BwKw*Q_+%>p^{Lg`zm0g&Fgx(pgb%5Ysd|6m~58$Sr>luOd ze0;F)a`|!>(b8Wo)uBEaRi%Ik`1V70aQSdDIloWZUyih25<7xH!YKNt2gCxIJ>-ShC;?=wN~2;rlb3MGzLvn^07`R2IA^11It&9ucH z@n5F6e3Mo7VY)h9xA&Y@j-7c|8k@df=1IM|@<`PNyKgxujgeiwyuVs&i+s$PUVJEBI9A3KVy7cMV62Ff@ek?^#XfFaP*&;}dY^UY z%0$mOai08WRrp*k*$gzZW~JKdHb1Hk)?s2;C}=GRnxL`{_&~mQZ2OV`DKv)qW4Eh2 zaGrNy*i^oJr@5wsqA2D)^f&VeNHcigrvBwr^$id}^#BUP$0!;GmZ^b4RPbdK5OJU~ z8D!}H#Sbi^MOE=S5YN{7& zfltZ#+!z&os+0@-p1lJP5vmiM+NCH5daaMT-~pT&5gU|`E`=FuAc*c7O{eTY>aeXh zvQUjUE`QB@z%GI~sy)x^d+?V#pTI9IXBGQbTlpBM5NiBz(>+CVi8I^iwLr3jO7izS z@5}tZ_*0IqiA8cB-`H7yui}nJ6H4~LRoDtH)P7Zm3ERPg`pQm2rbQ1`5pV2|;aAQT z1L#?I+tYz}u3DrUeKeVmoc`1CREM~rvZWERMR9a*{?74$IiC{wnielGXv{W10L>YM z&I!!xcr1~e4zPJxN?0A1@Z0w8u)$irL6oayk8O+MEesYDusYZtfJ=IRv-9AqF!pP> zQ8fRnZoK*7Yty||=-o?@Nm;#bK)rdWN3VcOs21k3SO)GE3Fx$H&Sj4ZZIB6V63hqV zjI##_=j-N9s~Zbz8MQp|`-l==e}6iT{}o5m|khavBUe0kl0;k6DilCx6> zTBjTICm?CKUoLri?Xaawq<4t?SYUj@qWpncU^D>GwY@-UN@$V3&}i+&>$~1Way8fn zBOI(GcZR_(^?{R;OAwcfvuE+w>`{f$<3(v#w#|ufx)%8DiY|Kl$-|wj2Pu+YjKhkC~{gTVVwNSsSp9Z123`&x&^S?N}9K+jIgKNv@3L0It3oQ zp&J-s@Y#&?%TQ)(nk~`H=z7}_vrbBUK>5qtySsmv3-`Vc4yAvs4gY=+2&?6UhB~l4 zLA!}F3k%efXONp8b}PzTKPuxf$_44R7=v6&Xp7bxgS?*pt3ZSlu8Kow(H{7KhAMT8SvZ(= zjpmd+XSCl4Xr=TlxN@ESdv!S&9)a0a2nuuRJm*LM%>)h>HG389oyjvtN67|!&`6Fd zzKQI-DJWqrPd#h@NNur~0Hb{V)oyY?Pvjl(7K5TgP~qq-qu5jlxW(6(K`+zWbxVE+ zGg0uY+c^oG$##f1P_Q#;YdkeR5kG1qES zXajh<=uh#yyU$wB#US1;<+0U5fJA9rXj2KGNz%C3gcu(xG$=J}rf->=QbHD&y$T$s z7?!!BBk4aaae1G&Pfcb8=1W6WK`GFW%MgQU!BTpFAY2V`;-%`SH6usv>~~oi4S|?b zy=Hh!aCz*PZ-ja#ULG9Lad)2RS^u5TRJsCR{&;g|>F*h*9x1(1S_t!+sUE~d1X>zC zdIY9`snYS)Wk(#(XRWE{+@*Wi^~`BqOdAKpy~T@b!R!1WdB)BMtu}mC|L*a8-s8nV z>n6KkJoiaK#ZC4bBCf;^&R)GsnY7~b3i*UE>FsNFZorpF z;)u_G*y#@a>jU~%g<(P269@^$I}e1W5yzq%emLj`a?%}!NIP}jXRDH7pLAvr_s*Db zyA8fj=od!CJR$*i`$=;tOnN*VCO1+goZeo4*C`X>jc*JHr`Bt(vwapY@8+3<6q$z+KEyk?&nl!N(1T6&g>F^^>b>AA znFq*q-s5-Sj+&}i!56C!0zPUy@a*igTN|6Xyb$Jtyf+hx4qYWz`fWwQ0vI6jhPY^F z4p7f)E>y83kGUr}WvC1RE;o{+1&fm+>vNb{{z7@;Ul6!e6P>)$m-vtfbX;8RrpEb@ zukUmki{|%5fXt_mBAARUuPXEbT1(+Ersp$vVlz)cCJvN)Kt2$XK%7?|e93;cpeS3& zskQ#joq`!jS%msc7A_hb54I#|78cnMJn1CASl*LWXfTLN*((Pi*mge08qg%e`~ph& zH9HOjVv;()Nb9q`ZS4PW*%s5#PcP73$7$CIa~KSC>K#u)`_vzV8IJ zE-oFI_gzijgtN;%I$h{=9gk^0(lcS)D*x|XaNgIUZV@h>pUlU5!c#pd-KJqLb;3PuG8ei!oFL$+4b)WU zu_==~1sG{4y^bUs+gowtRtYYRZxBA9Kl=xpoob-&O`-0!7YX8{W@ZYAO795$MumKi zgc?KwOt$JipA%ORxW2HStZrl#%6@lXloGCaf!?ZR+V=inGYuL<@>o&dGT1_T5Wqp+ z6x=9_C?+0VaJxZHF|Yj1kc3%K9`;Z7Ca@67I6d=N`6z_sO`7YMt3#tpN67KBVqu_l z=}v4H<|c&7q#IG1-FiUv_EwMx%5vnsW!kY){FS`{QA)D)@kW zqN!&!%L4@);21>(HJX2%T2XKa00ST%Fjcx))|rC8MiXxXqWbkN6)@EQxjeFSyC^rW zMTNoA6TA^c@`{1qhRxl&^>z7uy>+D($-lAU3QR@{`VtX1s)wYb-VBMmFwEZi8q;~x6{jH}dR_?&rukDPyL5vbF z3}4d(OyJE+w!j=;`B<`vQWN$sXG5^ZAof8FEW4}m<(|-bO-$uXkE*Z~d9u;*d130RXoQWC?+)|{2d_0GJ*osG2vchV_V7TNJdKzRoCZ?-U3}mwG^KgHc)!T7?9AAmi`?3m{NPPyOB)u!08&$SIg7 z?obcEp&kZoDySfb@4tCH4ma`hOBdrA`XiSdInC9!uLheawWr)?yRJmHlivP)A% zO@O7FJs>Yc%1uD_KsqbGfgAtKQm1-|Z&b29K_1h~@m=mn=fzkb<2f&)9+J0HA*0ar z1x5gzgeT17PF%)K94C`(wspv8fE*TZ2Us=%j`7}5x~zG$`A+8}^1d*)hRtX%7L%Yw zJSMNYf$e05DXD-v0lJN|kW>He$qN3jeWoc#D+_F^%msUoA!$2ohH%^yBt7PkNtgey ze+Ei)@~ia27ocH$J<0^@uN^fY{RA2VOqvsp-!QErVdF;je)gW8cE?%lMvVgE)iVna zhMR>?UMWZ!*oo+7^NfAg=xPgG#}24q2PBRc+?P)jgaay=bPO|!+T?5K0fnxsOC4x3DL1ys56>eaS1~_lj$uKwuo$_Ve>Gn91iYbBF}?HqH4x1elgPv?{Pz`# z_K%K2wUz=~`kbG`S2yaZ8E3Y~jg>KvieDt5#jH=x&mqnI>`JrG|5wr_CHWSoah)!Np7Wv=&ur758Fhansya<~KKjW;_ zp$~dbxxJB#fqDMG+3Twvf4PML;p_QK4Bu()5LYkMIV)jk6P1_cxzG#;P7lJw|JB`p z{DGv5p^5?g2(CW2{t6NSzylDo4TC?+ZFndBjSO)(4|l#$4-z}Cf=Ih z4Fd#3Gp4T>$PL7KuCE<5M&Bx7`SPKq#~eZZmxt7Q)DUR~V(9O`^#+`_)2rDBkHhUj zlNMDPvkDBD@u+_jRQ+7cl86hv4ZlF&52|?zYV!~v&)i1eH1O`)v~V+x-MvLg7OI6B z+azrDr=Dx4dW|FB%YYGG26B0*PO^q8{sx)t6J^;sb3k4WwWwR3wIn>Lq_1B&_d|AV zE@W|WBMv~W882|AY7*YinnOf;MoC@pS>%*kpL&KSLiiv;tuqV#Sm%aB1C2dqk+We45(i+AjoSLewa}O|U91slo9W~LK1%<@bT!XJL>!b#gWBZt7lw>$HpBg#l_6Cdl?OnNly+*f7v1KjA_t) zc|UvG>Xn5?YO~-dRf%V4d1P$O_`gVGPj%hBCGG=3Kajti@%yx;OWolp8lFfmJ z^fK>!!D5U~A<$O=0I~wuWhuaO1`gYOqshz+{jCk4>FF`XB<- ze_K)!ku~%aWp94IAbFm$0cLaE^{fG-_A=HZ-i<^RAKHMaXKe+`|n!g>q?#AW#nt1~bD@ls}&odrS0B>=D@wj|%+zP{0 z;Qws-3#=9n#?11O{)N?+lKQFfgPOtp1m0|77H*;gC^AV?f$`&j!%a3)DHR&eg|`w2 zCw6*jcJ{$8al$k>CH$hOUWta6zvJY47l4_4l^ml1eW0#(XU*^^r5WK&jF?f1vA_WG zLhpX=BF%PuHf~}-&k5!88CR5x^n%US&-6yiq;7zXw^&*I%A1 za0_B>4#4g-kziqpf3_dOdcio>>xu^*_D*lHuss04aZ@Mh0BhwHY(XEup|8-WCZSAy zYV7+xjfWUcLDm0PWK6zsZTlZ zh^Cb7h3^gm+YA*i7L+DWETH>;-w$~)Df`sAdEYQC7VOw}maAsj18^jt-oVVxwt6^2at`+Xo%OIbZT$zv}|T@cl=TIZO$`$#~V7L8(3KIE$A zfh@N23U~l$CHPX%eh6>Cy;uscc)vf98z+Mwo^Z1{9~g;3$NtzS+KUTmN+kjM+mmk; zq<{~Bs%mWmcLBjOK&}Z8`l~0=Q2YW@YLmYn3P-`LgZhUZspYdWSgUdk6B(KH8{`}z zJ3I3`AiCqh(mH@Aa>9MCi#NtLowc9q%I&HlkT|Uv3h+DMx#afAK{}{)4XE9d4)iS2 zcf)It>x}eyANDhT-pdYS!thRkR_7-o28zdKzgR^YJLd1gk&nBg;oEi1R1WypN|>+^ zqbqd=2^0}3!ax!RmZTgMzupX#&0|MaZeda+Yru|Bn*6Ipn*ZT1HW&tv(#Q(K@l9hW zqGUp%S@3f^?&b(akJEB6Yk zW(J{{z8g&j&!-VTmIldZo0)-w4Tj4@_{`@qA7y1b*Z3bM5I%PA^SkCjxE$P_T*?|n zQ~qm9U%98@*_y)KgrH#!PrRmnQ~Dfd zco>Jl!A=!>>Ep9L{PTDL?DRn)V0TL_^8FICA^!y_gYFj;k_OMY8An&sJ;=~d zx0gwuO0=~b21-4p3S~7gI!A?6^JXwwMDe2z=v<_uCj)uN6upx#cg}*mg?M`aEgsKb zmzrG>)YWEA5-z!K4ZPD7KOFtU znLv~3!@z@b>C}(`rj*Ei<>~SHu0amk{4QINFB@1Uqo}9(;7NMcF!l@dv%X`o*+n2S zLoyd9Tmritec^dbDfBk~}Va-dheY8+qrIv`yD9=-2e zc1DywBq(1KY*OiB0j@RZlDxI&X`m$36rOe{BvSV3!HZ6O`V67hJ7yxUnLdIH3MAG( z`TwUL1UL}Dcc(zZ^Ak(Fk5GP1O~4D z@k0)fV1-uY*V8?a`ptl_&yF$+Hu~rBRpX1=sPuIDh}@|5|7UXxjEp|iol)Fd=}O` zOj%*yJi!3?D&<%Pb|*AU=|1oZA}KCspC#KYeo;(;T+D>Xxc{E*#k`=;AK<|Kq$Jx} zW7@shjeNM8H?slV9^~2m4oU253>?0+6!C?buLn5P*MqQ3l<94Pw+`s}CDI?cg25}M za7#2j@Gl3B7sNzBJH`H^BJy&v=9J^@5I{`&={zIbB&-av-!{h*Zw@fHC7q3F+IlisWMUyW7@f=2bqP4{UFxQmmAnb zfNYi9{3yTzVzitS+V|6GmZVIPFQDBY7*vLiwrd^QPR!L~m5MkZ=2aPR7+{S?!zKShPSXw( zT#!=ofwWTf-nvOM25Cbd01aoCmY(Bk+xCe(>m}t;iwSWq5u}(*mJY4n+154Up0nSv zT5%6k3*1manQVB{pBJl!&76A6?-1i)Ub>R~x`MB|_85D3W7^z82mwMJL68;ssZez; z%fFs2dP9k`HTUMpWt~BAOZ764e0TA1=#Dq?Aso6Hb(b)>SE}tGVT1Y)E83|pX5j~G zz=rpnkOYVsvgZ|i&3H4YCz!A3OP^bP<;V3^uZ0%s5zyIBaRm^iK<_x~BB;yzU+>u# z7tj-K(?)?7v5w*a%ERSeJM+z`Pt6w8BoRm;(40fvfgCJaOUy`Iv6A*I;rHxQ!s+yh zd?z5Nk32BdpH>T|peLqT#$nsOrJ5f(8)uZ8qveQ`q3(u09^Oep`ed*;L$ovngNH;N{>CTZirX z-=2aF@-rN@GhhI7fj~R(Gmn1(S?dXIlOIb3+!pv><(p<@cc1!iFibm`7(o9F>P_%r zd+%X>VYTa$)kl0R%zH=NU6G1gf0Uw2X87HhiA~`Bp#q3;A5vKRz{G#_ptTcraN2aZ z=QEx}3j1DnwZ4AvklgtX)1-|5V$$@NszVbdNiyF5*3HAM8BNUGHA4jD%PTVm{f}^g ztJ3ni1HPsU6;o*pL0r2nlowJ%%4gjNJ~KAv9_Fm8FFjXaoaG-@Zo<4x6)s%-&bV%};P_sDKQe%B-U&cIvpa{C=m zeki3CIfGz%fV~77yx&g&W06IfR6c{(5|}J5Eifkg=cmAy_@d= zZ(M;_O6~B*!vDwKn}ElaUFU(lOI_Vs+>+W-Q|^9Ef{g-D1)u;f-E6UKkN~(f(I5$u zV3X`}0rgM|YeOwWfi2n|DR%6r#+#sw^x5OY&Lm@bM$SZboMqzJ);M0qpA*OSWa3H2 z$!IK3ynohsyv$_A^Ph9q_v%%>Dxk=2Ma55Q)O+tP=bn4+x#ymHmZ@vAufDX1`>6Eg z9OjG8v|CHtFI|20^>iBXACKHQIkT2HbM)xt&1-c2$NlI`rgFJE ziSviA){5shPac{-H}TT^R0cN;o26GXS7CZRpO~oC@=S-@#^c#b&9n zaclbgiQCOl&?b3y|zsE8=$3C+}xKZ7H5x6Eln3s-JZUh zchfT$SDLTpa)|A+dTsWl?U}>KM^vg$mtVsq;COI}WNfU{spi`9wc6zMX&_(~I-@?dnP+ad;JePL=7|##Nl(&s~7eb7H=9>qI_(>qI5< zQmK4pezmxEdiv_b#n~fS5W>Pb={YW4T%A8sJG_FdW>bf*aXh_Cr%HD=uFR}Wo!q<( z+BkEH&t>p?XPFWHr571C#EgQ!D*R{9Udo;#JtgGp_PE+~F2OwjHgL#|_pOah7z|W% zcd92y=6vzm=`*j-PA6Wvwr~hBIuVKo-YQdT+1I8k%hj_RGly2{XIIYEUw?HIzBZ>e zn~2hV4e>WGoI$+XCFIq~&(4>oFCM||@N4H`<1^7HOs(W!yH!|TPrbN0JF|Hi=i_q= z%vTGSa?np8V8L=@ZmA5LUviF1+^QU2e|4gCI{o@NWN4edeY$ZTar}^%vV53yI(9zF zO_=nYgONe%LIojyZ)Ymm)APu6gr$4_?EE$?m*9VcfY4biz>B%k>j=?)Vx8V?kbh0{ z^;3v*R6%eC_IMXSTCj=QrjqoCcG_nRPaOcq(@r>2hzKOe~ZprtZwIUP9Ei0@4soH1Cv= z(r_a^addlXaRa&F%2&6L8ufJud|MD23R7_3+dQ&bJaqCX4Eb))o!^>2SG$_Ny>e%2 zZliYc=(W=qQ-^Q4GqX!CUA%Z3R&6UU!awois|iXxan?Ptwt1zour+(=%;oa6izl}( zUdUxHr8eiUsK2u9ofFRFg>?*=tL=#%OdGut$yak zE7fa@N6Hs2K=E}UOFmw=ny)v?o7JV)ZWoZ9^7OU&^47^}W;?feE|)mJvU0VyGP8Pi zVkMWaBa-;S5&|*9Qvf+v7gB30M~bUy_9&2!6DV=axU4C(1Q<+qA7RfU&T+N)lJ$H5E&~`piNFXvY4hfqJ z(^oDY0WY|kSwe=#bgEISTuyDgzHxNx)uYJIvW-=n{=B|`4-CDSO2v+h}wk{P`Prh`noIY2( z1^Akvk>$+mr{->5nZw0Da;an~AgNnf-L4^a*&!HkAhG4ewbiBc>C4FUQm@ZlAseX0 z)LixQ`~>_+SCJKS?$sAprdB5oFCmsTc>0xBFU}T;rxnlT*P$cW1;1asTt>c}^$S}y z@URNvk=?$GytDXSZyZ{mE^eM$-a2{Z@~tZ?nS3_AiQK;zCoYw;mBs1Tr<)g{Te?7c zGuU{;_vJE9+t=n+FP%kBSU6=MBVZtFQhLorZRI07>M8w`s}&a$kt>1%-J(* zTR0wWPS3qwSwPy`*KsQWOM*F=mAV%yixPq`PJWnEaxA-yA#bmiysdDZ>2tOJqcs^N~4}!M_%pv&bfyvq54lCQMWf2`j62Y z_wX1b_T< zZ<7(GCi@=X=&3sjNBMVfm26yNPVm z?HlX$T)9NpC^xDahq)5UrkrBA>N**>1RvD`p$0fY!pAMlFt?yEjA@!IKJ?Z%f$BEIcD-;e+%Ct1vshlpVuWgLf_Z=Oc#sc)xc(B-xrdNi&sd>MOa8 zDyD$x6_|5V>sb%N9C%7PncQtqXbLmw6mqpX%@gLv&A8PXe()?*s^v^IRdm)|OpQkJ z{prkLEh@0~Lf=?>ItXj|?*h+J#4NaKG{4jKF8>+p)#|@T-?<{pmFi9k-YP&!dJ>Dh zvQ79aRU#YJa#4SAWJxL&bKHVkbW3&0OP!=Qk-&B);i{dcHmJF(Xb+C)l|s2*$gQas zE8Fyf3RMdANCex8Q_E$LtvwyRGj=TE;9u3PH>xEkF%?ZX6KHGFZC0Z3J7Z&!$N@+2 zvIZ?VwZOJ=^(-$ai=_p!s~GC9f$4FD4vfxXg=^bPL5-SQon%0fY@(7R!b}zLhxuug z-&Il|G4RNy9Kiu+DJfSs*bK4p4!uQqz`F2p8f`6i$F-XsbK*|IIpD+-z!cOij_8e; zN)1F`1J!dYgu1YQ2SjDJPAi0%SfRk+31ItZhWCw{Gq*I)_3cezQVi;VGgqrMiY~20 z+G(0tg2WmH^NXi*AgLOdD<(2kt){lQbD$}CJ5^|)mcd1HjK4MUsySJ8YuQxAjm8r( zLaHnc(x9QMJ^@pz&Vbn@kuIazQn{XG4qdjsH$?|YQ5xN-=H?r`FBBp9Oa{n&P6IF1@)mENC14)t0QnXg z5OSz>-JBjbXdg7aj@T6?{68ASGq%ZEG@6K6Gd+f7CNPCxsV1O1?o7-1r>^f9=+FQd z5GF6GKvs1HMN#plDX#gDd}TFyz`0yW11QyXt%2=`i3}DFQi^icLE2yzjB+{M%v1wV zsK>0j*OUDk%fN~*B=MYb1vS$QWwGMB&Cpg-_U)aWctTFk0q2Z03qI28a|+sL;Ew6t z#=Zc_i~Xi4s%i-=NdB+BE3RM15-X5w++dlk0cI!!Eh0i}2KJtCjQMpY$#s%cAli&6 zE}fYM$t0$|yA57WIL&b;XdjDL^}vVZ22`bK05=9H%LV<~{DSNg9XYaN{74mxDfBku z?JUmk$7M0qYAscC!POzhY&1$j@WdiSj0nh?G2Xb=!LMs#(RpFS%Bs~}?C3mhY9p!I z5Tjofo0Fuc1>&(p&cq!AUR80iInw*}2G~NWZtob&TpwU#NIv8)YZkny_zI4Wx!b8a zWHe`MvN}myfW($}vbfPS?WjZ%XxcAth~3aT;#guVx*Ve^p;dgq>7iHeKxMCDFl{~B zql-Cl1aPksci=o3hqQ}#*2ObiI8{;olYbd z5eGzDa0)#uI+E+T#0{nBL`PaTiNh?DqhE-^k|7RHfI+Ac4>`yvF{e;m(=rtm5gV{7 zNr$)+wiqM+ql`Sh%Eme#AQa)yY?@k<5cKhZx6Xi$>sf5xRTn#U4OkYN*#TZorY(=K zprs;Bs2vIlj;uCxNe?6v5)^V!is~`r*cloXEdLx&wSR+fYigKhL$y-VB=HFnQ_GC>yuy-F*RgM zhFOMC(Xp`t8nbY6y?`xFgX)2l#SO(LSf=qoPAp{kI@PD;ry!RSro=gaCKNC#lq}A2 z5~xs0Hfe!`N)^Y@=%~aw^YmlR!OZBvPMq1A(0U3dv<>i3wY`-qbz}f8uy{tBzgWa{ z4$BdHPP?!zDB&pOE%mOhL2Ajtr zPioAnfN4eOyrB5(Q+wGv9R}y^eObMDQ7eyRehk+fSMK%@$gu|-Fd0A=cqFz3$n6t> zjTT2+fpLY&fWyZ`!onq$lgpR?#EF$VYpDQFGmNG;vsw<^g9ON>zx6v@kFQI09kv)ym=X5PebTCf3TkBv0@Xh(9sS zKk3{HNDC10DyelhIvsPsnU+j9au1-!)IMNNdfWujx^L&?HktUM*AvsR#Pm(UmesQ0 z{->t}2sCv#Wlc^`Cj=GHHqq0T?(NmTvx~;ChoU)K;u7K(kr2M=Sp{WKF*C^$1yCeS zZsanJsvE^0QlA`;@{mYlM2%2^dahn@qod1i6?~wWB0UPt1`E@EiHJr<+!yCLlA6}b zMc@;Ye8jz2POG5GAfWq9g%vA=+6sz;P>m(v11bLRI>oZWhouKK59A`jg6*D zrBSQUb|D2-W^@$t<(SoLEnD7-j!7NzP}c|1(H2=j)IpaTLtP)Oj*x!`iQrP4|RP)(>m1k36W3=r$b$zt(awbY^dw2Cx^Pep{}ns)b$Ar zkQg!4_2K+J)b+JpT@7`8EMpIKeZneesOzKqo}sR9sO!_#g|GnJmp=yczHVli*}K_q z%KtD70`s56f5?9M)A);uN3~62b|O1=uC0;$=TI)?v*^r!k}8j#-T#By$o7zIr?Hm* zJU)8O6Z8K-zsmn({Jgmn&Hq#JDw_Xk{AfJ}Yg;!}+{u4IKBaMv+{yneJw5HcNSmEG zG&ytVh{td}v^89li`G`Z^T7umn7WLc>DttJSVJOpdl5Npp>xGGO*%C@1!Kjj3SXYh zPQEx*!!1%AdiPtYj9Z(6BC)bPg{&p+R5Dd#_4#CF``C-K$DAuUHY1*=J7L%`!LsdY zs#<~?`IvJOBdbe=GP)pZH=!-4rZNb23iUILH_}ec-E6>g4BGJMRyGF%BV4M9o9#G^ z$LkF;K!eVju5N4k4gGRtqrzI&N#{1$2n}{gZiy|rP=u}KYGc%9T7u}NC!I4J&UU%s zAm#)v^Pt~Olg(NVSMdC{f$KnV-M{UOrpW;QczG=kTd`4RD+|lpbu}>JM-m8}@Z`x? z+%BYGCPy`6(4$wjk1xXL8o$d`Sce?v|BiK=$VV}6W%wUF3Y)N^yVLrbbME$9IaN)c zft_!)+Ni)I;W578a(A+iwH`-q?{#+#)3pNVcBARv+70{hJRx@BjlnQ=EcP;nYUC07TWM^4n9HLo>x{ z=5_)u+_Q%=rBb%Jb?c>4bsd*9)0xWD3eqxf-*T%Zw~#zEGkf&N)XYmq;l??WIP@ZD zlmUYf!Hpj&exz7VHwx}6{CKEHUnBdjCtjYNVepaKlq=9M=m#!<_!<9sdG=88xOq5I zOVn1wi#V7TQ%RHWxM9AGH9m|B^KA>;mDE#_?MLVd z|7Qx6zl+MS!}>O%e;+9lE>#_SK*y~2?LUi=oz>UPdi$mxB^Bl4F|}1qRg$=*F0^j~ zrBro0xq&Wu6yq>Wz{Wp5ert<NwT89+N84|JLtdK!wRS4e*1d1 z=9RZkbQrj%9kFXNCTEK97*jZdXUO0vqaPGIMgrz}B#Yx@3AXtPGA{*RIlH_hKk^{t zil@RQcPm*f3xbm06m3%*HrY^dSw#NyZj}j=c0EfCws69`&#Gz`9DNOjnRy!P0j!D& ztYXbGTJFjc<*lpP5bwF<31o9<7%KJ20k< z)uBC$+_~Z;zD>L{GwH<6G%LB|R?B8vGi<0ABHH=X0}nu>hkvV2KBAAMeT&IVFxB>D zt_X?OxFMbx+3j{)?}T%SZ*n&#d>X<`qM`L$7LGM0Xho?m)p}91tFfUP7NUS?)@rOD z3bA;BgjlYSwKC6|=*r&E2txUh$7g1%gK~wp8(Gw>UxP{ua+}nw*YamKhM|C`<$ z@8VWy^$u79+5;q*9wX*jYuuW7Yn>yzn82v)K=*DzZ1=6_xI|K;pq=)jnr;ly=o!=7 zao_+0YRc~WAs-)uv4-wr4&6X!VT}eU0Wd_;t(Ic`vXWI_{-lHRckf}_?{aW9CoyIV z0g`-TmY^Vfc>Xc4GsV4}myOixX&DdHV-0se@))cMfgzC}f$JbfOGgd+y_teLIa}b> zREzT7W3j2xiQD(Eq=W*PG{7Fg+a9RIppU$QS2j(KKG9m3;Wn&YpUdfjdp`0ej0CPA zmr#570iC4C4}oSzLevX-;aO(Yu#wu=!u5*T7Mz{bEaQAM11uj`KV7CCJe&uON656)n#0^+ymxzR-ZL{z&*WE z^C6pHBR?P&Js>m9Yt=(=hb@9rcMyVrlw*RYWWwd?OYhuB`%t5p+kR zhc@g^{to8Cn-HU93+%%)SwE?q`Zq+zMS>j^&Afz2E$#^w8Br{UQ{wc1eC zu$hwVY~faL0KBFNvWi(ng!Yq*CMbo4=eH>wY=VHy(xtuPzo1>v-@rOtmtCybzI(wHR zhzt>vT2oq7Dt5f?_Ue=L?&Z^pdvCdu+=rfY>kM4t)D^cFA$SvN=)fS!T(JVxUp=F=xlMqRG4Ye-F=q{QpM( z`6B&CdlUQ?p1vdhCH!|_(dR8Mhb8Uh;Ei~l|1vsk^OBH3=ap+jP>6U60iXX1f938W z=P91K2)?acHoAp>e`cYXD#CZ*n6q52Gz#pR0Hc`lRz0g?j(01f-Ar2DO2LujdjM58 z4-^%cedZUm&&YRj6)Q0Nx6e6+at00#xpf3fPrHb#zJUnsKCof8BO(iP=&_Vt0OICt zw+dGcI5WVE5h1S-JAAW&L^x~JT%$M{A&a2)1}StatcSQucw($=GiIXMr(556uOZqo z2)_4yVVeG?CLR&F9bN<^)LzUt_KGRpp82=%uf z-#+fFWhd_UI3{#QOSg+~K#hp%49 zet!3moos{byEJ|;M{caSnOx~jEH6g!UFQZP`AtBI-}O}H&BXNG$m5yOXnhQkyKbZk zm23)uQR`#TImADuA7halxZ^cV=$W`jt$Q)^uR<|{;G#HRBd5t@xa~v;shuS?dEW^V zTp;v}g9m#i&!jZ?V>n46OTh?@bVP+nw3rXlYrwq>mTYjnLYP8lq&^aJMkJnIai&Mu zI#IA{L@h+TUJC9vGUxC&8FI0R7}!MwjiQ+RgqU1nY6S0J|em?&-dihcuR z{kEiZl{_N*BburnAzZ2DC?33X_D8y7=@v)hwxw8*2dZKo2uw!QWHy z?t^;}tDiF9faBIp%gjC=dcWGzd&#HKZCDS*9Mg7-p1K1SG4!UOvtN0!|AB#l`GG*% zwjl3Np!;AR<+Y*4A)mZMhz@KBhZO_~ZZ_ULXhFIks;gfw1MO`V_Ogg8_TP}_j*f@p5 z0P^36lsH1REQ)jh4RX5{j@|Ag!mPu0qnd+JIyPch`mEs$Qs0iy4xUAMK<2KCOa{F7 zM|nu1B|eEjaDZkXaYx}HEM5NOfNAd)0ZNzW7iwd%h!_&Nimz3LV0+7ToE1nH3_q(L5!Sr8uFOX*M+gdhE|NiwEfSK?;s=qQT3_ELtK*(o@bs zGnl{+)=A<}N{^E>BL=k}?9`B9ovqGgu#jK!q0Q10DisxAQQY2s1trfxA2~;2slmVPRLj>5j|C_2el)tv6m^vjYRRjgb9V z3@2o3k^%|&TdyJ^5lMI%5O2z<73i1_$8jC8L8iU~8|8zzKHje(0Xf37ZIfObsmyVG zgo`7b$92VsKPAX|3SR1@b7<2ynB{Qoo`GY{_&w|dMD#7b=?^+R29%lT2VI)rT76Xu zfG(VZw#+gQq@dGtxK>f=!M*7xYf$~vHuw-gS`bYso=X$F7I7(fVUgrNyNedB>D^Uz zpyt#5iQDBy_Jh85!a3<3gJJ~)bJE8RZp@5ZF9U!MpHHhZYd(!A^;{&IOyGh^+-V{I zR^7R=o<=(ArD&ZJJSzSdT26z^g5N&|R=SI<-36GB8XQ?*n;m(JHFP5a$PuV3>F7yR zr(#{GM883H%RSx9ROd`l8}|n>78dSTk6qE6ufq93T`Mjd=$JBpdtlgY z+piVwmDCfyI<1KdB=cuhK+-1nl}@e&^|hj*ZbdX*<^PgKy)Xa&_BD92DfyToEek@! zKaN1e7q$!=uz!DZ4uaF&H%WS$aD+)ia(e6rM1W{qUaHPH^|8B}t?ahC9vRQ+6Ho7r z+x(TlK^kt;q-ij&5Rjj6AHi%vUbA$)UeT8_h%hB?7T8drh76XhYRhflN<@fMBrla4 zRU|{_6njEa!XEk70iY3`|2iNUB(#tIJeYl05qWp+L?rarg0P$aE*SVJ8wX4xi~#aG z?XNy#y;|K5LkHZvAVRUDV);$tN~r>K5hT5>L^$1$`a*X!RFcAV#oF>GM*`d7{H(|j z&&^dudvJZD{B^iUQY}`t=>-)+iaL>JQRhjQ=^ll@rIVP7Ca@4xQpG!zeGjg^DwQ>Y z3zHm9gv4HcoQHlACFUt#r%9+zPh^hgrfN9|>+4xcaBr%?3Z@Eae1md(qUb1+)8}qs zKNOj-(St}w&#gx#fWq(yM@7y)!$&gyCGtW}iq~=!TsG#+QPxN?+yI|N;Xf{NR~#_; zJf%gBG{1r6q9+3|cd0@|LIR;Y&#ITY2`mGJ@ic6Y&{LUGZ*t6Lh7_X^;g={mqk|@g#&YROTN_A8!$kTCd&7(I9!A*pZHhb~d%GK# zco~;METfcnZ|b_QfD{aojb;-9qi@)-Jx@5z@u2-z#t9H9n+eE(V}rnsl`pv7Hw1Iz zndzx0!y!;JJ*JaJv!F0OH%>;(JZip;Nz%nq5X9Z1lq*q!R=YQ4GTH7xdjS0<<$WMo zz=#(zGd+vhIJ&!Zq_?+4#d-89GF9zjdrw1F&q5@Fr4X?;WLuYuS7z-XOX51FNWpKU zKQU^`C4HTO9Nrv{YVl~oNsM6=!ynr8bCPvZGm?9;93gsIzCL{uZBPnsgyv3{qJ%|> z8+?j6Gma2j=)hs+Elkj@OX}rBuOL60VUP3>gj^ zsECH8v>l+|l4>kT<3yMqqM>PS-`04CAZ|$;Mf>Mr8ZuxFHt<42=wTnc^lc2oG?UH( z5M|(hRmVwz=T)Pf*(0GD*zPnDLdXylMiqTaS1sI$gtc_3oLs*AC+<+*`f<^P?o^A( z2wqUCM@K=upmdt>W6r_M=)v}>7qG}JU+$YoLzdfcl1a)+lT13tk2|ADgnG`ElF3oQ z)`%U|TsIv(lsJ4?Rz85!uDhOt5J;pC9N`p%b)ZO_oYwdYNgM37glFDX7=cS9DkY}* z_X_>wU-T04BAl5xm~(VGwi0uel!SsFFX7a^i?1bND9rL~NDPpD+~D z0uI73AaUcfk{9Et`$kxg(GKR@<-|K`JVuiy(UnQ2OQmEggEl=P1?%c*w$0{_DWpP5 z41kudjXNnT{nQ#?_?hdxb;#syeT$5MXCR7p03@RclFiWqL`ex79GP^t z5WvJvBWP>?3YtS5r>8FYnlV=+D%^iib}L5#)yw2YF4L&?pY_alB|vjSXKoz*Uz=Y5 z*>ms-HhiYBEBpbSj0V6oDn|qmNE3vM67PVSGzdWRRbb}&bnMtoQ@P+GC_p-Tebn?Z z8XGN@My)bUb|8z6)~!yr;+A=bcV61crJIUXN+A?WU z781U7s4W|6%hZY*YRhPg#)Yx;+_V)6%vAU?1$@}(`Q*K$QuW0XH(6oGibHjmN-9ZG z6-gChS{@+8+25O2xQEj}9j7UQjI)7=)!GVcs4c72lS*g7+V7#ZjA?nOE#o|Y&QM!6 z)RqZN-cVZx#_-l@%d~+TTM|x%SQ1jKqx=uUC@ue4{0AYc@}I_En8n4kS)B5j_8P|J zKZkN{(eOS=m0@K03GLc6Cfo5FPxl)TPZ?_l1=wqSNSY+ZjlW-9hQCWu^gW6h)Oto1 zI%daF(xpaF>V=y-6tpXX5m*uIR4Bg2nz4UvU4<$&E-fhIWI7!uGb_HvinB%{UaR05 zU?b*Ailoc)MfZy++zvW2A{&GISwt%D4+e#ZY}%H^!cO z8{sZQ^=w%So%n|P)EyP(D*L1iQ1*n^m@%4tuX@oMxm+W`2p2Y1JP37(j1~+AiX4ff)uP<2!?^{7@v+DGbG}8 z6t>}}%y%@THsL@QFh8_IUBGyCc@WKh@moG)8aAUZiP0D6PhUo*h3W8u`xYy%(WP3ll;7jQXTxVosM7*ihk*#Fp#=Kjor<~@9 z2#Ye(9682QPp&ZMxKnGWd+64fy|>N`Y%CNw>y8iC#=Rl`%g8IE?Cv)V0L)oG?yKfy zk3mt&{<@hW)hBy3JYk{Jbkg#??h0q?ooW))qBAcvX)(~B8W_-ziRrfBRd2e2n%{@$ zJ_@BxQ=6gt;ekQ-;4#y53l9M>8D_3_2%9OAowqe##9HK%GOhws5!j01II568hWLjR zRHsSyT4UA+XJZsEw2wgF^}KWV(}2alo7&`tK!#mI8h+Z4p*1YSDK^f)W*9d6Yfa){#sQd#Ee+fFIjAw~!Y89>gTRp;Lc0-{{t(HPx?lYD;r*Hm>Gb z3V@yHwSCl-q&@rds?u6rp+H1^V{~ z2DDoHy8V`V(-ounM<`lHhj@v9IWXwnp-9evr(XrY7tR^1xwDp#;SArd;yI+?kX&-p zccI{nh)P5asjXE2|C;Bgf*Ljl1Irp?VyeO0U^oc^t*E&4ZG z$QNEE_tJVY2VHJX`rpc368vAr>QFCG<_7!Pt=xTcDOryv?&=~dI;1X?u`pQSFnY8% zk^D|E=o+vr7zA3ozhZf0Bo$20y8iE?Wc z`c?OVJkxoS)L^<5@eU|`4+oTAr^f9`QECfoS{__cK;xGew%Y@PEupMddnQ=}N^2LD zJ%etGVe>G^Sq++hdx!lU0~_`;d|nJ(bJqB}mFhl_C+&r+M&y0z9oqK~Y-o=%o3KV9 zUvvlfeF1Dm!5#R`3;y3782D}cUh#(B`Mt$h0{Q)i=|&HH^hUwPfF^8daz>FTD8r6<-_S-0~+3w^RTyw|qB;O*P=_ep>!7 z0icKPomRINE{*J%Z<8HqGl3+S)4Uk6A)cc-aw;9uZ*3uw3)GWu=CGSu(xV8)-zFX2 z&n`7KS^oPS%-UYgvR@e0GLD5zBZ%x6 zCbnK*X)~lS+gBYu45o{Hz*2X*faC@(Wk9NpFE)U#efhvqd{9RSgbx??s2N4o5NA{jh*E;+;dm2-s2n3=id3}2869I|h$Wcp z11%yGOFNdll=@OArFPdAeu>CcL|(L(l;N;b@(3ljes&ZBv!zghM4aMy9dycmgeqDb zS3G0op7C)=i`$ybU$PkU!aM4VzBaDWx zxOAn6>$zCOZNf=jn_fYo4o9*gi<08{$i5d9Zi_0^zqxse7(lGKv)^I@@A^=i{|4}1 zearb!LdTt?pL$kW{9#}I+kCY<(^!5P?Y7<_kwJIN`LCyIkg>CWVyI35!&DdR2VoXy z{nZOV0mPxURACA-P3KRyUf#d+3D`ooA>iG_?pb-q0}rU6D}pvDWQ($p z6R}EUTuEtiPnjw>OCLo;Vv_a}FXH4-1j<60fEHlWXtF zR1|){be30!;>&K8&NrlYGObd_Lf1_jAS`UyWIB^{IUNgo2;Xt5g=mZLN zMb_6Ob>+y%8*vmeE~3w%v~Yu^uc}IpqAlnLVRfCZk4HsB4Euu$D8f)&hrZz^1}&xbhe@|CwV{b7;M(4+7oXP_l%3S0BACdok^7F~@ht}>Ki7fF{vEzcM%QgAlJ zS3p#(nixPYuEKJq$f;^uK_0~DR&^x{ixLhpXw?3_JTGwVHGty*b%GpyS19da|K7gC z{dI6I{=@xs=-^Kr*=v++7H=DO0N?a*099Et08@9@4*tXa)!s&-q#y3Dslqn0f~N|@ z{gp(zd$hmm(>E*H|2rr#x+&T_`UiYYYd_RQyI23w)j!~&pVi8?ACc|&f#}yiK%M3T z{R2i=NRLZ#I?m!tyk3s8IF0yIZX9|l%k*B9*W$MjLp|cRDDShPH@4`#SkcEW$v`b6 zAd_Hh2Wed{=W58mNQvz^l(JGA_E$;Ib^bR9&HM8IbI5cntNN#YPfyUVa}~>~es%@$ z`r+eq1%|?)`zo)V;NWzXyOHuCua0pvjO%Zg1J$+&ezhon>^% z-nIX!2vK3+C_bd`<|=~r+b-w2l+bwRS$=x=5FTiQP~XnA&b3|5sY@6MvAV08C40|! zW|XYHaYQ9+aB=glRBEw$n>FncQte z*wRW+(lv}U+29T_%MxRjRbAJdT!#U92b;-9s5iw7#e;X$ulVYQuke|d^f*<=yuvx} zap0J2Rz=oc!G%ERs=WYK^@N2NH6G79@31ZmY*=l#Kz<;@8IpyuK*~5oOkSJXQcy^E z5UI_fhIsE~1dAkf)<&bSf$UB2QmeXpi+F!fZ42eW-+}F%4@cI0T`8})Lv2CCW8>T%qxt#IyeDLQc!B;>bXVJ~fR zb|dqE(A~=Gn3}YbrNrLqLXj1JR+eqLpn>Nc@@o^3N~N6egsS6(RO(^=5qu9XN|aZl zhX8z&5%{g7(jpNV?3L=)b!iC^6Wv;!BT+yB?835+V+Gf@E1Y>;s8Lz|vfLPXv{a{t zq~K67maA#lOG9Z4*hD};9f{JbkgORy__ceFMr&E$kKVAdzR$PNgDyM+$}A0bzO8W& zy5+vdsLpS|#3$ZPWT@H3+Y77!{DyPqi+{B%(`vmevPBaQ(bALLF!iyMq$xXhuo5Qq z#`(U0Ml3=L{EX536aR|n<2?1xe09UO&8r3zs$`g^BQg=Bpb{RMr1U4_kH2M0F%cI`3hKdQw`uZ2`omAW_19IPqD- zu!!$1JLtdnnJ`HWD>c{%_hbJN6Vlg}HJOoKN_R7ZiDs3=n9O~?U$VkkCY0NwB$=^V~I53O(U<4uM1&LyN<|MGuL>wwPl@NA0 zW<_P_v9yMp*-#Nc@8vN2LuWOGSVJ(=I6=n_bJ z0Yte9%(wWJl(&)cN(E&x;&(Fn5++O7hV3~6qSfj!7b5SYBIV667b4P9>m)>E49C%2 z=?KW|tz&d|i=cG67cx^BW<`8EWJR=R2PUD)AoMFPKO!+n)*BC#z73PUsmz{=nuUn% z4Xwzgw8JpgbY>hTedGLSyxCJKv>X!TQKUao@~$_kReB80Y`1K(sfjcUoUn}3sqs-9 zn8hidBHO4WX*ho;aEV$?ZP#A*c4!jqwfDuuDmG0hF9|MB@KC<|vg3w+btHZB=2P>~ zu@!JtODKLzsAH58osMn6nPz1=S1DJ^RCCeUaaN%qsjSXEN{LUYaHnK-=toT5f=tB6 z6X;EqYX!cN1ZOgHB4Rhy#}OHNEl=*Xrj-PQU0{eZp#I6-hAA3?dI*wg68+H^ZD2OAX`=kdwr~bS!N4SA8>9CY#5-r%?iH075;&g8D6F+ zq@RGrN=%4+4NC+TljiOd6V4zpA(9ggGAW_V&MP>a${pKZQbJxBV$rA>@+T$KV;9b2 zv_6m>Fjs68d&>~0lM{S6wF|)!{JaD#9Qc47eogJh{Qu( zkWVggg zq(&wy1v=2BoI(y~JMdA%QDx>UmgI3rb5oddo6D+GfELtERlAr>bsWHrQC>+yZE{<# zgb)@Gaa59crJo(@f`+;vmA;&8yQ^*mHmXo)kgd1tXl;i)A$rcx;%FcbkyLsb4p=g+ ziOQ1h#N&dmQ7#S?X;)p4_YHlKG){zRYbv;t_LFmxbtpLQLLC!r|2#}-hF#`>54F6j zz{kOd;h`?bB;Oh8f`+=F!cZ49)CECVV*;zNdQOP#S~wf(g0{-lTiQ7VUNUe=!O^b> zy)9byf%hied>Spr?hp` z_sMqrmTCR^)GL!T<5QpQk`?axlRS+a#xVzxE@fP;oZ5QUEeaPuSg7?-Qe!m#1scr0 z{7;7xa-ZayKkzW zZ_H4z^@XHa=JuCa|Lc~TgFZ)YHDj>H^9M?Z|{=wi+h9eoX6`bF1-NqQJ?TKfn; zg5(RnRc~z=2YVWo+D3XT?VX&4uXpd^#FjBs@T7+h>*-LS^X@5Q=fdS}*tr`pT@UmS8)ine0&kSrt4`Y#AK=We&T>g{;hZTK1lsIfv zrzh0@wVuIKDF+0Hu~QCoT9c0(E~ICl|15I7UVJK!&fK&SWBAmTU){ega9c=rG3(W(4c^oZ_qqIOGGY=Hx2`T0MQt z1pg2;(_PT&zNJ2OL-TNJ3eA>!;8L!%PFHl!ExN;I(VS9rD#t{f0uG{fPh~au`3FAC zs-OR_XR4=thh*LT9}j}rklm>^vQtqV5dVn%g=LC0zh`p?!WdY4dh9%PPh$LgnYx)D z2||OJx^MNzdVn9h%vpipBQkZ5@OvMLMMyJiGPMYeo>KWxOe7BI)fO?I<1QJWRT0&FCF1m{*mx(yKoc8~kbzV2=z14}G5-iaHpHtN( zk$RjyKr%#>7kT)XvyW7(vvj&fjFV(eM>)Y9;~>A4&A}iK8gLo<6sJVaPhN4?a~rvJ zB?TEBcgM7Mf7QqOtc~jflu8($6*@yX4?%5T9lm-|{oTIS!#ARTlNvP3;7xWJ7Ck8gK z@ji%B!_exdR=_NWZ6tYYL!tgO0Q)m$Cf0AZ5`+kg~&Y2bI&)aA4e zf0wn*_;=X=Q1LJNnmIb1q|M5*P@(s=)t^8FQ?<3}bFtjlDgpy{BQwqmPCSACOymDT z8A-pfQ}J8<+4Jef?Q|J7nlEq_^HaP27o>-II*Utr}wh z*UE)-ZM%p+Z_eGlVLfH;QgB@R&BonW@Of}JgCzMVv?5peSI`V0+6xjvi39hf8D#cP z17Hr{x2&cEXE1*iu1hM~vovJm2@}Dg)m1elM6L6X)=k z-On!d6t(VWub8R#e4SU16GRP$2xwdVRzn14rgjtF>r)>XhW9d8mmV)7_NxeRBC>qE zhAy4F{D&@`Lzm86I*p^t@u5p6dj=qM4P~}2;r~$zW`LAewI~wMg4HC2eZ<&UOuDw> z2cjm_NEaiW67MACF3D}-6jW>!qFeH%uEzYSX^N^^!b?(x=aAn;e3fB%FAljkbm<(r zbPioQMS^8Ib6GjEi9zLHschxRKHzwwE@_9?VR$dFVk=?+VX{CDr6Sw7k{l-z7B0y} zY8f#+!R+}@+$j{-oN;&s)#~h2$6mWS$fr!-4VNl7rc)V_EwtU6H@Zx)NMI!EUq(RhpT{?&1y(s2dTR619C|rE#5!sUvL7`5bZJ;?Ke-SuLxv^;{wqbZLgtx*n zzy8%7-iw9QVPLK3D0x%Cv6Jxuw!G|Cv0oJV_)MC#Mx9gN$}DZ91of-XMAbA$q??K^ z@dd7G&$;B*okoRQlh;Ob+|wK=5XX-@Zncc_$5Jys6QlpAonr3#bZnY7qZv^ej|qB= zCq!>P;UGbkXRYmQ?s_hkL!28?g*G?($8Sxm`qhLgC_CdZ%u*0NTt*+V8kxK9`7|rq z5~#C>D)q!0{ADAFM*xy;BC;g5RNRMLPaFeq21&?447W$??u{#El2Biwq6qGnDr6@4 zm=v9hag(xoMmDdpNumE}X#7F+ghseAIm^y+6<2xOAw{>t6+DawYq0*UZ@D-tb9ft( z(T*EZ(dZHamY&1lsd_U3^#~*Rs@b)#Mr+B$g76=y_X(8hF#D1iwHP5C59r5q|H$)^{;SGEFI?KVON_7(In{+8kiZB_E5T9bsj3YLF zpOyzAv5H+O&dnrTNexeMV+Ay3H(nt586oY*5RGgiK^z-CCWWDbcBr5oDrh;W1VXFS zou)|>;nkJm&?B^`DwnWPqY9;{keO&%`j)O*xI+akNADWuU#JiBFVHekH^(xu0~8*^ z{0rbR2{%3~c*!!Jdb&v$=0r-2czfnw(CUg|=7XVvcBr5oDrmvk8VI{@G}c;SO`3C~ z2lXm~{W{LC0tKx$7iR1E5!mo{v!3r52=jSu{JV=lnBTjjjlrLl?f8M{HxQ<>CpLjF zjp2Cfd13Vp)nc5Y0L4>rJ@IiF_cE1rV5_|U=8jcZn12TZ$xLNOjA3&GhRs$;OBIo` zv1S1fqm7rk2QkKBRTod^iY_v?mti3huatAOTDcTgu2nk*7FCaLV^9zDt?R)Pf$M2k zE7bFW_0;b@E*%83Ps(_0U7~|NyPT?WE`fP@?ZXcXn+?9>6OoS)AtJ1pCb0Zvn%jN( zOCdC-;)4Frf3K-xnX6cFLI2&HgZQ%ykXqvWpm63ym**G8oNS5%9jX-E>_1BDU!Afd zFj&NiAy+~ygtcu428#7u1wln`r>eOWqKnoh9Zn3Vn=K-gU9NPSuiz+pA_Cl{YY_y^ z2Su&HzNL;StWjuf;o70w;R#c{lJltrbse1(8Afp111D76{FIIJ>Ed7pYMd%sgK7~o znW71`BR2#@LI^0cFc7R;LmE(neUC`7I;?`l!O(y;s6n;3mr*@olcZkAEzj$K_6?^~ zT-4@7eoMXS3VMDYMNxSN_De8}C4()7?!O)wbkBxNwShXUWWZ>`>DxjY z?Ol?--?DHcKLr^45|thOuk{$#5KL}%vL7W0k9Oc&LUKC$`7dG@-j@#?#Roo;&fRu$ z>Ervc+qT6T>F`x!o@e}@?;f%rYlF-aNAE&&uyLc{ zZq%7+I5%X>2Kqrh3QKt2sHWE6yrJX`|H^X^hfI9~-?^(A=(FMyRqU%LtJfK-tU6}M zy-mFVZt7!-Ua*(mC;=s$zI6Y1XwM(9tmS~sO0XqCR{J*>b4>`UCT>29xdD4E8So+S zL&+&uQP>$NjZ8Y&PsI~$)g*xP@m$7w#xC3_a#oqCfRj3*RWe@c6qG@>QR_QJ&&(>wCww z0kAc&Cc)VitnK(|wF?t+<8J@prQ>%#>pd9k9(nI&gHVf}EG)Et>pGn5uPL#kWE$a3 zXy3rVUAx^vW0dCLXU$5SA)e(=X4)sGRZMf9Q0rYGLw>6OFfYf;(@snI0G5zoY z2`KYycN~}oT45!FU@#}0hk;B*A^clY1w(el2YooF`8h)zYFNysA2&0myJ%T21HcSl z99CyUiEZcHBa7s?R;txgFsc?wTD-~Yp;&4ZpqvUgsbZpbTU`$@ze!N-%a{8?Bc0%X z(V)>9nU=s?Wfk~`;~|ZcoQ;|E3!%rIY%<}0If0im-j}f@-}5poz)iG1G_PpnzW1wf z$@F*^i0sCqT90*?;C^*l3lSDtwFI|1iGz(4;@UAM6T4_VBU{!&uiPNl0OCqsBtkJ# zgT}J9k;7*ey+lYnxP8l@vXc?wS;ApTGs=Fa5F z14L92U4`UFJN^ni`#^;IB98}|M-2b%Dkc8sz6D@~#(An8(TdoDK6&Zkulw2!=TBd} zswqGL#r)~REJhkNmuGS~d|0dAjw!0Q$H34*VR{o7vBvYF|AX#Q~qZDE?;yL-E0$R;)GD9xHSme7^b+b{nbt zTQ-d|=ls_L8(Wt^k!@3KCgxyITuIGUkEOlS_qzidV!#1#cg#@(7<8uGU6TPM5H2WL zTrY6nyNrF0)?&4c>p7?;i0SKnZltHFL+n?`^pNGnj)*3t--+Bz&}!h;hDzjlh$}s~ zy9Mr|DB)5(6vRnkGfx6e=8vI9J+~3KjL_GR{_R#ADj@5rZ8<&3*N^r<{n8Tl@GOgn z6pEeP;BIk<+)i8lHe=4(;hCW6(&IxN(Q6iJw?dfqho2K7Zotmc<9dFYgwtNoJMY8B|b)$R|c6bmQ4l~(% z7H0-FoabmbUDl;FzR;rG2mCJ23Rhc%@2z*33j-VGNA|){EFA2uo$d$sn&W=9a_G4 zc_S`$ZI%@if3g*TZH7vg00fiW?E%74&_Xd-)b+~_Y@#5_I5oFU)=jwI#9IVZf*Jvb_*w%I^tJe8-64(8 z#ZrlKFBp@$S2E{wR%q@Kan@=cNOK^I|I)WggY=^T zW#$Jlh1PHe(_Y`>u}z!?Lr>P276;VgUPkq9FL_(g`M(79qK}VVkG4PKBcX7~^!E&p zQMAR9=`)?zo&|ZgQr$<KR0l zZSN7{QFf}mPI!NZQ*YCce4w3GQYEiNn2RkwZy0A zYV2o7+mzXA+BYo-*z~gKV#le$Fu02IuS^q;!!_q0Qw*K&%j#7~C}l@&gW`1S-v@<- zfT~w7M^tfaCHl0wFc1i>=^Rjln2yIC-zhji)fiA_kua%7y?bm~LmE_zeUHf^@F(oa zGZgK49ngL_3IDO-kQNE+`=`}KvH&}2TXs?Q3~AD}Y)qX*iJ=h~*}BkxEHfJ3!{1=u;OYQ45Qn@Bka!b%ipALjI5=g?+jc25UHt=?6ZLAYMx{i&ATx5 zyRk;8)<}V&l2w5a_${snp^5}&PgSchmd1&pjza>+;{m7gIBnJsEPh-NLrG z)%G%ZO22@%t1iwnaJpcOoq#z6i3Y0^RWvtI)p?E|4A$C4ew2g=)jv|L6 zz*uwD=2tCmA^B5DCAS+{#oc22=}7K!(vJyhzclL9%lZuSUjJAv9^U>9{N|f|tkp77 zdGNeq&-mq?vTyg*3g3(N|B0R?)g|vm&vu^)({C%RWcR_e?J)ALpzXbPpx-yJfkq4s zS%b3Qb|1it-j&un;i*a7eFI*U{OG_?@+dC}3mfu9cSO9)vxL;>d~dxV|IENZex~z^ zwZ_q{RQJI>xT*$(U*19d`oIP;(GO?QK(zX*7BI|kQO05t7AH5N%y~6D1r5+Z6h1xV0AC2H1vtSV`Cca+p&B&eh>j)aNK&`TVN=N6i&BBClB zV_PPI26km|I8)w*iiw7n)6>)nEeekI-sihdqq@#LaY9emySR$E&TYlWaSc{gwF>N{ zffF5WLoj7E0?bq@t*@K=tE2~&e;&O9?&s)_6;z?SxJIV<^WG6iZNBEjt@9DD+KPNZ zWA!nM@zq%qxmL@; z3&~l}mUHWDT4;>pp!ssuaQmpChm!w#F{Q`*p3=4N4uaoI={NbkD>Bh(Oey6%o_1n4 zHgOk|cIwWJjJqjPOlOd`O@7CY8uYyxo96lr#8Ff&G;iRL!|4=)oh{yKFf^u_XwL1C zXsZ7p2Y2q_m37p#BJ%MyhVMrN$fg;cesBeW>ScGrh&YoZ<#K&Yuwj~Z`Gli%j6 zA3j;%W+qE@&XW}}SO3-+?6(2nhEIjnoi!D2S)_`;0ep2AzUayzFjB?$KKfqTKLbbc zVI8T0OEEJ+TLm~G^Ux2{+m5c^ye=HA>B;$GiGZi9dRvJir%Q?kc@Dor|tard{kiV z5>L@~?rl?1RM02yu>Zu@Zusu;g*$qn3Mk$^9-K6rM)prZxazC&)d=4ytfm7O%U>?$ zsC`3*v!r~>Sam$jAi?murcuaIcaWx7qoZ~34kUl0v zu*mt!5P3bV=x;c|Qm3j5&pI~OJaq(8bw=tV5j0IofgDBhgzFxH7qQyPSSm9gVdIqw z%v|7S0N#Mup{WR@N;{6LG@C*9bTbGq2ymLBY)w81o}^rqs9Z#`9b8~?W<9N+sHAeZ zkrc>5fb&B-0=VPyij>BKaj8deu~Y@!H**l8g&%^BTav099`*`x zh~3YqweZ4N77z3=71MxUN2tH?lJ(%|PGNNa@GhGYTu#!Pg=+)4Al)1N( z{^gUF1ekQlSr%QDgomQ7xXOtY6QLfcRlsM17rW$&fT48_EFF%xOsl3 z{nclzSE~meec%B~#8k^=isf87dPgQ(mN|J6Q_%!+#mSUB@jH~qnTiKxXXke;2$Jo- zZ0CT}B=atEd!!p2N>5C)opKWMl$5RlX^c#kUl!32a`+12vCt@%9Fc38v&B&My7e-` zQc~D&4E7XeLT z8oFLXXiUhuBDapiDf~pDG+oxfW8q*7d5{xGu@_GOx$xi=o|#aSlXoWqWO|+1h_G7=? zBrs%`%yWnAQmsU6Izx6jWS6OJw>o5(^-7~I*`=0)`Ka`Z5X8IP6n9Kj^>bQ+S9%q% z>LLF*$g(LrJpxR{@}I;@m{R=e59<4s|3S9n2cq9pRZ7;jv=!!J>UURInt^DilvyH3 z7`9G?Y)3>6+QIADYPpf2kQ_2Jx{!Ynb;J1Vc|0aYSRjI0Fa~jl(jQTpBq2yk6(hGr zq7XEa4P;@__aP)nQ9r&gwGaoC9uqUE5*uvP*cJS2YP}304Ek6Rzs=i((LH`- zFJrcje0ysLN2o7pN?FQ|Ed}eE0?IrcjCKpMP9=i+G{@3z2k1ZZf$Ak`A2DaiDCmp7 zpeb36fk)USdZH?)?hMT}XID+%;|IK#RJ(`msdjp`up0EWD@J?K$m|;!@Q>>?Wx;H{ z3<5Pk$6_Wyu`eh$7Y4FQEw~2M;9kabfY?kJ&(M29tEb`t@Pz9{td*j8HCBq@(PMMQ zjMU51%wYy`MpXC;OjjQ@^Z@gxi4yna7yBYevJd`0%u2W5Hx?(O5sqR;_MtK!H~pM& zn$bkOIaWth+E_idJfPAk*OM-dEp)2w+w7}2X!b`+#z-(4r`1(RtOoWA~rox{lYuYPY!ILH!NSd zfs?g`pL^R+SG0Bw(e-x*hRHTdD?detZ#dRsvlzDFbnz9~K{pB;WYI)?2=b;3*dKF7 z6#r9+BTN*HeO;F#MA~RQ1bze$H1voca8bVLqyJWMX2Ea24FESB z{Z@At`ptg%MucOQiv1FMWPR+$2?SALL%+BPsKPsEBMOfSY@<#iniylhaw{Tg%jtWn1L%`!p>2uT)-X|WD_dw4T3&-fq!D8 z--A{s;McOKR2sLjV^2zsdDYBsH-;O)WBeCTO@vn!WW4(?7&6x>nr30MMn~ObL_6Wa9FHw zlMaot*f;9R-dQgt+z(cBO&nWl%5N%yRiLzUEHIGKa}K79B5H8(T5+PKGV2yamV}6I zA3Y;5@OlcF(S!vOKJN2MUhdRvke-+;oGwjZEYb;NYySau+sgSuxYAoe3fS@*yaPtn zxSU8e3Uwz9qX|E+;;ny!Tuxv!0zQa4k4%H&z7uQQro;O3c0CItZgp`o>0Dxy84@C- zxlXPIdv9r|U3H~BH!)O8W)Se{`37KMed{u4A!~OS5_!LZzOA~3)twx`h%KTSNOPFl z|JJwig4kR@nFYe(o^fxDXFv`1JtAvKKOIa77Lc7v1ohe*Q~r4$`oo#>1HY(mZPdJk zF=bV*Pp14E1A`3-a)@5KEg=iby_62ZcmV4*Be&-H-2{tStya(eFG0QZHm`p&Fx>fX zV?~)LXwGUb>ACFl zUzd{}lbn%RWhlOlasw?WLulC`x&DYqIhkn{qd2o&*> z^lmC7uClY#{yMU8PJ50B<{fgU)BS_lBqsYCu0^{2)&vE8*hdIPbJEpP`=GB{ILms} zuq@SQ7|T-S`ea#02L~I|kA>hz#fu=k1u&jA_@8c_(Cly5v}l1dh}QZZi{>;>x8?`2 zEUfViroFw4=mUXk)B>?XfuKG$CvK^rAX0^=9<`{=7o+Kck!>4G_7h?_OSV?4VadC3 z0vLPvfd>vamy8#<&`v37{1}`3lj2v{>q-k*SlE&(9Dgdg@uqYPz`b7;;kTkJwc{pQ zTKLB5P$Ba>Hp7=Kus(g9HOkPvkFzFzygtrm-NH&DDgAw-%Q3EvUJkI6XEm3}A|(>i zBq-NV5cWlO;31pQG;G3)o9U`1C>l&*5_{sf=DWGVIYhlCiBuhifiGM zdXCER3kz>5nH8IpDkvXKImQQVbIl|f)Hemf$Tpn!K7Ls@FX;ng0-XZ$>^u>@-b}{o z$(xoLIu%3jC?o;W6Te3Hz70Z_H$4{p?f{PVBMh*xU8pv>* z5o$m>g!yi}$l#dRsn+*#*f}MPO*haoHZ~(^o;`c2R)h#6R!8H}#%yFJnC_8-C!*&=Y7_M>% z7hx8;<`&9ZlaUix2V02ALWg4VJfOdna)EUx8;DebJHHxAYE_FB%7w1^CnIyPH><;a zfl|Ckor_YPh@7S}_;JnQoTkFl0c#Cjz{0Zt5vGV8pal-yf&tO8MUEra=u^%Qbkx>a zaKH_Ncm5k6%?2sr1Io?r}c>7zjUfKN+%ofAdTU zn^u~2P-_3i0-_ZLjU?{ropJ@s0DBTnd$?>jiyNlR<&s=cDePZW?1WXaCV+JSwniB_ z4c^RRcl59YY^Y?4)5adK)`&yU7jTEk$Yq?^GtLU^tIO3zf=O+e044?70O(ESVt1SF zI&Yc0XrXjPKFD1Cc@{+|cCNf}-Oi>?x3lYRAtmK>E-r?!|>G{ng6B@)=oBmy0z zVfBxtSgKS-bI_|+3gvnsx276gFLwG;*`}gYy;7*lLX|?YUM?4IfeB1vJ1o~{k#tCo zq3PCU)6iIXv~p6q77;jfxB#!7YZ$O&7_eg)uwxjogHO+XS0*XrLk=+^RsItV*ulJW zo*kwc6=52P;T6a5ibGv4;IDQ4AXU6yO;;SwRFp24M1-xearG0PrgZ;?&`!9nlA5;~ z9a%(R0$yhUIyYWgnWXySxt)WfCh*&KF^C>ncZ0vUTO6MmuS+QG>qa9SS)QYOX;!t8 zA1fWJJ_&IN=(tp5eFl#YNy$puO$J>)k~=9y0>f=&qsod6dLTsyLTDG)qy%Q*LF#4B zLF5l<<#vo4W;HHv@p@{FFR%_Eq!RasfM`4i?E$yM{oyiDeSHb`nK#FE$SycNCB_gi z3xDhoS)@LdzJ+3|;GULo6^Aw;0kb@e$uKyL~R}|}u zTc?S!f{G<#0b#|K5$CHT1O-4~LsUT2DLuaSJ|*&qnA?U+tYG;%)whR>#M^fJvU!K` zr=q-Z=rZiEuwN}S(g^U&-Bh5Xu181ZM6vSwm@^vVJH@t(XGsB`k4ZY402ulc^?acS zcycJO%0OKW5iJankJ%cRU?yValf1!ojx-P=fSW2IDVavkeaKG5gMyPm;ahS9qpZu$ zsfup`)$~mytY)d4oJ9T;rv>DUo9=WVH;J-E#QZDthA?SWupEixHk@R#lq$N(q;veZ zGnz~m!4i_mQLzvXU~yfRq0+qiRPmh%9JdhZXyUNK?Ez=rT_jb#5DSwIV`T<)%4@T%wYi?%?d0YCZ`jExQKW3 z$Rxd;i6vurrKD9HZ0m^C&*+poC?0nvnJ$%*sSLWq@b9?QG9vIT!5#yH7nnJvcM{M= z$5MoeTuj(hxELQt-_aHiHzohB||Pph?0(?bkW6r_M=s`?t zG1ZJpKq#OnVFe_;Od1jzjH=Ihn<+xP&gF;AgKsZHdS|dN9sZq14eLC!2Mey)K)vfl_D^vo z(F3W4lC?&4gE$066;sm{1K)7Ba_M^Z_;d{UwqSFGebh}KUqn7`H?|I1Ilf+;yq&|~ zb2Sgd%|Z(L=;-K*jHB-z&$j%!Yz5XI9eX))FOfIbeo-rd>VyWHRPR43?j0G;>%|p< z0J(hLnz3WCuB2|!LPaKqS^>!zc{e1gpPk3jD&txs-@yGo?Si&5V3QRm7WF z9f$N1!OftlI}lb96Rh(~OUx?pfm&BYNHBlX+8$|A*E2;Lkcxl0HeJ{8fBrAztAH_B{8XGm}998y^1BF-8p%32nw_bRy z@Anzr*+BfZzxBdveeVt48Vq)#Di!AH@HR#sMTWOA!`qnQZ44bRh3;nY8{Wo1X)?Tx5ota-xTmd$_iGrHj#oLf4R2$Hw=u)pnBi>< z%wSp9FuaW!-o`K?DDlFh0n_(4N|Pk*734LAGrWx%-o^}XW4xDA_5ylqZY1u_rQYy1 zW_TOJJB3#}KD>?b;ltc9^mbd&?c%+!+av2<#kxIef9r+U`hK6`weD3cc-!B4;kCZ^ z2Cux0A^)CF{iEsw{7)r?-Issnh3*cl9i8vL78QlFv2q3M!}c z@5v+G3y<+QY8`=b2Km~@82YkS`(PP|8Y@MoWt&fZ-j6imX7g`N888hk4S$3X>zaOPhU8OD}` zDyF6a6ZBh6d!FUb5iRV?p9!H!6^~%QtEp&_t61>}-oMfYb527T{L#R1O~7%L{`BQf zKjMW*qS*MOuS9NaR8#A3-e8-DQ~|!|!a@D6e&y8Pn7NA!@%1-m!pk;MR{O8to5nR( z*x%g^nVPU%Kr=1Rlt}~`fA^@!1+;Ew>#0>>Y`Kwx@fy=09^r_tT~E7Y+iCdb&qT^= zJ-Du@6~DYg{3c&5FI%&n`-u)IBio4|(}Pl7a-ckwH;0x_@E~;0t?;r~7^-y@Ue9n1 z#S?61Ln)*z&}fOY;rqGMu80PJWF*;g4F-fJCkYH%U4^C4a(X2B&rm=6^8ZC&Xe3zY z4H_+2&Eok)T?EaR;vXXVg)+ph8Mg75fZnYAmU;u){rf)JwHQaD@8K#^*+ot7g#J?>RN;(i z?ZKy1z#cUuW=tRII0F_wx)kb;A{8vLYwW~-Ik3TejX%J+V+|tUV^`q2W}x`30mAI3 zW)IA5AG^ZbdX!g!qBHsArJX+=80e3Q1!uvl-gF1@5n7=NM)BYU@$u1qq%GQaJCXOJ z%n~dJ<%_?K4P@1MplLEVG?DcMT+oazijc6NUqO_%z(lVO0$7@e) zk2^Eo?DhkpN}xs>^?|rgz)J;46hUdFN>ITAs6v1ch^l`AJn@25350ln-??}0$Bf5o zJNr@6`ek-~=YE`f?m6dv&G{YRli-{9OTLlGJRldyeU*`YV3X--bYSht6l?+pM63KF z?U-q0c!|e_e$1PK5k~mWNCRPjRWAmE!$}X=!`-f%|6gTM^vpb)2>f*G`+? zMqA2qOKkeEGGc6gfoR2#z*>4?_T)=_ZE1}7^qIE*VS5_3*pdy)5tPd<`RXI2DLx8T z*HHkRoo6*#SFrG6A40bBLR4Obz&B|qj^ZpOCMs&Vm5-KN*cxGape+Tr9@?I0l(e{g z8Be}V0fi$HOp^C{=xynm)6M_OrpNWuLUZHkQ*I(271%v8+lt5^zk-EFzXs#KfOmz9e~u&*+* zv&=Gnr>op|w2a?g?ra%vk(QA*q^Z_%tt@dG-?(-fueQ;sEadyK4XIsx321|ILwd~k zd|*7YWIxCErrOrD?Tx-k#mkjvD)o!-K6{q-v~hcxwqH%(u2MY)Dl%A2+U6Bx3Y#f7 z8`<)?oH|STICd>A6Tj#x6KmV+*GMqdu-A`2O3s*MbyqCHHv~8U9J22qpz7Jq(KGpG zmKLALM`)EAP^A`dVt;Donn~=C0S4#y3EQkpdN|C86AQiQSDb6_CrWp>?5}@M@<}w! zEc+UZbdgV5V};9~7E3d-VQH`8#Q$y6h(QHF#{Yo-M9k53qf0s_^S;p8c&b`Hv1 z0jDm`<({27B5daLG*eZcQv)wnCrqWS>Aa@&Th$^2eR3+kS*KOts3L`}3{vvgw5Zzj zky3PoThw3*N1TVY4Gqcd>h`&u&~y4%>U79n9CU6^@UydBbPAUxiRE~boyWK#nD7yTx2sps60LVH?&>iqKh)$%V0}$FVegAqO zT@$hEgI-A4eF-Jd=FVMWB!m{J1S!JI=$uK^(OHqi?cI-*(g*^W(%e9YUb6C#{Y)XU zyDDf6XsV#L5!0ihb6E4q2=$18!$RQTIyld~9L`V6V~{>d$PO^>d=1=L`xtBOMemOl zue7eH34fR!Qiw5%en}FX1`WhP{?bFtL% zC4p*blxKT^tDKsJdil8qUu`(_iZ@dHYrECzug(@N*5HQnlDYc+@ zgilujBox-gw2{@er;LUeVqi}Z?sU9UTBPtWb`(yH<|~1v1*5SUaqC3rH#Cd}#jiwk zt(XrFW$P3lJ@5eHJ^@M;~AR+%0#$V8uJg;~^?5!jtP znRc0e1sa4ZSqcKxcnslDL=KKMWSq)B%(Si@FZGCV%17u(Qc8k7!njuIz~ti;;yer+ zUjzi911vhXQtwxoB(9h|_x*hLzALtm{9^gvD?lClECZz3la)2wX<5@7+ zX~N?k;7Zeszmd4oY+fAzOT%<&u+tk0EWMCBhFdenXquE6?l@sy=RR6oX?WCO<%Eu> zK}yHn?KR_J&hUzV^>tq{Y3 zeL86wvk%irM`IQKD4w-?FTMdq7zxCpw{YlQZPx0>GUBYbp4>hbT<+Wzi0vD{DWRBG zv`C>KEh||VxU$u-Su`@Oz_AR%1jw2=05$TnbGzqld|)G95AGBOcM5@Bw*q^L4tNnD z4>6}^j}7h=26qb4b*#3Y7Y7}KI|ba5M)nn4!k6!ale7lbGPA^kSd~12D54z3V@VET zRbH>LDw$jl?i2=h3h^+N@m)7xcc$Gv4DJ+EBuj0YC4?U_)$*8%gFA(F2akkIZvA00 zvyX#2g*!Goi00r`&X3Yr!wU1F427$cw+pUaVnXBAy(kIy+8pkT(EsO1hLq@ zb@>Gd1)7%a@>q5(&~??eygIri+-a_{wDhEL{zHRt(D`>4p&*yeNets}{w{~{pR7oE zB%G8{-HT=wA9S~_wuE;!9CZL>G=)qf^oBlDsa$bjAZYma%*-^3B_AQiYZTqP-~;3d zpb1&mTbe26?wXw`mX4o1Zs+V1rNvS)XIpdgC-1&%e&NL8-NpI2`Pq}X`CKuJDmcDf z+%>(tRh<#iuyqYe0SdRSO^E6KX-I2NxY691KfkeqtRn)vr!--2L{-wDB}`$NTij_0hxf}NW$q$$ip>m^qx!ul&x0>1vb zAh;)@5fi{W@tIQ>6fU?=3&GuJw(BDNTP4EtQldIjMsom(uvTogw_-wswUWJx@UJgE z9zoRTGNnz8EYLvPTmd0Impx~kE>|qis=4)m92Sa5GtO4*x*f?itbf6un>(5H1FH`C zEoSXva|R&_oVncW@foc&FO`XC5qm(=oHG$nrvD_qS6Jc#EO7ffO$<+NN}q)AZ&K|_ zBQ~i4sL91X)uc>nvK6DKtIh9}+C0^p{4=%DiapU=F`+hE$zIiF_2Q%Tz;laD7U!4T z-p*TCSz%SB%dSLu^$l+IpIEjlfqTrjkTssd*95?VQ4_%B%a^l09l$Ty9-MS)GfjVH z(RDA)oV@$Q@rC)^+}y&#>_VDZ|I!B0A_RQH>Qf@UVO2tizuu=1XN9frjl;Sq{y~Z2 z^S#Lw6Gg4q<=%=3QPfH*QB>Qmlwb+YPHG{xe4(8KkC&iIh6~v1@_kSSF8 z!!xuG%E*0?irJzn01j5Cy#P%D@r_j5_DyYZ#P&_2a<D4Yr>0()i7vEWp? zRCf{nA)Ej(TUkr6X%!HP20C?sZ9&)W!MS~3;P8p%8#tFcPwC+f&hu9JPMY1fg%gFQ zN3c+4l%5aAL<(G4>{dS96@}~ZTjAcKTYxu0)z88k0aI+f*a~-i)v7jaUv2Ux^Wn%6 zO}Q36I70c6B0d1Yd|PYa$8O#XwvF{m_&FN=YfH~$B&7$3aV4#@_WAP4nedE{<%o(W^O?Xj&Onk zJ((&g++Kk+jTiA1n<*s@9AycZnrsh_4m4(yEG6&|_kzYSZAkP@3ECLKugL3QauJ8~9 zs%A>1lH{9ygNFA?cz{t;srxpT5N;h3M?5OFUI}-5)@At<8n?$^tp~7iWx&iasJT{n zW7Q=IAMAF0P`jvTX;bZGWNaT9-_m{#2@_RV-o> zB2(~6c!OPEZsnVc;Vy0hpn8xZ+8PBTf@oA zkp6<(tOptT4=Dd5;ir>XEAyJiK{MPJ<3!y8IAJ>1oZVv;UVWn zSZ8M&J)S;*$CLCpPmgo-_zQ4;oIlay+#x(3qsJL~e32fbx8t#s9#=k#$G7OQoqqn; zz~eM9-JOT%aW6ei(BnfagPecR;|E0A>v%N75u!U-ZE$`t%JYosJfk?zsLeA<^Nh+o zqcG2?%QMRIjH*1ND9@ZID>Tpz;{!jynvB7C?e!*ShIvB4fMR4@gTX@UUo6q-&%KCY&E3eN}Sg~6&Vx>afY zSk_M^5@qg@SdAm1RaR(UtbQyBynxmq`;&D=Z-&BAOm@sZ(5${2-(^=}SkMP7tahFz zyMgqp5an;SF3`kcd6+|>CO+m_-k_ZGV#&K@GBa8DeiGAgG-J_nFx*qBnY#87znY8L F{{f;nwP*kU diff --git a/doc/LectureNotes/_build/.doctrees/chapter12.doctree b/doc/LectureNotes/_build/.doctrees/chapter12.doctree new file mode 100644 index 0000000000000000000000000000000000000000..4aa5180751f8d9c4fb2c451b21c2606055b93003 GIT binary patch literal 193999 zcmeFaY0NBFb{IA@T!!pfEY6JHM59d9q&|(l_xioB_l+Vs)BC>fJ>)#q)?HOyT~%F6 zZ#3+ZVu);;H*{hWL6cVGF1*{47KDfG|o52!NBiR%l3rbUTn)MvZb zXo=G2jHo^P`DYJ*>e)xn&UddX#7dQPg<_uVJ_Ri(mJ?`&5ubek55I`oYn-57m;<~7 zt?j<-E4zR9oj0F6@fN$as&~Q(jF-?gX-;SyMF_&iJ7q*hAvA{eP84bG%}P{5q!_R9 zI`28FX|npZ-#_IvRwpkgY3_&jNzlap`_N~17`mXP3vI1= zy-%LJ_l*7Q2hZ5ocQ1FDHG=Q^YHok@8OApI3j6BrRha<%YR}lu>m;%B5SpfNq^`mG zp!Il(qgBBD?z5CYs4DyjpI;G)x$)^WT9=(KBtgv-W`f(iY9Q#@?q!6cXS>(ebKz}O zCeXURCM%4}C`;ySkLZNYvC*Y9z0k5HA&GJu{0+rf0rSE6vU~&hW|2E zhEPQG9Tvo2WhhNon7RbB_B*S=$s3V`83>%nJga@_$Jqz$OYEoFmvj==<+Cbu;v~^U zKJ2S#&CcQBD;lQ>jO)?v>lsO0N&--yBoczR&gcsMqpc)mrW%X=#&xY6v`1hrA;35L zRX{TPLqI7%4F7!{{`(R5@68XM>FkfQ0rpYttvY+oK7`g!@T^~l#UiE(A+xT@4N2gz z{rQQ;{6xl>pZ7ddud5HeD@I|wG_zy`Nd`8cbp=r9)mX+0tE+ivh9YRjD^2iEuu4l# z(p4`7x*Y44oTSc!&_yD(p~ z6&e62&C9HbxeN@?&50@F!L-UvfbG$QR4+>`8Sfl{2B6Me)6gVI!2RcvszD1xVvNUr zql}=#Kmj#g;6*-X-`HhNfa_;AEu3aJppZ18ZT7s*KB@z)ys`VV$9V~m_VW#LCs}Xj zCA$+1cx0-V!2+!DsPZWcZvHfM=K|+cBi;?3x9`pXE*S1J%H8Ju-u<}GHTV0Dbhr6` z^)mK%IQG&ehi_!Al<(gH`F>{0cT+Q^3`2;0Wmx|VNOeneE*WLxRk=BbM5HEpC57fh z0)9KtL>C^AjvFj(vB1-1B+ijKK!Q+Xky(BEkz_+jg2gqF1VLJeIuQ>PdAhQT$gekACpTzFHc1;QSlgMlZ) zBS@-hzsGy-);1k!qRol*L!=AQtC13g7CIQ4Prz^#L8&qHL-={aC?3GC7tB!HP~&9P z4|WzcQvv@jjf_UO=}%#%SR)!s?5SJI+?XCA%Yfl?WOO0)%fu9GyT@KI4`>c4SFo{> zzV$L1h5mc!Xt2=j>B_~Icj*nB@rSO{PlpYDqI-8zc1`zQ!`x!tE?ty81tYmYIL&x> zgC%nUes+O!lHu+KN%j;{#RbY~#=9FVxswPt7ceIp@NUo)P9$Vq@SJSOyFv7=`-*!P zDEA-hZZM=zpm7|d=@g?K!g0NQ<-6Rz`XYGEj~;<01ZxQ#Kg|dtsNe?9u%if0r7Un1 z*e($H(C65y0qsp_9;E9HLkJsM*y#kDXvK11Hi3>uCJ%VXU~MoW1)(l*dliiUR~6}L z_{cG;hZEs38p!=}Y!IpV?V>XeFbYpt25d3|6k;yvUcIS6ao%Yy3-gP?{KBt2Bd^X*bS8VLlvzxCap_nM(@Z`F!` zBJU8Q;Zp`&RYKUPoce*CwOFlI7dj_FX2h>*IyiuepP56x!w+c+kT}8nHb?DKRCBeF#L(Rx~kvh zVbUK5wp`@&@w|_Hz<&)W;Tq}se4E!Huf^c#1>`@hTo>f4E^fElR+{0q-E3`s`xido zA07aFdCp?@DgX&7g=f2zl}o!bRiXq4|KsS@k7_?*vbv4eqv37)DNdMJQQ5(<&&tW1~TyFOYW)5pD%x?~gt;Y}e%#AU}C!p!hkFa(NcDn(NE?mHV8qAXC z>GyiEXrZ5dPAu+fDG|rcyi-Y{L9P+BmqSrTWYt2}6{2HGSh|!@6L*X%9facMeu%e{s)lGF5BsZ`Rl*4P;C6(}UOF zfSq^_`ndSvn-)J8G_~JbS!m*eKVSwK(rYmud4UaBLZ9| zhy+6hQdB{gqRIe>ia&bv7)TaE!9cnm!n*`N5cDj3F(co&Gj{h-cpE*K>jFe@1rEkF zQ=%}G!mW|&RHY}V+5kN=1MBCY*}b|r6Qvb+fXMwq-q%Cq9vWeD;1e~Po)LwvrgyaLKcxVnxAQf5>0;B@a62Py3b6gxC zYQ|(K7?}`OkVZyxmE?IJIQ(&y0MRe;< zxBh*bD;^xDGK(oLdu;Q>?y?r}+CO>l+RKFpsvkgRa>U{oYsOesylzvx3vSns#~^&( zi+mmnZ|v6AqI}#83h6V)>x_XZEx?!zbbp$hr1Ym!kCNu(TV2C}V&t5b6Eh0q= zHDW49c_8Ks8GcaZ7hb5#17(a1D9CiL2YUNRb=I*q-?}%>9Rj`oSV!Qvo{ZnI><;N}FLH6Uh2E~0d zWRfB~(Mq3Az>1u3Qy}YyUc*|1wK@5?&N7^QXjqlcgYV-uMz6LCQKa)dYgJx1yI$jb z@t;NQT>W0Q`|+>AN6YwqZiT*!SIG1MAYuwmg<`}+i8X{8Q9#r1cChn+92xMWaB}LL zxtLy{l2aPhoPzuU_Wnc(s= zuY$?IoQv53LhA|x^MJTFBvqkmcjm18|1V&1i055{cz)v6#FMs&CviLCvHLm1bEVkl zKZC}1$qJX`cj7gF2{dAtg>3*X69EToAfSj7?-B@qh@l|s2E_o5MQ-fS1w;P?7%H9# zL^&WfVb<7TL4j=&h)bfetXgwOe|sUKfQb)LmL|zSZ&S2M1lnM;1_duXK;URH8k7TI zI|$P`N~2$RJE%wz3?Bk4sHvBrmtgClw2Y}-P&OVCLK+kjnl=+W!MS$K3v+lmN+K~3 z+<^*C;3|59W~WNR5{-uoEpavTW3RwLF#@EEAT|WH-I7BA6Et%Vl*}_wZQv@r2hf3? z3@8Dw6e{J!m6wt(pm-7d3+0KxuGaPocxcCfJb-Di-)K&y6sQhB=A@P3feipgXB~^qbvN-I5D}qz&!cT_kpv9 zSpH;e=z{XZ1K$V6#)*Z43(AuZeIGb|w-H*l3fY;%Ie)a~c<4Bvz30KAi;Yo+RHFR#Jabjw5 z!Pq$U(D#A!iw9Kf$dbb+N8WP1xTstuE{4Acrg93!@T^^q;FOucJ}BKW+$3aqs@#_G zo`pm2BY#-+Iv>uw=iw0Yq?yO?D=s>M4=@PwvMfjHA&MA!36Htk=3oqoVw#b6egI1B2#1z)&8zg4$mNI8;8wdS=~ zyOh2^FS@3EiqY-^&DSm$3$9sS)#}LG`TrFb*or>xzIKGPOz~n-*i}vT3GH`JM`%BM zg=}-der2;Gz#sEpj}lVuB=XZW(-RGNADB}2mgX*aPB7SgU~%ac*QDIP9vOX~^ncLN zLe8hKMfI0F-6#0BUIJO^s%g20WPS5mJ?Mh-291w^e>39WN79ctsBu1p9o1{0>)Lkv zh)bRhaj)Bw!i6B$k4F%3y?JSCzoXvh-yEQ59|{p76V0Qdv@%3O;eZWm3piu}P-GD~ zf3Dp_hM@z+XkOT3zR+PWv#@#7n=x#%#}Mr_jWT4cqMgv(63V=gkGq21Nl+&&*n_e< zgib|$PJ&GahNSZjkMRz3aI`TR8&xvw$mUS78Y;J+aGC}|Qzt0-g*|v&XgqiTsB9lB z+%cLu(xz}C9J%IpvLSB`mCKvUo?^{hK%Hj1`#|Ko4FTCq4FMv|4>zQ{=jrHrmK<3I zsf#5)XWKD9iI1_OrTN?WQlZz*z3u%r{vM2%J>H+$pSb(Xo*vB1PIB!&e21GuI!B@2ee1dPd&@{| zzxx&};9Kv#BSWreBQVeqf^$!hxAnF+aFJx@@Qiyek1G_s!MCqp-*^1nd++#V^corJ`j9ZtycG-Y{dW?tSqnt4$c& z-c__|02zOf!gq|m)V=5DVu2G328{92%lq!sG2`+`oBV0;hBKICjlJ-m*WqkRn-?HR497X(N5%#@ zyg3vf7=fHDFvAtv*&l<0>p=g`79LcYF^51jE>AH|kuV0sVR#e?HzBgli~?g3pG|?b z)8KcZ#2*G z*Q73Oa_hIcWXum=u@tU%U)k))`}aeyM>Bi)i0n6xX9R7gz<~qh0Hv3ElxUx{ne`Jb zinfrAvwlC|J>RD!7mUw8I|A4-L(Y1`UjFVYM@iHMYwIl-t7QAPvQ3 z5lcgB;C*CQSauSA(_v~J^7wEtiLs3cg>VfS0$Z~Qn2NCt+IWo-mNw5)fygmpb#$z= znW4uPnXOb*?^)2y$OpaFhX7>cVS6w|Kq-@##3!wIkZ)y9^YC;gw2=y71c0`W&cfyt zc2xjYFq`ZW33H=34COvk6k_F;ZAb`kNESv1CIrW#bNrSc?j9n`Sr!*vUfB!?=Gg&z z93#;qZStpCc-KTvHR7#da>=vI3Fy!T(n*H94?OSOhbLTs+;5yC5FAMOBiv^Nf4+R| znJoyhg#SwiBzz+YuUZn`B5o|SEYKW>vBDY z{=%UMwABO3+{}72(7UkZo4hIn@nxI-RxP2+?1aK)G+|Kjb{!tFBG8sj z!*4L&3e+GB6py*~{OO>yPVK3PEXP#K_*f6W%q=5efieh-w-9b@Ky@E~SxbNBAD#G~o; zT=sZ>W-q^T=b3$UFf+#=_%$SVj-)0nd2{F7UK2o1x>5rq&_7%k(K)R!)_1%4Y z#sOsaRpj;%f_)J2lco9uY#H?#VO^_dH38qlyb%x1sx+IpZrt<1UJ>hz$(x*j`9oE7 zwU2WU2C2hsm3wDkUeUrv4FAW`IzQn5?Q3v@%HhzRfazZ}7wC`R4$gr%!xdp(TN8WRAC@FLq0(iNw3j*b#P(<5xuM(un4Uz!g zZoojk3c|mTq z-Uq70ouz~=^mlh38D=lg+tImJ*8mQFDm;Oo~9M(DEOtB*hX zrALoS^=7a8=#lr_z4zJ5PlnInPF|#NP-GLM6y08k&!&S*d?4_Mm82`+iQ~GU)Y0KS zPLTzKHH{ExIP};$Ck=f>0Zv?0V5r{x4d34O{Pe5)n)AxJTNMY#r~gym`$e{4+kGEQ=E&k*FTZTm{zH?fuJR&K5r}zYq22HQ zu=`!fv%_zJ4Gq_VHR^rDwNMg)Okm?iQ}07;3>qwJ9?FHe)=Y5#A6f|*d|(SYeGCRL z4N@?2(Xl92MFlRyz^sibqaJ(F1?SKjo%Dqd72CU46^gA^$a;nLa7em!vOMB%Fz?-E z8qmPF{dMoXSZttsXq*}>^Oyy67MXEwJhF^UYaj3Z1B3bO+b%A$N-9DhoOwAAIFML@ zY7BG~JphL6`(Ox4)&+EURt{?+gEm34{J-}k5hab(fPab5D@I2%~Rdf8)}e6c=x?>3Zc>67Ec`{wohXTN)Q zgT_Y?aJ@XXr{*;QyP-U```u6;@BW)dkJ`Cv4}`Hx_!^fVLzO9GTzk0UkUiv7$Xme& zIIIQjV+L7H~zc`C%e1~bq|$6lom%&FZ_=-B;kDs;ecYc?8HWC6-XsL{N}-LU=8 zjekZkkcLZr;6yw)?-inv=yF%%-WsR$6VBp;8|wvk70Q17F;w6f1{fOQm<<+;S*Dl$ z0c@~KZLI(LVAb3*2Ek;p&&&9Wvna-QSeCzdFu?UPrenz%>)lw!{M7dxcP^6qK9~%k z*22$m3HRXJN0-`Ku*)9XONgc4|8kqvv!vhg1%wOZ?6IvI#SS63o@ec`fBAMiYxlb$ z&kp|tcHHtA#I)Q6TvLGp^_wTQBeciCZtrcseES$Pf(d|4fwOPhg{&4&20lQCzTv}@ zu?J^b3&DW7s}3Evslb@B1kM^RiF3WqF;C#QJ79lgb3jixJCm783S1Ly6{^?jrB2t{ zFbl310EKV+05incdvoDUp*lF&5d&Kbp^_dFJN3O|_>4VDom!|p{?JA?mLi}1>>Z+C zN0B{z0BrdQhaiS|jzesme}bed#K`l+e!bGMN%0@wPU+bF9Hn#R%dE=|>?k8j$v>A} z;UR?w4yASNB$l2a-r>L+Fbs`Eiy?1ehm!GOqDb?-W}dyI0O%1!Ph99_ zf2T{BonkbQT8|IJ%CU6xkv2bmQ{Zie+TFOzky%~2;y5`pu++-21oKwzln#L%mpe6CQzWX1;tqi680}Ie%qcpHNhUtDdwHnyz zKp_iw845b1A_dXDf)gDRfOmSKVVod|#d02ZSlBpOmk^+`-n3*~6UFC$yMxc@hEi;# z;L9z{*f-QsG;pNaylo8KZ((flLs1Psayu+QaPA9NtH3S=n7U`et-++RCXWI#duPsJ z>jY2%p<;hNvo{JV_D5%jFtoAdc&ZR^2|5f4SDI7kFF=IxgOK1d!Az`K7&h%f)nmr) z;f{5+b12#I+CgWO4 zlsdQz&AFy}lHqO*jjPflZ%fpB(Z36%Q;m2Zs4^#DM;AyZ8SXyt~tVfhc_f8SYpVrx@)BG}jv&Rk&ZkC~<-N zP~bC|B2}Z()==Slmb76&o9P*2i@tT6iIvdCx6k1s8>FibEdb+yBd|rk4`*ht9{*?1 zYCYipi(4-mV=daBGP~X|Xm0oW&+UF!R!;0b=;AP#X@J6|GjN+2)H0w$;H-LIa}|yC zFwHo>V-}*W-~&z21vsEJ<`S&EEXk-^*IuL-{1yk{|AT?>zj|wgPc4N16&rC^vX)h< zV)wf#!sQ&Q8NoQkcQDGZ7Z#nogUdW%=dH;T$kww>C15ms2^_RDt5%$bb}cuo+|gQY zD}?m%zt~xpzhf-R-@f&-aMrT?#_g8H?swB=sk@d1)z?5ZCHjNhFnnZ*%M9OR1gQ9V z>~)yIbOvq0KlQKZlV2CX4e}^bi1E}_AAW~E4pQC zf@9&1-A}`PTW~0+VdSIJ1daU^NT(|dzOzi!;QmQ;;ih$ur;{i>$0squ9We^Geq#JF zu5d;-XkxbxiYE=V0%-@=vLaOhx<$~T0?lx>L4kiiOvPT`?~B=h#qjl8)0bq?*U|O< zpFz!gXHaGc#eW1c+i;{2)r_Nyk&rcpGudWf1)gIA4V_H^H}{gz%)EOW;wm^J29XRyQ=L=|)<%qM_)V6R50?s3|%G$gF)vfzrbptDNWz`*DHe z@{K;ecf$HVK3M;wLD%QoypKbMFADn(m%P~b9D)Bzk%#5$;!652!+thI=|HGX9f(o+ ziU`kLGK^#(He}%rEC!?-zGK)HerBB*tj8&bv@y%)(V{}M@L+AP*Du=h@H*;j-cJ0p+pxU}{&-ekw+muogEadI5V9?L2{`piMcQv)3z zz@KaMCEjJ({u|~l%Q5cYY?c|uA-<1<1}vz#s`gaSf|C#vhv2Fa0(aVgX0%rx99qw# zM-8~U4Tf)~~02nk-;M{7iyADg$d62g=r6#_~qL{NGRqu>#7LT7`fG6(+* zen&UgC}>KK)=Ax)fL!Y21cQN`m>tN8V|wEGHispy&$V#&4Smi

~_qpg;xGJQN*HBtei?VAFsR@Weil4>YlP-rvKwJypn{L-nB13Di4CI|v@@ zsG`uad%S0xa}73c7#Eh48>~do#RSz;&cwxsryUoT;4dHOv12;+NSm{pAjdWDo3%eO zpZ!g=FC%nYn%ekcvyD+~d;rdsYS}6_{|Pb6l|snR{y2QX7a%^Xn-`z){|MpsQH}f^mmBgN3$jLR>rjNllquNrT35u5c3 ztkAzWpoar;LbJ5V34hr~*S|XGeiL#kD{p-IQznY6*JFZu>w0v!fVfHPYXN-KK(7U& z^>rV}FTH+?aIeWTmjW5O!%EuI+1;i05hPs8hwkaSIMF$NB7wXiqmbQnOQ9|j>e&^z z+|xL-2NVLnjU9PwP{M|4t>7#k+x5Tu05&%GCum_F@V?uu4+V2pHWwnPOb1rP@a&0?%x>&v>VXpU+FXf+3*zDs>-U)W>zK)g# z`PT}g;RAx<&?prJ3KTf?-^Twnt?XIz6$8noTO;}Bo*tR!K9c=5lED>t`XTY|6OiN+ zZS&E0;IsJ=Ngabr9i-p7pA8OPgu(q6;g|l{5#U^l(9PKA0w6KXiD(gUPz8N87{~1$ z+JPp>_Nv|)C>aQtAlu5-$PnpZfV`N&Z5;8OvEniiC*>GZ}Z$ej>#PT-)_z_dZZ&O~Vf8!s`eEmH`*gWA+OWvLIZ{nY*oe{`?N6NRf`&q9Mu^Q) zVYlvQ19yj4KH&ctVB#uyW}bjo{_DSKQ^wEWE)K5@)3DzJBJ?=ZP6$X!K@b#t3u7ZV z1UL=oQ4A5nfIQqx?G2(7BPJtALxRDC0)>p`fqShHdqDv)L=90O6>^lg$QMGND{0S- zu{;!W3preI4M9MU^(u%^%9mjp0#YVvDsW8+)Vmn-M00~%4(Di^aHPiE-U;U7U?-k@ zVR=u2B+WooqG=m07m9;A?>1tfND6>ghO%!sf{R1Dco!<%uLAdU!&OQ~DH(FDawoy1 z%hEd0fS{>=;ecH_BeW8E4KS45Ei_z27e^T+wt`(USO^3~~h!Vzw# zANvTT*W1kEH_rCEV=+&%`A+PqGkmKUsri+adYzqCg zYvlL!{%-j<{+~V3{+!4A638t}JK@jv4ESG1^56mgs|RA?N-q){@W1ueXDk;Isgq-9 z40}`)jc^nb#v=ZUk%&KG9QxkJpTmI9uw!4|sjm$dM(p3eKVtt`=?IXH-rVK7pfns+ zabOVO=nOjO7PN~9rJb&ZDE|hTL^#{^EP95Q2I-CT{fBeOoKuVjr14J=NMk=f@#&~V zSnz2d|Nr8kwX54@)Y$TDO=_eW!5~ND1Expgqe+m)7fg}9 z_l++RAkT>PB?@1n4z0d`k@qp_@my`<-9SWq=|8gZ>LAEP$$!!DmRw|N z?l(-u9x#+p;QjZlXF>Z}(0pcTe(Sr_He|Oo#|a&@4O-tr&%GyX_ch10`gxFRUJJfG?ZiF&~BQFQh}ieT0}@LV9EI zC6}j8I5V!NbkAkM}e;9Zid>k^Ortg1rh8@^5g9eXwbN6~2 zw);7$j4$j>!4W09g9pIO=>y@jZ#a0I*;^Kb`=@=}Rt|=`ktvb>!b_HgYE1=8z|Xsp z<$_@U_iF+8p-a(h!E;56eek|>O7LF6i|m5S{NY-FUbpGO0>Jgl{)88&obW#0?HBPM zpqIGG$nxU%3F&KS9gfqj1;tpOZ~%rmgM zP=diR!S-yXGgIa9XQt&vSP2STI&POBxGbt4yV1ZdLc3uHSkwRH0L}X=`kFOYYyF%b z_E+mq9Sn0Lv5Kk}4?T9VT9pt!_ zqYo1AD1;0-3>~7tXoIh@nE`5RAqs7r>~SW%%lUZ6<377dCl`s|tUWCL-#Q@8eF}dC zPs1W_^V>eg{4|ya9orU%}U;lq@%lSfLvs7IiYF_(m6C-BtW7|Y^*&nkS?^#m%nMP)*XA> zQ1bsTTG5pv3nQW;eEZQ6})WAMzp zIl;4HIdt?dIM|{jK0yck!ZBoqesQao=d-6~4Lc;c;TRaig+}VWO+;3Kaj0_2+X^Y!Z!KI4Qtdzhy(JGceTGRL(xW!B0kwI{CuS7H6bEJP^ zrv}_02J@UVkd)p$#67XaizWwtE7Wg-gDh-t0va}VqZ@j0ck~KZf*K$(_ostL4ckD> z0RcEklVKM#91(>|XrULn9&Dj=3ghHW*pCZUE{*Z=y%Xf^pFL0@$K?BwHq6JevM!{2 zOfS4OMqGYndjO}qoR|)6@vwUlqaT6xdVTxXb5{zO-FLF67#%U86T6xS5{L#|pNkmI zRkLs0Far@jTi0EL>N-`&~V)DsQN9ce)T0H`t50dx0+j8u{&O^tV;i{~LnML;nzWaTN4!2B@-1;>~+bRC|9TODJ%A3gA(}EcbMe2 zetwSv2%wFCg3dUq3wC7}@=63cwLEaJ2O$=SGxWi-<(|a}4zBr3of-7P1a1 z1DhFf#?r+EAignoy^G5NL~s77hc5)OAlCj{GskGKKf!*B-OpwHR* z>4&oTkuiX=?Frv1VfOP_41*N~;vkem1^(V+OGJL~Omx%=+`J5m9P~Fj!qSdI{^$)r zbD8irY7T1e9X7S5hS~Is`%C14^zg|M zppN-j*66NS8H1}Vs^Tf9`jyAnm__{Jtc7dx$Dbbo=jv5=`I6a_FshA`-D$=<0@3vX(#1Y50r@$5 zzpn3{H=jK5=FIcvtV?G=TH3e!!3lIT)%)bhd-mA@x9VeK0gHhD00`si)DoB`5NCSE zo|(s!upWHo#-s9Qehc*V1O6x!|HeBsw}fM2-+k*Tp=(m`t@qyX!!OR1FK@6vzyIv+ z^Ly!VetY@kUDK+jw``-2JnN@u$DAomZRWc0ypON``OpC6Bk%hfG5s(I_4g>0?DV#n z@bm-kqvXH37A4mmEmM94q2?SIY;XDOQ#poz9-^XMlyHN8?K1>0zq|cg)$QNH%~j@I zQ-(bZz8dIEtf*OOE=?H`o#$j>3k__XqzL_RuoVS7kZFw!J<;~-&<1EYqSCm?`)vK4 zFc{rN`0~i0_^K(`%#Cz4GNjS5aA23C(<0&Bwz5YS#u~~9QQ4vBT|X5cekWww7b{5@ zXmnJimr^8E_2B*27v6nG9;ObLdNLFgTS3$pEOoeT)Oe}s7MRu-kz`HT}{I?W^ zuG!qW>ydfxFT=I*hc~{kAHKL3)&Bt;k%4`qra*Ur_S~Z*Q@=5a-@%1=cT^OvN!@Rp z`#^AUOKoNI$nLg1kIeFV)7vH1Tt=&H_3YHFI~r%~&^6+95XZ-H`^R1gS(p|Es3Ex6 z0xT9t`MT8fh1Ux5b8td6O7@~a0nVv{C2gEPq;YTw_ZgUxx>LiSyz|RlOMj0+0Hg05 zaLqBwJ<=xZton_Ccg^`u-H*)nKtv$yTGIJt{Kcj=?D*6VfW483_?n{_EkxX8XM(Gn zLwNh%NXYR<;0kwz*nH%H$c_(9+=!E3crAa!dTv2?m#+J`AOROwJAv1F6mJD=lfePe zmB#t!4X|CUR16rxaFzs=<~x*wE>tj5V@C8GjBJRqfftPY0;u-8@YV=%11H|kWiahU z*vt=p03$%bAZ&{9Qk+8R9J&Jw^P~90@GXE{FQyl;MGVR)!0N}P+i(Qv3>b0_qv3&3 z=nu|VI+)EKo9_=#G7zx$pa>yI0yt(L$~&O!!fn~Bkko_ho>MlFI|=YEo;lHgz(vXd z8yw^LBW=?6UkDdCrx@+lu()i)+(~G{1<;8GybnxgH=Y53*Sn#?)w1Ew zcEO{=wMsa-ro#OZi2EUTg>Ox9Ne%OaG?!ceXI+FO0$d?vZhS=Ep>-x30mmeO4mR(K zvYeMkkIQV-O<&%FU%oD z{Zu3`M5HaB?Ow|;f>4Lgu9LC>B6PeY|LXwM?hB|v3Een(v=#gM?hC+wD8u*MiQ7XK zF4Fli2rJ8iqzN1etcf(X#{>4Vq-dyAN(SQ^)Us^-gbFV`#=S0xdy!?0S{m27xEh%w zUdS8t35_8On#c2_uJS8cf~qU^itRx6dE^mcYiTqPfH%SgG%!Pyc7&WIiui%q{{mj? z(E{+wz(v5Lp?3%2!;hLy$bA60QD2V+ZxrPVSUtFWhhomP07PNM$6ojsqT?9T@8$_X zWgdDu3#DUR!h^e@ZJFx1xc@s$-e)Z7g(2k6Lyus1nR^s{q&@V&QeL2CJ=Y$4?ct1{ zHv%_5e-gNeKK6z#qQ-AXlbliwvk{zJAc_M7H-I%&xBFCux~(6!41y3y(@POG#o(gL$5{CBTCHSQKxpMCIb_k$v7 zWDh~7XbcG_)FR#TZ1;IoMvlHZeb0BFGdey+B}>o*4jz}`y1Az`p%H)(ILDX3ANkLG z5udJpzWV{Vc8gY@qP^}@MS{6J+r1*7gVmqyUWZHh7?A*R`|Kn5hOeRY%i{Fej`8=P zc0={oKzT4?39jk#cTu7Rd^&&4xU;KjUfJcRCCXm~4-*_bG-1{M6yIg%=XF>eMtRDt z848Yu^Fz_D4BvyHr{U<+zy*4bs-yQlMOFJNIQi|_zoU}7mk;I-*`>AS2Ov4|+3wAE z^4t_&1PX1-cq8G^I+RElTlj+k<2H=gvR%DXyPxv{!*jVJfBIpL(aq=6X~3 zG+e>|vWZM;1b@?kQrb6%52?nmogWn2T{1Kd(4qWh+)CF+!}f|SBm-nY;7Y}@K#6sk z3`Mq8zNObTt0_@z2dH8#R^22uciZYbxfyT#HF4H$qOmi>bZIcG!6&r~|EuO!xzt=< zp$X85oRDkv+Yzx5qRG*k?uQ2jaXa))%b8qxp6RA*)La^t%dJeQm1gUeL2Qs0GOfB? zZMQoFTgvwb8!4Y|bG^kh(H!uLSvQ^v$P12LwlkS>zgL;JW|hTU$X5uqUT%q*>4fIW zgb*a^QL?=z3revovFq`2SZod_^U<6vj1mc-FB*#a!l7A!Ud5A%^_WQ{qKQ~68B9hM zkz#9nwpie^iEeB<8jT_wdAb@-3WXZ68kLuPwoo6{a^bbi7Su+H90gYVpqZ)Hh*3Mw zg(EpK=PN0Zac-2%t!uFoQ%|Vt;EKq#C@!*$>#3Ky^W8;jJEsMRQfN|#h7G5{E&LUib##5zo>J*o$}Z3xC9Mryf7 zMgoCuj-fKjl=0UR%c4^9mC~b>f8~qLqf{iiB~znND!Puv7W1XfWHOn66biIiel5%K zcsv~Ds5R9{YGRLA1X{BWmDW~ee<44gEa#(bG}7!AhI47eMRH5FH=ailVSXl-H}ux$ zC$%;$i+nbx<InfUhy>5=sQ`J@8&k);DD%72?s8u3Z4KwM*rov@=0-4r$ zK0h0khoqct0tIIpW8Y{N<@tHM5s8&T_3k)K(xXrU)?z(waBbdKh@``*X)?cVhUsl6 zlB-YCv#3B$3woB$4RbvhJW>}z^T3+r7fM-LQT`ga%CE&jBb3Uk10tc0Mu}}X5?GU? z$XZUPbYG1c1*X%Rt#h@>7Yg-SDKD;hzA(#W;*s^5?_|<6OmeNHr*mJeHVRHx-AQ4d zBUTZBv74!n5~To;O-}XIMnE>x!KBcr5v^8r$rlUtQYjyX`4-edhK#J%{2-gICxEDw z?6eSqmj(G1--Y2i+Xyu4X42!tvAK`vLZ-MzYhNLAlYFV&*wnb@q)yG&xpgkkRy!(J zlr|-9O)EhdXj_`ERW%jmr`6>)v5lAXav)NVm3&2c-sIPtZF-nm>v4sq(xR^W3%~~p zb-<^gZE;#-V!=SNu+B77jd{A4s3Z!c8m^@qu`-vfaS?f|(~;#?3?!)WJhP}Sv_ZF+ z)j{~Sa&%uS`nN0}<~cYRZV?I&Lq00oZHB6o(u9eo_4t;_r#Uv8thdXn;xes7wtQ}) zv}#OoIQQ#*ZCs6%{ZV3~NA=mHNiU0wk-sX(qRD)p@q-Wu>QUOC;NqcTlVxdApT_(R zvKgKY{o#5m;Dc)%MKwsq!_t}_YW`(OjQiUDY;rVgMp9ZlJPr2aq0K~2EPaU%-ONNr z+f+K?V*|s)Mqf5_G^ek8mCP`j6I0_vX2K=6*>xmdW43-kQOlnxg;HxZt#PXnRWEDI zps9psLND4c`bx}%8IMRZtd}MurqQqV;?a_rZHIY2-SKk@;aenEiDk5+b@>l-Q{Q!WVhl(=eS0?xXwt0(b6}ZPeftRijT9zYQhW?x>{gD zRA@NgQrUW{-003Wj1b~``B9Ba%i(yAC#ht;sty-{VrH$>8_HJc_!XbXPq(pZLk?t? zi-g~wYB$9$nbm|~S5FJ$XmX%Y{&*H9#)kZp61i<`D0MOPQ6l=S9f}W!4CAX*^VM=B z<4>jI_Y1+$T=3Ng4P_eFDpYS- zS<lWW8aKv+5fXZ2s>-Am5owgA z%cFj5*kQKIC0`c%tBP3PthV7{z01}5%eXw3gGDM7lEmPe5@=mWaK1Xlhoa%F2y!N* z%F;U0?v&c8IMYdS)S})?>FM@zJtr%=wCvXlai$wv$@37~o>saMS)WlGwJOHDlQvmM z%@Gy@Fe8#jT;(COv01kk`4^>%XMavqtgMA3sLN5R#?u;`eN0Ap9^tmG$&$7 zvXqL`$x#oQX0wHGxzeaFw5k}*l(&>Nk%t;9f~sDZ{PMU#5?Z#L9L=C@YRiRZl~OxX z7L(a>b`VvD~(B?jS0n$Ezz zb?+^H^PKU-=oH=|*#u_S^-w3!7w2;p2k-&a zA^3bZKJ)d-;CyD|H%l;Foh}3wVit>Zma%+t46kS!G%j#q*aJ}?~O>Ank zz9fY10uWC2G*aztX0t$@&}DL68dbqM84CO=v#tcRo+gGCqfIi94c5w;MPDwC)5U%v zNv7&uWwn^L2L4hy-}d+Cv0A>&x5sI@60UDretog-4u#Z$kebyBH<2@XCm$6jiEY7` zCKFQ$)M~K0?rrB$u_Eh~yeMgEdnu=Kn^{aI8VhBig@f#>lPs}WVkQN$Vl>-{rnea? zNVfRNtU(3(F9ZXmpDDxZ zXA&LiDr_#JPNs5O(Iv6G?)WPeSs}P76*g$AQ%dJD<92s4o_BKzVq03v)FM{UCaGns zLC$Y&8sfR2;;gpjsX5G=9eQp>G0UyJFCwP}^Cz}eE_ z@+^?+NMb#Z>aT(ffZWqTm6gQ&W-@4|s*eg+r6;AliR2>dEN49zQ$aqg3I!lt+gXDGMry-I*U9Rlp|fPoJb^doFcVld&dOKUhx zPmmh7t}NL)J+7BWV?8h=h0(B)*b383IIA>k6G|Kl!#r6Dm&^HOuiYK>xeYN@z&YYJ z1tq?0RX8e4D85*CLPtfMkI6|T?>T_~h$ zgJifv1xJ2v$w#Kel3r1AlR`yr#VTA4Y?*F=({w+r$7wFHCYlP^EjkWfezUe&=Dod$$xg;Oe3BGi`}ks@%X9O zwe?7$nIhCwO{^(YD!htI(@2J2)ra7cM0siK=Nh4YpDsl8P9Z4hDjNe6NE4{)IK1Y3 zU=>fcwPhm`5kpBK^wt2ra1M#?EXZ~TQO$(!fR9R2MS|9Wx9WGVsF=~;mPetIX%qH!Z z!gRWko{K^!ovla9T`uTL=|yU!O_9C|EUJ+?1*U;d@Z}18a*{1}n>o#w8n(xq=0J-D z2F+x@Hw@0k?es7!B-RVIJP%35J_vzqx*B2ibwpk*q=YXO@5H+8h01Pxim(vqMLM!w zlAsI%U0=Dyezb1~GO1w(<$~k{DQY4y*S}?I`jzu|KS#-l7Q+SB%Z#Eq{z6dw` z%YKzv4rRZRLO89@)OOQptrf{mPPPm{p%8mo$PPY)= z4x7zZo+P==axO-bn(70edDw0SQu$iA)QxV^1KJl@0?)3Bl`X&JR5CsuBD;d<#JhE& zTdq(Gu-9s3TH@o?{32Y)PVyMJWu~IEYyMtJOHb%-Fj3cHsytt@DYBtuhud0pDzYPC z80-X^G#F3XMoVr4rX_(O4BibR`|ucT*Y z96cN6rtAEgYR%)FNMI226{}d6rn5!xE4GEXxYo+!xv~v*2&wCDFxd^5rv8-1k0yga zp(!*=ak-pn>LCp@%_JL7=F1y6ueTRV^p;%$2u&Q$#lA~ZgeW4 zcA^_v4wvEnT%am+r>X(o2WnVbfzr)I$EkU%$g*QHu_1%iXsk1i50$!aF{y3K>XzD; zw&f(F4{2?yCX~)NUFyt5i4QFV-+Z;~XXfJ!9jhwCdT_B!wmSZLIOUUz;pnOyuV{0f zU2GXH4_2wz-bh-O-sZ_3D{rU?#9o$}j$hETlT?2@iPJh;)jhzE?n+0$&xnV2N2HE7x{%!?Dz}SOffniiVU?~*CXAP0D@vx z>ePxQB>{F%e8o(}CKn7%lm2G0!-OV;Fl!B0Yd@hx{NSieXgWFE4!iwESJomydc|ku zpiKD2SyANsGd5GIL|O}RyvilXkk(P)wzFuafy_hSd@;`U!ogTnr`mk1I}3&UeIi?1 zG)JXyVv|+0Scz6TP}$V)hT~&>!6nog2UZiu0ZlZ+k+Bx-mFPge!7um`pI72?KiOg@ zT0Wy?8}pjPl*vSD*$pWjFs<{T`wH8oAVk?d&}|J|p8{7>)~h^EFQDGP84t_d2-joc z0j)X-c7kys5{YKPMrE`*nNRhHQ~(K%sZdVR{r0%u($U_*_o35fBf$6#1Ti-iU~Wci7bBT}_RZQfXmLnTu4kAk#H zSL4vGO&6Mp23RS~co59M=7#(P_|-ojEvKwbMX_JRWu@|h3dTw?CDtNBWih-M^7<&o zC-sE_HhZO_j1*pJ4Ct_`<-+6CV!R4~iN-9sO3b$@&dY$mj(&s#as6KKLZjUZpQ-lgU`AHQQ+&9H^k)Gv<(| z`<=3{-P2+VUG6k=HtFxQg8tbyERBGhk?%LlHE5LxBx78;oodki;;`lO%Ol3O0Xdse zYj}M+Ww0*m;K$?#b%BxR;{Xwdc_8C-Uv z44A)yAWo`Ub2y;u@|Y7WPA4_J zk!+P4kOpVK{st#%OYzP5V%^xV@n`@n&`NmHFK4LyB)wh55@Ix*jMsT)7|b=(srE1u zD)kfVpepgBV!B9{Le+R!3C1(q&a$|yw1?qvw-ZbEsA4bxF$Z8>aGKb;PG`f3!C2IK z>^9zyOHC#x%!ku%qB6|JhnY!rPapKbaGeZW!L=sW>dgV@FQt@;sDWsu8;jODQzbzT zvi^-E9zx-N6wR*~$il;H{#>7*i0!h{^7$XK$Q*ZQ$awAq>R zJ~~pU=Z1M-yRrfl5A{MeFfFOE2DzM$b7OD={AwkXk9NAbwWO|d{Y_`qMYO+J%zgdo zG_V3M-9Yh6FtSe9d%ct&6=A)#AhyNOVz3C`Y# z>^5pLz3D2d#KnE<_#iZDiv@w4Wk*|*gt%0c4Q&!qZIfmeVEWTci%5;YJOez|n+;ZB z7t2sZS1TMj2y{T(Z&%>~_`uW3bUP}8-!N4=ky)U?ko9q^CB-(Kauj^&#WpUd8z{z| z9?Z8zB_7L-CjBm@(_*R`^~r51I;hstOArF(Qm&R6NVROgJE|<$1sU!5bL|GHEqs-f zQ10<-t)nj?Iu)vsiQKYNZd94hCO;d{$$3J_RiXk<#$q{^Z7jFV+(=z7XH05SA@o^C zi7qOUkzS1!X2qH>TpKQtPmyT(D7Go2`BAvCE<~A5A-MokXzue1OpoE~vsO5QH9B)Hk7P{;}d)beX=C_xHL=Y(XZc{A8Q+ZS`<>F^~3}Nu+mq9yFxC+lSoA zLSAb57LFyX!;{6F9cj@RU&T(kkYbz9w*+J0`6rnWI!8FJ-yCDW~hBix`GS@6~T3Sui5rOnc4smp9B zEiL7B%`cAY-S)6P%Z39iJq$3-I8arY&egeUOO}I+8lQ$?Viie{yYum)s4W^$)FW); zRW>r0XT>P^CiEoHD{#y(R%wS>Y2^HE z2o#keMiyc@ADJPCgNC8M%8aOQ8!}faZDlRJ%qo#&K+7y^RdG~Xu2-O-N0 z?)BK>V33^2YBCrn7NSqf4(L8nSA}{+8uWs*u!8+vqEnE_Je5qadPss0RD&0he$lg| zQd{v!U|)dKn4w^90Y@%I>K(;SPL2i)Ixd=BbLbM=HWef4Sx=obDd`JjaDmgL& zmlgB9s&6qWNlH6VO@{b#Hv+!XYD@Ood5IMog=Do`oMcegyin_^8Fjl{C0eC6xAWx|u{ZJkc8zyX|X4Rp5i`SQ`A)Vp9~QhB_1q z%dKB+6r;t#YBd?@43%1hl(0Tt1dAaW2!>&%u?@sKm=QV5b(^2$!fqiZucRj;_uQ~ksdHqPYcXf%?48gLv!LEcKyLEom2#oTPjqT*1%b+ z__rag!K~tB)4!QVbV@5txUEh``EnpvZ4Ab%QLQ~s&vTRdd^=LB+@Q~pni32*eJn$* zw7eKgB+}bpa!ZHF>*-S?vW(z5|0NE(`>avBlt5An%N4hV^hPbWP-o=D`A@-|m%LC#hUr?#z3cNT@nv#5l^`JUpd^r~B- z6qYs%Q7IA-gUjZdd~%uW!F7|3d?ZQEa|QoQSF<^83%+fT$^=*GaIsjd6{%tw-1HMH#B_y(ah+0Crqrnx~VbU+`<$FeCKE!v61u;DpTD%NN zXow8)@t7J5@QUeItyxIEPNQOol|Qze?satsC(TEXI(^O$Rhh+UI+35G7%J^gk-ql4 z>l;N$-k*{qIdM8@pd9~5UlF6oDoV9S@zpXhO_aj5aEeVxVb!0H`ydJB+k{YlzeMIU z%Xoj)VB*1OqBs!;?dZ0Na_C)drO2rQEkx(F)O;e0+SRqh>$Q%rsh2v9Y_sNX&h=ho zlpE{mEgdFX>*9JjuB)N7GUdk2M3@;=e92WIF4jn~u$c_E)nPhX7$^MEdAqsFQq7TC z3oX-YfcftY7;syYBhq~b!%h|t(hdwqinp9mQuRSf*RxxoOo{uXa-6m z1j@rz+aWy0~bvh6l2D)>*NH6Xh z{YJo~cwgTxH|MxRqzniA92+zQiJBNGm#ju)U*aH5q(%x-zK$KHHD9foF-KQzRZ=>m zQ5tKwiX*;1N9=t@*bIl0wJjDOB8|!fZVf3Qgb6WdJ%ZFNhTuGOo-D`#&FSKfjloK$ zQO<*4d|MDQGTPytF67cMb={R*HXCL2QLRDG6Wnkd9B*TWSgssJYz;$Wg2oU z*@h4c_yQ>T(25#3!i!GbL!HZ3zsIf?UP=#vH^8?Xl(Y7fF?YpaSo z{$b)Gy1O?jsicMb1FQ_zTCPpG-XKRToEw2uxvoSYO@wPe9zeJp)d{)325HBr z_tH8FDLzC`kWp49NCI>q2}5Afqo87Qvvg?MWS+M)TxB>mn>(|H6O2}Ls*2!`Kplu~ zj93Wot@%N9!!{G}eh)gemK;|DY@ihM_aM7Scl&59SRJ}PBre6+LWHA~Yn@hSkUz9E zYAN_PTM{=87qCH1du+lrs>TXw;DK+GGlZ){0*+2rwv)yp5xO#waO=<}lLOegn0BZ( z=ILQga6_Hwv$(`@2568~3Mh@e!_eZ;nnU)8fiV~p2d_hWJVn&$Sto^z6w>OnyW{F;TbB>?cB6eIo)oV-DV8bY z1>`ZgO=^-&ArES)rMjLC@$#8l?Vl+;qMWCVi^D>~_C>^Ce_O+CK{U zn~)A!`lvvrWB}RXQ2rzM^5qZchN;9(p2hk3m8{Pn(tIfNxP=osU;c@gKWOMyqySFV zmw&v}-ummua|-Jp|KiIJ);|e(u)hobmhxd={>WXfsRn7I(U<-A@+{kb_>~0N|Kpq> z`ykQwhl@npV;f)1wEYM9W8bn*>9xmdIep0gy*!!m^8LJ(%g0~-P|@-+1@`^?NK}yk z{HwYw3{6-X=HaPI5keBsM?r%!uG-(^XHKYCx1ATEl{ z79|OwJX%rS*ZjQl#dq`4zIhp~?|MI1`Qq06-1`h_Q+#Rf7ecAD zT(;g^6gY)q1YxX(5hOzurH5a@fS~S+ykyu57=`>JJOkxbKd->&Pj737o4n<`{%}z= z)r6A8`S0cNdyxy^7v51(xQ(DrS^+Eh;&|b+T=pk7N2vt|Vqe^g<@_-9YiTd-Wslzr z%jn;FAm^@0kcanNir7+h%sUjJ(v{1>{SP0!?2UwK@b}Kcc_O3`sy_x*-X081iTP{4 zUSao=m9G~=dr}eZzFo5LpFbxH@8^@KMD+3d<75`o?o8(K+a;O*{d1D}^WPC_{d~y|@to|u_whX=_FsO#uxd{m+nZM#DD8^h5BgjmdgvYXxj*t#-*}}ycY7{) zYwUj3JfeDlBjc-uZy&$$azy2Kr}vLOr1w(4`(t0#@9qlSUb1kfoDq+xe<$tly!Jjk ztA6*FK<~R=H23?1n9HuW9_{)^HN1a5AA;9tcwt^d=3JTbsGjA}7%y@~4{##DKXY3Y zy$B3AD6HkG+MVk4qEN(cPO8~awJX#(IEw6^YTew|=RUvXUPb${ufF_#!N0urD{Nwi z2RqEAxOhJ&{fxD%6;^+MRlA(Y5IT`w>nAUGLHP2+c ze4D4Pbj{;_hSH?EmrEBrr1WQwK$!)+w6QzY-8)tZ{{!Ft17$;ab72YJ;YA+J;q&hI z$q}&{3Qi+OV9TRneC79#0mkw(C`lK)DmXn)t(9I0#@rX*{Vd!C(RV-i;I08EWBti- zwtimu4*nrR7BBe@?tKS8UIrwdFCMg9;AeX0h6@G#SsK<2CsIByT8$^9(I>p6UQmKvuaxSPJeIY7sLdzX>_9uLrYAs0@n zzXbcq>y@rYCFw7%&obbCxt8J||52?}NFCf9IlNj?%uO{wke)D_a{q^N>-Zo?^J+}T zAVpsLF|S5+qbu&V@P8i9p{Q7YFHzxBQE)ylNOI%nSfBt% z7s8RjV?^eP5We3MUwEaOaVGn+|@`lUF{52S>lS*2AzMRlM^?&Lvb4gOpnl7IIFQX=@NEj@*cA3Cqo z5<#VlSK7XuvyXxhOrCQ>d<{YfB|?j@S4ez(CoV0E(oTFIn0zZNsk<=BTRn5RYBtbG zuh$GgWxI|)^(%h?B-Sg!tFQ2~m7=J3q(6S+CB50Z)B6`6(tBZSzWnd*-Ek)~=bAh2 z6e}gaxPeXcY`NiJLqP!Ui_f66>F3}5B>#-!Uwo&y2p?|s=%2}v0>2ucy)+16TYKv! zuLXCHPQDW#r(N^^&n#X}lRxq3G-7@806~A_jhVhW z+}N88_a|?)kW0PxmJdE>|Jwg%-ZAC1`HIfHx|ZyJ_xSYx`Ly1}-=uec`-flI-|pA+ zl^-vd8m>PYK1?aTmQGii=J)#ErRMSPd{y%(REwX#^Kid`Zc+GlKl|=Y*(HARh`W#* zW`6D#s)u`YSl&i?aL_IC!tO8K9NoR2eNo(cc8kB#{rmDa9^vQlE!?8t{Oyk^zmIAO zf9w4pc%7CY{Ug}VyEzP|1@27eaF5X(tph*3RZ<1&>^o4K9^`T!I0V>ED_Z9+6UY`T zVN>SNJ6@9G%NG!xg>jmz6krJYI(R?ePGvL?DmtK$;+mzqo;F&ftQD!ph;f z(H9R!88nI`K4^}rxdn*J2oQFP1>!-Ddj93c2koVx6toK?fP#3%1U=T}xa4oD6G zo;!0ty=~>b-ZE=9;1YT`4Z%ZH(3QJ=?~p~o;d9?jIW#Af<#ym-9nKm6i#NGJ0;uEQ z8}^gL4NfQec&SAho^P$i^$!zPfFJyH?M&0 zyyWcWjQcJ+HV_e>Rg-F;`B#4&W& zH?Qmq_s?Db`B7GXw7m8}(wvz7%Job3KYvd4fA6E4S&7XzxcLgxub+{nPX75PZkr`a zpWM_t^Km(wf9$Ip`Dv7|{d76dfA~2E8hdN`QR>cjc=(+=5T?uTyehd$^t|GREAPA< zjzO{Fo=Nzf2J(3uy_^Dn?m4Hx@4PCl%iVhYhAZ9r#%uaVALs(5w|(WOEAP1+zOR8I zaq9Kr^JQoK2hZ7A-@Kx*l!(9j^HUl4%g@Qc50^Eob4R_rxO|1+#~t$}rRCmG`}I5b z^glwUy`y9PADe>u^$N%QgL6;BW9ObqH=H}W&?kQF-Rb+iN$19lWIY-yM%Cobhlz>f@U`C;sP39QnjuE-m%SgHFFbFTd>C_kQfLp?}mY{d(TT zuW?>~4Q$8rmXm)zQ(%7+-VU?px99)8xBl8mxqhwUUmP6#vFyq_FNZd{AKFuF;%z-0 za6gJ)q~}4v1TMl%$er=75^P?TuJ-cR>-Fc(EmqFYJbie7-@kUHt4qmPwHerc3F z!U_Jhub+-}7r>ezx{h&+`*;Av7VcvgMY_hP#q7wFCjP0Xv~@qPp4bk|Nc6#sd>}+$ zpB=zFc=)x``E*Jf|Ig0de0upSb8=2MoYu?Z0;kk^N#LB}(4~I^Tt|7|-y^fa@EtSa zTE_zp;Qk2m1I?%GIv82y_NI)^dWYqAmp`KezA6-XxJj%q25i>st~DswYWZ=|OyKVU ztSfi3gtxi#qCi-F@U|R!7&3PBo5I6%ff9XmUfq>CcrhywTW>$mA=9sjUKMVWJns*p z7^$V_ey+-=*fB}SRra^wQHqUIb|1`64V)>hZv*Hn98kPDyLuoN1xGRsa2IKTadNsG zQ+4xaFOiYK(EyI97`iEd7V_Q#e8l@}r5?Oz9ZD!b{*vbS@Ic|=y88&-3y)sw-}7R@ z-+sVKOXOXihJ`VDFt@L1u~+W-y^l_m5@~O6^IKC=vXNWQGbKv|KUa%S;p%4|Ss^8I zAHDSo9hV#6*Nf$L66$x~E+tR&V4}RyCP?0If~QGTY=S@i+J#+W?U5TFW$bIPN1WIy zK3_8RFFYqxzq?rPuh@%9JiY$D$6111?aWgC`I4o7`8ip7Ki@s?U-0ty{R)Y%-!@8% zm3#75Tq5Tg8hZ*at>+O6C5E1>#iwxf%`01biNvcvUwPl-I!tMExYuFq{~GEgow5f& zi@V}+IeqE7(XScbE2XNPXS$n&id`I20MC#K& z-n3wA{x$$i=MdXsp+SPicYe{$@lp=PjXei4_MPH5E%e6eld!XqBZ_uGAUgZ-M#(Y5 zb8bGmyL5B?WlH6ybu0@~u>Dc~2wJq2$3btcJZKs~fYkT^`xsEqKm6I7yqB-Fg~0oY zme3EZ4|7oOJa6zwm31PbxSj`6t&gIQ?vTH8YF~r_2LH{a|86VeH<$iz zF8$xAOaD^g{cE7`zRua5X@P_V(CW?loU*G?zj!U2<(@soRtBQn2RDMuQ(Ww!I$W@Q2lS+-+qR zr|K(t4^@(vez!K++Vz?>mRcU*0oFEcfTZHW80|IVL(f2sErDtV%d(<@#xXlEMmkE< z-Ui{b2+>(2V5!VDSTqp~lhU{8ep%J}{Xf0Qj6kB{DY~siMg;a=#PR zHqCL3H#;I10}@c1$yh8I(xXMnkr`4|Xd)v3H4~{K*gT4A8qiUPg0qo9stG;v3^b8w zwl?5Yae$7q6t8zVTiGrv3v&%GJkaSfu6KAkW9L8vN36z310xbV7BhC$RJksR7}ME+ z@DPSVO?hnqKbAObL^$06+z;Ixvb`#{SOm4KNdgSXi0MJ~{X;M#peFj9_ULZbSk^m) zNz_T1r2w@uZlh)r;0tuMs5ONt=NeebqHURQLuVSAyt4ufoPZ=H1FG1M@KwA=b`s7s zoUJG0wyHFI=yyTxw6SKjmZVfTO!QHv4u+z+!0?vquxd042II(wvFHw{3b`Djw7~(2 zG2up@fVhmw*-I`Sg(As8WorftId3(Mc?ICawQ;T4nzpQrq!W@&yE2r8_Lj-8j>C9% zS8G6-$ZRVhOmM71V2t1&acg>ZGA z6WEMplcCxGmdd)%0P6?@EhJ6-6mw;6_Rz;2! z>Sne`eLAGIUMvT*b`~NLie~|VqIkopt;b_10=@7X7!+m)1TabvXI{IlMABfR5bIshvl60N`r0q75Rs*bxl4Ju=q5{^{Xk$rI(L8YIR?IE~aSvD+%P^aX z{1}j*_g*%4Lun`n`Yg-Hh1T(qL0Vr{sl|S!W_C4TXH_iJ2FVf!P|yXyopl+EFYqo|NnLs{<7Fo}~7>xZi=jhyp@9+2Gzy_Cw6X_$kg$caBW@p9d*skJ zBoiR>dKuo?v$_T_D;ZVqj}TF64OS!*&e{~&U~#0jQY|)Y?~}CdIeVlU_j$wU^#Fr~ z4Qq5ZP!D0;;~TY1b6Zf(++Jt4P6jH{njZKGyF&F=2jQ`f8h4xnf?A_}R-Fw8d(Pfh zk+vK6J({Cp(WFN89Xm-$*0kFyA4#FKoFI|dCwqy^Tf044?b84?*Pf!wI+fCl3DxS! z=E0;4TH;u(VRw-c;GoY@DnXf~;xQq*WC4mh88tc`yfGqClUv)vQMEA?S{;M*BY;-{ zNR&_jaA<6WMfM&LJ(|JK`fYij}a(E)A%fwTAj&W)h4^ZbQx(!1cOa5tyZfH z!7yFDgQ&(HK^huEbt|sYn6re3wFP8}MD8F6*p%JVOoLiUau;v2+1iRIKvAraBf|yY zW2~J;UbPceHK{gfq}u~&WRmNMA%#ddEet$qXLp=+dt(DKCpSuUJVuj_95?{ZR*O0c zmbInYDl`B<7jIek)LYaKOe>g$tt_4`r<>J=U2(GmMJ{&pUQ|2%o-lGJ(jvt1I!*J9i6@xxp@Ua=vi~X> zwyecz6R%#kx?RsTcvA+xH44`DkJRfnD&iK!HoF`Q)}8zt4bC= zq3RK_v-ima&ytzj0JPp6Hj_hgK10}9f0oT$uSZ1{3T7kD@q(mfBZjU3=qx(~z>dYyXs`mw)XW$+kvF|)Hw`vU7!kg`_s0RZl}JNrs#?ZY zyL7V=W@zsq@2Pq+YRbncC7=bfKh8sMe(lNG8Vfby%}TuNUvzqSmUdz-Ui7$ zoy;>V$7oHWx!kL=*^Y0H_BCf18FT#*kA@B(Mv~NX06ul-#*%(T#eGl0{}fvH~rU zb+aNWLeh_6%=MwyYOX_Msg06Rm}Bg9NO$ZK5a%Bcjh3Kp0%j;I0SL6eR<{EH^{vwY z)&~88FOw}cL%Q`1fLMu*&7s!pjV)$2qUsKtdUUdi_)1t|m-Fdz(WvuHbJAKxAqA*$ znG#5#DT~g+1(@B$pSsgt6&L%nfbe@B^sPAQ=_ufuOoJi5n{OuzZVo`9u-(jskx*Go zCYi;^(+<)0hX8v6~E_1@g+`r&SZZ1(DEEM%GnC^(tT_ebqr78t2D9Bc_sAWI1vKeOCIZ!w{GCFZ2@>9G@7(2nM*8{ejX#IrNy(uPA?Y%zq zXNlL(a91UqmOfe-tzC^m{OPJUT7n_f>}&w(zRHlx3Sj00RSw(t0oRk62Uc27l`W37 zWo$h17ctuuM|~mQ9CBllv6mm;%)1d!C|u)boadh zTiK`bTKC$Upf4wCT^0liP%+m=4OApYS^176drHHd0T8 zs9T}C72Qsqv0k;9{jwT~F|*?4iniW6OtQ&9)wH z33*QKMN8}leJW9^&2C$)$S$6ZyD?eGR0nM5j;P}LY)GeKD!H&=c{Yk=fP14^#0)!; z4$#i7wC>E!RkX$z`@u-t^cpx=qQRiD7s#whq3+gefW~&$ zi<;D@EU)re&{Jj_5mtggpJ4rpx!5nq#s+3Wb7f)nM5yj&G^}ac^(z2?qwji(ysXL* zmI5yKbfxoj*o$lXrGm@!YRS|AOh+@vNm`5Rx@<22fY8y%14(J(P{`W#>DX1hVdFrJ zCNU4t-pv|qcpjj)4yz88?gdpJ%#glph!YGzO|1>>05-N2*J*@`+sOct`|csD>?f{M zvv!L`4NKf)7u&t@a%)??`gF(3Cg_GpfZzwqNLKysbjA04aVB+77domzKJ)~7CpG(@@`0XlZo9VKxz($}(Zmq3MZ(2Ob5P5sMKvytY-fKiN*jO9AvlEpCAPhGE zlg}{>MNSleP+$0%zcoXzBQ+9lG1U!sYK&6abVpWf&}x6z>;aHpzon3K0J3dk_aEi^w}$vr^r!gkScKT*;x*Kqn9dj)XJ%AwcR5`g#ITbZ25^30pBd1Wd2B5&?+wJ)qi zu}yO97?+lV`B-+D>S8RILUVVh)vB%CmXEzkk5CuEMxG5lM+Mv0>9{k*%R$joVV&8##P)kk+tzTUNH>7~nuRp(^wzJx1>* zy170u`-WpGErmvx9Je3u&>ip3dsVI4bLN2QH5V0x(xE+0Mf{d&TlWbFCD|{j6be>da5;lRtVYWVYCay2{S#cLT6sMs8zXsW|R( zKhHvddQ*m=F@sUxn`B@}?rL1Mb?A^>C3PgrB@nBtCN`jkqs}e@y|z9zajccFJwMVG z4PjgLN8Gk8use%ltG**p{ZO6&Ml{E7)6rrM;K3u`%DV8p)DMs~Y}<7ZmQ^ht;R|`2A#S( zK@&G>50g~rwMb`hFeh>ka~B(`PVK@;PmXG`KG@b_pXga>Z!|FreODPP?sSy-tJ)?& zVgA*rxjmU0>U2pb3-FlHq_-oNdT)yk`Gp41-9m_wTYXvYP3iVl)aQiNjaAp(!}exQ zmJD8==JcEft37cD?;ADHf8t1M}d`4a4Y^Qf-q{f+O@CJ!&E zO#FryEb5!)LB=R{;d;nI8nlM`aylb=E!FosMnVr3Oc44UWcaF7T z*!qIn?uhYRArwru(||K3?Qy)D4U_(QhxQ_l0Pn|oLCvk&vJ%Pt$Zlz-bx^jOD%eMY z-Jb`&YIBlQ`cp*-tJU^$8JOTOY?En7nmk=MvZT$r>}r$YI2bMf%u0eES(U@BOwrS9 zx1p*SSm@Sjmf*W-1^oPdiUw)kCc4|9u$meurqa#XY-iRmlHH?`#I4Qwh>E$4p3T)= zRO!mywIMm1_Qt?6zrAe^Sa3&m+=CK1?X3`JQwpr|XaSN^-^Tbf=u0*oXkeyL`-3iV z_JZ2C=|(%_sn|ydUh(`%V+jLCFqW}g~rP?$rY$}^oHk%Cr?S5bfeN3VIE8R1( z`5F%@gMC<)6*=zF1AWIftl>f}`H`0WK2BBenJ#Y^%xvO}q`jQZtTobg2b3_MTdVC5 zu=iS>4h;aphbSE^u!yIelxql>0Lnhn4(cN5k(rUXWMi;W7jCpR$^L-j(;+BffKO^`oI!GS%I5Q7k~oTEM%i$< zS=P4_c)222sZ@>Wjwg!Y1A6leV+UK=S-X95kkBrpFag;BeajBCMY{zh7fHhz_3g-W zLTR=hfHG*>i+rD!5Lc*sVDLnI4eRR7T}!UHFvI3}ZKnVhc*aZ&z0dJcSZxQ4RcUBV zv#$8*U?a}$n5-T2zPu#{!hz`}3^5XhIMyeV#sr+J!eneC!}i3(6WOjrJZ;Rki|wwG zZZ;h!ZOue+*mPXnI}DVD5Y?nPV9x9F8J^qrTc@we?1pl@sXx`A?`gkP$(jntK^SX_ zowh1W;DSM3u{wRP#)7&O%(%s#;k&A^t@C3pX!Rx-zY}4#9Y8J)_oC=7vV9d*j&|&( z(wR40+^L7?5EFI11v~Ac(rYNvN5PBWFfs zv*ty9TSZzDHXCHj1|3dRy;@0Ib5Sv1&kM)S#t;R&M!Rc3I(Bp$PXuKM(^+3wuG*cO zvnT>Bzeh(w-||~c|6uWh1yNm8=j2`n`g_^XY)sXD)SOG31_$!ro>lrteZkQ@(Hg{y znapU=7S=sDyRHEuQ_QwqhLoBhYyIX7r+H`S9rggJ3t*$$@uI(xr-agt6;QtIbu>wP za<#WjTgqgRfNa}rM~RYj4@-1D;+IG|t8-0s@6LNWGVqyQC7Wjq3x0z-fVa-Fc;Bac zLYo>2Raa>dh(Xo)wz-Z2U!c9&FoYn5p1OkWW&@q*VPL-qfbv}DTYwkplV-m|iV|gG zTWq_7J+0MhR>5l{>`)oza<{idu&&?t3EwBCyCvP34v|!-FIl0YW9F9EbWo|Qj$hq~ z8@ju*EPXh^VJtJ?{~i-yp0?6XZ^JwzAWi zLDcIq$%RwRnb@r@*>{Ab>1~;zM9i#(lBJV$n4nv2Lm<`Qa1dr@xUch+yxYJolTtbl zXy3j!A=x>#u5>qBuUB7h_jM$)=0m*`IMvNUO<7UnHXWKLSD=^dO^OfSUsuCktHT~s^c2T_!~CwFK`}K zwDq{2f(;O{L6q)D*T=yrAGf_=t85zsM7Q=0Mlq+Y?x-owJC)_3k7C_PXJ;h#qE3Nt zN*gAd3{}TTGtgTtVzbBR7$#Tcwvr43!E~dI!K29vtYK4imz}J=_fS)q45O{y=qs9` z_=}YylWmKusH8RBa4Nmw>`Yv(51j$e?btA?%~U4zh5CqA$BnF>brL|x?n#^!H^7&! zE(ilL^w=Q?6W^^>g~0n3j;!WRZ@yel=Ywgz*;#KY`>Eeu+wL&vZ6{0AW4DvuT%mRc zH;Wm>p&RsQGKpZFN?ZqQbBx7D+)QgMXuy-7^fuIrSaXN&0Ar#t+FyD4YB2+wsDf+r z17jqK1pB0_#$@Uu_M{xEoB0s5glM>s1z@Vxaqx;|4Mhfk8*vNVr1{RJ zPhlX<5~Ni_`r;J)P@U$~tIoVmPx9FVYsFMnna{S{7RnD=QjGxoX8~={f>v*=_6CVm zTEqyOqQq($^0a^r)R`_ge2@?aZPed|bD}Oc`zsAIlv$j_noqcPhjQnmm1Wbd6+a3< zh%}h?z^-Qu=naCz4a1Iq+ddxw_sQjR|Gh<3+Zzo7NWq z&fOYgQExw=9jfejfp%S-uEc0Y*HaSW`mi)Iz{7?NgBq2t=){yoHQ5azSQMl+qi@Kw zF}NQhovebp4g$(5Yk~3=4*Z5Jk+NZF7#pO~G+`*vU+oQeOCfITi-?QQ)JVm`w&XJH zVPH-$w>R5aU76{-c(Xd6{e!o^#`}S~7stdua_GLBYu~vOVR*)6VV}j?6LjwX6^(6ti-gMrZR@w}qO}f+Z z%5X7dzL;-WlNc^|9HFskx3a6y%NgYp&6yLetG(TzGZYsbCSbU;a5i&v2eO=IGl!+T z!%}Z9ImO&jS+~8lhje$)?zMz)v)xeK!D2?xXFLx30oXV|LwMj6$7l>W2R7hpwXzDR znKWR*mm<@~%!R{aY;!ka=kXLvE##05CJQwYTd)pxj1ihW#qC!7&BBbet($6_ZDp@6 z%*tvhPX)TUSAD|~9Cs6#gQdE~i9^dIr-N-3-w*4}e%sgG9>_qg>&X*$31H5Ax{yHx zj%FP_jZJ!KPghzum6-Nnlc_Yw(lxvywrvIlkmUpT5(o8kCe7SlZclj?C6CoX5U`f9 zLvij$SRiX7ske=tS&;6WUaP0Eb++Ssz4_Rhw`E(#^xnjY8eP5{Gj%QEB@4^yvfh!L z9*?WT8BVB>5ya0cMn{}X^bqO0fxp`6OjQY8aoQj639q-Bpl!!h^ww0494w_)t~DgU zWQX_(e*klaowR!4yl?JjT}=-I9^yRJRNMAYHQen6I~dDqOCmRtUunjkZwoLk0nCj` z&-H9x?N?gH%p;gxbH}!8Es0fyd4EK+x~+nK;HeXl-+_CJC7qd-OoFZLQA9p3`2na7 zVl6U^xz!vrciwc~oz}aZt}E+y3tUS4IJ7GQXpb2_^|64eLfkZV2DQ}V(OjJe2z#%u zj=Bp|N_jTxW%GF#wI_4%KSZvoD9$LVixxH$8~b4=Xiqa*h`@6Peu8i^p2B*btJ`Y( zK!X4k1c;LZ9QOgADGO_+Sb7s;ua2C6g9$mTV7~?21=9BG=xB6fs zE`&ZL-7E%*ruGLJrRF{za{#k;ChpTUQ=4#X*Khm)b79 zv{sEpYhJH(s{B+iDQ=9T5L)k9t!yzecMve$?6_mWt-8m~=S?}u<#X(Hr?Df{^rog&-NDq61+5Cc?Sv&gNtQI>$2{>;t@?r^^YeX5PX*K``+HQ+B+ucHy~apAV^B-7Fau{Mfi_bq!Uv<>a!-=T-iI(? zAgl?(rgI*@&cIEZEBwLxFSq!Nc8XEV(yVWKdu|7fe zm03c#CNf)PM0GCnY0zQ4pEy$Lidg60ck@B>W%k9liY}O!fa*TTTdYDkggo| zAUKF-aurlSAOT~5!}(f*hZ!0ed^DpW0&mIj)RtUx1UVLvG$0z4i7f@R)f>_W3?dbT zHkIN!cpG~t-U-l31$7cij48H~4P9OrJ$|azL;(qfNo>NkRyhNv6M% zdh0A}F}ncK=5oR$K`Rh3lF=F9f#<=;k@gb})lo5_nMFLD=|nb6Gad3G2o+*0B5Ljv z(v(b-*G8VIbPot!Tc@N969&|zm4wm6nyL!58QsZNjNwa=t8(ZM@Lm@kyWVcPH2Z<# zcDC}~6srrGN3rQ{Ri6o=I+(OfN?I+Pi7Lj?FcFznlYxj~)`FA^BrweuwWT|_Q(N@* z`^e5*lTWgMY;{at5SDhUH|&UeBC9a5u{UPRgIU>2!~is(y~?*0t^+e-ZwVdSU1qX9 zQb~gbEr*s?aUE@qRt=qC7pNIwoIoS{bR?NIh1}~{vhz^1FEuE>HxiJMMXD@ zC%cf~=~A@;GYpviXf;lFx|2d`5~XqYLDxe}B*8r`#@c~wauRLokShmU$5>LCA;zX* zW;CQj<6td7y(sBLZrT{Gdi1J3;_$txsB6eEm1;~Rv@3fZC+179N)8dcG1%i|3xnLx zd6E0s9##e|F3yXE|NxSJ7sdxDz0Wr_R;~|C&>fl}S z>TkSfmLju4hrwvJQW;3+OqkBdmgt0DHijnK>8$E5WCIW#jOiMccAl@h&pnUm%B&6O zh+czYTBT5rtOTG)x4NbbV>DJ;RzNP&p}A|ZC@0xEXERBj$1B#yqCD)@GH*th<3^l> zD4%U@M_8FiL~SUhjBB*?8DLF%rUfR8oH z+L>z3F*zN;3wU}}V`>sHA`;A5#prOou+du6QrjMg} zvb`L+y34Pohe)9;+D68s3O9;5nd}TWGv?}5P!F*-Da0HnYY=3g5dza*q6a4xVKN-n zS$ouJ=xEx;IguT+SyD3>WP{+aaMxkbF-s)1_6TW?>SmQSgH_Y0QN|7#5DiFP#k9s~ zzi|>>g`}m46t~QJyx+qkIyzZ{c_MDtm3CZn=?Y+8b3;i)(*Ek8Lq;9y;bz~h5pAL- zkaiW%q%7u{8tf}fHa*Z?tI;+g4K-$J3j$3Sb75NTAs|_qy_<2>WSDhpvmG}9d#*y@ zj2P60lMY2&o5i@I%38~8WRT)J0@t&Pb_}NCYmgO-%=Gz=98ToeTEa%iGM(*e%Jh)I zRLx=yMVk$K2>$tfxQA|b@dJ2z1O`%VhPJV) zEjUcD-Z+$9F?c$zPm>0UD+62^wdIVm(Zm>MG1HUC$8m(7|R9L2ldX0J0w?p<~)?r@xa?!b;jx$sJC> zt9G=11hbjzjA)@QZ%htkJW=ULtF?JZwqUD_TNOKWHZs95vh_wPbTVTvlJ(wd z!7b2{J46JO^Q5&)u#_#ES|i&{x>e_}ii)IQclDT$a>Ndn+qatG-`MjQ)ohmEXE>Q-Ap|u-Zw=95~4#C1EV0x zGYa^{s+n-o(xY8N&0s1d)rL|LYc8x^v_4o7$`qYds?Zlk+9%kG2fh(KZ5aM&loIhM z(m~f1kfahpHow{?n`~NZ?^@cR%ZJR~Oef?pX>5&f4inShGie0L-vJ~%d%6zi9Eh|I zd&7YA2JuMk;yXj9y%7i|6_<%Q#CJw*|*PDV|i#hUL7XBlLppyv zR7)Qf`zP{)J3pEK^Hb#`JofK~Z-2u6Y54b#m+oJG{dkUP{o`MJ`N8@pfAP!p?}EQS z4S#D&wtB4ovbRVQGL{hV_ui1%5Ci7!!LhGgY=Wnqr=wt^5y$^^_!xY_pct?I~_B> z*51p-sr)Mxu=&K;1DqU`ocUxMK&coDK7QhxpM)`#r#Y54hI^p&)hEYtHJ0{CQE?`O z|B7-kp8&Fy7s53+{8Bmf*vn<<4S-p7e8bNIbk^M~@(MH;uP6#ioL-S5W#zzlAKbm; z_Wm6o!b|Rk1A2drH&)Ue#^=M(vn&x?BQp-OVg>jBQ zU%rH&{KaFPu=OW-wJ)gb@$rL``)llU;pLA*3h^iBYCcf@Sx{{QJXxnw7O(vMeA@3d zO?=D#;G3^M1(^3s1^Q+3tsgw~%Rf;(QmTCQ*TlSl5a4j!=9QyMg9WI8dG%`72dpuu z*9>K|J>&Mw%Po|URtiW$sE=sgKy{%4yAUot;25eSt)MDV7m5~zaP}G&4U{s17eRw} zPki)|X+f@R@X<#%06=YdfK8@Cjqk6t^wCEf12XrVk3PD6(T5U8Ma5~yQ1qg(bxvTh zCU0L%UljdY0GK@occnrQjb~{ORyhshP_7ntt(M4@d-AS(ZAX`Aef-`lbX=Cmd9Qn# zsqpDMCt-8^mfd~8z~v5C-YoOI@vi_p228}+{X{%5SCq#2$yZK}`?tP)%}rMrS^v%R zD*VQAew|o3eLeH@@^l57`Rr}jTK|n#^R)iPx&5NQPW+zAoxOg*Plt2iuAhGGqA2yx zBR4+MN5{2w?xVY}XC7XD<8;Hf?DV<%=;eF2CHmpZ6&fE*$o`4K_xksb79IR2--fEk zCge}OdV9Hl?aSBQ^*AfjGb_{kHVan%)n{YnQgwK+DvKhNr6rlmhNDcoEJ8`&Oh5m? z`q&0gfbQ)_xBU-`FHnx-Ge925K{4Q8@3#Aa`?2?7{{!n2_hTEt0Y1Gs@%PTppJ!ju zE58inz3$BW%Wphd-;=h_J!Jo<`QUxa{*||xI>iJC z^ecVxZWG`%^!;Kgy!{0D%JXOTiV5&vK79iGkw1Bb*^)N&=Z86XUk>Pz*F1ET2=tPC zA{1Is2+C&;?+rR>sswrtrvU|+000)?Tl2CqFkM_oxd#pA)^L=-%ON@(OAVCZ0ChJ! zD9#9tf;I*16@?x1GLl8<$o%2_eMMcGT=OjIIu@|aF96jfhb_54UH((wZ&cpzUoXG^ zXoFSpKRj3!4}{7Y&*MG!o|9tA{Vxw5d?PLAPyh0HlAT^$XgOamM)Lj*FYhiqMxgy` zIX*HJ1*9C*i8Z9F9LeCMU?CqYnpO??xG>rK-f5%bWo;vombF0{@ zzr3GV_Z|C=TQ!nPX$0hTF16obtA6@`TKykC(7zy`ftyx=$_g8$@lWdA6S~7 z_;&oTYl(d!~bmY$o+yU3LgWil4%(Z7{idQ4YjO~#nmRu5jkc*Mr8qdFg zEuMnU=nfoFH}c!Vo6!G61L2p0gBKQgm}|i~F6Z6X+Z=biWRB!A>%wCIueizYIXV=; zX`p|i1qyf<^iOXE5Q{E=cZFL+14Pern;=bZL)Z5~Z}L`vBCW3s@B>8PCIS8FV}L0) zc5#6c3aFfGWn0{ovl3da1yc6b2VYUKI{>vEAF2d^#Lmme-grhFfXl@*V4?(@V;yKq zHXg`dp7!3F zpOV>Ke};KnV(3|#dkQ~|=U7uEhMuRrr*PDIo&{dw>A6~b3RktK?>8lmo};y=aPz|_ zoW*?WJIlV87niTJe=p`wafGs~{};gP_U~Pa!-tljq=@O^ z!G-_6yZ_=vE-xIzgQLv1FZ6F?mG4x+U!B+F&xweFSSwJf!8`Dfl%oE*4{(XMYfIO` zDeou;AQ`S4jzaAPG)BI-^&rSoNax%(ExZr~q#}@3Krr69h*KjsS3&AVP~oQZ{AW3& zKzN(el@s?}tO6t-Z!ScmnoD`GeBIm`59R-TsP7M!>rvd@QJ`9YBoLP5*)#NZX@=CF zqdAyaf9eh7*_C_#z?+SGiQqSV;tEZd*62TeIhRf<<-^P8#Z>6qzx063*V+;%=jVTX zzlKg-P}r$IT$;Wm4lgc0%EmX2^ZrEs>FXug|Ne85{qj`tKi@-619SXxIV^wuIfsRP=gq3rcTZ^KnL6#q^G>_6ai03| zmA_wh?caXRuKnSRZ2pcY+xNJ%HeV-xv^h)<-FtTg{hR#%*A1 z!MX)EavpM6$DjhjI66C`fxgmjxpw5`nF%?$WgX+>nl7s&1t1Vu`MHGzd_{f)X7=4f zuhJs&M2^C|zI$oWRUhAO9e`2F>C8v=h_qO=b{FO@7FQm}|5xr5uc=o2Rblu~Eq%`LDg5=UQ{|h&t<@slU``uyeszxwU;ABN^ zW`$pztS}^3GVcDl{R~j*0AnpT({c;#<8wUy=?$HGuP`1KFw#$S*8j>Myzovxl%p>{ zF3i*1@tPy#S&oy(#sL)Xt^;zZbGA5-HYIHOZ}-rdCwraG+;7?D+f3jhzVfTXD_q=< z{mY-oh5sku?mef$o&5gyF^A%w+>vnQo(DmPdzb#31RZ`)>!^TS1|1H!6G&(T_x4E- zeeAaTZu;kr-Smea8U0fL;%~+0&iSW{M@j*RUjj7={MnJOD~G@J&;D7^VgiVR=RW*6 zj|PBz&-49`YET$!>j!QRNT^sJJ@+?7_5{q6Tn&P}!F!a#(quWQ5|I*a@;t;m&QRzM zE5n0Wfb;Q<1@ZX24TuGR-$a3+p&2_x^c6fBrfF$b9GxqZWj1ZI7#wUQzg8) zf7hqCy*PwS$09802a)1M&f#N7SOp#mb|6-A7hot)XV8ppigzD_9hP?9;_Ej@*c#&ayD5--ow-cvZLKf}r{G4w3WJ&B)Z*k#K6JV$d+;itUgou%E&^3^M? z-%I&dMI8R8OZoRu#gTsH4t?0oZT<7{2GDrcAfjxLB6-jo%0dcV{GSTv6Lo0Uz6hh$`;{Wt^dW={cPgdN(&F39I zw=|#%2NZ+>X%}w&+`RzO#m%Kx;m62R1&%U9F-?%xAVjqF4TR#s* zAfmr@09V`6K88k=5UQ`|sR}B%42}{Pppy$;?~ajx(NiKp;qpIw910ZgcOA>pa(G%hFjIf^4J6`~dz#NOol1;6 zQ-iPN=+D&t{%^WMypmezYXjoYM@7>(L=GEN%+|w4^ z{VQHRwWX(U(Rhw^U*hF?+ItE|zwp#esKm|F+jRe_sT;HTk9w*hOvNWv&cD9$d1U|oM)j82|S;(?ClL(t;hGjR%e zKvig2o?+-mCCCr*v=d;Ym=@5|Er962On}28cZU7FX}*BGhwni*mUg1=)f-@) zSMnM4Nb=y7d(`j!7?=3}|Ke?L-4`X@=8t|qOvm#s@$&nEoGbl#FAQE~u>JkZ4eKig z+aEh_TB-qN7c6iHIfCioIR9^ZUmD{|cAY1UHOu2H8jVLY)@D(&_^}_mNmg-xQjgX9 zN;aF#ZnFDnK#|4b*4(;^WRtXI*l_@lB04|fMw|ftc%p zP@pUb-~@1t#4+O7$#?Fp<#OqrGh+qsNyDz?)?Lpz_uR8`|5~`TgF-NGWr!k0TP#9z zpfJ~CdYow-?;es^uB$@A$j&O`M4#IqGs9@2DvutG6o5N3Rr%;qtJ#DZaS8WKIjW;O zIpvg-kXEjufoj5(S;bj~(I)B~`;zX&9zrKf$G!qA(#e3DUNbo(6CUEkiQLy39WJ@X znTRz`Lqt>!B5Bx*&13xB+ky^-d@{IH)h2!ND$Ju{Tn4!*8tS(yWIo<^N=)3zK2w@C zkX%a^?sOr7^1O3H!!YKZ%QYysZQ54{?VG`BFah-S>miVY)7dn9BQPKz*ZmvN$th)C zpv{k#Q|P+=Y+Ajx5A@3;FlQw`|`Z+##CZRKLZOAg8pqgJF8|d{^`A=-BY|a3q z%3ryD;p`sVpzxG2UJtrL=WNg&wW3&cxEk4?V62(`t@&@vJ8{QPbb!xFp z>}f%5waar(+uLzAm09z`M121YOLEnD`UYVNp81WDqqc#;SH>9vj>Y0z2Pwwt5!&WT z&_kFo^k(Xk_g2@d|B)c+jq3NW>AfipcTH;(jN-sV16X3%SaB+R5bEXeQEx?FRn9xpR$x52^e45KQaow{ z<1id_bl^MZ!~V$pS~) zMy}QeQXAL~X&l4xcO(lgaYdNxJa2Ytr1xYjhJy;22u_!aPATM%OyW2bE;bt;=UNwM zWBB?)`d6`f0AFHgSc!5};ElzPqr4}O=}}-05Co%VI9@Rx$F%BZj}0b=^r}<4O~yz! zJn7Cm$Woj7;y3i6#2VSBX_I!nv*-*&rJ#(+AK3~l*wL}_N2ZD)|Kt8Vr2MQWN z=F{)qXhj6Tz2OIdAbAXzM$z=;kwrE!bnK}Gw2c0Ib*#c0A?J_S^vCQFqd%XS04rgT zQ(jIP&@}Wk+c3|mql129I^de4zwGtsG$dy^4IWGbDcQk{^L_DZoDt^ewqM?Q0)_MG z`fN~D=>4o}yw9j!Fe!)7FZC)b##??kWg@P| zJOOZi>}GUT=-f@en9{4!<$2zq)h2RV_oGYl3$t93H!s;2gz;TkWXgbUJk72f?>pAu zhd2LbO3$w6Mg+P)l^gjCaU=YcVT-5P{tmMtNW!@R7T5wS#t_6DCNy!gCj=*fP@8Om znJk31Y|a>vnJqMmFyCrpGiJKX3Mg!YC~dxp__ihN-6gX0q7bQsMh??(3B1lIlK~o$ zbLJrqhoQ8_m=H3U)|#DC8S-?d9yQId9IQXQ@MNbTdeJ)?K5UTk5ph(xZ3(N|>FcoYyG2oy9!xoE1=faef}kf$Y)2gc3gSi!h?Cd4BCj0c6V zgcgoTp#?j+m^1`>ylw>+37``N^0Z**92Q)S8(km{5?4T4WX0@^(Gz}rF%A=~eZD{f zDmggCb3u#(T8QIIa$_0Rmyo8}sy#&ba8kG^Q-Z^*K+-|q@$6l}6@SImpD=oE9$$6Su$xCw{lG$SlT8+$*tA@Dh$>(Dk(&zXsu46cT(}kKU>On~;yc6=dPkt; z2BtFM!L(?Y<7j&QP9fGlMPN4kMWUI8#Rp>pM>O^9pl(O81Lx0!#By@Ytl0dkkGbXp zUUWR*57Adfok5WuR6X}L<6uk5Im=Q57WHQxk}@&XXOEP9oUHq8!T2{m%nl0R_2ISy zi2AWHh$_EmLFn^e%WF>WdzOo>b#Fl@lTCTYYPeiBg_!cpnd74TPWj#PkCEEMG13Kr zK1S}mL{{&HcduilSKM;_dZ2zJpv*L&{*|RsGbb1|0qzi~k!A%46L2?e>mbFwAGtx5 z?#Ma)tB8J4qj*~YM+4BgXNMrgVxMyxC{jmrv|v6b;GZnJPgphCN_~svFf&f*P*+=r zp=XvvyBfN~%xsMQ#GxS=Ei3-)}QU1B84b<=4T z@a*Q_Oq+ly#wKQuOlc_2YRX5jio%dSlIEt(hOM=K-iRA&f`WB#gMsx3H8p1j0@HS> z@fEoqp#=b&dY*ZR1RiT-2grv>PFsjThtmKFQEXgfTMSGAbEkB^q2~qoDIagptF$S&Ogy}%Mz4-@#ql_ZYF?hRvpZD4Oya|YGpa0RT36d}Y*Oi<$ zAyf8rv-J@Jgq0c4J)x^JsqQ}G`P`*6Sm@;yg{HM_1J}!j#WE-3CPb__%8)_dW9JkGG=s|SGnVI!J=}&%^U0K2 zuV*U-dSXD80gL^7Vs0 zJX~-F(#5S1B{2t^` z%ZPtq^@e%TupXIgw7~Bf(j0z7CjTDB@`_v_6R;c9hdTh70fh82GqF-2kB9f6W%teV zCy?2t&6P7-O`3bt4T|&SNHbx0ZPrOIsn+vQevVZ{#!^VlKz>Ff`3JAg6a&cZ2>x`0 zD$?<_Sfk(;l=cyvC1W;GvBTmub0hYeX6z*js=PGLh36x`zet!~lGjK;EL95;oiD7L|An=eW2tJE-4IAxe$!Spr8rc=tS31t25uqO;=Mit(AL;|C{HWN$`$26M??=vO}ba79-6b3Yl z+U_%&6$=;dP9lWi%%r+|jfZW$_aj&0cxF-Ey~Z;G(kYH-7S-KnJf9vX;}$P4oOm^* z9h>X9%whSRQ5J!lR@WbB#AJ>BXXdm?Z3878@ZL+(qCTHIHceNz1`WJfpE zKhW)vp>*|MPduysuJ9=Hl}~-*6K_LI*+L{pNc<=jDCKr+!A+YSajC7&E1x^7K>2_l6gm?r=EXM!*T!b8)v{9nn%LM`Qs} zGq{Qa0?8JFZ5ejq%&6SaXnA-UkB$fwF5ev0f{+p|&;!%b9o!P)NUHf}^VIRK-8Zm$ zl*r0~j(IdCLE%~TCl8C25_;glA7Vluz7Ioumn6?iGHRx(VaHKxA}Qa9{}Cj$C9;NF zG?{kYLxr;Zv5R+#W&7s*B}M{hs^#(s&B1v;_ART#!=%bO*g1MjRr1GeVlms)2Qo+D zg$%noLyL+1&X3p3nV(w$lCINsK+>5g6P!0^i@8mn{jFs8gzYu@lgIP)KTL5$J%=<^ zf8W6ZjkR5G@d7kAjV!-LbaRR{l4V|L<_*`-&hs|rQ2Z^Y8;<@OOl#oJuX`xPnL0OT z)@lves#W}kzqP)hnNZ42ir7Zc;!RL7CI-y40R;}ThiD#IYK*4mFxUcl^5ZE6h{Z>s z0J~WS2P%wBC}aQ{8pVgGhrI%e4mep1VvWK4Ix7(2)7)d70nE_qQQ#Aov4p&DPe$v0 zf9|oviGKu!dM8il;*#c_K~&_H=B!sV|E`D4V)3ECnYb{bOO5H;rGbdcttQSKAfAg4DQ%mow}mQ@>bIu4-r6N#d+dC-@Rsx4QGgrk?UTy;?_<5F zuhjIMK>?oJimDY1A;EJjJ&1hKGKA7)?j7q4Mw$dsh|U%`@8{~LZFTB`mI{(=ws zj&*Q1kFcYf74=)J}~O(F}QB*A@K?con3K(x!9(wAtIs`n5AA>A7T8>lw6kn`J{B3Tq0~JtL_?kjlG4Y;@t(a3=S#|j!XAu zSr9O9wbSZjBg(2hRq3=8OLI(+iFcF5bhhd~Ka^ zXj~^82?cuikDCDpol8AcfA3=WfbEE0sy6d8$R=GmTHZ^Z`*t=;%_aPc9~_p~4okQ? zJIBvTa%Jh5o^N#2))`&wWs>XZ&15PspZE&$djDj9Iewf;p655BzWhe5vbA|qQyTGB zUJeX)tNWc;|GbpjO!}0~SZKE&ZHr}h>(Ty6-y3V3rV>>5N@jU0or&Q}PvK{G?R;&i z-a4la?5-Zx*7lE*fySO+$;j1O=;(AavR7!Ggf`O&|6XWkXIn0Ww%Y6Y<4nERPU@-c z#{Tls+Ch5xWG#0d-bgo=cVsmkYWhn3!%B2*B_eN0;ii<%g-Yea_V&)o?$+wrwp2^| z^yNl#aJ+Na-stq?*qPed(JSd%q?;<`S7V#*{=n^48mr2naUNNVH4=UAcGzF@?kQ3K zAhFvoq7KaE+Dg~2C7R3oOH1clu`LaQD6C1P<^7dX?woFy+3nI^C3n8mT-uK-s#{sf z)$^Sb_i-bob&mAdfvVKj8|7B)9HU#`OLg+G<#;}ph*e_^sp{M71RAYDs8B!h#s{&z z>K4ur&2~}hte&na-kos0*x1vLz23gw_pgWLPA|BA63C_Y&UXfp{6@~L6jMs1?>$JmbGHR zeO%c}1n{4v`8u6SBCW0$+}oWk_wHs|?$)>5TN_(@%Sy5#h4s@;b-#WRO2vB7Cx7bRK6A$pcGOCslHU(_*TdVTqtqD+r|a!*p@zQa zdR}j39}P zc6+|$=}Duw-dp!>wBwnLwdh7~CA!($Q~Hr`7mVu8Nvao#_oE4aS}8Oz85nDw#!=a- z1UGxzk$7UYP;Uj5;GP-^RubhWUgcB`Y*>w&~x zb^WxzJ&2zNOK~mdmWpY)Q_O|@(WKmMhmWg)>TxBY#??%>u$^vEA^lw`1Dc4xr6@wigdXqux$>OI_KjbgO%H&7V^f z{?>X-Z^RA`labw(9d|3dau~%po5$tAPGwhJ?`>uPVBMHE5iO@siNj2TpZ#G(uelWDv->oZ$={G|MEsOrmMQwZ0CX*CesYLj$GL8tB^I0LvX#yP31(*fyo>EuCPt8DG%>YcW~RZMyh z{H<_xWu>&dB%LQQ&Xv%%wzRSoUy@46!==(r0JqofJ8MVS?>n>&l~(uT$7@GRTPvLv z+%9dV+Wyt^y^huir$eEr(mC2WO9yKwxs0L=_7S+Hl|GV+yNLreb&#*8&(htD*2WfA%QG2cGJd>txYXRxS9UPu z4BhUpHtYJ*&eGayM%OZOGp-lay+ky#+m^Nb0d~B~YAFyu@E7xPL4!hZ^}Hh;OB+r9 zZemN-3tM}IKsdgmudZ(tY6qKsIT}_oXN^vzli3AqrTV#~vKLv2oOCjWK{+{4!g0V_ zKa$xC21A9N+F{$jUg=?80cV9sM_L;64%A4qaOt)`dP_g9v*5^k54eW~=)`qIv_wp79GI^C`< zF`yzCi-hBW(DLqq5A)vy%u2h3o_+$}u&DZLp;ow?$z=Lo|H*E3`(%CR>?{&IPR3Fp zcjK&;uL52&?X)z&`WH*h^iey%6FrQ}M|)>yjdn7*DMu@Va>Cp8_9Km*R=(cW&Z7N6 zr=jf0ilS~84x?)3NGjy=+TIqZsv@PrgVU}yQ+S^~Z)t3bn~hX>Np>q`ccvBuzK07P zT8C~X98}KQ-JD#}{F&_)B@kZU)x$djU5a-)yJw;FSs;24&1WQEo6(m2sJ54rPIi>= zju%MM*;@`J4*coOa-dji)G|ligG!~?h;(-k-9EYI~z8ZM5=`Te5zJ4_AZB{Y2*E?8px=R`f(WtV+O{u)7GHIafB9&x+Wj zJB6i4@a*U?=uRC3l};_)(T-{-pdFc``cbG92HopLjsl6*u+%t>spaVANuvt>Y9j~U zNXhH1LMH6?o+;7%zFgYu?Df^ot>OCCw6mJ)93FN98+@OL_d*H4f>+iD)`hNoa#XD1Mrk-QCP?$K9=k&N}`us%SLib}M(54sT_u2PdhumK5=y zxs|}7K*w*fwl|>%@v~s^z+1{!+-~;g+c(Q2Jw-^>6++-Wr!aTj-qHXL{LLAzXgxYBh^fVewCNm>+>elONox!fakNr0I?cGcX=hJvU zb8|YY$;IGN=;XM%-mNFP*p6{FtgWX`4?6qxm6Z_@g>cSSt3N^q{m;?Q=fxv`^^3Us zcJ)j6{Xi(sl4L-4ReqB)W_%78U%-D~!hc4tx#3IPNF}R4p3%P8d4_~W|9e92^UIdp zXH0JN2n|lijs7Qn4|D1Xp_8qwq<&PT@sEcO6tz~%!g?3Np-(ADO3VE4ev{WnnmKNL zVhXXQXz8w1()}WoblgPA3a#%srLg*@;?7jB&2z&{3iyDIKDNpHG6pJ3iG)_u0EfP9YA&5n!CDHm{n2-$J@QKRpA@E-I_FCljmzv zwg%1R^tDD}Cdv%J)wu0u76w}?c2o*$jS)|2QY^q-DX`=i6I1_^iI_t1#Y|@s$Jm_)g@N0{%bHh5Q;mBgoP%?WMbY*pwRQOPVnT@lQgIP!@+gYfJ zD@?6AYSu@tE?n+vi(g0Q$i-hXX|~Al(G$VfwavUHz?E#`c0#B649yl^tR(jrv3zV979-9wvLG3OY zrR^~qnolAGq*;ckBqi!*)h*hW^GxF?Li|mxt)4DgSC(qa{81+Jta|p zW=PbiLh^UOl3iupeyKw8-%RjwV~pih3d!WpSqjO2Y1A{`iI0c3jDfcV$#Qc0dGOSN z<7Jji$#XUQVc~YNjOXM#OqN;o%)=-mCVd&9T{Y?(F}3!5$4_t*;$(u-iT@1rjs&b7c$$m*PHe4OJ0 zpCdCI@X>r;7KLk=Nm1sKMrrXOS-U+PABOFKw)jv}Yn_MlPRw%yR#pPbw`ZpC zalxo+YX3!s%0dF$PvDj0>@|3VJYWkG0JS8kMAuOYO+@Ic+kNe~M z@NxNHv-r3_`Y8Fh>n-{JKEjzGIVES(K;J>WaS&_jE*BX@n{*v~3f)>%d=3u^B)nW~ z=Bp5&@NJ51RfeTAz8tl4wyNSL%~Y()8LiQBb{o7PRf-OxYyUs2_0VLkCjr}2KxXM}mHv$Yd32+4 ze*TUEhcDs7QRUGs1PUVLMc?X-0?31MhNnY?p zoW9WGVC1pS?+N*RvK)Bq+%mGJQ8s8VQ7^LaZDY%*dzDrvYozDQmJqP9;8B#vQb2y6 zIjK8SOx3kcS)}uDvWHI^R88hNtH5o6A#YzwY&lm|wdIU6Q3d`mQ3ZluF>$-og)*!0 z_#8Rnn>mz=aQ17SlTv3Tafm$&7T(O)J&s8eZKR=rtfY|hd!b$M!uq=0Z1_D9FF7?Xm@a%?CbjXJQ>SIS^2iOm z_a6I$!N*Rr08i&MQm;K`!41Ay)4qvl2PHT-LCJ;bN5C>1H_7xerQ^0HZOOvpLnU?|qe|Q46*il{c)@v31lZAU! ztDH5)%@!|9fyo${MS|};;}lvN3Lw&H#df!n&ONRSWJR3`iUa|zCYdjbK8bVT;H z>hs7!pYICq0MmcLo?g2v-+f``|B%Il4{q_Qe>6Cs?u-Qe9o>r=ZH*4mH#S5m8VKBV zx);a!8K zClC$<#)c^QL(*NR`@L(|*yr*2e3D~wk^P~MY>@>-_IrGRP-uJxf+6__bdke>DTo{m z_$Cn9Cr9qO$k!t>E%LNA_W3`aHIDe;v@}YrB~a@h&^3-qQxG{Kg@fZm^aVqAUE{Ca z1d*pM@!iolb@%;Pl08xgTlwf3--B5H+RXRk7hbs4jvNk6ATkE&_l5jpgS-#9{^|`@ zdDmk%bL8DtRK|P-JZUazwf-vHsW>IVw+Ja#Z&CqVo76!`xrKD=J^V$dbo5 zxgn#;I}_`}TVk@X$U!;k35F;3D_M%%mGAny9|9`h4ws|;;5g?+!wma^6Wem+?!4Fa zBwND1Jh{+P!H` zWUmc&`r0!TTD>zi-*%A&Y?eF$UwHfs75c$tucN`ht8bWi1;U{~ z*em;_NEAG_A5k*;tYZ)yv&uvDufa^HQ&Zn#w}Cpnb$sE8^i{uXbU(yCxO6B}U(hF( z7Kv`~-&g&C`aG+Pzn!odx}=W| zr+ql}t^Ki~BA)W)SN);7Pk25jTu)xodeHO;P!**o*7Va2SKPA4_@RYm<0Ck|Y=TV{ zH5Dqt^?A09?ncue&_NTnJ(VVD_5_~$m%zFa5 zj!6{da6~iWf)7e@-r1XX_C>uuH0aF8&r<3mjvGh`Q9l^ILXTg80~Z`uxSPtz6Y}gr z^tp1USgfh|jKVHwdCn+2&edBr)w+de6!~UlSz~w$xw@W(;>vs=Hbn168nQuct*5k)lr#gA|mfMH4rdV04-3q-l?@KM!-zW4_hpOL`hOarnR(y$-KyFixNz8 zZLmX0|CEyS$eJzzDl9z4#BtXaK88HBG!3Dg1#&bY!t?8)iqn<%oak5pAJPV8cHa0) z)wS!bEE!7DwF!4NY7j&Sjar@NJvQB_gc4SFp~Qn)t*Hs`ZqQ``jnVBO>(pqc@rdYU zg>{ReF9BJ$3~#2IDz;|zmB*6I>ivcybmp;eJ$Wh8cywg?E=8X~gGr&Egc_`NbJSw? zJU5k26TV$H9~YVDZ;$l|fTcGzrm^NKRj-OzkD3=&@>z4eCW$~6wzTjA&0-t^C3pn& zDbVE6qto+(K8_jAhym}$H^vl*GlwDsc_!Ggf^wbI#q25lkk+z^5b>E>4tDEfQ)vOy zWnh@CR@yM-X3A5ljkPd3vDdFN$CCx@z6{_-@PsOb(Gq9`UELf%*mMd#GDkv_`^b1+ zr`Z+CSX&4yWR;@17fM|RG`y&_qeKkY#bc`0sAz1FL>7ihAeJi8B!zV2%uSgd-hA+C z4`jPSYIl%x1caTe%jk_bE7y(dBJ=M)GGriJFuTb2#H%qODv6YeeJR!7c5YElMM`#% zgSCN~9hzGY7O-!^P6DPDFbmThp+!VyUZ8cM z8==w3OEzru&%(Z_L>xV*f4HEHORWi8*VSV#c523udEc<>3EQ+>N55F@M$KdqLig-8 zP`{q=3EdPKX7)YJLlU!2pi3quwWe~4{2m&TnzIe>@TvXx*>StlMoNs?P zj~a&zDH`HKGG~>%>Uj)N+C3TXRqKx)6rv&VNWr>7=oW`#K4OiNsoFUiRpa}wB1k}` zMFbgpffYHzgu6SCW1I$}A-~b2(PaaWI7~9*J`O}YPKnM=g&qJz5vF695DQX0G@Ij4 zhU!I@kD5^0I8mBYJUOF_Q>U3A-^3}@Y45MFz65F%SWH;Du&@dJ2iRrJ_gDw3jMZfw zwtSi3?Dz<4C0gTxFN5~c_GlcdubGB%z;Xs76GVB8cg`~5BnzFct|LGf!RZ>wF|ocT z(KUC;@$FS)w{Edh1f!!gghA5CX>8hRQh%mzVYlA1EUqFLCA_n!A%|rHWC0UK7+;U^ zcN|Qe!KjFX1}0D+>#(P#Kdf?_%NUiZ1^l=vqZWw66Y`sqhb@d*%aP&KZmh!wp~;` zsr9vNqMu#kL9AWqoyQQ3P=<>xl0q2sXin%Dli+lQMiJbEw#)u94_|u;gyj(_II1;w zNj3zq!98;PrC~CpBjb8w%rq<3JZ2H2d++oBCxDK=#y$a!GruBsI;Wd=BbavGie3zV z6yMQYPF1Zuc3!ALP_GX?2-sJIAYg*)L%?!<7;~MtDhQbAFJUK&{j(4Rtcy+eZD+Tl zci@jO8OErjRSMvWbDB~{BqGRVb-K$p;b>k)W<;b70eZ7ciC{1DIEeL;=7yiHp=`1f z=9uYy%#RUdOm84>4}Oq+r%h>YxaiWfK?nNW)YWi~2Rpjcmpt(bc~sz#jVvxBPK`!{ z2j+@6TEuojG|CVfLLY=)|oeF)V+%VMmrYqZ~}p@H-5A_B03 z>gRfkIWUndeau_k3V@}ezcuH`^=MJEMuM0W4GB!MbII^_vP<+?JSo>(?|cKAw|DI4 zJ?nXm8PwA&J8=wx;M{R2;tbwpB=~-2qc9^HJjFnyJ{mOHf1BW^4>#IhT?f&So^9vEq>%L_aqW%;Uv+9}9xSGLxdl0J#Wc?4V4Hd8{rKJ}#q ztktg(oV-zed=0!(&wS|FUwZpRGof~vePSon9{w+@DamIhAjINALj(s_oH^!UTttga z>FIc0KuidVGK&EO&te|4ju0zm7hw6OSrHF&`7{E_GH1_9w^D#E1A_b}f(6lsobw|F z!Ki^mbznuP={E4)e#2`s+Gb9a2=ouewbpmw+)_hG)vn6c2$FFuH3W8zrn3o^N-fuN z=CPzIQdHwz-Oen%I*SPqlCRFDKCJGhK@7^Sc==JhlP`Z}_(_M|5X*u!rObQxTMN5^ z;eBhm^%%@p#u(`eV><1HXN!7EkPwD4lj`m>9`9|z(?a&)tv{X8Pn*<^N4+K*@paIM zi%}ZE3D{kNN}obkWQGN{EFLI_YrAN~uC&SN4WmsP)!Bzhm`RA4VR0}`1KEvO#GtE0 zZit>b49e5-na8P^=pF$yuH|6R<225@Bh4H1&y2ro+M4+l=(hREnEW$U$?1=fS=4 z!Xop)R)#A^(n0nW+vlAmHwHpc#16(*Fr?u7H#Ul&zg3^U|I>f|HrYh~=Y5%C<^vMCXPLEm#4 zawLQKWwN!mZCjo5a^Kl+c5r$iYaPHhED$w{b5>A$tSq%<$hL%~dBQu!Hy;x0`KBjI ze!8O8B>teUs6{B){_!_KCB{j&NEKX6EZG%Uf6wB6e z2>ZuR(osvV^qiE;faTSoye0;1=hily?u+Mr#Ib{=6Hk_r!v<5Y!#J)5#Ug?kKX!u6 zYs1`~;_a-koDggi5d#$ie_6Ot^KAX`cEVcr;m6w#>`cF5fzC~Lrr-Pr7QC42jAQAN znff@RW5Zb@K??#_L%7cLA?@5LamDN;z?Pf^_;&KV^VzamDV0%{k>u=orO+;uItkK- zEV8h`9HnCf-@@sqEATO`0I1n--I|*Hi)qyCE_}8IvS%g%V1ISbNG<^OY)T#g zq7^PbrVR8#j6rWi>lZ?_FS=~n0_E&Ph2nnavcmCC6yrOjD-^h*-4DNdNNaZ4=}^@3O+WKAruM-Yb&#gBa7sAs$rv*cehe;bHy?%BFZ=J$pWgj@O%+>&=j|7up0 zv=TX|f7M`$=qrOKGPxm>4>CC*uJvF~8GFmi30w|U#k@oGGWeuZlC}~LQ))ulrNZzZ zyb9x;45b#Y4;Ep0ykf}K2FKm9@+$)s3H^qbCv41DAH*Sj;kaC1~)V@4&G_bb`d+2E20Aki%ITd9T=E_kE04$ ztW~5u;aWUn%B?Lo-W)E+QM1nrTW|#nH=p?^yic1A2PLJ*UQoV;N_P@ zt*4=qwNESm1lSDWAwe0Wl?d5tZaKmMplHf*C^`d5Fg)Rh8J>#|0PO%)belCKL?k%n z$5oe&)YxqCf8fF#u#mWSiVjPg8xAczCnZ0iI`Gc)(P5&YN)d=dm3l_X!4=_Dg&0dji`eDs*SCsDkcrbrwK!0T%VOF%X`n(4A6d zeKznVjA&Lh-g->t9*>c)&H~(pG0mpF`;2Jm-nb_WX9ktsXDll-paQ~ZW>VdK#h5EWPwR`UBHl3m(`3?tSb{<7cNE9pFx^P0b|k zqnugwDh2j4L5oF88}*ELVwMNEVSkAqjOdhs0~`|Uf#-8s9GbzKz{``2#|#o^nyQ%` zm(AHpJ~=Q4?FCLND$ZJ5Y^yaprLq&YgCk6vc@p_Jdtfbi^(Sbq->CMjrMsyD;I(g9 z>t!nd?ts&oH%*b5hfs}jAzFDP79Uc^^9j{6%azzJa*H9@;t=!bIY3r+U0p#G0weYK z3KCQ4V0J05xQmPoD1uIKf_*u-AR4%sGLfJT;>7c+`~0jKj1@ z?h{NyIqsAtgh(R0qQ%QCk1V;?(lIBU+{h#BqrdBE{F*|-ty`U@5U+<|tz^|KZ( z{G3tGcqi^pyY7NpGH{E`49NJ#WdO3r_$y`(g^>>BatFQ{UO5lBi_P@!0Kt~)(L-2H zuy27M4@X|`8Vm!6hiep_%&66H^m%By09lVKb=MQ0hw^~Jtb_VpQ%jI$AvvnD_z*@v z5K(EQB*X{Y&5Ll~Foi?UEfh6_!i}O9H<{yx6$n6P}Y# zEt6EdAM+cqt@BO40ilgAjU4{ReIIyZuHh>P&m~t8Opj^G5he8%=$p&J1C{9EaI~^< zPlt(~#omfDGmbYPb%W%slehb2j?o+o(szNCQV@c5j?CCTIef*CI%SRL@!?D66Egm| zh!0=DWRYdRj+m~6rULO)g0Wn>Vm_6;qFI*Vr1-|(30SE(+U5D=j>LxH783%biaSU)CX8 zBX{W@>FqD@$J(X_ z^J3@+Y8N}t3?1cM&ANSd_!+f_cxf07ys6DX&kmn0Af;CcpT9!ct}s_9fq*{si+J^W za6tZG_zKq%BKSv>Op7mu4?6AQLSzA<4=#pZ9DSK(fppDqe3)SBqk`zUpXL&|tX<2q ztQNq_*qgB`s{a>QHhhKGJNfk&M_-J6Jbaafsl*JGF*h{??Y$Vj49i4ByDF)e>H_Yc zQ5zS-ABI6G)B%Xb1M|BAnyIiUeh!EM+YC(3gGwO_=cHn#M*)CeA*;r${b=}11<>?z zp@V3O7Q|sj*#ihdG1ssxT0vm(QD+P@WsUgu#$k3zP1m_{&ByO0SK<0aIUTsV(GbHv+p* zUtXdoWD1ofpdLEQ?RHCl?Dd|XpTioSGPHS`S_#1fyIz#ky%)pJ(ic=CeUWXe5OV`# zE`~4Q`NF%t0H);?t*DGOLr?5xzGybnMz(j|Q&GWzQ#0juy@n1w#?D`( z-Tz|vsalgD{3RXg-!`I#0&jJE`NQm<--6kPs)^6wm!KI!pggP+$0w{95gvqg(oQ=q zbmkQh9p;~G;Q6-!Buxa?D`Kfl#D9%Qf!@iFmU~r&;;aB%?4zx+3Y!1z;b#@N2Ou~` z9j;|r2*nYa5C;_W?}yYz_X6HK!xuOSPzgR>g+XYA45hPesLoW76s-AY&=8=a%@hd~ zd`iFg7D8Bm8bMJDEY{xwUFjF)2g5hVi?VPQ&4x`apB;Y6AM^)Jqc?stx=BaBG@Wgp zY*E~@s$qOa+X9C48M|xsN~1#yQjOrXX%IGiMv9m{pv%$rw=QdcO0}2tpfh}JWG2W| z{E}I#hS1#99&b`VXnBg}=fmfSoM5WIbuoON9`b8f_1}WvRezg)e&$*H{1pA9U%*d_ ze%|_F{Ct^y{{4&i`Ca$s3f9_Iq^2M*C?RG8=7|u4uGX5;t^)FN?&5EziqJg=>h3 zjPWP50hr}DVu??9IiMRzOg-O3&@qEvv7)b!J+w+c7%BF^Y?XcV+DQG_#I-hY4WAva z%XssNp#$3!!)OqL;fsbREeIlbljm2O9okxe$=?FLBxx%k8Ald?tz&284O+X@$m18S d$Bf803bb(=dkisf!&i&-tcWi(U!AoFnw_q?x27?Te(P$L72KRjn z0t46&0~kiWx%}pT$}s%s2Lp!x009OJ1BQL$%goB`QcJSB>%kBGp|T=)-M{|s z?fXCJ{bgvTK8(M6{}WInOtUiT_g|Y$|`uLcc5@FZZ~Pdw-0hm!xm17rqJgI*eaF-0tOVI*#q|a~Qs7 zV>$(2hfM{8`!%4-_n%+A`B?IjG(G6}B^|5sB~1NxjC%z8I%>Wi*YV}$XFvN_-=%;2 z%kR=ZdH)Aiygujm|Esb6o9|v%JN?7-kKX@L>x1UD~-X8#&#NCn*L=3 zS3cO18JyRq9^NG7a~w4|w^q2{*?xH=Fi^$-kZ;N0Rs8AD~LbN`hLF4`yZ>v zUo+UhYc@a>|LXXY*9i+h&PIRUnjfjdAI>KJd(RjP&e(tU{TchHWw;MU?P-|U7a+X9 zR)M^{H8t(4m$GS!;RR@t$4fPZ=}Vav;5>YJfZqJ7;(7NHuVLJdKNZIjg_IJ0k_%K3Q=KOc$xk1(b$r07TK4lH`~4;_dfR`~1RW?jCRz;D;j zKVsxx2>+ja-j>e-{6*mpd;N!n5NMK*ivEW}=>FNi^^>0fSsPw}!GDd(ztA2{JF^@U>3qG0;YHP`UOCO_#==5knY`^Pu;ydZSm9M3~@Kb0J9A*O#&tw zWT0bkrpma!k14o60D$S!Sfu{bs=P_EHI9BZWE)tGS7S1KJb7S>PXhz2{L`F)b2UFL z&;U&0bK$^AOZ@)p7qRKz#H(MmW&C++FQX66?f?e-I*@lS0HeIZTyT4^Og=E8&CBrG z2<*l1=JmesUMjzMt`xXy1&;RE$5jlBAK0g4DxY}srS<{J0S349>-*&2W3VX=nCS34 z-XGWZ`(67U`92r69?Dmv`rN&jp^f7({n^<3Yy@}tLLK}FqVdIP+W#2c0rCGg|ByQP zVFlqw5zjAX@*{QlkC@9B3PSi%j>(s^`Efe@&1Umo{FcY{i+TLkUHxV=;C_3B@x>&5 zjNX2;dHk2Zt=9Tt7QcO8zu6r2KZ4@?Vj4e6cfZ+8nBQD|e})aeMJGQT^*;Oi9anfKsNd1w?PSj*%zI-{vZG3C;t+# zQf=9cWflND^JG5Wy!nfl%joyON2pprs5~(S;9&{?AOQ4uEdtkd1fU-HuZ=#H)l=0z zo<(*0spxaxU$>9vU0z$1|H#^lW_&-S_W>jDgX_&APNlsN!+_3nfJ z4n8ZeDkbpzpX}TZTYdfN(0||fb&39tnjgCPbeq$&(|0eIS6nz|06+a5&3^R;JeUi> zbeC5t0a)hUi+Zt6?_MO+{`KuY-LGi@lm>XRA6}k+e}CmZzE7p!f3E)8=I?0q^(*)J z={{rgZ3w{g9Ux{vZ@#<%e}D1H%*4;FuEF_x!g#R209XP_Z+#QR$*13~=JZ!km z^5TB&w{2WUua$n0{XBa2%dbGO_bbI83i}uU*%}De*M8sokGJku?>=96U%h$r+UYkh z_#5rzn-^ra+r6%&)q*Sfh%(pM_tiu^+t!cW%q^>!)PDjgqfkFNU;Po_ zpz4QjZvd{&>UV%~96^sC%6_r?xz)b=Iat4s*H-&;4O~BW257+7b$*FU0PKM;^I?x( zdwIp>&z^v5_1fKYW*-*wS@7;Tjkt~d@$K{S7e7PZ{qo)GCVcf_6kq^fw0IrY7fqhm zztZOALo4^)>&?NAKlwZ$HQ!6chpD~Z;dMlyCb;jftN0w<$9m7(xF1FW=v_dG$8TTz z0Ydfh%h#`^zu1BGL4ddP+Tddu^2@KlTtII>?BQAT?BMzNgZ5t(y*7XIdhWppJ|A_k zaj%8Xn8VxekMi58&c@*z41IE%K+}HvI<9ZtA|Iv#oZRne$Z!6Ss{4kUx1LE+yh9CD45JGJero%Vjz`T12{4q?weLA+^AS4jTxDT2k z{s#RhG6uM97CuGyLvMhRe_ns=@xxwxtn;_3JQp4ujt?#3=y~j(VG^K>fQK5t{m{q9 z#;=m|@%vZr{52cC*?}p%4*U{6o%v7Q$ImnKZ2w7WUO&ChLkH~u3sHX@<7;EkQ&vau z3OWG?^Y!be@^1de}m@#*9Sh~6TAAWjKcdjA@IDveFcQy z`9BPy|DS+g;Qoh?Uj6^^F|zVE@Biu3Ti0Jh*uUOg|C{&!-sdXZR7WMqQuxC4fB(~O zKg6q_NfU41|NC|DA#VbZ1!Ek5kYN3+{r;akQyZR_pBuk@|8IY2`R({r#sR@A979)>re7A2y7Pj(uxmX0 zt6!Oh`@h_O@{{b!>E^OKO815Zf7-=P1^W)ZxeNFokMCLU`8f|)^jW~_t|>aQX$9zQ z7opfp9fR`f(gjEs^npl-cL3@Gi+kZTf>E9u!5j z53B>3`=fbd%L^_Hg-}$^uPZB*dD^$RIaWw;E!VKtiSDvLUoK&=P(hMVm2(mk8Rf41 zU0g%Ap)Na3!>)yJFN)^DWvb^$dU~2Sv zXB{%9xC#m6+lR~1H;Z$SNq0gxV@O<*%5%)RUHkbubT3Z9v}3qnpe{}v|w#HwxGE(XS~O{ zoLQ1xQ^{nto$2M+3D(rv}`=~bZLxND-Vg+4)xQPX~Khn{mJ9J0)FE4B)1Ay%+Om>|s>r{UNt#{?1oIBtF=~ zV2-f}UxbU5IoZRmJn4SevD%%(#evh<0S_dRqP^UZjNUtETQXZ%bUhETMQ=bOom$!M zSfM<4QkohN#LEz)GFQ?kk1OkCvwU$*v@e}bo^%?(zf&;Tlm~BSN;z|VlB5#`e%EjK zBYJSTnz1Z_p*!ZT3C6b5#H)|A)6J&%yTED_%~Va>-Oeb*BS{(%(7-P2?jc^ndu+0| z^Nz)pU5PSUDBwjz2yGy&6czC(N_DUhE(6wp(gk17kwEy5?6TGd*4!xB7^;eY#Gu>r zo^6KXUehAMyN4|;?3#cxqY@4bJ)YNXtNY1uPmwJ4eTvv+-v>0^~J6TD6 zo0s^^T=pfEKkoaPC~QcnSkbswA|D(xAnpTkf{)e+p~ca@?#|R~oi}KSx1Ax)$s`1p zGHph8TQ8-;2kwq%_bhzHyNf08v101JhPQG(v7@4;%)~bG5i-!kuhVRIx+?qDv4R=) zwTn|Lbg)?1+!JSu+?PPQ%5^q!QK`1*3e~;tTdYQkVnJn+wRK7Yr5-reu)dGdYCG52 zQSZi)*d-XyMHd1ly4hn$<7y{{fwrhjhpp>i{B4KOH~4za1kqJ?7M%!H7wj*I#FZ!eB+qd2>h+ z>5eZvkPCX4a-(o7Z(lE({fH*hhht~BiQSg$cl#Q*4PT<44=E2UZqkdR~na*R+y> z&PXtBBvBq{qmKFB(T-Mhj^cEN(tQkHjQeC+eO3h;sx92Tz=tdTFzdiV(=v%jesj#r zL7eZU-*g&A6#7w`;%EVQD!=Hf)kj8y+~iBn*;E)IY6dwf!p1&P#5J?;`qnQh#7Q+h zyq@1X;KezB~ zfxWb1UaOB&b?L{4EA{wRa@q}TY%|k4l6;7}d6)Eq&&YJP%dD87+hgffu zD0X!qNIjUnC?wJzj5|bF58Khy$oF$+Zx$uzfo-#;Z_RnWX=y!26VT@~3Q?nN*qfla z8`eCOcIS%neb~EFO?0~>R1r4n=MWC3X|Xn>Dul)u zx>Yo}Vf#uf=WQ{w>aoX72-OdG@fgE^f#hpXMYz$B&`5;ziJN)3&3W}QDGg!Q=Nq)^ z&jwJoHxEF>DHc`6-z8J55~x{0m$pe zQJA1(g$jD=EYZ~lSOr^G*P3_a0Y3I64?)v%sIg>HyNOrpfyX+b+HiOhh_WFsx%{Z< zzS?J+2MoV?AEPL5@s9A}8rVN(_-N#K546XciCDqI`xNA^c{?9gM9W z-J=ZM_tl+iYZ6W}Qr)w&*}C+7JTkinb`zW3y+YFz;PEbB zPSsg%?nVCnXm00eK{{^6uF1`La4nh%dw0qFdvFiVd-&FD?QVA(*=VnwEbp-BClXHbBy}?uz#tCCc1I6gu}> zGiS@X^%3F<<5X(-?iO1JZsPuxXBAu?4&KUiDOV-8qYiN6Nq1<7dc@9prkg9DEI_Zw zULqsaj1wCS={~`Pfy_7PIl11CjNJs4=r!n!>uzd6Co|k#g-X}Mq(!^p0YCAWy>KVC z-dF2{JY-JPlulJHZK<;UQZ$v#ws#4?cUK~sk~C-H?1{V5c?cxdFqV*OZDF5h#AEfk zxL4xsc5mH4iJ=sa<+>Z}WeMjQS3HxaF^)_TvLgv0jiX0>Y|iQvU-G1!#;PjG!+znk zczZaPghq{cvX`|__l+kL@v2R6wNum#Zu3Jp%dr*c)e%?S z$)DGzl%`M`Rh86ppey26%sCHUv~4DSv}VLtAX$JZd;kb!Z(Tc##?&m{PZ1K`;g~!E zZPMO&3*o(`F9Cjs6$j;;7~0+8&^TX-bws!5G;j``+{XlnFnKWL1U=~l(V{>b`66__ z-qr3bIb+V5{atGY@p?sK2{W(bh9cw9et6YzK~)_9T*z|RsUbz%NQ?w(C+*^?z!1+1 z>`+iB(#hj-pG|6khRRKLx9oNluPtF6xIT$*MZB)~y{A?D;>K2p*jrY%fuT55D92Eff(T>Ke!-z+iLQ zwZg?9!jMZv z3>tg_ii=Gd252#%0=;k>Hc?v7H%xj07B%WuK?d1)vQG#OvRzl3f~1A6mL{GZxCf(@pxC==oOMv0d}dA z5Csp&NG@@PO6?7~03|+^iIS{Rdhm=&t>b-O(noC{MEV2wtyYZJx$3n_3$|ch39M#J z;1zWH2aMh|3{VsS<3B0}=8i~J<5r?u*d`|dk*X-racFs&&Ypt+&L&C*qs-jEATWst z%YqRrLWeW59ivqz+VIaj)_?=)g23{>X~*0#@aP8O(*#)ZP1EwqvngZT`~*0vIaZ|b4R&Sc#RUMRyX$n;PXxO zZQ*RkOIbU4(b@6r@goKtJGW&QxUS*F$7tsI=YHT!B&j;xX`ovNwRS zwJnPTN(r%hyziB17e#6-iP>W!dXKEmW2%Dvva=;aQd~Tv<`OaPl?JUlrGY2)k#$|M zPj*Xq>g~x&cRl9^ElyyJIspt5-Knx~&8fPg{)piySMnFUC(XkFy@?2buvP{h_o9yu zU@?54TCG#373JhyMbuyeN#(AW_>v;of7r_Yb_~lb^VQ)52(o*y+x*~4D>cVSlHLHF%{&IRpRG-0 z`tyS+?%7Hv(;~aG!DTB}g+%c^?5j73vYGtZ|IVb6*a0*>t_oksAe0FE{ zmt*E^B_JI$fV~CjP`0`$=uAC^qcyiKOUK0lQR5DCZll{_aVVS{j&9B5T*)CZr>tq5 z$cn!XIWrTXgVSv-GNs-tN?RNC;YJ43ZgnM{81^VvF&I#Y7c$fr34md2$K@=yoK_jx z5jMf^*qMkR4d9gvz{9RC_WKRku8iAAsjiHalk)i_vZH_jEr`Gp9$>6OEh`SMV4az{ z#j)%NJe0-=I7&Gz3%s9bbX%nOL^+p}dKIAS!U6ERxB3x~F-K@QiZt&7UQ`YqF}ff+ zl!p9;QmIFCu9z}o@NEwPE+=HmI><#qGpI7E&po|d5ns>RdF9~P3ej$T?9F|F0$(6+ z-0dvqV{i{e8+V-xUx>`DW6|UT7M7Na8utRujn%}I7a4C`)|7*`2zeKd^`3O^2n?2z}@~GZQ)h-!8PP ztV<3sNzzSjkXJ14&L@Q$=&KEggdy19!ij$RxR+?&Z6Rt6Z&r31MEWa2Y zi{z9j@m@-^li06FT5veW<-sv=!)+`fTFfUsVs2>d!-7dQFnVy!L&2PS>@Z-$@t}K` z>r@YJe3JW1<@k9jlcSQm$)&6jSy*py>Xe0#yJn`SF1L3hXD%p#p;QXa+v_ZU-p8D~x9;FX5(UaTn$@23DeV1jTp&&c66GoEsA3bVG4gp%}k1m8DGs>LiKoY_M6m{>iyOMy_DK{+*=Z|&P+sO))UA< zRLY(Bf@Dzlmbl~neuNC)#|B)hSbapV zJ~yY3zfy$Vy7IIHWhCAQ9+Fqn}q8%E^-0Ev2 zk$L_|+APjzLdfiw>^>GpgF|xjp5lii2Y0KwomZu()E$sOSd-V0gR^<7DMJFDOa8#v zK_^E#3Jeo&EjE;QGaOpi2UI%@6J{k8CiQlSy08tR-7vFFZ>2|a;*f|a&IkTX#I*Ww z&qR9COW*Z6^G<5hJ)*|F9~xNJo+Rtk*OX}F6>J-tIotRE&_a}mN1(sN8#G{w18jIL zQT3Ky-E=KF$SvuOL0er_UAVrTh~lEf4yGe19csyx?9OuAD;rL0tT3U#6;)kytEf?j zYhxFBj&Ce-bScYYj^Cy+C{68vk@B9!kA^O%*TbH2-1}9WJut0X0OS<#-1}%R9^*x2 z$Qz#komLSBbdmtCZ+nrvB=BaJSc>9);4uqA<(YX}OX|@-;C0u=!4yDI?@bN~g;u=* z@?fb+t`56cUo&KkdWqgF7W7f%s$6JBls8PGbnn&6yPdrd^$c$5c%jf*46w(2Cz%W1Ui!~WE z8Kt9>)>EZJF?&D@Yp^PchkM9y7*jL5nb)rJHlAdlmkI-_d4|n+zI8a)9k(D4SpA|v zyNyi{MCYX|Ei7bH#EzM^kRu#=+GyiFjgagvk?CHB0bpT!Y=6%$mmty}$p{vTXaY)` zc8uSHz|qRa(ZsEVUoS+~(|LEz8Gt(E&Zir&G)P&<_uYWS1$N6W9O5&|dLLy~e=KOi z;iE(iHYBP%LkIDJ#xpm&5u}^qIMFcrA?|aL*`rOkTwPJ$6~(0Bk3EiqtI0)@@o*a0 z6*dz2*26OFmX9!u@WQ%ZAcxR(0k&kHIJI$K}O~$v)JpwPUY*5azXXAlb;~bH9C++E)yUf(#;!d_qSOvxig&Il>4|iQ0 zxr><$M^aA;ny@vr>hv1+2~^Q5K_hai_p!^Kj`A%-1iarZSkhn1(h^B}+i2fES_`@& zI4yOAvXW)c0)}pE^~L3pVxz_ipD66wc8+CTsT{HLO@)n>4jzZ4n467Zh7)iDbks(H zu3@$VtdTvV&Uu_ZOxgE%*QqFkMW0+mZV@a+&J$H~`5n2CDF98&y~57El-?m=ja1v1 zqVduaXVW&^$~?6wQs3O(x-#P7DE0FQ-%6Nhxd71AC)W_IY767lGLisq&$p2#LqMp? zETK{KStKZc>Bl*bSQS2~A!(qf#ITEi$vu+|NW#J=H<*Fy2F9Dh?zF1nj|9Zr8x>V< z&M^?oDRzxjn>QM9;5ES~EKHKXja6e$8uyWi^!&UV^;51Mq|Q!SDG_!Rsqf?b+!A{{ z2ok9il9QEdxAeA)MUNes6O@eoa$Xsg06-2H57->xcowc)G|9JiLe4E#9Pa1_xO70{ zbIT|)pqd>Doa*p|k; zLwD0u`_yd^wZbWz7WET0xLURa88gVHKVK2n4Df50^3h|&X`sK*RvNXv&Y*DxLYllQ zXUQR>cw1&0QNKxrkLizH>&rfigvn!M9A>(xdFBEa$N`wq!DWz2sWHVt|YYi8@$6Mkl~j;BptGHS7S1&Tp+=GQ>7I_(5pN zltHJQ*n+qPemO9^z*p_pc+a&RbfEMqCv1C#=KQuhz?`qq8$YcqfiH9%f(VOcjd_ur zueD|GfQ;J8E@5xpGO#z%3*A+}a4JysH`~gB+_C#>)CN9u2t{e0nI`wg9BSk)bGTjU z-T)`C0OEoj9}_@qAU_B86!7>qPx&q}t)fwY;IQoHSfp%ogEI0oYZf*==7l053=)MB zLASsqK!9Hc!M~Y2LP^8wJ+j2X$sv&9nEEFM$A6lXDJboDx)96~7txSVQQdXUp#g!!Tko`>ewnK(8&nuBZ=F5Dk9WKSM5 z{w$j@r^wcWGRadkMW!$`qRkP20&!R-wd|V>Z205I>D_|G!)<}Kz?=*q%*F!6AjL=| z6xlBJ80`zO@0|@Ei!0@PNcKu+;Z1aJGU*tDrNi58+DW#9db|ham#L{$aQr|X2>aMM zeqz-%j71(``QcfigzG5!5f)AjGL@y%pcQorkiFa8$HNRW7gvwbHTCWq(aQ?Y?({io z9NZH*Ig+Sy9B9A6;x%$7eRDyGrPQLdOLsW!1qy;5!eOLYnsZsBIooDox;8LyIC#XO zR11*X)r;l~hziafSWa$6)m0B50?WgMMprI?!)%}7;yi<;$hd?wE&KtpqBwRBfYKt@ z<%9zy=(9QRf7hn;6i9(%Sg z_P3L?j*FU{ka`YT|l@6)$_hcnx;WmH38`d_ZEauM`gIp zTXW5k-MWfAAFX3`Eho9z0(!mbq77kAfkS$jbqvtIQKwTOU3zGu&a>QWkhh)-wRGri z78Q*e{T8S)VwtH5B4+flBoU7F6~&LeN|<*GLKAG1iHGvodC=ZpWb}5@48|K~0*tA( zE4iU89gdMUHU?LDMB^16MhaPDy-{!0VuTD~ESdx;?;`>6gWVLwzPyAn3drDfx^UWV z?|2~P4hhRtbMM(%CH+uJMtbr0I;7Q&3_^V%KrXui2yG9wIr)b@hSUr@TEoT7T8Hel zffTOLDSD>Am<0miP=**4l$r>;j5=R**4cr8o0Sh6X>UC>!-9-><52-AUA%u&4H2*y z&7%U5o_&HyiF5ra?RK!P3lZv?wzyhc;N&jl;!*DC$dX&no6`!y zP66M$QOJ%{jij4F&S!nt+&kmhchc-wnm?Eg^lIxt&ZQ=MJuP9e z!;ho9SQq0K<-VmA(q9MoKwJ9Juz8)M>tE+{oIJ_bk5IhK}b6=rp` z%D88a6%}a5I%JNcDl2fXHTwNJ!7)#&=F!K)y2a0;94xmHI%#x(C0j8wV|{KVy~U$} z>Y4hWvfKlRoBRMOkP=r$UqP~#(p;Zm$(FQXrZu=R1JHSNmjYAKQ*%31B_M#4In$7g zhR$3(yQD{=+Cjo__9RbL$sikF^s}5AR6mmQ?d}kK-Wia<*pu5bdvH<#;)?DOF}7OuJb?Hs$gIj#a@`49A0M|RRi1J8r+Yy& z(mviJCp`#DS*{KQT_y%_QXf+&1Lk-Hd|BDe%6z$VyJD0D3EvSX#9ASP%XZL?32##g z_*^%6NS#Fo5vovz%s;^(JOmx0o6=DZ^@PC{7EadoT^5aJfYoM)ubHlj4^814tvPa?cgTn-kVx4(gRjD6At}1l|dCBIw3M+HYm&(<){In7v%kQLiZe-;n zli!?D=>z(R^@m2uwd9J^#5A6J6ubeZQaz;B<5RpfvD|0(I=y?a(-=u~!geOqji`L` zpJ}V!pofQuf}`6WGzYnqXE!CRX*un}$L`|mfiF38wmUaW!v#j1Q@U8qcBe4$d;yzx z?l>|I6RlrIK$t7kc^>y`PBn>vA?3|}B=$VR=Z$wfdccnxNF8;x`)Wp&8b6AD8vzE! zcqHD!J^=BV-DWs3w})=+M$-J_^yEmWo=E0dibzO1s>F`<1dt_r!?SqQk9y((Hk40W zoA%RN*o>S|0t9acMWT5b$hhEQCUkGkRdX_ILlc~rxX=xNPn5|yUaC&U92Y=rIsvv2 z%`Ue^HPovrF>d-T76bt86Db4g1is3{fCV;;LkVxF3?{1gkmBkEr;mw5K@FH`B;&**@OHB4ah%mz~lWD1R55(E2$s?nWVgIVW`qWI4!IQsN|=QK4*c$ z{tzy>hj3yJQHk6ISkUyfs+nVF1PFfD^A#kHNu?5#aDfLSNM;N(kW8dfC>r_D9?{pa z;Ow;8n~nsc z-^&S@Px!E0a73Jtp{G@t_AWF^Sx5(0x~uMK3eXgQo%W*^BoXF4cQEzb9(s_UqVuXw z!+V6I0}kph-Xn_I$W|HkDmvh)i9M6doXHudj_DwS3C8;gn<-qFF{H0zgoLjg#2rJR zQIk@P0Oy?c5Eet@%9~|S@oC)9*2Ggs;Sr^ah6%e~RErZD9LJ{ftLxtNy+gtRPt8pG zVWw$TMeSq@_aH&{9G}tkGAta+our5ctkZ&sp09hpZMI(p^(PBXofsE^&X}(h(3ra%y`TKUK4TvdxAr9O->jR5WTXP zNTexFe!9$^GqV!|T~{+4(0Plt!jK2a>^0s5&w5aoEa8kwOXdlSBlwc)9VppFqrk#3nZ!AY_QIDbf<6#xk>kM&RZ=Y?OOeM@OztvahrS9zon};uY|4HaMDGbRlnPo9wdlaK0KPi0`W0WHDFp z{BLrY#npl(khSgmQQ@T)tZX2Uy)CruXLc4}nN@rDsXn!(GQvsQ#6)`b1tIns$?8VPUqJFuR@0G>Z6_`|+Eh|CJ5 zQ#to`;GE7#vWp*D1#%B8(Ew1&EfHpdc;re(G`zEE9mbgjatxS_gPXicQ~^i!tQ?r- zkxiYDM~hm^4IG?SNTqH=%#`2}6S^bLSF(i$v~jT#rDXil=c#u~0xj>G(~TC|U;k-axqVQZzKcOb{svz)3E_Xwv*0J3)gB(D5U9SeUS z+gHR4jGEImc^Tu!Jgi>2W*x}0(_!)9%zjNUC@_uIhD2Bmk|e<^Q$p~xlFRPH?Iz*H zy(7krGgJp;hlS`N){f2X>0g2Gdz(gCGS@+N;

U%0OhnGv|A2;rW5-?uD@>*=1tq zK?T{C;iyt^JSWw7BRc8kBTHiJyhC7sNGvO#Z-v$H(q0A>nSpYyZ4Ry-)!|0zCULV? z5&}3eo{{Cjz!In8nnV!*L|=_WC-3P%D(RLkEd=g3M7^^LR%||Xc))HMwhjnLJp^p= z393AbNdj7QE@p87YqDN(AvP*s-xLH;ynP~bk`2)tWSL95d+Zk4D)&=yi?_w@S0S$U z{_fIo1}?Kl!kOi(#PWGj!n;_I!X#=Z7Sm@!64NElNE%I8?m(RM8!2Km@vs6NY4AXlHu`8i>{(Zgt_a>nu*0kd6Z;9nqqgmeHat!d zAM2{?L5DdsWd>|5Az_?U(-v{+bvFV!(+F<{jfJ~jQH?6tKsH)+2hS*_=QB~XAm8I; z1>mtNng_X$hmff`AB{)~NDQsp2806|CWy(}@1z-%XZsrY2NHrb3PV-LAJJx~@i@7` z2AV#~W_JwpG)-yz3X&tq^MIlqp+b-kl9$IN5{??P98n+g%=~0#mKsK^-BA3S}2OwIidLYxa=X3dgHKLQkxX#<$^g zp3*JjNN9DcH4JUhDMl3}NxLKsgC~7<`K@XBuDy#0DdzSDlBBP(=womU(M zFvTKjdZxEm_Oyum5NuNvifth3*e1R!A6LChCYTsKTYAv+t<3;TMwr{Gf+rsK(@8b* z`IhNcS6q*84lz#FhO-`8J0;%=9yhg6l5I;!s3Ah+r|M89*RlM zmPRV3#Xj(yQGvENycv?ts>A)a%0pbQGj8PHD^90XWSjhrRN^k}~h>SRybi;iG zE-(m-m^yKo=mO&JNK-BNd1@{veu;}64<52pEde}!B&*>7Yully32FbtymHM*lZ>GF zGXX_41u&jT#YC4Tm2G#$9rF7C+wz-d3AN~u~+QWFqauJRdzw; zK$6JX4d8mAJO=B6q`(~MW}6}wBHXg`{x#=2)+^QWj`|H`+?=4o<%bSV=%KA-HQwK- z$d9pe)0D`hEAzN63y|UCmI6b2SQ(RSv>-`I55$9JEm!%{^hN6bW$)d399Or*us!jN z?dgmIj{{7c3=)^mV0?NX?%ljo zRV0mVNlrA*{r1O+$-6EW+3g^G3o0Snr&dN>fMZ(x4^;#My$!0Yt2|^EaQ=0*xsa-Oa=O2&%>RSWX?*n)exwQFfTjl9#52!TVRkD zxJZWwdnZ#pVYWq5PwjZA1Qr?`HjD&97fMLgJIQ)%xM_iqAI`UAOY&HeL91h79LJyq zUup=g=54bFE&?($$O?_1Vl1^l7y?%lA6c44ka5an!hm&I9?7t{xg+>W%A(&PscN5P zwQNG5NAK7&+Zs4D0`b8hOi54>sBM#J9AE|50!@$XR_!%tb1{jZwoz~rawvSkPqj%F z3Yyj1mlJ&4+4SSkR%DThI+@PyTg=?S4~JHi$|7z=lpGE7Wl;*=o={aPx5=`=O?qI5 z;8!?v$u*(Q+TDRXHrquhT4mpqAvfEaGMTn@jQF7fAE)Q|A&P=>=ac@9bz-rDwsW<|spy?jW z-~A}75t5|KL~^^~mPcv}5GBfdIHt$;rN5r@_it^f-bGrs%ue^QFo%5>97hTwce{EB zj$~c(pdQAU;Z2>RN;~<&awfhrFO0lU3qJy0sLZ{%vvJ#5e??fU1RJVO$CZwuARQ?c z)OaQ}78e%7=l&S{q#@?o;~?e{w?L$0b_Cl4NMcKyq-+&iT#%y`8$;}1udp;T>@eHz zbR85(+uY}FZ(wgo;y5c;Jruk=Ay#&qCwRhSGJywUJ;yqm5=1ouO@W>dHV(KuxBU_= zTq9o)^msWPwzv8|Hb#u-8HVc|3oqMOxINOqcaI}jw1`?$&=?bxJCzRAW@`1VZE;*u zMj^Xd81PC;two^_n0^7Cx4jXCU~CF0FodF~(GG?5*#ofYn2dGH^_*WT`^jvMY81$7 z&eXuMZVyG{jhE7k0mMtLJ@dHm-6F{PEIKg=r#mg`k?tF2huU;0ftjmOSKd%NabL4w zLl-(e!EUgrEsf18OqP{hjv%6A#usQVPLm=4&Fi@F11DO|+;dOJ8+f|{o#}63z>|*Ao&-EN*vzeB<)eDLyijO#OH0vff=}#ESqz#ww z=BwUwd+I4a!+*CgqXLYU&)! z{jCiwgw;`j&=@Of82V+K81YM@^1&N?n)rOgb9^6N%>u45qW())W=+@ImK-A)45rU`Qa+tXLd%Q z>PQBLaMp#K0sMgjR$wy=`&-!rr{}#~>!3M{!n`})8GLMywV;K!D@eBBZ1W{#u-M|@ zeAy{l@oMQ+kmeq#*ifQFi2L17O*LLwD-xWIRke*W`4NMUCBt4AGdNiDN<~L#DGZ%) zMw?2s%C*Xy$q@dfh?uwB5z_(V)Z5YAB6~ZBH$m-n=<9|Ru8N~ULzL^XrAoL1Q4(!X zp4OiBX-uOi-o`X)QL9`^#1!?qkP(0^NnICrY->0-%hvLUCg`eLR;=DPR1i=#FWt}f zExK}@<%S8#c!090;a&gl~m%HWA0WNcO6e(m=dkMNZ}dG2u~O_@udTeETe(Xw!M_JKZ^j(bWP8`{E-3!sWd6a4G#Wx7 zcqtI^p3#O#*7<^k=&dmE6@%LA8z5~YUYo2$YQ}!=c8@hS zOlfd45vF*T6O6TXuu4ehF-g^KyI+B)+9lw|J9(Z+km(T@qyaPRKEzE&CjeQ(@sF40Rhw*Rh&xF%bpZl)slVeB}F@#ZGh^ajTHQ`hiS` z$dpS4o23P5G+Y8R(j6(qk~xplqc664Lq~4Wb%zlk!X4aPYY)fjG?n`+?C29+H%B_7 zTwREUsqVTKnxRV7H>0YPir`SKk!)zhEd&F+KzTVuEfbY|sy+ubo5aD=Lg!++; z7nLd4Qi%3pkGI>ax*&vBs!l*@fuUm8beRsd4||MYAVXUiiDrLJ`TagwVk771$z9e! zW=mkG7ah_eJ9R;>5k>}Wa@be1xz2zQxI84>co7Nv#n4h~*I)V5w2ARb6HbzaVq{3v z)Z9p3hU39TlxGPpPDN7UAXP^nay*cuV=N^dK2*9!C9k&-L1Czo$`q{;^ipOpD6|oS z{6}wxMxY!Q{oQO5B|^2Gnvfz0jM0wP8YBH8qF3kyK+T6O!w~A;l3RCXQ)|~*2brQM zOvFN{nFEpNMVE%4=6Ux3QEnyckq0g1h-9*0%2`_F5ztr_SM?4=ISdMF;STho%=>Le zVbh6{qwdn+x3j{sHacF;$u-PEr$2X{>0Xyh8r_Qc65I8QMZ8~w-=(pZTKuL}9S5q` zg`hRaK~iJ~d(3RYvK`ZN4cryW{9sozjqJ}nYC7Mz7VnYa@z@8_Ue%Q46>-!icI!T* zMv6GdJwWVMpr7p6gbcS*HKbOk1^P3ltxcf-mPA4v5I{3=Za2qE` zLhst?ae_L`Jfi!+`EPk0$&xiSNSAC+S}#E*w)MIis9Ow*2`rGO+vviuq8-F?B57?g zzyoMpmdKeRI-_yAKSm1Q>+A=eRe~c&A(Ka2(d)Eqa=R`?Tyw>T9&{ zAydhL;WyZ}PbI}t(4fct!zNI~Lu7My=2$oz%zMV<;vTLpq3^s57(|hs+ik z^uq@I$wKpbRh>b+Hj)mGEeBmeq9A&n=#x@dht3}IG%>s~cE{3i*l!8uaZn4@c+M=4 z)d<5uf1-m$cDs_syKE2Mr0&r*O$JP40{Bv+o;zD^O$3aN_N2pVOW@7GtW4?zIxIGR zl7ZJxH}JvF%SOQQY%JA5C-ZfiO=iaxD;;*-?aCP+AsT+^5@iR}4JyCbqeKM(!HU`Q z%j{?rV8VgLg-;gca;8G8Z>Ia*^=iHgDy)TiL{|hgMXIZw>F+(tosS^Vi;qyQ#t)s* z#2~}8!+`oYg|OSWMg$ftx{eirpAwjB9Z@xUJM0KyO_CpvHw3wcel;YQ{W_TItz;)2 z3Gkqn2e1=IRd)=`>!cEhJD?$N!0x8&ONb?0 zLjVAdWI58?wU@|r%PieRx)_lYX=oZKiEP?l?&77rkQ0s`jKWNDyU!_Vd2OL)Lkm-?bICg~O1Ur^HMl*i*pH z7Y;&f&(T2Q4`m-I#T4CDhv9)#iX74z_#-K{0&4{c!gN~k3SvJS^enNKwDtM`;ff3J z>dMs(nQD4Cpf^##jlrXn(|A%fgoQX;u(STYP47%@-(D9nq&Qn8EVUdE;wYX?^`4QG z#=tsmTMBc~7>n~Jo!K^?)H$wM0Yia`Xu#B>8CEND8dKvX#3O+>LA33~?bZ-fZIthE z2}HA6t1XiQdoayMHKjtflaxKmL#pr35OK+uNr^bTd#L7ft3yEn$d!|c8cz ziGxvVHmh3OW2bHxB5BaX9&$V_lCHO8ItK_{$@pVQQUGt^)Lyp)n>Y;_Vg~B$;H~%I z1`W{-@hs3mweNK#XMre3eIhL}9&%P;1D>=-Z8r+15RrKB_`Jyn=SnGv1yWHJ~v zal!R`iY?TL06$m}xPN}a?|m6!__|uIwNqzAB+C>Z!L{Itfz5ikcWauRAQJ;D*&VZ3w!AtQphfm?8)8#ZwB>p+VdM zI$rQu*9OfVNO#xnwa6mEA%1Mw1yk;9I-45fy@wgG$>T`gMTw$)KrqtPVl zZ#@%O^46G^#p!C|b1Tv_fxQO@yoduFIrBJyXdFcn7lT4eK(tcy+L_mL8=O)LWt?tT z#1>a<5W7%gMit}?f_r++9yIk^B?g&{0>kS1+{-|*Qe<5f>wR1%#aJBDEUO{qBnAaVpwpQYk2uFz4vr(@$oU7266dqV zcW7d0{i)&P*mSA1A+CLILC(&Vy9IZYeMqkr2GZ)SsfB%9WaBZhrx}c5h~3ybx*8-v zYp)^LcRql;n$@CY!$J&gq%h*eT0X>`yytCJ>W*25h#zq>NlbB~*Xlv8HaP~rGu2E$ z;X)ewoX`g>x-WTf>%k^q`|WS0n#wyPh!7)qeVxTrLd^Iz+Qn3KV4GTCQ`<2%JwSRQ z29!diGeUd5?e((haiL}|Ou}g=i{zp!Ds>FupX;D6X|CUB@yuzp1_L5=autT#T1bEe z&8Z;hB}p<*K!@+nU7LiQjuAiOCVss}_QQydmfAX9BNbm$HuweU(iq7`g8_jM=%lqF ztYaCj$b7Tug5S-gZAqY*oi^~QmIV=*NTKWT(O+?#0P;koDx1AARb^t&xpwO*4 z2R?s}t|5}Ekf;jw@42?_s(BqvNwFB!j>NPkU3V(%T((w|UN{rLuW;|J@Md6n8FV0qTf*HPIUcT!bS26-k& zAWk5Iac*GscmodL8*DPg%=+l~h?9`iAU^ROeJLS9zq;bOIi*6(`oZa`0XCn>{Y2Sd zanBq(NH-`^aQWsSLJquNz_tGvpy0|lF2zni!leaMdle`dR)GG)#%?fl^4txi-fmd}za$5HgM+eXUNvdt8kWG+bH@*F;Q*y)*LNsME>|~oE zpoGsVBOjO~ANHn&-D{bUcyODZ;{kc%LepI&!G*B6)Y z6_WCgA|ZCgML(5nY%|4MjK-$;HW&ggrMN?hWC(~~F2J#OJD3q3ldUoo@9l{CaIoY4 z!0R&Gs>9`S#{_S;9y(gcZX1l4iap%L^NNR9!W!Ih_#PRtX+BLxUJ?q&w&~i_TvEVO z#qnIoS~Eu`OL`7m@g%}AkpJ{vItwdE4iI%i9M8AylHdse#|}i~2qnxto=|cbct7x)mniV0jfY$-90v|R8u3G^ z4Z-vYe*{%NMeh}C9?ypklyZR_S9qQcXLN=^n%5SD`@*tcm$|LCPc((s>9HQtC@5)Z zoMKp#Cf%%G7_{6E>lJ93#VByvYa7-y0ejK{<=ehk&X1hUyO4*&?}v~AMGTN2<;NiQ zx$DCoPbcUMauyzB&{T-S^uRL^Jvm@kUJ$WzB0d0{7wm8gDJvjvnNRU!j0eB`{wA*Y-Eks< zDVid;bqYC$%42{m!ST~3j`RHxNjg?Sm`(gIGUg1kW}WT+1i^qP!vQ$q6@41w^QQu6xocALz{r_{uRJ$`KrhOQHB#@{nbTkA2V{Hj z;-M;AR?-hSP(x!GD~!crKL+FV{^+qbxTbVmD>&HrAT$vzmBEr4cZAJo6AiaQPs&q> z`mI6fB8-<#)YxOdPuClUlR6AZX(AK|S24*% z5Ec>i592nrnHXETTB+f|N4(K;mCBjnH@ei$67pqMvuIdVD`q`BZsXlf?aRV^hOYer zvi?a{*OrbQ%T+BvU0<~y$NF6YzDG=Tp{~6drW~DRc29p&5IyHVkSadnD zQ7DFlX(MIewYx#MtGHQ)Fb=-XC#stt#^Bp+Oa~hHPM6N%=+&hGasbJ+8AhEVP)5nc zr-jm9&V^c9%@?gwJ1mGTX>lm{Yg1tK@^~TJwB1D@wDH}fUiYQIhTpS3K`eWGdm!yW zP>(%iW2`e~jJAsv>WpWk-l^5G(Y5;!3j~_ljzcmtR$C4CwI+4f^ZuM~;GMIVT(t{ksJ$<42GTNVvw{cZ*1F;QS_7PiiBC`@wB%6cV z=uXqvA_u!fvLr(Qf?d}pDDg{Dh_{G5sQRFTN4H~U<(k5vO%I9o+TB3zukCo;VfM4i z&RK$KQj%a{J7tYX?Wg-O*nMRTBno!SE5Y7gQ`uSPLyU$!3lbu7@usH^Jr{Bfx9mWL z97OAkoDMa}EHi>FoH>5hsBLg*LZRx$x) zBsi;&L7MJ}BYQRI+FPaVwI_Tx>92r~Vaf#y`R)^JQ29L?I1+xuqm!;*b~QuZ?WtwH zg%s;-+AYh$2;Iyf2Qg9Eot?U{V_yJ!e%7%=sSomc>O-R(FF^jyl!APi#i0gUHUo7E z7-d|JKz|y|1GUD+M%oXKvDn^h3um4PeGg3fyD%T&zBms90`iuFYZ@f760B;l2auo)81W~&Ys;TvOI*-}Ovqd# zrY+jgAZgdCjVhf~KG3ZY8I0D-ZVhoE0eIvY*uZbwb0lnu#3Uz3+BaEhOm`O$;Efst1+l6=X7(V0r&Z0v0n|B& zO|=CfBZ84CM1R225FCu}ok7&6A@6@LX>u?_{Qy;k6sjuQgO*Y3Nnq!p{X0TW@?^P#`}QHxqh-F^8Hcz;E}>z8*-k zoxLOQXo@A&dNCk53*!He8P^A85D=k>2EoMzWL;AP@*vFuc1O;8>=AhOXtQTkOy9-c z1|9jJsMFlk7*OCatjgQoaJ7@SpkixcRZMbjNea83&oChnLA$$B`V<&?tEf6e!y_1N zBjBJR&#~Z3EMM~z&_SvkBm`Nus~#k>tVOOVi|DN_us{`LTCrjtVtkd2=tA!F^|VWdAQY~Qy;X^jkqR7TMIQ49 z06R)iz57~#|Q6tW0IvdQ|8LP}`a-ld%gI90>x zaFBxrjNTk*r9;{q3B1VGhwWyyqyYw@gLzsXLM%3;Ww++(qiRjby)sj#_S}{#CH;vw5V#3Kk*uO|d(CaxwGJ|MyPxP+vP z>rKZ5x}(!67Ys+mhJkc=k!3LB)U0Z&n$j2=Q|lVkvBd5uiDWDg5Kb<-dKYQMA`vh` zp~2Gc&w9nIn6gg2oT0OQurHT2FD^#;+!$~u3p%8JpFJ)ht7JzW>DE{r^Ssd{9& zj?<^MN5##l(l>jSGHK65Wv=YDW{yLyQb_FtS#L&&v=%11k4zo)mb(?<{$u1F67WoL)PSK#-`qKAo_eNh51z;F**GXKwP-N}LaNHiO!HG1_)a zl!EM_b6)phH`F0HQ?KoeD4rB#V!ajg`Mia?M{V92^dys++PsE!6|MUZBmz?^dGt| zl+;z+5{f*-AIR{#iynrdwQF8_3(s^F<=dvNcA2{mMc_iA-ll9)Q`fmOnL|la=wk^L zOgCv$WA-6~kQ9K=gmB64?Oj-$ss(T0s(E_k*AEY>Dp2q6^B>{?63{mPiHF{Zf1_<4 z+|;z7PBwffX`0)>!43ewzW?3B4lF4j>d=AefNX0nz37*d{qDdU?PQTv!JFwipzo75bk@uOI=O>i2^zR-NK-0s0Y6E+o1fr2a>p6cmxE;S?YZ90(fwmvfK}E zPc?Wy`O*aj_LCbA1akr5;iX`BkAEJD3k>+DFmR6;d4aLeHU&_JtQp??*HBKGqFZmY zrW){Ru|B^JBlCUn$vx}^FaZL!4F%Uws5tzUOXi3F2sU#Xd-(nV&*2v&?t$)L?LL3M2%d)7Keel@(8*2yooPJ$=zov>3s);fvb**g7Wt>e_4tusH;I?LUQ znbwcB&JuUR&i-iYUp*uL(~ z7IF97I@8=22J3!oor(1egGJm;AYO&aw$#UxUgs%vW!@7jjC!29;;NUOK*59qAL5|4KFaAAGGM_0g>VoR?>q zyUFmY><)KJ)y!+`4v>=RYw>@XlMqky@?@B~Ti9n_V|QSvd&w~KD!T)9uiA}ymED23 zcO^2fvOC<5tykF{sCz{d=2dnF>TUw@8ZrQLw-uFn6)I2M%Xze3h05di4r1$7sQlf= zmDa0JdF-qCw2Nw_b*A#4^$a8#{N7EZ^(xf*Zpo+hD%2XgcW;AKzc0_A&|mLnc;TB` zuR*P8?(T*D8q}KR?%ms3uR*P8_FinUuR*QpyM=xBHK;Xxx3JH?2DPT|cDQ6;gD0o& zHifgVLFMVzy_*jNlfD8u{d!aQWy@vHRQ~f@F5S9&p}z{Xrtj6Sv#&y}>3g?a_Eo6$ z-EtfED%ARJlQ#D%)cWfqL@o>p_bSwyyjLf{y$ZGddUNH4{%~h%{RR5-_03-g<8`R+ zy=)oxD!ldA2MArU^(xf*ZvO)ARjBpdwqvMh_6j@t*Ms%;8Z~q#*PmZf)Yl7O|33B( zf`B;|=Wv3haS~E+{+JH@k05$`1M%B`1cAIwK=g#+Wh|ZyHlL-w;z7^V+fD5UCXqi55N2H_6PmX{~G%%5>LK=xgTf|qRy`kUx93{ zK1PLp@c`mF&%iyrO*VM}0oRbat9Y=@IDUxDy!iHm@%Hb0^UVop0;)WiI}}2~A+9|~ z*EQ-x`Hh{w2W;*kdtI6ahbrRIosGedpP?EWW;GPkPTlxD1@+M=l%VkzB;~|$?p;=& zAcU~*Q{znX&y$T)#_n%Vr&QA1ee>skjsF!%ocqDhrx$K+fBFb>eIyA}$30xn{)(iM z-&{`;$7>GZe{=cW<@o7^k8hktI=^}4)58W(XpLw_^|ud9>vV=EP0x}nE^c0U{9G1q zZm+++Jo5<{-(7D!gZkT>COi`_47?)+2- zKN$bh(`xz8Q8P6mm#72f2jdV5SJVaM$06UbXdV{s_Zg4`(|2<;F^gt4oF8e9K3yA^ z+0p>?HiyOO9=>}x{jI-yaLmH|?%`MF&d=e`ucE3sIstmKd`Jv$X60!LG_CxLOQ(|e z_9m;}I~yA^J3yL;_h#z6cU%};+blM_+iCxZeE#6xUVlXYM^pNzaP>4l0l3Hc*{mYR zJ+08obp7l)Y5MT1Yaf~p-we{zpq^26bL(kjiA39#w{z>Gw@%av-fTYfv)*ck;R|1C zHiVm7k6$`<;;|R!fxCI`7Jx-*4D)F?E{C_f1M~rJEdW)Xh{p$v%%i+g+KcMT(6kV6bsXIghd3%~S9#MBaY3Og5UeBJedU}mY zewq$lcX;^ldB?ea_&QKu!n)}=C!{yuzI^S9^Ai|1*Kg5rbNO z4ZnZiFvsuTUqNiT^D{T$2NHk2Zm+0m052euQ}g#aeUa0ya~hwIX4%tRW|9--zJPK& zF@8Sj1fZT%i(8(Gr) zZ08v)n9RFP)7p79e`$WbZ#KX8*B)Iy{y4*~=)YWlT$ne6^K$E_CSL={6K?}uc@#>T zMSi~fT(luCyxC0`Z&{#*8l{jz3|O`JylO9yJOckwmv14w9e~TXpMmkg_-|itsoY|` z`Rd#AVkye(yN5H4Yf^kQ{K;j5IYEB2l|4{w!^}MG>!+Rrg?eHTWA{X@K1Rvmmc=+V z`#6UmC-GmAOhVis<)?6UGpZE#oM*ZWUGfEy^SvFocJv;<6_y@H?-{5+XK~+-?+y5u z!)FVL;+oa?$PC`D?Gu6?k^HK5+E`P+5=GeEsvEEIPdk1Lqh_1*Akm)u)q1GT4vd1S3tJF-2)V) zFT(GgFoA4pkS7o_iJi~~vgI$oy;<4N@Chr|33$QQ)8zf_13c2qhEFE%b*-iFk><5) z6OZfq+2}qksOJ;sanzd~d+ z+!)DxahE^CVuQA?$^2+Oq-B!Tkil?g*4NJ8wEFqOhUfZMzyC&Z?&mq%r3d-uKFe>x z{s*{8K4!ThxBhsxk`(=%*?q+Jvn}JJ?ef~m1oqc5Nl#qZWso0lrLnsQD%9ZnI^7yY z<>lo03jg`!3E=&dN4|miyfeJYrrrnv>gGu+@LjuLoH_mrJUSi1Y3fW>mUbqh=`{}}M z2I|xYB5@D4o1F+>b0yImOdT*}#-SfTK4AnNgpAhTH%W#)bPmi# zj*ftTgKCC}X`@gM(++@NLr15-?$9-NX>$%%0(1xr2&AD_HbtZ6JY{D_*Cm)X+}(Tk z;M!&3qBbN8hI5>JPrk=F;$4>dAM)F7;Ljj^)8xl)l3j=ChadjwKktP;eBdDmwc`Ut z5(k21&nc|&hsN^oTQI4H39y}L)2vbcqi?TygvCFyWx;COS$Z4RY=Ce8*__7sd#Vat(eBg-YO)tZD#Irco?R^%<3p zN!y^pm@`O;_1v^P2xf$tazuB_9aIR#vyj6EeXY;vnKmC=hEX2c!^3pSOx49;dVpFE znKDeP3`&#-gLbl5s54TW?!_n~RNgRfYHg%V0?JdR1|;BwyW%@+F>MrAY} zq|yS)Dk#Y+Blk!(@3QnURgM!6(WDlcc#~rqtNJ`ti(Shj+^Q`LkyRn>;XD|L20buG zlTgL`T03T@3Dn|@6sxyo<&mv=vKhhq_K}wNSrJY0R8vg`tY4v;36WCTGAb%-Qi969 zJh>OG%5AqW42i>8M#M|Si|1T>cRWZ@4%J|geWbd4P0Q>uhWZcLAX%dMe3IK^N}k7u zYQH|}l)J7rf@YlK6~?QTc6Ix+1=lZbIAP*+m7iJV@HQ^BiqRtX0jQEs;R zgkLVZE5b?4gf6WLs*z+}Mn%VtIU$$ko>?6E@xiorl{W4|!LPcIldYV!C+yN5c~A&b zFWVBW=`P2NBUdek@xq&L(t3*U3B~WCu;R(8kMO;=9#GwNH6r;5R9vJ+EnI|39ff4> z+B;-x#rxRfdtSl;hPE@DQi}qxDEl=hYfu_PUFN8(kA%u+;KSM);9k0U5n0i`}+9t+X9v#+}OA|0?1C+cWV zCix9Iue--eNV~Wrm~&YmyYQF?)!`#TBat;1SpH%%#CO#Qs!92^?Y6Z_OtWLMk;SMc za0hB$7!AG@s7{kZxw1KKMv+57eQAJ)KhR?qDu8BGx7?aL11Ec>>hybywL$Sc9hbTx z(i--zkqjP$G7)%103w640$841DCpls!vcM+el@ay0 zku#_J*w!U>!+BVD4WCE&!soScM)v}JVmZ-qVemfNLAL3Ju5E8&>a>gn8=zMMlwXDW zZK3GgYz1{=!pa(vMb&|GP3CnABS@{8zff*|UpZB$7_I|PT-P|>Gum{NvFUh~M(b>j z%%RSc>YD0N#yFQ;6#`bOcrxp=PdlRBgAt$BG(VoX7q$z zPkhtm9cmzM-E_&dX*)7j!F*`2jF(JC$Go*5m7|@dhe9>BsG1JyZDJYhPDC)Ed;g!) zq#vD2Kc7Cf{W%KdC8J@jt~7GEcbQ{LlLur3h0^vjm=n&pGWQ+L;zv+?W7%~n$%@K~ zJGQbtPjO=x3uKrApQU3*nx$|h-^X>R7altlI@u!@Y;fZ=9F3=gl-V%d z;NWpZIM~2Ddzxm4LaG*%c(A};d5?Ob`EcTczO-Lb<4#Jkv`OSw7F>qz%;BuYpg3a%r|4p%Mc0aw!|*Pa|!x{h^8-iFH1rXOuJxjRf@pAnZk zW~b@id||hzR4&chx`w;D#k$gwYPaNLnaG1konp`C&#`oOmB1O}Op2EBfR>>I(UGQ{ z$#x!@3%ToOtS)VHy;qyw>Y%YMzGMu1AvM!xo2=4RVv1TF%TNuI;1~JA@8QFBYIj!j za<8U+g>84LJ(D5Iiaf|ds*TF&0Ik$YX46uZp$Jell;RM`b!b$bNk`wN*#SwEK@^%e z6X=M(!iVl8|)^=vAw4X7ARb7Q+8 zu^By&w8c;drfJn)SA2{22!3bBgjM8(LHkE^UGyg%ZeX*Sy4p>n&Yl&iF1=l6j=o^q zGfL>z+|uTUwAaU2KCTV=AkRQ5m?_H%&9yTu}1?yiSSuj=w> zJ)^nJAR(=7$@f}bt0R;`+3NN8P8fka!}OFL)Pf2sn;opVxrxUOk1Tb0Ax*YPMpTOD zu|++cxliv5Myb76L#@T$i0QDMQnu}uuPM7lN0A9Amgc8yhme)Xq2;09E89zUzmR~L z6ekFA+>pG*?6$bO@Kkw#0T0QkTX%a57qm$FbAn&mTQk#C7pgxVSwZ5RvR#^OvXaT} zer*Pv&2o;lHo`+aJeYKk+S?&isUtVVeD9W-12no`eb7T}8WVYDR#UXHNsR~~nH+d-kks5FsEmnHUFI?X)FD6Ak_>{^koPjp(}A1H5rkCN4|q0;eV@{-Wi%ux$q1uuOo`jUwkQLx%WVf2UcM(*8baoaaS1eqSt}Chtmz$7 zu9!B;u?1dJSXZ~IrH-UH7js>Y(s$a{0G0=I0P=XKwrzqC`xy{=x(b8fr9xZDcxJLo%M3WNg?|eGc(ruYZ;&B)pf|OYy z8V)?H=5{CYlI`GCZ#hJ>4p+7(6mo#V#~R_$z&4m=*HZ{f2wBqv`@5?lF}0vpy)8ob zqOgSZ-`QIuaaS<3`Db|~PQ z5&AIaM_UDDR$Zu5dn_dhGzE;yjt6y?AO(m?#ZH&M zW$?@OpTie|Uya)TDtH@w8~oY&A2;WJ5d59eGM_c{!@q00;LLPx;e&bGZqv-4HLv|y z@P9S0o?80V;G5ENpEvP`O%u=Gg^o4NHWkI7{GGjV+z-%P@P9yC|J#?^`r#j%-=C|1 zeeWJjaGQ6b%}Zb59_Ry`YY$KNF8yyBMxd`mdG2fQ{kfyTcYxvsXBPy%4e;xQAO10) zLPHRkk!_&F9$2X#n?0fWPk-cr|MJ77)%CylqXs$a-@>1d(fSb{0}SAs{jZm?_^Znp$#?;5B9E0;uu_-r402W?Au&o=W+>NzbMHatPc= zA1t>i-{&;O+^0@Ll|88HmqzKPN*~T44NYrVQ0JkYpIl?#I2r_ zTN|ft!biuia>c^?_!>fPlGkADT&OatyJdiH!mULaH z>;HKrUzhFa-+Xlb|6I?F`5%7s&6~e?=rz7UCIp$-Cz9se5`+8=5ckG`=;C?;F8bNy zD~&D6eTXkcsE4B9xL4H0ja=XVg;2L(UjF9h6yPs``udUt;4`f@)7 z7UT0zULS!fr$F0xV7A+Rsm=2TuP>acnSS@6J{B|meET0kaw^XWZ=Kiy!02}mLsc7n z_aM&Z%`n0&D?)IN@J}08gO*FH;E)FRz2f4`mc55ZVUKAhOLK5}zwufvpoQzuKgDN( z2VHZsc>%)u-n==D=F|50ra^JT^!(I3)7H^%z{Ui%G9>vvFA6TBzh65l;g z@E_{I*0=Y-=j!cWe~-O`Dw0rBgTiQv`|hDRXCYXXAfYrib2`Tgh!@Cfj$zjlT z>-;bzH*SF+8+|#2N1?VZ3tao@WwwP8EtbMa>U7F66xeqNnrwi?-(d_va0JaXA8P6x z6X0r2L$mN5{2js2IL2{!^BMdd*}|Y@?$kT{9R+1h;5JU4?$I0$9@5;YGx)m}#z04z z*6+SOaRb4h{w;y|TLM#^N!`1@B`|+WU|x{GJThh{9{xZ32}v*b%iy1_{{iru>wgb^ zHFD|y4eVC^C>>n+qhK+ zE_>gIp#MF%nKvR;W!9&C^J4)M*p5@Jco5aVHRn|D8Q74I(ePnyZz_F>`CB-R-Oyk*ZzYe5+p_d-s}2#5USzXjh{B&O3i0( zzyAgh)X2@-(gmN#MwG2DqBnf^$_6(4LUZdRV}k=da2pNt0eyS}w=UQ?%k#ibTs^_z z!Ny@59{ldgIyR!e8Rwfv`M>#kTEBVH0W^w^w+*Lr(+b3SpPFfKx-P*5900z^{|^_? zK5D^?Hy7^e)RcJ$^KY;HIWxka>CPKx18jd2cne+mcs$HJFCmryE(3$xAn`mnr@01h z*D1`99HQl2=Scy;YxmC9TS4>w#$ciUcaIC~%W8nnJj36;YHoXSe`CLQPp)LG5&!RA zzqft4zp;DzBHXUzucjn7{du7V@99(TW$4;Xr(UYXdwTWT`^fA~Z|-gBo?ZwqLhWxl z^Fj^Y(!%UA7!H@$h0=I-fF?}c{cM;`fymum4dz4}QVrM&yo zKltXxz;e-2J{ej5M+kjsltaMY6ism5&iN4r^KA7v@pug@c4EzfMoRis_`*f-BFu0c}g03Ye_1owb1+O@Z(bjMbA1?MP?~UoGn`j`8=wI5<~bnr ziA#Kh?UCJo^Qh>3locKxXKJ{l2BX1ReNrbvH~IYG#B!e};BBLq20t2*N2G#A77+dhCVbuCs1b}H zh!L3SlbN|O+kt8AtWK^P*1Li)gb=k0W81)XZ3m>Grkw`8(BIDtUL$#cEzl`J$T4k@ zoSHfQj9fPJ|2pSEJ~Vd#PO{mgdQ>Yjddz9@G7{5|=mFE7&EUHv)H@B8?J z+y1;nbNBS8eLt^q)18-S?VjHB8g~7Dw&|uvFV*5bz4{mTa&b5PxxcM@dIBn=mtZGv z`twpP-qS1WQHJ=r-0hR#{QJNA8AyLxME;x4ipW3Tk>}t1$v5AChsAg{;g300(g8sHydEj2+rhXAXzNGh8AqzYoh;M)W@bIQdqtGO)Z2mSsC%2OP*N^AT zwWg7`&$7_Ks||%ZiQy+3!J`!hu7-_g%1ORH%Tvz{H_uvbTE9qc&#r$4;I|;sKq`>S zm!EtQ-Pnc1M({llw;`)5xa@$p&&h-I%zr#93eK|NMQSyl+yfB#y6^bQinY1$S2@B{7CxOxxe@JCA$r#l_-vsfP`YL;@G*e&>AWeCIpg`JQdxc1Se%$L4fW#yd4m-facw zqF#4CFi0C(2tSJhEV-f#tWX1Dru>tMnvkNpr8am8h1F#QKyw}+YZ)j z2Lr%gD)~tA0Cf}fUx3V%5o!gR4eT4O7->Tjr0m2MY#DkUOI9h{9r1xnR7(R(gL$Mm zdwHl^mgnYdyQ>-O68Prf2m9>X%(FH1EZ70s&5Ev6SA*X)4LLu4+nicZm9@mP0FaZ= z(wz8s9f7Z(Wa!d%&r6n2R>l3=TUFL^cpFmhB@Tda4b$FXYNGjrR-H(;FFHXQpZ0!) zN0Jg}Ln@j4in7yUdkN!_%`Q%Q3-X{`DHfq6)K92DVl$1kJk6wpVFNi%a)d?09dIq* zE|hbUcOxtLk)iW~KbvSEv)+raEtfR;4r1Xk;IVn*IjTK3f$WSj($9baU7@ZC{}oH% zu<++A746EC!1>2&MTP&ME%qU;=aHrkTEQ5wo{Y;-3Rm{S3~=c7a;c;pIFalGM(H{x zfM#>dy7f2=STRRorwH5$>Gp7CtAjK3z?bP8xr10u2z05kwojN(%1VAyv{nbSZDE?MB7}y*WKl z)qEP7I^wNb&wp}pP(JqoTdN~XNLxZ)v?Hqwu_C7g@}#Oavfi>h-UFJuVWh2k;DA_J zTGBvd`zx)e8iZ^p-Ek9K>@2q*XiV`P9%mFK69sxULf=|t*fIv?Xe)cA6?t&ZC{H1g}%jm}yG(*Ul5 zX|Q`F9iGe>+&Bx06s(x&XJwZx^vo99+I^O_ALARcSW9*W*w4(Ru~_N^2u+#G6xEc0 zbHXi!Q-XYz25~_S`I(HpDDGzsJv@nnXU|H!Fh7uPPMlwd=gqb!t zK@&n%yX>T>YrEnS7(9Y!aQ4W43^tL%jl;&V8v0#RfICO>NWsf`7r13Pv5>m6*YNN4 z1=SYcIK=CAaEig~HM)+Rmoj{?P0vU05bY7jhX#qtI>2kYN3G$*4W6WM#QBZXTlY>E z^KdC^G~tm%|8q5^in(Y$m*(r)nN9SQ)BWV6pBWsV=Dq9;BJ?(A%s$hCfxt1&#?wm> z;hH-y#(P7IlTlyW|>}sAjie*keG`? zSQwsOg0w!y+=r%@py?&(O}hkHo0SAaee%HGsW0LKqP`1ng#(d>42U}S$)~N4=U>)9 z5)O$9jA-5W=IcmA0_%dw5fYP@1Z~28ZZ?ld-lS(S=}Aobk73f2WM5IWHF+;zEp2(P zP^IpBuTrIU+PgykO5BqBX`%H^wL2jcyVTX6=UgAI{@j4oCZjMKe5b`4OsMm@uI7rDj5u%TS$#lu~L$LjpzKlc9hb^o*3qu_Bp4-dG`h)Z#-H zl(z8`c9O9K&YCjb&{!4N{B}REh}lOKQVn%S=Z?`D*N}0|LcJ7cffNP0ZGyZDR7J}B zpw+%=Vx?7r;!&5Ag=UB8#nlDMDt;|kRR;wUBNO$}549lS>`*GTpYlf`8Lnhpv1<^w*qE)o;+AinKQBiP~P_qihGgRmQt2G*2gN z=f<|QrJS`T!cVN1+I>2z6+aCfE#C<(iShAXue9hGUfGOHTrff*W3j&Jcl?qJ@QA1} z+_XTdXyB4;NbJezZ0W*mh)%mJ=b@@m<`1=pQFezxoO)_xoNDO$ z(ynX`X4`v#$~!dk7{qBn(M&>5C6b9CHwmbNs-Yma2bWc46k%=>HNR5OO-+_#lDu~9 znx1b=_u|TR+L)aO%h&P8O#Wq74kGSw=0^}L=P!goXt*%Rw=ra~su}MIAvrjO8-1yO zfMGk_p|X)4fk%K^Y9tw})TCd_HSJu%j;6Am6cv(T!?>3QQsNSjR$a`6tl_VyLr*}9 zMLdL!?IR!=tl-T`ql482*(iEZ-BL#^5VG39q}MtfOuCvxHay~;7TdCleid4>HWGf* z?}FUS5bVZQd&JnG3H;j9b^PZ7cU1IxYlx@44kMN&aJZi$Wq1QfU$GMqMo~L`gh+_% zxF8dNv5YKJ^pbPvW}RO_8EEB}KwWu6C+`MSE1qE{MOb6}e5nyP z2{%0pUVX}&#qgRLrG`)QQ)dm-T4-y!;EB&^pPS2Y3~B8NaKy7D-@7Qvj$=5r#I^`& z^N^GUqY(w{jN|2Wcu#nB@cOMZRT&lr-cFtm%!3C z`I;6HQ;6a!AyXA}7ir1rGv{Tq@(nz#(H3yVcY!bhgR4eLEvUQyA!}(9S7s?369io#L)D)JnP zoWpzy2H_`oQGs;Fm@Bl;s=QJF0l!Ha*fEQ0NWm#)UR6tn&7x&0?2$D@NMRFDT3kM{ zWIG9*4k2jp>hGQSAUZ&(N(B^4ZxvJps_?kKTvE9tAR(+Zn0KLp+ash@;l-4$!AamT z!&lH5oCn2?%Z|u8H)c}s#vwXtX4WfhTA|}s-1Q>L@=CDam70x0+0O!l808*?7Y;4U zaV-QW z>`J}>Ae-*Um$ZU5Cy%!EBN_6HdWOn+wNiTK3YHE<8sQ!g3=&~^zJCe@E2gLkzQ^kLk1+GWj?WBF+YmjIh}V?nlu(s<}5S)+9IQ24n%n0+t{Os819w zN$B7#?M5>oYau6-q*L)g@HF5onLboXyG)8n@&d}%=lT_F13B37>!MJ<&CfNx)I(>{ z@Af^t)Z-{&aZ|9X>7`yB0$LiFUh1`5?etO)hiavkuxGQ8O{bUo>7^bj;_0P+dZ`Z# zB_hU7FZI()y{n%OA00-AG`-aGQa-)ZXQr2Wtvs1t>Y=Dm%KErVz4Z$a7m!~c;1m$= z0`hr!6ohKZ4C?~&+3&H=1^-Y3naBl%9tz=+I9YK&kF2=Qp^C|dvDZp$oYuMY)mc&{ z$8blgY!O4nZ1_x&R76z(lrfQfw=9jaq4XlyK3 zArJ{0slh@wDUrIsiPbvEF9>RP|m zyPht$+fDz}v13J4(W&NJ85kgrwJS}35fB#5S-xoBUsMW1{G$>z&pGL{lAvKH-NN&U zz=KE8zp|UJf5zOHHZLTyog9P`0yr{8PWr6pli1u2O3A>R1f!2k%4r;ICWkc%CeJ6q z@*HfEfj0?8F9=4H@?Qs~gaA&0)0xRn0|%ibpiP3!vy&Z64knXAngojv2gmJL=c9wh z#GuB<<6!q-t0a}43Z>mo@0!9^-S^tVH)5?b9=QD*SRr~ZAcw0<_ZjI_9gtxu*)7%8 zJ%Ay0T9w`IhbI&qSgEm^VaN05KKBb&+BWB~DsPu@R^~298og(E;7M(YIJzFus4C_H zH&Qr&5AQ4dn}?LIFfGw5ilN2X_+5)M%$CX~ZGtE8V4By$RMHAO%jnT$r)Zkj!c7XG z;^^UU=-!}|AI94;rfUI)Bf4bLUDl@BRfa{)o5iP0A!8B_U{{=Y+orxS4wXGifXv11 zQXY3il_1AmAKcGg2=1!PgF&TVa7{ISb-D(rzL&C1^k$0sDR_zyg>d$mGCT_5$Aa6i zhinmW;(;R=HxYQ#GG=qqv>4(XLswPtETbQWk=?|dr?L*mjRpqR3Q;A~+Tb3m@(;;y zI3)Lv-Q!M94QE;~@>x9rvjf7+mfd6C8I!Xw5gY@(%K`#WdS9b-)Ua5)9b9wJ~>U(_~xc*Wc-|aU7B8JP4dP& zpUKgP<~>U=z0OXrv(xMBjFa_pdY!exr#N&>ud~zW$fTkpr`OqcTu|inI!oo|H0U$+ z_6qv6rfu;Ly#zyY)Irm=TgUr{UbJ>^<02Kdd{-a4Yu~=S3x~<4{tQOt-}pUiu|BVX zM7yspqH1I4U>ChJV2lL-iI{<8XCn06mx_Vqf?_b{%iZD~?<4U&rE~ zDX~l`E~*1-XlUmxq6m{8Gdtj_CB`y1)NXDz>hNAwX;=*Y{oFc~r3V4u=NnMHT`o6T z?bH>h=)4Q4Wr}PB>GPMbT$qy>>X(qL!OhV2u{xsv(=T26*qnA1#kl2tqV@==W9L&lwhm0LQS;sy$(U~#R162`}BetUEAroXt+>L5KGY>s>6O0BufZ7!V%twf6ExJ{ zzZR$ZH^-Rj-x_kN9Y4G33+$(tl?C#M5hq+}fR1*~Lh>wSxC<8Yj3MuE((8CwY_zs;WX{F9Z!r4=rT_sU>J5DW&j28zH-L;kBSB!I?aIweqqT9YSzJH1{PfaOnWdGdPdt^u*Jp!6`?&n+|INou@#D5)#iG~1sVg!urVj7t4 z2ForEbVqg>K1kp{yzavCKN8zmr;ZX&)Fh$yDSCrN~l zgy3@aB6l$yXRajFjp!f0RD5)dx&+<&w6}g%yO0DmoKB^UU2`|ec^c4$2PQ% z=*XW7HDqqBlJ`|IOvmv(JBz4-@~l(OQU?}HF!n@CZ7vTrdJNilq+fIjxXQdx1Og#G z&qAC7>tDus>u*9IToX{@cneq;#;R1wmjW=@3Si&YJR( zM?6(1LH4Z-O5mz6A(cv1Rb(zAULpq-?#eWN4dEBz$eL+gW|yt-a{_gl*BhO1s1Vp` zpe|7XL!v|xf@P=t71|c9v{6Qm{_$>nLtc$5zufmAQ*MW$!%~2Zds>MSM?-kaPAg$( zo@k(;HBuTVrCpMdVe4D27e0QEtsu#YO{Buy<+Tp;<|C&}b{4O>rvbh)%uF%Q(ZDPN z4qi8WS)Z}NQp+gyX@jS4gM+f?tPuqCk${n6BE}zRqNif?P?Xxu_UxMM2s8`k#H$5I z%w#8EvGJy!fYbE*@Z|a0jF;ll+DupK+!6*x#W(U5)SwmD+IyqtWE!k3omn5^uub3( z7S&%w!j7NDTg3$J^-fM5s!bfGzRdELTHVN)ywFUh5B5O$0c36@| zJalv=IFlK!P@-Lv)p7b%L(yDaYGHQr~O8E3?^X3%SVO=7fXVDY`QWc#^fy)x|iULm^ z`V1Jf4T;)w9rAjd(gPRU(bg<`%G>$-2zNRPAj3gjj79E0RX| zo&N$nN&>>YE=&KQ;LBq%?n&JeX^&=gdU|{+gmvHZAyXSiwIxXKV*r8Lgc$ zrv_h~j8lUziZCkQ*QvqR^JZpd>~0bl4PTYQG`lNi|CvIBbEo7&8aR#YFyT=L-pp{U znAsM&Z${jr!AJ3*O-H1v5St$O?^apsJ49AQTdj=H1&dA7wdu)(BExUV$uu?iiW((r z^14)BM`2pKa}0sT?3S2T15T@{!585Y%7dwAf;rKndqzzSzO1%9HTX{Jt?RlmZ{K?B zQ-klEu_>6zCW3{Ppm-K4{ydE~C3hDB*eVDxA7Hsa>F|EGPZwDVCihWFlMJcL+SydH?v_3!}No{`>_B=KC z!dHd+Q51Ar$kV{2P?$#SRGFZu!B>p%#meT}#NZo_WPX-W$!q=Nm*W%7eXEUsHsSDL z2>lbyy)kq5K1q0UxcamP677DZL~|y(IY^=t1V?w%lCNx$o_GFYW4&)mIp4`Cr`{27 zJ<00U&!dp>{fXNV*f`!@F52ZK=_uyNBAP?UibNJ6GAL zBXi1b_YnNR%Fcrl6B2cwu#h9X3Mtnd(4Gbz9`uEoRka-Ddvt=E1(V{W1mt77T2g0PQPrbW+#o$OVc}*vJ2Yz`i5!Ycr@+$Z=Zh7- zj}&ou1?U;L8SktTI^cZjZ9y)FE33f3*@0Da+Dd6<{gf`FTk5=JFl`f0ZzJ<#3N0ENsy-T~GvCgDDloMoq=~cc z23~`x7F=SEZXXrjUgYt^l?DS6j~?GUmTKo)sN?N>M|X~9Ojw8Ql+nsf$ppkJQMCbS z5T|fsEx%T&RoXk=(PnxZPC|1>5mnksRZ$v59?c!qH9)xD_`lxJ{YmnpzKh}XgB^L$Yuu!SG_j zCyIk);-DwN^Gg4d?u}3UD9^e#KJm9kJ?$K1U+E8jypxn^r~;bopKCQ}odAMN&R3J1oR!g~sbDzWao!$?`h8kjGZSFHhiT-&gTp4- zqHHjLM)p%ObP!YDV}?5PadEGRnGQ((AO>c5<@W>qIfJ|U5=K0oB;p^LR0MV~oE%on zhD5PbLwvY#E9J)^z^bE1DdT)i2AG1NtG z-#M!ZGGma7-oi*&1)~}5JuHmr)m-HUFN`x}XJPixseRz3K!J0*2u+|5?En^P6-uB+ z>xR{^4Qyx8to|_P`f&Br_$R7cjohfqOSn$o{c$_XKP0aN`nK*r2`Ss+#s}4#Qm2{t z=1$%3AT0Z41$F??9kMvX@!Z6Hr}DLpMyt{;Z&I7mgpE&fPG5Ve(I~D%r34K|32LN# z?RvUT4$tFDCo?N2PcAbX^IQr(*DFiQ$C25YWg$ck+yE#Hsa+}5N^^Z_`X?gv7^dlg zlTFPi_~*cOc2Nd5#ftrGWKctGlKsK*8Kl%E8D(7@o{X?GQI8I_p1io2Ud<+nJ6B@b z9F8XiXC(bv#Pk`?|N3YTIT`*G^GmQqF+ZZK-x_*Rsvkz~?e38w2$vOSsu^bLoSeYodbiWvJu>k#FJ)eI~@&1A8{Z zV*SSmb;fPJm^RBJPq{OuFA~*(rOhUCvsZjqYw%ELZOz7wJPl|%@&h{hv&fX} z%|*Y$*7N7?54fnAF5#kw!nEbgLiCq76k~J=26|wy#FCv$j%1w?CJA*C?3`WXjLv-; z13i2>yKBP`0zTQr7j4P6q!h<7$Isr&tt9v796t zj}PQWLGRrm8pj~EH=}V*sQV1(v&+`Ck7D2sK5d+}b55HFtWD&J4?VuP=)Lgqjyhko zg%O@9jaCunT^Qq7{=@ec7oSa;1ZRg=Gik;@E7$?o9(ReHH2(or+&JJ^=7H5V1jw$8}|D$4tWR3vtG#8KGDb z-!KqKXo6Gq`#jt$i;!=So2o5_=yn61=d~IoEsR0=9KagwX5?C@PqH{4Xn{tqZIFpX zB;t$6x!QsF#5P9Op*&`i5*Dr79G%4)b;Y29 z^ooquI&DA>8*eThPM91_5W!z1S)gW=IhW!XW=xxl2`{aKUgDsC_{csGHU5l@u5&(| z9FO)KyvBtPGwP7kQT4cl>Zac#cKq$g@(v|-%=}}^Bh1o^l=-f>ZRB7W|9i~%_a-uD z*3TP$k;EQ#Mw%?#NiaMVVH}p>ccZ_=^fFiqah5Xn{2oc7&_p)UI~E_2LjD=ZaZD*> z;C^-^MvP{QgPJ9^YjR%bj(`Mr6wg*pXTZ9e|?u}5Zh`qqe zr$hu$Ttg&1ptp>5%l>;mlllVC*yV(s69g&_yrMKSVC(PYyaW zod$Nsi@q#fj!~ruk$=5*y^YasT#I-6J@4tGfq zD9HUgG1Kk|7i7DzU<;p>A zVboN?AHyByYZy2)8bfc$NEn2C(+Df~72IChDfz~<{Hn+R_Lej#H5-NUT(9C2Dvukb zQZsUk0h3~+R$E3Vu;V5L^Mo-t0K!8xKzQd77?G7wm^Vv|l{zaq9mG9rEnh%Aav+YO zW95rGC|3o8x55<}AAIkn)2oQ~K{G@xiS>F5{x!I^pp!y7zlNvI^$FK1JlRBL;?wH9 z3eF*2HyzPvm3BF0?|cirxXvPo$SH*&s}9XEdR;3O@`&=K0=bZ{!HXw0HL<*~MK&%#s| zN+}Pqg5pspzjATn6x!>+LzY%151tR$#3h8_)i>5VHHppi+92D76n%6-ROkT)0OUKc zW62{Rj5lx&S)$&A{x}cLlKNf=dyO^EO0o#XHUQkJ9Td73y}hC(te1xXG;)c+DT}jC zdSz&&^dh*R&=CACFg6U#Z#U4yzzyv$i7+8W}6> zyplA>b7Y?6VM8SO=^;d)m^K%}OSK29k72`3Cuu$(m`9r7-Y$pW4P$CtyrN0Hc= zqKAWFqF^V%@0Fy*AqUCiVNZgoHQdICX^3PTSx|Ejy@nrEj=$EIc7{R%466F)IXC+;+`b1XXX z+W6!9baZ@So%k=t>%=#{V;K?XS7-zW)l9 z=B4#~r-nUVZdBkjOWpI)n{=zOx~}*1Y34B6zD=<4e;~5)!(8;Pn}&ztQ+Nh;BQFlc zK|lMa7H8A3aL{{*k%ixtuQ7ug%rBh|-VR*p7Y33ERusE3#(V#B-?D#LAApmCxRTSr zPO@;NUmJgX{~$WP5Ldc-H(Yn)8PlFjge;3(YHjV-3%7H(wqJv*m)Fc0&P81__*M;h z;oyO%if<^U)$i{o_Jk*4fwx`e*AI^LnO^o5rQ>jn!AZ^RPWEGV)7gL} zVj%Gi zAqy-o-eg?4M6DWkL$NM$Km~-YsxVZ`_+Pn_FmA!}bd!e-ZvID+6C=*QBc{zqlbUh| zzvN(!jF+R5dU|Xcuw1-5K8%==4?bUiNKz` zBP{NLhsM5@{BCr7q4Txdjz3%jd4GJ_{V9E%J=O0xdy6^`Pwh7joZ5k>$M18B_c%R% z9!G*)uD5B$Kk9lf@&HkWeQ`1`vYrN7Z*=l-4rs$LPm{N~n2Ya4#YbI@9R%ayAS&dU zxD`JmI2|cj+o`m74aEt{-uYT%N3s+A#SYJ;zG+IHUOJvxdS>~_XCzOF=LMNax~s_! z+F_bWLk0ty$081L`HN}uzP>Z*40n%4Blqku?Yq-%9#wveffh~}@~*hGH5aS+A1$qS z<9|n=FGS|9{{>8C4msKq5-EMD;3f52wx$zfNPCkp|cY99(*B?{{lgyl&6>-n;AU# zj#1F2WaGkTrcMtMyH}ARMEf7Hao`5SUP5+UT*)bu!I}-1F7cT{W*eqoHXc8a=8#~7 z4mP4?!DGn=0>_@(4pVDycHn7Ngr^u<5OPQP3pMKE)K%!TAW|~NN23W&1JSd@B<>Qs zO1B{;wc24*_{0q4Z{{lqey){L*NAYyKeo2EGVIF;wrfbvooTc-j)4i01Np}^s_^p3 zsRYWIa(lA||F$a)Ah<)TJ^aA{6dX%%G@u|_Goz0bOi_ZgEJj`uO=J8>Rnpi*w&@~X zgO^q@lX_m#mv|rVAhp*iZ{{o+DF(j=(2LqBjGj_Fx^)^CWj=IPqq51E=2WF#07xtY z7mK$-EUHc0ZKe6}x^2Qij1E|v;Jx^`;07Y4^32f=e?^2#m&OGxl-a=Y71|&&_?k)N zP-e!vc3KmPnMiiUDGAmo-`cL+l!eK!`Nx)@T3XI5EiIp1QW+f?c$5nEgTw6Hr`U<# z8Q~3aqIOIhol7{G4d#q4S-2zP=Wy?{iS2p^y##?yg4@M}`H+KQ;-DwN^EugIlkrCf zw?x2=jZauo*iWu)Bm?!uIcL?6hpT@hvbzVJ{2wtV|G1}sD;4}nAQc!6qNDzUV}%qpp)q*_t@6bYWMdsJf$Y+&2t}Zrda={;UaYi`=!?8FRK4bUU5>)e(5|ef=ELQWe_eZD7^%~97y*npAc>*k~0#w6TvZ0 zOMu+pP#mYxT1UcIN#iJSAbz`3+>yJP8@PgdSOYV|_Xru+kPEA4FJF~&-BXw^ zKOCV$v!#2U+a25O`3XaLJhGsJ#MBdp`Hn>GE=T@Szz7Vbbk+jaYWSvGS&yzv&THf! zR7gUkwOXj|`xW1VZxy%&6G3yw*D7l$tA|QkW_AX&vU62^hVyc``qa?VLq5lG{#k&Y zGtMuYTs5#bFhj^!Bj5k8`QH7U8NQ#=pBNuzJ|pp5bH_unm3q@W3Rn)Gx7W>cSUsDy zMjKO*Y3}e7e@4;MlwxH8qq>12cF^3ZS*zuDU*C-5~R{XnaO=84&AP} zn1Wu$a_@DR#h1eTs3j7^6vDfxe<{qn->`?`3mQnY`;kgv8j2Hx$^6T}#n~axua>sk zbUxGxkGVn0sEgUMN>FIrs2UCSkAw}9cXxbd_CqEgv)0J~v$J2V5dFi|4Lg-e77b5i zG<7}q+hYgsHTEHcJ+K~nzg>Ot?tS~teC)*+U$~UJeD>R4fN#smCHzU9Ieq21kD5m- zCr+kbc;(`AAH9s8Y`Sz15vr=do#0WPFl%r%!JEC{DN>HOOE(;khM==i}2p^y2 zm8UW%=DcI-gUyF2^NzK^Tw!@Qg_-Bo>SW0Ia*AK({2F}q{B)n`ao21Pli68cua(jc zoy=v{^6f%79gvBs=QE`!OK?+)vQwe=z2X8xQsGvuAPmR|>Nrs3r`> zDp3UOvHU+(?rh+nO_-&n9I`c#JEm3TnkXq@Oed#7kkY9}~4C9Kt6RHk66 zN_M>UymHip#kr|5-f48CS742l(HO!S?58(STN`bf?TDYj?)YrE~E< zKPv3K)`;r$KeR;Azc^=1o7H5O*TFDp$Rp!uH^-yhSCXbW2hZeTPlD;{*xNyf*VzzK zfY!nD+}MzNHrnX)>a67fy-O`m@0uqu^EOyx4gdepx3vZ&#cSNoQ?JIZ~Z?t@B-$*ebeWz(sTZ^s($!)<7p}#e$YgO(Wxgya= zXNy^Hz|KvgdTk-0Uw4X^WaZbb*flt(_C3+9v?^H%c3%4E%G0k=VdHx%Paj1oqU}=6 zcO3sNB#NvV=t^8Tt2$%c!7I1C!94iY!HGUIUeq`kr|X zfx|1$UjYa6nUyR(N0&NYD~<35@lKeJGEoJ*4*tzz7jt-P-g_R>C!Fx8(f!W?0jKLXvq* zO2NVM2ZlLIrgXAr4 zk0GEl$_Y-0_{{Prs%K=Y6KFV? zcu(j^7Q5x8B|DVP<{E>RuuufyV<5o4k+&O}W``u>$A5-XyQRa7@Tk$6(k$Pr3R&TKuUVDH(L2( z1vGA4c;iQ8!I*(4iOHGsOIk&nermzPf5DWSiOKtZ2_lbrQB8@OKrfs1(yO?v$&2B4 z^&mmhv|`J~19eCda`X-QStqv2o}(6@+YElY$N&gANA?20;i9+(GrI-{0-8mCvudZB z9ah)I0?sa>f`kzf!FS`fcldDnV{X*~Vx^3aMw;8HKuaz6CK+4PA8@5J1mgcy*h z-ew@j1#fxSmzqEp7-nZ7D3)f2>?yoYG-dV>M1LagY1%_w!_x{T7Ce%(&;zyKTAVyS zB%YHm#ma)W@^!Ej%f~@-`2XbbQP*PmYjr7x#4BLo*;(Y_Ezj!RG|UD7OTm?kn_X=H z)Qj!37*Y(4lNM5^a@tf*o62cZIc+MZQ48Nr!wVY;EdZIYI1jS+0jyu@j;i6SH8Vzb#x7^677B@e+Q#WjP=I* znbS~RKpz6t4({mUMTDYth~C8i2Bh}@O+N~skXYcItQ7*;JcWSXN<^{qHpo#xIroWKVy!s>y0P5m^(ZcVah>SE$urA5NdBqq* zT3@o%YOoMv2(%=s(8EYe?kvTa0Agk!E~43t)!7t}b{}vF&N6}U;~4mZHT%vancav< z8eX%%i`)j(?1yNgzji;=Y_vV+1ydjjoQYNCduV~uMiDni`7^4{$70D?C9&u|QANGcguYeVK%o1iw+gDEKxt3KCL_3%IiyE}_PlyCy_9(p z9q*}TvlBc}f`0R6_${5RSYmv!#&Yfb1#D%wfb(#Fjm~s`j-(!+?oV~qo$k*FGfRAb z+Cy9<`JaJ+6BVUhu_oRj^rx&?G^!;3$!|Phf>8VK3+6GlZk zF`CI4;wu>%!q5;c?YvcgivvGg{Y^Uw!$!n>>a<0E9GRzkIgsMBfkbbF9=HsfxUaNr zh^m8dHddNNKYOLsk&Hd{8^ua1JA3}ptci`dGqCNP39bDBCM>$xgK6#e>@<%`Yo9IK z>HZxJB-;I?v^KQ7+RcR}P=pYcF>!g~OOp52OIvW%uE87IYphk_tO8GRC<$2R5ZW4veAi|8jPun55bQix-}8v@ zn|Je{k-`;z<5%otjm2+1S7;$8Tn=6r5U_V#*Pj}mm;B6`N9lk33e7c|aKMDaK+6SXANrZo#r$S^xwHuLY>4IunQK)F}xHb6#T}Oh{)Gel-hO3h*=S$yYdMrUN zr*clD(6^JyaL2lnAqKa_L>PdGI=}e>G7aVn2>gaGUXaronK9rS2Nj;*g!30&%CHN< zrAE@s!U%^q)Ez|}JYU#`k=?wA#DTq05}b#WnTMc+!DGD>>FA8&euePzf~6BByj1@b zo{~1y{h`o8m^~GFYRR=5`2pZpBjESen|%d+BVhQA{r4H!&dNU!5gn^W$o+L>LB$t;Rr<7XqYr4eWk4^lr@tK2As-dR9= zU;rVc$0H!a^WTcD?ZgXP`W0;Ys30;}4*Ca{RhZ2gK7#t&8o&62J%xTr1BrG&sT?%? zt?|!$O&qfNa8R%5)ekSEiffRc2h)QC1qm6C<5g35cLJk4Gn&MPeOP%{NY%;;rGYh4R>F*yWtCWXgAnfLAPk`+hRYb$_{Zb zaB^Rl7z)M=@b-}q`WjMu*J(mB$%!GJBQ{#cz1WQ9Ua8qAl(ou_si4m# z*PC;SB?%RW&6n-U^*5Erw0U2D^esJg_h=N;^WbCdvDYoFjCIW2k{BK+u#iyDXIY=D zhme(2J*O-G__=l?r!|`;{&+IQ*qR^%4-PvO4U|!VE$M6V?=B#>4WfmDo~~Op=vz7l zyEJm}J@)802j9bZE1V%=*n@B8C+zY)sDUJX@C94_tNMB??ln&M3-oCwa7!}*Uallp z2DdnK85l1Lqk6-=yS9_!RbGXZNxlOZjYBU&_uu55T9g9R27Cm>Vq`sUy_N@Tl(VX= zGl&>zDsi7@E87BMy_3#umi(tuD-{vBbg2Z#AC3+2J5W;)QnArN5dn!+OR;4Kanht` zh93uRI~Nn40*47D4jTL*V+pH2CyHrvKFNh~P)ru?$oLtl66eV3AZmdlmZ2B8Vhy4g z2S=pQOo|Tab``TaJ!zj>;XC8ROe*!H~3*Z9Y|`}MpU z9a0YvI{>1q<$614c@Vm3+UA13ZXX)0ddER0a*GfMCIHmWHP($30G=;~P?^+>X+i6! zfE?0kR!xanibg9VRKq$jIVng;Uao>>O%F1L5DI!0BLlG*k2aDJy>8OehbaqXhX8=8#^2|JE36*Hk-j?3cWbmxI(Y?8Jm!gjykiXA^SzBL|-$f z48%1^PZ(b_ND|ajgtUH=aisICVU}N+L#nt;|?!(EmQsi##I2=KrUTT0_YL} zc5|5khWUBi=1TMPr@XVs(Ff;?LajqjVqD&E50jDsjNw@D*5FeN0hUz?Sm}-~#<(5w zc4x1ZayyiBfQq5jWN~x^`lKO4(0<+0P5*0IOq)~VPrQTABv4|;Uj1$u6|E6^KiAjj zfYlef(YpG_!_{sC|M0GH4F!zQ_-o2)dFk-|#?ox&Ml8*bM2X44wfDCe3_v|SS1Qv( zD6Zn^v8gnegYjX+jC}9~&6%{ZE@*!MpAX*2^iD42;Bb-ik;qjm@Y3RwxuEp4xO7PR zZDu*r_AO?tnT5_5xhtt|v1P-N4Ho-cj#tA%ShF==#bO*qa)Ml$DU@AdV{1{yQp zDn6kSEnJW{R9X|Hia2h3+^NQ>ka6I?xKTGj#nF?I9JiD#ChFjdcU`F2itaqbp;(9`m9F7rC#P-^KX=Wb`3^$p!0aVkJ6!d+Lo zIntA&_Ud$rLo4$&wZxY1h>-KkV7pQ6u*+=Y{l-6Mnf0hb&RW)T?7y#pM7y8VDjO)L zKYJNzcgbTqP1LC^6>c;eNNy>a!QlH@X`m*ll%OW_5~)T7b)t+lU$Rn#&uo_YcFIw2 zLo%V?7j{vb+G->|gN_Q4hzLB8VzwA{%A*-s%HX#RCfGtnRl2Gnau7+}4D3LQd?C@X zI_F)&fN|vfj$Qr!qDoAgbIHx0gIr>!|)Q z9Mwm>{*)zzA4~M9V86h;M)e#HAcJBq_|czrTjCI0uWX}n!_PGH?Q*7y4VMmD6V!q? zi;dXEVH7;a8&I?g_{?*5qXy9r!5uPd?+?MVy>IuS+j;O(w$Jmuf!W@JaqRsnChGm5BH~rn1KKTQd1$^<2ADAEL zbyhZeo>5m#bBi0;&dyo&@MExJAFjTO|BMv$@Tt#P#K+=&|4;{(3j%3Ysqss=Iw*aG z7V#~ihyoeTbvVwm-nHu@{e`w}w1Kn`lPJAWg8M`WJcW3b92WeIHe>$99IHm`m&*vt z7UiVY4Z-Mv29_nZ#W_$x{{HS zXC?`c8CoCg&CC2*Kn8DHtd8hu?Y$Y=`PS>eTM;6n0_P8BZXi*qTMQe`c^~waPcU=m zQg~*9GbF>qjA5sxoH~ZG!EgGB1HB0muZ>&P6|9Ja56HrKx8$GObX33PtQcw`$vWOP zSF_kxG=a=88MYju4+9PKyu(}z^X@5@+nrdybc5wnbD7viVLCgcm| zPoH%$FHg5{ovd*%mzr*2P}GR*BDkT6)Re~YAHC-fRx^Ci3Js%5O`rW&R(P1vK%(6z zr)K!^E3Ef}vly;toA6;nISWLRDmOBnCp+WK&%dhNTWRT#-!>~7Wq7BVn09I$co_K& zSU#vez!`*4)kdvIlgm0j<5-h!kcQf%l*-rOZBa!1X0e*!2W=5);T-cTtl$x77>*7z z%wXNR!?lNO_q<&ur4Ih@12Guw_ff<1lS#}}W6%A%CVZbpM4pve)lRu82-u-4Jp(|2pH~jmmn!YgUsTrL#?wh76MblwJA$`plR%7m}SiOT*oS0mooCcvF92)zb7> zoBDTy%NMKZ;v_;fU8CYdRw^0=gC-FbA#M)(onpvCFnA$jh2o%PNZiH6%4r??DV0)} zzuqoTtx>Lp_LtCmmKS|Z;%3QDSm-Z}#X^6j6iLxl(TBV&L+ok)9)HyS;P7w0y z89 z6O^39IiL$o`a94AA@#bpXcfw|ZqufflFWWA%+hAS6`O}f3r3F+U=hyfGs7xp63dau z#5jCAVZdN&zip|lKiiIJvl>Ew;>B`MOd9gYIGSCDbv&OW4LLX_3wII>KR6s=TfWvE z@`ac&4L&ZvhyrEe7j(Ef&T)D5m+y}F)R6hq+c{;hPAdkGmBLRf5>(1b0j?~Sr}EWr z7g6-b1dywD5r2nMkdb#(2&sx)S>0ZJo2S(c6^Hz0zEDapvXBpgB|4i~-8&#CZ8E_F zR?rvRT84a8gOV=bhF|NHa^iUdaDWgA+E92d2PiOmL8+(a{m?FMt_Ysj{a7$ zz0)jZfyp`!kG3sHqrKGoA)k_<7R~mp-&APLt+N#T40Hk7%rkYi7ujP_wdSu=M>(Pi+a&X0qC4Tlf)N8W+6$HV+lY#nMmH zC|7T0_@X}a=8(}M_Nl;e`M&$vx_&OBRO0edALq|FxEdz{qjk1Q?T2y|9nhL@03$ko zRE~3-*YN6O;U;%ymu2-1He9JeC zqo4dHyft1zfXDu;JeD%oj8k`LC9U`D)tXY1P_JR**Y(PPF`6~3hP>1Z38B0i*k#N~+g zI}@f|>wkV|+O0^mgrH!xMXkdD1<8-6Oa_NF;XWKKNl0;Bo0D} zgPsJ>CE$sK9NfOFi==qRUK`j!WMPzzAGaD|3-@pVZl4~BLUn*!KMH;SDVXs3vLOf6 z0SzZvfe%f@?CkdKP6j6igTd-LXIg*ckP@q~@rM>-uD*QFzI`H!XwIMYR#r}=OonWG zR~lZlQE;*j%+Xa*ygsNuu8Q!)NRK5GqePr;tN!Yi>9(?LHI|0no~-7r-B$LD71idiK>&%~`(42} z-Yx1^t=M9O%&=(PU$uGWJFRs6D;h|&`^4O$uD*`T>gf&mV8Z7~Td>!~K+gzFvBXo0 z2)9a~0in3gU65pd^Tv+f@p)aN*xAXK)=nSgA^kO#p6qNc`z4hfv2m+~DX^?-?4GMhQMSQkcF14m39?LEkR ze`v{4`<#aA9vo1sYp#vvtKAP>^8}FoeFRdNyxk4Lo1-pqaOrz3ZJUwE&G9{b=*dB~ zZ<83T;@nG3f6mSD=rGjk3}LwTG2;nWmpGv4-_ElB>ddlfaJc$^lbq#m?44yps}7cX zwTi)Q@3}V253MfP?U2N#b_Sd<;7M@2m@unxuuL5EBzT?`dsQMVFd+K`fyUrA_;%|s zr?GCgM{$-q;wG+a$KgcscD%_YC0>bzP*5IZ^>pUN*c+}+=WDoYOTYv~9)0FrFidEx+<-tz$xe(fl-{%;sN$Xjto=O|#|NkWamZ7>gS{k|nuhldBoxmDhG;2H+AmwU1C zw%|34OGarMjEZ(N5Q1yRG6H-+cPgp_v1V&Ka23W4soB5_yaKG1V3|W|8;6*94T2l; z6=vr1Q8$rfiI1?tZIBw*U=>4|hkELo9IK^mn!k9ZSwkT~1f;dEr_1ej(?50W*k--} z_vn(T`LKzbNeRJfh(b9A7l*}mV=)*^X%Y93MP%&ZMP>0O`faopQEaVU#?`J;SY({^ z;ySE!{-WG#7W0c5KWvi4d=WVdS(`0iW9jj&M(f70xfE_X=kh*=f2P&gs@FynLBo7GjiD~oEV1_4KZU?{QV2+HJk8mP&Tx)Y>qMA7OnT%~_8Opd;@n#G|8rOpkejQ=T@X$FVq z#e}S-)VdR75jQkMO!{C*CJs>w{C5JY>b-%*YlMd%<)YGzZ zId}`G4=d0QOI8$k#2Xhy#Q9em^frWZp>=qtYoO?ov%0-*#(YHh>SBHNB!j8)BuBI+tmHq2>JD9T~%&z;ZvOoFfRvP=f1`_Q)F;#Z=8OF{U zB{nk&;IplzgIc+`HiYOO@m%@Zj$eTq_J==@TH5?mzVG@jcKZaN?1WeUEipb^{bM_O zN1CS=CFuQOB>w=nMP zRTNW{QbSHESg?bYdE}iwE-#IX4?#hH%uxwF=yPLnFF|%(2%MhZ#bZ;`XE? zFyIVl5P-~03nvPk#PW*wRo zxkhf}>;7)O{7vAG@4vpQf02+_{mTdN%j4H6A(x*36I*%pUc)V$L@;A2J#Nc=v>sl2Ou2o=_8 z-^}UftKA396G&vG-PP{>2yo+6`n%mni;V)bUNt`h`zy2(_2O>#z+YnYpuhX+U7cEf zX|;P$qt|HR{ewsz0{d=$vxzScsBVz)u6_ewQ~GPCRl~Q3+KmFTIpO&EKuO*sFcVR zU~%;^Wb~+Cun!(&ik?ty~Wa6 zX9MsKZK-TRXaQ^T=I(0sPf<7P`?`lDDi&pfQ8)opx!XO6JaLOpFQO>kZugtRKjuoU z77_y@RJ>R#wJ^aPW1+po0w_85YJ(TaD-emBodv^uY^iZ+0+00pr!;H!UId>sXam^l?rRuJE1(+eGtgdGeOMo zX#NoJB{DhY`15zksG6l_4(WC2BLGbo+C0c7RJr9y)LqZ07PhvwGR>WKxlzwFS{uh; ztvrU7{;}QeyZHto@{Jtw1z?s@nxT6?o-clI={Tn4P;0#q>4r~&Zob)c1AlgG&q@h0 z1iLA>H*4tPU^~AC+Ap@tyD#70eLo0lGiNuI9ez%n>UY1tdss$;2;@?W%0y5c=cu^* zeccCI`7QeuJMIyGr{2zQ=gP>MRb%F?-R^$6)9-d4^f&X^NFVQD-}-p-8|1tCitKod zkCqvHKawJ}@&(-f)qcW?k@4j4_Ki*xgE<7I)2_5JJ!+qSKZvAJpm8wR_>Ykl_?@+I zyGKe$(10Qc?H%-0E+L=7_jlio9Q*kjIV5GM)N=V^5%LpR!S{9VDb;W8u6EYC_bV2F ztp_TC{=WjcZlm%Tl&NhQ@uTPnRM8gwKPY6~-@Uz??mi41X0ZV8mi8h)p~m;Y?t7w5 zD|H-8je5W>@9pkiSvq;bD8AH}unh1C?B3`hEQdo+kM7Y>{VRBlN+F>1XfQP7JMVBo zs^5j5Z84C$mzT^4_%Yo75B2Lm25g@Zbh?j)W}==)AY%NiRd1ua*b)CA$HC=UH?MaO zFtatL`u1-3K0Z{R)71)3QDo`fSAF_k{B?qV{p11s^>_G}4;5Rr$-i=J@*4ko9KfsJ z!oU7I0ZW&G09s`RodJ**1!Re`)JP*(-wsz6&6 zNUNRl`#>==!1AJuuKe%S(7u%;m7)DKM=C?R$&t#?C`+iJ{m?;tlA%%jk)cV7gHHD$ zcVElQJX8?N6!tM@OFbd)HSH8lyH8X*a5wDk&9z3&vI=SXuE;~%`d|p+LDQ?e^jHYK zCl?EV%DEZZbUoG}isQcQ26(=UZU7peY}R mlIqYN5TVBp*vGQJ;R%K_OS5;%PTfb=H*+qja=toing0)hhmH6E literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/.doctrees/chapteroptimization.doctree b/doc/LectureNotes/_build/.doctrees/chapteroptimization.doctree index 322d1fe100a9bec4adf28c005a2a78521ba8859c..2c60b3f7d6dbb98b5d496743918166348974794d 100644 GIT binary patch delta 162369 zcmcG13A`Is^}l)TwDeI*3+-!5Y5Q6VElu0(TY=K-`<|DL(vm%ymwkU>2_PbB*gBN~ zQDjp@1=+MJg2+#CMV6nt;>J((hk}5({y_g{CT}v6NnY~O_x^l7N;#D-?aSt(vC^^Dl47WK3_Eu2RmUzrwkwIW zj-9`4@7_s+$7-33r_!;>P^Fy9gvzN%D4m{}OvJLWVyGO8PR5J5%%mn4v1cQ($x^OT zgg?8I<#N8XpT|q2%E?N2UnG~|0lyqHA^$ds59f~0UYd;Oia>cXSMmU?3KGQd4Cn9X_OJaL%sJ2tDwGmyc&J>)lpOWy*0Q$T$68AX$&X=AO>9`%T3!w%vY|}uSaKY@ofDd9 zElsDgv18WLb|xp1OOl-Al1eza;^vF%oHaN9$|e%SRUwc~t|xkJBj{!m{M!uww!*({ z7ayx6cP9DC-PY~4zEe1YN=Z|kyH_Mle=um-8P`Uro|aQ z#t;A=Vl}{)Av;zwuVPYUs|TL*v!3%Z2@eM80gyW=kR(3>3U)uTV-1rN0dNZYC9;9D z20L}ddi6vywO}63Wd<>u$J|N)E$%kIhXnWRvU7UD;SWE)Y#nC}{+mxNTMO{sw_tdM z<@1E?QtTe9ZRRqfxUYakfIXUeSTZ?ANpm@Jo`axEBrS4@fx41fojv1KnIA-Jy+)2w<60-+4E zt&(B+Q?>F5bSvjQ?_nySPb}=y27B$)E&E4(m{td-T`g|*dAwu0ttB%@QtiyQrv14q zI-~npsD}sIy|aO~Bg|4Vp1rerOFtmJv9R+TnN-^0kcP|QQ()m!H&o{^sONNLF2dh> zu#!-}x@JQ^s0pN?Ij9oFYa&iK_7v!6}g2C<*PHan_ojeB$ z8T4*K6}zp%3RTN=T>0&ZDt_3^nyJOZfH-mu4Sa&2J-oF~Ee<>D(I$O&oYcPhH zWJpO}0a2-zozi(W{4`%2Y*neO0DVL|7@ zC3QyqKz!~-pB{vMch7K=NXmVk1@lktpIe#OS0+zNtm#%{o~_8{ASfdsv2WXinb(eE zj%}MXeXM^}1#ZW#JbU{J%Av_`*gM-!0Xw{9kpN${{T!^moqzrbgI&|wgWYs!9rn-d zPF*jN-XP45!Bme@F&MoEyXmYuAzuo1d=#?u7eUU^vb5{Jdb0HHvwsH!SDzCHEBO{n zakGIOyYrlrpw0c~YzF1Nz-lu*h=*UDP0|#3(#cQVxkuH9V;?J^9_s{9+KKdF1Nx2) zkl$u);17!g6Ww(abR8SQ@UEkTW^~=ba~}dNzIpCvq3bwHhIQRp-36AZxQ6qdp3eK% z?t?(`JnjXy(}5sF?KQ+7#>CO!-hn)Cx?0{#_goC$`-kPktlpZ|udqA!@*n-(o{w-0 zP-Kow{+d4Iv2X5^0PN@X?ecYk9?EYEuy14z*YzJPY0mZpPoh&VwRVeybqC)It z&vK)ktT|G`JZbWjCxKuelwAq>I$3_X^?CyD1p1+oU=wt|-hs`a`$M@M=)NRZG3@g8 zHiz3r=I~4(4v#*mz=^KD>pT^9>vh;3)TD|2Qaz zP|xmNmaq14Rl1*OmwL3WyofOPAE=Ijv7ffIJ3I9=_TDzwo$6aarrsO9#!k0k7<*px z(StU@3L5lvr4-!?4T`3gM!c=(mF{QShh=Zn!PcvUP0fWIXF#ejZGhTv=Ye z-#UTD0p;9D{o-StcX`Pjv!zrL#^6M+m|pxp$XW2(ZFZ{aWbBiMy<23O2hA{yN{+fYwiTO2lLGnX_-0a)J&J5d!Og96`&F1UCw~nzot)Fl8 zw!vO9-vS-PzA?Ome!G2)g$G1@+_DewylUAEB7SzLh)q_7`<9VSGO6rL*_||#ilw8e zY=W{{`a-A6&?gBUOrT$3siMc1+V;D3_EjuV4vZDpyg{7Tts)TTpVqVXbXbrn>^nn6 zWB1-^x3bAY74wko5RgB`9uC;#X;8{04?^z}i}XBbM0(I>L6+*Lo4-4iGNe=bC7 za_EHJHMI%e6>M89z}Rx{ZiwkLj@c~K(HMF@(HreyTTg-!FA9t$#QXo3yxXuJc)2hy z(t~AwdRx;{V>YK6yTa#$%zUCmuoZryE;!-Gf9gNFkjMWPFkr6*Tno{{LF};WAoh6B zwh$s}?BgyqcHKn_Qf2gz0lVmsYa#mBcCi54aPfJNP1rp$Je$xi+DXbv?DmU~LY&!m z__IWIV_9#%IMdq(a~_dmh9d`w496lc9FwgRHYiLGTc1BdB=PevA(HrKf#lo;NWUcR z5>t_gA_-|=EW`(r0p9kGqyFh8M`#bg$ahAu@F-;h|kA}8N{E)HbX#snbl^nR73>7 z`hJRehXFZE3)eoSh`{Tqc%sme#h#8}IMpn?#=P8U7O;FG&DIth` zFeR|AT1NKhO5)E*^K*CqolO_a@X6E$%<7?{Z=YhrKs@N1b$=PGztLbLaPfKhU?RWKF&r z#hCsOVPPEZ55L7IC3F~&{%}Tt7`d}~4)+I|9>aD&QurgN@yA62_Why@RCyT-W?0IACBK=1?AUD%aXA&C8nd5GQH279&2hwksWF@^1`Z3g<5+L=(w z9cR%V-t%wMh$-4+Ez8+MkKtSJ1(ZPDrv}~Z{@Osi_NE(kOm_W1xJ5>Ski0Mtt(pIyD5KzjqJFeskie;xvC!k;^Aj*~xM; z#!zSHQkTBwo&uuf>F9I~_S%fMzdiUGM8G}L*nl0Xtpshnd*ZUNMCmsJPh)H2XSw0- zKGS*(lOvp@Gx=b;bSD5WUb@4vemUuN>xe%i<+gv))=ZOz6!FTXJ|O+(rFwir5FzT7 zvw-y64o#F==dkj`*l)XByMy{Kmw~$R>rvzk(6xw#IN2FWwN@TVgff}Xk?F|;lbv-! z-50xU@O&1np}yQSowfp@2Bs8}wlgyp@KCQ#s0NfbvpTL%zcHxO%4H-=OmM~bIcttK zH-KGwSm0qf_ns!PoLhO-dYEdvn00%oY^JreXcTQyw6)m5E7oF9G`FAGk16H%*x|dl zWQ2#o=Ha_!P&4Ki3jy}vmBgEF3KXSIrodnr?_Df*y~RQg=QS-&4YqO=;a|EInkh|U zKfdZZ5SiU@c#kub&g}6=KYca%e(`hfy#eysoh;GVX@STJy=|~(t}$RwTtf^HdvEp% zNw;ByK;!#Npj!G?Pqbfo2)3Lg!*K}s^xC}ci`_o=I7^nHcDcc{fi_GE31OJn?rVwl zzSJe!EGUy~adgzoBYf(H@%>R@^hZI=m;dV84GU4R;Qg0?<*=m~ZaECC(3S&%_!sYw zK_%eA4qm3l_FT7`HKF(h$URzA-p=ntJem&_UC0M+Kwue?Cy77z>E-LO&wXGG_~?61 z>dq%j9|b8_ux=0Se3Q`E;ZD&e``-S+I5-A%snhp;=CXR*V6T1fY5>E&F@D`+>KFis~#ME zdYEp*h+LVQ$|o+y^x}yTxp~(@#Q4U|#}@MV?~WR=UmSJATqUifxvOBh4XwzQ2HSGI z2KyXFn4tHb+c z*gkF4*i#=?V?V{6usE{M?Vg3jbQ^|(wY5|_4Ld>0_(6QxdhAEH?!-QOE1_+=_1xN~ z+t3s-`E9pAkJGnCd%U$9bAEg+w&f!>&^MdNaD5-30~Ax=*zu2ifGAFHzXW3B%WQQ| zVV}R9c%A#i?UVE*7Wv}tPpqcHBcz4~K=C0XWbmU!5Qw@&MaSU+G3YS`dUXBAzCakz z_wUd_Um+`4iLXzb>eFTqru^6*{JiU7UHCxnNo}a_ z+&waEhKc?9PCoYIJNLtofTBt%lpc`v4hcky2LIQ09UQJL-J-Gk+}+ZJXsd9K5lh}f zgy9}-4YU(l;qdk?aEBV(f3I^PM9#%NcE@h)&3mO&y-0>T0>hM;j?gK$Z^ADArp-t>D;?GF4JeqE@)Km=B z)qWW)4#f_BM*OJg)8j-CJn)%1R9jE8_|T!C#Zh;LVrtebm@JXE##!MHpOq+Xp_7N$ar!d3km+ZD0s-S9QMTx#L?o+bb5M*?h8^a%g0BtL*gysoISmi znDeE{x7y$P^>wEo(Ps%Q%nn@GMtH^u&^D9X%KKw$&j-K^b&ov_v^hFzwU)xcAYGD? z-}_32-Tb*t;Cv5!?hGgmBqK;LSb)vQ7CoGu7v?s$~g#(g~Af|Ds8-tQoPn#ZW z-&!In;;!?D!-^k{)n< zA_?85<3MY$%f6_Bg}wYm&>lXP@6?%8WhsI1eoD ze;(gwn?RSH+%`q3*9Y1Xx|C?W+vK3liK0x7@hV`|wuP%o)S~PY?zDDfX?qx^yWDD6hX^can zZg=MFw{AbXc425{y_EE&RZkNyU3=kR`=54$^fx^10_ksC7{5*yT7z-_Yu6Cz+ob^| zJ*!Y4BkN}uhK4EqFaC?zJ=QCIr!$rj3oxJ}pT$Fc?e31RE(DN>;!b8t<{q`SPxpg| zJ@oY!bj}6e_z<9fVIkbRm@gw1jSJ4D6B+DVXJdTvms{msA8g$W&#R0q)0J22->MSx z4uAeOv0`xb%I>7uZ;Gk64fdt)IKV7=ZqSwVpj@$?#dBbyCKINM&e9am3YjZD^j#v- zQP;ZdhBTWcnj@XfndIkgw-PTL$};jOuQizTd&F+W9w>b(D7p=!g8Jz9b_|qcVD@z^ zTnvzc)TruNVwWimarOmBr)OJBT=Yy1`MF!8;e|t?H2R-siDA;*PzI``vTz)fN}l@u z2JHCvw=bl3Z+NbVz3;ipPGyOMt$tnuuK0`RcVIKm@7q0r9-Sv@?1kqA&7J5?MDyLI ze(phxflt~qDdh9T=Q0*pF|I+tW$Si$P+_oI$&4!4^)GOD_7v+6vcy3Vh>YiAlP_*N z`r=X$9C`74=;6<^S`CZ`RN?NULjuKx$ZqW60(Gyw6_PkKlO-S(ZTbWbQzd{SoW2zIxcvIa8GwNd#yuP)x~^>!&}2bJl)% zHl!`;G94SS6+hY(U(-7IP&O1!hbAHYGSV?w{rq7*K<0(xgFhmoNe_lTL9tJpIj8e_ z+IFH-pQ&6od6+OM*V0qElU-j0&r7ajKPJ{s4Ztxd|4l3k3^H1qelmIDICd=_jz9fG zGZ05>NFLt5a437)dARol7u`#YboGu8(a_-NF16u??V;tB*+K+SLC`piT zdhpMP>EM6=jF=8SvPe|dV2Pg-$2rpSQn?$u>*v3LaqSD(FaG-l_A;vCqH%xlrCt5G zzxoofPkQ4o_kytRTQqhz|B}eaJ;DwQEer#g{MBx3{jbCTiA{o)Ao{E|W<*_Pe!y<| z)t=rQcpppR*&Mj%*W24UaP_Ybfa^TSYBex4Q8_S7M}LY-zZ^*28z~1eXftJe^zXmU z6QhUZZ;3(nGc45eOmxq&9vdhuIRJ>#l2Sa|$P;=oZ4fXhMAN55#;yj}XJ{lQ7T2ivokJm+tsq%|euU=BwvG!eEOrJYg{0g&9n- z>tB5gV(Eupy)W8PJbD!&?F8B!NoeA&+%z2{nM^wKjDN#E{+bTM{&XBze(W_PcI-7b zgwE?(eELlQ^|rybzD_Kz?Y+@ke$j0@p%eCpy?(=j9{)2B`=386pf70Z^L^cv>8~a% z`3A88)bpkklyZC?O6hHbt$a&~EqRMLk*fD*uVUyn48{EXEfeTrChM=m!KKAwnpuwNN9S2wc1MB|46i?MNH5vg$zh6B=-5aT% zVbErJ2lnb;e*&QY{I|2PSN^saBISEd?aqa;rGN8A&UV;EcW@(T8z^=KtHD6Y$l_&& z7K@@zh=nh|3?b@u>RP9GnZn-q`&yW1SlVZ3e&%9v@3qHn9POjt-v19`oZEc|u+J}U zixved8MiO^XSyGbK1q3gR3ng1pp}sT6N%|^+Wr}&`|NJN=w0H((JSBGcHVVuUf05(`7Gsh zeWJ6J^S#(F-ZgTRkDl}IU7Xb){)7isTf%=tpYMW|H&g%F0o`&3O9XiHd;NdNYL4)@ z3+jj23oY(rJuuwoJv1VU8|m{~PvQ{o_Ni;M&*Pz!IFoS7#p*i#*>xP^eejnTi|L1d z$+;K2rxrDSaGAtihzW7Gc5h~S!E4zS@brdUDuPhbe=>% z0v{{91&Q1%<$$6n=OaXS}(KP{#y%&PZAzV0&o?J!|&idBSEqdCUF| zZkDFH6@?z_k@&s%w&fh|+J4gFmn`R8$eF_LT+TTIgnfKDhY0DGkwheNlb;sR&=C=A ze>MhD*XE2tU~NYhi)mkLV(oUR#JB|*9$uIzB8`+>T~=!bj9Ik2e#|He3HD|7~@{4=s|)-mo>k)<8|nVan4H4>HXbk*GkT}_d*$MiIthLxBVT0 z#@ASSg;IaZDV#H6us)Tj112w+?5za8!+K_*)MWL4i0*xgAyEln?O(~EE-^a)yMO@- zf$;?XM}^?*!}A1v_!G^}V5g0m06kDmRQbV>mk~mhAUfs$?SgApUlmYoTKFYv zIXcLT_pRk{2}@YZ*}_@?chyMxApGzWS|68p^Z_~2u#T+LscVcddBr*oakkOD>o~;1 zsbh=9v2TuKvuA0$U!lSfsL>Hdb&XWUs1b=1%#w=6#A0{|(NEN<%J?Tkb z8d)V_x)VO%;XDvC>41#K9-$s{4E{l2N>;|BLuAF__jWI7(o;DnlPUU8ntW|BJEhZg zt>dKR)XvXFRz{Ro#*Zke$WiR9Nm3UXCfPkv_}ZedBnGRW-N>HQFCLL2Ab`sheR6E9vIL4H>J7xnFHfV+8o->CY|G_rK$3e;Wcz@ODgd_ zn>e2apZM`6&V9}8gbF6m$&oZcMC&+h3p8;$2(;Fga+%oPQYw>A$M)unxo|p`DN$RS z;cR~L{$#V=V3N^*wd0vFk44XvG5D-*S0sDml`QPF%Vn87X75ch?{$;kXQH<}57<#n z85RD$&73o5&m|*1pQBQ@^{0eCLy{HogWsm`_d1E{0QpE#d0f1Ovy1puMK!M6!cpUQ zZ{;{Inn3NW9_jZIs<#b$tslDuypzCflVpzi_$22{I5Kku4j(qdUZEo_h695f^?D*o z%R{ju=k&(6aee?VY^ZCUfUu@_j-77PsdCrg8@6*Ef>MgUH{Ull3_yf}seO3IPd|&} z<#2As(H$Hf==w~2+gY45@h|S+?A|wlUOR8m(Yx@~XLBr?&N|a1t$?d(etpEG?$WBj z?>w7B9ADmhr&mdI8-|j;b`HmY{pq1`{Au{G5JETZ<;yLp5x;2 zvDoKY9#!_C3sK$5H3|eN;RNhuw)c=Puq}I!645R zk}^vC0FPs)5)6Eva)<~CCQ!jhf)EM%le8c-CvdBmc^vrdH2ifQCy!66$-`AI1mc5z zi*1CD+}N=JnmF{8O2By-!s`y)BH--6SAG!E&DlcEPUtc_OMqE}#7{W`frH`krjWEo zKdaU7{(AZg9V8SBvcERsR|+^A@i7r+C#+teZc#neH=D9}LzNj4aULVm5bF-BpZjz( z167xPE)jFy57G)Ghy!%eV9}*?a>;odLMPJ_a(4B-tX9Ky@(o%i6bmvdpD9I%ZHLsg zjxtE^nZOTAk#S%^|IcFmyrF@&v>;(GFkrYh0 z^lz6g@0(K2R3LERJ>FCxhXMW%M~43vw+~%_f8l-@VXnbX-OpL)_^W&qpz;0?9loY{+|P!J^0K4&U=B^y9YQ)P~F+U zhB?FAPKFy#63i~^z^}THb2|ROg`AZj@IF@K;Tqh2R|gZtiPRwXAZH7{{UB!-gjebY zrN(~YwYLrKJ%|vSoqFzcrZfh=g*PpVDCGRbK_!O>jJ-hcgGvOBQ^4~|WFH_sv?wfz zVu^WNKl*LrRP{dWyJO-;GA7a(86$yr^qdX2O@*w69;O@2w*Y7KaFN$$sl13f^h!`BA1*(2uI6y#KcKL@0T7`Jk^GitgE+wd+A{4_Y~1n3YhE z;zb+H1b@)Rk*>T5XtYjI$I@wI7I(Ti8;+l3=llS+F&%%&!TBl&f>&}N7g&OHcJiFo zN$F5FQ3)kt$66<)@-yXRE-N|)GazW3P{afpA^wmiN@c6=sM{Kk0E8o{Y`#LAd)XOD z?I6#jL_@^mQ1@0k@DI-tgm;n`;aWGm@45(|c5}YBR3;Nij-Th@e3vucf;JG+cA+=m ztG%4bGiJYEehmFE+_|n4ZY_<5%AsRu3paT=MrD+*kVoSpp`3rxzg1ddK5=`y#q)2EX^;QK z$ML_j{{B13wV3ar$&&5yuxD&Hr-fhd8QamE1)W6NZz7ZHiQT&!p#xZFo3&QvDrL|k z1$GJ157z+8ZVg^VT!AiOJ2f0wM|4G-2BR+ywtq+yZ4%GH&Xd{4=UQprT1t>%JiiUU z>y5GXXYWK0wFyw^fF?kPJp9?Iu}xG0g3o6+f6#vD#SYhYQPXWjwB59iG9?nwTOaM% z48;*_=3<~jWxKXIccI~)YiNSHgcrPH7lF4w>m54+KJf}%XX}m0obU;>3XRYj(USIq zm*MLmKR_>q1`PY}GXJr!lcF3r7u5gjSwbMomGH4!7W93cOXzj*@nSIX_7%bxm`1w! z?Xj~?x)1Jw;oXlL-X6G;53us}7-$0v+@*;(wnf{?}o79KL-3 z{UZGTI!5~;c8p);KWQDD<1lNuv$7MS{|gB9GhFl=aHB_ev*t?ai?+7zG70@2`{CA# zNDRO4jj=VG2bwJYn^(t(V&mVhj%{q7J3;!!PU6o933<2av_H6#uE0uTf_m9>Ct#tco<3zsPLv)p7mJk~STiax4kPOr_W#O&mu1aBp3C!l@RC8SV6LaKO2`=iDP@P*d0Qn?rlWsadY&3=nQN;rld#c%ub*beWk|NsAW z`dMKJS+4BJ(jD>#Iz6R;6L5NnJoCs?tyR8cs63er<@2#@EP5eTrn4{8CHp4`IVRA1 zI(O?%#1KH6O;UqWT`kJm@8SnAIdxUx8(TqZ!i7(sm*Wl+uLo9F&HsE#uhhw z!orH~DzIrDW0Zjm-G8^E`w<+A>ah7c7JkngW9!Zu;8avP#@|Jd$?@5ewzaW@Kew5) z@jxiqyT%-8Ij;*dBAAw=)Nz0Ls zfkXY@a>RnawH)!n^ye7_RYu+76_JT zbQE=BdTMqVHFb$GI|U3U@CQyOU%0&sTp?TSUo5V@YZhn#RG0w0tRjBqt`tf|C(F4> z{EZa|v6G)}*^Y{X^+!{~4dV#$Gd}F+DVypYBN3`2f+|CGM8~$vN*HxNK8|RiOE@PZ zN|-db1a8f3CjEYN^6GcG45m#NjON~xkq6+ts26|mWW#J*StnET9uy10s#^HjE0J^X{i_fGXq>u3 z8P{-)Gst#n{0plPBWV0Fa{I_?zuVNoOcMvS-*+nVE)ainHKNAo+HRHxpyK#S1&+R z`|Dyc?mO|$7N2GO{f^ILbaI!0p1+QaH=1>b9RKn*>03LdO7j3Wn_7?Tf#|jlKe8TKhu^jyIScxL z%MyX!A>Ue(x&Wn0X7Y2#%*eu2%zARL@I)qj5zYc8YZ8iWw0%-c-|k}rV|8C=4w9Zr zVvz5W`{NssFM)0Y8<7u!lUi7?saM#H6)xZtQ><3Qh5G?59L0hR5LcXmOuG88?S5-W zYLt48>9Fk|m}#xZ9xA6YvC?Fg8d$$^2C@NwrWXyUdlNz&c{l*Xk`$METMfnmpSumB zxo{}6MMm$h4+zLoX^Qqsy(lK3{F02av z(Pm^BOvmFdZ6UM$r&uZg@yo7#ja9 zz*ISj2efq!)ivYsd@$MIjBg%CTs*%*iWC4)HaKj4=KcOVV`ee({) z0)Dw2K#%5^W0H<{&~zc!U3fMEKP`!8&PH}S#Dpp)P~k`#A(HiJhx!l)(7!($Nda-^ zIYF<_V@Oo3!pdbM2ID{SM7unt-cf40xscTfo=zsjpNgYJyarib|)EG0<4z9 zBa86U9T*fFGO{RkA^V||scTeZ8Q#eZf^=tqzMkBLJPI#K?;OY9JQoc8V_QJJ|Lj6C z)FPGQ$Qo3=(1A{K0u8=*H==|R=PdmC-N;$^tGf{a=hdy~6VD z2|Vp2hqg5*vK7qe30AA&x-9BCC@2=BT|UJ_&Vc|)U8C%>-_Wp68$15+Uc`>)_{ha0 z6JbPIa&m^T@)uI@ON%98-#WODD9oQ2ZZ9{Z8+D+r!S@Og6TU-;c;IK!=mvAo-Oz1l zBCtmM@IF`s^b;W>1X1ZGvt;NsfP<;@1Fx-w91nI7ZKIpSn{0TrinjJm8VpYGCink6RcR;N- zyEyz=mKLZ~`ox7~D*e`l2yvXwk65jS>*_^*hdafBEK8Ufgd7i2cPXtwQk{UQ|8R_$ zVVq19Ls2|_5ZMDDdRo#cV9-woytXLVnajX?fv}c=|7THH5>;HkW#B#RyTe^OFVl?} zDTuiYoNh4RJjCeIE^8gQ4199asCN5XU&nH2HV{B=P$OTMdl@(%_%O@bezjRo8*-G- zUIu;vi_&mgf9r}4Vu}SB7iO1%Q`b5c&Rz!YSS*fxvttkYZgbg0dLiA2HkXzXe?g5X z@fjUL{4hG*WbQ(aZbOs7WqM=}zE6)3yMO5h^R+sLa=Xmob9#h0T;?4;at4gF8Y~sI z!x(WO*h)9D6=o&g%W5#ZSN~4;Dn*@)U>oq~^{^N0IRiqRy+hriJGZkSi8D>jVZ*2H z3Cmj+2hAAFCsmEec2F!E$MEFCkdIa@B%ha!hzIocx)Ff`6iws{x6c9G(UQ;DCp#`d z6NmBKt0v?@V%G9D3qqVK`c;-5y1Na;`WCCf@NPTp*$!ulI_ZputcVHvi@Mg^Ujz3N z{d`eyIA;guW!fBwfq9uY*s=#$x0{k)+S6u=NIbjnJ8Z~uP%3Ofn#7;6A*(>nHx~u) zTq&prNH^HcEVOhmXemoM{7udBb@&^fTYeILy&WkGH3N`l<(b{l{e;b+Z-g8oO*^5| zjc94`R~?9dPWKyS#@Mv$YksT42_X>mjGNX-$l% zt*?1tUBeeW2p{4Ro5=7m%ZNvGB!n<4nnK`L1@Hq?$bGE$u4PchXwi22+ntz4^GGUh z@gWC+h0=#y;JB91Fr36WZ$(opVT7Ab?Hxt{{yrPEj*bjmrRqZ*YCYygt$W+Z?;aVs zE7gZMAcu`whlyxu;OOwxL1ZmVSUxlqIeTwb_@+L@>5U3=@6CF;EzVOTiUWJIipTq~ z1bJX@RvP4i{a91@moGw22YJ3fR37$$4OjoN4{_*;!JD#v-4^DTBMJkv4{#>)>Kxf z3X7dpbOTlt;>N>>96G^y7~$d%97e`fD>jo3w;cY=?ab{Z1jNBlkGMNXmy(Zw?*Dlh z`77bSmmo&`E1KowxC%bOyUuk4X~yD@eq){9Hu$L_Smm_mdZ4o!K0*HIZPU9*k8VQ; zR{Z)9(pt##mxZBFDTR^U5K(Cc^Boa9)~zZ+6R<#d(5bekMiAnVKUoCX(bTv5Ma$CR z;EIBnF#8hCRyF(ZkdCEJ>|;E6;g-&$eUB%^{}DmFJieLT0%5@Mt1 zyN`$7FGa~uFB1oK-=9KW1_7@}$pQTn9f-5l+7$jcN-l@~8Hy0+Qa!_J&@Dl~<;b;5TBPN-|hYj#AkOmt!-k> z^FdY;{_VFqdZ+0!N~IO03hehT!-g4ZVZrNJWWup>3+ZU%#2-eo8{E%CpnmJmefWVK zo*Z%jpyw&1QA{V*$3Sw zU^N&lF0p#%v;!R|6m@dK?-t>mLic=_Z*iCpw{c2Yr$Pwt>bU1h$isl`sxqPhrA@Q&KsWugjPRks zZ_2O?VQ&Q?&dMpXS`F{3wRB%mEQr3s;Ah+WbNxbv zcDNQ9V$e!N?}3d>)IcA_}2MPYx zKk(f-{_FhglSLGB(Wq zj2d-~5gU}3kwZCw>-$(9qqpr)Gu$8=^&#YTQ1E#zm`4z{5aQS4o@c@B*0LK0 zHmnB2wS0`$GDV%#vU0LgN@Wv_7d@M=M>72}+;KfJ0Z0WGEnf#c{ij94a0+I7{|20Q z19|2hg^udz;fiI5Mk^L#JfK;tYeroU3fA2@f(pH#6njM z{@EMh#q0RZhzksK9nfbEe)`VzvD5PI49%R97Co6 z%?-z3$Ts<5g!pan=qNC#6Zz*t(r+??4TR}7dtpwk&sI1Fd8U2iXWoLe0RC@oL3sF2 zZb1}aB$u<`gOPOCyVtTB3|I3PXtSiKlV@;_riFruzn*8^&m#^|c6l)i*ZDf9(u_RzF)N)k#L z^g5L*6*5;{4Zbmz*7|HNsVFB+8j@k9F;hypl;V`Rpif1#TBEy`aJr4kw9K1GB)NR4 zFB7jSa>9b!Q;^2|(tNg1s7PZXZcNI}7xRS*@wHHtN~PIsAr`Y{qXw7OJ)N->_{zG{ zH61G?@X*7^uBO{=v4$=BVAfUT@uHsHJA<6 zGaf-En66r74u6d&=LR!DFB*%t2L)xm1qW3hMLc=vgaB+d(e`b)|u7j{8Y*4R9fq$I9C;}+2awO zOCl0+-71qppeS0(RgE+ztI6x!pfBLal&5`Sl^~-?iyJY8#cInJgI3fob7ZQqw4@l+ zqPB2A7)DF-U^FZYd8}n=Je&zM8u}SUCeq|LN&;8=cS4Jbr1``Gi zzwFRdW2hq>1_eoUs3Ds%$ffdnN$FRa1=Xac0S6jd1?6-w2O81HXX<%DAy^V6?FBKv zR99qCO{r+)2GhZ6$P_UoMOI$Lm2vZJ4w2oHiBDPUO)-C_#Pw#P8E;@ZT}}q`F`ZZ* zPzA*LVol_iL?p7ROrL0Q#j#+~<7-IdjgpaTs2Sz9q_JV~g+%^v8Fe>i08}8Hu=yLI zMnmYamS%*NLc@{b=G4KgPmyVe;|-p_=u?Pdj!c}-&D!LiU^b|3X0vFqVXqg1)u6kg z=0(E3up%Vn zXH8qxX?Qh9OzFz06g9g;X)S4L5pOMSRffcAvz8xKhHKWUIudcz?P8l_hNls!q+EyG z8Bkeks!BqyP)6+;kFvA3F($i;?o!e|I)8d+K06-X;& zN^7O5oXM$6HDx+sGpH)|Y8|}Q;Z*YyGP&7qZ^#JSRMy2Y85+@g({;bAs*idyHFY%^ ztte#%Wk#-a30?AdqoUG?{hoNu3kL19)Mt2hu35?hY-&x)5zq<6df9YdCQ`(TNxMxe zOc-)r*K}3fR9O<`P(5iCYXmh-IFU7I0)~jHnkqGlu8J}%j`RG=DmQEmiA5!&BchJk zi#0vBA*p&rV!I>B6WCQ@q1(!>H)>^`hL>}>9D21}lWRC)sL6v`X+~6)n_{ZGSY1iR0y>#UDd1UCg|dZfkyI->fn!FJA9oC|`B9qljHH9pqN~(n> zYf2Hfl&bQaDHC;NHNtqZp%VJjBC&&~<_Dq~PlZ?Uf%SWW;($Jv@#U4g>AZ;QdHq3R4RAO zmj?BO+y<4^ZaBm*xi~3R@6dO3M?P z0OiR==4pweXby?3DrwPD5lMuqK-eJkDV3C5`EE>!PcutS0Sd?2E>2%o;v1aoEPpuwTSfU25NC{a@SExFDN?Tpwh-jPX zw168D2IAJDRuORfr&BebZ`xVSsY7zxbi`e(@dNd`qNemGRep`a>B>suSz(2rRdOK` zI(%VYJyMq@O}<)^?+qlqUZt52R@;z>l!{nD7%(Iq7OvCk6AMc=gSDE>`_OEpUgA2e zG8Lp4S+lBbC_~cNOjQ;1lzXCBIdew=_Irt;B%3g1khzHq}VUi%z##T~2t@XgFr@ z=reIG01}rO zeL*edP8Zc7sU-|cvHXigu6>@Xaqg2K;-cm6el%S<#$!M9jmX%3yO3X9aV#;hL9#NabanxHg ziIb~-0ENP@*sP^?$UOW_Jn9Ftho?n0?p^Z1lmy9#n4WCU+arH2|~3Idv3T?ybn+d6vJdsYNk2f1dK(CS&3@Wa{rP2yh#(2{1lAuAML)GB%4K+iE zkGky=UMiXNII{BTg3cCH32J7)-BYoPY*vNBR`WTzI<7odN)&Tw!DY!56OmkM3Y9^( zXt^a(B|e=Em8MWhA>d3JQ)cijy)mUtOjlAKXPUTBFt%@aZC-_5Y1L~S>ZDT~%NPP7 zqg&?-T7_|YC>x0jZ3c-~=U3}BdA`{yvNe1egVAkrd%>pMaeY2jwx-Q4{N#s_Gsd-0 z?Py(klS_%8{1aG5W6a0o##%{HwaE-qjo3`sP%(p1LE=s5X5u=R-ZhigY1J{SJyDA4 zWMD~}L_DT)*KI~+z@?34z!)Ods6?Tcn;U3YBTvRaH-=IoX-pe+Q-v&8j6ZO( z&Bzyv8zo_&5fVrRq4boR-wb4oZne~8s?{3Onh#uDYO@xFGLOh3nvRLNk%~sC$;Pvm zlrbd>y7cOp%_xRs;n3K^8dXj2(CacPX~dZlr;IL>N34{1B0OIEhF==sH zEYU%knQ}`_L77*i^yt+AD0f69KG!RaNv2cAq?uRBM`|L2z&ah*X=ds|4P4}B?J~YD zsdu?e&YDZ>obJ}$dHAY_ko8UaVp;=@Qd1G5QybJ7(;Ai5Wh?|8s*GNf^GPceO;ut| z=Uo!FxrB04-YNHVVOki|*d6*BoKszkm(p&rMWoa_4Ebc#uTFc^T9q~*bTq_{NG8=F z+oyUAAilMLUt>gjuDp(nzABX<4zVF3ar7nmiXx zij&3)eQVcr0@<2}o5^seGXW@FJ00v(2cUnoI#WbW!AQ}V zveXMXmv0ITa4O*=oJVU?wR<-;;>yLTD1*xqbak;0Awy4Qo(dNKORi;AD zROS=*Gwt?FIW_UTJDErsr!%>PPv%a0z(!0ar&1xDHVeV~)$XLKm^XQ6N_lNiKaHvc zVXt#KmEq?C#*`^vD41kc0bv(9lUw4CW~ADtJDE!weT8C4l&FEt>0M==Cs=i*&3d&l z6$)i$VhuZqnx8hM6~aI+5J(yGX1`fh5;)B>)2?Zc%gYb*gXRnXu)932IE;zRhLSqs zu!hlCLjXB76R0P7kw(cN3=5rAR8%uq$OtoCYzAc}Q=p`bM-&Qvk}oc}T`nbzFfuAW z6lYbX*Ad}?$nI(~<}$lxytZkDwwM+dc#cwHhG(!9xie4@h_ba%so~1Yjeb>@>)=Lf z%DCAOh(VZ>N-U_rEA;T);b4GQ%^77D3C~^^OCybpA?j~t9AbzQ#&A@U7x=W+NHyYB z+70mpWQveJj5f@TV8fL67rh0q&!|lCrw!gnmCqANec56#}tf zS}u>;#Db(EP!jWOE)Cb}E(duAziTSm5L8q;k)|&6WowoQ53;jZoov=L)}Txg&7xkp zKj;x>v!a=q6hGn3XgsDWuu^c9PJ^W`RX7WJucV+)7DZ^-P!-4oJg7?&e6u$t^u?7T zakeHZDjKCYuWA>IWM1h)HXpbB63t}{D?emw^eyup1|g)#zhTL(bC9=o6&4d zA94gFXv|e>n8O8U9BS=|9I|DcYfxGhx=cXsPEM!1GlqyWoJkt(GLs?`^VtQVMpVV~ zrQFl0oLv?!$?X|l)*ca6%??vTk>$B#Jbg3~7lktoQG^%d@iPjsOJZ~IxKnbGOqX^k zWV(8=IaRZmlKvPB+otSFRkR_mzyM4WFbZXHInP>6g!!PVVoEN^N~|fDsN9J7!KGax z4=Sw`)HR_}XcZ>Q9*;EU%mwTkw?q^4m2(NJ&!QD5GEy-V**urR(om)4i9)7fZ`jH@ zuc0K#aP?+kM9_3tCHkBq?2g%WaSvLQR}2s!lA^rT7ZkecB7-99Dp|{1u|ygaIek`T zA`}q%EeU%?C9BzBfSyVx%yCUJQi>#viRq9v<$(-g$V+)#kEs?bXYzrHCKylzB4(~l zp0;HyDv^$BbMh);i9GF&G|MxR;7rLN2no=1O{_{*&Hk`4B~~b=r$Y^HRbMa|G*Sa^ zDxz13xiMoQN5pT1$RJT=y*|4no#H3Wd^BMUimTG1F(c%OOX+knB`|1a0+v+8Cu=z5 zUZ*6jFjZnX=#d7`VE5E{Dsd>LQ2Ucjk1%G;`CJWuIcSm=oDxmmSeO#?@;r0gUdkB? zQ<_Lg$Te}f@?erDkGS*kbVDQ&@vYOM8ca<@lVyXaDh>&GmMJc(G#B!kl(kYQS)I~| zd&XU>In%o0Of(wu2T+k&kppw^8;Z(8I8qjC^KxFZ*x=g3$+AuDHDnrS(IB>jH1)K$ zuBc?Jd{>-T(v>rHD7s35NYtAoY87tW$uxjiqBs2o01G&(H_Mw_09COuORmaPRvO%$&c z!qJd6G;PmEB@%xmDAnl|f^4-KHUi>OpqA&$svd={=qfs*XhLrl7po;p+#c2nJ+2tv zWNTQGJUwsPZkO>iGw!?@m1P1(o7FiZYoscn8NXmEDb%}FvUCN^F`N{dnx%$7piS%j zI-y<~4BO%gPl?M5B;&D?6OCukXhBr+iG;pjoM+C3JTgf{VN=w@GhTi)mh~G8N*T9VDT3j3z!-99187NCfFjf_i&}ERlqsB6hf3~YPcQO%gBp64qEGQ|5_g%CTf26v&D~ zehFHyg<%*t<<+GW8AVv;FzIuClXJ#ZQTr7JW2zny+rxr-E|fqW(qt|yx5?}vfn+-3 zkV#^)u#W36)Z_uK-xd+uyrLOf)9)3^WDQ?Q7qZ($ns`AURW<5)Pf9q$g((A<(=RA` zMM(Q5`VZbq#awTCKW}8{8ZWQfGktGs!p=o;+P5Zc!NKFxwH!HSq zwd%`ftZ6}|?(jzQwzS_{YgoK6Tbv3R^^JrC4ZFQw6mnirRj&HNejSe|iw284sX!gz zRiaTjk>h8|nzXCz3YcYjozEk#%fbpM;Y==Xw5-bI8|Fx0y5gyuLIM#~U?LIEBooGL z^+q#Nkr|>5g``?c%Xx)VmTN&{DYrQvMp0B$4kp}jUCrbaz=+1+%mibpSdCjPB+Al2 zspv|f_L?Ls529X$NgQzTpa73WM2R>|Cq-rgX+xzroi@kari4zTRoFc0iis;t#|kk~ z#xDvs>`+O2nzl?d9}Ak|%A7f`O-&ai9y@=!9*uD8AzN-HT+Ie-YH`e(bEF+8nzb2Z zxqwL)u;*)W2P!r5qw+w;C!I;yjPaVzU698dB2O~xl!q&#oX9PiE;z-hRJI&*>NSZe zFEKf*5Ji+(bylEHOWo75roNDD6zqX$x&~!b)+!ar{JOdfCU+Dvp^Y~cjbtkxzs)Fe z7J2o6s>&^iDygZ#V zTB-smDov{NC8a>FwI%Gugf%V6C#MZIrNibF2drj)T9XPVWeSxdYVy>>Mwp_~WL;%x zO(3fj9L7={+`3%PISguhoEMLJ;1?1-P4F{WFU+GQ;3Y=9 zrd22OFg+5{W|9qQ3SQRuO%7c$V-j1e29YHbb);kNV5DYEC`z)JKvb|Q6$Z0V5v!&x zSzel3bBjg!YAxrHM8Yz!(BV!ABz1FIEs#Zg+EU1nh{C*UwkfxA^}b|dCYf~WU9NC8 zS>*C{eqSZZo${H@QG=d~Ci39>MiW#ghbv}uTRb5?O-F58hu0vNCw9Z|}u5(uv z#J*98IE0`BTf7py2!bFICE@{5Fye)HA&Lq{oTwL3lflGzA%efP|Fi#xopELoabLW9 zt#`evs_UtGp67S?em`|hAqdf(Iuoj^Aonl1ndY5?LC`tj{!Z5NybgX*t(6TsdtKci z)As85ezzZ2EqlawPw_Q(urfEZsKrt&ZnsI7Zwfn^)21?DA@Vi#Oqd))D%I@aCuaZ9 z?#s9LW8K4!b#v-!Of3!Q)9{d7KWbB}?GOB!sZ57fP2|I&4vq3^ z*rGCoIrIZnj49^3i_px2m|&@rVfGH?t?HhlSxe0ut=L8*9bQDi2S zEVI--Ze`c&cM92;mxj5Bael@(Pv0((CM?17)_h181q;e85o=^hQ6K7r_5w?4;f^UC zHj7N+zzm$sm(X69f_Y32uA2(F+NSFQ<(-E!ppzh+*?#)G%F~OEY*TwhELx7b^~&%Y zk_gfiRw1Es^8M(hRWjK5L41By^@6YFk)pk@@}Vwqdznar(g8O02g{BsH0?yW9@MTv{B#?TN75UJYqGgZ6> zsxwZfZdrQ1hZEyMoxd#zIKXDFYux?K_41pUJ5rqj5;wW`FhJ9Uzo<@Q zW6EyD@e#U)S19(8vs~P(tD9oAx~A)gr_2j!k^IwS)6zgU`<((}c zXf$Z34C;z0!@Yx6i3(w@bpmV4^?D5TlN0$$jhEg<39C8*<$r}|}Ist?|0U;Q~hm`I3<7M#pUNPD&fO;A+Xk_hG+-qWRQXbWdP zoD@%T_TIYD5&AzD);!>Dd-R!bs5nR6<}NP9Zt!Y6fEL`rN7snAAQd;;v{Hy^NR*vu zkoST-qr~L1d1*eWKgc~|UHFiapaazmbQ(LpLem81Emcy#AYv)Ju6`M%?kgyz4$ob4 z5(7fy3|-v?wKf}FOMBmo9GOz6J9gE9)lf|>yQQgACSrRGLF5LB>10q26CS%%o4MNw z=gM(}R-LEcYTXdIq%a%PwkD1V)^)@OhTCU^5BmURhoZCk9qAIHMEI#kQSqsxTT|}r zsG;i~$MMh?i4o6e23hll!2iY-s*}h@V^-%=bWLm7+uSy2aH(>ej$_(J%1zg~4>RGf zB!SM6bmv3PJ*9;5!tPIkC*n6Ptl2F!Uf!wT=%Vm9+J9dRy98^P2uNMdH#(M1S$tA5KcY8zH+uk5dIqr7&*=hWw$Ae#bW`jJx z+M5wtK5l$=>ygPEo+Dm53BuX-VDSDV(8nudI#nrQ8;pWwZscIT6>NL$!V`hK>@7;hVW&FZNi70h zAoit(eQ68ND4_}r*|VsikoaX;mK$Ue(HAa22PylYsRPFy0^G)5H9id-YmnR;Aulw&s2|_W*ghK9YTa---8Lyamnc zWL?*(9XGrS)q_I9r+Bu=Qkm>RvJ;9Z&GJZKi4?o1#~HWz#9HxW`JJ~`rG~g2l;LHN*C_*)0W!%j(X*wqS-{bhI&Vx8Y<`^&Zjh*BvzuM zuy!~WJ0Kt1<&RKq4^`GvycLUiCNj~j^M>0^Hz^sK;m|98$4)b_%@Kh%16s?<VaNw)*P*qvYsyrUv64b$&Wbeoh#5IceQ44^V3}O1*01X2PU5H>ju21= z=ZBcQy`@At?m!+$qM@tt!Oj?a#`g8ecj3#dhnXE>?Bu10YOm*BS%%N1$zOpa1D*L@ zpiTi4CooHb)lc%FslX%f0J9^eHPV}gpbTRYHLv;O<;V>iJm&5J&-Q_y(}1^7H1KzK z*}^N?$gM&oc&qx1;S?lkxwwbZ-D>ze5_XpFr=$y=UczlY#<)WXRuA*5+pVqzwF7E` zKF)(TUrkrxTwT;~$5lssWN%ztq?2xCbKs-hGmGLDc|m~%yCv!M95q=I%Jar}i33;u zx^Y6q5u?)P!F<^3RO)%wo=F{9`~zKYEcsOpB|i##BqgYmb%_}pJJdG>+cMj+cVmVr z5dOt&q56DzTYcJE`zciK=(&z$)V0k;rIX{KhdO^kubLA$Pt|KvT>mOAql&fN=C5)b zWNB~u*%0wf#HP~R_)1;O^m0E*2&)kLhr-(n%iH-i>)R0~?5-zb(^tc_X0O-Tb%yqJ z$mZm(rA!Gm2F&Ne@r_yS{c#r}Z$Pr@MnyXwA?9Og8v!jbZ$(?Q8Pf+x7W;i8kb8lc zgzl6sY-OhuZQH4FUQD~JE_?md46M!m_SAUQ@Po0^?Z~4{=s85UqpvvaA;X#HZR$YZ zRo|-tmC`JYuV^+yd9E&emwb?Q*>D@FqOAJtthrH{jO{Cims>)Khe$0fQ7>^chkZiW z@7?j-TR}6WIIVi}@l)|6p#_Sg?lfEzKCqe#o8s6yUO?m8WO5(iP zAR~BE>Y!Uz1j?3>r*Hv7@lTN_yRD*4cu}rc-qPuX%92QG;e`tBB$FbDr7F@$Ca9!# z(0^=H?T%*1flgkkQ=>>)&Dsrx==A6dRmsPb-bHKAbrZf-qIZn!!TJ3o?^_JpG*3%w-% zj5~(};p+=_v!CkCJP8hShC-E)xkGldjA|!|omzK0v3xpUm8C{_Sw=s|g?zq^9NrHo z=lzTz4lW&TN7d<=uAZhxM_pHv+QtZdC?IE>!{}vfS_5$urXafo_r@S@YQP^r<7A{w z^Tc7&PRFF3-K}I=}$wFZCcxy$qsx)N{n?* zuvWMIJ7!-_r+#>zWp8}SM}yg<0z@0KomEepZW`Q*(9<<_>JCcqO?DF&R74ySX&1&y zH;ypb(jOrraWangA=cPrh-a)*2?{Hh&MtzDjPI)cJf<2us;gT~KRQ84e|G|uSZR8m zG2w^|3i=9&iICPVMHvlU5VJ*|2x5#QNs>>kQyRxV_7CIKE;j3VSoP||#B~f>T2@sJ z@#@Gd5u|A|nLO81?fX?1#r#g*^fmjmAP%KcPp6;DvQ+bFL?((Re1(Hn*PEJ^ntM*r zyYLE(>zJeWb+9rj=QjhQqdfJs0t4C23ybb&Cc+orxWuTXI90;h@w*Hd`m)L)nx>M) zPCVM;2O`1*XM$M7pB`M>+&AZbyM<>Kh9AY995`Fv>Gy3-x=T>j@(y z4y2+r@ub%jS_t#!9USZTG)&bkJ0MtRot{D~rj6H6bBy8onJF&UzMQA<7U4x7Tjym8 zL5)MqK8l_Kp4}z|ZOKD`u5Z~&m6U*P4jDYs45m@)lapEPC^xbVk|ofiZ)NPFF)z(S zdgR_QTJ*WT`6Xd+v<(@G{$bQI8<3iR}ezck3Kpm@S`Z`wCXNUBDG+M|iANG(f=lcnBp$Nqmq^?L*ZatRE zXKQ=&NFUE%MFi{yxgguH1!_@}C3XCXxhSa|Q~E^5ULqwM$BA!*>rB#h(k)kt`GqHC z7d7YZpt%9r`)?%jjnbOvmkUw4?selEeJb@Lf&OL`xd>4r2&n0v%n}-x!|4NsUIrQW zhCRj4N%q2kgKEU#=A?NGAy5y>W250Kk+lZCE zJmP)e(`K(tBr${ZG3~6_cm!u6Bb49Du^gyyXDNys$(BPj3?3cpBO<6$Qq+32Pu=nI zrKigCQM5u$Zxz_Fq6S?k8rJyv;_8t6>tzTBscrN1qCC)%p_+@)Xstgic7!JGN}D^h zqS=guR$W#__pI04>SieN)FWoMM%LoYv;qPbQ{!DV+CQKy)be{HNL9PvjMZjEn+hpabeum{(ad@`RMC zwO`@Gyc`vGl{>>w7q^~lyJC$hS3wmczMAJNH&DcA@(wCzcig?W*VRamY3rDE=ASQ4 z?;`W)54iIJL6WCFhf2OU$kcq;s2A?lt-B%+_Y;y{s>LZ_ga-p%(8CmPkn0hAhaQDj z{l37?xxi%U9c#S2cqvGE)z6o6-CLH0^HyZ5_X79XgR0z#cDdCr<$YnsqrwwJ(p|d+ zj`{xXm?gHK=UTfyK&t8<6Q;ExD|DpkLai~6hgcht3U@sePG8K|>ehQE21>9e3VQfg z6W9`#gCgx zeYa%|Rp#gUb5n2C+^HvNB50ABwbDM?dOy$4%PI58neuv1EiSiY@?2ebSngmrAgzH0 zV0K^(*vmZ-_Iw?p?k;&ii`sX`d-Y!`ncJ!VS-sEghCe}Y_N1qvqN~Z!Ecz2H5r`Mh zHVBOhtlu#*hsZmntwyf1$C(LG2(M-4`lvvmMqlLcE8KS3l06~{+E9>nng@&mwN@2_ zHXsL??)h=JfUu3Wp^!Fi;U2Cu9(HaK#|?Z^5f@ERYC0mDdkAe(9}sSU(E)>^3ewK! zcWf$`CzpfvN9b>{u5aTBJ8g}*&phJ^1&C6_IR0qN}kjF*l5xTQ) zH4{yp9;0QXE#0QR3>x_a0V-Qk$*A2tZ95m8)9_%#INIvB|H*&z&A;$bt45Oa2xR&e zmFstP%I8b?3`dGBgxm?p4eAq6Csj^E zT^7oEKiv%&FxrMH#(RCY@24(GhdqEos+Y2YS#|5$k0I4>r_)h}uZfU)t)L#DJV(REGS4$mU1oz8)9h)cL_><8hFcEQqkYjU+dq zlH@aXiD6?#+*aqZgPiOE=aWy)WnCHEUYlh^@GBgk&{*t3re`?Rm(m&}h)3u7RVU5; zvmL>5T_WmTkDv#?gXMrWUi+d#Eb;I@k2W~3Uw)7;p?N%CdMdd|rsIXg`LWhRS0^X* z>z5MRbwV9V96>=tEW^e1SdyUpeC+8?X6T)BrxWKDta0N~0jT3g6;N zFOh|P}>^JS*4G414mAcVclHY9T(E<9ck;?X%1NABUacP)I=WoeU??8L;R3q#d2f#JFm5J@$ceod;O=0v{b9a_WWvtX=tAVq zE$en)StvpcU2$;~ z{QrgzyDH`L0+Q=g)S-Nvhp?!e-Yjd5%H`^|#GP~uSd@wi)I(p|^FqFg-$|k$_3_{s zNBi4f_^$z_4sz(f>ti+or&LF%A)_b-yWee}n&Vx)WDdJHUQa5%FoB7QuE3wr@tbwH z)GyeZ?E7%uMe2m)htg8=Id`50RybXC{W9w5m$uyqKL!O+hk=+eXP*u?H`xB}wDSbJ zO|!94-i!Jo$GQjf<#JhJWFE2Ts(LuODgOK?L#>4g4Sbl!!%~@;g76 z_N6X`um6s<3_;a=Z4QUO^QWDf|9`yF{qz0H&wubv_n&#C`+xK!r|Xx|^}qYE(e(#T z+5Z^4s^JgZ+~o)U@~7OfKVkL#*p2-Ae)$RSWB+woe}DAHZ*>3OF#MC>|0(nv`|bbm zE8qOVZ~vWN0r4o&+q-7Me_X_zVn9vXMgdVe+bO<-~ZkB-tZq^<#!kPgJb@P zm-mwcet(f*A^t@ew(lueU?_*TVE)Fg=%0UnzuHosi{>0kRUdCk)= zm;e0NckCbk2tiC^GBb3;LN@a26bf8oQk82F@l<`=*7MT13};ozH} znNMN)XW>}ozxnmYzxDOUFTo!$?mu7tIr!qAE&px!^H2WNqPfPM}}> zRcercdvoVM`QthDqtkx>8r^^7fBg<=_BVc(pGG{u zhyCaNzn}8^H#z^YpS)C|{7--GyS3|wr~lb;f6~7Wzv6%Y$rb(7r2ZMS-GBJMeN%mp zwu7(Vz=8Q!;4=Q-r|TCK^KSr1{>dMY+)vH}WTb!TFMl(^Qi%N(*cboAUjv*c4qpK* zFZ}8^ zA{_PmAN;r{%ue#8H^Z~w8s`W;c~zxi_uWPr`tG|Fhrvfc?~ge{w}Y8oK`VZyLCw|KP8GQ@|7UxBrpf>F0m4CHyH^$bZ8v=^y^ul5n6husr>Te{D-5IGiV7 zgZjd85U^n}9L+I2|NVx=5j;Hmip!xqRp)=t_;S+_=h+F~w`>1?J$gzCZR8SFzEpWoLfZ(Oxq$Dc$MymPk$0 zu=T0AI6)9?w26^I9UmOm8!@BlM;JEIF53}dzh@xiVjVSV@le5vHR zDO@RK&*2+{xQ#l)FNfep)3TUb$YGA^6uTJ#PUkCWy#-2YbCFY-)Y+c=>mk}#FZvLP zdEnp15~KHy%(!!DkrD}>0wmD(*oAyB`>L=IAqeoFhEC2#laT`CMC3@qRU4`o1$-Gi z7d-+C_~7+H!ZZO$SdbRbAmo19ZTS5s5fE{srFS@V4^hU(#s)smWPERu+ub6=KFrhoy>M4B+?y;Y7&T&WR<+xnp8f&+u ziLkC6m<5#Jk6nsR48G36vM3w|9&!waD&Q%u*d^NyD&Fx?)ILI%9(}~u2%ifEehf-5 zw8zjJnZbwwy?p+ZDHugtnaWM2XLL|sBSzL=b+{QY667j9BF68Ob4@HpWZidjYdQb1 zfWn*~N^{Ssf&}o+jRG=>(c)-7;s%-{l=hZN>M-#!YSPC_8 z%Pm~@if$%jFcx8-g@EzuSF9uo6eOW(`Zl!4uGMiLcSKuIo)4CXqIp#ewajHrGYMo5 zBMOg8%w(C}4msO)E-QHPVSXRzHhHkc@X2+ct*onL`>AvR1j(tTIm;3X&Zt==JP8p8 z0@9_r%aS$=E*I_E+i9pJ(Q+`khuMknpDyY@cWZe!lt||Dr~vBbYORZ;2n6F~h#MZxndRkI~FdSzd%y}uqLx0#=<$4-@q!e z1TeYq%Js<|vSLUL7XFz`MeLr2&efk^I=IhTK8jfF3g!+>@Y1oMAPF&loinvN1nWBjI zO?FKv*~l;G@xie-(C)7U!NZTwsKVYTaX6y7Csc^7lu~-gR(@k6f#%>xid7r5%pce?i9!6?#9(pW+9 zkVy`m@6@c*faXBX40z{xM0GirOa)~df@H{qls7?WS7frn9V2mR2%Hz9BEPugPK_T< z0dx_*>i2Eh4gN|BU3{7f@+pE;MH;v?!;6Fme#1dsHB~vjJtztC0fX=t`A{GPtLa*N zh>ml1O7}Ugkr^CaOj>9ezjLBkWHk$Bq4yd}>s#N0=lyWeT(O7t1+0ppNcqc!ocEM|bxi{1UG(_OYU>y{EPs5d<*S$@7+eY= zYXXGC3J%IX5Lw+Zbpb@id(wd2r14U(vZyN>;q^#Nz{)8u0q=YUgZ;RZKAE;tnYxJ8NiLM^UGSlRsLIri^#b*DrlUfulCdZHUQ23p1n@%R zFyBLbjk)4!v(VFe48+93!<7x(jxJOFSXi@euT92t{QD4oiU&=2^gP}f7t`2N#GJHb z7j**ez0zL1wgUqh&bCzUcoG)`J(?ikRv8(0b*_M~foIm5uO#+3sGjIx8wu*LLjWKa zLMp*Qlqd-+D>K^O^SD2=(Yc(B7vF2AXYBLF+DaeustqZ64 z;e~BuRGiL_%kaALdSlTYta8fK`AJK8Frx#-UKfsn`OQ+Ab)rG&aC^n=mI8ZW2nz0~ zYvv9(pEVOQKGb$IYJ|@%RlNWWm;fs8!<9m`8Xb?Ec-&Jge zQ&shJ&Tpn>SuK4L2+;lM?S^i#N z@Zk)wSAv!J;|1kaeGuMxKd`l!--?%&WI8lSGJ21%xJ}0TdBU>Qrd)qBC-gOPhX>dQ zdSnBz(E|%(1buPNO-Nyv%*2*LM~`VqEM#71(RLt^!8r*P4O(L4sN=YG*nqYkXl?2_0r}ujW?eSl-#HaPyGCS%5K)3y zQpDTVXv_K5g`SXbQdY97)wB8CJbNQCg4X8g3xLIO*$Plz(CUF+f^1#9h%xl!bCzl~ie#*Yv#i z#!v{C8U(Hl&fY;S63*gQTqHr&np!|tm`YkXPQhK>rMIfg*=MGMFsZQvta&#T2c6xX zYP9TEcSkifW}I}q5P|}f10WXH&C8)b0Wa!>SOI#ped89>&gB3Uj7t9g|Gf+S@X$Cy zn{|xT9TdEUipR?`O$6LG&P!@yTijeOqtmAMpRno1PXEHf48atII?J_ccfK8iBV-i7 z#CTqg!dElleEv~JAwot0c#K1+3g_FoxZ2=f1_(%>{>p_ql?}2z5$ev6CZ~BjPtj%c`o$zMqL$&jQ9($ z?6vy@j?FWC{~E_e>Js}2(+XTZXvdbE?kS<%I1pf5t>7)0q5`g-bQaH)H9;#dzl5M(s2q{csKaeW zxkq}8%6NTa>jWQ^Mekp27%Ka+uRlUc1oj!ET3fuED%odWItJjN?I)8#2HoPuP`jT& z2rx2fN){hr3sqO~irL4!_-?$#n+e0uGTBGK|5a>^ayx$ty#$~75y+2-Fc5dc z&~!H_fr40@kwKvIgT27hcI)u32dSS0KNc&z)aGT3z+M9m8A~bF4A)w?2gaq&@D~eY z#yw9=!3BYB4XXkuPgLg!lo?jOf2}TGjZWnRniUX2d}a_R2P_cpv{?G$Jl>lCQvf#b zW!60D>>}+4YB8T!aW2p7GyM)n6l}9?$pfApZRO&wZg~6RB?;f*V1O?3H#0*%Kbl?_ z{a#(poAFM>E3d>`%I{q-=M+nm@9tz2&q?TzVh1D|_#%^&PS8w?zuZ{|XKIkD%~{Cl_kSFzWy? zr;mxqK;tRDsjj1Xp8oV$f+4uUv~Js}s^XPxThYR20{E1*&!Ax~svF?k5NoCY^tFJi zkOE}GnKCPB_E$S|-t4FHWww0`8ZuM+Wdt8XW;5r~_nIA|Za}gWB+4^TnXpbdNH)x) z#q+&tW1GCX9jZ}uJUxLG`WUy20jd1ZpNE7^!@ju8$^embN@fsMMq_>kf=I3&PY)zn z0#z|)raJb<_L-ICsS%LtO4f=vmSATJTTlm7np*R4OJnMw(vYCwC3XR-;)G4+=D5iM zGw-JFs)~YuzV3*UxD-(gPizEOt|#Shh{q4>Ru1G5BKGENv3e13C)Th|yHuy{u5tYH zOswQbFk%3W9uVOki}YJ~+6+^og~g@E;XH}g9eg$|V=+@e+?wH89d!wIe!J~Kd<@6| z)d84Bjb#iJb$kk2$!GM79s<5JLy?Vt8h z@5+-|OPuuO`8+g6blu_8M%+`>xe4}g5m*OA@YH0;yZ6w|iJqo!Ba&Re$9SX&Js*Q1r|V z+l&a$G(!`;*9yxX;BsaNx^2#1g{&o828_N6J06c7C`$-Kctz*4IoBx^ZsN8KF(NR* zuGPKm@zfc5k{vDraS@-uDRvCVjA($o7~$I1682!$`cvav=Es_|kn5Oxjb;0-|1vJ! zp(JwmWm$CFY8}V{=ls+ij8teA?MU81;ye@|enWdopiZR4NyjMCtw_=m! z(&>&VR)A}Aal>%$+~@UjrVpy#iL}x%I3Qx0kJg*@Qy8wv3PQ-Q@!{PLY-);YMl}nS zVCt}5TpyeaXP12!&;9OzSSS3t>K9x!R^AsN9MyGFqab%Tgj8d8Ha3o80uRJHCzrhu zri(-ITl5t_box9bz#$UBR>Eou96GQs}m%`bss%gb7?RcKjt2SU!ZJN&g6qu(cq5uI$(R_+gU%_K89~U`~@fytD z(|Pf)Y$YES;LbMw=}0Dt^O1Pj)bqqnwSxc*vZ)g>_SJ}X1t4D1m4xF(A%G!`Vk$i@ z%L$t!05|(%pmWSy+a0;EM*7@ZEB-q9NWoNGJAeacz~6uxkVLt=P$=_cubzvwb8NLW z#*Y{Uv2-DdE(vzF?d)AL#q4CC8jF%?>g z4Udr3LgXIiLaZ18C1PoX!-Aib(h!&UNfl^7Ii-jVM2T*ayRVBUZ*x(rg|E(BLb|y_ zjY9gU@y|JfXZ(hHgq%)CmlKG4h0Do0h6YCIgte@1zKgpVsz~ZU)QaTKpxY)58*5eB zNwaG}00@vU_hUGoP$`7q>~tN&4FH`(&J+YjztQxCLCk+!POioq{eA%;VdxE4@vS@h zN3|m(Wx%W+r`% zN`jI+2$bo0Nb{Ys;vPp9KBSl&N@Sw1cWpJJ6nG{ zk4RXL@7&@<5~9R|`<7S(2oXRRE4o5LNlBas?8>+5%3zsrpIXa!1s^`a0tZ6Z3C+qK zXf;HZ;FPRpgm5(;LjRV)tA}Q5KsoG$%hI9ZhMqoJ!G@))UnLoWFxgD686ZwbD6`5d z?F>n3-7hcUrl*uFD}kge zm&SRdI>D{y^J9tRbS#|S5+F+Mr+6L(H5B^L)oLVQjz?F;or$-x;(CZGisgZ)m&O8c zie4klr$up9#=9((>DASb-QYsSLVO#oFmlH-7rf>(wZRb2G_ryYpUg-u1|t?4vyFRc z-ITL1XT0yU*fe&{2T7PMUeEOD!lgmOfh<=R;g@e5#;VejZf7z9=E{=FszeyAGeOGZ%<@=$_5^c~V)RSNq3PX%ctBTtqKaxXdhNaDu9+H)UXm`@<$O$J8rV$u8OO=EgFSu9` z3EdvOkpYE3yPZk$Hqh)fxm5=y3_euHcxU#35ht+aJ_2)`cA3z*E3*y-7=xgNVXB~& zZrxe8Odum@uXlgvHzVupm9{VNqz8BDBuM&%b9n4U|31bN{T74#NQ$OXH*r)`ef4}@ z-5W7zLz#Z49SB&UE+r^>gP`8t>RL96$*;>P1a*7V6DDj}%A^{P15uYi&Rs4@)NF zFUxBKTFx7)xU_D+gDp#nwg3uIp3qT`^k&S7m7EC&wUr>qO&?$_<>mZ#>C}l_KfV>( z-Yj_}SVm z@K^8XMJMG{ti_s zy1Zrn=8V$o3eQ{fSZ3mq;GD+>(3gUV-wh%<)s`}1b`(R)c_=?Tt`6|_i0k_znOj5C z*htFYxZ7W?$%Ccbq>n@7R$BymXV^I=1|b+;llTaQ`=YU4o*z!h6hRtj>Ib}0#ur}k z{cy_x_u5^I>;$}slDr}GMZroH&&=f@`rWmDfdhZR&#%wn+1|V)$l%eJ4Em+{Dmbd0 z4HD6->c45IXS#qcuA(G(FB>3APRZ_)JGe zeAshQ*_$STK)VhJ@kLCEu|`)w+mTimkQal{o*(CtDzG+?JuU#~+PNn+en={)9a;yR zX$$h5nvYEo#K-NdL#&kSuj{=z`vVWJ#=vENJ!q&*Xl@(w#B-~2`ACv3<#6oqN))|q zn%F!e_d|7DwZ{ccaTch&B5CnlUReSo$d7l!8DT1_d#k+q7I%xv(apYT2-SZT9Fuw* z_+f;rSF|aF(3c?64_AO5-C>KF$%mU#X$JHfS7iWD5aqdCSEPHt;bhUvLKP*GHV%Rr@0zK#p!pvZ?TiOX|tF=!{jGS&m+gWF4PBCcsAM7V?+_l`2d=Gh@Zmu08 zk&6#Ej?@??0W3EtzJap)sR*8wYn-g0+^;<*cR$XgW5O|NHxnAe&vVwOgFFog-);D( z4pxh)(Kc$gd}4)i2*aDUkZ9ws40B)rdTo4C><#<}A*l(=bD9e^$abh~>-$)sGjJ zGJ{|+l=l3RtPGI)D)aF4yAO7qnZ}SeHeMLj0=x8Kgm@&23l(0&@RnYiGBOU|cd&q# z{@nZi<8yZyH3IC7yJSou3-=>X05%BJPIqRed;}xyJ`bHjVw!sn?jo^}a|P=B;0IC> zL4J#o@D8HNeM8}B^6wp1zfHesHf>@IdVjRE@7o(&>nIbW>`fL}qqI?t*p$i-+05)d z_BD{-_k>8H##6A73uZ)!=wNah_auTo#|Cx^GQ*Z}dIZXfl06ixm)=Gf)wH+yseGafaPVy(TKA~?xZeE-_7<%- z+!b+;BTy`eGm(vqZ3g{OeDxKXxYX%&1@4B^SJ?_l`r<28xKx_ew zHS4?`6z4JGmK@JGyr@E+8y83xJ(zpMc+5s|#Zc$^k*bBWz?@oBGnPs9NZbKhy5Ug= z;l)^6J~R0;KBHJ)u=RdB(>;L-;Oj&8f*QJ0@|v_E91kZ3iaU?D749y30HMh;xcd_~ zD{;(%vP91;BA#I5~}}hWaI$rMNbcFlxYk) zMGMR3&=uYLDZclLnd8E9pMV~jXm<+Qyja`krUR;8VO#%r%B+*N-n>3k zU+qz^4Ie0SJiwIEw4iEGaz*3m0HAOU$7Sn|y@xRtlkk>d!j6c*jYVSpnj1nB1(XXl z)4sjUTQRt$qZ}v^sI_O>J07rI?c6ziZxh(Rb(6`4mj#&ZdvT_WsP1V-=oHn7#TV{C z>;o_O2%ivA$%P=OrMNj+DBo6ldtWfZB zChW3FFc%+JrC+@lEq}rTl)Yi&nvO4U(zH&8NGcezG^oSzQ&|hX0;n_KGYF&IqBy_- zB*1$q8*&Bn9|2o+^1MOv^US+r&4LHF0GZRBVNVd6aK=%e0f&V2sv}%QdcJ^WNLVZu zUqd^yf)n6P@Xu^B_A%a*JW-S(k3YlBh|MQQ`JQo+gGuJxR0FmLiA*lU+(i1 zxZu3`%um@I13GBNh@Et28yiM?n-%#Qfko_{-x@EMT8_h9JrT|Htj}ZMg*Ch!qUdUZ zZD!sw3EJVWjjKydpxhdrxLtL{K-}6gO4v=m4kXfASaN0g2 z+c8mmJ>1o|kXr9I1I)8KAZOpn{X%VP9x9ff#PJz=B>^2@dAFFK{T4l|&`NCpGo6IP zy0opqCRI8g#L#+em$m|=vYnYp>+rs}Y&*Y(F^+W+vK1ZPq?n%TuM9eZQv3m7%APAF z$8G`e*$VdLos$PSW@ms9wYrH|&`lRMy~Nn+?8jH7rC#8)4kx!KDyf`C68who=`r+R zBd>#R4dEVCD0=AMs#I zpp|s8A;(kH;Q<{7z5+M(tAg_db(Z9+aDX>ay$zkw{2WWrBmaEX4UOK9!H#KoNu*@1 zHhS8RUS@IXGmt0i;f9%g5Nq;btJm9Y#Gzr?*zeOUyz~>w?;q$Up2G!^OH5b4Iveng z67v54u=nOcvtw7CpsVZ>rdUk%Kmo?!&&CGZDwk5bWE&WZYd?Dq)aK5 zN^L0v$4tKU@gb-JQ_MwyIY|Lj5HjCrlW zhBTX^)A{KZbbs?26!I<$QzIqgB|s3ga15{4QK{yFAv~VwV1NQ36ht|uY0aRH_%Tv1 zjO|Gb8hTvO$ORqoEkNjSMt!5>(o7tVA>jbvw_d5HjUa@wcnjg zN4r@D$ zWR@B4g~kjH;_IYaq8mL&JwhEs)^esAG?jL1{Z*Jt@LdCr6xG34KIW)u)e~itB=$y! zjCqpmuZdL)ALI6VH1MjsD!j&zA(H{ftUMgcIyexfm2|ccJXk^yI50LME`wY3Ej%m~ zlKCEtm*J8~atZL6Y-nH<>m@44{T0{*Zg(kk;7ZwZ6tz{EHm5--bflT>6%jWb&Ot1f zxxoUi8#7UqMuAV3S~A*->tVYCH$wg<>xK<=RvpXypu2IY9V|_LT+X_1;OuX1wz-E! zBYEBOd-YDQoUFqNm{zT#MQ92~`9%7gk zBB?@bCWXx*bP`)E%SpZk=n5vGxV0g)VE2=_&3I=q;a*a475z_{^Pe+Maa2R>F;hDy_DEEkY5piX)FdSQ%M zhh>H27%vUE(UPdUqagYcfGDtl1&0wtIn3rUU^(RgrQlElRbsm&V`)JTc8<}~S9|8j zstA)-2*?YdJ|e|tMsQ!89S^5X2+e5TBSd?DIY#?C<-^GR)flX2%K-L)h(QBAV1F{ z>FY_kSqT()6I#ntu;&4j{wXSd_QH7ht3=kabW7K?? z96`46xue^A9aB1Rvs>k;W<+L8)-Zy!ui}t-LZCT()P_5Xh2QVtG-PIqM7WZ@nG*m) zefki-aVg^EsC2^Fth=525cnoydfSA1J=Ubj;qktY?3Oa?M}dtA!E^#%ne$*yVh}eK>Km(~ z!Lw(!r%Ib>XNFc!cc*gM2lr5`6iwhg2@SUT^K5C84B##;v-Kj*Y^oMkoh>A)$wzR} z1i@)iHC8$mQeE`YI!-{c*cBvtt>u`^YW`Ghhy1(&kC}JyO1f>PF5D_J!IqfP00o$> zI#tdAP(Vn#P|ip;q6vK=Ew`AM%j(40K&bja@_;xumpcW@$q-%xiNhfAfgcEaNKsga z%-HDhn6{V!)SBF=LR85_h2;lfidZv5xs~B&BNN~QB6kcv5dfLf=VQnpCV*WgQtb}0 zD@N{ADre<7hQQ)>N8q+Abz=|aYeqyNgbR}Kuryc2-9FsbwZ{y$(%o5I5tquo%g~NA z@$@BW7L}BNb49%exh}+G5V|=~;xwvzE;HQ~5bZuJ2ehYetx7tf>_uj+jzLA6c_VB_ zGHabGUULNg$BfFO#lgi=PXla>}_SA$@FA4o-5nM zu&adwz9Ujgqs9kTST05>Al2Z!K}bx>b5o40bkiQShIA`^DIs}yf8ey>LAek&;8bn2 zAWC1h>c(6dr<07r01ZaiguSHJKN7GSDRWjZBREt8BwV%Ma)mSl|Hrs6dpwrI#cwxQ zOT9pbNPhr-6Ev2ZS0K9CAiOk{S1B`ycr~>~RGVG&Mx@%xyPaM_W3|%5iw@jSg`=>9 zP>nV!`Vau=w?~jtv)=~~sRrnbJk=q@CFBH{I04m;V&Fz8s0V4xq)tZad$Zaek z@~Iu2!gXFSd=LCDcg61ovngc{N12zP7|E4r0x(COG6Jj{)`rj!(oE}+nzjZnA!=xZ zsui!Mv}F@->Dv%4gvOA&)z{bPeB@Pg2ulolWw#F*2V!N(p*A3542J;p)wTLQDy&xf zWkr$uNs{Ut8?r)VE?_+%N~2#@qh4w?0exM*#`iv@ZzKWAMrJG8Ya*6 z_m8LU?FZ4f9_1Y$MB}&LJb~ zv;^*#A71@71fyOHA7A&L=YV_{g~!~#IQoKHuOi*I9$zKG8_s9W-$&niuJ7W9Z+IK> z_E$W0105g!+(FR&?Pt<{bR6%~eh7bF_`UDV-YU?W8Q*?`xja?zt6y+;dVueL)z$AV zQY1{@_SnmwcixWF9(%)6E^?cY6IA`T++zOuThn8rgg<--(gVu5_J_{C^$QQrehuQm zYu9hTQt-~Xy7I8wzm+e+x}g2MqvM0u=l}Yh$YYN^{}=B>KIfRI;QXg^8qVhdxPF=h z_praXzYiF6XU(ra)%?=q{Q1|h@A+?k7ZP2=vY)xai6hItyoRu^ zeCoy<+l@1Cd-#-vy!PBi6c_Lgx_vlnA??G@c9Ah~ z?q6Ri|3I8`FF1GJ--&Z_4{1FHue#5_Jm(p_>i+3IBElo-|IkMSczpfuAEsCLn84tL zy8P||^2*0vb*0P0PYK8yp|?L4kf&h^k*_>|*nBh5!hObgEd7EV-gxZnQu=~dfRX?$ zbN6`9HI@Hr>v1S@lk<;-7gbMs;Y%NeuzRxM4@9K(I1KeFCHG(Dml*q}w`S!5SNWxy z_m$R<4UvC$%_@J}6$Ttv`7exM;XQTujS)f}-mD_;RG;>%SBl+d0&k{~@h^n*yqlwt zP7Tos%lE5rprRDy!c&S157C{dy^`HBIW9((el)zkiTO_{gfYw-K~ zjsErw-neHw_iN@F@=qeUzcyji@kH@1kb>k+DY$j0sGiH;6nVwVUZ%P*g;Bho0|3u) zHs{7_Wm{*Xi;-u`v3+ydO$6Hqr>vEdh zW0f=OW|cQTdv@x_+ddiFaC3IrR?b$(F6ZkYSchi`G-HEkL2AtOD1{-=WXwTOK$KDt zto0cr(NET~SK8K-^EJpC0JC_(-UHMVZyf^Z36LH_1IHF4$PIq{8pg6a3(~oJ7OX*% zZO8HEC%TgLlXhmTz!iQ|Xpho(`oV!w;gt%k2?&({0#9NN>vR_y_9W>g){GlW}%z z=vd}j`kp!4t<$sITdmGq+lZgsNA~(i!I5W28WTGXPW{?PI$-^VH+zkb{XwGvMAyCb zw0>_7=gC`hboM6iS^L>D@Uh)w=-N3GU;sykeCC^eP&kI=9oPNYxj391#bFPnKl4pL z^voHQsVBsizBUz9sGWjyKbB0G+Z*Z}FY<1;gbE>69K>jb1J z-d&QtdA#0k-wG1pf#QM|q4;{8K&Ch&f=bVxb&nOFyhR=;K%fAG{S2VGK(LMt0ZvG4 z0I1^@*yx-Y;SNRyt$+qRjTBbM*-_r?XP&g5T|9e663?75)UgCkaL=AiZq8t|&W{2D z<00-?0q3hCfOem}SO>5K_I7*{^fT`$h{w6RwH)$wygYM2)xyY6VgS({z9`Ix0q{ay=#lPD07~43O1tpi&TsI%X;zhh+brScQp3^1KJ~Z6uLa3 z3nl%cb@b%{UEkdPp>+NuO;Pnag}hHr3i1JWj7#IWwzY?A?8y16CyeWCnrj8_UFUnw zk@Od{cikMz9x_%wapTb&yF-d@C5ODmJiBWs`(vKFcRlJhdTCxBvaRF(cV$n0Bq6Ik z=_5zxD;J z=Kb;D^B`vPrO~`lTMyjSrK#E9%b9T3Zgo-_ci8VQ+I+t?9ytF$apQ zly7~*&0(F-#65k-CvVRO&YAK8JbC|N<07rYSGgxY_3ye!_wY#<837Bw=Sp8N{=1GX zcb7T*6A!5$zRf$`Z(aTQ{&V=j>&ZQQg^zq1{OEt}BOeCRe)<7OySvQcRVx@BvO-30 zd)Ou}wCLeOE9CXyX}_!a@wo%dfAu}Cy8ihU%I`ga#~Z)zxZucnpXtkCZ5@8?>yfv- z=3ayx{%L@G*?Hn``25vC_P=^b`adr1$F9j=eoo-IcwU+Bw_KCI{L=6))+}U`4nt%L zsp6Z5SA9G3`oj-}$Quqn|Lw@<=^rl;C_2Cd9ZvgJz_493^xbc{G?#qWyx3$5^MtU@1JiL%tk_^y80C*f}Sky%@9qf5CM>7!Vh-c=J&E z02=y|px?2C|8|G`pO1lxe(mA05<-wZ`|FXn0{Opjg?#t+`n&NsUOAtTk$Sx{r6vwy!o*ECggL0-hcH{^n0>( z?=p_=BH*bTPaC0iyw#h#>ouHF4xjl3 zXx6Kf_W+vplCWOZtcO?qW8@Ek?6-a!(mA~0+Ykke)AS1M*V#sQm-+Df;lT5E-*!6i z-2Lm_$GM9#m)7-fy&q=cSKg1j9Twz8for#qYYfZZz0lGZV+8yD?H@q?8I1A&{Q&Y? zU|4<_hWBuWOL~>~SFF%MZp1D&G|MEi*;4?pcO&?$xV>gg@94+J3cOb6;q5b_U#9!>E{ztwH zhIcEZ@~V0BM^~!dd(6i(#sBdq7xdh!eDj?7NZ?(BT;mS7yUgLcz7rvyxu*7o zS@2n3hd%?>CHQqtV>$fQcOp-NsQtT_WCTZhK>8<$@{VgrxaR;a7Ql__;YV*EAX(pq zNT7`F9^>8X=%UO;Gl!r2F61MRQvY|q8~NJ9C%+r%ULzG(l+88k@bdKD_KjTw{^y(U zSmWH40moCA6Mu2(tLXdMWH=aY@_Sh?L&fW9_ho_!H`j>xe9fQYT z|JC9{&#~ ziGJqz?&CGL8oH`vu4368e)Ml1|KbZ2yK~iY(Lb!v8y`k~gj34P~n8ejOH z=$bN(!~ghUq;b%{?cd}vxOnmIi714!-ge}6wR zc$7xI@duDMq1Q0vVyz>>**nh8&W(t}pZoywMX=PDS2%d*9AA0v;U1OMKRA2(+^ulV zm6Mr={~%&L$_PI7gGdDOdfw*6(cyeW+<3+Et%-YX1l|0{ojbw%A9XOVyyc&I>hNFu z5JFu?%{7Yag5rxwz3~bNo4ORHf9v0{8ZJuT64~1`beEH4{LRl@+~)rHqmJ$N(Ej+J zB5#73ze>pc_1LAEKVO_M^VR38Ka9NpaX5|E58@BQdieYwLx!+v{l*o7uQQwOE^|2i z*hy92{mb2|{-VqU;}71CKU)2_e-!x$>{u6Vzp!SxD09*OjoQKZ5m?W|k0COwhKnK( z*UaI6_}I-8-9s_)f{eo_ege7iDE)7K68WA-ssD{Xg>Z-Tr;ysw8*p_H$Vg z$rnX#&iehCd}&mdnf(0k{Veh;N2_4>a|i=&@+F7=`InH_Uq5rN{$()ppE`_x8R0>A|Lce8_a5Dj5C7dSBXel? z-~2M7P3|1qpS?tVJazbAe+7}RAC>s4$eW<|{8vwxqyO7W)#HtqCvUjqe82fmu)D5` z;bm>}RyYP-b8fpdU3aLP-t)+tkLu=EJ_&o=&wTQ<$GzgscWz;zbAI7BkS{v2_ot9A zglYS{D+TVabI=Q&bKd$<=X~hTzwJw4i#z}7_OiOhGQFlu^YF7jft(%Q_Up)39bWb8 zi1N@aU8wWJ|NiUXB>SHpv61y}AkTt;+(qhD{=NOB;@?64P0*9W-$dv~8T;@2<|!26 zD%qE%>UyENG^-avb&WINP51Q%sLvb!Ir5&z;c4G*|2EG7WDZhZFKKK$h0JpPn_ zJ7vYWU|ckE>9ycT;BCq=it6TD9JtUrJ%@u-bMVf~g7+=(kj8+=NO!!o*`8kKz^&Ku zwNALs4}bHYAzyUsv0<17CcH_3H!hdsuHePY@wE@c@}0le*`B=t%$PTvet=InXxXFZ z>G+cH122lC&p*Bxx2aPAi$kNIB;`r?{27)O^25#DyWocDX$394WEYFPE>U)|mb?jYs1 zH3Otvy;%FztE4JL$@8m(Xhui{C%xS@@3M zhuhpgJ&xyT|4-o0z0}~bx8s}K+V|dO>mQ%0yeKvNKICOD`^vL!5UmfLzj)${51;e> zPrUxn`fm{L@Lm7U6YIwl_fY+}PcVn{58_JX{Q)%a-XDD8Er<0VA@pP6;bVV< z{MqM)@3kX%!n*~do~|6K&mqmjjXy@-Cx7Kx9U3~mO?12kAelh$T%&Mhky7X zhoPa$u4OgJQ;LQwegBd{hv>rKS76-;>Z;gg?2KK%HTPagi{N1ynT!*~496W@OL zt4||e{@J%Y)$cV-JU@+`^V6#~b}GwNBKBUpwfsKfAIAWxfDTD{yTY;Eu!9x_Y^XKSEkYb|b4 z!B8Aek<^KbXL*j~d4{Edi03Y4(7H6x!()Gn{3pmqU`+mv!7!2suc5g2;?G9m;<@eR`af{9{HOo+@#f=S{`SLbKla4O_i^4_H37Sp3MEMLspn%} zCo#^lLKo6lN;6$uR$Hxnlo}%ma=^`-GoSRE=Aa)BCz3Go)DE3Q+gXz1bXuSK^JO4d z%lU|hsiw&+SJie?}bNv6B0=Pw07u^kKj{b+H*B0vF9Ii^>MV2Vz#3bPFi zZfQe_`mnFD3BaCLx0FOyL#y4clz~3c?e&aqjMnR+yPS4Nz`b<5(Ojwu<#q?j3yEz> z0I2Ff44M2CDL0(FO=&>rD=ozkdDq2s}0pwX2hzZoy%QoFZV?fSn z)3Kuzy^KwDXAY2{-jv{nl~UpX)WUC< ziPC}2PjZc>9l@+-dA$@&NGU4!fIQWg%p){kYd2g?A;o@M70kveuVuZs!UyqUxT(rq zLtCWLQd9vuywk3(xQUVvuzEGnLT`)jxtdo6>*>hi2pE@_iqnhC(O+hSfT7n7-lkx50ahTLKr z5)*YH=hoE9=CX}dJ84Z&f{6(LoovjSq&^20HA6snzyUEvwWZ!Bv(X7f=Pk&PNYNG5 z%W5PQ0%oBl&-olCC0_DITmW*05ezI0=H1PEnrHc8S~q6Pa&(e>7O<>l6tJ=7jW%mm zVC!O#c#5K!{Q){~V!FRs4FEwj?Ib+4b?m&;skULD0|LZ;yu>=R185OjvRUD0Io+QS zdR*Z!YMc?)CKLhoYQ4vM8E=IXlffZDB8yL(wu0s9df1zV9TmkQoysZ`D=qjgnpN0B z!t&4`l{h5t+z~`~qOSGca0hu?2PQW{dk&v<%KoMb`KFz!7hBl~D@-2p*Sm60T*!Rc zFQ%1n>n}srRtCA@?zbb<@3?r$nM9}3TADCbx0Ld1t(XNspov|vwsShc z&}U;x+Egc~4tc!y0M20*)vO9|JvB%&8?0zo*U%o$=XMPpH7#YQ4;EE)Hkkp&`N*`3 zs2#6TiE9oPeY;*1IHmwtXA+1Dzgl(;otR7`G3WtWYY4z*!#X*vRC*faDL81urbpWa znG150L3O)^<;ETm5vkQYpXG5*m}uE3l&ozPV$$j?S);7P3ni^}iUHc2RtU~UQMXy8 zKzVZwms&U#kWU|A?2}xh7MN=lLqHY?EobTY+YvX4gBobM3A-@VJ{jqd__ICBI7ddC zq@C^5CdwH5n!svXQ1AUF>mPGb4ncVzb7`)cck1|B-^lt!bttq^!Be_`(=e=zmQlU1 zvyR86IVNO*67=+OuB@r~Xo4pu;95fx<8iA2C=MhMv8~~%2WhAmBNx7RyWJ*Waql5r zwO6}|x_#8;kN_M0bxMv2<&MbReJFQ?j2?OJF%R_`YR#Zhy+*5r8}OUDZmLoljg}}{ z&f))pxs*8Sh~_O)6Dr3Rt9d7kMMyDfOSRFgQ>o34o0d|p^7YI8lNGa2O`IHPxsiB=>N+nn7yvh7?08)jGRicG(~S z*n6vhY|nrtQlCepFm38B$o<-tsEV>^$@O|*R9fyrmO<2p^)?`fH+29X$f#-$6i!|7 z$6N?!fmu=VDADql+7YunRtAotK(gaSqZK6Ej$m#{Qik7por2CdG3SeP=QOAtSspp( zr=r+1fx!BB-UWE*)~$W{x~bjYd;f0M+R80~Sb{*D5WN*>?!g+rrtOiM)#tL%0Ucrj zytufR0-l8}weE{7WV1zKXXCko=m1dlGIDEVdjKmfz;JRUR~cCEVp`QG0pLWBvfzhZ zo9pE~A6CninaOqtNS!OEl{Xp}ZTN=Jpa4{IYPkT)vzr&2(%2F4hDjIgc5m-Bz1^q= z8P}~!ORRRw3c%K}E0{)o$NI&VnztM7!W96kT&#G2XsU;^a$eJN&rDdYa}v~iIT{K8 zF+N9Yy?kqCQ>AD(K=Lcc(6Hs|xd)3U)%X>@fQYTe`<(N7^RV zn9Fl>9GCoXz>@tPps@pX)N}=jz*pV+P21|aIlRi|wlem6er=u4>l1CoP5ChD;d+0n z0N8qOM0nlpu$rXBVmA}3`w%cRWfC2rYR{c+gC4A3NI|b?yQ=F&T`JDv!N$!*JpoKK zlEa4md>q99Wxu258f{JhJO0?{plL{c-R|L=&1NQ%#&GGVjz{zcnn-qN1#(4$0*X4LWD26sQ;Ak-q@CtS1fWAK#q?@41AtRz zwxOzRqO?R!8Y;50s)vO{@ynJnE%-dC9+lQ;iS4kX{z&1aFoi7hfbHAD0J%!GqFLXI=M<+cv6iMZC%BLT))=>PjcH)Q z+LkPo*=%qr*=yQxYKvMU?&@ld@y4re*s9s+dOTV>QPrAw+1ydfh*p#xvpLE_b7OQ- zY~e(PTv@bZh0KgeH;88%*BvfR*XuL&!KPmolxb#8sLdLF0CQaRybV!>AL@cXRC}Be zhxEo=lzVH|!aI%31r;m|0e!q_L85hi7m5dfwP$t-;XN2z)HW#FFely7+;t5&XQ~*lDPes za@|Z?XbsRm^hJ#%i6U6=-Na}c>Y}-EnU^A^!-XbcbbqQjv?N7Wdw;wwAfz(=vs=JTq^Q4Y}w25!DfyV!&Zx36WmyQs3}ccVF+j;})S7NPc3z+sF_Bu%9;GY+ za^yQ@8K=ONoeQB5VKG$dN@q4^sCIia%4^G#3IJ)2cRFo;7pk3AEE8c03UySB{K-6s zNsV6R+|t+#P)sUJ+fgO0hYh7pD*?ofqi}Z=yPBKLaEB?AFl+0q;>X=N3CPJ9W~k#b zB8Vkt10GPu1_`rTU}#5f;1NL5WZ9|=U9dlwoD?Q3HdM83zq?t1zpUw1^li}%N4te% z3uUw{dX8z2@EVw`G_I)(zM_{>)}%Aj)d7#21@yaI@;9S3ww%Q^=ypFBY0U=oV7FT_ zht7OGE@3UXmF7v?(XMeDJ`K3$hY}+5f-uP3malf8rdLYI?fd32gCp~sKG1*^!X7_wQ`D1 zJI-o7z*wR_MZ>~r%d*MSfbQJJwxzlAHd#fgV#dD9g3qRB8Om-u1dG52a5$=H*g00P zb#y9Vklnuk1?yol0Ic>QKe{B%2!UZIb;g&7F-eL5Xp%Fy3rcIP4WyZemB~69*j)>t z33kIV9r?3yrCaH=H-VL{2eTQU>XYeK;7G&H_aU_rdTV-vTK!(MV^;Piw!@AKuzi%3 zc?CM#(!aCqqL3aKMC3tInrtv}?bg{{mQ6d9*e#w*!EDC+Yf%)lh~DO28jnrY2o* zwpp*~lV~BJV@&KP8otyS*RE~hoJ4@dG+MP8DU)~e&|j~O-rA@V1F=jq0Mrfnq{hr* zx$g~dv>U;dN?y$~0E%fcklu)08=GLy=_700${FxoiCT3S_|A}?jz$xfGIIgoppuHd zY%$FUumR`%wkMm5cF--ne#P1WyoX%}AmM=_GHE*#(vGKWqAX4aO~&oGDmz!AU?);` zi27+z*%nPc?hX}Pm3U<|oH7%@#n~$uw^pM_pRQ9&r?=C%uT4pO*NJU8oRjM~P1jP$ z%{nY#R;Xn`cmX%({1_9^j-GXPA#RlEq`B~!oDKP{ldXLPPWE1p%KJTz<~mb}*r?!! zP%3dB70K>)WvFn#Uo{6DIq!r2V;7G{1Zc2Ds77o;GNfMVOaXsn+c5_GK-&P`AJK~> zauz38;)gVrEh~gc6Ky8zB(&BcOE;2U2UmXbuh14hTWVA!0 zfnZnLU>g7`H6gBxpugJf>wKn1Gun|w-b^_dz*MR`l99Db)GN5G7T9d36Biy;kx*Vp z4d@^a{NdabILF#<`3kA|W@YEiM>!gr-R^Q-)|rwp=vFk$Be}v5tKlfr05=q)!@gH< zm<>4Qm@Z2ZEXI}l$^f&lcHxu&;5q5^&@vvHxKjzxLS>f~I+HQJGR6{#A8y;Sh}XAU zoNUUd!VZ=xhM8db0&JYq8TDN78#VyCcd!`S)lLNJlIwPdv-YObA6AJh6Q!0=Yfna| zp#!dBnKjum&***X5Kht=7=Y5lax=h4_hk-aHIEQbhO!2jP&aE_m&X$$+if>Qi(~0b z5Y}$93?ne*X2V8f(a@?Tr)F8+M1x>y^=A2SB}Z5zTn%hm#L^&LWMaW{sk$X9g(@{P zce-R6A@6|v0SYCmw!l6~2abkWSy-1u4a|QGKtc^lrNK2Q4Z7Ss3MF-HMR{eh^hNO9 zY=;gl51X7w3(U?18>8y0-c$+92>@ko38szh=)OeQ6W{6T7`ZJRxKnT}dW=W)jl;-G zk>fdYZ=q@^bvyGJ=)?pod*h8{WpqJ@>5~f1t3R4nQfPO41h~{MRCx1w8BtoGn+0*eV8}X1!&3A3MNa7Y}cD>I^g?-(TA!+#iA22 zkOB1$ZIfym5}Oe7_*#UqvRr2BO6A8k+8a5=ZW~kmGH_{D9G0XKP8WqUhzHFI=&oYF zwyQPpmSee}FDqpXzMp1PTcljOHz`Ff81jQTF6EtC!Av=SK?*_v9>#3oV3Wu;*$5rs zop|L7^v>vW%1B#{rUh+u{oWA_(I=MuMYYjcbkPt-0FJH5tFp5)k)h39CJ(~)9wQxZ zFyK+}WINM=shLEbVbN(f-!PHFp@2H-wgxNSag#MOn$$*UrCIdlpxIQpb_U4pqs}M} zhkB)CM;y4O#)_~g-Lbx6t#S&`xu%{aVvj2e${w4I0&7(_y()H7#xjLWv8NinN}|XrXNq%*wkXxgj~rT}5vR0KL0OR&x*AyId{m!A`dH zY-??|I(1?Ku9$Y_)l(K7G90~&Wjx{TE%8Pvz}E?#?K!vcT*0uNLT4Bj@^@r(-RZ^j*fa9gxHdP&Xen%Z!~ z4nLhXP*Z5oxL}*kZqyd|QPc!Yw+_Mnulg?D$#A||6#67jz0uwrwn!&uX0x`5)#Oqv zJCsaHS&EXfm5zO-tu{St-kz9lyphEXKU3{8VyFclS&WBZn!PlD3WnN7$!X+rX(4eG`sVMnmr5m{lKqQOJP@C&1>>v!qpQx z(?dY}8|YZgQ`GsY9w-5x2~+I$?`s&_q#B%I8#!@?iR|NYNEg zq6a6z$#6?fH%{nS)NrLWJ=LuYG;Px{aK5)5FEp)JE|k60wWyX=Z4`s7?Wj8ClSZ@| zv%8wPX-56}rdRb%p<}t^A{g4!CYf>SWR?OBc3qx`(YlschE$)=XkB$|T>?RKTue;c zW7s%+yg`zD&9a7Ir*su9(#C)^okg_R9n_cTq@df{o*@#`exuZNC9SI zXz}Hmcep+;dmTVFM{Q2RwiYQQYrf+UlQeQ9&j}nX3%Utf+GBnVD?%HCzeZZr`!hf% zoj1F);ZOm%tadXN7oC|gQTqW?qJ4$l=z3!ApnnQmMTCeg%95e*0gq4Sr88l}ZXb>* z4SF2NOcu^Fj3d+zRv|f*VY3N4T-(daf_1@LCRQ0=*ky2;mPM3rG{8q>Z_+^*&^4F7 z4IW9et+xuAbuGZ}ENkU(I4KhfUp2USecp=qqy|TBfVkZ3*aU80E8&=2jp_nsw-&*A zCgK~9S^@yL*H5cSq@||85)B&ASqgzWRAERr45L5bC zy|P|OaIrEXi&_)ykNc`Z%50Au`(m5fmn6B4SXK#lat&wbWi7$%MW<0LDq<26N^>JM zEBZWBRnAhYXw zhu2q0xU2X&MvHRkh=bWgWf+Ez8==u*h@8dX>P<$w96AAj^$w1$$}uT&%DB&~yKWM( zgKg=ju9rUO6u-@#0Z(+Np7mf+AV`FZxHoGz3Ce&edlT{106_X=4!H^sW zaTUBx5wLXR7NwEI3|5yG@53$z2l1eeakSdY2$35)eVJB6Kj}L;OEo2@*C^cHu)sIF zidLvJAlxmcq?$Vg_-Ji<1w)TKhmQwkf6}n~G}@4{dW5lni*r9uqN3G zd^#R*OKdsN1W)UwdjNF~%r)D>GQ6v|MhPEFQR0SZUK)z(EGgc@K;e}g+?80FCz@nh z$azMF&8|CZ^I2vM7F z=kqxzqKNB=OlB)&=sIPOb3goh9NfTRxb>R*qQ}o zV_wBUTypw>m}ZAjW96RdQ;; z%e&)!-!`dOH92SpC=O_hI^QBPP3dQ|z-4UOKIwNHvSIzm#NvSq3z!unCuKad^SK`o~8OlIv zH^;KP>Pw;&+N2Z{vZ+)Eevz(awyu#AG{Aj53j~!baeuZYU9e7z4l@wf&7e<@DahMD z8aqO_>My2~rDVEle`Oy>CBUeX{#b;g2LTs9^J#xe3^OJm_;SqlF?7a|7*>}`N6Toc zH!4_r$rGX@k~|nrv!rVU&6QvG!==BjZK@(%Ae(Z)hrFH`F+c7FBESq9TVlUW;3g{0 zYD%)Q0UffjqT#yI$k&XH_jl7lnvmgiTG1*jgJwRP+Z8MdM7g7~5P-qh9<7n;tU#mg zM)w&G+}cODN(<*pA0wjxG`BKCr>;+KN`m2LsR$a6WoCQ4LbHUj1=G&7^^Hk{ zJsrRtJ6OZ(wbmP9=?|ppB(1fmPJ1zB%+;{M%>p>`TWBxKW=(jBRr5IdJRTWfr$@NsU!s3lh!yKX(+=4N4v`o3#e&I=qKB)%&yuzV@6zHWg z))WpKjPteJA~qc~CGm2QV3OIySg%8jy~%)&=z0?;*Tu3UF|0IaVsLz9>jnmfC>^&d zGOM#RAbJO`6irx%vM2P~mQtRUCEc(G_2Wer+%d#Bx1Y1kCe5z{L{P^XAeF9l$qF z1Iy6x$!hAeDlhh0k+d2%DM;8Ht=N6cl&-gK4;ayjyESJ%ADRR3@^_PlokkIDcO+kN z(UoNq(%R&7z=dFFSD_tD9zozoD=kaOtI&i`%a&;t7R0;Y1iRev@wg{23R|~pBcL(rRvQJjHtAJslvykOLE7U0Uh%zxEV%ea0E%ysZaaif=h{P1uixd;*yFAPZSu6)(R&hYCgKg zm+eIgwsAwi%hj6MlLlxB!Dj_MN+zvtjp;X+W8U>SeqEGNOvh!~;3-@CvW)6mg>&YDWV0DP5PfY_Su^$eL~xqXwB96aQa0=T zNxhZ?9i2PY=ENVHMc+h7ZOiB<+CEf*XHknBvpD;!RDG%_j2fGS*AcEw;R z*nMFHTBSW_{iVxJD~nZsBPoO4DBpUdCUWVpDEvypt)vZ%A*KNTtbrDtudFF1n1MvI zlG$Cr`-{Du(`l%v9*H}!Ku8_rZW}oaK?aqi-iOQgA>Hy?;0IvD+|R7-2F|^?UTw7n z)$&)OEC_ZPte4Fg6(_b)x&(ljM;VizuHnhHnECj~Pqu==sr0S~Hot|btf`Xrb};iR z>wUW=T77m-VGX07E~v7xVTcf|L=|rCSamC$S*uQ8k=06@vv-Xh@6j36g?MphFw6Pv zh$RxUEl7kfPP!YH^Ow^uZ!WEYp$p!~F7#etw;+>bISIh)lc=_dDuyb>TbJ%nm!*RE>Qq_7t zQPjFRs17K%veCEAL>Ur00=xO@e%<@j*XhDB=ib$%nJn~})0R%(@*Zp1yAF3q7P z>=vmSt`rJxHCEv8%O^#_&eRP`ie!xl$4xHt+or_C!H8K&bw`o5yQh(rJ#Aqz17^)Oym}Z_NPg*Dd%W zPyneZ;HE+7K;VF^=YwiJv~a$~>#nG^Fgu)W0i(Htc@91@88oR)J&;Y^ZmbD$qhbSX z#|6Baj~J~{hY&9-UwFZ$o6nZ!CWok8Z#i{aHJA^y9LWw@od~E!>U-Xp2xjTdsCE&G z1>R6Zc{(28HoMKS*ihRY)fmldJ;Isu`Z(TH{lfBTe7s|w2@ZSemNu46dDd{Vflkyb zUNlMtdxO_AE4JKKOQGgCsmgj|L9r#A_sG={BYaF&;R0G_;(@f6NpocO0Mpr^v&mo> zp(SlVC^=pw6L36RD`T5>XWP+ES)v20?yW0o+K75I*jQVU&p3TPm^-U-=v1)A&Y!Ys zeJXRgmINrhreiS3^*H8TF=RI@xFJ(Cbx`k*wrq8ztnJM*+3a(pAr&t4dbDJW$h1`u)bTf17~LIwb;NDZM~lI+JLntC5>mDXsf49 zquC|=h7i|w>zZmXD6S=wsRQwp={j|IP4`)C)GqOQi%#0r{ZfcbEYan1sA0ZWGme+X z%~^yOcy|RCeR8?T88(K9+X7v7X>APmRvD=jBM1UCgqadXSZ%eibpgyHIAyZyOy>Fl zS=xg!yV-)*aJDcrUqRI!LoEx5F;R_$=z^T?b-Vx?H<1yfGEZQ1H& zg6JqDx@z}yTXWTpqQv~vZk5$JTAkB2*?UMR6Xc|6t1LEUw* zv>()Y#^^yPNsx2fZ8v3_B01j>VOc7pl=nASSFranp<^w3l`~aOB)7F}VM;ZK0~po( zde82`y~(_4uVFkT&Q^xlR*K*xF&t*?ZD(DNrWtCn9lXDYm`qx`JqtV#;1lY)DWwzo zw5r(*x`VLoMwy#5vucc_a0$`QHJVtp(fV}eD0?!%%xM^qt1;j3!D1TI$B4)om1oWp z0@<`6aZO588?~};hM727G_00e>V~nIwOI(T?MF|J{)x3&XU?29GiS~?YzA$M8a4zcdi$*YX5aMKklqyx7Kcm!Fo|wmtvy6r&$R%+{K!z997YAnCirg zBQ9g3MIN1K>2kZ2W}DgD-5&S5b!`yw2JwwtfjG|zp=O5tsQ9a1jAE(U0w|Yue5bq?cDr!(H>ZI9v!yU`z#P+(BIMD1nVA+c6rwr ztjzi$f*E4O+earYrf8GeHe#A`cLjAFqp+t0!Re#Q(dM4Io~h1ZjY{v11srYtow`s9 zL`CYSVLLajtydYwO<;s$VMSmDjDKh%7ExJ&L~Sm6!<46GMj39Mgw5y1s;Z`8KZIHh zb=t-nsvua;sj|Vol&0U**XC|@xqR(jvnuR$yF!z7#&B>1`aT|xxta$0{ZpErR-4kQ zHV^d!axR_T3&^!kX_T6HzfliSId1##aGRRM^=d5raPym@xyh&Lw+_{{^|uFoYS1C3 zp|)UaAB+8kNJc;~03pHwcbB%idp;89pl~v-IG!c2cuBz9eEt@FkFjTFIOg?P6%(W0 zs$RVdI&T{fhXeht(WqJDQMHAf?Y-I#h?-Y)d*~3(ba$(#l+L(W-96DXS!Ip7RN663 zGaPT}s_Jrg4EE`4y5`m?gJZBR*sOs$d!x#%w`#kly2m<0eGq;(9B3V}c}$vmZG)ms z(-xSSY%%o(V$NQ@VYu7h(F;zm$22gaAE@habk+@bR4MwM-GLTZx(&fpYO2%go^0>1 z#2W_OJ$loKbFjU`Iy&I?^y-^T{i8aoN!#1n6l|{Q)C2=brt9g}={vfjnsJB&^y<6{ zO{1!_4mLiGFcjnC?c+m3JyE64lf+cp7tDSEn0 zqkaC4&JaY;TB_oTPJAtd zcIyY!_2HOprcpPe3dM}$@_2X(&IYwd8`Xo&F!@yY+)aj&P*@SR^;>%)qvMeoU$@E- zfar0t81@hLxZub|)E^!1sp>K)C!*Rml{PvB=LjY&us6})qw0oD^^PiA%ghuwvuf?M z-&rSz$ssHWM{RCV)v&GI5H~kidrciGU7LD(w0k(JR(IHa zqa#7BJ33>To^B8O6djI!bPkig!2r?B0MC zwk}##o%N%`eM4|`q@^j?W9zXGHqLa9jE2IE5J3-HEAGjVrL}u{Bm^799aBDt?Qlc1 zsKaFrHun!Yl>=R2r>V=~8*UjKXdY;Dwlt|H^%DVqT~Il#lt;qms4)x&(86uTjv-(7 zG&oTc-Cc3@jL#X1D3vhfg_ez)fxb?2t0`h__L~%XeVrZRf2P|VLG`FtuUFKMI@^Y- ztbP51tr7e9@HqSp>v<4p*8{%fz)98Q}ct9~e6tkK~+k@>69~fP)*&Xxsc19=VRnr4K9`h(f z@r*iQpS813Yjzqs)I(NJtR7^=58^gswe@J?Fo_Rzdf?cQx+OR>);OtfOtrS_jB0gf zPe462eHKth}Pb>^6HXmXR)qh;M3(2kYuujm{pm9Xvx- zd!tG>s&AB!j5L4;t{c+~>Zc5_jpWjM1HD>fY|zm-)uV>ts%!Uk*gB{Bd_VzDSX-r1 zMh&p_)nOl0wT7H6V|EDT7-)2wn*8;!p>OPP^iF}D(HN(OEZUGMAV^aj#A#%-YS26y z)~LE1x=>q_QxnyARWVy^SZ8QzYME?_4i1)+6lqH4aLxev$6&dU6 zbUSSQW?cy8nGs)exHldcneNef)viuQAZm(st6R+SX1&2^uUF|Nx>VDhx(=064r18v zv&muBY4jM!8f=#7%}dDY!Hz-;2|3bp8D!7u;q@MgKpKwO1peY%g&gD09^4+F4=?|c~eO~$c0!TSgo|!=*_a^uGsV={3YTP9?2Vd?e4HG z3TXubaX4p9ZuY&n+!cYN!h7oK!Vb7MHv$O#u0i4GTioTvD+aJ33%L& zkdPr{Uzb0gf479(U98SGQvKVc{Jj##trl3#PFO1@QKF!SYwvR+VubcWX<|I zpHzcUk>n~#pm>UZM1zUgt0fN$qY417S|mTlDMJcWT5P=}A7}DSx(3LW%|t{B5cxH! zOVL<8e8oBF!XldS1>XmM9^M8CV76aOXbI8PY1v7HTqvwE=(}xU{zmv3cGGB0>UPf> z5Z+k}ODB`qPH$J+ycgb9z-viEA^w&tS4}EOY-Yw4{DC!SJ7hDveGS^GogsWx=9z|n z=Hn@rXC+j!j%5sv(khTE{-0~m>i|w(irVn*QqADl zfO@JF$qZ$l6A~!tT3#|tp4B8Dccm^OV8~h^?c-x>(M5P_E$V_)VeA8+W+#i@5XuM) zivPYAT@ML8gm1a^j!;IZpFm>)uQxCi77Gr01*0I;Nx~IagpEH8_%5Ec4yJdP3`la& zA;*5rc_;#Td@cB2gUE!hI}e?W|6xMp;;)D4xaFc{){DOsX@j0(tTVBH2$4$yjz!QO zW0~io)QF&(L3^Hi0lF4gck2b{gIIPUH7fT(mvj3M*>vXppW=0t035uD zYcE7G0M6~E%JEwgQbI0P^KL{gxVm&V>c=JJh}=H*9Z9K$HRQLy&$rH+NO~!ve6#Gb zH&%ctMhW4vUB@W`FYesj!{w-*T=v$ApD9PJxTg}4TZw)yK|h`coXfkP>81% zx!>^B3M9jWb*LJYkx(Sr4T(%;$>1y+MnR-N89iNx#z7r4$&nL$w?63o()7>^f95rT z0N16tNr5^5Y^MUX8f}E6Wgg3tC`+94Uv65T=@$adFDuY@0QegU^ff%9qzW{!WW?Xm zW&sWg^t(!=0pQOmkqYlup%UZeN%Z4OM!(RLr3FAAtI*xh!oCJ{Cy@M_C1bw!cow*D z`N)ArR7H|;KiGsi@%>GRWVF6bf^|0Cn5E2Ce7q5D#fR0X8iXdJK$_41JD!rXvalZ9 z@c`ck2AxhbcQvCuOGcX)6BE9<8SMlT+}VuEB#GR=vtl@2vIkXT(;n0aej-Dj8MpcA z%OhF}*Ll6a3G5HI7m@3{@&$vB??rML0BQY&^?_&r1i1y~JZm5F0s&+DkPDde?Ikm3 z{j2=I3UGlrTlS+3ggL)(0GRWh1JrOA)TA4uY{bhfgX=CrR|4rXzhvIMA(Ro3UW-rf zM_Q~nh{(M(LXq6|ODH3N!LJ-d8}N$<(N2&Mp#X1I&eR|^xGLqi>HsRoehoSstjh(G z9xp5?+TsmN2eL+TdRnXiV@3%VWb?E{;M0a{mlm1GMMf84g%%cm9&AN=@U-?z(9bqt znPu?7HuMRgbmo`L0TarIDD7+qp1GtQk^A$60=b7vC?f!Y+lclsM;y2mIeF{!Ano1UVwkc$}#Q3l*113-EBf4f#8WYZ0QA= zx~`wflu#tMObBHJF!;a#DCC9#s*r^ODIg~79YDQQqXA`V@b3rEHhr1r4=YBQ?f9R) zXa~L|j7so_2GOpeOo}YbJR-6S;^FxutbejR@A#Mr9iGS7>JMWUTbr2dzTh66R((CaDhS8Y}eeW<`oZgjxGd5{6;K9J+G+ADO zCFzd>ZItr@&$hDSATTpmqp@cM-B?iiwNX@D0HW6daFaXNJcFe#JNHNmEG%=O%lL*F z^qi)i6=1?9VXbVYUIbn==9;-b9YSATh2YLY*iWXrV;k|t!=O9fJc7vOg?33lm{^OY zI>1zF?q`8I377@tC@JN!aL{L+7Ud_IW zS5y)jOBgN#7>oLCkn11cZ$VdpSrtm=RzX4;kqYu#(e=xzueMRsCBR-{`=fT$h5PJO zkLC^J=l10x@h=CsYkzf6cP(EeV2N-2C9uTzy|LwiQQ?a(fr|^1tz=0 zg}T9Y%oj*vA3l8v+J{TrNVgmwdDRW%{gIna@AJh4-|ImK@m-$fVRGR(+F{Bhh(s4< z@d8C6D^^9!#wGp_zHJ;mx-S6t^64FLdB?y+6t3&B%Z#Bw(Bia^TRCLq{rZ6#@}i=e zT*OnNY1Qb3C>t$-pvB+x(mCG0BuXWl4$D%e4gX>s{F0CP&;X2kmI4`&f|)>B(YmkO)lpWMrk$&FfaZOs*T@fNd!R)O`q=L6^+F#n|!Fml`kb+Y#m zsPrC?+_cCngRh%F*MgvCe#x9i2xUZ+91fui!BY^vrCK-P;~~@pI6i+Z+J*l!gx11D z!z96RVY_#w(0SGbv3pn-M)k`<`)6Ua3Ge%GQ3-wt{sPn(^c=oM7Wo#TM#d#a#KROF zvfLe=FXG`z>RzS+hlq#urOF)#_SHdNnFA%vuh<@i?pz#2XF(XmRr$AgLfRsDnpfWl zVGy@Y0{m1M#Pd-U#Q$TaE7CX4+ZJ&=6{$E5&t2f(12^ADnn*gHLdVjb|I4RP5A&Yk zZ!WeB?WS`3yFv!(Hq}Bz_-kxQ@J?x0dx%fS@w=`b2eL$ zSq5Ks6m7#-9YqzjSwIL*?HPyRUMb6dd2KV}zgLc;^&mvQTd{r|{2)3HJnIY`1thX~ z)_}o3Rt$qzKZqJZ!(?EPzL`aRZlR1wG4{sMf$U>{GLF_+Awp6izvQwSCBQpFKj%9a&VvS7`g!1Gk6T`0-9B?Sc|E+5`iAMO_5MWpc(kX*UW%F9J`$QeL|6? zfx*L9zy!f?1)U(|4dkUO(6!(Y-@V9QNJp0FbDA+mw^}i^(&EKIozoE zFd~;COVL=^;SnhsL0=2i5?sg^uAvT&5PwSEC7qtM;L~an<|^`L=69eDUWK*-j~=-S zZPH#%I20@!{IeL3=>-R`96v;>fJ*-6RcQ4pfcNM}&@Dj7SqaZ)Q;=E8wBR-W0TEw6 z`6%jJG7y2!@mD?uvzvQAM!7soD;XZQP(}pg>I49ZC+O5sD3DuJgfaq<#8&+3f50AS z)ipHCK`62`F!=a2RMlkEH{nOGK@C9mC$EA1p>5Zqvq0ZGC87Po8tz45Kv@&S+NG{W zX0PTmc0w7x^VCDFKI@YDBN2$irt32|U56S0!Piy_L45gjXb&h6q4lNF6}AcjSHo7p z{_D};a`^4(>*+>FzG&dvj-%P-wExW;fK|VI!}9q3*a_INm^zW%v5<_AppZmC&}ngM zA{HV#A&0lVTQR?ena5lIWdf8=nI{eS%d<2-x#&i^1l*WE@YkillaBc@kSuV=P56?V z&~9*(+vaT{+dA;C3E-qVE?^G8-?#}`0C*Qh7Xw_=lHtDdH`8@1`V=(t)~)C+K>x-i!>u=Fft#`SanHPP=iU3zPC)|_ zc7NtJ%I<%;jk5b!@(11`1r8iJeLLy_&S}QS%)mJ>-Hz&kFptgKMmC0TBcP=W4=XBx zJJ64S;Heqg4*+iZjO|2V!#enW?VYF$EX2!_?+cr-{@eL>8E|UC;7(_lC9qe#2{Yj> zCzG=TI@dZ)aIG>=`_!Srm3jS6UmFR1ylr^&#%6&24vXuHIe+0j?UKQp(EIsdCA9PR*HY~ zNu-*efUC)7Qp#0HB!8si+^{^H-}k;Zts>Q7FS#H{s8H z7TKUT=X?%XflP5pM-~>VAwg9!_;hXQ!Ox){U{Ll>&{e!pafjj1t!Te9A-qWEh#T@n z%1+KtF$@S+i6VOLS>QPKLR5~&G>a%QSmOOsEc-kJPteuj?eG^6Q7E-oUK0^f;59H~ zAOAd>fWbNQKI8-Y^%bB)?inqyU)7RzP3sf99TDI%*2llN5B8Vo8B;Lc=UD6(xb8X_ zar@jej!@=FP|-YDn2R%50HD+t@HzaEsILYNjyvo%X@^Ytk8oo=e3a3Tx<%ru?!HP1?(pAt4I^ZYoCii3bdiUi`LuVgDF^aq}J zFVZ?5&HII@6IgzOSzx*6mNn9Mpd&g?p^}1KrLJPWb-G&jdxC*z*TqwGCXRj)?S~z2JA3KGf#;W_#k3k&SC&uK$_+_I4 zJq{|seKUnuZXTrjP@aziNzyU;HLbaU96ZQQuupy&{IyJiov+L!*tv6PHxO*g99oYD z=Fko}*1K6!Y*7T86gtM5Aq1Oy`y1$jRda8C1J$hpg0WAFCzuHC+7w=kB$%k?f&@GD z5W2r$cLs-DB%uUw7_cY)?ITE0lng3)>k&Ak`o<$j33O|hlwK6wrUkmO)+pUvkD^H7 z`DGsVl2MGD!hZWPB!e+q`#7qGW=EISZ1NO#j%M-qABTzlGqk zOH^~g!MgnkR9%?K-A5&KAnM?c-$g?(acRf*J%P4k*Z0sA5bR1x!9|VJj4)2DAv#Vq zPol38&So#!I4w*p5yY9L5ld7vNvt?g1@pG(IS9%&U5gMcoOJGlnu&9Q%nZ~}GaxK1 z3ty53LcF|ONwX*j8h##wgU@^xRlp|T1`W2n4m!v9EILy=NBR%pjPTC_!tJ8F^5<@5 z^T_*Y6|fPvJ&Q_L6&%N>P9p`##%rfhPc6iyrU=VMCHGK!PU1r^po<`LOe(p?l|mzr zrJzs?P*5%SJDw+tDdMaEYbKk+nx)J-i#HsQfywoP4Yzomfsh+-_yMW}2Q*9RjFoAj z4DW!J;-f!6S1+gjMK98=7Xfx|2UsX0w4XSLZ+#B-OuBwZ_e_K$O9O*X|B!}=m)Q`EVfZhYyd%j?GFKckD!c@IPHOGpMTytKZc zaB}%cBIzR{o|=Se@HbwfTN>M6hAoZtFQa#9w*^=|MIA z>lLJnUzS8Qwq#Uq5>TDw+nbl<3{_Fh!)<)kd0By3Em1Fp0RyFf_N#~^M;==6A6^Dq zBL4;Y07%OTNvE=D<1A&`@S#^>)41w2x@nxHK!ySq%7_$T8$LmJ6>zYgIhm%NTzfg_%M9aiq2cpX)*FY|m$LcEmA zYy1^NlF6S%tD*S&e}y(`bVAbj7E6rZ0HQj@FO1ngLINz{cF?%nn(I&UUs9(L4=$@I#@io``4%$I)Ccd;P5~2293aa6L8Bdr`cA( zZ`hOOx$tT&`Ww1qa`ZP47XSU{YEX)lecp`4N7?KMzSz;>}){J)^ zr|6aWvAKJHi=KfakLJg4aGKjT_tbCEXA0x#OBxqJpL25*EUrLeCeI{*^-RG7?3rf_ z{sj{6gNjKKGaZsnF3)99&LU08WjVhas#WS<_z_RF<`f`US~vz((tGLoF#pPPHT+3d zY!b;=<(_MC!4HbhExs9kdlGodp9^<#pN7AW&U!wJd+#ptZC0y~$ZLas=WJM%oYHe^ zvi$RZE^M3I`8IlSwDoUaq1l*7&CFz$qV}L-qBtB0IV`?e&-JNac1TS*>$w5%?co|( zF3fi|0j7wSj)8{cs7Qy@^8{dB|dzUnInsPx=@E1o27d3#s(MQvDe= z2mbV1g{AY$AZ{7qz6By!Fv{HwBKQ}6#BwunW*K~Xl!`#+mrM~9$}pY)F~0zR>1J*h ze(VrO_B(|li*+mudnm6E@-9;Z9+;av%ssklb*cG*Rd`~W+dnsbDfdybl(xAsPbt^{ z74tEIlyTOE1t};?0a{@xc+JlJ`rVO&RA2VkO9C@jGr=309nIb91W;feZgykmSOTj&t8D04{U_LV4+8 zJKqx~cjtaU|7-@NF@zi|RiU zrZyqp`j9Z<7eP*gUy5)fQ&7HO@SRakiE)(M55gk_l5Rt@NwfCNm5^p|Ud^R*1C!iF zI07`+H_5Fl#GfDHNDjhZz~JU3&#&-Y!DudF;T%&dD$o6Ew(`E!&v+SF)YNLRzE$ut zF7ockbE-2$p8w4EMM8}Ea1(J}jFavXf9_&m79IQ3TeLcUkYrYkGmw0Ou7iH7{7R!NE7 zF(w;pJTm2SdmU1Ew6L2%rhm~gGPi7>Od(IUo2>;0Ela+Tnr>)UkN_p5G4+EsPRpd${@x?|zmx3oOtPmhKaS?B1BVx-1LG3I@3AE3 z?4gT!9XQDAjg_>K&`csS=)$Y6<2G)g+$pm}WGNPxxx;&8%G&0JCb_Z%7hK0}W^~F` zXjZg-xx%X%u$*vK0AFS1-Y+a^h{)sT$+HBt%4nL0T3s2l``XpqL;*~(4$&!=dhXhf za`j}2h4W>%*+sEi4sN^RO2H*N&eL-x*$v;3;Ht+#d#170zmaPsYhbA!5})E;zJp6( z7)F)3=VlXFG+<)T?`?A>wE zQk@~J@h0DwC9nn~Kpw2I!1Cy~Zscx(g(34z93DMe4Zd-i=S=dCD8M%zPlpK&v{gG;4dPkUQEx+&TEh9$Rt_X4fAQ>|kg#w}3M3KX9@xdK-XAHtsc5TUb#SWN0MB!!qZcQj;iD?7V zyJZ2Z$6<@e>;dq}@!g*QD))Yp3klV*;%nT76K{=iC%$N1jsNsXZfD_V3-Dha;M&$S zH7OhF6pH%#h6Z)LLWP}oa|39vve5@4hK*m~s_@7?oTWgGAH0X#SezVP{Pw-vd2@fd zhg*Ga;juyrXQu>CZ7{a!klaVE$%B6hyfFarRc=#*te$?LZ|i+yp@5J5_OXqB_F}KH z-skoO1EB~$^&qz%ANm5f9Z!Fq+X(0o6fmH$9zXnbuI%h-Fs(2Nky!{$2;SRq?Uy-j zpyq%~MVnIi2;UN9eADDXU#fhE_`e%{6tUF%i^=;W>MGxU;YXuSnS_4iL2gY!13vg! zZrcViz)CSdQnVWT9|Qzv6P*;a!Uuzi*L;)PitqRYCp$dr`1d)F5;q{lpoBkrdHzh- zq4RD;Gp5c%*KeI?Iu7c1?&R&vE0cGcd^!g%m6zDgax)#XSusx8@=4E?E8k5|3i;_2hY z`d#`6EE{u=&}CzxKoW(8myLhvUzxEt|FB^0@kh8d#scrd5z9ara zo}8?+649G)+4!9sg%N*Y1xMWf1V^I49)5z;$Nx&;!b&cW=VIlp@LMZE^FmhVs z0KLg>D>-wq<4hS-vemST$g6&AnB1Q0w|S#>2fZ;iXbD9ijW;>}2*)3j=`^h|S=ber zB2j{_^?@mJ(XI^)xX&`4ym~iW0_%#{;wd_J6=d7QGCeG@%Az!?u(FbQ3YC@g#A(Tx zI~0z{9McwG(CeUZ!*E+~IO>grlf(#w>~6m$6q9)!7I+t?`8~rz`p(wHpd1(DoDF5c zbx$k`;DYdAK=!BD4`Q=`?m6z}6cu7+R2k$eOOa26WoDsfRw%t`3N;z~o65tSJx&uO zwpT!y)=F1%l35yy)7&Mn6YC2N0iNeXF)NoAv?iK8(MVvS5YxI4^rFt2UHIkETrlE` z;kmRyr8HuyA^UMzaz;T!AR=$MoSLE8g}fT`wX5IvzMV3O#)!~!N46-rJDP3`xZ$vI zSVoriL61O!#=jNq!T)tNcRs%DiQ)_J+#t7cPfH*ifsf@R0by$EBela(uBesQ`70{@ z!P;=tS6&{gG0P6Z{nb#eva-IS1YiF@MS;SI3v1peTE_+5{>gIl;1PW3GsS!GBX<;S zTQzvZj32tSNM19xqs{Gf`01R7?l*Kg;6iQC6M9P|O#IXy~`zw!Oz z$M6d$i`L<5ZY%l-{^Rq-TlOZG4BjK^3KF#fl*lx-DY;cg&dA3ouYH)nrvsTk+NPcw zHR@Q0cqx+r$mUpUc(c!hQ6iuAj_?+ImR1p2@JHxX?=Ypd1;B)ZX?FA0d==PN{F<|PQ`{1ST!R*y zOP0Flo*Y`V1|}V~GD85g2)QO5tUqk5K>cvgVRMhgWU!qG6)YiVlw>m?Um(x6EMgfa zegH@rh;7I{2_C{EGz(YX5-Sc>BQj7>Q!a;J- zW{=K7RLcK)RDqFd?@5UOv#^V^|6h>QN*A9T_P6ml} zqG7%w2^wHlH&$(~re-PK^roBKWPx|Z=2m)BJzydqa!i0(2FaC3HB1E}E_Vo&1=9ja z^I9#dr#hozK{H)lpET4LFh3*HV8^Ou=4#S(#FE8qZ(dVU;y>aD25hb{xBv}uteGut z!-;2$FEj3xwSapO3q)mOZf6vf6C5Cc3p>Dhi8w;CDNBq*J%r&G(OA(S?H){az#Fkf z$vpvKqN*H3Em|!Ro9iMH93sOPK3BY^P+y5JJyCof?s~4cvOtd`&lOj}KX*P?T(+C` zL|;*vr6=xc*);s0?91uriZAO)83yx0%=jKJzQ>FIW?q!ex4ut3iQFnbr{DGzZ#92jtM*5HOzRY)d{hp3R*5w*G@3%3tAoy*9SxG39?hi;jK7I~5ucpTC2;0DasUa>( z4O@(Wq)sf|lTab$EDcg;MpTkyXA&i65;NpK?3%i}ZfZNVTxTPkDBo?AlRu0B0 zV)47mr)71r`q~N-vj+Qx#L9UCPInm6PaOdpXm^vVlKkQFDTmwXiiE4d8x2My;gsP6 z+Zv6K-z3eo)navf-4RgI@iEZaUW?V?1>H@(%TN@&O`DA_1%a~};2V+oz{~a4iZ?SE z-hiP!5GhYKSPlLv#h@aEC9kc$fiRC=3a$7~*Cg#HcFMF-w-+osP`5rNvs)sNjx17J zk|ZCr57p@oUHPFyzykHvGDWQdo)B5s)O2z635D~#^WcM8T`jADB?S0KUaM#jK9Cyn zT6rV=tdu7|#Gyu$3SQOMs+tKzW%I=sgAO|WGks3P#REgO)ePl zcXRn+JYe#YPTZvi1UOM9XHvQ z4G}-HTp?#stE{b>{i(VmqA5MWpNSvg6F@>y!kQi=O~K@Efu@<)@}7R6g7uz$cuzm@ z>yZCH>WBDB>j!=%i>};rdluOEi|5LHPy{ve-uVkX%lkluDL6Sc{?6dn8R*WRo_8gQ z@08xY$dz0Nn^`r?j@N`7PFUaygLflx9!ZhpephCiP?3u!_=#fhbj^WxNs|t0z#A5W zPcBO^Uo^EpMvF+C(v89RyNiJk2~FVmbr;<96t}e_9f*F1 zfx6UXu2soZ7X~47s{@iZ1fn6EW7bsx9w~M_#hD7^a}Penon26PNR6L*n)^`UrF-Uj zpW##m1r>8wexGv{HmKwc%mZFcf24EKEm^q;Z-1UE^9YD~ZYDzwnaHEoMClYbh_*l! zynCP9AB{M|v!0K`XMWALu)c}4Nd8Q3?{nGPJNZ1f{@g6>;b)%bYByo1l(pT@?!o7u z<|^WQp@656JnlRL9=DOl-nH;hlZTQ#qhJd>{<#?*t{w1jkjJBt>e2HM zd4wwA5g-o_c{s`AbUi$tC68l}FWYmJJf0*!zf(`1ry%Q==kw%I0qpI$kUSIwqgwL# zBl-Dz@~9v`FWiGqpXSb`cpE6r28yqN;%cCH8Yqqiil2evW}tW(C{6~7kAdQ1pm-Q4 z3I^J|fi`WR&B7aK(hzlRfQ3~`Bv(z6LbGwm#+M|~Cke$Ui9Q6`QtMMC2kKAQ3!B3g9G#NG3%>p&jp|hvJhY YBI24P5t(WNiQw^e^W2LsaH9qP7id=AKL7v# delta 149067 zcmcG%2b>$_nLnPfJ?<3Su-IOgwJ~n8t=^~}^)9Wtgu$pwqu#ZmEN~DYQ7|xuAqlwv zDUe1@;#69a%iX0xE|<&Qr6-rpY zY~0dWU5Zo^h1%)#CgOR-dO^LjrWQ#RBKgGW^f{eXxlAE(+P?V!aePH&ReC(V@#!a5 zs#mNW>*$FWSLzALYL8?*eJqWnSEdg;(uW-NXnL%JtUrD0>6=bpfBIk=O|OQhI1Pw1 ztM_eWUnPFMdbbyz3v!;*use>VcThdC7z%0C~vzjxN9( z*6!y4`1*P0BV*)izeUdjgykh8+`H~#9wPa5yFdz^bvuE^ElZ~HyLAT_CjrxX2M;*5 ziXL1txZ@jk63Pt+rWc_i>=13qy7U^bHy$%RGhcjL=d{zK8->JgmFtOP8-+Z==rf0Z znJ=|DiT(G+Ba2hjjb~j-G|w^&MVK5<|Ibnp&KW^ij`R50CgP)KyBEjEk#pV&M&B2f z5<|nw5q5alNbv{WdzAR&Id4ELR1$wbM@j72q*smO8<2OrgUvoqIOJ(V{Ntuw7ccZ- zmN5RbNjA;%c+Yk_E2mCoPS4tJ_xHX4jqm569vy2ZW@BxSnN{6z_NmRg_<#(C!rpV; zkUbL(8Mugu1`EISL%nPi)cpf_VE}6vYH7<>KBz1Z;vNVw2ZU=Bhp?V7hgUId9?G<;dF$G-{~&~0 zH%^S>cL9I(=v*dC-0c`6cC6UCBYhCRlaj&=DD8=hDI2D2a8@BNLIr z1S1Oi0tjS?7}pg})H3-*b)rP;@$KDPA-0K@4y%i5ExAXEY}vhbA|I($GOY>9JO|;- z*ix`(OHWQvwxnGi48#R{6nrY;$(;-p=6 zSND!Xx?%)2=OC5Uh7l^Ey-)(N#d_gI#HS8z1YO^F|l4B92}3AaMAdiynYX`cdF+cqSF&4?^U`AAHsR7Fy0Q9^ zgGZo1r!VzlHIIJ{w84lChXRlljfDNey~M=_E+Rg8=qw07-(MbRo#Vtc2QWf^*bZ9d z5+AKqnq8Jwe{lGTRb!nGtS9o~Eb(W-<)GZ(k5ujfUgbuA%T+FM=aJ)-%^bPRfvkia zHje*&L2`gZZmDcS-ofqn5Frr$2JH^ApEe%*CSn@L&!YNg%`OesJ=Jl8r(@zuksJWu zEt1%G%>dr9;C@>J{o<#dK39AT)E-Zdi)#q6PDT}@hoR%)E_8@b%9fi|gYqB>vV8!X zknOQwIs^OS1;f7QB)4CHjmTFaV9l=+6JiH(LjGamO$CMBv`Fj^zmrP?hQ=qAF2MeT z@&@qqAO|*7)XWG4a$baUf4G)ms?YM&r)ZMB&bxV>U1j3Gpo+Xf>KunUz?n&;jEL!; z_9@_Kv-(EhXuG-^=%q0HS_=6%KD8hQC<>qMF~Fj5)x}Pr@TrS!_B&?!y=}q$p5f{D zX~QKXRU-fR(mNpl-plEeZ-!#94e{a2ZohP)5BC!3SVu*C=Mok1;N=ELdxO0Xmat44 zrW0b~3aW@@Zp|ihruIRSy=ptjDKtLMVSBWVeZD8k9?5!i1xzY`sDFkn1Xy@Sumb&B|sB@2WOT2oL5)Q8fbCe-+An6FWt z&b)!^P0tX&vEB_Gw{5qB7u*URv#U8iU*u_{C4@E|aiiS@5rTVrv?jm%78ezadbT=_ z0V<>8FtGc9k?cbWnDWQ<>rE6Uu?q545wC!q7IT_O9oW>9}) z6zT!coA2lL3!qm`s-WL*P;X0F{q>?}7s8e>uSU ztZ=XmQSn_4fovGy{5 z5WH#t63>X1X~QH2;yeBwAe7(v$6+M98SQt?1)yRObV0cThlk1uKTHW=_Ejo35nZ$_ zFji8p{{I%RL0Q5uKKINI)21h!v5uB_uUkv}OK@^&o%{$od2fiSA{Z(QLqe3pIwBo* zETs$VN)w^F(!G=}&OM{ z#yB5bmgfS|Dj-Am9iT6j>+aIUULgM0p9v(EPyycd0`-bU=H=^&P zW>MabHW1?XiEidvB=qQ&-0nd~-lPF0J9ZLRCwCHGND5#+;u{>?vonvxIjOb41kew?l14z& zuPjnrH-C&qOj7`H8E^@RYaijlVa5#KX8$`Sh;jVw1<8Zb^*t|gdj|vkGyd<;`wPTm zZYyyzyP9|<`y?>1VfErn_2EBrNdNhFS|k%M=(!|-iBj=Xz{IZ7JrG#b9MpV)Wv~q~UOr50 zF3TX~4&EG`aADdoNszd)d<5KuxkXR7bYFz^xr>*BakRU9H%GJGBhYmhV}+Ut;L;rJ zE=+$cWBz*OWzdwKc&VZ%-mH2+n0XFRK4A{FdHU9x3W4Dl_s(co-|w;6gSCMkB|xDI zbxVA+P35ZC04CM6Pyzoukb4AN>x5GRWf-IAw9AaiN1)QRJ-2njp!Rz+9 z)~@M#*lOy>f^xwx7;9y^hIFvy`T%sj>v|(+2zwq-nA?Y`0_+I?!~)Taj0_!MVfzh~ z?2q3-E!^41K@YD~3O7*0xp&_%4r)2dxjoty-}pk0DBbsrE3($@&~H@e2DC5ELoKZC z`*?Cr|Hsj>&MHH(!d??H^EX(qp2G*Q>Aaa*ynXh&F93ITaBh!g^Zyt&>At&J=i4`` zK&td5nlT`^{U&ODV)|hvkc%uExs5j;BX)dfJ#p5})SGY~vOO+AnYHC2JDBwcD35h? z&BO$337ClFnvtpM1o5|+*>#hNkV#dmE2^}o)MEGNXg$+Z3iC zC4P3FmU#1iY95;B_P~2&rVYzVzyDqn@vZk#qGfI~;|lJuf@#C*BJ@6L2AH|Ez{gL% z|0rSo*?Qud_a6ljbGsQW;@wOfVvCsg!Tax6GuAoiDAp3>rkhu9As&BVGx44WB0Dtr)Iwp?hkJTTWzo%9I z_*u$?e*ZxOgxWuGVDg#JU>hR;U>d|RaHGE-U%Re9k&G6BfDr-RcUJ`QhYo|K(3fZt z49ChcG~{6s@t23F+&0ife@VY@*$^WiI?hk7SIUDGcV^nKIypo<^Ff%R{HVe=*vV*PXIT#0*n7qFUBnHK zTtfWdqtt8b>mIqBs6Ju>>(6o&z-Li|Z3yg9J)wHk2@)T?IXKv0+A!P_&p#^34?aGc zPbuRe44=$nopY_^{KUto*~o8x zY^UbEl(@!m5`N5Gi8Hg2Y6k1+?julj3qEd#&Za(Yx$2Rb&OSo@SkT1FCH>vfb2_xD zgGyNFNkl#=d)oVn^;Doc`Nr0%cMu)J=7<4qrdUP5L zYbDIiF}=_H3Bsfs4GU@mZ5ZquPrzcLbToRc`}(VUn~VA{!qCyrY`@3&{c!$2>|JAa9=~msag>5K~4l>nK^Aw|qZnFN%vcTx7c@;GY%XHtF`I}GC zJtgALP~>OFC0q;Kuzvpjv9r6$+rn#tvqOD85%Gk1#^RWm)matE<@#9b{ymhn&W75= z2@uFZ(Gl?>O8hHf&ph$%C$>ZO+rI$LhB8J-pF9l7mciVcxhX%n8v?-HPwoP8>SZJM z=93}_{R8CYDMsRnr?kW)PuU??F1Cx#2I8fEI-k%#eGZ>G8M_*`w&v<(5yv$3eg=g- zd~udx;D4sUOn+dX^Q$6Pi~ls`>vK_3t_gJYQQ-863;!(eoy z)27d;zy`TEn8eL@iV5}FoaM_@4yBVFar!e~1Ixbdv)hP^KewK^{f0C&@uslD{{rJki=#FJm%4+aWriM}vKy!K^k7u|*p^G|p)X<;s+ z)6X0uE?&2uxbc}|JNSsx6(jNLGrMM&(7>;U0mH6k!w`Fxs*VO3r)lF~q&9%e=6>!j z74fpb=*FMj&*}IT(0uN4Q2F$8Vtc<~XqQHtK>oaiFg|}SD0dyP`-L$O>g3XT>;=Cu z;)~By3sDAzO1$+vwfZeA&p|_`?3feB@{ycF}3vyrD8Io|#%waaTz z*FE8{rj|TF$vumQ{QQE&RFG|TQO5)dFKbzlv*ZuRQAfiqG zEaXg`{${y=5S#wxQey4D7{EWcvKgI6Sy`nokG}U`8q}=9x!<4`;~^XSlNFRk1Jmb& zZHWK+h6~JM;09Bb4$BH#I5dYQX6h(Bi;c<3G|hT9D}3^s`-kG_tkj+CZKCY{-ZQ+e zpI@|eD66}NXN?hoZykY(iH6rR;i2+mRZL(0*1n;f49&CH(%Aqmx)P0jo7xRJz(!BA zot188o~HYIzeGJthcYWsa?@8=Q)8dGu?&?-a_K;5nf&ZKTZtchhuWArfMvewef-4= z@zEErJBQN+A$~~*zWDY_`-u0wbPSU8Kg<&~@y1Ky>4W%9RC9j+phh`sk4#8JBH1C< zq9@ihh`3ySMn@HvD{f?m72>h)3JwfZ=O5&-gZ~Lq;~@h3w>>ilBM|%l?NU(jM>)-g zMg+Q4pJajpO@_*E+yMf8Z)RH}bxtLRNxo%wtiIVyKE2_42dSM`vhPm->Ss8pnHkxk zhWT~QV?&wkhCdI(DNS?6S>OErIPv=TFM{kuU+={oj5z!s0;PpG}e7ypD>!_ZhZa!>t)O1F$o=YAK|va<-mp{KNZuHRa3KJRnfO09j#08&b@oD2;((~=;nw7@#|hJ~FM=R30B3#* z9wUDA>!ZZ?eyxPCHqZq|?EcNx7!=Sg>g69bhU_2ZOe~#|*)!)R4RH8h=J%ISqW#i4i})wvxmOLur(Zb(#GZN8Onl~5YJ1=f96Ef{JA-YAW*$*69mKbK3~C9<`7KykH_~7jG4d7kq}fh#4~@q z3?%s1KPJJ+|C4inXojcDnI?mP?w_xmq3jF!bng^fNs=yTCaA&h)w_RylL1Z z#xo*6>zsw=$2q7E+G9VCnFH4z{eRT(w*L-bpI^k@w=7t@5&P;lb9^{>av+1X=T$wl zot3St;l$sWSCQS{`*Zfi!vMpkTuw}<=AGw|E^+r;TZr4=+R3lp&%d`9KpKk$p$U@lzb+j45~4QtozH>uSlYh1~lhLT$OcpYz0Mf4_x6LX+$I`|)+i*t&Z! z^uppz_>cVIxd`>vlWxMeKe=`jG6ARAp4%e7HHJ_xdOxvj82*kR9|lhvBubYFa}E@! z8tj>6!9jU6dF4vvDCu5_P<81b8u9}xk?!1N>&R4hb=_cr{o=A;@&=zFZV}mB1xG4<)b|D)bndml9Y{GD_f3>~|dl zE~ZHIS#ynv7VjL076*BCN}A6?{slyelu;@HKgAI#RQy+*jciZAqEf0Nn7C|$stNil z#V>N68Om^X5bz#G@ialIC?IA&OG95`>HT+r0g8b2De@<9NSAXQ|Mqgx>})(XaqmsY z`Io>?PrBHI)kTq7Hwg{GprdVPP4Zw0q|sgB4h!7LXU{>Xqg{TsY@oQStnhD9U9;6Q zP|%a!bCGkSFe{omNNI}u_VN$Qg^iAqgW?%1)mCp>NcN#Z^Bk5z5}Od}h>k&`)bQ{m z|L}0zvQfWwGcrL|HY3!wgFy)76Ppp(cR;?l8KK@}9a%QA>MaPhUWZF@Xjn*7r3Xuj zkI(9To;jTL~u-k}RKs437x#Y7h#EPh$RQ$kLjk8I(uL0ab{PRM=#d_E$ebbdavi?f`qvLMbW zqraQsywKwu!b)bWTZ_}zSn=?KV+foEM1E}yp_W12x?B`_^B|WzN3MLOFN>jUkD;My zfi6Z^Po{fM@|qtVjLBbL0OJyjT(=d0GoDEC)~?Tde8D0i7$tnPM|mjbuB)*g`w;z@ zYsBLD*)pH?=m=iP{o9ahrkSam4c%OPBG-LEF*}9Rcdh4+-IXifSgza9|LT{(>q~<(J(I>p#FVZ* zuq5|YT5|I<2iB8}Im|elVvY|V(1c51M2f!bOX-rWY(M& zGb_fTb8f6yXe3%kll4NZmMIq4G-mHju#vztVy-}h@| zGxC$bj}d99I|KLr9yMIpeI$MKjBht`5S9y&H%uV+T{(^)=ct13ZPQ>I?t(pT3wZfJ z7WZ_M({p=}9psrk$bQ(~c zF;aaY@&r^$%)R+e%CZ1aQl+=Yoq+Kt8`8p$w05+36oA@d}NeQrma`~1YcqFyb?5QbRzp2LU%hL8#~`RY;R0`l?0$Zqm10kYop z6-vM3`1A8N7Hab+Rj^6|Jd}XNlmM9oBmBGovBNoL-&rIdnj3g}2R@=lkT|>)nE6`m zPdK1w&$1@ZI*P2#z-edfuP;`(UtjzU=i#9tp*wDOf24M*Jxj0 zg7;k8U0EHnl|@J4&c)gv$|*VPrfNcf?z@(5#n?0qd<@2dl!VAvd$lMFckix}uzv}y9i!NE3UNrrry zN>m(FqZP|S)hC^z9Jvi-|0Ox<0GUdU?Xy; z3K5b2sYEXZg>i3>Rv1fejKaWKu2!K3K_9oN(0$-6j{@h5ah996ucl9hWO@f@S))ex zL+|IP(QV=0hz0)wCEs!Ua|;qP&4kL=h*>BH&FvH3B7tG01r}$}IdI?$uPM){~b%6i;lGAU$|3El-h0|cP z|9plaO!waPA1Tm8WaM`)MUR7h(YI))8Es#zei;h@)r2oYVLbu);AO~r$q!tPQYW9T zK5ubG_QGfRWp?}u zB*OAY?|<9ejp~(C{y5* zC$$K5R3&q7zLh;o!+n+vmHlDzuUcdqQ{KNxy`=x-;jUE|Kn{xuoj+f-hBtIRsYA?8 zIA#mZqG8@g&HM>+xq%~fK06y|gAv%aG4iAy*$A*F^~m|;<$81@29LLISWWc%!q^YjewtzWQPCagL@z1 zA;+u+>8vPL=#_ocuS{j}e=`ieF>eOD2QGC7yZ_8X5;**k1<3((PhN@o$PZePEs($7 zasJ{|r1?D$2~g45He?(~+c@g+G2LTp2g3+{3YMSIgH7^mJCdcR z{NVQ{u(E5BtVA#4p$4q{%-+opn;ggymuQBSV+&@b66fh0RPi1M;)fXy?Rs+31XDMU zI}jmx*ojaj#ib+p*u(oViksifkRoq$A_~NI<{2kKogRMXZ71?HLS{VOEEgI|;40R4 zPdjUKkwU5-NhMB0$yl1IrHcjWX_!;N12Y2g_5?y_tNw7?SszQ}awju|Qk^>O5>`bV zPBU}8xSM($O5vw^$eptt!h1{`xz!7A&TQo6UgVprByy$n%-KHV8;I_DXak0D5TAx$ zI%g+ZiCDdsI9W+l>pA#%>)L#x7Kuk{k<<8W%j-|$?}VneSEHR(vp2|{0mQs15*Le- z>WD-oy8LvNYDG2!$S%QbWBTz~LL1|mYAF|)IyuwD9nd3wJ^5S!`N$5r;-utQ2|giO ztuwUnPPfIGn}Wy({(8al4|W$%zJs~nZA!|0D-I*qlh^oG?3?ez_jk_+ z#Y@z4uy1Ad@wry3cUDo|u%6#fzW7u0f{PB~_L&ao*v)jnggx>>|B7+if#LUyTwj}c z=qo*{Gc``XJ+Y-gPwhSYpFQiLDT4Jl$W5=V*m9l+x}$@}j8yR;d1+up41&~yffXkq zeg6kE;fjb&hjBJM1x@iZ)t+&I@4=rl;f>z~@EkPgnm&)^KXuhR*3qHvrP+=Ed>MY_ zplV0Z7kFSH`JL#{e0n#)#6uvPt;Z-rJob5~^67+D4# z!9NTg;UA&?_fhJ9Jx6>L{<;JI82tZsR{IflOuqE~wdcb@53`2*6eEe3p(8%S#Xk!- z21Ge)uC(|VYwNF+@Go;8?yQR?$nXCY-L!M4$&!z~yn-q_zVY&kZPVMwy1ucM`mvy# z_QHXlqS;mom^g~&v)EoMGWNR_u*{si{dX%4f$1Ir7)vnSLp?4QVY=UyIC>oIpY4c? zg)8%JfEXd|yIxsw0dV-}D=Vl4I;I}P`G$j^*L$$of*ukMRIjf1C{X;#t1BJ`nO?Ot znTC6S7a`L(u6dvbKG2itV#2}dYORup-0z*Z5X^ zwWq&%8lUlv6?cL0{osui)Q;{)fg;z57LbcR(gVB*WyQ^mPQKLB z$pV~+R^%d_=)xgckxs4T=T@T=Xtz8ie+0jBPqAlKRt#CkL5kO)hhQ+YO-sHcLATmj zj`(+qXZWNo{21mIR4GVprP{lBJzY(`*?k0tabH=3egGUSvKD<9<}^24(4V;Z=9&iD zVBN2%k~_{vsp;0AY(}Xi^jkSS^(%$#v=lmO>EMM7I+_GE&osM|n!d!EX1ZI9j*%zM z>ry>uefK4kV7aIcu5Vxf(7^+Qb2jyXxoRX6pQsfl$WN?Ccfo20rsYgr943DS!8EJ>(1tkiY+2^lc#V;3iZ{lABOF$o~P3Soq{W*oNG(8NCbSKX8ZF%OB&= z7%lqfV?73F65ZM4Z=HwkB;#Aq^M}yx_x0zOi*{$tk=cV-d$WtoB?zxHPTCNty`>}} zM$cmhA268jEf*jXgt2SOdt6`~?Xl+0=#0YZzK?6uHuUqrwRJmsoIET=){{2)4P5pz4g>tFV!%lZoQ9)0 zy@lbFrqYcV2gcC}2y^tco_F@YHtdRbpbbV&kE7e-aKd-tL@kp~R3}&;xamG})w1FI z>o`iCkvNEfp4sTE%m~Dcalr5W#!*^2l(nZIyg&WwlDqU!tnc9V}rWPLGxVu{>yq6;zusiG^x{dtd z9u#)vlfT-7QfGTS%xN{+=pMH8$kQacMmITuQYUB7*Lp_BytrSx0)oKIQ4|Q*s6MkS zI8f>h`fl=zyU^X_!9D0vaDo9mJWep!hJ4Q+l-eObaEDijFD?ssY5_%QFM2+i+KW;f zUk7P3ZZZ74;a@Br5A7Da$#ZvuFppe_9yRbl8Y)aCEBAm4Cnm`9<;YI*OBbSJ=vasS z_a@S0K&Th-Z!R7Fj8l_0>;r?Z??W$yUb*5N?b0ku?{n#2>_c7PL9gyZk8@ml%eKY2 z^i$=YPcf7rlm74`6h1^ruHTOyc3lL0L(y{~^@Ej3hdV4)5WH|dPv;PsZrP7!pz~Av z(GZ6X@gmvy?z23UfQ`owpjM#t)&Z1SCW>)5m( z-n%jB^@C7?{N^CK7xYixpaaur{j+*yv;uKlKg^5J*J#`18<6s}agvuFL!DG`-aw*al=^NjPpg4%7cgy@ z2u)2?v6du%d$~B|ExH*1ywgDA-7=GD)I&MeF_I4+LyhEP64bYNX2;0Oq-YQ_EJI=z z$NXxQH>-9?61$RN2YWauH-#WR40C%H0hSVEZ~j|tH|1-3WQM8H9?3FJ zwx5vw%h;r)M zbvCn%eXvpAGIs9m(F$Y9jZqjRrv7E@F5rAI;|s~hd$Ee?9kMw8GWIAX-*Nn!1&Ns| zOEfR>kO3z8m$4TX$%OkaJiP-GLzc1MIK#;e3+5!c`z$)R_X(_j8GDD*Z@>S*GWL5p z4MzJ1ZL|obMr_>2!rSkT&VNv>ai$#$K^LaJv_qhOSuu@v;DB zuUH=h!nb1mwPm48m4*n`lDvlvT{eMUQC#rmf4#ToED zr+a3@kb?k&=+Mv3y<&Y2P-BkmkALH~k+SnidVh=S{WJDEEKrs#GYkDlH z_SwQ-6H1+(Q#7I5VfdEi$ZjTzZ6!;d?t9t?UEQ%ojnithP9I@(N|Wg7)MiGZ z2r6Cr2BX;Clnj!kCs^UP{^`}*mIuoUh?M_p?heAaI7a6p7I%znAs6{As25}#v7kEg z_m=LP!v_KGVsg<_KkqpOLjuN$0W10#HKDrNj#A%Bd4eMi9{oWU|2(JFX#Ksg?rgez zphq_)*bx`ZPDgVI^3uQ zLihmfd1{3`$Aikq)gJWnc`HMk3}{oNm0HP_6WID8GX zSjmI4;RztbEGmZ=lDHSH^eLXvDVg@7j-?3nH81LibjVf6=#b3{XiPkXkbSogg)cFX z5BShW$k+VckevW2EGA@sSJaD{3<;>df&uh6khms*O37~q(Dkk+C1yCbbl%dYU-SMv zz(WC;;MuMA4~t~t4fvG9?4)2H6MehY?ww(PSTF-CKFZTOFaW#NuBH;F88MJ&htahp z9`35*p^;qhZ&Ta+Egm||evP@esXaZz*^~3;thY^V@Bi_T1lC}i+BIjDu0NSQLc1Te zWi1U;$j^>s?nu95-AP4MIQ?b(99|W%cB{Ewn&IO+^X7v#F^z_&^BEHplF#|z(3~5u zLiduct56ga2KyuT^{yTRo_;ivCkZc4?hFrE+N;TPuSO@<&2Ag&Y$IQkpxczNRfpMo zm0k~WVb)6yTb_Bx)u;-P-+eVIAYZu}U9Wj_MpSq*hB-lM#SLXxUDN^M6z9!HOo5602;)6N;Z_66h3 zGI%XLqC?rF&#+`YITEiifnEoAoe8waIzu%%13JE7(0K-QWMQE5cR70=CF(s&`#$d~ zTKWuCmVPK-oG~?Oz9WS;fVXuiG{fTU#u?sjSTJuzhBt-`?w~gSz*o;x zNRW)AQ4cH#Kb|LD|AX!z-<^h-`Ij_GeLCPCz%tAhnOMoYTklkl725mz&1C3qy^7>a zPwt)Bj<{GxY*trVPJKt3dJli|k9%y=XsDs=nd`FXRs`yD`XV!kB_GYf@^ttf z+lg2tH*u}w`h$Rwd#v@pE(FOiAiT3qkL{F=&L0EF$H-6QVf6RFsWt1#Pr`51Yhez| zp?=jpT#h9#TEDPy<`lW7fEvN6jucQO`Cy@2p1lm6b4`ZP0ktfhzdXAKJ(sRv7!s`V zY+bb;OLxyhr>%l@rDqWM+Z1o(_*)zn**0;sf3GoJH=1y%>s_ zb-PBf$6ug5<>BcaJmabo`XT6j_Q3mX(0kvsD@GnIqtx5|tIFsx@SVM!25i0t*`iGS zg?5iH-FtV|X2lWq0bJByAU3)MWA{DRG@Qtj>no@QUV0eFO?7lT`LPnrMSh@yQs1hT zFBdLqugH#JKuA{=-A%7^fZwS(C)4s!AMFP$VfKs^UTMI=BUSWC(9+{IR0rYX1P2ey zz^$pHB4}_<9Tsw2S?`|XlHjx&t;?@6x}-^TXHYkNb@eWOvcH@m`#XxPs?jCeS~jw$ z8t6Mg_cRpRXhw^X#Yaz!R5-b&iBjK<`A!qX!PV{tpu;1HjLC)6B*W}j=(`W~ES~9| zi6rEATIdnlfZ%t9>qC@8#_@+1Bp9lS{P{ogPy#-DQ|M=ak87sTkC0EayJ7M1k<9SN zjW>SJLjnwL>$Rv8NTjbtsV@;c%YmN8h}X|MAMU^QTl73o(LZzUk2bXx7i^-#G2MCB z)MmeoM_;3L4i^6HThOgg(yY~zkw0{a{`ayG{qc3^5#WMLbhM$dxL}(C>ASwWW$q8x zcPGsMj{_8#**J|JT}z+hO=8pNMIr9-oo{oV8ZA?lktt1*lIiUBIQkMxq<}&ON(Ay! zVE^3R{mEg`1j%Qo(F%0Pr8ruiEDjiXg27*RBl>3mdfScYugNQK?i&0dKs(%f`3-*a z*$r+LFOGmcWz(9d1kcu_9l8zXo8f!R={zh zcQ;_;;_q%o&mq7158bV1bOTy@qh-nJy^qo3x1jK`PV&K9U`a4}3wj~AcbEfxz}w(` zPK?uLGWHk5Z*YEsZOLajYMH0Iz<%+bffvR$fCfoh@U$1rCXtF zghPA2ek-a($V+bT8q9UTz;J_6@P>Oyr>7-`2ovr*RnmC}i1MFqMSJo+y5@ZoWszE4Y(G2;#zyxKbv zoGo?9o8HxpsE;le81kp@LcI_HxBy05EsHz0w8`mrqwfdtPIh3b!_+~kZwEflK|3H` z0PwGzHlxLBV8lxkpu|g_{T}ol0Uyy`1-tr0Dw5AfXqmc{Yt9D*KUy{ff;+pTD;gE8 z)X_3!vBby}qUwWpqE~`U|9U4HfO6QzBWO(N&xovtYh&pRdMB!|z-Wk2bjoZgS##=ZKjMj1#*-V!oG@`DS zciw}Vz_jRVw2Z;Drtayk3%>uJ?%wtN%SG`%0u@p7rkwtUi-n$f0kg!3?wX2$=P~kr z0@YD*oD2^$qgiFNot@Ecl;b6X5C7s1MNm<7w1Dita_Jufh8k z0)zfY!yJm^ozUO{VSCCPgLGE+Y-1*m+=q4m{_FR_*0|r?hpNFw3LN;{nz+fiKU&I3 z#wh8|yGHqO67|CLK7Flclss>Q2ijny;(k;N&@aCqrT{zlcc%dFTrOz5V&`IDiyh_= z_%;HwIPViX_FnWbV9&i5J>Ytj0zHm@bV1muQB;-@E7SR~je;;aGwPq|RhPTS= z$tQk^*3aDaKJ-f~Nyo2OQ&Xs401R`7N|=;=5Z;>M4^jW)JMipGj|JM1`)y9ZNkVr^N{ zMNc)Xbt&xyr!XmYI~4ksq8t_}O3HdUAqYz9WreU*X$0$vQdyx;6bj`?(k^xD-TGKQ zXRc>4x89R=Y01nF(1X)yPuv)hH0>>?POTQUR4qZlkHscc;;PSWt3)$uPf}7XB}K(h zHEnM@)k1p#PqcM`h{R=T2}|Kz*c^`*lr?o*EviN9t!CROap$A?us;^__#HZja?0MW zdvrx-*6+3&ZB||0FS1E7S4@*=>eSO%sIC#o^v--FR8m@sSg2$!mL{7T3~MWz(U>OJ zE-8xwnV?;CHJskMS=~~5+IW0Y5|wz`E@fJtt6_SXxGEAvB)(c+T~UN>UQat9FV+Mi zbGzJ5v~z)wq+H9(0;;L1qaJL#Rjq2Zl&{&Nj_`CC4~fF@rp&Hv#M|0PSmG_V6RM~^ zQHYP2E>|op0jdSVw5}bPa)U^sxw;2BDi~zZ zjJt{9sd_`J6zZh9s5CN}PfDY01At2ahgE-5U{a>5R)@Dyiz~hHhNrESNvg_1+EHp1 zfR-Z=2z!H$M6P8D)bn9+Eu0tVr-Wi>RV{4jy)LCsnNb;3(&`j8-ER3ycvu&RO5&AN zL+B{j!HA;%Y}r>A)N=-vCfqbdQr2o*q-z=~T3<14@M#JmZMvCo;c~4J3&)Hynb2dx z5_Qa1)VP{5DW)#Tl6bUfC^v;kb;=UNBnjhGJCzcun-vq@bR{&nOdrRx!sK*Y6>~K4 zX4IwENt>}eR+DJ3n6}ciTAD%3*Tj^Wa8WlYHd<1qf+p`QG%YcsO_?+$(`JE9W(;64 zyQW>lTp=yqEa-(;SY{ThV}60I(QF8evSPv@scR)MrKFWID>cEXLPTIz)ufV1aY$=u z+Nb@P!GsA^nzRf~K5e=HKoD!luw*ILR(b-MuxZx1(uu0Np3B7?vUn>v8L46>Su$CS z>ryc(CbM{x(N?1=2iQ*tD1l)pR`+LCR1J^ zshCt6gDlu+HTBX`XiBLsq!dY=z%0dbIEX1QRZqB+7OaVWj)5J$|LGSoGN zd_JG>dL8vtJA^r>r-JtS6sV-#6vj2px;T=<4ML|zRw$aI<^t|=Vwsr4D4kTR9D-n5 zufi%#dkrg1wQY&il&l0&$t6sMO5GrFdF44lI;V>1Elq736NmjxLlv8pIg?W=vojzq zq^fq0JTK9Sj8jv=GB`%E)R=aZ^qPoCAIbzLMXIT?)Fe`-Z1p6j(Ml}(vN~zYHsiif z+bLJ3lrB*-RdKbwRZX&4GpK!vxK!N~=WDn{r^B2Y8@Oso>@>zFb!8teYj}fsVK$+u zx)kMjC}k>x;FJ}4zUFb~0v!J--cbW!JR=1T>KMj{uhr(zaQrqn2jb3vQT+7`63 zCFP{A8Z<_{IiECIPX&|VDNQqJbI8gvt;yF`3Nsl^33qv$*^Cv-2Sr+eR<7|xL>Z8r zKU~m@(@vE%9TWshp>|TNZ9Bydfz%#vB?bA2S>V@Cwf?fp*%7VXk&V6?8bN(xfXc3~5DLXaHsOlhSG+4jdfu)tnfu5l7vieiHb}qL&L7L3hRw(#qLa-RE>tp;c_bL z5>>lu4_UI}oLT3qg`<-}oh1@98uK<`Mp<%1svfx|t1YWFlNxDIS=u#oTNzA_huz-281K2@I#*@gA0 z#wUq1M26|64A+a>L9Y}GCLn`hm|alIh3g4XtS0uj^^kUpPNlG=lNkzFyqOG&!js-$ zE21it?LxC$Ur9M|N7OCW6jX_XFC3E@8`OrjNwYVTvQ2sg z=_al$M{5m@6VzFp4%Bj9g(qCGM718du05GZm=nP%Z!l$%*Ibw{VUnq3nk1%{YCSQT zHe70i6Gf{|l`Pa7wL)AvWh_>0vOoX}+BKF^MC%v18kpbih`OYyqzcmrq6%ACZ%XN1 zkj*Tid|jZ#>l!TCR%#^4mPa;?#j%nQOC>d7O;(aJCu>f;9cbyD4xwLT6S^ZsTUMC$ z>hn5_ykONh!(M;W42|PzK_FZyDVqhKS}%}Qe9b}`FT3q|TQyPCPG)QYhej``sHI7X zwq$g=n>o8>QsmZ~b0)1`V|05=Zi^@D*1OC({mhL_z9MLA6zY1rlxl_?9=vGRhmBMA zyvvBYlCg$AUdf3a0d2rFS=1Zsg|(TnqNeF=(Ol3$ z?IW^J1@h{AB@zp(!9QYch(dXB97?g0$?hwLbS=HgRxlT!YQUVBLsn|0S{ZZNY;E~e zp(w7@m@Ng9H!gLkjP0V(kLl7zx4on>n?jLraxyFvtHlL(I4vnzat?>mRkDgBRjb}I zEiz}U9&b(WO_y?hOyR`x3Wr@OP~g&_#9VI*OX5hwFOBAH8GXuT@td>~Oc*lA)46b} zjtQ$;TeuQ-VHKk}qfhJIK>?Pn)P-2R9armec4O8R6Gp|E)|5G8uIc?naiM0CVWp|;pPNZl@}d?cDxDdPGZrf zMrz3Dos?8HK5GHj#gdcOCX{^5FqDf4VY+3lX@w#a#SUJ{>CN$0E`cQ_p-3bU!lxlt zDDpmWvKp`$^f9|fA2#?ho{-(%sv4qL(ipZ>j8b1hDQIb=CbhNVR|qp2Pb_1`>m^UV zVh9&PZk0Bd%G+v6Ux6Z$5@kG-c8D{!x<)C3>kY5gY}C6=7H``a5hrDuJZ6qXj1edk zo6{bdL6NcwH4VGG2JwfIlMLjPkEcqprqm>s<*Ry^!Bkd*xIGoIrD*Z^GUmJ=)A}5G zx7OlrrZKnGAIDo&ZEDi5aqE-Kcvh%)rv0g6D3mc94Aq!MSZswPx~#{VX=sGWlv0&( zYkZ=JCq13Yn5#aYSY{B2wRlM4oT{hIqG(E>Hx!GLX>-nEkGZ8qsWe*<2(><6wdszT z@I)*UNvE~?j4wMS*EQU3aon9X)f82O!>)1GBT|*iI1f_7moYR4)!N5Qw z(+l#_$y!+yv8OPft!UG?1dh50H??fmmLcp6`g~4_*Q~dw1j%5qaPFybd zCKZ~5%u_OFJ?UZ^YNB*`GGCnz8}X`N;ZWH85bilP?FPn~Y&v znYmGK;FVytFquqeQxKU-N?qO^ln19LldY@^3v|motv#NM=~6aRI@~h4-BzKy)(R#R zwx+mNQYzh|cB)~iSgIb0RE8CFQcnykgDbjHNm(?B3u-E@yz8p=l0H>S7CmA`pq0|v zg5tKdDUZSM(r5A--6{APi@8detszufr+qC&TrCXwb1J_?ZkrOR8}VFID-*QLZArV~ zO&dcJeL7|FS?z6|#VDx=auK05?Vj|z-1$;56>vk7g4hy)L=_5()DopyWt|iz?Uq>5 zRuP26%4l69Xz6s~hNT>oCS|&Mp>!3aXo$!quuZ z1?^HGo|I}!A%87zsz@U>dDv6I>t2bF8xj0s6CY^SdU7GSbwK{<DSe=QM>h?VhV&^e_jLy!oA+p6VRuUe*>^aw)^fkj%0XH+41*q}BylEJ1< zBTy)$MZGSiOqq1GmN@Ay7%`Y|N#`9+SvH$0$YbDYcq5V1%4Ee#RnyX2YT3FEliKW4 z;;JAl3ks)IiITts zDP&V}PcmMW3nEjlL|xv9RiycNMjp1MqSBaHrYJ{BxJf*vR|%ccP$KAPsmx7{q8d)5 z1eLZ4=29fFc-D~A;o|8+Qqjyn1PV`voZ3VwnAfCacBsM~=4y4SVv`ASxv`7BxA~&VuicBG$HTgvHoTK1yt99j=BM?h8Rnl5Z?ZR~BL^&pp zMx;)SC6dd?{cW41npX#`9(_%pOiYJ0`mn;`Gq_t0bFP*s$@L+Lt66IXEulsuuk^Ns zO>0#pZuqp0nnPZa8lwt((`HhZC+n43p;{=5RSAK=CDq{#S$Iln517JPRlplHifdVy zCRFg0^wqey60oZM=2%+kSL7oC7)Xb!4Yx;94NaTnx{%0;H-v4oLaLP36E2lVDJclj zimJqI((3$vsUTK%HliZ8N){GiQXWR$IMsk2F3RammV}s!=44 zm=ivyvtG3;GS!I5Ep3&RO?^D+gd)iZQ6!-*Oqn88WzlX|O$!ATjZ7$YN#*V8lps-^ zvMEv}i!~O=W=o+EUM*=QqHMKNNLk7?jbCpM3yl!bD&?9#rjmO~>;*wyRnI4IakdpV2t;y6)$a}%GEz%8B*LZIu+^xwdT?C|zMtZr_C~5HQ8c7V z*t}(1uL>=g>?CS2&$I->$fDDF{5r{(3VH^qPV!0Oz0C4h2HG37z}avSV*B=cd9a?c3K8CL?Ev7R3!qNK;TeI8cxNu z(wP=}UFuX>qLI~7ji6enR@YQsFjZ68+A3wDYPBrmG3)EOXeOsK>64ftmxQEb%w)<{ zfjKVBm2|aYSd>!Wfsg>kA#I@}>{SS-d@y||*C<1>x+xCUEA+sOiZC3=#J$3{+~yEU zntG=^J1rLaG?r`$b4QfAj7wK9sx)yb{d)4{x~&q*Se@By##9pP>?y4|Yji2Xids%B z4O&FPWGp5MD%I6w#4C@BN)eyi5iQlTWvi?a^<*kKrNR#WpYjFe%~~#33K`TkFttoW zm~hmRf)MTyX7keurQ2)LG)hXFu;fxzgz=ilN2wv63>na&xJPm!d&)+^wycvkpp9v78HLhp>RxD>BM;l8_u-{C{cjtt831oZg5xZ&NjJx7Q{O8p`Ql0Nx>laiPF~ z3)NB+?o=l2DwnrhlM6EqlfCQ^wkp%)+d7+2r}ugU&2mAe_NimZR!-*1*>$*k zDj;=2&DaW7O4*XPTC7giYo5uBr{;1^7LqByxKRm68`5c&C~D7%lM;2cA#a7`ex(8C z7_=%SROdn}H#F*Pzucb>`rKi$Cg3wu!#s1+V6%CA=_wqhab&r6(`E_!g}SORAea)C zj0I!VByx*A?MN&kv&AD8t0$gpDV0g1s(|T*b!o(v^%UCSmM2!3wm0&*d=;i+{V+9~ zlIO&2ToUw{ipuiF~p)56hgH56#5l$KCc0^=8bC=gYrtaXh!Ar}}8n5AG*`&s`l{ZP zzgUswBDl@00&eo+a7~7*gh`7&>S~vrGMF>UxfME)cTCupB!ViDB3Do-D*~UX(85hM zhtL@cY1MhDOrr=}Br1VgC=UlMVy{4~R+byNB97N{VOuZ@!%VGd5@wXOFm)m*)wnLmOL>dNZODatX%TxJ6 zQzuP?WolKzS5FEXCP}0su20z-b!`#yrLUgVx(wB7G*NKZG6kzEug4Ni6O5-Nn69e9 zn^-U`hiQkROjHin>(imhw5%A*h?JF*JYiSmTPAlkYHUaxVL?=BlOx5VmXX z(phjR(Z9J+aCp=b&M3i3oDEvtv6UelS}$-c{e3{pdLmsFUn(@F(WVSrCb+3NHW-VJ zZZqXZlfq;Vg7sG|m>c^I*o_NMPV3+uqCqW+iwK9e0^BRV@M{b-$ zX`cPcCoMGw!hkBvV;}K4$MUIHTFBvT6p!mT$KHljyZdpE-*+Yl*ZVBP2*o99+ zMdg-jy8$M~Q(e;Uyg^`-TLl`=+vYC2U3^o`FY;1ug0()GZJDmB-aPx37#Mi2B1Wzx z$@5i#gp<87yH@9G4ALpO4&^Z8R_kGOZY0dB4-SmKGvh#^X5R6Ea9jgx6=+kp*QRW} zx_?T&dwpLui-pLTpQjDY%xkqEudnt31wyA|@{&bzGjfu&1cf6}cnHHw@S~`P=6npp zbjJ-Yw9d7bTK(v9w0ccAp`dhh$0jh*nS{`;Qc111f~iL3LF4M9sz=e7qM6*kCzF&N z4rO$aLbr9B(WTKX(k)9GSvNdGX;!?We0(4&g6zF|j9vNU!^|E%>=_}jM(wKe=}gEK ztFy_rqr|YCqkV#p!!YKuK^P?;Iy@3j{=q#ayL-PC+v9rXaIE!F(tU3ScHEHz-)i(O zZ?q*`qG!eSuiVj}PnbJhEWB%N8p84>nZD+26baeSWyf21Tp1k^)e>|q^o2~kUH_|nZt5UU(Lu3fvQnE^F5wRp!a@?pWRY>vNU2&^{3E-J!5)K~HUN5@)X6(p$A; zFB*pB%CxxXU%E0QuZmGM{n>pziUWI16evN_Dnq~K+Fr-WxaE|I(9t^H>#fmbqd3E;~y_2G-V^1%N zJGOWXoAn_dx~24?OSJ`3#Od;8rVProkG<=}9?7J(jkjTcz0S?5r^A_l-7NclpZrj1 zi{8cRskg<2nCHC;*Ej2aJW!j4=Jb@LE|SZx#uE=tlCQ{ui>4@@Pt}dY1}bPCYKTNo zu15$c6bG?O*df}~>AQ{n3T~zw!nN<8P>v*9jfZ7Ub4@0XY?D;ivyNsD-}Dp}N^SNK zmp)r(r`@ba?)BARVl9f%+&d;zQfpQ8#kA?iK0kz$4*`9JdfC;Kh5^-eW(#1WOiPyD zbaTz}kXU-3SWB=o6pe!wN`te{j_}B+{B}D!y?`FM$%c%Bb8|qAK;+u~ zm4)+?taw|G-)9!}!+FUDyVEqc@}NW39xIS#L^}KewHJY@*KLx<(&{YtcH0Lgq$`6b zAFTTQSvxP5+wDDMJ!tgmBA+XG&LM_67_3?ni5cXZNmqH=?a#HU9@T3T5dyh8!n=$T*xIXB2*}WcNt)xlFJ^!<|MO;SIk=O?s%<5?i775Fa_yjU#T_ zgru8VLbkJ^C_U>C=GrjrlnO1M3AspkZ!*<}Ax#^yiz$A8W^?|+_pJftyeYeYI>O_2 z;(AyP)*5*|sq2O=oC6Ufrao$vK0JmMk zNS5g#B#L|4nMCJf;;=1C@I3aG>f9r+j1;;aE5@TWwD}#H3ku-klge^-J_VQ7ik$@r~aD`&qKPTj!X{s+(arx3Qp0^@+Vw<)98{QeRZ&Auz&7diG&h zW6gp6N7tfcKwc5bgAgm388wx>Ho{Dp$cXxm;kz*0TjVn7ZbKdjFV{}$vK~G*aw4xL zLP|t1DyhrcqA%-f7)&ibd*U7fpnHSqOYgS#f$^_*T|!rxex}#zN~j}d8ySmpJy%wO z4W-q`bt+<)j&18M-}9@Zu7LpQuw+N-7UY z)U*A#&Vl2&2Pj!S8YuY3neXJb%6H2HwU?Z9WaXxHM|Adi1uYjSL|86Q6D&ui^7|Pv zHUA>gNj&T8p~g9KGKa1N=@Q3Z$x<_GmUAg z0o^Td@QL@I!xE!(yIzv1anHURy+lt}TEagJb&mD0BRjipci7w7-1!#quCr3fav$zlZitQ= zyyVdA=%@Xdu$F=Vbd_uWM9tj8qL2u0NHTG77S=4J^i9$r%@Sx_D$@=lqB>DeSa5iG@@+N5@Nm=Q8s^)b zyzOqPBQi{Ve+2dOfr@i_sEj1ZA=ILA- zHQn6wL9zB%qf%AJJXEn<&W()o&iF><_S(a~p-Q83pBfY$>prNi24yo}P~{qNM#?UB zj??s6cA9uxZ+c*$!pVmS-5X+(9kTLxbZ~5EK9$RITG-2lW;F^orOcL_6RdO#r z4p~h5>gMx}O$zR9F34UP!jUdpq{DL)851bmV8YXjrzU;UL9*eVnV+7bIcTWc$QDHq zx`CjYe>x4FboPYGtI|w88BoWxV#++>3rQYj)32AXO)|nsLBiDY8Rtv}L}AWHKR4Jz z7l%n)zFqvxNH1n8L-rhLmo585xk+H5B68ggu+-VmPCJ)Z(z8x+Jp zJ?ohE%yXqsJQHs2+~c9oL|s3uENL})SF@}#jhz8$uuvJYr(lxth#1hni`X;X|lI|CL0#A?pi{kG=F10r{Y^gxsw>OV=;ka;1Qq&=&Ew6 z?r45-j^~n@`7Dou0e1mgF5`9w1v6L&_cGTddqF*TcAjY9Vc(B{5{pQPg_F^j>IIZ?1uIZbOIcaEAh9FwGHngQ9qC zY@J)GgVqb!NuLoAen9<6*9jSPJW%l_8rgi-(**60>0`H>%@mTnm<7|KK`<#@pp(U! zi+p(b=s*{F)$XZXW=1DH=4xID8%ArYsGW_hI=ylZCvs53c!iy4AgaSgI@egJbzm%l zGBT0P%{3z5Ti3{klz^z67m-%kU(tN+Ttwx@fgcagsm;^s#ilbUy390Fv8JFJTBb!r zE)~*b85u)wfE5qQSA7?7{!54bWaC~%g?Flighc4c=G>aoHp+7TK;!t^WJ%tbM4I<+S z6JmB^JN^ur{Zp{FcFvX5wcMl6EmYX;y;`W3Ep*W?_M&{(MJz%+A>ZAyk(}hz40|~U z6Zk|rIU3RzpcV2#?8en+mr^@Z5J4H+Bw`yJ`0c!Tq>Y03B;P_Z_VM+d<)^5;K$quY z+{cPXf!PfxZsZKbQj!Jv=Z%uL8*wd_-Ecy?2&;z>#8`W~RX~jZx#(eeT&xp)xxxPy z^>XK>oj98Xo!5m@*rj_<97%n}-W6GgBi;;B$;nCr8cHr+X{=&}#iRQol8=wBrJF+I_v_1ps zEGu(+x9w9QxF+HUhW3%-QqOHCrMxa;+&;BHgLOZbT*2QN zN3vpk`xxW(F$Q57?nGnISc4ABINr{5hXpDe>0(upavC4@^DW1vM_xF|yeS|ST#c7M z!aK4H8&r6f0=a8aCX|`wf~Dplvho=^#%`wbRIKymvFU_U-VU3zTH0<$Z#7 ze}MFCx2r(YXbu-;H$I1wCF!$fU9H1d&96GV2;wSiWKPO*r^4ext__FPzjp#T$3q2;SqBO#Y?L7HPMW@HVpa7rC>38e3w<(tuE%9IN2uhk@G*^6GyxQK zNmHE1BhIgy*R{_~5VkzupP<1SO%(YV>>z&e6ygZI9^Pa%GR5w84ax0%x`vllhRwrv zGfPQ>ZV_nUJpmOrq;~Hh;`D?DgPpp4K8VqaJW3J&DpV~AZq8AP(^pX%u=H89?L91Q zFV+dj3q~RgT;^5{$fLp$~pv1r3i{N6!cy- zMJF*gHEcr+mm5_!vXiDVK8PV-jrAr%tzm=)RGwjJmeH(wMOnzr)JB>Th47{A+h5Aj zPIF+|t?=g9lF9LDO??)c-o1Hkpf|_$JwimYahPh7TiuXp$A)bS_2lv&YGND?~QbE}(HbVcjbdCA8%v1*@{;t|@(rhj{ zR;@M*kAyk(;a<3sZnEQ`0*dtVN>6%)wS?0a-RM6?I;O?@a8tA00hEzYs(Lhwf@t8% zxwY~~)|8AbN?rtg2C*YVN=J;m6tj{c-qQ>;e3MR_;=QpVL*hdQA%Ko(k_26ph_28@ z@8tR-UkI{mA$zV&F|VPJGwhgq@!W0mw!(fIT}4Wb&>`EEiFkytN{84hzFF)}WQa$TPOjxq`3H+pGU|oH2f{w z*X0On#%gg#;&#D$?KfU546i-pqbv=)7`IEN`C9mh#ii2Mq~2dpSBLU7sG0Y6eFaU} zsZi?ATHwQ_xF)B|;fsIg=Rf_iH!M`3`9Aq;wp#5S**<(Hsq%bT_8Cen3~VB3C?b+V zNI+MFuBO57bX!vg$75_4CU$NV#}z-B?cpP+i651cp3WfGrq<9jr{W&kM_A_fvVEB) z=fwpV^IVTNFn%>+pX9pN+o5!}~T`wEH-~kCy-OZ}1&|uQmJYqe0p`+w|?r2pZ|qVKlmrUS!&-t+LvDH?*=h`#lm2}Fn$pbZr}VxU_byA zpZ`vC2wyeF_ja)Iw;DZPw&8dB z`}g*w-+c6Z@jv~-r$6#Xf6GDh#eev}e)@ATO8%w)?b9zopUJ*@=)VD9`u*yU6JOFP zKmYs{m+~{$qy5@9zxU?8-qSzejeq&y{i=(6`?Nps>o1J`EC2iF*Z%&-Yxyqj8(iz3 z`G-H_m+vJ1O&=>fxeflT9_>m3p zTEQ=Wl7M^j7vUcMzsKkYQ1mzF-u$)y;;Xj%&Zz(-_V<7J(*#em|J$E_3@9N#{k0YX zlFWbhw?F*}_<-?ipZg#tZUBAw_5b`X+v!*T<*zRHyN>=_tw6u;?|u3k-~R(Y z;{R9Q|9gJV7yriJ|G^*o+5hO@`}D`Y@x`C|1(I_18FgKPzU?*G@7Dsm46nN#quY<`0L&` z{`l`N|4sM@goOXr2WF)GQTE62KiRdnZ;js-_LV>N?a%)i{~L$z`@fiPQ$`+L^<9(^ zdQHNRT)2c^s@u-6_N>zD&qk<@Rekji`+d*6nC>AQpLptLP|>jblwxmlTYzsOxjkA) zheYMbMYmWu9NX3Kj?DQq>>mAD=l8oKu`9{$r0fs3ldw~Sm+^K=V{`u*|3k|RES`vlY<@PglswdNJCtzLO4s{ojZIE_Mu$( z;chwImBVL8tpED3dn{WEF3}u(;CEnp zTvO)R`CA@>lse~=kR?Lmsvn;(>3N1NcoX*Up(ku2q{BA9QY5GQ(6eMvGg9F1O~`2& z6YV+ckeUW9)zK%w?tKCDN1#JN6?QPk+b(|#I6Jb#4BrWodT2ec3@Zm-OgU%BV!!7= zE~1bQdSRCoc9Iux&J19sV!*n;UNb>mEkn>(QQkTCcH4|8xao@7-pX+|Z4rA~y_W;3 zQ*BGrRWk&dQWiC@_vdR_i@W}%J>P`DQG(N&Pb_zE#jgy1`%wLpr$@(IXK=y7%(3ji-;vN zP2uMqutzSN2<(y61=7O%mgO$VrG(B2OOw<(O3h-4AaH^O(k?hq4xZc#iKTdeOp@N@ z_!dl03z7sq`oK}x%bN-p@aj|E0HgwCswWo$#-&l3selJEC>5{XX>w57H1NWu#HLpY z7tA2~lj3#(_dc`KM6Odnk7>}vKA>0lu#I9kQEHmoF4J#Tk@7f;+KjH6e#5tYCXgT5 z2*e`JAx28z(UJW#zzQU+!fp6F7!(`oH4gX-G)6q9tL`6c&tN=XJ5O-S z&Qg*jDBp8jbb=QcfI(;u8kZ}y!b55Khb|G76;U%zx!HPDZxOjecd_GNZrtVQynAWC zWA@wXA*M-jgbXZ_qyN-36lBgPWCvHxDE+-BcLkz8!&P&*eBy5x5L)Nbt9*>8$oVC} zKsd3y1=(@qki>k>pz>k3tC<6r#T<72DDvx`6l7DPcC&Dx3g(9Ko^#{5x1dtX0Tn9d zOd^n|7AM49pW_aSwtET$wubzi58U46oO}Xkfwb&Ee0DD>)Lor&%em`Co=XhOL5&D? zK6MzyX*Ix}ne40;s6ZHELjIx{gL<-$@gH2%@YKCAS!0s9P$N1eY=!60$TTQ5h6@~14=CJItZsc@nv z!2yqE|B7>~=cfBLy$MX`tyd2^iw~kii-R<{Am3D|l!EdtkJSC>0L7xvkzDZCPV;D= z5@q|qMeNN+J=GX{%5W&u&jggd2I&(da(T%QJN>O$^$Qi~pfSNPU2TwIpJMQh@E^c{S846VvtxPQ84$CX!GPGQb6LnGFyVH%jh_-s$ErNyZJ&r5LSQ${g_(S|>ZA z1^4uymt68!jmGQ6bt%(^1a5q6pSi@KZ~yT$FQnG$`$P=a+*6aC4CzI4qd0zmG%uwu z;_k_&G>AcBL+_Wgt!#xV5*$NU@HcwTnBJT~8$N!E_Oc*2CAX2rg0LB&0#BsBe5qo-TB@vHo#cm zAVD@a(n~IQbQPDA{CGb=NILI^;weL?uI#!6^P44QkV%d_p2I0bz3A+~;LnuXcK2s` zK)B$VF3toe**Xy&xYR9fLc`Z5$k#EmI@Kpv?ZQ^MLyCV|3Z6p`V2ch2l{;_zx~4^&B72oM~VfBR2~x4LUAnJC8_h=w<*XgFM&vaFc9pyOaJ7UPPO|M(URDST#WAiiDkQ14p?qydnkjAyG)oeu~1z=H=VOlP<6ihY;`s$igOApppd6?GWa(g7vu=vopXzq!!?GAO<)iA!}6&_acz9I|u5z z2Slk^X=>E9rBrL5Vo-WkT}~E<_;Gujj$Af<6a`u?zi&4SKvs=IFW~1i4i0$mMn^^+ zNUQq0V%5u6d#+$%(tQys(Y&NQ(Q5}RKhFa^2iTVzy?I;B$xa@Jy@%gm&7blkgSK-q zJ&a{~%A`WUuxJSm@BQ5whTvr0Dw-r6V0GCz;EoEvyue)wewPIk4=bG=JObCg&L}r< zVhmb(2WNb)>e~r~7f06WV&^71#FN39*+kP8;h$&+E%m}joz4}2aw zWvYOZiH@&*z(Pbi_u$s0{r+7{y#exphe=^}!N)Hl5@45-l1uEkj}+(3d?y77Yh*Ld zEA??dD`_v`e5i31fO5Dvwamp*uC_AH3=uhCq-f$9kU6%!M^;8q`y0fSS=vCv+iD-B zwpWUqYB_s;|6!$l-?1sbAqA(6$=$Im3rrl&Jo^(+iJa_YANklmUi9h0TYN^Mr|6^f z{OW8F;#eoJ|9t*i!Q9ZlQlqElzJ*Q33VQ;Zc|9Q=HIlLXt$N*}W2V<1OvB!HT zoP2zycz3N!g5m2>yGj8p1=ulsKt`bU4y2Mo5k7-L_Fz^9K|!(mHjksSVYjgdy+8$I zEs#ariu?Tovh(G4uk8m0LHl5_WPtIj0nEp4+6GGlus)zTeZ5QRSvn@RX`kM&y47MC zy%~~_3IvoY!UM$J)JmEd^O%zXM;{=BHg^1VXTa~~>){dKyO!7Uot&claaElXMEhsJ z`At4dbUPSk#Q|oJ0wgle@vwbh7rHhhU8tcw71G~MP@fG+7B*5?59f!ilDxYmy9GMX zln4-{;0@nj>;TH&)peKV)c!-vrkRq=B=ibm4cH!pgz-_TUt7Nzr%t^Ioak)cWyX7Y|$q>ug*9$tgH_@ueBKOP-C_dVbr0MeZv-`JQQMRb2r_nH=_+;#3h0U;k@PaGUQdY7K}03P zbS}(q0q7&@4Ukyu45Z0v{y-H0O%%cquwqnD6@=D{ng^M0sPH|G_Ve9St=OKHF`^Uy)1vnBxf#N(K?~=)j z{&VNEACHB}_wbJo@zAO0d9%J!og2+nceeJ{mGCj7_Fr`k6A84ybT)KtK`z7OI-tQi zb}oPskiyOT=n6C2{WNk92795jU0~43B`a*a6ua{J(H(I&KZB9>0k8^CH}-8RnHvpM zkJAIWJ|>0<<*WS+$Ih8YHwR6KjkCvfI4 zrOeXY0_l>pON(<4NHQzZoWQGX$99fs$h&uv`QQS<4fIp;KAA2)>CW}YmWEHZ;S;X) z0}zw}39=yxN_iZqGTrgSouQ@pDR-(@>Da>%6NYQ{9WlEXO}v5>roPuB$wNTg%@>z3 z$d42Zn7j5H@>1aeU(?V`@t#=IeG>rvQ}QHDrqy@&_)wBCHgSir_zI{KNg=?A%RSpi zcUC2j4>_S7`-U$JZJ|$(aD%i__~a9qWkJxhgQ%CwwYaJ@f?Kqqls1yHQ2wI@Njfq28@tYVFVYn4{hxPe<5VX34QQ0}Z zNZxdg;E5baHsID>izO(D+m?EODVqQJjduAae3}Hev)`QZeEW*DJ0Zm($86Aacy|I| zf0jb|jt^$}ow%7NZ92v1i-WmcPi-)m(}wM=FDkLsiiy_21OFyY<)BDkAd9m1cYd<- zs2yNflU?!X=Q6*WC}~fXXLt8Pw(sG+zZC@Jxz5?)8u8G{=ERMbWOecvpyEh9a?F_u zthayyhoB$mp?|@|xeS6^*1+~PaR+9vqa%a05bIEnNnIJx3m#zID2PpI|8#`CnSNR6 zirLD`LAnCnD7_zEM%|+dIDrAnGWVd0J7m>-%F~jT+Z;G&FbD`s?e%Co$+&8q-?($W zG>~e+^Z|C@q5izM9Olr!)7}PJ32~gjmzYiQ) zKdNv!fSJp^>3}!UM@EJYGlo*yq^4d*3BOCwo1|yU{YJzJ*cIN>p)df)7<9;jT>_X! zr;|Aioh*Va{1I`+(hbwg6eF0EdoOxHtlnf}Rd~Tl(cMjYfkiAD(uQ_{@|jwy>w;D^ zoPz`ge;~*B3wBJDd(E~yaB*0coM<7VV22jY2(+EY$&$?Oq{LByv*B1$#yv!LZL96XX_?3C=%lPdFt78xfP)l^8L$Lr1u&c* zK9NG9+a(p6KH|`EZHQH>kRZ}{Oc?y?0@2odQwC61ro7*-({-RDTW=_u&Iat7!Esv; zhyo2~MIm(i#4^A}qDvRDjh^j&r-#kf#q7r1NgaR;^SS9F9c#eFupR`!E}0gnxYh_o zro@v3=SmFNu{#i|J6uUXlbhzcme_ksw*;i>3(YhK+4yKOobdeHmDi}kC}-8Z=&AAW z`ZU8+IEf-z5GV8;5@X>`4v#B`T{-v4i{|;_y7sBYhLVAycWKEMTnc_bz;w*InW-dp z={k6;6=Bn~M3F7$-nfYGn49EcmfN1v{3 zp@@_*5pSsqk|e<8ePwhIhHLc4$tErA_v)n1%xxpl0+;;&vjB#WXPvY8_;jTQx{Q6N zZM$9v!xq*kgJuP_cy6+DN2F<>69?o~SP5yiTte)J5AWdcd{CZyT2vbxRih75X`Xl= zVH)UYka43hjKpPGfQiP#lsK>$fcqB8;GjxEih_B(D&yWj}g zh~QB|d^#teLt zG}!VA!!60>78slk;Ks_keh~W>RLRFHo?*fmwxk!4Go)MhcOg&kcMOu-ILIHg80+xu z9A*gM@SA-dSYYS-z~G{kv53%LwMXFFbidG>TQye5uE0iPfbu&6-^7&h!9hvC>ZnPb z&K-N8)itM;>uS%$gpW@{z=K`63O*#|l2<)~m@SufLG+gI6q4BUtY70!bS>2J?5ns# znrS6MYsPo1Qsgv-s{XjnTT7zPv$#C7f`yif5%l`tRNe7abh-dmL%=trz>|#tn7APW zn`VbR`*4Kmlr%|@)gw=x@Wmabr_P|EwSTzb@A3-qQ!uV%=w<3O@gITVTrPUhjG0@; zhWboiaoQvqaBEO<>tGGKI~*iu2-@@>I5VixhMv49d#sOPw(3BPd?m=TvQ(<#w7d7+ z6JWDs*Q0Oop(kp{zOvy#Oi!lfkD>V9s@GeL#bOn@m~jzCKiCHEP-WrW<=^w8@8Y5@-YP4x!_m?e zV|B}`E2ilf*>H)ne^-Yc_CfXKfhw6{L4BKR$`TW|W|T~NUOH8Ilr+a0EywZseAa^G z?4dd&j3aZdm5jhtU~JF;zv_4>@7!JCwl{WAATf93(q1DNU9R7q`#S4s-iKV3EM8V@ z0A2-JkBUdU_b^yd!SQhc@*Oe4^#z8euz_qq@@ni})DcbdR4%IePJ|HuWPr=<$)49U zi2IQoxLJB^Ot$Ttc*UwD%P6I`fEK7tcarFY!e~FP;l2{Vup+oqEiI?Y;CzDhh*M z6}XH}k#o;#OynNV?!K6DjypDP+#gOp4$^gd^t=aq2c5CPKT%NX@5g&DyYAWDwH8lP zT0tfPpB8|w$E%S(95@VE((E8S19Uj>&e^d0&JKKc-dk$tpx3BZ-db`){UOMY1!W$0 z0D0jv5h`kv4#=Ph-lg%lT)~SGT+7@*Uh8-UwnTYY`=>2r^g3#D`MM(2)4rEB=?-HF z&eW5{0DNI)!qX{eWM-e*cUQ$4^O~G5>;x2PvQ&hlv>XjNAm2yjV4&(8t4ALxW@qT_ z!zm)V^&t&Tk%AidE_f$3SeF+KNvhsmnZCwvT>}fyU73tS6Rud*)-rp0wKD?Mz5dLS zYYT?cLX7k=pmunvp0%^c%AA?yHxM2340+$%=TH%nL_Ke0Gy((67$~S3^X}O z)C@HGw7jlh_Tm7pBNl|VM{zBJpu=Jl#!Nv8o)?c6zM7y1GvEy#4`U(jo&&VI8D5%W z`UDLBlmXs6H-VTZ(P0E0jv_<>nK`&J4)b5`lh!i0)pJuu`G}KOZ<$Z=-5K|6_jI<$ zK$~&18~VjoLs3z*<0^I%21tyhcyvxQ^8%G?F6o$0sqvYsirFgd^{eG>@U|AzF7nZsst zFJo!M(o$7sN~ffZQe=?fyLxKaMPzi8v2&xvCAC#4e-y|Ic3XmTA`PVK+;9F4Aka|Y zKCs8*g7oxBI=b}KX2&=1=!C5I0+iOUV5`H7@ z8A8ymQ@pCHO1v-Hj*|16lI+b@Lxk5FaUBNIh(6H$m6HV|V)u_6a#%wL5UxAGT9|$e zkd@d!`m#h2YWs1})z)#c?5t$6Sy8I@tTQE$u{%o<`p8P~MGc zI)T*qL-KmyDq1cQ<)#rZgG09`bx#1U(2<{O9;zYOKpsdrq^J)`o`s@b?72u{tTh<( z-5d`K*e5_Kpp!JG=cf!gQtwM>Jzq=m<)feFj zb@$vH_rCW|Vn)DjN20YuRi(bp6;;o&L@CU3UoFfVa4fJoSI)+0ykO+uvq7d1+)sl7RNs-B0-b23I#GUw;SE!fRtR6@o8J4lF5c2I&lD=B??(xa&dZIY{8 ziMEL=$=67<1&~1}%TwH>*-TI(?0>`ch`l+L*-!ci;5zvpJxhSQ7E6#=CY8Ug%?sZA z0zu>%xrBg(LGn(5u{f?o2m2n**aL2ddU852Z(P^kPu`?^52C-N!M$->EdkAs>J%dP z#PWemXOrKztwf#()Mu<4n$A)cW^b%#2uLs-V7=|<*HF^*9Q6&nR|k;Fl?Ft%p6W*G z)%39~nvD!-{0|)E@*sg|9^+&Y0T2kU*0vZm)9&~tEn{$R2N9)X-Pv=&zNQAF75mSl zUJ;d)YgQaSd&op1HJ0)28#eZ>Uu9O&$u_AIlIO3-x)+#dB3ZOJqdr8$pdGk9c;RIM zDTTZsk&G$2En!iF>5ugqk5Q1*M@VWRO|s)58C~D;anrRSbmTI6Fea>V@xK{!@~m@JUj=&Okgo95Z+;uHDq~Z$eNV_ zlKgb;J@=eG_x8QrZvT_+)qP&2+I#=@>$ms*?eAxk&V1b*jnvHYioV8-e1halGYG{2 zcGyR=p4|?_X0m`oowhRwLwl?3T&Dzakht{5oDy+I`9P)|HQMqCX)LzA3Fw-S<{&e? z921@SmUb;`!ucRGG(e(cffk#Np*95}?Kq%O13UX!DS(<=ICjR-lFvtQ->(97MBgK< z^)dhzH+{tkQ&TO?u^FUJXsxgg2cpwcvuKh|+2xM?ZBIKmnYJNd!ATH!b!c}1^5X3) zz73bTrYl>T$x$?>`);knY&OJF&WfB24iBXOG$V)%MEST#sS$F+95}!+%_tDacY>ub zIqSD06Q$k5^=eJf?sI0P0z9HXm%K(;yr0`rJ2jP?(DJ zu-(R4SZ;yD2n81-!7~}k=mG}C2o8F7N!D-eT7^2VI2EO&r9kfL6r4?*R6^*!hsg?? zL7ZUd@p4s|ZlZ-CnJf>w=?>p|(NY_-&1QToR`YNkYT-HFXuUN0pr+Vudu33Wu!n)h zOu@40I+b8pR;D#N4T4<&yW`1vN&=cmujFjWZWcx@02giw*WF-yugU3!P$C7D)cvkD ztzio@f}LP=5QmN=%936t}*Yn z!oEA+*${TJgG1f{)gz03A##qJg1DVB+;CJcSoE9S-M-B)EoTjvLd)UU85Ucv%<)}U z0u8#|0b9V%tRpVeenAqrQDk$2-5w8uKSwFk#=3qw*iHJFy#!$ZY1@TS4upU4GKZkN zgQ~*q&4oN`T24pWjt{`9C_(ylIKam{0h>*Q-G~_j%V=rLWj0PbaDvcRBui?h?XuU* zcW}~S4B%XG2+F%6sE!H1y@`qlSsZ&puNAMxE1iK`gwqK~iaKzf3!VXW-o+mHgVDv; zR_`|F2Lb`$=nRB8&ZLnpC<>hq61#H<1USbb$ICOp1T@8O2N4V)4jJC@pwAwmF^w?r zaN__k?fe`dI*oleK1rsuDMOF}wqDvb%#iK0_Q^AGkh1s)!agInM15+tKL;%=ayU&^ zX=KfmAR~>2EvXW?C6=D=e1jD41SI|9;d}$$=X_!N2P$^3Lxx)^4)J$oAXMkzg{@`+ z7sF)uH6@Usg4xLf%?}-ukx2-{F@~KHjcEp);m^eZ>=&$Zu!OlnXapjZE^eNO<}?uD zqz&;}I|xjmOzUi!M1!Fe zV&@HKIJHpkiQ)bX&-|}~4S;4R*ovNk+z($V<35{+N48KW&@g6Lnx?Ls>RqM{S}Ga2 z*mJPCDQR<6iEP7K!wL4Hx$JfWICvt0$==n6aZ@|Th;So*1s=#2uSb{#8HdFv1cYn? zS2$2hELNc{K%g#QIp>TDyC1YrVbdjyEquUh3iEJj0zw2NX0m3t zS1`Rf?B6Z$F0VigIMEz*$K!-dH|u&A#+l6@AU1B@0VNxr+e6@2)~bcWv^cO^HEj`+ zN3*`6dgPdoB&7-AimDe(4oThKZB^>n;kqtI)nd^-qjA4#;vk*XB3MD0O*zsJd?gp^HN!?+sIno|x&=9toTjxk^&gC?a zjT!C%xnobc3>UoP)L)STI|X_kUWX8~9c|-$m=0Z-Pq4L+97rAYOMhe;GmT_GJ&dn2 zU@x{|ZxkjluRVo}<%QNNr~!mab+VAQgpLMLx$+hP=t`6A_0~Q}l~8gh6VpJ?Y`DyT zfurH`T`W%WR2)jF2PYa-OKxvqqo2vc z7PJ$a9_&CYCmT{tNC)&Cv~*}VustpbWmqbu?^0>#R-)NO&G`z1q|kNTTZnygY(#m) zHXSk6gR%ps^(H$%6t&)$p>BjGwgUl!%|;iHaaDr|lx>;oSSPpx3GzlE9oU_bD9^$Vu(SsQdJ1=uJYt>pGp^+|L@j^PFj$#&pKE?#1= z{$02mOsHnTkqm6=L6k{W#eybFv2z!@k#H z=DaBiPwPR4n(Je=(gkd+&vv6ZV39x%<2(yiEHzi76~Hny&cM&$uZ6T~#~3&l@}%`# zqu|6Yu~*ngZPN&fb!&tP4zvAWJ1N#A9B5-eS!mI)M_ua}NH!J|YTw-g0|R2<e_5jeTwKc+em965XNE?9Co0XEjTCI!$ zP;HjjpwCQ*0?@p0P65G*5T>x7%pnu7&boa?>%N}T@gc60mY@R61hWo1&UlYM{{u>c z>R6)NfXR8s%idpn&ny1ct-p2t=SmOZ+MTzDNh6@oQ5)g(=|>)U&DCx07hK&Ye8b(_ zgipT*`oP=Vmsb!!gWKF+@_^gimsgZe?`9h4Baef?!xN{Uf^VtU!?#~{p~kRy8C<+} zzw?!MF2XKee!fx(mr+0GQal0fa=-YiKpx^%r!Qn1Ujet45#uy^#Y$_wF&vn<6U zw==MK%Txb}Z47U{{?SF_Zh9B@%=dQ;etBE=tmCkLTSJ6`he!s+MQ4dJ8+4FfFq zZ*DyQtSt8hSC+d>@4|AQ78<=xi&5c~Ujl!Fq3qI54>bM*%`lf6z4LYTo0flgFTZBkU%6wa zXW7fIee$8LwW~J%-F18tKMrt`Q1Hbk3F1PVT-+lc4$DVrsxbdME5RXNd&s^3;^jBbw%W8b`WsdJ`^Chqp z4|mi=PVX`ruZIpKJ*T|gXH|wa233#$(T_7GHZ+i`eO06R)XU%5 z_{A52#V-GLS$hw+*tHk0o}0z4ee$6eTYPony=N(q?N>Lx_SR|ZHC}f7@Hw@|q7Ob7 zYh297Uvy=P?|E)HzV^vfy4%SgXrl;!6=d^iQ~BBZx$Ssee)81u8~95vTs9ECLQdK% zUi#==m+N!C@`eL<I(yKs+R zS?;GUKC*br-E{up>Em^yclx~gqP>2sZVXNzts4{evFO+C82PeI!Q6T4WmlQF7{Tv- z=7jy1jqijh?&e=EZT8Im))P<994;Q z3icnqwlR6zbA837aLMA))7O7p;|b_&_q_hvboT;iBhN6~{XaKy{=oi!G24CVl|?So zEM5p>`02yn-uUv@J}4unZ#_01yI2&!)A0QpAlt8c{q6R9S)ZR-`jGsSx9+37beX}+ zx8JDmFMk3m{#u84Gc?O<#XC34+Z7IiIPd)WhV{ZnpX{DK{o%$Fr}ut+BXG-8IZrO4mApcKUz6p@Ez}^bL(S zLreRcZ)m*r^q1ezV4=COH;i__PH^utC;uB8UkN6^=P!3#%9FR2mz^8FyX#S1bSm*i znh&oi;&1Mj?=s24eF0Scm;8gq>!62Z)*Jg%O(cj zM^HcBL+j`M!dR`>zxq<-=_)l?P5#n1fgcMs@)zIS_(tfs*$uc03r4gB=z zdm3Nyz&t;BOS#*QlpF2nBcGKlU$mot{hkK);C#F=LGR||;`^t!>5o1CyuA5R_w8Ak z@1K54WATt2x8Ak7wA~BO-#3fAYp`|XV;Wc3ff zz44}#{l3P_A-}Ks(&su~-Y4C2viG`8_hjJFCm(eZ|M4n#+*@omS@8Jj7rvwM<_8;um~e-9W^Z&u#37*el|B-e-3)2Bbs z_;twkD?ZrhpC0*OV+qxo4Wbpii7FZfOP3jNr++XgP{;ORX%TElbqh~AIS9|nnQ;uWvCT#g!dUUV}r zH>JBl#Ql-azY^`fG}W~g-CLe|*AF#*`s@!s_QQ?$LtR#P^Z3kj`hA}1oPP9&8lBTy zexxye&M&z%2DrjM`6CxT*?khY$EUk`=Gy1K<)1XZ{rRLn`lpRILOox-`yT1?hVuB^ zAAkI=TXFg0(>wbQ-Z0|RtNF%>@x`Xve^1}7+?QXbe$myvb|{amV9wJj@|y@>E-&l=Tok8v0id#{}j#~f3!i}FE{rYmM`sbt=T^M z)vNh(f@EUX5agld*_U+ zXRdXzxBvL_`}`|@;`x344}aofoVv=}GmleO&s@v@$DX>q?0ZhuyY~67`{#`(p)X#& z`#GlnT|WuqUyF?>ER8U0j)J@tR8(K_!N+$;(IbhbhF4bRn=`kAZ2=AiehoO~2519i;e=f1&X>r1-0!wG==17aLy$Q{`px?>3#gM+8saiZ5qv`0nXb_V0go zvT;7P`S>q3^!u0m3qEzR70i69@r6+GPk(ljgcN`7Q;jb;J@u)^6ZcQ{FFw_H8yNhJ z|FXgHk3}zh<8vM7p4PU$`__N_ywi{W%Z3eaeAO>CTqwxrKEF5K&dx>e|HLmfwELIg zb-&zrBcv$)^2KTB>pxp5KKa7@_1E^%Z~qA6^vyZhr}h0W{FTO= z&VBzqzY25F@mDYAqIcZL|Kj>w1QzYx`1`~A|8HLP|I3$OSoCv$_{CoUGw9{-?skg% z_>cE_rhEGOf8Kcf^tXS#@nxq!{`q^KHZLgpB_2>7J*1u}J z6&lD@0+-I~wYePZmw(pm_m@`;evhhwd8kvN%s~iVs|hfAXvU-rd#O z2kyM+St4L=;8>oCNOt}2ac4>gC z)!Eal|K^^=Z5ZDLPVB9B1JExU!PQId7e-$G+Xe~)&e#3h#uL{f$A9;n>&K$sfiDkg z5a$5ubJ)?p{s(vK?%!N|PR{?_`1_|f{plm`eDxFA9N5tF$HR0JKc0D@ZIeH7 z`kFs|O{O|er zOF#OuJKlix|DPI1V&u!r%cK0*r)_;8b;k!-aPw%|wS$6B^ zLUww$S|yJ!lQKv%(B1)(6ZKY{ZW0_#9=S8hiFhkRa3szWj|0l--p2DXcphU2mSN8% zLgKB>CWT`h3m?rFLGIjcXB$Xj?q7fRy{~@%wM#Cyho$2g`1w#$BG4$FmQLo+?<7Rg z6nPt-crF9rs91`9E;yK)u|Al1(7t^oourV^F(18WaAjYyRB zy#&<47psZM&w0C=Pn|q9w*HECO>Q0J0pq26xEPm52Mq3Pa``CF^BGViK&lc?KoW?- z^Zmqih~3tAodO5E{J7WRr}kJF^X&l$%&)`=P-HarNOczxU#q%m$GTDnz`Kb^fNJaO znucqjHVeuuAgT)*8d{-eAb2hN(kyH8AYv|!=-ayRo6W_&?}c<*)Es`g(1!5IGL zOSta6ZdV{&Y$?s1qz-5xJOBqch4*xh1wfNJ{3?a3;JKaTz+m>_GHI(;;o=z88}ARs zlALPoReRwz3#tP`X8g7qhJcOn$ShHi)ySXkN0vA`h>@I^yhgWHojDJJ^d-QHWO$ce z_b4nolu;j~o?;ztrjAg>6$`sG#rW7`4NlAYN`J$094^eIlEFdI94-}?ty*?m!mR3m z(7ai*95RC(ZXzFSMt5op*bx#CkW6CFp+L~u%#vUX$g35|dRJaWK(SK0bjO9_Cy&j&JP474Is00jeZ zs#-zHQ1qxW_E!Sc1EEIvH>B42s)@&Vyol8$Js9Piz1R@}G!4R}E`MN(rZu0Yb4P8v zBayJ98O@-=ey$qbL%|i7AbB3rV9 zTTt?>Ig=b)p8>n%2qY3zU|ag8%2^64>OCezyc+X3%j1h)w!(!y*DPs}I9;6UxLQEn zwSnxE&%5NXrsr~r);VbvXN?AwH3NP{Nl25f0|xO(zibh+)&|0rH5S%GY#%Xm8?{1OsQ;En-Lb@x@rCdoZPx_!-K2yKayF4@^g-JuS;VKaPRBHWPe zAA=o`;!U4GKsF|aJJvb5_JAWs?n1aouXdNa*23z$Kw8)%b%BE_K2pdCs*`Pjqn386 zOSRne#u+*~lNBb=>PU*o#InF6yHG(wTn$?T5TV|;+b&m_cFWpZ0Dp+{n1^@ms3S>( z*gda|kOLk`Z5mV)6%y-hifW~TB9+<8I zwbUVIc#98t9e_7I(6@pc?B)m%73Ch8#Z8M`dD|t`$DzZmV{tDVYJaz5Nz&xEz>=T} zADBR1F(j4oT$&Nnc^!bf)!L41z{nA^<)H=I+0LvE#)HFRF_Cny9GTRj**Xr2*=Bd7y-Ju7g=O>u{2{xx6-Hx2Z4y|H@k`x9zPv zVTDd}UY?DUo@MZLKp~7go8j!z5umRTGiKgLCdJl1%PiT}NO#c*O(xut>>$#(8wXqW ztn;zRsEgaHy*pfx@#w7kF>c=m4faOMI6Y*}ZYM2RG)!vaOtt8VX0N^X3y^RelM}=? z*WGob^`kvAoL4hxQ|)=sFWJU;UIRb|*H<*q1_qPc+9Ags%o1m%i#E&>XQhH?F`1mP z3%7wK(t_^nLF{8y0xeIEC%DKC7bwv1ToWXJC`fo^Gva;^I#6D_X9X;lAu10{xs+YB zJIetGG8+n|FVa#QxRKzk1Cp=3Rac_>%^FBrG|?FbnD{gYMx&RV?PW#HChnh=M%N1Tf80)NE?sjv zsA3#s#7_j30x2&TiV?5b0woksWF2y?*?2X*QpH_PwY8j6L!nn zA3$6tA^?1+Dh1UAQMH?@ z5Co9f{x0qcKtZb*R`%nL9l3tpa$xL`%;S1HV;4(fIVihJ{X#fqxZ#nVE(cnnz};@B z0%*&<~!-{p;Kd6m*61b%%7kxX?1IuxL<@>5J(~ z-iQ;(r1Sb=lU|$u192tAZ4OM3}XNy z3=k&SgSK96&v#6Y;(+Z0av#neI6QAM;_47G^SL2=3(yh;0FG2;Kmmki?Q=2o^k`rC z;%1j0_Y^g#=hz`o$%m`nJRlXqbIg(>EuDjeVt{ryDgj}ES?!Ifq~Obvjs?* z57s+u+@x9)B>|5^pSs>+JD}RsVYi4t;$zBomKx^8=DwxS`LzM84EV)yv=w&Nh;Ig? zIL@K8?L;?nj~p@%r{}c}u)B)w_#R1h_5kCdN+uu+YwwyMI*d5B&FlssxNgxkT_kdD zvoc7n6uUvSD^jnCWIoS2_(pVXbBZyCuEowOkkp8pYK%tv7}QRW+X>&Yo4pyiHthY} zt<4G>sdcj5M9Z!k)1z`hSW3lt{4RHZsj;57Mpi;?l2wi7&1uzJEiip5qWrEYqZS2P z8Nq;BfM%;T-7;=cICCIhsN*eGQ9eB^-8p=UO#zO!9#8c_3_v<nH9@2-|W+CexjY}wYbhnBNkqWTC(QLS-0Z*ucZ zUaFHUEuAsU3+=-MM&0(N*~~TD!<#WmOwh#>(!=isp`5&i6W!(|shV1Hqx_Y(^5EKcq?E zYBJzbay3nhBr8NIK_+urKu4ZdE>oF^J|a*ffdq8E@1KaQr^teZ|bz@c!>SvhGRu%mD6EFk#pXtO<4_P#mKeK{>XalIu; zhADbuvriH}vE%csUm~Q6Gd>lfR9#sx+iirT7FVm#PjX6Qrs|gMn<~qrs?TFC?cgY# zSpnuZ^{iMGW|5n_1!#0FCgj*Oc%q$yAP)fHL|W>_Ss~E6t`CE49EXfGDf)nUL49>Q z7#sw&){a;A$es(MURM;?{mGltX^kWp!Fcfnk7r+cP*e`)eJ!G69bjS$g{|_+1YN!j*}F$j1gIq$=xUhLe?R& zbpSC)PR4j+7UVPSYVVH+)Ajghic@+5V&x93Q3x!j*M4YCO<+PvBn*S5Ec-2Snu+}c zMOU7gk2P^KY;!iM1ayWwdOi%TX1FJeE?Zc}q=5DBoL_Tz*$&uAu~9A721t#6XpUr& zXsxF~&rGC^K2kkmlInSS1mbK8t9g(?6PB%sIu(?IvI21+w>jO`z{H+`#;I6XE+UBL zB;SU@sMNh;XUYqv8{@{TKdy*%w={qb(TdZ+F#5ycSedEh8Up}vN69IKu+zXg3)u17 zzPz%nEdvUFUc2SENO1J)Wg2tt*avz?G~+-mYP^%XxvN+0c^}Ov2W=gk6$5Yp0t90t zve>K?!SXRX=_V_-YsY64w>SwvA*x7sNIyh5(h)EY)tXYfjAnbHW2T}W5};K~;K^Y@ z8yE~!ohVdxPJesE`5nN51Wz0h6$7*8Y~+#Kpt*$cWvOp5Vo4$`5c)Lj5eC~S3&{`r zfH^T^65s81d)_MQGTu=+EjOvX8_Ou_iz!kLNWrdVRZbYobgz2ic<+{5#+l*Bg5Fky z6R}jhRtk+i3I}atpfkfEZr8aq0m5hA6rs&_WesYg7-!9-7<9%QfYt(a5Os;9xhE*c z+DA}MCBckswN6@xlAd~i4NrE~no->;_^VozlzTJ6UIzQ|pqx@Ga>@+$2$XFIdvCqv ziZ6~XH8a|@P%i@!nOZ_I>=#szX@T@(0=_P?cRd0OfU3Y#O}S{oa{h2T2_j;sdE*!~ zeW?Yk1r`8Iz&A|-kh;x$hJr9St}u*N;w;Mc`&`}*ld7iLF`3{!u|AADYLRS~>!~?C zO1@*-_KGM8Yh+*>9LQzjc-{-erku9=_z;S?+`$w`fv(db4W$xWPZ8GX9Pk_nW}T`G ziUQ>W*9qj|Ov@9A=o(=6`{l$1whj;pB+Ozvvv$s=pdz1}?M4yD9ZZ^X;&e66oD9z}W%C|>e z(v(Y>KP{t-+3pra-7)BP*Vr80m-1oX7l88+plQ4xfE@6KNyfutC;>!uJOfRq#lT-q z9J-B+%~r`VD}sqbH0>EHcxhf$iMXrRh=b0@+|D?J{d|;lb3BvXjmEpylZMXM;U7iQX1o2w3CCha6u+C zn<=|Z*+c7o)2}CN$9A}Rz1k3*a}ZcWvq9q*cJOv-2I9(75Wz;Eume{Eg?~n-nQX5` zmIWws-3!#6vXLtkiFT4TmF(t>>$(D8uzU&hZ3{zL@z^tJygxQM(d>x6RvUrhThqRk z>@b#=Rsg~dvSg|E1kIJSAyN0ZMbbsqby@6jBJ0bjQzk$(?T~0K!BVKy$N?9GyKHw@ z4-^Sd@*{C}z^X`UZJ9R8qgV+JtD#JcY~Sxkhu+at58(Ya2f*Rk4|9a82?W_{AqQ+$ zXf|BF$t8d#*2#U;WPu4@7!;dxdNbIh3b%%VDc8m%Z7-r zV>RV@v)A%1o3vY7H`tBms;0#fHrdlv)Jcz?TlFO^*aGp)XeL!YV=$lH6VnY-(^!pG z++53v*$Pkeg=`sPeU6P`N4Q;Yyw1Af$Ma67!`Fi*C5scLhK;BL?7RdX5L83J+ED<( z6bNo+8qq##cPM-?Y!yI0YAq|qwsKT6k01lrkHHrB#>N>itOl6V*&!8>D3Z$=5U@H^ zJ!EGf_DX6)zuR)%S_J899xogvLc};}j|vbl+@WnU>XB2xXpB15px+7>S`P$fV}Zvw z4aD2B!?}I-D~+KmI*-dqp;_ieI&#Pq94&EiSd=iy1_i_5y$bOHpfkb1HZS`94&qE) zra2vs57tl|A#Rx2N>BimKvYGW7}KH{68d6z2u4D}6D;2wO(IY>1vL8(w}wVVx3TT8 zGzAR$mE_@3f8qdgXh#k_O*=BW!h%GuZ&}c6I{q517h;Ioi#0AsC?WXpn$F&U4@5fh`~1|T(P zFbTAJL`NvH)Cp{i9QozgER9aS=<6m9PDVdMG)nTPGjp~WSAY@Dro^b7L@{aB5}uFd zfP87A^O#k~rM-hgki_g`qc%%19u2G!5-5S?c9{0MEKuw!6JE$!A&ujhhs<Gf z$!Z2k22cxBeduJhrT9)_EJAk4CF`?VKGsLk#Ue&*cD^UK!Vn~>*ZGp2jsP_&D+{-Z zmec@{O~J9{P#~hdVfu9l=RgO1NX%1H<}$(W>|#P^Hr=Yjab^cL*WnyO3o_WR@5h~z zK$TU^Ooj`bjVIfbo#a5pSfQmvZz~=c z7$)y~#}$R~Si0KI%+UsS+Ibf!2Mf{O5zPssTVkaQ3EZVu*PTtqfTM8hVaji)q{$B$I0n)% zSvzi(YQn|kfT$f+A{T3EnlI%kvG0{}HC;19n^X4fffd#45@;bVG1;y{5=)oaa%D0i z*Ml{}tiRopcsDf?*XhLlv1M2t71&$DzR#d-7lcm>+B23$KGZg4u-!`xmjvxSZN~%R zSoF$Zr3^65&wT}?FvG6fnMJmoi-Qeb?)GF3yZ<{@H((1?g;I7&O{IanTOQz?!`E}( znx?L%^tWOcYr^8ABg{sfzI{*!S;t#PEg0Fk^@I_~QK8QV^sXmvVjPVRD8lFx${s7V zMtwvLSh>HJFjUYsBZ77VaJ?3EFyJj>KU5XNbSugjEAjxOImJPhP5K7kB$}3v=&c?y z>1M0M#o#!HK(-arLyMdtm}-g5SXx(Ua?XvI1=d}mKsxo>(=hj^u!OBk9Q^T{mWcH;s+8+8*aY$ED|*!HvRdF6TRUh~uzpeqeD8u|w4@J9Voj)6id&iVTAK z$i`oq62f}+V0NJCmJ8^zUIAXUEd-?>$KzQA=q)J zb9LX2qxpIkcksPhj|L&4X~6OUW%fo(hX>msp|?sCZ0%y2=w-a$;FDI>%A6UQW7id4zz&mK-4x zoT%e^TXKQJYSx>&8;0g4VHFA1H@kiniXE8)$@RLF=4jSkNePnyluy)3GA0t5p3hT8 zOZ+}~M)iK;Bh*&RL?j<C|lv(|m-8b!?v7g|k@p z#A4U>K%P17_o!?Gs@(fk?UgX4hoxioj~#8v?GbRr1C5*oO>z(5J45Ys5P@+^hRq{W zVHRs{p$ERN*l-*vAEZOjWoCsjTH>3PICZv&KG+Fe!(2$rq&=?Z9z%}A((SKGiO@={ z(`7wP2AEt}Ek^Yg2ydj7cn8=~hd$jzK9(NVLUOgmc(qD^WYrMG#45G;#O zK@nIv$90Cuj4XiGHk9(?1RH}~@!HsiGy0(S46aQtw$^0S*2}U>Pb2_Mpt{vMlsAPMR zs*d~J)&3wbA+V*CA{^RQ!NNB^J*Ouc4HN*n?0`r#vfo-p6{5^|LhiRsBd8WYmBeDS zqo-4LS8m&b{76nkBn7TVPz-1!DS$t=B=)Ps*n=2wJ)bfC5U|c2_+<&FSKcHHjdJb} z`6&!Fp@N1afrLnswIa53Hxjb*b-KTynrJU4@uri4^Q(l0GfH`knd-w)EEK(kMiQW^ zo^LfJ8y_)j3nxHEKr4pQT2PD0$g;65P)_B++?vP>VpWs``0Y5bs3#7}+Ik=LLDadT zknKzcMjyk|=poMbDXZg%3xO}DyCVE0IG9SzBF!CT@8mpP%qF?KA5T(aw9-?Uj^j~> zW9#fFLxcj=wdQc_*M@+HqD)KK%hgtM)S2S`G#Ms7xtsPx@I*SB-XJ3x5L`A&K$E0! z?%qtA-ufWqfjYxTCL8h4v6rc4Vb;+06w2ABB8<|eh6MX6@jJjG9`={jWlRV2tct8q(6`3&d}AS3%<42^KIWzoMNN7#WXGh4Tfei!NxQ|&SN6WR{DHFjs`~r zZI#Pv1`#(R2pad39h)trqNvUrj$3xx2hskaF3SBrD{NQ5sN|&qLt1e3hFIcNHUCc~b?-A1UnwxauU&;Yv;d5kt^c4xGCzfz^s;Y`;Xg+N%!k<``o;pF!Zz zNiWpq7Imu_&ZYvX$V|Xjy4?aNltr;CaA$bn=@uNWmm?Jj=_Nm&@ihdG@B=3{OGYUZ zLIxs~3Hs=HA_9R5aVl+AAI!-l-=V77jMGxll#7jN9rF>=KsOn>J&sU7uv&Es+W;7X zo4Y9N!pdQQqG(%0TMX@SZARi;dpe(Hk`7R(s1J@m;x-A=*0%Ci1y{KkjjbXKvmjiv zv1JG~rE~%wWejqHQqh4f*>(yWn$r|)B_WOfZK3J9f7f)+M5DQ9dJg2RF*_;ejl`3=1?)~Y?p7rkMK zD@x5~9eT3x2SB1Rt-9vVi3Y$7Q@!q}$fRzftPc;EJvcznn3t$o~c!}y|iv`4Ak+6!OS3BA_Xu%sc{Yv8IRW!A` zHE5YDFkOW6sC3l5sA7CrpnjCPb=ed`I0GG#NDh7q%#)B0 z32gIFC5I;-5Z0zs9nR451?TOpKA_i*b%&x;c8e<^hd`HBAwq`R>FHtV?|Y8YqI+$p zsgyZC#5N`t9_%uRbzTa_d%;JQu^-|lSwolENUN23XlsC~+xo0jB7H#ek;QI9ip z%5kJS`X)PS#Bqs(4m z=;S~H=ZOYt?Ro_R%(y(XrO9!)G!==b0r=H~JqM3!E=0@ZkO(5#k{Y%H#w=NL@z`2s z(AG(xT@{$u=Q{W>frIkWbNe)cjAogkwa@R_Nu+P^(sIjk7>6*>!`U_&5;0=rgo?z) zkd+ccWwu(gEUG*->?5AkodZK-v}E$2N- zhLVcCY`dkXss&g&8}G__K`~2I$hDa|+7570oBP-nLa(;eF65ZBD#mIs&k9Ni;?+Fv zF2>Tp+SXPUN9Hl6GuA}CLk3ZBV#rBAoDJ(bUrn=+z(O6tnu{@;CyE5;siblkl%cSk z(1NbEn}?7I8Ys!bNxM<||6~5=-`3JnD{gt_xUV z@F?PFBz3nhefpo_fu%+2!tZFTl=A^q^Q-raZ?WZNi zEC9{4?v!2+Hi~E$_UsIBU)>R+?0}`ra{WyUVN@;K(Ed0;wuG~!yn_r2p-dm+hEMkK z_Hj2)gk;C39m5()T~TPSC1UBLT{t@)^=(+305{X^@A`XxpKpTQuDxA*aIQy3L%!8< z$7K@1IUNycq|w)CPicDUwuj8oaxE4>EKL_?r)gL1DY5FY3lk`adSvp;HE>a*9cLeq zl7NVH7)sUyRFey~A;)=c}q!~iD-sMXQLU~3h{>E)gfYc?XiK`gSeXA z(v2w<9U1G6*d6u)aCx|3nnMI7-YtBTsU;zgDR!2xptZaE2xz{LQ5;&C26)5LIP!VN zMVmmMRkGD=2)qx?U?*A#Aaq-?)flLGH83MYzE=++Q0Bm+r0oOFP?ETvxS6(KQ*sRa z#F!GB5XM^C3gHrKpxA`YbUo0FvfNCg794-82;$U%f(Eu@n>F1QLi?z|vsFPNFi~YKOfY*DkgPY_hQj)Y(m+ zQGz@VSve!?btb964w-n44~PnhuXS3;mM$z`21qNWT0r)jRT+}-{-AZ-4JZCU-PuEf z8jKE(Jg6ae0(3MBZ5Bh-x|)VLBF#q5=eDL5Q@W zPvwLM<_lq_^C8Q_yjvB(Dpc{|N+t8k>YnGiw%ed z8Jq*r3Z|%+*m8x@0c^BP!>zjoxD&;Vi~)q?!F%{P0@5A1Ke}sb>C*c(Dz!2u3mhih zC96mT2Fw69ml0GZa}UVQt9Zrwv#u%W>v6;?n^5R8?Ao_PI9XmJyH*B}-B6v?BOhB@ zG2-;5u<^!q?Q!a?FmMkgu<)EE+zn9V2F-0Rm<#^Q9LvY)5CEwB$T245M1t5%TU6Af zEl#R@v|3LJ&M^+cQX5IY!5p-vSTKda_tkkRv=hk4Ta8vzy49X2R*)C7P7CmY05kD` zf!W%d<1WyZSEGXS&hHRMtT@|ym^y8Zol$pZ`$ifsjtU^t3_-;237Nkh<#-3X29fpi zbD*GP^GOH5bg(Nht4(4X!*F2RO-ULX<8HAC*Xp1mD84MpEK*wYF032(W1nRA)%F~a zHW3d{08+znA3w4NLSnFh8_j?~%?=>s(OmTnMcHRspKmH1v^C>^4KomI*<5TLZ_T(D zVVZMx2GOk}704$tteSRON+A@2aTtV4m#gk%D9{~_hj!T-tf(3E&DN@2@5qpZ^Kxa} zwfn}VsMhuoqG#ul1p(CRoiMugQd1NP0MkMs1-3k6d~%U5G)Q!{5?7>|`sFCDc0D>A zclAk^OvWZQ?k+dVLoXrR&!WfMCWWgD8|Nx2^?3%RURD>JEGi09j%pF^5f~d_MoMtF z2Vs7~ZVW+}wN!;i1R{e6YAc>O@hlndO$~Cn>J<+_6NTta$kmpzx3-;IYxOb2vfhhv#);k=3tW#2-g z*g5LMx{t3-NntW+GoxT_A{b(ALR@sjs zsuY3=ab+JUvZjf>d0e1HQb6bt#Ct=4edTpfIANJjRR+#K0=PfXoz=d|2gg|-b?9Km zz$&G+VYC1O=u`#j)!DTH@~E$RNH>cigGtgO%yO?&(@J+);I0ZDbmRfoFJnZAI@%%B zA#4nS)ncL#CtNMgtH;&2sL7GnmaG;FoWHIzU@K!_dmWBk%==NNTX&C6KNOgNN_4Ua znur_%ICLQG#V|2f1U@l_Fpf79KGb7LoUF;D8fLoN8w`SjOM13F(DFD|30v>>^7_zR z5|JNzsNc(cj^tMvgfu{OB4=^g{>=XyY)23x(=>H?(O(z&PG`(x?&$z;S340b73NtU ztJG@B%0l2YZOzQ%uvTk>6IlS!b;BhFO>s|&SM{ta6AJuA(tUJ@aPopJMlt97K ztDU&Ymn0!CC$c&Q6c@mo*APt9L+5R;r%5zn%c_H8k_HEttdCM`YH$Uv3?R~I(*=mx zY^=A-ZLA(Nf2i#9!Aj=g^n_xHs0oL65Ry(KJ#R1@+ne2SWGm&$BX?s%f<$&+3$1*Q zDQH(MIFduneL@%fqFSi!i7H|oPQtZ`f>2qF-^1;ng%uZJtSBr!^*hPBMl^!yQVT{b z7Cog6$S|x;=%L;XU`jM+)0Pr1|G(az1U!l&YbPP8PDBtwLLh(xh#a{mH;0moB#;|I zLO3VMiRT#r>37Tguxl@-+AUEN+M}u z-(TEiwq+G}H?}1AruQu?tuL-i7EAjU_ji_;6~f-E^6V;8a$iSpSz%FXbAN4bUUI8t zLr+st5uC2rQc;{+SG%GprJ^Bk*r$~JTrG_{o0 zRn+CxwO3mVeU&XsdvdFraDd5Bb5`{)D(&vCU6z*D-q>j{=h)g|-5OT#mze0w!qSaP4VKE>MLB&ru!7&6 zzPP@mrLS~xSyPQ;kAPo+3hPyu^(Xfh!)BKDp1k6&s;XXctXbaT>Y9u~E1ow4U1D?Y z9hdF#^mdS$pXZptKJJm0p6v3eOv%San(*7XrrS)T5Iop8C zcZB=0t-QT`ZFhgCY0!?(o(mKB0cT{Vx9h%O1`XHDL032rIJ*vh*2<0pAP1buwu`e( z>OBptGRPpVs~fgz8@syO8WUTr#-=t?M|WbAsjCtG4jNn8F&uGN7mwny;E4i0KLx|X z`5SmeJR+%OjPYn39*9Sgd5dS$P4C6<$Cpj-7fwk#n+s_bNICj;JbE8sK9_(7bK=D1 z1fcBHBdu&=$}(^o54I;IB^UEP4Tfh30;Mk zC7}|?e8gUO%Jad?u+87V#6oOIKnwANWJD5f@gnZCcJVSC41ORPO@T}o{GG4qsbtI% z$vcw7K_=G76x0oJv!$R;NGCf$8^xWp$Pp6BeCIn6o%0BZkZ)Yt)d{_3#6=h3`<_6M zQFh0+lDTW+#QQwL2Q?0dljzNm+epYMkuN=21Ih$%r&5y zt03j>@ZgG4;TpgP4QLx6T9}5mg3zAzh=>SHI|pwxfjkEqSI!Bf*}Ebg-4KFE+R#~$ zd+10eYLAZ-j{_1HyWm-u!W~J&oXHk&WfqDC6*;Y_;I2^}XBjR87c;F$qK9Fl`hOq` zkrcY@nJ3j(mEly5PFdA%a!?9C^is}n)pOUpQRf|O6!>urnj1ds8F))N%D^vVqkJ$y z6{#8-dw3a{3FhV?lCPb=b8o`DjI92cx#-Sd>c2e~wL^*?4x6Ru!7JyXNi8w$na5&&>EXFpf%d&2h$q4_#gApWnhZo z3#eb5H*D-#7NG86T50l?=;pxd=i?gI?>XB!zhB%j8i%g#1x z-Jvr_tuP-*m)zY0Q0#DacZ46A_Fhyc&MiUEh1^sep`s{h6Iq0E9lmWv(#m< zeG#$)*Qz&?pBK-Ptb2|W~9=2kOvy9xXyvkL21zSDAZQ z(n9*%wfi|8JjLvskfCCf03LzU>Av6KWu$&17f&uhlcD|Qm7qzG!Sa0YggFmoNWiNL zQ5=4*1eJi^bJS9|vTzvDJrN;BO;9xQ~i=G@tqCtYXAq*?PcgC0FKMhVH{C`$l-8T1xUX&a=ccMiZ@iC zTtLxZfzo9MMN~OBsqmYV>r*w*04KSXXdj>{twe)(Qx)Z8wO3AZTn7%$G0OHj4HUd9 zs2dMQJYnNfREX27(O&`S+NG!%FJFqtIU;5SM_TSuT?U_9ib}z#RBv)IF{+LjdnAk1 zdatDkQ+LjY0y5|s@Q#DS;n;5lYVS^SuTA2VVWxrnxn(F8zqt%eE6^ax)zGM&vC1-+ zD*1VP6h4-MqHtvm3WrY7dDmWpE&(IlHEbk*Q-c!lXEi7jJSQi|z31d*WUgV|azu`o z;P3pbpHPcZfGcHv@2*AG5Zw4ds~@RF?H9+`S429-LksW|l@NJk)uBSL)MH-tTieqd zdRS_8jtqvAZ`Gj*q~p)82X&rXkI2CYrxXpOrOp~<=HipfA@rHO5>3Inm8i&XNU}yb zxe_ex<&~%+7$B9a(0s5j6{)%S{#7U&^l}zHx&qCzDUuO?sbJr`Nj-mD5-vmLHfUo7 zc+i$LiRAa60y#*X^Ki-_SO(su?T)NQHIQu-k6wqiffu?Y!L{$zYBqHlJky9u@Dw8= z$GfUutMl#iGP3si&Is!BZzEM7UckL2@iH;K*qT>alQBRzhq8O;Hoq$I+-PkNbavRu{hoECHnG_AZ9bfvHrku#2) zd{8%a8GN#p%2)kHt!ccBOiA8tL)rMPHk1ea@d6G_@y_2VZT^N#B3e$zKkLzU;O!nx}ORISQF zBlh18mn`tVET|fEMv2k8&d7wzZ36n~TRPDl(1~oqTT)OBPO%^X;}kRo-?RZufS&pd zpxpDAKzp|Q^)IB(M21d1TmFGZ_&(2;zZVzlX0|*Qe`7@#vtx=sveJ3;FNO!}`zow- z-h3TC+J%y!^_NB1 z$B9vZ#P?}*817C|RPb)87xE-}7&f<|0xQ5n1(!%cYko%to+}T8dG)>M$xx8%sH+h< z2|isxw^pd2E`z6DgXZJdYtSNKUG$Ydteu;%a-app+%Ul<_{#2#2-j&#EIX*A7?z1;&!-7 z&Mp|qsrZK0feFpsx1$Tt{cN+-5ng1HqMy~6UeYLY75>v+6oY@b9m0a$cc3!Rbd6G~ z^H6vhE_gg`8@dAK2KYNE{#>;UWdW({e}OK?Pj5qGtK-BO3VOZwRin5J7z)}|jY-lk zYc*kACmN5_2GF=*SlBXv7Q)vo48EHvL1Ru^MjUA%x8GwF0o(2)Sf3-z5RpchN>uPY zMl8PgE*@e2-<>qVTs}NlLseJ@aM(e#4i|5S^^EHdqA+OWOAkVr2@hsMyl(P{*ZqeY zVFZyQ!j!Q%fM45=Rso7xJ5U`!?+Fn4*t@i$pV@)z5Wn{0sv)!h?;k`ZfaInCkxYA9 z0|`WpWjj$VOfZpClEGGX0(95t*!9?-J&O0axztN`qltLLZge?}4pc3|xkITb zYpzaAyOwo1(!JEsP6(N z%9SQeK9C7U*e8BQV`i0{HF{EBM%GyO{~Y}+82rcfpgjEa9#k3(kb(OkV7vJ~8uM~0 z-G@-TjEs{t_rq|i=6)Iu@B)4UIdeZ+rlGd7n9EJbC39ii`}1mc!D{YGq!AYX%$7WJ zL|rZ)+9r@Md1b+q#}E#`{Q#N*O8V^sC@!xqnMP>K;g6^OnjJ1RpS#_qvLJeLW#`7{VAk+5) zkcs<)19Eadnu=fEkK#eeITrV-#mmSjNq7{I-jl!Mk>;Z)1N!h8`2Gjc41DBKx;lEV zLTui9(JOg#G9B-6X_>p#A_yjVjRHCATf;|WLpkUhp zIw%NF85XShDy(!+a2;qk3lXg7=ivx~vHT*0F zVeasV*1Z`$MDQrh2quyCJ%dh5qtOQexJz)7yW^6$@z9+jyv`Oj4mzvH6eYa(q=&{& zWQZAf(v$8uJ8>cehwPEmk;=w2bQHPPAdP9*z3cGdxxgtJ#qkr8c0CJyGlVyhSO>pg z%2Y+1My#eTgMa=kO2&iFq8x}&RIhXKyU(JiH8J*3_3-%Zz**s#G=<9}5T;r75r993 z$<}e>D%ekgqsCdAkfRPSxmYC1VsPAZDBZJ4j3A3(63z6+mFBQiR|WQ4J#CIY8fXq9 z^Xanjt@t~_5tp-U9gOR&u*%fg)z)t5U_|lF4Q(DJcqiwHj4j1{;5m?uB4f{YI@4yo^jG zHoSn+aO(?bLEu1g@!1zpBe3(&7tnHi&x>dz2&+QDj(0sd%-tBHl&CiT>_z&$DSO8K z7_NK?#Ws@tB=po&)xMyHVI$$Sm*}*IiUbY2<7H$*zU*bx1Tx|8d{rQsOt=EUM;s?! zMjJrj3;%%3&|}>QjJgkQNsndF{CfELE2WNuLuXozN56ui*^-TYl(ETZ)>}He+stj7 zOjh+?TiNKG&j2u35Fv~)TgHM9WQ_VL$H62A10 zD7!LFd|pw^qcMqJMgq{;i~qt2WN2tt@hX1eRrDHeJdWOkzJR@AX2qM#-H=NL_h~0x z?v;-=pSTr7;!4p|wB`h|T|?9q*y|@yX=sW{U>_(X0RrRFwnyW4PoQY&J2l5G-tsz{ z4ui{&6;*u_;%P2KhMEX*NPim52pt-K8YPE<5ZNo=g(!pjo_|7=)$}UFcm9eF>1L{g zING4nIuIg`J%dui=q@LG*%?@@j5&kSKyERL(mu)UEiN~Pjmiz5LERzIaUy%jBu2Ko z>(3%RD1Po)lmKYw_=VQF-Q5jZ{M}jj{PN#tQ64mw618`Ymq8urq{>H)m(}#zSjW$y zgb=lhC{xIRxQNN`qvbGWScK1ED&|#w4>>+C> z@4}KnT7EC>2cM((|Y^DNe*rIkHA@-?HL%y!AZn;hZII8A%264o9-X359k7I*om5tN=r! z6@hA$8EI5Z7{{k zVY{DV8qw8vI84 z2}hgktn9_vvFJ}$GhvEURWtg-=l+ArfYhXK&|=#X2dO1~llmDab&-V6qhJ}SvYH8n zQdN%)&Uzvlm%LfPv(Nt)3A%_Fd;ZdXbAzQFzxxq}BJO=1FT=s$PrgTU@CVDJx=_CLIfUV zOqsawqy})9;iwD|DgpQdAwnt4aGVa1^pLkTpabb8p+dYN#vWeN)z;A>n}U>{05AVg z@InIbgZ~ytMy_L_0?EkrsiK5OZrQMWY)BlNt!EgBM(wz+g>*9P5mOKES|EeRTSqL% zV?GIq8n+ZO#xWam%teTGL&ru4e+>zZsrx-XU=c1GIzK|#A7XP=mC@;*RAu!bpH326 z0EO5J7m_-wmSm`l6GuXI$Fv4>5U!#T+o7CMp0Z3NwW~>O$euD=l2C*b5X=&6fR_qZ zHcF4ge)tKwrNnC;k7kKB_+cN})YjG6ZtP#%WQ195@iurSUW<>`>ZV1Acf-xKgW|n- z>b@}Zq^zv9DM_6jErVUMtbU^1QDIA+u5f7KNZ~K_1RQ}M0}DL$*LY>#L(;nU~B#!Q|imN|ehwd6pcKYX}Vm`bL=|Ij8(frX$NNn_l1 zJL)ociYVL&9jN+^diI-_VLAzO%V$J^`Z`78@%P^gQ$Y=((Jt7Q;9z64GGdW-NOK7NA`SviBy7bi}4lF6bh*Ot?AwAPQM_VQ8P%5M}#k|^sd zocfTEv+L(V*wF5qg+J&(^RfWFQbKa1UZSgXiTVIE@A`F7lUV$j>ICFtbjAH64X)gV zH}h{3HvKf3cRlB2iNuR*V|vs)CV*kryrC0Ygwh)?lKAI< zK#~Oq48(G$&AjB@Ty+GsrMEt-WVG_P-yAXlz+a)ai zX-s-AXYB=vHHB^25WV3@>Wo+3TmR$!p)Sz5>(ei%JKOyM? z_kKK4pndZENb+wg{L7E5h%AUKj9eR;7g-9wZTXQ)IAinW#LOqe%=3XStuiu5Vm^T( z2gST12+5}E-8eK^F`cjQd;~X@F=}fKv+Jh% a?30P~GxXJ^sTC~{|Q)xtR@)>ae z?{^Uj*}3o5wFOtff!TExDn@N?vMgx>E06;#PyzD`Rw0FDBYEba2?~P)wpLEqT0dZE z$v;mHEYA;M8f{rBhgGVEWpgYzD3e@ii(l53VvnDSra>FgGuxIy+5&1tlWVwd3z3#}AH0QI%h$V^Ut1W>P=PD`EU7fwLKJ5-K_FgpvUZWgBC z@AnB2>kUa+`nImQ`n0U9G(%EG5C_#pHp-N`#=!w-FVZ{7EjzNAV*9M*t)^bC}pcFI+yE&4Ovh z!|nKvLqc(=(Q3kP9ulSr&ZKazj}z)QJMdrQH~ufZ;9rebKPfEIgExRpGI~>=(cB3K z%)mYetI5*rNIwN}pre${T`6fzSF}6m-0C--Uu)4RmV@JB1E1FLnM63Em(?cwOVjbG z5yB+hbUgJ@SVW(WH$NpzyK1@~{_9(5Sgl{6Pm82?Rydp1+M(~8V~C8L-kiObocslE z$)8!x*|XtcAKYdqrNb|L-DY7TPJBv;g?*R*T?|o*CGtHW%OE_>ZmB7J?U}BWt(1k7 zO6q&J6OfV?rGep-=fcK&Hm#wmlY*X1WQ@TpPYTnA@F`(*2u!v;Bhl)sd5!Io=;P+) z(V36`ix5U8OfO*LUBW!P_AkQI3W5JAID!9BV!~H}SIPuF?OutYS0sV^>)P?j!@{`y zQMujS*0zS8Zd0MvYO%ukV5W`6_8vG`Z`RCQtJT<_XX%@%w={^R#%?{Fey8uS=#8w3 zerA)UdnQg8608D)gC7_YuE2jB5~hblhv3hLgu+pVjI6ZejP%UZ%*@QJOkDW1uym5S zqcd)0iW&Z&mzHi$a{e|O3CdkZgz-4?gfKERH7NzB9ucCV=A~ttQ<73-RaWDvzZVkm z(Wiy=_{TSda8fQhJck-6KJbh%ZfM;RVMJ6&cqk6eu$utb zG^p83!uP)DaVCa{F`Tlh>+$SQZ?Q-XwRq6Q_ZY#9ZEv#&DHy=9)qR;I=9U@8`;uX}_P-vNV3;)xf1L3BY2h`96JB{!*bB?tc% z-5WY=cu2^mtB{+|2)lL8fTr#ZY07#CoVYnQ&at-W2} zVA30#noLazq$}t&T49rBPrK2oZ?*L5yI~`V#S9OjOi#CkhJL+m-K}~{ZwI`AvtRXa zm?p%*HWLj9$%(LCQaJoy!{&mFM%6YlCn?@WL>4FBA~k`p3S?a^iJcoZA0XK$5boi` zLpb=hsjaygqW+HVHn@dt?~biYq2P}(eAqlG-X$3q*(b~Q6|wzG3^4xw(ug9R9v6;@ zn5mnF&0`{pi(EH9m5rTA9dTT1sAIQ+tL@6w5JRD)y11V%C=GRTcI zV4<61LvyqZ!#=v#Vr`-aBPWtyT`s$kMIBTlOyGCNM~t_Hz#SW^*h37NY$GuF>54AO z9l9|bow=<8;x;!3dm4J|W4n49;Jo7Q9@188JB+wDHezDjMF85a0Y)5~gCC2Hm~Gn! zf)ei|m%Cs_QQSr@31i_hn_Mm@m#O6Pbqrj-AeRf1;PNTCteFOvmER&?Mm8>b|u@Am%C|cySrw(NLCfAYN1g~7Fm3gMY8yGuNuXA z7wg4(vN#&p4x%7IE&{`D3whYEp(F^5BtV?V2n5&&VEssd01lAYKmr3n;s}PLUx^bK z&dbQD;`83-eRNMNQj~4%>?K*><9z2k?{mJd{`6P=!vFp2U&{Vn{iN?|y1jWWNRsVH zvj6JpL&*_COSXeofBx0eKlAGIS5K}!@`TuTLQj-mU402!h?;Ino@~GRAw2wvw0)qP z{`36+UxwDlzS>u={*_<)?kAt*8hp2tQ*=|#31Q$^LZFL+X(l;Uwq;KUWGSb3j+LuA zV&4|!+-|zu6DVXz6pNo!#!h8-iIsSe6X#Y!2aXc6}rv;Xo6V1>MWKXx% z=aTb0*aW%UC!hTCEA6X4e5HMK^*%3e(gps(0`AvdW%$;u)+HaXfAv+-6nr0kgwJ2G1#9=|Ln(AmUzUQn@?<4z^T7^9udd!t zk@V{7qm5<$z;}goXFqg3*_XXYeidGQH4xNvgjd?5s}Bxa-$BRl+()~P7sz(g5=4}j z1t11nMZ4Kwxg!gnoqmTcK|8V-gr3}U0BZDXKXf;-mjHsP+w!aKH@~laTl=#1p7!N% z2|M#uAA0GIeMUjr2kEXofrnoS^uUzQ9$h_Vj{BSwY$-Rk{m_L)=sr-?0h-;ef8&9T zPrHBvWJN%~_A`KU?T-NE{4x0N=i$Haz<=NU;j2*lzLwXXb-&lso@h^@^(WaHK7zdy zR8MfVGf-!L7dVZyav-ATERz0fep_A5y_qh?-GrTFYw z3iY#RzHaHJ;K6W@_MPF0Zf6UCNm4#fr+s1rMf@NGCD4Inb1}>-3uZ0`CeMb2CEPL= z@U$R3eV!Zp0JoWZoR00MD@x%2m|*yn#6vR^DF9`*;FS)f0V_;VBc$R*2?0SsWx1ss z#4@bSbpVTg3apURbXEIA0?2G1ngCoGgFMfu=!y1?tM)tG#aBmad$+>^Eml&V(w_9R zXFZ_GZ(P0i=rkFy)awnncTG{J`L5pm*cTRX+X{g-pS8b~A))ZbM1Ho2x9I#DlpldS z4LrwI&qTx32Rr&b$f?8E6Kx!Rf#F`BZ|mKn>4zYi9v?(gMh+Pc-cPypY+1YSuR;1N zJM9k|{F|>cE?Lyo#Ocx9AIxDm(GBB ztL}GT_*)kx-Vw=PzxMbHjvEhPhCh2Bs&6(p;`Kyr$DeMF_g1L>6M*V3B(~4i`^Cq4 zZ4+)6jAvrw(=VnuPN@BY1KouF?hW}9=luUkN*KWZc{LVeYoo(a2O<|pX<32*Z+2ALx zgL^jJ%_pyoekST(U*kb4fAhkl)5czU3iJH!^Htn0t&xMY&K9>*+t1Hd@*bf325Rmn zf#aaBk-%&LHtG4cr6wWRRc96`d`)f0Km%iSPY7V?tv&$(ZG*jac=+tuqmR!lx{Qu) z*o)6PrjtnLeV*ro$_Vsy=O&vrXthB7HE~aLy9^{;5Ab^C) zEgi5PLAT1b8fY*Ln0&D;tZX@Tke)w+WrCp?>#({d*qgd9hVVd2^?>Do*(k{{jG0Rf zM=!O2<=o@dW`je6w?l?Wb-M^8tsiKRB-M>h)*Zw~e0w7JM)gjjyGxpLJiy?f{E-~$?N{(QvA z)y*e>BJNF4q@|9;1-AS4Eu#N4^KC6|V(5NFew_X_MSk_`W#5OW?Z;^>B@Ke8dIV98 z$M)kaqH_pu>~tb1L0?OQIKB%}natcvJ%7-I@Y~~d?w4}*V+fTT;z_44(s^*of1aDl zpe>iOnM;F!2Q=iC38>z5ELoMkY+urt$+s@TcTPr^8^AUhH@3+j;D@6T`<{K+d-!xj zdd33&jgEJ!Cu7e7_+CRDr_GG8{F|cj1j^N$_q}(~U&%Jx=&v-`(PGhE4>XyL*Qp0tzPK%i_Z!l=U#}C z6F>yFoqO^5^GAo>xxK-0tr@lcJFsDQ#hR}^u$>rU%CG)q_!L@8V6L9_3)(M24BGg& z(#?L>Ery3MbZStX`+Bnvp#_93Q!Nd#U|r0;W(4lIIE#a3RxU(fReKlgb!;bUYG4 zN(7KQ$imvYaV)`2W7{xDYQE=WTZEL92X=Vw(;V|ee+rYvnhvsNH{s54c&tDEB+z!z z@E!DzUo4f}=B55Pm2v5cQ$rqngT0M@GRr^xLKrz?@h>7y`g3;?%^CD}x4X2OuLF=r zmGJdzS09A((4>slfs5$_1MAb)EKPiJ{ zv@0ihX+o~|%uoYqvo9j}D1Gu0($UsykI#bRBk*n@S?mS7th5?tVZ(MJfJLWN9fY8>p0TV2Ru@)sKg}G0@s9+2_afG5yJy{FKl|9v@ZjUY=Gal! z8Tpi1$g%GH;zOu7wM6%227v};N~xusMa=dY)a(aHuh@aE=(2PWy6<45BSMYeNWuTM z@mKb%I569tIMC8GQtPmbf9Z&TJ3ASB#2x!R6mcQ1LEr+S7?u;sDZ9z83FS#QaJjD( z5gm|yx(y-woDc!ut65D;n!vb;>=rKz}%cZA)od4+ta<1!+Fg51)Zsg5i+&{X}^KR*} zx0SgAW)Jgby5nnEFz&FP69HWR{Q|UiVmA|WhY63U{qci@ze2Jy)*95yWrbr|_m{4Aqj}8R>MtzP8$sD6cU%oFKv@hk<9`B<-+M~?pe%2lSHiVWBfveL3 zzWYm(9_4iD)9=aaAFQ(c?T#eA_shS8!lM(|4`_KE*gx|2z>dy$UNSyd^?*ov`NjYbl3dH*-3P!9(`S+kc>{Evt?`YzU0Cv^ zsKEiQg9!+2K0IvD+0>`sE{tnj3%mW%+qd-~5ASMnr0lD^S^*S4e53u?N9Qi=$Nk#i z(CLCOeIv=f*NJb`=ZKC>8+i9J`fb{v<$dElF!?Vm;TO*J!G7=LLxtCCI^lt>uY>(( z-X3iK8rau0!+&#!X1KYKy>=+3+Ch49Q$K)4xUMn2|M}BYWq<|s@-ySp0%(LMsje_S z&wTvH<%?ppgnQs3R^xQkbJw*y%I z>J3=#)}A|Q-TLPtA+^_^hqYw-^Bb@2%o$29JiLI5OS7RRfi$49{xjxJCy0QRqQn>mTJ=J6DHG>iYJKRd3{#= ze5W#3smg5cKBpP`PgiN{!@uM2-%lUhuZ=T33G=)*#BQ42%hhqjbijKx?+XYidg-Y{ z@Ca9TYTzFs<~7sgIz9fc_tN9Nn)@%Lba{*Bp3Na#6oXoX_|>`XbYlk}AF9XGXhtrA zdK2(LK@B^io}K?o>G!Mx>?2gIWG2Hd^Y?Ks1M#|2f3!Dc z4(|7^R0ay^;izwrR>Y@z?ONGhhAKD!>;e)Gt2)^>{-bl_=Dg$nu;{*u9~^s#2t!?d z7GBR#ccF-0&@KNFm_imL(JXzN)dTHLm+oeU!HxqxPDRaQ*wnLC9*wH~DjzLnQAnLv zSX6pGz>}ehKRw;Kum5=#z|O%j&b@heva~+fk=U7TKKue2?#u7r6*%}~caY`5h`O`Q zb$F9p&DXC$mhcM9OP@iUjX@%xqsUGGc!0nRFocGKgf*NB>LH`_qV+O$#o}e^j7*I zQx6xlL#iCI%}9%_(Kj6YY-w-Y6;`U>*y&3+ztH9@naVqxd;i0Q5pTq7Gc+7X?<>1+ z*NN}58z8-@I6Z)yiPLXg#P}KDw=}qSA@3h|4N$iGa(x;9>N{J;o$lHGRMD;aCx=Fh;mx9J5quB+j%U-JwOn7;Ar5#?7m9>DPb^BZlzKD>FG z-TvO$QE%;kxB&c}QamkSI1}N=Als=rpXrxuF&}LuYl9@ZR4Z#&)M}c zck0h<;(zbxiySBZ@!zl7iJt-J?>>i$f#zoeqIaiJ)q?g-&t($ z7vCP-|M(iX*JFFXes^r|d=2~19-ap4cnCpc;XNc*xh2ZC3znQk2N79Ne457SBMa=<1VWVDS4-(~!!8gN+wJLH3IRW9|D-U)b{c4TgIGuspr3 zreyY`9r`Ro>L0)zy3V1*y&QUPwDYg0oO)Zdvkk18-MN-tFL8=}WkEFf3GO@0F6M)q z*EG2QP1T%mcWn22m>k$mv->=mU|>>v6|Jj4iu;BW?X`f5F-@(|QQP zJ$jr+Up|dpCOCsd@K@mRo=8?;MEhICEw&|LjeJ`9K|K zYrMV9g>_uA;%=@L+Hmih_|D*c_hY~DI?uvJ#9ML2*>c`;fD15Rw`_mr7REc+ez!h9 zO1`UGo51AW8 zLh5Ye-{q(msNrr-J)jj@oy*N560iMwVf6bQkrOhH{=mr*;p*A-6v8o)ljZNOW%?}0 z&}NCSv-+K9`$W#6YA1rbMt8T6WwempGjVa`Gqiu}asyc7zk7pbu9MtPo#%T};11;X z`hz1DGgAByZw&h&f&QPL1o{E2OrZZ{8j3u_$l1bPdvsw*XSYCod#6KhqVlk++a4d+ zc6D0|nD)2dWXb8pDy>`Ad*eQs*S6?>GCU1@B*Wh~xAgA;THewv{jdJdTinv8=S3&k zmhN}-z#Ff*r*F{XxY-#Y|L)s^|6gAN|C*b6^;hqxKe@D^y{}57zUm9eAiw;Kfhx|= zZnEc#&tDdPrG2d|WnV9HZ<$ES-FH=I{(lJK>pS?r-@AkNx-ow@-N{?rn5#h#Y9m2F zW#^6#C1tKIi%>=h?T=ShpF zx0;<@lDHQ<+2!PiYaw&01A7n7r{b8V6Q52%zn}I!19>g&$u#4=m`=CV~x$NqVx?Nc9{X233_^=~}1+`L#P%B94^qBkIhm-#So0duK?+80s z0J|Jh>e%NVGyCg(&QG)NYLytpyZoCsDE6A*zEdjx%^N)*B)R|LNpc@%&LsC&_j`5* z_3@|spu9RVP0sMP8#dWgz z`|px$-g|tuf$-%5D({!GXH4|h_P{+*&YtyrsGR-hMuF`5xk8q{DrOh*!2L6Fc9!6D z)yc_H_H&Yx=ALq*Ccup+yTlX3RKM^z$6YZ#_-a;=@qYT}jS4b;_auGZ+jo8-;?8=W z5O?QJ?QbSIQ*8(5MEm%LXQCAjKV1DZlfH2-!*$tpJqKT;0hLSxwa0a*KO(-9xJf8}Y0s zdhB_(jrga*@7`ZZ2i~x#Iq4DQ)Ii){Sa)`qCr$MqDGh=%>F0gd?9#gQ%@%M<=@~=` zGVAhL?g^Zh&ffoVIyjKN9x%<%0|%#XZhU&8)}Ouv$r*KCehwIZd4r}NPL0})o)4nN ze|)0G!^{~q{^0FVcDBkdGRh@feEs}xoDUCMa}bxOA5Qdt`VGe0z7dA@3ESH+^a~Fo zh!ZFe>~LY-_jB19kS~tBayJ3&J+ZT%59P8&IlJrnwX^@blV*DQ?ndCd^rbZrl}h>O z@*ogS&FM1C<@i<$z}4t+ha!&{zfY zGW9~9U?1o3r)O6zrj&f{d-#Fl?mUmQ)06bp@9c7so7XL-uY25iF9O`cztOGGIx|am z?`4HzK7W_Db72ZuI!dEI3`;qZsPW&YTmNn2zk3r#%cS1_b>gzW_h#gC*7HO@chc*@ zn>sTBQ=jGL?KZRY%~2f)1i}q9khg`ZNeA9JZ0&L+>3h?5FM5D057O7zrs2X=z8&A# z2Hi682uI1&zwmD9M_dARm~i>34yWe9Z*jq|@jM}cyWO%n%JgjvX|Qi4yV*;JLBqko zkmpVIZxKvA8UR7cUd{U`gC{#`4(8=9EC?^(P188(cyqpRAcRMan;y<}T ziI>W@F0|>s)2%vN;5#1pjaPV9n8v+p0yzJaoxu%#76~@Il2LfJd%;pV+DF?}pSp>wGss?lc440D1;Jn4WBTAR9>1R`>-ZB4 zhTj1CZd-KkFMhdojItdTl-Z)c_^{nQTi`=`Tv+zq=sgoK-@b*IP6)ZJ#f4e#XRkBl zoY?E?>sA79Be0jx?KBwr>gq#AHq9PX>g(zArtOBo#YWmkS6_#hy1_-; z=IigO`kh~Zn{Hjx2~2$n0iX0Hq(_h7{l5;pFx%8x%FBXnv;s5_w?2%Tpte*rFa#w^gy(#+Y zLlbfpA#4*6o9<>NANDHEPcKuJhbY{U^AEgoo%f+O97yn`p3>keLHl`lZPa(*zwiDq z8{~&+?`N$agAmL9YMRA4BVQJGnZcm?UNdp=`}$R8IZk?Giz10v)6^>4x(U}j(`gq zGfm`XN-c1bqx?Fln(jND?@aW)-+~pXQ$IatGkp$(vk0b^bPR z6I%AIkbX;Yav(lGjeY~exhJ4~1eiUWekcc_XP-ltX3b8s{b1+C9`OX>lobBW5$4@I z>277?WiW%j^7IWjCp*>n7~&(j=oP99ln(K+Di<#``Dk#{|w-6W5!R~Bu|2Hz_! zD>UH+i7D0t`K1lPAHjTb2FS;dUb!*PWm-)4;{4xXUv_KsGE`*}>=FFSm|`#XUhW9= z<(|^O#D19q34DJGpQK7WjjDdid!hU=V0P1I<7T~X@CgsX)dD#WZxL~F;0XYEW|`2# z`zcSLWjH);SPEwWw(7t?2mU@IzB5iHKF$$8e7eI&+Ov3}=jkbS;pydZp$Ha#er;s@ z!F>Uy!Z}RP5$Fz1v8FHFP2XwrVpGc!K{V=#KJhN-{)2CJyNQ{{B zwNTF0hcDrN4;aCJ^}|+Qdu`aZe(@m z`#4Evdx5hL*K7!>YJFw=Hh>Kd)sw5AO5?fy%cUT$(s%pV(yOblnCVHLS63e?x(Q|o z)c3sl9KL0N9n`heS62!;hC*>4?Lyp0wwsn9qI~LVfL(}ov%hjDjqIe~B}YU%;D3Z3 zEHaRN^yM601UEm=_z}QYWE<^R^v}P8JE;wO2fsj?K&}&FQQQ zpL`zvuTzU_Wy_5LfExVItPLhZ-0p8_d0COBi>0igSP`>iio)`ILn~R8M%(uo({gPf`>sG60SuI~Lbmo!DC4*$?Tbo5WDJ+o{J@qTouGrGFX|bLx7S4Dy_eUGS zW}W4_jZG$!xtJ{aqyCT?jmo_|jd2kt7ctbQia0ZBCX02~tr1FIUzIINq7i~1$n7?8 zJrA7*~$G7K6lbpJTG|daA0Gb+*=^Wv0VQC~9v9 zjvk`{z8p9zDuR!sj2blu*6q%G(Nn8P9jS1IH9dZUUoY>_U5m`DjvW+>OFvePJ>dCTb} zP=u)5r^-rx0HjIcb-9cNy`@zE(kMqIa*B~fK4#HP!6T(oQrMUtX;EcPEJxi9H7<5s zP51a>Qi$-LP%P-)B40*fz3mvqqYgbp(;i9@E$fX~;jo})YjvPSXjc#f5+&zoEW*BN z(=wk_KrHo~su!SJQjYQkuQOZ5Rf*7Q&%bRHmw=z1-TC z;*#ZJ6p&3avgI;R6A~sHw%Qa21B98WD|&=)<7%T^Yd1BZXEZ6*LZ(!!m-}c%;n%f* zm6~%N_kqp>#82|WszX^dqQp`STjk{SIA|)U(Lk!Jsod?TiUc9yZiQo)i;XJJdPsoU zp)ekoqXboFRF%detWPfmZ!Y45N!2lxLss6n2r@+^l|s0g*(w>=$N@_=^UK(@T2zA% z2govRp~Z599^fD}X#WHL%UoBQ6gfo>&L}GD; zDq|i$t?P{%-scMic#T2KA$i56(VAj-(!h2H3)*N-(NbS5>&*fRVyzvOIiymnw+e0;5({6>7%$9B(Yow)=R)Ki#iC7H-LpM|xt=XFj!#CIpy+i^GrIrD)we48a z@k$l%Sf!cB1V}?MjGn-mQCvm1sDgkhB_64$7%G`F=GB2`NE z9QGkVYfB|Um#aKGt1}hgGoD>fCzWBQQ|(4G>?)~lH4T-4`p2=}Q>GJZ!*8)dp{;BR zs_*;VGQ%euS&3|O0DLwq4py8y0bw!Zd9+?_pj$PM8Qx(`7PhIM$P0BmaToL5*t#g{ zt5iRgn;ovt&S7;hC#+)x5AyH;e(!KhZN53z=bJiRk>+@{Uz<-_F*&Q&`wZr8s`zX| zc=@_tx0Q+0QM$q=>8i77zr0l~c0_g8z4CZsmZ~D7`(B(l`AS^k@t{Trs(94@NR!lx z{dRXKR|iZrY1Gg@I;&bDhlVwl3#1*4k=~uRlIeyc1Kwsf-bS|xLCOzRpK4Fk8l{e> zNHbAuXt;8hB!mSmwG~8~m zhF=*jajsiqsr*cxh1DU|Tx~^=2Xz_r*=);CBi|g9S(I|SvV^DmlF?BW-#AUmsmvL+ z##H69VT594D;Y7;83-M&wr-n>_fxh-0V3A<5>WYn~Q zg(;6fYb(4_k0%kXirs=B7nz_lucM5zW$Y0GdWT>IB#(K^nKENBT4%Xo8R(U&Ha7jT z+){$h0u^mikwGw9z*Dqlaur7&;uuwls$dVP^;NlrmRSQ2nPLpQ)NJ9sT8miWTtgp} zSaLzS*dpSEsW)x33u1RM+oB3u&=#-(aw!?kdvTjn^sd?g>|zxo4it{wkYop`+YP*= z4;9dbrBr81!z#ed@|Y*4e1i8I@w(Zo1x10hwGkEaGra@0cm>@~Lp1QKbdQh>v^CPn zhiIWCOXs z@CLe3G^e$h&P3IgIBhH!=-2{%YHWGc>xE!o27!q19R>+|os~HZtB4%&W4AkIMI@p( zG>-Bmt}1~M!Ql*pC3UK*o69~uDQH!uB5vH7#+E!g8BXxUbj@mkMr^~OI+8c_a?HAf zLefls#w;kWw8dwkNN)v~WE@tS)vbi1Y&Y10^8$q+YM?pm^)%`6F)R)UCD zzr0dg9yu#+aT6RN0u)`D=37AXUR!gt=DHx+{A|lQ;gGI`gR-&L(CAwGpgiY8;_DU~_O`BafN&YMGi+ zORr#uNWZJ%mMrDf#-z6%AgU`n`La6kDbm>11EBRaQfztz=}}bCHoi(D1!fHDL9*)wC(vTM|KX1hv@*2czmL@zf= zRdMl2#B5nYAvVs~3>?wTlZj3a!V*32Y!U~nC^LzcXmUF;Be_^{MjGx;!3P^#VL?mm zrf0X%j<-!vDeyN9dxlX$)uS;pTrqe;>0;9cZ<^vO3!<;IoG{_ZYAh2`Nm_JS!kyU! zqLzIH{H5BuZj+IT(A%|*(6teX%|mCTEb2v(3*?Zbh*Bht+KAL%Hb@;@v5q%NR`Y1# z<@x5YPRSOBuclq96q3e3QX;CfwIkJ7@v&YXiH)$`?_r)sB=St@wiY-iZRGGKCAvw=4++W)-Ea6uW(8EW{&`T+LUS zASAW2DDz1kn@&l5*`yL_B`)9+S)+O=i}Fg3P()1d20mnmU<~8ErSDZRg6p8+yi_o$rqT0oq^c)D zFS0RHWm#ctj;C9!+w&(hLa#u~=art=-g3^0DDjLIa*hN@-N@AoR4yQC1;h={VxMgJ?M~ zEL!Ucg)fy&souumAS73aR~iH$iz#m*Er_lay7j4OZY9R3%^WV87*r9WpGdceNrp8i zfaeqj_j}vMlxl+fw6q3igoatCmHxO~wxM6%U4T5?tm@NI%P~6J?UrnfOj4-_?KWDL z*Np|SqI+WB#kK+3Yw1)UoCfffTQQ?7LR%NdxPY#QafES*+f$O6X*>43?&JferF4Ww z8+0Z@%2EuLRe&}bu_yVHv00ghE)fnev8e@kl}1aUR~3mSjpFo{;>L8LNiAG`(PqSn z7n38uQLh*9xzOt@8K>CeP6RWKK&b&F}y>W$D^;l;l z50mPOUl4T(+k`+jrIc>gv&D8$C@)$uKZ=CrIJA13g^FQfUac!cL*?2oP1*H`Shu-? z2UhQ-xquK=5tWQ;tH0PEn}y-B;TKzoJth%uthSjoMkFrqkZ7QzPPNE& z8{RbEM?`Od>d0DmDib>DVO=6F?)U&1Rf?OE#drGcNjTc%=e|^!m8djbYoJn`ewTxBNsTGJC zyl+pVh>EAGw7Blg2Ru_WsA0x~oeui=|rl99K|nBXg3 zze=l#Ew$@Rp&>P!Y!&RWI5oQ_#UYCe(rV6|t!=!muRC-MW+rEW3^EGyhO?B=0zQqZ za?IDF*_N&g1;f+WjVR1ot}9MCNFRvY!su_%XgjidTF7H))I!af%-F_wtSb4|re?<0 zRGfOfSXr5)$yg0t5iPN6tBiE;f?Y8|U)7lbyDDsX-QM;){Ftz{$yShh4Sb>~#bH@= zM-xxl4r(MZt#B6jhMv|LgK;17J%w+8l{=JY)BFe_dfw1zu+y5oW-Pp46DG@z%Xeu2 zd$<%Od^zhkd+wr+Gxg!34xR(HHCrortFD)}4_jbWW)qGL>B)RD(7ABdGsxD!Mj5@n zs_E;*88yRp701`6<{&XSsDXg67h8x!sbC~lqo|=&eTcEibg}5xl`4kOnr5>TXQ|Z3 zcz3xm*rh{>8^J0eVrkYQmiUI9cgj>m6NuCI^s-t?X=|}T^L{u_Dve^kPt8YaF)qy) z3vbqQ6e9!h4b81VKQ_y8Yg>~0f!A0IeblYj@xCw^O-dW3CRM2>#NK#%JD07> zhV+$&CAuZEq>#v5or9O&E4MijVu&k2!iA#L1-U4e#2J-`IpmtxPd3P~1ChTzQJSr5 z1lBB(K9Aa?VIZ=iYDc6<&bb=i;%W_X+>3Eu)#wfHlQoQtV^DkGQgykBAk-k}Y*Q89 zX!YCU$zmXM`-I{rF29ONO4H5O08?6z^TX@wyCMtFgkqdjdh6lWp}zP(Sy+REP41|&x4Rm~)533So4(WR51 z!{+O1jT!L0ah2^!`uSbs6V%wudE8+DZtXc!Eqf9}HPuccF6SlhHl{fQZ#T9}^W1LqCo1qaU zHL+@9JiBpvs^l6Qa_wVUuP%$`Xh>{iQ#KgU#7Hwqs%6*j2}z;s4t(&YR^U_UmI8U1 z(PROZN6?OtMN4Qdl2orDDs=4>uvxSWQh!o-4e;Sa2K5BH$OTG2iI5 z9l{2exuq`JqZt-$3U!X)n@C&6ipV4!(wiQYbmC&A=JJBrFtKgRL{thh>fnXwgFahu z=UjCyi=;7)nbx{uGt?+w*ziKFAPW$CuawuLyitXK$$A4Gr^#ya)Y^d>}6l`eL-3%i#-Y)7T8TfSG zT#cH8NzW+=O4tMYanxMTR81N8htpYWv?@&NUZ*`~#_U+AG#R`*URe?sOwH6z9%9N2 zb1EEZbefDVlqYgLk{69`JSUimRB;dtT$)XxmtcmEmxjO*^)lolOpd7_4NYmts511*%I@TFQP8*j7D5J3l$b!HhN4O?S;iW3q(?s$7Zy(rexrh^RTw|#7cV8YFonQC~n$|NGT~`A1zRh z11CH$lm|9VxvfwsRReV1JzTRn^L3Lg*aBR zOyrS*+>p@302_8H6h=#NSZnC*lrGsW$V6KzZpdWYFSf^mN6?D}9dX{Q%Wmb;h_UAE zaDucJRR)}yx;qy*Z!;hrJn7AhWX7{mxQ95zcTz3_FCb5Y4U3QG;3R)YuhOU({wT)KD9h zZnJG0(PRN(!6vg>+h)OALAr~M2|%Tvpf!jP=0%LQO;4s0tP|28So#aaiATDP=C=mK z!1@Dk0dc}ccROz&(#jn#mN99{Dn{}yJ(?z*yv00R%((hWL2yrmf`k! zh*fv7ATLn}U7+38kRm7BD6qSvFfG$1wN(hHZP5fF8%^^`UQ=h4294u{W~4$s zV7%G#e1Fgbzs;k^7LzCuIkqcS!8cI9z6`em$Y)BNR7hiV$h;D*Vh8EkHl+|#IJ(gf zXxlPp6k+;gql>p!tJ5nYxFT#Vk&s7F@tS8z zjQ~9ba;t}K>9V6VxM<=9s5ZW|B}nGvO61^Se* zv{s4itwTxfklUy+2hZMLVsnWIDuM(4`-+30b+sKC+f`L>L@Go``u;*~&COP;7KLD> z6fn6+pz(GPbr_~$8Df(xj)qvpmoUkfDW!pxJ+c6yYR(R-g>Gpq^rz7>#9Y2PDJA*A z8duz9QtZiXph;hG<}KPT&(@0DA8vf6hi|N*2W!~$VzI>~6Ou+%YdM~-OU1IwmTOaf zicTD?JlOc81jG@8stacjXphM;3Ta^o%%Kyqf=pZXd{rQsIvrFwL!Wm=Tog;=Wra*O zJ(*`jw{K5~K;-fsj?eSjjNUr=HdP2s&>5Y^n5tWB8RTlLwn3j(M)l2lh_5FQr3- zD0fFe+ig^P7}2XZlfJa-_F9HFR(b~Tux3MypxJlh$r6laX(|ku=3s~-jK8d6C5T;X zMom=FidHIMQ69pyisX9)B+0jsz8Ra_Xs}!~#}?!vHXR&l1?WjJDJu;hgH1+wYUY_6 zzCQNNz+5)Hq(e%E)guj+IDftQz&GJCWSO!+iP~YnbWh0$#m34-6mN9|8AR@ ze4j3Ez~CVrh<+IxbS^K9Y9fad7bO~De&8ShzOe<>s854lS>zinBw8<~w!W#g@->Pw z^6NR#U^=t8&9}7W7UDuJkPD4U9xdV_AuqP#Pz$Ldy;RC8g;)Iw->dbpgiZOrPK+R^ z?^Z_QZ0ZfF)ndt*SGMS20rB;f(5ek(9hpF$u5b5)nBpPR*J44muHmgvQoR>8gn7AF z?y@a5iDFsmx2t2zB7KpF$7T<($gX*BTCcC7s$SxSZPah6E4^Qai`Z%=6AD@k zJyflAFlJkj&1MJAni#W=O#x7T(Cj9SPOr~UxMfW!ly-(wVd4&lVDyM) zC>ovqXwp*3qLYk+>evj0+FZ7mUPD~A>Ad=VnMGt8okkZZK_!-T6v zEoPOst6GK0H&@jv>_}Y43```3%6v2P3+>cTpG06vO?+m%PKxyr#59NDG60<_OxA{l zqY*?Ow;Q*m&z2Lsgr(6DEZWY=BG@KEftY%_Uux^@KnnX?wCB&uW2#Sv6|g}`QJH*~p6+dS~P<=0?qId ztdYQ`K?AZ^rR}8aZIu;{gt#*=jVGe#EuBiA7>4o$<=N#XHaTxQUMz;=nW?$Ww!)ZB zui7omZ4XPi+QDW4#2;JYs<6tpw!NB96pQ9S08PIZ z0<^Q0Xlm8j(lj|AOv4VP^ERRu>%x2mXXuU}OKy4G92AnNl23!9lN#f;n3}z6 zHdtFMRHo*%J8UyUy*jKI0yo|croi`RX$I9Ud1{laykrz{;(A0t1z>6D55Y$*&l-Y= zV;yuD2~=BIGgPsp73MR|O2$4?m{m%};?f-OW;};7fP{1KO*~!&^rXZf5S;FGbewF0 ze%RCptTr`Tj2N`B*u*9adM%EzPBg55B{wsu6-01n6E>hBIH+NCvJ|;mX;AYzOkR!Y zsxB_d4cnZSoA#7WcoA(+=BeGoH76uObBNTi^lpDOWa@Kvu{K7t(sJqOOSBdd#Vsn} zAp{!)H(YzgO-~&0xUnStVbDlGGN2(Tv&?waE)@s$ywbwzhKjEozBQTw`H$<`%4~Jf z%3K(W`2mhjCjQ9f{ejw9YQ=7SLY68nLP}*j8HXWRBL+~y13`|33;z0`v8{v4C~h`o zGiu08VLN2OpNd^$Dg-qgY{4=Nzc^1|S+YwZGfR9Z;_S;q@B8{Q75EgRt z)oPuR{3-}uy55==k(yB)3=!Md7$iPxtlV0sIrGYB3`qm4)IgRrxWZ5Nk^EwmCDY(ps*9jV;R#T~N4+4nd>|PR!ZQ3Mn{u$qKN z_Q*<#4ZT!ff;*+)c^8tu#Udw9*QP8%CNH7b2(_nGKOZ|iC7yzg%5F@&8)f=HAR0UjVEw;gMkc=SK+lTU+?Sl29vMNA~tf}P9PfG#maMH;hCmiNz>2}pB))$C)MZm zc~2Eum3XNqlxa(q22(XAs8UAE#h6c;F149z(;8H+xzfDrY7n8N#o55_&|*^RrZz&E2srcx^#qLjzFl&EO2RYk>hByHP9)u;ps8R2F*Jd|a5q!dHmY(gSTz$14v0Q~Tsc01~{yHxCQj9tou zy_;apC~$@WGnLVLn)@0sF2!RtDB(1%K%7-t{cgwIg3itRmDKcBOT5l^=!z>hz+xMA zz`0%ygW}9mS(E@9a#jsRpPzIgmeg{kv9&P`@C*Eb+;pQ^U*Gn`E!4GD+a?832+1Q_ z3t}N)J#$GV+)^bWFg-R=Uz_#dVkQ^-VlkSiBb|%oK0CH(86x0Ytfa9meC#$>5P}bT z8<5a53a28HY*O1T9xC2C=p9_V9-!dp#wu_*aazcLzl)^H4Zqtt_ivZZmU z>p~F}VS_v!6WAQC9;rjEMWYAGrd(Y16NO!pG!_F3)w=BjA~l3n=P3*dWT0lMA`n3} zg}@nL)6i((jyHfUXNa0q@3Kv-jH7me4SHgiFifV*H++2C8_dB32$H#F5zbVmYrtq? zt1bzXE+n!FkRyS7;(%GDX>r2pFM$l(eA(*yAlFv`)8u%(8L>;QJ08lW##)v?n-)pk ztSqLCNl5)3rz{$EDE?FZeydN&(sX;ObBx6&kO&}g=Rg{7?tptY9#-*(S zp~jd(tK877m!Ld3Vp?S~t+C=jG*{5_G_8qZl;V08Z;B0wW|gbGkys#LPlhYPX>*mq zIBa_HVn#Dk-ybmbL2WH82%8Z^h%#H#5nQ$v4jOf2XY}9T?z_F6p6AU zDUu|L@bpu+XFb!mZ!6*aRbSPay-2m)+v+?mZSWM)_+#}-?wiu|4hU&Sq>8bcy zC+PxTufgTRC1*{f+26O?QFVb^lB-kh5st^-8elAgVt;^`-niOPF!ra13Q0RMc{{nJ zJEww0-QY~la{S(9563-KQuIR!w>DwPIRpz*<~uunKYQo^ex=J(WTX#{=qw$rclSj?816 zY(o>jCVuZ)xxEfkj+r0l8TZ`ql4L~7UalVU&N&>EqSm!l*V8iqr7v@8RmR!Mb(Fni zTS@b_!(iuiM`P{GVNdcexzN{IbExq3P~$f|hTZ+9nFnHgXsn=BLN>!}OMR#8nx_5J z<*WV-B<}s{EYq_zXE;;*RF1t~rP8ocAEH>Ha}X@?fZn?+E+-Y-Og4j1o%gt2ipBCXz-<)zOvNb#Up$w%9ZM>4tGV7z(%%~Ml^#6} zHm<O&?+8|>+c=s%xU%c;7*b2&^`PxbbJ{m!FC2U)XmxV_ zAOcu?x7v^x1)@c_McJ_~zI)>9Sz~5X)c5TC)9L1rJIjm#P~R=C^_TEDeeP(_v z_$ZH>yWf2E0ES~c?eYOC4tzH6L4!5$&#K|5`iip*#)OTW6)`tPFnPUFcA>f>2zbBQ z%>SGNb^7B59}by<8Z~eaxZZFB3&h9I{pr$r(G~g|ac%RP(@-#U^|8kxZojuznx^;f ztEs}<;hc!+*P?QIO<8%dLfxPa!u@GYx8h9mg=tx1XI+N!^XFM8_w7UyPy=;c z5SXeg!{1f9`9(>oMe|d^YZ;BvO&ZQX_j_GLSApOCEW(H}ZxIk%!)rdlt4>2pv;6e7 zM8hs>^!4Y|?0sjB$BrisEhtlVIGy4=-gWUqiWzQ`REO6!oa`mdz1Pw6BEFJ4p3lb5 zz|BL}eG_{O?G5Yi=3KvF49Y4mF0Wut>&BbL-8rZBM&;znZs6*xIDQ4)FumsOh9)rG zCBF__0La+hG54>saV(8AjJ@a2H#Sf8QnZ|8(PHx0ev$tZpN}Umxy#kW3!2|@jZ@B%C0{%PXHdQdiGp{`mr z2R>Dl+Jh9pR*IL?BmZWAmto1v%b=R+4$sY+j|e;M&&|!6EGv&?6O2NDON6%V0dvOv z%EWH~B!~;jH@v*)*?sbtjpbT-KVz!`{M$;^0&6etj9$IlpsS0!8S)p>LG*_f?M`bk z)c~4Tszrc36p_bW*laA%EWbfd@N>){qA#ueZ9VSzvfCxsasHL|N1UxZxik@6IlICL z&JOd<_#~P|36`muV;0_WD!Z>5iAzuWGQJTn`%x)jA(W0cB_VaxSlhm9l48(;CpE+U%>5yqp5e`K0|m#Y<{;{OP!TPj+yUA}-;d2O)Gn?X|vGUQ?Vd z@h7;)!N*ykFA68UlKuNJL9Q#?^cTB|uRhxm)6m)L>XXgD++F*Ph*L4Y%uDgS#tUBz zj;Kk3ad>r;i4ev(^>{6I~++d<;G+@ zOX@0e$`=l`emhn0F5yAYg~n80^I&mNzxdTb+9}>jJ0mLcU`0eq5G}>G`-wbC(L)bEM99xk2bRW+-07690N}O z?n6y|!+O5(RYl?)o?Nb!FtsTlUG&nRoJR|hkYdueZ8H;r;?CikFKuI{OZs9eJC zs1a(m`uX%kw$UVLR8yFXqkRV1QUyt0`H8zo$0U()s&flxteg)ea7|*vti;VkToTa~J@D+!OGmG4t8-u3b!HaxH7Z>}-eKuj6i+Np;NCudC^jb~xf@YtX^!phx0 zZcHKAdm7MA*M}!ES-s-?GMoFOy%*C7r^?v&kwn<;@9BJxk)RCmhsDpLWZwmW&)JM@ zE;7b&6)$(OyK-c6`D1y`3WevQJi`t!jKQo7_2F47`Yi+ghg|$aOIX*?vKwuEKexR*iKl};CE9nP5B}zt ztTQabMm5aF+;hR@FuUPxn|zG4)`Ce^&JlM85p1m|GIFd7l3%bV$X}XFC!F8n`XrNh z_HE8GG@gHmok;j&i3A5<`RRI0_iPE49tG|~yauIwE z!>q!5r~yNJIJQu$L2bOE;d<)RLvXBVP1L*w>U^{TAG-xJ0f+($l=L!a?LORx()l8* zWK^AMN&1O&kQGqDhMaV6xwzLs11}ZioE(N4SOShMF#-(L*L+#K-SglU_*{nbeL9kh zZQh)`?;b8_kgwwE>bh@5`pWK}GjFfo9hb=pU(bohcKc(I-gJca#PgK`f9^pvFFbCD zo`Nps5to8)0t8Febg}6(t`mLAr2}Crx2+I1C+??Yvh?+S=<91)lo6j;$cvrq{qZn1-_V znJy@?EQbp?C;$3RPqX;bM3M=`_-Y3Rfp}z!#A$SV#`)z_T)=mzrXxcR&Rnmy*3Ykl z(-N>Dm50sDHxIWIWO_`J?`yZCJSMtDV#o&v=_Ss1A^5qNlsoeQaVsyLEDeE*5C89N z#sR~&wJ&Dx{vN)xLpvLW@mP-_;E?%O2Ko_0upe1<5H|B2LcqOUafZ*AE|c+(ha|q- zEi!(Hr()hAUC<34M$Bx=EO)^u95eNJwW z9^_%y{*IU4o#;f_1MxeF)urRd0+2-zteguzxK#{7t9t!i#)#K}Ma+6y%9jj1VJil} zQh|o`7@?i*^uL*GHAMJG6lf)rcpgObB0&57-JTZ+AHWRv6MViWL-uEQg+!CPVR)1x z2kjQ0>DaC26N2Yc5gvF?%b9q)h3e!ydaXmbI6;ehoekzdrli&ypTqaN7hVce+QJlmQJ8RbDzJSSbF7`@8!E^zj-5tK zdF=mgel2-YPM;$78v3RNzV7$v8MEY+@!@SvDT-%GmDJNGBah_xcnh|ZfBMh(3N^mJ zzy-fnIDLcoc5*mfOI+)x(Oj+vchjxb*ydoH$`Z5xkiJT7op;Ea+g$ ziu_}ZiAUPEVpjhuuA_xa|)As9DIIpIiDK5U8oTBP~^y9^Y+Sq-~rjp(x6oS335!VSC z0{NZsNdQE~JFy5-jYoqAgK^48AM0u^C<}N|jWtD)#XApT1>%33Zi2^r{_OWJ^5-}v z>_^7?((T9$9p(J!qJ$D;85EA3PDwfsw_;hy|R_;VkaD;>sA*0(U zZK%G^i|)ipFjcj>F6|r=%}d6+(Y@AqH(pbMVWlIZw}r1Y7jfP!ic{{_R7 z%{kfXbW99=29c8~HrF{r+eIQy6GCCOs!tbix0?}vCc!Hq$ajbcj4)xrK|p1fx9J?j zK|fA!%OR$~o7@1|6hp&R=6?i}zpKn!-^?Ibl=7!vrtTBU@~Oa+2Gz)cT(iFWQ`=hj zoRPeFHX5oeF714R$Bh6}ND-%OcdmozWFQJZ-*kL;F8ngah%nbiK>5aRGmU z%J?eO>2X$_!CVjIQ{tb>S+NvrdUto+6al-Yt@SXB`iMEo4o6cF`}Bri2X_8qR%LT$ zh;^U(Bb7B;vzH|DCmR)FQ&k!;o%%&Ag0>)V-o0~DXMi{rvsZy z{HyQR+U!rJwX~K$oOBJ2+)Fg69dGW-f}W4tm1Temkgp*<`=D0$9U~JzH?dNf440+Jk1UY zeS61N67YzK$(y#>M`0ACaa8V*Vv8}`(D#A&?DCWGm_&XK*Rl)W320l&Y8Gur5Jc>U zx?FnpD`tX2y{J|uW21|qB^!GP>3gl~w$DA<_a?QK?ZkdMn(C?RLpaSLEA{HQt-5VYgH+uVzM&)(1 z{8V;K*drvQ%6Z=XvN%fhg_cR#`+e)5_LAa&i`aLf7)9!fY(6BH;;dN+d|EW$x;6a0 zm;RL9-JSi!t5z3)%bfht^}Z;g$;LzV^Y%tJ1w8Bg?cc1|qn2tRKz{Q`Sgeq&uD zLU2O=*1A#`x9CWs&L07Z6HHXWTJZ2Xc1E}&G4vh8<*q$uxIcSi2i7#j{Is;aa)$m1 zPP!0_P!wejj&Ql($si$+&>XkxUv7D**OOHIooBup2h*<<#}&u ziBl*{3faVLiZlX7(S4>djY|JqIO)?c&f)KSA0__ubKN#8{i!dgjl|rQ2d$|-gL#0! ze9;jcX)Li}HJN=T*Ij!L=&KP?gE_JAM3yU37f0zYLpgs`x01hE3)KDQBvEL?*SXU53g1=RTi#zboSSWN|AFXRDzO`B5G!=i9XEgZ z)qKVLRQz}4sd;!GyC-BRsq%YS9VEhk^7hff?Phv-eW=6x{Tq+Zaaa2((lM?xXu7*| z!628ZYcpa zoysbnTlS9{ZbC1;0EJ$F&UiK~dZA#ZtAn4vKH+V&aH4|V6WY-ta}2F^Q-s!1CjaQ+W+n$JeRwI zw?qRut?wgx#>|0NqS5`OcfdurLyrBgxO!^m)$SM}v(hK|!H+o7_xbR3t)>^2+Hk5t zk~w-jW6rT-ZBf&-JMejuv|WYhc5y)r`5m@U^7{vWVZ`}VX>8*+F9?zhP~P&W1Q23Q za}#5CLq2X#+3@K1JhN%ryT~RU4)IAxl=c!lw;x%mnT-C922$cNy(F)h)^Rww)B2Xo z^O=1OhWB{mbwT{)5l_gqBbB#Ral1s2_k{)tV7$8KucwSsB;}mZDhU@HM+Bw^i*eqA zRx(V}ss%zu*FRKkkF27a!LEUrCUUv@cb;3+8=WGgVXBs^{$$-&7=`a1?2RjfV~>wB z;GY>F!1)ML9B`nJ+p+mMxc)Q(J35c$S^GCLfbB1J*MHL13p2xb(COR$FE=oadur7Y z!mR5~kbZHJT*36e$k2>9%V?wa7hTpSG^pWK$f!N*!VCGRkB*3^VGa@u(9R3^w$zbX zlswYZt;q?G(|JuEo6{-U8dWiUi}FA$w0b2}FTM^hhMCS8j%4S&A+L;r^N{wzy_21B z_I7I!2agohGxT6|ubb~7oNL%QaA2S)&sneEEW`uWB-3_>X zMvoYYQ{@M8))yO#LKCg*i@XPyWFlGyez@er@@MXH`F0Y4`g{lX4tV#sHoM(7O+(<| zV2mX;`pczvzXY*}{$X+3?ZAP5-|B>?R_E?~cHvY) zJ;RIcW~W|{!WmL?GZESo4CAFcZi}DWT~&XSF8P#~dVXD;a&>y)&|lYrG`2_uo4C^q zCPdi;h472>PPea>-LQ|}+XKxHpGu(C%)b2!l?wslDD-Cq6@Y*51`4B9#8T7DBnvoMiJ%A8yY)JxNB-w%PVq z7gW|Ca3C?h8d{Wx)u!=z$?*|XR=*E#{L?!cwQiHDH-(YTm-pa=sOYq{S5LYk=%yV~ zozOIY3lh1DqtT?#sfPpUkGAB%mUJ7I>va{ke&&plJN>+!Mf8v+mEXCy*YBa* z7v&`;ci*wDJWV*i7I~}RHhB6^4U3}VicUOD`l(A#aPnNVoF<_14&t2+k_)YO??y^{ z_lvR#aP|_9M7SK=b>$qoDV8FcP#AC0%oFQ6kshpVF+a0yYrdwIa+O0itWr+Sj((oI z`*L=}{n>o-#f?`6Xj+={c`JzHkv0xo+}4$I&W3h;imj0~sWV>k_HU>z;$Qr4uB`jf z5-0j8BafT2O^RR1G*-S6e!B~-2b}#TzD8rO!@S

T zVsRrfyWXG}P;zt+CH_}1y?HFlOio_}6IY~uKevQ%Wdt+zTsjsFeES5C)3lkWM^_&qTK3 zIjb&@N&d#(KVD=?a#P0?EHqBUuMxtra;+Z|@ zrfB(8))5UP;yn)@qj1(z3HOgypOK^LsFy*obyFh}1uTm=;lyU!o zx&+5KOa0=A*S&Fa0UZmz01>Ucdx);#kbO4ZROqBC%X!zN{h`~Hg536noJI=PUQ(|xHC+1+ z5p&x?_xKtp6YJ>Acp@gI0=j1Hlj__fF6!o*jN)WcJyF-xPmC&4AS8Q5EpMH>?&gQB zWxw})#+Uxm@(TV5Q+eR=`i5b;lZZiN^#sj!X6Of@?q4ZVxg0b5XJClmAU$D1&E@lJ zZA?#x=2>D3Nwql-0P`-tn!`1G9CwAhl_z+(ZaJwR{bTz`;-y-Ad(UFtFnqDk4MUmi zYz4m8&qfhNdy+%8PKwQC^N!ML(h^p^2(QnP&V}pkl%gYII45j-c>GOE1*CNz!?IC5 zNSijB+cSJ*0@HF~i@OQZHsc4g|D}KBB0X=w4w7U;AlQDT6xSxARnhie7To8KS@uFB z#~+B#X9$~^CxWLRy>s%ZgTa^my64MZ;L2nmy^pkgEf^j7eCPO74yc*HA0gk!-aFY@ z9B=sON#eIRwZonsklh74^Ov7T%VZzUzmxQ|vPn7VAXKG;3d8Mup`%u7#yz&J z>g^ouzc_7tu8$hcrE`435q_%%C&u0(1o+(JU76Ko9kM7e!965$JXdUS7b*M+pUgddxP4C$yFBt22vS@ z%O|)%w^sPwb|*UzKF_`{jNiH<=TYq=Wf;^oA`5pebQ?ww<$$R~a8JuGV$bD^eZCPQ zP&M=vu*|!!dJY8PAMhSW%}0B2tq)}mr^$GS7&Ikf-}ibO_rp=R^jsKuE$zyF57qUr ztkT1qD-QOzU$wKe-S7k&4*YpHWoUGB>_zWoRFK?d^rRxHueVJ+pLP)$eXLGWG+H2> z`iLSI%jWRd?2c2;{~kxpCvT@qKF|VH*QW=})VuAq=VN>UC!Hbk_0^5wGj8AL?fcd8 zJww)9L&@1HTE+!t?2L=@?_K+3D)vYnVFz|>$I&+w!|+D*{l!n=P983YVmSY-MsRt{ zvGtncnFCeqwlM5+b5W-+edKdFF-S+Lr<5)eBXNFDxhdBT?=T68RE4jeAMmYdzk6zl z4#@V6z9@7RjX&s7znXq3Umfj(sA%efEL?5m_`-+xv2iOwGNPJ*)nmc!ZzXt7? zVsL8mi>9$6aLQ9`qHf?AoCaz^m!F~|Qh7`3w!PlItm71Y{sH<)*!zBZT?DOb8);0u zK5YD+pTU>j8opS@lM|p#q+=IE{R5KDhDre^1_i)4`3TvY)a8?J^IS(UrkG3m;6h@l z+vH{&O1Nud@&vWU^6+yRY2-2ayqVSp3-{uZ!{E}7KfUvj1O#;dSxNa@_1!-oWC#K3 z&>A6VDvhN{t}nvhhKtd!$Kv}&#fb>DZC^i5B(m^^*}ao+A?Y3Sb|tb+z8?J1rZThn zi~vDra7O{JSWA!9DP?MOF{k*0=t^;}p$6t|E`;$?!bYuCI?< z*(Vj%3BE8N&yj8S9CIbSSw&6>*GE_cRUOYm4Xt2f1xp$CDyKJV&9v1m6uMiv(7c*k z`kk5r)-R8MbKW|ksuscCh62C4>ef>K*JlC_&Z$2v7s#EGJ?+ElUx!F1&{r(q4w_pP zNHetvLSDJxp{=Alrvx0@kojRnnMBPHhF0ATZ-=D$F@6K7RKPbRZf5Bn9rYg*u{tvI=-FV zOA5Q)8@r{bh%P$Q|#owP=YELHjycwc*<3nHtTh@6Tc( zaHszA+IG01Bk9D7uU}vxYj?FO*vQc4>&4(khezX7fOgGHp)y!q%J$J*| z1R@;3J#bgW4Da&kb$p*x)$6ZcX3SWAg<%2E%FvX>^W@y7I+Buw@`M}q8qvIvWPuCmg+>wP2 zQeS3K$NY4ke_7pU^!oVOaLW$gO5J(BdS4h^{OxP;PH%A6HhVxfjXDjdZG(Le$aH(v z+)AZ`+RXle-#mkI77py zJ+mUtTz#GVY1LCURcYrh#|G;((zkglCPfs+;$jO-pP~7ReSU6bCko!XLRU5PZ;ILh zJQl=oV4P(BJ(toVS*rHrtxCm81}d9!*S~-7msHV3dNd$3y$U_n{f}dPB&B~-XW~Va zdEQs=yeAT{S#jQ=mgoK>j{y5o)p#d%Z7(6IJY9dK*v&tVZZAqd7Zsn4C-V4??x;je ziUp4Oqu=UOQ@divax<{CG>bMA_F8oE-aR<;^mS2sTO2m`f{$*IRQBmkDW%xtglEZt zXC7S?qI*dqlcb(AW0F5gm5GRmPcxb1f~>P#;zAh5PJzkt_aPw}4{m*HM|N=biewA! zL4V%vQXGf!KIpQ)=dEJww4i)OV6v=T>#WaY+Og^nqiEY%7X0t$2-?PELFnOR!tTx| z=&CW;?6SYB0iB)Dktpc1TPpj*v1G&J2rX2(!e6fr?9cud#(9&pFxXBXdW4VRtZ}!J zu!z^c!m1`2ey$ntS366mw(`$|SIykn-ak_|D)hE^+)gbr)A2~4sOE<6k-vhZ1PiWJ zq)!}t4vp^55pAJt-)?WkcDfyXeFvQ1%@2awhNS0BNllfl)%`HeHlFR_?_Z?*e5Yky zJ3cu64Kw4^p^V+xeYzhr4;evzv?H$FbZ;Hso_HY0wXWsa)Oh5yuk3+DO|S(|ghOU3a|3(eOhY_7ovmNCLl+DMyO72XfD8O#*~6uR2M4K+88&`0j;W28c>Ay=+- zth{zxid?WEk7>2ISMId%Uxcx})g>#lhrV@JI|SF%2a0W-{+B@O2fVaf{$?>{%z6T{ z(w*&#`A46&>lDj9Vv*mZwOL|+wEgd2-#~X@pa-LpElamAMaSo0q-NN2hl|8wim)c? z@yi35&g(r(+CskfIl6bow7ka0->v2pkn!x>q@%yS!d9jC^xi=~sXkgc=S^E$+*y;) zl)W|R>>3lC1uYg`cUKt24*PI32tlQ45S<$NwH8+tHUF$@-lzr_)j$BX>RK4~t&Pw? zN#0RKXg?vEvZ~`jf!O@My_Dp>zhLyd?Gyjp9^T>Z8gzXyi|}|0j=2=*o$B*RTQ4CT z_lr)U8$_G^4z4prDavcclUC(r{l<_sS_nJA3otWyL1+4HmYqp94CL1a-1JoKxL2g3 z|FQ=BA!zFU16E4>P9Eum;{N2ZsJQV8jXV}f@<5i`#k;!T{c~lgn}0^01I-FmDdxL+GYMoLp0I#~QrA8wG_yuB!ND%YCS z?{#6~a$sT7G44gtt^ImLXj&mLdrG1#oq~&gi?Y2O2z|k$Q_m7&^`zU&&b*Sh%ifVr zCaQEys8L9xq1Uj|&cC!Ga<1-AE9)2RGkfHomL1#jbYQ7LOkWotTW+-+!m)T0I-~NA1b< z$(KS&_03&l5Y!gR#&S*?btxXvBU#4t{mN3WYL&dY%TOV|<>Kuu5KuF5$=P!Gr`Mi3 z^n7WPav^CN5C-xC2UBBj{qbAcI4dI{Z^Zi?-C9t{<0$GqpU}oEp*e)wSX>T})+i(X zqOcC_If@!lr-~3?uXu-&zj>m;aH^(3oIauD{B^i9GtkPABGYk3L^f_Oyg8Hssh6@+p6 zF?bb(O8Z+e`~01$ta!=FNEd^7lhcHBbZ8bfbJ({L5Kb-|OBZ$&|nNPpbRthK$3B#Ih^5=n3EN zi3#lG^_^wG0IR1lq|teHKbPAU5S;H<7F#T3g74YjdBb;P`zivVMy?yxUSpjLsO|Cz zyDRlmAlp6i^N-dl3cZ=k9`DBT9nUj&sLt|(twSX_)Yrsm%+K!HiSp7-jf{DLzejqbydA zMPZ?8fw7wguj&!G7cD8c8mg>@R=!w*N5P{T@DCR;k?0eUR3xq@Uf-R0K@4fuyWZG~ ze_dc_NXG7a_aYILIPcGsPo1qGL1vUP2s1>=#3xRi#~0ls2aVCY#EAx-k8n&ck)w;M3AS-sctVk4v}A!ol6D6%YUf!`H7wi zc2$!!7MQpXRaN}L(AmS)+3ybG0}TP_m{_U!6JOmNW{YQc-1!bZvqw(*uiKEYw_03j zn`L-9x4?iV6SkQwBx+Gil73lgb3Iz4{Mdm*`vlD;eY2z4OtbD0MxBnwlkYe{0ImYX zuMff1dGz?{j-|o8fnfaZj&feJLm5BfHq;V4XVU#a-F8n$$f(plL8*NpoKGsK!J+CU zayZ8PL>hr52FYOc#i(_}@zR_|9NE7K-*wH@HqO^-aTqG!8d5b+{v7q7dxFHK(cQ}Z z^&tK0==-n*!ZXOX(m~=L`!~t|tpa+UmDgX_^|JnzzE>qpA9W0AqibsDiM_Ra!~AXt z6FJ8HPe-*$$=@41e`hx2PX77<`~6{BI&dd<0xggv*%|}n#?ibZ*Wx*7=KOw#vn*}T z_@?As2MFD!g7o_V-roDcTkz+1!%Y|3-1QIncTk`|Qn;Q+RQvXy#LED^9Dtu7vU|Y7 z%Hc6jljm!k@ti*{fTe4wEx%Gv{oa!bmvP6ucWT;v^`9R}hXVNSu zXrO2@OPQ#SBU~k|t z8Ve+_h#+9#kA~?3xgVo?X?njf04)IuR@dE4i}cy_4rIQ|SSlQr-4&fT*iw3tu4InsqeTE!RCaBy+W}pn zw%?%(2HhDq7X+Auh}ZD*>3Q5eP%(rRUr_6ETwZk=4E@@(OP>NOyQ43;%8DOs zJHoO($@}1YAV@B?^S=&gTRa9fI`-mHn?@`|e1P92e)lN06XVd~Y~fwDgZ$a$qrVy) z@*_y@%>|l9Qv;!F3;opEkvX_HRu~RkpUG}c_AGB?D)p~gGfc4(9*g@z_VZl5kDvWy z-9P*N<9nQ0> z7ujTwBje4>FOORt;zp^F$<5-5$Pv5DX#8dSxF*Sd*GkvUA(1Iw z_eu*Ku;3MfxemJ@st85zvn^B$L>uTys zkcVwSy_E5{Q&rpxKQF~6&Z2MsZ;9zTPDki;0kXGX_>kPQhCe?kQgX1a zUvqZCE-|}C0Dt>68SH`KCnC8oO1A`Be~aXKh{ZIjeK-;ux@b@-686|_;Utywfj}2u$*~kZmrpn8b00o_E(s;6CTQd|HOeR1U#Y7GCDpG zAPE{+h%clbMf716-wxBxZNIcG1r948d#jLcpW7wMkxxgu$k>TkSMYs-wighnU#R9P zB`4OQry1QBRhot7hMHABMI93|zDFlbsH+w7=)MA9pr#jPuN zn0tl?%NJ}YW~lNwcIOq~Af1t_L!WPL8g%1sm*l;=Ii!&65&k0JnZlHRif=;3Vuo}o zI*g1u_O$(B`o8d*Ryp&rkEwnqpZl!W-GaPNXDoUa z#)`e_C>F~@#P<GqV@!(I97&oTG0Pn&XO_S$L?!E83{_vp#A8R=XJ0cvy&&hTN{1*rb0`GHh)Ud z)6@%^lfT~UmtcPdl>>Nrm|Y%y8U$qi)-A;|zYZFzXv6?39o^XUv10Dtev!4hV*A1D zp-Ak&D*A453n)idZzzQ7QiHAks%Vf{=~oj;Atw5a_|~uSb*wjcckmA% z;m)?Z?Sc-{F9TZQF8XkszkfRe&`7uSTvynaZ{x61QmM8)ci2r5h~Cu6>ENOxk_9c> zC8w!q^1J2mD|}n)fTqMSMwPB^OKHG|1-2JP$zQ2s6#RflIWAGYJp(&ogTr)-NCU5? zQ?QmjXAKOE*R8pL306Porg;AZ*ChX~nh-70-A8S3;c}DEtp2P%QS9&|hWSVdnfCLlI9hi$8r3t@ z;xx$mF!+n^&aCw8h%(q4_cp2x!&NVmFOVNNUd|7OdhAB+X$s_xuch>`*UU5z>gg;n zBD``8)2=jrhyfe=_NZBe^<95^k3v5s1wbgoXl*gm<1q=~cvJeVkxwh__I{0`4yc10 zf_TB@`Po(Z6E!rSYlhu;-hfB1l)PXsBJ3DjTztLUhf&7Tso^ty7ks#;aSP(4O_??B zIk#unp|ctqDT1J(7Xkp8+`*@}V#KA>oBFzIY4G>#%t~|;Zy4NFpJ%S@?Rjc_r{@0_ z&#H04xZ75|_SrYzRpy!6*rspM5BFnbc*+kS>wfV!J+|l0V#()Mj-)6C3wiv4-A+}d z&{9RlE|JHg!XFIY66UPcsj)aP)(MvhXDnZDP84=;)Q{x$mm~RpZ~3jJJB#U`x35HJ z=TD%L))SRnzTI!`Sv+Vq8AVVjjm#d;UcMakPaqsmO2{7g&X)4v`#!hVA?>L`- zN>G4aQ0+725>CHO0nz9mPgwc@(x=U_8E9``OUqwE{c?11OyQD}9v`_4sqV>`Diqy1 zH!4=w@Rvc=E^BZcjd`F*5I*bjGKsJRy&of^0W?VyKU(PFv9WPyq@9gFTZ zIq-aJc=-@P_B8*a>P)s()v_)6K@<>>tY``X0s@lNNEHM`a`^f?_K8wdUW*nl;>J09 zE37r=7`;z8vIVdDxg6eSEY7)}eb}0fvy}g)FVovxiyssHf@kF!&EI$LDb<%NGEO_n zKXLi-NfoC#l8k_jz`?G$c21G?r+?z*1AquPgh+n$%|Xyz?6mBCjV)!=>@@FH2?y*L z_Bxj>_e40c<&xqo**5 zTz%O-^lI!O!u?P*oKbtMBmWqZ-J8_uBU}4A7eA$r`53fuLGW6#OdrrHX%&Mx3~?@H zn}#U?V&)XXUS-Q&wzBJcC$DE_bGRM&5f1Fst&^L?A$ zSXi&FViLpa5q%A*qmHM4Ok1e>j$kBf$)M}}hqVts{9>%r;{Tw$MlMW~y)C1AqKrig$$>$iuYF9mtO<)8?TM#^##zpBs!a{ z>lcb>J*QEESBOYBv|iK>)xUIbRk)Fv=h669G?+$oCCv#qf%aJNu7P%9aebxv={#4N z+_~UzA}v<_{${c`*KNYDT|1815MhP6Y@D>&8{Qw>f1}f9Id*=+Tx0##)7Y8|KiCR- zcrRU#^KS0R&U=)hPdT6tKWDw>!Y;yCA{$J@s?QUG0N%c1ACw?CcD@=ZG#SQoW8%sq zhG5?BL6!EH-NQR&o}U*l^ws%4L5j|YHBx*vNWGuvC?fg{BID=rfK~dSMc~jvLT)k4 zPEgas4vTt>zOD(!L@YArCbFk7jgO08A@6U5&DM}lBbvsW*76f|k^yrec}uS``e#nn z5!s+X-KBl$-r+ej?3@pWFwg*ag+eivJj{IHp=tF#v1NKWnxB%{#5p3r|~ijIZa^;hh}L(#ODFXc+ed zzRG5DxuxR{t}tJ%i!0M7I9AfOd44{>`og}W!&-jbg}UmTyLHxi73msD@u1+KKD=Eu z26!DrY%co>D9I_?zozShLY9Tcf9}BEt|$BF`z6o0c&Gn8%I{yf-<@DAXkDCoPHurc zQNLI4X8&XAhRg`X$W_G+a0MHO9!p@Y4O2wb)wyh#6T5+Rv=rQ!+V14g$ItiICkIxw zAkyO+Sqw+3>@-U6;nCiIDCMNsWj=Oy>|K6hIl7lREiQhG?xD#`ndgpVdcx%%aBz@V zxg3q=0#Vi@-|yOn|IL@ifQ}++PZ)5ta9_Fe=PN|d68`af&!`}NUkIgHN&YN^2*kOFFp{sX?@@-A-gi<$9prcj~ivTjGitAG;A|DnHSXz$y+ZqZHq_ zv2*%EE4;mCoM|u@JUmH*${paqIC{Q2jmQ?vxjQ5Wxpv3jbbK|sY92~uC@zM%R$nzn z4^L5+80p!aS5BY6R8aLK(*lJr9sj?UKyo`ro>QtaA$xA70|-`t5Z=7Ux8N$lF%SH-ZOE?cZY>Ux zuP1g7i^u8451j{0gXFVI^H$aGPg{9Ky5X0B<$8k8#}`1`gX1g{QvO|Ht%{#T!{R(w z(2yXm_E#+$MP1WN`nz%TYd%j+QCld!kgv1xdA4NMc9kvsZ!7(l`iboy(ztT+|7Vpu}s*%nkT-4WInU-4y|hc{tBfF6Lfwf zZ*VreH~fXzLH`x^Hm2hKF`1pIjz~#aD96HAeZ{pd{kAZ2D?Y847tw3ulP#@bw$=;go zSZsoCA9Cqxa^YPmv+!1JaI|5-+eECp6-)1;?L%_a0*dB3P4BYS&W6Q zhU4eh*?;@{5BqFA6vZIE1mXF(EJJld$W@rX@dvRSXYEh1!Rg$=kL=!e$*f?xs`8>J zsV2>f4zB1~I49%k?H%WdPV{v(+(V5o%YzB!lV#)-rJ%QGnDH&d zexK4HvAh12oi`NjaPQcC2LUWW;;)BwE~eFVewKv8isgW=k~f9bLb_h(K)nCs=#zh3 z5&XT+f0>Lc|-mjBX|*s0<;&{Fm0d;{dLVp z?*5#g5YG{Lgq+1>%Kmr@Nt7%^z)Kpr3S~0O&iOIznCyFb>_5UeU%D4*Hd{$lL(Z@J z4{dOi47sO7B$!d2-ZHXb!17=#{Rx)-#SWVXugq6}-gkel`t82|DoNk9N3D098!%%v zLt!7lbDWA?v^6=9vG z9YTe|Tk$a8_M-d7(jV3vc9%pw9W-SZ0djD7+P1aqH(70L78RlJ+HmeS=f1}-dHz(t zI3n@VXol?f6@KM!%%6by*AHUEZ~YJ0MQ?lHQu8Db=zH9%`dVw(=0q?%>sIm58+t_2 zcxlq1ug<UK(J9)Zc}`Cne3VW@ zCcqQ

zgL?~?b~p4(nvhg2!f$287EE*Uo1XRYZlTS$a|sXrij=Hi0P+$0b|D&Jh5 z&l~(clN|pl&3s2kENJno!|p4bKES_1LD2`s4$SF56YbzQl5umwiAlQFrY-N7J z?}F=Te4{<~5DzmwhsG&z+rS2*e zu{(a8wgJnPII0Jp=8Vi9n)u@Q81bH-7jT%W43{bnpT(J% z-z<71Wfi1!!(3i*{wkf|2&YAP|Av2At9H3aB6I;qUOq)TkG}ko9Iy7LFOy@_9Mk>q zFnF*jB~Aen64Z-xxhq)jp_j7vd!ta9DSOBfn|By9d)tsK*pY*Tj;|WGG6kH4;bVoN zhC_ekZ;zP1yYL?4+V}^YbyJKCTk$tij0_m1@xDK$b1U0BWOBSOY{KY65S<&W`07htBp+vjH!;A?pUweZ2Scew-;sFvP8MyoIWEub4k2Bh!( zyZ83y)@8?kR(RU@7Wv8W%hE&`^`K#&?nt#5Hdv)iR!TmG#=9KJ4zsG#vXe$^6WVi% z-rI0{!JXc`9did~MX0cu@yU!@QyFKsNTZ`%{c7;MFSAN^b1v!2CrxiQpD(dS6-T^> z9p?o6Vi>#ya5kGmyJwN<@jqXR*iL|kIE!k)8EzX0es-~h88cSKkJIAbwmqJ|?1a0b zHHycd+>n=UvL=GBi0<3dgE4U-NS!zOFq1A4NqF9(318odmuZD_ayKNIP0Sky-cctR)GkpmY+~nd43P?i=8Q& z7(LnQRICP50vw0zu~Sb`Ft*XSpn#u=k|V47B1_MVyA&8+R!{57eMXo5F!A@rdw()p@qi>Ud`N1=y|M=HztI1|F%EC@c-4w zI{APLyLZ(@4DAb;=do*`s0~V4y*r{4a=KSXy z>54sIpJJ^ltI6L*N12;WmaERB6t)SulNute==diYOXB(xwn#HwaIfBt4>4FFguqMW ztx0lqQx^7TYtsJ0$8_K0dmPSa;?C?{)#k%ne!6b78%G^qf%dq&DmVY1H?qdx8hfVu zPB9V=LPZo`k#TSO41_91UeAe<3Hpx1p31*s*Z@R5Z+1Mr--@0&R`_c$4H?{TU)8zL z3O6^2ziY?Xv2lF5fuzNhM;rO-*v9jy_MV?kl(>=ai=D5M!M0u zyI9ZYJb>*iE;sZ`$OgWEIeml#K>6(*7(5AgQrw{j$zb%z@xDd-$IfgY=m+ROXjR~< zg&$$V`&H>tdFTb6g#+5;exulnL=-Y4y@|xOHbLgyh|Rod6%{-VEwZfF+s4W#`)M`j z1Ptd1$|L%7V1$-geeMZSjQy8Ccedbcb?RXa`~BtlL@KLQ@$aiWp6glA?HobZLbJl? zy?c}mm!4Xx2g7D$PAKE_6<8p^ik#Uye81~apGw<+<93E45QR#m#p}^Fj^G%BUTC2F z{W_qN-FrQTXi5e2G#Gt}4v33)4RDJ7H9siT*D6|ZUu{n?=XI8Y`;2R-1F!}|&2 z>!AIj$D%y^;f~AnEO;(_tKRPMIitQuUvK$e!-FsP#RYT;Qxj8rFb=CC;W5n7k4gXg zd#mVPM(B!LLA1jauQ6`z>>yI~0tu*$BOY`I{S}AcvIN2zv-h}T9`E6NsVe){tNm?7 zhZ?&xg#7jpq0lPwUC0RI5|~l8305qHGK?6@WrEqj{wsuzlVZM#rBlN4bB?>`5t7xI zxlr4dT>78jjfzQ059wn+KBQgb3wlcDgY-$5^LYg)VVEc^l1drjX<3ChZ-Yk1RRv** zNv&J-hTa9VzyY>+$!qqr0D;R(l-#0Z6{GKjTXu z@*eqJ+?nsYCFSgTYP4oe6nG9GK@GpTHnIk<7tQ1*331AgA)Bl(kA)1rm_S+QLy~{7 z+*XTd(_Z|m^&^h$3g7siRS?Nm>>N~Lo2zxCD@{3p&MD~;&H|Uezh2~G#dGoy~oe`yio7&w% z72vLlKG4b#yKlUk;52=vIp|!hZ`716bbnY&YVMH+?G8 z6a6bbFBytfxB=s5FLmy6?9a4%aTT3)C?5CGhYJooxNj0Drkr_@C+4K`)Q-m|oaJiW zLi>0-0(-PI?;nxe@0p)H`}C#~F&M^-*|cB0w`{};a0%;>rDh)JW!0QQX+&GfUy7hOhOvwQ39ZfqVJ^sftGgCjWY8F4J6-!u2o* zk)RmxTAt5uWS++Ldcdf`{n@SSrV$30Plv^upDlYc#JIj!f;>k6-g-UC_5S+YS@)hi zu6Qkr^VT&DZ&ES%_F^97&wh0SVgqF(G#IPbpK4BO0-L#DMMYA486f03gORP{a4)q2sIQyaU(9jXpIc*h zyH_0r_E@yg0gxC0@Rv2?{PY@nNGBbbC?8hsN!qV3Vcc-1GGFoaw+&+4GE#F&Dk%Ku zDyFPbr}|U>vp0WEDopHS`5|)ej^GnWfefBXA6opW_rf;Th?1q&!%61-1d`uBHjo*J zA6WtPOR?8QGf^?Tl>1RoMCqP`ni`8gjeJZ4)CdsO-w7b-z$7IxvX_l0z}JBklRz0% z>}kUWcVawKrslf5Befs>Pb7fH-{Z@Gwi#zWc20(8$Lr_68XjXRf()4RPbUuKB+Gb+ z@inJ35f~H3GY6`idJLC9x^!?TC+I|1GXt6Q47(HYL@o7Z(jLujN3coA?L8Et9D@RU zlY>Ww9}!+=G)lD1GvTT2!FjI%*ZyhyknOAQmI4?i>;MivMxQ6xAfRkzU)3>3<8)(< z6TnOTk-9!zPe`fP8k=LE(%$Bc#5L2xD|af3P73&5`;bmwBb^u73k+1W(0VDqvb@6yqS!JoKnoFrk0hUokD%vb>0?9YtQU!Qb45{1rO6 zV%S?#(~y~)7E{|RrU@)x`D1nCryc;z@3><_B`$_=M;Lq9$TO2iIQ9~^>;*PLf;XA1 z)(DK1e}f(y!nZUSAfoKi)YVKsHkapS_tO>F5vi2869rfB+NH=;1P!cOM_~*V3BdTsX20`h3I`6`tMD23KwsD#N*~!;ls1OCART2gcX!(F%`CMWOifsjS|d- z?7k0~7?WpqWN#OI{J-zeEIa-7`k}0YJ!)sOz|m8ZAiLsM=)cu_GXx}JZs?Q5;z#tU zmqG(t2@EoKX403yZJ$6Fz}h z-H&D{| z)xQsGG@Qty>FgAW3bYQIAMREDd_p4q7+jleu5nZgAR`d8i+eYT$sw?PHJK8iPDC92 zrMn>8*0g~6X!t|U@ZLygeI$0~v?9Zh6ugtTlXb3XIOM)L;$e0) z08~j&=K{YkzC|VugN!6Iq^z&!zRk;z+N24W|ytUUV za;nB3{Gh_*S9^GL=$QRDS%NGQmPGI1$e6inHu(tG<3s2eFZWZfSG;b6dBG%Vdr!j< z?Bw(1c+ELBZ0^~%$N#CWD&94n+3dNWi4TBFb=wwPVtlyQEVLWj9*}l_@{RHQhHy?h zf`t~ph3Xjr&{e7HnV08+zHlMa6eDUE@J5eqTDC`~FqQ|pb?fW51p{oBb0rB`Mdd+L z_D}Qr$NN)$-f-Q*`)T(%dBw12Aa03Kkt(nKqy3Vm!desvTRQ)Jx&bq&red3heZ5fJ z2GK8CfxV9)ZVr~IQ#mfli|WDa&G=2B=@(IiYSvSl>^|3M<5O0Q1Ay*-_o!sw1UcPZ z#Fa=KA*lEaOcV+xKku9A{`cLfXt`lQLVt^Q2h1uC;ZO7KGUDCw-9mq$&^~gGdzrYU zGe2R2If{!9A~&X9!Oq3X8Pc+#jd7NiM4GfG11E8k7=i#AGxl8KiK|)%88+6Pu*Tl) zi5(1QEn0=qfi96#Jb&?Ooyr_lQa<#0uFT(ejf~(mCRz8E3s;IeR|4R%V4voSutsV= zRe?3d*u)9te$qnvT5PnqBXS9UWFKDAC`Sf?e7qYbR=n!vQO% zOT2>Ne1t0Sxk#TyG^6%Z`oP2qo_oUegUGyH2&I z-Js=Tu0odK8RATo0Or>tmCe$Zxv9cVUKV3fp@MM2tDZnx_$i%Lz(3OgE^*|LhzK~d z3ziVi@#CCq{v{pB>KoH2+1tZVUXKZsbdEfX;v>2nX92&+l`|U}r~CI7&)kPIOFX)) zA^$gn29qDUs;ecW*TuSCeIH{bRRVA7nm*GfWl5j5dU|i`ecE%6JFz53+Qcy#OW}!l zLj^Vy?60O$dW2$uKE1w2KyIOJj^0G>8{}45bSk80t*OEtKG<>W9V7gxA7bHhwW>8Z z0l}m}ax2b;q6Cz^y(|b0KJk794B~NX$qU0x5?K1S$F>CI38Adk&D9nT$rNwbQK(*L z3Os{%tnQh~W3we#q60Jzt80o^ygLKQ@scpdIk)`1m{OPW;M$?D`uM}Yf2-ESNYZi* zcJJ<~^Q$NrrF&SF^A*OMQk24~Hy{M?O z_DRHgJy3k;#hlCVyAdSz0L~`DHT8F#M$Unr>ihH!vSyc?V{>=E=REzZWOlvCFLmUu zH>eXCem>;qUr(gtekx!d5-d*Yaw>?ouHR0JzT#YL)@KZ3+`Z%5BnH4haf6X_%pxu1 zEf=mCiXSdfPz_)e z(#!)pNcNXLp5PEAH*0u%SsY&A-T324{zea29q~FMd9fg@L2@E;=(%*sIq{cR>xX~+ zok~u*37?tnf6h4WtmF=c*W`)mFYXo-@L)}^1DpZSxF8h5=SzO9W@!z%M&`h-8=j%x zty&<)UBWT$*`I`HDR8BmG0ffxp1qG=JVqCkgxcs&S;KsBbf=Z$w3}@#khgcjEVhSq zYj@Rhq$n>V64`i$Vmo2}K_0SnIoA_E*=*uqUP${i4#8B7A3%b0CAlrxwYQEQeL8%Y z+Tg|4-B=O8T2*dB%iX14!@C+L|6R<+T(FZK)GGbU7-D@r^*LSAIkr+wnOE~l_yFU8 z@I)Ke?m7nv21N-?hYY%G7UeETcngl{5nlD(iV4l_YN^h+i|xx;sTh5jijBc{hMREp zpZair<(W;vnlTY>E#*xj8S%UB&fk#)K?eoE7|k=dWCg+w^Pd)?-It+@9q|( zKE432^R>?O$xJoXe~v`l*{+Q)_Iqp?;iJCLc;@YJ zsQD=%E!cRm=maZ%BN^Aa7U^H|P9xFB73H<^0(-jR8&s+&2O-Hg`28Us|F{%IUAEE* zTgr`59uGm3HoB#oGlhZdXye2HoA!&3&cJ05%t1iu`0VbHZ%>=#@o57pM!|4&T46Ys z{@L1qa3)O@w^yU|CE=LlO*tok%YR_z=ABh=9* zS^4Wt(zM)XAs?44UGsEmUhR}cx%u9uoAXnXPVJP_>l00#69w;w%W5t*5D9PsPw>Q* zsQb`I=`v7Y69TGone!{(8JoR9k2!~Ojd zjrOww?P~EhDqQG3tw$amoH3YUE%glU!z7Q8p<%nJzzWa zu`o-bZMlzPTefrPKrk+EjZMVuG`#isaK;j91?Rb*xL zke(iBu7^YG74yP(U=_^Ese~Q+bIqawowZ5pw(vqAp8j5qp1?D0DVuL?mJnaP_XjjF z4&NV(YV=;euvd@51lB3!__aUxD&WNttKqO9BI@-!>`O-RXh9WfJE-0wqIBZSwqp8u z+u@Z;4%o@`@ge`q_wXZw?hMA(7t8(KRHGcdVDn=oNEzC*!NyH+KU-y&&-lrNbV#Hh z9Gb3bSHR6@OtlVl-3ehIs!`vE<6Ow_X2;f?Oo_WdWHs;)_NSG@&~k8?}|3%(DNpI*u3g_ zuM6DW*-poXuQb8%oz_ng3DI!g2tj)e`AFjT$WCc@`h$Zv*2TS|(f#$r`DnWR;(Rdh zQ`k)eTt()K#40~ck3#cVV)A7&uwlFKI=s>Cn8s(VKh`3B@W-PKO&EI;aPxjnRD7G< zvQN8lHn|trvBGCgt$igA1ufBNqB`$J#`-CBFt&Yd63CD)-a+y1QIo7$aK`RH@=KEn zZ@`~47npRIBN6(59ISzZ1Bty=&3rJLt3b5XW8buJE-GMRCh!bVK8+IgV$&}vSlHJ0zye|*+Ef6- zp~9Dsgg^E*zyyWl#>~0Wi`&m0;^1EMcWHd7d!wGW@-wb|#S$A8pY~Nfe_pF(9L@d8 z=smg(IK28>1=`>}H~alwCXs3`b5?=B^KE$6z`dTPb`8n>0-7datOPRh^Cc(A#TQ8P zmIfUlKl@qy%Pg(QvBfG1SYwG_G9^B=8=CmS#Qh4B)T6ms`Y5%F?qQ3Ai2hmoc7nZ) zU8shG)b$v3aVUn*Z~Og@{z~A=sWkGDES4)Z^UcS0TK_r&^20YY=2|Jo^;q^p%D~sA zmb{tJkxYDmh?wa((mGYhmm+>Eg|_|M;_y|yRAcUd`N%tiL=_y{xI5rJ-|wEPfqV-1 zI+nw<-7!ayMMJK9RJQ76xNag;hqc=eVp*vWDPq0*?nkAwMeLzP)cmM9M@1tQ+#@hv zd~6C}xu8#`pP>k!hz8_hO9;1S4?vpp>0^INjXB_BPWG_y``SBB2l^Ut>j4eK=f|Ep z9Qnzfa>PDv70M1>Y>!BDJH9axJu=Hq0*6sQsPJ}`=C4SJe+HkH&Li~6 zA2YnL4#`gbz^2zXyj*ylWUw~7`!o)$yB^h7zP}vL7?O?d#Z=v zG$SLLP__lwr9Fh4`DSu9|JAGD!=WMog0V=F2UDSm#(ov~=xM4|?9z9nBTv^g&RllA z|425Yz{|alk>_Imk>hHHa(?7C8{)^t^U}^@itnN*it+b7{4#G2#WRSiCMLc(s<;oiK5&W(w9iX&Lt1ZBu^Zf_ec@KpBI``D}Y$oP$jVg8(JWR6nCxoaz z{pMW#yVXWSk5`r6RT4WsA&tg+@a%Ity~ey?Jj*tR_VD0bh3ve+-2*KruB$s5eae5| z4bNCuysz7IrqE@i8a0^A12aM{pUA}Xb4^Ze=2lyX8L=d07k}Y*riQcWgs%4!ZZyLo zY~#0GB&Xees&$V^!2SC|Gj@CAj^IybN{;YCcow7g9US7v^sAqLM1w@Z9O7?xU?>1_ z3fB~~fIGUAdh=QsZ6@&?8#O@!gu|=otdMXQxe*3*w%LJ0b?pGBkiO5#qbg~EFigMq zSzgQl^zGs&`Sj7d*}X@v zF9WvHu7@Y}Ys?7a@~`8L%0jh|?ORN&jFkeyl?48)Co6kEjGkwhQUXn2r58mz^$oz- zJ*;8j|DO@xNU`E`mow#3#q7N6Z^oNVoBO4$L9u=a&{}W5Hska7N9-6>xqj2&m1u3o zh*ThKQe<<4`5b|!*MM^X(SM5}g-DKcdo=j=7b$h31f=FdyAdAAygr_6HZe|C(CE-i z%HA&=@(!*SESlSUy97ks78{p-xL=;FZ+YFvnC2L=G227Vb!V>gOBZ54J>bp|#P?jd z%kTK~8Ig34zT?P~hI6cu*PijO^Azt<-z+oiQoiquLpkXo5rp|1a0s|+&rj*H($D|P z17Pi@n|_YFW4JGQ<<{KMdWn*Xqkzxsc`SIx9pCT=T8af{CtPyjo&XWI>s``m+JGA_Lv9ENgS&cnBF|6?^m z8nSXWkjs2N@66>i`+=f9={uu~K)-Z2tkHN$@(YFJn%582f}Qj?%9&=n-ZKw>67SSt zj~C+-wo4uUOZCklJYF2W-eY##T<*Zk^AZv0E0||8BSzFXYHqDtxx{xiN}&7MY98ll z`Lkb#t{1@Yt%J6(uV{X##R~076MwyS!%o%M2imSYfh)?%N=r*B4I{ zSN#2vY!u04pKJ3LlKE&{szZ&(AY0BRbN(IA0ExML1f$9md|I;fR=H|RCjf6J;?h7a$Ke*e`Yk7S_8SH7^ zcuMSchc;v64?Jp*iHLz`NV9V=X$gdtt(O}llopGB_cok1(lh@RY&@hN-ur;b=aWJPDI{BZw+f7X2Q$K3$VwD(-Yqxc&KB(iy3ytB7tt}? z^nQ#j@x8+oti(*C!B-DIXAI8b^Ioh=1BrR+if8}N0l+VVI}^XNzd* z(XlX<_(EioB)9M72dlf)ugg8Z46nyov{rfZ_yfoH=e$9}Ov27K*aM;b%ZwurHnGT( z`?8_%T5}wnttYDocs;~-`LiJ}_~rH#jmx!C;gKPBD-TGFH?U9Jrk=G$3#VKjqYmAEy8ttg7FoYK+m} zdnxA1rz3wNn1$^mjkHIT(~cj>1`+IdszVYo#3MC{FSFLb(BAc!Qwe z+5Kkj67%GV83Z0&w>| zPfxwVxG06iD;xIFiIUu96kpPWI2#{HjLCq|^3Kjj{6j))N6Pl`OK}5_{g&IV2D5tC zi^a~ijqmbhx2MGkAsS0eu7^g?1=i$(e0;68yJU_ebGUWSZ? z*X&$@^?9|Zy{g(n?+02{{IuB{v1DfFkn zAe#MQZ_$KbOMXCT;|DvxjO-oeJ*4DGiRJ_0zIB2lwfVAbzrVih@pq9WiAybzN8L9H z6}C8vX_ZF4JULf;-_#}`+f%vt3!$iJk$IK$Q{v`uuZ@^eew>@b6(rpV#Q% z#Mdq5;Yt`msHpAoxQnp^9nizLP4pSpZvs28-274jN0t|0I_ZJ;KS{!^mm$M5ijtE` zkL50`$VBTuJ-HGS>t?u{D!=t_K8!_$$lqb)HGw@^UYO{p&v?8H8Y7cz`4~*`G?3XD zJPas_#_>Wy;BJ}kfXADIz2#)BFd%nh7N_LStlb6@i6rTN{>j5F0jY@kVV9T}Wx6N6 zgMArPY&B%4s9Tloit78UaD_5Q><@FSB)&*1wM}(>B<4~t0Jucl>tX568F{Hu5&Y?V za?k-Pi4<{?T<>~3d{_W6-cYjs#DQ8aF@t$>r6+czUOq&WNah8PN_+Q2uI7-@C|bHW zh15G?5!CH!lHc}$)(>(eI8SGPM#u6Z$041G1-EmA# z{PdM;kL-Mgw7I}fmB2LeOy)-L-8Cv`W}@>m62!pd!_M)C*Ad*L*Nf6FefL`#>~NZC z*^pZZBch)3jZ!kq;8$^lD%a~__>w<*t|t(#(nn5(pAR$>Z00m^7e1W$kj_GF!llLX zjC&@JL(PMTAj6m!HPUtGe!oAOcBojn%cG4>D0e@cw>Z8+sPhw3y%d(8kGYS-3fC^t zXHhC1mZRSK*X1NxR1=+7do;qb!5fCTSks~BcwH!c-u1^5dCJD_F>!Z})HB$F_j?Uz zT;!Vrg~z`@^@ke)8x>sQ=M}1xj-APQP0^b32@h?x% zGO&~OQfrP69W0zN8J_VjW4Q%49&nk=a*RLWld`EV+o$!U%Pdg<(PVz7vM9dT3 z0Ky?taoLCB%ae&JTB+0eEAa*kKh13#Gv(;XJ-gTxz8-Q5{pUgxsTa)G(}@} z>PS3%??L3{JA%U5ndWuQoY#1JcB%JMCEDSuNXwl?1 z(F@b!92CZ;#D0N3X>7ymTHL2o(3 zY?g^Zfc9^xmFdniq4jRgkzefj%tH@p`*cCyPG$t6RVIXL0`JtG07b95)j!?*dKx7k^UZIj0cnE0H#Tz@6BP zJ!UO`8J{@K-@>meLIv3FxkYE-8c~^}CwhTLJD+j@sRBa8MxnLIqZ@dKEk+L;61)t{ z4|IpE(&rfC;mF-kT0g^ z?tMW@^JcPM1iy>tL`wFtIcbQ7T8mSwC-Qe(`H6q>Jh`_k>`>bo-@`LW7UhvDyubW^ zB73FHBGGqA+CPRQk#Lmzmnk8zn{>a-UWX*%qGEuSEx_=j#=B64f@AK%#91=JyN*XD z^jho0sr+p9JEZU36J9W0?C%D??+zV5kKbUpisOn+^*8G8I~6qmS)3@hy<*$6C}hqDPsx6gNkcQ$lJ63)%M028nYVSd+lm? zw!tus`S&}8=`;#_+~p!hBIL&kM`ZK%?|ln^8_3XJt;a=Ajq~4q8SRgvhYY!oM};gS zhr!v6jpeO4fA$4<8R#)8a3>Ud)4P}8o)d0_L0n|pn}oS2=sC+C!W+#@LS-As#Hh^x zjqeoXUVqZ$*cX)q-R~n3PROaUrI3p4$XMr6^t@I0n{!sn_2@3>_`3iEyPcez4?|l2 zEfccsRPMLYj5Q3NjpOTswU+&Skm(VPvN$(GVReeuqu1?i`NvM>G8IqV7@d^h-M$&c6c;h8C7!niK)O>l&NWI1OiE)DL;%M>qbE1S6t`p#3r2T%R7 zr-@zv`gwTyq->&54QMu_S>sm-!6Q>eQ?J6%Nj{4a6W>Py)Vd=LZGaHce zM(oQxAgNLI{d?wK5P^pUgJzh-UOMh!tTgZkS_N3ijfi8-6$>vBa#vaFw0R)%uFUr6%adBVr~dhyv6=!(@RB%c*T!Mujo@QMxWO8?Xf z+hH{;V9;DLm4|Rh=)u~9h*g2JuQrV7dcRluh$dI-%#$Irt6?C~z`Nt7yo|N?8Sj)c zc^Ie7KP&F4%?a`pi7WJ>Qkv<9Nn` z&hBfDvs%LA$@3qcu-#%N!i2r9f>9Wp{7p8^X?B1-dpjwJfI2)~=oGK%^f{bmmcL-9 zc_Mxn#3PUg9Zpnl(^`QuCziE1)rFH9<>XP!vB3vlj=X;!h5SB!gs5(qh#))6DpEyg z0mUj7apJMGgU`2QmwnSd2?O%n9I=V=_PoC>K!*8_ewIAJd(+w4vHndq08c%ykZol9 zX%ER3VmXk!=eDZ#m?tu4+9dK%p(KSg>Sw&pnqjwp`@_^ImpBlsK5t@WbgK?qX$u`J=LhKlt7i zUEtg~SM5wdHCyS(lDEebzYWL_+rLQH63`iz_WFLjN%s9=pqTy3veM&QkqPbe4cS1| zwcP$;TyrL_ebXXHXHhx(rm8qB>Z2!+k5wi$8iAAqXO_8R0l5*uz2=i8fLW&DS0)D5 z)eFMH1B-jBk2g+__LH;MC<~h$KVW~iPkQ-k#j8UGGG^fS-I=#!t=f|uaYG8wyndb3 zMJ9;=H_@J{H^F`$?HF^k#TRGEe>=G*WbNc@XtybZkYj=&bv0ImBUTNxWk8x|PxsI( zz=TL#1UOrDyPsdtAXztp`Y=Lfc0!~HO_pD*%I)Z*(3HoU@<3$L-6G#4Q8&|3&LeB% z9e71|e&U%I38U^~hHoEGl^UblpWiLH8+85yhF^$)7%ayi+>BJvB+n z%8`7Wt;JxM%EIk!dj|+xPXSvx7{4YLJR4rI;({Cr^p1LZo}iDJK5Qh}B#+P#B7;uk zw8t|kd*=7JA?G5V7a0VzPe-vb2%M9ym*H|Q47Ih?+i>NbM<-y`RgTzqv@f;eZ+N8< zykrvoU2}vmMfN7&a6Q~lGRZ941P;gvmc(XqV8@c5UO#rc*8(R0z+H5jcv)dYQ0^I# zT&Lj0-r#0RN1di1kX>x`wX0QFrYF;g4KGk|Z%HQmt=OPuaIuR1nY8itZn9Asw@=h= zJd1-srZ=D^ymo+x6nU3Ug6vTE>5f{{w{`#R;Dh0u3{$w%=i;vxF=c?E6F6hWZq23C zf`!{mds&5L7U7fujdm~6geQjqhgx+8a#YWtJE)8Z76~G&z)BIpd^3+y0JWJoKtaW~TzwG*)zcUM9wc_jYK;rr2y;F4~PiN3ID$FH>= z3`mgfyN_z2tb>l=DhDKFBP`wpit4Nwo7(l#_?K8*z+|T;Ac5=&b0JlGzBjCWG~CPM zuG~Swv?sa&-W0?VyGQ>%An0$^7wwl>8C0>uFg8D_MLa#dqc(BsA9uqK2P1&D?*vZU zud2xC8i9m9=gjZz)3bsB`bN~cXKbST#@Ln4$5FzGyC;6X2Z`wUZthf%!PDo9bcAP; z9|DvEDq&y^;c&O816Tmy$noFoZSbu3SwSS`+fQe`5c||2-WUxGC)T-y!%hTowK~Ea zd&X1lOVu=cAn-qbej~XmtLig5J*)s0Nh8pz@4=o_f;vqW! zvVzy}NUB4!Q55%sME)qLD(g(%O{|xvySJ|E6a2uj_{(}Ot5>S`44ZC!yS&p+7`T=9 zSW=%j7~l2t6D$CRd+%?jgbIl-GfRE3IWQgYd*vO-zRvHnv=v$cC(`Bo!Wkcktdb6d z@gU4zc~)nXyG7t}+= z=NuLwr``JUZHS%*P5-S?idD{-gNh77{#y8ls2WP;^*u+CU5{#C#DI96PhW+LPNj$# z9iY(L9JJ}n!>VZ5J$A{vr4JPRp493jq52H&KAqi2Ocf@r1^c_=(|t2_Twpt!)}wFL zP{V$(7Xf<<=~V!HSfY=HZ229JqN%ry&AAzEr5=#5{o-wOc(;)VuoTZbQ)2D}%q5?Q zDyjRL?{QpWc^%+Hp_2O6zT`_;40cuhI&m+<#1+$(E{G z7DYdZ2DM^SL_jG8DSLoQAvLJL*S{4vJK4;UneW{jp>WRLYt4z|xKKhO+q@A%sf+T$ zI;1?Slo}DZ$Xe=5y2$QCB1R}8n0^+6zpZZ$@@T@DWrc49_CXo(Nw=uS&joiuA)$#S&ToyE@#Qkyy?sJh$rpPv4eMU#R0unu%|K=BmdYS;_!@cJYzSkAG z)H(*533#^caXuG^ns!lJ!wHhvdCV4zmSBn)cd2-Ss&G`|)K(rwQL^?dR=T{5fa_u8fXK2jO6x)AZ? zOKl<#-!H1=K5(}IfYY7=p2+xRkB>^4s(bq9oUBo_{`MlZikNX8>TrnZKK{#&pN$BB zl3{=voqSLD9s1~(js$1Hsua`6Y+w~AboC?n>s_u|r^V3{F}RPYU%s`!NV#~6&?0jA3Ngf zVPNzDhGE|W19{=^e$^3pK0pImy?Yj!sW0|Och^0B!h{3kw`{>Owb1(Id*sPJFT(tL zC*&bF^u$iqgQmf5(oYSgmsW30uzwJ z4Ew4EvEO7!3x2Tdsp8i2IQDPCyahI1PY4&;(#ZkKjs2GQ14jhQyU|Ibxoeg|ep|u# z88c>T-MrK@yDfIoBJ0M4Zo1PBGW8np#NnQ9gz2`u+lz}a>GD`CboFzmsns`Mj@|Os zk^KN#IOtd~^d;+-PyP~Mt6M*{`HP@>^}#0{MRJq_pGM<1#uE}FOXGK%PJ+1!x&rwV z(fRnGwt?B=Q+m+cd7Qg}B;RlPOg^q)Yonu$Q#kKveC>NIK8eWrC1IeRfdt)tMu_L{ zFJbR6V7`L4KVpf5JG^)L3@Spd^kN$nMr+}N(!!U}7dHBtJ&F^D{FHw`p^=>U@cy8W z3VKx=B7erp>9+?{?@jE(vU_^pY)gy$dDVS3y-Xao?|PZa`yAy0#%ng}2FVx}a~Z~y zWl}>)3Ae*iqbyt{aPVEHu(;M&|8qE=zam=|y*XJ~y~lt@Kazmy{;h=hx8&ydS*_d) zu-+}+6&jz(w1-Ey$0~ieabv&xT#uj4j8H8+BNL4hldSs6G=p$N-&16wPo>?L+leF^ z>PNrEtnh#R!%;bvJI=SGO)^Ebu`K&sNE!_`Av_J?Icc4RS7E1q#($qDClPiP*DGba zL^SfS2+-_~?urcCCF&=+@W-&;rvj2$`>Uoer;c-9>{6{PJ7HgEHUHTz%iwSt(GoG0<3ddU4)Qk!O-aT1y%-sT#*nP zr`t(9%x<-zCRn|=JF&Be)C(#-tOatA?eELF0I6F!HnDqt)0Lk;AZdZv5N^mjE!^Mz zH9}#N8n}arok##u7BXstX0p|UlZ!>omxIbIWutnu(gp9~`VAP&M#yWT2ox$8guC-) z$@HwyTvr}huc>vaT1;aQ5@0>A#!urioO+DfFEE3fN$)DRd z-+4V^P7;c1!d(6B0;#KmzQQ$oxPP%*}jrGfG|4@QjxB4+GFFe75fqb$LL| ze2Dq01f2uTkWvDZ9ObBCu97ih8+YDu!zaRLLyKCK{Um;uC$WF57#Mf2wkJ1ClmGRf z?oI4K!a6S79SQr?;tsgI0L7px*_p*oqrr7f^1u6tg00dGotv~!cM#;zzmW(;z*wd# zG3$JGDjwctLDgDzoL{AWYNLIQ!V>l&(83|jqJr3->{arjj`YSCN7A77QquyW=wO>E zp}YP=iefr}6@>!7*`Kh0>W1%^1R$OGKDH8Z;7Yrclx~YN@n{KwmGUQO=Ac@lgB%S> zh&HC+(>T4=KLvPgLj4Kb7tc;3DJkx|mhTCfW2d5WbjAeOPA%}DeEhJb5i#7iuc;h1*1$c??$^~))Tgm*|$J_(6E% zPDO9|ToeV+^&U8b3g3$IPJef%zJy-?m_B=61+%&`lQ&?oV5r26_WNZs`5lt5T{1pHvZNno@g!qSGkYce9y1O-wl7v5`y8LDHN+ho zE1#VQkYu_51=rB%M_KK9sYM{+=-W^v9q$5N#q_fou|2{B>$@-YcHIcXtpP zrMFM!084X6=nwn$&?KSC@NI_MyTx`)b%M}0VJb+4tonBUxhafc%;wMy}tv`i@4iB0~36OeSNJ%C% zQco0;+QUu48~m=g6Ket$;B~jX6h=3rQNCH-q~}G3Ea;-}@p;K096aCmRIty1-|#3K zcim4EgZr<3wH|`F#-60xlN`1u(@&Ee7a{$_vMljr4$o)R5Lx{UcGBhjWK=weM;AAy ziEj}xiKWL6<-IyozR_*ZRbLz6b}xn&<2&an0s|nAw9ht{zwD8Npc%Gw4OW|_6;M3J zZWyrHjm~$!TGKv~?k%iD+n!i7!_C<-=dr-kt@j+Yt)GslkY`?JX49MF{B~+&vqLa0 z+R4Wu_^HvvX`5oI3E#TQZafr=mLkt}2ZTTK_#nAN4^<%O%T*~7KfOE;AR45}?h;#6 z-w7pkOI2_pr}M8OTH;3IE56v~*<8TIA;~zE$<~@vzZQ%~UtemKh)2T&?Ah2Fr&fav z&$10y$wCMw1f-K&^O-tvkoD@e-pB*0LiF$XXp5cz+f-){0(nn=)c$a*WV}~zA!mJ0 z(iO6w?=J*AS=8&5KfFD1pU`jn!9l9$>=)Cn<@!?EBaMXC2V9105NvGx@;Yms20Z{k zE5tGbWqzN0fT^)9Ks;Kn1R?X!DU3h35d3v`R(zk%E)du(0D$xja0-MK9UTYuQ3E48 zl;A{)6&Di@_wYNND3t|tu^oKmJFa+Rg6oRl3wPg{BTLWU%;;cz`9WPqVFDtNzIw_C zL`tz&GpI=ib{XPq0$i#i;KU`veh}5-3UL*T{Gg+k^F7*aAz-6!OKp7VWG(ya@y6O- zTZ8xbQuky5R?{B+0gb;lrVDCNq;cwF3)CdAxy3*q&Dy1+M5TFF(zPn{O66Ki~uq3Bji)Z#>7l8z0dewm^$vt zRc9|?KG46w6Y}X9=?}hF74-;i>hHFRtZmNb#<3 zphIcE3IseR!{fXM9~f2D154cL-q`IapAD4Hc95L@iQMJmWf^~YHd|M6o0`<`VPwE% zBg+pNNvI$vr<#KbM87YDfw?9`)Y;OO6QC)$+kILAM*w0$0V3ZYml^lgB?w0 z_UM>W)R-by{(Mgy5%;3lGyWT~#^L7jD-^C_Ro&VHKc;SiI~wk`=F}qQBG2qGa&BR6 z>1Fc%z;6ghS>EC~a+{LDcEolIfk8tz{z-+GhYNC09~`Lz?rtLQzaz=>A0=xQu_JTx z*Lq(|=G-o@+@!$=X9M@>xEv=}I2B_5;N7wFh`!c%~!Rse1(a z3jxGbPj&yad^1v(t}n@KNz!uLs@IDL5uS-(CR4=f%Cy5gcfH)}(7sN7J0F=f1)> z5;l@Ndjf1&pF?`PKI$uYx?abPfe0d$76+0vkqz##dp^WvHby#(zo0V20F>`;u7{Gx z!>Ls9VJQsxod?PSUfCe;pHfvjgoQQ?SaE&<%Hgu|9r*y%(VJQ1Y>nNb#Sm#J*?R1KJz`zZ8LUwnDN0ms>7$FK6o&y+vFJXCkT$NMo$WgKt# zScfEuf!noQ`YO2g?7;_S1R35s+;@71vdg|(xjj|g-OwqxTF9Q$;RpDVsm@dICQroz&-Qp`-Dl0Ac9aCj*6MTqETl^NAwZrm zL9wq^JHu%11*IIik;H{PK18UTc&#yiDd>Q_WjxB$?JsviTsXshSZgb*5tXc3QB1yG;H@J`vIx!LZc1~mz^;U?Yib;GTW<|=f9&$hz?EyS# z%>)6vs9MXv^YVy)qM_^3kL8nwjUYD8?C#4uAM-T<k2o89b?o`-B}?ec5sPn1MP?SOVD{J}Q&#~ZcWzs{|c?1@2@t}_sXO?8D}t=BN2 zFTcu#syP;PF|<|o4^X$<8>$KMcpO6QUVb{NECHN!Aymz7)2n%20cZnpH=zSH{fI(b z$Rwd+{dK~;DL1Q4rO$W69x-h>D{ufv_}tkfIg4Pnk<9Hy54t=2iCXa zQRKlEALV}YwBxZ7(}+2XnZGeKRe!I5ky~16-!IYD*+`nMe3-6zk$Y9hbR>+>f?kPQEUTndWLD+HG9>W2f`8I2$$+ zs7DWjH5!M6Now$H+}*IH>V*YSU;vjHojDyY!uljbRXZRb^B1`|Z)7N99?zH>udN}1 z3d>|KSig?TRG)-9yhHlVsL10>Bt;W=i7x~0$4D+twP77|T*w_g?jGhO;TNL4AMQ4Y zZ??5K*98K-zj~i*!quV^S)ip|^5Mbhfan=9hES5T0*Dw)6B zl8L_7w)Gf5Clyx}yQZc0;EC;Dd0++$8>;aRpxeXI1pi#YtZfso)^)6DJyd4LziPqR z>Vi*ES%6aCay*fcJVix>fAAn};6xe(LJqOmhm$k8J5_Fk@l7L@- zxZJ!R{^c98uS*u<_m)YHX+@YQBEu-WRt0XVc`;uH?(w3CBSVz9Ce58c!|aD$!VbI4 z1=&v+X&|1of>3}I#sk-~#H_8iH6W!#cvcwk4v=b&W`I_#_$3;RK z%#$%Rcr4=2Di65Nhx)Xu*L#q>OCfTZll9g9G~zhZToM|EBHy9KQGJ(kJKRHX6EtLj z4ZnGxtDqjo=h-pYVTSDKB*@pHyA7psD#X{_I7Ui>X{>POetWn`F5NvwfE}3|T3Vw8 zcF?ib7_`W{6NrOITA(d?)P$HuUqYv61mRxRY^60I>Z;rSq8_sK~hvEKCn z+ddfBBCbgSWg{G`$hK;T;r@OMM!6H_IAb^d-Wtnd z)}ns*7eqkUa0Co;2Jyl{D$Tm}Zs|tEHwh=^An=tmWN{y*4;p;?_%2^hbKR*XI0ue5 z>CG2?v&R|pN`0c7Uw32vm=*9_$Lf{PZKLb!X=`F0-3sHr>|SAZoK#1{{d?aUfs0N= zjjq;oo!(SVow_&Hp~dA~qml|}()V6X+UB3NC^+m@ldJQ-@?LGWpauT=-KCfR!+XV_ zQz0kj@orjf1t+ROk1JCpSgc=hZI1&x^%ds(>1C<6uo<<_C*3_<#!*$rTdF54gjjt zS831x6x^djMb65F=Yt_5Hn~ka1$-CDY`!!UT&LvYqHZ?jD(`J0KJ^2&%=w%Qa z(=w&{{A3gSBy;D0Rm56gU;sAYAWfx;RommE5Q2|cwaBu8!$em5ZTGjY2&%rfu{CqB zq_Q-8ZxI7$&yDhP0gpZvzmIfQ*!*gY(f&IivWLovZAnPptR3V=$YIr&bw^WY+A*C$ zL^G*gKWIBiFiw}BupXNrABPXL0EkYCdEH-FCHZyHO9C>9XT~QG&Z*&I{&%&Vk8vw8 z*l>OM8u@|;xD|nWzl#j!SKIY&Ei+DUXfGsdZlJ$gaco3N~E zBOo?*NgD<;^`c;2xZgC$4qX2j6hBY}8hB{7w#lZ0p`()n{@4nf)E*~iMW6Q7(f>%v z)wf@rb3oP~uoCQEzJ$LfX<(Wi`fu>53CO$m&tPTykR8^7{*iC9WjjwDZvaJ+JFEQb zYt?QfABFj_|JP*)3KtBC6|U2gq|Yq zItb}39YUgf|V(xb_e?>D6jcp6UKbTSHqP_w3tre5L~iX9YMx0E`@AH=oyFDpvMmhN)g$1ysaClvcu(P@ z9fcian8?I015elZeO6{Dg2x7y*!93)#T^Bjdsklj0U3Ov`j( zzdfdt%Tg-9@lQ{Nk?9_}-+hF*Wui~a_aU`gj~Ta$gU5t`r5%Pdwd0?d!~a!WCKQYO zyJ@?)8I>=w8Ql-_dvsCs{w(r18bW_j5hB2H^bN~RgPtzLpnKCRhu)E5h?dIlIdIOm zk72ADZaj`iFocVGqdl^Xc=;o!M zT8t?BF)z$e5yyByZM(bWnYGr>IPT=*_W0SX@q1eB@2-)q_BxpISf+<@M-}1vhqB-4 zU~wJ4#DPNgCX1Jw-(O`?!wZaGG>1#u##-p--~N<4r}z6kkk%|gn&Y#ba;k@OJ1c%^ z^m@nI{oQIsUGf;F>C>U5WDABENuF^l=%0dR9F27E5;n9 zUT-XE?rHc106#vU+7r}SuyITWh;Gx0AX!sP*w`-@5 z_v0r%7sKUd>s_9z#W>(JxC=iz)>b3*XGfZdpmwot&tx2h7{y-(k#Swz?*>T??)i+v zl$FGain~(2+_uF4#x}63z)ZEH305i^%mMWdg3gouUpBYJ+;fK+^P%~vADo|uVEo;c z05UV|knqT$Y zkleI>Av9l+XSv(>L+rl$+YX-sx^j#qM>hs6!1Vn2J;11n`ureO;9@?LMB!g|EU*ec zQvq@j>ys(#9RtVV!RzmtB7}gQ-^ySgVaKSZGPY#m1>NaC?*Nwn1Q^~kcE;!Qn>_vT zdNdej&~bPk-y%u4^dHZoWslT`k?`MH+=|yL5X*?*H1OG%*4@WY|9txBwl*Z=#n;`w zLib4o?{ z@4A17KM#fL0-sGDl+p(7`9`aoKLG=Xl219b_NQ3Ad{gdzn-g{VVE%X!k{qGQj;I=H z{yvT(nEr%|yz=L+ZO2RN1Oy6KN&vY1oG}zYuV|nouRbve2`VcZ;#R(~pmcdcQ(R(y zM2n~;O}=Kjm&Z?5bMzv1w0L_d^j4Zzc0K0Tp6|~QZ%t5c{~j2)A@K}0KaN-x*cN<| z8#%h7*&BSp>2&H%5fvstpmGF(12Hafwk)5YWd6L|lfx)!bl|-|n1y*6mO2WmGVq}E z>@sI5K4PBhWeDfSWkNoTv7&wh6ipp4`Ec%FaX~lz*>+WLh?_3ma6J0sCv*qyt&+3Y zBGgJR*vA1!t%wQETKx6SO@BYjo4((nazfyqOm0R$#)p=Kw*)@K$K^$oKxEoaTp zDG{(OhL!$cea(p8p5v6lYOlyOnd~2@_4&u1#4JHwuKt#g;b zz-qVa;Ys+*k76x@^<^}7uAz*RzncYEy|*Si>95ouk9!bu56zAtaASm;Y*)3$(aA}U z8}|)bBe@2T$yt*e5Y^EeD+(zz#%pJN(?7ltU$^GGBWA(Rpm%7DDE>)|cdM7b-w^?Y?)-SNJ=e;%~NVp9%1tp@e2S)mX4(G+#4D?0li|d50V9%FRHO zDBZ9OJ^o`*KDev-lQ_i*F+H)$A+~^FO;IkuV8ZP|syV+8waLLOVG|@WNNPK>mA< zfn+m-OB-utHv~Ht+X&(&M&pGX+k-jDsZtx5gGMq2>PrOz)~dVkiza2_>Wk{{^%iOaz~lZ7Si%;;215o1 zp{EI5yYT3k<}F2@6L8~QQIyo5<65S!w*>{cK={DW@@iA`bw982)Mte=hwp80^)eQOj6Tp?o%*t>GuRDn|jv|@CR5fVlo=$ zC@Oq(Zi@nboFEA8l^0lGmPmKI(7|qDTzdm^L<=E=fPu#8a7}a}y zj>!PLU?t5(^xywHIBDtTc?1-kZL|9?^xAh0krKqe(4QQ=1$n@AAB6KL+mlcnzKV$Z zdnBwwL!pJ)gLB(vtViL#Q$LW~v#GWhmrI42H}uAdKfhl$@B9w6IfLOKK(}6J{+(5} z1c%Xg2T(${p@}y&H}E(Q)W5!sDz|)RKM4c|PmoIYqlDsV^eh$8cs3 z3q+pe8h&q5eK^sAOzAATiPbYcarB1@{+KE@Y7V7ovZrf?mrOZH*lmRpX@jg;hmLSg zTfAuoFmmUTbpQYP30cvv-hEW~9ny!z!}+z6ZipQ*!M*9=H1CskT`H=LluP^w8FJ&u zzH(=$!K@E?s*jq;gX#R{^8_;+#zKhNy9y#mrgK9%LezPQ*?X5zZ8F@k4a$Z7x=Fw> zNcS)G=7J$@PspM3vtrx}yQgnL7P&`Cn|7sa2zIc(VIVYvyb?a-Ta_%WzMOi+xr3Py z-!xj&fEfo5pk?Xbb}=2dR<1C6BfssfPb1DN+bNm1h{QW^x-@7o7v_;5U7KvzUy7Nt z*=d*yKUdj8zVwevz<{}o3mm#t$mg967px5JgjF-ce$O<^ATJ9~8&-4zsB*|Eliy7` zgYkr%wr;=q+p|$NoR)(-35qZSU}^9L31X^L4N-y_hYvL5*k`rdOmw2hTQu89KjDpA za}T|=z-Q>5@Hbw#t*yt`+DDVDA-m63j~!GIJf-oibQ!8 zJoRKmd&G&NxmpBqO@q=djzU-BC~o!Z8+l*s5t92*Tv&UV<&2uE5KZ|hBr_9R^zU#s2&S12&f$!2o9u%vDt+C& z$Is!W{?vW$iFhKixY!^|*2Ee>AV=iXgG-vM6Uo1DU-Uzh5 zY9~~GCqyCX;>-!U-6H~W?BYA++NuQcdWv-TzWsCwL#*;OoaHYNx;D&RiE02W@YPGd zBVd#;ers0fP|)Vsj9nx z=yx&p@xjm&G|^+gTsZUH$|DsD4+5|+j1sWmK=@QC7*$ z)90AFBBaenCB2@^&!G?Mqli1l8TwVkHxfxPj)KnqCiBHEo zFgq%gzC0{_^fge+_s;3M6EJx=q-6?Kk*XohgUv0I@8jk4>3Zi!&1AHXEx-BaE^`>0 zaoV%4C&2zWPxR&fSfu~kuPo1mR9(L#ReEc zmd}u6paBBW`JV1uVgZim4Os#J*P_1TMCq6YEcW&te9TmaM0a;f0$6|O$jSflFu;ez zo$IiogqarOI$+;|?0hD(c>iN=lbS2>@gz?cRQaN@NAJ%op%M+}boJ2}iN}V2R)UDT zZbyKs%`@?$U-dK~Zv7)Z2B9djngK9MYuZj_t4# zB>s1M3e0qL{s7CunFO6-@wy)uAcBF*%y*|N>&wVS z6%5K6p6de~2uzxxGf@}Ft`VuIVXq2;-d2w81X?dA9kn#^hZ_vcW5d8Rc)^TxyxHg; zSLk%`e_lJ{x1+D%u4A60A@^ft^FUnavYA40&T)c%03L>(BmkQ+T$*v0_zmu>7eWCn z|1T$oZeQ?WchzFd9Y-9y!dH|V20S#Q1+|S|?lp3!a(y5;@Fx>$*f6^w^{Bbr5=Bqx zgSP;(M2&fAv4n@zV?a!i9T8)!ewr=3%f|v?w&7JzjLz?8-mt)j2>@L&!2NCC%`xk* zA?g5DDUvUAKET^u4woADjYBFq2MkqNalz&NcY)7se?V6@NxH)eMeIwz@%_8rI$j~n z2Gp=`W#OunZ~{VSdsvxQyBR;+ChaVoDXSg*WN%=z$TFG0 zrM5i{{vhn+a>x0o%AFy@2&Qw9oqqZ&>U#pts!n+~hx217#rUTDrenFiyo$xzTTF+~ zAHzR(o7b40&tg;U<)(gO(5!>`_&t$xdDgnygF>mrZ{rrNMK2O?N>+h~L0k3?oin8& z!X}#cAVT14RTDp6$&=WA;BPRnWo;T?cb<^vHU6eW)xQ)GqO6gp1cYDS?~r*CYqX0Tl+)-MjH1!-xoWFgBg-#zu!hB>FxF* zF${dW-s=mNkxE=^ow@q$iSRekM?ycS~R#Sz^nGFUNe zNDymTFYqkc#=OLqeLP)v^ZU#yrtVx91{xGBFbYhAeTeC0KfSgXjO*$qbRXxf7tITu zNws|#eCBe2v?FIp-BYo`cn@^3FIn&VOu+8+{$jbSie&KPJ@8wYcgwthe4o^jq(x3;j1Q!kxzGZ!B^fPZD^a8+E@` zDMmf+j!Nx;EN!E9eufkL<>7+qr9R4K(xcR!^FZ?7qC*onk|((Fz5#cSxbqQ%DUa$9 zJpn6+8s=Z5F$rzNKYU<})W7ZIC4HR_pO%WJ!_i_0^tU})m6h9~8ao-C^)!FmOfSNk ziNLoi@GFh|kfDYA_a%&ruHg8xE`5aV$4VWygIOrrl~ojb4?~g#=J_|zuHCY(!{57O zdScJqa-~l&-s!l+>K@*}rTUHFXh~;p@n^VvWm5V(N89%gP+=SPeD3mOp7ja{yZ8u} z9lUReAFVj@$1Oz=iu;R{>AFf_7!Rl=-CfjG`uv$WTXTTatd~^Gg~6>xZS}xfN(FG= z9Y%;x+3>UV09~b(-WC7AkI=+p%(@n%l^y}CSk8`cKbx6!E-+n({$%Wq>DM}V?$F;c zubZG;Rs17Ra`EZOtdX`w6Rftg&8O32!$Q#s6AyW;hG%Y1fA8+48qS_DB$Uf=y|LES zKz|(5-imiVqV>?YW%;Lzt-I z9&_${MFoSGy#9t$iaA^uewRHyEszGn_rQx?9JQ^#WoZ?sd;edlp9aI{9u?SBP z{|qnlqvh^>%GtWRKuA1y%0>FiodgQYV~zC3l+wN~z8{w2*Ht*OH%XoQ1j|-9R~o$e ze!o2l@2W8L&HVHbS|oSwbH0vkk0p*{K?1JqyVC&1{ALsKKm}*;AGgAjo5x05JmXy0jx zii3WC-u6efyww7LUf+psHsVDj-p_<{L%vF(H{)A(+E?fK?L{+o!N_Xde%m?^f!L#C zc}q0v#oX}GT94a&Rd4USb1z6@3f|?3B;*~##tkCvWnSSMz$Lv`_^yhEKxg9Vuit_G z!PYfnE<50zoo@TtUyT|~6q+@ESZ~ZS`rq7$nzn8(4R6|j#)>nATb1f_AnmA{(ehME zIbZUH*y|I(?%m6Y*0TMZy+L*=G>^Ir*ZABWiG=(+O8_p*u*}lcId4S%bw3Qh@jO}G zd0eXu5|(LxeP2mt*P;!gK>7O=@GEeq5-nV?EDE#!nbQ=-fPKd%80@Taqb+;vI=JdRn{vPg_qjWC3d{r*|*C|QGeZZ0ZTiudr}}z5%tu-;lT~|{7yI1 z{BxqNaP20S01jk-*qI&kLmq$eFDT;sYi*n(VT{ew<$6d;&i@P_zq8L&eI96F$_|d} zJYy3ZK@ee`77Mz;%h?aeGQ+Wn+)v|B1EZc*$AEJ1KJ~ytWLyOM{*fe~M2% z;e`3_n?r%BbhH2dd4%tKTq(acPA+(yzjQc|sO!%W$6#+yyAv_bJpo|(m!n>Dj?X~_ zup0DQaPM9N0Xc_Hb&!)d@5eAEB-exT`!$Fku_R_QsBr5z@O{7g+v$*1QM~x&r`9j7 ze*68p+eD0{Gagy@Jq1UgqeYt0>xjJo1K=II4Q#zthbymnj_F?)X24)Y{=X!u48$eMTSg0}z~~wC$Ibx{^BZ&pkdQGl z|NM=dK`;F6^&1~!8HJmue|zGD%y;<;%{w9pV2CaQ#=h4_c!Sb3YS7*EdfgiL1vQFt z3(oorWvKFn3F>M&RZ#-$VL^ac3eiNkBI#_vuCrXl!C_%3` z+XYAUk^lK>S$&(P?(Tbf?EQM>Ym`FD9hDbmdLQLx)+{CmQx+%JOp<7}#Qq|4d!|8OZNFs;(~8JeVj(J= zeYiLRU)@N|;Z6J|?|wv}#@xB&RSQpu(bHP-WYSZe@MCiE7&a5D8t>VLe&eSqMR)J< zrQ)L20@ylBeRWAgBHcV@KCRbK1yBz^07jd6uhl$-;?S>M zF-62WD_X9mAI*bagNPc?Zkfa^s)Ct`>k5F9zcui_xmAfaSZJsSY|7RB#k2gIWqlFl zgW7#BIND#z#))mLzP%~de%J_yPFBYbNN@Wh9?y!M~dG7AUJGhrsgE&%LxQ(cwO zdW2H;$_&Qr*f;DH@YsBw$aCK5ku!K@7J4-rh8=hd17~*s>N)HmJkR=X8H-`@FsiuWd!tKDGPng`*ca1X8^ohJ z8Ez`)A~LQwx|=@hx`3hklk+6&w9b;d`ILO^?oBS$n;(E4*34Oh;~ONStOIW;7#_05 zp7_taFJK2!|C~-M*afyh#5{6tEPQ7GBcTxz7gk9_w9bAlgbnP{^3TMh{IN(GqPe#^ zmqT@TK0xsc9s9J086MfGS?r@K+xWxbtoP-S6N1J-JR}eUOi=fHR_2JlYkX zb#wudIbLImj51{8!E39|S3kMyxJf{b;Jdf{>{J{{-+tq|8x^oyd2B;9x-2~IU{#*k z=N}F}4@u`{G4Ku8XI?h&8wE+@Eq(ROAvp7&Rgdq%N?|}5YHI>du6Ej=7rf_^BOEPH zON@#EYgT;nbWK?5I1i7ed0v1zN|J#3q4gu;?@kDp_H~|Ci1tqE7E3g%Otf|tr+4bXAx{&hvy(;~&q${jk12UuWEo!Q@LSae{n6l-TI`q_AwwwhPdQrfDS!3V&q>w$JF~ER zlK6I8ualPp_H&4yGrbf1F~k1+KbW`M^UnYu^=X_c?=Kr>o}*LvI)@me@@QRqk(%#Z?Uo!Up)Oy3d;qb;Y0 zz&1xIwimM!JLY^)?$S+#ZdMbN+PuDlZ-q~tm+Z$kmeL7byp;DGNRP{R^N}~T(RE0t z<3mbJSd?e)Egifl`K%>ZYov4kP@l9I{z)-oK#*YtPOe;Zqvf6%nd1p>7nD|9$cnP? z$kq=HdGD$_<$f86`ZV2Z@2~5(Ju~o}MiIq>uIhD2T>t#rVYP8nSA{S109iO|pT%*H zfhKX;!B|gggGy&MdVET1&Is1-_-yFXxKIfW_z8}H;-(#VpYzzJ@l&be4{zuEC={l4Kg?JeR zRt44#zyGEVpj|lK4HVX_&k11FhnIgT?lEX{Njx{+T0{M!rpNh&nASUb7QERfr!2J3 z`ihUNjQNLfy4TTB*NM*#x^z1J^8v}8&ybY$Vo`0C&^SIHv;oCwypYnX%g7Z$x5cw7bBTYvfcs$P;Q0Tjf#w3uK4n#cnJN+po$$b;tb;&)f$kxv6rL3Kb7R^z}hFEJ!;7jr&! zP?6%Ssl=!ww(syHK!SjGpgp$wi|xk+8d_4HNZdgWIM;wjk`?ij zF2@?YZv^a`YkLh`lp^4u9Kiw_&MzSADYDNII;fDLjZDTU9KJq8~&<5viI=rGg-J(L+Ef zr4lK=KGuCXGCMgU8Zq9xSK*w!*P8Pfrw@v8zXc`dk!w<$v=hq!=U|R>4?C>_}sc(yk?b7*}VcGk7F?+5N5*0kfgQS$Ik}} zbg7<_C49eYsDsAWqs_PR@&578qrIE@@{Yc^6>WwE`IEly7VSEXx?t4~Ty)HN3QEkl zOUAArhkdqxV?6YQC;sL_-q23S;xBiprju;iusFy=I{3_d=0EL*c7MLVJb-_Cb7x0hI&;u-|OL5mB94@EbXnt@DH$}+^zF)8YTNf zn#W7gkMV6!Nv_LK9Rcwj`*Yg7U=fb2J|p(uGXMn}rew_uxprPim*37SmI;3@1tmxD zX;Wj2z)0u*@3Y5`L-L3nz-Y%SsEwqkmH_E0pdTY&b=$Q2z`%X!G0XVJpbCZjcR_k* zJi{BapsTyH`C0B0yde+# z?gcXH<|Naf_pUy|SC04aOyIeO;R*{S4u+_^W3(4{69z-C9l>G&KXDSYx+ML1JUGO6 zp-W;!+AHyDc%3SOh83#La9@5XfUBLF4Rl^F2kJxLX~1b+##ew*`)d;Tj zIVP3@L;}oB{TY9YhZ+OIbXADmsx4(XOtRe)c)+u&T_-3uNCM%46K&B4Z5-AuOEQ~tJkV-;yvp-Gyxxn;m zP)&Eetv&SLJ8i{VBsq8?@=5-Vyg1bhdQrhGj&~o;b%!ir^l1#t80DK*vo$<6v zW|sm9bx@YwR%J=?re7B>YO~jaew*~>4)7BM>HG@o={m06F6xZ@hT{@cYoEi{@rdLx zAtWQLkNv?<@KGm!@VtP*7q1ag%+lv%erZ22C=S{DT-YdN_f41E?54+j((p;K`xg^T zDaSDA*{f&j-N#^1)K2&Spc?W#%xkz!`v_<`5ufwO8HWeGsaT@b9%R9C7GVT}Bh#`rX)Ecqc*fqgiy@$*yN_c0 zIXk=6v2o{IFEShbW8M#7i|)R#uw?=YVBcDNP^bB+R`1u)dT64roM7_@*CM_fHebf} zRAs^+#pt2lc@~cB9B5Ek`YLWZZSkuDdXTlb`mAy(HNZ0d+qsX!ved|az$k6v+W2se zcz+%qdx`!1Wo=#{fpcWG6_~~eD=gUj=KnyRw|VaxCLfuwkZ!N~6eD01I`Z?lYRyIw z$0_W14v$YgIDtux5G0w9JzVz))wI_I?Q?QDZtnuYOAe;8@od;6{j2qeM)m<3yCCId zm3a^76&2?JrgE{Grrp7OHu=VErZunLQ=f;2vty9*ihKL`KKtlg#HNQT?JYrNzRxp# zXlg#ZU|)h~B%Y)0UIhoz=Bs)1=M#ok3dugN$_LCdn~c9BsUGlAvTLY;3IF!lzekhZ z%#?Ze4(4yQ;2UU-*0Wi)?kl2esP4e*1#f$N!H(LW#XrYYhBKrXzmM#LD&BGz)y>(1 zhEJ~-z#iZc4}UY%wc>Mo3k7lCr)<{HS64@LK=b-+X28Tfjl&UH5$^uYe2OPv)E?sP z`uA+z&F%g6)67mgyEpwDVnHTx5R#V?z|D#Mq04z}P&9?KUY+q3!XrV8IH!0dxF`vp zoQ*qbhwPUAT1^^U0Aj=C0kz$%4m>LLlGpR5iSbq>A7B4`qv$~Ly%$N1DIaguO2@T4 zkLMZ}qjRxo1Wv=NcpA;?^=w8!9HYH9=;<(HwrCFRN zZo<8OvJ}0zi%{G9# zu3FEg8v7D5(Tt5_WIm%gIku7Z>2aRb`67{@?q0tfjmk9gx7@p2P`|$Sx;foN#Bd@7 zU8>W2ym;57y_n%y`viKMx`A|$EW(2Nvoh{|H*MX=SX^|?#XwlFyH~O=#4@z2O6~28 zz24W+2%bBnh^ZvfK?Gd#{k(F}o{)gpe^T4+M|xen3ra%6`HiDU5A|0(C{87xpB)~( z$doloc)#ZMr=I$)?!Ujrn5XPCP!tEq;x_ka5^Ipk$rS0--2T00xly&R1D4iU1-;eD z5(``sVUlYfFOpY5GEEjD!R(3k44SKyC$NSs8MPJ03A6X29OUlBpQ4wh{|YnsJ5R?t zuzR`wg7e|CaVcSJHh{_F_e0pXU4aEya-4BA@nCauF%j**Z3ABG7Ien3e>2Ou5n-9Y zjPri2k#CccbvAD3@(^#e2|nNN(&vny9YD@55ixSVha2=(p(EV)#fLs!and}HHzrba zuD*7)G1J@eX9onj1b%I)ccVtkkWjW*xZR0G3^U{z9WJzoMnH?=)(^><9L^ z{s!HQtfCR`ibpBNB|cA(6sDEiWgh7RAoHqoV`O!0K zk0mShR<+mt%A0=$&Nd6NDLHg1=HIEcUkmseG$M^75UkTmG35yySCco6BP=(4*4uJ2 z4F39(zn%>w0Tqci+-G_`V#=7m8q$f5>G10dwrnFz|Al_>iWNqAJ1Y!e^>-{hAjJ`f zFfZH@1=er3NcH(v2ku8n`s{F1Kf80h#J7$?UM^_ki+yt~Wp%FRufe7OMJT88Chp`a z$n^Xk=&Bq$b9GzNVkjt)VLa%q{uV*m8qiaZyrFTADU`aL+nxKY@Ji}+-Wj)L%)D)I z+;aN}rAFw_PS3H|fHM7XoUvUNHcjgs>;rJ3mZHfjHcxxpy2Kwbyi?&IgNe2&ZF9_(F z2t_Z)Amq-Kplm3}YX_;RH@9-q?_IXO=X`%R3H&)Y3+F~~q$YM6rbckjsnT0NeBHox+to5g^7HU}k%5LS1C1;MW?}EfXpVGFJ+cfd zpBJ0&5v9OCGg{xAKUfsNjc8o)+scjZH9l?9LM&Q(UIp7)nnJQDV|moK76x4o*H8C- zw<~pkBt+pHEJuI!VFozwV_GzxVefWHmUby&MLNt)uNM&mWE%@+^56_TdDhj(d6!+a zm0FK??rDb>ps-?uO;@x!t5|y<*NsOp_rV+lkpl*hW-_v$LpPWlN z`*<(g7_eZbw0fF%8$nTq6L`Q*ISW}a8W6&&+WQ|tf=BPgdjwjLhE3qN%Y#EyCe;s$_p!YRp5cc2zPcb;Xi>VGmI?*!QmP0X<5U6?($22 zw{NS%wo)0-tso}Sal@f2_4(V?F99PVex%l5auESADAqpwfu$fmqAz`-+(vk!2YQqT zMo?t*`-%uWbt5w7I#E3|V?#ND*~$4G{ZbLVS{2N%PRKj3w_LP$WSUNgND9u^ zd*2!eZIja!PVcjRy*zFx8AA;U{2St_@e4Vwox*d zFnWX+@ad*6sc#4@zBvZWN!dr%afx)Xz-M6)LuPz&P4);B(=@);A)mRxgKdJQ3c zmBZ_B`uTFW4CL+HD~0w1cM7nO{Jf;?BHgvFNXq9KstL6Ycc z_P%ky+YcRIxygl)8cqBjQHZMAq`Yj-2b!()Zu-~fNgpiS!5D_h-TJt9Tk$j1)B~li zNvu%oWXUp`+HEtvFl%jv31zLvV93q@d5$ z6mS>@UIZu-pJNTFCXiN!|2gdS2|F$+m;XY%Z0p!6(%mL0z#=L-G@_qZClr^#;THe8OOuh93?w>1a3O(k*xVdf1`L~&O%>$^3WU*F-- z=D0nB7mrmVf!Q`7S~Xh23;S(RDzh8-<{*0fbNCntgbFQyiB7p|VVqYH6b(f77utt*2Q%%J?^X(!fxr_+nwC6ay z=hWZ);vV4%*6Om{M+~B_SWZ0YZ>)OGC#-8#_7UJZ;RuCv`myUgcSW-+lM*+I?Q=Zn z14bbF%f<814QWjFPrRVCEZT|}X_*se9M(791kOU$XY@mk-T2w;jb6NuSfg0e@43J| zJIMyZ&(;3hZmG5J#_OTG(%t@I?Z0iZC~s9_dc$X$5E(!aiRuDIUnu)YN3wufpK-AC&VWQw9M{!%G6T`B@V~Db%;?c$+vKJUtH`p|js!`mEM?jp;Pv zc2}14dc&k|fGxNZY(U`JU#arW75Osw))904niX5T7~O=uN6dG-sZ(k`4DB%> z0}oi_t(F0_7|UB$i z@ci-8hcXj`oNqVZfjT~|b`K3*+V*od_ksGuaDCvgIAH_5df@ZpPhAMNxq2Y-inE3xVoKaWt`lE4hIDSn zuf@t*bz6E5YFj7@Mez?ieZu!!6-%V>Y2kYdm-hWW9={$? zk$1w{TL*tL`p8I^tJ7IEYaU$8CPpQN6xJ`3_iFaj#Wcfd5~;^`C{<9Qojhj1v`4q+pUzSXiFp>YA$lnF$rbq68&#orHOJEbF zkgeaCMu@5CX8I+`Gzv)kogxosA!yec)JI1qQ(n(5juNk%o%7W=7d_5XGN?o4yL28s zTt3C-dSGN8#X-nUorHz){o7z;2 zS8-or*;ro`?$C{Ou!;B2Qorf-sED1e&;y~rNqKS1y$OEnKA)2SI-%OQA#4kj=A`0Y zT+3x2-EJ=Ta4}0#vxE9Rya2?Du%VE!%ESfsvyu2iKE8ZF@xM-q7obbq&K7V=7G7*` zb&oVe7RC{a4VMm}L9bPVs>EadtI`ptfA5G-BDf=cq;dV5tXZ+0NJD*CFQ47OjV$@7 zMlxsPUoqhPN^ZX>E0ng9vh%5WI_56$E;jLvqf1I}@8K^9w!{%L({Gj^gQJ$1w05wphOrqS5&jSxJX~Fas(`P64 zcGoO{4_;pvz;9MwL`kMTsvH?T6NP}6pTq7KPF>p5C~zgl!q4}d5`57y?2E8BBG&A1Y9_!BPdDWQRiEJR?rmtDBzM zy93PE{^V%byxcI?l77*QIb*Y4D6?_nP|Z~x#HThvqJ1D`ysR6dY>{z$_gMQFHXN1d zo{!<6CH?-xGYr}NEIUpPU*4#AC?w$K(XPjKXCE>;`snqGyV+DCt-3~U!}~rT=;#4> z$ybG8?sjL6aMd0Uukc!Rn6qiu9sCuprab|bdu?~Pjc7>Xyp;W+CF!2C#DCfJh}`wQ z5v*Qs!d}9q_zfg0c#QtXKb0=I%jPm3y3=%b$b{d6v;h?U_u? z(AF>($f{NU^r(d#pxhN;(;bkVHD}G;1FKbAi{1~7shUaP_Rgq$qCt#DEC%fZSs^U6 zCK)>sZ6*OG2d*U(n;B?9sypsEtQC$5<;Pg8 z$_L#$aoDpR>s)w?mT`@wLlCpO5G;^aps?#l#HaLei23+sc%;?;9!8LG*Vj2j4^j2q zCVv#ed`T^B7wxX9$FZ=IvnQHsKGc_rpO%>H3Xh~SeBVPHHr@Tf#dqP6N>Mz4^0GwR zv2{`|cVwSIg~-O`=@t{;V}}GF2ZO^el8x%@xR)Dd_}lSCox5Cd`mFN{nIP~m*#}l{ z;$yA2w#kD#K{hvBiMdt4=h)qAD{qCVb66j;0FBP4%TdShu=C^QE!g)By^co`cTy#Z zdt>s|GIuLlmmi<5eilkut2cb}R}7KY2A_xXCg)gpwC#ak+b)Q)$9=#titb zn^n!O$G~{JUc>UJCU^9jgK!hawUYaZp!xa7u6vz`_DDtGx)<^r;WGeP54$i`UqM~} z5@~jf3W2-(>;@F_+PfV&xKq0pDFSx=kN6^h&}Y#TWdQ|wV$jsW_|mJ&ZY$~zkH-FO zkeA@L9$b-aK!>yC6|gW+Y7}p>a8J+jxPZ2;6pmw_&0~hM(E`+Slr=~Oe+-|;)6)$T zn>QDa0|lgiJl|C3L3zg%bRZT_j+6SJ!*~2m-A>3pBH)$Mu@{g#P~9BN5QA97M?mhH zs@j|EIZR)t@so{^Sno1LKhKT@G|j%V)!_+1a(~@-=Dfn)qeMM^S~TVk0?iH=SOLWz zKKnb~Y51Ar8DF>T5edfWzF&e^y8KP7_Cs-O2sKvV8b87z+`x8obVkPCQS<&n48hy7 zn%{%OrFq9sBWQz;Ol*RYyUEnO7L4;a78VXhSy<_Zx96TH*d{yQ@h4K>9}O+Mm6`qFk;3JDQ(b~uXAK=~(GKY{3hkRx3xJnCt~j;)km2Jyy_xXLLK>PvF2Jc{pb95}m5G$%ALqdc{${y?g2Qsfj)WcX#rDdB>bg z@;z1azwLV2vS0Q`K!$k;iQN-ljrz8KXrsIvm3lw3_apVX z(7Q3YsP*RpUHo|Bpp4ODyC@yxkj4uZB<{|W?>%vw$J)zV@{?!HP7u~FIreHenMN~Z zR+Ao)R91TgdC%rJeUnptiy#)070~3m@d?3T7rC*Jt1&-2vH$b-tEk^l_OpvhZTi?1 zsb3hCMKiUs1gwZ3KijZBGYxw^ZRB-e;$<&M*j5Xzsop&Z|0*Yf)d_P-`zM_B`sQ$c zLA+h2b#g|Ecld8|)nU2sgIubRbGC-EzhZ;L%Ab4jxphy?EuTixG~_(hkO0lgAcb9hH|9tS)hgG$L2cg%f#4PQkNXXnd#zjf=Up!|GG9-`kAIX@Kq3)sAxEL0`%jbO zrv&8|uE&}AyL^V&r9A_xjgqT{C+U`l!&5=<*Sid(Y_WJAtef4K|nRF1Wp z`;>FvK31aRWJ|y+_g?dhu*wn^en&lgU&n)&7*8(j+)86htJs~#_Yt|A(5a$wSM4y- zbEU@%D|W0mDOm>)E^nCDe4$=`z-5vY&vH;Bc>KlBrce92O#^~cNPX`vJeCW$1DRKu zNn<|%Q?UQom)F~CvxWUPG0d{H4g-eIl_nG)Q^Qgxm@v6Mh8;F``(_9WFx^NUM>kV3aXgJNtHs&R;Wb)dij#Cn zcV_^Ns~sk}OHmpHj>)06tP(J!M%~+0hW04`!Jh1F)<=|y!IhbxDURk23S6u@%x-_b z8)WUzrTPqxek?O|Pk&v*R?Wi^Hw;*6q?2>1$gSA+7;UaqtA{FwrRGMv&KX@&_tQ|9z@Xq_wN*1zGhkuU{}=#(p}+uB**dHRV* zfTn|}st&~AUQ2q{PH<%bh=Nm?q{~#MoE6A5?(BUmF-yp>HESVbJ<^*6V0uJ!RqmP5 zF#A;uAeFXajx`0t^=-b`_Z*#tMj5^eurF;LH>GB$ykg#>GqNl z0`0$fI1fVpm(tdb2RFLVi8k&O>ZZ-7la7IlCCM(%>-EzppJ!;WTH-ruKV&Gnz>HS- zzxf}P7Rkh-oD)36?ipK>jf;-`u~OD@3h(;K#eo{4pabenBG=emwX527pYj^*g4(m&M`=!gA^ma2nD(uS2Dxq$e_&fPc2 z=w17|!>+>;^N?J7MBK56y+KNI!D7p7)xpSYxM)>b9V{T29{E90 zLw7vjG`v4?&VV5!!XNa@_}xz**-sQ1J=msM5OvtnnuJVMDRvn8r|;Jifh04?KM>Ch z4Zo1{ss07o4sQ8Peqe5b*|C2HOHy14SpbzQ7g^C4tB2D(BBD{$q59a4EWgw^%#5w} z4xDJ~Ca$4dZlR6}pz&i6uc|cMY*ypLM1RhQRA*DSIV2x`PSmUHOwozP;4`ws3NCUbjY4ET+oJFxr49rt@0#ZjAXQYf`QdjPr4 z?z0rP?Gwy0zSYFPZ%h#g@U)w9#geYGtKci{>-)T0-(5e&R)c#fuY~$5f7%nxoKr}TeXMSn0?;kIPdf~xKh#Xqnvi`B)4eT>oU|%~*ZW2GF5(_p6g4^CBn5FM;<9 z?Yvb?jg<~Zw?n%jZrBgCpMm4*q7wh~sT-N(?aI)gjfeIwhc=jO1Z zIG3L~n9*b$Xc~AS+kz%d?i|bE*yQfhC9{58#T)TpFK2p*d*KazEDIUV*uxCCq((oX zht|fsDIKBHiF&x6Umv%a_GOp$mJnYii~a7+YTMpDN!YitvJ?b3%d$C+%(a|$?}-Ul zup&BhIjX46l-1Si&k@>!`;nBn5tB$Yd39xOtlA6CiN5!u8D0Qq{LHC4w>~#uXp#5Dt*nth$-LjtXh3h z#h**5x9_>y3R&K_!|(LAZy!lbNsQF)+k|@C9l_QERhc)&XOqi4T=+IRV*ypL#_Y4)LiekM=C ze7!e_1c;6;J6?W2mYapzhO%CL*j=5L zzwBf7-#j^3JUExloXS#cWPb8ge?%IE0qig$Yhi#mTw_DylOye;0lgbb{f|;zpd~os z$)X1aeTI@4Y{R43T2AJ-ugCL3Y%>MurQ_(Z37>>U3_!)>(< zzCRwJQ&uwMHk#{s0@jXRM8)$7-#vf62RCSbFLq|z?AUV5ayuj%&9s#wz+aj~))F(N z+Z`}JnmL<~A&6v9n`;B}eASl~SIU{clFv6OIG>a|_rd4I;l=EZm$@u;Kd!+L_}%Ae z2F0+#^iw9x_siyj&&O(aDej`1y<SW=zSi%)# z3{X|#ge~%#8l^TLus2vNOTMY~)FOr%TDP+KbphN0-fbTbeZBmgZ=TW^jef2evT31` zSo;_5vDGHxE=Q=h36D_tsi0Fh^XdMU5eDk1&2c4yQ~*>*z@~r`*7O@=c`5Z47%kBa zw`TORJC)`VE>_Py2A`x>8%M$+$~`H0%|c@Qg|2NB*nn?JYX4d>vgQOCtMs(u{*v{@^^to z?Vuq#PRtdsgjb1y1A9FdsYI2Y{slFDYp$2TlzJ z+#q-y#)dg|9~BjOG-|jWIe)YQhUemIz0l3|!?7=!SQdatf39{<^;l0P<9q=5opX z!OWEV=yx2hH$Ab=w*T{+!>8SxORu+k;GPv^H&(R^-z4SPLW>EmM_%^UyDq)})`x%_ zx!0$7k8edM48|$ulW@lGn{-~uaRuWzx1uo`8h_A^`NrLGM41?WpSU&=#KEX<#S7B z?bRywZwmm#m}io`(lmU^&=@{P?Tr^uuJ~&`lqRq6UvuwUgY$Ypnb>1tnXh+Q%1L+s zKralw!T6;KQ|q}iFbsqmVj3WxaAd8ovmk2>)`&hJ8U7#O?vV8t%uPuEDkp>M_5)6- zm%?;&R6x&{-~n3T=O))@Jb$(pL|+B<#D@vm!c-Z+3mC*sBl6qJS9&nLDg_B99AK_r z_DcAn|BP5il5&kH5cY7iSh5M{|Z^?~JZ`^ys5Y@v+ zu*VH0N6Bk|s6D%oC?sE4y7N6E)q=;9rTK~@4|&A#`-4)q-cu@jB@uP~4&oW3?hl%V z0FM%46yYka9M6ER^c?0zb31+TND6ya;@uzl2=F~|0Lgu`-Z*+WRcHP+{>w9bBB}qp zOBuIs@@73dhrAK=$JWBg%qs*?v<|yK87Fi80UxtU1kK?nNF@E07H2P#+QPlHwl?(_ z9?5pr;?5$F07K|lhC2&#aDHC|3(P&p52n{*Y;)WoQpNTwIy8!^l(l=UX`i-Fj$Oi< z5r@Fh`!S@558<%2E*k#!zNTZwyv@G?n`JOsvms#*Rw)M)I5fX6gMI3+%0el}DuKG^ zU$eyd;g{PRD8eNk@8sh;y$t@9e=vJ}eB1PDDcmHtJA{}yriz{P!0zFpARp*VaJyT4 zarK}rMETLG!VxdWhfOM%1M@(L9zO@LMarF`BRZA*Vg+8`Z7w5n?#)(AJsZzL!SAtz z^!yxZhU5_yv#SNB8z1%*vOWX$I{)seJF~H;1WCriZ_CG29@L39?+6ivyBEWhr=nM` zh%iJ`g1+H+?3#hkz-Gm6^CJ0joM=OdR85c!r29+5-oDj)-S?Y)!2`m#?j zc|~8q<=Z`2fJxI>`|Q@Q6TCTZzOlPy^4Y&Z(~&2*fW4zhVAk~JMCu3%z*@&7vEHR> z4$?i=W7D;V_T+euRdX$Ctt;>C8ws$@edE&?eF~UPrx8e;%il9rn}|pJm{bjCB6mb- zCVXD{XLM=Kk^8(FVA^KAN4Ge*nExk*gIG`Li@EH9a)6O{dFQwAc)oh*kzTi_`c2BW@*1C z$<^cLPAJy!yxhB3OQ z6-iND%iOOfpbwm|#_uI+$O*WVUSs8vAoFiFj8+yK_Iq6Nre69NcT;33MtpeofQx9& z0tL=d`oV>PlKHur5AD=FjuKQ}6ObERC3ktq7YGo}+JiNd=q=Cb)7Qf!Vj#9wad287hxL60h_SnvKs5g@DF>hImaY(9K+x8;NQRD9@O zO5ZG4!02YU53W-j?nH}i-!14j)CjaJ2Eqqoz62RQ!NhM_+2l=M2G)O))DYUcR>!{h zLe9ih;3_uk(FoAj;_XF1MUH&lFzcd1IxV-YeorsG>13r9)=0%^=azY~DX&85A zvEREUZ+=CCo;_NybguY_`3>S}Gvf|%mMTw4vrAzC*LzjDyI5q(IOf@4_mfV&M?vKfGfah7$pL27A5UE0-l-ijna@5qI@pe2MRP zo!h_E- z;g6RS$j=(V0tZBMFE?w~H)dy=k~qib2{p(4bG&(dZ@m2n{snc|gWpEqUI9bSU`nC< zDXsQJ|GD6J3shm3OoTiYIS=J_s96uJf(>-2AO<_oNv?lq309(j2d-$t67s)2Fc{0| z7TqI9FmB=3JKT1Xf9u{bmaGZZ$^a-nE9PV`@VM|!gp=2hkPO`0vG+j+7|3iE1JHs72b$@H01_P_ae z_ZuILNg&^aPBKuUp-}re62m#yvWa&wqwXUNKTP?(olvgRjW1rfKw^d%wzJUr!l9>KxVfB&3Us zDPohtR0W4dPn*0j`wfvj|DEa3PaET@|2A5z3&7FxIo=YUd)O{F551#A`a!8M@-JkA zw7<_kFa0nc$zkU-kek`$CXt&?R86RKd0iiPQ4C&hMve}VEOxsjsL0?^D=|mhP(2bx zJfBhFtZ28hnnJ$sn5s%hX-=opSDY<NjS#;Wj-0xg%LC|dFZF&MeQgZT#MgnDT2qif74{N zPs9~?bLYq1uYWe@`k_+ZAaW#D*C5%1_KxdQ2y0@#KQ9 z3_R^uUOCY9b2v++-JDDZmNRpeujS6D`IDq_kRR^jSJ$h7hfMZd`DQ z^aUYp#z*s>0Ad?H1!p49#C_VcKO8;bmvU`vRSiaoiPGA-r{0BKYpo6Q7wq)&%Am~A z#u2a*2hT1+K3<9ima@E#Wqe{BS3>^yc_Y>HDaDOTTG^SLq;&V@YlLa!XHnB917En{NZMHKH7V0FixZ#x!t*MEDrfnkPseIp%&M9XJ` ziKjg%%)WeEc+9q@`H(~9NJz8biBom)I_`VHG)2;gj3R(O)5Vmx{HW6%R^E4?r6GAI zQuh9+!vR8_tM0m%mz&gXxa&k*#1rTNVkS6%Em52h{302Nwy`*77Jm?r{94!r66REF z4)2ezOh@a+JrSR=;~spNqHFaaeP>5}nc-i9$j#z0>Z!s5F}}+~(-Q-*YXF)d2dQMp zREGLfuwTyyh*c#^T5w$lUjbOJ7lKw>gGvi*6}&1?yLy)QzrfIqZht$p?Cv}xG7y+g z(D^bU(k6#8Oa3}(CPf$1AmVdHJ`3(aTm&9EBb+mVNEVh$W7qdiP$9&cr+=Zzw0AEz*X{$JSs zv(+~GuQ+}+zg`do)9~79pR^}RMlTS5D87xL7ck~a4>x7PQ0?}65tI--X+COHO3l~cM<8Z@p7^imyu%x7a?&c_Q|Tak?#|h} zlE>9AUxpT*wDdQTCPEz>&AY8DjR19JV`4t)ptzKiSb{U#0;MzKg9jGNpA`@?sg zFgO1e;HTteY3#!en7YpJJ6tVIIWtjVHFZ7N8uIwK@bFI`5ys84Mbsa6IkjodIwR3^ z4|bsC{+;2O598H9Dp0s&D?Gj#SDbAK24}AkK-T*yca4X(-ywLxAe6~cv!5vuLu2ob zN`u!lzXkL8hJrN}sA8rHPV6@QhK_8H9pZ8n7@>c?LliAu=k%nWFcys zsJ~c$#becj*5Z_(D+3E0g(TR|dcm&AzC^_p&C zAH)80`UW-myVhW8)cUuiyRwZHbkBkxWe-n8c8OG_w0!%i=U-Ek)}W;sa%m%$_&v5> z?3F48{H-$wGe007PrC>%YS;cLP)IksdP)Q4v$4+g_4^pptOJTCMNNXY+0SN%N0QyN z$yRqB$$JVsy%exhHLPbcR{Bro7mgG%AICR9HDB!OkQpHI)4V;}e8CF5O0lehT0Hh@ zYS`1!Wei=`)g6>7aG2zAq(Bb?3`|8Otu!R<%Y9D&8h3Y_2H6Np1a0$K(_FuE(p-Wp#1AZ#5XHxyrFDR#rW_Bu$JBVQWVth17WJEM2c_! zo=xmh;v9?1xOu%o4$xO`ZAY9-s&{iV!(|e%<1G$Lx1hBB+tWX3J>7b2-})vv{tY4w zl>BM8In4sBb(21Zq|aL1{03eEbfCD|YAO1y@5Kc)7j_(YWLI zPLlaA>-cx*U&jT^nQVPe8^}!9l>-s0DOnS z(=)=i1*LKV;+mySs6m_5IEHBOlJxdp(kJMh97(CC@bE#(PFz9=4iWC4!6gr+O<%VU zM!&a@;Sls8BGPqtAX@Z}xnT^_z5&Z(>$2emwO zMTFfaS12MDf@;QGP@+6(e_*25A?M2KvVFZ9=3^C1s)c?JGQH7O@gW?RfC>cUuhCg^ z!Fl4%^mM#b+^C@7PQ}8%mx1Jmh;bBip_fu8!16CmWnc&D+=0 zm`US@^=H`V{#x+Zzjuipab@#D(apQOiLB4`r%}HY!KH#o^Bd--cP`jsW5vh4Bsb{X zgxJqeG4=Kx?B9Jy!Gam+farvyNA@@K(E80CP2y4W&hP@`_~8}1_ok@$!UoO$cMNYT z;@2lyxqEo#8Kz_>9b}%L3}rxoEfyB~DuRU@iDD|U(mE-er2_pxHfc)L_- zz56Q#&4n|0v57$ublsP&@%Zq$f-zsJ8N|E>);>Nm&A*_@ed0A}vT!EcxvC6vyXSY9ua@8niAacYFixp(T*|0wFFCQumkOD{#v{?>g7s z>XPW2zNo1+*L+_mb{u1XR1*h1MCS3W>{HP%-F?l`^081o>!| z)lAxuDyRjsJ)f<63qmpZ%%k3b6_i_a9&>vQX<6;&kTH(ed@UT@FgBgRL=lk%n;e($ zY@{jp%RC;6^+DTk?DQ}bU9@Jr2Vgjvo{KD?`*TB z3oZvHWVh5ncw{!xeY^+2BRTcR=g;*{DbE`qwr@-EIfuK^0S>ACRocYv4&(ac*_yCe z=<-k#@7ZZv=*vt*YTAnZO+k;Dlu8fKr zIE}0t0YZ5MUHL{S7=*INnmnZtNPeHZ{$ zyMfzkw~k0G1^xbgC?~|b{%&}Q)n1?BQmvK3NUV}pcfq3K_D|IDc}WIGr^W@xOr}9I zhK==ZzJwEKl5V#F>XS$gRPGS_MoR@D&5cEINvopKCzr>XJzg^Ktg+6+I8U(Qq~#(! zK8o~7CwCc49*Nt+&|+;kT8O+450rM-dCHM6bS!@aqs?EltiYqNKgd_qBg=1*DeA?c zO5GQj=kw98FU#9h%dM2P2~lia80v7qJXOX`0i3mt#soo_=5e9S!w+pJOtJ0Hdl+kpuQvxo$8TN!< z!^#}%@ndPjv-)KKBTO9S1oKkx%KHK4p%_TQt&|53VNb4Us|J%>_nL+Ty_fH>OxL$J z1!lxGp#Mzyo)<#PjJ>0{}#d9&^`1;OkzKcG+mnH}ikF6ap0Gm5^^xcc$x z=`x37_tNh*){Gr>K(QJ$2kV<^^zpM@t-*jA`sJ22(A`;}oN5>FE?%BWOjI9sA=^^gPdW=hJl@*Ra{SCL$KdDzBiN5O!uq9bVrEXwKoL zgnVVw%TN|FHm)6*#}=wqCTd6QXUA@iwRw8AV89tpv+T$(DdWxaXo&mxLgrw{)EBUe z;1s_cs_2}+z)(f*L}nFU1-G}kRaT@0)_qYu6^23H8=gB9VLvgG_e9DLYkp@-QY+2J z({)nM*El2G3w=p$PNZbAcReTW{Rc4 z%bAC|lMWfA{j@EuvczuE7xe1)VD`M%Jbc<5fI*}3DL{#SzO3Alr-&sym6p2}IIvmQ zxhUutEjdu({yaybK710eT#MpLf6fLYC(UGpc#`#Dz9)iEUyKKc^#>oi0;RAf8nXDO z+aXU4Qd8=Ri}uDb_WISfHbNiMc67S!YkmmK&UbF4BDT9rndG(0`5RYJun@;LIr@yI z>=2OOc>mSBmI4J_4odT`$)<=**-^3=2@j1E1`#c)E8#g^BPxd&RO$orKt}Ks=P0D| zjaFz#$+}6P-}2@GAM}wM+o1xSzW{b^J1|E@O;$5)A<#s9-M9v~Y*d$X=y)K$AfYv{ zc6XNsa^4YPX7WI>_DH#23TPsO83FkFu$!JR@6_ZqeaiYeN8ZfQ!AYhPufG*oo_+~y z6Z&PJ*zQ-BE~|z~EH*T}H)>0I$4p!)+L6v3*Tu=p5R9i2k39Ajp~GwljM_1Q(oPPZ z({3SIwzsAU*lJWGcs5fMwcqRW{G>r%iGH1&4Was?23chTs~ce^ z{1uRZ?KL2?N6;MTG;E&@CvdZ)r^q`(b{6hQC*UIbt~F4s=ZWhOQ`E9{-Ckx3)@`N> zC~gtZH;PPjm>!+rC^2m4@Ugx02jv121!Twr%VR=az?#L?Ebp%&x+wN_>-*Jf?wb@e zYecfX!${+NdDlwb!WaNcf4~=ZL(3ATdx}x@I;p!p?EJfXctHfHK^qt{ zQz{=%HRjGm3150gzCjfF*cKNs_znl4Y`EP4lqHfM5fvmp~x~Rqw4*NB=)6SkV0d(ns19TRk$t{-h0;W+jC{5P)t~3o*HOh0n67%Z1 zzg>qqRO0lmVZATwE|_aZ?D?EOt6)eMvN4wXBXm?(>U@_x@^%jp9&Sr4@(eX!`4j8QQ)YkSz6xu|v zyRB_iveL=n;!a#pPLc4^h;@II^1n5=$O1p?ZohSUtiJ38ktCGxtcAx@ z;7i(q3<{Tqblo0}q_FoK7bjh0Oz;&ruhPd=1v+u17vQ zM7=7jbOLvB*)}i}d24iF;oZJ-0eRANo2GcL&u5c?O3OF$e6wmDs(qkhMB6^w`EoWl zE--#Mrg;$1AX+(>?u2^#*&(^Xyl>c;=mqk-ash%q*aQ=Ckb5K9hc@)k&cwSjj=#IG#kdL=hp$xXGK?}tZRWk zB9{fC*u$Q2RYfAx&UJn`kNxJnrX~!H=r;`0^m?+MuN^k3d+iGD5->|T0e|HVm_*oC zgMGoG2CPOYae0Ko=>_ba$A^md|P;*e-*3O_KU)w|h2^6;gzt_;7 zwSB4TSGA9t`o6d^fKcH66L$@w*Sl~Yh`uO}M;0OH zogpETBd>5+>Bz#8VJpK9(Nt@P5t{AGs}$J94x>1YVEV+B4KJVdVtE$gElO)RmOWSS z;szyTGoQ9gf#2H_bA|( zVG7Q*6pW)AuNu)WCfu!3fj8Yft`8`(9$=_i+dFD~Em?PD^TxCpXYi0DmI1*wO2}5I zj0iB%#w6fAOL9OR6R6UKj-4zMLV?tX1>nx-`pB7agX;D{? ze%6f9B408b=@qDb$OLG9^2cH%bfUeIs_rHwgs$6ACs*Kf;5Lv?^Tf2FXb<|0Qe$S! zp*cjlr^@@qdD%kLadH&t|{0k)v1a^miBfpzEiIy`SuTFy95A{iBU{3y}Pj@x@W}dB?Ievoypti@LWBK$eh7RlZJP0L?2cp zKw@T0bLF{$j5{T1I1y~OHOQEWKA3IIoESJ?zQDw~(t>g6b25iZqRMROc+ICeFkHvFfsH0gLfQd6+aNy-K*w6wLBqZ|WBA5l00ijc0?_H9)a5M{c!bVub0{X0M zXIJCV$M3cSrnIDY*HPwN7+X!lL5+mq#i7H2)6o)^Oz-&tVQ zKGF@lH-w`n<4Pt6J2v+JTxm@UNhyg6Vw2 z=_yq5t}e3Iq^U8~oVc;)f^P2=7HIR6?Zaj!1EjCGtx6D&*=IQV;LY!Hi$!WmxDki* z9MN7e1Bf{%AC)27?6K##bnJjnwFi&T`ZcnRbqpjbcZ{CN&(E(ft+rsPSjoul_fe8BJ;{wGC*)Oy$LwY+B z?!e-luZ5wAuEK%1`XMaWwbczC0;_stIhSKx9T0K9mdem&X8e&kwqE?w*aSoCTpkyF zt4>QBbvO?QoCN9^;W~f7T%N{S+3)W`~hE0bu>P5dA%}Gmlw+?4t+W z_2PnnziPG&bw-GR+EZAXXqQ~xNYh2IoeO9(%q}di#(Jh56Hx4FhwM-RCycEWk?y(E zhy~J2@B-4$27HF#r;fiTvt}(4vZ_P4AIPmE3ya;{@afT>s6>oW%Ttc%s=Kv2AWx2k z>Jg#P~N&6;w3HH?c6&nmHC-hFZcCvG&uoGQ2%))Y7)xdOaCldeg1=6iR!+I_|h^ zbH}=V6HEiLi+%>=D7oUMN`@;3{WCfEL?-C-<`8j?3|kJ1BT-Ut-Cun zkE@#YI8TuXptUDiA#S55$g(;5sZC=vaRfQ?hXQ`?{Hh#-8m1m1c}Y5ftv?D={3mRq zE-4I@W;ZOJ)QtA7eIZfPZ7KfUBn*ReUCA8QwhR&ZMwU!T*tj|2^RNKZ)Ue(IWM&9k z8W4po3i>>Oe7xh%H*!XoR|$vv57qN%@YgoE6f|*{RoLU9_O(Sl#Fm4pB;TrTjD4cT zTI=O(VrXFafK(fy9Wm6ct7K)qEDKGm1`SmzgwG&Ohr*lKwk+RuO7sY?!uELuNMgGB zs2o%kf4)9BsFM%4+cX`+Z7k7zju3G#*l;tBw8t9J>DRhE}- zuLq6MDTGpj2HXq$aRHY@q)u+m`GR^aRGNZsc+aJmi|!V>kXyTag*u^cb9W^2LQ{O- zABX;ZE((86E=UWZULeO}ipQN$g+91AS!UA^ZzZm-V5i(Rs` z*ja55>E4ZbW`rI6Dzy3>9P8xTbOD5sgCIDYfzz1@RL$rV9!oAE zK7U+eX3tAt+Cts{2SNKG%L;#lEhOK-@QA^jZW*<#ag?$BG0A;aj(WH604Ojm1##AN z_fRX$Fl?W`AObwekM0#CaS$!<^QM7Q)b}d|%s9 zxe{j`F-?dn+G#Dzz9ogPJ%3{BsnJ3l9+Rsh-m=n_IQiH|V^9Z_8ACGd$Qk>-z1>=j zf|P|EymUT3kCx*8eu&=Z2B93XGi3I$eH;Oib)^U{Xz%?Fe#mDEKjP1%Ysi$5J8VZ` z1FAevSvnb5h2u(%Gwgl+2!G!bm1&rQ5v6&AB5n91+st5L2;_im%@qSa;V@9DXc zklP$}L88E{Y>;JpamlYDLfOl(#XX(w37k`HVhNH{i1pH!6h_Cr3T zOgGwbv)LXw>6uJ1hz}+Uhnc0kIQY)dXan`a&q+; zM2B01x7q3OC|$;4R?pc|TIm}AMaHx2n{Y5Qiz=EV0%GBve~y-rO7LR;T3lehGAuP& zuO}@B-ytBp&k_7CFQGXeGdQ{Q@zi-xa3)NLs^oq*f8095WAhNK&)LB;^p1 zF_-qC*z2L3hSrEBB|b(Qm@^yn{N3n9iVUwNZBHiXd(iiq4ATc#b^W#vQJvxVdP^eT z{XfsX$Ax#_vc;H>x1UlD+mX+3&M8(|%J+87VPBKjv+wPSA0VBUB_#wmTIj%4L?*>o zmxcyx@d~;Y-+wl_WMs%|6|2=3{{!*w|Kj7%=kA|;PXEQ<`^7K*Y2*FmNB5gQ{<;p! zAgsgs^EZDKgpu3j?PqK)!qyGk*8QCR@7U|B|K{_T-~6%vK#6_Tgu&3@wk{A_1@xA$?|R~3H#=I{ECApHD3 zp8f6d{*yoY_H2GUULxX(yuacfezUPabp6yO;U|E)`tZ~HqBUXrX$U_xty{NW+=~jP zFkuP5>-gh+f1dsMKPn(yZa%qr{HU>e@$1j;tM+B`C*SsfAZh>R$Pkz z_lHZNCcjeQ)B7ji{J|GL9s_sl_rB*(e&?ir+~=F$^WyJ0O3MDhN4xpBN-2+DJ{kr- zKl|}mAD{onfBgOB{q`Jxe#`&*J!alV`qiHLe|~5z-+#xCZ}%s^due~XV!!9b-*e_a zZ!CZ9^OOJb=O6xk+vqUo!L|OrS$z8#r2p0LZt{P!$^K`5_ZPqTqWrpX-)*G%i%-EF z4W+q1&^CVa(UN}Mz!W0HTYS_dwPF3<&V2F3fBJ4-wOa;{B7c3lm-qJW=JzT5^yunO zKH6ISxChM_W%cWC-}LJy41+JJ88!dviyvP8?j!!{$9MV3)^+r6K!FQP~NDZ}@EUxWC4!rxz>um19jPx$kG zz5MCx-(BJFUVgvj{ZTmU*~k08-zWHSpC50oYN8;oAx?c0;`+WYY#I5`7r+@Ur z={A3ry|;Yzt6xz+9RK@$Kd#q%kLw+-Uk%Tzt?W%~)HYmYK+aGBrT(SY6Goe=t>d;6)YJ|*boKVG?`!ymsr zWb@t8zC8dM)W;ioH}7zO_vheX-+$8kpg;Q{oXi*Bz4&$R;?sZD41Uszf_KOIn_uD_ zfBDf0%5eN>1o`8Eua?x0E>1pf?svE8)B8l;_b>!n;q~2zx=nMBaZ}s(HF%%PcOU)! zy5C0eQe8PX8 z+uYG=@!X|&Byp;^RdI1Izxue-KYZ+OKF!1Vx2@~@ZC}@q;p=ZN{!d>0o7(cb-Q1%e zzDDz1)A`4rzCY}@P5%A1_n+^#e%H2s(%OF362E`j&(10P;^RF(zo&myzT4^VzW-y$ zO8(?;`>?<5!~V7p``bS3UpXGXJEngl`>-Ek!;eVxmxx6F`jq3R@n7(O@bE7}$UpxfgvIpbW5)6GAT}NFzMsuF-aG&Hz4Nd3%YXOpd_V8`)9;S+*H7YK zf5!5AqSG(`#_;sNN30#)V|4#j-u@atb#?gVS6{dzw&1s4yFu`E(_xwT(PDE~-k)9g zeJJ*`h~V3ozWn*X^3}(1e1C^rzjxPf$2E8Sb>q7&V&88=t)Cy`({FzB>HZg=X21Q5 zpN(#4ZXa>k?|t+9ci;RGz2HmTf9EhzY$YyUnf;pjc7XrM`TP(`|J7f9oWf7SKWxCq zeDZ(uOAj$~_6~dAJBIDo(0S$ImwzUG1j1W{K2Qn9@AyK0$8d;U9-mg<2k?J}-QHKe zNgl(OUwuE|{_S1C#QEQxyYllcWcUBK3z7bHx{x#TLl?68p$kd>7xXWGZ9@9L{je$h z=lJorKc;um{{z2&^Y;-gW0v>&`u+HPPXAAA`!NCZ@4Y8&&DS0pbc}{u2A{wALpW(A z?dSCW!W)rc`oG`Dh)A=+OqEm~bsLtu!u3hxJ()v0CzX$X!(-?|nvCCrhff|uzeUHQ zK3bSbf9-Ym99+1rdf}1(Ivhj4YeVw82N}D3P0hZZ{kkgS&&^K~PwBt>*_nRPVunHD zi`>i4-~8!6mOgr}PtALV%s@d$@%*RZowk{O634LlFOcxM7j7Jq@59=!|LG5YalbCL z^DsMXHF^IW)-`LeRWQhEE+_o6QT<-ACx%nbc~>=jHNEnC4) zje-9iH^W9OssSgkd1w1Jr|X$1wMhs)F|%whTw)=g!#a1ro<|&N@vSRtvLkb=?!-ch z;jx~^VkfdvVWLFyMlZFkvwoQd7*bCKtb^D+p2wF49|WK;cL0c9kZ8vmLV{X&EK7t7 z(LU3GeZ|Vz+_`!M8QuB-o{aO~*)1X{>|@!g);K z2eLgJ4z9yQTL@Uh?smgWu!34HrZ(>D5PtkF!)`<*Gt-=5wad~p_p*vU-dCoIa-y@3 z?dOXQZQ?T8eY-yv1812`DCXv=!bqajJ9Zu|&!i}N*16ZeJ=fDkXKHcHpJAFbR`;Bm zCUTfPD%+kFyM=9ru5C`jh&n;{R*zL$)|0LVlg*OWVAK6tk71=3v0N3L7s8o~%&Zo! zE;P+Iy=jFfZJN&@s);^gfm~KB_!QEajEcb~t}rxb66WEBTOAl^5=thtUD*SC0FTDY_AEbx#R7P?S&R7OYWD%>pbn4bz zx|UQ1+4MD_5@#CrAiRqLGhfHos9<8li*u|Bbpw@-eH`dEfG8y2q7V%}1EM_WST7K_ zKt)7+{1^UsdoRaf>DT-H;8LyZ>@`C+Y@lF*6G!uawHg+uY2lA~jT28}jwj!;rwK>uy^b95l zWV6!aj0_;M?APIGjZ5|1?N8!iSoe!y(Z?+h6$NS7xEDg+%a{97<~X^7190|~Ny}d@ zo7y2`(TMlSo~Lm=d#mPp{(yqv?8zS>gNp<{B2lj>H%m=w0)fX$7Kc)vDnrKtPp}>C zag+4Hu&B9^pxCkto{SD+kWM6vHq}ohuZHV-5O-)@gT|{t-=a2AA(>)RBxSq~mpZML z>SgKh7159_*1F1jF9h^JEonP&dOI3v=85%0i_5m;W}3sb&bf&I9)ailn&@ok(4~wi zQ*jZu<=CV@*+cnKmilpu_&Kysd5G7SLw0McslSS3h5I|F=cU;5a<&v`mF&+13Lc+x zKG5&BWRk&kR^vfw8-CVr3y_A#B1w(ik>8-6Am2Wm8(nXUEs3Xf3ojvYanRn+?&7#; z(M*DK)Nf@EdNGBbZ5_!bpN3R8yBE9GCwtfne5~V1W@ckO=II{#V$zTLQ=$tx z_M^~8Z1toZ#Qw_Ayh2FPwm9(MfgNL#88)dN##E1z=?GB&=Tlz-jhKqYjpwnVN3wn@lk>iL>yRvi=DwVvztrBJwM-`nY@xu>8hAkNSMapN2X|Xa zC(3kNJaukMrsZo3=7Wv?uFp#$jmDJg7sN?pVzS*XqkP%%Z#SOVjci4R&5rd1uH|!*_7@QdI6WWwX@qs@dV2Tfn9jJM(yov#_OeYP8RBir5Zg16bh_h|5*h5~ox1rovY z4$rEd-YP*kCTO%p3gqEyMd`}@{oR<<&wBQ_-?qYp`g!V>XM@0tWE0~XDe}vPVGFsw zDYsK6hSJKNd|ns>$a%q=jc^R(zz~zT%iIqeu6ns=z(?i*i z$E^;KTnOlC%6a5CF{9A|JkQaVK|)EwsQeCNUKuUmE4J>-{W=2z(|k;%E^yTp46>Kg z6X~+FY}}jtZ5p_0xZLPEl8V{GNmm$R}&(yns>t^#tb_dphaIwB*mBSmxIw9Bd4@jG=*0BLF*HmSn4MASJ-DFY*8z_h^X+tB0Mnc44iS*L#%i&f(Xk5=UBG z5BvVg!LE3GR0j+IkONKA>);5p>jv~zQtX9w>kH9|J#AQ2m1L{sa3Gn)ysy2J_@qdZ zS@$X_v>ry$P>XhX>4Ms@n#DnYHnf>u@*yj=9pCBR+*0uLw!97MUkEUddV=D)7fbKC zLBHU+#GJKZQ$^}vUGgyn&zF=5+{-{dnbAR6ug8caboBe}eCV$#qod&Wm4$JQa&JcV zTo!b0OF(ZGCkBd&)0UZ&exqa#E3zs2Ie}dGBir;eDhGS_3H6AzIwXUY&-eZrR;f|s zqhVuAS)gy74wl@7d{y;HH>^)-iQ?KsIzIR8_0rxRH2EY>1}uw4u6w@YS9QHnSxMoa z{e5i%vaF#ldMyB$_bQ4`q>8!n_%VJpZv_O_S*5I$fe{d0yYhbS9~&1Tf7M4s~W8bOL!dtt!9Y5mtxFFs?&< z##)x79nV&%Mtg5Bv>j@pE+=EccAPI;p>E>69dS5bFhaY+d2Ik^5^@_*aAh}6)>A&d zylesYMH+5)H8Ax4j2UsfEZm@!67Iyk(8LGBi;C^RRt4M>u;#qE0`GV@l1mCP_Ollek9TAz z;(m@J;8%!&z3y-ZxMGS^JfmJb%Pp`A zE`#|>f8U`RJ|hYv6{#r0_;z*HX?L|m0Ai9f>a8_bhL|V0j6NGYtVc1!vS2ZWAJ+=1 zJ0m>w3*iE*Q&ow`N8ZgL%u1YitIH{*MFVcucs^l@He_PV5kLh_C?MsDg?6D0{<)xI zpIOPh+tlw+URrCyic5z`MC~dJo|f-w0e) z;@mrC)Rm`0u&5A#WdYxLZi)r=se|(tITOZePC2T2Hja z$du!mQilzv&4bL{+hbYz!4W7dX3Cy=eU)Atd5Go*F3#oy7;7F31-iQ)+&NJ}lTAGZ zQ^9$06S(VD_xGrWSAvD=mC1?TmDWYY!t5ytan%UiBdbuTYTEJ*QC?Q@%*Hd>Y8WK>q)|IQ6L!#KrXP-%~E8oh)Z3`_X zgIFMTWXjn1Tev5Ua07y#Zs>0hi0`r!xxX+|LqRJkpYBYE;53~zP+D4^$j?H!TyUGC z!bhBOjMf^<2=o>zpkRNjmN>a1z_g7$9H{jbR*(cqc6OAU8gkD$j@;)$BvhJ&^SgOn zxV^*m$%TzH$P{H_?E@l*&YbWDZ^_N*S9A|EPUX2iR$P+0y{Q1f(ryy#->4@eF!rgTHBW(T>fE-|k}8po`UEK)}j6U=Lawl4d2-W|C) z)V7t*F_5T{{$N}27SydVxs7WhWv;FjE;h%bxdKQQXc3BZMjlA?V5|{kTq0*e-~Ac~ z8$I)6Gy2}Xg^haId9QHE9IuFT7<;io;()r4EfJF&`RICq2RGIE`sK!cPnXGI@qlX{ z9x#S3<|>-y_B~z-_cTY6^8~%QQBW5il7;d>39Z7sjv>Yw4`Jst1;V!GIAx-vlHg7YxpK~bJAtt?$cFD!-r?TbfCt8nM794$NLlXq1I0X!;bo6s_qo- zbZ+IrJ1yoSyZ6KnwXnT1t%iBn1yx#ium=zgvo&SKQ|XkN2b?NwX6r>o_AEIGvvTgU zLc#9%wNRHMd*3yB+%7jf49wehAb=h}qynMO%Z#BRJex_6hbSyqauY*{C^(()9s^)1 zriNX6OyAegbdJ%SeJs?Qu;y;!SC^;n44@CiC#KW*<@Wm2u1D@@$h$Cs+k0qm$2%jbPRzb4gc zdcmq?7vCi9Ce$45IV9(2Hk6AqUOS#Zp#G|B@&w-*%)nE*W*|X4rCk_ zN^EA27eG}7#z+$k?aB9EGlh^dIAhk~s9zq1M-A&-lJ$ealC!$fVNfFFPm zI81?hL{EEBHt>qBIoOh9TaJ3cuE9lHd!eoAwL1#wE!gb9X9Sx2w9c_RAH0E68>Kzm z9B?HN+g@~$a>LDz@y`eAGO|lu&(9qxE;)&cXB7KF5@B+~*P; ziPg2|$p=H3=LDz?o^eJWwE>b}bnMxQ7p`=hOX7?6AD2uaU){o30x5YQjb#W{lm;@j zP-Ghp27EZ zylWuVg5^@(Xx+jy%*Fe={N9D16U7K}FS{Mngc^M+M89=DE#Ce9vM^L3cn z)2;UqfIMU6$tu^_lQs}I#T%`7RQ$*vQL_!T=24$CN^xIH-kxu7L>Ui^tEh}Q>;Z9d z$=z)$=%|HvV)8wduQ^Q!f$HNPw@ug{ErJQ!EV1Be8Hc)e6D|SRH#S^i1#_idJr~b= zCnMANL{CUS(Vu$hEFw@2-+Cq%XA+z{z3yj>z?t(494SE^Lb*EpjSba2&3F9EfI^Gf zx7m^iprH@Kd=FzLTo12R6j}#Bh7ZpDv37wcNNHpcq|w3*ltw0gx+o%@rISuY*JyEI zS1Kr7D}qk}SmpN)AqO@SLLtE(1+5oc5~CFjq!)Np>d0pzM@OmlTF+JiZFQP3FZCL0 z9PEZX1i8Ti{0qz2nP1fl2qgm}naZ9LVKHU{k(*FZ^X;o1vEFgsKSn^%&B>Gx;3^9~ z0dqS)##I(v= z67&phS&O92uqFVWj;uMW?_lq?Snh_%N{%bJ(~Z%&)x!~V^;0Au09_K?o;cG+ywR&C zL9`c3tMFMO)=H#{W{AegIx8B1SxN^yENJORx_lhtO9fzLy5uf1 zd3Zk)_7p?WNDB06rkk_tQ~|_UpOM;|_Mn;SXYWCajhzEAayO;()Ftv%-Hptr@R;kv z(Pl7iWwPYXbTL@h@TzX%ZM1+VUwnS81P)9&=!*!2y~9Y}r_FvSgO<)85$|FY8ZO~U znA63fk*Bre>q<~;m!^W@r2)yUP3|x1R6Uo&Ypp%K3`!5b;5M@t^BiLgF)xIllw}Rl zR@Br1Y|)ookfw8exxg$%ieA#Yin%v|Gv3!)XAPCnOxNys^B8y`)>rZHP>>WF*QKOB zd3KuGh{99NyqqKptgYl;HjjC-?@t<+F0`pVX{)NI7uWn$CNlgr)mN=8D`NW~wL#!S%y@58zETEBK7U!((q^VnK7i1mnE7?Hu)48eaY`4+u zv406iP$>4dG3V#}c0|I#Qnrx?2P6M>9f#Tq#^8y>BL87``ix*8=dM>+e1pe!G2W4` z*iZga5<{O(9v67lfH=^Mu$Y{WuXMe?2Zz;(ot;MR$WSTRP6tJ~4a2lP0XWiTVRgE6 zQ&>pLJWqr=<#E zwx2An7`??)5Q2QUPF)sYltq8KE|Uew{%&MzW19Awf#(hGWMd3SXJ_O`n2m5ZP$gc@ z*Txg>|YJ>2S>k=?%V%q=i1_0)j&eg{JDv+sCpS->$k8=7#QN+Kfj# zDW1M<9|`u=F8jL%6JR9Vk7luqH%qvrHk7xZXH+t60RWN?uy--fmt3L>PQ~0OxAxv0 z9`crDA^TVDvia*GRgd^3HheLqfZ@Y^hdP|j-RA80xHa+Idnj4_!aPZxDbj>A1yEwu z-gx!}Uze$UMriVk5$yXq@?v!LkogCH8ea>oxZOQ|^c_I*7hXE4Jg{20|Qr2pY8c%MXRKVAoWXN`F zs*t@$6j~1T?x&D%dGRtw<>%YnfJqaxd&0GwAevj*TW~{QyE7lZ((4+P3{ho_Bdm7? zI1Ry1eD2##R=7e5iz&Z&z+5YvcB_o?-O%-JaqewlU^O-Aanpp<6TFuL*PPE68B3w) zV2^Wn0Ts@+1DhM%%7+Lv)kR&+sZIMrY2Gu%O@SK7(l_D6HPEmy#~ zS;5g@$y?==Im$)y;&1^8OB(XSRs#ooE{#4#IYM?^`>PY*Y!aexD%Z?DlN;$_l1zImmn(nUUVQQVI5z3jp3B{4c9(B^FXom6Bh2hOpi&EB-(5UQ z>z1S|tc2w)uHNKffx|Fzs@i;dU8sVpiAG6psON(@yY z?VF%uyReU{2)aWmmMD91Q&? z1VLcnV|iKvUEE)L+v{Wz&?%e4RF<8;3+n!qdjosQj;}&xAuu@CQHP1{mWK!7bZ02K z&@ZYFvfsP5W3a<%w%WNH0yjfxU)%j)Z_+KZv+i%{xQm|pD8T+{39ZYH` zaFWd9aXuQ}<3!!P$7}Lx7C!02ZI@yy&3f1CdbZOK>jIo+8|!)csFn@}%W=(vyCs0m zx~>L+KJ4a6x%W){*0~(Ha@;0ek@Y6Hkn&>jSVoaet&1)i;231_Gny3n1|XJT4vPrk zC66%vLN5NCl}nGL#`M8u!_ce*2x>h8r2*~^xqxXpNJZ{#j-0*hDolwF6FZ0P?;sqo z=l}zW*Q6iiE7}ZP%CPjT=FV(?rJJ#SA~7sBpy|Aw?FvRdJYSYIn8dZvg>xL||aBRKO=%9`dc=p}QvePfccxr;{Sez;WId7FLt#VlHr75lnF&3-&z88Hl&wRG+vkzRR1@jT6tV@gO?tLmsApH9NKQf z_vI{1%h?$KP6KwfdeNQYh2ZAW=0@90fE?y!B2n;C7X@P`6pj37f9ahFtln^cO}OQW zC9C`M3IC`jS`*;h01m01+`41cmGttetG8>f+(xI%@qoc<+YGdRI4Wb-9pc5(L+1E^ zJW?@Om<=ATKJ7H8uy>b%hWeu(-AdSV?JX0uD{Ogz;pBzNEn$tmVch*eirj}E)L7s} z=k2h!n$z+Cyh)6iJTboR6qnEJdFS}(OkEqU#nVNMbw!=%mzgU^c(5{ux^8lu--2q_ z;CCk4%xu`G3q>iWc7&AF@vk_=`LRF zU9G@+K;3NV-P5Cm3*-~aN(ZI80;j(m3V9EZ&^brG{Fc6&Jxa1xCUXx%xDQSORU8Bgv8T%G zas~1XWYP@hnXg$puyPkir|H=kQ;{V5c*``Gn?}qglAdGn@T_#RS0X$cVxN^FopKRl zvoP!=BI9Xswiji-dv8|SvX^exQud-Gv{71POiDdc8n}~^PdlKZ0#bVclR07(IX$`dY()EI zA<(Fl0~>m~WrftlOm-&$1`-_|%_`#NLQ7edc|kzE*M3;a<GcSXO^{son}YwJ%wEaTzE|@oRt)odi+JY z->>MK{4^gsRdJnb2?xcn0ZL^^B=g)N>Dj_s_PDcNbJRexl7}Q5YyoLY->+s)l@ypa zoDic?7indws3&2JogRf{he@H}EFLF>2zkOU$8!q@f<3sYg1<_xfyoGWqJe`mVuHrm zpUmxP&WbIGfh=9-sBDUv3Dv4k8 zxYVNk?y7F~I!HtE;p7eyidq%_KuO4pF#(+3IG;+8w2gpV72QQED!G*~fY88?C_)z( zlvL`Kl*#Itb6)3`aDThqdJnCfj+}mEGmux(#*#QgM!p*HFe*LD{k@jC3n&%Cg+)pN z{rTK_Y)q|%Gevz^NTdvp^7+y%msq89^22pJW)8UMOUV>ttqGDQX~^ zZhF0dhw)L2v$D*QI6huGBfke@vihx8V!;GMkGbnt0 z*X_w0ywLAn!{O}ORjZN=!T|L<>bors6GGWHkYh-@`o!^Q7txT44=}34Fh8ddZYJu^ zY|g#^whgGK{&~ET^QE(X$KN3)c6gX zxj?)F6V$dvu<76LwV;^Jen>l9kOgtiact1bRVQVs5s!vA^d1QDiee zRO&jAv;RZA;XB1QoYg-E30tf^7jG}{S{&t?@SozB92j+filqLxHxB_Xy~`H`xM)p+ z^x0MKo!MbBYfgBO-Se+?%o={WqfPYz*8@u0O4KDB?pd?niut=QWG$VaC$X2_fN&HXsT!jJ=7gmf+4)I-jXHE6?~g+tcvvWF+ zz_(ahs@Bwl3W1t6ppYNpnfiV7=x8`ojA{4zBgtLt__9vX7RsP3?@OXc&>Cq^5w&MX ztSc}gsvUDQdEF+I^+l^d8CuHYI@(Q#o5OlmBM>rnJvE?zAtk|~u$rvs)=NcM*X7%* zB~|oV&;gwDVLt8ZmT%ek!B3~_JTYBVxI`|OXn#7C!ZPnw;!vR{lPiFvMTI9PSU>F4qnCugAT4C zcjiqU&VTD9qoc_CGJR+1aRt&%h7|1T3eM1NNy+xL@7LD4x3|-D5c>0;d|99M3gfvD zl$M=e@Ja5kDBEJ$o*dR%VU8E*2#oxN*UoVx4ahwJ<6j&7t#?<9d;q92yKQ93`w2!; zYX5^PC-rNS+uDt+OeXp*Cn>$}8mZ(&k+M{50t zMZUNT2-Dh8=Wm_Q9C$~s06=;k4d_c*NGX?!Wo_rwWFObxh|h_~wjb!qy~@4dvEQRO z-h?Bn-T$OuvXd`y-YOzK%IHTfD`3pII=}8-xJQ$ueb@n|6Y0f+{3yS>q2KkFKW!V9 zX(`okeEEv?2t#bPb(e>g7kAhDia55&ExkZ&5yQE-XeZFasrF|*hhBKSP!m{*P<#IF zq2~u$GVBB9pIHBl#qRE`K>J3}T|GR`cY2WAnbj*rX`&+Y2-3_W$WMcPnXF&5 zptg7fk`8{-Dl;>ba6sdb@Am8S|Jfc36#BNwx5A8ralse*3C|zBACBWwuW&OO-bg6i zBKi#b|Kh)@ANX%McT;%hnAX;Pwn!i2WrV^IT+NH`aaEz-T+o~AElvCdBl@>|e_i;L zNP{CkxOGU!2w3LHRQD5%8MnpP_Y@7^_S)SpsFa(*^yEhjrB!#3e*O36kto+Vk6%r1 zFBBVVdkq9|$%z}kc~+nE?)B>q)hedBy#6-Be6tDPucSx434Ac8U`^wbOq=zYV%}{S z7U97d}a%lw|ISbHQ7?cy`SI24ZcRguyXa1U2!$pl zP(*Q8YJ_e+&ePBwekq;D$~E0W>7sA~wD`kkwHy72hnDSX2LFSCb#re+OMSdKLlIn) z)25;L-m`l#G~KRNbF0wK8`n4e^@B%DNxZH5@he9f@>8MAp?LuIZ!)Bfb9oKB5v`yp z9**Y6Rm1}NKX&ff<#-$!zDAqkbjm8haO++x?U+&dlqqW5L#p#57W>zi)uE7to#pMU z7W0j5%HFGhPlHq@g{!k5D&3I>_2K zJJvqQ_4if7Nxo0Aurjjj)Jh-g)K3Ud8W@DCK|}n=?Xj?R{5Fbra)jHoi#A9nvVR66 zGZH{6ig2g=&2)4W1J+Eaj{eT(gGMzVVQ7@L$FBeLG~oRLIR46iyDwH9X7i>&Bl;Yo=@Li3h>!>W!GcFk1&=^B0FuULw4HLz&-vAQJK!c87uK)13DR!P{(5xg zs*Wy>>zTY?JooS&As%N0cDP(s__*ZJ`vh>sf!+he^}x7Sg4((VoAkI0(TCSn`^nOO z{dyUFa7waF1m42Mc$z#Kb;#!pTU>%YOWWz212sCsTf0|r54G8KDbZ{;#?}?%z^cQ! z*1s%P1t!)#AA};Xn(yvUr+6U_(!M;%BmRX_Z7I@ql|mae@xN(u!kquidak zscEggQiu10BHJQOf^fo~Duy;CZX9$vS5WZ732#WlgZYwu53LO6PLB&yc8jZ$>^s?S zq@CUwBd%P|oJs*1c%6cct{kCb7>*}4wj2B#rAH$q7P2btDKR#jV zbYto^?(X%AA6;9;MN*4V+k%;9|l6UD1yfu$I`J^ezC}iy!Jd`b!cXdBy{N!fABtK7%!Kc@cv%UEKgD)S3P*R zMdQn(n=k7@fD2-dp9DN|vFKFyD)Cq_rAC+fpw_i4zKv>{AA_%a7Ci@WAssYZ(-*1> zh?dN30@kBHxg*}%+Kq{Ppk5M^Y&XH7m_-;Hgd#ui&uW@~tFGB8J8g!=lvY`<_ z3*dTZzFTYAk7@z{1LYO~OQhVxCHuEAv0Yn9)oPMu^?QEw{s!_R03_s8=M z#&M=wC^(ztNQi!;cBwUo8n15iY@)+`c#Uzr8kDfrC}I&%VHf(&Goj^u^tx_HAHn;MlF7G6f8yhLuQ;*3sp6jBzQ^ws4X|4S z%f5c{p}4)#d&)W`-FFAk+bQ(^l?g|)I%@Ifx~O>5J@Z_m4>2R1p|-DcYaa%PW;tOY zboH?bpg;8*g&fDDYW}$CtB2^OHyD)OoZY*x2?~q*W@LOx4yRMHIk(?!j_%uf?K)=e z)V7dluLfv8KOmU&MvdD_iP{OExPDuAN%T%xN*L;cKnrYm{C>8gq(D*M5wA=1*u~Re z3vWZ0svh5|yLi-@Wn$R<8ZXin7jBH!qF@n^%j6eDBqyvg%$$6BXXlDL5{>m4qmK`P{v>}2L(+nFTplP-A=mvl7Nk;(NAdj-WiQ|! zWPP%j8S{iSo|H5^6tFj<1e6>bU!}8ugs64rkP2=Bagl7j#kZXPGT-QBbw7mleu` z?l@}ei60nALX7U^aMYl|PRsfdrvi2e9e3>~?ch2al-Hl1j&OVZK(o!T&++Z?V6j1r zn!XrnAoZJ{M5;V5haxjc-bRy@v}z2Z1jHk!Y=HAzY|;K<%qdOap4zZy@3QV{XX78f6_d#2tWa2(%mO+L7w$tpW*2O0c~7j=Nj z6Z=kva-UOZmDPOU?zi{s%Qj@r`U^h1I5(|n^-ey8usGiK6HSKpmh%KXtAuhYjwR)>Bw7mJ z&ZYGdm|j46?4Ev?#u$dtbWgmKpetyp{8@z4F8bZzahp{?y$ktuRy_cHpOu8hCd3^_ z>qq_h^cNnC*9f~lLTs-Ed43;v9{mobYY+tVIjsrNU0;O6y&wm_Ut_SH0{C$(_V?Po zLJutP#u`G=sTTwGpdrH?amY3SDMvyeiUK8wVP1CWrxkQqHvIZK#CPRRP(QVT4H898 z*9mdW#d(C{TIs{b3%clg)Y|-_hR}*hZFAm*dv-cIzP%iD1Y(Jr#cuX#A6Mm;t*FZjJDFM^{(r21uR=?gIm%xj68-a^UHH7f1SoNz`PjEyr z=zi082EBcr;z6U_i{fK=2EbV}p8KQn;Kd94paJugK%?HfZ_g^AbzaRynw<01dN9`d8`{F^%V511ms~`9l~>7@TutWhiP1h ztxC7iL_JA+-O1A`$mRggNqxH$+^c$yOA`&)&d>e2o;sLT&Z~8IgZef~mUVyV&bUbF z`h_HhQY=ajxFd|Y0Cewm2Xilb!yEh4v}?QTfjYAecXx*6qH@&nTWx&z^O)|2x5`41 zK%2;LGr`mR_PLa=uy4k?8jwt}VcteVNVj@^y=wd#YdgRb5Ofbz3fOrJXzYNR@+A&0 zL*a-f8nxt?918VmDc~pT1I((o2?c}wZ^LK2$~ni$j7omHXB>=0CthoA&^8N+wGWBs z&0mUIeG-*a$seD8 z;nJ9Kn?h)(9YxO3MN z3^UR^AJ?LISlE+9pOg5!o5?kxt}~k&)9jnWIo5Rkm|6q;rG+dt7!sZDJ?EJn1JCY5 zigyvS!*}K#pk8~1Y3Ef${%HF234@boq#yQxnfJ7H2Yyfc=H(^iJ(g4I-q4lNzneR` zmL|Yq&);Ki#XtA-y3?}CBRhJ#6l(gJuhB*PEY~5=+Sd>HXqp$T&Jz&P85E#=<)kE$c~bqW@j;E~k?8i%oCX;@NqZG78L!9f zRvu}U!$-ZrJkg21Or>Qlf;}JZ+LzDmzNmgcOdR$LlIT9DPp-uQtz2r=)3a7C+h;uy zny*5;)4!-Uy(>)cHq`mdk`0Y3Hk=gkiF}2r-0%Z^o-gZmQ0!zs#s zJ0EQ-!o3jgtMpVpcsJ#c>t*PM!r|v9Q5SZ0iB>Q9K;%4mePV)KRVs!{BL5w5;5Uke ze`6vcOb-4iKbae9DdvYq+?0plc64114~_o z{%mNu@wlJNlc*_p4-PVY?R%$^`+8bY%yV3JWvF?}9`&u?TlGxYDZlDP)1Iy7XJ~N$ zJxaICqFHwv#d&w8LquoC5VoL!=e0SYmxxO)sM2UKhDJAgqBDEH_m^Yw-b0kCq+(b{ z)KMSDW*0y9o3+o3Uj#2ffkkBG2$&m;@v_AlGwM=?$Q0^W3B#LL(Vy}cEQ`wj91V4Z z2jvv|I}Motdyn*`%uQNU$l{9>xEpJq`MC~gWYypn8nsq^GRMWE)wW-A+W+y!! zD#{1hKJ9Xmud6Osm1~_|E7yGNmi(i#89Farj*+ycwO$pmC+mPo-XUd?Ju7b-0?^K zo{ul~S4AS4uO)^=)QXc(E1;iNonhMFjlq$5(O0}g!h>FK9glvWFy=nEPa}5$jgwqq zOtn|3ZA~vwH4Dnh1=sIh0kpF{7EQtJEGQUk4OVKymlxd zc%O&|Uzi)q`8HmGWtaB7`wa$^{a}y(nRZn6ioSb@;-?d12fdG)QwGZO!PCCIM>4ec zF&0#sw=)XWHktDFuf&YiZ!Z8bF7GXsOFH2m&i8^Y&Ckn6RA)coqnlojNa#K$$({yS zQ1;sTmX3AxOR^r9Ig#+|asKdU15$=4`qGw%`}~bB>rd7E`ff-^vco&1n@P6mY8tGU zNx!sl@KmRqywX%i`+DX%IK)sSU=de-?it)K-VK1mNAGNVk-oj+MEqSSOZ^y=L0Ux>9rD>AW ztT4M^XWl@H3hk4RMb54ZUbNQT7V_e8hmIo`?6?) z$3q@F1*Lt%q7rO?dWb*&`>DQ&;S{y)k5p1# zuZewq58OF6?{{-nur_($R=>Ma-nJ9V-(vQ2&a+ANQ_tdeT3c7dO?$6Dkvyh&Fe%be zOalJB2v4ki4^()iNFzpub&RZ|J7Rat2Mt&&lHB_5u0gBX?(2=r*Buv)w4sx1+1S;}gjF{ZONiJG(JNQL{L( z@Q%V44JJHW-@D^8x$t$^3`>-szrF-e$uy0IL+@r|zP|+1f}MbGZKkNUzdw&LRNPs) z6iV8W4ZNLXi}#QZD|iLh6GQ`9PRH2=7iz`2<6{Bz@xl;lQ2s-<#!ZI<*F#JbS(K3+ z?<*hG+2%K^xi(*4oii_%9d zH-rVYB@iwPSstO#{@TgmJ^URG`qajr1bN_sF9Ib5+yodpRFp-Py5EKaYYZp_trC!Sn1O#Xf`cDbu{O`iKac=vzd z6CgWYcYE>BZpT^Z%$2um>}TxKHv{#l77>}WuV3vYTjD`5ee2|vdM|bmQ=+xfUo4Sm zUSjF#NaSKe($ zPjOUdHAiY^+)&L}2!CD(Zn?a6KU*NjO9rAu{ipAJS(~0y9gUFa85i4#4H^@w7MhBBSpVx6GqE&fv2_q5$E=6R#Jb1uq1Z*@>(g!i(Oc zWokyd&qq#VAAP3LAm{Mshb_NQcU%({$H7(l?rgwZATI}?1HYNil;lKKF zAN^B2?C|Z$Rrd?R$klsB_WAjxGgj>!JcM|%=qy2Ns&W#<8AlzWMEj)Poh+9aY zgX0`<5O)rrRGZ$!)m-E0`eBT}u54(8F6uOIS+SM_KqUt|f4rmae|FgJYvi|x2*Gl| z|8OK#w}KJuBSZBc@?rK?v=_e70o`p=Vhx+TPxDK1rQmdwl0sPjQD&aY5tYbCw zUoD{ycbB?Z9et7Dqcft`S?rO7Z(&{yr&Qm8H>2{r8=aHzEag{~N?GJgi*aRZ)W+}c zRUpZ{<0~>eOh^DnbUUCK$e4MgAWJ&_w6|H0U1*>uDgqFL0Jn)9kOkDsM1Hv(hLDIQ zt4v|iN-@en-Ck_Koz>k2pW8vWAFLOeW*P==Zq>*%(){KhZ}*k_=})6Qg2qEtw_~cP z2%Z~Wy89(2(ba7azbLh#2Ykn!p2zQMHqFH>L-=o^`S-%y^R^xGMi8ii<8oh_-4_6A zY1189-rMi5HI)CXqKxY!L`R~%Gop_Y+_vHO)wEDP#T@&xo_i_jPuP6kE9%QRRqbHHMptuiy0tr?Q*z2D%vZ#-~JSvZ3>nJ)F+PUk*9Yc5#H9svZXS0mY#4X(8(+`j zjx2o-d2D21(=&D=dSi7eY_Ruayn}8h>#`g}MT~za$t(iCTA{_x%AtngewtMYcB2wm z&6~e3YByyQiM_k`veu5Ddpx^noIhaijgp=z&D9Xc7R(1s+}YRXoLd1bjc0eC7AUHE zE`}w}mng69Vd>u^{M@+MHHXUeV&Ii>{ag-ofxzQY9LUo;+_2|rMhHHR|8o{C;Ty!N z=AU*H)(jCFvG>+7jE{4R-!Ecx)I2B^J5_&DJ9-HlbujzC+~DQm=XuUE$9GdNy9sNhT4N;!EK-p*L* zkKZ!HS;{ux?%>0tEphw^k4ERrTS_?Mqq87k_PS|ZuSC>pNtR7{Ka_;>!c&)-tE(oX zoDji%MN&8gb&dLZiwfPsBs=Dm{%nFz=Bz~-PW^I_y`JxG<#U!57`fK!z27e4ZjW8W zE+y&RH(gG+fbN=&MeOIwD~uevn)6W@v{`ymZw%^g?bc^@O!}RL7=WUjQHH&GAn_!+ z_u)+P+`v^@ipdBcDvDQiwXnr88qe3BYcy!NKa|OZ>xf>W)fQIlK!3u4FX?yBbj&4Q zib|~yHW~KI{J!x#jMYW-qeB^`n;fC*iomL*?y#$G+R!MEkP~SqUKJr-h~q zzgk>{x;bCP%@HqJ&=+)g@eaHcAC13k6>?}Lmhc4!CP>LFk~00cYB>Mm=+VHlB)#ZP zgT8S!C$>Jd{4_>#jM?IVHyrh9DByd1GWH~b7x>eOmF1{Dd;k8d(g*@(%bRD=-F->l zBt_6f_?Gs?6ZRd{tIc;Nw^S2dQ-&P}J(TWb^6 zNfJ*8QXz2)dYGZgmdx21){EUL46F6{iu=s~7O_*jVfH&qd$8j@i}mp2ql(eo_8*Cu z*b96L@B++_IxvLdy!!3YeQ|36(e9-hxRC%f8|c1VzwgT>4E@17hX>5xjjGFc9a`oG zmDc$>;_e)+;~(`tcwlM;v-d zPBrRVPC7-!8G?Jb8i8f!htYBPQ18KIXopVagrFQDbZKjCUkc0VK0ZlZn0~xpbP0fk z)do9ox;q(x7PztPa7i3S^(#6gzROyFM82u2^5Yne%PGg;M~ni82$85dpXm21MRZ8I zB)X_i>lc=y{Me_*2ioH@FX@cBXHGF%-nD(L(;s9JdGfCQ_V{LH*thYNy_N>!)1m=|*%#;m)X44NH^h@9#nH$F|Ct2tGyhwST*#q{bCf z34^DppBmWV@w&R}(S8Zsa^@0)h?7NZC!KI^-@}e<*>o4C%~QB_{<>yS^XzuttiJ1q z%L+x&VJ1y%<3qJG4Rp3WJHn}A%*e#Ke160wV?XtDw7fM1)Ra!b*Xw=@JHlIU_Bj&P z^+3}33E%LO_^~rDizfm;Aoyg^p^WP~;X}O&s(hv8@1W$*%N)dUjw}D^=iy%aI1yEP zA%K4rz}EVc$AI4(AU~TDz)$Z3cOxwin%omPozoKBuUlOW2SRsl!;eGeXNKopKfRy_E&L(Bnu3ognElK8Uo$n{EaNk+AjrxfSls@yM zHzOTE1AF4a>#8c@81)96FU~Um(S_){o?5Ry(;y_ZA0M|xYR1im^%1kpG+NbM)7q{PDn1W zHj5m|l(YoLKO|JQACbiSbCQR^VLNZ}0*|Q3>)U5~<70*0#_;(5{#cOuOFi*-5L9Cu zt`u>n-Htq9vfw7x)<%c=N+Q2@9^9zJmB5-r$)pKG!O4@?wuVMuSQR@zFve+p*}NB2 zXXI+!J{>EgA)|F+ZR{gctFk&DnunMU5DbF6+UZqL_Ok|szz zS73jYfXp7Sjl?%6D?i`SIwAIl^oLft6E97L;$^vT7Y6NEDowv)L;gK=a~yAc%BN$( zw%dohsximUd+}*}{sIr7co8Z&F_>0qC1!0{V$IKWJ_(jC9{gR}2z(+X>B}N~L(r%9 zUitJoUI@(vbL)P>8v{n5w?8b7^f7h{tCu(rf4hsbTa1%p=wHv%o-#Cx|3p@y>6A@eX4J4>Jbo+GDg5MEn$-njDz-p|r^6snha0dkg_|iMoldJ}U#>W7ju3t5s zzx~wJtUJNOel;>i;qO$daO0#rje^4V=^l@8CI3H`QUBF8_UDD zneq0gWvU;;I-+wtfs@BS{bAQv&?!t;s192X0+2X?D`uXGk#=6b(*696msk3h4Sr^E z0eBGD4S)m3uqc;ijrccK6QBLnLyuc}FW16zLzNFta@~m0ZsK2+C=!+%w`}o#i!=BD zqan6;;1EQ6GWZgz&iuGFt7ukgB`LJ zlA|V5jv1)6S|m+&H8EHlb=!^B%Rz0nmaqWBl}5*1C+K>@ovC)5Jt_Gj0i{5^yym_k z-M0fCQ1I^;MYZq3jjqP8oP+rCfeXibnx+CU*6x0EUHil~W#{3U0v0YUDe$u|&%Ri%{gs;U%@pbay;BCzc`)fP74*$-`>p_bD7eY zfXEqg1|EyJf?VJJ-FK4#t}#HGd3YK5o#l9Y&Rd-L=u0gTy)KJ(|49DDfDt9k`M{_X zhMmBB`W!wHqT^t76#AUp1XPnU>io{tXB5+1g?(1!fIuKEc_I8%QoXgmOD{_md+^zC zzJ(fIYl+2>w0M4q6x{>q`j|ep$+C+kBU=`W=>>h3*zDd8>^<%lMbG!|^4#;(!X6^( z8%DwQX(PMNVq-d#GZ|Ym7oRBDAbofisoy*AH|{Z;te4TnZ>s&>DqTvSY!b)A4}N78 z-h54WV!vqT?M3ctQT%-?%LluS(Xnf3oXk1ptO{-IOljHMo@#4#_?@>42_4=*>fq`A z&|VfOgYwwQJQrMcs;YH7=kQp+$bVd#KfdARXuS4E35+#0v48@5*cD%0JnSFb{J!JC zYs8#FL*{^2O+N(oeEH}-W84~FG_?0srAZd#siE1*8M-e0n7s)}qUdKE`^!!0bG;BC z*gb>KW_!*Da9@s$x!L(w zOXkI~Igh_IXv2DE-G1+DM7^s1c6u_>=oK}QS{I)VT!(|~nNH{HFgI5xOdZ-C{MQcu zPmavt7yAy#>{4I`hdzw6*9NH&{^K9eu$@n~nOK;M3RcC^5<>Z<@a&bO;4gV*#&D{@We2U%=>c|972hRV4bzBPOqYxduoDMtTbR+(D zH{Z`uJh-11o2`+*fPd2*&PV$6R*#Gkzuzyba~Or(g5ucQO6^{&m*{>!@s%+z0v3gt zUIy4<_;sTlt2NLRzVR2LXm_feUdlQIb%k?7Hs0sIX+g~9JrF+yt+&jxz2P2TOfHh% zwlwB7&VV^0t!e2l)7^cZ{B`%t#|2=$Mz@A9Pi~&uOxp9w;X;Lx zdT!*1cn%_ZbEDI(NK%*8fg?iE9uqu|geqE&fSfJ?j_9j0G*<6D^J(aK^xIyx!rF@W znCN@<@2m#Ok{?0rd*b|gn+%6OYy-sAyDv66x}E8?Z#W$g1^umf&>0=#+@&~k>!Lrs zDMiB4vGVx9$))gx(1fXR?H9R>HgMs2)IQq(G=A2FY8t{^&Pk&%Ot zGX3}IMRza>hMTB4Uv&8v2#pov1kEdB`8e93~_eu9_%lUmmPWXBys7l|9 z*tMtlWBe|RP?fXVSufb<0=dY&`v(tusM{XCzck>s@PQB{!XD+YJ=r@a0Ejt5kdmD< z_JH9Yt9?*1pEadA?js;IHhjrC|{v_m)S8I)ZX;6~&W zDh@Ut@MY!Myw9kk2BPDZ30ad>+_q-GqejOvam4%z-_G#8j(h!ae33{UA4QS+mfu~F zAlKFUqSNk$^QS%^%iHC(08}y!im(jAXeGDNp}kv*WWgd^-hMbEfDjV(%_|Y_SvXJ>v;-$aoz`zH}WT{o_P5dg&yiFu^B_{KB zy7$AS|MU?mot6`YIpyA4{joP>CuI@G3sk8 zhM4T)@A1%fMx*Y`XOEMzH6pjmCS_K!f)Ry;21fO82O}xu;`wF*Q5vyw6$Qk1IMQz< zWi_nP&)-?tMRA51Rn!xJw68CRNf(#W_{s*XF4bh`KF-LBs6GjQ@pKVorh|TmajSn_ zi}v;cDr>R@-b-~7tI-Hq*DH!unV*&c79bx86|YwsUFe15cWyD)*CJn>vw&;ol_&Z85Q8XHM3xkuO0c$5{mv|*}G}acHQ5q>F-E! zFqe1c_joMtzHrjU-M3%4aB^bo>~HY_^sDgnRewGwp4J>IkMcVTtUS$*b~mPXdK)}1 zXJD26D_-!cha=Twcu~fc{LYUXO45z-Fl^bXM#oJygK)|5oGNj!%^ln|N0weC-Qr9y zygS)i!k3o_SBowdXk}1h1Ue27?E^D({d82y%4=-xb1wPIf2!D-QT-Qr3v|m!NJdS( zTH_8EyGT30g^GOCWqFJ?%*i`M%uMMoYu`Ny0(ZbP*A6@i9FjOpR5>KE(MP`6VmAoCukzSa?zdUjMe-1 z{za14TqS3$uW@x%Nd$>6#`CLu9aeV}yS*Mu4Q&(I-mkpAWUFC4(JG#xz3$UP1}wRE zbiW@1+|?5=!tWA|k(q(^m>QwUr7>U0MQoB7DweS-n}vq>4|sk(q4 zY5xec*HC7DSoB_VcrMfJvsO^xtz+$}&dZVGFh!wCq-ddqriIjM`@jVng8*>-)eKT*O^?Wi%G} zuj0?X&#ceE1Y#Fc%OHf$u!Uo%56d-Jh-uVcRhWjHRh{aXMKR68`l+^j9Ic(;p@ZUA z_xCS!_RJUa+&_05awl)n<*tC2@#+<36v=;YvX}&N`$Shr>f6=+p(c*&|}uA!^L^~Q`L0l;d=Yx zer?{)k;BWSrT)z746Wrt%gf+Uq=ZDpqrT_m^U|dXQ)R%L5*Yc-$^mrNb@PUc(%YQu5ZFf)QIpPv@4_gRYCy7Paudb2vj=7#Xs%XHf~&`OM#j1EW2U{z6mc)MNY>t~xIV#c755teFY-u9;_;Iz0#epC`0*Mw-i!0qtfGrKIn+ zx|^Q-ZvFElo(AbF^!{mK8Iwdq3R69G`(rT|QX+ZLQ=`@&*7EX4dD!=__3uahHI5SI z-{Y$%=JdYq-@lujiQJFcdS%-}$~mE_W=Evf{ngJS>UM8|g@&VM+c>5Sgi!Fh$xdinyR z#(F=gew+8#lU=|hfF;IJO%B=LVmPOWe8=A(%euo7NL!>`>oB4-qDLBrCN+R!-|;!b$0gnF7vx59q>Ecpmr?v@tL_1jRZAvn9!U2%&glTMFQ1RTpCvU zaG%%`)aM>Xvfu(}D<$3d#ON*7j{HFVPSnr(g@$S9fel`cDcC^!Wwi212??Y(;wU>e z3Q^E+o>buSSD}|i(Jc>7Gj4%zVW3`b7wRzLEq+^3{j9X!jl}BOIh)quF#WWQ^*gue zPJ4NQh85FTU)d*&(J~M?q4Q-|r=Vj++1<@4yyZl6&BF8LeQg?dpY19C|m2$#3r)pMvtPF$P5@6D%6oQi2h`W_& z@zKlCmWJFguvs?+xeLbihh{Wf`U%{eAsA2PJ>L!v`=inUtfA*|1yWZGUZwGyu-h+$ zOOk-u126O+PEOJ;uK&FgK(Wn;NGhi{Es6lA!1d4>!|Piw!(t)Zz2%Ln9O)19AljlZ zwy<;D5cL^PCf->;>v-L@&iPschR+&39 zPg5wNka!nKw(~Hie$KnTWEv8ILbq%=C+)I}whYfHzPUf$8|~wc>Wf~Yc~L9)55oDq z3{u*h0ii=*%g|0K^5BrL$qVYV3w~BPSR;NwGIcxe%_n676j!|a)#oDjhtC@s$^EO| zqaTPIV-py4?ElZZi}86gDp=8qd5QD&6dg!hZ{9(F>k&*K6CW4I%cMRQU{q_rlci99xw&W&-mxm%`Xp940Q#JN?k0pVTpFEfl~HZ-G=*{ z134dL3bz~0-702tomh)YINbIMzHDNSc9eT2($Fuj?iaK^HnMY^(od;w{$Cb|WoY5B zlz_UjHH_K!$AMsR*CIY;e#uK6KpHceh^tGec;ismQ2#(s0DIEjFE#Cw{9S*56@qh+ zHaGK{k-%L&oxf~~aiy4na|W@)DNLR}VQ>6QjKf#g%WTxLK3u@Cfm^{Z zw>(*__^$na5t*Y)4;LOcgx?5OC;Oe)U^~tM^;dM`oy_Q_N72;(Wrqm`V!!(Qbw0c? z+FV?doqaWekMlw+BZ{D;5RT12mAVpaWL5KiLwV{fC`#mvoguk>NNFp&`iD?yzNfjE zd7YZ*F&=`;qDUXbnA-hz>rqem3kaVI5g^XqM&iX8e+Asmv9XD{F(~OP2&;!k2^U+f z&f^b_Y2bqHP9)Pfw;kgQL7>=@u25Ho)0+tX$j^+y1fU1xe901Y7Lab0r!B_lMD^Xr zu>KOX4W2h?`JFufXT3q5fPzmK(I;%&=t4x$FHkf&3q;S`lW%&yyPH2kH9!G1JG;0| zle^OhGaV`K^x6#$B9T1y$ME%{UsvvL0YTvM{*j)$JNzC*>t4jX4s%nHpN{~n2l@Mr z=r1BeG_WQhOtceN&Ib2@@k-s}#6+*#L$bWmd_S-JwmO~Ww}Z2}iJ+fx5m)l-d~E?5 zF_I^fRo0QRkJLM09`5y!f?NB?zlPS&KB}ZxZTHXD^73mA!5%=B7Wl5;=`BlxOmgHa=_4)o6JWdxSd)c;+glWOw$amdJ z6udp2HO44oEG_qu{{8o6^+njg3sG99=Q`0o!j6Hpw^GyeP{EN zk3@Q!l{Ixv#HHoNhXgNo>rgUx#f~i-1V2|#DEHZN_5D`1N}q>L8d(B3^x(1FYPLh4 zhEZvOF9JVBV*hd>qYqrM>?MI4{deGYZ~_0B=LV={8_BXoe6b%u4XMB%jaf#aV+MPF z?%Lqj2;OkosE{he`=jxyEveu9?R|%zRT3r;Ul#9*qiP8{ zLaER=eNy?jIgkImkxbDb!0Ih_{I`3Se$eQt?R^x48q4bdRTJ1FK^!N zlr73SlSczlkB}Pj75Y&1YoBC%=dba*nqOaC1png}GB51X3jmG?)d+uQmjkJ!@O;== z(@1>pqe<{N?8f~X#i6J1vKu!*re9t<6nBqtESCO$w8~od3fI-s|pTLC|o=yVE0Qm~#o+-!+7w8K##dGN2 zxvJVtl21QOJmg>P0(asOr0!>nh~++BL6#^nd7hA%sEO0z{X>_;fayo*98gb)(X)KP z{m0aqY%8i|QS^goP*+WuqT2dAS#6vU!Uv7c#UjkHeN*Bt8mWVYt6Y!c$+CF zoLt;}Xdco7T6uGyMdgJ~bvkj}!T4d9W<-8A!r`L*Kvgpyy&GQ=N#D0**6(iB-S*o3 z&een=d>eCGVDCdG^%E7G&*Bvs3i&LHsIXopO=bI+t$sa^S#eWuOv%*37gDpg1o24W<))ZIudf|ns(RveDHJmVatvH=;Y5zxY{}ZNy@W0Baco|F?9f7 zE#KWH+Y2e_22Ea9f^JIGY9-dKhn-wtTUSOI4u6b{VtN;KvTPF_R7Q}R*9_jqrYqT{ zKdOpcE@*28;ChYJp5}9#JND%LVj zbRhs|Be`Bg;5Q9O(DGFiI<^v@9N}RCk8Xcp55rqF&v*WrZPOwhjTv}hgE~@i+UF zOUB=0{au`f_y(Xp>7QSHP7xQ5+VA zhYBn2YFv~rzk80SS~TOU<}Wx?DlL}a*2_K3&1vN=lo^V~=FxI!YpQYz(>ez2o(K40 z<%e_jJ_qU(RsN^4FR*1iF4rgg;@j6c=2$vW7kL=U z@Kvx?3Ppt`O}7AgG$7*-Zvfg}9-9Ewwe@Pd0*t6WK9djT^eG#iyWdwU*wgwh-%`f{ z5_^my=jtDCZlaL-VxVOwx<^00R)|hOk%z9!ody00Raq%sc0ek5&AP3!b9WP9COLf)@N$&MqAzTL~j;ld=qN}R?n5uBSV08!!1XrC!Gb!igV8O)2Ax4l+BuD-+y)ulNSJUtXA zW1zp{7gRD0pNYfYs8c*T>Tj{Y$!Y4>))Y5i`y`2ZtIv4Me$>2kz3oDE z`wE``o_p?5%JS!}lzo^Q>OR4_x}DMD#u)~JAmhEQ4LZof<6#xh=mEz4fzDU#^r`O% z7gDd%rpx^{u3O>*@g{rY<&zjg0y#inc#M6fRwtQPWS)L-8`%}57_ZplI7at+7jVF9 zG_LztYt2Sbdl}{EQ$ZQL^%AxDisyge#TOiEwdYqWkZ?=B>CLCet0pcJpVMu&U`~3D zLFz%=&h_#vEk!37z;pYC^zJ8LY3OcoupjJH(HmtpctbZ6U4EE31f`pLd4Adl zlxstO@y+A;%Q%AEB20TO-Sux5F?HbP45gYBhLZ`}Wqv>UNH?V-n^#LeB$s*v26Vn{ zfrptVVG>gKEqK!<^9%0sx`WQmIXiw%XX6VWX?Stn+&6GYKCC}8ycHL4bM5j;!9!u; zH%MItPHDf-Q`IyI+IXYxc9{jXm2wg3LS2SSgu5xQt3M`DAB=L9UhjeXdgFH-2r56X zE*F0AuFijIufm~&HDvcZJ$_{ zz)7wW9zt#qdl=7Dh50JKsDt)^Id7W(w|DMP=*XrnwL4E56ot-1Q#!N^3hf$hA zPYzK12uw)&Xbu5leSYLHfcBi=F0jD*H7;@Pq?a2?Zo;m6>=wLs9@c|SxX&aK+fB$xAzmyqK_2FU*Z}~$9hzv?tF+@ z)YtQ#+~>XR9+7UjF@K+LnG=>fxC?eF+&@J+%5s;di}^UDANeoc`Qflj%qg(ZQ~$*+ zz~;bR_GT?LSh0Wp)<4|<;sQaiXI)5Sho2+-{$ zE|lQ_&`#Zcxo3C`zL{?fJ46u#k2j)}`mHFYJNuf}=gS9z=#}jjX=NHjPZJ3e3qi}=#5?Dg1p@L0n7lthDEQiFeXn;-qj&=cyN2jrR+KI<=&J@PcB zQOWm$>nC4*F$_5a5+;=VhaErI6Fog9{QRi9lSc>JDJAsI2#-EDS)Y4nd@a~Sf+SDn zeq-qjE})mH`D$)p1PlN-}k~?Y?zEVtglO4&6w+8fsL)#HO8>*{IK@B zs7_uhB$YT5O-@E^0mbewwszy02^o%=`^1l)*?xCER<1W3h@V;%e)9$979xH;YqeF= z3ti>9cSr6zJ0wu!$q^)_Y+`xR0vWd#Wzyx5s&3IU4V=HaI;y{O>Na6UEjtK zjUysQ$J^O4F>+XTx_RnLU`^@uGLGvJXILaBcYg4WIl)9P8=ol(Ye>6f@#5V43mlM? z%yg~C$>~PpV0tl0HLed$WI`O2Wly%8mV@$I`e@s4wT?@uG@nvmX!sSvq6EAv|K&>{ zR|&U2FYgB#9`VgbG+G9QL|5N(dBn(K-(Kc8-;%;>s&fV-1h|H z>lsl?=Po{e2y$Y7cetioda2Zu*E8<+q8{tVR7?R4rL`xv@gjq-f^eka#o-sU6<-}r z^X-!=!x9FC`L#NTzkE=G?)>-HjTB;!y+eG+&zpm#Bs3qPAxbmSsB=>L-f0Gz9}ycl z6{?u~rtflCfq!aNQ6H}#plOHc_jz1C;0 z-x{ErMNICsG$BZ~qYud1*jErIX45tz7lGp+g~@_KZ@e#G$z!?G4_dc5)}gY3UtOeP zyM76z-DJ}wOwm?$K8-0l&!V3GSzTg>ueZA-8XeL!G zuHSJyz4;`Z&Ci8`x0<0L;I8wx8(kmu^YCedQGGT2kzFKWNJwV55MbA|`p)prTd>Gw zlc*zU%Wc3sWbr0?SS;}O!rT!)emirgXUA&ou@}hpy`c+r)fbF%y5TPvHP?Ht20aSI z4bJr%!aTy^`N9ZwF{bjuR}JBWdOu80q`KewgSEh|=XN}#5WXxtSyO%%1TGdi3`Xnk zrbZ=qOA|H9aY~>gYD54t;Npt`*$)h^{QF~UA6|aEruL*+eg8V$-XdBS7OE^fGh;@% zzes<4@^-4kqgu`Q9FTfMV+<3+5@vjbc5iP=v7DI81+nL|TEiKo~e%j+k@cPaLM#&maH-=gWh z?{?PV+$YoE_B)B#I!eN z3Uy*eZK$|NaR2PmVuaL>i9_aD-%d;#e{NihK5wa{cR)GV8^@(IP3pI8yWUZEM=pFr z^_{{}Z24KtO-!D7774G=3Woa;)q!kbk!kGpv)R|@Uf4bRPxc22V`k)Q)>s77>v}!k zzf!eaVz_`f7!0hbRE(wmU?&rtwKT zA=f5Uy_^h`If^an@0tA2E&-0QrQyqUk6_9-0H=gF- zEpTQsxCQCSzN0O8zjJDNY|9@waR`Oc=J`PN^=`Vc_Ak?}^VgP`Z%9v^e51nKLCtQF zl%Yx^F^brozqgxJ^8w}@ts2PZWWkW*ejDh;gA8h-t@hcsmj4;n%k>yxHFz^(IQv@o zan{)BHti- zjeY)>8I_i=CSc&v!JnSGSUsM1TItN!B_iJFec5lQcVPtp!hp0gET`-dVsIey4pD)WdYuEt1&^@uUb%fmN zddN(}rR2hr=kDT}s_qRmm3F}up{6S?dQavy*qA#j_-`jgN5yA_DP`B5IPR+gA#Aq| zz3Yc_<+DVjBz>Hh`Q9GXg|)sG*n+PBET`is@0T*9n`Hgnj}wOaGu9B_F+Fmd(Y_iR zt>>&Nszi@)H{dV%?@h0~NC2l{y|hxjJl$e>uB2d9fnH7VWQNtVRAJHdvLV#c*$x%gId zyrzz_6(7MB+`CsMxkjfe?i^A6N#A6{J>mpE%60Jgxp?c(T=PBeE7I9Rpzodt5Kh}& zrN2?!Z9wJ; zMJC;if+G4UYE|qHoF4Lv{YB17L??R% z;ql}~?3jd?3qWY{a^sj6c&q1B!2GI#M>#e!I=(6ihNss{SX;-unLcBfb?<@{wVEgD zzP+kP3OF?olD#_koYqAfnmVl8QeO$I=*vn@KUu%OVPkfm6ONwm`1@gO?cSn6oc0t$ zSA6~D_8om4aau_rnKDpyY~qziX4bLi!&#QzG_BrT8kDOAo2c*Z<>oJVan#4&`$USf zZ*)REXothQYYBQ6!;tqJ&BZ%-M%ldfAUld0ck_>J|J(-l&zuQ?>I{{QBJJ_fyd7`1 z<$~i~&4rBgkj5sFrzWOeiQb2&5Cbfv4}|u>0r~Y!ZWi->=7$r#*0?d}=mXz`<6LNI z2L`DoM1L+z%NK^Un?E@t7>n5|XLEvAH|hpjz&#?nQ3sz(0&9R<_SbSTWrE{{AnT1U z%4PRa>DPNpHCAwRX|R%95?@I|bS$(JGW$D;xuUrs8@7*1w%<~_)XC}Gc8;E#NLL`} zSgefF2)Ruy7XIkD^_%btx6lRSl#i6K2J}C3kTh=&ZP{uJOSnv{PpMs;_p!aTbl_Tl zUPj=GmegiH%DqKt?e86Ra*YWW=bu&`0HTCq?}BsU?fNLB>GSP~bD$MOSY8vhAtkvG zLhXBm1zE(EdJ~`*)q>OVC8G1^EnPkz1#qTsYEYjpKU#;=oAVAyuMu7i-6n=lr_+y8 z?45EweOvNkZ@iF|v&c#QxaETEdxV?I2EIsjYuZ0%fL5AI6(trZ970%On?-qDyWm@7 z7P{#=X#LNR#Nm5MA(GEU>^ZRVh))+_a!+J&Tv`C1+=sFcjnkKJrQsKO6wU%ggXD%E z6qFc&dZI^-2I&ESTGNJ4>a{#H(6LXOERW^ff45qL%&Bb{nZDxH4x||Lc@;#PIm4cn z_V3yKe0$Onfgm{Mj%iaCec*hv{d0}>dn!~PAbAzwHfoH)~FPV{N)u|oL4dB}9x zn0Ukyjp;KcDe+4^Kj&&*aCZ52YI-GVp55;j=b78ANWs#y*ZjihG{$Y8z^Z-_2%3K# zhbP2+UaAldT+{ox*ySwVqdq<<;*d+55yC}IY_Dtoo&1d5%hgn(4rU?YdxWZxZVX5F zE3#t6ml~h8XX`zFXDhIF$5s09kJ~QJ!q=;c`g8d)>RjC-wvR(XicirEixEK#btFiy z%V9cD6`2@2TH-?=>pwJ3Lbd<`zIx&QEpNBqZF(eDNX@Jl1QDD6B)VUaZIF!Hs~qFO z8nhJinVXAVJ6cP^u5{+{Fd+GreO|IGd>}OI^c$Y`GLwcVa1*J$ig6G9}Sy6)n>#wX#i=WTRo2_(q*dj?8?Z3Qv z$2-NlA^`+B@1ft_hHgFmKms0NrC;wZaQ_Nb!%;caWI^Bw@MZ8_Iqnq~XBg>H=}y0j zh$IS>WzenYL?3wfPG+dm*LMA}KhadJUshtb#-06jUU0O%YBt3lqovJZfYKg(&I>njXHKkxNWD!DV}B%6^sWQ~QxY07ATL~Ku4hWGyV zA`bEaX7EeWGY)JjyTQHKjR5$Gg4*l%UdjChRo2wJNc^>b{&i?qRe9Wl_-iuw1{{+4 zNm?oXeQTt@`%AGbvx$SpVVonkOL_k^hgX3{gl@si#+gywK8W|--KL^#Mz;c|%~*J9{qLdG*nIpXc*J8JL}$i>n)=l{(A2rmAo}h%bGhI(9rd@f5xjU`u(>Tqk-h3(d+k^$B{8(}x3%Arlr8 zqx0ra3vM~%JFDWTV46KwsGdnH#%#40geRJb=5$@W0X^0&IHR5qfS-ix8u2{u-`*W` z`!RMv&Z^TWJiLk8EA1(Iox;YGKeBp6q6`3m)DF~)2pW6uqm!{RiLoAiX9A4;X7 zH>bkC)n@jmfW)|1ujp9-YsGxAFiaYw@%Fj=y}gk9jZN&hzh@O$$LZdeE|0wpQ`2~E z*>^HDYi*Nb^58YcTee(r=fHhRPdLJ+$LlenF>#MXheJdohaF-fq!S{c5$g)tfOE=} zBhOZ1ZBsDf)i6Q$vWzf%Vw=v9)(Zoa=c(3jeBTRxy8mkZvb$L)PnFA^#Zu2y?N5x( zuf`3okvf92%nC4!$bOd=yGo&SzmF+x)i>`A*`+A!;SeArZt8b-jZVdK@a&a7f2FK$ zhsUVV#cMp*u-n^5?)vfj9C+erd!W^Hvh3W99Qt#!Z*(r(_z5{nC=nc6eLQZmSCks} z+W|sp3XFcSqJl3H!jAGy+va!6x#bPil5otvpDQX5A@Pi&SdZ4%_u+A0C*~h0{(yL9 z4}D3lqsPX#^jb}KB?O6)xz5~E1#-iGT)Uq2>t8JWE^oct_f4ACi=mc8TsaZwRiGYu z_cb3n@!vb(`ZUuR`V0bJD{1S<^h$RM>h+VfmA4&^i(Yuy4*c8+&V@gucz}nW#Xd|s z@@kgr_QFI;vb5D0VyPw1ho~=qzA!&3!atz9odVj%GZwkWP(z-5t$&6=1JvyDsg)`2 z6^HIA0SXy_CZR@lhY1I_&r}~t_8@^~{8ExaMP_M2voqcw^$`1z{VCwP)=qCY+u3+T zaJ;9JTTgEm;5#^8UzP~rNSoaasfn*`^*d^z`|>bD`##MVyxSoB+|RHwvgvUaEXauM zs3{Z;U!_1?mYqPK=Ia~i7mO_DdvxslVfg9UcK7YE13_k1s5Cq)?0WNe-{@y=%K<+< zralXwuP*SEbS3W(f4eOQeD)HE)$ea9Ie5z{`FjtnYI@W`o9R0ZNLpBdD=pL#Ee|Gw zs9I^%>jlqMn?59SWj-8*kStSouPXHenFKTs2dLCJt|kFd&wbab6X zEu-SKU`J9o#u+p)Q(r3}Ij>8SDsQc$g$FwX(skJdHkaWDH^pc@zt_k4bR6^qjwo}+ zCL>bfXOrFrr~_^r&-T^1OG_B54R@nob2FN0R;pV~YtmuekR;8!!8dxBFPu0cMwAK7Hz)L-FeEb@hrdcv<%& z(01NkTmEKjEs6-*u34)VoRb<`l|cHFMC<18BC;34-;!}iThM;spH2aBJl(UnKLc5xXe_k zi>y5zDm_gH^Diy#tA* z$fg~d$MD@ZgJ3#%P4GSyOdzyE8L59hqfQHAHOwpW3r(Kiow-uwL{|g2hF;UCYLx3`2qM)ivjB6AnuU`F6=b@8# zk7B>4M(TI9c(p%YY9xVaqIsJ7_L=(fYy;H0XxL$H6nVzAyrRO&upSg{**xpmAPi;m zhl*|<)#`nOiE5xc;Fz3yinO1R9BppK-A8bsDoZqp?t1{qWxZ^I?k@}b)Q^UOfEQW;ONd!Qg=m4~EXSqe1M!7R?Xd$@0<7Gmb z^|u!zEx*qB>kvn$%qd;N6@bFo{oLXpc}=GThozzHz$21Zd>x)@ljzrrOHGIoYNMr9 zNM!9Md=6f(?zp|L_SLh|On-ka_KNNVXQP=Cd83L@(swzGvT|cMx4Ggjj1a~7(V-ad z!Z5>r$qh|>Wa%-1P81}kc|?^2*`t&4_T^C25rV;I8z15;Gg}Mdn@k>xfg1%SH_j*;~jtbONLB9)y%O%kNx*1Au5j8Htrbgt5Ta^BwU5X zmhay+3+-!_IWPHeb1jB=(&no<>OR9isQJ`6UMKAXd&2@RiP?0$?T;5t+bRAPk7B{f zA1V2s$vLdpplhf4Dn39|LpAL4(}9;bYu>)Wh3f3BRZRH!dUKI{DDj)^micK3#P)%V z*T3KKN~!}YI%_eojk`on-{C}^Fn_+0yPI3} z=RqAg=c!_wx@b1N#|U8jzAu6U=Rvu@1kEcM=x7Tt+(E-Q^=PCcCZ1Xnfm)oRXi%d* zeJc20szyi5o4emn;IDQ2o!6{aTUPPa@(4@qw*vcAuQJ`J6gL?l!XF{xm`9#(6}g;~ z^(4-Wyu8K7!kE+r&*>x>2T(5xZL79YWL+-{)&>a*+{8%8xlSq1%P^bREwL zA+h8ge81LrynV6vmC3IVCh4gh;U!B7bF|u#*$G$84ow zLpr_J=cAgS^eaX$i<%5MFjN0Db{v*XQ=3QD8T;FU{>Jh3&b*!E(20GVzKg9qKLbfV?m>l6?T7LY3 z(W7OLXqfaPULC`?xfb7M(^PyEr8PJM73Bp=<2dG-^N`fn7&AuD}W*PEy@ z@&?Go>%_(KA2Pxd3e;;o_#`Ng11 z=J|S*!k?z2|GNi&Y>${G?`@2lJ~X>cvzMoyKxUi%ZWrdvLb)!}(nI(%A=s$P=s_j9 z=YqA0_62)9c-VaM*XGK1`vW1qI%M8CJo8wioiYB9?sq6{FT(>pLkttcnpx@R;dy$J=D>bLqg33CBE|1C^~WFXOgeTHRMirIhAql5uZY_szwW;q z(@i?^GW1+Wx<0W_+#sB{SY^AXmX1|@sEY%0;%h+!lwGrCk0;LT?xUE!RscHAY)O)=(t5kj=@<)z?a-m#+(z`B=Kdn(?d9SEvNXbsr@u3S z8dST2w5fZVra$3}5FdN+Hud+paM+nU`NmZ~8n4Maj&z?rxgS`7%G9thiXUR(HI2`X z4v)_%6L^3-_8V|F-U)t9G+0`see3Bf=12v3AWHrU@4CMyzD?+M!DIpWbrAK@60li zB~{jMWsn5=65opp?$+M-*Y5fA|30UWP-PFMFt&0J=gC*t;$LDnpU9sI9E|RN#g3Pq z5pV7@_Q$8d8`)CN@Vj3Rs5WN$|9!U2`=1%$%;}qqqWW>|aVIOZqko|fuMeP*>V{VD z+f>+2>$0Kq~(N;t<`)F*7y|FpD zc(B-QjIvK|i@k3P$71-I>~H99&ot0$F|+X#)P(wTwH(ZYmkPfb^Ht;bm^U}HIX$h@ ze5i|ZBrt+w?knkTBlB*w7-;V!T+53bys-ef_?Ll#_^aFB*_M0ka!K263~<^@OM4#Z z)!@3snB6(knL`4&-@_GlcP>-j*Xs8u;|GbDUAx{n z0^g-asuWP#D5KZza>%L<;K49*hu)3oLYTL7U18d=xVasqih2z9+v)ZNK)Af)t{q4c?^i*& zlvaj@Npve=sTQQg_}N|fFJ!0y6>F^vytPJg*+=jyX#rJopPvY5`Fkx}5o2KdX7_42 zG9_Dqq|>}<%|9^#P+q@Wq1+;BS~h-OF`E|7!$*@CxFkvsdC*OK>Zso8R;4 z0CezRJV7j1(-Vk}HXEgO$OM$ZSgwxtuslOkbOXKDihXzgcRt>5VjZ&=F?eLZMDlL0 z9KoTh5!4@jyvvf4WXYrdx)^u&qwep3RfN41Ny6P(z@7@7`t>>ihL^Q-cRte_6AJS$ z51&JFEN(c^tc_$BBmg1@P84~g-aAr6@b$AwC0FE?`9tR7ePQ9wA+?hH-Zg2jUpe;) zl`eI_2mkjp19I#cE9PNisvZZ^XSm}b{pvSTf8y*F@cSpu-vS?`DVWLeO*Z1t;M@n% zrBwWQ!P@5=`rV?1?E(GgHV^XE4GZV>Ahf`WKwfjJojMG7>0sj2B`8}ymZ5wYS_sFr zWq9&oSCvn}8dMgfkIj$DjrKF_$yD=Nfj)LTAHN}L(7581_--iNED=ZV*PZfD!6#G{ zE{GV>H67r2fga`o+Y)G4tyq&P^C<5qpo8giwwGVZ^ZYtte(2^7l3~*JXGl5Td%#qisIXTLcy9q8x8Wux_=xu%^E~GnYXb%L`8we&#T09@7bx+Tu+Bpv6-Gwbkdc4^2r|mE0 z>T9=4YS_nC>N;%_2l|Mx2EgsR&x?DckihHEjP&-0 zrEjTM?iMbi4PB*Q`X1*oWEbW_j}SEpp4fngj_>*(%|Pbi_;u?AO_tK!a!<<8kD`KV3b%*G`rw99|Rij``}- zv?g>@UnB7QPI#hJ5guwmKtDRi-T)^JM9nu;LfsYU(N4ZHvvk*CLVG2L+XsVH?W>8(!?7mc__cvf_EUMZFbmJa zdIOEgPZw&R2;$E(+`u{uLRp!1j~p}6XI?W8zbj$nP3LUra2!k|pT^0TzhhVE<>;Z^ z*%R1~xOslw@I-vKd&qmI>$z>nP((F+%CLXkt3q;g@c(~$&AvM{pO&{dx{zX5PD1~! zXz-c5u3A3*HAb8%rfWMk9-zul#tNr1Ml;FEK4|WpeIhs67r~o}fq@UaDTIY8Lh>!0 z>~zO(w~IbVQ1CRj`Tpg76YHjBM5O9RS)7DtSpS^p%W@1^_vMcHb^kY_lO+iAaCOrx za)o|$5|Ijtz~Fz7CVhnu%UyH=lR}EKO+g;xGk;50IOhR1{DiKD{A0Ob&cCy{w})~a z$y_K20ftvvs~4(Qyl&9tVLv2a4)?AG85GU>f(U8AL2pKQrp8O%lCV*{g~thiJws(p z0dM!WO;IPrkY1NfbK7fzbmDt=AYPI7$oDu1oWd($TsMs7tXGzyB0gs8j6#|^`J^t; z*jbvEPwP7u!GX!c7pG=qs!}PJI)20nj=nU&hRkj#4cp(9I@XAWb%@C6ZAkb^&q>2s zRK{vkoEdmEW^7uhr^Nz5{-vn9W&czdQd!)~y+|D<5K``SNQkW*;du#S;T(zPH6_mY7z_R_^O_T@c$Iv>)MfRw zu|E2u;=eE%pXMuvgQfKVv=!7WvvU(oKTSTBCJ_NjV! zE0}_0b>Ad%y=xCKMkTMkhNvFlGXx8}LcN5#JPB9l6OzxzNj?uArR{A?qoeL6NwYBy#; zzEagnwz-&1ZbJ}qP(vC~^6u?s?!LnAvKC|j*6dyPZB{u2dGeGG{x!R7()W1nADkKD z`S-Lw#f=^>jLgq4nY(ZunlACqdrAwBcz|U=saBekM#Z&(AmRqT_pl7YAXzJ&a#= z`9;eO0lZN=0e^=JxZ{)-^U9Vzm3VK63)*eh*-v4oxp$n8%Dcj`+OC~gJk_d?PF`lqJ`lf>JR zPCXu4Koh&R$lJ9z)Rh3zyy7Jq@AZS#uC&9%t7<>5@SzK!>}JAIo~6IKEl9+vl8t*-=rGBLF%Iok|xDcYnSDuoPr0P zefQV5+j{p^*zkYsltVOZo*IbBT!Be3j;?RI z4^o__;svu#`*(KCUcTB^E$l*$m|dFRse4O5b@vG!K#7N7JDw+l0W+W zOKIth6Kd6#GamdSc&l@G2@T$ZA~`!I4Hm=aDibO*|I0S<5&&1?!Cw4YF+fyDd`zLbANVR$#m=c2UOONa-*CVVW8 zS?LNySaqLb_lk=efpQ8z+B1xvuqg`x%lv(Qs2TtrK#M9SII9Mo=1u^p3~ml&irIw` z<6+wGxu;QO_Tl$ElEgyFHQC*X^3YxnPwCOOKN5w$fA3_GvdM70!21e(aW9de_47Ml zdBK=72xy2zh5NI#kU42+EXH$aqX!>gZ{t&9*kk7h5BCKtmvpL*2hAxETacd2&XIZt z7bah&i2L~^Sg?I~y##a=VZ{LdP&de&t`}p#G;I&a6E07_sU2U3Jgcpiy?^xf^^4@b z|7NV^IVV<&G>*#Tow`daZFj+5kvM7Db-yuPj!xrYy}z}mxgU^ed@7I^%^6?Q8FK)^ zbUr&|SnAQ$S|6F~6xwY8oATXq`AmxZ4*Y1Mz^s8jd3N7Xzkwxr2)VuRmQuH$aZrD0 z?8lfLFO`bvs3O8A{QR-2Hp(HK&f;(He2wdZPshf<>#9SiwzX!9Kw>)Mx{^RS%hT(S^X04X?PL5xA-B6oy8zv36Mu=14eCRohWnN#GX9iU>_U%eiwgS z0i&^X`!yb;qJn$`>9Y!c0qH$4hh z|E5PGT%S*m*oPuOCkxAu{v{lMv0>WJ@_yn5REM@n(ex>&(W!Zyn)HcP>aOf#LSi?t zLVVs_w@B6A@`aa_<3xqp!UxXz-Veg29qP_Q=8?x(;u~he8+@G$d7HlUI z8)OuF&NlkX7s<*QlzPK+@xTEGI~oxZXTxN}(NR8sJIf3&HZ*4m4cREn-A@>T&+C2N z`MbA*$f<=BZZf;gZ7tt>ZXHuqk&x2xM<2zs>|^1Gto|+LxN9do4l5H=!`O-*g)t1t zDTT$1FE=~cEv~l!x;(|E55 zGNl1srsi7v?*1L%JcU2G3eXD=@iMC!dZ6LzWQ%HCj|f0!i}3Tf7dC-CORJ;H_=tG?q;=y$OpB4hlynM_u)M( zHRA4>g+p|NaVP2LXRn=+fg_^4%c%#RKedOLY-0h6_{}CQRQTQWwPlaOH4gXucPrnp z``ulu$9g>;GZn_0H)DMVAL9C4xQ|Voo#;`oq`}7g6~4#M6(26*n<4T=Tr&y&mk7d~ zhEWsohL<77-5rpK?u4Q}YXjXKb7#;xyOn$SW!RZp1Wn!ZkPr zKvvu!iseQU%HY$XH8tnQ#%>PNCWJddOlK-sISY3+F_L}2&0{D^!sxq`+o3DE)*4Be z<~Uk+9K7x`&~7^+utP5|9MHE7WXeBSQP zd{BlQG4;!WY%ba(nG7E@-H_yl!2|9=dw~P1`Pq%ElyuAXa7B^^WS^5^0$~=Ol$@I6 zI+99RtrxyDh{ww^-KDoRu(O2S?$@|P8eg!WdAI2%a_y`EYMYCpeGcaJ(kZ|R zcG}JdVwd)2X`zPMKhxhbzgMU!=f@6z+;c?}z`8Kc9bWt%QP>QJLn~OHZwx?o#YZ=H zSS92Z}qiiGF?mJusaf9btLDq4~_zaY+gVBoq!!eiT`lYL9AGPeU2YE z`?0rb;I@O&9bM!1%ud{3V}E@d@E~+1bh$rnf2|)u5&)iIDEL6Uq5A8UoWwU~P4IIdV1D7eOpI-glZYdpfD~NIM zcUJdvYNz-FwEv^&%$60^vMBmNJkUw^XhScJbSiJO(hDkxe0|N6H|n7xDx&Vq$~>vC z_gZs~@ffZ#&!#jZkp3$xZ(`XYnvF-IwyU-DGGg>%K+kvXkdK+Z5zXA427=ac1)4s8 znE=F({w}?}esd|%uwS#XcV`u2mt&5ChoQQA2%q&z;e0>+q}Di(EHlsh9U!N#yGhLL zL*Of|oK2Gm%T63!zkGM~*Mgf?!cr0PpLgdrV8pGK(j@-q*XEHa50|z1%VJ#@zveVn zeSkhA*&!8)mbE9c>$&$CBb?|u1;qgum>Z_~hxf~(0@ZN8+ywQ!*`_xUEcytypVPzG zPB^m@pWP*Hh!oUMh2zd#z3dF8r=x=za0~)xF=E9}+!b2$YQ-Ey7rb)Zoab84w_RKx zb8YL6Z`JO9lT1KV+{((HRe>;X+DK3}to0EpCZO=1KL|dq&@5)o7j)WAYskI!+4h9= zN*U*qN+*&g#e~N$==sRp$m6H6*R0L&OG2HZ(e8kC)8XChC2!M;8kVQ$K*4kiNJIUX z#hjE$xm<|ycNT6x_fEVx_xx%m=khdD#T`&CDX@+ag;QBN4jL85lJLM-{@#{R=@AsYcz!@w&%-p_D%&M&jS4 zF{2#y4o7p*7?i;-J&YCbJ>&z_6GHM~qMSCV|ItSIJbFrJ%@zU``z1mZ4$dH1RS|s~ z|8B3Z_&HoUxX~=VO-|)i8CI`*;yu^BZ%<{DG)~hozGVTb;9V*RZC>(5D0@yy21zlG zAK}gj+K1=;jL@$kO_`7#`-serMU&o@fd;y9xAw8@wOM+prj&U*8R3-8vE$7R_$< zJR5{?feP@WKl0O;9UjO%!VBX4fQy>28-nfn_)6Hfvfi?l$2&wU3RAk3o_MO+;hylz zlu09^u~>%P&Az9a(}5MfkL$bh;E;?IM?VnKwY#RY<7&UtVVBHKd`7VB-?=BlK1X~| zYy3-b1f-Pg5_%ZgHR%;lr;Gg}K}NY&PrMi9zxOl;fEw9HAb;I{5&bLU`xzw#LCZ?V z40$;PWmCOu7b>-x{_iny-AD81Dy-xz2oSBobp1vuW*~6e4ys!|pZXjPa4kbj_W;Qh zR$H`&wTd0yFGxBT=*(3%we4>R4Pm5uJ?2+@=dh=8P>qy}MLyyb4-OF#unoC%26ueQ zjGVb3Nxv|+UG%dBTH&_0Y#Wa7BMk1rQN57h8`$>#)6C|J`?k~MSa) T4Vwk^xK3 z`UvvE`HjD^PhMO!lJN^<3wreGs;6=_onwYD^mkE2{H9s&aoj%AMK!`0!3oB#Uq0&x zkCJUrr;NJH(0;vcV5tGKxrc01RsSsNA|e4u*afE7k4ZcZgp-r*6M+Ad^12O)WPX(K zm^iCH1e?+J4W3v(p!(}!%0uKaWA>d$TAPf``O5h>{Mjc1hJZH;5gckKPx~Gt(|kD% zV*lPm!T*D8ikU$o!vW}ErA`PFh+3!4P;E&gvEofZ9;}12zyncu)F$RTGqt&B*-{lh zI-04=l0kE~z+k{c=ZD!Pwl?a{;aH&zkH{*N_tJ};aeydayY+N`Z;luLROGgS*KUw? z`}bY}Tc^{mBTt=?pT(KONwG(i@X$CxzyYOnnWI&07aT40$m?n3m16}4D9kEeS8i?%aMlN(G4^!5J*^g|BF0yqpZ7<;CoBYjn6IR&!D($jJXp3q zxB&GN=%*Hso5md!J$N{uo;lqMqnPCrfdM%=mU-hZ-Fe1Z8?*MiQJa|fbu{0U$4f-M zW4vH%3i@x$C$q;@y1pZcrzqoNISq-wmE}j&jL@-}eu@Y{5ee8TT`x zqfn~ADvR_Sj9GM<^7!>LwY#oohx5qa{=dQ%3=EOwx)n29oa$sPN^`#7&K=nK z03|Had2{#6+Td_KHm4QAFz{4=c2hlu`)0=P7{p1#I;C4J-z)UjzdftfPH<4|^?21{ z%fQTwj1TmxZAYRmYL-QaYwX(FT~KY%y;Gc+&l1+*2e5#C{(w8nQK*+COnu=h&*wxN zvgb2h&VGxGX)?B^4?c=**}-SMoE-pUHwQ%qo)!n}JgQmC+|bk$0rAu~S0HDtZ$M5B zE}kL8kNq72Aj!W^t&IK#xUY}32)p~bKe{ndx-r?~+xO%|bP*&j_{jc#v_Hy5WFxuA zrOdF9%C&(N$#=P@KkaRKZGL&X`B(#N5D{1%?JF3G6=z|paj`j^29%7xgVzCDPK)*R zf@?e;8#r%q0LpBXv;9h(j(@=iU_?BR8{sF2|4Mi*{JFLPtddHW5waCs+fn2ucVhMu0TMKNRNrd3sS)1s)m`RKt?S0vy}98d)K<1vksD26lb;!UKzFzc2+GvmBRa5+ z0kr4QWr%QKuJ}wx$2$4z4tQ&z*8hebqp}9}`L&A(K^l7n77*Z$uFEX^+qX9`(SCO9 zMol~BwXEoAMZLaCd+V^s`yjV=>Op$&TY`3)X*32)oaUZ$o--Nk-FUX0!n~-GL}N7Z zL0Euk4Frz+Z;S)~j2YujdWO*A}L^-)9ya}1TY_EBbm6W8kOi$F~5Ol8ktPCGtu z%<@Y*HA68<1QLBkA{E_>2st22N52y}Nb&NcVnQjD`*|XL{CY)VbB`X~t6w}ZUvJbq z$%(VyLLRj3#IL@jqxN2%kEm5aNqaWBVr^uvoV&%gEbQh6-DDgZV?Ddgs z0h*&J!LvXCsm=MmP92EX8fD`CcR}qBd)@|lq=~eQ7~@9il|@JS(mZXT$-w9C<azv^Wat;?{Sle<&OidDGc2VLOO6%MA+65kE<^6ATO0e&kO9 z-)*-f{o5%z2RuWN|EKUL*y^tw8-{fpkN~(^eO;Otr%3U9WUPiEL+^#tcZFdr_OQ1J zo5%k9Oo+?Ee^?a;(ve^a@Bk*j~ZFRmZ&Jn^11zqMpA z_tqbZ=@N2dC@@?uShX+sDF1!BFz<@7W6csmqqIo&!y7rqwiuc={_9CY*ZP`wK|7S> z`No+{|86{pR?j#i)Z7Im-Ji3|zF9R!Xjja2OM@*%PIQ`#kJ*6n=(!~}`ZLq3b~X@U z#IW1FIPW|sTv3+$)J<*Ac#FgL#S-tpVqxU9|9B1LjwbP<*3^!gaw5j%@n3FWEmk>q zsi*hauCut54HMEV9}jBak%+#sSZEN0bP|u5jnae=X`~#(zB8yyF~&1v-bRGHnj3M| zy^5FKa%r3^d5-diU~XBguBb7*VO@L6qw?<5JC8jFcjWhx>BnAMBb&{-75{3U;vk*J zAtbaQt@3@A*lfOfr#nm8=U58LijB;-5gvmw2%VthZ0R+u~JDCTe~_tQ$A z8;SeypZEceK>{q`p;iB0zOBb+`k_E!Agn25f#!j5-?e4R?AHf?s^xNcuEYA5%icU@ zfAi1lArN(diyk~4+Ixsl$`y`LL@QelQf8m{%OmlyV4!PVj z$1t6Wczm_J`1pDFF|-#dvLgrJa@g01x4Eo4$Is#huGU8N|GuFnjs$c-KjubHlD-WC zGyCN`Y2P4*-(hojdj56)J^L;EogMlRI=Uffs>M7BWN91*mSV=QZ%TuCYk*LL(qggV z4EnwlU9Gvo-FU;Z0i=QXnv!5|XC%(!tb+TeO!0X+KR2Sxk#4x@E>Y5YBk((tYkot@ z&AuQh--5iK8H)S_A4)>npg1QXS=j9ZQK)QW`cU3|H93!u;6r`Fp{Go$x_yY2Tnj`u z(%oGPIPxnXZ^z~IJL+hzJOsBv{8pH<)6Cn0j?q0elG=7}Pjm(>YBZX_eKx@X^_*o` zC3c`qI@XQ3lOAl200U(PhM;i!ayOLBHg&VW3%UQS@m+rKDMtjb9}SmzKKm`?f8vLJ z7ujmSd?jn&G+vBq6~0(?DN=1)3`vbZRt;svKm0i@nNg6M~dE`J`P3^;hiBIVPQ zKC5N<&hwneZ^aE))1)Q4hjJcgkU`oMh4%rkPm6YsNbUtpK_780<9AQl3%*}ve51Pz z`3-akn3wUd5|YlRixcL)!V>8RzKNU#j(Y#1baz#}-N%5y{3)3xI4++fe5B{3zX;de z?TH?PMS)?RW1dMO&@{8Km)_amdCap9Den0%Wuz6R6Te52&e5JNJ~B;wJ09__ zl9R~AQ^~g-=s~t|IU_mn_3H~}MnKI>Xmqr}YVeMF#K8k`ZLI9m-g>`4FYRy?ekGK| zL0)`5N)39EQWpe^)HcF7JRVKjJh=S%?|ec>Hy7U#s!6rv6poF(nZ5M zm_G405_E`HrsIfpwSMs)8A4idr0SLg(s4Tbc`)W}P8X}|CmXJ|W3Jx@J%r9$`)Eq3 zWB>SasxYM3=omlsLIdY1*i9RbO86PsujKn~hOWHr?|5&Ts6$?U5%v{q7oqJ)u6}T{ z4=tq>KJmL8^sMG@(X};pUl?$Y@vzZK|}))Z;85>Kk41-aai?KGC1~>5ugwni6R(?nd1M2SHpQ z!2Zs-?b8-viY87q{2SiUv=ifopP$XFRJ6MHf|s<{V1o#DB6QY%fv7xofDztz;=Y6m zt|_$NugU&+=MB=c&_xp;EIkj_-~p#OMAM&p2YbR->DzPZkm z+;_o^E&Vjtb*Gt?$8oftP1;~W%lpRo`wSU46B;%~Z+FG_L_j3xu>+*O3yJE;G4<{0 zv9pY0GjT5^P^N8Y&U%Wv0$Cfq>~)I@06j4J$59dYUQ#XIi6LMPjdvVk(b$ue=y?s( zr|#6xK*(FQ2=``sNsWR3a7F52hu@o1Q9gDfC!g!9%U&W@w}OSNaO+o`J1 z#?>s`Gm+omI#g{%(R8s*xfvZ@%-ya!Uw_k7E$tczADdP!j&l%u`!VJlJ7kXkV6VCE zCQrwg>w5I~zqtx04~o%tKql4}Qu|Y?b(;Qt9HZRRbS5I=fHq#XLTNV}c*<{%nJZuh zKx4IS_XCDMUyJ7UCvAlzX%}XtdHwt~CoWOEK8jJ8!jnrgj|!U3@`N7-1YxfW1x0&w zkY#_2V$(Y8fcD=Q zAq{{ST9s_2%#wJ!YALh^?+Y`B9I^E||K2J45%&$bok2dvilF8@c3(0EIDQn&lg4X* zEFDmOuVn3!{Lj8WRL6a_jM*RMMn(F6FDnjJ_hMvYAJN(0-hXILlu0nNw=bebk8eBt zB=nWCX*G~@Pj`fKYH)w6zt}koLoi#IPu{&ZV<)*f2KmEfic3ls;LQ$tm&yxx5WKiQ z#Ts$MoChP1(u>tky@~S8clJ8vf9%`QT^MN3lidhyYt}qk_f+lA+zs56TaAMLTmF^dfPXeUt=D^2k9=Kk zw})aRG!U?1`2 z)TSPsKuFE~!u(;!Dc+fWq8N_49MEiDqgzzGRfh6$T}r?MYkh{%@8or-D@QNK&NG^r zNtW(ZF9oa;5#mirsa4szejVNk^l?|S3YGIbhP6hQfA@>Cg?5p5AQ}PdhQ0f9*#h=c zR{9lWM$Gsbu@B*?@GsH045jf_znXcz+0~;kz)b36FHVk$KWrZ#?L1RsQ*wtIE22f^ zuII&NACSc7{`U^7@6Ad&c?3R5L0EmoZ}2Ji;K9R&ynn07w^ZUy_~c2&~TufS(V z{Cp*#!26HhzPqS+q_=vytOZ8OIKN5NZ&ueASMZKC|{^?>}NbPK} z2c1@{efOp^WS0pc47{`Uh>vhb^j8K2W~MVolhagynX5}%q&2w!Y!>ugZ45tZ|^ovd#+yY@Wy2V)!WAeDbU4jXd z9sN3k;Qf-$hlu!^=m)WH&4+)8X^~m`>k9{5WM>JzooJb14q&x^aks}g=Fkyf&96xM!}O^UyVJ3IvpHIwpI@Ijz=*)O__KfaOgP$j z&s|QT{|pfQRgbN`gD>rNf97W9o@E|iq30@&g{u4d{`XW230`f4-QjFS3bdo{zB40q z#)HjNQIo7c0*24=8oLSgeyBxI61n}WV_60noaOUOeY+i4@CnsD<=tk!Lp5j2%qk<{^@uM*lp5y`a#*TfPLGrDL;&Y`VN(f5)aLx- zT&KXnR;^`AE6Se{LtU~c-d{(p-s3suy=^HK2J!c5uetM$I-F@*I-*To=M>nq%mSm3 z;uonIuj1npWab-V-jdfmbib$T6bfmieuFJlqF%$8^|f~b-!|pyF)<|uH??wYhaD2` z=jXhP!@cga5u_A=)9b5z=H2euQ?V}J8Q%G0Y)~6G5+XFGD-G^3Y7J(GI_GImmCG_o z2&03zisd;9qu9UJXY9p3^a;ccsOE@c3Kt^$o#?o1@MDnN9aUyr8|E1v75{yg%KozxcM^Hj%S$^MH&o-zBLgZ%w?;A5=HX8osCrmomn~FYvzNd%8UFFPf@p+i2?}z_m z9X@E>TVj$EG1914fm~=H)9UGQxlS!A0JQ5$}EQ;vdx^yH)$g7l4g5EbhjqdsfbF7av>^zYnHI zFqQj&-19a(yev<1{4>!OLoYF?Ct1a3fB?nK9d(eY*Ax_q=d(4jN2{zo*j%x30E~Oc zN|drBSN&2y$kCp303Ox-oaR&|xQQR)_eo@Y$o=t1KS6kTyaG%thx|!iO7fXcp*>EI zWJkgX;Mi=q=P^?N2fsR+=^8eh5HV`AfMCb(K1ZKiKX1g?cdqELhUa6*PKwmR=fbBL zU$Ax_-g1)dpW3Lh;`~J-w()CO7Vqbo+=6|Pz2aZj%Oa(V=8}L2FVoMjJs{>)9!mCK_)F+;hBJ^qE%v)obq-a< zyAOM8glU6=7L9hoe)lnJJA_^zq?BQYwPj&du+P79D>R!r>kE8h)n7V-xOseo^iSka zv+;N`oMQg_#RT?|7zpO{ze}zy)5oK4Vw^89D06b6N5>IG8X%wW_@_L?9$zo$A0j4_ zkH7&gh`Lc$Zy{OCw==nOP=Kp1#`kVv^8~3u{|FrUuI}-=AKX}BRmlDZJhEX4UKP7shK9c&{sd&R0SV%^&0I?dTx5AJGd2$^g zFHX#Y+=*EVQ6y$0%{wz6AA}=0yq+E|FxZ6=7I} zOp~pkt@I-6rB}$zrWhqrw0gq6?yC@B;i9%n%`$pFo-DB@I7evpFw5ea>%SP*(wJKgdd#_EUZ**4W@`?*?(({nm)^Swp* zWI#=INB|g6<+R7BEZtbt#SKi9lB76+o!MggtKyEz(4Q&6^G7_2qS!)VfkdA=1&FZd^}N_-KF7F5v3!d8v$Jd++OszlW7rm`Jnl?1u;Wl%@Er z`YxwjIWAwOmeCxK*hEU8J^Ow`NY?!|$n?E&{pm>BvEJQd`CZQr~F8ONM7tSBmutnQ(u0L4#fN1@8@#> zqJ~G8Az1+`*kDz_?LT)YEJj#Up7Btw&ybmi#u>|AbydqM;M(!aGZt*;*b zeD-vY;Xc7TahA(d%I(p&^mBc(pC0zy4fyUCZ@gp-Y(X~vP{`yt2jO)IueFV*=x6s+ z*ZNUdp`gy^*IDXug_Pt9pKsKuBMZJuY?&)ryKMO#Udrbc(W=TJ$k z2QEXqlMnHb@blC=yo-c_X2PSe2KB9reIDe3XUBicXbExv`t9bLs%|gt9_4_xi{K#N z9=v?AVQm$Q^Toa35(d%=YL1}H+Ofr6%YxK=lV!%HcZ$P_S6EV#){C>y+%;Sz3qF%a zTnX&Ef19}$1h>dLujWzDPt|oPm`oe#!#+5!lb4}w`N?_h`soeuxUGmDwk)8c%+6s+My3w)o`IRwyz@usj&>J%3u9dZl4o%@m)S>rmxCTo%?V&3RoQ?exFZMvOjC7&B#2yUoiliIrz6i;@}(QrDF7d&fU96r}PM$TV-V*D%dF0m_p)A_DK zL~Ac{YPG9uU7mB})fkmwwDrBcW~OLUgm2s+LOdyP*Q+TkfY-M&W?onfDvNTE&XhvQ zSh|9deJ;=U>din;P_js-L+r7k($oEQFp*Uv@H~8HFODy#^kSc6z^Ows?{VF{tmi96=eaj00Q-JaJD$lu>b-^2=eK?aV`U9yAz zaua=*d|ErbD^WI$`A*ImmgG^1nITib_N&B<*|N7PX(#KEx*hAm@;6aZy>)u~H>GXMw{uFYk zlm&VLf@_*I!iE2J!Ry;CH}I>kuzY^AsXMmk>sfxUH~=-DYuncOxX)p(kVtKJynscX z@7f>)=Y+d`0Q8peNokb*Bp=B6GMea}4x@CNB5?J8Cz{7gG1ddmmpV^Vv^_)4j{Z)pb@u7Uy?^3jZlphu_l<{Y@s-l)HikHH z-74?h9$KA5^1P`zJn!GX8O7^(+RecJu!8O2nX_l;dv&y|>RR7paz;Z(;~&f8P&x9f zSsD6gX4HjX`letJk(d>t8xS)T0@V-zx2J1rSWe}1oF*d{vkJo7RM#an>seShiRwA` z7&*U_W&6q*7n|E-QfK-`c6w(Pf&!WhR<8z`RV>+3Quwy?v!I+#$bG}0bgdHK|8$F4 zA}9roU0?tVd2CC4uK(r%@-zN{)lg!|N7WB3j(lC~>1z9+#))2}fQk7$J?}|1#^cvj zp4Dp?SDo?Pf#OOV*aP!7@sgG8@*=qNbNIlJ>ntqHi<#)>mwotcB0B-51$7X2?jP;f z+hAc%4yv#HP|hJ<0k!qe1$sDb};41SIC z^QzhuWnq`Z-9g?ghWWg_vcaC7Xnv*!g&D=o!blrkzq0bBk4o*-*tooYtVfjIMfkET zxmn-BJu}!ZCQ^2JN&678+-F??<9oS@LBx!~sVf~(N{@_Gsa||j>2gF>H{K{B0*M3& zjPErXIzhZrSCsMo9_uzrH?NIZX!=)kM#R4sF&2D+v=1Y8JbUZ`{_>okGNsoW!b8{g z8a@ZX-kVrP#{OHd*vFKy1E{bKWaL0ND?~bWe**N|knahX#!!CKU zc=2E82mRua_tAcNcW_9|VKxYd1Au+PcsJ?gayVUBjQ}9k1dy)$mSpewUFPne=k!CW z%k8KoOlxlE;FbY>AI2%+W)LN`zrt$?wM5xLEr@4GAxqO}B<{3-JqP>xrK=1jaOCRf z!&?M4`}ql(x5&o5Y=-SC!>nIl%J(dRjb7{q`5NPClop5rAwHL_@cd{zbcz@}f5&kyv=qHXVn{=1C#f7@vH zFHit>8#vQ347f-4nwCe)wBGRHT)(@84{C2)k`rRQ?*r2OU^H0ONVEwCJEgS5hRvCl{^do2f2Z*ge0CoZfJ3 z^o=d57lx3O7?P%zz}o?m!8trfv+O9BrF%NONOs5WZbxycdFEAN3KxMp;Sta29FCte zkB2S;46*5Q6L*@Ex29sufOk6J00FjILbZ|tZG01Ca*40Y&SheNh@4#@226{4idwF4 zM_a*YtQ~p>$_5_>=4gv4Y@c(TIuOw5{pWRxAvV}Q&Un;*X^d8vGyGrU!KboYIIt(N zz^Au&FUHAe^q*D#>5IwIt3v*A7=IXe+xmWfI1n>b5cz&o2IIQF66jx6)J>Tv$v9lH zPn6_cHk?9Zpj*+T+dpYT>FYS2ceF$_p8CmNk7^TJ_Cr+(T2GH3I7*$%7c6lo%NGjw zxSoV%ox}nhsv?+_w^euuJ@qjc?{X79P8PnN#r-skaFG^j^E$lW9e)#EBu{fEIWc(c zR)gbyXpo^p#~dtos|g`M`3*Re$`10(Tb0SjXPPj+oSr_)>u*sWDH{Ysl?MrpO+2a; zBmk^Mi!Y7iguiPGka2c|vLDYk2S_*Mc~jgYV49h9K>hcx-{Xj|>9e1@Q(fectB~Ei zMD{+b_$>&NqOC8YnIzA`-82MXDw@Xv)3fXyHMS|{0N(|mlF`~DG)DPgga|1fF&Gu`hKGWCmaHUo!JaY@|(ChSjq$i z?qCs931~lHr*k?A(HR4Xf?P#Xb7W(B00hg^0-PBec*C=-^5e_a4&w5DN`QlFe~+G( zxqH7$aKX?XB>!{GKdyMmnRs=AF}5!6*YdH5QYTo1Fi-o&d*A0^t;<&P1O~OK)?w@0 z3oU$7K9lxFcsRu}1&SE-fce)G+R-`;l&Um{9TV!kbxi;jK$7xvUUun*{HwX&|Ml2V zf5t@t%B0Q%(BP%~`NNJH_@!&S@M68;nI$>OUQFu7*P|bLk;o;`^JVp_S1-cXSpu1a ztT;ctH}sT-ipnrHyi2>Uqu|Pf_ufVs7Eb@(K{rv`F9=+&^YYCuXSNZ%brB&pQM>?x0Erw#y;mN#{^|7r|Sy)pkwEUJQ$iyfe25UW9 zD?2c7%7it39RiJ=H8$$Df9GEl30|53hcoh?Z^&eO8bNNAf5wkVeh2bVUP5HJUnY0# z59p4l`;-`h#mtEaSjDtHVkvqq;((bCRB&HdjK59(gOY4=`6_x2;@klC#_jm`mD|=; z%gY|^WsWpI5}CKmSm)N^D-EKtyvs4Zdfyu9=M z*Uo9F&4u|4>C6@G9PA#zX#_yu$LICUahQ9=nUe10^ySSIna1_!Q3qLY?!!X#)F+yy zj~GN@z(V@Rw{G+M+};jn<-q(f{ra6|pd?NK8590*^pJax+D>XZ?VTR(8}~Du47dn$ zJ!R%v7w)@5|;RL8JoHIgWKs{($ru_B| ztuV8562{%8vfjOlAIXOTYc&EZk&WWt`M4~ zeUDdM0e+c$;E>-(Q|K7#-2#`PcQ~+vpUL8Fs$HL$2A*xI>Q}N(B)s3$O7k${5zhX= zVf8HGKfHe4?UdtsJ+5alKb9q`SZiV!Ar*3-JJ?U+^Smbaw_4v7w&^60UvC%5QkZKc zJC8oxohx2J5ilOk$Dgt{Lb}IZ_|kR?V{y&6ONB2K=~dwVP6->i_u0gz)j?!o(T2aS zAA4>%9L^w1P$6tF0vq%_F}skBRC3?yhJYzB5Oi9FtAI_wwMGlj>A`?ePMd#Z@mV?C zq2DT=#qas}pn>t{ZaV?9Xz|YLDal^p&n}W_)~?dPR4UNdW!;^`0X&A^Oz~zOOtXhL zODbw>pCP&SAUixo$DM6L+Ta|+OsGeW z8CGfeYgp*%1PA-Vj@1cg_Ug!g-$$$^LDJp9k=M}e`|O;ja|L-p_{&zPV7#oIDP$8< zr_@T7xl?c2fX;2+Z4b~!9AkWR9hMejGCgqAq!kalMdb9qHv`#nVm;n{Y`bnT>qGzZ zt}7HR$E(U<=6SVOSaokzp`6pJTOHD^qUqgKKNY!*1Z?`PAEGs zz-qc2i*BO;9v1bh~--{<{{79J4zUes1 ztgA%)CcsH2Z=G;Fq;yv1Dn-$Ox}!elP`tEqgB2Sq&$kf)|0P8{hFyTZM*N1mnlJk+ zc<_z3$Y(x>BZnMUzTRa<&7DO$hOkQ#%C@Z=VbjZi=c;Y**ca&(T@OxCTAk3|7Yp7U zgqIukyfG7u@V8f0^~=dNRqv;JQOaFkP4WiwdH+SD4ihO09{Z>le=%q72o*zu!kSC# ze#J7Co!vl9-U__uOgb8D@(CnjdMgsPnb|tsBTV)Bzg+*F=0pMb{)u{SF$~KN^J~3$ zJ>l1Sj>t9zPhR!fgF5Vo)2xmCAo8y2n)ax0gS(MH>A)3t8a(M+u)j1i@6^d4T%K{R zL^U$)$GF3~rcVfser(K@J71TE`vI=8!GCmzKmG8fbNOK_k_%aOI1G_J$`j^j5Y#o-KJKFMyXrcKlVvDo-9X0+4>G%=>*)G0SC@|<8P3U<0^UwjJSriN~q?=q?X6-azwZSBoUD4 z7G%6MiWEh*&d)TCop4Ky%sz^HGmq#&6K{LF2@A;sk;t>IBjOFI-jm%xEMGggL=Z*= z5T!XICd!i-MX!p>jUcYgK2a<#+Obc`jKC}u3^FdA%ffw&*{~%)(9OWrwaTAL`D(VypZ9R*jd*?kr7*3;Ou*cfU57t* z^+)g9FBr7SJ->4L^B#UfGvimD)0KVE?NHeU3Qn_n{Czwke6}E5^wWeDFA8n|bj1Kl zEDm;_FOtBDWpUNW>1ZHC{2RgJHabj@4mgrLP|tc>z~k>1@>Y{3}ZC0zwuQM%N3MK2GL)VT!$|C22} zetXB#@zy(V>xZQ=YY}PuKq^Vp3o@yJS23=SpoX7>=eNO_`1H@arF#@tX1dGAUXJRFtD3i@qQhq`!5Hi}1EQ*)ztf z)Dler3<&_ZlABV=quCzQ7!Y-U%UvKlm>lIQiXl;nBd8*zIhPJ~HhMA!T%V2wVn>vI#HUFZ@)T^@=Xd z6-1K5?t@SqckbJH6lxNo04hLyaKHIBKae5{t<)@%P1ScM>$IX#js}Ak3$p-5Cu2%| zkAxkXPGkU5nFu%9_uYcet&ZW30UDpNWbr3@PgWuB-q04}vWeTydh*9fM7yXyGzYIc zudUUo(s>Slzgf&5f(gd+uBvg+Wm#l~U3v0J+pMa?w`j&i<@x*k)b_bh3$ zdu13jqJ?CJy51GIa7Q4JD?Tz_74z7#<%hYT(`VAo&A|frQ7J1z!*eXBx91{4~2O^9${&Qjae|S6Q&UM^)^Saeed((d<&`*GIl%4oBI4MC0{d)sO41#jZ=ml7jol0VN)l z6&*ky#pm-c5e5!_Qg8>3m`SxqVD@fp-t*XvT%>nBYeF;KcP|0lNoD=x^+`8?(G=re zxVVK!kthw++LbVzc1C#t_VkP9%=13!JVF^-@HKufnP3+)6_B~nKUf@6b1>BFZ`|v` z$l{XiU*Pil!}`|m*slu(@28Sux_M%hA9=a0U(vk0hSC)O=A8Q@^VexOa)$u=w3dQ7 zVT6-sOJxYVG&mGMuyiQGoQnLY$_gJqjU?o?`~3~Uci&yS{7c2uFHBD!(k_+p)o#&6 z`%I{T#pjbgVut-e?C*>_4@RhXjM23#;_^mxCo!M4i3m69)Up)8J6Me+b%vHEGzn zC+qe!jfaB&KMl?qoprPX3Q0FOWM9ka7HvW7?VaP<+|M0!1c&nJfplWP8qdKOPxxWCHT&*LQXgl) zx^WNq=lMQ2zhQrrJI3Fw^XIZs;3)J=S)~f?qT2zLG~q|32?3Wbx0{RF>!Cd$aRHzP2WM6O=;T+H4+Q z!&uk+*r`|%c$-V6@RWDP_pBiQnW7n3R(E#O@27T%hj7@xM=)2U#}GgF1n@Cnp~>b! zrP%uUbKe#Nb5@UGEB*}v^@fn#8kc>}H`3owOKo0aGr*dA?X;6d+48&pts!XU$Xwfu z^B4h;MiixPi;t>4dU%;CN6b0ePnupy{OUs6$i?2JTMYg|cG#;wK;P|CYhd4I78?WJ zAK)zd+d>`3Teor7Ve96?l-wA6E3KS)@{h&0Cg21tVk!udGva}({wXzlLowA2+sD&@ zcE&rn&`iX5;nSqfNx?!D$caLkUZlwT2Ri13PUXsw)%EqG>?6#PZ_2V+=kGDt5pu{F z@JIRONbdN3)nxas{d3Cf_J<8S;mSx{w%k24tn~kK`fUf)C3}>AO&2}#|1otY+p1z& z6#XC@fK<{HMFa$-E_zf-DYc4UpXODEsOBslgCDAwcH5gT_qCWB*4Uc&Y?bl}uEBJ>sg;Eqzw6{iYund}*Zf`s>2S zOSYe98*E8a*~9RL1XMT!a#CxzT+)Kw29!yIV~*7&mbXBg)sR2!QU}?0T6sJlxGu_- z%=k1Lm3XRnOf~X_OaGy5%F3Jn=6EPQBTfC5G+J4&pq)yVDi_tPHtST(#MeKW6ma(;TFI_3a5J?|V%kOc}> zB1B;A@BMS@1#jaI3w;WL5sETmLAxpo7qn00e|&8d2yoK&7$mr7+l}u%U(@aGOM(`J zQ}5h-OCLW@J{oX7-W|_PGQv0r1`OoyqTv%*$BM2sBY;39%bh-AEZo=k!(6;x59I0z zY0&p>(tARz3c6VcK71VP7I3E&_n`u{ZgXuYPb-lObhe8aa8EgP?Z(sTo^NBDawkxew{_Zv$@JO1^y;=IRdHmlP{Gg!kgFw;(=tJqv=+s#68&=A5SULUj{_0 z3y6}4-o*Q~ufL*TKJD-8lSkma62<9=cdMlIs3b0y7b3O_)s92^G>T3hnXo(>Jkr6j z1nvCcEl|3ey-NTt);ATYC=c0+AXMRoi~7Tvar2r%MsB9Y)v@po((SWd;)`bZ2>E@9 z%Qn;60Y12+P*jDX2)Dm|7?p4nqOABst$*g;)se3{xHL#g@mgUYdazS@Uv^GXHK*+M zfaA{<8nGooNpLf^$LKf7i@Dk|Ecly9?ODhM_A^-1@$TgC#rJQYQ9;ZEdC8V92G{}= zHelu<6o>tiY{%j}2+i~RDIgtARpH!iu1soQW<5wcBou(CBR)q|K68F8Ke|BVRDks` z#gf4P#Dyeq{8gczOz-VHrZp!^>5de-mj>Rn7^CA4GhK~~^(6e$GbrEn_EAXa%>Ep; z7_mD!kZ4!>b1eIYHMqRH?2F>e;+XG0tB|#%UKf(^04wWs)BsU^I+cN|V>C(jHU_*ZM5i=vNCkZ2 ztL88Qan~wvt9LCb!B0|RENM`iBj%Vlh2P8mdyyWOam4zjg7pX6qZKUi6_kn&RP|gT z&WDS*oNA?Q*uR2zKK_7wKV5Fr3vC?sjx|oxS2#FWk^Ge3Z&&riRUY}48JfaTA8t)l zn`AvJG2v@w&UOM!3NL&%=xei(5%cNW2yC^jSnDf zKXQ&3N<{;?a*w&~$~>aIe!k)I`?t%Y(>Yq4UI`ypu_8UnLb2wLpGcYWI6aWisV&>I z2x4nPGI@vUH8GStlW?#%c4Rp1xfAVT`A47e)&Z9hYVxkxo%1!4cY1YO@=xD=)H|rW z;Fn)sBlLaC>v4#gsE>Sl+TUy({|b30*x`UhTxC2FSOqLM*RYkHXtSMTF=EZtMM|9+G% zuAi)XI(lfp3*aRE$i1?bSG+-*g8<&GeTQ7&_thWQ5ylH8(T2KL(@%;{vPV_Qp;{!> z)}o|U#W#4#2VujzK!rAXi=6#v9pvDT7YPN#vxfr^#0i;#t_UA0o(9pEE`@S13CutK zpixJB(Egnt45m;2=D!yyHlHC6RXm*Z+V!s9@$qO;k`G(@kdyHR`5XLuW;wb9y5iyv zi@>@3xA#i0?@04mS&qHA!ch|72aaX!fNappl#+qGQbMQO%f8`vmh(BJ$?!)WO6o1* zsrHEx%g%dq&wlzBidpgl;05IQZ%9RZ^X{QN&AC2)2GxTt`fNE;lMW||035o&-Q?7u z#))44b0}duk_c3_-A~s}sIu9`eureo-&`A#auJ-uMa{0Z-&boK*UW^i2AZyua&%*K zI3P24z{Q%2@d#n>G98|^DrYU-Boac&39^Z=Tc|@Q5kRAJ?ez7wEh)v4d07*@nWtU3 z4&;rZkR8e1!j9vSBiqMQhFr>%Oz-p1M;NlbC+%%~Uo~#xr8KXqz(3;&)41s>A`;+( z?Hi8!Nm;|)Gg=^~15@sKy{{8Es>ruKlN4!^^7=+Lqo5ss0CFm2Y|A;uK5s_8iZ_7J z?k|c7J{F=Oo8CF`XSV5F2-HZp+1svr;^cKU8k#gMc5#($woeQ#{iIUVRLfK1oFQbl zQEJS9!3JsXNT;*+`TjXFtEI+3AmhJWGNrPwA86@(QWE-WQ^0au6TAfDcYX7-FMvcGDHwziN z+)jib%LQQD$xjS1$`NO{?6J#94qIb}?(?;UF=Exib{t0iO0y@IvNPBDw@eV=jOz&?6A-+_PtG z_HQ3YJ|IS3(4J`@ktYAFliTZ%QSR7IS4ywN>!8QZFT)2pENH~bkUNiGv=oq^AsJ5P z)nZ-})qTkx=$lKnw&+4I6yM^ZQS}$VN4nzqVxkva#!p6)U=hVSB#9Fzfv*Tn;TH}O z>VC2Q=8xzgnc+1kVecXRXqZim2e#g9IXUwSb6>iHALb-=EkhiQa|} zSNdh5ym-y%xPt_YeFh&pg{t(a|0 zHrcGL%Hy+2p=47XVnF0XCt1}$ZXiI8r{CvymZSMnn4P^tub$gKrD62D1|aSR?eed- z2aAUUp9n9G*AFSFy?;wP(!E6UU;iDU)At~`y;e3m?vZ?`C0FcCr*_Ix&DCGe&cCe> z)<}cx1@1Me#`M7y_#CUIxMwBI-b?p@EE+axUuXyNgJ8eeuza0sBZF^*ddhcQNu{D+QIR+H00#~`7>KV_q@ zM*8WEa9k|&PPZ9gZYM2^+P~c1;f85v&5lNjJo6#LQ!5_f&&?~}tg}!9Wb*kGb}TO z(sl_^JOG6{!)ee@wFP#x58;eo`@J z`r|idD)TdX*2!g}r`K8OeNCQVmv$B|Mg7=n*vg?z`YC-_>Bs24~`9_oT#EO=KC z<|b9O$_5bf(_6Pno%}v2nSIvje3P~c@Gd{e`%cH0qSqi(S@U7P1z_oXbvb$WiBZc$ zs>31w_mPLr3VnpA>#(kqu$*-3Hqvr+IiF`?vCcdiCXRbZ{V6ctQ#CSs`2yu=BfLzy92fvI@VM->}Wu;zzfsRYS{8_*o!VUs`UAK*zMtsxtuBH zc_jqU`7CVV4XZ|>k=pOTAK#mOcRU=r4QKI03Al#SxGRVTrB&Znx(RPZP!82(&7zk> zfH4g2iV0nv;CYGb-MQ0R>p^G!C!qk|^U9VA?GPIq!z|gv-5qLGg`o{s0@8o{KFkhK z&A@CRIQ)7g=y(VE1^-2j_(EZcKGRz;s`b8^vdfcgRRow|RxQ!vkhk-GPwU9%3!|cu zU`X8u@OzGjFgjTpoLr5t2}k&hy`!jHxm^~?aBY-6w>BTdEJM7=a6gsy!ivA<=$qU) zKvwlud|3K6Jr9p?0*3M*n^0Y^O_rD@%!sSmfRh7_ZD>G7`&EolTR~@d4BkTDaeVH^P^vU9*LJZmiQF`KUI&NjzajJetjLw1=m*pPXAMnkVti z!qjc;l-ck7!ejSLE1NW^jAa6JRIRzHU*Z-FcFP5{o`pODw$ZTmVsWSni(!Mb62 zKrt=b()U4XI^M-9a&xm^`2l z9V5ROByQgDFSr5%GKJ!IT<_tmd; zyx^rr=M+}nhReoC@dsG?q)82e@D2OH_mg9MQvdlvaGy(ePua4OPdC?v`@z`*9mdvh z@!UczeZ(1EddHd%=+h3p`+a40Gm!76h!jwOuxuvTw>bLR4@y7FkIh6rRkFrir@>*V z&*;c0o!fz5CKlwy2v)focVA2w$x=lO=z_C37g>e)_xpx^Tq<{dn;ZtNLq<5h`|Nej zL_1j3$)5=jpV$~UU7bqcR_%JG1Tpvac>gX>HyB1s2>WQ~etYIZGBt7MxQ|Qon|ZbV zeDdEtaZfDeQu`jF)(>#2bxf6+0-Ve6;#r?6>C$r>);W5jKe3ykE|l-Y%zp6P z($Kukb4m9&PvZ;5S@L(kEPWP(FOS>QT6Z7DzwGB$!my4*PSdzoV+XcFq;Q|`x#DT0 z#no`X=myn>f-!Lq^0>WkUwntQ5)bxr=Ka7oQDmww(z!H`*nM4763A>%yXttth@nq{ zLlnAq(Y=ZSSa-RjL5s7LvRVHQn8g)`>3)w!3lNrE`ct+`TCtoDPnn@DL!uVDMwv&L zPdLT=+Q4XVu>FW&0wr9VG5AJZ?CgVad~40P z4>s`WEk1rl(({e^do5?e^Lf82yJx2F#Y#UqyQ5+(@0(Gb$-D-1HQ`YY8@*Rf`7b}D z231#w&JRtZrPD{GkX$A_Mglz*%?TMjHFI^_#*v48KeX#0xE9u;oUg^TzTR# z$ocC9oLVS<4BfKpsBWZk{`qmxJ4gdP7{--86(#RKBR^+;Ll^Y?{V}bU4@L)<^DFbK zc{)kmugDiWrOIRftc2ha;6ouwB7J+mrTbU>?Vh_`PPi{&sSDfEJOm4a`mIQdbNGFm z*(*PM-seg2qI)JCzRqoj3Qi4ka^RgXqJjMbYDi}M5cKqnpa@8;D0Hq^vV6|B>HSU$ zC$W+p2iy{(8{D5qh0Cobia~{Hyb(A8;_OCRB7schB5#84P*1D2<0cN z-`q&+9|{->{bkUYXq$r;3+mMa;QC;d8gvb^zKxZ`s&d>2g(E&MOp6wv)3)B&)I*Y`lDL` zCd#OH$G9bq0#BK2kIc)t@Vx!q9~sm(tge%60nBoSs;}b>6Uo|X_c?(`w0-Ml>PlQW znf*>o@q44Q1*efaZ1s*gKHx>ZA*YXcHno0(of73o6Hai%XPM%ffIVUGpuN4)#j>p$VhQYkyLxzQP9Z(h7UhT)3nOzFZru~6&2 zU#ttU-zr4C=RBAQer0NL3D$iLD%sCyfne4u((~CTW*Asp(u;e(Nc+TI}_&Igp!s5s~ZI!(3edpcc!f`wPy>|dy@eD*i z$W-!jDfwl#3a2y1q0s*UUvaP||CPVl^)owHkD1jXnBhPq%^fDIqdr9Rc=^GbCws*MX-HsL`RwZNOuTE4RABFGp%AK6f9~u1H zC(>}zg3qA3D^vg!?Hf=jH%ZJq8~7#MePLc$H9`-nT{wG?9KQ)ntviS{5PeY(0`Bg5 zGv3ek4-B)R_%=Q>HZOwb&{)Qt1J5^Sd&jgPMv;)gFs15Hy$nH!;-2DQS~EX2BXXYZ z6iLfeOH_%OPj&mVaAe_|I$jF>XtbEv8tw{po*9&w=VU3%-!dmzdLmCF zpa@!{o?B;)qLvm23yZp*ckI*Fqh1=gD-+_|a^wUQy4>e`gU^Nr$5)8N_=C~~iv_h@ z+#4E8K!QM>@e^F$z~cG7a2;~hKB`Z5QO@CDA3Vj+rjoX>gyMLAm0#|~Cb<1yDH z7X`Jmf27-UfZ%rB{Om)pY7!6^IF$@%YSfM#_~sythy?tKr-}R3Cln>1gH2%&gEq$( z_wH$=X zgUbv)H}(X$zv~DM%=Rz>X^Vv0!{wF8S$y@A)~M6vM(HD-$@l5a$OjYBoYSoJawS`(IJ~+BgVj zF@L_=<+9O895XwknzidKUMK#m&~ik-sfUUh{BdM)KzSeEhqgcB6AePl>$kssY09HD zfu{R~BXo|UHvqNmfVYO9oL&pmtA-1zuWPhx0zV-%w=1rivhU3{+^?@iQS268+fKSh z9PVR-c|k-_^qrgWNa3&eoz{z&zt`B zkDoNtmfs1H!&QlIR~U-9;qj=0>(})fmJ_K)ZNFOr{rF})KR`Od;5NCB_4ttVHF~QU zRaIsc7_a199;P4+o5ZX}sRVFWjAVH<24rogzzaI3%3{2w^!si=Nfb*kj9N^76PDuod8GuIjhabk`qClpD?+;R%)R#1tWq~ec zwXjZK)0^^)%n}cKsHw78E7H{kJkT1d^!UpUl=V^@+P{$?jwVRi}B#WUMQq*9qo$_*6{33#ll4 zjo^7pq;duI;wj?6e7G?#6FRS!O>%+9?*AQ5uac+ERQm=mW-z5A1S5}Z^E_TfZkfb< zntTgCR?SUl&#~A-P$7{X+Q5ayv_nmD+V>*EZ-i6Es`tANVgsN7mL-~IVsg%_C?D0} zj*gqPeR8zfbsd>8OA%tRdy`FX5h~U+YTk>FJ#G|_w@SiM6ZT(R1^n|~ddBi#UVRds zjgxXQ)r+d&V^TG{H^757IF0h9vr6G!CJ?oZ0nnz9P%I|5>OUxvpb{X~%7b&y^g-z0B6X8U8OqQNct7iF@}&i28Hq1~#lB zPkv~P2MCe*C=#>raOg}6SwLoPz8W1mkoRAEks2TO*+uHuRe31|yJ$bJ;yvh;OeKFk z?E8_Rh0`n!X)2>!3&5O#hQHXIS+11lCp9Ar>~R3 zxc2wju}8PWfR`-rV~R*few*$+P)>1V#;5MaGLShvI9(jn%f0#Pv7P1}i-Bw`@1NQ^ z(yiw{w$f0PpV)q@Tu+f`v0%x z@2@Hx=6WE837H`}nSx)%@u#oaa}u%w+_ksgy~N&oW~VpsVqx5EG9leec;8V-wcUBR zmE>fdIykPvma7COC#*ko>a!YT1WDcT=sS!>Q)Hc7;~(hn9}ws{0!)Fsd;r(}&g?UZ z(hAFf;88+*0=Iz)h0&2Hid-6-xspI`JQ;(n6V0@ozz-uGJd5o(eL1ARiYF*u7xq>H z%ZQ=XlAPo#nBSB5Y3GA23ZL`YlQ7w&0AdFupv1OpWj=#@1UH#h<#UtMCZ?^)-T6D6 zy&>P$q>KL3+@&q?YxiX$qj3jJwW3r*yj{!RetLx@uUN)7K2up9o@4duw#O;y=F4(g zHH%BMy4fsMaU|40vNylT_cpq@7dZ_Y;}E@M25-Fn**4(zef7Y90NSkfm0 zPE);)q>$gUKT0S#_I4|NRV!5yhu+`ny;mw2ff!!#PCWOxkr@lq>t_dJ#X+p_uYqYj z>`I6st)}rqr0?n&XIT@o-ymn6g|v#71j7FEen&VZ9&c1;S$9JI^YOU@g?JT(>g|u; z;Vft!{0E7uTu4E?OWi00Eht&E6?`89CpK^>jBaA|4MQpv!qRaSp)P)}pFBn0UpBx^ zif6-Hd^aH`83Nat`=motS=yfdIBos|B|}!sNbEOqNNzvabo&|yP8-J|1%<)Rlp*Xj z6jYiIZ1xutySvN~*@c#K z>RTRJ25Mb89)0IU(H`=}_~(w+?eRIO0=L+cH(+#+L)@tl9hHBVVrU*82G zMcKlXn9rYWknLcMxG6poJGv@fr9XcI@jw^wBtsMrU`xY0sc{AIb3!mBQfBedovg_G z{XCLo|dI6!c1lE31(Qzxx5fy2eiwH8SJL z53=g-l_!0;`~~Z{I6M7)H-rjczp3>DE{d_Dz$yu@7h*jKNy3nQ6^eSfmFR6KOpVii zjg!M^ko7>`tvb6t0Q_rAp$(=U`m5@A9su5!aP2t3ri9FLKNrNi|Im`+$uoP$H_(F4 z<&?V+hzx1pEZe4GFIf-#31pFYzq+x7_KOH7vn3+`qZh+{#24UpDdbCuuZ_n;*xH$G zss^#vY+o{;p2~SbpD&Sz_H%3^^f8F@xX$Q9#l!Bn?LH@qJwWT@ml=$-NkYY6cxr+A zeD&yVX)l1ZpXujs#wha{-mERSHf;ag`)^Utc@g==Ki9kT_cn)0%<79rSCpcQwOf;E(lt{OMWy zGE{)cpTkV++2bmupkWW&nZ5vOQL?{yNHTS;u^bP!A@~+$;9-%emCv*EwTcTmY{43b zRQ|K=bs8a|1^Vi)qa4*Aj#y!aAD0*#|vzsV)1BQOJpYL zTWVKxP`T0GQOsk1k*+9O2_#FDubP7aY;=&zxP7VX(zYKn@%!c#;qmBO*xJ2z>FZmJ z-sz#TERZn=>C&^p9mTafbH6^EU*>w3>{d~~DQt|+D@iw%&}}lDUEB`UsnyS;aX!2f zIAxHe;(}Lw6Uh^~{@{x``b$-@%flL!_yzZ!`r7+#3pLQblTtVgK>!+?!+X ztA|jSf_L#QmS;@~;?eurD!Nh{ak9yMD}x*0fcvHeAdW5h~o-0LX= zFPApv3GN{|RqOJw{T9_Ig;&bC8N?krJx@wRok{RPSgxJHJ9+-zP#!wR)G-*B#up4a z+0lqYiJ^x``kK##vrgPK{r)EK*$6LDuGjk;Ozp(Jul(tFRk6l}5Ubd^g>ohmIK1|M zOv6vyMc#<3)a}|kXX(&>XGe0dYD5_Z=b*gctda^?;uZn0-y02}w4FliR4ADC?poWr)uWQt@O5e z!TqtKpxTz}qJZYiSab&$j=N1|H$cC}2Rrp|9N6Hp!C=**IJoZL)1z4lVc^)!{X$O7 znt?U$IX|1&S>Un46;0@~9Hl5^MkJbG2WdwfcG*{^W;~kznw2;XZo7-X2XDm+MAaMN zEL_d3VD=<+N{9TcmiycJk!C+#5+T?zcZKzoYZT9?OD(^KpAJeQf-an9y+6D8R9(#D z<$a_-NLlP3pH1GdXmk`Yoc0;0}MT_9_DrWtx4iq)^E?doDkll*`}`a+b;Q$1x_DmvF06Z5zuW^Wh0Bq(C7!*qye zuIRyhSgwysdje6;{Thb{esJGo+sJrh@jqJX@AWNggcjnk@8;u$1qlSSbXTG$fz!GF zwzGZt^U-7Rmm~dkHl9#7gf)hbP=g^uDBkwMJq$PM=RjRIP>?^Iw)|p$8!Hy3nfk$X z!-rTO(O*47a6Z~I0Zy{?Pz>^dOqW9l-#x*Zl^t{DCf%ybpJAM4F7-{k@0M8SMJASb!0|XS$>L5kt_>@Q)&W_&mFlI1OYCaq`WCa>s zeb?TY^7aE8;0Vl-+*3>ryyB%tt<^q`Wg}-!_mbY?p1)z5MN=m^0F$9X1XH>>XLV-Q z;ci32_vC)bpQ}375Xan82ngxf@2+#+k3ZY{=s&lW_VzEbI`RCCKqRBeFcIr*q~XrDAAq`)@kB`LyKg7ek7^9BsQ)z9;^Y zKh&tLNuc{A@bkBN^PBfM0KL+|=LvvCpf*2|Nc#kF8gu+a8ty$F_Alb{?f=eNdVv<1 z{SGaBftPNV=5i}f%AG7H}sLP{6W8BsbupUurB?3i_mQ%{$OrxFh?zrudSh$ZZfix!$*WWdOq@ zJU#xXmY1^@cDsAMpNsLaG5$*08g8uX*QK*f_TKb-57KjpVxD^HE#*b%4slOE9*X0G zzH)lTBLw+lg*Nk)RZDKMKY0ZmQoGsN?HjTAj30UwhI`p~G^YUuf1z+9o|g5v?;r2h zq>2-NJ;0Z>ik3r5q{OW*;CQAy+dfXueK!<1f1ET+D{cl5^x?=^l(=Yk#Bs*?xfhPQ zB#k8JLQv;4`(8dcSCP-INq-XNMq}3Sb%)K7At5T}1haXsbqllRU*^x;RdUz+{TZ{U z?Tcp6W#!oU0G5%K5jM)spMlGNkEufkdiRY4PtlQ>EDz|T@ASBY3|4~#7p#^O+)gNn zBiAJ*m~m>N1O`fht3=xk6lwl$H@lL;hm|6aaxDU>xJNU@2guowwfOq|h&i|=n2o+% zf|a;i9)n>2=H+`9IJA3po08J(Zg^kiH0TsWHBj(Ra9H?fUHM zduBJF0{cyRrF*R&+Ae>9%&Y0yc6$W1NKNsR9fjvi#R8eZB|Xk*m(nhq=ck z1e=P@RgrxcGk13%`n=!e8wY^&a-$5K+ral;z!}`DGtq1B=&&|#*vOLuECyo3&6e$TJAlD&XxQM+Og`b*mc&^G^)Ax0=} zo5%1v@BtBc>K0jE3Aeg@dQY8lWbz()qvO+hX9w1mcDk|GCPA!F6@@s z7?0s7C>N95xKqz!=7gJGlj0v4BxMtM?_3tbp$5JjZUM(T#p%Q2I6UWA+;6ZpVNsHp z3dN`kwcZa}clP$>iW9JrzoqM1FfS*B4H@k`9DsI`9uh*6L>);dSD|5dJtE?0OyfKx zf}GM!)0e<%6!;)PPK9~3KldkFRMKrX-V;h-Z|@KHNMS+XKkYD~h~p^JoelCh31%)Dzl5b}Ah;zz=t~*=b>zy}-aOe6+~dylzL5sdlQ~>9H?b{lKwfdgK}UM|}B+(jO?G^m;!w`JLPG2426`>?K9>k)Pe-XKx_ zJ!^*R!vDEUwE#cOM)fmlKSx=)T|_L?0{LMM9)7jF>?KaYd>V!p#bBJ?_hS+7MT$>% zhamfXmGzM^SKrdIDd z&=ukFhR0{69mp{u?nAf0;O_5aK=y6e4VqPu{rI$8W?l=)+wH>O?;Jr5C3dk~e*nGS#aP$j zP98qMmt;0_(ZZ|ERA+2w@j@b9_hrmGj*i7L9-aMIe&ZWs9vj} z+#*tI{unrqud5KZC0pnAf|Q;&6)bdt6D3eMZcy<|*fLn^93YD)U9Q~hr6GdT|9 z0u(FOw=}NP_u=rg51WA6*fR-68fU@LF>NG^HhrtOhPc)i7U%>>cl#)a>?v}XmF6vr zvZO{>AbxF&l%cVv0ni9E4G8|bi;&oBn{f?@8z0TP_ERodl! zrvl#RT#s4&Wxz4|w@>D#S!C4DpDBoY zzVY_>(ny&XUn(<%gG9(_&2;y=wQ&0cl>yZBfn@B(pU^k{9Wf7-W4eo(`#=rODSuUx zdL)BOiU$2xr3uhdwH9&r(Ei5XH!^`o7^REcyWYRVths zI@XL$Hv`T|MpL_MAM5xl%s)v99fCjA!9F$8CB>i*Ntw}18;E@1wubQhu|3DW(_&}< zsP{s@&Gc#r)AReJXUfk$BL(;OC6W_LbMmEc{yyinMH6AV7=<|pdK(W;b3=YL+LPk% zRYKkH5Vr%c1&0SXs8sXxN5cDxRO~6#!yWq+$7OG=c@`F#LI?`tag#VErLUIG zcKVs;w9dQgDt>RD8n<7k3H#ieJ=NVA9yHpW24{ohBqRIdo0id?(>rkQujc1&y%*B^ zxAeaKs6B0_TqqGZWduRagZjQ#@9>4Uwt}1h>+1)!39*gc4ShFb@C-CuZfkI z%f?Oa)YfiZo~Zt+**En2@v(Zox9na!g69MLMrGNk%k#_^^5fpWW)?bws?A1p7w^sc zeOdk4ar0qq{8oQaU?nk)<@+RAr_%#B^Z7e#jFHnZ9MU_I-iq;RUy64WeeWY9`K^p~ zs&n2D7<|4^7SRwE{B`r@brK*A__!z*(Ov%-6{$CEg^b-~CuC(nUt6H3{B6t`|M4iRGyLQd_j7?l5!r zq}X<1dzjAnpnHeru{@{)_ttGQ-T?G7a3-;}*fWW+O&|NCh}>JfM@gy)L?48`KmVk> zg>5cqXchGrq3u(EH&%G<>_u9UE~Ghh`;#}B*eR+*FAzKJiiNfIoCd z&FKm7)ys7MW2OFaOQNy~Ug;SH6%OtM`r!T2w1a=@gQP@rvJFSE#|mXe{aK-KV~^_l zy~F2qLIK;MYc$%Pl;bB);j`&MmZVyZmOyjGB*(wHmjL9uq#5a9y!42fLUySF3BxwE zQ$}t0H;>UH`=&KVYz;_n*ZjDiM{#$?gLdIo&*<;`(oHr1Xcb0#C%n&;e^>Dz(P%9V6{oqByp^ zRlxQ$OT~I~Z5SG~B8}Dd9`YgPVMzku`~^1!$urnVJwE=16R8we*~3KU2e9$0@RU*o z*I!Y3VN%Fyr%UXg*H`fZyn(x8H|ye%sEc0*d!^;}M{On2Nn1ZjHdi!|-6nlGz0kLp zIK%Rh-%#+3pUig1R+v#<`xpMqmf`xi8=&jPVIST%g}oyq8~8ZX;rS*IpMSGS@lP8N zQ*n4HPD-$J*17IN#!gF*pDI3?^56PT+5*_3zxpt!F(8^9dLDezQ&Nq;zn>K0NkIQgj1t?sZ<| zuH$O}6|DD*qISFI#f3HVJ`~$TzI1Qi;(g?;WE#!_C!CLJgm)IhfzkEHg%iem)x3c|{cRUJrJO`sekf9$x3isC+)gg>o$&L)CLqR*KVy z62BqA6*$eP4qTszlHT7@)jsoLv%B2;wK`#|q2EP92v+RKGI+@N_5A!`5astBu9Dl+ znech%-r=7MsV5Prv6Y5Y7xaYMGEyg0K zl2`5-@~WcwdjQFrrNP7M}nOEuXo;{ zxp%OnQC9hafZF{-1E-j(`EOD_c$=4>Ga?DbH{_@cpT9f%sXv3}Hg!vP8#XVaw)6b+ z`*R*%cNfMWTomb5scn&TaFMJy@OJdlmk_Wt>WN3EyNk2|L!Qy?Lqn*NeY}{8jO?Zo z5Dk_~H_Rc?0Z!;{${0@MteI9aA>tz*HS6;-X@^s9;_V=lPP4K7_N5{Httz8}X3Ox4 z_Hws>=Z_~GzJNV#Z4Qz0|{J^PvP9naW#aO!8S8)AsdIJ#pgwC^rNu^Bl+b+zUP zuh0)2!xKl;*5m751(Pieny~|t<#c+nWN8s}`p%WsClA_=Y*HD?xH8&!J@WAU zS^4=1@7(Y3#dgZi$(%la_vNd^Ul)2oOdm{Y9&dZ(E)I^}IS<5)mTO=j0*!WFHa zveST;Kizp9@|`G_vJN)XLeq3*4ita6zuGf+;J#SxF_XtLN|@P#m?XX=&LAjsNL`UU zhU#;Hr(bi3>=;E5Kq3?b2Ft4Q8|U+K8n}%2L0|QsQYbJyAM`<({V%{sh)?9+1cz*e zt3P1MHucl59ggJUzIHqI^Fnv^Bw~^h5`PqdvxT(E@x#R*VWggKt9p(D?*8ZUGm><4 zqf;DGzoBkQcqicgGI1|)w9nGyrU5=r70Q;#4}I0Hp|~r(J(1o2>DySO>B*+MwSI?h zBrnx- z0n8H*a%2EGA)vLqOxb?&Kv+3pm?~0xNYf7BQLbsX4`Fl8U=vo)u4y3-*!M6x)fAp) z_e?W!Pc@q@d=Vh%vJ|IvIi}Ye_2%m5%)Wb?RX^*=%9c^0R%@mo)7fU=d=fXedhAJV zx6Epe?3pM5_49E|jq!0Lb5!Md!c96pD)o7yH6ns;>X-;=s^yf?N;MN+nDN^>B;aeF zxd9&a=ICPX=*x4`4HJQnLy;=YeF#(Vygwe@W zHyEVaGI2Yl?W$wrXUfIb$G*rQFTEP_*PW^Kn`E+K=aCDFo)b(j(XvPNK)V^6QI_vk z3i5WyzlHJkwuxN$jK*!AJ~fLF3Dob;sBT!@=I+Qg)*;8m>~I`GNJp=t943GQoNF)2 z|rDnsGExmQDb9C->SEwQSCsK!YwoIDTDIAZoap0jm9`eOv()1&@p6hq% zaCIRE#+2c&+g%qafvIfjw@NeBx z-Lf~SQsN;`w@~(Vee>xPIJZeYwynyH0**XGi=w;p_0m8wqq~>zTRWVe%C^e0bwo`i zAYt`W$BD;-1#f1GIp1;=&e-HI?bGmiY++^3J|!wGp`&^BM%(p~?*eoY7nU+o)pQcBsPwE7WvKjNzliP=tUHmKK5h#y! z2?;sd#Ec9H{@l=q#}Y|2e2WPO}0!C9&*XvzcJ$8nm-*u?_8r>$C z`xiF9+%G(&A;imaKD(~n#_g}I!MDK;OHdYmY6xLQ`K82SqF8{~4D*z!M^KQcDWA_t zChCTvo+@SutC7gsoV}^y8JA!y`{Oph2BJ8Zr2vka_0u>ytI!=I`nuSPc5#~%@F$_R zlk*aWa@y=hd5fgGI&)8LAZd4i@$;Fy*~p5KPfv>U5ejs7TS0WOFK!OwYOS$qqzxc} z1Wa3!Ie6kL$0X+0;C2sf%CC1(1fJ%aqd8vGM+aJmXsFE$bv1f2)+s*ivK$_HV>ls9 z7^kCrUczkosKXM4EQZJ$DC#&MiqmHBc4-~=Ekt}u0`(a9){`RtH` z_^0r7grcsG#V12@{c=A&Ac#il@-k|c)lJd;9#)pd>Jqub z8gCrJi#!0tesQM_wvvfnTW=PSdgqoPxUto>k+%n-8Q3clTX)c5ywA_eD9~Ei-%z+w zxto7gV2-!Gt*X2$P3T*>&RMOumsT=EE0v7Na=Q@sQ)pD#d@XHdd~NmM0heh2tNnUg z#5VLRU{nZ}Gk27=;0eKkGFAyx#}%OBjjt)5!|SMXyQPsL z=`nR#&u(1d_6YCu^<09Xpt3iq?erl-7!pbqP<~T|sJ*dmpHfpSZuWlGrpUoOGM}Qh z^VZ#$y4;WGJC_*`)YUfx4P4YCNqBa<)}l+qQqGP$`2&U=^4iJ6>MB zN^aZUIp{v}$o&k$5nBi{jzQ`!nF6r?+iE}GLt*L+TuLJzDJXNOBOmrJ7Xw{+T=gumcVx_13Nqf*Vd}649aqI!(STbecXlI~$)*F%)X0$YX#vQ* zq>?Mb8X4#WQdU$AkoLzVO?0bD3?AsNX}j5_uDf)v7v{NS1$QYkUCf^4$e&ssbF!=W zh>GTpU8F`glOkph{}t_YYDQfY0gJ0n%N4W&CY(J!+HtV%AOudLbbMMbSI}A&Cw*cr zP64vF+wF9W6yf2%@~=-|@KEFfB2fo*@pAJ}bE4P{m?k9TU4rb8-(6xmjyL9(4lZO>C+WaHY1cvDXO(efkpAjn z?&gUHS4hP}EqW89e(VyjFR1(TDA}%KwAavdnMy1-yl{qk!JrkvUY{ueqsNA;Hjp$t z!in13XlH^u`_--I#xk-`=Myyjmy`QG$&*uFWGz8Y0~*(+CZX` zte;z8Anp^Gzb~wO+eYG)`_!_p9GQ6zcM{yIl#BMHd>M(u0KS4MY(8!xZG`=t>;h z?QC;83F>;=ZjnyQAH?=)t6rn(SABe*J-}Y7G}nV8*->nQP*a44f(M$iQj2pYH36ws;i`h| zwa`A6{u(;rL}H%S9ViL$#8}X)q+=!ToG4QSyb%AID2Iu@Ujg8MSege1=BnkH2X@fs z;V+#U;&VbTfoPHJjGjUUH?$jtx|R)h+8}`8%_X~&Q*av(D<)wkCX*jU<(L4--&K`N zE;`otkr=qqA$zN*%vMs>ZFqcIEQH7(tMxNlaKI?`0_Hx*{Ksp@FHKF6B^7naEV|ci z#mbl4F#_xc*tq)Ig;-2&A9Z@v)}sTopL&{P+p_K z@o*l1NMe=s5N`uN3Ov32c5V~eOmf;52o3v2?pGSXW2e{oK}+UpDfs>#e&vIgU*a|! z@_N&indiVS4l=3@^xjnDHtUKyl7bDjGvjosnP}$lz?3c*jmW_psRrq1*aj5IRpG7d zLn8RuD4tBfkV@yiGdKMWSgJLzLXA*P9cbT}0PpU?5JX(gCT$ZEqyoc}s9{;CZN9Lja*eA$GJ(toWhSq;p=R0X7 zjm*is_Z#>i&ey!PsQm(RLa@?U3Tj%&plymE@olv%Jv&?-s0163)+jh#<}mMBp=h1K zC$UMkYR-aL+!dE`1zpqyAD-ISf%ZQ!QO3O0VF4wSV%ZFBWDiYVLr3EHW7K~`<_#=OVUncyD2&K{nG(;c}Yg) zZ0U(W6(F)IBpc;Vm(-0D(&lFeUQd4EtdUGMlr&mFUCcDfMz*I{a4x&0Lf%%O=^cC# zwM}p~PrRShZAnI)FxQd#sqa0QYTy>=v&nI(~ zJf~JE5EV3-XdBel-6zdGfMgN(Wa&fTFt=|{`3MG1a-7wQChSmy)Jqd9Hnm+H%tyK2 z(HfLqciTl}e0NKib10Ogle= zS2gQ~P)mxXs8THuWeC^G*wN$xYwF6|Nb`srJiRzZSPeC5$fQ~(1eLNAa%+Krhsx1m z&3Rev&IdMYrF&Z=nn$SBLiKcA^@g)7FVf_~j(V~7sX{*ni^gVwXBRl>uER{{E&|bf zw&(0_64zYl5HpRN=asMvFCf`46LK@axA=R$=;T zG)L}WhBjqb!D@2AgLT$O3B?EDv^^dzE8d0hon7B|VmdRr6;NFvbW~C&rvh?XSnbh| zHY~K6AtiGU1%Exu#^x#FY5$UC0|sd2oKX9+=A8bZZ<>4a#)6{*19L{Q!S0HUwWE(0 z2KLhYd7;8Hu|DgEiI7{J253j87GA;>v+Y!zqZYNm18McLBBmZDKuxV~Wbf-c{Z12J}o; z#n4k(ZOeFDR@d!flVr)c)+cDNZ(EZHKP>zoU?0@D!nSY(U6a@7vRxfY8v5u4Yhm5z3zz$I%WP8_nRU z?#$IaIEx#m?P_c8ZWMcZP&O=*VgQC{>s7R$KGn(cNt*c;aP(2EY+#R6QQDKW7sqlK z3#2-wZ}Kb8>0}|M=m>~mTqj#dlq}{#=xheuFTaY%Pm}hMQHMtc0)LN2p!{qrPG7aiI8746D@)GFPZq z0aEG1<&)Z)RCrFMM|HlzLkg_N#%*2EyQB_7x=e$jOB!EgS=e*tBS$@OLY~u*9K|Fu zk61K8CqFXvFxs)mM3p5tnKrL&9&>`kTnvx6aTK7O-GvVTR-|zx1OYg5prav- zzF+~k5a`QAv|#5EH?V-~#!^g^8*a!eVyqo=u9KYt-Uw;bQ92F%BfTNt@;z(^J>5syUfJCxIQJL?-NzWTP zxDq$%i2{A-?sw0zPpFflV1dF*2O>06P-3)f*@WPu1iBZN+v0GRH$(yl@7BeN2ULuhqxU?;sv~`JfvCV7T5*d-}Er-LyXY1 zT7F&KrruunuZ=sGGo`L%-##4EN$56H{WQTcX6-Gg?8Yz!;grnbq{VmGI5|nZnw>Is zZXss(+G2B?1F#~Cnb=+ScW#X zU0Sc`sX$uW6LZ+kVH!0fwO&zcnxAJx86m`>A2D%U?ObuP9v`yO_jkr#PemoAtQpVm z8+7w#0n^ZQwNaL`@K6q$UEH8*?Ro4%T1PD3%i{ui zil}7ap136!37W^+qD~od?el%HWC?Xj?#PSa0p-DhUd{qFRV}&_GR+|pqucN<>|x#J zq%OZKfJcCzl{R2sOX2E4b;^A1j&u`6GlT6DiPS0XCR&2*@~+>WhBcuXPog<{=*O#- z(gdsIk}g}RTeXp@P-B|4G=HSykxk1me^pjgs9ftwH7%hb&1&;@TNhAVGdVWT zb#OF{!y1<164TOUw9bQmw1lWC!)K}CYKuyS_;Q!~&{(%Z$l~t7C)TSwDQjwEm&F7K z#LaFrn~&z|dNme_b&^;fcTv0LIIPxC+UOwKl1h8coJi&!8Whh{bfes&TflY=g}n(G zg>YOOYm#EthXTI#TiqRs$6If8hVlF?llM&{If5{zBr4g|3LMbIr0WqJYIW&pOwj|c z1x#cb!=y#@?u2P1hrI{UBvfv@OE;qfNW%>A&Sa}iDQ14x$m3?yJ5%^Hx3J8!o;C|w zZO%OQ@;wLbJy|Nd+svGaHVb>$LR0#{jCXfH{cf@g;kz2aGKqwb0}r5aw#n(u>=7E9 z?QwicM&~{PZ%=^#n7|gpIC_)>fCUf~1&07}bhm1B;-2`K_n16fax9Un(W5+FLaw-j zd#PLFfDC)sIuPR})2#KT+#$N~K$yIo9yKk)AbRT1Y;o*RRv>w!v_dUMa4TQ9r%0}P zfZNCk1a^@~P4GBCrj4a(p*kjNk8uUn{|iqPk}7?GOmzZd|K0^)~s&r?9L}(XRc=&zr8)} zoii&o8bs=zynu(KsbvuMm|e@mh~m%f9n+8^O7Jqh#0wp04q+`=VY}LH3K_WEy~)O# zF`P2`Ey86+Q;r1crZB6;^K<2ijksfb$5U1KbTULs%R?Q4AQ!tQEu5U?xiVygM*_x4KENffs3uw*nggcfGgX3jvR)VtKq^gm+2Da zfMcqn>H{Nd9nwVgQaaTm|8k{HnY1K5?M(99^?rG^MMmDs{1JXG>f_>o(Iyc5ZL-i- zmW}C8A4h4c$1^EUwpHI8jtoD)BlHtG=)I|ceVL~~=EjvwyHk{LnB^1D*L??1>3Q{p zmi;MxIM64uXX`0-VTuE)E$vw$cN?a@!-aFuyE+k>RTPJ?UY#`N0qz`hc33_am7r3_ zmLN%{HrcMmhtxFT=h|0tpnAbkx%oQKw}203TOB&3;|qIC&tS__^E*>u%*2i%3H@^Y zNQE<}o(MlK3i&wnC&5w#o=nb0S{v~47&!78swV+V)_~=6SEd!s?LH6vQE(R;RB{h& zC6$#6P5+~C1Rxih>M`U5_79h*Da5BcuBouhQ`LC~E-zMygEp4b zE=beo4@*pfYs3avv!D{%R1#L*+9LuAiV-C>@#j4|Cb+0W-WKBjbV(w1MJZp|E|%&> z@diI?`iYn{Yi_%N&)`rJ1BSxkurj69<9vrrcZj*aEmsqJ8>0>h4U^0Ix<#J%yx2LX z{dr%B?1?tllT)h8eDw@mx{t3qTh2AQis zOzM%&A`NHI;uNIHrro)gt7RaiCz1$nPNUmLtBBvag6m(vE|5uu3Ojpe=+Pa9!6%id zk*x1ULk3Liv|JMHon;|~(TM2t?XI|&l0yhra$4nNgBX0xP7;6C$4jc)UgddnXd3>( zwZf6@ggP87Wmkjj!LTly-{;dHrh!jB%<}LqvZI&{@}+xudeMGXr7M8$k$atsQ+0K^ zrPpGaZhLmgK!WmwS*7q7=KMU6EtE5-u{J!jSfDQprGJ3id=&kSc)wgG&y#P{M{rw6 zDc@e2>EzC#@+ynR^8z|SG2BUF_=Keqh?iKBN_T5sFb7Em=8&1yt9g1|aQFDR-9JgW zBNjHW^5^>KSTd@>G|HzQBXyi}4gsYQdR2L;nNZB z$08$%=nNN0m`^gPDe-AQY*HTPVy6S3u86M6)A5)tcNFB*%mT$SDH1e}(nvTj9T@c?oNV=P@4oe(>u!i?`KmzT^CfkzZtl&E3H^B|G$toi6QYU~^6ePac8ke z5>w_9G2R3+_9=KV%?6lCX+L1jbJ>LVHq7U0PN)O}T-K*-S)v@_t~d_!VNMZJf4_(U zdp(|VI?E^niHO;}eU`Ubykf9K4B_0dA2*`B;}-Y9I{iT{Zce$qKo`^ZNXzeJTViA; zp0U@3d3Zu@R4T~*324WH3W7^qVVGbyjm3B5PTEs)KfWk^?wjPpTV89V98YCy1Hd0Y zMUHU%t=bVPznqVT8r`5#lI8jRalSQhFEA%XPU#LQU$=gyh_F8;l$mygkYL7C5)vn6 zy(KGt57Q035V_Qb)n(54CF}uaz~hpr+_C%pP%Pkf$4ESTr~3kBz<{`kK5=&sT`672 zO+$`yZcffvz8Jw=wzlaU>N=#hunckPw360@noPOzZUUM!SQJ95!*uCFK)g~CBcLy% z@&t%8n@DGkrd&Q+_pmo)@8X%Wav5+G*Dnt60VM|9AT)hh)q4mcF!uI3ogEwzxot~4 zw(@?XBO{n)i`M0OnvSxxE#P-O;z)pL_rPXd){}vtTv1JLuWv`F&IxbkA{pc;o$ke5 zgRrs>6Nj&m{x%USvM5D@cM>5Jd<9DfYJLdCA$(YvqOGd^W>d^s0V(|>$c<2xTwSvS zwbprX*e$2Gv}gMj>&ewZc)*c~Bmi)9tL2zaxeY{0k(Ptz=QOQH9L3ANJn{&y-8?Vi z-8Ek|(|sx0>rBW>7E1v3Y1V!R8L-a7HC$Q8;#spkq!fE*e;Dvw(CZ-|1oV|`Lhfz~ zsp~UoeUQLK3Qh2q%0w|x)5aPP9EoSNF$zXli*=0oVLb*TrsBLvqYpCEi%Ipo_I!1? zrl{>w4V2D-`XY!KS9IoLL<{9}4FG+4Naif6zig5?GTf(A#s$wB-dh`B^GM|4oYpgH zJ(;?5&^%MO6>I41vw#lU(`6<(H5}&fDp~o37Xerd&UKZjY+4mO89l%Q(cpB3;}ygw zm~5df_{V_EA`9|^_faG5!TX`*{iqd}qeHe7$TLSsytjQ?W0sIckC>dZE^k2KYYP!y zX+F#swd-VheDeXtI@XabmLqXG+NHL<>o0f)HbJIL zv?z%e0L=sk+{P-=l8p+50+{lw>oxRF+)K0A`9#^QuKoOk;({?x?<`4$^{&H0A%+re za9!VN5jSP{9A9Yb6vV8Hadb6C8+Ki4b}S9p4%sVf6z2FmM44N=I)<7%v;*~8H(uos zRp99xMan&7o+ZgPTv>_Dww>L#1L>Fst&S3G;}qXB?am zMhbMA9H>bgxCz$w8@SOxtJQWk_NAvl!nL=ycTT!F9;i}_xxxTK?ETjTd$MgnZ zQPSe(ygW@QNGhS%EOhe`40`2yGcXf~4II<6sD}n!z2kuA^p23xjhN2oF03gx4I%Ss z3d_72K1_PWEgbk0O{wkrW{s{VFHjGz$Fm{p>#52I+SXZ3rISJJx-<^6eYeAP=Buf$ z2=*dq^BvgbI_76K+XV9ZVJi|Ua)%3wawGF>si}g?c{Ij{J>!1iWR_-pSRe zEUn$WW0Mdc_j5d06y#AZIl$E*OD%3=)JxzaHz)w@04Lf?NDvs>Q$HA}wWIO{SJGwV zPBjKLa+-FjH==sq9YcL$ti*E}Kx=05AU0g=E<_*q4?CEzkj~MYBd10X$}n$4fHBss zX<@g1>WyYEU+LL{SYJaW?nhAt9q&L5Co3QsJmCc5B6brsw#8i7+8!6Y9z5 z`6EHqaeI$}>QJ%ujiwCKL8ZKu&c1+S<5`a2bn=R9=@}2PnU4a*nj#|#0OQPtAzb5K z6;lriX|)Dn&t}=vj3gMa($wpLr}JozeBQEUFl8*H+vaI7`r&bfZaUP+>AdD(etmd6 zK)BBKBrs?wE-pbX*ycO9xl+K481!l~^A=pwG`T({k&Am!YhpT8j#10$7}k`#NTj>x z7P8kwij*Z3yf>Jhh~~!O1ZHd<0e{9FD#H?>lc=XdjZ;I+9J6DZ%r@|In6nMXQT`p+ zoe&^pE;e?z<#~HNI*NDR?X3WyQJ-#ZGhb!x)#YqO{V};`6R{fIU`!DW$Im4T(g(O4J*xd-o;RTWoL6F+f<4oy!KNC zwbz3}w$TkpDG5v0i~1mrE|RbO?G8L!QXyWHf{ew*X)c`T>ST02Wh8jLI$Pby5@sGGmO(R!ZACY3AJV9;Me3Y@9SZ}X zn+vU1qnK5sR@e2YfyBXtCk^EgNY~8pCKGKV;o)%F1mqGnhipv*3z#=dL(kvtp`elw zQ1rcWxK2-gDH$o0oSRyoC=A`t&G`&_o$LNupZMNEZb@cZ!7IZRuUQ)G-h%^R2gx!9$!(X2h04IYKkl zS=aJ6K-E0uXe;D2zO|deJ7bKdH(25M4bPntk=+3VZ!z?S3?5e%dtsA)9 ztcl$*6-&=1Bh%b|vb{fJBD#1iUdMG%K_P1959hm2qp@TjD_$o#??47f9XzU-D^PF9 zTW4m;*^?-zY&Sce@pZ7qCo-9l_c!g_tMMo8*l1_AT99-#0!NAsejqQ4K9hO)sSr2}CS5a`DWYd!sApV$gR=s)f&kLZPSi z8S=JRJrSc##@jXI(S?c7ZYMp$NQD@30l76Av%vPrpmX`*fo2!5^TR69++eySG-FEY zTOaBE;95=WxSq`8>EO5FM>mHSjU%;PRR=95w^mTg)#DLOSvW+|SB&Ch_& z?Cwu~>^D|3p@T7VTdjOV(zf_C@}7c~=t2Tc)*|Xk?TF<98Gj&rnSOd;S_dm>Os<5JG$De?n(U-~aNF-( z_Lc_YB)Bv?4!&W&;=(Fi6rNKj<9)}MRSIJYawbz;N*`iW6;`F^Q)EeGKfczqM=utO zV|$$WM2c%i@>WvwEqYg)`na(qh8s;4j6+h;j#5yb)FlU3lt~if1x*@Q$lq6*KbE-_ z07StUeh_nVw8j2V;;f!ovZiI%`tGCcnntFFo$svs|q>WyWVD1p!#tC?D9N=}y+)_6bhr&F#X<>R4F#h#Ius6Wg|#t*Q7(Uhq-s!7eEN&N^2 zCV@O;m^O1r*PjAkqAUXy#(Nd&n+^J0>;pnsv8VemzYH;gy@9^Kcg|BAV58s6UqP+S zY{g$-{=&0r?065XtT9(3-ql8D{Nc^>V(d6%U&^&p@8N>DuXZDRjp0$o&+_{+2!fyf z^z;AZfBvJ-UcbJn{^FbHpZp7-efEzaK=yM1x{(d`eTpZ^}-`N8dPR6v@2+*I^`V^jO% z28Yl8m&51(Fq*vm&}$n%UVTc0 zQRNR`{^b5AFAhqp`6G0T7kmi9yY3@-@pF88RQczwUD_|%BTUQU%NOJ3<=%^p|Bn(c zUm75IULO8S^1xfz1VFzAL&(1T8bB?{%-~yEFOFkmtVGDUKz#yO$rjVNpV()hm98QxBaR znvZcl*f$OfyGUMlI~?lp*1N5L^7)Ukcl=g_Nf_ICSav`D$*|FIWZj#yekmWrJHsKq z@24+clrXj9xckX3IV>lxiqgx!0(-}c-yfUpIFHhTk0zF2Ha)pa10tKU~@2 z^xhrHCr647vvDdx>bXOw;n&7~?Ss$#FfYoN41axhE?{FkaK5+X%NMx&;gaFv4CjOI z!#Sn!${EfaLnwVT!==c*%){_N_kI5EaMAy`2CsWe(83E&HNzoXA+-L2yC{5Z>2>(! zp6%R*3-;oAMVRB2^GMOh7%PtVIj({IlGtsSRLP5-40qsgm?3)Z&1m`Zo8jjD;`Rq$ zQ@_I4{%8N-KYcU0|JgtI&tAUy_rH02Ykd8aU*WUw?~8A6H{6h<`$Np~Lw=dqDHMUW{pGn}uj=r}R|Jvt-Y5a8x##yP~ z*PQgxd3}Fv{w8O(dw*shPm;JV-rc#yaBKW^Cd!Xaar2#x|GG2qcim@y^{9Mz1*3oI zqr36zzxC~j{B_DeOTYMs4>Q6q{tdnU-~YAl-QWMK?_J^7dz^gK-M?-NzsdN~zw;7f z{CxU6`!I-p*%R%f^I3mq+durY<#$ix7)W7$(f0Hxae6P>{k52P@ zZumDjNA2C*_B}-L%I7bxF~S8o6Ir@_j*^#}r_ zGgc_?mLhLfTwg^0&M&+dIUl`c{o~*H?6c1i{eATz-h27!3r$gcrj%L_&*ybxYtiu9__R|;YeH+7}rXL?_VJBJa zeSDCaz&`qP*Dn{F94dH414Q4v3V8KS(Or9XN3v!B1;=esRGIVfyO zfBt@xKYn@J1)ogT!!qmsdM+P2;r#{p*?rgvPVVCaAU`?tH|_uNuol505NnY)%eD^- zwb%XsDp&7U?6zV0_@ujsQy)I-e(3U#F4r%1=4%7!8eCjBU4QYeGu@xR{OO0GH=Mcq z^B?{A$IScwd)LM9=C5M71oxqLhIiie!<%K+%dn1mvo3vq{=Z~M6bY7e-s`y`pY~xi zy?g(w{Ly@c9`;)7@sllnmChXw9s};%$NuLp@0$O`etP$pwPk#9INQJv)G5O$RLzbe&PRc@^%r7g>m`Oy!Q9sPjP?o!w>TU zOiS&z=kCSW+xv}%oBPul@E7+q4P7kc%lFIfVNC!1Pe1e*A6hJa_@lSs^KWP8-_Fjj z53S$M&TkWpznz`mJ+OW|JO6(-JHLq zzs1X+fAgVS^FQGCuYb2F@oY;_>PYPb6%YLGq8x+YVR(QafBP?aPV%3BTps#=wI=k@ zx&OWQ=l-p}`>Sd~?>g*5$A7xyioVC1(AR*cy=L)WQ}Ol-VrVQIUVefc{hvOv5~YtG zOBob`{&bk>i_hOiRYQH^b;}{Q|C)#Y@@4In#Y+|=kQm}|1m<>(!az~Q<@*f%pZqF2 z`)G0ft8I_5x_m!Y|GL@u!?!;9>2>Na|tjsJ)L#rx6yZqKjT_}_igOCO!VyLZ0h z7{4o%`L4B(^6UJs*X8dgfvYLY<|3@A38?OBS1LRKqFu+0}i_0(Z zs>(eq%k5z$g5SQhUH7Y^x(?$FZ&%Qwth{&Y^S326Y>5E<&7Z#bbUE;&H`#(A(*4el zz6p};_RGStODqQ7tk^znV+gIopS(~%|H-%4Ca=r8@7$RF#f@Lfe>l|e7n-r5AaCO@ z)R)YgNdKebdAFP>e)eathwy%V@%jdK^WyyUhu7G4?syKN*S;*g@~bi|WABSUdaX~s z>|bxqp_aCKGiqNZZwivQxBm#A8M?hdA@+;+;r?$g2`ZrfKe;6DZ|~PDDXXEU$?j>lHHw{3}Gil7v z86_|w40?F166g+VSp{}dmDJj^cmT$(YBDeK&+xUqV|Zh+B;ibTX3DegWcMjCT4pd~3XfXq_-&ok zv9ch2gG}71yn%k!d?UG;jHc2^BB8}EBr-`u ze^}ds?L3tyM=EoV$4nXL0pwXrTi|n(C?S@qiS>zko_GjsW$sSFf1jLAb?;p8z`}t+ z4$YQ{N^JF!l3OR&CRt024n*a_c(lq`pBwjj1Zdp!nZ)`-JUs7PspK% zj>)4DXoF7j`0z~qN!=LSmbAY;*#uF;vtFs!XCkbE!#~}nj)@rj=w+g`_k7v#kP*qRQM)T!Bvvt^-My({v|TN4DRHS&!?K%J%Ad651(qPVyOU9hgc~ z(!_7)=aI`PWWBn{BDc~<*lYnwgOcHj z7y*;roi>dzQX#6N(0Lw)5hcO4UfKN3+M;Ft5zB zjM^OhugQe2AGK}M#!RYtK#p(KW{W;z$?$q-_Z{2#w35RyqpZ1EF)2X!AtjevqhXBc zdg3#iE6n+B#zJRvQ9YqQ>QqpVj#IGdgYT7HLbhR9-RdNyTPT}Rd__Vs5pzD2f;AsH z?W(4-QL!cAz=0PeFd82=;v>}=gbB_d5vj4VBA=K26Q0gQ zJg%S;#9!ix%Mi;HYHPZ5!W^Yw4q@4Jh8cO=*Y4ObYxxO?`kuWw<}g>&%hmSGapcsP zkBl27T9QUwt23jUqNdS%U*6@iR*nxbYEtGy6?bdhosTP-(4IRI^ zayMoDbotQAp%&^SA$-J=awM=ADziH&tW6?JXBx?un8#RfWXJJQpRQ%HqE+wAM30HO z7&p}p7*`fI8FNh}L0^n&uLm;UvPlZu8kl&4K7M6Kht|mUF2igp zE$+30hsAzg%O^Ag_ty16oiZ1WEmxL9}V04lr{(`YIjLNoq}$el59=IUZ$-1PP#1uR~gP0cFnaj2K3ZPb=nLO>4QU zVj~!N7{ujh9Up|dvzyjWZJ1<-@pJ0Z(^lCZQcf4WTnD8u?8&rJ(^45?BJ#NeVfA)Z z;cLp37)#2*9LsS3q0~G1;0*!FH~O9$OTxNgbpdy$$_&rB7Mgq4@$5`Gy>EGA++%p0 zoR0YxmX$M)S)@=*u8p%Qan}oZ+ZlKEetv|@Kre3=9z7t5y9a$_Nhf0EkD%KdkBf0V zDrK0)m-8Tw<(s^S1)?MGU>mt$wo=1df;4^S+hm>Q-H$O&BPkK2a%aMs%h;@NV6Q@+n+ z#Qli(@7wCwVRC-EA9i&a=|kL)HNsSkw@`e+I^d{w>pY4#mAHU<-agz?no;`M$!hfq zBiy6Lr4Xyb=iq>3sT;1TJD*$8+EId&XV{S%zIOZo<>?7Vkzb zbRa}H#^89wVwHqP!)I!HtXpuh+~*D3=vZqouwb%?b|=9__;s9!1#=H6cSjU6uZrQ( z?PuNe@=VDay~cqg(4~DQ9LpUD5VVehtNHHKFcJ)le#>af*@Dq!!n1s;t|JDVI}yG$ ziDXRA7u$(pU=%ye@Fsw1R(jDi!GmI94556z)+7%1d z_2cD}z7~g=-NQ~jvidsj!-vGtBe)In{n(JsVHadx?fTLEc}c~(sJUue%iJa;r+QOJ z)6>jLg0W7X#x2j{7%z;=+I0w?YJFnWW8M*TwI$&clapEndyce*fsjWYrdqWgfmpVL zMqu5A3Fv?>QI$nU!C6{He6`Qbuq3Jfho$pab{0#5@B^`s@UWDS0O5_WJG}7TK7H5y zXBHFDG11Xij&rKAvhv%Cjo$O%4n6g98`JRy@DAIe3}r1mLQy;7JQ?53C3#kY9#WNU$o3sK zO5B0?iI(mRhfuyV>BLoq#q*2$dtMrfMcE#KXAWXsH-lj2J*8O$5Blf59Y41PLVQgz zxY=x-Sswgb0Z_F?iLsDUkvL>PzJZd4Y;~D0W3~%GI6BO>oQ2o}T3xdIT(g-UfHFc( z*yo$(E=2bnV2mGZX~5nZN-I2s@&ae66SwXat}3>0EQf#ef{Tr=|0=YT zup_Kt4C(C?#8B1Y@|?nJs#m|nBbVL*zWQ#2WqzhClJ-O|qrc(jU-t7A=1??0m!B0; z>;f@ad1nO0g-)|oT)(Q(LnoIuK7&lz3+qB(nB}ggM;+OLv30hB7 zB}8D0dNrXu@{3c$#V(`s1(zQHDYK0GREehF-SUQkjn(;u6+wlaEl`434)daDFZ}F>9p(K`y^YYM|%EQtZLLfrTjU zkBo*a!ME^=AaCCX7`1gl_Ff)dW|iE{_4Wa#+Cp|F9gU{7uDkjM+8f}2cp(JR$CCOh zejSsAQ;rY0+xohgq6c-e#sIplO2ww06LLnKWcazC9U9K;@3lTwB>ndrt>BS}fvg8u zL75_80bG7(kC#PVPns|Hm>+HoqY^30K-d>{tep1#RoBs%RS(U@tVafr0}O*3a6+ zce}7y!1|oDhZrOJ+Ei4e?!2R=@LSMaz+I&jdpzI|PPYwR|K39c?_qRuo`~3toHtrDwO=_zh&6dz^Ua zcDxrKbcld{>7SWiBL}j{l4uXrH=!g2_9O9UJIzA^2Q=O64^nlkY`gWKQqKQ>a9S03Kl^4`~+MJ#oQp}lpEIFHs;|$9*{0j zFeOcIexMDOGj%i>qxf;w@dm-8rfuB+&U}uXU*8$^S{YB_aG9p?;KeQfC(yc+qV5r?CRF1LAo3^8F$xd$*}od6B?m zKqunEdS0O85OYvX2*Y`X$XM%#RiR$JCCGhZf6Mx!81%uaL)2hGLYp~6T(Rfb3WdQJ z^;%^$R^FW4QH*f9$M=A_#)*6#e!gatNc0iB9NED&;QmPS;Q{E`aP0;?qa38FkKw;U z>K)&(tAGV=qtLTR9I8d9A@B?^zS?S+C|g)<5I+t$^zHK$Kmy1r|HpXo#jX^;$F;LPl>F|t zC>)v&&nBAhmf2xvX`T)ccvIIR+9E{UE+u z_xmAaScz|E!=$)$=h3mFp2ZEgcL0l)znB)iO;J`byrGEp06L)q?V^(?nXC)Vcwq9} zem&`7p~u;Ed^_GPq=VypV(?$v4R8NBGg*v6;G*HZ060DPDBVLspwc>;3yJ_r zv*WKPdc{v20?J4ZDjL8E+`lZOu-R21(l#!oQo4Mwh>&^x4PMecQ^}N0S;10Z|^D;yaVM0hwuYG`GACtCRQ2jx)G5L2_ zZ?4F>J(f#CG>xi zU4_&GJEome70m|pxY50P4?;X&I%CFLCXNvU@Q`)@pFvqbUgHJNE43yq1t~VEvo<&& zv5=0nT?h^wDI}-yZGZ@zg&4FVKYl{0`O#xx6;)D>)&Z=m!kt2-Pxr zBDseU!1Zcb^g|J^=iUQf*=%vrnj!J3NG8h%Mj~Le043P5szhm+T=6)MO?3?6zW`ul z1w+LTF^TVh!>T$%)S1KkRI4DUE*e49veyz-6L_ixARrb&z60Hp_DIk#oBNfJqe$Vf z(<}F`j1O1PcAE=-;{(JallzgbmqEF~+)c~5@iS4Go!x<2ru(YfoRnjR5tD{Oj#ga^?b!Jq0r$%l+e4& zRCq_?{2Y-t1V9uDM=tEIZuHAf2(&mL`fK~B=c2*v?#Cdu3wGn+)DGkV!6ESOWs`NCYKJe))_5oa|4pBF%Zo zP+pW3kNGvkD;t3K0G2e=XYHkZm^(lu_-E+_7z=6JBBT(@xAl3&>#|k_I@>M8W)@gH zvHs3NF2!$J*GFC%DaS|ZViA1K3&(9MIxH7gJOy!VbAKc`BanF3NsvzE-5HyEOnzIa zHRv1Vt`p=%w$tsFtyTDvbXDf=A75PZ=_{)VN>S^a?8;D1h;;xl(gGmaGC@;m3#6>3 zMKa(%FSx(&{U|(rfLxL%lL9*&YUgxmRh90otMm0Eg3CT0tY0&@lj4b?*ht8%h_Lq0l_bE72 z(@_enI!})S{9&Zl14ax?EypXQV7~$q4G>7-a}Y{|&s=v)PhB$|X2VD7=WqS#?D>s! zIOO>P`YLi&0nZe9h&G6Dbr3N7s7G^P@6)_Zrln*4kZ+k8>Cd|}Zp1B`jTdnXyB96C z1R}OSlZzBPg$r_bs#uos3igWnZ3)nmj13&`se{!Wt1Y*D**r$09IF?0k;JERVIGC_QU zut3A1b+94mFcjN?kL&?>L9zpcH z(V^6H&M>xBLCvn7FhBnr?%%?tqa9D2ed!62kGz|hhWYh7c1;-#!orIP*omUw8S!1I zbglC6$QN-0OVB5v712dU+Su59p5sdos9hU%niAxc`amuO&^XFDj&%Pbqt8wy#PVZb zh*=f@940D2`fcHE3y90= zKr>0P=cN>x;RF-x!ac~m9@h#LJwHD zJ1^nngHXP(fEl#tfRHtN-Jxu**CTrz#s z{=DYPo4LJTJQ+d*MZ)PZd?E5Xq$-R2*x%)Y%7UBr`kuHYLImTIcHNZRvn_%H2%bH% z2Xgv#viI3Oc^QD`%-wAk=^Z7_d_Xf4e?v;O*CkQddT;DsvL#SAO2F+wVZM++BK#jv z4gxdZkllPp`xCgE=eD{Y*pC?Rg{sws^?26tQ$v1-1W{N5LyA{`9Z4hnA<^E7c?H`O zt_j@$23!YsjA`g~AsPU3FyH!;K@;I*;en8K2zhRnILNB6QpP!lkI(!6sse>#M8g$v~jVXA!#K69#WhAH4f*V>9jh-eqt z04oH*QnN*d$d12ONSOPw#ma-WXW?XcEZ#IL!43kDqdKHlfj%{D=4(XewB!HaP$G=u zG)Sic37mgbQ5 zYez%^sw2aZo~rv@Gr3dN<1t_pqj)!%EJL~}2V@sO-{M>2w$8Ji55Kud8A(jx`u%1q z$pX*jWZY~b9M3H;hV%iPP3!at(e=K3LD;0Cg8sQyKz1JeJFdA`$vSJ?<75jHzzWW; z_9dYD4+&#mj8(58yIHM&yQXL+JCAbxUJ52hr8^d_sTv_0i}PU9zXec(2s}K&r?Udz zRh124L<-6+S|O}|UexgUtDem;Ut?MP0VsuAOrkOE%o8R~mMuRVcE5QJ$quSUyoCca zOUldon;Xka0EZLl-EDq_W)3?TX0;lzL4ws`6EWKCv%@DhaB%w4=a=hwZ9t^V|oABYj z-L~y>-vKqOp1RvYF9uHIUqdSUL^^B)2SLOfleynD!L9}T*)^xgA~T$%3Yp-?Zxf z=^`^C9myDS&C`R=FL-}}P~*+7%HFYcVX`@$ZI0QueIho?(tHs!*Gv&8QzM$dy=)g&cgY9@~2 z@*Wfv^4RmQ4{mLcOTWBO0~(@taV>lgA(XAWCAy8LUp*HqFkcoMn$iY-;hhW7|9~Kt zalH*RuN;9EY>L1AINZm5AJ^M&CSyQ=jqmn+!z^Ef(o%VdqVkjq&@yUVzkRY;vG(vf zpJEJWB-dCEBgpE-W-|CuqFr?bqWY(!#GyKC?=J611HKhOG7c3`W=coEVoT@?L8bWU zTJG3GYfQCntoQQdxqG#3P-;OKwwblvl!gu5C3W2#(}4{Jo;DBaoE8LP!Nu@SEAz3v zg_u1Om?*NtZv~qM^(t?p;Sz*SK%WZNB=lxrE}NMoy7V^h#=M%Suw>h94X=rB!5~}$ zjt>Wh`?jcA;*ZdXbsDs1_Ms5&C@;b@@1`nwiQN(Pd1KX&E9HMP0M2c%oB4ch+`gHY2foaxQ0B*AL}81o(pN$y4G}houOd ztozLl@6%qI;Kd@eOpHvEqxE6~lpW;zQlAoj$w6)=nBT|N)Et%e3-+%G=8|K@fs!ap zHx_^ydpdJA86w8?SRz3B9@tb=H?i~I1sY+!hpnRVy}^00LG&p8dixG2C_k;dQHVa; z%EJN}P@vshhXe;Lw3y}toR8_TaU+d2I}lVV?&D`Mq5%G6G_(s;W5It0Ghi>=ZmFQq z0Cmm9ZGj)tge^q_In&gOO!ga=eTLgr6Lsr*2)-lG7LyiKh3n%30G?_x@g$2hc+|yR zn!8ufELZCf-vfc4;DnOH8<_E8-__n z*8yf%yu)1NdjpRRh29990^`{$M5sFiJum8xE|x+Elh|(N`^_>=JvV|=$+!1c16TO> z(fmlokeS5FMsAnO9s`69B|C|}AST1Hc@yhdt|!39Sa0L7-_PoZL2u&6XPVamK~=jO zqx}ywYG#4}Qaav$DKIEW>@~TjXzT>DTTot^esl2YVpA35A*Z6{XA zW%;Ha+uQj&U71aNUEBxh#>`&3b6d1XH4*G!qNrc)Xsx&zrqmdw*@#BZrf%k>~&_HwClqmuiXRe~N zWlYmrQh?6ZmGuoU96?Cb`Z!`QhQ9nxIrG<5b>OHos&&4}uP~pu>6Yy-c#ZFnsa>hP@H0b~V=)+jrKV7g$kFk$%e?DOJyRsiaL@P>_3Kk;J zneTMN-{DT_5L)3MnE_~D{c(*&{$uaTZ0rfD2k%&Po&|{%2GSXboW#C|~##sE}T_q38vx3Uh*5|DtT zm0e?q+lTdIEn{6W)2G}hi#LE8c1Et8ifzfy<9P$373@_^qA1S#wSyUyC*e!7Bn|iW5u+`;;b58|k>~7YH0(r6k*TM|_OU6M|TkomI z3U9HZA~*Q8O`LYhZSr2@1t|Bt5HYvV6WQ$0)8LbMmvo57ye7h7%@wBVaYI4GeK%RZ zl{T+ISHhby()#Ty=*}=`-E8TgW6%H~dnc^5DM~baZ@LZP*puyO#(cj6nKu}B3p@zm z%elP>sAGRnAB2)!IJ7IOzzr&uH)PybfN5aR^MgI7j|8tX?7wgPF7u@+_6psL<37%n&TR^72w0rl!F*7XRIT-RErc60e@yfZ| z{(Q(N%5?|RFdw65x)*MLo$m|ug@}D2ME`)m@{d9vsQEoG#Sn;^;LT5@rjHCvYWAqd zocTP|>3WX^BZ@X8;Xg4HGxgAJ?kDuDnE*%lY*-Qw4uc}WF2=0 zsX~bU(5j}FouBh(w=jg|=wCPIFW}!Y)v@0^z)np+_*>E!hs`6$>qwZA$P4&nV$~>q zFuTP_{sd5wA3&FdkIgN_pSWMlmZrdro=XF8GGLY4wR|(wN{@jY-dvR;f5yjM5%wni zlB3w`uyS=kIhgC}hGS%u!szR-4|j$b{$D%YPXo1K;);MPf(u*)+{>vU+W8UA>3avrF}to@~s$SK`NPML=d# z)SV1`7yy6W_D(3j>0Q5F=k>dwveQ^>GzyFW8rpg!*Cl=gn73q+I@rnbvN!dK!|7*z zt6XNh6X3`2p1lt-+_F`t7IQRSrg$fOQ1JQ5`h>k!yH+0_-4b#^nclo-p*ZjS7 zttH0&Z@q9e?~Owi|vVd7en~3?G5bdYy-_=6EcE z^Co0UJohBd2T_cT2Dj1v?d2xBJJA*x>JXn5XfG zVPUb@C?istuNc5DX@QTw1_Uo9c&M@=VDWQWe^-?fFbF5B)DQS|8AC6A_=mc1JSSh( z{u2QoWJ)@_JSz9AW;rs(W%8UvMqSW8VFJj2{N&tLBHaQLRQdaid)x0NM zA;ARNy@SXr|2}4DS;OfgN~i(5=Ja)q;A+6G)j*~OYf6zupm~4ImvDe#1+hY!RR3)| z<2EpgB^Q__m?Xi}?I$A`*l9uJKnf{iG!3{Zm`}dQUyFXi@<{~I(80`G#gfL;Yu=o_ zdiJZZDw9Whrra3X&7E^$N_LV0QwD%-I$v4yS@l&zPt&AqO8_JeR#z9@{8mFPN90mc7QEJA2=Sp`lj-yd3@luE1g;=cmh> zHJJvyy0;G>GQxK;Tr&nXOnMQe==#xW^jq@aZpBvjc4K<_a}LcTyh?42Qh@J-+)A;OODEadE_WzvK%Kj@^O3n4J0SqF5A=wfw|hfr~Q*7^0Wo z0821$_dNsWFeaf1-p@q)g@(<7mCtMSNvjq>&vqz)?bi0eYXC37uQ^bT@XfeU5_+ATp zSQPy4pnZ=g9{EE9P9+c0ynbW=blE@*sjZS_J*~$%^Mz@|?&W;ezo%qm-|ps{FP94} zdFC)IJM zYg^tT;}LeLrNISVS;gTIqhpC%6zwx4<$Ze3=au2VX+K059d(bHvLvVU4o^Sc?nQyW zWDX_s>+a`c(o~fSr+k{LpCXJ-Fo85Z!CdU(17xHC6Uoh>^E$-sfJw!%f0od*I#@cT zcks+aH(f(*!cU0^7%05dgUzJ)K{qbk6%!^_jSx9j&~36IpP_Vg3J<)FQF;fImRLTx zy4JWj+cs#P$;Qp4QijgJ zx(ByQVi&Ep{vNlz1LE8ZSUu{&LyMu_f660G%9=sifZ~7BEIz^-d#JEfTb3R66pl_j zyoa&zgP`mKSflRnn!I#;9@p`CGKUljz=+ONW3YMi@a6>^IEa8%uzPn~W3|7@mG&6( zzYrw$w7NuocXdN0BY4M$kcSUO;wESt?NOfOQt*n(uXIjkomg%FW%ucSNh}E>HNOY2*xA)={kGG5kV^!5L53;h z%ZHhtbhWxdinyN!(e|5JK|*MVkf@;@g8^bY!hmZKOfzJxu*jB=zA?QFJwi#h*!ykNjwkz=0Ea4G9SAOrDp_`cfm+-$He<4BA7 z1?#Ju@}?^d=JIinjO&%~piwC%T?E+YW2c^;eBQu30DHyQC&4SVB^NI$VN0 zjh_eMt41!5jT2bY5x@-j)bu?3w!T)Uu+TwWA5*uZcQ{<_)jMnT>11+Kf8l6=7r-%E z;UZ!jX5sm477)P!yGOyj&kW%w@SxI)pPX>d_dUtMcZjSG*9;Lc_2JdRd zD)=E_NF}m5XDFJ}WS&0Tl`_(!j40Uq*_8?>$nvIbziErWE+)AbuPZ{H<`=N$w^=Rt0woQG&Yc^LrJZ|9 z69fJbqYGkfC^s6w&Z`AKx;Yy=-9C*fdf)oy0iSCFV+7d+3gL5|=2sh$;5#z$njuuJ zzJas!d>AOuN+Vdcdvc)Z+cGnjt+bx4Vh#~>k)eYa?p@MIoTQ|FNx@+&jGcTPH2)A9 znP<(%T2M8KaxkYb7xel~pV?VB$nZGk30PKF#WdVvU|z*%VL>=u@s_a9)H}66rB6AL zi31B)Y-^45fVX0;G3vJ~JT9H0q2|xrS{S*M{p40e191|GZ9FL)N3}To0q|FWF){VA z_pMLp_+pmR3c|7cwUH5C8Ct+y2FxNCP;m`@C>8E-!i_`jy z-MS0P8#KY*o$Skh1>tBdZx@SRvwYF<$0mvsgF>2oLIfT)|1Jk~3IcQ*Dwwrhlh8$o zz?X8^opEr326%PZc^lB;Hy>wg?Um|zI~1JZ;okWxRzM2(D@bHIYZ3E+1R6FIMw&cQL%=APxy3snf+2NIib zjSx?p{U^*(ig}!^6g{Ro#a7&*{A4`8M>9fiTNY^dc-;l$!^*ph*u-c(!4uMY7IlYBy)MY_ao>NX57ik&;hiTeT>~6_hc!k&SimOyP%v;%&#C_z z<&o#i1wt@}SZg#khPG1s!8A5`6(qcOlA-_l1H--s4t!79@ceeL7(oSi^P`+Am>>gb zd%>O?6Na7K$d7YM+#<^hEK<~&!+g;6L(#VCFlkiORyTVM$43UlY7PCFgEXiOTh~(z zizmI;dew7wVW9iijAeO6Jqj z&|1hzhl>6)GpOeZoEv}GFQ^KY^hqXXE%r?a&kZWHjOgms{H`KIB*BHxyBy~>S0ZjN zwmK13+F_lrZ#a=k>b`7EoWRq{o*GblXfe)zlh3SF?hgK)>la8opnLF7=kYWf(g3Rx zHjLXsj(jvmE|^W&z6e09CguK|K}>ein-lrGmL@jXIOePFhZhgV~P0k zGrWYPd3Y5oS>@7N{l3jb_d{n67fEfZYFungkE6Y2NzP{5TROh4TC;=_OxqREPwZC} zd?;LdUr{m?zj(*nSbnqg{m(;annD(P>QLLY4i5`+UD$Dg-xqQ&P?ILl)d9l|-rys{ z>@s*6Gv---?oZIS-kuDTC`eU;+DfkNRw+CX%y2hX}~b*f6%v~twVd%{Lxo{&y_#^ASjf6D|2-)9Iutl+-5 zQ)dg4VlnavWOWpLg0^Js-sf;{-r*$H@SVM@h0S7(GJ(2`vzOM&F{{JFL@X{3u7s&& zR7m+S2fvyE=m~>s8lS6O!1{!2SO-}1BiI8;F%5%KgQ`E*ZM^w>3>Z!gmOLjqLc$-A zV&CJbWPnp069^ID8QU8_)Dw0_p)Jxm%C*RcESyPkS8eJoZ|~8nMEge-j&eoD$3cJS z(}1n<@icYN>5>PmwkhbDelB%o{;1E1WLc)(+py_=WSXFf45$R}Zck_!jKF~8pa!R* zhL7}hmDb$+8a(YsbeMZ%0Ot1uj|1yjJs0t#fN;%p`8pTf>z^j8;Je(FaCr)357zu^us+EDc4Qf0h@?)3+%ut# zCgZ9&>oyomsS|{BE+?=ibqHpwGIi<1_Y7N~8HchV1>-FKL&Gcze=@_YtSYQO!UiSV z5-4(MMDfYNZ_};e9d`GYXSiSez^T=~lpYF4QYQ%H4djnZEC%b4RwjQnQx;3D$D;R& zucfI4kB=9AgQfR9mDi6kNHPxYXx5|OXbE!CJ|x%~O!j$#xBL8o(Ga#Hn4UBx1c}h) ztUsr1r6Z85D{zN^Z3}%~9A`6yzQ#~cF1_NlwX6`ZvH#tYE9`Lb=$tyz`ZPr0eNd_I zbyv5VKC~Obe$}l)RJemlcl-Axb=$GNABBlmQXNT$$PiTAu8ZK}8#A5$J|}o*aJxTK z<;DTweIYR1t9cpL7QRRKe)Ql1xNo94EbpeV0$4J9ire}eqh9~eMB#TUCB3X2;y&O< zTAuV93j5N2Ag=-ZBB@DWKA>Qe$LEPxyBDa0-9KMN>KMOE!DQtfdED89TnnQwL6UxV z+2G}N5c$>>-kb%qfNUa%A_BbxM(KA`a?q^GF z4qPjJpXZ`1jrd&MHmKuuL#w{zpbW|zs;=q-W=gBde$>(sQ|-_-{C*P@6gF;o$oBbG zsv31p2kfe&^?1;5i}64d<`Wxz_uq&Ie=_3}d~LJbqP86xmdmHsl;hIi9D=Fk+I)mg z&tD~W*DNSAm>;5E9~XAL@p8R$;?jpa*;Mk%!8(vb1`&2hJdl_#%&K9}ZU4Hz9%ds= zHXK3D~;_|t&Z73@CT zj#{wIA%|^bnP1Up#b}Ki^Y!?e(S75FJoUriA}!3ZM)iz#u=YxiDJ-Bphs}g}?9kWb zJx)s!ciQ*Jb(+yX+!)Sue#6SK;s>T$a|wmw$zWtC4K{$US~D} z%L#z#Mbw91*tE^dDKp$5<@1>cmoUJtZvIp4ha@Cv8gb zVm^O`TGqo`P8!Dz;DnN$r~e+o@zP`-ytxzP-YZrCfsafUL5l`)LdcdtPl?a44)eFWC2n!O3L|RU3pAY1 z8^qB-@WSwGsoW4bh?FRwIAgMU<$)<|e$j(w=&2-TcLw51UwUXXP$TSX)ak5^Pi4IR zq6qv$fQt98&!pV2hyy?26Vi!1Fq%?&62%wT`)@f(J#H^h)FBOMCZ$wnLyl8y&(Yn1 z5-ptlAcjVKxMvD|^@+Q#m3rTHW3Wa1JRrv6$-L*U^MmRU^rm7J=25f>p*K3$~Kmy_R$>9qZ#7* zBM){cgV!k)b7cj1wg}ToIpo~%{K8(4@<|{pNMQr6JoQ!$u8`(D_vo1f9bG2VUx8Yjc^^#SHEp_>MK#_weBoLot+2 zXxW6kz8^E1Tv0yi?n$(IDL{}bhci$|eGjPE zLK8u#PC>BG0GUh)6N^*Nqac+Cm08G=Y=j)qgB|C)T|1wQ8Z(=wdV=wS6N2XR>LQ+F zs4wFybVFbsET#^cT)s<|3|dEhzLg@J1n2oK1Y&cx-1$7xHG$44qkHf@`!%L7U(~|1 za;+pr4HXKLsnIo_AzHcWfxh>jnenoHM81S0bf$M~8aKwb{8b)9X+Q%KGH4&cPua1% zoXKS^f8*QIf19>|Q)1pBl8-1_!d8NMFYr zxG!QuXk1yT_dnevOz3+E`;_&hxX@6DX|+N1zT?^qrmO>X*dQ`~&Q}v)6`zWT%$>xn z>0M!hc}u^4WmB(&`><`PIV6s8BD8bAd2#5fg@Ik$f_3l7|JFNi<+kSs}w#`=TV1V7@3o}u~k#+kviqx}HZsPfcK9}fQk|!Y- zg_9*`LBxdJK^mYT7bW%{6OULDmo_I|qM<3)oWtg1t-QcXKpZ6XMQ|{~1$Fg$UtqiW z?aH;wNfu&ON6&pV8y$ZK)skmN z+UK}VzP&fjm5&nnJla~v&J|E-)Q2T zv;m}r2?wg*C)%Kv8_`2Lta-!tSEB+PdVzO1$lz zZ&B_Xag$FxVH<~SMq#lFaq7OQTGGQ~gFUNyr~o@?K0w}iu*@-xz7_bS$wQm)Zhpo6 zC(5J3Gz1;Y_%f)m-NN_Sa8E^$z-3cGp31XR)7(SXR&{U-qMR_ODZrn5x4^^6vVPmY zD@jgl7S=%~8281U_06H61s&uxM{TnA`DEmyF}W!K%Oh-ifI=J~M#P!N0fUB$&Z|q4 z`#bmd@3>QRNXYjglL~f%8Q7Uq%((K}Sqd-f2`ict%UGY?8!|ZV)1_MDiwl2*%>iYRfdGh)QHxZ>YR25Ugt)&ZhA@&YT{DtmoaSY2_p<$*ZrvP%msBcP zZugWN3EP*GDIgs*OB|#&f~;>uEb^a=?b}81_>vtDFa)5H!OH zCQr)u2if$N*GYeW5BEF1f0tf=m&N^@x-W8h%w(mm5wpL^^#CHz`!&y^Uv7Qrd3WPw z@?m}zdNwQqBEBD1F3?%wCIhAX{yc&5CEBEOM zS5NgtB_TMOux=gFXJE2upAZp-3>T=9dh7n4d+|L96oJ=^)1z?Hu={@5w7H_uH#!RH z2FCf~Kb4T9Uf4Tc$oagX(NldNV(i6NA6-X=@jL(ENaewwpP9loc4T>XR3>h8NnQjN zNW&fr(D!Aq4*C6(ZdXp@{&)`>-=W8;MX$e8e2cxJIayd#EdHc6ACy7EpWGt%a&>BC z6UMG6&L7_|hS9uI>z>FBEeB8MTB+V8%G6V5>r`NIhl9U-W58>#7cwEti8j#J9bQXO zg9#rx`TO}(3AaRPIx}}Acpnz7i!=a{*MVST$ zray-%XfJzz8yI{^-pu>6R6MSk%7|RKGFs}Q_x`pv&5?ZTaXFYXi*bgSrmlASTTU$8 zmm<(FYTKDPCS8nf$Jh6k6Tb4(c@)sc`JR-M-cqszK71PWqfYTVipw)jaqFG2td{}wl>aczV*c(>IIcZZ zRQqwg?+{M53+imw?pC{*@j!zeOa*+bt2^Ca4@Dz0&qmWf#qpy*z8i<95%%`uE$d)R z=rhWEN!QNOqLRz6RX=a+Dc|yOuzTVyDKW{CpHTzP4JoMsknb;`?M9r_~a*OZgUyKD#lm zYXuV5vCmddsXn#EG(JPUqG!3VMI+^EnQz8=cZeis)>Z4YpKxhkWPRocd=Nu3csQMNR9E06^-j!Jo^i)A57GpMrNh-Xgn-SiViK4$SCaP3y~yK zz?8}#)}nM+FWr<4M?9;bxq}eS`^h?-NebmX+H?Palhbwh#XxS5+V6gQt6qp4RJmcS zo+j+X^sW>y(V>4Y(NJ6o|7>fB16*L|_>|vZ?Fj4?cj!WTXD}-aTee@3V-I$MoWw!) zYUFRHvzeK#Pf^;L;IqudD0iZ)zb@|qAjfnOW4>f4>$+AsOD>A`$`*%EqSqU;~d;wv~9=6AXE z{LFiQHYz?wD)2>GX8~P^AvMS_L$L?vzj%hWWIfe5^Aex_P!mkkAi`s~Q-uK*dP90w zTA#EEedgtSNw+_h#{Cz+J`_m@(k0}3+tuYH_Xw;T@Bd%$xPFi%FI60^KrO{pG4 z^1z%=-<_+-%XE^C$9f&oP}DZ{E1w=9SkVa8XY6{&%4T-tJGU;8yS^WlW_&D%5X1#6 za0gqo*h57R-O?R^G+(^U#{LQ;QJCcFeyeKv&325`@CIg7_Hyk)dX)9tLkT8 z5oG|2$y1Wa|Gu=OR?lA=Na$t#<(Y$1A%Dm#ZDa@n(HCT>z6y%q@?XWXyAU7qGcowc z&vvzMNGkLD0H!I&xS)We&Dr>|{Ns^!Ei9&RnNFSt_vL`K+acE#KT6r3D zZ+)S-KNQ}VdXU@Cq|YZYW`5pssRaNdEGy1Q0ORw_ehDYP!%P8b8b`**@40g1Hy@+H zdpr*NoifoeJP13*fNcjHyDr1b{%+@hSx=_gV385!lWrZ&O?8T^YI>EW;!GrsqeWf1 zyc{LuNAKOVZr+LdMNNe};_82^`fqDRe$*(ZHC6#ZCzl#5+#Q@fPi=@a)F1cp*{qQR z_)M4jb+v*d^XUy1DiNS-=BHMy{GmG~)>R!4)xjf7)!xDJquRsKRU@-bm<;SNJfD9` zBhsydxAm`cVt^q=S5q;f>)#1wEWydjziRI-0Z*fblrqFAsBR_9Cl~(6t0LF2YG~b} zRrcTVjXrRvPN;4PyE0%6FUUueop(80Oqps}^EQNe%e}<5Qi7vFy1%zenlbMs`(PcYS(3EP6F0cC|`+mX^g`OQ63Db2DcM%EInt|CDLzz zjCyP=FM;(c`-up}jkY0*3dy}l^fh?Ba`LpSnlaJC%!!h!rm4FRO{|lw8vN9f z*kKLcc+HN~iKa$ua=<@_UG4gAyE}2X`8hu0Sb>b4j-3WIFcPnxDc6o=_3SMU-^Nvf zW9(c{&)5fFYP5%oVp;~7-_B}wmD@OS%u1@%+hNWhNm8|)$}vhUAPIh5&bc)h-RqsYCHp*Ar{M@vd_ zFSLMJ+(4&G!Z?&2fa7$l68iV>E-<47YbCnJX9>N;rk}N2SLwjluQjqPt##goz;<6R zFmOH2pTqllaVs8Kp@txQEpqoJf71QcL>Y3U7?F?4G!W{iI0N=2DU&9= zmLt8te4odX^dHoEamV{1K&xlx#C~SP#kc{VDsa5Vn>^nALOZR_LBrU;elqE_ycpq1sNz$vTy^YCa`CIe@%#o>5(m(aHvM zg?vaC_kFmHO3brg;H=UAMahCha~d`GtG%X&CvHNWwccJdRh@f99QoqXU#bf?-J`s| zRkiZDL|PeJUqYvBCn@3p z%g({kDEZV6E(#@FDXMI7%xk}<$7rqFW{e{)-ljo%SVG>P`;zR1>y5_^PPo5)&7vr@pUoPltWLVjmSmEml`P@-9o=< zf{ubbe7K`tE}3%Fsks0OVO~{R{H%74*p*&p>E+BISV19Q@DqpU?`pl=TNvw3S;u&^ zEA;U&LGYyk5WQ1ag;M(~qxp)1z(MlM6BlDyrp>4u&@-4p2KC3fCEhjvp0eDbY})uq ztOgg)zP&yX9DDm61sbng$d5pKu7oS){47qj6g6=~V{c}v#J#Ioy(Rzr4Zk|9Xwgv5 zt@dHaSrGF0UQwno?%(6iP(C-OCx53ua%Z%HxVRXBM*wk%jzDyHIgS7`+WaAdo%!8U zmydivaRyHwawna^Z5xo54(O-n`I(bG%8v(!K$dQxc?~l0L9x6`YtH+vrB<-Ntca1{S&j+ULSrpyNIb*|A zFXqK1dbF!!52PP6(hVl2gGfJI&IiHHo&)j$es3k>D_l#a-T!6g^LazUQEXsLSYPzH z33;BvnI?IDlKdbcIgo5YcYnEPGUcWYkOdy2`-evV+Z$W9;*elAq&Wv+hE-w2m9ybnk!M#EekeION!R^;SYN2}Ug?qQ_ zfttLDp4xKl*`ZNpbP8#gow>gq@O*f1xMRL>NlmbdSC^RtC?KhYUCW^z#pybb;)mZZ zGC=)(TdA|}f4A>UYUgj+Dnflre~dHdLqaqC`*g!)@)UvKTM&mGGJgCI#nVsv*azp+ z9`25_7-$hRD2;%58-DMqCb?| z7MN)py6@Y)yWZg5$Wesd`;U7tb8f9Ds&_wyq!CJ!FC&z!4hpTjY$oo<=yZDo->ccW zR~KD+*H~!!?}SlaoHHpHhuFXK?WrQd_DMRtDQBtiM0#D!orBFOk{(@N&_E zzH0{?AKQU{R|i|3`#GVJ1GpXw@jRM-F`fnDj-Ztff-y0C06t&q6|jv+@@1SLlieXW z11$w^g6*qVfTMbOV)yzS!EGT92JuqepmF6Tz7PsVRNmW#(^A8V)C_cuvLkRHS6lf;VHy!hjVR#DRVep-D6 zbnEkoUVEda4zT+HmQ|U>{vj+xKug;azANLA?k4bnb~~}zUH^bU1NX;GO7}-1OC|6( zn_)9rsX+<}#m?v8wh`lIC9h?hS z{dR9Mnqf5Ot*4C_-OK`g)6?!|@A!N51i$EyHQ_9`Csz?Zyj2G`J`?MSK6g^WGH!?e zEx|J0=XruV_UUd+jeRC0BS7hTn{S}0wxG+#MW61Dw+Fv#6wX!y^}_Lh)EevFzv`A; zfXN0P*zgI-7uVx*PqsL!Bef)kMW8M9g9#wB1ItQyu*}V^yJcV0wdG?k@%&>t58L5G zjr5CRkZeJ4mf!oXm?xp^Z_y14SG@-u@yMI@mYKwyt`~UFfEvN>z~;bVTuSMtO53P~ zYq9xNeT(yFf36g_te^4$@59dW3!)0t2gDXlZ+%dM*xfPSnb8uIFZ@omtRGlj;kHOs zAqQb5)pZ$rS-X0!?95;^l6MW})=LjmFMfI$a?cPT@xx$Pbph^M#ifJkqsSr>krbGS zO2_L($tlLFm^w*)!`pE0T>S+WDf(%E`%kVLD!1!eUM5#nj|+O)_JuX6~`qg^y+LHfTw{d)<-BW-7COe!sLES7BjyYs?8?NRqf!;V0f=3jCI( z5I7#@sXH$82fuyvxI|xmdsHAl5c*))6x%tdBnij?W{|gl`oF+-$I=#CKH_#Jw3cFY zM0^N%xg z=GDg+v;bg7p8VZ(LkF16f!}8kevXzd-N9~hT9LRZ)I4Swa#gB0#a&oC@ADBUPW!$0 zyf!SrNW|xVEBtnH{_=J(hOSCtOQ{9GU#?LvWW&T=%&R#6uQm|PPL}+6lkjJ1MCK(; zsMu$27=L)jleMxgtigTm?bG{$fxo8Bgb<)rlfiya@4gVY0e-=6${<7e95QWuE9mUvb5EUJF9`TCRWNp)9&F#K zg?K2k0&c{oO}9xAT899Oo9OY($$l)rx>g#}?xORAGM{N#+otOgfu)h96KAPcQ0bS| zz`bnh(FyNuVLw)9G#=;&SJJ!p-d$AF)}~vp=)0Vnk@t!ddoPna3d34S+^x@J-vS8h zjpt@M7x&wIE_s5(!yZ6_^uyl8;QXG8HV9~j@~j;eYTMOX3wxhn@0*%GV=em&naY{e1SLsS~V9Qe9fxBfU$Kn*>+D;lD}7F|N46Ko_d zo#BWQ(I)!*x0=y-Lx=3o@nQJ}t8ruokneYDdG~Q?qxq^tA_vw+x!5s|bor4S*278PDyfo-nez@A1!&{$;7hc!CWLd) z{%(0Y;UD`L{#0$vUeiMu&SNJx(xiRL+vXQrm;Rw8~fX-C(^+D?@5b?9A7PVV%iI#KG$rATSYx2n1nvpiAnt20GS* zIt8pST*%~hCo2je8V5hV>~!*%lh4o|HPbt_o6#g_4mU>z#opvBHb;*>^O(D*Ap=H% zEIEkMsrfU;HAG!!^?9@gPz=DeUT>XM{_#>#7qvt+^HHT%rAdAE*&bQF2~<~{2Lvoz zQLCwY){0R8g8QffW$c&UpYib%wcx7<7u&P%kG2M*j*Pq|vfO>!aPl(;Udoql55!-_ zx^f@R{rW=Z?a$xAkHMuNcYC;D`*0&X7J+SEzFtSuZF^+VUj+|jsQmq%k;{2T%gINB z*um4`_~-KhRQkhUk7(dwPSCL}bWv6ale-qC2DNrH8PpM0xBP&*;sgD+ z#05e8-F~?Khmg8%_TKMafYh}cJJfy|U}DV&74Ahg<-Pvkp9cbve$!B1mkaK|okcIp z`%)~Qi$m|KV?27hs7sN9$_Qng_kUy`Uf}s%;=Z?zV|d2Wd&LCwc7py*2D8-@K-iKD zPXL}$mG`dILV=`s$f_3z__dzR@ir~|bDSRnt{fvnOV596GQnag6|ZG<^jqRpMO9ydmw3O7Pttvr z!->4V+~#Ryk=I!@m3+EoIv#EKhQNaFU?e(MRM$8UjH`3QPTY-$Il@=sMwi?`D{(Rf z(#YG%c1u5NFr_^fysc(~eCW1bj4ckn_n;ucg+?Y@*IFltLXVzdU{g~t>fJXYhCpp_ z>iSeKug)*%zJSi?gX3y;e}2^ws#t2qQmp>V9W?Z0{dEVu3$pejmhBA-y-Cs{A5*J4 zRq>CQfj1rC$KwOP4jsTNdtI{QTm1?*tpaY@6(5M(d7#nw{f1i>RbL;K3GZr+a?In0 zaxy)gU$S<<)$E6$Xtk#gM@96dQ zuS)jmxXXL;4_AUa>U;JRm~-%FuY_SWGp~0=Xvt<)Ni04bnR`yZ9qCiJ7PZ6gtRL%V z783@OeV?Cm>nh&XIlhsgY6h5=52$)xGkaPisrxWk88s{QgK!B7&BFfn^b(^!1kAa9 zrJ8kE^vMGNgIAPyQRsP!7mh||EYFB7xyw7p5tCy*xz`Lmb=?6d>A15NqfICTd35dA z13##3E`AyUUY}QJyq$-`SM88qN-wi`P9wRTK!MbVv1!3|t#3~uhCEzAUa81&`%egz z^2@4Qz}Gnad&zj$Qn(`oV-4^jOz_2OCVmDzM8C3bTQzo6x_@-*2}y6b#p(>7IO42% zE8?4Hocq7t;-0rvnj1l;!4-&nZu()i@g1foyL@)1ebUr@2R@1!@5xMczbT<40B%mu!kk&9AHj|PyflkkEHRs?zJi;yt`lrx}L~L zYw)Dn*HSiD{s`=XYEQj@nF5WKr}4O4aCoA_SoGqCiuAqgh|T=5HPPii0OmU%EX=;) z>4O&(Fmj(i10;Zh)jcx1-6Z+|Ok6+D*0t&r_M8X@uqB{?A|H13dVOieT`BSrijNN{ za~a$C*wZ%nIHjQ47T7_}R0QD0yPO;cpU(NrarAj?#xjpH9b z`UFT#-xkjObl~S=;(sG?JC-mvQEgS^xA?EuCqi}60c?AA$mcIu@CQfqPojPO2Z_pI zaSB6?e;^Xv#yCW6=H(7l?6%mO9>DWGQS7^SQIK@fVo!I9d>>l(#%+hF&0aJvezzNR z3?DmMQH}wd=Y1+YdXED1SLH0Hu}C2Phh6rh5>?Z;2yM|@PO27$CB|`3tE{zf6diSi z#d-IIo9uvTa7m-wakp&}Glav;6`hK=S$KE-H*z*Hop0B%Cg48^TPeBSu097i)q^g+ zgxJX(y5%=o#?f*2v!>0z6~Fr<`}0B3>_L6k_32LT!zX&#B0Q9ebnSt{9}U0}ZH8vO z{IQD@)jbfq$6n%3(NEQJajBu_xk6W3v#m)Wnx8H(OLWTc1s)()W%KkA8UxVg7W<~z z*0syZIGAR><`>B^1xpD&WrmVP}lZ}r6Ohtzk%T3oSL@`4x&My zM5)+Zbe9`fpBvLcE#uFJqiJ7ed7x*@5^A4=(}9GWuynLD>fDSTNVt5yf~~t(GH%m~ zy#NiDnLw8<5i+b8COzcYB#sK%lI}u)<2y~e-(f)z9qX%+Ex2a`M0r8l>oygLo$g^N zaP9%~mwhjN_1bIlNH&SZ4+Vp&Wc4|L9idp&{eGg5t+{@Q_Q}M86U{FxFuf8@`@f4u*h2?97PrboDu<> z^|Jm1uK|=fwU^`UJo#8nP4`k&Rrjj&0?J~r2D))j2JRhoSa$*UdN>Y`;mk-~D*<~a zfILY{`?T1kw;|3$XT3DeK!74M4XO0j@P@T?w6#?J<1l@AtRsz3cHL4ym-i z#L{E=_MRusq0M|iH4BSJj;*`G1}5HcoA2)NK(BZ4UqM&?rl6GAbe5|6tp1T}U~tM)C*ZF0ld+O8raXDZ z==Yq#OCC6#JbqwHu`dk~w8yy#f+g+0%5JU`*11FmLLt8)eRC)Q;M|HPQW{tuV)5#8 zB!Dz0s0pu=Avay5Do;?ZyuR|(lYmejDrG=Q((;NJXmPwn2JgVK(tez`su@^^kvV9Ym73CLf=%sV%8-cpTC*ZtDz! z)fCvfTK7cC-=(2E=?mz+LV7;(=?mlqvS)BUR|Xnf_!@m-qu-8FcV~CRvQTjsJzlvC zs0!H4KIln2bn%L@XQDT`5X}31zwM9EAmNP&V=^X(okCyU0w|j7XddCJzeZw=Lod$j zbNl(RnJk`9x<1%8@|+Cn9lIyjoOZS&q-AGfH0)tC;*8a)t3K1#(ojQx(YaCev2hyK z{ryPi*&NG;&5U8(WpKBPUh8!q!5A{=BYglOM)`%xW708ANcT0SZYmVtz~P_gdu5yx znLpnt)QCU}ZhmiLX*IHVhFaD>Eo1_ogc`qzL%2pPHQzakN%TwS-2s@~KcQ+^>X$R% zqo4vvK|e0?g+93h;hZFyg(fe53SE2dF6?DUaJ_MIa^sbxK~s8vl;Y|5-3H9WpY{Wa zjqAj2y-#~pOM59>cG@cwT5l}tfE{#lxL?E9%ZTBSW~T5I2TG>K4%RR&K1*<`B0l_d zmd2PWo*kdVpK~H$e$VO5qFjeliCiIFwBe!@?3u@G{IPZ-^C#=^KDZwv!n+@^jYUF1 z4F7yGcYr9@XV#D|&bq|aZ{U{njpcg16i|p)CIh4qp7D&fEI^?K;1HYs-M;4b2D7m?LP|AP z@>gHu;nG}1E*GkJIhpR4G<1=$2KK{Z-V`zE&u|td=x*(0P8*=>ahwcNGJHCSCT0lj9^f2Zk*XF+fp z_N?%6f9)}uPEmLu(amW&FcA#(K-xbE&uZ~}UiUFVnm3ag4$8jK#+{h>incYXD~Z6ueF=Ynvb9M)L+{jT`3?!hA>g z@ua8h?YspWQ9aRFbTjWUg%(7ukBL^A;MOKv9|k6 z7mLu`u_eOU=Rc|-NphC;QK$vkRx))3D}Q}LaC&-uM3xmT6f+vPh1tR~7UcJ_u8_@B z`MY%;^g4W0D@JS8=gIoP<5%*@C2!6xgAwQ=bjCpIaQ(h;p!=IC_F!rh}m z)w_(wV&3DSCV(--^Up`zb*vmkvy?TQ=>eJZ=kOtJ%>ZuI@X5jQjjWR5CIjeJe8d%W zD>`%#5;RCDlTkXkE&(RRJ_opZbiSp?Dl)S0!cn6_t|G-PGE`o<3dxp(S#?*OALooN z6qPueYS_<%n50Q76PC^0-Pu>Q0@wGC<-z{tj=pwdMv*w2=fFYFtx_l92RKjH<9GfTAc<{W?K$CZ2j{6iLpUqQ-hEGe%G z*fje&9<8r?YWcuSo=okuy*==~_S3Qd`Bg@K^Aj~6YH%|XmkMSwJu6Edq$YydA^3N_(U(|@DDS~Q{Vf$ zfj_?m8`{L+$g+|Yi&eL`tzU2+KRRr_^K-cymyV}p?y&u7z(%+IGHHzAz4V6XFXe+h zue}S)CnP>K-+B2ICpO`8+CX2qa*UDk`B>m646;v|6P~?uw7$oi4dr=Pi~Sq97o*By zexHn#I2*>D+}QOqKi_3~+H8DKc#KV^bW&e-C7;rDwtiIjHl|pAt5R@Ay}6pa9^HDl zQuxPegp9H(4N*0XHks{fCh6EZooHW)q%YTwD<0ulae#6CUJ8Ap|M-t197cwO$mBZl zci$ljbLdb>`?(c)<|6+4us#fJQ4`X8zx}j7eww$Y1O#0-CtBC{hWDN1h5Mva|74JA zN2X!FSmI*1QpYP@0{-587xmG2T(4TA}q zpB``>9=QzWx0vMsXQ*4@$N2`O0gQir0jVvIre`!*18mOLfP6)LxZ>kbNsT~}Y_N}) zj1xz#R&-!EuLCDH!kG@SEZSEXp|<(idl41NTypH3$oQe{a+EybfvxXIF&6nsu+49K z49>G-bBAfN-sC#eAJru0_OQ=Aiv;(W)~U0jtbv6bk5wr-N^+++4|PO z%_JFY=?V`pHFXTUia+;59rDz4KQYtAd-C}wO@DXL_E34aOu~=abX2u%PTUXph3zYJ zPkLG2YVh>m<>91cK!(colsslds!PY0dFtr&7w{myQI!zkE+kUeI^Gq`4MPPd))n4p{;UBGhdZ06aV8mp@gQCWy8Q7xpX||DK3=%Tt$q)` z5CZRnys9^8O~JHC*t@hHD1y~FLhze|x?QkMw+kVMq5Wb$pGS4~bMR(x0>$PnFykT5 zV2esz;M^VgMUE7HZ4r zmGaJyUU#1gG{Hn2D{4?8U++R&JPYseLnYk5id&`N{l!y-`8bBm{bANf7SBjlB45_(RO`EUGr7_348JPTFrY`#uYtT0MBXK+3cw#0Ne7H2u0w}~NC~`WB|oe78M3$E zI(%*(y8x^F-Vc`@sN1Y|7w)g>Fn^i`87A(;*lct0*k(s<<`BJ6qI~24SMBWvpLefK zVf8$f*VC2f^7JCUvKr|uhs(7b5{59TwM@*|K=IF#f^?>zeHhb^CoVb1! zQ)1P_9WrZTe2C-fp8wudPZ13;LwwxZln|ot?&{jcuC>Qbp+#$f?UO(Z}uq=LIY!1$}rq6r8f)PTUOB~_yUVXUQqQOg99UA{bT0kX{5hi zPW$8MUBc!eV*V=YeAmM9>j~lEgu3Aid8gk7znkUlQRL1Q92;@pd(MCa;H-JdF5ycn zQYH!Uu~){y*L$6FXNb`68eY+ERv zSokAuCFxOKEaQHKkRq7*t+8z+eVFaza5_fA#zC5cJ?Ubc;W{`cIMC+Ms$YOR^tkrEsHsgCLx?^5}?9EV(fk5|TEQrT&lj|=rQ2qghGabg(|%+Ae1 zd9#8iY2r@tZJ^o%ZXWz~rA$uAI{mP12fb15z6)TEm(Sh82mVqvA{A>h#-=II9f9~0 zl*iO7WhFifKFmfNQM>D5^yY^%l(jeq+Esh?9jic!-O2l zcUO(MeP9RhH@`vrdFJ!Aq6X>51NBHwLjg7D>opCeJ0A|iPBV>_I^~9-;E6hZK3i4H zSnmSK+hr>!dmjVc?zI>m#)ZI&?Ld5p?&SI^5U|?3r z1m8P@gO`gZcedPiUeDw}O|_?h#Pthc&RyDbH+tQ{2-5RwlWox#9%l_U$@>6pxOpSb zKjJnv;;ecGdAULX%)S~$4Whu0lymuKS;;zt>9S*F; z#JLXKFBklq!@#CBKjnO;dDS}cLx9FZCO#f@f8UlzVq2mvALIcX8w_LD8fpHckZZ{Jny^GzYd@2#A4FV z-;4Nhk6r*|3#7USNJsh_$-X#(kPKrNdA%&xlZ-UpWv1HI4BqWpbe|E%zu(Qbom5Is z`i+;-iP)ZJtjvRp%CL;a)Zh5we0Cj%Z=VxS1_?y!FRNQvJ37tV_0vRHWo(u(){2a+IWC!BdmHU$ukxh}s3{ zvt8uX`Bd;q`T#Ta!F9(_Ck8tmL<@lT8bz$FYzA1E9eCUfXm~~qPpSw(yRNT&zW}cF z9LP!DuwVJ}S*ILCM?%0eWO!@n#M8f@JgW0QJDKL8zk*&bH$O!D9+@?-Bw%kJg`hBR zh5{@H^R0EAooVa{bl;D~U|w?y%8r!MTC;WB2Fd2M{;dKO{-z(I7n*XeW~GH z06T9}{P}kgZrk*D@khnuHuhGpNT^s2c1oWktpMoA@^{cgp2Cx!!mE&%oAHgEwVjMe zEY*xVpLcwvTPCnr(m~xfTX5|9ZG32K(e9GKlM06DC-?=2Bdyl1&?R+8ems3K^QlED z0`1)1CJuzRu;JUWKnnAKcwbD1s$Dv(si}=xxhwt5;^R;0r=N-EXz+~-=r!d1t+Y#@JN%Y7{yruXbKIfd z%AKtK`~O{&QpIZdX-*&Y4yzrCiyCxZScF#llsBZmZqHpeF@z*N-Xyv2p`opoIi!9f zd9g|!+v0=)QnP#GX(}Jt7Y)Vc-Nvb)`L#a%!0<-cKMt=o$Hh@)x*b~P!tZJT*`^K2 zk>5ZNGGE68lpAbIEjMu>_~1U{;hK?dZ+9gvG>Czp1NSv-&t zh7;oz-6MlPv7I12z3%kb(khUWh#xDQ7f(!1_(GZGA@(h2n)$@I*|!F$gs5m=A~Te^ z!V63aUMZc|gWKf?8u8Br!!k4$kf3{r{lxoK)sAdvmjdFM(|wx-dWbIsUo{(RcBP7u*#*Q@?hcKY!r~Hv64A020LYFi|i4G}8d!lPCWG zU-+tApNR%b%~rNhq=fA)B88rNU-grEH9@&!o>vHHyb23?^ETeEixZw&6C#$Nded@C zfL;3NH^`_&=c7K`fuhuf8_}A8_vjaSN5ZB*BUTFNGe4y7b_Gwrj%z?gzzoA1EFRDc z1xWuLUN5}tD=Z-Yv0SXHD;e3O-%?atj~KV4(Fb|CLtB)bj)FeT5uSQPBI%{WT(7bw z^9!I6s}2fCZ{N_lf2es_vNCE0+t7{#<{fQj&A+$Vmg1idyx#wzuS#U;YI%Cpfi)gx z?^$GeAKDV26zDJAp zm@Xv8AB?#4IQw|7*JBb0jkE(fD?AN9vV1JgW9*#XTdSg%F;ki z=oItj`A3oAOi7O-xUEI`*8#*c>w-+?!PpRC zLFGAnqPwDBL6#3c7!&*Z-Gsw66FM`JxBYTq=Q~KUh^%tl&cpo&axg?7#G}?FJ23=@ z>CGJ}b$R?(YSRLFc3D|`bGyE7nz9XfOLr3@m2X2t1kKFa^ zD~*p&6U3xriA{!dZqM>^za`>kdgY#e<3H*Y-Q>-F)PE2PAp>41k|eJ)9-VuG`SHy; z8E|p-S{v;M2T*$7*}8c-+-J?Wq#EH3!}xn1bj?ho_7YGmO~Y+}{N_7*zn-}J?fd>w zM!dg}lrI=>p1F7_f1_t`xB1UAb$I!OTQsk5;vtn^P<>vl+g)&tk8D9hbREqv3=WlPbqOc^ zP#r&^zkFEUDN6~4@+b}?kvbpZuWXd5cFj4)gYXq%_Vw)CAfu~5#`Orfp_p=A+XD85 zU~2l>p?~7wsiBL}?>T@58ACY_hakY}#UTZ|#&Q)EbfMKi59_X9M{u%UfkMSSGH+Lf z=E>CGm_5Hwzdu*0>IgH6VxIOh`F@q;izkj9r+PRlbl>(nT|Z}$X+E0-cCQ6}9}#}8 z>{D8s{pX``ht_)@Q9i8NO3FnmR0B(Co3c0|g?Re?PAdRk_2gsmqjFj|aLQWHzvFMv z4@Yi(+rRzwU_H<;+NNiH>97bM)Lc1EK6gw9dk_5=?*IEeK3A+fY4l>h^rirVL;fk` zh8-BQWR-k}c;2$^$jTVTwTtn9%*%w6#hs0@I)jc+E-`QU?rBfuV=71v0ih8NH?4l% z4+CZ(U|5pxat;YUmWULL{SjtGZjI3qkT5el%|wQV1s6n>@Jzs4bs#!H8>Gi5HOB&D{z zjTrI~ef%}{3&nhk6Zjy2l1Dc^APCm@JVu|KI(~Ft-_?h~%s8O46}-Lhka_3V_eYyO zMMAXoNCS2IN>&_+XwY&Cp|Q=Gk=nQK}oYqaSnL;#M|srd0AnAbI3l}@BQFticO2VwRPbLRQ`{H;0T zedYGY^oaua$GbibP>Q>@h^d{V!H$%?rY+_@_(s5C_1Osf!jz9-*s>dH`##Ipj+>u% z(0D9s$xg>h?j7&QYf7peRJo-5Zf(U>4gL+cMEckgUEUUoX2!D$k4?VxVsg9k*7Lya zY{Wg#$GX4MjEMjPzK2T%1r-H@UC7^+a3foq;J@Q7w~!mLzHMaDoteBh0jJ+qnkbf$ z{)YGchd^I59(?7Z!SA8rs{$z4!dvay2c2*8yKy>;K70NA$I^LhD~g3t_<w7}KG55mq$6jItPxa$yN3)cABJ+-Pc-G z=I;`xpUi*Qn8aG7D>7{AF-OB>kq3F5+McMc(K`Fb+rpxuO*Cpg=D~>|04>Q)ropzF z{XK(_FAzI%K`cG@CFMl3cSK~=W%FitR`M#Nn!uLCdQ5o2xa?%@c*K4=Ke7bwSjIAL zR*+y&uk)&WkFUcuCjA*~&wYuk-~MhOof2kfJ+ZEi(&QF7?7pY73CYBH37Umoxj)z6 z7cqf57Fm=?@(l|qM3k}37M0UrQ(l$llk`1E>j7s_Q@)547#D-H&+q6f#@P+TBLriV zfj;i3ZTLM^lJyTmKCXNH7Gm1@pz46Gp4U=rea$7TgQ4V} zCqMkF?xVs)V=vFpth6ypjx}?Ae|n9Z(d=|rquQy@;n*Cvu+_yd`<(K{+E^?=E8^0; z0Iq>B?^crIH6g0<8RyXU?i!@s8lhNxw^hfcaF5L#s6EyWo$LQS;@@lPqtOxHoxIPnlWA9H{@x^z zSPGEF{MGc1_Vw@7Jj0YF92w-{IPgLic(9T6{yb-`(0J>O6E<~=HRP>(AK~gZx%n8_ zeS&{xHP{{J3nvdFW`1g{`wcb|byZ&y}ev=CJ7PkRR+%re#JazRWH;W-?Od$XNl z08pQMvaL_MZA%Fr_n)+W&R6o=b;knepqV~{rI8C0F?o(rPf|yQFrqJt{9#G27x)CP zKs@c*S|HAEMU8cEEO|!I1a#H!Z&EGu#cGLl^y_-v) zkiMXN!#JLlGvB3`19KlSt#Z9LwNm<$;hB;@l!yf3AM<(gU{LcLvAFyxP2dZ;Y>3HF z=8^fA8IAeL(=Bh|-~-Sfi?+mmzRcPT@agtHHI7xCn=u>)dH5>^mj?4w_W&{53~H-8 zo2j}dcB#}iiI36oI%%_J+-NDmMGaoBuxT z1o+eTgt`+*fpg^mHf!meIW=I4Y)4nqp`P)nMz_HEDt>K ze=O+qyUrH^NKEbZiF09fFV}pZN%!nFi*i%DDEcyfXn@2i3_x{{C)qkkQ5_m zSIiEDBOGh)**6PJU=R>?hZrqigo8dlNu>Y<*z z&D#@etR-*L39?J396V;tL0-6h)hE!5Sm_8nSxWrheV23LPKPAbpD9Ru3vXX7>XizS zfbsI%YL2%gp@G}XZM@EX$tEPIr*Z8u7dTh|3KVZ*Um_*@Rs{8>FGjTTVF{j9n0pT8 zFtt1NWZICZk*MD=(!_BqO*u)vU&vWJuaCcsY6$V|S}8Gd#6MJiSYEcy)#LMi?Yieg z?#F04l+3LU4Psfy%bk_Na=5o75+~1)B+W?C?68j)gV)*$7(=w7cDX6NcI$4xwa>|z z_Qz&u!zW-+hrsk(b#0AX$dgO1eICJ=LQWgdIiC(!ga)$LD{|IJiP*VindeuE8(%mB zKpn`t=k2qE>kVJJ8D01LE!PN^{$4S6O70v`ffa#7;j6sC*!0xXS-u={%IfL*YDGSGqE0J)lM$e*n_{(1R&KWfH@2cHrtcH~rFFQzU z&2N`h{P6YV+wh^7goC2p5TeHbFJdb+k714t!wq7hZUoxUuRFc|d;>%+pC}@URQi#f zgW{lFm{>OiPI?U$R_v^Jl$exDtl z?e3G=S)~z(&l#~c1rZFD;c)4+S;$vGH47SNycVs8SP7SCm4afnniubTIl*_2H2jm= z+HHr0p?hBpgQe){PT(gsUCTC?F3a(%xCCYKP98GP1#H;$-p>2e>+jnHIw!2L&){vT zTB@i5WbFwesqAmdT$}h#SeKb>S$*rinLm(6F2B?C*bxi){rO$h2W3K18(?rU&|t9D z!Cvjg#@9o}{96zFeM!0dVvy95?BWb4uH=Xyi>?+#(obFf0Y)E4N*5=W;$*_lOX zm_u{d(K5QrPNujF_VE0SinT;%>4bUw>E{n(FT@ACi%=y?YY-EATJ`{bHO_Cu{nbE` zl=r|@(`?K^McB!`251Q-3zhdc9=vSbKQM)il6?;z%62KK{^F?2`;GM0)H~Sr{Q0g3 z-uZcUOp=!qMw4g4EKBaHVr+4Hy}yiCHqc6e?Y@43r;*(6%<)@0ZIkj{3y97MIx$tC zNDl5qHH<5-fGZvyLhw$B7hCcmJ4oRn+#>31v|%yHqAFW^{cB>-qZVyJ_^-W9u5paL zH}fl^Fvhe|gFkLIzm8(Jm*8v^&zuDj_e=#>7->G-aD7_N61Sx^L-3)^#qlDEhA z5p>VZf@U}F1^0P$rSz2`#~G-$eETKz!9qzRC3(zLMLVgKdZMGL22xhaOB;ckyd zC|@s3j(E22%&+SM^pGtp(w+XfR%fv#^m$g28~5;Ew^QDAT=;s~gQui?7O;Hd9pCsg zT_J!XEDp}RTJ@JSw69Gft3TFLb_g!N^S_0xr<~C7*xWJtr)%N+t}hvE0Y4HvR#uF6 z18VZ&vOK&vYJoy3pZjo*utB^`)A?funLPKKNADY@NAb4n zw^JLmkE}JRu_Df{rKnCTow~A;g1D6t8Q<=u?hgGxzUN)%%+!0x;qJjmKj)fB-l*tW zVLHeLQVWh&Wh5MPFF@{h*J!bzKE7F`m@Jn4DMZy>xRMqNo3-bicEc?vzpN63t@%)K z+(|cDBWv|T+Arq*d&ZLTF8&maw|B=?wUwI#{50MQLwF?$L^wOalxR4)Qb(Kytl)XY z_AK+pvu3^=mQn%UkLN(o2^)-1}hbo6%O)nBF*_*yVuqBKO+9DFv@$mW4mD)WG z0!(>j7E_Xez6xO=3s(4_qDi6^LriNEz-0a0R+_BI)Tc1?L3t#?#LoviOFaVDHwFefuRgj z|1#13C3W1YSG(`EFA}5Qv!}i~dre-m@!j)OnUR_6zsKf~FijAc(Rez?^JQFKi7WWuztNj{NeMqIl7f2d zzT;=tVHSqmw=f2jB~v*iZIwgdjb3G@ApTvREO;h)#_j-3>F)1=el~3kY(iO{Ke$xI z{Qcrw(LC&JhrBF`74V7x)79z9fyUi#_b!o< zYewn9;nxJ;!D}C~!r4kRu`yG*b(R7!E3?H6lKxcT#Zxbnu=x$L# zAb!ZZbX2wNJpDGcUEr4s06#(SJNDYA^YR#>CHioc34{N%r=fr(|$BD>}xKunwDFF zbKB@vGpHWehz@(i3>?658fK{*z}pr}r(lqe#Iruk3-d8%gFA1WoeNmLdbHmGCi?|! zpf%HO{klmb-X%$nnT9_eUg8%TqvM_QhWzd1G7iGWmrfv5RLti9AFL#+eF|t*?A-Ay zs1U!kbBlMAxtaUX7n%7?Ema^Zu&A|HGOzG!#i49jf{b0~a@tg!ltuhh7^rFrCfh|cl$U!Znl zg#cV-_pFr9eYjFhhEN+gpZCKxD=6_EhijTwA^F=F#DlM;NJP;-zhuYYQ9GkrJl3Q8 zSLBK$lE|hxT(R?jOMKvaySScrI@ZX*AWO{c2qfR3lzxO`G;Ngn11rC{Z1k-dacb5t zE&K0l!!**{<8pX==UcNF65)H``A~4EF0A~axg=~aT@x^5RFHXly61b7z7h!5x)kQk zRl7m&+deZhc7AWSSaz4k?c?NT$7ZLekcxz_|IwP1)~1IGqJ1y}qLrj_Pq~n`M`zvc zEI~iYsV8(!_I1R{?8NF@Riy=Ha=IvhMg9hU|80n>IFB&){8S6XYU}!b6fgCOAiUGF zsEXl1gS-TeHC+w6og*#}He7d+yvsRByq>iCp)Sw+U#l$THnb;DK;xZ{bVA*HuV2o$ zI`GUy3yf+)mfOT(SrIsx9b|^60Api3Kc}dVFAXvXKK>Ik9(f-)@iKjs3vO*^K!VoH z9S7V8l5`Kf901_lEWY+X>GT%Q!v`En=mglOTNMxhKdW#mPoElS5hI>IH<7D3Fs4Z8(Qfgavde{F zACmDTn(pcM=T8!SHX8qR;yuZ6$vBJHqNpg8D4o14n$l?C&ZzQp|O96qU zk4UXL!_qQj$M5Q2j#XVSoFO$Sb}KpUl~@M3rVOj2W0dkt&O<%RH22fb6B`b_X32~X z1f!mTfBJV0+`H?&B*8m-w>O?SK{;cy(nOID0nBsJUzfU1b$dc4Bn)`^z_ArDR~3*1 zZ*>-z;m4m54XP!O=#nbU6K+wS-`_}%FR@MOo3A9O0v$2J1QhCCsbd`UJ zXdi~_-`$m>5(TfF^AW`yydX_t%p?Cixfx7W$V7-LC*nO|73@f}?WwqFHol)$wMK zu~xrXCMTM5Rx&Td8_KNpV}4*ZUR;E&xpyLG_K$+ZH&ia!@MOIl3GNoe(adm zRL5-hFwuNK;gdW0M7?kGC0z_IX+VOrPCF~QN*MS5l7oh&Wt<%MFLmae#erlnKc0BH zq?Mi}A=ggMFBm36fja0+)7bXbU)U@@oaVT{V8prKf3OjN&qziN{mFc`i+O)X5&ZK} z3|l6UXIDme;eY2l7TIF2W(yDT2oT8;F!>9AtPYRL)$m!qr@x*66rFMRv`)QKOM}au zl;aNVytvdw($W|(ej{ba>}+5qu0sMLXEoa$?I4Gwd-LR7!&Gf|=Q*gfr7A!I(%jvS z+=a@RW88F+3>)jP2lDZOrVII0;?+%m`IX&WI9=K#L(AwLG3}%;aZjE`quo<*e=P;f z*hyX^n`2`d3e@evQ2XAY=*_nfQTmV*d=lVzf(#OHY zARC^UgHA@!kaO=@jgEVtkW;g#XCzNoVHi z5@@$vTY#3|@cz3~yDirn@af+nRf`h1Hex-?x%L8;y7kkx0$|OX?|pRAKdMe*GKVwE z*18weVUNpW<*aD=RB(Z5&?7ABRG&j9HQ8aZ?+rLZcdB{w`)TI~%Fh6U46Yg?%f};U z3mpFqFdnfE-tJj2Tlmc(A3n^2Cq1eB5>`*~KxAnekQ5%22?`YF)c>UEr*KaChUWcs zuDK0fawePrOtBsb_|h-j6+(V(A5UbTiQQ2gz2q&`Ya_q=b=fo9+}=&$HnQJG|B_8; z{=l{)F3$5%C(4VtXc92Mr00RaMPwIVpnAp*XaURw8ioiTB98-sy-#ueelS_Uk1CRJ zy~Ke5H=gL`6MaPgQ_4?$Cdf%B&BUMHIkFt2PXK!D&sjl{Sf21%JatfAu_kUA;j1B& zu9|l@i>v=?@;wM9V9sYFdj8|Afu|T4D!WM>2Lp;rsvJT)E;u+$o%5%mJ3&NVDpt%H zC`pblq*uS)73Z!}?I{fQ)IhynTl-GGfAo_IKZ)ET4>%$IF5#HpqX>@*5e!!(*GLYE za&C2MeZWryjz-icO^Xr8*|^%L&o4U*@4|<-?yn}^oBINOw{gY#8elg45mwy2{P~~H z$#6wG{vE*<3s&sf%<~+^>-8Av$!}Leu5=!#H@f1EqUJ|~>`)5|jpYEOEY4q$rJAvA z#j`*18AS)U9yjukleas0$p~lgXg5C+2olY6=*Vc;a~kpAOm(Z?5KICg?+?}uf{$Fh zU@V7XwGZHSZ`&v*i<2}77F&Jyn;bTNAquSZ0J98n=O0O?jEGGT?w}#v&7tdaazdZz zx`xO=M!1;(0N4!AY|;Gz%g=oWWeT2g$Oa+6)qk16N2H?um>(xZ1Q3KB;F~|j`JOCDm+Af&Y|ZWd^)MY70fn7ti8|Ievh^Eyc5(yFN$m^}tRgh~ zR>J4X?A2X-u(?-51jqeOo${I8KgIE^HCzxQ94Tf%!6m|ApS&6!Da=7?BR zE2>l-T86_x-rGh>fyTCK>5-~|7~a*mrBK^AJ!!kpSATOb{=ny*lCtYpWcvA%J=Pt> z;kQS;zH*(!Gk+DKsYB53x!yJ0cv8qIlA{ZMUj0NNd^TBi1{w`%n%=LCYtmT|Hu-JR zGjI%c^md`tqU*)~ji#~XW>G8ikq?A>7LsG5o2ZE6}Y~z9dEpO zr2P$jE|p!d#lGZAvt*#+i~4Iz!W~R8P=KjJda}sxnI?_>x#;Za?i@e~@b?OTulG-e zTNhiMcjs9UaYGyg3xs#b&iK=CsA$*Fsepth zLUyTku}mOuT+M%TTClP!`9i=!Y(QLMR1v@M$6Oj9_^zI8{MS3YRZlyG@KI^uO3@{v6rgrJ82qKFwR9E7lgc864tM0;`*!P`BzpDbwGK4Q=C3{h zjp;hpgh5X`#))?i1~5AAhfVJkQBqe4TdpH}cAws-ys)0!QX=J1|9wIAdlu8Qdxxt9 z`mclh>z*yYGCp7V?Xm)|ea^R+FV;MsG{!dL@AY`irOjNYX)K#y5YOUQ&^OBeBX_ zXe`FzzIb-j`fBY}Ya{n&xq#iEQzhqL&P;g?pr;_c6GpDttVPKX{T%6w?=5GZCGwb&uP?WC-sj<`ix(uQjAx|! zc@1*8e#lNbML#nE253FI$)$L!%TS^>Stf|w(!))Ed2G_1`{;t)xzne_RGOx2iiiiZ zr^PFzfM!921%yu@IS#Z)o+7{vu2w-*L>{!lwppp<2e-)iv_jIq_4Rom)_Lr77o?X_ z{gRM9U0Hc#y?AHE>i*yWPxVT!Xb5fx=mv&S&B@1Cv|pOU3s^&MVORp_`sVMZCd!Yn z-<43p2zJd;IJ2?nkLyR=&Fh{+m|Lt59XX%NK0hSQofZ{Llyk)_@3&^!lM5X=?*~sF zte*rqcC!fVy7c!S_CX>;%=D9Z#LtZ29@f1d*ISub(a15vpvPg8+im-8v-h?ZYU1U4 z8#*xmovMf}%oZ$NC@(&?+1Bhw#c`STZto;A;H7K;0otR+NYPmzCyh#O`(wwv=g6s@e zX!~zvRcrJF zFgBonQSa*gus!?!(-bmw?K8}n?nVO$g5gRL4S^tcw8rAtzy@cyFC|L=1U}O4r0k>5 z+0cK7r{|(4pA+Z%MVbA(imgF9bABhS6MbL+RPf#GH9MeEk{e0LBF^UU+LsS>>o?Ks z0vbz;vw$qY9?5Z7zWo{{>`+ltZ`e-!ruYG{mc3D4PMmA$ZkZ1XESB( z9g^HufFZ0DABgy+pwBk&ds+(s5VxN3cxbOd)R^FGOKfW<<%2&YFObxmle&>0EW{Y# z3#~i80bIK;pYUt2xz=0n)Lyg*={J~U?9R~Vid?0X5#E8z2;7|s<>3LNr=CL8^F@w= zHT0F4IB3Ik+4VKvu+lm(C8W)QSn>S@kKXP18Q2euFp@m4JhB`lx%iD$&^^kvZ?NTW z54|PDCeXkx;chfpTGsli6)knKRrUdB-b*{E;)7n>FtqxfoKG1&{T;CFl`f>L^B#9v zXq}!7>j`cfj2oi2AQA()@g4HqFucnH_Xuv1mFfUUvm3q#%~VKr_byYNiYXzIUw^gS z@|uxlBl1Y&_AeCfYiaC0M7ZzNSS}0$TNF9dVHuZ@I0YAyRIHV~)7p)nH>AhX473ds}q`uCP!DJ%%tY?gL8 zU+rFGfJOIEcvap-0tT$Md~GBK!?2VajrdrbcWT}q!x97xQI9JGj-x-RMl{qIGX`Rd zC?(O&9;bzs{+4LtZkZt8qoYfgC=5z*7(Pb2pb6-*tM`>jkrK1Z=WW@Q%&$Czm!rm8 ze*@4;y~M~Xw_{|35qBBDIYR9rI5hSfx`QozNp&-5e(El_-wn#t=pGN4J3sr7B2F(H zP;^DL+W8~ZC&dBJA#4JOAEs5@K4C|Q3>SVg$G~c$6geRTG;F;_r2g6!NLYo2AH@~m zIyIbZCgsBLBPHIFI5^e6QtH9U92TWlJQRxX(}#nJiC*%th7Ym?EuIczX{`4zGu6 zL_{4_{wr3uL#UiAM%c&8+kAwbNueG*Vd}sfKpchs96u(^IDs0A>TE|1#bNc@t7Bu8 zmH*~u%bN>!&M2n-mTaqv5e?XC&&jSYSN#b$%-$rFT_&>WrKG)l9rvmeJpqzhE3&1H z*OA?oZVk#UPrhc; zn|%n~)DU^k9u!7;(a58PPWZ}dblc{WhkZsluK=gK(mx5wOLZ2YhAxA|ssW-8j`opL z6bG*A*8n~Ioc-;5KC6r8VE<+`O2IXH@9d}es=v86U+syKnDmWMzm->F4F3ntRQG>+ zgRm1dh!eg=5!GXL(OFl^;W^1X0ou(?@4t}HJCB-D-(#5Qu50o9{ue(E)GH{ZineOd zG2z5fbS%537m>+3{s4iE2f$BCzCY)~(Kc^bCZTKQp*Wm_j`6~narJ9vjLNNS+~TS> zIr3Z;>l@~z%N8?IUo(8W(7cJ)!-IcPsH3r4Cy zf9MTEQxI#Cl@hqf1uO-Il1@J0f7$i2vwFHom46J~>0rNd;zthyDcSUcXT=k0S}b=Y zB4DLpAje7L_z;n9G)p50^C1aG>A8vlOqs+c6?mX~IJjP3w``RM_( z&&sIH?U!4ks4guU3@&%369H&nm|X8XWr`H)A$hLh~5|HiMb`&qY|? z4N4pBp~Lu^-wqhmj#PSM!UKsQ3vISM+W;QqQ~;y)GNRE47)6*UCMpm}O0vyE;+glh z;OyWC2|rp0TS{wW%LZ%#T?Pl;K%`}Rk)dCiQ9?u!x~ko`Hcr)zF>qFjteIV15!Rwm zB@Q3;cRNPS+4L(U{D!C4njjL8?!fL|`EX{!7s@+!l9q059Y1cAv zAS%voIlR*$CpEkM5uIHSm-UV>(7JnroA9iQIbWlhFmEM2<*UmSV&+EQl6gZ8~awe z<%IKC4<9==erQ$0Y);Eg$SpE71_{=eo9E_Ue;V9)ZA^KwhUxs)u(+rKI6e(|Y9^zu zkMp!r75l7CpL^&yor(cZU$SyBaIIWi4boxuf^ z$zL~f?zU|@RgcDZ_?*nww!-lH&5!4!0zKJ>Zu+R)jk}r`oe=8I7tIetZPEf z4uYTJr_+UV><_7UTJ^h!AoP-iWrKK&M9J7hgCM!*odBy_f9GH+YqTVMM=KE`kT%rYw4lWeNSCEJO3@ZVnnrx!DC*c6x;K%+DOFY6S3 ztNa1z`7ND^^DaNF2es3iYCLZ#32S@fr$UsUO$ql zWsWRj>kp)^v!bW>)FC&GtOqN>n3dz}ym9Gm=X zszGd#`@7JKP05yJBF zI-96lFxf-)5cM>E`CzI%0871cU0&Keb&_j5EIY}T=0x8(wlim~_b4B%|Elp0tt`sPk8~ek=E`$138;qd-9E($UDDeKdtd__~L^l$AcsIoEF>M?)jGmd#J0c-a;9YR|_U#*^#H{jw7YY z*pkBE)DRe7%oPN?OrGq+=AR^Qolm{(<1}ySI_(k5hxeSYPhF2v1>8FgY|f|K37dxg z?xMXX@p4AS-c*wNLh6T{*jRGCkzZCRg^RNzVWD)R)q}VUz-ZyMu;8seoFnLqa5|br zy?#Q*h>pmzp1wDAa0t`_FQhB;(3#FafmBf@mdSw;iFX!E_d4QKSv>3@%&X=HqV9d! zZGz)VI?0X;{oBS95_XxV>vM%~1l|3$9+J+=Q~P@@D=kAbFkhmu#xd%U)ukWrz7J3c&-J!(dDraTELb=I ziyv+HKm1gdv2ui7B7_+rY4e8Z$feR|`j7`mrzWLqvYJ2a*%^)ei{&iJ6AaVf>LnMQU0q6lyN>Gm^$Eb$y);pxxb9K0rk^E_BufKB+ zb?~2_R=}NKjCK(roqfc873p57279_kUGn>@ZJJ=a?H_{!G6%#wPf25ZF4oaigZVbv zZhb%^0hunWBmM1#4j=626K3bw%8+oUD-@Ua177!11w1x{Z2F7OcQ0CqszDt0@suhX zJRR(}_d=8KYwF!!zCxpu!eiW>#T|KG*H*&VczF!rP0cZV9J-zrKyJ zBzc|=S5-~^0Sn$KuzYF;Oo#~I~>AlCp4$iQ)6Vzo{uhqL+!Fjzc zzV>X&Skvxk=QXz2+g6HR(oy-{+MJ|y6ImdL~uGK;!g&@yQ!@6?1l{EnI~#; z|Fwg$y8hAc@d7oh{n2vi)9`m+!eGYfz?=6u%?#13x(viXnq$P1eycm{o+i!RA4)5RL;vT$v;(lM!5Y{B4el?|f ze3TvX$(^j)OMTH0_F@L&G$Dy}%%3)|IZpS(L;IZ| zN+}G*o0QW#1!GD@1BNP`UTX5Ye~!>{y9kz$r{rOQJ|a;Knj23YY4;%IV|Q!n0~5Qt zFZGc~USCb`!hL}(j49kTYBAmUWHk2X6RFxCK7XQbNAkR}rvq1h>0XOn`_PMkg7N$x z#{qS$tl+FK4Cj~uVaD44n%(*I0SK(MAS^U^Q|=$cXEWu#pp~wam@nnZDWU9(juTqP zctrhtgik%ls1?EBIvQK)MQTS4uj>1BKYX>eqM|pmjb=XSzF^+ZgQ}rP{rkNO7aHRO z&zO?v_w3#&edbnBnYF}NsGWX^r%lNU&vHn%uE|Hlf-gNC=f_nZxigbBVri0uehiJ3 z@gE^DXS*gVP#Rp^Qz!y|)uKjGg0w)y8)ATvm}E}POLA1nGrK*L`Wu|u;uD^r>mIrD zKW9phGcpOmp6f=0U+v)Gk&a4IHYN2yDqB(flFcxYEPa)>$~un zk*Iw!#bd{3!+RbHr;~>{9iHxs6`3NgKiNZ;tg}-yE3tp$F>yGxVBGgb&tOJmlJHkn zCrmtiZM@H~?vB8hsAy*USG;Qt&ajAAW=H?De|0*3FuxlcdpxKStrPrMG)UPxNaX$L(IAI=Tk>jM^#vEXGt#?4b?Wu$hqIa+f54sa$+ zSrPXsO6C6eJ_Mog)YnI}{pk}_77}6bvcR4^i{w3diRVt*+Rl-=CnF^((=Oz@tjQ|2!z4ac|a!=VVf!1reNS)T<|>;{d4p= zW$gEGIyOqXsF1)bk+A=nIkF!Kf(72ZxO@LJYS5`oCznbAktBexxP24}Yz5eA)CYN%aG!ed6oO)@z3hkdH149}9ri#na=H0zXi; z-q=GbMW1BB&MO#dzD|Mn5TJg&sjs3Xsq*T46fxAT<}AK~OrNZ6%**i!Q5g73W(bA9 zkK#{CvGWW$URXnND<=XWRhm~EPusCS-bX}?zJnV~h}(6}ZF0_YO1!go^_9sX-vKPc>rXa^qbDzSG{i_p( z>M>G(6055%pcfCD4^o3412rSaVtk36<>4{KM1IP@kd2<}9|dg4-DdfzWc(HJ8)5K) z-l4teFv-HGprsvP)O82U|M4RGAI^Ap77@gDCHM_ujc<^cz{4nTac!ncHwDG<6{Or| zyfYI5j+f;Rr?6g5HXW}y+Y4{YnS$y`8Uuj@e+QP9P=luxaX9iP8x{ zS={?)sYeN1_HA_yP(um$WOmcdFuV2U5$+=-+*oUnJz=!b@AFOhEB&Is?N5>)slYKL zxKznGVuE}hj@N*5hk^Rzc zHCy2@T3BEEsmBhkG6(nb8`;^Ro#rl~y>RW+)y|^Zv^iB-w6nn=pL|C^PZD`T#- zZ~dMwg@S1|`#WVfhs92$R)Tx7SB?IQzm1ox%U6|6Su$sUnUU-GcXlV}Ejm z;b5EzIn~_Um)ko!O5yVgIH5$2NnxJ$8MTxQG3CP#xs?#+e>=4~ecp5uMg7b4GX2zk zNO0GuiW2_V0`i2LPZC;&zqxtxg}#kJ^tt6_@_J}m@u8h}5fnpH35k3lJh6G0moIby zyY96FS+q+Z@WmC^qKmv<$>6iNc}2+|;8kjdErj?=e^T`d9UN3Qm`R{M;FjMzy=@QP zMc-{2*@HKr?eL#kR#URG-Zivn-T5M0A#~$e_NTLp4x3Kv1kEV0JEI*0jDQm&1OcuY zXZu@NJiHFpXUiGndV&9q$>Uz`S18tWz*tRi(c_bAM8{2dF}W^VR@^vUvq7my~YHJ|U> z4XH8;V4?wg{*lN)Tt}6bNNxHGA<&QpQ!YU*)DOt?A|7h26KAa+=cezEXip-4Pe|i$ z9xd+J8cbQ7Hc0ciT27nqtgFaYjJK*(=Is@47(?HD zz03spY7-z}XwMFTWJ(AMV+lDR6=nGl|DD^e@%ML2kKs1SJ!`Rf@5-Q#o5p58qk*S& z%u?{N@Amj4usQvy(14MdPA$g--fV6fmZ!VJDD;$EKgdYYj|M-J<=zQ|`O?zeZy!1$>{7nOGH%u z-hgS3@;BiWq_;!*%QT&9hy96eIR8(7pB|$>Ic3t(f=Y^g_(koM9-e;wyZ{SSUf!yL!ez>k2#qi~3&ml5osl|GKnDNu`POM-@W%mrE>-1e z#JD5g#4Yw9qYj?z>3Uxnx%weOZDxI`{9$ka8|K(w_zdQ_< zqrV^aqvDh{twsgO>UR0jD>XJO_xozn9L9z;IcYmHT&i@$R>e=L6gv zS41NDgCUA9L?!uwxrhLauNjirL6A9))ZzKY(~q%noxEAIJD+yR`>X8_gMKj&>&4y! z?L^TOG#`=PHr{)m$<`6xol2j(S~%JvfHUmxiBI^>aFv$^gH<#fmUTxs%9simR~fH2F(RYk8hT-9$l^(D zOjtmZ>Lj)Mge5gZ&YUNLgX#epP$86UiX?jE@69AuPe8r#QXnGKsb_zkK#VKn+xqURAMgbRaQgGZjQzC&z- ziCX^cb5qkgfD8Vkh%M3A^lhH^M>FeLS7Hf7(?3BTBQJ-`RoS!V?j+N|kDHx-lMCgl z0fmL@bD6-L)KU|6W;<^0R@&agoq3crUueH?Y^^V{k{nwiLYkbP-P<6UC^0>~(A6I7 z>H`f$d?IQ7Pjeqq%EzC_oFW#Xfxq~Z4rh_#FP&tEt>8odp&=eZeLwX5xZOAv9J;L7 zPG?d&YtZBSa7P*G&+t#u3X3deF`(i5SB=tyfj&XSsbgG%Jyqt0)!=-85)>l~U3ftc zgOq^TKZK-ytgLZ;A?d+wYYbS&axYn*n+HtV?e9Y ziK2ahtwtP9f4@|MB|LprNc3|JKy3Vr`GI=#svalvjG!+V>H<+f)*?Kv^ovKP41s}cIzufIS{5Pv4~MVy6{J){)=#pGf2#o<-T&ND|pO^ za~Vor^||-=_3du@x}!g?W8-5=;3EElOEmx&ge4z;z#2t{Cv78ZL_kGWfQr|MafDDz z1}DJHnenRdPB5jr_eI)|%e(<4# zAouOozw&4Gy?ZkZXj5wChF5j`0{yMoq5*4aMz1O1c zT6s&`T`}gavuP_MDMq*#c&HvzSzId6#SofzH<;WykraP zfo-tk8|j_q!81*eM~iF3e6dJ2jOs06-ei(rG`WFmuMOa`Hd@cCXlPBkQeSt4R?aUN zDz-C&HA0um>MbgyR1eit_0ms90$9~p|Lr_38pWniU1Z-YA#In03~B!FJAPn(06TL( zN+6UpB8**ZqMp~$7P5YNqwv6;sVQEq&q2%NFM z{%X3(ILe+gh>OdM?ybXxc5i!YIL41Ws%Z*(IimVZvEr~W4~SZQ>?`? zmKyGf_{7cyo9gc-r{R_S0Ybg|YX-;`Wse{2hIqRdZRDuQse3bv;uBK|JVF4S;!0ly6B%Hi;SQJVt*&v3v1E z|EfzIq4IvhQ4^$tSU&&Vg?9wApfc(^3{2HeXyJjGIF7V;wCf$T5JZ3xq?5?l&IN|A zh<9n%Nr$*b@7A56T73XGbob#TEg}?{BDn*>2zHJp12C^xZwTgYe%G3 zY-dKZGr#a`O74{yh-13%D?+wEQ3dsv{swO$4*QbB8E4qkPs@S z&CcTQnAY=yg!<<4*A>OZ>JZo^w`MWA3!o4sz#_eDH4!zMpv z5Qpsb#hIbdu$#`%YW7spc`d}azxC%Hcl-0@0O`fBUW@ma5QP>EQ1ra~hkm&L{|L4W z)aa?aB+P_kYBEp}EL@fcwfJvCQKM1P!w+kDiF#c>^yN~gQ=}x%7_F3_U@BPDJJD@` zry`9P=(07mr<{s5i>f!gsE{`>Q;^{kSYAtf*q(51yaSlO+h5H7$ ze=bEcZnZtKWA4xwY+wD7&kLmM;US75jbcN)HM;iMqFZ(0{X3qKpZhKlg2S$s7=Nzg zCN{|w6#+m@&;Hbgw-#y?^fsO(PQr&NW699@x+iZ~8L-|kV`7M8r+KCEl@mQE7z}X* z)2-rXw1+$4e7@~Hq4eUsGLPp34RaAaP>dGdw=DDACBm!>*|+f5#fwc6V@d2n;)_Bm zf3a=u2~f}Ei|Bo6_;W^Q174XKRRVxUuX|uNw%2m6lR892QM#?Pq#xfW;p!m1mnM9> zAo$YmBmY{KOLGU&h7Ef#4pEPpZr#f!6C;}yv%Da7pkF=_(mQKF8Y(O6g?BuYX}2G1 zxasvsP1sDQy4%C`iXtXQQI_t5fCU65kvXY-l@VN zkQIG)%5JAcFF?g*WpFWpY3f`SKO4iU_U%8<&{oLCwtRhmNO+xd_Oirwif6{Yht>#9 zCR`l!%SLej@)|)>2`R7w=Bk3S7QZx1bsL@qNfDGSq&t$Pj;!8u?C?2ivo+ zo3KF-;=GjsS4H-xzCbzW^R@p>-ZJPc_1|~-YoUNrWVr2NdGCIL#ZOZ2Q-w!ILThNK zp(gRPln+3sSOIuBv>=LsJv4a3bE(YT&mPN1PYGztCQU`%ta^|9ilh99*ROg_%bXPt zVLyra9@h+=M^OLO5ZBq)(RLoFXOe_C@%}oBL=R#QBrCF+RM%6?!$V9Qo*iOJ z^yu|%H=prrNhWMIt(;`9Z>AY+k-H0R>xmyg@ZR)SErPI_srfX&jPE#D`- zurG+kR4&dSac68eY@@%yW9{NXpGI5|WFOB}hBIZ{FpRq>!BtYMIa}YG(gpjl zP_6LItNCGF1P;Jed^1g5wR0f)FYJS zgROrbJ^E4-!t{CV`(>mDmjr{a{_%sl{`E&Md-D75do4F#)}6p~BMck6ep!ci{k)aLwuSV?3zvZoJo^!9O!8wZ<;D<3-Qp zHGQrLL0IdTAoq_6Eamj}lLShmj`#tH6vB8ueh+CfJAbo*;BW4vOYfe3KVD%Eh~X|4 zlw>~Vpus1P*jQ8#`IilyV6-J`swZYRZj7YKSz^B_?I_jbE6jpj@$z2~CWl9PSp?fp~<<-KFif3BdqXB~xI z!2En6taZd?&h2d(0;mt{XT?SNrkj^dJr{EA%a2d%2(aNBzM z&3Kh&=VB-zoOts*!jAjY^*Q~`_vs7LGlQR5dxu=lvElV(IbY7moKYZ{cXYd9@~> z@b$>c199B#`j=Ruo8N1(s>6PLw~~Z=>SyzaO=et{mrG|O?;O(g^HWDo+l^pfDLB_1 z*c}n}4J3Dka@Evk#AV|(lm`qiS;-@40O`e7L9zwO{fNMtaOA09$HU(LB=d!(19w@k z!QYzs`;p!GlK=IBArYl(CY=|fQCC2_E(`QYWG&VjtQq`(#ec$-nluc{d(dW?A+Ee1nzl1 zBiD3kc=_LR`z#Psw>AxREIjI0VNeXhdFAbaJlNmQ!;$@7;a=K(9|~Z!QZDZX*dG#9 z5D`NpQk$7#oBE-a5r3aw!V&gA_{P9y8q6%{RaG^xaB>&+@9UBX&k8SwIzLb=>3=Tg zu|TjllC6Wu>HhQ82iNG#D4lL@%ZLak*5XN?OP)^Wf<)Fz=l)=Vae_QyC3MDs7J zR=Fe&GuYxzV0q3DJbWS>y;$1A86`M9NmAcQ`uM#f`7gw&E+CZ*I~;o)PY>S#1))}) zJS;Ac-Z(ZczicYXR~w$sj_3uyrHbnJU$*j&Gf^ge{#J-M(<4gyMD8tI&d=SkW;&yL z%YY^Nh<_+D+aWq5l*ts6ovN#m@{00K2%wMU98>YF=Q-=iir_Q*XN)UI0uVjJ%+MFY zW2H+|=6OU}dtux^ekQ{WCVeWO&fo6=Or4oDv4@jm7gyg;4#vL6;3j%*G0yWG@Mt@s z8e6X4k%x%mW0>w&)@1~Y>X!Ic>ei3>;~b$cyuT>S54Bf|h1h*4yfF4b7igF z3hYz0^tInOFTfGI?I0rei2SUazaKN{==G^wz=mj^sUdJXBJmEf^^ta0XUBj>rXxnV zeoREFZuLrE2`f15o?0_yR!7(+s3YYy{|a}dWOdIi3K*0|v0uA@1lr*Owj)^=K8M%P zk+~+o*qh#PfGS3~NY^p3#hsg5GJg19^fb`?ND=KFC2crJ@9ZB7ac-FLC#SpMP6sC) z45az1#H!1z&O;oC4*_2MUuCApIrqhu7eZpyhe29{hU|ex%82mc{Qp>)V!d0vF1Rh8mC)J4m^UJ(D4 zYHIgK0EiNQ@RlFXk>ISN56#ZRPCCH|=gCbCj6UO{)W#mVZcjKhx@w=tHAkrOV*V5y zDz%vf9b<3L*>m~G9<%80q}nDQ>DH$SXweIH7^CWsv{jb(OW7H&nlS@7O~W~}rEw=X zm^FY3_X%!TW_P9?&e%ck74O+&T<}qeMrb*G%U4m__rz#$RbpJkz#uMhltljvx@phTA0_j69S7lBai2RCXXK0u2jEygGFVM%iLqmEVOHUFjrcImsOnbr5nq*d#^8^` zz`CNPwLfMQB4s5t^xs;a-MUeiI2%j8hA#x2ZzJ0)(K8-)zXx)VpKO$tui318q^E4w zuF2G<&p5tE9y+-O_qJXc@2Beb`+ZsX-`E}wSQPC@D$&6bxvu)ONd^DFBCI3p<&|YR z9B>#wgFi_m8J7X*JAWsj2g}=9T&^31sQ(dM_1AH>bxTsJEVr{)fuE>ZUj5rj(1N*z zPvpQD2qg+4sebmhoCm>ZNKjjsx?wdiD-1f){Nc zo!!4}9$3~uTm|48#Nqt8gT#CGmGker{np#&VDxKUdqy({<|x8-pg&wpIE(9pK7wsL zupfSMzmJ&zo9`K^tv{%+-dEVg*iOHPWM%)U5`N@5&@Ir`SF*p%!}(zc?*_sSqJ`xY z;+9`;puETK`3!@dx~I-3=aStz#qdk7(>x^YAL49#CV1Ykk66$qtM>~MgQBJ!KLWHe zm`f^bpC1_K`lH#Bo?tM~_4K4gzZ2;K1n=YQIbIQ^M%w(aVtFOg0ZYZ_FJm94<%PKgBIJj1y?^!y*SYjHd4H_&TP5HQB z?qj0`28lhOj!|tRI?=2S=s!vueNu6Yz$kA4q84bhyh-@dG#1T8`}{mu^CngrNkE@o zeh_pzo=c1=5A_fj8G4C7TezXDI9?xVk`vZ-I&dRYQ47i&fajtsL55#;PaHtS^Fi!N zExoQ6oJ7>|ubWriD2N_dojFjQt7D!H$kS8@A0FvYfq)+q?%tIbePViCb$b*_HDTOj z9AgiE)ChLO>#jAWDxO#GyT#ET>*=xE&k?xn`GUXKi8}^*J!&*XPK^z^#irG|`it>G zb7Z(j(qbv^yEN^WJ+1sUdx3lYu(OjsF&aE>m_Dej$)0c3&-IPA*+&mz#Y~G_-DG#! z_tY(zz|h1H^7cL%gKN##qcPNCAO^|d5g>o$FiUu9?y>m_iW5AbpYewE3O*Wiy?TR2 zhXni*=#=)ART8J^*L{0=6NhS7PU?S{!s(1NwOlry{rf$@w-n41(5%@GK{Rfae&58c z_Z}0u5Arqc-KZ`-t90{<80A5+MT_3kSYci2%7RLc~5}u@9eCVnSBU zL7ESlpM8<<$G?K_cR6B6jd$~n5oDd=Q8YC1N>Kmuj^K@hn3wm~XtnqB`K8XFN37dn z=JLzez+QXH_4AzHmf19&{xL;`;=+hq`@@fKF^%TnY>I%y(R%nBiOU7HDG#g9ok7n0myY#q@{aye)i$w<*4^GO;#6Sq#Rg>Px)JYhtoM5&%&D@ zHwW6Dg|^}9|41O(>R!qtO0SzyHMlf-yP2jtYv4;>a#kw zZEOB&{9ft+!vx>3j=o~WGL$p-`6(&TUE@dKm~qKHi*vP&Jc4?tI)FClk~iqi~gk@hsjPi>-9`b?K0)#ZUdIzi z()~yqQeW@CKW3Gw$HDk9!eYnMN!pAXdG1{)EBAGl&QuFj@G2JU8?Vg4>6yyHw)gbs z&j9LN=+$HjjgMR(qZ}~!&b9D%zLVbclHBr{k@?~gWo<2*EyQ>B$(aZ5@-+KXdBps; z8iR^WJ2p8#{RzGOnI5W*WWzmkCh4?WD767W%{O@Jj>OZFqsRG{j;UlE-EV*Dg~YT} zYy67}>=}B{kLrt6!`F0B#jk!_J`3Vf-Hv4Z=kcPxPIxYT!#_vww?5hV3U&-$-PkYT zXbQIVD~j!tbZ6?B@V+4SLM~87K@YrsgQ!C>66_Id_`T!?_KREIOb)W78NQ8r-cKG1 zj&^D%+qEX}qf_9AB5uS^2fA5eE2?A89tjzd_}#nBP?Wi{^j1G4}GKx5+1KUmwB3u45}J< zN!K*d0+R@3Qf0chc77Zcv8pZXnnzBnPCxk381!;X+oroK)<(r?p7rM)W*Koz{WV^A zgl5d0Vw5M+z??ze-~H<*z@eUgYQA#yEm_l6vPDjArf+m@C&0Ci_#OQMOP8Q>pqk6` zK7X!X2>?&zyN&oQ<-%)gn5Jk=vRj4nX>7ZvPF(rGA7)zrO@LV%wo;_WEp8azyBa%| z63A99%d@!jyKu!5&Hgf+RVfIlVj-yr8qd5Ws3^JD2cKW0PkW|Arua_%NH{CDC!u_0KKl6s;K ziGfR*|R9X(A#9Tj@LxTMq{=)R6W{Uhb1@KeRkZdu=OJh82Zh|%({{SIg2Ux;V6 z@%zOGP$hKX>6Z9c$i?Wuc=BAK3b*-ov;SURaPurahQWGA~ z7{PtE?N(FuNsmjcu7C+A!}>SUPIA2V;psPS+1NdW63+E^z@NIN}= zZ+3o1(WRQum6y~g19hn+dOp{Ow!zGUIW{mK_nMzM?mfEg>}tnSBo~r?}xFX z)Qh#4|AG;;4kY`f!i?R*`1LL-U3S3J?PTEC--r$~uWEM)WX|^&1WT=>-2G%H)<}pK z*bS{HVbL&J%&>E50s$*~3gYeR^!9qv^wtc|!?t%k^dXd*Pg3sj;3xrTp$wYc@69;E z{qx9Bbt8j7KjSU^gNB1zIwm;3cz9cI62bclAMqdiCUu>U-(leFXZzcCyT_gNe6$4I z6vn~a;DyP`z}JvJ71@+#;CrAIbGO$V_ecQ(^*JPHUv4PH)BECT?(H zJRstFyD9}90DbJe?}KH@MyB9Q;GXQr)-OZ zl54xo+KOou56YqCTk8lb-CMTtgVYbMcP;oUPfxW-eNpgAnFH|y{JKpuHuHWTDpnnK zCj_Qd8vi^rkv5V3io>S)GW!L%_hH#c%)Y%mlgL|szxFD1+_|OXcYP2pbkaQOV}K%+ zc1~V!MfaYMdn9&CoK5X^2w#u=63Z{EL&~p&*NHJmb5lO|KW86j7{@uK{|;WMV^%ce z1y+LxJjpp-v`e|*6`pFD5SjZM43CF4A!ijm*!;vX^AR~Fk3nkde!G&TkApLLuQW6Equzb^vnW}K5b`@gvyrDI6rj#?!J(j{J; z`(Au*9mXl5GO;EafVd4;&FHG8Qzb|>4vnYW{IztOLl|_&8TO|M-Sl5dq3MjuL|!Pj zn4W+*h^rU?%0m3n;(ZVMA56`u>{VklET5w@8PBSupq(}i;-}1m-`rlW<8N1MKEg&l zwwgS$lb{n?yFIqTQ|sz6U8N@|cSRQ5FGycMT!CC)Wt`ikD7vVC0e zi;yupx+J;lQi6h2SuRz0pZM&B)7xjb1KWKiva$N4{n?CX@9r{xtQq#Yt)~{Eo$qD4G5X#HMlp%_ za-nV44bl(#-7aBc^vYdshsUSj!N`s+5a@90r!f@Q+Yjr&YiaIp=Kl4|Zfgvui#F@b zBA5t(S{8zZ(;qLQhXYV&Nf++30*=(0vl zRq#8%c`G+=E^HI@KCxN}K>ZLz08{vq5pDYMZDWw{A`OPlC`*Vk==Ij(d;2vF6C$ZA zjNQjS4nc6)u7-V#h&aL6k|*_~-2V(AF$zwry^aEDsY2#MMYu*|f)Xxc@uiF4$wUkN zn`uYeo~ZsAvQh2$@I0AVXY_R&t??d>N8}H&qEsRxm3BYODqfWp{bi_sD4kd4>&mmD zAIZB$1(b${SCe@pn7z}^0}mv3;angsd{7?2>QB^V@@XnyQUh1Lh0-jR)JvMQl=0g)^)b1B zt5#wk?r3_Inj{$M+V8QRBM9{nlf<X|yX+g~?VdoQ$lWS>7CykhszesbDW+=Ke(9~-SDb6ZY5$J3F=$p;q!h3I0son!o3d)vBk)Q{Cs>C864!ceY8qs zId#;;Fm`d}@^054*&$;Yy*?XO_WJzDGo+_jn3y-i&24pj)klnN57>gmYg#betg&(@ zUP%L0ax;{tnF>9iV#i-emJkhLE1`CKJ9Jgz&xc*{{6c6#cs&|xC&DOB1OK-bZW6a zuZC)Kg!>RV`r{xKXnolg0ISv(d{nZ0?l%JV3FA552O!PSw8`tE4W{2K;P-v-Xr}dY z(uJKWDx_Qljgp%$RT&o_T(id`9v^oku-UJ8-kf|IDy#-K=j)Xv@O74sdB!Y8$H^6? z@KwbjShGj!J$$FL`Q8jSuaexnrZxwv+^F>SJjKMc^4|9Dxk?hp>Jiw3(qS(kyu!sj zMHJ%PoNec|)V^M?@SDB(=UK2L@5fR+e^J@bU+`&x2K%Y%jprYf3ID%i-3Xv6oLS_A z&zJkHA}_zKH91fJAi!#VL)=^QdpDMFa14X|9y-%8$iTsSe#VUapUdk*8=aH3F9t9` znL+I98@KH4n5HvB?7`^Bi1KHj44^6h-iDB&0S& zy8TD|HmJp!rr-7DiW7h70p-ERK%ldzyze`2 zqi{T7j^7vlp3@b>VQk^HAv{x82h|F!3iFULcnGIi&IO1dN|hg}(gVm2 z!6GnM&5_63FI`^IXkqX`Ve3WTypp*}G4c=K;-BAa{WhOTuF%7~^(1q0!{l`MoHL=6 zdaFpLghopq`a%bBYvH|7B0~C;jHhYx9Wqrth@{IGB-H2PR~WZVAU>Y@1cc_5E3KBc z4bEPayPR#=5X@vYehMjU9IGMgVhUkzE!Dcy&C{A%nAY%IlXhWcHhpwqhVB?SBrf7 z2_sj0uk7=c6U}^j&-$5UXSv707g;phu+~ zmeFtrauP3?_|Jb=>kSX~cz7tcKc@X_!LQK+zmqetk(#inb}zs(T)e|G`vWR_r}sDk z5A{Q2%>5%gF=zXQ7uRWzYjub4E(I4Odt{pr+Uj@*EO2sse+x*z|K}`bv$yA1QAdA} zq<)0Dp?!8;h95f!>Kc`JISGV&K}8lkWfa13rvi__{l+{V--g40$z@{{nBZo9<6bO? z0IvLeMo2u+(w;+wI*fS$8E?`}V|@1XX6J9RFS^iIp9YBs_QRJt-7qWaIAKXRYUQ~x zAU-=<3sr!KW`}R64#20nNL`n^5s?Gxg!~#DFW?T9 zO&+}P2PKFv7~`D6Dy`S!_NK%!zZlj_nHdehP4Dln<-R7QcNh>tVW&xOxD2%V^}65C zvjQhq2#E9i@e-xE-1i|+k9VCs3VJbS+GRaL;*p~3i`nh9R6LLY0nn>Xd{ zI3p`nQ}MAu4s)0a#2|5}i-^p%b;2 z2trX4M!MX`??H)!G>r)9d9^KiX9jL0_cXQ>X@$WeP4FEEMtr7YS=M@*x6NT3M5&n|+dT`g6fVMh0oG*NpB z01PQW*LF@l^&JuXctY#}TL}<(WYDHqA$C)EBL?-A2oHg=xs0Kshn2Bqx&OX3{boW4 zY>4P6dwA3im6H(;D^+fPVFUw_z!U2%G!R_ZW}tS zlLd`3`8zj^6yD>19#8+zBT8`6sGRdde(9X>@i$Xjau~?3G!lvTzpVD>gACT|BLN>4 zLU6liH_#$`r&Y|W+BP3Ye*+VR_zHQ3Cm{KlM{;UzWt<_I-#8~3f1$=B8i3qJ46^Nf zTMF`__m|kbbr3vNs&AZ1r=Lw=ywIlsFSQCc_0RX&>VxMV4*L7%=2RY z&|J;3_R3HjJ$y(jM$!4M5O3!F9bdfN9bLZNi$o#J(+%8zq1=#Vio%lUw&iC2ea2+) z{&?>PiUsck%QrE9<~I1{=&MK&3w{c$^Z$A_h0h~~vsDnSnGt*;9|r2{4p>LN2h(nLgfW=dWTmsN242zz%49L+*HoSD5zQ;@IKic#NC=x8{hW z7u4hu_0bs%Td#IK$NT<%-KUAPBa^ZC9iX85HvX=CkGhZ0^X*=g+ZC?Oxz)-tp! zxq)5(*)-po8=7~0_caLMx}&?iTvqTz*kWtYjc9Ik{;Lb*1MFi9M9pak0BOLDvsW$w zFJ*^U8~ujn4gu^g!G&!fWmF0#VzA`T)3$rLjeNr*dV07Xa(?;_J+^rH_N$ZSsbf@t z^)hB=Jd@FTtl1kxkH9@^Ss3N1Dpa2bZ-c|+YEgd?mvaIJZI2Un4JSh^i9s&snE1Q9 z^Uhi}vmVCXJyxZd_r55mg5({M;cR=GLpA&rnL@((V&La&|j7-C2py~Za81f+MPW9NKH$jfTNTq<|TE1SerEMW$}K^ zc>76fjroD@5Z@KA5G?Qn8oYS6No~MRd={cR+(fb5dY>dI~_h)@1Ty z>o{v;XHDwmY$1nFQ*tEZKy%JOJQ0dNcNot_2jO$`Ffbl9=UzOouCC!FUyY)2waH?B%x$$i<7;B&$MriJA-pZJ znkh%4=3iNK#Yi%rg8i#740YKL#-*ChzmfS-R5+qG$7+#s@;vOwWF|rF*{FHNTVU+1}AHadRg*oiu!I0Asd5kd0(bj}^4-0$PEp zEP9sVtiw;EVV$voCbr^blMYN z8Y%#oJ@5(Qco}7ewtW~)rUmpVq>SAe>Kjd)nf@R}de+4B$@Y74x>v*V9pZ|CL{f2) zT{P~(99(;k`xyN_bz_^2FSqVP>}Ps?^(o09yl_Q->G(nyS-%YXHf3vICrvGcfK^1Y|ZVkV(*yW^J&``?)j!thf+&yOR2mk4wt zDlN#b>eF7*n39nVDu?}PHSgQ2{WTt0e~EA>;$ATy#_>mRJppj0)gOM0n%KywUX&!S$ehOmwW|*)@YcE^ojQs)Xh@ z0c%#N8(ocIm`?Zfc;Zk6^Zs(Z4D61kZrn4&-YEoo!cERRd$r( zC+5vSnme$hX1WLtU-O8l%gVjN*jX=8uO3*BG$y4DyTU)AqiBsub~Ko2}F*O1>bx6chNJmQlca0h~Fqj+`7h zW4GPH-n*uK_=DzetOQWUFm(CbW42kyHfZbIDJ~{XrXtdqZUa+Uam~ zrV9t^{hv>LZGREnUkX;U)B)Th78oIx7uD?LeNX+dZL;%ds1hZM6psx%*IgSrFIA`B zeqV40Wr0Y*NCv-D@!)Y%)d+Ll&*d)f#er40X}%=M<&rk%RRd-XN2$UR;$>vO{i>24 zm1C>>K*vj9n+k6&8oO>leAc86$Ag&rx|djrgJOv2$OLT3TkV(S`i1LTag zPkx_w8K=M{#e|W!AAVs$)eZhA_+UzwjAw-uLm40O?f5dICb<{)S9du_rgJr-*AMvg z!|r=JKe5Ov=88PDM#3O*>ZK0cbd50t2N*NDfcD{b(;#{&H~Bcd>ZA7>rD}aT*GqDG zDtD^BJTvb6Df0I3mdtWmq^#(yYe$f+`rYdRfP~p6?fQp@SKnlO`qmW+rk8qv z5>Ngpy7I=Zv;{Mqs}9ZNZ|&oIM8RPXLFJ`>2dx3|O6Y(s;e2l;kjCs5nj;G?R=f#& z^hY%KXRg*68I8YEMs=N!!}YacRsF}~%u5BvhI!H;B+DuWeesNBN1?sY7&bO6&OJTC zu?&qBe8n7Q)^~X1P z#@ruTB3Hj%J^cz3j$l5Qh|U&%d#tzk{LTjkzT$7NS#Nh75)$m+4up}$4@osQcLe@4 zuNw8q8(+U~ymMN=*|Ocn&V8Q5OBPAzt~(iT>kP+^xt+vB(O#7TIOih}jQ(YT^{w9c z<$}9iSqf6XeP!2x0W$_o594esg2oKC$OdB97iK7-3~VlYJl?Oe&hBW23{P-8k=Qlo z9=IbvG}6^5MxXPn6L8J5 z(KSTFQkkH9_42>>h=I81z%K1e2-@>WoB`%N85z2_i&lAXmX|x}FiR%@6z9{CC6+>) zs}(z5I@PZWGJQBC%DjzhmLqFbaM&bN%>?E_3OqMt=wI5O^*uTFNZ0RI<^=wv98L_= zTAzcyVKR1LKCXhYR(H3M0(p(cS}(^l?b4fc;%74H-cLH{lhY53O*9Ztr1g#O?@wI{pap*o7>CP(#BUE2&Eme23G-q|+2!WqRdAcm4h9hBo} zd0~uD;7wRweziE?xkHCPBF zf5X82dNN95?@6@w9P3^sdAL^LpGUM>>ixIM17Ku##n=PhwP zOkfIp``LI;9T3t!Yyl1;Jv6(lf;`5`fJLc3k1@%{S!wCpQCn2^7G2lA}Jp||@C zV`nxNXrGLsJR5*gjrg*j@Z%gHpFHowSV0%}kYqP!{|P&=$iODMgTU24j}^s_mo<1^ z6DD+ZqemBt=dUrro|s}cu?$7aSW%s(Y`~Aywumj5=bY4{1S=rWSZ8~$cKvRLFJ&#q zC_-rJ{^SXCmpGDbT5Y{c2+GIj`D_^4Jsxl8iLwswCyqta&8IDHfRy{JUtB+VjpO4O z6Aps^jnsDj*S!e40$q2>4%YSpNP+gMohjV?=x8^IM^b!0du>LnneRif$yKqb@7nJ& z>X;jv0lLxJsDCYQ#hm62<-7CQ#1!Wx9#a{asyk zn_>u`*tBT7A-j+bcC8-K3R-IR5sP(zR?*5Yj9q%1N89t-$GcSHTfffeJ?LeM!SuT& zDTQ5gDesu$Fy}AqBvT$wozr}L!EgKCjS0)YQN?(+_QRz zM;zUj2h+$Gan*5gJ>uow@efV}Pk8008+FFHRs2#n%?`o*Cl2Z*i7`6nnJ35Zv=uTQ zTwfWhD$nfVzD|43&RUh%?gfAD7lTxsvpRj2WX2p-5|G^(U*XT83@y4z@7y?rO?M#+ zVaMNEZ@jeK?#n&NpTqNbRnbA^rcmJKne%x+a%=(U+oBK8J68CiWC_zpmG9V{98icl zFq166D{=-{d`fcc3}qxPMgGYz+HggQCEa>+fJjYVq2pN2!i1_&Y}wof``rzcd2w&2Q!|^|bn@4ei{w%qzNZ&X zh4PtM5fL=wFSR@{`+ykm?z&%}JfElPox3mAebUkASJ!z~oE9HYBbq;O>0>UAb)V;p z^DBl!UL7cVe#$aX`UU-IpC8_)<%jJbt3|(I*dN(>^>{t`pRdUje)g~FpR3^fh0`a9 z8$BHnOVv%cy=( zA-Ft7;R{I`K2${~jFxumDbsJqfVh8vzdJdM&;PKx#|o=~m@NYPN-{Ap!` ztMo+&P?i^k-Ezm^7r|n90jq$-?|ITyoE#_UUG8sPGU^8&xGI?sJdUbwCE0+qH_r{GQoGacU70h0{8)eqp zj(WFyM3QrXmIHqh-07NqOf!A>cZM>TIHu^+;l}LY^f?6utv^9uec1U^{)tCSIcx4< z!lJzoJV15#?K902@SSM@eNWkdwG2a7%l2u-%Ug#owqKu^3ckSpCW`^DcdoU(s~rTB zb;nxwahf0mykOM-^cHQGvrW`jWmmggVnO? zjk0B?JKz`dDBX5u$}b!o4$IR!Si$AJJSi@45vY|Yl$oezdxp^v%3jl+HhMYIZ^g^D zQ2!r$Z_+!vo~LyaBd=;0>^2!ibo%hpsdqGY&Cce!^NgF}vI58= zf<9U%CxV66UkL-5QJ!6(s!2SDV69F;dtAbV zh#Y7je{y6tA2`Z=ChyYW*G8?anI%B?`wi+xex)o!7Dayi7eBhl5Bd&VoLjt~`;7tW z7DKa{^4ci5M~&xW?3uQ5@es@21LJVKq9?)}%7#>SDgzP8lgX24Q;~@s(L&$621GtM zlR4=*%pe*09YtC(rmakD6JRJN>Sn4=ALri6rfPqE zdEB6enT-gcC9d-*8SQcI{Z|7|cnCixw*@gl1IA+R4{7q!s4{NUWv?e zE=W=4Qe;<4l(4-VVh5qZeUmn9S*j^e7ybT-y3B*#P5Lsjo0}y2{Czmx;zzU_9FfXz znbR%X=$`msyV(Ue&YtRnY8p0E>lDxD`R=bU_s(vb{cP14T|Y;@w03kx7P9d1*?4iT zxoIdK!*z%GR|)8BJpfpI2OvM2hY{+&tz-6Q$Psc>?Tw1wS&&nPZZ(5-KtopVp>CJ|p4sdi@z`vzJkE>yLrD}W>Pun_tc zgQCF@^&9fw4TrcQ|Grqr7E>zYViG}L$|m=XF1vG%FQ7QmJ1~ZMZLq{FE`I*B=q#Rg9AE_o*N(spyc z)jbSXz#PiqLRcP1!FdlF(oB<)mo|Ey1q{O2z@iu1jXS1y=K>daCe>q{l%S%XHD{f^ z#Ea&GH7NK-!oK2Hj5IFkaC+0mV#Rd{^?d8Cuz%a(J-JaNkKjpXG-87CIEHhWDukO8 zVA7H97KMUyL`>b~^_JY2%?r%rXm>;0cODGNS~V~L3@&Pa-1PSqz>0hIyxZGX{)Ldk zCGN>Zwct)gkL*ifb#B&Zk1FL$d~ZkJ6quBQhm29}aRd-!{ z=5bc)=pb0%Zh_BUn&Z{EY&W~R&$oyNlho)U(Ci?1CrnIJWkx$Tpfh-|c9+6i=WuE4 z*c?XU)$Vw`_~{V%DaHME?0i;kY zQ*(2@82$2%ftL7UY4|>QC0!dQ?{E&`YFqVPqIJjW?E$`e&B)nb*cnnIHq&&5_Tdov zdP#J9S+v?Ggv94`TaXqK2I2SOjDkmosDSY+Nj?F$ug-P2A(HcPLVMise2lIVZk`jHa>ZvsvRS85~e1njhikXP-N4YE>Q0}+_ERIr$E`wApkdy zsgj(|q8P=ugkucc!o=>38#)E4_RcOzKP{CZ8Z^C`X6}78bEDD>+erEoQn^OeZEbF) zzqSRpJudFq-eOG=;psFbXHJ2PvGW0{V1Rx#j9cUo&EjA;q1_gu*oz^pK(w^P6y7jM5? zyr}%dMD9g~irUhp_jlVcP?^3Ea!`S9U2v~SINSQOq)u_WkQwbkC1SzsO{d9iA5 zsG6yQ*yYLIVW3WQUPGL~i@}g{cW^~(Af@ZA%ltxp%nsG=*6JG?wbRj9K}}P#)zTC1 zVRAh#X2eu#1Tr8dDKQZB)Sfr6A7(=HN(qykgWz(OjH;lsOX1+2S1eL>*Y#}+$o4C9 zpMDllOy4gBD+=b_eCF1`b>U%8qce@C9op>TmBi-1dsWP3GFoW{#6nU!Zr!zi=3hn+ z0Um5Wr|OJ{{_KrSRjjLl&X##k2)PW#6G{?PgoKU4PihT(I8MyogOIb2yysT+hQb(9 z-T*#4g%;u<7ERMO(v#WNz%b3VdGl!nw~_Vkz)r!7rmo7)Mw z73OW67j)^o_MhMN{i|TiJ7mR0vmf%yp$A$NMe(yOeEhffu8$*IIGeTbLNJ$Zx5t)^ zIaYK@Hg~wJjk$wt(Jx6;URrw2lzsQuY@UZx(edN{IdtZTICx8Qth;k}{1Foe+r0vy zvgK3sjXX!Dr(5i90MUX&oVS5KkSdA;;N9ANOdIbZWP~B`I^Fn z;P$+WVuGMFRZhA{JP%&nt24lVGRW13+>j3fL+o%I(kHo$HOY&QdLq4Rd3w#WiXdxl zk?4a6k^y9esEcU^(ufH^Pf)6(jX^#m^1GD*I&IIP_Nlk+&5esjQKju^qdTwu34ElTcnP0C;DdrjmjQ~EBLjP^UmhAl}y z01{kou1DTzsDkb-QZNZ{t`qBpafZ7em!r$w(KhV)^#y51(V)Qi?n!J<22OP?IDID) z%a$FP@h%l5CXu_l+4k8+8|+v7h4Zd6p@|IV=eRso?4i>M5wbaW$~Y*xgRBeg&eH4l za8jf!iw;zol~>$*{Q2lD`T8RAz6z@a@-!g#zj>p zD%wxV3LTI2yLAje73pDp_4W>IeVIcEjyqJSflP}@>!YKAX~tvNTx%gpy#2*c>p$-C;^O`c^LL=wH}o4W{4tzxHdTNQ~?9)1f0u@hmn44Aiqz~BuA)ncJ!vR zU8>6_jD(`aB^?#bUCcSlnZEhR{JvPTC~W!t-WX7enmS>#7+tSM&0f063Vk{*%m~CYzbIn zRaAj_-ev3S8y1o6MO3>zqO}V4Goer=c(WB$mu^?ejYZikmf~TH62Mv5yDM-W zv_Up~*|%*axTXc8SqBMS#jP#d3zjuWghYggOnkN7D`RcevAlIA4vOd!;FAfkuJ!r* z6ie(XWRwd>xZd6qd5gam!m>fc#DZ3u<d)<`ew#-y&Bo8A~+TDV>DD-xBd0tM|h!%iz(^q|6hZwS&FA`pg z=^&+?p-&rhKJ>FwZTZ_s!c{`nfDoefQ5|>CypJ0{jR?KE-Zxy|^xOFH^_=!i<53>A zkt=Qk<KQywzfOgVGxH-(!56>&;KDr(0M7?Sv-94+9Bf8d@Ui=bv(sHbR;Bt!)RUg&^DL%AfUIDYwV9$;wfQmv zqENAmh`TpDvreRCOd%lg!uN9{oYzkVrh$+&5JD9^V1V3m^+EAB^Q(PoPXq-ZcK!@) z7X(ae0%P0EPdy&b{_^1PL;gVO+4rhu}fA17!yU{@rjcuUqBBLFOc6y_mU=VG^xSKp(f-&Kk|!OJ*dTV0pLU~ zZ&&M5ZZ}IH97YQWFdWqPO|s7@=3h#%37jQ^%4eCX%Pg!N>lw_{iKsSndVdh)?A>js zONt|vy*rEoQDom7OJIRHyJoL;%k5}XzMoTF4wQG`Ep%i*!FE^n!9*@xADxYlQjpZ21`aHYK z%;fgn{A>p+5D!l((Vo0|QM0{Cx07V%qp^GLo&{p=e79B%b+4i;ZS2hv|Jz+u$2g^i z?`<0481w$-B$IQ|uOFv*DII5{c}BNe+L@8!L09G+Ul*W2*r^*f^$bU*5J6~g!E{Q= z-u_zcA%dr>1$>YonJx0Ty1t5YszDRZ!PPgPVg^;`N3ox{Es~#tV}q#!)My{7Yzfqs z`+l>OOg__i-7c5+jpmRnUHhXaAdb_#BR7;z=r*j_Jw=ouX=7Xg?14OpwPDmd#c%EU zEZhR>Aa7~=WbJ@l;ZGHY)pFam>}CN?&!EScR~)H@_YS0#raVF;7B1N@s8LeSunHol zIzMR7tlX6c&w;6qzQ|<9iyLvN8yl^4RG7ldxw_=)RUPY4aY}fqQ40YHMi;m5O>a|< zXh7Wxk{lF()99GcH3bjt=`~TmbN6@DA?LO07($zxn@g}gRoASV@axyv(uG3D4aZx%(M9%&eldY+_DyEJz5Bs zg}8aU^BVV9xzck|(jA%+Tq*^oqdWlfnzsSE;w#VK^yIBP-?xD(XT%4fb^M_=-md=T zdA39mv$3JP#?6akU_y`&r8Tko=kz_?B>&=!tIVf^bGi#)&flRfcZq<~ZjXt2u4|(V znHNG%cGSEG&}P!X8*2fwDvBJVj+b`yx=CZ8T&@p*nf4mKS-ttZtBoy0p$r z$5!zlS5ka#Rj*0?`-&By+=y>hNMt@ljPkijS%PJwfYhBjI)I=!Y^BVk#skR35Ay>3 znRD|~Cu=EO{a zd=f>z(SnJ0rhUb|>{|^>V17d!;5+lzugHlVuR^TJii@4K&)y6PaWY#k!<;vcBXm0W zt4B;Xq#iR2GFmUnE`v)mdF;FQ0J5o}KhL&j+?3px1LUJ!JY74RibMH!z~}vLj+bOm zy<6+)=s0tEedHtv`%&w|xDtG@gHOMV_eE@p z_VW_Gr>n9=*YbI6=

9MC&J)NgUk}y&(dgJB3+L3xbb3e6uil zzuvsUo2HA68#ucWVV*V4%X$AvRu<|oaZB{_msW(dqo~)#_-gH7+8Z2wv6osXgm#}g zgfZ3xoXGULH9+&XP#J83N|DvDdS1yPF&?K9~Te%9|P07?v z`R*|yn>BmQ5LPAB*9iI^!slPWrUqL*mZwBm!hR77-2zxA6}!;kdgDDGNCf^gF*pO4 zbK3`0G<5>}Y#2*6U=^Yci(vm0D!`zff_ zNv!N-J4Lrqo?F^|(|FLML9A2T3!>5bk(BGrEkH)mZJ}3{-V63+gtfJ~8Zol}Br(m| z*FCqz9HJz|?r_|bqSBN>y$eL`^=8oK;}kHV_h2Li`r~Y{q)mOMcR`He31^5$UffY@ zGJ43&dpJtC`?DU4xQl{2cH>5Yh~-v4qRrEKEr?T}vQUC=s7s)C4y zI>5BZBWHTeJC4YtRcNM`7KHvqpD?Q^f#-&LS-KwZf?a1Vk7m)eyZcqjSZ|Lx4|~W* z8TNqVL>vch?LSVpDHv~K(OyzD; z_t*Nt-PZ>(6*9Z%9Ar`@)f&)%w0N814jbMe9urttix`!IjzCXof*T&4%aa zJ4wRjr?y>wHuWoYeT5AB`Dk-?J^4p zGVWqvO`H?nyVPu3OU7Z6ZH8MFa0+1}76gH1hL>444 z8s#wLkbq;yJ`u2NmXrA zO2n18;gY*j$PNXXdv`#rw@hpBqjiPX=UbGp(|XOr_K_StnFjY^ULWeWt1*_Ti9X&g5iMFnp@|1oHaUEO)sUY;`9LX0I)g5e ztNMVEEObp!>EUdi++OS5dHV@JTwu&>7?X^4NTtg5=5rtQR5vgAYePT+3KC2NY4LhF z;NG0UuLMWY`;c1I8d(q1NL?%#_(nQ3A5PLr&tuj@2|?!1Gk4RMa~vo6*q%11FBJ?g zsogDAU)Q*B^~)&h^u4}50Xn)?O1lCLd-akxUbM-sh}!NUblp@328p#gq`_Lh(01V3 z!4}kVj?v9lU%#e=h6;!31+I!YmIGK=ccdLkqKZ;b^ z9ppWQ@<4r|!)K)H=}V}#UCkzGK&8-Sb!})aMPQgG5DJS}x7Tm!%9DNX0~KXwj|=hU z+hQ4-eK9SDtNdIP!)g=8p?19Rk#lrTFuQ2$FS1q?OuM6(J*sj$=Kj6=aQ6e(w%^=?~9i4C< z^|f8VFcK5D^CG6CNv_li!9+Me*~?>sAULZpQv$}@?PW-miLl!szuxl4mY?+1*704j zS+j$*=@?umsa(I7?VKl1_mJr;40G$eMpNv73poKix@xlNv`@H3yb|nGPtMMbcb|Fb zi3 z$$C+tO+dgs>5mvtquMBg>v1|+DOk~{Q>?tKY4iF~RpfSk_b6mb?$d2GP>eF6ITA0& z6NfRjT@rIdqMZg;udla$Y5cG&@It{u4J*e zEdu?hcRFf44tfrA!GqeV)fi+d$Q9x><$Ae{ZZd375#2v!Nx9voBG|oPZ@V2f%gbPC z!x$mqJYHs-vp3!V8S*VXBBTW~uMiO@-FMw^*A(~#n%&mK)70Fo-~h95*mO@Cn$FB< zot{d3wTE_9#2!m!)dv1eMMAOf6({6O>c%U6pcP95$31sB-TXtq z3_UmoBmk-c+NR(QG0gzNXI(AGm%n5#VliU8a~Y2+O|7o#)Unq3yvJM&spjR0e)XSz zH#b|s(ut06xGoBFeS7qv^DX(>#SqfPJbt~skk9)%KT)>g34u`zkx%N~QlE|5jIqH1 ztIbcuJh!PyW{+#u&+~!kpyAl`**xEF#YI5vT^DlmTn5e6Y@eW)?RtT=PzEb(?Y?Kn zMNe`2G?iU)b)a8M(j*AeqGFh|NBv_&#G-g5uq8VJMK znTu%HT4XK)46kUzktC0=cGuvZ)#veJzhDdM9kb^bv5fT?s2HH+7{TXNy1(JJ4@d=S z$>0vK%AG}6TEBXMTnm2YcxOJ(u{vDpc7wsMrE^lKJS;tf6orcXoGN?6t(T0by=d}D z4d(#kI-M>a@5;Ht|0XqAn_+0$u}wLq15c^g!|CO^0M_i(KB+bMmOJ|xYe!XnQ!@xq z15c~nWtI>YX@~RBfpS#j$Xe;AZT$^BtR*rw`k`{31#-5^CWzZa5IQ0hM zA7Ct7N9P=Y>4(P&Mi=EPOyLN5*nP}N^|?TdVU0|+thps(zFn-|;C|h9xR1Ra>t@g| z;_MMOoi}+;8xzH~fK5xB(aUJ^GPVjt@t02_A(oBIO1uX|?SSukTW&&8clq9o#>68I z&Rl96Ku@Em9nvpCa87Xwh~830kx5WvhKtvByMTe)+OZaed6sgi_*;lCQ-*LuB+#%x#Dg(K~Gs>3L@0~DLHQzZWcGj)N&-AwB{28$KV2_ z3~ik{DJbgF4d?aXcyGd1BJdG{@pTtSS&p}uz$q+QE+)GYf=1FR&&z^$@4}N4@IwpO?76*Ss%TW*{fIH@dW?s04t?sCfAR*vM^X6${fP7RX*8SLA?C9s z-)=4mf14q=6bl64)Kke6IZ%<3v zYA+l#Bq{ut4=s;?GY49hAgEY$A1()=c{PJR@4ug$y`wjzjpx}b_Rr;+Ptep`W?e4GB!J4rx93@yl4NktfOl(vvK@- z?OqaeQyWGUQIa&s#~~JGU~p?!G?c!K!+OgVwrb|Ao@^Ee0wP;6TUo=X^;ZewZjO#P ziNO%7jS6Gy17;th*_@(hbArvyb*pj5$e~oDc`=OM4X)8`x?T+@ENY`lmNXXKhVx3al`TxA^bhmy9QI5hP_RNVM+GpL zBV+E+E~H|5>)Y{F-UZsIHUR$z>Z2&78Ue>X^ODrutRTm=r>eivCJmaOqThn#=*Yfy z>7$M2doSIR?>uZAL|pq8kAzu~L$WEtH@jtrD_G|BnXlr;ZgpCswf z`W@z<*N`_@iYD{sou7BjyfR-v2#OSdS4RPI+W4F&cy9ShjgF@zjpy+>HLiDYw}zF< z(^X?do?gA5u>L~ttgbmRp=sEz9AIJq8-<>}Zh|oB=cSy7~Nyu=KJl%)#UcX zl>D+`^8hY2i6n&6~zU~C1WOg zLA%a%ZP}8yhoTUK#S!u(qX_F@0};>jnBt9Qdi1^SCEWTej{#0*MaY0>$~{I87pH9w zoQd0`2x&HhnvPZOG1Lf@5CBemeJZ=Cfgw!P`ZDu)90=DFnxR}3=#~^T%g_GmmATL6~`ZE zISOve#@<%77b&oJ0Lms&&ks=oc@H}p74YDh1LzmsU#Y;()RINHug zJTI?hYjmUdtWf=Cv@X|}fYc7l4H(yVKCYPp9Xj0`UqVk%K48DhH87~l;j%w6uW01B zTzzLbTRR6#u;TW__m2GuQNEl4eKFlB-?*OuVeCmgU*tRtk_#X`3CRyKP;1EcguwZQ z|LSZP*6m3*$MKSl;s$f}i>5DwEhg^U^c3ZjwkEFV!!6S4YQCqF7jI`q?2HtY>;MX-u4?d?O08I!L zTj(N(*g)YgVu<$+9`U74qa4Ex-6g-dD1FzL=BCsEJ_ugK*{VkYVq>=QFN5Blk)3*pG+6rtD9oG zJ1z(0KhqP3Ir&}cCoWr_ug@?(hzr~e`$K|cm8Svl(cx1^<>PiFk6FF6k{cep_hshm zthI%BxjKMc0-YW!FD{#9f5uoM*6@%+2>_XewT-Brhw`?jvw`O3GUFzy;-7Y`RCeVb z08%b}*J%muQF;0*2Oqb%Bn^AXpUoiwB|j?=cqE@*t6JpJm@99QT3VoXrv92=Mq0X< zl;m*O()TodM}Sf3!d z_A&pWZz$U((;P;Z>#Keq9{|Ffpq=E~gI z)4KsBZNWoLzkx&PDcrTMlIBxj{g41( z8;LF^B1BU2;$ZP8A(2A9Td>S&f5|XV9i9wogM-LtLUgM!HVzJ=>(Y;o!Wl*!q|g1& zD!B9fI8(s_iKBYHNo)}&g&e*DLZ2MFLM;8m6vYW3^eTKD>tMV6Tq|B$a%ph6wUg@j z@;s`_zCk_m(A~<=4XBN_JBExcdl32aGzDWvIUykl_18{~ZW|LGP9b`CQ{Dq&ToFkJ zSIk7w(5;v6{UUp!&THTqM;-bVz*zQi25K8&ye6z-&(n(*p97;>oh>uz?kb=uA=3M8 z`5-orD+`ay>gcXiOs?duM)1U;s=P^9qUZNN24?M;!!Wx-Lu>@&t=x2!?K~qd`5MsABpH8_{#rFe%uL(nR$cYB zQaXk60BDC|`@FFl+dJ87f|F)5I|#S@P<`g%mnC($G`3Gu?_jol3gL_Oh@Q5N8`ho8 zfY8~Y4w6Y7`o*hb^jK_dQM)1fld9&N7j?|Np9`^qJ_!C+b$^w~OD5;WO@fj$W1+ao z?l(<19fRhkjm+T=;b4kvMEM!$z%VW)AyL@Z7WAR{s6C>qJB%aXVJ_+$i-NCB;}jom zVDmk2pR}3DNqZ?Xkht~~We-a@gbnOL-gN6Bt?qeLI(!gt47{zH+nA zQ7OIJpqDAuj@mu^q(QCE(L=3$Z#HknrHS#=dkY!91d|fk&k^$7 z8!PVKF+rA~f5$WG`0~lpv+nS~agXF-0JV^lnbxF~AmvT}Y^LbtLaPr;>f-s>AJ!H? z9c<_e@k6W$uD-ixMi^kr2Gn^}ucI8NK00~*<4u|$UrQZ(Uf~@` z|9UBiXR)Ugrhox_6US8rB{kapGkp*Dv9YgPqPCY~{tnp&4idP;iUk~HkYQnnN3=^-?l z?(KCX&Vy*8S{_VLE?wo##bN2Zo*onn4L?rYT8AZ^L`ud^J;bJalwIJFICqEOV%R?5 z_u0;jQNVut3fcJ3AfPFDk#9If#RD}ouVuq#Kmyk7hoSwM)J?`MjDldfL}g1=kE$wt zdbEmlIk)C&;@0kSdvq%tv@=9U9VqoPx4xR@e!XzUe5c%-ttcbbqGQlzlyAxUy>Rn< zf%cYuUnrh_U~c67cDZ~srf=@yijtRg>-!w@W3*ivHMOaLU6cT~)4P}R07X4*H&Y)A z6f!;#kRFk+ILb?MbLgQgrRAH?2u6*Rs=4UGl>wPcNG`^Ge)w3j8OuD~=+2?-?zr%z z_j;?K^2|KO(F!n=p-v;ZNW(J*?gHg(%Sor6c)u2iw!0yUhTDAr8|dXGY)nQ*GYd$- zP{SpnS>^j4!zT>|tHY;Y_^Dg(BMF0tX8+OuEDZf!%FqQ{+u!%W@dP`*v8Qj+8#yT1Fk>`|dHS$VLr!|P2SD>WLL6`JGSJ&` z!Eo?sx#m!?PI)4bO9=P(p<0=Xe&<=tFw3Z2e=;)ZG3}ALoG7=$xgg2Rd93A^m)~A5 z_7*FwksRs#(s({kKKn<}Qy5~w6wl3t9JUWc!DCu!ZDth4%22uAZdw!6(~c_^Tk<#> zuSNhBwK|7xs@F=(1>{X2q-14~DSPGLPj@}H;zOrd2(jj2abNn{z11&M85x@ym|Eq@ zBgq`oo_rjR%xPIr`hG$5kx|yQZs@2ra?5~DK7ILOuT*{lNzC$8km~mM1bAZL&5f9> zufbBZM%AgO^;R>I9khIPhxXExr$_6^HU2G_-nn~ZFX_6_4T$awfpx81O}8M-9}X6C z*_Uv4I=bo}%f#0jZn+q?Z?IAVr}k$=M1$F2*0;OCb7$-1Zku8DD>#>o^sXpqY*F5B zsb}jaVldvpD3lWqOa`CLi}pahgv0q=z@0jS16(!6^SmK9%sqI>&{-`aHi$%Hx7S<&NQLPRxW*U_c&#y7_^=Rc2>U=hS$n;ZF$FrM;!5e? zKoXk}EVk`JC|!2Hu%cMJ=*hjLae@H=_P%%Y2~w)lEm$HKPs!=?`yi7qgk`B#{XW;z zwgj~*@QYPe5&`-4@cfyvD@jvdX*xB3aH0!q;#WB0O3^A_Z$vj zkzhY=pd%-;8^j-V?~r&JP2S7jm5RuCDR?XE>>3~M327c%&Lx?dxF#z}SS1t^Bup4C zL=Licez?6w9)ZY&Y~J?CfkxXibqbU0+Os}8w)s>n7gVkcI zKo6zsrTjDw)uA5btxKLq#0Ru-#4;Fgo`@ScaNAiRXC_&EP&~x>v%K4e+Mc7^54+HoV zbfS_=8(O@)2Z8kT?3!g_(efgW#P=v7(%Iu4Efw)oT#^jI<;fXosJy526VrVE4y z?Vz_oYHHXIl=c7+_#WTxkQhb$ZgIxh4N6!@F&2FD!zo;%RuXNJs0E*ptH7aM&U@7k zJ@3?f(gL`X3hAw4F`G0|q|PC{msmL%+v^{Hp7bt3!+l%g4FCm}r@(fn0buY&y#>Rg z=%bE0y-J6keLiIiI|%}$qZ%v0g&u`>KuHNKr#``RU?D+`vUS5~TLObm=tH7@eC#MZ z@4;5$M){op$?9yMENCVVz^x%t`y^&~IbDth`-oM<+tK?7w@}2xvP06*R~2@p2d}zG z%CNDpnlG2aINZTf?Khsrb5}r&q)pJ9#Fc@eChx3?N}uoxodnFU*=kYR?DBDIJ(f5$ z;ORDQh&CrJBc<^1s;KvT-!T_hw-of`fmeQ7OVMTR0OSj5NCc9(@fkScVL@kQX4eJxZ_Bo6t z!?KQO_6Xzv3;i)_`YjdcN3-bm5LnDSIYID9wP9k%_4aCXaf8_nD%&Eih;+oh)%mxY95JAX1yvc%l=?2>rR z^(zKY_jseDXKGfxjWP5DWW=4P5|hwUike3!!Cdx%d2pFAf$Ek8rdt|TI+CG`HZAF+ zG5(BI_HwTHJ5uN$2Gb;}xUo)+Ql$At=P-ACQXuh$Hw*Y_?zSc6{WU}DxTn}1L~WCM zWYl^>IY?vWH+x*a7CMBs7riwZ_}^!l;wj&;m! z=+IYzJvaKx#5ALh2tthJrt0_#k{J!+5cU1hXSLF?Zt4~uwGxi8=Tn&g_1wE@;|ZJX z-pmR16!6O>63UK6ydQ}8wcgOMrICh(Qo#lMM6J=f_a)l3LPH}(1`N>hoy;MBDZ@>+Kfx?@#2JRBN0`4cZJN@ z-PxsdM?Lp$3976-F3~a~(k0@UtlRK87f02TwhZM~%kc;tnp&x)xK)u4uHV*ZCmN6O zBrQ$spY=MC8-GtK*%KxoLOS6*SsLIqQA~S%*yj1NaiD5{~syyL!O zS0#NW%1S?)Ci0NSFULs$4Ptx&r9r#WmwqPJxOj-C{LOy)A>c{2AAmp(#UMBam|yE) z@+)O4n1)3z&89Sj&vJ9(V9wZU)k~7%J^PSx!aZ;i`gH-y&>}Y4{-b-vBe>@W*lt|c zC)>?v;=NYfT(9gjt*#fDED%QSWe5Vd+4yv0t4l>F$~9oad^d1=;o{xRxzI@eLA!YU zW=cn1K?u8GotEUMj=}{I%ZnVJQxvhy<=t*~6t=@@LuOuTUa->CWpO@^rUi(w%dq+} z#J+$?3V90}7~vw&BkRi8nB|-Kd^X$=*QV!crC(lMb(eFLp8 zB5F~J`Lca7LhF#1du{G1;7z*V*%N1whwx0^H^SjDwd}mr$esw{a%?-GP>h#y#h>Qx ztsN2yzZZ@Zj&I|w26gpiADZuXP3#*l%;epdG5$_b06SBJ3&y&Nmm8!0Ht+d!xzH4g zwat+=O;VtqH4!$7a=Gqp2y zBZ#^ugi34;Bzdf7jIVWh5?TZ|q{lU>`nIrQ9s$^wNddesi$@>Dk~m=Tk$lQ5xxCmt zf&ybxnyknDxlP{nV?AD8GlY`!+d-I#lhm(q!&kO2ii#E*M9K)8_xfGO=5jr<>%blw z-Y%L1fcTXR^K50ZCk>3$(m2#)B2G=yZ$v|im(~5As%XyL4-as5dE^l772DK_6|o|p z&I*&tgXYe1+-3Rw@kujU!L6$HpY2Q%^mR!v2)FT?Bx807As5=q@b1m!35xj+(b3mB<@ftS&ndrBi* zLKi8EN1y7;d4S{c?#+Y*bU*INLhcR;;Ms51s+%TLB7tvE={B46h-92?^6=~ddfppZ z4{IFX^%mevm4L#g)?MZL*v2aoTwTKI&2`J8qO~v)b+b&FVN3aObESl=+lS6ur^iZ1zWIjT47DXbHoI+`Gu;l_8|* zHhVvgda=fRW{)|R6LX!tF94a zea8z!wB8tU|2PTTq&T5uQcuDY?6AkCPS2|v$H_%I{C!|a&QfA&x6|%i$9V0{B1un5 zxaIxcCT||+$xVyx&9X|UfFf4#8v}E5y6$k@z))y!*)@)JRy2b062L$Mnux?x5s0yYm;Q5uVzuYS`cAY8!tbFd3p!Pox`oGFO6m{N55)WYnJgn57!R}eD*6P{j zc737V@AqH*>i7Sf`k(yXmp|W6fAM|(KmEPm`@MfY1mFDA&;Mta?|3&`4;UE8H{=ehrKmX?a>A#Wwo%HYi`S^w%2EVEvzt{fOl>R~fFR+yK57qzrfBM_Mm;NICW%`fv|LXVg%HK-= z_7wO(TU7pk;I00*3;cZkzx#atALrwbANsP4Kh%D23gVxC_&@v0AO6kX596}@_4sPz z?|<{JhfNfJ|5={*!}9*g-~C}Fep+6B#c#0rpN;!*OY{Hquf7z1^ODE^{onh&C{Dhs z{cMhZT~x7O55E96%>SeB>R*TDG>maS{EGdf?<)WK>kR+LAG4+&enl-7fArnhlz5>I z<6lwn9}BWT$6t?G6@T}u?>>M1$>+x}e);=fep~-~_yFYN;g7zH@NzwT zmWDTezVc6o6pq3l-}d#p@jLd*OaEcr{t3P;YN|gOV8Z(ay`ZUIe)&xp*JIyg(bwht z*-!5b(*_2OUwreeKW)_?eb>ir>0|BpemTUy{G;#w^v}O6FUqhD*s9O+u&8(3H^VRf z`epp`$IVKb{=4G4to{ybc>jFg*VX@Vr+jwI=RNhe@A+|0eDjvi+dkipFJ63EmCp;G zKcCM=KYjM6UH6wh{CV$}1rT3W-4A{^n15DdcmMf!fBfBVch#R2pI3hQhkr=_?0dd` z{>$cnK2`kr=ip$KemHzTZq~0$KZwhp?VoRUar8N3fAt4hJ^sNryXRlB=|kn0I4wS# zPQ}zuTmSX-U-!-9*I5nM;$MEp-(=r^wku1%Y{<8p_D{e2y7(W?-Ot;;{`vZwAGiOT zkNuTB_VuklTgT#uJ@#4L&-dD&)t`O(S3mQ^`#)Rr+w1J7BmVQt@0+9E_VN7d-yT*h z__zQ5ldx%DxbD7g(BE`F&2cz3{jWc_0xa&g7r-~?+;128S@h?9zm77nSh41R-Ff>j zIq+Xs4~OTk*-yXvuK25m=JSzn*AgfD=l=0IUw^!Wzb^Fa-#=SPyq)^#;C$Zl+kN)A zEdKO!c)ndc`Lk{O>63rc9r}6S-*6}VwHNW-J%1<|f z&+q?++x7KK$LD``Wq%g&^>;tJa{kJ@{-!(nv&8?GSNXRq@#6-5v&la@(LZnf{P}Cw z`J1c#^Pa!vO#W*=_tUBL^#sI)lq7K<I`)i3bZ=SKeZJp=CJKfmhn6#9JW z=g;RV`tfo2?Xv#qPtWR~UrwMd)#ERcKiD+&9QXG)`pzG}x&QpL-`KmG2Xee1p`IBZ}<|N1oex|lv5r@sD6`|6K=yZ*xuyXWf{ zZL{b*5cIyoqQ0!@=id0wetuj0i=Wo~^JSm!`TFVq53BhvTfOhU3?={3?}kvn8$x|O zqrd+Bxlev`8~NFt^XIpQAFlErhM2z_LJi~39t7XqRDZtLem8`Qhi}G!Ur)Q=4WY0n zem8`|J>_>psNW5tJ{6JwzYn4Qi|>CbSN-Gse?W=sFW1z*t)`{_ar&R+J<3=4fFGY) zSb)D#Tl??-N^R{g73Lmz-(M-r{rTs^f2jVq|JQE|d;jA9sj&C2T$}r;*7uu#^Ha$i z{urgKKla|5N$beym5PfBZu+@|*AY zkA8e!X7&Bc7ftmrwQ-M0dK~?68T);W-~8~Mzxd5R9OEaT*r@N_>!wGo@gG+Hn11s@ z{5c4}`DU44R_@zne)r8Xf4-i_|KRjP)inLve|asxZt-ucuYYG~0FsEmPk;H@$iMZQ ze;7_Z=0fAIe|-J)n}6{2l`^a2?@zz^dqX^q*p%V>-~6Mf38(S@uIpNQ+qi+S<5ad~ zS+cCuEsEMeF9n)|tQ?Xe=(VTTg%3US(gFmv%hgiehqB~G@*&3n2{5L5p=1h3-xhdw=T5nIG}1U&YX#zF z9w#5CqU7$_>PQ@W0Z2{N&zTqtN9iF4XlnWHBKR-#2HLVv0PVzk%v0oIfe zx(SWwP+)Bx>5YpIXe3LUi!F%uHH>N)mg!2gh6lxZ0M^l}$dE|}n^O;gb~D4nzXh#~ z!Yedlld?&T)duIS6|$OJN^d2B74TGDndm9j@kY)Q?nvFr!^R=vr*wkO7`TAX%Y*5# zMiY@nI@Q5%M=P}w=u?$e;I^DFWG*3^ZJU0GtzDU4X0!EreYLv7xrFR0FBY>^Q51o-sFXV0OQQ4s|@Vi>X&bJ2*gc@8ht%0^yHY|{iH`c}^2 z0-=rF^$}gdpiq%LtkU3R5KDLpMyYZuj2Oos0qWawg~p5! zd#tulPv!3KVI+B=vj{`o`2U0>g29)=I(TE1&Q%DPyo0P*DGP4rL6XZ`p;D<6A;Yjx zJ|euM$0~d6Zpt|wRgnO$2P;BST*I!h=OU57L1e+0pFt3;!Xh9-H`w4YyemYfYgoVE z+nVy7adDr%-9^=zW~yz_?9tdTK5M#D5-ih^`vJCU>m6W=-S2ShH&Q*( zq{H7Q0(k;F-{n=;?9nkothY*@O9lbHDg|>!A27`x{>nSCfPa7z-?~3JoXG-_3mV4X lh*$nOX(Me1JZQn*QI10n{&k$>XAv4lsklGxtgmu@^*@~c&Da0{ literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/.doctrees/environment.pickle b/doc/LectureNotes/_build/.doctrees/environment.pickle index 09789998a43133652b4221789c7007aaf23756b5..80d37cae602c4169bded2393ec6c52f13709aa05 100644 GIT binary patch literal 200875 zcmeFa37lL}jCRYT4N101usylceP_B`y}57qNQ3PJ zvVavjF@b?Vcw~Lq9|Q;lLXt1MBrhZoUUqnp0D(Z3m%QXl9wg+2!26#%cd2{p_ROu) zv_2Al{{5_(>09^oIp=@s)TvXas$Mn!O}E@K=N9^}v)XGEOSNl*Zf&B}tkV*itEZlu>hH{T8jY!QoxVan-)g#Uq12q}oEdu5bDQ4K*?P0()=pQQ z{Lp3B$%F3r&{^@*J>xpf8vTv;hR(S8R=eq*tG8TlXk?VWYiQ6X=uLGNc+I?^d*}w} zf=s?%8!L@Zb(Z-e27fO&#t%Z77S|`-X0udqJt5+vic=eJJL4|oT;7-*C!KgBUTd=A z5_3XdQ=PtIt6CXp72PU6UB#b{jMnQ{g3ne*4MysXR;gZN@+&;(B3~RCb($kB_Zrl_ z=92itY86YKMI;6X2d6sAD^9yc?b@wY@b2mwbSA!}RBO4-F(;2NUzo2ro>$64($P|_ z;5Lix(UEquGSyjIY_%HR!J(n*BtIFfH=&T_<#uBduZQh!nd;1kB%|)s_0Hmaz2flu z#cl1*(uUJ2jx{bP5YSo*Q{3VYDUy`p^8;#;5IPnI@OD#|zEY&j` z0BLK8*uOSNze13*R_WDiC)|q0pu?QgbGt z-l@*v3-zmR(=Aw|lh%WdRcyLrhqnd%`dSbQhhDb5=bw?U7j*(IgYROMM-&xo8+!2{s0T@)dmL8yswD<)E5}&W4&r6=yc0C{6sq5{| zdSNeKz1_^al~V1>h}Rw)D_x^+T~KRR$&{b(Y-~6+x8jXBg#sB{%Y(Fyk-X;-S+Ct_ zG+oadxyqf*n|cx=R42U_dRNsc!2q4WZc8n)=6jAb8kG|CbKGe;))7*s2OD&11>oW^9cG+u;B&)c(W&u)AqWUAE1>rsfJh%ub;%6jB?v9Tu-dM)&=c|_z-QEL(ziX|Sx*Wd zacj;f?2|aFd7|%=h)dA9>a~$E7i8c<3iV3GX;#t0(2EK4(%2*r^V*{x=(fpcKyNL_ zyHY86El9dj&<4{Z9&}U%D?}B&qEu-?#q-Ft(U*mVqxpLGnwuA7Mx08eesu(HuHF>3 z57DxDu+bw_A;N3*HWX1W?cOiuJ4Li&67dsp_K9)bJghWquDD$-~LJq{mIc zC*0m03H%jsoCos(kDDS=K2nkqbe2{e_(W)Lyi|jR7BvcE;*%-vWm1C72^ZAv%=g?@Ta0%JAlLW~zf~WH8}fU0I1Ern2tHdVAgjS(mj=oq zk3%qvk%Wc|INr_*|Ife@;p6;IWcj8#>-p0`d^#uw0scE2=Fq3eLrfLdcQ*P2RIRzi z{lx>t)#r+9iffDOitCFTiW`f2irb2NpD*saUcA5fK=EMlQ1QXy;o?h*4;5cpJW@P) zy?6=@9>)Kti;on~K3_anJYRgY_*n6quNPl&z4%1&$>LMPcN9m^;9H7LakQ8(7CH;B zxr|eB?D^t&vDjHBYiz`GD~JWir+jpf9}HN7PN7<_mB{!93(b0?P`_Hkr!8lEq=+#Z zeisI66-pC>@RJq(Q+jUC@Z7iXhyYu>Oo2a{ro{+-v-o=XweUmq7vD`6;K{2cm?!N2 zR&rpAMrf2Q!S}uqe?0Ys{mkBh=kA&swq7%JajN(%ee{(2(Y^9Vubt{F;a=hgA4`0E zY1qP7mq+<2^;|M#>UzR`be6jfLx?DD6I zZ*6y$@h~?sRwth*VzGrDe-E7HCH~F28v-rBXov_Bgie;m2gOJ8TjX$|)XVf!eAJh( z7hHR^QqMy#eP`f8;i2hCTXGr*W#GsixXleI{cX@`l<+N=(C94MgdyX6j)!QNn2%oA ztWOnxqO<6DJ>M1)v}jj+$2oXse7^8A1*ox3{J!I3QHh&UTA~=@0xn` zRPp_A`V>Hu-S{6YCiRiy;7>3V92te3B4%{0JYojVoqGO}uj9Y#*Pm}qjTV0%@w)h? z_jgu$EvH4oBQ6u;Yd~`;h8(9dE`8{Bj$U*pO72ywK4x7CU$d?voU<;vo>N7*03BX- z^Tk@}X#_ALRyYG^?KG_;m2nr5n$O7d3M0$&MW=zzuv_{@$QpdSC;j8S=^yWlf4s@3 zO_6rB^hyW}_Yspe_?rFF$8P7Ilg)Y+qK#AFgm!rz)B3Sr_3|fi;T0EUb0L@4R0kj_+KFxQZfVfFwO| zI~$K<*cO3^Qz^A3A#efR67tUY1rJDc@C7RZ40m<;JOOUlK7nrdxeTw{S$EuZ8)3{D zs3gXu``W3|&Z4lx6n_quUS5LfEP9)G6m}hcv?6*Wbs~PYCVHm!5^k~~Y7*}+{CG?B zI54n41Ki+FwLzc?Zje(O1UlgcJJbe&@pFTFqXyG-18zGMwGH?UIs`Y^t2PMinj74w zHV7=78yr#_1Xjuo9*P>M_R39;MNI-W14HBnr=kX-DFr6UErwHC#GyH#(jtz{rIZ$N za2^j^AX*%0VoEkud>4MJx-ADISZApiYl9)Jv#>mBi}0^K+UeuTER7^n#dma8&^(~* zT-%EfK_o8l_QEJ}&{^4N)-n0;9>(nW7|r;nI=e6^?7=G|{-bAo60yIZ<#1-iX}Zpo z=XF+acz|yeW0jaf;OqO45-7rFg5*^3fi82rBE}Y{vtYuh!1eP0jjt}lPhw2IAP7u# z<|3Cgb?&uO6hf98q#uMVtNeBlE|?@@zJLh};%sV*P_x|f+b%>phCC!@6yf^|n+O## zVUs_b->Mg!N%@n-;**iFYHR9T@G8RG;8z4r^}K^=8PZE4{8`9yO5vjwlP^i-UK?L6sk(t z4K=bN__mQzT(e>h=t`=y+13gxb;?vc5=%avJp9 zIqKXi`7@fR`pJ&xro@A#Ri{SDGEbxmBXeDZ`CX%wzcM*>U9?;7|2CB_g$%S|NL<^pjmj4p(iGS$H z>gb7-3J)LqFN&0;_`>kX67iy+cf@EyREZ#S8OR6=MgB2-$kSYKg;_7AP*c)-{tP%8 zf)0motq@;@1VgP=8Y@wbd11SDrH14~M48#))Z0|~|HvXP60f(Bh33zLagSxo(+b1X z&QQzz={TCZ(x*P-O*fpMhc7U9NW7!F`g8Z-S@CtnPACOyI!J*goBDb~Qo!#ba|0qB z7LA@D-xV1$E1I$h7`I`0ZzGul*_bK#p%M5CbaJUHtrhC1A~X??My{3$)Fq>LSynNa zAe~85`ce&3OMFFuF}Dz@a#|GtQ^Av!f;g6I^39T1SV>^P&oL~(%^?j}Zzi6v67OGa zBF9u4rx6ijdml2}rB~t=rxLP2nX%Bnt`KPvVco%i6g;EsS@=70XTk4SEkJlP0wJ5N z5hQdmVoMKs0g0ED!r_3@ZNcl5Zwr6_p5ph0zrRp?eeiqm6*N`P2YmH+E}4#K!B8fp zHHVN4ChAk2m)#)MC@mV%JY`DLPpd|hQdS|gf&)N1>PFNbRAYBaPKr%bFSth9!U9Zw=WS zt({;=tvOO36|)PGPz&jCUzBJ?Uxg)4bh+r!h*K6!(!2B-O{wAR+afK9v>_`o`hK^wcyc=7n!hV z*qF3=ooCRS7{`i@)G}JySVe0U;atZ;=pNS{r@O`MZR+JOAg&7LaTZ26r{N+wdE#25 zADMIvS39j|`Yim{#KKgwX7PuE=qeRNoBczt7`*4+hn~9Yndka?l(uafu*l4g*Yn3|aY%ebpbAtc&_+yh8i&Ha1v-cLIdpiuZe2yn zpH|2%2yD^!K)UFQ@XR-FP9<-9_{7B%c9`zj_E1O}dL*8SOR%wZYZ}XPlr z-U!#=*4;(A)2(6oeFi98k+Z7z9o_}$u3^;WP~0| zezM+1Nri7@(Zlh2O9DVxVC-R}aOoL;BVl!_-eO~vzLQL%KWY;6BElH`V9=wXt$)W8 zwH-TUO$!?X6{0#Q{^(~jWKELt2qbRy?6a24IRELhDifu*;^H&SLCQMx(^o~*sclT8 z!A9FF_DiqF+Y&eN?znxs{AEc#h(5cEGXxS-7vj8P&y#V|irLV+^q=y+D#CNZ@VL1Z z(~_@Sw^r~T$6}fgpFok_!%k~E`8MK^9>r*p!1R4s^B1KvUccM}{Wk*;Vs8>Rz$>z) ztw%k7G`@WF>xyVo*)&dIP6w~9*VvCC#=ISvG5OA zrC}h}Z=@jxy+_tc8P!YN&$vfN>|PYH3`SH$=_M#*+=6=}rI5pPChDbvMU^skvt1Kz zQjEVCU1_o!@+o~WN;iF*+V(_k+cfOS?|2x#-Tqwzmc5&;pDovqDx{W(2Bz9!Y|3#i z%PD28=Zma$6kv1dBUL&e%tBD+Aqy5on>-WYTpg;Wf=IS=>!1~p@FQw2l?)R-Q6%g~ zyZl^A9|uu1v*4FnB6-mi(Voa;`Gt105K!>b6Hvb#uA|5$6!|tWp`c0vQAi*{%vwFD z2Q6>96$z2}m%^X-w5R$@Od<`K$27}{P2{mb10}!%ol2dWsgG9 ziRNIjk6a*5>eO zG_`FxO?*lz(lE`nA!sHh&*-%^59<)esEC#(lgoIP^-%uA0PKYsDV zrAsfF3Rzeez3ne3VST!a+3%Sn=T1F(_{1kw@~X0 z=tr=`C#o zw(broSWiG=e`)9yXJAUTfm0~OxboyPZ3>-5HMQ$SL%G!anRX5N1QZof*N9r&Z6OIt zo?ImPM9hUD2wBtcJD))Eqg8)`;$bY%A-O(I$?0dFfSYiyQmP0gx6eF*UP4itN2&Mc zo}n0k{(3I@q9;(2iUd9tB|a0C~;PFu`_601gA z$eZ&6QS}NhkMguq6J|_lEuUu8235`eno?&|^lHZRWUqA zkd&STHL~1Yqz6~)%_~G~cz*H~s&A*#T-MXZ=v({;k&K;NpV~U*i1%-cnl;gZFgBss z5SeDK&^`6i=7+>0jcB_VCgvyZr~vI9odvvDiggZNxVNB$;vr{vPRpmhjNXVkGWXQY z^kLPxg5(st1zJnTZ`cmt_vJNIbzO1Auo-3(%SYsKauqszsWv7y6~u}V0-nSw5Y}xL z%*7U!JI^CFf}}3`d6@ENll4mvmYpqmRDFrGXua)C1p=%NzDD(qD}zUp%Mof?A3R9) zZXx55S~`n@Rdcqibpe4I#6uBCsREbQ_H{$=qqv$iN6rRm(1rILw!d}Tz26cIILkyU zKPp6vdGI>dqQ`5*W6Gw6F%*SY!Kw@~Aie`@l}dOOH0rxXSyF_1EqU2;MIPHIMo^P4 z)=gmA(kQr^mKWfzx;$P6xDdJC@tQ+Yir?yEkOr&p*xs>_hWQFI ztewS_R6{Hd3+gPQ`WqIB&ZihG{6MLma zsEv8Cu0DeG^1u=JZ6a-L$Tu3C>ZQ0NzO){E!z$6Hn_|||)9F=%1_&S9^JyHNfL;tsDU3AmNJ@Cc3I?b_3A=om|v zg^?CU3BSZ6tS9KKLoYzLbSn)6LbZZl1TrPMT4!MO&!9Vs03do? za3?6Qi$M+h4&0iJ?iV)O7&Y_1F<3tC%-J0^TOKtN$@g5 zh?Wo^6EZ)&J=FG^L)bSqR4ic+36@2JS0s&vborfC;XA>D=q)SyB1|a4-7)^YojTTl zBZaSoS+S+Y3K6J?NPI4gbQKLT@m8J1+#?VxAagHFHEfi=q9W#*f(VVJ!CX|D!aR+D zgt|!r!qmB>erGLzjeYBf+Qg4kPx3qk$(}MH|A9wy9Hn8f^>^Ym;3<5!+Xk}Y`LM|bL83sj5P$H) zo=w{I6Af%kMQ*~Sd{GOPNC7!9s5fe|QTm=j9ThdS{f0s@iQP4#4X-I9G8Cx{iNsp* z*#CUQpIl9q$H*@RATWu*D|nNr!VtA>!E<%nTk)~*W&Q#R(-C)KLnz15QQCzS5j^(* zGB347EtU%wMZoHp?S{lz0YQW}A}0T06F~C^l4~Y!|T+ZA0_7WcmA~Fxn1szAs7x(gv`=A<(9-kf)Q85wDT< zrqTAA2BiF7^-d>;+RJKRA*b1XG%G;u*H61z*|O5Z@4s-sbOzjo@ADH=$il zSYRvB&=W&wMYvmQf~$c-^2N#GYr?O(P5P=a%*~yvE+vTljfmkp*aYeCz#{D`0AA{>aroB_IhuXt(bn00veJ%3z&>PH8 z4c{7Uvfv1MlARN5D~leMXkLSO8P9^#7eZ<{Tw!=#SQ!(1%%v!3zbWzU zWoN?SDKW9(Zx{`~iJUHdzAo_=$4FDdbCvI>U3+*T$rg44wX^78f4nI)b)3Z$7829+W~08PxxvOl*9@bVby_p;Qz4x{hiKbek)v z=fKRFwz<>3EOgiBaS{RQq$v#JV+X7tO@8(2)j^hsQm8|S5Qosx8-k0YH^NeO>J3Yq zV|j@Na{GKfLJLz;Z?NRH#sm!-3g~@m9eaPd@RiZZN4bMxtg{^bM8xYO*C;|EMbH!< zE;TvENph}*J{Ph~St~c1C@T9-9qByrRQ?-6)S+HUP zcu?IaW*OLUOm)U1L7{QGvk0?dDtBQp0;AtOb?V6fxbiQ}wfBsL9bpfD_PT}NA$JbZ z?v1beqx-{l`?%ek|Lsqfho9}|&))LXg0F|49pKO2dj0yJho9Z&fA;sQ?+ib?pFjJ7 zPkww$_}K&e+1q~T*;eQ~1SfC*?)5K7eV#x2-e>2=yovbqhZekKuH;MjvlaKQkev#D zxbnw;v%GoUEw|vW%IXIn`RLu{+k(Fyf2{TU<-Xvr{K1PC%Ikx_#zwEay}Tm$Yy5pb zxTd^3_^W)nbhh{oL9l%0_zE1cfnr=*Evn@yn^=59XNkX60{MK}QOkwf=ru^A%q6Gt zMr`23F5B{AkbD7q-}uKe{;`sOtl}T5`Ntamv6g?V;~yLN$436KiGOV2AGeDiFcE*b z8D-6n;-m7*@eh4@XBpPEC>z6p#?%Yol42*?58*d`3{5-pd>NSG6ZnYw{bGu7uxk}n zW%TEKo-3byI){zHBId#1X166Prext%=l7r4M#IszgVr|g@TjHP=DQsF5c@s`ckiJO zt4M)T5`;dbuzl#79lb$aqFSPp5X5MYHW6Ly7^PiMal(6_1Ih3p7%>AN!hYMm)VMb4 z5Aqm;Y451pq!tk|(bd5S?~kBo@LAiQLris&by9BmKPT|>?EAKquj1!$?nR=6Q)x63z=H#ABsr z=CKYIw7v3$G$sAp3U09WMWUpasY)7tJ*!|2baYXDeD?iw`1!4PPSc%fg7oq_DM;V) zB2g(#`k<5YPy0WA7C+CfUt0bz_&NMyalp<60F1`%&H|DD6zRn><$gq_ zlxhjQLE0mReAax?0vRp;c;UrO=c>QE63ZA!N#bl^EYDIQ(uaw_yvsQrl3%_Nd78lz$sv&9VwUv3CA3d;;-) zkGS4^kxmEUGu2S{RPQR@bPdZN2dVO3;vdLZ{sexKRz8WJ_?kcAAD`wQpXDE);~#%6 zehlNF&hi)WYxytm5BR3!%nW?5md=Jd%g30-;Ye%1eEyU85)(e>C-|iN$qan1Ia41O zC*gHfY-$VUbpCu(jpF3om_{kdF$1SNyBtD?9g4_!(ws(ylm%)21O8cJg4o!#~F}?6=BO=J0|shszQiQvP5D4iEWb zs(+5>fb}qTC17=aoWMEKY@(t>3{6$k=vo)VLWy+}JAP4~n(#t5M2RIIF_!$+gyfVo zm_hRX;2;hwC>h|Lgb@A;cFNaji#*PF!r3q}XPf;smZ_#KQ+(W@^u`R5Jb1$2LqnLM zz+==I#U?|X_<6bLqDEifcZmuRsJH^w7(4hqF5QihVu_#CmbmOkA#)NaQdVOI+1Cmb zvA;q{d8#QY!s0TeH(_31r_E~|9ZIasz~N#FU+EOOM1PS!XI|cVgS=1@X9ixji%UL4 z6oFoh-BTy)O454uJX&wEWS=sYY*j)s%7)A!*^%>7$=iSkbn+0B!U3xDBVSFy zV)D)n3w3cQCct?C)wsN~K##TX*Tz~{n9u^HLuSyzUB|-1sfCArw1yi?+~!1y&T|Rx z8HtUs*m0e@$vD=%{xVkH!Ueh=-5>ne3Aa0axY%Sok?#?S7S4N6I)XC^ zG~q9cxjId#%VI7}lhCr5KhjjLEM{Re6)B5Z1cm8k5n)p}To#cmg@7JkYU zY?MWuKts7$=qS@bDwZ_LG#K$%K`vQTZk5TsiK?wKxdTzLRi-W>s%^rP@voT!T1FA9EcY!&U0 zqXQJ+A{-o-)F^g&nVDG}Rw{ODCQ?i(i7~mymH(LF5gDX=6DBcp28qhW5GP~kK@lT% zVvMz$*dHM>e|=n-FLGi?dQp&9{sR7CE9ywh^OtYe{&JsEiq@E-B`B6R<3}n2| zv5#~%<*tH9yX4`l0ZR6{HqJj6cj!$?0N$zsSl4Dr0kFbqzj<9{#}VYvXv00WFyeq7 zY!_+PAvMjssiG9o0^dv)Mv_rX-SZxf)A7%ta>_zp#qA>+91hN9@eL)9&ZhvAZvo=*R$Z z76c!Z=r8@TCE;8zn&QWOM8of=FbXOR*cb@&yj+ja)peb&X zg+dS~bOWLd{c6C9JxGA$ke>9ti6`90f#UHV{uQ5Yn zESe{Fa>gTfqxQis32JRk3u7tlWo@y{dMPObMlgU_j$ z^Def6)0pE_1r&n{F|U3fDX+=Sb^-bUJDibrz^;u+FvfG{?lGn65gG187Kt!Txz|)no z!xYQL1X8T$*!3}+HjukEWV5lc(sS(^%SH$Hk!&%0ND1uUrOmP8QQl!nB54mgoy6xN z8mZW?8IXv$m|>(coed6LqO+)JGq?zB#6mOLamBf}bP4%ooWPe7^60(FHuwc? zII`NHofD^OlO$m%WS43-mUo0CFwKHZXI?8o(tLF&`-_2!e#A}>vJ)yWtem%J^sVe#3J6a*A#R?XLKAcg7Ttd4k9rn=aELzEc#OWJD6iu|D*&U$U< z$rlsqEGGp7zMS-{FQ+XPpV~r9$vhUR=5axrX~jIwnv&?bc|1TvZD1W|#RV~!5Kcjv z)(JW)!9s~<5KWWWP<19wLZH*sVmR!;K{&7saS4v?v5dA$GTM$8 z&KSr}X#LffQL>E1s%5mbc~&f=X-XoqWf(7(Ek1!G?{H^%vdB~VoS}QWwhURJ>&wxx zd(49bMV|`A4`}nCK=J*8#7#*BaLQ&^px}enC6^=OcEh5h$}q$Rg|@g!}bO8PhzoS0?DAJ&Ch>Xn^y(aUo<5V^{`)H%b4v# zfd?Y|ak4f!;YmvM;_A_0^|N5%SeXhAuf(%hzB^_JH$aCi;tSd;%4!i0L>9p!+9aY4 z5rYNNf*p$3HKpH|wg&e(ZKf5|_>3uuo}0!Uk!hedjIK_cW+h;z#tib}#l4y@-4TIY zii2OGOV<31hs8$lP(Yt8COxk+Qb38IK-bSd6Bi_*+Zh{+>i!4u9~*e zGD6ikkb_vEY{=cove8Tc$JGhhXx$%qJf1b+r2AmCd0tw~az&e81>~YBiKq*^Y$vlF zv(SDbixPP43RVmzoJyOn=b#x=-Qxq2v$_Bbpz_l=nU4S$BxIR_FdXAa39bXEh}*AbG#Nzyis2S zZ?-pq11Y1I!31_h?Tokq*9(UN}tviDJx2=bK=GavEr73 zP|BkHr?h!d5c-5EiJl|0oe&ZLp&N+7cIMAcSbH6_t=fOh~wKVk^?t_M(4 z)f$2%v9&OcaOSrd;vGGMxL=BRJjtsv*fReT#wkl&cWHB|bmFb1BzlhV{*&z{KyK1y zve>8A!tueJdnW<_;Nu8Jc?M1+(Nxny^Z`{SZ`DP?i1rp=TB-W5|4JqK?sY9d8m^(wZ~rU$p_ zO&G8@YYUbYuys`VNSxWkSz2hDvfA`UZFUr>UT;dG=TK!$;Y@o}7Q^;S+CpZ9ZCN16Pp(4y~=hle@U+CAeAB$5_kuwoc3 zI`XoV0f~rnBA~Rsd}IQ z_)APlMDYgWd_(a@kNo9k%zCWR5^BoBd@*)}72NvRSlmRWYsfZpLR(K+d*c?~;v{oP z`_`CC$%sJfM=k2UKaAy+A3gPM|(P#-f;Wo?170<|iaPjV!| zld}3cuFZ-9Pr;N#&*52rmX4rC9D;iXP>n`q(X@{+-mkhfVyIrw7A`AP8*+3&HpL-0 zu7tTu?EIWRoU)YK(Pl^i?7At5o&&a1046rn(8@UND&j4l2Pwg0ofca``OKwQgre~t z!}?xr6=a2VC&MbqfQogoZB?w>lt_f+u~GBW)=A&3&7uPIJ55Ps2HH62Tpv`d^C{dH z_>TER;MuJaWB5sJ>9S(DA*@jMMBWZ*+cMqM9p&rh52q}Seq5U&1+hOAB)Z0Df#rvIv~!mOAc3^7eF(-moY zIAe&3Y(0q?Zt{!4o)#v5MVo5{_%EB1h`Q=OvhB?Fg#J)uAxGr^&=LV4ih}4+>H?Pc zJo0ih#;K&J-j{?6->}1A!S_RQUXcln9-!n#mBXoSB$1$O5$c3&6&id zcsFb`#st}DUeH#Wfzc!vmyL`jB}35BW?nIx>!u`nZZvmBp5};ucr+E>H(gXBsi}e) zTQl76)fP7^+;>JkBCIDur9H8$!8FLmMhRV>C>fB5xZs?i z0f~qUUhp&^5pnS<(?tw_8CzVDar2h3Q!l=hb1~(mSX}0Q@PD)|CA}Yzh^gz?Ytq)S z|5^K66%+rGAaN6C;WKKrliGsSylMID%!w2=cM^+m3)1Gk>$SgKQTG~C5>YQ&DM-xv za@_*4-!U%~^LO6iJQDHZ7khX6MZ zXYV7YkK;Q7wZ*H#3pj8Nw-$H1{B-uovyD8jtllvEK#9?D zWi_u$8wUCv+M;CzdVTI{z?+>Hyd~oC1;Z&*tDn*4M?vc+O-UrtG6-U$IG6(_0}>Gz z|6m%n`EjtgAnxYH!5SB+$D-pcVRZbL+Q_9FBMF`w9dApEj=!M&t%}KgPLME&j*S-! zH$FUxjkS%6Q^WRIT5NDC6|6@&t$3ENdo%9-3s%fdpsZ*dw{R6B4u#tWhe+9h!_Z$Z zN{gQ7YO|!kaf={f0Eg*`+#4w-!{y}I!GdE3>8t{b*m=iG9O~P>8Kcp!EqX@#2O5+t zO>hXe3=U;9((t%jn<)j4ZKfn5Uw9`&I@>FGtBzQsI5-mHW^nUZy#J&;XQ<9!p zj}mezQ`Y~c&69%MubGnQIdc8SOJifMxU1gRkBDE-;*@H)i9N3#l~rNsKXGyU_UT^R z5xvBy{x5Cuv!c2qR|xpGWqhlGe>>dgDv#MI^W6Wb&7cDDUz(EWImD|d9In=pm%!=E zDfg44JZIQeuk6)yWVHx@1y4cosfblW6(Q`1hn)6z~g?Qc~q?TR4LRmHPk8oiPi|EM0s5n7IW2K6y_{?}`Zno+@> zRsMn?^>hbysjigISe%y4_#SOm6s>=^DT%0Oy_SKS?K$eoQ*KQx7M*mRRvT4t33!yp z4A1+t1-X`b&6ZPpYhx0sShLTL~+Mu8{y zUjq^m7c&fx#{PHR5$l+r(c?pgac3$b26;8I)1?jD&qZwwXYKjxk=_e3d(4{>&7>rX z&TI3d7|j_$;wHM=yB;ff?ch2dqBr8OBacDEW!N|T$^IIf+DEi;$ZBdkb51A$-xGl4XWIXcYyNPjipXCG&mXh5 zlmzmJwOLfG?KcF8o9O!Qro8a6BNs2DTE&M^oCO~rl;aK}<2#Jo-)bu*D{k9G{y6V6 zTXx91z%M>%%kDq*ptHZ$=1_s{FHA{9-Sf{G`Pp{=Tf5*Jh3|1}Gqh)1SFP?<+`g?F zuF+P*IHti;_?zb3GUpchPr96Jxi*^$xJyh)^c>uc$8beeJG|-mRH;@%*>b^6oZ{cT z8AEwMTfnScbQ3OL@i`Qu_Bc3188LAvO}cjj!xi`I zwCc2>Pt=`L!LV3?MLi)d=BQ2^iQgbCHi1`Yt17Dryd>udS%aH$>1HLnMdu4UqN1Gk zFN)Q8U)E`Y_xWkH>^eV)={Y0&WTVp1LO(HC} zP9NVJ#S8HPWQMkEZXIonXEirm+seEOn*y(PsjxSS4`jEKvcP;@n=i$fUL#1{#0c(? zw9CM9#vSZCsMW9Xr3LW-T)-!$Ro21%>20+L?|-egJ*8e zSpT86z*(`jat?DG)P;!Pfh$Fr;TWDl{3nHdzo*Tcg6GFfNhI+!aOu&g!0yC=M8rj} zMuppu_vd0i+U_K7+N5dz0NsRgJ3mvo48etoiNQGG^__%Tbvp^CETIg=wV# zIc-i9ZCj=!q7HMrDT%1tGUl_;Z4F37TyQap0f|T#MbouN;sTeZ58vE^qx^}Q=T=8C zwelmJgE$RPT+ed}89jVVnMey$t+P&TQvAUl?8G&AgsN-d;A@ZO(*tyKn#vD^HA@w3vq|qpq_WhSrI)7FES0psRp~Ngg2YV>S?@ejv(DoN*@=>SmBx)E zXz_St#@6h`UZ<^yjOy=DIAYg*erfc;ellTXwh~_UrFpgIwK-ED`YuxvQBVGMMtQb_ z%Y{dsain#|&LDf^^24y>E7J> z)fx>Rd}F~u>sXQYpwTI#$d;UOCtOr?^G)=zDS5op%mzUQ_Mf%2nHAWhK{*sjZ9{51 zyr;p=`$CJ^T7`rbp*C_bvH5wFgMlTa`O7b9bFbLKKbVq;`s&}Al8E9jw#XZbzh>~- z#vWt&MeI;VV1)Ft>*37kSiw#5Asbcy+S!?)De+BbMGjjw!40k632r1`o>F3Sw>Be+ zeQXmXZl15OX{E-&8M0R3sZkRzR>e6{=c92l4GqnA8LUUNb(GZu*kVlwveO0lE1Akoz+ z%>Leu!>4h~0k(Ke;LQ4xs5u#s>uTu?kxNgv(bWpJ+icdG)-lXZt&^$e+TS28M)vL6 zO3aGv;an+@)gEJ6<)U1OYJ0M%*d*q)!YyJk?9;r+4`?&4p#S}*BqA>|#RfFnQ>?)h zGl|#dh?Siq1xNJVcz@P?nGNCBw3U(75C&5WAzrW}617gj5w0MPd`hPOSG74+kpE>< z5%GdT|E0DfvZ9VtE__L7z93R;I8&Y> zMjQb-($;AEhEq#JzM##f0{Q1mNhBdR81JKyfd?D|5)l_O%nwZ05Qb0T-n0^y(j~+5 zHyVmNi!ZfYw}DU{8$7){nhgbm61Fafulmp8b~&q**=#qi>(#_$IETYzgdQTZ71rv< zx}L8FOmKx7!T}4rp2Ii&XR;?tDLq)HErep!t4&Gt+?;lXHX%kRkzkik;p|q8sPP_~ z!eMO{Wc6S>Q%pfVHZ!d_u`lh$tb^JtDnQ?7O5*<$pcA2rk9*uJqygRKJqCJITLm`) zbRt0UahH2^%0*iv+AJzSKVeFu=Rj|J`6Gz`5Q@IW7+=9&0V(N&r_LF z!NpBn{zA!xW~r7hH4soz?zCQ`U^Kk_r2oRPBRgXbru=ZY5dRn2D5jevDIs+s{(Ra( z{GV%ot73kCCP>`G1k}FMR4iL)=YyrHWA*TUXUaYut2di&g%2SLk4KNGy<sj!Dw7#q!%-6LQ<8@wJzN~m{%(a+5(d8O>oSEVCCxMo7F6J3+jug;N3lcZc zciwgxOZ#E+4QCe9;$=D>(>G;Mp4L`DR#0vi`{|-BlFVr;GHG6~rp=gw%@tD;QHLrr zytD1~Ha?D>%QW}}H5}BZXp2&Okn7%z!F#i|fLX!Yl)K6t+CjYq^(w)k+@;by;TyG? zQh5kSgfZ^eSiaqP2E!q}CwK$D1s-&HXBC1Rj zKg=p+HjiJ@R%2H4ID-P~P!GcCvL0X|fgWtu1MRtEJ+N;M^njM39%2@i;-){KEr()J z?=vNlv?zn=Q8dHi!NPz<#6^$7uyvgE%46C?t_Wj{I=pvj!?yOf+6vBUYwL5I1_N() zm!UnSSm&>``B7}ntWac2Shb;7v#aB|@j!0u=9c9ab1RaYYk_bHl91b;Ai1dw zP?B5nHYxQS%eA>z>}H86iJsfdTI${7CFtP`<1?ly}G9{52D)TAVQ3qE{Ac~;yLE38@higN(R*cvywB^f+*hW-Z z=daM{4*t?_^;(j)4E1ttjug-y6(nxrlxxN5TAsG)U}u{c9^()wPg(WPX$zWF^(&EN z3i+WSFZcSF>bRxm-4HI5s()sc8Pf?yXzgg<;TOd zygeIdXA(o=rLN^Ym9~~Qr2VamVGRfpH!(Q6?WBvL4oPTQAh2rFsJAnHQ|{(3(^f%x zH&+zjxji=~af&;G$q-Vm4qlcPL7mfPOF?GXltk3o9%gW7JA%6H7;br~S8$@6xUJIf zBIjIO64|^GkEf<@$`DRy3z{85y2B;pG=X6h1}{s?OMBXEDG)YHN%S1TO&8sK8%vfb zR+zR6PScLTdz-e1S;5#LkeP_6(nwA@UfjM zM(hbU-@-mMoZiK0aFOJ6^4P*6{*I4fSzltD7H;ZMB-q)GJ?&KQ;&YE<<(PZkh!im| z!fooV^fihQ6YxoE5Z?3oMk3eL{V&DoZo z)Yf}eTe^dW26|_Z`0ObR%9Q{jo}KC8{Qg8ZZ@iKrV-n39N`3EST{q%%2w+-;U7f`ihrQ3hO8*w$tW_nBC-UxbYxPgW(#g*eA1%J-_>SKLFji(Nkl&8w;ANw zjxP5fMLn80Fsp=97wh9VY0+&CSYxFo_82RD-Ni`}YUzw24F>+7wN;Z9`2D$2Up5<+ z9)WB)1OuXB>pRx&<<1<67Bh#G`1MQL3@hgF52hq~ZVq>zETObB0X(X7L+!+JGBdVj zh;Q56s|lo)8zX)bXyOK;klz@ZDa)Okw0Tp|TyILE=VGzJo7Xl z5plr_Z3ZMFE_Rw`+=vUTou0e7Yo~|Klxip#q|GPpXww<69!BtkqD$;z7_*Kvn{?G5 zg+o=^kaA(NRm53ysn<`J$HH~i*J@i-de;wDC&OM^X= zY6KF0#6IaKv_;IQ*v_(WkE7rubUU}EMUOwG&4!}sA2uZsb+orLShF2H+NV)X-E85+ zdz|Y{nOtH1el8k^l5*#0VAxSl#MgY6LH($w^y+($gs!F9T{VHE#gZPBu#xE@8hbf%TRt}y00EnJT+EwA31 zw!HekwE0oc`k$sGdXCo0bM2~sgOnqNsCcZWK4y&8ZJC{*T^W};t8z8sh!=U7BdIf` z#BHm!SyA9wVM?Os@NDDNZ^?Z=#!GqUkwO!b?Zl#LmKPYpgW5u8?PfWDP2BHhlB29g zTuY#)EVkaK&71=2K2s8zK{Z~0S$oQ9dtS+@Stlx`D(0wa%#z-OksHyLEGu&Ba^pT{ zwkvTaVU@DJ@`N@!3Rd4FNOX-BXMKHT=b1<2yS;c}rBtJJ6_?_5q^na7ThMrqp?bBp zZn8qPGgoQHcW#L^v@Zfxq9E^_IGN$r;nZc4Z`Ec}0q_}95>aQnW=bNObFvxT(43P) zVFMBo7d-VbAQ9=}TTSByf98As=FWWkFS|~@NHbk8Uvvvd^7H;m+Hr_8F=z=ByAexH ze4VG<4yU;v*2X@)n~>azX|8XohmaEBF8LeU-=$dle-$M3-IeixvEp&py;7O9F8S(> z2WiSv7W6N)1KQdKHCwT+02=u^m*DGC`zAWN+NPzUt`>6JDYGj zqq9FiXYVfi66y+Z;}ePu_r_tGp)KQeuePXJ`^OzVUi$;Qz^fPVYVTEhOTRWN3UGIu zlIS^b>lwHMRs`1pd-tw5V%-`sROhvY%L>&7AF2ZqK!Q7^bDh!VLBZ&>DT$tAw1F|Y zPr_*TUVC@K`*m%_D0$lAWkqSDkJ5b-O3a@EQ$w2x1*WPgiJJw}{Sr)jcG-LO#ru*E zliG@5`hIQkbYZ$*f{FQ4V4BiqLV@Y~OiA<{raQSeJs`t$pKYB-5jG80yW?=p*qUMc zC2euD!gi^QHiFi#7`iK>zlQ4$z(mp!@ATdr|>PwqbyFXlo~H{|Nxv69FW6QvkY4n*{}+ zt)?VyRu9@60<>qpz2|{cfRb$(pkZy%bOG8M0>r#206nbDf&$P9QxZJ~h%*fP_F3m} zwXvAn?zR&iF1-oEQ`Z(OD?EM@V&6V&#A42D;!HuOqRoMVPRW!+&(ZM*m;Dhs_uISE z{admP^%qKgOHDr(ugto6K&yiF}g3p zh`CcR`XAanC>Z^*DTyRT2CGfcf)yv)4M;>>eA+bKA92BpDmTQ%|8pZ;pkVaE&0RKo z@I*zNnkUXRxX`SRI-{jZsWr*R%T9`Fxl6R?85i@>$+O3umJ{B!5$i4G?+BODtUG3B zhC{kYETxGufbw^zRgB)Q{jEx0*epnNT~wR><(^H)>s4&?;i6n@_VCqTN}jkiO*?i* z4`~aZ?u-ky|*xn9lZ6(5lOIl+R$f zS!^vUl=6v9Whu`Yse-mhS&>?WD;5M#q6$N>BmtCC1L|nAq5$-iDT$r~wDwY~jy-hb zw=8ks`Di8CtJ0e=OxLvq%L>!FoELJ2(~nV;AUKntO4$YU8f|tIsJ_FLM9-l*oCa06 zZIhf24)3qg2`>Kb^FqnP>8dSk>2$nAzq>(N4E{T{Rh1R|!>Qnhn?6Za?Am2n{cg;n zCayV~lXjrb&uX)+7|BnWlIXdSJfv$RP$TZ|XxH0bikaLnH8zw#)K*tkLwQKoP$F>^ zQ%Naq{XK2Q6;t_`DT$t&%I3?o+q;e9MG&~+hU_S4nT&<3o#`4fz+cf8GAqDa#DO9a zm$cV6h`yuKMCJ^qRJ(pzn<)jne>5f0bMRJQz|jqEvxOL#ieN7sKba^mPiw$n-F|0} z<{h|g4Cwe=QC(}JFeYu;n3Hyj`etor6p%KUlIS@|yQ6JY7>lv5YE+y|866IT!$zx? z{3zb>4Blsmk7}zVYk%A=ZLg9U_rx%aV_--mTYe(<(v%~JAJS%3F@Oh6N%Y(R)`i;# zVj78UzVFh8fgINsEh~`gqYVTx-lPCK<@(-&Ha`kljwy+rqqXtGHNMaa_0QAv%I?h= zvyQfaSuxv`b0ZGBcCwV4eXnb?q`>wXQxZLgZ8c!SRx7bJ2Xk25lam|@QyMT-@75M7 zD^zO;s(>rLy(cylE>W*vey27w3P?X|N}}f=-KR4zsk+#3m4>7-6^8rc+Um&)_kB9^ z5E3uNB$lcs@rT+BD<<)KrX+f95~p=cB98;1>A3qUt_!OL369`~zIfC$i*(s+{#9Fr zS%cdlHZb#cN6$++=)^RD$wobNdICE7w z&N#~pjJ##_YO0i@sZzjoY$#7Vf_2XDauw9uwV6{u-E2zY-!rHuw1v*vo#*9Bh28Re zXN8K|QSEP6PM1ebNSz9exaos19P(m)7<&x7- z8G7$Z)egqBxmE0-U`nFrc5rBB*m)m!4cUTeCtEi}iS6PAZ8c@Ji$fWlxEQ8c%$T9b zZeo>c9vy9_74x`mO5(+39`DswQ&#h!;b4!9^J*36cWZyUg7Z5~N%S1&hqAhXD8D~V z-sOg=u{-#rwz{(7{ZLkS5Q*E>C9F|R<>T6nE2i>?rX+f9Dlg4qD&lrKD?Hz88e6$> za%?PL(^gnkV|i&7W8v%kLV>$l%Uac1{#BcE#ag~%N}}i1ayW~%&`GJIrCPl@eLD9B zX|bK;w)SeGcsPrlhyzu9QM($+I@L%lZMGF7x!sh+H-?d1sFysiUi)Xw zs84H0k`kN9!`h0<>Pik~F_8ufYI|MnW4&r0C$xE1?Bl2@i5HuFRJ9eA)jlW=-7CkT z8&ssr+TX4qJ#I>(=SZ(R>$*4iF$Rq!Szi4kiu zRvT5UUeM-7!K!0QqUTucNW;oPZ6hC%Mm~DHUGft3jG5nJJm0S^epWnpq~U3!T#?x) z=gaI%3Hwbd#P8K+P=WZ}rX+d}ao@496UO_X{D6V_Q*9x#0<|QU-rqK>V0==W2?dOg zo08}`7(3JY+W>B^%GYrVD@p_1g5^%onp+$zjrSPJIoo;_BKN2EIavbRmq6-tTU4CC zW(v~L@W{GI|{!r0lOT%G-N}@=iK#m?f|! z3BsaqNdgJx+fZ9|h)NZ3SfY%M`5clLMgJRRkZ_{&oey6Q(43j^LrJ z9d*FMy`63JXRm}GDeK%fM2Wj|Lt9N*aXyr}JKHR#Er}_0@Hh3`s$slAn`Ol?UN9xm zbHg~C-7sh->^ap2PX7&N!|~wm25GT@d{A3eSq%RQ^<(am7?VX-cB!rgHGOi%a=R6j#s=qhtPbkp2wo>Vkt0Y6YiRz&ZUBB@u_j zoym<5Vgs3%>($ip5H1xBq@*27!K4>bMs;{%is9jQB$5&*`3F);gUvS8IOb?Gtr*AG z{(s}3>dkIe#>TNzThCd&2Teux%cDh3MR~jSw<{>;Oi8?$T);VPCF!7iKt}m473E>= zZ&y%$*p$SJ31v@PNjfOsC!>6~igH8y+ZB|nrX+ff^04`EJ}~`cVOA-#Pk)QH8nfEL z@C^+3(@i9{tLF43Z6OqMdV?v6o}1H+1a+}F#ElSQWBCH;d&Lp^tjiLNWoT1wq#IWrY&YxP;ZNaYKMH<&Dyv;6LYHj@h2 zZ!#s(bFlB72J8Wgce}XP#6n%7n`^zvaDPZ!4YLC`?_mkWkl-Fv;ri(Kx?2TpK>OKLy{nn3Cu@zC+kejmcPWmhdIF zf`bdO?Zbziv%J=+Ad{4sifF&hi2u5_IVP^n#TtEh#;A(%l$CKCFd)fTtwG$vccdM%z1)Oe3Q@*Zs! zWbKvrW`)BzlhQ z#v^T9W+YWmkNGE)#=C6yW{lOd+5%>UXj9IKa~M`X%YpGh6}CxjmK4|~OiA<{w&QZq zdjOeOgu7ZS<%{u^^k}Kov%F%xT`5?n;hq!IqS+zI=I|rhipy#aCr}o{yT9c^c(HOL zB<~tZ+bp?Vf>V#psSc^8^Ml&#E2i@{QxZKloehr*3&9v2Glqxa9lmQT2KYC%#mfpX z?zbiWX#DL8*@G%%zpl-Y0@;U5N%S1Dtq<3)Qmq>-S5&i|MQM{;tGQ9fj)Rw>J;V4n z+9GF#aa*ofze?3>;91nCVS~KjIhx(d{`;_s=wE5`rXc!7QxZK#blKy@No%xH&tJh6 zl!>mFc*aPr+|jFf%rbPiNju<02IVCxD9g0jP(bN3CGm|1%6@H8vUVR4n8x;gJfwoL zNBip)FosM?^c;+1L4j{HGh^q6b3*dsVmRLYM|Ho62+;}xqPSO_6^h&&zgb&tS%E(u zmi0F*5fz|kwOLUBnlvTxjSJ9!))px%K*HO`_Fx@VLHQBwuUA0%K~oan zxS;&Dwn$o_#P+xxQ$hJn?XOor`E^qgJqKm^X-cosX;>+H*OL#~iT$0nFj?VPLDwtF z+(_xr<0>$Jqs@o{%wL(3=s7ThNBDT7xJIn2rB+d_HxFR@5zd874?}ccW?=sE6dFC*AITCcZgv7=#CU94>s z;z4G56UOjZA(QerqW=s8r&LYNwuVaG8_JY#U4 z)D|TxILmV(FoG8el~XDz->l7tg39BjBzlg@x)>@0R@2Rw8i_n~mo|*jw`+@*6{U4? zlx&|h39N@zu)a;39R;jsO-b|+tp4)vVHvHnB7s)C7b#B}p`R4;FoAh$@fCk0H+9RO zz?VHY)nEQ3FX7F?y55=un8`Y-(<+qz*%XK9h}9o4CDD5*mptO+uUx?$*zSN8hcWhq zaryo15OULAK)51T4p>&o;2u%o`|qZ@kKp^LDTyR}I_mKK!Dkj=LHpyd|MKQLD9|$? z5pl6WkZ?5mmBdARwEQx`2RPdK>M81%zk|Pv+sYr~?s;dI2mR%{yF4l1)9rz9Gixuq zPQHlc0kM90s_7JxBX;=>^8@v)+&MdOFv-~Ib87iwy-C}3r;6KrB^&~?48=0-?^3*b zpCD1*+(iNX&`!%N!2XT@+wu0`Dy+}lpbJ?@^YR8Y>!+}nbC1=9=KJSmu-H6_t=Oc$p4txotU zqjFW7{j8`g%8mPeQ&D?M`%4wIKW$1Psdj^5EgBiwml}|WxL9Z^2yuat@#1tN0 z#h2Y{EleJ-#0%TYKO7E+@6r}1-J(danTEr6Xn&VtNIzprB7*QI1&LW7H}{??)vkC{ zWPz(C+zGg3Wb)c5SwK|67xX+@D@`CsDYYi)(9!c=r5<MO2tw0T z4Un&UtuDFu=^AoZyyKqu{9@L$-r3@x?}xyNx*c&TCDjR$C#U*{mk-YgCbtnNTeO){ zK-nlr7=U6r5!rr%kB2x&H(ff-Nh@EWcySE(yohZA*a=*Go*kuVoD+jRy4@X?0|eOHidX|UpF8Taj|ZC zlQH(xM{p9mTdC7J2u4Lp%UZ|+ScN)$P~&m2#^a*L>#3v20$Q|f(iu<5WXu9Rw#GMW zBbU`0kHYTlyExm#4bz zSiM48*dd5eDv0pa%QjTUZ@dZpWpgO=q5M)7HFp|hfx%VA*> zT*uP{!U0BH$6#Hc!dla2Pl5G{DT$uLdfRzMk0uT?WPPS@%22*pThOdf-k$Rj1E=#FDAPqXyOl(}8GzGo*M-^StRdi{? zRhsRz!E_M*U(RWknAQ5Uo%mk-@nlB$D7ynW_A(HmeH!e{D*l=kRa8O#3LC zu7jxL7)=kF)^RNR4Olf`E_TtTfS&awhI*~tt69W$-fJnixATH~5n|e4o|kVGeEZay z=qhdg6nvMPlIS_U_na)%aOx8(3zb#<>7!7c7a8XVw3U#xOW&Kr_3MEYiC#Tjw7NtE z`+zo+3fOy1N%S1-9ekb~Hj$SmxU?(SDn8x$a+%*^n4i)XKP${T{PX4_{=jrSvs_ZZO)gT0zM+>>*#6NhD> z6^K9vN>wKcLFMegDi!Iq+B_;quQDakbENm5L0JZ$dF9bwE3XY*ArFZyG$Q#%vkEaw zEVyn1Rl{658%N!c23x>`+N#Ogrw?F1Rw$de0w$D=6N^+NAWmK)*}}45*&0@>*6@Hf zzlt>+FeQ<+27@)pXjzlD4jGV$xcDd24NSxZws_ulb2o|Yxm2%+#nR)Yu`#y^XJ5kB zuoF*XO%4Z~dlnn|aWeEXlz4`H#0$H_ioE$Ns4Pm;~k_J*YjC~|+!7C8t9wawn68Dr4lVKRJBCY29 z4ca^@ki1|@BI<}8Ms>Dp&Np3jY2jX+0PL53VNGA%N;XY9M(%^!B4$UfDf1|bz5*U4 z=P+g4}yeN%S1Km0^foaJ@V_UCfbn)W?j|XSD^&iqonnzz#T);7KV3`BQCH z6nH*qN}}iR+(t>Ba7UKs4@*>9dH(o`I8@U&W!UBo%}x}pj7FW?MY4xDrOIpD=T!7E zab04Nr&}?cQt2^An=J*xuk{>4T%3F-Hy<-Ea<2qusJZz5akja}MmnMJ!!w zS4Xk(f&jZ%Diqurx9|qIHX83CB@wLt%ZZqD_m zvT={0_bOxkBifqCinX1K1rc!Uk|cJ6C9y+EB)5`MMD>H(Y$}+)O^~>Gj(+R0dKHDC zVP4Il*uZU~v#2P zZnrYm0zVXR2mHt?PwT{Mw0TjKzS5LL)QOh~60;tGuRX_$8#t8i>2|3p?gB~FLZ&xi zoDOLVmbIs>%LOy27-uoCQu15(Ycr&PwcnIP5-bCE8F^gprv@Y?yPs}`!2by z7R6fahS<3r_KRGKjr2K0Ni^_CUT`*Jv9h2*o_ z4KYm$JO$6E=*~KlPdp;=$kPk)B&C|b5n`H&+=S@jO-S)doNkqBStQbzI*#2d0 zMiuk>MN<-y`OPqDm;%55qU+&USe(E`^)zzy8(IJ#&o4?Yf+~!7^lnIl&EN~#s>x~w z2e7T*myPOdWZ6P{;Eb*)xd>&G+)+wN_vf_vRjlDNrX-TqVBkq2XT*!|1|%Xbs-_Df z#05$&`fhH?#qG!HwTXJAO$8R1m`>-@%6|}6SKP6CcIG@JY-)AIC)27cwrGE=VrCl! ziLT+z>`y5-Bs6MGc-FCV=Mtku*H-Kg4r>dZ?hh1ocQ#_`Lgz1s#Z~r%XXk4*X?DLd zE&MpB&5;7deWoO$zP69iob{>-K1+;lm@iOzUhHN|L2Xm_c8uGowuo7A+w7k>MmNeM zdaT=mM+Lc*S?7p0PYQBRn3BkhoNsU-6yV+$cc3T9CMj-fl=5O)P)v?H$DOM`f~BuTthSaYjun!KVE-!}inK zipmPx5c2Bb=xF<=V0%~t3B<7z;)G$+%Hg?bZu2L!SyeFoF;fyz=lfwci`jOY-_!+s zET!OL!-`0(UZM)$MjaPNP!@)EG+)3nMZHkU(}e&Oard7@=v~6PD2`LDd023)dOPEx zbq~LX4eGyZt2nDcJ>JEj0u_Zt(1D6XaRpQ+R74d%P!WCz4cR!*)z?sz7b3$;@%kUt z7D+L@-!dhUG(3awI*QQQr5TWjxad*Tu;KF6y1Z0sogXb@S4J|@>(+`*@9Wx1&T4u% z|2NK`UHAEuoK{MW*jKeVQY`0ROiA<{vyEr#O|fa_c(hm#*W@NZ>)wn}yK7I6rbC@g zxhgp1sd`vWz#K}jrBqmL)n-Y7?G95CJ%{a%lkFzLDIAm_!!~JMMC8{@+z-{6sWC%% zT3gtx9q-QE7;`H-2V9(lJBXND3CNVHnUmU#DL@`GC6O6O<9PiN1?Z^B#QEFkhy}Oh zlqv%};i5$WDf~k0$Wzszq*J^$^YJJ>`3AO`nzmlE+RUXKO%PCriId#W{aG(O$D_4` zm|BvX<>;;H&sbTRcC_jhZDABUD+&@fak{aAR)x-vCSm8N74ASq!X{*!n%%3@Kp!oGFQ(gLUtPCN|=s z-U3rL7gPD{HCHPae6rYq#+2xD7b5MJl}s8`6@!y$ZwES#qOr;(5G57a^wx}5u+*yTFDwv}n{~Pu7RcWEy|LyKtpya5^bYAn$ zypxawgieOXK$uM44<3?%$dC+q$Ox=R()4t9rl;uXZu*f-bWuSiGg^`;y)3Y@!f^$0 z4YK&yMUT3;iwhDF7gT%!t|)t8MGzzEs_ggO|5kTZS9j7?%;fBG&Y8a7t-AHs|G4+o zU;n*zZ^$z%F0JqMOQP7y-XVsYY}ajmAHHE2L);M|a9Q50teGko6LU>?7O+}#E$9j* zU?>}h<;+&biMzowOD?m$&o7B7H`}>z;t*n2^X#@p_waL+L^cz+d?XtS^fAzmwf!Q9 zo>(27bIjV=1m7SnsQ~wSR#mkX;LUXOw5)hD-op=8AglFR1S$q)g?F!IEqQykH|{c? z-#>ch+f_?G<(I^i*OKmSDyGIc@M`R|Qhg{1j#ht}*!~I63aHlhr*|bOK@VrmXE>Bn z$;!6b4ejN=i+a&e9lq~g3^-+onle>4H_Nv&G7 zg`4k{RI4)QrT)xXH95Y$%b7B<##n(T*+QXEQ3g6f+Qh|;sHb~o#8pfFEXqB0JB^-X z(|TV7?rR2Lx~X|z<<^ZlYH6{^sh$;4ZHo@rEfOm7TbQm??5{h@Ib&U(IdhpP;Fm

A?&V#3L?WyuknY(< ziF#~JvP=cA+rNxgcadjSUG{&A7_U+jt!P!hlaE^@p3SKd{e7kL1WQkfK}J1GS*<}@ zyCixIZhD3>*}$Rhat+S#%!*6l!+uE=8(hRMiQIU+oYL%lkSKB?&j%kQin@^J zw+|9J-qL!ccuU3F@7pct(>ocex63nSGeg8)Fhw=M&r$htW+<^YuqA{|dhwCHwG3P! z6dz9FYt?Mb`DKvtav=!wInR}%d@G?s$_8OxD;I>h&+}bf4dS38aV&!{gIO%Gr*^w4 zyEc{Uv~)xN=~>h&6^tMZ28xcZ3C^o%E#Bh~@FuvPJ z8zT zmg{26gu?ng^W>^O8~u`)dds1QHFCq;3X-4aj&Sq`8wJLa5$7w^g39H@a!Jo3R&P1< zxxyn>_!1s_G>^8nUuH&U+%r!u%Z>OYG3A!)z9fppvE{WGFOh+Z;U$LBh;0w!!$|c!Mf$BCd80f`1KorD8%w?ssiM5t_G!;D zS8Lk<9<3J7#U5Ha06m%Eh`s%mSvu`Uo;h>5^@;#KRDsW9 zNndz|I$PpVON)i3t(hv%Ie@W3wc3U(om=3yU@eD*$~n=0dgC_wgI^NGM)#Uu5=AFk zYRXhP(Y~90`xd<3B(k~Dz)*-Er6SvoV*M0k+gL zFRsSCM3Jc2m@7|x^4ps0FWEB4<#tj|eHRalng>0LR&5X3(1nlxxFSx<-Vp1{HN@?n znQ-ZMi(eAOhPYWwR4L%&*AOjz8~e5dlBq0qOL=EB?KDT}NioWpXJM)}N-Op#4~_N| zxv{w=_2ptcInS)POq2FYqSQ1#I=EsVDGksEi6R$M6liGKp5~5?T%j~Ok}8Qxm7bIe za*t<~R$oC<7B@YL8(Re_vu4>{o*8jfk5Bj|G3AC?zy-|YO9$IhJMQltj!;g_^_XW7 zt2NicE-pf*c(gAEqll+_h8n`mw4D3nPeJ2)6;Zy3^gJK;EOC{3#vm}afRdFPLq*OC zzQF8qkBX0ZX2)fKTm6zKHnf}lk|;KJsRnPTx$k)+T;zsg2fbH9->&IS)V(-2t=bsM zh5~(9w{dS~L~3Q}yr?q+7ruS4XYg$UE0?cc-Mb1uflyY>s=73R{esgNDcj3ARogQ0 zayiW^ckIwWRgQ zxMNu}=PA+U?>viGjV{e*xRf?FT$(-X`L-_2{@O2zVvGNk7-zD>WbM{tj(fFXLzL2< zxy*Sn#tG{t#lS z0N;fKxId{i1Ggl)c=Y08yNG9rtFql9z5ONG?E$+zT;xo%+rtUNnY_z>A z*+NprH)XF zShQBnvhOLd<1)uxo^S0k$0z)fC^d%<|G)SOAuZYmi6R$Aacg|{$a61|{f;7mw?)IT zM3V8PQs1UR8L1yX@T}pg>c>3HR8t!7EHJ zO@|H(YXxDtox`awb6%AF2hYM*rRF6Df%_f_jW1zH-1SJ+rcYhtI6&h zG1L;p7C8ZJnE1#L)?RTngo>raIw!855?7z2F=Vbs8>z^g%SOk0=D=m6`F=^1+Q>(D zSL`vRN%|mBe z$lfo>=Oy`~B>$okvlfmYJk~s3$m;01vXbn`cW*W8xff;xd)MY~$Rn4HGJc1a&0Iqk z%Z3aklUP3VhJ4hVEn_p$T_bV1+PDl_H~xx0SKudV){ln9BGDAKf8P8${>-{?2p$Yp zvWq=vHl{;+Y}r}E@#Ii`!mO2zv-9I-vnH<(OqlhuyLL2^A3z8dAF|=L$wYi_eq5XX zBHp>CZrZf1MxFZo9;2yRgPU-2%Cy#4aM?stwV08N&+RIxDNR1JN72xuP7OV3deYFA z=V$&uQ&BzUrlt^mUoI6(=TF2D%Yt?+MReuvDL_xtBfYKd?SAj@aLoa$@AxC z{2Zxn{?w`YpZ=w2evLzIYb&VjUaIK6qp0Xbr;1+uOHt7}rJ_a*IqQL<3QBsIO8Vwe zlyumsq{DwHN?Na!)L^yeWzMX$@4{JW;Dsz(c)7;>!8e1gU%B0@dCg-*@88F_;WR`IWlNrWBCMOyv zFlkqtcn!1|Tw-RR!QeNW108Bacwk2C;6P)}Y$2DKXjq>58Tvb>{W*(#Z1KSK59E#Q zC*tDi1JiHF8##e90B;jG6Yy&SX8}GZum-Tw+aFxKhfNvK# z5AfXrj|2RK!1;g=3tRyBOMwdkI~FTq#{;evcmm*+0^bC9oxl?T?-F-!JeKzqt-xNu<4;kPp!21QB4fuV5=K%gu;JJW{PE*9*40xfy^8l|FxB>8hz&^k) z2s|I~hXOAEd|lv1z>~Wbv9|zj5_lnCLSR4OO#&|h{EEO$fX@rud_z8GTF$97pc!aD z|GW@HXQ&4BV}Wcy(~nn2*?>+J$ObeZkPRp$kPYag8V*d~hdUH~J-NqB++#;AsA0z+ z6n>vT-s6)R@;c+2R%Qk=bLv!i-hGXRs?e}x$jZkxRLB3_%JAaDk|C1|>lGa`d7ePF z@`ymT@(F=#<@X9?D}P)=Mf(b)poA6+F7{ZY{} zD>b_{VD|x@uTktiEs*TaoUM+M-BUDFy0}a-ce$@}bPMGjvk zK!wY#4E1@Lm4QBucUhTP$lPINYLI!z%GBD`zDmnc3pvhc!7XZ)9NPp^j;uh+ajQVG z{#AisJ!h7E!w_rMf$YyP%L$8Iv*Om{DLv?(@%1~Edk_>CWGXhxyX2Br<71n@LHB^@lSQ%VeH2rF= zvUpIU4b_!9tqgCvUow>X^8zX84+K)sKMSOwU2TdW1-(ch1TEfsjlOpS z?tLfEW8-EN{f0o^;YESGLvy<-fIb6EtgtfVC@dM?`vV%PLZ7xWEc7GEkgGpws0uCa zP-JTcSg7C1u=2&N3@hL5lA$DD(@9_?r%zlV%@8uI{t)}Az#0MH_KtBNwL(=s$chI#Wqt4Yalwm`~ol|agHy@raXyR8g)I%H+Y)1M?m=@uWS zNK&AFf#ftUkeuGAp(6P?D?^e`Ss9XSn6KzSpqy!cgOip#8_eIg79}vv%P!n{EnG9s z50OH%5^kSB3ila-6z)3$$@OmqlI!^k)Me;F!Ns{&hWsTYLwOEps0uwO84C9^4b|~_ zK75VH1R;cW^ zDw3)p7izlYu(X5S91CD&age-CAldzzK(hOsKr%IV70PztqO}UBi>?&Ni{7mvS<2~m z&RrwJ#dl7#O$XhBIvmXx(b&Nqcw=@(yNyCr*EnM2(I^Dij6xL2s2Kjpm~AS&9?T|# z>8RSlmi18Gdp{h`g9lW+T|-9QH6%A0GSaLeIn$7lQ4JX%)sRtA4H+xdkP%Z2$-RaQ z5^6|EG-OmvLrSF~LpvHWz@s6X3W^*u=9b!Q{I)`i;{*8@2fV%&g3TaA7EH5-)h z+tS-okhldq5~bpyY;-%cFq*-U+18Q1^f2Q_c!J_I~rnE1tj)Qu{^#Q&e* z);4KsV87^?U6jI@6vbm?3Rg2Sg@lnQB#cZUVPpykBU4BinL@(I6cR?JkT5cZgpsMg zxvp)R`a_-}DkKb1Az_FL2}4v!7@|VLy}*$$M1_PQDkPl1zeDu^=r3j%)NHqL0FpuH zb)%Tx%E7Q}3#Kv-;8oOCq!}}?f|wJatS1*!zHueqxRP#M2{*1}8&{%@E6K){VB<=z zaV6Hcl4?T9GOk3KP?Ah2LB^FF<4TNiCB?WBVqD2E9y>UZD^#c%sl7HqjDJ(|6wc1X zDzo;}R!yCm$wqkGY~m^r9HB{K0aOUD^-&uS4RO_K7OBT7wPI)E`=B0MY&K_7SfFxj zX*`Lqa-(SEK`gVM$e@OS%=UD0Y%c~nyN#z%+H4KRL+{)h#1uPKfJ2~Wty~Ya%L2IZ zyjinJ)ue3xy1emYTxa}*KTq@L8T{-+^m%As9^;bOPFIx#=X<%1wd63A`a=}!F1gm6 zjn%hd*Fa_J&)cZiX0V)6IEEk`4pt)BG^h#%wugqJ`EvZeWTWU{vXo`BQxEq$n53K7 z$o{5i0;PAYd_4MojvE-iP%I)xUNytW{f4>2`kYlu%o+^eq2049L6AKcRd%fjbA%Ys ztVNGF8j>D{b$Y+FStM+;NZ4kPu+1W2n?=Gli-c_!3EM0Zwpk=>qe$2)k+4-FVXH*K zR*8hI5(!)7e#~QJ&Fnw#fm``^8yaZs$S4$?$(v2OvgNWPs3&a~V$7PoH>UVsvk}`q z$dLN}JbL6vTn4m_`RAbGHE&GrNyL+(2(QRUF|#9?9vS8cZ%~mBVy|H;0ORAMsi1xo znN8?-gIIu!gXTQjG>Vnuim=ii~c1qDmGDqSg39hn*5&D)~3L-{>q;7=9P_R|QAfAtz z476nInhw>qL`E`-ugu;=76pxeor$AOxpX|pNd}yJ9=ptJjYY9CTVfaw$8ao(nFd?U zcI!|ko*NGC$|b@$*bvK(#)DYBEreGW66)NAM|>g)PE@ae^~~@%#I%7-ZU~<~W?^V5 z!g!2jTW~Ol1@y5x1nMx3euqcf_9WAhOb~lV2S-N|xok8)@Gzdq^AbZ)B|kfjMgXGW zU<#rtKV&{mDTP{RGPzy5M#dlseV1Eew;eD$QG`~9Ni)GcBaz`KlnEOtqS#V{Y*}?g zo^9+MYeunhMKs^v_te$DzvjDU$gE4}5^`w6X-|Ikt|uSqGHdnHb>=L7>5A%>$%VsF zxEvAAfZ*ei&zXMIT1DoAUynB%7csY?_1AYET=pM#7@LqYHuGlyKk!eY>2xw3#B8~| zd1Wsq52Z7`*zOm#XcOi&_P&jiKVX_(J?GN;c%T;zz4u~l+?-2Cx55CK-k|bKdugKH zbTkDLnO;3UxB~tAFj^-200)0JUAkbQ=5NDC7XA9pyVjKQXKVqNQ^wdz%@}(n2V*z? z&uy)mu`_=A)mxitUoK$`+GZc-xagJ*4}Mi&)cMCtzwz9}w33S^rdFEOS{nAM4#sZ1 z=5G&a#@bK1zx&+_pFOsWtsZksYaNh^R)SqEEx|Lj#0nyooMnHFA`e6~DWJ13j1;w&o78lU`N&DK4} zJI+~n_{a9{@%*vfi*~NtS?C^PA$!m0?BsS#HpjY?TfR&)Odo~145H^kFC6cUvtXXTCUlm&*We$9C)!wv(>-2_JCq5hM^ahk5|3q- zUx0{&a+Z5DyN8#Ijlv0UkbEiu@1s$$k%}VIOqaQr9&QBAH%_WNBM)O%25|_u%(%fE z_#*VP;OQz?ElZD6g^ci-C;S=piWw}tqs+A*9l?U^iEJ{>S6}mZ`x(9(MBwt;&Ud6j z3B1b&!x{W*%}tmma5`)dTWXC)p}`Ek2@6N<=iBL%r}?J9&4J-Fr}D9Tazji14`u9) A(f|Me literal 184041 zcmd?S37lL2CKTX)w-% zuvwvlu_w>fEL7t=luV zN^|u9`}ebErf=QT=bZnkQ>RXys(RJDXJ*ZsJ&XS9tZvqerRt>tw|b$}s8uK2YOC8> zd8l2g6pl(Cy}7&n)!iq$eVsW@z1}_5SzM^)TMgGOlp5X6i5(9$-9~fA$y%f3R_~v1 z@;lDDP9Ai}cbpVI-4m|UsM6nfZ^sEY-)cA9Q?-`c+%Ymr-?d}FBiQVA<~JL8LHEEF z&;^-%tvXg3?{=1XBKm*NKgRvM}KCxQGQqv+50|Nuy&hm=Wu2Q>ptL4ADx(c0%FDX@9Zez^JRi$v~|Eg)A?(>yvmrXg90dnFmQm-R|YiqI|95 z@cYFr?atD=(<+X%Y9qj>*)4AAEN{5=TC>!uH75B>9`e5=Uz@1ci<97_IWS&of%-tH zmf8SFTRVvTO9S*PbSiz(Xv2Xjp#2G_3C5wa@mg)X;*K~~r!v{XH;$AF#NARTwBd|Y zoeNNJw{!4x?V{Uo3)bkQb+=;`8}8V_Ek3`V7KFl~mo4`^z-qA$0fM`CIQMjYa$_~9 zy+QO>7HbpkNFBy8QmR5N`RyLaIuAycI` zUh8%i(vN|96$ZG{y_B!C3#7;v6brr{fooZN>#YN&`eb!~8-yXb7OJu%uGD2##~_8eWea~(hj6$jn1mLKtHPe8-)I8e+|!Nr(!p#&EotVDb; z>NH*ICQ$GS*e-W-&quxoXvsF&AXuLJGA?#c52ShoKh}=B2SoAl7V;HbJ*d zJ_CAdInDExQnLj~R|?u-dZY;*O@I}mie6Eww4ma-WZLMc3o;{4rBb^% z0ykG{2wMrCkR7`db%?kUs;{+M^>z#14t@ks&utcK7tt5P=B?6%i$>j{8#>Fp9yF4N zlXppvoBU6>y*uLjE8sX6<^vu#g`_;BBqQi7tvK+B(B62d3Joo+7skXVUG8O4mmT5H zpCsNS^vPXyJ4dcycI~eBBr^rKei|acZ zJp!uM+~U6C?Zwrniff8%i|dN(iyMj?i@S?kihG_c?!8>Rvv^l=fAK)^?&87XJ;i&A zFDMQck6kVvM}zzD|NX@WiYK2eo+>_Ae5m+v@uioGFS}ekSA3-S=+F(t5j1#t(J77= z^Tk4E!6lb*Dvmu_94{6->tv0MG~Ehf0rDxI9^eQ4)__x(s8vg3`~!tXtzM{Itm4y_ zGd@zp7!AJ*1GNgJ3j^?z75-CtZcp>vv+$4rTf9txKbfM%2z|5odik~BL-ZHVO&8$F zCrU6+*#9-;z!r|sC|QEjgJW|WIMFcI{6`wr??~KnEoUP^0B3S0v`}o6!$AH28@Vvqj$ekD3 z;Qw{qS9gmahSR42n(W5=U=gX090z}bpW2cE-!moGor>W&sa zhsjgZy?3ZzB)*AEqS>A8cagbN5rGR;Q7(~@R4Nt{A_XfOto!pvOH`OwQ_#EI(+P#g)b2|Sg$tl z&668!RvY++$_;K%8~7&64Yq_0rZ8S^yESa<^Xr>2H@H=8;9Da%7*HGdcF7HPs||eP z;s&>?4ScKN2K&PXiv4hldlFhi^?oR5f#7STff-J>_{;ch!fiPi5IRf6(B+R1odxAl zTSQas(avI?82^T-t*XSL6Zk_JVL8-dS01)DX)z@55yCFioJlot^Np zyYb41_vn=#iOAotLMSC1)E5w67$5Nt5-D6TVLjJnlbx;&F^|Pjvlv%R>;L_^khD zXCXEB;PpQ&K3#mq{~aN;m^@?lfPtSTW1U6q)|h>#-NfA4Z$-hZ|9fX?!5wojiG!tK z>~>M6*dda+$Y#s zPIEjm)h124i(=k*R-GjwpMvgEaQ5t|lty>34euGaa|cC9Hh4de%tv#F7bsEB<7^k^ zOg{N;=V4Q_^~nO#5YQ22Bvrz0ppg~+w~dSdFKNT^Xvcmidt2W%qM zMA0}V8|dIJrCJ{826Pr9fE{rWsn^COyAYqE>qS3ZEzpJsfOcCWn6Qq^wy?YoTX2vq z;~Weo0`^nsjp`00`+wB35FjgBY7uv+?f#Nnu@Gv~1*ZivNNxrvvYV7I);cTvL4 zT~l`8wik-THHGMugP8+pFwqi|9Jd{)XPKCCQKm`wyz)!QClkg?#RK0nAAi9@k&d6$ znMun@;`E!5VW7+bQuM`DMgXwPY0&|BvHoB`f751MM-&pJf zQn04|jAFd0r#H;8y)H7xC(>cj=n2wCp&_%PX;O}H8*hKUpb=WA!87D2a87 z7#92-!vfqKvRbu9?D;D3{>27THq~(&5izzeMxwa%3cTV}0v0II6!_N_BFiAG+aHkp zXOxTzen%?G{~gJ9gf}A)ve6nreiS3N^pMwMc$Fp?4k&x&zfS3^;P)RbzA5A1G!bA-tD~b3aN%!#*pT5Q<`3uGNhESsHYVi0NPPE zB=?{xW1b5Av}i~%AvLAJG8m$SJgq0{7MPjcadK5WMtXha6U2d^P5a)OS3C==^79E}p2=HSHKkF_s zW$5R~3U$`9rUv|B$y-KSL-s~X5m=#WjMPTO>_X(H0(#sRC0gNEVFeLgE_^g1mQXs^ zeBwi)Je)(6J&Ugcufrl|)FLt9buI^A%FoD#M>uSk1mtfO-i)7-h~aa}R0nie8T9S& zs7R&I+A7UqqCAl6_Vbs4ckp^U5m%ovUBN>*#|jk__@aw`>=r)b^(JzdupKe2TNTNA zBfP}~Z`t7rLN>}b(U)L46!vGDa8A_W#kKFm6{yB(Ynn|(&JjSGASm7J`EZL zU_6~oQlo}Dff3YeK@a6GpmrmO=3A2^{<~YHcj+^lQp4G|MV1Y#bxs2T6)%upFEvH9 zfVm--$AUCC3A0XW!J`?k*K56r^$w2eMI2J&pmf=dlDoXtaa~%tzdsKIvJr=XK z?u(y7T;ER1kY-9@hN=%soe64My2wp))cw(wsA>pYFB#UBo!t5gte_U(Atz^%94 z`{>P&Khd}Sl`lK@$hmWm>=^I2ww*h7^VV(K4_G^PST}FACS0f56p7f2MNA_tM7EU8 z^@uHgV)0_MJB-+P6!RzRV$rQy4sy2jNsEQGu;Q90TW|{l){9D&iZ$w5bz~$!176gs zVnoF+PRqLJ1TBds?5152ZK~FI!x)xv@lg_(GNkOT=!DlI%thKm8RQokvS3t zZgqle5f8B@fM;xl{3QI86myiUFWQ*Qj=tTuy2CI!P};Jk-y$1Q$G;=Ezmi@&!NL3HR~cW=(ON$L12r%2hxRKglC?4b7pqSeMiq6wS#oemU{!r z&?E6oT!M|8Zc1WVZhRl}E!xU51ia;uVrsdb1mq}SzEn5^n-k{Rbe zJyvC+^j1`Sra3@ahd%nMkUF)Eh%``dH;aAJ>(REvO|(01-70@soDZVU?&1W2#MFg2 zFWdb{l(b?t^e+9UyswJzgfKjAZbh`@>DH|lnlHlIln|dlk=?^~Yb*IS;*cIiXpzA5 zeON*ll_SHsFi7--k+2u-@^dMD>_^eef>*hSc#Kj+&7`G+LVF29DKgo|D1Z1SAG{Jw>Ae)!>Mh{Y2Z^zkp^k54Sq8*c}B0THnA>ILxynE zv4>8auucu0JZjy2^yJ|ECtfgk=RE zPQ0K}qDt5BwPK-ofsD0$hEz0+e}w5S=CwOfpXjCD`4bd5!{EfU+smC_%Mak|xbTc? z|4`1?o~U|RcW)(-nq0zc7YS_fC7bxoR;^xfFSy8GaUBcX53=&4?X}z>KHV43Jepz} z%89*esx{8$ui@9kBg!Bk&5o3zcnhV&fPMr^e4?lkQ&3dWA(*5xgYJvp3h{;KBZq$r zm3g4n0n-D&g@vUh_)jq>;GBXjRgl?&wslKD!8!+ty``a-oq#D-`;Vit;rt_yw<&ZM z#mR0n9LlBUkGHGHC!j`$x<=UI77IyG^5i1PCt@xPLCBg0-+2znk5=s*#lu*jLvnqb zlGBf$gPU+KQmP0QtdE~VFQF){NvZcI9;X<9{(2((qI0P5L;{~`{2mWzlU7i6=r1B3 zBwO!~K7|*dq)_l-Nbwewa}=&Xncb!Ua6JPk<%s;;Gd(W8p~$A?nE-}j6eWjVTaZ}E zB>0(^y^@UsGZ+C4jKgaWr!D3|u~nmM$(!>7QA7$ak7}<{17=KVEsti{21UZ&no?&| z_-ezYYN6Ih(RJX+gBMrHEfB>ZRWUSMkd&VIC8yk7qz4ykjq^loXkPpkDi^0pSJuEmZFgBrf51D2zcs>4t#&3&78qszUOw3E%Q9akQo%y_2 ziggZNxVNB$;sIx9cFUu_jNS-4GWXQY^x=ea9?2sF`jH|8pC_>jgms&L!dsmiA4F^fNnP~wAmz^{>y;iXJ6UQ{F(cBV zwRW@X3$WV%8r3_l^dCtsN2qDN{~*!31&oJk=`8eD&DpZn`2?yE4@DrQ3S3&-(+$0k zT4mN8IUA%w7uZsI!oke<`y?<-xqDL3yPH(vM49 z*bU(nMnuU5!Vh1R<$14G9O8^z*dr}MZOn^x^%1O>`;NeC6KZQizFy~4FU1|vrFH)s zR*5#f6tk9|POTa=K={}m2k*7>SYNwb+(P5%8hVo-2z#RaN&d4|m#PB;hh>K(R)!?dkoHI<5}}L%++_6mhVWf3vG85-e}?xYz^z+UIF~NK1&137MDP-qCJ0c3>OUj$#R0GO#S_zanWY zpv&*93f}P_gl}2l7hysXY&P+>!PKw@94dSz%!(~FQiwoBMB;N{q^oF%iMHx2;vRum z0hxOds|JmdS5(A2QxKuC)Srt=Q<%pPkWiP2FcM5!R(g*`Jr!a~xw2=e_e?}I=pEG> zc6o&}w6*eMDH!r;7cUks`M;NkY4|)VjiKd-@JBdJEkBGugDGYCMffY2aF<^k`RgT- zzg~*JBr-3H{&^06mLH*iyjfcLQSpcL3GJWoeKGB!2!6+&ir{zbvj~2FY2cEu3&a0Z z-mt^IaMbsNt7v}}(l#}!Pop|}u{P=Z=4E)wb8Q-VP)5Ligrnu^umS3tkoG|r!P=(( zK5ZfL-mh2M7=~gs4r{~bVqC?Dg~@wok=PG_nP4d(MH@;YWG7rqC9#-E^O#6&gjl-f z(FT=2=P^E25IhC%_S%nCd@yLTL69iWEW{i9umzGf(S!pVQ<0l+DPPz^B~n064C)P= zY?QvIP(wux?Pj4+Ok#J9Xv1sDhzvz4Ln5(OJoY{x@g`T@@(al?`XDd~-zzjHQH3FD z+x+M1F0$go!OQ#w6s9BY#QsW-qr>u3dk2Hi?0v9 z>N@GG#xOT`F1nN;_V)D!?_f`%x1ou&j|Ag5ru7JXDCrkqR=iyNk$`aUf}bA1E+~p9 z(G>$J+9()b##uB`kApaCXf`c4Q(n#cgd=cTvYwB`4edoeRelNj8L$@BngfWSxK?|? zY410Ge^7B@aS@d!cNSvkjqW zK#UwWmHsxnKh_>Ck3u8VM^<`D;fY>zAm1Ij#@~VHZ$BOYA5~Pgx!68B+uv^$J}l7; z1(7eF`Nt9j)Nty+(A=QL#s8R#O3;2&?Ay!E1&1fM#D=$%GWaHPpY-{<*jpU!bcg0B z-%s1w@Iss|Y?H;u#pclL;@Y7*+nu#uL{6>~w!{@asL)s)`5gIJ_=d{}ziPZIoAPr| z3N1-cPl7VBBM1`@QO$;;OX%w|>L$G|M*7ABY2HRiU)1PyZP^ggwY zyuVy{y>Jbqd{J~1Sigw8M=nvUL5iTsI-Ga()5S#xHTWVu3WwEMFJen)L00gK-6mtUXwxz1z5x*?B-C2k^EET5+g_pmL zso3$s&z=AG#@buQ%Kyjz>+!!Cx~Ba9`F~yh$mE0NfARl%r|v0)H9!=@#Q}SgyF4^H5WHJ*a+9of?F0={hVml%2>4_5F^8`o+r-X=jmI!-o_fX^N zs5fL`M4^p^Zi8Bc#Duwn5w7;9XXv+Eo1tEPtLTfg&kI2?LAR5|%zslt2NbqJ+)Qvmuh= zW%fG1o@jw7wRgbgqK0$P+Yp7!Bhq|09TO`mR6FpW@NJ#BXE9Tx zN%^W1SUA822UPNVXV-{xeF(DGQp1GjC{m%CgI2fv!)VbS#c6<2bpqb(%qfXd1Mf^p z@b?I}?%a&h_-&s(> zB-XlKhfg5ellaluD$X567R++2W7rpO9ji5PmSMpNF8u1tL(|e}x3t6U&) zj+Dm42@tIkq&SMo0#UYRaeZ~<@SLb@CInc{XThnNoXcZ!(#&%jIX9o7QyBOtDAbqK zdfMbv4Vmwc8uN|w1ta*-WN{k4S4&4)o#fM(qWVv2zd&>$cD%1_MJXFxIJp` zhBR2(^~TaJiAhUSrfH;I;f=l6F+pQ*tluh6nZsL*Ib0g!kmfVfa5(s&w4B;6;K)P& z6fn@LFF`~m9Y4_6!jdYI@z^~!5yfT(=&=^|8f#%eObaxjnMMnb4yHcJx!*eWl3{!J z?9iTF`}XbFi+?O^E+#X6s9F+BCOA6~T6?frsr6f@Cp%1a{$Zj<0SuJqk*aq5!Otgj@CLYmVXeLiW1UTPq-pVEbj}oOEFH?*u*6qs_sfjiFGDR9< zy}nGNuvn`v(`YBw>C5Et#TtE?e3!^Gm8n;YwfQpj1+gw)CL0lJ@?}Cmq!G$Oew-jC zmn86%f5~XOQgM0bXOJj}&7VbXU=i&N9l?G`I#f7mn%#$jG_GAj0g0D@SVcPrXk#e` zO9#hD)Qde{W@Z)zbsxQ&iK%=-_Cbcf{G+5%F(dyaXh3hKN`(jTO{j@NNeC)b$J!0l zjZz5*@)@FFQ6wIaTp;&YekcC%%=TH*w)oax(Ee7B#QOpgKP^a<-;E!Mx-S1zk0<4y z@AcpVy&ediF1?@XwfrM}Wp#Fh zYqOzf`u9yqycaLBGCn0p^n|3(6q8LaqJvp*f=fKSyf^BFr)b9v{DZ4>uQ|=;o zv`bBFv!waAYvbrwaT`xpLhc$BxqsAVNkQ&^vD&X*AK5mDX)WzF#O@88O@K<-Mh#L^ zKttt67$*6SlPEf=-(sxR&CjZ5_2nFUEaczz`L}U`0r77K{L9cKb-UHtJSyO=FeMRo zyQP9e&u(Yh>(=?b&cRt6wSq;54pw44u16b2aKE-_X?xqcptm_T@n#F&B0X&=p|9Pc z&5#1uUQ-frxLl3wxW~o2(9c=3+~W;Mgj~$LukPdZg9XtSo+)t?9wS7j#Xjbw9?+lmcT{1L1B+sqIb42az>k$gaB{y9tp9^D-s zfBX++gndUndx37m>nZ6ua8iCP{qs8d=k@sKfi1_^d%=Ror_YhbMt>x$N?cAh4cm<7`_? zvuQV+YeP00TVk57U1izmkRp;TVh;(C{D3yciap$BN+NC#I-SJhA{?jKs~M08xtM00 zGM)bQ57W7uv|SE|1i}PqVvhrC&*B6?amF9rUwRg&4J8CTdatq#j%ve^)&}jII6;&o z2?8OzRJE~qDI|eu7Hm4-QwfpgsRP-FHk*p!oiinoIpjCefOiNb2)LpR#~zD`nn>ul zm*`SDzBn%^Cz-Z21N#PTank~8iIHSf@N0YgastQaS8^lsRV-ht&6$Gbt4&E{j^+CM zBmlhyd)lcf2OgbXjTpIK)D|u+a_e&uxI{oe%t?4HQ1SYCZGIHIe%6#k=6D?t_Xv`= zg*Gfc2aAG$0?n!UXmR8$UF>F#Rz}f9l2K5vh!P|JXWD8?i~NBc&b4dj$rlsqEGGp7 zo}BcnC#NkHfZ0M!$vhUS=JChcOe^N`X;TuJo5x)=)cV$OQXGaqjBpCdw2sn7S_@@T zel$&HLlsikCrc;CM0)%c&|%Z~S8WxgHI4l_8iakz5C{I-O_tFXcWT>CGng@uozR-9 zC!=H;i&V?_XKkJp%lJoA5~(f2cy(;iQ5^4s>rPQf9)Vi=oT0lG_cZ8DqS8XQI7dee zF%J?Hi&ZE#YV)8#u}+Ye zUuU=uYO5+OTss4}Z0|%2yIr?EfxLbCc0?c<)TH_Oer;YASnn_;5%#dXY#B3M5^z_D zKTZ)PCp<|rB3!fPFLxF!96C_JL0xzj$#zE!;R@)mMT}~zD6K`@6$@?-7+BIvcG# zM2HKVD@8}2^c+Zg<~fZcm9)FaWUpENnV^X6kF<>^xo42niA8L`m{i2}2io7NSpDw_ z5-bK($uKjJ4YgZMslM$3}o zjjwAnrGWBPQ&3D3s#}k87Hz+U18Q+{H0~qAK0cg&%vVFu^)EPqE4EJ}?MsZ+@+!AdL72p<{k_i3gJVByow=+d}E#*&#Yhx{3 zBHN?CB{yO8_Gk;1wx_KVnbIb6mfXjZLbsjT3@KpQrX=EE8H|(RP|JPYfJDf}U$eXD zHMcMx69z+IsA&eO!BYgIgffo}+T17@tu-Z)IYwI!7je!6-M}oR1%%u4&Pv5;ZX*3Fp#zhyvCG7=FqH1-EE_E$+9Nel~xJGk=~WAk!Yh=BZle&+QOxU zYJCosv*6B-F&9BBp)}(C+8il}z0Z_H95I9ZOqk-~`MLp#kc(+jJf?HPb@xwTDld+x z!woqIjV7>vJ~pf9(T1(&i`oiKZ#CGz#k|=vZ<5s{%pv|tn;*qy{=$?*=4fp@dcmon zPTijkN@}rC78}g!qXTN{w;0j6OR@@f`*NUcqPMI)c*{aQu0$9$J zMCP4x*~6tK-4vP>6vdt~Jg2lpNej>N+=U1)5-JH3jv;M66jbgrC6PHQ*UF_%me>hQ zy#}Sv8J||X%V|FC-Z5?_>}NVm}}Ivxl-_(FeQ;WezBetiDP5W7^Ampi;@vyezfNbTjXkuu}bZt$kGhqkk?pR zP5*U9^f$E?k`~cjxzRRG)lOQ`qrF#wL?VNO3+5q_1b@OzU&@{Zn$5vszSV7n?VKQt)?V0hj=6T>oZ4BJQPAZ=1i1u zCw3%?>fMY%e4)00X+hj1d~(CBv_tSb4y9psnF`w}ZI%?+hD=Fh4%?bTP76KLFV#<& zsU)^wur6qel@_eExl!WF_N(%lFA1mRDo#ypZWNsArX(`QX~7Ycdf^K1Xm1KWWjx-Y z&3;-u7Ul}x_e&V8P%(I`HU|m@&zO?P9D`Njpkq2?|8S+mccDjoTf%e3<+rs(N{h?t z9FEQ{l)w|pk3F6wgjT8u{iZfA3PQhON+NTFwh!XO&AMHnjc7>oHtVQY!qM`Sral!d z9F6uPjrSPQztL7fT10QfQJlUEv;yJFK&fgDlY>G~d3v}?Mf%IyJSs?k(Ue5yNbfs= ztL!1=vWb&{0@;Ei zba@gYSkJRX!EOB!(3AmaceMGlMI(NdFzk?iI9s=n(meHHi?NlxU`Q`G%koY zxsFR7n9Bb(*f4fP8^UD2MH)!lF!qt84P%4a->TT&J%YqlEI!{H>`gj~+tcZ09lAuV z;O66(l1$Z*T}577{FF-XY!3Dy(G~9=lQ=kpm<+;zm z=E$uKLTubpN!KYw<23a#ea$rJ3z zYI@g9qF~W_@W|09R8u!)*gm5zXj<5=7s;MrACI$W=nza4^2s= zhR`^gcnM+X1;iX8W8lC!hV^#K67~B17R@=Z3m36;c;mYXmTAk-eL{$r?TNC zRIGeUTO!5q{z;JN87Iy72H!CHIbExZ0T*-a@kZ@ps~9zhsTwk#o0iYaj7o`3r7)=; zFll>CO5S{4QlPY6n=1vAHKrs&XRy+gL^y9^%ebO>Q%2$1%@2ulHT^9zN81%F_TuIg z^4ho?G--56_X^w91KPSv>nCo>@p1kh=eA3n)14`T^Q6%xp&;tGHhYSJ9Wf;l8rU?@ z8jm*p!%~ny14f~Qil}C(h6{15)3p+=ZLV7WG00Jmq4z3dUDMV?TC8zqE=$6&!m&$| z*mag9IM7*k^a({&6>T;Z%u9mA)pPVW(fNtkg@LU!qWZ$2*Z?;*($$7^l_RcPmvauC z6zv(Zr?qvF7P2kamhJJ(gSbP3HS>%Uy9CdY`(Kdc{@Jjq1i6dI52Z{y#S6HaIa9bbP61Yk5-1 z-p8~VQ|#%Zf<(`r-}~$&)9o57&Q8`5>5nC!$D=%D1iqpzXj%kT=33x~65|O8lZ8p0 z_)FTnC`$i=DT%NXf1Yuh>15a1Q@prg(fw^Dx-`8SKV2cY3FEYAMOIPwx|~0Qif|@* z+=WT!D$LhrNC9h(DTz2(2JSNSxZF<-NQ7Ku6_wo>B)2IUK#mN7Y|lV!+SY7I`?a;6 zw#VNXq`5H}5Pny%8#rA#+DfRCy+fNZ#iI5K5J`MNK& zA^xbgKGPcFj>xQzqzRk~PZ@faTr3|-sM!7yZAKOIdxI&7(EO$uHB5oucgE%08&Pn9 zbDpK>H?RP{4_=g9_*EFu=-rS8o58PWt0t`(+>UMio@`WSBg+=p17~za$weTW(N*c^fifR^W^Q(Y7&y+;ig|87LW<1mtF)S?r&>=6lL!#2g zjKrnPU9DMaVOA39aGmL!GsZi$1y0!=J2#2dL7!t>5&@2>=0@T;7#HRy&2VjP))Y8z zH6@Wboa+vWi(9E1P+vx8u!bK#62-7b8wTznZPC&Kw;r1caH%Zas92=FNE46dg+e%c zoSSsU{~2w56to^RC6PH=s}7?a0{0~0eBDH(5}q?kuh14LElR7AwFgh){M!VC66!TB zYV)EX)G{TJIYL_rApsD&kqAicuUrHW+QHJk#8|#ZTllnCZWCAv zDACbGNkqx#o_Zj9B6BY}%!Im#cWN`J0Q@#n5}5zpkyCwD|AMjj?Q$qw{2=6Gd1w z(e>%xBwsYtK|wTm$W2%t|Ee~(iY@%LDT&N&Ve?7XZHdwLaE&e)qtgM{jbDlaK2<|T zb@{5S<}ugiCcveLkn#bS?5;1#;3XVNvP7FH1-yl(Br*qY?TJ!V+;=8wAUszcg)O-W z1GYz7u(aK99X1UK&Nyue&f=kM!otW-ZFUr>Y*P}MLzOm#)0wIv!}elrA=APZJLP9? zQd0RL?Qd65I%7&AbCd@C4n=(lXRCTiHg6~_HT`0vCZ&gP7b<0pqFI$_@0$U7jQJDV zDocy`p`fc$FAZh(#>i6BFIJLdj%AW$7o3oIeuXygip5+sC6T$s^dCV5mpD80!4t#Q zSfe(9TVfD3JJNfV?clxIib!h*HZCq;N$gq$^Ib@SyI&+p zunr+fB8AThXN$Z?n@t7scbbyO9P%B9aF0Oq%ddJHCI4zDaS@ZFlqvd-E#BUi_Fabk z_q3If9`;d^hGHucMa+{LwAvtkqYKb#l2ed-dcxTxpVVekf&JsABr=EnPJe7r;1|(X zTKsR1kO}QzIwEWc-_TZ1T0@|H-W;+;4TAWx(^~y0b)mWc&Tg6%-n)E4uCRl9Tx_V}2ek5Vy zV&h*VEjH$~zg4ji!6{HW1)dNpF0 z%G$!Eg=qt7LYO-$2?=6xX{~l%(&FB@HbV+v1yd5K0W&Vumt7Q&2v=NGC#eA=^^~?$ zX_1OeqUR;8;&rsYU4iAYAkouf&3Nxvbf{KqVFKXPqf=bzbJpyC(UvW(W*6s110Ezl zH7BV^;RD)SC>nmhDT&bV-)Bl93_KX;D+)X^@|T-2{lQhqP7_53Ug8+$QE+QxV^I^C zsv+CVm$mhj)@H61yP6{LlAJHsl;VEcEz}_T}JCVRc{+79ud}+ce zX;Yga1+lsy(K8;M`5E-xzKZuJm*`r3$jEOe9}4TWjy0U>dD@*+O_*_C87ao}t=cL~ zi|PIV)8u+xk*|j{rcOF0#0-v2U96TKYsV|tu80!b$8Tz@DXo1R2<;;w&LuH9s~?Do+dTp?WxtS= zK==)9wiN^Uuqlbm4dg^DrZu4lLKBKd;Wp-Xp&lgDu~`j>2oMWOYKT}=!jW`e)RscAsJ}8Lk-0@33N4Bk zguxzxWm>?TXzqZoSx*W-9;;YOwvrGtPrZ$>{48eA7<`tvaYDyw=qrou< z9O&=221TJRs*_NGk4v6#F0hg+n6@>;{X%VV)51-MCNRGUMyReBg+(a2Cw7(G!NR2M z!6|Ll6flQONyNc4$i{{VU7jczkO;ZpoS*@TkPBYm5QGPI5#RsoKUJsTKcd zq*%wBdGf5#TQake7b0GxtQbl|5vGM239O|_R}2a5X6RYFb7NqBtkCUWa`ztIQSY0JFi|{=l0=to%Tao4`bO1TRl%Y z`68~3#VPtV?BsSD^w+rMlqRA+to)Bbbo^RvJv*~}-jnNslhm???S7k-o>o$1-kszGbiZDFgn<vW>PV^b*3aT2OHhKSsQCvd0IiBD}owPOcS0nbT7~rNyjY^Pq+X#;7LL# zVLkMqHZKZ7`%Ot?j?ktdw^4N~9Q#zUu7grW7uCY?oVPX+ZqHYE{9 z-5?AOBWX@a7?23Lc-(YK;N_oYUETbXbp+QriUR{%4R`vq({n-EY59hkiML7K#I)0V zI^4PZF8ab}gEfmK+TW^J+Co9XAnjzD=UB;$f8-+^i?kf|4C-U<{I<5J$(>(OFgEvy zvrffYf`k26;3x>K5^qkpRhtz>>)T98ggxtK25zRa87q&wRk2uf%yn9ARKdmIQ64iq zXS4-M56?JrWRLkAN$@1hDj(ElMSU zYRj1xwQF;u9-laVC5+iLkr;7$Y{*-t2~9y1S5$&zB0TENqL)y9GG6 zXos1uF(da|+QOzq?#7(BX_2^)Oi9F{G>96*z?1v0 z0f~@{X@*B*|GRF`I_zc7@;uo&tHdxp+OYlngSLj#+Ru7qX8p__^QJ^I35lX_X!D~O z&DRBqtLScTez??ZW9RWJXf+tA9*Z#Oj{y_y-05Cnh*oXPD46fuoVyTmF6zj|*ce4k zcG-!STrAh-Pl0TSDT%O$EfgeX{49^$g8;N)U34Zzy_2Lbfi&qW7L%rWgOR;mTkN!* z@8(>M__m2}${9#}2RKV*MvI0L@4MKe&7XqoPE!(bWDVSJ=)u_~7?23L$jXEF4OYf$ z$nqB__%;XW{=i`NPyQrkW$9mIQybUDA+4!x&pCkvd|?2VpDE&N*XeQ%ZklZxUp0GdpBbQ|GTz;X%XCn%U3)O z#b7-S4pBW!97=Pp#M9FLRGTRUxIZ!_kvVV&hv`}s*E&6k^XpI^O!w=wYP63}l$#&H zRz9)tiZVi6%rP-#0DgtE*aZGfTUBXI;GSGl$ZFSxtXT6YpxBMh7j{G;Ic-}Mi}0ST zv6)uXP7a@vrS_lHNL za{)ci8vO%8rO_sFTi|`#d@H~oH6;=D-$QIWGadS2uQ;Rb6@2uI2|w3>2t`JF@bt|Y z>$vw!YJv({(xGNO%R}l(I;IQ(6ItOyv`5PTsA} zm10Qm5F~nz2s57OTXv+>bP5-6tD7?(PqxIKvF3kATgJ4SUyg!2nHQeDT%Pd{Dvusu-h``Gtg}fNQ7K)4T=GYP#5z|S22hST$=uGSNFV!{LyODofyT` z%DcT_KMnyD*YgZxmW+=n0ZCJ>lTLL~{J|dV=p}fB3D?4T*SO)SI^K`>y({t_Xp0x& z-V!fFSRND&E!sRYK`p5)u~cbYQmN8>?Qd1O%p5_Yr-SOfL(a5R>BhmT^&s{gUMRU2 zY21i|7L7-yZOvY+Pg@bmUQAJchr$t?_DK@IGZT8b*vk*mQ{Qbe$vN&l8{{d|d6bz1=l1Pn#@!~m( z`-Bqw^M_;Mm-?7tX=qE778a`g6CC*wycB0GPC96!rp=0iPeqXE>BeR}&N}4PCQZ`4 zxwVT`8a(*2g#FgxB5ghM^0Ft~3oZ(|`6l|vlswvLW`ZCC+tt=)T3`?PRZt|g4XN$m zdImf12`y%86%ty6+Q`8~=I3D!29}WIFQ3-tUa^HYnUVKjc-gz*_ZW ze1%ObH4cuBwR}&Fv_Hk7-tD3u8po2*(0rG{`kJ4+H66%e`!1eNZX{8>vl@Ft znbg_8qRprR=9f%Kgq{5hrX<47&L;Ie+1alTr!|gssMIKkt$ar(UF%^)w9!H6+IU;+ z-wRr@ZEd_Zqlr!j)y>`n3{|$HU=(}y+({QjKVVaG3JEnA>$I6t>}a(h(bFl+{58{>-)l-D^dh_1fM$A%HIQH?(Xt$| zvNKq4MBk0}XWf_C5Jt3>k=76f5)2_)ry~-zPQekbAc}lKrvIEarwZ~fF(r{X^8LUR z`#<3ye7}f;e?6G{5lS>se;-ucMRC`Al~I4Kwj$D^j>9cHNoc+xQfxR%o*_mY0XdS^ zXcrG9mWI4qn@t7sA2KBohumPi4?_kXa12O&hUe`s6n7R6 zw_LZ5P#ya^n|U>Rx5J(E3ILg~S;XbYhj^)H!{$lRQ^2R0!_D3M^758v!ngsAZzo5Eje zt01i@Y)>!+`LxWWn#9FP7iImw+AJzS|G6oN|0_VpLKP49s8>h=y2pDA^mE!OxDuda z0g8va+@llj*ZM!&EGj_%yD5pxf!^}s z(*9P({GJdbu3`de@BLIPTWII~rK-cV;96(OJ{_(#8g7NRp2yd-731{{ZTZsTwK3OX{zR9n=W#@d$DagR!qFsO*XBq8?W=;sRrHQl5uDH2Ym9#Ta zM3u3CW=1KqdAwL#jcLu}1PZJJJqV}EdVq!adazj!wC9fXz`ohn16l@ph*(sDn|?@J z4#lF*n39NFl)>~UoMG``VL&3}BBL;D9cR7rnD&q>!Wg3t?>*YEtzFhua9UeipW`$b zc(Z#9?Fq#?uh-^Bv6cYZY77SEPw_Jm`v&+|S!Dn4&l zoQCzVQ)#<&7$$YPCWf9`H9FGF2t~Gp4`{0`ttA}Ejr($AH@7Uem|KzDTnmJ|kA&Rz z1(KV}042F4ZxoKW(dhm7}@`>Em&G) z*X5{Zi)sv+GYP7MrK>;HW=DbQk4#CVhRS@(b;!ZZ5{M!we316qM*HoCUac6hf76yP zEn*u{X`Me$qdWLZzRYV$(lXS)Xmg~1_DwIe)A1k zO{`WT$rSKIL!z9TNZjAHL7Nvv>1$0%ggs@IATi@}DX(f60eOL9mnb;#hm6g=+QOvm z7Jf-Faic<$P)BsPHY*A=cbSsN9Gb;^BZmr${D2`TXbX`Rk|o}q8!8+LQw>L(4F!%z zO-aPzFqkKVQw?^K1|&i*GMZ|vd=Mi>!)m$tVzu;GJHAy|ear^(jJ8_S8ptZ|s6UA# zDey>GVgGS$Rum(7%9KPL9s`6!BjJS~0}>$@uP{xa5*JwU`}eE6;3|^X)jsAOWwiIOk)|5op+5U#Xo#{2W>ki{`ms$lUx>07+ z^18?=7k5K8&PU^^shcu{Yi^vG$XDq*fRL_k2{?^m7>2=1lk(Clwb@c2TxLola|kz` zar12~S)y2B$}TuXI|lDgZ4uMZpPn#zNx!tBDGDmKM7Y^ZO zTv3BkS9q8GLQF}yNytJro^n)YfkM`9D`~@-6(xHU>>r1scQZRdwDT&mW87F7f zi>o~=&Ljd^93Yr?>!@d`#xU#Eh#~u7ZRyfNwjn33>=fMDGItVU37OCTq|K0m*eeBz zs~CK2<%$ve0$(qV)4MngE|Q#19$Q$%-_bEF?MsZ)Piw0sElyjpr=2QGJnnI<9CObb zkwWHW*pgzCpVa110q)(VB*L!t4#s|_W0SRmfg*ZcK9}5t(fe=Of~7@oT`sh*q*AV> z*hG|&@A+MAh7_=V$CN}IEQ5((ICtc}Za^aBVw!N)*gMnmr4{->OLEax-^mlFqZOQ; z>6^1HeMejGX>I8SzKN19T8?{dd!ka81KWgkkZ)`ArI^&W1c{!Gd&YCNcZ<`pPzFH@ z920aVmXN#2M?|)(*m~G#Vk#nTJHJ$dpTyK8xyb3tNHMb4Sy|0k?#_+j955S_(ozXY zYO|zb*(4B@uXXnYrDtOKUGn^i$A@mx=37C2y(x*X8?P}X5jqpLzwb$Ba^#5HC|&Ri zm1)t74w|gvJWyeiR1zgFEO2Cx6GmOQ^S0ntq5;UvkYv+6sjd99PU&c_;7KlQRV?>O zl8a(6aovH#SH!EHOGqx+aKbs44`{QmSnzQ{qNneg`QsCA5EcRWFJQ(-tLf;j77igo zsaK<2iIwn8*O*bPX{#YEiZ?Qf%&mwl!7Uw`gma7qw=zCS(Pc%OH3gxPDT&a>j4{YF z9bN7_gnBe_U{DI3M8np1tli6 zy0*A!A+~a3#BU5uTpSee8$mN+x${HXyeVjY(3C{xXl|Eof+81vC_Z)vwdv8}S>ruM z_zT)9NQ>~Txn_756gh6C#kb)H z0mVPwBQhkZkJ&>V))qC{Ln#WzZR_#FNWyGIVlCPWv{_NKe$bRe*!A`^aJ}M5CVsDak z`pa;wLW%zHrK2WsjNg%_vdB)Ah6 z=(cGysla`+DT&m*+BoFBcDPkTJ{gB==BGJ>amtpA=Y!gErp5C*45vPy3aIjcny^Z7 zLYpfE!21P>o-@T6kBM(Q-Kb%F6esN?#_=T&x@FYIPTQK%c}!amY0yqFiI5DOQXk+D+<+AJ=9=(eH1Wk_bEEM;M}B2_DmV3wT_7E#(JIwr0dD*u8_4EdRuh&L7*#!PY{89WAPJ|8ZqQ~#F^{#TBr*qP(_p(* zqe8O0RVa;(xwKcJl(3vXMLUM;UTqQ6_UFwx$LGb&9s+O-4qj@&mz=+oU$! z$yQ9-iY>W$ruA&_T^F>!OR>(TAkh<+nUA=Z`bU(i1wYY8>=fRrEn-S_c9sQ4iV98? z}Jv>7HVIW;)zj6)Ymx+ASR76W=VJ@SO4ZsJ2LH@mQS`r{+*RTlFCxX8?|<|5b-yishcuX|5IDgv`}4-@JHfQ zR6k0bDyaPrZB7)_{?e30YSfGe8nMkGkK-Jhu7z}+h26cDT)z>ERi|&x@Xft>W};VR zAnDvBc11A9HaNDyvF&keQ^iTMt3Wtgn;Qkf{}2#f#i7Q=T4bw4`BU2QfP%isW{C@n zy_ubeQfXi>I4vjI!8G4x$ZpYAQraFjKx>x1Ea-16i|BZ=EVPeQ$fDr4MVmDRzZ*?S zgkA7DL851@XPP`%=?8TF2ol9oeavv(uPsnoxK?2YqA1qlli)C>sXgkL_O~mD95y8p zN5o)W5Kb+)UmK7JxtJ!(F?P-C&d_j*`xdRUbSh4*QX4PDL!BON*hD6^HJsK&)?>|+ zd9%g&I6iMm&%L0{f?_94LEq0v5pvGqxKENteB zZh>}Wy}paTS}w*q>f-d*q86@V!sScn=})(_6elWH+68y4RN=SF|9UgBK>tSndw5D0Uxs4*zu)$6u-cv&#nhzG9YXd5wbA(6TD3CSebTdlzol<}?fhA@PL*FT{(aM2eBdeZ>v))@ z;uZ%%94l)+>ReF7-9uBWZvkg(@y}FB`gBxDpYCWW>EzeueD7&#A&MUAID~i?o0s?3 z?#N$zB7f}_f35La$^mht**^T0WRm@)=mGj?C;hXV{@F|a+>U>yQvR2s%Ky?2kn(Sj zXzq?4nma{WIz5e+{ywUuzyE&M5?r2VX?H>`j^g9WMJU9X!m)ibs*rDfzbk}>1WzM( z3A0(`{k3an^iS&1NgeQ2WJW(s|Gah@TY4_4y63W2ox$KNjqf7mVL&1r-|MD{FK^Z5 zU*|xr+B*h}XIuxo;?u#(xQqC*-?|SAE*R!;Bg>dI*l0MDoPn93%XPd+^qA|k+Kt$} zto-76U|fvO?}t&eN1d`p__9zOV~@cVLBjk7!pcUeTP9V+mQ=**UwH&yr39Jp)BaW^ z$ov^WqNn!%uP?6rfwqXr!Mvi__~J^i$a+muVaxAnv!Q7ElcprXj`nc|Yo=#i_WigS zqJa$uEi60IsZ`=*1Mgg|qTe~{$n!hnu`bZje3yI6KWM8WEvN&zk}r#Y2@Ux7PucQi zK?d2AMM6Dc!}~Y1`BYHq*2+`uiTb4In2s2tV)wm@ln+NvDpvGqxj-}g9@ z;7Qoua=SJw3OsvENn{Ss7Cy;Sa-R?Lv4jueI3Tfx6I)_S^8!QosJ75)ACb8JP~L$6lZ9$2r_(0LFjw6nN$FLk12_;v%S-l zL^$VUGrFQVCx^lYBtkBD>SI76)Wv&EqdRZr`_ET*=G%9c^58Vn_0!{gR~#n4=TQ_w z$1x(QS;CZ5K3SqXKF^=#{=GK#$=!tHj!kntQw=Kz|5p3E6l?z*K|S{Bg z!1S~!iK_+Eof1sDciOx6M*ETnliG@5`iQo8x-i`-!NmM2F#Vb~6ADbfYDyw=m~Q0W zbe9a%9k%sgzEz{aYF8AlXz3VO+wmWQ8))2e)E_J;6D{WpB^!~z> zMCRzN5$NsR8Q`_ozB7tgVhcuTPG45h_gY42@6G@i;!EjRv$Ppdp!x3iEHvvFnq2`j zyLQ>T_C>+z(T3sKrmdZ{ooKxW&#nL-=1l?UW^EP}fNnA+k$K2vEEY160!%O&6d&0YJ=~ z0#HSp1qGmzDT&Mh;#9-lz1Vbnf#JWiaEGmjToZOYYUeaA}`sn_x2DX=1#%rbJ{#87=6~1#MQ#+ju4~W zyY1b#M+YGfBc%~z^qjVEx)|LNV#M4j82uk@9u$oJ-IPQeBZFn9aOH|K?gk`6E@qof z8A2|2b>)h<__FC5kGFpI+|^w_yZb0km&QI5aak)4*&B66OBFhJ<1Ag;#nm~(;U?JV zu^y4$Qf>!pYDc!u%mkEl5nEFe3(DnJ;;WRtFsS{lN?*7~khqHLKAVo<5FhM~6ID=j z);FtP*&jAVJ9b8SZQ+xhk)ra>=3Ie!6xB3Q9)som*-4B0FW2Tt0pt-=5}{joDPua* zOF^s7)=)=-b!Ty6O`(*J-ISH^oRNA`Tcor|t;)5SCsB?eSdsurCUCol)fS>kMv_pE`X}0KD@O8%rX(^ql6!TH1Zr%Rs_k04nP4VYOpOiY+uG_% zYbf{X8cHaxVk!w$uHVvTTrrh@G9{6@scc5@YUSIwGa2Qr7hG|PiWk>LLe|by4H@9; zZp|o^?Oe;}0R>#rakPH)9iB=%dnlpob(1zz3V7>HNn{S*YRp1VtKC8jOx3Wbj~t7Q z+DQ!8;Kcmfz0@9zDlE@sSJ9OqH z6E1dMB_U}{h2j2=wtCXSeTU9Ggv3iQiKVJZd|R7g#U#FEN+NTUxL?O4{6kCm;twx^ z5@{i10isdU4ANz@x$(BFW;gfgn2mo5s;2@Ga0MEWT+1@mj;_;|K(V7urX(`Aqb-;U z`BOsch!lBR$J$j~%YcA8Y9MJ|VC0Wz3!T? zNqj$pTGAFeEvR#IrNSB52ch^MI7^IjX4vPQ`GI7MijWS zzDZjxX>r{vl2Ae}o8^+zP$_!vO4SbDsLicn2Tz)k$lMMNOb>{xVEa&I+cTI?1a`{d{KKE$vV|Yj%c&37|Eb1 ziSG>~IbAC?aSHdBU-h=8HHAM(6^44Ww#6y2iBz-|mDWV|r!kQ_3u-re+Q)j;K1$j= zEA}yFO5*uuA5Uv5Dy@A`9J)u2LpP{Mze)Ss6{O#2N+NTl*PV1-zB3UOa(>G6rf5>I zM;q?DAJP^rEjDX&6W~ou5<}KxtTw7xeNdYl1*=~+C6PH++mf)tWi8%uZ{(xLaSL56 z=b!p5#`E*q;-|%PTN0kQ*Tp~5G+=Z6x^9pv6B;Gn&xEsI#nud| zGenXu>0e`%AJA4nTF<(j&K+h6Y)OKkC|r_2g84cX=HuEdDli{0CGmp-b4^d zb*~%%U9Tco(f)P?!ICM7%n>}0wxjl2PQKMff5w%(?WCiouZR+N=dQMz(&Bs|b$7N| zOj{CD>fkr1=JB*P(~5b#$&^Iq=5beg^T4&gR&BKDHZCOW>be3tY#P6=t)jH1aaVfN zfQYs%qGT91s)q3)ZI%_o_@F6?%njpUdc&a1Xw#XfS6o!tVb7mZLUo0-*g(FZt*W#J zaxlGtP-c`xFqvXr!A$)EH>%CHVkOfhgh zrjQax`ukE!#<4{;j$5>uR*YkdDT&Pe$dzCknO|NBAvTVa+Db}m95fZ#Cyy3673BxC zzgbsN1J8EEM}RK z$lNTJpMgGV6Bd#QICeg^Fc^Qx5ZK{nn`4!o^-z)tPYjTlJ>fF4Qbmm*uM~;*CuRFu30&)$0K;pIyH&b}wAQfBoH`!$%2T#vP}|yKrUmu7D5!S8 zr`@QI%f9tC6~BfyR|vZs!a0o4xZ`2CW-mLQ?L;f*sC8UM? zwy8R|fE-fTo)i+;whHz~wV71F{&iClnS*`X6kzvTyxYaSBo^vo-CXNUhWjhpYM2?g zc@Ikj~EVvi#%xca=v*NqtA$o_3<9zLJS8$wTN+NR{Z3Ed+wqG+9IdzqBl+HksD5Rrwr&$70}zXSyKS*GbQo;3+S-6$Y}wchfau_ zIVEqpO9kz;_SY+*oiru!{R`S9ZIQJ=iyRQLTLrDH{q+iH4O0@|zo5NKTVyTJBHQ@) zsGz-F`|B0Z-eO83bI`U!7|McQAl06O24 z#1AH*yR_AjwlfPrBl|(_Pyrp#{(1$_+e}Gh4(Rq_od1DJ?SeajlMGu(=6e;HNa#1M zwzyrVKG`bPs?mg?#(V6MAJ$euS`cr|HH8eQos?uC-;88`(-tz=o($4Be5Z=^ur`kh z(x**HWRA4Z6S#rAs zUmlrC9Z*f@6WZ)6rt>jV5}BLMh8GD7!O$ErhI^wOzGo{2`0upEOA9crwI%*&*zF0~ z-6~{X(`HD4>?@`uGKcJ@`)U`d#0{1!%G*w&qRFjR-LPXv!AsGeVO+60t69#LT(NeM ziq^ohC`-e>c)@cxsg?crK^4)Z+Po=wAoNV889XBy$8xmv_(k^iU>?2TR!ep!FX8v>lHADO-W=9 z#$ms%H=K~M^TY8Vd2t^cZ~CKh-&llb`2kVXE6xZ-?u|dBt+uql9|@{`CAqn-H;~RWB+!EvwY*Q<$r05qyC#Br*qPV31EWifY8VSZWo;GIKv)b)6iB=)TOr-l46GwEb)#=N(=YmBuD%#JV%z zWgQ43;eJ%beXlm33huj1No0=u+Or5Y57lZdTH~l&6E2oCVl~dmO&G&-+JdFUaGkjQ zWz^@)_BfNEI;KMP5^Z)As2(;YkvUY$0+{NUVMiwdv1bg>e@7Q#GA6DPX(^YYD z^-aYcCLY{3{u<_MF69h<8Y)5-SBZ+q6#7*e3oq*YPjyw5b3YhedUuKa@*ecPw%oDbPeaQ(I^bC}@zEz?yIcBC7%_Re%2Es+L~M&7l- zb@4IS2;N-YbwebL*W}`A-{r62S1w<r+v4Try)a#<4^(vj(^2&?d4M8z2&H&@-1%ItLckOjUdVGkiBViLxI%Ix-kF%ul< zaQ@2V0_P1T?ar%ATAdl_76Wb0o0MvunUorxDkdGyYuwr9yskO_qRBB${>G%yIl-jf zInJcbd5g(_%&rG!NhleZ>G>_>|T{oC;`;C|r6fiMJ#e`yV@xY9amYf2n^#d~o zX6z|B2Nli)d{kjI;2#yv0<6DG^40+MDy#*3kHR{@VTJX8_bO}vd|Y88;GYyW0XE^2 zoG5rU;Btk{fZG+e0N$yv74WkP+W>#8upRKf6wU!`!DnWmtOIbB!cM^VDLe=8Lki~t zenH_pz^4?>2YgB4xq$6>H8GSe09>nZA>eHa&jZ}8@O;1r6kY)MbA^ilUsl)!*ok+X zLD_|X>l7{qyhC9(;71f*1o%aT7X$u6;S#`O3NHbihoAUESr6bl6kZA#QFs~P9)(K* zzpQW>;J+&D1$l&%m4IJUxC-#s3ReTZrf?15`FP9? z%GLs2r|@#Xgu*KTeTC})zp3y_z-JX+1^9--cK~+b<{6Y-4fsxl*8n;SuLazva6RC+ z6>b3hjl$~y|EBPIz;0ZCL)k{acPV@);Gn`A06(d46W~89d>7yg3O55bA;>_(jeAO- zUyH~WNhjFH(Sc^71O4t|9Gxj0sA`EocA$$DvIE_ykR2$ikR7O`kR9kd1`f>FixTQ% z$w&^f^%bU!YLxNs7@7yFrHom%0$Iiq19_e^5C}6N>{o%MKVqO{`jZNza(@AXX-u63Q_pLI zMzDgK4GL-M4uv%6V+v`*Hx!cTGYZM{b%kWQs9lti=|+WQno>xnA6LkD^sqw4qvsSd z9=)j$@hGgBRfcX2=)QLjN~jUKcPS*@&nYC`Ckzx{99Mzd=Xc17q!-8$)6RHZ`*mIhfQgXLN=K9E39ZRR~Q?bV8g>a z-Xu0Wr;s+hsgO1-I$ts%hNI+-fj~~FKp>|>D$u&e6w;s<6_RPg1)_&cml`N4w*>-K zdVxTd52^rzLievT)MtbGTRc8ns9&^5AgOOwNa`7dXa5VChX=qJ?aG z4U|lGs6gtw4V3*41OiX~c_5Jb%YlG^=J^f5z_{G7ZwC7}IiNHP`$Y{3Md`*s5PzsZ zyFO!}Wcq#}Fw+Zxz>;elMb}Je@=F7Op>$gyAe1^@Ak;xP6bSVY9t(s92(PF>XP(m} zis{TN71EiOLb~i8h4j)x3fUBoC}dMSu8^bG{Mn+6qu136IeJAEa`f7(khAHpDCBJV zR|+|sKB17a>4nXr472GnR|k`j7Pz{=3@zg7g9_=;M-|exKPsec^(~T@wq0hRc>FdM zXy|T*H1rDwN|s-%K&xLhQ1&lq6_xb^tgHbQ=#N1ICDZ*X&^bR+2EmWOH!HbW&CObF zwsNzLnz+IFo%*2>#aFO`n7B}-xZkh1VkNU5R3;zNl%LWzVz ziOfQY6hnzzLy4qAiR?p(W`q*$2_+g9O0+PPXlf|Y=1`*XlAED(x?sTTCCv z-mU&@Hx4^T$7-C&K8oSO<yuaO#d9*wb3$ zfZB8pF$rUzX{ub?rz#mc%6kc226S=@!Y+wJnmc zOA|OgTc)dmnDcv4=yzB--IWnwRwC`$Y|MU5jQ76*{aOUF!H5P1w$gpt)sV2OAz@cT!mfsdT@4Al z8WMIjB}me)k~%4xx9|rUv0Zx8ygOhT|1dsQR`W zFcvbtVhMcL##F3;wt=|4uY{NxPs>0Fp0L+%-k2TEq_dGY&u}%HKPQ_{CAb!2iF(V+ zr)X;f1D0h53%?1G(TZg=1>EuA(Wb#sx4<2k3V?w~xd_(d^L-p+N`A|hIAR~<>ordh zIsJNs__&?7^K8GZcxOJ|=P($_@3c^nqopyw9i~LnwuOT1j4S;qd9yz!J{Tz^E!@V; z4x=YXrz-mG<$K*+1YhPWR%VUEGz=LnzZHd2n=6*a)E)r zJ=o=@y@bWbbg{D`Sr|-PcnmaxOJpkQ*nvSflLZs$;quKikZE?kDAt(^sAvWj=ex|? zf}K{}me0)Ljz`J)KKHf_XY+B_!dr{1!BhrcS||6;If3ChAC(+A*OOv=I&5(qRU% zgkhI9ZFp|yUv@p?NBp|Hm(gA8FFE@42ao=&+pjgxz$PPpgX_g&Hs%BIQqhyR&p^EN z@~SG)aM!~-=QztKt-pR<^y`1Ve~HrzDH(D4kYMIu=kwXTmCm9e-rm0*P0sD#lFg&_ zY#xln`h%PK{afU=xP22M5#n&7AAPz1CQK;2yuB5Ucl#}wNcOX8`tx=UD%}3@Dqc?G+%!*-8hHxS)0@3*VIQ^C$z4vuG!)(S(5ai@aTKRl6cHndugeg3PVi>GowSW7$3k<9E|9IiC&p){KZDh5|uwqoMVD;&j4z(Iqmz{X@U{mcY z<*d*o8Ne&fII#ZlN6i@>f8GA%i(^&gXN+m3pDpjMF?Mh~sbF<**JqwKtlAfStLN_* zJpVSbT5DKwc&lXf+^26*R@WZyJHB$u&fRY#tIG{5j|+6KAOpmMofDQ^D!}=RY`RICcJ^Dt1No`AM91 z$C>67-q2NEo`3FyAr2R)ytu?5nXUH^W#WB~hc{4R2BZUJ?@-Df zUh24btCl~vJgXBKiny_SDp!zM)<{8y99)LV{Hxy`N-P~2#JsLSn#=>(9gElU%T|C+l!?I0q Nd@T7u@*ywU_kZHO3jqKC diff --git a/doc/LectureNotes/_build/.doctrees/intro.doctree b/doc/LectureNotes/_build/.doctrees/intro.doctree index 7f74a15322d8df209e004f4d990f539b311e4679..2f62b739c386661d2e796f2008595050f2356b5f 100644 GIT binary patch delta 252 zcmZ3`&3wO`nWces>XnTwVml}6?c!Fkn9?@IuZJr+r?j{vwJ0+$9mr43GUj4nh@GO5 zwG>EaEuUPlOJuU!P6ftQlhb!50?Cs*C)xV-a3*IY763IF8iCD#bB$4q*atG=0EjpQ zB94HFV?YxP8BYRDGi2O2dFD=iAp7J_>CN)H&6pYgZVubGmzl+!n}K0+qK(L8?L+d6 zrjxx7$uXKu&N`&d;trEoc}Ni`ar%%cqse5(!xD^clcf%8v0VpQaA~sF;S9#>lQ$o> MW4yHa)8TcD0JEB2QUCw| delta 204 zcmccL&AgzSnWces>eP)aVmoF0dN`6Z5(`RFi!7$JO-al$=3-!ooszW_NF`48-D$wM zV)DaXhLhKWSr2wj5>16F(a72ZRFkz2L>!pBewQKRVUSA3^^-U3)CaO3?3CUdx7&=F z`#VrY4_|6gQGU_n#C^h>H|<-%%xF0I;vtF2*@xs9^(S`$NrTBN52-Uc0!1x=B3y?} p8TBSR9F|~om>hXni|r!Fk~5P#4`(o5oc!sq9pjnJhDX*h0sx)>P}cwe diff --git a/doc/LectureNotes/_build/html/_images/chapter10_39_1.png b/doc/LectureNotes/_build/html/_images/chapter10_39_1.png new file mode 100644 index 0000000000000000000000000000000000000000..91a4496c5e66ab2c962e8d247a1291c2d93fd1c3 GIT binary patch literal 2976 zcmb_e3s6&68ji)<)sqdZ zKouffjDd=j@`?=@LV`)KfDscwq)AFlK*0!vS2Yj_2<)Yu+0Jy`+1XBK?&I8xiQg!FsKQ;>Qq!(ESv6ZGMCvQ6@Ue@RD==xZ+3BAuDc1)2V{L;$lor=629_N*ZZ+^dZtozI2 zn*S`PL$i^dda6 zr>*`)QiAyOtj2(b(lHoGT;BvkQ(9#5z?_*gr+Wk0JArI3fPDd!ae=)Z-%ySHK0XQf&ek&VX*#$nx09OJnyTb`i!t5@RrfOen}SC(oQ1 zGguDJ#oOPLOMDoIxkXU0UES(Md8QKv1*Lmpq@7inIrvO5&se2YV;zR)9fqM{ZYj6m z>63*r@rM9A54`eGVdrG2RZwk7)X4_X0AcA4cXcrVpV>m$lhDhO-+?UaU2wT24#NlV zUbe{9tw;$~rMk7Lzpi}92D!Q!DX~RfgodnKx!x*A%i$(NvDdkb0r ze3UfNVYnSK!KeVh*{`GA!V8;FUE=OOEdUo7_!ozD|17m>`oW)uafD1ZuutG)0Uim6IBl{YX<&;6gswLRXcD9uSs}k*03DqN_oKeD(~a z^LWP3NmDt|q#QdW5d_PHe&siADi1dBZfFwUU)_$(u|+0#q--fK1g#S(m&}!YtnF#; zfOkKEbT+5}a&=^d1vkMHzvwGu_-sK+tdOr^-2FFTP)(;{90_6{Ob!|&VL_{J_d9N? ztn^$gz!qk$=s-FEh%w*ZNM-vld|kWb{`ky2fVlem;yG~P8<4&m7_>&J9EQ;t!}7T} zmpI$*uB&riR{a(e7)9J(`-F2v`Y*x(fIuSVj|b0tdp>cK7q~^UU2q_Ff>n zg=gf+V+uf(15lXN9V+$C@c>pl0Wq?FU3wMI*tNBOWB^=fSE_w%mopqO*tkV+C0hPy z!MtC_(mXqWzojHBJuolqN?KEzA0-%x!DpU$OIme@C2xyr{b3QGAfEY23JYQ^U3op5 zGW(uxF5|~6FHE_+P;Ht(K9fqbUG&u$0}5jh`AN4Ajdb5fJ+pMlvYORGCbs;AsZ@Mm zQThOK#rIMv(l?RZ4=dOMdto~HO_v~_wAqzTx%^F+<%z}tYZT8Je40o$xC+Z-O?gR{; zA1`-iH~>#i`xfM4P}EC>dW)Gk!P%UXipzmj%iJ8xLFE1L)O9_^v+Y)b?#I#NRBBTg|JJRT>GbgjRUz8WJZl*)EiDb! z)+;3A9uNl0F+VTE*>j`P_dLB`7W&m>oI*scSn4_N_Q4mJ(2j1#YIL98P+HxTm|#Luq!G$+EHOK5L#QCaR{F!%5w`| z8G8PlQbQ(@>NHKlw6_MNcJC^1=`^^h;ap^4&{+J|cO?)jLnStH!QrnR~!w+Mv<4lYosQU$J==p%IxDLjDMD3K7! zZgz!%wA|cW9s96CwCh@S4%*3ynQ<^TYnIq=C}W0}7X_9$Gf8#f;o$)^1r%EW+gjR5 z_wt@&e`J^2H^6pttP)TNJm1B(8K`nUXg#zv|drCV~ccujri@{_ge-0u^@Gd lCgsJNArP99|CI*D93~?k>=eh%z^7$|zi$wpbKtWt{{>fyiKGAk literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/html/_images/chapter10_59_1.png b/doc/LectureNotes/_build/html/_images/chapter10_59_1.png new file mode 100644 index 0000000000000000000000000000000000000000..6d146702945cbe319dd1eaa069902b9573ea2737 GIT binary patch literal 22294 zcmb5WcUV(P+b@i|?E<52tI?~xi6>AeLACAuvrDoB?a>77XLL`6V) z4M>*~N@!97B#^9cg8Dq}_q^YAo%06?S#@UCteN{)?s=)Dq0D%Q{SX5K10(FtO&tb? z-Adr^-hq8!i)HN*dGICee(SEgu9Ky^=Y3ZT2KD>y&h}33_BIdBA}w6qY@8g$gvEu$ zE}gY@cXxJ^5fO3t&jG?tu2v!~2{+rpMGiXOF?3^KILt!-+r`R zg<(&xY;|AWdA%nk#~*#(OYfNtqIlBEjg_V$jZG8 z4EL@ho%Vy0d>1Y_Tm~fbcbhySC&o!^ph}1*JzD;`ZOPl9huE$SZ_ujwW?!m+_}YrH;9WSOqft zsT9=s%L`Q;e=`i7(0H@U^R1|P{Y<|VM!z{yh}0yAotbP5BX%YSaH6+eB*1mzWjwkv zb<=rL8Ix$66U+_+MKBH-cP*ShwI@yebg^}(l5weH1W)z)fL+X0mn5D{U-AmOnB{93 z_nG(48Bg2RzdjYplir(-an<=_;X-->N=48h z=j&UA-EXTeAKkrpSvi;!U*)|j{@}|2KZv@KbvHlBvOOUe<4=L@+O^B*!@W=X?fv=Y z0SVqyr&=+Jh+qXu#_c!k9{RD9lMe~4vGjX)UBLJzfofjl=ZCpXx8d93WsAL*AGF3u zs454Yfl1}{^ysxliz(+C73g8x>n4Y3io-S_xo%t;=v;Zt$luBs9d+Rvol8Cr^J7AY=5!CpaH^n`5Dh_n5KfZ zj!r0jBfW$;>Uu2wffd_y-v*_L;Nej4y}O^8Q}4+>M#oGphP!**o<5RQs|#c$%*C#E z&3C1~DzWcRY7DzD_x;n8fl5!TfL?|(-VJn`l&(}&)zGGJ{$%gfsnp7a08Z4MP`wg+ zL*5G)1Qis_vf)^Rx!zpD(vk=awY}UxBK08g;_1Ux?K9B}Z+k+p5~ z=8v%f@Z30k=0)|fW~P~$nJP|3qXd>52T9`!2OjTzvXZgtp_9l;`6qc${$RJr@%DG3 zH(tJcX**PwpHg&4S558p`r@!47Z+E%BxKc|Am3+#sPb~DtpE?cc7=d@qMvPG^W*y` z6lFG@)NzA3(`$L$sLVN$r?IcE?*la>Q?6-kpJAA4t8~s6%SEu_Zq&b4SjF>wYiHPt1{OmBjhxhdKxM#!mGo9%Gt&p`; zv!x*j&+BQ55G+P680qI4>4UdPA6(a>u)oN0SO(Sw`X0DulwF=@xk*!$2!`GhU|pbh zVNZ=#c+B;@zrM#~{+l+TDWW@&RZtH11Uw$wkt%Q3auXE|4FimVpB#LWegx>Kx;Jk= z{rvg!l{L?OXSeR1{cGqGYJEQQe(m#2i{?n;NOdK6hB>tX%vLiBoPKNCw{G6dP>+=) zb|gMI!_=T3Ro5OTt;?*q{b8|YYcYG=_`|)&!X{)(HeI{Jc_y#ow&_yP-6dWXOD>V*Eohbbn)Q796TH=s7L zH`h2D+%pS~O-O%$2bHU9Xvn@1z;ueT1>SIHvfMovyS_X;=zl#G9(FLB4e6DQ4LBIX zs?PK;^p`lq?gMwNd&P$EKru1UK=--lazP`m!wy@W7Is0iiQt;4m#Kr=S}0{betdGF zgH{YmX16-k$}V9WE?|%|v*64y^y%b*T?`D(4}y*|FnqYQ56o{L3w~~D3YF6H<#B>L z1$>t%F_Et3_y=A-F;4&L-##lZGWJ2gLdh z`LqSWVXBYE5|~!Z!g&S3rO&RGxl=`Mx7``Z`|9Nb(RbXq1*VvjSBIzcpH|5qO+5b> z1H+}}!9Ai349)>AjWP(C>+}Qeo?xZVLHDNg%|~wkvEjSBm@?RXb}*TK;*m1jBcS}d zf0lo|2h5_Eon7hM&TjoY;N2xgaG70t^f_*qlpZ+e1A_p)&L3qEp&z<__VCRWz^i3zPTC5@ur2Q=TtH(R72qq{7hCOUi?Ryv) z9-{T03TO3}RVDb(iArz#dfc;0xlJOgEKjp^J8Z33waGl={KdjU=fwrL2Muzyz2&LB$u?974(=W8xJW>RU) zO^G$;6&cnqo%`n{bKjL;cT;S9K!u#8<*B#linbwztl%vT-R);~lMu`bobs-Qqx5s3 zV{hAinNuG1h1&~Of@`auI7`&fsZ`<(i#KGPICX#=yciw{O)Gl$whoXJH8^GG3~5M{ z-bS45lPf3+e#)kNNhU3LtG!~~4*gJ>W5`2o)IVP(bZyE?GxJ{l?gUH#TVuMS3?roN11az+ zq7fwGs0nZLiO5#V?mR_qiS^p0h`4ZKs{IwFuv8&FPnrqJX1*JRU9}<_IXp^Ys+*a; z9&C!wo1yNNaR1bt)twc1-!DpPU}iF3jA&r@mLj)SVvzhgJK82wuxyo2u_!`ZbF&<+Em1@jE`$r8h0sFG+#7G4O&~$rh zl)_@l1}6Ufv@I@qB0z&UyUQWZ7G89-?78piKenYA5APy2N3`Mw6K=kYmIh=9_J*lV`@mbhGU~8L*Bbd zEAJ&y*im~AKl|4~$_brf)m)NA{H~t<9)9`xBlFZ^l>4@c7#}UE^tPNZ3^g8Iv9g?> zZ5-f2>>U#$lVy9xW@Se1>@9u#_-#rPW3z30$rG7%%_5%Jt(Vz7AN)w!1I6 zpOYrcFdl}`bQ_9_z!t4<``>9`GMR_?aT%YI^|7{n%N^Y39lrs-Y*)tJ&;kqTf_uNaDoCiJ7&=!=WkiXb#j;_})abFjZ z%>-9FXz}8+6D{UQ_UO<2u{O+3VhcUrz6oG)+uQ%+gH{0u!&3!GXTx zI#)3df)ds*HJp)6j{EfZ(2+xz<2cFl_*0=N0*p;&#f(wisqh9*{RIR4BHGsI@$wC? zsr?Dp4;^pHe%IVYxsco@VCBrTcWOl{{A&ZF+Exm@+!0p0`f7+JOMWlYTs5|mAAQ%6 zTJDYGV=}W=nLl+d#o4UxOtrhwbPRPAot84U2Kv6)Jmg@Ag+!X6$$W@}el)h$Q6@EY zCsd$M#KEg3I5^lJQK%ZWuRRKj4IYW^y#dBm3Fs9jg7x^taAna3;bui5I~nIK3ZdYW zOLl!rxcRP>PlqQ#)5;<|;oHx0LeP(uyjk7)KN24Hl&>MSp45c7lk6aLjGUQiy2ck< zYM0^_iILYQ{*E-h5R6&9)Nr#wz$%Yn@6_5x9H;Ct4}%NBTO8C;RrMkll4EL`3~8{Q znm|e%E610ZGrr-h`dYLZBC3{oKpmrCDpI``x&t)?j3pP|JpBIgag4Z4=&5riQLT<) zvhk-@G^TThANqcS{4$}Tjii58CiNQN#+F*{(IN}ob9fxXw7UOXLU65e1Tnnl?P3@{ zoqS*~;b4z0RMg@aDz9g={FI339Wq8rHb&1|wLqcYHG~0BG1ursIs5(!xbcwp>3~IF&%FyccWhW&pKN;~$J!Cui#j418-O|CR z@IqLUL{zhb*ut1Y+L5Pe8u3|%g_fBBv)GQ-R1cIoVL9bd)>AFfAgl}mZ2(uBv>`CJ zFBl4IT?}r+ywuh4T~U|EsnixUc`lP*y16)5@I*GGMLdW;?oj{grCjRvn73T>-b0qxAmyQmQ;C*= z*%au+s?)c;n7|0(dBc)^dlmIY85TlvaDs*+6e~yTUJ;ozEa9J<+bD~o&X-)k6FpVN`kXs7my<5WZV}06KvQ$O?QkoJQcH4ISp^(E} z|5dCXOaMVOb3ovv#6CB>8%r(1GgofuWmqe~bXJl2#rH{$H)78`_Gee1@#mV7OP^OQ zzZnbsK=fFI2m7m&Q0-XKYG{s!(U05jxWhjIK#(TsFpy!{8guC2!H`xbh3{)gsSLO8H@OL-IAZH@fn`hJb78UTG^v( zdTulXz_snzDRj+vMSFQzoUF(7WV3`ssRl(ML_ly7Q+(Hpnr^-GNf~A*d#_h>p7I}_ z7D=cuC|{ZEdAEcJ8E#1PL*FJgZ%oCq`0o3$2Em6X=ccnW_K32N_&qR!f)|q#NRCO6 zA_c2}*eKz#p>7O{Lj|hYOYYMeW*r%9xZYTVLKJeFE3os$h^}7JXH(Su$uJ`6$J;pt zH0A3Oe&R`kgd?7Tyh*WcO&TqFNRbIk!ud^Wn1YkjXIn)o(n!#!lW%6kB!r-2npyDV z)00pqGf{NY<;@nkwP>5osXKIbPCbyezEd|!YftP%LdCa@3lih0rv$WXGR!uAxR7im z$Da>g)Vp-^!gD#KOMdzSBl=?M=jRzg|?>E>=7}wsC3&p=0_RZ7`d|_3T=%anS7z+aYFVI3OEXPnJ>(mC}_)4aj671SLB>wK*yYB{yY|MKXL7eXR zLRJ+7;!kA9Y=sM*Z``7DSvvsWQ@pc8lwrnC{BssyflIG+L16#!<7|mW{1=&Mz<`-N z{s{mKGc+E=tAVIK?`O~tuo*xQd$o>%WA>Ry06y>+sCfKJ8o&vLey$y$@V!Xu-xvCx z1%M61;rBaeWixN*2f(I(+0o(5q4ADW* z$K5+s*(2yTYa4myzyiA;ru4=ScF3d=fVJ$c-){he?N@o)-&gJO8yJR{qYoMlJ-4Y!e>X!HMTD%n_4~SLDw=@ybZOt z*1e+nVkEQo&UJs9YlR8QeBy7aH|6Q{^xi#B#Ic4}5~kuXtI)q&G{#DL4vQp4HA{wL zhLtPZZ_T|KJs}{Be+N-NC9-Rc9os9tO>nIw^_DCZuiA(6*qE=v-Q~{pb|c3}NJj3H zn!0Xf9E^w9H0RKmS5zFW!JUG8G?F=T=QbX#BEH}gZt$&NV-<5}AKe^lJl ztj9WYWBja>qppxWiBBUtURiKP)-GmO=U-UsT{@iCguAJgVJ0#<|9~c3UFjD>lVM8@ zVcu5uB(zN1z^`7$mc+?qD8yRD#Mk21lWn+_%@8?gUHSZz-nW0ut2&|f8WY>RkIZX1%YChZ-39~u64JZviNS;t-qI(CeG?^{E)q56yBTmZ9Jh}%UXu;P*Op0N1%DJi1#DeJ-7YP@woTk{^!fSgLyORzb+Q4HG7|9}-x~mPTp%Ybxem4*#kW`tq z&$jkU*mFtQsd)TL982pFj#DoH>XLc3*cqg&E#pOd&0{mL=wR!odFn=N1=yN+*s6#) zqZpb(P+rfPCXz!_I?j~$lvyA2FcTf@DHBs!_%KeHm>1;;RNdNhdG+Io;!8#&9aEn= zd^{#UpQ5@x!0^nbXUL;mx}`!>RLHNs5|B2i;q;;(iI8r)j)z6Nk|(eF95hi+6EW-U zNOMf|ai7`lZ>FFzs64Z?vk#zAeWiGKi>TC(BRYlG4pKc9GlITgLV5h$yuxBmWZkpY zP5$T?_*ya5L)3={mYob4K%?CPoT;vCz03{%QL2uq74b%=3yqndMTtqh9Mlq=G+U7K zQ40{^gbJBySyQ*p=h?dPEEe_NT#DeK`udid^~>~i)b~v#e~K6&)+(ZVUVgc2vDZLx zJ($Lc-OallQK@C*k-o znmE$Fh2La^+@A3?Hdyvi-tA#0Piw9e4@x8&D4X7ab%j%7t3umz1;WMdXuCv>lqHR~ z3w~>d0%`5By-;yXmix%jI=%}wUwidKh1a1hve^qc^QU_!dzZhcQn}(!W}5^t5Y|Wl z?NkU_?TS~cdH%6BR&cU#|9G{E_nrbp28~1a!38pcX-1CU+LArt25RHpxpFnlJ)2Ge z_+V;TmxK>}yLDho&TxZX)Dn#O40 z>tCk#JiJ$i6l!LFGMeMqnRJU?$}vtySC`IG%abR=o@17P2;o#siqz53(fe@kIwO~Y z$)`_!Tq!8@MdbbujeMm;@LW%`^~{fbj_@a+H*BXyM)AY|{+I&0>>5-?_4d4ir(oW2ZbyaBc;(Z14&Fc zwT{<&V%H2w7YJoJkSr@UaoNXT^xXJsbCUTepvtPpix&z!>$?L&iyhid$*;q-DDOUE{ORl;Z89w=As z9hN{rAa!a zHFEq)igLxO-*TJMpGzX>U%A@T-OCrNQ`m8OEWhmTGs0Jbp++ghk~a_e^`}9> z7ZUV$L8_Q{O50C7gr&`1Mv>5J4|14HUUXun&-13nv#;j&>t9t?Agqx3W`FR6;B+TK2Ai>ZZb0-=qjJ|s$IrJLNKa}_D^X?57{)JBYZuZg-V0!F%dlSTJPUU#>?Ha9Xj=i z*x)}F_&9JREXA#%Yo9;8xrgz)868&GHu{$1U#eV<6@bYUNo$lV`LUYu1<3e%m(pj< zlH|Y)y|A;xtM`QQv!@=QI1Nqh?Q_m^b7N6o>e)4=ZYwJb@=SIuNr{W=0paCxk@rGz zpZL9x3_#U0p6kQH1DH4*%h0++Z!xPjy@ntT3G0rt`k6X)uT4inbzd$MOKCoDvil5} zDoq1~Y}vjvXTQ6JnK42MIq$w)m4{Y6Q8*L};fKe?eu7>pel>iuNhTuLPCEWL zwy#vU=K_8ZjJTa+Wnx5}MNJcdKVw6%R4+Dy#r+DuhP+fu@B6^k@Y;sNhwv@Kd5!c2+LK;aexVy&f zbBx6Xb9$M8(JtsqeDCSOsZ6y+B~>MgdDn{_W9|-zF}OeA9-z4t;oEAsWn~}zEr(2;^371ttau+ zQSIJIj3BxGO+kLjDvb`sRsxKClq_9U)?;6}2m%CF<&tclrHt37?=urxP0rl%xj)E~ zwlG)i(}2*YhNOJ|ey{fCG*Gc^fOUXf&g%ouEKp?WuP)ZCnkV&**ogm@1F%?lhNf(8 zdf~J5RdEn)%VWc701@%x#Q`8~4wV5M^g|$Ou*xno@5~PqRiNgJTeh5xSMW2EcAe}f zuxLI~7g4!XW84tT)u#w;Cj-%SE*;~q1I!rM!aDI@nip`16g>U#;WBAq5FRhXRLeE&-;_lcywCe zCo_=vO44x+|3!ov5qgPLWU;H6`ggckdVXuw(ix-6qnb2Ym#JrY&(^cQ_U=!o+JD*| z;J-bh+1RM_aw{H1j<`uCM`Idr#Wu-UKJ+X${P=9bxG>3&K-^|)akC!tRV16X;H)sJ zrcV7dMVRfTbJojKL!8+g5cag6I6)Pin(|FAr%YF*Dm3Gx;0i*#J+W?; zIyt>$&{=6h9J!!Y^YPs_$GRpy#Y#kMMbQQFGIL(E*#i& z=`aU`v;Sbz!lt02k)L_frF6t!LccuktKXC-vNdL!8?9IxIJ(d~Cn6Ied)HMaH8I(* z$irvAia3BbB@Pbr8=ny1yG#9sJK>mNEo#+1ApYR)qkYx!@3Cq1nfJ~`)oh>t*fF)? zpb#V9jHp$vx7%iO$uf}FPgZC;2QylIg+0--+Wp~}3&m9@E;Q7hvL2hWD(tnMqs|?$ z-}?LD!I-PO8e@A+W7Y_Ga(grZo5(#b;iwdsWuS?lc}3=uegM~cYdpdC#hcTRpnfe0 zYL73TofzANqAvXP2KNm@_{}<57n;Wg*F+Q2KY?>Cm8v*160$_OQmH}bgTI9f-eDIz zH?sOw#py3l__fX-42)i~*AZqd=oQumXdRSWwi$8b_LsSC!64}Cs|F~YWn3;e$8{T{ zAjnARfOC(iZQCjPQI{ta$vinHLX$1SN#6Nz$rB~{RMW%YN_)JVr%0TNDjFN z-9s?`76;4ecq=FYu={-Y-k+Nsw2_ zGU3%f$EHjxo=dTw*oR0>xzija+mq*4@Xr(8N>fz6QxXVhmv0L|O-{zXdIc%E&qSt1 zlk^J=%tD}%YK1I4a>2G;x^;IwP{9XgxhsR$x(+`k_DZCusguIGXWyvNI4GmayebuX zWp|7mTa8k!@vP*fK|6R|lZGZf*q2?QeURnd(a4sD2HPOs;kA&DO66D0T1+7d# z)2Gis%xP}hxD}=M6`rk`vxXNTM%;jYNw~2m8_d{ov?-Gd{*AF5DjrND>YE%otZwX| z5u}!p->%Zxr{X#Glb{2)6Hm~4t;i|I!8`^7iG(=5LV$bo| zwuXU8_W`~90^KDh^^T6<3DO`qJz?px>>KpL!`H)NA47x*Xu>j%S}=i*K8MbHV39t; z#f}~0YM3n*sxf+ZD+prg)Y-Hs4|sNmZQMSv^3ukN#Sq0K*0dogT}WiJGY?d%tzIRU z(}n+PR8Lv_4Q9nDt4xOKKHaPce0G&~mLQm#Ag%~CFnE9g&se=o|{kJl=z$RiuOuZ9)dUSBuso1-3f zfs&5vlzrQr>fS!PWfB6RWqD_ZOLyb5eKh(VbhO^8G9fYzSAlUZKI73DojjAS^e@hb06OjywwBt;k>T0^H^nNdOovB-V%(gWugg}&X+9V`7R)@(^N7GCTBp)Wy zJj+wo7CENfZqYQ6DqTLHWbGCWI4riO$U6{ag4`}`RcgRB`%U!u6AqNpu&;p9zoy?X z?PpP_TK;6%byH;`eeso6W~(!|i~< zYK277PuGZFYY}S)ekV;}T8h|W%6Rqcc?D@>G)iXT;cNBl*BuF8T{6{utBz}*(^rp8 z^&0S%=tq3|B+kq(scQ@1TTKeWo_mVFdNDo-!R*LNQm?;=osCdy@9@yp<3x_O8lVPHv_q{>fkpE zw$s(u;aVSxT+6YG{EJ=kpuytzZlO2SIU#l7W;C&G0!jzt4}rX88M1x&xeD40Ij@Wf z{|9?@ePTRSfYroyP)-QPBHCpY<{K`1mom#1Yv%KbKj4Pz)s#qe6Qlfrytd%VydgYC zBe6lD>)jQ1&&uHf(=$jmK?AjkhTuM6JOnN{zIK#T*2=Xk8f{QHB*X?6bnDf&UUsBQ zP(x-IvU*4=eSEwtGF@{6Ub`=|pg%>%L$?T3d;|oUk`Sh;I0CLb$#CJp9NQ(YYE9mL2%T^ z%waTn#`@ua-EzP!CVYlP+z)R`xH=YhJY(|}m;=VrD;RYj7QzCUzDZC86*VCdv+r8* z6ho`e)&wv{b9G76G!ZV_?G@vj5Cyz#ox2tBt>+uity#hgo6TuALTs8xFRf`)_rH1a z?p>Hp9~(!7v*?CMI(a7Kxp2R|&g|B((Yo8fk`S-HQT0gPiz|laM|oW45y24xN|L1q zd86~q8*Hf*5(*}Wd^UQ<@ z8U2%#G*7X<$@B&~zrcDKop9qY+h!vnv?;lc$Ebok0xM}k3sgAOPHe``^OC3pj{aq_l3J7sTU=H|l zbGBP_*8nLhSSMa5z9JJv=}%EBf7*K?%uLKM6=D&a4X($=b_t);m_wJEReXamua9)R zJ7~kgccRsEW@|4~xv69Xe^i#EU#J`vBEMr;pf%^|rK=aurDd!ZHb!?tO>t}=r_^gG z#DWPZ;uTd9^^nOAwY-VAI+|F=wuQ5oPN%=LXyo#yrh?5 z+S5Vg0;b9(Tu9bebIEG4A!RqdwCc=uN?Tt4s^27?2CQ5gIIOXEQ`M?H)l>mzhc!iV zm1e<_bE%6qtVyp=%(lcGvNMogS3NErxqP}hXyx$!=n|}=QMLI%O_zDowL77b_TS!j zbZ8CxELA6XXlrZJy$K_}tF6WZ29`&j76i7iAFyDJmN?oZaK-LyxczJ9D_ z5MsC|G3WFAW3B$ZPO&A}_}tb(I7&@67Rddr*}bfn?*53}e;tH|r=HoEg0TBLQ&~`> zxZ$*nG6+VG?AZBE4jqKMML(mi>|yZl8$Z`DxMn z=@k6EqbGf({X`0X#_l_(oZT`%3$FT0{d?3r4dB2p&21;JeM{Be(fNk{01ezb zSNRP${)~%voRrtrqd*k@%=>ACNsi6rVXIehY4x(ed$nE>6BfUyrZ|;<|tniXi(H$@a=}y$Yk?^CeW&6|G6`>4Zm$k)bMI`vG8v+2f_9$gCaMJ z=9{|udI3qv^(@k-PoEAkF|A+10?V?5ZI4!hoHq|lJx07UlvlMU8!ocr&1F4#G6SgY zDxu&bauJFBLQfCyY7OVt6-Um0%kJGE;#GmYfBlj&ofzTyQh0`)Jqu8QUXjdP3OT#? z9-4V0HPSJPhH?SAv;*!JsUgK3c=B)@Ztp(Zbqly>t8J+S{8<j=n7#%ADt z9;oszOjD0dTOl;hO$00Ub|l`AaG&XzTg1>c$saL-nvYFYy}ZhR7ku0>=;cdoYwHXv zX&#=Nz>`}FV5ta0k`ju0$??!7On)!AAo; zC~W|jNwet~+mDZSsoc4v1&Rc+36S8X^n8ljo->TB#wGTdkwV7oy?)DeYzYuNL+kn| zc*%qu!gj>xpKz9&1SwFrMRq(15w-^4INWo(^e_wy|DiIP=qj-{v2oCduPQ|zVaeM zGmA{M)OE+waENvW_1^BCFST%Lxe`Y$u{!&1#^8R(szKqf-eg)yij zXC#~XKr%$K_u~&k6fcw%$y(}mzSTsl#;#I+yBeM9htT!e*_y5b{7BFjUxPN&^U!=8 zdc0iEf&Fx<4E0cU-MjH7)~SxA?gvL4bizyqE>qqStBmfdD~}|9W}fVFV$r-4N~5fY z4{4Of_`3(w|Kec6RMIfNQ;O?g8^*(KK-tlQ!@Ap;WuXb7WpuUQE9hZ6vecl(BYQ(D z)(mRNE6{g{k(RMbP;QKu(h{lO$QYTEy1(zl?;?X~c z$gt2wyHMqT-Y-oHHEUCgNSLcC|FSSl$2Lh7scf{DCq?ajQ;Fc&*kQiPV0G_T`!6m& z44n0T_|y~!^BfgO2IPu4V^CQl^Yyf z==auZU`l5+!C|UljIr>`MKG8KzTwH#>{{b0@FmIy3phPC0fD4;&D*nh+q<`&kXudj z9b)mV4kNXLj$XF*T`4ejS!7O}Mmk8S$k|%LA$V0I_2@}7Ah#v^PRMzw;^Zg$nFT;v z%Av!DyNAl%ihVX5_47;&!BAPbz|(T&M_m!R&tcj2q}hGK5bsKR8@U0arhji&fR*%R z+zn9YRK7Bxo}H1N&!V8mjA-@e$ot7(39i|l-z#}xdj+S~cgj;^@@M;jGBp+TknsnpL*#0f4IJy=3C5xg z?cR~*8easgv>xqtqxfh9$6rMnTnLIM6_IiNtwqbzrYhORls{r9<_3_G6{ z_uuvcDMM<S7$gzc z_GBc2JPj~f-x>Aa%4Irp^?ic8kEO|N2Is@VSfojtB~E;rFrRpnD!q{s^QK1m`k4O! zm1>jA;jb6``VwEPQ10+7^`(*6B^}JktyN?Pu3<-GmC;cr;UhnKvZLdZ0OX*Kqo~V+o#yGi_Z` zXAXcQ4OJjy0AD5+CRwcD9+i*0baypd}FS&*yFpOoSH?w#1J$cXCyOynl<> zF>u#`JYJUN&ZwI&Q?A~AE_sqMglVy&$agX2_&e1V=CZZ4cPEz&ULMHo<+j0L3NH*B z$>}$pdWbA46`9&Jj0n6)G!#C{p0heV9ua;|uJ{yqmP@Y}Qfi?u8Bie$Fp%3KGrr!G zisN3}UTwEq94hbI_6|9J3*@9cnRBcqxHbY@^z1NOuUNYrH>gZ|dz{9!(9^>Vr?T(W z#mSUkxIP`ss~Wm4ESvmU|IHGS{+d}@RsG$TR=taJ*w;+@2FD8XI=&OpZa4RZB}?&x zbtLCsFr8Ten>~p$$u|0-5~G#+HEH>+<+@!n@L`n~s&<9$k;cqDQR!DABkWCanyKdl zvpP&|rq^Pi^cczQ?b1Z`plgbZu|xWE2HUBL*fz_f;f%u{&WpRxXr-p4Sc8{_ZueD* z63zvaJpHYbst&7vb9xR3QL%KlCg^&qp~!`S)Lnb_Wq{-*NCCxAroOA(Pe0k}dM<~H zUY=g5>oZxsWY2T)15xi=CxWtPzxo_EQ%F}SZo@`6aYPRH@!?DqvIZ3${3lB?ZQ$=5 zI6a37Ti@zPuYGhgbV|_D;*6zjg^DlxmFnmY3utK(huYI__zcA?=Nn_umhijUvFuc3 z_T?mF$0*~C$cTZB7SxloFd0u74KBuQgFOl;r5Yx#TO884V@|%we_I@ytMeSlvf9eG zCEa8MZs%kp<_PWFfF`emEu+4dGHBsXuR5&?Wbgf5XlTD^7k?Hv^JA=bpxUQ&I^V8O z7(^;+w*rrMg1j*&lroM+$<8v!B^uJEF=+S6ug3rsUW$Bz^`jjl!o_v3WPuX{0DVMm;ev{(PW3bzFfxQ=x%*tk)FeH>1PQ1pDCIi zUC^oT|M;%5>;FsDx>~g^1#e0H!PUOrp>^LGZ4y+nZC6Kz(m+1T9`o2{COjjhHAN_>0h*s(_JC_Ypjy z`@keA(w|g#;2AaixzR=QK6%1YmuxU&-+*^)tHv^-@N+)q6jcN!VWg*x z!=m`7e!$w1lwOXEr-xsrO>HgmzV`bfQVs1A@4L~4-D&PeRwX!l_3*s zf!WUO*eE~z*IWcle$BD+7%FY;aG;E{Qah91O4^|NR>rHp$N$C`+apMs>7#nh!vEjPGslPypou2K)9w!f^ zCaWYLSQsflG^}$(@d$C^Oc*g4e)^RL!?80BFvYnjC#h(T2WeSdW&f<(_hXaURuOAt zSNR^%_-!BY-rz6;+g7R5txTfbcN3Sg#e+H$5F&G8dhs%Y*rpc_sQitrx$>y9!=%)Ay%CTM&vn0P;ACei>{DaQ!a;&Yx|@kc6#0|a<6(N91L6_u zN~zLlI%x?%C(^!*a;V42-GZc&3hSwoYF0rQypv!_wpwdwf~1A*2zKb)C;D@=e2U4; zah|ubgmB%CPtzCLJSvOasE+zJ#}iW#xlJ?TSK?SHoU_eqfpqX%1k%eR1oTya7^(~M zu8*HQIYWlxFHU`h5k%hg6`FwZ*Co`v|FX#=a@!(dhWkPU?ybZsD3mf+jZ09U9m~lx z86sx!Y17)r>QXUyN;vZ#&cgSX*@4&|}m%spPp|zrAE? z+Ep>d%p>=n)!=wfWF4@eT+2X1G|EhJ@EVABGPDwvYzIqnL7H%GiNjzPfV)y7kJ#)@ zYi^`wkESbaJW~xdl7l`-UK$uDWV94|^fN`|nJGPkq9913>-n?ZucL?ja31~0h&&fV z2x*tYc-X&sR#K=^LMO_TD~gA3ur)WWUEyH{?PiZqvV$Vk=C;78U#0v^zFACMeqoEK zdh~rHuuiXFz>nh5xWs3H^vUVixP#%3YVQLn?R1U+L^Sl~laBXXzwoqBG@reb&ojR%AJB~D*nNbU9bxb{t zL$vw@pkI7-mwbhoA(s5`Wqq|lb)B}?-GJwBT$ts^Vs+CXA@CUgo{qz+R zq?(m5<+<`-fT|o>PbWf74rO{qniW}x&~wH?9AyXShCcgJ(2`(5f*)xmjh;ZEek42c zlI4Q9ZO=uzUca)sstY_KdetZo`eF&skry-*dIGroy}Ace=|tC}7u`hyoLAu&G&%R~ z+m{85K1Kx(8}%3HnZH0cA6`Rd($#BjmJ6y4|C7u4A1utt1ThbyUIf4HZB_xjvRSGa zosuvUvuHa0hC>!mK-DOc&eBM=d^5;?mmEwr&L|sptX%<+qR77giXRCNm+{{&bNsm& z#Jwp-)=Kx;&_yYA6EnuplpjBw9r|5o9Y;k)MGrADk}ioD7Tg5?qvrD)!b3xoW@fDE zY1zO(R<=kxMK3Y7eC7DJ;vV2tFt2~zIoq8c!L7_BWL%;KtP=^-({wHcq;vDYLPA1_ zL*=WC`>+2Umb#1KW5nV|5mUy)hjmA5{P5*&R`mRHA)_KKV922JTvYI=AsPK{+yicI zAfWfw!R^6UWIf#eZe%|qU%Nck8}IDKL(5JXYV0fik_j&{uX;K8Ks%;Ebi%_OEA zc1#2oI~)ELReg*kE#|CZcXs?@VGRG18vLiw{x7QVUs1y!yyU;br$0Hw|Aci-4|W2g zM{NDRzJN-s`ns@&{A;9kRKaa0sQP93=Pvb7QTkctf5kBmZ9t&(Guhx@_j=q)SUAwK zlX?9svHHuOyw7(9z&rg81ea5@!H-}041cn!zpwabG;^6wt^F>PV+MFBesib49Q`|t z)(bk-`P;q!r?G)M>Ob|+K34JER$Xv5`V+_G54V|*Tmhuc)d^O#!nxrRDxXK+W5uAE zSnXHpL04AqN}~m*g+p+xE5CxBrZB`YHHmY#3Zh`%-pO zh)T2)I$3!$R4@4!D`_h$>H!mG%|6{}__0daTWec?D3X;zOWS#_7v(|pF&iOLIXeu! z?kXgh>GV9dmf!ls0#am+vfe%yI{jWI*kD5`Ji4KYY%J~hay$1edU5wBl!Xp+^`PU^ z1b*s2NlbAag*Px&vy#IK#H6QXH$8*~;eNI?nYO`tI;5!xUYLb#M2{3VTb41wA9&Pv zB9jn>eM++#T^E%qOXvIY{Tg^-uNp+)wHIs=_&og$K8j0MJB2W)ZW-_{Gbaug;T8pE z1~S~{Orkt)v9I%$v@m=h4{*mwO4`AVashhhh-0!pJ@ZS8?$E%3#Qw>3|fl zw#K_-pM?(chayBn(&d`LN4S{h``u4mPd25{gAkp8!xv@qU1@Y?4J|myrBn3i!FiGR z3Kfxtx#Ip}Zw%+6o~CTyLS*e|;y`fkTQOe!(BmM;FlaN$mKb%^>))?BJ50tBA%U8t zFlEiy*hw6iQI#nmi;|ID{7$I2AI078$EW@D)S<___pbFCJK2DAAIqoCs`f~q3PjbM zYefrl{o(&M&EP`G=_#*j$q7Wl`SM}*jls*+Vpxp7alR>kBLLW*18+KFoTOAjk$Hou z@pGP5(Yv0|g9$NG&$l>fH*qj-%9DC@QN+x2aPKu)*R#jnCR0|}TIN8qB1n_fL})$m z4P{Hd5*)Ew>bm$h+4vkZQ!CX5LYv)B_K@nbyVrcbG!sWRK z*GC;2``_JtGearg*S44~;`v%H-__Gb35V5BQgL}Rc%^4>%tA(R+KEoYl`7G!%pXXM zN4JYRFE+=NxrHzCdq&mcuIO*T`SaS*r$LHisJPo#Io6ADnk>lIJwGt}Y?|Kp4-{J9 zKr`$sCTlGq98(X<-p(3LNnjtkAO1iye#5dtsuhG3f;r-b15?OYcoYR7_2Z{cXM?pt zY{AMdGH6;ASgi%!JZLjN^LF{uu8$mT3oY#F(N~_dHZ%ati7yB@Ok2cW4`Wsz>}yxu z0@~HuJJgLj0LXo42*6m0d4fs8v6n+DQ?xl=>N;2;=_AiiDE?u1*M9}8ol)(p(nd%M zebW8~&Hpry-R|W-urq1&{-o}IA>yCVbn&UvGpWNnkoDIZOFyBZD19*for7iXOSf+Q z9yI?v|8(r7skE=pn0D3n`~Cj&crf^UkN5R@y`Moy{plIZnmuOhi*GKd*qqA5 z+^x{JH30yps|&epLRHH452x-W*;|CfBa*ey3KXc=o({lVIXxpEbFhv~GmMiHS0!t@ zIzsh?CPfO3=)F(dzOC41MDOaT5@mnk0uM1o0XCp8==H)T^N2t zQbC~<<yUBB1ql|NYlthr14o^tDVb&whg&T!Ce z&a?V?=^3;%yAVOIExZ~%XV{IYtZG$bVU2K7aJ??e8yk{S&qs=IsWp_9H(~5bcsZnk zdiJQxl9)g-WmX0N3k`ua)OL-0*khRc>(+B=f_{^V@|>ew2Hu8sZH_xqc^C7PnR>gK z^ihSK(2{3}E`ANNtrvxIl4#rVV^f!z3TywJ$QWJG3o!E^@=>4Ii0YGBWtD}{viR-+ zbvOBrR0!j@O}d-u^c&Hs+UjdnTlD$Q&vb7enYyr6hj-O~=yeH^s_wD-$rs5wi>xh2 z=a_{LwXwoq&~qks)qXD(qUhEh^`zNlBrZk$oLAeY1=n+W8W#E8f0w_Wa#=`Z#@kuk zurIZJ6qDlBzg4P=Xp5ro_q!)l9eBM@|6ulWml3xRcJ}hsZ;F|X{l4gRu88V^*4sQ% z7!>L4j_*KU;GDH_-n{wqgJ6v%e5WfZT171i5m$>BvE2T8@^##Cqamo5M!9Ee#g{Hi zA}j+V0X@>I;#`%CL#X$Ahl${gMq7XDN>ZYN(Kgsnwt}K%GCk=-lwPzJ87bP#QXs}| zBTyf|#<<7qfqym1EmHTnRD-( z4KA6cpTL@Lx_B|yWU#nAhoNHrnb?nMfv#6HonG`+dD^23^y$tQc7bW%tGiVdq(@B! zR)!)UOqb9+N8?>*yvxNjcAhTe=ry8>fA*uhMyR>_MhGA9!~ET8a_Wx6RUm33-V53_ zSxSGz`dT5>NJKb#H@6kOIG?g+n-CTY8;A<}tfko#le0H$_XU%sWz!2Y+qX3{#)BDa zgT;R}NQfGP_WPlACBaIFH+OX3Ycxo#eIF1g>OemB4c@$eNNYI~-d)XJAMh~x`GcoM z!3rZ95Vk5BC~=SAzApkYs|aRy+4Z|lahr7dA9m&dwx_4h9&iWM>UpT4$M_&;`EYd~ zMi0yK1lW5yZNM%iEG>k)TaA%*T!wBBBGxlZT?!#vghM@Sph)O0WAefi?amrzAzD9z z)jcsIBZE{k!#za;Fuuk^1M>cbPm|6XDq}cJs*7X|0^mZ3_pQ9yT^+Pli`nRocKj*% zSy&PXZ2-APU0>gYxHZs0I|H)D=Ikhhnil}yTp{yfBbT8At9~!B7ml~n+xq&#*BN|2-TqPcq4o^scHTFg_&0!hGiGyQzu36xp~}ZI)__FYy5Rd)$!C!ihDRK1WR@(+ z?(>MSjf#reXDH8mF%W@9TZhf@I}NKyAhv>_xDtXG9&^|?9*&gRggpO`D_Q31=Y@=i zs^+~y(X`5{-Dv!TTlLOdT(2;yQZP9uIT8E|@)8_q7P%<;570Dy6$J|)zs*HEk7#iq zg~4D{W8*>F!nYL1BR+Sv&Dk*z-U8Uy{T+R}AXU#lTt{h~DvyC}>uTaBQV6@Z_}H;y zVYF3F4bOVN9_Dj@$j;8L$DQ}~@o}l#VY^V?&_PX24LyG)Fp>(!lXs2|NL-V`lq8{P z(1FY9ms+|s7ZFQjHHRMPK zXXhjUNA8a7vC+e&hcn3mq{WF)RgcZ*9hHd!Yi4Ffz;k4=0eVjaO|#1|&5rax%MU&| zOxTJLiO7u|kXV4_*$!LMf`GN>PgPO5l#qYCnADx5O_%^8u?X|M0f`ppS1%s-!SteK zb>-wr4we#&q3uRc)yH2yY5I~xSOU4UH+gAJ;CSGtRZJlsdX?-kX;v$Ssl~|_s|x*e5at^;>|G0G*F~<{}~edjH{-pX@g;z%Y*A_ z$r%4YL{w8!`kC+b(_EBu&d5};5|m-rzAVOk&PQfMim>*9!5Qzp}V| zz8S_A2gLIsgZ&Sh>4(9}fV=>OUvo&5B(=7CR93fHKsYXo=(Az&YzF(qg`! zksk<}c-TompSS^vR_ZQ=Qj&R}_{w1l<4&$$m2c}3a_7=RP`KqO%~j-=)z;2MSF%lN mc8BrdxqrvI&i+R4Tk-Ojzf784E|bEw6tmi7XI{F|^T=-=B1vxm literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/html/_images/chapter10_59_2.png b/doc/LectureNotes/_build/html/_images/chapter10_59_2.png new file mode 100644 index 0000000000000000000000000000000000000000..b7c47b451d2004ef6e10feb36f91a8b9a80a8c27 GIT binary patch literal 28628 zcmbrm2UJsCw>AnQO+ZAX3kZlvk*f4A2uM>wnslUhf^>*VFM^2l4oZLS8_ zmtTbMhMlLU8%R<>!1WSAClAv^ zox7o%P3nm}PhD2fWVC$dhue!9nUZ^H2XTz|qN;8CwoYu6yAf9c*eVDP6=JfN}7Z!9w5J zP&%KTUNOxHNzf9xkdRPMwp{l51f)9P&}00oGnu@fpX7Y!oB43opk@Rj`qxm2h{Mm@ zrFyIPMzk{}6REkh#7ndjZfSb(AFPcfWHjv^j{!3iB@cGM z#$!E4d#i>uc2uCHo|ft9?ChYU$gVEcBz}|b4{8a^gN2mN6JM>5_tyikho~B-v3Cl= zM3n)D+vI9jn&&#AxgY0U{HUH>pi`*TlOZvfO46Gtm0b1=QsslT3En}+5Aka3242(NF~a*^>uyCWV5(85m5Es?%%;ERpnD5z$<97fsHA!`y>en5 z=qWz;ez;^ZH8nNqrAv9hH@R#7BP1J)P5t6HBJ8{UJn7CeuPJBe(a*0;pkC+!6;>gu zPIA0}fPfSU&@EuR{et?-qm@>p>-($a5CcAAiFLs{cY1&F-?-6yh*M$l4FP8QV2%QT z5yYhzXg1P<-pAM1qS7E^oxIH)9?Ps-^yn2Z(NgqHeF;A~Y)sa$Yh*`{cmj^z4`0)1q`;g>hx|Nj` zhOhTrkjIuS83&$k!8;oaoosjNKI!*M+* z>{Pw?nTHnZPNF$$`x|h#`6rU0yuuqu7~q;CCW?Oh=3Am|FKF1jx!C^<$itic7T~hI z>7}xE@~QtdN)2P*;S^}`AD8~SRiR3TG>$VD|8D;L{accb8fRaD;5OA&px3yMxkA7{ zp-OwZv$t=ebbfzdjk|_Mzt8$JhWebmvmp^bI{#D}#ijrB_w|$oQD={plx0appc8f$ z`9Hn-YALAxeu*|dA7W%5BQ?+w8t=~`MKoYE;lIQGJ>)S(4GnVOfs(5nP1}S%G)?heR%BCZzgbl{WaO+g;B%U;4d=d(dgsU1o5*&;^=0#pdUj#j z?EGp6(nKXPD3BD@SCBS-*V!c0CGIC2kKa^vz7efH_GLX{2mAK3{4FhT43~d^e0T8< zf9wpbc&g!2-~-Q2u4FNP2+OUbRKpA@Q0Bbc;bS;DyXtDK=gIW1vySvAT%PK2%k7%r*IDCCsHO!L{g@xd5t1!%2{8?~*kqhIMa(8;%X zu>PdP!uLq&i(5NPb=xw0XRm`vXdwnmQS<6*Qa6_G9$&^qCi_ILF z+1n%s(9;9glJSGYkJ<~T7>rM~_rc>lvu7EzzTazJT%7WoingGSJ!o+UOmYXQDbpue zp1~*MILvoTJ1fH?@cHwb+H$8gAPFI%__uGbpgipCZo9j?_bp!KeE9b5+vffCiQ-4O z7u1va7XcqHHVNZVlz;R}nmqO7cD_HXfBwY-kLS}uM-3%^G{)6=(Jqjgw6n%m`+KylfGG+k|PajU({vaDM^Q^^ul zax3F-n3K2_-Q`?`lB8ne^D!y(}jTPu)qNkDHsQB=!&_^8Dm}0}?EGnij)0 z+w6Ws?wXxzQYmcFAmMuB;7hTCk=X~`+lAU$994Vbs5?@e3JQlFA`5T$8)SX>Psbl5 zxCy4p-Z!$b(=XK}aRp}8vC*Wn(R9uI7g6tTcO@`STbrYB`Q0*{brp+K3@l)-OWoP& zY_2k0tJ=K;-*xMf{N4nvrQ(PeV-g)#`za-l2UbLB_q_wSE@2e(Ttm{U>y z&8@_-!(-XGgPRw&dUsjv#>=$Ayw+JATdTB(tGp@?HG@EFT1$;P6k!(T5T>yPqX?7dE2q+o)-;RT!yx!!et+VS(&oqL&)74WwKC**iikdA~3d6tI8vIT*Z zaKAUaTXQ+uCdh+{+y@B{*G{Z(i}P|;6q-;|6b5`m?U-yFc;YSO+DZcl?V!kF^*n)f22bJjjJlQ&PA8d-)W{o*}lQqSS=Z)@ZsEq)DrR zix(;Ev!W+TFvCVY9lK51^yH1-$1$}2$>Kqa065>?5j2;a4Q3D?9-i?2{erR9!-wp5@9uhJJBzlqwWR{Pd9%Ph z8eqTq!JyJoEN001z7-gEDuzfF;9_ILFBy6WEK>@`yEzXNdBlR;Xvw(W#eHbw%0Q^0 zxw@F?<>gJ~2De82`}+xUY!bQ);I2le$ve1Q<()y_=F*KAuFM%Z_BTn#K_y9T_jZa9P>$hfP_r)z% z;Hk`catgTef=_CKSFB)Xrq{RKpPx)6Ns3tkY;? z--J;S$iF$V)`-Ko4BTR@DQ)E{37=ndwjS(GN8jK{lt z{gcKcO8ajDj$UuGvSh+9RHp+NM8y8b&36e2=z{~>jwqTK7MXEhSche<>vYo@WCE6x zO<#sux+nv0hCWD5*{&}`0@&PNe980l)1$g7j(BdTTilQkQHvUtejv-Pn(qc(~_}*j~!frvG_p zvQ2cjv;1~VgfD=zq{E|3uHzn#w(carXQd4HxYi&jPX!fo&{8r+5sh$3rJ<#LpsRbW z(Qhvgz*;qqBe4+?B!JoAz&5?osH|as+))~fnXhpeifV3_XYpUFWO5ndq{$ttwyg%X z94DuznybgVEB8@-nJW{J3f_8m6SeSIom?9=lt+tVONOj_QZ(ubZt=0r8*7QOqSkXTnoWxoct~ zeRnrTJBf^r|G5LZj^0G=kpR!6PE_m1>sD`^kMFX3t+1vB1!N{sNgvvHo335WT$jCw zFN)n3quJnpIBOZ}d&e0%d4DZ#=|>azrNDfFY`1m^WM@g;Y_W(A*Es}!oV!E=#|=Ca z$6B#0bhuDgFQTV+=P&c<3MkB8CB(Pe>1u2*AAPq1Prhvyk=6gT#o^0LIwE|(k!j1S zXVY+KYQhCrnnhP0XS8}tEbV>q{VZBp^40nX4aG@nw5fxB0T1Y(&QIdk!7M%RnvgE( z!y7q@U*@hgt^TOod>l8r`PJqKEq7;1BUqFQv*Zy_SUz&%;^orEQfcNqF96ob?WWlb zHgTka+JqOs*$H$T5=91}5!d%*eeUV^QF(|Z>xK}K)5`;xw+O%`Y;0@>e6&}osSg*E z%_5?rJb=YGRBTn4dPO3bN`!c3eYH2fQ7y)Q+p1d+8r`zFzf}C7;&gTXxN(?*kCq7L z?;Cb(2HUXd{#<7`wKp;MGZNIWGj91Hc0CLdN2hW*(|nSbjQd&TmB$>Cf?Ko2o)|M{ z#kSyDh#KLBvxjeN*A9U#NHRT>2mD0`t|emeUE_hq=B7CI_#M5NTm3vnYSW55cd9y!@ zJ05}eN1Apv519CZ7k7Mo{VVs=FD;bFsa0Vq-83z?I)g;@Ex4F@Vr@y_E@*F zkBz4-J8PGZ(Pm=7o71pYz_8a>Z?Abtfls!@%(QR=%8fWzEzWGtqeB57dk<}uHR4#2 zpk>?ljnLcuF)I(Ahl64CQzM|^crNjmYSF}2UyMc@_XJrR8Rqkl)24u{S8S@{VGI8TomwyRhAX8syY3$E6 zkn^XB-v7diu<6V1-Nu?6Xr@tBfhN(2K1MPC_5vQNd^{7tTU`_@-9G@lW$7Ve3$pe; zhi5)~PeaZ?+k%#OI^wDBAAF~Dj$gw%&pv9m@zKg`2eH!tP^>PB=M1x1S{~#`MxvB> zfY%;0=Pf7|_D2J~_~89Hw0(0%7XCeKFPAvGkX<7CPXjyuy@7vUp#-~khFRzE|FDif zzNegl#!+&UM~{JF-Gu)^ot_HHz`&>|bIw8K=!@US@fq6ZsB+-?8BqS`?2oyX1zK5bDL8`gFK)9pRL^e z-Do?(A299pPba_e=q*t`e&|$8N(%jWjs1Oqqe&65)e1X?xJ*4v<~LdXo=b3ge89!Y zxfnK~`}+d#hJ2N{tIW*3lXajoh7q8oB%t1#qF;RH--yxQwY#F8#FzX0+q*L&M{Kfu z={J!P$%`WS_~CD{K-_qK1sJ6a8GqWB z02M=h?V4xXDev!@1WCQ;NSnZ=-S=5mSomFGcF=fTMoJ36Cq;lH?%sW0TPr?j6-LRb zHQf}*AYwy~#bN`{9drQR`pujO)s59j;gkX1YXul}*q**#aP#B!N(24_gdq9gb|@L0 z&&tQ-Gd>P5cTb8?Fe)3IWj|POx{6KwJ^l$}nTuXBv$L~Kqn}&qGTy&eva>4!`2vsK zh3-V)W{}{q1Z*iF0}rN{T=Ww@Dk~{1#Oed|?b(Xd(pow>+$lAvd>ux?B)JJ&Er$Z* zHt)}p!3)5h9_SW70c`v9oZ8rEC*uhV4W*)?QLZp;R8?2ccN{4PZszw2GdUs(#xs8S zjCW>`_7McAs~mZJfFB06t@E7ODBkH0TY;?E00>l1EbMXqgS!qtmkYiY|6Ya~PTuCq zw@ZAqKAf!|{m18BuJKC;BB%bY*Yl}w7kfsl{6n~`g`MBU1)o3kNpJA4n_1Mwz$sn8 zO0WO$&4iOd4}#xhYU(7H)xJ}r=XUGP(9flh{!9Y}o)TIn4S3C2)Laq9=zG3_fxabb z>JL$fxFO5glJ#eYGY8X?RGoJmpVZ#HUn1(>4i=7|g$1;wdV)>_^jsgL&(Vmd`f+35 z&yyedQYkbA#gq?4Jv?j`PtNL0_Mb~>1hswf0>K@C%iBKP^J)jP$D_c9qW4b(hU^}$ z&e8C*;s)WqM}-|150B7(>q*J;IH_1eDY1Hvm}kS{4dnfL_OC0F#iX=Y7CR`+Y$IUC z<|G38uF9s_#-rp?9AZI;;RMpY=KEIAhUjas^K&C$cxcgJYnMwfyNe&NLZ?yF=lCM)`@r>$7Jh>K&8yi8g9d^1f2ANHYar*57Emknv#LWfQvy$q?4@IdkZ;! zjv*J2?{$a+E(~;X^i9plo`~=v=7)F{UK9QjV++!(4?WS4V8Hj5w<7TY0ofJZF1Rl) z^@As^bhbPsGIWb_*W(3=VQaz?2{+Y+?c+m{a(mu-{uFqV4i|%I1%CgCV{;cPOzcYu zgK0{ken4A6h|k~=+lvj(*)@A2{Gf_w7elNuw!x(0&Xit&2RF8pyaXAN42JSxUn?{04$hII<4S$yYzKeXVfVuOFqBy` z9iQ69ZU#-`bq+i92bb7Z;d)5J^z6GqPt&%$HxU`mCk+j$1D}ZnTrg?(NWp`pZW74i z!AL!X9A3_#$y0jWI;vUhtBp(ZNs9+NsCApN<^7NId$@p8BJz^ym&qe3X1IH;WFmHk zog?7qWs*M6?$l&Skpb+pXS67JL!syZtQ=%b54j1;mYZk%ny21ly#F!dxldUbdBxCM zs?{bDzt?{5>iAYuN?jUQJF6D@uGD$d?ABGCYJoCc7e>0R2 zJGj#8_L}T?3sFjaB7A(2g7})-S2dU&>Ui18GujR=h5Kj>eiKG5bXTKvJ5YZtv6A*avM4!oF|t8i{U=p;FCW3A?+O@aHOT?=9o#j6yaLw?{!w{y&lJa& zyIWxx{gHBSu5mco47W>C|A0dqV7Y{P3pD9*$E8f0UJ6-9a{ zA$q1Y_LtU2J>Rj@c|-Cxx35BLFY$|Q*YQ4NL*^Ifi;^-lwQQ#=PdXW8C-8UY_+74<1!>P&C87!(C8QCWWAZ`FTyDWu_M`bdt**Pa(*F{6P_MO zR}u2OP1oM2jmE>pEw=p(>Dlfp*aSuVSJx$y=Zv+)lNC+P^?`3Tu@3e1@yue3f<<(?<W;9eJrmm2gEN#!)rY#&@ zC61K6Dv&W-JSs5eeQRtn5XO9Ikz%211yO+uacsoyEZ9ut5;RaBQp+AWCthQ62l;{Ez=te-3@ zb-||}26OFHyZKzGKE7^=fD{%_NYTHXJZ!X=kbXbIF01cqR7J(9__E^y(Sxu((YB2f zT<#$E?x7!>R6-nq;Q9f@HOfnQ%QVv`c}>qA?yYQ6t)bu|Uw&B!!d?$wHU7NQ=orU(>z4MCib*Nq|nFnP=8H&)@MU| z>V&C-AecLei^R2rjw0&)Oz~57JD8oQLfr|yUwC0vgk#D;g9O zMa)H0FcOpZbD6e13i3|lX?{kRje)TjNG$oLA{vdx`GFvq!9r3*;2~3hPnL8>gIm_l zN-~#}-t9+k`}8T24L`qifed~gH3=bFAeu2YVpR8XE(H9}h$mK5JYeH}@oTE3?BoQx zeh@Ng$ylFFJVcALr;U^L#*_CR_!3*5?@4pp>Vy5cAeI-J;8 z3fsq7!HP?VRTK<~u?~QSYz>+vdXkviv!#@arW4_EZxf1_Fx0@D+#G~sM8?p5r-0J{ z9xojp#L#*u#H7Fs;LOlR5Q%pmy{r*CYK7$ujV^aKox50etnlXgvu>^Z@TZga*=R_% zgw54u%Z2>;Mm7-l-ARU|^@(q(HM&36ylB_4(TusFCc`)!k9I_|y-WYtyr{=w<=njY zVLtlIMO369BqZuRRvT`zs?N9C`-iQo?JvAjDgxuMXVLX68UO7rj<^&T8UKCHGx$6n zd|X7U7jadg1y9+E19Ms8~V{ih+m-@?WxU>~K_Iwn$cM<=W03p33Pvl2RI z#CwkYE&SxpEwdBP=K@1y*K(DR0l@WNiKdx_llRw&V(JSefC-7er8>swB$uk%dN{ay z`&njDL>S(+T|_UgTi5zqQ&~C1oScFGSp%lAFqN@irP4KspPerBF`s;KPtjZw^Q?0* zaxaP1^?{SuM6~A$^ZkqTa!9-v-P>`GiWvjIqX8!)*T*ymCR=nbUnb7cYnh`bx-RYi zV`!>zeVAobWp4{`2`t|F){9v&6}ZO~>5{ziak|Cb`&O|d;OeU%>4!dZH`0PT-epdh zOr7Eu;P;P44)n3(q5Z?3`(j^6xfj(>lE^ZoR#a2=PyJ#W za*+~CYl8UEv#*bksUo(^1Np>295>IVHx1|O&sop_V)C;d#+1L4Han0FC^cQvmiYE| zGwHFkU<4%XYfdjJ8}ECuv2s@FVlS?b+@z#jpWPQ1_w$N%OW0G{O|N zk;aL_b*Bk9c1|(P?`0iNYBXN$*(bc!9gsX~T#%tZ|!=5@Wh+}QFw$~(8POMgI za@T*X;Cb>qPQ_1Lm6!)(lU*~>+C|e@(CsBqJM3PPvf(ut#C4dw?%pMV-s-1mbN(wB zN)uR$rSG=TQr1^bgF~tr)u606yD%7pve=8M0@w8V4V*IVYjw#4iGx587eXsrTYC%U zp8xDSU>Nce@X8+e*UkQN;|J)R8=a!g3KRYOjaY>Kb9qhps@!Z3LlzE+KEh$+WiK8c zy6^Tdp!P*sBKzHj$JWgcV5d(bZYirvYGogIG#n_G9VX5B2K$sK@Q(9k5Xz&36Mcm9 zL{0U0Rr<1QM&l3>a{i1Z9j${yzXqCgeM@P1pT)8+c4P~i`ptOJ2W)mvG-?W2LG=TwK)e?-auLiWtx1jf6aKOc+!$MOFhR3FfGIsjb!`lDiFO z97&b$cS;3QbrEp-85;s$w*?doaUO+wA(obwJ^(US)7CEZ-b6~DY_;_re|4Vd+?s96 zM11@9?IIx|dT#{S@rhPj|K=pJ7J>Dwq@q%7-f{uZC#?Y5mKVQ%=4zx0Dp(RMh&|_6H9iUIKJX48z1kL|5tQmyJy!F3c}hhdIT?>Ho&# z**Q2wq`iLqEdKfFX*8f9LWLdc|L)gC3VKYOD3!f*}4fv9et?9$;4_N^MWfqXc6w1H4kUD-&V7RB3gg2LSNlRx? zFo}vM0~!Jn3X0zE8-Um?A9%*3B4M`Kui1d68AgA{6`uZ2+(X(peOL=1I4Cx4^ecdr z{JvWoJ{A@hO3KOuCHexAFMcUOz1D#_lLJU@oRAF+ZW+Rx^Yi!1jq8LPO@KJ~1HBiL zC45Mo-YJtSVgoNiJek?F3sy;d%ip$!o7BT>O2TWM%%;UsXUcrq{Cf7Kdmyq!qgPp!MXRp)hO8HhQWpRZ(hEtsJ|P6 zdyc3eQn#W1P^b|9?mI{KYuwX*oE%sbvqVi0J>-7E>es2LYN3+OYDGSLM?_UUbk6#E z+yT0mMf)YIC7U1PhXRGeCtF85Z&9DDa4Y(PwrrTi*H1buo?p92EV+>mz0!0-#BUnX zy*RsPF|)dQB$GAzib}`!7Aq<-a4B|ifm{=!B zNyRV@^@o}__Sge&~Wrtn9y9={BV{j%}yZH{05R*=|sJg1d(vPu34| zQOIVRZ(&r)1i(%o<=G5`+XAQ(e?}8kBSn`FszT|I)gIo=WM)m9b~|uwBF7|pX_?_x zb)7pO3R-`KZbU3Bab|}kceXDshcT8A1??|~{?QF=59x-cdZWu$|Hty;>9`r~ZcRHGime>jKImq1U zIa!w8`!(uw%q)i|o3^2@8j-1OlYweG=&!V^qv2rR? zUZy8a<6-U{G#}Tz;4r#ANvx)f>rCLvvwkdW&7f=x38G8gS|HTxQ)_cU$m-{B?_wY> zRgdzdLulOj#9VB*R(YaVUR&bY!Pt!X>1b379JL)tCm{ZbdnMTgIkwD%{;GL)wrLd1 zLdpOJOlGE(`Gb8SS1uU}n>XPu1UJA%>h(d-oTe{&CkB6Kk6nN$JR^gZweFsXVIy%r zc5rit2)NJb0Z}i@=eJT7ge60Y2ZeWjx-8Aza2e=_wM^0EC_RR6-)Ej(-Ryw}t!fqN zQ@08*4=zzy>`AH++JE!#*;P<^(d7`TpA~xfjxj5|>}Xxgl_v?JQ(D9^)5kn$aM%dp z#;!}1P3jCju#2#=&L>(qxxT7w#3;Sv$)hckdZ`)xoXp<-t(5n^@8+>s*lc||v~JDu z*n2t<9?zj-_p^u!c-DBA<4$(^eYaYOO@`h$O1|j1aeKjo@J3NiC>d&IPGSqH%ig=_ zI{QkMwSc@%RX%6_jr)vLtm|bjruW4*A2rQbomK<`b$NpDMHxN&Se{a8$H_^MZqqfK zIP}n6K=n&tiE!kUhlgz(+DtKTs@_Rea0t=Mw!||}O-!1%#nFbzI(66tci+n~GVxaO zaMZe~(DXVvIr#oetAud-^t?SiYp4hobt?t3vm;E>O*ypj!UWKZP^-nJ;M~hFpu=a& z*t;6^mRH`6G=FY;OBy?(F=rtjc&VV_IqIkT?LaY4KWTq*-kUcSb9vtlf4(9P8g3l} zg@Jtd^75?g*4!>!BMlE#XS>te`t4e9AaU+P!ey~*SK}0VNqk&h`dik~s3h=(gqa4d zhlkK-$T-eUN@TQICGw7AJYG?flG3)eQ8bw>-8V`L)#0YSL@T(p|9S-3)j{dlVE_F_ z=3K|dOKq<@ZvJADH>`45fb{A;pwL5qzfV~SNRv^4*@641y!BfZeD237g}bG6vB;W1+X;5|fxdgYoE z(X8WSLLj~d(cV6(owb_4u9?#TJ#vDi00%bL&n+SSYcc6os5N^7to1(TMu_@QIa52> zM<76o*ffjC3Z+mIejOBCej*BSV5?b)Uj%>=d9Y(2N*M0?*)z5U@B%TZjvuYP$yncr z0#f;Bl1|glzaJ=*wcRol_hz)Tv5BK>1M_6+SDT{0xoJP8$J~~dxlk`Vivd(kj2NH$ zMv|oycmoy9C-!bUgtvkgqOzu0!cHaO*eFcNgVB`<-b6aH{rO5P)_{-b)hi-dWO5uD zAz-qw+F>h^X=$;v=A?TWOBV*nX?mxO-;tCVR)@vO9z_6CSlG7jIuOP%0hHpGQV{(c zSFby;aUOceJ&9$&pzzIL2x2?b113%$!_0)>Rmcvz1+1m++9)PaQf1#XNJWTztDB|c ziaZ)c8L9&pfctIJUtAFCTJ)~#9j2h|))ghWvu5Bjj-1&F5>L309`x1CjEumQm86Se zFP&)(Gk7Yn(c{q$_8p^=E5P8!@jmiM-BKaA>q3b>o^^_{I-GI&Ja#?dLv?xp+Y&}w zVjdPi4skx=3WC>%>9@1$;(bD{rWmiUTjlEMkoiOEB%_|`+$Mil9&x%XMAGeeWd`g! zH3oWA!o!ClY04n#-2jzRUJm*GIySdTx~^q}cpUOl4pJ`~hGXaJnHjA_zz+@Hg*Nz7 zoK!^MCMAmWdOLURQHMUid>JQKG4JT;Nnqs%9JoR!d{iRX&EH=I1S16mu zU2_~{KE! zTtk|uk+>~YeJ5WQb8%c0bbU4Hjro`Z{HA@|%gqtVrR&yoUp6Z%U!*4nhhNv8R2GuG zTPrs8b7@qFOq+5awe}HX8~6)xsyX=CzBLkEUOS^drCL2K)i{uB3jMXL_^XPIg>r2SolgdWZIf@?{!Pw!4L7zQ?b27R1^(% zLleibs@uZ6(Dv+UzooCP)HhsY_)=UrWtbJo6sB{%VmX^j?RfK%-Zvvkk_-&Kw7-Tx ztgM*&uExn?qawpuG5ornUJg{|2}hJ z3z%_ToQZrUob$6yWd3-vlz=qm+BN>!T36(A_(@JF3u85d;m(xv>XCY3zgZM) zws|s=NT2~Vib~@olIx`R@t5Lf-GaTMy_ERb9KyhtPMjWe_w&ScHJt+m25lIOIqh&7 zOF4EACJumn^74_dYduwZ!VIIE$)S)_Bs4u01LS z_D;r~gPX45^ZV5haK8MSfN8*1uE5F)ZPc}|B6Fc+?W~o;UdH@3L7prxD`<~Co5xdn z5wLH36~F@9){Rz=ps(AHHg{UZ6{Lj?yCehn!4>xar<}-{4`A_L=1KoD z3V?yctE{XH2@88t?`e;!=TM0i3_S8Q^;`LvKCY*CQ}Lb5^QY|ZP5zHR%6|`QC8<6& zU}%!p9UWCh)>n;;MHBJ?)Wa|gsIiv|5^exMIDUeYNz?vJilARh&}Zer&|fZc7FJjJ zqXyUrsjf3tK39?d72f~BCug$#b69XDVyC8*^f&#t+Wg=6xF`4)>Az+1|A|Qch~#&; zf5U9*w$HU|ULpWsv>Pm-08(Yl0a+Zw#&oqUCBPqk01|4X_eZTV0J!#liOG8*UFnIm zWe;zj9_?9ud&hZ(g@LH{lpFLMZ}ofzRP1W2!)5s{Q}q{#iK(w#kw+xmG5qS3x`PGM zeXat>ZDADn^n&JilyWCq6p)f{XS$C$Q2;Rm86(dPSpP)x|C{`ofcWyG&*loI0cd3a zxj!g=@)3~oEl?a({0=bJ_Ldq}+YOf*hD`u3G}Zy_3@u{u(mMeW^g z?B?D(~@0K!tda1M2 zk5q*7u z`QYB#jHW@?;@3DY$iP?MeYIj5m@OQqQ<})ldiXYt$XcBthCVHg4ckxWgYIB=^*B`g z23;ffztzitlM8EFQ&+_gw&?#*SH1&LXzjfAwNEBWrdMmmB*16O#wMauWvVVv1;*lO08fg6uWEHM^bdU^-HMpSr+#e$$_Jzm&ZmLxUKOWXG-1y;1v0lD zMHpJl4xvpoe0n>P1Xr$+?8xLHcX*lHQd$@B;R7}Zzl|SpD?Yw`u-L9Yg z_OFCjB8x2O-&#?kK z^aW{_v6w=Z(};z6+oGoxFRmhqL=_rB1ESF0KWXp&V0v6#5LU4Og)F88i^89O~z3J zCP&WoC*?J0O5RGCp>NLpeRU%0d98#BPdwjCix+a9M_;&Z?0>bb)=SwHHFwj4&{wC* z7axxt`f5Fo`C0udnci5Lspek^GM^Nr#KySw`W~uM!BrGaf3plOQBy%H$IYSDu`lTQ zgZn==*iM@f>G5j#@+W#{X;^n;c&>e2(;+Q0gkF>S+CdGz&G52<&MC(p0o8Q=@nkSE zXvgtgTsFS>$iB}uO;<1klGqErZoU!og`Q}1oe1iE>k4fUimN%*Lde(~1Yyz(DbUXD zTlkhxIp%bY`$>q$V)x^w0N?Ip0qr`E#oIu(Ux62p+Rsgw{~pO3)=%EWUoYQ?_|h?gM4xxat7Ctm9}%q&$<~j{Co)D)dcRhF2VKp z)}?nsGIu>A0$QRc@%8+?s?BWUylKxSH>+mV6<4)R}4zmdU{>k^YXa7^HFz=!SIQi=e`X3ZLBy@c(9iSQSl~L3- zCbv+>nbu8l zLptcBLuQ_NvmThzR^9=%s%!m2~9jFa_tx6R^52 zkN3@VbMMPQ$5Nrq5BpsVk$V%0==lLOlUMDqCv64qTm_3op;?6|;B%vgF04N*q`qcn zUfCR7ad>r4mywXHw!9yb=-%5F*OBJF-n99S+f(~ST^m0op>uk+YPr1Ycz^-bvrjDo zz^<3~R%F%sePL;=meptl^)b!ibbO~SrBS)zVfBPa`OePHY+XDv2`R-wM^RnDad#4>?axtMC8lH=vxhP< z95zed&f!&`7NqJ<;G%rPB-RP2)`4^hhv8EDdffNi`+XtHerHx{I^BN;81?}`++zTJ zc2^=V9iXf{lMT9Phg=F}bV7O^n#iH)FD~69*#bE0HHq57Pb~z_%pY<2YJ%4Fi8=D{ zfcWi?6y1qlHTTH3`eZ?bG_Y_uE3M7v#VAa|J3ipbEf^1$acIrc$)DG-hh#%F zR_8{t^BksI4FXFI0$AKdHy4AvQTwNtX>$t=~zDfMfoR+K$fjZ7MY&lO(1=F$GFx!Xd^6y zaC^LV zWaDFBFnK|l&CJZAu5l{@Leg)EyvaMV6U>6Cd8T)QYhiqAatj7ou=a-u{=L&A0HrnE zg3NHwpl=P&HnN}k8QXCIdSH|yJVlmH0dTebv_|%0cm2tuU(OxuVpfq>RtQmE;>!}U z%S}<}yxGR35$hj9WCTPgk50K$9af{eU#K3B^@*7oKi^P^eU^NA<*utGLR9UFyunaI z#^{SI5tZv|NF>d-Yo8L`?RfWM-c*y)eKSJ_NSe5*fiG8p$TLR=DPo;e*}!!#OE)pj zkIKUmPbb!IGJ8pzfe(itEcz|Qg|b_hu8ldNc1hummg=RMCl+s|x?1A{i4by?77&IH zCU-Fsoeze>#!%0iJNLjk=neL3{AsK&y)qrI9?xIaVZz~=b!xA4^vgNf_8`bK)E-S8 zcMA)C;uMe;QBiv&Y9mxG#!G@~Z;Y)AU$^9mSdS}C=66g9^&}Mh5 zY=pP_VFsz&xs>)Rk7_=*@CtnJz(jBFI8E7IAEm-k^2joyg`_U8a!8Iwy z$lcNC!okR6@vH=Y0rN^l)kJCC6^7U$)P8ofhig_QBrttqcmm^9K=DlS+U@7Fxu^z- zpmuXCbfvGlB`CHM4T_-+CR;-^PBu!C}%xaBfCJc zJMZ(u9(7cfPATkrQZ<3>r>W#{Jr>1j7DrM8kXt7BEOa;G(WbNvBxmMj*LM07yr#vnV=8NiKuGF>oJ-;Ki#~ zOS}z09%Qve8{kWxJh_^io7=YtBr>0+mXDO1;H%^2bCms*qa z%!O2UTdcuzAh{hdW~2QSP_<(D1Pm|^_G49xn$9|Z$d*5dFX(rv001BU4z;tW|JD;& zdQ{7WrDgsb^PV#{{~*bKCp`Qoko+AY{s*Jx0R=LEAL*C>uCQTaIXINkMT$Tn_JTOZL@!JRQ|EVzigH_hypSa{t1tt zN7nxr(ER_u_k}(nSL{Ae;{qUB2!Z-DbuLiWAj~UZFKy$H{`=l`F>n5FdW`}vprXk< zka6ApcWF{blewmTaha0*HC(3d<|c@bkAEhqJKI3oiCMOjoQX3UP0sldXP~Bns+!uj z&$2+4Fpw~b^02gI2lChY7J;qP+}xZ-T&j$}D8LNmIShRQL=)%9A)wjkD~8oJLO=x% z@>LEF4&S4d!b}9P6^LH+p!jx{Akvp9b+$A_Z2N8ktqmR@EGrdxr87#477)wU1&lI5 zvb|Zr*`UIH+fTh+0$CqbQ{8N#Tkmq)%MPQHr5csdQOc2N8 zMrxK!3BQ)jub)dmq&GghOvNmb2`UsYu3oQZmF{aQ3&%M8Sgd-!aRb~b5crBzThn%A z^Vs<3>N9=li+e{+$SJDLrC<#oOQX(taHgnUNoXN*{k~G$CA?CzBVyLe*<|uV4-$Rm z*2B@;`|OJtds&|i>iu?RH{SrUe6MJpUEew~*(T)LlwZWMg2-8=gjGZn>@s?2f#(0I z?9Ah#-rN7Lv`2d(Tc=1Odt@6YC8>}U3Q0m#cE+xavL_X?Wyz8c*-Y58C8NBC3)Xmt9z=rGKb*Co7M7OpVb<5f7SM7MugFgC~u}d+r(f^o&NZA zl6%GO{)tITN}Gnan)R!iJ{(W}({Am=C?&;&J_sH3$|gEcYF)z^{avGUu>?$)@!AD; zMR7~KQ_IOqIYw3EMjh;+yfTi$8%piM{g+)N)vp&_dANd!Key6;M*e1%G z&?Ajbes!w2C0Xmlvb>m zo1Ea%^FHJ)!EU?3`g4=4yA5TRxA%DGIN#xw6H-^41dq*lhF4t+|N4O`G#4`b5I_!2 z{@gg)`JFBqHW$pYJhpc+D8fOH);gbyVnr^Dow5u+O}Hw6^ID@hy?3H5`ko9at$h!t zBtJcgBV!gn*~YFiLyZ*TKVfz06_dCpxrXnS_J!)P7y2t#g-ziDT zB=-@g{6@^zMb!&ng0s$Zw33#yvx|bqA3$sgJPl#-z|c@(Ma38d`~$3@o$}X*@P2@? z5;rS}gG@dE#^ltG9I=mHaci}R`a$EPuP3ntMLbat73|@+vd&Yk;G29Gs*59*r<$%O ztEJ?^$CefK7(eU84%zd>=JlE9`Rn}*QqEht*>#+p@77#K8|*tLH)f!41UIcKXVE?? zcpf*T&@>muP9cx^3OeoXd317)Zq{;Lpfrrr>psEdIw4_>Ut6$9q3H%5|B^OP@2@K% z=M9siSFUf2Dd^aH)lF&I&&<)p@bgp>U4~TYILeUWqr)up`OzmM3o&X~THZX6h~9W6V+Z z&Q5{mg)k{dg@J;9hSIZMTl5K#y-2NszM4&x8LJ}g_F>^!Uy3e-ZNAyaf01O|p$lY$ z!W>aP7Rv}2C;W6czs_KDPSf3O2fn@^a(esvwN!F)@=!|_7npO&0Mvqe4JnS3x9{?< zA-dMIHUryB2J(RD(GJm6qr(q3@HTm{UHP8e`KmoRh{Et~*H97>OU- ztKnN-Fs?~`_tkC1y;ahKNmobZalyNB2mjERh;-T4UKr;>D}QdpICVs5T$RkdJfrK1M_FbHCqG9_TL2C zh$j|S&PIO;KUk`U5hVJO28zDgr7KU}4gw5bI%qP|T;b9;4{!sTk|iWkVmhpzh^R~A zzpDqhA~dmP(JE|}LbtbU7S2H%a3Xy>SI>RCD=d4Xh{Nur3oEnUGSLJTLK6>i^hx_Z zq7a*5lrD}rz*8UA&6F?B>9P?wSYLVYc0Q?RZRe|8qgM(lZ&_akBO*)>xr+O*4&Lyt zwL8kNgik%H^ajng7mNSwy4>d?T`)X+taLD+IBW64;In>Hp43xTrBgh)FpQB;RFTOQ zOAm`5EZxoEuVQAAhhz#45WkEkpU#x3k4NdAP0`yX!C$GIW!CeZvcl~~N38#5k`ml~ z`OEX$?I~?hf&1z|oM*p3OI!T~ga2Van0=|P+>1oWkC~q5n+qK)^&*s%2BxI9O)+-t zH$6vXbUTlIn>u^)n2S3-EKyQef_vwBVBvv9{7l_{U30c+Y)Aez$j5!1C*Xtx4jsFt zJ`0?N;C>O|Sq`px(^{9<&n+ju4vcAZJ|)E6IMHPqVzR7|_Jdb*tp^ck)tg;zRC|S%y~%pQOrzq8spvA?)(`yK{(SB^ zz_#z~{*d0sLAmr9uOilX13C#!)IR@hQ;%;+|FH9xY4wcm~lEUb+QfX@#c@58X3QUYwcMEKu=8Dr?Pww{?LpgZkP&8=kFDE|V;G7=p5gAEQ9V}g zw?oj(zL$miNGul7&$bc`@TLi|+j11!#rkbKV0{0sPhi?uf~sqnp#XQ)yFj1sKPD@l z*jZd=W%9KF_Jp-M!VsBki@TtE7vsJ@!KZQ&8`%=h{`e!)5w2p-yNn`>aSU z(U5V4#}SFDeJXGJ=1O$icM9{!QkT-80g=UkKw;oJR&2r`yxD5whIUBU*SLykf3ogd=;J{@V^y4kn>XrRDoU zG@ANWDdy38T9w+RezG38)msVVeSLGMlCFb=88f#+w@Y?@VN5sqi1F#3zPj;4VT@rI z(RVEy#>MAeItwE?mQWy=)$%b;q2w|-K$XHVV}^`7WNkJ1xk?xK85I#eS|NV6do8ne zkYfT>1Fuh15>QO4Ar4GncdN^~9{@E@zt$Q;&OgWZ-f#$^{vU?gSYM#kM79yw!fTPYGtUC)Gz0j z(kc7eq*Uw>!js^oe`}&pZW|vUeC^O0YDoxlYcF9&ZyQ+PM>OmNkpVBM$ir^;9^gDw zO#)(}>f!>IpufJj^A&^@3j9UtHlJBYwEw~#?p%QO$u7nY`n?z90{@^N{5J=9QP=JA z1wlRhEM%`;%=A{zE)`w`_b3Yg@muAERf7JerH6=GiU=$|#MVVt#7~OC|H&!;huY&W zZ~swUTYa1(nyWnYdb&;_ZvAdMb6ss$G?z-y?@oU0_qc}-mTE?RPrzSY$bbLW`H@Jf z4*b7Q@b@hH-l7G4zz6=ld-n#&-{|<1tg(KuHYT!%`B=>GbBT`^&}?g<>_SUhySPVw zG3XUzj;Kcd3;U1-aVvycgg_J!h)16l#PC zs_9(1^cD0b3rhZldWpYDPOhG~0wIRAYu7qT+zSZU!o_9n84@185dvi9K*I&WkW)91 z7#vuO3x-(xTa2yV4r>AM)S3YE=qIek481+Rj30(iW3CUK$;Sn0WjQZ$K$za00`_S6^z+wQSDN>-(uO`FlCW=g*&qI`YLJ zxHdJ?8V-P7z2_&k9}5@IW-%F%7zQ?EfFV%M0*LwCmD+JQw|iIZ#(**cTPY5GYdP#i zVyd7T1+XJ6C+OZ$6wF~VRf5>s;ondQf!^c=@Fvx0adqd7Dj2!c{9cOAqNm?@T96RnhJAyy1(MdAm7$^V&p{u2IH_ z)Yin=yUx}UNSq|nD{ma*UgBvl%vR!yQu$$k{&-IER>fuWsx-h)GG)(5rWVTFjZN!I zTnjsUqEpb66MXo4#(OupcCXnmuJe_ev#~F+HBn2~$3_1J+eecA(STapj!B;noKNmfZrE403E~Dp8zU1U} z9JPF0D|P%sJ&jDY_&7OvYAon6r}bB3Qs(Itp~MnKzU=1VAL^^Y?zev5ln27bA-Yds zcjN~V`-;vlzVFBAjV+^|^QMfHtk4epSgy~jS-0q#Y1ab+%5nyI8Y`6j=&@j>u-*Sx z2ejWk=|b_#{<X=HFf{6h9qgX|?U!sU*rLp8)16N^%2tvvyGOg|OFba^EJDvS zzcsuJZNGAXAneAKs7>2ZCiR-g$?Woe@agib>E{{a=Y5HaJIY)Y(9YGLjG#acmL(em zj&rT*c0zpGrVFnK;a*n_E}1o=1`kq?Q~^uxURb2^KIA#-x7b*9yzzV~TGbah>(S_G zjnj${l%~+3y0U;D444p)eRE-R$2fwzBl~9h+YVFBGA~7V3-P0ROi(-gZg<{duIQ)A za)uYH&C9ac%4J^hoKF*ctH^?+nOgju!T>9vwz~HsOF@b0bP(88fahKL4iLoL0D=Kz z%QkVN2T^9eF(4Li-fsHgoo&9!WR)w%`?FP=HuwiIla+>l_clJI(AW}gOvyBOe@c9i zjK!uh%tU<~Lc1d^R#*55XSF!hnekx3?g zhB^C)L>RC8_}hx=m@1Rs-z=`xb0&%H&63UeME_rG&QH{+timf{ry+z3>FiYqbUK7z z`AJ)wQDrEvCisLVjs6@ud!I{{jC+N|vBV)XSULgQOWz=Ta8yk;HVWmt z+}=zQqHUMw^<_nk^A9zg8r8ZIslfa}4JUN046b-DyVXmnm66Z1@A6{iy`;g+8}9l;rM*q)ti`IWLmvI_K>+Fx*6r zedAqYNxx7$?-7N_PdyJ;099O(WtL~9ZAd}j#xgZ`_Nxnc@h>o?!kK}bu%W6yIIWJW z8`!^iZ&fWGsI@9Xx7&XEpHu%xaQw|?S*(9c`<;;0t3^O9>Mnor_ZJncR!_wbfL`w} zMI2-31z1bJG6TQTAB+0E|D-BwEY{s2nmL$K`9Ey2rpE{fX+cqk{PpNhD%U~{WN*&W zGc4Xfg?Z)W<)F9Wh1gsv>|L2o7BG(+k;Io`uw>xu=*j##kS9^LYK;%X3zx5wlln@NGg zEzsIF0yUbKVzyxXET~?AU+xs}14dF|Of}V8;z(f?mmMW|0X559=qxatnVtc_;CN+p z2^e8Z@GQxUHb87$+ba&>DmDO|w!b#No@*_3C(vQykiOeeW zTr=u9+=^)c>G2^0A@I*jIfja=o@{17GyFrH|w(e^*lft0440 zED%5(zcce=_}5ukz&zPH!OFr@D|uN(P#oHMtFh}(=W7aRG!#LXTN-qbLB#s%MVL!_ z$rFa+TxDqPq6vHX3By(h3pIa8HFEg#f0c$x;B(*nB8mTAk}2kQx$Gabs=o|s1T}8u zwy+qFI;kuz%Ky1Weuj%)|ZaQn8fE1gJZ*WtV&j*^Np* zT`60WI&Rp0Z;KY7^-q}FclvgD%=RcfBsmC;D|AJ6-xGs#E4x z2K|_WJ9>F|xDPiA&phQhoDyrxewvc-8Lz@RpS&|f=-Vg9N{pxfn_q4qr~SGwF*H?W z-|7!Q-vvF=bI7@^ShWg4r9&z%18Ry*i(DMfah*~R+78bvO?LX6)YrdZ-L732Lf+A* zG4ihju6?A^uJ~Sj)75Twre8CJ?z?Rxhn=Rw)lC)xK_w|An{V~b^e@_oh^VpQ&4L*V z1x>}UD6bRWh7Ju~g$@wM!CaZ?_EQrx%)SCG4??)5-)|>Ls#0%=vXN~{tNHr& z=uG0U$#nHV+5LuO?pEt{1mC>CAlHu*9S?g(X=CF+n3;@|){cp0eci_VYlh(eoor0j_|~2$@?*HA55Rl9 zAmIZZugoDNDpE2o?ZnIj82wh(j9wQ-HOA@SN$LJF5y*rMxf177uC}WSjh>XdF#}l& z{KUIMt8_;1U=k(Yy6|qL>kfQKNXgzn{mZ;UmJ9P#o^?~9HujxmdV`>f`-AZkdKeH0 zE%Ms;8NJ@6{ZtOB+Q0=CSL#1X&ud2)ucK<}Qi!1Jd))f{FP5_DiwcUS1rFq| zGooqb_P^h9wb_e`g8w*v7AyZRw~hS=Zn55#2%?LSmFst0v0dyh&>w~doM&=MN{ljE z0@P`}lMQOtGZYd}2M4#*%>^~i&k_zP6Ld`~)IRB9?M!dqxwCf7nrD#26gPfb+l=`1 zus9pxmOEv?NF^-)|7XZOfZMnX3>=HJ8O(z0q0(IKVr7=!}diZV{gEE@|wcfMft`OWW!298ZClbJpWam{3|%%=bM%^zPLaN?RQ)3 zK=CU;wS+BLEZYfxzN8ZQT}txLKPJU)`b{3;h(?=GKm?1xpP{s;5GN*~09|8{jR%L7 z2Yn1nBJoFg&5+PwPH-Y^dw}@}O+twHA76|)1W}zNl0zW?hCaW&VGJUuB}oXrQ?h?G=a(>*ZHX?U2&6wO<*BI*PQx~kHx^>E5zXjw~Vx6$lzOWr#b)e&^zVg9INX4YnKyMMzg93$LkSW5i4c;S-M%x69JRpTdA{{6URgo+vXaoiZ-o1PGP}GqlM*@R`oh`ym zMnV<39H4|J?RtA|J!_nZ4TttgGSEavVfw=l=ommFu;^-_Le~L52dKQx=qQt6Q0wm9 zzdr~R&js+#qrkHOWG@0dx3RIA8g2=GD16dsym+PvcTFM(njyirAaz)pVSGuBeU%&n zDs3dvL*nu6NvCoVc*qWNF383#t7k!vrGZdT<*#!KpLpZ|tIG}&+Tf}?^?%rmfJo5j zDofD4>L#iC1Kv3ShwI$|QaJJ$wtKIA7rwtCF%g>bAbvga8$x3n2w;Wq$Obg1vEl%; zx@a4%Wto(UZT4wcqzm0~ zCdpL|4dKwGp*!UmyUMLCNvHlbx(08_@fQ51-{As7y7Rz38lg}MI-%tXH>_$X2~AB) zn}7~r`rwKoGqkFWE`^?Bb)Zt@0eY==to%R)mzfJ1YcdEya74mxf_IMq>CbD29`$fV zJ+^0Bk$aIH0ouPydF@6xw*wF>bwgwOcmOYUKx4~S zqL?%bq|+4i0f`?0L1O)pjjH{X7YlV@Dc=tcM)1ne*ayp#8 z6h8jX#%pk^B3;>zr@gTwJq1v0?zL74G+N_m|64t{{bDBI{LqJz<|mS76iPOz0OjHA z6Vk`y@fqjy(li-gU)=Bao_i&|x%v?(9lyh3N;Vq+L;5J(nbnWL4g(p5qQh4<>xKlF z1l-E&;eniv5TIojJiH||=jyMEHQbt}Ayjo5#$ye`>%h}`gYk32Sx}j%pQOGLq{0-6 zUEuxB9WZpiSuu3AI-6w>3i?mB)9`2Q=p7M!N5EMyF$8-LM1_6GYs}6v%1MU9{h@^s rNBnYd4|WTjSdtn3-w*FEEcP288R7Dp_uQbv9-Eei&e3f3OSk_YJgk{0 literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/html/_images/chapter10_63_0.png b/doc/LectureNotes/_build/html/_images/chapter10_63_0.png new file mode 100644 index 0000000000000000000000000000000000000000..59f332230a14b7ff2beb4e1adb4c808af1a8b277 GIT binary patch literal 26114 zcmb5W1z40_+ci9j0@9(H%x&-jo5EC8v z#k>(m1o#kek=Ali1Dm_J8#$SQ6pdUQY{4$JR>rh$W=_slV0$h$ZZ<9!T1yuf2WLTc zcDsL0U;{f@uy>_P!GN3Ga(Jfg3<6;jqyAn4C8v^tKxSZBDRFg=)XhoH)QCl7>+Z1c zQrA1Ocdjj8AHE~CF>R;rP>Q`x=VvfV_b6^9C6*xUZcrN$)UD&Woau8bRkt`g6LV4= zF7qXpFEiJd=`=x`-E)K>b=iNJs>nR+k+a4IDgStu8_%*yUrdyWpJm*~bOd zUF=~$kc*|&{HhCL(XZi$BZvFT!3OD`OJw$S@FV8o;ra>rYf0-k&H zGpkbYg8}7@k>bFwdexjhCk}!xD^F5*?M5n{8A11-zBBw)s11^mmVWHIre5W?DL0U# zs9oW355$%bu4&*Kx73|7@L7#f-)C34%6&WC$VWb&CDVSg%4K8Zz32Xt9X1% z{Nl??$7$c=>|yptkHRc6eBCq4rJS5Ne^?LAl~4Q0Pal1X6768j@QHcU z`b^5{u4|B#J*Pk7l#%&Gq2XLpSfNgNr1emKvB$2lDEvUpX|ba@U!#D{y9em-%49Vk zv*y<HOH-X-)3NAi);=j+3%B~=_@voG4Dye^)m$wm9@5JqVYW-1lqPx zy$zku&G7pu8H&fES9Lo;3~>_J7>YlTB@3Yt#G{*|;g)%}z@YZ!CC`SN^1#MuDdV)? zIji$h*X+)0Bc-rMG|*f9qtv*cz)*qJaTJ6>#pQR%#lZg_sQDSWD9*BWYL_iP??XIKbcbIv*-Wktoqn!{RZ>|kJ;5oV2hmi@nvDA7Uegxh~EUQlZ zP=O|zVfi@gcvM)}Jz&koK2i(8y2G@ynwwGLw)rxiMLWhQO-hQJo56{Ayv&Y5#QP`< zcr~|~)Zc85m(M#@a=Ow)kn*6uwf=ee*KA z@uy#2{z&8lQ=4_hH*?@XFZSd?Zrf9euym24im6REwQq*verKzUpkH70yqix@$CJ6O zB+Bh4^K>gYGko@B&umo6?e&0{`D%QVft57^m|D38?}xwW@U=wID915rJba$@EC*^% z7vr3FpWca>g2NCr-x`%`H(n-;IGG>JQw;=bMhuROGXUjPrtf)@d^Pyqj(Q|M_12-ASl*AzC zv5rkIw(ifm)!yFjvN^`1X24F^uI+MK^Ckl|!i>u4S-$5-0n4H?_4V~QG@=u&@8Lqz z{z#GgGLfd6V?PpbVPS7Bq^a%^ijh!IbiN_H&+j;Q!@fMFt?e0VXWCopUSID;6kDWw zh7{EylG`DSsO4f1dY_K(F|b`oNzsqGjg38+-BC&tEcSz++1RTcU&f9MSp^09$B%bQ4vmbAf`Ws! ze??FU9lae73lA^V^(CjKR zE0+2Jg7CcD1mc6dv z)=f8^uLL}b`&C~_yW_7KP3Cp9A=?^B#jb-qw(b3KoAqVv$;rvVA`n4L`Gbz!uYzE3 zN&%9?$-Ki7b0g!S>c<Sge3FWlvocjk@MPmbT3<#dE$ig`k>g`7~nc+dZ4#SKMj5q zrb)-f)Pc8$V3lX)`;2M4psHQOt=SQ-7*6_fWTR0{A<4}{D-7e!8m|iA=m}YJV zK^otEaZ%Fx6uSSAah}N2;$V*@lHYmgvtGPtEjb}6>Cd9NW-g<>R(eLAY2-0?Er2Vw z8n_joKTlKeJtxMa6vlgU&O2n~3cm9?5KX{gho6|i|6Swkp0ozy$Jk+KpUsR&x^sQK z7DJS_ueOe*m%*JXm!eQB3G26k<&1t^^|h@&w|657CQF!V_17c}RcPzrK0)p9>HDX) z9jtv#0ggo)_=QSW;`_`iexN5ho&F z@^{YOrQeRk+;=-czJy-S6c)%KHVI+NQm*EEBjEK`U-G5?i?8ZQ4lT9ADd^qII=`Z* z%HCYl%X$2vlRKxT;;^k2 &w9owBou1BbtG;9d zc1*tcVvW0vjt73L_3LZ{g*v`+@$66Q#$dZ1Y44>bsbm8qe}F1JDG4C>7ER8Eeec1y z&9`nWGDicwbz53wyxUtoL?20`_+j{)H#@UtzAb-I&uZf&YvD4~tDCuRYqm;w-1{zk z3@Wbj^@-p?&A862JcFtXW}c^}_R+RLOY!|%phCSPR>kdzl2}LnR0Znl_#ntKh`-{P z^d{C~y?wdrHwWr9p8TJsfg~OxM_nqP^ab!X5D*i84`}ljotnU$F9pC`+LUzFs=LrB zvp*AP+#K1whC?x)v|8lb6gI-8P3~---}m7=8>8U+GZ3Y6u*dgUiKgpu(5uBHhU^N@8W5`IAmsTIuQO zuYE)Qbi}&b7BOl6saYgWt7OBbCtb0g+o(ThrDkI8i!yQ%$-uzf( z*`G6Jwm9Ze&>4dCZTy8Rru~c0Ml)@38@xD?w4a#M{+&d##PjfY3R9%BlB4Em*+!p& z{CqLNVC0(-T5A+dt9dD~w*uG__s!e4RY#CgEsys;O|5ztGm%m9^zP}pK}&dYG}Pe{ z0+O~}&74TG{?|p&k*I-HhS??oeJ}IR!}C2Xv(o#7{ueQ4tqd_jU^WS744vmq;JUf? zy}?3Fw#Lox8|sjt6R9%r6y(P>i;{-sJz^SXLEqD+U9JT@?0ekG-^@HVie|r(<96tz z8*tFQ^ZO*kS+eZ%(zReYE|E*k!$W^gi9UzDwKd~`@|K~5WMF@2tFZ}jSVXN>4$?ol z1YRJ?pJp!?|M1zXi^ny*W!S-3OS8EdQJnBvSgl@!0--)V4I|s<rzL2j zrAH2A%T2vZL=#&y>UyVt`)yk%ObDOLX0CPWmOf{MCZ`1UU6z@4#*7=ZOiXX(;)JJp z4LoLVn#0mJBM82Bd?QOF>xy=_*eP(Xbh^p8H`H^RT{~KK)beE68mIAR*UU|aO7I55 zI#uk-p7u>W#;p;dgH*Tg{E;C)&%nnq^w!ifoC`ywb|(Uxxyfsbc;u)q08 zwFX4Y;H`AxRvnSdW4~BuqS*)T)dhfBvq>$vx$B5_!~RRt1O18`)*H)M3#X2H5B2kD zA+3c+Pd$CeW7pC4QFeUxU=E@`5;r>k+X%XOP6mCv`*!GjbCxDcm% zljjLLbVds4L)hh=-8+c=XH^ZRV;c;J6Duq|&hpO=Qlu6zdWhGQW1NNd;d*+`jOmZJ-(HopO&3-)P_ZCbV+_%#7jF+j*dw!c$BN}>toXc*KNGG6F>*B>JD_H6H0;RdyQ7o(tx}CaLUIQR{gdiF2u0F z(`q1IK2k4y0<>%HCVz@Up^w;}i)$6shDA|NGQ0j8eya->0?R^^Rm`8zj0DCQ+=XQ1bP6SjS{&2madjkuOq6WG%|baDA9;+_ig=Lp@o{{wvulKLSMa_4U3W6ui`TjI}*WaK99%*l0V zu(Uv6<%V?X)(!E{!H)#gPmpmW zJ;!V%Qgthm2JCkxfv{w<;W9BjCJ82?_OY+XsuSeMW9GCi2@7E`F5T z1LijBZ5V_mW-DdLnqREb>`s#i8kS=?uq@p!Qqqz+b&@6%JwN6?(dN=m27z ziSZKX--VXkho5-QWw}! zVMQp-X{eLqU~}rA=)B=hC#dGUO9H@~J>Jt1jhjyU@MUi;K~F0C^7e3ig-qo7>1 zF5FWU#tjhqFrX+?xln1?sOETU?9{b3bePBF3Z*-ZL6J zR73I+=mbPadPnX~*)Z4Kt~I^e*kwt}kKNSLLPSNSsH;l}u-lK);m?6r`S$iBr^az> z)$?qYHyqyI(qLqbj!1wPE+Id(%RO2I*VHc1i!;K{PfGc`&Gonfzqs5o2%S-*+4dbO zI6q&C(y1*gdYO&yZD&BXJEmbG{q}Yykk6PJO9R+Y8_#M_KZ+$ea_M$2vQ}k&1b#eW zy&^Aj<`v1EI#;abpX4WQ1S&%s+r&*M}$jw0!9RE*ObZTYK z^MA6dmHfy5^J@jqCD*23R=eV2x_+^YyBW!Efd^bfT+yw}f|mcuzA~rDiGe%pqWw

v>x!Q4|E8z*E<=|@G&1*h9{KlBGRTLc2L0OApi78Vp)UW2O_uw)XrOxb zXN<1W6HWLJFK>R=e)6v&JnPc{diLLXYI*r+fc#!wbrBze8r>!dNVYWa`47c?e)&57 zdE`WukN*Fy32M$kz+ovT;onq$QO1)9`S~-@skZ5d_g(70Qhl?H#LY#Mi+?2(T6L@4 zj&*;PDX_Z$_x0-!T2>HyG=;q&Js;tFc=}|?HdrSNF7fE)|B75wsA@7KrvpcY^k`u)V}eDH3i>6pL-mgFmx%bWJqBU91#o!$>i$+_=c`=y}W2 z)_aw0cdWl4(>Ikw(=wJm`%?$vDc?}bOT;bjG~E>Xd~pQ94%qv#F>$U%5c1x43R`T0 zLrYKy6x#SfoeUzXEXZzyq|h8YF?9uri!(IKryP*3&?%EXAr@t z!o)ffm*%X82`RjQJ$4lQAVs#qJ6KV;=@0E#2*X za5l|-s(#g_ztlpR+V8}ua~{Yqn*&KcASM0w4s%P;En-Y;?COSJ!m)(cd(uM$ipE!v zuTzRkCxS?Lw0XzR7)FlK3Jr`oY*SPEwkyK&Z_+4Kp6uC8n{pr?QRFI5rGnEb9FM-Y zzm~Q4sxvfMC2BBfwFy;h(bTyk)h1+5Z=5l>E zB0{>*ybiG#mlo601$AmKQ4&e>r5r<53X0{dmmU1i72}njWsbM$;-ub{ThO~!=sm2q z6xyvc7nO|TB^3J#9PD($NK##HmT|_I9+E`7i9^0cyM=N}SB7c-^36ciQrp{1 z=mkZ+M;H-Y9!GW*an@uk$;SFd;iI8-X~!j>Mn<$4l+(K!g0ZzLogRdfurKvy0`S44 zHPUQnroK?WHks3`g9CV7HujoS_Y9BS(aT>1&^-|Dj2KVc7_l|f???9&vs5XrlC5`u zIYm?}`b}I@!blapH7!GdXP^c~3ks_^C#>gFI%0__903G1+IW@D9gr?7%JT<$Whf@a*JbEcDhqF>&?^g}mCb zo|b}auc04334Hs*ZeuJSn6?;o&d)#AL^P1B8C1K{iuoa3m@y~buI)vnlsOXCj+$E`L-EPg^S6}1NcUgv`*1w8Tr?)BN~_`S z;BNFXP{pDfgt&OBNXC5Rm}04dZ2_yY!pm&RjIUm@4E!F&FQi=dE@{t`3!UquGs2p|Fe=+Ui!{bd*gsF~RO z(vUQHA|ZU6#b-A{mzJ`Jks^y8l1|M|Y_+$_M8RmHh;`=`J0B@O75XyKJ^y>898Bjv zJ9?d~C%|kCxR{NOdAE32!P7qzu3=APtcZ2@@knuB(_%oDRGVg-%qyg1u5#i6eqBXs z(YM^MpWCC?C42)VakgkIE!H4-PNANn7Z}j3)9-cJuj}12svbIrE(baeC$L>FQI(ic zsF8&>kVLs_83hiSDqFB?=2_@Dyb-T{Ro_MGmfp*OR!)Hc8)Jfawu(!=Qy{w{F%H!; zM{C!lrs8~+SQ+Ot4Nsbn3^)Rh{B^S0TjH*zzHwEp!1O8Zi=RS#+NwF3ATIu9<(N4N=?S=Vu7h@&)~e=V>b5PD&Y$azXL5m!sQGi z!^7_jU(8W()6u;Kvf>Rp|ra;npNg(4iR+gQCkj<1cr`3nRZ`W0zRS}KeB``jz zfuMIe`y*`aBs9qGW(({AQelx;iDp}=A~}=3k=y7B*hc#e+!BpAPg&X`xNz^jlQkOO zeLRgvs&HDA<~>%Or_Xp!iImsd z{ZWy{I-x&00}VB5k!J|$&e{qtqlw1-Gbh>DdkEKnDjSuMTa7Jzdikhg(!O&-a)6t) z^Ugygnj(GNc#9(=Vr^>xSHsN_^#0MxPuUVO3{#*R@0% zrJX)nl-Q=UZUpHka-6P)_8d5kiX$8XKP3!`?FPv{qsFYtLWDw{RnH=UeSM#DyL#-# zUSAh?46zZ+jl}NkrV&2(Hw=kG^K_iP$+Q~%IR7ja{)>`rV?E`xfC*2<*OF}U0vR~( zH72;LV31Qq{%f5}=+Vm!=kNlUZCBdeC&$;=)_A(1qejZ(brn9@Wd>id2CK6+i_&Du z#7NG7IA%_C_pV#_t!|KX_}#^EaGjz-WK_gC^jWh z%pjl3@43ecvq3D9lNfw;Bs2`|t?4bUOZ!+p@=TUjo4c<)%!DDa_n;nR&D)(E`Q&X9 zkH86hnt$}bkDM)6w*DjUmOm3ouJJ^n2Upyy0b$}`=u1dTHAvVYsE^w3vgOVyP^599X2Sf4YzkTahwRNy&*NNC9vWQf-_^6< zMY;-Ye-|F+E3)#ZaM!DWD$M;4x<#S&?~5E(FL~mBNX(xLF6)=OI^>rm5F6eU0<`A8 zRr3C!I{#~(@9(2D|00Bc9lheWf0Is2%d2vuY3DnYNnL2<&xC#-ssQCthcm$&H1fNy zAkn)k>mZ*Fqa5Ie41vX?<724%6&IYtC^5TiR!O9vu_VBq{^4_1CCz`>-zB5^hnQtv zlInjt{HIx0mD1qPmq&p*=fCOY6@UEa0ask^zkU7d@!gm8*j=>WPguGv$^K!g4cxv| zua5tEwMDQiGJ9EdZvtCgjuFd$=y)$Kr=rJ}M&O=VrlzJ?6_fz^Rmfuvxly13WjWYd zTeqxHK7=J5BI(8qJGwyqlq%4|cK-~w_l)H~x*8UF?|%9Ao*A=a!g%k3faJ7cMuDzI zSRlYR6i32IJoJ3RWqsjDQ5uoCQgl6WSDz!2JFvt|Pnb(Mc*4H`S+e-5P>W2;;hXGg zzkP`4dkL+?<>EU9*R{*pq6fM2RHnKIl(PwLFTlM_d4Y5S=Rv2@ipXF~4l80G{WM%` zm`eC?o98yK{jMuLH1lk^>x?lqghU_PuwP#3m(NU=sUw8XTubaO6ftFZBtgMt;9lYq z4?%aGxNtWHf##>NXt{5^fNq=Ck1LgJa*ULSoTuJb%HSpC6D2Xx7lvJU%HC$*GC%7w zluz1*;v4pbiYs`DBx!R&K07Bs!XQr9cA81t;)^g%`SK9Z;bjY711aLQ_DeIU|_|J`}NkCC^t z``~DUFHdbC%QDEKQX37z+J}x8x?IfLJ$d8C6GK|=LX#3J`J+><)1`3`9dpGa?S8e{ zqfJVmJ*yAd2n@WDJnaE#sR|3TMs%eznQ=#c!$t-nd^bmeyXd?WI26fp;Y)Z1>JJ8z za*h!`-8S1J%A%)1_@XB$eN$tJAApjkux1S?1e&rG_fux_P6L1uo(aC!n^RfzX@_b^ z%;Fc)BUQX_Cw#N&8Goug=QBB|7Q-4Iq^ORM-)*9_X3c~GFSLGDD$gmjeN2&;Qt6pe zh@t^$>a!iE2Z-PbehNZDlF+?|M#Y#IoEY}c{>^Xgq35Cj^Q|IDU!#UG<{U`r8OSLG ztmg-<0%u`Cy#>k-otMzxGe#lP8B3XqT!I*sQriF>lYq|&2foMwLBWeJa{e2Q_+kf7 zG3n^``0R-}tH9}-G0Gvy8VYBJE{_*(3h5!)L5=9A4GPycIW`q@VsjObE2b(1g5A+~=JNKtJQ$Ojqymr4 zZ(7v!*|u=w7Qs)GHK$5+%506A-`)XqT7VQ!X?v>n78ceV^n9zahHTFm*iZAcg4&h6 z+5Og9(*nNLFl62%>7;+qn5Lm9_`~fw0R=v|yX-wXPGoC61TIXRd(FJ3T(wH-NFbLa z%%RkMyE&?!co*GsKRHPEIdZ`?@8yu}`it~?MJFDCqt35yVFxw@PjJ_aCy7>8NjqaW zFE74}j27FKd)mgWh|@T*UVZpWCrQ*-5XFN5ZOQ7ov{X~|+Aq%0AFVUTpVAkz3+%W* zgE!ln(gLO=H&W&ISYWB(d1#J34qAL++3qh}SZiDR4J~NT(*o}jWtqHRX>3OuxHBuN zu;t!0o>zlK%Rm~!vB9vdS0#pR5E*z=oZDvZC&vd>NyZGjVo35@(t3$&N?IEh8(8zc z{E6DrHUN)%Z`UROy1r6CU3gnRC$c7w^Mqt zZDW9tN#&<$)6VUuwWJcqGLol<&a?A!z8ubr|AF{>ecrYp=i|G z30O};kMOn%XFr1LRH}}h#Q)Tex||D2}*femZ#^x?1CwNx2p))C?$v)cc59YpUwx3iJ=gpl;>IQ&7&i zA69m*>%VGk^@@#~?JI~;vX~g{lD-Q+R1Ov0zbaDpGH}n8UxkwJlv!&wu*e?kF`o=DMUyg6b2owvM70{+P%F3LcHu5MbFeU%FSE2b)3#g_KdtFy5G z9ctn(v%i2&=C=a(cO(8Cyk1;|r3Ihg;mJPlA<)u4v6K1gj+K>#+NB|Y)D)=h0mV=) zhtc^u#2GU{BXR)(j1thM0yHjpT>Ua5%Ax?&2&WI>pE9o4b9&YuWWYkG&D`nbuC)V-wy7buxg6 zgHW^<>$X8S8*iEnB8eY34jV%ugq`e=PMj??uWhtfP{2sXXjw? z%^OU&&9OM>MJtWJN`-?_y7!g3&XyP23{wbnBN6YxlLk@C-IBpwTafwbHN*gghkHtM?lt|cwTM~_|V9g zdZ&5pzCJNrQ&!X{lCe7m<@}iW7&ZTY!^i?#z843uD_r∓o=hfVOS@d;Xf%t+yiu zt|mM9>h!-RVBFVBT>8(Hmi(O;7rnYj?y|b@52)?G0=0il@fXP~tf&$ET{QUn34fNw zRdFPnf(cbC`DX!S3P=FgUaHH0596zahZ4SBqOK#2hX!}O+z(y3rxszZ7()gqTrf?9 z3-0>%eradWu8YflZ=oz+`&*acELPx*;X|D<(*+gCg^`0GVT%IihT0igreWWhHb>Y#lcnCW807nshkjDlDi1=mkK^a!l1 zRKC`P8~uh@ZDOcaoh))3kYiDlp9m6d?=M#ct`+^pRqy9*YaX|BSDo6+-Q`Q-p7a_$ zh}<^(MHi?InPACS%rT5dgi@vUSCs!w<|`g8fW%5Mf2LkT+Y7NH|Iv1T^Ml?>nj5|i{5&A(R4410958@WHI!XwnbTCu69&5 zD~FurJi|+TGy(;yX605U$Y1gvxzbN9|7Xk)5#o!_DzdXIDs8+Wt{J3>3G}W^31|HU&}@!)*I-+a0JT5QqGM^jlokllFp?rQF<_%j-Q zf+rElN)3%7%-i-eGX<7Hco?>0x1TMuSp@~Z>PD9g$?2`BY$VZWcL`ao6*H(_>Ky?> zLK3eXIiS)9^w=s;A5SLrye9zJduRX^ejp!T^OcH9)F&}IngFOCHuPu9kJkB%@mLRj z0K5dqDx#^q1_D@}f#3Q7hfhPsI$nO=+V&}5?vNM*-rJ|T7xYX-c*_84ijk$EE_mK& zir}PZjZC@Cj>Rm>>%foGL+?ecQ`+~zD^~U;x$T&-VY#GRk`)Ds#r?UMv(V5KdPXvO zMu@2Ji{g*rcbH$l5wTav%4-ife8o?R9u|f!6E()~J7(C#m6`j%bP_4PEXs>T66EEc?1OYZYR62{Tq)9fiOgeS^E!BDc95rH%WLUrK zqH^5dd^H8OX`h2WnN)tq*SvOPJ42cVgp`yDDE-MqWhpAoiK-N0Zj9ONXreQ2-3VIb zxrJM)#qfx1tI*oX-$prU#3NB~oYo+b@za5+7_cnUTg`n8RjN#n+R(2_NhNMfdhenk zrE0{dY8dVTIX?lie05hR17;boq~qlq#COe~=S8FAQO^;sc$ z-j}ehxd1o$SGk+%oYIq`d%QglJmYiy4SVyG!i;{#XrK?6dkYdV5*dyP2L9?sp}M6s zrK7D&R3|f=%p*QnV39WOycZNl<1jtK4bO4BCpUL zrWG#M>PqvcmO!imG9G32lX5^lJ5Q^a?hcbW?Lt4>KF@c{zSlC;os<*{WiEeH^w zx3;~%U%3rEM|d6ph&}2K6No*^fy*=&Rf~)Z&`fvU-xnq2sc+fSw(p1yX{|~U9)yLA z2a&5X!0>ln+|EReIgJY=j-tF6wD33Vh&1|Ic6-F8n+_Zww0GN0Hf;>S9j^TZhMtB1&Wvn!B#_gg z6mSZ98bLnk(7QFi2tE;@qZ>`5CeU@nBoC$2}z-<@5DD$%51ee;#s{V#|eP2$iDOGU9VVGl!~S0 z!=ZeQ&IJ`zZMQ~VtoR-S3D|B{Cq=(!`cOC`Vv1f>K>bHlhy^CZ6L2TmOfoSMq~6RiDnNq`|- zaQX|b{xvXv&b}Ix-=X}EB;ns3D!f7_?WcpkjcJ#FrnvV?T>k%Z&2PN@Z_zsQRier1 zH&l`MH<fSxHw=8iL2hK3I_@Ulh3!B!iZ~*#%zXb^<0D4PS%)( zN~f?}-lLm!R*~^u2v<7mbQWq+x8=u)-@uRr(mCiNj_KbxU?v4GZtm??(f0R$(Dfu~ zOqaX&uWz6P*dVUkISxQo8nn3eePFNH5a<3meS-UDfSI!`piU^k5f&U&Y@3cm<`&@a z7V%>0i%JsghHea!*-r3ZeN0 z)3iJI$RPiF%C$fkE4?4=k(m zGXqhue}~UyPaaS&05!q^1N^xWLbL%~+>~m|+_H=>V}5QWzUOX$@kbJIaeB>iwB*71 zaFGQ-KjNKG1{~lYHHfqI;U9Xq5!Z5+DHJF(!u#0Mm*GIhig|0PHmQ=u%f0ioMuW` zsCs=5*7w-cQw)lNyW?a$qH(td)bdovn-BPeT`zXvPq6Ordit7U6)DLZ4ZIY>I5N#B zf6-6I$2|QkbKUu#@ZHuj|`pWI?4;@egTK_I3W?vTxV2# zsy}7|ACW}u9x0;FXOuXenI4^kP}rqENcWx3uJCrZ;z!HJe9lv)Wk{Mje8bhy`WnH< zN#*ABs_SfwYHZ(;pJZ$ox^4D;y~{eN+vvX~CyYD5i2m3`ogA{1MWou*{ju%`d{S&g ztCT-_xiy#5-iv9-raH+pbCcauEc$h@B14zL;-b}O+m{p{$}%Fx5JRLuHjRjwSitLG z#mqk}EG#~8Zf*_}A79xZ^35AsUfy5N&4C?$!m*V~{maY4s`X^wsbX!*{}Xj4CS;-G zQ(}I2s>nD?0zI6Z{8_Kr=SGP)^8HbCk6u3}Hd+d92#z8kRt{y)-;27a;0hS;sDAXK zU#Vy5kc}fLsx-* zedf0AZFZ6;nMBt>gVt0{Utv^<2{j;lm`>mzJ*?{cZA_f16RnqT!v+8$L`AA0OcZYD z=5OI(bMxWzhSG_Oi1x_tki`?EU+)KFSIBFU9&w&6-c!fWTxhOx!*L(Fq`srK*onf< zB(OH-B+kJDY!NWTF9bd{&IhlE@Xb2JB%Yhkq7~BH4Z{#SAU7RzaaXibn}Z!Qp_7EC z(y`hNUF9gIY`W%4IJ+3`w?TM$ATN`qyXs0qagl3z_%?LU6yN*EeW&e#-SlVFdO>s> zZ%tHk+x*%nsRO)^FFPtH?d8k5xfMJ2UZG)(R5;!T)Wmg}@N-j3TL7=TBYoUJQr)AX zn;P-vO*r^s#{sfHAGl!JKQMoXxe9T5NbU4V17|6waDootb z4nbE{WjjL{blf>|+ZP}Mt314z3)RYWfb6%UFGFON-zS8-?C)X;?G~fYN-Ky?8@8@; z@TXwj#1el3su5s&LuGJ7r2rZ}_n;KkzN1i+;xkJ^p>`=vcqW2hDIv1{S`udrudTT& zHwF`z%b_|Gb^{i!22X$D26pBsZq=T!uc)m`YpcG_H8!O9=pHrJU8qM5P_I5U4U9Df zgz_Cy$v#ybE$vzm3F(_~yGm-+$8-x@# zDp_yZTX0{IOd-+PNYo2vKe}h!PGuv7>psk^%$$c?iRSkm?th1eyRs*WkJpLxcc0yP zwQA?z84}PrhWPII$_FkDa?jtiC@AyS&=-D(vS$K0$AmBV*x02kB!HIRbv7yYhThzmuv*T3+G_?)xg=5+jOULG93!t^e!SozFuW$v@x^0MuIdD#TpYe-uorbi-WdhZxwS6ZWXI`GRQ<+OQ1w{ z0J-J~k+{bsWB%dZ18ph81Bh*#O%NM&SjbJuWa#Y&+de|hqEDMLPb(|ysv)xM=tiWy zC;H1~cK$P%7>|_s6ECJ|fwPdl0nT_`F+SyV@MTxy9Dqq8k+UwJlc|@zY*!B)wB;>>%M+!r^!o3aSiL~&m{Rsiax48wj1}jjb`{YM(?K13 z{lul5mwK@EIH98QPu)I*gbcS5%8NPP)I|-j zxH;{@?UM~*4Bd6Tu4VAI8WS~VN=!vHX&q?^-{CZM#qS*&)YvpJ2W{r&zKubL*WW)- zU`OcX(n-JNa9L3SqJcQz?X?`p!PUrD&jb>W7l7#>S&^@ei1b}bvPk5%B0|~C0VjGc zuviv46QTekuX!TYesHq8;Ak~pz$Y0I_SP##)@`0DY-BRhJ3$YyIT9Ak94lhRkZZW) zf+Hmlq6gJsvOAr2ZcOTJq7j+aiX<4v=mgG#11Ef6eyA0EL>Ue)Fj{W&BVj}yG+lJdSV{dV&Jlb&P5pB=BQ;fM zk?i`|c^u@rG>+49sp>`<$PK(-W1y=9@fAvqeTPF^ou@vqkl;&jo@;Ts@A}kBW|pWnlOtU_<1TJ$^Gb~8M>lqsgO8AX$+T;TFL1`x@4E*Ol5u1xcA(Y7 z;66g^A|(QU3cqFX^`N>|Dbt&fh*BBe?{cVajrETs7;VrhxB|<>mSW24jE!gylPfrI zPS(Of@i2S^l-lanhnO*_JM*l?SeacX@Shxv0=6e0U3t@RsVfP{S88{}0d8`@5Ner#oo zIbh+{17g;^QR1aRV9%!>>Gasr0js`##;N}GskjfqllGEPnzum`4E$2ah;+60HTJ8i zc<*-OHLM2EH7lZvrpej9i*RSW`Pit+0y=OO=f+!DHqU#nq$H&kJ%{i%j_k7GQY>vG z<&jVHVE*>pD{4G>FM-kxdFJF(iko;o^M(Tx>biIjwYr|>8r@43+%g}E-9N~P#|WUZ z85k*MhzNLs*>2Liw5uyMLG;AwV~Xo`7Quc2MI*Xdffrlm4-9iZ_RI>ndJdS_@c)y7 zBoM)Sy*Jkk1WBkU+1NWJI?7@h-5M6!s6lF;vo9@u22?T~>-TDS8cShA%xK!)nQ+bg zjgQFSql}pAVCC*+sK~Vn-QEwGko2f*b6LjS??U^nbam54^NpiGAgMzRST(hfcBS5K zs#r~*h2t`#jZ}>7o8?NF@ztUW0x!Mr(X05f>B>+p`7uQOceh{6?2GZO6~!Vb2Q{QI$brW%02 zqAfpC#qIr_KLU$jK?&{F^^APIDwj<81h%QEFF>TyE!uG2ovw@bHUEJU*qd@9sVxAG z{l1g*4{cn#GDQEDykAw;|Iui3Yrp&-GJ^km+W0R`{a@^kGzXdWSLxoAc@_N_c z-;G!ac?%>3{!w!Lo29b+TdMw7n}Yv$0?)2v9)u{8#RnV=T;|WBQ9L`y`X-8C-?`ZR zj`|w=vCRA)VGDk~_(JV$RBSHa}_6xwiyotWJ%2QF9i@=EFI&F^A{EAFeq7)_VEb%nBZdgio z;9rKT$^*VRlVXSA0q#c!2d6(;(`1!IvbhtR;?MNHC$15;xi9<3DxOns>vIcSvA{6d zfqRR)sB5a}bLldxnLfo}{K9!Ow9>Bhp_6kLI1c z7{aqbg7mnf!M@s_YU%h;E&G!a?ShK(a=r~%RO3@5s3??>$~8o z13c;tACg3dN1v5)p!>JZ@u@LB_@=CVhn8d2i@&1ecS+rai1obKL_YtKBGYH1&It21 zf~hj#r_1k+#^QA1c^8m`9wPvs07WgO+0y5s1w1d2$uYHQ-&T+LBz##>_uym1`XqnN zHfg81pWmp-{pro-_7SccE-%l!G8+#N5Q67VF=-86O$eV_lju_)T=U&dYumkl>%eOb z+Sw6T#rj%v`Dk$~UN!#k@TK}kz2h_C^A&}&AIVaeo@VQrFF@yfZUSlK?8tXyWp6|` za|!mBA9;!NU6eRwcLZ_So3oR17ny2L7b^0goS&^i%Ab&EVAbrUF9~s#NsBOw25jG# zoW^V9Rqs49#O7ffGq0*y&FH`pGqc_{dn1YXo-3!Glwl&>{#!-hM+3D(Y3j@d4Jnxx zZ!aHPM@70n7<#a}!|+(9$mIf?%f96kcSWn0Et2a(|9Q;7Nu81!S-&rX`;=bf7;c9* z^95iUhZ3ZFmfZQ&QkW%^am;_$IT^V=)b>0_z5VsU`an>w3|l5F;P}+A&rRPe^F9c7 zEg@H}IvIzeI8g?3HKuk_z@2MC|kXj5NEURpvTJs5Bak04p^JlRUnI{bu+)M&8o~J zHETjeP3dITgSBaBV#xMlF(Qyw`GQSyS-zKcWtpB$so$wmnf=9R$<$rLXlDB8pR_`+ zUb$_&a_jF;)ejTln$S4CdvxKIdcQdLnpWAV%+?p3zUSuCv;15B=6JHp1DIGiv^7tt zds3?taq|haW2#ikOD?$9z3&U!D5#zj3y)-^Xw*K;Q04*_%A z@_?(@oLdTi8XI)fi&n=q$Y$taBNVOmbbsU#=ta?ax_9!+d3V4C?=f#eL=*!W@t@(p ziM`NbU*1=u{UDwNnOwU3oI^2@+ZByMY|?ksuOyIMk;!r9ypi&p2QR?&|EcWE@@am z495K4AIkT>y6^A(xbJ`QaXz2(IiGXR`~7~so+lUbb>T%~BINmO;WrEu5d+<^S=Xny zbk#@Ocw1Z^oBL@qWx1||pRmEW4`pg%i&`gpbnWQFm9_lO(w)Kmem=+kBe>tmQ9GJE zF@(Xegls6cUr7!aD(B|oBLe9ut9=Z7xY6m?#Tg&w-mlrVh1YD`U!tDXcYJ)+^U%%c z1`AqNEBvUttts2ynz9J0ht6Sv=W%W;pWjTO+z%~i>@qrmn#$&+piof}ru1%a7e1zw zlrAgxm6YqSw5gvRw3x^DN@V2^62((94hyBk*EI_ZF0?uo9zcCFSSm zrJgapZWUa*hnBkf4|+qdxmK!p+*6se<5{~@W;Pi-sa)Y6PjATb8KAKo{4^|Gc<`WS zUHrE)my+GN7K(U_$EsNVogW|}iyjEmJ$&QcVSp(i2BNw+rEYLNhY_tT7A_TuQRian zm`68U!|Mj>#_4_dzLfe>+W0V*twcJvtWNTYsl~$CGO_`~Z|P)DU78^O?P+f8y9nhj zuLJjfToDgRs*^ocR(1EZeA1!=ZJhJQ4lh5PNTT~pn%1T^W;AW8S;J^S<`7BH@_v^7 z2gHG1!Z0MeEn91}J+S#?fKvQ2T+Kd3*DbZkph@U@Fp3Pr@pb!ntDceaQ_p2@M20id zs4I_K^FLvn#`+bQ%|szl2eC!@w&NLPUv@ts&f~kbx4s~PLtg2TIm2y(E6>3cSL@H0 zL?BR9yOD#!YrQhcv0$AUBqk|8+{koqyaNY<=b5U5ShUph+HyWQP2Z!*jp5rlS^Gvu zEUuE|GAT4xM}NESS?9(4A!0^pYWo8#{oS^IJyr64QuX@fNUiU|X{Y(RIdZ9Yt{mF4 zLpEBA^NX{XqCTD3O&VW5?cRFux|e*9Xqdf7Bw>_m{^EgwmpvsfIcP^h#Y0i-{LCgq zP9>?{2CHkLI*)hv(DqLUS!<~$col%v-iMiazno`?o5(bKMP;;b&U8hA=18T|z+xcg z*0@QRr}@F5-3n)Y*%h0E%+<84)ZgeI5K{~e2(D;?2l#TSw{_<4zi&`b9I@fLEA2SY zu2ctE|B=kjh&}BdC{BKs6T|Yf!b? zYy)A>gPKOl$6P}|{o>=}(@5UJ!eW|B^NwtEYiHY~|MoJ0nXiv-hWH4lai zuEu;09&L9Kykth)Cg&}yG0+}xCH;aolkCa2HJsh3oX{iDO48y~2Tg)}0nJolqcDQ@*gJl+H zXNO8|uNB96oX8yUOIZiUs(0MDzAZ2Fb9h5@A8PmRa-P1T?73Rz;uH3HmTVob?kw3f z9)B7Cr}k25k-hso>gkjbi)6zW()=!WYyE)m7fkUkc-3>5zzUs zEPtAEAU)X9UGQUuleFm5V?Hs|$=Lbf_zp$1r_>f#)XddcM%Rc`b@8c@gDY}5%n#?8 z0xP0>!&oV=FJ~Su^Xs@2w_&0w+i+*VxyKFhMl#%Ai%zReR&$_oZjVtP59~Dk{57^^ z;|@0dfPpbwD`lP)BjemF8nXF|Y5x*EYfGy??N}@;mXvri&tSh~@*!sK5`c0^eZz$e zMaX+`kV4|On>ScMe}f}E}-qkHqf*?v0_e|8oZWx6{zf4`L~^C$g&vN1+TLLwNU z6FLuReTh|w>N-=%K@GzQ&pfIXt_zB{<*fO*JAL0IqEwo!Y(naZR|5tS{Zbf(a+WL> zdX~%79f^MKd!ci5spP*0Y>nE<);wNIxbbf?DwefI#UvGCWb4w(9whvDg|d9?rF2FO z2?f<=_wXRGi0PW?dR=!^gQM2h{UliZ)cyS~zGDdf3;-Exv7w&Ls-%1!p|#M2CyD$l z{{2gmFQU0x82*m}YR$~NUK;*)5cSvUc6pVw8NL=bnXZWh*Bkm(Y5W<373Lziu_~e^ zG4kZQ+us8IICdk;%_P;6mLRS_be~$)r2~NU% zbA~QHMa6fUMvUxSWc&5iP|e<>J>MY}U~c`8zO1jm{8Po(gmOF0`mlIT2 zK!1{1V7MkY{NHtel@%2nz{?}>a&UYECM7H`dk-ta0<__Ry1MD-=Un$Dy6BNhx@*p2E`Ytk$*?jx zUPeDtX&OX$-P3*Z4*bu+Jl~7p2L7w053wLY{{FjD0m2Jn0;#1HfJ${c?LmvUrU_Jc zc-`{;jsc|CZ1ts`2Q`=y6B9u{*uB$1XRSWpy_RzjweMH;YmHeQMZeUnztyz=uM&Yb z_Kk9vtXclgxq`SBL>RHIU|4NrJ=7ogYt1bGlRWSrHNonS*DLjFRrlX-X$=ne>vIul z8l!A2R$a@q82mfaGO`L%SpSHplWK>)aTNNr5tD{brtf)p#?`ysIkfuG&`YmVLI8p5 z`cctSg2}OKQx#Xkxvxgphi>dbNON1vaPl53)#_AZ^QXiMkPO&_eJh8Z_` z5^ulSuo~A-%*`1+Q^@^h&v71qh3XkdA5YTYUtS5r(%Va9iid8!mz&Qs`1US({qaiq0pT`G8EtCys)W6)uj*+Y18Mq@}2hYZ2LBQCKPwb z_~GSP-X?zuZLvh{q9f(Jz!nSoBRovxx^T4P#9YdmnTxOHh;7%B`rr1*do!*ry5UsA zBJ+*@5-ytLT{3z;GIi?yZLHuR747kYz(4|UPVz4-)Psrja3kcU?%Z=o+eB-;TBtRLbx>JeGdh7X<*#&bTIlKR2cNeEnANVOU-Ms@C|z!UkM|8fth^kT+8Ex4 zjS+CuLr_}!SNk25a<@K+)XX7E$CqvwkHjwYaq>8N*$EWP3<{iZ%Mv=jGM{0);k7>1 zwRT4O?PB2OV@D+zA*rlev!)DZ54hU3PQ-kd(ntIIlrwNa1g{En#;nSpp8QLbSAG4J zJOu8`tPHC=4Q&@X;c#KGp8O3cfX31EZr? za`Yby@-s3=)qHwdqIRddEUt}^N@UECm2;H9_VV7L`wJ{UtnBR8prX?~I4 z}I)WAuZqy0Pe*%U66WuIfz7UP-9F`XaX4X0j%aDY}kofHM3ihNnou4ka z20@X+b=$D&^t-v&mK!#0+eZv1-24aqMQ+{^6CHm!dn1Gym-Y%u^za_3P9t9*?9bM* zGsu3_pF89z8|{^2BC?MX3V5rWfHndnkG`O^XZc5ju{4pR=4OG@KySY~Y5zUYg{y06 zZT=3XAgp$fzEjf}*5H`AStK~S5fvt2hW2~b%s!GnGsJ}&8crgj(#jRu2UNEJ0wE2jd zfBUnI^(n^N6Ls%9cUltk{?JSko7-BmZ<8{eE${T?n7GlKGtF1psip5rXL1$JH5d0s zC`IOC3vPZ9DGA!Zyt%%>+4@Gly(Z``N4iSnz^!2kNZi?xrb?uzr4D_OwE51fO6X?y z42p^9?!`?mh}K*$@;#vAAsOFriNGeI6Qh2?tZ{oS7tKR=^x=kbUUidCGqs1^)Eu7_ zw*+rsFLwDhq>W;5Fvr@~)?L^B?pi=It;CDQ2JX=~nc!+AE93nwrYmi>P zb*uik6gMw%BjC1sLbMfosNI;#0jDeAY(O~3fH$^B8&Llkjbh=j+9TxLA`~h8qsq}( z?YmB<)XII!i^?m@uwTw!E})}etFcKjZ{@LDsa=Pz-2?LcoMYWLxek4zZ6BBn!V-1y zMr*vIWgY2{9efTAt4!B&hfXi4Fd*NQ|J(=vE~s;|U9~T+Q-w5|F!rxsujkp3UG~M_ zH2%`p_QGCaeMQgzX$hG6x&HrVdih1p`Q;G!_0Rt0p8UPIVEJQhFTne=7I6IE6s6yG zAiq~(er>_IQfwAU%JIm4T4?R&))7xXTmMxt`MJaYxgYs&X#Dz}dO$n};x$mKz-E*6 zf!u@cgxxh#lUBp>&$%2nlD^Y+0vYR+=C@$oD8`pf6&}$^S=9;V+Y@2a?!^~KLR5c< zVuoyrHU!hZO=sarz;35PRdpF8vIMs33{Y!mz@Gdc5cZ;J1L61i0xcxz!#`YpnRbA| z9UuQEu3Mi0%Sd5AcGO@l zNwLhHT8e!Rdb#6(%?6(Q#RL`KVW3EWX)obQk}82sQ_^2jg=_wYH$1AOfNtvZvAV z?z_Wl&)>TB8ZJ+7O4XKfpSFPA`Vi%E@i;`DEb(p=UGHqkfwY;SrPBfv;L_QHydMzI zZ`!lG!96r%>Iy0VL4(N4-v>o8f(D@-7ntCdbA1EFH5|z9lNk&^V0$f3 zRf^ttSLMgyZfs)mCkT^;bFE2(U7i!k7lH+lmjlw|3gF>@GHnXFCp;qJLT8~1;!e7I znip(6kARJHxzzi!Xw#(w0e!Tyi1Pv1D-eb23VrE5Zx|I3_j|#B zeCN;|i<~V0b$_H0q)8g^;r#;xwTw?`HsJ@i?Gw8hQRqUs3IKTIv;qZcN1txeh81PL z1j;qMkpc`c^$Qn}6%6EK!O-xctmu>v^bvCK00?8@o5({x9?%g;f*Y!_u@MOWeNEa* z$yUTjWQ>6NpbXRq`hau?AV3P}Zsn;R&d6^d1yQ>&)u*nhIRIR70quA(ypbw#FxF)=vV4o#H7Ki-N7dt%CF$@{qAWnD@cLHWXeUamnGMV zC~)#*82BBM@f6_7gH1MwJ!v`?20=DhE|HTal$Du|-FP=y%a%}z0N@cEJviyWw$TI> z`*dCWI3=q%1@a@X;`xCxtLN_N*T$uauo9Fa?OQ~^EG4@YW>gO2`c;hg!mq@o|81s5 g3fJr1NLRAMUS;yM{A&=-V_{N1uXQd{#l+`-06857Qvd(} literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/html/_images/chapter10_63_1.png b/doc/LectureNotes/_build/html/_images/chapter10_63_1.png new file mode 100644 index 0000000000000000000000000000000000000000..10b90707a29331afc5f626165be5c8003070e6a7 GIT binary patch literal 28453 zcmbTe1yodD`vnY&w4@T!f*^u)*9Zn6rJ!`DNH<6fNH+*bGoq9tQYzggT}pQi2n@|I zOnn#e=l}J$-uGMI`dEv(%*^H7=bm%#xqI(tKPU2$y5eQxYs5G>IG2@`?rGxSTu=ah zO$qUVPpsQWWr2;P`+Z$^EhlStFEdvw95pj{XL~1ids}l>Pb*h9TPH_hJ`p})Ue;&s z?#^yf{QM4ocHnbzwc+o}xi<(jLgcKZ=Z1qrLVfm&i<6N>hlAtzO8K7r6Ys3;S)Z)f zBV^a!xc|VGg|)q~MKSMHDus}(s4W$4?x+NNJb+}vP4xM_cMoE{cUuVF z8`XLK+z%z8b$o6xUFB2=#$t5Ph)+g!Hw~)=s5w=uf0W(7Cv@d5gq_0`TKxDO{yW9^ z0`I*g?8csn|IyXnRDK)O$(}97uQ?ExgM*{Yc9c{5lVKzTGG7wHbN!Xs`VV!Eiy6{h zd?tQ-m-tenKk8MEl$wBuuik23>(8W@a=*!!N)niA5|B=Hu zmpfy5b;|9%98T&Lq=zGwCY{Xio6P>U%X^BBqfpNo&t(lr6Nw>8}b)F8jp4&b9 ztG%T+U*gd487g5=2<|6E6tN8AYX^fMjoTsC{TUrBU{p(MC7+tQ!NQ^e?B?&`13*QBhZUMu0)ybaXo2nv_8wj^c>ePb5&XKiCD@dGz54_t+;R72xV2BqqLK z`n~8ej{Eu$TmO+oXH3mnBXhvX;`g0!GNzt*5awI8%ko4M7^JMM%)!Z7;jyU=tJ{%d z_FllnIg74D{|io$cF8poTE0A&!7eq1BG11^09~2S z*VW!mK}jhOjK+K81}P90C2TkL(QIp?oY&y%)`#h-dLLom#*-xy;2vxz z2ceojJT2D!^86}rJuOc=HLZS2WPeihDCmaD>x8VVnBLW;?W*~;&C;gEpQrYd6?7Lcq>7hRM8oul$k6ocQO++7ICb+3&efijcUHZx>B17%P7k1imDc^&&c@!|T?F`sy@Wxlt*y;=zEM^! zLxhckBV>L3*~3)6e&7aF3njivC+8>ORKJH09GO?ILcn$9+xIRphpFUzl~m0(@$xh7_>G+XP@z!Vo@d7)N>^E!R&T!ZiXN4Xa!E3B3yxpH`Qw#|Gp)iqy(nr#KYy*)pCEI zI`-vlbTlwqd&f#C0LM396pz@RHqf)ZG`TY>!iv{Msh)}K6PGI+YLZI`1Q%K6c z54`mYJdYul{K=KGSaE+6{@Qy7)%)~($ME;RBA_{CJnJQ(+4G}F_!qL}od?4AyG5^G z2Rgy|9arSyHigWCzx#G$Bn^l~x7r<94{Vjz3gd?Euil#1*!&c~%(BpBQWr0{zkP{= zlOtd9EA&kPk7(NOcxKhio<3m z@6Iy!(l7LF*`&Q6yeYO1y&|m<2JU6{$)j+X)@}ne4`9%Oq%2>P+uJRB)4G^>I!6a( zUfL>Xz6vh4XtaXEEM5ybHH{`GaSaNty}O!2ihV7s*+{|vr8KUoNg7K&k3Ee-*~uBl z6lSJs^kbLfwaa|R1r_dI+(5jLh1E(Eh-J1!Sxu)ObiClVay{r7<9)C>cX^k*-Wvwb z@;Gt>e?MTHaA|)515ccVSw2bHn3=gZfUfuvHFWx=_Jm*pVK@HxL4#y!yPJ;BHgbWU zY)h)MUKy14DYIeEL7h=Lsa9sE@`qp3da8T8bc1ch=lIBPGz#%SYINTZNT$TD^$)id z+M<6h>%`O*-{H8+^|fGsxr2ApZVVjZhj82P(X!Y$IqXWlnS_lJ^r|rE$F3TCR41gV zA~{)xw-H1#sC9I5v1?OdYm*h_WaW@WyBnz^DBbhv{OSaV%NA`N%+opR;Uu!tzoDA{ zf?RK`>gUsVYQ<&m)$&~T67j4Tw^{O)Hc&Z47_o>5!h-S5BX8t(srOze5u+@X;54avQG6O<0S5Q(h3x9@oYs#zF_##` zc|ozR*APvbN#ef!1$U>F`?8LOoycEM1=5;)P_Va`+1A&{8|~G4HdG{XKYI1(!7cIa zks45>=Tm&QtsUymu+iNp7q3}{eqR&Mn$sGS1KHX!CiMpGl$)-5m(3nfB+4c;?||AC z)JLD`*wJ-iB=2t;dz8|7>Ezy=%ftw!hSsagE?y|nKU9^%?ng*zL> z@CqcnjS&I8f@1=%NxbHvVl4Pc{=k(N`JBW~8|A3yRLOvM2?^W?;Z02}0hj;|u0n5) z-%QGJc+-!me`Lz|byT17 zYg;2|H+3s5Gp*3on1eKlXSg_%@7ngrciH#sr*?{V?vaBG6O8KOTu*jwacFLzhGvMe zl*PDkNF$t2G}W^o;+Voey|Wz5xdZ~iRg}74d1-w$l&9ez@CM`cB;Rg^WvA|&)I0Nt zVm&ZYjOq{kcE8-f+S49jPu@AvV>ce+R6xJI1P8JZ>1^Dbv2{evl(z2c*^SD<3HWgM zq~XiL12rbKBj~NUfCP3h1jn@dqsJ2`-Jek|N08EQ`~2c%Ynj`xkI0i72~tNp%J_{J zlWxd98%7A)f9)Gqb}{$f>YbMHw6&ja^yf8c%(Cc;Gpn48h>Cjay4nL^yBRGu!>5*? z2+iY7o;!3h$8(ABMkEZ~>0Qm$m_uF*6uL^R$Bf->H7P=!1oxeMrS+_fE!jM-SPVBh zyAG>=puEtY5gA7;OYsiag`J(Qckx%-(w7cZcdO(FWb`6sU8Ot_?ZXlZZNWs{RF*aO zc5UaexQ}WdCh~k;bgf-KdaQEmhkwME-mh-Y=JyWCQDTuX#Oz|6avqXmVmZ8eFA0f= zlp18*Q780qCZ2Ki`w!K|N@njqjEZKItQdNKU~w2=L3YGoh)`Tnr@eYry{~DX9PNea z8gNEc^s+EX$#&L4W)T;wvp5^(pDU$&xPP)yXv8SxJyNNRQj|QftZQ)t^Wo$d(=?bf zz}%Xyru?+3cLUkLKDIN*su;<+Y?0=gwS-s_eKur99%f&{N&fU?V&A(C66;_G7x00nLHGC+5HLq=;!t+gU-=q-}Eio5pEMmXm4NLNay1G~ID z=8$D5O~$8E(CT$yqVH80)vpt#;^`M2JuP71wDV=v@3yafhYGNjCkRbk!m+yBAho<8z4+SwFJ zsm>G+RWKJSrghBKoDCo0nsBF}rq)P&>!X?K_8^Rs1)M`d`>_jj>sD6Fj$8)_49T;J z*8`@K-R6rv-PzJSrS+QBfm@Sz%O~yePNosNZB8;7UEr&3DAN1^W8x&(xVq#x7ej)`zQ*^ z*GO_qzWeTBu%;avqwWht#T$?EaU%`9h7)|^U35#b4@WUWohbs(j+lvJU-T__v?3c`v>Znrq zOjgA$#Icf$NouIt#p2eJqC1wB9ARd_CDC?zw7D_YP{*ZET_9XYMK_G)IVA(rfWXp< z6*3PGdGpFF#cqa!!kFS-_HG++t6(4^%iDiM}5~&ZgdS6V|eIS!pC0) zQC;q|iinGQqnVF<|72r?DX761`SK(>yE*0-A77%`-P9qlsTO<>t=Uv0J)~pW~ zGc!%8zjYZEx_4i3_t|Qzj6PySCUM-i&wPf9XJhOg8Fk_3iwjWEx|5&a%=(l8HA%O9 zMt0x6l@cO;BPqB^HcSp4UiHSU1YU|biM$9MwOSYUtKC;ySgOHJJ}18y;F~3x()>-l zaiygE_ACPH_G+=g+HF1<;q9R$EG5q9)8947cyODEKxAz+U$z`Mse91x`MQ5{J$HT8 zQ&3g7WRk6Fes8%;ugZ~0P*AYikPmoR-3Q1GaGs4D4ziCcOr-AJqz`i0?>i!}GVg{% zk39*Ett9-{mmNnJn&3rMcXx9ZSe+CXp3ZMEtqr3cPPv-8j-MXGE;3K+=*xJH>jGp7 zP!f*6!_Hv-Clv_qZGc74c(u+N=Da;e_mKQ^>^?)}<>nLh3-~WpKKTXs2S@S+0d!yP zoY6SSwU@1W#tks{e}VUMXT&2&yO+>a;Clq^Z>(Q6c*bD#c-n0p=GWbL`z2{O(Crmwb7ZWe`?EGFK!ADO?+1S! zx*PR71ln3V)w2*rwf+kI-~0+(dv^N&7dU3)1JK+V13Dvpy3c-Xfb%~;55se|mDs28 zdkB6)K1BihSqA*>zO`SY_NV{dLVyqeGWT2XJEOe7*k}B@1pXYe@YiVk->8fLlo|N> zXOwc!2hA(3BbrvL%F*adN$5)#E{LCmwgbcsgd#VO)#;i=R~nrMCRDz zT^tK&0MIPbMeS%vXn0KrvLv@=>&AuFX1(U~?Z!Xx>VJ;7aEVyJb|i1pQ7825jA!=F z1SCMo>&_76VPj+a{>dm4Pzdxofm;Jmws0iC7#Vqa`SICL=cgJv8tnh-ObO#R3k?sa zW@gT*Wu&IQYiViu)Ah-dD}ZQOB~#$FGxyncG>q+T7zH550dk_xEV}rY>RFmD<#7u@ ziVf!efR3>-lCSc!qIb1bfY0cmu-a&a-(u^fxfh$a<*+EXhsifvlDW0Kmt)1#1k74R z;iU@eZygv&*VMl*JJZcPZO(Iuzw+{KiG?n~Q6oArLZaZc(y53(iv;Jf zm0m&4aCkZ%UJLsd(hp)ix;jQ)4ytAy&~6DP&f!b;A{#XK9z}>^LE{Bwt`CI5F2Ag# z6A2JaV61WQ+k^S2GmC09*XwsYT%g2VX-soE1BHt znv4l`fi0u6D8f@6SQC27vV*h`IYS<7ZG`Sl?`mEZNyjP^BLmzZ*!#UxMe}2hh-LRe zqJE^Gn;K(-g`UohLoKrfY$3e*E)vVCkpaZ@M*tQUkB*Twa$+eVB;(o{X zBN60pw>+DJ$&yRo%fYi*R<(|E9xi~yHYRPYd~+!Cj(fs@m)1@?`dF zH=Qfw!&!?LCn9|*M{R#dXJyf4ois0=X1o0}F4?(rr8rSp2B}Rk%Nh1cHZ}ID)+=5M zMrBU7aHBW(=UJuVFXw(^_iSW_G9PRiw74@fC_u~EL}1sH9u>)>v#Lk8j}RPKn=PJ>;2*i*18_F3IAl$;Jo`a_5%yP~6Ra%VZ@ zG)TD)gYOhzzTBcnih;lP?W>ROYTUsK9)CcOs+nA=B6Z!`;aFT;Trz{F!$U16u5>(*s{vO*n8rmV>bYXUe29z$;4Yz*iNTcMR;W@Y=uPDfO*+ z;Lo+GJt@F14I$qWys6!D|2R68izVQD2R{R;CZqEyhrOQNyK!H#K>{$t*35HPIGQ45 z+^GHO2b(gVlt`aR{$}?eqAagLdG-yN6N2g{P<2K6-<0>_v%=Z?LukQF>Q|Mk^+lDa0OpU-Cpv0I-9@b4_ya(%i&NZ2po zMCgY=%{Tn$FoI7<02+_ZM<;0Nj?uUboPTh3_2mjl!jdysQtOkS@l3a;W2i5m^l{22 zy}f>iM|^|H&+;zUt!S$^7GPOEduC+qoy76rM6H^oV zm;rb;*2Cv~-8aW#@h@K!aGH||Bc*qp-Tpa3=PX21p=d1SQ>oaBxED+knP<$*^Q7If zQ0qw5dDdF(h0mD*o{P0Lz@jYuCH zJ5yd;3vgK%YxTb{uQg#h`Y`Eb#|(d16UN@Ws_;vp^k}+nQbbnjKKY<+Lh^b*3kk7H zDG90AvkA!rBH2M|D#ry^dF0}liiv@C9>wdn&Wl%t$3|~0h9vPy@-vn3N^Wy-Wk?KU z;u+S1DcaygT4hc~EcKS3l z-5L$~j4A0`)mUc-r}Jjoj@Z=4wp4C?f9@z?n}E!=SU$$5+m+{{rJi?rT%DYl8^AB_ zii$_Ct|0Zg-I-Wg8H5$yAIE@9>U~@G2VAyMmLEh1??jqd)+!yGFr==6_wNW9tYs~x z3;H}0y}^>7dB1E4t*e3&t%I&~*m}7vevH0tlB0}mcA^IQN=+x@y@laxTv%=H znv;O#>)5IO%W@1WFgmds@2zl8q4eE2TcRCCMk7Zi zhj96W>%G>->{PPO4QkkRuH6c86qGtwiHP>;W;L?CP`$bSy=O&;kJQvOzX1p1gwF=~ zR5~@qt4kMx`OxZ~_JZ8HeX{ZtZ(J`1mvW|YwBL255_xV%acvFLTVwu}$HVYJg6PP? z&?gl{7es()-~w*yYLi!SQXNZK5_^?&m*P)krMtOMkD5GR&HHWy5|Tl_A8e%`#-XwL$~Xly1Jn}Ymwn{OXv$`0+wVlHvA8OGy^+}oYjr&TlF zYa5(5!jVCxWp9IOijMQTv=ACIU6>KqsV-(>8up_!ZCjiJ&V(0R3{|3pm))@T2>T?Z z9gJiWwi(bN&QhgQU+hLJtW=GFpr<)*0%vAkKA3#qwjF6=vRu{F0lW4wZ}IjN1&xFyJ+6^ z3Y>(aQxaFAj4iS3Cg^3`_7;*msK0U$$Zx5KcQ-<)ziBODj#k z-&)Ot4q;i4q9&PFN==#E#v97Kq~CX8#(U$?8YY>3{*&b5L%h;=c@SRVvVYT0 zu&09oQeDRg;&UyxE{~iY^hY{Z#)-K?#j6vZ3Hhf*Q!CDttaU*IZyE^uKi@iW?*We& zTxmqh(Az{Q9~+A0_}z{eRW$0u-i#cun57OK<5#zCqayGG1uqB$pO)fL_{Sr?Do>U< zDlEl|F!pz9+u>NU8&IXxZA=3~hQTJQGu@mjrx$Xqbd43`O$>^WRjzyttEz6|m+jqA zSuRJ?<5`zKe(&#DG0${oM3NQ+JSpCTXF{I@DJtAV+T(?7A7kacS=Wag<~c314nULj zXf+fQLpCpZCQ|s4>x!87u_y>YsOi#Dq0B6GgHQ;qG{UD`SQO65g#P9c9~a>wdWs7JilED za5JThEZcxGg|**FG2Y)3xbGh-DB4X(bWT{efOlh$%2u@8TIHF z#Ci%P7L6x8om&Xc3l~+1=PdTE#knXKclE&_jHI9KOriz8)x(S!=2uIT9F8p|D?9G3 zL&Kh5Q9nNw^T;l}Me?Y}kRFCDb$Q^wWx?B^lZ`a6N_I3vd zCu(S42EVao^2R9dteidD_TWcQOxRI?DuS0H{37uc_hIyxgAfc4HuM0k_n9>?@J=<- zkv6+Fhf8Kg%6cKtv;r!yF>~}1`cgyj^v-=2w_9ZR^*dd=LEOAqFjf=hq+#l<*MgY= zf@wm%10m#0ev;gw4_DRjFMEwAwhkoCkGf2H>#OI%glWZ6|Y_fIjb+fm>hjL!Ai7#2m^}Q_@Xq#uYDUJLPcwX+U>ZyM z%57R{lL0cz_1$}N*$H>%GHWsFm?U?f||=CCwK6(;cXxB;qyLI3>f%LCe( zSv*Cdyu3T6fzX4K(lG}i@7)R%#Btr+_8KCU-=ctdJR_z5J1QI7GoNTqkr1?x^`Vy0 z#oIUO!%jXZTan%*_<$~FxRuN%itQ?{j?T6WN7}?b51J*z#XS0Q;p0imfe%Wj(GTU1 zu4(e9%x(?MUg?KkcoWcOsaQTG$LWr1sae6z_MeZ2eKJp)ChHc+GWA2vy%Ugl8FdPMM_1*AIpsi z>@F~|XOvtsHa>~H9NxythZ#vjs5snP6L|j^K_*cl4rD`}PC}x0c^_?ZgPDCtAa(l+ zKceWNUe3Io)ww8fjCo!<_#KyOYh|;A2IBFuG6>dVr+NGCDtQe*&&+5~)4j)DI_tX~ zC@A>ubIgsX*4C>FNA3aQBB4;EKeq`#ZNnS*f z!!$}FU}knhzj1~Ih)r&8VTCAI14OnID+euqUy@+vvodsmeQ28Tz%U!77OmJZR9>6NTx?Iq7*g!241X=LbuGbT>I|1 zH%l(2FYA`lROXd7^O&<~yZW#Pjzxr{c(CCr86qXn9HfT~ja-gB`*p@fgs&i z*Jvkj*5FGGE~fD6}0zBSn^dw-bg5G>yvwuD=5yc68jCxF9omJ8cv z5i+#clKu00y69$7wlx1Lcqv5wwLsFF-hB<#kfj@1-fur4N5&&{gWqdikbLpIbNHQD zC-`TMmiuXPQ17L<71r9O*OHv7NaFZpSb?p%A#WX^cnqHGE&IS{y(Y`d?*4q?^x@H1 z$1&(KMsCFzGk;zB2Q#3?S!mpucEn_U9QRXlgRUKJdWxqP-#y)jlHcT!#0+HA8mvymnq~P>;}pvu+$B zaS4mO_H+DD_oS*XHNL471n-r}Y8?P=Gs>+DEN*t-J}G*Zz3H}}7d!47^2%8d%Wr*2 zv*ZCW`4u-Iw_{0Qu4^u&rYah5mQQ)konAn=4`dw7Uc9++W)(Zrdw1p_;Pqm1$Fvto>6hk!FA^vgKiKk21zrO?Q1`=#TlP0wy_t5G+NrW zRw=}SE3F%l$F|`YVE|xvWZ?>rqpO$g8<>ekfcH{jCrRw9Rc{*2tn~Npvj|NM49Mbp zO3P?Y`6Jz5tn4`DX;8z%j{sE4L{`niPr7|EJnl}D8LX}y$2#Cr<(iuyczwLzpT}R} zdi@?B%6~$3uN>_*RHj`U64|B-sS_0L+4FKintT%Oal=*%`xD2+GN95>daT^s3DQ;3 z#tnmRTSc*nEcgc-cwR@9&OxAPT71*mHxt3?QXUO=Oy77&j~3#)uEiueRt-W2y+n+@ z`igeYUf!K(46r+i>pD)MiNB(NvpH76e(P40LMU z`2gB9TqLWG@3s&c@Q*t~n^o!O5YdHerhk?D9E}ZX{*AtVgo zCFKHYZ5Aft7Jvfzy~H3@|I2ehx3xZ=fJQ)?)c8Uql|i@SiylY)v$A?4Onob{pHyBX7H z@v91FNLf^?P~8f!mFj%lnW+&rs&!X3ii?b76A}{gkOZ!P?dhsQJ}h8qUFl0tlJh?; zv*;otrr}j;3P684Q&@o}%on@CwWoh6?SNU7t~0+{b@VfDVP0OD%kl&3zBGBDPv}LT zU%4AjW(CABKGSrbV9EfST&T-1tZ^*|46ff-Cnj{?zJ05i%FfPS1I_WhX_gaN#`5hkZk4o9(cxP_nGaD&z*0^UTSinzO z2lM>#%QGo$45T$@>%0m9iA{o$Ea$~fZXiD+U+1~KKJ|qM$W%d><3R;Z^Nm>`a1IdA zUJC(>p;uj)t#v*2=8}|WQ`KDx%Dw6X>sLS~FQbz0ETQ+o&?ny89gHY!*eUmCdUh0c zb_*H(%11)-RRG)Zb@PZZ^*~fI7Pbc z?&jA;$1w`uG#cqBVk0BB*_$shaI$H&36gkqnV80X|3N9q8L{v&K?sB8ae{(4z2>*y zB8zDW$-S^2&6XcsXXpQ-kpW8TTaM577PwgR^d}*1;nG4$uD}ZlKjDk}t3l*l23__O z#1Ma6tq090z2l1*X3Qbeth8`gd4nCit-o6j=Jm~BQc~b z>!z4P%l$P$df}E+jQ1$Nm>guatC~D1U6wmtu~(X2W`-ru>>^WN&WiDTX=*U9-W#u~ z7%jYx4ti2FYlOTL#HRBz-u{YtG+RlEk8l&KuQ))AzSn7t1QZ9ClRbT7(^E< zFC(X#sw!HOGI_6v;zGb29yv`A3Nh0=DE9Kke2~wi=m^O3Zm19d`x{W+SK-k{6>aFs z2Va^U!*Rex`ncMt1%wQS2Z%kT$!V?0F)7ykzTr&vV77f_n0g~(z_HuEi!WHQr#hlB z&9}dYFTl{I%|)+a+4&9@j`As~WIyssrnH~3FH|z4Mewc77v%=;XrCJF&o@jzNEcFn z%jfC;;fcE0wv-paHXO7yVb7Uua=E}`nnDgj6F9mNtLg}9JDf?aGOD7;kns@$9N7hc zef(@1b)2o;+bD!oJpXYE@TR!8NlQ5|-~h8Gfhq7NRc&JdrSFgD-HqzCIA zBY$X>>hbn^KaVST7ne3OpxkA}97fVqUbu$A((rzvPH)S5V3itvy-C*G-2UEuqbNzC z5e~K%*1ZZ;G>u335v_DrTn#^NKxN-Krf=R5xv4ePU6u<)JbQ9IQw*{9!w;-c$X2yp z>lV@(&oW5B;&%tgwMcmHvetR+SdV`)LY*wfZ%tMb1R`N|@%(_V|HJeN>R>Qk&R+^B zb^$6r+z!_tGlNksK(R}g2^f99P(9nxpv<*LFu@(L*V2d zLM|6t;J{|%S#%W2{nljgk)Pm5XHF0{6(zQm^Z zZoJ~VHtuF}5E&V&!G)xB5uDHVCCyU5dGM(7CqC{y#hQuo3i>*JyXX|GW{(Co|PMMLpP>^dO)X|x* zr9s9~>U;410$n9JT)oh z()z{#PC>=D2J*MY5iOP$AU)X(jO~WhK`-67(So{!c~bg%Ps*ZkKtSyvLn{TS=?HCG zd;@Hr0EHiK??-D^JDa`a=T9%SI9wmLpQ%m+yo_d5)3_5gZd^c(NIn33++j0_f|s65 zb=ZQ=`3M#OjYB*n7CzMrd?sgk8P^84l)D3w#|VDf zYOcqiCo>%kr3Do3d+06Scc_Ry$C0m3PaEIMZa#$cs%>Ji$A~N6GQ09Lb`BUNpIc1q zvT~}qYtWoNZv-9Co?6tBM$u~I8jN#XxCpp7=#Cy!fMI2cugo8ndP?xw`^kgnq|O$Oxg+dQ|&Z--zIP!<4krJR0ogQ~|dN-8w^A#{P?%R7LnQ!V+n zftZI6P&CFUmzyn3JFPRq+n+`458Y7Tb+*->VJth!`Y3o{BO3=Ij{9lA?CyY>k9{GN=; z!8G7>YF|=6d2?4|nClm48r1xyXns7068{4o{L6gR(-(-n4+ow9r{C+}u=pQC*53x9 zzok&^zac~D-(u&(U&8VqN78xwe~ee>8aALt{|5iRJU%D9=dgz7A9VA#*X*oh2l$a= zz3Ul5CjCn=mQ17C0t#(@zG43b)MNq*8<<||gigIW+hn_kor%hlt9?sn`_OCbJo+6I zKhOfuha60QV<4Jyl=YAD`~UC!{$?|O``-RP_Q`)6M3TRC?mv{|ztfoCL`CMrLzsr& zSQRi-yay`Kglz`ue^&n}*3kkA@ffBGeht_+rX4_Xh+&j`RoZwO6&Q$hhEb&+*&mUGa{^VJR1 z$e>1N^MVeVPJ%DAjBv0MTo>n8K_}I4?A(1HMKbA00Z6r7*uBEXe@)c9Kd%L8%W^0qoZbPbp*B0io=P7V`w z1o&q{!cATz0=0zy$?6Q4g&n3u&I%_VzUK95L+U6JMnntKVdN<;&dCizN2$JLcXilM z2lHBdMVs3UY~2a-Py2QfNtEo%5t_*U5?A6RKDNv`X^)y(vq?yk@(K$A)rj-pB^q~iJ&7F`4UWCvsmd|2SMaTb+BMRo%6 zx%fxY`1xOorAHA7XCaf*?7{PO=tdY6PNjIMkbhJOl z#p#2rhW8Tf#A_@C? zO{d*8E-}F8wE%|HcJ(nhQPJV~bJ5j{^(+kbb2d4AlYko`Pu;Nkq@!*o00GYjYISw| z)Uu_1P$m5`5;kSK%}ykeW4sUCO*{@A(Z}s%)>?d6Uo!FgL-%i|S$C zJmbO>pNV?`ooPmge}JnxHEAGtzQYZ>zy^4*}3;6E@G| zWDrKi^bimr8_G9DI@%{9qH5ij6dz=8aME#bzIx&F@!4ap11NzrDox&Z(_QHKtZNASg`_;;E&rW=5 z5?`Py*8fFi&K0N89JMjM3cwR$jQ^qeal$>RI3hKN{!a!8 zs%?DqrMDdc+Z6LyFZRu>3F9>xr~SP<3}Lt_LZf?LM%WWtZrD=yYwj3tX`Hse=Nfql zt0st@c?W@|ZJg)g4|ClSF^}ntk7k;-CRi}NE1Bt>PO)BtB>D}_E0yw`4WJ;-?aON# zBJ@+;95M`7_^fuv<6=fB_m7|f52%@#)Br21?T-&v$-;vH-V_Bad@uymU;|48JOorX z?5O8x14R$ujRySGZvg%6{ndG(o`YNGli`b<)3E#Z)3+vEHYS~~kFoOhaY&quq_y9> z`B*4a%7f{>g&c%R$-BC{iU-C0R8y zDs(-%aAIvv6}iWmONp-tmvoU-+ov78;}p){!+Z(6Epmdb3UuLO<%sr$bz$og*7?GC zK#R<7r+B<+&n=^tA?!VtJ62Haduse#GfsJ|6gK*`^Wz5fkq$utxEr_v$Wm;>Jvrm| z3O#HH;>W&8%nsWp0+mnstHMB|BzVT2u$_qum!g5kDZKX9Wz#u4r3f#LD^4?GtRj8r z%GFA>>j&NW_V^zc-V6J~X#qbF@^ny8DP8T-S8K_3ZfXkZRqBpx$gJ5&yqFTM22TM&z=M7`IYjWlb1?IBhW zur!#tbHl3WI^mmV^j>UN+$Q|%$Nd~M>tA~G8NplUwkg0Si)SI$A#!nmf(I#}@~z$dSOM!5nb9!36+U6r{>y*BLfV zmp&a9T{T#kcLyfJH@EJe^G?wrhK{-KBoe06bm`1VAb^uf!psZHQyC}0!v~hb5LkQ1 z>bX_6tQvIdsn)XtP0d^eg)2q^(*(^wS(XQ8p zifP|=)p*-jng)_)e}ZdS}J3*fZ>4!#jlibluyF_8H=WG!G5JEaTCMJZ*_|om1k@uvCJZ&E*Pc z^`Yhqupq5N?Hoq@E?0K$IE#A{X2N^#j3TEq=pPA5xLmQ074kWthO;19Xwp&D6YYcK z3atwpariX{42DV~>0*5x#}P;&tr8p3o*$}^mkY_lDz*0F?_}VR8ZWI{N9;WFPoWVD zyDV{T%=L!<^77{kh0sT*dnc-|0hBcSQBPQ7 zM;qX0j^CN26mQC|UnB?KwA)y{@y$H@gPQaox%)i7QR!}bR#EfueDjB5ise>-!)m|yvaN#q%lxFLNGrEg#m|F#SZYK>T z?2PWFx8=-2epB*)%v0``r|K%dC&kX& z{wHA&D);Lj|8)0hVeuJR|5vflKfbI#YQW!Y`R_F*^3SW#{*f{MNB8`$8T(z0^v?lY z5&w6hKM9SVe6<$Thuek#MdsjbiM}FcVddZJJ5;SS$FcV@R8a*6vVx^9`-CA?W`RXb zwx(VL#v}XK5HH)3xMyCSt)NibMGZrFFMqO#*h_3G*NBYUo zNb6NX!hM^aop8DzP_P7}x<)9lI>c?gz_|WflnXXCJ1x|tIiFvKkaWKm>}U3k;Id0@ z7Fm3x%6OL(+`CZ;y=^hKGZHvajTfe2vf91tq*wD0K3scX0jx^1H$De&^y=LYUDz*P z8P29VE*NqD+c;*6E$%**a+h`nJ3>i-uDiGq#JFA6SzjxeM^`$y5rpg!}--VsmpP@qu#^(Ln6U&s=Fn51IW&rlh~zCY{Ps7Uo512S z3w1RN>Bw%c98wVag{z+4^ zmH&Z`oy9@raCs+%)R=cFFnl>1n!Q?!^A!>Hxrg5WPh;mD)x_4daRe1Bh|;B8K}Dq~ zy@S$K1SyJ&fOL^AA=D5B1nB}wFCrp>NR{41N`L^NNs-<=A+!+Ez7x3Ry?4F$UEd!r zSU5A8%$##(_OqY;+j(q$m719&XX>S)Ym8q_zPNzBkEvotd!hQ-M#F_QW?#+3>~NPH zYosFST-8sVn%17`dneCC5=62yYu1(&FUVU7w|l}nCI&s?vALlkRETdt;ZU_-WQ~PMJH2LJ>y7tGNVe z5BTtL{aoA&OCnM}b==!bWF;{yW9WFQPRS&Q1aLl-vBJZnG{2<=8(me5U@;7vn~#+G zRg&kx7LCqb{)WCAJ(`D_ohgZq6DC@Za_xMyY!huq>QyxurJNut1~s#(p`7j6Hiub% z#jLg$)SB6dt}UG9+F0*oPEvGxxlLbtvviT>GT!|tm&b?mR75MN>29S-SAiLPR|5AY zHc;Vqic%LB3ZtfKfl`WKKna%-&;Po|w(PTl{tv=Mnr?NVz>?usHX}i-0 z8N}jmd|0={YAly3FWkZw;7k2DaQO37w`(3~Zv|xJvKo-fj|rq!28km}4Ey@+9tY%I zBsZ6f&I#X%E+EboJ)5{6(cmL1w>~aUC?~VhMj#GcbNrbnr<3;CvaN$gSPs|3c)Ek{ z%(x?;h#_-FQf2SSD@NzJnS$r$zM#L>CWgL;yi!`;-8iC7mqPudg)E_yt`)@JB<@|o zfn>IuL7++bIkkBj4)=wKO#3*Erqu1b3nq=-$;%UkhX#r_E(Ox39)8mG;cKsVPMl?E z{ls*=sfo*?J~b7XUKhN!1$J=dCQ7#zAd;3yCJW35S#s4?qp2HE`$1GB3~}JW`rwsk zaz+yYh+%^(iu~4juH24+(P2nK5O zafx~Egg$QQb9eX&Dji&5Pnppce{hEE!;WFVxbVCP7#9Vi{sD&=PP0E{!!CS(l|$-3 ze&BiyLAoV@_qd;eZ9QK|1?F)-LW%`W0>G5)`DN3FBpDEiyDSPkRH8n5@>qVTi;R)J zpwa6KyhD1~P6{zO&MXI|ivqeg$`?1!Vo&CtkgB^TBIA1oA;d`@h;vsedh9_^Bt5x2 zb``%8j6f5J*Tk1%8dj}&FG;<)B_0wbZ~dSG0jpF|dv)gQ*;Go*uN@4*APW;z=ubwucZ4~ORP392WvZSg1AMErp`5h-e|wTnfg zLfJ&+KzYWXU5Qv;piFXZ;;)YC3#(=WzN-Q$>%3=c@k9yLSdyItZ#!9R88Y&K1XYyH zxH5|H%Io;J6m5PaPO zayiCX8~a%uS(FyRA>x-G{gzM_$pG;xxk4q)qXghe z)Wnr4S)3v2;yQODhpciW?M8;sTMKG)L9pFHf6U1&|;XjQ~; zY8(+*ALA(&ahAztjZu|L=xs%ksJ28$ii~=_(eGr=8Id2^@BaDKk{(4Thh-9 zcvrc{)lrz0vP=!GihkAx3|!0o(id_Q@fUob!y&o#%cSBN1KqORkE|)oV+~EKtsjE= z*@hz3KelqdU765q1(ibpn)q0V1-Oka{5GyzDgE1T-$%kQgsNQs1Ws8e89o3?OVTvn1xoQGI{zj0z(tr8J z_4k#zxoZ!Ep=9VKBeOg7XMJS9`@MSZVgR{MmC$#oC8Bn@IJ6~R{B0fQ5`%MrB}t`` zXIT*vwc-`t`5vJH-oE_i@Tl=G=+cdqrV+MJN2mu1eYjPF=Xg;@s~+}SDOZpc+|ZG= zsU=0+wXZT|d@R=OT&-uqZf_6^Lq!dqZG5VAAAeajT`d)xaihLFhv-pisp;fI#U1V$ zE^Z4Ib|0sXy2{+L$MQ(!LL%+?Fwci>3K(x5|58id2p9CFD#_UmIj9 z&&-T{$?ASDhT3v+dqJQfeAcaH9P$~B7Am;4i_uWO1Vk|XFZWNrxZ!tL7&3pCvS#O- z*1Jz0MVlz?F)1qB$G-;IV~(#)&A)sQ;FjD3yMUhkIf3fJVX(Qlof2ZA8SC2O+MI4b zvD}6`brUC2tz0YEk#y_HbfSxgZQI5U4)45~8hru|qr=L_#Ttykf;+<0Og1pLt#Wy9 zs~j<(bps=?0E?>k-X1+ouL@t%N|i^wN8P{n&4q?Qu;U1qt{*xRqay|vb1e2q0{7&} z&}zMRjXTZMs5g6NkE-2c>T0#Co6z~v#`vD2-a8%CyRfwrJ|t*3mrP?mX`?*vDOUy7 zRs+F21x|QSuWxPl{io2>9)|jBaT2RuP_jpZa@SZzS(%E0JNziksLf&rx!ERw?qM78 zl}lHVfxNMUY*5pk)>E9EH!@mZW$BkYEt-36#i@E9PN1iCy0|UC4c!U#5tXSlL2o0j zYB2R0s=Cm7Tag7<0yG0V`R&*Zst~db; z&^D+!`u&&X(8C=H5hR7Q>VLB>#VqdA+^z{8iw3Eilt3=e*Mf#6PTR|az0?a$ zt6zxPF%unIJ5c~EndvV6z`+-{3yT-AlqGr!bZQpMBhf$5WW^-(A&x-dKRdydJ_-^0V z_h-DAwokbDW5@e{KhFJ{o>RZ4q+|CJkEZ*v^S{~Gb}ekcHv;MAy-e~0)=vusd5Hz? z7_-H`ueSj+6cBP}nH0$YCHl1YGsDTV5+6azB?X! zgaMBy#|uC{1)Pb4z-#&!uEJyD70c7^k1b3~fQ%`K1a#c`Yr3&_fIE|1TV##u&eG!x zX1p9V3k8JCJ%ETuJ})B|myc>!bPRay_)lM^fVr8OnLBW>UIH#t*zRU|8qvC0so7)w z8&DwFc^#)Iz?nf7GzEY%6B@EX`N6_LNyE3s$R|>^>0gkdP%!WRi_Q`?3-Afi?|_ikqdhR z8qkgRT*d!e7W#*JGx9Q3Aldj2A?WXp;lG#H{X^N|-yg#~@hShXSNtP;zb`la-IQ?u zA7~d5BOn2p|JRdvw{KhiLongzu7HgKxAt>at`F_wvmlhf^gGhBb@@;SS);}}<9v!t zE@-FC_d1uas~5o9=?;q#-&BUoW(@J!AMH5(+UCc{Qmdkwp_LRZbj(|?O@&8pJ}1aj zvhWq@j^-O78k!n~p;Q#)Gua~jz&X2H;!4$oP=U#7fWV zP{a#*y8!qLML5ytO(dsc<)pibeQ3K?r;Q4Ku)!7T@1K}zMG8=MRJZP5zEz1$XTJ;Gj0hPTyJKMuT;MAsE!Qc6}RMZrX&eNKZ-wDA|uH%oxq7)66PZ zQ&bds^r>Ayof~ta*35<6oje zCo^bGrsho$9t$J0l5$peH@d2HOX&07uGBZvr8)}{|pmxuv4S*rVt+w14GT@&3Dg;QW!%|jvNRg!a z6pU^|=|vuOX3tPqK22%$Ey)6C6o2hc|XxjrT~( z&Ca9=O2JpDSGawm9e&d4Zevc%t^4D#-Hui)pK9?;oc!CFj?wfU9`i*pl5K3kHlC|U zq)3O!+)z&2)P;d!4@LEDE}ADTJLu1t<#b8;Ce)Z#UJEBH_7}vAKAHNvRcYh}!%I}> z9{S#_8P`BV9KLkV94}Zx)pJPCcUS{CLN8s*8Of?%7_H;S?7TQFO$FYE{OzO*$LFlE z?p3APkS()i(hQaQHiBwxYx-yJ)9q%aDfTM;WXqoZe5(m&e_jxQAw@N(53X z5=8kX<==L-UpCtKOSTYkW)e@ya;i7ClQ?_h+)J>$OmWW#f*Ie!!Z9uQHpG8NrQ|E= z%nQHD2r&8ORJqIh_hpM?ZN=Uj26qVB`gj2lmxSD8aOlm06_La$0m2 zvLH~4ft^7~nLuE*L<92?q*=ByPt^xUrTp~!e=g`_Kc zLc~=fLr7Q8NAL5 z{RgNNh&VR29y!MOufCNf33-M&w3In|6~TzcbSoh@QEwa{TGT8jNqJXK!MB8EC0Ej| zHi8F;%LiW_*3Igw2Zv=+kMf)85vo4-xu=4??xF8Mfpe<*dc{gFLq+u{3~L08(b~GY zr-2d8tm}j7uot=-lnj*uqxS$Hgx2K`b`yvu#`(j|ai8+~O#8ex^kTuP;bCiK5KzjA za5+@jS=4mhn7DI+XT!4gD<+dKvHiOyud_9KamMA)fQ=-W6b zW0?ia_HC6T2CwDaeK|Y|KMBpXB_{9a%>m#tq~83PJcJ%v31A_s8l2I!4-~-aJCMK0 zLIrggMvlR`K4_H7mdcYHg%KTZctr$UrL8Sktx-vQ3ntq0&GSdp?)V&yMNV(grA9jm zt+X_{Re%B6;yhTnom5`*d>cZ2GpJ?s_!Z7Zf{QOl`PJg39vN(&`0R9K4?zr01Kuy9 zCp9K2<83cJBKdGR-h20E?TH$hAT(7%$E%*QyqSWz!o)7O+(pRco9(=5>)=u7yxl8} z#DL4KepbFM*hVpG(kY4+p5katRB5?F|AZAdW`x!}ldxo_UD&^Eb*g510E@5@1>%6DSkt2=S*y;KlylEzoAT+4zn`)c2$I#=| z3S?gCg$`K1m%L#OIhu!_<-B&?C91{Z+|~-m5)aAGkZ+cad5nT^ZVxiKYV~f2>v74E zwK(utPk&YveDL5Qs#nzp%%_Ysdn`H)Rkv{901%mAi2X{i|@% z1hJjLo`c_wJ&S3wxxKtC*W2-NvU3K>zy7n>c_oZm#i{}MiJBZUd6H?D;G>u1I z`3PboxvgG3(843a8@EoW90u6Z@08{lLnZbAV#73PHpMpTAV;*SrMz%b7P|+D+U0qW z1D>Id2!2caW7jq^(#ugOoXlxE=5_w>hu(yv!qO*tW?r{))}{XpUVmErAu9rwKBeE0 zQeMP&n=}NpdA2T(V=zVZ3lne};(fF}*p~*@Y@dfjJ{NVLlixf0 zQoC2CBzEva(yoLPXgSeeiCM<|@zHavgD%XDVU8<4xnx+>#E7+%Nl>NxmftMI$83Ni zV{}qiRAI$ZefrP70C?&mr*8U`BSb|P?jh8?WO@-ESECqUy29sVl0|@!%T9tfq1r{( z7lYhF6I($mY_%Ap6ZKDijpLR_cUe@COdoDVKj#>Ry^S2(x-&BN(Z{6Fawd!=*6oDB zY!dq$=6cN~C3hK0jm#Jf%LyFEk|4?h@wslbrz@!7bM6_+X6oeO+nr$&7Zs_aJlfx-dX)$3~KVmgcYgG#nT_n{NLCI?OWWkcI+lVU* z=(Vy>KAo6Sp8IG0D(esb{(p@( z|B);2-YYhZY(s(mKyE?@DcsP<|LDW;S1TZ3srdIkL4W^GhaaE^PnKb+Q1P>$W+25e zN{5)DAd)~0kThieO{p@b4D=1r%`=t<9eEI-N@{$?NzMTjn^5Y(Jhv8wEn68K1E<8% zwPb~AFYGpym8&02ez37Rcx|A_IFz(isq#ALu5!QYn~mOLZ&v+yogZl9F>D3=2a@yu zYHVLx>6DuUZCf%xB`AlK)Ayk?_hBG1;6MdhoFZHyz_hc(-mr$aZAdA?atxehI4kL3 z0nVEOCIx~xMN|5jeGimryf0PW`0TpWCk!WfgOZQgmAi7SVt42`q`qUv;1Q{*XkrUx zOoJ>BrH&0$0Q<2RyT9c2*?9@J_LLPXzXKjFH-PIg11xP8?FsMRygBu(Kerv&QmZ&) z5Z(Zv3cB08`26{jW8kE7WMt$fC>sVQeFBk4X$7Pn&VhkG;L^)|EDai`1OP-fpLR;a z0t66ICs*?20RA{Ul2^SuO_`RmJ5U{I-``1;pmgQ|$O(689@OskkR#<5fsQ~w#>P^? z#=3L|YDX5I_e<=~~i3MoSyG7o|Nn0hbt421=SK;Av1`>?FnU z?b**@z(5PV6fOsU||Fz*;@dW?fPmcxpzV`N|Mbp&rMm?77J|>Vk}z- zKsHrQl(2UvZuPgMD%O_PW6D4aszQemnQ$)oR)9QP00YX3a@{+U6G87NcUi`~OZT!F zxxLp8n3|e`h6TwKCndNWbwj2ep*;%}@+2h@2V}uL>=P;#y^=pIp?ePEN5L=K+1V{V zx3kO9Homxi4LGmv^{@hR z8Bk0_!`Q_q(<2njz`y~Y(EvWN4V3o*z_StM`zVMTT(a&+qIB^Am4Rm%85_(a0QM%i5tMKsDZZ??D8=zHDH=t62L=$+o zeXpOTJ4%N%2UQC%$@7c~$3zz2!^w?jAC2v9|!$c~99RU#7>Ud=ETO yL{8TC3jRiUfTjOKBK*CQ>-Wdm|6I_C+<8@qXF{QfHPEt->ZYoeO0Loq-~R(6BYrSloN=K6~%;?Qie1@425|sw&>ParXuR0l_Wk^QRgF1ecA$uOTrZ zxWcub{~7#|a97ZEf8}K9?q%j`L7-yh?riVmZf|3L&(p%y&Bn=5Sm2?6FyB3EcXwyE zM-Yg^{|*pva~95V9!#&z#L&FJL2nVF)>jl|8Oow}-e&wHXYo@V!Mgx(ga8PFj_*;N@hPrSePaBJ{uIFd02)by$AlP>mtFw8f_?cC?fhk z4FrnFq$>4>BG|G%wksppxE1(}xhdqVspO7@;3eX4XV|n4ibgK?uAH|lyyOA=ukWRhLJtY%k-PwGny&@*-zfhH=owqD~T-*C^ut?F%<(7UG^I~~GluNBJ zD3T;-nf-{#`s$ys^fh=*Ya0uE;1Qhs1Gy`z522(^6#&L~x~y`2CU5!50%u`?XR*L* zS>SPU#JyoEvXbzZ@zaWY*ICXIr`7BYwuB1C_7M~?&URs)b$+dt_t4)ga+ zB_8m>2ddgs9KZTg=$#+wPxLEHxSb+IUs5St6fTp+UuDqT`q$7*)QR;XY`jE6AWL8r zW>h5m*J<94LUO_Qu}sMgT{-hrLppDQ_|!8$g4|?eppGezv-AT>@7p!h-qJn>VQbT@N zip>LGQ?^f>Lk#nT^Q%h%pRYx5dt%DpzO_r}7=3&-`P$htbItt~^WpN)nZxNNsSy>` zQ+}Tr_Rc2hsBWaZ>&bfOx+I5M8W}R`3>)ky%O3ZWx)WpH80<57_s$o?Be$TjP?gQg z{&C5Nj00J1p0GfnsmtFSN^NdEm!i2_WD#JPWXMeNb}WdeJ=;XloIWKLc}_g;%fIzs-sx7x|H!2R%ACtAVVUjaHYi+@jlSOGts|v%g5$ndXQJo#qU? zF#4OGC5;wos<2X`=c`Q=^e@7eLeFRi!rP+O7T7%7h&a{6xT??>&rsB^q+jZTZ|$Tt z-=k1_3Vb_`)v|xhN3g?zX44j_RWBqUh0d;!u-)kB?VM^NIIbMuW`1IxLmzY=WbqjI z8QZ_)L8hi!9F=@w?aGvRX@V`)p10VkQJJrPdg;m{$2SV+$9q3Zj7o{1#U6a8Bl~{d zLaiyy-{e& zRJtz7S^d`NxzwO1L{Jt&FaotVnSn~pdOdffhh1re8aK*(;@n(}+TV{`3Mk&bexa?j zMgN?tvg5gZWIck5l&EO=q+fjtZ4&D6L;BPGMxsvvy?UM9I>z1GX{3LY`&LERs``00 zr<@#q2L?awOdx$jZ4lfY^o%_%X|&>V>7hd|lQYAo4hfv zv$u6q&#+9*PV53O*1uc&u?LAv)2l^RGm!*!>{yuSCd9biM1=H`s_F%dp*{6p5C@y_ z*VU30ln2vaGkGGwBZbOIJ~o4)Sc{aW@{?{r4uKgJ!%rpM|3L?A8~bj@EVRs%?q zjqK}9jF6<41GznGi{A>5mCC3>JWrVBKP_R?F75D%I@pb>BSk&yOmO_2U7Z(j|*Mhdbel{-d1oS67w_XtzT$L(bwr%eNHvSX5;p3vMWVET;Tj$ z^X_zlTw{A*r}@}Qz7C=wY;1fQf0zpPqdDss+aYWBa|R7(4j3Qv+cs;1yinRtw9h|0 z?loVXxh_>5yD8g|7&bOpRoVe09T?oUh@D@; zLav-d$ES(VM0+^M+tpx=-eTHSk4!pzF^IOXh!gg{rfX|P<}+%n7)RoyJnup$$?*XT z=GC+g??RI!uF$HF>A6}|3USZWE0Wv#mf++q??zy3o_|zAjhwoC9jm!P9vI=^>^I%TTjhw~%MtG*Fr=L5e4EPJLFUL}{aB=907WrJ zpt1bQP>&ZHlSHAQuKvl#zACu8sJDj#lg}2(X>;u%|JOwh3Zl)pQRY!K;)NdamXGGu zW3jRV#kYFvPUP@M|$rCVRz%|187D5?Y2 z{^*8YHgRQE-*ZR%q%bQC4w>h`=7JHM+hOE##>8eUpUU+1&@cUsDlRkeRi*T^mfjM{ zXnPb+(I2`wB}+3F-6o`Gcz-i^OWAZLa?nm`OHKc8N5}B49Pt>O{1?0I*M^|B#j@iv zy{SMu`6J=}s5?finBB0fq~1y=c^0@W3!GD)I7*&4?0Iw^zY-?z=l=6>$IoOe{T^CdwF8}dCZx<2{QLa&^xrPpv$*&StN0Yzj)}4^pB^bJnB>`uWxON zho+}J-+EAV4=p-mP9YgZ0!7|6HhLpwd77Yx(v7tOi&Mz⩔>4!BuxJG(Ednq4_ln zyl~7ptzh>EHfkee19ElwZ$0_wS7V-9qcMHpA8?G?4Z zP2Hu(qM{$#(C+Qk`}v^uls9L*Xq=TJe(Ui=@xp5=Mb$jv58qc0hy8}{r+wUPvow&@ z27M}p;%KBPu^BT3E0z;+M}6{Lo8arsnO~yjvcn{6G;-F8DE?`$P!)qQsUkc2I>K?% zan{gu{pQAk#X<;-N`W$i>(Pg{gV~7m?>dQW);i6bbQ-|b z#NQo=&5oA--ELlBf!B3@%_tak^BaLm&F>S)5wCvnX0MZwx^yO4JIr3&SkIob{MB38 zw3}j#?y>o*)IFa%*r(x=uTyGN3g>T!pNF?>mu7dv$yK?kR9B;PML)19^;EIIU&#|o zu%JDNB@yC}y;O`jTo}4-I@?DllK2SO*C9JSM({mkN+%rj^0^= zqVD8lW09(^lJ=Bx-tlb)T-6S3=Y99kRWkr1k2*X0HaI)tpnPFQQIQ>zK|cZFCO_&K zZdZ}ZWxe?>j%X8<{UYveW=y5PD@UC2JbKl`=W>l8yoB;G@prJ*@vu23ALoWU+q?c- zxG{QWZe6MOcyk0Yna-6chr07iGU_zh=y`Y}vLa$L&i_SW_p9diPW47|xm+eW@$@#z zGg}cTQXz>5@aBc8xgXc(Ta*1y)gQ*R5$PIVoqf?bRW_-=>LNY$QiXywjYN*v<1H*& zNRkCUEKht3(SMr+VMUAZ4rjV8C;kBbMLB)Ckgc>&>F&?Equ$NL;#)JML$U34tZZUI zj%>5DU99LEi^cZid&rbF&Zo~1$8gl&C7&eLIS^9Svuvs2YV7EZ%8DWt%ae#U146GT zaqWUX`-}>MJQQi}65(xJldst#&~!~MZU-S#0&MCiPj>XB_Y!QWKvW;J}sIwvZI^l650fzNv-eMV$X9};O%UrALm$on!29{o`_&Zfk!mC1U9L3Iulb(cMprlNWO4^z_Q8JN*ra zZu3g8!?3;m31LVw4%kec-O=^Q@#2xUQA2FK%=@-dgGDIAdrvJPHCc*|VI2r!K1#8|uG@K3j6lJI0G_vP2H(jzosPIDOj;{!Z&jB9PB;OaQ1!longX)L#(n;Q z-18nf(^w)DBRMam=X$kHhf0B7NU4}gIYRT`KKfE<`hk&g!q3|fs14W-zu4O@dBpZi zYqr`w52@Vf;Ke>LJfzhKx&>MFVb773=fa;}D+zoOi_ok>u-212_kVZzR=3ryNxl+Fjph%MsJcBr>Yx-LJ!c!umiJD#)co4P#z?ul z10l=Rjgf-tpBW*z?gtOK^4LnbVE54fZHPp>r26eh2-I(t9T;1l{9A8Ilfj5Dmj>; zNJe1$C--Ns*xZYH&+WD8TH$ib-pljnM{`z@(ubziGoFjz-jkl3pN-H!j9&nifA{wj znGU8aR5;Egj+wwxzRQQWPTJ&@ZWh&-`D0w`Jhx9y)yMa;{bE%%&lP>dbi7r2Q z^P9ZReZ9r8e*0ORfKmJdvlh!VuO?MFMCOgPs-unvo+s(OzDbgzh3&EtlQs=;ek%!9 zxdzn&-Ek1BqZzN&n#G9M>qA-YJJSg;?CG4L*NlhM!Jk)W+fK08yA4N{1K*y&$=4>z zIgh5@$d2Y<*xhQaa!VDUPFDzX;Pa!M8J~j@9f_TqMezkVrT4!<#oFD*)3x!^Mdlq@ z2qcn3pe6{?bcPUhn0(+gD@9N>7wFe`wx{gs>Uz9Y-e0qxo#egWD<-xnR0h^HGun6U zdx-bxcJ-xrA&VQ7oT`}`SxQaJiX-3UiB1l;N!S|wwlbqs&3}c{{m`$p{XCc8ae-NN z>z6(nXz=q&4LH~^@`q3 zu<#n!G!wt(l?^n(U^1s$!j0#L2KibA&&G<3^Z;yXYipZe((<03qSvlnBQOlaEE@(K zj4%ZJ8~nFBmuBG9Z~$|3D{eS6AIgN@yz?NarA2PC%AvmRraDz2y5OE;?J~{b91J!a zcKTvh(HBt#Y!1%`ubBWmU=Thb#SQ{a}v0 zQy;6e08v^KfAlWVSn=q$Cs%y`t^F+RU{VIi6<^PcBBztcNnBGe(2O_Sm+kZ z&9L;`#YBN!L1WNx%rF8D^#^eIw?53d!?kIFiz>S9g%IWlNx3{991CcKM(d$LcaTyp zo>A_O(H63f1>VR4|I`WFj2<}$#FLd&#(?%E6|ZRX5hFNH=b9v3i<3&Bxv{6y&iDku z7UO22jRf62ig+E=mSghZ{nCKV{Incb9{2(#fUC1k`L-P2nO^)T!~|%UBam z^o_s#B}SmjOS~XO@nLhGyyfZq{L*^G?K)#MX_^OnDMYA<`%sPAk!%%u&lwLLf=BLa z&6&_B0`bG~*Vt9$UUttj;QdDy{86NQ1*g-RlG{FaGES>scQgBOC^p!(F@kU}Qx63J zs8Q>>Jcmt7NjX0y(=C>fm6S|+_wJo;SxjYxbd3xt%hmMrq8u5LI|sAxT{^x3@(ph< zfL9rjTDk8CRM5@6kLiwUV+5-b!+P=D^E%7b8%GThC+DiG^8M^R3pk~qSC22vB9 z^vRJ4<Hk7IYY%8tH<_st}TF8Y<&wwKi`K1XD_wxB9O&bV<{ z8*$QOmD%A7)a`9URnlx9${+@79c)CZh%mg2V3A|U)T!DTzfX_HTiBrW!@k5QT+G6< zF74mJ%*x~RwTaTo)A&&9wyNJK`kpH^UeZfID_?Ws+oq56`J=76{=smJEvJ6?_LGY) z-rt3W{5#JPYz`GGy-C6z8=8B2d#DHv0ZkwQTyYxk;4|JNFDuh69W${JpSKTg!V+&s zHVORq%=EP3WQ7f-SNM(I>bqkZ=YcbKqRLr&JEWfc>{`aVj;;q)$;84Nwrq5v)M_n| zA>+-qBM!pxy&h8OyZqQrc<1a}%M50(KOnpu9){^~!+-F_dep`S4;ns$9a~SkfUpcM z^N!I7De4ds_47*%_f2lm;zdQULJ>k=+6$t~%F1=iRx2Ndt~}Ui?f9STc30e|vEsih zofMo4`c*9UfpnEGqB9Bj^7S*av80Jn(- zwcA~>u(B%sHazk$bnnjoAmx81fknCfh|!&5v8?L*!chcnp@z!69pGDAd@EjciO&Y@ ze+8bs`A_u{Z->m04C8|)7(D$<>%ZrlQI%g^UCR>2(2$1$iS0FN_{iO~LQh`xJ6nJA z%gRBeVS$X2S{$dvXfLYrI&SpvLVjEBSch6W4tZG;VPhPVi(g*RrBzaU1j{bv0{+tH z1Q)w{J2{HawH|UOb{?zw{lX6x3>&i?zzht>lUKb7`%ZS7dZhz@of};Lk`&eZ<4|WX z)0&VHuZNu(dh*31X5UAYEwO)?PQGOT_O$uTXPgAhnzpyx@?}@KVfFX*oE6^HLtonM zgeUj^4r2r>zK?p5;Z?o}0T=U=lUo0I>I`H$KcYO9ruSk1S;!JdnMhSk?u`5{B0?yM zGwVuh(otKxd%B`7Wg_Oa{LupLLO4kKCokAaL08zKr(E8Y6k9L zp!sWH>L2>cN@sP$X*T)~KA1FZQR8%?Vhz)|;V!Wu6__m%)7Uttjw|;bfNPq?8lTcU zkA-{pIEB{>;udk3H8)2qeQk(P4fkCpMbd_b;=O2Y3NGH&;@uxUj2qyC2{qkv2a08e z{zk>f8AZsXnOHwN)WO-Md0P*uk!xAW^J095B5_#_Rb6cI38$=*V3ksWw#$-y<-vD}s#2S_$1 z-y~i%*9-41P%E1cWleoJyDP%70jtJAL5rNGINn}8gXeX1?Z=gZK(mv1F}x8P%_!;& zff)gFjX&`83ol#;^{MCX2`G*MUC@>GHg|190a$y%ASq{%=iXZ;TJ55WV5OKyWrRy(LOmO0# z!uEmK)gg0?_)7Tkz5iqa33;kB*q%SRGTo;aQ@G{mx*n#JXscZ;DzBfc9A>c?f7BX+ z_fOK>cHYn1v)lbI!ZynPy~3fAhYT3-L*YIDo#`_MeLnhb`Y#zDZV-I{nX+`;3>{ezOh^$OjyD`CF^nD7c*0t#4HJL)_T&TnmryjaIEA6*+N=53YZXb^-x zRW+=gRafXD44+gr%DgRdJ!gtcwJWae%bw^=s{?>=1AYH^_R7 zetT&9hNYsxgQiFv(k(6n^`{yYSQ~R;Jp44bUU$MT@XN4ihVF8f^s4Xrp9fpF$IEV~ zjY-DPkc5=|>$vpaC{r{K(Iiseh7K_4AF?r(xIRbuWgS@g|7?3S*UI@Bwo9SN#8z z`x~VdQ8ATImo_4iK(kL&ezsbSXB#CjR(OiphuSS&pJ@}s!CjC_h3g$=!W#{epYLPd z>teda@EWuOy8Z4Dc}C)vk+_6MfPSfWj67qNO&@2aS|$eRq=)IQ#t((k6ua6cu@)(X z`(myuLJ>p3?FGq`0rj!|8k<)W`_F@8q6qP83XB@7dW3@XgxP*MYQ(uT>q?l8#HdX@ zjlbqTZfIgmR4}fR%De%IMN!KgD-)Z&AU1O+UWg%=ixGE?_F}mT1n{gVik!j0-reTj zayu`4;AYL`HBbZ_+@lwl7?I!!m9BD9NK5P(_V3gAktijOiz_W_mxht}E1I`hmIy|I z)&-Zjj^v0dB&5*v5hSxnLLBb`Abg0~Ls2UXKAe}C7c(U+c@Uberfe(#cQzw7vj#uL z#>V-tV|o2{1`?|`jh?nDWa$3e7RLD?uO)P`@YkcqV&85JP~p074NJ?QGQSNfbFR=w zqSgcVMg+TK$S;Q^`%=qiZ2#WyqUTGZ#g)lCnV>NvMSLt0nvUcO-FsUdBp|qy`%-_T z_-7=eV}{ZKMRtRaJdVfmzo58`n=Ylu6OYIdUlJ$3Ln|L~W3{Fg+a?(kk=fbbaPE5@ z8tclW_=?_#CHddPp0IBe2XH?M_9-L8P)6q2LnA5yDw$ z#Tz`i=0D&wrheIws1;wn%c#kt-T% zPjCd3=?eC!1doz0AlXlEbzyEhVwqrkjR!BQ#=nc9*JGijI zTP((Bte+u`b-yp4ztek2>G!~@3;v%^Q)3XXqg-RAYE`EIQwM4L?k5 z{}_kG)2UEmyYl9U=PoOq_U64wHJ{W@*$903L)VSU(y$5Wg6UDaCSX^zo+{vTG&idr zQj_N(vEt3yVO;5Em)XsoeSe$@UC(JCG5V*A#j9hcnC zMGyVz?8=@jC3~56E!+q5ES)P<5+Ki}AC>ia)cLd_eqieksqV4pod2l>&Ilzx8i)g; zP^~sDOK&7^_Q*H3=r`U7n_g6w3c{dVX1{*Ar)W@I#_!-KZhfLh`HUyu6p|r7&gE~n z88^xNt}%h(>nt1KKb5!`g%nDrbXDCJNb$^b^{+&e%7_XMFb9pul=~Zvq$mk@Oo;#V z(IQ?}ERbbiC50x9eKVFlQC5zj!{S7X$*rA-TL0YWj^FQ7`SJTmv4S0{56tK-axG6us6C%x zNS%xGlJOS9KXEH8uIuUk>x<6xY2OM)v|3<7W4%w%-nwm9zKNt2|(o zs?l%T@y3lXlq#TYK0afmPx+Ewti^*e$#p+y8=CG=;7S8?Gqi>+{P8&@bEXp4w^1GJ zo5{=g$dj5#5phl? zp;t0;gta{D`7d7B`HVvqQ?#jeJVZh)Zhb%E?N`@ainLZnbjgOrnZK&sG|@F|5V7ik z!N-WOR5&xblG~Nhop~=lzrIjT`k~i@Su$SX)1&hOML}0|yK?Cb1LkH_VZ;)0jX%}< zbRSO>*%T9^@TV|wRXL0si6c3fdd#% zQtM~*Ye?U~4L!spb&eUw%fj6to2b>4UAd(HX8HClWE#{h_E!pMQS|nqvi=QPGRHc> z7--=~K1-j~KHhJdQbuTk27a`5K9dX4lJ-Kb4R-mQIUAoxdcpGk(9eaL!xKwrC7w{9UOAv&y2Gle?!faRI6V0@$iF4!a3QtkK81< zl^?PME9`4qON5b3>%vF`c%wecP*Kse<8)K8L~BfTN&ho>T00`)HrpzN?ajoQQ_%^` zF&Wv6a{DX0hLDa$2c%j2YFT#S1O5R|fTP0L?&?&!%1t!}QyKX7xI{si7Tn9@KjB8=2Ho7Q)xRIPM*Cd30us*f@^WLIE(T$ z`HZ_>)F(eT3lo@*Kjk?>9^5Lpadz7Qs&P{8%`N=l@!{8_SHgU&@M~)Oe{`DKaLzs` z^X7IFnf&^rFV0!1kM`!;SV*T^93CSc;8wXu!`qgP&$S|_HjaUIS3d++$FXsL2A-SX z8Dl#wk(>~GVcrcbM!#(Ogm-EoP{Ci4QNCjNV%l(B9q}+RF>^ zoVl8n9MT0+Ju1b4-G4CMC{=do5VpiS&p&q}-uY~}B0Ss0O`S|&TO>T@+6R{$1lu~; z8u7?hO-BwKa75g^Vk5claDi!@vxPvFARt#kP7SXZFt^F_HZ*@^x#B&{JQT~8bsO+n z+z&qSY@!Jf`oAwKLuxluo`k2>a_wj$*e-#m6h}61t9qvf4>IiZ`XH2z8GfZxV{o%| zqOx4`6*yadV$;bMh_}$uTaUM<$C|CBz7t71D7IiAFguR!jFWHG(Xt{ za^OylYXGF}E#HFnul?tanuUXf zGek8T{%#w%oAt8_p274cT& zmk+O{5`Ij#28WJFG*aYGW-h@(wEbMXmQ!CO9ZQqJE?(inbXk*u)!5*&Pjfj7d{>@W z8kFS9#^AWZ|J^5Syvj%Y?t8nK#!|1O;ydCW&2$b56vb)@=+FwSBD(9+F4ft!V|(4K~(Y( zovrxVsOY=jXE=jADm)7gbCX>GP|-!+m&F0;rWG17n!V3n(mH5JcaVN@wp+XN`Rhe| z6`qhYE3aRwla|XJ4z;qC`ZYf&yZ5iz1Shr&aHWk={-0pV)EwWRa=s%zq4lzNyT6#M z;?_R;JD>5;$-{{c&c_W~HU4+RMvjBJjhXtk+IewI(e;=HlJ{^j?fSOr!j@L?kZ1b? z0T{*)Ur~U&53&TnA+AR(@Dw>>gJ5z#`+QxwAl4nuhvTUo1u{P~O<<^5HO@BNJZ7VM z-{goZ<%z{UkUzWhK8W+}Z1WO%%O(r_{MBs@C6bu@)=!X^30g?)BWNnqU)Hqn1UfGs zs0N|l-0uwypMN3TBFXogrDKyUSZs4RO+K$XNO(p z_=i?DI0(?)w=%*V(D7y*4!+bX>UW=eX4_xt?2x}Ba4ZT^UbTWU*77+WYRJ{+mfU%R z$b6`i|GH8s!uA91qz;xV>A41>_!6mg9sSX=R9~5%EV|n3+39jVU~!)9CwoM}+(*o!$=hnE zVL86@V0=@F)Nt=ojy8P{dqZ%!=|ny*;)gVC=4}0$YXHi^z`@^7&0ZFxu z3$bfZTY-y&0%Q6o>R&tjKDO^T$@diwskAHl_OJ zufOvC7nX)we{x zL%ENCLU@xN{YU`*SA}?Cmj%uW&g;k#p9Yin-C{u!`x9uYJW=I7cbJGN!K%0${)sEF zh4oSw`}bE|>&Agqi4`|r6P$d5pyLWB!RNQj&EoT)xI!BRPCsf8POR!5JCN&~O-8-_ zz>nEi9$60LdYx5f&*8rZx|B0UrW8gVyGiJn0ZsHfhqYf!-#gz(!npt z-dS~&w^v&Q-qDYN>!iPd7m8!g)ZK3l+_omz0%uX5O=R|rq*F4SsZ|;LWyjhNq|whZ zv`3cHbbx87%7rxOgZzn;Th7$A5` zhAy-hn}SG!t~JZeqd>2M4jgIZ3RUH8_1Ca0(4bfKf7`{oy04vKg|YtgFcssgfy0=f z-s%{XidJFpfvGN?<=3tpj{4?>qXE=8ug|wmPs16`B+p*E;Zl#8nkewTx(7mw(D;6? zSJK_dAcDPCHOhOFA&jk zG!Skr9<30{G|n97YfdAu(A~g<_VWN3j()j6@EL3Hh>Vj)1b#f(Z(2>DVMcpn)7B+D zwQ*{4gJT>T4)_E)A+}51=ky@9z%SBtZ#oO-tgN7R<eR=ONcR$Fl3d@+2aNT`}j2?%k>5@oW5eCO@*4cPTA_78RHpq}!N#t#Znj#DHA*(%B!MMXMI24H@fOIP@ zTfp>R8vL0W=%tiD8;YN=|9p{LDUPGy&!#}WQIygAU%$K)@KK24{@vQ|A7A;Au8c`2 zFRF4tCqX{qrgRr40kygaC-P^GL6d^I8B30|$Vcw|*!Gkchzii>*2o?|DlXae_``(d z38;ppvGeXrRIc7@GSxx|flWXc+v(g@KO^W&DP+hgM=id|of-&;p9s@w0|GQ}fGMKj z1Vl50DUht6@m6c~`>Q>=HOa$%q?WToS}r+JY=t2}%0rfB7O&==)!{e)qWtSNA9M5@ z{i0JNvs@@Us~H9r_)iqOMLPL>iQo70go--{#LT;*ADONASAJN9l)SNcGQG|Q1^sJ; zkd`(L1Lj_Zl+OJ2^Qmrq z9;}+$@d0x4wL+j7P7FKn`-`}kTOCr@B^gwv)V=neb-3I-vmwP5d0N*La4J&+Om@BB zG6dz)_~C=e$P?OP&$F-n9sMhzI*mEs2KLyY>n$ku7+Q&#`Lg04jT2X6QD2| zCjy|XtDs9{;hz}sXRn206UUXq6w5uZiP}qRl>G(Ph=(sMPBT?2@0Jx(!Ma2`N2T#o zl2?3tYZ|sK!{m(0O9*s<0StU}DoK;kq~CY6lVz7Vie^P4K|TMtzc}!dWCEL(I8ft$ zt}$7ke_V-zvOt=TFl^RWpc*C~K}!VsmtX`J7?GYkNYLjS`7-17*vd>B#-ML8*6Z1@ z-&!;Pw8jUpemsc8&kH|}u8(ZE>?4yT8b&S`!Q9w(BjRarYLEjp6kgTqrTc3YwKvh6 ze_l-FU)q?J{fl0sbK#82bnQp6Ydtlnc!AuGfAzsH_B^GP99#2}1PeN&l5tAZf+IORWhYb33AB~;X<_)_Fb&S(U7$0T3D2%?S$B#m_h%~Bs(r5=6X*PE_&vsD6ouCUxZ)o+ z(JN?p?w;5Bi`gH6w71G=+%{gl$FMs=r#sp53`@MBCmFFR3l+1P`VT)G+07{zrYj_m zx;=Qc!XE~-z%^kru_L}t;>*-LkmC%79YbHr1_TQCmK`D@kgAw@6J{SQS zuF%b@^9ASW;Xl7mQv+3)tPYWwWb{9B8i8({H!K){9tTr-k_`K7l~!a6VJp(d4u?{G z{+`5PI=YQ)HuB&oWK5p`=i_R{Jjs3fMr+JN%ADSX>D9*96Z!9O-T=K-C{Kft+J_9L zZ$HB?`Oj|n1jZ+KVEV}{a53A-#?1<3IK-1$wJsbDdOwquaheHZY3czrX{)ZDDFzgo zfX64DQv`zKcfMi5)i6JLdHp5KXyTgAq%j{9aL}o+L?bF(4$p)c+<6OgjuxW${f51^ zZWisFU-_V*j+?__xsCC$2I15x3;hA#l^jKB zx9Tl$Lp*U(bO33dlT$6bwf)Y~osbGCIDNc4&DS?w?tvSkjT>U3E$Z%f^M*zJ9E#-Q%k~}wwEV{qoj=Td z%fw5Cvwrc-JmX=_KydJPB?K!>y;+xWCwqmP- zJDCP4P{TiVcRv(lx>MUb?N$X>fO|9;Q#mhjp~lzM|=iWMTjPig9ZkRB>Zmx@xuEWq324h zTGc_X{9285O83LXz#Ds(JxkTBDOQuyPm18cSTd`z&gDgOBn-OF!Anotcq_s$v5w@| zUxh-0iN-Z6Rd195Y))OHmRuRME*=s^5cvLb!6JsH`#M^E(q3|NCRwE$)a3TP6!5VT zCp$=5dvb&j(l=x^CLbm%c3XC6 zOR&>AbOTGb2_q7Je^LwV?)kvv4&mN!6GT~Imcn9(}N=E#| zOrMY8m)L=0$i$-f$=A1M5AbD#&HGHGw}QI+Ybu4_3@+PS$v6F(6b9Ep6N9_8LYA^` zU0y_c&vO~(YvpZ%h|#q1X+V*`#hoMA zqqphzaRyzO^Bb#E9Ym(D{T3H~-u0j|v1KB_bZl7MY+V^SHxEt4_*20GeZ;%9soPRi z5u=^AAKpEURN!S}O00itvoGlC$KPha9#`XO+#OMYi_Zk^t84y(3*psyuPTDn z?535%eCC}0v6={(gIgJfg!HeQ}V>L z{;DJT2R^k!j9U%!Ms>16Uv@cqLF&r9(T8Hs^UrU(WjGM|qmXRL>EBY-j~wySyy7)! zcO{^#7U;r2mvv$$ox6BT`b8M@{&G9%G==%i9V4b>?36@F^R-PITW@^^}n}7?^Etl&#`z&e} zGo8z7uwUKp!CN?BPBSnE)!Fy9b?2R9WGVgP`m60-66(z_~s919s}4v<=1#h zes=Cte3*OJyLh9p=kC9|t5QddBym0i4Vh)2BG4=q*?nA7A{&#q)3O-D^rjyg>9Un! zf>xeIfHcVy0+>s)Trm0k(v~M-oMlt1Z0u~`dgP(Se47MFahiQ#g|FYs5n?!hz!1oM z`sTdZPEX8jvwZh&OLY|B*E|N0C5LQT9_Nq{TQw^0cky}`@A3Oz1VSzj`?&U`*NlfO z!ImNup}(tAlPjx5@6cNwvy%Z1+_{Yozt=0V*8)ppAs!aTR@h0ye|yv61-BD8}ea|bfz<-Pv0& zXQzlaT5kaWc%*S7v>OV4*L`Ewn__BlsO=vPY~xP`?+<#6%7j3=0LN{V5u#6H^x;t^ z!RJM*ZONC;JXS`MPk*1jh+hZ9H45rUC_N7^$zjuVRsXLkZaKql?UmCfM>2N4Oc*e zOSM)Oy^HL|Y_>Mskqp39Cb;(nY!0g1svM_CHS3qGah%#SkNY`y78eJF!Ty?C1+2S` zo84%tQk*|jd)Nr0Hv0bTWTR5*5OWof5>5dj^$eDnzVk2dX8KkT$ww0lVI;?P#l^b+ zt!evj;0ExiGKItp6Wb$H(^isjB5&ZMNcvq^bmQyuMo`xSdeNXGsZUcrlwcmr^%P-( zAY+hm5L9p+!#RTIK2R`Au3I|SA9L@<5%OJ>8=><^q}AX4)1B2QK_+jA78?j?rI_jb zH_UsGGJ&-YnuELOwDfx2gAKjuf2h?SlZ~}F&D+2b?vcdGoUSYr_3;Bs(r&t6m9i;6 z&yTQSk&3+^L97XZGA>hmN%MaFrpJ<@&=;Q1Rm+FzA-}f+Zd4=xUf&1Wbnydi+Vd6; zHS3RsZ(!XyPgf!qPty8Pou^KyMfG7^B;3T!LTKVn+N!yQ@uVKh?>~?RGSaum^^|GcXb6^9Sqz9-@>u!=uQ5uRC+Z z6f-CVCS9o!+E6GLi$q0O`3iRoLbw+JLbw@6Y~^~(jWhn%SWVRJ$z43cn9nw1DNg)l zxp7hem4QY9@ta+LzL5)|aEmF%)@y@F_WOqm(^LD`6q_<{f=x@NyH24%rCLB@%PZp? zml3(51lMb6(_W$h!76N_>7YoPBmh3{BA=K#|CFdhW--`j<$5<@95d7EovTQ;Mca(ZX&T@J`sb`Py0 z%n2A}rNTSXyuaWo4n~!sM>yxbTGsxqS}i&MuD>&X;-j+F`TN^PUaN~wWW`U|v%s5e zHjA1q%X)Pz#6;LDl76l0yi#n^le768g@@e|FmTr6Q{< zGretCrj`y9GM9hKN}z276P16PbxamLGRwa3g2|lk@dDSy1OMkGcNI+~uEc>eJ6EvXqGmj&2a>^J z%*bH9ecBF2mHZN%E~y_Lw+8fOO_~G?HVg(bG|k(rNY{|11Cdio(c>zzGAw&-fd^frdSjRauTJ*jbJN+04~*d~+S(dKtfyW`5OdNS?#Xoh46I=H zg}@M&u(9#tY~6z4pOS}&es6c{uStw&V6bK$ZIUMtxA*W1sqNiU4_w zeo7CP?@LG<3s4D064-%5LE^(QiJ`lPmsC7zg02{cyxWx6L#&q}U(-Qq!+_($MTZms zu%C4w-?%KlB_d$-Jt1sj(RO^qM`9w2*+o4{93Z124dB}5PVH9*x2BTrF24Om5+?hs zTvw}cmr&iwgT|o;%6pol$)al?pbOK@ls1CsY7rpN^ zD`|bQw2Ij~k)2roY`2iRYi9aG=Huq^$_y01;9Nre5aOrVRM_RFyUNjIe2pP}A#>UU zx22=yxrHWBU@omuy&yLiNkk<|J<=L{U}@a;=Aq?~h@vsVNDE?adVm z?(jxOnv4vX6}qftitAUa88Rr%%QeEr)~x&5vrFx{pP+YHloWCFn(sqHk*U$HUut zzcEpg@9}AgMaS+xpPaWZ<-^$_r4aQlNhe+Sn5Gdte_~~^99xW=f^+)0^Xe~-MD1kk zpE1Hn0V@)|(w}P<^e79h9GX`@u@EaAS?bRAWK<^A^3VsN>Bn&fEANo;ciIB$1x{|a z#nbs8-G!W`DH3JuA@5pFomgATXf1YasRT;lg1D(jv;~~~6Y-i$Rs*sxys|bqBoh_h zBnwtAyLGz>#c!E|wbg?xMV!P?kkq#?8jkptSvaG=VV`*0E1dA^$C_rLNKkB75Hghr zvVj1+Hdi!J&h0hgMlV|;nl`|C?o-s$i7=p+66v`?R?wIP5S061ip z+7x#f@_?Sxa_>rQ1w~rZXi|S`-z~w9!{O0j|0<~ac+Kkl8< zmR6qIFo^8S!201(4VBklbK`&S0TTeQJCKAd9g-@L zIryQ@;iC0)v;cQ8RIpzC(~E_KRg$6K$vl$5Yw@2fygW#ckbgUS^<)hUSXaKkUHYmudnUbe^bYcp1}!3RT-sp5BNtxZ@}c?Kmr!EH`2Fg6CZtskeujho=Y6>TNa z-?K{$^L*BfU26JMcetTxQf3PI@lp7cP0zwl>hBXT71u{MWLsFvGk*_fkXuqfNC}hAiO*&(caFUOM|5&z$X`_j{qnh?i@L$_HK+q~ zzcoQR&KfBAFXpCcEOvWlcDnUoq|Wh%&;gT z92CIW8ctom|CV+JV1!@He}qDNbeBLUy6MerGyw#Q-XO93Oz}Q5UhPtqLV{~wxl5}) z{+;=X<59^Vg1skgx&VTH2He=cmECQHe2YfYm~FW^&hm}IBx=*LKMl^G)>eki`t28| zj~%=KplXY+HT=QEhb-p;u>R@*6;WN@4jFX9Mf~}fAqiiIez%LJYbqSh{Emnl3cxIM zWlZ_AGvz*F#@>ucCtd+>JkSt#eMkt;78CEm|Cs-Jd+ZgYR;s-01{K&TZtAbHiLXzv z+wZRh|7oF#)s1l|_}I5vRDY*x#RI%L$E|jNInSn|KXL$g3C!m|=3f9#qE&%2b9VeQ+7Bd`E3gEWfj@k9!wMgb6fnR{uu?Tl%;j;=8zYvvZ~Va zfxUj8_kMWQ(${mBZPXrV#x8mDIx)zF|73KttNE+sBl3)Z#$_hA*8)-!Jp6sPX~S}O z>buTv(GnJ=(ttV2z^=>>ZauK8XlJ{4KsfwF4ErZ|Fi zM^tT~9{O&>$c|s-7d>IA(2Kd+8~X8ouJa5YPFI+zbfn$UmAXI2dvk>PYSvWOUK3AY z%xkNoz#6& zss5&$t$32RmZO{a5RVH-*}QZp5*-MgNOGPF3kg{@P1m;Z?6NKxowmb7w}1KglrZXV zT!I-=7!Nc407Z=420vb8bWJxeVPrTwo6|__eQ#I(!>9b!+@5r@RaGvnB3Q_?g96>` z#6EOq5D#`RoKdaxoXhR8StS$9ak^RP&y^D~P+B>1y}I!^PHn>{ko4KR=yR^_tKd}-PUx)5>d7@sif6H9fMOZEtV&-1vD1zw z?`Efc2StyIPKiSI2DY6OcAkhPYVW#WD< zk__iVU5UkL2T)=Jr?E7G^84^Vt;07&`y2=C$auC=L~hIS+}@cog|LxLS-jk}yp|Mk zDM(8OQgmwxa_cH=r+s4vye#j8!aBmrt!@^4m?R=2!hCqN3UXod73Z%2Mdfs;=EaI* zmXVjaMw6u0>fej+Xa#X1a=UIAj4a%gTPSAi&x<~ECRG4~&5Xv!idwBo7wRv6<|3jc z1Gw?=XRq1eYG34x%-YC3`IZ8&`tH(tnFV?W)+9o+mlp4~xb=Dx5xq-&BqQU>PEJoc zd2GT)u52hlL)KI*YZwPDmhctUj=fM}YD)p^u(_nAqCY_hA^))3S(`D-Wjbnx*e5k< zW9M-a3fGy$QpbUCt-U$b-2H8aP@{b{zv#}NMW-apxOMWb3ieu88`;=lMwisg!0PJl z;?EoDaJ3N&(V3gwOS*+tY$61Ux~{o~N=G2#m~q6?JQf){>ZJr)_cg-eecuP zL6epJc}cY7nP=9jLkPmAKl$5&=jNEN9p^y4-fywLquxtUO4w0Br$3(LB3sHuGzuYv zenb%VAK9c)hr|1-(Z(wz;Xa>O&;Y8EVnmjm1mLOT@d~MdDrno*9_NU$Z14PHZV($# zu+MW{`Yo19zg`2U(Bs678QUJxy#pVQLnp@nAUXxVh0q_My#PuV{dWcu$dvvEH|qb# zUjjfuqpJvPRPt7?9AnzPRyrJGucVUaFYQVBcku6B*$8?gRf%%ht?cXN-!Ps z284JcDzt(80TcQOh3Da&awqxSPxFV+LTqaEx1O}%vsw3we((ousn9B29Bh|$nasbX zOxqp6Wc!Lqtq|jl>)z01HH=p}$Fm!tk;3al-%r5 zGV0(EF^KZckGmJQ$2~*M&4*oFr5KZ1No)-!Z!xRxpDW$sw(9jh#3enejyiNc(m@Sx zPN|hYq}n^W;NSBgfp^HwSCwmJj)uaj+9L|cIF6!^eT=EplKvSeWX)6rxNA|lFO1I3 z-xUOOUM#9Tl*zUm*VkC>@?UGLnNU@7d$Po*kRHPf90uBQ8q5Jf(Qzi#i1~MaVr*+~ zUhia5KH~UB2z@Lk)U^1f?)s&msT!$bg+XKDct3r--k){yq!*Vrhm#`L$C~a7D{xiJ zgWCB^phr&Txaax6DtJk+yixhFxd5i!S4=Mf)KJUxBR)@Zeu~-Zgq0kEu2LLNAds8- z%$hbW(xUK4)CKF)(=imq&|V9*q}w@hSX%3+XPO@@iECdJ8u9izQmKe1G&Y^`iYe~R zkK%qy{rKD+*tS#v0x((dwaZx?GfLcWr9~W-Ir5EehD&)Hjwh&MlC>YOLn;zM>-)1c z>qrBp2OAa9jLs~Bc4R=&sjnQRTBdR)i>a}&VYA^4`6ihY2w~YX>PTVuCJ^vdAmGkP z84l0FCd?>xmzLjnx&+kV$C1Ne=AVyE0sMPMovG}$NeY;OYBWK}5l{!s3*pVEosYzs zeIyw;Y+5cI-3wrH1zcdy6rQ;VcbWD?+tvcIS=LA<_Z=>ua?0~+00Q4+ZZW8?D=Aq16$VOpu(u+2 zlmZa2?GtZKttbudMFHXwl&~HU8@MMv6bi=>x$^%RKwuhxV~wft3uv@tQr=){1im>` z>4wTZOF3$Yg6Yuy@_0)Z#21+g*s@Z@)Byn!IG7vCw2hJX7)+?#g9zD(-?t*+v>+-N zF!vvGJaP>c0;=a4GN9nnc#^;7L=7F0D)FYSyJ<%R=oy!FIq@dbfQ~=;Br7mtS6Y6q zZGnKt*I8B5T2r+3cBcP^P`u|qEG*C!;D4u%hNN44dXXZk;(F;64$xg6L8>@y>0!+ZY%aca)XnwJ|WTOu;{mTX^7! z%`pKZ_$B74pzo>UV&my!;cktgZsF2ugSyrH`9HOBCe6&t7)d76vQ$`6Sn=3jXd;)PwOueC6-1;xN2Cd_q_GUH z^ww#d!+lL{AI`l?^;yVVHJRTQLJ;vID8zdk8kj{fD9T5q)89g{|MJMv=7d*OS4>*4 z9m`b>8#)jgIEXZ4-s3=|`6JS1;Vv(cu@IdY2#=s~@JpzlWP80+F=V+%?Ksix(r0}~ za8~BtwQY<&G-lk5xTd+6Mo^GX@HC^iC#I^psmlACYQkQ4vs76qpQ$NhN!6Rsd|AS| zJi)qhH{VdMmX`rkvt0D6xm4qYSj9CX`Spx!|ItF*rUu?;zw%5U^g*Q2wQ!r`KD)z7 z5`%Tck1&R?If{geDoGDd8i%+fyHLbu~3f=yyoyE%L*v(~ufJhx4hN{u0nQH`Y- zmM$9x%krTbDl7FdWWaoZIT|n+GA+TQ4If&V;dTzdfJwbR|@MrZ)u3QgBMR!0(ipe^!F$sV&?opGZu7lyfe~oc=rY30J#kBVk(l+7-B-a|@ua4cAkFrV$7_efF4}w~r?)WuhE(uD_Du&)^N#V|a{BUO< zF8OYSJa&IVbhRIj!MV^_3_mU>_G3P8BB}|vLxa4$me0}4KR3afO6tEjVW4@tPnUr| z{L{6eDAa4l{v4P8&T4u;Ty*QlcF+`lfl-V<8%v?9Nj&tRc-BN8i-9jiDSx zhi1eZJ^XXHuu*-<@3#sU8;kRNf*B64CIyBzHq>F(o1*-9oR}A(6~=rR-)ufo#m^TH z5ziGTYA%&vUM!j55&Q1s>gQWu8NjTs*!~+>Gduqa-{)Z}NDKCUY0!NzMTmqm{b?MW z7ab5t-4d66cW6cSez|cg!I&571+OEX=XR*cvblow9^KX3pv@8d&N;LoO>hxi(Z#VK z?5ehG9W%uDggJouJni^GwZi|7?Jisu3);AU{2%|l_Pq~FM-SR7Lj()FJb1J9oU0EF zG|nqdB{t~Kdd>2q^tvTHuHIF+iQTH~8ZR_klQQ9I@3EqPHrpWk)C!g`vjNBK!&Sk~ zb2YuV?&lZO4!icVHN@O$OU5zYY8>1N;}K=Qhh_V^ntkY99-et?8wjdqc^E2eI0eE(%fwrwaymIlzXN(W4@T8-OY5$A+)Qa z&RJ?lZgwJL|H;n2gwPJtvBpO9Om8z@gdbmTKYWVdQHw$A70hJYSZ%aP6!$I_XG}$c zA4dVTPXuMF)*PA3fZfi5&_R}Sc*XC{B)>PlAFTtV2k=-&B!ZX^Oh+he*quBPxuTVX-UJGxj4mVsOL9oPtt@ zt{krdO_TP{1|@dm7K#IFki~GqIk*EIY^}Z-TS}lm(NJYt4W9!W!u>4XO%s}E>wV*3Tz}izYk7fUUpL`O>UnrASs21#s>?pxCx4&s zut`*sc7Q(Oc>2$pDfjqd2m?)WzjfK135%a5^?^pS4&fCYoZfI}&0Unf?Vs^LuaBVd zi@|_d3xh?`X-^^1d(UZS%T4>P<2R=i2KcsjJkp*9g~h|K%TxwBH{ys2&N0mVuCLkC zh5r-XDdg*Qos8)$!W(etcwO-!0AuIrE!#(%1UuKwxMx zj{bWzc*!IX(`PN(Or|l<37d!egodT3K7oz?BFKq8J}_$WDM)9&6f_=T(%-lY@iEtk z=p`C>D$t8e9zvnh3tEk99LdyvC!OxkN%Jvr`mi4fOFzPN)OcK#BTfTfqOx0)Ba;uK z>l3P#S%SVn&l!ffQlhdlYC+>8On#R3wYZi)YD376LrFlPa;cxo)j{1hQm-qv zeS6QZ&qUcJxZ3x{OdfZ;)ArnNw}4M_YM8-iTE=3`Nagp@;D7#CK-Pgs4%oZ2^;9Xyx z-wbW`tha-cfBuR-%e#%McaUYt9n9u{7)V!Wjo{MtC^S>tqC_fee?SPjtwk$P);dm; z+P&n_Bg$8UgbQ}_s(KGqQ4H9%ePq5plrLlQ1?z^_)8#{ki-0p* z(=u!6%+orXV5t;*P{;`*h`?$G8eJ?G0pd3Btu@p0rLguHFJ(lRIJsEKg2#eq*>6HY z>m9tL{&kH3ivZXBjr7MYTL_xhI`ttxMzZ>rJo=q!+i3Q`Kx|@?aw_U+zp9;WFFbx(~s7BQM~}y>8X|DvMUJ^Y4>s@J}xI*>GV*s z-tntz462TSXo)s-%yfwj9pX7h z`E^@g*yj(O}U{9@@mDg-$mQ*WZA<{+O_7L)(`k1I|t@r=jYIAp_AwYblOIw|qUD8e~ix zJ8ZdH1PPxs^`VMy$SfYEO&|4ewb=+OwhETYGIVKrU2*YfPoqoXSN~-?4J=M(SM^rBLRcnfsWDI&4Wf#1v z^Sy&9P6sU&MugKsKQ}USNKf|&RamsBBGR-GX&*!zdiT~Flvv%4YIg9oVls)ux11hx|sho_UYlk0mP;)VDYP6zB>U{5eW$6U5(M;7DYtbpBVHg#*$<*Zml%7?m?#9T^q{f@>^F=J+J`Ipupa)4#P`>^#wZQ+HjttBnduRdfh6ho zqa5l1H=(&rIe!Y<$gAN>y4zD*L2+85_ayd7iWn3^K>L#}{qBKCyIAt~mxlPx0}lqmnA4us1Cm zh%_ar+C$i(p7#+JdkjQD5ax4#HE#pdPSMbGk&!Jgy zRgtT(^Aoq3uT0C?4c^iSzpD@$DAJAC6aFh;a!RtGRrGxKcy2Qyh&y$VrNY)NqH%@J zR_~`33|qN;q_k^%OcQZ>VCdX5v|=%LXUD@I*ETp?&|ymsM&b|{A;=?wWLRw(3Z8&Kl-3+u$}coi$OCs*~>|y0l>cRU70k)ut*4 zWo{o&mW;hNtMlpY=gZ5gu&XI@T>taQw~`k+D-rX7bv)Vhn`C)pTPkY+z(!N5I53=5*!QH@0W_ zlT3%f)m2M6{wy+37I}AIbsuDu*yj^6wZ{CLD za+z%Z62X3_R9H`At7pwN;G^TU7tCtNW=9J}y3Sa6x{D~U{waM*3VxV>|L-?Jq)9Bh zYD(qvq8DBg5s{IRN^w*?hMp~k8B3`y`0~5o46C>Zsd+vBHx>gKzlwh4EffuAot7JEJMVl%I!A==OpB} z;;`MVAD@vZ79T(G*j=A(mN{Ji>j6nXi*ce~ppj`eQcQceF}jlB(uA4w?2{b)1o`ff z^Hkb9-ulSKfMYCvn?4#|_&>P;nd`ubDu?6a(}Iq!E}arXA#H7K3{me*8X%H&MH6Pal*!4+$?b>o`)6eyi@G7@KMFgkEFfa-C#!id_E!cAtb0>nAy=oBj^iJ^ zHb$0CJw`{BfilB$M!SkF4@;qb{@I5;)boGi4n5#AKC?lJj*i?>QBjq4zh40+)5$qB zTz@N2?~WL`?Dh!`{wgz*G4)?#H>`TuIaTKYLHueC2{}7hYsY5}{C6Bg$!nY@>@>me zJS8gbwchb>zP;{rIb&_APB1&XV#JFu-#D;Hy|DM*4|*zvA_z~0V6;YT3{#24j6 zjFpD2de61C?db+(4UK_4i38|H)M(5q2C4g)HxARl>iZY)AIWT~HvIIbS2QXR$jmUC@>o0)bT84@G?W!UimR zb>$!N{X4(5jt-{p!EZ%BWE4m3)!9b6xEEJh7IAD{6l$58h@$P73 zv;uF}dknwW>opEOU5cR-imt5{ov5_;7#I{0WJEi)w8z1!Rx~xAhMF1?@Gk4^sX8&! zX1O=FF^K3MaZYY{?aXABnl!i{Py1X4na;PpiHeWE9`)jDI;Z`UTOHfC3*y+%zWPv%~SFdK)ceAUi7S(U(ZOpiBj6wQ5Tp!v8stdfG=Fa_%T~t5yLOnRn_YO{Jx95yUOZLcwVN3SRP%w)S z`}o!^U^}wKy%JvohXU-k0+~VBuIs9zc$k@c8@q!Y7h2inD_aq4StrLnL4fzjMM^W~ zh35#v2KttBm$l7OyO_FJnu=dE6|UD;m#1{!Tu%*kD+Bb8Hr}3|i2~Aln!x&Wz{8s+ zA%O@NlG2)yU}%YxbBUAbH{Gv+LB;jdru{vI_lGC`@hB6}9iqg$nBPEFjne24x18@t zGs^^5t7WWkwrZusp8ee7M1jawNzKe>@2!bShtW6?yqLf8)#jtqEf=dcDOb|h{3 z(lAA3ragw#Mcn#@MxPbE;K}k^rWMJ}7BmZqA9ax>nKRjG&JDUa8UGftTUDI)C;TIQ z6Z?aC8Tl>>Z;1~8jIYxFF>D$n)EpaBvlyRm+n4>Y`^_3b!aVSST~$e4Jr8*CBZm>9 z(BWa-<-zR1lidZs%fr!hNk0J$)l^>V?howp3JO{c-cC$G2U=Xuza`a-2eHXCYgp3o z;}<%`j9bLiQ5U$H*vE`x7_Uif$xKKp62yJC^faqU1X{+)qZPDqU5FI{81^KARRI-A z*G-%G8O~Ta1{F3Pot>9K!IRZa4-6|gfB*hHT%;FYVpMY`?w!?LL(1piH0sFvGQ%w1 zuawR>@J?@m@Tar-E0|g!tPl&O;e@-%?LT#c1rSz#!MeH>7#0>5U-I*>HZF>J2_FRq zxHi(qKwQ%W*Q){#x}3W}(jpKC)NO_fwb<_8Cu3$FOoKqD;udwdOw%7Z`rYZhN3Y}L zB%^Vk$wwj%sP38lMCAhz4xf}0?@tBp_Z$1K>Oz|R@5=Ksr;brT-a?tDm(pwTwWq&xh>!Jr_|_D?}k(c|CT>cwy-y~Md&f5S#<&DUf zKkH@6f6D=XtnS3RaCh^Vd8^)n2Non1FE()o~DlIe+dZvm%0NrnF=$Nyf)Lnf>8OiZ=>_#TmDbSh-u9reF~FJOQvp5@b$ zPEzGt{Ss&+P}d?i;5dwsuQ|-x;tppsQuU9}Ix1V+Ds^rU`ASBdyvzC=F4ghT?Iu12 zbCF&Vyv~zRd0=*fF-o(n?l!vcfoEx5t`}__fc0{3_)`>Rwqx+PO+jy}ML;u1g>R@3 zg;$GN(W3^pNJth|-)L(8VX~YKADq6CMy_*%yUGy|&N@pnJQEXEK-2ypNLf}v!Ni0} zAcW_dF5K`Yrn4)KpIW)mp{*&U!gDTnGxHv0na6*mOo(|Z&1bBacj@m3uX!^758n0Q zGF>VBn=Dd3Jbcf)+xA9~A?;mpMbdc-2FG0-_92oVyFRi0z)ng>y70Z0JiVC?0iD#b z&TI>v4>#Hl2HGZ(e;Quid>X=;5d2;}#BLaMI`spXN0GO2-6rK@J%!o9*BjAQxlH}o zxL9F9{V=UEo{+$$8%~~p$Awis!$qr~HCYb7p#8ODu+Vqu)9O#xqpaBsvNim%Vzgb@ z$SKPty~l+z4PLH4^ZbM+yO<4_)AzIzZOD++h&sUTP(Pd4LLn^@9Fgrk&TtT~ND`+o zJt@DL?ZRbxnj@<#+VJrpUw#6!T4Mxl0#PtmIm1DsB58uc_+J!yE)EDK5r`J)rrlJ= z2mAB!qfrsG&ydRGAd};Hn~z@D4m)JUp&*)+vMlg9zxXSsSf*V0iQww%zk@eC2!H`^ zg>zo+1xd^0!@sDtlp=L@du-o)zBe}Ui}r8=lGl7AvI3W>w5uPOx+HnKZ;SA2_swFd zg}$e<^H>QTLcTF%_UB__&%01I3Fo5ZW3EHi^K$1>;VvKikFxgeUIHsF>$vWYmgUe< zxx+U!cLXTX!$q_q3K5WH*zM_$4?J6d!gVe@+2)fHNI-= zS8`r8l~x7XxyWAX!UK!-TRDY?gTlv#8#gmQX`#yBXP=Qvue=$ZZPQDXPq@*(5>7_R zM@_*;(OF-QBAXf{*z9pb78J*-Fip`Bw!r1LXm=wZ9}x;r91$DT3=>u1B&r*eDIugY6_SGvIE7E%*ejMjSy(KAC6vc9<`Q10%tgQhP0LVhyN=euMhUf&7EAMG2LKb7t5)lA}f5t=8&Jd8Hye>%H+_qN1m zT7MkS@h=3SwSdC{$Z9wF67{~6ly%&5j_W&}xgpyH$f`|l>{$8vd;KYJK!pq27%*}A z?M|q^@g=5ZqK}*Bw)qXiOn~7hP7?l#jrolQHrLJ!& zTpjS9W1Wjd4dlx899q9(id?3_+tC}DT4lpugC3z^kZcafV0`%JO}f#VbaeJqx7&@( zk0{G9Tu%?D4H8U~lfLdeHvEQm>_zUczPOp@{p8wUncXk6-P@w2zJN6DS!x+xJ)s>sCR7_tCgwjQQWM?3RcrDFxIls ztxdI5mQd1v)Q8rvdjufcXU*s@nrj-;Sad@+7fETp{+zR?(*5`uw>^H;yBiLaz|>#X zi~--d8gFx4-&7(q zOg$;@*ka@Pjdq2*&vtK{mw>mF#Ya$vy<6yu`yG+|Zr?V&;Xz7mW}<4aC)&doWji0X zRISg&__L#J)v*I~RGa_YGF^9_H=5mfVNn|`42>j7bFE?dud$ zg^Wn7Cx1rim$dmalF}*$Vmv$(P(1pj2CZBa{JwftWSB>*vq>Dy=E(jWosoip>Tc0O zYyZ_Z=qH*+k)svW;Q|!(bz~*k#PTiYL)b2uQDMKRHH}cPX6p<_t*4M zoYtJeeQBXw81b0>B~^Dq`R9bqR&G)14fFICvQBflTN2uxLwXPcdDM`PuR2tecyZqQ-g9_M31k_T-j&W?!v=C+<}tiYyf{OL>z{#A(7sDV z+8glS`SH%NS6`01^`$$}!|{y5M0{nCchJ_7OQCO|dxtH8@i%l&_A#`NF}=*Tx zIb}Er*Zr#96i2HY1DOiiP$yD#P+k0d_1*T(WCBR8av#8plbA-uRp%vD4_f$SRjJ*> zlfP~T$kD-HReZoD8suI1p-Q;Xmfzw;N3ub7@S5o>dGWs?rz@;wC!dShP z^7VI#)LKSG5EoX3zHf5&I&Z%pS;i%vU}a!DO(U+P22}~jqyPOa@p^(sv8i0%-m7fL z{|g<|EWqUQZ{GUV{!ryx&KqU9jMtm*c#JM0aiqXI-oeTG%OieaKZh3>==MLO75pkI zS}(GpNGBk|uQYdTV*ZPh5gO7Ga`KUs$Y_N8f0I{~N8^?Zw5Ob33hEe@0b_PweF?TQ zMlI!|@E^E2-r21lqjdu`{R`BLE`XO(FuQ|z#&^!N6oEw9gMCZ*bk2_U=Ebh|K%^ZnOIz7;c z@n=A#Hc-Bk{nLfB869$^TD&MJc;F!r$4D-N&c{kEI=df+)_$IK+n@dnPXG5<9Xa=d;D#@Kz}Gz} zQNK$_vZzr?Qn}{ib>$l~vQhGNC#&Q^4aQd$dh$2T7s_^SoaOFUU*%Gh=`~`Ta5J^e zpD%5Qm78PYl}mj>7U>p-e~EiKOW1)#wc^py2_PjUpEd z?*nUC%_ru!KE>!VNlEtE?uQD?m`_tBJBgOfqb`E-D)-Um?M{#<3uk^Ee5?qj5GrZ_R!9eeWY0GoBG3>x%X`o5}kdU zfr3|x*YX(C^iEXhT+XvH=~Ej}qI9?btz;FB96r$?Yn@MMEMHqgD|iGq+-(Ar)72{IDmKMCcCj+h_GUoVk2eHSPj@9qV}a1uYd^&$*DBLG=d(qYQ4Dn z2m8P08SaO?7SHSG?SoFJsroX}E=M{Ft*5D@%Yk|}z6kDyaca^tPk z+p3W*c@XcV&vwbOIZboLGQLeAk~t82D`tu4utwgdh~oGY_nzFA{M7v53OQ`3~;^d`ggG>%Un?tPQ3164Xz1AA#yyiSu? z?}tq{OKL_3%NqfB2X*p^aaeThn4hUnsnjVx6cO)+E*ij|DC*(2sROgPH(lBR^F@v_ z|Lvenn+@3Yk*8+4{8m%wQqAvW#~f4xHX7kLlzeXLo47UQMf!xLGGo~f-n~E@kZty> zZ&X0cr(vgTGUx|onrqfB&2_~}u znpfxAKUqBCc7x2PPdinosGmnh9$n{_+R|6Ny^OE)WVGXBWo=dNRK1XEy)W{k=78N( z>`JOx!wl_;34x!G>{qQcDzj$Z z+85E!AC~J$b^R`MH>Nz6t{B=m@TNb#qSLXPW_Vf=!O_AASRJ; zDB=43V#!lREQTed?|(08?UFU?B2(fc|LOM(1|;&}Yut#b2~->sUGj9VGk$1BFx8?R ze+{h{PVjt|%kwmm;o-9=-g9Y-O{6HAF&NlC?3$7Orr11S5t3{e7cV7IB-ftOK(#|O zfa%NL{B4TPeO@*{Q<-o;FYy-*Dl6d9=7s5RjUDoB$Rqt-nG{EfO*EcXfN;Mm(`Wx< zB-1ZsK}d5rB&$92XBtiI1@P~?@+K1*3va%;4VLrKNtKO^tpalUz%=Y10Sh(S+NA_tlUvT=(O6URh{DtdVgoFkCDI_Nz{iZhp zky7#za4Ymcc|)?iEmThyQZd=s3hFbJKz1AjEX;-11g3>suI$>m%QT%p^Uy4~t9Pnm zY3k!ZGNnI%7Lz@IHx*Bk@1Qv_205)ow~CTuW2WuW0(#=vA^&IS@ZJQdPOkwubA_r9 z`nKFUui35`{n~!CdO%b6L(B78qIoB?&t7A(cuNVmTdu&mkV-1 zo#9}Q46u=aDR1E3W`w5Qwt-@WdiLH@rMfc*=mnhOgE8JaF0I1NsrYSO<&JwKeG|Sd zXkZBeK%WBz>s9`UJ-v%`m|+x8kWvKL0@lLSTn*2TT;Dmrk=&p(Rbm&%u>r%}!OhC;ioFy;<`q-`C_z=n!*tMrc-8 zl)zAz^`K>u3Bo7=n-=1Y^{$4|8>Q-S8lV-%EdIX!OM>_Z1Jnu3`v>pS86<=MZ0Um9 zLk<|Cl7cICWh6}3idpl15MrS{^?g3`5EVEg1hW6q$z#vodRTefmv@%(DNxd{5iOxS z(3#!KQ<@`qk)PNee!hD8&!nnzbojBz0$vikUauWcX0a}vz$-KDNW{Wfl@x2$fZoJtUGrw;7@r4ekJ?L2STnnG$ee2C{4^;vV^|oOXG= zrml}We`$u<7rOZpg)&P2c{p@zK+Qi_RTKZB(O=LeCas;5E)2OhC?8|Ka4~!8_nR0! z@BN-1IFq2jG{m08(sxKKsZtEge6r|*knPgsFModetz{+fWP@mAQ+nB(3v`&}oMU{S z;~!yT$3RqLAeXTaTtTyL8jog(%_oS>{MF@oP`0+5swZh*$*j&)qU`LyK|ia1fpP44 zH{!+6cRpmWyB%m>BE>9#%}g zL$tCJB$vRB0dw>F$iRLUQ1*L7&wqLBs^g=Vt248y-vbgbEuQ? z<8O@MWnt%;Mo*tR=s#o~w|5n+tc?$lgg&U=@|igg%0&A{3rJb8fxj+~Pxntn>zT=I z`Yez=)2I+dwU61|#pktt`Q81UU_lgl8bhtfZPgn_jtaE|(1c+BkcfN^$!z*;GjTsl z@U^eqPgb(TLnuHk_hoQi=ANq&V0TKBnJ&L|N$%%1d^@P_8)#>j8&mT^)xfR!AgG!b zH0E|jcvf|p?9w|wzIBNdp3K2tr;}*c#9Xe#?V-^brrCc5vBBl1KA}4y7<(B*3(i2M zs96*)NytVyPe4YnEVQ$Ko(XF4z$WDM~JIOn7WZa6hewo)=Jac|&4&Q&NU>CjxN_BAmt zxg>89m&OoZGU7^*wIrH4VbA)!M5BA+@pRCjdo@pDS_5=bf;kKLo;l%~mq?|Y3OH=x zLDfiiT8~&imB_lSN=CBUzdbFr3(30nqun@0+(@aWanDqQ9%@4mHH9FIZDZSP;%ItbKcRBFu=<9wSVw$#_O_hER!9t_Gt4M- zK-Sgb zQgbnWf;0jKjCC65$3+M61X(DN=LHS9QKk!FQ1=C;0}cPf0aP3zIotzWg9PUu=P*2D zs%5srJ^(kV5@mkNW9jNz)E)*{{?X*G9TR~|1XB_&5Z9qiDC_)Ak09r3)zJfotwdRm z9Ex9bwGXp@MB$VQ970BeWHZ0y!S(;?G11niVRvbw(~5D*B=R|}(txWtZlPs~I!>h! zX?M@*^xTESYJ$M4h$uo|&s8$*p@XGw;5!%Ynob8!{!yC!Z^vEbwwUeU>Ir6$(HAA} z(jXF*(UtwxvdBqz770g*4=TOXa@I8eJu#b;p1b8r;rq+*Jfi9dd~0GPy-ZHvm;iCz zIF?V>4UV~t4%Qik_#K*}y-L+x0{N!OJE7_b>fmJNu+?@!#7?HGG7`Qaljq*XHS_RD z@cPvL!6fm0bo3d&-vH<#|uC14zDs<`+%lp4b-YNYrYoPk(k!8k*_mfM* z>?%ZM`}!TIyx5jpM-PLFjMS_s=#KH9jA{;qhtUB8)0G88kz8jA<(ASpNOokzL({Mx z9=|s(kzzl>I6@3n{Oi3?nQRf1r=%j`Z`yfgNvRCp&v!OkjeK+p6bed2qe3=-$l5$5 zvD!Kr1x-hbXKNPl>vKaJ7x6jN!rh?t%j*2iO)S5E-`LfWtTB3Ex!gi^%;OOnt5F?t z`KggJ`$9L|_=1B1mA$9_cTCixQ6b32iK5)U5SDQ^AN8R1_)W9<^hhRL!lDGdE;A^n zPhP)b|Fn;B`~K!)*N-PB-pe)!p4lz*x=^t0)#p8hU)w_KjOjfO*$a02ep)+D`Angl z^}}1R?uBx%;-@38smyb{41yMt!+KrCMgw<+!_>B+gzZd)Ox zei5G@B`Eo%B$> z3ad#Al*{}?T{zg)>)&~UC*m>mJIq+e6+8aods<@`+G)eoI#oN&Xt5b(5FI0P?cX({ zl%~42E|=ZsPLyjB!RrR7*KM`l%#Z9uDTxiFxnqw7uw_Y{4K66j{g~{&IeCmaX%INf zX;-8emxyovM#8ZzD>>bqF+B3ua|2WebDH|9rBl<^`nVmZ9ofFP*-ZC zQYhHl5Kxpbz3t7)4V>brAq1A7!cBp9OzusLPDR`u7h?sdH?JeTmO zVVJvWeJ7g!ZI7Lm>=sZkRutsdwpZ;O=1b?REVsjafuPG^U|u;D!}`fJkWlb}p283` zwaX@U6Pf-QXOM5L-1kdndKYAP*?CN4c-UBxgKg8qcUf&)7s7~xSPt1%_^x3VcUafz z;ka7!Of$`S5GJs({S+B#1zJ*U&-~ivBKYnevQd{^MPeRiFKu`J$4H7W%A_-o=>ePB zW|UY~7W1w;GD=e2OB>f+)Q6^v^M3zPZqFwZAL=%NtP&Fk=6KF0fV8gL408}^?#K5U z6*Par5EN|own}_iRlXw|cplE{NV{4m&io$sDT-sWnQx76_zIknL(L$WsmaR=fXy@k z6@ZL$SG70!Q%#pbro~m60B2S*)-t9v?z6I*0?}L9zVUm~M?KJq&uTE8kNVi)8*pKW z*B|F0kscWdB9bidHpOd+kj|vS*4zNI`T3Uteup*BiL#sfx2!HLQ2Osyahn-7c_jxHly{zn3^rx+D`e`C?`^) zRz9)3OE0%*M){f?=$|QZa%y4MUq^K1?^>@r7&8RG&YR4BPW9tY14+rWfg{K%tckm> zl=*6F{L5Uq^N~V*ZYGRSAHMY+O(FtC;=$;xZ3YE>q(y{0yweYte06s^5RG0aE>OyN z$@S>9^SxU#O&QsiSBiOs^4k~QOdCfX4Jc7pfvDl1xu~CvTF5huw-vJPkkY3p)m(Xu zS6&?e7b}8O|3w;%!pc zRPW!z)=@?a1b{sGZYnx z1G=rG-C2-dS3!2}_;*BtyMN;CpFj^yvrg=3?bk-OJi%28jw$fTDRM=UsrHIoN&U-d zPdx3PIs0vWJP^KTQ&YF%yJ|C^$+MXQp_B$dskbot-v7f3huPea%aygdTc7VqUK~f@ z(c}V1`9MGMmy@-QoC>oh5MQY5%T~V6Y2}PKKwU(}!iaf^w?uU0B1(UYroI%Ov@u`3 zA23#5q)K~<>~Hn)z^}W+Q9h3Y8d{`cf~2@P8?I`dgsbpFp_#(Q-P&`5F&pxh}KxRd;VsT#NEHKk6mK>SWX)Oiu(+|uu&6Z=+g6eB0>C`LqZRpsJm z`QP;ZyZA(1SJA_gb!jb@o4W0Z!hl(TR|y_^wSdSSaub+HTw`B9W!zqeW^Y=pdkxBv z7buTfjI~ULC6xWMJ7a^(o&V_a^&BJ1FP>gOa|+sItbQETbbv&BSbU<{(huz}Kl7ig zHqN4R=m{XUSpABI{eA^K%BoBZ%)G**Mr7rz922HBFTF>tVT^JozcRI;+I_t?4JK&l ziaH&Y^4vD&zQK>12u5{BSx<8V$!no(^BhMI?sb!I)M}r*eD)3M_6yN8a#1r1{^0)F z;%JL^T3LAUk0GjnzTdO72ZQb#T7o8&#czb{-TN#vPkT3kA%Kc{gdOrG~c_pcUE zIcFF2^+>xzgeKccX34$G*%wrURdoGXr_TnV=bv!UDg`Zv$djjA4)e=b6k`pMGCje{ z6WuuVM;X1_xlw2upq)p$n|UT8S5U@T>mZ!?@Q8zjCCvG9xtveB8)Z0Yl){?+))IPd zswOb%oL2N4Gl+V_Q0etoloe`~MF|v*MjM~jsvyp$EuX7m>6k72%ssD1ES)F{r=Te- zKjk)$4RW7KXY5j$;l1(79U74kp^RE=4ir*+Z~;isAqDcQ@Su)!FP~bGOdR&Evges4 zRfWh}4Wj~^C~(2Z2HpTF-Zk~{LmB?uZO$I5gI|}Erx*M#MJSE#f#ySGZ7+@8v3O;0 zL|f5YNcC!fv5^$mg_bN<&Av$Zn6m9HN17nHUKXBV^{N^+zqyB8qT-YzO1OK+;{2JI)aS_brQ;uI`ZRKIt{- zn+|+W-<+10O+%KDGp7Ow>*ADRpEc~Bup+y9M8eJsSUd*`IrFyL*ON2C(QS2x_LW9oeK z2lXX8{d_zl-}$%sGo`aT5kb4o1>~gNLP7DVkvI`#LOCmJg}+nsA71qq<3W|wRFH^4 zTS2dBX%vDkMi+r|Ux~klldb(ktYosE-^q#0evQ5TTIisS@qL%8xiO~gw=QV7&-Dm>3w zoKFJpZyc`!tL@5wGKFmHcIul3#N&n1VUu%O4+r9~MI7fdOW}}`=?#>1LO`*T&_Ydm zC$lNMXy)_DNYusiO{b645(AB|srLF0)X^-VfEfoLnq$pZ8-zo;D?#&qkErq6&cfEN zgP+Z!yGDL~9Y_SI{}aJ0wGwaF+3Yl|PG8I8p@X9452WwBT@|nW7(_v%&y$r538IJX zB&irz>bgVMp+7le#zv*lt$4=mJ-u{B=Y&+(lm-VY3n-)IU+IKd{&K=Go_hB(BgEW! zi7!%FqNm@i&*sldMo&K0Z4~EoO9ZcrW?yNTY5DHR-S2>_WQ@I@lJR9RQ=2Y)y{*sz z4qw1(LTk5uVmTyvq6W#b=IdT&tO>d?YF<^we4#)QYC^%=r%&31E4?pNN03)0e1ern zYQY9SUYA}j|3D!NV4D?1$dlp$iH~N>Blw#Xqh@pOe&)!@piqtMe#^h5xxjG}{zJj> zC-%=6Q^O<^jZaS*$G2wvHz5$sQqhqRP-VCR_44!ywQs??wscx$)=YaU%DCOsDC173{Pk{f ztWr^}-(G7k6G8|$k9*e#O1*9DLIutu4_GQ8O@H-B(D;B~-J96jG`Vc7!G%O5Q1~6C z1bPZ+W0R7Ges`^1W~{vuRN2lRthBt&6PH-MICMntj6ObQ{U8EFmlt^H&oL#GQdmh& zG>^N@T^^?x!MmKRyrHa#n&a+_o>LS^IweD?8AS(oT@;cok&KPMHXh7vPkEnK42-e3 ziNZyzJUfNj0M`6q4)N{tkIK&@{;l+scwYGnH^kqs&(x5|LZtyEZ&v7B3Z`pk@9=~~ z*s1mGO2^gK)W31=6lWPEa9aXdAU$gVl&CWJwllp-0=b(S*8!cnB>mdnA;VL?={3|G ze$<>gtrhWFAF}y`-+`HDx8qavm3HP;{jQI_P=1X%wUB44=^1`~USP>(B3qWbBUp%Z z34~Znkz9U{B-SrB*G!(Ps(J1EX*zpOZ6r>M5ra16b{iHb$Y9n1m(|6L`gbC>n@JPBW6W|* zKdFzo*9Qxxno;ezf~w)<0m@_^T8CsHuq`?t?wjs~_7d?< zgcVsP&u7g-yu^Q9>dOT4iiBehjr?nwd&7V>S{O=;rjcAYnfQ-0R_wifu>^YqTY9`U z>Xv%P9c7Z{fQEL-Q5y2=TnG~$Y%O{HAo+Wgy@FZ6SOO&q`U#Ps&!ZuK0j}Z!N<}_W zQ|I_v30g#V0$$U%+j;~v*AZnj-*NDo0`)&iu5J=*`nF4*f4YtcRSucO_AxWR-BjxX zhRXMis1loll@}C5q}_bDs%@Fgaup40G}rfrdO}(wVmE5{+U+mkc5k0H%cCwOMk)p0 zjt`Fu`qZwdD_$M`6*ntSZ{A)~$dcfg*zjjoF5M*=0XvHIre7CKzP`j+D*bgbS02kr zm!Z=cDQ-)OLp0^C4JcyafLLT%#|sZ{shNMc)``{p(nvp3&PORLioDBNVT6y)*vYU^ zt{d1*Bic+aDZs2#AY~FCGI;U9g{;}H2}J`XeeOQk-v4sOzCg!Ctk-9$Otx{^!f^GE`1{@*dM}*4UWR0N6o2G zp!SkJ^&J(xO&z)1@V(}QEnmjvN;0DXkK25d6g7~y65Zp$=D8jbyR7PP+BaFbXCtJ>`@eM~Hbj`ghhHcOn{N}oRrQB5eN?yV-1nOv zif7K9L2hV;*d3^{$)cS5qygl^E}Ggao%N3;YP|m>S6modyqGUL`B5x`lYi0#S#zRC zTXAbuq2DJ)|ApJqG(Uy+z1M0+Gb0L{0~Jj-E_$9esETQcOd_7KpNT?0n|QNYGU3UzR{f2E$bSJt}PJ$lJ0l&sKM87bg82Wxo98 zBMm`)f<;Eedb=gr#eDnxon_v`e_mE*+Y?s;J_n5b@9T^Jysf52%79cuN^pNE!+bjf zYs)m(lU+@{nU^*WfM>K*|3A%KX*iVa+eh^%iN_Yo zl0mk@pzKRR$d;0AG%=PeS;oF(Df^nrmYqu3myjjKl5Ol{XJV{1lRZY{f8Epn)BApT zKfa&lnB%zb>prh@xvq2hoo7ogK4jS&zjiGHmijz1TVXLm1& z?H)znsDfB{7NR%z^5yd*YwoK`ucN=fNJ<3H)=uRXMdWe!*fZei3NVgBd{#Buy&kG8 zLGAA*Rv)fEALQ>hT(BNNn^CQvkA#t+E1&O``uTRm(fO?3mzm59IkF=@>vu=dZ(xj> zBIR?2#1b2!cnfBb%g#Wr+xcKqVqD|O{LvFd(!on6w?X@w4St z+I}}LZAMM96toVMs%4N>M2VksxqPsx{${KpEkYsx(e6rIyW+UUG@SF?G<5oEm^Iz0gHt`z^BhS+0o?Y!q8xO(tfNhwaZb^Z)xP? z<2iDWug8bWEcIEt3biVfSS1O~5*=H)%-ci0OS__aWX$3mJ6DywCB46xfm`kq6hWzN zg+-NUgmK|i%fbjn9_Pjd;@%B)jUE1Kc~U%6J_+cB5H<{n0W9|`|1t8TyG+cLC5VnE z({1v;ms_;D9B?RZUgP2|pB1SO*>R-4TJndRanuosKDaAh$qs#ABfZZ-D3&nFNee+UC41mI2SgGKH zk~6#9$4QD70#((Tl4k3K2+}78cWNbl)kDi#eAFWO40bb`oVxmGf6-*YISZ4Vs)1nM zJJroCWxY9Qtfi%}43<+MFBh2W(3ULaYYTIfJM3BRl9RH)rQnYpF@=dPF9Nqhr#IEM z$XC&RQhlG;%HfJY#rs)(C%Q7dqoj4W#aTZmjw59!^i%L$e-va2`V8Tg7B9 z80|d!Gj9h!vWBdqH-AZE@Mr9d~ckq60JI}VYEF?IFM`q#$x9A~C88-m_TeXauo1Zi%)QCJ}@#2iw7^468*wTGC zB_VXj1FT6weo*c8{ivnx&a8*X+U`c9RbMa8+a253&m715RD?pL5vJXdPf4(KsPkMk@SrsU{>K^w$K#y7F>7*Hs$YJ`Fi zwWp@qW^&4X38=os8#9?(ya3~)B|I6t>LsR1bTq>74M6&-*>zh}&*ocioKv<^DmCGB z;p@+QDb7094JkQeNx~0b*g+#nxBc~%Cr74yXoRBj-EM-wTZANRs)^#-RAF#8 z=-&Yv+-Qr$JexznD`R0W)IEENIY6e7^vL%p_5v#%lonPv2b6C;s$0*ke(8mJC(mt7{V*RH+)7 zxunkqO;OYEFQ)>HK(BjJ@Ont4irfa6Cx9QB1?V=g@vn)Y)`4c9GS^p}-mWHIn=yV! zGY)?ixx@EydC%Ut@$6b zhJ+hcc#|eKkxX9OEtL?VS9){*oU+PY%N!&)N0uym-RrgkH2h(~qz+;1#-_9;EdZ1i z7*BWj=S|wzOr2se-h(oprxIAQdcwNh;nz9uR&gR+xksI-v&3ujwUsueL9XQkjSlq% z6UPLbdP3m0z~G)F5$WlA&!Y7c01K7zEI&#p7V+`f`bvAEhby%r>fOk-LophD?%=$n zT+-~|M|tKeYk-cMfu?{LVZrto^RX$Up0`CDr017z>(}a-H)n@b;Zv&vrN_g?mMdT* z?~}?;w!$(|7_%LZCUzuJi(%ui6rk*3!4;VGu_=1@`X=a9I~k+IN9nG+&wP z&XIK^Oa?u7hHrl=!ysQNRZ!+d%iyTT79I#1O%vav!w*Y*s;O)#L|mKnsJ@+YB<>TO zp?DhBBCI$ofx=UQDh;Zq{7=?f^eheEN)lg~k@$X;zN@XWTe!X5{g zYcJ08PPD%V+$NMl4lZKH5n2>R*=2?$=u)%G$j1Z4HT*)rhe^2CDa?Dr^ti^>ZyrFg z9{``!9vM)9OqR|5Qz9RKR*oG3{WCs8r<)hc1N-N~+(PWrBu9eR=yNEs3uEMCd^xi3 z`Jw6}nwaGyDqNnqqTQc2G_Snz=KCJc5flZ2j?juR2^TC6*fxI8$X~GcOqN)4=taZJ z2Hz&mA1S?wA=~QHiGJRwe&;UIv`ofxofJlMpErZd!o>9GiZz2D+IGx3&Gc*JcoD{P zNr*oVmrS%8B*@$+%4w9W<~JgoDX%8P@gBB65WLU+8h2s^_W>8t3zd&St*hM(+gcI< zZ97V2?^}hC!X0~Fi#~4VX?f#j`ZTgPuckVhm9GWTqars~9^=17S(ipCc8&1c-L+dc z>FxG8QnFSe-|uJK1n!Qo)donPu+KdgDGA|eb>$AVv3xWAkN`&lipXNa<^+Y+ZrDe5|p(*FRbl|)<)lEI_9(83s})M67!@n`F!zGePlz(3G&4r zX)PjqE%S_sx1`lP9Vnlx)Q8>YPuSKZSiR=V)La~rIh_zLH!iEJfA0u=`mDEn4Gy|K zK_zyQJLp9ec+HmNe7>Et)eIZ=*2`Ug-gi`9Dy{rYn?d<3sL%ch zz^YjDiu4MscZKyd159)2=kSj@MThG~bp4n&1uAQPbNCkLFxb*;Jb{%g+{FwK@?$=+ zG_Y4Wu@-r8=Cf@o82ZUd``8*DbV*=TcCi^2iJo$yJH~g(Ow-JoY&@31C$HP~ZdnxL z{4>61&F%RW8qkDxYwjJ9fxd>(fsYY+Af6) z{Gu4t-CU=ek37=vw$r4z$)lUdf?>#(-Q_Pqr4VgrqAlKVOb^5*y4O`<5QSNYm}^`* zaUvP`7Khr1F1A|U6|ylgxT*Wq+uWGp=@7;B?X!Rutnx5(Ub_)ltLqgX{3{Z};Jc;X zUh4PlPjMwoCk~`R<`Vfy6x=Lz>GW{hNzp)LU5s3}$SR|3jHBXqq@F(J{D)xs(Jw-l zZyg#q_ln8aY$Q@kPuFg_<0#gmCVj1_*3GR)pU`JwH6@tFv-$MCp@R^M?|wU5(o?ogr^934D7 zvPsJ01XORO1p(2V8n3hRZe#M*@+JF3^$n>{3?o1o9*H znh~x)pZ2XRFm>$Z$)ZP=(W1Ir+qFF6Aq*-(2)V05!IgMqfXM3 zO^tZ5qp;*o0rv{KYh0+wfHmrSF4K}o?%%*|Q9yE=f=8haIF^OnqIAqxU6a}s`vWl( zDr``mdRlVn@?Sg5x!>Sq>EP`YM|Ax#eTQr_d{S)OTo1E3j}Lo{fyfds{guQ5*_#HX zroZD`{@?ul>*=ziew{GiCRu7zQE!ppi@o+u``mp@$8SgrK~nmMFU6K`vp7EfP%L^n za$)H#XipoPT6SJ}9yA=Vsr*{tkJk2=<40Nh0<|kK|7)(!QM1bo-6hli@ucxe41iof z8qEOt2Ox4G`;=f3PbdNum=LH~Q!s<$QLL|M3>JWBnbw!UkM3+2yEYoGU+=r}1&!); zLg}ES(c!N%mT!mus21;d!;W&^v}rPUmF{Z=4f{0(BM)q1)0Th4<_fa@D9`Iig?FUd z%#qNw7iDio!I$Mxy-KLw9w$+67ju`Ab7{(#XeUnIqlSgpsC?ELx2M;kpmk*sA0W=O z9HwA>hZzNb9vxSM-NKO)h;^}t3a&BJb7k7>At7JrDa@ck16r(G~1j%yHwf z*eMPw*la&nZ;*;(j!?NoI@V%(EMh8h{1isRk!b7qSVElR6VHgJGeuKve4Pp$r6Y@^ zKF1^5&*VsSawJ-=ch{+?bKB9X*ZG!ED9{|z61HtV{hO5TiUenK3u7xUN&i>${>;u=iPJ-HO-QWlUZ@@i?h8qH-e!zTF^MD}bWvvzB$#?H%FI~9wEtmRazk4tp-bQQY8 z9j6amkqVLAaMO$w(r+oWJ7>3iUDjMjD%LI9xF|rE?|B1hnAK;@EPc5#F(n{5-ItM0 z>ckY)sbJZT)Vi^$T@t5gD4-W{?#iiB3I~dpv2e-a>dr0MbnAiY$4}m~lyR!Or7aLy zXgnc1@^R-m$e6)&n7D1fl zV_6h>Y^Zl9;wV|l4qv8|(9#>Fo^+y9k76gOMk$wnU(T~`fxba>Kv0Z=0;Xh#8dWW2 zvrT=!i;DNU0GB8gXu$OTE%)ejw_6q)O87)Gh4=T&hJi&HFq`aaakWuNwNXeSrcKy_ zBrN@-YzXtVBh?k9L+i>@-q9(0Qx~uc%x%<+h1&#AVQjPCz3N2(VUI?pRA2wfHga~K zbLFKV4orY#M{(^u_`}j)P&IYpV#vu1Z{ZjEXj%OSl-d+XpIgR;B{9ucxM|R`$o2@d zq<(R=V=SC0WJyJC5C`V_bguEcEN)eAAs^-d^l!gtsa;7mHR3EMRV=(M__~S~s+aDY z(Iu)G+}IC+XW;l!3*a05YmcAEp78%+_BZ*h#bXL#A1Q;J0(T;qTTY>+uBTS2`ta$0 E0LgD~`2YX_ literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/html/_images/chapter11_58_3.png b/doc/LectureNotes/_build/html/_images/chapter11_58_3.png new file mode 100644 index 0000000000000000000000000000000000000000..6d89cdf1ed3793fe53f5101867d7685dc83523f8 GIT binary patch literal 29238 zcmZ_02Rzh&{5WpQ&Ww-}Niym(&MrjBs3fw(*&|2Jb_hjQh083fGPC7y2+27@_RP4< zvqxwAU&rVB|NXv?$N%q950A(D{k-Svx##P=)YsKyqCZPdMn=YTM@#(y85xBu_-}fO z20T$cd$|Jqf_iEgc|LT5d3sxU*plg3dAd8hc{)2hJ^$R+1McAF3X!-W0l9kK-qX_^ zE-xwR^8W%zxOvz~V$;>T01`TPEn_$t83Q}%KRMa^RBke|XIXdDZyF#{m&d#j9JBvg z*9dQJU;aRKi>Yqs%J~PJ9Gv9$3oZ|y_LJ09>Yx5K-8J4qBf~*$z)?%_ann3|pqtH? zDI49O0*gP*ek#u9`5PkKtR^AN`}sC1ZD>g0;rKN?pCI^Q+i%*JP*n#%9=98Hz%L>7 z%hfLgTmW7Bp!mK-; z^H2dR-b$L*uu!aX!h}~UBV^GLM(4ACcDi$Em@j&u9h*2~E6z6R@vUg)&tjoW*~;FQ zugD*pN(jub6T6*kynClVZn0z5W}Gx&w?0U2?EnRG5$ zL!!F6m49G+C`KZcV3k)&(mo|wrK)xK=;dZa9iZ|jVX)ZuLz*IM`&O{+jL`zoK^tZ@ zTulY8h7DJ9LuFCknA)rU`a|~)KRgtFm#i@OVQ@qYzI~34@(X3uDBWhVscOSuKBaaV z{Bt1JebtGPiyYxTSO(bh3#)XiZ2HXhjC^F5P{t_6EL~>ji+9P#kO!E15T^u(gd9qX zTM>cE9mJX+eoq?IW8T1ZReUxn3uwOCA@+kXvdD%J${-4b;2PBd#_89z=~Rc9k;ovb zY%*G;5`uR}5EF$7$8<%h#$z^WDd;c(m`jstllLb#Fy+rFH;}%VhG2C|es@^-*&>QV z`siA=YGt*N5Aze8h?U!uUl^A)koaI}jIJe{{-)7JS_^SNYSny+jEkalr4=UVdY4=7tgnC+3n5C5qFTU+6;Y^x z+2d&ypt|=HcFu{6nfp{h%Siq|%kb?I#@_L>$$5jSBf}W@4ppEo6B=JgxlBp1{F)-R zn7W>EKLEX`H@7p{kMVD{yQb$AOoy~>px(WzW6%QHmA zi}j(av9**P)*`Dsr_(+hn4`Ts)hz!pe|pooE;qHM-0OL@$pidIha1?7$)`|V$8V(Dxz=RatV&!)&hiN$SSBcL+xWVwhtCI) zjdJe#T^_%E7|!V8ojUn%W5vcGdNPBNw zt`uICBtGIrDf!(Q=L!|DuH6tfFS*SAsZ85)cOG#e|B+=){jKvisE7H-lb+mRCh+f5 z6E^PCOI~Kg0y7dwHavs&st*j`&P94<@{FJHnz*;IL9Wl|cCZk&X0nc*;1L%WTKK4TQMe|zRYN@HB1&}i(uIy=e!;yYg-W$e;{wbRZT`H;|Q&SOm;B# z@&vt|z0OlDxav)p88AukMeh9t{_97%c*|h!2}F{&bexONrM}dRC1z`!wl|hQ%`uaK zxm!+4Xo!?Xa^_whPmgASye3jc$iAAU+t*D0ptM0>OCcxHJY5$28`)6%=b$ZlO{GZ_ znQ>iFSyJBwG5PGCCADN)C)%HGG|}oG5qe!p=+Cka14FrV*VD6_X@q;t3R5oKP1hND zZ%(RsdvJ{g;#R9!OH@|96)atH*N&*s8J&J z6G8D)3^bp@sx;4s6oigQV+MHA{lr%tCfCj~N5oB=1%0DfT&w>iLY@QK8DlfZ#~Jqz&aE1RSIYAVSEv2;&1l(> zr!g0ikE*F00c`VgoS|@Q=aP?O1-sg884iv60LEA=RmYNlW|J;pXlnk$`lGJQu zA_x@RIDe_RBrn)%NHK`pn6_%E|Euh&{oXep0_cz>Z$iDC6_CrqnnSL(8>3L0vb09x z{?4iW0Em=C@4gL>drT#>?b<)_;ANh3u_`}3P?0-&+BNr@kC>vdV+SDjjK68@MaytDyO?y#>49$gyRbpT0O<416T!0FG(%M z3E@pWa`Dc%)tx}gCQRXh3lq z_ocqs!^s6Lro!h@b6@XrO~dRS=KlLgiSIR_y<+!enj9U)@39a$YYlt+ekhf(*QqI< z04(44uVCT=CYiDKfWdA0jaeakurADymC(@I72Jz0pcyxR14XXs+8l_!_P#tXiXX*g zVLR#&7Dc^S=MN~ev`(jUzGDT6^Tn$7Ax?I%-)r^fTlr?C%lwY6z-LP37w`*0{X}df zRiIsk>*Jr@>1kIG5%B9*&I~5<{o50Z!at&}gyJjhem(zAB&3dnR<$Wi6El2x0`F-vIx zA@pTPic0^~vd_?f8+x)~Yb5U~*N!+|nHZNE0<^r}pD zTPd}hH+=c(u*da@2xqb{G!j_3?6c!RPeq*g$E~KKy}rxgadhQ`76lG>t(L2~Ydb{V zQ(SJ-2aio;Rs+S)+Yuh?Iw~nVEc}J5*|PZ>od)k%laZ_X!%s8vy6W25=$(n(59j>_ z7rUOL;Xa_Q>n#-i2PNJ(BIfy>vkSSkM}bz0(}XLp66w$@^5^@pcaK%&25VVk4oLfJ z_vN1D*$5lc2<1kFr6<3kkLeL_g6d;=2EKYB@a!XV_mo^07I(eO9TFu|oKdiAt-Mjficy1c*}-O4aRc&G+LMr%O$u(p zbXwA7Wk?8o{X6E&iXUbJW(buE%A=|0h_$QF`xBr=kS^1LEWYwa?DW1#S0L!mNI+`4 z(1(*vodqvZX>9fxl&RLRuSliGRRY$&Eo(B|cYxz^jt4c>OzBLvV{WHl)>qi=wVM>O z?~C=qFHO3Picp=4?b_tlbw7B9drd3RHo`C{k^c-^5EO3vjh|3=rt22hU0`&j7`w10XN(zj;@!rlEDmrVwqozyCGX){gNd+(}tyob_;Qxs;||K zHlg_bskG)j1Iv_NMmIuNo2F0TTvy*OG!rA;lI;zMm@5nqqdyh#eUksFE`=a=$qK!7 zK_tdWVLDYCQ%m+&&C+1fzU#seZu(mP2X3@du>$rg7eXka!Wu@2y(+QF|MjAj91{WJ zTZBrpg2f}IR>{V%cQ`X^PW)fGRz6jr8nDXTB|LQy0cUBeQalXxet}a&i>cdDhtJ*) zs9lqZxwux3kZdLrpm{6IeK+_CacxJdxJMmp{t9^JKV}Y|GUMjxfi>K-C;m_2Uf;`m zS8rJ|pc!sdP6m8Pq>o;|FwR+=j}%yAmOba<8?}l%LPb|i*}wAEHFQPL5$cXW2RCh| z-z~BFjd;p5fKSe|M|m}s4#7M4a!4`!jZsi4TxH5EV6OsIfqVM)Ven^IrHDS!1y}P3 zS5t_vSn;0X|5$tG?`&$vddUa)iaw$^dPl=!G!;HUE=k!imA0w~?e;t$^-S-1U6*2A z*D7wYmeP&iB+NTz(E+*hC+;C7;kN`j&Wug21uCo3E95;Ge^5P!>eRMCdan#WMZ;HJ zS^72@#`n~-R=1!2rjdaD+G`$pQ_JtB*V={Is9S$rzJT!o+D-R_`B{?wA&$-Yz3ywf)fG@)`V}^$EHMb z*u$O&PP&`(pzGwVIft_|8Tg)~nGl*E3N7!uv&V<5_@dP|#8z>iYZ@m!)YlCyyVjY} zV#yYp72NG!@&;Fqd-w9Tlh&Tftj)vcgK3RN(e2k~1CuU*mmc>ZcDT_$sZkwY3iYX~ z&PqE3m^4Ur%AH`5lLa; z7hz#k32)vUNaUzS#>8AwR!;x%;|HIL=J8CyL+HWK4-riwv}uuYiI18}&=eTX>s(Yh_> z9_l(ZWID}zd@R4qbQvMD@6IG=7ts|G6b#7-Iz-W)Lj>Q?x;?w# zmwh}Ex-dJNWC6n_Un46psfq#mV&&xA+VQa|G^v`)%Lt@E*W)GXcc03*j{ay2r7c^6 zEDt*s&jQLmxJ}ffj}D3GgY6N`fCJHox!pBzd_x{5FE0ZIm!`lY=YGB;QM?&@I3AUh za;&SF>RFpEBXe$*Kt+|KeaIUTy$|hkxw|&)v-wN&=vrs5uEOiz`Hvx1O;kNSJ@!4>?f0GBakfM6+8T}y+`f4&wkBV* zHmdWLHmiNEG{4t*4^NtcY5f?ifs5GweER{McGVo63~1$p?_YWJg-ptSch$MAcKxSV z&1R2w&BB-b!*g8h?9D4|2pG4$JVH9*=$wpw_xW%} zp7os;x`^*BE!RB%>i^qX)C5*qv->BCyc*cb-ax})i$h-8?I%x$@8BHzvCt$DcIHbi z!{yH+iYQ3qJob$Ni=ba6R%#6$KiDn&*QhN5wm1a>cdhE{T@4AJQJtQ+igri;v}4D9 zF)Us++T=YE&{q9ydS7BT`B)d(`hK(T9`8$BX!DFoIgSfI%E0)HfHMAw6918V-~mZF zv%A-eeGkSG4lr%3a}8=N!wOM=I+KJn{X0HIr9F~n9 zF`zs2MmFS=EnY7drV1xFaL2h&o!Xbk7^CWRE^l`_1 z-lume9h@3j+}MeIPfj2UNQIkFhO!5L;kg|}D?@cS?hJcJ(N#z#H21hr)7r|)*)5R& zcQ1Rg${|BT2VhyW#IV?0r#YOdX64(W{b=iA zY09f-&a+tZh61(tEY=dOdiO`uU@f`s+r4dkE<>fZ(cITUswM(cq9ndWf)GF+_x}CQ za)(}SSy#STrEPBDlJJ%OGgRxP3URC$o6LHYaPp8eOy)Z_oa(j@_hkmOD-4cxrU`~i za8~o|lJ7Eb&!?JjBXGT{ED#f#%~OiZ^!GJhm3-_cJ1dafyg;qlFjWZTm0JB?+NlRb zRI(>kuAK|N^U41X6i=vxbKdZ&Z0m%2&tDrZrY`Etb>Ul$CF)W!=cUJsQO_Z7YS%gzVY>o!5R&-#6^H2h&cxKzRL}(3VfX6ls`~>5ds(x3i&Xu%w-UT< zsnr|yl?Qf}E~d-J(s+QmTs>QQMTsC3?P=&w44KFQWNDFSrC{-;XT8o|t3zlmi1_QS zkGH*)F#kzN0M!+5~X*b#Rg$hXwne6q{WIwFZ8Q)mZY0xIw zGKG4hILi&Ei8PHVrcb*Ae%0k6J|5ZNj2RW`Dn(0}v)ePJcfGP-5lwc1Nf$wmbV^lN zN#VI8qdQY);NEeuu!~QXVwNuB-}__AW?udMYhUR)_GLAZArPc+(dhmL{kH<&7_SYH2Ne!>4ccrV$BVA5tqBPU#l3wy<1I>k%hU4)c+j@R2hQ)C zL8lCE_3%0$?NO6bFP%?(e0*PlaWCOIy)^%oPBmNWj_YDYEU&%yTX9Ss2NIg34MA#% z$+`UJ+x*$=tzX!n(K$lv_>*3wkLW%{c&{+gtV3ai8`-EVmjvMfh<`T^?W9a+rNIz+xr>fIcYD66$a? zyR+Z;&N-c!H8D#v$5Z<58}~cl#UkzRp5lua;vNI$V{{rjH90#HpZbnc_l-!Sl;{{v z)Dw~#lG5e4iGF8u=1xyEfq$c^}ZnO-Dx>74E+!KcBA-@z7-#cpBbx+|4z_}I&YGm z-Y9&Sw$|eNAYghYdwKLfk*fnl`d@Lf>?=J+N-G*C3OfIBk}FKU!ln89>T?65f7kd% z7f%!VoM-f^EDgd7V0cW&k+*Y_`pV(l~4QJ=o~F}LUchiCU5 zp#L}2=~S)heVM?c)MNjS>;lx7M#=x)%^8FmjBH+<9~t;}eC#d|*$)(tu>3?MyktdT z%-HA;of$1>`$=I?h*uDM_5fUJpcgK+#<~+8X2us31 zPb|SdcarOtP4}m7f9bF6zuNdJ8MM z^=I!ZU}|VzY~IB1gsGW};9P6ichCBGgEOt+0_i&^NHhVGPejqqy=w*R&pI@l4wp~J z-viNJFc*O`5%3VuAN0w&*qh-jNQ@`!BB-9@KtFCv!cSsoM9Uj z5l=g8cGMxf&M*kp`Sybc55^7W-we-M?_OMC`$;hS**H6W;^XT^-88b0C<**@q%D|FzJgoK2o_ST~VNb!aCcQze*3ul3tKyNubNt4Qi^}x9( z-@rhthM-AvsoJ#TG{gT4&En)L%x&w%hNFJIWPkQD>c5lprD&_P+dY%}uvcsm2<5n0 z&iofIQTM;}o=z|mN(uCDJW&A4tgZL?i^1)x0T6AeGBCc3L^08oKfX~$HK{xK0V5|& z>CzH>4)gckn}AmAT*{DQCa=3DP{du|N~fmklA^a}*UoOco_JpSMOGhaEBt6qoBagU zce~z7mdhzEt70B`-$HV<)aCq4%=G%O8H4hNUO&@`B@@D=I{w_LIkg-QKHPjiYNE&F zfz7sGT*67clR(QcN*`G&{Hg@Kt$H`x)vhaA?>}{c{6XF`TfktHY@SBh(D3m%4$+^d zuA;~`Z%Noc=Y7p~r*LMnN8m&j9w-3c`-ym7rslfy(fogb#WZ))5aa2nk8=CimDQA} z@+@WUB(2N{0z|FY$mJW!0Y#_os2m5^_z?BRLNfV0vy1i23TcC!7L6-9C$?QfdhsfT z(axe{@f6%)DS7q3C@OK^T`Uu~*dL!^#`_W0z(Tw8pS@B5{8uD$PiZ?bWg87kZ0j8T zI8nx#%hjBgcBw-t(D@3e-25Xgy%WEJ-l2D;HfsKvvs*W+@pil+v9ASG{iK|(n*dlF z$R=_MReLP$YM6zRlCC_!U!)!S)1QAV#lysIvcKyjC_w1|8dIa>`<1;FOV2fiw#&A^ z0Ud;0r>?q{={-Ud{S|V#Zh?0YbrO#~KsKgFe!M@mRAXw}FRy z;}sVjS7_ZWtB%vg4?2B!F`+AOqhZE{NcB8|u+Om6Nz`G_oHUHw{QHc#w`cLqdfVdv zgfEX&a6N7|4NOBx(1aa#YHuKmXu zkj0M*`8t)3p8OJG)tScsB6AiH-VDz90qWYXI?)Pi)`Ikz;}Gw`0eCh=B;P+QM>;lLV3g%181{N9Sva{pb)a@8Hmf<0th+dq_yi{_-e97hhFAm#q`P z@F3v?)AjrAZyG9!%)=+1O6LA;bjj}Goj)ct0c+?1|N#C0;@o9D8L*H0kM5 z?mO;B*(}1(#X~t8c8~L-P3Gh!&B#+MS$`ZT2bb=a+3jne2#Du$b-T)@+v610A`xM> zOHFecC(p_0UDsK1UfuS{Y&pMOBe<0Dsg5-5YP{8`Q|fsq2^M{qaBt@0{Sv>jW1XF% zcTIS`U>jAI-AdMEdPVf%_=)mwHtNKD+?h|?gBEf+^p3v>B_4ZHcK1W~H_mAfvKSlQ z)>2niN_!vOZuVlwnf$vVmJQ{RNeA@e;h$M z1>SKu*yI zikx1zEN)eNAIS9i^XJvEx?@2<_yiR2?DK& zUiBdtYjT`y9iwco-9JJ2zord!NR*CD871twcW&ixn9KxrE_o=LvDvzFNd#iTwQF{% zcp+&?Lo<9sp8y-JIC31UV+}lrJz4z?yL;pE@<^}=(yq*bFqi5ymFo1yYVZIf ziL3dBkwmur35A?B%)D3kkY@__U5A&R4sya5rlV|fE;S|c46f8k&l9IZ`yj@;G$42i z*$_b)pjWL5bzsRDNIuf8OEzP*wOVo^1tXGTsGpRiPtOGlbUNpvm~c|)5V-3_)k*KY zrAwBu&`#%YRHxS6yFaHr81mlFzJeR$TSsf%$ehzz9-8me3XwWSaih=?2V9LIW(cDL z>)%6&Os4WKq&iKfIW=DU{(iCkb%iPiVaL8NZ4C2g8rL%{r|geAO3}FguQ|Z5*n49Ncac?n z%hUu_YRd#vCv`6Qggm~U<=(bKW&}!{(wFL7R2Me7?ca^LWlANj%TEOAYX!F5c51JZ z*lshuAXo4^SBF>Dx;5H5_Oi(A+SjOLnZ3uYTzj(pj^|T%J|1f|j1Q86`m9jiKt1;1 z0i9XZ&Zmytr&~O{W3;e(7N@*jvjk8MAU{rCs>!wS6x!Kx#vF`vS-btZYd+!nnf5?J z8`vyH-~ElL*Ufyy!sGlOl(aNAd!FuYfPx*g%c4>oqe72gyx@u5acvqPrj&ld&Pz=l zSuWBybdX-32CoOCUrV;+xa2?Enq#=b5F6s=`gnpALuynTb=JQt+4b86#mj|r@}J7T z)HJGhY)(Qm!1dBEKU92G+x4X@NT$lp&zWI&ihQv4H=z_H;9J1eXHXr(hFMlQJ)>y9 z^D7vM-T8@QZ(-{JXLf}}0FoTA0<~gN6+N?3cxyrlX=tB%np(E~p^M}9o?=_hB9j0b z(Huw2;K&8xp%c6b0B;Sk%QZMEaxUjDujL5+?g8|eQ#w!$B;bE0MbA}27S zamz*r5I2l8RaU8CeR1mTkNm|rly zUpm-VX{t)Zs_n@!g0-}e6sok`wVdjiw~mY{=lfCM5SMXv+|*TsQk#um2h9?=7%2G3D(5oUfk5 zp_g&(!i_Hm2_p3-KM&Kpn#YB9XP+I*ckMMezi?G*dQJKDP&EWKz}2Q&dqHYi$w;=7 z&;vZsADHCLLY>z}I5*=LAJ`w4<__`em)^~EtKv9jpxqltVDr%HIi+Cp>$X5sO1v_| z%c#jNP#KXdZvxQYEoO23{YdS=^gzqY{e*G)v)kcxU6{&u#~Ml~1{x9~CEwv^Ek64x z8baPjl3^N6vfiKE!01hsq(C8cjj%O)LTka$w^;AFOKLlsma~Xt*`8wp*8vA%(YjvK za^{WNOr?*PM{c~6$N zMa=Jmdi)XVgKqbuYesReQ8~b^c}dqR-$r#=xNQ6C&RNBC{c96Z4!7)LHzmKg-pBpeQArK->d3vIqa% z9}R#h9h!c9N8oY}VXnGms>bat%QrZEa*$A0ND8XX4)zjOc|K*E1|~CvWlkO%;|YH( zT{eMTl7yJp!>VlU{ra%|DMP84E~w9=hOqjM;YWG*a}xIPDH==KEE}#76>$FjZHr_7 zgI@UG)f|LLk9x%eCrvd>DT^}BVqBI4gBq&9)>&BNgA!7*+;YH%r?sOGN9aHGpL=3K z{cs|f34W|JuxvDThvRg!Q14S-~S|@LGz{2{K1Y@!;1O_>j`X|2@Yk z?s#|Ju-@iIl~-|xWEA_J*BZ>;U%5|-J@9~K$q0WeZz$JWfJ<=g)<_$!=2t|x0$xS| z-vjR8VMbI<8XVttU;m`0q)utBmZB{=4`g3LEkw0xJ0Nv! zlUtfgAae z(NU%PuD|=a)V(0uex03Tp0hwgxn<`L3W?X^KQCHH3JHtz>js^=YZzYa8a89rmL3d> zD?Q*--7ind3FE}-2$oC5NWp9FhbARn)X_EPNVU*?5CgR7T_0Tbax+RV+L}hJ<>d&i z=!U;f%fvq{vEjS7n=vs9eB9;^a2sLBG$>4f0;Yo|#Mfvl`5DC}BIxv*Evyg3!A3)f z0U)yf{YtE{BF*udqag)kz?l*vx8p+yd2vnc{F-EgHrTa5K}*fyDC?cC){^i`aeeDn zPY=KP?dBGNn>N>WH?I#ij1kzt%>OWV^3sbZYru;Uu4-Hb6D^SrPIX9OF~2F7Hu>E@ zXSMV;sp_ zYy{~q8|*H?2IaaY1U1x2T{1h}U;SD>Qhi>vA-fKYYaA1Kx%w~VWiEycb7sG)T@$b- z<8TD`LwFchOruD)(&rt8`sR@@TcYkmc=|#qWoqMQT;d<6*PydSfZEH(61Hz~1T&B{ ziB3^Qb?Yb89VqPY#x-cXiq!f5B6`9dFxhZpvhS=9{XDw6c9l7oX2ooH zpUpmq{aye&ENICs{-jraY4gGL1$TN)2@g;NzG3?M=*Amq&ac7$C zk~qWY%?nrgBoMTBA4kMLZo+LHa*2Yj5i~1W%qSi`i|)7IX05BYdWQ-ozD_t@esWfV zpIo$k{9UdnF`)1v;93HlJgtBAN{B2?xuCFg8n4Rxc4Xg;;tNH}o4oYAFuwpa|F=7J zpkt7D;LZ-!t@v|ybxETWl~VGityMyPw0n~8?>{muKl#J))nj>=0H$>@#;?UZ)CPwA zuX~AKv@1{;?cO_Q-`!E0G5>R|{;EBC_` z{i1XJ%BL!ex69Ol5G_6UMzICaC~29pC$L+zFGGnGMzo$DxZmD5FK{j68SWAFA?@b1 zGN*O)-T3qU9~~Xe&5uRWX}>|tC)q~uE_g<)#5R4DwCZ69d`DtZ>-(>>X>g^O9vRBy z_(jf_VVR(TwB8=(M{jmqfB#s#WuEB@f{EYt#p?~=$RBR8fAY?4cmXu6)$yyw5w@+Z z8~&2R5Y`&>Pv!$iyQ7EmeEqIt-k->Q8~%*F4eYBZv8_3QSLlbj{(^Bayk#&=Je@^eN+^#?9{>6ZO_D#w6zl4|Z5+B|;+BTGkPW|6?8p}8 zUgpiooevqs!2|1+H{!b=7CK)uM`u$9xeT|2T60Y@o4wWlc6L*M*(9ksc@b2C$DbAA zm#&85&4GxhR-WU2gWrt%H@tCm@Aaf#g}rs%>VPlKd+|t%AwlJ(G^$_5zUfb&7#&J? zv_Uc!I^#BZgJD(-bmy+jvT$d?9dnLLY(HHUvLwtF+eig2s_r>)D!elEL(8nxl*6u5 z!Lc7`$@hQgVZbiwLHq`>IO(!VSpN{VNT!Sh=@$HPPd`sf3zS*r=xS=tySL%fZDoVs z@WBI?G)4|}WVf{F%z!d1ip`=!@SH!mz1(OQ^N&O01(0#ChgF>i;@g^7{; z%9I!7b?(3PXcySdoQ{Jawc3%)qnZLU>2dCc5W*Q}`BD8s{#4@Cf?euBA8Z2!NpCYZ zs^3vRf#QMW$EeH6{{-VOnTlU@vN4Dm^z9q5k}YEyUADG8>CH@qv^P_nCS#K<56>LC z--io%jfH33rJAQXGQYuHRou@HHvy+*UB`pORSSDmSHGPTCQ1RFJSHOdNh1ydlIkejW&b$DX@|%D@ZT#kL*=T zQ(jW@xcDI#xC?nxOcUH4+M#miFQFWyV|<2F0=M@UQ)?Aj7THDhK`@A^#T9f7z-6VD zx_(FS-hI1MbYm=qDuX4YoTK3`2*2kOdzD<}@GzQ{>{YPByKT-T{2*?uJ4Z(8?4!wc zx1*>37F;5Dzm$h;n1}psXpUvsdz={=Nma;4E6du>Z)MdAKO-$tfA7BQK7#9IZ32s| zOas;M1l7ZdupxoH#~`Iq34@y!0&k;ZW;(^5l!-v!rKq5E?mh`m!R;XU9G@fIR)VRP zN4Z$zn?a=W@5y|6C%ryXwAavWdY-@~;Cd=H_^|nWuAsjR*>kt;!rQ>gB|wf;Ug-Tu z4?_3k*qwZC1@Gpm@TXth+fQkY(_JhMHrVK$3EoYOmc1&S5W7Qdu=`5crM#bvy!2TeMR zY1QlQYDRLKe!M^Xf=M}rYQhl!29W^co#gvxMswfoPV7YO!F|F_EI7rPKs*5{#pUaR zZK7dTWaKWmaw-&=%yU#*!UM8}dq?Du^C;>cPENx?5g9lO~4_J5gn>v`2e$ z#TR)M#+aCVeRd#b(D9^y>gwMGfOKvyfE`42JzQKlwKV)b1Y#O@nu`YCKsUS4h!3?S zIv(2)*p6Rf`@RCrS6+5%S;r*rT^%jia94}xuAZ@WpC50b2T6ov3NySQJD%raJ=ZFh zRQd7V*UPTE_FM`(wtrKroL#C{m9$K$EXF@Yae_RGRAg|4ZKtDz-w%a25A!Au*+3L5 z!9``q|KA&Uje=k`NU988E9}7Aen7MH>`vKxeFHNEt6xb{^VBDlCM5ZdhLbDB_S7>~ zb0TD>RUr(t=9D;^v*bzdjk8oY{?D9TklK84!4^^d_+p@0>W};eah1}q&4t}Fx4?wO z=wFr!se-5nqx=6oGrulfL7k|8H*l~p%D>d!f9z1-bRPCBI8Vj^OA!rhIX>7|JR!QdDhD? zM#yvnUN$H21-C2FQ)aPpSz(m>5w^DM7J|y(mj_&oDAorzTOf_xqgSJ>+5-A3;I5zG zMX%vSI;N(k5^sh7G=L2y8k#BXFdxIKoPNjSZaB_I`*G-Dv(=&pH(V(@kN6nm{h61R zjIMO5zZqkvkxa-2*%V{pU<~2Af0532Z|R?$_!m)6N-Pf~&h0r)#lMzTxY?Cw*)Es7 zT7E2^bh_3_nd8fPomc6rsdnYNxBr{AiwP{SubJ)K=B%FGl=qjh=FiYI@w2fWY3zPV zc5hc;U%Eeo6q5DSXMTruI#YFXUbchLVJ@l)1;bZ#Ao-`TWOpg%Vb2x1e?Y4`u&y+L zWKGDORCvU5F-4~68)Z(x6{<(*FBU?BW8-z_;Qh;!Q^j08B@ga^B4JrNxv{3}W{-sw z?9|&r%30ojPx1ku%Ox1R{&%Heg+q7k=gnz~6M(ej_dAqR+LB4Fm59UKXIysZus)^jk%J^M>U7MNU~ zxFVZ`zraEo)5JJ6Bx27n56s%-fWJ~?gEgo5w`^f;8NwX$+6MH`mo?D1*vs|JlY>dw zkO1)*l$!*at6e9zvSc26t!!Xp>aDb<%xw;2luF1Gv#I2-%m89azyHt2d(U-{-mO;BCDsM?h= zr>%=>*vcdM#5EGy0@982-^HR2AG=JW1QPe*VW7|5JEQ-ZI-2j4cF>QVv%viDAS2ON zZWFm#6qtCVs8mvSByR*>3TDR>z&UWQ5e17Q3{~ZS55ag-+pG!FlBVQ zgb(@vaEp_mg#;C&@sf@=8w?*I4)bypk9vD95{k(51(}QX&w_qGRx-@1cVE;Hw9Fu@ zWyjI6Kn@8_bEbWl(vyOWTgy}=_UsT*pUEiOZoOPz{Y4!o)tm8DLwyEph6P{fBa+uV z8(^lxl~;-nDns%bEcUxr4NDWwjK4}m#^NHF;QpTbOC0F=qaHhr*QZ8>H->A2gBnMSZaMjl znBqDGasO^w8OilLBUV=>K~b|$%%=vip5E=NbX{}q)cw_)ZdyP8 zNH79%kn~3dnf?Ih^$19M;(xRYH}(X5g`f}V5<8hBdTgSM z9PAo9!Q`MOXj8H0dPJ3nS6$Jqo?i57rF2xS6lmMhNncWFK=F8I7-x*&K6U)yp&Q+3 z84U`rT4zElxqYU!M7Rys4<|j*P^Z5LDj#SF>X~M&@90q0xh%UvJT4xtrK7Flkxl;^ zt#FlZl(HEY%I`!HLv|bq^VKom+h(LpYSB4_amnbsAPh(3_c0djvn6=@M(B7K?d0gP z#y6=0f=j&~R>>>6>r&RIRmGcVVh`;Q`J-$_+?2%1##QqYrz{oF`fz|-eS#hap$Y?Y z6Ln|T#zJ&PH%Su!7`@wCp%v!x;G4h8J|lHQ8Mgqv_&~J_rWIj#dnly+v9cQQEetN2rKs*$Ql-Q`dd|)Lzv|lG1Baz{zVU@L z>N89cui=x^3{x0aivF?#xrU>aJs8VC$?< z2c;B)KOp>mwQmN%kazq<=5tW6HOM5Sl=!lN^qnn4eE11`KM8nIyy-L8^ea-L)|OeG zTldZ_4RFg{?caa;cjIgUA4`TA^JiNB&kxmw-jZZo1kJLd4mTfqZ~M}(dUILSdF+j7 zY6Y4P=SP=##CWkdtS{7Jv%GK5&?mS^p>WAo6dZoauoE*4Ja&S zZ1^Ug;(ZCeX7XmJ8h#Xi(X*Q8n+pAgN<^{i0|YxOlm*{n-YOe z^mHSTt?B+X=D*vg!OXxZGN^7FBB)V`UQ55Y}L;G!% z7Hojr2vqoeQ3G|MA0(;O+uyIakzqQLu0;Ew#s;wH-04ZoFFFc|@ovKISdA*ty9o*! zllb!Qy;0ARVLA{KK>M&}w@|cTIN<^s)yTu57GYxfZv?DbNT4WSYg+Y=rZptc^iYR+ z)BS!ML!o8ps6CBRdhl~u%-eyfya>*5b@l7VSO-99avOkp;;RADt0QQldlnC9?R9II z5B+%p18z;}s0)FSq`LoouzAT~c8%pRz3xe`En`dXW~V|~NZUy0YTV5W$Om?iO!{*- zZVPXBnoQKIpUsavG%B|mm})JNlG~xShmu`VWMV(+Y5?vY0(MG~yI-E0(kb)$U(pb3 zs$NPHy=v63;cjijow{@VMlBVXxZm^rRV5FAktE=v+ckguWp)i-X==C+jXX?FDwzhr za$rpN-jqy5h2o9HMxib%YXeEB`kxFdxdEwqpP$B?9^wpO#bbfh*RJy61n6J?LyU#p z3+NzG;ZL%}n^~a7Q0Di)^0g(a`p=jH*0gNd-5NnPYr z-NGzatGvXf1Kj#yW9ZNLQT5gDmmW0upz@@V3_n--u_mG|+ z76mBC%3PPVL2MV=uoNb8KPET$&gAQ9eQL>nycdweG96Jp0)o{Fn7S~!FKsPuhS0*&jL{3=wJJo}C!F4(n?YOXlVxN&TSe=&5-=VbcP@i>MT;FpFD? zgX!j_pxF(C9fcCV29Q)_c>((-f6Uk(&C@^Y?>jpM-x&JcilPMiTH`1ek{h=wV8++Bpt(iQu%J)%*CYbQpSp}D2+ zOO|OSlkJWhkAmQkbNMG#DuXMeZ;dG?k0{g0l+-@^Hiw5!p+Jm=tq7|xO^@s*+o^Z| zK#2cVoNf#xOZ!Cp*M+k9e>4RMrve%+gSxF32acACa5T@?E$Adh^MlRYc8tO1Syuw? zSx-v(4JcBYTv|1Fe$Ewp#sx}5mV`w_w8y?s;gSLwXfgbJ>6ZeX;6eH14y02rC*u0# zx@nh`YCp}&mLGlH9;BLu*Wu;d1ln-fS7c)N1x$avAZ}>%>BaxVp$5Hj9w@)i0JtJm z)!zAm9>I3@)DF{Mm_Xo^+MVe;pve5#c$0CS;UP@x!VdFLEolLjf#Cqh?>Th4eIrGD z)ST$E4^Cs)V_-^|BE;+-ZMEd=dFfxmEyKo`X^{7@XD+-fWJq7I+fdcsSmxTeee`1E z>JbG4E#j7YKl^ub6S2Fa7&^=%3!K%=T!}C}l1PWJeQhgcIAOfve@9Lhfu*HcJdj$U zvR2v-rgxi2QW?UxS_2@MjUx>RfHdL2Fu{GJ5KWN)qN)P{UF9jR1Oeg$_L65mzjY*B zX<89e=Ay~Wk_kSnjXK&lJq>~Cd(-(Ax;ay*OLu(9z711OvwE;^$AxbLPY#tXTAYZj zka$=!hdmA6KwuEFQsu9iXsf|b+lu_&#`^)NpMC6zZoWQ`1w)5QpAQN^?9dm0 zA>g|^(8J$eR`&e8%cj_nj3tMwuYCLg864fGlOTs*tZQhqVa8c1?Mh zx=ohc2%wb>pC@#qnD(y8yK9d2(|uiE6!3qfyxcEkaBLKsfB*o})@y;V7 z$7eLn*S{kvrQWbeIkPaIIT#5pps63y9BZmATCs4QKS#S34>ZJiH$ab_E?&@_e)~$C zS>F8&V+|q^U>nsp;Ikf_K>u-J{9LhqLhX1VU1cu7QU#<&<=~LD6{DAKPKp9LJWJC< z@w{sb6CEKpEj%t#?U6>gx{upT6CZ^GZ50eXfggAqW{X1XklF<9RKroN@oh`J%0Ata zeAge>Z$H_|=ESfq+kN_Lx6+VhmQnYjyf+X=T1Me3EC>Z;97Wf5t z9)KMHSf7?}YOf?5mz$)S{@@2W+ zYRktTfS4s>^ex6ST4x*`K=E>X!1$e)5{UHhYf-k*+^}5@Xm~WB6zp!rX*lN~Q(EdC ze!Y{5F>`gK007vv(d(17t3R7oH-#$i#Dz`?fDNMrWB3_b2a%;S#!n^3LV}VIE3vl( z2Z|_R5sf4(*KnRDTOmficKc=fh6N`MJFH(6Ua+E-MB7*L)K`rKS9eHuDXTC5*zkjk zQb$6%lJp~U)cVLBXgsLG0kzg$rRIX8BLiU);%)XT+3rIJy9QgFw*zM4>tl`GB|rG$ zsB{lPMl-`zPi28Kiz1p)QaLoriJW!Kr>vtUU# z8eq=j?B@hz3wijqr!4CL6c$}D>@Y^Jra6_{H`7Qa0F z&Zl+TC!P;R0jB+yZ6=W3U<>Eoj--0ZRz{whV|qjEB8g z02^CuY&fU-&pv6l2pe_QFg1KMEQ3NZQTJvYj~cv8aa#%{((AORglAc+ zo=o$Km~lSz!M;&R`EaXvlsjA%3a@F`?ztsE;W$;@M&QGH5a*a0b>iWFB#V|qo@uYFKK?2)6`3bk5_q`49P*%=P(!@ zF(kV$l>d?4g$L2DS-cJnrL6ruj^wvl=Z7=o-Q&Tdp&~ahP!;5S03ID$R$$Q)p5N+> z_Lh#&Q#d8yyT1IT$RPz9`1*KY7eIUebO43Tq95sWnBCE`Y1GKQ@&foY3P!-fL!<~! z=p>1A08bx2A53k~Tfjnt+W$f3^m%(p{f`rNQy!9$&TBtq^phSYwV(6ok(U^GQ zXALiwXus%+`CaMZsLxL&u|t!t*R4V$A=egm@ttM_KmIuqSzuutP!%Vh<~jhk=F>TM z!w?Gb0IvWLK>k3nfNJPvZNVtOZ5~h3m!>tWWmu9JX};N9P%p%^wB)V7Sp~gw4iLc7 zp1$&uKmPI5Cg77b=ezM`ir_fi0)<+~f>UwHM{ypY$Ce7$YiK`#7vPilxHY^7l2HSZ zPd2OKb=rKL9rRdzf*&?;S`~h7YoxxXpKLm> zKZb^$4590^d<644q2uXR0}c(DeGcwZl=$aGv|g?vWWlL4Rg$}gDWOwzkVFzTVx+R3 zam&|L(G+WV288@9xai%($yGP>>Q|8QJ~WK*c-RNPD&O9){;pjn*YHStY}1NGt-pxHo`LI9_J(BatZK40m>waMAO8cNAmhNp~5u~F}axv;|MK0;?qAqt<2 z{GeU2Q=1lPdniFh{o(9>zx!?9BU@@V)#G0RB|8ApQ3SU2V1F~@Vsrw-&*b~P)g9qS zE@tzQ&maz53lx`UoDC~{fV#hO_(CPCM%inR^lju)^D2__(Qq%QOW=Va0LcNSMJ_&n zC3IFlt4OXCK~yH&85QrbK2x5%U&D%SyQxZ$sx=IJ2;yb{gNByt;8iMpb>4I1R>l^XS z)M~e6C*aq>ju5U|76oObk&fY`^x@~#{>8w1O5{SM5a2HGH z?XtHY4f-j?-2n_g`+rnfR6;4=O0gc(t}^>?O;-oS{pUWtw$}*b9@^YB*sBvyBw29X zGfY!W8^aZa$=v?PkBzyqB{OIK6Rpjha@B zH0R3KWGAI$CmXbr&BVln#s?7OBQhM-%Y9&IN1;t5^;4}y-}0;{ESEmyrwvrCGz|{!?8#>Syf}@3ql>p!~KD>mF{7U^DBsitfEIY{wc0Hhb1@A{D^gf$`MAWKx z*iiYD-r?-$1dr*6bpRx8crVeI=MOKt#==OVQX7`6#@gz8GMD_5u@x`Pb%roz1eiQ2 zd!C{TO-`hwhaBWyv7;&xp{j~C#bd#(clVw7HGCp9BjlR&z4=k)GKoHgN3Au+m?!Ni zL_SD9t#`UcF4-35m;4G85hn0e^0TMM(4IdrRBrSuZ9l#1L0c$ha~(=M5mrUw)i9^! z*7~dMgqQp+>p|lVr)3L9MS`w>$~RsDk>_nhBp|4O*>6n$?Yl);U7mJv<&K^TxWTTQ z*)4usJz?a?zBCxZ)Eo}q{OC}gFS-$!5AI47O{rkWkG_WBhg}nnI$w4rUmq65jmF!g zU2A6ISQt(KVDg?}rfQdrp8d}{1(4R3Y3uO^UMzOIaftTU;e??4Yzj7sNUvB15gQSr zFgDv`KDBp~eQ<_{WA$EUgWK9%Y4tX|>v`=df1aO&rFy%YEP z&m%aXTO1|%Uj6!L-@7CG-?c0w^U9mrscYC+8#lYVtbnSA1ldr4MBf5*MjxaA9i6iS z#0IJ{WQDRS({^_Yc{hAwr(mC|WuDO&;w!2ASgU%+K`_K;#MOv1Q^9BEs?h_DiH}dA z1_b_8joAxPQgDKj1fWN>sIgD( zs6LzTGbCLzmQw2qXSLBF3|ODpp~sh7z<;1j4Ss##?{oR6((~I4%z`NE#}-(9{?yLq z>78}$%lfQ)HD|Q-P8G>I&?xa1m|zw+Gh}9a^5{UY`oT0aN}f?D3N+a~p7pcs^y>7P zqNi}@3cyEOcHtwm9;!&)=E^d?t~-Ol#qR=#Im@^F6uK^55!`am?;J#5L`;Ae_^wDZGi6x1j0 zrt6Kz*$;I@=Td@+Jl}O_cWs`!?6bp>mGf*aQokrnvZc`E$2Y?Vg3KKNXmNa2Wf^l9 z3DY9Dd>mi}#?|PX;_riUf>8cbhAROe%nQw~yXk zz>z}5C_S;E#BwK7UpyL>NLZ!1?aK;_xQ44r8$KJlgLAi$+0I)15hGrG)M8n>h)`VL z(HiP1fe15P24J6WPL7q&tyFNmlIG!_TujdRuypRVLSOU|sSy&EZq6<0JfYTWJ$y6Y zu^B2qz?FTxjtX7H7aC4oK9MDgg6XHjZQw;7Sf)&81Ed~s&!;+03+NX4 zFit-Tx4+Z!7V`bB{6Os*l&kjsom=|lL4r7&k7u_`%zz^S`p_;k=gssi7ICOs8!O2p zhy%IJu&`HS;afcw^IzV6ZO#@r&P6~zz<7}_*=@W+!d{#!RzFK7?cmN?=H#XOGu(?~ z`KJY#%S@n($qhU9&M|BWh?Lw8dxWBZH+VetvkM9EJOvL))sO)kua(kkAEq2V|Nc?P z6GBeY&3WFuO~Llx5pYn7AGn(HzCf7^P+%Z0|Gb6(uiHVLjS)eQ#^#=HZufk)=B=Sv zjHhqj%p{-HZ|@7S8ZPZuGSqFPf9W7$|6DhU!i}p52N&^soWGMGRR!k=j*5M?_r8_zW zF^&!7rKbTub;rA(!7NzCH!lvEb9Th5=KHyJ8r@#>7Jaz6J@Ac z@KADC=E&xND*G23)`P+l{rq~gUa7le`qRRvn7mEvf!N!(or!Be!Sf3pZ41MiNMVc1 z87Ir;l0=Y!_^Uv1IF{h$p5p74wA(Mwy*1FQeAL#K50wIKQ%ZbVF<}A8)E|Y~^w84v z`qM|_)F~MLo)jh7cEc31Mt-dOe%isyt~udQVfV)9A7`kuI2-4Sy`iV?XQHmKkFl1S*CQlskkO3builHND!Djv}?)gx{Pb@XJrCZ)9EnJ z&~Wnfo9Pq=T^}iu=fBZ1`*`8{Zdu$t5o>&r50BRoL0%Fe{oCuEN7p;BymAk5Y?Qq# zW+2a6n^NU(<4L1cpnSe237KY`%YU`NKnvGIf8pfCM;W67f*y@!-88}J0ZOyXQNHz( zL86zMp7gmmt}7nT2^B=trcCstHwC_e_0#W_=3OTlo|OmXrI7AW^-=E!mBb;Vsi0)5 zYuRH3UuO2HVv9~@J9D)Ie7k>(z75Ps0fpS4j+!W`@`&(;Y zzO%Y;PIUiK=w-r}ogux*YdxiJB0?mQHvR1h4^Ky?)TDrXEFT9wq`aUr80ZsJPp~ba z2bG(U;C;1AVr=|UW_pOTx2K7*BL>{i;)pbhIRnqc4d<4PoOi0tl#LOE1dvuPiayBoM(zx1~WhH?lTK>cya{%gF7< zQ=mL!W&ts>Yab!83=(ErG?kw2dA+Y7$8fv}ehEx4vww{} zpJ&?j=qAtc_v+L0>X{!h;m>v%fQjy;p_FvEAfBu@9ey-iqUyywY}ropcd8`_poJeN ztjSxyB||k+uLR|GOZROzE@^0tSM4T2VwjU#daA2dM-VLC>3MYcSLFpA{asMs1!7?3 z>#;_HpdDXRsv1j^brYwWQI^TNS~Ss)0>RjB0s`xvix}^_pK@H8N}leZ9;#4;x6|J6`E3#N}@C5`$X5qi~0)t{6ACNWlM6P zYa=U@oPdADX&J!Qk?s?^33TABmdLB_=3fd!t$#1#3oJrcfzrH|jPi!3=QzLkc7dwR z0B88usn&L3&7qFjhemxcR#%>L=3O84m@CCEYnJUzKhx#AF&x3hdvY20Zb!K`R-;CS znI%NXf%u5p3mde{y0-#BMhCJ-8l%74sYfN$`S23ZtKWbG$Z#PZ_eFa8@;znAT7|zF zi7yfzunDJ0rHrrS%W*O;pj&?!$ z*0(1hr2!o%Mb&`}^)_XE`Puhs0BYUTzFVP^QtJ$~0$j)LDLzWsM?dO&cZVlIHiLfT zPu3Wy`f{L;U)?#wwuf%kshv5sds08xbq|feW zMyx>7Ct%5dFnr(PzIEHMBsS*i&D$t)>E6w)Z!YQEruo1YGO3eA`vM9XP)>_dyMEE>;e@51-lKC+ClK+S5!ESTru!bdmx_{klsNn7Xu>>|!3mOPi4qc)4U z`6JT^NJ9&K0sz)1Y?J-v>dE?v%bfi5S6}GMjB(=(WZ=2P4=4i5nM`=P`VeK8&kk)# z;Zo#M^dKdwtkGC&6Ve%^u1BS!2DBe2U!*@;qfZq9cyfW0g)m zBDJ#LCv_V@Nb;@jFpkONh9YlwrjlQEz%Ee`mtCtDHX*f-ce3@AD3oJjqPm-}SJG<* z+RfH5gQ7mZ#VwnFid2t_w(WG6wJ2Cp$mm&=4CF2&In{Lhi|}FbJ^`7mzpLuz{G*;U zIbb_r?q3nQGW}Hvrn{OW&1XUYK^3sp&N3ot+DHfut%X9rr#k)6>h4agFy9{q=R1!t zv$XzEw=!mL`NrjtHLpQvP$|=#;j|YK9;81G-LjGsp*N-~Z%++6RBhGUJfyg#PUI^B zI-pR$emZXCCV*U79jS2KtbW62D5j}?`*-c@HT7zJhl5XE0{i#7FVoT92pM>CG{TA$ z?;XYZ28fp@Qx0LqBhDE;$CjKiu#sl_J%g^2`{~5bE=`8TEE9mX^1=umcF2anro8qD0<9~ubJ^b{Vju}nV9!%C{T9)KCP4l-9p0>pjbW2CiIGX7Vu>n ze=nhj;62)1&+@*)T(z47hW?KA=3}%M=s-=3`Gt2i6dPX`sHgaGL*QFZ+RX-p0?*6c&e+1i~taW3T`dlc|pwmMK7_w4_lxJ{<9E}w3 zuDXq@yt8Is5w$WnX!4wE>-GQso)`belPLL!gTgUH`p6qVN$63r!^gPg>=Uc5O!4Yq zux5QmEVv?ryXeuGawW0_DmA1G+svW-q8?3nGe=)L0;gNu3f=*zWBVH4I_Na^iecz_ zx)Rjf8l?n?nICOxQX{pZYMf?XkvprK_9(AlX+q8mxK52!C?RX(!aM)SO2a`Xj;O17 zF=dPzQxG!<)O=B)ei$h@(z9?PWaZ90&)eMUwt46%^;?LIs8vQxw$AOs*C*uz;sx?C zIf-_|@oW(%v#d?W&+7l&&vBg@AMbZD{yd|Zpdi+?eyMtu0m&&nMA$QcJCY@a68<3G zd`!wcQJu=d{@S{|U_UCx`|uYFl&}U#rH3fGyA_$+=al~(k(z-&z#Ok1YYOG-C#(A( z-Mc|UBcMqB@1OfRY4Hp2dWdfSPwVghualjyyM{_B@M12LI~;Yl5hm&!b-`>3Lh)ni zPw3EJ3|_pByJg?@dRl83!5FWtltym5+ki0#t#)?|L)dP$bMIIr67&8YjW-hhr|0>< zcCWw8Jnwociu=F+;2)QYSvH`!p)Z^rs|DD_e{YJN7yj?U36-kE{&xQ@ck|x1*V2^H zY=Y74MD1oNi3iWjI}Wmoix9nzt)e4*=5glcj5ANYgYId>g(bR(7bDC|yD&Uct}lb` zQJ0!#VyyELJI)Bk=i;-AMX&s;8R7DvYt4&62hn2tG4V0$ceM67iQ;Wn2mX?eUU~_A ze$zTG_K?Kc0V__FqR5M%sbCY1SDHMa*}3Q|An4`z`8Fo+>Z)|tAfk_HHg(j6K>~r# z8zL42weMt=gq?{GAJj7F?NC9DmWRt$JV?qWe=_JUqxI*|GUQ$q8?9G0ILC-^iG(o{ z#cI2T78e~cPbSd&KM`eetM(LUQ#-{OZXkB^2!;qF3F+30%dhkEwoi$fd~vcB@^jK? z=U$n9Tp@Mg8;0ugDQhCF^)gH&=;lwm;*EV}H@Zn-+mc05B-}I^SYI^Be$%mYt#-7J zV08MK3L!#Q*j$H1iqj3wxxkNc{PQq}Eapn_nz_VJOaZ2Bo}v&f7?1Q1t|v8-w@-2s zmh)|kw%*w?L6zMMXPsZBOkSNEF+;HRL}^(cyYiJpBh|pXwysF^Ib0 zF38)?MQCvbed;_3Pg4JR+)#J5aKYL3R!0P70uh?}7pad}@hGUR|5Gl}nsTyQ-c#9c z#~oxxd=*<{UQMO2)r^|=Qn`^y4I;|KQ!NEBj-L$%2vSL}>m$b4;OZ_|??e%L26@D= zj}0(zBwKI$mEQpbDb5v)D~0@Y0-JD7BS=KfbDU{_Sj>42xDku>y*%40qIf0L!$yXo6aJ`T01`TPEn_$t83Q}%KRMa^RBke|XIXdDZyF#{m&d#j9JBvg z*9dQJU;aRKi>Yqs%J~PJ9Gv9$3oZ|y_LJ09>Yx5K-8J4qBf~*$z)?%_ann3|pqtH? zDI49O0*gP*ek#u9`5PkKtR^AN`}sC1ZD>g0;rKN?pCI^Q+i%*JP*n#%9=98Hz%L>7 z%hfLgTmW7Bp!mK-; z^H2dR-b$L*uu!aX!h}~UBV^GLM(4ACcDi$Em@j&u9h*2~E6z6R@vUg)&tjoW*~;FQ zugD*pN(jub6T6*kynClVZn0z5W}Gx&w?0U2?EnRG5$ zL!!F6m49G+C`KZcV3k)&(mo|wrK)xK=;dZa9iZ|jVX)ZuLz*IM`&O{+jL`zoK^tZ@ zTulY8h7DJ9LuFCknA)rU`a|~)KRgtFm#i@OVQ@qYzI~34@(X3uDBWhVscOSuKBaaV z{Bt1JebtGPiyYxTSO(bh3#)XiZ2HXhjC^F5P{t_6EL~>ji+9P#kO!E15T^u(gd9qX zTM>cE9mJX+eoq?IW8T1ZReUxn3uwOCA@+kXvdD%J${-4b;2PBd#_89z=~Rc9k;ovb zY%*G;5`uR}5EF$7$8<%h#$z^WDd;c(m`jstllLb#Fy+rFH;}%VhG2C|es@^-*&>QV z`siA=YGt*N5Aze8h?U!uUl^A)koaI}jIJe{{-)7JS_^SNYSny+jEkalr4=UVdY4=7tgnC+3n5C5qFTU+6;Y^x z+2d&ypt|=HcFu{6nfp{h%Siq|%kb?I#@_L>$$5jSBf}W@4ppEo6B=JgxlBp1{F)-R zn7W>EKLEX`H@7p{kMVD{yQb$AOoy~>px(WzW6%QHmA zi}j(av9**P)*`Dsr_(+hn4`Ts)hz!pe|pooE;qHM-0OL@$pidIha1?7$)`|V$8V(Dxz=RatV&!)&hiN$SSBcL+xWVwhtCI) zjdJe#T^_%E7|!V8ojUn%W5vcGdNPBNw zt`uICBtGIrDf!(Q=L!|DuH6tfFS*SAsZ85)cOG#e|B+=){jKvisE7H-lb+mRCh+f5 z6E^PCOI~Kg0y7dwHavs&st*j`&P94<@{FJHnz*;IL9Wl|cCZk&X0nc*;1L%WTKK4TQMe|zRYN@HB1&}i(uIy=e!;yYg-W$e;{wbRZT`H;|Q&SOm;B# z@&vt|z0OlDxav)p88AukMeh9t{_97%c*|h!2}F{&bexONrM}dRC1z`!wl|hQ%`uaK zxm!+4Xo!?Xa^_whPmgASye3jc$iAAU+t*D0ptM0>OCcxHJY5$28`)6%=b$ZlO{GZ_ znQ>iFSyJBwG5PGCCADN)C)%HGG|}oG5qe!p=+Cka14FrV*VD6_X@q;t3R5oKP1hND zZ%(RsdvJ{g;#R9!OH@|96)atH*N&*s8J&J z6G8D)3^bp@sx;4s6oigQV+MHA{lr%tCfCj~N5oB=1%0DfT&w>iLY@QK8DlfZ#~Jqz&aE1RSIYAVSEv2;&1l(> zr!g0ikE*F00c`VgoS|@Q=aP?O1-sg884iv60LEA=RmYNlW|J;pXlnk$`lGJQu zA_x@RIDe_RBrn)%NHK`pn6_%E|Euh&{oXep0_cz>Z$iDC6_CrqnnSL(8>3L0vb09x z{?4iW0Em=C@4gL>drT#>?b<)_;ANh3u_`}3P?0-&+BNr@kC>vdV+SDjjK68@MaytDyO?y#>49$gyRbpT0O<416T!0FG(%M z3E@pWa`Dc%)tx}gCQRXh3lq z_ocqs!^s6Lro!h@b6@XrO~dRS=KlLgiSIR_y<+!enj9U)@39a$YYlt+ekhf(*QqI< z04(44uVCT=CYiDKfWdA0jaeakurADymC(@I72Jz0pcyxR14XXs+8l_!_P#tXiXX*g zVLR#&7Dc^S=MN~ev`(jUzGDT6^Tn$7Ax?I%-)r^fTlr?C%lwY6z-LP37w`*0{X}df zRiIsk>*Jr@>1kIG5%B9*&I~5<{o50Z!at&}gyJjhem(zAB&3dnR<$Wi6El2x0`F-vIx zA@pTPic0^~vd_?f8+x)~Yb5U~*N!+|nHZNE0<^r}pD zTPd}hH+=c(u*da@2xqb{G!j_3?6c!RPeq*g$E~KKy}rxgadhQ`76lG>t(L2~Ydb{V zQ(SJ-2aio;Rs+S)+Yuh?Iw~nVEc}J5*|PZ>od)k%laZ_X!%s8vy6W25=$(n(59j>_ z7rUOL;Xa_Q>n#-i2PNJ(BIfy>vkSSkM}bz0(}XLp66w$@^5^@pcaK%&25VVk4oLfJ z_vN1D*$5lc2<1kFr6<3kkLeL_g6d;=2EKYB@a!XV_mo^07I(eO9TFu|oKdiAt-Mjficy1c*}-O4aRc&G+LMr%O$u(p zbXwA7Wk?8o{X6E&iXUbJW(buE%A=|0h_$QF`xBr=kS^1LEWYwa?DW1#S0L!mNI+`4 z(1(*vodqvZX>9fxl&RLRuSliGRRY$&Eo(B|cYxz^jt4c>OzBLvV{WHl)>qi=wVM>O z?~C=qFHO3Picp=4?b_tlbw7B9drd3RHo`C{k^c-^5EO3vjh|3=rt22hU0`&j7`w10XN(zj;@!rlEDmrVwqozyCGX){gNd+(}tyob_;Qxs;||K zHlg_bskG)j1Iv_NMmIuNo2F0TTvy*OG!rA;lI;zMm@5nqqdyh#eUksFE`=a=$qK!7 zK_tdWVLDYCQ%m+&&C+1fzU#seZu(mP2X3@du>$rg7eXka!Wu@2y(+QF|MjAj91{WJ zTZBrpg2f}IR>{V%cQ`X^PW)fGRz6jr8nDXTB|LQy0cUBeQalXxet}a&i>cdDhtJ*) zs9lqZxwux3kZdLrpm{6IeK+_CacxJdxJMmp{t9^JKV}Y|GUMjxfi>K-C;m_2Uf;`m zS8rJ|pc!sdP6m8Pq>o;|FwR+=j}%yAmOba<8?}l%LPb|i*}wAEHFQPL5$cXW2RCh| z-z~BFjd;p5fKSe|M|m}s4#7M4a!4`!jZsi4TxH5EV6OsIfqVM)Ven^IrHDS!1y}P3 zS5t_vSn;0X|5$tG?`&$vddUa)iaw$^dPl=!G!;HUE=k!imA0w~?e;t$^-S-1U6*2A z*D7wYmeP&iB+NTz(E+*hC+;C7;kN`j&Wug21uCo3E95;Ge^5P!>eRMCdan#WMZ;HJ zS^72@#`n~-R=1!2rjdaD+G`$pQ_JtB*V={Is9S$rzJT!o+D-R_`B{?wA&$-Yz3ywf)fG@)`V}^$EHMb z*u$O&PP&`(pzGwVIft_|8Tg)~nGl*E3N7!uv&V<5_@dP|#8z>iYZ@m!)YlCyyVjY} zV#yYp72NG!@&;Fqd-w9Tlh&Tftj)vcgK3RN(e2k~1CuU*mmc>ZcDT_$sZkwY3iYX~ z&PqE3m^4Ur%AH`5lLa; z7hz#k32)vUNaUzS#>8AwR!;x%;|HIL=J8CyL+HWK4-riwv}uuYiI18}&=eTX>s(Yh_> z9_l(ZWID}zd@R4qbQvMD@6IG=7ts|G6b#7-Iz-W)Lj>Q?x;?w# zmwh}Ex-dJNWC6n_Un46psfq#mV&&xA+VQa|G^v`)%Lt@E*W)GXcc03*j{ay2r7c^6 zEDt*s&jQLmxJ}ffj}D3GgY6N`fCJHox!pBzd_x{5FE0ZIm!`lY=YGB;QM?&@I3AUh za;&SF>RFpEBXe$*Kt+|KeaIUTy$|hkxw|&)v-wN&=vrs5uEOiz`Hvx1O;kNSJ@!4>?f0GBakfM6+8T}y+`f4&wkBV* zHmdWLHmiNEG{4t*4^NtcY5f?ifs5GweER{McGVo63~1$p?_YWJg-ptSch$MAcKxSV z&1R2w&BB-b!*g8h?9D4|2pG4$JVH9*=$wpw_xW%} zp7os;x`^*BE!RB%>i^qX)C5*qv->BCyc*cb-ax})i$h-8?I%x$@8BHzvCt$DcIHbi z!{yH+iYQ3qJob$Ni=ba6R%#6$KiDn&*QhN5wm1a>cdhE{T@4AJQJtQ+igri;v}4D9 zF)Us++T=YE&{q9ydS7BT`B)d(`hK(T9`8$BX!DFoIgSfI%E0)HfHMAw6918V-~mZF zv%A-eeGkSG4lr%3a}8=N!wOM=I+KJn{X0HIr9F~n9 zF`zs2MmFS=EnY7drV1xFaL2h&o!Xbk7^CWRE^l`_1 z-lume9h@3j+}MeIPfj2UNQIkFhO!5L;kg|}D?@cS?hJcJ(N#z#H21hr)7r|)*)5R& zcQ1Rg${|BT2VhyW#IV?0r#YOdX64(W{b=iA zY09f-&a+tZh61(tEY=dOdiO`uU@f`s+r4dkE<>fZ(cITUswM(cq9ndWf)GF+_x}CQ za)(}SSy#STrEPBDlJJ%OGgRxP3URC$o6LHYaPp8eOy)Z_oa(j@_hkmOD-4cxrU`~i za8~o|lJ7Eb&!?JjBXGT{ED#f#%~OiZ^!GJhm3-_cJ1dafyg;qlFjWZTm0JB?+NlRb zRI(>kuAK|N^U41X6i=vxbKdZ&Z0m%2&tDrZrY`Etb>Ul$CF)W!=cUJsQO_Z7YS%gzVY>o!5R&-#6^H2h&cxKzRL}(3VfX6ls`~>5ds(x3i&Xu%w-UT< zsnr|yl?Qf}E~d-J(s+QmTs>QQMTsC3?P=&w44KFQWNDFSrC{-;XT8o|t3zlmi1_QS zkGH*)F#kzN0M!+5~X*b#Rg$hXwne6q{WIwFZ8Q)mZY0xIw zGKG4hILi&Ei8PHVrcb*Ae%0k6J|5ZNj2RW`Dn(0}v)ePJcfGP-5lwc1Nf$wmbV^lN zN#VI8qdQY);NEeuu!~QXVwNuB-}__AW?udMYhUR)_GLAZArPc+(dhmL{kH<&7_SYH2Ne!>4ccrV$BVA5tqBPU#l3wy<1I>k%hU4)c+j@R2hQ)C zL8lCE_3%0$?NO6bFP%?(e0*PlaWCOIy)^%oPBmNWj_YDYEU&%yTX9Ss2NIg34MA#% z$+`UJ+x*$=tzX!n(K$lv_>*3wkLW%{c&{+gtV3ai8`-EVmjvMfh<`T^?W9a+rNIz+xr>fIcYD66$a? zyR+Z;&N-c!H8D#v$5Z<58}~cl#UkzRp5lua;vNI$V{{rjH90#HpZbnc_l-!Sl;{{v z)Dw~#lG5e4iGF8u=1xyEfq$c^}ZnO-Dx>74E+!KcBA-@z7-#cpBbx+|4z_}I&YGm z-Y9&Sw$|eNAYghYdwKLfk*fnl`d@Lf>?=J+N-G*C3OfIBk}FKU!ln89>T?65f7kd% z7f%!VoM-f^EDgd7V0cW&k+*Y_`pV(l~4QJ=o~F}LUchiCU5 zp#L}2=~S)heVM?c)MNjS>;lx7M#=x)%^8FmjBH+<9~t;}eC#d|*$)(tu>3?MyktdT z%-HA;of$1>`$=I?h*uDM_5fUJpcgK+#<~+8X2us31 zPb|SdcarOtP4}m7f9bF6zuNdJ8MM z^=I!ZU}|VzY~IB1gsGW};9P6ichCBGgEOt+0_i&^NHhVGPejqqy=w*R&pI@l4wp~J z-viNJFc*O`5%3VuAN0w&*qh-jNQ@`!BB-9@KtFCv!cSsoM9Uj z5l=g8cGMxf&M*kp`Sybc55^7W-we-M?_OMC`$;hS**H6W;^XT^-88b0C<**@q%D|FzJgoK2o_ST~VNb!aCcQze*3ul3tKyNubNt4Qi^}x9( z-@rhthM-AvsoJ#TG{gT4&En)L%x&w%hNFJIWPkQD>c5lprD&_P+dY%}uvcsm2<5n0 z&iofIQTM;}o=z|mN(uCDJW&A4tgZL?i^1)x0T6AeGBCc3L^08oKfX~$HK{xK0V5|& z>CzH>4)gckn}AmAT*{DQCa=3DP{du|N~fmklA^a}*UoOco_JpSMOGhaEBt6qoBagU zce~z7mdhzEt70B`-$HV<)aCq4%=G%O8H4hNUO&@`B@@D=I{w_LIkg-QKHPjiYNE&F zfz7sGT*67clR(QcN*`G&{Hg@Kt$H`x)vhaA?>}{c{6XF`TfktHY@SBh(D3m%4$+^d zuA;~`Z%Noc=Y7p~r*LMnN8m&j9w-3c`-ym7rslfy(fogb#WZ))5aa2nk8=CimDQA} z@+@WUB(2N{0z|FY$mJW!0Y#_os2m5^_z?BRLNfV0vy1i23TcC!7L6-9C$?QfdhsfT z(axe{@f6%)DS7q3C@OK^T`Uu~*dL!^#`_W0z(Tw8pS@B5{8uD$PiZ?bWg87kZ0j8T zI8nx#%hjBgcBw-t(D@3e-25Xgy%WEJ-l2D;HfsKvvs*W+@pil+v9ASG{iK|(n*dlF z$R=_MReLP$YM6zRlCC_!U!)!S)1QAV#lysIvcKyjC_w1|8dIa>`<1;FOV2fiw#&A^ z0Ud;0r>?q{={-Ud{S|V#Zh?0YbrO#~KsKgFe!M@mRAXw}FRy z;}sVjS7_ZWtB%vg4?2B!F`+AOqhZE{NcB8|u+Om6Nz`G_oHUHw{QHc#w`cLqdfVdv zgfEX&a6N7|4NOBx(1aa#YHuKmXu zkj0M*`8t)3p8OJG)tScsB6AiH-VDz90qWYXI?)Pi)`Ikz;}Gw`0eCh=B;P+QM>;lLV3g%181{N9Sva{pb)a@8Hmf<0th+dq_yi{_-e97hhFAm#q`P z@F3v?)AjrAZyG9!%)=+1O6LA;bjj}Goj)ct0c+?1|N#C0;@o9D8L*H0kM5 z?mO;B*(}1(#X~t8c8~L-P3Gh!&B#+MS$`ZT2bb=a+3jne2#Du$b-T)@+v610A`xM> zOHFecC(p_0UDsK1UfuS{Y&pMOBe<0Dsg5-5YP{8`Q|fsq2^M{qaBt@0{Sv>jW1XF% zcTIS`U>jAI-AdMEdPVf%_=)mwHtNKD+?h|?gBEf+^p3v>B_4ZHcK1W~H_mAfvKSlQ z)>2niN_!vOZuVlwnf$vVmJQ{RNeA@e;h$M z1>SKu*yI zikx1zEN)eNAIS9i^XJvEx?@2<_yiR2?DK& zUiBdtYjT`y9iwco-9JJ2zord!NR*CD871twcW&ixn9KxrE_o=LvDvzFNd#iTwQF{% zcp+&?Lo<9sp8y-JIC31UV+}lrJz4z?yL;pE@<^}=(yq*bFqi5ymFo1yYVZIf ziL3dBkwmur35A?B%)D3kkY@__U5A&R4sya5rlV|fE;S|c46f8k&l9IZ`yj@;G$42i z*$_b)pjWL5bzsRDNIuf8OEzP*wOVo^1tXGTsGpRiPtOGlbUNpvm~c|)5V-3_)k*KY zrAwBu&`#%YRHxS6yFaHr81mlFzJeR$TSsf%$ehzz9-8me3XwWSaih=?2V9LIW(cDL z>)%6&Os4WKq&iKfIW=DU{(iCkb%iPiVaL8NZ4C2g8rL%{r|geAO3}FguQ|Z5*n49Ncac?n z%hUu_YRd#vCv`6Qggm~U<=(bKW&}!{(wFL7R2Me7?ca^LWlANj%TEOAYX!F5c51JZ z*lshuAXo4^SBF>Dx;5H5_Oi(A+SjOLnZ3uYTzj(pj^|T%J|1f|j1Q86`m9jiKt1;1 z0i9XZ&Zmytr&~O{W3;e(7N@*jvjk8MAU{rCs>!wS6x!Kx#vF`vS-btZYd+!nnf5?J z8`vyH-~ElL*Ufyy!sGlOl(aNAd!FuYfPx*g%c4>oqe72gyx@u5acvqPrj&ld&Pz=l zSuWBybdX-32CoOCUrV;+xa2?Enq#=b5F6s=`gnpALuynTb=JQt+4b86#mj|r@}J7T z)HJGhY)(Qm!1dBEKU92G+x4X@NT$lp&zWI&ihQv4H=z_H;9J1eXHXr(hFMlQJ)>y9 z^D7vM-T8@QZ(-{JXLf}}0FoTA0<~gN6+N?3cxyrlX=tB%np(E~p^M}9o?=_hB9j0b z(Huw2;K&8xp%c6b0B;Sk%QZMEaxUjDujL5+?g8|eQ#w!$B;bE0MbA}27S zamz*r5I2l8RaU8CeR1mTkNm|rly zUpm-VX{t)Zs_n@!g0-}e6sok`wVdjiw~mY{=lfCM5SMXv+|*TsQk#um2h9?=7%2G3D(5oUfk5 zp_g&(!i_Hm2_p3-KM&Kpn#YB9XP+I*ckMMezi?G*dQJKDP&EWKz}2Q&dqHYi$w;=7 z&;vZsADHCLLY>z}I5*=LAJ`w4<__`em)^~EtKv9jpxqltVDr%HIi+Cp>$X5sO1v_| z%c#jNP#KXdZvxQYEoO23{YdS=^gzqY{e*G)v)kcxU6{&u#~Ml~1{x9~CEwv^Ek64x z8baPjl3^N6vfiKE!01hsq(C8cjj%O)LTka$w^;AFOKLlsma~Xt*`8wp*8vA%(YjvK za^{WNOr?*PM{c~6$N zMa=Jmdi)XVgKqbuYesReQ8~b^c}dqR-$r#=xNQ6C&RNBC{c96Z4!7)LHzmKg-pBpeQArK->d3vIqa% z9}R#h9h!c9N8oY}VXnGms>bat%QrZEa*$A0ND8XX4)zjOc|K*E1|~CvWlkO%;|YH( zT{eMTl7yJp!>VlU{ra%|DMP84E~w9=hOqjM;YWG*a}xIPDH==KEE}#76>$FjZHr_7 zgI@UG)f|LLk9x%eCrvd>DT^}BVqBI4gBq&9)>&BNgA!7*+;YH%r?sOGN9aHGpL=3K z{cs|f34W|JuxvDThvRg!Q14S-~S|@LGz{2{K1Y@!;1O_>j`X|2@Yk z?s#|Ju-@iIl~-|xWEA_J*BZ>;U%5|-J@9~K$q0WeZz$JWfJ<=g)<_$!=2t|x0$xS| z-vjR8VMbI<8XVttU;m`0q)utBmZB{=4`g3LEkw0xJ0Nv! zlUtfgAae z(NU%PuD|=a)V(0uex03Tp0hwgxn<`L3W?X^KQCHH3JHtz>js^=YZzYa8a89rmL3d> zD?Q*--7ind3FE}-2$oC5NWp9FhbARn)X_EPNVU*?5CgR7T_0Tbax+RV+L}hJ<>d&i z=!U;f%fvq{vEjS7n=vs9eB9;^a2sLBG$>4f0;Yo|#Mfvl`5DC}BIxv*Evyg3!A3)f z0U)yf{YtE{BF*udqag)kz?l*vx8p+yd2vnc{F-EgHrTa5K}*fyDC?cC){^i`aeeDn zPY=KP?dBGNn>N>WH?I#ij1kzt%>OWV^3sbZYru;Uu4-Hb6D^SrPIX9OF~2F7Hu>E@ zXSMV;sp_ zYy{~q8|*H?2IaaY1U1x2T{1h}U;SD>Qhi>vA-fKYYaA1Kx%w~VWiEycb7sG)T@$b- z<8TD`LwFchOruD)(&rt8`sR@@TcYkmc=|#qWoqMQT;d<6*PydSfZEH(61Hz~1T&B{ ziB3^Qb?Yb89VqPY#x-cXiq!f5B6`9dFxhZpvhS=9{XDw6c9l7oX2ooH zpUpmq{aye&ENICs{-jraY4gGL1$TN)2@g;NzG3?M=*Amq&ac7$C zk~qWY%?nrgBoMTBA4kMLZo+LHa*2Yj5i~1W%qSi`i|)7IX05BYdWQ-ozD_t@esWfV zpIo$k{9UdnF`)1v;93HlJgtBAN{B2?xuCFg8n4Rxc4Xg;;tNH}o4oYAFuwpa|F=7J zpkt7D;LZ-!t@v|ybxETWl~VGityMyPw0n~8?>{muKl#J))nj>=0H$>@#;?UZ)CPwA zuX~AKv@1{;?cO_Q-`!E0G5>R|{;EBC_` z{i1XJ%BL!ex69Ol5G_6UMzICaC~29pC$L+zFGGnGMzo$DxZmD5FK{j68SWAFA?@b1 zGN*O)-T3qU9~~Xe&5uRWX}>|tC)q~uE_g<)#5R4DwCZ69d`DtZ>-(>>X>g^O9vRBy z_(jf_VVR(TwB8=(M{jmqfB#s#WuEB@f{EYt#p?~=$RBR8fAY?4cmXu6)$yyw5w@+Z z8~&2R5Y`&>Pv!$iyQ7EmeEqIt-k->Q8~%*F4eYBZv8_3QSLlbj{(^Bayk#&=Je@^eN+^#?9{>6ZO_D#w6zl4|Z5+B|;+BTGkPW|6?8p}8 zUgpiooevqs!2|1+H{!b=7CK)uM`u$9xeT|2T60Y@o4wWlc6L*M*(9ksc@b2C$DbAA zm#&85&4GxhR-WU2gWrt%H@tCm@Aaf#g}rs%>VPlKd+|t%AwlJ(G^$_5zUfb&7#&J? zv_Uc!I^#BZgJD(-bmy+jvT$d?9dnLLY(HHUvLwtF+eig2s_r>)D!elEL(8nxl*6u5 z!Lc7`$@hQgVZbiwLHq`>IO(!VSpN{VNT!Sh=@$HPPd`sf3zS*r=xS=tySL%fZDoVs z@WBI?G)4|}WVf{F%z!d1ip`=!@SH!mz1(OQ^N&O01(0#ChgF>i;@g^7{; z%9I!7b?(3PXcySdoQ{Jawc3%)qnZLU>2dCc5W*Q}`BD8s{#4@Cf?euBA8Z2!NpCYZ zs^3vRf#QMW$EeH6{{-VOnTlU@vN4Dm^z9q5k}YEyUADG8>CH@qv^P_nCS#K<56>LC z--io%jfH33rJAQXGQYuHRou@HHvy+*UB`pORSSDmSHGPTCQ1RFJSHOdNh1ydlIkejW&b$DX@|%D@ZT#kL*=T zQ(jW@xcDI#xC?nxOcUH4+M#miFQFWyV|<2F0=M@UQ)?Aj7THDhK`@A^#T9f7z-6VD zx_(FS-hI1MbYm=qDuX4YoTK3`2*2kOdzD<}@GzQ{>{YPByKT-T{2*?uJ4Z(8?4!wc zx1*>37F;5Dzm$h;n1}psXpUvsdz={=Nma;4E6du>Z)MdAKO-$tfA7BQK7#9IZ32s| zOas;M1l7ZdupxoH#~`Iq34@y!0&k;ZW;(^5l!-v!rKq5E?mh`m!R;XU9G@fIR)VRP zN4Z$zn?a=W@5y|6C%ryXwAavWdY-@~;Cd=H_^|nWuAsjR*>kt;!rQ>gB|wf;Ug-Tu z4?_3k*qwZC1@Gpm@TXth+fQkY(_JhMHrVK$3EoYOmc1&S5W7Qdu=`5crM#bvy!2TeMR zY1QlQYDRLKe!M^Xf=M}rYQhl!29W^co#gvxMswfoPV7YO!F|F_EI7rPKs*5{#pUaR zZK7dTWaKWmaw-&=%yU#*!UM8}dq?Du^C;>cPENx?5g9lO~4_J5gn>v`2e$ z#TR)M#+aCVeRd#b(D9^y>gwMGfOKvyfE`42JzQKlwKV)b1Y#O@nu`YCKsUS4h!3?S zIv(2)*p6Rf`@RCrS6+5%S;r*rT^%jia94}xuAZ@WpC50b2T6ov3NySQJD%raJ=ZFh zRQd7V*UPTE_FM`(wtrKroL#C{m9$K$EXF@Yae_RGRAg|4ZKtDz-w%a25A!Au*+3L5 z!9``q|KA&Uje=k`NU988E9}7Aen7MH>`vKxeFHNEt6xb{^VBDlCM5ZdhLbDB_S7>~ zb0TD>RUr(t=9D;^v*bzdjk8oY{?D9TklK84!4^^d_+p@0>W};eah1}q&4t}Fx4?wO z=wFr!se-5nqx=6oGrulfL7k|8H*l~p%D>d!f9z1-bRPCBI8Vj^OA!rhIX>7|JR!QdDhD? zM#yvnUN$H21-C2FQ)aPpSz(m>5w^DM7J|y(mj_&oDAorzTOf_xqgSJ>+5-A3;I5zG zMX%vSI;N(k5^sh7G=L2y8k#BXFdxIKoPNjSZaB_I`*G-Dv(=&pH(V(@kN6nm{h61R zjIMO5zZqkvkxa-2*%V{pU<~2Af0532Z|R?$_!m)6N-Pf~&h0r)#lMzTxY?Cw*)Es7 zT7E2^bh_3_nd8fPomc6rsdnYNxBr{AiwP{SubJ)K=B%FGl=qjh=FiYI@w2fWY3zPV zc5hc;U%Eeo6q5DSXMTruI#YFXUbchLVJ@l)1;bZ#Ao-`TWOpg%Vb2x1e?Y4`u&y+L zWKGDORCvU5F-4~68)Z(x6{<(*FBU?BW8-z_;Qh;!Q^j08B@ga^B4JrNxv{3}W{-sw z?9|&r%30ojPx1ku%Ox1R{&%Heg+q7k=gnz~6M(ej_dAqR+LB4Fm59UKXIysZus)^jk%J^M>U7MNU~ zxFVZ`zraEo)5JJ6Bx27n56s%-fWJ~?gEgo5w`^f;8NwX$+6MH`mo?D1*vs|JlY>dw zkO1)*l$!*at6e9zvSc26t!!Xp>aDb<%xw;2luF1Gv#I2-%m89azyHt2d(U-{-mO;BCDsM?h= zr>%=>*vcdM#5EGy0@982-^HR2AG=JW1QPe*VW7|5JEQ-ZI-2j4cF>QVv%viDAS2ON zZWFm#6qtCVs8mvSByR*>3TDR>z&UWQ5e17Q3{~ZS55ag-+pG!FlBVQ zgb(@vaEp_mg#;C&@sf@=8w?*I4)bypk9vD95{k(51(}QX&w_qGRx-@1cVE;Hw9Fu@ zWyjI6Kn@8_bEbWl(vyOWTgy}=_UsT*pUEiOZoOPz{Y4!o)tm8DLwyEph6P{fBa+uV z8(^lxl~;-nDns%bEcUxr4NDWwjK4}m#^NHF;QpTbOC0F=qaHhr*QZ8>H->A2gBnMSZaMjl znBqDGasO^w8OilLBUV=>K~b|$%%=vip5E=NbX{}q)cw_)ZdyP8 zNH79%kn~3dnf?Ih^$19M;(xRYH}(X5g`f}V5<8hBdTgSM z9PAo9!Q`MOXj8H0dPJ3nS6$Jqo?i57rF2xS6lmMhNncWFK=F8I7-x*&K6U)yp&Q+3 z84U`rT4zElxqYU!M7Rys4<|j*P^Z5LDj#SF>X~M&@90q0xh%UvJT4xtrK7Flkxl;^ zt#FlZl(HEY%I`!HLv|bq^VKom+h(LpYSB4_amnbsAPh(3_c0djvn6=@M(B7K?d0gP z#y6=0f=j&~R>>>6>r&RIRmGcVVh`;Q`J-$_+?2%1##QqYrz{oF`fz|-eS#hap$Y?Y z6Ln|T#zJ&PH%Su!7`@wCp%v!x;G4h8J|lHQ8Mgqv_&~J_rWIj#dnly+v9cQQEetN2rKs*$Ql-Q`dd|)Lzv|lG1Baz{zVU@L z>N89cui=x^3{x0aivF?#xrU>aJs8VC$?< z2c;B)KOp>mwQmN%kazq<=5tW6HOM5Sl=!lN^qnn4eE11`KM8nIyy-L8^ea-L)|OeG zTldZ_4RFg{?caa;cjIgUA4`TA^JiNB&kxmw-jZZo1kJLd4mTfqZ~M}(dUILSdF+j7 zY6Y4P=SP=##CWkdtS{7Jv%GK5&?mS^p>WAo6dZoauoE*4Ja&S zZ1^Ug;(ZCeX7XmJ8h#Xi(X*Q8n+pAgN<^{i0|YxOlm*{n-YOe z^mHSTt?B+X=D*vg!OXxZGN^7FBB)V`UQ55Y}L;G!% z7Hojr2vqoeQ3G|MA0(;O+uyIakzqQLu0;Ew#s;wH-04ZoFFFc|@ovKISdA*ty9o*! zllb!Qy;0ARVLA{KK>M&}w@|cTIN<^s)yTu57GYxfZv?DbNT4WSYg+Y=rZptc^iYR+ z)BS!ML!o8ps6CBRdhl~u%-eyfya>*5b@l7VSO-99avOkp;;RADt0QQldlnC9?R9II z5B+%p18z;}s0)FSq`LoouzAT~c8%pRz3xe`En`dXW~V|~NZUy0YTV5W$Om?iO!{*- zZVPXBnoQKIpUsavG%B|mm})JNlG~xShmu`VWMV(+Y5?vY0(MG~yI-E0(kb)$U(pb3 zs$NPHy=v63;cjijow{@VMlBVXxZm^rRV5FAktE=v+ckguWp)i-X==C+jXX?FDwzhr za$rpN-jqy5h2o9HMxib%YXeEB`kxFdxdEwqpP$B?9^wpO#bbfh*RJy61n6J?LyU#p z3+NzG;ZL%}n^~a7Q0Di)^0g(a`p=jH*0gNd-5NnPYr z-NGzatGvXf1Kj#yW9ZNLQT5gDmmW0upz@@V3_n--u_mG|+ z76mBC%3PPVL2MV=uoNb8KPET$&gAQ9eQL>nycdweG96Jp0)o{Fn7S~!FKsPuhS0*&jL{3=wJJo}C!F4(n?YOXlVxN&TSe=&5-=VbcP@i>MT;FpFD? zgX!j_pxF(C9fcCV29Q)_c>((-f6Uk(&C@^Y?>jpM-x&JcilPMiTH`1ek{h=wV8++Bpt(iQu%J)%*CYbQpSp}D2+ zOO|OSlkJWhkAmQkbNMG#DuXMeZ;dG?k0{g0l+-@^Hiw5!p+Jm=tq7|xO^@s*+o^Z| zK#2cVoNf#xOZ!Cp*M+k9e>4RMrve%+gSxF32acACa5T@?E$Adh^MlRYc8tO1Syuw? zSx-v(4JcBYTv|1Fe$Ewp#sx}5mV`w_w8y?s;gSLwXfgbJ>6ZeX;6eH14y02rC*u0# zx@nh`YCp}&mLGlH9;BLu*Wu;d1ln-fS7c)N1x$avAZ}>%>BaxVp$5Hj9w@)i0JtJm z)!zAm9>I3@)DF{Mm_Xo^+MVe;pve5#c$0CS;UP@x!VdFLEolLjf#Cqh?>Th4eIrGD z)ST$E4^Cs)V_-^|BE;+-ZMEd=dFfxmEyKo`X^{7@XD+-fWJq7I+fdcsSmxTeee`1E z>JbG4E#j7YKl^ub6S2Fa7&^=%3!K%=T!}C}l1PWJeQhgcIAOfve@9Lhfu*HcJdj$U zvR2v-rgxi2QW?UxS_2@MjUx>RfHdL2Fu{GJ5KWN)qN)P{UF9jR1Oeg$_L65mzjY*B zX<89e=Ay~Wk_kSnjXK&lJq>~Cd(-(Ax;ay*OLu(9z711OvwE;^$AxbLPY#tXTAYZj zka$=!hdmA6KwuEFQsu9iXsf|b+lu_&#`^)NpMC6zZoWQ`1w)5QpAQN^?9dm0 zA>g|^(8J$eR`&e8%cj_nj3tMwuYCLg864fGlOTs*tZQhqVa8c1?Mh zx=ohc2%wb>pC@#qnD(y8yK9d2(|uiE6!3qfyxcEkaBLKsfB*o})@y;V7 z$7eLn*S{kvrQWbeIkPaIIT#5pps63y9BZmATCs4QKS#S34>ZJiH$ab_E?&@_e)~$C zS>F8&V+|q^U>nsp;Ikf_K>u-J{9LhqLhX1VU1cu7QU#<&<=~LD6{DAKPKp9LJWJC< z@w{sb6CEKpEj%t#?U6>gx{upT6CZ^GZ50eXfggAqW{X1XklF<9RKroN@oh`J%0Ata zeAge>Z$H_|=ESfq+kN_Lx6+VhmQnYjyf+X=T1Me3EC>Z;97Wf5t z9)KMHSf7?}YOf?5mz$)S{@@2W+ zYRktTfS4s>^ex6ST4x*`K=E>X!1$e)5{UHhYf-k*+^}5@Xm~WB6zp!rX*lN~Q(EdC ze!Y{5F>`gK007vv(d(17t3R7oH-#$i#Dz`?fDNMrWB3_b2a%;S#!n^3LV}VIE3vl( z2Z|_R5sf4(*KnRDTOmficKc=fh6N`MJFH(6Ua+E-MB7*L)K`rKS9eHuDXTC5*zkjk zQb$6%lJp~U)cVLBXgsLG0kzg$rRIX8BLiU);%)XT+3rIJy9QgFw*zM4>tl`GB|rG$ zsB{lPMl-`zPi28Kiz1p)QaLoriJW!Kr>vtUU# z8eq=j?B@hz3wijqr!4CL6c$}D>@Y^Jra6_{H`7Qa0F z&Zl+TC!P;R0jB+yZ6=W3U<>Eoj--0ZRz{whV|qjEB8g z02^CuY&fU-&pv6l2pe_QFg1KMEQ3NZQTJvYj~cv8aa#%{((AORglAc+ zo=o$Km~lSz!M;&R`EaXvlsjA%3a@F`?ztsE;W$;@M&QGH5a*a0b>iWFB#V|qo@uYFKK?2)6`3bk5_q`49P*%=P(!@ zF(kV$l>d?4g$L2DS-cJnrL6ruj^wvl=Z7=o-Q&Tdp&~ahP!;5S03ID$R$$Q)p5N+> z_Lh#&Q#d8yyT1IT$RPz9`1*KY7eIUebO43Tq95sWnBCE`Y1GKQ@&foY3P!-fL!<~! z=p>1A08bx2A53k~Tfjnt+W$f3^m%(p{f`rNQy!9$&TBtq^phSYwV(6ok(U^GQ zXALiwXus%+`CaMZsLxL&u|t!t*R4V$A=egm@ttM_KmIuqSzuutP!%Vh<~jhk=F>TM z!w?Gb0IvWLK>k3nfNJPvZNVtOZ5~h3m!>tWWmu9JX};N9P%p%^wB)V7Sp~gw4iLc7 zp1$&uKmPI5Cg77b=ezM`ir_fi0)<+~f>UwHM{ypY$Ce7$YiK`#7vPilxHY^7l2HSZ zPd2OKb=rKL9rRdzf*&?;S`~h7YoxxXpKLm> zKZb^$4590^d<644q2uXR0}c(DeGcwZl=$aGv|g?vWWlL4Rg$}gDWOwzkVFzTVx+R3 zam&|L(G+WV288@9xai%($yGP>>Q|8QJ~WK*c-RNPD&O9){;pjn*YHStY}1NGt-pxHo`LI9_J(BatZK40m>waMAO8cNAmhNp~5u~F}axv;|MK0;?qAqt<2 z{GeU2Q=1lPdniFh{o(9>zx!?9BU@@V)#G0RB|8ApQ3SU2V1F~@Vsrw-&*b~P)g9qS zE@tzQ&maz53lx`UoDC~{fV#hO_(CPCM%inR^lju)^D2__(Qq%QOW=Va0LcNSMJ_&n zC3IFlt4OXCK~yH&85QrbK2x5%U&D%SyQxZ$sx=IJ2;yb{gNByt;8iMpb>4I1R>l^XS z)M~e6C*aq>ju5U|76oObk&fY`^x@~#{>8w1O5{SM5a2HGH z?XtHY4f-j?-2n_g`+rnfR6;4=O0gc(t}^>?O;-oS{pUWtw$}*b9@^YB*sBvyBw29X zGfY!W8^aZa$=v?PkBzyqB{OIK6Rpjha@B zH0R3KWGAI$CmXbr&BVln#s?7OBQhM-%Y9&IN1;t5^;4}y-}0;{ESEmyrwvrCGz|{!?8#>Syf}@3ql>p!~KD>mF{7U^DBsitfEIY{wc0Hhb1@A{D^gf$`MAWKx z*iiYD-r?-$1dr*6bpRx8crVeI=MOKt#==OVQX7`6#@gz8GMD_5u@x`Pb%roz1eiQ2 zd!C{TO-`hwhaBWyv7;&xp{j~C#bd#(clVw7HGCp9BjlR&z4=k)GKoHgN3Au+m?!Ni zL_SD9t#`UcF4-35m;4G85hn0e^0TMM(4IdrRBrSuZ9l#1L0c$ha~(=M5mrUw)i9^! z*7~dMgqQp+>p|lVr)3L9MS`w>$~RsDk>_nhBp|4O*>6n$?Yl);U7mJv<&K^TxWTTQ z*)4usJz?a?zBCxZ)Eo}q{OC}gFS-$!5AI47O{rkWkG_WBhg}nnI$w4rUmq65jmF!g zU2A6ISQt(KVDg?}rfQdrp8d}{1(4R3Y3uO^UMzOIaftTU;e??4Yzj7sNUvB15gQSr zFgDv`KDBp~eQ<_{WA$EUgWK9%Y4tX|>v`=df1aO&rFy%YEP z&m%aXTO1|%Uj6!L-@7CG-?c0w^U9mrscYC+8#lYVtbnSA1ldr4MBf5*MjxaA9i6iS z#0IJ{WQDRS({^_Yc{hAwr(mC|WuDO&;w!2ASgU%+K`_K;#MOv1Q^9BEs?h_DiH}dA z1_b_8joAxPQgDKj1fWN>sIgD( zs6LzTGbCLzmQw2qXSLBF3|ODpp~sh7z<;1j4Ss##?{oR6((~I4%z`NE#}-(9{?yLq z>78}$%lfQ)HD|Q-P8G>I&?xa1m|zw+Gh}9a^5{UY`oT0aN}f?D3N+a~p7pcs^y>7P zqNi}@3cyEOcHtwm9;!&)=E^d?t~-Ol#qR=#Im@^F6uK^55!`am?;J#5L`;Ae_^wDZGi6x1j0 zrt6Kz*$;I@=Td@+Jl}O_cWs`!?6bp>mGf*aQokrnvZc`E$2Y?Vg3KKNXmNa2Wf^l9 z3DY9Dd>mi}#?|PX;_riUf>8cbhAROe%nQw~yXk zz>z}5C_S;E#BwK7UpyL>NLZ!1?aK;_xQ44r8$KJlgLAi$+0I)15hGrG)M8n>h)`VL z(HiP1fe15P24J6WPL7q&tyFNmlIG!_TujdRuypRVLSOU|sSy&EZq6<0JfYTWJ$y6Y zu^B2qz?FTxjtX7H7aC4oK9MDgg6XHjZQw;7Sf)&81Ed~s&!;+03+NX4 zFit-Tx4+Z!7V`bB{6Os*l&kjsom=|lL4r7&k7u_`%zz^S`p_;k=gssi7ICOs8!O2p zhy%IJu&`HS;afcw^IzV6ZO#@r&P6~zz<7}_*=@W+!d{#!RzFK7?cmN?=H#XOGu(?~ z`KJY#%S@n($qhU9&M|BWh?Lw8dxWBZH+VetvkM9EJOvL))sO)kua(kkAEq2V|Nc?P z6GBeY&3WFuO~Llx5pYn7AGn(HzCf7^P+%Z0|Gb6(uiHVLjS)eQ#^#=HZufk)=B=Sv zjHhqj%p{-HZ|@7S8ZPZuGSqFPf9W7$|6DhU!i}p52N&^soWGMGRR!k=j*5M?_r8_zW zF^&!7rKbTub;rA(!7NzCH!lvEb9Th5=KHyJ8r@#>7Jaz6J@Ac z@KADC=E&xND*G23)`P+l{rq~gUa7le`qRRvn7mEvf!N!(or!Be!Sf3pZ41MiNMVc1 z87Ir;l0=Y!_^Uv1IF{h$p5p74wA(Mwy*1FQeAL#K50wIKQ%ZbVF<}A8)E|Y~^w84v z`qM|_)F~MLo)jh7cEc31Mt-dOe%isyt~udQVfV)9A7`kuI2-4Sy`iV?XQHmKkFl1S*CQlskkO3builHND!Djv}?)gx{Pb@XJrCZ)9EnJ z&~Wnfo9Pq=T^}iu=fBZ1`*`8{Zdu$t5o>&r50BRoL0%Fe{oCuEN7p;BymAk5Y?Qq# zW+2a6n^NU(<4L1cpnSe237KY`%YU`NKnvGIf8pfCM;W67f*y@!-88}J0ZOyXQNHz( zL86zMp7gmmt}7nT2^B=trcCstHwC_e_0#W_=3OTlo|OmXrI7AW^-=E!mBb;Vsi0)5 zYuRH3UuO2HVv9~@J9D)Ie7k>(z75Ps0fpS4j+!W`@`&(;Y zzO%Y;PIUiK=w-r}ogux*YdxiJB0?mQHvR1h4^Ky?)TDrXEFT9wq`aUr80ZsJPp~ba z2bG(U;C;1AVr=|UW_pOTx2K7*BL>{i;)pbhIRnqc4d<4PoOi0tl#LOE1dvuPiayBoM(zx1~WhH?lTK>cya{%gF7< zQ=mL!W&ts>Yab!83=(ErG?kw2dA+Y7$8fv}ehEx4vww{} zpJ&?j=qAtc_v+L0>X{!h;m>v%fQjy;p_FvEAfBu@9ey-iqUyywY}ropcd8`_poJeN ztjSxyB||k+uLR|GOZROzE@^0tSM4T2VwjU#daA2dM-VLC>3MYcSLFpA{asMs1!7?3 z>#;_HpdDXRsv1j^brYwWQI^TNS~Ss)0>RjB0s`xvix}^_pK@H8N}leZ9;#4;x6|J6`E3#N}@C5`$X5qi~0)t{6ACNWlM6P zYa=U@oPdADX&J!Qk?s?^33TABmdLB_=3fd!t$#1#3oJrcfzrH|jPi!3=QzLkc7dwR z0B88usn&L3&7qFjhemxcR#%>L=3O84m@CCEYnJUzKhx#AF&x3hdvY20Zb!K`R-;CS znI%NXf%u5p3mde{y0-#BMhCJ-8l%74sYfN$`S23ZtKWbG$Z#PZ_eFa8@;znAT7|zF zi7yfzunDJ0rHrrS%W*O;pj&?!$ z*0(1hr2!o%Mb&`}^)_XE`Puhs0BYUTzFVP^QtJ$~0$j)LDLzWsM?dO&cZVlIHiLfT zPu3Wy`f{L;U)?#wwuf%kshv5sds08xbq|feW zMyx>7Ct%5dFnr(PzIEHMBsS*i&D$t)>E6w)Z!YQEruo1YGO3eA`vM9XP)>_dyMEE>;e@51-lKC+ClK+S5!ESTru!bdmx_{klsNn7Xu>>|!3mOPi4qc)4U z`6JT^NJ9&K0sz)1Y?J-v>dE?v%bfi5S6}GMjB(=(WZ=2P4=4i5nM`=P`VeK8&kk)# z;Zo#M^dKdwtkGC&6Ve%^u1BS!2DBe2U!*@;qfZq9cyfW0g)m zBDJ#LCv_V@Nb;@jFpkONh9YlwrjlQEz%Ee`mtCtDHX*f-ce3@AD3oJjqPm-}SJG<* z+RfH5gQ7mZ#VwnFid2t_w(WG6wJ2Cp$mm&=4CF2&In{Lhi|}FbJ^`7mzpLuz{G*;U zIbb_r?q3nQGW}Hvrn{OW&1XUYK^3sp&N3ot+DHfut%X9rr#k)6>h4agFy9{q=R1!t zv$XzEw=!mL`NrjtHLpQvP$|=#;j|YK9;81G-LjGsp*N-~Z%++6RBhGUJfyg#PUI^B zI-pR$emZXCCV*U79jS2KtbW62D5j}?`*-c@HT7zJhl5XE0{i#7FVoT92pM>CG{TA$ z?;XYZ28fp@Qx0LqBhDE;$CjKiu#sl_J%g^2`{~5bE=`8TEE9mX^1=umcF2anro8qD0<9~ubJ^b{Vju}nV9!%C{T9)KCP4l-9p0>pjbW2CiIGX7Vu>n ze=nhj;62)1&+@*)T(z47hW?KA=3}%M=s-=3`Gt2i6dPX`sHgaGL*QFZ+RX-p0?*6c&e+1i~taW3T`dlc|pwmMK7_w4_lxJ{<9E}w3 zuDXq@yt8Is5w$WnX!4wE>-GQso)`belPLL!gTgUH`p6qVN$63r!^gPg>=Uc5O!4Yq zux5QmEVv?ryXeuGawW0_DmA1G+svW-q8?3nGe=)L0;gNu3f=*zWBVH4I_Na^iecz_ zx)Rjf8l?n?nICOxQX{pZYMf?XkvprK_9(AlX+q8mxK52!C?RX(!aM)SO2a`Xj;O17 zF=dPzQxG!<)O=B)ei$h@(z9?PWaZ90&)eMUwt46%^;?LIs8vQxw$AOs*C*uz;sx?C zIf-_|@oW(%v#d?W&+7l&&vBg@AMbZD{yd|Zpdi+?eyMtu0m&&nMA$QcJCY@a68<3G zd`!wcQJu=d{@S{|U_UCx`|uYFl&}U#rH3fGyA_$+=al~(k(z-&z#Ok1YYOG-C#(A( z-Mc|UBcMqB@1OfRY4Hp2dWdfSPwVghualjyyM{_B@M12LI~;Yl5hm&!b-`>3Lh)ni zPw3EJ3|_pByJg?@dRl83!5FWtltym5+ki0#t#)?|L)dP$bMIIr67&8YjW-hhr|0>< zcCWw8Jnwociu=F+;2)QYSvH`!p)Z^rs|DD_e{YJN7yj?U36-kE{&xQ@ck|x1*V2^H zY=Y74MD1oNi3iWjI}Wmoix9nzt)e4*=5glcj5ANYgYId>g(bR(7bDC|yD&Uct}lb` zQJ0!#VyyELJI)Bk=i;-AMX&s;8R7DvYt4&62hn2tG4V0$ceM67iQ;Wn2mX?eUU~_A ze$zTG_K?Kc0V__FqR5M%sbCY1SDHMa*}3Q|An4`z`8Fo+>Z)|tAfk_HHg(j6K>~r# z8zL42weMt=gq?{GAJj7F?NC9DmWRt$JV?qWe=_JUqxI*|GUQ$q8?9G0ILC-^iG(o{ z#cI2T78e~cPbSd&KM`eetM(LUQ#-{OZXkB^2!;qF3F+30%dhkEwoi$fd~vcB@^jK? z=U$n9Tp@Mg8;0ugDQhCF^)gH&=;lwm;*EV}H@Zn-+mc05B-}I^SYI^Be$%mYt#-7J zV08MK3L!#Q*j$H1iqj3wxxkNc{PQq}Eapn_nz_VJOaZ2Bo}v&f7?1Q1t|v8-w@-2s zmh)|kw%*w?L6zMMXPsZBOkSNEF+;HRL}^(cyYiJpBh|pXwysF^Ib0 zF38)?MQCvbed;_3Pg4JR+)#J5aKYL3R!0P70uh?}7pad}@hGUR|5Gl}nsTyQ-c#9c z#~oxxd=*<{UQMO2)r^|=Qn`^y4I;|KQ!NEBj-L$%2vSL}>m$b4;OZ_|??e%L26@D= zj}0(zBwKI$mEQpbDb5v)D~0@Y0-JD7BS=KfbDU{_Sj>42xDku>y*%40qIf0L!$yXo6aJ`L@%NDD}pgdoiUDME&EDL_-Pp+tLBZI?;jO*PTPu?%Ze~u-R`zz>?9bV`S)W+CxHve!;NYs(YmEE?Br|{Q4fW;-1I&DUiq- zDLZfxz4aoW_KAYJ*yBp0gAH0{&5rl2h|EaLPo7B=;N^xadSkND1kmRu`TD1Q%u*L% z+@enzCBcf-FNnJFbzf|~cr&P-81xbRX%OMFKzoFThZkd$v&ukAOB*X!*boXHtm8A= zf&bDr28N}A|4OrG|L3s>zo3}nGtJUuLNc;HyCm>;w7&Y?T~8#Mq3By1wmq}U&d!#Q zkl+^#2H*8*kV0_`?J^A#!v4P&jp1l>Bml(8lQJ?CO-<>Un3zVQVi_+lFCS4*L=+Tk z@nrsEYl@zW3*X=0|CP8nq=#QnvD{pT2m*mfyne0P=5u8uqEsO(DIu}`IX5>~xz(Jbwln25VMXwPI) z%h#J|>1gzf3*+>E2p zV)<05!Hah)d{YgpkoLQC@|~%Q0^`nL1bRkBwHA+~5`&xhM(0w!##j;G>$IiB&!4^S zx4=Iee5{cF?O&30&}1y@Wy}5b4zVpYpWXabCI?UVYfVj}APhp2iF}2m7P|l>l-N`LZ*e(4)$WUavs*l~#-G?N#T2d}j`rJF@SbwcYi#q;jP%ZJ`?M<7!5LBt zb|Im8fGr0%EPx|D+pUpw^%BkD8OU+G+?^m#PiZ|X%dKkfPU!ze@qd9FhsCZZxgr9h z(vxhPG$T4jQuFj?R2C|qj(P41>DlG&+2!sLa{hKs+mkHWliWJvPwb}d2LObpwbsXI z7x#``Yuf*jrLB&p?K0sqHv%+5@Q`MVun-4}vqybYWQ%l}Z?O9NyQOM>VmRuEDKzI< z2j8G}85qN42dhU+VNGNYNA4T(Do3kJkrU1G5GUSI&D?k)#MSs`V9i?}%)>Oi-u(H6 zix0kTL@Ym!oKs$&+RYq9km8soPHDx?3N+JUM5u z!$EiMrZC=GJGnA!DB^j@qMU>TeS7oSq^{Li79x-J&*hp?5#%hRZ|{X*w)`c+OKRoEmwhD2pJMI;SvyHio>U?@ptV)A+IXLvEg`h=^*et6k{hY4X^!Tns^A#5%Bh(Qc`39J}Q#GRhP<% zWO*KS6I%iQUSmGII+iV7Yc;VM4D*Eb8+Wsb{u#TJoP667$-(PW3U}C^b38(%&VdaL z{20XS5t*6P&2D=pXMcWa3Af3U&aFR=V^nI}b#z~FB}PWYS_bAM)IPkllo=Qp=ubIU zYo$izv5bgAB_w@yyb&51nFqu|ykIk)D+61}-2am%Qv94_Te%tI7r}d-wZy(Q@peJM zDBxE!Ci3KnxwyCr^_zJ)+Ae7oK0j|53(MeqA| zXKJoCQ|+Bj+mf!`ts`{obu=&YqNYkz1)IyvFzbAEKcWOMdYqmr%03=Ug&_j3+0XJi zilV=w{eGau6L#IQxba(~C_RDY4T5OJOYM&O!Pf%tO@Gwu4n!xIuD7R7V9|1Oi!V`i zbbhC((5!Zo#wXgf_k`w0RS7RV=-g+oZX%@H#M857V}{xVQzz{d!6Ug>@meX;$2ui`p8HiH^SozFeFXId3*Ni>arSnA6NE97BBS-@e z7Sx-c>&9NI(b9!i)D^=suj$TY2((Z&4}Mx3PG=kRVu@k9@pE;f{~H$XuFrt`iv+%g z%Xw3NvP{?A&+zqYRGX>tjRp55v(w){w(9L?YeTmu3Tj+;H1m}*M}RG-<1Mh)I=%mJ zW<&D5b;rK5{m_GI%_ekgYy#X{tnv1A*+hWkrGR51Ib=DJz{Jf=|P_e~0Sg z{MMMeX-^7H*r)RKbycgSCT_b2?Bs!(e8yDQYKXK(es$OjfP5*42lVWu-Ovh1+3 zvZ5&=5vay3BxFmca^r8}okEJmvKWZg?7Q+)2{tiKT9f9A$!SEaicB zn5mY%BIFtNFWo&X#MM@Qp=T>AQeU9gfhJUN-f$H%99M`(C0vGbY_ z%lLPc+Wd-s2rhShmHDXB^P=&InJTz%W#;Ek?(35V8A3YcQ>DYBBN~4G%cc>)tZ^9& znhIA($X-A4vp@G(ag*%@aBtWM953U>V3NCAgpWdntaEZmGr8~g4=LUq>1~S}Ix$q8 z`)fAolpqO^a6%;HWBg4{^(ql1!%zHZc)()Y+nrq7{HVT>*zCR$ zIgQ`D?=N3n-9-%oGO*V)6oRSpA3k|kzO%pg>HjOqe~)_qJbkvi)gJ-y2058om%d&Ip!tF*Z^wHC`UI|5Xv2mne7yRwi`d(P9Y-a zZW#}fj9bTMO|*xbbP<)ugieD6L#tD;eNYf{jm3oRPqZhi8S4*PJOaw+auc}QUCq? zwneBR&(3PoPFQj6HHR_--3J+RQKx_0y=1my&+_klq&i-c?A;eBh^c7|?a|?-)Y<&E zITQ7HJ+U&b0Cg6^j#F2u-!o2+15#4t^-hBS!@r87Ghz=3>T?X^xhfAFZNlFNDrrju z(GHyENi{j}9b$qv@Pz-wf1B%!wAzW{%sPtm&>;e5xB8F5D?mXaE0b}-I>F?;XYDe` zEng}T*V&}r;RR%1<_FMgmtA(@MSV z;YK*2(REW!e2Hj0&Nk=X^Z|W7;|syhfP)4ELOx=Xh-|~oN0U@xW`^<@A6U*AzG)BX zU1a=+M`cH6Nb3&T+KTz5$m+ANsiH4G{KRToyrA3G0g{B5xQh9!nYG%joLt z_K{=!5No)ILPoxrCQ+QG)hh$w+izvNhl9@SNxmO7JWkw;>=7;H_T}=`@o*!Kag<8? zw;K?^f?NwV-+w`ANp3rTM$*~gbpfrsG(WTXk3_OoH@~+C&Hr9_lH4t*gqQwFw!g`J zoDJJNUAuoKzGftf5ilzNgwlP6jY~r}Xwnlb?Qmi0u;E8f9=^S^=;-zwFxw9dguPt# z=>2mHw(kI9RjlEa`O#xsPty-@hG?GBb_OghLlv8{D4v^`hbfwRDMC zn{U&9|CLJY2laWU0K2cUD+hbuYF(ueAKG6D@u*ECxA@|x=%gqr{^h3I7^LVY2@r+> zlA1lPn-VgpCMi@k5~8G6*%}5hpFr_njf6y-9(ebYIPbpqU7$!w z*y}|Hs!LtPt_j&EsHW|8CXKzf25qeq(R0mH5c12vVyilE=)}D=Fq@9``i#vu$uF1z zz`l;41?wpjP}5*}}?yTC0&Iw}pvl(`b4&?F-Cc@Gv( zPXuRAMBk#}IH+TUP+LCv%8Q+gh-T4oo=_+G4wBUTBB?>K#1#5dcw5fgqG!yEN@(PD zzN0!X+*mTZXKH-3H#^uSKm;6^}nGfD`)Nr6b^9tQ_pJmkFH;c&j@2rkU zsgG+dz<=q&*w{_>}qgZZe!Xg!0>Bb@m*KJ1&o=)b`9K&l_(3 zT!O8>_1@u3LB2GgJpPC;`-HSIb+Z(&VnL)ka+OAB*|UZEzgB3bnV__$G@Tzz<)K(#6xe?@KH46ph!ph-ssYIhJs(IHHiQ-y8p>XB%DGA6 z5oVgq{oe2I_~X7B)otp#1N?QY1;~vMfxq~aVs^9^+;=kfo@}9aSjOu1abw_gyf$M# z9JAhFA>;vK7O}Ns$>g^EXF57FC-qkkI1BaoRI8HfjtI6;;R0w@b{wR;=EGQVkjF2< z?MYkG%-&F|m60|7vq&v7BJF1K0=!g(Mp!TO#b#Lb!KH^@Z7dRE9;s?6o<*69-|SKP z$#-}t)CWA_iDc}bmTCnX)~Bz(Rh_-sJ9{G}mmaU)ws`%NREJbi{uvMhpKLc9?lusW z6{*h9tjF#xuUavYxX&P7N=(POZ1&$IQy7Ju){w155pPsfg%jz%!y6k#cVb@leQ zG~dIBO=p|JiIZ{P@~17zY!3-m#m0p)rpLoKc+Uc8_K}FU2h+S2a!OoaB)DH(A?Qfo zuHQsgl(qZd|8f?Wg2iNuAH< z{QiEQ<~5sft_gPMIv|b)GQe7?PWP9<$49LmihS>4zmlwK#Z0914=r58sZ|4Q_niT= z>71X(y8AA!-6$H|2?-_Mvl-uID$dV`IIc;798OUd&i|A+;Hqlx; zl;RK9jjXW-qwZI7;eO3Y7zni?HbA7dOf`*~mbSmIWx4+|#KrpbS>6P9GRaZY2@+^$ z_VECcXxDtqa_X;`+Yh4JESsgu<{DUjRnn|HN&UhrzzA2R9yejVPnK=Mldv0a?mKGd zrj>n}(OGfyz9G}`>x(o3xaiA)f<%^A_Iqrx-|JMfgvB{B5$~PYc;MaqU zA3^`iyhJx!=5J7+uwwe@`5!$&@j)V0-qsXi3-2cvby4I8h-hSBw!4yO{DNYsS@mp! zE-E&`Oux25yGH7_BYUVo2(iMLd$Btk_|hdaf(G z9f_?#xE?``J}C8K>X{6Us8asD^HY>8z3>9d%=n?xg$Zd{C8t+#TWkdC@#*TFNY6MM zsC2ktG9iFfy|(IqgT?;nwT~tlx4ZvA+B>*hB>`*l0AIOg<`A2;D*wHbiCdXJ1-XZ3 ziK8;3vhM#@!w0M7TlXXU34UyH-9)E7+5O>h;dB&DJ}2Y&nvRDoDCocag-L}hDJpzzeS(-f${!6gPSXo7flzB;$yybogD}=X2CTX3$*mB z!uVnTcFJwbRag7DXArKLkqKFeNqrTIThhPP^1y0puHqOfUvptk4U<+0q%$iQFU`y# zDuYIVS_2l?-M~L9i;95u9$otH;aZ+Q^2LwUesqP_J4)&P>aSrlg7-=-TDd$t8;*Rt ze)u0?VQof@mvL$mExo;>-RgvM-VSI%gKk@Xzp0_;=97qx&A6(#dzvb$SnnJb9s?T2E&NjIKuxoJ9Tt6^<<%)wX9FVb_p7 z)en!~4Gd>yNvd+G)hW^PaPx#rz)1!H(-7d}6JI)fq)Gj8V|lyFpIRAMkUX9VckHF# z)M*+n9H?7G4d}jP57ze0fuqO&@HisdcumSOBYr3l`@kx&2uKqo-ss)PK9*Wv`9;g4 z>4mv>3~v<5<}MAr5c}lUHWG5a2E$*AD{MeVxFZjCxYlC^!ROAqAcQ!tIcj5NT3a(s zyPpHium1{;tuLz#y#Fa_t!y}ir2{IXPB|75XN$I5zMf;7sF^tP!gUB{3X%Ux+AFBi z^WISg!()<*a{I&M6bbwZd=KazxxnA(sXo8n0&00vox`>3J~`?~B=X%vN)87p+_zqb zT8WbEgEMfVSD-zVMy%QeGXL&>0WFF2-PpR{{t>HWp1gJC&>;fYw0qy*9IBs$!0~^NJMM3bp=bDy&re!T)9n1wZC~y&w~~-#_5mxMaj+I2 zK>;A>@1?lvvc(_Uz_@`1guJUtnpv8xE^SIQ3o@+S`#**tg2(3$1zLATMEm?QLyat~ zj=#1EUo)61qvF0UqsZHUSAkCNI>S=UbOtLEY6kbBK~I|UlOJW$9-{ony(gE$jz7+` zq+kDPaBe<|=G&Jj;cHX-lK1Y%{2{BjN86i9&g?)L(jpthOAR_5ub@L-(4k7qx}-|h zod;s)OWo3e^dx)!Urjp2|~k#);kjRAOd zam)Dsn_wd-BVA6A)R1ap4t-^{@q^C>UXVf0ktl2YiP5%~I0NHPSvTLl@Y_JX3p0Ar z_8l_@?Xa?%q}BQ~p*`|%r0)7(sdg0$RiSf=v&p-2z6`~3$^Yp^H0H=OvQX<;AUx&u z8P2i5J(is$Gv7;R zOAuIfbq_b)5URXxSL}%fF&`#bRjoMwtO1X>p}-t9a*ibn2~4nr|PXdtU2mY)K_*W4QuvJ>q;`=313p~D#MhSX|wF*jmPn9OZrq@ zDHsnb=Ltsd>B&G2zDK+f2s+YH@;f!8wwJ&czoQR?3<& zdTKG6A}l}8`=jcwoje0-vvcQVlCo40HAroaix?^`$y6?6t@Vp_^G^IxWJxJ9bBm6) zT5jx83;?Vr0d|<06hc1gQr5Fr=qw-I5S&+u@Hq+y#q+#_$Vb?RwAJak&LmH~2tb8^ zQn$i=+z5~C*t6P)2duN=uLgL0YBpC;7J5`!&pDNdN=JeVv3=TaynE3IfkzVuZdw%5 zbNF517r!riq|*Jgzb&JNB{q+JPH+Cqb2iNo_sRCo{;s$vY`A(t3LE-sL8|!`)0jU7o@oo0AYan`ff7`ba{MJri>z%QT zJm^uWt_%GC+SG^k7o6Dub&CLXe7W*8hQW2uMoS}mr|~_{XBDkIIN}StJ0eBZN~B#E zwQo=@R7d!q7l8K-vcUVhZM=j`nq%Qw{*65{o(sau`9}?m6c)9*GWg>J9yXu_^%qZr z08iK_7f0(cI0-u5&k|AQl=SChXd<%~(*w(3iQdff10Vnzd#*e6qQd2|p+4Wm4*J0~ zr5-OAFI^d}NT>KkbwhqE?~S&4YpT&yB5_psrF5N2{CgdgD_!hD^9vs3-aI(n^hbMt zI;Y%J1HOzIKQ{=`;%f4cQ+%4S+KPQ3z*`77X9ouy+$Qp!9}H?;xVgY_^-HzA|Lm*`Rk|fGD#0^#CqVw z$ZomEJKRoP4b#QRI0=fd*19+!r0fY2{g+y9vP7?#T4)mk>7 zM%$69wYg8vvO_jSTjok0SeJV^Uhk1Va`#raHGxU6fd8Lt0A6rbwl=;Iq!(9S{nqhY zbh@2Y05g59>cw!t-UeWaSnL*3Inr=*u1ZIpHeK&PUlnw)JY?)lp>H7T`+!nI#fUGfP|K&KsM~+aWe2X#sjG9Z z^YFxF>&$Zs!ek$FJa+6jEfW4sWTQ~E0RyTTO(Vj#==c(>uLqK)^^adrT0OJ$pZd)a zc8B>+9hJSQ3CWU{6xtH){M|E35QpD+`SBp$uK3xR%6r{*5?_Bv#Q(GkQ zX3&+fOEfS^vrR(wby#OLi02Kogna$rEDyWn!Y2^NDpPZ7BWy&g26vV>0}j5!AjSPK z{#b{=XkP#IhAaSPFey-QiiZRf+ZVqE)nO)^pu-*`YJ4#7XvZST^Qh=-Ep3jr#d{t> z6E}YLQs61WRUG3ern2<#nx>e$3;ZdT)o)!}_TLI2g=vKtW^Pu^(mmT%ONQG^M#6pr z++Ns$Z%td>X4mK+swSy-xcHj6zK_1pD?YD+q~+gp5}9eCwad<6pSk;wA^6*0-l~YA z^04&c?$FIR-oDs0W0`vVXC8-zaqJsMAdZ>f;Zc6Hz+?A5V;#5>;20YIVB7id^vraq zg;INxM-dlk?8xl!_(Nm#iC&Jy(fQ$Ko(4yZnVG=fJzy$35)`1Ho~*B&8<$QKcOEq7 zl;3r|e>vv&nBtA%Sb&)j-u;6erLwJFVbK@=^99*-0|gi-EPwTE?(1ubVl>A_72o!% zTo&*`t`r*LRCR~dR-oM@mKivN!OrNXQ`;*G-k9cQxaen+rz0draR!KO$LrG|aM>mOt-ZRf5d z`Dw1wf0MEOxwNZ95%~Cm^RJt}hCb zVT7mVL-RXn@%0j}mR_Q7FUbzpQb`xyKJO)n<~Ck?&>IAg9AGN2s*2&|eW=|#P%7vW zd^K0@tXMZW`p(}f`G({y{8zqVf}i}1K+y1yR7wIcT%`{ILK@sAr;^{mNAZN-vyXF? zLsbn9-j8j#@;4Gr`hKH3qt0$HbToK#g}M3mfDSQ3<%=Pkp_p|cBv3!T zo?X!0=j##j`PP;c0qKo^q*lXRoYnmt+lrqe!y7X8n$)Xf+g$)C-8stqk2i&1;zhp~ z`gO=uCt+_qyKjZl562?G|1QB`(;0|Dps?V{LO*;5$-hRqS*l_!u{+Q7JjY@!-}(`i zaOC8^7HR0NzZ9C$Hg;yq--@Q`+o3>c_eC;=sHJ{II4WImGa2p;a5gJf&2=WZ-frwV z-Q<7+Y-qVK=neW{HLocw4Pp1e06%jXK|Ye8Ie*G}X)so48}jX}zdbtWx9eXE;DNcH&f z`sLWFvhYqqHkjuuer^wsKi#1qon1$KritR`i+>TJ{+f?mLDdW2zSOr9VhkK0Mb}1H zDx?R&5J`}2kPH^>o5z0nmC>OeuO#-Op^-G>Kr?;Kk;&(3>)VdtOy^+T!@C)}!z~YH zqT;^F+0JBtOA)zfc2@~Kz-frXy2}%_01YuhsC+KOybxj@2r-v9zmM%nmR^P|2kk5VZHsxe$=o~}!??c+&2VkgF1&-DBC$tF9dp5~wxTVW4_nt{rz>xN& z0+gQI9+Q}w9lc$%D56wP-GcdKq(fjUgdi?U<0ymelz5k^{^Zd8ScQ4Jja2Uxv(p>e_wR;gL__-L80Q4aKp)Q^B$SN?(s-i5&vDJb?5mDCy7?Zn z){_V$@tpwft2eX=bk@;X&XyKE71X2EeP(WothBVpON9+G84mt)vX75JPB5Q71@oF< zM6kPi_{II(F50(h&YnZr6RpBGxy(vz-eJBL=K>53fS4-~q7cp4RGiccb@PpTlEmGx zrh80vYur5;+MLBK(HAsO2zs_J++2EHayj)&kL0FRIa>p9?0|FMo;`b!gQ_%z2+++v zc$@H=W9$~M@CSh(Irfboa+Ya8EL{HZ9@^V&Xs$*69AE8!k?fpUh_qYWBke_C-0L z0e_Ddn;Hn$N>z74dr>DJ2<^%}xW#R7HbR6&Ic+bV3o-z3HM%j|#TJl2L4NK!LZ5fE zasYD_dkIop3tEYTz!_YzbAq~%KcW(;%e*b%JeDSUE;LbOCx=K<%EYMPi1* zUrReiQ=@B+`ux*+I!PMLkm3swx%Y#U?+_l`pmDbid(aZldj5$n=<915LD>h0zNZ8B zQxjZYF8!&Uui`#Q#uIitWrVVZI)VD?j{w4Vx!{vmam3n=J}7InJu{H6KnWW~04^FG zb02yIHO)Z>?zU-f-M?LVMY+M2Hf<5R=0H?bJKKF@ab9H)r)}Yi4K!0~mEdN;0tZZ) zlE*_0x$Beb3eXekyFDN-o+f(Hh9zj;nYlJKqg17z5X3Bvo(nxHY# zrvVJ9O}Q~p^o}fXWA0aoz$4%N9(K)!G+VQviRP7pn-N@1OU))yC0?J{JgFou2jlkgU^o| zh!Yb|4R8Hm_|BH4%AuDDbnY9EFnN6utj~g;LXAd|I_fn4I7epCwMg*iXhxXGohFjE zM+5K23skNJ8XHR6V$?lD3o@FM{%P?S96cSw2QT~IaIP%^a}Zh(CS5WYdg=F4==P>F zO}-^SU>$VW*nuaz3X3ifRB|hVw*zl$`*GCVJ+5XnH61SAS=DD!mnu&ea8lRayvseM zr@Fs0j^&QEzcm0^(g9FL+eD5csWlqf@%j4&`htay+!lW(b)swe_Y>a6lMnl-D{LYSgV`W&ZkMC z*<}?XiZ>kvx*}gkTS3OSr0N*wQ{))*#RU`!(MkJ^%rxC1#I{bF14^AOH$#u^ROxi$RB+dy>mKte4f6 zy_YK?n`lt^xioN!?jhlO3@52LCwW8nKrofvbyiU_oEyN{!`!E}V+(d>OpDnZaCpN z|E!Rp2nx$%BwvQPe6&WR%2$vj6M0L%05CqHy1K&~=dw3iQ2)DGZE!W>kEPBeAIP*? zyV@QOR#R26?#PAY5ja+UM``gW^d<4%4K<(1u)NW4@R9p{OSYSVIk+g&-uUK+b<6Cn z2CtO8Ip}Kqb+uC)pW8IJdv4v><|LeQ1XB}p-r|YA9-dKrCEIkzKJUT*lN3SD@WVoT z#?m}fEy2Z9Yo@@>7N_Tp>CFOsgDoY#Yn#vrCZxxMRB6ieH%iZxUr6DH@h8`Z2-+`c zrqWf(2%W7F-3X&_quP0)$^HsT>3rffdZqurBilb6cxrjC@=|Eyst@1aREX9D;8Kz+ z&~H62SB|%6Qs0=eWxO)EdU>NiJ;CQ~hElQn4a4!BZSFS9uwk}!OtH|{U8eK&8H;xB zFmSZn^{f5-VhwAF&>^__LC8ADoOxFeWu`;DuKYTN!cl4P*riM-mT&XGBvP0t8zyJO zd76%8f%AQ61vnWH0FV8eFOJR*&DLXM(qsgn|JHQ*s+Grvz&iNZA>|ISC;4;KLx$Li z2uO>ouI&Kf(b~5n^3bsQiLMreY__)_2+waZ{98QzococUdRFXtOFWf4njY_!9<5#D z15?r1ExkPrD|_gWEOZDK0a=KIL`Fc$A|USM&^AOrL?7oT1=3N6pz9bXNbbP?^aEPk zoS2t+;vM^)o79{U^5zNA%H-Pdf9AQB@6#B)J&%g zR3lpeZvur*=>Chp^}}65Mh-VCns?n-;KosI?``Jw%_u09WpQZiv-p+cXtewS&o94= z$Dl*LQ9Ka@T%%WO<{$%X+(K{Xa}M@9JTa!X6YsE)XAv^Vp&3r{ z&+)cEvFQ3Ifvqb}^sTw!Pk|eK{z|OVJF*dqY6XH=VeN0j4M(p__?}T~XY|56(mIbq z_S}_#MG%yKZ6HMXqnmgJR2_}HBKBwugJd`BEv@3l#!8PA^3K}Y_K5FNIU|Ip(~p>A z3ahCF(R;IVd}`F5eOc!n`X0lwv5?1MJzA(zc>NMMjZZ(-Jh`e#)Zk#;?UI#drqeH0 zyr34^@KH6Otwl78>LzFOXlSVHoRWX+kgCudjnx~|?cT@Fxze9=Z7zb5izc?<-Xko6 zRgma4;O-aT&KIqewy58foGo|F)wOU z^an2Nx8Xme?t~xFwwUsBJogMB?A79AH%YtOX979qEDs^LDP@4Tk1~Sf*a2+cppKR0 zM|Eic&Jg1&{=SWV47^PFGoM~6N@3HE>3uD>WdD|hRlb=rb~Iz@SF@A-exVx}k=-Ve zdYe!GRfvuL4gnv4M`mm6_vS=1Nq(;Qk0p-I+z~svAzVSejs63uikUTQ#7O?wn*83E zU%p`=M2Cnf){GB(xDJ<;ihf=E3lqKV&*7=ke#F0b`g@Vd9eA12W0q{`J2T==5^YfR zmjYWcjkayJ_`DlD58Za^(b-9ca@s`)s+@aw|7y_{T%Ri!KO0Ak*wzULCm~4cEk}PT zHBhaHXD_B#?%Ga6wr)2ODi9cIQ^kT4zV$t&laW`dJ@AFA3$(l%73+B(Zl3p;U3qN# z5!s1awPS+d_9#PG+j#3rKRX~h!d5sD*#h@)=-8sKdiSyxI4>t`LcSQ-vOk|jft$mV zX#e&U@q)d}2Sc6Y*S^S$C^cv-X#(vfI@{(#Glw#XRQdyfkp%yk4!T zblnn=ZkL(B|E(?Kzq?}+F=HDsV-exG`F>9_0umkp@vecf?-t(DP7MqXAKJAyJ-G6A z2Hl@f1^MP{nW=%!xw`7_Pf=Oane{^J-?Vm@PwTfdtV-Ur6@v~~()xeh6{N-#dJxg- zkOS$VynOTrSTwTh!T)(>{nN|+QWtsCo-c5vB!LJyk=(w?}Am+W@ zU}MMkqwxA+6f{Xw=2`nKhn2tfol?DzHQb4Rl>2u(inPwjt?^DJ(X0%499C8Gf4f&W zH3lTE>F|VON%g~qx6;X?iJ;PmZXExE;K1U9LSp^t4X@!kZB~^grzyoGOX(5t2@p`pI0cA_S_Gy3m{| zne$dKk$lpCck3dWHtXkCQ{T*Y@YOdOm=4wT9gQMmW*yvUx}G+eIEFuX#eOMF!k=+> z!UUCPdbiu2!|skZSS?b+$^r)Zhgn%qLV^gd7~w!~%t1t;YtvVfZK7n{5^k@4_0G2P z)%cPj-QyFsow<^QR-k zj!o5)cOC_X`k>~u__@2MCA#8unN*ul-vH%YTm6RdUlsOKFHDXKFC97sNr__;DMd6c zLTwavNRI>=G?)zfngsgV^nk-EBJ=?jvO%8+Lq~Nf*78du#7ct8#p=@b`_u#MtQ?3r z#~9?s9WUu;+Z%MMx4NO*cv2~CBf#i_pI5UyG<^17!=ECUZ*;b2BZ$Z#s4E)5vdGnIL@eJ+^DxUiX6-yQ$|Ew;Ub~n%TJpc_o zMNoOJ8cAY!9IbR*r-do4{Mb(ItKM2~p)we|usK8zv_j?}D_!1M8NAtB?49aNijjNm z#IP|$$PTVuH3o#GO5+r2)p5d_8&Scjxy=ttd$*^9?GH|Gi0~CVqTR*Kd#?1KV#cqx z)*XPO#@$dkYC5)w5v5xo6e-XQUjHOWmXrrhMzz#<;0~Tod)j?lc9=5?LT-oIRKD8F znvJj%`TS80PpIisC4mpj{y>FB51P0hWfpA3@rPS0R^*{V(5-&Yoh6hNapR4f%Cp{Z zw*~bT27|Z9w1c!sM|}s;mQnC8Wxo4~;Bu&V65#dQ0=J%)|72< zWkHzNyy68-%3;u5^|b64&o#}RzPJbaYj`#B~Mon(emH`FYp0_{fqzQrx>Wmo27n_}PJI=fETuQf-e;pJ+I#U*q&p$ zd%(9~&-)0Zko1`Wq53OB+5VJHa^1Ql6DC+YisftHo-*6h(v|}qcA)_6*SOmL8JMI+b&U1}_rf9b!-V#mUx_NJXsnShU~cX3y@Gijfg?>q z81Z`9+@H#oJ{^P9`iXnKXF3GIw-|Q&oJHgmOP3YmO-uEEzXUgU z2pk~`Hc2Ly;m7iCJU`B)-U}x$2cu{N)0}h+QZp5E zfriALGraKy7xGIm$d&CJ`!2){W${*gIt@dWWbRmKe--fLGM|y+a?LQrg=r~>?@ep= zF$3)?xDzCy_o<+noO<3M6KRnu;?hkRoyjdDjra-Y^!aS9vOw}U+Bxg(6pj9?=0o!m zz8U=1AiVI`4(xkre`$h)ump}OPmz2sm(RT@qGVRLNp&k(LA=6THvG?XLI zd{-g{RnLt0r8?3;;{Slew={GWJ!2Jav_h!TgNUISxs3rCdO{iRzZ~ z0k0BliUzpIBapkz_<0F-65}$`3?o+9OG>O4!&#qiWn&r3do5!Cb0xOH>EhpHXbV~% z(NQiZ9U{ZQBY?R|_c~FM&Uvv4DjpbheZhm{LJ_nlR#!mFhEo+59e@@uJU@#pK`oS&%39NbTBHJ63g&;8aU$IYYG|-a$uCzk8PI!lgz%lFV1eF#tk!b9)-p9R-E4ww@8#s$jH@|uClL-EJI{!t zC%Dro1oAk&^+_+Yh7v0Q5ktREKyLi|ulK3OP6+;HWSE#4H(H)Hx^-*^wVojh7H-^c zV*s|K6+yb%Z)Wh@Al=Ih^JpD6b%uJcqex(Wer59_`{<$eUCdr{eQCJik2-X#&Su+1 zvxAh@`Q}3d;79S$fRg*ozzw8JOC#SF;RVv8VK00&ZVGp9Xx1S4*eXO@6y1*uF@<=k z!d2R4(e{S@W@KLtu42&OkI^es&*C6J{R#Cy705_$`~`_Sx$h?V&51GFilCd{87=;V zZtsiu82n-K*~% za31I7<8~+KjTod#qd$nY}p#rMCcyyYhyDL>D4JmJ@`Jud|`el}W!Z2`&Ha z@@b=b@6z*IySa}O;)5%x2A`ac_-uyIFo`*B&=y~)Fz7oi-Xcps`yvp+4_oSJAifVL<41XPUPM2k7V z3pjxbT@uHiRQR<1ry?P!@Ov+;{ua}HC@@g1?$~W}415`H?bOzStbEFedfwpqG+^gD>`A3_RZ z6&)|$H;2lGH4Oy;yUT=&=o!F-pzjVoyq&7X`zSTp?JRCLPuf%0lSP}NZ5tge(V({Z zWhko8_zD4-N;G(XTS$`?N^qV51sDX*bE(7sQ`=icRkej}!-SNSbb}zGbV;{@fFK|U zNTZZUgRtq877&n<5^0fE*mQSF#|Abn-CgfodY&izh=`lBZl1e(AisxX1W zaMLeDN*iv!_?r$OVKks9o)Mj64C+>{T%^UI4Bvd5&NXFF>?$F-b;_C>tLg;CE|Qe^ z{+cx$UgH=Nm zLm^YFx(!C`xv)*X>{bA?0Srm=L2WBV1;v4?xfnNTiRQ<co0r>jRC5=8dvc+i+Y9|)n z2+8yx3(|*GDK%9!Scr3+5r$hm9Zi=O+-!CN;iF3jD(NKY^1f4Z4A0aC}rtP*(*}ZW5J`1^YX8yU?{z zL>wdl~g^RtN+1G@zT|rNQIpV9UD;JB4Y!{lzW)B0OGq zvmT_+X%@Z}sQ+__(M8pTr^6!)JbEdh9adqQtm=W>qFyq(=G0Hf@#gI>=TrK?!kL2Ovd@hwndT|+ zlc~RKX??deVH5; zy$$I-c^{@kjwvxg7^fKzl%yVErydn7J(ww#Z$$lMB80Eh2%B^xM3_M!}e#wbv z+qmBx+;+rZ@>LxF3N-2T&PoTMgHbEuLotRyvMj2<+|RS?A?$?B;v4{Pc(72Y59c#- zxsFk0kIldh`d%BVP>%#aj*n;Elq6;!CtZ@R+9?m}dCk*#&BJ+fypNCB+7q8sT!sQD zN=)6(eUsi&Ac6#NC`6@u?_nmMbJcinU&e#}#cH<5bXRwG)4o;)K0*YyU#_W@>&^vC z2A7?-Jt5V4c?*oVd`Fo;ii{M1e1aba223{HXm2672_(lN*nkgWdWB^FDX!yR& z#$y<(bqC|#J!LB*Oz;r>-kH8#-GMKN=`!(HZMv0wD!tCm-tHVC(uj>aki1l5v8Bz1RS?x;y?0$?*u#T5c=sCAD$+gaNCMwM3OSZ$G&4PBbc2lgn{Qf0pEL z=4#&+pgb!nVqvrf@~=A<-iun8aQigB&P^MNbwcHueuS(7-7b3`@c#hTz+z`D{1j$ zPy%{ALDKiNc+8PYU~&Dyq*5sl{6ZUK%v}=5-R}oAm*Q8HiQ^v>H(~TyHMQyOX5O3yXuA>D9=nWYe z8J9>drb;2M9&o)9JDlR7H@s?@%%b(I))XE&Ug~T3U=uTY)sQ~7Y>sgKx{Y2tb8Z84 zLf$kYP&YqLCPDWVZD&%O4S~J(@t+|UX;6)(C@SXn^{HjK>JYM*@KcI>MHZd%JJXg* zlKxeCYRBT*&E&gpB?M-Sw*ga#?0={Y#)(O3?MQ zTrdUipK+NKW$`4ZGeF%1cc$!Sj(L)F4xyEQvY&T);Txr;NpR~Vi~aN((?Y5*Aj6OE z@Di2Hfu1A0W@QHI)`6zP+KrMA=&-=P_4vHSBsLQ4I2r zGG%>*U|zq1q>h(%^}{d%jFEV6rEa_Q2C3>b?M1A@w83%TsrHedS#Wl{9$2Mf;7#lO zL7SrRN_I&KBuhlW52^mN9L_(_SNn1IMA@(d5YdXfV|Zc>bvC_93P>t;2Up+{?djg zhJ+k|=pdv8$oU`(n(%>8g)sN^Pl$t%e!%$AFXyCX5W^UOEa2K*t@#v(Asws!JaNj4 zP0lln$Md&+{oIvTzXj>v_=>0tVkvui%A-TlB0}CXZ4($ZspVlZNtiruL|)e5kVpCN zoJ)VRVLUHGHA@<@x&8c^(0trz@$UM%HlR%ooP7i=4p5Y15@`p3my`4HOe0rphRgb> z-%>kw*?Vx7`ySjmR}R`cUBl-3OHNXnb{Cs;2QTay_Adws;GebJ> zgIOs=I)d8Z?;3KL5cfbX8Th5L zX=og|LI25EkDx$4o8EKujGcIxgi6@%E-1r^JjnbDKp=9s4cxW!_vUhg0zOy|4wPPe ze*fUP|Hc+!on!z#!(-E1o(S6GD@ z=e!k1ueJ-E7@Up==AqyKkZung!xZWv>*dO@s56$Vt&^ONZ2Nt4FbYt8>$N(?*IDqq$H0(g8YiI2F9x_gXMd6+^Pq?pN-?_$pg{9G8u;njPx>By?ab&OFvKcb$m zuP85hu)W>zb~wVdlN-7h@#!u0=G*Ynq!J;{dg@D%ih)qeK}Yl1`9aHW&Z(Ol53+m| zP&Ehv zUGjWmmARfpoGt5uEXT!#d3V=erMP)(?#U(Zbipv^+%OxQOr!dF696ODP$2p?y~_U% zff5>mTQ=?)pO>pfH`$TNpDb*0TUfMqbevdAh*ZW)xZQr5rX$_pbaUK;L<;-D920)wlrEl6EvkXwk?&Rx*wkx$y}kx!lr^C zC<<+3z@5mM+nOzG_7IQaD5#|da3hS2m-piEQiML;+vAGSmUVL2m^5;z!*raEq_ZGZzduZAK`;D9b4(b-B>}jYspSM-#22b!Md*Tc|JUd-)8)g zMK0;zT04-?;3gEB-7$)qroMGBYv)1556j*7EF=V*7P1TQ_B$j!{f5q1v%;UfQTd2_ zIEB}${XZ87b5SSiGJ_U!eBU0nSUCHOYUC%a(WTp`i(G4@wK~wYyW;#=wKZxPD9E#e zbNl)|!;X+!5~Dy6kJrijrySHxkb(|055W5YJujf-m0+9S1gLpsZ#!74Yim;CE>y(C z#^!F52BHqz9Mo@JlbsAq@4o8N`e?};6!C(FiU)>rF|ZADc}CQA|L;Kf+j+h@%bCy2 z(Ms9DY;WG+o2+c#6=;zI>{qAq!k_jhXeGYIqE0>eEuN!mN}#s>KYmXvJ7ftBoUa&* zk=q1I3DKOC6L5}nZmG^fh9c9ba*DhLHG8;C;c&Ns@jUK`!KLW%l$Wy3P1#?c2bg-! z^~2zRL!QPhEIk3s#C>cbyrwx6G-_6GeE2NeWX4%#>jN|9Dj`7muGsyC?Y1oHli#KK z@(|V&Ad^%fy)2Eezi9nv@%$%8#JxUQWFU=N&Q6E%xGso(BUVqL>uINaD~=b$g{BIw znzgo98vYj>h>ig)@0Gs}Z!+-jFraJ6O$#6fjqq(ddnDeKoJ->w%o_B6qsvX9+px>t zXfBcZ`c$=d#{_QIgVruY)i%rT0mU&ct(*2PkBJ<3p_Ry`G6AK|hYcUCWx7xpwy#9} zEi7#BvvRgf{MQ;pae(rw)RS>R2s77IYSJf zwt($`B&~?Lgdps2g`PkTVmNW>P}$wJ_WMoQF zWprnz2M@&eI!HiMTSP1)L^uhuEHSW(Cf6;6fAq_lK@X$PcRXBbWiDszt}eS7Tc$RUAkk{n83uK7eqrZQ1bIm^W^zTzj!hBx+B!Jx~?)MU69_% z%;VUsDmfdV(cgZ#;<+Lz+={vYK@KRI<1P6TT^kY@oR#6GQ)IC6hk z9}4vl<=wL7%dTrjckhh5zwHjE#gQMSMMv4*VPJCmleuEnlsj$kU;J(@4?bR5oH$Gm zRPuszJ`N3nRt31+Tf6o!6VnSGZ`$9as<0N{0quj8OM@&kc<0;xbqV7ocjcarwR#JY zasr0zG>g~mKd4$l+U^M_xeh^tz)HN_Z5V+>Eki=EEjsQ*>of5R1SI&(HXVj!j&P7P zf`sQqzN?Hy$GP67%&Swhu_B|>dRLwHGmnM&?G~r!X_+2p+mt3LscHbH{Xby$+y_8R z`$i3*RfX&d`X0a@-Q8E_6MFutzp{X^rk}lwX*uJDwAY|~O2cnq(7;0*!12ugBK8&fcBcRf*;K}s&wp6-}H;Sbtht4i` zUwWO|!b^eJh93Jda_#AW+F(zh;XzoZ<{I=kzP%GaV&e!8xRF!{O#}c(BCsm^=;Uf#seDW+m z=MnPReE{MV5wWqhXD>SribTXm*6y*S^Sh>rwawseuk@J>M8`xgY`*_jK$a~E0FX}* z@}+{fnn_Y5HI1PV87p-hyUezc>TmP={GHGX*r{$kATKf*khJ+GK&OWTn(JOuOx9DdDc9P2 z#B0MesgH9Sk;8WdQnlHS9>ACRk!y=UO6@ES(p_Id0W4PfjaNwwPalD{$i*64J163~ zdrtTdn7iK_zh&3r9Z$pj3!a*~x;3v;EOXDzu}6_&JxL zk7+yLyyV!av)A55mPiI#I!9Tp_%;e3dgK;H4eRD=+k~X^TTKxl7RkkWk3E39(!1+H zvQ$n926wu+Ot}AY#s*DA;Fer#M#}#8k^iMH7s0#YWzs8Y(o1fle1&^V_pfRISY1GF zE`--Sn%CU!crK7G&PcX34M+vG=xQ$IVts-7-v&m7Wd|paTIJz zQLpkh+JRyKYJ=Gg7gLPY$V0l$fqQy9aGi%F+O*#~u-GTum}bG$@fBkE_C=JH*`)SB3udflGMYFr)I5vvREI@~F02LO^W zr@VJjju!7rYU3ovu0oy|BZYm3C9YB`HGMwUwfSSV4iAMRD1nwd%w>H&bdfQZ5o2e`G~@k5*w|-~U&Nyxd6?P*XBr z;<0spy!hhalN@$gA{k@5!)>t`&EFsCtQhEd8)|a96^!c9J`;X6muRNEcFd%+tk+_f zIiJ~HazMeEe*cXHL2^eQB|q6)bW(H`)Jzmr6abszZKp({Ti;WS^<@M&N&rST_UOh$ zqIz2Bj3sVbkz>?jb)(7qO2(TRIP2Q=EwV6G^?gC-g{mGZ?YX;ZH9Yih^@s>z<0{#zvmL&{?BKo*)A;*_^$RznVa&0V{%fNuK@ZLkYQ!w$h*xCP)ywU<>$hQYZLweL5KzBM?fBSUO6gbY7-iT<@!((IFjW9e*dJqI}kbUj_ zp#Ue0zk z&}pMJu)4V3I>mgbj`~Fs#n~2%TgpP7+yQh7q3L1`@s%Z3Y-8`-R74H0s;|AQyQS(< z1cl!g@->|R4CD&P8Y$02+W^+P3djVwQo|-hXtZkW*zN1(zW%No+%Q+Z}6%Yhqzyvuv&~4aXWchCN zqE;?-5vdY$Ux;g>8%7_jD?U)6zlJ=mMW) z_Wv1T^noC~NQ>S9tbAP>uPM;WtyaU#HeUl1MgayX!JZ00*}Fh-MmW|zD47k>`s9fI z8z_ePFno@~5%UR(+i591s_?_Z-|>6e@(8^2*59c|hrfz%+po)YbGqgNaLU|wiau$Z z`hhN*;We$a_BfU}p1-!(p>u}<(`ty#5C~Qu-0)X)=fsWtQ9%ZuIcS`rS-%$e#MrCY zC1(rNv_OK=c^{Z0lvX(4!kiwmga%~;^H7av3NPJQ@!b~4=L^t)u+>D7e@bI0Q(d$6GI zgskocEK&bGJ51xuBAl_I?1T`^B1Nh1tHlhT_*5w$qg=|(UW1tqN4S1F{Af{_67~t; zsUhtHfw0ljlO{{W63g2^&hPZoerV1BBX+jKDn=7YGgxx}d%{EX6Ur4WJ@-3MS&D=e z;>~zV97O1?wL^hMXDVI9#~*mpC_#M;M9IWTC%0$Z@@Ag^()IZqmW5e!k&!jYIej?F zTyw=JCG`w0M)<0yYqZtZzgEAWp7K#?zHaV#->dZn$YkNUW*9(EfZm5;pdfwI7}VGI zMk|U>-8;s?j?#_pAk%bDkUP$y_v<-uBa8gvNQ}qz?N9tguWVH3{n?-w1Ckzal|)sH zfR(`OJx>o5uVtdq48;d4h|y^h+B$~M<|0y+#Vu(XOKvP~yHUK6O(i2zqL)iu{hEJX z)qNOV^)2TJU+#$K=XyhnwLqZO;Odoz?c=X2^NY(zU6llTU&B7y4*X}DO zUx>!PJ()-aZnAod*@R+qrEyIby6c7wz7N44zp#+M2SU^&4~zZz972Hp$+kKx64$?Z z-A&5jbQW92XEWDO=*hq|ZboQ&Y9)sWEHWkY?}jY!P$lVH!X;yX{M53k=WUzsxAsg| z*+94m6qbRS_7oQr$AsN}6^rjMAm<)9+m7JVPvFdi zv}9*l@VPBB0=Je9UwRMD^%nq@%F%zZ+F&c5L}-<6I=;xom3 zqQ{4luTmvGG2X*qgZ=Wt(k@B@Q*QY;<)uXMB1yf9bnY8*g{L`fzE91lChLjYuDnv{ zA`D7vC~0`(1s;s4jWuvUJ*;E1X``#@+ScKcZQNHERLpJCYv+TPjCt<-aE~Qr*Dj%d ze$7$;rRVJ(?#Z5?zvQ8oHApk@tPK269{lxdKJ*u{;2cgcRHnPPZS2XOk^r)t*HP?n zjPb$C>FPW%adDKR?LleGQksAJoGbEPG}XrlobM_G^SF-_wztgmW2e=N265?ahx<2AZE9-cDpnI^eci@;SKQn}w z&7=M0pDGk>XReiFgVK^i2*~nZ`ZH49;MXl5PJ_XV%gT%giYw4yruU8S{tPT^)Z9U> z52PhCa%BDc;%NP*G7drcc3!ii*Faz?1xVWghNz=QW*I`g@{zY;zuRcy=QLB`Z@h?s zl03rj$R%i$-en8;8)6TXife4WoF~1K)8Fyp#HKMHeQ-u2wClJ;S19`S_dLdIwBFC< zw|c@nS18e(rm?zva*Tu^mURv~-{Y#gV>Ahf0U901^O=s#>YRF<@z);PpKEVLCDe=` z8FZE*PoGZgOIRnPhQ2_OV2|4Uii4LuZ|bYcv}tqu&-6Ka%0h%agLcMfUvH0*WSN=1 z0Ghm*f?V<^Q`sqe3mV5s(+Q7mb!SQUxXpagy?1)*45y>Hwhm;#iak zfOC%Ed~YF{S5>QYow@OD`YAghFmTM~d_!Eqmm$lUH#4rag!XKjvj)!fZ^^~m$~d&> zLgvAXUzJ=jgU>2JAtHG3ntD0&EWOAHDHlI`EX2zMS~A~aGuK`f-HRIY`TWUugR;?{ zb@kip3uV1fu?l(~wfgKWR{dYeHpN=^RsTlW;1h2u=}ODNAqqf4DiQFtNm-F{>6lFr zhGp=LNTv5%Ajc64Q#N0y2+gv{9&UK%6Ese*!kGS8$a^pGszN(oub~p(-u@(r&A{e< zkvi5cyx(rK6>zyhpd7N~rlUjdvn|&5Ss+-amOl*0@{`AfIRFcP|HBY%fL2$RU6gf7 z(D(Hm$8A?~W7n;DygX6lITnw8nAv1n{gpr-PU{KTczh z6_9a1gA$3oI9K3ZAG`A)tl@^&I*-FnmlcBQEROlSuUxOij~|%bj-QV{j~W#DS$?Gz z)TtbN)i9mbymg7e7h@B9Iks+f!J=Z7y`uYX7thqqo+`5rE!SiC+4a*j^sgk)&!gX}*jgtTjum?Y&kVX-5(CIrThnYSBvjLl^7MJsac z1v~c)>rZF}Aedr*pdX1o)c-WYkd)imR_(bNru1fVVLyiXgd_-4KO z9`u=o;ng8*uFW2BEv=EzD?9iwfJt!jN8FcB;BgvI)=GU9*fdzH?BpJNl;dn~CBCKe z9SUTANd!&{lEj!a75|wFp!TPErxpMJ_fQ-Y&92bX`DQ*c*0XX2oBgB%IdA^wW#%mq z%4AvweuImgvg(^YW|rEz2-UeT2gDRPqI9OiyorFc*AgJGpRE__Q3$wdm`rQkO2eXJ zRTDnkk-=|k-t>^F0*Mw>UUZBgkWDvPpSlNS{pE^lAIOhPq=D}OSlw?JbT!zX=2|T5 zk;TRsQGXI^ z_0NYfjkDgDh&`KD;WO)dJw_)QkWfQo@Gjoec(Lpen^CLxu)BWy+R`wj1Og%!N8xK8 zpoBD3_Za3Lc=QdFqmCP1U*b%E4dNW0Un1w(R?CRk(tJ0%jZ8gI3R~9xZyM;wDbJ9= zA3#^fhtGIyWZa!w5#2*I-aLNZkynj#WgKJax&ys+{5r0#jQL6VFWJ>20R7~TRt62K zA?k61

u@Q8=Zf5k$L(<#Cl$S6?6N*`Ji$NGtB z=DS#e3@HBG3|HimRo_!r{D7d>qv)ghcSQ1&uLU^NT&#%UVQLb|mnBTgb-*4L(3j50{YB6zsHh$dqsJ z-dBK_hql0NZ3Q4Irf+gs9ZF0h3tQ>VNlLyd3y)OeH;d-C&fNXCJPtfPWfR1f9=C-o z4jf{J`SUedK26gkEXRvxvm&=ncbW-W>5#c~QoJ5F)}S}RIFmW5@%jb8Gi@WRIQVbDr!?-&T!pA6^7k$Ui zj*xr`s%S9ohvRr`&OgbjzOtQjZL|Hi3pfCo03gB2I!+&qDpKxp-U|o56oB+q!1sTE zd^x3L8i8w^n;*aur=%lJWEXHi7O}7rCNwPeLx>DlWH-*-{Wh(R8N0&;`IAGg>Ep&b z(~f#^q7!3kM-Gj76Z-#LpKJ;T(4Wk%$$SN0BvpdRMJL9GrYDF2w*+#6TU+1BbL~;F zByd^;t9I5&3X;IKD@AfKf}mbh#u@T}AVk?aICPq*LlyQo+<^|Cf)a`lA-3fkcE{Ir z8M4nMBA)#9v9kKl-aTaj5Ze;hRaWwykOdIcZ`%g#0yQ7-L#f{rvaDZpkmZB#A$ZT; z@I&=6V}uO2d%l8{;gDeCdBisXTFF8jD$6@nV_FNxTtOOoHq*HAz1M<85DLFOkS@7J z?w=dLFFsa^*ciln(&B0RtO`7L*>sjIXEQlI7u@Adk&5}#0;k?#%x$RHm=$A_8}2!ta`RP4Xs zQs8o6W(k!OQ!Rblp$MGH6Z3evP!zCF<#F&Fvhani*Ec&0#6!fVN66w{gjnnr@ARJI z!8cGag(d}{^ay2wxSU=*;R?x%U+YZ5^}j1-iXXo0_0HBUr6aX()OY4;W`({JLuOBM z$4p17Pia%A(L-A3E)J!&&KRbNGWM>38gVBYpoVVLZ8{mEZDV{Z=RN?lJ1B~m19uxx zkKhlr1kzDqa$+ibAZm{p;$!`@C9~08v9mCx#k&3JekFu#gd8j2LW7}V?-4=@jJEl% zxNTRCfc)X~+a3vkO zbOoORZEsIhm(JfLUM2j2WecR2@J(2bvwRG~ne~>S%eoIMCp=q7yYP0@w%T|ES;D&j^9OavV< zAWo4^KbUJ1$X6rfCcN;>j8BW}-|t+8ObDdtv1Vq!;ie{#SM;hn1|lcZ%aY@LW!CIM zn+B#HOtAL?re?kgQZL_Lomh=NR$)sTZ_*5()<+)skXGhGk^)yAGDuK?H`C!SuZ%-c zK_}n6U7`IQX0$Tf;`hr#=&J+q^1=+(Sn{T}w}2H~`~86}^4GWgL9$?8n9!kI|p7B9mHr46|EX znxwAN9GNADDkSpO=k6Ej^Y7ZL|E@*T=Cn=l(tP)E@0K?zIS{S8b}znCb%zY*?8P&8 z7N2bisN#HTGtLSk4>Te`JJF-%q^qp#m4_oIdt@O}4Z%pz&cF=lJId?_ zm%MFPVH%QO#evp9#TyD^cG&&fpY1P0G<*F2%v8MienH+cANMH17g3E)xPOBDaKhR1?z6cdgsVs3))wbEA&w`Hw_;}+P?lEILQ!K@|{K7K-aj}&-a_i(89Po0x>O4}x%oevOj*fj|X1rxkIyA$P z+v8kGsp8b`p7MZ-(*h!Nr{>{;V_t!N9?EWGlvJYx`pKi81OdrS&ttN3@>9|mz(Qg@ zWuv9cw?8};9xhkBg{ZAc&TtHE0&l{4X1!)PsB5ESeYqgqve;%q@;h}{ysQfW4=AOu2uzv@4XF_xLsZm%(B9r1#2i3V@3?eery`g zMMi8+mlFA|CF#_=Ir?95W9W5+6|PrW%DZQ}IGr0&dtK!);!xVzXZ?jsnXjkF`caKE)Mc?N3w)0p1vyN>$ zGsRD_gn8ky<~7%?l_1vfZ|qwUs)h@L>~ZTq5cYxhIy#cRDR*5~%B zv(nSb{X6WKl`4D7An^aJ5){%?Q<*F*JVFsV{$XBHajOe#-HFj$Ul>d3gH^QJ7-q$T zAKUB3JJLsJn7-i9wZ)P+$!z-s8!i5}P(>Lm&k1k3HuSzIqQi?<;w+d1)*d5k69K0g zFW+cCx@=E1SXtrEc%zBo@pVTO`vY#p zm@I!D;5wMeJ^R4FCFjAu6%wklF5YSjx-Kc&aLp(f3xTRZ{B)Y zA@B!Gh95&ri1vbU5e!6o+P^NMWLpV;ed~8omsj;J91FikwD(dLF&id2-8Xvf*apuC zNem6SNY*hD`=0xN$U$3{HZo+DX(7~nd?Iq)m2e|8gj>F~{8zo_Pcr9<*bvu;Oe%7% zLbEH^@m^yz2y#XyQQroPZ44LG24bR`75o|sc>eKGa^sx9uTDV?3)LXM^v>Ry#@yZ7 z=%9jf?t~66>Qh}Oc5A7lLuMvH6hbtH{$4#_BWst`t(^Yx?j5uNiCPda z@}|e!b_>4HJJzwY*Gs8uEba9a;m`Gz_q|w&s3JTK{^3qNafe9ni@{r(s&}e<2l>6U z1y`q!2FI7Er(Z}ElljhJUE>Ik_JT-DLgGvl8J=`@TiSdop}ioN8|S^eEXs!OZJrqf z-?Wmsck24VrHk&rUn*=Y(7yDnb(wzC@pg^l`0Sc;cQiAPvzC8Bs9P!oBAOMP8%B2@R+&Xb*fd8yQSjtev`tr{7Lmcvx=x8s|{uIG^~F4)^WdS)BwH3k>P|W zG@mb{M>UahtvtH{jn^xm^DusHmd`%P4tGLp#nwX~bNJc`1~D9?g80NfIZer&r1jX(Ep2d7r;w zFt6j&dmE?r=P`gSQp2>s{%c2yiU>UE6CM&Ba(WhWS{@=yO%x?3t8Ifw3vvBcA#yR! z^rokF&h5eOYoy=QkJ-qT8?%_Oe&EHlE74Ey*fZ=#HTsyZ*fi2K2EUu%D)zhJcOu-q zv-?2%+P~K`Y+X=@ety zZ3@Ov;qs+f_bu#WvkGdkKP8nDIk3)&i@3(GU%W*bFk7kDB72xG;hOg{X10dHZ-eO# zgS6~>xmHfxkI5+2$+}5dR$;*X&Sv(eplxGG(h&`y1^bCnP@ZG&?uEFvhm$bZ(Qsig hLF?Q9fA6eMeRO80J5qid@t}Y|igGHlMURdB{}1!eGV%Zb literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/html/_images/chapter11_79_3.png b/doc/LectureNotes/_build/html/_images/chapter11_79_3.png new file mode 100644 index 0000000000000000000000000000000000000000..4f89c99e972be14ce55273350dd90da75ce36d6f GIT binary patch literal 27834 zcmZs@cR1C5_&;t%5<-QnLNswm)1-r*aB&DXQ& zExcl31R04hnZmL^HaBFniF|eZWL0;#qy|^BP}#noTf175TacPtpg&UZy@2|G&()QB z-dkU;T)b7EG|eGY1tV8@#$(of;>yl0=zv$o#=9@|CrG$#z=m~Y!B@J~r)rv;oSdBW zA(}1FFIZnvGSJb{**&?f41Q`O{we@|qNDiVe{^VK8X9BT$%ZX{hb2=EcxMwGvPCpDc)3IRip=)~om$9$9c3belm*AL`-p8?m=O?pB`#yhNfJ-lC3ZHsPB@zv!4QYLcX|Afj-6;?uRE?`ab+ ze<4*u!TfGannWE?FZ^nZ^&s5wP{YM42teU#^_y`w}9Va`YZ`ogxJ)qzj zNwA^Wr1(n(XPGzi{qX(Lo#xUXVdUrJ^X`N*>Y#nBmtX|NDcR@+IO*ht(++n-3g53! z4F8%nvEO7AEjI|r^)1J`RuYYjBsedhd(YRetNvYe8$$TH`>r<;|8=;z|317na>>T$ zp!yEUf23yag@n+9>Yw{k93zkHCu)6SeY5Jrjf4equ)76Kxlf3Tu2q#|%d&i?MLg=L zV{mFd*N|9EE}s;Vg!)DcYFpL%qe2oX>0U%H*#q0#5q@SiON2iO?Em2#sOrP-wo5$h zaG#*ZH*R5F}O#_`amSk<2sQK1{I%Jsh0Sd&IZWHz>pvWXL4 z_PoiT9CucZwS3<6-EByHtM0luo2l#Mj6OSsPpnUz+Yr93G;GlwKTT3kTME~$!-`aK z%;{fud0ZuRS^L82z5n9RP@^<*9DYo(qM;>pFW^MObwQjo=9#qzayEAOox58aUw)(8rCsg!0`pIHu zbZnN0Wx|R)*f*tk+nebBR+(B>ek)5NW+&OO+H{{Lw{G2WD*)g3ns<&x%al38%4mqY zki&f>_&xkf8y24fVUM^DNpkHq&&gWflT{Uoi4*P5bqBET&A5~KG^>P!!z!9ucGmUk zgDmfUQnKzw^80Ec_-AKq5n)Tzdya6H1&z8`jryJb=2E*GK}*z9C6Qn8l}#jYn-|$g zgTuz$O5ew>RK zb-TtIIWlW{QNN!VyR`Z0?$l7M+cxTUn=#>62r+8s8 z>6|2a@80DgVjkB*wdT^923CwXviQJ0&<#RVN(#~WOT3f~309(ITYK5_Tw}8?a{6!5 z<7;Y>tQXs6#$Iw{`Kl1;Bh4F|OAl~GIP&CYB`3B$M|UQYbdWEem53}+ zVsTl2?<#ZE_3UvVsUloz+IPtRgb~)uPcC9`X_CnzXZKm)j0diG92p$v(dafr;XdMf z3yF0!dxV6mk!~S}3z?Ayc+xr?n%~D2dn7UII(Hs+ur;}HHWlbz+W47#f*hW)ZUo28 z3BYg9rngR>-(9UgPbdltZPMuOm>nC|TS<~W7C7)`{?&XU>g{iKh7uch&J~+rhJWJa zxR`su8bh4K(jX#S5oUMj^pn(v`E;jwXrt1d(d$97N@mc#Mb- z$M0H#eZ$dWBL&8wKmcF%BXqKZj>E+d7v5TGcPZCpiV8_c%{0Hg*6J2p>T8e3Abb-hSMRKT7Z(c95d%! zA?HO9cUPTCohi2L*!894l~aUmYHzgd$W{MhDjjFq znQA@lmuajlHaUh}u|P3fpjLd%5QJkoucevf#sUuq9kwker^`4`8TWdENQJdaw#b?7 z;FiZbbwhc4#r&_v^3cfwmLiO9ZDXYQH1a&Z{5Eo5cEtOf#hUAeK>K+lb{;1{FC zJ?*9PKhMd9vAQQqZabrClk!r@jD%ZL^&`T2`++8?V6;QsZ^Ny%22~Q%xv@L!eFpGa zM|WYt{JY^N5gy+Y4wNVZ9Xoay2aCJgcLprZSc8YhK|N5~TC@yJg#$7pGks9Hn_qjhWj48yj>qIlpKP(7 zY^TFaXJ<&>Sh(m|G@9kFU(%z6TcTE`I`Qyb_r`MNdND)vPUOOEWLO4#)V6_VGBvMma~UxW znNjrzb_!=s%dT(^E9cVT3JUg_2@K-Q=>a2V%Vlq5N84f@4)58-EtsNUtVUwn>rNsZ z7>B6Qo46Tv7l+EEYNV8SVTxqG?#Z)O=1^G2%#rM061e-fs7+Rc^KYlT3ls5XzANas zA4sW1&opcqmn51iUq+hbm>7{?zV0(e+b*H&Ww9=2vEGiP@vUM(w%49N(&MLnIE{|M z3{>=iK0vnNLae?mk}MOiBOh@cZif9T8vT4 z&WQD=5&eXrl}S~tx~c1JlGTU~m=QH@9MecVi=G4fK`he1*5w9*GZYrR<>7xk3zHVd zba=L-<5HL~N9dMNm>&w3RzDO=oW+7ruXF!mEzy0}KIgi{NW_FFK<_Yqut1U>`niyz zTwK)-RPQ(K6hFm~SH^!flaU;8cUAT4`PH)5p({aAbrplHE)MNOpu`%nf>Ys3)!FSD z?~iXF_+V&RCd}RIC0neM6LCvhtOxel2TL(X=BjZfp(ZAVz$H6&)z2d*0d?*c8%;Z` zhO_#ZL7$E-RtG2V)(PZD>jOlu^rlDecEa^jY!Xsx+it%of(s`d>eV5W0fOO7k_=` zNPET_-r+2KWcS7*chdu5dLy~sf_6@f=e>Rp`yY{w+UsgRSOS)MDBZW}#3~N@w=XB# zSX+~xe_rCM=bDQXil|g*q zM2}Svd!l!3?r!h8&%p5bSL%(DPLCb9ku!jE?Fcqx?}UhciFAI`GFe{|e_eI*11b9rQ6D>rfr-m%|4tCPY= zgcrVDJEHlv+(qA;2xC`xZFqbSDaCgdc;JO;arlsxBeya4equ3AvS2Zf!m9^)-pN2m z`2Zb9jKuy;%b#=Ty&#BBUNOrr?;CUHx9Y8>!0EsZ8-7ZRpVBjx@hZ!b08p{wbO+llC-PnNR+US6(scB8vEwEFt*HnsmFlLdjVr8k@^tGtBSNS@>!J2qL zP*70kD`v!vFurYJPu9DDa@Gfk17D=~jKEKvG-Q)7=r4ofIk~xAJw0iusVz=ld>9!R zWaQ+?BO@bK8bYBDC{(n{(T>`PG4MXA$G8L#u5l%3Vw!iv?MGj*d7n5?#(s=4+T7tVzv6l5j4<>-XxX8(g@TX42Umb!*UYs4*? z!v%itt}45^Fj0cO%T)W(QVPbdgH668jEz=e8iLgM*-7=`?B~XYjhx(q*#H*n!{eq? z8Sv?NF$W&tYCf4jnuQiBezJdvFq1xEX5dv#uc+8(;xL~>l@If}tldwO3oQw3=z|uB z4=bJ5b;&O?{S}wXbzk_Zg#-}QsF|IF^pp(0}#fwJYVM0QW_en z+A0@j$`@pR|99n;)>BRW+pj7|e9a4%rx#v*VNj_KO-*FF7nFMMLBO{n?hh@9pP{H9e4N*DXJ)Ch zH}8dQE+bpgW`lx)dGGNgcg7)8=jemNRBk@z^Q}5`ZoAD5Vo2p9jQdfiMu`pY345Y) z_(7o&qWi(|F2`WETB^cd4d54ZnTofP8R0313F_xVm*( zw!pyefR2}p?6|v1k;QSHqRN^Nj9zW|KX0dFkA9-5%oP2oNU936Db+ zqj_L9Soq-3kSoAY{9~&dh>oy@Xf>%HKYs>6xrNnb(ym~xLLBU-BOj~B*7}Edr^vVp zPsVPk36i63ONl2QE(aC%sCV4K5CRLr!!BAl+Ri-rb=Tp_M88)^fsH}ias2eH^L;{8 z+%Mad_`^^a?@P7+Rcv@>QU{oOOU*t2Nn-vJqrqP&4SuBJ`};@B@WS`Z%z#f+j1XYG zb`qvHX977YtRG855FI4{@YwTN-wvaOc61ZYk7Jf`Dd~l__S=};#ZFecOBM&`pPF~9 z&9JSpu;akOE6hJC*^g54@*V_GvyeA+Mskf+Sg{a+h})K5vl$N z>$?RSM@h~}?l0Z9l(^MjtP3q^6uA`Q6gX9XLLve}j4zobKYxLxfM0cBGn+hiadUp* znAC0Kv>_4jF*|&))LLSKy*^@a`_f3{v;V%c#mpD#Zo_lHXIXQjNcJT??yc`Xn6X*+ z>dmM;_buCp0eSVkc0!|%jzv%f2EDPg`Z6ji`8b7JygWPsEiKQk6(io|XA~7h#KkSv zZ#X3b6eHdq*krw5)M<-ZpXW&OZlxZ30DX|FtLxRPSF6J4H;s*rJ3Bky4_lRGT%j}nQ8Q(6*Y)&4OU?_|vX1&m`vnu( z032z+;tj{6`aDm8KywL>#m2(jzrS~EY}xLvD}O$tFs@H&wOwsH6zU7@RDp)w4I3=^{;Y^a!_v)sow> zt4vsyovR{xNM{8U>57ukt76CcEvNnG=~0pgZZZ6XZYOTKlz*8fV6f2O*4ihkG2Mya zcHa7?Yi5Z*5plYT$|tIA`e!$0$fFDz{qw8E3b=v~zkps%f#I6BRP<BX_Ly!>x%28c%@Wj!D;%)iewnRfS1oeGp*6p}#YC>bpL zjy%)Lx}xOG-r zt$J;@gvYQypxMRNV?j^qXzAha;T8CQ^d3+Fp~3AK!V}HnexoS%+z){U9 z>E63t$pgkbB?3(rV|`Oz*7>}6m_qKq!-JaS&Muvz`o>@`ds#{JJjQ#VR6}AU``KsM zE@30h@`Fg&P$l8h0oJ46i8J!Q3@F9CY$x7_dx*2`EN#ATIf&o#qfk%^0a6})l8jJaseuA1}t*Hj9HE-KXTNIUB$V%z$dOSgU?#XfRD9uz*)#){Q z6|qLeS&E?`})?Xrw&ojjo-zHcU@fpVy99FmXype-ZvTTgslrD7JPy z@_bD~dr>^96E<*NPWG9>Ld=n-)Z?!qt2azTPZ>w_Jbnb++SbsQOIF1CPYYG--@h(> zs(&x%gPuISISk04G|$ML?vRp9`uI(BQOzq^36q>@6m+V$m@QJAjdx1aJ?Fzq9Sf~G z(!eNRf*FFoB;o9cXL9xCS{P z@~C~UZGm;u=}y6kKvKqruC6qS+A!`uy6bX<__GA7Eg4bIAseL4KCXZv_)!8dlmB&# zv9o=f710AT543`DftR1%m`;I)B2`?cwxBgK=`1pdX=kC&V{0K6*y#~8P5Fn_h&wkp zvLwY$_S70hcU8??BR9*eR=wSEle3s>z0lKdvq(VD)UbI~;Rk-VgWuY+ZiB7GAEr_)Q)w5| z&Jb6x$T*XR1?nh_e+NuUIrq2-0}d`YPD;d38w($`oXd2MrilN;Z_AO(*o z5>Nb26hgwC*_1rK_xOMAWIGb#8S&`nrJYtbfl?o*{Ctn35yD4hc>Lk;_`Sc+--4y? z6iMBswJoFTbd*n>+G|I54x(4I%c8Odz56mmrZS9zKI(-F;om7Ow)fugj2GcJksMxS zHJ)ws&}kX;opg)csT=X^V~VCpB!%0jO9-O%z*f@|rK9)q<*(JJ&$$mZ@l!1g-iZp& zbolu9t7CHu>O+5CWFu$UMg3S>pe=c5Lcg?e%u-mt`vqjOz=fWN>WHjF>qFkIX`d8r zi|{JUsIJ72u0*%4#64l*^78Fqg@~NaH&0ij)i~>N;&fWs7q*oO2L)t*aKk^ck2H2} zj2a|X>}S;-%y{eb(wl$bSJGzxm5*Jxe6z6`p60_C3Y+l36Vb9DOb-R3gUG6*s8cj{ z3eCTaG%a;Vwq96DOfw3477?tPK16M!&K%iUgegFrms|tz@%YTIG|Krs9LCeb#Bf26 ztnRfpxrJ3s`Qsto1j;%Rk7?bL09v77g)0+{Yi!`@O`xPxa9+|rN58mh2u@-48Gnc_B~Geh_7q@VwVOWDSc(c>f+ZWsptHqex!s3|I-#@0J;WKlJx{GXcG9$$nVT1 zBYUcFe&U^mJ2fngvotP1#y^#;Wjm9jSKpS7R~)I9UYz==5sy4^DEl00&!+gyA7&a{ zUNO*kY47zdI!e9asFQL26>-8yFExu&_nu9zk78O)GLlWq&)Qh`kGCs6QX;z`-+@h0 z7UXymO?@^o3|6-Cn)gzDXY{grPwwv8;DFP;EyNV&gmj`dx%mP`^85lXenhOTO$-Vs zxbSOB?^F638?P{t*?zqsBt z`%0tdn~rYtjXg?=BlfFSLW-)t1Y`$g=?2oLH*Y*2&=+%UU$2us5E=>Q_6J)4g{GhP zr{uBIYFufyQv8k$eh${>p95}1nF`t6<@Uy_w6wG`Z*IBhRDGz&DbS~aGQxdRlX3m+ z!F1NI?00O1yQh+j1_UZ<8SaPIzm7+5Dj8;$-sL?0sx($5)5@qcF?3y7_SB%gAoQxF z=%==jq+a$@7rv@l9`J#V2R}wcU-X~y`i;qA8~Mx*d<91$x!a&t$55im>h6M&+O4`8 ze+&=2S!}vmv-OH%?ux*w#2Wj7l4{H`?2d@Tg0l)8#5l8#jt1JoR+14&(m8c`vztr2eVN zJNgd(hG5!7i$vqChY){`;S$^!F1y%B)?kxNa%f18H|h$*a03)SGQiU*8hvoCm=e|Q5$QxlO7X5XjO*6DoSvJje8>O;o|IKaezT$eGf+q()FEA7 zR)_@h8J>q_%=pE5bR`wcDFi7o*$PsqHiU2Gy_=dFdHGUrMm&n_7SO~Fqidhs;A{Iv zrfruZI5@;HNx`2cy1;m3b3(Lqp9||fPt%r&AtY+nnpC%a z-T}-V0h!zEvF9;8>49fcmVSZhVJBt5To9{)r65~@dvsCI9dv(Va`^Rp`y_>r(Ed*J zm7OhzV#=w1C{MJV)+rXKk#FC&ii<0Hu?1DHA#-7M(7e;shOU9 zBvB^lrmQ~f3Ay~rF7T<>*vRlSPQ{6GKBSKx4zwyJU8%*f-E*YZGKZXIF7&4HIO4|< z|Bh?77)t!yal}qGOmY1$)e6F1r|NA1?hgHTaF%oxO|38VNB#M0kFqZ}%o;#cI*VJe zuT;nuKBu^_Jtu)$*s|bjm@^crhHakXz$_|SL$8BQ%yfp5Z8QoVIYS|pUR3qliIwsR zrx;rI6IUmT-SuqW^j5_6S#>6*V9G6GCfLn&I(Ww}WWTUdPZHakaM^%hH zKtSJbnwlV~`I7g|S7h5mqYq#YPR}Kj0 zHUcQAwuM)JQOyi0T&$ZB41aD=^9~O|a zcLZLySI#S+ho5*FTVA7Ngg?_pR)M~0Lsm9=!s#C3-eU3VR;I33z+Rm&9nlj-xv!q+ zZLCPdfZ0zVvOj~(x(ziT?*-UuS0jo(8OH4r0G z^dI0f1KISmw#C@)Zhl$iZQ0}#ff>3;XxySe+*xy?;ral4)OTaVye<46<%8qDx6!eu zu?z89Lz3=!K&IF2onHcSDdtREVsJ=ch36;t6)F7EyuXXt==8%{hd$S{Z5k+{Cgq$}1zU!G1H8h83iHlszvHk#f% zz*PCO%c$7`W;T0?9%8R$UuGJi<^`ar>k6T{I$*MqG#}_>w7GCl6~;9?(lVzp8ucjB z=s8CT;cYxlbT;rGWz5-$YEALyZgX!gL7rx4$-yXntghZi+;BYaH1evA7Sb&G!O?6Z ztJa}lk3@>h@NzbYCo+F)gxO0=`e1O9WgWpq(t zmKjspwHs)KRS=Yst;e(RwaYdlr38Oz`XMQ>$BFd$D%LK68dy@R4de8Jx}_WCmMfg9 zqg$dDQ9MHy+a{1wWmRQTmceYY_@vUGc>syCKY;b8)eUr1Mkgv?nx}Tv%^HE&_}KEp z2z8zR@VC>|Ee4?b_Ctr1GcK9c;S%>2{kDvBP$=oIx+U8(1OGG}>Hv$XK}Z$J(<}ct zXU}ddGpl`^XrB*G_>_zD2WbM>@RcpgguDPz3uOSwYp;bh>%D}~OoRL>l<2B3ZhFnx zx>lx#0|Ig%K_LF#*`hjtl{kw@$PrM7s_~HKNgIeP4d9u<{~gAGyqZlMXTfD&h;|`kCk$xS`*CSv~4Fh)a|EVJ8 ziZa-9cb45t$5c0h+{Qf*#q__xk%u&Usba{Y-5l%w)3PiMjq5-eo1~dA7 zWW#Od9Ej?dyG?!P-LC`_r4)SB?|;#J>n`W5PkoBfOzOM0C|+~}Ttjz$pY?+Jz+AJY zwHDI*{ott40Z2?|yMbQL6)UU>t)@k!&VosS(mXH#7NWh! z0gwQ$5Jz6w-dG!n|8M{L8$o^^*Cwcs@P}gr(Qa#~+uKb3$m zl;w5P_Xr2ppZ#-Gl^ZPlI`5Bw+%0)PL-zZRPK?x!hTAuf-dzfT0WjDH2WfpE1g~9I z%bL3meDnd*ys4I>t|Okp&`1d_=Ex-22ZBBu1LC3R+t)mUTC~#*a~S~Sr+hYeVz<5% zN{ZI#&YE2>VEc5sc#VR68pLiH?#^HUVD&MsJm!KLA?n;zLU?GSy^RN~1~@|%6mYGJ zaZh(AkHP|Amu^A4*3Q%xZHIlAMq`|BWT#=A*yLryzPtUpu*(@M!Y+Di~z^y$v) z{24u2(wTw}!Zu>1z*Z=T^?6|zK*S4S)T>TVoG70S>n_62-UO6Hc1IHww2gBBZ0xT_ zQr@+E@vSZ5jKluBW-HSt5@6SxyUj~GaSeFN3KzKVZ_3!}FfL9N$M;NW87Xy(;vr>_ z?QfQ5RiWm?y_EH}$(TXqM1c-l_S?^n(G^yKVA(vkF{i8MP(FIvrrYD4(vUEam$~ad zeI@zJhImxaBR`O3vQhU4AM2880Vp`YKt##O;dyjzh>HC-zw6~B)x%`qr9qM;UVTMW zwrLVDh8x5!b@S~782&6sK|_8#Lue0{uHdu!=q>%x%!(sOrcc#?Clz|#Hi&tOzmPI` z$;oy+fNY zMcAD#Nc$hMs??HuAEvAQkQ$1s8R1X=MVmc}e(1R9uCsuoOM{G4C{XS{pd9hW-V(>m zJBgIDG#lO$2X9F7S4~>@v=E4;8|XXQkklfz*utgW$;J|i29BgG>ho5rQio!-XKn({XgME-|C;cw_)pauBP` zx||sO!gCa#DMv7)9V~LGLTFR7~C-!JXGYE^G$7PwuAPV|;Dmn-lh03ccr! zi=yCsZ5>dSV*pvs5O+BQThk^=ce6bA#Dq#HG(REg?3r9iPJzy#CqwACnhQy9_D`@4FZ%-I?{Ra zHB?{R&`wvyl0LZl>lSXdPgH(2Md)Aka1jf}GCSeWTr z$m>|hXJlqpSihi?E_?fjJd@4it5uRJPesQa2zV*TK-i7{YNPf*V0}L-@n0aGTGj6- z+NKpLE#KGp9t+D%1Iw#JNsEWIW@o|L8qY@@Sk7u?WuNIS1}D>oJwm;DyJJH6hHMvx ze#eYR_4({mxr%vkakGu|{ zo^;`LId@-U0)6z8a3QD_2_g$Jn9FkTk>&iaeht(BXf)?Q5~f7r-o+MqAF9NSzJoYD zff9#veD`LF>)LqfgcGYd4`?e#-b|wQ2=Uq2RLuUwL7yENmg|HVjI| zKPoAY6IZ#Cm_a*f|DRBH;cjy5N|yCPigzUd?Z1PFw)?sHR_sh`8iNhuOIND~%K$n` zS#(j>lGx>3{jLCN0EP$<(xQ)+_By&APyCde;k`l!g%R1$WQ_vy|I6jw(z)N|=~IE) z)Y4`6)+I=kPdRQd0bE4vngl&5NiaAamto!UO-U808D7GrmKI>oNFuFxPh!a~#8HbF zh(+jPj%bmm)-48m4lWVCgx{~0AcQ~tj``B_lRGNvIi@;{Qw7`ynQe+1*+|R1%RPgd z{s@Jn!j&LZ1tXc0;LGC&P)ff7(ubAh*}g~E^x30{@lYPuzrd}4ESSxSl1&-bvj~;l zN4_AXv%EPuo^pKD?ihFOKJrSIyL0!3v>zuurQuN&$T4IPqxVMv50%FV^a&EmJjEmb z?AVD6fPDiK4v9a+qT3Z0&K-BDCUJ)XVxiy(dcBSt=+0?ypt8v4_y2R~ZWbAxT(~?d zNDh_$r#Tk;vd;clLq=&~R68z^j3(V4>{ui3q;^fpi3DW6IA)or7zZZx+K^D(NR=v= zJb2tYNG@eq6%^ewZT2P{eFr@h*^GZ{0zIK5x5PT>q0a z6i1Qarj2b1wck=BrJH1V|55zJ95P=W2rB~fQzv+vBlxhXdHbGV?3B_|q?w>vE!dIJ zQNH5g49Pdog4J2FyIm7{YqAOx@m zbyE43)6MoJBj-s;k&?@gk3K+_YRhmBguMV0mKW$@)4zJ2kNfQkN)&0F)BX=)Uz%NZ zFEIt)AOCKIIt8d!xIeC=-4^sPJc3~;rC^Q^jKH#FK6!ViFTCx@A~+|?u7Xy~{P}0Y z`jpG1v2ochzW-_nQN-_Z5ga1m7Z=`&8Zi$I1-f1PNf%JlTV!t-0*1_&HGw*^4Ktt# zyMMjUj_rBfKay@Og0j4Z@`;dlVf|aqS(oEvWISm7`1c+vdV{ug@X}*T%*^4(rLj0i z*1KoC5ZbmM!k_|Ca^R_;Qyl=?rhtzAb_nOq?Q1WdvIC)Bmgc@`I!K*jkS_o@#N_Ue z#X|%^K?RQqjWeGZ+e@r^wFHJOZ4gMZnubT#u2_|Ku$XAw1 z5}`&JJ9mKI{lH_ae(gOmg4ORHvkYNwOXWk80;l{}@h;%`4)G_`!l3cEUNWqHx`8j^ zNzB{X0JD;8x}qStDmOpej~iGf5tx{&&v5fX^nEE)C5%$AVi#oMbaRxE+M;8??>ytu z0GK_1V)}*E)dx--XUT#LN_Ypa8KAO4={uF`8$NYvDfTSfZBQ^anK?`&)cZWP$@OI3 z8OuW^{&rieo)(uD2t2_CH#oUBUGg_kFN14hkw$c)st_`HmtNjKV^| zfPK3w?u7z5))(9Zrj)fUp^%l;O`rbKlU){hmEU97=}QDykPKc16Lb2*hQNN?p`@jlP<2kj>vfX#M!95UVCq z8d#*^MQ!9Z7NoGb{J0aSlQ{y^5pxrv6APL8bi&lIZuhu@`ZnUX&OZzBAx4wLlA48c zM@wF{GL_#3u1(Y4@1AlLeBP#Z@{nl`@<^@(5VA4pEul)U3jiHqX4d8!Ey9ziySMk&{^4v^V_|G*sCDD*pIJ~g{4WDR zt)pcoR1EtKz29iEe*HLr8X8%T90G7hQRG!`uv8cic@fuXWa&LuDXXD!EH+NX!`aNw z0~-UU@&?T<^i;&WZB;lo&hf9+uv5J135xjNp@M%##zq*^lz{zaId~EhDYxd?v7^$N zx8pS@9ulOGup$CQD1S{DJv}(i4egqD#L+JZJpmhx^eN-5keePeTxV`yEX%(9FbRYG zC<$)AN&-G^dF5XS2bG#}?~fA?pd2kbu9p?81rp1#b}Q4-H-JJ(s>Z`0%CCk+83%vb z%J9$xs*r$_dQV?%#LR8w(dYE#dltyjueHpA<96I>A`}P?-m8!SS+fjxt4TXs>9f_^ zPze-{TZO4P-wF)RKAmnBT#j@0gM@kg5H%5q|C5lNm*dEG`+c^*VrK$jQTcduot4#_ zmxr?(n2N6P${#CkupV8v*o#ar{OPZ#aR2W8tb^6YQppnDvrIi`whNkGp7e$jePUr0 zRiy_xkvsjN$2u`s8jg20`Uupsf?TH9)4h1pE~4=_P$$EMjZ)|2GmU`l9G7JXyDWxs z2^v~vwUo6*#b9U4wr|V9$-s@jXTw^BXP^2_rC()DT>z^sK;!a4;xbRE>HP&0lY%rd zfM-fYP+NiPZ zpVZKMMh&2d-{R%x4;-j9cx!UPup;=j?w@sX5pMkZ17Vx`;-b@x;863HZtIn8>Wbs2 zX|NXLoSjA)$*&Qq(-t@-ao+*PQy438m7JrRervKCpKeMGWz9DH*DRVJ@>VqM?azTC zY(U++M>dn6nxkBk!!CeZgCSLU1O6;M`>(~#Ei5!Bqa%u)|7fA^dxig5nZA{+qy~YI z!_O@fW{d0VYKr16ip1 zDLpm4_Z60ZK^M~^eWEy0RF>4)5~s((QI>Tqvd{jCu-^1t+d2Q2xO_DJnBSRNSKVKq zniGHV5^(u`@W-r_=~a1L-&upavT+Gy6Jp-trT0Yk|9Q`dD%zUcgDH)h1p(gfaJzxf z#B$&K{b!i&Y=vXgB8u6gpACvtvUF=d9^#iZCdG5y&9`S27(!v|z6m~`eeZlH3L+L~ zL0l)IePbcL<@zG>y6*0b5-MM(wd7V~Dnj|=KY4d=Wpha=-+*1{(UYgVC;z~x>3-8t zlil!m>M;Wf#^u`+3X{w)Cv3lxioBkioqcPer?!h$39+eD3E_bLmou;FP&x9#uQ*N4G?p^QU>Grl{+A$9}g zhEF_f6DFwY%;p7K1WL7n+bcJw263 zQC@j06M~QIKN6Fs_F-L5wb!TWisqD_!%}SlKZ!5LdHjIv^7Ix@gXBa@EnTI{ClD%W z*&Oow#9l;omn>Tyo`AP39D>V62S+w|L!b33Hj=Qx?}3VPX~Jx%-k7bTpdWMyq@#(P8Mb{OPf(LP70w0EiJfz{&r%1NgKE*Z#KcW3AFQsy4P}b0M6OOQC?~$Jhq#Wwh<>btNC@3D*7pcR2y#VB}JFM&P z@+-mr5#Wm_S|T-nB35)ADLWl;)!PWS`o8jzV?N;#d5Zm~eKJnchJGoU}?&Kec zqs1cZew%^U4>{gbEv)^GXf8KAY2#j(v^v1 z%v&2Qh$}W(eE7shIZ5P5TthNK9PQfyUPd|Q`KBP`VJH2G8#a$((dPxm`H+2vCM|NG z^5{?`G1O4frg-aLzE1=GI|iRuPwv^mZNG+>1V8E;&q#sg*;6LC>p#^*sT%Tf&MGl` z25J~_W&deD>d4E!ohR|~HQrwMSF7$D8qEr~dy%Ghjy4Nfxnq3IrZ=Ga_lqhVW$dnL zGtRg&*NOO(ZuHq_$rrpYDN-McAu$j@w~<!8#YZw@5O>$5rgWc#5@RL1bvH9B)8eRt|if9XEsZ4nmn`iltQ3xd!FK-S1-RHTW6Z%K=U!#*WWoF_R4KULKgDBiv5s1tC z_E1yvOKli^k%w*z3Z@YX!-c{UP%vq$cgGp%xNBJN9TZH)GhY6qjLyo_V;k=naM!ex z_0hl9FXAdFg0C_I@-41cLmd7C9A=tinjYO`sTyS(+H^?EZ=xI?ztx2IiErrUYDSDr z&<^>M$|h~fK%M-v|3-Wni0+IZX3TN>_Wb|trIuVfGRd@w-W>{rlliW$-gC<%Fygo< zetEC`8#$i+_d(7uM4@f%xA{HY?%3N8*gErF#4zqtGkTMn>Ho%Hj%X!u6&eD&a>`(p49Vv&=(xkF%r^1gLtD1n zH^D0FA;~clq67td)%3jS&7PS6+L6M5l&^Bwdei7SrR}h8>UDS%pE|QRxLyg+LZ-m+ zh|XuWkBW_#Qdxz);%9YUxiC5|!S}$|_AllCT)@JvgcCKAh=Xflm@P@+;qg}u-Q2$a zr?>Bpr~3W-7x|!~k5h>d9V-%!B90L`_KqSlkC9n~hLJKlviHc0>^+WF8=ODTYCkrnW1x=ln%LYcVaLk9-)6BUIzVT zyqC?-#6=~}V=^_kUY=*U^Ey~J)P-*e?F6|Cm`n4s5>GuA=%|hQ9zshT$1C2W&pfa^ z7;-*OOKXLxqOqEO--TIvu#8r!1MYF{y-#AnCghKccz182EjQskXt2*3NGhZ9otfDt zfulY#vP!JRXv)l41=6H}W)qJOl^X(;#c$t?0jZ_B3ceDp^ltlxzzRnc2a|lTM^a{)L%=b=^CEF_e;h$dXXl?6`NO-<=3smjQL zMm++!4+xlQ@9JyGjAX~!o>}RfRJ4RbA*8DIpgDckqNU|H-Jm9^FQ9DX1r|w}TkqA^ zGT)<2^dw|4q_TG(f2-f!wV4GWjL0S*mq+73f9R(jX-5?u-vq}Bhy#1hj8O!oH2Z2+ zxEBHSB*USy-yFw3p8l+pbDhFa{yE0`cvW|i-!x{EHARDB?p7rD81>%n!QvGk6U&Dy z(2+}}O!lNVGj-Js>=M8>(qNm0S@R^pOh@kbFAWq`Y~$f=NYe>V!c?eU=nHvkYJpcU zx_Y>J`JJ7(S659x{FEs)?ky(@Z4vZU;63h){RvL% zk-HmS)db`Xc&S}W@$P3MF+Fp()SB!_L@V-xX{+C&;-338p!g`kOZJU3>(f`RNJKe{ z`}cJ*Kz!MX8c7nzbz}#EMyyXkQ`_JzvpOG7$k0ax-0*<3Bd+ufE`YY_{V7LbzGuu| zRzT2k*s){bsVz63YBA1(nca`Z&IAx-ss&9k!{!v8Y=xKeU# zt3N?KBTOhi9P~E}tW}JS4hT-yweS+$__&$HASV}Tmxgqv9JARF(J1`}o(tf&lF?!W zdutpkA(sV;Zjg3Y`JSFJX%4H>TB732_y&z~SVrjh^{+6AWyUC8&~)*S zfAHF11Z7Z?Wovo02x;nsj4@EX1DK+Sn6?~DMhlEi&&T)y^mv@YTmY4sm! zD9wvu8e+KZS=v*UkKFtgs?d|Ia%o&*|E9QD=n*vmQe7Cq~R!CkuucPF+CMk6*Tn>5Vk*WciyUUU}>tZ z^*!b3K^{&d;Gw$b&@>m!42fOT#(n zz&n1I$yzjRs4t8HIA}@-I*hFm5p}?$Q4pXma zgyrNZr#m|+4Edp&18#L1+{!faqwMAgk<=f{6(V6)3hB?Oxx0ISIVVc&YXFgfqSmur z5Gf{yL-N~7F6(8inGK01M0;6XjWi%BbZFcYRhssKz`R2e|4cppLw|zZq^DRsa zh;z(`4ug0{Afl>KwJ$Fpe2ps1 z-uqaptN=l|pgi0uSQ8VghtD&ZM!(YnhcWXxs(x?E*fLr2_$kB^q`HHPR3zu^_In%< z<>1zer^*W~jJqF3IY|ch^}%i{yXVLBZHwDW0%D-v<_mYEfK}L!XUpmDC|@S*Vj;(v zy)L#;z!AF_uE#V&F_+`rrpe6PYBHJlY)5e6Oy#o`2r|W;e7zndv!MB2rmda~92n>s z`Lf+kR{`Cg^l@0tob(&Y4TVvZ4Fh?on=L5w!*hQ3^~1*KweW>o#)a?;unQJ*k!pPA zaH_qM1-2+XT-x)?c(cO|!H&p0E{;4g*LkU?{O`;%cR5sOa`43wml=~RG^Zc=2E|Xp z=ZM|kIdtNCKtTHfwAoSD#`3lb;!B^}XKF0$V@!Zwv zGBe*HX=Zxm3m?N9Q7lJR=-v-h)emS%-qAcadT=S_(T=LOj}<@YA}X!1_X371+SXuR z#1DwWd-3XXvS+Rw~alzG-iztzcKmp z0~;Icf3f1lOh^orWi}?=A_aCiZHkh{ztY@gcsc-8hu{=Ka?}{rE)wq+UK@0d5C#@| zBBXpD`|@7CiNU}<_9hr_LrUkn^8?rFMUKo0yo;|F%eYL6T}xrfV@HS!?nprhMv3pb zoxg#+)l+cVvNx*A^cuyU<_7#9WE^4G2thi92ydhQ#%jNEYEW|oqz~Newij<}nPTUk z4J<*5N`aDFp@TEk?HHaA224qEe(tfc)K3cDMS+BXd;`c_hyHzc(D@`Yx2X=~3XXun zV3NY6rK+qe@ynKvlI?-X*Kc!gCJm|OET!qvp*q*Ty_7c5b?ZUMbDnC~E!fuFQQ2NZ zX^%ePd3uKc-N)qD=&LI|10inN#5aC8g;DugRQfu!GL627|tXhQQ!+?IjKyT{{)g5Z;$K-g_kme@8Ay)Vx0>2xEb9~o0!1< z3zf;(pP=Lh;QukAA=&WB9=Q}2CD~!!`__Rg;TJj(gk+y^nU8>W`Y?8Q51f|)>{GVe zJExd4_GS6XEd&ECtd}We6}?(>M-)_@0bXc#hlBV01Lf)c+M>w(fZGSBAftsL!L`yW ze$HaI{3Qqo>#d|q*>12;GnOM6S-hmZ?+1fp0w84li)_dM2hT!zof zB{)|@iUnz;ydo5Hm(iroKZ+ zhaLZhc?bJnG)z#gAE%JoQ@NdrJJ|uj3u~faQPJVpt1txyiw0HLdNM^(oo2h0&cf`k z1I#dB?v&*GsEB($6TLybaO@)(%tya;u!!z zZ3Lnsn`6Y>VmY*z3^zopdF~hCTg;nU=W1!iL={cnc zc`F$m19rT4AV2HYsO02*W8VTt@5*YHAM&|@*wxqxP+AX0n6|C|`qR5R8JGHvzRs@elqv=FH!W zuy++p8-|0n%`pVHNl? zCHs*?*iwz(nA`iGk{I`$y|l!w5*B2l;|I<$*xyhnDO(xxNk~5z>I(UEHvsJ6?g=ne=ffk`=)4zUGe5}~gbvx^59pa$?vqqTfB?GD5+FSQXsGL~+pGKc zMlX^86qv#$KKZteKLGWjImV@?{XCCwr~7L)XYxgsm&_(;(Hvm7GJkh9DwJ0Zmvf2S zR@fNk<^kw#$?IY2eAl$`Z&j;qD%^Qr^crg2a7;b)w~qZsj2>^%ApOvpik!Ld9;kak zFQF@j#mpr)Uglf7vu#J^o0v?6<74LTNqvjmP%i&#u6|c?>>Q_E!F=kTU-{Y@QGy&S z0zry*_Rc#t^!Q!Z1$I*Xk-F~Rq9NspCuEa~(|Rk?($ipH)UkueZV_%+Lt~@w6m_jO z9YKe|ch*E-YG{oo9*dHmtii|=bWyOxE_gdDXC4#j59`KP+}9_}Od8I=+**W^h#-sj zXu=hO47^r4cEJ+UgIo%~)Hk2b**n9W*1t(F5_O4DZiWalA*JZZLRMp&?D^uu3En{Z z_SNndI4tS0Hl0GW`OT}{`3XEkJunI2Z{4G{-n5ZBO1?(HsAH-|H@J{3+%LMUuQP{M z%DGE*+Gzk$GEa*S>x$9hf07^v*cvE%X+es%3H-Qo80Z0}n{X{Xvi3N&V1g};jv?{RvT=4Ad6xDbb*5!S>nhB zMx20qUy3Xwx#y7V=}|RqVKUXWIUfqu?STBMk9h!VeMEQ_>UndhHq~hj!o&+t-RwuV zWL@ilo3!(h$V^d}$O?afr2pQ%kfMbLQJ5g()>Q}CgWq{5H}NxK_|b0{w;4bbO{&vU z1j(0SG%mLzQ)>&tOCS`KG8ktJVBs)gfg|(B{!DN3OE!wS>sQ~aK9f@y9fWn6uvWZa zOvi7~lcQ4+)WZX)(lH=gGH+NC`NIPs!pHVR;l1Cy@H={~PGXrd;D-x5CMVL}mM4a7 zMsMr~5RRo=3&h?n(iiQ4C#y&RmVlL9KPued56870{$zJkIJbke%eEPidgu3c|05vG zDL|OwUt_KyH@qn(lL311L%(Ai8e099mD^uWia?Z=idY_P^L#VRYkfO%bJHHaw}@ts zi9oE-Xy#RZXXcrhEN^lg^~!$WqijXd8DUrm;{BFUaSB>r@j|B!)_+O;cfC-4D%9J3yWHxK(J80Xe6G%h^6cOgf|izh zMZ|l#tRjMm*Abj`-eBz8y;p~4UBWwBdu!pOB+dx;^^)qRB3mP&3Fipx2gGcPi=A$V zXE8_af(weu;h(qm34qY#ai*b(5N)arY}I&eupncn=Z(j(q%}QGb6RfZLnA6&V+mJV zFdQA~%s<|Lt*c%s64`YE14E#yJWNx;VgQSjUYp(^DhS{wNh6!Y3CfJ1Qmx0w%)g@T za!JW|Oi}aaWgv(u935xx=|p^gy64Xu#H>ECm~zZ@2~CMulGX=XAdJ19ftYPmQDF+fbz*I@c}U*~Fb*)G7}0hmjsx?v6Y!(oc6o zI=aV{$Hc?p*IYrEW|h~Q`awiG#JV`9f#oLK$|%sfn)+pvZ^iQWtVF9CTF`o=AAX*l zGDy#2`N_qe0)C_gv@gbXy8Y4NwR8_w_6zib3ZTG+Ikt#Q@wHe8B+!%N=m=gsn3Pnq zJwx`b=fo~JhwmAF zIK%h~h6j-+KDrX=vu#B#j7EQg_Xx^+zlSg&xM<#7L__ILaNLs-^D!cLd5dm)qe*7y zQo1|QXG7(=X0mD!>C z_(DoOuGF*1fnSy>;~^h)B&@87_hrn(N`du0<%b{;r=_}N^7AJMvpII5FdO<1wcUe1 zwADF-C3!26|AKiC+B7cocPzH(c&>c~(GdcCN_)MHjHwXV=wHV+`i+|Qb|@zH628E2 z8m$zb>0K83W{E(rz0dHqw=30s@7N`IqZSQf?Zwee;Cid3A_nB}wXXa^-ra=FQ7G?9 zOQmEr_NOoj)36Q#?T?Du4I@%k-G;@_s@rsy)R5Kka2)~WO&ILX-e&eE`vroZLg7M} zf!ny$Fc&R*IHG6IjC5wYvpvGpt^|TPQJzQvmYlr&4}0mBx|c-*7Jov`qu^WCCD)Hx|w$ ztuw>n#v4O`VGhZhqOFRm406=wF_A2F=-%7R9mW_QtsqihnJ@L*|8(etoO8I$UPX;iWWNl1?CJXJ>~47KGr`4fzux zRliTSCOFA0h{mLF3SjTf`LckAj8su(`aG1n-eeM&b$ z<{wyo-uN@U$ zwksMX8=ST>c`SwAX}?QbFH zeoE8>N6|ryaD+1^O54_hFq=kMHRZxRcj8%MPvXxEP@V?Ut(?n&gki>}$k`c)nG!hf z;!t5k{mkhHgG)%$UsEsuNA<$lz_&LPNnHE^GGwXR4SH=|+bgLJay=^@EO7bBs&`I$pE2A}&=5P*`B)Kpxc`@X_+37;j3o@&!-BS&I^*Brf?0D zU=*{LP*SbhcI87NO%2Vt^b8QKH%)BP3%pZeR8;LU9n`Fm?fgkU^x|ys+w;Cj9&mjP zvIo}+qHI}W8XRT2`77z3p2^(}lfGb7gxWxSNX5cp5!!fF=@KTmJ+N;8BwE&~c}%XC z&Ux)|mvoyYeS|rBr=$>0w5&skmKjDs*5oHTG&014=o#j3>=iOxu#TIiL~k*kty_ka z(=HSd4&5YpATv`5eaE66n%X*lBjTSZyZu(Cw~&_Xu=JmqnvUWfs?GTuL-4&t->u>( z@$%bOvRZ2)EW{=~vg9&{AL2t0Xzv4zKx_43YFgUt{^OMF;vVM+kY^E+F|fOCWs_v= z{+#8nAPG3Y1FKq>+5Ck2r*pxeK_9TFF}s4lH_x8pOJhFl-hytJ5l?^u+OH;gZS=Fp zU77m&c34r~SGBt5_%puwv1B4r;udoN_N+-q3}E!{yGgsuoWc_;<6B$dnm|k%gNiP_ zX!k#bUq)I~HXjaH#?-R{O(tVO9S<;5$m<$C4j^BF*U|(TmQ%@y0d{gRyg=GK_P$f1 z+TJwHF}Iv<+N4)a%Q7F0<2R5$0e%4k0tKj2gO+Rw0z(|`_m#_njSYa^ydZg6}8?amT><^g#O=&c1m2Du(NUtXz-EYu!CB*;+?2tY0 z0G7!HDhM8}@MVbpuX=~@F=M=y6w692!SmH09`&cT@10rbWCj@ik!-yOrr)|rrt=f$ zZocK;_6|HD{J^GM*CxmF;_C(K*;pEJI|(`x#pW13$qpxNinEK@@A{}i0=Fe$_!|x2dd)ds`D#0i~}mV=u3v^OFkthC--{|l)H}Vy=z2R z-InFDyZ}s-+)^02m`{-Lw{^lSZuO`8d%66Q>oF7nQ!wVN%hXJ*5vms2x{MATd2K@# zygH)=@;*qut)tpWN%j98I77ZsDtZC><(4%eqo_hzDHg0s6pHiIC(7qJ_2Q3D=sd6G z5Ty|@&Kp~3RDoF2qu#R0?f2@AQvxFLXSP=xn#GRgC=zyo!nOFwTj(g zxqj{_ZD#6Ksmi{VK5z8pfswvu&XW(RY_5U26HslD|Fre!(SIxpC(L{ZW`kao3FP(x zMZquQEUsEq(y&f^Fo!n^kMck27F<(Ti}r_yTY?p?|29vS)`2xmIR<5sjk2glS%jlz zGXhm^HOJJtW)uiC2RsSA(Rb6N;^A+D%b>vws@^e}KEole&$%_rXcv$r)a;gVeZwa^ zo%bTP!wlOYi0uGldVb)$=&j=l53C;tycne~`B9~k?-F_=f*zYF(7cFh&P8`PS*~nd z(f^MEpMPg~yjAPpeN8jP7ewmy#7^!oqbK__;y$U+bUwSa>M_cBMpg9zUvmumq{*bM z&63pQKE8`VDQ-uvf=U;g$9ziVuVtZTOqtd9?;Ga@wkUfOst4cNQjz^fpW0s=Din$M z%cniT%<5=7%_Y;I%7?jS8@XkB)fX?4FxbVT`fkpYkv=)S%2Swez0s#Ioi|$9b1=6| zlw?5fI^%?OyI_&j2UIf&Rh?vVx*gV+&Soj&dE#871JRJB{l9C644%$~4)p(++rKnv zki;35%6AT{f__4?s=zpV%31YA-X?iiAnIuVN;v?fQ~IFtdtZe4I;#LlE5&_MFm!sL zOjTU;3?LP)-J0@#gw=GV?;PP#yLeA!+yq;3*b_j_m;UR+x(2-8)xakZMOftd;98{56tadV zKld9amU~|NJP}V%!BjY~Y)eSKGMoAJ3w)Plrf<8L6S0`hr<7sS3+gJC=*(3pjtzSzfTP=L{O*yd4B_gMzKHu*vW<*yj%D>Dd z4>c=cOs+v8Zl7njY4gW%5%AY8^J)ajf&+{I_b|;HBk(#=3N(NAoO_?i9Ef^RSMXZl z$&q1!i9e7<3=`$du~f!`3Zi4FJf1=gdf31}sCWH8ME1Y`NChy@Zcr-M97B&)`HZqC zLs^6n9wHI@PQ~|WsQ?T*L56z%S4CIJz+syMJ1x}-puZ67pMULNC*|=3<#Bo~p`h() z9-4iva020p5qE6@%3cjfJo_|&s!0t`7JKpyjJ#)-M}+?U_fNDZ4yW84bItRT&C*75 z%oF28l*PL;B6e^XplVj?AX5g0Uc+;3|Bv6=`hQ$(=M{%AAxQWM$`t&L7>S~+8Ycga H@tgkwaTP7+ literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/html/_images/chapter11_91_3.png b/doc/LectureNotes/_build/html/_images/chapter11_91_3.png new file mode 100644 index 0000000000000000000000000000000000000000..4f89c99e972be14ce55273350dd90da75ce36d6f GIT binary patch literal 27834 zcmZs@cR1C5_&;t%5<-QnLNswm)1-r*aB&DXQ& zExcl31R04hnZmL^HaBFniF|eZWL0;#qy|^BP}#noTf175TacPtpg&UZy@2|G&()QB z-dkU;T)b7EG|eGY1tV8@#$(of;>yl0=zv$o#=9@|CrG$#z=m~Y!B@J~r)rv;oSdBW zA(}1FFIZnvGSJb{**&?f41Q`O{we@|qNDiVe{^VK8X9BT$%ZX{hb2=EcxMwGvPCpDc)3IRip=)~om$9$9c3belm*AL`-p8?m=O?pB`#yhNfJ-lC3ZHsPB@zv!4QYLcX|Afj-6;?uRE?`ab+ ze<4*u!TfGannWE?FZ^nZ^&s5wP{YM42teU#^_y`w}9Va`YZ`ogxJ)qzj zNwA^Wr1(n(XPGzi{qX(Lo#xUXVdUrJ^X`N*>Y#nBmtX|NDcR@+IO*ht(++n-3g53! z4F8%nvEO7AEjI|r^)1J`RuYYjBsedhd(YRetNvYe8$$TH`>r<;|8=;z|317na>>T$ zp!yEUf23yag@n+9>Yw{k93zkHCu)6SeY5Jrjf4equ)76Kxlf3Tu2q#|%d&i?MLg=L zV{mFd*N|9EE}s;Vg!)DcYFpL%qe2oX>0U%H*#q0#5q@SiON2iO?Em2#sOrP-wo5$h zaG#*ZH*R5F}O#_`amSk<2sQK1{I%Jsh0Sd&IZWHz>pvWXL4 z_PoiT9CucZwS3<6-EByHtM0luo2l#Mj6OSsPpnUz+Yr93G;GlwKTT3kTME~$!-`aK z%;{fud0ZuRS^L82z5n9RP@^<*9DYo(qM;>pFW^MObwQjo=9#qzayEAOox58aUw)(8rCsg!0`pIHu zbZnN0Wx|R)*f*tk+nebBR+(B>ek)5NW+&OO+H{{Lw{G2WD*)g3ns<&x%al38%4mqY zki&f>_&xkf8y24fVUM^DNpkHq&&gWflT{Uoi4*P5bqBET&A5~KG^>P!!z!9ucGmUk zgDmfUQnKzw^80Ec_-AKq5n)Tzdya6H1&z8`jryJb=2E*GK}*z9C6Qn8l}#jYn-|$g zgTuz$O5ew>RK zb-TtIIWlW{QNN!VyR`Z0?$l7M+cxTUn=#>62r+8s8 z>6|2a@80DgVjkB*wdT^923CwXviQJ0&<#RVN(#~WOT3f~309(ITYK5_Tw}8?a{6!5 z<7;Y>tQXs6#$Iw{`Kl1;Bh4F|OAl~GIP&CYB`3B$M|UQYbdWEem53}+ zVsTl2?<#ZE_3UvVsUloz+IPtRgb~)uPcC9`X_CnzXZKm)j0diG92p$v(dafr;XdMf z3yF0!dxV6mk!~S}3z?Ayc+xr?n%~D2dn7UII(Hs+ur;}HHWlbz+W47#f*hW)ZUo28 z3BYg9rngR>-(9UgPbdltZPMuOm>nC|TS<~W7C7)`{?&XU>g{iKh7uch&J~+rhJWJa zxR`su8bh4K(jX#S5oUMj^pn(v`E;jwXrt1d(d$97N@mc#Mb- z$M0H#eZ$dWBL&8wKmcF%BXqKZj>E+d7v5TGcPZCpiV8_c%{0Hg*6J2p>T8e3Abb-hSMRKT7Z(c95d%! zA?HO9cUPTCohi2L*!894l~aUmYHzgd$W{MhDjjFq znQA@lmuajlHaUh}u|P3fpjLd%5QJkoucevf#sUuq9kwker^`4`8TWdENQJdaw#b?7 z;FiZbbwhc4#r&_v^3cfwmLiO9ZDXYQH1a&Z{5Eo5cEtOf#hUAeK>K+lb{;1{FC zJ?*9PKhMd9vAQQqZabrClk!r@jD%ZL^&`T2`++8?V6;QsZ^Ny%22~Q%xv@L!eFpGa zM|WYt{JY^N5gy+Y4wNVZ9Xoay2aCJgcLprZSc8YhK|N5~TC@yJg#$7pGks9Hn_qjhWj48yj>qIlpKP(7 zY^TFaXJ<&>Sh(m|G@9kFU(%z6TcTE`I`Qyb_r`MNdND)vPUOOEWLO4#)V6_VGBvMma~UxW znNjrzb_!=s%dT(^E9cVT3JUg_2@K-Q=>a2V%Vlq5N84f@4)58-EtsNUtVUwn>rNsZ z7>B6Qo46Tv7l+EEYNV8SVTxqG?#Z)O=1^G2%#rM061e-fs7+Rc^KYlT3ls5XzANas zA4sW1&opcqmn51iUq+hbm>7{?zV0(e+b*H&Ww9=2vEGiP@vUM(w%49N(&MLnIE{|M z3{>=iK0vnNLae?mk}MOiBOh@cZif9T8vT4 z&WQD=5&eXrl}S~tx~c1JlGTU~m=QH@9MecVi=G4fK`he1*5w9*GZYrR<>7xk3zHVd zba=L-<5HL~N9dMNm>&w3RzDO=oW+7ruXF!mEzy0}KIgi{NW_FFK<_Yqut1U>`niyz zTwK)-RPQ(K6hFm~SH^!flaU;8cUAT4`PH)5p({aAbrplHE)MNOpu`%nf>Ys3)!FSD z?~iXF_+V&RCd}RIC0neM6LCvhtOxel2TL(X=BjZfp(ZAVz$H6&)z2d*0d?*c8%;Z` zhO_#ZL7$E-RtG2V)(PZD>jOlu^rlDecEa^jY!Xsx+it%of(s`d>eV5W0fOO7k_=` zNPET_-r+2KWcS7*chdu5dLy~sf_6@f=e>Rp`yY{w+UsgRSOS)MDBZW}#3~N@w=XB# zSX+~xe_rCM=bDQXil|g*q zM2}Svd!l!3?r!h8&%p5bSL%(DPLCb9ku!jE?Fcqx?}UhciFAI`GFe{|e_eI*11b9rQ6D>rfr-m%|4tCPY= zgcrVDJEHlv+(qA;2xC`xZFqbSDaCgdc;JO;arlsxBeya4equ3AvS2Zf!m9^)-pN2m z`2Zb9jKuy;%b#=Ty&#BBUNOrr?;CUHx9Y8>!0EsZ8-7ZRpVBjx@hZ!b08p{wbO+llC-PnNR+US6(scB8vEwEFt*HnsmFlLdjVr8k@^tGtBSNS@>!J2qL zP*70kD`v!vFurYJPu9DDa@Gfk17D=~jKEKvG-Q)7=r4ofIk~xAJw0iusVz=ld>9!R zWaQ+?BO@bK8bYBDC{(n{(T>`PG4MXA$G8L#u5l%3Vw!iv?MGj*d7n5?#(s=4+T7tVzv6l5j4<>-XxX8(g@TX42Umb!*UYs4*? z!v%itt}45^Fj0cO%T)W(QVPbdgH668jEz=e8iLgM*-7=`?B~XYjhx(q*#H*n!{eq? z8Sv?NF$W&tYCf4jnuQiBezJdvFq1xEX5dv#uc+8(;xL~>l@If}tldwO3oQw3=z|uB z4=bJ5b;&O?{S}wXbzk_Zg#-}QsF|IF^pp(0}#fwJYVM0QW_en z+A0@j$`@pR|99n;)>BRW+pj7|e9a4%rx#v*VNj_KO-*FF7nFMMLBO{n?hh@9pP{H9e4N*DXJ)Ch zH}8dQE+bpgW`lx)dGGNgcg7)8=jemNRBk@z^Q}5`ZoAD5Vo2p9jQdfiMu`pY345Y) z_(7o&qWi(|F2`WETB^cd4d54ZnTofP8R0313F_xVm*( zw!pyefR2}p?6|v1k;QSHqRN^Nj9zW|KX0dFkA9-5%oP2oNU936Db+ zqj_L9Soq-3kSoAY{9~&dh>oy@Xf>%HKYs>6xrNnb(ym~xLLBU-BOj~B*7}Edr^vVp zPsVPk36i63ONl2QE(aC%sCV4K5CRLr!!BAl+Ri-rb=Tp_M88)^fsH}ias2eH^L;{8 z+%Mad_`^^a?@P7+Rcv@>QU{oOOU*t2Nn-vJqrqP&4SuBJ`};@B@WS`Z%z#f+j1XYG zb`qvHX977YtRG855FI4{@YwTN-wvaOc61ZYk7Jf`Dd~l__S=};#ZFecOBM&`pPF~9 z&9JSpu;akOE6hJC*^g54@*V_GvyeA+Mskf+Sg{a+h})K5vl$N z>$?RSM@h~}?l0Z9l(^MjtP3q^6uA`Q6gX9XLLve}j4zobKYxLxfM0cBGn+hiadUp* znAC0Kv>_4jF*|&))LLSKy*^@a`_f3{v;V%c#mpD#Zo_lHXIXQjNcJT??yc`Xn6X*+ z>dmM;_buCp0eSVkc0!|%jzv%f2EDPg`Z6ji`8b7JygWPsEiKQk6(io|XA~7h#KkSv zZ#X3b6eHdq*krw5)M<-ZpXW&OZlxZ30DX|FtLxRPSF6J4H;s*rJ3Bky4_lRGT%j}nQ8Q(6*Y)&4OU?_|vX1&m`vnu( z032z+;tj{6`aDm8KywL>#m2(jzrS~EY}xLvD}O$tFs@H&wOwsH6zU7@RDp)w4I3=^{;Y^a!_v)sow> zt4vsyovR{xNM{8U>57ukt76CcEvNnG=~0pgZZZ6XZYOTKlz*8fV6f2O*4ihkG2Mya zcHa7?Yi5Z*5plYT$|tIA`e!$0$fFDz{qw8E3b=v~zkps%f#I6BRP<BX_Ly!>x%28c%@Wj!D;%)iewnRfS1oeGp*6p}#YC>bpL zjy%)Lx}xOG-r zt$J;@gvYQypxMRNV?j^qXzAha;T8CQ^d3+Fp~3AK!V}HnexoS%+z){U9 z>E63t$pgkbB?3(rV|`Oz*7>}6m_qKq!-JaS&Muvz`o>@`ds#{JJjQ#VR6}AU``KsM zE@30h@`Fg&P$l8h0oJ46i8J!Q3@F9CY$x7_dx*2`EN#ATIf&o#qfk%^0a6})l8jJaseuA1}t*Hj9HE-KXTNIUB$V%z$dOSgU?#XfRD9uz*)#){Q z6|qLeS&E?`})?Xrw&ojjo-zHcU@fpVy99FmXype-ZvTTgslrD7JPy z@_bD~dr>^96E<*NPWG9>Ld=n-)Z?!qt2azTPZ>w_Jbnb++SbsQOIF1CPYYG--@h(> zs(&x%gPuISISk04G|$ML?vRp9`uI(BQOzq^36q>@6m+V$m@QJAjdx1aJ?Fzq9Sf~G z(!eNRf*FFoB;o9cXL9xCS{P z@~C~UZGm;u=}y6kKvKqruC6qS+A!`uy6bX<__GA7Eg4bIAseL4KCXZv_)!8dlmB&# zv9o=f710AT543`DftR1%m`;I)B2`?cwxBgK=`1pdX=kC&V{0K6*y#~8P5Fn_h&wkp zvLwY$_S70hcU8??BR9*eR=wSEle3s>z0lKdvq(VD)UbI~;Rk-VgWuY+ZiB7GAEr_)Q)w5| z&Jb6x$T*XR1?nh_e+NuUIrq2-0}d`YPD;d38w($`oXd2MrilN;Z_AO(*o z5>Nb26hgwC*_1rK_xOMAWIGb#8S&`nrJYtbfl?o*{Ctn35yD4hc>Lk;_`Sc+--4y? z6iMBswJoFTbd*n>+G|I54x(4I%c8Odz56mmrZS9zKI(-F;om7Ow)fugj2GcJksMxS zHJ)ws&}kX;opg)csT=X^V~VCpB!%0jO9-O%z*f@|rK9)q<*(JJ&$$mZ@l!1g-iZp& zbolu9t7CHu>O+5CWFu$UMg3S>pe=c5Lcg?e%u-mt`vqjOz=fWN>WHjF>qFkIX`d8r zi|{JUsIJ72u0*%4#64l*^78Fqg@~NaH&0ij)i~>N;&fWs7q*oO2L)t*aKk^ck2H2} zj2a|X>}S;-%y{eb(wl$bSJGzxm5*Jxe6z6`p60_C3Y+l36Vb9DOb-R3gUG6*s8cj{ z3eCTaG%a;Vwq96DOfw3477?tPK16M!&K%iUgegFrms|tz@%YTIG|Krs9LCeb#Bf26 ztnRfpxrJ3s`Qsto1j;%Rk7?bL09v77g)0+{Yi!`@O`xPxa9+|rN58mh2u@-48Gnc_B~Geh_7q@VwVOWDSc(c>f+ZWsptHqex!s3|I-#@0J;WKlJx{GXcG9$$nVT1 zBYUcFe&U^mJ2fngvotP1#y^#;Wjm9jSKpS7R~)I9UYz==5sy4^DEl00&!+gyA7&a{ zUNO*kY47zdI!e9asFQL26>-8yFExu&_nu9zk78O)GLlWq&)Qh`kGCs6QX;z`-+@h0 z7UXymO?@^o3|6-Cn)gzDXY{grPwwv8;DFP;EyNV&gmj`dx%mP`^85lXenhOTO$-Vs zxbSOB?^F638?P{t*?zqsBt z`%0tdn~rYtjXg?=BlfFSLW-)t1Y`$g=?2oLH*Y*2&=+%UU$2us5E=>Q_6J)4g{GhP zr{uBIYFufyQv8k$eh${>p95}1nF`t6<@Uy_w6wG`Z*IBhRDGz&DbS~aGQxdRlX3m+ z!F1NI?00O1yQh+j1_UZ<8SaPIzm7+5Dj8;$-sL?0sx($5)5@qcF?3y7_SB%gAoQxF z=%==jq+a$@7rv@l9`J#V2R}wcU-X~y`i;qA8~Mx*d<91$x!a&t$55im>h6M&+O4`8 ze+&=2S!}vmv-OH%?ux*w#2Wj7l4{H`?2d@Tg0l)8#5l8#jt1JoR+14&(m8c`vztr2eVN zJNgd(hG5!7i$vqChY){`;S$^!F1y%B)?kxNa%f18H|h$*a03)SGQiU*8hvoCm=e|Q5$QxlO7X5XjO*6DoSvJje8>O;o|IKaezT$eGf+q()FEA7 zR)_@h8J>q_%=pE5bR`wcDFi7o*$PsqHiU2Gy_=dFdHGUrMm&n_7SO~Fqidhs;A{Iv zrfruZI5@;HNx`2cy1;m3b3(Lqp9||fPt%r&AtY+nnpC%a z-T}-V0h!zEvF9;8>49fcmVSZhVJBt5To9{)r65~@dvsCI9dv(Va`^Rp`y_>r(Ed*J zm7OhzV#=w1C{MJV)+rXKk#FC&ii<0Hu?1DHA#-7M(7e;shOU9 zBvB^lrmQ~f3Ay~rF7T<>*vRlSPQ{6GKBSKx4zwyJU8%*f-E*YZGKZXIF7&4HIO4|< z|Bh?77)t!yal}qGOmY1$)e6F1r|NA1?hgHTaF%oxO|38VNB#M0kFqZ}%o;#cI*VJe zuT;nuKBu^_Jtu)$*s|bjm@^crhHakXz$_|SL$8BQ%yfp5Z8QoVIYS|pUR3qliIwsR zrx;rI6IUmT-SuqW^j5_6S#>6*V9G6GCfLn&I(Ww}WWTUdPZHakaM^%hH zKtSJbnwlV~`I7g|S7h5mqYq#YPR}Kj0 zHUcQAwuM)JQOyi0T&$ZB41aD=^9~O|a zcLZLySI#S+ho5*FTVA7Ngg?_pR)M~0Lsm9=!s#C3-eU3VR;I33z+Rm&9nlj-xv!q+ zZLCPdfZ0zVvOj~(x(ziT?*-UuS0jo(8OH4r0G z^dI0f1KISmw#C@)Zhl$iZQ0}#ff>3;XxySe+*xy?;ral4)OTaVye<46<%8qDx6!eu zu?z89Lz3=!K&IF2onHcSDdtREVsJ=ch36;t6)F7EyuXXt==8%{hd$S{Z5k+{Cgq$}1zU!G1H8h83iHlszvHk#f% zz*PCO%c$7`W;T0?9%8R$UuGJi<^`ar>k6T{I$*MqG#}_>w7GCl6~;9?(lVzp8ucjB z=s8CT;cYxlbT;rGWz5-$YEALyZgX!gL7rx4$-yXntghZi+;BYaH1evA7Sb&G!O?6Z ztJa}lk3@>h@NzbYCo+F)gxO0=`e1O9WgWpq(t zmKjspwHs)KRS=Yst;e(RwaYdlr38Oz`XMQ>$BFd$D%LK68dy@R4de8Jx}_WCmMfg9 zqg$dDQ9MHy+a{1wWmRQTmceYY_@vUGc>syCKY;b8)eUr1Mkgv?nx}Tv%^HE&_}KEp z2z8zR@VC>|Ee4?b_Ctr1GcK9c;S%>2{kDvBP$=oIx+U8(1OGG}>Hv$XK}Z$J(<}ct zXU}ddGpl`^XrB*G_>_zD2WbM>@RcpgguDPz3uOSwYp;bh>%D}~OoRL>l<2B3ZhFnx zx>lx#0|Ig%K_LF#*`hjtl{kw@$PrM7s_~HKNgIeP4d9u<{~gAGyqZlMXTfD&h;|`kCk$xS`*CSv~4Fh)a|EVJ8 ziZa-9cb45t$5c0h+{Qf*#q__xk%u&Usba{Y-5l%w)3PiMjq5-eo1~dA7 zWW#Od9Ej?dyG?!P-LC`_r4)SB?|;#J>n`W5PkoBfOzOM0C|+~}Ttjz$pY?+Jz+AJY zwHDI*{ott40Z2?|yMbQL6)UU>t)@k!&VosS(mXH#7NWh! z0gwQ$5Jz6w-dG!n|8M{L8$o^^*Cwcs@P}gr(Qa#~+uKb3$m zl;w5P_Xr2ppZ#-Gl^ZPlI`5Bw+%0)PL-zZRPK?x!hTAuf-dzfT0WjDH2WfpE1g~9I z%bL3meDnd*ys4I>t|Okp&`1d_=Ex-22ZBBu1LC3R+t)mUTC~#*a~S~Sr+hYeVz<5% zN{ZI#&YE2>VEc5sc#VR68pLiH?#^HUVD&MsJm!KLA?n;zLU?GSy^RN~1~@|%6mYGJ zaZh(AkHP|Amu^A4*3Q%xZHIlAMq`|BWT#=A*yLryzPtUpu*(@M!Y+Di~z^y$v) z{24u2(wTw}!Zu>1z*Z=T^?6|zK*S4S)T>TVoG70S>n_62-UO6Hc1IHww2gBBZ0xT_ zQr@+E@vSZ5jKluBW-HSt5@6SxyUj~GaSeFN3KzKVZ_3!}FfL9N$M;NW87Xy(;vr>_ z?QfQ5RiWm?y_EH}$(TXqM1c-l_S?^n(G^yKVA(vkF{i8MP(FIvrrYD4(vUEam$~ad zeI@zJhImxaBR`O3vQhU4AM2880Vp`YKt##O;dyjzh>HC-zw6~B)x%`qr9qM;UVTMW zwrLVDh8x5!b@S~782&6sK|_8#Lue0{uHdu!=q>%x%!(sOrcc#?Clz|#Hi&tOzmPI` z$;oy+fNY zMcAD#Nc$hMs??HuAEvAQkQ$1s8R1X=MVmc}e(1R9uCsuoOM{G4C{XS{pd9hW-V(>m zJBgIDG#lO$2X9F7S4~>@v=E4;8|XXQkklfz*utgW$;J|i29BgG>ho5rQio!-XKn({XgME-|C;cw_)pauBP` zx||sO!gCa#DMv7)9V~LGLTFR7~C-!JXGYE^G$7PwuAPV|;Dmn-lh03ccr! zi=yCsZ5>dSV*pvs5O+BQThk^=ce6bA#Dq#HG(REg?3r9iPJzy#CqwACnhQy9_D`@4FZ%-I?{Ra zHB?{R&`wvyl0LZl>lSXdPgH(2Md)Aka1jf}GCSeWTr z$m>|hXJlqpSihi?E_?fjJd@4it5uRJPesQa2zV*TK-i7{YNPf*V0}L-@n0aGTGj6- z+NKpLE#KGp9t+D%1Iw#JNsEWIW@o|L8qY@@Sk7u?WuNIS1}D>oJwm;DyJJH6hHMvx ze#eYR_4({mxr%vkakGu|{ zo^;`LId@-U0)6z8a3QD_2_g$Jn9FkTk>&iaeht(BXf)?Q5~f7r-o+MqAF9NSzJoYD zff9#veD`LF>)LqfgcGYd4`?e#-b|wQ2=Uq2RLuUwL7yENmg|HVjI| zKPoAY6IZ#Cm_a*f|DRBH;cjy5N|yCPigzUd?Z1PFw)?sHR_sh`8iNhuOIND~%K$n` zS#(j>lGx>3{jLCN0EP$<(xQ)+_By&APyCde;k`l!g%R1$WQ_vy|I6jw(z)N|=~IE) z)Y4`6)+I=kPdRQd0bE4vngl&5NiaAamto!UO-U808D7GrmKI>oNFuFxPh!a~#8HbF zh(+jPj%bmm)-48m4lWVCgx{~0AcQ~tj``B_lRGNvIi@;{Qw7`ynQe+1*+|R1%RPgd z{s@Jn!j&LZ1tXc0;LGC&P)ff7(ubAh*}g~E^x30{@lYPuzrd}4ESSxSl1&-bvj~;l zN4_AXv%EPuo^pKD?ihFOKJrSIyL0!3v>zuurQuN&$T4IPqxVMv50%FV^a&EmJjEmb z?AVD6fPDiK4v9a+qT3Z0&K-BDCUJ)XVxiy(dcBSt=+0?ypt8v4_y2R~ZWbAxT(~?d zNDh_$r#Tk;vd;clLq=&~R68z^j3(V4>{ui3q;^fpi3DW6IA)or7zZZx+K^D(NR=v= zJb2tYNG@eq6%^ewZT2P{eFr@h*^GZ{0zIK5x5PT>q0a z6i1Qarj2b1wck=BrJH1V|55zJ95P=W2rB~fQzv+vBlxhXdHbGV?3B_|q?w>vE!dIJ zQNH5g49Pdog4J2FyIm7{YqAOx@m zbyE43)6MoJBj-s;k&?@gk3K+_YRhmBguMV0mKW$@)4zJ2kNfQkN)&0F)BX=)Uz%NZ zFEIt)AOCKIIt8d!xIeC=-4^sPJc3~;rC^Q^jKH#FK6!ViFTCx@A~+|?u7Xy~{P}0Y z`jpG1v2ochzW-_nQN-_Z5ga1m7Z=`&8Zi$I1-f1PNf%JlTV!t-0*1_&HGw*^4Ktt# zyMMjUj_rBfKay@Og0j4Z@`;dlVf|aqS(oEvWISm7`1c+vdV{ug@X}*T%*^4(rLj0i z*1KoC5ZbmM!k_|Ca^R_;Qyl=?rhtzAb_nOq?Q1WdvIC)Bmgc@`I!K*jkS_o@#N_Ue z#X|%^K?RQqjWeGZ+e@r^wFHJOZ4gMZnubT#u2_|Ku$XAw1 z5}`&JJ9mKI{lH_ae(gOmg4ORHvkYNwOXWk80;l{}@h;%`4)G_`!l3cEUNWqHx`8j^ zNzB{X0JD;8x}qStDmOpej~iGf5tx{&&v5fX^nEE)C5%$AVi#oMbaRxE+M;8??>ytu z0GK_1V)}*E)dx--XUT#LN_Ypa8KAO4={uF`8$NYvDfTSfZBQ^anK?`&)cZWP$@OI3 z8OuW^{&rieo)(uD2t2_CH#oUBUGg_kFN14hkw$c)st_`HmtNjKV^| zfPK3w?u7z5))(9Zrj)fUp^%l;O`rbKlU){hmEU97=}QDykPKc16Lb2*hQNN?p`@jlP<2kj>vfX#M!95UVCq z8d#*^MQ!9Z7NoGb{J0aSlQ{y^5pxrv6APL8bi&lIZuhu@`ZnUX&OZzBAx4wLlA48c zM@wF{GL_#3u1(Y4@1AlLeBP#Z@{nl`@<^@(5VA4pEul)U3jiHqX4d8!Ey9ziySMk&{^4v^V_|G*sCDD*pIJ~g{4WDR zt)pcoR1EtKz29iEe*HLr8X8%T90G7hQRG!`uv8cic@fuXWa&LuDXXD!EH+NX!`aNw z0~-UU@&?T<^i;&WZB;lo&hf9+uv5J135xjNp@M%##zq*^lz{zaId~EhDYxd?v7^$N zx8pS@9ulOGup$CQD1S{DJv}(i4egqD#L+JZJpmhx^eN-5keePeTxV`yEX%(9FbRYG zC<$)AN&-G^dF5XS2bG#}?~fA?pd2kbu9p?81rp1#b}Q4-H-JJ(s>Z`0%CCk+83%vb z%J9$xs*r$_dQV?%#LR8w(dYE#dltyjueHpA<96I>A`}P?-m8!SS+fjxt4TXs>9f_^ zPze-{TZO4P-wF)RKAmnBT#j@0gM@kg5H%5q|C5lNm*dEG`+c^*VrK$jQTcduot4#_ zmxr?(n2N6P${#CkupV8v*o#ar{OPZ#aR2W8tb^6YQppnDvrIi`whNkGp7e$jePUr0 zRiy_xkvsjN$2u`s8jg20`Uupsf?TH9)4h1pE~4=_P$$EMjZ)|2GmU`l9G7JXyDWxs z2^v~vwUo6*#b9U4wr|V9$-s@jXTw^BXP^2_rC()DT>z^sK;!a4;xbRE>HP&0lY%rd zfM-fYP+NiPZ zpVZKMMh&2d-{R%x4;-j9cx!UPup;=j?w@sX5pMkZ17Vx`;-b@x;863HZtIn8>Wbs2 zX|NXLoSjA)$*&Qq(-t@-ao+*PQy438m7JrRervKCpKeMGWz9DH*DRVJ@>VqM?azTC zY(U++M>dn6nxkBk!!CeZgCSLU1O6;M`>(~#Ei5!Bqa%u)|7fA^dxig5nZA{+qy~YI z!_O@fW{d0VYKr16ip1 zDLpm4_Z60ZK^M~^eWEy0RF>4)5~s((QI>Tqvd{jCu-^1t+d2Q2xO_DJnBSRNSKVKq zniGHV5^(u`@W-r_=~a1L-&upavT+Gy6Jp-trT0Yk|9Q`dD%zUcgDH)h1p(gfaJzxf z#B$&K{b!i&Y=vXgB8u6gpACvtvUF=d9^#iZCdG5y&9`S27(!v|z6m~`eeZlH3L+L~ zL0l)IePbcL<@zG>y6*0b5-MM(wd7V~Dnj|=KY4d=Wpha=-+*1{(UYgVC;z~x>3-8t zlil!m>M;Wf#^u`+3X{w)Cv3lxioBkioqcPer?!h$39+eD3E_bLmou;FP&x9#uQ*N4G?p^QU>Grl{+A$9}g zhEF_f6DFwY%;p7K1WL7n+bcJw263 zQC@j06M~QIKN6Fs_F-L5wb!TWisqD_!%}SlKZ!5LdHjIv^7Ix@gXBa@EnTI{ClD%W z*&Oow#9l;omn>Tyo`AP39D>V62S+w|L!b33Hj=Qx?}3VPX~Jx%-k7bTpdWMyq@#(P8Mb{OPf(LP70w0EiJfz{&r%1NgKE*Z#KcW3AFQsy4P}b0M6OOQC?~$Jhq#Wwh<>btNC@3D*7pcR2y#VB}JFM&P z@+-mr5#Wm_S|T-nB35)ADLWl;)!PWS`o8jzV?N;#d5Zm~eKJnchJGoU}?&Kec zqs1cZew%^U4>{gbEv)^GXf8KAY2#j(v^v1 z%v&2Qh$}W(eE7shIZ5P5TthNK9PQfyUPd|Q`KBP`VJH2G8#a$((dPxm`H+2vCM|NG z^5{?`G1O4frg-aLzE1=GI|iRuPwv^mZNG+>1V8E;&q#sg*;6LC>p#^*sT%Tf&MGl` z25J~_W&deD>d4E!ohR|~HQrwMSF7$D8qEr~dy%Ghjy4Nfxnq3IrZ=Ga_lqhVW$dnL zGtRg&*NOO(ZuHq_$rrpYDN-McAu$j@w~<!8#YZw@5O>$5rgWc#5@RL1bvH9B)8eRt|if9XEsZ4nmn`iltQ3xd!FK-S1-RHTW6Z%K=U!#*WWoF_R4KULKgDBiv5s1tC z_E1yvOKli^k%w*z3Z@YX!-c{UP%vq$cgGp%xNBJN9TZH)GhY6qjLyo_V;k=naM!ex z_0hl9FXAdFg0C_I@-41cLmd7C9A=tinjYO`sTyS(+H^?EZ=xI?ztx2IiErrUYDSDr z&<^>M$|h~fK%M-v|3-Wni0+IZX3TN>_Wb|trIuVfGRd@w-W>{rlliW$-gC<%Fygo< zetEC`8#$i+_d(7uM4@f%xA{HY?%3N8*gErF#4zqtGkTMn>Ho%Hj%X!u6&eD&a>`(p49Vv&=(xkF%r^1gLtD1n zH^D0FA;~clq67td)%3jS&7PS6+L6M5l&^Bwdei7SrR}h8>UDS%pE|QRxLyg+LZ-m+ zh|XuWkBW_#Qdxz);%9YUxiC5|!S}$|_AllCT)@JvgcCKAh=Xflm@P@+;qg}u-Q2$a zr?>Bpr~3W-7x|!~k5h>d9V-%!B90L`_KqSlkC9n~hLJKlviHc0>^+WF8=ODTYCkrnW1x=ln%LYcVaLk9-)6BUIzVT zyqC?-#6=~}V=^_kUY=*U^Ey~J)P-*e?F6|Cm`n4s5>GuA=%|hQ9zshT$1C2W&pfa^ z7;-*OOKXLxqOqEO--TIvu#8r!1MYF{y-#AnCghKccz182EjQskXt2*3NGhZ9otfDt zfulY#vP!JRXv)l41=6H}W)qJOl^X(;#c$t?0jZ_B3ceDp^ltlxzzRnc2a|lTM^a{)L%=b=^CEF_e;h$dXXl?6`NO-<=3smjQL zMm++!4+xlQ@9JyGjAX~!o>}RfRJ4RbA*8DIpgDckqNU|H-Jm9^FQ9DX1r|w}TkqA^ zGT)<2^dw|4q_TG(f2-f!wV4GWjL0S*mq+73f9R(jX-5?u-vq}Bhy#1hj8O!oH2Z2+ zxEBHSB*USy-yFw3p8l+pbDhFa{yE0`cvW|i-!x{EHARDB?p7rD81>%n!QvGk6U&Dy z(2+}}O!lNVGj-Js>=M8>(qNm0S@R^pOh@kbFAWq`Y~$f=NYe>V!c?eU=nHvkYJpcU zx_Y>J`JJ7(S659x{FEs)?ky(@Z4vZU;63h){RvL% zk-HmS)db`Xc&S}W@$P3MF+Fp()SB!_L@V-xX{+C&;-338p!g`kOZJU3>(f`RNJKe{ z`}cJ*Kz!MX8c7nzbz}#EMyyXkQ`_JzvpOG7$k0ax-0*<3Bd+ufE`YY_{V7LbzGuu| zRzT2k*s){bsVz63YBA1(nca`Z&IAx-ss&9k!{!v8Y=xKeU# zt3N?KBTOhi9P~E}tW}JS4hT-yweS+$__&$HASV}Tmxgqv9JARF(J1`}o(tf&lF?!W zdutpkA(sV;Zjg3Y`JSFJX%4H>TB732_y&z~SVrjh^{+6AWyUC8&~)*S zfAHF11Z7Z?Wovo02x;nsj4@EX1DK+Sn6?~DMhlEi&&T)y^mv@YTmY4sm! zD9wvu8e+KZS=v*UkKFtgs?d|Ia%o&*|E9QD=n*vmQe7Cq~R!CkuucPF+CMk6*Tn>5Vk*WciyUUU}>tZ z^*!b3K^{&d;Gw$b&@>m!42fOT#(n zz&n1I$yzjRs4t8HIA}@-I*hFm5p}?$Q4pXma zgyrNZr#m|+4Edp&18#L1+{!faqwMAgk<=f{6(V6)3hB?Oxx0ISIVVc&YXFgfqSmur z5Gf{yL-N~7F6(8inGK01M0;6XjWi%BbZFcYRhssKz`R2e|4cppLw|zZq^DRsa zh;z(`4ug0{Afl>KwJ$Fpe2ps1 z-uqaptN=l|pgi0uSQ8VghtD&ZM!(YnhcWXxs(x?E*fLr2_$kB^q`HHPR3zu^_In%< z<>1zer^*W~jJqF3IY|ch^}%i{yXVLBZHwDW0%D-v<_mYEfK}L!XUpmDC|@S*Vj;(v zy)L#;z!AF_uE#V&F_+`rrpe6PYBHJlY)5e6Oy#o`2r|W;e7zndv!MB2rmda~92n>s z`Lf+kR{`Cg^l@0tob(&Y4TVvZ4Fh?on=L5w!*hQ3^~1*KweW>o#)a?;unQJ*k!pPA zaH_qM1-2+XT-x)?c(cO|!H&p0E{;4g*LkU?{O`;%cR5sOa`43wml=~RG^Zc=2E|Xp z=ZM|kIdtNCKtTHfwAoSD#`3lb;!B^}XKF0$V@!Zwv zGBe*HX=Zxm3m?N9Q7lJR=-v-h)emS%-qAcadT=S_(T=LOj}<@YA}X!1_X371+SXuR z#1DwWd-3XXvS+Rw~alzG-iztzcKmp z0~;Icf3f1lOh^orWi}?=A_aCiZHkh{ztY@gcsc-8hu{=Ka?}{rE)wq+UK@0d5C#@| zBBXpD`|@7CiNU}<_9hr_LrUkn^8?rFMUKo0yo;|F%eYL6T}xrfV@HS!?nprhMv3pb zoxg#+)l+cVvNx*A^cuyU<_7#9WE^4G2thi92ydhQ#%jNEYEW|oqz~Newij<}nPTUk z4J<*5N`aDFp@TEk?HHaA224qEe(tfc)K3cDMS+BXd;`c_hyHzc(D@`Yx2X=~3XXun zV3NY6rK+qe@ynKvlI?-X*Kc!gCJm|OET!qvp*q*Ty_7c5b?ZUMbDnC~E!fuFQQ2NZ zX^%ePd3uKc-N)qD=&LI|10inN#5aC8g;DugRQfu!GL627|tXhQQ!+?IjKyT{{)g5Z;$K-g_kme@8Ay)Vx0>2xEb9~o0!1< z3zf;(pP=Lh;QukAA=&WB9=Q}2CD~!!`__Rg;TJj(gk+y^nU8>W`Y?8Q51f|)>{GVe zJExd4_GS6XEd&ECtd}We6}?(>M-)_@0bXc#hlBV01Lf)c+M>w(fZGSBAftsL!L`yW ze$HaI{3Qqo>#d|q*>12;GnOM6S-hmZ?+1fp0w84li)_dM2hT!zof zB{)|@iUnz;ydo5Hm(iroKZ+ zhaLZhc?bJnG)z#gAE%JoQ@NdrJJ|uj3u~faQPJVpt1txyiw0HLdNM^(oo2h0&cf`k z1I#dB?v&*GsEB($6TLybaO@)(%tya;u!!z zZ3Lnsn`6Y>VmY*z3^zopdF~hCTg;nU=W1!iL={cnc zc`F$m19rT4AV2HYsO02*W8VTt@5*YHAM&|@*wxqxP+AX0n6|C|`qR5R8JGHvzRs@elqv=FH!W zuy++p8-|0n%`pVHNl? zCHs*?*iwz(nA`iGk{I`$y|l!w5*B2l;|I<$*xyhnDO(xxNk~5z>I(UEHvsJ6?g=ne=ffk`=)4zUGe5}~gbvx^59pa$?vqqTfB?GD5+FSQXsGL~+pGKc zMlX^86qv#$KKZteKLGWjImV@?{XCCwr~7L)XYxgsm&_(;(Hvm7GJkh9DwJ0Zmvf2S zR@fNk<^kw#$?IY2eAl$`Z&j;qD%^Qr^crg2a7;b)w~qZsj2>^%ApOvpik!Ld9;kak zFQF@j#mpr)Uglf7vu#J^o0v?6<74LTNqvjmP%i&#u6|c?>>Q_E!F=kTU-{Y@QGy&S z0zry*_Rc#t^!Q!Z1$I*Xk-F~Rq9NspCuEa~(|Rk?($ipH)UkueZV_%+Lt~@w6m_jO z9YKe|ch*E-YG{oo9*dHmtii|=bWyOxE_gdDXC4#j59`KP+}9_}Od8I=+**W^h#-sj zXu=hO47^r4cEJ+UgIo%~)Hk2b**n9W*1t(F5_O4DZiWalA*JZZLRMp&?D^uu3En{Z z_SNndI4tS0Hl0GW`OT}{`3XEkJunI2Z{4G{-n5ZBO1?(HsAH-|H@J{3+%LMUuQP{M z%DGE*+Gzk$GEa*S>x$9hf07^v*cvE%X+es%3H-Qo80Z0}n{X{Xvi3N&V1g};jv?{RvT=4Ad6xDbb*5!S>nhB zMx20qUy3Xwx#y7V=}|RqVKUXWIUfqu?STBMk9h!VeMEQ_>UndhHq~hj!o&+t-RwuV zWL@ilo3!(h$V^d}$O?afr2pQ%kfMbLQJ5g()>Q}CgWq{5H}NxK_|b0{w;4bbO{&vU z1j(0SG%mLzQ)>&tOCS`KG8ktJVBs)gfg|(B{!DN3OE!wS>sQ~aK9f@y9fWn6uvWZa zOvi7~lcQ4+)WZX)(lH=gGH+NC`NIPs!pHVR;l1Cy@H={~PGXrd;D-x5CMVL}mM4a7 zMsMr~5RRo=3&h?n(iiQ4C#y&RmVlL9KPued56870{$zJkIJbke%eEPidgu3c|05vG zDL|OwUt_KyH@qn(lL311L%(Ai8e099mD^uWia?Z=idY_P^L#VRYkfO%bJHHaw}@ts zi9oE-Xy#RZXXcrhEN^lg^~!$WqijXd8DUrm;{BFUaSB>r@j|B!)_+O;cfC-4D%9J3yWHxK(J80Xe6G%h^6cOgf|izh zMZ|l#tRjMm*Abj`-eBz8y;p~4UBWwBdu!pOB+dx;^^)qRB3mP&3Fipx2gGcPi=A$V zXE8_af(weu;h(qm34qY#ai*b(5N)arY}I&eupncn=Z(j(q%}QGb6RfZLnA6&V+mJV zFdQA~%s<|Lt*c%s64`YE14E#yJWNx;VgQSjUYp(^DhS{wNh6!Y3CfJ1Qmx0w%)g@T za!JW|Oi}aaWgv(u935xx=|p^gy64Xu#H>ECm~zZ@2~CMulGX=XAdJ19ftYPmQDF+fbz*I@c}U*~Fb*)G7}0hmjsx?v6Y!(oc6o zI=aV{$Hc?p*IYrEW|h~Q`awiG#JV`9f#oLK$|%sfn)+pvZ^iQWtVF9CTF`o=AAX*l zGDy#2`N_qe0)C_gv@gbXy8Y4NwR8_w_6zib3ZTG+Ikt#Q@wHe8B+!%N=m=gsn3Pnq zJwx`b=fo~JhwmAF zIK%h~h6j-+KDrX=vu#B#j7EQg_Xx^+zlSg&xM<#7L__ILaNLs-^D!cLd5dm)qe*7y zQo1|QXG7(=X0mD!>C z_(DoOuGF*1fnSy>;~^h)B&@87_hrn(N`du0<%b{;r=_}N^7AJMvpII5FdO<1wcUe1 zwADF-C3!26|AKiC+B7cocPzH(c&>c~(GdcCN_)MHjHwXV=wHV+`i+|Qb|@zH628E2 z8m$zb>0K83W{E(rz0dHqw=30s@7N`IqZSQf?Zwee;Cid3A_nB}wXXa^-ra=FQ7G?9 zOQmEr_NOoj)36Q#?T?Du4I@%k-G;@_s@rsy)R5Kka2)~WO&ILX-e&eE`vroZLg7M} zf!ny$Fc&R*IHG6IjC5wYvpvGpt^|TPQJzQvmYlr&4}0mBx|c-*7Jov`qu^WCCD)Hx|w$ ztuw>n#v4O`VGhZhqOFRm406=wF_A2F=-%7R9mW_QtsqihnJ@L*|8(etoO8I$UPX;iWWNl1?CJXJ>~47KGr`4fzux zRliTSCOFA0h{mLF3SjTf`LckAj8su(`aG1n-eeM&b$ z<{wyo-uN@U$ zwksMX8=ST>c`SwAX}?QbFH zeoE8>N6|ryaD+1^O54_hFq=kMHRZxRcj8%MPvXxEP@V?Ut(?n&gki>}$k`c)nG!hf z;!t5k{mkhHgG)%$UsEsuNA<$lz_&LPNnHE^GGwXR4SH=|+bgLJay=^@EO7bBs&`I$pE2A}&=5P*`B)Kpxc`@X_+37;j3o@&!-BS&I^*Brf?0D zU=*{LP*SbhcI87NO%2Vt^b8QKH%)BP3%pZeR8;LU9n`Fm?fgkU^x|ys+w;Cj9&mjP zvIo}+qHI}W8XRT2`77z3p2^(}lfGb7gxWxSNX5cp5!!fF=@KTmJ+N;8BwE&~c}%XC z&Ux)|mvoyYeS|rBr=$>0w5&skmKjDs*5oHTG&014=o#j3>=iOxu#TIiL~k*kty_ka z(=HSd4&5YpATv`5eaE66n%X*lBjTSZyZu(Cw~&_Xu=JmqnvUWfs?GTuL-4&t->u>( z@$%bOvRZ2)EW{=~vg9&{AL2t0Xzv4zKx_43YFgUt{^OMF;vVM+kY^E+F|fOCWs_v= z{+#8nAPG3Y1FKq>+5Ck2r*pxeK_9TFF}s4lH_x8pOJhFl-hytJ5l?^u+OH;gZS=Fp zU77m&c34r~SGBt5_%puwv1B4r;udoN_N+-q3}E!{yGgsuoWc_;<6B$dnm|k%gNiP_ zX!k#bUq)I~HXjaH#?-R{O(tVO9S<;5$m<$C4j^BF*U|(TmQ%@y0d{gRyg=GK_P$f1 z+TJwHF}Iv<+N4)a%Q7F0<2R5$0e%4k0tKj2gO+Rw0z(|`_m#_njSYa^ydZg6}8?amT><^g#O=&c1m2Du(NUtXz-EYu!CB*;+?2tY0 z0G7!HDhM8}@MVbpuX=~@F=M=y6w692!SmH09`&cT@10rbWCj@ik!-yOrr)|rrt=f$ zZocK;_6|HD{J^GM*CxmF;_C(K*;pEJI|(`x#pW13$qpxNinEK@@A{}i0=Fe$_!|x2dd)ds`D#0i~}mV=u3v^OFkthC--{|l)H}Vy=z2R z-InFDyZ}s-+)^02m`{-Lw{^lSZuO`8d%66Q>oF7nQ!wVN%hXJ*5vms2x{MATd2K@# zygH)=@;*qut)tpWN%j98I77ZsDtZC><(4%eqo_hzDHg0s6pHiIC(7qJ_2Q3D=sd6G z5Ty|@&Kp~3RDoF2qu#R0?f2@AQvxFLXSP=xn#GRgC=zyo!nOFwTj(g zxqj{_ZD#6Ksmi{VK5z8pfswvu&XW(RY_5U26HslD|Fre!(SIxpC(L{ZW`kao3FP(x zMZquQEUsEq(y&f^Fo!n^kMck27F<(Ti}r_yTY?p?|29vS)`2xmIR<5sjk2glS%jlz zGXhm^HOJJtW)uiC2RsSA(Rb6N;^A+D%b>vws@^e}KEole&$%_rXcv$r)a;gVeZwa^ zo%bTP!wlOYi0uGldVb)$=&j=l53C;tycne~`B9~k?-F_=f*zYF(7cFh&P8`PS*~nd z(f^MEpMPg~yjAPpeN8jP7ewmy#7^!oqbK__;y$U+bUwSa>M_cBMpg9zUvmumq{*bM z&63pQKE8`VDQ-uvf=U;g$9ziVuVtZTOqtd9?;Ga@wkUfOst4cNQjz^fpW0s=Din$M z%cniT%<5=7%_Y;I%7?jS8@XkB)fX?4FxbVT`fkpYkv=)S%2Swez0s#Ioi|$9b1=6| zlw?5fI^%?OyI_&j2UIf&Rh?vVx*gV+&Soj&dE#871JRJB{l9C644%$~4)p(++rKnv zki;35%6AT{f__4?s=zpV%31YA-X?iiAnIuVN;v?fQ~IFtdtZe4I;#LlE5&_MFm!sL zOjTU;3?LP)-J0@#gw=GV?;PP#yLeA!+yq;3*b_j_m;UR+x(2-8)xakZMOftd;98{56tadV zKld9amU~|NJP}V%!BjY~Y)eSKGMoAJ3w)Plrf<8L6S0`hr<7sS3+gJC=*(3pjtzSzfTP=L{O*yd4B_gMzKHu*vW<*yj%D>Dd z4>c=cOs+v8Zl7njY4gW%5%AY8^J)ajf&+{I_b|;HBk(#=3N(NAoO_?i9Ef^RSMXZl z$&q1!i9e7<3=`$du~f!`3Zi4FJf1=gdf31}sCWH8ME1Y`NChy@Zcr-M97B&)`HZqC zLs^6n9wHI@PQ~|WsQ?T*L56z%S4CIJz+syMJ1x}-puZ67pMULNC*|=3<#Bo~p`h() z9-4iva020p5qE6@%3cjfJo_|&s!0t`7JKpyjJ#)-M}+?U_fNDZ4yW84bItRT&C*75 z%oF28l*PL;B6e^XplVj?AX5g0Uc+;3|Bv6=`hQ$(=M{%AAxQWM$`t&L7>S~+8Ycga H@tgkwaTP7+ literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/html/_images/chapter11_91_4.png b/doc/LectureNotes/_build/html/_images/chapter11_91_4.png new file mode 100644 index 0000000000000000000000000000000000000000..5d106940e37126b360c8c18743918fbd1e1839a2 GIT binary patch literal 27519 zcmZ_01ys~s_%4b8D2NECG$<)3UD6+lbSNkt(%m)GAfSYlbc1w#lpxb-`lIuxJ0?dY(7-#=wsXl6W{|I2afhc+yhhN*EY-mBF{@11#{4vWr#^ z_`&b^LCsOw#@NwC&)x__UeD3i(#Fx!O#g+mk-dYNjWri5H!Ihh7p9JmwhjVpY*zpG z0#+M)6Sn>o@gcCuLt80z2Mi2cBJ}qijD#c-3=H!fX>qa7kfhyt7s$lg^34ItVX)^e zp~RH*3%w!syAJ{$lu>?rRJ}qqkzc7&q+3}v@wl=mL#3l}JLN6n-N*m@Ub!P1dj{2q zkodo-ncuyD^TVOq#H#fC(hIic_LuxUuECYh3BW&oUMkof8t`vK&Ok<7Ts-qGcQ*JT z&ivp1`K3p(i0$>oiIuZ+RRKO5_?(ip!+QU;UXhh;E{vaCd3t)fKSg+U!k-vy&ctWX zKcnlGOtnq~UgcqgFo7T8IKy#-|6ZCba?#V!5a!+W#vtdl{9REo?)39>`Rb}6Cl{Br zl+-KKtf^dJK)_YIA0D}syga?2Ah|&>f+CM$Qp0&~t_Qr^-P6N_n%&Y90o$g&Vqu{d z7S?{xJV;_7rKl*n{W^k78A#~=`{lFL&^0Iw{n+qSSJb@A`RwA2vz$$0a`HeZrC{i} zfnthKyt1P3N!(&n-IhDr0;`ffe_zl_h8nJRhZifS`xK)^5s%}sm>h2MbZ4#K;S_M* z=^jpd&&0%Z=WENiJJOz9`^&3qYj&*<8A}a&2r*b2_TO38EMs9krsy8vTLha3wei5T?zK!7 zY4Tqmk8O=+;cC}8>djP`VFXhNCp0t&p+#s9B*MQm!TIq{3$pyfaeF*)Fj?@Z#OoUO z+q2gy?2!Ghb&gx_P8X5_ntKpJhk&f5($*Jz`MQr8d zOr(N9536QXKlnf}Dc4Sm_r0RZNrgD}zbW>;OuQtIs32adx}KF_CD-6vc*`uduUNgw z5S2wyrJ&1R#iWL&mX@WU^Ny*@&XitJWtHpEy7T4fuIL5V0EpVhR6=JhNEhUS75J5E ziOwl-1Nt*cO8P-Rf9??LdgzUfj_zEXAgo?JEo*c~RVn8vR6?5oh>SVRI-NCS}Y@I=p4S~$#@<=h#rbud{UNR-smdpVXZZ*X;XfW44i zSh&+78b&QjRRX&#M_rz8q#n&V4Bc5eam&-L=f%JmIeTH#c=8+r0V^>%KU~Yq$)PSQ z`VjQIP^0oE@Bu6d*!dBqK$MTqU0&A76G8p`au{{ayS)iK7P-nf zk8z*B`P%*KWlK|mwtNCN|30s%(3@!>6Np;Kk`s$Y#aF;29w!s3{qbD>DZ=h|KPoA` zYxBbkJ43nA{ev#SD<-C`7E$-cg?so%=N=-h%j_*f(C@cP)dvtEY$);o@&L>Cdz;?& zcwU>!qNhuDm^v_qJxU(HSyA*lYHKVk*0VRL;{}&1%*~uUlbiuPY9G(JS_n zrVC~ic!O=>CdcdMD|rh&g+r_|8fwpqnEcJJn!lajR?hZz6PsDOZO zJ&G+HC8xf@L1Ta&wAwITuj||eUKW;+q$CO*_g$XOFzT?%7!X?{S+cQhP4mCSd?6r| zYi=$O4}ZLS`s~>s7o^ViWRYwL8IM|-;X^Lt{dv4A{&kd2^QDAv8k58Z+-*t0&4hUyZp`%pIU*PgpQ9dcGjjjd7;sr`qa~Mt|t7> zJuGx20`_XXr|O^Lb>m9qu`g!t;IK7Y%?1E{-hm2_i|a;|G!Fte$)O)JQ;G1l@nZ{n zOetUs({|x--24dElX4n%d)s_1d0>F@a`A9NjAZydE~e>O=?F4gY-&V2vRnO# zYUVHwt*q)wvo3j!=69NBzd1l2p;5Z?FJ}IKU%HJd5QLKuRq4t2W<_DizG8X(yTXu| zKCAu}%X~RfRb7Ps#zW=`GwLFU3GewQ!dD9@-ZUkd_eN2E*HPbn?^_1oYNU$Y5?MQ4 zcSRT+qdDIF)bi#U=|z3Y``-U?mf2V~hL+n_)|_n{p5x~5a<0haYENV>vgs0nY(z1S zQ&^!>YyKy83L$n486Wzn`?9C_sn=|;fgF}>Sy}E(!t4+nriV{Ik-f^MtGGQ)&CJg2XJbwaFk(YEw(ufA8Aka=Ddauwz0 z8#VPpEc7NYf~b(5-%|RIUPKW+y`^;3FH50uUY&@LFhiTWJt<_FkVvUhhRCE}?|znG z^*rQ}l9r?A|MR>@+Ki4dJ3K-wc6D`zjuA$mCE=;0v<;Un^yU!N)vG@(T$`&_fX~$4 zuKbvpHmoGkBK2}oQUFnH3^*VvCdPi=31)Y`7OPyK!cttnC$Qj-6joAFf@~zan2zTX zL^8;)fVW$bsK}I*K@gZy84@9n8%h8Rfyhy>vLt=@@ZsvlMr2}QUn6RvZ)dukA2sJ7 zEiJ8gal92w!r^ndS06?t?6yB5No|KHswTwwk*nJ*lInR%%4IURdVwg($;|v77416@+O1MF(`4BU!7m~vHKCUz_lAOOsuij>7ioLQm=Hk?U5!t*AKM3EE zrkhR_|H&6`sLR>Y^fZFVJR;&_WYj(19NwOuN@?lh_e%DZ9zB&W|2(Ig@M$0SyhX?g z=x2zMWaqw-TE5Z!U?k=oi#h%Ad8Ta_KHHJ9T2)MI*|7KQ)0msvY9?I2n$pWuh~1IZ z)piiV_2r3^IiIO2o>$x5{c&Z*PbE6SGBPro)8&i?U7=aIxd8y14xq?!7?bBaID>~d z%vx2Cl<0~Y_s4m2_%WtHeBAeH{k^W>)YuEE=H|@zupTX4qZUn$H%A(-4*Ssja{%u; z+Hb?BCQ-zmZSoY1)pjOT&X#-0$mp+K?|f&tSX(e#F5YKo0}hh*+N7q#UuKizr zCd{-&-J~g3#kQ6uV~1ou`H^+!XYaeGSL}YLw};qmYZphEbdbF0oeY(TumouxbNX{r z4aRs4X%XH%re$PgU(IeN;(RFkvetQ2T?o3KLpNEdJJQ^_d9ch%~@%>(xOQ{^fy5f1KFu%{6{QiQCEcol-#O403TThiiQtolhRz z@4Yn%6GMYeQm@mmq-L+YAdh^X>(9v7gychv8+PpC?Wa*#Oo!M^b4P8_srop5hbX+H z>yp>6@NOWFqIb#PcL{uhl8BKyDdk32AlG;zJu(?~FBg4p&%12k8OG_vsi;`5(t7SE zD?T~K_Cv8$P#E$N)!Zprbt9C_OVEWg#a@dt(tywP&`{+1SUFoURRLrg685hcSy@?h zbaWIDsY%2M;Ula&XD20I19*IME#2X?@j|YgE(@+3Lkk-RUDQJ$iJu+zv4MmIips50 zyvdpOB3JI0yVYE_OaCpnAy_60)!V+^xyO995n_y1cI|kp7gf7eusAlS+iAcuwA_}7 zTeC5E`)L(F8nJ6Z=jJ738R20#E}f~ORFsPMn;L6qNGD|n=!0LfLDJNBMMB32iHAU` z45;Hf-!D>hbKmu z6TssXZK%|V^?cF$f|aUFjp?UrTb`{W5fYtDlAYvH^e|0c4} z$@g;0Ci23&xrk5n`)S7@RtKcP{nP#Mtb!hoTl>x=w=@61)hRq`kt9iKXMEx;(U zp!COgzZ66^L;`q4hKGxRH_)=Yv~dBoxII9r9T1utGW~;Cr#o6z$90K(*lYN=*gXb? zr0zHlg9rX?+?G?n6h+RzCtBA9J|tq;AM(111Ql_f{Y}fKel_=FQFSF!x8qGclcAK| zRfC`aiV#MV#i485)YY>H&OL+!u}g{NkSrI>PG#uL9@+d>DSl)}1SUDkzSCf=Coffe z%&nU1b&daRg^+&}#~H=vAY!&`&;t~6<+r2rH;}#UXh;+(K(9}^eZ$w;|7Y^_?f5Pn z&h;&zo1=8{Ff6ay;kK2L^pjSnD3(Zn$dSh3Xup$|a4EePC=L?`pdN}Ft}`7WJD9fPiO zN-^EJ1W5MvN~^*dopvH3H}*PBKSX=L{%o2R$ry|8tz1c)D;}#sEin{zs^&xQu9Xw` zSrDCLuAO6cR#&PexcI!DdErem*z6|;L-lyvW$!jXrtKb?&JH{2x3hQdSO2M{SY%Gd z&aPZfKUR+4#yf<;6xy)hmk%lEZ_sLCB;xSeFKg1OYd6GWH^g&qqX^-t+CD=Dklmjm zjy5VVu#fbyD`d4nNQ0-a17418Z)~orQ|S&lE#mq+qWCkY23CEcEyI>+qk z=?^GGIe8{Ir0V|HRzauJoX=K7o>iw1tY+5pP{{L>BH-h=iq*SV^t@}-9ew9#aD;YF zM-n>BLCPI+@}uwpRdai#t7fxNtGmgQQ{n?h-P5!TM1jA0{MY^&L- zM^r*_pg6zF{z**(r|HL9%#2 zAk&Fj*BzCH(a{HT{<;TRTk2Q48Cgk_Sxkxwo6-Yx$yH7jp*CMqo5Kdy3Zi2sn{M04 z@S78yU%T^qA_Q2N2SBG2s|$^kTh{@g@4^`qBZkRrY{mo;<>e=Qbl$)w25$`J7)!JDxB+j`#s~ z&2>hfD|A;fNz=U6dg^u3xz4w9^3%h8{&}9v{BJ{u5%te0fE;a89so-Y1a=xaE8HDybB}iqB!~r8zWI(Wqo9&p7eoh{_ zC=!)jG_;crv7||)$HGdsWdVH`6Tu}4{PKjLV)&ED!==}?(FvVhB~4!6ieBGr2*_tD zp^?%*9oL-l&?cpKW|UGWYBbb#k4WpR^a_%Rh@z$o$8|U8*9qG>taA_9PoPiMcZX} z6TN#KLdiToha$cDD3PqjAM5>uT%_5|bLeUmg56_LHh(ca6OI;ZSxBP=ewGluacLGI zM6lTGHTCu@c$B#qLe|m z4@RM1!APoDIWvKtkufqp-u1IhMvlaj@Lbe#`mH^pzj>7N$Z{Ps6!Bv16C8_X_d%zG?oa4&%LVQD&COP&P{SdfM2xyM*%^(AJkB2v%{yVb zzq+OxGA^Omc8nlgQsRbv2i%FI-!wdg9~=}+dl{g%*|c*4qcm$fqd1IfIE?c+jDK*f z$F$8A=Ws9>29v6~2GY>n>b{^@nnW?~uVnWmAyFK9OBTVNPQ-$^eURk{_}e^fT3Dcc zR2^SI-#rs2cs*WT#bezzl~jKV(d%bMf-&_9L`<=?p-cwB#1ImaJB}EGyq%6`KW48f z&uYqOKZs+1HeT!Y^zFjpIVH@`oa5{}j1;vZ5bO;r-jNO4aVsWTBf&$C$B8D*cn`%G z4T~;oH7T-REzZIp5+fax8SKT^YB?ux)%1$Ajfzh0vE9pfY*(*)&jw?b`H!Ob{cl%g zjauiOW^x0%J-gX2i`;Hv%XQTxt~I0^phmhgyb4aqubw$BAMk5Azk6&mIAjFreIlap z;Gm^|_NCgofc$D{FIP6_w-fAZXxmLJ<=5aI3Vu3zyf=rwxbOTnIxU1WYTF}=jM9Hikklb)I;Wn0yoqxUIKR)JJX3HvwySSMs9utRta_t<)dV%=8 zXmU3ZYM)5e($^Ws)ADvnv@>o*)KhYDCUA0w3Vh*_alft7CkP~$t%eR^B9j!vN&~vM z6xRE`lb`qb_r1+>AWEq#Wvq;F40!)WMq!`xz(=TTdqV&8r-kWOUPs7mvtf@astzC| z^DsD1{XYu>xlj%Ug15L3)DpRxg+pQG^yG}?lGBpv*R6kFv(!fYi92L-$C^yZZYR?@q{hP0 zB)ib`12xh#o8GPFGK6C)LKyfDecls@F{yEL)G=^n)#H$~T0OULt3DWSs9s$V2So44 ztCiPg{AsX30Shj`u3Gi|;Yspq*q@K^uF(1Rs|T1M51^}BO+E5;HfrrbT7<|~$Cf@L z#)j52Rn*5F{DV=W#w}P~6GA-j3EyL@zO8xAIBpxdMk0*^jQX>s5Qk%m&nroQt=r;Mr3b#x>@0W)Qz_nU*4SsSk7)oYb|nhEO@S3=V$J@^ z@|#2C%EHY2)YOuQwWkZyy;6_%VTDU+Tuq19XB8Ocq> zUn1C7#hp=kOR>%fsdXBy{f@E*9A+m0P73ooMhD7kzK)VU{UH+{=fKOhCz85hTnH~C zvahl6ASP_MaHNw&exJlUo1N0iF6qtkC+%gF_Va4w#p%UCi!x%uMv!OkpmH4+B+^8p z`>F*_S-jR1{T^boUcFAKSZtQ=i43%|bZ}+O3?-?i;JUIDDImg8s`&z+rOF&V-y+jdRi6$Ow`EYG+ z53H7?vB1|y6YJ`{Wn@S;Gm6(bvlyLnl6fB95I(f%(T^(<~L zWN$_1(bjOcQ%d{q`z8MVL%Ry~5?gOHuPsJ}q_xV|<#~r(M*;BO0^sC10^pn-JcAUj zjfQ%yB*AbWsP`499xvBC-zq+$^P7-4JUIR#oEJI%%V(fDdn&P|q^U91=UHlBy9PJ8Jt(j@Rf2kX}$SC33th0Ry;=cm|ISE9i(O@rJ1OibK-J_m)_(e zw>;iOK|qCIbYRF-I-!{Nv~LK7@A@&uq`r4{lh>&)V^cpduThA6J6iXNnTT!k?{<-u znYyz8SA@sac{0}@Oikd-NB=%dC&nIrn>3q@l_!mU_K9`)pr?tW z-sv{H8;^QOQ+ofbfcCHMs(`#cy0-Y7fNvt)VtDI3cv`X2@ujHN&Qw!lvqj&|)G#)C zjx(K7mrXcYYb?g!qoV<}{q})B5cv_hnvnVP+Kbjp^NcRpcfU6wXmhggF)^yoE}6dd z*|nxE6lvL{<0!H#_kQm|vB_k8EP_8ba}-^zW}VIY$A0|!hNW%ekKnKNM!5aKcKiVS zT@r&D2SZ7$>Y=ZLqp!^@&F!y?w+a*Ns}bCR1YqK&q?hV-NkScCy(%{ryrJs6!sk0X zoUfOUcoTlFfvWAjiA#pVSazX~1D=i|O|!-gjbO9a2yic&7xR8yrSHz2TsNB$Rmf?$ zlWKEXI7~lugDBD{%B06KG9LdHlVQlxEdJ_0)K$576(7N)3@jTp2DHSfMfwI!8@);1 zA+=H;BmJGQ$wG2_$jkB^9m&fvFD%;i!buKq}af9i$7-^2rLW zz=Ifnpe`nz(%9IO{w$EA%GG+VtrosywB@2$KN$Wh3&gf$Rz=}A(f*ns2E9HQdCBkh zk=#(8(kx(jgHfSI1|Ex$HWQY}n5Jz3$#gVXQbbFNGz9acuzR-Vlr_B#aqrsLUKS2C zH#idb_2qLS{?+Wm?H7jpSQn38(X3V3o?i;po7|yobpn!jL3w`DQzlM21ASlSI9tnz zK}DU<8a%j;?!fp7e*k4OweH>!?wxJl<`P$VRG;I_@F=V$L~7Iz66Tf8@DQ3tx(Zaj zV>jEq)!LAHiiU>0>mj^AZT+F04`pj_tJ|DlF>auUCrUPh9#DtlB@Ii*J7bRn8{ox`zh_AcdW?E>J3Tgsqj;`(?s}XKv3GN zrTtD7Y-$J}FEyH;>@%BZkG8jQHjfV@qlv?0U>1)1wqcAY5S_1TBJTy++w=)+FpZKY7Ic725ipR zNh0AS9NHg2$FRoMbs?+8C>@37&G&BCV~d=#QFcmaZ=dg(^$Wx6ekJ|(N6}S>RM>GjpIS2K60P!nhXAMcd zp|SBu0ZAHkwSuwV6D4{W$nw>;hIVn!^6z5Tx)SZkhJY-%>Y)KMvDspm5vCGJ&Vn1Q z?t}RI-Y6LBfa-;rk{=#k9G1rq=kPabW`gju>)beD|9u^B>(vlkSsY2{VN&IKtKx)B(H)M2s|1xs6UV$+1RYpC} zk49~^_$8wr)KJY}_yYiU!W?7IqZcJu)m$%<+WM`M&u6Cw#{qBAh>m7DykmSLc28OS z8-Z*tF#iOxL!&Z4M@?DYg%s2=4gokx1(X>`djrUw0|njIY}+Vc)%Vb0xHrS=m`qQ2 z(CIvseEwN7LSl#Isbd5T>)|9pchW;2yN6Lj2zn*wW%!&uX1Lpy# zt>uBxN}u3|Gh>Chywqpa+Yr(_z;*f&C$Y90cLDTQJbSnWJh6Ob6o{+y<8`7PV zY9Uc6tPfbGOthCVK}$UCwvnm)lte7AtBsM1+BTUs6utUam`GD-Pty~tAa{aO!=sIn zWcE%#oPqpQVau7JjAO$#aTP{>p|ODuXi@ZGGbLw;Dloms*`KHzJBN3Na!XABgnThV z6Oi%w8%-4tU_5liABdTT;dObefg?mUS(MuH>#;n^bXFdMIXrGMUyqsLAQ+Cc(I^y;bOA)7UM8&XPHK_$YS7F`8oA&B?<>8U+RQ=Ood@mDpO3B9MiDvKiJ0VQr zrcWOqEcwU&=|Q~o8dFc267W56jV~?`Us1C6iJg0HvIU8M3o2>CAL|M?w6{DT9N$>T zH#OsWQDy)Mw8&tz{@Iuz@p2p=W}nv$hMS|88ueDOEr)(78ELtQYg!kw7R(ZsM`WTM zXCa&b%c6sn0hcKQmyOU-tcRo6^yGcQMp@u*)4nj6oc7ym(-WeCIUa3${QRF~pA1J- zz2Ky$qiKcw?lNwhK$Qoa+3pNx=PdDSxaCG`=%RuL?Nvf=?SdMEt)uZOohEfI@5R)) zl>Ry%Et9}*DF2DYio6IB!12Ju0q21@U3A6{t`GlA%a?Pn-I|?%wTvMOMW5LNr2YdvCR``0w90TM~u$=jC--_!{ zEwBK3`SLq=*pdGaBI!R=>xJ%ar6?42i@QqFp0)ECuH-pniuNalM3g1E2Ahxl|uIrpyM zzxP$^s0}KBAHoByDyx9znnl3w#=@)rv+_F*7-$Y6soE_X`ZXO0`0y+gov#xB>Q^5S zdQ#O@2qcdGTAQDsM*9sEHiUtNYbVmg9ItyMdqc$>`%M4-@GRF>4V2;!*$tPE^y%~v zBlt1<9F(8TXfJzL^?UkxUBDuVa=WsH-`AKVQ7sS!GR&84KY5TU7mo%q(j}Sp3pz2j zPPOh{*_{f15BC3H!M4(wwre`_I|lKFfFGxm1j|Jv+7H@RubGX2#FONJt@RcX9Utn_ zpG(b8qz=k!IM_8)z@%yHA1NSHq&1+p>u0T&>gR#r66`w=LM{rnO{yVR$KpyvKFE_y1qzDb>Ky!SIB`DtjmjWg;| z^q2l{BOfS?U+DwdE$ul-?Z1rDI@>#2^8S9iHJ{NAY>aeBTw>~;2ZUK(?2!2rBqZ@~ zjkt>|#Xdi{@h0@IPe08GHsOkt+?+fObOzax+syti@XGT>z&!Z@BAP)pDs{2$O?4r{ zI&2n`IxSAVvm@D`@)67gd350R$$w~npYfqB0h0d8)HteSW!@0~7+ z<@6vm+8K_FH}A`EaxJJc zQ>EsJw|kVSvOZ`D)X`4n50L;)PIPLJD;zPgA;32Ff@143UheO{4b?qCig#sKYBPf8 z3pQ#pRC>MDF`mc)_9X;q;4_zIX$Ur-hg|ZnSf$%7EuP=e2s(m1EWjzhBHXF~NuaNp zOjvGjG@Do}-A&uQu66z>sYKXV94Vfe5IiWDvJ-KCVLk(Hq#p?I!-IoV@A92(Vi1n| z1`A&8r&33+BLfp^5?wLY0wSR|38)4TTj&ksdi0nKvPt)K&Z9TVBG9At1;N6kHoz~AH zhc*mq4PzhRAF}Ly(ktrlWn)q$xH-*ocS*ppK^5K3Ox$O5Wp}YHxRg5HBP;wU0A8@ z9puf(T&ql%A8nn~M%(e)R7oRp$IX{yyeSRX&aQpqWVmtH6(Hk$7%kDER{S<*Vd-RX z+2n6gd`)QO%$D3X$^T))S$*j+5Dq%5k`E~@k_tknHtR3X)l>ko09^i(rYD~D?pQ;&8! zg$IcLPNO6b-)}qMJOYrc80GpM^x3e$mHTa2jiBJi0tkw>>^b(@ z*P|Jqp7)l$aLj@h(E;ip{OeXNk3j1{mgyF9^D`s;&L9+rHtPwEg%_RJeTYb>dIV6Se_LnP$ z%gvDTJOtc=;ViSjayoK|i+o~yv^}H^9u8{hy!)vh&RnvDo@dp`?Rf76el1NjYtYy` zZo_2K6_Oq9K#-c?>GH>y3Eq(rPx~k*K1bLUU zSE;*@&&S(}{GU28NlRHDCOhc-SdgH)$xQ>+yi?+NDp+;qVL8kBGtsZIjYK<|F#IPe ztel7+Y?co;qsU0dE00qv`&k(AS-|A+zxivVI33opsSYt5*=1egzg13UpG><3oMRuH zlInq5->AcDN!o?hUceGR;-YKw)bx_Boz;E$|-+cg5^0vP(Q0o0}P@pA?{k>K-YL>B?UG z&`qL(6pFRLu5<=*#<5+&N;>|!ds$OAP9A8T4l)nLkCR2wp~MtI&Qo4^KULRAg~CsC z?0j;vU{I>w10Af;N{z&0Ne~nbtuLukj@TNWPww%j>f)Jh)k%r#&uyk$n;ig%rTs=w zoMQqwtW{V}dY!e9|6bnX)tciAJJyg!tK5la3Hz3rt~GfEvJYr8X`+FXUBBNI;`XB9 zDb#Zqan*8r7mA=E2)rjP!p2e#^5gmk82=$I2;1J}`jXqh)%&^SyH_aGGc?;_aN|7Nj$5;UA5dK-J>#^(Z3ie09Axxm?7pl}3Q;lIah zNJEu$|5ZxiTI-J{5kw7W@j^)qHYW~fM&HF$J2uFP15oil(kzR`hBZmL4Zk0Dcn&|} zL?>?wvP3lg+5lR1v_QQI1@op=c9F{~)El||)~cH;XDLY!o$J@MG!rH2Zg>$y5-TW@ z8@{8|Vuw}6<7lx};_o=s2gB<<+>g(s@;E}31^Ccu&(2b9VT=0|6c6C(nV`=)$3%Kw zXsXadn5G53C;C-)!8!hknH(`2b?oyToz_~NLMcFvzxw2=Ugan?*`fQDY`XM?DOQEq z5ulTS=c1+m{~hoVvwj12Mr} zvu>!M3bZrmZ&Ago!lC`SI{+?QK+IK>U=9kHD;Q7Olt6}@LeXe#G0>e?Xd#*05eh?K zRe~uU&0$dI`r5A(5V!Rzb%TNKAZ}ayK9n5Q4KTXfD0iYZW#KbDz~JC)S|a(WIm51~ z&N?|I8$1Ejpp`l^0)k`Dh3}Q3%4v6*(>{asd z8}@S%>D?zg$BIi}G*`2P%<;43^vm?<6 zY!`a|zX-JLa?cv5W~!!K8v18(9aU0alPMF%7Bz5oy<0 zH+vRA8=;^}T+X^nw9DI2azB!&|M#i*!BcRjy(i1bhhKPA# zz!xF%+pfj8WSu{Fb9~AvB0%cL@nB=X%*(#n*9^4^fwJJ4E+S`F&s7*84{gZ1<=X^S z4oJ}YKI6>3ycN}9@X85|&9er}RPX-KbcG;3bM|>;=7i;VAuiA!V=nxp!I{?s5E7pU zH_A^0!bS6m)Ov@Auzi@7uszy8CCMmIq9G*rLs8U&hM`0|r=2o{DUh5Vz-Vf()-aZC zgxP@`9C-k0CCKA$6XZz~6T@ARW)5VKJz)AgH3;(ke)gGmJK;Gu3yPBL0(=_<|tzHYFPf1oaw4wpQLZG8p$FX;2-eaGpxGlM}9G68r^f3($xdP7-} zG`?QbzT;cUxZL4Chp4o3s|_hjJ=R>eycu+okpp_faT;x>o-bhM z2_DwisSyL_*VPhVQPpw22ZHhq%Em64aO^l*LSJG^x8Jv5A>FR!zYtu~g}gt2{Rncv zmD*fl8IvqNsbO#^%4lpRC*6OxAEc?i&UIErJtW^Is2_~Z4l7#MtB<4HgbKAz0)ft; zYvy?Qu`JP_&*NRp;``m>qb*o|6Piy0hG`65V3ezPtk=*vgWcpHi1Nih3mY#>o!I&C zY)U}f(_EgI!cr5`*pFP^I3^R8AItd>p2*j*gnjK}FS z-h@AUD5#aw{zf}KA{TX-!&f>0=4i8dSJrBRFn$^u0ze+JZZ!l29(q^cuJcAa9RQO# zrl9J6`<`nBt3tMBB1eT)61vi(Tj9=~4*bpWM*AQQ=#j}m|7o{&2->Gp;=eoFd6@Xu z3JoOj%*g@2yX+2Y#G$hKpcE7@(oSrK*QP(Kc%9qvjWuWVO{3pGWyi~R?ZzMfP%m{y zTLrxvBCv-~+5AzWbMgQ<`(FbJj*HfJF2HPTj=dpcw}~ErbwQ% zxGy@%^pC_v7P)hh;63=77@5jff5Hk z=Y6K#|DnqS3^EA*n;4z6wwIes`!%?C$fpJqv<->|&_ zSFEPDc+9k7T6^0Yi)v3s`U&9YJl>cfJIHE`@IE2_!?j4cyk{9PdkuyKe+(s%`MZSuxs=?T4Z%FI@*#m9z3Eh9A)kkjMon zSwH$2aw%M1cerd^R$>yAwRf@7()2f98~Z@cgwm+V2CuN_mfZq)hYrs?duFR0$_ehA4qDF`zy8;vvh_ z?n$ZB(HpQKDDi1Vv6YdAL9q9xFbpVH&A+N9ZnW_40Y<;hML0ZS3KS{?j1+jqfm?_Ve>*Hu${!!*{d6LtmY8PIk+*S`=hJbX7=oT9~FT8Sp(xG|o3CUq!& zpDbUULf}IX=ASIz_7nB#X4tii=587NyR`(o&@U~k@EiJ@^|g@E)W=~bg>gV)0i2h! zfp7Nx@~R7HRg*JQmxu`RnDHVsl$TCQq4S?%OrI2i{JliDDVf&na{BYHdj<;8Ns7+c zh)?9sxA?x>jT*WOKsW7b4VzBc@k*R7)vNj5$=U$S?G+8DZBjUzO^ci`Czz>>H zB0|D3F!LJ6pESv0`|s7qZ2`u7@KkY#+r|9Zn^k{C_KNqkXiBn66O+-D5u#ElzG-)o z`3%N;8&x*RU4ll50Q0d&ib4colIT#&e_s$RhS9HeS__ZZ1b8157F~P%u4Q4goOFVx z%_%fMYHo8{?*&h*-a0aFLx4Vii+s2v?@HLhwbGWK@~1gR#UdCp&!A{%CbB%o1Po*7 zOGm5c!4qG@R9XLD^RL>@IM+)rd9F^!ysOWFA4;IE8kdip<;}uqp6;{@x zZk@4ysn^C61}&T);)5~8K9aQcJGdO7yU?qkOA{OHLqbL-;UQb zTkZYfhUhjNEE$N~k)cM6+h(}?ok|OEqneN)P_}XAgr4Q8@pAD8@LwsYpyypsg?Xw& zzs^U7i*a@5#5!KJ9L7}~#;2#d7sl0)(*u}G`H02-u0TrPMKw5LrXj4>;FY7zcoP_% zru{!#U@a{n9}V8;y*`%cjMG|r_%*81c_VEhywW+nvdX`*O41h#FEmS4{~O*9i2X#p z;RQ>PhOR_Lg(14svg?C$WR88W6p@t@I|zW5h=5?J#@RKK?QuB-X%E0Ct;okRvE5S} z_EGRD!=Js9&8SbaAXWn~;+>RDl~jDAox>1OxgZ@*7z4+iN4&Fl=7ax?tV1_v;n%?& z<0!*Yk-r~nT&}|x|AT@`D}Nwz@hUmWHtxSsBZ^pM&@=@EP-L3z?qPUT8%6+VWPrW& z;hi>TuWEdq-N|ixq`M6I(^8t`#KpC?<}RLM7#Cg7*hwFQ9ASR2qw3X)L4SG|tI}c< zkc2oiU3E5;8%Hf>y#&-7PL5@TpKFuBpPm{YXb3#d^oKmM$NP|G|j)gtN9Z>shp8&+W?S&45OKu=UQdmiAVEZ z#ece%h+LYuT?2ng{zb)25o7(0>yVwaGaIs~{#7z7b}Qy+l|cZL@bkz}vCP zc{37=_(o_Quoy^}UpjSFTFNzZ#)_x%slVKFRbWZ#~Bu+YvCe-^@& z#~GP@6TYkCJ1zL@-;@DJCizj2-dn<(TO~oibP^CNsEC;fa4uZU=et&;-oXZAl?3U* ziGM&q)cbq7xXx!nmh=B85xwqUI`~p;<3~chyWQ497Bp{4@$*OgJshfn-kJGn;x zKTR|p+CQx`G6`SiD||J*BtUNtY?kG&e-k;5@0XWqhc_^0fey0pjE}S_GhS=Z|3BxyRhZd+W`OwAim7W*^XB@8BXM9 zl(_)6Jh*m2L(}#91N{Fg?kmHh?7qDTMMXkT6v;d*OUNn|-gn_HXrCdoC0GG24_0S4e*i z=t|H)H_wHBvHAMjvNel?c@f^~SxNX!Sqfkr@^fVFP^YdEg)pnA)F(<^6j)YupC38h zDHmlX$$P}2=`H}mL-IP_+p#Zt#t041t3$#GPFREmNIZc@XM90FE?L?u%>$A*uR(o_ z2AC|aj%_u33yI$bf#M|?tpli5|2HG1`ih5Wq0UjjYD_Q)9_XrF@a_iOTFN$$Df^jR zxo~i(srtBxmy8I3n(VZZOb2x*^$7*TW7gX&ubW>|__c z!k|htP`H^E0qS^Vo&C(NmrXBEC2u5D1i8Ds~|+1WAh4Zt0iz z+^wyB9t{$t5PG<@XQ)VX>BuWw$Jxd?;cs@uSFpT@eW*A+J^k^|8%>xta{dCtXhk2| zf>sa*NbzGhg{;POSPXYWF{H-jy81F8Y=d;I>e(w?p#fGXCtj+&+U1 zwrw$QUgw&h<$lbNdoN4ZE!%V3g5qMFH$dYHK-@Er7wc^!l!19Ob2_lk1Ms7fD;a7` zD|t+E88RXUQgg-5Pan?yo7hMZ4kXtVm*MayU;3?-ajG_+KjD6 z8WXB9YA`G4(0U>P6h7nyziq%76;Sfs)<@azJ!vPDgT!`gUH_GUL_}4I0ZTDP_;AN3 z8r%`ko%4G;K#!S!ihgwg$^<|HVil#G!#GC2zyk%mAVV1CFjYGAc$ERQ_QsdKvriXdptF}Nm{ zaegXw+2;ah14&w{0?;tISfiYyRu*K;q4x%iBlQ3$EW>QqodkjYSs$*z7SY7pZQS^G zG<9PB!7aL^_K5}xhy%Z5_xEy05a!eTowp;wPTtQDON)6`tiyF9L-mUq|A~~_BUy^R z4z=5A8&u+)Ovokuio{47MB!b1;LN34D0U5qimw`G2DFaYx--9bLVtv=`F!Nu z_K=`fqQ-aCmx8~AIbMKu5rtYJ0h~X@DrbhV3S_%b29b>>+g_F18R)?gNw0Iz8d2mL zPZYr3Xzg1l3V@*g#&Yl@E79=P)x#o-F_GPNGdW%vZJR$zkao@Jnw&fbjz=fh!2s4rA$8Kd& z0@t%(+;bUJEiDu;JiT4->bA&KcZERjHAJ9?3N691XVA$)M81}x63&dYH~6#PjOQHs zc}CpGdUd8vSm2Za#VR>JZw1^7b@l`bkZp6|&_D<(Z#Nad^%&98~+!w?*-`J*0pB{m>2hc$D zOY6>+xh^`};q<$`_F^R*U5ijsg6&zlWgk_H8->Di&tJkFLYO?kJwj5D_A2GDg^El6 z`tT40K&eRQ$=Af#YEa2TaVcw~-8=^!P0l>29B7P8kUQ8D0#BAT&x)i<_1R%>i(IQy zwpRwryefV)-xcsqz}vJ1a8$z5{4CotIl(0McDZn6o6}p+f@Qz5Sxc=ZL7(ncF!QX& zEFFdwXmVv33?98;e3<2-zbKf6qzk%Qe29Ht?JM9>{?X3J1-_lEgzR}*{y>6)gk3V2 z>`-TN_r%TQ(UA|AZdUOZMZ-2FU41dGjR;$I2>fmvOT~`&4-(C`-HaHM_p|woKZij2 zDoX6bsl5#KQ%-L|ACkSv zYB62I^M*hhLY1J)XOMdaJCX78DrrOM4r|BcUtxeEx4oXJ(no#m+e=ZP*B9`y-M6rA z`aEOX?*Ketk~Cn_?|a|689lCkX+%VBO7_DzK&C6Ksu5u;-1BE?UBJDyE2!DzOrUb< z7?fr}4IKKC^v?1-8Fxf)x&M5zTGAl)E$Qv!CkEeylZ&4QMyu3a0nfdGd{_ug6?iw| z09_jBInLQ{q1fS9({#Y+A^J{}H#m(s5tdH+;m=cHlotXUJ;ne+Ns)H`Y@x;6jtZ-BN@|{M7{bV zefA-Y3~I=`FWW?$cIe8FZn*CqGKYvyPXn_+*wS$U>FV-yi>lQt96O^A0+k5soSGi~ z{8LjQe19uJJ&=tJ$ptcC!;kK1dVmoZ!89aYMq!nxfGwL6$&Ifr4evo(7&4EvZ44YH z6{CyBoqHfU%1_3rhaEUiiroG1M$^Ml5Z~Spa|$=l|C_R9e49gvC(j#DW%aAqNA=+q zHjzc?l@VDeL}Ei0KktkLUTd>u_G*k(4wCM5TybJ|<%W&$x@G&>*9S141m7hlD@nJM zmYXF1XA#TE0gu(2HhxRbdl)natO^8wY`a^~DxzX*=ozW%`|~ux2hEPE&w8p>N7{Ix z9lyW30TUI@uWZ%DQxc?<*yNO~TEw6IqBmM?z2)MFN_`kqf`rrxm=uwdAZjxBlQJ8% z0z^R4`M3T+W~=GWXO)FQV-$?aq~&A}E(5f7scASMDvN{l?TrC1H%8(Q%B|Y3x^qF3 z4~UTzr`VM~Z!v1V#{e$H7AtlH`$y?F)HzbQJvC5fbq8&k04b6z5oz`xc?udq7UQ#% zaut9SO^IS{G+RWP!NwK$nq1hw{G~n|Qw?0zLY;k(E4Io&(vf!iXEl^AUvvn)*G8uQ z8i|7(^7g#y_Z%b}yRFnr@#?GqEgSun&E>ravBdzY_?E5u1iMWi%yd@86{lal(@lRN208xhpO zE$*1CdT(d+;aer$KeRoV)G>lJ{dj#c#0nZBVH0W+Biv8~bG$k=ChyMPM9oR|V}w*t z_`~R^B{*mzY1z~dd`C-FVKPoK&N&LCM*bd1#?@B)hI=GBXr8b@w=6|v5u+Juc6>%N zs2UvcDuddyl`c!43^PGR=j~N6LHh~P2%jVPvuV(t#w4Zz;Chm9>Q}y&d(frET7S^> z<}#;dfNk2GdAX{{>^^;y?iR@Nash}2r2O5Y*7_j#mGEDxZqD36mx|QLjOkD+6{jA< z$;17lXxg!hdyCg>$?cS$Je8bdV4UwxRZKX^#|~rP^4fYjJq%!xycsymnNba$K2kDY zjW6V`4=uX2UN1)-n1egCzP|{{P7DcW6JClTp zn16j8#RJ}Y5y16+ZxR#lU(KT!@Fd8HK2m<&ldH=&2;IJHZIvwE??IsD_ILYaRZ}o^ zEI_1v?nwOd#H+ikAW{5(yN^1zcz!7xciDXJGkmn)dZwS=IS{_DjG>G+NbBxb%|_*` zr63<%w6G5ALgH?bm=ohQt>X@V#OC>=PoO@_3SxdAJb-)yFx9hOBrz{NA<$!0cY8oz>O;lLLO2m3NXBxq>GoU-Mzmck*e$q#v)@_Wl zIsQIpngdBKjS#yMZNheuEmFj}@Pqdeh>f_CQ;5Z$0QbWE=QeOJC`5m1h7Cr)dK)bJ z%4+h5AW>7wejGR^un1{Qy2mUEqNbJHFS|;4?m^lxn5kmcVP8yaexI?~UQhKw_bwt; zy}7fQz+st&m=>P)e=gGrS@PA9!rRxqdl<$5DrxI@>HNlQ69=BBt-a#R?fiH-9FCDy zZvcI0c?UC^!dBY3qaF)FIW7`0A%b$lqp7fhy!V-*LBIeVC9qeS1P!#|`XC+lib0LW z%y!UO{Em*ifiasoB{QslGgT{XhR*qxEUGx@sS^0J*?M~nzsrSmzEeYqVuqsN3sHYN zTOZbnzPDY|>zu5*yhE>g=E9r9h6Ype7#BKD_NG4A35K9w=ulHx1fO6_YZ#H z&oz;Tch-N0n=Gv%tqOWT=p~2k^fmv=mx1xMBza&rZUEa^zeATmkfdO=3xzQwAO9@l zfkz`q=O!-*XQ^5$J`J8!_-+*N@X^#S=N;QrsLmsmIaJlNMBP#uz{>P9Zty9J>xp6# zfyn8JaX8*S5f&5dNXe8XXlP7da|Bv|3zK)g)NGr{tTgDGe_)cc-gB5D4Ymveu>^ux zA>~Ve@H}w-mRZB&$oA4Kg`QQ}on;;%Zxf^K*`OO*Meqv1kL6D6RGC;nBH^P6-SkB@ z!R<^n_;%Iv3KP~i_gu9;9y*S5#!92Q%NE6(U-L$!DNQ@({zse2#;#z+F8MAihy!N3 z@n7fe!7iDV=aBcbqmbL$fP7~v#y+#q*!qbTD=0!ZZ(?Kaf!%` z=kJKU+&tLCsN=x0ckjxVtXxjXIv3Cu0-UCz@BwBiprYnI;(vZsVMg|IagiRxg%9(EefGlp%YK(juQlrm#UBA=Z&*|0u!j1`INtlO%gA@G5*8W+Q zpw}*jd>ET=HsI+k;*DDR_J<8>eub=7(&yr-*bhigKD^jCCtWsD10#R*w4u?1Nv_+z*e_$T$3`->~j}}uq`5S94+y}}+}ueoCYKW&eE!k6roQDR zii&*KtkW;Om~tsGaj@WX3#bw*vV{{HY&4)uXF_IGK6V9=dOh#+?{3|F?!I zo=F7kv$J*0hkXXUlq4KgId=wTGfj@mVkFVs3Bfk|t};;S3D)>&7ySI8x8kZ1wgNW| zr-N^?Ia!PavJ>~LY%q*-b}By4&i~9&!D9M)U}$iMom*@a)*Vv3xOdkTO^a$iJ9Q($ z#j_3YxCTo5T|xyN4m!OBYEi03*5;EyY7k}OwU5d|>#dQ)>{`oxpSd6t@vV$UjHrHgkiftQ-m+lcmgbbvlgJWc*KME9h z-JYr=#}cYT~Ek0xiI~f_PT^cA*{x7BV&gW#0;pp$NFC-JB)yR1|3tsKThlX za_@)&YD0tIoG$&h_n1ggcLTW5897J|xhHA=*xDp2PO0{|<>-MvKp;E$J9uH*)T+Ca z$nn#!-NLK*`1Xl^-reO8djKO9A+u3i!&qTyTcz6gBJrgZ z-e4Ut?+0DQizhSRK8;WWX_uKtuEsckMPy?-1_ryrN~Fg961&Q$``o;Z3|Tmq8k=G+ zR_j(mt`tO`~VY}HF4&OX>2$WeLTrlpICkIrA;zp3J?t7BJwG9(l9)Own zLOHaq_Dq=Z*9I4Tc*QfFT5oo~MvvuZU*FgieT8B=nh>GssW74+Q=>qQfgahBX9<5g zST{-9>SumK47|m@Yc&(`H4RZf9#^N#c@2}7QCeek)9}q$)N{S)pPiI&v`!mMOY6yh z@m59nG$8mXYUPgN;gW#7Xy9?*{lP&b;Gf2ww)js6XA~ZPat2qPiPTW`GvZ{O8%Rfm z1n~udqyvP(>?%dP^k@2P&;7X7n43dbuAF#@`b1`N$&wKoC|3wGPzO(yLyYj5ejct6 zu87KKDy(WK^QP54MqE~|?}M+icXdcO;@}gaAXF2GF&ie&;m?b`ibBQngTuqgJC!=8 z`=lTP3ymnp+_wNwBXR0Nq9;cgBNqaMT$aEYz)k&D4x9d3k1@o;P4mKOcA?hH40RaiCoU?GL7rB!K| zIi4wH!0FMgsalVFYQLqo)dNyG~e#s{mR`XM7jlFqZuPg)_VuZsw#p_~uBaH15 z3wCZnQZ?F3FR7V(72OEJBPs>d%C$d79iDoJV#x{(VPeZ*)*Gy`=j7uIDiWt=6u9r4 zycNoy?fuD-b*76aHO=tAqTw`-v`_OI{!XMwIJU025tN2>IxoPqkX*z%_|3NV$H=Kc z57Fg##TZ%^*P&}xt4w&xpcb_8bEi`)+Gsg>B2kA^?v!Lrv)78eq^14M-<`Ve4`GGh z#9tFrYBa)LxVi2CtATyq)++7Ud$_&v;DY021woz>|H42FtOnW}3mJ+g z=C?~dr}f4;gEEo3msPxv9!9ms@u?hUK#l5o+cUXVwKACvd`<@ctfl0HrM zn9{rY=)$~*&dn`5%FF1S*o1&3b(z+(Jxus;%=3bBZD1ry-oZo=uFtOmc?Qv{=pi)_UiNd_w~ypPp?Upk3~R^~w_1eHh7VvBg|&ARe2ttrcU5kVvA^Nuya$ZbBfapv zfA6%MY&EBATu&03V}S9isx0K>xamP*IN&kh)J<$Jlx=W4Cl2KAV4Njv0HkSw6Ua6{ zQqgBe)TFx`FdKDppQm%Ae$^nu7}1-Rb36%I@L;BZl(lp37|1K?j6nMq=`R~arIaJC z&?pin{IZl)->K-&-Es9YNH`azHNZ2@d9HmLdw~CTE{}%FakI4fqcY%bBIfPDoS)fC2hjm=tF+|MPvo34Z!6+z@iRy16HnI9CG8drtS23H_=M;3irNX+*M z5-{!@!rWa1ulo{Kvjur3Ic#tv#f`eyZmYWZ(M*>`zf;uFJ6TOeyMIEU-vUiV{A=m@ z7mlVA5AsG9<({T?_(1BuovT^eh=AP`F^G~{Ub>C=P3_IQU*p^ay?&U&+hqEe)0R)X zBbsssPwLRJqE>1n@Ma4BKQnh|K;C^3utoN4mGuai;Z$2_0_{}dxRId5nJoK%dOLEC zKb?NYf7VfkxYTYK6l&}d+2V%>+HvdwOQ|EtbD398@8^P!sZ-{&e|iswMuCohm>q^} z!ypwfNbWFX4b!h(9R2o>zqLaXGlT4(6zQ3|)SQu!`Sm*v*Ll z^&(nVpEOa?{z)B^Yi5*4MAv>#lbP}hVy`xB{=8JEJr0xHSXEG1<^99dXhg+^kKDC?osTpZ6=td0RV1@E$qBjzE-QnnF$fdt<$Fr*q=?**;|c)g$ZwDLKl%{bd6Xg%{v?U~=mZ)B+6 zd3erja;nDmzRCtf6sW4~T5X^pZ_h-rK%ZZJfhA??$#m`DpBM^S~Ja z<~HlnG37JtB;bwgS#wkYFXft}0O=O)9Tuw|%L;^5ipl+G3$M=+v)Vm!_d^wuy^}ur zeA3y&9qfXO-^INXbwlv5eU-E0?HZN`l+drBPm&2DecLvlG9M*nx z@>)r^V>3O9j2_j*hr7#<^VFWkY-Tg1Hd`^G*sr6SW_(ih=F<66=us)WxR+qbpMdfD zzdE)>m=#0cYg!j7iD>=sepC{*eO)a{o6@DoLMJ1+e?GLhF;@GudN?7Cli}!I-(jl2b#Hw zn#sNsRcn~*F>wzZIZ$n6S2;8LR%z}ljdBfmz3@{F@F#+yA!HM-wMeiRxhVH;YA2iYtj%7*Onts0Dfy zPi}SHAN7>Kb2E=Tj4mUPW}n_@f<}D?N^kd3y85A`jsX zv6bgpPgTKR!4C~u%=p+TJh(G(^ow-M_wgfg#56r$n@)XU{_HPxxAkb_7MB*eM+!eK zqk7drs*kRw>%Jqzq5pbGupHlfC45gnwYGcL#U`xlYzmRI7TQHqO}7CYd5F~2?c`lP zb<)eQ3p(hT;<(m7>fZ;9MGC8)K8i$|k$*Y+1)I+>U#r4Ha%{HmRnZTISgk%VBP!f! z=PxCB6-5LD5zL5-Fi0UBR_e#yAJeJd7W9AkAI&V!FixP0ruC-N>=%OfLy_6nH`wi( zjxW~hFl~yLjV)-Q0r)3dR$EH=GxPP_#Df}1lZ?VPucNGpI*CIIYWY%P7R9wYo45n$ zQ4GY^ej1}XoD%cD(Ox5l??K-gJYHFW=Rl;CkMZ#1^lDFbBg*kPQOabRL><5X-Y3s{ z0?@WjG~{>kyP1}@QutA2cg(hUq?KmM-wvJn3Hogs1oe4R6)iM1VfLr0{rsWJ{6GsI z4omp$;ks;wUZXM}v~Qu`rbQ6t+J;RM9TLkD?HjJ{QY^t@dFdkcHY9X{pz8$u$N%ex iIKWWN{}kpE>e!!sX35C90Ptg2L~>7+rHY>z`TrmDXPKe^ literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/html/_images/chapter12_35_0.png b/doc/LectureNotes/_build/html/_images/chapter12_35_0.png new file mode 100644 index 0000000000000000000000000000000000000000..282fbd25e708eacf218db601f47abf2805ca21ae GIT binary patch literal 7811 zcmc(Ec{r4B`?q~f3|XQG)ns2LM4@FuS+fffWea29$5LYKm7>W=lx;9$%g&H3HB9zp z3`3TpVWeR!>Am$l$MbyO<9EF8pYQv}%-nO__jTRZd7an!IX~y;Ofoak=iw6NVqjq4 zxnTe`XJBBA0=TTtlTfcp%_cZ2-AVL{%WE~i572LyV; zd?AYG6(RDcJc5G!0=1NseE#!*A}qjN3I7^O04Cw|Gq4L}VBi)w{4g@SLWwXioTT1> zUa<^AQF47!9c_XW^3)DupTwVa&SdF5n;&rFvJ@Yiz)kzY$InmmysN!+qr^bas``!D zt)!c8sI<3e=pOS;uVk@74k;_M(kD;QMbFJ&#SfXG&Pjww-Ojd7Tdei>_Ubi3_`A`1 zwL_O&+LI(-*h#c98_lO-$?f%!AyIMyV=2sk#CyY$C3yrH@!=MO;NY z9>P*p(wsXqdS2>PlEqw&q;08bDn%e61v;ooN2={OC7j(kEtZrgnc4)WLXgF&OTArd-E4b6~EG}9LFDilkK_?-KaD>B?^d-nzz zsTpVx<(@NPftDQ+-gx zwdYmjdh2!)-r*wA{T90RDip;w&AETqEqdoA;We+({iS?F13%r;&G*ubCKwD3+}omD zpK?!CQQ!k@yDcqv=Lt?03V_ODl^A2f%O{xcEp^~8jkM0Nl_w+A&UlNtrrL>|3Hi=K z6>gVC?j&iZYc^j@M@)=NlIm@VJtD3`CP^X(VzHr2yw|&alL)>n>J0amtjVHe63G8p zm}rB#W6`jPE4tdFgMf!I`lDRy80>`}d=_!V_kA_8cTM$V;cipuIsfqgy4&*f9+6=V zp{W0-kKY}9C;X{dKj}CQ=R7`mKAEa_|$pz7WGZCafE)upXvn(^?&!r?l6Vdr46Q z&k(hHQg~Aidr9A=nKzj;8aQ52ob*=wrLZ5pHT$2+uTc>bN4(i4D(`mQc)yr|4L@V? zLZ6hFA{T%3rp z4b0suK#=vjWZ7K)WFvPL?T$|JluLxiC|0`H1>RrkZ|`Tw%*+HAPN}gve~c@R?n

  • jEC5UUcy8 z_gU6y84Uc@_Z@d!ZaY_H2#&=ui1*=5@%|Gh+i4`!nO|66k-%jI)^EnM&?3u7>N^a76y0}&aO^3@^3H*_FU=)nV-x8fj!_{)@q*rZQs zX54Xl`)=N4C9M{El!e_7$hyZOT&BssPx0l7(Zg_|9;(%R@w+Cv@hp*cTx)D9CY07n z5*FIOTB3htD6B5v#5>U)&ZcsH9ACm(!r2E{`%_0rw8yMCzD}`#n-``k6r-<#H58&> zP!jyk7W3;CX6AT(>7yk94?t4Fxg`0L^1k%(_@IT9)!^2DuZd=pm$=?9+|&YGtJ`ei4O)3wLa(-2Aog4c(`TRJSkFl%JrjpH8v_>(MHCOj=~)SaGL7 zw|?6-DVw`qf8r?@7;tS5-L1CBR8(@Qx*+-q#^8>748DghwEqyn)@;6Eq1lK+`v$y1 z)OEq$F{);wZ)>4f>fv`glnmn4-@U!Oyl}peT^Ti6D;<3;X9$UE-+IINweWB_OMas+ z)Z%xXF>T=8F4O~4W4?bcUHfsmV-Rc`@bu|?QYHq(R7IE3Yc4^d%=ZgQD@xu3{&k{3 zER^%P1ss_v&{HEV>QI(n5ykyQvr(stEc~wfLNUINhhpeLFBrsF?$<7!K6Yn7Itrrn zh??M6OEg1SXqOFM&@7}UjTf^No$S=u99pt;T3C3uDkLSzmz?JdM?;jF>sN^s0q*E4 z3&=VqqAa+08hIWh3)Z+S*lB|?9aRJ~endIs0UKFB#DLQSt?SVy>K01Q>c^S{2n+vm z0_P~gIpUb*?63GweKOs=74+|zK>I#70npc?ZK3^VCDyd!_<1lvo9{)Y$M<|C<%W8} z`)u!m3qH`O?q{TYlMubqF1;u6oc@#X&-_qSyDCH!OqN)o>cQ_73KmgP__6WhcIUH> zH(w{dcs#JF>CEl7dZ~9h7il9{U4Qy1?AEafYx!3X8*UfLCt#bu02X-Rnv4^J+`y1^ zrmgG?;{iqeUPzCdS4}yKcRh-BZ}wsW19HO$6Ii-iNnkZsIyM6V5RNj?MsnlPWJEux zN?WRKozz_KvMH2NK7(iyZ~GZ@Rj?BavsR4edfpslX@W8J;yi%28>((fkxk=>%Ua41 z*Z{r{k8)@Z@hMz-apfdoEXm3Kt)t_^-0Env$mXDXXONNalF9D>WCd#8lI5hs zcqcZw#pJoS##k87Mi~c?98QvA+@RhoKi10bHY=`BB6!X$l$4#TtFwO8ARc|K&kb&V zFWUqf#n^DnRshr-m%&)Zpc*LW$3tC1T;RIIOe0R+ATI5hMWxT!uS5Nd0fX^EdAJ*C_ z)O6^4MmYp$4uAU~Hjgg(T6pN%Z{n%>Cc0SPx<2-LX@`!v==6k-GM*{Ke@*)X3@aXOI1dgD5Q>5b@1A}a z;+0@Jena@avlmwn55-19AvAzXqgeLH1Q>|Fj}qTVUrg9M7Y+FO7oN|LlNC?)C_Dr( z@Mg-qJJ^P|kbdPYjoNFpp+ILHbeA5huMpB5wREyO4i)Uo#(Tvh>)r$hz@0mk5Wc<1 ze&`Gx=GrD>(egy4vaC|a5^+dtJvkeCaQYpa1l!QU>tDM?!THT|!9wR=Kz#c5&)f6j zD!B52JY)II*TYFQG8otZUUb(bPgG3@t5I&|>W_NM)22J*kPK>n)WRt;OpWA98%RHv@1O<4)`4acwT9&QY075)AD*vY}? znPO4nmwvJOG*q{F?raftD#^mo-wen4KboTA>}G4*#M{~fYBDaA!|H4RkoQy^R=4bv z`BWPHh%*GSCx5$MMB@@>FFdCEKC{fU%joftf5$^7zThKHYFtAXG)aoNaqzhQwa642_5P}b_*_n- znK1tYFSM=;PF-@Uy5N|u+4zv>^32*H{shtV9Aq2L?%vj-jC4xOI0*3k3+A9suy;B? zBk1U-PQhhHVm`7#8nxJ)Euw$35wtb9qBKJKFF5D_-Ys#ZEBqam4Rzpk+Pb_hB&^ID z;>e3rOrIlMfll*-GW5IBHFYu&4Kh+8*Sj8p{QWtb4by~H=RO|-FJCY9dX1>(Ms1cG zR@>Yw{*Na4XSfcIX<`EI!=_{LaqZbv9ZCi4wi7SzIv8A8VbWs$Yl=o)K6QvOgusuZ z?G>72adIl+LUBB$FupwOwtL{!$`@DaA`5PS$0uPW0q+9#DDnDqaK9FL@acAQbKY+j zP?e@soqpF=Yvi`Ir-RH$N?moq?S2Y?Gy++dk&JVXv-bO14VT{`DG~j<#dv%UBv2Is z9>+Km18Y7F-Q(wf6(K!U8lA&E%H?)7v|!bNf-^zFM z!aYk*2j!K^`#(d_nfzob&q{?bOE6nA0(HrMIaWNWFu|MaTv{MnAiy$mNFiG7C9)YU zgzh!mNa2WfyAz5c2!xq(+8ZJ{3_3nyfy~t+9vwJ8?xDTEF%;=Ol?4^J7eRi(?l52s48SsV%E0w3w~)MJvfa15Xv4t0;W5J(m-1mKb#G+e#Xu8{1?> z<8Z1qt2pvKHGkfo$~`<)Tkp8>z>l$}%`W`0SueF874Lz-o?uOz!g|&0%{-?k={FAz z&5kNWW~XZ&MXy8*+aF`K3A}now&4tT-0J!Z%XIIm+eJl$L-K`an?cA9lybn%b=s~Z zwsEAsZK@v)F6c4*31H0AQL(2znxk`RyImg4vZ}6Cxe;{8mRd-!;hF;d`d|iiRbX(* zdPHWat??vN zk>6llcLY6o^+)2%obX#pKRxDAXp-2~jm+^Er5V7sUo%x-Jq$SL>doEKXxA!7k`bn6 z#_XF(4s5PV4#NAW`x3x`&JD<1b~4m|=_$uWk`YoC{9}6U(g%&r0<4C)#Lm_C9%$_4 zMniV1{?m=FSXjNOJYZF}zHiB4qKpnalYf7Y99&~#^$l})XRy0w^nPGjj!(6CTTrcG z3is$Cmhe@dl*|2{Rfkc#Fq*w?{2}JY@F6$I0_$$0NpYLZ&TI1hW z2#%VA7cA@1m_lhx;_T2hrv*ZUh|(cq-Q!#Keqb7bcz#)PR3C`=!o;?Zu5_kOZNM1@ zIn6;M(ot4vFIL>#^_pqMtEg$j@2Qfpg+uJ*`)$Hzbv0da(nydn_Ny^cvMkGPR&jXT zZrJnwyp04veTKZXqZaG%MImQp>SvQf-*9>ZsW9V^6G_aC>s!O1GSMEnsDUbOSNb!O z?a}Y}n@|UF&}<6A5wy`^r-M5$brcGe^W*x46OI8N(dSl<;cjeX+N76fG-aiG#q0Ve z*~ke;K1A3uMu|2Ync#`ikXrkQPt4H#wT5r;s@lp@Rq!1j)@=0L93AXm7$L%5Nbj!{ zIr7FFRcCBg-P}Wlv(Tmdg5x$7FOG0(qA3wv&*#B`0g$CKf$GGzpe->j672?OhZFlH zt)J1M+cmD?aOfpIkW(7M1|M9Fm^c9I5G)d}HYc4>G~j%$k2Q zIgSa^-nTJdsOSBB(uvVvhDi<_5a+A;O1W^| zhE}ebEKPRDmu^HAU82^{2=26W^(}bDTHKFZtYDo#^#R1;~p*W=gpH%0 zTL?Rn?Dd@=`zm=ZC1t^r9YVq1**iSxJ0DG-i%d+H>n$!MY?axM!Ei4Y#ZxEwW)Gu4 z@nruwgU!q91JUqdT{j%sc+o?cCV)lf9Ac_zO>@vn&I?l-fXo-BtaOL1mln`D6v4y7 zp^CIy^f)DaMU|O$D?Nmr$85rKEg`_57vI?xkDftb@Ui8|1rca$>fC2^!5DZ@^Fm?} zzU8Any_yxj8}fc0%>U4+f}Z3;N2_*s&}G_yis+|E+sfTjqDsXAy1AJa*8}hI!X<;@ z;<|sCmb%oJqFgUkWed6J+J{}CP zZ|$hjYhOosx4$z3tG!3lGuNh!c7+5>N4?0j$Or*E$bZMv&mQGZ^4}89it8$In|cISD6CoA&)aIJYPH+HaLdY&*8TJ5J9h?5V8O@ zU^|5CUj?!RAl#*_o$-NU3>%Yk?sWa?UY*$}LKvYnmSet;bTbwEe#w z-}x1|{Q6P(om*Hye3E!N*2zB6xXe)IwcYsYy@b0*=;2LN$$0YbPdcW5bR|mK(klb5 z`*lnblwxL>mTmunr3ST$^+e545xEZCU>cdQvzoUP5=?a0{nI$=!-Q&zU}eBesE?ry|8XE~HM%G7PLqf*k~xm>z$Ef0QFp&+ zepx}1Uenm-3ckXv>E`F$<;HebLfw0!vLVZAiGp<`>x-izZ14P+58kZ` zNdpvlkuz7d?k%aa73l2NR7hk0GC)AUH96`&CHf!j|Nn~`{eNmi{9`fkFH&|E5n+r} zoA&Vb7)IPvr0&bbhCfWNSzfcI15&@s4^h`tO@E<_AO4)8rs1bKqTWX83gccPvDFiR z&Y#fDbuik#+&rGg9v%F283IV|0x4YI8QkwLxiTPkY@sb4>0kNjdk6zE0kXN&Xd(j2 ziR&j3uYopNGrftTu&kv~Vt^-beA)~Lk^W~uoR#05BAlz!j2SBi3I z?-e0Ax&*so3L=JGadk!jq?C^EA*r}C&L$(+V`Eqk)FFR-pN0s3K&`U4rv7X3$JRIf zU4fQ^YY+23{hsw6keU|(YY`KIAl;{nV$8lPIx)&piq^F?r@6mv!b0G1WvRB4AYqv) zyJuf%;R_ApdR;Xjf8+iwTF2Gh6QFFpuHT?4h}2p+sb@%@JabTrpywdM09BqRIV9`! zzm=u2H2H2dc}Vu6a3vF+mt5HHMP?)~0;l>6)#_BNVeEPd(J`N(%Z-|BZ7X=JlW}4@ zqg|aW8r&@BundV!jN>8g36~x|qQMk1(t3yc2fK9{vF&5@A0|JQO4oEkiq}Md_#BKW zovlz@uTiu?jeVLKHMqzvZ<9`3#_xv=9II?*zfd0_W?1uN^$4}OJ^Q7! z@I7SJ6CE5gJ;3ci<4AymY<<;v?(cz2#rjZ&Vimsqx4}7fStm}vS<72~QXpD~VvRXT z{q}K>L?W2{db!w@w6$D+JoRW6q?Zy1EoYu#^RAe{=-7P>J~&RsBk0A51`R0;cC0Dd z)*!E*L6|8rHZgYl{*qIy0G&8z zf{%r{WoK3md7W)6qeVA6ZdrHGHA{ed#T44YPnY+*?zUDoQr8Bo2OOsq;(}vqP?Z9L ziDGrz_Vwc#qUpV*yJSD;G^+!PyiJFbK^}}j=k+7<76w5#B{Q*c=6=0-i^qOIGIyOx zOnQDFVawz2`OQe@xlo4jP&raI1ABGZTBDJsZ=SRZGxa_>_j6dS#wY(h6mr>pDI6It zP91Mwmv^m7d`u!bF-Gf1S?hIe#*Q;)So*r(5E@$k) z3(3&yij2dm*v{e3KtlDpnwtpqsuNZIhwX*r4vxE%)$KYl$HFA3?j%I0o$g)lIJmeR zFdIJVwA8`TFus>eIyuPCb$X*r*i8wByc9&DNW7NL6XfTndjbEOcK1etC(x4>=*q<} so)}W;5ea1aS9kOup!7f6d(=PYV&gRSi_VS%4Pk~G*G-_9tIiMq7wcwOLI3~& literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/html/_images/chapter12_51_0.png b/doc/LectureNotes/_build/html/_images/chapter12_51_0.png new file mode 100644 index 0000000000000000000000000000000000000000..cd49564e7f1028f093d19f8db6a6ed3fd039a271 GIT binary patch literal 9850 zcmd6NXIRru*CtiEB2}8GNbiJR|DtrHL+GGDkdE{kny7T8hpHeo^w3dy5l8^(A%xy* zkQM}F!}ILEyL;`sd+oQ~4=Iz(Z|1bQ=bm#WMo&kLikz7o4-bz@L;ZyT9v*%O?)w$# z9o)OmBlcq4hm4PksgI!t$jAScmjm9*S3aJu9zL#4uOIn2czHW{xC4a5g#ZGN-uU=< zddmt6yZuK8ArCJ{VR+t)QQRP8p6X`acz6`Fw=aCWtegjUc$}LWFP<3%0s$i@^Vp)!^RN z9wMTCWVwRhWb4SxqaRC3%xp*c;FG0U|FoVxi(MbVaK}@vI?ls|lCb&U#Za@ugSPPn zg~iK*Kt+HY*nbgvp0gUfcqp@Z;R{ETMLr@;SB!2Yd`3<5j9D2I^@vpLF_98!SH7uqbW200!Ip&HI=)vrOU?I%w zr4NAb*9L$#!T@Tlf`5lg`sgf?D}nUIT8ePs-{bs65F<{|ba6Sqy?|Nt4B{lO!PvYD zu7lrBc*X61GgN<`N1S>9{t1^PVD~?#cptif#Ws5^w*N@`OZ<#_EgZ7%d42?0aN*P( zfT!cz+-aA#+QXl}{?f)?ZsS3i4nfXI&fUdHw4uhLFMH=orUr#pk{p(BoSJzB%9!3) ztQ%{@%^!I&@t*3YDZGimKMOhX$Ag_f60iA^VTr0!4&h1=K-1h`sO^X|s{w-m_TaBV z=X*;S)9m-LM%=)WwA^BD|7TnO@4fK<CNf+?E08y32+*AYqu8yrWkZ6drdX?`Wc29cE|Cqj+sn96BH<<+VuYSSXYU(kI(B3 zDKtKbaF-T*c*nz<;B@z|G!;8*H8N*^LwaM1Kcm+DGKS@ar_T z+|z3fDK1`5^2ECMfh)R)b`t*So5#q(84M$P0LSi3PW=O`?6iEPkj&wm6NV}Q@Xy`g z#nq5Y&e6J_oL+sM4c?#)?ki*w3nxNXVq;)e^pG!q;4}qzq@;*d9Z{6n&pZsqiU6;+ z1ziQ)SABnU>?Q@$tC^+Q!ox1QT%>m=>uJ#nm-mi--~48iWN142v#|KKec!Hu&Fn;U zQC~6XM)rcaJp|1nb8O}`@O|^^^Y1Hmi_89h&SlVAxb#vjp#~ z#0Rcuq$`BhJUkZsUeTOFNFv3>cr}p7y6PW`!Wz|yvfEz&Qo|zD+?Usf4_A~}|7edN z5y%H&oo>yrv7Wz%DL-YEKE?LC4g+ib?*EyJUCKs^@zvfGw1qjm*E%EEyn6+{i&@gn zUq6^3oFR-)O3ELbyve@#ea-!QboR7C@H=LJ-F9^Kyz@OkcMG6H=igi~J2){sQ?nD= zW-8GruhG`_ccvt8`E0j&^C-Wk#c6G5YuFvLayMFLeYU*U zt}1`uKom5NG!z4O~1pN)->|F4i}%TjZHmXH;HVL`dA(hhM}ODF%R zf%>U#0#Ajz&2bSA{DbT`%A?6|NrOwK8crQEFfR|R3TTW_7To{`7sTY!1&pZ@@(qYn2e(K>mBu&YepJf=x@Sl;l)7zAn@#Ft@`PsWDQ)3>!27E1p&q6+DE2l3fnG zS47Wm*h@M_#m{9D1mqxB2cE&XDfWhuE9gNEPyN0T-` zg5c!Ak_~~+PhA=Lyo*+l50#sO3j0s|Mou=Ua+#n;NLV!O<>ZjA_(o2i+XRGP%R^fh zUAO#U>E4nu3)oCe?5UIoX>Op{kqehh1QT>G$;@t4h&Uxj`zq_qo@*|-O2f4&h@<}< zKS3Hc@GFbAQV>TiAxvp-Fei}wSd{~;+z~w#Uxb+w-+!-B(sRO=dEpk!`B|f?*1L69 z#zuuJhBcF>LxnzKV~}lXh_v1rm=XeiPTIx(VyE6%rg7&Z{kpSM3-u(_>Q`@-=Sa5C zYasDcqfuks`rv*2^Dt55VKY~mCnLyF*Pve zZffDmZ%`_`aKl;55eUv#Qdw1{{rl4LO{jzd?JSJK%I~f50})qjZa=wI!Fz$bHqN7d z8V%ZIREsQ+sbxeQUO^y8%%yL^6U~yI(mvgqZpL&IOuK?y1D5QX;mz()v-Xt_vX6#E z@m0^E;!rRDXDo!Q=|}mP#IlaN=9Tycm6gF)_vDE=OdDq{PNU5BTtjU5H~+cmyV?=d zsZWjo7vwgc`E5(}2!V-dI*sUmS=v+(mg>ME3AM^CG&ctQlj8A}H<`OKomck!3uMh` z{WIs{=3^hIlyhnk{Xd3+hI^fp(#Q42bl!3O2JCN3#kXIq7-#6apY|0+a%!j-41NBi zZ4p5Tdpn|)Bn{^|Dj#X8`8d8UG+v{PWXjx$d@FmDl1@H?o1bSQ&Za|Q`Jlm$28CMy z+uh_H>OZ=x_mSgM?y7wgZ*(q(MxC-3^sN+t(WMW;UwOzB-r>Bx_KQXK_`SFQ0J=r> zmZzNONOPrAfVsp?)zRqQSBoF_?S^Ex#U4|0XRn*kFn`8s_*c)t;^?`pPf=7|haxg@ zHYQLjhxTaID{WKYo!%HA(}nZ&66~}# z;ZbvWxmYdz(!SC0xO`qjns4+Nc-EUQ>p08dvqt3j;;s2R-`qXP`&2K?OD_vsUVe z^k0xh1cA`1HYy_v$p$*}1q64wGD47C0F*ljb$+;*UlVMFJS(=oKMAIIg|yUC7$m#r z?vYq`(t7})&EF{Y961NLspz0`0B#;6Bi`q6;kpDix%$VsE?^t!7XkYH9jxo6GF} zqd3!Fa^)$9&Z&vc;>xycrRfm6Vz(Khjx-)NKpR;ztEmepI3kH)7;iq50&{067bJ-< zPiDC)B=goz2X33J4B8ZzZ&6^0Cll@^X)4KI)08R;?4ix}ssGEHk*;PkJGKJbhX&nlU&r3cYkK2*Q#-=Aq<@PO(f% zChO8qPju3jeZzJ33bzDbQ+iU;PElse`hAUk@HsVQ>|4H6ilqsp@d0P_n`9`0uS|favO}=oJ7&mWV{Vni8f~Rwr*Kc`>w7RlY{M? zAhIhi{UCf|5db6C`~fZV_aYDWgQd`5osHrke{URrk=wlP@o3l8sx{v*cr^s!uJN9R zzU*VD`G&X7r@mBwI`{K)PCGWHUjX?d-7r^O+bMd>bYKTrml*Bve(9bb(vL#_4(PZ@ z4~NsxN6)s*%fz-%xc#Q8R1GDGj8=f^+Ok8A!9us%Ue{>HXbmq)c)AuQi5-4jW3f~pftS44hmL>n~R%9~6im!Lu7W43l(qaM9v_-1E0 zgV}psL>WV(_uir0Y zV=SS1Uv&pmT@b9Cq7#;EXg^o}#Kf7U9qv=&X(VOG@Xld~O9s)a7>{#fJX5nv_vs%u zauaOT+|-vC?PMLV(@-6^R{lSdA$_n)e)vT?ANlyE;#GRmq>>wbacIz8B z&e)KE@@b0eW#-s`u4J_06KN-cY) ztT+uG`jibTWX9dvM-sQ+%<&CzxHxZb`AM|$u+bi@896GH*2R70&D)54rIxC*35m6* zW|*Ss`{wc_<%PqY(%j>29yYDLP8_9SF5(dJF!jw(sXmHs%WA=)^0%;d7gfotyHBk- zg}Hy(=YmXhlsBOFIkTTRjBk^fV7Uay6c}$ggVUX2^{cILCjM*k4vI7m74B?}#6zR$ zp2L`(174Iik6s;aK z5hRVg9h~Y+uzt%@g9Cc^!hOkYZfml3x^jB(tL_5xA`o;j#*3ydH^=szkM9Anp)6*6 zP(i?30n^!e7`)q|KnOtDgK+7A%fHu`DLz$;k_iA^{|6s6NyXckt%@rTdih_K*&;(t zKy$IKSb|WF?oL-)thryyzI+-bJ|S7|AS639RW%fWT%1z( zt5!aO6`O-rf(7S(+~qL#_;05++k(c;mnptk#z*1~3L$1)(qFMLack>zvE(nEh*em@ z3;b7=oejSABMzPT{)-u<`+*ZVPEdsh&wWm;bXI1fQxHV!Pq`eT@uMM)FH;k7Bxy#> z&0=s>3YHx{9MJ%3WW@5+PH@O8*>?U3Wpvx+ll1h zrl1M@$qz3|O`c_G=os2MJ9B4@_FDUVp==y^U;PsoHSA>NB0?&ui3j+DPHS zWA70uH_a8yujs`Q71F=r_KtIBcHns<#4JhKRf$`Nly_ zP^+P4$Y<)>KLq!YqECld9_^m}ixs~l(UWORzAlt75^8bp>Dad4@PBfZ()k9Z^uN1~y@OFr{);@fQx&BebthkbUGOZn|={ z{B=4kDLOl#=*3MOw&lOy*^+CSknExEo9B{2!UWNSQ#vT=2?o-xusf~NAz!g(V7uvD zCn#?B*O#5+xC=eQ1qNBkzWSGPse**@vcv)P#TscY1vxcea0;t$vD=Qh>}MyrC#3~G zlfDk(MUhi08NkP)Quam@(h{B1u-kY0^>R^3OF4Io96brtGEgs+pL#Ms?y6SJ96W2 z@qH5g=!iit^uf>S)5rIBg0NE*X;`uzj}#@8@)5s}zJCf^>WoQ{J*Zj|mY;=u2)JCL zJhX8Kk-%LYua7@V&RJ0w=LDA1M-&GzKN9!&nEdI^7#>KGskkCw;b@qHXZyqh03Q zU=f2-{+vFiY73MX);3zSr#Py@VmMaR`Ov>(2Aza2MF?!dw9wdZP%RTap_m!gyDH`O zBQ}hK-~v$WX!p>1Le8zNx!a>q?LQKjvceKDIr!c#=qwVc2!~5TkbVGEd)UoihF1TO z(quzDcl>A#b-p9REGbK$d|&>M478*DAgHwuZdre{h7d2`*7}HwIG(?LvXs&Zbi5S# zAC3=#K8IL6Ft0t->Q%2MI3>pmSUCS9_Q3nsi|ubVZ~^14MT#6b%%x0cR1{>Y_k>WFvQBNJv|i>E1{ShIQWZ%H_e?1j>p8GWcZ5V> z#|T#$PpTSU3;{rHxWe23f-LfFOR699yDWW&mrH#jgOFBI0up-FO!b3@vwJ%fYjLEcvBtE&(R+*U0hKx-uvbBm9v ziHVi001@w#sni0ri$l*0S9X!kcfQom8s1|+9>xsnlcq9dBB#dn)5m^_#C<0l*0vV( zCd*K>Hqb`G3{ieP-%{v)El;a3x?;O*Kzh}u%rQtw zeE-lGFeN{XkEU9c$oSe7mv-u~N~kjj`Ta5-iusWrkS1NN+G>}di}O>w5R1Mki*=y- zI|0oS4P_eAh@X%QI|i9@Q3{T+TT3SwnqO?QTC^H;b$crrLmElrN_b&EjZZOv`N4lh zgpp*(KBO@#^-|ef(9l%=<-^+KQCKBKM?x?3{xeRnjOzB5Yg@U7j%;n*0qi$YGA%~3 zz(+O8z{KMPFL;Q+uzW4`s#lk}_KEkLbBM(KBES7%THTay`dc2yuL}x5fJ(zfkELQ9S!2%8|cDBzZ;Y!u8nO z=zK@f-o8I8iu!8XKHwyGkTtX0&EsqK+KF6C$dHEVSF=u>O^x(aJ#e_)>P6FP7~!MF zy7PKGEhT3MkIuNx?43g*k!)~djcb*75J$Brzu`g2$k9t1dgF9oKEN-bS0$B@A9HZ9 zGbk9o7X`Rwv@w6Ktw4TnS@wnQ483Eu;%h9`Y1Q@XjDWODhPcN7$EC0OzZH7U38}EO z8{b*d#m7-u0uM15MTwQ)ZK(-HhJ`Dmti+j9M%HS-Ardc$WJy41_Z?BdQ z%gWy`4vo%G<~o~Ar7D4E6}h4tCN)M1_eV1B;0^#m2A?xpm$CY5s)c*0P^6trl5 zg^8hJOba2Wi4H+xS_<93-Ep};(){dbMBqB%p5>93wE)X8OlBVy*4q{AC-5h8AW^YD zR?QFgb$Ozwa^&`s8C16&^5z+MbQ&e!H@Jc2(Polyv_T!fIMeoa4pi}?6T&~)l zkIwZ**xJ%4IMp7`&yGaMtVivcwtUtivO6=JKH|6OiEdLGDU`Yq_?3CM!MZqbmIl=5 zmuGY%{Ts9t5wUnqAPgCh*o_z=`x{HoA9!qdxcQvcW<{l~W5~=eKp&NjiL~*OwaE#g zQj%L0wER(8iGat_Lj#6!9b03vlM@2-m9lTF+tY(z*jcx)JYD!bdFYMq&1mN7%FI7| z*l{v(;j!-0a;}ZY95Bi0%_g>MuMH7A&piSmV4>r@mce_3mOyX}BNyv2;}Gg{Xt7x;rU?0=^dlu()eU=$h+?Fj<d#fqId_&ZBEbIlq+kV(Wf9~$!b-?tA&m4R4xqW1j*M!dzUu>1u6`D>NOXE@U_ zGw@-7gf^u%VfX=P0wrPG6$jI&4EE#rBR=P$cn9sH@R7`QS(3j^5E+b_e+Rhno;d7f zXYrqz=b*C*+C7x{(lYH;Q=w+O%)Qs}K+gg@MUO@)IC}Fc19T?1RKc|HM+8IcZv*h$ zw>tpOQRW}9`iIrzQMZ$QA3%HLI&SKc0#JF`7d-trB%&MgrtzZptZ4FAeL z;@>(CDih!6h6A&Zqv62m4qO>q6y|m+;YhFufXRik9ltVB>Z0NL_xx`{ z;m_UvHU9Xc|LG=zsyPO+Hw8K~yv-?${`}n#t2=pkD27YyU%RFR#$O;#P5mLrbHv^g z6(yAYY$i$7B{xXY3FM)U?C7&qw3CDlBV0=$Xa~@u26~_oG5`xLhg>&6(E3Ri`?280 z7zo-HbPs}zj}WMI$!tqnyEjI7fS*SqKyrX5l;ej`UD^%D&%jqQI+yFp#H|za>pw%R z{qmmZ8~jFm4?Wzkq1J@+RIa6AO3%@UM0S6vG5NbQyWwgP>pShjp7R}4mXufa>E{+x zHTu@eHspJ6&x6s|4?F?JWgnhZ-ElvOMTJZFws)3_`M?kUhUW9x`m=cItSB}jLJk0( z!QsLHEuo(uMe{{(gfR5}H^fFVLNS-KlE+LiLMQ?rZdgi$KauMgP!I0u$G4rXK=;?9&*MKXxp!n^ODkjbig@=H)NKMQQvf%8^ z5o9#;h7udzrfU+{@!3()?jfNNzV+Q4qN`50yZ8A`(`>HA(+$7|5MM4L?CureQa0$! z%3rDZXQ<(L`TK;rr9>^C|s*8|L|bc z_k5EejO?oIK0|QkBJ3L2IShA&!%gso@%^|D9JAp#;Qcc9%NFEFa6{TG{Yfm39U zeDS}M`cnBTspd;7&{^W2YeA#?EG!WUo%hS>yMKy}iiQydNMg2w`sBvB;}PC)t=Nlr zB-%e4xro;mPJ_*9OL9#p4_w$(B2x4K`5QoF6_*Y;ti+ITcLE`j=`5u6QemfjJhm)M&xI@WT5T0XeDUwC*LDmpK!lx-vb3l08Ui~s-t literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/html/_images/chapter12_67_1.png b/doc/LectureNotes/_build/html/_images/chapter12_67_1.png new file mode 100644 index 0000000000000000000000000000000000000000..91a4496c5e66ab2c962e8d247a1291c2d93fd1c3 GIT binary patch literal 2976 zcmb_e3s6&68ji)<)sqdZ zKouffjDd=j@`?=@LV`)KfDscwq)AFlK*0!vS2Yj_2<)Yu+0Jy`+1XBK?&I8xiQg!FsKQ;>Qq!(ESv6ZGMCvQ6@Ue@RD==xZ+3BAuDc1)2V{L;$lor=629_N*ZZ+^dZtozI2 zn*S`PL$i^dda6 zr>*`)QiAyOtj2(b(lHoGT;BvkQ(9#5z?_*gr+Wk0JArI3fPDd!ae=)Z-%ySHK0XQf&ek&VX*#$nx09OJnyTb`i!t5@RrfOen}SC(oQ1 zGguDJ#oOPLOMDoIxkXU0UES(Md8QKv1*Lmpq@7inIrvO5&se2YV;zR)9fqM{ZYj6m z>63*r@rM9A54`eGVdrG2RZwk7)X4_X0AcA4cXcrVpV>m$lhDhO-+?UaU2wT24#NlV zUbe{9tw;$~rMk7Lzpi}92D!Q!DX~RfgodnKx!x*A%i$(NvDdkb0r ze3UfNVYnSK!KeVh*{`GA!V8;FUE=OOEdUo7_!ozD|17m>`oW)uafD1ZuutG)0Uim6IBl{YX<&;6gswLRXcD9uSs}k*03DqN_oKeD(~a z^LWP3NmDt|q#QdW5d_PHe&siADi1dBZfFwUU)_$(u|+0#q--fK1g#S(m&}!YtnF#; zfOkKEbT+5}a&=^d1vkMHzvwGu_-sK+tdOr^-2FFTP)(;{90_6{Ob!|&VL_{J_d9N? ztn^$gz!qk$=s-FEh%w*ZNM-vld|kWb{`ky2fVlem;yG~P8<4&m7_>&J9EQ;t!}7T} zmpI$*uB&riR{a(e7)9J(`-F2v`Y*x(fIuSVj|b0tdp>cK7q~^UU2q_Ff>n zg=gf+V+uf(15lXN9V+$C@c>pl0Wq?FU3wMI*tNBOWB^=fSE_w%mopqO*tkV+C0hPy z!MtC_(mXqWzojHBJuolqN?KEzA0-%x!DpU$OIme@C2xyr{b3QGAfEY23JYQ^U3op5 zGW(uxF5|~6FHE_+P;Ht(K9fqbUG&u$0}5jh`AN4Ajdb5fJ+pMlvYORGCbs;AsZ@Mm zQThOK#rIMv(l?RZ4=dOMdto~HO_v~_wAqzTx%^F+<%z}tYZT8Je40o$xC+Z-O?gR{; zA1`-iH~>#i`xfM4P}EC>dW)Gk!P%UXipzmj%iJ8xLFE1L)O9_^v+Y)b?#I#NRBBTg|JJRT>GbgjRUz8WJZl*)EiDb! z)+;3A9uNl0F+VTE*>j`P_dLB`7W&m>oI*scSn4_N_Q4mJ(2j1#YIL98P+HxTm|#Luq!G$+EHOK5L#QCaR{F!%5w`| z8G8PlQbQ(@>NHKlw6_MNcJC^1=`^^h;ap^4&{+J|cO?)jLnStH!QrnR~!w+Mv<4lYosQU$J==p%IxDLjDMD3K7! zZgz!%wA|cW9s96CwCh@S4%*3ynQ<^TYnIq=C}W0}7X_9$Gf8#f;o$)^1r%EW+gjR5 z_wt@&e`J^2H^6pttP)TNJm1B(8K`nUXg#zv|drCV~ccujri@{_ge-0u^@Gd lCgsJNArP99|CI*D93~?k>=eh%z^7$|zi$wpbKtWt{{>fyiKGAk literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/html/_images/chapter13_3_0.png b/doc/LectureNotes/_build/html/_images/chapter13_3_0.png new file mode 100644 index 0000000000000000000000000000000000000000..2619cfba803df616e52c284fe277e5d50ec2f1cc GIT binary patch literal 19939 zcmZ6yWl$Vl)HOP|1q%*Af(;TvaEIV-!QF$qyCt|wa0u@14jEj7yA19O!3MwcykFh> z)^~sO^mJF(>0PH!@4ePut0PsEq%qM+(E$JermT#_Hvj<65B495iVXX`tT(8G?fBdz zwcXSlzq@&wxL5!bP28O99Np}!O{qLATwJXk9XLL7e&+Z@W##7PoAmxSht336|_U-z6*g*C1IAp@O`#3Y-0KR~U?=dX1 z1jmTRSqHuu4Y8h8WRYbl5pv_>P{ z2tP$eZ1`--F(llA6U}p}?5QC(oP5pw+iOhv+i%2_Fyt`2S18--O|QmrP1FD~ERW-KV8^^F1OVrVdUo*MR|`zQb`IUzoIYM8`JS8}9>tTJP|HQ_fGY-1 z{-y*dM#W7@cZ{|^`{l^8e!9Urbo2tW00=7h6T-P9VT!^CQDm^gH%Pmi<~zNDZS58< zl!AoU?-O;)w6U}n28H#w&VTt!UmcxY_U{SFF#5(b!1re0Lol2+ALuryg-vIPGCe~Ma!mJpu2(4=fH!?<@>?~)$8fiobanLEj_1|IU|x6 zb!r@q(HRlS_m&?j%ZKycT1iC$9_5Xu@s47&j_E~!ufnuBakc2gEST@gs>(r0EGUVv z80s#n{cFv%%WF86AWN6RA&%UG&0Y)H9{aA3Wfbpwq503KuiaL*9hJD~C#hI9nc**D z=ze%j^rYR$c;GTl%ouP(Y44v3a#i2Arbuxok1Y?Y?7UrDAy9-NXlV^H*;PVY4*oMN zGCV_iotQpAam%Rtl|hl8w8G}}YAUHA-CD|4N{J9U+FM(08-eBvfG&`2fj6-=A5|Cr zs%hBPfR|*0Sw9S=?`Pt%d|Qq#6qYbV+7M*!+zpY@D<5GI+oT z)#qNk3FIg#5!+jb^~Zy6g2JAm)n;;v^W;8cuRnmjGSJV8{5u(q9y|c!bawZ#Mu}E0p|_*=>6z0D@A?+jZv(R1qtw5h}E)|!~JG$7sZ2RRgs(TI(MYd=`APp>+wJoP<(<9tPFs* z<7T?_PLFuM#K)i$eW#|OoIXYY6-I+(gMyrR7HGcBTB9pz@h+^^-h66a&-cc98IJ> zd6x>Xw`6-VyRt;C(?#C~I;Em$X@f6CQ*m1LbM}R@W~iHTq^{e;x**+c-D|6ib@7nU z0bjS&PP9^A_b2XE2tM?~JTlMR)Hzn?i5lk<1^2uPnywObcVgMHd#wa_?e3{lT}WYo z%kRFB+Iq%WI;1a+G{EL>ZOOjkFM(UB1kxUk`Gb9HsP0EcX%NbL8V9+FQB}gUHs|*% z-Vv7rPGt?;2QTz&^k#^{xb7bdyd|2#A~bPlssCB>4xf6f!6`=rll=wv z_6j)Wtd|AKl^U+XZzT(45ZbHzUPWldk?eZbC18~b6M(8+r{=qs4-S6otzU+KU0kcdUV z5u$PPl38g~yY2n<@pM3h|J(QL0J{~>dAIh)jYt9#_7&mP`^o@tDn;eXmD$+c{n%+H zz&fvXE4tth{EfBI2n+KD`$nSGELuw#WoSec+&j2F3?1I2h+nuf3e+c#E;0XGb~LAP zXaoctXEmGI*1CbSVV79UWZeNKzi=CFyYs&{eQQ5?kmS9uN3yO^^jdZ=Lzm|K4AKqm zbvLrG3of<#fd(t2$lLaS-tRHTbK)#;e`DFWQTuiQn;iUDW_J8$RX^A?zp1O!R`|q? zPDVN@@>gI6&d~d!aTj53k#mJ``b7%4@Xi2Q&ub+{jfCCZKCG;rv+d;bwcV6^o%vR0 zxBY9EBz{s3G^`MVJ=pz^OlL-BG2Mk*)5HQ3!~z9=xo}kR5vx(WtwuO8&k%B-<0E|v zO$U)552trt<+@fgEmf&sTWvvUgvh@5PT%n5(li5A6uE6ZH3nLa72~B0l?`#h#o~Zm zl)5msyE4&?J2^g_nJ@cYPhGis_=5Q=TYXS^^6=qBTj-(4D_@Pjb3LfgoKh3M`&-xn zK@@jyXxdMa7|BV3_hxa;MOWH z99G-w^A^y!Y_=xHBe!cjwTxdbqGH&O%{gx|W0+G&%$`$Qu)=$0vDbx=yoWX#-Nxbc zhPRtv3mXe?$zNgwa;=xyj;)LmG~rLaT2#m2+Xk(EBG7R6vY*jhzgwJ58I7!xH=QB| z2`d_ZF3eXKy54%sij@sHIU$3*IJ`O;QI0dPN_Po2SZvLtXE113@3X^I-)AJAIq#r9 z4c}{yX-tLDayvDK=v&WTMZf8FvGlhtTX9t<9$czR$&&*Udna|no#zNmLAmJT4efmJ zn-LvkPODo7!-QQUT<@KmNMA(`tA;xa2xMR0l(EDWr*#?y?jHJPNZZl1M7Pd$xu=vf zvPbxXYk837c_3U5R$Dg?vx)CT5-(dQ5CJJ#w9=sYt;qF=^b7B*5(*-r2PD`EO{p^& z;)_ZyJY80vlAl_6zVKWlCs$kR5WmQaUE=&m+Cb7>UMacTmD2sLQE9u?E;|jf@waHM z&ko4PR#?*0KU?^*Qe`!Tf%N)y`c03Z5%cs((DAnPdXDYWh6j#(EBSywC4HD@k_qe1 z5fOgW7oL;LQhg_4$*oh;!^5J9tWQsf0mvxNz4=>+dvpy0JgM|^8Bq&=m#*IS;4kfq4#b(ic)T|b;Xxjes~6L|T` zW?WN-|4?2!>nC?)jrRu@EZgWT&_SY(jp&}GeuQDCw{N2J`7!*>ayx6Y=9ly(JE&TT zb>zMr&N;j#2*~~2@MeX%2@P{xY{=T`XVxhN^GqrG4g2?)usZm=T7PRtCR~t_aDT%7 zMYkrBGqgWyexnmljqiCqu10U!dakUXpUd1QA70;PTh-HEOc{_(3&&bud!p`hF7pVR zh^q-p_P6S>oXaYiQSSz&?bD~LP>w~X@j-f5q!sQ)f8NS)1_yB-mtK5}*+?|Mjg2(! zXI|NtOz+Fa@v-;7Q48DByed5Cqf%+CZ1w(bYG)s@yl%qIP#8Akr~KW~z27{}h}1=z z4@W2&aSW1Hi*iZrsxvCalC-PR5tpCHA7#tVSu@T8<^8WBPl!D=OC*B^fyd*Me#uHL z^46j_s%LcRj=#atjo@oVey&?gFW8Loud9Wi7 zZw_9A{w7LDRaTSx>@l%+Lucmli8;%UHp~r~x@c`L0?fqzEiJ8S$ZCPr>(0NZiXya^ zFHU3g?YwSPgjuC=o;RJal4N|Ldn|RFx>D)6Yixn}nfdrV>Pn(JX%AlH^ct5|{H^@KGN;dTw$_`TeCA3^N{|z!*Y8Cje|Q2hVkfyoDp6L_`?z;cpByk}w(*AZ5jxYg7JdVCfU5hb`Y z$ke(@65`#tODsx{S_s2MG~YHW-7}hfTD|*mep50^-q4dzIsQOY<|q%<9C_(YBitRc zBwA6bO0v#=7_lsQnj;tz$bw%c>0W1_lrP2Vb0jhIhl>F?ap2z0rSf5aW!>M31?0YW zGSuSL{WHOK9P#0i)I0tMZedsd*CxdWdh$TBuzNr*WH|n6vgD;FmnWjgls|M0r9lRS z{ik!XvClH*+&qRwRagt4jqp3UW*HGsTgPC8U?nR--j%zCsq{#MAm8vb_JjUTyL8CdUEFO~uKIVX8!Q#jN|IBO^|fxW#QJ4PFED&;%o$ zGR(aH0TOjGt(AB|_L-L!G69T5h|&%jA20(q`FqkrD?5tbUY~~AtTCLYLHJL$g-v`{cNY$yoG?uGzY#QOy3D$r=W(U zHT=*Yi}5ZPRF+-4nVfPnlJGj_#e`ZEIm-rLV%t>FR%?-7c4a&>=tBk$+n`29PWMRQ zh99VY)MMi6%e_OyzTs*`@4gaE-cJEMAaR4lSyRN!CNZh_1O$;~hC5f}zqZs=S-P+U zd)9oY=niF(JP6Oe44LW%BJ5&p35F-P;9?MnSSup!u3cpj5(Aa7nVT79kQ-mN+2(n^ ztiR^98Tk-zi1J)k?m6)Il$N*@vHp<{2MA&tW15|*hMH0W+H|iLN#M3|%wi zV7UL#-_m;ZS;DvQCBoo6?akOd_2d9UXu7OkX}xC*MN^4R8JMzCHr8_%MosYu1AkhZ z+y0!1NLoUq+t7XZhJs7_$_Su`<4unE#q>6WJ7Z3rS(TCjXG{}>3CKlqN)Ec_KTr(S zo<9~7$gZxa9zK8532UUt$m>Bz3o2!s)~?6%?CxYYS)0$WH48o^B@VQ@oDXxn4Uy56 zuvDp$4QS(f<`TeTsd2x>ER$8GYM0Eq1OBKRp=Tv8l;6L7IhA(5FUHE%AQ@UdtkeE9 zRPb&4d+nhd0gX@7&=T2;=j5C%^zDKB8m|b_l$vE^^oMor_mm05of5WIN-wHa8^8UF zr~beo%jz%Bb&K=b$AS(l;G)M93CnXfGIisZ|qG zrDOdR7~Q&a)jk@T;eBMl_I9flxEM)?{_OM#3buwyWybQ4+TiPoHihM>vxc4{8sCF$ z1n-W0q=(1xU8sLpyY4LgVsgd8Ij3CZELeTJ35)s6(Qe-$eI zso;bPe9M5{Pi{XS)AF>IZQg6fr(%j&J4RSwn!T%K-O2iL?SdLV^(uVV%`OR_$FRCL ziO1;|rmS^2G;5Ed_AT7a)NWRGbFo3Tht++gXN8fBb{sR1wr4Tn>im~EYmR#-)8BH9 z-56&)L0yA1oV+3Qg)k#kjp6efC7?-84^<5P%%21wmxD2bFpLrUH-VV}O&yRjyt(9$ z?Cx!}K4v3(*=5bGJ|_@!F<_hbhwI1U4u zt(^*(CI+>~v-H78|JCBO^rISF|4r{bo)&AV-j;rpQFegetVb!M{l=#*bY`XZ9c|dRekWu>!4n^kZbUY?NzJ;PM z+Q{zUVy-v)<%7xh_&(2XzrGcMv#K4`6=?#(QL)ek!C>{EP8}}-!aMTvA-(9(y*pR(o$wb@Z>( zL%cjL_${Wp}lY#XyHF9St-SIq8=%1?I%DE^m+vbOocj znY*hw%-VL%%fI3Hu7RIaWrC+gw^m+eA(QHU=U;sH@5EoTMZQLSIo2jvYUSRwLr4Oi zbHKg0^RlHv6!;6Ie@T%BXp1pJ9t|-jeGsIF|JA=)#P-!X{f?#0a$C=94IDlQd*VJ9 zvT0L(!lCfkc1|pZ956k{6`S4sS)eHCDj>aH)IkZA=kZZoiKKG3oplbG85j7(?MJ~v z)`<`O2D%^Gq?w{Nr1w7d^4iT5;tj8iF%nx1|DxfnG%NcV7!$JlQ;Tr_HemK$-Mc`c ztCiZTH$(kw=S^BA#2&rmIJ}!-+Z3YitySL!8|i~Mb8q$n=iJV8g<1Jwnoev1gOX2E z^26t$YNZ*IE)D67R?7q_UC+%*Ya1s>`L(0{a<3z@zA2O`ds{QKEdAZsj}_hv5XmR> zqr<)HRLoVIxV*de<>V5aO|y%ZRvA|Ec;05bs2h;ysiuw^Q7y;xP$r`w_pqTLX^re~ zxn2pVq$RmdU&wsA^ZU-ly=LYwMK0fX_1%fy>EWS&G-#}aBK~z_s%_^f%MkZ_b`hS6 zm(S46a9U~Wpe0?0TLc)9Kx3ut?)0&ZCu(@o#vv|uCwaav4a~)K&TldAE_U~a7&GLgGKByBPPcIHpZlC9x zW9(my=aBWImlm?WU+|ny@0hv#uqO;U*Eln{vAee+4bagmiGq+jy3{B;2?uZ2EAHp# z1;;B`PISIsGuWBNDBNyMQ;Nl8;T;*LvPlU@%)^uI-~|?n<%)q@wn+0S*?1?v6S{e6 z0$S&U16Cp8l=6oiX>#OmQd^r{lA<2qm6CInQg75yyV(_QhRjm8dz04zFPbboEy45k z@;dj`**gXPAHR`JRE)Hdyc3H^`7`dlp}X#~YySjqyeS@WLyvGJI>3gp@>y~75Ve@i z!O3XuoxA=Sn_G7{La1h$xF@sMRd3E}Vl^jC_sVg4aNiOIa3s2J{sTG^Ut*E1Ys2iX za4SsxKxTivwWQCyX}br6_ymO8o`-i=hLi{rbZmja5qCJao|@4SO27i~O#F!Z2;N$w zBSnS>iYD^b2US}T|Mf-C(X@H?p zL)fLeXtGsf$fgACsyV*IgsBBdJ+y|6c&0EGyE&42tmyiE5D?I1`tAEivok-@!)te znZoL7l(n%rsLzD4*IzCMu)ILS+0#CFO3QoxNS2C*PQ?AbfHbNUffupsVi>~?mPG-nuZ7WojZpm)VC?f$iU|je$>fsTp_dlf>4Lh zcS&qk>Gd<>ND9CM|8=RxKux=wccEh{{qUP2ux-h_iCd?ep0p@N!G_DyX=erD>zv=c z!NjqJF2NFpWG;zp;P34wH}(q8$(_lkWPLzR2V%#hj|I^S)yf5buE=f<0S*w%6+5HBQ46cQ#3{IJA&EK zY)9m{?!c*29sA7pJf;5`^(gQXSWnQTnX@rowg{Wn*pjoMTQr~FP0??+bW^@|CZ-79 zRW9NP;+l*DD-5mB?rb!Du>)n0hCVk^~)C|JP+;)e^fCdpR<9-NzT7X9!RT5kS z<^QAN?0o|;6Og@f0<`J?(gm|ipW++OL>_oX)8_huYCa?N+&Mi`86D$8$6Lq|0bRXz zD7kuVGee|s_pLe$=xf}Khl%FZ;57k9apZKjJMwB=Ql5>PcH8I3XZ4?&?=Cm_!A~zl zm`?85b8o_wJY73}Y{hwP1QteH-h`Pva_6gBA1%#d6q}ac5DOf#7zfW||Mu3OSE28r zB_j{5WB5&4cK2b2;5=GADET${l@@!36Itl^Pp`U1H|yfsFKNJpg?P;ce*TBDV-H~XTI zJ@P70umJXeX8iUy58-nV``G+nqJRewK=IsJ9snCW!aPUlw`kJJSk_*h`j8? zBjXBm>*lZD%(*_by1IXcN8*=CR9kO)2~uJK6a_>v%)@V;iyIfQTs38p^zswL8?X(i zfIP{*YwCp;az78M{Zu<&OpcFpVd@SG+$g(P|EJ0A*Lg|N7+{7^`&px_;!2jMQ@8Z| z^$_DJ>%wvE6QyVDX;$5NRgY@0NK2rv^dYs&Onitf+?_c{`8Jw$4}PmyHoUND>gC+p z>xl>mwAXrKxzso04_Q%0Siet(a9US#)&yV;G9)Jy%MQ1s#W}ZADgLEPce}ZD(N;7> zO<*m_CVBGf{~ZTiIif%dr<0J@S61d9ooO$C-_m)3pFflJD%Y!+Y|JNs4%?hK&mnQw4D)DisW2?z-yj1xJ(wZ(o7w{Ql!&uJX=Wa;JniskcRc_My93fs&1A>|0AGAd(l%VN zX0S`K8*lwN*gYAka%N9+5=;;~cX2HFl@!yH2KUeE)9}tK zT4c26j|?}&4>TK)%$Ku(i*<%44=ajJqK9@|edBFH4BESRES4App`7nss{z~Ef9|PJ z{Ror`m+|Fcx|_Q`UsolIKy@bmpw(5h;S*w2cs(C(6gds5A-{CxsUWM_{XxHRSFNg{ zQqtc#_Tw`lQ`RasoYhTc!H=|ZY3lKlr_)ks+s$7N)>E7hX!7X%-awtq+2nn6&9|7p zDo48+;AZ8eaU3}JU~{nBAFbSUJLHg3%5Cr*RxU#3Y3eKJbQLMvTi?SumFH4N zk_xBTBbT5?XJwJ)FSAXYKnA)ny-Xea1`lU4eFVAQP@eZPYCqYW$FMvx!vUl}NDR-@ z{IQsv;$YkF!u!&Z=FWS5$E}%?xdy2|r4BLUy7juwsut@Gkywc~)0y%bZp;UtMxlX& z;}?J5Z*chIK2~~s7;1S*U9LMs_3Yg+|11a-zD2#fmCoMHOf<E zO>!mLmyvmDjf>Uk)|ZFbzFK9DW6=wz=X>@eL@)+MZ7zC@daiO#cjZ`f0LIcXusQIV zi{iV3L0xdMGU?AWh9+FPzwt8;(vzmtGzvuB&K{cT3k6$3dE0Ek&K~n0P{ZRR<#k!* zKyM2=-H?M=8kKMB{MLCw$r)avL<5II5k$2ws%MQJ^KbEa@BY24f7^DgvjoMX`x#Q( znI*?Pu(@*fy3PiNHWABUBfNE-FFU=|Ij%-_9nZ744)-$w`eF!no_7||j`$P3Rgt(X z9h4AZ%?H`#l1;NsMtUsQi@xn&3K63viu|?q$gIa-$Fo$Ib6+#ME(Vf}N32~pfe z`+xN(ySS4@)p(JYbU#ALZ?4ony!$qlX}E>Wlm|QTp*$CGP{j4+!DV`Lfw6n9?{07&*`}mfB)1?JGWXv;Xv2#BDT^ zx7bqe-Nh{Xs{pYtD}Z~Q9o8v$5?W?m>+WfR0ad3~Q7=OpVl%X*;@M&iv$MkqajWC` z2DYAbmy%-%+hM}kFCDEfL?IeMTzx*p=dF5J+r!HKk+m0sc;vdAL-}KEeXP0va6c2z z$zK5?7>j0Z~3Y|R7n(J zg^lZ63@4fK|Jq~rQ}ITp1Cne_!Nd zB|G()A-&HgtpCx*q7r~uDlAB}Pp|;kA${GrtRCRB za4-h@#N)LIkKqAL`Zfk;>*W(BvzS(yY%IhKN>Kd(tZ>A(4R3;g?vy|tcrUrX-k9}r z6L0`LWY2*)Elf$1LVdUSDs*+n5$B(=Dhak1Yt^tPh>6&#;lZGR_kCievHTpUCEST> z`Rv~lYP2>yS!9G@woYVlT5>l_*fDstk!cGHeK0_SxRNyEgruOiR{)E?28(O=VVcKe z?bQsbJxWkT@Eg_*q5yn3esHv-j1SMNY+dNF1tPk;&1%LBzzhz3om;7cM4wilH>Sjg z>&$IAImIM3>_d{&4OL?`1hCM`DY5Ozn>W}93_S|IefUgOV46(*pWSG${v|U)_q{60 zP&(^O-lkENj?Cow|pIs3HT#+>KBJSJZ( zC7IF}Xu27;jEcG~!t)frNG0}loL-gAY~JXwKml!`&ilkmpY6rAYSoz-CL5ptvTsNH zKGal1`xC{s1X`yus3q~Xzq+0gg3Q!P zwF}BqcX=aFG070E2ZS9vR!c3iVH(Yx#b$0rDyXf=-0m-}^g|*-M zyj!FP9QIxoSZU*(#+WPK^EiEWKKidQ-Lq1EY0=RpSeZg_l2^6*^FGaC7|gW$Gt9_t z`SkaY-}`K;Z+0N%g(8;AJD1uxHg57hHvj`8qw@m1ARI@LEwkQ!3O~bB&h6MMxt{Su z-jr-+S*N)bFhxsUPuNL`(~rfM`D`%4IjZa)^>T33b~P{0qsvllTFWyx@?VsV{_BJm z0LWqPKpRqHKY=%{hgt1vO2Jt{0>go>rtoT$K_?t}rM8VQ1=IFPTMEjk95HfNMk~Uz zBe%_3SC2Y5E`NSl8(^z*ke^|zPbngWY6sO!f&2Si;^>`mxTwzbGQqsm;Jk+?$Jw5@ zg`m%aahK1F)A-g9Vh<)+kH;I5vfst;u&Ky!UZ>LC>wsZfJzPBR|58fd6w6hkny=IS z8pm<^CCtjBkt8J%$LXiBEghdx*a*~I@@XALv=F`)NtQ-;8&?oiQmIKyYwVZ1!aWYL zm8d{`MFG@kcDYLdc=ys?C~zz(J+gwjIs0z zm0~X;+gi>p>VlM;z`orYYboiHt7gYW3Z_lHH+SVm@y9>ad|E^=J${NIzS1-<(%Cn5 zh}9<7dq~@N&BS%E%&>4YbNhXyC#Uv7=sO0izE>p)@`c-j1DKsz12_ON2z78@>4M&X zJ6%$|vCY+`byP$I3+_8RnMc(|dMl`AOb)ZkyLNE%&f~ zDO;8AzXpHYkD^%SMVNVP+%u*k2u_U=t}Fev zmOhui)FAuVPd`}CTRU-4r1$0o!rD?@8Mf)4{&2qMf`4Ec1U~rLj=f{3OzT}f!ntT%8iV@Re6qx(Qh+f%#NCA?UP=ssg5v@dq(^2D4)?f)B$)T%aP{4a9{ZVO_kW z1yFmvptmytYs?jlYujZZAaC$s^g{37UkI0CM|&*WEOGuq4|W_cGIK6ZOvmgMWxRY9 zUD*0QRDjWX@#N(G#{>6n!_5||E5WGt_yhwamKk*epTl{BPtP>7h(4%j6g9QxI|p>V zk~Ge8TNUw_2O0Pfa&c_b5_oC0zE;LQAoC@(=KxTn@7f+fJFS_x077c52`rnrS* zpwDsHQbnNQt>vT7t}wpx18NpmwBOD7_=hc;?L7g1Qxi_+7Y-}()yk+t*K zz_C&1tG$V6!}XALRHw(%qBCp#F8VHpu)s>h-btzo`m_3QddoPSxBwVhP!jfpmsF0p zeXO9rzJJz=7A(#xO%X;;xhixM`QaM=$Pgpke*O>kV9ty z2$Ia&VYPj6TqL7i!N~`sj26+LZ_-V=d|4_&?%A#Pv2;P^>l8{U1;5$3Vf*pzE8NWN znX4cmdf3h(;vthAq7zEWAO(D(6UH@3pkLOV4VXNn63krX=S?NhwO^`{&!@aUUw=KH zsaAZZTWk5tZymm16=oS0`KtK3v1RG+Xdp{AzZh8u#we5NgZL;Sym87aNV?&>tT$e} zQp-LN{|6fmZ*0St9Efw@k4wPrwR2Ap$PW}E0GrH;;=%BqP|n_;B0SdK4eFAZlg8|* zCAWL-A(~GF%xV=KMmgrTe_yyl(n$Y0R94_^8=~q8Z_Yh=Vf&sJ88ysLuFx+ZXn0YW zDq^^>y_~#vbFk9B5hd%NY3zM5Lg(*p;yDO`bL<0V^op>EbD~7~}yav`T<*_`&L><-W|(MZ|(Sy7~1>zU^>SuJF0;hNV~%S5DIu1}W;cn&NmZx(7x zlU=*|0c-RNn-qgf=afZ?vD=c-SQ`B&9!6-b;J0F6Erdv0sZ}E3RV4Prh((sUR|Z*w z`Q)+Jzm*0JL64VviRG0+SR#3#9Y#tz772VI>q*yc^%<02-`hu%xFp60Nd}~VAQt`- zF>SZz98~KUP#-Y}W?X~=1U{MP>}mvwavVoUtPwuN&u^DeYiDyNb|f%q{Cj;=-Ebam z2h!SWC5M=Q9%5;ezFeVgtDn4R)of=RiQS$z+!RWZz!{@G2yOvqwS`62v=oACf*tt) zpH`bFQ@Ms@Kei3;+RXuPiRasq=-(Y2^rLY)rv4ffHhNeuShnPm-&M2FqS)-_`sWh* zq~AuDlic$CUa4}uh=`Jy{HK& zx(rA?8{stMtcGeL&-jvu&mQA&|9MZ>pZdqVbPP=V*Oq0`9q)XpDCjfNcDdhaOA73v zedsj!d;ayea_13yfY?7*)!FLQ&QSEdlf=Q?0LPN~qx%T2&GQZ>TYKoSi|;dQ@iQq_x<1}r5Vq^o}BF-gIR7+@^1@g&CJHh3j7_z`{?1pMPVNH8BHueF)zOz z96zW$o40Lfm`+bn1461S*ahxQk)K>o>WRPB5y@Vu*q-C?8cpwxOawIgU9R5Vp1S~} zB2dVUv`ENe|}v` ztG93G`+!3%A)dBa`(`9b!vqk1xqs41;H z3I}FW7`_1&mDnruRZ2o{d=F;eZc?bH0F*C@TOj+-|T9>FzQzLxXfv$dUjDXmyzj+d}l z1Domg4+#=GREmwHlZ6%g4HHlSvHv9Fc_+wm&k|tLjm&Fd2NS}9E4QeIgG9Pp7~FCn z@fs>X;)Xs54R8Z5VnM7J5C9!l)i(5C7;Kg;Dysu{=50;SIIbgW%y~GSTWUPXtUEsI z@jwn#LmqJeedXOz|G{@yjbyMm^s|&D3AkQlHyPfwPVMT{wxcn%;`e&2NOpobJfI$a zJVL7zjl-YLcvuy!aBx&Bl>jZ)J!y<oTmpg5`I8iEq6mIr>SS@&PhNU{8q^^ z=Qx{QZ<r7Dn=j`MYUV!gRZ;zArBEt#GvY@*lMaP~50Ity%`FH$sb;yRtZpMUza3S#E^^WsK zbDd-Qc#C4VxL>Cq3%B4$pPOO(!B0oXh3A!|i^D{U!*II^A=CoUVb$Y_Tqmv<#O9IC z<{|MQi13vHx0%4n;d3$J)kJ8N6{b=2LcwpC_MQpxpEG>g#1?E~-3VE?;yGRC=aQxP z6J`)ReF{uO%@3FSyicVHr1Gr&MW=^l(}Uzm=T?DZ0y28{n+Vq(rH;Ih08leeNL6qL z@ZcCC#>EuBk=#`#ym&XHoI}-514Q!IW`@A}d~w4-tbP*Uhr_o>`}c@1;|}C!Hqmgz zOER8WG)VQ{73K)k?DITNr%0%t*{8(HX80BI!73{A6!nUk{Ma^ z$w2ShrOWgohE2Fuee%g)$1`**R{9);5X3det^UIq^{LoLV0w@EN>qN>B{{HV#`|>L zTiROIatf{!zg6}!JLE`qO#vu2`r7(%W#&ta($BKcjC#Pdck*#pp9BV2Jp?PfhN~72`sanOy9?%Z;gDauVz;L%d(l zB>Lr-%ED2hs?N;WYrXy*l}SPK5QHCzn$NrWIe%vd5U=i7rFJr8ff*Ef0_uj4?sjBH zdPI=K?sGQn+|+HR)1-YCfpOBXRowUG)M;VB|`92(z>U zBYKA@p9tED_~mfB5IHg)s@VxJ0|q|@$WwpK}F>#>`?Bb1xNmUgp7x6 zwdlaDwvDLco8OT3thRV`8D}r2o&Rzx0Ozgs3UwfHl9u4!8*u`J;-jbh%ciR`NX8?1 zX2*@}@6>sK6K@;GvV2q_Qe{X1C00--4?%pdWp99uALlWmJM@Hbfj}it$78PsPvFrn z>y-RVdG$MevXmRBw3iPPpi;{~|9$CfpeUJ%1k&m1Q`ly&=4P`(3`j^LQP?^gRI^url!mG(tsd;-*qo9Wwg+f;RPIE;x^)E>$$t9m zMR1<(CPA_xf1ou#LP*F={D#+^B^0d+>&dEEe}z04eybQnJpr zbL^t}UUd9%y+*L1EXj@=tSbxz?UGw6q^gaEO{5!dBtfu`0#uYXU~dT-tQ!|4^;K*$y3ZgL%! zV6+AKQl-*n>*jmgcY@`!*0X2@_fe=fOO!=KEA209X6G+vGo}6}9hIgSAL0KmI1?FB z!uXViH=}}km?|Obd5@hZEA0r1FG%H(`m=!TD$e~=b33010+)1e9FwnVcu-|`_X!fo zfYO%?m_qoA-6uhPQp)T>5o9>lO9m&nf7`V(WB^MI;WM=QnG^sn4bx@B*b4B{i5*n8 z-)xWRIQ&+dY@~pNhqFaCl&kS$zv{FB2P{wXDK_-=Fo z#`s0vUrLyJlMdC8CSx}qa|@bYn3B#S6jT~z%UA(Pq&@aXlh(ly>P`&~cTc8nmVc)8=+4MKn4)R*ru;N#1w$F(G^y|1LrI8g3VfKS&c3RObnc_{wl>ylMps# zK4TVk>`F*(pIBTgmQr3m=*J~h{J`mcPhNEK%bK42K0*%(#NW4&p!u;w?S2|ui@O^%kh)$Xy{IH)@x2Zg%y4gP9NvR8rdi+<)=OGI z)al#Os{;!3G8d&Qyw=RJxLqH*f5y7ZG|2k>SyX-G$+D=lIX$Q394MRiNPf=V+hd5b zsWqad72`x2{hmXS9bT?Po*UFSmnKm#8Y2>hb3B`w!NWjE0Yy);2gEdakP|*wJT89i>i<44N=gt9#PeEoO z*pfpxId1jUXD+U#>hRiIM8b-AzL*Z(#nnmolDf$%`*C4km)$vq87Uy_TW#6SBbpG< zKViwlmvFF|Uc>8(zNBI1-tdWAy;h`Wo2g?1+d@z#A8{6Lj?>RSNR!`U$378W1T@1s z=3E4Jjf$Ijr#gw18tlKpab@g$Wi8H?R17Yv29zgci4(6E7a#8a2%hsn0rqGn{NY@a z?6COGP%$Fg0Pf@s!~LFVL2tujsCvi)`?4I4QaP02wX2;k@yBkiNFBoG5A(PhA1=$k z6tp}!PG7`kO&w)yjxoGDninJ-hPfqRG03)n*WRi%bXC;A#HypF?L{hqTB3}M-H*`OvyFqRlNF~z~ zl`t0`zu+w*Lkf#XT=l6cV0Li^F;7xQ!}ffk28So^jso$MLRs{-i%cyT_)9G-ohWGP zvo{~^jRTPZ&Qh229p)G?&qL4$pKCC^C-QSbL7Jeoc#8H+ceQB8Ob`tW!if2i^-ShT ziU=?;%f|Q{*1AT=dhe1!!H4@Df%7h|sQ3DRv1_-!d;m5%UOe(<$o*HrFC3MnPfJXt zxTRR5Fi_~E%l5BeUZ=j1-8Iy5`3l$r6pyrpns&Q29Z6$gT=IhM>Om1q4Ac^3YKT3g zcYR~nThU>8WRbtAcu;_r+q5RI4q2G-4R4GdnpqdOV?$y`VMDYlG2f%N~haqiJjZhaizgHduF znOw^Kp29FLgWTqc#+^h($SoPS5OSSFMs6LK2&pDTL{#Lw#1xGhA;J(L8Zs&qoeV1P z(0G-ydN;FO&Y zts1l+XlJs1n>&B4JeXsSJr&9T$on?RTiq8H&h3P4;|pYV*~5fe_$(U0es-X?8eGf& z=FuwkYwqqWX4bt*C8Xzj&{eBFcXQ+E*ruyBZ-m-5J_P(y4vKq{uMXz4Y4M1XTZslU z0<=*d+R@DJC>s$*d%<#2aN46`G9ybix!Jcew7Yb#y7YC{mD8Kf#PNM+B3*VQn$}RY zLX=eQ2%%CizFxfb)q2ksi|hdV!SY%F5I<*9(WQb}qwLf^ey(fZ9!B2+V=}r!jPo7m zf<~L#M-x5_?~3;A40pL~*fc^v-|C}}66eg^Q8>4>qTPEl4$b*2;b)96UrQ*r!14O* zLM7Qk2Bp%M|JlX0R*yajQJTd4J{E^fiv0wl&TBEBB*nPE)MU#Lyx3Trk?nUp*Ve(Ecmu$@Kyk>6roKuFrsiW#X{3x5AHmTC4UF0$p zruIVEx7Bk05%yx`<^&7;aQjt<=Z@Hg5+diy&Ni3n@jz&G1muf<82#GG&1V?j%1}f8E`$dLw#wy=?un{C;VLt=Jd3%${rJ~L^*CnYq z;1+KZJ`%Ngkel6Agpcr@?-II?o@oo<__MEOz|#X4*D95GIeZ!0rFxc#ej~xZCq6zp zeB5=^zp_h)=k9wC44UczMIRv50Zne8z}h~Iqm3GZ&!DY#JH->+htUn+<0kJ_owm^I zlPzfz^MrFBS_`RRp`~#CnX}|h)RGoP7Xq?lO~SD_<;L#kc%%0-^4DHhCCRgPOE^>* zF}`BrlDs-f4-|aeLRf5o^5 zoGwxkw#Rd*x^xZqvetsR-9~_7$$~5BD&UJUi&~L6Y533Tk9A9I$M{`{miEvXPKyL(+y!&bx6dJlVfUwq5C=(*ffe!R2czv`*E1 zEwcjmHhMPFWs* zEdfcE&PvVk#Y3r(v+Qi@#Gba8&WObIvNr&-=E*_ASLK1hi$@A_hvqN9M+4*8Q&m>; z4&QE#jiy?Gy0W?1iC=TI1G<7+1K!L2Ln?XUonOPZiibO!Pak}(eqfw3f2Q|Gz1N8I z)Q$KBCDY)?6~p}Y$aJ0;F|Ho11JfTyE z{n6aJ!#B_%bF+Hcr1ZL><^&;_li#3VZv?xd0dr|;GPa`J9Ujve%u%Ve{!IdWqpKyoR(-qR{l9+6xb1#|ejsk6 zWI9MWgB?1k+Z)7c+I_LA*67$vIP%z4U?xp}R~$O4iM!M9^1$^e0k`TkD$5O@-{7f| zQ?-Q4o%kIV#`NC}({~s(g=DX6i=i@=PYCq*k7KW>!i90g2+mGYJGh9U*$C2ekZebQ zBL_Y!Wii`C33pz@mI>@LaDyN0=@u+QrIq7LzsfhIDztb>cU|oEUHzxjTEZ!1lC4kv z<#KW)FyWgv0Y8DA5+zxtU*pV6v>9s$`1qz?yBDTcxb)zQ%gIrNK0!4M*Ah$F@u$Q~ zoqD7Ig^ZIxU+u1t1r*Lz0(_c^qiiQI$v)e%WerWY=sSb-I=^^D%d{R_qpH@u>dNT* zkNqXA_HzaUpejAw4-Aza*)(E_sQHViu08jkB12cTf8HMlOtQrL6pBiMwY7V z%%FX!Iz@^ggjIg`2MYOL@C*9)5eQpG9??kgIGr3-H7K-5{y6b%cyc#Xh=-<70~z#H zCvRO;lM-c9bl^BMIqy{}vE6=wp^^DfP$5{XnW#efGXPdM6cUw~14WCX>YTpYD`pj5 z;M1mAt_Tk(Etr9i2sv4*4){5ELd$|Nf}lDvqvT0Ts9w|$ZIU|uyE^z)llY~|GX+8V zV$=Gea>K~eYa<-A2~Fdf3Dx%{sXZXf$#kAONOF#7h2@@90XaoW;fNOf5QcycmUI)i z1vlf`t-zF=)Xfs`iYKDtol%;7XCAXZAbS`%t;`3SzyKrIvZc@OfbjOQmfzOB+%7#4 zm{wq}@PKd~T8*S%83-|dl%%smfhFK$LYl{x;S+kHp*_w|*(N}n7A)bn4K+h_dx3mi zLXJdWEwBWa>iVmgWjGGHPt0nZaRsiZ8%}eO#|| zG0i*4?P6e0l^DORhY9br5D+X4J=s1d1L%mh>XOC^MarG+U-fip&D3d?HXOSE2#(nbBl(~#EJppRW~4z+;hxko!CHb%ZU8jkC*N>Rhn z8C-FfF#0@HXDDOc%KwL+M$94~xm44LE64_Nzxp%n;r?6oW4u<3j|*=*RoM7zX2s-X z5%l-_7}}(>{*v3pb56g$I5%h9-0y&hkVl1D4VlEMpnmRt-#(`U0F>Sv5cn*DT!eoDR0&P@}NUUs9kUaKjH$XQ;K z0!zeZZwm+s4N048L8=Kluu}xjPhWPUFSNw;q>UcgzN)vx)sRD8S1aq|YLJp|4}|P- zisb6d!Tx^B=-j=p824sAN}(S*B2hU`Z&|^;;r9ruubPB)-_MHt;j@OIo>-{Qqb^FN ze|#N^Bi*KVoB?k^3AfLa<;P8P2C?d&8-#=cmoIRHsSD(Ug|zijgaEHo&BWp=ctlSn z{?a8i0XMEVwDVG-(+ORYfylL6)dyV4sieg literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/html/_images/chapter13_3_192.png b/doc/LectureNotes/_build/html/_images/chapter13_3_192.png new file mode 100644 index 0000000000000000000000000000000000000000..8e81d8d7844d86a5a99340fcfb76fd34b8871d1d GIT binary patch literal 3541 zcmd56mWzklYP!^TPAX*d(h%ANhEFz2uSY!|hi|l2m5Viy%(TdOF0uuq1 zC9P~SD2oD-B``<}&0}j(RwKk3K@mbgfglJS_1JgX({tXR?H{xJanHTKx!?W1`^~u{ zPIgN2YVrU8C_(lITmXQOjK8m}lg01U?b}N5hdI^Ooq9AXh??LV69_o^QlrD8sNo@g z+v5XcVnd=LjrI5H8}Hu!6_pwtYhhpz@q2)NR7|izSHXc^JjwcK`{S_yprHKrA^_L& zRPl;mKnM1_Cgx4^eg0ECf3jnCv9$4HHP*p%tPD{_0A=6`_vh=%+QlJ`Ho0E(YU!pU zHbtAyY|+LOX_!i^Ig#KfJ}aXff}?gPmBp28oscRk^o+5yddYiz(MOoGd zx%Qa^dGJkZPSFmk=%$G4dJbW!T zH}_o-vNGXe9k13>d-67$`MM|d}g=c6Mc1TUV+sQ+^ zyp4=ph90sT7?UCcN8q!JCs;RTDW(W|=GEMgn)q_r7BrIbG@0O&J8}RiihHaVp;Na0 zv;pL(nhb^B`^(<=ivNxfzawJSl*8N?$P&0%5xuGnr69sGuoU5&zxh%JV!4}0pgO`v zV42CqBA^9*%7TfY9&J#$yIyh@%sHIo2K7m&c|INkx{mcfM`;RX@*3`SC5(-_>&03E zB>~@6Hw$zOuoou)mAlQoRjunDyunJD#+Wf?icaP~W$)y*g0awePk~iqd!`N)W(Z1- zKd$zOU$GTHf<>mal*oCGKJ)rJv<)_)z;}#|jY(!G7_!OcRLeW4SifYgxFkqjdhnB_ zcvJK|_26aDu`NTu1{T0!tJO2oMK@qLsW(i4t^a8^~rdcNB}ra!>oC#+Qwnjnz-_mYR3W{ zS(P=22vC*>w3H``b#1fJEU0 z!7Nkg4qI^ox&yJ(STjm9=XDH(ctd?^I0st@S1Qr_@VrX&X0xjB?rBULo;Uh8%-#3M z5T6INO)Hw1p2I~_`=vc`TcVQ?wyybA;l(WSm&j>o9O=rpqQ^%lJ0Jr%=6CM-*G?sV z9&IH)hLM;p4l(_W2 z)!Pt7yyQf;hx&wnW~J|=LFP88O2@CsP~T<6^{XF*bJYjY#BvxmGxO&Vjl)Jc0ivnl zJ0y#8Fht7c6no3o^1zNU0!|3d*b8O2|1o;)7CLQ$yTuE4&_3=;*cLZ{<%rg7&$ zmy{g~@Fei_gr4x5uheXCWK2PcF2f3nC$7ox<@wFj{qXc^%OcBCafMZ#QO+mPw*<9(B z@@GNlzL8LVO}a{#CjxT-j#NjszI}|2c%3*4rG5R{ABVB_FA26zvP1l(pcMor(9rld z?b)E$4cA)|>Pkaye*Ufc`g+Hu5#&`$mQd(naN}h0Ezsnj!l$=RWn4S!V8Wf*fEKn0~$cHkG3WS=dx!RR#! zz}CQ|g;OPu8Y%$qu_-P6O`;$Fwdj{guYPtk>8{)tW${p- zitu+UbCWLS?rFPDpwB*?-D;UH#0NgIJx|@Ymg|07WDJcu#dIF*;bf*w*&?}!g8& zcVo_`@E$&$L^pv%f^E4-~4h8jc z&(UW&7^h>V7l;CK!WX7qRFP8UJ>@Lv1uw%U$7w!~>6A3va*^!^sMeT%z16VIX5spKV{@?8np5px(Sp*>|FRfQew$8iEt%ta z_h%DI>zNd`Pv9$4iCfL2H#kg4UT;>zjEzXsvL+oP1-NF~($8_wbbA`Cn-pIjw0^Ka!ZbOl!H-k0cY|ng_hb?YZL>KJcJ>enT@S(0%W- z<-;F{U%UTKM2!~RP(eepV^v--4o;wxcIrlt+dp|7ESyJa%8AB2f2;2bM!XQ1a_->k082*a|K(z>Nf*tpVt5Y literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/html/_images/chapteroptimization_123_1.png b/doc/LectureNotes/_build/html/_images/chapteroptimization_123_1.png new file mode 100644 index 0000000000000000000000000000000000000000..fcf4c6806bc9b6341be72e93bceb25da03f4f055 GIT binary patch literal 11310 zcmb_?cQl-DwFbIhjhCvW@ z^ub{62-E+=bcb$9Ix_`WD*4poW_Uw1}{p=mDtF1~-%1DZbhexiirlgODho6Xh z=PiZR0eO3fz-(sw zcJv`iR{fE*CfzMUVXCk9=pyflnI=*=J-feN6~~~f7hlq#DtqU>9-Sy_YiX5g%%?j! z-%<$Py{~$cckelMA0hQalHiwj*fH9fV9a%?Q>u1l);4&%X1`#0v*R*nt7f~Vv!-^Z zzOtaQK-gbZNvSNmqlw@iRmyfzG&=`J%46Gi@6@<77&thn-~UJHW!K7(aJAanTc=>c{E49>6%+`qB($NH#l z+JO|u;A0SHX3z35_`VPnRmKvh_K2Hoehgku7)E+^PlADgFoaHmrfT9C42Zw|n4?<1 z?;al9B^+rE+g!Y6^_L<{^K?iS(3ur5cnU6-GcOG6lyhFn z%9*DIn%jZapo5m~pfus7LN^c)?$QMw148v4tX1U9w~p=V0T*6_D8cg)9w$u)s372i z3&`QO$xwmq)ehVR-$P^OTybpI3TSQ*N`UXm3lHWyfyP#(>P4Vz4vEryoE!F_vv`jH ze;_6WEI=;rod!N78~Pv&T?hHuo1~iCg0f=P2J!78Yx{jKybDmfZ-AIMaGfZ06TZv2 za=_Vd%PBnL?7Pq+0v(0B*tU^di$Nz|!=VE8wZPTO2ynhTXd>?TI%o#%pA5d1%Uh-a z`8_WP*n#glgU4~YY^PcqEL#Blt2?#Egz_+QAr@G#5Mw255xP8%uGo=%qDkE zZrxB^Jzj&NZYL3v1q8P(Qki;MG7b7lej+`$Y@-;u<&LNNIwV{=k}~E;_-zwHpSweX zUmTCX>&0;#^Qf@RU60p;pMVj{E7;P$yzYBQg5 zBX@+Cup|MD0i=JdY^=}(*6{bWn&;i_ZI(Kt**$}<J(-8tmv5ohRcG&So1`}HDvr5?4t@d< za#Kg>P^A+Uh(eWNx3hL|S%%hBI9)9vXrCkv*$1czcSMyf8P{xQKjjMa4S7K|| z0)*;zd2w0y@!`8NNU67}W|j<_KTJKFqp|LHvGs6<9s#~_II2~2(VAk6=9mo*5w$b9 zt6(|L*KTa^1Q#}%z$7lj0K$C%VOKx;p&o)8Vu=aFvJjLhvZW)27Ix4=G6tdVwa>N4 zq)Hb82nw9!JzZ~ni^P+c50U3`o=;f3uF3=YhvPHYfqY@gFj>%y{MBN$q+DYT5*7sM zY~8dmaS6@Dr|iUZdVLUq$`NvREkx|#oYvpk8H6C|UQWgj_d(}_{Nxpcog4arndYh< z!&}obPs67WYzw&GI7G)pJ&>cJS;P^oCf|#S%+I9;;J;Fjbs{BMMNDt*dKgH2sUvJ7oukbZTVi=y5uz;y zP2hhsb;bRbCfQW7qLU=s21Jer68jDZ>>?Yv6*L$cb33tk=Q>EIw>w*WB=rg58AWoO zg%kM8!cZ+jUpjvWxVPLv;9LD~q&6%ck3o|D)+)Mv7gD|Wt`9tDsm=`imq}mXv67qf z1L4dq z@5q*y&#iA;5rV+;D#$|Er&l}F9pn;^EV3}(5Y(f$1lI$E4#y4n%fuaV#4D48S|#k~ z+N#;}a|hm7g#(s4PPP5;_Y4Md;apV)ropAd9mY}XeU{Aj4HAsd`KA7N2QOO-N`qC~Pr@pedge*jKFymXsi>md;p)mBj> z51D_V$^m4}MV>vtuZi^=j*Hv+)%`+HG(kff=F6QQNkAwF=xo*OWOQpX{+${io`(#$ zb32i^{)2E=r;ZOgWnaz<38V1e1aNTdrK^yvsUfvsGC*@OW+E9|5OL+b1Y90ZKPO0E zymmwuwV-XM7`FCn(~^{xlu9&9O!q8dFKn{G0^(4ej9@S>@%J=l2`z@cNI6s-Wr=$C z&L?mGgzkSJf&ZDj{txzhu*`#4ikOZLB zDgCnFnwpB8{e&xR{P9YmvDX9=mDqdl~q{zg6?rHvZi`Ll>RAJLKdx zbXWNjpMMwy5M*~|g|mYcBZ(KU+aN1zktr}`R`!o6oT@?I-rj+4?^9Llfy9Oos(wCl z)uOec&}0I7ybpS*G4I}$@nuBYf=VMBZn^uT>jo<5sZvh3Cn0A5n@2)$cxLW=Wds)g z@)lMI+79wFXkWwGXcBKQj{TwE3?b(2S$rHEhc(eJ^*M0X^j~b3i`QsLtD{4lo=W{W zxldX>uFg}Vb}GvC!C7|-*Ux9-TYu|6^{Pm>sSKRer|J?Q%J^_~Ay+X`hq^HzFI7re zB8#~Z2}kZI|C1uG;k#_0v*+h%nAZ@_F;ZKCxib0j(XwbY zpVhK|Jj%vr=2HW{!Q%B}8;x@-r7|zWd0FcAfZF5TD8V7Io`2kn2r|YP!tUX4j?IS= z|D#c>c7UuA4$(DJzWc4TVBz>sQr@^N!piPEIQgCHlH;^3nHQQCZ)G{^Nb3z~4Gx)y z=NQ+SWtc>8OesuzUCS?*SB71C=~&yM)gYmcENCmyvAwaWm#c%%{l-Hi-o+=2}Y* zjh+Y^9nVA*;^)XF*#$BKc{@Ia(hPdT*jKP|coWLtWa?P8jBoz;+}@~3H->`OlcpgE z;?oihwJPbB-Gi;3yiM^hrNa~RSasB(A2Hg^1?_znKII;unx=zYms$R7uevlakRimM zZ5#-m*G1y{%L78NiZ&lQ!zbX~L?_bCVQU3o#O=geMA`FRNGW763;{ahwc$Nj`D+&>jKW-K{HI$x z*fbvEx|~b^d8VvwU$^+MR`w@<`Ze8~eaR!kyjFneNbjk$$$Ec;?U(We4uI^LI^)F7 zV3lY8pYWd^HUSr_PfGqqfT7%tg<{)AjmUuyChfGDJ33{Es@lpQlD)j7Y(!*ujLe%|soF${~E&SC)R- zroQ3?S^TC=BVGOe2i2`+RMiyaOM#YyLHFH#3or{D6^ow}d4F{NIQcaRLEA;xNz`NR zhHQMD7qR-D<_%yQyirU-9UN(-mhOY@h$gQyLrTeb&>A5}TZU3mWp9r%(lIa_Jrn4pumlkQRlZoRkRgN% zPe)IFHY@9wa7A&g^50jTi45A@^S>+=mtC*>om5N9_iJ5cIQ234hRNWaH-`*Ky-wWR z`g>D)6GY%*GJ8NoE+oP zj$w8~M8oyXv~+@?)9wi_CwgwOls4{b=69d%qH<>$8Q%ggV`Hzxp&6RpuRU%qf?Ed8 z4-XELvqZ8p-3VV?o+_8v-Qohw1 zik%J42{~gq4xK%-yvVY4l3733?(~TdUAT|Cbf8wALO=eBpnhB*WySbvj;^x>bu@&^ zLoG8QextT$cV*{Skyb+h`8xEEo6}a&i=G<{$#RRE`N?`#hhTcCuW=uy9A`K8)t5`} zp^r+KPeuZGOBH{87BDk63th3cI>KHY7-Es^!0Tt`ofx|zzwjmOT6FczP{YL0spd>; z_=ROh`paMZvvTP+!^R|vT<^YiT-{W3J<4| z$5U;0rN#-o7JV7krOwyQH<|lqzqHMux|~45mTq59Ez9POjmbt|_T7swAsVN!bLBQl zA~bu=%rwvJ);GMlDrYmcz_PI z*=*>?o=_}LSAjV5V&`YX#FBfxwR{cl4M4m^t;Re_0^OWV9b!SEXc_g+=aK!Ng8rTD zw@cZLO|KGnB?|}bjHd!@*~VGL^OlHD-DZVf>Fw96YlL#x+|B$hSsM0e%RSs>eHTDCh?wkFAzT}Qu*(N0|LfF8mf|2R<`R@JYJgZ zXCY>K0pAImrDr|Wp$wi|{^>isujQ?VAjJ+uxL=L~5Pade8J+k_x0f3fnrCgJN$ehc zPe$r}ro=-5P9AWR@pftiv?u{cX8W6b+YigrDlQLY3l_Q_oH=w^2ORKYFXAdL-^%y2 zRdO4M{-nvkye@i+nytEwrh*Vy6N(YkMhpj5JRlY!7*mWT;|)}dZwo$Qv*eaB=P*~L z@NwNC5AG=a_W35JWATlQM^ZQ%p>;F2H*r4hDm~ixKAzX%RV{MLahit=`3z|ddsf8c zA@8AHJb~*yxQAs-Ks;~ZY+f5a7gp+7Lc)|Tdwc#>Fj?lhuAmFe!i%t8fOy5#W1TFf zJ$|&6`R{KZ*RF z1Q3^MWTo{QM9hE95Yl&k=?tpGZzZV2TZoYE%eV~eo~SadQ_5^0v3~?DYF01aS`DK% zyRY{uu4GK%SkxaO%WAj&Wme+6jyQwW?taDr*E4*lBGbA~d7?!E8GIR*LE)!$0cC?q zj!z_Cs~v8cnWt&d-4i%t*0P-yFq;T9o>)B|l7~+stU>YgZb6RZiode>OT?tdTUj+T zf4V`}&FEF1a#v>o)YV@PY;*krd@wXaC>PH`gG>c}t`7zhIA92PlF*r#tcO-0zI9=P z?$gJHg`AC{o6BAWy4F)5?Flny^aZ3w6&(#rEAPsgLWDk5ON)wZl&; zDzD5@E+Y%;gPc9tn+xKu%fVJuX6ni>HGWJ!UsmAe+R)}2j(+;KNc2ZTq~fZ{o8Z3` z`9F|;uOfM}ALYdSNb6{ZUGd8_T>OOjxBPB!6xv?V171F$v)vBs5pEpDUhWNr9*>L- z4;VQ?*LG1wU9{&@?4I0--!hg!XYR0OSSXBgG1Po_cIdrsxqk*&M)D7x?bZ}B$X9c; z`$yF+AHjqQ0lN{`1h8=PU96ek{RYf4yrk`xcY~#wlM)?FsPkQ+OSWmjd^~Bhl)Co^ zhF^`gSn3#V5it{o(3z0)69YbQ+GQNo{GnEfY3b3{vd~g=w&(_kQ`85K4N>Ipw_1yh zWx-7f{IY|6n#xS}Q!B#aBvX*w)myMyn0$mguBC7%3Zrw^XDXHIGV}S&vkiytj7|$EZ;D^jKCfq`L+M-aHEkMwCMneqmJl$? zQ@(U+m(hjPmw)T6XfB^F3_ak+4)o}pCQ#&W5&!yyV3V!D+`Wlu)jq{EfY*2E8j^Wt z+9-D~a=NWNm4`O-o6Ig)G9z(}RA)xnJ@v#QYgXXREaLkD;a5gI$49DHcB(R~Q9D)$ z*{zSbi@CrBX=r2 z)(cfVS9>TE1WliLMA`W@;>~^LWH7FGkk-k*#}(@ZH+Rxu9!M{iRf(0nJIeR0twDM--p&rC5O(-c_4;9OC>km5Z~nXR!Of@T z>-7iS+w;>b=5D!X5S`)?bjzOc{!qg9ukbNkk@8!qj?7)BJn%Dc^Nji1(bvhh89k#P z&N2xf;e(yZ0``9G zo=&LB>l|RtRiS+Ln)$4Yt2J}^lb@&Ri_6Js#JsjYYhDp|cr99FfwD*gJ1XAXcCQ-^ zJ+K@vKJ;s!WF2rj=X2PqNUc8l!hyprdF*g`L9u_0X~o9noUtseC{)mX5#@{BMGMFV zy&P1iGC^oM$h>)}0d<;J)#4&U;vrd)rZ(&zD#csQa<)p6KPFB~Aq~r|F6E<2yo;>^y$n_W;yz#=D|L6Bf6-90q4zL5 zzo~?^-VLqT&}7)(ljeMJ828JpXv?{?WAVFv!Fib{M=`2_1J^_A?<_6CDTqMrnC}PI z^RU^)>#hsA(*3c!*|^Lx?Xxvilr>30GjaskHM(nj+>l$~@B@3Das2WsM=>xaFEoF~ zE9=iR$FleIv}<4`jWK$oTGn?7VGV@ZgT&y7LITFf+l~VUr-MlXns4V$wjWh!g=F%E zFZHG0jyw3t)X&hr+@680pkMF`ud37ZQJ?+D-d^Zi>^54Sudm5aEQpsj24M|&(8j+W zAl0?U)C%00y$kk21y#WJhIY03=LdLwHp$0jJn(783q~@$>q{`dWQI$Mi(Sf@cqgMt zgxr{25FHNLsqH?`YH+>uCiPEyH4QWWW?|eN#o@#-AFdmvOom9ty5^~|2qf-yeXJc1 zNFSu!A6k$T%`3Q8A!Mrw7C^({J`ZYAo4EG~0Y(~|MLhey!b{sSShVt$6I?{jXYK{j zOvC1H&Di7Vo}^b78wBSk=4_ic&a8H0t79@P7ZTmlcK1IRe<*V3DF_DXCsp>)20ypz zKFm0Z?$HqSbNTqy+&rpBgKmn-^JgB<>Gu7)vJqs4B;S>IVc=K!u-}|vCRxUQ;+c|P zM!kA=alPr*`>mVpvhY_0&1t+sX7BS?*;PODy1RTRTe%s_0*kF zk{7J>Fdl!B$9^yADkRr)^8O}~t3&5}Q(a&?s;On`Y-K^h*^E0@3~Fw7HSheeMME#N zexvmw@bV$9kWPHr@jXEx4`_q`q0+V3bGJ9|V5L=eR&>bd+i;q>0)tLP8 zhY8g&l~PSiXO_~}X~;{GQtI>o%7J=uze$-b(~7GwQLM{S;e(xITVll4h_?2!JN^fr zy3#{MVy|C3u?EYP-RDPf6k~`h;p$-C_X6_E=K#y1a&GKqSzA+2u(}eC%hS;pBXo*5Q#dOKOpQ#bqE zR8rRrzUZ5A`o{rJ$SZ4;a zUWA?Kg`elIz~)%ZU9JeShfSuxm!VUad za2JuvTlhTr?uQ`9;u*oNCRK-ai&9kg2Cpqwar&khy`=O)w_~UL6|_BUPf{xkv>dpU z!9ua$^LkM(nH|CNl=jCYwF+a+%0nYav>y4+!&ME2808CgRdB`6GwcK6^vrw#IftoR z*xn1Rn}VCqpO2cZ5=33S=pe4wwr3L+9cz zo$Jq=x%J=iEm` z-t5O|CLmK;Oou!8p>4mvs%xA$3m_mTGa}+DEah%KE0QHI)y70^O>X=x^ zW9)%}Wb;G_5%XkLLYRkCp>-I!{LZnj*a>qq!BV;AL1Zk^wp-`z&a!7&q!*b8G0M@P zFw5di`X=9NEslX{o_Bx%P?z3WwV|F`a$!lz^P z*4ROZrK6_s&BaIIL-;xY{w?hI=Hh-?2jgkU#^wQjO@9RAiNB?96#Z4@H; z>vH&1TOa?*8h0?YvM=x{dEUaQE#vZ+=)pKjGeI8SZ3%594qR)XR7+RC zu`f7*1ol@>c5wN}ct;7W59E_CemP*4J4$OcQf-U~s4q3PD{p^S#xd;>l-0j6D+b)# zh+!!c9Ut zvggx4XU~G=dhCuVDy~CVXS+h5IP9VC6SGd`qpiY8d$PTyu7h0Gr8l+hHv}d=fy~`0 zF2|BJq&XX6p{OJoXyDa(7h4`dFXnJPUl!?22E9IOj@w~sIhkVKj9o)$f`XN#=4wNQqqshj*s_eAZeRCOh+K=#)9Wg@@!wxR9-Y~c14WiF%emW#?M8sZ8 z)9Ka^8G&lcN$rht5`0KKje;sI``W1582{wD-vTlbCldS_JWLEdzDfj$ClMwk3g%d3 zy=k1Dnny>Iv=?qdawn9y;(k)cf-UjB?C*QST@1Uo7DG9NsNRB_d)(wYLll(NiKfjI z3N%&u#+1tp)S=Oyj}F3s(rkb5cO5`!i`S_?IT(e@Jcc5g1I}dqAk@+Clv2(3c>Q|@ z5tQEOV%PwzM_-HXBc?mHr8}RI(PmYN#X`C4hensFtMUVBF*QLX~1t<@{0K@N&M>t%xS&i7tkubPmY*gdO~c zNQ$cZR&${cX?|DbAzq0EiH45*zc9Yf2Tx_aJ>sr9o|yfypj5Ux9oF~Q=d9qQyeNcZ zyO$X4nqN-pPE{@R_qZ&OV@p#ZhT2dyD4&)}{n;K*q6PY8Q-0SFj;elD{d1)nlRX}? zZ{cTFkHP7RQzRNnTq=&}m$}_s7=3+*a1Q-}nucgS610|2^!5{_G7TeR61zP!*(ft5 zF79cgzJPUF-(q%-)YNSa25GsX6_J=@nNqZYCC&YnlcY5P@ER&IX!ZQBkF= zPC-tVZd+{a>tvf++a!Un`w{eI3~9K5Qi>U_0x@pG(5zr{BVu64rd1qz-;)xGet7IH z9{l8W2Jvxt&KM+cy2dDe=n)4;dv_mQ{s1>uy`Kr<<0Wt-pzFXS|9FoZ7nl5FH6FYN+Q3|Gwp)~Mb!Wv--D6ZN0=tNt%*SO4F@)sM)4Os=2_@O%R3tXahFuOM*s z9%$zF`E3tY4>F-ac#=BbUuOBos0XWI3HvvVohZB;`Zl3~0Nk2bL_IGcSm+b~+O-$5 zX*VA3!Yl*`=|sQ_)E~AaG2%hArQhAT?+{YMuA-agS(_;lH}Et~geG>KVFN?vQF!MC zp%4`0&t|$0lhW`UtYut<#4;#&4%X$YCfdn4TBVv%Fc%!&2qCA_|7w(D>IFkGfhu@D z7Y<=mZ>e~1$Vezj$)7uphZhK=YUu#8whgodRgYw?G_{;ZpKSQ9Hz`_F&x7<%Sl ztMyCjIOigyZ=L1sf7$BAz=JWzvM zFgrc@T#r0=0tzy$e1pLF!SySfXE81ldN6{$3zt++kQP=BY0c|0;T=H*0|pLOcDt)2 z0#8GMukxxJp zP|I^ay525s^__2G)m3|7domAW@T=j`zoYKEFZ4+;ph*e7*UO2Gvd4d4bJvA>$8^e5 z-Sm){sC|!8sW3rLXs9u?cib7a+6wuhbm3y5VL4NIM>v>?m{k}mN$2CQ571ka>4$HC z=dH(f=cwhG;=YXvL#<$MkV}cZ>aG*7p4cw)8<}B1hK{J*6r+)DN8C_6En=uqWuPOx zVqR1&_pxR4@7zcFXpX1xU-*H+#J$N!ki=ex4ooe`@7@6=Fj!0`L7j7)CxXa-*#)#o zfF@8?zQQqLI)jN&MaUi}3Rdr#zTn=?O)3B4uA+zgCSLtz@i7RcLf>U-r#qZAe~oi* zN&a6#3i-h`-=$V&51u!VG>^QC2-RBf@DCTg!blwuzvZxf;@N>w@n2@X!9M&x1}DOO zF-{w8*$|HKw+qm0oR&GOBSN87r1RpMDciVjLEK3lc!h)qjjmlwPoVU+15J|modb@87RX9hWcLH?1fEJI!)EVpyW_E;jbocDpHpz` zk3Ag^fp&k!1)#;C?ve3S#eY?LbSQ8U(1Y*BFQf&*IBaK?$>`9tgU;qXuC!oLgw5B2 zx6C6)Nkhd3BpPmC67+}wBP>}@UQ6CNSCoM89Z36Q&EI>5-D&HC`{6G{B*@MsJaG-a z6>=}&8>01fh|K3bN02{N)8Ydg&}igNgxiCs|Cs@*wdi!T7V-sBAL)n-a1yfeiA@7H8-Yad$?2Z4krQY;o1vHAD1l}5NvrMr}C7JXr@eMuYI zx0VXMWH{_gaWJWGa8{yAyi%C}K%|=16gO`Qg%EU&q#&fla`?GZK5on-9is!teQ{9M zC;&PuNLQrh<-<*5{O%Ms`LTJFcM1}AlUo!z>2latNd2?G^Z&#jZsp}h-nK~R*SHec S4!66Dr>?B6RR7%O?f(KlMKw?W literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/html/_images/chapteroptimization_132_1.png b/doc/LectureNotes/_build/html/_images/chapteroptimization_132_1.png new file mode 100644 index 0000000000000000000000000000000000000000..bca109752117934179cce4328a79c468821f9ea9 GIT binary patch literal 10420 zcmbt)cT`hP*KP;`B8s3OAWe$WYv^62iGtF5mrxA|p%Vxe2wen$P!&NsD4_>P6cB;X zo0LElr3eI&5+DR_e((3)ciq13y7!NhtT|_9&z^nG%slfvJK>Ru!KDk=F8~05OZNV$JWa@S8JU#VJaQ9n(>Ypl9&jxDl4~B-i26_ODU7-Pf{!l+}w;LfIfkEE>5RkNj zG)VG>7Ze&0q$VTtg zHlzDq#7Lv}u9dC=NJm3dU)86Zvsm=)^Wr;GoB=X^Et}HQ9p{Netx|KE0w)NxnKe@+KTXxGt1Ofq-w+I31>Xz`a$?EC~BY<%T#5q$e3v2p~3!H+2 zS9EFa>gqldb-_IaH!a|txGIx3YLgK;TxxtNhhm<)SF7bO2`m7X<@o1WpLw!2rkBH`5 z6VF3BdVsfN)OkJRP;}Tu0A`cO&_bT#X=+`-g?y!1jXmV#AIaGwuAs?eFq*$F8>p{` zoOy}$z{bP7;CEwpW3z$e$JL-Zf5yz#Uyoe03AGUG2E(b~<%^-(02Ssin(f*`b5Ynk zxan>10hG{zotvkqg~ogl(heZ~CZ0ZSpSJ`b#0+i>fSY&^jX{wqND3Cmr;Lgm+!)Jx zQsfTi#`#qtYkZKQ6-Z-Yt)j=^MLCqg;6^++B+zZa7<`}wA~zv5UBS*El-|yU|JNA) zl&u@i`G0vyY2#-IB!zqXOV*J=&ddtV4~47&p|tPeBGZw^J&QZHLFByd_UxNuQFX`; zvBJ(eBFc@!1WfMTHBmwtgF{^NGti5;1)gDh8cBu))|hM=j}tJ)53HO!(*-`* z0v|-~?0NQ%r#_6TlS*;-2Ky_a8h7MQkVp!tTZwxu!a&fmP7yVZ+bG)!k%1ghYC)(N zL^BBnA~z=QF(YU6z#$K#q@$*A%=c`Gtyqjm^ss;TxU(C05rpdfiIKTi9h8BrQ9}9C zs>3}?OW%FQ^8-#3L<1C>Ml-9ZgGs`i!N3O$QrE)s5o0uBi(Thxyr5F;!% z=<+XY0GC5;h~fmfVuxOqQAa`_w(e_D(PfSE?MhCkUM}3*+}KXto{MO>_19e)x?4X< z_u(~I@0}(m_82FgVGLsnLzwi(n3E&gopw3wTq*w{U|Wj7LJ%dGxR`7BpKsx9c_FI2 zFG=vkitU`(!-Ia37yu$YTiL*efB`ri_I!YY#@2f*#}bA2d=%qhRoFt`&eJge_62WU zj<)AldygnjItT6$oCt&1C_@#y0-j6p5F;W&1V=#Bz_yjqGB2BKEN2l*uFEK=xc0>6F|I8`=$h;9rAs+@73LF zz=!F4vI~qSuz{viMiu4gn5)|>3E}>>p>z>$(gkgysW=;_xw|!O&$9Bab zMLCuPNHWW6)$(wr_hTq5$T@IxaXdNwb=WfW5Ep}3(`g|6e6!=Y0Envcm|djVGKo5M zi!wc7{pg?f1V+>H_NL?R&tZnIz5CtWf15$Dy8&VWzHSRF0ovQ^J1hGMixE=WiQV<_ zSLyP&Ft+Pk_t-=`=jw4%*t{z%UnAA?v)2!q7|fwzw;ZW?p*?x^%h1M}3!k@zHTDPI` zCvs^?Y&5uyNpOg-gTr4@QzF>Zt)qt6sUD31oswPLPKUCfw_+AGvA2rd3$m8iudX>V zZGewCn}f~`VmNkIZhEhIEj1FOZb%odC3(_t8wcXaUmTv8C} z?Be%cm@dc9l2V;OJi+xNp5mMk$i_cpQ-W`;N0xsle(P@dRsST0do2~HPuEI*ud64` zuZ&t$MA7~<>R&=6rq8Ofgnh@yK)^DB(D=1RGJ>@1i#0VQ2yPDdG4{fChtJS-7;aYbcNA65r z_pS^rgjC-5_e|u%PnOByjr&ofAe1#NhBxPfq)5)p`p@~bxdey?#MqV?=+cNx0p`rO zftXrv$BLF~PU99h`B#)#CVA&&lb|tdVU|&;&Bv14w?OJ@oqge5b8qN_7-kReX-NnvvUi#EecO>n9i)LC;S1`w_ggYLu%f(@Z6c{R@wrdz7pjK z)Hc=g@bOd)#bk@d2g!}nZ8{N#&#QRO!x%nZKMZlW7+}`#wk05LXTuP6>5$xgjE)5% z>;|ia`UMNUj)!&Zt=r(!;r^vErV#nMPO3yBkf-Nu(Z0A zhdk;sFus-C>QUw~A{s9s*m#YE3hUH!(wz|fd0aoPh@f{{rDsKsGYgBysXZ${Jcwas zAG|kYA$(I%@b-WF`dA7#dW{P5b8}0ma|sGI29h_M{hyM03bOs`tZ3Z*{E{mwD(W)? z1kEJCQ?nq9i1_O(|06y^APiaPF0!&R7Q+RohX2=Ks$?7P3bxLjxeE^Q>~Ggr1SzAc z<1tAHL%ltr_^0fnLgINjGp5)ocnZw$IRb$*`$5x%$K2bC`fbH85OM7z-#4lcw51cS zIWt>;vo)gjMVpY9NMq#8#PVPs`IQ%DOjwTmvSIN|lH-*{LGIt@)e{Mm!z8*Q~tkIHVebb zq9g`41VCtz+~!^I!Br4B9qH%~W?(O1W@SYdME{bl1)4lTh6n{zqqX@D#kOm;N~kCn z{B9fmgSdE(4}v^U3|(Z8X=hidUxgwN-!?4XF)v+)*F7FoK(T|BJiz98%Kk+6dMY5U zn4re93hsz~JS9);{EF|z!=iS6_E7HUBM=Hm=c&}e4F>|0z)mE3lv4Znl6gfIw_!mj zzz*PH23+1$98KJNZ@a08mBQ}g{4$UQ3@82s9fCdx-G!5uQR5X9lvjVbB0CSW?f>=g zT8A?$Yo9f{-Ms{a;U!U*|LXt=cmEPjPWe3YXfISg2sh#5*9<7Vq$Mh7#+{Mz(T#2c z5#KrYQQ-LE$EfiACVQ6ORH(0J+vsy#yztT8K%wK?rj;b=9Zwv>P=s4KL|HR!(@OR~ z%lEVYRlfG73Q0%(zSB*t>f(O^yLc88QRrhV#B^kd5TnDdn^3tJJ zw{jIxGS_{Y@!`8;(|x%M3|3`j?^Dy#$P*J5Gkq+qVuiK`?b3B~;1D!AZCGBf-xYzd z7+duU{ZCVgiIvL#^p{>)Wn&+;mZ4Ai`t93Z1BE0bqgl=$XV_@@QL1xqW~g9%s~IA- zPmhHA92D&mNy5@*#;4F z?j-2MR@aVwva5w7Wqv5`lBq<2KE&X*kRxAjl@Uf8cAk@XYE1Z%)#nK;N?nY(9`=ufCGffP8xvWvSM>cmVCA}j?YwMhlxNMnnXD)#9qyk@Xr4@9%j#naex^Tqd;ZdX}qsozH7(_X@=3sGau)noI1~M=GPT1s^7%|<8Y3a z-Y|<2C%fk!iVT{+Ub&6ge5l@1lOH>ZvZ)si{!3pU&%fA#R;?N_?Sc4Fw*-1ynGTe7 zT^t<~*d*p>f{&7VVM?|7;ed2rYc+Y{LoImwt1-We`rtamGbahzNnY&iP}RA(AJ|hf zl9B?9`*vf!G|c-bFl=_5+Wt?)XKwnEao#9Fo$s$)RrE6zTjGAVzfr9A%+%yu=kl2D zoepS}S>(Q9=RWEbysD6UC(VnU>#@7LshmaC=;$g$abV<81Tw)ETBct9v$t63*&UJ4 z1;$>U@!wi@@zwF7^=vj1B?b+NhMpZ(xkGPUbzZBUe=o+6zP#@2FYWe6%|@q&;i(0d zh3hf(xm9(r3B-xiRtxNYW39x1ux=NOSD0vF&!xKkcD-~=VQWg&#*Dc5AM-&!2Aoq9-(^Xs zJkyIE^sro$65Jml-oDep_7M5>1%BG%@~DYCgK5}D_@2>b39ovwi)nf%JN^-tCH(+w ze>PI<*SXWs+T0-($psqvD5FS+Agc-n?M%gHA4`|~jp&M--Tw@rE{EPCX~*#m*R1am z1CD-=&nYZ99#|XG{G=cH<^*%Q!q40FM9g`q>dqm)OHSURh$$SWdh z$p@nk*&ryX%U%EI-{o`Q!o_rbAZMeNxp>YbfbvHn+wXO|$Njxol*ok#-aaD?v~02^ z_W!izplk$v zJl#B_1MS8%B%CfeG3WVNz~{COmV>}g>jqepnPH_kSg5|m_moY_;cgMB35E}2D?6Z} zwEKxqGvRDA7)_qim_E?Yxa%p3V^uog(`AN6lVA&r<3xFUDn9g z$`{N)>j@k_mkPL+J2O)=&`Q1@${$MF=}F=ssUyuiEw?U@-oHBh3XJ4}c}x{`__S55 zpM)dPhr8PGpAwYFYaZW&6nptDhU*qMIbqjhAKubB)7st%SuZycOmZ+WErpdC#iq;tRfo$q!u!kwA@G41NWC44OU2PquAkIQ3%;tivnp-yv-`$; z`r1pjv$TYxbkH;O_@L5iZz@6mcJ0g5f3Wrz5u-QpiC6_bfPm&Ohb4VFe^$H-@JeSJ zyM`#w!oCG?ZKP6(Gl4tS%}YV(?a)AZnimIrmpL)quTDDHB*@WF=|wsF_$TZU_L|Gp z024mje2A0y>+39*QdQC|3rm_?_ZFk(QUisAM*D5`lq9UP)a`to=BnHa%u_~s)spjK z$#Cvi5=|NHFpU;{b)OLHJL(=NhU?Znm~8JoeiL)jyJjru{$*P34_eN-cXgpH;p@QS z-z;QT+;j3Xx^a%hYMnV_z!3RM{)&);WxQ!lG<~wWKt!f*e|uxNu;5-PT;S#E-o<5X z(juudyYpBc+!PR)6E4TY)kktGytSpz5DuxUR2`;yWsN;w(bWQ4aLt|Gv$=BXb^e<}VkW4!`UfpWLjnG3-CEmw@s|tH5Z(vzAuyt2c%>_vL>f_9m;< zh^^$|zeb4jBSncTQ}71Yy9f0NS(fUd)IH+n{d(&lzpc%K96GDjWtiMUruJ}UwQ{nM zL8*H9WAo#Ev-Am`N6_D%c01dIwZC2DSu358sEYN3L4P^xFz6}>&AOq&B}(iH>SOX zr@#6pF5zWbg<(Px)!?m1v|L>Y+CFF)LeLM4Vc~aYB9yy z?&>rZo;0h9ora!2T(IqJ+(>%LPg^&U1k~rsH8p>hPu9up#uH$iDkPGw0^e5%QCz_lwkuoU+B z)!V8FCrqe(hn_P_(ure|RY=DyPbswl-id9uZ50|MlIzJV^y|y32lrhHbiCjy&y0`G zAx5^IDB&MBt}?l$tM(RG>|2Sk$^Q9}=ayY8qZaOm$%C`li7lw;CwQQMcV@poU?!qN z*dybM-VonNyg#C}+_+||Y^l(=ApR1lk8eOr_)+4Cy?SMM7so0TG&!=vr zaKkqc+sO?t;e-lLFLoza>=rTcYhaho36!Mrn#L*7N}e-UaO zo$!aW{t1g)v^*1#quCYNJCTHC+v?F3LHKagEwaRiYjTRjQ*`V2hQi0fM2(Wv3%Kxq zEx6uTHF>_F%!5i8)@!=0blO!>O|0bs#eVURfX;&l3fhuhj~^eSU!IObePT-mFIQwd z^M}$4xbQGUakN}GqzRz=DC^P6j%AZ=gszP_FgtnIOE09XD2eZiE)`AJlYqq9^l zG$o$)W)V?I!{Gr}=-nyWXZi;3|1L4}g`Zw^M3`t9rczQLo&3+VU+lG9{9-yp0Chsw=TdM@C>G;8NmQGSn z&mo*jqLi(w%k@WcHn(n>S%+u(?yoBb1alHK-`FcL-!0q8(fS-dK3<3EB*?r*RZd?m z4|+RsKB$S=9oldhxY-a06|M2ptg`V|zI!o!hg|TKK58ea=Vql>r3g!(u~RVT{sm6T zYD@N1E9CRD)jRtW=HufRHUc>8?oj~4ghxul`Eutk0l_mr9_fCl7(9C(4Ruj?Xzklfa(3FSg%Rr^(sDlAKpkm8#o{r*iDHJ z3rdJaziU`uxZ3L6^&-homi=C%kMfjh74~O(b0>Rki=badWUu?P@@lPyDDjG9xhma~ zdJAF8%!cAubWAQqu-vjnF}@=LLtYTe<}*Ech94yDk^JYYH*ItxKG~(}c?rrZi@7uy zNnALZC?oVsfRYSqJDOB=9H6EL%Xz?V&ok#BxXQ-IsLs1qrZYF7A#CYmqAn%(B40dq zn;pEm{t1=6b%|vl%fr7?OoxRbFCjrxr~P!lr^Hz^9W~hjF(}auQg(qp{n0`uF7tHP zokbjgJmH>(jngX2RuMtsr^a z2_(`WTGd-0AvkQYzpx}o=W24WM{Im!VORBzZJp~kvf3a0z+B?iss?jLgrv2Bl@O3} zO`b4eRLSjK6K5vr0WRH67X09d&fR*b4zbv0d?Txh#%FFc(Sw6#H)2ahm6bzJX^p z%f3x*Ty(PpG^Wz9Ytk<#pt?=s)8=O^VCia8t2DG1g4?;^Z^@#=G z$h$Y><0q6{=A(jw;9)0Qw`_Yk(Oho4?veb0d!+oXP7TE%S|OqF*7J_t3`L3bdf*zX zni6Jpzj^+s0I)=b$AiC&Rv%vtvClQU%)4+Z-7eTsr)Xl-|;G`wD@+qEz&sz2xo#fV#n2_!W2SxG~>9yD|_9Z znoLugg$uwBa(}9AcTdEx=`|d%d+*($cl@qfa>Zzn%B-eiec^9EV@TR3E^&2-HhZ$~ z^(kGNByY#bgV<02@(m-n=?m@y&d+D}8C}3a_-Me=J#Y5h zn(M}otL)g`v4WFIe`=-MN=Uin%&cMW5~Cy0zvur=%qER<_-wAfD(&ZR-ajvsO3%yI zr-xKc&IV%K!RxWUv5WGkgu>>m>XB-5z0l{muxkcAFu_()DVG+i%uX>3<)m8AmB09m$XI0pet4N+Co?^w7lh^FvpwooQ~^F5A5`=1m*q9*vr&N{JIiA(oqec zP#4^WyOgq0pJX`v2idjS^q|c#{l)A`65?EiCze`Nt1<*mXgTW&KdRBMdJ^#=lusxv zHKmlpQZeF165=AfUB9ZvAN#FqB&JI^p^8K54o;>D(e|}%8tySN88pM+p^v5wJfok zs8)JG&np?1TJ=4|@SiEZ zV9lB?jl&!HTec)3GK-^W?y}bk3YJnMPG#o72QuKMDI8HA#q`X|;$;=WP^=&4x&f4i zlALKwfTtt4RANh(xPzXqk?HKn4JsQL5OZ?M2(o9Aq&clw>c1}gNVjB5+>}aIx?`E( zb7spmvM4c7-fVk#(Bk+lLBaGf+BhUHAc{E*jn-aJTf|SdkXz7cGEVI+XN+vDtZ#o& z*=Q!jvz`)kOed~^$`40+G`*H5WMJ(=&+_WWsM3Qg)uVPc6^2785Lzg@z{)Lxn%t2h zZ+{Pe(Z-g{LFJ<}ov3t(;64@K{%?hf|38NQf097N6sggx_$Nsrq#5aG0k)&M)G-E( zLk`lOUf%X0c)1{vypC4?c-kQ!#3=(LhLDO{$>!KbEb`_D16|$O9Os{%*#OclEq|bi zpW`>26+q%=+QZzL0+`{PpA@huvj71w@{IoTO8=4Cu2nWvOC~KPlS@|8BX>B5&`EDY z>jE|>YB@o_fbXy2ta-<5;}xEbA)D1oL1~+rw!)2!D&jjwhJ?=7V^rOPm)f$E;p8<^ za~yX-L!DqY{}IHo#FBYfHj=`+{Sd1`Fbc&~b@})vKD3q29EzG0CJ)O#CBPMAfXFW zHUUDI9Gi#Nq8I}LPEIFNpkIroX_LeQH6GGKRz2|1A5b1gAh>^KfJO|h3SSGzJ$h{g z?4ovGTbXv;_PCYn^-yAdUOa7Y@7CpW(RO={s0*seuLSN4ozq%Mw~u{}+t|hile0`h z&r;FaS7O@Vl>6Vq3@+zb{0VEap?5HUWGCNBR*sFIlQer7gmPDt2!zD(3`@RIE0pS2 zQ{DKhPRZZyO8O-n<_tc_(>=?Sx&I)#0=?)79tJ=ZP(|ILavmkSWNbN_ z3Z2K{G5`!)3&g2yW||AzjMohBovvG&xyL><=yJ0tPoOdY67qg8XdK6U*SnvEN$W*ri09|s7N^>`NDo4Bmlo!Mo8Y2058B8p=GXd2Cz5S$ zx8D8)Yi)xF$OqP)Jmd8^U$5GhBgntLBr^hpa8qiW1ITb|A%;Pvu^Y`%sE&^G=KaAlylsA2HhQ~4!1~;dq}j#v|dWZF=1CGSJ{8GY0szFEX-Yi>sY<%_T*O3I^*vFKR31cm?Jf!MVduZN8Z zrC3#L+TccN*ldrkGQ-RKqU+anscC9d8IP*L`TV0s{gboyf0WOVFAu}d)g>-s7ICLd z8wv?*rF&E*Q;`HAbnNH^$pE6ue(fRH^ff#5zODP_Y!c=kQDLJ zjNw9ykFRc*!3D$c=bf+fihri3L4W1u6*4k1dM!;=12Qu5 zB+_&JGBs%=p!*$|^dsZ1X6A1Q2KhtmUpSNL+WY%>g8e<+9Bu_VzwmPddjo~Vg@F%l zx%&J2_{oZhc>Vhe!r&J!BB%mYG)V}pkEXdF8QE2qi-(--Z5{_1nNWw8s-O zic9;KY7~bfgOphI%@Aod4pz2Hs>`pTWND7lD@UiqKRlkXitfb~%}p*?bZ;Rq%70?F z?Cm09?Zn0zmjZ)nN;*HMxdi}xRHju?Ri${|d5tOUafYa>D&IAJIwmGs)qfj)%`kw% zi6PgX_cGlDa)LpeA5v6g1^DUi-ve5DfCz)0HE=I6r0rYt?b0RYw9O1rzAL89Q1JYN z`K^xp;n-0bxOsM|^J-9+bC77?)OiGd!#lWx{`WKo67~Miq!5F`z?E z;KsN+!d48q72hCmw{=dzH+(#I$^=M&!w)>!ROg*jGL_h zWhxnhikc#VocOE!7Exf{VBTroeZHo{lzB#ok|@!&K&RC$PuIY9SF00O0P2jBeF4(i2KC!fV2 z3ES62MKQOZ2hE}m$!aKPB5UeG=W(fxgu4)MAYLQNxT86J+ieYRbc+TrlzXDHNji-eeu8HG>22$sJtt=8y<1hLIxTmQ7fe z9_3B|1nh%vCxb?b-N*uO&EVQ*FxlkVQ39AV2}s17phfrA?X0Cds?!@stE!7F+(&uM z+x~ckj&sUteT$kKNA3=ov-pNM3gh_6)rPw{Z^SRmW*dTcjNI)oOD|7BZQcRZ@jX}j zoOo2fv0VP~;X|bcXxL&ew!^oB6W1o)zfe5Jygs?9dBlE_;KY zE?#GGW>+LWVx|{W9*LktPzYjLMRvh6Ss<1^Ny;-+rRfOtPI@?2wdH1PcUw|W0J`Up zSJ{pLV_$w4yWG%f)Z0iqsVCo+R%N7f^PNx#?m6 zo+j$}Hn+xI?MTKP^H=cXyV#zzimauUYYkU|9{5h|`^^(Tl9xMBvG6J9HAx4MDSYaW zDg}mKoZkkZ@x1f3W+Rk)M|4;AI6LZ`y5P1AzaO<|4Sg;_bXR>hzk5cFM{gSabY6X4 zqq{xcR<{MZ{r(!mo!o88I2iA!N=Fh`eLYoB^pW*5R*pP1s>JDn{{0Dw6L_dkY`iwN`7{ckNfCH2vdv^#|iDyl_A4{Tb3 znwuF>ZB8KmOi}d|E-f!FuV3~sSOzQ5GCQnn(}}vJatG4dxPB|x zHxN7*(PrLT1d<1as8_-?X<8@~nI(&{vR&rKzcDQX6;>XUE7MQTeu%v3oy7LlVMHNelhEKh|?7+m77I}q8#t(_0 z<@og%3UEvE!*9JxQBzfYDWqCItr6)GDF&+hhVmZ7E2^pTg$B2G`QSM}hblgr6C)`A zCq82NzYEs?ix~d@HO#k7+lAs0zlf^hYpvTkQ&)h{VHD906t>452ZJpaUxRS8UlIl% zU=2Iga74*@w)vkF-K4{j`2p?p!B2JkG}%^I!zIVtvXgcF+Z2vzQAO%g2}~SFvJd4x zSXozHT^(s357Ydt$r204P>E9jM;WQwX5`Kwt)#tLdKHg5=*f+cbd!op6^C_Wjy#e-)X zd~GZ(IRi-3AE>7!3B-?=m)mVkKhYQse;6+!bHm7}<5!ue@1o^)X6APmM-R}@Y+m3V zsBRL|`}<}w$+L?5t8C}$@QKDla&b&|3~CU#v)A|SVVY|R4P;(O|1mvfmbr}kyK<>c zY;3#utB*;!{HbX-m20k(JGd|F$bxxLS4tUO@XY*1O>B9&Y}2%0DrxscLCzkR3#7$t z>`aW+3?l2airq_e;%fpvOx02zZpXQeE^djxk~e{fz$d0$5Lpv#kLNjE$+V63;enXM9^HIkc}bbe;97 z#v1w9ht}TFp9Rk~gv&{%z+4O?9PxfE+>dl0#vWz?+$T*tucb9O2)#=zeMhGTov}

    j7XRk*9Z2>>H=kOw4ejdh zI6A;aDv7<%dP|u6n6154dL4Qq?a06p0|*yoUOOiFjZ;hF9tTJ2H z8Jz||2wMn1VdW~RBURnlQ4mcnusEc<0jdbBxHHQR@*msaKNt+>anFJsLnftm6=%60`(0 z0uYYEIxGqOa8Gk;pnfG*B8zh9GeCg%PjGIU$l};vWk!!uKsT9V8y0+KhL;BN?9p)Y z?Ee~>>$U6(sH)eGka8)4gsrWQFoGI^x*@L<$G671p4zb$UY~{ znx_G=vUtL#x^`bvu0k-{!`-Kw#Wn}v$DVcYj$KR;NsH3a$!_jVmay!e(3N*D5^p2B zy99Rb1Nh&b^Ckp1qBu`WB|*+1#RbOkWi_9^F5+l*Yj1E7dA~irhU3{2$wYC!{>Y?N z?jDk=*L`1HAQ-M%aun8`99+rYUN2EVkE^>-D>m{6Q0We1c0?EzYw2(H=DyGLL3+Yc zpE)_k+F?Z%Pi;V1Mte?7(1y6w)Aa2uL9z1mwiu*1OdY?sLy(#D1j8Z#cjE11`;wtd zBL4YIoOfZYMFth%!jLBbx{1nKS*i|RF`6Z!=I-Ft{g27KQu>=pSkaZHf||kMz~xA! zBL12h#VfNq5f$;SB{mS3|NV|NP`uE~8Z+ls)3arKkc9R;ouxFtGM7}RIzK%>$KvQ& zKO1KWIP-LRZ8tveAEH6ed-!T+VDK~>9o{=%ZJ$sA?MV(cEbmdMS$jj*cY_E^Rgbh<(-Bcsq-E2unLE6!VHW3)rYu@;FTPA<=Vp6V3A;deGQp>Gtp z8rst&?ibVQYw{|7B%ChOj#3E~^!n!hFU5nYWOMBN=OQ7>JE zM|Uq?=lmVmBh+zyRCp+$`bY|2vM6*&-%D*>9mue!AmO$brFPU;NlJex9&-S^FOI5^0iUdE!_ZcruynS*5G022j~1a1FaeEU{Fg!hrzH)@_}>$J2D>o5WS;hgic zbACl*G4qBMe0=HQO6NsKOCHI-lzoq=QY;8G5&lkc6Buv3F&u<}CiIk@p~(&YoQ%FB zuls1Fb!&MB~>lRYz1B0q#qIep9ia{9v}6h@aE_Hj85_X7mmJouM3={Gn&+%xc5?JQr=5q|boVqC?123nB{l%1 za&RWa#Mr&O+*!nlorM_FMlted_!PPBK!PrN#W+nB5mgupyRW#QtlQJ6FS5M_{(2{w z+w4i`OD>gN!%#rjBJ?YP$XCCM9HZlOeiQ_&oyOl0^SzG!vZ)uyft?*fVZVGa$s^MJ z9DA_HaP1GQ88IP<{2;lp<Wf%za-nLZ zOOP^TUKH0exs2y}e*}irjDAKC<%OtDObihjs;mk2><;3Zm^e-mNuNW}9PC7Vr+Zsd z^aqlx09X;IWBj$7bq)t=C7sJ*7tUlHk|Hc-m72Y=#AIV)B(kx9n!aMX@ga9kf^&ir zTP)bnQ&ORVIQCBna*mv=mkOeE%>P>CT%41`+cXV!%=f4;#XxjFtA%TbZ3&Z-G%0FD zRB8>LLBh~FYsmz`T$N#l2jTBrtGpdsV|%Qtfs%dL8SrDR@d=oS-fs?zNSfmtG!*be z4QkZ8-a9w5<^yB2VAnw|jsIpVOrrF`!uc5SfCyo=fefp0e5HI|mEOb6k@;c4C11V5 zaSBQgenv}Zi>=cV_*_Mu%RW*{zFZ`BYI}G4dN1aUQuz#vld|J$+Z^iO0+q8D?mig_ zl$544Q^eAmpA>+(d$rS5&QzV2PsFdJ)gmbsrWD`C(O|*~wQ8k(Qf!s5g{8wks-9Ii z__-m7LNoKVvA*#nxYX8P2UkR{49nUY-#3~Ai+n%0Gbwl`_lxw}Z%$<8OY=mXr_PUp ze-yyhoU>T4W2S=xT)p#c=N7!wSV%8B*=EC$^UJSPHAi9~w#-l@mcyPy z8{%d^Wi5Fg-ye=Lz-Wb?zeQxnBMr2kGKJl{+eUP(I``}?>A3N3e%`km0sLkQMxCDf zcn$@O5}A{mdfiGj@*FwO_!VaZse4qcz;|n|unYpRU@xGiA0Ukc!@1q%o zJL}oD1JxN49N&;+k1O=v>}RA@xT^df$lY2cn!vJ$90myt3_ncVjcONG(YAF`s-2EP zr69(0$;_nZipag)pT=KY*nDcTrD0=V9N$(r4ZxbEkSbUw7@A7hFZo47HDXEEH;Jr{bku9aN*D zpubCJoV)l^s|_5&fRb0~uHX?)D~U`|)jNWnNXLZlyNvwuvn5;uM^f^SJmQk-eCP@E zXO*MZ?;L`$fP?`B{9HG?!(~7m3<9g0LQJ&uv~?->yKR%Gb*BN~Y)}zm`NxOmjYJXN zlXEs5xx!^X_`p+ath}$^xPx5V$~0-FBBf#?f75bQdz;Xu)N+eqNNEX9yMA2k-gMrG0vdi-pW*@NsximJt^u{_EJ(X$Oic&1raYPlcOBVnpOrxb` z+A2rSMABW}u8MJ8)qnuAi9-T6nb7PzPm8E#MG;v`;?bRIcvE=0uvcEOa25dga?+)T zaR>2(l3p@Zda{N?6!r9qp`&FfPKi{-k9FYyO*{P*b4?Auw9PS#6ss_)((^s>0IgPy zCa#doU7-a5K}78Fj#WOc4N1PK;mF&n)}a$M~Td2 zW_sR433cEc?!{dxAMUNGU*t`I-_$L{(Xd}BH(G0IJi&4-1aqBqf82u?0FIFCB8a@6 zE`x^2Oluk8cDhkaeelEKp=l}Q_dw#_9qK-7DgX^y*^g z63h6sHk1uZ&YuFtDus)^`_DO9j{PbrH^QFrxoM^_Ln&y$sMI$?IaKUdbw!L^TBMw+ z)=zkrKgwG#Ymz=vgaBN-voMdrp^~G)pwaXQBJ;ZM(O(PJ5K+>w$7Xnq{M=%gq`}iP zb5oS!MF&%TZ<0bjD>Ra;K2zY&+dR!e&kji$O1Da785h~_-qz)NpQCFcsRo$ATJ~4i z!nRDh!a+Z^J(l$YGhFJbu#cv)1IYVyv@PD|T9{ceN(e!BtU zJ&Xm$rF~mIkH+d!ed7a`ap4d)ThEmDK_>KZNl|)#P5}FiypG@qS5^=pH!*%D>Jr77 zn1Vw-R5r0DP5(-Pi2!Fy;DDD}K<@K0?WlUn!Sel?8ND_vo3o ze1TMY&sEfrerO&-@{nmN(ytMHH6+zWPUuvibnN6Xk zU-b23d-f1EWn&b0NJFvk9i&)~q(E&6hLTRVKGY(Z<0g`7gyB8HYoKEdDWQx*b+ z_c$bsy1412?!S6c$}}Gg%<^CC$cC6PNcz;S z*iK6UpF80GvCc@-Xh?!84W09|qH=JpI0#zW#nu1;(AQbm5=O2=H)^NHuL@3aRYJQf zIn?mM+@=OWt$>RJU+IYVRB1A_7=7Gqnn-ReCQ}(9Fe;=slg*(5W=)_3rOs9I;y)?e z@iFI_S$dt4My=Jh_OsRsPND2^kAs`A#z}gffamFgAPU+F9 zMsbz#JHiLu>>W&(83gDk|6@en7`e{?lzKHucUpGdDf1kxitJu@ilz|Az^@{ZeN}?c z-5=KD^3vyIw%4(X;@izxpw$meEP-;Z{)*+m60qCN{48Pt4+fwl0;B0S@g)s~AUP$yIy5q5i#2>krr#YD=iPHE?yoA(6=OQ%~HFN?VLxJ7wU? zg$v!txWqfMZY-={Ve{|eW6}|c>1;{=ZB3)y?-;AJvWZ*a^;`xYltc60XQkq?;7QA8 zwTUhL>96!qQ1b3)11;Bq`zoDhiaH<12#xE^oZ0YJ3tu6e2i!`teEBo#e?Ed-$`ta= z(-oV`KQVL+=fpD9{^duy9q#V!DV3k&5E=z=lMvW2oPTXWzPJC^GuzK(H_3#n1B1X2ij%S5kE z1o-qU3VvsA#QY5e4CR6KEd`CT6QIUI<_K;POq;L)gBM12O@p+tuh&!u$M{8#I_R6= z{gIT1EMNFxb5JBZZdm-aX@yNWaW1%Yf8en4$pE&AQ$4nZ0xF=wf|mk5NdZjhe>X7h zBRtOq7G5P)H!1XL0y{+OlN_V^cLUcK3e@Uuqv)o%BSDp@s~;c#fP5!KUgc(Ftw+;K z`%gmO4j2v#S8z7ot3dYtw`}7{mBG&oV(v^=yBZhPnL9g10e765yg+&HEeTF1cbnOj+gCA1TOa}@HD$-7)N z#!}&BC*XJM_&s#T3)d3IVjCxtg>;}y4mg(C&gi6X7*abjf3diPJ zp)m+fRChW<>BNdd>rQeyU8vmp2>bTUD=y1AaRLOu*QaLTAk>4XG-Z{IJy$Vyvi!d@ zHHZxeyjuT$V3JpiIGdER!1~3MyQ?vrIjPlm{_69@oZ;tfJp1);KG;WW=*vEy~gH z0B!a5Gd=tA;cZpYqtZwKTXrX3xIjM(Cns}|Ma%i)9;8Xg{`aIES3Nz<+m^)D3?SGW zbfWR(dW-0hqDnmiw>mDV(bV3`;>)Qj={5ix;( z79XC^r+PVJJ+{!oLSKjlbrE@Qrt^ro_45^Ak}&7G>@U?fbckTkeCIH&Up?F;q?R}` zoJqHIZfd}(md=B({S_P%$3wKb?JHI?8;2`BOz^cE=`LpTN#cD96~iQfXXS{w^jqB5 zD9m_mJwYBd4EFBt{Uwz-JxUB-jeUW|m7MPVKZWxvWbXIgs0(8#>d`I~PNq+umi-O; z3n*@m#5SjNGIR0d{$7^dk9HY58-H$Yxr{h9>QyPqu6(Sm!{E%%_c_tu?0cPGjb(CmO&!)Q5zo_=Y(Ph+UaZD$H7n$wnTD1w zp#Y4NWP}U-&idH6fQ<84t-!Y|rf_y_{uu}DWs$fU{AgalT#W;iKpEaBJT`)%J^Iw% z9?y64?-I_p-j4i=WIVum)fDVeZ1CZVyZQZ|FebN85rIAS_O(E+xOpoj{}|V_g3!1K zp!O9qdbfXe>$VqDuKe@@aI7Bgx8duTvhC2#bFe4gsVa$`15??ZRv5{>A)<&62Te$$)>_>2Oigu}ew04dSb;{b~PC zr_C9qrxCK`2PeRmw!@$q)bKWw`FylbIJOo}Nky^rnN3v1q{0}bb5f(~jUJ!56by`l zdg+u!J}Tyc+ltwNvHZ;AN2NPa#i);Et>dv)Z~M8?n&4}8c`ns7`|pWDWkcXt(QrLd z^PnDKTYm5tOhs)tD-e~(%FOa9Bwu=1# zAvWc9@kdt@AXfdh(I`e*bC=HgGLdN!GOC5%56^%pw2 zFc0+uVLc4nux5#&*E)~AliHm-2tX$Aj~|R|`aFsHh3DEm#jO)48d>A(sfID)i`_A- z)ZwpcO_%feRa}+Id-|lyI6j~_t~V1)IV+5or&?-2Yjjz0lDg>{8xdx0%vcB8J!cp; z-in1pLEHYFWtGXJsYwcLtL18v4iuO)MB`KYwJ`#hBc*}`b==K4e||$n@_`dGlzi;B z`7yt_Nx7^9q0!az2K)*~$d)LAv=XLZx-9ikR&hxd-Nl9Ej+KV_z4d;feGe8nnoSJW5qIx z&D*d}j5ni%awHk>yt1RP4-Z}evU4II2v%rFFMp{s9gCSVZ3U~(qtEx0+G?N9`TG)< zorr|-HTyo-?iQZA6*4;@zhMH#!{Rc)uPUU=336;Gk<8l!e9%Re8_Oa1kEaG&vG7?g z*LR2kQ&O|%fK>C!mMtHzkj7{$`rw-IHsJ6FoMv{r6g29VW!!i>E$0gaT!s}G1STbp zPokD=I|Wn#Ga8Nk_8iNwNwSk?ijW3_qEiaw>04*P(+X#K6E(Zg>g}I+xx@X#Q?XSc zAEei0m0za|xt>^LD!TX#FmZ|fM!MTRnF%kRZG4e0=lAEM@WfKPjqLfZQHx|+=@T9R zqeG4Dp04gBt6NCqwFYrGaJwM>#3RQfv;bG1Bk>y?)d{6Z0X;xvsB!$B86<~)J|Iz% zo1nx)cMd!8Gi?=cj#Gkp?lz{G=;@$*oV1N@UDlA7@OyE1zt>g%vpS-xq(BCinqL8QGZis1Vx`l}=!HS&hHba=^U8-?J~jls@sfT9C@{!89ec z$4HED_S7VH$)MDohV#NR=n0B}M+8jNX?qltZ7HrvF!2Ych|N-0Ow@AqU4;C)e|pYW zXmYvuTl>^5U(0U&Ne_udC;kjdJch;cMZ6s`h5y6SS%yW~eQp01X$fg5MFHvVMwA*# zMyVkbkQjRCR-~k1fB`9`JBKc5q`N`78>B&>?f-qhaqt0{i)*jF;yix~h!~8TT&5rA z(5dtPT1Xy_xUYU;lJyBF0uRJ1{?;Dr@m1;SHZ5R0U8*X63cOJLaE%)CNtQ`7mY4YL z*XF6t-KUV#yWMUuYyx_Fk{i41gN}P({;c?4LnhrjynhzSigUF+5e(JT?eJ4%*5l8> z&IG|Vd3Un2@#&xJzA|Y_4M%zTa{B8AxE`6tz^ux+;42Dc&=7u=rR|xKy4;oh^kn`e z52CWld@0?kX&1%w)r=WE3J;00R#0L*I$Ce4*@nt)DW5=M<4_rPgZmLq%^&w4WiJ6` zMb&}A(sKpG>YuJQRyGd{H;9pV@y?lRfY7*}XAe-Fmoi!JN1v*w0edKzQulDMw9n!j zR#%S`=-DcUk0Gst(Q|ui=Uu=U2NG+hz!#97eAl0xJnp6z2JdtR{xGdS`GHo1y*<78 zSU|?t$5C>iG4r^-rzh1|eM?1d5kABEGzPlDwv17jTLu~dxG&|GdahR3vkLQ7*uZnh zG5?+?o~kY9h}5;-xv_YkgxZTjU*BOu>J8&r7Wm=|(2ktww%1lFaQmSyjYy82#k<~G z=(l1Q?G|N%2YF@zsU(39Q3_ji8&*rw7TT8LF^U`x&X9Ky)N1r@_nX`~qeDt5Hbag7 z6bt9+v*WOVkM1?p;m%S)Z+rG~_M{&cCeV}^ul+w)Uk?I0sMb~bxc{;h=U+hn!?d~3 zga?Ojq}9mSrR;UtcjmS#zQa7BY46zf(?BC->pTyEsc3J?C?TRH*?tiS$k0McKY_8@J#+V1HK<}^p* zA92W_+&s>r%9q#0pJX999)aam>_%o*2ZzC;R}H}r{!=zi@l11Q?UEXEqKA21{-hSmmd_JuR&Equ8{ zbkXX+)P^n3?_B{$wUE&q-H8)bf)f6wk7ohJ@xTMnmVDaGa=FBsO?9PvUq3Uv9UfA3 zH1)AIgwG|lVf^-JBYMh?NGv65un9+nPP96tYLK}bHvgW`g?>i#Zr_~C1{F^ML{IJT zE?zdit}+Q#O}W=`LBx?cYqQZ>*oQC8FxhuM3qn_vTfsZ$u8q_#DKP{yrWc}KGAtPz zy+$n2XRTS6M~f9kqLr>yc3M%tf}5ZHW{Ry`yIu}&S60`w0wU4(+DKHSC#dONeoOX1 zIX*N!L61ZoWvvCiu?6ZO#_U86mdFQc->AmG7@T0VAb6T34|^d&1OlEXq6K7SnefPJRMv1@ z{EKnZ*^BJ2cp|sygaHt~V)i&^m#x?wy)``WPJdPJfJtB^^Chl7x}VJ_$VhBWSY6lGP|4=n<$gwX(@mE>(bopQTrP@8+;7J?fG)EW%=#-#XTE&^ zW{Y>8u7O~T^F=slLjArU!#Asy7B$t!Ao9-8Pw9JG1UU}FYLp&2Npj%Ef3Sx} zYn32&*}hdeNas$%*fYzudDS_3uNC0;(@T5sb;e!&p^+-7l=Xvg3oa;^YVJ?IYXWS& zb<>GF1|fT>e9wyc?M(MxsjUr^%sFb$V3PDfy!oH&+MI^Z3{ye;9Qj28u9FmTIZP*X z6C;msrM_S&YibbSK+7ZskFppdCDo@KdlcazEDN=NMV)>$WV47R)-ME>Q_IPgQdi94 zUoBY%K})vb#VTc!vv#^$O?P;pn?94YVX6HZZW(0vXz&eE;c|88%@db`o9;k)hEfD{ zmsGC*erYid8L<5T%fqvG19#Yg(Wm=!Q-e4LGszCCqQ;4FziFj`=t1djzH`H&>$vEB zCe`WW;Fp0Ha`{|(#P;GrcJ`OL=Rj+u=6mgPtcmf1j>n zEw#uK{VncooWtr)MH&G)#6qlpO^nyw%EQ91G-DFiTXDbUDkTN9`YAjya1= zzcF#fQc_h<&vLINwJcuMOuqal7V%|F2K-DJvEv**2j-y;|h0>W6tvh7EgAY9Gp(wOlLT$5Y zrfie6Q~eVGRR}8ip7Q$deJA7L$#Iy(;H3#l#|bZRqI$hiOeA5Bd?t+d>VY$ zQmk^|+oH?a>;IDvG z$$0`=PRX+;`|(A}`IJxOrMwk(ZwGwEJ9DZ42fyPDQmr)P}Jw~Cjw8~LYSoJn){e}>q_=WGbhiO&_H<(XSg zQ>t{}^EVsWU5{R9*3oxymg?@-)?YBN@lBFmhay&X7RF%s=awj^Q_CN}Z)4_v8&{PEN{K*KFZ$EV~(^m51DRs`DgYu3i#cnL@zIqj7l3(GS_~|w>WB7Ju ztS`$$85-Arf^WhGTYK!dZ4BKQEQQ-DjDN<-h&I-RMptYmsSJABhTYMSE3}EoeMhavaz8p zH#q3}cH+;Z1Dp?`!P~;H&apl>>wjLnn#zh3}JS>*D$- zOyESc+;ugjLeaWq|4n_3bvUu>i3E5W>v@fY^eJ3v6A@S7LEdEfcyY(b&DlWYmCZHq zQ*-Ut!jscNo|L4qOmO9ZQPR|AE!)iKr?)#EGdnQAxZzVw5t_fFAmd_W`TX2^0Ff{(&FW8KsQSXOb z)$4H(mW8lfGiA4wR;fV^cv{||;ATpYscC)NU>idIU$c)Vh+g6iygpVLDgn2&eREa& zFQ#sqcHRjv52E^}$6T5^7Y0H93cC!<)dBus-~@dx(H^di8;qwq8rs`Z+FaHpU~Nm3 zL#-IwM*Un@*D9dHFJtQW_BeU3CM*V}{+qp!MPx4hL$+35(KWuFMjJNLGi9OtlR8ag zGt`EN?4je}Umgwj4)xDqLd;3Rq|er3Q1~=lHYeUiZ$V#XccyjKaMB=(+xB%upoXRTL4MkUH&_IpQ`xm5}^2IFU+Gx1<5H6#v#1DeoL0xeqxhD`%!YNf$*6G@GS9_rrta}Ive zT!N3ezucsKpTj+hcbH$AjtJ3bh$giagosjf8Av=%Mt+7HzfSuwk)W!g)<^uaAVn7M z`PbNr)D0|{^|^)EP-!Iz;kSxj(G)Fr{4B)1+bmx@#N3_1$J*8?tDILQT;TdoT>Hdf z{L~ml+txC|nEE~T>04BSJweJZ+@sc!I30VUVH(gw;AIn2!mmUKffi@CJLG7zPP)`S z0#~XBxRy(Q(e>|-b$vC@rWh`yxA(2Ki?nk#1;YWF=585pFC6C7PqDJ!{YulE8j2SX zT})$w7=eQjU}__eU*DxdxqB7^rw?1K!BBE8ORLrrCF1GRK2E45WWaX(C8BMP%I-p7 zfGdqukg%m=-aJc4@WEG&7ChSapTH%M}e(6pBFUc z7h)U3E>ZIMA(+qg)@dfv#}ufU#Pl>{Cb9bvO9BuBkK;aCLy-Q7712i^+w{oKSHJYu z?_Fg(`FLyet8lxil=*JYOaybsdu!)?mLUSZUoQ7D?)HWIcUBT6$arVkrvvMh{{hPk zQDfBjl#T?6&Up?nWoPeCT$8BNRBFL0tBc&8u^7VYLgY-b%2~EMrO|Do=Ak$+iPQ+| zZUOD2r$cF0F$olC1N5vT4NrD;KZGhPqMYtImhsZ@e7E)j)#>nR-4W=3?=P zxf3WY#MJUKRE`$kHqku4uL29RIYmDW&l+SCiSbJJa_gT`zJyVSwu#{_SR33j(Gu>Y zs+e)Li6-;=0iky$C*hE39rbs=cKC~Byc{$6B62x=(5N673*G!@C|}-#`iB+T3gh76 ztcDN!n}4@bd#DDjt+x_50!GMonCMv8me5ONBQOj4_kvTn2F?PO!FlzFJ(xv;3VU+) zDQ(lV+8_MOJD!x4s$|Ayud`@i;CZlXYe#1RybG`JtX}RC&%9j1Mzq2FyC&KU^Y8<&M^``I4gQ zVq#CS+(syzDrljBAypeLeNF+9g?ag4LneKQYD^P#bEDn&dDF>m0K&j7_XDBYJHEtt z=Vu^;d5?rU8Y1e`cH%~vU$aczO>Pp=F<&x$`gk_)FSZ(G^51Eeu_oh3%oNPicOJg` z)im=%GEM!gT-3~BU5^x$2Z2nrhWr#zF8&Pe&fOkVnVz#m8lC@!#fmy4jV}DmTqJnt z@(@_)(pk2JQghQEB2QKLfEAJY}xy~&@N3Z)OKJnw8>JB6wV zRHu#$ZwbNVBVcYy{VMSA65~hOjzAYyjNY=P;hfKUHwoG&OJMSX+GM7)-IkiF}sNw0T3Al)f^N{L-_02)Nk(S$DTK9{$q_ zFPM*==T#jH;cFfJV}pJq0HC9_D4#pfQY;sMfcD(Cy4sG5QhG)bQ1!pm)VdwKQ3UF( zf4<-!C-ZFDbAbM^I;GcNlvi6e{-KV7l)d%eZAT?CE9q9BGpYB|ET#Di^mDfM7Ye&j zyJ9jY-+aIFBT!$1ccU8~SwO2ftGn6CX1L0E!u+B*thh=ZvekW%E)M??*b6jS2v{_E zP=<;0i@dnLgHT8Vjy@hrzeIT!m%R8VknNZsO7#zKK6Ja?ZBKusoX+I|-|5#IvBk8@ zeeI@^O5j)gH&JZ0^Ma|psAFYXDxziP+gb8cjbcGPJ8a3S`S)Il{7U%TMWTvH0C|Rc zdGeKe_3f!nvs-FHDe)Jn5TT=}#hKOARJ@^5H>J?fzXw&e|EM0&`qrjYAW?ZR#@U>cxr(_x zn5>zs4}5s~;~T+$se(eFcKKW4@5SQyfW^01qriE;7?ke^{=wPogk&PaK(Xy^*EG-> z|NP_M2tyz+s3BSLzz-XPr)^L`@VSeHwmTjJ1cxk-w(Kh-EB@m0cn8yy{4sJpIClRD zNTPsk#Y)<<(@`KRZyp1<&w+yiM^ON9KblrM&V$jU*0#2C?;qCMoH@Y0$7K@Y%j&j@ z^6<&7h0V%Tu37#)Cpqr@oL^^C&yR}-6w-BP!tW$%IyM-d@^IJ@kSb0UayD-!Qe5Dx zQnGTA*X5fLTBQDEd z6DL`0^85*u2(!AgF;43q=EVaO{&)~bWDYeDUjp$J1lQc7?Lf3WDJj9w>KdVx%?0w5 zACFz(L63p;h~tLLj*gjih%gs)Fm*(5Quc*#arHrlR?Tp5Srv$JUH zc-WniUsKK-O+Gxk2zTv|fm-7m|5O=pK$#XL*S?i|7>q0ksGRg7j?b)li(QFuZ1dpy zY!=R(cbGsy`E(c7TzBW2x|d-vHmg>Wwi7V8)}|ZU>%kk?>q875o)vGpHCSbcLvS7g&~k86p&JwX?O-rWbcxLE6fI_7PgS#vC$ zvBqDN63zP~l@53J91ev6RDeGQVED#$N? zXrKO45(3HVKwMdpvKvlmH-Gn*2YbGyyR~EDQ{n7GUD}6T6%wj!RXO^nOB!x+DA1Qf zDq;RTN|j3T>n_UMl9%@HFgx&Cjq?>)s#%m+QY~#|$mg9k!LlKO0@lE22%U?Q)6(&T zlN9hCHYsDPR$-!us*+9z6?lx}(rh#_)&u;y&XXqf5>Kn6De`?IW(A7Fue? z@ti^!HF;Bw=kS8fH|;DJzsQEeCAm2}!=Z|Wl8GC3A}oe_y<%i~*a8W6aswe#pOrVv z@k;iGcH|l4a4n`AC-IaXY*skKtAze8igjMF3eTiT+D9hbAS&Pjzua#YhOewLn|bDqDL!!;eDm> zOdD9>K|NqNHy9f#v~Gtl3mRc>Eg#ys=BAi>a*@_?Oe`3CKb7-N1jCXIj=mLJW0J>QAwFxbTd`^J8LEL zIe=dAecTG$_1-o}h)1EvVufU+elz>}L}46$AbpFL={b&Hn|Z@!uD6`>T`t!YJ&$YH z(?;(SX81DWBdt^neZoVA2oNB#a+$)xgeg4)W_0-S+)pC6vQsZ;eD z;j(s}c!xmNFL>NbMSUgZz@i05#v90_X}$_cep!4(@SrsQsYk=VCX}_~cSq zq`vhSGn=_fe3{FZOLGY!I&e?LXr}Hx>OXU{g)-8IL8SV+;k-&0oPK#iB99#+IL{bD z{~LU_CcP2XHViT2kL;?;D3=qLP;- zPlJdTnhvuBrO+Ezxia;9Ywwf%0(}|Rc9z2zFArRNkH1m?Oi!sjAX_oHLmUuwog2K& zMBcEc;5J0Y4-#57ku7_L%GQ0FK_cUWhJb3T`Sh2x;kHERH|b+HXK_lFH{T%QT5?5W z1U&dJwe{jQ`&}N~*W8oj4)ptdZ)$UJTUH0KimtJ#X3)Q_wpq zgCFSm!4JsHa+uxmGeK&r(~rW=yV=rnw}d1|+lE8EyY%GWgw6`;O${{1TASd-b>P0# zuDeFZk#cbw6}!8VUTXBR*I0ov)if8poUh>l{2d zF07hJRkUd$&6!t=Qiut)CP`I7Vm{~O4p)6oXkimFl28rt?qMx{WFZC-r>%d@c1`%? z9UDqA*U+^1L6YWoT`Noib8aPj=YRHD5BOGxG-$55uW#_>HV~p{?wQB~)-y!nWYbPf zc{yAKn781VkB7eP9L-LCnG(hU7DHl<9dktekH%Q zx`^J7B>go*O*U1Lg$*z>W+*X>ufwN1=CKc8k;nf5z*`|fI?pC^tX#uv`A9$Q=Y{F+ z)A^xCtG}Da=A+jJnMA_Jn|M?SRp>wM*26VvWmvwN^6jY!RAU46o@GZx4pclR=zaK;OE>QO-z*P*P*gmFNvNt&!i<|Z54G9 zpDNFtrp^gy1`HFx%rjz4jH-QSV0%1n^qQ(xtDI2dg*;!;I%uYx5c+~) z!s=6!dC3Xohp}3AsHd-yzU`ZDS=L4&u|IWgM@m!IcQwSQ{lP3kKlJM5J4rQ`6R`!` zqjiCWI_>L8-qncxW!v8`-lyrgt$>|E%}L^c6y?i4=p%e`cz{ZQXS;@0onq__0F}u%kjkUPeLnLADGU5xyK*R9^j% zc3!qGFFUD3>Rq~|U`FkM3^?a#6SMS>M$H+ubdfFsdr0?+At?{J%kfB8mL=gGxo*l%U`I>1_ zlUl`P$BLRVAS?Lp^mDlvoJ+)$T9}Y{zDjetpxM|HFq`ct+F-wgBh)(}20w;_CTNlRE$Co}DRf zz9RD)s8!|mRnFpD>LuInr;nnp@>jGAMwLz1IvS26_CYcgK4xeU=iTdw40I z*v$9eT3rXWG3Nt7~I zfQyL<9~V1~wx+f^<%A_`VBuI$+WW+~t-FA*LiHB56ABPpfh{7qK8IO*c9?)7LHi~k zt>}sN)PIl7>K(cT&>xWNqec+sw7H-Z|(807naS&+sNE$2{A zbqYGq%0|b(mcyG6y)Y0;titT}J~HL8vjLsUE7uJ1S%Uk`?m3DQj(`3ejDeVjGZzXC zvgmbQWn-%p-%QoXaFA9;-H&39e(-b<J-}{z%=agkCM=KCx*^#mXQ!y6&SvnV&g?pPq|v>=xS{~>IbfBasy56>8%4{B#$s#- zL;#i(Q?p|>IfeKXYS_s{*=*gshhz1_+xzb-$UOlc#2D~+#v*)RF$H~$>Sx>>sWYFW z2k#X1S)A9|be{3b!s>zMhMaJ9XU1b&b!}yM`zJY#w}x01>+;SZ%$oh_$Ycg!5s;b7 z2Tn#VG|m&`RX#moR^ZiPDGE2vqyRa4UD^BxFpUO8%PBi?vOVo0Q8FRA*lwCK^~$2T zqpw+5h5J9LpDIl$0@vSrWVuXF4`d)ao)Tw_z|dkGw{N6&Z3PDKaj+^8Ga$jp5X`ZQ zrWpnO{MdLlU0a-2&E12%h^`qq5Wm}kz<(^ZwQWWdM}cSDo7WWf zHc^15f(aQ7^Nv>k15|=U94AuZF|-e@<)yXEu2vKhh>0xr)S#g9{RkX1J&<-V#_HR) z+k-%>@*P>u0asGvxW;G(xJgUA|B_=C8-nBG&AMrytlwa{nXE((To0)VA%%#@blZ`f+CwZ~K(d5R3qa zcG`wjI_4}>T854JN$ot)Ll*=9{Qf~!=01)r(mgePNoKK{@iohx$_{j!gXnN*9E8^o~ z^o$fS9AS|v)4BIM=BlJ>Q^Z(o!=CJXvPM8cjTo#Hsry7-_7b4h0i(pbCRIQ7??rp?UF@QbOI`v3*Lag+b}O=myZK0qER7`rOk9eky|m*kEW0 zt=EV6jr|2YWus?-OMzqb09rlB>V)#GiXEI9;z6X46ChK5URHyw=+V%!Gs`mto-T&O4Q2`dxEBBH=}i70P)%=lyl9GW@!NAq8nF!!v`VF51Kv(x zt9Gxt-+%=0fE0^SxiKQCXX_sb!(9r3)8gFIm)S#I33R=ow@+gY~!6 z+VBD=h1lFGKn9hP^al=Pv^W}P|0BlP1%{7C1E?2RuaJWJhYt8?X-~((p5BnwvVKkXiipic-?TF)@DyoCBiKH)5W?R&geji`p9uM6k83xPE zf~w9nq=HO8T7iHgu7qD-eyB@88p%>(?qg=(2Fl0c>D4|9FUf}UbpIQH+}Zzc74}~9 z`?JJq%-dH!S%>cMQ#7)|Hzkof0+ABv(29ycGhD57xuKu)jM@yS55mI=xw6P_W8H|S zX|lslN#Dsz;Iqck-LeXryFleOhV)wkbPEMw}vE zkDOwR8knlQ)I*yAO9Or@6W38(76mH?38_2s4z6y7&l&kkw2uRotZqGPvIA?NHPSm& zP<4#xK*V{aKVu^_(}Z;qw?p*NdckKh!p zhY7nebv8xXL&>JmH7Qdz3#{gffb!tD&xnnzFj_weduvYgs9vi_Z+k30&wo$p<+ZF; zN`zLkvgomx0{@X(L7oT_(BasWT@lfLq;KUtFV^gNZ-0l)MiF(uq39g5ZT4&)Ds8GA zkyq+%8czEdRlD$S&c z>}YgG8i>X!8NcPq<>~`VR1GfSn+j-V#Hu`TEGZ+WpYY|V7==fh8VhAtPj11i5;!d; z7I7;&-2ais_fevI^Pg*X@xikkCaLs{L5d-Xo-|LfI`0nA|CzV0$DvY~4Gzzm^`_h(thln(@B$STNbKP;-X$l3EEt>ctD zo!q^xJaTl@K`=E&i>BBR-AL~N94_F)&elh`8c_p-maLJLc*G~)b|0TiS^-tVZMM>s zx)TQ!8BS=td2nAtY=bb{p;osv-jUvV|9AbEZYam4YUIq{TCv?Qzwcg4gMQz&Q~9#w zI~7X(a+&N8Bb7PAlp&MiDDAC*x?-@c=un?b0)!|Pi-z05iI)m5Sy1D63xYYqDDAbP zYMOMgGUPJ&a1UXe-!oRI);K#OT`H)5pCv+~kf05}C0QdMP)wl?PyqW7`Q zUw6uxYKcXv@0CkI^sKP|#hficZ|t#@;nOcW^;?zWV2e_JgkFht1CQozkf>1GzVXKM zKY*Gps|UB?ShGYv^~)N?-DP!+kVUT9SvlGx-%Oq%YzY)Ya;UC2tK?{aX|m;U-X5=50s&YFUz@}*Ds6ai}|ZARcs6Xum0@l ztOA>=Y`J`9rD(#d&UR}V+N0#ZSog7Mj$%LgIF(6ICnhBLSJG?RGg_Cfc~?;|U+ z_Qm!}D#2bDbS*<6ru42mQEVkckM(3dz}F_4F+W0QZ7hgKB#DZu&AGvE9Jw?`KSxC} zPButmcNR+c*rj%*uz(z0IKD|Ue8C347dhZfmk=jp<1Dp9^JjmE`10V)1!E3rCpows z$ZetdLWFnakL4UNg_%yDzvwv=Q&!1V4z8#>#AjQ!f_n3h;6QT%xQ_M!hF235D#) zs4c=fg+Rk3Ew-CQEyE1=MY%n^?E5FqxJwU-9dO*aK3x=5@Ey-!9R!~ zjpMU%_NjojN%96or0EV{tFM}syf;!hZsv8UL-6O0ngp4F(+?Xtx8Zz%?Wf35mT%RX zM6VJwsec#!fa7WIX&n4{?6LY*v|=YT+$_AcCazYNX6u>~#TG1i zqt{>idlx;XyZ3A*!>Y_JofL*zIa>h2=s6~{ff)mJEM+4nkIUpKwT~pbIs2-Iu`Lu*eV?!y)&s-qRh-eREX@V&|yrCnS7u+ng@&1GHmU`9CkE?T9X zvbsVvEqBdq0QKad@cmh@%tx6^>s&oq25=7pJ!>B0tQUE8UTF@9Z25fS6kO}}s=zly zqw(923PxKj1h?Y6O8ch={?YAv5D^DlDe631XYbLB6;5{LUea!D8<)nQW5&=9w8GHydQd z#(@$k_;HjPk!YpQg6{YLRf64K2SecF2!zD4{CwppnRl2ijomlXv#shG@OwI@0C^=i9Um{(s;9PHNcKy;# zq-(YvIj6_=>l@+B91ij;eH6q^!&_&Zxr^{99?;{|#(rZsN@!bBT=Ug}0%dl(5lB?! zcc$LL#66RowO0}lzWO|syMyr!3td?^YujJ?|$`tO9N+TICS+!f0GVcS)nHjr@^ zOUo{D@y3`!`MuXWZ8N_h39cGy>v-G#r%5LCYV{&A(Sn(4s;itF>~akL+;=m3`2{{rhDy99l7ZzJ<-Lr-`0CpVA8dL zxguV#tdTXi8BQWNIBwT|>AKHABA3!Pk4t||n|*v1V+I$qFq)V~{XFHusx}kYtN-o& zWHE-;mX2y(oMLw>^~Fy;ra?bF#-Dn4QsI1b>Zd_Bwx%!IACkP=MOpCeU8ZzrlY@YU z-drt+(!-0NY&?Chu%$wmX2v!O89Sy|-xPyT_kyqJz|jOQuHNSYY91DgNAsQ*9xL^= zvy>Di+0)xN?vb6u_ED_t17Z4HHq5l$*%LsF)=5l7l?_Z+l?F4sTugYD#j8%DJ+)qx zd^U1PGLmVU<3XDu_2gO+`>ZEW$+bW-BlJk%--$k|d+m!0w6XC*9}h=A!P@77-^BS9 z`?6k@x(qN;6y3Oe(>Fzu=XGUnJo(Yssc{hXlYKy+`1y48$_^|z!sv@N$3ZGfZFL5# zb)JT$MQsp1neDVx*o{>p z#vfB04kgo{)Y}lt?ZDo=4f4=F*%VQi9{c+@_oCa9FjI8XKT}MmS!9LSXa+Wz=}Y$D zt`v#>qxJMJ*3|d)JgKsSTNo+Uk#0J_}=$A$#Ym<0d|tMk!LVr;9OV zA5=#0I%4aEGcbIN3%fbF5Vpz6C{5a)A{#7W#Wy5bAnoI57v7bMD$r~voRhvtdLO91 z#EWa__k8f#MhNDc{x^Jzp%usm}y#S z25^hZ4wXC5M=3-3hB*EN|EO<2uu9f(t*?!oW@W{)U0m*k1#eDC+^#EHcsuiN#-~08 zaaNZy>Q#VLh*1t}-J+;D(cGVkxkeuvJ~b6OefKje?Kzt>47OXf>qawwHs-qAT@JsP z-XsL{2#3d>&+bI`{?zmQz>3;mXLaC}vc$5vVAlBkuF=CURD;i{m;G-Y$O zEuJm9fH~`GeV;;oGthlp^jXN0N*_DA!7pHN{Pw**W!2<|z}jzT_cf18+A|@prw1vWmV_6I zcz)LCU&mjw9iQFkEH?hUv2L?iu8d&%|*gDyYturb=pr@8ClMo-{$|P_-TpGH2 zB-^XWIc%d^C`jIj{AP7g)3(<3A?A21`H1EAtoRLgQRU2*rz%ul!eQG}7yyIUh^@t; z4_;Lh=E2CsdDYU%-iEKx#dXdYoCu&RUrk|a2@7Lo=d8}93R!PBdMlHvyGu-zR8R$DAC)+{H>o6Y5>QxzdqON@HT$3JDZ}& zCgJ~||1itYYRZ6-?AE2^kCBZcgqi^pnx|0)me&69bXK@#=-CNGCWiVrYk9*{2b$!2 zF-rppk-3Y=6w_m)yH0&kxP4%@WiTEzj2?!O)e~hGD?!w@W^B%xXn(h|rc;R;ERv&e zJ{6MJbdw;s$GanpK4q_+VwZQPc8HZ8{02KlSW3;#%SX<><}f3Soc>B0QFgr0fBz}g zBl2*XK!O|m{`%&ZnmU$TLHhPakHAB%Yn*(}VU@PH_x<%eedj!_{Af=*W9OCEAw9xn zdfA!^n@$x z=dw@~0Zh8u6dbY+kHRs zPWNBcRYl@+z8rEw*o4&%2Sk1dZT5h-u(G?~t$aF*jIw0|`6-zh((1Ryzx{9I^O7MQ zt3HK&u0N`>)VY!K!CX ze29{n9WR5$z2#X-zumIg^I9KDCm(dMZL3!>&;Sm-pv}m5pERB_;N-hGOGCf7k$a(d zJ5cO2m=Uh0ZOqYW)y>EugcBQAY}7*A0307+f6)6h9S|NcC4bwT=fc~^@!@sPnzymI z{j2?i-?|HBZV$>tg}pCk<4oJs0+A`1T&TL&1tp z>KQ3T1wHt9G|gZgAvwibm3dRH*f%pebttSv&F_(l3&t@zF&oQ|(Hx3~NjANk+ka#2 z?$HposS8$RYzK3*pi_oxzGe%hbEpOptLLc3%8h$LykDPp@#EAsPHynnrHv9B0Onwx zujF$gF zm9TWS(yIqH3x_%d(MPE>0J5s}aqq#W!d-egMS`$D2ZN6yjE7H-e8MWUoqceIs;ONi zUA1ACX#?=L{FZeFM%E&9JK+~ZIk#CMr8Je`O|0VbJ-l)$v3D)=BaYg9B`?1;%c?(r zPfDLp9U?87=5!&M^Q1OKL5u}WU`k-S*mWAfwJafA+>*1YPtb5LdEt}M5>%*C?7>g= za+Nciu!+cS>xTQ+e!(wJROuB%6sx&{W$6wh}$&s_^Cu1VO<3N zxYyqfI1w(z175*z&byUYIoV!HPnodIjwm5Mp041(`%x>WXZ`EfH`00{5OYEPzp2>+ zf@7_RxM}gKW}J}QkcnNYLbz#<-2%-QV#<(Nipc^|B696zR!zyz=L@aE9!lIB{L2d#Ja>_#6 zZ+g&B%Z&At>p+U4{cF-+SA26$p=o71Qjw~``cf>4e6hGfmtg}5$B{=KWF z-QC}E33tk&BiLq41q0RZQ5cbJ=vO4ygMa?@yTgNwEHfj_Qdba7hu9FBn8l$FD5C?aDUo5;U<=#=&z?HG;k>1uy%bfj8$}+bnOt>P*ev z-nIrzx#4&_(;#*QF#;S#hYDDHyZlkk1x+p4<0cSSpUmKF0-Uk9zZ+-!>+>CUyk31! z1ATiZTQ%}3KkHR7{!gIai7yX@heF@TV>M|Ha?DA^RI#j-8o>u<8oxi8WeT);gr8(7 z6JgE4Ettl0+K7?49Uu$~qd#V1o7sENUm@_RXuMJqPhIOorpV35=E1MpvbLco;U2t^ zJ@{8epuKb9?wdJP`(opj2dF+W9E@yl8ogLGy_-#AbcE6^PA|UcuX6SxY^nn24%0fP zQJx)lM`K$a3Bk61CPa87(@DbofAp_ zmP0B~o0(Z&9kppEw8MMjt6T*-PH_#AJ&YXrORv0ibbj_F>4Ey??CQEx8m@N=YKGSk zhqHwjVT(R?UqC;x%wqV&eYNe=w}mI5mh$!f*w2J&HSLQn!x<`p&pF=LF&hY+paix7 zUE3?x`)Gszqw2fkss8@>KZ!)7>@7vey++wCN>O%{ajy}{xUP#E;o4Qb-ru2@36egZuvyF4Ez&w~pL5$b_^AFylTs3m z5?%UR5(Zv=sNRsRQ268GAOFsn!f@WE>*MwZXN#*o-aT7;$15w~?lYYkw|^tI^Ilwz zLimH$)3Hj&u+lP6uP>%28&in0D;{xRQufIb&$SUc-5V1qlmcXtT&itHgL$g4cHf&W zJe`L)!|0e|#0FZ;5b5s44}g}k!rLWJ@EP7!z%+S!NocYYVZ?)UIv+i2v4ZgQ#37b2 z&5B%U8>q{G6m$d9f@B&xZg=;m(Ky#3M{t^oHI`oI>oi#z`V+-CP<75QfB9^BUC^0T zoBUm)8~gf8Ix)Y%V3dLU2_wwd@F1F++t_Gts-QQUn@L#pP=6U;Vd%)xBxv+by5L_ySc$Uf@zi@O^2gE-{n2`(9#{!oaDW?GGxiswxjR%vFw~H; z2Ig!xqk{W|4YiAEg3_EgHwokC(34iBd>akZjv``}z>~33bu`!Tp$5|kh?a?= zRo7Y1kf;o{O3&!WT^tGCOn>HM?9wqo`q?jwhoaVrj^Kg1UN^G6C^RcEh&llU| zgqW${3}hXrkKOyT9x-6zni&VNT<*`0PeZPhBX^4#y_$LWtm&!(-+5gAoL2_RsGjk} zS?N-pLQy({-{H##bP9l)<)Z>q&t11YTM==o)^OUKb zyTilCRPZG8`{b(vS%J!!UqF^?m;dk?3<7P`j1XoLb6-NFlH@bXEo*Mj*7_~IL=HW# zV%ut}x*=0_PD8(M%MnrAq2liv+R-HA?>8HiaN(s%UKE~8=8a5R6znUT`n!5AQ(&JylhVToAM`*2GvNkxq2oE9PUf~-Qptc9$+D@TTcQ%- ztqUV8f0{2IXLz*r`>OaK()d2Fg|itu1lwC$){0^N2F0GVh-g?8W;Kyhe&y5`16uIW zggts_Ep!YlK7v^|Vpd*Nu}f1jIXt`)8y#C<$K)wvs+0zDm5VY;03%_1?`NDt;JfPl z4rh8Ww(8H!1L?LKf9>Yf0Dq`+EL#-m*iAqxQQ9mYMl z@GhMch-nmN{Cv-l>vl7#nMis5FL!8{Q~gTSc|W(^R3zeO^d%z%UXFJlSp|CHez_blPr=?E~y^R^8KPHJwpc8XlUP!nanG0@=Z92J*m@>CGO>ISWeA_D!Y#QY3&WyAgoIMe~`Hg<|!AqGwgD)v? z`1$Y*#&D#5zZ(U>b^IzdDhmV4++<>Ld^(#Kx6YIBTrg+wSEHY{u(Una%yfO@`}gj7 z`3_EN%F%V|%Sfwo4^~%fzD@^0J}N8aRBgZx>w5}Le}AR{kErVpge8aM*z1`OFjgJuH@Z*7lO#sjcMz0NdwSK?*#5yibP;VYi@P<3Oj zngG-a&%_890JiE@o)Q`#WZcTimsNA%ZR&$Lc`b@QIOYe~27%%VjMS{Na~e2f8}6nK zo(Um-OSd)5097s7MSF78#AIgLnG&1#B9=K|n(V~Q#3GG<6Za+lE+w?YYc%%19=Or% zKaZBw^_S-@A)+X;{I}~nU2*bYmq8lFNq5JC`ck&qxP@Vk?1+s+ zs>{0Qw?F^J_l`A+twso`u2Lbp01W$Vvff7XZ)C{da zfs?6xO{t@OC$?n9$6}*VHxb-v+r_H!=4 zKmjI{c{DJ<+l~gQ|8olsBQ=&XpDtz7*ZLuYPxmIS+HFVP1GRHC5&6usU-Kjh7O*IYH&zy?a8ljqi2$QMNt~IKpo0;0RMmqmskoezygCEy^ z6+;U0zJnWV9rw@(4sqbfM>YW0o|n6jn@|+R!}oL2+h#B?B6UW_AE~uBSh)B&$32;P z4~CmCcCE#leufQnN=a`sHp=E}E1Q~qMm|x`s7=Bcypux5=8RQ8Lll_ShLdS9DF+y0R>@Ma?X@JnG2Cr?11GN@(0}6ZfU9nqz}Aq(!rS zIBi;)Mp>DXgR+%*Wz9va z8tZ?XK6r_{*kf63&=Rd1N4AOHi;}DL(_EtYIS2~>fdk01%x46)J?F-Q+;=Lo2i0s% zZ!|U~@;jvP6KMqAH9C4AAWUx+wWyQq@CjoIN!tf4=SsQWd_4uC=b7-?Wm!4{_OWS` z=PE0RjkF1s8IQDQcFYk<-`0on%FJ>{ta|?K{an3TgS(%a@HBzHP@2s+D?mJUPS$JY zp6_ikl|nInc1TooC~EX*s#_jSUU-4K$|kMxxftT z#u>^L!-rQpe5N6{_Le-O7is3>%4>rzmyM0b3&GihsrDul;UEBq@h)^smu- zO5tB4Q=>++j7vYa%uiYd-Fefgl<8}|K&cPkWFL%Oknz_a_zp#kG0|I#YDqjWP#Jmi zwvHC_e5|7HBFvU~z8Z@R2Eg(=*K|)C#17BWSrQxZji()9Z5j@648Yj8py6%)|613C z_D1x)YXWhk?rU>1kTb~!u!a$V1GgoW#pe+}+LJXPt;T}`3O=6PKQAe@YIIMIDOeBD zZ1AYX8&?;PKI=6jVH&`R=%H)9If<-t0|Rey9UY@eNf>4pP`7Q!IcS*Yah_t(7TAWo z!Qgbo7{{`>EMUUkn$~!r;>OV;|D9~t85f>F?2ywp<7{7^OFY(QP5GNc6M%2wTJAUl z@#J#l^_C5_S5z?`{{W{Xr_>_#ZEwRQcl3T6L;QqL8tJI^Sn=Bd3{4lfmG}X6qQMTr`4p1 z7^-<^ZZ^8n-h1vop#XuWU845w)qasF>a$p#yFcukzTvyQbt@W;Ih2|i@d^do0z>Oo zl{k7A13@jHFB#cq7lYSJ#iTeAd=}sLEKu3}WcT#;e}mSrcO#W1EwTWPODvCw#a4B+ zL2_0{cT_`V-4ET)Cq|2}H#BY^|4uH_+R`jl(b)SUGIn;i{?MBDckTg;9ZR&$RWF%` zrJ$&*ePHW>J-n!Y8;O-UoDE7_k3t@b3Ei<0(TRPIEqpq%v1Js4H3}DjBVzkGqh>%N zfw=fmqRkWKy!Al&)Xw*2M4^_X|3S^(sMr;-eVtOQY@5+NduqJlX~#ED;URzxwgUjz zwKqfc{HPK~0Q3U{qmNmKWaLSWo~Pme?>-#WTjEryo`zfB7*qFN?y4Et+*?S9I3o{E zu#F8;EhWt3J=5SFYR9I2ti5}l58wRfvg$$lc~+ps_YjJq5fOm_eoFutI*a6-QV$N6 zd+@q$3#jr>)9P_1`;HtQ91ad@Y$a)fOTV=Jc#C#6J=Q*s7V$m|C*mjwKsOIM=Xv1?RPPO2R{tFzk z(Tl(sAXCZsaIff#9gbG&d+!$+afWF}{QE>{o@Wa@Hs}wZshm~r^Ph@a+3$CpDMp1D zrM%x&uBRE>V8I_QZEd;e2dOjuM$pKD@>r)P`1 z9ihrokpHS2BW2p&?0;gZI$DY?-4r~hQ4PMe<9eHEovkCUltJ-7TSDu6`cFd&oJ$AR zUT(k8g`;AtTaCgID2%aGY;3879B0{!M~86P&DoXBjH8c>&FY4zAwHok_O8b*nFCZ4_+T+y)o!d2K)dRV`D3B>Cy8Xr(sWudz$?X9dk-% zSZ7jTt+jJqhkVWx#Gzv!T?eQ}B}}*eOkLqJKiSHBatj^S5f11o1)Zt&auLdB0)919w@$%PPOx1b#~eQ0 z7`Drf5%bfPk$Ii#^YByLc!G#JtxF@rbx&X-kVtJST93H)6sFKA+yQ~A!m z-`+u$H*cI_av3D(T>oE=AhDeHp1r^Ymh;8I&vRGX;G1gk`OD@hx|Y`OF4kt`!u{=y ziuNM;CcYStQrtiOa{|aRa=#S-o_;GKxVk@QdrO$CG+%f3_f z0#DX5bxMvkF*FtmXTL9WB{KsYgW`^_RMMZip)bWZ+m0(ma0pW24CuJQR94~~L!Gz8 zv}t0fa5gUur3p8R&FM{OU;Lq+$f8EHOh_V8VU7j(2?o5+K?iMdhR@{u=r<-BA_r6A zTAxENgps`<&yG@$K8~v&IQJ~g+a8wxIr@hTy2pJ@MS-Pb0EfcJU2W|SPIxz2S9|hf z8z{ozns+WLh2wiR*J7S8B+)^|>FKdwvAdS-ZIJt1J)DNsJ4K5Os)z$5QtK^&H+FrN=%4i5As++!iJ^l6V=uDV zC4KQXHv7W2mSMB=s}n-CwI4KK9mPk}X{Me8hz|na`bPM7GB_H!b?+DxEd1jTNB=D+PD~$s_L{r1FYfDW_`|1au~V27}CcH6nFB@g0nYh7w2MyPKrg~|qhqo>Bk$AdXc zDxNkG0C*hZI;6y0c+_M!ih$y8z(dKkA5m<7nZ&{ z`U~_nprnd^viN_<_p?LJ{DqXhX<2?Ty^BHD+?U<^&~%Ixxx+wa%|*B_LTs7Y0Os5X zb6GH^>1-OMfs# zm<=*s3^f|%jYdnpy`-D_22wazs-b06$y>N~`NiX;L7-c1S7#U-0cY%wTw0q*lVNus zZY^C$q{VEd%y!=Mp}%r5n(>mU52<)2Z@QS>vId_5Ff#7OeAb?MlRyl$7UAw#@VqHQ znth;JD}-$GC@g%!)l?Pgx|a5kJNk){g0gWae_Z)oj<>ZRVC|%0DdtCJ3gp9GEyjMw z8YctoGHq`RY)5P}xqeFq1Ib9l*2&LEtI;NpRq@WF-yKf5e}R=tx=@HE{8*#ih`dPJ zRd@5Ta&_}re9L2NnAF<(dzPhA#!g>X)@ARc%lbDbespQ0QQf0$VlQqt2G^<)anu$k zJgZXcPgmbzYVH7SHT57fjo_o!huu<^3e|odWO_vNY6L%nom5dXK_G}}lF5cYeWF3IGWf-(IF;o+t^CZd8f`)EM=S?3~)@I zZcvhoD~JQ1^LXjUJsGR)zn#v->8rQ_LnNs*zOUjzfsLWgqz6!Yvj@0!no%%1b0AFS z_k|TcL#Uzd#~bFoqNq&o__T_Fb#b%^j`w6wZhg=*h(vygsRJHEn{Rd;gW+Jby z?(qdc@18#$Vc(wgogf{f&12YTvzr~Pv zhlmuJ80G`-bL(VPiKh6KFVjN1XVWHH9mci+1LzmGinYpa0YaI8c!iXsk}CDsZ)!kN zdp9S$pR0j&KmH+F{E`q4Ov4Q~TKsQ$a-5-dSobuvRNujjsQ)*;vWKiSRVAYJmOAC_LXHpif{n zRr?Niwuv(}w=ScZmgG07@8su|uSo)JNw(78prKf!tMe@Bc72!4wn}amO11x3l<&B8 z3;N5z6s{fqCM)mjb)B!$xdv`2^g@Mn$2|?Nnx|jJvX(Kumbrz-Y3SkJRQG0Oo0*=H z>nfTYNOq-*t~gfa;MP~nrBB_?jn_{@+ABT>ix`5B%eb1TIF(;RqXx|pBpCp*!k%V7 z7!O@|K^ImM-cM{=?PH%LAS+~~_=oH22CxDW^NHql^q&#W9z3)-cWP(dsTXfxK1I^} zy3S!eaY(^?`2D4lnXsRif2Zgu@b7iWCq2}$FXZk!ZAnp#ar=<7or*~X;szeA|5Vy} zHA*DqX`a6|b1!aNf>$wEm zD!wi1LbLrKhR(jCg^zwe9tvG$P?u~Xl8bIk++wJcd6y#4e(Q`y0CjY7X?7;<*P)kS zTz>BU)njtJYw?gNV6hHQwpjYPX>Kvh0qg@Ydp@x4zt3Q;8GR93;aZ~5r`Ekxdb{-& zM{5F56VxFyLE@$389T9B3d9FR%7Xjom$9m@R@Y7>^ev?6=tG6YlX6&U4>yr52CQtx zrgFqa58xNmFdF=nQ1rBQ<^p>qYYwJ6W)1&V$$6=F(_GWMWNja47?A^6*$>wGiMFD2 za`?9uhOx$1eA#wQZN4cE&^QRHUI>GD1!kI{plzLa-irl@N zQ_fljON?IM7?_C9`;yXpJtl)D`M;qh>K#+wUG=Nxle6tb(2)>zxI#EBkX`wK{fy|v zk2PdclQ$kz1otaWohgN*CN|msxd~>=(mOA79L{WS{qX17TTZJ2$%@Obn-=O8HNWn@ zHlO-l@b2`MOBo!&Sk5X;b08gn8Wm7eQ*leQ=+4=W%=!heyj}jbFqKPe*a#D)``*uS zSB2Mss+bkX44^r<%+u#PN zjN&P<)8hU1k6RNhp{`43htV~%58>e>6Ry2aM;iU`9=)VQtmKa?`y6xq=LOQ$y*#Fi zCuwui@PbX)Px@xHmeYTxY=HJ6*lduH@oyjQCwIzT&bcH1KK@l{h0L9_*7Qvj+jrc% zse1eTO!49vVVM%|#`r1JN0?j-X*^#Oi9 zaVHvgr^snwY1-?Eqv zycwX?7d|tCUk>48xNnjdsL{SDWz+LgL+f<_>o{@mOWBWa$$b^f-4UYDSXF@|py&ZU z_3EUX&jGXt(YM7jp_tlB!~I#KZ5X!LlzDN`$PB(BbvYV7%PYdqP=J!`YR)d=Do^b; zkh0`ZTN*Bp4z{_c?@&f8>S3o-gU7MRw1!>j@Nler-JwaE^-R99_$JhpcI5R?$4whG zi~DFg1ee2k=pco)J+(|M@r(WYT>AN@^@Ro`h%)$j+p;`AraJjv^k0TXBD~)2{l&ie? ziOdHFUn_9%_MbZunmTL)kY(^uWm>=E|K}1u53p8-Q;+&;pHicO> zMvVveP9Cb(xj|a8Z^}(?Ua$5XH>9trzbS&!wdH6xprc59EBQx{aiJne6xMZKvHcb# zd+EEt%$g&*sDed$yZQ=#9T@b!$TB=E1|5wS|rv#uhUK)Lq zm&e8Hv-zmL`O`eq?v9GL1SlP(F`o2*|8)dz$S0eB>?)}1gbyQ6Q&%pD%xQ|Si2#kw zy7Tl%4YuH4@VAV{-QZCoL3oA$ik&rWESpOA<94I>pG_#g@DQAfx)f;l+y>J71khGs zE%k+r96uE!HIT z*d({V`?jhmOxIU76C4E!isoP7-y4SfjqX6mep;2+j!XTrIpE2;csw51c0*QO+zpJ- z016n}4@>-=E?R|Jx_OJyRq^TczfSev3kyIL&5XV53#vxDVVI{(F3AoA!~9PZziUKr zTAL(${52H=mWBksC9%*Zy-G>8!m8Oz6aF%6xQFm2TfN>m$Bv9IQlnfAz1_Q;q-Dz3 zDUex#8dt&xOH8;ZcPK*nCU}cwHI_YP5|iPL!eT?bL2~Vlgcg)d`Wh_8^`y>!H-K+U z`GyP61*pc{*Qkb4I^aHWzxEC&JA2V|8hs@h1%l^9P!^*O9W6u_{d7T`UKKEo!bEHw zZ0Jxm|Cx$}8^jq(LnqU}+){s=o}0}?GTJLpi+yAz{ixYA`yNLiDguME0R;lbJ%UiW zSrbR+Z<GFWiAe9&eqADqg-@WPG-ic2q<NeiBMQ27&&G7NQ^^0B?@zxQgLP8ERBBmqGvxwY8jw*9}GG&cDaLmP8xZh_!$ zxg#4t+fp$G?-DDoK2FF|(^1*kFpsGICH&tFDx%C4HWo744Y%b-GP*vbAvocTOGuTy z?Yr!L$E?G42xBvqPrnjnjwyI`SQ7=8uh)Dv0y%CETtM`nz!H6pqRo65u@NGuup zbKtYm{!Umt;=uOQi9g1i(VzQWYfLJG zR7cZ8y%nN@r?oIg74RWcJI0GMflpxR$LYBZf656X&EvfNk<%9T?e)3<(g~q3N2f^f z^~P5oErr*>sWUB*{VQ3+Uhs&!p++h1}6 zydB2uu|t84>ot6fquc#T zbRzs_$^kcrcA6ShiqhuG(@^mO$qr531r8wSlwvOnmmu!wp={|F%#m+<&#RgJVkTI5 zTyaql$C#^ilzx4wW1AJx$~bhR@K$sVM@>C{z5~QY{}(4Imf!9xsC9T=vlz#ceD4MV zvEunaXX4wvqK#_i{mpWr-D5u~f)cnb#dQ_*no3oo zqP8F(|0TY~?Wq+RoiOhI@fRI5aJ&Q{UMz-IEULq#*H1w?%Z6wj^yiQ&i*TtUaI zzSh$p0Af;nhDJ;wz!SUO)|YcQvO~uESqp3c?jN@29$KSefrz2jK9U|_!Lxecl1?8Q z7oUl2eJC_Tz8!8;DxWm(Mj;9F^7Z(y$W7A>b(q=`YX|1UE;!z7lM1~1<(+qC&}+fK zrr?JieZYkMRP}@D1WER-sFUqHuJqEF5vlnx=P#m)1{qxg%9(h;>CjN?| zyC>32ZV5m~B+IsEODO(Wn67%0zOKVKA^!nn{L+v{Gb604xikj4Ar`+(He3Ocwzev})+9U`U;%+YudK`jYfHNZ#AR;WUR00js zROsr*yWvw^vtd{Z$%{4@xPJgo+9n8D%&72tDb$c z059;IvY$Si$=}m=MCY%7@;*>20Qc?!>l*s4@|(E3he{TpQmIn0%AaNOLMtmoUsMWp zhu;a;8vcY3i_6O3q8wr^Q%c;8S#aEKYJHsdf_u>n4s$U*zeu)PKGyCvo1i|QUvHH?&uGH}wmja%GT#&p zMDfHXXeh&5Uv=Q3f2tPMd^gbG!l2R1gHBLS`sG&CPfNv5^v!~Dn&q@CoYtQTbX-gB z$hFUaTX10gyhOKflocM=%rjl8#hfNc{;EAontgA)@byn-jv$5afY(Tkqv`J?h1IkD z9XOMQ5N@s!DHET{Yk%%Hlg&n#0AudCYp)(_Y)^+Ce2zCvZIK6A4M3qyla*oV^CR}> zS84+Kk|f{57G$XY->3!Sn<^tiwK zY*1O=BQQAcqEe@&3G(o)S;EZqcEnz&xKo%2BjYeDNQvjmrPyh2$5sw76PWROneOK1 zC;&gpv5b;$U4ijT*Vj0{FlYPdy?xoUozJ<1>Hd%B#GM>Ka%E$?hQ|5Nzcl+$FTjx# zR@0eN$*z^Jwb-nf(*<0t@wmKKzPbzYO+>8@kG(^3KH#7-KgW$NQ9ec73BS{d(M30Z zaAX9sTUN;FbxFoulv;N74KYHGj=nVKYdwnj_Nl^mQePBA z6LA%|HHjCHU?jT|etJ z<)*c&@9zh;-I1nxb`zYu${7&=Ht3%|$MG;lby*#$38~UEAA_x4A=8NUmcc3qzYcAv|f{|9u8VW)Sgc z3eEfg^ek*@Y2T%C49qSyKB%B;-YTNByxwSPMDWREI-jTGKVMt82FURv319}bN)@JY z6JnP=Uow%f`%U;&(>{Hg7c*}e%y0cbL1;Tt!@%>!}Zd z8noZ_Zh)+zr{DdefzUu@;135vGaoNm9&f{b!=YId<#&3Zu+G;Fobz;uwch`JC#)(H zEa)DB2-3m}{B31O*j6%b@iyu@IcxjXG6A*#Z|EoJHtDvr3kiaW8phJKE1#koOX}@u z$}h(kS(PB-jHD3}vLO_Z^BQ7J#*>C1W+2B@pfy_hLrdShl89(uKx+j(c-4fsD#2SO z886*I8hpg>KLj_2TRwi8;8cVS%x^As$rRm~1X^KUOK5e8RA1JoRV^VWczB%fqDLAR z1?;&tNL^NxUmpn%#^Nabek}hhy%3|<)R0E#JGuRnu`WLN$XJKQ3&&5Iw@Q&KWLJ|0 zZWk<}#a3l1A)gnQjl2KB*xd^dxnUrNk@2g!B4}^z-~EN8Fo#@Dy6dF{Weu*70cw7G zD;4cniumXFM3|i3-tzHPE}k}RSjwWA2{MjZT3>&&*F7;4u8T9yc(4OH3G#@70mdQ` zHTvyfvj>T)S~Nzg3y5-xf$ywF1;uVnD1X2xpzOU7t}9ZFuN+4T%|-QdID!SA{iSQs!SH59Yh7~av- zn&5f6VVf^XY#3pGu2sxh35IS^X9nfvRmhYre}`$(lS-e4=jzj^jb0aRhF`r>-gH}- zS>q<;Lw2byl*$~Qu>*0?NlmcNAfQ200r7bf(l}*KWu3 za)IFRH!$YVtJV?=nl@YcosXM8UuTB^?kmWrZ(RwePNH#tq|hYLD%oFxXV+Vn+BQ^up7 zzh?i`X@H%1hX2T$s!anCo5(^$TWOZ=JlQmhDEq~3 znQX+ZEugbBzbZDHH3cdJb}!ok$JDA{nBAz4i&W-7GPX(YG%sqm??N~EO_cJAHNIQ$ zxQ0)GvOvcmY$`WT3bd&J(|cdmT-T-ZypaZv&%A$8O(J&s-6?D;e$a2w7!{Db@gmvb zG{VV1&cGRI_kPIuwTFLBn6+x5vU?jO0TgT|&*zednN>Fcjreoh`~aHRq|qvj+s(T@ z#m*t)a9#~r6n~FPcqQiVD{1=K=DW$4@+HJxJaXVa-;r^F6jB*dQjl0q7zinmF`@T+ z-dQ3~om^1IF@hilJ71!%&82%4_vY6>?u8_FPk9{OV=~iKeyZpwYg6I#`cGhlb7%p$ z12c;mH_;QF1CrUd(4KYr4eD@$RG{hJsn1B{9Om4!_(3@tttUjaoMX#W$Z{dzq6-Q( zMVHI{`@0qs&)9Y0doguwnw!ljCy@62Z7v}o5ez6O7p`8${h_yh&}j)T8fTMfuA&Cf zKas$m*_M1>WO{|K3@{v;al7|icpSxCDbum+YY;!i)iM_xblsFlr9M5%>OD&t0LICy z=ngL(?A-spDSx$U1dC|jTUmkUU6( z$$w-6$G${(xJ~;(pV-_pDw+K~@X}quKQc8Ojzew79mZu(8!HwiaYu|!OF`|u#mMMK zn_r~qMwFw`(3+leAh4lfakb)h>3?s3nyw$r*+kihnvJS*-S1#R9su8GW08&_m#(dR zbhhWIOSm=s7bmMzi>CB-o_hT$1=h-6%zRvCGg2S7C@7E%@7d>8E;MxVWIx)9{no^~ z!V?2P9y{G@`s|m0#HxRj)#C%hJ6TX$!Y$$9l?88Cl8KAGG(2FDVD)<$V7<3mjaZ`v z<6HBDG2B+=?AOEumqtq<)gdxKu{Kf-&6NR4N@6IFOqFtGR=q1kiWBV!glwgmd#7a_ zZJ;&;(h^F#`Wn@DX)b=R6#Q_C!{5nchbW%YJ0kgMcE<|IWN~x;(+rV&dR}ok$hR3U zYSO~&KUtINhgdjKzxSL3j)fGX#!t_H;yY~gB>k$*P6mI)DQ zEEweu)r!idvvZB=rPp3_6RfsTKL|WFJ-IDq zip1)bMfv(D(WH$1_DJsf$HtK7*K3VelP{FU4}p}ke3Bg{9_shBH6ssLFWc?yi3 zpL&6N+vTheEsRlIlw2|2rM10#`4+5f;awxyY>e z>Yu8MjFQsDJw@?1bV6IBO*)ICOjFa5L z8nzvbp`g%{)Y9UOWct@ivt2d^D6qJSA5EtXuBaj6S+&m(Q5_XGtW6HNXmzuxYH1N&m}m5Q;VY(!n?nV5qM%#@!R2>k*}0~fQg3*)w-#1CuovB;xrBjr zgc(dTaiM|ZS6#oK{f3;s_(oU)ySgFbiP3d;&G2yC3Yc}dOvO81-(sM8KP5*{Eqi}6 zkS0@ju~G8}NP`nr;}ZTpL0eD91PT;mrC? zt~sfZ2zAJ(ffX05vaz&M_Rh<+8r4=!JsmVDP@81Dr)$)1S^8zij#jn=aShi}axRm9 z@WSNll3e-Jg)*gxo&^8i-hiuPzWn{hKU$}TEFCWL3|~Ru?=NZS+5=+WHwCxoV&O1Q zsoYecH@FKPgQkj`NLfQMD%OlrNBRO87gaj>#VP_+h4Z@!(s?B(R9E(y`neAdD5izo zG7CbfXfXc+BYHsQhy6zUKwcj3{~bPfLTouO+-UaaA#Z1k&OO^HK14ddG#b!?xnugo z2Y?woFf+DBqaBh^G?P1!=Ycr-)9|6J2iVB-{pydmgTC)R+)-t?qPyxfNWwS*1ED<{ zM8Ri12A*ZjqG|yWe5B7MRzL*zri=q^O}g;E_zr=5c2d#@)!@r&Hen^na&d1QP2VJZ zzSre7_>iN;|6uB!#Zu|;?tbC3u{pg7l?717Nnl+7W|JYJn~&eD#>6EUg)vBg4X0&k z5z+?U8HYIi=b>lao3SvXd6E4BI!48BJxqgXrh0hu3rYv^t65F0gOErp)+_ztTWx8V zy#Q1}huqU`PV-Vb5a?wp)W#EU$9-djFjrKr+O< z3Sl0l6sId2->sbBKchrKaFtws{z zju|DN*G+bOVn%-biJ~mhr9Bq$Pl5!RosS>{m?5H#UMG!4}{1SE`{(yCs{8-#frJ4QHb~e)!~pz#yksMl`V^% z^NBr#4f9Krgs)Kxs z_}2ej?_@0+uX0aes_(js;AXIs=rrXwqhmxnF_H$c?sdPwpJ+UKw0H8Mm%u?Z2ihMf zR>{12wirC4$Cb_SVXy3orV_dSKAP8rBzWPp1^L6PA z)YsI1yJGfLI{UU~t7YWQ^O3tYbb+{sMo)i5eMEj0MBR3A>@|~lQz}O)VO}v$1BnAr zi$T@`RYAx4beb3&VgAN%=yfLZf4dWkGrxBcMK~_>j^^4?wP~T#oKf0fJcnL5WpX4fHbJ@|KddB{AzD*RcHm2dEH;+8)1XcC57mtECg3#Kj8xC^ zH^mw$S5*@3OsFISDt*8H<9nPm9-7-+&1~{~Xmf)*1#x5geEaopw3l;0PzJC@S-*p# z$gMxkdWQxp&zZjN8sC24bPY-@``BX>ulX`MJInjcXIFI>!+7mOJ9zhI=fdf6lef>| z?<-_t@}&NbDuGkgv)Ys!lMwtNA{{gq(FP6_CLWrZlv3iLj0 zG^9FrcxfLPMaO&QM-VBp;suYTsWvc=L|vFcgA?C!x%%6?PXTTJm4I}lhJcqWirznd zhHEF>xhQh03v{$D!&d|tJeG4en=u2j(C*lNVzL^E7*Y0Tx1ig`64p? zi-X&&j7U;Rvhd*^oDNd;H+LYF#KALZ^^Hy9;ygYV7DgR z6Z}0^f19+gtN6W~_bwrs`3I-92V}X(vKwI0qJn)H@ z<-u3>=qOT+FQ=-&XGONUdf2Eof&8Ez0Z~{du4C3XCxsr>G$dP`2GI#SC5X*eLnB;dOcsQ zdI`3J2tf^(g|;WJ3aXs!1I)rag3576%WQ&mRPe2B;2)_vU(nUR1KY_3+L>nG-0mUk zja5hxELg_&&a7zy<^rH|9#liqt&JFDMlF{-2p*=Ys7AapS^WW*1Bbv>0&8tM<{HuDRLPLC=1(5~CbY$H($7xPgMhUQ?8U9Re_xbJ!v!ZZ*z zn2%%DqYh2_I8E=36mu59>Dm=@^NB7uTEgX0g86~($?%5Q`AASWmMSkO5YdoOse~lH zvtpX!8&LX9KfdM?+@R?RfP4hCkHs`5Lp z{oFLPP*L<$Zhao1J|SAF)|Y6mt z9zHti4Z58mpgz$;GPY@j%iwn*Qwja{;4q`l%_lJu+qYDc1k)L_d3ba4tCw&GrlB_l z?%|2*-a0wG*E6Pu&CT>qLIc*`_blLX-qZ|BF=G@fKXN8EW5mXIUkStFpF$%5$L42f8JZ1O*>B<-(Spgm3E^&3mY+aXN5Qn7anyqC zS4zZ}ltZJ}g%qN|8o4$XdvHk@{&h0+v+Kp5bZOV)kCIyDcvm)_4z8W!l<}4s@jCSP zSM%^zybqK7PKSxxf0k`3D;@^Xgj^)6&c$01Z@H!f3ZPNG8uhTlfGE$%nm<6c>lYI)Z!#IbuNLYuiE zzNOdIv>Sqbt2vbt>Co@>6ey-~qt=Bu2Z+?~6Aa}E2!qOZ#8WMww5wjRoh@~2Toj+f20kwxG8OE8;nZK&UlH<{5lwpbi`(WTfkS z#<$rrMk14{j6Cj=c=ExZNtyyW{s&iVjm9L*2mavw3)_FUgVFA~kjrw`0HT(h?o{t} z(;$f9+``M);EjxvVEd@U+TVPe#vb9;vgK51a)mPe%}3O6P9 z+djGYCB*d~Lx*tP+h>Q-csuTPJ>S&q>^;10FDNDElGZ-&S*v}}SZgFYMu${fXO2aN zS}vHsdgXQ}NCcgOh3pdNfJn+^N91;o=d8?w947zSD4Dh0(o;Y|pFBZ}? zfIvp+?1ZQ3MynHNhIU+ConvQ=RY+m9Nnc-8hbyJC9>C7#)NW27!i{!KalmE=fVf^! zgG~TYEBnRjT6}`={?e_!`h*O2K%BHXS0s_RIo>%gv8>yAK0bP-yswP)0!tB%z2n{= z?@L5lYNXas<0cQoBUU`@fwwAt((|8V#H!-(Czzhd!NJ_l^_JcO&x&1zi_oxW=FXR6 zt?!m~9a^i+_cY3@xC6%N3qLkQZ}?Ao-ut}F%J%c&LK|RL@7&m^k=7!6ScRwRzSa^q zbl1z%)A{fX=F%^dtwhO2uFw!75RQj7XTYnss$zWU!}%8Lc;>Ki4>?#=R`J z?f9fR40V5NQQ8L?xEyc2-+q2Ao*2UIkSQOLlLneosPnOvMVL?W{~wJ~Tl=%#FyqZ$ zs;5mQomEir4_t%Kh()})0int1Qd;WzcQ|qO!F&S|d%VK~i@|7hh!`Nq z=p{^Z-1b9_q|sI$irmPEFOnE}cwdNx-d8fe>Ur*q4MTenlZzy z9Y40gnt=7mKNu%|7-dOUad1ZP{O+tC=oxAj&MvmMbRRAvs7=UU#)sG!G4YN7RzUQ! zm}zW6v}W|$P*}d-H=@g$0@J@Yr>AVT`DJX~=b(%S+VJ5?v6{Tq9(FU=4n5IiLbENC zCUT;WFKxS^yrL=j5xM?=XgNJiy-{mUPm>pap$H+dHRQj6+c*3C-KK-XC@k3GMbbuz zRpj8$a@m~%XC+2e^b8)w<*fs7_n$G#*aS!}?HhX3sw`uC`HM$F`9TgXg={iI5OrN* z3pEbUgH~_HzcgmZ1EG?2qK;PaTfqk zft0aiCiVuzwKaj>MP@d;nw($L2s{uXzgfI@01{f2U-Kt0SS~m4z2%fIUHQV@8`g68 z_xB-k?XHIczzTvDlu6%?h8f{4=)3aFH|dhTzoL#yvQ1H7sSf_}8VDc#|pz?C&0}nRFSH#_d;qO0&oIIUVxCx z_O|Sd$J$y4i7b6KOQ2Luh2J&Fnp0PF98a>~umMQ%qqx^^LlWcJ-Rz)ZB-JxVp(p+= zLX-<*)ojlFb@tFc)AB9lK}~znaM$WRm}sFTKkM|X`kbw~hJ-p7n2 zLF?jP1jSnBYq%|cm@2+K4Y52gx%@9LUgnV?omIGqbQbNKcSlmQGQ;nDnPb2vfRu?Y zVMQ|PV%b}f)(nho)}{}lTeq1iSpGF5U>TKd%+3ZV7SDJ|U&JTgq_(u_1YOgp_uK%f zkAwdV2yw=b>1)!F&zPKsBXd0|;M>mBJJFKMrut`gsqNRhU@@s+G)28djzPpE zDKaN#9Z@LH<pavd1j}&sq6}Sctu(`dvs_>hx%$>L*0~&_*gaG9xOh4~)2ZxLta-y|3Y+PUT za#X%(hSf#=T;bWB#ONrix7cCS(AJqv_vktMX1vqsIQb{s$@ba>_Q9=Rn$J!m<2Y%o z224_;H7vhMCQqI{bhH0inbggu7YE%EI&{}nCcssAAvI0HHB{1j#3n|FH#h^)*_h1L zTrh4%mk0@5)KbOs>%{xq)IVT4wb2{UTu7iut>(te45@#Hxm4TQ0P96}Z%4H?K!8m@RBFpaS^Yap&pMJ25UKD_j}F{!%WyT|aLm`YG7%@TLI%YQ&Q8!9K(jnf3UgxbpIc9jQzzx)w7M~@32DOMN^t=yH} zG+8n4YQ?V4b;X>+wLH65JTP{j*UdH+7(DDpsA>>Ew+(f`BOkUlV}WKtauz7X zb-8hrEeNA8YjBt4?SEp7e;SU)Pd!#?u{tIBsHhqpG8x+ei-}j2Edz9#O(S zb9irHh8-YiME99nIRhV>IHzpgIOX_QkE{>&J(2>5P_6{?+WXIE#cyQa-J+%-F}aVHWaiEPLjv#s3szOxd)8gNqdPjc7e!6@FQ4jVMq$N3xG-Udkh;q4w4 z@%kQD5vG^($_Vl%5pT09Wo|Cn)mNg7(K%(wTWr=p4e7*Z6}X?R=1fGsSGkX$6PlKX zXV4l0EVU8q5ho4Cez7L>lKFbUSYDA@=WJL3$H;pcHMFk4$4r3=ldneD9$I?AgvUV3~z?S>QGf=#WwD{Bpa`O~aq)3m7XIqO>O@)EU;4JhDJ z9tMp{1j;&tRu*Qn(E6T8%tY!v8Io`Pg72#WM>ZTWZW>ch z`;To6%svpVNGsq1Lb0zNyu65FQWpdOk}u3|N~!^qV?^8*0OB83G|dOdKfoec)7|7g z<^q7?WWAl?+*~z*4>(VpCkDIjMA_)YQFf~JqageKsI_!0;$LeE=z89a(YR`4^<6t+ znQ(>GU5uO~uMlbO473|M$1+JN9t(lkA>=K3X1Z?LW@QWNgcI z5_(s-MRs;#y(`x|>VX%JvJOFM4~nD?6}dAwYFAM!`jTh?8^8#;UrHrhFL03&T8->8 zt=X@U8nO1QPci~XRUkdekr_X-x3uYjR`3yl{QyASYBGdw0BGvZ6grjhhlG*-JG0${ zZm|g$^`=&A<|zqC`g&jl18E=EziyHsr5CGCy#~K2`2B71rVuX zd-EiM)xa=Y{6JM1?^YH?n|aXnq_uozaJrN)rk=Y8Ou|-RK>P@-qTn?K?m>Ye0BX2d zG5{uAZ6IT|A6@TY?UA|f^`LK>`1!)WZy#>kfy&cm`}qrp_njaTIW~UU3m8NiY~42>Rh=TrBJ#)8f0$qFC|D2E}fOo`y8jTAJ$8H!zP_6wadT#<^h=z;JrET zBYawuW6~w`VMIPCmCFr98~Et&bT|X1&Ls99_h7QjJeT4B*!YWu_g}ZyPBgGQf=vnJ zk}D~EX$FWwSLonXTtxgn1F-ld5i#`D&40(k#rAMX{Nc5@AELN%?z=HNU3V6HXdeN; zIq!U5TqMNB?U=mt%tpMj2j*p>x-UlE?)NVJ@9;C8e~DWF{w>}HJkp{6wxM7U_jfHF z=Vou4rYD$y_t+UY5vms7IXHi1mxoKj4#9_9D7Ja$;Q>F8V-#)#H#9<8}(Bl>gCHnpPOfy z!)L1T{8~b}@&XLL&5XqrrghGBkSd$ z31P%Ky1#X|8pDNt?lB2>SXI*eWHotecW1Oi3m9f=rcV;3mu_Wnz4hRA0w|=vCoj)| z#eYzghqYO&BPgD_PUNAwK=p)XD!n41q$L;OCrFA(`+n&A!U^(3d>mXAWAVi*_+g0M zsjSfo-Op>ULX-W_Dc@M7;391HftcO-y9Mm$r_#BqPKFHn97Nm`H>{-zdvgYb{4hNi zYN{z(%SadXuWTf7avF}zcs{K=C)+(#83v9gUlAb((*N=PN*LQquW4|WefaaG(c*UF zY5f;wyS1VnUG;L(#E|lrZu5z$e9<5&8Y}}%GU9<~^7(r0g@wWElBjE&ZNX9hbSWES z5oI)+ItK^pULOY_{=>l1ZY0&8?Oxaf8y&EgdTo>%+Q=Fk)EY*2*=VfJyGf?j6fyG* zZoPlXEtHWvXFYJlKgfyfgL0TPd5Jq1KB4i3*-of9d>QtAFM^gP*nuteZ)caWHkEF` zX#>NTiII{+rm+~x5~DZ2qj~QVAjMqR8>#8xn3@HVuMD;_eK}>6_M=e7Uw01p&@MS; zd6fNWB@fc1c)2X$!|^8lss?`)H537?0uvrU{lQjyMwo2G3=CzJd5pF^M$KwPfL_pc zKRvkbdegHXq$pimhGa@5k?#m|aVG-$JOJlI2Q%mMc9m!Kq}(pg>V$oren%LsR!gZT zxPH)|`K=Zgt76OU&6fT2HnAt%_0!QJJP>*=6Edd#Wg-Q{fB+|9qCVn!X-P0@2hXDG zEvGG5U5Ef@Ken6zP-BPE*uO2)g7S+u!j82UJR4b<9Hs_y-5#MjC&r*sA-Dr1qTvze z=9QD(&x7b4fdo>x?gpgC6C-GMnbyaVo+WER!Z>P~5aw}XlVCX!tCXE8@DkoL846IqLvstB#z> z^Bk_E$cnHmKXBdp1F`ni>F%H&1 zgL}V=&EOf)=*yedVD=K#(A%%-Wo+rxro65>qwsXEVB zWp|4Wia%T5Pwz8X$Bn25SA|8I3IbNK6_%+4m2DaGDB@Jd+G5zEyxQ102qCaD&xF;I z40|9LV&WIx!xecJWz|q`ybusIx(va~PqxG}_~SJ1d;^3m^}L;BJ)|wGM7$B>%gd>; zl*0PK+(120UK2{pwRTMTbI8cxACtS(R^XYZw_j%fVM{Fsl!{P@T4d}<(yVR+1PnQI zTt*YKcO!;2jw```Em3Cv2&@?Iu@l0KYX1CnJXH5%6+5|Z8>R4&Q&^67_i)!|vWxAq z6-`Swv#LvYGrJIPt{g+-Z$6ZePeXh=ftvvzI&^iHq@NG^pZ{&?gq2q@BxSR<9pVbP zrzj6@8%qz-hb~I@Qq|9vrro#GofRd0kK`=%g_~2~QO0 z`QAN~STkCV0Ono~(s(8F(nk$YojijSRn90xt9O0Mi5wgxmzy{4O&qJAJ;k$ECuIuA z`)}8nI$zRA|3Co#o==#B&+5B$YHfA|5n|onGIp3Iain(`n@9JF2v%b9m}jF z28mt~A?kM_K+7u{?^Z%>V3A?bjN&IEZrTV8Dk(=76+E%%7~$&{o<Ww{rKJI=O z;YvXgQf`V@DGFGsspl5563PN@EJeSm!*z*Q_!|J#{gdCm>;e@7N4}SF-a5-`DS}tU zV(3yvuEU6mvMD+RjsQLj58AZ_{2lS>c^pamiWc|szF}X{xOqoX8EPNzZH>zYuClHd zzn(5qiR*gL$b`lE3k^-(ngp#C1Hh8Q7z}8s_NxTGM<`Yj5%I&E`jW1L#3c; z@m?&|;J(4ro;sb1rh|EsI7~_TMv6!)^V+Q~?5jHCSSn7Uktt`jaOWHWX$I^7U zHT+&ZOPDJE2V0wNWodTZsWdB2Z&Q`bpNO6uo860gqu>yw`1=g3{W6#3#4L33VpPqa zDe1BKEywYNXw3l?Va4*V@*GB-c__AIl!dQD@!+y(?md+$nQeHEQ6ah^(s}tz~Mjr2JwxSkba2W~-*Hnew65 zS+O+udAF$m-(6n1M@TdjQ%zCq+dDB$?eR*XpODo#h2{R&?=LYayf`b=ueO-^If%-t z+ZnnCjZ3!{af^@L?r%Ah_(vdnBg`zA&pJ_&VHwpDQS)@1lh|@;q1=u?>%>Do4T8NB zCbaowB1m5^+oCrQlO>ODy_4$;T@O6s&6F1xS}vS{rE8*HFO&JCYWD3g`;F!^s$m)Y|ej^LL`Rs zENYFjM)Qv6jD}U2LeoUVlQM?U6Gie$VN)2p*Id5`mXx)YQ|G@>ofzlf+L#msSJK}h z?GXJ^$?fi_%wm0cZ?s~nu~uqZfj4Ul5wQ`$JZic8-;%PwJp{FinB>ww#>1B9?)&GL zs5hI|JVV2an|%(WEqFpCzl%cQc@n5>tCmdUBw^+KR@NX!8Hc}mXpFXSchod9S_I#XdL*=wS zsYA7Qym&P~5SxHTtY!YdY|sCPs7dVhMS^sVX_asUhRI{PR|s>YhuNNDjI-?N9;1rO z-=i088X18UWU|i{D3Ej2xOFE6#rzysmd;46*iCi7Ll`Z9RA} zJR$rrH;W0vM9s*y6g^bdE2$sQj?Skr=M1GA6iU>Z%O+&&cqv%<@Ix-cW)KmhXcEMs z(x#{b?wB)j7XUdzKl4|)N5(fr7TDOGJ}HUHV%qGl7PZx?eul183t0O2;GLW@Hc(Z@ ztds^rmqAFiXzW+^m9Z2%fa+o!aq*()DG(iZ5ob%NYW{@PK%x?+(FQ}68z!YzMD9O{iN+GT95+ zy39(Mj)y0S(+qW}2@0^zUL97gx*P{=7@~{x{dXl%sGwzlIcKGl`JCU%pO9U%{7cDI z{$rV!W?j6n;#2XGz3UdO4=)@aDzd!B!7^Q)kghU#+{BQt&%S?+GdDLU8vNRuQl-kn zAmPvWa*}ddR(7!b-2j4IWOlFT2;uBT`JeZ#Ca-#1mGQH4xEm8b=p*`~R1=vOsYDBU z^IPA;%JjIUWBExaTre+PmSA8(Ih*x#XrSfRD7CeWnKyZst#~~L#D)Jv!`Ys3lKfTh zXOUX1W22^JDz*)I$UX1;uUGUbtDF9#60>(%lO+W{Pfd3cuL$hwaPu(c368u?TR9s{ zYNAIp?b-asN=x-us`bZBOiJRYQ<`fXMaT~rj8^-X*p6rBWf8jJwlcF1PZ4)Mz}pag zlE^Hlz^kO>nm@>($nmU+rOhmc25+$|RH|WOYpYJYIX5ZbzbbV**}?;2je0J@>2GV( z+M?QxMSqn~?#xcy&m1d%L0f=s54O!F{7_u_bwp!&+xDr!wdNyca>-A~t7X zZJ`=MFd5-xvYssdH1(0x(j$R4$6E8&AE_qE%}&?bgd@Zzk1kK7YC6iL)r=^0mhMZJ ze6&K*plGSmN5G50gPg^|eO0U*oy_WOKDb%kGDQXOp9rq(1_mCe(K3Qm!rQEp~8Gmr@nRhBl z2u>D_$7SzJjP1KkaM)Id3`yYDVVbxW33Fh!rIbOJbM11G94ob{Zx zj5|@2JyUqk1gC$8suCqZiuGV+^?6Y?V{UHsA^h}r0{3zg_AH4$*G*Hu%F;6+_)y5u z5H+YTw`|#tNvn1{qeSSOb1`@-a4Q!u;nguKU-&|8yzfP#dlV)3Gs?fjV%>2@ zpjY4T>Avkwmd|u9i%851RQ+u>qcZBG`TUrVTeSI=i7hQZ$%707taJT_l$NbU$%U&L zG#8{>t@y8$aymBx71Au0t5o}SNDh9 z6Az>VHRk<9++%Y-k7a+GH}{lIqVZ{wu&lB)+Z9)4nP=#U$iYwyqmP^J`z5C;|%^db7Ych+&j2UQX-&lz1B~8J~v<2I7Zv zD^{t-q@ncZ7!^pmNM;4*$Q}q~Z5XgN5>33aX%H;{vGhbP(weSna>*h>5dtIJdZ2vU zbW^mb5iij2ctDX)=Phf&WS5HXKD&;1#ymiTWyGazT0MWUu)$R-Ji?>2NiH$m(*V9$QajeewLEzbJ}m;ChI^}x83 zZ_v6>ETgz#n04NcR$QGSGQKI1zYM45wsSOXeZ&#o<7sB2=()W3?TyQ<@K zjTI53Gjm((+H)pIlUv!5nQCzBkjs#g(v(o^lXXrEYZC?sXD@tg@w4qVoz{~JK+C34 zUDQWq+xocY_UNlF&VRz5{+mD_Ovnoax94kD zS{IyjU8b0G5F=$J*bbGY)`~Z)@J?sSW2svsge)Q-Qa@+n+~k^Fd<_A0)^3T}ak?w< z^*(X)+xiiPRCTX>fg@u|L1it_Mdofz6wjxr`&f7ze41klatjD;g+ zN#Nt5f#X~|75Tx6>kuO}>g*msGJTvBOi20u%e1l1{5}!*N=tvkun{XKS-5eEOx!P< ziZ7;o;M?@v-0ER**87$ui|5PSg>AR|Dcy)j)T?;LaEC|}m6HVITGKeA;MGiS?63l& zz+5w%!H31B`%}ocD97AvlT`nb+?LJwf5nn` z!rukik(<8@5A+bP3MW2g-Slls?@{ zv*VCTX4MXlV?zFLDP^j9rq!jdY4UiVG%>G#elMt{-e{-uEUEOj+1Tegp;&<}MG6$w zoJhK7s#pR)J*5jZytc$$7ptK)(AV6&_lN>LJaueWode22uj8m}IWwk%2(j@db^E2g zyNWGch4%MkXd#%#S(W=dddJ`#qnOcLz%a^%d~Bn@0F1!nDI|_um#^*-xkfT0d&UP)gIF^Md>#RJ({)o^%NZmCZ{>!`Cj@zB&O_vh7;nx*y}-$MA6^#-?2 zNM(M_d$~OQIT0bAyz{gtT`G^w#OcRM_oP2R$7I9o*E?VQG`l0NNL7>=*ST z#9X@AbD8=+mXxuvK!iQR`j6{35Yl$mxvkMCm6bTOO)RzifOp|n(xftBLlFcO_K{kH z7y0MN+dGLRzXAe5rQ3kqSn+Ln8M_75v-f9}5Qsrwe`h+ix70q{cIzvYP_}$Ny4Cc0 znd?u8$~#Ys)($?kZ+F2w0QPRJn(6OM9ZxPKeg2@NecyyZJj0@L=9lHWlVw(u>^+F% z2^wL)-;^Z*n|;cSA#2RG%?lcgc;{TMpttE$`z#y96~M#SP)$==wVJ(8&*h$2V0GV0 z%+W|$m)4nAv*$I$dm-9^6dXjoJs$mg?AJe45(^x216=;Y;8kFsdD`fn{{1bj1}iem zDK7nBlcFpnTlvcUCo~qj7ip%WOs0op#gl!7@P-9_WZA62WR zt9t>;5f-~;!pOF2gv2_dZ^JOZVfI~Rg`SCqhSc>Gda9w-y^bW`m^BG;gFipV{7Q{* zVJRo4!_A|6OaDDIafNJ=){b6>I*B6)3TB0*-Q&nMGh2y=Jn^lYZ^Mu}Zh}ER4m=C!ZcF z7H;TYywzu$Ewa`s?v@NT(&`ZEl#8WCTeX4aK=4#B7t%F`o5C{o-Xxhp#9mKLqU3=^ z14cPaKZR14kvK+3GVwH_ug>8!>!7v1eF{~0fU+Wz*=HXJ-_TF4mN3`QFn-BD4y04BXKH z&fswYz4>bXwD@c@i%G2MH<1j(!TpmoA^l!`D~Xanaa*y|!Ck1XjRS^v8VOO+?S73Q zn#Cl0Jxqj5xiO2B@`jq^f#!KWA!RQ`Lzc!#>w;> zMG>vCRaOEV1Nqfcku_;4_D)UO9Udfag6WfswK+&zuQp=x`r#-EFwY1FH7gZg+GbLd z%V`a1)S;eo5^Vi4>ekxxlo6L%IJH|_%LrPak2mh-zDpSWC=)(d_qzr+>>616X z5-lxynRVJcc4Xi;tsUekU&Y7sBWge;$bM2#Y}{#{p$`x&NwOb8gUFMDS7(?X563%g zUz^6W@-~czgXvF{BTL|>rPSuN3zeqqii`@7iS&r@1qC}4NniH;Hba6UhRRd=69f2A z=_Lrp*N6C1OO$<6M|SCT!HO~4&}q!2o|IBQ+w}yoDpHJKR}ppoOqrO7V@yc-St#65 z@1k)>JZ%sE7dzpsH`s|kR&jl?%&>9q@d$<|=#JRQz4qDjH#?^*&?U0Jr+2*xSoqwe z^?0zLuUYZ-OHG`m_jm`F0>*Q)fWn*@sUrG)a4AT%&*}B7Pb?>C6I0Ek@+6Y6yY=yN zxre}##)(Z4*q*vSgwlwy%!r2N)Kyw>zw0e3FOyF2I}OuTE;WVNzSLHn6~dSH&$cD$ zOk&mk)h4sYjLW#vAvm3Pqto0A83`2>Hg0htH%5pfVn1#Vp3jd>k!vQRX^e`ZJ3gsF zbQV;M1}pG5`MT=j?VfPdUBI)wwz2k_n`l`FBDSpY!2c-j82*=5q>0)x((euZHu!P0 z%6+0N=`?CmhpkS>a9S^^=_olEJq<8ws@}I9(@@8!aoled`1Q~G1Or(6#*U!xdLc?D z{!1p^$vt~eO)(AK{cIXm=#0(?YUopAi`3dQ#i#ZSiJph&&H9hFZ!-mR*kFzHY3lFV zk>$c`zn%=8!X>u)X1yOqP&oX$BSPatpCPuNztgz6*AXZkV~X-eTadHSSta_QWnA(Z zoSJ@K^z0;BDvSI!VDk(UL45qiL^I8rsNQuD$!w` zBH5&)uP3@C;A}2!G5uLB$$7R%pJzY7d+U}Em$IC+&Tq3VyWK_n_M_Z=JDv-uUi_F9 zXIT5<`J1OahcD-lKfl@M$tf!&skj*)P_FBQt=(%c>x1=rtSt3;_rBJR`)_W#kItcMMYbWo+t6F&swJVzeLo%c5mnC$Tvap z!K%|RtW&P2{9{bfU0u=OY_E$L5H;#cF)YB{V*0Jc!}W9H7N;jn(^cK4Zxz{BX!;Gg zlo?~QXF_1g_Gm(gElxy8J^87Hyz)?-9GsuHNU7RiQlA~6EuoVvOK+a9&cSK%oR^RE zUBUHK5Phw3ao${zT-95Zoi+isDCIKKfjrHTAnipR;UbVDsRRDXCgkkbKYE_e(DO7E zI9G2x8QOiEP1sh|$ag~Y%srBow=!~3ElwIUai-RLbl|*i+1#0`@141u&h*G`dEe;1 ze+a5^3OT*gURmDBi5y}cc6oD`|3IZ1!da7{qOt7LAcnV86e7 zRVL=M|K$!C6__~ohZXd3?GMkpUo0qupF5JyG4&)htyekLN`mf_4wul;@bGBeu19M9 zc=_!Ne#<-=Z4e(^S5QI2ujoF7$TwAxM5TJ_D83b4WHAAv&p+-kA}V5ERl^(%1| zWx{_c&*GP+^Zl^3eb{nQ>iBFV-2Vrw0&dQ)(y@lZ747NiX( z@yFyDjs3!Wks2gIHRf3|w6qFCH)_nkWwR9NLMO_yzNMo0_KG^TEc*&K7P}icsYiK1 zE3F`BGot?dGtVM_L3Z98;|d6Z$+BV2(~?<+Nif(md9obY1qg9Dxv9gyqg3?FQaJe<_8{%Nb$vVAPQ;t13y=k4@GKW%ECV^%rUTccb$`9m(S?5bhI1^mnD_c~e~8HN39V{t^}1I8AojS`V5+#h|TUGRiz~ z0bblRL=l9+-?v}YmXmmb-)#>YWKv}NJH6)9Ys*{+_vIA&;7R_%N5bqMip_2^YA62X zzDh}(ayA_|qTA~up;3pc%>@F2LmaY?h$K~WV}ek42^kWq!ZbtVQ^#q(Nox}9PZ5ul zQ(Rq{$Ax0fnw@Q3xCu?OzS*7KA@r;H{bovaEx2e_#CiAOy&Hh$&cBFR# z@j=P0gvnjATtCURHPqXC#66m$Th&mC>*aSu(}={gyJ_&Bjc_Ad4&v#-Ng)K4 z_nD#nsjN_zAVrD>lBH_UrGQFQKR**ok6GXoZ9}Lc-VO3#wV2~>&5{9rMzcQGi?x^c8@8Ff#Kfz107QOBy zRz;;|Y{_k5_at`2TUwS^y$=t++=+i}=;-9>s5V(+iTBs2YyWPee!=?3u7(wy7wNg* zNpdF&^vznojg`zH=b3<8ywVLuFSeCtS9;@~K-2P0_JF=5s+wLDlzQ=X;!NKozy(&+ z$j-n`CaW(I1H-tOcn3n{pCx3UEHZun`PC&}e#O#?@@VZWbQn)pZL(!GcZt7=omP$` zM{OT&EBbX;;cbCJ(t8Iw^Tuxec!MnrzV{oLXN6yjMD`EJNtyC|=jC1)KCy0yGsfAr zXsXa8Ws>Z{X%6q}oN{!~7;b>`pu$ksgs=mtjE08~e*TW%u<()U-A>VAcrh@ff9d>A ze^*(=`=hVSUBI#0QHWl0?siqZDf@G|pb!^#K$LjaTa!ND!P+sUBigSg#X90*C!6V+ zAw_J&nHdbqkgmegsw?Tv=!(-y5dPNUP7-ejJQ@CStpmLP$H{?FPPC7ld*tu20!~;_~<03XLFh|$z<^v&$ z;~U0gqS<%vek+4m$#15(4wTv+dwE>WP6a%Zp zt3b0N(Pp8zuSBvWhIN*)l8QMkl>x{J&iti4des?QYWa*(>FRvfCT)wV?JuHhA;S^3 zG7OF{tv$N=Mnv^JE+#7~n6jx}6k)C$&Ifao*vdta8Lx}8i9s%R^hAVqI?<^>QqzAf zzVOp<#gE6H#S7bIs~UH+gRw_f3MUlb>EEZez6bWyq;9AVqrd2e+|Uy>mp6U?dsKe;d#jSSOQoNejh+ly&w#9$N*%zA#s)uV_K& zIc@M5u?uGc^Q^lT5n3S3P;s1=4Lxm2hrUxR!$8s-hK?x}#cy?vz=axWzx$%BvJ|Jo zIGuwMO&~hw9!7B1XUp8SOMfGO86TY+@i=iexEC>LQM~P9OP*sBJFO7ZQ?hVxMa<{x zUdUH^IlFqU7U$~c2Je`jKI(zmxMp`o8f68VPT=Z9ziIt8jGy9YxF3HWltTE6eeh!i z6T8rJhDFVBb6fTE{zLH=*9I3p7|XOe+0fX(XCBH`q^l;voryNn^dP~9-P7VD(7JL~ zNw6rJdG5k7zZW8etRptWN({P{L*^c_QU=LA!*w4uePG23m-e7^&4F>y@l`%2xY+)7 zFQs7Q_wh|&;tYMs7?E_6`KyhjaPKEuN$`4aAjQ>FI+i&e3==1A%f)2EdKF4@wk5-^ z(p&k~hD)FO7?3u(tA8=d^Y9*DzC4zQ@ID%Sw`iQJyLS8`hYt~aruMcNRMg2bFG#dS z7O6mOj02f{ZuqocaK?a2!K8#1Vlp^nOZsA&N!vrs_cGtY*R5{UvF%;l@SC8_=aVM+ z*?Qek*=Zz`YNm_gT9oBodv}KIB=4@p|KHoD;eb@XP{+iHd}66&fQwv z^!&iGitrF%(2UIe-bPsy(gQ97Vaf1JiP^PuhIcO(7+LPOG$5pMXs^K(-oxS7QnPLhR$jXV>#k_2{a5||VprK=#+^&Z5d;Z+*i#&8l!%lcHunx^ zFiQc8<&Fr+Z_xtOpSKAQAntwlO%P5^8?H4pF0DGPGY{)FuAGD9i)k_w2&L@#KIN~7v3y&=&rtUDdkDA+cn+hjf1`O@B(%Q7Yz6lf z*DEGb>(~W=3#mjuh0A0VLJ#xccDt=RYW}cLNHT7#2?$!iv~b{D>V+{m>y%_T+F~NT zh~dR3Yc`hlZn$vxfzcP4VVRt%xM$uJl6{}2aIM63ff@4woki>c>k}2?K+Tx~!L^U& zRpVOUKeoi^5Cv?dbn&S*2uFaXO?X!GX1bt*b$DEuF>jsyW!&6GnI=gJ5=YfjRh7^r z*0rX>M_>=z^Gw8`8$OcXO4!6BT7%rUb|GC60Yz_%cMX}$81VxhyO(p1a9e5@jLkYy zNsF4|E+{Ak8-6<-OWOoRnBYsHo57Gu|rCtMgZ)g{3r?k)U83o+@k$D{tNW_8$>c&_>n zSR2l<`WVV;<^jq>{a&#{N3yr}t=S6#CM9-?q>;l>qpYx!b|#~56WCXx!M%4s{ZCup z83H%jsXTn|hpc-}tM5vGUNRK&wSRH2Cjx>F!}c zE@R$kZ6l)&sP;?Qkpj^$!_QQ4p+)c@xSMnW`D9+04GsM#iy8$|P2K&YK{w&X@6k^1 z-NVg@)xIj*ix0aomM_F4n=co+H4PW0L@8#LgXfq-W8Vt@$v@N1_oRQawm9fXf4jS? zxd9aV9-J`bu!Cf?6DCP_OKoqc0Z+FmI?xjRj_`B{qP+ZdVhc>%zu$6I;^=2aBO-(5 zALneO06oCd7zy~!>k=V}CO`K;spHv4;AK<@MRMdWFUy1i6uQ2wP~?*pZ}gKWoyp90 z{Zuo1l0$_7p6B;RSk|5p8Njiv2E7_L3ei9B0$^Ui7&U8g($v~9vgOi9_r3;&O783< ztYBYg*mFb}c{B+ur4QaAb|O8)?l}G|3D0w=5+DD@P@mVAg<~!wrJ`RbMs0=v*`^rH z{=u*=D5>(hkWwu4B-=i^)p=|&bVZbK(7JTv;0lt?`-}u$1Z({XbS`U2MQQKqe*J)= z-sH=qQgKa4sPTB}hYf`P?9_e;=C;Ce=;6Swnnk_zr$YN>5i8pdd6i7zq~&FTQ*;WP z&6-8I=rBt#=%T9Xbp(!tECQOoTR@&|k_;4HKzvA!{p+XTclPg_)CddF zYe#>~)uSfMeGq<^HZ55w-%T%)V_q~PLr6t>UV5ujV0i2LCsudcy4&7`+bJFiSY1o= z62^Nv*|)4T;_W#Qq8p=p5W;o$TC17~`V6h&bKiI`bG{Po#s@4J3Ls2?dIZo%p3Rpx z*ulI{RQT1ZpQah^>lf8&zl(Ru+=xxGlW_|d!&zs-K&EbIR@fbxL!SADj_mSxLiW+p z$;roU2}&hKck@}LAurzy5kAm;%aFufJFnGvj)>9$>H=>52f(y=6*sUsV7eM7()`rAqJS1FJd4hJmf+{5SysQ8FkwVjrtbQ%?CL%1WrgKC4I z@{KBmqB(M%i!SY+=Tbe+e4n{>5AP=q^Gq8F`y?Iwxb4$eSTAJEIsqs}#v-qYGfkHd zG08yx=VetYsUnV$XZ<(1dyo`fPybKz+VRDb2d1n$x$6|B)h@;cp8PR)sPLDaA>KSI2E3?j5VZ z&vLbj33-!~IUZwy$Rp3jxpHT4n&rL6(AY-w1&!DdS+>EY0(T5Er&^>yF0* zbBT?J9v%5BeeY7YTd(@rCngF7goqhi4Ebz6ahw&xW=mTr9+ zT%QS0tgAswhn;mx2l(H`y4SJaqP3sS9fp00bIP}CEl?bT@bauHaMWuAMHtc$%@L5j zbA3Zp4UOJO?&R|IptiDwDxC=4jS{3|g9hH7W0GHv13PsfMhPrw$E_ugmE>o@W89ZLY2EH5h#g1V`2?|iNUN|Iu_ zQkFonk(v+^aa|nLA}^lCZmgT#;n41SAi?<#W|x|f5UFX9s;XY$n&)dhF*-#jS0ZE# zVp$Fr_O8bee#vQ?gG_&)f9Wvt2K@od>2)<|6Rf@ikUg{6kSCSO?y+Tfk>0I8Qy$Zx*jIvIgg%z%~_jB(b;pssNo>w`Fkqm3E`2#zv%^g`|r_hU!{K?87!o5FQ3UsDb@lK z^=UET0MA%0fWUvBek`)wA2tl`NR`bm()JSUT3#y4ju|s12qYsOGmbiQB-F`{$kMDP zd_#k!>!t$47N_!f^%(=7zH=r;?gOmL#B!pF?}UW06BaP#8dUsvO9c4Q zQHOXL2q4G|Gn5i&-lRCU7uR!U47?x=GY{f+U6MIT3x3Qtpq=Fok<7N=#AS*VG2|ZV zxizcX(K#x38U|sF)_9Z+s!*ojwD(ZS9YwvM%I2@Y@5ebLoPQswJ(-K3-FEl=hP-_L z)hW{;xwI$z$=-S52@Y_sV7H4Z@dwN*uBxFr>LWwa6o-1_6xh4(Nm{=IQRFE?DT@bK ztaurS;)Sn%9+tK0orQ6(mdZ}WwXwL+Xz(PfjV&Hxa<$3T`)dUZoBG9sE|x==M`c2( zbl(Dn&)~}Sfy#BET@Z1N0<~zGNlBlf-iW<(?FYx2r$&<0C^31C)QCcnw>C-3*j_|W z39(dNM5-4Ku49O6E2YeRNczQFjg>P=@11t>1subzKuD9nVPF-dy7>N}5xM(^PtboO zbfq#qnHN`E`0)5DZ(`lxKQq$Wdzm=6&2KE#{$MkL6)8L?pMCM=z1YCkR=%Nd9xeIY zIu1~lc4M1j|Ak2FDxR|8H8QPiO1Cs$dS+@S9PaQFSas%g8@8Fpv5O*$w+K~KS6(xy zSb!{gNqgW>jG(3Ber`w!yX|EXzCoGc^M$X>kfn_Cg`xmTctMwf|Czzn%-wOwhPsgQTS6SWPD!3i6h;=Q z_l+Pi<<`nTUElFuvsa!3frf6gI){(Een>2Xv==alK>IcdIf%C5Xii$w+w{Fu3ExZG`XLkzAx%j$&f!rm z8iXw=*F9?1Gu5Fnotw{7PxL0B2#+pF8WmeKFIf zSjb`7N?cA4@_!(eY_J$gFKEgmj~lC(O{G{S`>kR@Lu*g?HC?msl=nC1$oNC$9EVib z;JX~yVOaxfhAC&0`zmUBoLpn{kAoaZECGO>yfi}#!%r$7`PTmD&fDmYw<-Sokx(^{ zgmb8rhX0d69-X>Msm0*Z+k@rfz~n28eoooy*q)E)J4fuDG|Jie>ka)0UKrrT)0)tC z^3F6f7so}c@P_UV)P1r+Qs(`t8CozDGNZNvxj?r&MWd^*xKV6zboWzxH~+0*horX* zJCWxR?wxuqM1s6ugF9pnT?24 z-Bf0J?{!m-bn;;Xm3v{ss>+5pf@(kC)O4)}v-|*Qod5QL)wy4z%c>`@F9*T-B3(c# zo)@oXX~>+Wz)YU$G$Tu_?~ZnSjJv`%5sQj3%9@91kl>x(-238xGDt;|wb6%Ify;-j z$)?xScujuR=9Ct&6SF?1k9epwwJDb*Y{<23k;X?A$gA7WkS*1&Nm~qL-IuSi0I5hX zYeNoiPdOCHqs#4vsK-xNuVlvP9r@beo>R`43 z9{~43fdX+&cx_lGL9rm0ENbOM6xm!gsLQj^XYm=x@P;wek4psTiRAg9FJqVQD)m5( z>*jZ2EJ0n2?i>GIqi|$HZC8WPrE3w9e4)EUL)BHG(UQWKsQ_Bq@ZXPjb#fWQme5ST zt9s*fJq0D7^1o5GA)>|_is&X%DVqE%JA?-&H^V=nNGX)N5ET6D((M8x_Qm!=jHX)^ z-x{7a=Nm0V>P~8^>qC=+{c}a3N(7e z396-q_G#~Q5~Lt@>*O}rJmrD~b(BpG?_nP8)xmhd?27O+5KG+x`baHEu?wBknD(#}~|>Q^f{+v;iuT`{TLN>8lshs>>RuKc~gLaTk z=1az$5B&-T2$;VQLq~vNmRL#90(WQJ#@cu{&tt)=l zD0LV|d4{boD{_t=e^8q_KseMiey^!P)o?%J*;dt{s7{ocCWntN;Y4a(t>4+416UY# zB0E63ui(Q%)F~3x6lzJ0@caQVCXwH~fAEz+j8MzZsz#ANJNyv%;zIXOM;dYmI$Gd~ z0AQfu{b!WEgPXdOX5thJvrWfVTPxJckDXx|XG1ok;ZF_yE~yMrBoH6@zL=Wp)hfNQ zw4N&ZGmN>7*W8C%6G8Yw&6~RZ@TpV%Y9G(?ps#~*M*u~f64=Qb^3ZsM*G;;g?;Hd7 zW3^iHjYF5ISEZQ}B@#y@Z4yaI|L=efnu#Ayk({WHTl9`xxp;$~gB7lHHvy4qIZ6tJg< zv#lWR2#efXfYUR#^Sx$CGk$C(7W&MCTdch^AwI#!8?tS zOv@GxaORlcn?*I_Rr=zJ=Dtu;lT10~HIrIBX_G=RBPm?Zt>N2YWr+Fre@U*;hBp<% zOM6^D=p3qPCj?>blITVKmm_N%jt(haix{r`z8|^_a*J#sWFbI{-y6EaoWpMAM2?X7 zh)ySH0H8g9{}58qN(B24<3Vi;V!fjGGM*)JINkiNmBxGcv3U*QXRdgKMY#K+H-bgLD&#O0x zWoAaX4c!|kUWxC_f?1q~Vl{T=@K!3t$}N2lRY6-p0Z^&6__YzuAz8|+W;z;9@g?&s z{ys0=ic-bXqUhFs^FQ55gDz2$d1Wq*R13+|SjGB#p=~`gz$uOz$Dh?)T(ypI!;++U z2^1kqeUav~Np>qKXlvTf#{%A^HXSzbdBkP&4$Nl(0NqO^_SJ3oo|K;qjDdA3TfS z)hEnyJZ04nt2`DY{QOgrIyOn%MN4ZpWKOB4)cn<)rdS#_QmV2o1!uX*C1?jInn z@=&ct+py1^qsD>y*AF8ravNY-e34MeNe0fLF|4wS=mzy`UeDQ@7TC_?rN=qCg3*sd zC&NzhViLkTG{wvlJ%r4vhPiLuNGoZI?~gDLm$E)VsrTM6pPM|a$9b&d z#R4!K;rL%wP(W~-uisIg;C1aV1mG?ZRwh5D>5mL_U@!Dap1z+=ACX<@l{7G3&43c_ zdWJvWG?g!7eZW#pT(si82Ea6OpRb|QFk1q*0>{SbDFP`tutdS zoT?I@{V=W31d5yPB#SC>Tk|Wfi&5fW1qTB9@ItBrs+*`{H&E0U4>C^I0d9`sur9j; zddViH0fwi0hX`7EDf|p=x?QEk6pm$Lp9iX76SJVB-p#PUTz~wAUrhj)n3GtDsqf?k3TmBO!IzhRSVE&(L4`Iua+T_J=5Y3Hp(i7k7b;fc;Bf z+lV44YV%qd{p`*I8OsI{>V9d$W$CZ_1x1ERn4Z9)`g-{D&vBQ8qn+ZGW5BzYqp@X} z=smLg&9C)`ag{YS^^V^UiEQHv>rWI~6SZ0?5-as;zy!~x!r?cWHG+*to`4VtI8ET>@v${f#;uUPH{7S7NwK&wycHPt3o1?^Oa81I3hDry z=o6KWi80Tws!&G`s4s`y&9=ozwy7{5sAq``cL@4*OTewiEnO|9anRG4#aafuvl+}h z&C?qF>Xi1v=h)L~B2z_w_f;PE73haYbp*dFWjw{HpRpM?{tub6tM14w@Hf=VMH>5X z_dbi`{X0p%;bX%TJl**IM+!oocBQQoYBm4z_J%zNkO(Bvag%j}h5T{9Nb;+aaqX9- zHukm!7DTkgZueBRlw|F=MT|XQ&l(fTWCP;<7U-v$?32p;Ez|#`%s1w$;DXNDQzHXT zkkLSzXDqG3+D($(Rds(}7oAAM zKPY`M8$Qr*^{C80(-qkF0xX{diDeQ8ZMx%&d-b_XDi_sd-Wj}!1=dXKMx9m<@_g?A z`lEE0hamo3%kmS;%e-;o-i7U$Ik(Hs2%dz~%B#xJHD8<%W|)>80Rcp5WE+M(YgeD^ zf+$Kb98i!|oHfpSF8$8=-{X*ksuk`@MLmq5Cb43{AZ-ghN*`?9k-a;upEO|DyV5a6 z`^*$Rwk2b*AqnIZ@M>BwX0UnUs1YbL+eD0=y={Ykm})sxW9^!|l43YDob~c^kX`#6 z?_gqB%6LF~{s<*Z!xKLB|R>s2Mhg zjph?_#US#p2R=&*T{0UCaMgMkay6~LUKuQM@?G04r+SQ_x=3IUyRHi-HIR5Wzmikp zFSVs}H8LIMLr-rLbH#&o)76N9ll*V3W~Zr7K*6`X*B7toY_pGP_*}zQdd^|<qn=SuV8AwHPgjwB<;@BB}<@30xpmk?Ig?JJ$5 z7Xw#zB<%uf`kSkSBoB{b4tY<4LqG=d^~EjGf6_Z2phjuJ4{Ji%G%Gevb4U^}_oZXI z(%bYDa5nj=GE}AS3wNEd^KAQ6Ga>7S@;8%XuCM(x!^$$*LaxYbnn;#RZ})nf>jh{* z&I7(m9SH>reUM_2+QAA0Wrd*cQ@E6GNSmLq3i3+Ghne%8Ne)#z6Ltpts$6LLt^N7; z;y|&e4iL1y8u=r%%ILeL>f$n*${iZeP0IXiJ6BD)RNzDjTvLm zPm2|zZM=82AdLwSeZl)$q8^?>>JrurYpuRphEARRnHL@kc52)Nps3&`qyd>OudOc2 zc&*9nK%o}30A3dAFjR5{##r+WU9!(UaqYpq?f-kkmzwooyeFi_D^Obw`Q`zfQcMb!B_I2Fu=v zTLHR_$_26evQO^ZIk`1wpm8bv{3v(>O$pE^pu5c%L9sXV9_VL!dLrwlZ0O-toTp#@ zl-WJ+Lzz+Mz2nxlo}aAAVzH9;pl96R512~E_oyLG&FJViX^GHX`I37Q6RBWuJ?}sf z;1!Ua&}AC8w^w^mTasvsgAv_7g7z$U5^bR0CpmbNBE(M3gZ`*GzLe!=Cr7QH(RIeB(l{l3Z*_&3-n^eH~3cEID}uTN5| zi}KhMJgR9!!)2B+MouaLnvn?2h=n%kVva&N zmfl}kE1YEus`ek4N@U%^QmgS*F@73se{Y)z#GY?99M@*jA5Yfnrs{9tG6M|2OB1lo zxD(o3B&xVcTQ7LZ$M+vT*pZBE6)Oid6FMcS!+d+fs_;DG>wHa_X53C)7ja=CEso~; zq2V|_u6@l zb4@#@s=wW&y^K!|v!6fn-1|jT&#LcK|E{XhvToo^w0uK0;OC&k?w)t_Al1>{-obuh zN#fw0Oe*^oM9Ve1<5_B_=_HMFo|Yf`YG)($BjVx(KpugvEN-8ipGc}oP21}562d0_ zRNSMG_9HFycj-IeLYb5#dNE7M&nn^3$#FO#*TKqeV&EkHK5HAC>H$;la0ul9?!P~> zABYElEEE7YzpBQ+YgIF@^OrNIpyw~emgV@ObVmfNKgD@TXIMt(W5uXQrJ-73YXbhX z^S<>c#;g@TTKLrVA+h0u-pu>lkVW-MFiQ;#h&EpaiSghUokB6GwKj;qNi z5Fqv&dJWgc&sB(hLU;Gy26atM(N3VOFH94XU=7wolrWr%HO;nOKq5-I8-)?KGwj;1 z7Ve^Vq2~cN;%_&HjGcf^Rl$7UcJSF!=lvYyO%0rW%pdz?dLs+cn>PjlmJF2R*g{=MB76F3*<1_st#oXsL z_3w9>xyheQlGXqIQp?M;td4uc6!Pz||9)^`x&H45Mt4c+|9g&E)1ypq(^bzNKAz=& zSD{xISq=3C-z1|rx_-qDf^S^JSHL5IZ-9N!%RtW0Z=lSlABr_f0}VgWUe$I=biDA(WuU=Um4tegIgP|ROe}{rHTJ@ z!6O+-aErc!1XQolpPTu3$q$3LM@QcEyi(=)_e>{UE{0G4tbtpLWKj5~=>7K@2k-vB zXZ%_pOTdgtB3Z&>ZWojJc%zIv1RTmbG|NwO3~vc$sN9&nZ$vnI?GBFr3uc3^H- z4<*^dW5!I!OXi_MNMxvFemx062V@*q&{Ktw5Hh!ye;phH#~{6jyIkqPbtYCM&}Ae` zjCjmxY`1b0j z1=06pKDsT$UT;G6geJnSlvW0j2^V!GGY$7?b$N^Kr({`4W&91 z+y5FEfXO9ZBCWtNk~&_a6KBD8!e?&hSSW5G&e+eQr^47QG-F4y`O+(Zz-6NCb9NNaIs@8E#Q_54lDCVR&Dzf4BY%5-ZW05h7EdH$`y;Y!NaS>ZyT z1oT(13De^Y*$=#VfG*EXXk+sek0D@g&%EUhPjHgluoSVTZrN(Nc?7@W|@6-6wZmpbG4T z_DF!PG)}jWIG8gwZ|(5?zVbhN_n6yxumT>UWc)=A$ZeNGNUlRXm%o zN(>=$$jg)00i5uw%#7m$daB%n09i;KH(WgQq6~wy`TmgwK8sUEz&!9Z;Dn&%Qhh%* znqcAs7~fxq8CTd%X0o$3{&E-&^uI+|-A~H*-y)o`%`73Fn~*}XRDK63r#gBQm~hz0 z=BwWon2C*fu)rqsk@0K58B&?!W-4ARS40x~278~l7rW!h0*}NZ%IlpXM*vd@+HFCh zfO7k_Z|m}fO9bXW&OkcHfk{1Dr49F4=ORlW1zn$@@N z53eI*m7LzjJby)i`uwd(3#yx^yZa~03f)hLPXE|t&rZ)r(4!G|s_iGOPZrvK78Cr& zVUc$PiR1%`fjiwE)(UjpMkfa6mkB~pj(exx73v}G$*4}3ItJ1~ei zxHLYpc>-Ak6ML$@yi)FKA1{LJ9&x|}4vP$aZ$w!$JU#mgYbl4tl)Y_ysX5yXmPAN%%)&_KOI}t|J?~<>)B4Esz3QsddzJ&z4vQ6T`iK*Co)O z0bi7O>IJhK`m->?r@i6R6HB(8{TWqM(7d(@p{3cKi)v%vUMWI$_@gg;+UJ4}2?0NR zf`5Dn-EUfG(g5cMbXEm^IRo|O0&}FN4XDL6yOXx{T)Ymos05cDVRzu)3m?PyiqY=_ zzM|xH_S)tUxs1Le9SAmrj?Nf1>I(D=29X`-qdYmnrv>PTcBRbN;1)qhOxe}DI6k%2 zfndVppYNRRkNP`H-x2j^{F{ipM>oI<*cVQuUUj>8>Lj{v>UzRe4WdVXL^;OdMbip? zqWF%^_chr0qRubdKak*B{7PpwUl#4*iC_*rfY1v431tqe5+(3O^^b!m+~Y(CuZQSe zNzk7oW2{Gk)$A^mYi5&e?#0K8-D}2G?O+7;<-?KI021?YDtFwp;lO^@Ah(x#;t#TO z%r=lh2eDOSznX|Db=(xxu)E`k`gmZZU2!ChHU8=7fjnqcJ)itova2cRRW;82*kbvC zdR6;Ii$h&vKDyEJ6aG>4m}Xbir$F?bVCjHf*FgGf$Dk+pZB7TOgofmm{vS)R(wR%g zgM9MMkY?2TUTlfPeAEs@+CB21K-_zSizS-lk++?Cd)h~r9a75D^mk}dIMSZDvTY(? zh=S<9hkQUONAE20>A>@AynRv&ylj=IWDy!c=8Lp6Swn41?kgXjdVRV_#9@w;q}8g4tl~Jbo3-FJ2-0G_RTE| z-6=bJj4Xpn;@k_Z?scK@65SIX&pI|CcLg3%(1(3B=BkDHq%8R=qQq}pY&~n*{7#c zJ`1xr1pfVOSH54+)eTWRUlk>kMTzBM;7FF_K@vK;*q=dhZP|tQXCn~*S{v9Wlu-WF zr#OtbtFH@J*oJ4dkROQ{)tzw|b7x(h==Z?A)A%f?fvL_NJuOqzS;WnwKmH*&+VL0+ z{tYe_g^tcqoLyk+9EFzKk|{qs49iF1riMP|@fCl6?0*zJrQF{zrhsaP|7CR7V<2b4N2@-OqigL> z;;`bbHN=l^=dk)9{!Q|;Ayt{$h0q5I=_ZmI$BdTtrUOAiE0i>Gu*{KJ;dWtxLzAPSiBm9aj-dMTr@R(1UtiE3=S_@IoF(vWBNe3;deVZ*VUQ*}4)Ij+%BMjJSKMpm)d_ZZz&U#PSu57>w~tY> z>|20y(ZWA2Qlu~{)cF5fVc{)<*&xly1L>}T74Q5C)BAqujREp5A*V?CFX8~PISX96 z(Up(>sL?RQ(M6<{bu4_GzhWUGT>288E&h|LN`QPMiC!IR(7?E<#JEK+_N^pwB5^c5yn z4!g|;m+pL7U(CMJ{Y1I7ntG2AYC`>f1lR3dL}-rM zO`}g#>~9`(TWQWFUT0n@$lshwqdmzrOc=|-Fm{5{zc4s)JidZ3EWX8Ue0oH0Lq0Tg z8dYrMzt&xNHitF^Y$oiV6R(DoU87Dn7XLtr!o>ZII_bR(*@dtkg^yVs3K$PB7w(L- z`(^{BU1m=S;M32p-M>{oR`OY3+&czI2b&F18}NKwA$r7hN&3qHf4rt`L{wd9U3`%a zAzkxTI@mB?sve@;B!tFcJUo@~ZI4_b#*b{iTUVIGL}J3H(_f?xBmD>O>=|_TD50b9 zNW>9)@wG#jAY=Y|QW#_xSd4}kk;keps)wfotv>)fAoyRJm-ulVYT(Eq8v23g_u>G1 zaWg^j^zi@11Bz08z~M>829&QpGdo*=RXyh#L@4<`C+F7T=|&5D{iDd+>jC1y_c@^M zrjCn>#Er@Sg$`UWh_=JkHB2w_{|{5V2T+El#C8VODS$FQ#|+T?_Vxju_^g25++ZP- zH_lbBU}Oj(mYa3u%wrq#j^=k9fJf+FoEOEVS6vR`sx@sVz03j*|Gt|aXs>6dbN(MR zBk{VqUZ7xGbXo!%KHdGqbD%192v<9ag8m13)?ak58z(P!D%D?h!JIo$p~SGs{wXlOk*$L!Ateag>iU1pmAjP<{e=^aLH)_`S#`w2~~ z5o}GAEMIgc_lH(-Gb>%p{Rj37dbB5OGoQ<{u8Adw$5p_f&YnuV`B;bSbolfjMr|;y zBG!Ju3dI?Fmm(HI{Xc`Kp1fE!6~YjG`yDnMOvRsP3t+J8C|-M}TeA&x%gz3bPiCOQ zPbRb!6wrW+&_hq)a{>SnI*{N$ z+56uEUOLz@p%Ff|*9&+X``r~KFH67K^P)NC{m3DWWx(HWM-6pZHAX=O?kVGZr16BZO#<+9# z=a|H2ck%LfnV_ZCq`&I(hZXbwr37UU8L{FdQoiMP9kuJ?w6@YZvl5XGV~pb}MjZP}-TZh;x{r$Lkz}^AZ z%DB3I*{#aMLrIuf- zJCdu8u3vOne}DX#LW<4U|sBFoySOI|+0Ubr*#gr(9P%s4Du283JyuEk?~Kx;?8!>ploya~C= z+c`?nVaRR#3v3U@ut;ljUsgRicASij`Yz9~4kbLb-lj~)TN)c|uY_>LA_57-bRne@ zi(g6kwfY_%YaeZVm-_ghc`9ZJxxc6joDSgll6O^vYC9*~Jslcef2ce4HBUN9pMChY20WJlO6z*oV;nH#%>oGy3R|f^ECq44a>ldqoiS7L$rn`r+883S{^;CB%?28d>E5iK0h$r3+QC!un*0Xv40~6u@_m~bS^2Ezi@AtA1~g96DuaVgOL`)o|DEThYd+TL0Ol_`{Mpr0ZPPshrHE56 zIy~*iS8D+w=Nld>cLAX%*j&ZSj;p)V5?R3`S9!!O1uuO(+dwP!YMw=kK#aX)+q&=n zB9rqw+pMj2YKOzoULY>k*9hi#l{q2ePw2T zTDb-!zUc;;QM=`hMQvY^UxGwG0z318b-r-T2OJvx5^=Kqno|l-hGZCxWzp&SjQ)*u zfVA%BhMUTrjMY~npPds1%8dt$BVb9(T1kvrrZ#{nYa}CQv&4iFk*V!hMR6B0Aw^$b`g{xDzVDBM3J6(HT}k!3 zu$sZiooy6Fp=%C!;SK9B z@ho~T^^Cx+YSjnI00Hw~-&h=Xz$C6*o!jaK);8^O%X~?u3V(XqO|=0bE@L7W89oBG!P z)Vjm@5H>vc5Ei~d6%|9Q7d)aTy*>OZ!Y=>35N9?^fz3s!JZIL4Y{TWB5^)ZpTY%}Z~>!&LtSW+tU z1g*nw{G}@l+X0QXmW3Sz<1)1Y`OEm#hvhN9DPCZu1up%yZ#llicR9-54fb9b<5;dO z8%KUc4^TPZd$2wJCmm2dguNz0&xGENjN1>LWcAeBXrFQ2>w_XlPIFVG)Qod5o8GZk zRb1XouZ{a&q7r{I>S&3yT+GRGp6c(ZB$TawT(Mf40K@KeIF~vpO6{ zjC2A)>Oy98XdWxr*4f&#hj-|Nwy(kHCy4!edW{gTVzt;mNB^Iujog@Pb+yuINZ`q- zkOwQJ`+zBegm)+=)b2u&To!()Zoi+u*AOrYVz<~7I zc8dP|I!TddV6*bu-5IxA@Qd_rbIRh{3g#qpc{_d@`WPV-3C?awz~8l(j47ysWb(Zo zL{NwI!6WUdtGtj^aK45fudj;CG2l+dASu_0hh+jHO$FDIE6)n@Uy1xSdA+|J;=5|R zq5ev+mo$fAe*dCHX%@x4N~6uL10fs8$H%lleps2OIxF33#Bjk|S+>z*(jS8+{-XtiXcq)WZ75a zUoSVQp*?NzY}B>Gq(G1FDxe(n?$k(iv9|2->)lz3@roJH?PnNA*s-gR{%LNc-VhV6 z_<;Mhm&x+^4(USMj>JKrgKtV)X2d%!3aw<~cvF^h!b7Qq@o7Tb?5n*NP&iOu(3{Kq zI-Q8TI+V){J&=8RlXLq5r}`In2BdzA?RYOa{++mq^tZ%Isc(r_9RGaZ%Y2|-Xkvf% zW|Z*{yHClLh&t{z)noTYfu(@D>v}np(?MwLZxFlJzhUl;Z)S~auFWLL=~>#^ccfX_ zS#chUln-pIJStck(NIdi+3p%r4J}^F#kj&8Qv;_8OJ|P)W$E!Dmob|_StBdn>ID&) zp55oB2%NDl1=Jmph_JjdMd|I)&ndai!@NV$Qz3G>&j)I+7sSQSi}0cN0t7^h!}D}- zjLNZp;aIw+8Q(C~R5W14dfELHPUYF+kq-Au5zguwLFT2qb2wo3%6-)+ew=L{nmrT= z7k`{YF(3_T^e>D|wqluLhh$B%w%eY1O-78(ZXsV|4}|ikAX$BRpEi4Sdq+u})l!+{7qb!*fr`TxQ1bmW>gMt;)HwD(t*4y|$QC^A=Aa{h& zb|lZZej9Ae$Fxo7ASqm$^`YjDvaqzUJT+Y^?xQ%-=~B}V(~^6uuldwfYHOLsRA3M< zVR?i_22;HpkRJ#VCT50Wk{yi?_>AK%^{ue>71_gu4d$p+`1rWIEK2)kc@ACbsn!olqT~na2V47tLFOK3z zn_w9iOsfUe&3${(EU)Xl*cqzzmtTpWlQe#^+m%zxhr~x&y=?mwv0(`K{&(8_S)$@* z5x{aqJ$IDPYW$5F-NUu}2)gRGPIjI!46bYI|0OnUiFOiH^qT0`K1DXLxL+ZU(o;GN zWsaA?iHfT$Zg>xwP(v)|@v8P3nNri@Z9dH_L^BWsTj;$lJb>M2ZRv6xaG6Rb^d8N3 zH70ehs-q_QNJl<%d($tJ?GLbd0$?Y7nsw(J_p62O&b~~URhGYT4YGn&_*H>YJjZ%F z`!kL{Q1*-ujt~zte)kpTXnmpZ>flnpD6Cz%KRT0YquvCX@s*(bf>CzXlxt`ZSMDQh zAD;wmqTiisWuE42--UXh(aRP(%EmRQ5_OhCB0#{2SFgb-D4AzqcYHaMVVdLW)1ltF zy(TIw{W$s>*m6z65p4~8CePD>RLLb3_&LooeNiXvbMnjP@E%A6==bQffx)7M|Cj0| z93oDVV%*fb|HwwtIUdy(_oTzEn)`sN5Hq@NE6qo)&rY&Vwh$)_EAGLw2FgJarAU*s z)qVQrD}{9r+m`F>WP4~O_GLTXq)tet=B%-=oZMu^kCdH6kHf|D!A8<|Ekb$)Dm=p< zaP3r1a&7&Ev2a)|sj>THp2wfZ8y}0a8_`{k_KPbMy&rc5%)Fy7?1v3gI-j|H(OQ(j zx}AMZkk}B=lNru3U}=k=LNm~)a~L){E%~^ktu;?oY^D&sr$-8Z#f}?O`?FE7W3P59 z_QWo>LSyth?qr^QjgV>$X>(eitoU2o@CwqZN`kkP{mKdU`uOWPY#hK2ZkvvqievjD zh!)w^Fi!R$~n+%oc|v{0AZ!NAv+->?@gWXqIvKMOeg z$l30!*7AIT{ry9;c8*62$j;QB&_@`KO5FXP9tQnXvdI(N zDOoW)FZ;#BQ}8+QkPYnhYr8X18p&s)1s16_cn3}n@I+eJjX1f3FBdYZ z4*1Ngg_B+5Aal>0nmOFTQ#8A5Sz9dSaVD-(Z(-}oZVC?;c59<4e2E);^vLP*o8b8+_!IT}P{I)T#S7O#C!`=*> zR8hn@(iRz3_q2FbY26H=Z6aE91Ya6wN3JmI_+kYveo?Foy!p(fAa2FuyceJ+FD4gzYg#WDBp z8lojdwRdcf?9LYS@<$d)BBI%}7YYV!%lv^5>;1W7Jast=2(!Tck9FAkll3 z-?%9>^idJXQ-~&>oe}6w%YLfS&plf?1N}8|VZh#S;cwwAJOsI2MQh?Zxc$27MpS9y zsPE}*PR2%Bb=Z>I=T8mR~Xs_n6Fo zg{`yZ>35u6S;t%f$sI{V2RrIWKiz1Y9#L`H^!@6Ozgr`*9YJhD9ZPI-R6p@>Vd$&D zf50EPP=1}sitcq67=BaY7~n6KcHn_b>MyKj3~tkUnd5;B-@<2gk2+PrP&oOA(IbvsS+8;4Uy5Qv3sIF(lsp4!_thnrHH7k+eVf)j2$cE>& z6V<3N8W3ll?Rh@K$u(dReHL9V;;U2Y7;l&BaO`5cT&=?CymhAt4KEAhmaNoyrgaZk z=g1^nzYj5S&C$Wx7=BZk>rP8VmQM@vhJAWb&neUhf5sVJJKg=u>2lTdpQ$IAv;)8xWB1*ywH}%KxQp+?g*g&M$mLVlv3f$qE9*z8F|`Bq z8?(J-rhu@6=#ez<;FO*^8=6Av%g*haWUmmO<8E*mW>hT)SE-%y`94 zsBr8j#e4qyIa^(a3ZE^er-OgWM?g0cq3lM+)W?6Cnt=L09iRaSTOL;yDEN`j)%}uR z3d+8B*co8QswQn~=j&-C9qU?K0_OvnX>`VaTOYNu0%b@mGWyyX$rjkE>EU1G;1Aop zKMXh2x_o`>toT>VZ)E@UCZ+B=p%17zkZtuNnvq#K8D;eKMUMEy+f-7K3qpFqq+-Z< zs@fLvlb^D=G7u-f;s|qg1C^vynn9BEg;&UyDQM}-NkUpOJ*nK5k-8Bs7VDwT0QdNE zL3!&THjeq+pETBg2Epm=HOI(0_jEyyo7t)g%`~jV8qh+;uSD1S2nz<<;*N^B1c47R z)rEd8_D-C5`oVBczk%X&d>7%D&Jf-YF!}RflRz)JoJ(4{f=a#Cq$(nd-9aqzw2U+j+1`QMVCXemF z_J0*bb=mtSbDd*s7ysl&7EHUmOG?eU@lfJ8{*Dk%D55A4Eenle8`7m`+E-vdQzKH5 z;TgBaAnUv;#q2nW79FoRzd7pkNP1ecB?mQ44b+%eCZ8OX`2v8B&{K9h`w=}J=bmXS zuAPJqtXK)#MF}LoCUuFt0lE;Kcf6MmgKG~hs4HXVyB^cA2R&;OI6S$mv+WJ{+>GEV^A`JN&u%n0m4`#Obty^iz@K z+E!ik{#B1-NQl1MX07?-JH4_4pC-k<)VJ90=op^epaB|sTBq(095LkI9}0Zzdr3S@bdV}RwTs>Ii!XBnLiOLVv$4{m(y8K*Ee$=Qtiji#^bhL&!W zQzxn}DztMv4WWj0*KySgn}z4hwzEMkVN(@|>jZ^m*Nkt>bp(m=rahn`Yb?6utaoF- z%P(JF)^|5>>UG3Is^>Z$MYqB!%rGm*Op-}_2!S9^O>Po4t3A9vJdR=BEi15!yuGhM zHyr@j!sTi zRZ+v*^4NcnU}Q?dauC(B-cIf0MF`r~fHR-ZTIt zxDvAL{|K!;a?j}65KrNE7?piP^J1Y)J0cT~01yXBXhLgV61NBk+ZM!!TE@Dmv%7zR zABwERCFdw>0d1z|vo)gAxXyO}eoC}XuYce$v&}g^ZJ-l+-(NkHWf!osY>%Z842g)B z8NFm%!=B(=6^(J_@Q=_?*RqLA629gX@k;pINcMrq4q!@BR0#U5l^v4{KkTa!Yx(f$ z*+MEf5Cx{CFRMk9)yF{`&uAkBXYI^z^6Xvx8pkg|%;$DADg_N|rylZ*PEMRoT-nO6 zrxZp)lp&vg*e%z*439uWsEE7GQ8Deu3wS8jrd`O$H*MEVp5qwch&-zAqoG?pF;{)srpsRp3;( z-f*l6n_S|EDjsE-{cU6TP6npb7iDLj}(&oEEg@M~9&58dcY_f+J;e z&Ja+;#{=XQx`EHteYd{U<#-fF1GP0kmYZNZ@7%~sg+*U=rg(j)>cX0ftkPkt1}1olLD#_AL-8p zTPd4;-E*}7JFlpmP)iDsCjcu#a;Da($X-=R_;-dD2KVx`{VAT!I8|uo3OfY`wh%lb zuFtrlLu(=$;x}phcXl}w1)w(jU|W4sIMxJEy=s6> z+57x@p%vuOhIXcGxM~i9%38cJuD8lY&X2+=hsA}=6e~bQ3 z2gkUx#qL8C=_|zU&x6a}v{!+D`^}K&q1u{1(Kv5w_JnZog!vh&HUIVsh zewBGW-ul&*U5i_ai}J!u<@yL}+!pYnrRIaUC)vu4hza&v$bsX#+S6ZRG&e@PdT0n` zX7Ts8E;1+jlX|bm`O8nlH@7M8w`p_>yj`J6$y@tzuH%LW0*l9>Y22E9;#sr_t^0HO zYhr5cmG*yvhV4#yo##i70gvyW5(9?}dRf1h>r)4Z@(}`5v1!hKR4dRh^;)xv)JUcu zB$S)A@P!?p7tC}^We1NGcnmIP%K@#`8W=3vKtG8rrq3hDmOWX5m5bB_1XMWlz4id< zEI`m{qx0+kb_mhgI7il92Q2^gQQHw{0+e8LBdb0 zR0U0+n_)w6M`UHeqH^u@W&={aNDF5|6m08ZRLTiB4S~mo5G~CwKI>5a{H8Dj8sk%% z{RUapAyc%S@!=brEcn;T2A|X;@gnmsP_Ad;0^7l(RIItD6xnL<7D*Dugr7-b&pHpP zfnn**Y2mii_*hWVg)X3?UHBWbQiG@!H+9V*ZYH~!Gd{>>j!@8oO-p7&dI5)y z`(@QDM<08&oDlh9kao4MD<2Tg$gy8E1$Uy{!>L91`|l-=&rtH8?st&lV;9an2iJ#p zsZ1+Bd?+1bkXHrdKh2N(S8-3D9)*(76kA`@eylX>X$iY6Cl!sA4|%X6nUca6HlrPx zzqEKM)jrIDjN+I8sp2>VIcO1sm z5S?lx#e`piPu<84mH&zd8KQ;U+1qlIVO&&L6WZ}>73jVkRPY&ter=V?5i>XvtlxR< z+-J8rmG}N>k1~Z!9@`s%7MRDum4`#;*O@H?XYa%*(04=>u`f%UjewT&itFM5C`N0H z6^us}>^FZlWfHeG`Z<za@G;D4qzt^N%k3^gs~FBrt6v# zB0g0Yo60fnYN64&TqW#{6;Llq9`r>qbHPrsS=N|_>|Y%#^k`u-b7hWWfFf8t1t>82 zQUaBOFU!gi=Fw<?5ouv2x!?+d=g0A33!J#{o>Yh zzD-^?s#Stddse-0N8UOJ>h&^l@%8g2Xf6bg+1jE{wLN#`RQZJ~!Jf12ZC=MP;6W41 zmJ+CfTR2)RsXVEm3`?6fppNfu;7a22;bsV5XHD1hq@D5;mr!jQ8F)d&_@xSk0}v*D z?0kAnJSZ*d^;~(q0@CYMm3(&qMm_7VeE-GX{S~U`gE>2MYvtgJyL4vWSu&Ga9COqg zB^XyDx&qVQGqKYpFFC8U3K6s16FLk-iYo2#=+;R|ob0L)@@Fqom?5g}5;%Vq-oRpJ zOk7T+oBVa(gF=7%#!gm2Pu0?Pj914lPzx;S|9($_z{ue<=NoZNBJY+yXI#;#LVkgH z1VcmhEk{D&9#OWjx-f{W#Al)mRY4GRU-i8fm% zb?5;5V59EhsvIh<)7CPzL*C(?TFxmtRgnbCI?IMGtkEsEMDjU(i@^cO~jGqaih-!`F(cp;L)+)KC$McF~ zbBQ_(ObJh(Uj*koudDqw{kF2kfZE)QK1~B7Z;XwL&3%YTU{nM>;Cjfr zg}EXt)Sf*rqti9}k=0NjK-_QjtwY@W2e6?gSkgL9l<1!AxF6ei0UCyF-QD@=A~_*E ztyyDXCt|V_t@i?q*TMKPT0e4z7=MQ8t5~pG&;mEU)|R_gYDE*#h!l322`A2|gBt&y z*|Q>oUui^TcActQp5iauN3HPI?FS(mRUoMhS;2#UA8KzF%AGb^%4;uSlREgxue4Z* zyQh>w#~>pEo}4V1OCGjRouh$rAt=q=VbXnSnLj6ECo|}=5<{%N5=#&o6=}38Wq)Uo0>5&Pa5|$gapof@zw@&UkhATmtpp0wAlI04jCgjf{Fhn74AU z(@G;|!4cn(i(BaltwMp2Mv{Or5xYu!w<01Y0G9M}b=Y*SiJV7;ZTNxHxBwPzE@$9f zA%Yg!a>Sn?Fa^=13jOuv6*(Hzq;l(b1;Wi1wT^&j08)PbIWB1@aeTTfDs&(b{ zTRDc za1v9oSm7itJ3OOJ?vw3`jQ?{wuHfmvLu>-CGN>~HcL$rf{4(`|w+^>W!7Xb;K}aHg-9 z>p49XXz!BJnT3#Bb?;isiJ(|D*Iz`?t)~Gp%Ho+TL1LRAP{Jmccb!OPb@YB7vGo6P z3Ej$@$A#juD zmVP()WR_%EpvHLFwHC5~()sMA0Jb3;X^YBNQer?izK;Y??Vs{oEL#I2TDw!f=(%6D zb4Vf;9hgC+zYWdr(P+_sc3p-ky6J~e4<%0JGD&jUX3gJj%e*hDSHq5Y@oPfxRh{fq zL{5PIM|NHIH)#?{oXfUKBHw@Ylr|9!+0wk{ChS)tbHJZ7RcQVB+uFu>5HCI-}?R{Cd&r$8c|i0 z!_4?)3Q_<;v2hVfwA+sqmKQGj$$>7EwVb?J3pKC)Mi5$CN7aU8PQpKtJa(|*ZBt9d z9(+NhP54Ng`cnviaiv_#8PUH+@R2u}@rK#zQ(%S)7Im%ljYzf#B|`B0lhU%-IB;mP z1!C2Jz|+gb%7bsM@mfeXyPVC+hr39ys2X3uJu&Rzu>%mAWaD`Gw?azh87q-Ne9>OZ&wDtZB8^6nPlKH$~7 z8U)MrdS*H{1K6YT!WwIqmF$m1WMP<=Nu3ZFAe)NhrDjbbZ3B;&4pO3bot?=4+yKT$ z@4tL*hsJahQS(aQJfb3@os=F?K1q{pee7Ri`B#mf>XYU~hv1PX&p!VU*iT3W+8FwG>aOb;n%}> zwZwjSxQud=F%V6wP?=x2G-(T{8}()smir2#Rs}Acc)VX5Sa=E!V~tfHuqpO3(n@EmPFA8a90|{$x+%V>b zPOuDv0dBsnUG($w9e{4AI;2_q9Vrep8oURRnd@_@{phly&vabB&FQJ_KB5vv$G$voRkW^kZ3 zh}Y{P-c_S8+a{)TT#i4B3jYTERTu7$XscEG5dw00cu4V%olK8zY?9H9Hcx!YG>6n}Ps*|UD)Sp= z<-w|0Od;34D-T+Dw!+cardN4z5*Z8D17nvgjv{I2izDqig0 z+iS;972PL&bu=nWAkJW`9eq~vVsJ(OQMteyJu4Kt5Q zc~)C3zX|UkXqxbtCf2ht0+_~jRtLV*TQmYaP8~R&CX*dNaL2Yn$$&;iYq#&dCb>Rp zWNSkSis+M18rf%ATqed`b6Q6&y2!|H1C|o zkXpgG-!%3hUa~X$wI;5&^ZZFh$Wy+Mbw$1Rwm+Vaj&pHCHRu}fCbwFc-`N5o0Sxn~ed)OAZIr3mg0+nR+~ z1RmHz-R{$BYHzP> zNN*i%UT0yQ-gQ5GhaAEgJAa@3%5(eZ(DtUUZ|#TELWLXzLk+73YWYcfdqp855PZI2 z6{YfQ=bLp2C)1uftL#YzF{km&-nC0oRD;u^0-7#X3M#%xSh6)Y*!9=)b2oX7lz3BL z6mjw&{sX6)7GAl8-qQn3a#R~46ik>2e>M>&kw}Vg7e&#c6Uo+s?Oj$;;CJ z#L{BLYm08SE4~rzvl5x|iNTs@@jpT}f0eRyl4G^F=N~w~Ib*&0e5)a2M0UO&vdp&Q zG{6cr!zxi3vMocWSuA`xCttesVn0qZt3c&)~-b&2U;8`WX9dU}s>Q|L`dwmM@2a74;Hv_Deq8A1#oPxkB5zE^stfLq0Tk})Il$W zoVEPPRBUZ%f-bVgnU*~(CNpcSZiKeuXj%dgf8~&xncvXa>>I_)BGuI7f4>coZccx* zWkh+Go0l(2;P`}V*TF*R0b-m#_tL!H{>mOKP(_2!m+bG@VWdnn;8JB^k<7eEIGtvG zw_?6lyH{X9(TEK8Lg`ERJE>v9f1`~cJ};tk3g*fEan=xfON6W5C%2+*9U{EW;WT!I_vQ( zgKtyf$~j9h39XHYtu1zJJzeZ1_0LYxigXtS@~sxWO{CgR;6-#KJP!xmmwR)0N}sBss#79>gMyo(>QN>n$0ZbB*f*c}APVhhfIo z+n-hp=#yW*R*pMGqekfK9FvvbV@~$l)KA&%GlhaU94n&8_uXZ)OJ&3s&3S!C@d_u9Ga5oqIY3o*Y)~L~ z*cXT{6!51cS>U8e_EoViu;kF;or{Q+~ z%SFk2LbyturvjD~tkkR}UV$Ox*AILb3j3HJo0BDF&JNr#Mx4L#3Tso59JPrE0hbrw z$CTDwYq{cOJs84Oi;}W!It#VFi^(V9MYEe$4{JY-zUX+`5xH6Ryu)_9id4V#yOF*@ z!>`0K*CY+9B<1)N`F(ff?v0BqJx$qWX(n+Dnr+*Vol9n~R%pFDnx{vCOiqo+&>%RT zTd=>T3_&4ye1@^y!Q!+@p=msG>j_JYx9RXbwnw+a^khwCTHuSgQcW9}g# zh>;oIwc(WvV;}GEt~#QG)J;rtZ~v);3KN5vnvY^h1;g*%^+$#MweI+=xhY$Yz_tOs zp1Qjjphh=itOT`>H(yDcZ zWJ@-@WYt=WiH7i37LWh3 zVmbq?w@RKA@Hz~r&81=hVT(?-Amw@yicoy zCw6w5LnBz6boR6GI^7GO)KZ$KAb+k+YI|K1(dL^BkWSZ-kHn|L(*%bkuez{e6F%=y zZ5GSHHZonKh9Jwr{Bf5trcev3XSA_%wbl0Fwj97~3(m>FMjS@Bx+P>@Hncl zPVnm{&qf8*mctkfNHGdlPjk!H3oc0JVKDc;s*`=J?E{5jT3aPSeua^Url+#28ti4N zr^*{Tj=V90UQ2koi9T5{G|7U$eh!i>WXt?!B8vmF55(o|X{idlGKEFxZJvxts9`jG z66aQJv_$nQ7J^mNFVpc|!M*tEVFZ1Eh3AcD@9xB)mP<-;S)%?c!O=&kXQ-?Z5d;rV zit3i0(0Kc6QPhkyaMnWFMq?pu8iJ|NFdk1GJzImtRBA>1Is!gg@rKn}A@E>XwEP6^ zztjE&l-5enQib#9N_EHAMQa~o!XqX)IDEgs*K|ty3miTyOTzdYD+}ZO2BeFyKQVvW3#bs+qTu% zZPKRa`JHvvI{(1DnP=Vm-XB~${59=Jg**YHOq#~=^=%FbiBv*?2TDEaL+Wg<{0%j%`ga z39bhBZ=%~Y9;7@7AfSZU#^bp=(y}Cuc>$!CE|oP5xD&*aAD*8PQTR)0tI^aH?k)@P zIuB!cS0l2G?Cyo>tj|aJb1mj$IDmLRFcSe;v5@PaFWp|*>}ZK!L7hn2OuObQ^7s-r z+&5`syP9XpR0E0)0vO%TF<1=uj;I>1-=&-rp>SR@5aswdIM>PGOt!0QZj*5ECGU1R z;}0Fu_m8)X0#wVZws=5G)N40&g8_(1Jen)* z=|J<51a{kjsuRQDjucU@f+Ju}prWQ^8$;^_XWCX0&ZQY9N!6>Wp0JJelX5@I>Nucl zo*0TWPjFoV9l@@EW;*P+iuLM4tpHQNnh)XSV+qpp5p}m0MFj?SoKLSLm6Nrj;7+1* zEOy@?&bs$#%f{^#w-rZ2m}Y}S84`v02-!e%`k4M`%c()_0!}|&(+ieyAaNWewppuK zddXcfU*-+JU+=!I664LYhBXIJgY&)D%_i^<%lyA@>&p`tXOe#^89Ye<{>#NP!W9R~VZ*dg>$Qi;zI_54?}f zN*)O%A4YX?O>7z)}b_+^W{LF5%LX%_&|os~POWixKf10a&%1~5to~y}jsq>AYI%oJt;%Gh z3md-Is`;S*s!>k12aoP)y*_l)AG+vUV9=me3|O5__yP%(5}xlx5OGcy{i?1Bla3AG zvg-&;Eg%Ge9CpLF!JX$cZS9==c})P=*}Pzeq_^9=vY(=H@2q1Jk(ayNO3D?90nZZC}%DtI*s9|`={5o=EDC?9^k zJoLlvH)nDKnr?~ysUG)Uf4RKcioxUVxmd&fUFsZr#fH_fp_^=CeCW*zJhia=U_(8D z4NV|}&B$Lyf7OcEcI1`+pxXbnNIMpSfA=;VI}Le-DY#y^wI;?{lF5@T{2+2Ybvq^Y zG-O5erOfCYulI=O?g;lkZsl`$`SoZ2zg7{+){_D>KKcW&&#^f4VPzzp3%~X!01%ni z()XJI)-QWQX0E{a=_Oyca=`1QV;Kr>-dAh^x)>SG2&jkIih?OwBjb+f*aqJeIX$8{ z;vo9WJb|>fBlZ`Pe(K@#G=@d#y8-qod`##>!FYxrQkwP-R??e$JXC64Gy_(FV#NJ| zDHFSh!a<;*>)bQ)+W4fnD&NR7+kGBv6)4600xX{(PVY!H-jhQ zJJ+-MvTt1j{TYr`!ACgZzK7o*u9uWbL;5(v?CP zghzYmhljcqv0}x4BpsiY{I=RB1U1`{eP^9{N`qvjh*I`Df1!8#m)UgY+|9~}vl(%M zMPHjtTzVfD^Kt}}|J<9Kxrtz4!AEb)U*K@zmwaWYaJ~5giHY+q@OLnYu6h$W@--km z99d6$qv%fxw04zl)H7|T=Q3`J6Yc8b^fxIbaB%rf1B^7ZT`Ox1T;Z7Hb*ryD9QcbZ zmJMp6slRj3X02MzEp%(XI#+!HVkSU8F^IX5;ZrkgOE?nHcmjIL9|v>)_1}OG04L-| zm|qf#+txB{PPO+i+BwA=0G4(2@xnRWJDf?Lyy!=r^m$(Y;p@ixe| zTpl^Ds3z}tKrV5l!G(Evh2F|J85@7V-n!(6s@k4EUc4iz9PW#mw&13BPSbyt9WGGF zGOtea&Rb2~jUM1pG6`aP$uQ^}bEqKurDXHrpPLy+FU`9$TM>yUZYLf)eYMaRYF-0s z9oUsWt+@NxneH4E1(@QtT(7je8Q4g!*i{q&k3GI*Eu$E`MLM5V+|?sO&ZGdi^8Bp} zWpkN)Y=}a{C8qxAZnpkFf9e%>`forlAAjqvFQe98wY#|}qf+^IWZiIGL}HXsaeM@( z&~<_?0o_b@p)^`ldj8d3xwBtQ+X(U*ZccC7xrXn|j=g`4gStV$4z!O9H#=t0tUvA` zOI(O#B1%X2oOFYm3AxCITbM_rzhL=VQBC-gvW*{3*caFs|d%x^u7JQK_1=t-|oHNp;U=G%H|42+w> zJo3n;>&BzpmZ!0DPa0DZI)UUg3Xp|O)!-6}FoquT^OPis9U5RkS0WfvgI%Bt745(P zA^J851VF_aCIUYTJ~{xkcto)6^uH@_uktq@*-q~JR5N?%9I{c5hgE#7$y&iu=5HOe zFiO(2&|D9t>sTy6fYoXJ#ev%IK0JPR7OPlx(ZD-?>libwE~6p0zfx~>P=%pi2*T+Y zA{b_89jlCOUE1rUk*6(g;Zlf76_}Y|)J&Z$)rMRkpCPaoF0y(R|#D$n}^ArexvvP1YnJyaeMVUS#)SmKUw;31ax*>9evz zb4%6;X!%kpQAyClSPer$xA{ivnVVKnQ`?PPwDQP0R^tmqC2r*Q=vpLva9H_ z@sY}8$Fz3K-OW>)I;$j`K{`V>%(}q3<^Xpk&1cT_8swBP%LxeO?nFLKZFiRWn$}iJ zLs(C}gM2@;re~-ZU$m9e2YiswP>#H&XF{7+x-^^60g&GLrq|}VClxpp1FEv zda!`I-ITR&$g@oX)A}c@)_4nj_E?nUF6s$|gDT6?Yb=52+?Ci7{)kS`0NHwB6@66& z5&y!;C`PJ|q)*!~Yd-#(!9KRA#Dk#{#PPg#v6{9UzFzIq8{{Vk&!IU{>3mnQoJdga zggHQUDFNUFYcU)Fo3u>0@s94rh887sGR8I4#aFw*iw|fum(p;{V9cKMgGqQ3$;^AOy@s)&{=36aickjhojk#lKb zzQbd4dRJ_-MeCs=5zy{m@g6pznM9lTmN6$wJUH{C_VeV-+8E zj{z;p$s$gU)n#voCd{aVoDMEg)bhQeeAzq=CfrQplwu_(KV}B(Ok-@TTvO;JCbYwi zUMW8ksiTYlLREuSdpFs=8ub8*c}K0E`E|VQ4z6r2HgrGEY8a&2)m$IdAx&@ApASn| z*}F0cn{FLKt(+R7pS+`Kb_?)T=0SkEJd7iPO_Ulh87EsD)q6z&n1-w3P#O2^RJO! zh#>>x*81b0gg}bfCsO)AYej9Oj#Hk03&|Bq$-;HmL_W?1?5yRuVu}2KO&+ zlgb-$CVu8OJ@s=ac6yDaUPjSQGZGLFTOlp$U{7ujEhp zxOzktDeis|4*6Uor)wpUnpe!$B*y{$uR?J=l|>dx(_-XlL_|NL5!sZZ5S=b(*iG8! zAge_?foXv7=?Bb@8f4G}UImrSq`iagj;v7PDqcOD<7P_!RxjmjYpV3O#xG_d?XN8% zjDxj>p@t!^1q$d%<06wv(Zdh~8#nMzE2Z>aMF;M4eb3y5wDqi`M>=6Y!Ay!BctcJd!lH40@!yzMR4YXe%MA?loco*f6C6K ztEO$WmLAuj+k4APKLuL2izuEeZ%AllUX%pG@L}P*Z%Z&`_?Zp~*j}<3s7mbYnh!|A zSt{El+Vb=tUB$Cw&b2i>op=Ic+GQY(KR5IcXRr0Ot}erqFW_ZYTlCLm^Fs$fGE!nh zY8;kwUFuK-$Svu3PczR_fUd{y$Y`k#B@1n-I6^OqZbU9io;BdK!a!B`NP5?WU!G!rlv z4WLT_5%S5pZcEwS^3fXXx-Zu@PM&TmKDR(JG%a&5C(%01FaW5WIW}I(N;Cd41A0D8 zO@Dd*cOZP<$3-~*TDp2P^@p&)@arK;-bpscUib~tqlw9zK+KbL(tq*16j^gFSq>X+ z7qS_XRf=>_v#~=Kq_!4qNSg>>#vFmMp%$Yw^KM%mOQzE#rtF~5_o-D7R75wgN|$9ds)M=kMxKqvK6zCUp1>oZ0{FLq)?~3 zO%CIlC5~Ud*S7L#p6G`^CPt3EiRU(T(V;Zo*&X8g6<53aCyQ_&So3=>-bhEfu_g8npqb);y@&)wYfR3d6 zeKHV0r)L1#Rgh$N2rn%YYM!vjAT|mbQ2gYqxO7x>L=Uc%_+<+bPbOg2PEOmR7S>XT z&Y>r~WmiFqum17TO?*x+sZI02g_N)YP)PpLr`^jfJO13jc;$gmSUf5~(6=xvd-Y_> zN3@AnbsSKUD>9E9r&>`{8|pBaj2ux5*mmf<>1lxGyIr5#SvzWBERZoOOWOpt$VN?N zuIL6VU4{-bF*9oapnV(sRrQb1$?6jwfb5huGquaBeg8ua{{N~AXltKNy#24ez6G&n zTVyBL`m$skz{WOGxO;v7P@9)RevPnz(QPv@(@Pgj>G1_((I05REtw>7+~4xXSXnzWz!k7Oil*q+Wo*v+t94iAyx5AI(N( zbb%SS=MU%yoQ|JcN)g}Bb^HSVWUV_RypXS_ye#oizwAJi_{Zg59143Vi1o2ph>-Eb z;BU)vO!ogl{;KmVQ7Aal$BNq$YL?FVq=vPiagUm{T&u$XHN`3Q*oWY`7WLGF4JRd0 zR=&;XT6|u5w>=J&UsEV_p z_P_!xlAjYV9or2paPUcfh5{RCs$jtsy!I`XDvR6o#@AYtEwdg>prDXa>5o)f^H`4y z+yffAcF;d9L;@@yTXh|98xEiIQN3bcPl1?#iYG1@&DII96Hn2-`FOA!He%XWVt}w7 zPKgWyO_*VuIHskUU@DxOW>o6)us)g^?$C0T>TFAeK*Sa( zHkOatcq0lRJw*r>Y%vfjZ#SPS15qT!))SC|!a~EI+VZlk{_R%MOuuh$eLCWSaT{4* zo~WPm^sjCQM>14Pm+kI23%PLf8?iV%EQ+NcmrsY1Tj+}ywaOLfc?koL-xlsf$N9uMbhzNoRG7b4S{r!kZ4HwLZ_v=Ro$0px^I*QjE zefS@u<9ExGd`>ORz@cGr;`Fs+m;z^Y8%YDZ4InJ-!O%?0f@*8LXTWhb;C?i~ABp3C z2vp-DtmV;6>(7&HfxBycjjFAJar???L>_o=Dd4cw!CzFbcemx2|N4f=4A3x)_*zt5 z^k=9%Z*Mpbe?8lQ1AoTVY9E!&v0G}=xt{NZ`EZ`Gx9fo=$o#sIMEK61`fb}MM_goI zVa>F7l&d=Uu+iFvSTXoyoh)L!#_}nJMLk_jK^&AN=c23idOtkT8-P06OQvIjlZSJx z)hK*uhhVLp?_r0P__kVuuMncLJg@H=)bRmQCBG^IJ;d77{xyy1HJ$o&Q>g*fMyvWk zo#vFYV22sUHC{(f`YDnp(4#<2Cfdqes!&Zh8>N5~^J34abz=w2fQzp$B8yI&cmor00P208pM^(n>yp~i#dpY>-xVYLnq$uxi; z!amL~q6vWV#Pp`#+4s*Q|4p{65tSZ=nI%Rx06xS?)@N5p;NkinqqGhY3~aokSySoB2DL&G z)VsBdk?9}yXm~LWYz+WFiCRY>4hcQ>imP^IG-fVQs%DF|(ragDZ6axqXvB}Ao@)^E zGb{#;RX@HK{=@t9h*jXrwJIoTfvRkh`R$pO0Z(CMfG`6~>jm5(k(36nPhn+hHfYYP z@X0EdR)1W9jdENevtV+buzj-KsICWpHINQ6QACORhaKS4c=rR662vD=ou}}en}0_j zs4ru;!-(ywUeDynRQ?JUTGtxGPe{w2^se-WGjSJoD>1k7f)iTZJ5}An$Q9gCCykQFK z&hu=QEq@9zex8W2Mp~Y}vHWrp;|br{j2>SWo+A>hyW99YfwPu70M(|b(mr5YzRTl_ z3A}HFZdMli^Uo7sn7$2VWtwZimVm-Wjv$_QuKmkDV5*G8-MNlNYu<_7CTUPE)G8ZS zb1fWjW*vKD(qt~fNi%b$jqU5o3@+D#mQz_jj1q*L8i2PlZifOw)S<49&cQc&%uO&o zL9P)g4^JWWcE08O-E&6=&p-`wjg$`H6abx?H3g776%QcwOHg>hY|oX^qh$@kwb}u) z13FOR^=^>?Z^zY<+NuChncAvHzJ>DrO+0y>x}CJWOTlEMGKCZ47TAcOWDETTw>;ce z+9Kw*j1{$I_YNqEzHzFhLdprvU-@XB1y@@pnhbYVd_G669+vx53CVJrELA3K=4!ND zDg}a~Sj3bHalE%RXC|iR+pBn*oXQv$z^bs3)EPsi-Az5McloC&oyQY z!TYO6Tj=|=#I1yXd9KC{IvR&RAu{i-BdeONe)P4rj}2>6XZ0R{r2*g$*BRBK$Qu2h zU>7rTy!(Lf!|9D=pJjOZ^dzs7A$`}jGmY2e#OIAKwPMJ49Zq=5)V*P3Huvu?Kr+eR z3=Fxv*F|iEBgu1JIQ10nC%Ty%=k%*llo>DYDz<9pYGrc)`vNebyCo~8Yk{y5)fj6< zJb72`4^DFH7fH`<6H*qdLVr>RTCja{bg{LgSo@umucVb$SPF9`yACz*kSEo@cVU!& zF|Q*DyGMoQqkO8w%m?Fp*TgN`93T*$4~^=f9klKY6=NP3hlc3S@E3|lfRUziH$*C! z83r-v5aqK-c|v%Y#M9aXq|_`QgYk~f8)N?<6lpyeKEnvp<VeGkbAWt3@+y&0l9e#Lz3$yK=^mfw1C1T zd$*1>!F*h;|KX1g;QHpOeI4Slfc6TT@%nJ11JK`hc8mumJIZV$&`i5B8z7%7K`Ldp zT!t^)X9A!h**HxSu3pT~zK_J20nhbpWY8*oyOR=3l>b(BVv|XB@z8}P6_N+`HW1@1 z#TX>FUw-)V99D^?Wp2weuKbretTb(*r%c+wOfc$p2RaexHfQ?r5q;EJf>6ToTLW_; zH65=^Fwe=?>w6OYW(&#fls-e?Kq+?sv~-2>zLT)j2>Z=!eTUn(Tw#yfo(R_wMP0us zE+OWjck*#X0EmR-s6}e=rRAr{^WOXD$Q8z=XyW9+DEW9oUj|mf3Ot z8yqv{fp_GRz1v=I1g91xlV)@~6bx7j+HOAQzI^xa|H%kTza1rz&>OHm@0i&;hcK>|txMfMrDBfex(!lY`sqb?CMB3f+kd z;mRB}p&&b^K~aGS;Z~`h4tWqL(Ip1-{B)4KV9HF)dkfmwV?q;LaUAjp=u3)7!z}bx=gb9ROhnlQ6nSBX!c5oNwT>i8VW)qKG zcD=GH>c?)|X&4F&q_Lr^(KECy3!l@n&^*{junrcB5l_3xj*ML?a~N=cMA0J~8qyc9 zZJ6VhDS(~(~HBIXG=VVXI!CS7lZWe>xLvX zmAa2X`-_N&R)$)BPDyu=u#pukCGnPohU8(dKECf8!8dDP&8)##9q3Pe$AEr5Bt5=K zOf}z(51&f&3{$eg7Y+-rq@L;!r$N*+c^*cz+rBcYfj4b;T~>r6c&PRIUj^$NHPapG z$JJ#1`~rI*>?P->e5TI@o7KQ&3F%j0>o^zm1*&C019b^}m~XM_&CKeQ0I*a(k+9zA zX59bKn-lq;aY^bjcdl=i9j8xNlbDs=$Z0J<5$e8q8W|lq7&pk<%~J;(-yH91>kqi41n_0~gq7g?;nht)gqH0>*` zg?Ws9uN!v{>k-+aB>jK~K|PEM4 zP(o)6@i>SyDB0pw-T2hybleTGAYlh-Q!Gno{ntor=G{qsfs|`8Hv0Wf@WfZpr#pKWPlHWq<`$ue0%W*?dy zoKyj{Z2I7)A>vWJL5d+^D~oCN^!}+C5RvRJ=PsEtUxMCENIfn_8jY_N2DiBh`cW^aHoSM4Lu;ckJ&(+sMZ;vMk zp8uvIqkXd<|Irv7+fwQ9CbK-&gIO{>?Q~nf@(pZXkanPSm`|@*pzy3sf7nL8nhB7L z%onL<6z(bFa5R~B>xT|>>?bso8lj-JmazF!zgh*EM%zL5X+W9pxxnI+IE5Tx4hgpoSwMI$#J9>@qcni`e4^~zAM~}G$F14ARk{m$MbP0)WOk)r zfZ#@ttzcsOoMw*Z(zZaYQ}2XR1B#fSjXUt2nD|`a|2nwGKYukc-VMxYz9WKNEnDXw z{^|3*lz74W0=(WfQbK7qPrv07Kjv6hAvlB+>mFmhjehmpdjBA;|2a|zSAI5MGs34* zjE*7fj^e|nd!5ienfA2lLUxsj=_x{y9n?0Ql<$nbno`Pj)#;0G%>+Z7L;|fTs`Qu8 zdktuB7z4`wVRMhusO}cl)OW1$q4%v(KQwIVe4H9ZiWk2b;br zUWA;zJrkzZ2}`v}2u7$M=uU~Mo@pI`dtT49+jP;1LXwMha=oAmp%kHSdAUDNQCnZL z)JZFM>>X*A$~46cSDYBfpN^7>g7FfrQ!Q{55ZuQzuuYb53Syot)I#_eHT3pvm;Bqi z%q+BOPETz6;r0p(!f**Lu4vIP7k1`CmMrH^(XvS^;^YR%#+tvs6C{Hh1;+_#e~T}w znV}Xy3RtAK>lv6N*~0j^f!in&I7S@IuB73hI5PLU1%OxsxkS!*pH%`Xan4%@E4$C# zQE=zSUVRRWbkp3`bH^FScx)z{hiaW8O4E|l46IkNwg}h#O{MfqaxwS$?5{`WG47SH z0G;92<34)44eb{>nv`;6}t{T&gcdP+Ls&~}97uWnyexJ$>#dGFy_ zX%ZR*l_xB}Zk^iKAy4s@$T4jS?jDO7xC-h;a?O`_89aZ12Gb8fY1UWphCsg#ltWgq zhJ;n$t5=z*SSwW0V74#Dh16#UYgR#rAc0wmS(msG7B?9D`)LZRxx=GzY$1PYtI<3R zI6}r9iu0%OEXQ$RC8+EAZ}Ep_e0W<#9(f!V-ofXc0^l7FaAA({hOg4$^21U?q^0wK z2IrBI^;B~><@QCr5Mh0_(8LS~4}F$h-W_l#%RX_pw{cqWPOKA`0j7v80&8ax^vO(N z`$5mnp8%(1K0Dps#noCV8CNg$mk-kr>=r?tLsqFX=ePoxYLK3p=6$cnA_a<|Y8$X> zg^_k7!{_EmK9Tf|xInpx@qK0`Ff}u}SzJk-2ui~#QO`_L0?-z*bBGE~)wGngxOYz~ zPg~_;BpQOsUTyaKHl=JZ@q5_`9N7&xl@wv<{)5mz1r=yUrxjdq%nVsh*0TUGOY_Ov zQUu%gJ?r>e!yAVr?RS<@E4zUGA%|lt{lmqGO(0l-?5IaZt*4X6mYXe@_-P}xgP}3# zT`nR<&|+tUdUrp&OT>T#B=}vDT5QR+(&(J7%jj zDpKn;CvlL{7@bVhA%s%O&W>IGLu#1HeZ{6m(f6c2JN<==t4*~EJDxKZp8R;KbLfRc zro!AVnMl3!bA8@7>kO&?G_|KL1O23fTknOTSNSikg6x>%$1gIlhyGYwbeN$O6D=V5 z;7S~oqVQHPcse4N$0OV40fF{Y4Mnfv{Cw! zU$9xHk-L5|uH8|)=><9uHV(Be)I0mbD@Z)sM2?yZ>pgPUIF^Q++05oA(b6-yfx-4A za-fSE%j}{yKz7KX%Bf={kG38IxGPQ(KwJVv(BckzHC$c;a6fBG=wti6aatfLmYE$l ziMTZK%QYsSz)eZ1e$Bg0MKz1;xsHp7Bok7_iC)|{OAUz>cs-JPV@-MDG>T17%GJ!0 za8+ALHoVjE%reW|3Yx(jNB9^PQ1ygDh&ADe?Kcj*_>!o5m}<0XwQ#eD<-QYejIQFg z_bo{THCvq{@hkwu3~Q2z5dAe^7BJew@WXh66kBV%^_zX;5|G&kyq6P~GA~oK+qjrc zdYY$izr(p~guUA&*(RI}_qIm8Q)>R0SsnfRa7#Pq7y0%_&(#8Uu1A1|)f`4}Z+e?o zpRBfVNza^f<4Ecaj+}5MK)K^TqfKdhWvHx8kt<7@MjBu0;7=di-FyC4_jvqOlOcDZ zji9Vd!@)-3jV5&k*RH_qE1N7cky0u5sz4aS^;qwfdV5Uu$~c2p7{+spFaB8$fDZ+| zQIoMPF{vDLg(#BW#8K1x=fZ(4is40-`O`mH>0^Yi(xLLj!|7L3Am;0&YK>rbhhe**Kh{y*~EWm2~DoH>2CY z=>Gp$jfb*@qO6T9S2S?8Y4v+mKtvXF*z7c3sRv=7BjU;S>rSyxX*vbSx%h|kM}v!O zje}CAI78RdCFRHIjfy$9Xx4IFPBe`KrqQ1=2%~dIw_1&la%R+t+}%l>{g+s?i}WQ9 zt7Br5lgn~NCR^4sTN{zbUSHvtgwnL^nPGbz)p0nW{4Tf`unaCd6$1S#ndO*=QFg0^T7C0@{ zKYTUt`IeA;_ifVXS$w>$2Ts_n3XTB;i@2c2F1D8ABqhsGB(n>R)^cEi^(Su|gm?mg zg054JCV%WIqJRv9pVDo&a!%i!7QTx@#cH4eFn?~o_I~)&9#KCli^gkpR(YshgIep- z5SXkoXO@V{*Xy6F&Kfp-cy$PjB!oe107{nbu(#pX*|Mca%cAKgpHNv;38(Y5WvJHA zqU#$EQ4uQ26MRQAtExvXIg3VkP|Vhm13Y)Y=4o9HyO2ku!Cyo*i3^P9MN!04Hd6%H ziT>1p$?w|oL{4L+M)=2XSR}agtFRXA+Iu=Z37`%vY+b@mM@bCR<%_i^A{l+0%}u>4 zo}~-=&2XVnn>dwZM#WRV6(@bb2|pYGLDWs#Sxb#aow(+r^tu?U)gcV{=(Tp{Fzg6M zsXrL)c}Eg!Ym4Zxp?HDe!h#X=L`vF}q?!l!tO4#G%&J*8nYx{FsRPls z7?VamZj-XP+t=5xT}w7psr7FYsTzu!>Kf2k&30I@)5p;G;SF}HMIYMN9H z;I?+T3E+G6TF^%7)}Hmxr4M?Y3<)fTgd48!9yPLxwu4t!!W|Mcg*FSZ+f1YWif7wq zsQwgag27+a;etskWEbk(I=TN}B}1w8O_ z6ZO~}F9M`707XU&+yd?|-6HJ$F#!M&keH1Q+}S+-e~9wgnt6ojYi;ls;d`F!4i3qbX46C* zX?jD7iUA)bSy*hI5pcSNJ-)c)q#z(lGOtRX@>eAPE>|OB$*v2pXC_Ffx3->_7GJ+n zq`c<)LEc9lWx0fWse|qPn_Z_`X2+qB8HIH8hhL7HMTi?0mQ$CptUlhv%Uq{FR^Ru5 zisiXO5F}HAL^GVi3pZ4mapySorU=}AyRM)fKbpLLD)B@xne55Ts*WC!2*H_$D?&?! zm~j))&!!cYue8a=j|rrNUX#5`uH~TrH_ue-a2?D#6N?222rWM(Hgz}yWM@WJs)u;&J!NohuIl#f&^NR5hUxF4{QO~{0m?ld;qp& z9dw4&<7)d!Rvm3Nv2bJEDn-837M|zaIN|639uI-)zHY|F>l>v5rxHialR0{Gz|7Pt zAj1Lls>&$A=!PXOCj61AIlk0F+%eOW;zWstYMj4(*q(~gzX@a-gW}1)Xd_@TG zs9yno4ApjG=8ceB##2PO{=dF&V1_5`zEsc&P07-yU0XqmsaaUjPYW22;t6kNha)n1 zExT5{I{*^yOIDe6o=ib{<+N-27sAi<)jjT zHVg?;#}OR+DD|`;S=13GVhgarZwk$Wm#s3|(FyG;Qkn#@8U{=~UBxTfuyh zo^++wWK~p3mg{>8ypQul8h8?zaIL%i31hyQE;Nb^6I;SA&nPZ}csnZ+b^NA=LqA#A zUIB#CCS+-Ntsqp zVO}1~BNHp=r{=FlmY@3l&lR+@ir^xCenYxPl5px4D0S!?|WO)-GPr; z0oa1~k>V1>&lZ%|Hjr{A>4A?5(DvQsXa4KSx_Mi!w%QI4|ToG}7gUi3qt93P1 zho2%WQ)44J;l?2VZw-dhfYSjyAFsenV%W!mt68sw65jA@#u&dEh| zAeN!BY*yH~s@Pn>VJS0Tj{Obau&?GhEg!7IOfiVTPgFi&R9kfF_H`&diz?_5QCR_X zRXSTZCY3tUE6c?m<@7+B;|r>p6rMD}8WrZUdLtvmcQ zDYRhYs|V?8pe0TcTEs8!Yg4EqUkL}wGRc0QBpbuY$N$trtuk>gw0}y+)itX6Ey>>C z$n)~(v35$ykNmDuZTm~{*Gz16MxEC^yXy^edxH{zu*}QZ-R*_-o7wy#+7#c>i_<^u zT6~k!esIQxR-Her@x_%(XGi?a(b>nSfi)ILA`Ry_y^gv|xRWVjAl6y29)~R>(jxSo zuXIl@mMU)X!PjfU!mIN`3x!^#50@$`Px+r;?&_*XJx1=* zrD(f4f3bGVxq7BGXqFzg%2`S*m%H_P=P6m?RKX1T$jMTJ%ZAHU$nZ|{=Pj5mF6p(T z*Vz-@-RCZ*e|+@|M1N^s)dn%+)Vb#}E);=Q&NYYp-;fpLl|wI*pJ>_R%*dHznB}#; z#ZWe}OEoe-ajp)7^{Dyz#E59kJ+;kt)TK_|us6)A>U=50Y~)1yeyrB3WQ(CANXg3D zq)byQYFd&MoVw{%GPTwA#<$mrb+sl~Z5Cgl8x(vU;{d*!*#7_2>AzwiPEtBGiz|2* zuI-Ng&>8=7_+owYW#dXBvru=!QeA500+a0XKA0~7q)Yef2)nq(LZ{L)_;&c=g%P0Y(V)1;JpFw2y5W*s`Rlsq@0T4MJBR35=W+b*|b9t(Zxmy+O zYfw^Pf^50=+3QHXxhS=-9xc^L*EG+r-C=}}5B!J|ZS4!N(QvqNe}0*rkIW)LlXNh2 zW4vBS&!d_dSqo3+6Hq{ZQy6Co?c?A=Edb+=iYv^3>Y2s;N#>p`PEw$Y4-kPOf=P^M zMw_!WiNQJQaExEBGWL9wavBR-?L>GaA-}t(omS~`P)7!-4~s@g2lz_P^tFUM-`vJa zE@VAMD9j26zIPU3tS)3s;hs+2fEO$NeYFPd2JgNFJO!Z~l zPX`0a>5h6x5p>xIH5^z{zHYj~DE^R<2fCR_;dK8MC5n>$i)*p^`v5Y2CI0WdTi6aW z{BQZDxHcahH8k9;&}VONQ4@@p4nGQtnpW41SlMDrauN(v4RA?`?9g$-N%D_8b7g;{ zrXFcv4#P|sRbw`Q5Rv(*w+^6GUi_lef%ib*X{G+Wr1d(nkDp<0{rw+r2KwGa^(t&Sx-x@ zKR@^xe0+=?uT&py^0)y-a(TU4M`+44l+P~3-uXdI zm5-3dBZ8tnh0Xv>F>Ux5LQtHo{&3A3p2F7_o9&p~D2!?}_e6C~ie8TIKuwgEs<`DG zYZGVjDjr>Kf7v8^mZA*22W6Mf86BmW&Zbw)@F#}J|4%iiCyCJyrvMxc59Q3k$Y3g0 z;b`)tEL1e$)ogeuB8C6@u zi$gl6c3eIgoek+vy}RTU>K{G5UP##vg^`UZ#)V7ZKT*)?;7+QtpS*wx?AsEfc68UMW z z)gJ4lZx?BsIW{kc`vgX>UX?_T$Uh%bkrn@h%`DjE3R|twU%~WR!fo<#QNrD!;f`SX zL9WGH?(jbkBV6%aIy9K#8!92y{eLZS#^pa$+80N9gJ9j=v4KCg!71(R&SGkqCU#i5 z0m%c-4&x%5e|j%MG?YtHk7uUyrXX!nDuK-XG2tC^W*8-Xa*{eCqPPe&v);&OJ;QjS z$eKVBH-`f6X5t^S*DrbWF5-seQDsYX{rll8EZ8rgQvOc$-y{DPDS5XSTK6B1Z}TJ( zO`HAjE2_*?i(31C!~~Er<0QAO)lSkFAJ0<>5Fj`Xv7%RykO3 zG{p7zqIB}6XK$~^#3c3cW26M;_7e_iov|$32ir#ZpKqoFdJhlLW<|D^^1&e9vO2$A zx+{-4WfVtmd{!giI2sGau=gcAjon~xWTz%YJ^S+F-EWW5*hRce+*73@vBEdE;wt#hnN% zyHp&@CFZUhnpzb%$Pz2H(>M91gOVviXR<1NHISaVB)xGO7oYUY+dO12WkbYVCv(Qh ziJ~l!J(LHzpbCpTp797D@Y9eV|3s!d2~Ao=T&<)Rkk$9(79C||XUrBU>oG1;Kx$I0 zjTDFm#c~9U%>w7aDF0h?YLS1JRpHaX;9gOp^@=Z-n-lYx5n<6%lueWoNQJEb%^hA7 z_k8YFLo#WKy0x-y8}$DCCBlqLD=XL@gO*~AJzAz%W@0pgOw*N#=lM>jOKZo7|;iubJWq?K6jzNzu9&~cCD3`U) z{hAjLeBE(&oIJ2Lh_U@3M}+qDc?e`6qT1CR7kEz%EGy&vAKv4L)9F;rp_9M--_k29 zqdyc9>%}M{PMZJe|2W1sqNo3%AO-%z%EnLk!NsOcnrt!NOpM}gk<1G$;h?H?sqg~R zjBeq9(ap1FB3lfM?e-8Qtn3uJ+oH%RwF!OY)$xHuOZGmvm7Y8F2q*Y|MW1eENM~{l zi|pG_op%arvW7}Xa8U<}C2Mgx>9u}srYVO06+Wn+32=!F0-mq<$iBKu^{+@!Y8g$z zdWO@a%KRshVKr!ZN|r>}TqXPw6@Qv#p6%$i5Oh6HbzeW*=h9}c(^tKh9?Yj)j~b^i zV^v)d?nifW?^CLh45?ZcnwdKF4Q!rT&SCA$0Rg{6vuas>nOsV!PDuy{5^W27EFbor z_-~xUCPBi96!n)&<@EoyZ5bBc&e`22iGQ6(RbRBnz6@(OD0cC@5CP*Pd>)t{7S#>m ztR6!9)7LM|Bj^)Km8J|8f5#W(gM1$qMFjpJQXj>V9D2kuC>=$~vq{;0YQ@*vAboa)%$rCTm(sYDKlQVy1@Cd&D3NC74u9|IWw}jp($iW7IT)ofL2O!;B#@ z4AW1ZiV$tQr4@8~l9(Be3OiufI;W(GCf10$?TYao*|sxoisSMa(j@VLP&#yTlb{64 zPb7i;d+2<(%ZEmt!K&rkn=PFKTyo-ssLw)b6|>W5k=PCU7zgPN6*4&$N`r{o4;ZN> znyL%Su|d8EN4*}T999JbaPWE6vM$W$6LEHAmzlnbB|> zOl#xlE@|s}0}AzTeia$vh83yM3Fp5-!^Wnc_+ z%bE9m3t60~ZhMzjNkVG=xB!2?LAJ|@rOxH>tE+w1&nOzaN_-4|Wz%T(6>8Uvq>s(qzdCP$|wl{9I_GR0&) zatukHN3{3EHKVtvW=4$k_8vbVuy8_e)RJg)j8(w($hqC8lD1!h&pgCvHCT&@`3a~+ zDIOgJPXd`2=6PCb(I)~&y?1EbRZR}u4xUB|UtYZSs_O!jO)Lr%%(c zWeWE_W690`(XWf$JyI(1zW*7fMD}-mBxvb1EOHOW8I~Swvia+1xq28sQuq_Z#kfP3#}94pEZZA3XDr?vj|$f8V4i z3wl3if3d8cUyu%px0}-ZEVPmfxl2|}n($w1$<=?;j0nB*1of&FP%S{~Z+5;BSpN!gKf-ugCCa3MJ6|U!MuO;vZRfq> zTX#u0o|9O2#rfVL&2Lj&u6GjnDe(F?sEB0q!h=P9Jc6}rDzFL+;)+)K_4L$IKUYUN zs)@=^pHFV0y99Z7XSwi8-t&*eAWLJmbFF)vIZ&M5Lq@Udw*ste2sb^Yh0=}phTjA; zcgXZ`ibR{{@XS#)i}(sQ8*_)M-(4>x3d zs8w$d!s9WC_6SI}C4Lbm_pVP}U#o;`Vv@>LFP~IP$=j^=6Ni@pcZZBhF3w_`#e(@%BlGzrC5pi6=E z1icvjYqO;D>aLMTK*gWFzMBFPo-b1CBQtSNi)}GgOGt@7RIL4WD5N-wRRjj}Yqd%p zex}J##ZbB|kQ2vF>4!1NN1U&cpWUN}{+I>TcPh3wL@8I9I8=Ulx>TG(fJR!O;gnaI zQFD|?yzsZ@w2<&=6QzIb`bzMkIFUz79EXiznrT)YMMK@=s=gqQaE!Pj$%rGe0RL^Z z=pxKNpmK7j^AU$5;!>zJmQM4c^AQ%o-=X<(-6Q9PtE=qdg-)`Cg(6K;tly1r8}IzI z#(4JN<51}50j_Uo0$#z+mlR&UvAd=DM!Bs#u3M=gL^tZ_xPhBbt~V<136n_@=$E(0 z+_uz7C)m^B z@naTsNK$MH^!1`iJ+LDkFC~MK(c|~<(-Z$hhWSfr2wO--Y@KLUNUXIjqz`M|4VWdb>u9hoXf7ij{HI@|wPRaFXfRZ08U- z@6(G#ZC<{44KJ`Af6<<=XkB{kV!CUrY3pRz&Fl37mP7YpfW{&P7?a@}w9qYnjAVM| z@X|l+a)p%MOLFVXD+okN?F0e(S3o}gLxke`h$&)Lxhl2g9vdh~W2)e6R-3Wf7+G|+ zmt^8q7wI(mX3h2Hd&YL&8-33;+?fzri+|q3x&ViN^tTn6CV;)2_%lP^;;e~Gga|!t z@p)>tZsXdbIyh_+2C!EvXR?h4{5-*VFHI0KjTayzE9KoxTIam;5X}JKrZ~w)nZ_gZ*%=|1ZqySUvi?NUgl!N2zmp` zE$a-%$%7fL{-zD&-l;EWhP*gyu|~#tulh$*Gfk*XI zz$TyfoO9e(UFw<|5}iwAT~$n7+4MC!1UitAYf3MyaY0kxt~tnn4!|W^zZ441@y#fs zTL~_^1-D+k!}U;{of4QXESVC@=(g9W-o9xli;s~MXtvCvmrqndt40d%jJNle%WLTfM#?-58<25A8mJY*n9m~fyIhs49ZLsFUBXTzl7no zgFegn-&rbh=0v1L)3{V(($*^4G4z-31lT8qbR&5s?yzeUktYQ=&JOVSlgL~Bg9?Fh z5?%dPh>HL>Bi@kAlQG7zXKk8U9)S8}*88JAjCD7`I`HB<)hmew9@_b-Dbq*e57k_k zybDuQc+Re9pU#^`qpS5PSJuc8MQ=oN&$^x#xM>wBpThpQWE1r-9`u#|Sh)avJ!^V7u}6M10uF_#J3xea;jwQx4DQQtSH$Io~?b##U1gON`$lw9@0=Kb-s1A)@5K;jws@g$T$sywP&?R2NDDX8~ zY0Eespj>v7cR2VH7HTP7fa`({Dz-W^8)oA)UV{8=PnPN#7J;uh#gXCkmVN(VI8+QMNiXnJi4y2Q z(Sj5*7d+pi8z{KGSEXV&9JLjsXfWVKMOn2et=*3x^xR5&mD5jMLpOqg=)}LsB^r=g zr}tIiaKt*X=>5$OZ~MTpp((cRL&Ajw|7}epmy3@t9dl4lAdPZ)sT%-$>nmcqhJ&Lf zoSgeSS9&laaub}3m3zq}0GsFL^Ca|0!XX>Mh`lNkGSlrb@8~oC1mfLD>;JzhK-iDG zzTutMu|)!1AxweEKT}A0djz8|qW~Y#_f>B~eIlX38Efp5GQrj%N~$@#!obOmyR_LS zg5*;U|N2YXu~z3Vl5*o^mky+_x+4*?+3xWirv8nSbOedlI9OHR>H(JeMn_q72XB2i(FI=6E*-(DGrJ((Nv{d+l^+TuNw?36TmQUTqcvH8epnopbozb5 zT^a?2oon6+VD$^pbtY7ABXkf?4r>Ay*H%3Al-;U7ld1R zOMOLR_4M!3VKp?wzM3>nIl+*qke)n2H%IsUGAUyWT~t3h7ZRI~|DQ-_8}hZY`Bgwi zBq~yWtE2ed!~fhDX`GCbQcg6G%BZ7uV(m`fZH!nUHCbfA{dZ@t&$ryC`Usrjc=Ntz zZ~nzMF09mzfl@U*!&cGdb4)>xfY!!nes1Bsn!@H4;CV@J4C-mq5XY*KyXw~~gtg3x z)+_)_hBBQ|Wi&Bo+>&?zGbvY&I`JIwtpU9x?oiBVb?26!j#T-C8 zG7OPMMpVqx_!bt@gH$u_W4JY2({l42-`P6B4x|yOIN8hXEQt&sXCFS81^^N58pY+~ zvY0`(eDlnV#T_s(HB#zFmnnf zhiW0|ae}MaAUnOq^Evo4LX)r4ucaltvDEGTZ2PYxx7K<3QVSwUyKh%^ZdzGoOhv!W z=P()BiQIrcFuNjX4U*18?(x27J2*($h&vz;XqoYpIk_!AZo!jf#mOrS^P8XSI{c4Y zV60U9(*0CPouHTbC%D8KsgT^A&%F+rP=AI;S0IY?8F*QInC0?b@%{Ce!5{|C{hxb$ zTGMhj>_NxU7VPhmv2)uDekY%&ZnBtmal+G(R}I(ux&Qt2#`(-c#$ywIa>6j*r$;>g zJL326T23x>Z*O3e8Yf4J|M^2z#i?VkRT`X6AVUBHZiuL5s(kd!9!SWnCQbQoEX!hotp1jb0CQ@0z8$cDGmY?ZdaWLk!$!0D2H8kdn6QSgP?rAEpbYMQ zr;ZlIE}}YeWB+%}os|_`<15^X=-`sA3NE4$6twKds z?aI?zKq9+{<&-m^dOy+*9qQY`A#RxbAewlQfTnsGPLc{_6K}$!XEWvCrbcO>T7Vxo zkt;64jry1V&gf?y_r(M>NN&vuKu16+-D(Z|Fcukd-_)ES67W7uYg6c=zkO;C;67wH zfWBPwocM8x_k5xqoq}Be2&(q^+Bn5s&z5~vzpt`0kXS+vj9FMs=Z}jzND7qH+8>!H z*Vjc1b*N5Vz*3ZneC}#aSb^IcZ!5uZ$wtFnu88*BYUlP7sv4hq$uGC^Gv%#5*&2&L z+XsK7ILP1o9xe0+bUnn+W7;pMLS($$!E*M~W-8qxV9`s(w}(fC2MCUrJ&G?#^6WIB zm|j$~CM%;P@Gk)}^sPW)x^K!Y$FE^}@oR0NcaBP+i({y_Yx z2fV%0Z+RuFByl8$+;r=NmYK5~4gl^(Y!Vj$%LU%|(uHshI^>vbGAINwSjI zKAL4&S!*+Sv#fZ9?-eUVU;OF3_HLhqW~;cu+FVlTe=E2K)64G?-Gee=&s?dhAcY z1?2B+v?w(Gk;QpPmyLo`MOJEnz|m|Gm?R$CaHDAB6{N_NA1X41fH6U%l6fvOJ*u8n zty~+~$dPe1*613`MWS@cBYKcYFiJ=mE!2%^le(e{=!Q=7> zsnU^b=t2!+-nkAoz;>HDfw$J3ow<(*!}*%A8`+5%Mwj4Oa_-tTxsybXjcTeBQJ#X` z&**BB{S4^^Xirj^kcPbk>LKBPWFyE=C5s6iQ&c8H5x8`rGyq(soKhphBDHEo*DNHj zD&fQSSJ261U)DseLMtn4x9iQdf6>vdavT#c>0-ZVDZ7l&aDe4eecpu|evIvX=h#Ce z{SAOaxVf_Xj1RQdO==iP2gX%Zi7}GFs3fAP?71#;XCa7RN(UIzw$cM#eD)B!W3m{6 zACeT~MTA%FD8BPxpBS$IJK6b&qYYp;_`yIg-<$WA?D77=+xhdkt%GTm!_@o2JHhdd zHE`Ujla!YL^^`vE!6v0>NjwRIN%pZrihVso{zHK;_DR0C4cT!vZ%C;c+T%;qsZX5g zzeoPIozh)8`Z~oNs#UM(-0Rv6pPk~=zj=@N#Lk)7)jJVNdAHZBy-(%wUE5Dgn3WrQ zye#)=(!XI>DzWD+ltuuj0n4QR{vafdUJJUj>5}>C+P?Zy|YD z=7oZ=sr`qzLQ=cmsictmuSwz{Uy+YztrL62u*WKo%dLX`JJ6JeDCIB|OlGfIH}GJ6-GocvFUz2}wCOvwvnY9$+@J@x3$Bz6bySjj zHL?!Z1^S=oUB~vQ#V5RnQ|QuZ+nv*H4&j_lKUd8tbN@LHvi~u4vF?G`p+jj+R3^`x zM@vZmz_7gD?W8~EMf?n?+8z2gJ}Arw#?>`tlh$lX?{XFhnf8=O#Lqp@l_}UCnv@mD zfNHItHM=u7#O7hMlffbn_ut6{fc_y+e|8on@eOt#mW0*sn5M>}M&z0co(?OkMjbXGN9J>~3P`{QxmA=TJ{tQ^e4CDn3^CqKi6i<`o1UmWOak_51Syp1a8$9?dL zZiK%C6+PZNRXh=XaH97DY9+uV3^DbFo3bH+R(?>C6U4BEie2!#%n1MHi>%3}Dld#S z9s3T=oK|>q|F%u9vpHHTchIyDPx_kZVF{a2av1tUgKjfhDD0x$kPy}v5&+y9@-ad= zk2cD5yNY>Q0roy-p-w{+o|HbE+J@6o0-~c&9z_Wf8%(d+F=+q!v*PcshXa4XAZuZE zTLZTa28cC$VV#W2H4V5hqP4z&dpq}+TAAq5`alPXWLb1mD;Rk51#WJCko@1Aqiv9l zGl#lA99-Fcxo&KnA@_0210g>djn%UnkzahTUwKHN*`DQgScufmvKB z4&!w(oTqLP_jeIz>k`Q_0F%8{C{+~n0|EQUrEWgu{k7&fLyqfs2W_$8OM)eNy`j6s z6_@A#RIrXn<@sM#h-s{j*GXBd?XQ~JKpTIC=nkEJ-(z`DFO^SY2ygEk~#9Z)aJ6noy%{sc-BNqY$+f@nMcms_tU?Ejt zyDB?~f*E3>Z1MXne~2eLYSqfWIe z=*NUMNf9OmYx-trMrsU;xUA(`e|XdnXCPYkJ-M>0R!R@^d337=GDRiE%uIAOw;cil zfNsyzN(%02S;@jy$e>z0m>`G!Y(gFmP|HoZCF!=da0}GS8Y+N`=<)oYvEwzzo=`?xHIn*&XRUDMb6h?mjZ=p}5Irlhi3 zL@}{=w5A*xb@94ClRi6e2b-WD#lbg|P$of{I>8$+u_btZxf5AHzeYUFjq?3Rm1&;f z#)mhD&^P1cG3RIc2zrEj1mI)2GHP%z(EtlCZt8=wT(ZL^M$!cbskZwExpY z#+NTVzGugVw98B6E$*mF1qA2NVhw3kWujjQ84rX^x1X7>pgA`D5nz4QS)7(nIo=*j z(LM>}gs9;aQw!8eC=_(Yg-li7oSGjY!-eNwDp_#v$eXy|}ik^Vf| z1+=&c3Ew}0Qd2J+HZ(|hQo%0of{^vxOh6e101bJhL=WKtKG6Q-Kppa+3Z!Z3-I6K! zxTo8TTK|!sK1~G00*z3Axd!&!7jPcNZP9C|if`(uRSE(PU=~W~XD?9tTdI-ZBsYD$ zW%%bVBjjZxEPt=&&wrf!PA1Ojj?Ya+Ohp$4>8p15;1m+fNOag$FQm0GA+kKZJjs&KwamvG+?=%(p?I2!TbueW~1k_Dt=z2U- zBBNv(@fE(vNPLN+7#M4`pOfSCiuh}PyZrP+gcOZP5;Rj`l^Y^BiA2fcqD7c64dx+2pTXA*OxP~=ex@~YuI!2ml(jFmrW24L>gg^D8u?xK2) z;eu;!P5>i>R&y{gVpDsQG9Go%rPOkAUab3I;`a|xkplv?LJq~#ks>*Gc)%1;C~y9w zv42#~bnEFpS8XqB6*2=K6cR=%nrV{EcsN(S&6XxpGe(`eKDoTAMvfL6WU&GjM`Fy( zypxk53^Rxz!%4L1|6Ly$*EMJJOdlK1=?QdKHdD?mSjZsXrZ3(qzI=wZ(HY}N1i+kK zqYsZnCKMR;T=Vci|4b?**%rJI?k`dGp9YpU*YQ$#n+?Dl;$g-DO)^qXb@T+oRyzPuszIF$nM`= zC7K_A0ezD&|%1J>RoGxxzc z!2eJLzyDf$Zm7TBgiwCCY2}#?L!CY9bp@lKsG;4CAUry}ys6e;o}W|h;5F!JWfK|108Uml$5lv^nc{xzKz!LF#|C@5_;Q*LGq(}2!*$XiwJyE{bl-P z7%6}m&8l#mYQm;m#laHq#YsL&g(}L9gS)e-Zfd(Z@1ur^zyGtJw#q7GQ0yUOrct&y z!;%-PyeS+O0bj>km99-X3pMyxA!iKL07ErpL$nLOiUH#u#+hweo)65V-7L6a_@c(Y zQf_?RD+$O@yzdxpcU}&p$>cm{{f99R+70@o6sLo2$AMe&9`022pDdh`q+X>IUC+%nWZ^uT9*`F~FeO2rEiF z2IlBZa44Ei{z6s)J1Nclu%BWWg5H(};CBsZAvmm;pT~elKj_?_)L7T7Hvt2gnHA95 zo?iHuek!ioP{>d>k_mI80H%b?ok6O?{3j&X&qExNnl%Z?*k4uSD6uVn9V2v+pnwNV z%`gh_Y4&>p+fd|H=Mf9ZOG*;NN1SOrZr~PvQzIU9po`+%Oj>qiVzwrhq3B>Fqej-#@&BsdZQN$0z-O~AQ%e^DSIa`17m&1>e109gQsO1VGXTi zRIjB4cC*K<%=3e-eH;<$=--;1HavFdx28t92U*+Zk1iBhaT1i}KqQREiyBcyOKLP) ztwfjeIG4(w3snYupNU;Ja`g9x6D^9~w4hnCN)pQmX|#XIP9x1;)TxQzc`H?H8MOQq zSMB}JA3Yt=2n74PMJ%AJ0)~nihws0=?#c#fm#!oDW6!3pbOCYY{JazJ z{c*}>Wmo6YIP3v28`85EG%-9X4)W$iQ){Qswl&>%lUo-|@d7&~{_6EB`5Oa~{pUtTvn*vhrF@ z)efa`39MKEniR@+Z$nK`=jFrj-=u>O(is-7hlaeeL*ALb)m3rHOVyfZiitXbuFKUX z6hJifDl6q5iHlX+B8f|BvaOR|&eb9&B4W57h(wqQCl&nbyCc7s$3b8`YjgM*s3Jr{ zR4PxMC&ikgh7gx56DZX66G}%{x9^m*$2ET0Y{=^v=kSv;ADeQE#W>A(iYizvZ;OIu z`Am5>mteH?q`*8EUVuQLi%VhZ*D(~sv~ixd%W9lcsh#ZM&!h==yRZFClF-P-uXxD}uQjGA?i@ zL+X`M>q6_Gjj`+gSHE`exQ6uK8-C@7u;9O2hw;mLF+hAJ^&5JzqKaoCXv^!G*MYfR zqMI(>?GMrFQ+jbLW?ybB9^DRuamL~?VfrYeP5j>TqOGl>rxhL|;(t}mT%PYWQE*g= zEOPdz;^BYij=CPOw4_&v>$ij-OIxa+dI+9Wky4LveO@jH<1L1`C2Q0iSqy2sUedc! z{l$;Y-%E~0NL7a2!%(t|+=B}z95(ez(;dt)lH3_~& zO=}_1(#9NxG&6V2IsuvnD4rvikOOl0Bu8&4>?ZfQkj_1sxdKD~N5Odde&5^U9H^D%`c#uY3em{SYy8;>N0WEm4Lq|1WyF@q}KA2N- zGZpLjmPrvN1_UmEBZ}kt8WKEl7=#+H4YUe$TtkFho7)nAF{e<6+UEgntq!86XnfW| z(mD>nxQCeWnogt=ovxTz{*P~5DkE_qdBzW`Vy zXVZ9JfovMhm(a`jF78WQ{(nNB)E3rmvRndD0J|kZ5?xHodb>g*O?FjI|5v^58nJ*u zCeAzVadY!Cpql3+<`n3gxwptNsP2>A4e4^ig0tjt$mCNhSDn?jeeq0~SX6+{dBAHR z;>=vDp|wTYrOUPzdfZAh@pw&DwXZ5jI*A}O>#UdI>UHE1+*Ds)>X3x>+_)zBC0D`G z|7x*~gU{X~{J=@4D_n*?2+hsWWeaqf0 z^2OhgQ!^lJHFPMM6m7b{9&$Jj4Ee)Of7#+Yg@Q!t-Lm9L$;)Y|brjgGr!Uht_vP8- zicyF5;A`}=E+*AY5~3;0eVK}{zObgjkvf>}UZ)=)n`OcT#`Y$F`;3>c57=a6j!XmIY$4hk)auuudtm`sK|7_qgB_1DsQwXWKJn-Xf%S z$A~&A2eT_MjDu+&9yWI}zHIldi=DZgu^mhp6LNn2C0Wd6BxD)ya9>*NIh0bzs!!o{ z@nMN{6F^(4{WsbKiwzeN)7+ncyUty)b)3!x^X~$tn>#~Nudxig?fP?2mV@~!`C@w% z3d4)m26PPk@?T4HCozTAB}ez9v*i1pc*W75W?POkQr!MT*BIu}vz^8urywsMC+)Z4 zVc+)8F-0}b^$5PU!@9K;dmMe|rUFD())XM=vz;RVm{VqRn4;|XHH?SK{?RoUpxP(? z4mQtEkrCI8ggMgd6rbi+2^z2nDpKkzotqs4(8sizvfz)F1=Xb-(Vy}N_8^k7E^PX_ zVcN(cpS{bNk_!1&$OrvWJ#~G}N#Z2L^OQ7T#caMRlsGNl9;}+)Q7o8rGjO74lnOppR-`s;3fp65R8@KplErUx>KBr|oh+E@M00 zJp18Q)1#DgWk>jNgxT5n$F^-vS%ySvpf&w<6V(sy{CkHt=J__2rZ<}7(Z7oCRVF}* zw*TbtQOLV{@(puS=%bdQ;k$k3$w7VWb(gEW|HzCP0o>(rC18%VIHm#IOD5mY1K5y< z>!X2aSP@6@{ybXdW?^C6MV8<>OXp}tLM%!3$onBj37OMGM zMIh-Qp0P9zl$LG9r0-VA0`d82{=z<5W~l!y1Gu?@dqcBkyW@?wK+n$@ug8V@`B^+n zDw6ON*32{yxKte?4gIyIs{Gg*l>FD)HN=iTS6{Qe8PzFTyNW`VTK$k1_kG@;dh_TW ztjiqeeUBFUqoY${|Cy=^=Q}?IVTCjZN$hfz)=_%aN;q|#i2m2xsW^nm10Oz^Jj1@i zgt?d@v6aZ8SQL-A#{&uT5PAW65O|i>c;zb%a<4m{@#cUhqjEu&mU*V9bS~W84T~0F zy+#hCgB-8Cm(vN4cm2+f5n%I-wmST;9fl-Fqzvx)T?@)Jz;R(Zy7Np%CcF)Y{?99T zA)mkvJhBlZNI_PXxXwRFkCSQ?$e#hI)abHiE ze0y=2_EJ6&*z^CT&3g@Ul26M!drh{Dv1MgCteNiCJV9vIX|8pND$p-7!UjCjs(Y$> zwtBs@@&LK7)k7ge(I%3%-%I0vzq?`1-Yh-pKwfN?jzpgh4dhSdZ2;R_+td>2*=Gb@ zE>}$5X8LU2AYaS8?_4xQCjicO`K-)Am*_XlV%bo<9O9~^zEXMl-|PxgAAz@ zD^Ek!I(c9O%le5L5**uFUw&u>8zvJ>0d;pY!vOEM{mG+U731+!tNVuW#oM!$m9&^< z$PKgz)XZ_JHSeX$J(xg#E*~dSdWm**V-OD+-QcX4Wbw$cRPQZP!W?DJF7fmFd_17=fO3@uJ%l=h9{VIDJtXH$-CHQe5-&0wPuyN?3wr`VKrm&)BhdExSp6-TMUW+16DT9H> zu=I+hL9UVLM|0P6*!E;;LZ4ksKfKOTpe6bws6zuugfjgW3q(<7K*4Ffp3lTCD;kb! zW#T@Le<9E36*FmRlst=42>SZonG`cn08Jwgx92Yi-zrGL280=J5Mu)fSi9Zp?{+zUq?Y> zJgg%q#fi6R(DL^Xw~Oq5e8u0-+rI=UnD<4XX3Ncy;Bm7~@J^hf?9t4f6EV~R*< zv);bSxv4AYfv$%DGY3=vNPBRpK<;qTk{$kw%o75h_9^5}~!`*|*B@Dhnskr0_o9`&A$trJo{@1ck?tctQ+U=qVp{)PXkt8%RW%V`G`4IsP481f&Qd)*SWWU%DcoAAumtO1A9c&HtiPcJVIW|C)$3 zFVh^>26)g5uo3dK`{E3n>l(#@_)2}At9}X^Yw-7{l@&1>_JNUqvR#`%PLK+|I|w#X z0WZ`FlUowzV}VxRccOYWB^xbaH3k_sK>}k1nEdWSDY!Kyl*FL?ZI%1y;M3m(C?#bD zBm^)8I?8qK9AY(dYQKmFF{Al%`qr#%6l#A*dcW~IHAHCB#m5dJ1VTU(T+!;)zj7y& zz-7QKtT@`46Oka5@=s-op&gh@{7KmwF8W*Bh3IM{Lt&^>_F+Xc%0X)6Y`FWwzNgI7 zTW}p};`iUvM`fv!Y!{G%PBsG?*EGsRQ^Ac*A+0Up26-n+>@aa8NMeN^zOgP1a2~gw3@Q9F5*^raika-A5mDvEFiZkGMeQmdr$U!?On{jyhou3O&Gra*eD znLmzL5|h3S7z03r9C3FKUbashKyPi{D7oHv;i5X_1VS?3w9NuSL;a6A=a(~0BKZ*~ z`I7=Mi|HlHK!t2Jh>_}r*a-1OR=F}h?~SZ;H*FyYWmMUPV)Yi7$J-Ksml;dU5+mC2 zB{TOmkZ_Nqx9g2vvN*E!w}Ru|e`*;+6=L<5D zMDAl#YbF@{=b}{8YZXkFhP_s!quzeeEsTB2r0N)1UC|@Zy<}NC0;NkE3%*B{4k4q* zhVUzjm=~g7-k}ucy&*Xpe=Llbawe7(dW+~;+tEVidG>XEngZ2}+f#ifXv~>3WnwX6 zVHSX1A~sZgFts}b(2{Udq_1R-i$SQRKLO#MI`1hf2J>Zex6Y%j@beg-pUC`ZVgQbF zlpPiqP}2cc^QL!LSfS(tcWCdKV_K%>j>{eha6jwj=rZl%K3r^y1=G~J5=NL=*7n*M zrx*jrMT=CgL;M$KtQ?9$EAjNu=pA+u0wrhLRjc)%xOb(kUvWAl3P2`2&C#I)bR>XZ zwxw4vc#rMdum{(De0)}I3XNTH&XV?M ztO5x4&yfy#-22d`+FxAryf3F2eam7^bD;!7Hr{>vKi4dzBzMhx>`liH>p02m$sqW28S_||Rv9aN#0&0ZI$((cz+NGaE^Yze41)=l@b+kpIv5}~xD4W<7 zIT13<7a17=uaLx*JO^(E%GX~ZtMxziG!~N071!Z_{+2#iCX*m0At?zu|0*%fNv{2m ztm7;1U4K-OZ!tz{XIwM|wEkX7SX(qjzu=W`@Oed2qJ3AguS@%;7vM41Zv*|2_gI&` zJV~olM%$jtX6q7e?5j!6nXFWl{lu_D-C1{q%rdUOP3m`p%0oax4g%)WWbV*lfD>t` zw0qjQ6ced^d>+`fQ;oAYfo@+%PeSS!p$h~QlXv~J=Ev?k zRPJSX&(}WPWRx%{_cN2^NbWS&1UFun_dWk8Afi;DMsemALCOzIC#jI|co#f!3|3|W z3O!y5LeDi|@&qJ((`rFXq~h4ZK88ZbiGbgdvKA|jrJ8s~ao>1JpoATw=|5OMJKyEB ze<40s#|!WddbEPPeR^8LB!sO(-tyMX6{S&4JOIdq1i`{hQX(d2s5LeOX|q%aM~RBS z=jnxQPUH+bGeUqNOxt#qU%oZL0a4#BMXa()d09I2n38<$eN5w&9Wo^SZaSyRNc+SO z45c2tpxnqvvl^+X)4=3%)m(094w9tbD>i~t$MmW-z*{Jy*G?7a9w`P!e=*6j8xEK@ zSyM$U3%jUd-(Nn!BYhcOr;?X;b5A*~L4&$KH^o8-hJB7N0#d$Sz6Ql|-AF+TMcI#u zm=dh!q#fMohy6Lvm$w|8krs#l%s=CozE1?_;_2o1Ff(=v3YZbV4WuS2oDpTU@G^gpBc)!+LV*KJ zd4sj3xlR%-=%E_|=;eSKKu`!1$_7A>O0tI*-X^m6>9pkep!GF-S+=Z{GOz!R@;MkqSOmG?`^R2t*NR~ zuksRju(YU#z4QYUu2>=nk#A)1N3VzcUj?S=D2`mhN$ia$<^Zqi^ck9aTREN$f%dP@ z{RIRM7Wm-8A3QZG?up;hE@4R%pWb%cXn!M>@xBhz)AEC7Kd8dZeJxx?DYh0o`k4gf zTrEieWfnG)E&J5@L=*+BLJp8X$A9-6OCwu%_&s9{6z%DfZ1eO-sea;v>bZ04%%?B$ z)rLNe7v~rl^&H!+U7kN;*gEVehfJNJzr4Ars?OYo#W8FKW zi*!4-3urY{SUw3>5!)NL&@b}(WpX@*e3QC}4#xO6nuMB1AstJTiYbbao2*J44Nvb& zdmO|lGqc@seow|p+uH@YR%(Nat^se^^KqEOx@dp}0<`sol?Ckm+>jz|8QPO61YO|w z#2Ao_%q#%_f)ju4)_S2wA5hKx7A^6R6Ecek-L!|8Jod<_%0U=yYSlkn&Lr^p{=)w;K}HkxQ{YPTWsM&B^0H_H^VikPQY`bX zI7gzBB-(_et-Pk+q2B+nAUlK6fWN1}jj&LoS4%ILjcRF4q+u)#B}#31lFPyvK}BX2 zlXj@%ndR>B8t|Xm2PCT$A4Lzc?)rCG2~Yz!DqkA>iKg3y2Qsx$q98F#pVLg0A8vmb zK&GZaKoXk}Ing5N;?i{5Eei-hL^Rd?V3QLs4t(CvN{@!1$^)Rzk#j!Th=%m>X`0`)OZX=N z0d11oU&`0akTbI?6eXK5l4i ztzErA+J70d_&%%LFax?kG`u;60UzRnXpXOhZzsRvEyVfwA}4U65JCaB4j~G}_A6*c zP4DIsPq``)`3X)p!f_0U#4Rk4%L3CNs5~B&=$V~cX|JA+ng}EBQA-1D@er;8XvIb% z%9FWsUB<`WbZgY6h{7solz$aPpdwh8lL)aNi_*Cs0*;*a?zHk0I1`UFT8{{|fJ&%ZH*c&+>T|pS+eOQ5trOj@YK(3e)FX?RS|y0UrTZWDlQvxNeoU z@`ou#Y)K%|3`pPFT{RSAz<`l0;mguO>5%Wqqme>u-^8$ts~vzDwp;OlL7}{I0{knN zn23ya@je=bJ0EER!8>)F4EI*HSh4N?$k)ekjYaJ;1(>KP_izm6pnoBtx*FbeUiMYw zv-jxv?vzd23pqMg+`ZKijLT;GPDPhu@e7#y6dRO|^A3^D;ic)-Vjc(lekV;|PY`j@ zL}|e)J-S?wYftLhdZv1|K5fnNeZ{PVF>zyHAizD#kw2_-tfF2|nn)h^qg~O`&7iQ34f7kaA4|h%1idG_RO=zB9Ye0B@aCtSmc28p2>28pEm(Pdy2XFw#zV@}&9CM6wl)%Km;laIR3k-Ygcsk*3A=Ix5fQcJE_(bKg`iNQ%4|@-v z&n`XM-_$V~kT!7*+F$F?ZqmaI1*6|+cZc1_m&4}oi|dPLfwV7P=l}b_8{2ja-8#y8 z&ZPaq)et9Uj~=Ct;NDrkqg$l@x7Uds$STj-1Y_UZLTG|*xb`6Z7t7~3@GS+gR$8AA zn*biyV#KjGRxh;B&ml;1Lz0g~3=OS6zes$#wU6pnI!;Cc($ga5nELxnd#ONzhIRNt zSWVdU++y4UpXkKCt9*t*5J?#eCrY$|hib_hDXrBe*~RqHeK;60C=hjaKJ%QLFq{OO zGp4BvJ0$&GCc@5Cd+#P1>QTDuBaUb^49gLAOg*he0bk6n?RCpAFaN90nUF-eM8h}f z-N)W+?zO%siMVg%@bIT=s?f}8rB@Wo3l{ToLS5flWNP&voB1=qXK&T)$ZSA$omDYzQVC@oZ{wt=+eZP9q`yp=rp&REi_2LJT#-=LC&E-u2YQT6Vr7X7KG?Gu# z6E1iN%6u5eTDH^xOcGV?cRW|UE1^* z#6J3To0rW6I-&%@Os&Yux{O=-SyCDW5EUHt5(+7g#f)g8Biub8Z^awvRNiE05Q4GY z#7UWNK4eqQ&SVqz$L72N^nJA}=Ky_#>ZqV1=2IpQ1P=Pzm*l+ydQDh;od{s4bo{8| zw~O`ZgO3cj8~~}xp;OeUF7n^IG`quy*#R#TNpG6!#8Qd|cx3oY8TqxpXggPo2P;hy zJF0PAPENI#3X}Ed&WYI|&CmUI7w-AY-(gqRUW1|0@#I}Z_x}{4J=#tWT$lw5#m>nj zJD|x5UQBGe{RFT48PB!Oac}J~QkqTViieBSxZJi075j+xlXjp0;{`)==6@XwR(D7S z##+A=Jm-3xv&QrgsXf8W#;sM1*iVI@{i`xkL^OOm@T zS5KS6q?bY2q>etmnQA4R$hmPxCMkaj+!Lm?94Fz+(y5zfdu!CfZ{4937E5IjMB({D z7|plYejgr2XDoo^v0D5W^!=+V20f#0_9;CNbHYdVs1*w&ciel~-bAYKhy^LnHHX@0|awWphLFlj+;J;1j>rM0f<`(;kbaS-QJYu2)fiM{kO`ssxMa` zN?)_jFxP%ot0jlZDkS`@B?~QIA^9Xo1Fm-u{z&-+HyWDi18dghsK2k&^5tgI-;UeX zJy_X9Rw~UWG4o!ePuUU%*VJ83dE&;C&-@vR*wm`0R!Ay?$PVsIx_A|R@K;HreW-D6 zD5pKab@fsDVNi0Mad4%mg!j3`N>-e8bI_&*#VWG7A<%7iN(<0sP#5V!swK+ zmQikF^S`en^tSpuNu5Huq)Ja$p4lvVS5#k=6!bw4B1@(i&w+7z_s21Nr{5 z4Cb88O+3^Vvqnpn2A-AePpQ2s@wGj4Pb((>&B%Egb^ zXc=$k(na4L1ilB>v;q#{Gf=}AM4vCsntY)O!Z*hCk2y+*-n`Dg2sH3;`M~(+0#dNit`<=TAOce>G^d8TKnY|cWwy<;)URk zHyq!(7yaVah5fQ>3NuxItk4o8gCPMUR@~L|vw2|})65tdJhuO7T7_fW0F_wTa;ahz zmd}4i%XvuAvg(qP3izC=Mv3T$Y8$-6?&Na7Bn>jPdzVxZ402QQ(09{)rTizR0fr%x zaRZGg`Xf7rON(u(%=Cq|7K`+W+9P{?Sg(Qxdq|ptn+L(!hGs%X^!|l@L1d_`AwzT| zPT%}A=~=k^esA7&lRTHzCM9Tm;f?ve);8{JpYGD^QuRl3lGARt)Vb6pENBYKW69&3 zgH(3`CFRv%B`0rzmwqD+-Bf z8_56iEv=thSe4i>2zcJ@V&q8w=={L3G0cxxOS<0rB^uj|1s^%dLGHVJL;Jv|=sE=7U((@B;AhC9{$5h~{;^kVSIyBrrfU94(l z!Dl_-yZwGNF@};jX3*W8bwu_g^Tu1r-(p_9&zC}Lx<~?#<~Gw|D@R}?Dev^hEk8T* zLBQD~_`iVBA8&_!>dWxaEHXgLi9a!Fvd+&t8KN_>37rssOJhw<$w{~hFt}~b9XRqO zM|!BN0-Isr)mUDJ^a>x z;&^Fo^(26glYVP)Px+Wa8ONqm{2)qlG@ zmhr@$?cF>0vvti)I7#ZTxVt-b%?XPce8ZOLV(M!;sVpIBe!Q~S+8L;sUs;t{Cuj6O z@2IxkBZ&k1`_=%12xXfGTA_+4Y8bq}W@Nug#HP~Pz{8Sm#e!a^sITLB5o7k{4=}C& z_a4}j#QtDEQUbe*Ww{!_A_I&vKpu5v3n)dF?}_1wddttUpDe`n(9irr_$ax;X(69v z%c;`G3;E?XC*osW$-2nIPOo12o*Fv}ua80-oBrX|RpDVbw$O2(RW0-3DG)K<{+q=- z1CL2eY!N*Ni}KTHfI9*o#B@|wpU3x z!r>O$#+qNam}WqAD}EI~7Pt54>&=*d%NmV`1s<%h0oNCCW&dn#xeU`BK>quCGRz1%)6< zOoWU&I0(cA*ZfAFl^!mAP6bNR?uBT&PsYe_(XzOI$+}$hVOLD)*`p`*-+dh^ukkjH zsxZR`Q9zDY2RoIdETnfyvi8o{{0i>Oe zIV=XHO!`TE2k%o!|92^8HoR{9eL-0}xW_jCJIQfia*8RFNo}%=b6M4$A5qcSwy1=j zq{%2R9d0Q2jCfBiBi2Yq7MqJJE7D|cQE@*D2C9J-K><|^Xp%V-MxzszvlKmK_M9MY zMBVBUw|}usTP`$^5F|re7qv}?v+JtB9fj}aL@__$rYcYE#NTNqT*p@9y9wA>LXOC6?Bv;G2knp3hN%pX%Cj(drhg) zsO2T4gHiHl`?EgtZ|3n0I8O6?Bvsod-b6{uK;S|XBoU;s*aeaR2^z@^>auLC!|uc8 zIGWX4yFlJg6SK0iP1C>4+8sKF#-(S@U$x)+K_1| zH4~U>Ke>u5(l;uv$M< zN1!5u!QqriJa@2b#vBW{Nq)Wu(5ue4=Wj3QLb;T!9)?EKM>Z3iq5qr&^L^hPq4@C1 zPTeEXkj$J-lSd>VRjvI&Ut}Z7=Kvz&@A@-I@@v-z&z~Zr4_VN#qf#Cfzs?-C#4H|4%4N4C2iUnRG+14rH6w7g{G30E)@#t z7c3dN$Q(M6(uvX|C6y3lafGObXvbHP4u=7&#F?W^y;Pc{RpwY|r_pntb@5sa^%cEB zQ9*)y%}R+llCQA?5eN zd7-(GjL#({PuY2eCC?eL<(UQGRxgdf}$YL3dCR&CyeKf&$gTr6cK2sv)BeRGP>`l zSM@=boYN-fx=d6Mf+mZGIti48#Sg#qbf}`l;C=rW$0<^Ap}B2Pk(CN~rp%f*(Ck9$ zA=kz(RA;bsdeW;}sl~!$74oKyp_~R5fFLe%fIT4A+RqsC{Z@+!3|qVW zbee*AS|r~B1Eoc%RN27@9=^Q1JgfPtDB3rf<#;r)5Psq+6$Jcys&*edM#i*E+VE4b zPvg#Yotr5T=<6!A(HVRjRJuqu@HSs{cj%h0LEa8=AnFJDp#8hCD{Pt%5eCpXD|epA zE7uPtws`uQa0UQUPZaZMD@0f|Lb3V{4fIC^co5?T9#7lM)~Sy{H)3Bb9paeaC#5L? z`dFDM!L{w4)c3#82tJ-t^LG|GXkaI)MPZl(lQ*GbI4ovRhltlrCQE7Cqrrrpuk1cN z>T~sHG>bh8F)S^12snroQxwNdUk1J(VnW78$2L%)gLaj^Rxc$J$hv3Gy2iBx1M@V~}?vV{A2J@k<*-$=A>K+okeJo97VaoIju0iG+3=cAFAH`#OO|N>cF{9U57}kKh0Y?ABc2aTHBr%JiYdRD{=aXF@~h3banH zL%}WOXmDD4;}q>efpNlOzT1Ram6a8`XReOxo_?W;oeXk+qLTi**8X>1@I(><{Q+A_ z@r(Z?t-QEv{sh&1sQJf;ctYoHuT0nKW)E=nZtsI4I+ zh8=uyzar$ElA|xg##Ap4yUH~#5T8u{&lc>UqW5ZqRS;q#J_91vwV18 zz@##f%K%*!jZ9B1hRDf@i79meuXL3}+a?eENxUQzTJ)jzWLP(8PJ%Qk^_P%$Eq_plBWj*dP2Dx65nf}Kc3hOZ&A$;QT5{Sx(&vXY zxBMOcv0@RoHWe(#OuM#W-l5o1-?cxC6XKy+X+8KoAkTO;lKRi5&n~A`#$MQnc~-4^ z;}~aWY-_93R^O5{H?c9Hl709>AO$iVsYWvVB$fH6m+YqL-Mtl(|=ok5KNu*8b0umgM3`3 zEnG%*Rj8ye+8E8fF#T|>2p+#x9ygSYpMDpWfWUANb?$(UE@cLCB+3NniJ6Rooz@`i zMz2;8#YQX&lLoo*f_9SbNrbai$yyDkb#JUORtrhI|HN~hUbAOPbJ1e<-4B2XI?_O= zysYc)57mui@ASWAg?bj6oO{H&;mb3=4fPNvd%9DFXJmrvmgpVSbKS(ju$9zB`16!- zcAmJ&%7!lCx_4wHYF=TI7tksJQO16<*jRIc&UO-kAGrX^f7b*)1fp4m_)q&5F#AXS zBU9GSb;1QlN)es3ctr1STi5)VIGmB@T8%+GI? zl318P z$XRAcIqoq7GK-cDh5xn8&PNR!z;3g`uAC*BQRDT>s3;I5O1OQLW&7S<>8PBaZ}kSe zBUa>64P>XL<%(&)X;!MeUb5i(okKw?BS2DEExCIFxd%TA*7M-&!*|gmOPG>k^LUT5 z_!y~P;CIkxNmh44^zH5tN`C*nNnV2q_~$dcS&Ag~8SsS*xtX|DJ?08zBa_9-#H0S(c#UlQ^ z+osfZ`JE5eOJ2ZsJ{!l)2oJ=xWiQi(=Or%qbQ9-COG@+}vJMNRDW}^#ES_9CRFt<0 zIn^6pA^eHa6d(_f@Gp<3a%RX}`XX%2)imTY0Q1UiJv@^gp<3wV907dPcc(s$s_OiB z=qsH{K<1Ggp#rKb*!6SNK5T<=4Fq8Po-)7D_>1UYOF`e=%;Vf#B83+RcRv*{R5E8v<15#t$pB;m{R| zIJ)2Xl=-^??(RFq6A5%GX0w62jWfzMh&k>NuxYX*b(LQ>m2=gIbu6k9K88vdaWamI zVR81ONbSNe*VVH}u_CFLTBZ$3R0P(rJ!Y5Mrf@2-v6|QB7n%^>jtcY0iy0e`QHUZ$ zlzg}fmZrdp)j)L36i1z~6A>OLcTEJh01$_ctl`F^3k|Wt6!x!bU_w!)-i{vFziDGv zJ#+`uEzTaY#r0gbpF_&f`GoKTC9fwACQMADrVmQgWu2ef%&Myy?%JN8(aDX{h!gz zE&LImuZ9}13w6lti}q{6I_mSq*a0ME#LLnuvWW>+T3+DLN^!SWmOHbXNcD*?GWqSD zlODnBYpx2un?BC&fs0~TO5)?-5DmW>ZUm?L)A{yR{*XzL8U2L{dYR4GUasr*K!y()u0pL~CjkpMpu zWcB~h4oI9oti71(lCD^YB>*Q-4|w%^kz$lo8jXGcfJ#R;1W^Gy8X1P3vzBv#na zNGiU(t;mBeDuS{4TwN*CD#}adumeawTTB`u2CCVu5qwxz*F8TkiD@a*pIBHf(?Z*n zk|e3p4}XTxpsS1;T$wQ{n#ix3W?==-y-~1}aHEUZWdg@a0+ne{7uN1)GjbH@4n2xC zCsiD>3Cb~c*YyD{Jt}_QUre|V8v3(t*1AI%st)GGarF9t&wi&w-K^mrcY~m|?SsIx zSvTdpjY~XD@ZBkZR2?=~sN-aHU0pX?!2a7&ZM#cDzR}wIX4n;KR)VlB(Q032UXn*)nw|+pX|}v?3#)wvp--ie$t?BgkqWC+9ISdM!I`7qx3Xe- z{d`tApYuzR9U0VAO*J3~mn0O+W4YMj@Db5JhUuUHI*0;%)=a5IX$2T+n--}~Zp^os z@L`7Wsx*4Mwqr`$jzO6DUkA`2mc5YF0yp4ylL+?$76oDYzq<+&fXL|Y^#rPu4O5J( zCF!`}p#Zg1F{?Zfr-a-Hvq3}KXWZk-(RFYjCXQZ5mcn5lEIU7cKB_+AZ4+lu9ac`ucAv+Hi_jleE@&-B&UL%lz;%o@*8Rrj${+lgm_3q%Jb{;@vXhbzlN$BAIUa68T)=3*MFc4!&PC`>E zjS1MndKyW^D2Y%mCkyS_T`F$GzmSt%aDHcekfLW7;zLjt8tJS+ z=dz{TJa+B!Z(HkU0+Vq(q-5Ajjhvu0D6Y`{W;AElL{;{V`C&I@U;l z@;g2VEc`}92`(;Va|FbzqKO2$C%{FjISio>SM8$!0n#KXZ6wohBOme9iiJ@2Ufh8B+!cl%^icrFW+BR0%12tq{G(t20p3cqyBauF z3-fp*(D9eZirjYAQJP={_w&dKFX4av6$i6aMi~qxk_-nwUXk|ysldsH*P5LacFn9M zrA``(7$>Avivh!Zi|=ixBB#)~w3^S5 zqU@Sk!7Klk097>X`Q{6wF~6X4DZLuQH(d@D1|A?WMqv=}WUwhz5BHW65wc?ul}oolvA*k2+zqvl=SfmEnX3#uP(~=hAT{V!L!IND)OBaML%E`H| z`JnYzTBiYueXnus;WiRzfa1Vp#qla zQX>S2bvhs0!@HVoT4JIpMi;fakLJ~#h!{SE8T{$_a_Bh7C;u*Tds%X=CE0cDuF=tS zZuiIQV0awFs@|l9?18(^FnPnGT5akXB@>bn-k~3gxO$NtA%?Vs4G#vb z5++)jJfzfRxtCGH!(sQBNyd%0F7;nJ0e*gdN~apC^3SalQ57RapwB7M_`wY4wpKAS zUu=PEsP%?D^Lzh8kN%9@f!A}eEXw_C^hr_CXl!hY#6`z<>Rb%x@{x~JSoZA6KuUKk zFM`?C-{qR{Y0#p*eJof&l*6)NW>uLvBy>#21?4l9f@P=z4$;?JNCJ$U7H=d)g+5A^A zbD}HWSdK3$NfLjm1w-v8f#??z>ECVvHSlYii4$9h&4Gb5{lYbC>=y33Q)>A${QEr& zT>`1Huly}-Hz)26-(X`QQ;8Z#AVG7Ntl5AzU3X4!broccjk&fYlAA+w>nG8n*jf+e zB%#H;&BQ_(+*&)T!;%UZncc7F6jtA&l*>Qm3PrIZClvNbbJMq_)_*l%NC4f7|~%>e|cZS#uf6tDZHaj=I&kRM_A8a zD5=WfTmqG?+bJRD+6)|X4d{Nk*pq+#rddTs$_0K|+F*euyS_KmXBIsca2S60W9as; z-|W^mi_-oIr@=u^;H&k>Yvuu?wm8d8zj$01TNEi+8*unlSDrqW=`0q z7if{_&=bW9eEQa@@EG^11q+rBpmB9GM_A$F?fNVB39FXwfY*)swYNSsI>HwL85D2j z3o#t$Ru57Ck7rN*?^Cyt(~>U{&+Iw|G%S!lTtg&ffpi;B*Jp9eVID^w{ArYU+xod; zE93~*M$TTEL{w!21bOj9S* zw>1UtdIf_POBWaH&e!LGzm99GJPxmaXw&3Iu!-KjUYaee^y=tKx(lQ`C1Ga}_{YZN z3$$2g|GAPO55K!h&R^J~_`A@`plD*!3ox9w+zsz#^(m<`vDQ>K{8o4cO7e8$k7QL8DB?~2hEu3BYUKi9(FN|Ab#wg&9YW`` zS6-kn&+Hg>fi`8zd98G9d)v4!f5iOou{WmQ#OKEM>$yDQcl52=H?P!r(617*58%5s z;HS1y>#-K){WRXZPW}}Er(G$iYD^Ar)oX_pEyCzx%J|i9+k9lm@jdzv zf{9}TDZ!MkuL`Rc#dZ7ar`JPWTApu${ua0s#NZJ%zBFi;5P!3hQt0*%r)KhYLZf6; zLni!}R}sf+4V5G6%RNk8k1@JXfbi`DI+UKX<#^oS0;^SqF<#`1{{|`gNZOBNT3N~h zt;Ho&QpV(OlJbxQGA>BCbsv}z+q3nVd4*#)RqEQ*w!-Nn88U3~ei06Yiz)lP)yV)Z!6{4*sKmYh)I!QV8=(9J$sj zW)BPh8u}&H?6E0c0La|myriDmg3W;#W~4tP(z4py07;0K89d%~Yp5iiz5=S8$qKwri4={EnPqzB@tzhZ-h6 z)OoIFTAKNt-8vc3*cN&9N{yCAVTvg8lgGPss>m)17?7#L?kFjb%r7Yyfb9|SCiy*! zJ+v`fO&wu;jI1RONYph|d88yj{`(uPkXG>vnX*(ReKbU}Tft45=27^&#~KYN3LYCV zi>4^*)zMM;UIrcO>G(|WZ=meTSHY!4$T;#pL_IaTG4eVTV-BAD@=9xjVkp1<`^4F~@<2TkVuk4bg)YWYdbqTB zt#Vtgaxp?l6Y}(SD{ekCWHKE`yU(0#jT&cOm$W$Y+6Ub0yivB(rLA`^QH!>F^ zRq~AVqEOWv8H3Bq)8S631EzV!NzwT^DV#nG6`7Xy<@>L-WpVbgaZ2g?^&f@FDiduhW2E&!? zmj!#1@zITdON4Gtb?=FKwDYiHwdLSqvpzw7H7_CE7QqY+jrS!MnMF$?q++3jK~qHA{ng zm^`MLiJ(T8*9|B5djVJyZwJ$9LesVHi+(lH{V-uN;@@K?NMSzjc1>75;XYR4{`NMN zw6xX?N2{S1qse=&*9~yEVdGa;raOZ1so;h-KK0tqf5&kCTU%Tct#Q^+pDeK+bN%AkUCy1DkDF$PF zT;1&VIIZYSgSuYKBznE*aLsw4q>q29h^QNTMeqLW`6wcMhh9E6YvtgM`?&BHPlQDiUF5YNusRj9!2(ng zR`BsYA4|N?aN2g-&`>&2<;KE<3lCc+OH%`qD4|S)1RJessQzq#ok+Q`HtySB9RijD zSXTQ~Cm>lQ;-c>+>!y#nu1T0g1FGN*>kPeM$AC`d0eKPz<-Lb(lSk!QV>$}eeGT^C zvTWs?Hpadb=5KHKZxh~k{!Nx`nb`Zt-^gpGF@hu)v`Ax81+n z5R#7!{Y8jU<7zOra|$Vv}VyXbf)i=@ZjR&?wc*ZDihb_^7LAF65F)RKq5AV7)s3#1Op zw>VhB@iC@)RXz^=vXq0vi&&BW@g2&G@7Y3l5E3g#Jd%~=^*GpZR%a)Kb4RuEIPi?MG*Hn*w z$xSu>U20JSZg90-+mxzL$+Fr6%F_pVN@^EtzEL%56DfxJ%C{}CLBQOnqfpMv;#Z_a z6hZ;KZqHA9GURod8t9>l)3#H8{~%87!okgc6Dc{#MQuwE9v50oaWo4FUZ=eqU#5zIbE+(! zZ7&AbIlQGGAB`LIP~Ybc2z#LJ^&%8YpZi?T|Ly|)HC34Nhu8kkP*UUov&s14=|;i$ z6VKaSljhRPvL)%!Twj}y>iOr=aqQ;*KT;jS9G9vAZ^2Vk+(()dYg4}jxvU;0Qs!%{&g1T{M z`-F~73|$0hH=|QwO5lyTK#oh^Li`%7-o7$6AOZA(?L>Onj?iht1 zR}K{NSmdH3?;H)ZsaF=s%ZZJWWYah}fPE6ocP<6ZZcQqXdiD&3t!(1aa{8?fp*{p9 z>TdUVr$AQZQD^Nj+P{7PAfX&LQkeW&T!PshuR+>^s~^xF=^D zCsC(O-S@$TVolAW;MZkeFZdCG5l@}6gM!3Y=A(U$Pgk2IislA?!dr9+h+YyGUouxRyS z?`u#ll1rN-Nxlw)8|x>8X8R#%z>jG~K~#_Vy-T$hO1g}zLOn3)sXU}x0naaLq4=eH z&U{oYV{vJ8ohy=DBYXnr&n(!TpDYTs092q{GqV(D>Lnx4sB{oI>^Z`v$DkOJl%%+l zpL-24O?Ze!`~HWYzb4;VyoZWP<_)40R1c@+Z6;8{BOvn8<(U!@mxh^SZsud-zI;S{e7h~X*cFS6Y=$_~fH!+rP5HPpciw7xrlsV)|?%np* z!ote4DSET-elgzpCE$jD%xR(%vSfvIdQA3~Msa|z3utQLXtxoW3gB_7GdIVs1Pmc> zOk^eM{@!5O9nmpqm32*n19&&x+!2#8mb^t&@A7bPY~UrT%I4$s0iVcowL*~*ow8hY zXmeejL6`=TjlJU3lioW&Ys49+eZ#gQ9r^4QSvu?H$zikZ8!oPeSuP*~t!Nr_&AUw> z@l485A4ecu%Z4kEjSFd~4+pt(o|4Y4 zT)Sud9DuSOs-1)B1)nEyCWP*vGPbH@OUT{kxS z`@ErrOg3f}mjbF0O)xChos{q%-uNe(ciAuEsEB7WSl_IQ}122 z<050kp0zvsEMA>S19F^f8|hJcsG!bVtIIPg*Cp1s@@mMLLJA#sJ!lQEd(ij z$;Hw|KwcKS$|HPo25=klW=vXVVXBH!ILs zHl^Gzfq&c1HPPdB;ug5>EAQxnVq%ZGcZ~nzT^8XBuP2!Kilal&U;n!o$9_KVOjR-P zK1^N>30s_Biwe|omVNqk@D?0_Cv{`&BmV&i4bTTuqDGEyZo?D8*({g@Hr>V5&xuyM zxRNIejn#RlMrX12Oc|8T_@HtfVp0{RDCQ)RHw^p79##5%T0b#-^HOKIZ}DQ& z$eFxtiBm`zps)Y{z!&L(#Z}KiZ-7H^JZYkCYB6uE(t^l^-ht4MI1FD-R)2CU39pWe za7*Gw7;Mf%zqrwtl-tV7QCBVE?+E$X1UcHF6!i)}M;6RWVgPKO>+2Rvyir-G@6Uh% zk>MP@ze!6RK$nm>IM<{(F7>A}Twz}m!HqFcRw%`{ODF;W39cvm=1K$uK z5BkH8VZr2t^WX2?66QIRht-%9;hAoc zrh>)?%eLVU3M!x!cYx0Z1ao_D`ic26#ORRzBZuifX8I%8J%*Ank~%2|4Qt;Sck0!f zjS4}hQ{Vp#SEe~IbqO1NKyUVeP`Xzd+`!eDjdHziP|wb{?P50(gl_yKiL2&755TS$ z_;uy}KFrchjnI1&>)$c1{eIN?Cl9YbWg2E|`4LS7OEVWg`EA_g_L;0A#Tgs=e0X^2 zV6vZ3pSalU3Ij|`Ecb}gs;)p90XcF6zrwfsg`BJP6GVT%b;WK!;3)shRjIh~LGq<;w1}XxW zaoQzh=Uz|ygjNR4Sk`)e+j6ZS8jIz>p?&J@6#9V;S98FA8tu~Plql?%+y~!U5@n_{ z>*IFwxA*6gh-r5fPvw$Qs3gyR#Vnb=I2OT4D@vLFgW}vqJ85rl%Em`ICr+%}&& z1ik7Ecyt-5;CzV`DUIS1jy0%>pCy!q^Z(1q%Y6+EgIUe5NB}3RP)67r_V(Lb>(3nx zVy)l3CO)pVP7OvL%@q9vo0A8y_C@_mUXrf^E%JIfP&9^n`n_@Z;JoyMWNt=xPWIT} zUCY3izBo0qzM=wBIMRSnAsm5us|7%TiczWL}N%ttBkK>I3FLR^?QiR zE%IhRTtw~PvQ;YDsWfBYizuK$71}RX~X}f^4k9b2}}so zLJ0BCUo@lb$cuWl{a}5}lGkeeBYbXGh^w$#zsY)Nr8Q@jQoU5utd1$TO5coefk^Qp zwVt77=H15lvHj6D3!wqL+1|Fy`B}=@x_)oihju-^-RIT2gT9XAKiM2ESq!;vHZ*-Y z3oy9PABDjUM9k>R_a~y|Y&!#DAN7kyNcyP4zX07WE_~8EugQ(NuU7*+oCA!wLe zRN2+M$Wx$zF(LxfAHa*<8ew8evk?#g1p*wFSviG_>Ud2xjMU{3)>a^^-)TwC>t%C2G4#_@ z%#)MNpSJ}4Mb@R)wR(MCX6iUsGquLKyrQp5T+>tLcb<(10OqraSpZ2GKI>gfWAP!dAQx@t{ehN4=f z(Zs~p*V}L5+&mF+*0O0_+@Z&BCFUK_eR8&3Q->EHU5W0nHjxcqO|2rDR`Z_|bISw- zdL*RS2C-cVWRC`3y~!$Hug#wu{x}Mw8ib3zl-)MpC7kt?F0%u&E|{YFrYRa9w1Mo% z83;G?-D=55cX4vbj9Z8BzFw)vp>A=lmyPIUtT-T1V__@RrxPqs%NKCm66W5^8-b;` zR$K88g)Q{e$@*YxH+d~A-q0WuUM5`JWCl)zbL6<2TYhjNZRIcsD9e3=H^JfmIw*ng znUl_1lHV%K`{RVO1Z<%H$^e(XycK3iWI|fJY3Vf;g#BBu#-!N0wuax5faJ-q9A>|u zjv5{G(Vra+qTEAnfR0Qo}?|YNzptHBEmRO{#X=qLorCL7Y?&>;hf-h8& zj}HLz(i_1Ki>bTlR~ZdDV*{c(D5Oe;WhgbuQw+c1H#QbS*<`>`k2mxY@^LuBbrF>L ze#c9CUNooDHy011IUnJEhkZl|UuP&3v)h*T@9X-3s%8!zl%p!qMR>kst`nWtsulpg z`ytAttLwbDxA1MbYEk*$oMbBO&PV-VBZ_C?sZFSVrk-6;a=P=Ul+oW4JXO?fflTZy zKfG~_1j2z&@Dp(!_&iI|plLok`Vjv0OO`4kv@W#bRQp=1fe{;Jt`q64&6KxuDa*?t z9Bau9;NB4Qf;jc~YTWT*L$Q%};iV;I&jGLL1cIn*Ea@e{BXhIE#(^o2m*59ou)G+#jt>L7POxW+ht)b*E#-)ut=01tx@Du0Q1G;zs)Ky}oC3e#uMD>e9$dmzLnyj%rW-DBRYBqF710 zmch}2L#2Tjxa_+ZWD|2-BZ39FsBb4QoT8w~s{I7VK7%3FcF+cny0u(QZT!!F0KWP1 zw(~{p?CJi~mH)61=SjT|vv)nba`0;eyY)2DTl|4wz*+^`b!8n1LU+@wuSf-tkQFx| z$ID=j7E^DPEQx^G8yG*T1?Rz=B`bHp=ehaV&2ilq>moBQ0yHtOta8>fT=AAFVl?Yq zv*`WebAhw)N(cS5#bntzF-2tAZe;MLAO@MZt=GB0+QAu!Lq5@BgB+9EkAoCsJ zvTIn$ip_)Be3ED{WPHTJhF2v0b_Z4d-7J0Hll&tD~xlzO5}fL_!)Qq@`0zKsv6pAR!>Fbf?lF zAtl}2-QC?Fed+GJ^nIJ(d*gd!yuUvGa45<>hqKRKd#$;TLONd);$I|{ zTci$0`Kt$1`>h=lso+x1!F!0=X)3Wwy-dRxwTtl-ZJmu&fpih!E~H8T_*he^qsgXE z-grfmza_LD5`h;g$v#Rfu9 z52QWy2fB1L)6XVS7|a%zjSWc(D6(l(z9oH-9%jVj>}d7az*AbvxqZ0(EIUA8U;tP? zPR1kYu6#aw>Cyc`(a+bLPb}0rBOMYl)s$(cv@lmc;;GA1S=5ZZLt`r~#&C3ya!aXP zqRl6LrPJicCRF@FO)>M~g?De2h?o0&tDH$&zQR6fAH#4T3LC5kJs`c(1Dz9{cv1f8 z!-ReNml~{O|BCwjhoQEoH-nsuDfj4rUl>R8nHGX&X+dwxI<2~g^UT#=T)a|VPM^ho zN9PL5+=VDZON5-5>hl+M=$5xb?@5T-4EMckOzGd4aDIN7GXdmYEX80U?!QgyC&QsK zh(rNHl_DR&yO}ZP%JM6wzvEaG_f+!0Q}=yir-CspV<9+hu;V@*O-I*UJ^`Im!CcTV zMNoGC1N2?L$3!p5%m7->tjUj2j0Tf>i81E!-I{GbZ9oANZ|HS!{8INy#^hX;;ZK&v z{_So5(nrS%XyvGi<_H+@2a`CU!;w_lp<)5Vj_#DX=M%siqzC^4L<)V(0;7u9k)zGN znbF)n2stxC+LWNIRXP|-s=0z4RIjbG`-5wL{IOpkRh+>4!4{pz0FC!eBkb?s5A2%< zrXXqhsvzpg>0$T(K{2LWizDC0@L)GpVnw@aNP5x{mV2(eD>>a4_ns)b9#26zqOET< zRyXr_@rcr$oDeb7o!osi2zcFQT=WPJKZ|af)>UTHitbNJUVT|7-kf4n;&_sd`jgiW z$-VW$=CMRwZF0x^NYeAUq5{++E8Xul#Ps8kWfkc|RPA%6G6H~X40Ur@@(82F?JgrP z@a%*4<7Fu@y#@rZQ8_MGskt9s1?nQm8_OoMb`R?ifHsd7-~cQ47t_VS6S-jPxBiAK z73X+1>NVD1Up@{oVEz?Uv!rYhCH7^7PDu|#+RJ{I+O$N{Z4EJ9i{`>LAE|iH$uha8 zP)!wc2bx??xP40<0tUBRt)0{xL{8Rd0Ruq&- ztdZlW8%1O=i~TACDXLA$4m`|Dxg7NDogz z8nlUawhy}`j5NqJ%{Tcajr>eg?{|divowXFgb;avQ{T;QraY=Vxs-$&YC6^T$a(lV zOiD=oGTUKG5aKs1$E~%qvQ{WfMWe)Ceu3Kqj|a=3o$$x`MEuQX|?9^ezXumfgAy2bk2Mj z>!y(^)~~fxKFrHLoLC$jLfQp>Bcm5zTgqju4v0(}LaNF|uP>&LQt^cHqi%Hin`qf& z*^P~G8ziPHpiSt{K7;A&9fwyyk)uBT?IMgtTj^oW+l!yX2X(C)3(=y&{0Y~SLl`)c zqV&{8dJV4no{LX$qJPT~Gb0F)@$EdK+Oz+bnHvwNB_G+nAFf7k5h1=pztd6K zyIGGtFU&!L{wlus5EGpXUECzr_N@O!ffmh8)1#0b=h)aQN_mu;nzFyIQHr(I`v>)3 zjYmC9na_ZePpd`2&FSZ){eG5s^b}vL_rfCPFMgi!24iB)=AXB7d^hTV8#6k~;W)^7 zuC#M$q|Klo%s7|9_57Yu9q)PXS+b1!G3AOc{rbxe7xScY?cs9PNY0g3;a;Z&^*wbq zPVeh>0eX5qsu<^TU}eg$#T66{kOvmpg`Be*YIwW{i(1axd@#(w3xu0>py0|9Ltm# zqi5d?E?Zip4WiP2r97m%BQ8kN(FSqrzOe3Bi&L9SkK?q)P#5e@9W^cvZ0}uv_^W5= zJyEWmjSnm5`sYQ&9t~8bu#hHi?Ssmt+8CB;h29o?l#$^%q|AJivnBNj?r>xms5;T! zJTB3V0th3_gL(?`*oXUG*?J>`Usa~G#}+$!OpN`3_kyc4$`PY((?Qk=`U$m>^yN7A z*gx)-f3M3wtMrK%0b1^N8q8hoD=a+%FqF3lgHq*9mqC(0L06+iet-ReVQzFetn*OD z?|=O7y>v^MAph@DCZN$9+5O6>%%{3C;O_`U(A#gaDB}@EIJ0Jy8OZJ~MB$nJ?qynP zoNamZQ;eYo>G$qg%aitlZJUuVe$8=iZlV19H~QX^;>=-HsS5j=!^%j0F|Ci0!W7k+|9gds)~e1O(QKmL+*Rc!>Qq}{M10NARs*G#XcnLs>w=V#qLCnkm!xK6Bu;EOJ zYxyPj&$>iQ+jLHg0*gvl;jW6b6!HXCk5z9LpOR8G+JuSrJ68;9C22TLm+081%8!96 z=kklHD`VCv7L#w~#DFk`+KiHfj(6<)fznAt_D=qj)(oDe4u1M*CI$d_{#kIc-CvVJXe9&T$b^}c=n10eWi(;Pd31D$InAQs#0Z)6e@ z$UOHxT7%zAf4r#2UPDeZ!o*Qc_ZCYZk`E4KxVH2}yLo!@kj&uXZ7$2KGiVYMzegz$ zQ>ylSsYg?X1`4H_ndyv8{0Jl>ihE|39_DAcjJyXVNYhMXr%K7P@DrLDAXqU*<54SJ^uDdk zsMfEHMF0VwF61-QJ8T+?YQ2hy*{5G~D#WG=%AuM$t7_X4{hy^M0UiQa!-KI@JVZQJ zoc?bxV*5r$1K$JBxA;*yO>t14g13R4N1C4Ay4WRD_wXS?VkY%lOm82_MQXCI=nLr& z!iOA(p%wGoEW#Z{Oo~UvTITcn329<(dEW~Uh{as*@BO0H56+VJz z>%Ym!r!&i3CUC8q=<)%;(0bb-z~)_wGDGaF032qR`7={3$8!S}i1C9_BAE}I$a0~( z7ZAn4WoSpAWEP%Kphkoav+~uy8g|P^zv+>!KKJ_{cmY`Sh)CW~bL&cfmJT9Wg8EXr zMzXZ2sFQDl{iNIP6aywO-YmS$|HW)=?_#pFg#0U0N-Ho6pMlcMF44ljEQwdo6WE@~ zpg6B(%b+pfjxxz&2tGBper4|BS2^F27~dY7A~v#RS)x3#txJ^4cjgTId0*)T7{xOL zxLAamIL4Tmqa86?t|SV%_i&MU7P;axe|^Vdz)8%I`d)str)Tv0Ug)o_iCXODV2RIR z-Z9yKUdFxa*sgwqxhs%VoL3^O27O6AX!{FT`>gJ z>l+ozX8a44UHAA>O`VMl?=WyUutz5J$rb+XmjyyUvAN0?#Sv?x!qhTUQv;!s(oXMr z;6P)Yp35pHo+~W0jlWZP4O#6GO3LjhfqBYzV61;e+ra#bFjfogadoj(Y0DpXQfnD#fFOsvyR(-L*?(D-p`7_^`vr=>GwW z`f0^56ADWG??#PbZTZZdTBNTcWOZY1Uw zn771BZ{S6id0Zq6v?AutaVE-fjtHQ?6Dl@$5TT%eO-e@jJ;BP@zg_o1mLbvLN^|J~ zo_9ng@Y38!!dLBMcsV||-M%v8OLS(kW}y=!V!$8oY9_3uh@h$TIHwBE%VP;~+Nx-k zRqj19ss;$;U}L$(GkUej|26w`MAH&nvjrXf)9@BV(#K{O%21MG6`xb zlA)DU$J7N(F6AmVADME=RuJ+_6x^eQ=N~xUVvQFL9=X+Jy6JOrI)L#!QRBK=IojRP z(7FBASBa#bZDl3?UK_Lv4J z#N5qDQuiD2NIlaO`Hf=f6`@TjuM9o%7+f8sELU1iu&r@T=$KI21A4)Lxkdqnip0|J zVs>Bgj{W<)ia-AvfS%aJC5&nx8I#_lxx8$!U*lp=K)#dG;i%6#wf(jH53!T&a!0*|b2Vw?8H+rHKZN6p-)ia`Oegz&)hF0--^82oDx=`A zpXsovxRUa*IUqz{r`FPKW2%9HPnA-yn}b(9bNC&HmJPIHharhMq*Z*|WTlIXo28Dq zCP5;_Rn$gDw_&&E`cp>_V>gd6nD6{0pzYpRr>Kpl$DEIjmDv+RV60q`LCR^+ z5{?6T12dY0q#>s5*)Vq!F<)KKuPZ7Q=lG7D`4pic^-!SQLd`^es58u6ZfH=HnQ1ZI z1aC)Tv9Ks3js8`*N*h7w3hRM9qvBZW4Y$-Y!!dpW>K;?MB3&^``UFFvJa^HGrFE@~ z1ybCx%&|8Mi&W5gNz^GuNWA>uj%je8^teKTlO?&UY22M-vsi6)D11zkcWXE;Zd1@T z8|DCz&ba$Ly`#a*5{6^7YC)C~1%{XnErdcK?3*M0TD1BT_E0`) zIjaK((;76tUtmOlg=ty$3ad$}kIoS^v^IgAlmX5VCo3fRV{41hdqHc@)KF;5HQrJpr&yPX)E6y$-K2q^oh}JJkwatVpw-v6N%~y z`G@FPf1LyPU7fWY!wHd=`pD0PFRu^B9rJEw9-t`vV9QlhNHZvRCs_-82{Z>p9*x;;_j1>zpeAAf(F#U}Lncz@`cw_jsUKD6E@PtTY*u;1x% z_h>$|^(ejb-sgJxZ<;M%wf?9j42uYCWT5O=TJ3imT{GIlz?-9HrK^tZmhmaIrCP%3 zB1oU*+b`^zAK%9+bNasukkLHNoqx~|U!JRyWM0?sbUdI@nqafx!+RzukcD|Q*lr#0 z5>o|oyUS&$`iCX=lkXl6!R^Zj_rhyua5)IP9jP+}v981&!`A5a?Ib;@t3Y6`o$umA z$1AsfaOmwO&A9^tq|SuKZ+;)?HhEdhQ(FV;uK*z(RfOB)Pgz*+mMm`1ncZ@mmkz=m z>aS9?+H|y9;}hNr2~dZqj89m@VQYN(Fm5ha@5-YI=c63pA*iE6Q#>6le^_?x&*J@` zFs|KuSJS$1Mv2bY$nh^+P6#Lu{PbdPQ0 zVEkz-kfm{`w1q|lcq~Xx+kq|>n>l(1E8uJxvRR2DgZC|wDQTUKH+@%ic5feGkQU)R_~L;fP!DA4`pCj%gM4i&QP|$AUBG-cQUVhsV6q} z)4`jbzRwg&$mcQ$@bS0b62HECXOQ9%{UAx6H*uI+MQta4l5dZ3yB=7GFxFtTqKq)9 zqeg2dn4(TBRg^vRwz^26OG#fI!dMJDWnY9X(bn372HHylHxgTYr7YO~elA^o2361! zT&U?ce)Or*g2z-S{u0t6scER}NrR_`uhiroXsTYG2JYYZm5dEAL$8@q1@9zvgh(8f znPw1%R|pg zLfs~ywY+zzw;NQp8ZTp!l8GXU3ZlL70-^CBDV60qz;$L9m?o}GqfIq6)5k1RWs@Sb z+eb0*5-Fni{?f~JDLQsLJ3eUVTX4CO3QS~>Rs$cODj%hdb-FAS_J`WAG{Q{N{=n0~ z?;Vx5+tP?q?6}U6Y~=14 z(@B;<_|k~HqKvaYpE~WnRh>f|n{jadm!WS59sj(4dDk_nSFxGCtBl8<0gp=10AmRjbS@R%N6VW7F<@aaP=FY`8_Wm`5sZ>`Yw>WJgB{TmIpZ#n(oo3Z zm|I*bGX+cPRg>h5X1SBY_6hCFA^IPO2e$3NJMpoGn>|O=z+Tl?&MIfIK!d*b^$SqS_u&U(gqf6vB^ficVtE43`i%&u?Lhwh zl5Mvoa;|(9PDEf!`DDaH_REVCC@2i8dG!jXL2W}gVDi&uqzg<(~48Pz31_3_Zb{6sRC4NaB z`xC!iRhk$8$^3LWY}97Wd)_0ayx58NcoKyAOD~j2 z31fDhC|(Uh>uk?gsek7TVE<856S8-YHw7&)`Yv;Iyzb>2E}tzuC$dCgxRieUia8^? zHin9^F}HQ%bl zS~z#Yt7H-&5+<~s=-9zbT!i6617vEo^g=xrXoEYx*E%`e73%-`%xA%AQ3?`P(rRbN zOKt49(uqaAK|(RqJ_}>~pGlXP7pcR-Ee|7n8t?mTtm9l#m7IaWounf`8Nh%$T?m+C z2CWQEZ<=f)_6-HL$b^-myqYNES}cvF>rvs%SDXQnv6C_tWNyNT2Il>iSt*x!oB0fF zbY_5`gOl~jW8W446gmsaLd@A>wEL+jA#YT5IFOp2(rfC;UeC`s<7o;mAK@QRfS@5qe2$!fi{AoRgtN#Lx~DQ(UK)7| z^yqaE3OAyQCGX?X)!Rzk9#^3y!5|8&kv&^AH7U%O$UNK?Pfh16aH{80`kUQG`_x!s z`aJi(01c=`Xl>|q)RQ+^Hlp9F%J~t`7WkxA{hM`QW+%u!6sA?jI-d6&&PNiTobphw zJ8T5~3CcAdrfym&BVOTEL|p&AEep%iXkcan#tv97DFfp)xc2FAfVHBA-H<1l6 zA0o04v#LBog0$P%NFDeaD!pDK32r>+P><~xMF&lA1d;<7xGW_aO27+ttxgVhj>RW;ck-=D{?uh9`7?J2MFekE9joj^VK ziA5P+;v78<%LPCzJVTZsD`Jiyw8}7f+7)Kl2Fh&mx6^05pn}d@z%2=Gvgvv8;B-2A zuW)E^`1x{X>C27IWn)5-{OCfdH_A?55;i%A|ig7r`!7 z((J=c7oNRC0Sc&@e+VbKUb^F@f1e3Z!J?sXO%hz?&5mJEE&@speiq9+WFWJPFoLoy z<_;)0`h&0p29Jt&v`TbohIfg<8m zdbva_<6v5v;V;6uK%7Yrcf7Is?)`J1f)oC4H}ko0G?UiqE7Y~KpyL}R&G#_(;#=Hr zwnp*C{}3Pi`!fe(lf+Sfd9Ji8XLT)Ue?9O;05!25f#V#KaC_gi6S0I1W2CI66_}w-h|ufHecV=Xut)(J`Pk)AHD&2AK>MJfP{2>~V_N#a!@=Bk&v^E>*03CNB>Wd zcPyAe^@X7Tpb0LT&7|y_ln+t}Ke5tEf=ZW_jrq8Q0`fpjHZ*-#Ef0aKowpO>24I`> zRkG>5X=nR8RgjKqe##)Wt9X&_+x{%u$j15%=xo=~MtNf#G^ld7oFt z=GmzPNOj^xA9(AMQx%R?OJsmT{={M$F+JC6EPuC8&ZJdG&--msfpG&C(BnG%4vy8~ z=IPM6!A&r@4|R6oZ-xTya2&M`rL|p`TwJgGSJT(v%mT8q=QF05_hRTnt&>AcD%VxJ z=630rO}Ub@j0K~c)G8FO^!Uwffz77xFhZ87{10Yw?QCd??Tm2e7zxRQNM`>9s|=-F zhYEtmPXpfV_~fd9(3*0vYQH_kw@MuWWr(1?xA5hSbV}Clv$UnQv(umHQyRa2Q%m}X zX%Ptj7P?qlmY#n$(msh61q*cFR0Tbx%q1~f?R{lhY1aqkDyPsAmcxr=hNII8A_-xX zWOd?0=M@0*hsE#lbsoQ9L2t{?^4NTS-In7qJVpwXm4#2qZ)V;$bk?2Nl3Yt_2{i_r z=TbUqEjpE4Yz~ru6qS397?^+>Hpq45SxxdkOY4;8i+hg5Bv!{w6fe@o#JVGI1CC74 zD*9XOBXJ;w!Dm2-)A`i(ge==g>E*7B3rp5&XNFwGICU0YO;oF-l-y7zUNx_(P*>h5 zJ!n7YG;~z*4E6Yv0|qsi=mjX#QLku`i)#DlI$<4w#(<*v&+%P7I^L^Qg2OD0NlC4~ z*@|}$F!K4>-Lq|FVOfC!ew3!qo$(3YD*3(dWf6oj_8?QMe9c0$dxEOa4Sd7Y>q71k zd=!9^c}{9UKK+OWp+|jJJ(stJkTKhVztAbbW89dAr$fnlCoRlf>&DaL)J^S}+^`Ao zK0Tc_h1bW&-hwIKN%swi(76ktZTDkEh3p-qo%VY2*dPUG1E+tJd;eHkzK%%2b)v9l zTBO~~Fd78xhDB{m7o?f^5Y9{+4P36VZ;bq(Z4L^79*rjkUYw~)Nrr{BgNK(-p}$1*+-}N*mvu8Ipliz- zi_$Z)vgbtdg}%;jt%ctYMr@~K^OEYO{2dTf1V8)1`K`db)d(6ywHHw9`HrW5Vbx;Z zk0k!q_F)~(=Y%M;e6#RS{D!z)y>u8Sca7=r&tQfZ&Tho3o~)x9+K3y zAN(7%?(XmS_oec;79gjD{qu|p^Z^X~*!n&XOJTG|f^vm)&Q+Mj9hq_Wh?U2x07!za z*1mYkwK1@+$iE36#M=T$u9-(jUOO(}CTUF!MFdhu&|9LW1u|infZ+3kjwU230!(4g zzN^sElt32gQq&^`k5G;2t+6oFA|J_qSZxG47J6C`xo`Sf`K2@I5t>*}iyO+P@f-XV zpNqmn>d+JiHuOa09M*orRSB^?n%`afdp-2IJ=4ZRg8~lVd7PZzHiGBz95SGJ9n)&A z)X(#iu~pdZ=B=PB`fXhYE~)lJ9+JJ$Sp{fJoAB8T2pX)`XO78px_`9+WZ1&Qtw>yc9T z$wA|QKkmBg^^!?4>=Vt20J|O73tf6uKtXB5fIAv9MvLjUcsNboU&o_+>jteZWXi zFq2VSWZkS0Y%frkS&Qs@eu z$e)$t$f6Xha<>RmOQOK_QQ=N5ZG~uv;g77f)!fEtV*r^9l`K{)p4WD4A*DI)V2@pL zvrCsRL-oq8(w7)K)!f$_=8?n*-84(6XlTgll8!5#V<0v+_l1xX7Bk{Q(_<#rbx-^& z_`*?wXg~|no#4-|t}f%N%9q`xqo^NWYrm#RJ4GQ+OiZb4ZB0t(1RWFe3v*YKQG01Sj1@pfpkj7yNS8s<&wII0{*kihBTMGbnW z8KM+66B^{VORg771OFQ57r}@^uLi@<)e@$AJcoLI@S%ncgZvXmth$LUVx4v{Rt^03 zAhjfW+i*^=`lGA3^q*$K+7>ydTQhlt#B+E%0vNrC-vb&VZBqrG85u`m!WR{~nK}np zDZW^nhtJ|28v1kd=Z78+73WbP70tA!q>Cl~2fFn>e@BEbZeikt^&ZJsN~7cdPi2(uJOm(tsm72bE_iUM{H~Wr7n_ z#_O>x!)uZcR8^n+!kinw9@sg?4vZK!LKS9KT<+hKlX`Rls2X&NJ4Zu$TtXYBf%}X# zwk-fjJSKZ4f(YmX3Twh&<;el>sBvWC$`0<|zT#?(1&Ds!c;O;p}cD*l`m%MKO zDD#qX$_bf!cc<(56LwMJNe^wI^~G9^QR**QyobFM1UsVz{s-wH?B^0<(5<&oh3ZtVD& zN5k^G=FsEaY|c@JQu|_a_FVu?PwH8{9xQo}@8LafeMeS@tX)R&ZUr%=dCsKwje+)2 z(;svJaj$~u$qzl{A7mn2?n8ynVnXt)9B*6cVoqutqgJL2WcE@J!5(RvrWg9GD_Nq_ z%z3m_(LGVF_P}tQ^2AeG=6V~ubOfcRZj~`Qx-cmfEvcpKl!xrr&WS~>ACRHJLW1$~ zBne^>?=u|7WG}Kzc6Tf?-*?YTTSXn3#JE8SeUteqG}KfoV`*9D9+iCGv(*v5S$2&1 z6x5m;tv=*83#gWC(J7*lM9w^LsS+_J15~vYOvHgmoufs9e1s%*HQ?JV#s7m9eW5|Y zOcyj+nq1~LmLAN5s!sW8aL8)7Y)i--lnPdwum6z>!`NFqM~EQvRPd4~#8)xi^O?di zN)PurI#V3&C%?Wx`z!Q|z8(67ed%0*az9a3pY6hoV}2$A9Xzu>Fz8NX1M2|cI(H*M zFL87#dJ==ltXMAly_yFgbk@d+4wIWb#KJ~djb7&UgBx2W2=Bn4fG;mBp;74My}|Gd zRTC!Ytw(*d%b2IVGPZB(c-ge+Ji}NpD}8pj?2oU?dd^v^{z9g zz99AaZ87X{T91ZDjNi-vc`dGSxF;NeQh>Vu;P=<>T%#DTsjFeuo~WS|PY%gAwo0?C$Q*hSzppr&(_J?nDFn~7$c zW47D?or$kzG@$s8P<2^$Ir1R2lQ-t(8F15k02g&!JA8THG=~tTc`SLQuYdj^NJ`eP zdChd}T&5<3CP3G?+EfHnfjrD`Hj`G?{j2Q`91rZ#w^#_HV9&f1WFXEYr!1EO3knm*%b{DVHZxeQ`lYK}HqK+FsFd|CupE^Z}hsC5-H)WwV`KU}N~! z_ltch{C=a+b>n&A3_{Lm5!FX3(+XpxE|_k<25{bRXo}$isb^--g2|8LwGi^iULTMP zuBwds{KZg|L~!%G&Vpd7$;8Giwb5xI;3enpAajl}u<4?EcuSnt9&8x$DglXv~ znXy4?=~(9{8};#xDudkcAOL{ZhvpMHwnTooX&Lvtk|0<)>yRDNbcWU@ELzX-uLHsd z=;63I9j~}U#(*2RiT?qUaRsrxsh|9&jcwEcdr_+REVHm}KESb<7SSaM^n8qeD^kGG zt$|n1)U19})i4MEvv*8-M9`Ypl!9afZeiK@>`v1`ISW5i%lLeC!$HEe8ps1TUe0OU zr~5 z@wJ{xuQ2U`EEJwfu`z*3o5Dp#D`V;NO5(~5JiHW~WW&++vv&L+wuE{VQ{mZ20HHmd2*W(c3XFsl0 z!!Xu%WJt(Z;2ob{=KvY_++;in-~aQM6%BtKums4uI>D&dw(S*|P2eK0ni~l)_*1AP z8uuT6Mvbp_l;q&65>9R4ULRKsnT1!v*A0AyUns2Z0E@J|18kN703PK7gD zmzkm@Pxex7ah3uZtgaHLkHP0?v%Hp=zF1xUZ6z@L1c?LKP|g=MGK`nb+Z0&MeCu?c4P_Ou@x_U2XW6@y(Tj|9$Zo z1l>)X>;HV0?63d*t}Nzt(Ezv>@(D3Tr$6|UDzc&n)Z9f0nc^WIYZZs0lZ&Dge&$@V zrSSo|?2XS=8P=)+Mdw?JPS3l>>2oFupHW||me-q4;H+p?PysNe6%$3iol(&yT_FhzRj}kvl40gr6TP>>QXGLoZ zix2OuoBD+u)^oTc{RZJOaVvc1ZCx?NgTeCJR#Sj+FdX~pIsHaKtFw;R9**eXQ#k%I zCPZaeHWM(7vv}S$>_uS z-Ca=+{0HXa7QrKN0gBC^AqKjZrxCb~6h2r3tzTMo1-7yT81Gts!IAz5 zZP^RRCceP@3D+BCzo8WkSUA&}oDh|%L%73lefJf~LdC_YQ@H z1ui+@$o9l=NXn8-3hFAECv5y!#uv+Z8IE+Pn-x{G)s&nA5}2A_?(`chDd3jb(3cro zJsGpy(6*nk+%-xdD~c?xBtJ3wm58+pKXy~Mr`5U1<)Pnzk)OMR<$H0*eJpsr8nMgs z%hy16#^4ZE;fCpGg9FdbxJNnzm*j=kPF)l)AgbZjk3X?!4gd*yPJaj z92l{d9zm`7X^BkH*mkrIyYj-Y*1f^G7CY8`%6-f-b=#2wYMX~M?eR4+8A3FQho{H> zxq&yHELn}`i7^*U$M2Tm$Xd9fZmd@ga21*B+Yw7?DuEYp6nAdD%RcvIo9C- literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/html/_images/clustering_24_0.png b/doc/LectureNotes/_build/html/_images/clustering_24_0.png new file mode 100644 index 0000000000000000000000000000000000000000..e2dbae3dcb84b738c4d9e63a17113989842908d6 GIT binary patch literal 79456 zcmagFWmr_-7dA|aw6sVI$c%J%Dm6$A-QC??3L+q&IHW^6gh+QIT|wTV&&xg6@I&;q6XUE!W-RoZW#Av7~65>6>LqkI&R91QoMMFdP1U`=+KLUP{%M2?6 zzC^v{^}V&+Y`y&~JZ;caExg^G-MpP0EE#=mJiQ#;T=}^KxcE63?Y+I-y~Mb=UH;Dl zTyCCr+{0O~M}bao-IWZy(9rP7{(aEVGT=|q(9zJ8U(0Iy!}sq3U^W51)6t=!c2a%` zqI{ksKN`Q6d~YrhWG*%$4NM|gqn3OZ5&csLW2(#Cir`U7r3E#&H21s&kA!sh5xv5U zKILOf(wyREP3Gd}lBOo7k?(_|TdN}%Sy#793^#tv&#U=7iw1WGf3yXa>XUe&8rx6B zw_gW`-CQg#x7JS>^4Autx;SbD`6I83*m(ZCxG@*PKKbwGeiytAt*>*F1?QjU$@>e1 zfCmnk>cOAXfi_>~Ub$*9W&<~cYNHnlWbV;2ppHc_F+Yaht8y4rIz)QQTlx*yM*)mT zhK__hLwO)3haklf(A~u4L|$n%+ru+v;tq*>ICR%7Z1VI{1bBnAoEF4H6C(epfz6EF za4%!(dLlab5Tyr6-hyKyCb1Ed47WU^0dbkoyn>vHM-r-pkE3Ql*jS*MeS=30yo zI|qFP?&@t*?J?V?(}vUGkB+j@!c@R#m%_)l43lb@<;%zjNbxe>E!oQQwBbV+u@`ii zKnsGzXh)Ci@N+EP>mWwwT)9;gsioNuJ!mWN4f=|4g=rsM-`&f6O#>;;7B-zuO@?k0 z)7|JLL#LCWA&5y8phM5{?O&GdXf+Xb$c7Z?uCyM+L>qDdMuhf;<3NgKz-Pa<&dQ*> zC6Hp)(^WO(5x>HO6mzF%CqsA3)2{vwOZqE-&%Sh^uU<2n+y%RAKQL~m|W%;FBAr@48gU5 z-I8e;mEcd(wC5;{Fp@O%CG7i?+>16m3F2Xl2lk^d5aMkR^+Nc$8_pK;5-p7OlCI+d zom~d!l4h$ljMyH7Ekbl95pBE`uH|&M9btxfpEetFTWK`B$GZ}Sd2eNoeu=%34Ms?m zo^88c-_9$-cl*M#ABA>u=+;*+$N1MKrjOp?uZ%KX^vE6JLWfIZnI@w$^;VQ?xP5;y*} zIOB%hM%8#odDI*(S$d|94m^z-mb~Xhz_4%mS7>bSrO|HtAjJ$)0!xXQ(oVhCIEwJo zpzuEA_Cu$2#G`wa6#{pn0Lpfhl<{)k5^xU3=cRc~P4vKL>IouSz+2k$YDYeYecWbq zvo8%ZbZRZE9jTpqz+7Q|VDz(MhZJ*RbV}pgDwm!OZM8}h+y<1MeV-CTzh_@zgE=Sj zV|6f$8&VnWrPfT{1vTz8*DPb-woF|Em()kg%-WrPi(OB%v6mj*BTZ;;q#a7@Yo?s~ zpC8-&>+U*?=<=KB;RSkoPVGH#PK#^rSy$v&6wzy@q|0mD?0v<|utG^@L*8&;-X~3o z@y88)dS{n{t`0^#Gu%sS7z%P{8wwXY!pf>2J+u8H0Yu6RW+i4)!~Sbs)e!ooAh zy}apY$GFdhI+}pbmcfXHW{K_A89aBNlelB4a^|d+#knwamj1VYFrPMAlN#T*Mkg$a z{q^#WTV}hs6F3SJuR-%8AwEr`eo%x#+lyh2UoS#oG}!}L1~4|?%k+CSuUj3&BvmqW zIiTC;Ky~CoR@LdQq{B?n*VqVfAW(>4g2=5vFS>~LK^W0hbK1;Vv&eyF*e`bBkbBqO z>lDB#OLrGU5NpyIcZX~ZcCqVDsDhdsKC1bkvzYB{E~r~PLKhf>Vavy5YwhrFq4 zaJTrqO9x6gn+84kRTua2;iO;MoEQdexO?N{%xd5IY1^&S{C5e)2?U16& zotxcsM0?n;)?&xf2cv5JTW0Hv3hS%^ZuivD*G_jjrDutlaZ2vzb_pVXQzITqa>WjN zU2lwQrow>fIIK8CT3(I5a9b1@@mV=hod%rk!_MmJp{H7X72!&E?y`Dlcx9W7Gu{Sq z{qG3c8FX5})ycH%1qqe<;N22;nDKDmg@w2OfQb?2zzj7YcMVrp)sSL!5W+bp(HV(< z+E|X+ZUo+Zi7-VAT@xx?lxrBv-?t0@=gTpB*B{hLP}kF_#&VoPbl z+cfBIbTYIqX$5t`j!;9RmvcKnYlQA9J|VhJD1e;+`=tl|Euam}es>dCeV5o@eIFE^ zH4cQchayx*}M_T^H>Vf zUc%GBcOcbz>2Rt1oEvz<1)8vQStlU03k8rn37VLco~>LJIliqTwFu zrfBG0_29>3j4FnM9te{f{VH1H3?r1Y#4SsunB6S_4_ zZ5n*slejkdU!$=M=rf#IOGs{E&%@*@Nj7I;&Nk>8|!12*& z<<3VfiN3Wjg|-FXlZzL}594k%z-QTL4@?u1H##fCj-~52yyw6WORX`sv{tg_T4!<2 z`&A3~q={N`YC|7YL@eLQ_GSKWor@PU7t13VaULf_sWs52P`?`ft?yxHLCovrx$_7~ z&(gDJN6VPg;e!GBV z%HdjtY9V94)Bupl?S#m)QEH-6L?wioZ1+aCo-L%(CZ z?jT0{CFKeXT6o|^%xf}r+C#XKH>^IW+RqG@QR~``SR~076FhBeS<4?0MBj_u=FvL- zQ1v#o+~;zmIQ^z==(1t{Zl%AS;FjY^@O7X)y7bw9Yvb$ZTORW|y49o)+R`?)9(Hxc ze!Ev+Z-7#`S-N8!X{ZqGkhA!Ca}w*eZLnNcH(X=^do_@ zj@Ep=;F5slk?KQ5YJOoPulK>7Q^T}LZ+(^O-e&;06MtGvaBbjETc&GJL-WR1i`dJl zEnwJ&XO?&bxV`3df7&aWm9KP?^vi2)Q9bXuVGHk*vp~52_SZT zhp6BQEFrVDsh@S^hI{jYJ<;2eANZ%5N#2QA!M3!6zxD*WtBe|=+mG3gK|+OnOH6tX z4wvga!@YMuOTQ6v?V5}GRQP0M@S>J#^DJ?$*G2#CWy{Ub$(?N4FHBp%b>5{>Xq_T9 zLG61le8Hp^Yd6@FhS+4=j-JKUHbnwIt~DQhv4+{WS!$LSGIMO~kl?-oonwvuHILJ$ zseXzalbBiJqFwlQTmFX|1o&qw{fm8>|M&G%ZI4|kB)UY^+UmJO8%(b@9w< zNYe77P^~rxJd&4D)|IWA1h+tWsSj?**Nkl*HGE)2yadC-xRx(2*9ff^_72z8E>K3I zGGb@_3@_q>R^AJ@ZM{Faj<)fu#usVn0I@DFes8(wtQWF9Yo@#lUQ!Dw;=Otq2&I~6)*=!$%|se`~MAz`{%^3CzHAT7B#1vWYBzj1~$EcKxU_3qKH!yc;^BUDH$jfaa{w~C&)@ytH|hwA1Gt&%m5 zAJo8}dlKeuyW5rx8u!?=QdQ5!IbabPOaona?>_Cx|3->_wkSUgQ6h@LBiK97r> zdWI{KQ{-ayoz=_gs+=0`LHOH(eNw4GnQapEIpXK2=4taeO=#oIW~*Nxn5OlqqAc@Y z!0q6F#Z*J;rj;&U(Xy9*`aP27bt(vx-K`mm%tHEyk&J`>21x~p|8I=N;}bFVkBA@! z-3C9`hkTq>7PV}5kc@YwyB^B}Kqka9qo``Ka2s~J^x%YkfFqylNkf6e(G*(1H73UV z3|;%lJ^3!Ez4i3kNwZF!hfh!Yg zzk`OU7Vra{+a-0+L5my-eU>KSZ*$y}A#$U(tu*6_{NLMN_4pkIR$k^7rd%R~g=VQ= z4C@-Jjp~4X1`0=qp~S{Qfh6tcBSd)imqY=%e-eH*f0MOUKJ|QTPppVfU|CowN1%@0Ik^`@I7f-JW*e#^^q z`iC{Ay9xf=U1ze2y)rp5w00sS*+u<5L<9$QkB7y1M3ZNRGL2Th6&D^^zq9pS!mC() zXA`?*_j1?ua{g=MMY3+cux|5YNHIqPzmmU8=@5UP5sDfU>zirYRByG*2}*@)bO{+HZRc^v^4+PLX^0~Vo=gZ*=?7=zm^}z|K>{deSh=k zPTABwu&gbt6;-%2TptVMB^I@~{tA-%LAWPa#tg9-c_VjUSQUcY_XDo72wq={cqxST z9c^7e#a4LS^BE82T&@&4bkA|v<=wN3i{>3_+5UD03R~t=dH9wotQZmxb5d~|a`ug1lBhsN)VnO+^@9Py4cux^mZS{c-c)8H}LZKH~ zXFyj^wwWsJf zXIDc1uv<%b?V+Y=Piy2+Dw($>E>WewJ-e>T<$N{{f(RsXPowmGJRB{x7{kU6K(VAhhI0Mn!|qfH{jIDk5{O_*`pCXY2F-nJ71VKOW7zGyp^2-b!-W* zZ1^n%w9L=m6m!Y_J564C^(tQLTyz#cN>X+==8<*=!&}M?*6FCk`|RosrB) z!4ePI7+ayg=Y9-qcI-D1$mY@}5y5}lTfdNNyI$8~>x*ZH4LIwPV^Q`)nk#xeGz_S> zA=&f?i%JYAUHX9PZPP8!H(@$8$Bf~n0Xcl~iAfwp>+q|L_J_coS%NPgL7b0`gUm|# zK6;rpHTCgurIlRKxJqc0A4(L+I({BJLI0^-;Nrw{t^7d&9zmS!WZq*ds=S^07{XNH6=wP?&h1G6E90q^^a3#MYUAyyDe0-yE??kNN z8?;VQA}KwoOS1@ZwQ)m!qtlAgkD0P^D|3KB029tP%Bn z0gn=JLz$riAP`=B!epWz%Uy7SC&g9eTA@E zzY4PFAQy}53%oFe=5`AqsWuYnpMX5%`B_D7zauZ2;Bva9kXjnreQf&yN`fbEs`SaX zU~QbnPCsQWX7iCl8IW#>u*aMx1;a`Gg)|K7&{ZD(&ZE%uE+S(&WrcwmmH2HZ6+6H>J^ zI$U?r1&q4Mt&7Y|Eh74s58#t@q3uR$*S4dr9&(hd?OZq40~qeN*t1bBcla7GjZCs@ z#9bMO?xjSNp!aDZwpD-Vw^q4D+g(SP$lDpGzIV5iTrI(?DtRn8gn`DE2%VYC1K8f>uze38!0JT&p?j@mXw3&G-)~BLDujR&&aX$wO z6QnMXS=yPL$djCBX7 znUc@w#-N&h_&%4Iw+wp1%Y$|>OF4gsr4r#}z#)V=2(@7EDcO_M$gqH0%u}|4tl*R% zzrcThs9C`4-@Z|bV3i@y8FRfnsHUMHfrL$xLTaF~2B_5Exp;8!O%#xY?pS7mxc&X? zx(8;HmamGx2)s%ap1KJ>?i32p^bCH{tt-@iJtcGpTAy9#Eb~)vz93usku%21W<+88 zoy#D%u|jmE5-}GP>#cfl{@=Q0zkjk`=U<%fqQvZO{2_WJN>2GlJBQ4)7&EOGAGtYP z)XR!;>)SGECFkI-7glcCHfjp4M${cW*hohel;w{$yFlDMp-Sev2kkH@P;NlL&KsZvj75 zadWN^hy1KMGWpsvX*^HQ^MOB0Ojnq`d5oz1hp&fA4}ag+8&!s;b@EZ407pcRqu-mJ z+VQ51-NO$~nUAM6{Q)3l*(zQ@-$2X1Px6jK%Wdn<+!iJ6-{P-G0)fC%~3$s|~xmxJ9D+TMg_Z6~u{BFBBwN zPgZnBf98s`(ur9k?53nfUIz;;#>Qamkl{ylAARtv96# z58hW?5-+^}F6u_*yF`v^uR_Zls<`(NxmPCB-ef$w45ci}pJXAUP}`1$H&N$>Eo}~t zdi7dHIEhOB8B`*6BSt;>CbUmE12p3CFf~2=g>s>nK|U#nDFPBeTY;=&0u- zc#|T@SXugxouF@ews0!gGvh8K%JtkKl3s<7K?Qu$VxCWR8oy_fk*iXyBK8hre&UBu zU$=pBPc=1yIt5^Xe`Bzh0QQWxc?XSMKHncKeF!b^ zRRO^1O=Zw#GwR!J1H$fx6n-gWpY_&}rMxj0P1i*k?YxMW?X>w`2fgX}yFvIQe_~Ll zB)3Gs`u3Mx+WLzG_bCgN@D@u9wIEdIAe$S3by?WK;jasn_vnk4v~1*U%O!Dgg&a8? zQM%NwKmVXapR&Ov(L97dS#cVLW`itNP4$|GXMr4y;)hQ!mRfwHVaK`(VOf3O58vL6DBEKC ziV1>-7V$?pyR%qz@++bOa*01c_V2k4JRk)s^aekwrs69({de^UH?ZI5KWuMQi)=f=IGEhf(EB(@ z&2Xl9Pq2KK#554EF=ql*pvT(`WCrWVh+!b>arwd_puC*@Wo1J%Mw;x| z#@hDkWuc8n+Q-_nCJrIASq(mAP0}%Wd?i#1D>-!RNua}?Pr8+hGE3^SeRgU?)imAI?H(S9zt7WLVWdq&+`E#dBI3~~ed7h{ljNZw36CEm=~ug@T8w>Ud7;u)zvlN(?0?D`k!t&M($XS2XG2;n9z*TQ{ z6L1n#xkr>v-u9(r>>nu0_Xe(n>(=B)QmKtDjNREmLn_ziIE3YrT3AM6?+m&8X!hZ{ zYH*>H2EQQbJ22Zq#X9a&v8DKquo7JdATf{ZGQjm!Fu8IKs5mD4L*%_SzcKT>T!tRs zF7!;L;_iia`QuO9y#9i#bFyg7V)#2W+t$r_&pqU3LU4pk-;b9WTM1F}s6N6urK!)Y ze^mZpH4{u%!P02AzK1ateG}|k_V|I`r~935U9L+R?cWEuBsUt}1%doza#XGm_x0s& z5(k#1kuTw$j%c=7w6!+`sCm{TT8zZLBk_d6D z+-Fi2woGBi*MZsPrVeBxl%rYp9szd!BOnBsjXmUhTRfLVYj(vFy_Tcu?^;n|vqA%( zn5rZUeOIgv`GIpr1Qp`r#9Oa8pSHUNT4bzxl2cyIr*Dj-1t7sp4+TRd9&f+2mASgv z0Q*>|FS&ze)fj;T7CpsuuLpS-i&d$xEv=pNU(31m$f%}hL=KtFBu3n*WM#i!R`z!C zZ?3RymDI~-v!;Ib5))c{Uq!H4^OS9?_?ADrb?)J^Pc_k{IZ{rF%hyc86QPZNIp4wm zLH#evsWfao^y6K}>`mz-|K>McMw;Ap?DS4!Pt=2gSW4d9=BQ;`T-m#Egn?g z@iFr9U5dN%VD5XNuR2;obw>hD;S-O!?!UYL0v$U~n^ESNger*aN>I2NGMP8u{$OD| zXkqe3R&JZ`>7b8xMQ9I2;J3RoyX42clXpLF;b2J(#pW<83)_PGFCZz#L~F_iX_MKf zy>7pdvd@Hejj`*9j*ifbiLf?*S%0C?e66EUcNHrbC70|A%9X>%=JhdbE zLThADgORERs}y`AB8)of_9TP#R&x$QzicI)EYlb66Or1!k39K*=IeA4=MVj@~`UUht4j-NcP zPhwsdG7J7#7xkXn`R4>bjuktrl_K3|nk~`&7Q)lS{xe@>(C+~M-DN2d)>cEsQPE`L zY$GFD*vWiu{mVYuAR@I;1=0_`OGyo#18%9jFSNBLld(rit6FM0=bh$f^xB7q#vR(K z5V*#1)m}P*9=+S#ⅇFqEbc{#U!LnLJ>}yjyR)~f8bEZWtB{pC4#k∋3(x(w5m zqEnAOoCmstog05vD)gW8Y;Eq*z09hyXs+S^wl;fv-7NmMR}|tP6htEaE)5mpO){$4 zQZ0A8@;FqIssub=Aw8MR zofy;Mni*tbM9R8V>An7S|H83&SL9f=2Zy|YW7+=4Vr-%W>@pkvSotP<1D;s?n&T-t zqtB^4W?l~OiRN3=&UtM77`sHru&9e{ zm?58RnHZ>UI%LXVj%dsHx9DgX1G??<~&{r$KFB6`(F?C2|Yzhov6dKO$_TVrw_?1w|k1rk?xZ_^ectsRVC!`n;#1vj3fBVN)QtGovk$ zDl!C$4IitlNS?eZ3M8Ug{-`F%d zKaY9-9$bfA=JJ_})juOy_X8A91x)Ekzn57Fi$e+qm?r&60ibHt{&@8`+NEiRVVLnj zsQ<=xINi!a2`rGvANP{XaF6EkOT?r)hBU7G?qu!>OPsN z3I_-JW64{>|Pi(XyIr8V#iH{ZA&XdseCZd)K25N%U zisFyCoXx_YN2r*g)!SpKF~Vw{Ihvks66HSWc2~#y5(^Bb%fpLZc^90&RwwOiwe zN6Q|e3Ck@FeItyvx%5D6-WHM6Yn5G_qGtoL5ulR#ZhHn`uzwOu1$+#JYkIhxhaZFv zE-CRno$n$i^iPmaBah5dfu{iBS*|Z{@=0n&4agpg-XX=xh~CYG2n0cT@&grPOM|MX zR|!Z3ZU7BGHatzQ_WG8-rFT>Lrxk4D`brTaJd0V@gzzIYm+6tF0zCDyPPG89%6Q!$ zPvupC${?wNa>P`I1#FDK8K^gXwr(Wvt0Ir@_|oB!k`9UTbnOGEuaj0rJGi5-0~GS!&gTF%eBfn1CcYkjFS^)3^^>^Hh@gTd0_!4&$x4Z~({@2ekw3fr4$RU&mu zd8XjPd@)ZpCJNWa#8Kupcn%>YY$)?DTx7=>PL_Y_62tbDFtWUkuD_2jF^3gJC>&)w z8~SRCx|S&|V)cD7ya9*bj#d8;wp`D*O8?meHngv7a>X#j7^^%JZ6i&8+CiKr;UA@j zz4&RCCx2KJ z+qykp>PH4|)x#3qHyGnIZ=SOS8o|pl*C))WO1ItVzGfY7yvPX&Jd}AMT#2g>fT7K> zhe5%Kyp`@ZQ4Ij0D)^1MF1$>@?U6qlD1 zFP5|)!ZEGjK;1PF+fhx;A}Vjd0};eO3rB?oM{u{bB59gUu03S)*UXJ#Pw^EC|Adt| z^}5+GJngTY`U)xDgB17GPEmz3pe+^1uSTfKdN-ZVOJ4|HI9RHS92^aJp&MHCaF8eA5!fYXI=4s zIw}yPS6Nojy&n(BGm>6 zyE5pI2BYG}>yL{`E!Pt}5doHZ%@gdfzgo z)tBwKQ!jFUmcHVp4CmrkQbC`7{$;elD%ax0&kkGFaQ^tnSnxTPvmFCPxYV)3(-v@e zQH}q(u5XUVC@K0Wsln5U&;DJ1l(cybhXU%C-_P-`qHezOB@TWZdl|~H4;H@tt0Bb2(r<|-&R?->+SwFiJCCp<;O)=Q1%vn$Wvnc-Bp5ZN|td1^&ElaP6CvJ zHGD3H&$ASlR$iA}J2+K66K;{uFdp}fC_wVl>&(!kyc-^~Q((&j{ocU0MA{S={q!9# zffO_JAd@bsrQ6HdwuGzeoAndBZi9$DC9ww(xPl|D@q2U?hnVJDJFtSX!f!wQGTjQ8 z_6v?0_dR8<`%LyWf4e$V)AM_R;Fa*XRbgviw68EBrupFV25cpC$dwQL0l9GkRg z@ez?jg$Q2l6aqvX9?mpToj#nmdEX=<%U&ozbYxLV!)taLQ}veHbY|<;GBZGHq#kre z*m8Y98nv=hML^7)woJu1Z5T%9zpB<3;(TDr@-KpR8lYFF^Wz|l=TUTe#?d$BDj073o*$w?NBZ%;q$atF;Eaky`h!60zqrZJ08Te(xK@c!2k~iQ+L$ z9)SnOXTAbv>d~YedWcE|Z{kMFV9JB9iJXh9#BQmcye!l~Zi4)3rHB(AG?{Xxw-sqv zJUn1obth&Vrs>OsT<3FjF(~@F`W{R8*JqI5KH3&T>dL{0(U=H0My_?weYctAyy8sk zM+jloRVK>78OLM9kd2MbSp$~1Fis;*fTy!;@oD2mu+?QKkH@}VgG?<1wq-m^_v?G$ za3qm(E_I=3b*@VObI-<>euJVb4#8JjG*UE+Y4M@mj3ZYY#VG>eyNbqhDZNk1TyiP? zCc$W<%T50P@;eYDmpduX8cvCofCOrLb=SOiBFsaA%BGCG244k6i-Wk{v9Q()RO=+l zVf75kt(EU;JZ^Oo=6m}YRCTuPevx%TCmH_MXW zcAkChqKt%NA%JMf(Gegs4U8SJFPU;eluzo7SAWEj*RbEcqG87<@=6?#tGP@0sF(gO ziY;8u_jwcfC)Z4@LcDdl^k%0m$py>y8do=+t>zOryxK>OocrqoBsTVUVvL^~4ygov z{j!#k?UQYwC{>t8+IdZT(9)7G?E93Q-k_*j_)W|&c&4nZu00@Yopg>jg`W_&dnRXa zhch%0Wd}K?FE=zq@6BA+&25)BRWr%s8r^-!n*<6nR)pEEaDE7c%jJUFh819FmuScu zxD45oY8VGdUuNw;;!x3ajB-*D?6S!CTqEymFOD}_*RS${Z-$O#;~BWVgb4`<-4bSL z3OIx@m8ZrtK-?Y>uVcI~&e~AelS|4nDEW8mvfT)%wG9~E1RFVqI20GD>q!`R;(|qq ziP%XbHPlJ`t@e7wusc8*Mm{N-iqMq_gL?(I4HwVGYFi16+QKQ}@M4Wq*70os$lV{l z$35#nP&c8JF`BgU#`?f9_IMk9PW4)dg%XzIl<%o2AVE0VUz#;ZcI;4*c#B+G~wG>+|lGk4loywu3=XV?U<(aRPb?6Th30vG0vTae)xF4e3>gJ zHyM1Lf`ly_(N)Gr$#c4kh|;Wyo&vaNePZNO`uDzKY|+D$k+dcKKrJD5E;l#A5B$d| zb}ymfgY^^<+bgqq!xfyVKR~l|EY>yyZ+9BQz{+~(#7;Yp;9wKf!&_RUSp)T0cIDFt0(I7EHba7Sc>4EI8X6M?!6;a<{VK?x@Ac zF%+`ofj=$BFUG&zd?#>2SHD^s#`WjS!Az#8-q!yxBK+!nuj0gE$C%VdB_010tK{*g zT z+0tL2WGsuG9Ay$agx`h1R=l? zQ9uy<2C-Z*6nI6oT#Hb*GvG^L%?u0r^hAU*N*9_fpKi`9WB|Ssalw|)rG7z;5Taqm zZsWYI!v-0NO{l~7VpRV!$`h6GQBWl%aj2)4;#?*G$V&sVDjo~^OjcGSNBK;umBo%{ z#CpHQ8U{Hpa$>*s`04yRk3Bd15%QClpUc@DZ9D z81D!A1$en4Umm|y;GKvrBIg!LWKy-5BpW;ZUL~{N%Gn{hKzcSX!Ow@1Ai1YyCD#y( z%%tBp6|hn~(fLLiOnZO=jIq!c~QC$(?Off-9ZKd0;24^)Cffet*t+5mn^& zHl<}+f7n5 zK#@9m<_c;y_uzugL!Mmvrb)@K@u9;@j7)#&>Vne8Eu3m7-A7{O_#`-ETEp)oYPY-OqeOlfT)U?jUku?H&%a<- z;Q&M?xdByx;u*Aw5qeeXGAPHVOywvQ%Dgdg_@PvGm@(-Dv&_ZIvF`0uhFshlf?w@| z-!`PL*N4S^j?NB{R21qN25&cFUwicOj3~#gNlwmWl153XDZd7)Xf(}VUT&(<-)N#n zr7+wc*aw0+yaGn?vG;e`I~i~|*IlMQLCX@bj^Q$(_!fZ{Z*YyWjeG*im;}}EEF))4 zd<}cMIq#Jsu3`eIO&nLZ)^?r}@w)uL3 z@L!U&NvT9yDo4vDk{1`#8YDlJ`Aj!SU!Gy^AO`DkYGIFkR{k=_S#0KUm{gKeHJw5C zGq#P4{5A~*q?M;MF-~ru3q5s9|I}AAIh}24UA5|^C1!flyyf5&*Ug4vNmGr}gS*(6 zvyRQ<%}0BSN-rtrVi|%xV@iUU?=Q-Y*OBp34qQpy9w}DLHQfrrxx2IeW%A-l=dNBl zsVwX=V2(&GQ9&(MZoy}t(TD(+SXTqxSVa@0nkyfgO|@b``j`DpMunWA z=MYrXl>(<{$Yb?MS8R`@}eZ4|!E; z&iDFr)N3laKl)to2h&_u1#!>NAxibOddJX_&uB%Qwd2)T+InT|qmgBm&S{b_7{zBu zpY<0jt<=@Akakk9cK3F!ll+EO@~OyUG5@i1R*ZB0OJd^{-!q zo8ylgpMi|uSNCrXQEgEsOtu6@AFR&r<*z$>d(0P0+ivKP! z3(rvP=y|Z!mvGFnpSVmb$X?Cx)u*ShVXvm$15$u5vmqUZ8ZEq-y3dQlA2!&&`C^I9b%u z^s(M*N0!otb3o97NxLWCPvv}iozvj-l8y@>E&7!2Vc36Dzhbm)%d(JXx)rKPTO%!u=_FCAIt(uyju=gUc!{i?Z}7 z>-pPz1cvPC9ohWSW4G5Xb=0t4NzL9WEtXbCu6rGU1 z(p$B)TmiYj-)p=TMeA%xL?|IDc62J#9vZj~u5x&Y7Z3oQ(48Dkp(#e##9Ff&42ZCQ zsG>y(#+`-d_5b;3B@~2ff1yfDR+RS4FQ(iifttfOX<r zn(sE}cztuO|E{TOLan6c%uLzGYy#`HI`;3$5|lpiTD+5Qm}FNWDwL^gVa@)3?tB{6 z)j(E8Bk`qwdV>mt9f<8NFtT2P@l;!mAL*p{yW(;YL6#PFPG>wb-NeNeg$Ivl<3>bm z{L+qwk140ct?&o|;q(uVf!YNzMKE4zKc^Oj22)lbuB`cI3f5^cs}ve0L<(P%0h8=V ztX=i2%1(lO-gF#3hIkL`MW2GqLRHS1O4I+x(piQ@*@at}?od)fKyrYgyOB=mF6ow* zMp|hZhM~J#hHj+0C8fK&MbG=4bAH1`%o}^}^{jO-|Naz4(xgI)D%DPyuV~8OJ!*#a zw$6XwPL`4~AEf_X|MmGQ_IVxFM^z?*?Dh^@W!3xgBy2+NMgNM=R%*d@lN)9!4ISxl zWizlt(mP5rQktbw?9tM2kW$-80PMItAApmN@wuGm046J&MrEb9WoPGduZNSU5un`b z+dXKj0A}Ru^i3dHcxb2X0BB;IDusBl&diP7wdqi1uow;9%2G!jndP4<0No;$s& zv!B7i5haBl6Y~_BqkZp1PnT&+WflAKUIjihkBVDQ8xbe8bTMW-?U&otj;egdl*JUO zi77ex#V}psK|F=jZq2w6i{?~tr4WA3DF25S*9vkcVK2_LqzWy1l!{k=`g%Y%`X?YM zIjuSWlkA@O8AiT#)8_AcEXn;^H?oG{O0z_IChO7W25ZC}Of|DTsa}=Of`i#f&u%9| zQFJ&eN8%W+9HQ^AO}BI8(46Is;!OBWi_V^6B zQM!Pe5H#-FzPvFq@jcq5P91-V!UiYbliJDo+QbpVz?aBDt@@g}r>4Ikrhila0+7G80UPNd<-iNQ#1uFpn^Jka>rN3&>1#Hd1S?TC za;GDp_f{9UDKRrlQI$|~u-puAi4iX1n6%&nUI`5cqy@$a_oI+eNSV&xnFhScEIW6L zVkui_zWPITzQH9hPOX>6j9(H4LVcgnxq!2nT_n|@;X7DpjoI;UZtH(RD`7Kp7D`pW zKPox61Li`fm+ikHwt=i8)=mgP`E-+(&3`jyqMd)RQMKwNO6joX5T#UgF+Lq=75@y= zdacf`oW~8x_Sx-q7V6?2tn37dgj&(?_MrS$ViR@0j}8z&N^5kb!^Cr-! z2980j60C%hnJ9FtjOTxN=%hzlD)498B?OeQh6O;JH4k!JcB5U}gJ# zry~Z-t5QNd&Js|GX_ahub%vyFbkY$LaaCaOXisf2LWN~PNcs83^PRX@?)O28eTeva0*_LGB=Du=s!GL2POO~{ zc(^&Vb~R!Ak*E};Xq)HiP z)qZdK=A&UR;0B>{E%l`>@nnl>nc8>o2YIa|gUl&MA*l$o6~9kptr&n@g}G5Qu)~A5 zbH>&1C4lDz*RaxRBK|i>WtR{Ua~7|~ej4j@sg$xNXzTy|0!Va%SktN=*P*&DgjG-G z&!C$F0I#yx?CiOOoQP;sHa9`_Y2-PHC0xWMdZf_bMDpK{L#fuA%qKi8`*V0OK1Oq; zC{uU+1GF$#Kut;Y9G7QeX%g!}HJ#SGMmhTL-EqEDZ6G4&E?J8??LRjSBN7C@$9r%K z!<55#kisbDuKohy`Mf6FC1;4l5nJkhvGZafNqEP=V#1u7+y@CWJ~m4((xx_iTQ0_S zt&LqY=!>ejnF%DT&rbgAOEv~VO3@Vkh`4^Pv2?OF35r*=F}KNVt*1hCtGn?_^ANc} z=R3;B!li4ye~qFwTI<#hz0D85e9KF6N=n~uw>C(9@kS0M^Tc%QNL@9LoWH0uGb+lw z_-*iWq1xMb*Dq!DJ^iXbkN_)Ht%tD-8PY}Zy`gG>KCS314Aio1foqLOe1f+#NcMSRT|co>4<0##vask!lzv>hy{_Fim=H9!v876b2B7R`YP$$ zY=W?o1Z*_V0~ZFo!Dt!-zgAzjg@yC70#Vp34LNAk4JWJ2(SaaI9be9F8XyQD48naZ z$|mSyyuiw*dLK?oP_v!$phzY&F@#8B*X~U5%}{7+eS?>2`!8IV%0&)i*lElZW}aN*p)F7H9|Pq&gnJi zTp%#1mfBaKDfkDDLNL3uM!$N19{N}jMb7rbka^=;1CFXD(EToXp!#lqpo zcnO}}pM-na#}w9ob6_fC{c5HE$`8WTBJ$1GvCgIOVFu@?2b-Mz@UTJ3e5|rRbZdpg zC=4o?(xVrDN>J1?M9{#eL(bsj*#qldc6buux7xB0hIh90JkgE_40Z$Ay@P1}@9~z16eqCm1 z5PB}TVNhsbj#L>v9u#ZI+|#|Oe*j;NS&HGNRGxWxc6$#?v5N1XQ2$I?6t970sFM?s zKAGI{y0J>X@=@w~hatvGk;Kp2zgts`#uU6rQM7}q9Y|3WepdcK-I?>0%iEBO^w`Jv zr&$xdTjcU{SaEPQAr=DCv$Zi3L2p)5p^wfSSJf<)Q0Y7FLkpg@B;Ff9$yj0MzU=g7 zA8J0-pJOR-Hb8NrKGFQ^;b}5JcADB_jgiR_f=|EUaaaQftJ8aeZ2N3+pH?sXPmj$~WJ_CU z2jxv#vaRU%nfGLc4Nit9O5K#iMShdi{M~87Hi5+9k!XMKEZ#i%*;9e7#R>j8VvrXz zqSD>zopp5Ps4dUs;l|J)Fz|dYPeu6TW7g8y;2I)cCHZ>qAsKqB8C0W z^t$M>A2b}Ni9vFdJ{bS2)Q1FEe@DlI+k?|x>SnO+Gd|cAObQ7Z6@mFWEwvmHK~%{_ zkLC)f)F@)WZ%bR0@pWHhG`w88M(RoG88!f~?VtD>Al$JlF3nldc*>-A->!cT&e>HY zr3fZmw;35s#~B;RRL2kV@_8mTKW5v6#LN+OUiCM)2Ry0>qd=!#T}rmkEyF2|(q+iH zf)0@IW~pHaRitmczS)lKkdO4azgtUm#4tqvMKG$_-JpW%6b3UUq#Q!MmLXwSNy!R( zo0?m)*}*mlrj1aX^&a1Xj{43jtZ@(+WI_^+^%B4NMb4mnY=bPN-|YU4`yAo7}0(eMNcy>~B!a-SP)HMEh4zWjU0Xa+9xLsFwHkcutU z{n#@b^Y5&Mpwz=DBYIo&mU2XsYed#wlSN^aU`2D$As;dg_#uzl!1KsX6#2$UDGd8C zhs?~XkIaBeCST{$E zOGB;g1jZt1%M_Y5t>oo_i`Yf(b47l-LgW>(cRyX+Gg7YgyEXXkH+Wy8>U>e;Z!6j5 z_(a-){E|lGRL9}ae9AoQ3k2lcBFsLJQ8laGh^>>J;Qr7-?e!2*@s&#Pu8wb4E$!Nc zmH9MU?rC>$-O^YaaVZs{6-bk;PGMJ^KCp>u!6Kt-gxGHFB| z(W-kkt4*mjY1|dnaS<0M*%6Ai3q+JClqM@S4I*d^MDg>qNGz}Wiw5T8G#Ef}=ily4 zVCm845F1o-jYQDKrNo_9sV0xoXkfAuX1=BT2V)Y=bpGLwDj`Wk^g-rWu9&I>MY}-) z1*sNaCgK^Y_MLjIk2PN}!t5DR2!%;n<}>Yd1i1(`q2%ke4_CWDAPD{&18|&1pL0eR z@%u@P*d-7^Lm$h%t=uZ=u6x3~2gwXH+<~a(jZ)aTujeMr^e&8+_zx#QUmdsRx=UPB)ACOu$Y4Qfj+SCMlKK~D^U%9FQ_t)s^xUbr@?XZSOxasW$ZBM51{%JifTTY6N{E;xfvcuFt5PDy73- zq<@tWiy9laeOV&C#Ao~hCo@uBP5DK-OKD1&8UOnj{@uUzrPcWOlC;n-pRoImV$qR8 zw45cN2xBPe-Sw~QdX>Qp;KV#CIBsAc2_#vxjlY`tdLXYrkUn6^B8qyuM+&koo($q_ z0kI&hJ~F*~+8N{Pve~*!v&zef`S0&FPtetvnk3()l!3ol#uZ_~rJIHZD(&UYwpOCe z^WB_e`M#s($&7AkUb?=uFVEaTU3FvJe9h)q=qP=#Lez4z1BR~E#DlC*aUcYG$<2)x zbt#q>kS0)PQ7tqgV$O%7f$^q@U&%J}Rf$ld{SQh%_71lZCDt86R#o;>+$FxZaRc@t z6+}GdlGXkGL4S8}stfLzQ!-+V8d#{-uMc`mv>5*HS!MoC-3UCZ?Qf?RQc&i4NPKK} zA4*w6CjZ+_&Acbv`H1*~!F&+6uWca$#pJ7qy9yO%u29}ZXQTa9FbTenkfwY)oQ4>= zPQU%-DIZgF51ql$3$Y*`VR0sjd#_>rdpEP8UA)^0inO#=){pOKL`B2DRi26ubls=^ zsyd>$i`pxMu-%R+JE!aR*=UHcymFj*{Z{(5s-G(fGZAbF*RCZe8I`Q04cV6_W|V$$ zxrOCE@DMZ2>=;TkdSseJfLQ(IJH2+_OvupX@G4r{DV3U0MkPO$d5xxdrWFwT{GO5? z?Q$uWz>cuhQ8lLhMn(u&x?;R?fV_E8);rL{388Ykd&i)Q>9Tbm$$wrN$J10jy|zUx zz+|RDS=bv!zx5EW3L%ZePC?i=r)onukw%;`*CcoSMV|)fOW9&;TXRlBhD=+2OcoW? zNu&%)%$UDvy)>lM(#;p+86>O6ZR`l%{rVd1`YuW}Y2yUtU|fsvN&dZ+U!Y&3Y$kE6 z))E&^y|zMoyGZftRv`52giBD*Ue?MF?6v7!)5?5+JFIX>X#V1TRL|}bVb#lXkYFl? zW``@%#$;A|oz0&Q*3Q&6K)9)6QA6^}lmEuAoWz`$$Y7J-$u?*UX5rXfH1OUc+i(&C zA8nsYCvb4aMD+b{VN6AN$$DP*vk$_w1Z=y}9 zVKEcG8Bc!lkq`ENxi-&OuhFKY3zW}?+IJPmB`Q2QCqhWuoaQO_%1fCnG1*b%=45 z6O5vOvZ4_#T-78O;40VFq-FMcL+p7&>&ROOIbFtAOI-~%^bi;rtwAV{-B|0_R0ZY+ zjBt14)CmdS#%;Pt<5%IWhK>0M}*OcYlJCd%t>h@)s zB>d6PDw?NBSnF^bkJVfQ)kKfgC|za}u>Ll2nC$|T38_J;l#9ovMjuDZ?(I?B0s9FF zf9ovLniF#ah#+9E@bRx3++F2zslN9KY#6-b>}eq0uBY*2Grl(4Uz!;bWE(3UZM<-j z?Qgg=dHyV=DJgo*y8u!qB-IQ)zIJhb-HO*+|FOs*Ps7dC851_48>mH)+g-~>qRL~n zf;I@hpgiP7LF-P=2mh36x7?|*kkEQJsti~0{9VLe=3D(OSAB-$gR*R2`95SX8uVXA z+D-H03XmIDDR58(`8ie$R#b>ppTr3Yv9@Izp)%rotSXhg!fiSmWs)QZy1n+a-}B`>tYC9wHpJ<4pZfLr%M5Aw zY_?q;PZ_~iBQC_T8IUrz+cBU0vD6;xo1~Ok_QNMXc4?RGa+Ru^496DAHqW_mG|2<3@ufp zF00v!S~&4RnrIF0nUYRp^YCa7GvrQM#T+{JKUa{LEM=-6vC3<^Vn`L?SfHGXNXYT0 zY&r?4(m(4^tuVCB)8SU?OibeS2d){7`A70l|=V(^6PWw7&_UmVC~`gL@wgY^gj$?3VA1Q3y9CYdde=qXss8L&R;}gx>ifvTTgT2B&YGgKXb^!Vg*{X zXKQM_TbIDWZARE~9**a0-7qS$A`LDi-&JD$tq1oUIDFf2i~gSF!F-WuC;{Gfh~?R~ zy{s3WgQ}4-mMx+HtYL!p28sQ+{NdcGV%8+#@rrlMD05!#x>gw3I)_lf8m}m@3KXn= zcX*@f$KZVCNCl5;?rGad`9A0j8^#I4J${&g*tC8)(hz;+_Zp~;rTW8Pth_naWSVq* zeLT>6-_4I&eUsJhCK!x~vOe95JW=YR(^LXK7cRHnU6tnjs9Ge9R8 z+-yl=17>+fVX3zt`t)kfHVychY^Bzg$q`;zM9F_r^y)NCPu!h(=AI=8#xd@v8IFR4 z%7MngN`!OuH;5@gsTtXSKC#B$V^`a5FGt@A_BKTztIdWAE;KhnTa*33>E+B_A}Ssu zQi-uLMcd2&8BseAg{=%YW3e#%j>3u-HPmq_KTJm6&?f4f;SeS=7)mKC+S01p(ywv6 zQ4Pp@)2B(WadkHYMnY6l?A_~+l!q#%6nS7bymWnU2R%MDu-Eb7W6SD70ld@ogFEty zCa=_eb}}=*6z1}?xt7B&NF=kY3>v_pd|AK#VqNASc)92zKEZd`0?cIHvPNl5ROBJy z?pr)ITvM)pJ$gbWGm~;H<|5Yk5Oo<5B-y zYa{v5bf@6N$#5r2+H+%Ol5D-$ZX@Hb!Wq6BtjVT(kYl>Ww`t0oEWxFRBGDUkKaD1` zO5cWSewDLt(KDowTyR&*V6uMiY0T`VZp2&k>Fsr(CeJ|1s*?9am^x{;qo$1VwatGkN=tj!1TDQ&zpF)?#1%GKL-(9+Xy@B3Kciz7 zXdgMT7Ln0wDvOTub*Xn6~!N9I<=Rzm()6zOI-RoV<1rM)P;{xDt#P@fKj!TeG|4~N#-LQ7Vi zds^3T!3ApfCfEy!-6w^W&Zb08_yoo)Thm441%k57va8-@U)eo~bKrAOL;A1e-)2MG z=bB+adZV6&YMVFZgPh$_h^mHy=A?sdK(E>GZpUlDvIwBAAjW60Kq7aU?5w0;jXZ?1 zG3xA(&9mU)NQq<+bk*2W^h}vsX|AQ#RoDA=zG29AGP1hI70 z`{QW^Qt{{{#;aT1xN1PU>ENd863P4HtwsO?BV$Iud|?p^ujN=C%x)nv-kU|f&F#bkK@bQz}EU8Pl=Y@)_ObJl_E@<+?#i)vj|DV?PO z-W&<0A(L;V0q6NXPHCRk&+RovHyDo!7W;YZ5Iocrx(Sl)_a3^2U>k+KoOW18u~=7$ z*ktbTN_|Z~w=jah&h?|GYV9916{mQbOn!C>7}NejORDeFMarDWTQQ?e@Ff6cVF-&E z1-FCwvK`Y0y6$%dJ5cmrcSvasSL$8{Z^6bEP~E=^MWXnt-@c>qeDKFrE$UZw6ZEn4kYL#;Ezm*V(-DYje# zHw-cKl}39VF{wd|SNp(~yPB6vFzagWb#xRXIqI~(&=_nWwy#!s=_d&6e%h&@*zfqp$wh@E@79>-4gGs*Z<@v4jj8a1DG#9VBx6DNpg z@_6a25kGxAYe&fE(Wr95j)SB=Eyr_YdkGV%E!FfMo|Dvg_0*~H{vwR}XdYTP0@|$OozYtCVxs)${Q=;`L;f&Yz?693h3}VLA7+W|z;z6mWf_mMLi% z>c|jE?IOCH3X--4`9jSnEMK8~{mUb6x%<|Or&XPn6h*aQ|G%&8FGO2DSr5A%>UWEi z4P{1(pkqssC?ouG9D37IYSq&|Xt93`X3zt%<)FO=XlZkzF{Y61RuWdWX-J9h@EOS3 z`}-6{iIuG4uR5-B5v8i7Gi4*e!BBu0iOSx{oVmL~QZ^lB1Zxrd=04DXt7D;zFxN<& zhn(l^0LifZSV7To%gZr*4JqHB#xg0-lRgmfiC6vQ0StSMQ$W132HZ;Fp8!GL zQA!bZxCScV8BvIh6cHfHY_y!N^a-zy<4z`XE^2P4FlPqPH+sv`^CFgTxMW^xna@Kt zuXZ&W-Uz`|W`+NMmNg4TV6spU0|CsU`cC2O>s~?eDK$;@2|PBeTTy0f$qvy;^Zshp zygpX7oz!mv1Im8V3|_*kuTN`}5!_0H?tzU=#_r~!)dNAh_tYO=1pek) zQ!M53?~W(u$+!=rW!be?DdzH_o?`!a*12n=v#&#lyR&-dA>9(`NrRQFXe10Z-glKR zEnf2YamC#7FN|-o4XpIGhSBmyPc`ngb?CkAhm6m@STU7ZCW%o|5(In(9+!R)C#A3{(2I}v)mh=#G?ZYKi6o?3v$$NMPV6K zVJ*eJ^=C4tnG&? zWFNjGJb)kkvdmargb_$8v2dVSFbWCMd?knoQq}l?lts{vW0GRdBHKv0lE1YC<_p+! z5O>qP+RhRE*%f4)F*oM|0PHq-Z1)ai0fGv#xLf!mu zqd!MvdTZwFds8D?z|q`TqHLx3ht{iSv>hd83ZK{dvxff~pZU(@Z3LJQbPTsTPyq+| znR4AXS2=|Cz}M_w-p?_PPGWso>A=wpPzd`P8HD1j1{vPk8s_SG=s)| ziea)*jZq@DOj2IV&1ANuzPGFM@sW^GeHq3D3Hfs`6wfSDfogocB^e}m8Og^eXx}~W z9+x3-sf`!2q0;^93J;Q~fESv!jD+cXs>o5mrn-|7V z6}G{VFUyOEKH~_&Eu)vGkE@L#>J0zzBeiJv4o01Q(-G>=Ug<|rP4n*{<~6fD`aY)VSX z=^`swFmla$7B=4OA~HrHB_l!IVZl*mWmPfHA>8vb;pj@JA)C(nPY=p1@L;2}=!#9* z>luuy!UxaMzdr`3 zL&DoowQONSy1#BS$?Iwff7B3Mkm8;N_v9VF5(YCKK|O&~(|`a zN_sd|%AqogHkvH_4#r_=`nZ6^_?}Qo+C`r+E9kD$-dGe`yGKndd0dUfN5EV3*LNBE!D4g0;5WqCG%{TtGdhrfPMX~lM@>V zeF=P0x`xF3Pp=hq-2s*w=kR0SB>;`Wss_?4mQm>B&6>0RoktMIH%zEJI@Eg1ex{L9 zM|m>#@B15ul=A3BjizU3yh?Q3rWHn7&ws3w5{W5xG?hL}edCxH(;5{ia3uH=Ag|4q zZOQXt$2jkp)5t4tt{pD^v54#=BJm^xvoaXB(>ZZ}1}fxAOwkdZey+*m7P?Abw6%Q2 z^idI8P-6(>WTXM;ML^^S%NLLjx9Rs+S6>4OhW^M&Kz13Q3dAp6hRH&d-@&_yOUs|A z)TmuF@F|&hbjS^?%c4}{uHR<@uGb!?)4QW2^dgkgmmkkaJ4$7Q-Cd}EtT)uw61b=Z zMNaa(tFacu?n~)YV^@A$rcY-yq0EJ$<(mJ+d{YTu*RkEJM>z3O8*r7r%x-|;-6iee zH&~ZW#(d3YD%PmotTQoNPHyRR?Q4Byu(oubl+NxZZxY{z;;YL(9QEq|+JG@M?CzoEOoMnBW2 z6q54a480P>+yIT`Q)ZK8&h*P9#YrL+1(W<8S&=VG#PPp(dd< ztXe0EdYiJtx@9uu7q1m5M>gm4aw>r1DkPM2z3i8hWlp>FBLtfSa3zC??X5S2d67sL zbOD~7=mNlf+8O!J(A=lezuhF^4RG%s0n)0_JWd%po}%e13cu~I*@j#H0(|4rISe1^ zIRG@?Ak4vd@#y+SDdzZ;YtWX(>5i5t$&ZEo|7o%!e~rEvd+y$k(*65__=UWb+ACP| zh$$ooMbPVLE>QUNtCIi|N`%MN)5qRYSsWT%{=Qi@kH>`NAn8_wM?OS9rNq(O`F=X> zMs*e#c3nvXMZ71xX@QAvAY@v9=W4Yg zoqVgMOgTU9N*2?ObriahMcN&+ES1z;ZTIuKws73?eZjjTl=gCZUgp7@)yj-x$ImhSt&m>auEfK$2BUQW80i|Pb*e%ZB|s1? z76Ne7Y_6%^VDgaOGa74;SFd#gKk$kX)RhXu@+o#t@U(z*RJ2^j5f-kMa#l*ir|<%z zZF<|zJ)RHO6mYg2iC-6o1C#W%MkcQlDAlH3MIWMimh#9V1ODB1_VqM;Ex;U^OPsqvVBW!qG)Up7hhpOmH+N}G( zx^JRX+d{cUB@ee}m}r+6N|$H_l^Xz*I=+boI6ebco1Ozxbo}s{r7b>xtdI+CW#Etxww1$FP25S3NS8MR zv^BRXz;;fdB zkw~gbenBZj?_YBXOl@m;-c0-=aIuoCDS?F|DGfA486K|#jaz>YPWI-VHH_?%?9}X{ ze^w(5Oc>4Jf=V%mI7EY{egCwu6=Pmush*}I zIp*rBOKJ2`&6{mw!Ov<~R)?BABZb77mLh^MXL8{vrD71TqQ(@p?HqD~TRCvp8*uO+ zGZX-9V?ag1;#=$3q}VCqtb0F>0Zs1xs?JhH0NA+SqQ&!PN^2CrM)Zo@z9aQUyBQ!W z`f%YKlNAEx6BIDBEZ(}Dw*lCHer|HB-f#NI_|{wUDo->-`4w(^)1n6f>MMN`L2Hah z13LG|NAm@#e*j0P;cs1c4k{$oY)*^1>VvRJx1bK}hX~%WXc29$$ z?e0Ed4i~lf{n};DAFhWPv-hIDq+5vyXNT*w8wY4xI(SXie_W~V*fD}5 zKZqTr3a_X6Ou*=H_)o&W5k;MgJoT>)Vy7=yC8K)8*JZUJwQ@dhKrC(adAl7;$U|&XvBoC$ z1ISUCnw(zkD*K05t9n!qa1H}&IN$}ROx|47TY>IG_bs?Y>#BwL@ViAJ>&gUbZZzfmtf*^t&0W;~I-j=8MGx6yg})pL8*7!UZ^! zwK6ORix03K4e~+wH#nqY^P3=tN`7KK)qg(y`PSDF8XOG1!wc133h+?5e#>Ioni^i| z)4z`6FGpv5)6EhV(j(`_s&xNSqiRXuW;Z;8(;* z_t^=WofTnwVJtqE z@#E73hf+i5qx|loC(Ztui9oll<|UK;EsUc^HQl&=B6a>CvaV)Kv3v4v=Vh&2{r&l$ z=s6JCDaPsM1A52%3fl+^B}U%wtotn3h^K3<2P=H)87cRS4HoL~RJ#ItH&*oQe;=hk zGb~$$#(%cLOGdqHHDa{;WtMau=`l0l{G03NmWt^0;1`tY7mB)}v}aEH=_YTD5gL_j z`7b61wLI(2!U7$Lrg0-<_EaWhDELk)j znHxj{zHhn9Ii)09wfgv*?q#}57B*$im+C4X&oXwtj#)swv1G|sg{ExXI>fXJ{q^Db zm}#vo24td$Az)i?D8W910T9ok1hDCX%&9g0V+*;|wz;>RyysgJQ}to2Wl!unU7?mn zo&`|vrbzHyAa8VuUOK=_tQD9z7=)KrHp(yBXsE-WHpQI9+v{f(p$BlEkB{ z-kalJ*mL>sOA!peXodPUSOSQ0B}3oiSf6FRPWoF_C*{z@_sW7d8b*7Ezwq1rv%)@G zpBqk-eyWVXW89|S0 z*oHzazA_^CNrg81qI@PkNeg@8v+T6J6L$nXy`l7<2gj$N{H9Mu@*)vGz)0`VkML7vf~Q^ZeS zzUuIF7J;(`=L^YNfshQq@0R#8cE#4w6*SjTg?=}tl++&HZAB6fiMHV$r zqlFQ6m!uS$q4VB5)Mm_Y3X#^B4B1H=(RYf7df~~k0wZO9{4mt2?gE0voe0cnsVQ+EkN z%ddO9&0Zj$e=Z%7FidrVogRe{FEO*=ProRH?uPI0WXb&RLs4*6CA&{&_En?(@!M4q zwFZ;qCW2Iz76(l7UM-uws%m9tcvBWDGx-@WG(Bmi%40u*n%e1`-YIobi;oWT9;)Vb zKs{Ub*@+O@Yz{z|^iYKI$)a6m$2OS3bTgEq5~tpdoDf}=p9mV3^vB?lBh9o14?u$N zTu0|{y$cV~q`L{!TH#huUb@RtXSH-NwZCrrEg16g-0J6;MGJ?^KkO*2`iY_2VjI&X z{c2d;K`Mq0hMgAdp3I0@cEH0{vR`o$&kfXY)r^&X<=-bM$JwGBh5P=M ziIeIDqw9uoAwU7u_U2g!4rlMYzA2^hRn$#_= zDP03y#yFLPyvl(?EPyb^wbo`yqOta>9$>CoA{(fz?=f1N%s4f#Fnlm~oCoGHB5gYI zxj(EmuSiw6V=*z3kvhcg=6`8Es2Pnuczq*W+YKR@VkpI4C+x2SY z<1H(?W*2P=O6LBTgek#e4(d6#T7a^nVqUYHnP~mw9$(59GW_G6=bVpxFmD2CDQlf1 z^O{>?^nSI|lI;>sr9EvpU>2LOI{Xj;*~YJQe?}6ZH-h{&aaf)d5b+ z9-oyetL&idQu}PoV=L)+q&xCR*3a-Py2OC_S-jKur*02W{8rUzYZUOt7z&JQ{_7rS zlz+|&-gEqq-@)1@y{D42*VOb>7_kSq1MN*eibT`Tx>vVC9_;I@l7y6zdMi2f-)A{LTN+2CxtDl7xIyT#)eQdkd+=b$b(KyER;6$ z`x>~rSN9ae@Btg`Ex>*6n8l@cKky%vqUw7-NYP`QX5s8$#?u82{~edcs8J!5t9){XKlmunP(7BfQ5;K>Z_w! zWJQEy+P5t2$+9J0ydm_Z_-;MkQpVsAw)hg_VS zD--dykuqTD8@%dPd2;V;X4RHC#;IQ?R%`UtY`zwS?e!;FXg9`P;8u?r7!>cOGw{mp z!>1&$($?o4ZN9!HD>Ik%dAg)hAMy=N2fxay;MVIx451TAu$)vhYJZ}2>ikp)Rlxap z9~$uKtR1W{EJ-BTlJ_%OWg@GeyLdYTPb%+(rt?ZmQ_lR5(7mgGKd`+0RCJ=CWZytv z;c=#|4Vam4lqI8;*i`6~2oPDcCbz330!o%BgpI?+BGKcyFqZw8xY%{)0zh=|JuwzOb*UT%45uDHalY#@XKp z2IQd+vd`-{#_k?x@)fx7_MHdK2;e6VFJXyrM-3OWVcsB`5pj1e907Fr&o6LD!- zh++paj1Q$o_=9N$;dHHLjB`UqHVmJy|)4+rAb@vH%oJiI{qS6ACS%Wg=zvkQs8(Dkn+z&D(hJW+G;lR zVRNYW;1M{z=UZ+gt_dZei>T~f$NQS5L0+V<@+mUAh#M^ZMHAmOXlDld<${Zdcy!Xt zHVi%GF##|%z+0nX#&TK#dJq7f1HhGS=$IC#X)KpQ2Il4ggErNB?!X_i>a7ry35SLn zP3G9SwG+Ghbt+|&04Hkcyyh7yw+1mHHL6bt`@mI7s`KE>7MZr_px9jGAGBpH^!*8- zt4)Tl3-|4TMvrH%NI76T8GElh6_l#kg+2|mK?R-I{1vsslB6y+|0Hgs+2sG?h>it& z;!?~fJI5-Whas>@RwiGJ!RY!6uVl#iMLI8jZoj?rcilrK8@!@F@Vi>+>pi0|{quXD z-l+bC-KoRtyB*;vW>GG<*8sm?`m{>vmFr$5_>IPbRRkJmrJ_e#F?oC8|l^i#V&Vp{=Rk3Ud85a zDk`BLt@D17WJw$Bd7PAByqWr_dRD_OdrIJy8ze>YGuPs1F!hP`H0GvY7BJZL*yNbg zMlsp$m+usH7AaZKa%5a=_R56DZPzdEk1Vvk4sq1Fe5;NgG66t(`^nPa$sx!0N&P?uh*~9@s&L00;mI6Lu%u+&P?C=vwnf@9!7R`+I3P?IV61`C=acd>!!cH*~+dahmsgt&yH_)d2~Z z#V|J1K`$zNbmzHv*euy^{*P!Y1Xw_241QKPicL(cVoXHjNoU*f`UV)3GFS2adpbQe zf4`er^Uk36-+-Fgu{Pr|UE8-#?|6c(zd=+OL&!NGH5^ zg%UgC8d1aHwFrA-LYF<)+91euF+!ygDgmNH4I`Du-0L6pVo60yuUMo=35GmHrw!E} z0w>i4K7pbWP6bfkR4KlNCZdqCUUMf*?BfH1m&ieXnJVHBO*$_Vm7}h=qwT$sKI0_t zQCDdX71_N*vaHtaXeO7Xtw)I~WcX0lAAX_9fd%WILjQ!wY}@H#cIYH%-tUSM2j3s} z_~Uy=SO~qmrNu_os=A`sDx&r$*<#Q@)kx(=AG+-q`{oZqt*N}Vi=c|@emAUaYH)mc zqqGf6X#M|syIZn8Azuxp5`RJz<4Sa#?Eo|Xsu01X?X^`ZOHY61I#tX_( zUVm5MSPL}&Xa{^{O5pPic>FiHmV>GYvv~|$Ja2ox4UFQm92cvA!>Z4YveV9}5W@Dp z@w`HrQozWaE=4~?Y9-kg?B~bL z=iU8djJd$ASeI!I)x3WTg|JUf2yPy^r$t1|`x8kdq1yU>@Xseq>1VTi#fYLfki0v) zS4lIR%Hhw!HYp;ax6@I@|3Xu|CBpLsHh4^8M&iGm64zxISZOxzvnJTQR!y`eHzY*`*>xv( z;qL!M0~?bxj83y{LaRcp?uQk+{pMh(#U5&s0Y3EF7=HPFmyB$86IKW^vTO2Q2IL-B zH`-d+;e^@CNj$ReewPnsz%ly0{JtZ^Iqj7>&Kjho!j6EK8RtHD1Xlk%}m1 zX0f_^bPay8jYSlM5j{GE8O(l&4}R90KWcB#Wg2!DUp(DhAu%(k+SF%c>J4{XF*&2W zPh%D8Qyl1>|K>j^EnM(sgqJQ6tGRaZjg=mO-`~y>Wt!ltv z52xzHTma7O#?Q-C^Gr@X&nZJf#--RUi52h+8AG@tf7_&X{uUQ;Y(7z(4H2V7hGQD# zjZ~25eyTiE0TbgjFBV?gYH$KR8hu(ZK>l}1dim6?AtB=^M)BvOZ9k(fhq~*<7x|q7 z>Q{*XuPE)_OU^#-IYKW0v)!K}KA*x6l#%#_>asr6T9|*rliu>|T(VX4lD;+^UoOf; z**`y=ncw=Glq+qTFDxcrL_j8lOYnQ_=j{wB*7{E|B>kd&%Nnm7bzDS=CIlaNq-qk@uAa<=FS?h^C+Lj^xiVbBsRg!Ghh%F;f== zcK`mW8AWpa*Ty|Xm!0Y*+c9iBb$yViKeHxA<$kW8UZs019>y7XCU4BDP;7YV1fdLA z+1QdomA1e0L;UjR=}JY}iQMAB>P@uAwd}-r@>13mdprZ`(4C-M-kTC3H%JnmB}>FN zy%g4&dGUCSNZN4^!?4tH7w&lLpXw@38(#6wEV@kD9AO~TEUhb5`&XY;3^2;2>N3lQ zJ#%}k(6S)^xXeCt;rdtt4f3aWD_O72Gqvu(f4dewH~&yiYkn_>QxH3TNg^z1hThu9z6Zba!d6Q}Qnm=9k@7jW{S*gk+d~vqZ z=?}?}L_#WyesNL|-Y1OIls(kcy&45ZUmxk_BQQ*AeXC+7WU-l(?4NE5n47$N17rS+ z8Uh<7MoRmW4zu6di^s6jwmP}(#NSTvD=l3AJU2rpuTe-t{K_j;QvqD2Y&Pr7TQ8P? zm(4iLEUTd{A~h%M-=QZYjM4a+aDA+uODl^>GT#rh5uoT8xNE(5wr3n8A;)E2d$Aeu zl*E%l^@99A&z`DhI6^Y1l}7rEPD9+R#g*rf{B|hFc1D3Di5J@Maq7K8iG^#wwEkSQ zxWrNz@4CkZ;w^o6yWE>9x{#Se>X%2|cXE%^y8Y0StL}7`j0~q)WQH1(cBP?w0!Q`&;W< z>;3}^E|+=EJ!hZ2_j4XUKJ|?ADWlxx#9x%z@NkyRjTl@1|);0g5Y&;4d>r_AKL3_O!&qb98_yJVQjT+5b4@$vbKxH?Q>1McVoS=FY&(^ zQgC4eJQbf{U7Fa!N*~%;>Lt7sqryfIuxj!?rpyo7ijbagxyaQsf!Hun?~xygsz zCfZmA**G!Z^LS{NJD~5KJ{nZ^rt_ol;yOi{^;f908SvIO!lvXlBezf2VI-dN8Ogqj zwSEFGXp>G&7=EsX#hWX|VD*wad+~ogUR#HycvL?_iljX7iv-E~7c9?155h4qEgX-o z)fJS%zp{+dAl+rEh@eBy(v>F3=eh?%U;Kd`Xu)MF$w1HXe`C7UZz*LMi7Vc}d!LJY z>s!9aQigVGQ|}3-$Z_Tvp7*qa=r%{R)=N}uap}0KcMYN;pHSSSXDUr_V@Zo(qc>8y zO2&b&nfk=dO~x+oQrlQ)AuCh0@kPLKD0Sp|DmF5O5rWbU4GGZ_PW8 z66q5HJJr;#rZr>RjL`ZG-k{G_RD&$Z3?>h<)Ef&_j)kw)<4yu~)yT?XN zLgjxWi_V9+Q3jLeprk#Xd{fa!f^$L^UKF`rDvDJiviwf^JYgaH6;Vn_kAUg?^pTnY zCXE<&j^WOB3|{`cdZhT3PY0i!f2)WKoX$NXuiu?M-%GtMRH>5odF{E9y*De|lZtj6 zsZ~7+OAHP6v=Ju@z|tXN5;=D~x0M(L264EKRdb%wQ$(;@JYPuF86%#4^ihJO&>btv zRIF7ST$9M|6Bx~_wqA-*IhD^^3hf7e1qfmf;dO;w{1ECutgv5H3nm{P*AQcA%;uQ$ zAzai;11DbRcDv9@;Aj}$ZyME+brgeO^bIUKUXzoPaQl-Lm<>suuc1tXkHPBZA2XH9 z6V5$0ZGpPBzJ8Q_HFg2e%TY+ckB;6QgM_y{v@Os03CU{vz@Qg8JE7uI_Q%dg&03?} zwz_zmMJ_R1EA2=x&+q<*o?uOn39b=fw~l;YIb!C_Oc-jT zSWI5O{eB~EX)b_)SJFnkBX=qDF40NRuGKhXf*#SKm2DyDjY5k3ylbn4q&aEI>gNh- zOcGqCbVm-@zRq#aHSc6gC%#~}5nPLNJigVl==ArYvy2XQN(jqcnUoLlECACIp0@h> zc41M(681p2v#U!*sZp*otQ>tdfQ^8)N`HJ^Jri@?;Dfbl{yWxv*NQ8)ighE%mYRuR6{tjxrDFwC!QQji|&Dr2m12ZH+>+jAO0SNpX|sr z{KxZ}1Hz3el(xG?+DviZkrz&Xv2~8;Qn9&-8%DIqU`Bx^CVKqKvLPb1GW_9n8}Uf@ zMAa~8UqNz87J*r`o@Pe`uHIMCRUW{-M#~_#z3acd<0?8N?fv>Hdg{*~?nVt{AvWx>XyYBa9 zOYwEyM6D`2=^S9DT$*LSDE9Hl$R6YDqs=WW>2{ST=OVlc2L4Y%OcV}7J;`v|?(owM zdq=Z7(cv3D%a3;(XU_q{6VX&EoxR)F98o*QMwltIOO9kaT#c|Y6@GE2SPQ(O?GDu;X+`O{9GOYUDjx z=kqC2GHbnS$2mGR4?0f})I!w#NRwX><~S?f-j!#ww5u z67C0$*d^ND_3GsE;*Yi%9xYP4OiVvEW@QhbM+ zNE_~ec*2{3#gH?EnjE%6j+COV3f`Db{6%fUu;5D}M?cw91{VHZA$Jq>ScBl;5(s8) z=Jk2`B*#z(E66x!Qb@fhwNh~S=!r9|mSZJU;MI90TN@F0^^*BZ&0`^!S&=Al*3gFH zANI!n2JG57bvzb@)nmPl8tv8E>*}EyxVKgK)*8agg+-z^rk$y&r+sgtSUVe54Pty& zLnte;@$yy~v2?5{ne9%Up&%AChtoL`F4u!MdOH+?AVRXX02-L4v&@-t=M8X0ohQWg zYJNO+Qi~hBYj?Quj3YgztmdUkoS3U&kLHeIj;UtPEQ0jh1Srkq8PyIKqWALWyM4Ch zVBDZAjVEJm-u7g4ZkBa01PGkgHXOxPDH1|K{!PLfHVZbL8vsJ+H|=9bGs za-^Ys^v_eUp*p6#J--6MM$E*TaO86pmNEI+?2-~5#lkx+6%u!*D+RjvKj~QnN?>P^ zd?N_UnUFN1Cmg}g<74HYCB}tjfuiAuHX4O22}vPv=B|aQ0u7!JB-^$;p@fv^`BhNur-VhPLs@aqv5E=-iHhL0Ch5qrSUO9bs`0Sbh^Qz?F>(IJP zguaId@04yZ_vJA%Mwv&9FXg*K4Q6|Y+fy-3M(iL-(VODkgd!H}Siffqdy$P8j2ezg zwR^9QYddvH%c9RXy$d}UdA)db8a|~Doml7kG(ih@yg*TlE=??G^Y+c0_Tof@XsLIlJqVSr%vgOYUShZas~f8|tN2!uatMVJkc6b!I20v{Ds_S2>^dD%6;m zp0kS8B#Ws4xyk{9E0fOzU8FE8GCmr+m}sN~%t?CLOZ}Ql_1HEkA2xrP%9P=y*k#PJ zfKPG*+cK07oSo7irc;iHHQ(c_b7G(G>?wv6K`!(lFYh?e?XISmI zTnlf!=o?1G-F(9Tdiy1p_Q&qjD{5 z#DV(h7iqji3dKvrC{bX>5Ki_SKAfVOwqngMb1xxG7N0ngHhG*PqhVfj3bLz@SyQ*5&so7Ywuuf9Ve0&sP1Btvr(V^3~W}${2$MNY=_LzcO);fNO|$ z&W!_5vWxe)@-7C0V%`TSG;WEXNvzD4|EZp2GpDS26Lf{Y?}F)PfdX8GYQX|Bq#z%{ zgeza&KV%a-ps990l5Mb0Ob&jbpr`)><${5?^@@0_k z-B)|AuJXD3nSQ7-6LoCR@gz*Ikh$$X48gxK1X`-r~Fpvu`~`!Go`9sTQ}K~yHq)cYZ1+_LgsWE>34C6B5vPAGw zw6Q|3FJ6t1d$5DRC2H1_9jBMbMB97PrYZdAr7T|XxZ(4k?^PumJ}6+jz#K^2&}PKi z-}hrO$S)ODd2E?`>qI9zs8bU-!xMZm`N3XLW?ITH0XsY0SfNn)S)sdiTy8s$i}hgd zpj>}miMJTKp-2k@18j#`3Pc_`1S?IEV5RbHp6_On{sIhvcX(C~*tZuJ)0^~KH4#wO zb;I^3D2F)_#A=4*Hn59CTWd6qWVtWp?H?Wao7d~8EIO~L@ZI!TpCTC3PFrC#q(;#lm5=u zYoykeUB-X9Wi+!EPwYdX;2Byb}m0y7YGDqH@!uLrufsg9Oq6*2&`H6hS z6}{77@-By82{IfD(=hc$1djb@>Jdvv4v0dqZFrvp^=I`KX%MAJFO7wOJw z)`bWQgKCmD64#!(yL*OYAu3O!d`*xmdxFpMZ^2Z^ZMeT&Ba=~A)W>HBh|-6 z&L{4(eZ5VaF{<4r>)v1n#o(`jig_A!O+=HP;vFKav4SKcuV)e!-f>GoVS)HrJW zNS^s;eTTXYWZ5rsFZx8tgS3HH=-I_-mzUq#S75YUmWllUIxEv-Tv-ukdfmspaLx@S zF`F1Sg^!x(z2bLVGj10u^oh}UU1tDtY*6c^g)8m}^wG$f;EXr* zK6oZ~qP~y;UHx2j(f>+;Bd(PPc16Q)90+cq7K5M=!{N2uBGa8tr3pKyxh|1!Pbe~Q zi+MiF{9p|QjIKDzzt30MGo9GdqsIJ!m|MASR|Qma@l~6Pq8}R-(n1ZyIwr_3o!ThU z#IhIW_*KU%>XG2QbG#F;z5k*#or&Qyj;?T`)K5M(3-+|dhL!xM~hV|IXn+0QR zW6S^0i3;@jZNGJ=;PE{bfqqk9bk9%;?))-KHVucw)$H!(Hi@d9=9KHj0(r8@lM;9> zSLVB_k2wveF6LtYqkbs#pV<8u2OD3#DqeM}cT{s#z}i5x*yUBswK$Dmjrf-zu})6QFCm#~+@;C*$J%h8C{trkr){ zk+^I)<(rA>O=Z&=AGJ)nhqN~p;SaHVT;Wvfr@J41EngLGnnCgh16m?UB+We2_hT;f zL{9U98GsXAT&n^7<;>;LM^xPXM^NTQ*?*sIRhW#x3V%L16IUn*tq+lgW569P`)AMkwHUTE%VmG1kzW~CG$}ZWI z&Uo(5Csfbv5V1Db-Z8e-f4;j}W=rKBwK$^rAb5lM5l<-UtkQ^4SO8$8YFOWHY?{|T z1^g0pNqM97ZsSwhZdx)1kfbg1$L#L__bCS7ZOtG&*Y7wd8vVG~*1?i6D{ z{EO#qeG65uDCoiKz2w^6k)sl!qr?`syXZ!^$eOyw9STRD*2d(Cl>h4hx4{S!p-7Ay z+~XC8^4)9{WQA+Mo<#SpBPs}Ovhw_Mfw1wPvsgO*WU=Asi05=_LWH?zkYw+awA>cC zV4ryNuoWU|>4x(#Mv66uQnYo$AXCCJYoJ+stbp=z@Mpp5%w3&lVVUvtmh}0`$~%>F z-NCWv9#hpH^zw7?f2&lh2^#Bxf^g2hzeHr{`+*c+?z<M_ulR{tHj`HUB*<`d$%xSHJ)b@f5(Y`9l|%aDe7b&7+%qh^W5$6n1>P;a{3V= zx&qckUSxr|+&oG!*!#)(bOf)9V*+!WJDGr^og)}~I&G$d6G(h!jAd@jxk={9sjA9t zMgy&uBhl2WM9pTGp9$ZKPt>&CNko-XGW_0*7w@+1k zt;3ivrNzQlHiykS_=b7I=abvKg}$Kew~3qPSI!@1Z4=(HR;PqoZG_gOp~E%|5-?qxs^o-c=6iAT0OA;4S>rl;h;YohFA$=i` z@m^d+y~Mj5H31t{%Ima%^{pJig;DNvMLc&VHrCwJ*jQD^Ua=m4n4emhTiH9c;xT=JmHqlnxQWHcVUj27`aRqfqvW^+#>6D?z{ZgW7jJ6~ue<(QzuevGp1!st zi@?Cdv`5YlYgA*!Uug{wx+y=qL%*#YVQiZ-qCfOhN#=@2wDI+hP~kbc_nCeQh;b!N zF1GHa5rjykgIdJ8bW8m~J37XwniZ=gL&+L;T`!cn5;851^cB}Z&zV%Wqhuc&M*xUX z{bx19Vy`z^g zv+t1&QOBj5&F&<@c?I-7%DZ~$!OeU7G>Zcv@R)!Rctp{Y{^&ZHG?*W`pTluv!R}_p zX8B^#%Wja$>>*}&TN~B~ps^8}N1Kr#MU}~y`@5fbauNk>IUaNM(cq2Y#z3ieAaFQE z|5{S&?#{uHuM`c5lgGj3hWF%T(hEV-JQ4@=^>vHh*i`Y`6qn|sN!s{%iD;F6iK9!n zj+G&alN8#M%rGlvAwl(Nd`Baq-eyAbT_dudNkbYyCiQH!+R^o^Oz*C^0*ogJ)PAz> z5=ifHeRya6BKC|n=8NrS6Inh(tNJG2L54oxPl1tT#L<4}(2~?w;J-ZanVhObdzh9Z>wO7o`^UO({pF7}o``qwelv3?O_pDktcx3g1+=r~{!ePR)?wYy zkmg!YNyBrf#t*Ev68Jx!itF*owRz)_w9kTF*PDk1js`m_yEub|<{H_FhgqiJEvM`! zeaMm6D~3Zy6m}s~w8@KV>`Z~^=BXC(j3NVDqn<|pD3yfXbJ}>{c<V%{~SC&wp8o`8(+k5(hU?D1WpcukV=(q zydNM+)tEsAu%DYdL+fW^0a?psj;UcmU-{|J!NVir~Nq;RnE(VzF# zO7Pu+hX8kq1e-p4J1^ogZOMC4pik&EencwN?PDe6ik7Zr=;t70kR0D`;3o7*F-;kD z_C~K%ZF zd{?b{M?7mvgy@|~ff%RRtnHqFj1{SMY(rB7wCs(@-vQR->bbe$t|2N=hEPn~xh zz+>NR(DiZeSBJFLsCZ6)hDhF1ZFk;0UG(UTCu-Y@EGR5(!M_NfMZXi*iNdg<4VYB%rKzCwwPD-`tE1eBSY^=Y<%;H5N!O?Jqf?j57#^B z`(4O&=Wxcl0{@j9n3`YF?Ndwp)gaEvy z4WO{ZY>})wt8MW(Nl~gK3W_|QVPKdTu0=*IfeVFJgF;(FD70du-81>>P7WB6Z$9mc zQnnyPiu#SzCk5ZZX>{zsD86km`N#*U{#>_hw_#R;BG&xEWP`LyX$U;MY3`D)h0)6^ z?ZI z2zvN4!rL(BK|nxp$5VT_eHMx8d=O@Mcu2bS{|r18pa-Rle(}QD(v!wlU~x9YqKP&? z>X&A%>g0GI4MAS)2JSFJmxa||9@Hs%i5gRKu37GXJx^mFC*H3`w zW00)@4SmAxf6pB+{gjBRw&E}I1RnpE)Gji%LlLI&YOX5Dv$f#9BQU#%+{xs(ZNUkb z@=~l-_5)BeH+t!(WYB2u1!yR-OnK=JZ(U}!8ABkVGNh;{2N*!}c6+tcf<-=iEt1flYf;6j#DMu7Ne=Vf$kG@$$l1z$vC+bZlgg#Ut=Q!zh&q_!$ z$*sV6VWhf8wAgLSC-3Pgm1M-a4v&JF^7`a*+zbfyuRc+(cQYAypQ^sV{dqwxUaCjP zDtaWbs0;4v2+kBh_qB3=S(hOV$PpA}1|WxqUr^99cZzgdU37c>l~ngXomkG0(pf8D zz)IsC~mxP)_&4sjO&;@wc>%H2;Aa8R(%m;6szgV!exUD&{pNMGTJI#g|?Hi`kg4 zL`UhHwstC~h4N6n_+;Exe48XMGtO-f?>>p&i)-~R4!4s>GhSeEdy`ddvCxLE0wPfc z-_>e-iB*n@lY}e{#>)1E$-6vbuBP^(P3qfwSfIxR#r4RwEt z`@G$6E7)ykjKPg6DNY7Z6mI{1!~(|Re%Box?F$bFNDY$W*F|rjt=J0d<&}v)^^j~` zuza!N=-uT~h9`Yc3-JjtdUWh!7px<87I~RgE?&XKi((qnlEz@C;f({lD0H zuL86Ro8 z@CwoWVR5^mSY3S<4Z1m-6wnmv{nK1lo;;T`6)d*gy%6mSUf3Aa>z0*sN1&yRY+3vFaZzfx z*#h`NoNVlSO5oD2#4%FGHn8Y;mbBQ7-C1I?-K@XjA7ac9SBPy^oU)gE&0JW8EgZcZ zXRb10lDL_=Uq3aePI0(?ja^9V?3+DNC5ee=A>Jvidgj30HRH%ti(FAb!g#@A! z0p*~;?qsyALc_l?>PmIigxCQju8w$hmcn?4BTIshtUS;6t>66ozH6x8Io1!|q@;B7 za!R3pLd9rePtA+5t`I>kpet#=rA zok-L+6)$zGkMQU50pRG?&2w&3BCvuCJnIdR(KpyEzhcdwIPoZj8T>FdOT%jZ)6tJs zfeRD@uwP(`)e-is_q^XwCZ>~U!giImwjc#H(i#a)JZd}_yj#X1BxDLvoM=s0wBzP= z9p0Sl0+qdHJuq=d2f!OQ;SUDo##WD% z&LY+(?V%g-_lzohOIjdOGLw~s)MYDeAO%~g&RF4|)5YW-EW#Gm5XV@Y{o9i>zfvsC zl^+~nuHQ_v%*8=hvln0hdYXwHK9Gdb5)PGBB_18;&%Cm;xDE|kySV^=V_AQCpks=m z`~4+u$}~c~bj_Q}hk)8 zw8#24t^6;cL3=*N8I{D>gW1D4QY^LFnC1>|UjXe>8?)5_L>?ddSzTc(O#ZV*gh%jf z+O^Qa@N1ux@egDbC^X~pHD1$vswwitju}1C@iJ;v`P55;?jisqhfx~#slDmLd6`oJ zwrtuT49oog7)ClF^aN`v%puQ<>`3MG2Ly7=2tE&sEX^N1j z;a{ScLk8|kfg<}28fBsT3K~2e_4(rmoBog!Nr%2&{Bh^*-z#k=t6VEmBc7GsC4!MSHSUX9|6YcVni_G-5E#0jhuN1K; z3A*)e^DmZSmM)R?1*`gzFZxXKLpQiXSRwU#;%_l}nBrv^7KLL1FEjyUTJHLK+b<^Y z%6xq}Nh&JqspCi#PN!-?JGEH@dnkG{J56_UaiOI1?5?yQUt{scpcOS1^+bAMzb#_& znc@A&DD1B>19ZbGU+-Q~O8T)VV%Nhc4Ei7C6gz@i48G61MtqVRL0IU!T&#n5hPU!! zDs%kibcTrTXzvn57fG)Od*e!yHWf$9)bY%lHnfd!QPuJ*1^fX;iAMx5mo7Dg;r%Skf!^atRG322v7zmMldXEBI??dv{~_wkI+Btkon8T z6c3nJvvc2)MV~f8%S=DA0@5dN^~uUI;8I6`Em+Ba-`jsjPGPKkjY}15vr%4d5)+C# zU6=s-n-nUsD|j-3(Xx!%`}Kh-8sMZbw&IW*GO{#ta*ZNr1StI-7Wbw|L>8cU(i#lP zZvb(jhn(NpI3T%vHT96-6>wP8!4C$i1EDzeemWpLUwt})FENRj6`%925mg!$IbRjm)AEGCI=BD`kUtSF1k2s}!Z3kf>=^ zQ9I!8l5^8Ee%sio3YYfxSTBp2#s|s~P#r4yDyJib9%mk2;5r#qY92oTAcNb2%Ph$F zS3L8f{Q)b9)}m2qfkpH7;O?jDJ8N~1A7gKK)sh;X`XIC;^fJTNp0T}bga=!t%);C0 zqM|eD&d2K1gU^c^i-X@7-bz8a9ayK^sZ1L&^%RRCE*LNf$gZ(S^w(iz z>6{e5BaGB1C)agbueVQ|sOSsNB)Hjlclsz>943;LW4XasKdc3zf6nTdKN~Y&#t$eEc0~j zc0?IjF{&gb=KoxB1-;^8um;_S>YagkFkkn+FsKUXhzw5MMR4Kzn6G0iS(q`0TsB++ z?=x`IP;&v@ksdHxisI-On+PjEDIY2RgT!r83w;FF((1nRJ(AICXC<^5uKTqumg!P)1jtwHi|nO8O+vikQ7LTFEenwymH(CP=+JKFyplMc0{j51T1vLRO!>$FD`-xZ30#4s1)Z5Nqiv3nBGOCV)jtMWwN8iu58Ne( zxhVbJ#}ixX$+0V_i>Y6x-FHX9N~Sw?&(r7@bVJSF{Wdr_j|ui*I`$;(e4v8jDNXp9 zjeZ?IQB{4vZo`VA)cduZ)J6FB&wvc^5|$f-BsQ#J-2N;@G(}MSQzx-d^Ch2P-g#;b~kt#zMF$IPU6J~G?fv{cy(n;@Ab+DOV zwX)a&PfWOV(Y}l!QFJt%Vk$hhBFmzoUIDoI^$#FBcnN#$OHmd;dI0+%VCeHd5@8tE zJn=fce4ct(I$dE>l61^n+WB|xL4{3aO3qhkFZFfg5O)I+rM0X1KoIpjmHkQDQ3kl-d~`PRnAWk z{nS210iaVycwPATr8j^E&evUvj|#IWaks?vLxpNGV+ZHeFyWVy_!+$qB3MOf=@x*l z{4E;?uwI7a3r!Xwq!$+m=334tVHph8{9+fUp%G0MQ`t`$jQq_~txB9Zd= z)A*795sB*21!ask=kSXl6di7!TW*Z;OSr?p%tF!yY#R!j7{%b`r8cFnuXx)*r&JxI z?I$7|N>suTXz-;sz1DJK2T2F+Agh?^h~^CnD+Q}xdP&=)@;TMe<-Yd@o~XhmU2Xih z7%HC$j57UVlg?gE!e^fVE?u0=#N_K?R#sMvaS8PmH+B*i=6`=BEez;AD)K^|?%Cd^ z0^zva&GAqe5Z7ytp^Z3N{Q=Y1uo~04;(m6d@w?A^``%*8pUrBmA7<<>p0ZEtgqOAf z4vv}BlsQC9=vLO?yRrAizW|L#>swi^=PT)$^yQiF-c-} z7T)pESKRQlanQ(5>1a_Zb6zq)EDn38EO4_>2bej&TJ_yhuL81;(y;aGV{kNvdQms#}? zYSJ<4&dFtJ3D75tN3h2{-C!jBygol!1f?pm$QdeLg|BuJFW>6mf1}1N`t7H8*qGb# zgehC`I6&ZOL}&EPAl-6H^XYc`p9KK(nWMS5yzS1}KTBDo4?63Xv$<|=p*BzKhfU`t z9cGoe>BxJGpmhU`1+28G@5Y&Y^@1Dz$>{-p^rp4f@UJ*I;7D8Gvp)#TCa)l;z`|*o zZ;~4?b1Cr)kJ6+aLSBJff|NUl0VPEswgxM@>{4f6S|pI~nKTS+?W=t9^Ax;02^57c z4Wi}mied+sdAGqvzmvv9VymkoB7htgx`FhwHqvzpd|N1r){D&6yW#o-Uj9DnYmu#g ztPeyeK+OVV3n2LTa6EH&l^~rlz0ESVr1ds}#Gj7o4T7KAHM-N>--9X$+%rrjCpXJ0 zl5YIG0dARsYb{Ge(fxsMcz76#5Mj(Wd+IhQSdd?K<#ZIiP6pXc0FTmx!kn4$gDJ`M zE5gC~L-LJ#Fab4>`k#Oo`p3)w}mGt_l3f*_Nj>gRedexn1j{%-2Qe{e z?F(>GA3w`wp+13hGIT5tuq)ml=f&n@5k-U7pS2%|{0c=_Jwp|*6<-0vqD`VrAus@1 z$`r!s<^*kW0D6;(%9QR$A~OL(1KeM!a=%u1iIItE2+1={cR<_*Pz$|pJ__dZCLLUpUbCIOvP{%20-{p+0Q-(3g9aGH0BWLp4`I;#RadgKk`ny2 z^!05>H6S z)ykX)0UJFJ@+iB;{5dvva z%^Z#EVcTOCx{pjQUbnz5dh=oM4>=6F>cmoL+VVkTsJhiaz{{0xKU0AKfT?0sAsm(Eik2yN0Hmvi3F^UCzp`ni;xd-Vh*c8 zLdDa4Hi$pf@OY|ZBr}pmEDGcYM6NT__kR~g_$xe-4A^u30w9c|xlY+01Fe`~w}J7X zkuJ?4dXacezDJzb{>D*Dkj6Uq;ca()#OX?QY|3cif7V(IovI0th{ZCMiko9f`pe<3 z$RH};D^7~9L3%$Q%LXpNkAX|!y2WSS#e?$BJ>yB41sl#~z~^Y071KQ5Bw*(yMg^Rk zJHPEz{(_wm2&C!z^OgAjK3=kUL`g*r5Tu4Q?!-unBOH= zvEF|B4uQ2V1mNtc*cKpEfc9_U#3?DkrPSqh?7(|Nie4ad6!1z|L@_9G1tbBH8ZS&8 z^0|sLFuPXMGN?)QD@uJYUlp&hsaLfkTxMy1rJI|QFe*boQ=U`IW)#)FdVPVRicu_hLp+puwYxwLQFC!&Z_3jP;4y;i4Kh&?|Qjg3A)-p@s zHgaWRZ!C)d{3feK);1&H2R`a&ObiLw_l+sg9O?NfkBd`HOdJ{)NoUi+t(<`FyTW23 zit{_Z@we)x%Ubx%AOz>ehXdMT^Jcj-zWrxd>rd2TaaU(%R-!?C%6~J1nh{Z;Q7Kn+ zl7xXssi8CcS%H;@$(jDp(qBQ94O>e!)60}vgpC-=xL-~ivT zr=9rx)!R$8$z|r-1zOPNeXduLg!d&q;`#8Jl_ZNbujK)JQjzJ|r)`25XUMqz_&NDE zW_&*o1epX=Tp)P<#$PW_qMi%8V$se{N2NBAxKEgi0G zs-NQTlJ5fAg*e2-s=9Z@I$j)X(%v>9?<~<@aR#7F6Ee{0ai=U?S}U71H6s zB)P%1^Y{EcP{5KmFrth47tE%yr4ufIO(I@bf3sp7AK3Ql2N@$ZCm`~gpMiC!#Ntw9 z)JieCLn-fC|CfHKE3T%!c?c+f`Z^Ny9r9t3w;Q49Mo*X1Kn|$73`M?}^j&-^z!Fm^gboO>cPN`TH;rZA zP~L?3VHF^bsC^T%Xs8|mJQH;aW==K&1{0+P=Mip18gDe&kM{Ku-)-hxBk^yShSp>8EScnu-;dOY4MJ z`nwRYnpCuv0c+ApP818;cjB+BD-ziv5b;3BiPu z-4w3yiaLO|#=-$$0@FIexy4kE<6qLAJO5!8#EYd=DvZJrvBhZ!d+V2}Oduftvk(5A z*#A`ys9|!<)0Px?UP3&WV^j)R)Muq+0Iriepv56@o~~Yr8OCC8Zw(>;nqPP2K6pkl zKcW^N$y%)2$CmP|`;IUz>6Hjo;iv_v?v&^!$J5`37C$P}sk~Zx5#SnN6SIN@ok~n- zSY55edJQzkrZM{Eubt{q+y#xdqov)f?VVExZAw=!qD&3*Qj3i#Ax7Qmr%B2Gf8}!< zk8}7A+ms+UR2cn04&HzipZozhV@+3uN!T3*BQgc(L#=^Sg{w#0I!TTLMT zV!hyNRRJo>IxRgw_tJl=fRcAQJrI^7tI|73@F|4=F<_W~NXM8krzmKcqEJ-9~Ow0|h| z(PMD?I+Z#RaEwD~iX{l^L&(JY=7gjJ_z!(Xl_K>L6JohbI1m_hZKQI!F{+mRzklez zrSuW{W^Wi=t7Pln5M z-kc`1)^y*co{k2Gk1M<9B$1=;Jhl-s6{6Q^XM21h>iG8_2#~WKKs5I#$TkG_^p`L7y!aHu>+rHFwj<1CWMYh(6ySg(R6gukE9@s3l&Z@DBlO)KB?uACwrlO1gVzaxg{Z;RWV_LOdE#cXMym$Fdl=Tzf+3_zAA z$8w&V^;WVaaeer0<6?$u(!`O5s@+aYzgLWrVPl?T zI#k(pskRN?BE9#HfpToNgO=X=gw?V?mQ{%+*pxgxfY|`!ewzE_53~Ky^opSCA0z=H z6)Nd_U1FTscf038#sW0qOiV|QtmpM5cjGt8Jq*C4Pw9AR*mIcS(15 zN_V3)NOvRM9n#(JzMq+I=KIHSoYBD_o9jBywT`tm|B(JpW4 zmLMpnTQV~#6clN;=!=MNc^Xh223%iR^uIpiMU$@l%0()ZPa;7EN5OzKkyb2OAm40Q zBF%>}IvBe3bD~5bZ?7WE>d%NU=`t0dH0P=G*7xP?+3qu@4c8>eS*?iV-ovK6L1vX) zAr&SaM#?X^=N%T~yVNp(i0=2Ju1mn{ej57(PDrd)`6fLBV2Cwu@E)egEbV_dZE@H# zF@D290Eh}3R8Whw1;sNmrBO0n)bCr&s%TEE9sv2X}q2~`_4>K6X4s@lt6IQyi{8K!FtB(PUP}9tBIxVuCI8y!dhkiB&6Jvl-4qNkN-C~F# z0}^1oH8~7v(tdD& zJTk9D2oP5m+GXlW*%3Zx*sQd)d_dP8hi|l(XG=NU^q! zX8VS+P3{l7s^*1?g&!BYAW74wxqL#b`Ax3_h(pm*_u)DIX6C=Go*7JVgx%dr#YD4& zizn)nEH3tGY5N$~^lsCkS(#uu#zS^aMm#%CM!y~VWHC|3-sKUU{c8sU<9E|PPUYSa zfNO9~@x`WBa!Nd5r5Orknq~U=E4x&`D6KUY2?$W0F&)&piQ4tb+FhJBbHi5usX4$B zsye(BeuDxx-J2FQNOaNF@U8SUdc#clF{7rr?$frKc-Y4PbXP-Yz`;T*oy~eo-8Vvh zGER1ZAz^nh@=D%Ggz2A>Q+Vp|duUG1B7?kN{py^x(L+O1=153hGl2aIorXhCXwlgJ zX7^cMe#QzcwBQZrwT#{857x9uGmqh|J|oWq`ju43h2lTh@DcDYRoX`YNeufK z8<*N>jn6CQE@o{Xb?(*g*YHyHwddu1@;nUyBIgS12UwM&zYxJYGiRNY@)24X-03tZ z=LP(xPqc}Xzh0A8Dmv8sExKX}&&6+3X1}`V2iyHYHycR~g&ZWU>s5QTHDgP~lf@lY zx`Bp%eyY1A86#hO%g@OZYAw?0mhEI9Z&auG4TnHbK?1J0F(j9uRW*KFKB6o;gbs68 z;M$|W-iw#WHr+%)*bCt?0bZQc&8eR?g-l~Aie0pFzb%6$io0UIx-qqZ1|a-4p^5x1@+GCOOBW{} zg%%zl!G50_NS}-aKmB><$B^drW@;vF_NKX$SQpKQLpUy1V3pu#LIDGm;)_&WVC!lt zPH>lleOkgn;A(=dj5>TJJM|{~@46v1#uc~hjSNBPVm}*rXSBWeLR=ip(85Dz-1uXH z0Xw+*Sb$}4RQCfu1K6Be*-965y%wW1ga-J(n+W$Bcz^-=OCKeI3uMq%R5Mr8 zYV#NkLEIwlZ-e|_MI5$D>?SDYT!+&Nk6ursjkF8Ur!HrPv=P59m)OLQE7!2HPcA&i z)-#Y70OtWt5xbn%m!@k9h0tFZt~30Fha4sqE4Qu>t=O-pU(EJ$8g8;Z?15<+*mxEi z)7MK*0cgJDi4Ou^G&X13EaO{b!*wh+8TaG57cVHHb@}8<4zd-j>TV+Q@MqB(YfWn=?u$LaI;;|<$jMK9chDRD(5lOi8Xvgn z+8MEEKG@W}Z4^HRS3gDK1A@%_RBOw9p1Vnl-@^FAnJdg-zj(#zAPSY=E5CaHF7O_0 z2l=N9ZbC&5w|*xjOy_=KE`qVou0W61&Hphdx&)mMU7x!K>%-3 z$n)Opdb{J^)rxyKdf~`+Q;P^>3#%OK_>HQ#CF>`RQ<1>xns6RS69GW=cy_dg)3vvoB|2nDN_qZn*bP>J%d|!1MZQ=tfu_l8iDq ze;XKmvt#BZ8B?)%7f${$>t{pWP9m5~^ky^KVMiJkDs1cit{dhy{V}wU3z+JvcsMZk z66;H%^Ww9v=UOsqZWwK2VPcPCnh5~Ylb6>ei{v&r76M|gg>0fkuls0ulm>0p)UDh>q{7_3fbrJW!DX*Q>**7AQp&H`-!$RUwJ_n+%J+56J<|Fk;Aov#Ui zHAMmdkcA_GU%!G_2u;dhk6+U~NGDfVVhUVP!5WY6vRiRR&A?<>u*t^9y6|%UrQ=1C za=oijSFhok__*FGIcGUmcccaBI2@p0gs>CPm0%e=fROu^(fmNo?Es-b`#QrDH-i9y ze_)HPMgvDJgxd}?_%7Z=A^JzaOogw<*IMqG_TwoyD!qex#;H=ZKLrqFNC6cyT_x%) zIw?E%n%cJ`CO|_0WDP;oV2Eg>Oi;rNrQ4lujrG4~o>E;MFPEC$>b#E+d9o0X4d7I` zFVY&}V%cMDYgd(gMiL(@uT|9iX^!1zM~7$V$qBq?9t{Dm8A_p!llcQJ)6@hb1N$PU zVEPfavjc%6Tiv?djX)CQK_{vs6s`>SLe1bl61>nSeY`x!vD0rU?Nda~#nGh&Lom=0 zuX%o+SaHXh{#qN%ycnPV;x>;{E@wM=25U*B4zVE5{4~d!(ndc{O~m-3^`4hR5(`QH zf$guf(BVX|B2Ms+?+@>#|8(8^mBLP3d+3ztea<}?@CGw$yh`3TY-ScE8EIjz7_*){ z!rgCl2?neM*f%(onKX*Qt1T zy696b-d256E_#tZwK&2?A?4Au-C!+t{gA?kg&N`(F7QELx24i{u>M*Em6bWDXiz!j z>6zNWv>JbP)yv1nYQA_^c=K|xuh2>#(xYPQ#R{9aX;<{|;Vva*$nWjyf<;nmIM3uF zXLRi9thyqz>?;-TDXszvIs&wNmWZ&+M-^r+B=;;mh3w;})S!0~rD6_lG%>iyq>-jQ z8IYq6S_l{Rk#ri&MaaSd9c^brNK@9V(TrJxoMT-O`|WZ947ZKpW1GwDp7jZR^LX=e`v}mwG6x) z^Z^G|l{VQTSH*pt8#m!V%xfB1W3AO+nEg*ZzZOQKaAt(FO==JzCM2mPQ&Zn-{qcl7 zt7Tgto#&z6M#qvtG`0vf^N5^bAtjZj;X~BI@@ z{p0jJh<qzfH>-D12|<4olWiXzMxw&}I~}#C#R}`l`89 zoa5W){uZ^egD!}(OG+j8#F3vEue&1@Po9ykuF}gk_H3ETWF(GE#q81qJru`d{UC6M z4U&+9j+?!%uHwU7LkBkvlRShyoLL7~+`m{@>R7}3w9wIme<(3t5p&`_PYj^1-fgcI z&QN7p+!b2LH$8udzfNRzZ!__|)ahX#qW1YT>?~{rBInu+aPL@qqyN;%)+u5^ntAJ* z$7c~RY&+CHZy&~!71VYtB>%6 z>4wnUlYKhVZ94xq8ETvIn)B8?_~qD{)=R-fSznCte_qG77xypGtTOd!offPKjd7Km zGT>1c6W=r|cK)Hktrc1-Mt9*RBEHIsI^)k(gJq5zZxiO<01s`hf6A`M)`?sIcLSa^ z32F_}X2G$1)_-`*m1SG~9f|>6y7DoiMG)1Y5QZv~Qy0WrX!w0oUlkoWga9HB=rr6|lE!X^J;<{jy2H7<20Z8pYLCHRZ zS1ZIIZV=o!TKS883#+;^{O=Y_w8T2Eux+0Ai~tXIZj|q0_%8+b&@EeOqYp;S>p4E+ zs6Q?RFz)-D59VSH4*qK8hU!-Dlw#Funpg1flmS=ai>R4YFYDQJ+D=00_|jz+p@@oM(_?!_p9 zX`7pmgM&_3>qvz%ef{k_1;RMUkHrhx`}q>*lGcH{VoYt4k{2`yPYww!c_r0{rg zpntobj$ZGZwlj`NYEg+_4>?g04m4$C0JcZ{7u|fdCYXI{)8%G&mRL4BD~sG(*z7GE z#u*ZjVKF*iqZX^^@R8uoR>9iR`FR%)Xt{U8Non)X+aOK@azrRyl8qp#*3%dhbFuCw zT9Bgu8JrmCozC#9O{eq;E{%?%7+2rX%5erIDf8Y?OR~z=ndSg9kNP;17~=24jY~yi ze4b}DLMzm=B6xaG^G?7f8R_)8W>V75Wj#Das*erV&Bb?dpY;tal|Ay&eeT&7OtaQD zD~p$s>{a52G8M%oh>5{nBnLp&5Wp$oWvA+VhcV$J>Ikd+09&Emd< zg;=*^x>T%0-k~>i{^v54Vf8d6Uc>r2=`PwDJ>C6)Iat8rh1P`vSw0r21}OrN6=Ndk zh+p>NjvyKjrtR=qSs8IbjtzD@AZ^0qleqy7h_GH%|9-`c=&ov@IF#_*S<5rsk=&%&Ef?Wu5$%}Ar zoaFaUZpEfAO$Vt5#|<%z(SZ1E)rNr$se_Ifjh3so*V zpHMPArCV|Qmn!dAKk=OhB&3@tq)dxQaibi!W96?%`z!AX3bf@77yQ<#KNX2A<(PH0 zF%7E{KWJRKKd6-(fa>OE5kUeFR$A$-6(;IS1!)qy^FR%EyBFSzTh6IlPW3{vnKT%v z@b!BTq&x>=Q-^(kn=5v`rr(g=<<33M)tUh4fO(UV|8GPQfqbYw_9~fDz!(j8i7WfM zYv;tx_A9(DGv=*IKImmepeuJku=9_AnVx|rTuOAdf|NClSqBJmme4&-kOwzKhs zg#XAHdJJqgn^TS!1MJEM<1ypcl-M}HWLMFWZ-QMnUL_u$&z>Ta|4U#7J{W?t#MdF`|<6dc4~?gh6(-iL!4cuUtmw65MS8pQm)| z*g>&S(%gliQZNxQp}}G1t?%2qL3M@V^V0lzwGJtOuG+8A>-4aDuEJbhffH-|r*1!A z7LicAI3R}F=xQ;| zNitxlSjfnT?6?zfKY>3f$cOVZfK1x|Ml-$n!5ZXiF$D;Q#PUtiJ>79laNMvNM_trF zm6ukz_}uYWdc6})IE!X|*xg=+g7M-M*ejC|)SJZ`Zs2;HLCm%r78NY-umAt);ASY0 zLp1Gi8;nZ8r)Y*yPZSrk=+*WTnhyi8A(HLw3 zs%^%~mFz$LLvl5b(x%YzXT>nJ9j8GJ@_47}X^)Ek)NmpwEA?v-n~hRJE7?M+Awong zP@uM3T>92#kSsP%sg{lgBda9f$N6fr;EjR1lB^oj%nz)HKJjjLW8nU@!k&GkB8ADybJ^)^zBA9Ko1<@4fqE2kT}ZK3sE!BYyp5^meUkx^IPi6$eexvRQcF8DJ^eZnER z7*Bh9U|Se6{3S?8#ByVh=3lN{;-J;^P8vUzQCl6b{5x}x}8zQ=>!6r37k+zsqbKFA`n1q|BomHYGdpq^< zpHJSAztmR7kVh?(K)vNo4`kO#47}}{*dnKTdvrQh$V{TS*?zOu?{~lg1g$U@zXn^O z5>0$a5wp&rp)M611fMBRpDo7fEJCZ6Idp)D89e{3k}*6S$PFhy$2#5anYalE0U85@ z)PJaVyVz5gU}IIbr^Bcu6UG8T4sm@5D_)9)Nto6EU4Q!6ap_7aN2R!hVXC17TxixP z+I9m=$R5psreVzX6EWe*b3B}2;jyY(ww1WHpLoa^ud+5Jd2l-ws0YMIgV@-iS2~GU z&8GKPt_JMgdin!pe{tTnuy;7@R2xB{X`}5D!KF~7u3pr^ zi+}svIXi#AXjt&yKefsO?`sSW~x`#MSc6L(Gg36qR&j?8+Wy7XmWwxe6^2j z^Rkw<4kgdWT`Wf{wE9NN(b)fLm!m{B#&VqG+|Az0Lf9glg81t{&!xN3TUnXT7JB{K z0?Rm}Ix!tGb{{T=i-GZ-Y^Ro#)yuZ{Xz^RtQ6m2cv?_80`xkL^+i)tK{dfT@_8vE> zc<^8aDTCxstfTx`zVlYE# zDJ^bft-1nnCQjFsMZ8!_3ELv%M1k<0KWblk&gsK9208YVZ5AyIwAEH>!KFTbyQM6Y z{$T`*4RwUs)*n74-@7@y>XXU6cU0Mh`Ywu*rW6R8_#JcKQ zWTE;m+8LicyN{YCfT@50yO3il05*0Q!c>js+xS?RsBty*{3kd?&_hC>#)~oVZn`Q$ z20cCmRdIhDK+B;l3wCanuSrEa?b#(R?8faxz_TCkhq;);lIRptO3F0-JCzKF_FS%U z!Kh!9QpD;!bR{;8D~aZ4Alyxo&g4Lzvm$V_6p2a}S|)E1arnH&VY za8IAzq3iW#0o@ONzR)Nj0lBsJ;_jgo^D@=ZgrUud>WK;oP)og)gf299sbmxG;VwtY zFL(5)>z9Y`2@hl0Z3ffQ%+yZkO67420ZAe|(Way)<|@m!Pw}OoB#n|D18Z;y#0Wrj zLglrrQFhT`g)r^V$0?f(td|mn%%OwE{de40(VO2$E_>q{1X;)0hU7Z}teR7sX^dng z`E}b?^6_18#mOzGL|h1iSs)+W2DROzzC?WiruN#RcSzDSLe*isF+6ydVXcaHi~X}K z7G<=wjfy&g8CGVh2m!}s-*W#yQN*6NXm8HV`BY8TWEy3O=_K}n--x_kJNG)On(cXU zf~8!ouDxALax)Qq-d$qucvxM}s*Z-t^WF|-QZqT#T+Z6QvJWIQomYN2OPqClg5aMD zKBnmBag=D-jtur@h?%ed zS`@fx_k3Oo~Rt9=_LD~$FH_mlk-|7OC*u>-L zFlrE>|0^~uH=+?gTwXUl$MzL&X{6rX(DOtFJ-l?j_hZi-&{n$qLV@ zRRTInF2EJ;Zh|DfA6;L`hIaum9JB=O)9?f?QEYv0|GCPc%r*%rZXDX;bC1o>#Jo+e zrkQ5)7Q30;O)d~lyZU=IyMnjeW8+W%^IzhSW3Ar}1F?d;W>HYon1e-Ho$j9S8)Sf+ zU)C}ip%*=RPOwBm+?ZE?@hhE5S-&b3{7^+GFT-cvV9}{$^#^s5s(>O^vpPwrTnTH@ z@H}BWDd9Qxi$uw>@*#iDwPH(+TAK{{g)R;q1Q%iMJ9V?mybvy;Xmuu26>U3m{FkuQSsvminwx=J_VEF zxe^-Tz$}`JU2pstZ6k>4&F5E97NSY9pUBG4t!`Kr4MMvern7WR;2#M+TNTxy!*P%1 znd*)ZKP3g_xxu94doYXA8K7Jx#%T1xeX30%SZ&8X5-pgFZ`ASdG?OkI25RdS;%>{L zYlc3_j*F{r0nu*4)(``6!mB@qD?sZC(a$Ztc$IOyzyHfy)w5c}|I*MPAHVMh|E%9I z_ck!G)x?C)v^733l=^mY`X*Jx2D&fU6&CSNmF(#N90rVD5LX0)iS%V4&-Z9B(P~?y z>m?ZQ?@;g>jA!()zyBOHyFtVKU$IIs24OyXo^gtz3_SB92h5?L-ZVLi5y39A{D5W} zrO|?)WRIlg@W*gc>731xoM_tny&bS4n^Eb^pp0g{nTCv`@`+^NOy0W$R6kSeZ*p^E zd1@7l#Zyz18jsHy?LIby(T=b-t`Ww&)f{xi1?aj z(T|K&=9Bc$%@1s)t^>cf$Co$l78VZB1~g@o%kKi)O2*eP!q#~`GById$CsuFd%IC) zT!$(bTbJeSep6r#0%-=ED6k_Htru9QlyWDnd*L)1eDJv^l7}H!5S=nqOH^!+hNZt{#t~`tfbBghR-wfc@clpUo>p%q3%s$RK-Wgwu zDm;rm0TMSk$b0jhX?YM(*iv-2bYM(1#nXn3t1HpZtVPp*_V{g`c?I0RdPj=b7tx4V zfnK|`2;Qks$-C2df`17_jWv7wJN4%;X6c?C6@v7gEU}*oWjEg5KaR zJu8fYmr$8J=5qZZrGSS)i~%bK%6vI%^uWsD3Mq(`9&T$hikC}S_k*}uZ8Ys7<*;p< zJwH__l#Fdyo)U#@kCwUsGNRR7pM{}JJsLumRl~HHg;>$<#n-nntgJJk+lW-rCs>=c z`7_4{U+*-X{rhO4Pk#Q2oY4;8Ycyc*WjD!{nSNi%4&I{v6eL6F;Vw!9ACk^5qBj+5 zKNXJ$7MgUcR=g8K`7=6Xhl5&+obhGs3wIbh7GYFO$&+)MT)2eQn7;no@yf|s9}5BK zj{!qc<8q@}-x7D!ly<$IRt|^d!)>71JXL_(=PE~kiVe%Fqkl`!Wh^&qQnz=2%=irA zN8Myv@v;BT68`=B84mp~O72k4x=|_U9jHJ6t+~DrAEyFB7G!d8(zTbjS<4!J)xZ-KVU#$}oT(AmN=kx6>&BF=V-T_cO==mS~5 zNWsU`rKR2fcJvjn>I@JbzK_KUG~pEy*k)0DpcMG!%r~d2^Et(Qrdz-hD_@z?=N$AP z_b#vaajj>z-%ME1P3{xsh)cX8Z&b}a3i>G@`9i!ho;QQ$pQfvDa$G~9g9!{|@KH~h z)5${*IDlx;@SmU(g(2DtP~D+9oJaTz&}exo1(q5-M1)3K%IpnDkjcy`{WFlFZUxr;7zT^gmxCeKmsllf*kW2L>7x|{43Mi2V} zv2=hM_0j0_27?Ju2f$wdX4mkP5b-K@xRZI4%5wlPvCG_Zcft)6sFK19iK0bkVwTSBF57SN@ko zbF}$}%?0tm)w%DTE4Q%3b$&o3yMVCTxf+vCG^})$!?lWsv z6Ej1b^6k`>-_+td0R`)3*Y!CdWwUVQSQ6zNEOei1d^oe+$~b<6aJWWvdgcYSzrq73 zer6kdPe&+E6LE@cUTVS^xN3du7GtCB=I}gzIK^P$Ydgdqml_TANon3V{^6$Pwi(h4 zE5Qp~UpXf0B^(< z&(n354e2>Q#|W&CW!q)5Zv1V5{B`AQ1$)(Tq35@?Qtbkf%qNLOxS%{kkb6&oeSwYK zX3@5KhdGIVO%js#NlqedJdk+8A#J}D1Nw`XMzrJrPB7`~s#dU7D+O;Fvf+P+Vky$- zLZr5Ki0Uo3@VMR_n-shKPTM&OpPI`}I19re^={9d+bvWbk6lcRZM9iqV(FHlC+`5m zZ0$&xlVxcdO`R%2DxUIZ8Uuuhf^m)vZDMZ00gr{=@DQ$<(S`O95=iJ%D3o|Q_YbA6 z&M}HhuH8+Yhw2~cUmmTLgRCa6fuz?r*_5JnknP~bPrhi1WcKo^=`LvEJ6U^iHk`ZA zs0?Qxa~=v71#Jij`tA{NbAEYF7yb*&9z;vOhn8&)x7sdpOSp&sE24c}oS2l^1YNmx zvY=}4b)Zq&<+t#U*55Mh_Mc_9(S}Drzrr*>HLA#HSwB67-Ml*d_w{}P%%N?Z@~O{q zyj)lGJEn%XNbUlK1yr8?#Y%OJz9}tPt*1 zv{zq};`@IZq6x%F8`7v2zAGY)l1tdjr&Zg@6beBQ3Gci@22f|i`T#RSq$M-}tu@tl z0wBvYdufvFK+u%W6RTcN64t0YD;a-+Yn24}w72TOtni@v`-S=>Wlrd#zx) zq@VM!g<@}O=CMJ!^e!=d`y7}DSJ4yi2LC$RdhRJmTfM~i`My8DUH<--?rX^uUA%lp zI0Jm5+?_-_- zB)ic13wS7G3JHlBE=T%xBAq`K@PmIy$nyysF05mi;fEZD{s|ZvnkIp^ zALA5exdhOBM0_)JDeGnOj~74}eC8@Oh#-gs%23ADChQ3aW)QTk)ww`<0EqNea)9NN zk}YQtt{Maphsi*QSZ3aqe*-k#n3bFPGFX}{U6?ghA<2%j(qM%(x`K!UW};0#J18e# zD~te_Nf@7?1C#;iLuTGln-e|~mv)Hx+L&q*)sihBT+t-u;YO2wu9L5Wnq>-Z4X^rJ zAcz($hD!8}D}!b}j%@#e#l178zAn7oD>yF~j#z+f88bs;mzzwNKBabV|G)0{Vb8^- z_`HpPkh-RYE$o=>pRnEy#|W`zY3C=*_8b_<9)cg-e>VRPW|>OiJGROTI=fTKX41Jg z9xp{300oyNh2rOk-1r$awDU5whXFvc%yirjJzeQvUCC@FEIL8q4G)cp=__7wW}(B3 zKd}KU|B=g|I-KWwLV#%6GwG#1^naQ_ZzZ)4mSrn_6#B> z##9UXRxn`uRpz4My?uSl(CV75QxOZYk`?!Fw)(HXlH@*FC^>v-({tD56>uiwHSZxE zCIeY;m&yJ~7(mO$Lf31h{WVl;K|oGWqVNCOv8!@-)Qwy$+D%U}vpDMNRYu7bCk$W2 z+Skq$LG#swemM{O7WmBg8HpIn4brR@ABUZ&f;F^c%mdjHN*>SVb9M%)r|w;#RMJ2S zsCl^b;n!kfzJ-fduE!6_0Lgb%T7>JDg|$?oSh-<%Fm79(Wh!X`>AP%M9$j>U&oi3g z$(~oXCv;rvR}r@PK3;qu&75N%L|u;vam(@63@QAghkkZ-{>0 z6#X3azy*xknFvo%$7xd9BsN4lWK6ZK)z>}J%l-*`Lrv&V6CR3%{nSb!WPacDeH=f+ z3qCeb{{))Sj2P%;LJZ>#lVt*1`OHV+i;`XN!R-ONEv%V_CgR3E9Wl*Kp(pNvT(*Gx zE$I0nOLKI`V#%>p8KS(vjy!6L{x(hdZib@MmAGEJFDqxDVtxn~${(ML#{2jy+fSKg z!s%7ryez^r33eiMpJx_J`Y6j_6L<~5I7GVj0d|I5Du0OL#SgqRaDynQ_H$g!eolt? zvDP-gm}E^JzmpCTt&mAN-;M!SQ`9Q6OaNJ{j$?vy(}ZGe35=UbjB)p6V;tApTeH;FSO7>-qiFXg+Q4 z&U>wX-SO^g<86|$(nl_(qvY92b=Q6Yfo^@NV z1wj1Rel{eBXRT$sb&J2a*33SP^WeAqC8kXAbp_ywo~zz`#~H+Ho~Y$CjNzMtRXhUiO>(>33?0~>mw#l@lAiVVJS<2iEZ9N?NUJqLQ5v?y!%RCj{*6F0F3X4 zYLip;NRnD}!6BwK02Wd$2PC4=9jfsByG7yv^}`4$?i>ll;%^n z|1Mq}T4WK~y1kQ0P(ONUaiWrhMUfQKa=_FJLmt&08g|$x;LoiXp^3zv%aWE>aMB1` zBijba$=P~)7lJF3v%6)V2VW)!ICNOmgB{8${F9zOK6M$oo;&I^U}3JRsO0;NET^FJ z9{$;LAvs#Y|8Uu`P=1eIim`Xky>?l52~jJ{x~`NA8PK>(w zo+jMS(p?9~$$9G@g4$1j1G9BAKPfq!nxF5)$)&bmZDEefaWq}0mAASY7{;3FYE>2C z`1)>*scPHX1>492VgDcQ%6=yPD?7InX^L{NNN6Y2Gf}wDy+T2v2C8=*>^a5LQi#%r zEBS2wtT#3A*@7YF2QlDG6GY7T+i$mTO5!fEq!t(Sd~5q zf~#@Ph+fa#z%YN5vz@oy#$z-?Fw?ZCR6J2dk8V!9i|QZ>4yD=5ldQc|X9-HHkq!iW zOs#6$Gp%cQ+6vOhm`QTR$ROd+;g-dbUe;%rHdU`MA>B8X=Rq@e4jHb0f=XSUjrJ)) zEAP~*)9G6V9Jdt`Z-tOb!7J#~v+vt3*-FN?Mq3#jN%ko5HmU)zg8xhYsy{7)aLhT7CB*8lSHhVR-HNpAUNXb5~Z?oH$?>{kdDU$!cr zCD8?6%$On%7D|h8vl(`25eTHwmFX6hSAhy+b3?hP0rU=jG$=mIbfS zTkPzj7L|0uFtmt-Bw>=68NzQ1Os>*p^YD?5dcnwq7J%hu0n zZzoNE0(!dasHR7xl*EeF8q|+VvOCLr<-%hrxikfFv1>&ihWbS<5!|vVsS=74T3y}s zKO2@muV)LAx#3%qBPQQxNd@u33dhph6{^zSwMU({ONj(WsgCZ=3N?kIR4?^DJamOb1phAv;SeT`MrYt$!8T5JhQ@u&d<%t zx;tTzQf@x--X6~2`1#&3Y73Ewxa#h*tZ}U(d|y{uZL5l`*s@e>MvRUk&4=@Kh89TC z$g*AP%T6b=Z3GVnH8_cN7m}v{;*E7(vZ}v{@am2EI?xbRpUGk>@tnUyA>L3T%j|lI+1n4xU`Q8w2-AMWr(%T@?oZ7(!8?0x z?WlOYLbG9#LD`?#Xr|eL{Z;Lq>P0LlluWxMe#&{unv!Eg$JVE86qc@GL?$3S^PLV~ zyY-KZQ4rXS<|=EKbb#*n`tLcXaFgra?n)Ghn0dOYSrxVh2noUSf2J9BZ9YC81V>XQ zrkaB4G8O_bzcBKF2VY!>RTDi&N{!PO%sb7+FzuGY1!8kCR%KZvWC!hN^_9FMwFCmC zA3woxo<=KcLG_S=rZinBsgxMW4`?*qgJErK0hT|OPd2-M7WV64?fs0n!=D(~b$Zkg zrnpIrOygrR4A8%5W{&3ca_EBp$mQe0ahu>R@A9e*X5Eiy49m7eR%PiyhYzsUuD{X0 zyD56YiPC)8P;yO7i~~%wrY*gr?R7`q+p#1!A@ zc=HZ4AZr!y&$1~vGm=*TEnUMy3L4MnYn5Mz<*}HHi&PCd+|dpALPfHhz7zgzt=cL^ zeMbf1YlG||kR(xneY4g-0`eS?}vxhdmTN{o|7+pi9=gbp~7k4=-4HBE_Kamir zHQaUl^>N+R-E(jhv+u23s-z%27{0}9F-Tclp$9b=Vy6DBQLS+A6Aq>Or>W}SRY5>- zbV-W|s~WX+-U@=p1=UP~afNK&`FnF%8!|GT_KDOFe(&cUrUE6VXbq33stz409isZW z$!a5qG;zV?qY|W2(Kx4NQ}yv@Kc*CO;E$?9^YmcK*|y~few`Wd{*O$zA2XInkV3@@ zba0+#ySSs_+aN@7q)Wtcg5X3yh*>t|!J8yQd-4yNBx?4cm}i{SR1&e5)P_^d9t>h} z;_~%)8Du9tB1Gv0+?};gsG1_k&7_Wum5Sid;O%lzcc!@oWu&Ju2g86V2MCZZlk$RG zIT`!YbA=OQ<9Cdl#5b*E9~3worW|?T-nHb=#~OrowpU_=jujys$C1c>vCl7j z%$2+WuOJkqKpr6lO%1|49zprXuir_%iQoF=M$>Rt5cj88kM6i{maIbcb*NWX)#{yQ zdg;bDGI_-(%_m!(;P*#yGlQVpmK&4&oebj#?=UdyO5ddzO{lyH)bu4OH`5{HX2L6x z5!2tCfAB`d4kS5svXjrI(9xG%2YcY@G1l3=^o#?=>h{Au6P> z7GiWk$xJlE z#Idip%hG5u>2i58;?8Af{MXuoauG*AC*T5sMG-Psli?su9g z{=2@oCXti*^JON-aD0M%8}4`qzWcA|Fadp%@;>^zr|Z0Mb9};{?C&!jPPkTv@A4JJ zn3B#<8EHXT8n^NHJTPc`XjB_A(38y1C&}g!$CCPgXjhf-QQv%Qk%6I0nib{BP|H3! zK0a9dhqzgINx_dD^!)Sctej6n>w6`2kTZDWP>`3k)0s48dg)FvD&Lf8wusNEzL7t~ zDReQGu>4r3Fx%I(sF=K6Hg74~S#O82>69zfAO(MDRZYt!0{<&p2D*+tqVhEPl50w3 z$XeT+u5w@X0)zUBx)y1dmNlDbKSup6^zR;>-cIezGHEzDS*`>bbUB27Z@qDOt9bu# z?5{*F*+P{cnwXaJcJSh`*ysQrSRILw%lZGdU)^<#TY2=Sv^ zZi-t^4nEI7>!&lSAH(~SZYt(hs(_ zr6gO-z3J&9pRg`8l9N!wOu){}kGkDpNw-Dv({UF;sWBpZ=$o8;UX~C1{_}r(E{(Gx zV+apdglXBT=&beDY8$-BxABR5EzU}zXHn4idVNW=Ifn(_MyZI1M^DhCYbVQaxoGqF z;cqrtsR;>yaxUFkJ@K=kys&!z1HmektU`r447APgxqb+GXWy7_y3rE-v?LA^FuSp~ zwsaXk^ioQ|tsX?&DE5Wn>Uc`G4L4;78NcblX>UNMR=xY4jrk`pyc#Z5;G#E~YxD=5#SW2QUw3U^7*}f$Y5IeRAMWF} zSUlsDl|6C?ylk^kIfZ^smog`0 z#+y!xN&PV5!NCEYbGfRrY24A6trXTq2bMa9$DFG*8IhVBK6bs|Sm1|Mz!{2<4GXR| z-8CS{JLYY#DZUgLL(0BBH$+{o3G31H_AdTGiu4Y5!?VoItOBXMNwP~F5?z_DYtq~$ zQ85_sBEzz^vHIU;3FWvqQD6D75hGSg%W0axTT=(8y(UKeo4E*fhyN^yT}ltxhlNJ6Y_t@qbODg{tNQocH}zdd~U7 zoo=o200T@ShE|-vY9uJgStVdbYQR{4WKg4{Z`#@}wka0yBn^(0FPKk)8n`@5%%>grT?V~>F>t4Aed(D?8nU;_C(pZ- zd3vaxmIww~PE~s3C{Uw1L^eJs3<(lDmxI9{3&d}D>y#v6Ac2rZ7M}EEnETV*e|y_f zogn!A*RL{NrN^l+AqqS0N4YF)0YKB^-KhK?`!Lt|Aw3ve9NgFt=y+RU*bbLl5?d7J z`^4GJ9+rXZG$6r*#nJUZnuIg$spczl@epcrlRw_Jsu{+o2Ytd73Q7Eqf%FerP3pPX{~>?G8( zMivgh8UIoD{1i7AQ#=s16*@LfC0;xz;v)Wi7b5D^!)U=>ICa%CM-SZY>5a3>^}JG)N;LB?E%AG^h*> z5`uJ>bW4X0h;(-|Al*YrcZV=^N!{(e-*cb)_xejmICIX~d#(MhcfD(^<*!j=9UY1$ z%)>M9?C}}YL#Bs%t2`pLXSG+ilOy@87vXKlnqgSi61V6Hu{!QGc_L5|JfCnAoT666`VP;aPEv z^{DadE)n{`kBEefy;?T_=aGp+;sUhShOU(EJNLr0Z(qQHVAEzEdOyF?{4Be-j!Zw> z;goG&At}T|?ECR1Bq(3a(bE*6KqVG0z{4W5F!-%wo+i~|>G|_a5j60vIjMYcRL z{U*&SKpFt2MBfa}L-^ww%jJNiioU4z#p*y1F3sR5E?pC)#(G z_L03S6eU5aE}j#See z)*U?S4(SA1WEPNdi53Mgl2C>yJ9uT4=J`e_w*Oif9*iV|{aL29`uM5-0xe*8Ky+E+UVkwed6 zuAswJ9PIe51nPH$v}l&BiUmIOGum#t8DBqc>RAPcVndDtuLE!Sk9m}}gV%Wj zwhd~$PPe{S#@wIpnRznU#(uryFip2cS_5IXx9^tYx*YKRVE{I7!aJT^8Tyo%^JXo2 zDmsEe$r>A5~Sj~Qg@I*Cw&E?g>RKQgWSn3$cI<|`l=EWjf-hcbu)5MJ#>gkw)(GCrcaHBSnTQOtal%ovROex> zLo>;wCV2NmLR-bQpq*o|mB?hWq6!msr}D6B{<&QTh%&^dZv!IF(BrmyJ31_zxm6$- z7co2bW1ajW^VA?sQn~xesSOaVfTJ?aB2+m-lNC)Y-!br~N!JozA0N>!=kJuW4Sdcq zzhZ)7m@iXc|M-ub0-GcXbzpI--X^5c^f@E0(*C#qOVz9{7V(0o(K#~Xv3zG181k(a zAJO4&^^9lUtjhLDh<(Z?z-;O9Wz-SI%wC2axXd zmfMCyU)9H9EbRu8jml#Xf;Y?4@KTS;q|T1d790;fch?L%yG_|?PmBvzwa5Fc zgVt-%Y^9_;TJIQ|H_wE3-=s3IzTVGk)Iu4&~|4Pd0Be)C5-Qtn;5wV76H zB*5`fjSCN@i-S~I49=4ZRS`kryk7*wB5(F=l>or0*>89qMefE2MEbK1I)wcCZv zep)H#`2wd7__SJD8h69jBK@0o{+HKrS!>Ix4cT&oPFx&Y6+LE|nR)AQxyp0#7j>?m zecHyEkbqqA8gr3ii28Va(M`U(s{iB=Nrtx9tAFHaF#PFpo&{hTa(LCZQjv8c%AjpO zCZ%E>k>$jmV1fx^NDnzP9U!6iht=UZ*GbQ;Ti4j?zq~_JoH;LFuR?ax)+4rj@dzlG zuY`^s9@xoX?aC=43wZ=mWWXrP1ipQ%{sxX=7b_R6tP0QK6Sm*(0*V=10p%eHvUR?| zbT(y&Dp&XN3^3(ZT)dk-)0*J2QpTAGKTbzddz^@=XIrUiE~%-!`J)1G(CVB+AcziE z+{#l%7*|E~tP}RZXVXo? zHL!~{+T1Qlih8eD56-TeQVAL@<|a9fo~Nmum8Hr4-ZoHH%8<*yKvk!vGCtW5Hw%t1 zR@)r%vw+m5Zh3|M1k-rjS0A4!27UH;;;GMLcQ#naHFDjn^7}!ymI6v;&W4$0t8eI0 z(>lpd_hGvVkR2 zVevS_R{axaJ6sa)m~vjW{?XFaP8wa2!UeaBy{zHXR4~iH$kL3^-f){#m|a%nBeOB} zW2MlLEbJ~YsRqjh8XER@q87Hs8oqE#FB~DohQKD2YvnkwSXbXcyxi>DJag)FDn*)k z#0{3bBi?s(1{zH!^|*)}8PKT|LzbjTIE$3pEcYj@4kGair#y>QV`KieTQtzk8%2rb@Z!j4mqEy+IIXK%^ z=;7??5QUVU!)hp+hs_I$=zCXnOAj=&5kF`+$k}Q&urp{p8*(ldJB?O^u(+CCH^YD7 zX!g){teX8~k0iPMcp6>T;E_OJ9sm$;I|O~ctp9woMWy<^5-+n;M&-;q#zdZHNX(Mr z4!$RQkE?$vNQqb*|EWo(wPH%D;o|uQ*YrFrd(Eo(^N$M%3yhzX3_<=(-z*so7C<|`I^6+I1@;`3z`+8sE?Lfj8y{94fO*aB% zST*VQa{e{S`Rk&2$fTU-R#Wnw0;BOEYkX28r=!dqf%T#pU2bB1OvKcgMw6b1_392M z*jIPvhMVfJJyzlgTh`heM=6WSjvq0jEFMeqLfN|=Qs2?qhKZ-6wA`f4}tS} z5H?Y#p}(TFM_L-y+`#qLh#Q|QBsYfy)w#fp^$M{!w0>YS|MD}P%0{D$gp}n=V7;m| zl207-y~Ha&Q?>1V5*TZC!x^+2=G7%B_zzMSNN#L4+bD8ug4?_YYKJR8>hS&Uh?yJETre`!;z@A8GWdyZDkdc1$ zIY3)D;srL`)q}aQl`OxntFNu<*x0z{y{^6Wq5fxl(#oyg?0Zkzq_?HQtoDm{d~DJ` z-!Ya5mXRqlObXV?ay9(75%WFsq1=TRn(c9H$_yP2_S$}Vy8IFlAGzVVmt9kWz$?O$ zQEHK0bbR#`ZQP1mk&OsFOEJ@;)7(Ek^8L1l6CLljQk7>E`BJo4k0tZMlCyQ$>VCdA ztVDoGK^bz9LRys;-EZwIREc?3A{abRo8ab^h|qlYF8MwU`zw|xh#G_5Ct$6{CZG9( z^G}G0Qm_&%QqyxM3NsYo038lLCizYmFPzA#*s1CwqQ`!Mc`(1!G~^wBR$4q+}^{SD%nEM_bvXNbzbB|7sSSC7z+IT}PH6uJ}&d0T5e0g3335bLz_OqrtE;1KQj^Moh z>F$rpO&_g4;aS*w{{{^?&1Xqb&zxY+h2E(>w2tZGd|)&8A2W7?h-j$(7x{+N1RhPb~%&vmx{4Dk@_-oqu>GS#nLDDep@?`>;XN6zOyk` zoV9MXzWB{zQrj3_vW>-jWp>I0I2vy^R8oDj2OK~v3ck#N8s4~vs=u<~3RO2X*l>s{ zA$(&i3Jh#hG^?y+bJvxL$nKijwO;8K=l$wgbxNRAD#xRl^^qk1f~4l<`=9(@H?J0D5_@hg>#zy_L z0QeNx8Y8U&Yp)Om0GC-O#GsTpbPnsq%o9L8vhsBT6-(li{<*yQrR)`jf%Q#tm1sUd zFm4g2v&^{t9vZ|!056PpV2~WZtyHv~KUB_**JeGfkP+^or)EBshZM&qun^1`%jSeJ z=)mN@V@HnVYW6(5+Jl{1lLBpc>K#h2=n(6~h``vMQ0&`0v#n2ZvKhqh>__bH)bxFq zcBf(ff$ivRga+Uq|$8OfxKn(BOeT>L-hfmP91gG`W@lyQM!twEf zx8dL2UpPA2Y;Zz|hON8xwr{+~f{NpLKF7I))t@~jsu(Q2qs>RtVFw79ThWl7-g430qlwdjRR%m zwpon`DyL@@n-J|fjF+HG5qM#BB6z<}=l>K{PkiQQE^krV&d*w^Z#b$|-ev{y$$A&> zqugK8mS1eLWZ1(QNg!fxeP>eP|BcLrMP$2r$`)XoTI--N^K*kEr9!2UhaN~4IT^SrK-ED^{7j=n8V#1y(~lb++we?l2Q-|+bFQjp}4<3%Ysie4?i)Ux4MV#eaoXjLh6KK-4Rb7ao<` z+_5Wfs4%ITAo65qZCAJO0J;>`1a(A!5E|bo2$LUE>{4G<%wcx(x^`Np;FRWdS=dH_ zK0pDgZ>&3eahu7`$^_PHN5ehh$4nCph<{Vq$zZPd+Dxr~xTJ!YWqN*43{G4G`7T&d zlUa?(EZd6GWUq+ZYmbMcTB$heI6y6uN#xiwE&Te=$&sq4W2_eTujI;h`-TFsWR>caHZa9VwKeV{4C^ z1TIPM`IMbt0CxcLz1yJ{;)PyaHZDo_1rf!w*FXQ_P|6bqg@4Fo@1wq#n z361bK>VmzqZX3J~VdBghbsd8{N~mg$`>Jo=Odvy>${@r`{qZud~12;j{ka&*l;!EPAlar7@rSZ|NS2dE#&(k0I7o4is$&jk?p@O=cO#MV_W zbb7cBHrBrNBKCsjnR6~g!v}6z4t``1QKjh}<{4e&-PgY%yTfne4r%}T*)*_haAoqLy}pGvD^rsBK_8(+5TLdY5#AB!4Dqjt^P zi5Ghpbg{?8j(Eg$8+r4nhTNK*G7p$<#6X!8lS&pf>H2~qLmqjr0SCf>EA_IRcYFo~ zvMJ~#D5Gss9=nwr@Q6jVlPQWSK;{dg{=J<~*FCx0g3}*u4R)BKmburJS;J?VAMY(- zj67{9rmn$S@f{O3jpT;IWuz4D^C_>Xd@ghk2a$b~hHGei%Fi9`-glr2EIU?`5a#)n z1)+BoVKgO<4k%ISSFOX3ToXhh_2# zB)c0N-@T4L)%Pg<=~!497#~Y?NmQ4!W56*_A0d_M&3D=CCNc!vTQkqu;|k|Q=P9!e z3ZSm(2I`!_vz#N-Z4tbULD7a`-Tk6P7rqE%TtkCxtrZNS{$!m3suAa5GvFPyTyVHf z4(Ou^%pc0S01bwB!8xfl8M#TZyelcL+&>c=8HLzI}&00t*F^rnnbeCRjLM8wR+F%LFi;9E+Z_0C>q z%}V4QY;sTa%LsEi2PO^@T3Z_o4jOWC{!C$7MtEQ{Cw#6;Cn-qQXShP_$GmjGd!C-@ zvBw5a_X#;c_;+V@@*wLSJ_bq7S!Ph6gTJ!b+k|itb1BOHv*HHr++}wBxT1VD3-P%N z2-lIT*Y#;uVasftLRX(?jl-hIv-2qI(SOsrEe8MS9k;9%fx&@dM_=Q{Bz$`OL(d&>iCTtDK3(%q?Fk$2_@K^;<$f;` zt=+s*RCs{o_IW4M4#Zp)?{h%v%C>Y2FP^eIo{eXRO<-=R8hCCD_r1$GQNR&{^M+*G~D^H0UnI6A+_A3kK!@jY`VtfWGAnF^c%<%ln^GVRe^HYTjGux?oNF`82L z@W3jvtbrmLJyD2Pa9|cshlg=eEyc#jH zg*Kj3ZewPtDZ9ArgCzFKQD5|afMK6|yI4{<7baDqBNAk@(chUgYyHVXTP(3Z^IFr znEeCD$q$S5%44<_(+mH0N~siQqv`eAdI{Kc{g>j|&H4!|-M6H9nr` z>MeaA=P=V$0C3}PLjgX$`ptJcm zz>&|wKUojTP!c{QZ+kVV@#^TQ<8<^@Yj;B&v64b9$gHbxYrXkq0pzGp#-GR;jVuIa zlestX-QWT4c0tdLjO#2}UZwo2-kSv_ka$Z={dDwN6~E;p70D{749Hb4G#*5&x21{S01j4-Ml1|&Uo4Gsx_0EC#Dq=pCci|-A!{dl2$ji<9dh8Ss- z7=PjMkKsThm$Q#wd@R^2L*GeHOjq*AxjY*6a35^`29x9c%CyuAdOvVpURYr7EF9~` z#i_u-lJ9!AU^Z-NQwN(CUyFZ+$zQU4esFOWEHOG_%(a?9>`lJ*%=e%j0?@p?gK7^`!7hw2FFux?9JM5UkI>qEB#(<6o{rwQWZ5*g)=| z=g4j{$dRoP3YZXW85jt0K>kY#i3E+~P4+mBFWnrKrkA5~WB}ha@m{{lvA{K~2%c?{ z1QOoX?Pfq+IvrC<4F6eiOakOmWjY_$thYJrs0#N#nG3&v`OR?=Y)TW3xIk0E-O9 zUFJy;L$9AN*`f^$4pJ}IdWoV3YCVnJ;*~f`P;qT>5FZ$|-j^~0X^-Na=K+wpk_DMb zM=-$(!1pT}VhqUzqyrGK0r!_GsXmwk7frBvG$IH)eU=Vt@o zSj<5AT_3v-qwukehkxQC{ipnUVfx?h1b`WUvL-MovzDp3Q_;pOJ!HF;;&dT!-QNiQ zv)JU^qvclDYzDAb3484EYK#>@KSLLa78F;mX|88hA-G~#`T>xQ*87yTvwe95^UC5b z!**?k$a9X&OxeM*M(xs{ro6#v)jpbuCHhPO@zE|YQs^~#vTG0R%>&kT+w+zU+IzP5 ze00UPANdI`xJupbnoD>Dt%_5lzxG5_mk_>zXo#JL@1=5DJR1b3jLopvLDOlg5eTWw zU-H2Z+~0eLgGAZCjCpA!qU(bVr(CVuObTkjMj`@QqFFM6oFy8^}+{m7Ws1AKKik*F*$uEP>uyfaGz)e?}Q#nb^Bp-W5{H@ za`~i30Tauvy5)8SmSCvY1e7E&4)5Y*CfU&T3N3Hy3y)u1a;*5AXjidiN$kx!9~8T= zz-b!Ux#+s1yl2>H#3=}HcxY9E^2^p#?bVg7Th1-rPIe5#{(A$w-#+a7Dvch!$7GGq zG~QMJGhU~PXzhMadwes!A6Mz{VWIi^Lq*3M&i-58)f7Aa{1`b?JV#n6MQnA&6*-42 z;{*kH(%#J_McWeevaLCN(GDl5*;>@PM(<)-|7}qMm)rM)s?3z&!7|{&ep{99Up0`y zE$rikb|bE7(Ow)}-PFqY&}U!I28)jq81A<{H#XI&A|-NZH+O5iDKk=4W^J588+-k< zCz+x|y9A6v0w*S3^@%4XZi&n1;(H+f7h8K=^g>xb5!#2xDpKVpL@-RBl(5pslvQjvOmPDA>~>1|J)rXu&(?FdnE{Z`!?cd_lP}5 z?=<29ZM#BG9)iq7-{p}TJp~UO-bKt*{K_qC*U=g8)C)f>SkJav8vtWaU}iL5p_K>< zPx2RAN5-KVM3g{E0qj6^l`cc#s0n`|xc7u%@JA?J#IyP#kMhZ^KX&oMnYX(5hv0h> zMiH(A=X3SOf=nK1hi!GV;@RNfy9742(+9EcnxYBud+GjX`B&cGF(fY zFe9T!VS8#-;h`VI!8_*or!-E01vVx4?7Go5;Wy;)C8Pm4paaACrRwA<@0l8T&BPdv{h+Xjf{kn@E>k|6w!7L?4-7x9Z$N<9S+Y@BVa`AcCpZvQ{WY;!tBC zQkF*={dco}g(OfNEjFLdZl#uN493Vyr1l~~-Y_O2Ep+=(GyCsjo{sPc*>bI*z-vsN zx6!D_w#^`~6%n&+eYxw0V>(}WJXW2qcD~d1qo7i5g!L%0+;%wJ{lg*x3C>s``oTL% z1^F-lsFL2u$W^5>Rhfjo|zPx1Ey`QES+Srg8QE6|+ zDOXSm@+#oX3(QN$>O1#ixDNt(zr?%ik!Lt(lG|?WoSq?c&8g(1N6$L^qk{YoHvA;8 zs3Hhma=n9#QaWE)gN3e202)}pc_^Ca_9mxz;l}tkZAe-~M7NE}Y=h^5=+l6w3MsEO z5GP;2#mMZ~qjt%TAeJQd)yU_z;6rd_E&nKW)A5{tCx*CVb z$g?ivV=?)pPJYI2|zgImCn* z(C!SZZzT6AioFoM09=-O3hRmxQ-l<#N&q+k1=s4yv4F`7|6O8^&i?8{@-*NgCH^RKRlHl(*i~--WpTU9naBEVa3Y?|<%s?2-Ov z)c@RL;IIF^$BTDl_H-Tppbiw%P8ai#D*zI>Dn3>T#XS524N(b%)CNHA2JO-}S)K+Y zlR%r;1L`;f>evD<8oRx6G6Nt`GN>m*zy*9&ykAukQxyWe*1EeZ1ixAveWfUiM%Upp zeMfyQjd|FDL-(Eeu9yp7{|^-J|A6am&ouKd5Gcki^U@HSxnB!YfRIO1?n}aeUp|c4 zq7OWuT&U=O{X@C5e}6Li3L+bEM{seM6<>Of%nhwX1(WCT_2#c9YJJDPc-P~rV&mSP z#W?lxM~iP*+i!z??hjCHy5afN`o34|6H$|=y^!#wr9MucdexK!-p%?v*~cyG@R^*SMhdy`v0?zNC^3jr;ZDpygCn=1vDQ zMjRzYO{&)C@yiE;A^OUp7~}48B(3xkBd_-GZudgjoh2mL z6BW3efKA8y>+bP2nOa{LSd238o*`4QYTmAM=E6qgzXW~nbmcE!4x^`Cc|}5ghPVfN z+)utg3Jtlta8;?MmQz(^)x`lbihL68*?2!17kUaPaNYZnNKKG5>hWL;m<8?!yUPi()W?K_keKYI@v z;)Cajagp2YULfYWEOOK>2{z8J#RuL}^3%eoW2*bK_i_Uv%mENmOM+vr=u5@mAPDrw zM)72J{M`+BlDwzc*H>zN6s+s_cg#<1^?m81;_V;k5I~#e?tbI@T6Mc-Ww!Aie4-1O zy@Ow)>6bI2a28`E(C#qH{1&w(Xm6$EFKeUE->BfTnz963fYv=3FLv&v<=sw`qn(Id zF)mbm*`XoPSLs)_+3_tNp0boHSQkUSJ`=VqsCzAL1DnG9S@Cx;%)|G;hE$(TMPG#V zo(2=%{Kszf|NO_!!hvV{kDUQ$^#3yX)jN!Z@@@^@@_d" + ] + }, + { + "cell_type": "markdown", + "id": "64b4469b", + "metadata": { + "editable": true + }, "source": [ "# Building a Feed Forward Neural Network\n", "\n", @@ -27,7 +41,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a27e39fb", + "metadata": { + "editable": true + }, "source": [ "$$\n", "P(y = 0 \\mid \\hat{x}, \\hat{\\theta}) = \\frac{1}{1 + \\exp{(- \\hat{x}})} ,\n", @@ -36,14 +53,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6332f4a5", + "metadata": { + "editable": true + }, "source": [ "and" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "5d2a5fe5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "P(y = 1 \\mid \\hat{x}, \\hat{\\theta}) = 1 - P(y = 0 \\mid \\hat{x}, \\hat{\\theta}) ,\n", @@ -52,13 +75,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "62bf3ae6", + "metadata": { + "editable": true + }, "source": [ "where $y \\in \\{0, 1\\}$ and $\\hat{\\theta}$ represents the weights and biases\n", - "of our network.\n", - "\n", - "\n", - "\n", + "of our network." + ] + }, + { + "cell_type": "markdown", + "id": "5fdb1150", + "metadata": { + "editable": true + }, + "source": [ "## Defining the cost function\n", "\n", "Our cost function is given as (see the Logistic regression lectures)" @@ -66,7 +98,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "64cfe441", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathcal{C}(\\hat{\\theta}) = - \\ln P(\\mathcal{D} \\mid \\hat{\\theta}) = - \\sum_{i=1}^n\n", @@ -76,7 +111,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "dbd78c70", + "metadata": { + "editable": true + }, "source": [ "This last equality means that we can interpret our *cost* function as a sum over the *loss* function\n", "for each point in the dataset $\\mathcal{L}_i(\\hat{\\theta})$. \n", @@ -87,10 +125,8 @@ "\n", "$y = 5 \\quad \\rightarrow \\quad \\hat{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$ and\n", "\n", - "\n", "$y = 1 \\quad \\rightarrow \\quad \\hat{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$ \n", "\n", - "\n", "i.e. a binary bit string of length $C$, where $C = 10$ is the number of classes in the MNIST dataset (numbers from $0$ to $9$).. \n", "\n", "If $\\hat{x}_i$ is the $i$-th input (image), $y_{ic}$ refers to the $c$-th component of the $i$-th\n", @@ -100,7 +136,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "67834a87", + "metadata": { + "editable": true + }, "source": [ "$$\n", "P(y_{ic} = 1 \\mid \\hat{x}_i, \\hat{\\theta}) = \\frac{\\exp{((\\hat{a}_i^{hidden})^T \\hat{w}_c)}}\n", @@ -110,7 +149,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "0521db23", + "metadata": { + "editable": true + }, "source": [ "which reduces to the logistic function in the binary case. \n", "The likelihood of this $C$-class classifier\n", @@ -119,7 +161,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "12a92031", + "metadata": { + "editable": true + }, "source": [ "$$\n", "P(\\mathcal{D} \\mid \\hat{\\theta}) = \\prod_{i=1}^n \\prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .\n", @@ -128,14 +173,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e03ffaa9", + "metadata": { + "editable": true + }, "source": [ "Again we take the negative log-likelihood to define our cost function:" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "cfab4fa3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathcal{C}(\\hat{\\theta}) = - \\log{P(\\mathcal{D} \\mid \\hat{\\theta})}.\n", @@ -144,13 +195,23 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "864840d8", + "metadata": { + "editable": true + }, "source": [ "See the logistic regression lectures for a full definition of the cost function.\n", "\n", - "The back propagation equations need now only a small change, namely the definition of a new cost function. We are thus ready to use the same equations as before!\n", - "\n", - "\n", + "The back propagation equations need now only a small change, namely the definition of a new cost function. We are thus ready to use the same equations as before!" + ] + }, + { + "cell_type": "markdown", + "id": "496bdba3", + "metadata": { + "editable": true + }, + "source": [ "### Example: binary classification problem\n", "\n", "As an example of the above, relevant for project 2 as well, let us consider a binary class. As discussed in our logistic regression lectures, we defined a cost function in terms of the parameters $\\beta$ as" @@ -158,7 +219,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "8646c18f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathcal{C}(\\hat{\\beta}) = - \\sum_{i=1}^n \\left(y_i\\log{p(y_i \\vert x_i,\\hat{\\beta})}+(1-y_i)\\log{1-p(y_i \\vert x_i,\\hat{\\beta})}\\right),\n", @@ -167,14 +231,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "2dbfda71", + "metadata": { + "editable": true + }, "source": [ "where we had defined the logistic (sigmoid) function" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "5cd0a375", + "metadata": { + "editable": true + }, "source": [ "$$\n", "p(y_i =1\\vert x_i,\\hat{\\beta})=\\frac{\\exp{(\\beta_0+\\beta_1 x_i)}}{1+\\exp{(\\beta_0+\\beta_1 x_i)}},\n", @@ -183,14 +253,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "020de545", + "metadata": { + "editable": true + }, "source": [ "and" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "2efde2f5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "p(y_i =0\\vert x_i,\\hat{\\beta})=1-p(y_i =1\\vert x_i,\\hat{\\beta}).\n", @@ -199,7 +275,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "bf9a596d", + "metadata": { + "editable": true + }, "source": [ "The parameters $\\hat{\\beta}$ were defined using a minimization method like gradient descent or Newton-Raphson's method. \n", "\n", @@ -209,7 +288,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "0b392cc5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "a_i^l = y_i = \\frac{\\exp{(z_i^l)}}{1+\\exp{(z_i^l)}},\n", @@ -218,14 +300,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "5169434f", + "metadata": { + "editable": true + }, "source": [ "with" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "dcc8ed0a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "z_i^l = \\sum_{j}w_{ij}^l a_j^{l-1}+b_i^l,\n", @@ -234,7 +322,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "4010628a", + "metadata": { + "editable": true + }, "source": [ "where the superscript $l-1$ indicates that these are the outputs from layer $l-1$.\n", "Our cost function at the final layer $l=L$ is now" @@ -242,7 +333,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "7bf89431", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathcal{C}(\\hat{W}) = - \\sum_{i=1}^n \\left(t_i\\log{a_i^L}+(1-t_i)\\log{(1-a_i^L)}\\right),\n", @@ -251,14 +345,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "79bb56ee", + "metadata": { + "editable": true + }, "source": [ "where we have defined the targets $t_i$. The derivatives of the cost function with respect to the output $a_i^L$ are then easily calculated and we get" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "a27a06b5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial \\mathcal{C}(\\hat{W})}{\\partial a_i^L} = \\frac{a_i^L-t_i}{a_i^L(1-a_i^L)}.\n", @@ -267,12 +367,21 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "cd6acfaf", + "metadata": { + "editable": true + }, + "source": [ + "In case we use another activation function than the logistic one, we need to evaluate other derivatives." + ] + }, + { + "cell_type": "markdown", + "id": "b9e59acd", + "metadata": { + "editable": true + }, "source": [ - "In case we use another activation function than the logistic one, we need to evaluate other derivatives. \n", - "\n", - "\n", - "\n", "### The Softmax function\n", "\n", "In case we employ the more general case given by the Softmax equation, we need to evaluate the derivative of the activation function with respect to the activation $z_i^l$, that is we need" @@ -280,7 +389,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "eceaf7eb", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial f(z_i^l)}{\\partial w_{jk}^l} =\n", @@ -290,14 +402,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "bbc77522", + "metadata": { + "editable": true + }, "source": [ "For the Softmax function we have" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "88d4c18b", + "metadata": { + "editable": true + }, "source": [ "$$\n", "f(z_i^l) = \\frac{\\exp{(z_i^l)}}{\\sum_{m=1}^K\\exp{(z_m^l)}}.\n", @@ -306,14 +424,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b47f4092", + "metadata": { + "editable": true + }, "source": [ "Its derivative with respect to $z_j^l$ gives" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "65ec4336", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial f(z_i^l)}{\\partial z_j^l}= f(z_i^l)\\left(\\delta_{ij}-f(z_j^l)\\right),\n", @@ -322,14 +446,23 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "38f54e19", + "metadata": { + "editable": true + }, + "source": [ + "which in case of the simply binary model reduces to having $i=j$." + ] + }, + { + "cell_type": "markdown", + "id": "c0d8bc5e", + "metadata": { + "editable": true + }, "source": [ - "which in case of the simply binary model reduces to having $i=j$. \n", - "\n", - "\n", "## Developing a code for doing neural networks with back propagation\n", "\n", - "\n", "One can identify a set of key steps when using neural networks to solve supervised learning problems: \n", "\n", "1. Collect and pre-process data \n", @@ -342,8 +475,16 @@ "\n", "5. Evaluate model performance on test data \n", "\n", - "6. Adjust hyperparameters (if necessary, network architecture)\n", - "\n", + "6. Adjust hyperparameters (if necessary, network architecture)" + ] + }, + { + "cell_type": "markdown", + "id": "e3810222", + "metadata": { + "editable": true + }, + "source": [ "### Collect and pre-process data\n", "\n", "Here we will be using the MNIST dataset, which is readily available through the **scikit-learn**\n", @@ -388,7 +529,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, + "id": "5e7205ac", "metadata": { "collapsed": false, "editable": true @@ -443,7 +585,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "78721970", + "metadata": { + "editable": true + }, "source": [ "### Train and test datasets\n", "\n", @@ -460,7 +605,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, + "id": "dcc066a0", "metadata": { "collapsed": false, "editable": true @@ -498,7 +644,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "95cf3f87", + "metadata": { + "editable": true + }, "source": [ "### Define model and architecture\n", "\n", @@ -534,8 +683,16 @@ "\n", "$$ f(x) = \\sigma(x) = \\frac{1}{1 + e^{-x}} ,$$\n", "\n", - "which is inspired by probability theory (see logistic regression) and was most commonly used until about 2011. See the discussion below concerning other activation functions.\n", - "\n", + "which is inspired by probability theory (see logistic regression) and was most commonly used until about 2011. See the discussion below concerning other activation functions." + ] + }, + { + "cell_type": "markdown", + "id": "25c0cbe6", + "metadata": { + "editable": true + }, + "source": [ "### Layers\n", "\n", "* Input \n", @@ -568,7 +725,6 @@ "Since each neuron in the output layer is connected to the 50 inputs from the hidden layer we have 50x10 = 500\n", "weights to the output layer.\n", "\n", - "\n", "Typically weights are initialized with small values distributed around zero, drawn from a uniform\n", "or normal distribution. Setting all weights to zero means all neurons give the same output, making the network useless. \n", "\n", @@ -582,7 +738,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, + "id": "9f415ea2", "metadata": { "collapsed": false, "editable": true @@ -608,7 +765,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "afbff46b", + "metadata": { + "editable": true + }, "source": [ "### Feed-forward pass\n", "\n", @@ -630,7 +790,6 @@ "$$ a_{j}^{L} = \\frac{\\exp{(z_j^{L})}}\n", "{\\sum_{c=0}^{C-1} \\exp{(z_c^{L})}} .$$ \n", "\n", - "\n", "Since our data has the dimensions $X = (n_{inputs}, n_{features})$ and our weights to the hidden\n", "layer have the dimensions \n", "$W_{hidden} = (n_{features}, n_{hidden})$,\n", @@ -660,7 +819,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, + "id": "e05b2147", "metadata": { "collapsed": false, "editable": true @@ -706,7 +866,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6c8100ba", + "metadata": { + "editable": true + }, "source": [ "### Choose cost function and optimizer\n", "\n", @@ -719,10 +882,8 @@ "\n", "$$ y = 5 \\quad \\rightarrow \\quad \\hat{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$ \n", "\n", - "\n", "$$ y = 1 \\quad \\rightarrow \\quad \\hat{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$ \n", "\n", - "\n", "i.e. a binary bit string of length $C$, where $C = 10$ is the number of classes in the MNIST dataset. \n", "\n", "Let $y_{ic}$ denote the $c$-th component of the $i$-th one-hot vector. \n", @@ -731,10 +892,16 @@ "In the one-hot representation only one of the terms in the loss function is non-zero, namely the\n", "probability of the correct category $c'$ \n", "(i.e. the category $c'$ such that $y_{ic'} = 1$). This means that the cross entropy loss only punishes you for how wrong\n", - "you got the correct label. The probability of category $c$ is given by the softmax function. The vector $\\hat{\\theta}$ represents the parameters of our network, i.e. all the weights and biases. \n", - "\n", - "\n", - "\n", + "you got the correct label. The probability of category $c$ is given by the softmax function. The vector $\\hat{\\theta}$ represents the parameters of our network, i.e. all the weights and biases." + ] + }, + { + "cell_type": "markdown", + "id": "720d19fd", + "metadata": { + "editable": true + }, + "source": [ "### Optimizing the cost function\n", "\n", "The network is trained by finding the weights and biases that minimize the cost function. One of the most widely used classes of methods is *gradient descent* and its generalizations. The idea behind gradient descent\n", @@ -763,9 +930,16 @@ "\n", "2. It significantly speeds up the calculation, since we do not have to use the entire dataset to calculate the gradient. \n", "\n", - "The various optmization methods, with codes and algorithms, are discussed in our lectures on [Gradient descent approaches](https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html).\n", - "\n", - "\n", + "The various optmization methods, with codes and algorithms, are discussed in our lectures on [Gradient descent approaches](https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html)." + ] + }, + { + "cell_type": "markdown", + "id": "d0b1f84a", + "metadata": { + "editable": true + }, + "source": [ "### Regularization\n", "\n", "It is common to add an extra term to the cost function, proportional\n", @@ -783,7 +957,6 @@ "\n", "i.e. we sum up all the weights squared. The factor $\\lambda$ is known as a regularization parameter.\n", "\n", - "\n", "In order to train the model, we need to calculate the derivative of\n", "the cost function with respect to every bias and weight in the\n", "network. In total our network has $(64 + 1)\\times 50=3250$ weights in\n", @@ -791,9 +964,16 @@ "layer ($+1$ for the bias), and the gradient must be calculated for\n", "every parameter. We use the *backpropagation* algorithm discussed\n", "above. This is a clever use of the chain rule that allows us to\n", - "calculate the gradient efficently. \n", - "\n", - "\n", + "calculate the gradient efficently." + ] + }, + { + "cell_type": "markdown", + "id": "96417f62", + "metadata": { + "editable": true + }, + "source": [ "### Matrix multiplication\n", "\n", "To more efficently train our network these equations are implemented using matrix operations. \n", @@ -829,7 +1009,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, + "id": "c692ab5f", "metadata": { "collapsed": false, "editable": true @@ -908,7 +1089,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9d0ad486", + "metadata": { + "editable": true + }, "source": [ "## Improving performance\n", "\n", @@ -923,14 +1107,14 @@ "If this does not improve network performance, you may want to consider altering the network architecture, adding more neurons or hidden layers. \n", "Andrew Ng goes through some of these considerations in this [video](https://youtu.be/F1ka6a13S9I). You can find a summary of the video [here](https://kevinzakka.github.io/2016/09/26/applying-deep-learning/). \n", "\n", - "\n", "It is very natural to think of the network as an object, with specific instances of the network\n", "being realizations of this object with different hyperparameters. An implementation using Python classes provides a clean structure and interface, and the full implementation of our neural network is given below." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, + "id": "84088dcb", "metadata": { "collapsed": false, "editable": true @@ -1040,7 +1224,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "61dae78a", + "metadata": { + "editable": true + }, "source": [ "## Evaluate model performance on test data\n", "\n", @@ -1055,7 +1242,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, + "id": "999a01b6", "metadata": { "collapsed": false, "editable": true @@ -1082,7 +1270,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "12b8be76", + "metadata": { + "editable": true + }, "source": [ "## Adjust hyperparameters\n", "\n", @@ -1092,7 +1283,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, + "id": "f022ba3c", "metadata": { "collapsed": false, "editable": true @@ -1123,14 +1315,18 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "118ee392", + "metadata": { + "editable": true + }, "source": [ "## Visualization" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, + "id": "01cd7236", "metadata": { "collapsed": false, "editable": true @@ -1174,7 +1370,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "1cef52ca", + "metadata": { + "editable": true + }, "source": [ "## scikit-learn implementation\n", "\n", @@ -1193,7 +1392,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, + "id": "08650740", "metadata": { "collapsed": false, "editable": true @@ -1220,14 +1420,18 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9a5819b0", + "metadata": { + "editable": true + }, "source": [ "## Visualization" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, + "id": "c76390e1", "metadata": { "collapsed": false, "editable": true @@ -1272,7 +1476,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6b973f8c", + "metadata": { + "editable": true + }, "source": [ "## Building neural networks in Tensorflow and Keras\n", "\n", @@ -1284,7 +1491,6 @@ "clear how to build one using an arbitrary number of hidden layers, using data structures such as Python lists or\n", "NumPy arrays.\n", "\n", - "\n", "Tensorflow is an open source library machine learning library\n", "developed by the Google Brain team for internal use. It was released\n", "under the Apache 2.0 open source license in November 9, 2015.\n", @@ -1307,32 +1513,15 @@ "Then we will build (effectively) the same graph in Keras, to see just\n", "how simple solving a machine learning problem can be.\n", "\n", - "To install tensorflow on Unix/Linux systems, use pip as" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], - "source": [ - "pip3 install tensorflow" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ + "To install tensorflow on Unix/Linux systems, use pip as **pip3 install tensorflow**\n", "and/or if you use **anaconda**, just write (or install from the graphical user interface)\n", "(current release of CPU-only TensorFlow)" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, + "id": "cb71108d", "metadata": { "collapsed": false, "editable": true @@ -1345,14 +1534,18 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "8cf89ee7", + "metadata": { + "editable": true + }, "source": [ "To install the current release of GPU TensorFlow" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, + "id": "ace3d31e", "metadata": { "collapsed": false, "editable": true @@ -1365,7 +1558,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f5d7454d", + "metadata": { + "editable": true + }, "source": [ "Keras is a high level [neural network](https://en.wikipedia.org/wiki/Application_programming_interface)\n", "that supports Tensorflow, CTNK and Theano as backends. \n", @@ -1374,7 +1570,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, + "id": "024068e3", "metadata": { "collapsed": false, "editable": true @@ -1386,19 +1583,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e36b74d0", + "metadata": { + "editable": true + }, "source": [ "You can look up the [instructions here](https://keras.io/) for more information.\n", "\n", "We will to a large extent use **keras** in this course. \n", "\n", - "\n", "Let us look again at the MINST data set." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 15, + "id": "42dbd743", "metadata": { "collapsed": false, "editable": true @@ -1452,7 +1652,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 16, + "id": "eba6a34d", "metadata": { "collapsed": false, "editable": true @@ -1480,7 +1681,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 17, + "id": "da80e8b6", "metadata": { "collapsed": false, "editable": true @@ -1509,7 +1711,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 18, + "id": "87273539", "metadata": { "collapsed": false, "editable": true @@ -1535,7 +1738,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 19, + "id": "8cd653a0", "metadata": { "collapsed": false, "editable": true @@ -1577,14 +1781,18 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "31009a5d", + "metadata": { + "editable": true + }, "source": [ "## The Breast Cancer Data, now with Keras" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 20, + "id": "991bf288", "metadata": { "collapsed": false, "editable": true @@ -1761,7 +1969,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d197746e", + "metadata": { + "editable": true + }, "source": [ "## Fine-tuning neural network hyperparameters\n", "\n", @@ -1779,7 +1990,6 @@ "training a neural network on a large dataset takes a lot of time, you\n", "will only be able to explore a tiny part of the hyperparameter space.\n", "\n", - "\n", "* You can use randomized search.\n", "\n", "* Or use tools like [Oscar](http://oscar.calldesk.ai/), which implements more complex algorithms to help you find a good set of hyperparameters quickly. \n", @@ -1795,12 +2005,16 @@ "as large image classification or speech recognition, typically require networks with dozens of layers\n", "and they need a huge amount\n", "of training data. However, you will rarely have to train such networks from scratch: it is much more\n", - "common to reuse parts of a pretrained state-of-the-art network that performs a similar task.\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "common to reuse parts of a pretrained state-of-the-art network that performs a similar task." + ] + }, + { + "cell_type": "markdown", + "id": "3614fe93", + "metadata": { + "editable": true + }, + "source": [ "## Which activation function should I use?\n", "\n", "The Back propagation algorithm we derived above works by going from\n", @@ -1809,7 +2023,6 @@ "function with regards to each parameter in the network, it uses these\n", "gradients to update each parameter with a Gradient Descent (GD) step.\n", "\n", - "\n", "Unfortunately for us, the gradients often get smaller and smaller as the\n", "algorithm progresses down to the first hidden layers. As a result, the\n", "GD update leaves the lower layer connection weights\n", @@ -1825,9 +2038,6 @@ "neural networks suffer from unstable gradients, different layers may\n", "learn at widely different speeds\n", "\n", - "\n", - "\n", - "\n", "Although this unfortunate behavior has been empirically observed for\n", "quite a while (it was one of the reasons why deep neural networks were\n", "mostly abandoned for a long time), it is only around 2010 that\n", @@ -1850,8 +2060,6 @@ "(the hyperbolic tangent function has a mean of 0 and behaves slightly\n", "better than the logistic function in deep networks).\n", "\n", - "\n", - "\n", "Looking at the logistic activation function, when inputs become large\n", "(negative or positive), the function saturates at 0 or 1, with a\n", "derivative extremely close to 0. Thus when backpropagation kicks in,\n", @@ -1870,8 +2078,6 @@ "its inputs, and we also need the gradients to have equal variance\n", "before and after flowing through a layer in the reverse direction.\n", "\n", - "\n", - "\n", "One of the insights in the 2010 paper by Glorot and Bengio was that\n", "the vanishing/exploding gradients problems were in part due to a poor\n", "choice of activation function. Until then most people had assumed that\n", @@ -1880,9 +2086,16 @@ "that other activation functions behave much better in deep neural\n", "networks, in particular the ReLU activation function, mostly because\n", "it does not saturate for positive values (and also because it is quite\n", - "fast to compute).\n", - "\n", - "\n", + "fast to compute)." + ] + }, + { + "cell_type": "markdown", + "id": "0816093d", + "metadata": { + "editable": true + }, + "source": [ "## The RELU function family\n", "\n", "The ReLU activation function suffers from a problem known as the dying\n", @@ -1903,7 +2116,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d979c7db", + "metadata": { + "editable": true + }, "source": [ "$$\n", "ELU(z) = \\left\\{\\begin{array}{cc} \\alpha\\left( \\exp{(z)}-1\\right) & z < 0,\\\\ z & z \\ge 0.\\end{array}\\right.\n", @@ -1912,7 +2128,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "eadc7692", + "metadata": { + "editable": true + }, "source": [ "In general it seems that the ELU activation function is better than\n", "the leaky ReLU function (and its variants), which is better than\n", @@ -1927,8 +2146,6 @@ "spare time and computing power, you can use cross-validation or\n", "bootstrap to evaluate other activation functions.\n", "\n", - "\n", - "\n", "In most cases you can use the ReLU activation function in the hidden layers (or one of its variants).\n", "\n", "It is a bit faster to compute than other activation functions, and the gradient descent optimization does in general not get stuck.\n", @@ -1937,8 +2154,16 @@ "\n", "* For classification the softmax activation function is generally a good choice for classification tasks (when the classes are mutually exclusive).\n", "\n", - "* For regression tasks, you can simply use no activation function at all.\n", - "\n", + "* For regression tasks, you can simply use no activation function at all." + ] + }, + { + "cell_type": "markdown", + "id": "a78e9091", + "metadata": { + "editable": true + }, + "source": [ "## Batch Normalization\n", "\n", "Batch Normalization\n", @@ -1951,8 +2176,16 @@ "learn the optimal scale and mean of the inputs for each layer.\n", "In order to zero-center and normalize the inputs, the algorithm needs to estimate the inputs’ mean and\n", "standard deviation. It does so by evaluating the mean and standard deviation of the inputs over the current\n", - "mini-batch, from this the name batch normalization.\n", - "\n", + "mini-batch, from this the name batch normalization." + ] + }, + { + "cell_type": "markdown", + "id": "04e309c6", + "metadata": { + "editable": true + }, + "source": [ "## Dropout\n", "\n", "It is a fairly simple algorithm: at every training step, every neuron (including the input neurons but\n", @@ -1961,8 +2194,16 @@ "\n", "The\n", "hyperparameter $p$ is called the dropout rate, and it is typically set to 50%. After training, the neurons are not dropped anymore.\n", - " It is viewed as one of the most popular regularization techniques.\n", - "\n", + " It is viewed as one of the most popular regularization techniques." + ] + }, + { + "cell_type": "markdown", + "id": "f9eb2036", + "metadata": { + "editable": true + }, + "source": [ "## Gradient Clipping\n", "\n", "A popular technique to lessen the exploding gradients problem is to simply clip the gradients during\n", @@ -1972,12 +2213,18 @@ "This technique is called Gradient Clipping.\n", "\n", "In general however, Batch\n", - "Normalization is preferred.\n", - "\n", - "\n", + "Normalization is preferred." + ] + }, + { + "cell_type": "markdown", + "id": "95301882", + "metadata": { + "editable": true + }, + "source": [ "## A top-down perspective on Neural networks\n", "\n", - "\n", "The first thing we would like to do is divide the data into two or three\n", "parts. A training set, a validation or dev (development) set, and a\n", "test set. The test set is the data on which we want to make\n", @@ -1988,7 +2235,6 @@ "do not use any of the test data to train the algorithm. This is a\n", "cardinal sin in ML. Then:\n", "\n", - "\n", "* Estimate optimal error rate\n", "\n", "* Minimize underfitting (bias) on training data set.\n", @@ -2012,9 +2258,16 @@ "the test data. The difference between the performance of the algorithm\n", "on these two validation sets quantifies the train-test mismatch. This\n", "can serve as another important diagnostic when using DNNs for\n", - "supervised learning.\n", - "\n", - "\n", + "supervised learning." + ] + }, + { + "cell_type": "markdown", + "id": "e1da8c6e", + "metadata": { + "editable": true + }, + "source": [ "## Limitations of supervised learning with deep networks\n", "\n", "Like all statistical methods, supervised learning using neural\n", @@ -2027,8 +2280,6 @@ "\n", "Here we list some of the important limitations of supervised neural network based models. \n", "\n", - "\n", - "\n", "* **Need labeled data**. All supervised learning methods, DNNs for supervised learning require labeled data. Often, labeled data is harder to acquire than unlabeled data (e.g. one must pay for human experts to label images).\n", "\n", "* **Supervised neural networks are extremely data intensive.** DNNs are data hungry. They perform best when data is plentiful. This is doubly so for supervised methods where the data must also be labeled. The utility of DNNs is extremely limited if data is hard to acquire or the datasets are small (hundreds to a few thousand samples). In this case, the performance of other methods that utilize hand-engineered features can exceed that of DNNs.\n", @@ -2043,5 +2294,5 @@ ], "metadata": {}, "nbformat": 4, - "nbformat_minor": 4 + "nbformat_minor": 5 } diff --git a/doc/LectureNotes/_build/html/_sources/chapter11.ipynb b/doc/LectureNotes/_build/html/_sources/chapter11.ipynb index c03e4a368..00bf35796 100644 --- a/doc/LectureNotes/_build/html/_sources/chapter11.ipynb +++ b/doc/LectureNotes/_build/html/_sources/chapter11.ipynb @@ -2,7 +2,21 @@ "cells": [ { "cell_type": "markdown", - "metadata": {}, + "id": "7660a7d5", + "metadata": { + "editable": true + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "id": "7174820b", + "metadata": { + "editable": true + }, "source": [ "# Solving Differential Equations with Deep Learning\n", "\n", @@ -10,7 +24,6 @@ "approximate any function at a single hidden layer along with one input\n", "and output layer to any given precision. \n", "\n", - "\n", "An ordinary differential equation (ODE) is an equation involving functions having one variable.\n", "\n", "In general, an ordinary differential equation looks like" @@ -18,7 +31,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ac838a12", + "metadata": { + "editable": true + }, "source": [ "\n", "

    \n", @@ -32,7 +48,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ccee4286", + "metadata": { + "editable": true + }, "source": [ "where $g(x)$ is the function to find, and $g^{(n)}(x)$ is the $n$-th derivative of $g(x)$.\n", "\n", @@ -42,14 +61,15 @@ "Along with ([1](#ode)), some additional conditions of the function $g(x)$ are typically given\n", "for the solution to be unique.\n", "\n", - "\n", - "\n", "Let the trial solution $g_t(x)$ be" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "39d7dabd", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -64,7 +84,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "74f33170", + "metadata": { + "editable": true + }, "source": [ "where $h_1(x)$ is a function that makes $g_t(x)$ satisfy a given set\n", "of conditions, $N(x,P)$ a neural network with weights and biases\n", @@ -77,11 +100,8 @@ "\n", "But what about the network $N(x,P)$?\n", "\n", - "\n", "As described previously, an optimization method could be used to minimize the parameters of a neural network, that being its weights and biases, through backward propagation.\n", "\n", - "\n", - "\n", "For the minimization to be defined, we need to have a cost function at hand to minimize.\n", "\n", "It is given that $f\\left(x, \\, g(x), \\, g'(x), \\, g''(x), \\, \\dots \\, , \\, g^{(n)}(x)\\right)$ should be equal to zero in ([1](#ode)).\n", @@ -92,7 +112,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "2565ab16", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C\\left(x, P\\right) = \\big(f\\left(x, \\, g(x), \\, g'(x), \\, g''(x), \\, \\dots \\, , \\, g^{(n)}(x)\\right)\\big)^2\n", @@ -101,7 +124,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "83d4ee25", + "metadata": { + "editable": true + }, "source": [ "If $N$ inputs are given as a vector $\\boldsymbol{x}$ with elements $x_i$ for $i = 1,\\dots,N$,\n", "the cost function becomes" @@ -109,7 +135,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a7a3a709", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -123,20 +152,28 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d3ca8026", + "metadata": { + "editable": true + }, "source": [ "The neural net should then find the parameters $P$ that minimizes the cost function in\n", "([3](#cost)) for a set of $N$ training samples $x_i$.\n", "\n", - "\n", - "\n", "To perform the minimization using gradient descent, the gradient of $C\\left(\\boldsymbol{x}, P\\right)$ is needed.\n", "It might happen so that finding an analytical expression of the gradient of $C(\\boldsymbol{x}, P)$ from ([3](#cost)) gets too messy, depending on which cost function one desires to use.\n", "\n", "Luckily, there exists libraries that makes the job for us through automatic differentiation.\n", - "Automatic differentiation is a method of finding the derivatives numerically with very high precision.\n", - "\n", - "\n", + "Automatic differentiation is a method of finding the derivatives numerically with very high precision." + ] + }, + { + "cell_type": "markdown", + "id": "9bde4bd4", + "metadata": { + "editable": true + }, + "source": [ "### Example: Exponential decay\n", "\n", "An exponential decay of a quantity $g(x)$ is described by the equation" @@ -144,7 +181,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e74337c3", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -158,7 +198,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "273549a4", + "metadata": { + "editable": true + }, "source": [ "with $g(0) = g_0$ for some chosen initial value $g_0$.\n", "\n", @@ -167,7 +210,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "db3c6623", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -182,18 +228,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "8547e3c8", + "metadata": { + "editable": true + }, "source": [ "Having an analytical solution at hand, it is possible to use it to compare how well a neural network finds a solution of ([4](#solve_expdec)).\n", "\n", - "\n", - "\n", "The program will use a neural network to solve" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "48341fc6", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -207,19 +257,24 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d25b1e02", + "metadata": { + "editable": true + }, "source": [ "where $g(0) = g_0$ with $\\gamma$ and $g_0$ being some chosen values.\n", "\n", "In this example, $\\gamma = 2$ and $g_0 = 10$.\n", "\n", - "\n", "To begin with, a trial solution $g_t(t)$ must be chosen. A general trial solution for ordinary differential equations could be" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "7c5dd91e", + "metadata": { + "editable": true + }, "source": [ "$$\n", "g_t(x, P) = h_1(x) + h_2(x, N(x, P))\n", @@ -228,12 +283,13 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "24223062", + "metadata": { + "editable": true + }, "source": [ "with $h_1(x)$ ensuring that $g_t(x)$ satisfies some conditions and $h_2(x,N(x, P))$ an expression involving $x$ and the output from the neural network $N(x,P)$ with $P $ being the collection of the weights and biases for each layer. For now, it is assumed that the network consists of one input layer, one hidden layer, and one output layer.\n", "\n", - "\n", - "\n", "In this network, there are no weights and bias at the input layer, so $P = \\{ P_{\\text{hidden}}, P_{\\text{output}} \\}$.\n", "If there are $N_{\\text{hidden} }$ neurons in the hidden layer, then $P_{\\text{hidden}}$ is a $N_{\\text{hidden} } \\times (1 + N_{\\text{input}})$ matrix, given that there are $N_{\\text{input}}$ neurons in the input layer.\n", "\n", @@ -247,7 +303,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ebf04383", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -261,7 +320,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ea4a0013", + "metadata": { + "editable": true + }, "source": [ "### Reformulating the problem\n", "\n", @@ -277,7 +339,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "2351b84f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "g_t(x, P) = g_0 + x \\cdot N(x, P)\n", @@ -286,14 +351,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f6cc00e4", + "metadata": { + "editable": true + }, "source": [ "has been chosen such that it already solves the condition $g(0) = g_0$. What remains, is to find $P$ such that" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "84e066a1", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -307,11 +378,13 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "feff9ab3", + "metadata": { + "editable": true + }, "source": [ "is fulfilled as *best as possible*.\n", "\n", - "\n", "The left hand side and right hand side of ([8](#nnmin)) must be computed separately, and then the neural network must choose weights and biases, contained in $P$, such that the sides are equal as best as possible.\n", "This means that the absolute or squared difference between the sides must be as close to zero, ideally equal to zero.\n", "In this case, the difference squared shows to be an appropriate measurement of how erroneous the trial solution is with respect to $P$ of the neural network.\n", @@ -321,7 +394,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "0c6f0e79", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\min_{P}\\Big\\{ \\big(g_t'(x, P) - ( -\\gamma g_t(x, P) \\big)^2 \\Big\\}\n", @@ -330,7 +406,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9302a1dd", + "metadata": { + "editable": true + }, "source": [ "(the notation $\\min_{P}\\{ f(x, P) \\}$ means that we desire to find $P$ that yields the minimum of $f(x, P)$)\n", "\n", @@ -339,7 +418,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f7f204bb", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\min_{P_{\\text{hidden} }, \\ P_{\\text{output} }}\\Big\\{ \\big(g_t'(x, \\{ P_{\\text{hidden} }, P_{\\text{output} }\\}) - ( -\\gamma g_t(x, \\{ P_{\\text{hidden} }, P_{\\text{output} }\\}) \\big)^2 \\Big\\}\n", @@ -348,18 +430,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "8d61d75f", + "metadata": { + "editable": true + }, "source": [ "for an input value $x$.\n", "\n", - "\n", - "\n", "If the neural network evaluates $g_t(x, P)$ at more values for $x$, say $N$ values $x_i$ for $i = 1, \\dots, N$, then the *total* error to minimize becomes" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "10d3aec9", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -373,14 +459,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "5e296388", + "metadata": { + "editable": true + }, "source": [ "Letting $\\boldsymbol{x}$ be a vector with elements $x_i$ and $C(\\boldsymbol{x}, P) = \\frac{1}{N} \\sum_i \\big(g_t'(x_i, P) - ( -\\gamma g_t(x_i, P) \\big)^2$ denote the cost function, the minimization problem that our network must solve, becomes" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "fe010d79", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\min_{P} C(\\boldsymbol{x}, P)\n", @@ -389,7 +481,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "add715f9", + "metadata": { + "editable": true + }, "source": [ "In terms of $P_{\\text{hidden} }$ and $P_{\\text{output} }$, this could also be expressed as\n", "\n", @@ -397,20 +492,21 @@ "\\min_{P_{\\text{hidden} }, \\ P_{\\text{output} }} C(\\boldsymbol{x}, \\{P_{\\text{hidden} }, P_{\\text{output} }\\})\n", "$$\n", "\n", - "\n", "For simplicity, it is assumed that the input is an array $\\boldsymbol{x} = (x_1, \\dots, x_N)$ with $N$ elements. It is at these points the neural network should find $P$ such that it fulfills ([9](#min)).\n", "\n", "First, the neural network must feed forward the inputs.\n", "This means that $\\boldsymbol{x}s$ must be passed through an input layer, a hidden layer and a output layer. The input layer in this case, does not need to process the data any further.\n", "The input layer will consist of $N_{\\text{input} }$ neurons, passing its element to each neuron in the hidden layer. The number of neurons in the hidden layer will be $N_{\\text{hidden} }$.\n", "\n", - "\n", "For the $i$-th in the hidden layer with weight $w_i^{\\text{hidden} }$ and bias $b_i^{\\text{hidden} }$, the weighting from the $j$-th neuron at the input layer is:" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "cb9b22eb", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{aligned}\n", @@ -429,14 +525,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "49f3c493", + "metadata": { + "editable": true + }, "source": [ "The result after weighting the inputs at the $i$-th hidden neuron can be written as a vector:" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "a352bd61", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{aligned}\n", @@ -456,7 +558,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e5636ad7", + "metadata": { + "editable": true + }, "source": [ "The vector $\\boldsymbol{p}_{i, \\text{hidden}}^T$ constitutes each row in $P_{\\text{hidden} }$, which contains the weights for the neural network to minimize according to ([9](#min)).\n", "\n", @@ -467,7 +572,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "68bb8b9c", + "metadata": { + "editable": true + }, "source": [ "$$\n", "f(z) = \\frac{1}{1 + \\exp{(-z)}}\n", @@ -476,7 +584,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ff6e6536", + "metadata": { + "editable": true + }, "source": [ "It is possible to use other activations functions for the hidden layer also.\n", "\n", @@ -494,14 +605,15 @@ "and biases $b_i^{\\text{output}}$. In this case,\n", "it is assumes that the number of neurons in the output layer is one.\n", "\n", - "\n", - "\n", "The procedure of weighting the output neuron $j$ in the hidden layer to the $i$-th neuron in the output layer is similar as for the hidden layer described previously." ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "6fb4c55b", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{aligned}\n", @@ -519,14 +631,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "09c31d8d", + "metadata": { + "editable": true + }, "source": [ "Expressing $z_{1,j}^{\\text{output}}$ as a vector gives the following way of weighting the inputs from the hidden layer:" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "f81fe361", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{z}_{1}^{\\text{output}} =\n", @@ -542,11 +660,13 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "c309a4ce", + "metadata": { + "editable": true + }, "source": [ "In this case we seek a continuous range of values since we are approximating a function. This means that after computing $\\boldsymbol{z}_{1}^{\\text{output}}$ the neural network has finished its feed forward step, and $\\boldsymbol{z}_{1}^{\\text{output}}$ is the final output of the network.\n", "\n", - "\n", "The next step is to decide how the parameters should be changed such that they minimize the cost function.\n", "\n", "The chosen cost function for this problem is" @@ -554,7 +674,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ea47ae29", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C(\\boldsymbol{x}, P) = \\frac{1}{N} \\sum_i \\big(g_t'(x_i, P) - ( -\\gamma g_t(x_i, P) \\big)^2\n", @@ -563,12 +686,23 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9dd83767", + "metadata": { + "editable": true + }, "source": [ "In order to minimize the cost function, an optimization method must be chosen.\n", "\n", - "Here, gradient descent with a constant step size has been chosen.\n", - "\n", + "Here, gradient descent with a constant step size has been chosen." + ] + }, + { + "cell_type": "markdown", + "id": "531a7b4f", + "metadata": { + "editable": true + }, + "source": [ "### Gradient descent\n", "\n", "The idea of the gradient descent algorithm is to update parameters in\n", @@ -581,7 +715,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e10c204a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\omega}_{\\text{new} } = \\boldsymbol{\\omega} - \\lambda \\nabla_{\\boldsymbol{\\omega}} C(\\boldsymbol{x}, \\boldsymbol{\\omega})\n", @@ -590,7 +727,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9f4fa48e", + "metadata": { + "editable": true + }, "source": [ "for a number of iterations or until $ \\big|\\big| \\boldsymbol{\\omega}_{\\text{new} } - \\boldsymbol{\\omega} \\big|\\big|$ becomes smaller than some given tolerance.\n", "\n", @@ -609,7 +749,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "4652fc79", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{aligned}\n", @@ -621,14 +764,18 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "41ae0626", + "metadata": { + "editable": true + }, "source": [ "### The code for solving the ODE" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, + "id": "af7c165f", "metadata": { "collapsed": false, "editable": true @@ -785,7 +932,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "875a0c0b", + "metadata": { + "editable": true + }, "source": [ "## The network with one input layer, specified number of hidden layers, and one output layer\n", "\n", @@ -796,7 +946,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, + "id": "00684827", "metadata": { "collapsed": false, "editable": true @@ -965,7 +1116,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "5420c490", + "metadata": { + "editable": true + }, "source": [ "### Example: Population growth\n", "\n", @@ -975,7 +1129,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "1436ed3c", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -989,7 +1146,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a590bdb6", + "metadata": { + "editable": true + }, "source": [ "where $g(t)$ is the population density at time $t$, $\\alpha > 0$ the growth rate and $A > 0$ is the maximum population number in the environment.\n", "Also, at $t = 0$ the population has the size $g(0) = g_0$, where $g_0$ is some chosen constant.\n", @@ -999,15 +1159,16 @@ "using a library like TensorFlow is recommended.\n", "Here, we stay with a more simple approach and implement for comparison, the simple forward Euler method.\n", "\n", - "\n", - "\n", "Here, we will model a population $g(t)$ in an environment having carrying capacity $A$.\n", "The population follows the model" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "48d788d6", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -1021,13 +1182,15 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "169c6c25", + "metadata": { + "editable": true + }, "source": [ "where $g(0) = g_0$.\n", "\n", "In this example, we let $\\alpha = 2$, $A = 1$, and $g_0 = 1.2$.\n", "\n", - "\n", "We will get a slightly different trial solution, as the boundary conditions are different\n", "compared to the case for exponential decay.\n", "\n", @@ -1045,14 +1208,13 @@ "g(t) = \\frac{Ag_0}{g_0 + (A - g_0)\\exp(-\\alpha A t)}\n", "$$\n", "\n", - "\n", - "\n", "The network will be the similar as for the exponential decay example, but with some small modifications for our problem." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, + "id": "6d2e33bf", "metadata": { "collapsed": false, "editable": true @@ -1226,7 +1388,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e31ec549", + "metadata": { + "editable": true + }, "source": [ "## Using forward Euler to solve the ODE\n", "\n", @@ -1243,7 +1408,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "2e9ee105", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{aligned}\n", @@ -1255,7 +1423,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e876da16", + "metadata": { + "editable": true + }, "source": [ "along with the condition that $g(0) = g_0$.\n", "\n", @@ -1266,7 +1437,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b79a3def", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{aligned}\n", @@ -1279,14 +1453,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9d99cb4e", + "metadata": { + "editable": true + }, "source": [ "Now, if $g_i = g(t_i)$ then" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "3b9dcc24", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -1305,7 +1485,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "65ce688e", + "metadata": { + "editable": true + }, "source": [ "for $i \\geq 1$ and $g_0 = g(t_0) = g(0) = g_0$.\n", "\n", @@ -1315,7 +1498,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, + "id": "d5497948", "metadata": { "collapsed": false, "editable": true @@ -1391,7 +1575,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "fa8f0bb4", + "metadata": { + "editable": true + }, "source": [ "## Solving the one dimensional Poisson equation\n", "\n", @@ -1400,7 +1587,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f765b0ba", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -1414,7 +1604,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "bd63b92e", + "metadata": { + "editable": true + }, "source": [ "where $f(x)$ is a given function for $x \\in (0,1)$.\n", "\n", @@ -1423,7 +1616,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "c0a7face", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -1435,19 +1631,24 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f71c3cb9", + "metadata": { + "editable": true + }, "source": [ "This equation can be solved numerically using programs where e.g Autograd and TensorFlow are used.\n", "The results from the networks can then be compared to the analytical solution.\n", "In addition, it could be interesting to see how a typical method for numerically solving second order ODEs compares to the neural networks.\n", "\n", - "\n", "Here, the function $g(x)$ to solve for follows the equation" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "35aa6a37", + "metadata": { + "editable": true + }, "source": [ "$$\n", "-g''(x) = f(x),\\qquad x \\in (0,1)\n", @@ -1456,14 +1657,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f8b35111", + "metadata": { + "editable": true + }, "source": [ "where $f(x)$ is a given function, along with the chosen conditions" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "33813514", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -1477,7 +1684,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "c70aadd4", + "metadata": { + "editable": true + }, "source": [ "In this example, we consider the case when $f(x) = (3x + x^2)\\exp(x)$.\n", "\n", @@ -1486,7 +1696,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d5719dee", + "metadata": { + "editable": true + }, "source": [ "$$\n", "g_t(x) = x \\cdot (1-x) \\cdot N(P,x)\n", @@ -1495,14 +1708,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a683041b", + "metadata": { + "editable": true + }, "source": [ "The analytical solution for this problem is" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "672cdaff", + "metadata": { + "editable": true + }, "source": [ "$$\n", "g(x) = x(1 - x)\\exp(x)\n", @@ -1511,7 +1730,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, + "id": "66e6bebb", "metadata": { "collapsed": false, "editable": true @@ -1672,7 +1892,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d425cba5", + "metadata": { + "editable": true + }, "source": [ "### Comparing with a numerical scheme\n", "\n", @@ -1691,7 +1914,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a2efa110", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -1705,14 +1931,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "5011ee25", + "metadata": { + "editable": true + }, "source": [ "If $x_i = i \\Delta x = x_{i-1} + \\Delta x$ and $g_i = g(x_i)$ for $i = 1,\\dots N_x - 2$ with $N_x$ being the number of values for $x$, ([15](#approx)) becomes" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "705ee300", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{aligned}\n", @@ -1724,14 +1956,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b390796d", + "metadata": { + "editable": true + }, "source": [ "Since we know from our problem that" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "19c9ece4", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{aligned}\n", @@ -1743,7 +1981,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6ade1a7a", + "metadata": { + "editable": true + }, "source": [ "along with the conditions $g(0) = g(1) = 0$,\n", "the following scheme can be used to find an approximate solution for $g(x)$ numerically:" @@ -1751,7 +1992,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "78b16d02", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -1768,7 +2012,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f2bfcca4", + "metadata": { + "editable": true + }, "source": [ "for $i = 1, \\dots, N_x - 2$ where $g_0 = g_{N_x - 1} = 0$ and $f(x_i) = (3x_i + x_i^2)\\exp(x_i)$, which is given for our specific problem.\n", "\n", @@ -1777,7 +2024,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a6191528", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{aligned}\n", @@ -1811,17 +2061,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "aefef707", + "metadata": { + "editable": true + }, "source": [ "which makes it possible to solve for the vector $\\boldsymbol{g}$.\n", "\n", - "\n", "We can then compare the result from this numerical scheme with the output from our network using Autograd:" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, + "id": "471664cd", "metadata": { "collapsed": false, "editable": true @@ -2022,7 +2275,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6f02e86d", + "metadata": { + "editable": true + }, "source": [ "## Partial Differential Equations\n", "\n", @@ -2036,7 +2292,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ad5c63e8", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -2050,10 +2309,21 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "c7b98797", + "metadata": { + "editable": true + }, + "source": [ + "where $f$ is an expression involving all kinds of possible mixed derivatives of $g(x_1,\\dots,x_N)$ up to an order $n$. In order for the solution to be unique, some additional conditions must also be given." + ] + }, + { + "cell_type": "markdown", + "id": "52f9394e", + "metadata": { + "editable": true + }, "source": [ - "where $f$ is an expression involving all kinds of possible mixed derivatives of $g(x_1,\\dots,x_N)$ up to an order $n$. In order for the solution to be unique, some additional conditions must also be given.\n", - "\n", "### Type of problem\n", "\n", "The problem our network must solve for, is similar to the ODE case.\n", @@ -2064,7 +2334,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "4d489854", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -2075,15 +2348,24 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "82311538", + "metadata": { + "editable": true + }, "source": [ "where $h_1(x_1,\\dots,x_N)$ is a function that ensures $g_t(x_1,\\dots,x_N)$ satisfies some given conditions.\n", "The neural network $N(x_1,\\dots,x_N,P)$ has weights and biases described by $P$ and $h_2(x_1,\\dots,x_N,N(x_1,\\dots,x_N,P))$ is an expression using the output from the neural network in some way.\n", "\n", - "The role of the function $h_2(x_1,\\dots,x_N,N(x_1,\\dots,x_N,P))$, is to ensure that the output of $N(x_1,\\dots,x_N,P)$ is zero when $g_t(x_1,\\dots,x_N)$ is evaluated at the values of $x_1,\\dots,x_N$ where the given conditions must be satisfied. The function $h_1(x_1,\\dots,x_N)$ should alone make $g_t(x_1,\\dots,x_N)$ satisfy the conditions.\n", - "\n", - "\n", - "\n", + "The role of the function $h_2(x_1,\\dots,x_N,N(x_1,\\dots,x_N,P))$, is to ensure that the output of $N(x_1,\\dots,x_N,P)$ is zero when $g_t(x_1,\\dots,x_N)$ is evaluated at the values of $x_1,\\dots,x_N$ where the given conditions must be satisfied. The function $h_1(x_1,\\dots,x_N)$ should alone make $g_t(x_1,\\dots,x_N)$ satisfy the conditions." + ] + }, + { + "cell_type": "markdown", + "id": "9d134db4", + "metadata": { + "editable": true + }, + "source": [ "### Network requirements\n", "\n", "The network tries then the minimize the cost function following the\n", @@ -2099,7 +2381,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "5a463498", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C\\left(x_1, \\dots, x_N, P\\right) = \\left( f\\left(x_1, \\, \\dots \\, , x_N, \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_1}, \\dots , \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_N}, \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(x_1,\\dots,x_N) }{\\partial x_N^n} \\right) \\right)^2\n", @@ -2108,14 +2393,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "c40d8997", + "metadata": { + "editable": true + }, "source": [ "If we let $\\boldsymbol{x} = \\big( x_1, \\dots, x_N \\big)$ be an array containing the values for $x_1, \\dots, x_N$ respectively, the cost function can be reformulated into the following:" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "cc033de6", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C\\left(\\boldsymbol{x}, P\\right) = f\\left( \\left( \\boldsymbol{x}, \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_1}, \\dots , \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_N}, \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(\\boldsymbol{x}) }{\\partial x_N^n} \\right) \\right)^2\n", @@ -2124,14 +2415,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ae18b4f4", + "metadata": { + "editable": true + }, "source": [ "If we also have $M$ different sets of values for $x_1, \\dots, x_N$, that is $\\boldsymbol{x}_i = \\big(x_1^{(i)}, \\dots, x_N^{(i)}\\big)$ for $i = 1,\\dots,M$ being the rows in matrix $X$, the cost function can be generalized into" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "44ca21bd", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C\\left(X, P \\right) = \\sum_{i=1}^M f\\left( \\left( \\boldsymbol{x}_i, \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_1}, \\dots , \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_N}, \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(\\boldsymbol{x}_i) }{\\partial x_N^n} \\right) \\right)^2.\n", @@ -2140,7 +2437,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "fe94451e", + "metadata": { + "editable": true + }, "source": [ "## Example: The diffusion equation\n", "\n", @@ -2149,7 +2449,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "30a42273", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial g(x,t)}{\\partial t} = \\frac{\\partial^2 g(x,t)}{\\partial x^2}\n", @@ -2158,14 +2461,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "fd4077e7", + "metadata": { + "editable": true + }, "source": [ "where a possible choice of conditions are" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "dbbf2e4b", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -2178,18 +2487,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "83653db9", + "metadata": { + "editable": true + }, "source": [ "with $u(x)$ being some given function.\n", "\n", - "\n", - "\n", "For this case, we want to find $g(x,t)$ such that" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "d2c2ef4f", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -2203,14 +2516,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "8fb27bdb", + "metadata": { + "editable": true + }, "source": [ "and" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "dc9297ab", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -2223,7 +2542,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ab90784f", + "metadata": { + "editable": true + }, "source": [ "with $u(x) = \\sin(\\pi x)$.\n", "\n", @@ -2231,9 +2553,6 @@ "The deep neural network will follow the same structure as discussed in the examples solving the ODEs.\n", "First, we will look into how Autograd could be used in a network tailored to solve for bivariate functions.\n", "\n", - "\n", - "\n", - "\n", "The only change to do here, is to extend our network such that\n", "functions of multiple parameters are correctly handled. In this case\n", "we have two variables in our function to solve for, that is time $t$\n", @@ -2245,7 +2564,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, + "id": "b07e858c", "metadata": { "collapsed": false, "editable": true @@ -2300,7 +2620,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9a167ec1", + "metadata": { + "editable": true + }, "source": [ "The cost function must then iterate through the given arrays\n", "containing values for $x$ and $t$, defines a point $(x,t)$ the deep\n", @@ -2322,8 +2645,6 @@ "$$\n", "since $(0) = u(1) = 0$ and $u(x) = \\sin(\\pi x)$.\n", "\n", - "\n", - "\n", "The Jacobian is used because the program must find the derivative of\n", "the trial solution with respect to $x$ and $t$.\n", "\n", @@ -2345,7 +2666,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, + "id": "921e5969", "metadata": { "collapsed": false, "editable": true @@ -2392,7 +2714,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "0bc00b69", + "metadata": { + "editable": true + }, "source": [ "### Setting up the network using Autograd; The full program\n", "\n", @@ -2408,14 +2733,14 @@ "Be aware, though, that it is fairly slow for the parameters used.\n", "A better result is possible, but requires more iterations, and thus longer time to complete.\n", "\n", - "\n", "Indeed, the program below is not optimal in its implementation, but rather serves as an example on how to implement and use a neural network to solve a PDE.\n", "Using TensorFlow results in a much better execution time. Try it!" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, + "id": "20734418", "metadata": { "collapsed": false, "editable": true @@ -2649,7 +2974,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "143f1c80", + "metadata": { + "editable": true + }, "source": [ "## Solving the wave equation with Neural Networks\n", "\n", @@ -2658,7 +2986,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "190bd4f2", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial^2 g(x,t)}{\\partial t^2} = c^2\\frac{\\partial^2 g(x,t)}{\\partial x^2}\n", @@ -2667,7 +2998,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9719cfc5", + "metadata": { + "editable": true + }, "source": [ "with $c$ being the specified wave speed.\n", "\n", @@ -2676,7 +3010,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f69ec7fd", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -2690,17 +3027,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6ce8c5a8", + "metadata": { + "editable": true + }, "source": [ "where $\\frac{\\partial g(x,t)}{\\partial t} \\Big |_{t = 0}$ means the derivative of $g(x,t)$ with respect to $t$ is evaluated at $t = 0$, and $u(x)$ and $v(x)$ being given functions.\n", "\n", - "\n", "The wave equation to solve for, is" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "4be700d7", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -2714,7 +3056,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "993f93ba", + "metadata": { + "editable": true + }, "source": [ "where $c$ is the given wave speed.\n", "The chosen conditions for this equation are" @@ -2722,7 +3067,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "2cb2a80f", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -2739,12 +3087,13 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "3f1dcfd4", + "metadata": { + "editable": true + }, "source": [ "In this example, let $c = 1$ and $u(x) = \\sin(\\pi x)$ and $v(x) = -\\pi\\sin(\\pi x)$.\n", "\n", - "\n", - "\n", "Setting up the network is done in similar matter as for the example of solving the diffusion equation.\n", "The only things we have to change, is the trial solution such that it satisfies the conditions from ([20](#condwave)) and the cost function.\n", "\n", @@ -2762,7 +3111,6 @@ "\n", "Note that this trial solution satisfies the conditions only if $u(0) = v(0) = u(1) = v(1) = 0$, which is the case in this example.\n", "\n", - "\n", "The analytical solution for our specific problem, is\n", "\n", "$$\n", @@ -2772,7 +3120,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, + "id": "230a9aef", "metadata": { "collapsed": false, "editable": true @@ -3003,7 +3352,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a23bd19a", + "metadata": { + "editable": true + }, "source": [ "## Resources on differential equations and deep learning\n", "\n", @@ -3019,5 +3371,5 @@ ], "metadata": {}, "nbformat": 4, - "nbformat_minor": 4 + "nbformat_minor": 5 } diff --git a/doc/LectureNotes/_build/html/_sources/chapter12.ipynb b/doc/LectureNotes/_build/html/_sources/chapter12.ipynb new file mode 100644 index 000000000..c0569826b --- /dev/null +++ b/doc/LectureNotes/_build/html/_sources/chapter12.ipynb @@ -0,0 +1,1577 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "b1ad0b52", + "metadata": { + "editable": true + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "id": "9548423d", + "metadata": { + "editable": true + }, + "source": [ + "# Convolutional Neural Networks\n", + "\n", + "Convolutional neural networks (CNNs) were developed during the last\n", + "decade of the previous century, with a focus on character recognition\n", + "tasks. Nowadays, CNNs are a central element in the spectacular success\n", + "of deep learning methods. The success in for example image\n", + "classifications have made them a central tool for most machine\n", + "learning practitioners.\n", + "\n", + "CNNs are very similar to ordinary Neural Networks.\n", + "They are made up of neurons that have learnable weights and\n", + "biases. Each neuron receives some inputs, performs a dot product and\n", + "optionally follows it with a non-linearity. The whole network still\n", + "expresses a single differentiable score function: from the raw image\n", + "pixels on one end to class scores at the other. And they still have a\n", + "loss function (for example Softmax) on the last (fully-connected) layer\n", + "and all the tips/tricks we developed for learning regular Neural\n", + "Networks still apply (back propagation, gradient descent etc etc).\n", + "\n", + "**CNN architectures make the explicit assumption that\n", + "the inputs are images, which allows us to encode certain properties\n", + "into the architecture. These then make the forward function more\n", + "efficient to implement and vastly reduce the amount of parameters in\n", + "the network.**\n", + "\n", + "Here we provide only a superficial overview, for the more interested, we recommend highly the course\n", + "[IN5400 – Machine Learning for Image Analysis](https://www.uio.no/studier/emner/matnat/ifi/IN5400/index-eng.html)\n", + "and the slides of [CS231](http://cs231n.github.io/convolutional-networks/).\n", + "\n", + "Another good read is the article here ." + ] + }, + { + "cell_type": "markdown", + "id": "315b8308", + "metadata": { + "editable": true + }, + "source": [ + "## Neural Networks vs CNNs\n", + "\n", + "Neural networks are defined as **affine transformations**, that is \n", + "a vector is received as input and is multiplied with a matrix of so-called weights (our unknown paramters) to produce an\n", + "output (to which a bias vector is usually added before passing the result\n", + "through a nonlinear activation function). This is applicable to any type of input, be it an\n", + "image, a sound clip or an unordered collection of features: whatever their\n", + "dimensionality, their representation can always be flattened into a vector\n", + "before the transformation.\n", + "\n", + "However, when we consider images, sound clips and many other similar kinds of data, these data have an intrinsic\n", + "structure. More formally, they share these important properties:\n", + "* They are stored as multi-dimensional arrays (think of the pixels of a figure) .\n", + "\n", + "* They feature one or more axes for which ordering matters (e.g., width and height axes for an image, time axis for a sound clip).\n", + "\n", + "* One axis, called the channel axis, is used to access different views of the data (e.g., the red, green and blue channels of a color image, or the left and right channels of a stereo audio track).\n", + "\n", + "These properties are not exploited when an affine transformation is applied; in\n", + "fact, all the axes are treated in the same way and the topological information\n", + "is not taken into account. Still, taking advantage of the implicit structure of\n", + "the data may prove very handy in solving some tasks, like computer vision and\n", + "speech recognition, and in these cases it would be best to preserve it. This is\n", + "where discrete convolutions come into play.\n", + "\n", + "A discrete convolution is a linear transformation that preserves this notion of\n", + "ordering. It is sparse (only a few input units contribute to a given output\n", + "unit) and reuses parameters (the same weights are applied to multiple locations\n", + "in the input).\n", + "\n", + "As an example, consider\n", + "an image of size $32\\times 32\\times 3$ (32 wide, 32 high, 3 color channels), so a\n", + "single fully-connected neuron in a first hidden layer of a regular\n", + "Neural Network would have $32\\times 32\\times 3 = 3072$ weights. This amount still\n", + "seems manageable, but clearly this fully-connected structure does not\n", + "scale to larger images. For example, an image of more respectable\n", + "size, say $200\\times 200\\times 3$, would lead to neurons that have \n", + "$200\\times 200\\times 3 = 120,000$ weights. \n", + "\n", + "We could have\n", + "several such neurons, and the parameters would add up quickly! Clearly,\n", + "this full connectivity is wasteful and the huge number of parameters\n", + "would quickly lead to possible overfitting.\n", + "\n", + "\n", + "\n", + "\n", + "

    Figure 1: A regular 3-layer Neural Network.

    \n", + "\n", + "\n", + "Convolutional Neural Networks take advantage of the fact that the\n", + "input consists of images and they constrain the architecture in a more\n", + "sensible way. \n", + "\n", + "In particular, unlike a regular Neural Network, the\n", + "layers of a CNN have neurons arranged in 3 dimensions: width,\n", + "height, depth. (Note that the word depth here refers to the third\n", + "dimension of an activation volume, not to the depth of a full Neural\n", + "Network, which can refer to the total number of layers in a network.)\n", + "\n", + "To understand it better, the above example of an image \n", + "with an input volume of\n", + "activations has dimensions $32\\times 32\\times 3$ (width, height,\n", + "depth respectively). \n", + "\n", + "The neurons in a layer will\n", + "only be connected to a small region of the layer before it, instead of\n", + "all of the neurons in a fully-connected manner. Moreover, the final\n", + "output layer could for this specific image have dimensions $1\\times 1 \\times 10$, \n", + "because by the\n", + "end of the CNN architecture we will reduce the full image into a\n", + "single vector of class scores, arranged along the depth\n", + "dimension. \n", + "\n", + "\n", + "\n", + "\n", + "

    Figure 1: A CNN arranges its neurons in three dimensions (width, height, depth), as visualized in one of the layers. Every layer of a CNN transforms the 3D input volume to a 3D output volume of neuron activations. In this example, the red input layer holds the image, so its width and height would be the dimensions of the image, and the depth would be 3 (Red, Green, Blue channels).

    \n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "a142cd5d", + "metadata": { + "editable": true + }, + "source": [ + "## Layers used to build CNNs\n", + "\n", + "A simple CNN is a sequence of layers, and every layer of a CNN\n", + "transforms one volume of activations to another through a\n", + "differentiable function. We use three main types of layers to build\n", + "CNN architectures: Convolutional Layer, Pooling Layer, and\n", + "Fully-Connected Layer (exactly as seen in regular Neural Networks). We\n", + "will stack these layers to form a full CNN architecture.\n", + "\n", + "A simple CNN for image classification could have the architecture:\n", + "\n", + "* **INPUT** ($32\\times 32 \\times 3$) will hold the raw pixel values of the image, in this case an image of width 32, height 32, and with three color channels R,G,B.\n", + "\n", + "* **CONV** (convolutional )layer will compute the output of neurons that are connected to local regions in the input, each computing a dot product between their weights and a small region they are connected to in the input volume. This may result in volume such as $[32\\times 32\\times 12]$ if we decided to use 12 filters.\n", + "\n", + "* **RELU** layer will apply an elementwise activation function, such as the $max(0,x)$ thresholding at zero. This leaves the size of the volume unchanged ($[32\\times 32\\times 12]$).\n", + "\n", + "* **POOL** (pooling) layer will perform a downsampling operation along the spatial dimensions (width, height), resulting in volume such as $[16\\times 16\\times 12]$.\n", + "\n", + "* **FC** (i.e. fully-connected) layer will compute the class scores, resulting in volume of size $[1\\times 1\\times 10]$, where each of the 10 numbers correspond to a class score, such as among the 10 categories of the MNIST images we considered above . As with ordinary Neural Networks and as the name implies, each neuron in this layer will be connected to all the numbers in the previous volume.\n", + "\n", + "CNNs transform the original image layer by layer from the original\n", + "pixel values to the final class scores. \n", + "\n", + "Observe that some layers contain\n", + "parameters and other don’t. In particular, the CNN layers perform\n", + "transformations that are a function of not only the activations in the\n", + "input volume, but also of the parameters (the weights and biases of\n", + "the neurons). On the other hand, the RELU/POOL layers will implement a\n", + "fixed function. The parameters in the CONV/FC layers will be trained\n", + "with gradient descent so that the class scores that the CNN computes\n", + "are consistent with the labels in the training set for each image.\n", + "\n", + "In summary:\n", + "\n", + "* A CNN architecture is in the simplest case a list of Layers that transform the image volume into an output volume (e.g. holding the class scores)\n", + "\n", + "* There are a few distinct types of Layers (e.g. CONV/FC/RELU/POOL are by far the most popular)\n", + "\n", + "* Each Layer accepts an input 3D volume and transforms it to an output 3D volume through a differentiable function\n", + "\n", + "* Each Layer may or may not have parameters (e.g. CONV/FC do, RELU/POOL don’t)\n", + "\n", + "* Each Layer may or may not have additional hyperparameters (e.g. CONV/FC/POOL do, RELU doesn’t)\n", + "\n", + "A dense neural network is representd by an affine operation (like matrix-matrix multiplication) where all parameters are included.\n", + "\n", + "The key idea in CNNs for say imaging is that in images neighbor pixels tend to be related! So we connect\n", + "only neighboring neurons in the input instead of connecting all with the first hidden layer.\n", + "\n", + "We say we perform a filtering (convolution is the mathematical operation)." + ] + }, + { + "cell_type": "markdown", + "id": "bb1e3617", + "metadata": { + "editable": true + }, + "source": [ + "## Mathematics of CNNs\n", + "\n", + "The mathematics of CNNs is based on the mathematical operation of\n", + "**convolution**. In mathematics (in particular in functional analysis),\n", + "convolution is represented by matheematical operation (integration,\n", + "summation etc) on two function in order to produce a third function\n", + "that expresses how the shape of one gets modified by the other.\n", + "Convolution has a plethora of applications in a variety of disciplines, spanning from statistics to signal processing, computer vision, solutions of differential equations,linear algebra, engineering, and yes, machine learning.\n", + "\n", + "Mathematically, convolution is defined as follows (one-dimensional example):\n", + "Let us define a continuous function $y(t)$ given by" + ] + }, + { + "cell_type": "markdown", + "id": "051485e5", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "y(t) = \\int x(a) w(t-a) da,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "799b8e5f", + "metadata": { + "editable": true + }, + "source": [ + "where $x(a)$ represents a so-called input and $w(t-a)$ is normally called the weight function or kernel.\n", + "\n", + "The above integral is written in a more compact form as" + ] + }, + { + "cell_type": "markdown", + "id": "3353345f", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "y(t) = \\left(x * w\\right)(t).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "ef341ee6", + "metadata": { + "editable": true + }, + "source": [ + "The discretized version reads" + ] + }, + { + "cell_type": "markdown", + "id": "ca8f7582", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "y(t) = \\sum_{a=-\\infty}^{a=\\infty}x(a)w(t-a).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "216e011f", + "metadata": { + "editable": true + }, + "source": [ + "Computing the inverse of the above convolution operations is known as deconvolution.\n", + "\n", + "How can we use this? And what does it mean? Let us study some familiar examples first." + ] + }, + { + "cell_type": "markdown", + "id": "5545738c", + "metadata": { + "editable": true + }, + "source": [ + "### Convolution Examples: Polynomial multiplication\n", + "\n", + "We have already met such an example in project 1 when we tried to set\n", + "up the design matrix for a two-dimensional function. This was an\n", + "example of polynomial multiplication. Let us recast such a problem in terms of the convolution operation.\n", + "Let us look a the following polynomials to second and third order, respectively:" + ] + }, + { + "cell_type": "markdown", + "id": "9f317908", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(t) = \\alpha_0+\\alpha_1 t+\\alpha_2 t^2,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "eb6f1070", + "metadata": { + "editable": true + }, + "source": [ + "and" + ] + }, + { + "cell_type": "markdown", + "id": "9fe61b3c", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "s(t) = \\beta_0+\\beta_1 t+\\beta_2 t^2+\\beta_3 t^3.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "38c68ea7", + "metadata": { + "editable": true + }, + "source": [ + "The polynomial multiplication gives us a new polynomial of degree $5$" + ] + }, + { + "cell_type": "markdown", + "id": "3e91a9f1", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "z(t) = \\delta_0+\\delta_1 t+\\delta_2 t^2+\\delta_3 t^3+\\delta_4 t^4+\\delta_5 t^5.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "5e24ac44", + "metadata": { + "editable": true + }, + "source": [ + "Computing polynomial products can be implemented efficiently if we rewrite the more brute force multiplications using convolution.\n", + "We note first that the new coefficients are given as" + ] + }, + { + "cell_type": "markdown", + "id": "ac215eb9", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\begin{split}\n", + "\\delta_0=&\\alpha_0\\beta_0\\\\\n", + "\\delta_1=&\\alpha_1\\beta_0+\\alpha_1\\beta_0\\\\\n", + "\\delta_2=&\\alpha_0\\beta_2+\\alpha_1\\beta_1+\\alpha_2\\beta_0\\\\\n", + "\\delta_3=&\\alpha_1\\beta_2+\\alpha_2\\beta_1+\\alpha_0\\beta_3\\\\\n", + "\\delta_4=&\\alpha_2\\beta_2+\\alpha_1\\beta_3\\\\\n", + "\\delta_5=&\\alpha_2\\beta_3.\\\\\n", + "\\end{split}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "eca51025", + "metadata": { + "editable": true + }, + "source": [ + "We note that $\\alpha_i=0$ except for $i\\in \\left\\{0,1,2\\right\\}$ and $\\beta_i=0$ except for $i\\in\\left\\{0,1,2,3\\right\\}$.\n", + "\n", + "We can then rewrite the coefficients $\\delta_j$ using a discrete convolution as" + ] + }, + { + "cell_type": "markdown", + "id": "0d517816", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\delta_j = \\sum_{i=-\\infty}^{i=\\infty}\\alpha_i\\beta_{j-i}=(\\alpha * \\beta)_j,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "8cf1037e", + "metadata": { + "editable": true + }, + "source": [ + "or as a double sum with restriction $l=i+j$" + ] + }, + { + "cell_type": "markdown", + "id": "efe18d99", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\delta_l = \\sum_{ij}\\alpha_i\\beta_{j}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "14ae41db", + "metadata": { + "editable": true + }, + "source": [ + "Do you see a potential drawback with these equations?\n", + "\n", + "Since we only have a finite number of $\\alpha$ and $\\beta$ values\n", + "which are non-zero, we can rewrite the above convolution expressions\n", + "as a matrix-vector multiplication" + ] + }, + { + "cell_type": "markdown", + "id": "046e108b", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\boldsymbol{\\delta}=\\begin{bmatrix}\\alpha_0 & 0 & 0 & 0 \\\\\n", + " \\alpha_1 & \\alpha_0 & 0 & 0 \\\\\n", + "\t\t\t \\alpha_2 & \\alpha_1 & \\alpha_0 & 0 \\\\\n", + "\t\t\t 0 & \\alpha_2 & \\alpha_1 & \\alpha_0 \\\\\n", + "\t\t\t 0 & 0 & \\alpha_2 & \\alpha_1 \\\\\n", + "\t\t\t 0 & 0 & 0 & \\alpha_2\n", + "\t\t\t \\end{bmatrix}\\begin{bmatrix} \\beta_0 \\\\ \\beta_1 \\\\ \\beta_2 \\\\ \\beta_3\\end{bmatrix}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "0c73a726", + "metadata": { + "editable": true + }, + "source": [ + "The process is commutative and we can easily see that we can rewrite the multiplication in terms of a matrix holding $\\beta$ and a vector holding $\\alpha$.\n", + "In this case we have" + ] + }, + { + "cell_type": "markdown", + "id": "81bc84d0", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\boldsymbol{\\delta}=\\begin{bmatrix}\\beta_0 & 0 & 0 \\\\\n", + " \\beta_1 & \\beta_0 & 0 \\\\\n", + "\t\t\t \\beta_2 & \\beta_1 & \\beta_0 \\\\\n", + "\t\t\t \\beta_3 & \\beta_2 & \\beta_1 \\\\\n", + "\t\t\t 0 & \\beta_3 & \\beta_2 \\\\\n", + "\t\t\t 0 & 0 & \\beta_3\n", + "\t\t\t \\end{bmatrix}\\begin{bmatrix} \\alpha_0 \\\\ \\alpha_1 \\\\ \\alpha_2\\end{bmatrix}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "6f314582", + "metadata": { + "editable": true + }, + "source": [ + "Note that the use of these matrices is for mathematical purposes only and not implementation purposes.\n", + "When implementing the above equation we do not encode (and allocate memory) the matrices explicitely.\n", + "We rather code the convolutions in the minimal memory footprint that they require.\n", + "\n", + "Does the number of floating point operations change here when we use the commutative property?" + ] + }, + { + "cell_type": "markdown", + "id": "e01eb276", + "metadata": { + "editable": true + }, + "source": [ + "### Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)\n", + "\n", + "For problems with so-called harmonic oscillations, given by for example the following differential equation" + ] + }, + { + "cell_type": "markdown", + "id": "1016b422", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "m\\frac{d^2x}{dt^2}+\\eta\\frac{dx}{dt}+x(t)=F(t),\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "c237cb74", + "metadata": { + "editable": true + }, + "source": [ + "where $F(t)$ is an applied external force acting on the system (often called a driving force), one can use the theory of Fourier transformations to find the solutions of this type of equations.\n", + "\n", + "If one has several driving forces, $F(t)=\\sum_n F_n(t)$, one can find\n", + "the particular solution to each $F_n$, $x_{pn}(t)$, and the particular\n", + "solution for the entire driving force is then given by a series like" + ] + }, + { + "cell_type": "markdown", + "id": "4f2f2089", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + "x_p(t)=\\sum_nx_{pn}(t).\n", + "\\label{_auto1} \\tag{1}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "a32fa928", + "metadata": { + "editable": true + }, + "source": [ + "This is known as the principle of superposition. It only applies when\n", + "the homogenous equation is linear. If there were an anharmonic term\n", + "such as $x^3$ in the homogenous equation, then when one summed various\n", + "solutions, $x=(\\sum_n x_n)^2$, one would get cross\n", + "terms. Superposition is especially useful when $F(t)$ can be written\n", + "as a sum of sinusoidal terms, because the solutions for each\n", + "sinusoidal (sine or cosine) term is analytic. \n", + "\n", + "Driving forces are often periodic, even when they are not\n", + "sinusoidal. Periodicity implies that for some time $\\tau$" + ] + }, + { + "cell_type": "markdown", + "id": "0b6ca2c5", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\begin{eqnarray}\n", + "F(t+\\tau)=F(t). \n", + "\\end{eqnarray}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "789cd636", + "metadata": { + "editable": true + }, + "source": [ + "One example of a non-sinusoidal periodic force is a square wave. Many\n", + "components in electric circuits are non-linear, e.g. diodes, which\n", + "makes many wave forms non-sinusoidal even when the circuits are being\n", + "driven by purely sinusoidal sources.\n", + "\n", + "The code here shows a typical example of such a square wave generated using the functionality included in the **scipy** Python package. We have used a period of $\\tau=0.2$." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "2c90eb89", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "import numpy as np\n", + "import math\n", + "from scipy import signal\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# number of points \n", + "n = 500\n", + "# start and final times \n", + "t0 = 0.0\n", + "tn = 1.0\n", + "# Period \n", + "t = np.linspace(t0, tn, n, endpoint=False)\n", + "SqrSignal = np.zeros(n)\n", + "SqrSignal = 1.0+signal.square(2*np.pi*5*t)\n", + "plt.plot(t, SqrSignal)\n", + "plt.ylim(-0.5, 2.5)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "8e7b8f5c", + "metadata": { + "editable": true + }, + "source": [ + "For the sinusoidal example the\n", + "period is $\\tau=2\\pi/\\omega$. However, higher harmonics can also\n", + "satisfy the periodicity requirement. In general, any force that\n", + "satisfies the periodicity requirement can be expressed as a sum over\n", + "harmonics," + ] + }, + { + "cell_type": "markdown", + "id": "4453c025", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + "F(t)=\\frac{f_0}{2}+\\sum_{n>0} f_n\\cos(2n\\pi t/\\tau)+g_n\\sin(2n\\pi t/\\tau).\n", + "\\label{_auto2} \\tag{2}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "32d5f410", + "metadata": { + "editable": true + }, + "source": [ + "We can write down the answer for\n", + "$x_{pn}(t)$, by substituting $f_n/m$ or $g_n/m$ for $F_0/m$. By\n", + "writing each factor $2n\\pi t/\\tau$ as $n\\omega t$, with $\\omega\\equiv\n", + "2\\pi/\\tau$," + ] + }, + { + "cell_type": "markdown", + "id": "4a58698d", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + "\\label{eq:fourierdef1} \\tag{3}\n", + "F(t)=\\frac{f_0}{2}+\\sum_{n>0}f_n\\cos(n\\omega t)+g_n\\sin(n\\omega t).\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "5664f63d", + "metadata": { + "editable": true + }, + "source": [ + "The solutions for $x(t)$ then come from replacing $\\omega$ with\n", + "$n\\omega$ for each term in the particular solution," + ] + }, + { + "cell_type": "markdown", + "id": "0d9a2811", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\begin{eqnarray}\n", + "x_p(t)&=&\\frac{f_0}{2k}+\\sum_{n>0} \\alpha_n\\cos(n\\omega t-\\delta_n)+\\beta_n\\sin(n\\omega t-\\delta_n),\\\\\n", + "\\nonumber\n", + "\\alpha_n&=&\\frac{f_n/m}{\\sqrt{((n\\omega)^2-\\omega_0^2)+4\\beta^2n^2\\omega^2}},\\\\\n", + "\\nonumber\n", + "\\beta_n&=&\\frac{g_n/m}{\\sqrt{((n\\omega)^2-\\omega_0^2)+4\\beta^2n^2\\omega^2}},\\\\\n", + "\\nonumber\n", + "\\delta_n&=&\\tan^{-1}\\left(\\frac{2\\beta n\\omega}{\\omega_0^2-n^2\\omega^2}\\right).\n", + "\\end{eqnarray}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "ac8b5fff", + "metadata": { + "editable": true + }, + "source": [ + "Because the forces have been applied for a long time, any non-zero\n", + "damping eliminates the homogenous parts of the solution, so one need\n", + "only consider the particular solution for each $n$.\n", + "\n", + "The problem is considered solved if one can find expressions for the\n", + "coefficients $f_n$ and $g_n$, even though the solutions are expressed\n", + "as an infinite sum. The coefficients can be extracted from the\n", + "function $F(t)$ by" + ] + }, + { + "cell_type": "markdown", + "id": "5bb70ae9", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{eqnarray}\n", + "\\label{eq:fourierdef2} \\tag{4}\n", + "f_n&=&\\frac{2}{\\tau}\\int_{-\\tau/2}^{\\tau/2} dt~F(t)\\cos(2n\\pi t/\\tau),\\\\\n", + "\\nonumber\n", + "g_n&=&\\frac{2}{\\tau}\\int_{-\\tau/2}^{\\tau/2} dt~F(t)\\sin(2n\\pi t/\\tau).\n", + "\\end{eqnarray}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "4f64082e", + "metadata": { + "editable": true + }, + "source": [ + "To check the consistency of these expressions and to verify\n", + "Eq. ([4](#eq:fourierdef2)), one can insert the expansion of $F(t)$ in\n", + "Eq. ([3](#eq:fourierdef1)) into the expression for the coefficients in\n", + "Eq. ([4](#eq:fourierdef2)) and see whether" + ] + }, + { + "cell_type": "markdown", + "id": "bdd9e4e8", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\begin{eqnarray}\n", + "f_n&=?&\\frac{2}{\\tau}\\int_{-\\tau/2}^{\\tau/2} dt~\\left\\{\n", + "\\frac{f_0}{2}+\\sum_{m>0}f_m\\cos(m\\omega t)+g_m\\sin(m\\omega t)\n", + "\\right\\}\\cos(n\\omega t).\n", + "\\end{eqnarray}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "e64a4a4c", + "metadata": { + "editable": true + }, + "source": [ + "Immediately, one can throw away all the terms with $g_m$ because they\n", + "convolute an even and an odd function. The term with $f_0/2$\n", + "disappears because $\\cos(n\\omega t)$ is equally positive and negative\n", + "over the interval and will integrate to zero. For all the terms\n", + "$f_m\\cos(m\\omega t)$ appearing in the sum, one can use angle addition\n", + "formulas to see that $\\cos(m\\omega t)\\cos(n\\omega\n", + "t)=(1/2)(\\cos[(m+n)\\omega t]+\\cos[(m-n)\\omega t]$. This will integrate\n", + "to zero unless $m=n$. In that case the $m=n$ term gives" + ] + }, + { + "cell_type": "markdown", + "id": "d51a4f59", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + "\\int_{-\\tau/2}^{\\tau/2}dt~\\cos^2(m\\omega t)=\\frac{\\tau}{2},\n", + "\\label{_auto3} \\tag{5}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "44804e35", + "metadata": { + "editable": true + }, + "source": [ + "and" + ] + }, + { + "cell_type": "markdown", + "id": "7de0dbe5", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\begin{eqnarray}\n", + "f_n&=?&\\frac{2}{\\tau}\\int_{-\\tau/2}^{\\tau/2} dt~f_n/2\\\\\n", + "\\nonumber\n", + "&=&f_n~\\checkmark.\n", + "\\end{eqnarray}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "4d1a02e0", + "metadata": { + "editable": true + }, + "source": [ + "The same method can be used to check for the consistency of $g_n$.\n", + "\n", + "The code here uses the Fourier series applied to a \n", + "square wave signal. The code here\n", + "visualizes the various approximations given by Fourier series compared\n", + "with a square wave with period $T=0.2$ (dimensionless time), width $0.1$ and max value of the force $F=2$. We\n", + "see that when we increase the number of components in the Fourier\n", + "series, the Fourier series approximation gets closer and closer to the\n", + "square wave signal." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "4ae0ec42", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "import math\n", + "from scipy import signal\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# number of points \n", + "n = 500\n", + "# start and final times \n", + "t0 = 0.0\n", + "tn = 1.0\n", + "# Period \n", + "T =0.2\n", + "# Max value of square signal \n", + "Fmax= 2.0\n", + "# Width of signal \n", + "Width = 0.1\n", + "t = np.linspace(t0, tn, n, endpoint=False)\n", + "SqrSignal = np.zeros(n)\n", + "FourierSeriesSignal = np.zeros(n)\n", + "SqrSignal = 1.0+signal.square(2*np.pi*5*t+np.pi*Width/T)\n", + "a0 = Fmax*Width/T\n", + "FourierSeriesSignal = a0\n", + "Factor = 2.0*Fmax/np.pi\n", + "for i in range(1,500):\n", + " FourierSeriesSignal += Factor/(i)*np.sin(np.pi*i*Width/T)*np.cos(i*t*2*np.pi/T)\n", + "plt.plot(t, SqrSignal)\n", + "plt.plot(t, FourierSeriesSignal)\n", + "plt.ylim(-0.5, 2.5)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "acd75ab0", + "metadata": { + "editable": true + }, + "source": [ + "## Two-dimensional Objects\n", + "\n", + "We often use convolutions over more than one dimension at a time. If\n", + "we have a two-dimensional image $I$ as input, we can have a **filter**\n", + "defined by a two-dimensional **kernel** $K$. This leads to an output $S$" + ] + }, + { + "cell_type": "markdown", + "id": "0cdf3af8", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "S_(i,j)=(I * K)(i,j) = \\sum_m\\sum_n I(m,n)K(i-m,j-n).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "1640aae2", + "metadata": { + "editable": true + }, + "source": [ + "Convolution is a commutatitave process, which means we can rewrite this equation as" + ] + }, + { + "cell_type": "markdown", + "id": "11491f4c", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "S_(i,j)=(I * K)(i,j) = \\sum_m\\sum_n I(i-m,j-n)K(m,n).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "a1e3ef9d", + "metadata": { + "editable": true + }, + "source": [ + "Normally the latter is more straightforward to implement in a machine elarning library since there is less variation in the range of values of $m$ and $n$.\n", + "\n", + "Many deep learning libraries implement cross-correlation instead of convolution" + ] + }, + { + "cell_type": "markdown", + "id": "919fb5e9", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "S_(i,j)=(I * K)(i,j) = \\sum_m\\sum_n I(i+m,j-+)K(m,n).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "c42d55ac", + "metadata": { + "editable": true + }, + "source": [ + "## More on Dimensionalities\n", + "\n", + "In fields like signal processing (and imaging as well), one designs\n", + "so-called filters. These filters are defined by the convolutions and\n", + "are often hand-crafted. One may specify filters for smoothing, edge\n", + "detection, frequency reshaping, and similar operations. However with\n", + "neural networks the idea is to automatically learn the filters and use\n", + "many of them in conjunction with non-linear operations (activation\n", + "functions).\n", + "\n", + "As an example consider a neural network operating on sound sequence\n", + "data. Assume that we an input vector $\\boldsymbol{x}$ of length $d=10^6$. We\n", + "construct then a neural network with onle hidden layer only with\n", + "$10^4$ nodes. This means that we will have a weight matrix with\n", + "$10^4\\times 10^6=10^{10}$ weights to be determined, together with $10^4$ biases.\n", + "\n", + "Assume furthermore that we have an output layer which is meant to train whether the sound sequence represents a human voice (true) or something else (false).\n", + "It means that we have only one output node. But since this output node connects to $10^4$ nodes in the hidden layer, there are in total $10^4$ weights to be determined for the output layer, plus one bias. In total we have" + ] + }, + { + "cell_type": "markdown", + "id": "4ebd8c85", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathrm{NumberParameters}=10^{10}+10^4+10^4+1 \\approx 10^{10},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "6d886fa7", + "metadata": { + "editable": true + }, + "source": [ + "that is ten billion parameters to determine." + ] + }, + { + "cell_type": "markdown", + "id": "cd3b731e", + "metadata": { + "editable": true + }, + "source": [ + "## Further Dimensionality Remarks\n", + "\n", + "In today’s architecture one can train such neural networks, however\n", + "this is a huge number of parameters for the task at hand. In general,\n", + "it is a very wasteful and inefficient use of dense matrices as\n", + "parameters. Just as importantly, such trained network parameters are\n", + "very specific for the type of input data on which they were trained\n", + "and the network is not likely to generalize easily to variations in\n", + "the input.\n", + "\n", + "The main principles that justify convolutions is locality of\n", + "information and repetion of patterns within the signal. Sound samples\n", + "of the input in adjacent spots are much more likely to affect each\n", + "other than those that are very far away. Similarly, sounds are\n", + "repeated in multiple times in the signal. While slightly simplistic,\n", + "reasoning about such a sound example demonstrates this. The same\n", + "principles then apply to images and other similar data." + ] + }, + { + "cell_type": "markdown", + "id": "fc38055c", + "metadata": { + "editable": true + }, + "source": [ + "## CNNs in more detail, building convolutional neural networks in Tensorflow and Keras\n", + "\n", + "As discussed above, CNNs are neural networks built from the assumption that the inputs\n", + "to the network are 2D images. This is important because the number of features or pixels in images\n", + "grows very fast with the image size, and an enormous number of weights and biases are needed in order to build an accurate network. \n", + "\n", + "As before, we still have our input, a hidden layer and an output. What's novel about convolutional networks\n", + "are the **convolutional** and **pooling** layers stacked in pairs between the input and the hidden layer.\n", + "In addition, the data is no longer represented as a 2D feature matrix, instead each input is a number of 2D\n", + "matrices, typically 1 for each color dimension (Red, Green, Blue). \n", + "\n", + "It means that to represent the entire\n", + "dataset of images, we require a 4D matrix or **tensor**. This tensor has the dimensions:" + ] + }, + { + "cell_type": "markdown", + "id": "c153f6eb", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "(n_{inputs},\\, n_{pixels, width},\\, n_{pixels, height},\\, depth) .\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "f45ab21d", + "metadata": { + "editable": true + }, + "source": [ + "### The MNIST dataset again\n", + "\n", + "The MNIST dataset consists of grayscale images with a pixel size of\n", + "$28\\times 28$, meaning we require $28 \\times 28 = 724$ weights to each\n", + "neuron in the first hidden layer.\n", + "\n", + "If we were to analyze images of size $128\\times 128$ we would require\n", + "$128 \\times 128 = 16384$ weights to each neuron. Even worse if we were\n", + "dealing with color images, as most images are, we have an image matrix\n", + "of size $128\\times 128$ for each color dimension (Red, Green, Blue),\n", + "meaning 3 times the number of weights $= 49152$ are required for every\n", + "single neuron in the first hidden layer.\n", + "\n", + "Images typically have strong local correlations, meaning that a small\n", + "part of the image varies little from its neighboring regions. If for\n", + "example we have an image of a blue car, we can roughly assume that a\n", + "small blue part of the image is surrounded by other blue regions.\n", + "\n", + "Therefore, instead of connecting every single pixel to a neuron in the\n", + "first hidden layer, as we have previously done with deep neural\n", + "networks, we can instead connect each neuron to a small part of the\n", + "image (in all 3 RGB depth dimensions). The size of each small area is\n", + "fixed, and known as a [receptive](https://en.wikipedia.org/wiki/Receptive_field).\n", + "\n", + "The layers of a convolutional neural network arrange neurons in 3D: width, height and depth. \n", + "The input image is typically a square matrix of depth 3. \n", + "\n", + "A **convolution** is performed on the image which outputs\n", + "a 3D volume of neurons. The weights to the input are arranged in a number of 2D matrices, known as **filters**.\n", + "\n", + "Each filter slides along the input image, taking the dot product\n", + "between each small part of the image and the filter, in all depth\n", + "dimensions. This is then passed through a non-linear function,\n", + "typically the **Rectified Linear (ReLu)** function, which serves as the\n", + "activation of the neurons in the first convolutional layer. This is\n", + "further passed through a **pooling layer**, which reduces the size of the\n", + "convolutional layer, e.g. by taking the maximum or average across some\n", + "small regions, and this serves as input to the next convolutional\n", + "layer." + ] + }, + { + "cell_type": "markdown", + "id": "4af74ca7", + "metadata": { + "editable": true + }, + "source": [ + "### Systematic reduction\n", + "\n", + "By systematically reducing the size of the input volume, through\n", + "convolution and pooling, the network should create representations of\n", + "small parts of the input, and then from them assemble representations\n", + "of larger areas. The final pooling layer is flattened to serve as\n", + "input to a hidden layer, such that each neuron in the final pooling\n", + "layer is connected to every single neuron in the hidden layer. This\n", + "then serves as input to the output layer, e.g. a softmax output for\n", + "classification." + ] + }, + { + "cell_type": "markdown", + "id": "2b435dc0", + "metadata": { + "editable": true + }, + "source": [ + "### Prerequisites: Collect and pre-process data" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "ffb4904f", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# import necessary packages\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from sklearn import datasets\n", + "\n", + "\n", + "# ensure the same random numbers appear every time\n", + "np.random.seed(0)\n", + "\n", + "# display images in notebook\n", + "%matplotlib inline\n", + "plt.rcParams['figure.figsize'] = (12,12)\n", + "\n", + "\n", + "# download MNIST dataset\n", + "digits = datasets.load_digits()\n", + "\n", + "# define inputs and labels\n", + "inputs = digits.images\n", + "labels = digits.target\n", + "\n", + "# RGB images have a depth of 3\n", + "# our images are grayscale so they should have a depth of 1\n", + "inputs = inputs[:,:,:,np.newaxis]\n", + "\n", + "print(\"inputs = (n_inputs, pixel_width, pixel_height, depth) = \" + str(inputs.shape))\n", + "print(\"labels = (n_inputs) = \" + str(labels.shape))\n", + "\n", + "\n", + "# choose some random images to display\n", + "n_inputs = len(inputs)\n", + "indices = np.arange(n_inputs)\n", + "random_indices = np.random.choice(indices, size=5)\n", + "\n", + "for i, image in enumerate(digits.images[random_indices]):\n", + " plt.subplot(1, 5, i+1)\n", + " plt.axis('off')\n", + " plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')\n", + " plt.title(\"Label: %d\" % digits.target[random_indices[i]])\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "bb2db46c", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "from tensorflow.keras import datasets, layers, models\n", + "from tensorflow.keras.layers import Input\n", + "from tensorflow.keras.models import Sequential #This allows appending layers to existing models\n", + "from tensorflow.keras.layers import Dense #This allows defining the characteristics of a particular layer\n", + "from tensorflow.keras import optimizers #This allows using whichever optimiser we want (sgd,adam,RMSprop)\n", + "from tensorflow.keras import regularizers #This allows using whichever regularizer we want (l1,l2,l1_l2)\n", + "from tensorflow.keras.utils import to_categorical #This allows using categorical cross entropy as the cost function\n", + "#from tensorflow.keras import Conv2D\n", + "#from tensorflow.keras import MaxPooling2D\n", + "#from tensorflow.keras import Flatten\n", + "\n", + "from sklearn.model_selection import train_test_split\n", + "\n", + "# representation of labels\n", + "labels = to_categorical(labels)\n", + "\n", + "# split into train and test data\n", + "# one-liner from scikit-learn library\n", + "train_size = 0.8\n", + "test_size = 1 - train_size\n", + "X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,\n", + " test_size=test_size)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "100a8d6d", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def create_convolutional_neural_network_keras(input_shape, receptive_field,\n", + " n_filters, n_neurons_connected, n_categories,\n", + " eta, lmbd):\n", + " model = Sequential()\n", + " model.add(layers.Conv2D(n_filters, (receptive_field, receptive_field), input_shape=input_shape, padding='same',\n", + " activation='relu', kernel_regularizer=regularizers.l2(lmbd)))\n", + " model.add(layers.MaxPooling2D(pool_size=(2, 2)))\n", + " model.add(layers.Flatten())\n", + " model.add(layers.Dense(n_neurons_connected, activation='relu', kernel_regularizer=regularizers.l2(lmbd)))\n", + " model.add(layers.Dense(n_categories, activation='softmax', kernel_regularizer=regularizers.l2(lmbd)))\n", + " \n", + " sgd = optimizers.SGD(lr=eta)\n", + " model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])\n", + " \n", + " return model\n", + "\n", + "epochs = 100\n", + "batch_size = 100\n", + "input_shape = X_train.shape[1:4]\n", + "receptive_field = 3\n", + "n_filters = 10\n", + "n_neurons_connected = 50\n", + "n_categories = 10\n", + "\n", + "eta_vals = np.logspace(-5, 1, 7)\n", + "lmbd_vals = np.logspace(-5, 1, 7)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "635da5a7", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "CNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n", + " \n", + "for i, eta in enumerate(eta_vals):\n", + " for j, lmbd in enumerate(lmbd_vals):\n", + " CNN = create_convolutional_neural_network_keras(input_shape, receptive_field,\n", + " n_filters, n_neurons_connected, n_categories,\n", + " eta, lmbd)\n", + " CNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)\n", + " scores = CNN.evaluate(X_test, Y_test)\n", + " \n", + " CNN_keras[i][j] = CNN\n", + " \n", + " print(\"Learning rate = \", eta)\n", + " print(\"Lambda = \", lmbd)\n", + " print(\"Test accuracy: %.3f\" % scores[1])\n", + " print()" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "df145244", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# visual representation of grid search\n", + "# uses seaborn heatmap, could probably do this in matplotlib\n", + "import seaborn as sns\n", + "\n", + "sns.set()\n", + "\n", + "train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n", + "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n", + "\n", + "for i in range(len(eta_vals)):\n", + " for j in range(len(lmbd_vals)):\n", + " CNN = CNN_keras[i][j]\n", + "\n", + " train_accuracy[i][j] = CNN.evaluate(X_train, Y_train)[1]\n", + " test_accuracy[i][j] = CNN.evaluate(X_test, Y_test)[1]\n", + "\n", + " \n", + "fig, ax = plt.subplots(figsize = (10, 10))\n", + "sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n", + "ax.set_title(\"Training Accuracy\")\n", + "ax.set_ylabel(\"$\\eta$\")\n", + "ax.set_xlabel(\"$\\lambda$\")\n", + "plt.show()\n", + "\n", + "fig, ax = plt.subplots(figsize = (10, 10))\n", + "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n", + "ax.set_title(\"Test Accuracy\")\n", + "ax.set_ylabel(\"$\\eta$\")\n", + "ax.set_xlabel(\"$\\lambda$\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "a6724f1c", + "metadata": { + "editable": true + }, + "source": [ + "## The CIFAR01 data set\n", + "\n", + "The CIFAR10 dataset contains 60,000 color images in 10 classes, with\n", + "6,000 images in each class. The dataset is divided into 50,000\n", + "training images and 10,000 testing images. The classes are mutually\n", + "exclusive and there is no overlap between them." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "90c28005", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "import tensorflow as tf\n", + "\n", + "from tensorflow.keras import datasets, layers, models\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# We import the data set\n", + "(train_images, train_labels), (test_images, test_labels) = datasets.cifar10.load_data()\n", + "\n", + "# Normalize pixel values to be between 0 and 1 by dividing by 255. \n", + "train_images, test_images = train_images / 255.0, test_images / 255.0" + ] + }, + { + "cell_type": "markdown", + "id": "759ea77a", + "metadata": { + "editable": true + }, + "source": [ + "To verify that the dataset looks correct, let's plot the first 25 images from the training set and display the class name below each image." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "494edadd", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "class_names = ['airplane', 'automobile', 'bird', 'cat', 'deer',\n", + " 'dog', 'frog', 'horse', 'ship', 'truck']\n", + "​\n", + "plt.figure(figsize=(10,10))\n", + "for i in range(25):\n", + " plt.subplot(5,5,i+1)\n", + " plt.xticks([])\n", + " plt.yticks([])\n", + " plt.grid(False)\n", + " plt.imshow(train_images[i], cmap=plt.cm.binary)\n", + " # The CIFAR labels happen to be arrays, \n", + " # which is why you need the extra index\n", + " plt.xlabel(class_names[train_labels[i][0]])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "46d2ea5d", + "metadata": { + "editable": true + }, + "source": [ + "The six lines of code below define the convolutional base using a common pattern: a stack of Conv2D and MaxPooling2D layers.\n", + "\n", + "As input, a CNN takes tensors of shape (image_height, image_width, color_channels), ignoring the batch size. If you are new to these dimensions, color_channels refers to (R,G,B). In this example, you will configure our CNN to process inputs of shape (32, 32, 3), which is the format of CIFAR images. You can do this by passing the argument input_shape to our first layer." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "044310ec", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "model = models.Sequential()\n", + "model.add(layers.Conv2D(32, (3, 3), activation='relu', input_shape=(32, 32, 3)))\n", + "model.add(layers.MaxPooling2D((2, 2)))\n", + "model.add(layers.Conv2D(64, (3, 3), activation='relu'))\n", + "model.add(layers.MaxPooling2D((2, 2)))\n", + "model.add(layers.Conv2D(64, (3, 3), activation='relu'))\n", + "\n", + "# Let's display the architecture of our model so far.\n", + "\n", + "model.summary()" + ] + }, + { + "cell_type": "markdown", + "id": "738f34a7", + "metadata": { + "editable": true + }, + "source": [ + "You can see that the output of every Conv2D and MaxPooling2D layer is a 3D tensor of shape (height, width, channels). The width and height dimensions tend to shrink as you go deeper in the network. The number of output channels for each Conv2D layer is controlled by the first argument (e.g., 32 or 64). Typically, as the width and height shrink, you can afford (computationally) to add more output channels in each Conv2D layer.\n", + "\n", + "To complete our model, you will feed the last output tensor from the\n", + "convolutional base (of shape (4, 4, 64)) into one or more Dense layers\n", + "to perform classification. Dense layers take vectors as input (which\n", + "are 1D), while the current output is a 3D tensor. First, you will\n", + "flatten (or unroll) the 3D output to 1D, then add one or more Dense\n", + "layers on top. CIFAR has 10 output classes, so you use a final Dense\n", + "layer with 10 outputs and a softmax activation." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "e0fea435", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "model.add(layers.Flatten())\n", + "model.add(layers.Dense(64, activation='relu'))\n", + "model.add(layers.Dense(10))\n", + "Here's the complete architecture of our model.\n", + "\n", + "model.summary()" + ] + }, + { + "cell_type": "markdown", + "id": "62f1e50d", + "metadata": { + "editable": true + }, + "source": [ + "As you can see, our (4, 4, 64) outputs were flattened into vectors of shape (1024) before going through two Dense layers." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "e2d8f4f2", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "model.compile(optimizer='adam',\n", + " loss=tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True),\n", + " metrics=['accuracy'])\n", + "​\n", + "history = model.fit(train_images, train_labels, epochs=10, \n", + " validation_data=(test_images, test_labels))" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "d2965f40", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "plt.plot(history.history['accuracy'], label='accuracy')\n", + "plt.plot(history.history['val_accuracy'], label = 'val_accuracy')\n", + "plt.xlabel('Epoch')\n", + "plt.ylabel('Accuracy')\n", + "plt.ylim([0.5, 1])\n", + "plt.legend(loc='lower right')\n", + "\n", + "test_loss, test_acc = model.evaluate(test_images, test_labels, verbose=2)\n", + "\n", + "print(test_acc)" + ] + } + ], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/doc/LectureNotes/_build/html/_sources/chapter13.ipynb b/doc/LectureNotes/_build/html/_sources/chapter13.ipynb new file mode 100644 index 000000000..7d78135c1 --- /dev/null +++ b/doc/LectureNotes/_build/html/_sources/chapter13.ipynb @@ -0,0 +1,1873 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "6d2db899", + "metadata": { + "editable": true + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "id": "f4908a97", + "metadata": { + "editable": true + }, + "source": [ + "# Recurrent neural networks: Overarching view\n", + "\n", + "Till now our focus has been, including convolutional neural networks\n", + "as well, on feedforward neural networks. The output or the activations\n", + "flow only in one direction, from the input layer to the output layer.\n", + "\n", + "A recurrent neural network (RNN) looks very much like a feedforward\n", + "neural network, except that it also has connections pointing\n", + "backward. \n", + "\n", + "RNNs are used to analyze time series data such as stock prices, and\n", + "tell you when to buy or sell. In autonomous driving systems, they can\n", + "anticipate car trajectories and help avoid accidents. More generally,\n", + "they can work on sequences of arbitrary lengths, rather than on\n", + "fixed-sized inputs like all the nets we have discussed so far. For\n", + "example, they can take sentences, documents, or audio samples as\n", + "input, making them extremely useful for natural language processing\n", + "systems such as automatic translation and speech-to-text.\n", + "\n", + "More to text to be added" + ] + }, + { + "cell_type": "markdown", + "id": "43cb4913", + "metadata": { + "editable": true + }, + "source": [ + "## A simple example" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "cf6b9dab", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "# Start importing packages\n", + "import pandas as pd\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import tensorflow as tf\n", + "from tensorflow.keras import datasets, layers, models\n", + "from tensorflow.keras.layers import Input\n", + "from tensorflow.keras.models import Model, Sequential \n", + "from tensorflow.keras.layers import Dense, SimpleRNN, LSTM, GRU\n", + "from tensorflow.keras import optimizers \n", + "from tensorflow.keras import regularizers \n", + "from tensorflow.keras.utils import to_categorical \n", + "\n", + "\n", + "\n", + "# convert into dataset matrix\n", + "def convertToMatrix(data, step):\n", + " X, Y =[], []\n", + " for i in range(len(data)-step):\n", + " d=i+step \n", + " X.append(data[i:d,])\n", + " Y.append(data[d,])\n", + " return np.array(X), np.array(Y)\n", + "\n", + "step = 4\n", + "N = 1000 \n", + "Tp = 800 \n", + "\n", + "t=np.arange(0,N)\n", + "x=np.sin(0.02*t)+2*np.random.rand(N)\n", + "df = pd.DataFrame(x)\n", + "df.head()\n", + "\n", + "plt.plot(df)\n", + "plt.show()\n", + "\n", + "values=df.values\n", + "train,test = values[0:Tp,:], values[Tp:N,:]\n", + "\n", + "# add step elements into train and test\n", + "test = np.append(test,np.repeat(test[-1,],step))\n", + "train = np.append(train,np.repeat(train[-1,],step))\n", + " \n", + "trainX,trainY =convertToMatrix(train,step)\n", + "testX,testY =convertToMatrix(test,step)\n", + "trainX = np.reshape(trainX, (trainX.shape[0], 1, trainX.shape[1]))\n", + "testX = np.reshape(testX, (testX.shape[0], 1, testX.shape[1]))\n", + "\n", + "model = Sequential()\n", + "model.add(SimpleRNN(units=32, input_shape=(1,step), activation=\"relu\"))\n", + "model.add(Dense(8, activation=\"relu\")) \n", + "model.add(Dense(1))\n", + "model.compile(loss='mean_squared_error', optimizer='rmsprop')\n", + "model.summary()\n", + "\n", + "model.fit(trainX,trainY, epochs=100, batch_size=16, verbose=2)\n", + "trainPredict = model.predict(trainX)\n", + "testPredict= model.predict(testX)\n", + "predicted=np.concatenate((trainPredict,testPredict),axis=0)\n", + "\n", + "trainScore = model.evaluate(trainX, trainY, verbose=0)\n", + "print(trainScore)\n", + "\n", + "index = df.index.values\n", + "plt.plot(index,df)\n", + "plt.plot(index,predicted)\n", + "plt.axvline(df.index[Tp], c=\"r\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "897a47c7", + "metadata": { + "editable": true + }, + "source": [ + "## An extrapolation example\n", + "\n", + "The following code provides an example of how recurrent neural\n", + "networks can be used to extrapolate to unknown values of physics data\n", + "sets. Specifically, the data sets used in this program come from\n", + "a quantum mechanical many-body calculation of energies as functions of the number of particles." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "6776ae2a", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "\n", + "# For matrices and calculations\n", + "import numpy as np\n", + "# For machine learning (backend for keras)\n", + "import tensorflow as tf\n", + "# User-friendly machine learning library\n", + "# Front end for TensorFlow\n", + "import tensorflow.keras\n", + "# Different methods from Keras needed to create an RNN\n", + "# This is not necessary but it shortened function calls \n", + "# that need to be used in the code.\n", + "from tensorflow.keras import datasets, layers, models\n", + "from tensorflow.keras.layers import Input\n", + "from tensorflow.keras import regularizers\n", + "from tensorflow.keras.models import Model, Sequential\n", + "from tensorflow.keras.layers import Dense, SimpleRNN, LSTM, GRU\n", + "# For timing the code\n", + "from timeit import default_timer as timer\n", + "# For plotting\n", + "import matplotlib.pyplot as plt\n", + "\n", + "\n", + "# The data set\n", + "datatype='VaryDimension'\n", + "X_tot = np.arange(2, 42, 2)\n", + "y_tot = np.array([-0.03077640549, -0.08336233266, -0.1446729567, -0.2116753732, -0.2830637392, -0.3581341341, -0.436462435, -0.5177783846,\n", + "\t-0.6019067271, -0.6887363571, -0.7782028952, -0.8702784034, -0.9649652536, -1.062292565, -1.16231451, \n", + "\t-1.265109911, -1.370782966, -1.479465113, -1.591317992, -1.70653767])" + ] + }, + { + "cell_type": "markdown", + "id": "35227d36", + "metadata": { + "editable": true + }, + "source": [ + "The way the recurrent neural networks are trained in this program\n", + "differs from how machine learning algorithms are usually trained.\n", + "Typically a machine learning algorithm is trained by learning the\n", + "relationship between the x data and the y data. In this program, the\n", + "recurrent neural network will be trained to recognize the relationship\n", + "in a sequence of y values. This is type of data formatting is\n", + "typically used time series forcasting, but it can also be used in any\n", + "extrapolation (time series forecasting is just a specific type of\n", + "extrapolation along the time axis). This method of data formatting\n", + "does not use the x data and assumes that the y data are evenly spaced.\n", + "\n", + "For a standard machine learning algorithm, the training data has the\n", + "form of (x,y) so the machine learning algorithm learns to assiciate a\n", + "y value with a given x value. This is useful when the test data has x\n", + "values within the same range as the training data. However, for this\n", + "application, the x values of the test data are outside of the x values\n", + "of the training data and the traditional method of training a machine\n", + "learning algorithm does not work as well. For this reason, the\n", + "recurrent neural network is trained on sequences of y values of the\n", + "form ((y1, y2), y3), so that the network is concerned with learning\n", + "the pattern of the y data and not the relation between the x and y\n", + "data. As long as the pattern of y data outside of the training region\n", + "stays relatively stable compared to what was inside the training\n", + "region, this method of training can produce accurate extrapolations to\n", + "y values far removed from the training data set." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "7dc577d1", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# FORMAT_DATA\n", + "def format_data(data, length_of_sequence = 2): \n", + " \"\"\"\n", + " Inputs:\n", + " data(a numpy array): the data that will be the inputs to the recurrent neural\n", + " network\n", + " length_of_sequence (an int): the number of elements in one iteration of the\n", + " sequence patter. For a function approximator use length_of_sequence = 2.\n", + " Returns:\n", + " rnn_input (a 3D numpy array): the input data for the recurrent neural network. Its\n", + " dimensions are length of data - length of sequence, length of sequence, \n", + " dimnsion of data\n", + " rnn_output (a numpy array): the training data for the neural network\n", + " Formats data to be used in a recurrent neural network.\n", + " \"\"\"\n", + "\n", + " X, Y = [], []\n", + " for i in range(len(data)-length_of_sequence):\n", + " # Get the next length_of_sequence elements\n", + " a = data[i:i+length_of_sequence]\n", + " # Get the element that immediately follows that\n", + " b = data[i+length_of_sequence]\n", + " # Reshape so that each data point is contained in its own array\n", + " a = np.reshape (a, (len(a), 1))\n", + " X.append(a)\n", + " Y.append(b)\n", + " rnn_input = np.array(X)\n", + " rnn_output = np.array(Y)\n", + "\n", + " return rnn_input, rnn_output\n", + "\n", + "\n", + "# ## Defining the Recurrent Neural Network Using Keras\n", + "# \n", + "# The following method defines a simple recurrent neural network in keras consisting of one input layer, one hidden layer, and one output layer.\n", + "\n", + "def rnn(length_of_sequences, batch_size = None, stateful = False):\n", + " \"\"\"\n", + " Inputs:\n", + " length_of_sequences (an int): the number of y values in \"x data\". This is determined\n", + " when the data is formatted\n", + " batch_size (an int): Default value is None. See Keras documentation of SimpleRNN.\n", + " stateful (a boolean): Default value is False. See Keras documentation of SimpleRNN.\n", + " Returns:\n", + " model (a Keras model): The recurrent neural network that is built and compiled by this\n", + " method\n", + " Builds and compiles a recurrent neural network with one hidden layer and returns the model.\n", + " \"\"\"\n", + " # Number of neurons in the input and output layers\n", + " in_out_neurons = 1\n", + " # Number of neurons in the hidden layer\n", + " hidden_neurons = 200\n", + " # Define the input layer\n", + " inp = Input(batch_shape=(batch_size, \n", + " length_of_sequences, \n", + " in_out_neurons)) \n", + " # Define the hidden layer as a simple RNN layer with a set number of neurons and add it to \n", + " # the network immediately after the input layer\n", + " rnn = SimpleRNN(hidden_neurons, \n", + " return_sequences=False,\n", + " stateful = stateful,\n", + " name=\"RNN\")(inp)\n", + " # Define the output layer as a dense neural network layer (standard neural network layer)\n", + " #and add it to the network immediately after the hidden layer.\n", + " dens = Dense(in_out_neurons,name=\"dense\")(rnn)\n", + " # Create the machine learning model starting with the input layer and ending with the \n", + " # output layer\n", + " model = Model(inputs=[inp],outputs=[dens])\n", + " # Compile the machine learning model using the mean squared error function as the loss \n", + " # function and an Adams optimizer.\n", + " model.compile(loss=\"mean_squared_error\", optimizer=\"adam\") \n", + " return model" + ] + }, + { + "cell_type": "markdown", + "id": "1978b6a1", + "metadata": { + "editable": true + }, + "source": [ + "## Predicting New Points With A Trained Recurrent Neural Network" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "d4ad417a", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def test_rnn (x1, y_test, plot_min, plot_max):\n", + " \"\"\"\n", + " Inputs:\n", + " x1 (a list or numpy array): The complete x component of the data set\n", + " y_test (a list or numpy array): The complete y component of the data set\n", + " plot_min (an int or float): the smallest x value used in the training data\n", + " plot_max (an int or float): the largest x valye used in the training data\n", + " Returns:\n", + " None.\n", + " Uses a trained recurrent neural network model to predict future points in the \n", + " series. Computes the MSE of the predicted data set from the true data set, saves\n", + " the predicted data set to a csv file, and plots the predicted and true data sets w\n", + " while also displaying the data range used for training.\n", + " \"\"\"\n", + " # Add the training data as the first dim points in the predicted data array as these\n", + " # are known values.\n", + " y_pred = y_test[:dim].tolist()\n", + " # Generate the first input to the trained recurrent neural network using the last two \n", + " # points of the training data. Based on how the network was trained this means that it\n", + " # will predict the first point in the data set after the training data. All of the \n", + " # brackets are necessary for Tensorflow.\n", + " next_input = np.array([[[y_test[dim-2]], [y_test[dim-1]]]])\n", + " # Save the very last point in the training data set. This will be used later.\n", + " last = [y_test[dim-1]]\n", + "\n", + " # Iterate until the complete data set is created.\n", + " for i in range (dim, len(y_test)):\n", + " # Predict the next point in the data set using the previous two points.\n", + " next = model.predict(next_input)\n", + " # Append just the number of the predicted data set\n", + " y_pred.append(next[0][0])\n", + " # Create the input that will be used to predict the next data point in the data set.\n", + " next_input = np.array([[last, next[0]]], dtype=np.float64)\n", + " last = next\n", + "\n", + " # Print the mean squared error between the known data set and the predicted data set.\n", + " print('MSE: ', np.square(np.subtract(y_test, y_pred)).mean())\n", + " # Save the predicted data set as a csv file for later use\n", + " name = datatype + 'Predicted'+str(dim)+'.csv'\n", + " np.savetxt(name, y_pred, delimiter=',')\n", + " # Plot the known data set and the predicted data set. The red box represents the region that was used\n", + " # for the training data.\n", + " fig, ax = plt.subplots()\n", + " ax.plot(x1, y_test, label=\"true\", linewidth=3)\n", + " ax.plot(x1, y_pred, 'g-.',label=\"predicted\", linewidth=4)\n", + " ax.legend()\n", + " # Created a red region to represent the points used in the training data.\n", + " ax.axvspan(plot_min, plot_max, alpha=0.25, color='red')\n", + " plt.show()\n", + "\n", + "# Check to make sure the data set is complete\n", + "assert len(X_tot) == len(y_tot)\n", + "\n", + "# This is the number of points that will be used in as the training data\n", + "dim=12\n", + "\n", + "# Separate the training data from the whole data set\n", + "X_train = X_tot[:dim]\n", + "y_train = y_tot[:dim]\n", + "\n", + "\n", + "# Generate the training data for the RNN, using a sequence of 2\n", + "rnn_input, rnn_training = format_data(y_train, 2)\n", + "\n", + "\n", + "# Create a recurrent neural network in Keras and produce a summary of the \n", + "# machine learning model\n", + "model = rnn(length_of_sequences = rnn_input.shape[1])\n", + "model.summary()\n", + "\n", + "# Start the timer. Want to time training+testing\n", + "start = timer()\n", + "# Fit the model using the training data genenerated above using 150 training iterations and a 5%\n", + "# validation split. Setting verbose to True prints information about each training iteration.\n", + "hist = model.fit(rnn_input, rnn_training, batch_size=None, epochs=150, \n", + " verbose=True,validation_split=0.05)\n", + "\n", + "for label in [\"loss\",\"val_loss\"]:\n", + " plt.plot(hist.history[label],label=label)\n", + "\n", + "plt.ylabel(\"loss\")\n", + "plt.xlabel(\"epoch\")\n", + "plt.title(\"The final validation loss: {}\".format(hist.history[\"val_loss\"][-1]))\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "# Use the trained neural network to predict more points of the data set\n", + "test_rnn(X_tot, y_tot, X_tot[0], X_tot[dim-1])\n", + "# Stop the timer and calculate the total time needed.\n", + "end = timer()\n", + "print('Time: ', end-start)" + ] + }, + { + "cell_type": "markdown", + "id": "e2cad4fc", + "metadata": { + "editable": true + }, + "source": [ + "Changing the size of the recurrent neural network and its parameters\n", + "can drastically change the results you get from the model. The below\n", + "code takes the simple recurrent neural network from above and adds a\n", + "second hidden layer, changes the number of neurons in the hidden\n", + "layer, and explicitly declares the activation function of the hidden\n", + "layers to be a sigmoid function. The loss function and optimizer can\n", + "also be changed but are kept the same as the above network. These\n", + "parameters can be tuned to provide the optimal result from the\n", + "network. For some ideas on how to improve the performance of a\n", + "[recurrent neural network](https://danijar.com/tips-for-training-recurrent-neural-networks)." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "c39f1516", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def rnn_2layers(length_of_sequences, batch_size = None, stateful = False):\n", + " \"\"\"\n", + " Inputs:\n", + " length_of_sequences (an int): the number of y values in \"x data\". This is determined\n", + " when the data is formatted\n", + " batch_size (an int): Default value is None. See Keras documentation of SimpleRNN.\n", + " stateful (a boolean): Default value is False. See Keras documentation of SimpleRNN.\n", + " Returns:\n", + " model (a Keras model): The recurrent neural network that is built and compiled by this\n", + " method\n", + " Builds and compiles a recurrent neural network with two hidden layers and returns the model.\n", + " \"\"\"\n", + " # Number of neurons in the input and output layers\n", + " in_out_neurons = 1\n", + " # Number of neurons in the hidden layer, increased from the first network\n", + " hidden_neurons = 500\n", + " # Define the input layer\n", + " inp = Input(batch_shape=(batch_size, \n", + " length_of_sequences, \n", + " in_out_neurons)) \n", + " # Create two hidden layers instead of one hidden layer. Explicitly set the activation\n", + " # function to be the sigmoid function (the default value is hyperbolic tangent)\n", + " rnn1 = SimpleRNN(hidden_neurons, \n", + " return_sequences=True, # This needs to be True if another hidden layer is to follow\n", + " stateful = stateful, activation = 'sigmoid',\n", + " name=\"RNN1\")(inp)\n", + " rnn2 = SimpleRNN(hidden_neurons, \n", + " return_sequences=False, activation = 'sigmoid',\n", + " stateful = stateful,\n", + " name=\"RNN2\")(rnn1)\n", + " # Define the output layer as a dense neural network layer (standard neural network layer)\n", + " #and add it to the network immediately after the hidden layer.\n", + " dens = Dense(in_out_neurons,name=\"dense\")(rnn2)\n", + " # Create the machine learning model starting with the input layer and ending with the \n", + " # output layer\n", + " model = Model(inputs=[inp],outputs=[dens])\n", + " # Compile the machine learning model using the mean squared error function as the loss \n", + " # function and an Adams optimizer.\n", + " model.compile(loss=\"mean_squared_error\", optimizer=\"adam\") \n", + " return model\n", + "\n", + "# Check to make sure the data set is complete\n", + "assert len(X_tot) == len(y_tot)\n", + "\n", + "# This is the number of points that will be used in as the training data\n", + "dim=12\n", + "\n", + "# Separate the training data from the whole data set\n", + "X_train = X_tot[:dim]\n", + "y_train = y_tot[:dim]\n", + "\n", + "\n", + "# Generate the training data for the RNN, using a sequence of 2\n", + "rnn_input, rnn_training = format_data(y_train, 2)\n", + "\n", + "\n", + "# Create a recurrent neural network in Keras and produce a summary of the \n", + "# machine learning model\n", + "model = rnn_2layers(length_of_sequences = 2)\n", + "model.summary()\n", + "\n", + "# Start the timer. Want to time training+testing\n", + "start = timer()\n", + "# Fit the model using the training data genenerated above using 150 training iterations and a 5%\n", + "# validation split. Setting verbose to True prints information about each training iteration.\n", + "hist = model.fit(rnn_input, rnn_training, batch_size=None, epochs=150, \n", + " verbose=True,validation_split=0.05)\n", + "\n", + "\n", + "# This section plots the training loss and the validation loss as a function of training iteration.\n", + "# This is not required for analyzing the couple cluster data but can help determine if the network is\n", + "# being overtrained.\n", + "for label in [\"loss\",\"val_loss\"]:\n", + " plt.plot(hist.history[label],label=label)\n", + "\n", + "plt.ylabel(\"loss\")\n", + "plt.xlabel(\"epoch\")\n", + "plt.title(\"The final validation loss: {}\".format(hist.history[\"val_loss\"][-1]))\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "# Use the trained neural network to predict more points of the data set\n", + "test_rnn(X_tot, y_tot, X_tot[0], X_tot[dim-1])\n", + "# Stop the timer and calculate the total time needed.\n", + "end = timer()\n", + "print('Time: ', end-start)" + ] + }, + { + "cell_type": "markdown", + "id": "842c7602", + "metadata": { + "editable": true + }, + "source": [ + "## Other Types of Recurrent Neural Networks\n", + "\n", + "Besides a simple recurrent neural network layer, there are two other\n", + "commonly used types of recurrent neural network layers: Long Short\n", + "Term Memory (LSTM) and Gated Recurrent Unit (GRU). For a short\n", + "introduction to these layers see \n", + "and .\n", + "\n", + "The first network created below is similar to the previous network,\n", + "but it replaces the SimpleRNN layers with LSTM layers. The second\n", + "network below has two hidden layers made up of GRUs, which are\n", + "preceeded by two dense (feeddorward) neural network layers. These\n", + "dense layers \"preprocess\" the data before it reaches the recurrent\n", + "layers. This architecture has been shown to improve the performance\n", + "of recurrent neural networks (see the link above and also\n", + "." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "6f0e9b62", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def lstm_2layers(length_of_sequences, batch_size = None, stateful = False):\n", + " \"\"\"\n", + " Inputs:\n", + " length_of_sequences (an int): the number of y values in \"x data\". This is determined\n", + " when the data is formatted\n", + " batch_size (an int): Default value is None. See Keras documentation of SimpleRNN.\n", + " stateful (a boolean): Default value is False. See Keras documentation of SimpleRNN.\n", + " Returns:\n", + " model (a Keras model): The recurrent neural network that is built and compiled by this\n", + " method\n", + " Builds and compiles a recurrent neural network with two LSTM hidden layers and returns the model.\n", + " \"\"\"\n", + " # Number of neurons on the input/output layer and the number of neurons in the hidden layer\n", + " in_out_neurons = 1\n", + " hidden_neurons = 250\n", + " # Input Layer\n", + " inp = Input(batch_shape=(batch_size, \n", + " length_of_sequences, \n", + " in_out_neurons)) \n", + " # Hidden layers (in this case they are LSTM layers instead if SimpleRNN layers)\n", + " rnn= LSTM(hidden_neurons, \n", + " return_sequences=True,\n", + " stateful = stateful,\n", + " name=\"RNN\", use_bias=True, activation='tanh')(inp)\n", + " rnn1 = LSTM(hidden_neurons, \n", + " return_sequences=False,\n", + " stateful = stateful,\n", + " name=\"RNN1\", use_bias=True, activation='tanh')(rnn)\n", + " # Output layer\n", + " dens = Dense(in_out_neurons,name=\"dense\")(rnn1)\n", + " # Define the midel\n", + " model = Model(inputs=[inp],outputs=[dens])\n", + " # Compile the model\n", + " model.compile(loss='mean_squared_error', optimizer='adam') \n", + " # Return the model\n", + " return model\n", + "\n", + "def dnn2_gru2(length_of_sequences, batch_size = None, stateful = False):\n", + " \"\"\"\n", + " Inputs:\n", + " length_of_sequences (an int): the number of y values in \"x data\". This is determined\n", + " when the data is formatted\n", + " batch_size (an int): Default value is None. See Keras documentation of SimpleRNN.\n", + " stateful (a boolean): Default value is False. See Keras documentation of SimpleRNN.\n", + " Returns:\n", + " model (a Keras model): The recurrent neural network that is built and compiled by this\n", + " method\n", + " Builds and compiles a recurrent neural network with four hidden layers (two dense followed by\n", + " two GRU layers) and returns the model.\n", + " \"\"\" \n", + " # Number of neurons on the input/output layers and hidden layers\n", + " in_out_neurons = 1\n", + " hidden_neurons = 250\n", + " # Input layer\n", + " inp = Input(batch_shape=(batch_size, \n", + " length_of_sequences, \n", + " in_out_neurons)) \n", + " # Hidden Dense (feedforward) layers\n", + " dnn = Dense(hidden_neurons/2, activation='relu', name='dnn')(inp)\n", + " dnn1 = Dense(hidden_neurons/2, activation='relu', name='dnn1')(dnn)\n", + " # Hidden GRU layers\n", + " rnn1 = GRU(hidden_neurons, \n", + " return_sequences=True,\n", + " stateful = stateful,\n", + " name=\"RNN1\", use_bias=True)(dnn1)\n", + " rnn = GRU(hidden_neurons, \n", + " return_sequences=False,\n", + " stateful = stateful,\n", + " name=\"RNN\", use_bias=True)(rnn1)\n", + " # Output layer\n", + " dens = Dense(in_out_neurons,name=\"dense\")(rnn)\n", + " # Define the model\n", + " model = Model(inputs=[inp],outputs=[dens])\n", + " # Compile the mdoel\n", + " model.compile(loss='mean_squared_error', optimizer='adam') \n", + " # Return the model\n", + " return model\n", + "\n", + "# Check to make sure the data set is complete\n", + "assert len(X_tot) == len(y_tot)\n", + "\n", + "# This is the number of points that will be used in as the training data\n", + "dim=12\n", + "\n", + "# Separate the training data from the whole data set\n", + "X_train = X_tot[:dim]\n", + "y_train = y_tot[:dim]\n", + "\n", + "\n", + "# Generate the training data for the RNN, using a sequence of 2\n", + "rnn_input, rnn_training = format_data(y_train, 2)\n", + "\n", + "\n", + "# Create a recurrent neural network in Keras and produce a summary of the \n", + "# machine learning model\n", + "# Change the method name to reflect which network you want to use\n", + "model = dnn2_gru2(length_of_sequences = 2)\n", + "model.summary()\n", + "\n", + "# Start the timer. Want to time training+testing\n", + "start = timer()\n", + "# Fit the model using the training data genenerated above using 150 training iterations and a 5%\n", + "# validation split. Setting verbose to True prints information about each training iteration.\n", + "hist = model.fit(rnn_input, rnn_training, batch_size=None, epochs=150, \n", + " verbose=True,validation_split=0.05)\n", + "\n", + "\n", + "# This section plots the training loss and the validation loss as a function of training iteration.\n", + "# This is not required for analyzing the couple cluster data but can help determine if the network is\n", + "# being overtrained.\n", + "for label in [\"loss\",\"val_loss\"]:\n", + " plt.plot(hist.history[label],label=label)\n", + "\n", + "plt.ylabel(\"loss\")\n", + "plt.xlabel(\"epoch\")\n", + "plt.title(\"The final validation loss: {}\".format(hist.history[\"val_loss\"][-1]))\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "# Use the trained neural network to predict more points of the data set\n", + "test_rnn(X_tot, y_tot, X_tot[0], X_tot[dim-1])\n", + "# Stop the timer and calculate the total time needed.\n", + "end = timer()\n", + "print('Time: ', end-start)\n", + "\n", + "\n", + "# ### Training Recurrent Neural Networks in the Standard Way (i.e. learning the relationship between the X and Y data)\n", + "# \n", + "# Finally, comparing the performace of a recurrent neural network using the standard data formatting to the performance of the network with time sequence data formatting shows the benefit of this type of data formatting with extrapolation.\n", + "\n", + "# Check to make sure the data set is complete\n", + "assert len(X_tot) == len(y_tot)\n", + "\n", + "# This is the number of points that will be used in as the training data\n", + "dim=12\n", + "\n", + "# Separate the training data from the whole data set\n", + "X_train = X_tot[:dim]\n", + "y_train = y_tot[:dim]\n", + "\n", + "# Reshape the data for Keras specifications\n", + "X_train = X_train.reshape((dim, 1))\n", + "y_train = y_train.reshape((dim, 1))\n", + "\n", + "\n", + "# Create a recurrent neural network in Keras and produce a summary of the \n", + "# machine learning model\n", + "# Set the sequence length to 1 for regular data formatting \n", + "model = rnn(length_of_sequences = 1)\n", + "model.summary()\n", + "\n", + "# Start the timer. Want to time training+testing\n", + "start = timer()\n", + "# Fit the model using the training data genenerated above using 150 training iterations and a 5%\n", + "# validation split. Setting verbose to True prints information about each training iteration.\n", + "hist = model.fit(X_train, y_train, batch_size=None, epochs=150, \n", + " verbose=True,validation_split=0.05)\n", + "\n", + "\n", + "# This section plots the training loss and the validation loss as a function of training iteration.\n", + "# This is not required for analyzing the couple cluster data but can help determine if the network is\n", + "# being overtrained.\n", + "for label in [\"loss\",\"val_loss\"]:\n", + " plt.plot(hist.history[label],label=label)\n", + "\n", + "plt.ylabel(\"loss\")\n", + "plt.xlabel(\"epoch\")\n", + "plt.title(\"The final validation loss: {}\".format(hist.history[\"val_loss\"][-1]))\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "# Use the trained neural network to predict the remaining data points\n", + "X_pred = X_tot[dim:]\n", + "X_pred = X_pred.reshape((len(X_pred), 1))\n", + "y_model = model.predict(X_pred)\n", + "y_pred = np.concatenate((y_tot[:dim], y_model.flatten()))\n", + "\n", + "# Plot the known data set and the predicted data set. The red box represents the region that was used\n", + "# for the training data.\n", + "fig, ax = plt.subplots()\n", + "ax.plot(X_tot, y_tot, label=\"true\", linewidth=3)\n", + "ax.plot(X_tot, y_pred, 'g-.',label=\"predicted\", linewidth=4)\n", + "ax.legend()\n", + "# Created a red region to represent the points used in the training data.\n", + "ax.axvspan(X_tot[0], X_tot[dim], alpha=0.25, color='red')\n", + "plt.show()\n", + "\n", + "# Stop the timer and calculate the total time needed.\n", + "end = timer()\n", + "print('Time: ', end-start)" + ] + }, + { + "cell_type": "markdown", + "id": "0752ba7f", + "metadata": { + "editable": true + }, + "source": [ + "# Generative Models\n", + "\n", + "**Generative models** describe a class of statistical models that are a contrast\n", + "to **discriminative models**. Informally we say that generative models can\n", + "generate new data instances while discriminative models discriminate between\n", + "different kinds of data instances. A generative model could generate new photos\n", + "of animals that look like 'real' animals while a discriminative model could tell\n", + "a dog from a cat. More formally, given a data set $x$ and a set of labels /\n", + "targets $y$. Generative models capture the joint probability $p(x, y)$, or\n", + "just $p(x)$ if there are no labels, while discriminative models capture the\n", + "conditional probability $p(y | x)$. Discriminative models generally try to draw\n", + "boundaries in the data space (often high dimensional), while generative models\n", + "try to model how data is placed throughout the space.\n", + "\n", + "**Note**: this material is thanks to Linus Ekstrøm." + ] + }, + { + "cell_type": "markdown", + "id": "784138f8", + "metadata": { + "editable": true + }, + "source": [ + "## Generative Adversarial Networks\n", + "\n", + "**Generative Adversarial Networks** are a type of unsupervised machine learning\n", + "algorithm proposed by [Goodfellow et. al](https://arxiv.org/pdf/1406.2661.pdf)\n", + "in 2014 (short and good article).\n", + "\n", + "The simplest formulation of\n", + "the model is based on a game theoretic approach, *zero sum game*, where we pit\n", + "two neural networks against one another. We define two rival networks, one\n", + "generator $g$, and one discriminator $d$. The generator directly produces\n", + "samples" + ] + }, + { + "cell_type": "markdown", + "id": "a42f89ee", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " x = g(z; \\theta^{(g)})\n", + "\\label{_auto1} \\tag{1}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "abe7212f", + "metadata": { + "editable": true + }, + "source": [ + "The discriminator attempts to distinguish between samples drawn from the\n", + "training data and samples drawn from the generator. In other words, it tries to\n", + "tell the difference between the fake data produced by $g$ and the actual data\n", + "samples we want to do prediction on. The discriminator outputs a probability\n", + "value given by" + ] + }, + { + "cell_type": "markdown", + "id": "0821eaee", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " d(x; \\theta^{(d)})\n", + "\\label{_auto2} \\tag{2}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "55e0ccf6", + "metadata": { + "editable": true + }, + "source": [ + "indicating the probability that $x$ is a real training example rather than a\n", + "fake sample the generator has generated. The simplest way to formulate the\n", + "learning process in a generative adversarial network is a zero-sum game, in\n", + "which a function" + ] + }, + { + "cell_type": "markdown", + "id": "f37ece14", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " v(\\theta^{(g)}, \\theta^{(d)})\n", + "\\label{_auto3} \\tag{3}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "d6d6d5fa", + "metadata": { + "editable": true + }, + "source": [ + "determines the reward for the discriminator, while the generator gets the\n", + "conjugate reward" + ] + }, + { + "cell_type": "markdown", + "id": "3c74b45c", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " -v(\\theta^{(g)}, \\theta^{(d)})\n", + "\\label{_auto4} \\tag{4}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "605ac8c9", + "metadata": { + "editable": true + }, + "source": [ + "During learning both of the networks maximize their own reward function, so that\n", + "the generator gets better and better at tricking the discriminator, while the\n", + "discriminator gets better and better at telling the difference between the fake\n", + "and real data. The generator and discriminator alternate on which one trains at\n", + "one time (i.e. for one epoch). In other words, we keep the generator constant\n", + "and train the discriminator, then we keep the discriminator constant to train\n", + "the generator and repeat. It is this back and forth dynamic which lets GANs\n", + "tackle otherwise intractable generative problems. As the generator improves with\n", + " training, the discriminator's performance gets worse because it cannot easily\n", + " tell the difference between real and fake. If the generator ends up succeeding\n", + " perfectly, the the discriminator will do no better than random guessing i.e.\n", + " 50\\%. This progression in the training poses a problem for the convergence\n", + " criteria for GANs. The discriminator feedback gets less meaningful over time,\n", + " if we continue training after this point then the generator is effectively\n", + " training on junk data which can undo the learning up to that point. Therefore,\n", + " we stop training when the discriminator starts outputting $1/2$ everywhere.\n", + "\n", + "At convergence we have" + ] + }, + { + "cell_type": "markdown", + "id": "cfec7462", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " g^* = \\underset{g}{\\mathrm{argmin}}\\hspace{2pt}\n", + " \\underset{d}{\\mathrm{max}}v(\\theta^{(g)}, \\theta^{(d)})\n", + "\\label{_auto5} \\tag{5}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "37c65d4c", + "metadata": { + "editable": true + }, + "source": [ + "The default choice for $v$ is" + ] + }, + { + "cell_type": "markdown", + "id": "c868a092", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " v(\\theta^{(g)}, \\theta^{(d)}) = \\mathbb{E}_{x\\sim p_\\mathrm{data}}\\log d(x)\n", + " + \\mathbb{E}_{x\\sim p_\\mathrm{model}}\n", + " \\log (1 - d(x))\n", + "\\label{_auto6} \\tag{6}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "ad465af3", + "metadata": { + "editable": true + }, + "source": [ + "The main motivation for the design of GANs is that the learning process requires\n", + "neither approximate inference (variational autoencoders for example) nor\n", + "approximation of a partition function. In the case where" + ] + }, + { + "cell_type": "markdown", + "id": "27858a4e", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " \\underset{d}{\\mathrm{max}}v(\\theta^{(g)}, \\theta^{(d)})\n", + "\\label{_auto7} \\tag{7}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "86006023", + "metadata": { + "editable": true + }, + "source": [ + "is convex in $\\theta^{(g)} then the procedure is guaranteed to converge and is\n", + "asymptotically consistent\n", + "( [Seth Lloyd on QuGANs](https://arxiv.org/pdf/1804.09139.pdf) ).\n", + "\n", + "This is in\n", + "general not the case and it is possible to get situations where the training\n", + "process never converges because the generator and discriminator chase one\n", + "another around in the parameter space indefinitely. A much deeper discussion on\n", + "the currently open research problem of GAN convergence is available\n", + "[here](https://www.deeplearningbook.org/contents/generative_models.html). To\n", + "anyone interested in learning more about GANs it is a highly recommended read.\n", + "Direct quote: \"In this best-performing formulation, the generator aims to\n", + "increase the log probability that the discriminator makes a mistake, rather than\n", + "aiming to decrease the log probability that the discriminator makes the correct\n", + "prediction.\" [Another interesting read](https://arxiv.org/abs/1701.00160)" + ] + }, + { + "cell_type": "markdown", + "id": "2fee38bd", + "metadata": { + "editable": true + }, + "source": [ + "## Writing Our First Generative Adversarial Network\n", + "Let us now move on to actually implementing a GAN in tensorflow. We will study\n", + "the performance of our GAN on the MNIST dataset. This code is based on and\n", + "adapted from the\n", + "[google tutorial](https://www.tensorflow.org/tutorials/generative/dcgan)\n", + "\n", + "First we import our libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "004a0b53", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "import os\n", + "import time\n", + "import numpy as np\n", + "import tensorflow as tf\n", + "import matplotlib.pyplot as plt\n", + "from tensorflow.keras import layers\n", + "from tensorflow.keras.utils import plot_model" + ] + }, + { + "cell_type": "markdown", + "id": "353af161", + "metadata": { + "editable": true + }, + "source": [ + "Next we define our hyperparameters and import our data the usual way" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "8cbaf16a", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "BUFFER_SIZE = 60000\n", + "BATCH_SIZE = 256\n", + "EPOCHS = 30\n", + "\n", + "data = tf.keras.datasets.mnist.load_data()\n", + "(train_images, train_labels), (test_images, test_labels) = data\n", + "train_images = np.reshape(train_images, (train_images.shape[0],\n", + " 28,\n", + " 28,\n", + " 1)).astype('float32')\n", + "\n", + "# we normalize between -1 and 1\n", + "train_images = (train_images - 127.5) / 127.5\n", + "training_dataset = tf.data.Dataset.from_tensor_slices(\n", + " train_images).shuffle(BUFFER_SIZE).batch(BATCH_SIZE)" + ] + }, + { + "cell_type": "markdown", + "id": "822b8cc7", + "metadata": { + "editable": true + }, + "source": [ + "### MNIST and GANs\n", + "\n", + "Let's have a quick look" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "52b5965c", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "plt.imshow(train_images[0], cmap='Greys')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "21c5199c", + "metadata": { + "editable": true + }, + "source": [ + "Now we define our two models. This is where the 'magic' happens. There are a\n", + "huge amount of possible formulations for both models. A lot of engineering and\n", + "trial and error can be done here to try to produce better performing models. For\n", + "more advanced GANs this is by far the step where you can 'make or break' a\n", + "model.\n", + "\n", + "We start with the generator. As stated in the introductory text the generator\n", + "$g$ upsamples from a random sample to the shape of what we want to predict. In\n", + "our case we are trying to predict MNIST images ($28\\times 28$ pixels)." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "356759c7", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def generator_model():\n", + " \"\"\"\n", + " The generator uses upsampling layers tf.keras.layers.Conv2DTranspose() to\n", + " produce an image from a random seed. We start with a Dense layer taking this\n", + " random sample as an input and subsequently upsample through multiple\n", + " convolutional layers.\n", + " \"\"\"\n", + "\n", + " # we define our model\n", + " model = tf.keras.Sequential()\n", + "\n", + "\n", + " # adding our input layer. Dense means that every neuron is connected and\n", + " # the input shape is the shape of our random noise. The units need to match\n", + " # in some sense the upsampling strides to reach our desired output shape.\n", + " # we are using 100 random numbers as our seed\n", + " model.add(layers.Dense(units=7*7*BATCH_SIZE,\n", + " use_bias=False,\n", + " input_shape=(100, )))\n", + " # we normalize the output form the Dense layer\n", + " model.add(layers.BatchNormalization())\n", + " # and add an activation function to our 'layer'. LeakyReLU avoids vanishing\n", + " # gradient problem\n", + " model.add(layers.LeakyReLU())\n", + " model.add(layers.Reshape((7, 7, BATCH_SIZE)))\n", + " assert model.output_shape == (None, 7, 7, BATCH_SIZE)\n", + " # even though we just added four keras layers we think of everything above\n", + " # as 'one' layer\n", + "\n", + " # next we add our upscaling convolutional layers\n", + " model.add(layers.Conv2DTranspose(filters=128,\n", + " kernel_size=(5, 5),\n", + " strides=(1, 1),\n", + " padding='same',\n", + " use_bias=False))\n", + " model.add(layers.BatchNormalization())\n", + " model.add(layers.LeakyReLU())\n", + " assert model.output_shape == (None, 7, 7, 128)\n", + "\n", + " model.add(layers.Conv2DTranspose(filters=64,\n", + " kernel_size=(5, 5),\n", + " strides=(2, 2),\n", + " padding='same',\n", + " use_bias=False))\n", + " model.add(layers.BatchNormalization())\n", + " model.add(layers.LeakyReLU())\n", + " assert model.output_shape == (None, 14, 14, 64)\n", + "\n", + " model.add(layers.Conv2DTranspose(filters=1,\n", + " kernel_size=(5, 5),\n", + " strides=(2, 2),\n", + " padding='same',\n", + " use_bias=False,\n", + " activation='tanh'))\n", + " assert model.output_shape == (None, 28, 28, 1)\n", + "\n", + " return model" + ] + }, + { + "cell_type": "markdown", + "id": "854bcd6b", + "metadata": { + "editable": true + }, + "source": [ + "And there we have our 'simple' generator model. Now we move on to defining our\n", + "discriminator model $d$, which is a convolutional neural network based image\n", + "classifier." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "41473304", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def discriminator_model():\n", + " \"\"\"\n", + " The discriminator is a convolutional neural network based image classifier\n", + " \"\"\"\n", + "\n", + " # we define our model\n", + " model = tf.keras.Sequential()\n", + " model.add(layers.Conv2D(filters=64,\n", + " kernel_size=(5, 5),\n", + " strides=(2, 2),\n", + " padding='same',\n", + " input_shape=[28, 28, 1]))\n", + " model.add(layers.LeakyReLU())\n", + " # adding a dropout layer as you do in conv-nets\n", + " model.add(layers.Dropout(0.3))\n", + "\n", + "\n", + " model.add(layers.Conv2D(filters=128,\n", + " kernel_size=(5, 5),\n", + " strides=(2, 2),\n", + " padding='same'))\n", + " model.add(layers.LeakyReLU())\n", + " # adding a dropout layer as you do in conv-nets\n", + " model.add(layers.Dropout(0.3))\n", + "\n", + " model.add(layers.Flatten())\n", + " model.add(layers.Dense(1))\n", + "\n", + " return model" + ] + }, + { + "cell_type": "markdown", + "id": "353af567", + "metadata": { + "editable": true + }, + "source": [ + "Let us take a look at our models." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "f899d4e3", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "generator = generator_model()\n", + "plot_model(generator, show_shapes=True, rankdir='LR')" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "87ef384b", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "discriminator = discriminator_model()\n", + "plot_model(discriminator, show_shapes=True, rankdir='LR')" + ] + }, + { + "cell_type": "markdown", + "id": "b2bef82d", + "metadata": { + "editable": true + }, + "source": [ + "Next we need a few helper objects we will use in training" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "e397847a", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "cross_entropy = tf.keras.losses.BinaryCrossentropy(from_logits=True)\n", + "generator_optimizer = tf.keras.optimizers.Adam(1e-4)\n", + "discriminator_optimizer = tf.keras.optimizers.Adam(1e-4)" + ] + }, + { + "cell_type": "markdown", + "id": "db3396cc", + "metadata": { + "editable": true + }, + "source": [ + "The first object, *cross_entropy* is our loss function and the two others are\n", + "our optimizers. Notice we use the same learning rate for both $g$ and $d$. This\n", + "is because they need to improve their accuracy at approximately equal speeds to\n", + "get convergence (not necessarily exactly equal). Now we define our loss\n", + "functions" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "931eaced", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def generator_loss(fake_output):\n", + " loss = cross_entropy(tf.ones_like(fake_output), fake_output)\n", + "\n", + " return loss" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "0c4a44bb", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def discriminator_loss(real_output, fake_output):\n", + " real_loss = cross_entropy(tf.ones_like(real_output), real_output)\n", + " fake_loss = cross_entropy(tf.zeros_liks(fake_output), fake_output)\n", + " total_loss = real_loss + fake_loss\n", + "\n", + " return total_loss" + ] + }, + { + "cell_type": "markdown", + "id": "fcf8f066", + "metadata": { + "editable": true + }, + "source": [ + "Next we define a kind of seed to help us compare the learning process over\n", + "multiple training epochs." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "eea2bbee", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "noise_dimension = 100\n", + "n_examples_to_generate = 16\n", + "seed_images = tf.random.normal([n_examples_to_generate, noise_dimension])" + ] + }, + { + "cell_type": "markdown", + "id": "94a6e341", + "metadata": { + "editable": true + }, + "source": [ + "Now we have everything we need to define our training step, which we will apply\n", + "for every step in our training loop. Notice the @tf.function flag signifying\n", + "that the function is tensorflow 'compiled'. Removing this flag doubles the\n", + "computation time." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "8d48470b", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "@tf.function\n", + "def train_step(images):\n", + " noise = tf.random.normal([BATCH_SIZE, noise_dimension])\n", + "\n", + " with tf.GradientTape() as gen_tape, tf.GradientTape() as disc_tape:\n", + " generated_images = generator(noise, training=True)\n", + "\n", + " real_output = discriminator(images, training=True)\n", + " fake_output = discriminator(generated_images, training=True)\n", + "\n", + " gen_loss = generator_loss(fake_output)\n", + " disc_loss = discriminator_loss(real_output, fake_output)\n", + "\n", + " gradients_of_generator = gen_tape.gradient(gen_loss,\n", + " generator.trainable_variables)\n", + " gradients_of_discriminator = disc_tape.gradient(disc_loss,\n", + " discriminator.trainable_variables)\n", + " generator_optimizer.apply_gradients(zip(gradients_of_generator,\n", + " generator.trainable_variables))\n", + " discriminator_optimizer.apply_gradients(zip(gradients_of_discriminator,\n", + " discriminator.trainable_variables))\n", + "\n", + " return gen_loss, disc_loss" + ] + }, + { + "cell_type": "markdown", + "id": "62015b88", + "metadata": { + "editable": true + }, + "source": [ + "Next we define a helper function to produce an output over our training epochs\n", + "to see the predictive progression of our generator model. **Note**: I am including\n", + "this code here, but comment it out in the training loop." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "b189ed96", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def generate_and_save_images(model, epoch, test_input):\n", + " # we're making inferences here\n", + " predictions = model(test_input, training=False)\n", + "\n", + " fig = plt.figure(figsize=(4, 4))\n", + "\n", + " for i in range(predictions.shape[0]):\n", + " plt.subplot(4, 4, i+1)\n", + " plt.imshow(predictions[i, :, :, 0] * 127.5 + 127.5, cmap='gray')\n", + " plt.axis('off')\n", + "\n", + " plt.savefig(f'./images_from_seed_images/image_at_epoch_{str(epoch).zfill(3)}.png')\n", + " plt.close()\n", + " #plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "ba2c82d5", + "metadata": { + "editable": true + }, + "source": [ + "Setting up checkpoints to periodically save our model during training so that\n", + "everything is not lost even if the program were to somehow terminate while\n", + "training." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "a0e2fc8a", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# Setting up checkpoints to save model during training\n", + "checkpoint_dir = './training_checkpoints'\n", + "checkpoint_prefix = os.path.join(checkpoint_dir, 'ckpt')\n", + "checkpoint = tf.train.Checkpoint(generator_optimizer=generator_optimizer,\n", + " discriminator_optimizer=discriminator_optimizer,\n", + " generator=generator,\n", + " discriminator=discriminator)" + ] + }, + { + "cell_type": "markdown", + "id": "4d93a0f7", + "metadata": { + "editable": true + }, + "source": [ + "Now we define our training loop" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "a1275556", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def train(dataset, epochs):\n", + " generator_loss_list = []\n", + " discriminator_loss_list = []\n", + "\n", + " for epoch in range(epochs):\n", + " start = time.time()\n", + "\n", + " for image_batch in dataset:\n", + " gen_loss, disc_loss = train_step(image_batch)\n", + " generator_loss_list.append(gen_loss.numpy())\n", + " discriminator_loss_list.append(disc_loss.numpy())\n", + "\n", + " #generate_and_save_images(generator, epoch + 1, seed_images)\n", + "\n", + " if (epoch + 1) % 15 == 0:\n", + " checkpoint.save(file_prefix=checkpoint_prefix)\n", + "\n", + " print(f'Time for epoch {epoch} is {time.time() - start}')\n", + "\n", + " #generate_and_save_images(generator, epochs, seed_images)\n", + "\n", + " loss_file = './data/lossfile.txt'\n", + " with open(loss_file, 'w') as outfile:\n", + " outfile.write(str(generator_loss_list))\n", + " outfile.write('\\n')\n", + " outfile.write('\\n')\n", + " outfile.write(str(discriminator_loss_list))\n", + " outfile.write('\\n')\n", + " outfile.write('\\n')" + ] + }, + { + "cell_type": "markdown", + "id": "6ff3a75a", + "metadata": { + "editable": true + }, + "source": [ + "To train simply call this function. **Warning**: this might take a long time so\n", + "there is a folder of a pretrained network already included in the repository." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "371ed41a", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "train(train_dataset, EPOCHS)" + ] + }, + { + "cell_type": "markdown", + "id": "654399f1", + "metadata": { + "editable": true + }, + "source": [ + "Now to avoid having to train and everything, which will take a while depending\n", + "on your computer setup we now load in the model which produced the above gif." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "dec4b560", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "checkpoint.restore(tf.train.latest_checkpoint(checkpoint_dir))\n", + "restored_generator = checkpoint.generator\n", + "restored_discriminator = checkpoint.discriminator\n", + "\n", + "print(restored_generator)\n", + "print(restored_discriminator)" + ] + }, + { + "cell_type": "markdown", + "id": "296bfa5c", + "metadata": { + "editable": true + }, + "source": [ + "We have successfully loaded in our latest model. Let us now play around a bit\n", + "and see what kind of things we can learn about this model. Our generator takes\n", + "an array of 100 numbers. One idea can be to try to systematically change our\n", + "input. Let us try and see what we get" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "eecfbb1f", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def generate_latent_points(number=100, scale_means=1, scale_stds=1):\n", + " latent_dim = 100\n", + " means = scale_means * tf.linspace(-1, 1, num=latent_dim)\n", + " stds = scale_stds * tf.linspace(-1, 1, num=latent_dim)\n", + " latent_space_value_range = tf.random.normal([number, latent_dim],\n", + " means,\n", + " stds,\n", + " dtype=tf.float64)\n", + "\n", + " return latent_space_value_range\n", + "\n", + "def generate_images(latent_points):\n", + " # notice we set training to false because we are making inferences\n", + " generated_images = restored_generator.predict(latent_points)\n", + "\n", + " return generated_images" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "333a593d", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def plot_result(generated_images, number=100):\n", + " # obviously this assumes sqrt number is an int\n", + " fig, axs = plt.subplots(int(np.sqrt(number)), int(np.sqrt(number)),\n", + " figsize=(10, 10))\n", + "\n", + " for i in range(int(np.sqrt(number))):\n", + " for j in range(int(np.sqrt(number))):\n", + " axs[i, j].imshow(generated_images[i*j], cmap='Greys')\n", + " axs[i, j].axis('off')\n", + "\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "2f5f0154", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "generated_images = generate_images(generate_latent_points())\n", + "plot_result(generated_images)" + ] + }, + { + "cell_type": "markdown", + "id": "ff581bf2", + "metadata": { + "editable": true + }, + "source": [ + "We see that the generator generates images that look like MNIST\n", + "numbers: $1, 4, 7, 9$. Let's try to tweak it a bit more to see if we are able\n", + "to generate a similar plot where we generate every MNIST number. Let us now try\n", + "to 'move' a bit around in the latent space. **Note**: decrease the plot number if\n", + "these following cells take too long to run on your computer." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "d3617ad8", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "plot_number = 225\n", + "\n", + "generated_images = generate_images(generate_latent_points(number=plot_number,\n", + " scale_means=5,\n", + " scale_stds=1))\n", + "plot_result(generated_images, number=plot_number)\n", + "\n", + "generated_images = generate_images(generate_latent_points(number=plot_number,\n", + " scale_means=-5,\n", + " scale_stds=1))\n", + "plot_result(generated_images, number=plot_number)\n", + "\n", + "generated_images = generate_images(generate_latent_points(number=plot_number,\n", + " scale_means=1,\n", + " scale_stds=5))\n", + "plot_result(generated_images, number=plot_number)" + ] + }, + { + "cell_type": "markdown", + "id": "1a074f93", + "metadata": { + "editable": true + }, + "source": [ + "Again, we have found something interesting. *Moving* around using our means\n", + "takes us from digit to digit, while *moving* around using our standard\n", + "deviations seem to increase the number of different digits! In the last image\n", + "above, we can barely make out every MNIST digit. Let us make on last plot using\n", + "this information by upping the standard deviation of our Gaussian noises." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "4ef8937d", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "plot_number = 400\n", + "generated_images = generate_images(generate_latent_points(number=plot_number,\n", + " scale_means=1,\n", + " scale_stds=10))\n", + "plot_result(generated_images, number=plot_number)" + ] + }, + { + "cell_type": "markdown", + "id": "385a2d0a", + "metadata": { + "editable": true + }, + "source": [ + "A pretty cool result! We see that our generator indeed has learned a\n", + "distribution which qualitatively looks a whole lot like the MNIST dataset.\n", + "\n", + "Another interesting way to explore the latent space of our generator model is by\n", + "interpolating between the MNIST digits. This section is largely based on\n", + "[this excellent blogpost](https://machinelearningmastery.com/how-to-interpolate-and-perform-vector-arithmetic-with-faces-using-a-generative-adversarial-network/)\n", + "by Jason Brownlee.\n", + "\n", + "So let us start by defining a function to interpolate between two points in the\n", + "latent space." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "57de87b8", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def interpolation(point_1, point_2, n_steps=10):\n", + " ratios = np.linspace(0, 1, num=n_steps)\n", + " vectors = []\n", + " for i, ratio in enumerate(ratios):\n", + " vectors.append(((1.0 - ratio) * point_1 + ratio * point_2))\n", + "\n", + " return tf.stack(vectors)" + ] + }, + { + "cell_type": "markdown", + "id": "cfb76bb6", + "metadata": { + "editable": true + }, + "source": [ + "Now we have all we need to do our interpolation analysis." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "e25decef", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "plot_number = 100\n", + "latent_points = generate_latent_points(number=plot_number)\n", + "results = None\n", + "for i in range(0, 2*np.sqrt(plot_number), 2):\n", + " interpolated = interpolation(latent_points[i], latent_points[i+1])\n", + " generated_images = generate_images(interpolated)\n", + "\n", + " if results is None:\n", + " results = generated_images\n", + " else:\n", + " results = tf.stack((results, generated_images))\n", + "\n", + "plot_results(results, plot_number)" + ] + } + ], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/doc/LectureNotes/_build/html/_sources/chapteroptimization.ipynb b/doc/LectureNotes/_build/html/_sources/chapteroptimization.ipynb index e8dc9fc17..5d83c5b50 100644 --- a/doc/LectureNotes/_build/html/_sources/chapteroptimization.ipynb +++ b/doc/LectureNotes/_build/html/_sources/chapteroptimization.ipynb @@ -2,7 +2,21 @@ "cells": [ { "cell_type": "markdown", - "metadata": {}, + "id": "4d72e1df", + "metadata": { + "editable": true + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "id": "fb6e8fcd", + "metadata": { + "editable": true + }, "source": [ "# Optimization, the central part of any Machine Learning algortithm\n", "\n", @@ -15,9 +29,6 @@ "analytically, however this is not possible in general and we must use\n", "some approximative/numerical method to compute the minimum.\n", "\n", - "\n", - "\n", - "\n", "In our discussion on Logistic Regression we studied the \n", "case of\n", "two classes, with $y_i$ either\n", @@ -28,7 +39,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a507b82a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -40,12 +54,13 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "4071429e", + "metadata": { + "editable": true + }, "source": [ "where $\\boldsymbol{\\beta}$ are the weights we wish to extract from data, in our case $\\beta_0$ and $\\beta_1$. \n", "\n", - "\n", - "\n", "Our compact equations used a definition of a vector $\\boldsymbol{y}$ with $n$\n", "elements $y_i$, an $n\\times p$ matrix $\\boldsymbol{X}$ which contains the\n", "$x_i$ values and a vector $\\boldsymbol{p}$ of fitted probabilities\n", @@ -55,7 +70,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a3cca0b2", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = -\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{p}\\right).\n", @@ -64,7 +82,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "12a4ad28", + "metadata": { + "editable": true + }, "source": [ "If we in addition define a diagonal matrix $\\boldsymbol{W}$ with elements \n", "$p(y_i\\vert x_i,\\boldsymbol{\\beta})(1-p(y_i\\vert x_i,\\boldsymbol{\\beta})$, we can obtain a compact expression of the second derivative as" @@ -72,7 +93,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "5d6e7796", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T} = \\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X}.\n", @@ -81,12 +105,13 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b324ae78", + "metadata": { + "editable": true + }, "source": [ "This defines what is called the Hessian matrix.\n", "\n", - "\n", - "\n", "If we can set up these equations, Newton-Raphson's iterative method is normally the method of choice. It requires however that we can compute in an efficient way the matrices that define the first and second derivatives. \n", "\n", "Our iterative scheme is then given by" @@ -94,7 +119,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "7c39cc3f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\right)^{-1}_{\\boldsymbol{\\beta}^{\\mathrm{old}}}\\times \\left(\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}}\\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}},\n", @@ -103,14 +131,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "10749f5d", + "metadata": { + "editable": true + }, "source": [ "or in matrix form as" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "3ec50136", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X} \\right)^{-1}\\times \\left(-\\boldsymbol{X}^T(\\boldsymbol{y}-\\boldsymbol{p}) \\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}}.\n", @@ -119,13 +153,15 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "0145d9eb", + "metadata": { + "editable": true + }, "source": [ "The right-hand side is computed with the old values of $\\beta$. \n", "\n", "If we can compute these matrices, in particular the Hessian, the above is often the easiest method to implement. \n", "\n", - "\n", "Let us quickly remind ourselves how we derive the above method.\n", "\n", "Perhaps the most celebrated of all one-dimensional root-finding\n", @@ -136,8 +172,6 @@ "numerically and/or your function is not of the smooth type, we\n", "normally discourage the use of this method.\n", "\n", - "\n", - "\n", "The Newton-Raphson formula consists geometrically of extending the\n", "tangent line at a current point until it crosses zero, then setting\n", "the next guess to the abscissa of that zero-crossing. The mathematics\n", @@ -147,7 +181,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "43c17534", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -160,7 +197,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "32ef04f0", + "metadata": { + "editable": true + }, "source": [ "For small enough values of the function and for well-behaved\n", "functions, the terms beyond linear are unimportant, hence we obtain" @@ -168,7 +208,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6700017c", + "metadata": { + "editable": true + }, "source": [ "$$\n", "f(x)+(s-x)f'(x)\\approx 0,\n", @@ -177,14 +220,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "8791dec4", + "metadata": { + "editable": true + }, "source": [ "yielding" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "69008872", + "metadata": { + "editable": true + }, "source": [ "$$\n", "s\\approx x-\\frac{f(x)}{f'(x)}.\n", @@ -193,14 +242,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "fce4ef1f", + "metadata": { + "editable": true + }, "source": [ "Having in mind an iterative procedure, it is natural to start iterating with" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "e64aef7e", + "metadata": { + "editable": true + }, "source": [ "$$\n", "x_{n+1}=x_n-\\frac{f(x_n)}{f'(x_n)}.\n", @@ -209,7 +264,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9acecc44", + "metadata": { + "editable": true + }, "source": [ "The above is Newton-Raphson's method. It has a simple geometric\n", "interpretation, namely $x_{n+1}$ is the point where the tangent from\n", @@ -223,16 +281,16 @@ "guess near such a local extremum, so that the first derivative nearly\n", "vanishes, then Newton-Raphson may fail totally\n", "\n", - "\n", - "\n", - "\n", "Newton's method can be generalized to systems of several non-linear equations\n", "and variables. Consider the case with two equations" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "18bc9fd6", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{array}{cc} f_1(x_1,x_2) &=0\\\\\n", @@ -242,14 +300,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "7dcad370", + "metadata": { + "editable": true + }, "source": [ "which we Taylor expand to obtain" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "f1724121", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&f_1(x_1,x_2)+h_1\n", @@ -264,14 +328,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d04bfa9f", + "metadata": { + "editable": true + }, "source": [ "Defining the Jacobian matrix $\\boldsymbol{J}$ we have" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "a4d3a9e3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{J}=\\left( \\begin{array}{cc}\n", @@ -283,14 +353,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d9d6ff69", + "metadata": { + "editable": true + }, "source": [ "we can rephrase Newton's method as" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "362a86a3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\left(\\begin{array}{c} x_1^{n+1} \\\\ x_2^{n+1} \\end{array} \\right)=\n", @@ -301,14 +377,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "4b8c2937", + "metadata": { + "editable": true + }, "source": [ "where we have defined" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "7580aa9a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\left(\\begin{array}{c} h_1^{n} \\\\ h_2^{n} \\end{array} \\right)=\n", @@ -319,18 +401,26 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a2e3adc3", + "metadata": { + "editable": true + }, "source": [ "We need thus to compute the inverse of the Jacobian matrix and it\n", "is to understand that difficulties may\n", "arise in case $\\boldsymbol{J}$ is nearly singular.\n", "\n", "It is rather straightforward to extend the above scheme to systems of\n", - "more than two non-linear equations. In our case, the Jacobian matrix is given by the Hessian that represents the second derivative of cost function. \n", - "\n", - "\n", - "\n", - "\n", + "more than two non-linear equations. In our case, the Jacobian matrix is given by the Hessian that represents the second derivative of cost function." + ] + }, + { + "cell_type": "markdown", + "id": "83a585c9", + "metadata": { + "editable": true + }, + "source": [ "## Steepest descent\n", "\n", "The basic idea of gradient descent is\n", @@ -343,7 +433,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e127ea11", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k),\n", @@ -352,7 +445,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "bce435bc", + "metadata": { + "editable": true + }, "source": [ "with $\\gamma_k > 0$.\n", "\n", @@ -360,7 +456,6 @@ "F(\\mathbf{x}_k)$. This means that for a sufficiently small $\\gamma_k$\n", "we are always moving towards smaller function values, i.e a minimum.\n", "\n", - "\n", "The previous observation is the basis of the method of steepest\n", "descent, which is also referred to as just gradient descent (GD). One\n", "starts with an initial guess $\\mathbf{x}_0$ for a minimum of $F$ and\n", @@ -369,7 +464,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "2691da5f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k), \\ \\ k \\geq 0.\n", @@ -378,12 +476,14 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e7ae7322", + "metadata": { + "editable": true + }, "source": [ "The parameter $\\gamma_k$ is often referred to as the step length or\n", "the learning rate within the context of Machine Learning.\n", "\n", - "\n", "Ideally the sequence $\\{\\mathbf{x}_k \\}_{k=0}$ converges to a global\n", "minimum of the function $F$. In general we do not know if we are in a\n", "global or local minimum. In the special case when $F$ is a convex\n", @@ -402,9 +502,6 @@ "Note that the gradient is a function of $\\mathbf{x} =\n", "(x_1,\\cdots,x_n)$ which makes it expensive to compute numerically.\n", "\n", - "\n", - "\n", - "\n", "The gradient descent method \n", "is sensitive to the choice of learning rate $\\gamma_k$. This is due\n", "to the fact that we are only guaranteed that $F(\\mathbf{x}_{k+1}) \\leq\n", @@ -415,10 +512,16 @@ "\n", "Many of these shortcomings can be alleviated by introducing\n", "randomness. One such method is that of Stochastic Gradient Descent\n", - "(SGD), see below.\n", - "\n", - "\n", - "\n", + "(SGD), see below." + ] + }, + { + "cell_type": "markdown", + "id": "a6a44ea7", + "metadata": { + "editable": true + }, + "source": [ "## Convex functions\n", "\n", "Ideally we want our cost/loss function to be convex(concave).\n", @@ -433,11 +536,8 @@ "$\\mathbb{R}$. Examples of convex sets of $\\mathbb{R}^2$ are the\n", "regular polygons (triangles, rectangles, pentagons, etc...).\n", "\n", - "\n", - "\n", "**Convex function**: Let $X \\subset \\mathbb{R}^n$ be a convex set. Assume that the function $f: X \\rightarrow \\mathbb{R}$ is continuous, then $f$ is said to be convex if $$f(tx_1 + (1-t)x_2) \\leq tf(x_1) + (1-t)f(x_2) $$ for all $x_1, x_2 \\in X$ and for all $t \\in [0,1]$. If $\\leq$ is replaced with a strict inequaltiy in the definition, we demand $x_1 \\neq x_2$ and $t\\in(0,1)$ then $f$ is said to be strictly convex. For a single variable function, convexity means that if you draw a straight line connecting $f(x_1)$ and $f(x_2)$, the value of the function on the interval $[x_1,x_2]$ is always below the line as illustrated below.\n", "\n", - "\n", "In the following we state first and second-order conditions which\n", "ensures convexity of a function $f$. We write $D_f$ to denote the\n", "domain of $f$, i.e the subset of $R^n$ where $f$ is defined. For more\n", @@ -454,8 +554,6 @@ "make a drawing of $f(x) = x^2+1$ and draw the tangent line to $f(x)$ and\n", "note that it is always below the graph.\n", "\n", - "\n", - "\n", "**Second order condition.**\n", "\n", "Assume that $f$ is twice\n", @@ -465,12 +563,8 @@ "single-variable function this reduces to $f''(x) \\geq 0$. Geometrically this means that $f$ has nonnegative curvature\n", "everywhere.\n", "\n", - "\n", - "\n", "This condition is particularly useful since it gives us an procedure for determining if the function under consideration is convex, apart from using the definition.\n", "\n", - "\n", - "\n", "The next result is of great importance to us and the reason why we are\n", "going on about convex functions. In machine learning we frequently\n", "have to minimize a loss/cost function in order to find the best\n", @@ -487,11 +581,16 @@ "is minimal, where $f$ is convex and differentiable. Then, any point\n", "$x^*$ that satisfies $\\nabla f(x^*) = 0$ is a global minimum.\n", "\n", - "\n", - "\n", - "This result means that if we know that the cost/loss function is convex and we are able to find a minimum, we are guaranteed that it is a global minimum.\n", - "\n", - "\n", + "This result means that if we know that the cost/loss function is convex and we are able to find a minimum, we are guaranteed that it is a global minimum." + ] + }, + { + "cell_type": "markdown", + "id": "809f8f01", + "metadata": { + "editable": true + }, + "source": [ "### Some simple problems\n", "\n", "1. Show that $f(x)=x^2$ is convex for $x \\in \\mathbb{R}$ using the definition of convexity. Hint: If you re-write the definition, $f$ is convex if the following holds for all $x,y \\in D_f$ and any $\\lambda \\in [0,1]$ $\\lambda f(x)+(1-\\lambda)f(y)-f(\\lambda x + (1-\\lambda) y ) \\geq 0$.\n", @@ -502,7 +601,6 @@ "\n", " * $g(x) = -\\ln(x)$ is convex for $x \\in (0,\\infty)$.\n", "\n", - "\n", "3. Let $f(x) = x^2$ and $g(x) = e^x$. Show that $f(g(x))$ and $g(f(x))$ is convex for $x \\in \\mathbb{R}$. Also show that if $f(x)$ is any convex function than $h(x) = e^{f(x)}$ is convex.\n", "\n", "4. A norm is any function that satisfy the following properties\n", @@ -513,13 +611,18 @@ "\n", " * $f(x) \\leq 0$ for all $x \\in \\mathbb{R}^n$ with equality if and only if $x = 0$\n", "\n", - "\n", - "Using the definition of convexity, try to show that a function satisfying the properties above is convex (the third condition is not needed to show this).\n", - "\n", - "\n", + "Using the definition of convexity, try to show that a function satisfying the properties above is convex (the third condition is not needed to show this)." + ] + }, + { + "cell_type": "markdown", + "id": "f3b91277", + "metadata": { + "editable": true + }, + "source": [ "## Standard steepest descent\n", "\n", - "\n", "Before we proceed, we would like to discuss the approach called the\n", "**standard Steepest descent** (different from the above steepest descent discussion), which again leads to us having to be able\n", "to compute a matrix. It belongs to the class of Conjugate Gradient methods (CG).\n", @@ -533,7 +636,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ec752109", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{x} = \\boldsymbol{b}.\n", @@ -542,14 +648,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "eb64c8e7", + "metadata": { + "editable": true + }, "source": [ "In the iterative process we end up with a problem like" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "7e99eb7f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{r}= \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x},\n", @@ -558,20 +670,24 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "3a3f6414", + "metadata": { + "editable": true + }, "source": [ "where $\\boldsymbol{r}$ is the so-called residual or error in the iterative process.\n", "\n", "When we have found the exact solution, $\\boldsymbol{r}=0$.\n", "\n", - "\n", - "\n", "The residual is zero when we reach the minimum of the quadratic equation" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "a88175a4", + "metadata": { + "editable": true + }, "source": [ "$$\n", "P(\\boldsymbol{x})=\\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T\\boldsymbol{b},\n", @@ -580,19 +696,24 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6992cc4f", + "metadata": { + "editable": true + }, "source": [ "with the constraint that the matrix $\\boldsymbol{A}$ is positive definite and\n", "symmetric. This defines also the Hessian and we want it to be positive definite. \n", "\n", - "\n", "We denote the initial guess for $\\boldsymbol{x}$ as $\\boldsymbol{x}_0$. \n", "We can assume without loss of generality that" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "00e22e2b", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{x}_0=0,\n", @@ -601,14 +722,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "faab896d", + "metadata": { + "editable": true + }, "source": [ "or consider the system" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "02cb8061", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n", @@ -617,17 +744,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "fe52c448", + "metadata": { + "editable": true + }, "source": [ "instead.\n", "\n", - "\n", "One can show that the solution $\\boldsymbol{x}$ is also the unique minimizer of the quadratic form" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "f698b7fe", + "metadata": { + "editable": true + }, "source": [ "$$\n", "f(\\boldsymbol{x}) = \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T \\boldsymbol{x} , \\quad \\boldsymbol{x}\\in\\mathbf{R}^n.\n", @@ -636,7 +768,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "022bda7f", + "metadata": { + "editable": true + }, "source": [ "This suggests taking the first basis vector $\\boldsymbol{r}_1$ (see below for definition) \n", "to be the gradient of $f$ at $\\boldsymbol{x}=\\boldsymbol{x}_0$, \n", @@ -645,7 +780,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b64077bc", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n", @@ -654,18 +792,23 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "dec06904", + "metadata": { + "editable": true + }, "source": [ "and \n", "$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$.\n", "\n", - "\n", "We can compute the residual iteratively as" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "b566de75", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n", @@ -674,14 +817,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "2c2d16e7", + "metadata": { + "editable": true + }, "source": [ "which equals" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "6c97f03d", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_k),\n", @@ -690,14 +839,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "2b40818b", + "metadata": { + "editable": true + }, "source": [ "or" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "6619d064", + "metadata": { + "editable": true + }, "source": [ "$$\n", "(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{r}_k,\n", @@ -706,14 +861,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "467c71be", + "metadata": { + "editable": true + }, "source": [ "which gives" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "d58fd1af", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\alpha_k = \\frac{\\boldsymbol{r}_k^T\\boldsymbol{r}_k}{\\boldsymbol{r}_k^T\\boldsymbol{A}\\boldsymbol{r}_k}\n", @@ -722,14 +883,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "38e32957", + "metadata": { + "editable": true + }, "source": [ "leading to the iterative scheme" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "98043fd6", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{x}_{k+1}=\\boldsymbol{x}_k-\\alpha_k\\boldsymbol{r}_{k},\n", @@ -738,7 +905,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 1, + "id": "8c7efe84", "metadata": { "collapsed": false, "editable": true @@ -771,14 +939,18 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "3bdeb3c1", + "metadata": { + "editable": true + }, "source": [ "And then as countor plot" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 2, + "id": "e6e460db", "metadata": { "collapsed": false, "editable": true @@ -792,14 +964,18 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d165add7", + "metadata": { + "editable": true + }, "source": [ "Find guesses" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, + "id": "236615ae", "metadata": { "collapsed": false, "editable": true @@ -812,14 +988,18 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "4b90442c", + "metadata": { + "editable": true + }, "source": [ "Run it!" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, + "id": "0346fd1d", "metadata": { "collapsed": false, "editable": true @@ -837,14 +1017,18 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ecff8b5b", + "metadata": { + "editable": true + }, "source": [ "What happened?" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, + "id": "0d9b7732", "metadata": { "collapsed": false, "editable": true @@ -859,7 +1043,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b0f8920b", + "metadata": { + "editable": true + }, "source": [ "## Conjugate gradient method\n", "In the CG method we define so-called conjugate directions and two vectors \n", @@ -870,7 +1057,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "67b215c6", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{s}^T\\boldsymbol{A}\\boldsymbol{t}= 0.\n", @@ -879,7 +1069,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "efc1c192", + "metadata": { + "editable": true + }, "source": [ "The philosophy of the CG method is to perform searches in various conjugate directions\n", "of our vectors $\\boldsymbol{x}_i$ obeying the above criterion, namely" @@ -887,7 +1080,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "eb4e1832", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{x}_i^T\\boldsymbol{A}\\boldsymbol{x}_j= 0.\n", @@ -896,7 +1092,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "775cf999", + "metadata": { + "editable": true + }, "source": [ "Two vectors are conjugate if they are orthogonal with respect to \n", "this inner product. Being conjugate is a symmetric relation: if $\\boldsymbol{s}$ is conjugate to $\\boldsymbol{t}$, then $\\boldsymbol{t}$ is conjugate to $\\boldsymbol{s}$.\n", @@ -906,7 +1105,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "95893950", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{v}_i^T\\boldsymbol{A}\\boldsymbol{v}_j= \\lambda\\boldsymbol{v}_i^T\\boldsymbol{v}_j,\n", @@ -915,7 +1117,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "16bfad5c", + "metadata": { + "editable": true + }, "source": [ "which is zero unless $i=j$. \n", "\n", @@ -925,7 +1130,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e2577f1c", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{x}_{i+1}=\\boldsymbol{x}_{i}+\\alpha_i\\boldsymbol{p}_{i}.\n", @@ -934,7 +1142,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e4defaaf", + "metadata": { + "editable": true + }, "source": [ "We assume that $\\boldsymbol{p}_{i}$ is a sequence of $n$ mutually conjugate directions. \n", "Then the $\\boldsymbol{p}_{i}$ form a basis of $R^n$ and we can expand the solution \n", @@ -943,7 +1154,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b4632612", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{x} = \\sum^{n}_{i=1} \\alpha_i \\boldsymbol{p}_i.\n", @@ -952,14 +1166,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a0a06bf2", + "metadata": { + "editable": true + }, "source": [ "The coefficients are given by" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "1db7cc6a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathbf{A}\\mathbf{x} = \\sum^{n}_{i=1} \\alpha_i \\mathbf{A} \\mathbf{p}_i = \\mathbf{b}.\n", @@ -968,14 +1188,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e7aa5384", + "metadata": { + "editable": true + }, "source": [ "Multiplying with $\\boldsymbol{p}_k^T$ from the left gives" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "884580b0", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{x} = \\sum^{n}_{i=1} \\alpha_i\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{p}_i= \\boldsymbol{p}_k^T \\boldsymbol{b},\n", @@ -984,14 +1210,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "934990e4", + "metadata": { + "editable": true + }, "source": [ "and we can define the coefficients $\\alpha_k$ as" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "8be96384", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\alpha_k = \\frac{\\boldsymbol{p}_k^T \\boldsymbol{b}}{\\boldsymbol{p}_k^T \\boldsymbol{A} \\boldsymbol{p}_k}\n", @@ -1000,7 +1232,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "44f4d8d5", + "metadata": { + "editable": true + }, "source": [ "If we choose the conjugate vectors $\\boldsymbol{p}_k$ carefully, \n", "then we may not need all of them to obtain a good approximation to the solution \n", @@ -1015,7 +1250,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a8739d7d", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{x}_0=0,\n", @@ -1024,14 +1262,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d871e171", + "metadata": { + "editable": true + }, "source": [ "or consider the system" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "7ed84e84", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n", @@ -1040,7 +1284,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b690f75b", + "metadata": { + "editable": true + }, "source": [ "instead.\n", "\n", @@ -1049,7 +1296,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "86ce9e8a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "f(\\boldsymbol{x}) = \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T \\boldsymbol{x} , \\quad \\boldsymbol{x}\\in\\mathbf{R}^n.\n", @@ -1058,7 +1308,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "7968787f", + "metadata": { + "editable": true + }, "source": [ "This suggests taking the first basis vector $\\boldsymbol{p}_1$ \n", "to be the gradient of $f$ at $\\boldsymbol{x}=\\boldsymbol{x}_0$, \n", @@ -1067,7 +1320,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "0d510b11", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n", @@ -1076,7 +1332,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "c7c47a8e", + "metadata": { + "editable": true + }, "source": [ "and \n", "$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$.\n", @@ -1088,7 +1347,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "5dc0e4ac", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{r}_k=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k.\n", @@ -1097,7 +1359,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "0aecb4b3", + "metadata": { + "editable": true + }, "source": [ "Note that $\\boldsymbol{r}_k$ is the negative gradient of $f$ at \n", "$\\boldsymbol{x}=\\boldsymbol{x}_k$, \n", @@ -1110,7 +1375,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f3dfc701", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{p}_{k+1}=\\boldsymbol{r}_k-\\frac{\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{r}_k}{\\boldsymbol{p}_k^T\\boldsymbol{A}\\boldsymbol{p}_k} \\boldsymbol{p}_k.\n", @@ -1119,14 +1387,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "12e92892", + "metadata": { + "editable": true + }, "source": [ "We can also compute the residual iteratively as" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "1514b03f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n", @@ -1135,14 +1409,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "7b09db3d", + "metadata": { + "editable": true + }, "source": [ "which equals" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "4a0638f8", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{p}_k),\n", @@ -1151,14 +1431,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "298f5e46", + "metadata": { + "editable": true + }, "source": [ "or" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "acd35abb", + "metadata": { + "editable": true + }, "source": [ "$$\n", "(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{p}_k,\n", @@ -1167,14 +1453,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "79625f01", + "metadata": { + "editable": true + }, "source": [ "which gives" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "dc5888e2", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{r}_{k+1}=\\boldsymbol{r}_k-\\boldsymbol{A}\\boldsymbol{p}_{k},\n", @@ -1183,7 +1475,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d11b96a9", + "metadata": { + "editable": true + }, "source": [ "## Revisiting our Linear Regression Solvers\n", "\n", @@ -1203,7 +1498,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, + "id": "cf7c349e", "metadata": { "collapsed": false, "editable": true @@ -1217,7 +1513,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "adf34219", + "metadata": { + "editable": true + }, "source": [ "with $x_i \\in [0,1] $ is chosen randomly using a uniform distribution. Additionally we have a stochastic noise chosen according to a normal distribution $\\cal {N}(0,1)$. \n", "The linear regression model is given by" @@ -1225,7 +1524,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d28eb4e0", + "metadata": { + "editable": true + }, "source": [ "$$\n", "h_\\beta(x) = \\boldsymbol{y} = \\beta_0 + \\beta_1 x,\n", @@ -1234,14 +1536,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "60060fcb", + "metadata": { + "editable": true + }, "source": [ "such that" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "82983f16", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{y}_i = \\beta_0 + \\beta_1 x_i.\n", @@ -1250,7 +1558,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "60fc4bc0", + "metadata": { + "editable": true + }, "source": [ "Let $\\mathbf{y} = (y_1,\\cdots,y_n)^T$, $\\mathbf{\\boldsymbol{y}} = (\\boldsymbol{y}_1,\\cdots,\\boldsymbol{y}_n)^T$ and $\\beta = (\\beta_0, \\beta_1)^T$\n", "\n", @@ -1259,7 +1570,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "0c5dac72", + "metadata": { + "editable": true + }, "source": [ "$$\n", "X \\equiv \\begin{bmatrix}\n", @@ -1272,14 +1586,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "002d8c9b", + "metadata": { + "editable": true + }, "source": [ "The cost/loss/risk function is given by (" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "b91d8b5a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C(\\beta) = \\frac{1}{n}||X\\beta-\\mathbf{y}||_{2}^{2} = \\frac{1}{n}\\sum_{i=1}^{100}\\left[ (\\beta_0 + \\beta_1 x_i)^2 - 2 y_i (\\beta_0 + \\beta_1 x_i) + y_i^2\\right]\n", @@ -1288,17 +1608,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d0fc6c20", + "metadata": { + "editable": true + }, "source": [ "and we want to find $\\beta$ such that $C(\\beta)$ is minimized.\n", "\n", - "\n", "Computing $\\partial C(\\beta) / \\partial \\beta_0$ and $\\partial C(\\beta) / \\partial \\beta_1$ we can show that the gradient can be written as" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "3f99dab5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\nabla_{\\beta} C(\\beta) = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n", @@ -1309,17 +1634,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e1305a22", + "metadata": { + "editable": true + }, "source": [ "where $X$ is the design matrix defined above.\n", "\n", - "\n", "The Hessian matrix of $C(\\beta)$ is given by" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "ef62073f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{H} \\equiv \\begin{bmatrix}\n", @@ -1331,18 +1661,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "dfb78235", + "metadata": { + "editable": true + }, "source": [ "This result implies that $C(\\beta)$ is a convex function since the matrix $X^T X$ always is positive semi-definite.\n", "\n", - "\n", - "\n", "We can now write a program that minimizes $C(\\beta)$ using the gradient descent method with a constant learning rate $\\gamma$ according to" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "56cee86c", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\beta_{k+1} = \\beta_k - \\gamma \\nabla_\\beta C(\\beta_k), \\ k=0,1,\\cdots\n", @@ -1351,7 +1685,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6cc71454", + "metadata": { + "editable": true + }, "source": [ "We can use the expression we computed for the gradient and let use a\n", "$\\beta_0$ be chosen randomly and let $\\gamma = 0.001$. Stop iterating\n", @@ -1360,14 +1697,13 @@ "And finally we can compare our solution for $\\beta$ with the analytic result given by \n", "$\\beta= (X^TX)^{-1} X^T \\mathbf{y}$.\n", "\n", - "\n", - "\n", "Here is our simple example" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, + "id": "90fab6b7", "metadata": { "collapsed": false, "editable": true @@ -1424,14 +1760,18 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "48ba87fe", + "metadata": { + "editable": true + }, "source": [ "Alternatively, we can use **Scikit-Learn** as done here" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, + "id": "7522775d", "metadata": { "collapsed": false, "editable": true @@ -1458,14 +1798,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "90552e2f", + "metadata": { + "editable": true + }, "source": [ "We have also discussed Ridge regression where the loss function contains a regularized term given by the $L_2$ norm of $\\beta$," ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "5d7c032c", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C_{\\text{ridge}}(\\beta) = \\frac{1}{n}||X\\beta -\\mathbf{y}||^2 + \\lambda ||\\beta||^2, \\ \\lambda \\geq 0.\n", @@ -1474,14 +1820,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ed86f1ba", + "metadata": { + "editable": true + }, "source": [ "In order to minimize $C_{\\text{ridge}}(\\beta)$ using GD we only have adjust the gradient as follows" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "0386e23c", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\nabla_\\beta C_{\\text{ridge}}(\\beta) = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n", @@ -1492,14 +1844,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b65523fc", + "metadata": { + "editable": true + }, "source": [ "We can easily extend our program to minimize $C_{\\text{ridge}}(\\beta)$ using gradient descent and compare with the analytical solution given by" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "c62584ee", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\beta_{\\text{ridge}} = \\left(X^T X + \\lambda I_{2 \\times 2} \\right)^{-1} X^T \\mathbf{y}.\n", @@ -1508,7 +1866,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, + "id": "e8d43667", "metadata": { "collapsed": false, "editable": true @@ -1562,7 +1921,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "1ca83847", + "metadata": { + "editable": true + }, "source": [ "## Using gradient descent methods, limitations\n", "\n", @@ -1576,9 +1938,39 @@ "\n", "* **GD treats all directions in parameter space uniformly.** Another major drawback of GD is that unlike Newton's method, the learning rate for GD is the same in all directions in parameter space. For this reason, the maximum learning rate is set by the behavior of the steepest direction and this can significantly slow down training. Ideally, we would like to take large steps in flat directions and small steps in steep directions. Since we are exploring rugged landscapes where curvatures change, this requires us to keep track of not only the gradient but second derivatives. The ideal scenario would be to calculate the Hessian but this proves to be too computationally expensive. \n", "\n", - "* GD can take exponential time to escape saddle points, even with random initialization. As we mentioned, GD is extremely sensitive to initial condition since it determines the particular local minimum GD would eventually reach. However, even with a good initialization scheme, through the introduction of randomness, GD can still take exponential time to escape saddle points.\n", + "* GD can take exponential time to escape saddle points, even with random initialization. As we mentioned, GD is extremely sensitive to initial condition since it determines the particular local minimum GD would eventually reach. However, even with a good initialization scheme, through the introduction of randomness, GD can still take exponential time to escape saddle points." + ] + }, + { + "cell_type": "markdown", + "id": "dcf3e808", + "metadata": { + "editable": true + }, + "source": [ + "## Stochastic Gradient Descent (SGD)\n", "\n", - "## Stochastic Gradient Descent\n", + "In stochastic gradient descent, the extreme case is the case where we\n", + "have only one batch, that is we include the whole data set.\n", + "\n", + "This process is called Stochastic Gradient\n", + "Descent (SGD) (or also sometimes on-line gradient descent). This is\n", + "relatively less common to see because in practice due to vectorized\n", + "code optimizations it can be computationally much more efficient to\n", + "evaluate the gradient for 100 examples, than the gradient for one\n", + "example 100 times. Even though SGD technically refers to using a\n", + "single example at a time to evaluate the gradient, you will hear\n", + "people use the term SGD even when referring to mini-batch gradient\n", + "descent (i.e. mentions of MGD for “Minibatch Gradient Descent”, or BGD\n", + "for “Batch gradient descent” are rare to see), where it is usually\n", + "assumed that mini-batches are used. The size of the mini-batch is a\n", + "hyperparameter but it is not very common to cross-validate or bootstrap it. It is\n", + "usually based on memory constraints (if any), or set to some value,\n", + "e.g. 32, 64 or 128. We use powers of 2 in practice because many\n", + "vectorized operation implementations work faster when their inputs are\n", + "sized in powers of 2.\n", + "\n", + "In our notes with SGD we mean stochastic gradient descent with mini-batches.\n", "\n", "Stochastic gradient descent (SGD) and variants thereof address some of\n", "the shortcomings of the Gradient descent method discussed above.\n", @@ -1590,7 +1982,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "473b1af6", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C(\\mathbf{\\beta}) = \\sum_{i=1}^n c_i(\\mathbf{x}_i,\n", @@ -1600,7 +1995,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "3353fe2a", + "metadata": { + "editable": true + }, "source": [ "This in turn means that the gradient can be\n", "computed as a sum over $i$-gradients" @@ -1608,7 +2006,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6e8e47c3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\nabla_\\beta C(\\mathbf{\\beta}) = \\sum_i^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n", @@ -1618,7 +2019,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a2eeb6ad", + "metadata": { + "editable": true + }, "source": [ "Stochasticity/randomness is introduced by only taking the\n", "gradient on a subset of the data called minibatches. If there are $n$\n", @@ -1626,8 +2030,6 @@ "minibatches. We denote these minibatches by $B_k$ where\n", "$k=1,\\cdots,n/M$.\n", "\n", - "\n", - "\n", "As an example, suppose we have $10$ data points $(\\mathbf{x}_1,\\cdots, \\mathbf{x}_{10})$ \n", "and we choose to have $M=5$ minibathces,\n", "then each minibatch contains two data points. In particular we have\n", @@ -1644,7 +2046,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "5a7a0f8b", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\nabla_{\\beta}\n", @@ -1656,14 +2061,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b7b5884f", + "metadata": { + "editable": true + }, "source": [ "Thus a gradient descent step now looks like" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "6492d660", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\beta_{j+1} = \\beta_j - \\gamma_j \\sum_{i \\in B_k}^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n", @@ -1673,7 +2084,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "584164f4", + "metadata": { + "editable": true + }, "source": [ "where $k$ is picked at random with equal\n", "probability from $[1,n/M]$. An iteration over the number of\n", @@ -1684,7 +2098,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, + "id": "42d97cf8", "metadata": { "collapsed": false, "editable": true @@ -1694,7 +2109,7 @@ "import numpy as np \n", "\n", "n = 100 #100 datapoints \n", - "M = 5 #size of each minibatch\n", + "M = 5 #size of each mini-batche\n", "m = int(n/M) #number of minibatches\n", "n_epochs = 10 #number of epochs\n", "\n", @@ -1709,7 +2124,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ca9c6c58", + "metadata": { + "editable": true + }, "source": [ "Taking the gradient only on a subset of the data has two important\n", "benefits. First, it introduces randomness which decreases the chance\n", @@ -1719,8 +2137,6 @@ "cheaper since we sum over the datapoints in the $k-th$ minibatch and not\n", "all $n$ datapoints.\n", "\n", - "\n", - "\n", "A natural question is when do we stop the search for a new minimum?\n", "One possibility is to compute the full gradient after a given number\n", "of epochs and check if the norm of the gradient is smaller than some\n", @@ -1732,8 +2148,6 @@ "compare the values of the cost function and keep the $\\beta$ that\n", "gave the lowest value.\n", "\n", - "\n", - "\n", "Another approach is to let the step length $\\gamma_j$ depend on the\n", "number of epochs in such a way that it becomes very small after a\n", "reasonable time such that we do not move at all.\n", @@ -1749,7 +2163,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 11, + "id": "d2921658", "metadata": { "collapsed": false, "editable": true @@ -1784,48 +2199,62 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "84469eb8", + "metadata": { + "editable": true + }, + "source": [ + "We note that we have defined several hyperparameters. These are now the number of epochs, the number of mini-batches and the parameters $t_0$ and $t_1$." + ] + }, + { + "cell_type": "markdown", + "id": "b4b94e7a", + "metadata": { + "editable": true + }, "source": [ "### Program for stochastic gradient" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 12, + "id": "71dcdb35", "metadata": { "collapsed": false, "editable": true }, "outputs": [], "source": [ + "# Importing various packages\n", "# Importing various packages\n", "from math import exp, sqrt\n", "from random import random, seed\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", - "from sklearn.linear_model import SGDRegressor\n", "\n", - "m = 100\n", - "x = 2*np.random.rand(m,1)\n", - "y = 4+3*x+np.random.randn(m,1)\n", + "n = 100\n", + "x = 2*np.random.rand(n,1)\n", + "y = 4+3*x+np.random.randn(n,1)\n", "\n", - "X = np.c_[np.ones((m,1)), x]\n", + "X = np.c_[np.ones((n,1)), x]\n", + "XT_X = X.T @ X\n", "theta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y)\n", "print(\"Own inversion\")\n", "print(theta_linreg)\n", - "sgdreg = SGDRegressor(max_iter = 50, penalty=None, eta0=0.1)\n", - "sgdreg.fit(x,y.ravel())\n", - "print(\"sgdreg from scikit\")\n", - "print(sgdreg.intercept_, sgdreg.coef_)\n", - "\n", + "# Hessian matrix\n", + "H = (2.0/n)* XT_X\n", + "EigValues, EigVectors = np.linalg.eig(H)\n", + "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n", "\n", "theta = np.random.randn(2,1)\n", - "eta = 0.1\n", + "eta = 1.0/np.max(EigValues)\n", "Niterations = 1000\n", "\n", "\n", "for iter in range(Niterations):\n", - " gradients = 2.0/m*X.T @ ((X @ theta)-y)\n", + " gradients = 2.0/n*X.T @ ((X @ theta)-y)\n", " theta -= eta*gradients\n", "print(\"theta from own gd\")\n", "print(theta)\n", @@ -1835,8 +2264,9 @@ "ypredict = Xnew.dot(theta)\n", "ypredict2 = Xnew.dot(theta_linreg)\n", "\n", - "\n", "n_epochs = 50\n", + "M = 5 #size of each minibatch\n", + "m = int(n/M) #number of minibatches\n", "t0, t1 = 5, 50\n", "def learning_schedule(t):\n", " return t0/(t+t1)\n", @@ -1844,16 +2274,20 @@ "theta = np.random.randn(2,1)\n", "\n", "for epoch in range(n_epochs):\n", + "# Can you figure out a better way of setting up the contributions to each batch?\n", " for i in range(m):\n", - " random_index = np.random.randint(m)\n", - " xi = X[random_index:random_index+1]\n", - " yi = y[random_index:random_index+1]\n", - " gradients = 2 * xi.T @ ((xi @ theta)-yi)\n", + " random_index = M*np.random.randint(m)\n", + " xi = X[random_index:random_index+M]\n", + " yi = y[random_index:random_index+M]\n", + " gradients = (2.0/M)* xi.T @ ((xi @ theta)-yi)\n", " eta = learning_schedule(epoch*m+i)\n", " theta = theta - eta*gradients\n", "print(\"theta from own sdg\")\n", "print(theta)\n", "\n", + "\n", + "\n", + "\n", "plt.plot(xnew, ypredict, \"r-\")\n", "plt.plot(xnew, ypredict2, \"b-\")\n", "plt.plot(x, y ,'ro')\n", @@ -1866,7 +2300,23 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6231b86f", + "metadata": { + "editable": true + }, + "source": [ + "In the above code, we have use replacement in setting up the\n", + "mini-batches. The discussion\n", + "[here](https://sebastianraschka.com/faq/docs/sgd-methods.html) may be\n", + "useful. More material will be added later." + ] + }, + { + "cell_type": "markdown", + "id": "8d50214c", + "metadata": { + "editable": true + }, "source": [ "## Momentum based GD\n", "\n", @@ -1878,7 +2328,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "45d43ca3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t) \\nonumber\n", @@ -1887,7 +2340,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "dcdd91bf", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -1902,7 +2358,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "c7519d1e", + "metadata": { + "editable": true + }, "source": [ "where we have introduced a momentum parameter $\\gamma$, with\n", "$0\\le\\gamma\\le 1$, and for brevity we dropped the explicit notation to\n", @@ -1918,7 +2377,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f4d4340d", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\Delta \\boldsymbol{\\theta}_{t+1} = \\gamma \\Delta \\boldsymbol{\\theta}_t -\\ \\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t),\n", @@ -1927,12 +2389,13 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "41ad532a", + "metadata": { + "editable": true + }, "source": [ "where we have defined $\\Delta \\boldsymbol{\\theta}_{t}= \\boldsymbol{\\theta}_t-\\boldsymbol{\\theta}_{t-1}$.\n", "\n", - "\n", - "\n", "Let us try to get more intuition from these equations. It is helpful\n", "to consider a simple physical analogy with a particle of mass $m$\n", "moving in a viscous medium with drag coefficient $\\mu$ and potential\n", @@ -1942,7 +2405,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "eef8ae92", + "metadata": { + "editable": true + }, "source": [ "$$\n", "m {d^2 \\mathbf{w} \\over dt^2} + \\mu {d \\mathbf{w} \\over dt }= -\\nabla_w E(\\mathbf{w}).\n", @@ -1951,14 +2417,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "80481a6d", + "metadata": { + "editable": true + }, "source": [ "We can discretize this equation in the usual way to get" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "6aab8db7", + "metadata": { + "editable": true + }, "source": [ "$$\n", "m { \\mathbf{w}_{t+\\Delta t}-2 \\mathbf{w}_{t} +\\mathbf{w}_{t-\\Delta t} \\over (\\Delta t)^2}+\\mu {\\mathbf{w}_{t+\\Delta t}- \\mathbf{w}_{t} \\over \\Delta t} = -\\nabla_w E(\\mathbf{w}).\n", @@ -1967,14 +2439,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "dd6414d2", + "metadata": { + "editable": true + }, "source": [ "Rearranging this equation, we can rewrite this as" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "b76a8372", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\Delta \\mathbf{w}_{t +\\Delta t}= - { (\\Delta t)^2 \\over m +\\mu \\Delta t} \\nabla_w E(\\mathbf{w})+ {m \\over m +\\mu \\Delta t} \\Delta \\mathbf{w}_t.\n", @@ -1983,7 +2461,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "07bbe6db", + "metadata": { + "editable": true + }, "source": [ "Notice that this equation is identical to previous one if we identify\n", "the position of the particle, $\\mathbf{w}$, with the parameters\n", @@ -1994,7 +2475,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "7a9a2ecf", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\gamma= {m \\over m +\\mu \\Delta t }, \\qquad \\eta = {(\\Delta t)^2 \\over m +\\mu \\Delta t}.\n", @@ -2003,7 +2487,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "fe5a2bbc", + "metadata": { + "editable": true + }, "source": [ "Thus, as the name suggests, the momentum parameter is proportional to\n", "the mass of the particle and effectively provides inertia.\n", @@ -2033,7 +2520,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "04540023", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t +\\gamma \\mathbf{v}_{t-1}) \\nonumber\n", @@ -2042,7 +2532,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "dfbf53a5", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -2057,12 +2550,13 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "32ac3869", + "metadata": { + "editable": true + }, "source": [ "One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of $\\gamma$.\n", "\n", - "\n", - "\n", "In stochastic gradient descent, with and without momentum, we still\n", "have to specify a schedule for tuning the learning rates $\\eta_t$\n", "as a function of time. As discussed in the context of Newton's\n", @@ -2081,10 +2575,17 @@ "\n", "Recently, a number of methods have been introduced that accomplish\n", "this by tracking not only the gradient, but also the second moment of\n", - "the gradient. These methods include AdaGrad, AdaDelta, RMS-Prop, and\n", - "ADAM.\n", - "\n", - "\n", + "the gradient. These methods include AdaGrad, AdaDelta, Root Mean Squared Propagation (RMS-Prop), and\n", + "ADAM." + ] + }, + { + "cell_type": "markdown", + "id": "6f575b16", + "metadata": { + "editable": true + }, + "source": [ "### RMS prop\n", "\n", "In RMS prop, in addition to keeping a running average of the first\n", @@ -2095,7 +2596,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "274604c4", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -2110,7 +2614,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "cd679323", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathbf{s}_t =\\beta \\mathbf{s}_{t-1} +(1-\\beta)\\mathbf{g}_t^2 \\nonumber\n", @@ -2119,7 +2626,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "0a7f8e9d", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\mathbf{g}_t \\over \\sqrt{\\mathbf{s}_t +\\epsilon}}, \\nonumber\n", @@ -2128,7 +2638,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "48ba8fff", + "metadata": { + "editable": true + }, "source": [ "where $\\beta$ controls the averaging time of the second moment and is\n", "typically taken to be about $\\beta=0.9$, $\\eta_t$ is a learning rate\n", @@ -2138,8 +2651,16 @@ "is clear from this formula that the learning rate is reduced in\n", "directions where the norm of the gradient is consistently large. This\n", "greatly speeds up the convergence by allowing us to use a larger\n", - "learning rate for flat directions.\n", - "\n", + "learning rate for flat directions." + ] + }, + { + "cell_type": "markdown", + "id": "83140ab2", + "metadata": { + "editable": true + }, + "source": [ "### ADAM optimizer\n", "\n", "A related algorithm is the ADAM optimizer. In ADAM, we keep a running\n", @@ -2158,7 +2679,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "61874dc3", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -2173,7 +2697,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "24e19d86", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathbf{m}_t = \\beta_1 \\mathbf{m}_{t-1} + (1-\\beta_1) \\mathbf{g}_t \\nonumber\n", @@ -2182,7 +2709,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "506f78ea", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathbf{s}_t =\\beta_2 \\mathbf{s}_{t-1} +(1-\\beta_2)\\mathbf{g}_t^2 \\nonumber\n", @@ -2191,7 +2721,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "cb4b8585", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\mathbf{m}}_t={\\mathbf{m}_t \\over 1-\\beta_1^t} \\nonumber\n", @@ -2200,7 +2733,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9b5b11b1", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\mathbf{s}}_t ={\\mathbf{s}_t \\over1-\\beta_2^t} \\nonumber\n", @@ -2209,7 +2745,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "92292a73", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\boldsymbol{\\mathbf{m}}_t \\over \\sqrt{\\boldsymbol{\\mathbf{s}}_t} +\\epsilon}, \\nonumber\n", @@ -2218,7 +2757,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "1a264832", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -2232,7 +2774,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6a307202", + "metadata": { + "editable": true + }, "source": [ "where $\\beta_1$ and $\\beta_2$ set the memory lifetime of the first and\n", "second moment and are typically taken to be $0.9$ and $0.99$\n", @@ -2248,7 +2793,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "3285f010", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\Delta \\theta_{t+1}= -\\eta_t { \\boldsymbol{m}_t \\over \\sqrt{\\sigma_t^2 + m_t^2 }+\\epsilon}.\n", @@ -2257,7 +2805,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "657349da", + "metadata": { + "editable": true + }, "source": [ "## Practical tips\n", "\n", @@ -2267,8 +2818,16 @@ "\n", "* **Monitor the out-of-sample performance.** Always monitor the performance of your model on a validation set (a small portion of the training data that is held out of the training process to serve as a proxy for the test set. If the validation error starts increasing, then the model is beginning to overfit. Terminate the learning process. This *early stopping* significantly improves performance in many settings.\n", "\n", - "* **Adaptive optimization methods don't always have good generalization.** Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications.\n", - "\n", + "* **Adaptive optimization methods don't always have good generalization.** Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications." + ] + }, + { + "cell_type": "markdown", + "id": "65044ac7", + "metadata": { + "editable": true + }, + "source": [ "## Automatic differentiation\n", "\n", "[Automatic differentiation (AD)](https://en.wikipedia.org/wiki/Automatic_differentiation), \n", @@ -2296,15 +2855,16 @@ "while numerical differentiation can introduce round-off errors in the\n", "discretization process and cancellation\n", "\n", - "\n", - "\n", "Python has tools for so-called **automatic differentiation**.\n", "Consider the following example" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "dacf05cf", + "metadata": { + "editable": true + }, "source": [ "$$\n", "f(x) = \\sin\\left(2\\pi x + x^2\\right)\n", @@ -2313,14 +2873,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "da4ad36e", + "metadata": { + "editable": true + }, "source": [ "which has the following derivative" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "f4c3e6c4", + "metadata": { + "editable": true + }, "source": [ "$$\n", "f'(x) = \\cos\\left(2\\pi x + x^2\\right)\\left(2\\pi + 2x\\right)\n", @@ -2329,14 +2895,18 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "1c8bfd4a", + "metadata": { + "editable": true + }, "source": [ "Using **autograd** we have" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, + "id": "e1d91b8b", "metadata": { "collapsed": false, "editable": true @@ -2381,7 +2951,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "cd1158a5", + "metadata": { + "editable": true + }, "source": [ "Here we\n", "experiment with what kind of functions Autograd is capable\n", @@ -2392,7 +2965,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, + "id": "e2e9faff", "metadata": { "collapsed": false, "editable": true @@ -2420,7 +2994,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e4a83059", + "metadata": { + "editable": true + }, "source": [ "To differentiate with respect to two (or more) arguments of a Python\n", "function, Autograd need to know at which variable the function if\n", @@ -2429,7 +3006,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 15, + "id": "f65983d8", "metadata": { "collapsed": false, "editable": true @@ -2473,14 +3051,18 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "1d369f97", + "metadata": { + "editable": true + }, "source": [ "Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 16, + "id": "46ea0652", "metadata": { "collapsed": false, "editable": true @@ -2508,7 +3090,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9cc6674a", + "metadata": { + "editable": true + }, "source": [ "Note that in this case, when sending an array as input argument, the\n", "output from Autograd is another array. This is the true gradient of\n", @@ -2520,7 +3105,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 17, + "id": "17813055", "metadata": { "collapsed": false, "editable": true @@ -2548,7 +3134,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 18, + "id": "6da49540", "metadata": { "collapsed": false, "editable": true @@ -2572,39 +3159,45 @@ ] }, { - "cell_type": "markdown", - "metadata": {}, + "cell_type": "code", + "execution_count": 19, + "id": "a8ff2c17", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ - "1\n", - "8\n", - " \n", - "<\n", - "<\n", - "<\n", - "!\n", - "!\n", - "C\n", - "O\n", - "D\n", - "E\n", - "_\n", - "B\n", - "L\n", - "O\n", - "C\n", - "K\n", - " \n", - " \n", - "p\n", - "y\n", - "c\n", - "o\n", - "d" + "import autograd.numpy as np\n", + "from autograd import grad\n", + "def f6_for(x):\n", + " val = 0\n", + " for i in range(10):\n", + " val = val + x**i\n", + " return val\n", + "\n", + "def f6_while(x):\n", + " val = 0\n", + " i = 0\n", + " while i < 10:\n", + " val = val + x**i\n", + " i = i + 1\n", + " return val\n", + "\n", + "f6_for_grad = grad(f6_for)\n", + "f6_while_grad = grad(f6_while)\n", + "\n", + "x = 0.5\n", + "\n", + "# Print the computed derivaties of f6_for and f6_while\n", + "print(\"The computed derivative of f6_for at x = %g is: %g\"%(x,f6_for_grad(x)))\n", + "print(\"The computed derivative of f6_while at x = %g is: %g\"%(x,f6_while_grad(x)))" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 20, + "id": "ec67d4a3", "metadata": { "collapsed": false, "editable": true @@ -2624,7 +3217,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 21, + "id": "742a2d68", "metadata": { "collapsed": false, "editable": true @@ -2662,48 +3256,55 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e7be6348", + "metadata": { + "editable": true + }, "source": [ "Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input.\n", "\n", + "Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.\n", "\n", - "Autograd supports many features. However, there are some functions that are not supported (yet) by Autograd.\n", - "\n", - "Assigning a value to the variable being differentiated with respect to is an example thereof." + "Assigning a value to the variable being differentiated with respect to" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 22, + "id": "c551058c", "metadata": { "collapsed": false, "editable": true }, "outputs": [], "source": [ - "#import autograd.numpy as np\n", - "#from autograd import grad\n", - "#def f8(x): # Assume x is an array\n", - "# x[2] = 3\n", - "# return x*2\n", + "import autograd.numpy as np\n", + "from autograd import grad\n", + "def f8(x): # Assume x is an array\n", + " x[2] = 3\n", + " return x*2\n", "\n", - "#f8_grad = grad(f8)\n", + "f8_grad = grad(f8)\n", "\n", - "#x = 8.4\n", + "x = 8.4\n", "\n", - "#print(\"The derivative of f8 is:\",f8_grad(x))" + "print(\"The derivative of f8 is:\",f8_grad(x))" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "7a13b21d", + "metadata": { + "editable": true + }, "source": [ "Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 23, + "id": "19c7502b", "metadata": { "collapsed": false, "editable": true @@ -2725,7 +3326,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "4450885d", + "metadata": { + "editable": true + }, "source": [ "Here we are told that the 'dot' function does not belong to Autograd's\n", "version of a Numpy array. To overcome this, an alternative syntax\n", @@ -2734,7 +3338,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 24, + "id": "013fc7f8", "metadata": { "collapsed": false, "editable": true @@ -2759,14 +3364,18 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "8d360f7d", + "metadata": { + "editable": true + }, "source": [ "The documentation recommends to avoid inplace operations such as" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 25, + "id": "e29a24eb", "metadata": { "collapsed": false, "editable": true @@ -2781,13 +3390,233 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ad8fbbb7", + "metadata": { + "editable": true + }, "source": [ - "More examples will be added, in particular how to compare autograd with own codes for the gradients." + "## Using Autograd with OLS\n", + "\n", + "We conclude the part on optmization by showing how we can make codes\n", + "for linear regression and logistic regression using **autograd**. The\n", + "first example shows results with ordinary leats squares." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "904f65dc", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# Using Autograd to calculate gradients for OLS\n", + "from random import random, seed\n", + "import numpy as np\n", + "import autograd.numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from autograd import grad\n", + "\n", + "def CostOLS(beta):\n", + " return (1.0/n)*np.sum((y-X @ beta)**2)\n", + "\n", + "n = 100\n", + "x = 2*np.random.rand(n,1)\n", + "y = 4+3*x+np.random.randn(n,1)\n", + "\n", + "X = np.c_[np.ones((n,1)), x]\n", + "XT_X = X.T @ X\n", + "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n", + "print(\"Own inversion\")\n", + "print(theta_linreg)\n", + "# Hessian matrix\n", + "H = (2.0/n)* XT_X\n", + "EigValues, EigVectors = np.linalg.eig(H)\n", + "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n", + "\n", + "theta = np.random.randn(2,1)\n", + "eta = 1.0/np.max(EigValues)\n", + "Niterations = 1000\n", + "# define the gradient\n", + "training_gradient = grad(CostOLS)\n", + "\n", + "for iter in range(Niterations):\n", + " gradients = training_gradient(theta)\n", + " theta -= eta*gradients\n", + "print(\"theta from own gd\")\n", + "print(theta)\n", + "\n", + "xnew = np.array([[0],[2]])\n", + "Xnew = np.c_[np.ones((2,1)), xnew]\n", + "ypredict = Xnew.dot(theta)\n", + "ypredict2 = Xnew.dot(theta_linreg)\n", + "\n", + "plt.plot(xnew, ypredict, \"r-\")\n", + "plt.plot(xnew, ypredict2, \"b-\")\n", + "plt.plot(x, y ,'ro')\n", + "plt.axis([0,2.0,0, 15.0])\n", + "plt.xlabel(r'$x$')\n", + "plt.ylabel(r'$y$')\n", + "plt.title(r'Random numbers ')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "ce338980", + "metadata": { + "editable": true + }, + "source": [ + "### Including Stochastic Gradient Descent with Autograd\n", + "\n", + "In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "de261f10", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# Using Autograd to calculate gradients using SGD\n", + "# OLS example\n", + "from random import random, seed\n", + "import numpy as np\n", + "import autograd.numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from autograd import grad\n", + "\n", + "# Note change from previous example\n", + "def CostOLS(y,X,theta):\n", + " return np.sum((y-X @ theta)**2)\n", + "\n", + "n = 100\n", + "x = 2*np.random.rand(n,1)\n", + "y = 4+3*x+np.random.randn(n,1)\n", + "\n", + "X = np.c_[np.ones((n,1)), x]\n", + "XT_X = X.T @ X\n", + "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n", + "print(\"Own inversion\")\n", + "print(theta_linreg)\n", + "# Hessian matrix\n", + "H = (2.0/n)* XT_X\n", + "EigValues, EigVectors = np.linalg.eig(H)\n", + "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n", + "\n", + "theta = np.random.randn(2,1)\n", + "eta = 1.0/np.max(EigValues)\n", + "Niterations = 1000\n", + "\n", + "# Note that we request the derivative wrt third argument (theta, 2 here)\n", + "training_gradient = grad(CostOLS,2)\n", + "\n", + "for iter in range(Niterations):\n", + " gradients = (1.0/n)*training_gradient(y, X, theta)\n", + " theta -= eta*gradients\n", + "print(\"theta from own gd\")\n", + "print(theta)\n", + "\n", + "xnew = np.array([[0],[2]])\n", + "Xnew = np.c_[np.ones((2,1)), xnew]\n", + "ypredict = Xnew.dot(theta)\n", + "ypredict2 = Xnew.dot(theta_linreg)\n", + "\n", + "plt.plot(xnew, ypredict, \"r-\")\n", + "plt.plot(xnew, ypredict2, \"b-\")\n", + "plt.plot(x, y ,'ro')\n", + "plt.axis([0,2.0,0, 15.0])\n", + "plt.xlabel(r'$x$')\n", + "plt.ylabel(r'$y$')\n", + "plt.title(r'Random numbers ')\n", + "plt.show()\n", + "\n", + "n_epochs = 50\n", + "M = 5 #size of each minibatch\n", + "m = int(n/M) #number of minibatches\n", + "t0, t1 = 5, 50\n", + "def learning_schedule(t):\n", + " return t0/(t+t1)\n", + "\n", + "theta = np.random.randn(2,1)\n", + "\n", + "for epoch in range(n_epochs):\n", + "# Can you figure out a better way of setting up the contributions to each batch?\n", + " for i in range(m):\n", + " random_index = M*np.random.randint(m)\n", + " xi = X[random_index:random_index+M]\n", + " yi = y[random_index:random_index+M]\n", + " gradients = (1.0/M)*training_gradient(yi, xi, theta)\n", + " eta = learning_schedule(epoch*m+i)\n", + " theta = theta - eta*gradients\n", + "print(\"theta from own sdg\")\n", + "print(theta)" + ] + }, + { + "cell_type": "markdown", + "id": "ccd8829e", + "metadata": { + "editable": true + }, + "source": [ + "### And Logistic Regression" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "cc5811d1", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "import autograd.numpy as np\n", + "from autograd import grad\n", + "\n", + "def sigmoid(x):\n", + " return 0.5 * (np.tanh(x / 2.) + 1)\n", + "\n", + "def logistic_predictions(weights, inputs):\n", + " # Outputs probability of a label being true according to logistic model.\n", + " return sigmoid(np.dot(inputs, weights))\n", + "\n", + "def training_loss(weights):\n", + " # Training loss is the negative log-likelihood of the training labels.\n", + " preds = logistic_predictions(weights, inputs)\n", + " label_probabilities = preds * targets + (1 - preds) * (1 - targets)\n", + " return -np.sum(np.log(label_probabilities))\n", + "\n", + "# Build a toy dataset.\n", + "inputs = np.array([[0.52, 1.12, 0.77],\n", + " [0.88, -1.08, 0.15],\n", + " [0.52, 0.06, -1.30],\n", + " [0.74, -2.49, 1.39]])\n", + "targets = np.array([True, True, False, True])\n", + "\n", + "# Define a function that returns gradients of training loss using Autograd.\n", + "training_gradient_fun = grad(training_loss)\n", + "\n", + "# Optimize weights using gradient descent.\n", + "weights = np.array([0.0, 0.0, 0.0])\n", + "print(\"Initial loss:\", training_loss(weights))\n", + "for i in range(100):\n", + " weights -= training_gradient_fun(weights) * 0.01\n", + "\n", + "print(\"Trained loss:\", training_loss(weights))" ] } ], "metadata": {}, "nbformat": 4, - "nbformat_minor": 4 + "nbformat_minor": 5 } diff --git a/doc/LectureNotes/_build/html/_sources/clustering.ipynb b/doc/LectureNotes/_build/html/_sources/clustering.ipynb new file mode 100644 index 000000000..84bc644b4 --- /dev/null +++ b/doc/LectureNotes/_build/html/_sources/clustering.ipynb @@ -0,0 +1,649 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "c3edcae5", + "metadata": { + "editable": true + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "id": "4102577e", + "metadata": { + "editable": true + }, + "source": [ + "# Clustering and Unsupervised Learning\n", + "\n", + "In general terms cluster analysis, or clustering, is the task of grouping a\n", + "data-set into different distinct categories based on some measure of equality of\n", + "the data. This measure is often referred to as a **metric** or **similarity\n", + "measure** in the literature (note: sometimes we deal with a **dissimilarity\n", + "measure** instead). Usually, these metrics are formulated as some kind of\n", + "distance function between points in a high-dimensional space.\n", + "\n", + "The simplest, and also the most\n", + "common is the **Euclidean distance**.\n", + "\n", + "The simplest of all clustering algorithms is the **k-means algorithm**\n", + ", sometimes also referred to as *Lloyds algorithm*. It is the simplest and also\n", + "the most common. From its simplicity it obtains both strengths and weaknesses.\n", + "These will be discussed in more detail later. The $k$-means algorithm is a\n", + "**centroid based** clustering algorithm.\n", + "\n", + "Assume, we are given $n$ data points and we wish to split the data into $K < n$\n", + "different categories, or clusters. We label each cluster by an integer" + ] + }, + { + "cell_type": "markdown", + "id": "0deb3255", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "k\\in\\{1, \\cdots, K \\}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "cfd8fe00", + "metadata": { + "editable": true + }, + "source": [ + "In the basic k-means algorithm each point is assigned to only\n", + "one cluster $k$, and these assignments are *non-injective* i.e. many-to-one. We\n", + "can think of these mappings as an encoder $k = C(i)$, which assigns the $i$-th\n", + "data-point $\\bf x_i$ to the $k$-th cluster.\n", + "\n", + "$k$-means algorithm in words:\n", + "1. We start with guesses / random initializations of our $k$ cluster centers/centroids\n", + "\n", + "2. For each centroid the points that are most similar are identified\n", + "\n", + "3. Then we move / replace each centroid with a coordinate average of all the points that were assigned to that centroid.\n", + "\n", + "4. Iterate 2-3 until the centroids no longer move (to some tolerance)\n", + "\n", + "We assume we have $n$ data-points" + ] + }, + { + "cell_type": "markdown", + "id": "a29b7459", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\\label{eq:kmeanspoints} \\tag{1}\n", + " \\boldsymbol{x_i} = \\{x_{i, 1}, \\cdots, x_{i, p}\\}\\in\\mathbb{R}^p.\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "98f9e37b", + "metadata": { + "editable": true + }, + "source": [ + "which we wish to group into $K < n$ clusters. For our dissimilarity measure we\n", + "use the *squared Euclidean distance*" + ] + }, + { + "cell_type": "markdown", + "id": "d3c32572", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\\label{eq:squaredeuclidean} \\tag{2}\n", + " d(\\boldsymbol{x_i}, \\boldsymbol{x_i'}) = \\sum_{j=1}^p(x_{ij} - x_{i'j})^2\n", + " = ||\\boldsymbol{x_i} - \\boldsymbol{x_{i'}}||^2\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "29d24648", + "metadata": { + "editable": true + }, + "source": [ + "We define the so called *within-cluster point scatter* which gives us a\n", + "measure of how close each data point assigned to the same cluster tends to be to\n", + "the all the others." + ] + }, + { + "cell_type": "markdown", + "id": "fce5c797", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\\label{eq:withincluster} \\tag{3}\n", + " W(C) = \\frac{1}{2}\\sum_{k=1}^K\\sum_{C(i)=k}\n", + " \\sum_{C(i')=k}d(\\boldsymbol{x_i}, \\boldsymbol{x_{i'}}) =\n", + " \\sum_{k=1}^KN_k\\sum_{C(i)=k}||\\boldsymbol{x_i} - \\boldsymbol{\\overline{x_k}}||^2\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "674a26b7", + "metadata": { + "editable": true + }, + "source": [ + "where $\\boldsymbol{\\overline{x_k}}$ is the mean vector associated with the $k$-th\n", + "cluster, and $N_k = \\sum_{i=1}^nI(C(i) = k)$, where the $I()$ notation is\n", + "similar to the Kronecker delta (*Commonly used in statistics, it just means that\n", + "when $i = k$ we have the encoder $C(i)$*). In other words, the within-cluster\n", + "scatter measures the compactness of each cluster with respect to the data points\n", + "assigned to each cluster. This is the quantity that the $k$-means algorithm aims\n", + "to minimize. We refer to this quantity $W(C)$ as the within cluster scatter\n", + "because of its relation to the *total scatter*.\n", + "\n", + "We have" + ] + }, + { + "cell_type": "markdown", + "id": "f200e7ff", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\\label{eq:totalscatter} \\tag{4}\n", + " T = W(C) + B(C) = \\frac{1}{2}\\sum_{i=1}^n\n", + " \\sum_{i'=1}^nd(\\boldsymbol{x_i}, \\boldsymbol{x_{i'}})\n", + " = \\frac{1}{2}\\sum_{k=1}^K\\sum_{C(i)=k}\n", + " \\Big(\\sum_{C(i') = k}d(\\boldsymbol{x_i}, \\boldsymbol{x_{i'}})\n", + " + \\sum_{C(i')\\neq k}d(\\boldsymbol{x_i}, \\boldsymbol{x_{i'}})\\Big).\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "5471a94d", + "metadata": { + "editable": true + }, + "source": [ + "This is a quantity that is conserved throughout the $k$-means algorithm. It can\n", + "be thought of as the total amount of information in the data, and it is composed\n", + "of the aforementioned within-cluster scatter and the *between-cluster scatter*\n", + "$B(C)$. In methods such as principle component analysis the total scatter is not\n", + "conserved.\n", + "\n", + "Given a cluster mean $\\boldsymbol{m_k}$ we define the **total cluster variance**" + ] + }, + { + "cell_type": "markdown", + "id": "299a99ce", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\\label{eq:totalclustervariance} \\tag{5}\n", + " \\min_{C, \\{\\boldsymbol{m_k}\\}_1^K}\\sum_{k=1}^KN_k\\sum||\\boldsymbol{x_i} - \\boldsymbol{m_k}||^2\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "bdfa54ee", + "metadata": { + "editable": true + }, + "source": [ + "Now we have all the pieces necessary to formally revisit the $k$-means algorithm.\n", + "\n", + "The $k$-means clustering algorithm goes as follows \n", + "\n", + "1. For a given cluster assignment $C$, and $k$ cluster means $\\left\\{m_1, \\cdots, m_k\\right\\}$. We minimize the total cluster variance with respect to the cluster means $\\{m_k\\}$ yielding the means of the currently assigned clusters.\n", + "\n", + "2. Given a current set of $k$ means $\\{m_k\\}$ the total cluster variance is minimized by assigning each observation to the closest (current) cluster mean. That is $$C(i) = \\underset{1\\leq k\\leq K}{\\mathrm{argmin}} ||\\boldsymbol{x_i} - \\boldsymbol{m_k}||^2$$\n", + "\n", + "3. Steps 1 and 2 are repeated until the assignments do not change." + ] + }, + { + "cell_type": "markdown", + "id": "f5def86c", + "metadata": { + "editable": true + }, + "source": [ + "## Codes and Approaches\n", + "\n", + "1. Before we start we specify a number $k$ which is the number of clusters we want to try to separate our data into.\n", + "\n", + "2. We initially choose $k$ random data points in our data as our initial centroids, *or means* (this is where the name comes from).\n", + "\n", + "3. Assign each data point to their closest centroid, based on the squared Euclidean distance.\n", + "\n", + "4. For each of the $k$ cluster we update the centroid by calculating new mean values for all the data points in the cluster.\n", + "\n", + "5. Iteratively minimize the within cluster scatter by performing steps (3, 4) until the new assignments stop changing (can be to some tolerance) or until a maximum number of iterations have passed.\n", + "\n", + "Let us now program the most basic version of the algorithm using nothing but\n", + "Python with numpy arrays. This code is kept intentionally simple to gradually\n", + "progress our understanding. There is no vectorization of any kind, and even most\n", + "helper functions are not utilized.\n", + "\n", + "We need first a dataset to do our cluster analysis on. In our case\n", + "this is a plain *vanilla* data set using random numbers using a\n", + "Gaussian distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "b0260188", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "import time\n", + "import numpy as np\n", + "import tensorflow as tf\n", + "from matplotlib import image\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.cluster import KMeans\n", + "from IPython.display import display\n", + "\n", + "np.random.seed(2021)" + ] + }, + { + "cell_type": "markdown", + "id": "fe680e35", + "metadata": { + "editable": true + }, + "source": [ + "Next we define functions, for ease of use later, to generate Gaussians and to\n", + "set up our toy data set." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "9db2bbce", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def gaussian_points(dim=2, n_points=1000, mean_vector=np.array([0, 0]),\n", + " sample_variance=1):\n", + " \"\"\"\n", + " Very simple custom function to generate gaussian distributed point clusters\n", + " with variable dimension, number of points, means in each direction\n", + " (must match dim) and sample variance.\n", + "\n", + " Inputs:\n", + " dim (int)\n", + " n_points (int)\n", + " mean_vector (np.array) (where index 0 is x, index 1 is y etc.)\n", + " sample_variance (float)\n", + "\n", + " Returns:\n", + " data (np.array): with dimensions (dim x n_points)\n", + " \"\"\"\n", + "\n", + " mean_matrix = np.zeros(dim) + mean_vector\n", + " covariance_matrix = np.eye(dim) * sample_variance\n", + " data = np.random.multivariate_normal(mean_matrix, covariance_matrix,\n", + " n_points)\n", + " return data\n", + "\n", + "\n", + "\n", + "def generate_simple_clustering_dataset(dim=2, n_points=1000, plotting=True,\n", + " return_data=True):\n", + " \"\"\"\n", + " Toy model to illustrate k-means clustering\n", + " \"\"\"\n", + "\n", + " data1 = gaussian_points(mean_vector=np.array([5, 5]))\n", + " data2 = gaussian_points()\n", + " data3 = gaussian_points(mean_vector=np.array([1, 4.5]))\n", + " data4 = gaussian_points(mean_vector=np.array([5, 1]))\n", + " data = np.concatenate((data1, data2, data3, data4), axis=0)\n", + "\n", + " if plotting:\n", + " fig, ax = plt.subplots()\n", + " ax.scatter(data[:, 0], data[:, 1], alpha=0.2)\n", + " ax.set_title('Toy Model Dataset')\n", + " plt.show()\n", + "\n", + "\n", + " if return_data:\n", + " return data\n", + "\n", + "\n", + "data = generate_simple_clustering_dataset()" + ] + }, + { + "cell_type": "markdown", + "id": "c0bb8c76", + "metadata": { + "editable": true + }, + "source": [ + "With the above dataset we start\n", + "implementing the $k$-means algorithm." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "29a75065", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "\n", + "n_samples, dimensions = data.shape\n", + "n_clusters = 4\n", + "\n", + "# we randomly initialize our centroids\n", + "np.random.seed(2021)\n", + "centroids = data[np.random.choice(n_samples, n_clusters, replace=False), :]\n", + "distances = np.zeros((n_samples, n_clusters))\n", + "\n", + "# first we need to calculate the distance to each centroid from our data\n", + "for k in range(n_clusters):\n", + " for n in range(n_samples):\n", + " dist = 0\n", + " for d in range(dimensions):\n", + " dist += np.abs(data[n, d] - centroids[k, d])**2\n", + " distances[n, k] = dist\n", + "\n", + "# we initialize an array to keep track of to which cluster each point belongs\n", + "# the way we set it up here the index tracks which point and the value which\n", + "# cluster the point belongs to\n", + "cluster_labels = np.zeros(n_samples, dtype='int')\n", + "\n", + "# next we loop through our samples and for every point assign it to the cluster\n", + "# to which it has the smallest distance to\n", + "for n in range(n_samples):\n", + " # tracking variables (all of this is basically just an argmin)\n", + " smallest = 1e10\n", + " smallest_row_index = 1e10\n", + " for k in range(n_clusters):\n", + " if distances[n, k] < smallest:\n", + " smallest = distances[n, k]\n", + " smallest_row_index = k\n", + "\n", + " cluster_labels[n] = smallest_row_index" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "9fae7fc9", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "fig = plt.figure()\n", + "ax = fig.add_subplot()\n", + "unique_cluster_labels = np.unique(cluster_labels)\n", + "for i in unique_cluster_labels:\n", + " ax.scatter(data[cluster_labels == i, 0],\n", + " data[cluster_labels == i, 1],\n", + " label = i,\n", + " alpha = 0.2)\n", + " ax.scatter(centroids[:, 0], centroids[:, 1], c='black')\n", + "\n", + "ax.set_title(\"First Grouping of Points to Centroids\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "90d2a873", + "metadata": { + "editable": true + }, + "source": [ + "So what do we have so far? We have 'picked' $k$ centroids at random from our\n", + "data points. There are other ways of more intelligently choosing their\n", + "initializations, however for our purposes randomly is fine. Then we have\n", + "initialized an array 'distances' which holds the information of the distance,\n", + "*or dissimilarity*, of every point to of our centroids. Finally, we have\n", + "initialized an array 'cluster_labels' which according to our distances array\n", + "holds the information of to which centroid every point is assigned. This was the\n", + "first pass of our algorithm. Essentially, all we need to do now is repeat the\n", + "distance and assignment steps above until we have reached a desired convergence\n", + "or a maximum amount of iterations." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "378c29fc", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "\n", + "max_iterations = 100\n", + "tolerance = 1e-8\n", + "\n", + "for iteration in range(max_iterations):\n", + " prev_centroids = centroids.copy()\n", + " for k in range(n_clusters):\n", + " # this array will be used to update our centroid positions\n", + " vector_mean = np.zeros(dimensions)\n", + " mean_divisor = 0\n", + " for n in range(n_samples):\n", + " if cluster_labels[n] == k:\n", + " vector_mean += data[n, :]\n", + " mean_divisor += 1\n", + "\n", + " # update according to the k means\n", + " centroids[k, :] = vector_mean / mean_divisor\n", + "\n", + " # we find the dissimilarity\n", + " for k in range(n_clusters):\n", + " for n in range(n_samples):\n", + " dist = 0\n", + " for d in range(dimensions):\n", + " dist += np.abs(data[n, d] - centroids[k, d])**2\n", + " distances[n, k] = dist\n", + "\n", + " # assign each point\n", + " for n in range(n_samples):\n", + " smallest = 1e10\n", + " smallest_row_index = 1e10\n", + " for k in range(n_clusters):\n", + " if distances[n, k] < smallest:\n", + " smallest = distances[n, k]\n", + " smallest_row_index = k\n", + "\n", + " cluster_labels[n] = smallest_row_index\n", + "\n", + " # convergence criteria\n", + " centroid_difference = np.sum(np.abs(centroids - prev_centroids))\n", + " if centroid_difference < tolerance:\n", + " print(f'Converged at iteration {iteration}')\n", + " break\n", + "\n", + " elif iteration == max_iterations:\n", + " print(f'Did not converge in {max_iterations} iterations')" + ] + }, + { + "cell_type": "markdown", + "id": "545a6742", + "metadata": { + "editable": true + }, + "source": [ + "We now have a simple , un-optimized $k$-means\n", + "clustering implementation. Lets plot the final result" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "d9d3973b", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "fig = plt.figure()\n", + "ax = fig.add_subplot()\n", + "unique_cluster_labels = np.unique(cluster_labels)\n", + "for i in unique_cluster_labels:\n", + " ax.scatter(data[cluster_labels == i, 0],\n", + " data[cluster_labels == i, 1],\n", + " label = i,\n", + " alpha = 0.2)\n", + " ax.scatter(centroids[:, 0], centroids[:, 1], c='black')\n", + "\n", + "ax.set_title(\"Final Result of K-means Clustering\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "ee6a145f", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def naive_kmeans(data, n_clusters=4, max_iterations=100, tolerance=1e-8):\n", + " start_time = time.time()\n", + "\n", + " n_samples, dimensions = data.shape\n", + " n_clusters = 4\n", + " #np.random.seed(2021)\n", + " centroids = data[np.random.choice(n_samples, n_clusters, replace=False), :]\n", + " distances = np.zeros((n_samples, n_clusters))\n", + "\n", + " for k in range(n_clusters):\n", + " for n in range(n_samples):\n", + " dist = 0\n", + " for d in range(dimensions):\n", + " dist += np.abs(data[n, d] - centroids[k, d])**2\n", + " distances[n, k] = dist\n", + "\n", + " cluster_labels = np.zeros(n_samples, dtype='int')\n", + "\n", + " for n in range(n_samples):\n", + " smallest = 1e10\n", + " smallest_row_index = 1e10\n", + " for k in range(n_clusters):\n", + " if distances[n, k] < smallest:\n", + " smallest = distances[n, k]\n", + " smallest_row_index = k\n", + "\n", + " cluster_labels[n] = smallest_row_index\n", + "\n", + " for iteration in range(max_iterations):\n", + " prev_centroids = centroids.copy()\n", + " for k in range(n_clusters):\n", + " vector_mean = np.zeros(dimensions)\n", + " mean_divisor = 0\n", + " for n in range(n_samples):\n", + " if cluster_labels[n] == k:\n", + " vector_mean += data[n, :]\n", + " mean_divisor += 1\n", + "\n", + " centroids[k, :] = vector_mean / mean_divisor\n", + "\n", + " for k in range(n_clusters):\n", + " for n in range(n_samples):\n", + " dist = 0\n", + " for d in range(dimensions):\n", + " dist += np.abs(data[n, d] - centroids[k, d])**2\n", + " distances[n, k] = dist\n", + "\n", + " for n in range(n_samples):\n", + " smallest = 1e10\n", + " smallest_row_index = 1e10\n", + " for k in range(n_clusters):\n", + " if distances[n, k] < smallest:\n", + " smallest = distances[n, k]\n", + " smallest_row_index = k\n", + "\n", + " cluster_labels[n] = smallest_row_index\n", + "\n", + " centroid_difference = np.sum(np.abs(centroids - prev_centroids))\n", + " if centroid_difference < tolerance:\n", + " print(f'Converged at iteration {iteration}')\n", + " print(f'Runtime: {time.time() - start_time} seconds')\n", + "\n", + " return cluster_labels, centroids\n", + "\n", + " print(f'Did not converge in {max_iterations} iterations')\n", + " print(f'Runtime: {time.time() - start_time} seconds')\n", + "\n", + " return cluster_labels, centroids" + ] + } + ], + "metadata": {}, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/doc/LectureNotes/_build/html/chapter10.html b/doc/LectureNotes/_build/html/chapter10.html index bca7acf4b..3bc899723 100644 --- a/doc/LectureNotes/_build/html/chapter10.html +++ b/doc/LectureNotes/_build/html/chapter10.html @@ -5,7 +5,7 @@ - 13. Building a Feed Forward Neural Network — Applied Data Analysis and Machine Learning + 14. Building a Feed Forward Neural Network — Applied Data Analysis and Machine Learning @@ -53,8 +53,8 @@ - - + + @@ -199,6 +199,11 @@ 11. Basic ideas of the Principal Component Analysis (PCA)

    +X(b*aPvOUGV`e3wr%NJ+Jl5YxtmO4ubw{(ERrb!WZ-QKK!Hr3*n=i9`uZ&p zkx!$T^8r*F-M$}Q#CawwL@Qpi+5ZcVsh82C)}q-k$xq0!nF$I;{_yb2K@k@M^(xJ7 z?rS$%(EVW^4yS1*fXEPTo_>YIz*IfDVZR_8uO1j$r24s)U5{=t zCTw9p<;vh|=)9n6bAPt}gWdmHfN9tIii&sC~Lkv=2+9lJPJ#v0@ zrTS!A&X1v0&4|{q0!~k*dD{H&gS2W9@Sah0crk^N$oLC z5;ceWCBHtci^Y@C@5LSRI4pDt!Opw|YFAH0BPQ;171210`v%sq86iwG4#rx8@m`K= z3Ptz@-I%dI`FL8&D2>R$$CRJQ8`w%O5y>l`p3W%!s1rYa2a6G|q-96yGUs?b`Y!&4 zMbeR2HQ+$R_N&=^!*=oJPdUDdz;TP6FGa|2G>>ofbKHCz`b?Ei!(Oj}!zsPv25`~q z`o=^r=WK~iu!oWxPITPh`@QiO?s!wU&tLU&k?o(~>k&G?wazHxu8(uak}SmEhLXA) zAu?GHnQT_IK2W!unZ%3Vn!EzHrsm47cgS!z8rp{Ygt>nJO6~z@Z*x57NC+dm!+s zESOa^VX0qo51S@b))quHR-febORbmER=;KXmZ5~{j|*@0>-T3L#_rx=5%|2YOxw+4 zrt4V@+*^5G>2Z^R3;npFFyu(^u2nN>|UJ@?{jzC*l9x6O^70U8ZTN|{)UmAoqzB(FJTeIw3iB~Gun za-eZbuI}9x1q~C9Fu$t@BhqwfdVrZpn5W~-&gsIptvCy@)^4Ty8pB2j5$M@!0t`R3&m{4p;-vWiPd5dJFF93rfg29%^d+ZaDJb;X50$^II?(T5B> zS#E6e-CgOV$}EdSXPk~ynVR2NXOH^C96K$l`t*5|?B3rOL4V$VaCN0ml#;6%s}wjK z3UNU8!&<`uxw&y!>TTMeWB*j!lHUPxO%aBooPY8o~hU~d0~y1vi1eZ zq)-{dGzM%{<6~a~8E)~OzL#}#4iOG0@U;1yX&d%}r#>}*@K5zdscZxXZ|gZmes}tQ zi{FopQ*<0?_bXl-u|N5jx|>!X!K9*Y%{;Q)IvpV9spvzgI*dD@I6 zo-g?dMVru|#_JiPMQ5_pM$GxfPy*3K@K&@Z@bT>i=#uyOp2F3$xt{N*n+eWw0-GDk zt+pfJTKz`xmA!Mkn$nl;XP+Dge+fO9@MS#a8A#tg2alGxDDZLv?8y+6S)@);Ba#Q6 zW!iaJIjWqih-{iLC~Zi7!ztG-t8AOpoXLxrqwx|VSg!4RwseG}2- z@vdby?C6gUEaU6gVou%XCL$KjvoIo{A->>X=_+_xrOD6GJUA#VU7usuaUR%V^Nt}W4FuPE z{P3BaLpSW%PjE@GT#{YF!HkpHXC0xDpijf>#24@gLPCzMqTPGELuxePX8B0O!jDy% z{_)tfHKb@89oyb{E?HmYG7I$(V-79dr6!70N-2pess8I(mAvo z4d?@*B2&ZY7`SEso>f~fu(#h^H@A~gsDCwiRslcu2i8g$SGpyk4aJAnIg~by%jYm1 zF{yN`%LD3aKzrNrDXYYzQ0jEIx+y^LG!Ls!odpnj^XO%B`|FLLFG$feIJ=tcpR{_F zNAK=T*4T5ub3q4v$wz);yDcN6#M)MuxT|9FEDWoBcQ%OYBC$GK0}5Qe{6GX_yn&#O zWT|3eB@DzM?9>@Vvtw8O^C*6x262XvT z2RgrWI*1BqoZY|?{4kB0!#BhL0pGH`Z?4Nvx7te~OR8@jW`{V4FoODsV$!Q4Z$hw` z2pN{%iDzf;$@3I^A6SR9Am?|#YSp>5X-|dWKej>p#o2=6``?O^p-_>T9r{sViu&BC ze4OG##J70X*^K*XXRC9h0(Otb>>KKQM#XcD?D{sRHp})0IU4Dj?H4#1h$M^RBmxrV z^Z*lr$j1jgF;C-D8 z9w#Gd0=ehmG}$cBQ(cho8oE=#(d`|lwd;JIW0qmqieCBLT-=`b4Q(`0L1ivNIpCLM z5;K!YrqS!_nvyq~5AG{k@~E3uy%Pzj7>qX90+^RJsLZ0jDbR%dOtsyq(T4>G%&oS_ z5x8duT=yY|7VEaM0xJ=O6~G)aSl@MlJ=36dT$U`so{QS&35W8fu>1Bgm6J5~AKwUi zBae!L%d)({w=D(DwVR%o15CdVy62QNjWu=unl#oXJJ}5#_9_?KKT|#KL2)jhtym15bvkG zeZ+60_NJ2cBvl{I+qoB0N>8+s%R^&v$6uL@J(`AU#&ncJAQa5Bi_}h^=ZoE0hZPml7XEH|CUTH2_~I2# z@`h7{dDhh55y^<<(Y?@-Npr=fjkjI-?@wkJ&O3b3N2!WtOWM4)zXx>(ciFBS$iwOi z1`M`#?@}p?`ByyLuNW0ba=`UsvnYf*mnMn*4ChMKE8cr<#4kwhu4!Y&9L*2XTlk$(-1{PM{lhMM);p@2N4EMMoc+= zU$8!ONVPR-{BgeVH%H|3_apG++_licW4)lQ`=@gADhNJ#dw#lriid396+r-3c8ol4 zFZLl64n4o(5HUS~`WPKl9Zq-NS#x|H@51D`=DeWB{IfeXSN^naKzxOCB(6fQpXAoG!)1#N%4X2}o~~@f^gH}X2BKk2(BR;cC%1BS=46G0 zwCk_+y*9haC>gT#CHqWnJMox}l05_*$g8*v45{3YP(b$Zw);hGhi)a?5d;t9k{l8Z zpBltzay+)3ukS|G)N)CSjQ%AdnV&J-myTm|w=7+X!`MB>R4XRm@)WFy$k&ZT_*f^~ z$~i^hze+LiF6MYwg#C3xo=PEdw`XjsJda!e-#s{!>%0Fz0^nHBCM{f~Nhy*)Xloa7aJ5P(TS>*{<+oIFM6|SRumZ3cY zEB|blv~3<6=g6^Rnz%uHI|7<56|kK~Owp!q1_Z0ol&0ULsMI|an!SJkA z6H8JdjF-|cQY;>^P2Tp#?RbbqU1JN*{MWBC7kap_HZi+&9s){63_Jc_NDV>GTol>u zdu=%rdeA9OM#*9TkIskee^gIvLeT<10T74P7OF_9bb-4!`gp2 zF#aT$WTozs9Z3o1*?G$=zYVcv-MgA+xr1Jl-wRG-w{BcZpVk^x71CDpa ze$Gjy^~T;sVSS#;`yiN$%Ei->azz zP6-L|R5#)P6Z}|Kmh5g?M`NAG{t7Bs@ZWwrmG28%eZ=J>Fd$rbiO7-{b z7{Gs<@R1quXKJWnJxUtOrn1lG1kZo@EM59G&as{hmn8S&bg3 zYcmedY{&6(E6nf`kGO2x?Ho^%oo-%DD}Ridka67zj8=5Kv)SYJ)n1e4Lrj{!eJa|u zSJq>t1;>beGy|5kPhk|A@t2MvK~cxuX?|zKTo-}|a(p#hXYERNXjm5mwE6hKlVx&cHXy(sN`MQyi*0R^nAcM}%}eu-(lb z!_NNV!ioiK-Q14PAg#w#IS(gudn@c#MtO?rXM@fk^+t2TDqN03(*6w>paXH&5OmyU zZM(;rgM-R^zU8%!?aD1tldd1zU(*QmqTje5QB|L-{Y3Edx=NY@E2-3-z0*1)IQnD9 ziCkSw$}wXUCAPWpL0RZ%tiVG$Fd|{Cz2X9OpLGPM8Wq-c-P~1t!B=Ss*(Z1@U_aH} z8Hsu&G1Bap+T~jDZb@`~!;LtSFYk+g5*Wyx@ghw@fqHi{dSJ4#{iQ%%TcRVQr*>9pzWT7#3j3cAw+dpM3T5m!(zc?|KXK1<{JDy&^{w0^OmZ|Eh2o_r%8DEV#XZAF>ox zcocK&P0e$Hy8Mg7N@vP7v9B^kWo-%}P3l8NsCSJrzcom(mASklRc&t_OU2gUEO*H> zeUT*4&-KRib;EjtFlQ=utYoaBUjb}lqhto$bau&0Rli=R?PjQfUG}DE;C24WD}6Y;oSv zoxjQ9qqKgf7p?7EnHriIP}5n=6rr317_u2Y0Hh;Hp)RgGefpCtu$IOIxW{`3=9M!b z%gaEpdltscl0wqXtBTUL;7f%fWu5&g17UG+>bkFAE$-QlX>W}oS1o&sd%T(6U!E34 zRdSV5kuEijz04s4i8G~*=f)t#F-^~d%Qjvdv~(Zax13IgOpg|+D$3e?IZCVo049>6 zr}JIa8whE!lP5C9DksFV;qP|bU@%4K5&4a?>V)0LoK-2V6j^lS;4M-rmnP{pe)WAEsP?FX~omPIvJ&GeVN>#dlw zRpU$k!5rH>w}$J&gz@<(h>l{wsNk-PRTLDy_KpC3KhTM-Cj8DF{!m&a0;H1xhjQs)1#crVRbDw)&j>b9`QcX>B<})Z)_GaM4<;S`mw3 zXJpXQA+~iYTd3IkGXOv}Udy8Xy77$#b@|q0TCnBT+6y7TNRu>Z%18w1uVGIoB@53!+zx+rI zHZ7#8n!&g8v^nfTk1a zemX@8nFD_)MdAq^!b>l1**8CMtzj;Qe#0PuNXN+Upu>#jb}oAz03co63BrMEo5CQp zPg`ir80ZoOd6<~`D({he!jo?&aDIvvq5BAF0j#L1s1OSBBoPkSgF8i$*pBT;bQ1wL zj%X$rL3mejOVkWpW=CXds+VBW_7^mbK8M)mbH#o$5-|XI52|%zhwRfVrk&lGizGrP z1H!>hCPmJI^3+-kaE{p}-Ca|s1yls!8za@eMldnC<^JGoRZ}ez|9>Gm{NK?c{=?hM zZls+J40?Wqx4MIDQyyI>Y2v}>7<Kv&sn9~q{XBZ=;js8g(rH|gmE0ia*=>6RdWuT=+v-q+T{`XE0^WmIf{~qIBz&xi&=5+KCG`D9wE+yt>Tv1%jXHw_VA7VV zIsaF3X~i}CLPs&|;!GcW(BVjoe1r1LfCo@k(-1lA||_!!@7bH6hwv$N)nan z^MeZA!3d}K&+--oUrB4p%>Y)N~e!EYf2u zqF5rmJFa$=Rb@3Y9|`T&a;{RKsjcffdLC6(XBV+q`%7@Z zvccL9i>wRBuEQb~w8m%HTOREP5aYU=dRfUchi$GVts|P0!Vq?E zJ~T;2C!9>vRhm`n0y$}0xP$7(G~U}Fp6k(%0DiFEUdy5tZ`IVK*d9QY$DfykLPloT z8weyi;w5=!kP!2n!w1-&%)5RJ{_Rv|$5MwD`2@YTryoeV1)L6l6#@0kUJV z%~fXY`Z{%;q%6>QZcyh*W%IW8nQwyebXeH+E^hVL_n(YBH2krqMzJ-3!cxyNT5aIu zEU*x~ZhS;NdBm-7Z4Rxx3$7dfZaDGk&=`vPl6n1W-@A0zL#e)NvNYgUl@-jZAvybi?!un9$Xl-D z&8?r=bckswp=pFuMStFIk#OC!?l|dgd|18*H>+mcZCbW@o`>#MR8Mb9ll<>bUd$>t ze($g7PBh&>Oh}lz4gYVq;>%)4IcCH;-O<(EaiVEd$b6R0hC0V8<}v>c3y{)v|41h* zI!cKTyFqc z$M~IxLDIil9f!;E1gJy$_M!(%16c!YP#-Fb4@uM?qO+9|^kRx`QD2b67|mAWO4qa@-M@cPS=91q zr)itV4Mc&-@Txa6Gz-e;FPN~y-2aF4vU6U|rQDF8|9HJAlK0*hcnWprFXAY7vR7aAxngB%2U`&kz9TEjDAXU@Y@!+ZvQu$TGn z5jO3YVbM|A2anK6D~-F*SxJd8*_t_%{K_J2QFUA82C7wp8c#4)RW&L{o<90^M*0Rj z=oK?9z1O@X0u7#`#EVS0axrM)hRv;tu$Ec3v@o z_riMV%<%#s5ch~)0mn5Q2-rCy%xnr_5+6oRD7;HvSfv3`Vlh2eAZ)rNFSz>>=BqNk z?lVwTn;+&&2mT&&a8f}UXT-*H`;hRN#;-{m7Vs5>zLpiqWjR9!S!vnK+9g~i)o(Dt zkB})3TM6sk13SluX*6k5nELa;TuV2P#H(-e$9Q347EwiqScBP`(pXxsT0M{l$RLU* z+IESbHD%exLxQVp<)~jjRpqvid~BSYk0_>1=wXkXimbg^)HAy%uSuQyoD%bQI0Q^NMW|dy#r^sJJy}eUPPN6sK1Jw#{sv zL$)xf+R1s=p*(D^i+bf1y1-=#OX0l>eB7DyA(o1O7;SF$sxHtnP_fh9m{J8r<&N_u zNIkCsZI8xlkjkHnyK3q<8_N*tXoSIzOu@7Y<=B#qQ9}`AMysxb&^r{IDjS^$5PQ>o{(DvrU#Ahid|z_VGTY! zMbAbj{5504UO8reMMyoChONKnbZ4{p{_GUFYrErtTH-xBI0}6E0_&Vg=GfC;**GYD zi^v##Uk3X~;)k|g2S%;C(Vobe-`z7y%w40-cg9%z)K9jQmV3`9LFsb>t=NAt@>(to zSuJ(!RxQXM5`&`UY$89{2T*c97s6X?ziO#y##AyM__#skD%J zx-fU<)&_TOnf6m+g;vAQ>*m~1kJ&MHyKnFkcq3*qm;kxXHC1+!#$?wZJoLvQ@o4aA9iji_De9Y-v-c$17j#3LUM0 zLl#7J#ug`2A2rezM*+P$@T9ZMytQy09d~ZklyCnFymG?9C(0S+$OJX2lJF2fR5z1& zVmB->*O#6-p(F-Pr?@jDa!Lgbx8FM~#!7fR8!ibR=&3LtywVi9c_RR&p?1S8ToB^j zv1@4CBC{n!`mgnxnsh>6IbV?2H$p>7BW5TC7LM2f58%ecMGJM}F^`K|{xL zh3~BL>_mNNqF#y(7JYg?WU5V;fmu(Az_R00LVJYa{fB+UK;AmkT8K)W@(DhkD~;rk zpCOk=GZ(rf+0_dLw9O^g+|WRp!1`D0h+xrTZM_?0=ESQE^qHyz0@z4M&(Yg;rw%eD zIBL>Tp=>W%NhZ*e4Uv>J_V<}bn{4~{WOm{0qkrw`OrI()Z4!$A_ zshPFo{8rWh*IA1#)i(@R|Iq_=?{LHb&zUHLIvST7KuIccUB52y?A;0pH|F=Y@UH~9 z;r2BTG7^8>5$pL=L)Z5nW*`>nJf0iO2{>*Y=m>AOpZ)2~6rz%D6uo|$p~Uc@5f3ox zrIC5ePLAE{iGpqaMZ1hQ!;dY!F2Y7}9q5$~B0UP*9v8~M8!KF%SgEuIbT8NJ@sy1cGONv<#&qiJPNG>R^4#q19zC5q6{=nup0SS= zoXrr2UPd5x_vc?pHi+vk6aPfX>r5o0eH8z!_;8oGFuMHA6WOpx?9j!sRL0sUmY@xF zl90R#L=*Bu-a(Tx>Gn`NLIbWY9_O~5aPwn6X=>b_3*R;L9dScP3GUXX_Pb5a&aM)( zt?6h^d+Y=5%NC;5onknxtMl!6=lN4EMi|uWfB4fEOD|xF+}nzaEU{N3 zLYdmOu>{@W)II7!K4QCfWS-^Pp*nEW^TN)XUy|eu94ps#i|rApXFg)}PYb^gbZ-3o zX*#v1(Y{!J;<=5rXc2owHCO-Wh`b{ezHc|n;dFLOFD4TAl($rZm-3ux_qn$K?h7Zt=1VB*I~q<6Q>9@-%hNJ9Y1_HcD;n{>r*eVd^s^ zx`1b^G**yG?CQcIscr1)o=oV`6NdxnUg#q6WxTxC&P(GT(msxd8vI`Qyq9df#}4_9U(g z%qtCXZyE#kGSr|COVQ8Z82hvPwkL>S4pkP|F3sCAMva!>`bGuUIGM-71G^_}$&Q8E zYsgP1Brg>%gc5h4VgKV_3%{9zrQA@T2{u=#l9UCCMhuzadUz`aalj1J#0*QS1$<_2 z)%6-1dIH~3$7&XE#5|273K9^~%Uooqo0Fn1!by!ao3o2zVNGgyhNz~1Wv>q%xrfJw z_fmnY^&zK?_EZBj12$tHmXpUPIG{MT)=iNORqKaw_P0W*D>+vkr2-OZefE)2bYnzu zap13ORokx1$ZT=s1xp3ZkHKqn^BG&uQRyW{LUokp(nZ{E)laQg zV;{0Bs;<4fB;_EN5xvUbuMA)xD1H&~-hkX7E0_wh!bUjF2=)nr%X#h+(ty?@WnMyA z5TAcd;2>;^1`IKiLPxJR+B~ir>|+0v1@=*o8Q>EiuDi2u9C<(vE)PO@)&kR;!1jjV z2FDB)yP2$$?|{z{YO*$hN3jY`FG(ytHeY8LRGrLrXq!f@zpKSi7gh|5Jgx|2#{3ty_X}%`= z5z1cTI4z+TLHOc!ds%1=#jK0hf!)~QWl;a1BoGe}x!1vZakn|_iGH^h862KS6(9xr@C>_1GA*@WF0cHKhD$9Q3RrHq4cic0p^AVv&R}+yzdx zh=2R2@g3yrEXgN$U=u9mF-hj#Q!#chp#zgYH3A1)s0GUTG>-XfOLCILXWl)-6kEC# zZFZ%6H9YJ$VVsK;{lj$(9ndT**aYlMhzNfMUou^!0gu8ATKw?}hj3%ebHPu;)qCGz z$WjM1faqq+qNQHFKl2OwIqkMqjRfu}M@kVX7 zO-+aikzgh|tXq7W_$%U=DQgYQM{0$du!sZv4LmwD_ku+h50OliLI@6lL|y8L)JGXiV5V@H2TDfU7njR{ z(sPqt2KAv@(3!@Y0m!0thQZ$jA3V;Ip&BSYiT5e)ufn!rDn~KyIr8{r{NioE3R)MH zNaFM}iv4L2ulH=lJ}-Q9LGPz@a`zbQyr|TGNefw0P#cIkd0;O@9GT2Tk7=umeXi)- z2%Kn2KM9yVv56A?H0G7`a)-~!ozHS z{kjUbg|+_Ape-X}H!^+p;=y{YI*Sibc-}Utq2e?*0<8B&8WRi|qL6wdb+SzD)Ma z6raL0=}(3cH-)9wR*Xx5qmJATRus>|BBkWj2-P~gnsH^(SJqj!|%7K|H&m`EwlC;)HKNc_60Lahr(} zaDi%-vM$TqoR?1F_!rsl?z;OEpAY$UTqW}E#9r9m`~c4W+UYd$5N%g$0t=S1wi;F3 zssPD)@SMW*-84eY0J1`xL1bTEn<=F!NvIQf#NYp{zJ@vUHmO>T;Ypkl`0L+YEm3OA zvzwK}tilAYCvhf1ErA2G@j0yn9RYQ3i_(Zb*02?^AZS0`Ep7X2_7{ftDr8h}8E9^^ z`m&42q?zynjuL?BSB2`Ig!H5q46_F@vw=vS!ZYdru zKgE8Go3<-#^#CRM{NZoXxSm(U2!6{%wPILmE|?T~nQ|&}>1S^A%9Ek$%R<6Y_ZQeymro~uV5+)(nCfukn%0}Bb~zDyGl|H#LO6z} z9Wuyw>?r+BB^YD5a7ESR#;6YKbI3rJ0%beRU*YdR;~pVDdTouARZTJaQs7f9eF=QwuhVHA*x z0~KNnaNIAK()#gA*2`ZA&gCCA9yiz9VU6#{)l%5c^m;tJNcxV#$YSn-hzDGIwW+oi zaNx{es5SrOCFUeKA6d#Hb`a_E;MJDaTb6wE{wxEXQlC@y%k5Oec9P)eYWcIDg5_B* zuSFQM-(~7q*6>z~`i;VPugY3@q@>1q?N_N@yWlmj9+Q`=73aD;pa$C~k>9NUkdDR% zd|h#I{1G?VCz$}xegAI664@~5AoA6JQZn|_`9ys@bq`0XW1GAj%W9~*r9H#hiHo&% zW2WZE`SPj{xKC8szOJAoEF3<5J4X7(3h&M8nO5W%C*RXjA`gAs_vn3Qn_hAZn$6`1 z{&hbbejcERjr|Qd{Irn+2F6q9-XjpE$vw_awg-n1OJ0+mY%@7vVu zVjp2Y&Yw&n&?a|7?;FT^aZ?y>=wq+RuL}k26h}do(7M9#?c}xVsE_2kSaq%g@6W@P z+#=UIrUIYpz6}lX*y(3&p5PTP-4kRQB!f49O=6H2X~IJlbY8uR6VAT@tsnCf3Degt z)~IeHhpLjK5*2aF)#NlszZw-nuQ%6qo``>0uJD?1r+m)u2(N$5HJZ!)(R|r)xB~Zr z`JQLf#1?I^FF1(Oo1&bFiVgF%Oda6Qw+Hc=}8VJOw;Pj>J2h=Y!|2t{co|)qX+4*Bq z7B{Ssqd_)%cu}Q=y=YD4c-`^5VEix10Bg~hH~;QlT$vNt&C*aM{lQ9dlLY0&TDHDQ z@Rc^Y=xnTwvR~9#RB3qZp4!ZpNxi0|!qKYwHYpiyKiun{As1O{5Nd!yogdO?_NOow z6+?8~ZHM&;;v#v)HB!>?qLn#zKld%Mj8N!XTNh@rq_-m+UoP!`OqLUrwVZs{GE3NL zlq-6=JyR8;B!34V4TE@R3(mM_u*!>_d>CD8d!6jI+&6vU(INDZ>PPM3#HViGHwv^~ zCT`O-YLQP|QYyPY{+4Wvdv~?=wCRSMJ@mTBguQG$bymxAIQQ8{lcR%Yrk+_8?;&Pr*}V8OOQFGKi|x4AAEKUd zfeBwF@GutE9@yqCCegdx;0W9v(hf~3=K)$}I?;BS<#(m=Zb9C-W~c>~|ET=JAA3eu z|04abDCvViOQ_}AyIjMqo`@9x<7OAR==LPi*{>I8{$J&u#5H$<78OCJ3jR93CeqXD zHz0R$ci%2<wfk~4Dtkp6v*(mgjRUL|$VC$@8UaEAG=mn-sU9vm! zMNng{SMjb&qnv`3xJhR5Ui6UjO}0rA7J{zWfgrf9^F6FZG+H>Cvru`$%>AZ;i){^A zNu^j6SR-o7W-!^_l{@3N;Xe8VYdcsp5wB%|Ah1>6`7U_PICl2b~C>rq4-^i#0{D1imIcG@!czk>zt5QZQJLc ztryLQyXLRep#}{gng|(@FAvVgSq&$N5VV)|!t6z3$^LBF;FIY{H?kVF@fR*Va^AZs z3UVKhtjC)gc7*sj54uIC6b%jo_DeX2_b@fP_+fcXa7&_S9x`%McN9WH$8C#02ToDT|3k}+zTvw6XtxT09E0!=;* zpN_?YRBwW#j*5xds_VpM#|Qt#-R9mDo168)_@g9bri18LHGk9PLk;hpiy$dQPTF=S zd6ZM@ZsXBj?iUr_0&#OuIhEmH3Q$`8uFTJqg)dYyfm%jJzeX1drepFFjC!+9xv`3* z;3i#lZa$DVV-tDfl9AM+g>h}-J?=;G_R`Pq?tS(3#KsM6tsKy+fBVM(Q2uqF<7x=)J|Hh zf8EZoCMB;;GH(9(!v~6&)l~52UbF_agwrOR@Lj3d@_1IjrjjH@>ddPcH4A$X!`~=Vs#;UiR;cUgX<7zUSimm(H)GAic6?===se=n6rA(?6$>nux&dnWq^;QwiK1?91W&ee5%}* zl7KiHKI+^XqzNe55t7rXvxSp-+ua4%Hu71I7MoruKLW?qZB2Z_ZH7Es8Er7g1T2iz`zp@&vR+I=yNO~Pj<;z?w_=!-TJ7xAn)tNQBs4aTmTZeio zhDEEc$Gki7N*1b1ey)bi2>8+U|cwnt@HFT!tK(1Aa3&@@dq=DtBQjJ@_2f`_LF2ng(<{ zed$dHw_qt|rV7q)-UK)Bd1rq5G`zjpFwLc!5EYAu2|~y6wli%U?BJ5$D)PG zRKVnbh4^9DW8`DAhb$lNSSpqvtlNlOaaUU3L3 zEZ6K-Qc1DA2*W97)f;{G{)^ff-dDl4p){$E>6q`oc>q{0eWjTFg?c(viz*&~kvNY= zgKeWyt)qmIK-Dtl|9fCNj{Hq~tBwZ;TSt<_vfol)7p3HkJ8^ytPJeKT94TNu&zOW; zlE_*mCxDYIW*6Dv;LXFH!@{qjk}CRMyI3qK``lId$P`KMb%ZL_IllKD%^5&|(T#mx z-kI28nr0OVDcthQNc``HCJjHq>M#|k&;qa)tNEESms98O+yUXsmcIT5t1is|LOsc# zs9S=ua;P{$MxYQMzlbRx!1~< z#D&&vUlOa~vik4LCuF)%&2Yd@8GDRCFSg=&F7*cb*GVW5g+rIh+G=d!TA4m5Ku1Qv zZS!qrtHn2{V8hFcVx&p|lYnsjwde3y>p>;_v-U1P8*+KTEmQsf`6lV+ROpJ{nxY z%Knl)s=G^hB${dU~fQ)!O{pzDTAe8?(XOt3l9%E zu-+xT{EL(H&b6?on(V|QDe*m3+7Y8LWb7s?4lp!L695T`hs)UJFmX>h6L&Du(n2zh zgq*g`H<$?S)$$WzpDsIi6G9S=VB%#3YQcO~_P;pgVGxY?KvXo3k36}AE<_DN&%nku zaD{fGaFrLIO5;P?#wR(7JI+?2EqqN8bL&jU%xPM80*$Tlt#J0Sq zfb}VS66R*3OOR+0*1~+D z6S@?D9VgscqLnZQWUp@hP)-`4nXIa$-K+J=;tdtBjnqucca3~Z#V$?$ipgOfJ3MQp zk4?&(u_ixk8g^TpJ{emH%W&~lT;H3qeRnrq@2(FQM`V4aaX(PH`~ayzg|gk#8LRW$ z9ne3=7+3du`_MNS{?d#rr0ux)Reu0redBU(-Y^U8 zynbFCSsShlh=Kkoul*PP=Ge_|d3$Nq;(ox2Z6;4Xxo8tlhjMPsn;|)G4xYH#@d}pa zU3C#p)HjAz?mxN@KfD}`#qS{5SC2;4Km!t24Li*JNc-zs61?Fxg*LqGLr1{rqpc>} zXmCF$7h0~tx2LM-fx^1*kYIJhe}Ig=d@L5m5mN(rg()EXcuE18gxn)3yA;3!nfsMF zZvU7r^}YUDQ3u3b(}I5&*o#!<{E<5D&w>?bS_4imsbM=JYR3@dfWcY)->ZI{l1cug z1y5b%JFFJ>Pq%s#&f(`*eLMN}>2t`x9063!HX0w_4aqusk+hxO4Q|#N0gCcB8;E)@ zZ1={xf=Rvz^bNROqXStiL#P$L!X#gk=C2j1S!MW+QI*gdWGTJA8W7s%-$g+6QflSH zA&!qQ{nfe$WJ`bJzOy|dY0f`zBS*k~#{p{MFyd$AE>JKsXB^M~E=TjD=3E@eDF(`7 zNWk8Tqm@bZ37^q{o$6hFY!Z=B4Wz|<-$?5SW9U!EAbUc({!q5+rdoQV=^VH8|%+Flt%}quWBFfUM|!{><%i$x1r6NLCrJozA8BdlTi# z5#MKo@>l9YsEOj-wLTV^KGkW#r)Y`(rrzZ|YUyty8guv>>uh~gc*}OwRGF6ZTll>L zv1PM2f?(trb}n}~fkMW)VPcx&*3EhYY*J>?VY7OQs+tVPl!qSmGIX2Qr^J8*0tZ7= zbKcTWG=P??)OepwiZk!G*rW+j3n~m;2;7CGbfC2bnP_HMFz@qnlmA862clImOLcM1 zeweNq;~WA2LjQ4_gxI2nV?ThS%sD!+1dxtK-BDjK?oSMWibwFmd@Z7c@r(X__C4c)X-|t2=Bw&qqv33`Bq5pZ96{n=uJ$#wg~~xy@vr z#`wjGntha4CwWa(g2_OM(6mJ-(3yX>YZ?Fs{}&Y<>z4D=0vTdk!ehADiVwHLzXvd5 zx@yZd*lVKK>oxE0Q(^ReU$EX=IgzpH>s2&ULqQllh3QwKr%zj-un93_3V*HpW^diP zFO0uV1K5sEQi~j~T_=B_+Bc{pnYSQS4bK$rUFw1w3Y#yv6?%IWAdRs{$>^LyXt@CpZbQ@|3F zQgXpd@BMpchU;sUpWg!se#ZM^xBx_sp@5Zyk^S5>X-1J`7QhTW7y!p(H`?xraHlly z>&KKF0RV}pX!LM=zQ!xu;(QeOQ5{dgN1lRAo;6jJ7qP4Ofp5|~dgs~xN#RCG06&<& z-sP&OS%8e5ly2DpQRE$fUp3pM-@JJwd}H)8z9$!%T~8(LH4QMauE>iZh676?gZBXv z2ABdIjs49CKO|V3H#Np~;lslG9AH0Oy0<&FkbaXTtj#_()_ovsNzfh+VujHq|BBB7 z5TI8$0I>VgVs)NP#JPtv0cWcb4fwV1n@~dx9RMU52)4ts3@$&?bs0}*I9h8abY+#l zpN`2*cn_c-3A)pa&>sV6Nq)BgLC}wjkDx{x=Kl3x8wax6DhWWABCSwmTty>=Um7py z+;^rvh{hDZo<{M>%!n6u#E`_ag?MRv3M|);D>L#xW7lUA^y6yE%&j{JHf$MhGj0 zO309hlxAK7mA=Mf?ZYETTIvp^LNg3-pjNs2D*%$x{PjndjizPX|L~s04o9$fDatu4 z18dQ6HA4UyUF0Q^i9PBp;G(Y2fM^y*@yq{>6U^r4;G)gd%DWdj5fD25d4nCY`_s4M z!P_*Bt>foJLEz=9WFa8<1)P!t0qRf$I26memcOrYuxXFv=lUN%xDN~FSHz=R_%GV6 z*?{Q(pKE>z+Dqxi%WoteQT?MFq^Z9DT8Js+yejfrQUtVVey^i35q(!0uiqcm-!~_2 zApsWpaZ=kr^Op%%iCYC=rD}ldJhVQc5TFBU_R)!t%__ zH$sN}WMdYkeihygNg%m#L_ zvjCKU`zN_er#rQ#+dVPxZEImeqcY<-l?aG6=2MbeQm0R)8eD+0l6(DySbve>#lv$$ z$SA}tW9L=zruSp29#U&a=0etRnLbUO{g{pS%I#n^j7*KGAPcz5#itx*0EaF|@o+@( z$nIv}rj*d&#{Q79h}9D=hjLgibT|S$f7j=VY|NY!;k(KV2+IN?G3I;BtgQ7I3w0U3 zr8SASCa+&#D61IOND78>q8MwKEkMzF^$k?gEZIP=zQ_k~OSShMO#$anqmML7|xXlTpSB<@x7meK(=z`x}H zymC?YWmv`ea!v|2zAu=i0ti8Y$25{a#O`m;`VIi8{&gVK023y|B&B#;GF!ipF3^DT z9ii7;zPBZIbXnAvF|~j(Wq$`&;s*%M{o_#UUd~ZQ2@`ia1xL*AbTv6Rj`B-|s{Tihj zJi0a>DKm41E1z!oM!^mMqW^Q1)tqqZ@5Zj<8G*RL$3PDPTSTwJKjNOG>NU6zgEasQ z3>?{9l4gF>d+l2a5UJ(>pZ(R{PhR)B>8GHB36M@CzP^2l)!ww=o{&>{&;F#w%S1ktsi`*r%;!HB zF$i#Gk?csvrzH0;Wp~t4F)ear9#Zl+f0^Pto+?vY1$2O}gf#J}N_=30^iIj`euHvC zpXj=2sx>;Jj;zI#-2}KsP%AmLKV7P5*6-D3_0|lE$L>OTlK-XvtZT+@oHVDOVwT8eUKZ~N`LpeH zO3bkPg(sS1{*~AVf>^?#=>JBXh&!~cK!Hv$;WX$a7HOD_X}VXU#|Z$=*m^`p70iQo_=Pv%nas^b%`siFan#ZDwr{Eh;0f0UDzn~rS!u}@qf0U82Vy0ae zf15Ggb4YL^eagn>f#eh^f2Qnh=GdI|!;+CrlLXBOnkbU%H`|B-@y(?R36sMq)xH;k6 zM&(M!Hev>V)XD?eHJ=PoOkZ{HD0STw0QASw0aP=XRDjc;Vj|Vxlx8Q=9#b*PW7QHJ z>FC{7K7Gsg_IU=_XU^{ec^b8Jy!G?BG3`s#OO%uE=+}jU(W6esyoRQ%^MW!Ui1qIQ z4)(ePuBlut^_)<2`A+B`BFk3OR(Z8ULt{*VO>ZD_&t;(p0|M6COop4B<=l$Nq!g))&a=pPrzir7~@Sq z>7y-$y{<{X(=<8(j1z3Q9*2zMaQYPBhI}}V#2k%@3BVc(3V3CD4euZTZ_EZGudb=->+Q`^Ob7ZK*RrD< zJ*n9e;S%ZdAI$rkToojS-03UW*qL*zHg{HJ3`C+mVfVU-+2tzEYi$*K{?aPvS3M5o z)5FKl&$s7;VkV% zPhQ%-MGYTL0>t4g(D#j&zu9#2rasRM*@6EL(}Bs((fB$?1lQs9>(_M(@Z|A`DDd{z zhOn2Rz1}_#Fhh^*rHgq)`2D)OWP`r_VvQn+U8h@g zueGPvdaQR~!1V6+=6p1frQ{9+WR%*{ryXxT-U_zciK^A{NlBUcLg_LUB-}Wuq^(livE;_-=ekeS z9otSwi;9Z!^78h(ak;)^W*RJcGG#!~-+spXvr(AM$iWfqzB9w)ydsn3dnh|PHnuU} zCQ2ZA%?+B=cX_-Fi#9#op8oXt^R2Z=jU{qz&SPN}P7^@S%lox2o~Z_SZpr_0gK4*M z89$0Aub_a}r27FWr+)8xb^zk~;>fm@%0}(*LXfwi3-fs463u!cz)V!BF8yp;ot`R1 zQ5TM~9%&D~H}KXRoqUowy+EER7n^h=J#YOx9NR1%1=PZ>nS4tY z(5#W2M_aUG>-w=ooGC~XE2p7mB;iU zpdyQrT&d&j>G;;xR!P6rg6ah~eprHVt5T+jv}3^epHMS%^SHD$IbGf7(a-rsF1_2Y z>#~c(fT4vSY?9reP|3zmZNdzDvinR|E-sJmmb{(wI62C_^pJ8|{qn)9@uz}|*rtQD zAk#to0k4?8EODQ($VfU?)(8?dEpAH$CFnW7&CkQt0TxzPk>(TJCqzVV9m-uUnx>|- zmzI{!SCfrEo_9BA&xD{aoSd9~{`^UqIq?absNeVI^J9vq)YJ%N$(x@*&m4`M+ZYtj zq`bD+^>Jlwjn{4S_w&>MN86bKqI9HZv_(j&9l1xUQ8vUJ7~HyroxJ24G=o3mQt2?^ z1A1^c&%4y1q9CToUVXw;2C$zTh3fx8e{(OM55F?~PN#{9iNBw%94u6EODI{caFXGD^8C&H?r{X@Vxx|gH8+r(EeJw zBQM~emuGviJfEkgrk)xF{0t)mto=(y#$YIozf7T0Cg|^Y30bm%`!iWtSv(4XsCZ?G zrq6oaKFyh)61XjQkwBX}uk`>ZRf_F)rSBNM_Ra?F{pjYD#O`|+!4U}!Y$HZty?8lJ z*dKQ>s4@K?IAC0YvO)HW!hG2o8Fs*|-tF-epz@7bVeXh^k_N{GiQMm*w%HN~KZ)$- zniBzMXrD2HXQQA9w(lDa%S3Cgt?B;B3zniv`FY3;$Ygf8sp@eb{mlZ|Ct^_^rJ_wR zxCrPfp@e-EJ2PIIM?KS+;U>JG*l*G^UJsWcd_r)(##qWQR-m|i0H-O;$qCdd(>*|l z?oGw4xLij0hlJb>F&QwMQFSs-`;u+8`|@?gm;?({>4SPd4W?9=W-%ks3a7o@ zTd1OK<(TttN&IcSY%eWhgDhvSZ}%kKIecGz{ON9FXXP8vc_cXo(vutBhb^Yzm86Z* zn7;~p7arW}ZCAi3oED$CBl5-8YK@hjCzZUicX*a%bak3E%PP>u|2glqP6dm4roJnb znwl!TXB2RAqQ!Z#KJekg*4Qb{m~6CgqW_km@hvW0ucStk(Pc5`R`SsLaHG1lVP*Jg zVHDj)6kF+virfuANoW=)!=JyBCF>ppSKp+#s8Si>`^<)iSz&x z*TMLEBh?mn`}XTY`TMBwyGY$@B~H2*i7b5m@u4pei(cCN{`;Cw7ie2iUgVGlVWf zmabOwBsPl8S7MjGxt&ghQ;y3eXUH%mjc>%L94fFH*1|KOflf&Ua*AfB({F3J2rSJXv<# z+AyTV)u0dG-m-V58_8A0MK}kcy^JB0ATs;;&m=c_+m$+Cj6-Qn{pRnzcftt1Uu1R+ z%K%;?A=?0rmBOrt*viQ!uSbT3Ew&yZFmgQh=6!)63NkY@gHD?#R{^Ea;n5Kw&X7@o z$IZ#)(QkESr!GvgeLzt(925Dee3tka5AlRV%IK1J)ngdTL`L_sj8a4oteZIlvi3c& zcnc4>XN+7WA3x`pT-$KeX~-DlqRB&MZ2$#xZM@OU_Vo7JIOiM&mq-gVQ+OFt2_ma;qDkozK+c_BD%Opw!6+1)}z3uuf74L zxo*GhDX_nFEo}hi%BWJert4WlS~Vp{?BGaO-c(BNIvHzM>>W;W`MZL$ouL%9Vzt`E z%WpMEiFBuBSX@eq43O+&4YMj<5{Mr^N!EA99!lf?Zq(rq2-5!Z;9V4XSI6xM7iY)y z;rCbrzmxG<*D*zDfc@(_*Kk%D-0Z80j4aX+uJp zamu7r%e3ilg>uu~z8N5cAQR=LqUCBNxykEnsSbZwJB1NfLxKzYCzD2~n5P=Rc<6Wa z1-@^4sXzghZ<9i*kJ%Z?)ovvk3=9*$6qj$paTW9(w??t#2Pcxw%0)y)(Tj@e;YyQ` zoAx3QjJ&*~Kp6)xn{)a4vP0>DOmuV~OH0{Ns@G~}X7oepG*<+Y%=rl&Bf)yIfByVo zxK)b>hS4=i=kiPczn(7dc&Yi2un%28>tN%c6JZmzOyHXJ@gu?oDwO2qU>+s=1Hm2i z3fJK=VO)aol{H`H`eM!zC1tQvmTlU9N9FH_Kv`BXb)mM1t$GaY`~L%LyyZr?M30*O z=c)C-r2oCT z=q%k>9kaw?TXf(Muyd8*k!C~0U`1F47;Fu$)__=eiJH2VbUIV9fz_qV;zW^?Q@uKw zkQENX>3eeE88!4KSrbNnQ?f+!1g8{p2A!}IoFiZ5gg|RYd+--)ur3pYd*qA$WPP5R z67Oi6XFj%bvh!EH%jCX~K7sbbTGu_n+WSkyNIgf}GC|wuU^`1m*abD{7(FS0S1jj} z3l-2D;$s(sH9>AV@yzrv2)lFm!!jP`JYS6PD{(^WrJbDdAG2Npuxp2?>7DsZjPt9L zbJjx%j9GLAbazia{l`CguMN?Bf&V@*j>7)zCGaXL?9r2GbtrBtMUD3}Q-4@$?C1mC zJ9EGoOvmu1ww)w<{7S2r&*S?MNH-zd-rLeyFVZ-R&X7(auC-zo60cZMkQ10!9ik>> zmNz*%9u+ZoB>&3t1(7!1tVI;dp^}&_df8pITt%plUEU{nL;$iF46KHOj19|(P=_iP zk3je=;c3vJElKJEca9)bM1>-S1MCvTQ(_~c|G21EEE_Wqtq^S|a8GK5 z%ye-6Il@9c=fp_Mx=UQ(*(==Gt0AWee>Tw=$)e%wFc~m6HMw0>->F)Cnp&Kf(nH3^ zUjo!Z(h!^|9wSc%lau1V&TV7lH8fLPU`Y&dPyk0GN$R?7AXAhJ)FnEs6iWo{sFi3W z;?-71>8L?J+(Kg55Hb@c^MIQ&Ma?dQrBmk2uEW2R+H_FM5v%OoDxxN=_JIUe`Qb7L zwKDJ*PeJs57#eQE#%bk94h_4e+owW0kZuS)&R<;iGiSu6Mx59Dry8l)u$Sl}=v%F6 zqgVg*1SFLpo`P2p7--B1;p{s=UZVkVa1M>_5jH)cG=2;PS#nG}YC^MUK+i!Hje5SA zu-FO_wJtAwa*|Xd(?Ms#3sM=Zh`<9_%F_N_k?X$a}^woMzHe0ef?nR4Ip5tyci#Y z35R+Ymi+!gN#Ab?*@SV@fifA956#F;sT(L|Su}wew!}leUB?>))?pw~6i-MJ9ZNpz z{qrxY0h`PEAn}Km^6yzzv0QQAvq;i`)dR6#QRIa4SVXPL$Q9uXmteB2N<+-(5#z}c zPvcY;JqU$|$dA77*vS=DZ~Twfd*l5dKVk8IwV7L*Tq<;p6IL&FE+64R-Qy7vdG>72;-e^zrcoOY-r#{l7Qx zdU!kVjs8?X0Dt6>r?L?k3+u_V{~p*_8CjHASZ&2B3UayuS$ntsKkOiWvyVdKpi7y} zVodG<9)ipvTM)fcouMZ$A7Ou@cq+~5D>P1xw?i>Lg>&}XVP;(DLt6N>Ff4=B3ZF}r z5u2>`_a0W~?)G6F*R35U{7*lF zK~3Q6jr5DNP+YX1JNkTL4hqgeK||#C7odp!1({sGg9YFhIqyLJ2f%x^erJO)&}CHNIMq;e;d`_CR5FQ@+{ubt*7(|4=p+GTziDMkxs_kK`_t?Jof17P|{mf02K=;EsXTg}KZrojk|^ zVFoPys4I6RBO)To%ge_X7d7%H7*j{It7acP{M>6T09-sWGV<@=zZJ~&$J4<(9!oU* zcFeJ~v=#=7&Exo?%9=68w!XfurRdzl&ylRUaT@3irTr@Z(UAMCn%a{INAf0AY~?O| z-OkAG&i`O9hX7c04>nMCcvVG3O+$mCg#|-)b~cu9=GY6#%|Cz0OLU`*E8g;^zR@P{ zUafwHG~=Cp|2m6%MAP<#;_(8q<8qJrvKx-w5Z~!zrld_StYPEtpSr*AW^7`zy|aT8 zz$(uh#nff_-A7VGON+Rr@;x`j(5Cm^!9iXrXM*w_T?0$8 z3v5+~qR>-Zjj4C!4-~c2GBe+#*j-&;JBel@LfRM!erJSptMIi|azw>3<2q(+iC>?e zi)Iu_bi^w#VR1y^WPz@mYJn&+5$xg5ax~*0Ps`3Otg4D{Y!p4mV4Q@h;WiKCUX$Rl zf4aW}zE%eA$Ni7tz164Jsfzw8iQoFHftAKWi-4iDnVFfC;a&%OXdp;EdiItYDtF7P zs=&d)qsd$bwDs3^aA(Sg7J=d;9>JS3Ve1Z|pJdNrIidTrsVtEJQkqiq`06AGzw@&* zUpzTR>R7VqK7xoIj;QXTp+}qE>FR9jfA$htvO(AEgFxK9nR6O1N4g41OKWhDul2{$ zd|P{VvOJP?&0)Z3z>RxEe7ElbhB$w`KgBHFyc-oUN>O1UV1neX4u9Zo+)+Zy@R#(=N4>cHsGH=xB<83_q1FRz5vRjb6I4Sf1*LA1Fc z%Igkt$T9No)PI46;>4_lDQ9XT=OEP9Z z^@>?RyLZ!DBH)DhE;(8b7b#QaDWB-D-OgED`oN-kdK z*4-o7tJJ%P_b7{76&ZhU@I>U#z`@*MYjEX09prO2NCLca4_3X54z|+xh=fyL)~cw-#<9e;Y>aXkRp2RpyWq$E9-ymVG87d zP{v~GjBobsZOF{b3?&1D|NMKtI)mv2EV&%w5AVjcDs3eLp~mR2>(u*%{m;)r&$aFa zBqtfvFJ&K}21wO6HcrmZKYk4}XHOlesjGVfHSOO$lf*J(BoPO0@Lzc|NLy?*H#aZJ z&;NXR87Qo=zBQKFY+5N~wyp@TaFWDqr9eeRKUgJTgLJ&M$_d*2vv4i%#Ro8V7I#W_ zTNXD}7oV3y*DFFQ>oR6{3o9yOfrx(EeC04JOsJAbfQN&I z-wB|AZ0gm-R5mp=AyKIOva)D(wo~I@lc!m&ro43_X@!QB-eG>}h{fh_9FM=?=;IMz zh!4FO8_;(l=h6#3HV92x4!nPPkI1>=%N_`!ggmoUC&3GrVUWp*KR@>aZtqyTySuB) z`5fothxNTa>x3ZKLG`KY2l!TB4(M9R0Vq&7K-?`YEfwjP9hYc@L|O7*%+E^hFSJzF zH8(5E%p8+zH)-aT_C5O#bT_QjtsHh3=n zGFO8H?v?E8I?XwjnaOaatDWJBJM=P50roL~2NYPWrK8$^f+r$4;b#;FR1%=Up zWJPlXXoOvase$C%*kA#Y&yru6kt87BWgc!;Hr))t@Y2Uea2Zs-6B?~+5TPnu(oHi% zGFfm;rbn%wro9RiCTBF^zh2oa-QH`-Jsr4TyU*-6$K10v1g&54UHJ;ikq|um>;v@X z<2A(~2qbb~UDFACe-}bQK_M@J#9#G?z&jClnt4IF(s zIyN@3ysYKo!gbhjFVj-V4Eut6$Mg*Eqj5$5XMAEx8X9Jb==25flUE)Z{YY6jZnf9< zLZq&vh647t2e%v1&pRzKN4-J$TaeqyTc^2N7^5R zu9UMxQ`do2%Je?24A?HF>%dQnH~r@1;fH6NPaZt;j8^(|b9#SqeY3PbaI=te`|Kw7 zFc?jGCMFZz|F%WASk%zS*w-F5mmLh z0JP-)UJ?}zA6U1tvRW-!MpU|bLxLiY?=&ClE1b8C5&Vo&k{I2>uA^&g4C(Y=%CNMz zOVX9O4FtfiVIp^$9BzqU6}3S!rlpQ2g0Zyc75&trfS-SS&*~)Tk+* zJ%?y@-pbQk*~`skL@1(bU@#366V&^J zTN9(gEfY9Yt9W(VIeB~A3260HR8)c6FTzp=-HKNM!~irGbPxhW>54vZcC&K#eG-pS zbeU}XxXAmgepj6xxd3{&!eU|VhW-Ggv}Z{0_uF+^R0^13Giv5^w5qO5x^JzYsN;My zLdqPuN*s0|nUhWVIwePZ*h!-?e$vM*tPHl78rwAEEJ806eDNostjLMz#2rx^RwjPk z^aGru*@HPhpPQSr3=Uo(6%I&;ae4!D>hlMLQ>(*w?tfAoT0h- z9gv5mr8$Pl8Cq>%6!|1RG5z@L?7-;g)5XO_Tfy|%7WnD-$&12O1mwU8ZEm`3|Enw( zI_>5#DnuJBC@u(V(da~Xxp~d5Cy=;+t^*c$8;M8F{VOI4bStz=L@9R<^Kv=LT@SF| z)eiE?b-efxH&c+*y_{~kvU~@hy;$|=81i3k8DzM;JN(tqa0V6DF;SDIh?d~#nr(=m zg625zrbg>>Dsm>{1Z)QE)^$H$9_19taYW1fPYs2`y|*U|#jG==O~4)8gkdv3eGdkr zceyJMy}`lXBTl)tAk(AE{zXZnDPkpms7K4)Jx|w2@*J1mWmoWUdt{J?EmLzQup}Up zHQok+0??BL82gmD#z`N&DJ52eua+0<-Jln%W1EIh%c9%mCDzglc`ZkILg05(2u{ zLW}QiY!@9$4v`q%@fX@CZEpBx$~W#ru`=fT)Y9*(jf*miE8!P~PcoV(tiZR7uhWAv-vnD5HopQX%U%Chufx-TOdH@!mps zDX2v^(66mw!m+xwRZTLx{}2<_qpB0KmUS)sRXBA-Kvov9vch;4bo(Z^F^@y1Y#Kmr zL3aNW$M4l#uvqe~4%GPs<}+V991lF7j%jooqWtRp{ArreQh`p{)a*nQBY{sr5?kvS zf0poKdmCzV?RbqkHR77~ZKg(I&BsPvrr}&)@j2Hf*W6yj%~=Pc<4((BYjGt1ri9^& z7a!In+o2)4y}y6^TJ5oC79&}txbR~92y~g^Ds1L>rl;qPPRXD5oFaa<_ixkf?iD1O z=t|s%fjC+RfMWp69004be`573^pVTU4%XId$xat_e)CX0J)0n;Pq;TSrhMA?b9f%m zo3>*DuVD6XzpE;UO9{|8RCsIVw+`0g(ZE{HqAGJ!UA_lG!yJqPM{j4QTN$MZ^2dk}p} z%fL`qTf6qBwm5K&p%51J2*Y+>dprZcfc1g+9BL0~>5;qlvS;sa77(|z%*<6{PRtD8Uua$xuQLw!3CYl(C^ z=(8ioU`3?W&e=mH*mp#b0-CoUTSG=9cgfx1)3l{z@@>MmGWtAZLPd$X5a2v`_RY@^U5L4 z{l*_eD9wdY55KM)$(`g;UFZG2-ixauhRb?6Aw4|_Ny)X@x`C=Ebxlg-ax42c3IV}ziXSneQjSD*|>*#~89;?aLnT@<V(oFR2+BZZ;Dcny+#{2s|W2XG(Q_znkg3A=@P1! z$WiM=_xP*M*Zo_Y_VukViYm`(3)*yqrdE~5@c;z>NEAZ^^m$wB->D-#((rR=V+!5? zl!@2K+t|J^ifS{2{?r4BoayeK7meRC0LsCN!+pp72Zp;ie=3^4Th}rn*RnX0W#9bjAfWo&BZp6JD^y2kjSq ze1c+PN`HA&bWP4Ju43>%+b2Wmv`lxGa3}U*6EBe$FddzlO&Jl6Bna_%r8HrND29W#b|`CENTc6c zf^*b4;YEG=s3nlXl<(us$3u>3ca@^;KFciibDEVVv+C^mdvrM~UPJ19Rr$LQQy;cM zMFc*vq-#zf=eu{#Wh})JO;f?w-~YP0c@d@ZE$3{_-km~jwhRuue{dZsb)bb}&i#)| zMr>HDNzoohd;Zo>Bmo*p5(Jv?&Gv?>i)PyS`OT!`fnd}BxR+5VpM!PNj~E6xKdgDU z>h{3kvK_Iofxhq7%DTLa%3C?TZ1&rqH-TtbjYB?CI=2eG~JE!-0$w;ITp4Y(rwteQP0aoDEfF#P z4aMAkSzSADnL_7mlNS+zKm|!;scC^}sc{c$^AfM97bC4?sG_T({>oC+OfIlHD^Ucz zOTYpm-m`qk-q9T!-ScBuPsV?j>}7l}ra2^r@L&7Cl?I14NKjCgO0}!#^~crkj>1<9 zCx3gyn@XLz%iRQ<+PY@xHIFUr6B_nIGNR-ylt3;hh$-a(WJiL*e?*Ps3&Q~3eEW#F z&5z3>uY;*y=|xVXa5z)cTKcPkDsQ+!f{ytBbYxR7DJcoazln+C0;voOl(+MG+on%x zDJkItM~(iuYNlp;n5KbCV#(&?kxWRz8mYS(ZNGW?(sYKk`?M5?=3{%<-f=(xf0L?3 z(bwapr@Ig(%^wXYtD5R`CN?H3&GNvb+jS|LR{S=w(+?LLT)bQJ_5i;4fqm-%=LV!r zi625LNi}gS^(bf|PCh2&`?tKon|TVEoCy3nwVSo7JKl^^uvK-$NIvdA-$sE2l!}K^ z*=eXIsxHa0v@{Wc9{{3l^*LcGsAi14&v1+C&tdxt+&p2HdYc?fQ_z zx170g)n|2}F*b#oc>7-4bBK(lm2Drh_6i-E>;c<9&tW83j(_wkq}7UYx=!XWvm2^~ zsf_Mps;jF5SjzFGrO+*xwm}Jms;WepVb9VMJuqe>#@Oh`s&MQV+uFf@P5sdvBd-l; zQk8d~m0f z$}s6?RSVv{V=-?+N&HT%AsB#udY0@)B1jcq-3U|iFG}7#qYE}CzRlJ;5HYE|v^y^% z;w9+rz>>jdc_26UFqHlo9R{nz&FnO!hyO0qz-*Uh2`ZvtO0!A1eK(7_;rFApyVLlUr#r zmZ#fh0dHzZxu>2Qn_NefyYB-a8Y(1#0FrkhJEOQNKX$r8I*F2LMELpF)g>Z|nZ{;c zryrT9QzW*@~X^!KnTx|0TrR_g24JKg&DC2C(#cRer!`z#>)b z8pT>m;IHnvc#U`uzu`pd>z&1dxWcV&BGES&sY@Hi%heV9G{SX}cK{j^rY3Y>YP+0| zBSfIXWdn{r@XmxBtB?t}w3xV-C#P%=uFJEJ9ym{cBJ)INBmXp%Pzz-=gR!+?3O#@IO)jA?Xf>GJF&&MXSV+e|3-2QgrB5!>lvEd z4i`;K>5dFh53E2Q+p=sZze4SakT`O3HUxbh>eCY}5r@%L#GLtqBEH-jxYS_P>q@Ck zcqhVaP8q8u4y>O1*mc*kp?nB*T{}AE%lEIOUo$z|OPjg9LRZ%k6N649;~UIdrITMz z`P!=Zi2no4oRv|ev;7ql`l()qjMwVRqtKZ3tj)}8An(3&eGzdj;g(SZtH-NuKy@sg z6K?-k{*kUJ`T5Mo#>SMuFmE%ikjMfs`m?@UXf$$u{y#R_fvvF3apUyjBJCP;C?qa^ zG5IFX*rT?&=Cjr7cEio9ImXXsZt&PJ*TR_u%MXkBw42V^m5mg;PWg*xdR0iw(HKE%q)~aBk#AROA_q^I?4y996|6_m^q#QVt zS2VxvD^9)v|ARA<3HrgQ=Wa^bzw5V(3Cc3Fui#;`;i3HpEZo@lI$|Z0-kMhF*gR(f z9M?UWeZ%uE+pw*;84Bl_tqG0Yng`Lz>_!-cQHj6C6T)<<++L0X7n_m$Wf}3+^FKI=EZ)AZA2fGgcXp~wiR@z4Y$g)d z1=5dJP5z8oJ#F?HBEx=?dnnQOy6yp!X01KjN|W$X3rZ(zLv113d}V2rNkg$~-}@N8 zshv2%pT{vi;S7J@YP&sTWtGhMDOrY{o7&C6WEh8DQXcn+C^ zplGU&6w~~JsL$J$q)#0g`cz6$?YIjoi+bfbK_-@yq{8mx775-xp$yHzk2kRou11#} zp6EGU25yA*?+Ke~lLJZ@=5Sdlk;OrzGURi6iC&o=AWR^#!ew2Gnf>dK8+W(Ye_P-H zoQEs47|siN%zr?vzmst}dzc*b*<}4qT;2SXd1y3qXxdoPSZcH6{Gls$tnrl9vFAAU zl%}^L{U~ozoYMB8E6^N@O-0^oXNI{e%~pzn8v`-o1KC4?^4PL+9jS)me-)>&(VA&tFVScbJgyDD+G7rtGNh5iG2a@wrJ*0yq*#UgpPoV zqnB^qy!nU0FcW-A(&^Z4K%>#G$R7i}vrRy3A#UL^_-CvC;pFsm-}v}=`pB20yzMkt zx<2~*oa~S`r$LF>^QCl3HnPX!4SD;9`#g`Lk~xXD^a&mW_jb#n83(iGubi4DqLQh( zOdv7;{KmfH=W%~mIYaQ^<|)Q6v37D5Sh;sPT)slX z$Zo=y9f4SiZ$cf~{;h~BRV)>}t30}6PWqn6rw6b(R`ngx{=Bhdg!oi@2cEXM3kSt? zVvA&89a|JtS%X8Cl$E{e{x)8+bM}-P&0fX=oWy#SametC8Z+)fvv_x_L4Ty8d@qxn zsNZ>-k#WAMTWw3o>+z`Omt~@d?rJryb#H16ecGD<31-v#l7`7U%xvPsK~MPw1qGlK zG0gpX1+dhL2UCvCux|$%fGQBx#{>vr0Eyp5@!J8=?ioHI7@p=7 zDnkW3Tc;I{nZxdt+bmv4@4q_G}@oW|5$2dR-k(ZObHQTQ*ChKLkvX#TaZlf2=l^&fVT%CK3;K@5Sh0=MZ^0F2AL=hKDJ2&%R$Bz}%MTb{}Fu#@l?({zzOF z3yOayrZ1=64(C8&b6_UQPu$CaG_;>z68{ z-R^=0<+~uDd8|5kqYw!Q2Zf6+DY!H@N%8`syHFKi95v_>Ri2(%>#&GA-BRBJ4ZiVr z*CBV)WbaXKE@DFZ!FF?T&>FHE{ z{{A`CZnyj*O^gKhfM)$hj-*KImKy+W9#1}1+ulNo{+;fwEfh~30c~8#!4Ix^hDI{`R{bNb# zFhErJA1tgIgq;}#-rr&_NzUUx9ENQ<+~Xd#hFd+w>2SHdH<%yTSrB!!_ZZL0$jCF~ z_CDPjOVxyDO$%6rhj&DR4-XCmB_xLWqF<;KPkGQ@dT3>!-WosC9&UIDwf>qU9|;VS zf9rScdpvb^Ejtl6{n$Oybej7v%NO)zeA(Z^krGlsiXsWwB6ry)x`sbxPSP>z+TlZ97_GvhPFJ18js&l~^EutGf8#{Ctt2ibzu3-PhGl zb=ow8&O#<;l%AFep5?Z^#~nJL66A4yR4RqDw|d3m26)d+;AT$C);CuF+Qp{QP;7n*G#{4Fi2wXf--hHJ>Hmf9ksR#-V<;3wFK91m9nbBomPz&B$gD z*~?;z8KCStID5tV2!927;{PAB4mGvLZ69iFSmzQn6pzwlf-|4`Ub`vsAtHR z#8mETzV)0p$NL?bHwf4^nu9L|W$#aA5r_A8hv4=8SYoLILT)$8e) z#_+Fy#AY*g&H(nNU&VlEIeo+ahTAKl#Ns3YCHSS0V2lQ9tYW!qp0uJM#p;Q&>|(lb zsuDg&3MbHJ_UP!r*Ap?|G*jxpj5ceOkqUQc$G!R!J{ityldd!xO;fY(BND}_Gf)uhwInI)$|-<%#5>>nv+e&`ga1fZ#HlfP zD@|dgK>lFHpJ;GPZI3RCzphrJVrfG>wYZh1PuYS!r#i5|w!jP-Uc{~^7#Q<9n*dS4m1DCfOySh6grdXh8S14>^(F~Cu_t`B`Hm^XRqp!<{1EcRiBzU=momZG6Zmp|9V=F)EP&Awl zaKIRvn%V{g%pviPCC{bMp>&I$0Z=eaco)Fh_E{enn!JINLCdB&0q&{3sR^j7Lml^p zVYq1(ReXy%tMhXoz{>yp3bL^i*G&_EL92cJ>Vf8o;!Z5vE`@hl>DI1aJsVUS`r5!{ z5(?d0FK&f>-7X}2y25Xfr&IR6bcWzE#5U22s4md-B*`x&y9gzH2xL&hzVvxKSQy|t zYI^&+=qqE1*AiLvo6djEGq@Me`fbD-{y`ix3cG+HY$vXY+SiPUW`d_eChAXH(@YIn z0cc9D)5J|0|K&StWI{Wyv59rSf?&eC@7@jJY7|bQdM)$1Pt6?4t8mS<(vBs#_YA@=L~Nk^MU}yt$qHM_+7~erkFLBo^24^vx{2tYxWb zcayv;79eJjv9-1R0vHtl>J$FsQBi}*--}!1b00JI zBvq35G_en}>(*`qeqSULSp)^x*zEi{A|ad zfXAMokZhuniB8YFkP3T^NQw14`*{W;yg6y9mnIxFEe#_#J8a0{$ZMf!T^HX2b+|US z0Tk5G2>`Zu3jK7mMe9J9_@O?LMn88D<%kr$4~u6cQ0v4P-rpym>t_Sv-yh9% zx8lHOX51)OvJpT^kgY;wk8C#kAJPM<{*;KQ-FxHIE+Nd$u5UFR)mpe4TO@S0>6NLX zBSp4xw%`2kM_H>(^q?a|laAm5VZPs0qVH{F_8@-)6?Q_=@m`N*h^-4?Yt0o>A~ z9{zd20!0-*VMW=`M-}d6P1)~H6)xa-d(EA3X9{tF18e|p#{S{q>BX_l+qZ84*BOIx zvV0=T&e@eqtfLGt5;s{<0-i#^3N<)gWoFz0$r-GsNNDYSoYE#)96f`7}22FC=x9KO(NcScjgst8-oI zd>P$t z>nteIY%}z@;dZ(-p->EF23CuQ04JkJKuD+upf>^V?ZY%TGKu7a?@N3;I33kj1-zS8 z$pDYw_s>8tSt*`gyFwr8wcelpVnJG~JXe>~3jjNSxRV2lyJ}DZ)7n4DB3H#LXT|l) z{4M<)EpD-PTcU{nua=JCXZdvk%g3*=bTZ(5oT#s$td0H6k6XFlH5Jm0=PmvE$mRdK zYDj)b1o*2`eaSY5Gk;cv6oW%6fafnqle%2OdStC;~(?J1D*6Uy##8a z_|Wsfw(3u%B?LGCPf1=itHGA-W2_>oz2T$Ufr(j{2}BenDSg5|kKdzSJ_yOo={pEP z<^M-;zj=)m_oc+vjB-u#wa&#lR{l1U9|9;pUS7@di#;~_qW*^F%Uj1cf-fR|&ZvXj zsuF#!6g0mAu3A7YO-oDjG*+&XFCmWdz1x$$;oNLF`M8X9YM$NgL!ZL*0YN@8?=Mzx zMMXtSY-|We!zc{c^`au+x&SM+!?O4->}Ld-X3OhaU*#O!TYFkwVFPT_yOJ4Yg|Vr2 z5h`%M)c$s1P`(N`?Z$~`6>dFJ(<%wHP#aw(oneDs`2yfXK?=XOtXfKMAe>w)XTN?^ zUs|VMHt;-bnSb=~<|2fieW$@>zgkynZ8QQk0cY#z<=$gV(iH4y>AQ~KY8Go41azI! zQo;FU4N21VnO=ey5m$hY@=Zy8&mP`OYuPF-fLly4HsM$5-fZOXT zX~l}APF6M7eY(kvnDsQ}8zGtNi+=odttR)7)$&I4k z|0wfSot8x54**R;S!o#0e^eiNmxS>Ak-wx16`WTRCiiqUY^|6^CA^&$_E}t+xZy1H zPIlx_=B6z`d6R3C(5kvD;v}!l;6Ia2xhU0+Z} zV{bl|Pkn)cRGfC%=7w~R!Gfdl)FL#76id5&mS926D+|Cw<39hukCF2_-i*9cWUIIuc^jz z)eULldw>pcG)mFdJCleP<)Jt_g1?R$$dtJIyL@TZF5ZNB>v$18dLZFYXLJ*KAK|PG zu!JxO1}K?;%yC&*e7gQsgq;lK>uA9?wy_3~lj^ySGdbp|m(QD7BB!%)fk7GwfS`Hf zzx&Fd3FObyxNw|>Od~eh6HqkvsUif9x^dmM{gD)$5S~}t0#gEfNfmuDDFE}X+1mgh zNY9Fj%}DAI1Nu>ZSiL4}Vq>QF+j|_Jg8lZE<<(wPgHNHWWJottOno7lZh2zo!`eOi z&`z}7AxCu4wp5y#b*OI=-(tvU_K<{q%FKU5cjG(TP`hUuQ%3W1ZxdNkW}1dlhZi!9 zS0)z7FhyI?+kg~6E?cZEASNbqMBVRU~S-zj`xx2?1x%^=oe(_d1YLuZ&ONN3H9EQPk`ryci#C6SUi22c6*SV{QO`E zrdFYE6Bd?Jlne|Z%N!He%*8oB`=A{d>+n?{lGG*3j`9h2?BpQXD@d@S*$!FK zM-#>K&GEROXEV)E-12Q;k0pxwqIxqfYpH4T3s4v&eV!_5Oy32&M=ZPB`$|&@(E!SU z3u;R)=qRQ~#wgS=Gz^w5O0Dq#m|gl0uqQl8ss?~;w=r$y-wTdEXGwz*k8a8T+4Z%z zxBt%|t)`|1ID~&WQIFZ5s?+GetpN*x|0l*#f=~QBfNn{Gx7r~31PDx?krTCSlUd($ zF@r}f!ih7##9y`6dCsF?|M8TA{t<}S%7Htvd5~_DLb`< z|6nJ=zipF+c6vHwAC}@LDUp=Fa`uD@^mFi#DRLC30W>&G@b#k+tldu6Rp+ z-ZT%ITyAs)560zkj{3(C);5IaU2`a8T&WXYusOQL?_U$~LzNU@)KPay%uMYMz?_KF zRq!b14bC2Dd83c_@bO5sGOZ|^7u|z`f||WI9~)Gev(m>Wjci_=q;`z@hhhBRmrVy8 z!Z7B>aqYu+a)Vf5*v;-0C&?ceAlWX#W>Y6q1wUjjkxznsH`6>ARKTWjsA&S+8&bclm$wj8Te3=Eg}m@>K{o1!!tx-U)Je+?Ma>?O3rXz^{GOn9@9z=-l)} zo>=R#I$s6Y#hM_#;ha5$Gr2-Ux5%Jr`@qqryy{uJn&0c1#OH1x6d6Zp|7RrYd0ZWU zYXWs5ukG`IJ^77KyFt#Y z%XR0j@g|8ZWB?(KiyM3Z&RO@k-|vWBK18R6Zl_+P=Uk@0Fh|F*;mXL7*me@{wI3wO z>LjsjL)qu*7LI)0_MwAbSCp)#uu86BdndE`Dz00!cSI>woi>H~j0$Y~xK$UY9ZER)vm$)3rXcaOE5 zZzG!#QfB3L0Q}Fl-rHqOB?_6OA^@$n-}!2?C(;@okB9SLvj+|?uu@nxH%(y=y9&)- z(kB3=)x6;i?Sz|N8i9)mgu-Akc-aJ>9T*q;@mrmQGXWqF4gn1nXq1+#rTiA727cjV z#+nrMzCvGxJ?{cWZ@i}6GOzPHLsLyk9;)*ug;k3F1+Z_&fl@ITf3l}n&7v|2EaZ&Y zV-r7}S6BDQTHKEU+#eYwk|>huO^H_%8MfM3HvQ2o-aynDkQ(BA#Dc+KH*0)%Yid=e zoI+1+lt{ic1v(72G4$ra3j=JDMhvi!x0 zxbEUu?&4dhA=>D^GdS}p{t+}==1z?=Z4->ZmO<_j!gCwm6-r0qP?!& zV-i3}%DfVO+1F1>J0`q)Xj42~F_c!K^BDg6ZRI;_E4OIpimv?uu&xUskT!{2Dd{GQ z_5g;S-VY(t^xmVV_4+aPzG7NJYH0N|fcEFb#=_$|wcX(DC7U9H#x#?qmAg?Kqd`x6WaMpCtXNhbRF()Qnzis>#0T?VbOZ#Sj*89E)C_7|qkabl zUOo4J&)nDKhuhT|4I(=P7cZ)yyj zp?N$4QUU@*;uC(PK6~{3$s2_fbw2&Y4N?N58S77dxbAnZSvuK`M0r1jtxU-h}r(%7P-ztU;AD$ z%+JcPoWJRr5x*|CCjE9>jaS?DEHT3Adu93eUyrzzN>*a$vis*RqT_SUue$#E)oWLXeP`VsqJ>W9 zHz5qW4kk?Ss8LoAuz|o zwZuO9j(Q&rNIDlmz0I-a-|0Xh3rv6KI0SLPx3yGzl zU3Ad<{}%IHx7$d;65)ceH>Sf;X*abA4T*OKEPRq(uazFBa%a9?6e4l}$$Kbql@=M@ zu7(iBf%oWtdWPAPYLg5WkS%0UuJ-p?0kt%njLCy5&(J?(e?vN5zw|6z1nefcn)JML z>!W2AS#6{koAe*4w!KLHrsN9bYumY^%Ercb6=FxtW||OJK-p85j703NnyGclkv*_g z*?>g|U9|l)z$s=(eFvNuX!;n2D}`0WA98ls0T+?cK?CQafMZE70ej-aE(3I4qoz{F zK%|r~xf-Epz|=YEMc2bWo+A)FIK6bBk|b)p6v^E=w1PP-PC8ICZNN z_yQbzWaBm4TE4wA!;`bE9@){LdB|mQ?bsssX1ZBMM!9p>3Mn69lS{(L-_fYiFk|`q zT4jUsuQQm|I|Thbc9A(~ehTOp)~g?q9;05lLO8o_k#@t=)I-0AxSCMfewj6_6kbGW z-msyqu1B?~*a04}Q+4KyLhmS1ImV&scb>jUc~kz_%U^R;3KdJXKt&9K4FR(hi}tS) z4nXE6CAtX2oKTuKWddd@_Wh=kQfVsi);zfizlG5C)9){u#;=y*L;-r1mY^CI_ND9D zR^}oi?k#h(nIO*uKVTV*A@=dI`V|qmD)YEc5QML^keRU#Q#f(S-u&QfU&XC%@04YgS#{5e!bHflBH9AjZB&)LLTLE;_ z_E5o?U)C`TtT6%O$^W5}W-zgLZ-+vrD)ViAWF^ht3^|UKfkR)g*YDJs6mj4bgiL&@ zaeiEp^WX5UUQgLX76F;@&&%k|?st48woic*V8Z0Tj9pf|q2t2IfP6fiAyI2oG6M(z z3P$#UE~$X}AIJ|HQ1-wFi2p|0Pq6i8fM+mCV6GgR8XGw8NAa2`Su!bfRmmNo^JR$% z!xq2dEQ>6~&9agnLtm2wv;}rssux9masQCFO`E#=w5VsJY>V*uzvc_5MLQzwp6{SK zR5$3rS5ccK2LV1@k_HZxBNUiJ&M*Boc#~BD#2gQB{SNyR9?PLm(}p>PxJ(u@&5Eje z6h;-bE&Hrf1I>8PTrzX@`{-xdm;3*xV zG*G(ElD6tgY|vU*i}!Ct!903M|25&O?1g$+L_8wD;t@40(Xk70$SLX5^X?;SVnArS z{DIy&#sPQyoDS$`eu0OpPlZNyxy#)F@3*R`!N$ZM*;!HdzRIb@p>)Qoc&bCFTV@3e zut$hu&H4AM><@{kMNZFfctqwqwMd{svJ?{)D%)(yMjPv}oRTm= z)usz23*&-ZnLx81e&FOrc}0cS+0L|>b2>8N+9%sRXEL1Cj75!!S(?g4{Eg-AN*Zwd zw;z(T*FT&(EKHv4S~>X6fF}0?B4KOH&@D6HG-2qg?|(LGw+SkZ34E6bKT*WZJW;sS ze&Q&9>>$Z=~VDffmIoJ-z(2)-i-qb~=yr8_(w? zMr&&uwEhoIXBk#i7j0qb?rx-|Bo5tO(%m85AdMg(-65&eAq1qPL!_j;ySuvt;jZuA z=ed9P&$G{7bFMMRcqcmhDuR#d`;;H-4C(a^1P}k@=f5Q0$RnF z)j(zcf&8{MI!ctx+@tA^2sTqzA@ur4&w!L!G8Dvb9svP;G{1yvKXN!ts5#9po9PP0 zpj`n`U#yEq3$Sf@ac~u4>T5+bI>UyZ2zP?0Nu^kIRG__I7^7^y!N&H6*x_z6#fQZZ)Hqf=hQP{zXV#OR;3lgIu zW*9FqY~E3$?2cG|Z^%A?pYclpLBnZM3?MP^kCI~EQ;gL66%4dx(n|(XfizQg9ZAlx z;ga70IA4J1Yh~|70pBDzdp5lZZhYT8E#G3+Wt!g7=~YZ@|46XTG+ZiPR3kn)g3?o3 zm9%Edj}H@STtsfk^D>y(z)RTBMxhwVc1tkQdm$>8zu~vZqr0+Pr`2W3WNI2w8xm_{ z=x2ZLSCO9HBUWPsuzRnKV-|{VHLS1m2#mV{PwR|<# z{`XZ7=-+C3xIkG!_iPlxF*{=#I~>I!dK4t@>QCyaa#mv0UlQ6KR7>a%yKQ#LgaXs` z(L1(EymNnr9@=ZqtkKuV{CGCN=m~;E4VJMETc1JgMAC0?k!?+IhMo%nJyAlN2N+$U z?NeWHReESusum9dmZmIbmp{qRC0v8mRnd>dj)8nI0W-D+`Pj&VLvxm1VzPmu^ zc7?}2CY(=E;JES|u>C{RDV#*q(7f*Tb^J8=&Z9x2bmpQdXL|THu|H)8fzX#em7|A2 z?r#(S^4Rw(6FNdnT+I7S1HFyYZE|pDbUdNF9Nlpfrc9vScDveD2Ev7!b}9fE09kEl zbCU*m^NNfjR2>a4spx8csVF;e{{eo_hYPXuH=-h6pgf!J?Swhg^-iFr_+xp#qfi0j}cehc1j75ZqH5x9a zN2Ab(O<*+!Zd#CB1y;MRq76}?Zc0n4j{DfOH+rsL>rFuL&xHw>5ss?;6OpDgXb6=;t;{4Q=uQ^DqQBt`ZKZa3mj4IP&H#vd5k zQ^*mp(`3pm28OP!#>*{`aM1e=&gUt-;psSWcl%_Yqgc^9-Nk%in_zNviZ+^t@6q6X&(x3}4=wR}=-nAX^Fq2b{`$XES}sm8oZMk? z!FR&z8>5FfC+cD|vPm%~68JKmuMiDsmkot>9UKJPui8JwwcjJXy(r-GPb$*Qb$Wb! z1i=z8Cg}v@kq@dTac#81lvuzUSs0#GeDQpZ3l5VBo{=m*-g(hMx8%1MrAo9-R+*Wp z%4uw;KH#!#_aQxTO-YwIeC~wCc7*oMY7)pI@sRo^MPc$h?rcln_vzA*ZGLFBK_898 z>L+1U!x({bjmjDFI9LA;s7R_0jkJ$X*XahzNh!R)oc`~VMgFp~pPxK7rB};S5g&zB zwG64os&G;7v-{?2CvNSbuH$21nvm`EW_Pv$hoiu)trYv(_uO9u2zuahz3;4=6d4AD zBp_VTNl5ddSH@#x>UFy2>aThCwC&)y|(+=z8{`DuzEAyy%e(tu&emAVj zKxpRGC~rJ*-a=2OPK|fP~WTsb`~ySsLn>F>6|yO+4N^~T}`(+mre z@J{gc3JD1T#pE+!a!7_RRs~$J-|gufI4TJwS(mq`C{~P~l+tJ22wp_K`Q{Qsrek0H z_h7Hm)YV?&>-ogo#NhB^nsyaY z{Aa48Q??o34o`2t6f9&n_>F*p=hn8DVr3cdVdu~ipHEFq3<{;oB~|Qr^SWA(1uSXm zfx`a=;Tu9oTD|_CZ#kp9hsp^0xFAvpHE^i@T@PZ->|q+2rD59m+B==YG(C!`k5g!% z^|_ountI1xUenajbJ>d-=ALQMytyC0WZ(w3LIUDmbod;;Tj3j)Ft__9{~CV=|Ne?s zFxG~YW8*b);?*ja*abL9oP2zJSWg{T=Tl<;rl!j=yN|M{kEotIhhqwux1f95kgJXCd2!bMjwmCsEU&MpOdoz)&%AHPtwFC%N;IfT-o@ron8|Z3?+$q~61=Bu7 zSnGz+%|Z3G2J_4BQLn6M`!~%QNWsRU^K0hw7IQbAS@SZ?l%9X^o$O1qdzUgLk25`` zjWcyni)t3;RzFV8c@1!}>+fc>Y<;}lO~v~7{cX)2jJ+4?%ihaVE@P7X`Ak({D%C?0 zmB3VaH(EIsKkRcpH8K{0#J!9Jwn=N^iyqD06-`cA*?)KtN#wVS6d-kdjg8fGpaNgQ zEC{U9lsEZg=cz?-qI`>k>JzaaZw$h2ehq#{(mdWB)|@)?a{F|W@$8WyJ+92WZSC70 z$%^{z3+eF5?n7%kPdC;}#oD&Fjn}uoEnq+l7lWE}C-7h0ZS1E$@CgNe)A|)DIpR+s z+NeGCM#tWfYRBhp61gBCTV=%m%iEfU50PVAo4sKY@Gx>31F>GPwJe4pUhRIgnUWvg zSsA-^{>bRNJLeT8-DN~^WK-9;6;+-zgInY6cjMV`;p!aLTu;GVPkLrV>Iuy~`6gPm zbPzzq8o)~?Cf^HP&eh)rk}GgFM}|KE63dwhWdS|qYjTeIl@4K6N76D3{6)5^Ci-=b z@tOGIqtK9N%?jb#I;J$oIPNQ#oS$khIqz6NW*Zn$duSHsNh1F7{cOIdU~`jJ-|ljy zO7BB_IF1{V?uN0{-@e@{PSvT!$q z64&1BJWUi)R7qv+KIV;xEESWyM z?iK#xnOSU|XNzc({zuRM%g$$-WF|FT9tLkkkDdUJMtBnYm>PGzLi%khyY`OFz~I~$ zKJSOm?dM+|N!)M;u-KV>RxLu_KCL>@NQhCC@*B=Ne(m$M-G2KJIr0y0 z)&G~cFgcWm1jP9SY8Pu*FP^t)bY=f$XU!rGh5IcIq%$w)WPL9!i@o*4{i(Cs(D;WU z-nT(*w{saaUoDZ0D4h6owEDeV5A9U5h9L2zJ)EKn~1}cvhL( zSZ2>8V3Ay;!QjR4%o}?5iKSi;T)%+SPzwYjwQ?;KBse3|0~?TxR_bmuqCD|t%JF(x zI0#0{#WwDcK5}~94Tsk6V9+|5<>j&xz5mac1YesL_qx{KBV_GJVhRH6=^IymO@Zdb z3CCUZAXT5~ulYgih=)*z@4%VQt_r+AKf%$;@JFtZ%f^!I1`J2TCwC5kU0u^V8W##R z|0L3wvNAA$0?BthL&L4jo){ZMO3@c5xToXx-*SS~Np?}3?YepSwnnGX?k+dTQrHKI zGT0nMgHC(Q$Gc_A$1djMWW~#B8A}6OAEL-pNgXYZK3X#=yC_9U_Ybwr(Ed#cOiTD- z2^D?rdn>$66=;cFJ$CZ3VJc~f1O4~8{~3T!Srs-?Oe~}mSOtg;ZS{Em z6`HE6|6`XBAuvb?^Le1i(>{)&ksbZq-Y*EJ_zYO25n&_()c zE$|;KsP!P5zf!;o?5(AZ1Tq^N%c$Vp0-Tl^XP0Az8~6Ljh$r$LRB0&~o6WKbEj8`9 z221irC0T7A1|pp#=?OP?{~~pWrF9f26T3RR6-@RhnATUIp151p<@TXD0IhVJ=_|1Q zTUR=E+}-|da=dO&H{%GJ+p(~y zMru@oR?#Z=pIO;y(x=99);ERBZON)@L6jM@W2bDHdGO4jC8V3OtbWLa2${9gB6;C z$b^Lz;RnU+hRF0n)7~Sl_QZF>{VJ7;{YRTsFOPChqu0FMPU@mBnXmuY*q{1;_)%`y z+VQbwxS$9F7|3dW*$E!{d}74f)kS#-=(odDBRxGZGY=r+Kp?M-zbzT` z+sd=(o@@WT!7%Q%h$;XaT(!P_zUmOGO}x}zXEeEkr6MyB6#8!{D__j-qis?de{LmQ4v;*RpeP&p#T`M)~2lQ>n=A z8qVYCs29(dIAt&r?YUa>N}Y$FmrRqHke{xq*seaj?6SYC5Lw@^G{ecQT%~{73jk*y z^(%+g2;%U8>cbQHt*a)S@(G!ArOne}Q~)9PHj)E!AP@CUl*1LcDDc2~`+EPXrrLQm zlv3XspYnZ`Y`g*4HC3D|>65_n$nYF8G}Eoy&v!HCrkeVsnU z04f1MUZm8j1+>oajysJ8v|2^c58>22&?M~XmhfefTVENG04bv+AqtpIiu(gq8!|S7 zijMvK8kU?B7H}#??1eBq>NV?;-`obfx?a|$`3*-`|1)MNnN3r4^-1P#{;Shw%=$HV z?uc9SV*>p%Hkw#|8*i2}?oZ^UN4ZF-c)r%|Vwm}Afbw2o<`wVP5v=<2%gi}nOX6P7 zZVm?Y?t7eW4)?0S*{R#4f*mcZf}|yk~J}h&cv7zzoX>6pB9hS z>lhjKf{_R+SyTSKSoocOxO;?^NXUZjvq>~hSkf(1LL(Y+c<>n8Ml!r~MHJ?Bqil1V zyEM)I>toLe9IWc5^gjA1NAj<>$L9IH(<(`yu2&Jyp4L8vy&SA9Z=jiG?~EQZpT*v3 zmS^PU%${_Wq|W*H+5 z|8JG?YWh~i#X*wIT-_AOFUPfOuJMlZK99Lf1bxcft@E)}uw<4j6!!K~`ZGq1+-e=> zTF{NjFUri*2ExBW2F?7_eLG1oyxzA9iy~%uty?!Py+reTxI!4BUHwjP>r72e0q^V= zXYLZOgu~^^3VXZ*qLsEKH32l=-ZAIPfohn1_{WcS=DFT~4bPkDFH;$y)EsswVoh{O z#n$75x93F<0bJ%p6RyM(KJMJ1ZO*3^6jOvZ+{saHKes7@l7HEs)k(gV_W&P^4O>-xF3t-ScoM4nQGUz(<4-hrcen42CpNo=y z6IG)7<+RzutQ%^X`?B07O)rB+i4J$;@6CUR({|qWr@DpOjWrSMUF={B<<7k{!1C2F zE@HuvuEXc?=r%L2>PS6>&#KgPw1sG8YqTkNcd5=;uoMB*MHTtQK|Z8e@iUl;&PM6e z&Jx6xR=a6ub!#;m{y8A-Ep+8z7zynd%|F;K+d-dYpleyu{EuOf zOb@=laV`AXaFeCY!;DfG(a9wRUK2VTjDj-3fb5gVV`_>Au1J)Wbu ze&ZJ@H@vdSt}pG?42GqlV_N`awRQi`#Q9w;(A;d5diUiS0USY9t|d$;!KR``IEGb$ z+>lENsUbew@|jJ{bB6{9EUc`oAb<29W^C(%2odU19K~^u{H;}w_40f}Dm*;=Ticuq z7YU;EwJCs&f(Y1FFUILgYu`>KhpDl!B^a>IpjY0|>CX>+(6T?z%*O{^!ypDhIxCHB zBD&u=Bs=vp?q@fW0k&jxUjgPU_43lg;nVGh_zB+G_@V0}NnqhZ@ii`|OzYSE>cI$i zT^D-ZO23>eJ_{QSQAV0e5iGBiocc<~iES-|p!?&i-sD(zvwn*PO2k{y)wO}{2W{Ys z$sj)79h9e1mNED9#pCc_V_AwYB0KqBLEpP_KyO3NogG=zP&+pJj04QDM?{DeJYD%Y zn3N+G)TppZWJ178fV#ts#3=Cl-(UDgMgahgAnzC<^akU|z0PA?nA~)sl&k%gPI(tb z@DK2)FUlrdUmh&34S<(`T{xzh@AqXOunD+BPIy$n$R0@__k`1)$uM2m?)`)8&A4}P z;`rXlfhe8zwb`VMLmUIk*H&p-2{2%hr|;D>THD-Iqe`$zm#2rSNZ&pF(kkQm+q$?Q zG&pG=H@Fx>+`?^#sak`6>%q}jBf(5*<^O^W1Z*Sj+8<))*=w@i#WN&Gqt>C8z_(CU2w#L`q0qYSCf8*TI&f&}t)$G6;R-w{yePwlg21Z7dFiE3UuaVN3Pn+Cu zPfL$q>tz0gwz2QtUKUE47|;eb)M}S0hq0`nc-3foU1^K*B+{5x;=0FBw`Pi!pC5GM zd&w zISRXi`=o8qf6zjTqwhK{uHRUaS+a;b0O94XINgW8RdW1nXSQd9vEIi!JnV+;gH-=% zFv2xYrs)c}CBKG;0qyug^{cmE-;2$!j1~ygrq=yxc5psJz6Utg_1+yc^jK5L%WwfL zI_ZJ2#his~JH2^{7W#p|r#LH4Y=Gaje%F#cSAFL|Hp_miB|HdZBDfWbVKx_R)W2+- zu^Wz9^+!(r>qV_?sog2UpxFnm+>t#!q*RfPO;+Y=%*x2NMZT%t4TYS}987fdmPNyC z8Tb%tY-D(V)AjK3g4&V(KWiD}ZKY{~*Umn@vA&KYY+mylIl1r=O`QGZyv>^G1@m|IPi(5V8 zfSdm7)0FuU-RAbdcivp$%$x5EMFyXob0XJ9x}1Y6Qn*AL-+_u2IkOetgzh0lO>&*+ z6x|QoBtudEO=b%6lpIezuz!O}4V@iC4v8$uA_-xQk)QD5{o$;$;~WCVm&irrO5d79 z`-YPB40_<|Rzk+1?$>Iyn`X7E)7Zqrc}%_0BJ+>@;3QA2(jCyIinJ2{N@OCkLI#4Chwi`nm=1eeEecYyfhYrO+VKy zaPQxKFi26ad4T#dIXS*(9-{>3I*`KtZ6YVR25tOSu}H$cVj-h@pF|{BCPK%>&)*+M z#z#y+A(LhWxEvs_4UoESuC75);kKbuFp~?RmM6Tq7W;L;Bg%_Aq@V2%IOTD180^L^ z*TG_60b=zCHe$WITxtAH30k{G-oGYsHLu zcVi+j^VBji>>q4j4`ME*;sow(Qq)6pqZd%jhfj8-ez8a885VMHN)il<&8V+>m`Kg3 z!}EnO1v9C$5hboTKZz1)zdE|IC*(46C|l=T;!%F(9h6MHwvqU?9cDRTb7yw&ByKJ=nFO& z%kq10Lyj4+70!JaRauk7v1AA8Of5C%kWEg_O(ExZU*jv&RIx<@596ZoP_AVOCU%Mn z{h4Nd02lw3TPy!SIx!XSv3Y*@V1bX5J!=^|+JFxZ#q2i_7;uUyC4Sp!qKt`I1Msrd z4NmZFu~xX?ocmHRHX1s3J&xpDD$3Hr!@+PJ5CUUyI_pn=pLZ2Hd(YeC$}*mQTipS> z8xNUe>7yQEA(?Rvjg7!jEx^wYXrHNoU*6C-(#=O0vvK$MhA_s3+x-Pn{Kf5F`R)17 zM7>d(dP|3@1vJE*Ikd*2sDG4LpEmqu9~eyyUvH;nu8w^8(T<=z^)T24lis=saUifx zAT6X7U4#~QV--p|?y`VGP9f~qe{JMM1Jm7Hd=mV5k<=ep=S>)_AtV{UP0?a6RP;hA zGh`!MEbg|HZVrg6KPNhzDs^adB>SV96;|FRC+ReYxF$#WG==vosX1FzcJ%rv>eh)P zD`}TkZ$0hh<@ZaH6I#^2v&*4)BiW%kqlT+cbM=QX(R%jjVTY8ci>8UU?e(%js?ju^9u3#-T81*|oKSx^^63 zNif$7nj`?yTlKG>QcA*uj|s)izIL&xaTFl?!Chbd&c;8hVg>FhZ=U1m#HH2kq5kZ> z@>HT#raavyYlaqn7$9R+z5K1ZLTf)q1K>%GQhc$eZn0xCl`4l2YL8c+udCXdT_mzLY%|#d4a)t;-|5LlDnDADHXK$gp@H_%y{VP_4~i)VC*<7~ubFpHmt^8% zvfTu?V1BoFboemHG9T|07QaS?omvubzG=k1Xf5I8K{TNKXtfcPHy6f=0>4b7&Egr0 z^ox~>P+%}!eD0jolTN+ER!cqU9F-Zmgr-PAkeLOgMcmqt4ylA(9B6~@p>YCULfj?8 ziQSmTK~bpfL-VjaoiD5zF;fT`35EnVC#g0PzoraU7K^y{_0%K|7b!#6`X_95wI8@!Ev{myg?vHdN_GP=Wad=LkNQ8JHj&HA<0jh|IvBjh;Rr3U_4 zF50bWd}(+bhchPeSaJ0`G^_sU-{JOK9N-8pmbpN_0-&(e@UsEPmfSLCIoH_2-YxY} z^Gf)ezQqTd^v9{I=|fLvv7DlOi0{h;Bup{Wf9i^y+y=~V^Cz^v)pRiol@KDD%^fyG z51CahbhmR%?-kxwy&rQ3Yc^sBZzlKUY43si)9%=Lf!N;yd{l)0MMD1le(VDGB69m@ zm~63cclmAfGT=k~$9)3u%r0fRvDSDd)Q`{HpYh9-;}ty*qh;2- z!2B*RI<5u35I0-hG#;)0KBD}&cAe{mpiP2KiW@8D?-Uxm^pFCAx_jVUH74^i3_O|> zR~Eq$mP1_KptF%4Qk-W8a|oFP->2O)X-lb|v!r}?*c-0Cv|sb)vmUJef2MOd92)Iy zgRC41X9)T0cGCW~3_p9R%CR6gEDo{L&Q_4Fr0K*P*tz7+;87j(4zNzRj+>Wfdfuhn zP22L?snXj;$^G}~P~FGR5%R#8tf2mwu}8AtnFS11Z zR#Zd6cUP0{z}akS`l$jTa4gcFm< zQ}`D1yw`bTh;luG1t&Nja4O8GE#_*KZ({4^=J|)=iqAW;Q)v+wyRI8TqkLstA33HO zT8?|hJ%4o~D=$+I+RlW~798DXsOV@aGhW`0kku3`$Uh@nb;q##Ck99u*(0>+OO@{_ zM>LR+swvx)>;FB*=>Ano=kjWrA%vRWEPHIRL49hZy^X2W%~0j=L*^LX%C0{y-NG<+ zP!NHWl_@f-qxfXS{_#yFiENvAforV6sJe3*Q^-34tSn3)*n2#ukADyOCE61#S-UC; zWKLT1Rt!3Y#G31Qq_(8B|hu~NZjV5J7t=g;w_U?bIt>-$YRg`(O;eI1mxu&l?a4lF=x z!F*C$7XpK%m$rd0(d7Pr<)6jArY+Sjrz-9YqdgrT3H!@GQtG$3{AyKb$k!$1Vjot7 zo%QK-?c8m45>t#|DohxtkBB4p<4DV>HzXx45ib71F;%`YsE=Hu&*x)~%z0(2tkoGu zh9Tu%z{gB2Z+nA_4CWy;Nbm1|nb5h6!>@l46m3LnSMMH&Tq{x*Er|a}?cm_Zvfi$p z@)f#7W3TcJ5O>Imf2(KLv=7GeBdp?fdP|1zC~YRPvxiNoxPfiam5>R0D=jHrk!dp7 zFDvq$#4Rl6bg7M#-ZIx}c86emN*x6Y0-X7$=rweiAAQ@K)j(Ji7ZZ{AnA5H?Nv(ra z(w8RBcIdSLOJe!H7uLE=M;QZ`t>UBrl+c9=D!O(k_BNnrp!!L*mE^v$^c5d<1ZmAEp zBs;zdV2TC?6k1wZ`YlaK1&|rT}~l^3aa9`u88Xrk4Yy zCGtvtG=(uJOCWXUnf!SDu+lWHmY75zoV?M+_+vjru|8SO{V_=x7a3PnKM#g@c8_U} zv>%2l`gPDN_D{qZNet{-Qhfvpo4lkDc+hm=YH1Pt^1~wlHRmu+(7slJ2_LG)hKr2> z=6M#H5+1GRgQ(DL@Q4}(QCUXDoeUy_6)9MDELEYMB!YvU9!u9xjqC%Dfq-33YKRR_ z*A^V#_dp`9T^C7vVh6(hDUo)+?reK$zWS7C9RYKzCTl7Rx(6PBaZw$cpYba(6N1+= zm7_?5?CR@?ErH$4zbrR?_P(UgvOHChKyXPD7+}BC<5)R+;(-9z;;m>|agFykdQ;Y| z1}=i{V@^1Zf=h-ABElO>m8$%L=T!~>83@4+C`i&1P0Lz}-v$d2g#E4~FD@?Tyc~T( z(w2mpb#--{0i{OFCm`tJU95)G>wQnov?$!`mdurrB-F=Y6lP^Pko0B`)=nzKOr1Ril53~rEO8fFGW}J{ZR-Ys!;;FKBizh* z3h@p;#)(0m-Et)MZ$nwsHp+UJaO|;3(>8{n`p0&Q=TSn-YF&8m#(I#GzVH>nWI0~v zSE|%2p3u@;n3v$=@SMUAi{OrNJU+gtN78)9R?g8}J-qpsFoMw+1U*!y>oosutg>q< z7x0iUnzG`79@_VNn6|@Jq)d(-GwQz;lHV^&YvrrqwVczd$^100KtATTIkDJ%@z{&r ze-#4cy#C|$0&%BngU?|l3JPce!hug2vIYMkF0yf2+t1qyfL@KK#*1$4?H=3EmnfY` zA6#LCpgkAmM-M!O-@Y7fE71#D1hRY4XRHqV^wOijxyHuuAs+gZu`u{EyMnr9#6!3C zP+iLD6>J%l8o|PPNJ%r_giF)1K584otOOOKGcGoM9qqN>({$mh=;948g{Ca}Is+0a zPjT_uj;f%egQ^};e*A$5vwenjoyG2Y#guQMpZ?S)Sj-?~a3C&io)3f2k5u%I7U$dQN)pib9b2+mRRXsR}RDdx6@O;t@ z2Vkh32?^*1HBjnUE1arpevbT6JIh3p$*E5$-3@fOO_DnWMyY>~4Ci;yA~3m8p3>9T z&o3$po0ypRen^#T2sWFX!{g+lDd2+>M_m(=l{GqOo*6aD56=H7Ipx2}Fp|k#vL;1k zsK_DBJC^0Ny`TmwdLp#TN#f?KS7jDrm&(wJa z6T)UixvAkKY})BqQga<;1uz~xvA;qP&NCxI9)x6mPJFoH3Dumdbl44MMM1Q`Aa2x< zwVNJ4BFJhg`5{QZqTF0*5y=JZ8;b*sB%s-kMB%{0Yh08Rz&oTUI|>x6#(TwoKv+(* zgU?~U#ex`$2T1c;MX)+%p%+D_Ok@LuxL-bK_W)a?S*JYTFR(ld88y^A)Py~K87#8T5*A%m+2Si zD9LnfU|Us0jg?H{TfrMkq#9A9LX0G~^U&0}h`31=DV9a0$MDpLzU^9HOa!pUU2_BH z8^A8mnSvD{<67G62^hF22;k=>29Q-P8sG`c*DIrrhK(+Bx3he;U;uUq_%#V|DniJ& zS6Fu0PdsR3JI>yJu%Sw)``Pq6Z0yL~=H-?43}E*HL=nm15$v%Qma0MM+TDUT*y7U3 zfzF%?oUUmA`3+G9JBPqFu_$Spx9}q-2qiQ2^;jZ{PrN6zA5H-&otKY~g7jc`=(EAiI985Qp&Fh1Ivj?y-6T+LGl z6V>QQ!OZM@rbw#NgPuw2&`ey)j>hlF2R>C%N+wYTK+rJqG;|YxNeCOH+DpCOZtSOl z*eRNL6saiRQs=)$+Cnx+v2R11c14ohZ;9TFyJouGSbQ5(8}Vt}uDwVN*K zMwcIT>>fN@_@*UMDiG2g`wd2`EIdA+Igdvi-;Jag8{vkgWnWV35ZU={%@P_k6hG3O z$uldNsE|v00?DLg0|DocERL}|4mx5f9CYZjq09K6xG{%k4CzL!HWP_!M1JS2#^h{f zEDx(DAs#^J-UN0uDAW3#ACs;_?9ClV>#xy@p#tFy{q^1+b;>a|?)j(*RzyrE<<2U9J=R&4(k+LQrX(KG|&l;qJn}{CvIXPM> z8TnBdUW6;zHhLinDlRo~pn^D%=Dl|$2{-Y!`hzm}*%Ylu1$euYMZ+CGq7O1fej1r;MJ6*heF51YXk6|`M~Ki?mx ztdzO@Cv=1W!ZVA2JC4_b0v^YOA2k_C09$GbLpp(~kuGB{(TF&b*jX$YV?0X7Wr?A; zDWE?qvv^TM#&ek==aqc;LluoL1;f|b66)EQ=`2)g{zJBgcN$-NFv(6&0F)aC^*)C` zyN94L9iFZ{IOTPW!tB(m}g!7@g$u@1x|^FNU3*j>e0Qbm36_VncB zs%RKXIJJ5em52wth`9Uff2t@Yvf`JNhlZVLcZ`rk^ zRj~(7WKuuwXGODq?z0V|M^~%9jYNWF*o-^QcWk=2mqM=js;Decv3>4mS!aMUa3lxu zkWRo#pOD6;uN}kiVe1$&SvQ_i-ayrM6^Mm2A{3K^cyjxFCeE^lo)c*P>Ztx5*h%Ig z&wW$&K#I}*H=7!2xNcl(AopW?;s?T)F45$Cu=;Gg?e(^NG+H|Q*U}%<{PlGelJCbp zE^(;asfpfa^|YX|p{_v&ShdP&;$!>1BexG* zlT0R6WL14(tbk?wtzg2o=GV^=?~jLBwU>8R)(M|-R&fa9WCetU3-wsJ0Ksr{bX4=J znA2l5K&MN72e7JzMGRhAW?p(2?1b^7rpv6WZ@_(tIz(Le>ok4sPS}oG z*0GGN3`Qu_;KzXSrdrN2fjzz`nF`w##;9>R%od zOv=kG8lj+5hukIdWI5__Z}>U@th3moH5-RQvOGfyU5WyL{DJhnWvxCyh^yoG;CT8> zXvEDy2<~IT&4sbyU&AjG!EZETbo)5zzrTlq)=l3Zav0Bp4205W; zskNIozjg8M2R_|vV@C5BC3m=$b}E!cy(Web#DzmAr_t%)r2!+Y`OUQUubR-ZBY9|i zSt~YuB0RysD-;avTaCG_CRiNwA_W;IvnJ~8E4BJ>`mT@T9xwxBT{c>8=Il$dLiq6I zG|7l-$SO<_T;}P9f&|!^k&%<%NnL9E&`pHnJPZ#vLyinFlXa8$!|1@&B0kTU!j_Zw zL-~&%rMBidnRfIJDVHF7LVDg>Sh4OKduGuJN$`nqKvEWp?d4lkM$V}f1U1H$A_WP4 zHOXMLP}3r>Yp_6eUQvF+CaC?W#^PHj{^gf-plL{c?FZL)M`2*)Lgu90(qja0wv3;B z*Q+!m7CaJatz&q9Oiu20HOb^nImWd-*R$Ql1&TwM_J<1#R$Mw=CQk6I>yTmYZ7ks9 zdP3$vcK;n)1t;(P(DoBoTlNWX^5VvX>glb}WyfALdz%npMjDy3@-d;nJ&d!7R+ zPVPG?B=s-id{sv&`Ncy_EkR`@@Rk(Hb{1yI@6W?HAp|m0Ni(F$GlOLYR7==KK$K#4 zdDX+gGcE-UfkHSTsSLAuO4R7#!P{t=rOkY=6e*+<&rzbI^bFgs-KAtakxEIq+?j%f z7VWL!Ht3?uXd`g%VPWuf6KhVP%=fM`8r02+QYgU23Vj<&9-D<)42@LcQ$ikj)@*Hy zO!JGaScFFBFluQTBN+26Db_6MM_5k%5nOuLGdb~02`KhJ2`O)lV-#vX)KMBV;fC1G zjMDyF*+!+`oZvwFQ9PWYtoHLRoTuV(@W^fJ&i7!T4lvo>fVn2Wo_=)ar#b9%V}gZJ zvNTN+*i`pz?LKZTueFuTcz)1qzFNme%L|6Da?DnVNT@2K@LT3vInT(v_uxVOi1U`=L*i z(Vp3fhLV~DS@J$BH4CC#9wF>FMkb0p2vu_thE+oUcB{w2X#DJ$m_wL0XPEOGnqm<> zjrzj{ww#zS&SjWb5Z#%g3`4D@B-ki7C1fgq_XKCaow>ayqufATqk~2%G6y@nvH;b& zc9jsmnt!{c;v{^@=ntd+x4+Fsye~85Uf-x&$1Ada+b2mMhAcE9+0G6d{4PheKB?5Y zDAR_O#mJpQ$_O%V@lSNj4^>LbFf>7OEzEZesLfwx_gKkm7wYa*zyxB&Q?$Of%Sk3W zcaQtL?fk41AAMxsUwpl$D zqXCaUDBpj|dk){$qzicGtC{)vWr6%|x=O~sb-id8vZLLX3o1f>)@d~lI6&%#Nrx9r z|7xJwv&S3EC*^_Tfu?m>_6E7+4fS9XIvfHV0!mdOEh?96+q;<)32bz_h0m|$wX{+! z>>)$8iX-LvZ8)&(+z7fy+J!-6`k)7fp;Iql@DVQwd37V3oyVHb`_)#FqJ2!xSi3~Y znNC?E-MFb9Rr!h7o&q_K3>G&}(WI7=&??p*rjy9)+YBXzcH)G+3|;PYq3PDEgPkTi}U0HJD@ME9o=j=|+Vp*Mi z#qFHV$r-HDO5M8E%_3p5!O+drr^S_H>0ToFu@I;}@*HpJM zCXsvW!op;Zihw? za#c%bq36lM@<~s4d~+lfp=2oN*&kcX2$$(zZDY+8`keikz!BiiBbUI49KjljJs+>c zkWy4yle1PHR(aR;$_*TV`b(WRADM@g`WI9rbd}M+ ztn89WTffWxb8)M(JC-A%>rJIwZeqaXBtnGzy4Q$Y9mV;aqgqb!A^SrMF`i}G?qepf0mHV1`AQ zOAp1spkj&%mtUg1XHT=+%zxiXsjkEb{d+Bt_Xaz6Vp7o;~rT43l8X z^*D5ATR6BXA}U#ifR}6P^AXyUBdQE{b>U}dS(q#);-vP4yct1>4l$cSbcI}hKehsm z-UP82|sWYL564|~jSOtaA0dR3N=!Kj1ET8LUuNAcCq!-B-n91uRifdaE`ZA^V z@3cll#wU!aLpW^es65B+d5%1^9(1AxP4H4JO)XLO-?6RHg|g9+e~`(G6Hjz7>c&a7 z4388|#BmIK6Gua`XK8UklHg*DAdNOhbIKc#ma=S}fbLkjV;VrBe`G`&i7{hyb8L3GqltI<$FoDv=|#nlu0be^vV+1=S{$-Pkv*JY)cs7`muY0&*;&xXfgy5F zvVPz3N_xpHO15iSM;o+T_1Xl5lO$bf137RJQ8GX5=BN6+cG9 z24nQPBI17gq0e6Q1ovsOncpV%hklOA_k|j(q3Wk202KXhXKQOVTdw~u3t}fN=3is? zw#afP7M1torak3-mF~jAWDG5Q!yX>mL6eDi#TT}59s(%@-JnXALPxBjakV1VUaU|e zh)C?#U(0WfYAu-~!6ZFe!d%uUWhoLo=-)iBteMawJK%{#|4B+nSfqWS{YWK3*^`8u zPoign_!{21I6@C1$(+&|`DJ~ceOmoyRu^IO?y~m0oE`q1+S-YY~H03+D4&Yq^+pi48rU4S_L`@w^*pXPo^a{k8US7 zRGP-zQG^iUwofR@om8pJd}RLD&LS;(>8p7CquXD>^WXHw0{^s#njI03MML+nCkeDzBujoF;xNm+EoFGWRHDPLCW|nRF3nrwQ;T#9 zXqUDZ_AUO&CKXsi#O>h!wk#RhWpp|?IB5Pj$4G0sZn4CxYwS6rpP)Fx zQlj_<4d!KF*{`5t~xdxFAoj3nANG#k&|)^&>R1gaIg=QFCeZK zv}YMoV9;dE5P`#wOZEwsmLr;Cm>I9O5!19Un{V)^O0_Eb^>1*9!-L|r^hUy-Z!k2r zIId)1>z$}KLrOjrYB4`Yh80`-A4uC492%2_3R>FQ6Z7*vI&*lE)edt(j;eI-D%^<# zGM#t-x}-!?t3*G!ze!m6gz<8>_Gu_4!e1R94uPZ23_gkF6?)BIBCg1bCTB z1$ye6#gbVabVwb@62(+q66_S>8Jy?`7JD`OlRY2c%#lN5>}AFW^80?MVV9dUM9TN) z)wZTbPZEm+1V8J0n~GUo5VsU-sFQ+?IHZnq=CgIB9v(Lu`jp)bBG%K&l1Z))gY@(9 z-PdpG>l(bra|g#4R)+F-b#&Ns`fl5h^lI(jyy8AAb`_o&I63{#GC99rlv4E0_WkhiPf>3HRdx4#4=W)ENOyOMfN+rpi3?}ErjQV8}`8ulv87iC5Ld+OFMIDKlqvM-Ti!$%IlFfS7? zAdRS0!w=vlQ;*T-Xf8EQ7Jb0!t$IT6r*%})92ryo5f%(7x)45DM5 zAqjNd?S zsO@+bdS+#mtb`ng^RU6lV`qFq5C8bMl$smA2NtCi?QE3;m2Qg{JTt2T;PKmHvi zh17M0aW5ryEK!|hud|Ncd;JCg(Qt zcTfLHM@5@F)-5VaXt0El4wX)tB6C1=?BPc}&vu3cITTr@ zY~qrnPF}+s;g_RBDEzecl?k}G=cFBhVu)TobLbn z&AEB zj?>KnSkW%YPU!sKzp^SS6MJYXry^%N1+nR9{)nb-6W+JyJ0G(|C}x~?_V@FOi$jgL zLiZX6)A{27PQ>?K;)Fat9?IRU`#L{fhFbl)FdkJy_Im$KbnlwDB#e&!BwFFGv%h1C z*(xeBUQ|W)I(ia@fQd}!nU3m+lq+U|0W~>F1nT%%-!2YYXFIPUUq3tk&=1<2xHAGv zLByC--*^q^D8Y;RRwRPbujCrC_F)9)R?>e^*Q2{7otkXb(DkP(-^MUA2ZbrB($Y#R zD53w%l4TzKBEf@Q%>GLgx!96Wn6ziCqutVeivCLxssUbPz-Zsv_2*q&{cv9rhQ+Gj z6sNd3pL&u3$m|?3c3m}Sn+@&o-4XJTq6i(fR%c6rot+>#?Cl*3WdYz4r%>2nbRr}~ zll)1$J0@|R+~SDZh;(1jF<>+NU(EKt!EOBeo}JdFX=J+KtNnH-U9f$NN=itTjTx4e zG4Lh%P*7IMds&)03mbdL{;-M8B~e&Yev>n0r0<B|l(%dw}J zS(oGtgiV)W4;7+@2yLHKTPyIRa}p}fDS1(1d%Vx~l`%29{aL7|8k665KS?wyeV*r` z1fjWs>*ur4Dr|#aU!oz%^D0((ZP;sx(}r`<7dZN59$Hd`m8|9=An;%QMvC_xd;jSd z{?1?KM&BJ|_HUw!i6znlih1vO*u=Rw=R30%e_-UAhZr$=SK)OIteD2trv}pTRLLeU zJ>o|a((V)^BH*HZf>Oj;u(E_g8;o`kWOH!T-(&@PXK`cffyX6xLjfrZgGRa5P?Jqd z=FUW6wfPjQdbyswnHdXwYVS`6ESFm|K)3XDzG1Uv5)eTluO=Yi00m#9gtj)Bv9U4o z*~13v{nyu7kuQ4Qj0lr&1QP&7O}$LVO#x5h%*3_T(za+Qzo8)ooRG#tBF~QpVm8R% zNJo-`^k~U{{}q>&{X45GTPYhbIo6mFtcUP1Kkk$827=?W`*LJ<$b~Cf~f9L1LY!%!B~*l870$TWrHg|DJi#zJ@Y7bI1fjbkj`lJ zk|89Z({ut(9$liP2TvGO}HiC{Qs6?T|k)}eTm2I1}$!J>F|oa-l4 zKsqz-NVj46JG(pUt~qf#DvV>}sh@|!81C)%BK^!n8sHOtg;&ewyf64nM&QNZ&E$J> zTBDRnSX#$^ic0a%GHURTJ4{U$>Gc+>GDJN_4!UxE1h5@-3kwQ@Qd2*t+p;F)R9D9Z z1-*F2`ua6+>9mwlS*H}Ba~E*(;l=}rIN{w2ZY3U>(k?DnWSwlHWJX*hwN~>|US7g+ zOfZpytsuiCtfX0SR8lgs6QL-z|I}N`!b|h=0%BuhJIt2G#_asE9v`lBJF1&-@8@l< z#*);J1L@aqfd-%}t6VERIIi@~d!FeF^LB}X&-5#V2r0h4*Z+|+6iEDylMxac>WV{K zb!9305X(!YMB)Ta`@hsUu7n!5pUk?4A1u0)rTu|ANK> zVV{DqGbMT6{2FJb*;!+LL8HGy`Zhi~7#A~D8ef!H@9Wjok0ezTk^1-|_2i1dm~L9a zs5Kd1Gm>Ol`RNk`9BIhp_^0vS&cV{~>a7(6z%hq={HYm2%YH0Ok`f0)EP7P&k^c>r z=GOf5Pu=B5rP1Q^V5C?SW=j{2vl6^A&|*BG&~?p}rYFx4O`z4Ey;yCU$+&D$#1C{8 zQV^mnY;C3NwFA^>tuKZyPnktlP7WSU!H1$_jn|!XBD?M<>ch|a!cUkj*K6VALaxWn z<1qiX^jABmPOL1c&8L528RXD%m0-c#84H~ZwOelcvz7kiy(Ii@h; zWb?-i)v43y8O-y@cU}ZC1AzvYMFP(nyMY(M3L>mbh$_s=h|^8yABgit%#|IDIyS=> zO}p=R9k=Tkab|{CK#tL^|LM%+?^(L;Fx(7*B(q9LL;BFY)&#$8ULe$Amw&-CLTiGt z`e+5`qpsn|qlB152tGN?5$C(qY^?=V(oda^VK0=1FBe=oBcQ`Txa&^Mfli|*PVYP} zn?8hU-mZRi_jR)HD5(H>azXz_e_V=?8<#jLxNaY9L`_YND+ME*@D1syr1wG1%=JLq zz1-tt=$A!7=f2oSps3zGJ|UNj2P)k#L)&t0ibJ z!A9EfL2n(;&k27BrbI-SQZ^K$$; z_qs%?3pSC}pMyrF#(SJWzPY)HD%b0zlE+0t&qBM3UHoVb_S5#>K{p2U!%M0m)!!AU z=xOPclDmOw;!?8sIA1H!3yFB}q2UR+AE@-lP+3IgEOFI%W}COL=Tt=#&Fo8m`hQSM zpl@_f=FW|jkdAWLIfXX=tq4z1vEcVC%_y#!g6v!8(GwcpWj+8Y2I+Zig4`G+0lC_A zd~qHor~T!#ZM#zIc|TUvwbsAv5?1hpz#)Re+_Q~NuT=^a@yMOkTVM z8YDde5d{-Fs<-&(Phq?4!eTx_5-%^W{iT*PXgFcUm@F~NsrN01o?suA{#V)<3?wq@ zYufyHYGe{=>~a6}s=ZhEzSJjy!NulZ$Ga~Hgl42(b#p>7wJS&O$y;-9RD_Yx9*Q9) zB<v9JXb+HT1n-KHapGXPj{l8gaolCuqY+gkaQq1X^lKn3^(y{b{+_ zm>@~pt^yP8j)RHxgA(`Qi&{h4G=VY&@uj?4tF)msUcB&b%_^h*5YGgaluiHF!$FPe zAToPg9U6Cs5#%aZUdLs5-%Y)~S>{+8-m=z`GM>Cw;hFpfH8A(>ihcb|URsR+9|>pT zy{wpe>ULugDVkvjc}nSb->5RPAEZXQA6|rOLc+`g`tntL3sSd!7o?wF*$i8JZ0Ra6H8+x^pPJ(ImIh7iR9+)iTle>; zgo`=QaD@=hEhsJ#o96FS9*d&#@-3paYh`l0t3!eQeVk*CL|miw7-6tg2a zl)u5>B*mtFy_cFJ_?r40@eli3Jj;0rB`3(x`|u#edp7=ToUy8}i3&a?Sc3QxjU)hK z8+0?gcJi!?qBrntA`(`QWZ=FwM;#c69^#kTSqWtucM7d%DU~7CHIeye=_%-s6Zyqd zrHd!wF~T25xk3%GTVXXwE(A&^R+CO3EwS>N)V%PDo#@9Rm)$PN$)`wZH4_7sY z&@bfM8qD9N=W3g9ph|oKKNM3bzLum26bDU9GRYAQGK|g1FK&DqpJO|bNnSso_?V^K zDOY~*x&NO3el0Lb3t~gqM22Mt5=#xI@>`7Gl7~#-3hZh}pu}+1e4CG`{=+V~oG{8~ za6DgbXK#<}&E|wsZ*t1!&4eT8JDa7C@6wE?O4LjulV88OB5FIog{LZ~2$taDS&D&#% zd`-StuGwqVWwEb>iAi14hMKfw$>&@lI7RA6i-+A)x$Ql%{W!0*>zxTpQCpF+w`HIV z8~J@^O8Bd9XM{tJ_*CPQMyDoFl%t3F1AbylN7b!j38~CGGjoJbj7@d^>aQUeUg}9t znc%anPZ>~W?{?CaU4JXk=y7wI^vIEvZnE;*HhP9wv)*6cU8os)e#l$-`zN*N^{Nlq-RJf*&$EWBe@KtPj>$ zy)QQBZzctkxN3wV$}9rd5am_+>-~yI@@}{&yWSAc7lrw$zS4m}n%}2Pp}s@nn26%c z-ENE|ET^^9I=>;beivvCMGc1-P)q{#v?MsBZ-uEzF#{v9PZ<{-ucI9YZ6kKWlBkZu zmxf~hk^Q5n|ItkV^o4Frz@kWwEMdw)=W#WkIO0y6nz(DG#HW`rDiZa?*CkMy7fe+W zoGXeZce4|3%x0^z4m?P~){9XUkY3Nu)lB>V(-#GrC=di~`>T*8C1{pvO?Xt8rj9RP z&wvsJV8a~)+Ahz~+PuxU9rg;N&?XE z^hQ!h(&DJ9<>%#XIJH;A{Ag*(01OX4i9KT5g3kM&htv5@jUS^3Pw8TS)SAri@b4wr z7`Jws>$%Gv|9DE*g;(CQ`3ugP&k}=tA_ZkH#8_5yECkT}O3SH*iR5SA;)}hD>zMSH zhw*k6p>5;^Ia)#{B(KHtbY&Qbk-i2TPl)Xm$~a~Bu!jC&GZQBsZ-+|ADhB#bN=V*A zNO=7I75FEru#5_!WCw@DGC)z~Z>f<<5hg}fvq4d#ECCE1xtqfsBk%L`H}p+-s%r6Z z!~YcXK>r7WZGnd!w#Yq@iZXKGmtA}7?tWKX#>O-@Hw12cOAZnf*6PP-cbFXv=HgKn4l(*ip*3{GtW{H9p%u)+N zT*R$MDxW^dvJrwmqOe?QPRW&yiXAe6UF&FQ5W(lJKb8Sc7G$^F0Mbf^nBiVrT$ERH zTI*QPJnAdjx7%dheVavKX#{G?h2;|dV+xWN$f|^7v^y$C~Az{Dl4O2)$37? zBr)t!b$Q6L)Rg1G(mUF5#`)z?>nq@VzJB2W7X&aZ@$zL_Q0Iz z#)bEHd>2t7N5`kz6Dd4w1C2)7f1n-P4%o5EBE_*AT6^Cmn976U&VkIw+13bE?5vfQ)q>NEuIG`*GTG}dQ6xS48;3_nrl5&3 z6Mg}NmzOTz2q-;tjng{_rVTogk&&1niE=CyRZ_wlfbHnwQtf$j>acq!qOtKNxB+yK zVyO`#PD$^?%3SU~6O0_saJCf^5DQ|J9088?^u3tA+csy@OPZNU$n-q{R-!r$f>}tzXaeXr7OmCNV|%JS${z#8wo*T z;ou2d+r%!xERoVQ>BprFlP5)w-tLgfL8{q8fJpQ@=m>E~{xdl~=VV5^_{3|_l%`4l zQ6P=MQtOwCvtbHj(-p6hmY%G%25xN!a7E!l*yC+M3aI^F0~XlR0lw zloLwojx6V4-%0c5!*6@5vI!x(F?K>7LB1UHl&p=k6~cq!phjH$C9hxi z{pEkZ3Uc%v2H}a*NO9(@A%S%FXBwiNIX4c{AFX@s;4s<&)T}D==L7OCcv$b>_AuYJ z8AN8y_n#>rf{x}!qH=558KWqR9q?71tv$A^!>4osUn+^KO-H0q#egkRP*9v-U8$(6 zOF2355D*X;QmV?)<3f0ND#8A$PK+nT7`eK6@~%rVt)=+)RT?d{izwD{xO?)w+V3;O zKw^E?ZPyL*sG@8?gfhIM)ZLEuDY`D6q&%DV1t=ZHh=DA|Mc$aj+eK(AP1j+OS%(te zP8YEz-doxOF+>~UPhVsN4zBXwW_RY zu^`LC7AK$LOhW@- zjhFca1^<$L7J6uM@*TA?tNoJNyyX1KQAPQa6l+>12K1O9qiB$G&Zdx_wCBRJgC-nY z;KC{^=V~?Lz4XhHrgk0Jo|KP3XQ8Mo(~;{LL*Nm8T>t3Um>8f0z+(e*adNuYYitgZ z+iz_Zfg2sA=dqY|+ry=jPf%fdAk=!r3DiQhw2%urM*vEJb>q%o2jgpzJ-aUi0xpE>N0{({468!fL}8pN`_@u?{&m=$ni z^Z59*1GrN;-Vxl zbYwCFW~|9%F(04QwWDAH04KN0Exw5Rozur+61~s3%#Lm~b#)H=vu}aB09;-8=M5;A zaJy<+9`d?c?7dsMYE^P)?d%DZ298J}`qLki>ixy0t9a-$Iu-_D`wdiJe{8yqj+2A> z^R*x7ahW8SEX>VAq;d;&<-B*{`z(a}S?+g`*}FVk8~_j>oL*^eeBx{S$~U-VxJbUI z5Ie}{N=sZ34U-ngd>dQt}F;*jcEl1s6CvwNm-{ZgWaCOzN#cA^-5y@#P zRRiOh6xCkscwC1Ctr{!7!c#-VN6yQk_6ntDmRAo9FTvdIcrD8*q@*;eR#eVzuo^+C z&Ys+#%5avf?By(QRkl~iPg)+{yk(pQ`donpCy8^yAOaaP zAmG{dQR@vm-)vqo*1oH8IM&1peZ=T5r6~G^>bw2{0{!fPAb|{3vJ)nnKz+eyUP8EC z^MNG&UU}u_hebPMb}?G!(fWtcz~G#{ugX7|&8Z(EB(HJRkfE{|bi@OyBv@~Yg%lp* zWtV<^CbZEOrgFf4XF1~pM;*ZVdFp0ed_H@4ygOn_khPmq(>VEQ<7F}FG@6>0=Js^A z3N4SnOGR34wkcFxcYQHK9YN|HsqZtGLpfSjwL{uEl0*6&JhQRf$R-Tig-*Kg*giRm_wOe+4;ucZ%xC@+jaGDX@ASB=5bPOsP^wkk^AJA? z`S~M*G2jPCEdYHAoG}?18k(&YW{kO7g?|r#F?bSU`YI~;O_`2R+-sr{&&9S)#Ar8% zcja^%dV0@ODJ=)ZKko|2qg)xL{tM`#Sb=qAf=P=$3fpU3a9Q@!@w%Au{KuU|Qq8jk z6@IpM!iP@8zA;;A$Q0-Ck+aOk=neUC!<*S=B(I*E&cAY+=*5g3CyGMZ7To&w5 zmLCpXdJm#WRkH4kiWyiKI9ji1xlIOtG&bJ;D#(kE1?v&3P^bk|DXl52D8d(UX7yr1 z^R+wM+te{KD~;APrHk|oZ ztFl6Yjp*v?26P&jo123~B5N~J>ru7E4134wvD*p4(LzI~AcY64W_0wuyu7@@hBBr9!+BX*8QvGdT&wPl87}fK=rpb?z9=Ex zUp(*TmnnJo#AW+YM2??>wB_}oOPfbyly3coNP=s2e5|8@ya(uFm64HL@Bs=%283dA zYU-`i?xaJ*1wUO@Z5o&HpQ4|esxem}E^$vcHD|8P5;A^Ij)gUg;sT zA-}Igk6Vab#~5fk+}{3tb+`yF*)-M)WWm83t4)a-j>;ePkFQcZTUuO{hmgL}eCxkR zFkcH7c>WEh;AO%_wjvAV)11{~M{n-!X=A7}6jb!|M6kW68nQB(oUN=5qSMN;{n{S) z+89$lp88YWuQZd9bACgQT7at?)h0vmtuApp1n?_xs?qs!Nx0vo(3`wyW1bOLuS^z4 zCy7vwY~S~@Fik+vdB)({#!|Bzp2+N?UAnkZ-&ad6x0b8stjy(wp!GtKxKfsFy{su8 z`}_A#CzhyCc4Zo%wscqPQKG{z?^C?XgZW;b8J*6*H5Lu$<8m<0p|gg+;5{?B0^>Q* z<>_&+TVVic0t#%H!#6iJrc|Us74?0?vCoJLP`Qcmad8N#F-RM)*EVFJ-9(nmRhveI zGQ?%ACfIC~{DBdPkAfWmhhFy&api#Kc*g-n`*=GyNk*lP!NWln9abKmXJY7P+CYir*na_Eb& z<1A%!)+^}DT)Yi!#v;1mn&%EBi(sspv!p>ydCCB7X+X>iWbHPaD9E_n%8!Q=Q^URK zpZ6O~qAAB){1`g*8lOGhe)@t6VH8Gw5c2UB_Wet9>>#~%4S z-TiN;`8;m<^fdqY8gFYCO|~+i|Hw6v#IcpAZM{0v_Q(THMs5TW>8*gYJRW$sbubTm zA(UZ9cgQ(~$}I5QKF9$WHnJ>-#Lhsn`hJl`lq%c<3-GjdgZN3^{8&r*)!d6Hj_SNW zE2gDIQmMI*Br06q0X)32EKq<9GCdCY-&rs4Ws|zob#+S|sBG0scV`2 z`siq3W=0buqX?2Xy1EpA8{z#k#bUS81(IZPJ@QTJ6^NEAFtctIt5~lL>p9`5e5Al`%%aY&&maqiH@^zo-un)-WYxbl&kT<*`UuN`5j zoh*FWl4D_KfVE<>!e4 zc~H&=pKj~ModT5-Z7|mk8+|w+syX|KCh{7d8CPU07JcrCR6}FXXVOzrdTa35y5$x~ zZRF!4nz>bJyDAQX10$q@Io}8zg8(X`34l)#6M!<^Qz`{a+7+p<8i z5ghqa36YO50dY54xys|pT09#Y@OsMAYOu4&K`g@_5jq>JU}}sY4BN=0-k68-S}*j0 zaf|8eQ>heuT)kU<5&@q{#)=`c`f6%5E9IG1^zTHoc0EUR{eRGwgW@8B*XsE1%Euys z$8h_io#-URy9qZ#{hL1;v%kzH0z9Lj_At)8_yv!n7FAVMMScAdkW322_Ja?@X>VFd zLxYz#XUo1poTLiaKCRVnr8d``tAFe1;aql-!9Yh^aF52G5~JO==%uQEjp6{ zfJmD2pms;!e=Dp5nE2Lx!$!n!XYU77B?ER-JmZvixL?G;>VZ*98FU7{8cgH08JrewXO8t~j`_$q_sa|q_;2_L5gm_%8n8Hta_kL8GJfR3 z?!RoscN_IwSHUe3=yZXADE7#+INHw4yB5~Mlk?r;H&RhRk@&`q>jB7?=e7jZTA}E} zPW`qgj2dii8H~dZ;NJ>@XrQgtS`s{tX zElE@e+#OhEa6pEJG75{t&BoGls_N4Wjtt?Y8NHFVxugmKF;I=ED_RbC{0(Lw3Ntod>H*r5f$^Zc0 zj{W13k`jl@(6fT_qdPC#U%Ve{5a-~TIXG?!GfQkDfx6ww(i^)B6*y{@v$YFv)=@S*&nyRZIWWp= z-|+r^OOz>TAmciAL@x6j?2wl zocYaSU*8wfy+c}Foh()X?wlX=X2SA5_P6}|D|E#Bvf8jJQ$x=!5Ts!^EvDH%PHY@D z9Z_C9|F(tLqsDU>BTczl)^tcZq8*8T*!J|;A?Go~Gh+*0D|aFs&Bq9EXz^PA1`UK0 zlf_1-=7$3tQNyv|9A;2*_J4{gV}?SU3_TECEwYy$R9nqkC)k!9?OL$~(}ps~wrngc z*1;RBH7!4|!;9^c%XZ*&?rR0;|8;UYz!9}0%!H6DepuJ`aPX_9rseR-=V4FZ^x$tz z;M25I25_J*5NqJ2R5^YYnCUo8sli_$^lm0-z~dj>pM%hA03J=p=i#DrS1?j4cXDP% zMPDEGE{y>wk)U1(tZ8}+hcRiY&7H!me@Siko6sAE%$Fr4RVG8E;6RMZ_6L0s`$TQ&t~%Cd+1xWO$H%|6O?H9?VtVM`L96y`I~PA1&p!%8ziBNb94O}E=&C&S~!)p zT>iDw(gx@N(CEOnx?jK2i74E2zrV#Q5(c|m==e9{{bgNSKA?Cy94<;U%WAO@gcZH~)vY%+=7yaek@S;vzefX@9%#B?~l2r#$X&EDzE1+vT}FKZhcuyF}?Tcr&}W>RbcEC8+% zmi*m`_59+(u9w2)c*P&f9z00YPO3tnX{K8c%;$FEx^)CDngPq|w$tyV)=A!A|FS{6 z5cjwd2m7K$Shrx04mzV71OCMv#xh?o)G;Ags~K_UGGU;{UP!u9?vr00FcY z;4H2j%;M&K2QY#CMpe{zI(mBE!;+%z=gdH@GcDDH6;3qYEgt=Ay*pg@0tA46@r+hH zWKfNNCZ(D&~=tBS%U}2cAv)KYj&={2I1ZE$C0px=;j3kn9!oC9_a9UGM zTTMg5lR9xjCjXNSTdtM{z%20Qc<5{puvoa6S8hvgiD1v<&4dI+g& zIj{=MJV&8){RRTn{{k#HOIn)gsHRq2TAEi?g$o2mVPS9`H>foP9Aa{MI&-w&N#NJ7 zUl`%DAXf%VDM|3CIS$KfTf+3>j_56y4ur{tQbXVC0_tIp^}q1yy7m$t{{GI-!?r(A z?d<=G6KpWIuz+bDWzKxl2azy3?c4uJN}G*)W$STS_Zwtf6z(tZhfY`V2bz`og^58> zfrssNP^q*I%J;w{$6VTPZ3S)dOp0eK`fdZD0P0e?ap#?MMZoqt1^6Xp1ZY0cFIl8e zdn^>FeO5@j@Xq(|-@%_w{ihK%TQ?leKq=}?K5_>4gn&&JT1A6mN-Ur2P7vy2M|>X7 zz#mf*nXJp;;Dx&i4KKPZ4}mrSZXn>eo~11hg5Q)Vt6xJCxoQ|WSqtY_yL+rCBM9$C z4ekVr1t`A#esl*vQV2Zk=)yvT)qLOxP(OM_AMFU=e1cea=>a>3!)Y}&P+%eS?@Dml zZY+HvO7xKrjGqZ;EI&$1;h^cb?dh%!uch>i(BETR-{XJ>{-)MV2k*e=u!-7aaIv%f z{k5HXsivJDi-_iB1JJSHbmreb6O+N@cHY*L?{p76N7LUAp!SvjKXfslx_8;Je3_wf(^x8oN=q%U3=L`W5>k0tl z&cVSZ5Wm*1!tw18!kDf&Z7Eq@BG5gTx3YsN*MddwX+RcgjZ4DbinY9!n`5@{u%_o%PX0;XjJhGkJlzfE&5b zb+FHGJ91F|)(cbsDW_R6oUNcQtd_*Cxy&vYM8IFWUzk509z8~a7X!L^9Xa9t+V1e>1Y$x1?mjeeWk;3&u0}B7#?Ks9uko z|60E=hK~DA{yrcaz_F9}uEIf=+nG3#QrC{6P($!@a0SAa&!Z{)U;5eiBFUcOD|J;U zehef~>gvkX)P9s|2No|4a%SMTU&?kqzTNX&nZq+|Am^aCUCx;@xsyP3R+wY&gu2u; zba^bz)@j4|D8e?_b3(%Lq4q>}daG~*hEB-#864DHaGtk1zq|ye!q_$O`*pkA0$rNd zDfWTnb}(NDM<`&HvqSa9k;7>l!uiT=E2BIqVfg)Clxu+2uYwS43NRwj$WD$sv0&%1 zj7U*Jr>IAsTY}&*h}goQY|se7Ai+~mJ2WJ8IcsPWz?kteMvHZg7Jz_>Z%@w{pCerJ zvTR;4y2?{Md&IK+8PCNXW6=<;M1MsF9N5PfjB+gcD)yxM~A}V$z`b_iv%S|qIf5;rthSkd`oi~It zuh9ZZ0L8b9$@%}j37!(FlgAv}6hh0c41XdVB9{MuMU=XrVNX>2p*&BcBSXW_z{dxu Lf@GQaXTSdk9a)P_ literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/html/_images/chapteroptimization_63_0.png b/doc/LectureNotes/_build/html/_images/chapteroptimization_63_0.png new file mode 100644 index 0000000000000000000000000000000000000000..b1441ecf45660ca6870991f6ba7d6442d68619ff GIT binary patch literal 27781 zcmX`S1yoy27cNYT6pFh;@#5~*LV>0bDDLj=?q0mOTPg73?(Po73GOa|w7A^E_y6~1 zP3D}HH5u8n=h-?D-{ob{-;=zDgM&i{ef^>Y2lvJYcz;Aj0&15JltsWp&_znaMcLlW z#of@!6b@|Y;$UO%Vq#tEMv?94hYX_YGV|77-kr^%dyLXBCgEvkvz(?M2UnmlilSFG>Ti12n-?BV4KF z1Pf532_$9Dj#>W3DqB~0#H`~aX~V7-B5(q(Es=KwZ})eMrIfGJeWM*%7tC7c;65b3 z+0NOZBqU3~q5HP|lgQxwz;n_Wsk>*uo3nWXmUEK>qW~cXzJ5MG8J9M`L3;fxB1uBg z(a_LRP{KAziHL|;aM61BIXE~p=!t^t4Gavb=7A2`&-| zzl{@UpBCtrzXFd6T2OETEqMy9B`n#m@^yqB(!N^cq3?k&Od(6`poDiGpoHHtAy`A~ z7BKm|E~Q5J7mbqFVbLnF)laujsft3e9+>@$193mCjAe8X-nRbnd;^tDm~$%3wFPEj z0KL~l!}NaxN@xuPcSo^%m!K1MZC-xaYdMl7+tJ(9gG(K2Fa_Fif_a*$5i-7iL`9^+ z?({?qF+RbmY zbu2;Guq-ZczKE<|%un@yLdDXph^uwUUlRGUPnIVgPKeE86+@17(44fLGXx87Op$B!qorw5 zG?%m*an&4dlGIkv0)18rQ1~*kgdMfC97Zd=Y%K>2QPf35g1veyEe9p5<|`7I@{A^hhGD&pasF3Wg^!DqU{X4VV>S|^S!>W6 z0x=n6Nsp&PB^U`BFzKNl(ExMRf(ET>sWVM%=$ZKv(K8`Mi}a)zb?|MFur-?@vs%N1 zWA|*6k}Udy=$~xp>;kMMGn!X>!xE%rBXLuWIJvHLek)8q3vWag?Br&CO^TLy(t^A| z$Tk0zs)#q{a0*$z{f;#ML8$QaW6lRfq0gl*1mGk%QNH7b>)GQ@bl~q|*5YE;l(i6L z)3FVa$fBQW+$M8qmULh(aH3+J$^5BAHmmtaiJ;RSS&LInRz^V{KAS%j^$((kbmfmK zwq6331mN@zQXf&1lTnYm)W&UOs)mk~rig$-w%U@l7%5yA&}vNl~h0rsc5V z7vo2XLYC306*Cl+Hc0I3X}6)vgtMFPV(n&{(QlPOEl>-KkKt6?Y7sJ>~2J= zat+0f^uY(<3MCIE8DMyi%QU_BL!gvNmVRN=#MA&=Ua=K8zZ0g%#y6`@=HL(`p8R+v zrG8lyoNqxP3A81&gvUt<^cBCqmRMfxJ(f`n+12jU3OH)&2u#Rl5irQtv3a#J*ofn7an0E>&)DzKZMPf4#L?jyl%TD-)a~9Ncci^DC zddsxEQ=?)930~aRger*=tSP%@Wbi(DWK(*{053woBf@H$4CcO z0>`t^jil673502K?Iijln23M24#?yE8e9>GWDQTH4R5H8TnuRm@sHY}jb!+%=(r_t zx$UTupKHG4D9YdHS2L=nM;iTe5~p~|9rNwy?nZ*9)xi3Yb{19TboNPH#z{`?EYn7g zAsxrqmS1dF?3l$%a(qDxAAnKR^qJp46uOTY4A3_deNl4?sWzjcfb(U3wUy|bnk5Qz z!UIzk{{H$A1Z=Gb8L12BH1ZHzDv1RolCv0|n}n*OMv>aSHhvYJRl6rFD*kc|ojxI>AH-p_t{k8SoI zn>ti;KMF?Zd8n3{EUlgPll8a$?SYjwJbELNj@e?uUpVx20SRO-tFSwzBn!?_A4k25 zLs><$DCcqf{qOyE=?3(2z(g|6z&wyli$?zGZHs)!y4ImhNVXlZJ&?2t@NWts4 zk*CLj(1kHAdQG&`fww!TEMk>*=MH7C);M~9(BtFP zaIY6)G30Y6)E_07@GVekf{t3{RS(=LZ|$No-&`;uwIB3JmKJfP=b8uzkA9VRcc6$Bi4-dE_os*o z*HfR8csFx$+|zNFFH>|0NagGB!=(llFN-SZo##6ws1WEX!1tX~`cQ~RDAZaPDwt3x5}`z)+U}GMAJE4#3oN#_4P`|%#D=Zc4Kv0K6O4fw zgTW5Gh(YxJUF^(Pr?I%Sv>rNTPfZk9F#)GAthNtz54wwu@D?S4KnB&fQtw{G_ix*S zMGZeY1lG1dG|QC=r%!QD^04!6IN3RXqU+T8rlxmIHrE?*t+JAi(w-eP2I7+up%XM> zlLgczItfQU2}e2!={}LauD?;;Xp@K7oJW3aL4m9yFzZ?U*{3#e#ioHRl@&cg;Pasy1FN8_136YsfH>EO$9_>5sWdGp-3<}YfHr{MR^2y z2eQ;VPLMewQN_^zZ;RqybStunpr{YO+o<&U=bC}#2N2HI=u=8XeiXl;Vm;RmM8JI3 z`IS;~z?^gT23iciWr#J*gnUUA9%j zj-^<+E=x{YASG?TXJiKz0AE7u$BOcQP1Rz52Jb&HQ?+5c>)W99R5?0XMHECZVhqp= zkY(L!2HBO(WL4_~lazcR zHJO5(bGcGZ3>w=h%fdFahU(8?m;os%{8>4Ay#YVzRvxpVB7%Ox@2WQ!NM@l}Cv2DZ zY?}<-4tph(@2Q?WIK{kMIFn^-#f1g~mjvD!<7R!E{9d{0ap8ivL~v~8o0t4AkWcL) zGj$$Oi76F?AN4yDk*g2~q6DhK?_m3nNl=QamtBR-&ZeOiBLHxNH018zYnMUVzpsoZOX(4y^3@TCv+Pt43z)t>6HHgt znAsqaD`tJR4ciUN&?Os9?^e*_j%$)c;S}#;ocR$!*-)7l!1j-WCkH6 z-z)Ug-8H{rgv&BZNAGdtLt0)UI^6{Nd87SQ&Y{8^W5G7$!zRm<%aAdKJ#j*(_z{bJ z7qp8?``$BQfO^CzFzEhXtx9XcjEsQTTgu0lKsR~{rQU{*MqO<+1Dwz~Zzwg#-Y|Eq zW1fcsh@`4!)@0@*VxAbKmh!45y%e7k`KZ#*Ijc@XEzbR%iJ`u36i`-0oG4QaL^#+YlGodOE)*N5XPqF zAu;x>*R7gcNE70rmGJv~Kw!a18o3AZSETJA%)`+x%@^4l}>kEc~LTIE)u%l8kd?6yZ|R%wYr~h@xdC zU;8dnbwUHh~edvJY)@tF>V(Hjs>E>;5>0#m4W(o5EN{yx!%`ej0ww4Ch z0B!Aea8LWtkzKThf*rCSv9R7%4)IKZx1YL?O|1WmI@_{y3-dm5BW-bGGnwAsQb%|( zuiDyrflGrc`qS}boGQHUbP2u46&Ri6HeV9uudhBV?87(EmLyz}(6vEzojoqk7Wr!m zHfG8;V@Wm;NjG6hHxWrTpiVZTPNvS7>ev>gDo!+O3O7s5tR9nEI-)*x!gdlOY+pnQ zhmV_A(5#M_Ivs5`eVncfRy`|~IV9UQC0o3x z5I!YSyeLyVrBJsL;~C)+ohpgkqro@Xd8c?i8CT0M)T_dVa;Pln9^ws|uT5xbs;sOn zTnsDZ!1NdYLl-g(IN=ze#(6JF=yae~!e+v}x;mH=_&D|gy{rFdjzyTn8-jgqDASzE zm)f;#)ISt8plx@2W2n;B?(nT0b=rN;-p}0XYZ_o*#dSoUcifbGh{a zN_*kX_972e+P7i>(kMqhJ;oX$%v{kv_gHdGi-QITkp*%c6Q0orJTvge@lPLh{&^#s zjntb|)>zeP%yM-hp1zexpasMEBM-w#{P2G(hWr>t3u5~DPK+tV2`AU|lcK7ip!iV! zFq(`R4Ox1O10R8In%7~Y7BO;Yi}gGlGpR&*xrgKDaK|kcez}A%ZHqE(i$fD@qJ$lM zxnqv>LR0A)Ny^in@)J{+eYiuzOkSPjfGqK^4s?wHm)qMINh)*0=T~F*mf=WW)td%j z1x=d-!OzZ;MawyVZXXTicw-N9i$P8mMW}jGdGg z5F*_gK1I6>65AQK;;Z9Z9Ud$)Pww;43wggAIyrTeDAF%XrGcy4$Vad)~ zH|kxNTA)`jE31vIt+8%%$#H(3R^c(HPjH!RsfNkM9IbaT{SrU#Nc>k5Lq!Gq58ajL zdVEdwwIwZ~&j!Jc@bjA)G`d&>t#$evz2E0~6X_D3YXA7AK>`vLSumG z0KIEllWJ?NIB3TteNd0w+FJa8sA_mIM>`c0clmfrG<0A#9rB4UU1MWOrRD1~WOe3S zcTK(fXe&VyZ;VaNm&&}K%*n$9_)Y^jh*EU=N*|d@_2#%DORFMTOHAi#I~gj9P)0L4 z6RwrgCM$+{L1|MJa}9@#_$E=rnFG;lOvZ_ z>dU18eaM_h10T#V9~wPh4X0vxh5th7Q2uC5@~vf@w4{O~H99px_nIpB>smrw`i45Buiwic0{MqY`)8IXEYK(k(|NHmfz3*4KMtve#CZ zAOn$~{vgY$0p>r_NYXbEezDO+nm!R;u5mdv{lFDMh8Dq5a8*FhtCxX zBUcg9r%q@8Ig0b5HaDj+t1%M_#(+m~BZ*I;m- z1&Li*a+8~jqq93Eznk0iamm_gK%|x#SB{a7SkIDAP=rQ8iAE$)Mm!>2Iz1G<6KS!p zS}p#zB73iebg)V25mLn|-?)f+p|oZR*gCCwc}O7F4&cE33!X$9*oztwxKgT;g-{DdU^wBAzelH^be=Ez-*FCi<$V8B*yi3Fv3thnkr zIyul=FNV!mIdm)MFp~=b+@eSfUxbgH?pU$#`qxmK7WuB z8+YnB4yY&{WRezHoEBT07G0PYd6I4YSuj_1&L+VE#p4L$-QO9aye7`C`p!QB+8WPa z@Klq1XA?yPxyEs6B+&+3FZ@j;R#=TMna=kW-X`>MB&NO=}M41nv z^IGl{h(2&|AYHn|#;(9SeYv zQZOgZRp8>wH4w=#u@Rd*)Cr1j5xASVLmwp-k-yKB{M*1&T}n4zy1>Dl5v*aoYj)&7 zJ!vdy?&;(4!!0*eyzMO3D$@nbf#4rO6QXg|o64Fbz$rL(8KD`g@I`=^cL-_|U0d|x zN2ZqExgUlYcxY{x*HjWHU1dFzn;96374((5?~hG1H#aORJ;&UEeiV{^*!y3%5!dtz zo=G0-_;I83f*VgwX#;k#t>w_T^%jXX3lQh?ko;(suB_}#Mv=L7xP&G%L<8&#fl*(K z7=PJHZ@HDNiK_LFz(#3+8H}|Ivy~Qj1`9y)@{>+hRyo8bEgs&rj%@T<*V&t72Od^A6X0y`Lq)JR=&^)usPi)M<-nhV@ zG-lVo4)2uK4j{<}LQKMTaIs?*#+__LdZ#bbLmhG^j9%LbDt8EnNMvBcu&c5V9)bMRcnox+u9o$yQ7{6yDC&b?0@TWc=!U_6Im?4CDgZ7 zLyQq8@BH}oAfI{HTwDL$%7f6-@}iv!oH`1?41(zr@uI=FBK}rMqQN_8Q^$3IA{eAA zYV~!6P1z@{+8S#M8aJq(XqBvVs(ZKnEbqdLm-u;lWF-?(QMc|hNSD?(dM1-~ZFHw& zXU%@gYoMX^=$ir9Z@hz@BP`f^K5Gn+xu_fk*hAJ1TbqlM&HHBzwT7^mb|IuiyoPc| zBPTUV!yIDs7bq>F)PNCRO-)&7c3G>(SgD;_6EDe4$U1GSZk!H5yfPq{evDXO~du6f}= zpHRUw)y8@^0AS?-#)Tfnf6fu`N|7v>wUEGa5nl2OGGKN8MK;L=G8DoH8Z|kI-$>)ynHOd&JpD7 zg%!(y_TQ(0aWcJ@ml_&VR~Bxj3Cd$!ndW=39)*l-#Cn3?DO~>Pna#>sXhP6iTNs|O z_Go5{Tp@gqR_Ob2Mj|rTr>By7XrJ~1;g{@fj?KJMd1paQ%pX6;sES_mJ zzD(5?Ihxpn6~|%1b}y+WRs1fjmq}ZEcfQ$m*%eYfr@nfF&6!fRdxDESpnojoDje!=rT}GOZhf#FN!#FR%NA8!Wf(@ z#88PssFS#?N=g7ky?xjiYw zd@|l$=bF4g@f@Cqo?_9T>JhB?BbE!XBz}I~Bg&QM5KJ_15}Guj9Z{j}8MleFpnizF zx$VH{MW>K>L-_e6bRc5mr2oKi^F|2jbtIQ>s|z1ZGWQRuLzcD z4}dl)0C`M={HML?P)Od|W%TK3W%|_fK3G~`&939*bqvI9X!}24DSSy3aXI9{Bo~7@pAy*Wp4>aIejy4F8$9s@(8 zB1aR4!f%f{cSPKs@Kk3trtx-lGu2^};4%yQ|9lnnW)WuVKw*RX#OXh{gosUTxF(lW zqUElA8s!o}zZiG(8%7kImt1~a^mzfDZ}=xn-yzgO z#$(FbTC7hT2m!>Ie%o5tbc3$jTHkG=pB$mxmDz6dZe@hH z(1MPU{H~dTUZggGcz+X9oWh&75UklM*YUj%w-U(b_gyceUwB4XPt>7-XD5*L4Mk_z zPAHa~R05eW_r&F_GMPAc-{vq2os_=mk&6Z}iQioed zN2rqnN0?KfuOuJ2a5QE&Z)0RRxxz+cZ7?j*P3@XzVear`b&vx6SwZ+)~%PTpgc%J96DygolYgwk(Ns&<8IxJztAR|5Ku5pydm}K#|Ag_4iW_M&d zF{-vuX_H?}qf%!Wxc38M^Q)~R@cbIduFDfWFMMY*cEb7bFVE1Voa5hJys1-Sgl?;b z>Y}c6u(j|~ePeI~vv%s=rzGjzOle~zOu$4y(?bN~W>LgKd!G%j$w;TYGAzM03BrTPtH+f>f#vV3Tg_;JGSE++}CVr}t>=m?kgI4`8qTNRh%iI+++02nTF z(Y@Bv_8lqGa&&Xs8@MBzz&-|gK?j?xCz(M3(ef&6ly_^Z)h($_HfN?MVQis=pq9~6r1))F~7mMI$i&)C&VQU zV%%|qEcxm3^V^*7g@M@+`j ztNUBOO(7ZVWe$!?OP9TzLoN2a3gspf<&D7lGjq5zc=F(J(ufaiv|axudL^IxSzh-Ht7P`EJqKQwXWZJYO9fC&ESmATMNc1$%JY6r7D5kODf- zIr!}_4uCd)-4@P${DTW)u!6Yz>O|_ye=_I`Oh7&G0{)e0d9F;Vu3n|6hP)jF&kq1% z)bv};@7ML6`=5UF#*F)bP_8xIzv5PIvWU)XX^*0^@+H`G`0z^-&_^FI7N-DLIE1#w zR~hr7)s$Sgsr#8--3uJa1s44bcR$w}BX3(Ep|-F7O_crP z3dRt3xv4yq9%l;mCSR?wW_4d{44iBIz z<+(P0wW)7$&Ebdvs33*+nu2W0JdS(|;%m;B%F9=AwprO^zqwC(pXzhfRu}?!+sAk1 zf+)pZem+o&e`8Y4E8y+cwcqF_=da>5`$9BF3+(8-9Dz|_5Hl}6K=f>iHrZ~Tukg>{ zl~%FTsKZM_Pkz!cFx(Bs-9T46>(Xc=NSkh8&ns2Nv#l6A`zO}l)y8OX1rusmj#P5w z3V$mjUO}kubRvv8e=kZQsxs!XTcxM!vn3!9K%xhX7OWxBYi!2u8a2WdOXO-GVNDumM>+R=$S2i*82RN^AL)`MK5HKGd>fFp zw|VRJ-lA$FLi~_^>5yt}mu_{JX0<#u<@&=G0c9=rq=6aVNF0SwzXFBW7kc&G`;*qY zWXv;zzE9c>U~MNrFW5n*^0?eYe!1^hBNOD6lI$K}U-cEeXt5Q=Xlq#B*Hs?1N*`7U zx{UXv4?7^D%rSOi86E$Ub@%m{nlqI)!e9y9JR-w!+Ox4qkL9vs@34c~>Jqnd(!Dd= zVc#~}dPw2kQXW4=Kq!rUq!KH~r9hoRhdqWBXZH0=-IoKUaT%rl18&0X;1ODEtLy0* zg1m;Zz}OrP@-@R{Zwa2p+tf8=s!Zmqf^dwhvxn>WuX~X8%3%GwO$=ib?>AwaiytMB zuPI3Om^b`lcg%|{(L8T&A1V)Yo67ZPMoI~yOhm>YiL+?AIfl1#AzQQD(dZNTI@RQP z?3=$T+5#7@KTMo`&RBuxX+pHHxx_{Dte#uK6PHqqm?-=gKWdVd9w9KB$XPUGEEheV zD4(-&HfmM(r{Pz8PV&Uxzx=an8(%h#2}H&=*TJ3Nw>xDpU=z8gbR<)?j;_MFw@cap z0v9Y7sgeUp06!&%7;d-ubGM)opbQBLzq?>zkAunvS7Di!pX`p?e*}tSqn+<>@q&jK z(zE5++9}Yy56|s?6<0-6c1kaM_qw=*r-U}^e&xzB_3?;}i1(D9n&fh#?;TD@zO*pQ z2RmyAbn;gGt+F&VkbGCh?_y9f>%%vYFgiscI=<+COAVYP))V2Dn;cTjHmAG6TlAhP zDzkkhpDq2|-I29o6vVa1nRkt_bM3{&wfcIa&s(=WoER6R`_OemdGd6C@m$7ibcjt>;}6qPgb01G)Z$a0dJp-*&zmE5wVfKU&!DfR)z+W!laGY)rQ)b zW&CbN6?ND~HUB|(!Z9x|#Fr&S(s!;i7oenFF0-{dJ=Vy6=--u8I$^V^x2YFrNSlNk zUDLy^PAlk3$ycfWob+lVwpDOk@C7g(9=rZ)I$#bx{z+xBkj3mqz z8}Xq<{A6yQHX(e!R9_J1n%U;i0+?AYo$%h5AK+?{x=^I3%ukri`2wd>?sT$ zCdxFr8j9K4Um}hK{GaBBJh!?5wTH^@0Jq6$jVt1U6iA~`OyatE++XC#r1g6Me(oy* zG#MAE-^!kP9@_|0;(kF-ZSNQf@J=z9Gu^Li&MKH8wRLfW1pW;ZJaA_8M(y?9KSdRC z_cx==fmUSl%-U|(b+Cnbn=VVZ)M7VbV=6#aiH>dfoH=G;Fuz>A_<3rU3jo<%5!`&l z1ufIsb&mH+Ak!)3VvpTU_*3t59#d7C)zh6YU3i-=&j9q5<38(h^GL+dVDB)G%aX)) z=q|{}+0q0u{*S+6yRnV$bxPKDgR_F~r9$sC%pkk*TnHPRr5v1GQ&axcaWWSx3S2of zMAy(pVScCCvlES$#tOUb-Z6CWtbnISP%))YFD@n-J@FI{a!bq8IqT}>Gb>LMDQF^v z3&>e!A&LBT^=QoCvFYtCQ11>z<@;lG;ej?4HtRKSVO*_(jbz`Gxx8~lCxXS7hStp$ zXb^0cYl4Kun`6k^kfL91aQd-)f|=3^H&~gnvvbD>*_2D8D;Mh$l1pDt zs>uLkhW?4WhHYZra8iP>?XE9#;_MD$Z|nz7^z}}tQn(h46jp=*OJuxTJp?P)A9B(b zkPFwBTkiS~WVNe=1KeTtu4(OyIO#;0PP zg;x@;-b@e*G@B!rP4upuuMW%jJ<)3kla|`9*B+F<2Qq)nHhG|K25*;8edLfGAA|VX z0;Z6u)}N$fZIS){rDe-QFJ5j1;?~{a%E0^N?)Lkllxy-b3eC$!#4J?OlV5H}n%rQw zQyBTBrsp0TYUg*mE76Mj_@1mi`q3r0i}1k`Kk`SzeMvpo9Ugf%Osj!Fjg!vO^S0u}lfUaW*KSW+-z(u=XIH9>zgIw;zu`N|`+3qB zDHqx30Vq@)d6g>U_RHQS``eXJtlZYT3AW95hcp3pX5_iDlf~6KpM9_G%SrI?#kZ(g-AiffhcaOXUKntVEteI ziM87|b5^GYNg>L&cK+#``s^XMe-Ull1L*(%Xc@o6kLNM+733ow-w-U3n?uLWdv#1M zQEc;-80NeFi`CDIk%Ly5X5ag=LN!3Y|U8~-xYeU`P z{Aoj)JFaeT;6kuo4tUqO-`e0yjCU>6p!amOelb^m{73ne)-jb+WGzK=^W5ZKYkFY% zUX4{m?JWx{(SYBUZ$XZZ-Lk6-oKsD{|_>z9=Nh`Q~Qto^7?zZUmNuu2faUI zXh9R7z93W4f?6qV#s1K-!M4IS^+okOu4w)5#Qne45UKzy5nX z+{iiDcz)&-@ngunTYb0WBMEqBOSSc6p;aDw*;o>YVu&ILS#X`qAp-QE83sDgy-6YD zU0?x_zW?@_;P!B@e|_`#JIlw%r`+cx@%ssX2H>cpZrmxXK3!&qEs^T*nm~HP{mm0hHPwSV2`!|N4ARWEGqq9vYz= zFH_;s$+1YX1i&GE?V|ZE_MgwcDvIq)eXn23^z*EPx@|(co%S8wH_vy(>rY!JcT@gQ z3S-xTo`fOlOxK})qx}6Nwr#)K-)l|ZFisex`If? z)=qBwz>gKuIdrqSh}SO1O|pt9gp_QZkKam?TV>U1?R&pGqQR32Emc<(FYg1FTbNet z^`sUfr8{BC#nU_$%lmU802c@-hTI0fwwdw!qR(rFTeJfHHb}hZ(JMq#j9i%PUv%pTqGm!peH<%#StFIaaf% zbXMU9K{taWCkXP14ocX!Iga8u`ClJR7i^Cz8yS(1)RP-B+lGr!qe;r_tB?VeFsA&{u)#F5x9RdL!LmJoj_~(J>mC8NB>CzEy!Qn^9ev` zX|>-{n@c^MLh3vuWmf3NIYkR_TV|9)7(_w-bgvgQ5=@YuDLfdek#5syLDqT;r`ezU z3s+GecYqr^Z+<6wN`Tj`G7SwJz{tFwAO`1ozJem)%FT46fiK?(Ktc6N5y_^#(Yi#>pG0(rT^l>Br#I!*V?^CzQdc7|cIBA6ZjPS>?XUEOp7+lZk5iF3U zHiJS_WLYipmCk92e8DPHah4@)^8)dn4s;w(JM!KKuld5%_8i`?giHGX=>ua(nqJ71 z-U6D<;pS-x@l}ga1DKPexwOB47=YUHb%Wo}oj8>m&`>NUDB~v8CIVEKs-F{-AjSy5 zAoBzTTv)*8&9QF()|n~ZKL;DurZKqTgX|ki-FabxYU%!6Zc#P+yWcdDz~iA@1YA>jIETl5{L z70sr?Omj*>HCtui?h}awGDf>Yit5Qq{GQaMVk+w^GYW4sX4K>h#!`}%{f|RJQ*$Uy z08X@Tb2e@Omw3Krik*ABsI~hsY}}11&+`p*Zx^5Pz73cp0rDC<#i2^{m3^jg*-L@sXyK)o|NxzaBi-rk+{?uU#Q_vg#d*#ZN^)X;Nz`;HSLT@JsQ8xQGFOM{U z)-HCFZm-P51b}t-COCcy|8CX1GiJ>Apf2}?!>o=L&(cpxitivF!Xy zh^e+h1|Q5HjTO}Okob^B5_Q!Ev<^gaZvdCRf)BUd5^wiAzq^XZQ(^Y29e@AM*F9;c z>ioCI;Q44CejBRL856U3qqdUO+Lv~q5)O!{&g}FEqL;tsn0X&f#r~G@tF6!iBKr$+ zPuEM|j?Ye%g2PE$)lR{Sp*k>#EP%BbHN$3p7gJ)r;HIjbGXH;AFV{D5`NiB^92#E8 zRJSwwk6HFUmniF(ofD6fFMeIvOBglBZP!zM+6}C?U?u@m4diSQrvTR=G~scnwbEtIx#?Tvc!>o261l&ySVJvSxx3- z?YqBRgdd&SmN!}=jiu!)&-y&qZ2*>Jj{XaK6X{KQCHCNwB{7gb2`G2=d;U*rLlKij zw|`|`;sGUZ@y7|Nj&lgsw!0_VMy0-rFQPq}$VIFEH^J(pPF%dzy>CKsyv_?vRXka;zijlRDZfw3{M* zAFfqbqFW_rdHkSNQKk5#xb z@4E3F3_n=%9J3O;6n6i!4Eb(bhj#p`x?{wlRpI2ayoBBD0-@iA* zf>&;D?N@`u4@(;@$HIV4QK&**f`%NazHH*0g#`+H2w;Ct)%llXsQv%T9djN#JUq;7 zoZ5`xcCpIve_oMUdKkAPArbX?Ol*S2w(%P`rj^-d^x#MpJ|wn^OE)c37VZ=h9G%1|JqOF4m-_iY?pE`fxIuV5cKW|tQkgnxYT zdEZc;jHI}sF0f6!Gk9ga4yAZZ&2|Hg!b1wWes@*bDDAvo9sjW@`2sys; z@d+6^B=KX6-Ucv&Edh;ZcMHYuYGO?UHmq1*YXFNCTfgh6SapEG5kQb{Sl)f3OJ0l1 z-8|UX80!(09Ij2z+-M2BS$BqivR*E=&G{S(P#?Y9Jy6~N?e-@YH9bg)8H!KU4~X%9 zZ^cX72j2Q9BVV>GI{N^-Ofe0?!}RfI$9#g)?VBqjNZ8qRd80OU`J=L)^;l(^JK(1g zr5_vshHSyj83Xau^b%mFUTlmCi&x`!)qEaF*eOMMo*%?|ER@w`t-FD6KR!NqLmo~o zdBD|vviwb*2SRS^wMbO}4&$O%27F-|bB-h5nSQ`<0K84~brGa)=ne<(nrb|U-qRH9 z;Q$@c$ulW;@6^uQoI2al_Y~Za?@s4Z7&!4nj@TIOG*Z0c>~-cl3p?)tU!P#Q;W>>Y z!W^LyRE3<~Ls=S&j67#48higKdOOc4SDp~jdA>_9Rmg`#=50qv84v~O0S1t3DR;cM z@P*GE>al;hXLV^@u+sogH+@H0#7sHCqLlOVkRzA^*zx7x*qf?OOBj9 zJ6^A*0G?;R+s)6NS7+vo$)i4hD=S_-T|3p_(*%PDFp^=);9I)r#{#n{K?pvS$)OSPRkr9nyFb#|@O0n~2-SE{RH@t2La0^_0 z{kx^wy4(rjhb0eRb~bn45MdrLbeNmrHr(GkQiFQT+is=X|1p&G(lbS&^z|Cjk5>=m zSe3{iWLj{c%4!dn(wkX(!Ch^oTuKVLr+--Fot{7$>U5`Jf}<$dS+XF!bKVy4Cj$OH zW?$=N{%@PzFxrILVBC&P`Bm%qvI3kWTAzuz6rG;80J$%NT z>AwSRQ6rO_>AE_=9Odva3)`B-<|+|^qfh)|ZcpQDt)bESI46eF(<7^;J`yB_@^uD8#pYny>QZS51p%95X@~h|m7x2?ec{xd zHsk~G6el;fu^06q;5t8wAi^zx$)Qape#_dZAKa>+0sP2Qqh`Re4oNKv-Br2WWX?9= zy;vtb|GwNm5ej%&MFOG!uD?B`9*ZjrRP3U6Loq^r=+M?@m$} z2za?qL@sB3p5-y4-v$l}C&1yiP_msqm|W~65M*GtvaTBo$?yruY!Aus1W$|9b zz*!)Tq)P@OKD}Kp7MOJ~OCVr+HGT8Hu$j)a9+*nq$c(FV6MIT3p*3Lgkd9*FyIO;6 zr+TB7gZG($uG=XFaa&(xpXC4$C>b_0fkZ=oEzXSfB4}ymm71y)Mwg}lZq$Kx2`YW9 zk1cZXa!hf*lGyL=2%^$I4TGB@GR=^tKZ?9f?<|jyXXcKpyyKpn@MM|dM7rntUv~aSQwpzRfsMxzy}=?QgeUoR=M}(AijCpno7>+` zD~lxX0ZE*)AF z6G#xmsFzy1T0;(qHg)VcELRJg06`~;D)<}30m|}d9+K5&(Q8v)C2tzJDf+uh$?#i< zvCP*Z*k8A>=7Wxv=Ci?hjqx#a6PWaCde1aZ&$=Yd5>Ps&yHQG%7zF8|TUt5>P#Wp(29c6( z5D-wmh41;}oX=}t!;IIkS$pjjd#&fbe-C~jt&C>B$oUw_xu|Q1=q>r^n_$_`qd%`5 z^(fEF%gDi$g!w!MNBqqx{<*kckPef)SxW`u z6|>=-ghUC%zobGRz0O?!^C;5wa0Um3^Ax_5GeHMGr+t|!0G9pzaa*%c@wdm+cSZc- zlIzG--^YWZR@!wdmVKYG2x*bj1S+6LXOkpwlI35CLnv;RYJsb|lLQYCs4R84zkM4# zmL})e1Ymb}d0lL+iZoe8yXU`a=R&(FaSME}K+(Z}E*Y$&CGM1QCELe*yL#`rjU3-y z6j!dyT{##2V&fzJ`FnLRQSp5E%r(=E1P!Z5Zyki@GiKhT6c~$0GsVl-Ce2ng$I_J_ zta8q4k=&+E)uT2LLXYx;82s97Qy@eT9$93|e_^=bD=psOsM8z#WKXVVoy`QCj2TQx z#F=Spv!a0_=-1JOAsHj~9>#niPW`fb-3U*MpL?Ep8_(%xgzQ+lGu*=8L3s6EP*j9a z!pbiCvr$XHO=Y~YC_eJ3?*r%#XWbx@J5j?Y0~u&=2_2Q=&+#$+$^-XOy=OqI3=FK+ zHm5YwPS_t&j$W{@ARyW3ZXOOAfP%%1T5CtE2E_933OMfM6gM@K)^K{1t!LEU$NGb> zLu9}m^d(mqh$e0w3cRCvQ$9c3lCeq`U@S^n2=O6~1if5(_o;|tHY%x@b?qexxx&jF zt=c8%(j6pouytV8DJJGjeao@25HX&w{yD1you~F`k}a_y;64l5CirnQg{c3bw+0^0 zY$dRp@qO1dz{UrPMv$nHJ_+Lt>pqzjq-6m-WE<0NF20Qeck@Om5ZK*CC5!gIDO5Zvy}~fpj+uda!g+UqUtU$!b!~!tOBr(n*Kd3-5^3swt@M7H^qRd7 z4h<4i|MhO#_Lb;kmLTe)>fi7~qot~V7K5bF0s=2Xr8B$)C<64c&AmHE{;wUS@V{QX zNV}0K_}Zet53g4Tx)=kn(2OB9+3Qpqol%)*@;yDTt2$U&*`#w$(jXt4w|DP!t3Kls z5o?K7%r55aDWkj8Z7GTX4a(Z?Y&yJ^-8NYV{w#JlDcqTJtiJ|xl}aQ7qqarQ41wCm z-N)VBEh&!>H;VZF>vA{*I@aiPCA|3dx3FHIl8wpXQj!k@rd=$?^P>4hi10W>wM zr-vNUW^SM2*Ia?1Y4Z2r?p!76$#0;ovFp+gd@2_){OICqnEbEN46_n@f}FtA{3q;;vY@@frhIH$mRLHXz41bxt8~=_c@;M3xxr42D7yFQd zJ+T3|0yz?_G9ZNfmU`=pgS0q@_=zzW_9B^;;M=GvYt+Na=t^t zn5@`4)%LQ>msfjfS-RlYtkR&~+7xRsFZNM(&M)UPM=5-9o z%30s)cWe@=>&$-o*FyMzkjkAJ3+H1le)R`9W+wzClzalE`^$!)+%6t>;dQkqZwMKa zBJyb<$!4Cu8OukXxD;Ytc~eFEzI$y`@&v@#&48Oh53{oquGUCcC8}Ciq?PdP~1A zV!6;vdg1L7bT|Vd$!T}Wj|UWGwu?;`PX_<|sB!%~7vLn>V&lX9IMi?ajDfME5?n?d z!5^U@5(s^i^WQ&Y*VnB!rpXY;hIsv{(xtNe#gDu~C{omK+N5S8 z;Zu`35RvlTR6A;5AP?NSz5*Wk>Y_9Vel=E3?Ly2oSek>^~xcYW^7%Es34Eb90$i%-O5mm^t%Ye9wNE-m8G*r{_ty&_@QnfoIMvj^oCqC5??di`uZ;H<1k|6 zK(Dqg@}CqLvfjHYE#l)EWT5_awZdhmUJPhVnWxWRKS}#(Tb|mga#ING)%hbmA zDA?<44PU;?iUf;RMDV+GQZ9qaW{>~9NS>fhJwsmKv$ zOoxJplki_J5;jyL4i|dWjRg7RM2gEl7|xQe1jnZve4qZBun1o`yNvur%b}w23+rk~ zwaUsloJuvy1x||X&iyC&kLsfE$l#EsAH%!H=jDAb?+|_!h6#9bN_L2{)sR@fzYO}=b_0O1qFwCdxiKJEBYznKdYgV2Y4w7ooSrcjYA+i|pz)&`pS)GdeGv}guEr?S;u zwTJdCkJ?0r4>~)Wr!4D!3;djSGk5sXeRNW>01 z7#uzcCJ9KEN#WyDA5tFX6XY8Pzb73-t*HC=?L5bg?V-fR$<#rf4Cu&pM;A;6-WxL+ z)SUL&|h}GAk#Mfm`28-7|7|)+XZ%}b@SyeuP-gc~Qis8)GoL*MrW13np&o;@(K^Apm0y$1 zz<2b9lkrvAw&}+w0}}d4Luwyka_+L4KYoSs0B;e~uKTh6JXqo97NM)-ERuOsdk;^( z^7;Nglw7C+W}{a}wHZc^``h`WHT-U#{g&VQcbo{0_BnyA=b8D*ogo>Tw9%%vm^$iP z!3Ca6t-WDW99|H(Fs*MjZc{a$Z#5ox6{*H)J6|n$%~H?Eqhl}Y;|814dIDhH`X9Gc*o{}M zyRJkSPlYV^7#B>Dqskf9Z2bnp{RX_x3(*76F&Pxi?Y_=BBt(m_6qB11lbfE%PgqI} zRDpZ&bv5prC#j(|FSy)HygxjWfA3}M9u#}xhEeS;vM~0oAGnOZWHp)fMx>O(l!%i66rI?{ik2HuU2TF{KXjU!F!*^d98T9%O-|cO##9DUWlLd8sJMJ{gFyPz3+uFEmP`epJk& zqYSI9sdaJFzS~gmvw0Uj(fOX6ZV0bT9A|fi>cCu>L_*h6aKeyYg;WuV&ZEaOeUPNiB!|4UK2PaNB z5Pf9p!P0LWgT3TR=7h}0%t-qmPT%IWz|@W_J1VO;$!1!b{fX9safD5(jNog3ITZp$ zDU2Np;BBaAPAYc@B^f*nw_!3srPk!LPKCZjTKs5N-JHW`&TvKBCyiCq_>6*dQI$@% zzziC@o1Ow}>o~1eXg6sed5gGt+0Wu?7IulSo9IzdzKgG8f+)DW^b`}|jy(!!jxY&q z|C+z91^>Kh@y3jdShoyVvG6u}6BHql0~K#AQ$VwXq$Srco$r|2+0o7G&Ce`O4N0)r zmt6bN-%L~^K_;76cWwR-@IMR{#Gs4~^$#YYO9kWj#6VX*r4~+LQo(U&sj}3KX zLp}^R-?(^_ZB*qpM%ieqnMll^D~0h$HAw*l@p{Lx5b=OA=sYQbF*d~VmXvK0j1MGWp@A%d5Cbaq1e}L%wo*H}mUJm-6>cF5YoA7Y&uR5eBn?$Q)fjD(`OO`)y zk+Wk-dIw7CEijnLsBKtFJ&sp(fm5#98*p2hst?KJK*KiPJ|rT3R4i4Gu7EA{Tz0{< zaKcN9r%}bpddn<_eoJBHIeYU#Bq!PzULK(&+1rbeo#v(vMp{>3#){--I5C!_Q{6iZ1JD8pVKbebAB`xad_oZjAH@DCM@> zLx~Zqfl~o~XRE)8mw{kTv{2z6;jl<{tJn0pn|~O4Ee& zh^AfZU5hs#iDqB?mU)4Kj&8b+Z@RjfX`i>9{6`|-Iy?&|b5R`_KI$1+k_`*or6i;` z$~5v7n-ek86E&J^G6HV`${V+0m zvHRbeF>dU!bogWXG_#yP|LP;y-5$e-_GcM0GU>Cs=~qtl4?x&Xb3;$%f}*t@1tnMt zlM3NB%o#2vn8MTZ^t~j1`}UZ%+4-2&fRbIGw*HIQMCX(m;IwcmWn&8h=4ntmSDPx; z{QOfcZxzC1Qb*gWrsO`vdQoo4o#lBx=-<}a@f2yIMDMdvGb+(=YJIW2FHGE z4;^+CXp<`sfZ>EnW$1_v8^HSwxWLhE0GEcQS_r3G!eYUZm1~&R)@D{Sy8m;G%6=&! zV-Y!2_lV@<qBo$j?q;4|ECO_?LerRD_Yb`vUJJz{ z_%!e3Y`Le@*`HBl&Rflex;kbqGXs^H z)1UYH6T{s>$Ge=40(%ViOXKfpm6oZhu;UVU!DjB$uS&S50S?OT_~`N5&ywiczU|_l zyT18C7iFMNuv8XTET**K8t}KO_AQQi5XoDYy4wEV`FjS8?MkESXM<6IcQaIIjzi>6 z5USY>DN;i7#2DW5ShM>{+C1`b%WgAW}z6oXS;UrE3%FRuTk>eMAQ`vB}pm!VwCdz+E1@5+-oiPG(fJSy|D zVm~_AEXse;dZBs9jBv$-G0M~*pFeE9Psqs7xZsl5u+)+kuCWGw{dXnLnS8epBokV& z&4_w8*&8fDM;G8=k6&HMH4^+?@9#+plB8b1KzM_Q3PE|>Jbo;oAPwBU!oGl3N;WKg zwnWy1esVUZ5^L{2beiltQifBf20|2!Z)@0Pr4C*Upa^0SdYc?WuOXJ8ql3vTRrkOI zQiTgZKh-_JfuG2+TC3;MtF@p-=UD7J`l-_ny^8u#Pjc9QkKIy;G;>A47u9}*Ant}K zuw5!Y_}qCzHcF)vo`vk1NLSD&cIsJ#B~og;>8)SAYr$@lz!GE$`eKO6)mmbg3V8|? zL%4n~yuxrV@<~?Q$~QpVxCL&J1&CFv;MxN#35dHNQ7aB}<3BH8Z>4?9ZU^?e2&=2+ zro)|R+_AL7v`<5y%00U%ha1(rhT;m*7?%kFG#%3?Jm0AgiQ+JXewrKwwUfJnvDcrM^y*}2RM_;oW3 z`!9XISS{Dx6sm*2n`}HySynJU{Lp=EKx$VXp1kGpe)A-F>->hFWr=(w^Pb(>9S6?| zUzVLOA@l|jHhT)O(m>zI-=Ibe=itAoFO%iH;e2sUbSgTLfuRrZrZ~b#%xic=ZY)M6 zu5i)rE%PA0Eg`(;mz_fC;^MT?|DnD_8NC;X+>O<+;8ql+0-peCW+e~uFqx%&>ywdH z_ML(an*J`e&R-tXd#d7Z0M$$69T!n8zq`H+IjxKJXvL3=6zg*Il~{V)F}&Br%(rtM$hryOhN` z&Ea1?;X|HWLprc79W8E~AJ>X@-+1uHb_kBnrZBw$M$_?G4}LEP4|vqT5~1{h$UfgZ zKOO(E+hJO?*wV>4Pigvz3fv5s8v(ctuMVDS!u5(CR48RZrdB}| zpv(cp901K(zE6ZTyq9}Vm1*$3fuGYNhy<$W#e^h}@l8<>>vR|E1?6(*>U|;B>(1q+ ze#;e#i48M|W8OHt-7vmm~3aAT}+EWV}#%_vR>3 zFhiK&9Y^o!mxe93aucK-F8hKgPRZo=S$TLeRhtmEaj^DSpYjGud2L16k_^0tTakf} zBH}&?vr?B7&uJZCgb~DdU#6x;e^Z$$nHjqAB)` z050;h-h10XfF!e`7dlke~a-&VTGGQ7D+A=KdzC6;3tOm!w0q*hp_5%}- zmCwRQy7ZnFPsL^hqHj*?v;q26v-V={rE-6Xq+&{& zj-&loGn&3Te8yw35sC@`QVIyD<9oaL-IKEK(b%bV@WkHC95q0^bR%4}Y1DY6=mok9 zD345@s-{f&r@}=Kl9pk$P>byXh~ zjV-{Z#>V*(k`3*7ElQjCCq$aopW^jK`{MZHHFWcG<5_Lla5b|&ZiThpwm|yodQBn? zsZ0g*5BuVYowCT>Nh-F|myr*1Oe}KE`KHe#n$@@-C(v0zpSC%_ii_FBA4k#*aUu!l z+fM6z*dMMK38&L*5`}5e-N^moP?myE2h=Q+mUkbw&#G$_iADV~cr@~3H@ANlQBWMK zDu2sy*3hE3oD0lsfaIxu+x*2hx*--^R|{l`p21I9V?%w8V#2qXRJNi| z+PrwCjog;w7il)r182?Kn9>hK%wwDDr)-6_2Lw5I;jtx7wvH%(=%k`TQ$*RfKb&{b zwf|y42bx1oSLc;$ZXEw=or|2C*?;g>L+HNWto-LETaSmKBLH+2P-r2RW9W5y)Y?(9`&9TEV)3Z!xLXd){{qaf9dTTy%!?dJsDS~vP|lG#+RH~ z-@{s&Qc^86H?wK{tRW|Y*y+g5?~e(QLo>cj2k4DNd0Bf{57_$n$^j zS-`qY?t6B$)-R0pepV9Q6bjQPQ#q3ZoL>IfPA z;>Sn@C4={EcX0Ot(npoydXUnRlhUloMX6%x*Me=eBrvmYT{nsyivR@gsKLDhLV4_z zk&r}EWh(c(_QK-r$}fWfS<@(dZ@CQ;LyQgtAYyP-a4PpuGMN+Jt3~3^(pIE|%ff#u zR2rB!lUpn9_2C;lv($rd;+VHAKYjs3 zjENX0zkVk%(}~S1Dx-W=#OI;O))lxm6}Y+^`aYv}%qlO-1m$xd_uIQ9%(g+$ow{AF zWDo_2Uec;Baa5;t;1h)r%G|HC&<9sX`oD2XFtJ=QS|;CrGw1lC$A-_yVvW0!hjXNn z_C=#miNG|Ex>6(DnpIA2(BM=|w~C|+391eNhwGLw03{iJUaBYG?uyQjvoBkw%9BdHMA_Qm)!Q=}E8U!C*=yXPVhMMEvUwkR97>alg}H=TAV zBML0NxaHh>A9#(!N!dF?$eGd<(xJvf#w$r$*H!m3cR~9&>@^apx|O-xZg;d4BMQLe z3zPx?R*tT&rn=&I(wD6)HyEvs&W-1{d7=Wy*cxNG6M&2@D}{&wE3f!9+2uwz!NEwR zk91QR1Fby~;7iBH7~q%h8lo7fRagK~A8@flsG`WY8Hz)i6#s{cJqOdGH%k~IeNdo$ zkDcM6k)UFuXSnB)phZ?#o^I7Dx~#)VKjM4s?G}e8Mmrzu#7I5)$op`?Q18MlSwe11 zk}ShoclcUSrKK&fktA_8w11_`!excG!5MJOIaSjv0mmG>pfj``P}r-?1m<0m_GSi& z?O}9qG(~D}Ewpn>!&)lm69sER79QC=l^@h&a_4mJF!6h-8&Jt;!~SlC0~! zik-;kt+fg7-q5S|=e@Em6%V&b2AjJUV|^^4E1|ef%(@~-w$m`(wt(q+tV{>Ms?VFb ztV}M>3|JogXv;?PL|Ox(**Jd3=E?ITHNLgJSzO8fPXLb(Q1yNap@x z^?tBN-C*})aRG)Ou3Mo%`R1u~Z@4b68ERk?y~C^=?{&s~SDt`zWaM=hDL%md%Sn@2 zfLp3-{Ygr8assJ$kL|;Mz<((OyZV?SiAmqS1r)*O8p6*tVXw}g zQf7#6{JyCLis5Ls^dI)y4c03GTh8lpAYXxq>s@eFj&+1l3&{2{12okK;IMj};(+sM zFlNwICWIFx=cwkD%IDWBlviMHC+BiD8bHxU)g)SO=pX4_+4_+;ya3vou1fuY8BT$b zwZ@mrLX3UpaRg(1BwJ$@MsfGL#>Ay5W|6O8y}|nX9h|S1P)|?i#{BgiyIuhYV&T-VB+)lK%s z{E>-$fT`H3yQGaI3010Yz`mes4Q~eI{PHz7A|pBk?`q|%<;qw7I}U`ygp42wNiR!| zd0Zv#U3NoSOW4&N+6}WFQc43?c2y;xJV(P%=?Pl)>n4W56nD6yNN773$*5YZJw5+&Xi7`rG;#_sVu^wd+CFaq8 zt|5D0H+nc#&Zx~9%pK%;5%8WH<9?$IddD9`iPbujoUjjYx!5o8rinrQfV?VwtaC2VR`58^t%Itm0xg^>ws>u)-&y=AyC9Q*0~mg zB@`j-@wK1P|tE| zw|VmiL(SjGV4Eb-b6;~+0c=)b8hcadpEb>?;#KI4m}=dIGM1WOH4 zA!bg;CtNh!h1lCa8$bFD4+@sgY#F!%E^m(pomL11WHwFXb+SHFlEL~A0WoSj+-zHfdW$L!Dped&@E!{4Frmx z1u=G@HJ{N5vJaJmkL-xCQQP^dBn8w2Q2dhtXVj-_;!`9|Y*kU$))!({6L0!4R$c{tA7g+p0(Hsl=}F~WrB}-VE9X-|N_y~&1x--L)1?~Y zs^T;LshT_EfT5ts;lcG-XfNhMm&IuXrPbCoh7MBf#EkqRm&CNHUdvDj1tr3QFD*n4 za!>T`=A2``y%pq-yMgWWvopi*xkY?=A zF1DRu0*y`I-|F4N%@oYTE2)rMMOKq5;Q#QJj7Q&w!A`56yuD62D17oSC)Q(6w+RD< zZjcSDb!iX?0D*1oEALkl-YUA}vgEQnHIw*|67H@sW&w~D^oiA|64ccJ*Gq5|M#r|^flF4`D?h zbM=3_C&%WK+*IZ-5Ei~qhxqpYj>WXOAN3 z01nh2uJ{_4mHIG5hb9js*McB$r!>eF=nfnhPk=!P4 zAN_yll(we}T)nGY4#;@$SOxg&K*-_l_Dg56V5f@o2 zamt1toshB>1KGM`LkQ8BUK(>)PhawjQ_{b4mv5`@A9@~<#`m-xl2U`>x$F6txeP}c zh=Q%65AMc*D_>4I!}V%@mLFg<;zuS;}yxos!}Srp<}xo=IsEw0F{J6vrchm7w zUOiY*qzQX_`l$_cgwZ%b6Aby0_=Y27s~|wc_wU!oZ;U$6<`&-G*adF+pQ)M?2}a*1 zYY%3`zazFKiV)z&@pkKZUemWe>!(gya-ERGruAy{QVJvAg|45<%3Z;6dZkSif}tQy znb6psmWFHV<|Gn<3IkfTVcv+)<>3F%dc;VHzR(&rN^C zG(7Hk)8}NO1~k^;r3RCcqDXqEo6h;io?M~ma;MG~_( ze$fr#D$$gPJ%6sq+ZwHgrIe6d&$K(1>AVwG)rRBFG zO(&FJM!Q_}`jdn%V(`1mO9^yk) z#)u5hg$@n6te>q@R!}pc-^U1-j;E6ttXTVlqh8(xfaFp|FR-E;G*xNvj0ccSCjz>T z@d+QebXJIneJ#0xl&l6++B)3vWKmdU(hoiOBR8b`mpRbt9eN5s7Ax(fSYakf!BC-{ zLAVA3Ibk0SI=|dG*(>3&;q@F!L{8Z#j zcYTjm`Fd_}H74xBnw`lxwU&xR5}^{$`%2qDKLSYHsTAXp&wbcHdUv$VGmvqFV|6{) zs&jQ)n_fIBttZ8{V*Er^GKbaA*7aljCO~GV9&J=apE=3eD0ZH}Y)X@-P&O;u8cd@$ z*tba&1=L^`=b|Njm%J%O3B4>WL5SISacNH+9kKbzyT0S9W#kr(8S+C5-or-h0Cp~) zGY%WPWi%ApHedi0VrD=8bo9|;!`cxCyPKJY*{G4TVf?Il;ETw;p75>o7h-8A_A744WZW_ZwxSS_vL ziWuC+rSAGdip7?n8kfO!D-a8-fG>_qcRe36z-kR9aISx^eC;DkW?p_G+ zM)7Rv<9I1+6FAxvx_DID;-ht!72|OCWWz=HFr{*Wl`;3vOhdoUaf<)>tQovAzY?MJ zAVqY8se?%agY8QbCg<^Z(jC9~JmG^_nFE*YcR*-|q8}el2u_6MV`d|@%oqnNDd1jS z_23iL?-tq0;Nm|!F5LT|(R1i216Tor_YWMRr!v3X#gmf|P{Ug(Fercx<4vQ?dJ2cL z@D>Mr{s;KWWU{j6r?atwbX^WSs|I^y5~(E7XWl~(DW&sjD2IUB6Xd8D4{ZHO!x;T& z?-4^bn8ak0pe}>(u%6yyZQ*y}JEuA|kHD#V;(Z%rReE&32_JaMp7rJ@&`F|buv)Y# zI&Y~c@256QelE~c6K@~@LIZaddc<^4TkpW2DU^ESWvuk%BC$hB1|fW?m_s z$%qH6w!C?FmBMj5i{Nt^x1VgwdB7MWY+t%e6t0MZQZ)o*dYsP#e#bEpq~QQiiBsbS zsb89c`9m$;b-nK*B4rXp) zV28wpS-Wj6_oVMsQ#eHvP}~YTRlO}aplzvfQF&T=#&e`W5?CrSr;r^sUcs5e>3 z6c)f`N{wfVDR&t49`nX&q%s>7z15uP%O;ChUMFM8aIm=myWZ-52OKsLz4=9N;J zP&`DS(YA&wF_pGxMpJ$TFm-k_7FyXi4q-Nn7#0};iJ}*MLnX|fF;F@2J%#JM)uLLl zxeSVWx!&h5CWz1)DjI>20PwqFUM_fGsH*xyy3|wwlE9CnbBlPuo@1dTR*OwVhno=8 zt5?rz9WTRh;*mV%2W1=Z3aFvzdjVD(i8~!` zz~wcHD=DlNv9?x-o@Zck(c@wlp9a$Cb*0Rd$-Z>SDjcbJ9U+Rakh-fba~^(rphYi4 z$rsDhug`ank_{Bf;cHqDzhg$zbrcOFCbFCmLy>Av=tss0M~Z)@i&A;9jK}}G9uow5 z(_|djT+;rw?q0czrcn&0PEO-xLL-#ZjnINPUn8FA=H!$VoXV*;PMpfAQWWFn56y57 z+V<(Q3vUO4p}UTa>@QP^KmdH3=r!T?Cv&v(EAZ3d(jk<5p**_+a3ZcGcX6*vnyw$Q z|D+J$5_`=-0;hyh0D*4?d)&AH6t&rquD>2flv zjQcbz_^`i78i>??rz9<+R^B(~2@z59X&}F0C%xLcN5?oPJz;a9Dw8`zoJ>XP`pfl*h3rm zk?JyYBF%@M-ajfztw9`w;efp<#!LwE!0$a}c7UDEr6G#HhffT>uxUAv|7EL{yCRkjnxk%<&!53F zCs66ao_tY+nyRPRx{b{*-!Y%a3^G`ChrtVo2-ycX%|B@$*Hobcm#}CK3ZjU?A9a@& z64XhFbJF-r(#GuWJz^cNZ#xR}Y|)Pkow}ZZ=SWz&nY1L^m(#m8KX`K{n**?Bn(tzqkBt^JHBnPQPd!Sk6ABREcuZa zaEfk0DQ#q&;g|%|E6PVilRm8PS>$~NdpIRLKbTfGq9O+90vUS zIG8Tt7p?~Y_Es!@73M)kz~YO;@UbUU9XN)}dp3hf0sxo7U3l%0Sa3A;TIL@1)|EC!imcd^N9fz=uf+oEdXui*EJYV+;tugOOL6Zo> zUZxfWuoIY?hBDVATu+oKurlYE{N|aiF)8A_sA_J5-I?p z@ItKbGW42>kwJGhTAPWS@%6NeZEbV8}GYP0OjqnvGDW^O8CsM>)m3EPu`1bvfxt zkz~-KQJER%OKfHbmk%*kZWJLW@5up2@w67Mqo4l3VfbU=flysjBDBHHxo=j2&{RrE zW;z00hY+et!IV0taVKdteu!!O)hTW3-ZRE&9W+RxL=SV~Q`SmUOIk~50(g){V;l^m za*w}%x~m|lDP-2@jK$f!eM$uEcLq(Lv0j#17=!W@wS)$TiDnm5%&`tV%*>6- zSZno+*s@$>@+HznNF^?HTFcP@_&B6M0%!f0|9g#6it%4uns6L$^-MwDL3Q%C)j57z z0w()V1F6GJ%{+U`*3RPAsXNQ*kw-eqmzbBqBZ40%#A-U3Q2b!ajx2aV2XsI>o5ds> zietd1NJ$p)Mj+`zb_3?R@q?MKaDm3CEz44goF~ zAH3E{pfW1bo1(%^k;T!O-lQa1=2pZ($nJD$s%sZf)ORUZI)EN~!J?SJ?~FxJ_Y_$t zy-$jTyt3jg*JtnFz61I11?TKZI$dThK0Cb;dF7JYx>S77O3^||W#-0isk44YoKNu` zu*y@qp;>(gQe^Ewr;J&E^K@Ja;5-u^f*bTKyBAMZ^%NV=x{o z$Q}iWek(FG$b0phZq8D8)P5uTI8Q_421|#UCLmWGK0dywH^BCjR`}v~O6$@k(KJ(v z3B$%e(Y0r4+jPRq1RlC0!=KvD#)nYWP1QrAh+Ew!Ucu1$B`*}K^aOVNCY*t43^F%7 z^7D$V`80kHqj{oBLJKCXR$lYtac`N2s+^eUtu8EKC&5O~=u%9mP}6dgN8W)>zt)Rr z6z^Q&zu)W(ESJ4>OEplTw4eQL*yPNZuA?=CF@CBEx7{$Csv++c*n#rsPd$L7OA?E# z%;M}@S-IBTyqz-=a#T_i1VExcdtCF0!qTwZ?>1wG#K^=mwkABur)qvvDj7r|l}E59 zj76kMR_6*Tc$^);X%SG3Hqgq;%YcY*IAY`I7=pR$hlR=6Qj5}PtK3{X>Iq+2tHCEaWf{TWHCNi>1j}b_UvZ~B5KHH4aK1S2-r%TQa?k#g|()1L=7m||= zd`d+J33D8?rl6?l<~Y3yR_34UPsu`&%Mz7Ii>}FcU6WPrrkG&Uj!Cvs9ggT}IO98} zOPya=<`iKy;Ki;RgOyHk{*)x2246WYs#MuW-@Eh$0hJM>DdPsheUmj1)OXGD<(7x$ zGa^E$Qquu;Zvg#!4m(LGzHNp^VoQ}mf zJjvVuF$^;^hQ~^tteN%&o9b;cu3QqoU}C#e4%xb!3TXfVTeW0r&_T!N)J|-al+dXp z;m=!G^woPMEUiu(m5yPf)89S3s>^3g>uVjf=rrD;THGrsCRO&2i+t!=rf zn9I{6&%n$E2Scgo<~`!FQ;(^_**{FjGET<$6k`Z+@QT>+z+RHSB*E+02UE~O4L~y~ z!U=}xx8xGi@przcQ=k1c!iY&m{%y-Z zjhi$^Wh+U}f}{lFitS{lx}Hvm{l3;y_rp!ouZ2hGIBHbo z^|sPRi;r@XEYkJm3n*Hj)0UlvkIT@(rX#8_MrejOb&KgSJ~r(P{YWOiq%nQ-?%uhk z9Sv}u#<*Gs#BeMX)gnX5hg{R*-7|rmxORL?>6q`m=y7Or&WpqF*0OD56X=M`9L8T? zOnv!A*&$jwkR{!SYhlfSte(+YmXCJNXVvi2A=zZL{G+mJ*6z@9mOq`Y(p9GwGjo8N zKuY>B5xUFwNK<=17#Sc$-O@CLU^-S4^|ad>ls4KESz=`fL9w4}BUi&;{<{iIKG$u` zH-II-zg`Nsy*on=s9>Fhqzfm3#_C~4wJOu0Z*7bQE6kLN))VG9IYT=|oRA!LSS6jcaf{{iL(t?XQj6@7K`EI!P9G+7HEucH7NcTg|W~N z!;5WDygAT~9nNLjZCGr^rtEnKoyfg7f*5j1YB{^NYNTUnpQ+* zwAdlJ^7(Z%FkD2?$VSl1JS?JEZNaY)<1pTMck0V;N*KS03liVB@sBl1czs>MLu2ZT zwB?pST=EdRM1!2HJlC)QX?(`gW{;e~HiRkMtVGE?o`-(S=W;L6g;7lpIg>4=g_>q1 z7U3+{epnnprYAPc)FK%N+3s|6{;7~Tsr%>I=uIMMDK;=+pXm_feHn0itME9Wjo*I< zheZu%!I{O#>-xX7i?Ll)!L6mG)wHx%&&L|??j>-fa+qXF+S}SqXkm$zN5$qjTZ%uI zkNq)^Ys7$g@Q0+IdRi)zE{(qafLz?CD6?UU^UrCoAq{KTooK=DC3X^G{lq{GOL zqFM}%;0qCbzdP4lOK;qCtJ$J$5|5c>fEa@}GQk=vcNJQUJV7SS zm^?Vm=a7GBTSZ5qM(#DMj5O)&#hA@Im8VtgY}4GeY<;N6EC#RRRUgg?TkF2%<|qO= zV5%D;;9grN9;4SgsuDt|>GJ4bHR7XKSdq9&gRb!zX{9Tk&h{WteG8SBUpwqu&nh=CSGd~LK?E_Zl7^@aGd zMC4mTj4lx$SZzoXYhufaWv@~SWPL9kgfDhVs>totfRR|52>ha)$Wb;J=kEzJo&I%6 zTnCzXQnoAp+ETqvWm%f7{RE(v4SZ~j)#GDR!|L;Haf8ZVD=6&(-P?a^cc95-3hpBw z-1;`T^`p{pRTu*mDt>4+tCkFj-iGE&q0a~MXeQFxV%tO~Qhi3XZdQ*2sQk*0y^^epm2WU^Q;a`Ktyn&#gnpsCb1wuVcEVa)r&HHj8FF_y;Q zAg0e#%kCSh^0h`+y}v5O4EaTG3>z}yWfS^Q^mg}6jrUQiJwZ6gT3q%$P_zwd4;O~8 zta}qk@=Kz->(b9lgo2sWzV#2MCCZ7ja|V1FsE5UV@1_0#S03d}*;!y zpEK_pn#K;Mca}`2qXiBcPwWvc(J? z{PU6AMUr-q9O})K?N#W;Tj&t7e}XANM(|(#XTz1d!~_s|0sWKIT;z(K5*3WXA5ki+ zOAI=a4`~M3s511ch}_WS^lm)x4K~f&Bqy%hTD^$Ax}g8(U2*Ig_=dNXCJelE6TLrz z>3#vnK#UM^3!L$cMv3BPw3Qr`X0VAP(9G7wCyYwd2hr7qHaGty#H_R;`aiT;(OZ1) zdbLv@6SHN8as-%a(wl$$=2QD^imj#qyI})UscBeRRf(3tRP~QCr+ag3t-50YIS`5a zqx!LY2q$)U$j-cEjY4kkPs%DsXoj6g0beZ}1&ROfn0)=zs8>@r{=UX-z=s*!ORH5P&*^L54%04jXC({u%Tck@q! ztEo`>|G@R1%dO&!Mu6)*4x`$7-1ij83(f+ZnBmB+5p zUzPuowU72wf9dmLZA{wqpZcP(8$JM`FQ*WUs~2a*M%^cCewezioSXBCX|)n=qmW(h zii3A^#bS2H8V2@g10-uwnG*z!9i$6*%JJaqmWZvp3Hf?0h9E#?;$6VeHxdC>$~X*I zQ$Q%EMm1>e)88Q1WrsbPqO{4z?FF8*Yi_TnmL@R|gv9u8^0dzxfMHE?u^WmhHO$eM zr~0s~l7ehJb!V6@{m1*NiA#Z?MW2QbDk2KNY*WRa7*&?A8ZL0{FPvn4dlkboBO^2Q zjL-6aNfc|WUUL#`XDf$ulK-xuo{Ac7fT)3$)d8I0kk3)C!J}n%iF0hPSv&Xzn;S7G zXaR3IUX1AusIbUIUn0O2u*m;yHw|MWk`1oj8N^!c%>xsjxZcZUypzmRT?5fdvqcyo zL{EfI2HalbHENm55{2VqdIuv+_@b0UEKkkN<9#9o*_i3~ZvZm`b)xYwlGsCP`HGnd(GLC2sl= z7^o}FZfdSQG{aWfgd4h>AfI`ypP6Xw4PV4Dg{Pxp6Ec*jAQyFCzr7v#Rv}L;Y-wPs z#Uj9tu)#*{-aQ7!FDYj(>7S~4HMv5vwNZnrfnE2>5`fXIQuc4=-cVRcBJ706Cs|Jv#7KmaP&&!NMSG&*;QZ6_re&Q1uEGx_{ttDTHg!PAU~+ip01y zN;rF2y$;cntj`k=XB>U271sU4%B^0pNc^vJ+@?`Bu1fsRfGh2(FRypT$DmEcGy1}Q z{N(>@l-uKhH~0r%a}$cGgBJ#yvMSzc!Q5QFEd3x}(!9trp!rr>HdH|gR9vz8z8?Hh znhmzqOy*!{C+-YXq?5#hf1mzB7mrd~@n9SjFyJEAGX=D8>R09XrE&dI9CS#yoQe?D zAWZj2SYfo&M=4)lNRfYFPvsf+0Jw&1k-S8TF8S*Nb? zq1WT-eF$T)d*2{Cx!_msA|c1PFhbA6WD&4gEsrmjX4m6T6po&@i_G?o^O8dlkku$d z{yU(TE1={DCA(nhFX2+Jv~|k0I4WMN6?0&Me+|H#zoPhDH6s$0kzmjLbj*8zfHT+R zh16G6=6Mo341V%a5M?}<$H)KjElxXd9txI43{Q(Flo#1NKDLdDlAPzUZw30t)zsMr zNbmLrIh*jysmFb~KRkPuEOH&0EQ3{)CrqpnDEW23$FDc-kwQCDU+EurKA{007A9`W zq~`EKcaL4;JC}Y%c+c`hQtvpG*_c5f=0CFnmKGwgn8+1mRbL>lE__DJl7O(nfG+ZI z0c=L3m8>zrj^I*uve38gxvr-HHK)({mHdS=Yy{IwtRSMOJIespIqB)~kgv+oNv{lu zv9q>c_$1P7tV_#;P+{CXujM;hwQXhIN^?!HDk5by;d-KLOtzk0`e^^bagh4)3%Zqd zu8b`)FJRQ`ESleDEToI}gb9ibJ088w-WSJf75ksbrjqx@*nq9Nhu2ocoww^ICs3nw zTv_T2+8{?AJ}o*W;PfC`hnl`6_wYKls@yI~g~~zBe-J_OmM-2fmS1pS4fl%E5~EB3 zTrN2}|(#WD?V=ycG;>gbLu9cIpNFGxhz>2aX#sJDhBxVCv+(4?T9HuHJ1v zqMlIi2H@5Nvq9Cspv3#-<-!D#3Fm~TJ8W9&z>zjngvlA;+tnIqH}DEKpUim}Nq0+e zX7`qb?9;Tyhg-ju|44VopMGQ}`*eGA>2|tKa`xtY`Zn(Q5+@PMnp#Gx9U4*Ml+-@G zRH(T|<&TZuaUwu(^4}Z~-9B5b6Jn=;S$C~c)e;l6EbP+He3E|w@nlam7C{Xo@sq6B z;kj3`thDX3Zh3DF?AM$!CjI{SoASDMh}1R=*?;`{`w;bbBwIBu(nw_DziLh51k22m zxeY5BE1$7|n3tMPu%;mav5H9J{Kk~SYi`%J6&bX4>VU7Rt)$H%j{%Yx_bR;RWy<&~ zY!26-ztPSawt-ixuYOuj@xz8yc z1x)08vw=MoEP&KTshI@RS;1)KCyN!>8=q`Xwt>jsrIi`R@e2&Bq0r%kl4^lrts=MV zKGZ$hgd)Onq}U}p>o)+}KZWx9oWI+cP$%~#cLbl>mJ0b@lG+;G6$oW4M|QZYBNhY- zt<=>1E8De!{nmI*EdNqWji;6aMH60AmpX>FsY(!fAmCM@{s+u2=Ed2Of$)|ioWevK z=ye9$k`*kwm?1e;oQ6hCog#EU;Mgtxmt&8~JC)lk6}ldz_*XbgMS-PPZ>pkw*v4nf zwsscA6Pb^|nd)o__N_U3Wo<8Wym~+Dge0NU#>!?2iWd&2=ot$yTl-9H>XgG|rTyf; zmAXb^>GAiuracRvFLe$1XyYd=z8DQ|!@#o}FK$D+DiSr!6FsFQR6fOci%ER_*m;!= z+V;K0Ef!Lhf+I{xf=`(a-}qj}Ke{C)*w9pyNv1Fdo+D{Zy^d;T zx80tT+m`klb3tl_ek*;Nhqxa*#13Ax?wbAiqD_qW^aIzrR~>vvlb1TSz^-B3rD?%U zduAMx?LAKtUkRjC10NQ-WbYmO*Z3^*zuayvYr+mmT|7TxbP3;V`VU(GsgCJ{>t1g*Uhlu6m zhLxyQ`E1EK#kX$OWQla7SULq`bQFX1ZH|DuMRL*pn1uF186rTkOrA^PMnS);NC0=N z`MIL1uSJiI(U2LUUbeE*HS7GD(2m5VM_wp0y35q1AXi1W59SGK%WM{xhGY6vK^851i zh^(nn(y)@uNuI^?Li9B!fmkHI%&mQS+NTMr-K{}+eJPbd(SWhfVLVcEFZJZr&k1Gi z{l9AV27)$Kahsic_X57V8at`YX7NHqern}?WzlqIPdaFn-S+5eQ5^b|mOwTeCtnw1CdfGlZ9elHk$!bMra3O}%?d=m{XNL{+qul^FQg3s z5-Hw0Q>LSdp!-O6Wlu+zoac?CIO6DWClVGGmg{`~{v1625kG(P$LB`u)L*LLfr#Fi z!LeKJZf%gsrS%(3TGd|*&w?FO@=<{4L91W6pJa_C(%!FFRQpA|Z6{amHSNJ;02JtE zKKb4x%U&T{Ih`pgyT0W?06F`W}FdQ zP1RtlBT(c7d6gJZ76~TdtEotjRMNB|{F!3Y&ssa2jip>F%DP}(ACG*75*mU`4l$LY zvMQ#T?(js$E`-_|azyF)wk!h>?otqQx_k+L86QwP(C5_0oc{EjVPqaisohWedH0{c_Zx9%%}R6Mt}=;= zM&u;>pJ4C8d~2V^#BwSL;nF5etd-ByYVE)Y&VI$Bqi^~<6Qy?P%YVMr4MX1jYBxXl zZ}LHlvO#%!qrgK@!*B9K3p%pIWb=b{hSl4p-Q|_daH*GQ+QaaW_ToRT)&=vbEX&b% z^PvY)r-T6uVvFJQ_i43s&m{db`oG$zUoMTw4#GXep8bTks%lL)05e;3ayb%zL3p() zgfgj_GbZNiPh++kmJhr;&9&q}ZD#_Zud6$8VJ;^i%E1u!u53cV`G9xbGoO8`}eb3-!L}A8@!Pn2f<88F?6UKOd@vJJ+;AHYX7PrYF7RRLEzZ>hPk51KSL$kHzla-=!5v} z1M5#SLyorB*`jDjRj5;& z;hL!=HQjdl9JI3A0GaJm5EfPTD*qfAHIL4*kW)ueKPgMLj4qS4X_~YyS(IJXYmEAo zZBanjp}7vMI+yHJKD+t4DHvWWm5cN&(z6lDRy9PCCw=vA>#sElG5`=t+X4X-(=Qui z%&`S7p5>NXFUyla5%F9?)UjDZ7 z7ipxE%g$Y;mT)+)&eWB?QmmzTLsdbpOh>`8%?v%dTNg$QFasExE>(B)aNx$ zMTsyETMRNI1cb`g8G0%=(jKL?Xv%?>eWIQ?=AA5 zl}J9c@)w1btE|yoQt2m_uRE3)2~*Ga5_z)pgVJgil})f&ziX6%xH8g^l4ARbG~uh$=l2$V(zlnt%BMc( zrJff?SoTr}5`y*OSC~uw%*Nb(8?id3kuPNu+Ze|7#X5q+7jC55r#ck~8w>O^`kuMo zgMFBs%S|wMV00=F(jf#PQTa?l8g5%OCV@*WG?kjM7?=gFdbT~cJ&hIMpf z-S!Q;Q2raLKrR6iOQ2doB7%17)wFZIxcQ&RR5f@KDRLX{9F z`MhXjy0C@0*E_k;ud7)XR;*zQht`SbN7tGhtqMmiCB);zZt%?|AUcP)^; zr&D~{OYzYm2aTVJhGI(x*;rC3{r z9|QTeNo^sVAuzDct!yi|W?wRJJ)^JV#FM{j?i8mb6q`b*0N3*uZXh0rO7>A>d$Vsp zQ&6A2)sJwraOT+ia(?5NkozyYgq8Zi^l}xUCb^&F|DXZ#u@xP8dzM{zp7LO;d_;%( z9hdjz^LN)An^5Q>s_h-q#9yD+Nq~RnXXb5OZYJgu(xqPpig<^bpShk$se|{er8d0^{&efSO z(zbhV#=Le&yYhkf7L}R^6E(8bfY2u0_n*2@nR)Iulk;$4y(ESpJH2OuP*maFMw!J8HW*~I893r84+Tl1=Z9LhpSONKf4GH*}ce0;ux01Lzfy5 zqs^>YEI|@D1n?kvw&hRz5Y|^9h(pycT(PpU5ji}j`3okf0=C;m*^+0sE5iZcAY&|@ z{wVM<#T)Ng$x48_WK{2%Agww;(8tKk9+r=SrV_TeEF_(waRgcG*0{8G>w=~9BIoN) z{s+!~k60f>%8i@@`%yq`OoLqVb#QV(BJ?!(Yb;m~5-V{om#M{PFD_`LX1`+k-9`HS zizitLBJaZgIB>I@r{{^S+sOEgU-pjn{+uGs(|CHRN zcYiuL2rV2ILJYUeS>0Kq>Cl_sZax3~gXN)wkyH)p&j%TKjUi3ZX3o0Vst?cQ*G?ZX z5fGkT#`M%mmaBRndcd_enNTK!tPs*QDQhf$)%7Sd=Sz0NQ=w{952V^||40i$ZyC-wICzbzn zzdflTB$D?u)aSz9^OAxp8X2Wy*#H%X?ghtjS)FB8*jD_VZ!FYISWlGMSeu(k?!%YU z&QnnuluP}t84orIhYIHijkh3QPVZX0<3#om5#mGngUK4EKNXFtuOv6}e{r3fTc_2H zP>mwBy<3bv=`qu)2fa|7vu>KDR0PHUt;|;YIq8I4-mD!EIgmOz3J*!JKXfmA|9RPO zmGGxnf>d9ByYWvE<+w;_axbilEiW$Hw=k-U69TgCS7Fi2VS)i?U5tMy%=Mngqj=iQ zs}7Cq2wJXay>Q*LYKwPV%yl&zUUJ6S_R#DoqLa=b!l!bM()^FF1EIa?TG^$pv?>{F z^CG#m(rwkRUUz7ux3H;f1y&BeHwc9b6GmJ}YOZyXTkLcH*~d3{<9^0gQW35>{#>{z zTar>+B?BTiYAf0*yL~dBoH4LseWOt6l4dw0I;=Y&2wCrI@%Ra)Hy-UMNZ##8sL{hO zbDE*?(CY>@#kfDo2a^C>>wm6u7iaZxC;HcifND>`X6CZ{1QyVgRTiZmyip^5G!|NF z0~6C$Gu*7mHs2N&9<_Cpm5h$o@ziX2?29uLhOU1>O@2Wc5E2JNR1)vg_HKMn>-^5~ zob#(WSD*UtU_5ZvD1%zogi6+4+=)iJ|6dS$3C}5b>rGzO^FjM|Bf*B05r#>ofx2G* z^4`R7p@8d~jrM{EOujZ%aK3a19U-T29RT;5=J$zsdj6|MdX`#1D_xpv#oRgfJgfD= zF+bkC^pASbPn9FoH0}O(`1ef2+WV9Tf7ZSLotCWJr%D-gj~*9Ze+TV;AZU()D~dl) zW3jCo^ACQ%6hi~aJl>oBjLeoLG(ZRf;MXq8m(wn1 z${|7sIsLlBsVSN}VD;t3_kMco`CZ^Reo*|;)Uo9Kr+f@m!(+|wpSl0Jx%mWf5(?Q2 zOnREm@Zel7s>(`Mq;p@yr|KS;q&a`_zj5_)$ZitpV31~ru&D|YCac@BT@a~VjdAu->QcnbaE!6b<)z6rrxm5f?&?Q? z!cfkiH>(A_rV3xct|B#tvwHx%D^RlEG0#u0EAE7YCZunok$eJb^82L~jzSi^mT#uC zl;b*H=v=8yUH+gZk$aRUYUeml^CjjZDED}PWeJ1uL5bIMExmwekVT^8&~cSyhS^N- zQNqH_SUx$DfmW3kMbyVh+jo-=ZIe%A7Z^nI5lu#ejYfkQ-TpD-JEMS#d(p0vy%cXg z`WWfg4vBAR-4QX0`(i)oSoL|%(|63(v(wz6X(_wrIRfhIWgpknPvU85XSMjfYS#C5 z#R^Ugl}dE5w{N!)#EeO?uhSD8z_aN^@4p}vk8iPDf77G{&Xzp!C}sAf_5CDOWU!$2 z)}%MJg#gphpTiN@blZuKU(jQt!wPJlq2c5Q(I*-|V#e8${Jeb%eNIm6zsIZz zGW)%@&mdU0hkDMj)z9G|B;elwncOofzdG$_GS7r;2E|Dye+G9AeZ3aqsQrdgjE|MM zU#?{#a6en8JcW)%JNm1A?%ft>^*@$g+nzLWbVj@^3$=AxVIux>!ET*yfT+#8N!zw1 z+jmPP3mk`^o{DA0=p*9w?Ufn!S?)jLHj zpm>W1EyapUu;5Oy1b4R-mlU`E>GyZ@Uc3x*ZeS*J_Fm6g>yf=9?^K$3tOqU-*_@nNT=86KWCky&O23R+C=rM4YhI?&J{#9Xt^(aWC$HP6S3hmE;v z$1q*4h~E^`9_HVM&HpdJa{^I&w}?0KhlyJL+Bld z9EpI)i^7o%vF4U)SoiG5Zv40KVQjP~r>!*BpY3?kxwRNb9zqm=n0 z51JNB-@w}fIzs#23w1+Pqd2sQxz&?vYEi@fQO!M zqsiBmh4)?0!<_`hoIvwVlM5`rUMOL*Lm55cuLSThw-ViTL^6+iJWP!4_@-QP{Dq#? z`un^E|2@tudlbd_J(kj%kdOZa*naBI;Izw_d7iITMgDkddX#wbSHXB7eQeC*mS5lJ zamm*>62gA|{{5t9%}Gxdzs)OuODZYBKRcdyivx#RCxnVQCx9XG+)dTz@(&3Xo@lR@ z=sPw-(OzYck|eo;{+6AYMf|jzpnI8EIn5MqOnpLApCwzr)@CMlv2X$-pSKfWEodgw z#ecnF>A<0r^RjOmhA4mEaiUNn5e%1cp_y!io9E3-?aumFm~0L}vA`y}`@UAW` z1uZX#rA=xN+l-5g33V4Jzf{vTaBc8)21kgU@g4(xD4t>D$>KgIpQ%Op#I~4mhLcwp z$q-Ol%P}=sH_3fF1M>3&CpO@m1Emcu@y?ufH%R-{IGEP&RmePWc?B^272kgHM!urE zZk))fe{1T%d3kZ6^CT!Cy{`yG>gVnM0w2?bO2^O7GuoChT09Yn9`6zdpZYoVZ(Ii_ z&wzZGk5Us~W@qGV0Rqb>m%B`Rx_tQf=zvC*pmHv)GZCgO&S#pNq`2xQnK6PRbWyUn zTxlgw)yO`SSxMB$tGn*RrXf9XES}Sd$q&=FZY)W|#mDup;+udj87pX5U> zNB__h3Z)H1sDEV6v1LzWBvE3Es2@=;?U&E%m2d41zW8&iB+Z+OtkObw7G{FkQ{}%i zT^IH`ve8OH)Y?99HZd2GLO&86GU2;b^bAj8~7VviF71C9C1`ZPHt(&ut ziX?kFv)0=Bba`>PfLJ8igTE6S+tVbAJ&%oyZ!s4*To+r1pVo%-uQP%P<7|BCCD=4E0a&W+<4~899wk?Dl8>S|I+h* zC6l2JfnSNN{!+2=AjNJk_T5q5fr>3@|G#&F#>6a=KC{_#9$nVx(OUBKb3P24@BtK{ z%EI@W5OwxKg|Q&AHPXC?jqjevfjQ^Dt=pHZ8i?gD1Im|sKFg#%O+yqIvTqr%Z>4eN zM>?`gx{dC^^c+uq%v;08pu(zh2?pF-jl$aNCIyPj7GdLq^3jydx`$L$&tJ01pmv=g zEVk^bC@tS-i{)>8!Qh;mx~i)j&S$AbL*fEL-IjC_8v!j1Asvnx3zK;*<6fe@D$!_@ zY<8ew+;DO3XXEMlld8$6_!!#zoPCEVqZMam(Zs5pTK)lrEf;*&C3ipQ$rC)wb*XLh zzi~73o7NSe!xQM@4y`RjBMv3a%}w(}DCn>|VK9L}Z~Mp{>!=aE2-k8Kx4Zu)cTkpm zW=82K$dw^MNgsgNQp$zJS?p4r*K%v~i-O1zB(RxQ^Eg7@B`tOEAqNRB-V#oC_mUn$ zPi>QIZhY-G>8*6YA5B(7J^+iczvl(&h3pWZilR7EJ?s)xL!7FOoKHWr58Q>mDDNB_ zm8vM^O!nYR@!%wZ4R0~f%%XQ*_3hXDI|()IgPQjRn^-Qb9;torW_=+0MLhBHbbzeb zKsZ!uRRLm@BI9E>P9C!pr+Up0y*!#Pgf%7FT|M%(WBEVg2`HC!8b>~q z!#0h}`Zwb%Yqpq4A0vr+3TMzBHE7qluivggnjHZzrUw^cXBHDFQc$Fzs?A&>aUqrJ zbv~0(R`8^a$SbxAgx>E0%U7Hc#y4*&j%eJDe(<@Ip$4C48>eras*;-~`i|Khr>Hob=oh zaTJIr-~oHMIA84HQ;F~|e-kNbl|DFE-1Y3gZR|NW_NLCXSfh+HhiKq=;E!>Wwy&XY zV~ZxYW#CO8DS{#j6v-&wJ<6+=YZc3%Cf7U)i;q40W*gG8+D#uM67yFZ|5M?HMQskR z;Ci_7_-G_0JD*zbsE%b*R7sfU2G&njN#XriLT);p=kc5^qE3t6lS-&Rt&cv_Ue3lv z*ejs-jBpr+vSrV^-G3o=VuvF`cY~g}=0xof@xP4P5iW2_@Bk@^B<3f*&bxVw`J%A* z9k{~>I~vBsJ(2=|$?fhF#uW364^CrS&|86o+1;q&DL7lUQReok6S-P4T;KV0dYk*m z=}056OGoZ`!z84Jrbme=u!%*Vjom;;)-}B*%cJdIc|C4f``#C9a-Q2ng z7|eJ9#C17Y_916>ybnbV7WRUos8T#?t4kc-daiyff1Z1`-`tW z(;gq5OIB96sL@~6=Av)MsdzY%d^tm-6fu5atM~?xH?R<&zU8#@>u(oB$SV-KUrX7= zM!1CJ*QY)ajjYqA3qvO_|Qi7 zWXQ5MNkGY(jx5gEJHynQa;;`&-+gp9#|`UI3H?7QS7OV^Pm9x5WMR!G+)Uupk&~7U zI#wIX6{`88usTNzeI=i31SWdC|GS3V7^m>Sa-KWxW+V3cja=U-QOsAZs6C3vG_ikiUL0y9kO`49#-!uOS*IVXx1y2|0w$X+D9d#Kii2aAinrfQA55y+S??EzR)$^459l&1#dull@ap4KCG0wH^c4dcUBc2q7UK z7M#_lmO9qQl zNUs(L>BB2dPq&!?y5E9A$?q3JZdR_Vvp4#C|3?pdHx^yHxJQ*I+vnWDc)S@(=w43_ zaWOF&AM4X{49Y-PtLW+tOI9o%E+l#FZkgvCW3OL2qfPGWC1l&B>OnI{?NwP(%?OwsH>h4$31uuS* z&Itpy(x(Bjv?O|QK|$!I#~9hG90$YKb{lG2;khetwlCA3=(uXNWIRllPFRzRer z4Hi|I#NS}VvhoV2jrujwdjhMYtukSfUixDX%dw8c)ph^$ypQIN^|M%(+R5!86_R@- zL8H&mSI9wyg^aI@FL;DPBp_K9;g&+9!)Zwj4dD=!=t8T;| zn6?FnB!}KVGQ>19$wWn?^n8OYQdG81aRW8(85jPS)I~oW)1rTjt(#PLAWembCIlwR zri=p*5JAgxa~K~$8QW-Zs-M06tNRx#O%0OY70j~AkBbGO#anqp?ZpC*I!P)Q z7pxno<>esOnWTE#zAiR#Tb6MS;Es$^v6kwlZgqite?htJK@*50@S0gU^f@ur3x7`U z`yLB{aDA&*(iU&$!a5-UH30vU#>JPYVkLsJcf)mfI0>2aEN| z4{OSWIeJC-(h5tK&2l6RP9hAW%KxYHtkUgLG3qdjjIdtt*USW6vjXy#DzL+jM`{4mkO zX~?bAE#1*@j_UtL;(?^(`RaLaY~^B$*yAgp7AF;O!U+fzxO8l7&qvR1tCP8KBLUa1hobE#5PP{xc&T%A_SBA?kqmh2Xjm|%b2w`^zPx-8&=A_{$(kO z%z)<_ZX>UV{IR>;ew<(A{`J$tW8kB~xkQ6nxXj*XRJR`MW2Gsjh(1!4Od)i{6-7MsI!Gh;5wX7N?*Zx z1+^i9$tF=+pwAWTX(=i&v3z{F>sW8HgN6VrqgMQb<*#d(dD!KaO%(E%_>XA6R8_G5 zDTyhOC;UdGE=?eJHNG|(+Ryo43F7Rh!=dn^v$__K6S{m4|QF&L;8%)(7A z7VmZXvi#d}<45mqaN<-evyaa%i=>$Tu$z7EZ~+916s58`?p~i^>f)>mZ}aOI8DW6v z^HHPbPhV+N4xetW6LCMD5xVg6bdG44_GW>&fs3$Od|k3NGL8Ssi9+9>KVE5VAJ{8h zh@mD``|cNP6NfZ4*p7s-O;d2SeRK^yT3q>HH`ntf8JTUo4(86bU{75KoJjBk;_2Z` z2I28T?+{AZoSSZlKm(~BvUzfEU#;B{GJH^Z7rnB!ccBN=`mwj@+r74)@NkWI9{uP% zT4_OEOxL>yxn25K5OXAp(}c~ z6|g>7#o1|vr~8APJlR<&XtJTx!q!2Z#Ik=?cfj5aA*4^5ZAg1aK)jB>d+Uln<-pw$ z{fTnVBEMZ*%Ap3NKdAb4wJQ(`4NTW_?P)y_Ep2|S=aW%(_(uJc8+!#zJPTZ%0B%dL z$xX1TNTSPiti7>1-=i})m}=gi3D7YPDk+zoW_ZM(5%vCe&p;93<~W`3_P9I0Qm87w zyePi1AR*stC4y(~Y46u&`)V`o+`BPXyxpmMo=nH>t@#BLtwnf^=sB=G7tKqn6Rfqc0<)iQ)1O<+Wd+PV>UeyZ#+n*F+aIMJ;aPYioy< zEFGmxH{!)NqRKbo#n!FLrUoL;ld7LB{y0}sH&@|3D{NQoJ}T<24kS6rbM#JqSw#=sOY6=74KHiv+C zfNcsGF-*_cX}s6m5*(7zFyq5VO)8htST8)n!ozub3-t@H9~rs;`CcveMeg08Q}r$< zujGKiE}_GUle2|V!50iVhTGa;(#tCj6p$hN`F#up2%_Hz2H||x9(YFo&|8^R;`Psh zRIS`@``~vJAvyo0gaI>0r+s}m*|fYlL&u)_h?6VqA+HGLmBzY0p`)@fnz;AYk$|LJ z-S*mKn`K(m&984QPzGKczR3C>iRWfh(WOF4;&-wy9!`%w-=(QsS=c_PTT%-13oiUE z07m&94s&v7`_(&|E}JfG-PHxTIP0-c1&L&A?v4}brxrH0802OuRhjO21i%KD$|)}D z_x5R@hN*U~4m)A~2eyskR70_$68>T^XWTf0E{vV@#hhqs=ZZg)L0K|_w*=e^ar15i z*`L(~MrlbZG26d=)cRQoCXl~Gt=3V!L^(kjv-4W|c>i@*{sFF44I?vt8>15I3QLzy z>nI(S{H2uYkTqSGon#iTVv#gUvJyEE*fl%CSHHh+!2s_;_6~29CZ@RV#iUVC$;c?3 zUPjP4g~UAV?|4Q_3eRLtbTSn>nKODqgro?~NGLj`mveTf_b2lrz3dS5hgM7vR-meQ z#F+xGHLxg5%bnlxbc7AY#y)i^JJLAiYhw4bv5#`(5HJxF=vJj0xw~U_tvo#54yB&P z>H2OXJ>$DQ%!$m&LG2`y1M_DWhps0;P`VsVf6^qlF2;@yyk6(WF5q;nI65sCb8M+= zi{85d`iX6Bevlk^V0c=^X{?xI;K6nf(3~SuS}zd5zU@l(1Ty}>o6Z;RYFi=qJEXzC z99LPU{(++YKg`S4J)f(Ci^F3;sDO)&q$P)V%p{Pc+!b!4hv=!ji%Z1PYoJ9kIC{0% zYZJVEN}duW(iY&8=(=dI)jFaXnyJxuY3-F~lF8;CwDC#b#r1f8saz>OIk^~U#F(!_ zJkgoZK~L8r1f@@d-_1Su-k4f3JAW$4pouYbZ6Mhmfg~xe!)Uqq5Kp;>vA8V!WBKI{ z8Qq86gpJ!kC^ni2F_LPKJ~&31CO+%p7E+3sS5J(+V?H~_hcFBg2=oe~wc&W*1`TaF z=&};O+6&IhoI9A}?3$iaN|cO9*4gIB2fS?-3cmb6@WuF?w=2FwAWKkDK61g@gaLmh zQh`8C1{eNOM*qFFh*KOxho=nN7Two?Y}%@IdCy)-2JZ@`IE6c}bso2STNtIp`COoU9E9Haatl>tEVWdC}l^ zw+y1JG1eM*?gEaNq6r7j(_kG+_sW?yHU6I95ZDJbwfH+G>bp97 zfW=~d5rp?mfWdy(`>%kvwy8*4JC~1bIC4fK?o1DzXq5Iyiabor($~i=Au7=}DMjf0 z>88cGU+&<%!Gkk)$L0|w>9J8F#4xd8`T$HY5$rCCJXQT1DB5S%+CLo}J+edsP>nav z{Ju`}U#TDLN=&Z`qu2%^L`XP6}Er~N#2GTTY+6| zgwtWe?5r!Sdd51aq4(OwD&d2^b)*1Vj+83j0(1|guJU*_SMH|Smd zRJOCz5>kX5IURU64w%bX$ZBO$1)w`R(v(|vc<(H4I=hp?Ld=A9T8*8LXrPlY3 zBv#{>Lpr<}Hq|OQbuJgDh$RDTASPX_$r+R_9-g5yM^1b-Q~>!!Cfl1e)&9mNB{g6L z!`qsWdkqb~dxxM4pWSEgdJAo_)%2yjff*)5v_s zY#;Wv+GMTE66%R&8iX(!2RQ3BP?jAD8Z6k?v`tvIFH4O1fJ@SBEkygBM1~f1Qh+^! zdW7$2y^u@!1@hO~lW-W3Jlp;+=G^!xMfu|q#5Z-HzqvY5xg3my@|YDbvt&(h6YHz< z6jw&Ov(f2=KZ>zR=;=5-6pv&l5g5%j*TKAN7ZOq(Vto$__0b2uiNAxL=3~@YfGgkB zi==AFUX?3sv;0T(e2bqhOM94!l~jueTWRo$r~qIfk8}?{$bs+vOfwJ(`+8#gR9>^O ze``2UHC;UtBcS8TO(B8R;4u4Yud7J;i<8KeOl+8i?7Q%pY*I`2-~H z?OD9j9Ut{wTYr)hYzfscGx|AAd3=!J7>K^6@bQt+MQDlilV*!|r&eS!5YJrYQI_7` z2V68(Q|qNmRrB^Dr9Ni!NVvz<`6sRfp>WLG>jr1N(?$xel8bmwwu-nDA}NUyPNe#l zt`fmO*`3T7@7Zmi)HPRIKnS)WLE!Z*LHp@nrfjpcHRFbv%hraY=ouI1 z)4l^PmkQd|tH4tTU^zHhLA#;Y~v*N0p%Q2YXPAII568MlIst4yPG| z+WTT*U$1#zSBz@XUr?+&BF+>Q}s^t;lo*(QUz>3TkvD(M0d6dB-&v|BgOp zlJ2(>qiMZQQwMlVsBnUEBFcjhfT(T2+q^gVV-%wY@wD?1(%b_&Y$K{n-At6lcKJAl9@=@ zMV8yzyM0_;kC!qibrvj~e-}XbbK07QQQ0PRi7_YTl>gww?kb6iHk^PHnYVbS@R*4y z@FlL|F1I6RfP(zN5`}b!Cx>U?6*M| zz6&{hjNAX8<9j@xR-OgFBzqhpg88MPeZ^Y}=M(NRZu^O72|XI7kMOW+9z1ICi`G93 z3%rLaXY)vTM&^X*~=WOlf6{X$$;9Y1^Qs1@lC#0l9iz_AQ z^DOFRIIQ~&<0g?Zup)D9z!N6!7aU#+OdoK88`}+0)1g5wmB3QB_MN{AIBkxCGonaT z61Ro}Bj-HA{T(~z^+IE_m@}Hy>b)174(iBW#oN79BG8Fqvt>6dRJJc1B4;lU)Gqi2 z$mU}W6cY-$S; zwpV5x@sco^>95J6ZDeWVe3_ucknh2)k_o7$Wa@vZYTuAdti%aPSZskSMPoEtY~^Nxyl~UY z+~ey5uH_ck$iWEvyGH|Q2z2VU-_9TbkE!WTse0e5K2e?(1Jqp|FR3nq`D!tdBk+7c zz$A_1WH9UX{qfRGi$55GyqE+1zkgF_rq?(7II#!hLDgwdf1eC^pN`LftYT!9rNEAmX(H&OTe)7ObOTh z)`(r z^jBKCg_iv~I%<{3C~{hAdQdsy-7J-yTF$R8`xY*)w#9H8+X+2>Oh5#48f$*5=%@JJ zkBcw04U`^LqIYj7TRsK=7hvK)K_F6nuh*$G%+t2!;fAl&*6soVT7n!iE)EYpz~!QB zJC#IQCI&dgnb91?+?@J~EMC(->5Hc29zNxRcV`r(86W%lCxv?h6ME;w(STvG?dqQ^ z=A0;aCH=N;*~+!O+pKPA`CY_asEgv>WI(Mbu0}Mg$`>b)GMv~`09Zr6CJ$r$`dC-y+rKi z1f|qwe%L1y(7S@9LM>$hfn*DR_Mu^&aA+~-mKMdz#aw0hB;wpGqr4Sl+{{()ZOkIC z9NE|h?Il2^44N1eyPY^eAahTa?$g8^bq~w*;mu}S=SIo$L=eZ4;Vl7eaX*U`FgFt2 zb44C*1uV(IDPoCN(O~H%3m?!3Lz)?_CeEbz?hM$hhYwQv)cc+Fy;u>Wnd8yByqy4F zbqRn63M~KG64$nd!O{jHpf|G9h#<|8?B@{=`Hn`*nZfG@j@murQ(c``eQ7))ui8($ zZ0;AaQ|;pW0C+XuE{pltohxi6@&%t=aok>Mh<8f!-LObjO1(TUlHS3jOZl{Nhu86d z(IEuP-xrOcn>$dU|II%9at;R0OkqB`UwpWtg-z_A3IINC#ys!~3u)11-%aW5#Y*!) z2CnzFuvJ1*lFMXLZZy1f2q@fL4LUYl-8CGJ?Zzwic?EA5!*2IsD8Iu+&e8z2`_78&Vn#L?H=K z^1489yDlxR9~dtznpUn~J&po8*#%v7*f4Q-fW}a^zrpMKy3LC%?a1N z?|V@C2#m)DRPRM=-hQ_cJoq{|_VZrkq%qtgEdC@-p5OkPDn)+6 zi=Cu*qSOo-k%=RHe6NTf0gaop{@QsNqXW9L=}$(j8s#+G{5TF0I1WpM1GaMC)3OkJ zQi)bBp#CnC&jnXcRIr~DxMy{aT3QtiILJ0g%>F`u$OE}|H5IxA!-oqzCrm`7Mz%aB zRFlUi7oNH-ub{45C6?P8`m@fyRi@fRs&Eiz!^M#>eG=c(u2+Ryr-&?SvvxQT+pene zk5nf7B+n-KbNsGf=_A!)rhCU(7t@#j2%(Kcx>K5|pEO6JKQ&tnxvmp8bL4`?a9!G< zJd*riEkY#lGWZ@2@K3MGFwuD6ULQp}`kKqExgi$sI1)ShcAll;7&sPw+QZ3k(48u~luQn5h zTD+Vip<3ZUpf5MJ4NwZzHwL>NeGQcm8ktB%`E8Gj>m$_|l)i|S>Q=1GZQU&ZXlzhm zNl>O}>gpBHHWAi_iX+svx*~PG)5Q%ctDDTg&UuJFy+rxFU%eHDgTwNZ-HT3faMtx4 zC_?Ku(|5+t&dq}9PaW!Lri^&l^kYx+`A z`l}?Sg5wu{xo1n2a)P?8GmFx~*F7Io+Wwc+eYt4fykEhBSXo1E)>a|1$>q7F)-ZRh zt7j1D1Zhd7+;90hs_%h&jguybu-SBU`_O@aeg|NfdgF@j@7K>RJHlWKw&2R3pT$PS zX_kJu9l(_dupt`+XDT4K3}GJv+9k*%mxA3omg;t`Y0-1S`UvFlW`SXLi*Wzd7JnSd zU4r7E6%d65$K0o*IuJ)vTi^Rgx$O3)-|$|7g(;lMwswTiiZSXyOsp|mLo^pX;5Za` zT`UlII?vBAv~7G;cBKf+3 zC;aVyyX2gZ8x7{oz3ssV%r^&;0Bz<3tns(s53m5dL~%!#iee8byFs&z{6iepaZbpi zW-|4e&95#nTzN1}7<3TwqbB>CaKS;%+e5cCL{ znX#2>-ZD&@BccEk+jOj4T63&iu_&E~e!3;i5ksPKL_;_H18)v=+pe~sF1NJCqOO3! zh5toYumgm&f}0;iZ59v`s=s22I=c{JPR{)2yE4v;qhXI08=L#Zgc|%%+aMnrD%GDC zS5PVqleD$dEAooW99zG(uc)gs=Sld@>ZbtQ5TRe_tOU* zkx<5${;hlqVqD%A^K=EU6^n---S@$%dN*rVu8B$#&-yT_Jm)SMEfKcs`4fCvN}<;5 zF(taX!GBD`h=xxvS9(9j6Vzv;Xh+`r+Vv;a*M$94WceAOrY)^@k1 zLq?hFo7q{1sj+ z)%88-d%@EV>*F{opV*0iPYgv>avooSk*82F;=gBs8wVJ-YZ({5Xap!259mj&qRbnA zBinsH>nyHbth5XrwRvak?cFF!AFmfY4?alLzZ#yhSvFkRXfSK-q-}k8G=ug7imwl$ z8d3v1k^v_eEgT^=2kwtXew$$FiQB>qww)H)_$Pq*#jT(q*i zp|kwvrm-TP^ChBEr_tLlj)ezt+S5z!0evz~gQjN66*qb zTRHES|D%~uEbJx^jmu=i6+(Zu~whz?W3;uks)~ZlGz42q-=HbWCeQ?Az z-wxAT5Ft328`&lOSzw3>QI=$A$d;)3r?H}c+9i7GOcZz8anZcg{o>zAgbH?ku>PP) zt6+CxD#~~LloRgs#WsK}?$6==>0voFjnm}u-6LSY$0Il#RmpWa4&%r)E!Qmc+ZiUx z3ATl3NY-^-74R2s9rp!Lwwz8=RJOLN!vth88>_U|pe!W+i%PRhCj1%udW@EUpbVeo zmG!K>h5dcVE|sZvqnAZG2dQnNTYVSAQ(H&bJ`4}=J%>wDUsKpGXsI+yX&>t{6I$6< z|GqVmG_gewBenrRjS4=;%sbX|>;Q->^bQ9D!xWIkSpRtcR*lx>5LODwT3MhO!>?Fi znXmQYL{@Q&>PvM+=^uY0=w5D_mZZ}UW)(#b!Jsuhbm*fM>;;B^Y^kxeg=ze9E1E$m z1#iWJSKWj2!N~j-S^)})ra5DF8%@qa))cK=&r<7OvP$!VI^oiEBDrZmJ9G8N(78)= zRu;*^SWWdDa7=~WvQ%e0Q%bD&3Py~`$ymRIv(?NAzr(9CKk&GCmn?R10srWeBX)7l zlGg}<-#+BD!f@hu=jSh7*AEX}WHA}TR@L1iQnVmiKETgK3W<-;YkcX&r6p&tkPuZx zLjISvtryMCYeCuQe4C@7?M$fWa_hO#kx|Amo=}&}5+<&DZ`b12`ZyOY7`t%JdwDG* zHn`j_6}~YCp?v(YrBfIwe(vF)U57+dgKj7qlBvwj*kG{4(=n0FmUov%au6RHOYUcL zMy2+9OVfnAU`p-Jj)Q>YV#eIY7c%PgcR`+FHyfU_)EP<^Hc#cRn|fk!tWSD015KU2 z4sqMu?0Cg7lm5^wCL`S+7-Up-J)*ejEeb=(DFFyRmmbT7cN6w05`Jvlho*svU^qQb(|dzO>}(llFEl=CCpB97J31>sipl$XU+ zA5>pDJF8aLztJ5c58$*>QL!2xc|A5p{-+)t`(N_lcO_y8#){pS%QzL? zGh@^8%?f?RMMbe@$j#i!%IJE;XbCOcL`g*j+)k`yB_norw)?Uyw=H&l9+aMbjiLv( zd}H4!5*F=m>E*6#{P*w>lm;a~moz_neXy&mgZ!SMFC({gbZUqZ;Q8fA7UnBAde+gG zv^-*e|9X8JAl@XI{FeS+-NT5y7`o;4u{gBZj0Pl&bMYVlV(6#^_n*Bzt(8gj#VdMC zBr!pbmNYo^RgeTVefJ`{)L;Z3Lu<95(5|7yw!0vAgAas!fA9BSzQ?MOr`_{iX~SI( z=h=w$4<Ae5NQ}qVtFvWj z6xN)`vd21S`HC31FD2n~Qjqd*9v!=OPW6=nj*7{sJ4*)yK=<%DDv z3E1r=t#3GWj}KS?`1!%~-R;;3XCc1e`+I}f`g)R$?$$IRy0kGm8pQ&SxSp+=BOMYH zY!FY{SxJqSuw&9rYQKEsSB2x&<(x@e)(C@y!oj(FtpNCzm9|gLpOE6um->{jpX2@r zW)gxN9aSS+5iAIngaoy8XePPHVipjgfvpE)W79ti>Z1R~c#Mw^DGjl*2vs)Cn1_7U zyuG73zVPgsS-@dn2zn$cRzO5N_1-{J!NP*;A9#``Cl(bv{P?OxL=0C~KYR|&6FCnm zd%*rSlq`7h&DIk)5+w9-e0sjXd$0D_gSWThltR(`?tLZP>u>GUSwIXAm48|~xut{c zS16Rub~`-Hn9Rc7=4W<(S!{KcAPw(3r2-EJ2czN=hr+@p$lze%I~HjGi;EIY$H!Hj zLqj+`JjUYU&U}KCPk*$wW&p7FK$i>*7Viqt?E%<2LcO)C;^^!)!Nl?Co1Ae;iEQ~poW7e-hIgw<<6>6F+eT78QVfQ_US!=O^w)?1rQ-_)uP}MNrwL3A= zTm9gbcFGEZ`xUAKQ>~cSe-(doZ_I=$Wh!&Xs;ES>F$5Y)io~q7AvTkzU}uV0Hwf#A zIj-)Bx%B6Rp^@Z-U!jqYPl}oLCBAo_^gOZlc+QPO(i8LA`g-=!B31b>XSv7BvKHTzp0g=t<1`_ z*f}x++A*xGg2ct0+%Bp*mrR2i;f7X@;Asu&iRpPc8#zK<~4YF1GPqmB|)6pV$OotIh@;|n9@=^v|b5S9fjih#UrXT{R2j_l&{5}6R( zDP$S9hd(vhbtk9mwT$N9Dk%jW^%$DyXy|J^21P#0%;Y*jdv+j^_);Mlw|CS5ET6B# zK{dep{Vw~DD=#y1(IH8hnBb+a-#k9ew)~}=Pk2O=rFFiBPeW!>%s-C){_XEg338w_ z^A{#hpRB(C{p4$BXRgyI2NCidWHk&nplv{fXF@-ab^&-ZutNifRCUD$L=Q z&Mw1qwU)v2S-;_B{C_{zK}8310CxWcvv0_OoTX9BOroE=BcSXjt|%? zj5Lp-rK%1jhxty){%JKB9U05 z^NzVu2N3MW0Rm1=BUN>K?mK@ChEk??+qWgI&!ZbysjvpK%M2mX#ol|YN$IkpyH1NV zK5+<$GBjlM;^;78VsY`EwhV?^EVba9x(S07^&nH@qxbp?$^pg?Upz=iYPct8$&@{gt_XxA4bEdRKcMF$7RsYG~6$}=8UF=-jomoMF!7$=E` zvR^he8>@S(6BqB;FczhJ|8DqMweYR6ar8F}ZdnCCLWy|{eNv7`C62~l#q?#Jr0JB{ zm=tZWhE-pa(H`_~y5EOIH09=%%PILi?MDF01&X*`7p<*hl!XNFgOz!$*Q)KjZ%*;z_@KoZ924o#$3625<~m=vso zT^V2j!ZtoWrj`~@D1@Zxoy9{+{k?h6c27Qj=);qCTZ)#N7~|R~H2gjsiKEr*yzX)7 zr$K*Zb2e*40kiDGBvHlc9G?Ajn;;6>*RXsjb^-{f`)TICPbXvu8k-s`tg6kX#?YP% zp--$ociDGVg}$*T<4X+x2OGREwZm9AG((%SJ5)vsO?-UQ;6*!g=6Ez%HjUE1Nt892 zU29@cm^h<ivuYOh@#wGLv!6W|K2xU3NEa0jX$#xTCrC(C`SnZlCi3+w zFLIK7Rktea&z}*OS7IMr?gQvJ01e%wZ{jv8kxIc=@ND;4kUyT=xpA+hPm*aE#JL?VJzu3yKq`Q`F}dns)3`$H$h{ z6yhBe=D8H+t&+`Kf>yVr6%??8o-QqSk1A%_*-SEEzu|k+G2DeIfXy%*fTQ9_Smvb4 z3*sY7N)nxKF0OFcF-|1DMa(Z((i6Dn2!yI{0y1W5DcrG?So^ zPeP)plC3Qh`OcQLt=`{luEr)KK5;&u!*(?R5RSKEP8 zBV+F+V<z!@ z7JFcjMou7LPlhgntZzF(bP87$O}H~~856&o7sOe`;#&Ht3ezB_1?#+P4h$&va5IaF z>k=Q~22|t_cIIQ66Jarlse_L<+MZFBja*(=6Nl_x+!n2|uRV;sUmA^yg}lTnNXY7+ zxB?(F_1f82)Y$WGAJbMA<41WxFLYBncpbU;w?eMzP@@TU>!xQOxDq%`( z&Ho&g5GCR+nkoQB+dCgfYXEoocP~ZK9LW4-<#BQzc~qw%0x-_yrE~&LqkvS;wrj5R~fo7;lp|>L$+3xz5b9_-ewb`<_ zukYOYp?x&Gw?jFCANpl?klBGfy|~z+u)e9_!tR%2L3JDT+!sw}Q*pPIM&4I#roGUBPtQqcR6h6Aadp#aP7Dql{X9J_QBq@LcvFxxIay<- z|1CaVfm$k23w1x$4IQY zfxopUa zR}FM+ID_B|Jd%!hYQ$+FXZVm|r?%c_W7m4%b|<$-l`6adj!&JX6_-71akM5l4r3o1 zPvGSr&e}=*LMAm&%D^D8>A@6ro@X?$71J zU=A0}#B)sah>P69pv;YMb6OofIK0-DySVk1A4AF+hS) zk7GMKmto}$4zDX`n+6pc%%xje*pyXNTiM6#*syxvFMJy!uC4PL8(&mXNu1A`FsRhq z6r8MkZ@!>xs>X5lruWY5`th$OhZnzfSRerC;1O(xhx{P)zjol)XHD9))_1=Te5s_=Yn@*j zdj8@?(<@vb7XI<*KX$bH)WeTI9^W|y(iI^#JwR>WD!9pkIE$g(>)(ug97A>(7Z(RQ zpw^1Z8Q5B_R!x|gOy-QhXy$h`;w9|Awy^u50A$DkafPsr5A3>iTmVDyyBe`#gTpOc zt>l4iH^wcfx_ZkW%a!$yPewAo_rze!0_sYL!n$<#5r;zF%o?S;EtO%CsN-~Mnx}F+ z{+~B0Q0}c!XwUmu5Bc@M$0eIq&i50x>5>PCRv6i|6bUdK{-1-6I+y~#UlNa~=zPA7 z{_#+~uR03}kgf4b4yN`BL=e*KN6FIX{`i%mCYC51D2`pM`nkFE4Xp6FfRz^Bv>r1i z9pH;?k!?D0S-%U*TPd{(pZ3L`*^FO)GTT$deCO^i(I02)ekzN@#I(CwR$5B@J+I~K z*T3|f!{tIsiUkClw)zQp#&5MO@#n~iS&4Q#a+-^{-gR<6dm%Htj8r4#!d3+pJancpHcbcqk2KhgF)dk#Lh&IiWk^Qm!@GIi;cbXUB z{$yum%&H@kotE0348!Fyd@$aozh~^ag3}G}ji;n_EcTz?QsK90M5A-c9}F>xdSnCODuGwXuX#N_wyZ2g}XkUlx||9>o9Wl&sA(|r<> z0KwfM1ef40OCSVy4Z4BFHMqOGyL)hVcV}^z;K5xN`EK6&er*+1z}~q%-KWnvJ+u4{ z)y_yXA1^Pr{o>Z)@3Tisi$S^&SVUih{Nf@&<>uW=d)sj`%T!iK+*=#F+7Gh~m3{g8 zky&G#*D2b3e1-sxz-Flb$<8QXbK4UBtECPDEXt_nPJs|dbsV4Ykj+C0U3xE~uXm0x zK`J^~vuEC8I2}}k+9wx$x!V#D^X`%7a~uN?c3Q8s+eD1IQcy$yYw2E;{^qR0wS9dE zly({V@80n5DH9Dxho=#X76~Jr_q*9xMCl^5UVB#EhMPgXKOvjj4=2Az`Qt1n{L`;{a>;DQ)D#n6KVHfoO;Bh=AT&b-ZSAPUME__7^?}G6 z3ch7{8spLRBWv@M&#V>E_lxeBP~6GYvi0U6=B|(`j8lJPC&-Urq(Z^vb0iZh3mW$N z^s+j(n(2|@@%yzX3zPgHd2b5cj@u@exxjJl9|HjR{A#6aO5eptI65 z|4e5g6fNRb6tCDT*kr1~k@IE(fm}j@d3Vs#CViB#cYee_4OfiS%NF5Z-q=x_oF_Nb zZd%Ch?C(SbQV-dGKMK%Tp?3@6?jSl)#o+$al8+6?zURk0@4rAw84iDYn_HRxH!)lSg2&m?&ZDLcyg*&6vXN>%yv+eA|})@V?$+C8ZCD7kj7Ci`yE= z`thbr2ByEH{A4Y_j^v5g@YvI4T-VwD=j*2fJbv&6*4wI@#|&DtQY{`kwxk&vTM1bv z;R5XB6e3K5-SOY7pm5?{&aN|Etu+x%CDvj|s(hLR1>KUw{e!at9a)phM=wS6o5?!2qp+SVMVb<`%tE%Ro?E@up-i@_ zj;*_A`JEjDq`u$MD7d(J`H_od8usmD+UTQB0(}c#etT(f!@S(GR*Q+%advZcMq!|1 zDiNQ_Z{=3&)Wa3nnjg?zrIEh2$F*`+WHvOpE^cj^`eoz=3>>M_tHvkI#-(XU%89*S zI@rbDQOi>*fgbIdej7qS6X{t)Bsqw5K;s2}RffQa*t|bP6sU*>P?f!X9Rks2_afqp zXw+SQAvC$Ag-ebYx;M0mTvJ;bE%AwCEW&igH-&>Yn|nXEzCH{th<&l1CM9EUdei4I#<6BrIR$VAcZwx*__8&>hm}-togLH8=Fb z+jf$stJDjCc`E*r6pz{Qa>9|~qPn=0Tw^vxyC;Jv43-bNMWy4vrK+`o@e-!-o!`_z z`g0|yBUI1!ixp^jUHFnL`C}zynZ?22AiB7>Dco*6Zv=5Wm5R6Al~`f71-6Fky!n&7(dnlVg{_Xe_JJq42<1$jj)3%xb7Jf-BV z4!*JpNRML9FA=YYSmet8YT_r~Jbf3?vW4|0xTE{)tC_Si{QD(U>|HhGcmR)DaTWwP z48c@VIT|?zmU;r+`*7`jN!YNp|zp9)_@qK{5S-mLb>)vk-I0NN51YSPDjHOb)5e z8k-}rjN#htJHk{x1SEUC@p=d%*f zIN_BSFA5LdJT22E>Z{GM@uJJ4EE-rvA)>^`hPicoI7NU-X9?~*b6y;|pZnY7HUYVJg-M9DE`PEW^gyrr( z@M54JO8xxJ;EMO2G2tUsfD31SCIdAP_Oo{V_D;hbv@zxpzu^OMA z>y~@j+0nS&7S(tdW7a!ZF0Q0ho4g?GjT1!1#B{hixK#u@q-{wI(+GFP3Gn|d6$w#ZJOkB>+7@LpO?r~pc13~NMWuc!^u|{cl%7l2;>JngA&{pg$6?wh z590sorH!r{M7gXaf$uHVCxM2`9Q=uXy3|QhOF?0D0L6w_Fg8S~`19xKFpXM~5Yla! zn-5z+Xw#zmt%dyOO^Y}537>u?vtt!~VD+^9&+&GzeSyjU6GM4A7CbwT2S?cQA#PnA z<-5Qp7PjS}b46XV(bp}uH*2CE#RYC=*&sR8(+Xfk9p$33aq3Y??K!phz^Bnm!hJsWPB zJG$5eM;jgfH6d>v;{2o{l94{AETzGu{OKh2PKHpag@4z+!Rbzp(eg_M;qzmQE8ilo z#?O6=koHbvyM|z!RYm zK#aJiWEqqF#`_T{OgKQI+|jlG@e&A9ai@PF;HQd4oC(~-+nJ4GDWy;2v7rpZ60aE= zuMm;e61n~%w8u!?9V`L$lqy%Iv0G~7PRP&K2ex$zD}{f-sQAqX*90k?YMTd(b=Sz9 zS*5WtWQ}TjY^42wyB2@88U~F<-biKRD^_mKoj~(k4Hk3f%4@q7A8gNcLV0Cr8g`m@ zHiIZwRn;8A6$;ant3H0RUJG-bIRAqwDcaqS8T&(ikY@o{{Ojr3=tM#{-4a>J(|LRL*y$e{H@6f%GG{QUUKBj##K zYFxda*`sAkdW^c5K5;W=-3yN`TtHyxpG_DX9xYeZuxK%W!Z_j>1LsJrL+^}g&duUkB5n#&y1EbuER6y8YEA3HSE13 z6W9z|?7+`H{Ahm#M>~$1R#@j%S40dfa}kmK3HygtkyN#qstHRT)$;wOZFUjs_b5(V+(AicN)6PF(_tWX)_;?1OU9g*b z^3?7JL6&H4mDQHJ3S|+A7qbdcC&XY?wuT(NzB;Zj14H%8Ugn~ZFy_9oS#R^i@6{&V zL%LKyboEfOJe<<)hN*b?HGdtUU?p?RqXCp3u&J{e2d-8k-vQ`Hqg@|a+9==^YS{Fe z)g*QAW!IO%ywz?Ush~U8*GCIJZ8pV3bu?q(fjTx5=MCe-LBelX9e7TUcv^3uKz`gBuNp-tur4r)Az+SD@8bJ*kLv~Hv9C* zQU|L~++dAjv5Kgu3%hYQLhiuhwVNX0(F#u+cfz+;C7_G_4#fXGEi*L~S#K=g+mjwu z0ZU6tgxqG(Hkdy~)+2&1V`F?Y5n~GEFAhT&=<(=kLW-8$#Wqll&C(Utb>(#-z=_{m z$UU4YI66G|vj+)kjS^(iZQyZRyw>ddAm;ko4gUK|rbD7cFLg-AT$Yzh^HnER{hO(< z<(b)cEpa3#FuZ#Z?>5$P_!$eH02~Q?#=B*$RtbJ}86^vlWc7ne{BOU#TRB`&S>#V< zxkBU^nQ#M*^^P`=61d`M`7yBy`D#1&{4AEIzY51b9uz&sj3%V>ru3d#N~X)JXk7tG zu=zgqn+Cu`|@&877V<5c9`( zC*EA_?5q6)fn&f{1`A*oWiHcZXR2(;?b-g^cfo{QDbl@v(>)=RK{DWPD*WR|%5`g2 z!#vXj>G;+dup{)ZVjM?VS!N-9_++04A6RX}(HuQ|-94s$tVoF|v1&+C8Bis~W+_fd zTkWY0+<$2OLv$Q&>`jsB8OhV4^-8W9QKuyau{1xMn$MSWH8VfVt}phR;Bxq2p&k@p zackAmYCvlswNsP%Y`Oa}LRd>jki_18u7XU*gX9|J24MaNvy1o&s{vs;aUfZfP|rv& zJSD*fYSxPkq=##!&58r00BuP_Nx}Z+Icy`qU)EF zuUHerG>^BpuB9!;uKJ-bYlw=s;y=?y;%^kd{csnCW3yj#so(vySoUJG`VGkV-N=#0 zvQ*5aA4y2QmdKxn}Aj%#ZhfRw(cZ4lkbhxpgtjGD`hlxy4PtQ=mE;wcnU? zS;+6KfaNIOROqmUn&U+s>P!?G#$TPn!|0fbX=o=yIDz`m)~f zwbX=#2t6t2=o_=#jYjqq2ch)bjtUefc_Lh1i9E@f7I~7vYF*{!1##1WBpr5GOk0sx^5eO&ur1^^Q7!_4 z9DdDG%P}xC`&EZ`X7RsXQm>B84pcr@zQ2FXfMUbm6;!EI;_7g3Tl}_JMp(Tl{uGr! zhvX13Kd(M)zECb-$IrrEU(esK6i1G&yHSLZO|7hPgFPrbu54MSv8KBG+jAI zTRM$>=^^P?kDBXqyHEPQLKs+2h=iMw6@eQ-WuoEjh;G_mN*7F&h3F8qv@D0G{(;s# zY>Gx+5oJ5mk5q2{sW3o2lPqYihGQVY!qsI@<&_q@RerR$m*8#UPB=-!q-D13>z+zK zvLc0ECr_?Ff^3^(zroKuIOs6q;K<&?_6?63E1Ry>?ibY%* zzSJm&rP z9-PMKloov(qLmj5zoFon#;W{JJR*M2og{WB;^wA1$@6u--#o}Tq7h(Kh=i=;HVkRX06`%hRW zkbKjgl%K0F4qH7qCx)~ZH^N}5UUBgz=B7l&x3=i&$K5lXZ4JGRWBpd(98ldYe^l<4 z18eNel5y6-E9~Jx6i5BO=C)zDor+k6zI$q0!~J$wF*TL{2Zz_Y##NpU?kX+CxjtAH z88xUl_*{WIv&kCw)=^!o>h|sb94R6Q0Hv{4YaNxBm)HN?C=Xfg`$~yfZ}f0KObmLu zM*s39gHZ#&dz?G`sD7Zeb+-(*i%c{>n3I<`?oc{VWngMh`TdLkrxzIz*vrv>tB3FD zEpfByN&XvAu%^nO^+v|d-xrQLN=%?c8V;ARI$!5^gT1vY{)}xh-dcpyP~{+evHX%t z^B%pH#}{L29d4EKzvBq z&c*$Zl;boE;G}i^I7X2AcbjC#7o5x>Od*I!yy-JXB~f0hBQ>(*{x9O3DB}tr9qsMw z5s6O5lMlMX(+I*-K2XJrR8VfJFu}NJVt>)&k$)0cPFs?u2+71|`Exe`tZy|x=nv&PYZC7B^*;x;UM+gmRvle5b8$6Xy$r$wybzuc7@oAnn%c9&46zX1cc#b| z7%cfVJ733U`N%TA&h_5>Xv5QYN1n-% z7laH3h>QLl zv~FGG0;TVAQgqcpY`k_X86&YD>Ky72$hJrOc=bf(k)}-^7F4-wz05IT4U|gYnb2}S z-m8j`&qg-yjPMLq7gRWF4~p22*Bns`MEdhny0z`DoLAdDxjzAWF$V6y{dJestV9c+ zcO;C{Nv?Ykx_NgsTL<|6#d&N5h>VS;Pdl9W^2A&KtBrx$`2;+SmcGJxIsVgW2ZV4> zkiN3y&`8(Ai@BI!H$3ce6FAc<`-*HL|Al|+6(YZa{|D|X(Y+?Z#pCyrIPa6Micld- z43ReH;wxQ5f3)*GaoELG1Ejlbv)#ab=La>JyL)tn6)!hfC~{X?{H8?(u;4krwtMsq z;%pt5j<(;814L-~oqGhziTlNra3t|iS5Hsyk-GfPTi=)IIzaB}c)mw3iZX&2lnp-Z zDl&FhU3>E}PyzJx{oXs8+amHLh7kOt(Witw;Dg`0N|hc*vgmTL6%=_7S)$#MB3>&? z;h_l+vFkbid-WL{K5=Wcg=QS=A#26N8*w6*-?0EbKvW*(v(b0#-n@4B9|J&*0c!d252wVPdy(sFhhzc% zaGX+_KRfeYxu(CZAy-i2#dr2ola(juAg6&FThmpA)>h`J8x%vY(KqeQbUMYDuPn}(If9$6|y~L2snp{P%EDg z?*}ba^QY+f$O%0DIbPqv_6GO`=c92!047>>7z!ZaMjlhylF#DK(43tXY0(=m)#qtc zo5^&dhyWnE40ii2&5O?u08L@)VzuYXQ*a;C=F~W^u7KdJ+ZF&e?AQ+;UzY{Z&BG<3 zpGb%KMc=fb)z5=7@pyB3dX_yqF1;xNLd03Z?ho124^6!U>8lwcTh)v^Z10WK2K>Ln z&~ZJo3S*kV+MN43H_-MI6E&DzN2SDX?#Fys5y| zOye^#H7P3Sh}e7NN6E`r)R$fc{KvY^>-ytA+7WP!&Yy{yTUc+?tyg&8lmy*v#-%lb!w z&N4D6&1X{@;c57jD@<{8i*0m1S)Kv`IXR?Jf~<{M^;uwr(X_Kua^}v!UFpvnt*+Bv zZCukrZ(c2XqCRBeiHsdTywd#Vk6w9mz#dZS?N}b*3H=aY%$R^!A~~Ce{Z%%zXjx zxg#O&GDF#FO(GRLt05MV7Lq&1ImiY|yz{qv;b}M{_szXPwY6DFv~rWCNeKzqp~Q*H z(iGDL4y6|)vVmLV0jQT!Y6U!Nequojn_rEkurjz7151V^sJ5~|NG{rBU6N<8i3q=ag;Q;SSy)vUU%MN zlDH<|`4v+~M-~a(;pGjmnZN8Cb|%D)Sk2PGouGgR&bFINxl6m!6pk;!tz_W`#wU1q z3s;xYD?pWZe}m2_Aru;kn@UjH^SoOmJ*(e z>eERgmY^lR^n%PMmQ@c0^ELng`=xF1Hc*5l20D(Fg{SZ^r-xkiFsJPhnQKY#CP=$# zgHjL!;tkZv{l7{}`<7PvrQ(0nxj=O2rRYN3CTDYeoiH&!&8KXQZJSlPRF)o=rYmU6 zZn)DG^i3zgJ?O8ZCF>b@)ME{v=wN1we!bAy=dET)0UErrAun32YS?P{FwcHJOdU<-_mv+z5n z4+?d~6lG~lGMl@zf z8DhY7?t|WQr?lUp#P~$g8u##b#&2;c_2Tj>?BY1jPRN!r&S`zwucHGM*z{4qe{UpJ zWsoR=JYN5UITigO`ZEN9GIg~_sRHd4P-1+}0Kd3Y@z&!CP3`^i)brbP5d=B1k)5== zTSe7%(H&=@c>#Ps7%+_ET{8V)-pe!o+sXuaj6|}4PRnaPz`^q$?p<{btW9J8sRlhcSq#5mQ1DC)kvfpWSIqIXWn8)2X_e|KeP93guB zbtk-r{fZ0F=W%f=GGgv;2rk|mWHB77(z(2EMF*{ConO517lrAvNifFIOYo!)Z;m7O zk&TNMD`0R;`)M!?vUtkjKYmEXQ4Y{Zuy}gpp}Eb^EuhldtC3J!+I3;yYZiUzUMEwzHNlMUV21;4{l6L zAhzB~{%BnC4S=$MIk0u4E=UyAaBOkIl!~S@)fl`eVkeD}p>wS5-PFeFdzrd=c^Iph9`y68cy8G*zr02^4M{gkS)tFsa)yX#A z7iP;pDdG#t8tZ+W3sHJ=U$7oEo@G%^+8%ePm7qB6Y|CkGWLYcB3LhpFRz_e@YYL!o zI9+!v^Dw}r7(`AF0@STC*fon*Cx1v{B5ti(xc)&oR`p3<^=ViGAU1p0rIT!A<+s-( zISIiVm4_RR^u#15|-L+UOym~eEma*(n2oA8txt|}(O~*|dyPgmAq)I6*Np;z5F5lTzwL4lK*0wwOyWVhjYZ&9qgL9br z@K~D$jFN222n!bPepv-grFl`jtoT>@@tN@B{QgQ(r?a$RND(7J>`h4SA1y(d=Pm2q z+SC^W20*mgMtebkO($h>6iA>85KBWs5O;lo^dIRgfG+9$X`5(jdVXt3JrSL7eM2xV zLw7R9S7rsgJ-=nP=Hv*Z{?y7wz#YuMdKhr#*1%sb{c-kf5n5|>; zkbK9zE`(+7HlBJ0AIc6b~=Y z_8`DPJUC;BieJr4!Ps@Gzk%M$D+`~mppMgFaysuR#_<+fksv|&gJ1K{79^@Pi=x6a zvgv_;3uDJtqavkya*dAa3s+WLYb;MaLkd8)TBI{3xADX#9}R5nu(B+!1K??T0=Md5 zl!B6Yyk~4WdDltK@bm@(Uw>~-pL+kY=0UuY65bw0#9-G)c}m4Vo{M4LSc$67po6x1py=W?>tRmdo{!XO0k+G{g2qHF^qtie z>Nq;*?He6p{?z_U9L2JBOE%09fA;q`t2fe^l~5!Dqb3I9kB7}}Yc3#Nf(d+UqL+yK z*J#6u59{JzMxWFWE&zXDGs#zki)P@Hs0mKtKbDzOw|8dk>(eae1!K`1j`l zA{>Y=$>*WV#T?{ycT;#&Io!6(TTUKbgZi_L%s%nTvw@NM`2BTFpGGgQjj}qeiG{OM z$iB6WGd$1bJ<%v9z4c+K*8O$=NgwG*7sF&oYZh4I&v&fR_d_ka$1l6cM?!+4(%<+M zX98_{{c6t-uS8I}POmc!ZlCN!uWKJnj!an1G!c}OB0t+6RtXh=t<6tAF?4vh?OyxN@Iml+dD~_mYL=>l=&>zd@vgU zG}PiE#>&*1ReC-*E_?VYhlU=frq)M1tz2q0n*ve3KA zR3QX{?ANgj;py>8p6+gFk~DTz4cz;wtwrp1-)FP8m9{_L?*v!^!VH_~=`SlcGg4f< zkT?H*v@3Cbu11N+ov*$wv{`kA*1cKbHY!NCn9d^teE56a#&|5IV!t|Xr?*@)UGKS5 z371_C3;IRx5bx;|=s_>%{{f|!#z>784a9+DY58ShXQ6g)P_%+%cVPYs=hdtxs5C_V z6@SR!qpq_jgE8bv!)?VtP5TNqt%A^92!>wn4hA72+U-7YCqm|fkbxosZfniTAi}~2 zjl>n{>TrD`DCDUOTp(NdYU7C#RzcP~em9P9%Ka5plH@-f{@!%p&cc{E?+a zmNi=Uo#Mmw$!YAx+zM>5ot1Rs6Ah`G2QL%p^Kc_DCXoazjhGa{=)a|Ll0CV5;^b_& zy6!z1hL-Q0!b6f9oeetAu7iLBV`rj@05eteU{>-df6(Q_QPDA&Ff_R4JQ7-;jDe~l@;_|Ofxu+&)d(H4( zR9}ky3l^d_6T@`Tz4Ka?ozEW10qg12`KWYolf*}Ov(lG{AWtg6oZ!tV(CXFn)|(Ix zJcVS9?jU)KPc#MCXL=K5p0=P(2z+KOGyO;Nhli83^u?HWBIqPo1L;JASX>ilXjCMs z*t5Uvm5FU&N<-3WrA^4;H;CcapPj?Wy7N3PNKSpG46#XJ{JD7rap_n627P-mq-o-g z`sCA01ehW3USl%DBM~9f(~3MzXeWihP_5GU>1syD=U=}5-w6KgUl$w71wjrX7^Uv-sfPn^h2OhF=_~X5KL=k7sBy4B^GV_x%|>6pt9s7_vAeuJ zlmj#hsfz<0r10I1dD1A3`^yB#(NfC5ppF~bQUBHtR8atUuPZ^V2>^8rFz+_2b&g7% z7XV*-@vtw>LQEnNIQbnc9#+5IeoxhLT@vu>)DNUN5rlPj2siv~(ZvwNE;t17WZ`9d zVesK#C5};-HFV`PWu5tzY&Y zFOF{>Qg8&kR_*{`Xa}3QO6lMc$)hR)viaqWji<94ccGEk>eIb;AyXuNY}JYuAMhFk zj~`!n0Ip@M!;|>RDka!&Ww+Bl!*Y#yg?O+dOD;A|C0z6~ISVipbU+@SjO{OCBx~a*$0@AYKl54gU$}wS_d>yv4#5dm>Lz`mXn7rIUBy#lcvi_+8k% z+}<(_!oor7?yEu{e+(uY1onmSG8JT8`6{K>>^K`blnLIxKfKWa%=Q;gN!*(idcMC) ztu}Xo=wq(+g$HYo0n!cJ(PF z>HhjD=1?k%On?fs<-9#O{)-z`{vtMp>>_pibW%0|f;D7dv5SFdbe-?j0m}9f7{#T( z*iugGtNWYOchQ?7f^cJZx17ni`Lf7_@jPb5>iPn&KX_}`4w2hm2!TfKqPb+f8vGZc zk1p44w)q;RsJ<|8v*0nXSnVnBeC+FqtE?nKE)TjV(xX^)+08J2q;mjfn3#ncd=|HP z1@4dE8tEF4Ad=r-#PvQs?y^!3_@56kNW=eK4?wqgKBWYAR>N=nG|q$_4+xhs71Cf| zJ_-s=FE4gmLYWM19Uy_%0eD97R|j!KL&3~lUjFb-?JaLNKsTO&zJTp=tb&ru%hvnY zUj&ezldEWbm$+pqKlL1SZuzOx$8*fpO)AXEKpfanRAo69>Ze`w?5?z|UFU|mfy&&6Z zEH5_MdRXZ!0*o`QnOa@PAe-WUMvJz~bJwj%7XSq~JKaEZs=c($W9k1+JXwTJKK319f6-gKmBSLj%@=jR|?M>87g~4aOfBb7$@% z2pvEdOw`FgJocTU`EKbw9D;bU%0>Su|Kfu*BgFW_)p;5N%Vf3!AhlUMJ|PIT)#Aac zGi2W1i@84@3%Ro9>#%uxx^ZiD@c4!_V>Al1djqu?jQe2kB(d~5O4s1w7+kW&2M|pf zzhEkbI_w|fUMIs!R7z-Nz7%{aNWNU9AGs_k9x5#?sS>*q+Xn_DQVD;Wk@cRu=sU`OVcL9Jl))y8j8mf1{Oj*MmDd_bj%&{*9>% zA+N33TD5LU=dXPPJsnaXAHz!N<~=;p$v{FQU!3F(`(@$Eb54%*AC7O<#&kfTt(mDs z7gSGA2_zP;n;c=*1kgiqV{=MU@^@r{%`pJOz@}%#bJx+}K17mCXs+e_5(ou|9x9_< zd@C1M@xsI>1`*!E*$#$7v8uzX_b+Dsj^kj+Q)S?@@hJ+5vj;-Zb%5EzoE~`DG5o9b)~;7 zp@Wv@*8I5(=^tD6-;4{y02$)Pu=iB8n?PcO-~zO}hfnqwFNfa%F#6YJ&31Q`H8sy; zY{nkUYC4;B!>L=YKD2!d$8}MtI}vynBH{IJlRe z6vn#=4K+S{RHRLiituoJbye%T2hoGP3Ha1Ee~JGG$wNFq)_E*Jf<#np$`{X1nQZPBjr)=PRP_V9 z>1{Hg9$P2%;LzS9xsXs_vm6DJ7tfb8g&~|=#zrOL`-gmIyPN$jO{kk|<=KlQbMQFX zDNem1ir0gk3VnivKsu8ZvYSlbj|z+|!I#p%hkrYcFT@+EgI!MVLgye^csSqdlb*`t zGuJ5fSI_W{K&!yb#&?;EwEFI3IO0y33yb183Zddw51M09?z-5!s^$WNGj}hHdyy`Z z@wjt0FDvh}o)6{aLyM=FL&!Qoo=bO+)^OkM&tLcRL9;egn4XSC0m-blh8OEZt?+d~ zX{~mApxH_#untKqjC^wfct5uWk{kO=4y?^A@I-=l7TsBC&TTHP53K_!+rUDgPyfDF zmO$-6tU;D7pE%=%n}jyeW7Ciikp%F%4ON?LPIDH78s|I>FKMz1F}2yp}AJy)^KHroAr~@ zkm03njhC5u2{5v`m0;W$oP1Fkyp@T#Db)*%CIo#YR}ba4dX!?!f@K2z8R6v1xHx=& zcnmb8DGm;-nIJ`_+xCjb%Kt)*N9qCv3SudiLve3>3sE) z^+AV9yX!!3SifSWUH`-%@4JKPGu5dAifN;a`{QDZZYhZ3w33e67K#&kclId8SfxQ> zgkOf)_+5bf-;(`iEPIgNe+Fj*!S;0d$W_gEtjOB?GvS9pr<%L{#$7H;`89I}_k)32 zW&P{;Rhqvxb!VB)?t9Lyy(wtu`^>vAyFs>~w`sZc)gD6~c$3;2^rxx! zzR9N5n*Y|R(_jwIFg^rE)Bfq-@?0@mV^~){D;Z>t!?ZLny|C#Mr1CSza4R>ii<2Rq zwaI!_QUYvOIEtAldHLV>&sCN!GAwj8@8U(4a2cv7J}%>o}c)`3u`VC&CN5 z4r_-3>a-0koV)L43W|0R%h$l5@$Wm{qSX)r3c=Q?IS7Y)pl!`s>F-f3na%dy)=d!? z8h)utN#6;#CzV>|(=k}@zb6dj@AvBKFJLd_zQH|Z<+Yw%!x%UfRDjq_7mVp`+s$L) zBKRH4TlFOb7=uz<1AWh1F09oVvCbkPx2S6zFbl*xzjA|_m>>ShR8K^q+f}BIZ*y6= z`%mCyY5bd!iLSSH;h)_!5CwCyKTSt-#NVY}W?nI@Lk2<@vllJ*mm#RXJi!1SVrBJt zMM|=E?(wA%fzf;+W4jku)?lYp7cCj6=}0RR`~n)U|B^&n_9iYdd}~wQn*79`$-3w7_o+Yit@oQJ7@lIzj#00Z**1&6H z18Q{akyBpYKT;p}yTWAa{)OYKWp+n3bCJ4nC-q|FHvCL+`RS_;fIEIvarnmOx++1z z1ZlK7sQ=tZ@A$cB^erJ$*Y`d*CJj%RVSxI4mGm9e1bA?Zr&G!|ITe8W+f3lDflO|C zda*kK4K=<;=c}S4RjVi8cv%7@aCQmq>2}kT4eMj`Q9VwQDyc9+H|*}EtGSn8_3j15 zEA<#kBDW2s+!&0s(RQ-6v9L628H~V)2D3-2wG3cc^tla>u zrRks>9~ezox;oN`@W`cp+&;A&e5{nuR-uQ*JcnKRX}IffyzRcdv4I#O+=qG;(r|oMf`1prAjL6ALha@A_0iU@`5$#Gjiu(ts?Y{@J{py~8b; zH84dm*4)eMArSNkaw7o`|1+(_5evoph`z1m#E#-~;6N%?>3-Tx9dy&kxoC8FT_UrFeT#y^+;) zn6|>hWWq3_8NaB3`urxYlhsl9-5Hr1D&7VI1;m!t8QE^PH;$Rb))j$l;|?waUio#_ z#mdDKQIS>8{pLE*Gpz{i10ZL3ScCt~Pj|M}8V_{%9icH=fpV<6ph+juX_l}w z1b)z|$iyOxg(7((rsJ5_>_Ge$kHzbOmT$SBFJp{^#c`qs1F&Yu5f8WQwCf=L@0ksZ z)wT|;{OSYg6E%trfrGR*cloQ9vt{UMXv))v$VZT}gyN!rIjYQW`3Zw$!=ln!VZ%t` zsLSxP2e5tlJr+xsS;Hj0#pe^7Xo(-sJ<~#lF-~>%mj~a3HnC2-v4qwGasu%O5zbhV#|AO5bN9h?%Ikb^&JYHF6b*bsbdj(rx&Xe(pI)#fi&)3ZGd(9p5Bd^>!YG!Ay*23ngm z^&sX_a%%m%tIM7Ljxh29jxgfYNVtbLqux2bwtXw2%@J#8<@z2lx&DbEB^(?v{5Xvj z1{kvPs-NF(MHygnOk>SRM>`*PsHjNcZ11DWxGcQWXiR?=%KGej`^zHZReQ<%EOSM| z&JyX)%YBrL$?g}`S9x#}4AhZwxWzZ$4x~H-+NMW7bP!$i+6IYuG5!yE39JDq5^&TD zjUK{hfCsMw%ttBr6e)hUF%p!(@IkC?LpGSD$=cg7)(=B%_#qx=9u>c`JTC$qjkRP7 zhe*~XG#PR{ma`_W{t-xHulNr2hfU|Yz6~^8r)Lo?#`o6qvk**< zQxbD33a|Rxjo8@%94|EXQA`%GZKpnSHO1er6$O-2k#vmoOJD14dBn+>7JC)?{O%`y zP?ipu)aZqT{hTC+_mc+>Iv*&SfLrG0jGG(n1T9Q?Ke^H9<4uBW-$|#y!X%)a16J3$ zv?cAgd4=y{Tq=?q_9BI0fbV84w1$O_Q zPf254RLgw9aBZcN;1#0>n1*4+450+3qj#h!V+T3wfSKRnAi9r&O;LJ(Q;FVC7AlhSFF0!0`a0T)x81oj$_1p5-Q{*K%~$a|1Ae_SnnwFhG*e< zE>)zo3#IqXL4B$&{G^40dK#ftUDNC7L|IywMFU{Trkgo)7B=>s)_v~h;tNIgZ`BSB z`e%28%%z>c85xj$|F~bYBpQwGLmhe4@Ht8)JYHtmQO|D!qb@$oLXZ0mUbmip5@(cG zIk3<`&_fKr1|tD+)wAkT?d$#NrZpi+*+Jv()_MR;{XajI``fX%zTW0kn8W?YtVri4 zyz_6fp68&?joIzSSmq3+KHbxROm0pzKKF4&v!$w<%pGkJFeiu0q6FH{)p69p{c%Qg zG1RhymkRi(zR`V@4-S7Ep?>NSe633@Y-x%-r|V^5d)_8;0h_Yaa#0zS332v2c$u{| zL~?cXt`#5EZo&%w?CpEkX~`M8-9Co}-PqHIeg|M8QMg_!uG5?fb?}A-&D0x0eCv0U`(l=R{S1azRMmWNw(<6K`>W z*HtpR^|1@ADyJJVJt`E|`K0q4)oJ#I*i7A&5>|Q-{UaoNKk*ejsOJLhe4YaRCqWro z54?HB&oPwqbI-iyyYv-X^e-CdA__!16UA~i3CFKt_wwi+h2Y(-y7tk7yccou4r~!X zM*nPKY598DuhTC?Byw}Nmc38^!rt_!w(`z_YFfee|9{VucT&A!^R0H7PfI#Tos!AI zd~qE#+4*~8X1=hS8S$q{zPMJcQ5Ll~kXdyylv+3~S{K|RNp;*HI!Dn9E;+h#9{sy8 zXIaK@T4-hS@e5wBP*2)++C*+Nnu@OWcQ1)ngB=_s^smeED1Ys9XltQm;YDK`? zr@5?&kB_oSSj(JhHU~}A%d+Hyd7i${YX7cBC4G$YfeHq=og!9#y>0(U?193W&2)dm zS+8RXJgn#2KMXMv0#ukGq`y$AwsS%J-bAjme0e^&~e! zIlQKnpJo$$(+}U!?c$*mZ-yx4eBRc+$j%}I$z|lEIa~ad5w$bNdP^a|TMzp`p3Xa* z>i_@$l|l+3du1zoZz`hf@U}-0lD)^_96~lpNX97=viElEk#Wf0dyivt9M1VZeSX*V zyDoopxvs9`yq?e3W8NRP$K~g%3(Jd2t8PtRc7@90vaaKf5&NzmpLr%PTbdNau&S+f zs{tMmZ;ei#M?`A#6iB|mihzB2a>jx<0=a})bf|TZ{@2ZT_T`pQ-oXaPY zcXFg@mp`XzZE*KTmVrnU%uf>DA8j!51B3K{5#xVJ5J|+(z34Ai0lr~xh(L(;4R1V5 z5bvAd2ds*$@iYAKFP%`ERRr9(4}*#WWpG>TSd)bn%g~6tn^H!2>k0sUwUf@>P+&NH(a}`Om`_?#q!WS)LYy+OxU%;~Jt-;~^i)xpR5J z%}J%KZYWyv6wdkZSK@0k9pt%hvc6##bALPJn}|3GRU^);^jNr{hz!7YE}x68`@B2e zK!wGOq`7}dH;=8aX8c6Q2~R6fb=Xxey-3K1!zi$9(*7*%Oe`Vr2dyTA2dYR!06(C{ zt|LMpEEQ#(K4582tQJ8(8oV9_UU)h1C?zncg+JKl0sg02pj+A0Xs)9HBWJhod$UP- zxwI05r!gpfaKL^pVh(h5AFYIH?lpLn5$CFHX&Q-tw@O_KQ?H{X@@{aK0~hf+i%tG- z=s-1CHG8S89?>>2^V!701f4T5q&?b~Vz!=A`(cKo@Z_FksmR@HwY=5yu$}R#k!NGI zmdYB8V;JY}9;c6OkM7d0hQ=1HIcy#OvOFgC0HvaD#hE&J-LHxtxqS9dOzTsPiHI>^ zEwY)y5-%`sC;@B~Bi(V|TQa5*fFgQ5CHSL%qCF6}-85-QA3w-B4KtB2PhS29rV8Z7 zW(&yXVjY>kcRQx@(FzHDF0^2JQN)twa?pqwrGL+g*x`xX%H_3t;{y^RcS06PSk(>O18NUXPy7n%)$xCGV;WEQ zpDtPe5N#r*1|0=`vC_39{${7NvKJfgooD=a(YwpRFYCjq4wGku5<$rp3bhA@n7^5)J#kV(>m7=e zOR~=OP5)tUOT%;yh5N7)6yi>R>Br5L%2gYI02E~X||=@?A5M?wgSn~ApCTi|n(Q8*Xx%T`mdFCZKafh$Od z1DltyMl$Y`;ck2Q_;IfF;f`R;ZoLFoW`2&w*H4Y?r+e!7Z)VyRl6SA1uS+)c*Fi|& zBQ7t8R}2ePCGLW@JHMXBoHX6Eq*8ff^S1q>SS+V~y53L-^PQW-LGxF`OLubs+n}me zs1N^ss4O1f>d|e_2u}7}qSeHC&odoO(u^nb)b{44%H4(vbG6$h1I)N(>kpNcl{L8G z(U~i3%vOv7E1VU5o^3^f(`Vn&T8w?I^~IGlISgUk%ZM_?<$Ni!JYzpPP*k9h;`=5h zz}r|LWJ~(16s+XsZE_^~X(gJx(iG^)yq8n^GhN2q5cK(mUY_1bNlcqa_}fa~^;W8z z$ogu$tF%~UhYKWE(05@oU3PbQvn83y$sL^8iKG_ zx2-vd+3mGQc#SAEASMzR@B4b)G&Gx~F8_(Ta=CFc{L=3h^9Dm-TB&daS;>v{u$Tku z%QQi8f55Fh>|`lEsY*^-TCwg0?X9OK!`X$7ps=5TS#>h?XY_F$?ONfWwgCMzpcU$? zcceox`QpprnK8jnq%GtQc!W0xJx#G18+%_553c5qj$5mR%EdtnfyCMM%3rDT7Z+l0 z&AX6hT<)Fr{!yAT9Bze>UPc>~+>?+Of^|1pqs1I>d$&cB;#vhpJO|zGDl}9xQ@AT8 z0j(`sIwA5E*zWuGC{XDH{a1}Zs}()6huuRTcS`;BM(Wb zWuYG@p4s9PY)^dKHak(a$4f-KYQJtKLI><3^h&in(b>-G`boR`dlPL&ya+aL`_4uE zC?2fbb!7Ty;PmDf(h5GKt`nw^Vg;e;|kMicVVN)Zmfok5;>o@*qJ z^DVgm#-ze%PJk$|qq{s9pOek_{?`VI@mk=d{B84z*I4XR0>MA2QrH`Y8*ethM@ZHf z9?VhD6KIT;xmT@phS^fUBom6w=j4Aq>6GY;G08CQPHB96U5rVlY_IgHSQzCa{gGYR zaW!mVeOBFt{d(BhJP`;{Xh@;1mIW0kdaVJlz~E#JDu2JgFiZ2U?vX$Pak;?SlWe?3pfnID#C|#A zDyzL(wXQ)E7uixj-yce#e;Ltl3p&|o)>0j|Nr|z_gEd9O+x2%Xm)m0YI8tC<4?LK9 zol|}YEpA~zCO$LK5}8U+K5`S`!LR7CCUTwkgh#!|vUo_zaYBcLyB59dBldeP>vcu_ zyl4^V`amzc-4^Lcb=`@8&(C}J*w3ABJ|kOp$?@6x9;c*YGR}dy$D(AVQSM`TP;dFW zUZ;pOhKIpo*_LTJXkP5Yn93%$u+&f1v zZH7)D!{Rgp82M*?f`%MS=_lVMs}2f42NQPDkocl(dTqb4d1J#eMpJ&2vn(SH$?~ySryyUJ;@2G;-DKKh47Ld>r~Ep8wP)d9U?~mt2G`gMzuS$^NOy{MpM3>ZWqo zlRzaQ!W=B}RY2~tDw{t`h$KW>>$=;2dES3;)3J~*-Ey^{y5qYw^F6z2ho=w?>jXpL zQ)}1tN4w7nU0u{N!w&-V{Lgo&z|#~xef=bHX_o*-cKt{T=Nal(#84*Q#(iE*CNoke zl&?*Oe0s3d@>Uq?unzwmnReFk`VOF>An}t+j`~vIc7SG6h{_(Qj-tiSZ+|{5wsevz ze>I%|Gf=6PtQ9kFDBEJYu8>~Wj(NT7b^T9PiZf*q7Xs-fd3uq%7EDz4(ohehOi@%2 zn5^sMyt}n)x}nJF9ij1Eb5{qGB@PVYc+7m!bDrv8L)WC;9wK~Q9}bz#P8c5p(5PQ3Mc6BT-1vEcwDA-iU^Es zr90S9lkh9N`mWQTpP&GygZarxeuaBG<5YRQ8Z@r2*qZSSFBANz&JcI18K0`h{?M(T zCk;p1ZS59M2^W9{xYzrLuKg#}b!qdzM#Y+6m=A8xxdWZGiHqOP=PuZ++=81P7UlBQ zUnc5})jlt^oXE1YYi?uZ6Gwfyst)irz3vU{LG~rcj(5ys-U);}KtTNruM5!7tK*W+ zBVZd2Iw|Pe3rcccxS0lZ%A*hsiha>On!n%zw1Y|MuUTxO1B@ClQ%`$wsx8_f0w(o*~;rWeHKd!Lq~ z!*pk`8xB+-v<1K?n%8Y}EydZmBBP=rjO109J-dGqWmp_h_T(HI`l9X^HG1PuO$B2V z?}_~NJ-tA_civj~)U{UnrvF#34h;N%uYiDPXY+{=)t{D!W!zNrQh0HX`b}i8WT1`y zCC>Uwi9+I$%JAbJy>X6zB7+^1T{mr+2|z{4^}w@vZWf=1;2!Ao;{MreJ|_eXGP?q& z-~YeA%Z)7jEsKc!d-;9tTbOM)&tgI_EhUBW#(5yFyQvYKm+gS{QQ)fL%yiD}nleZd zxvqSEaRRj^@c_SYPtRrrWRO`1uEV&$8NRE7Cyf^9kLC?^w zy_B6cMUg8A#tE|sR(F;q^c=PMt`t(z72D1xtDp~-+e~5W4~yyp{sx}n$smsg?oAtc zUD1rqj4P1-0606yI5h5B6^fYobU<0R*r>!R#T61hIN^0o8O$wo?3kMR#hj86C9skg z24$0N4NeAHQcY&ojlHCU6*GnSbn_N>l&RuK4fe@x(DApAD_TEZRM%G!Ot7Z=Xgr%P zY+k$0MXt40wshJvX5<5t!Z=lmuyVtoGl-O@{> zzn5uO`qGQ}xg}|kBegbe)RLr9%AOh+*YV*_FN8BaLMw@X;=E`# zRmcE>mUf^%FB@>hz7vPb)drPa(sA}Nw=fp-c3Fn+%uYpenj_X#%DzMb2^X(D+~}pH zuZVZC4Dt`R1T>asbvbcS$=C2;)V_WKyKL7vK)5#KT}1oiknH*XQI5*_YE+hbx=b2@ zg|TdN4VcMt>$#`FiOq$8~>HH1^HE;x8J|~-g`T@K+LAU5t8Kdy@?Z)bDz5R)C)| zRrlJA{n_Z)&{q0=aF~LkLhb(s?%S)V{ZD66(L6SaPvD)33qOGh(f#>;EulHR^7#T3 z#Xt;hrEsvJJMwS^2aX+63E{FeV-%x0K$(QRhXLMKNx)*Gm&9RHa>2zWllRKuCct{b`vFmJb~ zCThB2hV_>eLa>=$R<>-9r}fW&K19jZ8~xA2VAq^tTBJcITs$DawC@n2K2yEIHl#f* zy-`WEt`}*N)5K}xEBmMk;y%vtADbED>{7i!RYYykSvUujG=k590jsD=VVA7VV9w0L zlu>wkfGjoRF>l%warLr@{M=h4d(v^|Wxe%M-yZwH<=?n=-ffc(^{COM(mT#k%O*>> z!L#Yv$CTR&GXhk8vjS_787?T)w)(S|9m(k#)GJxtAKOZG-Gi@jA2Z2p*gumTw(UCX z*u0z%IIT?7utXmsJ92B8Bh0of#WJ*j#NsStn$_l$EQfr6W3u)Wf+ucYmWbNZHmEyh z$6+i}V%#lF7b_*#l9cn^oFJh*z_RK1`l>imKwd$3CEzNx`9EgtJUuwpE@m?=KR>Br zMD54LHkiOoo{)tY>S}i%nDm*vto_rmH&y}kq_Y={d>V`mmy1t6KF1^{|Cgudf3Rj= zRUBn~@zG_^*RQGbSIUGUZNtG}F#wewP1KK*i?%8*S9*D?qIb}R3=~7X>x#QrRS#wa&T-UC?)Z3mMtll zo3UUU7e4l9j0`s7y`#hWWvMzjNw&L}mhdiLy5YokVXIX`OD7uGq^HY`I_Wy83YORy zX69c-Wf4OniZ#0(*^;J~Y?zU9G|-sYsJi8+crQzi$qF$yKGP5BDMdG+_nm?HltnK- zQI4grVcpsLda&niB3Y`CZts-d9Rmm{B}5vUyi1dq@x={?9ute1kdzm&djV|%rPnj~ zYy5OAjikse3Hdz-c`b#?h}@yMhW({4EX!IrPE*g#OT59Usg8g%tdfT3J%NUrkZyVU zXMpkzcFwW6+8)+kD}Q~q+o7ahj-DcMb67mUgPysXV6db*Eq={^ajw#M$>?(#vs&Xz z+^61$%w5Q?hh-L(rPT7MxGyUT1>-jj>}V}7=Sck18}AIMU7Wd`U|=vMC^ldXS(q78 zZ-O~;-PyDTcs-Hr3s)d-r^2vwn%%EeZ>eqDWSD)Z)!HHoTr^0KeMsC{B&U)WgrK)o zFqS9GhcUQfZHq~zsT5OT%cGZZ{aKP~j1J1HZLu=kgX=0ZH5h zn0T2osoQ5>Y~j=5t9hr91|SY#={a>N!M_sEvV}Q=WD22I?z2~5SgHvMB+TL*OFM7d zMBt`z^{8g0!q&7W<}e35>lY_8Zn)^1uAD5lr^mYvIv^NV*YdR(q*ME!I8yU$^6P>3 zs)9J%)~`=9{NKJ-c&^|n9F}Z8^C>5X5!Hks&+6sHTsmJ9$-{os)+VShV-x@V!_RPT2|!{)=j@-F;9$Hivwmc;y<}XGYhuOWJWiSB~5p%%j0) zpL-{#O*5tU7jTf_@%{lrKMD;9IHN*F3uvR&TNt))Jbp%3T%E7@w^JatWVJU7bOkMo zX!|SA)Vn?qD%69e3KRZS0iIvWF}gRyzmd0J4`qn)os*(#0ld%%(8<&Oa)MF=_*Y|# z4w#4c5364mnPHq4^lng`DRC3T>AvX1rh+OyIElB$w7!oyRydMBgI!9BT2l6Gx_Gz1 z&IfO-Vt z(Jv243|gbpb&V?gSTE?x{6imHgFI{n9CN^C1u%G6a=2%QXZai;M*s�=3&U(i$FS zVbmHvbQOH@&q<28sVYjbUYAC$1+HRYI)dE){ED&xyX2+G)Ni?1_RuG{}Hj`6}cS{`gsySPh@+Lzmx)PN!?XLJG9&DL&$n$^J^3 zF{SS6B(`iDT5=lUJ0ba=^YCKJ270xB10&IXO+jg(?<(Cn&HH9VvTKv~*!~T!PGkos zmel#3s(`UCrHVJQM@@Ng4|T56B>t4qpYJ6f$CZP;?|KwaK>o}`X4EPF{&YQJwY46Y zU(9yuG&WKDhg40b9QTcU}mv55GXaA$BA$|*NLOJ@w-Cvj~Tl{?>L(YJM{B9AH z6KWJuoUPCYj7jq_V&DHZW9cONU+{u9RuDHCD$RYMz7`k0ukj?Y%9TT_O( zo@ZXgGI-5tiB^WL;~u<@V)>>Y{?em&RvFtFds-zXQZVM`k=37KRIjIS&Qkc;)BbXN zu)IOqP(pYwABzN(dJzHnvW$j;Cq)QHavlS%jkEfSDv!e*EBfx2eCt(^-=!f zCjd70+3cs3ls-$IWt90mP%q%r)jkr)WnrSazmJ`61=Ba;IG67zP$tbzyi3|p6CQ7M zfs!DS`@Z9>xj&r~c0HF@SDzz<`&4>WR4MR8Z41466~Hi?6cSX*bX3IL^)Z#}{^RA_ zCrXqs?({|l_}WYdE4pPBV)pDNUpy~Dol zX+Cz0VXP3X8rGRt2IZiBPcX}IWepeCOuCMP0m~Ci+hw$w?vuD)sa@az>q2u+78&1v z@X+?Z%)+dW+`JYL4kyJYeB`ec&dvW|GcD0IdDTk`#&|@MVwR>LHg6=l&jfap%F(II z1-MIY&{rs^vz5N*%#iQ;F;eb(2Z4Y?R+ib{LeeflRHiN6qsK*ojzlXYA4PrY+U6e9m()g1hihciddN9p`YFusKRY~&hPs3rHX}dIqKFDL@xTIt;MgK@eB}#3k+ZUK z{8(H0*k+8=a5Ckjh<(Sju++N}tJV&^>8Qc@D{Wx)vd7_z)|&QY`TR2gD9}xcwY;1m z`(|OuY>=(fQM+ukW9FT7&PMwvUeFFI$%9IdD9?K6MPYZAS6) zQWbDo&=~j+xIsS%^W7Y`gG29yc!Q)R-`59~r&at-==}$fs*JY&;ZL^nb@&Ex^LX9Q z2~Qmqkn7A$?akV8)aDk-+TEyWS}%{6zL-L}G|3E&z5;C~|M&W+6);VCzK{_7^{e>) zsXfm{qasfKQsOR7(%PXXB7>kI%9C2_R8UV%93hrc!{JC#nL5{z`kX(I%Qzv{*Z{>N+@s zf7kfIp6ezaT9qO0vvR|PwcG@^e`Mzc!xdy&_hRnS&~28w?Xs^G zGt3GUfz_NVi|X$&Ba=bWtt@FR-BEsweSi-)0;H&51Pa>3-2pK4z zpWAO3^!?Y$Oin;*yMKzoln6?!bl6faqR#3`WrTiy9ygzT1rUVwdnp4ulW!YIE5Ve) z71H+nV4K3wknX72syu>j8caQ>7P(OZ^#JcLPX)4+=gj*-3f0-(PhM^2}xFX*S6O|0Mtg|ED<8W`!B6!F~iL^XKo-g!%-j zGO_rE3b%@i%J6Rwo53Yk(juijX7B_{WH5UVA!A)bvyZJte%(l#m5x|=iM$z5FP-gx z-n^fRP)1kXK|i8_vW0fb~^Z7rFWoE&^mezFoU9c9lB#p~)-IkAN%yi0)KVGVTUc8YFZ=atMayDdfwMR0LYgJoLxCOmCJJl+kqxko@3@l7cEfbjrr;#azog#sHhQvV(B0Z{tNqxRN^W%4 z@%lTx42_6bcc)Za_x@r5la2|^7P3cu|GTn@ zaF)KQtvlLBjoMp29&$*VEvQ*MeH;y!7W|Q%WY}KK%deb)Ay~ zn$y!7%#R4U?}LCa0X2Sn$IkleirzJ$$IeOYU(vjT&G^u8OUo#oiLDy1gF1xNot{Fy zFGf&Yq3ht^#a*q-cLP;Jzp!Ecop1J90c^F1osFP93LfMMccTY*uwaNTdTp2u zz&mT9C%2P|qxWW;l?YolhkgBzTW%T~OJ7f=Q}JQVi~-B12gA&~04R&faffSpU2Ep9 zU)0a(YdrYrj${Yj)h}+&JICx$m@yuzKO|*H8Yttk}D+P$&}|8cIewBa+}6 zpeIU8yV`*6bo$#%M=LQGCxc4+6u{i`4(xS8HI{}o>^$+uV=!`Gf2gcsih} zBh}V149gEA9-kA=cqMYNy#VqwxupI&fjB_B4FYx<5GvoziM^%^u4i-vPvL9#9Pz>R zVP^qGw<}aVjq&eB9+0vP@y1g;*G|*z=#hKO&WPj`D7+8WKIRmwExaWC2vz~mEk1i% zL%_KP<9(B_lXrbunI%aei}~Xhd-2D{Gq9>DrYJTjwaxw`2&9auHKLznZ7@wD{nOxX#3NBA(tQtsyNoxHltPL*sWhsoLOo-Q3@^TX*N+Aa(=<>N) z#J7jt=TdF1^dDEIP3pttzP239KEC!fs(G!$^YKPJ%0iAqFYk+~A7+PE?wpIoD#{ED z&vLN6ub~GsbCxTH^U$+L$vlz`GKup|3a|e2rI>?~%$zQ$w_eD`JtthUx_7=-&IZgT z`NO5wtGI#Aa%5E~C1s5N<4Dc>2G^dPfv9YK0afQaSPZ0pkC z)}op^LjE9;#uYMN& zxdWQ&%CTp*eaCN=G)Nf!9iravvhpKjr`LN8Lui(3h8kqXxydJWf0Y zN5=u9fEh4PqW$!VIMe}~S^_5K=jCYC#6e8n$aBI~~E`{Oazo+jN@(mF;}>-_C0SjpES zP57esF`=BJdIq4bbZIvwX6KiVz;@NiJ2J>v%gz7*e-Yb zTEObC?NU>k} zz_Ln-_25?3>HVRbV|Q81YtxRd88usB7ro3{CBC-gMFUB)CkqU>ARnuM%++%ndD!b* z3W)wL(_63lV()HOngitH`Oa`#nrwVRo!#^+fn95yz-?%)@oyN=!6fX;OB8 zM4WmA2;1fj?$J{KRwzVYA>%x>)>2UEOZ+#C^e_Ywcg^F&zo za>gAghr_^pnH3YTVfr*dF_O;yNBFi)kSO&(;l1{Y9Z0674kTmi;mv7VakCZ7e9b_< zMZL1L(Hn=dgko%`9SI||&qAfdxYgw%Dt-A9a%9LW4c%l;TUs?BsW6C(%It=q`j0GN zXL6bGyjlw7Ve^+=T5p}NATi1b1_)Rx?v!Btz3BJLsp7PidvLj#rgd-IDzpXmOd`Cq z+#f9xh6Y`Fnm_Q8sI6u4I4bk2==T2l)XOm3C4R)a3<204A>yKA*|7>ynYf^EHD)rC zK4oJW2Zx~*|{f@C;7wsfnht zQV>9VE)p=32O|?U*)du?rMk5750^IzZamm?ubXIg9SVd*6CP#7V># z{biIfXXERadV*#Yr&3f3K1&MZ{^};1?$sbi0)Ax8ycn47iRau+oemkbd!CKmyz#Ws zl#RCcOSH`^C1G|pqvxrvUgBV5efwQ!uJud@w!j4$EX7l$vxXQnG{`dLY%D0 z{K63T;MDcx8ds-ymq&M>qFe~N;Izx_<;%x0Ub4rY|9Wmw&!?>Rc{_{1yy;U+J4?Bg zeKwE6q+A+sidWIiHfbp6E}e6eU#e73z* zlxip(ZR@a1oW~8{^IwKY9Qg5GZo>{(DXf?sSFs4HuChb$%<LF5AeGdjd>T(-<=w@A&)aJk!cDJZ& zV)FA14_guJ(`7G-3O_OBD3WrGxS`Bsa4Ct68|l)Y#VF?_y`xKH2-T6kR~BY}eq!9n zhx;1&pK7S;Hg^ItsXIIJo$j5oyj!bFVe?VSIjz&n?bFN6)w-h*Nb(A-bh7VvW2 z9?R^TpR?RM<-AudF=?JaWtms0ddkSWFu3`a1kMC~e?u@{jq`;m)XnTP;B_+A~&%sTKsOiTXa8swj4Tc`QAT2~i-27!_*O1+R;h8U+3|n$>9q$+9 zZ(YW@iqdIdhY(oZK4m`K(l|V`mq#x8+Hw@)F8F)xUvnx4T$aPmAF>tZ1*bSfC|n)& z`maN(AH0ayYHEO6VE-OeHNla|=rIZB{eEXtF1UdEzBZ}FRW`-WEQEAqxs;(8dL&&O zfT5~2O__sI!?Bkv8U9WTy8*`TqG^kL_TIi2jQ7N(X6DcnsgpjY45;guo?toBZq7{Z zGTG|3P?2&|SrHW%-LhAw_iLms&IMI8NkxPgVY%5QIz>V-NCJ8~wQqLn-QoZh+Trev zLh~26+_)B3X1rzSg|hVinKXM)F(Af7g^ z)O^F&xphgxQ~oT;_G7^SLEhJ2o_9H;V&ku7qjym@J8vY~AoWajPwMpZfni9sU#F_Q zz_LykCf1o<@iRgEq7#riKbpVDN%nXm63M|j2P z{b}C#mMj2UmF$Wmtq1}Yh=aLl5&w012}6_EH-aC0_Of4@`>o!XWj36Xhj>R-BfP`h zZEYS?{h46EXMzDBSO&ALPaH~-RQCP>rrPm@C^RiXQH~+N zKO`#-?AfFqb`Vd26YbBL45!J6sB!+M*h}+xf4XaOoy#zE+WzrGNKx zlMUoy;azY#``-7!?H{dE0Sk<1J#?eV8SbWT^7)!LS@caNhO4dB+vE^hg;l?#| zvNhvq!1?&$1%n$K%zja%a0!(ca zmXh_^dk_>dYbf`;FNZ|-#^vaTbcy+IOZG6|L~ZUEr1R<#T%pw+sZ{~Foyjfi?wx9Y z@C}Ya31}Bfq)bfr^upzv^SG3m2kUuO=?nyTT~7<`ip&gu>)S6J7)hc>Xt>~X*4HOb zuFh|=G>|w-HNi_k{Hm?jl+lKh^hDUVCb>tku?7|{R{Gkxq>|3s>TzGErJ=MyXvE$x z=9+=Yx1GawUAyI~Ve^sYZ6EvX+V{kNioAzzscSuaaX3ldV;K96U5z)5ll&#wT~!qy znOCxx3xN{V^Qy?tIRVF2PtxN)Xo6FHFVi!-y{$fLXbZNu9=xXtBtawwbKy(5SOzw# zT*!~4Ig6+EX*jwsru*_YNoa}kN)^U}2&QMfOUlD?Kj_a-(<0Z?KHg%4Un+X?k!oVv zuvYBh-*r-vy7i3U9K(YB&Ta2&llp+fb{}2nzsl3)yEb{?)h3?uWIx#g@i%`Sp;0)t zFqw0&(}n$K3?yI%e5xUyAu{FzbJovc!~zmTiiTX3jaPh zUv$5Pbm-){1RQZ(P9ApyXT`LtN~~c|{iojjCUzLr*tTU89r0EGagdn6koK8Qf5;~m zcgjWWvpq|D-;Wr6)ee=%MBo`3H#aqrEyv+@$Ze5)KlFKgH$z{^ALZel2asD$TmNT) zoBEH6>N$-DT?WMIBei+jFH{p{eBQet<_2i;xJ6^XreJ7G?qVrOOQ0XVUWNHFe`|vy z6Kl@*WY_0XmIo@uwoW*`a^lt2a-0@I~zJbpSy@?y2xq1ky8dQD*I>Fx&&6T9_Y*OukF7YGT`6m z!+2TPUdE-o!Qnp5w}#c z)9|`3q^|myG-ZVjn_KHYR1Wmp+c)3_7?P0!uX*)1cdCvKc?f(?JMOBV6++F-WB1qS zy`_#$c|)IvM)YVl?T4~4)E7_9%tRg)8aN+}O%IQJAkOgpK#DjVUEW1GvnH;m&Np^c zThwc0>nyLXbD=R7zV}oA6DXvuZ5)7MqM~>Ulxe`0O#v7X&f#ZcN3W0*NQmrptPq~r zt#AcLeA3Kcg8Of>Cmm2yr_Mk{M*Wn)oZ{wfcTL24vSol^{EYjevVlPXc; z;~L@D*faP!Y~AA9N?uOa6y5{~X=JL!eK04F`O_^j4Re8~kaYbJo}d-&vfv`Hg<;C{ zFKSP8S2LBW?(XNwe|V4b_RWhhnF-jhxPUOoWO?on>CO>!sb{cfOiJ|mo$AD*OL3+cKdU?rN#R_hDC+TITXH!lV3)(`(Li> z{5%}|v^CEzDorUJT$gC-LDOd(&Bia8h+V6?{zc*E6U;lEAi z+$f{gIJ9znz=FjJ$SG^(m`%NM^oyDYx1o=BZ*WogfVAnD1_@_Ud7Ox=4A$$(kq+57}2$sjgV!{bLb`q+bETtjZwY)5*+Y zeWu>sR2regV(~2NwcGytAfoQX8#kg@UnxD)V~zvXcq1Z6JPYp?)ad*C;@GH|lZA;D z^h2s&V}v@tpyZPE(o+cvOg(M-u@$r%T9IuTIvV_^kKw8Wb1(doN1Mw7C#U z&FOoX_d1%-jw7Y-=)z>!A9o_7lxbwD$yV%tctb!=VG`>!zn0y!`N6fp-B%K~Skr3qjzRb@i}%|kXvvAS%wvvUn~Jlos>WPj8#r{GE|MYKaFu@Q3Ve=r;-39VtSHC1k$Te$4tXu8_s`)!NIo#>`1 zC*ICwKGWNTNs|G$1+;1+&*sv(5}*7S&zHJ7C)84q>s*;D5+?+P^0$+-+rbPgu(f1y ztG}cqt>j}FQ0v_hH!lc4PQnasL2cfR;cD@3b(KB;96lS{vj-LTc5Wzfu~9&kPtP}K zT>{=ils`91GQ2EpWMV5JvxUfYp8BON*ra*bvy3_Aim673)oVz~+U#huQKjCDGK(8^ zYPL*ZXUsCfRR3GKdd(8an&=h-d|es-uJyup8kh|VkM(*cS{5*-awx`&8^gYmaQ)+yk`rpasoje zZOVRDt#hSY`Qx&RlD0}U9#cfw-=#~EOhW$Zh-*`_b1b+Fk(qvEQ7lp84oMIJ6&M#N zSo<0|`*vXygc_Ge6vq{7TN0_P5>ACjSK}zR&A&vzxLjfC&>-A%S^CDlJ3_B9U}3&y zKVLgAV@Vin-p?bjx9kp=4xIh)WAb6GhkK&J`Gqx=K3ff=G88SM;=7sWI`ZVsPmrse zpHiAbVEBnTEe7WD-3Au&Az147>-qnyU`&oaVAK>5Pl$al+=T*GWL`lg*pzcW#rE`Y zG?{dp+;TquHdrSXrHOzUJ*r7GZthY3Q?> z9UzNa$sq8+j?dNfn%LTOuk)M-=x4xe(zxI>9qV8n3;0^o)#6M(fqeRmIazr0(r_viRmtf4EhA^z9#SH$hxL%4<`n@b$?Z`~>`T^I+wC zrL6ycj^=6GvlCn7ePuIvX}gF=2Q6or%fGcn{Gn3Wq-|a<5>145$V*?4rvbJkzb$as zs&iAQnj*2wIV)@U)3iPM<(2uv7hfV|r?-Ww#+D2CKN)6_mX^|G4}FGOq_#DK8=I8? z?c|iEWjK-_bfJ6^->m;-Qzmt$wz6k;d;8b$i`zFJN5E+oCL*3)gw5_-hJ zd%VR>u3;{E7kf~wE`jgjrmKfBC2$Ge{Ji_r^YtxL`V7U>eZ|mI8l-~!C!NP!4}15y z<{JmR=Tkw^O8)AY9dWvuHNop=nI{{e9u%Jum%(*>^zb@#Wr(p!Kwjm8(Dw2EUkZxL zL$xs1>6jfQkxOhf|Ir#+>cQ;{8KKr>3+Zm{xG3Yo784Zmz_!@j)}AY(KXW+&sebs^ z9pX9}?3W+rmHxK>@;{rbU zK)21KVr@0KSF8vGZ!?p3icF0_RR44I&jjp8YFija(*IXnEavp32FKA%O+b{qq7EjVWg1B8gNDP`Aia%Ftug;xzh9mj|NKf(pq$6aV&mv!7(^RB~*J z=8bPTYU4ih>E6iJ2{L6#a7ZCa895()GPE)BzCsmb$({PaK4&Ep#)+S116$79%oH=Z zzw~}3yraA0z%_Z7eR491J!3aUGW4=>(OJ1X>E~+!ye!81u|BkPM@tvYe`efjJHd+p zk{5T8n>IPOe(CCzRZbl2?kbF~5by>PdA@t(SeevhKTi zA1(`@)i?Fh#4kXdps?N_mu@FqOCDfG0u&f;Go-{KpYvOJakN`BK@)(VVIjN)_jmhf zaqUIC*knrY!;Y`E{c)GP(CSbHoCWkG{?`%VKJ22DR`oD!9x;%byhaw7tQmX2Bf$7O zzfF}pX;Hu&(Q`JJ3Kp`vz9~o$X!Hr}A~|Mx%g53aA)CX?1autCNNn;0l2Y9cWTOLe{AaO^NUXB^TC4tQ6Dy z9K!ebWj;RA&Ks!-uutGI(690GjCpBqVF=5KQ4I5&g#8F>1QuD^5!mcTTHCDwDiQDM zZ>b~?oF;`RiD<8anebI)@5guuO3pmff|v7AJni)*?=P!lvV|yGmVkHP>(;BKp&2~* zPyL+MRiWi6>mE?b3L~o@4hOmKhheL-4JMzfIK`0g)y~)?HHfJ*PIdJpWDp39R#DoM7lAcv@&&SYAqH<;&83Xc?Xz`XHZ& z>^t#h?b$^^w8r^$KHuKtbZJ&~I*)u8Ia6ESv1>vs_(BsFLqKGk+l zD{gqT`Ze%WKJFk$2uQZ~7JqO%NH>h&d?yMcB{=sg>+vD>#2R}TW1=pw`(ymi`G_us zKe{8hW=DDKmMeCna{F@O@Ro2&bTWvB^97hY*UK(foHx22G2O&=$^IRsqf7jvE!zuk zfP&anL9uXd;UF0A@^5b#EeiF>fct3n>^Hj8r21}``}qu&{Mn4WxqKr*!m~C__WrX0 z^`oi!VfNt{rX*}|AHR>u856->*1yf2T~5}dof{>3SMBrl?1`m;&k3-M&e4n+oODyV z?X6>4!!1`)&gc7k*m?PU2pY@G_{MT3&XhmlUEnVJxJk6L--lGU+E0&~7k-3Y5%_&e z+j-~TifdLse8-Axb@*JH^5~xXvn1-ahbGGriBF{D8Z|HQXO4+$Hg^AyrLT^P^83D~ zq`MoWTRMgiP=*u)ksOe2h7L)Q4<#K#4~T$BcXtjjba$tew3NP&-`~5|UHXs9HP5{# z_SyT~bJGZ;uY2FDx;LvyCRlJLu+eLf;S@!M3%~9qRk0B%j0l>;%*RYtidg*i%4G%s zMw4`+2eGtuAPU-8((Awo#pkao>=uP7YKWGFv-pi|+85>YhsB0>X<>8PJi1&vygQfH zxOc)~kPM9$6>*b*Pw;gnn`lD)2%0p+=hjzh77TKwx|6=;M5|GJaGt6TT5B(<;d_Vw z>S0`2M?ydOxshfwf`U8dp7HV3I4@Z(*RbT4of`T^JU_MiH2wo4usJr(a=rewK$G$> z6;vONT6Idr(lgigE@mkNKA2c@rhtjfEZUOa0VK@b!dw4i#DHG5<b!-jkGf4-J4Y zIO7Q}R+260m)1iS1z4#yfddlxhZv%CQHw^qICF9~$i_7`ywg=|qXW*4@z?zx;;!(U zMgq?J(c2z>OM+sPq@xx7{H{NOw6(?=6>f-VXLb_3+$;&bMu9^ATk4)iH zha44Gw=z&iH zfXSBQ4!=SK29g7bF+yZy6f+|OM^LtY)Gr#w3v(a1`7P=C&;DCz7*Fl=!BMYsjwI%r z-JM}{67$^TrAhk1!4jPDMDAO^&HVe6ffBcMpUU_45$!0;4Fi?%_++n{b3igM02{8U zR1DcY-eouScL|rSMa4jkV@fEQvBYA#a|;q1kqB~)5J{u@F-J?J+l+Fy4%yT)?d(2w zppMo?Qst~7_H)-F7Qb%Z_lS1_T-OyX#ozVdn_;b;KS3-1R}L?d-{nhGUKY8mv%z?U z*7i4f$LTi?(L;5Q2s$4A;0OQNd(#s|Z(5Y0pOe0kTy$gBcwh*L|25ip_G>QeSxG%8 z|B2C5Mrv4u6I_+)`QJC1HA!jY(b*VroHZciWP@b7$beqUnnt>MBURCy?c*?|wbrUG z0Cs=+!^nvsymq^K%j6Gks9+lTD2k=-rN1+DsEhp!J z#ihvL$mV4Ra1?5*hGh1@%_5Le>S?MLuMdnu4})}Pj$*}mU!*zeBKZkA*S>1I=#)zM zrbkxl4zd$;zJK=Pr7ruU9gQlv67C)D5P)Y&hOVvpXI=xC#5X>0iZ)OHn0UfIFV`+VZmiJn zSCl6p(>S* zP7M&yHAifC3Vq2ea1j%()(i$D8{HBeK3#4~UO?6bGSQ+_2IRYnxG_r>ccLm4laV<9 zd$Tpkyo*S*B4~Ufo@qrq0|Hy_`hC|@gv~o(uw7L%iLJ*w(A>O*lT%-@Ug5ZsK-%Q= zwwYa1Xx?)oOaFkYh5-?vS7A8>qxPStxQNKou{E{2wSb3qnsNbOk_xCw`y&T1TEt(h znu7d8j~eHiKl&sqR)0}^Zh7X*i6FW@{~h%lqDgkA7=~<|^Zh$a3c$#B#dFo^b=h*D z!OJ2eA>hI_RZlCN0)(nfdztA(B z?Ez`X{od?lwQi0}$4lVOwpQ{m?BH_g?qd4kt}jX`1^4a+#scu_-rog8=O35Ke4W9& z;dc)-7gEilwPW*Z?Y+B;1XjW{TBl4Kcv`2sT?x76u3yfw;d}L$wN@9_*?QvW$2D8ohV$D4;8g8yDAN73-#)lQkONch2;{+?ek6RgKegOHsQYdPjWx5g9oI z!m_oaBTfkr(mH&Pc50K+!FvVkF#3L*^e>DxdY!*H@h|?9;64qvhrL>)9)L~RKQ+Dmu0Q9LE z9roV}MZmVE)hihCRYQjgdadRx8V-!!NA0XtFXBs@3=qBN1Xut&QFX~|b6ZX&!2}j+ zjfSyetRSY=Re8X+JA%@5Rj*qQe%3TD`m-e3+DnZ*T14K3G3-&jA~$*>uQf#WF}@`8 ze~gKLprLgI)czqW^%eNy-rnjPU^mz%)UY)p5?QhQq=J6Lhx)fp9_qd(lN$SAyxDV2 z0UcMvJ3FS7jc20UiL!j95qAf0ija=lu?%E1q^Vx5SqHH#c=0$SWGX487C%1bC)j;E zHu`Iz@MBU2i+F9E7Qo8E5Qsz9^k(tSeu=TQ%@w#9iss45HgL?_2L@ENStNgs;l_5e zYJb){ACK2(o&Oa76aA ztu-(S;+YsXhFD+G)1E1EU~BMWG`l*7UC!$-*f&GLSTgj|6UcM)z?dt4Vhn@zFCI@f zm=aJIS6dGGdLv~HGU{WG>fmqDfn@NQ_l4@i7E_3z!wB`Snod*sD)so_- zBYVyJ8t`)Tp3t|M5tZ>eIq>N!hi?H6|M*fOyM!k|F?gpu?0izt?mC+#VC_dw86(0s=ZO zGVYigiyE6`+ed%;k!xeb8V&u4(j+`N+no5r*zzO}h$D9}!8B-v+wL5#`q31ogo!B~ zXZ)4N&tEA1;cYWN2`b*WxZf-Z??cNHUg%X(*UNZ$M%rq|RQW6@H@w|DDUEJ(bBkM? z6?AWoNq+FV>nnEC)VN9DPPtp_H|z)u$~5B(?f>em-$xjoVOS={GdM+Fa2*lNq=4jnk zbn@4JVo&Xwek}|@Tmbex7TlE7vQo6b{lc;wY;~#AV-hGZtwN z^x)b7;J-MM*>-_+76T?QD#wKb+G72L+H?}|DgqAhICdDuj=SnyBGQ@&<_RE~>w)%y zx20lBIQd59|IEj*$iNxSyW?S9(_F)LXvMBt^gBUH4mS)x0w|)O@ig&>7=&fw7=z8q zsei6k`x-O(7%?{6A|bFi4A&!TJ4hTm8<^$wi%is-(4qf4fv{=P;XOdhiZ_z+Rs5G> zvS4l_urRmzUQNm$9C)02VDJs^ln07m9*8w#|HK{y2Ej<A|PDqlv$n672tbCQ67g_t;iC2^dlM{o~WHOtZzaXa%H5M7Zzf z0XA761D`YaWV20yRFLeAwuqL=IxjjFKLpi|n&IxGY*-KT_7=MSK{)X6EjX}D`73ROm*rAB|qdip8^H^{OIk(riN!@%O!b_gi_~O_yi&hP2#ofRTVMY zGi6y#IR+kqghWmAQ@%K%mPAFcp4iGkuInVj*`l1M+h)?u*M$h6#{T_<3C|3>#!fpc z^VmHFdGMNNev9n?v3r$=nj-`1>z0LE;aQKZ8tp!1@vfvVf7f%_sQdZxW&sb-RY8KKenqmZ#AXl;@Vmv#i%UR-L4NhU&F1j3K8W-z*S;%?g=2VcSjz<@; zJta!n9v*y)eDMfhJId92WJ3)mw?pehe=Lna?O?`sH^cFz#73D9sf_$4d7E$gmkRZl zlJ-txM{uHxN#^tST$}Y7zmLz|ap-uDsk(xrNu!6@{un2od{K}w9qvHX;~9Okdc#E zGPfGOSOOcd1_>^3(89<6O*`8TK>-X+Pl)cl{1kzaZBt8FsuWQ;TQ++%OH?JJO!W zt`rjv`{CZg4The_>(h&JEdk=*-)Jhvo!p%LlCx@!tuC!GP{9u}^vlb=)$Q#uH?52K zg-x#hv3Ndn>86Q1s=3G!z`uRBHc%`B8NbgfW;a*&wMwK#+2R5qC}-hi*QIi}l<-vl z3^?-aL&p9{Ir|qFt!ZnNzUJ{J8DaqC_YI7uBk*IY9Y=g`!FDv~?M2oL`Ug7M(wDsF zWNDrl3X(`=^gnJJ>tDY84mj%kEB1-&%ip7Tzts;IU0B#f?&)<7W25Dlqw3QT<0UW$ zwv6~vZ&Cc&=8heakG{|EKeHd#n%gy+jSy#ompz*#rjjx-2#1~H6N+tLt?z7Vom#*qXs+4_qv@k*%|S-Fb7SLk&8N*I@||WM&}P@K!5|ZGElpC8>0wiZAJUO3tuYC0ICZ@Y&H9L zrH>^4jqKO>%seCw4#j+>{%+p>y|cY?zTP*TK>4Y}p#)?Y6ZfG?gi5bEYU2Fo$ERg~s#Vk5^ok=G}_ z5A9wLP8xCd>C`tuQa^k5tBF;2n#3Ac0Oo`+cupj5E^i%~-uyKF4=4{jf1g7yVzd z6hH=z(^Kz|DI=(lygj^aV$UEMn?I*0Q8>YVzgMDg;^I9MdG+102!dgV3tRD^rB8o9 zZamW_56-_{??j`gP&&^I>~nl#-C#lmCf+gtx5ggnIy>Y21FkzCr4l{k#_1XMYn2Cz zB{JLmyi)Zm$4HUnRX^+70(}3|qGv2bns2rjzc+0a9>4B)&ipo*us(zr5&rRXf|#Q` z+`~s-%EKcADMAN;LMJdo(e3ql-yc-Mc<;nv@@7|M3xihcI&k5}h8-v3_Qu__jjj_p z0u~&)&ftfRIJw(CSLxtFwJ$;p?^LC=_sVfZ1bX_FSzWU4rM?>B4@);86zZghegHV0 z!!vKeg(I7)`62oE=nhRRAa^KM_w0FpzAne0Gj_wN`mCzB>6sPsxlgej3RG<(jA=A! z(~---kqd5B(N$-9ox~dQz-SLOqC8vVL9ErgkO~a}PF1PqfQ*2SDa>^f<_bLrAXeQB z&ve=YLcgw>J+k+KELtzW$1Wu)ZjzauIaxKjzpQtvM1_yiq?Pu^EN#KmGm9vhL<9A) zsNKjuAdyN=SLDc-_ysUVr$|1D`?b=0`Yauu*5yx^4DP7`EwP4+G1WCBmiDs4OLOfM z%^acOlL|xtqK+Z(78Kv;{yJaPoSZ`XI7R3~g@%!zadZ6uegw*!t-;q4a7MhWJaT6jNgSm3 zcr?HQ*pnH5%4-2KN%5so&bT-?hnlom*Q7I(tnJt=JRl{uiIY{*Gi)a-4*)o5y$#gc zSUD;@v$@gvXM6mqd}Th~|1lQj1Mz<%pZ1>zU%3ECs@`kVP>%LjCyLBp)UKB-U$$QU z)pmKL3fcU3zogbN;OT;#ib{f5Nm6)Xh?6kp7x1RMNS1krhjnW0wBrmdL5qoA&hpE? z%ZG@n1JUf}`VqQ$s`SMKn+^OsxQyH)g3SNnTzUkOv$%5%rx4IAf5)Y-&AUraec|Dx zMT9{3|5}JyF-lmN-z|>4d39WMu=sMz_HR}06KfD?m2$3O+gV(qzV4OxykD`t$kM)f z)BLDPZq}rngg{o}ThZPvqyPG6fmtNxsS*}M2bY>zAp*H?KyBhJZ9qKIgAkHMvPf^@ zhrm-X91=C?R(h)O3yDTjQ3Ywl7Wnw35I_2zT6|Q>Ok)))yT9sNP83f%!0g0Iu)Kev zsq$9N{nRaueOT~M2DeB34hi{Hk9)FsuFuzI@<*i+eM;TDS1+kA%)Mz&5Nr z0H%WlsLV7PUJJiZNSY1IU4$Og@c_V0EjY=FRyIFfk|2tCmsK{pOVCY~93Kj7==|_S*mB`7dm(GbZLF?q72!No zuGUaBXvJ)c<|O@nV6COnqDmx6K;YxVrge7xCsJ^auMJ=*JA`bxWWd6j_G&vpNMS?KJaB#VkDu~pe)QB#* zF$BUf1gat8TeJVduWCDAKJ9)u;}GjT#ij3%GF;EJ$V`bLxSICEiBeX)lo5blv)>T* zX;uu4)BkCfvcR}WzgS21)%<5^s5praSaG*XrmN_se3+G}-NA*?;l)U!~E(oW2^KPCl z7h;{ix!P&aCI$qWXE|OPLvq(yauPeV0!^h6H=Z6AZE2HGDhd71kaW}io@3Ct25Pg0 z+22pOoHsXael@vP6@wYA$Tkn3FnJcB@y6BjNA&&;k(+y2M3$q1X={5|SQx?2SdMl9 zx?GUx@a03e0U_rPF*=!-LRa~W{khSBRo@;tNae z(~IC99m%-WuiIn~;NLSL+78zom8+TivCHagmrD4w6k4&jmyaFh;WFN1qh%g@r@|6? zXrh@c40^0uZwP<&y?)s)z?-%&@iEvTw)8TKoL5X2R|+fQQKq3NV%t*o$BuBtn6sM~ zG?@->*$S65`uKc7Qu27et11^gRE}pB(*1BFW7mkWiVCQ;w&L6^?EB}S* z^$-NqiZ$Iyq<6QRy42XMq~5<&Mp~BA?}_mK(cACIyQN+H5sC-2ppBX(nQ^@lOyVF` zBXO#}e@I4EAx-SH>9UvDsH1UPxLV-%!(ld#DBS&&h_p)j@7<5O@i2?9fDRT^w_>$o zNWMXZn)t90+@V~do(I+YQZCjsNk*=1cNYDPamIui^(|?H8haWWL%mMTCx;Y(W+@e`&M^tW)`C zgxw4-TB2x{wCWrh&Kx=p5OFbj>@)fCCw@@idrHw9xC>8}%(b+Mf1VWea5T5kQyi&K zjS9RyySh6*X1EZN+Ob|wAOdfBr7w1_`|K)P+is$T2IqB$*_MkOA!_Te5cJzNp7$P{F zb0J_-1Y@LHw@xHdC(#$wA34-@G?<1?ueh#+g3`Yx)8^w znIFh~wLV>lHPjct|9v=1Tw7{xqtA}Az<*uuz#ht9MSbEXGIP>*RznH5z`v_5wHqEUb)6+oy(uco%4F_zZp3L8Xyir7>E|%qUft%=NRaK z5XpB9@L!>M(F_!Cv(ebf_FUY^mVQ^Qv?&{(2FA2KF%-D7pO#@Xx7PFmhSi1C>FHab3OrV0a!!JIME)HTcduHnWtp&lsIZu`_qB2VM0KmW7bbBkaK5zqZ0?(Cio29n?DhF@ zw@}=T&o^zk%+x!(%~=HVpTpcXwPw@(-6(Uy>)*{yb={7QR86()1R~N4+uO}i3YtW> zHH>dA_TWluS%&#C*850Y|I{ZWZf zd|EO6{lbXTr7iI=cM641=AF@@uYw2(?`h7?iBBjHx9+qOF%>Kpa>g>XRG6 zrEQC*X@GLF36kx33@^A9a0YWX$}1KpOdr)xt{;A#cPv6U<|7rfLRtva=3rngs z&B<1loT`FJ-+h@5aL^X`F=Yr@86$AgRwJh!y3A*{t7xl?uNFq9euTePA5$&Bv+^KS zAKPQI=hWv)c0_f`Gho-}dRH+MRIqZ{$nY7(DE6o6mOVQYP?z=pa8?IV=2K?9j~^}T zb(niTh(TJ6cJ2u%LRvB=%&8+JQTve`9{*V^Hk3L@Tp3XW#fL#FV}VscNVjUr3v_V; zT2(BZEh~@hNE%14VcY4Lt+>&O6X4w5Hby5hO60dg2mE9YJk==0^G963>C2IV^)0Wy z&wda*5<8~5asx=jZu6Ib#Bo?J*r*4@AlxeY7<99l5+L~WpHD*LVmuT1QkrV2h6=;p zoK~Do*nKe|Fk)mn+a8Jv3V+gsmSIXtHx2*^3n=fwfWITKe9hO1l@~uxq#EAQq`1>? zV)^+71tgfKh2B!leSA7);Uy{lD7NQuezky76z(5sdy$=Cy1Vj7I~0HeL}CFjd# zQ~&%9DRwgt3XS%l<2z9y$~G+8ocNl{8VaYU{-w>O*VIA1ala)#ee}G={{~&Mk*5&yMh;03MuC{m7~RtYO0|{cS1v>n$lDDM%-Z<~0>)DJcmlFIc(UAXEu{Wjk}W6)Et4ey|}qQBUwtg3Q|8n?@PeB3%(;CZ)fn|B3}a`hUWVnx8pK9nTzrVIfY zEBQt8C`@Hntw2~wXL0KlFEvaj1YzE1Eittzy6KkwtC);U5x`p_{2m*XBJDYG(^m!}Ez2{q1rhJ0As8&LZMQDq^`52E5k z_yM6k6!P5F-aHu(k50oSf<&o`&P%4cDBgAeOOUQE+t^@#v5IlaW*f&_AQz1nq+@&9 z!`Ad?XM1f)^UJ3!t@epm3Pq}hbPC6=j3QedrB_T=pRZ2c5YSRs zu0jX=rPB}2Cr)Ze$9FPZggW}mxr`HM+O=_vD4tBQ0PA^@!$Oyn7AQ@Gbd1~XV)Td|weu$d=X2e8)J0B8zQc(*Z<;D|MFKJ*@V|m-r!{r#QJZ%T3k^v?C(sPH z{!i!ChlnuEQU^}%EJHO@y=2N#)ri%p5{D5`9W6zn8cYRXvNKqd65`;#;c$a+1D?O~ z(5VvGZ(|)ptq5Ifua9Nao(?_5^rhXtM=DjcF^%l98O#$W)xs;g7In*`Dvfxhst7P! z|A=2?My#MmR^rXIc>bx}w+)42T~{C0zEK!Tqh4si#Z-?}=jupeo@N}r*VKNs2vdx^ zy?t^i(wOa%9RqbhS~i>haPz>7>P{`pBbu(QvkJ@wPqsPodGPfcN5S%I8&S4+H1p0V zbzGjwdJ{lN_Cgc?yw81vwI6k_z zcw1_K-w9l zuAJZ2Wq2CI7>!`^+k|448{x133>0o*NdcUSmt5`rFf4PXseFdJQReq->L1f`RpnZ4 zF()6f`v?N9WYHjQp+PI*ney0i7_QV$%H{bVFuPgYI(~@+)1rZ|tL5UlKT_OZe>JE` z97-G9K^A!Ekg7M38Ui^fF_8^Ej8#IP!MsuRvykmjaMLUE95nhn+lF3GwqGq4h$g^_ zeVY_p<#~Mb0fi6KSz3YU4vy~)n)m^80#E_C~g7UB>tm`BEo}Q)HwT5Vfr6 z3-v|<6;AFpP*{D_m21qyij33>VzNVX>W*}ua$c&lN`Z|R^)>;~UA)N{ckPq+p1Y~O zp?A0c4bC2Lk)uWS z%4>leR>}wMPhU@xH?Z`nM6Zx*rH7qE*AT;OCGSYozm zv!BMz2aW`{z0!Y4vHhx{DSY2>=oFp2yu@$FQ;ngd0RU5qHzS`qH5sYm^#VEcIyB6oL6@nrq zEtd#5G#-{iNY~EbolS{;s2ElM_A?BQp&mkw457ZONg>`54p}4gmu@C{V6dCv(NlE$ zF43dm5^m5IkAL;i>GaW)NZPY?^WA5u3Q1x z9R5kUPbINL`hDJFYet1Ap6K@5d`VMVOTRy!;|QS6Y`ubFX~o}oSbU9k6&NSlOZymX z9qQg5H~n?LzxsI&?azK&p=s;-fF0Y%|GN>vnESW)r7bt*zUK#`as2Ci{U4H@E#1p_ zylm0z0NzFTfj(MPrO9Q%7R~+>xh&PdVh^1DK7X+wFA;z3vn@^oz-GzLs_v6fhM%Jx zYR%d0CX8`cUNw!S=-TAXwTxR!!;~V%BtPF2YtNrGR97O9Rz6s(guEF6QN^Rg?~b0^ zG_sz6%QVZa2KTKN_O1H%3lP?Yi{y*goQAl4hWLF3gab?S=nHQ^ek~jv zJ{LsoNALRMcj`KeJn9?)Jd3Uo%2Ojvt8gN?{B_ad8$q?J@_};G(w?vHEoVy4uIW4- zL}@A96~1zd52f-X<>c}w4N^whvduB6??)A0o`l~+vC*2!zyXA0azOfN4AV?|Rx}%_ z!9k4NS&aL>81sGM%Xi>Qmdk({?1cC9_;)7wKA=NyV}(!GDoOojG5zu}{qP0!^$1xL z#+w^&!O4^EAMa`@-w3x;?2UmVuYbJOA$O zD6kCx&v(7;G56UR(}sZWy17{=YZS+55HGCHc2DP{)AwvAnnqSV`v6)7M* zSVOaq&p6%-c-Yv(E|2KwuO5E)R>~OJKLFDkFx{YDaG%t9Uw`{BgS?gLcRxjw41-Be68spRu&Gb*NIy#b77Ze(2PcHeD5w`h;IZm=J?gB z^1Wlu9;r?qB#yDg?h|1%D*fQo3!R$Wt(iKhnOZjQJrm8>;~u2s1vZ8+Vyi5i)CqBB zXcucF_R18iH;5C6nR@xDkmepm!GRgQ^gH?gba+V&JZW#PeHWLf6)KlC%NNc3q(??$ znLWC(W4}iNT^M^F9tGp$zC~FrT<(q@5$dH`Wr#waY4Zs;_o|5e_8?IQ_C|E3AjTZ( zW9zB?=h@?zYs0kj4W9wXAp=GqCm{MYV)hc@-@$jY@NKGBt_Uwb5dYqVhMz5Jgx>c6L=lAQXD_cX`O&BC&{eVOxvP@#r(8G7!w=|zo z=Ky{Z00#<$gR+57#x2BkOl0HD!vNNDwSV--9bweYUd7yHaQw1b+VmG>!7F*@K$As0lO_nvps{*;{=2p!e1>==+32i$5}^hnHZMh!zjo?Hni1EaG0t}GAH zCOvcPz!vuzL@GwY3SHJ>8$Je0IJ34A<`bnPBvCfFPW?J%%D_s(*vh!EeL;o+$RU_Z zI4j|L`D__4YRJEcFhvS8#Wb)p!4$_L=Z9W5M#u&cakOWuh>ycZiG3Qp7h;M~-wy9; zc(zE*9NEqseN#;?Hv12#F-IcU6u-Uak(}Ay_x-?WLdYAU5sv4W1zE;^TQRRav`c?- zxN{!DxWa+%F-d*KS6NLAv&un@h%Lf;Slo82PSiZV8Rjve6#08c_TumA>PD``zZ?4> zAIIvC+8U|`opjyjV?b~jk%{pi(?fnT{jI!?D>&iAs70oT?WcD7qtn-MU85%qW94OJ zD(ZNS0XAfu_W*R0W%gTd*Gd&O(<#fYAFP{mTC>a;FTOyt1~kIi?q> zp^Zk+Zq(11n>8drlyAyu6qcj{LIem7K$v^fBqwd=dBU=T;^7MaR;WM(1q=cPeXwB7 zwBS!lp$?K+)ueCz8@_HnU@NihlYYKD+Qf$m6gw7VI(ICaR+?z_4{^F3zu*3CQxxd6 zn6MDD6FOw`cA2pUC;^?&y8dIJq@jh8HfzYs+l3Z?dcCDoy=bwoQ`@j;3YiTU1Q{>g zcW4j;vl>!x4{a5iv@U`6vp0!;wcLgxyh(MsWh(eDjmr}FQ;n6wJS$W{AE4^c+XxNf zDw_IR(!Bmp(-vKpA{Ih+Bp4wM?Fwvg)`SG=Kc~&Q?fVcN?j281;eRVf4U^LR#gX^hXgM84CjYE9loFd5 zMeR&etL@&695U1Qe*`-J&(_u23+TMdzYX_Zlg)r^A zJ!ZuJ?=tOQ*K_(^qgd6n2!oD6>C(~_+*4*W1~6;;s zF1Zg_h!*L?#zhrMb;vrltF>hoL@CKSJlmVl`!4;L-`gRpGNpGb3;2Q**o~;I2&i?> zna$K$cg3_e-+cOVlyEzPg%G(5dfb~z>%Jq4zN3P5>sLj(I(+j6_OQRmP08xxcFa7} z@^1i6K-d>9+xNSO5jdfUcP(Rv##e)K5*4e3$ijasrf`W;9R=1AQvYMB82?TiS6&Vb3&X$+p*sCT6;ML|r$~at zqi*Ij@y0>@(!pmTPo^*8y?iz&eqw*Gg)FYvaL~gbM7Yne9!&{-?p+VB``n*FozGl( zt6o+2H?`TYK0KLnv_bLJD54-C8D=T1A;jlx1?N1w!k7@k8($OrR)zyzHGoe?=3(IF zQ6m$5>1F`H42^&(G{S?@7#bHpK@x!Yy!fSPF_L{TrVyvFmZ-`-U++!PYRtGzkE7VM zx!5=TQsPg3?W&*;EZJiun!AyT45V#O$pJdN)LL3S*ONQ`4}dkXOzzZE@JKz8D2 z$1DW;_!9$~do+0vnmkBNVWc<9YN~~IFjnR4>-cH4c%&NeC7Su)1;lX*J<62G%3hN? z4V} zXOW8Prkiyj^z>WYKkI@{kPPiNcQEXDyDBGfJPU~;B>Lx_Rn(C?mynf}EvSJS3b;P= z-Rdd;vFwLmS70_aSJkT)n<^LSUK}P0{aH;Oe|*n0nmgnRTs*n_{n7=JxAMdCoui>D zo3D!{Tt&f;cmOV->3zL1Nr!D)_~K534egU^`JP=-?h}J)o%=JoA@cdgP`=lNvk|mm zp94Dx34eoJ>F~*i-`n(RL$SP<3Twc5W@Wwo|INQ?oc+v<`=5^Co}#vm&o?VIQvYNm zh984CSXL8rm2iYsEcUw!8{CpT$&5XdIboy@RT~fvjF_iR5*FI^ih&|XIbkHN zWJe8#wG+)mA*_&Osf!B?d&4h;{6PV#+ReOa;jC{9n)ugqEM-Q46856OWzY0m^WO0a zIj|ocKrdt7hG=o25fkTEI*q%$H_)W+7O@;pn3}WaM3ackd0?t4erTgGh z_p|Q!yoLI*#WgE7GSaDFO5<7YNLaqEaZSRwlSOA|Xf+`fZDEqD9AdPK(8s4omyQ6# zZ02N3r6^uAE5o9FV043U9u4(kmPc6OUy%2;X}WdDCba86eloaG~~$Bv`yvQvC2hgt4DRVbW>ZoGnf0&t`FJQSRuR>_U? zZ{$0C{acWw6_y0pm4BM)_@w4bGAI#GMt1D$FIn9Td#p)%JX9FqRn41+wyVW5<{lg2 z{wvM@nqBJ%T7dX| zFS4Z$)xuP28P%(4w6t4@K9LL4n3k$q{MI8gjmAmVTlL;0=Y7wTA(QBtqXOa#F>Ltt zHoPQjw_y_ODV0#l5bhM|CqKaVLTr+ zWA`kBxsIky?YS~{TE6b!TORTsK8zLVj z?R}A|N~KnSM>Ky4bC(jRWsJ~{2Q1H0XiJz5XjKNYw1-J_}7!80UnT*K{I@nkRB}i4W(Nne9<+f z`E82EkrBWJ^eYduA+`@?9B3)5g@#8_gv&lq4PQo?}e-qCUB|2 zY}5KjqACP18N7K$K@y4z6&MZNGY){}MCcz#f9dm&+EW?$=;IMGvLQF#G-9xU>37OYL3fr*Z>1N3yeCmFop6G;L@kYD@sr z*}J5k<8qQqzY+a4UQ*oY)RENAtMD6^Mc|0OaDL)TV zT1%-eME9kNUcC-=pg>z>%UgKMd&*iYpLi#Q=e;Dh^P@KO{W`O~eW}sAZhe;&zHY}J!%-j3MgnuF z@0@xNa+uY*m~yN>5H;{LasqQ#+ow!H7>ztW0e*E3Ni-1G;!0-C9wS5UGNE`T_z5!T zkpZk+P!>(ALWEKA*ASHw0}Iwf3)UP9*_``{c6!%E8c*qi8pDYaikUtR;~~+@L~6W5 zg9pDtje!JYchmfv_|?xwd2H_mgc!aEQs9!kP}wNg=UzNIF>{Hai_q38*0$v#-}4h( z!1Rru?5ZBq1ZQiK@B%7=P{ziTzR&ng);jHXlNt43Ec=pqL z>LgD<+|}+nz~1TtasL=R_rJRs+rShjkBTsKl&cKq>?^PBIoe3_3&_fvg&4nB4ZRTq zX8>u}{Lz~|OQ8yk#v%Q}h;oF*?%Rko##$IK-_e0(D0YJ|Zw~#NHdp$urVLkq*8|U) zpI&oY+}~d%HasKmaugQ+=`FnDX{K9TJbUzC?MF&hH_H5KtOdV_A(hT)aOZ0HtIAi; zleH`6qO2~Q*r&@7?@nerTg~5={xUW`UUN$Mr2KqHwjP`uP^>7L1&pdE8{3Jr#$!t2 z^6stU4YUIyapuk9*VKR;+zfm}WK^wVf{UoqPp_!<`OKt8o#J`+1ZeF8AYmti9reZp ze!O%dyIi$mP993Y`&_Vk#z7c{U$6K)*7)t9Hg;0*aeaq8;2r`*h3GEw{w)fPW?z8q*_$9#VM%4(8=)rP!#xL z6dbj=%-5vhr^^$zb2v_Apw4C(#lD;={YkUfYT?AJ@1)OqDnA7|q{{Ozzh*1wzHo$a5d?`woJ|Vg&VY>FB!X+=zz^VY|iT9Nn#jIbbJWp?c=$IeN zV#D*F@72Py34s8V?I+9Aob6r@7KB@i+%Av|m49LwhYEteQkb8RK;+daT!xUT1Xo-*<6>%+=znhqi3gzE=o%&qFw(F^d z?8Ue!+-WV670cBGlP!5OY(!u|8#xClYJLoQnDpW@He|Gg*$(-tb#KjtXl>bZz8WM~ zq~W0jdegBAU;zmWrl?tAWGc=AwVFSngtRi z1Fga)O56l4ReVIbgzF%yP=FL#x5mFpf$ne)LZ1;s(i)1>h*hK)zd*h?w38kS2F$^( zt^-fJJXJd_S)rAo)+ls=T$KXJhalqvTRJ;ac9qOdoK;QR)^1H4y&c*GMhNTl3ojSr z8yAa)=zf1%Vun2dJJH$yI$|i&r1Dk%Tjp0^*AnP?0Z0vOxu`yK;)@1-l3+oAkDhx- zZ#U#+z^umwiYy(0YKIJ0t%N*|yj$)=t+D_F0hb<8;o*1gFX=nGq zxznmO(-&%lD?U#vA;_43VjvUvQdx9%-%=@YE6n`d;n87HPcs6jVGa{M?FVebL4aVN zKXT0iXoG3T$vQScZF26}BepL}-ol1xhkSV&ry)U~fF$E0H0@lw(U>XdSkJYK1_Os0 z(}A|ww<4;81RWYzqp6xQC+tYm$+lAgg;=t(DZl!*GUKI7B=nnR+Wdog z1mk}A;`W<==Q2;TVu{}TcTGL8fr>f=zb)jUEBj%rkF-0d{{Ox8(=>T1M(VkMfO&<0 zh&)9|CF^BjMc>!;xK?;?})Q#?BSWq%s28i+3+4tZC_aF!-ae`9{Go1J+;lf!-f z`!#YU>mW()YL^gdQohA~*ZIUjryj|#7s*Gg#SKnJi<4!U^k$k+6I!o=13~zGco-!= zBZwp*Md^xHu9Ic6)}_nV5h};CZ0H=8C5}S1^*?-bWw6_D(V42j)~b|2i`YnooI&;c z#*YXoFM)+bUXh=4rC~n@e$G$|Q7QwFW5+h8w>4_ibAPL95O>6MMrIB>mqtp=qw9VRPIsOdET5_~5Rd3TNg%|Hq$NWb85+82;O9Yh7179WmXWSv8e z040mkwG`A}VCL88WLt}=yx38?#bdZS0;o_I;>%pGR2X+6`7%)jzy3z`G==;yZTX|i zG~z9^Pz9%8&F!^D^7G{L4FhfqIJgCn*cQju-|DPbGCW4!jGwct5J)px#x?Lindb=lfmx$-iU>A~T-~XeU$f9ea ztp^v-UA_Prn-4Z{$WyE4ObGo>OOj6>Ub>5XC)g1Q&ZL9q|L6T9BaW=6eP@QfZ0^L# zh0U_I01JmI9Nv739S^IPC*p`(XL;NCA7^UpY~3RD)>ywWh%lb2K%MSOo#2;-Wk<^* zcEn&v(ztVak$b@Rw``sYRl0*l@L{9&rmfW$PIbXA@``*3VU$&@}*)qJD~J1lmWy2dcqSK)YyrTZoAcxq1}tJ{%6@s!dz*%v$l7EFMoW;2`FUHR_kB zSbb1oQRd5dR*`@S+ZDX^B=-F3+VQyn9M#(2ZKX|M6Gb!cnI%^#-l=9)|0;pPg)$!! zxD$i?0gCaVvjkh;RP=Y>WCO2Im#e{7-dk&2s1XR1b1}G5%hO;`W!#xT-qs*3fX3cd zbHmAuRN>TH!4$PGA32dy6OXu!gDFB&VDBZ!6aMjL zKqEs(!lFM+$P~-gN#hFXyMX-h-{LcCAt$chG}xYv;XjwC5+~VnLNSNdRy7wLxY+l; zZ*hE488W3Bkuu-HT&RzKp~HrgwpEh0{S56@@Api4bdGE>4H~G5nmsaK+7l}QVKMHv zkf30&Hb3cjav~7x{~|;?1ji|L1p9G6&KVqczWnM}#=4OCL31J4-Svd&?6qtt8h7bZ)E+EGm*-s4*SrsT%qcK_9Go3OXES#CL7dBd#s>FSW-FP^S&VK|nEMy$Y#Rf@V^+nc|=z$B!T#hKOHzWpH8163$ygGX|be z>n-s^jfUMPjm+w_VaeCa_cJqdNBi*{aE5wgOu8iRe zUDPJ`8;K-ez)6w?^UBa}@xSd z1dSw4?z*kqyjqzoT?%F5s2?45)W|p+YVZfBfR( zfE^n}f_S^GAp<6jR&0Ebbd_OFL7;v;Zm_O&L*l-M5Hv(fS?CroK`+sesZ}+i!8PY+ zWbUmicWIyDo_M!;cOre{e-r9g)}6tG`^N;$!&ZNNe;F}|FU2|F6%bFXO;-Fah*`K| zONI?Mz)bRU+#bXMUuztvb4eDb!8uYm^S%3De+4I{BpI0QJ1-`MZsMCRbwd5%o_V*e zOo@tW+5GZ^c`6XFI;Oyah^lphs!jdX;HOxXt`TK|IXfn;K^sDyQdTy3#n#VD5am(S;aYbqp6BhKUg`Fq_`&4#ON?s$h0H@uOs1(M{g{&C8<@otJ?tK{p) zTy=)kU+YuG4+2HV9pEr&@+iA?yPNR*KPMH;ry}YMaddcL_~BIYMIkI>kOOC|Hr|6; zsDln-*ntqZsDeo`81a@T zHr!mW)HfU;D4dCU`D{EjMsseydig-B<|Iw8>k+(H^Br zl{;0j;fX`~SYXaeiN{Nr77uC}^JW;4(?~}x#W0No>!GG)9pK2xHGU#m#^D@BEYjc{ z%LTEUJ58I^vg(^o;)9(Zc(y}@2j?UEHHOGke!*yI>3i73+K(kc~xHagdhZ;8!V zwT)}EDw>~wzgo9Qtb`V7P^vT3Lo1DA=A^PDWQUVqKT&@D1RUip2bG#afHn?I8aYin zX#n8ICQupRFr-GmNMXVJ0m{1ta#8w463|p?GUG~mr!EbeA+~A2pE=Ak#b(=D-^2Zd zzhC1*&fFVqU|QeN-TZKL*8OT5^P8sQ{f`vs#np*ipsEmDo|t)+#L!Y+xcJUyC0hbA zp0{>9fI8fuis{nCQk{;#Pcs%N)f%BV$U)cqy^likdx7f7szn119RE1eYOETeyo8Yp zovKTRy9~weSTSiS2h`j0F=t#eN1oKmryLfEXGj5I3fxy#2aD3}TE{Q1RU9`s@$VlTVBd9d`khD}PenhzVTx&LF7}L%kCQ$@pB3F&WPKNjNW;Kh zP_ku!4F*RAJ133@G;GSzYH}Fe{#!`5;sSgOW|}QiY5U`96LnJSUQ_N2BBBrsX5t+7 zvPa007*3s!Qnrw0)>J87Sehu(mK|KJ&ciUh$*{Xgw@pnX#30u!tH~O#iC0qVtj=sM zZ@fvbbUuhWNMeA48)+0MQwtMQG7i5FOoDO0k@l9RRLUahQ2Thhh9&`-XMi64E~5NP zV(`)$X0vbrtjRwa#d;v_j)YY@?(*xD&Wo4jEv2~A}x32XlzNmJvlkjWJ?o`1aNKN zUqu1~jUuosCB)m~%@`WTF=a^KcQ069P3;c`nS75>-(eTubjVo4xBOmI7vJ*PUN-c6 zQ~DKBq3_f9xdsjfu1Ia~CD12^+fPI-IP%MMiU3nY)HFTk!_!hY>SgP+e&hizPS`IH8#%91mk=SST&4h97j>+^1gJ~EJB%945l2q0>Ug= zA0ng!^~)rn^Mjpse?0lv@@d8qGnGLeDSOVKowy%c@oKDb+brOZlAEeyff2u4GwLAX zmeskzUSQFSscGcz2I#p(kLLnE&Ma?bQ{z5(Pa$O2A9R~BB=nX;H4y64PB}oTnghmu}GxRbod}@`L zfQo|66f$d) zcxNaJf{d95;2g!@%oa3rT0+?EFRyK0OZ*P@pRch*)uHefM;`*Hjy3xF54E~z?X3eEF0a#{|Q;U)=Hl6$XL&roM2VSC|*eMMf{87be zsS8Mtlh|4d8-F7MGqB}E$Ck^X|B{GhH-t=?)#RsCl<}kk!r_xS+2ikp=j*EOEpxHlK?Y#TH3|%?#hvOVtB~Krgd+LNTjWYQ z{HdBZQYlp#q5j&ro)|CDsYb5KfXR$U68q^4J&nvz)uzU>0lGCui8`IiFfN_jX&iH? zeR!qffR5`Zw6@VfU+G)PO$f?R9Jv)p^2`E%yP90gK(pGBSWTu!Q+_U`m9p$8(c_Jg zps95#(p`VjjxJ6zg!+ICEnKpS%SVzY(VEGlrl)%j*oVT4>1YgSWqBDD8bhE$KuTF6 zbP5R^RY{~|$zbukF{rHY76n32K9`OLnMV$T#ASI$yO&*bpHt(*wSU6)EkLS}K1v}I zYf+`tr>}dBJ^!&`SUhSuP&Ew=mCAUI|BS+G)P=cz!=>V2vvu8^JAytghI53=gM#(@ zoQA3mJXzWwELi|6PNhB0nesWV3^*Soo@YL`)lPRHvZtKj{B@@#Wb^My)JAm@WG%J+{}o6&UPlPCe3@V?48{V8zb2e6%M zPmIW$lK@rd{#p~q@A)uqq*Wc`=H$|O`WE~|)GG0X#2pgjslzdfW`#4hb!p0VnGsVM z8Hk8C1ewmqUoCeTAoGMaEquq1e|*M<|+`@Y+g6gP_#bRh@cXUnp zMJwld(o+cRe#;)?=W+eM=jsU$)1liJI~)Tv%3ZRoNt3TpP3+v16QA&(4%9LEU`jO# zk5`8YaS3}p*kSmjXisd7&0$)|Xtn@Bk|^?u9IN1-HK{RCv&NK?)ntUbvf{Ze<54L$ zg?L8t2sF^3BBSLa2B#O^S6O`9IllJ?P$$e<)oe}^u+z_%nj#bC(*gOQV=j!7zq7xS z$JUoO{&x9vLKt>fu^aDYp}EMqU;}N%!78E{mP^yU{U_Nc_L03nE*MzUQ`%Z`S^>^w z#xI<2IrX(2U50JDb~t0MDnEZZ(wWHdx>B&2#rX%@H~Z(gG8MWzt^+k~3)x?t#703+ z@!!pr#%;9`H@<|G|E#boQcTlyDny@>9Y(S%(@wB>R?C_)Izd%b%W$8f*R>uZU}Y1 z;0RdN8Szibu`IkfMd<=_dcyR~pvf)zIhzxlI$PW`?wLdme&J7oEK!(I3Q`4+?+)kV zCT43h^_?4S3r_=t_wL1B4(RqKZ65}sg9=cid;co9b^{bX;sh{-65C=7QE5byN#yUs z{rH~fZ;AsQZbcr3E0fxTc@dHpS-a-5rr5T&b|2|g-eL1J(5UgIWuSiQGXWh7eC9Pq zU@xqxvwx;%;M3SyU7megwePd;=27g@-_Z|$pNy|bu}8G*&wGVgz}FW#;E}qBOS>EY z9I?E@)7(oY_d5xFNfGj-8W2}=46>8F-4~!>&iUIe6uD88VSYkI@JdHMpM@PQ^tnzXkSfnY!t0a&fX<%cxOU^toAF3~M=QgZ0s7`^@uA^V z#G+m&mZN~S2&d?gaXGQD3u%!pSBD`sB^3&srmfP<%l=1tMVT>a9MZFM2qS4cf#k7{ zQU!lb4r!%ma~O~JFTWw91sRmFm4L}fQg*w5v6REm7&QCuu{&hZ+eeu>210*asxLKs zyNNu$pJwvnd;fOJ5WV8=y5{e)VWn*fdXL}sd;W`lb$E#X@YoOg%Z)Cm`6}atR&bM> zc0MyFLsW}a;C_qTVK>B7pr9uCc@(9yhEF>Qp*9EAopGbYfdhQbPoLuL>)Y_gfznI# z__?|MDn|pE&{&S_M+w=#U(J17M6i~rzLVM;Wfvh4Rud$+VW-p zcLu2wDR#i>wEo_0Ph6Pgp>t8x&t3u@=h{Fg@>g)vm4|9NJXr6lXqS>^ZM%%ayTLD_ zqakDvqMLO&afL||gE=na)%@^uIr!ip(rTC8ME#Ni^Zu&rLzR(?>5#6X zz|=PL;Qf1yCgPjCuw^+0dchP0D;;a1!i3fYmCl)D#7T)l&=9sW$G3L5Eo*GBl(Txb zv`dz-dhAbsdF-GfNOC?J$E1`VL=|88>ou9&l00MpI6#LKOn?c{NX46>Kuds{hjR7BB#$!8i`PyvtF8bk+P0$ej&*yX{D-F%s^a zqMKyP(^@$XjG)!!(2V6+qs)9MI=g;V?%lI1=gJn^k&C=_kq|4ok#argmr$_PgV!Pu+S3r^ zi?5SsJ$qAd z;uomB=`-#H`dFc_lnz!pr(_Rb(n0yXz<8kV%J`M~8zOH#`}1(DF0H!+^{#f~rmth| z-BtB~bL{6OJF$J?-}zTEq-tNd z!dD=p*hZ5kR?+LtMb!JaS_vcAPOFK#zSvVj$B(#!&YT#YR#{X|;+%rC;@GL}n0;nk8e)uvm3;Il zeGJL7(AtPJadF_3Gy32!y^CBvlLh;o{65p6C|iXMDn9T;2Fe-k;4xCZ1;_f>9f1@< zbaK6CZ{U^X>r2KV3GXa>t=d=y{r%{3gUAkCr_s&r%fIT!3Ac`rYLx#Orf1Q6AW1U% zQrKshJ`dr2{T4^k6M)HGf@H%Vrj_)zex!PyrOgI9`=XG@d`t{v%`@i7)Fz^gzv6X$ zzCtvr^p*FSi}GhI%8L-pZoVU@)ab)QV(RdGJN^pfvy=qJvshU!sGI~Hb3lWL;Uho) z{IhD@EX@=ak1U`w5hY*?Rl~v!86W8=sT0rtT`E6uw2O_jacjdc&NuP}K;IGubjHbl zGfadNYPw#n_C9W`Pi#8W_}~)zy{c@}hX8|7v5FFc?NCU9%V59F5}s1EtRuSwCfwln zSV`CZ22o{Q1WpgKM`F1qko56UFJd|_0w$im$C%soSaI*?x3q4}y;*{{6cGZk{|I3dNbz*gk%!Lf~ zT|UC^f@^uC)O@5v??xW&(I+y+lUcSo*kwhB68 zE}uo8Lb4Zi?$k`=A6WU{CIm&h*LLweR7lvHD*&JYBhLuXtpNXC0#dbVsM+lI@(85n$Mp}afi6n@(KzugEa^{qT6|W zpOd_=8vrcMNljULmbdC)sT2EK2mFqZ92EuiwxmC^Dl0#GdCq~+a*alYYEP;PopRC@ zQ#>t1@OCmgqfJ}++8kvm$D98+22>~X)%)O`1Icx4>)?85){1ub@ zRZ5GDK|c;1X;;zXx~f|&X^7Pai4r8*M~zzL^SOevE=yaLPbDtcxFn%A-<$58uIn*s zyn3> z5!>+wmejdXH|iUZ4634>eSjXP1`S3_sZuWzPKUL3)52m_!6DaOqsc(XpQ>9Uzm@s( z3a_qskE*_rLs;?kX*nZ6wc9=zA2MtmaQL(nD&ba{piX=5Orf?k^>>v;dsS_vHNj0z z?%vshaUN69ae__muu@a<-`@qDa;1F!YJ7#G{&X(QA(t^<0Yl!2A;s^fK}ll6Py+eg zN;p3#=R}Fd*qMai)quM{o>%~>iyngiM@HZji+Y$wcFc4VP;eC#yaoq@aGBcYtWZVy z%ORWWK91l!5{|TUwK2b?H+2F##@p(hYs@~dw%>7Nc#Luxx=9v z`+xNH-u^7=1YVPrpJ-?H014+GQ6z$PPiT0<)RnAsl#Y=S%q1+aOj$(?zntbGCUiS; z|I5#+A|*{HZ@XlvMaCP~*14$3{Dq=M22k<3{G2v{!Bu3FI)@TH;*>6La0ZY%={NbL z8l%4s6JsHVN} zIh&0h)Rb4l9nrLtPhW*`g)9+z5aKw%CMVm*gR^PnGg`--#)C4E{$1G7Y+`YfywdSAh~<~8S`vh_L%a$b+_j_e zr0Uz3RVi-)Wvmar4`;M31}}n2MUMv<3K*+nX?1&PAkcOIdpk<1iShD?dGmLMuJdJ=-xA%M0YE-xUjT#k(i&m8g);f8Dg{7(V9Q zJ9TrI7O5p=IlU>#nj&^2o|Drw>ZVvn!$84{ly-FEYsR()nC52HlIL$)?HKV~P*a?J zZF}l);TaNIQ$A)gC}T9}8TiH;E*miTR(CoZs=xU8moA{Ezg}*lYDEA}yX2C&(N1e6 zyoh;mythiS95v9gotqb}EgchG zdkTF4+kJddUp{ZaKB-0zs4Y3Mq|3PL@+RvIOnS^6RHfJTmkL6fsAMtfz`9RsJ}AXedglbxxx z$jR{#g`cYpHUDcvA=f&G9bV=_iDrIB9szskz#oP_FDUT$Z!>{TzEY*K>LYw435O)o z6u;2nd1lRr3)6(fp*wnfk%ILUkQI}2PVsMKvKwz_{%x5IQl2jShC3T`C3eIxKo>}H z<78lURp~ZYb^4bdE!d9UR?6!5p1F=r^%$ZM8#czz^w&am{J+7|ypMPLEzH+kh!zRS1scew>Unh^KGp$hLkDtiJ!iX0yM}?p& zuB)pAx^T<4ZRWS+I%oW;f@!-{N?Ak#uC1`7HSLeFNZm@KK3}rH&QhwSFW`=?Al17{ zzO_s&N4d2zIE>C@v)e^4?yS#B4qS?qh1YZ%E(qm9Dvth!c0Ay=5$o>)uFbc3CvH-+`Ne>8W<)IM^|x{` zxg~=)`LAME6YMq?nIH>IEXxARn7@&1ShMb=$>-x9yxKw6meY|1dXTlj(l7f#Gw=bT z4#mo{a6YpZhMx)rB;|wd;Vh!;QhDTyPusmF)Mpgbd&!QVNpIQyFYJ2wvMi4?M94bq z&A3uJu7#di4nJ?XX&9)Ov2l&4KM32yYocKp^uuQQq~Ghui&Rag>3Vie1OD+f>e%N3%MdMsOxCn!nZ&j2fEw(z zT!)`@j-b0pk86MRq&~jZp79f+M`ioBn91MO)d>GHxPxbJ_B8X8xuHY(f^-BbEy>zm zaz=s0EOZd3K&_Y>{oa%c{+64fu)_>Viupkgt)+nLy+R%OUo-(MQ#{R~HK4kG6bW{8a!~zAGo$@w=6zZ?d3zMtz@lm%~L?yGcS?6zi zC!P>*tVOqR4`OnxMZLi>^)oVAelRelB)0LysVKqRZ9Ph-AN#vp1i z)W}c+-fr5{ESE|a&{#ol*VCRQiaCxDuk1{JY0&&Vj=z|WcaxvCZ_c3~gt z3y9I|ES)NQ7;;5|ED@^p+L4F4?OsjRz=ld&_)L=KPW$LSZcz5{kc)Jc2?g%cW?E76C{Tb)i z=m_;*x)thg^m4hk@_466QL9weUY>xBNLf(iHFc42Q7ae!&FyC&&d(mOyakr$+m?tG zv614=30hKo&4#JoUk&^o#uV@LQEZXksRv79IwQ1Sc_QxKz-_!7WIWAcYSx+@4kXhL zVxTqZ8B4?Pj;&S4GvX^PqgoS<%a5Js& z&$`YkppmK33wKBsdeX7yg^s9?t$Jv}){uV_AG-0^y$=J0V+B&)OwkKQx!Y^5pI1;3 z0|CWeg#wiEU#LHkpUmvEmt5v)l{IkBC(+$6o05cS%S&Y>`JaJFOKTXk&g17X%ZF&( z@i9n+u43BUHSQUP#NTRVde1+H+()ZVX4GueG*tC_${*_xF6v_286d>qDHeZI!-dyO z2oLD$vRTH^FDSaiO=8wwfj{MrYbPU*U)0`@o(Xl&bg zLQB%Av7}9r75+PH#8q5^@Mi>uxiO>OGG-A|(4B+Z@Jm#fdia#eD*fo)v?s-MK0!Jx z$E>7D?O8y+kN@DuY}wtLTkQD}e!xTmc3PG5ofKrwNE(xMHIRmim|0qcs%YAs?24d^;&OZpbiMa% zjE-jU2}iW3iZb0tmV|)w^_U>t{Xzj->4N^;;LYbtJGX3Vc|jcn{FKSK!^qCFxTC1d zZ6C>PWMnV#-KwKUY2%;Mp$fZz5t!r!sH8ZLZfkuz1Wpdgg`pwMkIQ0(S$a{#h@&EGU9TR~KzO}{A;H4BM zRa6&XLK2`;ErO#GwMY3U7P&eL8#t}q=IxPUOM|jWVh<8!Q3D3mR9E?fg}VR?!01Un0JA>drWQmB%vuq#iVqWv)?KE{ z>qVE;$VR2&mwStw$F$kfl3tqRzMBSYE}FmIENKiN?f28Nfl}dw+0k+4wjP#<0B_AXiop$ zD>Jo+i|q95f}fAGO63EkoZup{-!mAOM08&2u8iK%>ts3Kk!;LM@e#XsB|Ay{>7+PH zUf^AH_bWeJmpHA;HbCTA)S}KhEkXR55W)CHalBF6IKnCs@=VQG9=JNG^Fz-kveL z6yk1fSfWJ~mktZ5k1-Fbm*MmK{KnGR5i!jhcJrb3Nci^oUcC32!W;8ZWRv#;_k~lp z-)V+k`^+Pe>!*|I-me`@ev z#=Bu&31_x-lcD0!9U9$ypfDQk8_9CU{y~dNjvG41V*d3~$J$MLTB)Ytz@7sGHEdm~ z;sb_k=M{XgaDGEX^j2{8M+_`(su|dZLMXYv@__6|W+oQwti?ldgRI07N=f2IrWwSI zV1f&5h&CArH4!w!7+LtgX;h#MfgZGbWF-oXZ>*{P_4i>5kC!F)H+u~3`hKNn+npr1 zJY6Aa{83;yNcmak@vTUZGqN+ihtf>oUT>Db!3IoCD9o?69dEzykkLlCiC4#3Qm!D8^{2i~z9 zR9KMNGwH;{%97rM!w+d^vk?$b;s@@^4As?ou{U3(HP2sw9nTcdKI(YJraYK8&oO}w zI^;)3%KUD~MHHjWU}l9f(;%QL#O^$Q{&U*8QLbpv1N?%>pL&>Pm=g9qyttO&c-VH~ zfoG=+bWE=xNOR7s)C&uRibEzPUzDadO)|=Z(9T+T>In`CS#PFe8V7)!A`r zE9IODaCPdbsiM=4G{K8yn=#2ZTWB@>LbD=#9$C_j5tX^Z$5WFraf8MPczfZ#sM(u`5KsG9B-i1d9T?yc7Hklhc&fuyW@RYzUz(eLZ_Pl zB*TBw<6LwDZO`Gu2C`7Xg(#hD$VNovJ6hADmF@L6Ls6MXN<1m9hXTGv`EP#V#gANe z&pa!v(BU{Dg`#f;rRmLO={ZIAB7t_IAy?G=v5b6wpG8Ygk<6~0aK`uPGA3u2y!>e? z0fVH=&nSAZm8`Y4owCd8X3Kwz4m(ZRF&N#QF1!fL-q|DeNTi-a&7NcPeY)#>WUZ97 zd}^;_!JBN)%8%uj=O)Y9b+$3|wpzd-ze&0i_M{Hm<3PmF*3ehVK!fqc$j+#l@v@W1 zkqLUehh|q4hPH$J1?omdOI`8PWUezSPgj4KX&0&bMdFq>WuCXU(cg812RFC(;WZyd zXZ5u)D>5w=R|slXsHcUE=P6Z%jn^pEVbz4mrhTxuH@_ux4G2c~tz;GTwq29$Vhpj( zQ$l4S+NxOYHZ)F>woJYFY-%1esnnS>dqwL{{hQMofjeA*G**gt8R(0d)&jJ*kIxXy z#C;EauJ1wv@p;Lak!yIFP7_7O$0W#*QpBuFc#q>xzI{>oAzUCHm&!YoUv13$&TTra ziCOkR#$w}hroV6xP|mh9UFa2;YI+eXquR{%4dK%F)7>?hu)>X_!qYflnpONnZ{_hF z`HcK~Bu5uwmhZ=}?`qCBq@DZsyDkGx@+;v(=&*jPUhj(}&(998gpV7>Qd`kuRov6Ve*c-^@)*#u3cfq;vJ? z9s&aQ<8H7UTdzf^Tk0?Jn-x+!loVL7U0)x%HYShlYy0tZY%h1WeK18XUb|r)5Gbw^ zD6YC-Lx=1zA2DIheNem+F7AIc{~*0t_d8CyH~?7JU9GJ72mT1aul3fS3jUA&{sdCb&Q?8A@CyZ2preJA}Wa@O$< z%j&LmPIO+R*k6H&`6wU}(bt9eqI&+yxXQTw+JNM-OiuC6&xY_;e*c!zesC$o8al+h znSB373owOwvDxhMR$S-&;JNc>n%tg!h5{lyS?7A*WM=) zm3jnOT|tuwB8H8UigT~+jHI2AAav+Gg8}OweDN|BcbhkAc`klxJc+RPK;4GqPM%Ylpb_uK67TeR__M=}7s<%PbCaf@ysL$432 za2Y`wpBL|TJP0m-9Unz|H1puHQm>D?bkIE1tpwR#UWoyoy3s#u+@{K1$n|+Sblh)< zslast0qg3~Ui7?T9vXrn@()Da@31dn2HpRJc!fg#`-RTP`(yRNCdDDfP^FDG^37_m z^Y^m|l1Wy$_WON`tM?B%Fxlzue)N{y8L^tE zddAlX{?JA9yOWC9_mBX5*02}B9QHTp=X|(OcRqZ<$g``1?L>U}aQ@nXFIaw$j`>I& z3sbU|)17m%-gTAH9X{mu>E+vIiBX4k&pULD;_!LP_hB&~JvXbnJ@0d%s{dZ*<}*>wgIQ0L|w$|A$Hu jGH7lCin-c;1h{umvQ$1n5oL=w80ZTqr39#wFbw!V(cRb_ literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/html/_images/clustering_17_0.png b/doc/LectureNotes/_build/html/_images/clustering_17_0.png new file mode 100644 index 0000000000000000000000000000000000000000..1e6a8c796726cad4240af4d925bc4bd8ab338a8c GIT binary patch literal 79050 zcmY&^b+&@CzKk=}3b%QuL3h@f_3UNQNb9Z-kd(Ow_@c&-G z>*Q+7HnU)m0-D6R)XyR1WDHpKa(sAqJTt-LL%#V)Zbr{3=?M8e>BA8F}~K)tEG%_&ag1H zsJG6dP>p`vU*2E%J!<*wyVO)e3D!h>wm>m0PnnaI#elsNM+}vi%(9V}n|DtW@Y_9C zTetI0CKl{#&Z-W{;YL&j=0Vt0Ual;%`{e(*Yk)|$ARD6ocR$aW8{-P&5qE7jd7R=C zv;VxXw+?UP-y;}W;#5Jtz@-KV{K2OQe5lqS()9r12-e{pur&E zN<<<{XvWI%ARf!K@%>$mR5AbfKE3Mx_X$I_@FvZBG_gQg*U`EAiosJ++-^QRmNciUg$D+&3jxN5 zoB;?=!-xH?hzQhUEbukZzUBYQuV zABCjrP#=bBw0nAl7Q9Bk`vI%Pp^#MJHkfq%M&XP0-Gf=nrVn)(>FT$JtyL_&gUk7R zYK7Y-()XO9mx-k77t()io8W2i1+gI6AY)I`ctcx2p)`+JOsN!Zk9oGQ8x+1U&#o?#E8K3ATr*sJ&d2t@t_5~kO7r%n zdlHim-3;5G>XPK|;T=0dYx#H~fcSSEyz_HD68Jwr@8OOF-3eonW0gXI8~s5VWrjA| z9YB10(QI|}z>KgqL3`*z2wo@WOTT&83kV+l_P~g6!eh~6UOSnvsQT5t+Ka8}JP8lL zH$j`g1fi(^&fVX1HwOh&0E;y~oAhP&+)w-K_D~Z>s(sgChU>pEhnoE7)E90Oh@mZdqbv?XA@U0%2!xvU@(n3imkr>xz z-;wMOQqKKGH|bTdRM>e9+96uNOFS2*OIn0%BYX>ZDaL)9vH!UidcdI3jb|ln!00Bs zo5cCi*kHdXZ^rv7>3aA*k-fwFs$8@O5DH9k+1{o7U}9Z$*M-4?^1a)C?4^WP2Rv(J z-*sbo%kW6b!T{?Sn~6g-aJTvP=JTCMC2X-<7Woj?_!168J8+P^p){CX*r$IV z|9r<1dI_9l^RD1e(m%%*5`WBa^DtM+)l~v62QMY4ym}FS3mmoGT9i#LL7U^(tJ|$m z3XI#Xpa9GZp9@L&LREzLmKn|p=6w=OluTi1|IV@B8*zv(DQAZFvzwulf_4=Ls2KWKIBTzpunZ*3?^2!Y7{-T>1ZKV-T$MOTQ zaRy%icRw`x=Le8o?ta4GkpOWpKhq}{W1=hN#86G z^~&9@P)%!Xr^SBKh~{<$+-{KZCf{U6PyXocal>A9rJ%HX{ipY znW15wmh{#EjSOe=ny}_#(-X8KelY z{!clM{8x^F0{uv8?O)XY&nL)r0*`Q`LM{Kdwkw@d8z6*2Ep(jsod?8uc7DiE>t~(P z^_2P8v>dDLMYfm2Q?Clu4w&73?pjf-`&3A%SJ7SpvnK%e;L*m5Ah;0FJTN4 zmLIo=bHuhJ_iNZPbN~71%NX;Vv>*5Tn$C4KG^LxR?n;lOK>zbh0r^cav~%AcQoi%! z{{MRhv96X}T&5C5V84HR2rMc8yqpI```>S6i`AjjJvVWIFE#uGgeNr&+@-Ee#b)|4 zs31$BaO>oJ@P}&q*JX{NeZ!#39yZmbR1fxvBEl5$6BQ}s%JPF25kTZSV|2qVhaPa8 z%;foR$ADAoL(<_L2O8jMV-O)&W=tjQ0rB6f zyu`V2BB?Ha(6*9(CArl`Jmtr_w+Dh4s7wQlH8(Te`8eVM_qQB=i@+xo3{-`@?7n>f zc89rQ<=$}kKo-1x#D;LG)w_SP^fH_Ti~ux)%N8D>y5MnyyyVCfm-0&Z zV>*A3JKrIiR%J2rtB=-9cJ;x)@Tg;Dm(4&7Bi^6&36Dt45)BG=ayQsHdI=dsmL&#| zT<&(0xXix5zwOuhyaX&9v4$!OdD(2!mPgUvDzeUZcaD1tZ@c+OGUM$bJFLcgsF{Gr z=37~L>7RLa*Jw@UiX9(5*lSb=zn4HvO2=6OOWJ0PH=>uJW&7?SZka&g{yu+u?oe9A z{jnUZuDwl+<(Lv&l|Vm;Z&)5F)o;Y{-Y4Vn6+vwy>qC&?(elI%@V-D~uDZn4)okUj zX?xP<+j5`&Con^AQt6o(#+Z3q^020opDMs{C=Nk5{$R{Bb(-AG-^9rrZ-aQL#}pbbdo73Cu=U4z3ybzp6yoo??XfR{Jy3_arsnIf9{uSmQZCa`i87E zCLYGRSzsR!#9AA}|6pAZQa=Bu-?z%~W2dWSU=oJ?zF)(-@uW{u>PM0{&kTnv%j`m< zU>@#sV@7BOwFb4lcWnd99<{`uQDJ5N~yf>DMO;s=VX#)ubEV|P9|I!zZJXpA1E z>ltsPuGyuLUj@fH{7NMQYr8$2Z?XM{4@4-HhnkOApmRoqjbC#@-YGnrZ*K|LFT!@X<(YkDsTX=gNti z@yc(y#}QF_h(wC4eTxxSa8CYcjZ~M%q5#vUi=%?w3vb5+UcqAyynLmBBYwk;?cuL` z$$L^vTlcwEJ>F37t7|lFUu5s&!qS5)|BL6PH$NXAdhix<%+uSFz;@eC@@hUk?Q}00 zJm9p>_&z-`5sl%;Xyo#xXb9Fzjrs>7RX*Ll0w(tdRkr$z)c0`%Vk>~p_R!zCM^=1+I82|v`?GLR%I%BUJI zXzAcw7fZ$~57RJ<`m8dQEQx0w9iR31mY(x(&)Q=FiNO|DQcsG@q{Sm<=y>@tUeH6C zHg~9KHf^p+3D4zba&q`ox6*)%i2p#iEp0M-4t=Jn5@M#<5|MtJLi|rX=vg z)mRI2sG`z676QIk$#^BzbzoU#jruZP6CV-{e%0x>8K`Zf^OkDTji}Dd|NO;TgYtN# z|Kk?@kn`lJ8>Ua&E;VjmCi6G^px?CCUKr0^86YhHeaxcL32|0D5Z-l|5@ zPsO~A?8FqqzGQWHd&>Uj{uj4kTOZ9L>xAi8sn7%~=+@Pls9KbA7GcMU=bw`-7g@Y$ zIbc;YyziFccYT5r&IRPSlkr7dFYbsStp zY|AJUzP#LG0&rApX_}p~jAT)YlbM7ZTJBWQbQ+M$Rn@sf_r=a#ZuiA=$EJpVa)ZjIry_lU z76Q zJ{XtA!ONmZ-5N3A(t8C}>fm%;)fvi--ue{+q7vZST%xPw38vPBp>MrVEaXTWk|4KD z%w44iPAU{J!}Ts_Y8FSeN4Ul=j5lM+FvM?Z8a;o*i-arRH^=^}tmv%jwYF|J#B{vN zgMU~eXUiApt*k_PAW+L9G16+5NoHPie`43=*l_hX6H6eq==a865_PS?hMXe9iP1S+ zJ4=IaxWPctfc~NyY>b9SmC2(4voQ=dOrC{@!9=N>3%?E(Em9X%1tY#-k96vn8AfhIza+rSniC zPsu@zeTcpwDe=8ZoAf#}|4i?B=VgRi=@H;FlU1@e*bOx?fw)4T{qdp^Cej%bgEuE? zZWgW55AFGz?+~T2icbO*TppV|GwiPr!`(<_*A4z_@=*98gCrVh*pohSO2dYoY%&w& zJHaC&kw@tUnNeQTU!5mqfU?_r3S%9n2FZL>I&V?ezNl#xGSl!>0#ToIf|wnMk3tI; zi8HLT=0qcIduPD$4)mX=UrXZ4b?01r?bU!Y?5$zw%%*I zzE=OSa!n1%V;U$s(JC^ek9M#jxUo$9SM1e9DyHVArXP_KR@`tM)kr7{PJy}c7e`lSO#xUvHSm#cMjv+6kOQ_R##69@N zlNDd)Ia7G`MQuuFyf9WQ)F(Z>pxeLXnd0HuRf%E08aO9FnwVmyosCC0v1TiJM!3T3 z>Y8juqhX0aVkQ~{TRW>_NnLAVDe6=0;Rk_WHYs*e5PUxpErO)4?-fDMRENc@S|k#r zn&CDXX%tWkd-0-5LWAFQMvX4BKkr?NoDiy-!YBh zU|(%@9pVSo!s}-VUe|A!Cy`%8*}{z|QmxbU8=(c$O)_F3FvRd;z@cM@6SA@Ro1B_< zmuEO>@NR@qQZM!i(Cg4-+}!Z3X0N_b|9`>&YhUm9o5#t*3_A zF$nwu0aA0=QDPcY9TpP7L?o{RGti-lL|I65kA9MA-*&nqE#BwfS*ObM!Ay$K%q?b3 z{u1a`CQMWnfD2r4wi1J?K}ktwK1Z{bR~qqAK7O5g8-71l1^I}A9;Ylg1Ar#eKV%$9 zt6Ck283s=yAui215UIt>3d-SoJY(|4?v?3>P*N;{q-p*M!S8jGVVhLcY1tI1TL4a| zgr9%3-~Up?Rw|fwaZy^Go~Ym6va;5uA1^)^k1y4~CakQ6PNf71E2VHcB%G%&&Dj~i zOMFVIyC4F&i4D}&c?v~@oe?Wq539Y>qpKfz&5o^IpzUFb&4k zV?-8E`e5Z*x$#>jq`K3|thP)IzHwcV6yIUyMwtVfsD;NI5q7k4AL_U<$LRaTS8?vT zy;*k6?Dkrs(`_@b$WUf7?Rnkgj%H|*)U4NSUtTgc>64`Z8Nuy~T9KVL5iGMshN-CA z#il7U$yM8wwA(G?Hakr9*g&Yw5YSSVe?LUp+FV@w0(08Qq+4&J9TvyMh-&M7Nb@9ka{g5IBS7Jgf5xw~gW0%&+vCj??zCpp1S)f9nWcUYH8Ns-E4E*yc3;e37BxiPYm z!sqCIl(Lb#3`%bQI-8KjuEitqj@c61em`(q3+Ck+Fe1+5Z39znCL{HV0#2L)NM}!v z!S)8p_bDGb{jBqyWME^|V&7Fj8I+X%>I@_!3tKanVg(UGcA9p_<)$m?LiLYSPbIji|KW$6+-Hf0E zd!$n3Ud4DcD~%I;U_#jWx%y)2tFjuw#5p~HaOHKLU~z&je~z=X6~#o4RxN%w@g#n_ z9DQ`$!kBUZL%cJwxcAn) zWuZUpR~YZbyG5xXZ<5rE>%V=Sreh~6JZz9q!B4RYND?f^bT44LK{9~4)01G1p#m7} zST#=Zat0-akvd7*MoAP|Y&D!PizI5c)D{aj|*{ z@+5y*6|Fu2apk?UPu9!2AhyXd7Q9tAlT{Ww_qO*LYvw(C1L@23k9iywa5^D_Y}^3b zeqLf2`^~&<1ywTcYc&n=pDCS98*L*8-s<{`${fZ8z*an9p3Q!u90aFnsIdaPkQp|JqfH^{Mwo`%E1?8oh4`9Z&mM6c z?yL4>8?)Z`WVZo*g<8uK7+v!-aIW}^kR17gSH@hX&sS};-U87t$uL2XkTj*QJK$;= z(8~t)K5}oH`2B8v4K~iw`Pg?y!_)DaUxNT+b-O>7DZ4K;yrvfJeCIq6D<5@;kD>LH z>>~*|fKhjzXN$m{ztg+9@gwcG(^@1lT*P^R>0_Q2ngaid&K%SeS;P415zuR*>M@{Y zF%~JQW3I1QUvEIs?Im(HH=req*au8XOrx=Zt0$)f%nai#{=&$!aRD^~j7eMm3WLKd z?tT^^D{t3@1b|uQ>hHXaSe#90UYlq|u2<(tyN56`ntnOLyOF94APr^Fr3fpK6LRZJ zm%Kj6N*fG=l%$uP>-{tDRu=P7lLuWNFtezu9M+T~g-i`mkjsTz^*K$)tWMM1*QliPbSD)s|)=;;#Ip>A>M9TF;D zZay(JScRp)_Wm45(ht`${;VwrK25+VQB*DGq3`&@mvew>V`g9>1A>z+j2S1O8Q1s(CsJ7~!rhYDk|-onNp%#?&jKcjl@kD~6+4fw zCd(JT$xY}}je{|Z3SJD*Zl}E`F2y$P!+K{}jKP8xa0#X-@vo)I060Zi946Sx-4ngR z<@!#2C&Ei$-k&(7w+eg4BT~l~i4p(HV+eP!!H4N&BIxYIay_O{8;GLHi&EE`cx(lw~80&tTqO%YNgx_05_iWkggIqtdTP^7?7V@AnU7U4;#^&QcM z_I2|l*1%qx&=ep673hr&*1zL_gUPGPvtcVlwZ1muI8M;1pC%k~9T(>l&$9M?SRgZm zLKK;((~JOq4c7{4(?QM34IpR~LlHXxK?L6`bkCap(F3PQtN+-dc}{>Yzw z)5tt-|7k!jivJS-=Fp$C0_kYDssqk(^Hz8G;yamYkW$91F?vzWR5$BBkH9zc?pVyq z&wuGEr9MpXii4O`VJZ@nxJ07c0l7S(?H8lppaa0J)DHYRz3zqzo^aKxM5V2Lfiv29eaN$HGO5C zv0;hOaR23{8XB)L<7&VBj_LeaRr{H$-m&B%bDeh%zs95Yt4Q4QFHWW=&raD6nKiDK z?Umb|zmLBGk6(#jA8=YiDP6xW7Ld0pZKvJ|7!TrW)rinqQ&OkVsen+>f~m2c$lc`( zW)tSxmB>E>O!kb;f&MNkD8WI~MZ)XBa#zl=}xFQb7eZN1JU z%!H|FzV)@H35~jxpiG=Vk1EfZY4D||5O+(wFnAo8ELZ&=zIa|d141z2aeXh48N?j4Xx^I!7#zk+$!^D~=0N8eYLiuXUyg zqz54KLa&(xT3XTte&9PXB4FcW0QLjL+EkGT!vKn9Wrg;rXN}_B?kBDKsE4hHYzD1m zX}S{Zxp-TZH8n=G#8UAL8glf;pF5|~n=pVwEr>Rn{I)8VxN^jjTGmv{H)#U8E z?3<7DRGKHG84!-YwjlZ#@75Gg9s?8h>xZU_E|+K-(Fp^`Ue;(4pu?~B$R=!S+9*4} ztx=r(BPBuTWWqq4SL-v_Z0a%^GWuxDwX33zRDw?Jkx)j@L}@MWb@%H_re<(IXTvx^-z8EgFxq- zIDN0TxW+n<<)0^Ic^EdBl=z6{bN2)0Xn<0^DQRLG5g?a75yk7 zHOr~Xr+Zu;gX$>@u!f;|!w|lY?kdMoUj==)N6@LLy#R`H)MEXQ&19A5<#Z;KlS91s z2dMWVBAySs>k3Xh&R;MGoNJiwnca0{`(CE$So6v<$Lpl-WD^5NU^?jiEcUfNJUaqp zSbh}BhN3W&UPN}>Mbf(-QO3%BEk@*a;M?91X?`k_puS3_$6S%jc>Fm@9UK>QvM^32 zyFdr55bQ(le?QITx2My{9N+0qIMen5Q8hDr&b}gHQZP*O zhpUj4(IEy-LvV+xQUR8k__BqbuCV<$r51sb;jsSXIht7J&GpuoT$cfzzF$R)g<{+A zt^jdGgA5z?nRW$yRlZ}|Vs@XI9Ca`gz@*6=V6Y1e=;$7NXX3z)NY3%^<2Yp-@3u^{ zPcueuL&iY#rsFWKV*{1Uf77us&`0yJ=T0f(iT}Do$)u)|4@LR*+vz>VWrD&9ODGNW z=cpB2@0`OEYT{>r0Ffn!0{GUs_{Vw1_AWcOkG-Mubk8_JOd~W% zEUm8!+sFYVSJmxv)I}vMzyyyBEq2g-X_CR8;Tg#VSI5#wjCc=#CXuSz@t=2FOV@|X zE?k8Qrl=e;#nOQpPB67G7+=;0g6&P6=go26DxuQSvao*bqM)OzQ6JS_A9F&WMd05k zvT?i;T2)A|V0btHv_Ls7Uo98$VPGWa?_oneDwRC3R7V%X#SbZ7*XWXmu8rKMs8@_H zDlMmHp$BY$=}jba>O?dE0S)@=*?_^yVm2^FIGOxu5E;8fIFF=HxL++?vF91uyIDJp z#XAyTU5ByX59y0;K})oaT+htaSW#YUy4iEh;l3At$yC?WlmUjKWyvZf^%gmLvllNk z!7U>GD>BkgaYH@k3@@c<0-t5e@b55UoDG~wNqKk>dnDbzqZw1W#J1(O%c$x3{=Ag7 zW{F`6FNY{wlB3_L%d?xaoV2%IQcWVm>UPC;4o|AbKKsRhs%jw-{JX&A*G8;7^H#E- zF%+@g$g4A|855z5O+2i@hL~~rD1q>$j4Vex!^4+*ua?+sjdXwHDFf72bc`Gb7%c#z z^G8r`GKM8LGXq=WQxdIUKFWqMZE9$!VM*PmrUQ_?wK;TiCRX}fnRaj{xGz#NJy%w|_9O-+pmy%jY$rWdVeP?4pZ)sP}IDR?shD4U|6hdF)ONENW1f)RBTT?^;Iw0o- z<}W}|gBHgqeoPS#k?px=B~3d{)N7q}a8K$T{!FDDOTy!l%q{0E7va%Nt1OQ_GF+ya zUJ>~9I4^*6+C#{fHx>^M8YDGnpJ6X3`~j`M=GRoa-|>k6PP|kvO9lL!u9&S=NmX9x zSoI{TO1_t$XJkBB+e)vfsg`BqDM<&UVK2Dyifh(B>0}rJ*s9Onj z!;-7<9x!4^wXJMv)W{2=Xr8f$S*=WcRF+Xw?ew>ZtjTM;lkvT{D_ZoxHIrD}2G~h& zOP>w8$UB_6QadaeL&LA1Uhb);I6r3wvdlK47LGqW^1;#A!@s4n@V|Zm*MlpL|Wu^Un zlwo0_&TFHPZ`37f#wqT4PEAu9LSipx0l4^~KXjys>^Z^SJ*TD7_pr`sDobZsV~B#8 zpc**bFiZsu%t}7KM;hsnl6g8pK#Y*lb>W7woKvb-CFt0%$YunF`Jep6K$Sw;j}3c} zLqmM%xZMGu&`U0qAj-B9)=XIzN*X|SIfJ%6nIAytbhCr7D5W`!kd)j5lpax{ZDYxU zzG9$Fvec~5)Xx%fg2(SUtr;$*V0+I1Y^EX6M)8KW@2J?^De0tVEv3GmyBRaj_z;0V zyvB_j=}B>tf(bu_b-_TVW96b}P|7B^4(3hujqc^rG9P6JL*OQ3ed^2>S4 zxswIi-TzWtCZ4y&2@?NB4C3lrY_qKYy5Veeyb#MWS`|2xOH(e~87hYlV6@ijYM2|{ z0-SSG>we7pe4sj!=GSyp)li>NJiv5|0|-DExk(b|y<-xusy6|NsH>5wmjpzD(l!Ag zn_F9^UlPncJ5GI4gH`&StdqjZTGbT4+tmd+Og-s7&s4$<>-}urj~aj{i0d|DkdUf? z{;7dDJG?i@95;0$M>^c7JtMkKwqxmqM6E(1z#O0%OFFv6$zCHo)Ba<<!BEy8eug&o&E6Wm{06=7bG@0W{yC{b#7}fH{jIz~P?OpHL

    • +
  • + + 12. Clustering and Unsupervised Learning + +

    • @@ -208,17 +213,27 @@

    @@ -294,151 +309,151 @@ @@ -452,8 +467,9 @@
    -
    -

    13. Building a Feed Forward Neural Network

    +
    +

    14. Building a Feed Forward Neural Network

    We are now gong to develop an example based on the MNIST data base. This is a classification problem and we need to use our cross-entropy function we discussed in connection with logistic @@ -481,7 +497,7 @@ P(y = 1 \mid \hat{x}, \hat{\theta}) = 1 - P(y = 0 \mid \hat{x}, \hat{\theta}) ,

    where \(y \in \{0, 1\}\) and \(\hat{\theta}\) represents the weights and biases of our network.

    -

    13.1. Defining the cost function

    +

    14.1. Defining the cost function

    Our cost function is given as (see the Logistic regression lectures)

    \[ @@ -519,7 +535,7 @@ P(\mathcal{D} \mid \hat{\theta}) = \prod_{i=1}^n \prod_{c=0}^{C-1} [P(y_{ic} = 1

    See the logistic regression lectures for a full definition of the cost function.

    The back propagation equations need now only a small change, namely the definition of a new cost function. We are thus ready to use the same equations as before!

    -

    13.1.1. Example: binary classification problem

    +

    14.1.1. Example: binary classification problem

    As an example of the above, relevant for project 2 as well, let us consider a binary class. As discussed in our logistic regression lectures, we defined a cost function in terms of the parameters \(\beta\) as

    \[ @@ -561,7 +577,7 @@ Our cost function at the final layer

    In case we use another activation function than the logistic one, we need to evaluate other derivatives.

    -

    13.1.2. The Softmax function

    +

    14.1.2. The Softmax function

    In case we employ the more general case given by the Softmax equation, we need to evaluate the derivative of the activation function with respect to the activation \(z_i^l\), that is we need

    \[ @@ -582,7 +598,7 @@ f(z_i^l) = \frac{\exp{(z_i^l)}}{\sum_{m=1}^K\exp{(z_m^l)}}.
    -

    13.2. Developing a code for doing neural networks with back propagation

    +

    14.2. Developing a code for doing neural networks with back propagation

    One can identify a set of key steps when using neural networks to solve supervised learning problems:

    1. Collect and pre-process data

      2. @@ -593,7 +609,7 @@ f(z_i^l) = \frac{\exp{(z_i^l)}}{\sum_{m=1}^K\exp{(z_m^l)}}.

    2. Adjust hyperparameters (if necessary, network architecture)

    -

    13.2.1. Collect and pre-process data

    +

    14.2.1. Collect and pre-process data

    Here we will be using the MNIST dataset, which is readily available through the scikit-learn package. You may also find it for example here.
    The MNIST (Modified National Institute of Standards and Technology) database is a large database @@ -683,12 +699,12 @@ labels = (n_inputs) = (1797,) X = (n_inputs, n_features) = (1797, 64)

    -_images/chapter10_33_1.png +_images/chapter10_39_1.png
    -

    13.2.2. Train and test datasets

    +

    14.2.2. Train and test datasets

    Performing analysis before partitioning the dataset is a major error, that can lead to incorrect conclusions.

    We will reserve \(80 \%\) of our dataset for training and \(20 \%\) for testing.

    It is important that the train and test datasets are drawn randomly from our dataset, to ensure @@ -737,7 +753,7 @@ Number of test images: 360

    -

    13.2.3. Define model and architecture

    +

    14.2.3. Define model and architecture

    Our simple feed-forward neural network will consist of an input layer, a single hidden layer and an output layer. The activation \(y\) of each neuron is a weighted sum of inputs, passed through an activation function. In case of the simple perceptron model we have

    \[ z = \sum_{i=1}^n w_i a_i ,\]
    @@ -767,7 +783,7 @@ We will be using the sigmoid function which is inspired by probability theory (see logistic regression) and was most commonly used until about 2011. See the discussion below concerning other activation functions.

    -

    13.2.4. Layers

    +

    14.2.4. Layers

    • Input

    @@ -824,7 +840,7 @@ of values. Without it, any input with the value 0 will be mapped to zero (before
    -

    13.2.5. Feed-forward pass

    +

    14.2.5. Feed-forward pass

    Denote \(F\) the number of features, \(H\) the number of hidden neurons and \(C\) the number of categories.
    For each input image we calculate a weighted sum of input features (pixel values) to each neuron \(j\) in the hidden layer \(l\):

    @@ -917,7 +933,7 @@ correct label for image 0: 6
    -

    13.2.6. Choose cost function and optimizer

    +

    14.2.6. Choose cost function and optimizer

    To measure how well our neural network is doing we need to introduce a cost function.
    We will call the function that gives the error of a single sample output the loss function, and the function that gives the total error of our network across all samples the cost function. @@ -936,7 +952,7 @@ probability of the correct category \ you got the correct label. The probability of category \(c\) is given by the softmax function. The vector \(\hat{\theta}\) represents the parameters of our network, i.e. all the weights and biases.

    -

    13.2.7. Optimizing the cost function

    +

    14.2.7. Optimizing the cost function

    The network is trained by finding the weights and biases that minimize the cost function. One of the most widely used classes of methods is gradient descent and its generalizations. The idea behind gradient descent is simply to adjust the weights in the direction where the gradient of the cost function is large and negative. This ensures we flow toward a local minimum of the cost function.
    Each parameter \(\theta\) is iteratively adjusted according to the rule

    @@ -962,7 +978,7 @@ We denote each minibatch \(B_k\)The various optmization methods, with codes and algorithms, are discussed in our lectures on Gradient descent approaches.

    -

    13.2.8. Regularization

    +

    14.2.8. Regularization

    It is common to add an extra term to the cost function, proportional to the size of the weights. This is equivalent to constraining the size of the weights, so that they do not grow out of control. @@ -985,7 +1001,7 @@ above. This is a clever use of the chain rule that allows us to calculate the gradient efficently.

    -

    13.2.9. Matrix multiplication

    +

    14.2.9. Matrix multiplication

    To more efficently train our network these equations are implemented using matrix operations.
    The error in the output layer is calculated simply as, with \(\hat{t}\) being our targets,

    @@ -1086,7 +1102,7 @@ the Hadamard product, meaning element-wise multiplication.

    Old accuracy on training data: 0.1440501043841336
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1098,7 +1114,7 @@ the Hadamard product, meaning element-wise multiplication.
    -

    13.3. Improving performance

    +

    14.3. Improving performance

    As we can see the network does not seem to be learning at all. It seems to be just guessing the label for each image.
    In order to obtain a network that does something useful, we will have to do a bit more work.

    The choice of hyperparameters such as learning rate and regularization parameter is hugely influential for the performance of the network. Typically a grid-search is performed, wherein we test different hyperparameters separated by orders of magnitude. For example we could test the learning rates \(\eta = 10^{-6}, 10^{-5},...,10^{-1}\) with different regularization parameters \(\lambda = 10^{-6},...,10^{-0}\).

    @@ -1215,7 +1231,7 @@ being realizations of this object with different hyperparameters. An implementat
    -

    13.4. Evaluate model performance on test data

    +

    14.4. Evaluate model performance on test data

    To measure the performance of our network we evaluate how well it does it data it has never seen before, i.e. the test data.
    We measure the performance of the network using the accuracy score.
    The accuracy is as you would expect just the number of images correctly labeled divided by the total number of images. A perfect classifier will have an accuracy score of \(1\).

    @@ -1251,7 +1267,7 @@ The accuracy is as you would expect just the number of images correctly labeled
    -

    13.5. Adjust hyperparameters

    +

    14.5. Adjust hyperparameters

    We now perform a grid search to find the optimal hyperparameters for the network.
    Note that we are only using 1 layer with 50 neurons, and human performance is estimated to be around \(98\%\) (\(2\%\) error rate).

    @@ -1420,7 +1436,7 @@ Lambda = 10.0 Accuracy score on test set: 0.21944444444444444
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1429,7 +1445,7 @@ Lambda =  1e-05
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1438,7 +1454,7 @@ Lambda =  0.0001
 Accuracy score on test set:  0.10555555555555556
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1447,7 +1463,7 @@ Lambda =  0.001
 Accuracy score on test set:  0.08888888888888889
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1456,7 +1472,7 @@ Lambda =  0.01
 Accuracy score on test set:  0.11388888888888889
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1465,7 +1481,7 @@ Lambda =  0.1
 Accuracy score on test set:  0.08611111111111111
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1474,7 +1490,7 @@ Lambda =  1.0
 Accuracy score on test set:  0.125
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1483,11 +1499,11 @@ Lambda =  10.0
 Accuracy score on test set:  0.09166666666666666
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1496,11 +1512,11 @@ Lambda =  1e-05
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1509,11 +1525,11 @@ Lambda =  0.0001
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1522,11 +1538,11 @@ Lambda =  0.001
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1535,11 +1551,11 @@ Lambda =  0.01
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1548,7 +1564,7 @@ Lambda =  0.1
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
@@ -1557,11 +1573,11 @@ Lambda =  1.0
 Accuracy score on test set:  0.125
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1570,11 +1586,11 @@ Lambda =  10.0
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1583,11 +1599,11 @@ Lambda =  1e-05
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1596,11 +1612,11 @@ Lambda =  0.0001
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1609,11 +1625,11 @@ Lambda =  0.001
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1622,11 +1638,11 @@ Lambda =  0.01
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1635,11 +1651,11 @@ Lambda =  0.1
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1648,11 +1664,11 @@ Lambda =  1.0
 Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp
   exp_term = np.exp(self.z_o)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide
   self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)
 
    
 
    
@@ -1665,7 +1681,7 @@ Accuracy score on test set:  0.07777777777777778
    -

    13.6. Visualization

    +

    14.6. Visualization

    # visual representation of grid search
@@ -1705,25 +1721,25 @@ Accuracy score on test set:  0.07777777777777778
    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp
   return 1/(1 + np.exp(-x))
 
    
 
    
-_images/chapter10_49_1.png
-_images/chapter10_49_2.png
+_images/chapter10_59_1.png
+_images/chapter10_59_2.png
    -

    13.7. scikit-learn implementation

    +

    14.7. scikit-learn implementation

    scikit-learn focuses more on traditional machine learning methods, such as regression, clustering, decision trees, etc. As such, it has only two types of @@ -2058,13 +2074,13 @@ Accuracy score on test set: 0.2 Learning rate = 10.0 Lambda = 0.001 Accuracy score on test set: 0.10555555555555556 + +Learning rate = 10.0 +Lambda = 0.01 +Accuracy score on test set: 0.06388888888888888 

    Learning rate  =  10.0
-Lambda =  0.01
-Accuracy score on test set:  0.06388888888888888
-
-Learning rate  =  10.0
 Lambda =  0.1
 Accuracy score on test set:  0.08888888888888889
    @@ -2082,7 +2098,7 @@ Accuracy score on test set: 0.09166666666666666
    -

    13.8. Visualization

    +

    14.8. Visualization

    # optional
@@ -2123,13 +2139,13 @@ Accuracy score on test set:  0.09166666666666666
    -_images/chapter10_53_0.png -_images/chapter10_53_1.png +_images/chapter10_63_0.png +_images/chapter10_63_1.png
    -

    13.9. Building neural networks in Tensorflow and Keras

    +

    14.9. Building neural networks in Tensorflow and Keras

    Now we want to build on the experience gained from our neural network implementation in NumPy and scikit-learn and use it to construct a neural network in Tensorflow. Once we have constructed a neural network in NumPy and Tensorflow, building one in Keras is really quite trivial, though the performance may suffer.

    @@ -2154,23 +2170,8 @@ will give an introduction to the lower level Python Application Program Interfaces (APIs), and see how we use them to build our graph. Then we will build (effectively) the same graph in Keras, to see just how simple solving a machine learning problem can be.

    -

    To install tensorflow on Unix/Linux systems, use pip as

    -
    -
    -
    pip3 install tensorflow
-
    -
    -
    -
    -
      File "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/2357089093.py", line 1
-    pip3 install tensorflow
-         ^
-SyntaxError: invalid syntax
-
    -
    -
    -
    -

    and/or if you use anaconda, just write (or install from the graphical user interface) +

    To install tensorflow on Unix/Linux systems, use pip as pip3 install tensorflow +and/or if you use anaconda, just write (or install from the graphical user interface) (current release of CPU-only TensorFlow)

    @@ -2179,6 +2180,14 @@ how simple solving a machine learning problem can be.

    +
    +
      File "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/2259440937.py", line 1
+    conda create -n tf tensorflow
+          ^
+SyntaxError: invalid syntax
+
    +
    +

    To install the current release of GPU TensorFlow

    @@ -2357,7 +2366,7 @@ If you have Anaconda installed you may run the following command

    -

    13.10. The Breast Cancer Data, now with Keras

    +

    14.10. The Breast Cancer Data, now with Keras

    import tensorflow as tf
@@ -2531,7 +2540,7 @@ If you have Anaconda installed you may run the following command
    -

    13.11. Fine-tuning neural network hyperparameters

    +

    14.11. Fine-tuning neural network hyperparameters

    The flexibility of neural networks is also one of their main drawbacks: there are many hyperparameters to tweak. Not only can you use any imaginable network topology (how neurons/nodes are interconnected), @@ -2562,7 +2571,7 @@ of training data. However, you will rarely have to train such networks from scra common to reuse parts of a pretrained state-of-the-art network that performs a similar task.

    -

    13.12. Which activation function should I use?

    +

    14.12. Which activation function should I use?

    The Back propagation algorithm we derived above works by going from the output layer to the input layer, propagating the error gradient on the way. Once the algorithm has computed the gradient of the cost @@ -2627,7 +2636,7 @@ it does not saturate for positive values (and also because it is quite fast to compute).

    -

    13.13. The RELU function family

    +

    14.13. The RELU function family

    The ReLU activation function suffers from a problem known as the dying ReLUs: during training, some neurons effectively die, meaning they stop outputting anything other than 0.

    @@ -2664,7 +2673,7 @@ bootstrap to evaluate other activation functions.

    -

    13.14. Batch Normalization

    +

    14.14. Batch Normalization

    Batch Normalization aims to address the vanishing/exploding gradients problems, and more generally the problem that the distribution of each layer’s inputs changes during training, as the parameters of the previous layers change.

    @@ -2677,7 +2686,7 @@ standard deviation. It does so by evaluating the mean and standard deviation of mini-batch, from this the name batch normalization.

    -

    13.15. Dropout

    +

    14.15. Dropout

    It is a fairly simple algorithm: at every training step, every neuron (including the input neurons but excluding the output neurons) has a probability \(p\) of being temporarily dropped out, meaning it will be entirely ignored during this training step, but it may be active during the next step.

    @@ -2686,7 +2695,7 @@ hyperparameter \(p\) is called It is viewed as one of the most popular regularization techniques.

    -

    13.16. Gradient Clipping

    +

    14.16. Gradient Clipping

    A popular technique to lessen the exploding gradients problem is to simply clip the gradients during backpropagation so that they never exceed some threshold (this is mostly useful for recurrent neural networks).

    @@ -2695,7 +2704,7 @@ networks).

    Normalization is preferred.

    -

    13.17. A top-down perspective on Neural networks

    +

    14.17. A top-down perspective on Neural networks

    The first thing we would like to do is divide the data into two or three parts. A training set, a validation or dev (development) set, and a test set. The test set is the data on which we want to make @@ -2729,7 +2738,7 @@ can serve as another important diagnostic when using DNNs for supervised learning.

    -

    13.18. Limitations of supervised learning with deep networks

    +

    14.18. Limitations of supervised learning with deep networks

    Like all statistical methods, supervised learning using neural networks has important limitations. This is especially important when one seeks to apply these methods, especially to physics problems. Like @@ -2782,7 +2791,7 @@ features).

    previous

    -

    12. Neural networks

    +

    13. Neural networks

    @@ -2790,7 +2799,7 @@ features).

    next

    -

    14. Solving Differential Equations with Deep Learning

    +

    15. Solving Differential Equations with Deep Learning

     diff --git a/doc/LectureNotes/_build/html/chapter11.html b/doc/LectureNotes/_build/html/chapter11.html index 19cb926de..59a43e75a 100644 --- a/doc/LectureNotes/_build/html/chapter11.html +++ b/doc/LectureNotes/_build/html/chapter11.html @@ -5,7 +5,7 @@ - 14. Solving Differential Equations with Deep Learning — Applied Data Analysis and Machine Learning + 15. Solving Differential Equations with Deep Learning — Applied Data Analysis and Machine Learning @@ -53,7 +53,8 @@ - + + @@ -198,6 +199,11 @@ 11. Basic ideas of the Principal Component Analysis (PCA) +
  • + + 12. Clustering and Unsupervised Learning + +

    • @@ -207,17 +213,27 @@

    @@ -293,90 +309,90 @@ @@ -390,8 +406,9 @@
    -
    -

    14. Solving Differential Equations with Deep Learning

    +
    +

    15. Solving Differential Equations with Deep Learning

    The Universal Approximation Theorem states that a neural network can approximate any function at a single hidden layer along with one input and output layer to any given precision.

    @@ -457,7 +474,7 @@ It might happen so that finding an analytical expression of the gradient of Luckily, there exists libraries that makes the job for us through automatic differentiation. Automatic differentiation is a method of finding the derivatives numerically with very high precision.

    -

    14.1. Example: Exponential decay

    +

    15.1. Example: Exponential decay

    An exponential decay of a quantity \(g(x)\) is described by the equation

    @@ -512,7 +529,7 @@ g_t(x, P) = g_0 + x \cdot N(x, P) \]
    -

    14.2. Reformulating the problem

    +

    15.2. Reformulating the problem

    We wish that our neural network manages to minimize a given cost function.

    A reformulation of out equation, (6), must therefore be done, such that it describes the problem a neural network can solve for.

    @@ -657,7 +674,7 @@ C(\boldsymbol{x}, P) = \frac{1}{N} \sum_i \big(g_t'(x_i, P) - ( -\gamma g_t(x_i

    Here, gradient descent with a constant step size has been chosen.

    -

    14.3. Gradient descent

    +

    15.3. Gradient descent

    The idea of the gradient descent algorithm is to update parameters in a direction where the cost function decreases goes to a minimum.

    In general, the update of some parameters \(\boldsymbol{\omega}\) given a cost @@ -686,7 +703,7 @@ P_{\text{output},\text{new}} &= P_{\text{output}} - \lambda \nabla_{P_{\text \end{split}\]

    -

    14.4. The code for solving the ODE

    +

    15.4. The code for solving the ODE

    %matplotlib inline
@@ -846,12 +863,12 @@ P_{\text{output},\text{new}} &= P_{\text{output}} - \lambda \nabla_{P_{\text
 Max absolute difference: 0.0437499
    -_images/chapter11_47_2.png +_images/chapter11_50_2.png
    -

    14.5. The network with one input layer, specified number of hidden layers, and one output layer

    +

    15.5. The network with one input layer, specified number of hidden layers, and one output layer

    It is also possible to extend the construction of our network into a more general one, allowing the network to contain more than one hidden layers.

    The number of neurons within each hidden layer are given as a list of integers in the program below.

    @@ -1025,106 +1042,14 @@ Max absolute difference: 0.0437499 return array(a, dtype, copy=False, order=order)
    -
    ---------------------------------------------------------------------------
-KeyboardInterrupt                         Traceback (most recent call last)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42376/2971492148.py in <module>
-    144     lmb = 0.001
-    145 
---> 146     P = solve_ode_deep_neural_network(x, num_hidden_neurons, num_iter, lmb)
-    147 
-    148     res = g_trial_deep(x,P)
-
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42376/2971492148.py in solve_ode_deep_neural_network(x, num_neurons, num_iter, lmb)
-    119         # The cost_grad consist now of N_hidden + 1 arrays; the gradient w.r.t the weights and biases
-    120         # in the hidden layers and output layers evaluated at x.
---> 121         cost_deep_grad =  cost_function_deep_grad(P, x)
-    122 
-    123         for l in range(N_hidden+1):
-
-~/anaconda3/lib/python3.8/site-packages/autograd/wrap_util.py in nary_f(*args, **kwargs)
-     18             else:
-     19                 x = tuple(args[i] for i in argnum)
----> 20             return unary_operator(unary_f, x, *nary_op_args, **nary_op_kwargs)
-     21         return nary_f
-     22     return nary_operator
-
-~/anaconda3/lib/python3.8/site-packages/autograd/differential_operators.py in grad(fun, x)
-     23     arguments as `fun`, but returns the gradient instead. The function `fun`
-     24     should be scalar-valued. The gradient has the same type as the argument."""
----> 25     vjp, ans = _make_vjp(fun, x)
-     26     if not vspace(ans).size == 1:
-     27         raise TypeError("Grad only applies to real scalar-output functions. "
-
-~/anaconda3/lib/python3.8/site-packages/autograd/core.py in make_vjp(fun, x)
-      8 def make_vjp(fun, x):
-      9     start_node = VJPNode.new_root()
----> 10     end_value, end_node =  trace(start_node, fun, x)
-     11     if end_node is None:
-     12         def vjp(g): return vspace(x).zeros()
-
-~/anaconda3/lib/python3.8/site-packages/autograd/tracer.py in trace(start_node, fun, x)
-      8     with trace_stack.new_trace() as t:
-      9         start_box = new_box(x, t, start_node)
----> 10         end_box = fun(start_box)
-     11         if isbox(end_box) and end_box._trace == start_box._trace:
-     12             return end_box._value, end_box._node
-
-~/anaconda3/lib/python3.8/site-packages/autograd/wrap_util.py in unary_f(x)
-     13                 else:
-     14                     subargs = subvals(args, zip(argnum, x))
----> 15                 return fun(*subargs, **kwargs)
-     16             if isinstance(argnum, int):
-     17                 x = args[argnum]
-
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42376/2971492148.py in cost_function_deep(P, x)
-     67 
-     68     # Evaluate the trial function with the current parameters P
----> 69     g_t = g_trial_deep(x,P)
-     70 
-     71     # Find the derivative w.r.t x of the neural network
-
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42376/2971492148.py in g_trial_deep(x, params, g0)
-     57 # The trial solution using the deep neural network:
-     58 def g_trial_deep(x,params, g0 = 10):
----> 59     return g0 + x*deep_neural_network(params, x)
-     60 
-     61 # The right side of the ODE:
-
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42376/2971492148.py in deep_neural_network(deep_params, x)
-     37 
-     38         z_hidden = np.matmul(w_hidden, x_prev)
----> 39         x_hidden = sigmoid(z_hidden)
-     40 
-     41         # Update x_prev such that next layer can use the output from this layer
-
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42376/2971492148.py in sigmoid(z)
-      5 
-      6 def sigmoid(z):
-----> 7     return 1/(1 + np.exp(-z))
-      8 
-      9 # The neural network with one input layer and one output layer,
-
-~/anaconda3/lib/python3.8/site-packages/autograd/tracer.py in f_wrapped(*args, **kwargs)
-     40             if f_wrapped in notrace_primitives[node_constructor]:
-     41                 return f_wrapped(*argvals, **kwargs)
----> 42             parents = tuple(box._node for _     , box in boxed_args)
-     43             argnums = tuple(argnum    for argnum, _   in boxed_args)
-     44             ans = f_wrapped(*argvals, **kwargs)
-
-~/anaconda3/lib/python3.8/site-packages/autograd/tracer.py in <genexpr>(.0)
-     40             if f_wrapped in notrace_primitives[node_constructor]:
-     41                 return f_wrapped(*argvals, **kwargs)
----> 42             parents = tuple(box._node for _     , box in boxed_args)
-     43             argnums = tuple(argnum    for argnum, _   in boxed_args)
-     44             ans = f_wrapped(*argvals, **kwargs)
-
-KeyboardInterrupt: 
+
    Final cost: 0.119936
 
    
 
    
+_images/chapter11_52_3.png
    -

    14.5.1. Example: Population growth

    +

    15.5.1. Example: Population growth

    A logistic model of population growth assumes that a population converges toward an equilibrium. The population growth can be modeled by

    @@ -1335,11 +1260,25 @@ g(t) = \frac{Ag_0}{g_0 + (A - g_0)\exp(-\alpha A t)}
    +
    +
    Initial cost: 0.221805
+
    +
    +
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray
+  return array(a, dtype, copy=False, order=order)
+
    +
    +
    Final cost: 0.000417932
+The max absolute difference between the solutions is: 0.00424909
+
    +
    +_images/chapter11_58_3.png +
    -

    14.6. Using forward Euler to solve the ODE

    +

    15.6. Using forward Euler to solve the ODE

    A straightforward way of solving an ODE numerically, is to use Euler’s method.

    Euler’s method uses Taylor series to approximate the value at a function \(f\) at a step \(\Delta x\) from \(x\):

    @@ -1452,10 +1391,27 @@ extending the program that uses the network using Autograd:

    +
    +
    Initial cost: 0.221805
+
    +
    +
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray
+  return array(a, dtype, copy=False, order=order)
+
    +
    +
    Final cost: 0.000417932
+The max absolute difference between the solutions is: 0.00424909
+Max absolute difference between Euler method and analytical: 0.011225
+Max absolute difference between deep neural network and analytical: 0.00424909
+
    +
    +_images/chapter11_66_3.png +_images/chapter11_66_4.png +
    -

    14.7. Solving the one dimensional Poisson equation

    +

    15.7. Solving the one dimensional Poisson equation

    The Poisson equation for \(g(x)\) in one dimension is

    @@ -1657,9 +1613,23 @@ g(x) = x(1 - x)\exp(x)
    +
    +
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray
+  return array(a, dtype, copy=False, order=order)
+
    +
    +
    Initial cost: 457.256
+
    +
    +
    Final cost: 0.00310113
+The max absolute difference between the solutions is: 0.000464088
+
    +
    +_images/chapter11_79_3.png +
    -

    14.7.1. Comparing with a numerical scheme

    +

    15.7.1. Comparing with a numerical scheme

    The Poisson equation is possible to solve using Taylor series to approximate the second derivative.

    Using Taylor series, the second derivative can be expressed as

    @@ -1933,11 +1903,27 @@ f(x_{N_x - 2})
    +
    +
    Initial cost: 457.256
+
    +
    +
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray
+  return array(a, dtype, copy=False, order=order)
+
    +
    +
    Final cost: 0.00310113
+The max absolute difference between the analytical solution and DNN Autograd: 0.000464088
+The max absolute difference between the analytical solution and numerical scheme: 0.00266858
+
    +
    +_images/chapter11_91_3.png +_images/chapter11_91_4.png +
    -

    14.8. Partial Differential Equations

    +

    15.8. Partial Differential Equations

    A partial differential equation (PDE) has a solution here the function is defined by multiple variables. The equation may involve all kinds of combinations of which variables the function is differentiated with @@ -1953,7 +1939,7 @@ respect to.

    \]

    where \(f\) is an expression involving all kinds of possible mixed derivatives of \(g(x_1,\dots,x_N)\) up to an order \(n\). In order for the solution to be unique, some additional conditions must also be given.

    -

    14.8.1. Type of problem

    +

    15.8.1. Type of problem

    The problem our network must solve for, is similar to the ODE case. We must have a trial solution \(g_t\) at hand.

    For instance, the trial solution could be expressed as

    @@ -1968,7 +1954,7 @@ The neural network \(N(x_1,\dots,x_N,

    The role of the function \(h_2(x_1,\dots,x_N,N(x_1,\dots,x_N,P))\), is to ensure that the output of \(N(x_1,\dots,x_N,P)\) is zero when \(g_t(x_1,\dots,x_N)\) is evaluated at the values of \(x_1,\dots,x_N\) where the given conditions must be satisfied. The function \(h_1(x_1,\dots,x_N)\) should alone make \(g_t(x_1,\dots,x_N)\) satisfy the conditions.

    -

    14.8.2. Network requirements

    +

    15.8.2. Network requirements

    The network tries then the minimize the cost function following the same ideas as described for the ODE case, but now with more than one variables to consider. The concept still remains the same; find a set @@ -1994,7 +1980,7 @@ C\left(X, P \right) = \sum_{i=1}^M f\left( \left( \boldsymbol{x}_i, \frac{\parti

    -

    14.9. Example: The diffusion equation

    +

    15.9. Example: The diffusion equation

    In one spatial dimension, the equation reads

    \[ @@ -2162,7 +2148,7 @@ mixed derivatives of \(g(x,t)\)
    -

    14.9.1. Setting up the network using Autograd; The full program

    +

    15.9.1. Setting up the network using Autograd; The full program

    Having set up the network, along with the trial solution and cost function, we can now see how the deep neural network performs by comparing the results to the analytical solution.

    The analytical solution of our problem is

    @@ -2402,11 +2388,200 @@ Using TensorFlow results in a much better execution time. Try it!

    +
    +
    /Users/MortenImac/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray
+  return array(a, dtype, copy=False, order=order)
+
    +
    +
    Initial cost:  41.05505310046362
+
    +
    +
    ---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47448/73752910.py in <module>
+    141     lmb = 0.01
+    142 
+--> 143     P = solve_pde_deep_neural_network(x,t, num_hidden_neurons, num_iter, lmb)
+    144 
+    145     ## Store the results
+
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47448/73752910.py in solve_pde_deep_neural_network(x, t, num_neurons, num_iter, lmb)
+    118     # Let the update be done num_iter times
+    119     for i in range(num_iter):
+--> 120         cost_grad =  cost_function_grad(P, x , t)
+    121 
+    122         for l in range(N_hidden+1):
+
+~/anaconda3/lib/python3.8/site-packages/autograd/wrap_util.py in nary_f(*args, **kwargs)
+     18             else:
+     19                 x = tuple(args[i] for i in argnum)
+---> 20             return unary_operator(unary_f, x, *nary_op_args, **nary_op_kwargs)
+     21         return nary_f
+     22     return nary_operator
+
+~/anaconda3/lib/python3.8/site-packages/autograd/differential_operators.py in grad(fun, x)
+     23     arguments as `fun`, but returns the gradient instead. The function `fun`
+     24     should be scalar-valued. The gradient has the same type as the argument."""
+---> 25     vjp, ans = _make_vjp(fun, x)
+     26     if not vspace(ans).size == 1:
+     27         raise TypeError("Grad only applies to real scalar-output functions. "
+
+~/anaconda3/lib/python3.8/site-packages/autograd/core.py in make_vjp(fun, x)
+      8 def make_vjp(fun, x):
+      9     start_node = VJPNode.new_root()
+---> 10     end_value, end_node =  trace(start_node, fun, x)
+     11     if end_node is None:
+     12         def vjp(g): return vspace(x).zeros()
+
+~/anaconda3/lib/python3.8/site-packages/autograd/tracer.py in trace(start_node, fun, x)
+      8     with trace_stack.new_trace() as t:
+      9         start_box = new_box(x, t, start_node)
+---> 10         end_box = fun(start_box)
+     11         if isbox(end_box) and end_box._trace == start_box._trace:
+     12             return end_box._value, end_box._node
+
+~/anaconda3/lib/python3.8/site-packages/autograd/wrap_util.py in unary_f(x)
+     13                 else:
+     14                     subargs = subvals(args, zip(argnum, x))
+---> 15                 return fun(*subargs, **kwargs)
+     16             if isinstance(argnum, int):
+     17                 x = args[argnum]
+
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47448/73752910.py in cost_function(P, x, t)
+     78             g_t = g_trial(point,P)
+     79             g_t_jacobian = g_t_jacobian_func(point,P)
+---> 80             g_t_hessian = g_t_hessian_func(point,P)
+     81 
+     82             g_t_dt = g_t_jacobian[1]
+
+~/anaconda3/lib/python3.8/site-packages/autograd/wrap_util.py in nary_f(*args, **kwargs)
+     18             else:
+     19                 x = tuple(args[i] for i in argnum)
+---> 20             return unary_operator(unary_f, x, *nary_op_args, **nary_op_kwargs)
+     21         return nary_f
+     22     return nary_operator
+
+~/anaconda3/lib/python3.8/site-packages/autograd/differential_operators.py in hessian(fun, x)
+     76 def hessian(fun, x):
+     77     "Returns a function that computes the exact Hessian."
+---> 78     return jacobian(jacobian(fun))(x)
+     79 
+     80 @unary_to_nary
+
+~/anaconda3/lib/python3.8/site-packages/autograd/wrap_util.py in nary_f(*args, **kwargs)
+     18             else:
+     19                 x = tuple(args[i] for i in argnum)
+---> 20             return unary_operator(unary_f, x, *nary_op_args, **nary_op_kwargs)
+     21         return nary_f
+     22     return nary_operator
+
+~/anaconda3/lib/python3.8/site-packages/autograd/differential_operators.py in jacobian(fun, x)
+     59     jacobian_shape = ans_vspace.shape + vspace(x).shape
+     60     grads = map(vjp, ans_vspace.standard_basis())
+---> 61     return np.reshape(np.stack(grads), jacobian_shape)
+     62 
+     63 @unary_to_nary
+
+~/anaconda3/lib/python3.8/site-packages/autograd/numpy/numpy_wrapper.py in stack(arrays, axis)
+     86     # primitives defined in this file
+     87 
+---> 88     arrays = [array(arr) for arr in arrays]
+     89     if not arrays:
+     90         raise ValueError('need at least one array to stack')
+
+~/anaconda3/lib/python3.8/site-packages/autograd/numpy/numpy_wrapper.py in <listcomp>(.0)
+     86     # primitives defined in this file
+     87 
+---> 88     arrays = [array(arr) for arr in arrays]
+     89     if not arrays:
+     90         raise ValueError('need at least one array to stack')
+
+~/anaconda3/lib/python3.8/site-packages/autograd/core.py in vjp(g)
+     12         def vjp(g): return vspace(x).zeros()
+     13     else:
+---> 14         def vjp(g): return backward_pass(g, end_node)
+     15     return vjp, end_value
+     16 
+
+~/anaconda3/lib/python3.8/site-packages/autograd/core.py in backward_pass(g, end_node)
+     19     for node in toposort(end_node):
+     20         outgrad = outgrads.pop(node)
+---> 21         ingrads = node.vjp(outgrad[0])
+     22         for parent, ingrad in zip(node.parents, ingrads):
+     23             outgrads[parent] = add_outgrads(outgrads.get(parent), ingrad)
+
+~/anaconda3/lib/python3.8/site-packages/autograd/core.py in <lambda>(g)
+     65                     "VJP of {} wrt argnum 0 not defined".format(fun.__name__))
+     66             vjp = vjpfun(ans, *args, **kwargs)
+---> 67             return lambda g: (vjp(g),)
+     68         elif L == 2:
+     69             argnum_0, argnum_1 = argnums
+
+~/anaconda3/lib/python3.8/site-packages/autograd/numpy/numpy_vjps.py in <lambda>(g)
+    421     A_ndim = anp.ndim(A)
+    422     B_meta = anp.metadata(B)
+--> 423     return lambda g: matmul_adjoint_1(A, g, A_ndim, B_meta)
+    424 
+    425 defvjp(anp.matmul, matmul_vjp_0, matmul_vjp_1)
+
+~/anaconda3/lib/python3.8/site-packages/autograd/numpy/numpy_vjps.py in matmul_adjoint_1(A, G, A_ndim, B_meta)
+    408     else:  # We need to swap the last two axes of A
+    409         A = anp.swapaxes(A, A_ndim - 2, A_ndim - 1)
+--> 410     result = anp.matmul(A, G)
+    411     if B_is_vec:
+    412         result = anp.squeeze(result, anp.ndim(G) - 1)
+
+~/anaconda3/lib/python3.8/site-packages/autograd/tracer.py in f_wrapped(*args, **kwargs)
+     43             argnums = tuple(argnum    for argnum, _   in boxed_args)
+     44             ans = f_wrapped(*argvals, **kwargs)
+---> 45             node = node_constructor(ans, f_wrapped, argvals, kwargs, argnums, parents)
+     46             return new_box(ans, trace, node)
+     47         else:
+
+~/anaconda3/lib/python3.8/site-packages/autograd/core.py in __init__(self, value, fun, args, kwargs, parent_argnums, parents)
+     34             raise NotImplementedError("VJP of {} wrt argnums {} not defined"
+     35                                       .format(fun_name, parent_argnums))
+---> 36         self.vjp = vjpmaker(parent_argnums, value, args, kwargs)
+     37 
+     38     def initialize_root(self):
+
+~/anaconda3/lib/python3.8/site-packages/autograd/core.py in vjp_argnums(argnums, ans, args, kwargs)
+     75                     "VJP of {} wrt argnums 0, 1 not defined".format(fun.__name__))
+     76             vjp_0 = vjp_0_fun(ans, *args, **kwargs)
+---> 77             vjp_1 = vjp_1_fun(ans, *args, **kwargs)
+     78             return lambda g: (vjp_0(g), vjp_1(g))
+     79         else:
+
+~/anaconda3/lib/python3.8/site-packages/autograd/numpy/numpy_vjps.py in matmul_vjp_1(ans, A, B)
+    420 def matmul_vjp_1(ans, A, B):
+    421     A_ndim = anp.ndim(A)
+--> 422     B_meta = anp.metadata(B)
+    423     return lambda g: matmul_adjoint_1(A, g, A_ndim, B_meta)
+    424 
+
+~/anaconda3/lib/python3.8/site-packages/autograd/tracer.py in f_wrapped(*args, **kwargs)
+     59     def f_wrapped(*args, **kwargs):
+     60         argvals = map(getval, args)
+---> 61         return f_raw(*argvals, **kwargs)
+     62     f_wrapped._is_primitive = True
+     63     return f_wrapped
+
+~/anaconda3/lib/python3.8/site-packages/autograd/numpy/numpy_wrapper.py in metadata(A)
+    146 @notrace_primitive
+    147 def metadata(A):
+--> 148     return _np.shape(A), _np.ndim(A), _np.result_type(A), _np.iscomplexobj(A)
+    149 
+    150 @notrace_primitive
+
+KeyboardInterrupt: 
+
    +
    +
    -

    14.10. Solving the wave equation with Neural Networks

    +

    15.10. Solving the wave equation with Neural Networks

    The wave equation is

    \[ @@ -2693,7 +2868,7 @@ g(x,t) = \sin(\pi x)\cos(\pi t) - \sin(\pi x)\sin(\pi t)
    -

    14.11. Resources on differential equations and deep learning

    +

    15.11. Resources on differential equations and deep learning

    1. Artificial neural networks for solving ordinary and partial differential equations by I.E. Lagaris et al

    2. Neural networks for solving differential equations by A. Honchar

      3. @@ -2737,10 +2912,19 @@ g(x,t) = \sin(\pi x)\cos(\pi t) - \sin(\pi x)\sin(\pi t)

      previous

      -

      13. Building a Feed Forward Neural Network

      +

      14. Building a Feed Forward Neural Network

    + diff --git a/doc/LectureNotes/_build/html/chapter12.html b/doc/LectureNotes/_build/html/chapter12.html new file mode 100644 index 000000000..c1b605ab8 --- /dev/null +++ b/doc/LectureNotes/_build/html/chapter12.html @@ -0,0 +1,1509 @@ + + + + + + + + 16. Convolutional Neural Networks — Applied Data Analysis and Machine Learning + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    + +
    +
    +
    +
    + + + + +
    + + +
    + + + + + + +
    +
    + + + + + + + + + +
    + + +
    + +
    + Contents +
    + +
    +
    +
    +
    +
    + +
    + +
    +

    16. Convolutional Neural Networks

    +

    Convolutional neural networks (CNNs) were developed during the last +decade of the previous century, with a focus on character recognition +tasks. Nowadays, CNNs are a central element in the spectacular success +of deep learning methods. The success in for example image +classifications have made them a central tool for most machine +learning practitioners.

    +

    CNNs are very similar to ordinary Neural Networks. +They are made up of neurons that have learnable weights and +biases. Each neuron receives some inputs, performs a dot product and +optionally follows it with a non-linearity. The whole network still +expresses a single differentiable score function: from the raw image +pixels on one end to class scores at the other. And they still have a +loss function (for example Softmax) on the last (fully-connected) layer +and all the tips/tricks we developed for learning regular Neural +Networks still apply (back propagation, gradient descent etc etc).

    +

    CNN architectures make the explicit assumption that +the inputs are images, which allows us to encode certain properties +into the architecture. These then make the forward function more +efficient to implement and vastly reduce the amount of parameters in +the network.

    +

    Here we provide only a superficial overview, for the more interested, we recommend highly the course +IN5400 – Machine Learning for Image Analysis +and the slides of CS231.

    +

    Another good read is the article here https://arxiv.org/pdf/1603.07285.pdf.

    +
    +

    16.1. Neural Networks vs CNNs

    +

    Neural networks are defined as affine transformations, that is +a vector is received as input and is multiplied with a matrix of so-called weights (our unknown paramters) to produce an +output (to which a bias vector is usually added before passing the result +through a nonlinear activation function). This is applicable to any type of input, be it an +image, a sound clip or an unordered collection of features: whatever their +dimensionality, their representation can always be flattened into a vector +before the transformation.

    +

    However, when we consider images, sound clips and many other similar kinds of data, these data have an intrinsic +structure. More formally, they share these important properties:

    +
      +

    • They are stored as multi-dimensional arrays (think of the pixels of a figure) .

      • +

    • They feature one or more axes for which ordering matters (e.g., width and height axes for an image, time axis for a sound clip).

      • +

    • One axis, called the channel axis, is used to access different views of the data (e.g., the red, green and blue channels of a color image, or the left and right channels of a stereo audio track).

      • +
    +

    These properties are not exploited when an affine transformation is applied; in +fact, all the axes are treated in the same way and the topological information +is not taken into account. Still, taking advantage of the implicit structure of +the data may prove very handy in solving some tasks, like computer vision and +speech recognition, and in these cases it would be best to preserve it. This is +where discrete convolutions come into play.

    +

    A discrete convolution is a linear transformation that preserves this notion of +ordering. It is sparse (only a few input units contribute to a given output +unit) and reuses parameters (the same weights are applied to multiple locations +in the input).

    +

    As an example, consider +an image of size \(32\times 32\times 3\) (32 wide, 32 high, 3 color channels), so a +single fully-connected neuron in a first hidden layer of a regular +Neural Network would have \(32\times 32\times 3 = 3072\) weights. This amount still +seems manageable, but clearly this fully-connected structure does not +scale to larger images. For example, an image of more respectable +size, say \(200\times 200\times 3\), would lead to neurons that have +\(200\times 200\times 3 = 120,000\) weights.

    +

    We could have +several such neurons, and the parameters would add up quickly! Clearly, +this full connectivity is wasteful and the huge number of parameters +would quickly lead to possible overfitting.

    + + +

    Figure 1: A regular 3-layer Neural Network.

    + +

    Convolutional Neural Networks take advantage of the fact that the +input consists of images and they constrain the architecture in a more +sensible way.

    +

    In particular, unlike a regular Neural Network, the +layers of a CNN have neurons arranged in 3 dimensions: width, +height, depth. (Note that the word depth here refers to the third +dimension of an activation volume, not to the depth of a full Neural +Network, which can refer to the total number of layers in a network.)

    +

    To understand it better, the above example of an image +with an input volume of +activations has dimensions \(32\times 32\times 3\) (width, height, +depth respectively).

    +

    The neurons in a layer will +only be connected to a small region of the layer before it, instead of +all of the neurons in a fully-connected manner. Moreover, the final +output layer could for this specific image have dimensions \(1\times 1 \times 10\), +because by the +end of the CNN architecture we will reduce the full image into a +single vector of class scores, arranged along the depth +dimension.

    + + +

    Figure 1: A CNN arranges its neurons in three dimensions (width, height, depth), as visualized in one of the layers. Every layer of a CNN transforms the 3D input volume to a 3D output volume of neuron activations. In this example, the red input layer holds the image, so its width and height would be the dimensions of the image, and the depth would be 3 (Red, Green, Blue channels).

    +
    +
    +

    16.2. Layers used to build CNNs

    +

    A simple CNN is a sequence of layers, and every layer of a CNN +transforms one volume of activations to another through a +differentiable function. We use three main types of layers to build +CNN architectures: Convolutional Layer, Pooling Layer, and +Fully-Connected Layer (exactly as seen in regular Neural Networks). We +will stack these layers to form a full CNN architecture.

    +

    A simple CNN for image classification could have the architecture:

    +
      +

    • INPUT (\(32\times 32 \times 3\)) will hold the raw pixel values of the image, in this case an image of width 32, height 32, and with three color channels R,G,B.

      • +

    • CONV (convolutional )layer will compute the output of neurons that are connected to local regions in the input, each computing a dot product between their weights and a small region they are connected to in the input volume. This may result in volume such as \([32\times 32\times 12]\) if we decided to use 12 filters.

      • +

    • RELU layer will apply an elementwise activation function, such as the \(max(0,x)\) thresholding at zero. This leaves the size of the volume unchanged (\([32\times 32\times 12]\)).

      • +

    • POOL (pooling) layer will perform a downsampling operation along the spatial dimensions (width, height), resulting in volume such as \([16\times 16\times 12]\).

      • +

    • FC (i.e. fully-connected) layer will compute the class scores, resulting in volume of size \([1\times 1\times 10]\), where each of the 10 numbers correspond to a class score, such as among the 10 categories of the MNIST images we considered above . As with ordinary Neural Networks and as the name implies, each neuron in this layer will be connected to all the numbers in the previous volume.

      • +
    +

    CNNs transform the original image layer by layer from the original +pixel values to the final class scores.

    +

    Observe that some layers contain +parameters and other don’t. In particular, the CNN layers perform +transformations that are a function of not only the activations in the +input volume, but also of the parameters (the weights and biases of +the neurons). On the other hand, the RELU/POOL layers will implement a +fixed function. The parameters in the CONV/FC layers will be trained +with gradient descent so that the class scores that the CNN computes +are consistent with the labels in the training set for each image.

    +

    In summary:

    +
      +

    • A CNN architecture is in the simplest case a list of Layers that transform the image volume into an output volume (e.g. holding the class scores)

      • +

    • There are a few distinct types of Layers (e.g. CONV/FC/RELU/POOL are by far the most popular)

      • +

    • Each Layer accepts an input 3D volume and transforms it to an output 3D volume through a differentiable function

      • +

    • Each Layer may or may not have parameters (e.g. CONV/FC do, RELU/POOL don’t)

      • +

    • Each Layer may or may not have additional hyperparameters (e.g. CONV/FC/POOL do, RELU doesn’t)

      • +
    +

    A dense neural network is representd by an affine operation (like matrix-matrix multiplication) where all parameters are included.

    +

    The key idea in CNNs for say imaging is that in images neighbor pixels tend to be related! So we connect +only neighboring neurons in the input instead of connecting all with the first hidden layer.

    +

    We say we perform a filtering (convolution is the mathematical operation).

    +
    +
    +

    16.3. Mathematics of CNNs

    +

    The mathematics of CNNs is based on the mathematical operation of +convolution. In mathematics (in particular in functional analysis), +convolution is represented by matheematical operation (integration, +summation etc) on two function in order to produce a third function +that expresses how the shape of one gets modified by the other. +Convolution has a plethora of applications in a variety of disciplines, spanning from statistics to signal processing, computer vision, solutions of differential equations,linear algebra, engineering, and yes, machine learning.

    +

    Mathematically, convolution is defined as follows (one-dimensional example): +Let us define a continuous function \(y(t)\) given by

    +
    +\[ +y(t) = \int x(a) w(t-a) da, +\]
    +

    where \(x(a)\) represents a so-called input and \(w(t-a)\) is normally called the weight function or kernel.

    +

    The above integral is written in a more compact form as

    +
    +\[ +y(t) = \left(x * w\right)(t). +\]
    +

    The discretized version reads

    +
    +\[ +y(t) = \sum_{a=-\infty}^{a=\infty}x(a)w(t-a). +\]
    +

    Computing the inverse of the above convolution operations is known as deconvolution.

    +

    How can we use this? And what does it mean? Let us study some familiar examples first.

    +
    +

    16.3.1. Convolution Examples: Polynomial multiplication

    +

    We have already met such an example in project 1 when we tried to set +up the design matrix for a two-dimensional function. This was an +example of polynomial multiplication. Let us recast such a problem in terms of the convolution operation. +Let us look a the following polynomials to second and third order, respectively:

    +
    +\[ +p(t) = \alpha_0+\alpha_1 t+\alpha_2 t^2, +\]
    +

    and

    +
    +\[ +s(t) = \beta_0+\beta_1 t+\beta_2 t^2+\beta_3 t^3. +\]
    +

    The polynomial multiplication gives us a new polynomial of degree \(5\)

    +
    +\[ +z(t) = \delta_0+\delta_1 t+\delta_2 t^2+\delta_3 t^3+\delta_4 t^4+\delta_5 t^5. +\]
    +

    Computing polynomial products can be implemented efficiently if we rewrite the more brute force multiplications using convolution. +We note first that the new coefficients are given as

    +
    +\[\begin{split} +\begin{split} +\delta_0=&\alpha_0\beta_0\\ +\delta_1=&\alpha_1\beta_0+\alpha_1\beta_0\\ +\delta_2=&\alpha_0\beta_2+\alpha_1\beta_1+\alpha_2\beta_0\\ +\delta_3=&\alpha_1\beta_2+\alpha_2\beta_1+\alpha_0\beta_3\\ +\delta_4=&\alpha_2\beta_2+\alpha_1\beta_3\\ +\delta_5=&\alpha_2\beta_3.\\ +\end{split} +\end{split}\]
    +

    We note that \(\alpha_i=0\) except for \(i\in \left\{0,1,2\right\}\) and \(\beta_i=0\) except for \(i\in\left\{0,1,2,3\right\}\).

    +

    We can then rewrite the coefficients \(\delta_j\) using a discrete convolution as

    +
    +\[ +\delta_j = \sum_{i=-\infty}^{i=\infty}\alpha_i\beta_{j-i}=(\alpha * \beta)_j, +\]
    +

    or as a double sum with restriction \(l=i+j\)

    +
    +\[ +\delta_l = \sum_{ij}\alpha_i\beta_{j}. +\]
    +

    Do you see a potential drawback with these equations?

    +

    Since we only have a finite number of \(\alpha\) and \(\beta\) values +which are non-zero, we can rewrite the above convolution expressions +as a matrix-vector multiplication

    +
    +\[\begin{split} +\boldsymbol{\delta}=\begin{bmatrix}\alpha_0 & 0 & 0 & 0 \\ + \alpha_1 & \alpha_0 & 0 & 0 \\ + \alpha_2 & \alpha_1 & \alpha_0 & 0 \\ + 0 & \alpha_2 & \alpha_1 & \alpha_0 \\ + 0 & 0 & \alpha_2 & \alpha_1 \\ + 0 & 0 & 0 & \alpha_2 + \end{bmatrix}\begin{bmatrix} \beta_0 \\ \beta_1 \\ \beta_2 \\ \beta_3\end{bmatrix}. +\end{split}\]
    +

    The process is commutative and we can easily see that we can rewrite the multiplication in terms of a matrix holding \(\beta\) and a vector holding \(\alpha\). +In this case we have

    +
    +\[\begin{split} +\boldsymbol{\delta}=\begin{bmatrix}\beta_0 & 0 & 0 \\ + \beta_1 & \beta_0 & 0 \\ + \beta_2 & \beta_1 & \beta_0 \\ + \beta_3 & \beta_2 & \beta_1 \\ + 0 & \beta_3 & \beta_2 \\ + 0 & 0 & \beta_3 + \end{bmatrix}\begin{bmatrix} \alpha_0 \\ \alpha_1 \\ \alpha_2\end{bmatrix}. +\end{split}\]
    +

    Note that the use of these matrices is for mathematical purposes only and not implementation purposes. +When implementing the above equation we do not encode (and allocate memory) the matrices explicitely. +We rather code the convolutions in the minimal memory footprint that they require.

    +

    Does the number of floating point operations change here when we use the commutative property?

    +
    +
    +

    16.3.2. Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)

    +

    For problems with so-called harmonic oscillations, given by for example the following differential equation

    +
    +\[ +m\frac{d^2x}{dt^2}+\eta\frac{dx}{dt}+x(t)=F(t), +\]
    +

    where \(F(t)\) is an applied external force acting on the system (often called a driving force), one can use the theory of Fourier transformations to find the solutions of this type of equations.

    +

    If one has several driving forces, \(F(t)=\sum_n F_n(t)\), one can find +the particular solution to each \(F_n\), \(x_{pn}(t)\), and the particular +solution for the entire driving force is then given by a series like

    + +
    +
    +\[ +\begin{equation} +x_p(t)=\sum_nx_{pn}(t). +\label{_auto1} \tag{1} +\end{equation} +\]
    +

    This is known as the principle of superposition. It only applies when +the homogenous equation is linear. If there were an anharmonic term +such as \(x^3\) in the homogenous equation, then when one summed various +solutions, \(x=(\sum_n x_n)^2\), one would get cross +terms. Superposition is especially useful when \(F(t)\) can be written +as a sum of sinusoidal terms, because the solutions for each +sinusoidal (sine or cosine) term is analytic.

    +

    Driving forces are often periodic, even when they are not +sinusoidal. Periodicity implies that for some time \(\tau\)

    +
    +\[ +\begin{eqnarray} +F(t+\tau)=F(t). +\end{eqnarray} +\]
    +

    One example of a non-sinusoidal periodic force is a square wave. Many +components in electric circuits are non-linear, e.g. diodes, which +makes many wave forms non-sinusoidal even when the circuits are being +driven by purely sinusoidal sources.

    +

    The code here shows a typical example of such a square wave generated using the functionality included in the scipy Python package. We have used a period of \(\tau=0.2\).

    +
    +
    +
    %matplotlib inline
+
+import numpy as np
+import math
+from scipy import signal
+import matplotlib.pyplot as plt
+
+# number of points                                                                                       
+n = 500
+# start and final times                                                                                  
+t0 = 0.0
+tn = 1.0
+# Period                                                                                                 
+t = np.linspace(t0, tn, n, endpoint=False)
+SqrSignal = np.zeros(n)
+SqrSignal = 1.0+signal.square(2*np.pi*5*t)
+plt.plot(t, SqrSignal)
+plt.ylim(-0.5, 2.5)
+plt.show()
+
    +
    +
    +
    +_images/chapter12_35_0.png +
    +
    +

    For the sinusoidal example the +period is \(\tau=2\pi/\omega\). However, higher harmonics can also +satisfy the periodicity requirement. In general, any force that +satisfies the periodicity requirement can be expressed as a sum over +harmonics,

    + +
    +
    +\[ +\begin{equation} +F(t)=\frac{f_0}{2}+\sum_{n>0} f_n\cos(2n\pi t/\tau)+g_n\sin(2n\pi t/\tau). +\label{_auto2} \tag{2} +\end{equation} +\]
    +

    We can write down the answer for +\(x_{pn}(t)\), by substituting \(f_n/m\) or \(g_n/m\) for \(F_0/m\). By +writing each factor \(2n\pi t/\tau\) as \(n\omega t\), with \(\omega\equiv +2\pi/\tau\),

    + +
    +
    +\[ +\begin{equation} +\label{eq:fourierdef1} \tag{3} +F(t)=\frac{f_0}{2}+\sum_{n>0}f_n\cos(n\omega t)+g_n\sin(n\omega t). +\end{equation} +\]
    +

    The solutions for \(x(t)\) then come from replacing \(\omega\) with +\(n\omega\) for each term in the particular solution,

    +
    +\[\begin{split} +\begin{eqnarray} +x_p(t)&=&\frac{f_0}{2k}+\sum_{n>0} \alpha_n\cos(n\omega t-\delta_n)+\beta_n\sin(n\omega t-\delta_n),\\ +\nonumber +\alpha_n&=&\frac{f_n/m}{\sqrt{((n\omega)^2-\omega_0^2)+4\beta^2n^2\omega^2}},\\ +\nonumber +\beta_n&=&\frac{g_n/m}{\sqrt{((n\omega)^2-\omega_0^2)+4\beta^2n^2\omega^2}},\\ +\nonumber +\delta_n&=&\tan^{-1}\left(\frac{2\beta n\omega}{\omega_0^2-n^2\omega^2}\right). +\end{eqnarray} +\end{split}\]
    +

    Because the forces have been applied for a long time, any non-zero +damping eliminates the homogenous parts of the solution, so one need +only consider the particular solution for each \(n\).

    +

    The problem is considered solved if one can find expressions for the +coefficients \(f_n\) and \(g_n\), even though the solutions are expressed +as an infinite sum. The coefficients can be extracted from the +function \(F(t)\) by

    + +
    +
    +\[\begin{split} +\begin{eqnarray} +\label{eq:fourierdef2} \tag{4} +f_n&=&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~F(t)\cos(2n\pi t/\tau),\\ +\nonumber +g_n&=&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~F(t)\sin(2n\pi t/\tau). +\end{eqnarray} +\end{split}\]
    +

    To check the consistency of these expressions and to verify +Eq. (4), one can insert the expansion of \(F(t)\) in +Eq. (3) into the expression for the coefficients in +Eq. (4) and see whether

    +
    +\[ +\begin{eqnarray} +f_n&=?&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~\left\{ +\frac{f_0}{2}+\sum_{m>0}f_m\cos(m\omega t)+g_m\sin(m\omega t) +\right\}\cos(n\omega t). +\end{eqnarray} +\]
    +

    Immediately, one can throw away all the terms with \(g_m\) because they +convolute an even and an odd function. The term with \(f_0/2\) +disappears because \(\cos(n\omega t)\) is equally positive and negative +over the interval and will integrate to zero. For all the terms +\(f_m\cos(m\omega t)\) appearing in the sum, one can use angle addition +formulas to see that \(\cos(m\omega t)\cos(n\omega +t)=(1/2)(\cos[(m+n)\omega t]+\cos[(m-n)\omega t]\). This will integrate +to zero unless \(m=n\). In that case the \(m=n\) term gives

    + +
    +
    +\[ +\begin{equation} +\int_{-\tau/2}^{\tau/2}dt~\cos^2(m\omega t)=\frac{\tau}{2}, +\label{_auto3} \tag{5} +\end{equation} +\]
    +

    and

    +
    +\[\begin{split} +\begin{eqnarray} +f_n&=?&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~f_n/2\\ +\nonumber +&=&f_n~\checkmark. +\end{eqnarray} +\end{split}\]
    +

    The same method can be used to check for the consistency of \(g_n\).

    +

    The code here uses the Fourier series applied to a +square wave signal. The code here +visualizes the various approximations given by Fourier series compared +with a square wave with period \(T=0.2\) (dimensionless time), width \(0.1\) and max value of the force \(F=2\). We +see that when we increase the number of components in the Fourier +series, the Fourier series approximation gets closer and closer to the +square wave signal.

    +
    +
    +
    import numpy as np
+import math
+from scipy import signal
+import matplotlib.pyplot as plt
+
+# number of points                                                                                       
+n = 500
+# start and final times                                                                                  
+t0 = 0.0
+tn = 1.0
+# Period                                                                                                 
+T =0.2
+# Max value of square signal                                                                             
+Fmax= 2.0
+# Width of signal   
+Width = 0.1
+t = np.linspace(t0, tn, n, endpoint=False)
+SqrSignal = np.zeros(n)
+FourierSeriesSignal = np.zeros(n)
+SqrSignal = 1.0+signal.square(2*np.pi*5*t+np.pi*Width/T)
+a0 = Fmax*Width/T
+FourierSeriesSignal = a0
+Factor = 2.0*Fmax/np.pi
+for i in range(1,500):
+    FourierSeriesSignal += Factor/(i)*np.sin(np.pi*i*Width/T)*np.cos(i*t*2*np.pi/T)
+plt.plot(t, SqrSignal)
+plt.plot(t, FourierSeriesSignal)
+plt.ylim(-0.5, 2.5)
+plt.show()
+
    +
    +
    +
    +_images/chapter12_51_0.png +
    +
    +
    +
    +
    +

    16.4. Two-dimensional Objects

    +

    We often use convolutions over more than one dimension at a time. If +we have a two-dimensional image \(I\) as input, we can have a filter +defined by a two-dimensional kernel \(K\). This leads to an output \(S\)

    +
    +\[ +S_(i,j)=(I * K)(i,j) = \sum_m\sum_n I(m,n)K(i-m,j-n). +\]
    +

    Convolution is a commutatitave process, which means we can rewrite this equation as

    +
    +\[ +S_(i,j)=(I * K)(i,j) = \sum_m\sum_n I(i-m,j-n)K(m,n). +\]
    +

    Normally the latter is more straightforward to implement in a machine elarning library since there is less variation in the range of values of \(m\) and \(n\).

    +

    Many deep learning libraries implement cross-correlation instead of convolution

    +
    +\[ +S_(i,j)=(I * K)(i,j) = \sum_m\sum_n I(i+m,j-+)K(m,n). +\]
    +
    +
    +

    16.5. More on Dimensionalities

    +

    In fields like signal processing (and imaging as well), one designs +so-called filters. These filters are defined by the convolutions and +are often hand-crafted. One may specify filters for smoothing, edge +detection, frequency reshaping, and similar operations. However with +neural networks the idea is to automatically learn the filters and use +many of them in conjunction with non-linear operations (activation +functions).

    +

    As an example consider a neural network operating on sound sequence +data. Assume that we an input vector \(\boldsymbol{x}\) of length \(d=10^6\). We +construct then a neural network with onle hidden layer only with +\(10^4\) nodes. This means that we will have a weight matrix with +\(10^4\times 10^6=10^{10}\) weights to be determined, together with \(10^4\) biases.

    +

    Assume furthermore that we have an output layer which is meant to train whether the sound sequence represents a human voice (true) or something else (false). +It means that we have only one output node. But since this output node connects to \(10^4\) nodes in the hidden layer, there are in total \(10^4\) weights to be determined for the output layer, plus one bias. In total we have

    +
    +\[ +\mathrm{NumberParameters}=10^{10}+10^4+10^4+1 \approx 10^{10}, +\]
    +

    that is ten billion parameters to determine.

    +
    +
    +

    16.6. Further Dimensionality Remarks

    +

    In today’s architecture one can train such neural networks, however +this is a huge number of parameters for the task at hand. In general, +it is a very wasteful and inefficient use of dense matrices as +parameters. Just as importantly, such trained network parameters are +very specific for the type of input data on which they were trained +and the network is not likely to generalize easily to variations in +the input.

    +

    The main principles that justify convolutions is locality of +information and repetion of patterns within the signal. Sound samples +of the input in adjacent spots are much more likely to affect each +other than those that are very far away. Similarly, sounds are +repeated in multiple times in the signal. While slightly simplistic, +reasoning about such a sound example demonstrates this. The same +principles then apply to images and other similar data.

    +
    +
    +

    16.7. CNNs in more detail, building convolutional neural networks in Tensorflow and Keras

    +

    As discussed above, CNNs are neural networks built from the assumption that the inputs +to the network are 2D images. This is important because the number of features or pixels in images +grows very fast with the image size, and an enormous number of weights and biases are needed in order to build an accurate network.

    +

    As before, we still have our input, a hidden layer and an output. What’s novel about convolutional networks +are the convolutional and pooling layers stacked in pairs between the input and the hidden layer. +In addition, the data is no longer represented as a 2D feature matrix, instead each input is a number of 2D +matrices, typically 1 for each color dimension (Red, Green, Blue).

    +

    It means that to represent the entire +dataset of images, we require a 4D matrix or tensor. This tensor has the dimensions:

    +
    +\[ +(n_{inputs},\, n_{pixels, width},\, n_{pixels, height},\, depth) . +\]
    +
    +

    16.7.1. The MNIST dataset again

    +

    The MNIST dataset consists of grayscale images with a pixel size of +\(28\times 28\), meaning we require \(28 \times 28 = 724\) weights to each +neuron in the first hidden layer.

    +

    If we were to analyze images of size \(128\times 128\) we would require +\(128 \times 128 = 16384\) weights to each neuron. Even worse if we were +dealing with color images, as most images are, we have an image matrix +of size \(128\times 128\) for each color dimension (Red, Green, Blue), +meaning 3 times the number of weights \(= 49152\) are required for every +single neuron in the first hidden layer.

    +

    Images typically have strong local correlations, meaning that a small +part of the image varies little from its neighboring regions. If for +example we have an image of a blue car, we can roughly assume that a +small blue part of the image is surrounded by other blue regions.

    +

    Therefore, instead of connecting every single pixel to a neuron in the +first hidden layer, as we have previously done with deep neural +networks, we can instead connect each neuron to a small part of the +image (in all 3 RGB depth dimensions). The size of each small area is +fixed, and known as a receptive.

    +

    The layers of a convolutional neural network arrange neurons in 3D: width, height and depth.
    +The input image is typically a square matrix of depth 3.

    +

    A convolution is performed on the image which outputs +a 3D volume of neurons. The weights to the input are arranged in a number of 2D matrices, known as filters.

    +

    Each filter slides along the input image, taking the dot product +between each small part of the image and the filter, in all depth +dimensions. This is then passed through a non-linear function, +typically the Rectified Linear (ReLu) function, which serves as the +activation of the neurons in the first convolutional layer. This is +further passed through a pooling layer, which reduces the size of the +convolutional layer, e.g. by taking the maximum or average across some +small regions, and this serves as input to the next convolutional +layer.

    +
    +
    +

    16.7.2. Systematic reduction

    +

    By systematically reducing the size of the input volume, through +convolution and pooling, the network should create representations of +small parts of the input, and then from them assemble representations +of larger areas. The final pooling layer is flattened to serve as +input to a hidden layer, such that each neuron in the final pooling +layer is connected to every single neuron in the hidden layer. This +then serves as input to the output layer, e.g. a softmax output for +classification.

    +
    +
    +

    16.7.3. Prerequisites: Collect and pre-process data

    +
    +
    +
    # import necessary packages
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn import datasets
+
+
+# ensure the same random numbers appear every time
+np.random.seed(0)
+
+# display images in notebook
+%matplotlib inline
+plt.rcParams['figure.figsize'] = (12,12)
+
+
+# download MNIST dataset
+digits = datasets.load_digits()
+
+# define inputs and labels
+inputs = digits.images
+labels = digits.target
+
+# RGB images have a depth of 3
+# our images are grayscale so they should have a depth of 1
+inputs = inputs[:,:,:,np.newaxis]
+
+print("inputs = (n_inputs, pixel_width, pixel_height, depth) = " + str(inputs.shape))
+print("labels = (n_inputs) = " + str(labels.shape))
+
+
+# choose some random images to display
+n_inputs = len(inputs)
+indices = np.arange(n_inputs)
+random_indices = np.random.choice(indices, size=5)
+
+for i, image in enumerate(digits.images[random_indices]):
+    plt.subplot(1, 5, i+1)
+    plt.axis('off')
+    plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')
+    plt.title("Label: %d" % digits.target[random_indices[i]])
+plt.show()
+
    +
    +
    +
    +
    inputs = (n_inputs, pixel_width, pixel_height, depth) = (1797, 8, 8, 1)
+labels = (n_inputs) = (1797,)
+
    +
    +_images/chapter12_67_1.png +
    +
    +
    +
    +
    from tensorflow.keras import datasets, layers, models
+from tensorflow.keras.layers import Input
+from tensorflow.keras.models import Sequential      #This allows appending layers to existing models
+from tensorflow.keras.layers import Dense           #This allows defining the characteristics of a particular layer
+from tensorflow.keras import optimizers             #This allows using whichever optimiser we want (sgd,adam,RMSprop)
+from tensorflow.keras import regularizers           #This allows using whichever regularizer we want (l1,l2,l1_l2)
+from tensorflow.keras.utils import to_categorical   #This allows using categorical cross entropy as the cost function
+#from tensorflow.keras import Conv2D
+#from tensorflow.keras import MaxPooling2D
+#from tensorflow.keras import Flatten
+
+from sklearn.model_selection import train_test_split
+
+# representation of labels
+labels = to_categorical(labels)
+
+# split into train and test data
+# one-liner from scikit-learn library
+train_size = 0.8
+test_size = 1 - train_size
+X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,
+                                                    test_size=test_size)
+
    +
    +
    +
    +
    +
    +
    def create_convolutional_neural_network_keras(input_shape, receptive_field,
+                                              n_filters, n_neurons_connected, n_categories,
+                                              eta, lmbd):
+    model = Sequential()
+    model.add(layers.Conv2D(n_filters, (receptive_field, receptive_field), input_shape=input_shape, padding='same',
+              activation='relu', kernel_regularizer=regularizers.l2(lmbd)))
+    model.add(layers.MaxPooling2D(pool_size=(2, 2)))
+    model.add(layers.Flatten())
+    model.add(layers.Dense(n_neurons_connected, activation='relu', kernel_regularizer=regularizers.l2(lmbd)))
+    model.add(layers.Dense(n_categories, activation='softmax', kernel_regularizer=regularizers.l2(lmbd)))
+    
+    sgd = optimizers.SGD(lr=eta)
+    model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])
+    
+    return model
+
+epochs = 100
+batch_size = 100
+input_shape = X_train.shape[1:4]
+receptive_field = 3
+n_filters = 10
+n_neurons_connected = 50
+n_categories = 10
+
+eta_vals = np.logspace(-5, 1, 7)
+lmbd_vals = np.logspace(-5, 1, 7)
+
    +
    +
    +
    +
    +
    +
    CNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)
+        
+for i, eta in enumerate(eta_vals):
+    for j, lmbd in enumerate(lmbd_vals):
+        CNN = create_convolutional_neural_network_keras(input_shape, receptive_field,
+                                              n_filters, n_neurons_connected, n_categories,
+                                              eta, lmbd)
+        CNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)
+        scores = CNN.evaluate(X_test, Y_test)
+        
+        CNN_keras[i][j] = CNN
+        
+        print("Learning rate = ", eta)
+        print("Lambda = ", lmbd)
+        print("Test accuracy: %.3f" % scores[1])
+        print()
+
    +
    +
    +
    +
    2021-12-08 06:58:03.630224: I tensorflow/core/platform/cpu_feature_guard.cc:142] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations:  SSE4.1 SSE4.2 AVX AVX2 FMA
+To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.
+/Users/MortenImac/anaconda3/lib/python3.8/site-packages/keras/optimizer_v2/optimizer_v2.py:355: UserWarning: The `lr` argument is deprecated, use `learning_rate` instead.
+  warnings.warn(
+
    +
    +
    2021-12-08 06:58:04.114437: I tensorflow/compiler/mlir/mlir_graph_optimization_pass.cc:185] None of the MLIR Optimization Passes are enabled (registered 2)
+
    +
    +
     1/12 [=>............................] - ETA: 1s - loss: 2.4411 - accuracy: 0.2500
+
    +
    +
    
+12/12 [==============================] - 0s 853us/step - loss: 2.4410 - accuracy: 0.1944
+
    +
    +
    Learning rate =  1e-05
+Lambda =  1e-05
+Test accuracy: 0.194
+
    +
    +
     1/12 [=>............................] - ETA: 0s - loss: 4.2597 - accuracy: 0.0938
+
    +
    +
    
+12/12 [==============================] - 0s 842us/step - loss: 3.4744 - accuracy: 0.1361
+
    +
    +
    Learning rate =  1e-05
+Lambda =  0.0001
+Test accuracy: 0.136
+
    +
    +
     1/12 [=>............................] - ETA: 1s - loss: 3.0466 - accuracy: 0.1562
+
    +
    +
    
+12/12 [==============================] - 0s 743us/step - loss: 2.9400 - accuracy: 0.1028
+
    +
    +
    Learning rate =  1e-05
+Lambda =  0.001
+Test accuracy: 0.103
+
    +
    +
     1/12 [=>............................] - ETA: 1s - loss: 3.8064 - accuracy: 0.1250
+
    +
    +
    
+12/12 [==============================] - 0s 912us/step - loss: 3.8175 - accuracy: 0.1056
+
    +
    +
    Learning rate =  1e-05
+Lambda =  0.01
+Test accuracy: 0.106
+
    +
    +
     1/12 [=>............................] - ETA: 1s - loss: 12.1612 - accuracy: 0.0938
+
    +
    +
    
+12/12 [==============================] - 0s 763us/step - loss: 12.3063 - accuracy: 0.1361
+
    +
    +
    Learning rate =  1e-05
+Lambda =  0.1
+Test accuracy: 0.136
+
    +
    +
     1/12 [=>............................] - ETA: 0s - loss: 91.8768 - accuracy: 0.2812
+
    +
    +
    
+12/12 [==============================] - 0s 922us/step - loss: 92.0923 - accuracy: 0.2972
+
    +
    +
    Learning rate =  1e-05
+Lambda =  1.0
+Test accuracy: 0.297
+
    +
    +
     1/12 [=>............................] - ETA: 0s - loss: 529.5700 - accuracy: 0.2188
+
    +
    +
    
+12/12 [==============================] - 0s 935us/step - loss: 529.7050 - accuracy: 0.1861
+
    +
    +
    Learning rate =  1e-05
+Lambda =  10.0
+Test accuracy: 0.186
+
    +
    +
     1/12 [=>............................] - ETA: 1s - loss: 1.2495 - accuracy: 0.5312
+
    +
    +
    
+12/12 [==============================] - 0s 750us/step - loss: 1.5138 - accuracy: 0.4694
+
    +
    +
    Learning rate =  0.0001
+Lambda =  1e-05
+Test accuracy: 0.469
+
    +
    +
     1/12 [=>............................] - ETA: 0s - loss: 1.4077 - accuracy: 0.6562
+
    +
    +
    
+12/12 [==============================] - 0s 954us/step - loss: 1.4837 - accuracy: 0.5611
+
    +
    +
    Learning rate =  0.0001
+Lambda =  0.0001
+Test accuracy: 0.561
+
    +
    +
     1/12 [=>............................] - ETA: 0s - loss: 1.5539 - accuracy: 0.5625
+
    +
    +
    
+12/12 [==============================] - 0s 932us/step - loss: 1.5615 - accuracy: 0.5639
+
    +
    +
    Learning rate =  0.0001
+Lambda =  0.001
+Test accuracy: 0.564
+
    +
    +
    ---------------------------------------------------------------------------
+KeyboardInterrupt                         Traceback (most recent call last)
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47647/2018906331.py in <module>
+      6                                               n_filters, n_neurons_connected, n_categories,
+      7                                               eta, lmbd)
+----> 8         CNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)
+      9         scores = CNN.evaluate(X_test, Y_test)
+     10 
+
+~/anaconda3/lib/python3.8/site-packages/keras/engine/training.py in fit(self, x, y, batch_size, epochs, verbose, callbacks, validation_split, validation_data, shuffle, class_weight, sample_weight, initial_epoch, steps_per_epoch, validation_steps, validation_batch_size, validation_freq, max_queue_size, workers, use_multiprocessing)
+   1182                 _r=1):
+   1183               callbacks.on_train_batch_begin(step)
+-> 1184               tmp_logs = self.train_function(iterator)
+   1185               if data_handler.should_sync:
+   1186                 context.async_wait()
+
+~/anaconda3/lib/python3.8/site-packages/tensorflow/python/eager/def_function.py in __call__(self, *args, **kwds)
+    883 
+    884       with OptionalXlaContext(self._jit_compile):
+--> 885         result = self._call(*args, **kwds)
+    886 
+    887       new_tracing_count = self.experimental_get_tracing_count()
+
+~/anaconda3/lib/python3.8/site-packages/tensorflow/python/eager/def_function.py in _call(self, *args, **kwds)
+    915       # In this case we have created variables on the first call, so we run the
+    916       # defunned version which is guaranteed to never create variables.
+--> 917       return self._stateless_fn(*args, **kwds)  # pylint: disable=not-callable
+    918     elif self._stateful_fn is not None:
+    919       # Release the lock early so that multiple threads can perform the call
+
+~/anaconda3/lib/python3.8/site-packages/tensorflow/python/eager/function.py in __call__(self, *args, **kwargs)
+   3037       (graph_function,
+   3038        filtered_flat_args) = self._maybe_define_function(args, kwargs)
+-> 3039     return graph_function._call_flat(
+   3040         filtered_flat_args, captured_inputs=graph_function.captured_inputs)  # pylint: disable=protected-access
+   3041 
+
+~/anaconda3/lib/python3.8/site-packages/tensorflow/python/eager/function.py in _call_flat(self, args, captured_inputs, cancellation_manager)
+   1961         and executing_eagerly):
+   1962       # No tape is watching; skip to running the function.
+-> 1963       return self._build_call_outputs(self._inference_function.call(
+   1964           ctx, args, cancellation_manager=cancellation_manager))
+   1965     forward_backward = self._select_forward_and_backward_functions(
+
+~/anaconda3/lib/python3.8/site-packages/tensorflow/python/eager/function.py in call(self, ctx, args, cancellation_manager)
+    589       with _InterpolateFunctionError(self):
+    590         if cancellation_manager is None:
+--> 591           outputs = execute.execute(
+    592               str(self.signature.name),
+    593               num_outputs=self._num_outputs,
+
+~/anaconda3/lib/python3.8/site-packages/tensorflow/python/eager/execute.py in quick_execute(op_name, num_outputs, inputs, attrs, ctx, name)
+     57   try:
+     58     ctx.ensure_initialized()
+---> 59     tensors = pywrap_tfe.TFE_Py_Execute(ctx._handle, device_name, op_name,
+     60                                         inputs, attrs, num_outputs)
+     61   except core._NotOkStatusException as e:
+
+KeyboardInterrupt: 
+
    +
    +
    +
    +
    +
    +
    # visual representation of grid search
+# uses seaborn heatmap, could probably do this in matplotlib
+import seaborn as sns
+
+sns.set()
+
+train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))
+
+for i in range(len(eta_vals)):
+    for j in range(len(lmbd_vals)):
+        CNN = CNN_keras[i][j]
+
+        train_accuracy[i][j] = CNN.evaluate(X_train, Y_train)[1]
+        test_accuracy[i][j] = CNN.evaluate(X_test, Y_test)[1]
+
+        
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Training Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
+fig, ax = plt.subplots(figsize = (10, 10))
+sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis")
+ax.set_title("Test Accuracy")
+ax.set_ylabel("$\eta$")
+ax.set_xlabel("$\lambda$")
+plt.show()
+
    +
    +
    +
    +
    +
    +
    +

    16.8. The CIFAR01 data set

    +

    The CIFAR10 dataset contains 60,000 color images in 10 classes, with +6,000 images in each class. The dataset is divided into 50,000 +training images and 10,000 testing images. The classes are mutually +exclusive and there is no overlap between them.

    +
    +
    +
    import tensorflow as tf
+
+from tensorflow.keras import datasets, layers, models
+import matplotlib.pyplot as plt
+
+# We import the data set
+(train_images, train_labels), (test_images, test_labels) = datasets.cifar10.load_data()
+
+# Normalize pixel values to be between 0 and 1 by dividing by 255. 
+train_images, test_images = train_images / 255.0, test_images / 255.0
+
    +
    +
    +
    +

    To verify that the dataset looks correct, let’s plot the first 25 images from the training set and display the class name below each image.

    +
    +
    +
    class_names = ['airplane', 'automobile', 'bird', 'cat', 'deer',
+               'dog', 'frog', 'horse', 'ship', 'truck']
+​
+plt.figure(figsize=(10,10))
+for i in range(25):
+    plt.subplot(5,5,i+1)
+    plt.xticks([])
+    plt.yticks([])
+    plt.grid(False)
+    plt.imshow(train_images[i], cmap=plt.cm.binary)
+    # The CIFAR labels happen to be arrays, 
+    # which is why you need the extra index
+    plt.xlabel(class_names[train_labels[i][0]])
+plt.show()
+
    +
    +
    +
    +

    The six lines of code below define the convolutional base using a common pattern: a stack of Conv2D and MaxPooling2D layers.

    +

    As input, a CNN takes tensors of shape (image_height, image_width, color_channels), ignoring the batch size. If you are new to these dimensions, color_channels refers to (R,G,B). In this example, you will configure our CNN to process inputs of shape (32, 32, 3), which is the format of CIFAR images. You can do this by passing the argument input_shape to our first layer.

    +
    +
    +
    model = models.Sequential()
+model.add(layers.Conv2D(32, (3, 3), activation='relu', input_shape=(32, 32, 3)))
+model.add(layers.MaxPooling2D((2, 2)))
+model.add(layers.Conv2D(64, (3, 3), activation='relu'))
+model.add(layers.MaxPooling2D((2, 2)))
+model.add(layers.Conv2D(64, (3, 3), activation='relu'))
+
+# Let's display the architecture of our model so far.
+
+model.summary()
+
    +
    +
    +
    +

    You can see that the output of every Conv2D and MaxPooling2D layer is a 3D tensor of shape (height, width, channels). The width and height dimensions tend to shrink as you go deeper in the network. The number of output channels for each Conv2D layer is controlled by the first argument (e.g., 32 or 64). Typically, as the width and height shrink, you can afford (computationally) to add more output channels in each Conv2D layer.

    +

    To complete our model, you will feed the last output tensor from the +convolutional base (of shape (4, 4, 64)) into one or more Dense layers +to perform classification. Dense layers take vectors as input (which +are 1D), while the current output is a 3D tensor. First, you will +flatten (or unroll) the 3D output to 1D, then add one or more Dense +layers on top. CIFAR has 10 output classes, so you use a final Dense +layer with 10 outputs and a softmax activation.

    +
    +
    +
    model.add(layers.Flatten())
+model.add(layers.Dense(64, activation='relu'))
+model.add(layers.Dense(10))
+Here's the complete architecture of our model.
+
+model.summary()
+
    +
    +
    +
    +

    As you can see, our (4, 4, 64) outputs were flattened into vectors of shape (1024) before going through two Dense layers.

    +
    +
    +
    model.compile(optimizer='adam',
+              loss=tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True),
+              metrics=['accuracy'])
+​
+history = model.fit(train_images, train_labels, epochs=10, 
+                    validation_data=(test_images, test_labels))
+
    +
    +
    +
    +
    +
    +
    plt.plot(history.history['accuracy'], label='accuracy')
+plt.plot(history.history['val_accuracy'], label = 'val_accuracy')
+plt.xlabel('Epoch')
+plt.ylabel('Accuracy')
+plt.ylim([0.5, 1])
+plt.legend(loc='lower right')
+
+test_loss, test_acc = model.evaluate(test_images,  test_labels, verbose=2)
+
+print(test_acc)
+
    +
    +
    +
    +
    +
    + + + + +
    + + + + + + +
    + + + + +
    + +
    +
    +
    +
    +

    + + By Morten Hjorth-Jensen
    + + © Copyright 2021.
    +

    +
    +
    +
    + + +
    +
    + + + + + + \ No newline at end of file diff --git a/doc/LectureNotes/_build/html/chapter13.html b/doc/LectureNotes/_build/html/chapter13.html new file mode 100644 index 000000000..f7f0db19c --- /dev/null +++ b/doc/LectureNotes/_build/html/chapter13.html @@ -0,0 +1,2386 @@ + + + + + + + + 17. Recurrent neural networks: Overarching view — Applied Data Analysis and Machine Learning + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    + +
    +
    +
    +
    + + + + +
    + + +
    + + + + + + +
    +
    + + + + + + + + + +
    + + +
    + +
    + Contents +
    + +
    +
    +
    +
    +
    + +
    + +
    +

    17. Recurrent neural networks: Overarching view

    +

    Till now our focus has been, including convolutional neural networks +as well, on feedforward neural networks. The output or the activations +flow only in one direction, from the input layer to the output layer.

    +

    A recurrent neural network (RNN) looks very much like a feedforward +neural network, except that it also has connections pointing +backward.

    +

    RNNs are used to analyze time series data such as stock prices, and +tell you when to buy or sell. In autonomous driving systems, they can +anticipate car trajectories and help avoid accidents. More generally, +they can work on sequences of arbitrary lengths, rather than on +fixed-sized inputs like all the nets we have discussed so far. For +example, they can take sentences, documents, or audio samples as +input, making them extremely useful for natural language processing +systems such as automatic translation and speech-to-text.

    +

    More to text to be added

    +
    +

    17.1. A simple example

    +
    +
    +
    %matplotlib inline
+
+# Start importing packages
+import pandas as pd
+import numpy as np
+import matplotlib.pyplot as plt
+import tensorflow as tf
+from tensorflow.keras import datasets, layers, models
+from tensorflow.keras.layers import Input
+from tensorflow.keras.models import Model, Sequential 
+from tensorflow.keras.layers import Dense, SimpleRNN, LSTM, GRU
+from tensorflow.keras import optimizers     
+from tensorflow.keras import regularizers           
+from tensorflow.keras.utils import to_categorical 
+
+
+
+# convert into dataset matrix
+def convertToMatrix(data, step):
+ X, Y =[], []
+ for i in range(len(data)-step):
+  d=i+step  
+  X.append(data[i:d,])
+  Y.append(data[d,])
+ return np.array(X), np.array(Y)
+
+step = 4
+N = 1000    
+Tp = 800    
+
+t=np.arange(0,N)
+x=np.sin(0.02*t)+2*np.random.rand(N)
+df = pd.DataFrame(x)
+df.head()
+
+plt.plot(df)
+plt.show()
+
+values=df.values
+train,test = values[0:Tp,:], values[Tp:N,:]
+
+# add step elements into train and test
+test = np.append(test,np.repeat(test[-1,],step))
+train = np.append(train,np.repeat(train[-1,],step))
+ 
+trainX,trainY =convertToMatrix(train,step)
+testX,testY =convertToMatrix(test,step)
+trainX = np.reshape(trainX, (trainX.shape[0], 1, trainX.shape[1]))
+testX = np.reshape(testX, (testX.shape[0], 1, testX.shape[1]))
+
+model = Sequential()
+model.add(SimpleRNN(units=32, input_shape=(1,step), activation="relu"))
+model.add(Dense(8, activation="relu")) 
+model.add(Dense(1))
+model.compile(loss='mean_squared_error', optimizer='rmsprop')
+model.summary()
+
+model.fit(trainX,trainY, epochs=100, batch_size=16, verbose=2)
+trainPredict = model.predict(trainX)
+testPredict= model.predict(testX)
+predicted=np.concatenate((trainPredict,testPredict),axis=0)
+
+trainScore = model.evaluate(trainX, trainY, verbose=0)
+print(trainScore)
+
+index = df.index.values
+plt.plot(index,df)
+plt.plot(index,predicted)
+plt.axvline(df.index[Tp], c="r")
+plt.show()
+
    +
    +
    +
    +_images/chapter13_3_0.png +
    2021-12-08 06:58:41.160539: I tensorflow/core/platform/cpu_feature_guard.cc:142] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations:  SSE4.1 SSE4.2 AVX AVX2 FMA
+To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.
+2021-12-08 06:58:41.346810: I tensorflow/compiler/mlir/mlir_graph_optimization_pass.cc:185] None of the MLIR Optimization Passes are enabled (registered 2)
+
    +
    +
    Model: "sequential"
+_________________________________________________________________
+Layer (type)                 Output Shape              Param #   
+=================================================================
+simple_rnn (SimpleRNN)       (None, 32)                1184      
+_________________________________________________________________
+dense (Dense)                (None, 8)                 264       
+_________________________________________________________________
+dense_1 (Dense)              (None, 1)                 9         
+=================================================================
+Total params: 1,457
+Trainable params: 1,457
+Non-trainable params: 0
+_________________________________________________________________
+Epoch 1/100
+
    +
    +
    50/50 - 1s - loss: 0.4255
+
    +
    +
    Epoch 2/100
+50/50 - 0s - loss: 0.4030
+
    +
    +
    Epoch 3/100
+50/50 - 0s - loss: 0.3958
+
    +
    +
    Epoch 4/100
+50/50 - 0s - loss: 0.3931
+
    +
    +
    Epoch 5/100
+50/50 - 0s - loss: 0.3914
+
    +
    +
    Epoch 6/100
+50/50 - 0s - loss: 0.3898
+
    +
    +
    Epoch 7/100
+50/50 - 0s - loss: 0.3882
+
    +
    +
    Epoch 8/100
+50/50 - 0s - loss: 0.3885
+
    +
    +
    Epoch 9/100
+
    +
    +
    50/50 - 0s - loss: 0.3871
+
    +
    +
    Epoch 10/100
+
    +
    +
    50/50 - 0s - loss: 0.3876
+
    +
    +
    Epoch 11/100
+
    +
    +
    50/50 - 0s - loss: 0.3867
+
    +
    +
    Epoch 12/100
+
    +
    +
    50/50 - 0s - loss: 0.3850
+
    +
    +
    Epoch 13/100
+
    +
    +
    50/50 - 0s - loss: 0.3854
+
    +
    +
    Epoch 14/100
+
    +
    +
    50/50 - 0s - loss: 0.3802
+
    +
    +
    Epoch 15/100
+
    +
    +
    50/50 - 0s - loss: 0.3842
+
    +
    +
    Epoch 16/100
+
    +
    +
    50/50 - 0s - loss: 0.3820
+
    +
    +
    Epoch 17/100
+
    +
    +
    50/50 - 0s - loss: 0.3842
+
    +
    +
    Epoch 18/100
+
    +
    +
    50/50 - 0s - loss: 0.3827
+
    +
    +
    Epoch 19/100
+
    +
    +
    50/50 - 0s - loss: 0.3819
+
    +
    +
    Epoch 20/100
+
    +
    +
    50/50 - 0s - loss: 0.3818
+
    +
    +
    Epoch 21/100
+
    +
    +
    50/50 - 0s - loss: 0.3803
+
    +
    +
    Epoch 22/100
+
    +
    +
    50/50 - 0s - loss: 0.3833
+
    +
    +
    Epoch 23/100
+
    +
    +
    50/50 - 0s - loss: 0.3804
+
    +
    +
    Epoch 24/100
+
    +
    +
    50/50 - 0s - loss: 0.3811
+
    +
    +
    Epoch 25/100
+
    +
    +
    50/50 - 0s - loss: 0.3805
+
    +
    +
    Epoch 26/100
+
    +
    +
    50/50 - 0s - loss: 0.3779
+
    +
    +
    Epoch 27/100
+
    +
    +
    50/50 - 0s - loss: 0.3791
+
    +
    +
    Epoch 28/100
+50/50 - 0s - loss: 0.3805
+
    +
    +
    Epoch 29/100
+
    +
    +
    50/50 - 0s - loss: 0.3794
+
    +
    +
    Epoch 30/100
+
    +
    +
    50/50 - 0s - loss: 0.3776
+
    +
    +
    Epoch 31/100
+
    +
    +
    50/50 - 0s - loss: 0.3784
+
    +
    +
    Epoch 32/100
+
    +
    +
    50/50 - 0s - loss: 0.3748
+
    +
    +
    Epoch 33/100
+
    +
    +
    50/50 - 0s - loss: 0.3773
+
    +
    +
    Epoch 34/100
+
    +
    +
    50/50 - 0s - loss: 0.3759
+
    +
    +
    Epoch 35/100
+
    +
    +
    50/50 - 0s - loss: 0.3765
+
    +
    +
    Epoch 36/100
+
    +
    +
    50/50 - 0s - loss: 0.3772
+
    +
    +
    Epoch 37/100
+
    +
    +
    50/50 - 0s - loss: 0.3760
+
    +
    +
    Epoch 38/100
+
    +
    +
    50/50 - 0s - loss: 0.3753
+
    +
    +
    Epoch 39/100
+
    +
    +
    50/50 - 0s - loss: 0.3739
+
    +
    +
    Epoch 40/100
+
    +
    +
    50/50 - 0s - loss: 0.3753
+
    +
    +
    Epoch 41/100
+
    +
    +
    50/50 - 0s - loss: 0.3729
+
    +
    +
    Epoch 42/100
+
    +
    +
    50/50 - 0s - loss: 0.3748
+
    +
    +
    Epoch 43/100
+
    +
    +
    50/50 - 0s - loss: 0.3749
+
    +
    +
    Epoch 44/100
+50/50 - 0s - loss: 0.3725
+
    +
    +
    Epoch 45/100
+
    +
    +
    50/50 - 0s - loss: 0.3713
+
    +
    +
    Epoch 46/100
+
    +
    +
    50/50 - 0s - loss: 0.3722
+
    +
    +
    Epoch 47/100
+
    +
    +
    50/50 - 0s - loss: 0.3721
+
    +
    +
    Epoch 48/100
+
    +
    +
    50/50 - 0s - loss: 0.3711
+
    +
    +
    Epoch 49/100
+
    +
    +
    50/50 - 0s - loss: 0.3688
+
    +
    +
    Epoch 50/100
+
    +
    +
    50/50 - 0s - loss: 0.3718
+
    +
    +
    Epoch 51/100
+
    +
    +
    50/50 - 0s - loss: 0.3679
+
    +
    +
    Epoch 52/100
+
    +
    +
    50/50 - 0s - loss: 0.3704
+
    +
    +
    Epoch 53/100
+
    +
    +
    50/50 - 0s - loss: 0.3687
+
    +
    +
    Epoch 54/100
+
    +
    +
    50/50 - 0s - loss: 0.3672
+
    +
    +
    Epoch 55/100
+
    +
    +
    50/50 - 0s - loss: 0.3674
+
    +
    +
    Epoch 56/100
+
    +
    +
    50/50 - 0s - loss: 0.3669
+
    +
    +
    Epoch 57/100
+
    +
    +
    50/50 - 0s - loss: 0.3684
+
    +
    +
    Epoch 58/100
+
    +
    +
    
+
    +
    +
    50/50 - 0s - loss: 0.3668
+
    +
    +
    Epoch 59/100
+
    +
    +
    50/50 - 0s - loss: 0.3673
+
    +
    +
    Epoch 60/100
+
    +
    +
    50/50 - 0s - loss: 0.3655
+
    +
    +
    Epoch 61/100
+
    +
    +
    50/50 - 0s - loss: 0.3659
+
    +
    +
    Epoch 62/100
+
    +
    +
    50/50 - 0s - loss: 0.3647
+
    +
    +
    Epoch 63/100
+
    +
    +
    50/50 - 0s - loss: 0.3646
+
    +
    +
    Epoch 64/100
+
    +
    +
    50/50 - 0s - loss: 0.3628
+
    +
    +
    Epoch 65/100
+
    +
    +
    50/50 - 0s - loss: 0.3646
+
    +
    +
    Epoch 66/100
+
    +
    +
    50/50 - 0s - loss: 0.3643
+
    +
    +
    Epoch 67/100
+
    +
    +
    50/50 - 0s - loss: 0.3645
+
    +
    +
    Epoch 68/100
+
    +
    +
    50/50 - 0s - loss: 0.3627
+
    +
    +
    Epoch 69/100
+
    +
    +
    50/50 - 0s - loss: 0.3624
+
    +
    +
    Epoch 70/100
+
    +
    +
    50/50 - 0s - loss: 0.3615
+
    +
    +
    Epoch 71/100
+
    +
    +
    50/50 - 0s - loss: 0.3605
+
    +
    +
    Epoch 72/100
+
    +
    +
    50/50 - 0s - loss: 0.3609
+
    +
    +
    Epoch 73/100
+50/50 - 0s - loss: 0.3617
+
    +
    +
    Epoch 74/100
+
    +
    +
    50/50 - 0s - loss: 0.3604
+
    +
    +
    Epoch 75/100
+
    +
    +
    50/50 - 0s - loss: 0.3606
+
    +
    +
    Epoch 76/100
+
    +
    +
    50/50 - 0s - loss: 0.3598
+
    +
    +
    Epoch 77/100
+
    +
    +
    50/50 - 0s - loss: 0.3595
+
    +
    +
    Epoch 78/100
+
    +
    +
    50/50 - 0s - loss: 0.3593
+
    +
    +
    Epoch 79/100
+
    +
    +
    50/50 - 0s - loss: 0.3585
+
    +
    +
    Epoch 80/100
+
    +
    +
    50/50 - 0s - loss: 0.3587
+
    +
    +
    Epoch 81/100
+
    +
    +
    50/50 - 0s - loss: 0.3572
+
    +
    +
    Epoch 82/100
+
    +
    +
    50/50 - 0s - loss: 0.3567
+
    +
    +
    Epoch 83/100
+
    +
    +
    50/50 - 0s - loss: 0.3576
+
    +
    +
    Epoch 84/100
+
    +
    +
    50/50 - 0s - loss: 0.3577
+
    +
    +
    Epoch 85/100
+
    +
    +
    50/50 - 0s - loss: 0.3548
+
    +
    +
    Epoch 86/100
+50/50 - 0s - loss: 0.3575
+
    +
    +
    Epoch 87/100
+
    +
    +
    50/50 - 0s - loss: 0.3551
+
    +
    +
    Epoch 88/100
+
    +
    +
    50/50 - 0s - loss: 0.3556
+
    +
    +
    Epoch 89/100
+
    +
    +
    50/50 - 0s - loss: 0.3546
+
    +
    +
    Epoch 90/100
+
    +
    +
    50/50 - 0s - loss: 0.3560
+
    +
    +
    Epoch 91/100
+
    +
    +
    50/50 - 0s - loss: 0.3558
+
    +
    +
    Epoch 92/100
+
    +
    +
    50/50 - 0s - loss: 0.3538
+
    +
    +
    Epoch 93/100
+
    +
    +
    50/50 - 0s - loss: 0.3525
+
    +
    +
    Epoch 94/100
+50/50 - 0s - loss: 0.3525
+
    +
    +
    Epoch 95/100
+
    +
    +
    50/50 - 0s - loss: 0.3543
+
    +
    +
    Epoch 96/100
+
    +
    +
    50/50 - 0s - loss: 0.3514
+
    +
    +
    Epoch 97/100
+
    +
    +
    50/50 - 0s - loss: 0.3529
+
    +
    +
    Epoch 98/100
+
    +
    +
    50/50 - 0s - loss: 0.3522
+
    +
    +
    Epoch 99/100
+
    +
    +
    50/50 - 0s - loss: 0.3522
+
    +
    +
    Epoch 100/100
+50/50 - 0s - loss: 0.3498
+
    +
    +
    0.3469819128513336
+
    +
    +
    ---------------------------------------------------------------------------
+KeyError                                  Traceback (most recent call last)
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47724/2517560119.py in <module>
+     65 
+     66 index = df.index.values
+---> 67 plt.plot(index,df)
+     68 plt.plot(index,predicted)
+     69 plt.axvline(df.index[Tp], c="r")
+
+~/anaconda3/lib/python3.8/site-packages/matplotlib/pyplot.py in plot(scalex, scaley, data, *args, **kwargs)
+   3017 @_copy_docstring_and_deprecators(Axes.plot)
+   3018 def plot(*args, scalex=True, scaley=True, data=None, **kwargs):
+-> 3019     return gca().plot(
+   3020         *args, scalex=scalex, scaley=scaley,
+   3021         **({"data": data} if data is not None else {}), **kwargs)
+
+~/anaconda3/lib/python3.8/site-packages/matplotlib/axes/_axes.py in plot(self, scalex, scaley, data, *args, **kwargs)
+   1603         """
+   1604         kwargs = cbook.normalize_kwargs(kwargs, mlines.Line2D)
+-> 1605         lines = [*self._get_lines(*args, data=data, **kwargs)]
+   1606         for line in lines:
+   1607             self.add_line(line)
+
+~/anaconda3/lib/python3.8/site-packages/matplotlib/axes/_base.py in __call__(self, data, *args, **kwargs)
+    313                 this += args[0],
+    314                 args = args[1:]
+--> 315             yield from self._plot_args(this, kwargs)
+    316 
+    317     def get_next_color(self):
+
+~/anaconda3/lib/python3.8/site-packages/matplotlib/axes/_base.py in _plot_args(self, tup, kwargs, return_kwargs)
+    489         if len(xy) == 2:
+    490             x = _check_1d(xy[0])
+--> 491             y = _check_1d(xy[1])
+    492         else:
+    493             x, y = index_of(xy[-1])
+
+~/anaconda3/lib/python3.8/site-packages/matplotlib/cbook/__init__.py in _check_1d(x)
+   1360                     message='Support for multi-dimensional indexing')
+   1361 
+-> 1362                 ndim = x[:, None].ndim
+   1363                 # we have definitely hit a pandas index or series object
+   1364                 # cast to a numpy array.
+
+~/anaconda3/lib/python3.8/site-packages/pandas/core/frame.py in __getitem__(self, key)
+   3456             if self.columns.nlevels > 1:
+   3457                 return self._getitem_multilevel(key)
+-> 3458             indexer = self.columns.get_loc(key)
+   3459             if is_integer(indexer):
+   3460                 indexer = [indexer]
+
+~/anaconda3/lib/python3.8/site-packages/pandas/core/indexes/range.py in get_loc(self, key, method, tolerance)
+    386                 except ValueError as err:
+    387                     raise KeyError(key) from err
+--> 388             raise KeyError(key)
+    389         return super().get_loc(key, method=method, tolerance=tolerance)
+    390 
+
+KeyError: (slice(None, None, None), None)
+
    +
    +_images/chapter13_3_192.png +
    +
    +
    +
    +

    17.2. An extrapolation example

    +

    The following code provides an example of how recurrent neural +networks can be used to extrapolate to unknown values of physics data +sets. Specifically, the data sets used in this program come from +a quantum mechanical many-body calculation of energies as functions of the number of particles.

    +
    +
    +
    # For matrices and calculations
+import numpy as np
+# For machine learning (backend for keras)
+import tensorflow as tf
+# User-friendly machine learning library
+# Front end for TensorFlow
+import tensorflow.keras
+# Different methods from Keras needed to create an RNN
+# This is not necessary but it shortened function calls 
+# that need to be used in the code.
+from tensorflow.keras import datasets, layers, models
+from tensorflow.keras.layers import Input
+from tensorflow.keras import regularizers
+from tensorflow.keras.models import Model, Sequential
+from tensorflow.keras.layers import Dense, SimpleRNN, LSTM, GRU
+# For timing the code
+from timeit import default_timer as timer
+# For plotting
+import matplotlib.pyplot as plt
+
+
+# The data set
+datatype='VaryDimension'
+X_tot = np.arange(2, 42, 2)
+y_tot = np.array([-0.03077640549, -0.08336233266, -0.1446729567, -0.2116753732, -0.2830637392, -0.3581341341, -0.436462435, -0.5177783846,
+	-0.6019067271, -0.6887363571, -0.7782028952, -0.8702784034, -0.9649652536, -1.062292565, -1.16231451, 
+	-1.265109911, -1.370782966, -1.479465113, -1.591317992, -1.70653767])
+
    +
    +
    +
    +

    The way the recurrent neural networks are trained in this program +differs from how machine learning algorithms are usually trained. +Typically a machine learning algorithm is trained by learning the +relationship between the x data and the y data. In this program, the +recurrent neural network will be trained to recognize the relationship +in a sequence of y values. This is type of data formatting is +typically used time series forcasting, but it can also be used in any +extrapolation (time series forecasting is just a specific type of +extrapolation along the time axis). This method of data formatting +does not use the x data and assumes that the y data are evenly spaced.

    +

    For a standard machine learning algorithm, the training data has the +form of (x,y) so the machine learning algorithm learns to assiciate a +y value with a given x value. This is useful when the test data has x +values within the same range as the training data. However, for this +application, the x values of the test data are outside of the x values +of the training data and the traditional method of training a machine +learning algorithm does not work as well. For this reason, the +recurrent neural network is trained on sequences of y values of the +form ((y1, y2), y3), so that the network is concerned with learning +the pattern of the y data and not the relation between the x and y +data. As long as the pattern of y data outside of the training region +stays relatively stable compared to what was inside the training +region, this method of training can produce accurate extrapolations to +y values far removed from the training data set.

    +
    +
    +
    # FORMAT_DATA
+def format_data(data, length_of_sequence = 2):  
+    """
+        Inputs:
+            data(a numpy array): the data that will be the inputs to the recurrent neural
+                network
+            length_of_sequence (an int): the number of elements in one iteration of the
+                sequence patter.  For a function approximator use length_of_sequence = 2.
+        Returns:
+            rnn_input (a 3D numpy array): the input data for the recurrent neural network.  Its
+                dimensions are length of data - length of sequence, length of sequence, 
+                dimnsion of data
+            rnn_output (a numpy array): the training data for the neural network
+        Formats data to be used in a recurrent neural network.
+    """
+
+    X, Y = [], []
+    for i in range(len(data)-length_of_sequence):
+        # Get the next length_of_sequence elements
+        a = data[i:i+length_of_sequence]
+        # Get the element that immediately follows that
+        b = data[i+length_of_sequence]
+        # Reshape so that each data point is contained in its own array
+        a = np.reshape (a, (len(a), 1))
+        X.append(a)
+        Y.append(b)
+    rnn_input = np.array(X)
+    rnn_output = np.array(Y)
+
+    return rnn_input, rnn_output
+
+
+# ## Defining the Recurrent Neural Network Using Keras
+# 
+# The following method defines a simple recurrent neural network in keras consisting of one input layer, one hidden layer, and one output layer.
+
+def rnn(length_of_sequences, batch_size = None, stateful = False):
+    """
+        Inputs:
+            length_of_sequences (an int): the number of y values in "x data".  This is determined
+                when the data is formatted
+            batch_size (an int): Default value is None.  See Keras documentation of SimpleRNN.
+            stateful (a boolean): Default value is False.  See Keras documentation of SimpleRNN.
+        Returns:
+            model (a Keras model): The recurrent neural network that is built and compiled by this
+                method
+        Builds and compiles a recurrent neural network with one hidden layer and returns the model.
+    """
+    # Number of neurons in the input and output layers
+    in_out_neurons = 1
+    # Number of neurons in the hidden layer
+    hidden_neurons = 200
+    # Define the input layer
+    inp = Input(batch_shape=(batch_size, 
+                length_of_sequences, 
+                in_out_neurons))  
+    # Define the hidden layer as a simple RNN layer with a set number of neurons and add it to 
+    # the network immediately after the input layer
+    rnn = SimpleRNN(hidden_neurons, 
+                    return_sequences=False,
+                    stateful = stateful,
+                    name="RNN")(inp)
+    # Define the output layer as a dense neural network layer (standard neural network layer)
+    #and add it to the network immediately after the hidden layer.
+    dens = Dense(in_out_neurons,name="dense")(rnn)
+    # Create the machine learning model starting with the input layer and ending with the 
+    # output layer
+    model = Model(inputs=[inp],outputs=[dens])
+    # Compile the machine learning model using the mean squared error function as the loss 
+    # function and an Adams optimizer.
+    model.compile(loss="mean_squared_error", optimizer="adam")  
+    return model
+
    +
    +
    +
    +
    +
    +

    17.3. Predicting New Points With A Trained Recurrent Neural Network

    +
    +
    +
    def test_rnn (x1, y_test, plot_min, plot_max):
+    """
+        Inputs:
+            x1 (a list or numpy array): The complete x component of the data set
+            y_test (a list or numpy array): The complete y component of the data set
+            plot_min (an int or float): the smallest x value used in the training data
+            plot_max (an int or float): the largest x valye used in the training data
+        Returns:
+            None.
+        Uses a trained recurrent neural network model to predict future points in the 
+        series.  Computes the MSE of the predicted data set from the true data set, saves
+        the predicted data set to a csv file, and plots the predicted and true data sets w
+        while also displaying the data range used for training.
+    """
+    # Add the training data as the first dim points in the predicted data array as these
+    # are known values.
+    y_pred = y_test[:dim].tolist()
+    # Generate the first input to the trained recurrent neural network using the last two 
+    # points of the training data.  Based on how the network was trained this means that it
+    # will predict the first point in the data set after the training data.  All of the 
+    # brackets are necessary for Tensorflow.
+    next_input = np.array([[[y_test[dim-2]], [y_test[dim-1]]]])
+    # Save the very last point in the training data set.  This will be used later.
+    last = [y_test[dim-1]]
+
+    # Iterate until the complete data set is created.
+    for i in range (dim, len(y_test)):
+        # Predict the next point in the data set using the previous two points.
+        next = model.predict(next_input)
+        # Append just the number of the predicted data set
+        y_pred.append(next[0][0])
+        # Create the input that will be used to predict the next data point in the data set.
+        next_input = np.array([[last, next[0]]], dtype=np.float64)
+        last = next
+
+    # Print the mean squared error between the known data set and the predicted data set.
+    print('MSE: ', np.square(np.subtract(y_test, y_pred)).mean())
+    # Save the predicted data set as a csv file for later use
+    name = datatype + 'Predicted'+str(dim)+'.csv'
+    np.savetxt(name, y_pred, delimiter=',')
+    # Plot the known data set and the predicted data set.  The red box represents the region that was used
+    # for the training data.
+    fig, ax = plt.subplots()
+    ax.plot(x1, y_test, label="true", linewidth=3)
+    ax.plot(x1, y_pred, 'g-.',label="predicted", linewidth=4)
+    ax.legend()
+    # Created a red region to represent the points used in the training data.
+    ax.axvspan(plot_min, plot_max, alpha=0.25, color='red')
+    plt.show()
+
+# Check to make sure the data set is complete
+assert len(X_tot) == len(y_tot)
+
+# This is the number of points that will be used in as the training data
+dim=12
+
+# Separate the training data from the whole data set
+X_train = X_tot[:dim]
+y_train = y_tot[:dim]
+
+
+# Generate the training data for the RNN, using a sequence of 2
+rnn_input, rnn_training = format_data(y_train, 2)
+
+
+# Create a recurrent neural network in Keras and produce a summary of the 
+# machine learning model
+model = rnn(length_of_sequences = rnn_input.shape[1])
+model.summary()
+
+# Start the timer.  Want to time training+testing
+start = timer()
+# Fit the model using the training data genenerated above using 150 training iterations and a 5%
+# validation split.  Setting verbose to True prints information about each training iteration.
+hist = model.fit(rnn_input, rnn_training, batch_size=None, epochs=150, 
+                 verbose=True,validation_split=0.05)
+
+for label in ["loss","val_loss"]:
+    plt.plot(hist.history[label],label=label)
+
+plt.ylabel("loss")
+plt.xlabel("epoch")
+plt.title("The final validation loss: {}".format(hist.history["val_loss"][-1]))
+plt.legend()
+plt.show()
+
+# Use the trained neural network to predict more points of the data set
+test_rnn(X_tot, y_tot, X_tot[0], X_tot[dim-1])
+# Stop the timer and calculate the total time needed.
+end = timer()
+print('Time: ', end-start)
+
    +
    +
    +
    +

    Changing the size of the recurrent neural network and its parameters +can drastically change the results you get from the model. The below +code takes the simple recurrent neural network from above and adds a +second hidden layer, changes the number of neurons in the hidden +layer, and explicitly declares the activation function of the hidden +layers to be a sigmoid function. The loss function and optimizer can +also be changed but are kept the same as the above network. These +parameters can be tuned to provide the optimal result from the +network. For some ideas on how to improve the performance of a +recurrent neural network.

    +
    +
    +
    def rnn_2layers(length_of_sequences, batch_size = None, stateful = False):
+    """
+        Inputs:
+            length_of_sequences (an int): the number of y values in "x data".  This is determined
+                when the data is formatted
+            batch_size (an int): Default value is None.  See Keras documentation of SimpleRNN.
+            stateful (a boolean): Default value is False.  See Keras documentation of SimpleRNN.
+        Returns:
+            model (a Keras model): The recurrent neural network that is built and compiled by this
+                method
+        Builds and compiles a recurrent neural network with two hidden layers and returns the model.
+    """
+    # Number of neurons in the input and output layers
+    in_out_neurons = 1
+    # Number of neurons in the hidden layer, increased from the first network
+    hidden_neurons = 500
+    # Define the input layer
+    inp = Input(batch_shape=(batch_size, 
+                length_of_sequences, 
+                in_out_neurons))  
+    # Create two hidden layers instead of one hidden layer.  Explicitly set the activation
+    # function to be the sigmoid function (the default value is hyperbolic tangent)
+    rnn1 = SimpleRNN(hidden_neurons, 
+                    return_sequences=True,  # This needs to be True if another hidden layer is to follow
+                    stateful = stateful, activation = 'sigmoid',
+                    name="RNN1")(inp)
+    rnn2 = SimpleRNN(hidden_neurons, 
+                    return_sequences=False, activation = 'sigmoid',
+                    stateful = stateful,
+                    name="RNN2")(rnn1)
+    # Define the output layer as a dense neural network layer (standard neural network layer)
+    #and add it to the network immediately after the hidden layer.
+    dens = Dense(in_out_neurons,name="dense")(rnn2)
+    # Create the machine learning model starting with the input layer and ending with the 
+    # output layer
+    model = Model(inputs=[inp],outputs=[dens])
+    # Compile the machine learning model using the mean squared error function as the loss 
+    # function and an Adams optimizer.
+    model.compile(loss="mean_squared_error", optimizer="adam")  
+    return model
+
+# Check to make sure the data set is complete
+assert len(X_tot) == len(y_tot)
+
+# This is the number of points that will be used in as the training data
+dim=12
+
+# Separate the training data from the whole data set
+X_train = X_tot[:dim]
+y_train = y_tot[:dim]
+
+
+# Generate the training data for the RNN, using a sequence of 2
+rnn_input, rnn_training = format_data(y_train, 2)
+
+
+# Create a recurrent neural network in Keras and produce a summary of the 
+# machine learning model
+model = rnn_2layers(length_of_sequences = 2)
+model.summary()
+
+# Start the timer.  Want to time training+testing
+start = timer()
+# Fit the model using the training data genenerated above using 150 training iterations and a 5%
+# validation split.  Setting verbose to True prints information about each training iteration.
+hist = model.fit(rnn_input, rnn_training, batch_size=None, epochs=150, 
+                 verbose=True,validation_split=0.05)
+
+
+# This section plots the training loss and the validation loss as a function of training iteration.
+# This is not required for analyzing the couple cluster data but can help determine if the network is
+# being overtrained.
+for label in ["loss","val_loss"]:
+    plt.plot(hist.history[label],label=label)
+
+plt.ylabel("loss")
+plt.xlabel("epoch")
+plt.title("The final validation loss: {}".format(hist.history["val_loss"][-1]))
+plt.legend()
+plt.show()
+
+# Use the trained neural network to predict more points of the data set
+test_rnn(X_tot, y_tot, X_tot[0], X_tot[dim-1])
+# Stop the timer and calculate the total time needed.
+end = timer()
+print('Time: ', end-start)
+
    +
    +
    +
    +
    +
    +

    17.4. Other Types of Recurrent Neural Networks

    +

    Besides a simple recurrent neural network layer, there are two other +commonly used types of recurrent neural network layers: Long Short +Term Memory (LSTM) and Gated Recurrent Unit (GRU). For a short +introduction to these layers see https://medium.com/mindboard/lstm-vs-gru-experimental-comparison-955820c21e8b +and https://medium.com/mindboard/lstm-vs-gru-experimental-comparison-955820c21e8b.

    +

    The first network created below is similar to the previous network, +but it replaces the SimpleRNN layers with LSTM layers. The second +network below has two hidden layers made up of GRUs, which are +preceeded by two dense (feeddorward) neural network layers. These +dense layers “preprocess” the data before it reaches the recurrent +layers. This architecture has been shown to improve the performance +of recurrent neural networks (see the link above and also +https://arxiv.org/pdf/1807.02857.pdf.

    +
    +
    +
    def lstm_2layers(length_of_sequences, batch_size = None, stateful = False):
+    """
+        Inputs:
+            length_of_sequences (an int): the number of y values in "x data".  This is determined
+                when the data is formatted
+            batch_size (an int): Default value is None.  See Keras documentation of SimpleRNN.
+            stateful (a boolean): Default value is False.  See Keras documentation of SimpleRNN.
+        Returns:
+            model (a Keras model): The recurrent neural network that is built and compiled by this
+                method
+        Builds and compiles a recurrent neural network with two LSTM hidden layers and returns the model.
+    """
+    # Number of neurons on the input/output layer and the number of neurons in the hidden layer
+    in_out_neurons = 1
+    hidden_neurons = 250
+    # Input Layer
+    inp = Input(batch_shape=(batch_size, 
+                length_of_sequences, 
+                in_out_neurons)) 
+    # Hidden layers (in this case they are LSTM layers instead if SimpleRNN layers)
+    rnn= LSTM(hidden_neurons, 
+                    return_sequences=True,
+                    stateful = stateful,
+                    name="RNN", use_bias=True, activation='tanh')(inp)
+    rnn1 = LSTM(hidden_neurons, 
+                    return_sequences=False,
+                    stateful = stateful,
+                    name="RNN1", use_bias=True, activation='tanh')(rnn)
+    # Output layer
+    dens = Dense(in_out_neurons,name="dense")(rnn1)
+    # Define the midel
+    model = Model(inputs=[inp],outputs=[dens])
+    # Compile the model
+    model.compile(loss='mean_squared_error', optimizer='adam')  
+    # Return the model
+    return model
+
+def dnn2_gru2(length_of_sequences, batch_size = None, stateful = False):
+    """
+        Inputs:
+            length_of_sequences (an int): the number of y values in "x data".  This is determined
+                when the data is formatted
+            batch_size (an int): Default value is None.  See Keras documentation of SimpleRNN.
+            stateful (a boolean): Default value is False.  See Keras documentation of SimpleRNN.
+        Returns:
+            model (a Keras model): The recurrent neural network that is built and compiled by this
+                method
+        Builds and compiles a recurrent neural network with four hidden layers (two dense followed by
+        two GRU layers) and returns the model.
+    """    
+    # Number of neurons on the input/output layers and hidden layers
+    in_out_neurons = 1
+    hidden_neurons = 250
+    # Input layer
+    inp = Input(batch_shape=(batch_size, 
+                length_of_sequences, 
+                in_out_neurons)) 
+    # Hidden Dense (feedforward) layers
+    dnn = Dense(hidden_neurons/2, activation='relu', name='dnn')(inp)
+    dnn1 = Dense(hidden_neurons/2, activation='relu', name='dnn1')(dnn)
+    # Hidden GRU layers
+    rnn1 = GRU(hidden_neurons, 
+                    return_sequences=True,
+                    stateful = stateful,
+                    name="RNN1", use_bias=True)(dnn1)
+    rnn = GRU(hidden_neurons, 
+                    return_sequences=False,
+                    stateful = stateful,
+                    name="RNN", use_bias=True)(rnn1)
+    # Output layer
+    dens = Dense(in_out_neurons,name="dense")(rnn)
+    # Define the model
+    model = Model(inputs=[inp],outputs=[dens])
+    # Compile the mdoel
+    model.compile(loss='mean_squared_error', optimizer='adam')  
+    # Return the model
+    return model
+
+# Check to make sure the data set is complete
+assert len(X_tot) == len(y_tot)
+
+# This is the number of points that will be used in as the training data
+dim=12
+
+# Separate the training data from the whole data set
+X_train = X_tot[:dim]
+y_train = y_tot[:dim]
+
+
+# Generate the training data for the RNN, using a sequence of 2
+rnn_input, rnn_training = format_data(y_train, 2)
+
+
+# Create a recurrent neural network in Keras and produce a summary of the 
+# machine learning model
+# Change the method name to reflect which network you want to use
+model = dnn2_gru2(length_of_sequences = 2)
+model.summary()
+
+# Start the timer.  Want to time training+testing
+start = timer()
+# Fit the model using the training data genenerated above using 150 training iterations and a 5%
+# validation split.  Setting verbose to True prints information about each training iteration.
+hist = model.fit(rnn_input, rnn_training, batch_size=None, epochs=150, 
+                 verbose=True,validation_split=0.05)
+
+
+# This section plots the training loss and the validation loss as a function of training iteration.
+# This is not required for analyzing the couple cluster data but can help determine if the network is
+# being overtrained.
+for label in ["loss","val_loss"]:
+    plt.plot(hist.history[label],label=label)
+
+plt.ylabel("loss")
+plt.xlabel("epoch")
+plt.title("The final validation loss: {}".format(hist.history["val_loss"][-1]))
+plt.legend()
+plt.show()
+
+# Use the trained neural network to predict more points of the data set
+test_rnn(X_tot, y_tot, X_tot[0], X_tot[dim-1])
+# Stop the timer and calculate the total time needed.
+end = timer()
+print('Time: ', end-start)
+
+
+# ### Training Recurrent Neural Networks in the Standard Way (i.e. learning the relationship between the X and Y data)
+# 
+# Finally, comparing the performace of a recurrent neural network using the standard data formatting to the performance of the network with time sequence data formatting shows the benefit of this type of data formatting with extrapolation.
+
+# Check to make sure the data set is complete
+assert len(X_tot) == len(y_tot)
+
+# This is the number of points that will be used in as the training data
+dim=12
+
+# Separate the training data from the whole data set
+X_train = X_tot[:dim]
+y_train = y_tot[:dim]
+
+# Reshape the data for Keras specifications
+X_train = X_train.reshape((dim, 1))
+y_train = y_train.reshape((dim, 1))
+
+
+# Create a recurrent neural network in Keras and produce a summary of the 
+# machine learning model
+# Set the sequence length to 1 for regular data formatting 
+model = rnn(length_of_sequences = 1)
+model.summary()
+
+# Start the timer.  Want to time training+testing
+start = timer()
+# Fit the model using the training data genenerated above using 150 training iterations and a 5%
+# validation split.  Setting verbose to True prints information about each training iteration.
+hist = model.fit(X_train, y_train, batch_size=None, epochs=150, 
+                 verbose=True,validation_split=0.05)
+
+
+# This section plots the training loss and the validation loss as a function of training iteration.
+# This is not required for analyzing the couple cluster data but can help determine if the network is
+# being overtrained.
+for label in ["loss","val_loss"]:
+    plt.plot(hist.history[label],label=label)
+
+plt.ylabel("loss")
+plt.xlabel("epoch")
+plt.title("The final validation loss: {}".format(hist.history["val_loss"][-1]))
+plt.legend()
+plt.show()
+
+# Use the trained neural network to predict the remaining data points
+X_pred = X_tot[dim:]
+X_pred = X_pred.reshape((len(X_pred), 1))
+y_model = model.predict(X_pred)
+y_pred = np.concatenate((y_tot[:dim], y_model.flatten()))
+
+# Plot the known data set and the predicted data set.  The red box represents the region that was used
+# for the training data.
+fig, ax = plt.subplots()
+ax.plot(X_tot, y_tot, label="true", linewidth=3)
+ax.plot(X_tot, y_pred, 'g-.',label="predicted", linewidth=4)
+ax.legend()
+# Created a red region to represent the points used in the training data.
+ax.axvspan(X_tot[0], X_tot[dim], alpha=0.25, color='red')
+plt.show()
+
+# Stop the timer and calculate the total time needed.
+end = timer()
+print('Time: ', end-start)
+
    +
    +
    +
    +
    +
    +
    +

    18. Generative Models

    +

    Generative models describe a class of statistical models that are a contrast +to discriminative models. Informally we say that generative models can +generate new data instances while discriminative models discriminate between +different kinds of data instances. A generative model could generate new photos +of animals that look like ‘real’ animals while a discriminative model could tell +a dog from a cat. More formally, given a data set \(x\) and a set of labels / +targets \(y\). Generative models capture the joint probability \(p(x, y)\), or +just \(p(x)\) if there are no labels, while discriminative models capture the +conditional probability \(p(y | x)\). Discriminative models generally try to draw +boundaries in the data space (often high dimensional), while generative models +try to model how data is placed throughout the space.

    +

    Note: this material is thanks to Linus Ekstrøm.

    +
    +

    18.1. Generative Adversarial Networks

    +

    Generative Adversarial Networks are a type of unsupervised machine learning +algorithm proposed by Goodfellow et. al +in 2014 (short and good article).

    +

    The simplest formulation of +the model is based on a game theoretic approach, zero sum game, where we pit +two neural networks against one another. We define two rival networks, one +generator \(g\), and one discriminator \(d\). The generator directly produces +samples

    + +
    +
    +\[ +\begin{equation} + x = g(z; \theta^{(g)}) +\label{_auto1} \tag{1} +\end{equation} +\]
    +

    The discriminator attempts to distinguish between samples drawn from the +training data and samples drawn from the generator. In other words, it tries to +tell the difference between the fake data produced by \(g\) and the actual data +samples we want to do prediction on. The discriminator outputs a probability +value given by

    + +
    +
    +\[ +\begin{equation} + d(x; \theta^{(d)}) +\label{_auto2} \tag{2} +\end{equation} +\]
    +

    indicating the probability that \(x\) is a real training example rather than a +fake sample the generator has generated. The simplest way to formulate the +learning process in a generative adversarial network is a zero-sum game, in +which a function

    + +
    +
    +\[ +\begin{equation} + v(\theta^{(g)}, \theta^{(d)}) +\label{_auto3} \tag{3} +\end{equation} +\]
    +

    determines the reward for the discriminator, while the generator gets the +conjugate reward

    + +
    +
    +\[ +\begin{equation} + -v(\theta^{(g)}, \theta^{(d)}) +\label{_auto4} \tag{4} +\end{equation} +\]
    +

    During learning both of the networks maximize their own reward function, so that +the generator gets better and better at tricking the discriminator, while the +discriminator gets better and better at telling the difference between the fake +and real data. The generator and discriminator alternate on which one trains at +one time (i.e. for one epoch). In other words, we keep the generator constant +and train the discriminator, then we keep the discriminator constant to train +the generator and repeat. It is this back and forth dynamic which lets GANs +tackle otherwise intractable generative problems. As the generator improves with +training, the discriminator’s performance gets worse because it cannot easily +tell the difference between real and fake. If the generator ends up succeeding +perfectly, the the discriminator will do no better than random guessing i.e. +50%. This progression in the training poses a problem for the convergence +criteria for GANs. The discriminator feedback gets less meaningful over time, +if we continue training after this point then the generator is effectively +training on junk data which can undo the learning up to that point. Therefore, +we stop training when the discriminator starts outputting \(1/2\) everywhere.

    +

    At convergence we have

    + +
    +
    +\[ +\begin{equation} + g^* = \underset{g}{\mathrm{argmin}}\hspace{2pt} + \underset{d}{\mathrm{max}}v(\theta^{(g)}, \theta^{(d)}) +\label{_auto5} \tag{5} +\end{equation} +\]
    +

    The default choice for \(v\) is

    + +
    +
    +\[ +\begin{equation} + v(\theta^{(g)}, \theta^{(d)}) = \mathbb{E}_{x\sim p_\mathrm{data}}\log d(x) + + \mathbb{E}_{x\sim p_\mathrm{model}} + \log (1 - d(x)) +\label{_auto6} \tag{6} +\end{equation} +\]
    +

    The main motivation for the design of GANs is that the learning process requires +neither approximate inference (variational autoencoders for example) nor +approximation of a partition function. In the case where

    + +
    +
    +\[ +\begin{equation} + \underset{d}{\mathrm{max}}v(\theta^{(g)}, \theta^{(d)}) +\label{_auto7} \tag{7} +\end{equation} +\]
    +

    is convex in $\theta^{(g)} then the procedure is guaranteed to converge and is +asymptotically consistent +( Seth Lloyd on QuGANs ).

    +

    This is in +general not the case and it is possible to get situations where the training +process never converges because the generator and discriminator chase one +another around in the parameter space indefinitely. A much deeper discussion on +the currently open research problem of GAN convergence is available +here. To +anyone interested in learning more about GANs it is a highly recommended read. +Direct quote: “In this best-performing formulation, the generator aims to +increase the log probability that the discriminator makes a mistake, rather than +aiming to decrease the log probability that the discriminator makes the correct +prediction.” Another interesting read

    +
    +
    +

    18.2. Writing Our First Generative Adversarial Network

    +

    Let us now move on to actually implementing a GAN in tensorflow. We will study +the performance of our GAN on the MNIST dataset. This code is based on and +adapted from the +google tutorial

    +

    First we import our libraries

    +
    +
    +
    import os
+import time
+import numpy as np
+import tensorflow as tf
+import matplotlib.pyplot as plt
+from tensorflow.keras import layers
+from tensorflow.keras.utils import plot_model
+
    +
    +
    +
    +

    Next we define our hyperparameters and import our data the usual way

    +
    +
    +
    BUFFER_SIZE = 60000
+BATCH_SIZE = 256
+EPOCHS = 30
+
+data = tf.keras.datasets.mnist.load_data()
+(train_images, train_labels), (test_images, test_labels) = data
+train_images = np.reshape(train_images, (train_images.shape[0],
+                                         28,
+                                         28,
+                                         1)).astype('float32')
+
+# we normalize between -1 and 1
+train_images = (train_images - 127.5) / 127.5
+training_dataset = tf.data.Dataset.from_tensor_slices(
+                      train_images).shuffle(BUFFER_SIZE).batch(BATCH_SIZE)
+
    +
    +
    +
    +
    +

    18.2.1. MNIST and GANs

    +

    Let’s have a quick look

    +
    +
    +
    plt.imshow(train_images[0], cmap='Greys')
+plt.show()
+
    +
    +
    +
    +

    Now we define our two models. This is where the ‘magic’ happens. There are a +huge amount of possible formulations for both models. A lot of engineering and +trial and error can be done here to try to produce better performing models. For +more advanced GANs this is by far the step where you can ‘make or break’ a +model.

    +

    We start with the generator. As stated in the introductory text the generator +\(g\) upsamples from a random sample to the shape of what we want to predict. In +our case we are trying to predict MNIST images (\(28\times 28\) pixels).

    +
    +
    +
    def generator_model():
+    """
+    The generator uses upsampling layers tf.keras.layers.Conv2DTranspose() to
+    produce an image from a random seed. We start with a Dense layer taking this
+    random sample as an input and subsequently upsample through multiple
+    convolutional layers.
+    """
+
+    # we define our model
+    model = tf.keras.Sequential()
+
+
+    # adding our input layer. Dense means that every neuron is connected and
+    # the input shape is the shape of our random noise. The units need to match
+    # in some sense the upsampling strides to reach our desired output shape.
+    # we are using 100 random numbers as our seed
+    model.add(layers.Dense(units=7*7*BATCH_SIZE,
+                           use_bias=False,
+                           input_shape=(100, )))
+    # we normalize the output form the Dense layer
+    model.add(layers.BatchNormalization())
+    # and add an activation function to our 'layer'. LeakyReLU avoids vanishing
+    # gradient problem
+    model.add(layers.LeakyReLU())
+    model.add(layers.Reshape((7, 7, BATCH_SIZE)))
+    assert model.output_shape == (None, 7, 7, BATCH_SIZE)
+    # even though we just added four keras layers we think of everything above
+    # as 'one' layer
+
+    # next we add our upscaling convolutional layers
+    model.add(layers.Conv2DTranspose(filters=128,
+                                     kernel_size=(5, 5),
+                                     strides=(1, 1),
+                                     padding='same',
+                                     use_bias=False))
+    model.add(layers.BatchNormalization())
+    model.add(layers.LeakyReLU())
+    assert model.output_shape == (None, 7, 7, 128)
+
+    model.add(layers.Conv2DTranspose(filters=64,
+                                     kernel_size=(5, 5),
+                                     strides=(2, 2),
+                                     padding='same',
+                                     use_bias=False))
+    model.add(layers.BatchNormalization())
+    model.add(layers.LeakyReLU())
+    assert model.output_shape == (None, 14, 14, 64)
+
+    model.add(layers.Conv2DTranspose(filters=1,
+                                     kernel_size=(5, 5),
+                                     strides=(2, 2),
+                                     padding='same',
+                                     use_bias=False,
+                                     activation='tanh'))
+    assert model.output_shape == (None, 28, 28, 1)
+
+    return model
+
    +
    +
    +
    +

    And there we have our ‘simple’ generator model. Now we move on to defining our +discriminator model \(d\), which is a convolutional neural network based image +classifier.

    +
    +
    +
    def discriminator_model():
+    """
+    The discriminator is a convolutional neural network based image classifier
+    """
+
+    # we define our model
+    model = tf.keras.Sequential()
+    model.add(layers.Conv2D(filters=64,
+                            kernel_size=(5, 5),
+                            strides=(2, 2),
+                            padding='same',
+                            input_shape=[28, 28, 1]))
+    model.add(layers.LeakyReLU())
+    # adding a dropout layer as you do in conv-nets
+    model.add(layers.Dropout(0.3))
+
+
+    model.add(layers.Conv2D(filters=128,
+                            kernel_size=(5, 5),
+                            strides=(2, 2),
+                            padding='same'))
+    model.add(layers.LeakyReLU())
+    # adding a dropout layer as you do in conv-nets
+    model.add(layers.Dropout(0.3))
+
+    model.add(layers.Flatten())
+    model.add(layers.Dense(1))
+
+    return model
+
    +
    +
    +
    +

    Let us take a look at our models.

    +
    +
    +
    generator = generator_model()
+plot_model(generator, show_shapes=True, rankdir='LR')
+
    +
    +
    +
    +
    +
    +
    discriminator = discriminator_model()
+plot_model(discriminator, show_shapes=True, rankdir='LR')
+
    +
    +
    +
    +

    Next we need a few helper objects we will use in training

    +
    +
    +
    cross_entropy = tf.keras.losses.BinaryCrossentropy(from_logits=True)
+generator_optimizer = tf.keras.optimizers.Adam(1e-4)
+discriminator_optimizer = tf.keras.optimizers.Adam(1e-4)
+
    +
    +
    +
    +

    The first object, cross_entropy is our loss function and the two others are +our optimizers. Notice we use the same learning rate for both \(g\) and \(d\). This +is because they need to improve their accuracy at approximately equal speeds to +get convergence (not necessarily exactly equal). Now we define our loss +functions

    +
    +
    +
    def generator_loss(fake_output):
+    loss = cross_entropy(tf.ones_like(fake_output), fake_output)
+
+    return loss
+
    +
    +
    +
    +
    +
    +
    def discriminator_loss(real_output, fake_output):
+    real_loss = cross_entropy(tf.ones_like(real_output), real_output)
+    fake_loss = cross_entropy(tf.zeros_liks(fake_output), fake_output)
+    total_loss = real_loss + fake_loss
+
+    return total_loss
+
    +
    +
    +
    +

    Next we define a kind of seed to help us compare the learning process over +multiple training epochs.

    +
    +
    +
    noise_dimension = 100
+n_examples_to_generate = 16
+seed_images = tf.random.normal([n_examples_to_generate, noise_dimension])
+
    +
    +
    +
    +

    Now we have everything we need to define our training step, which we will apply +for every step in our training loop. Notice the @tf.function flag signifying +that the function is tensorflow ‘compiled’. Removing this flag doubles the +computation time.

    +
    +
    +
    @tf.function
+def train_step(images):
+    noise = tf.random.normal([BATCH_SIZE, noise_dimension])
+
+    with tf.GradientTape() as gen_tape, tf.GradientTape() as disc_tape:
+        generated_images = generator(noise, training=True)
+
+        real_output = discriminator(images, training=True)
+        fake_output = discriminator(generated_images, training=True)
+
+        gen_loss = generator_loss(fake_output)
+        disc_loss = discriminator_loss(real_output, fake_output)
+
+    gradients_of_generator = gen_tape.gradient(gen_loss,
+                                            generator.trainable_variables)
+    gradients_of_discriminator = disc_tape.gradient(disc_loss,
+                                            discriminator.trainable_variables)
+    generator_optimizer.apply_gradients(zip(gradients_of_generator,
+                                            generator.trainable_variables))
+    discriminator_optimizer.apply_gradients(zip(gradients_of_discriminator,
+                                            discriminator.trainable_variables))
+
+    return gen_loss, disc_loss
+
    +
    +
    +
    +

    Next we define a helper function to produce an output over our training epochs +to see the predictive progression of our generator model. Note: I am including +this code here, but comment it out in the training loop.

    +
    +
    +
    def generate_and_save_images(model, epoch, test_input):
+    # we're making inferences here
+    predictions = model(test_input, training=False)
+
+    fig = plt.figure(figsize=(4, 4))
+
+    for i in range(predictions.shape[0]):
+        plt.subplot(4, 4, i+1)
+        plt.imshow(predictions[i, :, :, 0] * 127.5 + 127.5, cmap='gray')
+        plt.axis('off')
+
+    plt.savefig(f'./images_from_seed_images/image_at_epoch_{str(epoch).zfill(3)}.png')
+    plt.close()
+    #plt.show()
+
    +
    +
    +
    +

    Setting up checkpoints to periodically save our model during training so that +everything is not lost even if the program were to somehow terminate while +training.

    +
    +
    +
    # Setting up checkpoints to save model during training
+checkpoint_dir = './training_checkpoints'
+checkpoint_prefix = os.path.join(checkpoint_dir, 'ckpt')
+checkpoint = tf.train.Checkpoint(generator_optimizer=generator_optimizer,
+                            discriminator_optimizer=discriminator_optimizer,
+                            generator=generator,
+                            discriminator=discriminator)
+
    +
    +
    +
    +

    Now we define our training loop

    +
    +
    +
    def train(dataset, epochs):
+    generator_loss_list = []
+    discriminator_loss_list = []
+
+    for epoch in range(epochs):
+        start = time.time()
+
+        for image_batch in dataset:
+            gen_loss, disc_loss = train_step(image_batch)
+            generator_loss_list.append(gen_loss.numpy())
+            discriminator_loss_list.append(disc_loss.numpy())
+
+        #generate_and_save_images(generator, epoch + 1, seed_images)
+
+        if (epoch + 1) % 15 == 0:
+            checkpoint.save(file_prefix=checkpoint_prefix)
+
+        print(f'Time for epoch {epoch} is {time.time() - start}')
+
+    #generate_and_save_images(generator, epochs, seed_images)
+
+    loss_file = './data/lossfile.txt'
+    with open(loss_file, 'w') as outfile:
+        outfile.write(str(generator_loss_list))
+        outfile.write('\n')
+        outfile.write('\n')
+        outfile.write(str(discriminator_loss_list))
+        outfile.write('\n')
+        outfile.write('\n')
+
    +
    +
    +
    +

    To train simply call this function. Warning: this might take a long time so +there is a folder of a pretrained network already included in the repository.

    +
    +
    +
    train(train_dataset, EPOCHS)
+
    +
    +
    +
    +

    Now to avoid having to train and everything, which will take a while depending +on your computer setup we now load in the model which produced the above gif.

    +
    +
    +
    checkpoint.restore(tf.train.latest_checkpoint(checkpoint_dir))
+restored_generator = checkpoint.generator
+restored_discriminator = checkpoint.discriminator
+
+print(restored_generator)
+print(restored_discriminator)
+
    +
    +
    +
    +

    We have successfully loaded in our latest model. Let us now play around a bit +and see what kind of things we can learn about this model. Our generator takes +an array of 100 numbers. One idea can be to try to systematically change our +input. Let us try and see what we get

    +
    +
    +
    def generate_latent_points(number=100, scale_means=1, scale_stds=1):
+    latent_dim = 100
+    means = scale_means * tf.linspace(-1, 1, num=latent_dim)
+    stds = scale_stds * tf.linspace(-1, 1, num=latent_dim)
+    latent_space_value_range = tf.random.normal([number, latent_dim],
+                                                means,
+                                                stds,
+                                                dtype=tf.float64)
+
+    return latent_space_value_range
+
+def generate_images(latent_points):
+    # notice we set training to false because we are making inferences
+    generated_images = restored_generator.predict(latent_points)
+
+    return generated_images
+
    +
    +
    +
    +
    +
    +
    def plot_result(generated_images, number=100):
+    # obviously this assumes sqrt number is an int
+    fig, axs = plt.subplots(int(np.sqrt(number)), int(np.sqrt(number)),
+                            figsize=(10, 10))
+
+    for i in range(int(np.sqrt(number))):
+        for j in range(int(np.sqrt(number))):
+            axs[i, j].imshow(generated_images[i*j], cmap='Greys')
+            axs[i, j].axis('off')
+
+    plt.show()
+
    +
    +
    +
    +
    +
    +
    generated_images = generate_images(generate_latent_points())
+plot_result(generated_images)
+
    +
    +
    +
    +

    We see that the generator generates images that look like MNIST +numbers: \(1, 4, 7, 9\). Let’s try to tweak it a bit more to see if we are able +to generate a similar plot where we generate every MNIST number. Let us now try +to ‘move’ a bit around in the latent space. Note: decrease the plot number if +these following cells take too long to run on your computer.

    +
    +
    +
    plot_number = 225
+
+generated_images = generate_images(generate_latent_points(number=plot_number,
+                                                          scale_means=5,
+                                                          scale_stds=1))
+plot_result(generated_images, number=plot_number)
+
+generated_images = generate_images(generate_latent_points(number=plot_number,
+                                                          scale_means=-5,
+                                                          scale_stds=1))
+plot_result(generated_images, number=plot_number)
+
+generated_images = generate_images(generate_latent_points(number=plot_number,
+                                                          scale_means=1,
+                                                          scale_stds=5))
+plot_result(generated_images, number=plot_number)
+
    +
    +
    +
    +

    Again, we have found something interesting. Moving around using our means +takes us from digit to digit, while moving around using our standard +deviations seem to increase the number of different digits! In the last image +above, we can barely make out every MNIST digit. Let us make on last plot using +this information by upping the standard deviation of our Gaussian noises.

    +
    +
    +
    plot_number = 400
+generated_images = generate_images(generate_latent_points(number=plot_number,
+                                                          scale_means=1,
+                                                          scale_stds=10))
+plot_result(generated_images, number=plot_number)
+
    +
    +
    +
    +

    A pretty cool result! We see that our generator indeed has learned a +distribution which qualitatively looks a whole lot like the MNIST dataset.

    +

    Another interesting way to explore the latent space of our generator model is by +interpolating between the MNIST digits. This section is largely based on +this excellent blogpost +by Jason Brownlee.

    +

    So let us start by defining a function to interpolate between two points in the +latent space.

    +
    +
    +
    def interpolation(point_1, point_2, n_steps=10):
+    ratios = np.linspace(0, 1, num=n_steps)
+    vectors = []
+    for i, ratio in enumerate(ratios):
+        vectors.append(((1.0 - ratio) * point_1 + ratio * point_2))
+
+    return tf.stack(vectors)
+
    +
    +
    +
    +

    Now we have all we need to do our interpolation analysis.

    +
    +
    +
    plot_number = 100
+latent_points = generate_latent_points(number=plot_number)
+results = None
+for i in range(0, 2*np.sqrt(plot_number), 2):
+    interpolated = interpolation(latent_points[i], latent_points[i+1])
+    generated_images = generate_images(interpolated)
+
+    if results is None:
+        results = generated_images
+    else:
+        results = tf.stack((results, generated_images))
+
+plot_results(results, plot_number)
+
    +
    +
    +
    +
    +
    +
    + + + + +
    + + + + + + +
    + + + +
    + +
    +
    +
    +
    +

    + + By Morten Hjorth-Jensen
    + + © Copyright 2021.
    +

    +
    +
    +
    + + +
    +
    + + + + + + \ No newline at end of file diff --git a/doc/LectureNotes/_build/html/chapter9.html b/doc/LectureNotes/_build/html/chapter9.html index 3aac078fa..aca38d4f7 100644 --- a/doc/LectureNotes/_build/html/chapter9.html +++ b/doc/LectureNotes/_build/html/chapter9.html @@ -5,7 +5,7 @@ - 12. Neural networks — Applied Data Analysis and Machine Learning + 13. Neural networks — Applied Data Analysis and Machine Learning @@ -53,8 +53,8 @@ - - + + @@ -199,6 +199,11 @@ 11. Basic ideas of the Principal Component Analysis (PCA) +
  • + + 12. Clustering and Unsupervised Learning + +

    • @@ -208,17 +213,27 @@

    @@ -294,76 +309,76 @@

    @@ -208,17 +213,27 @@

    @@ -330,8 +345,8 @@
  • - - 7.7. Stochastic Gradient Descent + + 7.7. Stochastic Gradient Descent (SGD) @@ -379,7 +411,8 @@
    -
    +

    7. Optimization, the central part of any Machine Learning algortithm

    Almost every problem in machine learning and data science starts with a dataset \(X\), a model \(g(\beta)\), which is a function of the @@ -750,14 +783,14 @@ which equals

    -
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42573/483257001.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
+
    /var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47735/483257001.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().
   ax = fig.gca(projection="3d")
 
    
 
    
-
    <mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x7fad10f9a280>
+
    <mpl_toolkits.mplot3d.art3d.Poly3DCollection at 0x7fd098df3280>
 
    
 
    
-_images/chapteroptimization_56_2.png
+_images/chapteroptimization_61_2.png
 
    
 
    
 
    And then as countor plot
    
@@ -770,7 +803,7 @@ which equals
    -_images/chapteroptimization_58_0.png +_images/chapteroptimization_63_0.png

    Find guesses

    @@ -812,10 +845,10 @@ which equals

    -
    [<matplotlib.lines.Line2D at 0x7fad20f69be0>]
+
    [<matplotlib.lines.Line2D at 0x7fd0a9063be0>]
 
    
 
    
-_images/chapteroptimization_64_1.png
+_images/chapteroptimization_69_1.png
    @@ -1069,16 +1102,14 @@ when \(||\nabla_\beta C(\beta_k) || \
    -
    [0.32903042 4.1484256 ]
-[[4.04621521]
- [3.00415763]]
+
    [0.28001319 4.21265216]
+[[3.96987657]
+ [3.02493054]]
+[[3.96987657]
+ [3.02493054]]
 
    
 
    
-
    [[4.04621521]
- [3.00415763]]
-
    
-
    
-_images/chapteroptimization_118_2.png
+_images/chapteroptimization_123_1.png

    Alternatively, we can use Scikit-Learn as done here

    @@ -1104,9 +1135,9 @@ when \(||\nabla_\beta C(\beta_k) || \
    -
    [[3.97230501]
- [3.14741468]]
-[3.94735055] [3.17084902]
+
    [[4.00275135]
+ [2.99724883]]
+[3.97065296] [3.07656896]
    @@ -1177,13 +1208,13 @@ C_{\text{ridge}}(\beta) = \frac{1}{n}||X\beta -\mathbf{y}||^2 + \lambda ||\beta|
    -
    [[3.92343595]
- [3.15258907]]
-[[3.815563  ]
- [3.23522201]]
+
    [[4.1533795 ]
+ [2.92819235]]
+[[4.06858699]
+ [2.99829953]]
 
    
 
    
-_images/chapteroptimization_127_1.png
+_images/chapteroptimization_132_1.png
    @@ -1198,8 +1229,27 @@ C_{\text{ridge}}(\beta) = \frac{1}{n}||X\beta -\mathbf{y}||^2 + \lambda ||\beta|

  • GD can take exponential time to escape saddle points, even with random initialization. As we mentioned, GD is extremely sensitive to initial condition since it determines the particular local minimum GD would eventually reach. However, even with a good initialization scheme, through the introduction of randomness, GD can still take exponential time to escape saddle points.

    • -
    -

    7.7. Stochastic Gradient Descent

    +
    +

    7.7. Stochastic Gradient Descent (SGD)

    +

    In stochastic gradient descent, the extreme case is the case where we +have only one batch, that is we include the whole data set.

    +

    This process is called Stochastic Gradient +Descent (SGD) (or also sometimes on-line gradient descent). This is +relatively less common to see because in practice due to vectorized +code optimizations it can be computationally much more efficient to +evaluate the gradient for 100 examples, than the gradient for one +example 100 times. Even though SGD technically refers to using a +single example at a time to evaluate the gradient, you will hear +people use the term SGD even when referring to mini-batch gradient +descent (i.e. mentions of MGD for “Minibatch Gradient Descent”, or BGD +for “Batch gradient descent” are rare to see), where it is usually +assumed that mini-batches are used. The size of the mini-batch is a +hyperparameter but it is not very common to cross-validate or bootstrap it. It is +usually based on memory constraints (if any), or set to some value, +e.g. 32, 64 or 128. We use powers of 2 in practice because many +vectorized operation implementations work faster when their inputs are +sized in powers of 2.

    +

    In our notes with SGD we mean stochastic gradient descent with mini-batches.

    Stochastic gradient descent (SGD) and variants thereof address some of the shortcomings of the Gradient descent method discussed above.

    The underlying idea of SGD comes from the observation that the cost @@ -1256,7 +1306,7 @@ the number of minibatches, as exemplified in the code below.

    import numpy as np 
 
 n = 100 #100 datapoints 
-M = 5   #size of each minibatch
+M = 5   #size of each mini-batche
 m = int(n/M) #number of minibatches
 n_epochs = 10 #number of epochs
 
@@ -1332,38 +1382,39 @@ function.
    +

    We note that we have defined several hyperparameters. These are now the number of epochs, the number of mini-batches and the parameters \(t_0\) and \(t_1\).

    7.7.1. Program for stochastic gradient

    # Importing various packages
+# Importing various packages
 from math import exp, sqrt
 from random import random, seed
 import numpy as np
 import matplotlib.pyplot as plt
-from sklearn.linear_model import SGDRegressor
 
-m = 100
-x = 2*np.random.rand(m,1)
-y = 4+3*x+np.random.randn(m,1)
+n = 100
+x = 2*np.random.rand(n,1)
+y = 4+3*x+np.random.randn(n,1)
 
-X = np.c_[np.ones((m,1)), x]
+X = np.c_[np.ones((n,1)), x]
+XT_X = X.T @ X
 theta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y)
 print("Own inversion")
 print(theta_linreg)
-sgdreg = SGDRegressor(max_iter = 50, penalty=None, eta0=0.1)
-sgdreg.fit(x,y.ravel())
-print("sgdreg from scikit")
-print(sgdreg.intercept_, sgdreg.coef_)
-
+# Hessian matrix
+H = (2.0/n)* XT_X
+EigValues, EigVectors = np.linalg.eig(H)
+print(f"Eigenvalues of Hessian Matrix:{EigValues}")
 
 theta = np.random.randn(2,1)
-eta = 0.1
+eta = 1.0/np.max(EigValues)
 Niterations = 1000
 
 
 for iter in range(Niterations):
-    gradients = 2.0/m*X.T @ ((X @ theta)-y)
+    gradients = 2.0/n*X.T @ ((X @ theta)-y)
     theta -= eta*gradients
 print("theta from own gd")
 print(theta)
@@ -1373,8 +1424,9 @@ function.
    
 ypredict = Xnew.dot(theta)
 ypredict2 = Xnew.dot(theta_linreg)
 
-
 n_epochs = 50
+M = 5   #size of each minibatch
+m = int(n/M) #number of minibatches
 t0, t1 = 5, 50
 def learning_schedule(t):
     return t0/(t+t1)
@@ -1382,16 +1434,20 @@ function.
    
 theta = np.random.randn(2,1)
 
 for epoch in range(n_epochs):
+# Can you figure out a better way of setting up the contributions to each batch?
     for i in range(m):
-        random_index = np.random.randint(m)
-        xi = X[random_index:random_index+1]
-        yi = y[random_index:random_index+1]
-        gradients = 2 * xi.T @ ((xi @ theta)-yi)
+        random_index = M*np.random.randint(m)
+        xi = X[random_index:random_index+M]
+        yi = y[random_index:random_index+M]
+        gradients = (2.0/M)* xi.T @ ((xi @ theta)-yi)
         eta = learning_schedule(epoch*m+i)
         theta = theta - eta*gradients
 print("theta from own sdg")
 print(theta)
 
+
+
+
 plt.plot(xnew, ypredict, "r-")
 plt.plot(xnew, ypredict2, "b-")
 plt.plot(x, y ,'ro')
@@ -1405,23 +1461,24 @@ function.
    
 
    Own inversion
-[[4.15629539]
- [2.7293182 ]]
-sgdreg from scikit
-[4.0728785] [2.66410989]
+[[3.99775949]
+ [2.94659383]]
+Eigenvalues of Hessian Matrix:[0.36102113 4.18276924]
 theta from own gd
-[[4.15629539]
- [2.7293182 ]]
+[[3.99775949]
+ [2.94659383]]
+theta from own sdg
+[[3.96489434]
+ [2.98399675]]
    -
    theta from own sdg
-[[4.15454301]
- [2.72522848]]
-
    -
    -_images/chapteroptimization_141_2.png +_images/chapteroptimization_148_1.png
    +

    In the above code, we have use replacement in setting up the +mini-batches. The discussion +here may be +useful. More material will be added later.

    @@ -1538,7 +1595,7 @@ the steep computational price of calculating or approximating Hessians.

    Recently, a number of methods have been introduced that accomplish this by tracking not only the gradient, but also the second moment of -the gradient. These methods include AdaGrad, AdaDelta, RMS-Prop, and +the gradient. These methods include AdaGrad, AdaDelta, Root Mean Squared Propagation (RMS-Prop), and ADAM.

    7.8.1. RMS prop

    @@ -1724,7 +1781,7 @@ f'(x) = \cos\left(2\pi x + x^2\right)\left(2\pi + 2x\right)
    -_images/chapteroptimization_177_0.png +_images/chapteroptimization_188_0.png 
    The max absolute difference is: 1.77636e-15
    @@ -1907,28 +1964,42 @@ The analytical gradient of f4 at x = 2.7 is: 13.8759
    -

    1 -8

    -

    < -< -< -! -! -C -O -D -E -_ -B -L -O -C -K

    -

    p -y -c -o -d

    +
    +
    +
    import autograd.numpy as np
+from autograd import grad
+def f6_for(x):
+    val = 0
+    for i in range(10):
+        val = val + x**i
+    return val
+
+def f6_while(x):
+    val = 0
+    i = 0
+    while i < 10:
+        val = val + x**i
+        i = i + 1
+    return val
+
+f6_for_grad = grad(f6_for)
+f6_while_grad = grad(f6_while)
+
+x = 0.5
+
+# Print the computed derivaties of f6_for and f6_while
+print("The computed derivative of f6_for at x = %g is: %g"%(x,f6_for_grad(x)))
+print("The computed derivative of f6_while at x = %g is: %g"%(x,f6_while_grad(x)))
+
    +
    +
    +
    +
    The computed derivative of f6_for at x = 0.5 is: 3.95703
+The computed derivative of f6_while at x = 0.5 is: 3.95703
+
    +
    +
    +
    import autograd.numpy as np
@@ -1944,7 +2015,7 @@ d
    -
    The analytical derivative of f6 at x = 2.7 is: 37732.5
+
    The analytical derivative of f6 at x = 0.5 is: 3.95703
    @@ -1989,49 +2060,31 @@ The analytical derivative of f7 at n = 2 is: 1

    Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input.

    -

    Autograd supports many features. However, there are some functions that are not supported (yet) by Autograd.

    -

    Assigning a value to the variable being differentiated with respect to is an example thereof.

    -
    -
    -
    #import autograd.numpy as np
-#from autograd import grad
-#def f8(x): # Assume x is an array
-#    x[2] = 3
-#    return x*2
-
-#f8_grad = grad(f8)
-
-#x = 8.4
-
-#print("The derivative of f8 is:",f8_grad(x))
-
    -
    -
    -
    -

    Here, Autograd tells us that an ‘ArrayBox’ does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible.

    +

    Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.

    +

    Assigning a value to the variable being differentiated with respect to

    import autograd.numpy as np
 from autograd import grad
-def f9(a): # Assume a is an array with 2 elements
-    b = np.array([1.0,2.0])
-    return a.dot(b)
+def f8(x): # Assume x is an array
+    x[2] = 3
+    return x*2
 
-f9_grad = grad(f9)
+f8_grad = grad(f8)
 
-x = np.array([1.0,0.0])
+x = 8.4
 
-print("The derivative of f9 is:",f9_grad(x))
+print("The derivative of f8 is:",f8_grad(x))
 
    ---------------------------------------------------------------------------
-AttributeError                            Traceback (most recent call last)
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42573/546166676.py in <module>
-      9 x = np.array([1.0,0.0])
+TypeError                                 Traceback (most recent call last)
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47735/1122558214.py in <module>
+      9 x = 8.4
      10 
----> 11 print("The derivative of f9 is:",f9_grad(x))
+---> 11 print("The derivative of f8 is:",f8_grad(x))
 
 ~/anaconda3/lib/python3.8/site-packages/autograd/wrap_util.py in nary_f(*args, **kwargs)
      18             else:
@@ -2068,14 +2121,32 @@ AttributeError                            Traceback (most recent call last)
      16             if isinstance(argnum, int):
      17                 x = args[argnum]
 
-/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42573/546166676.py in f9(a)
-      3 def f9(a): # Assume a is an array with 2 elements
-      4     b = np.array([1.0,2.0])
-----> 5     return a.dot(b)
+/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47735/1122558214.py in f8(x)
+      2 from autograd import grad
+      3 def f8(x): # Assume x is an array
+----> 4     x[2] = 3
+      5     return x*2
       6 
-      7 f9_grad = grad(f9)
 
-AttributeError: 'ArrayBox' object has no attribute 'dot'
+TypeError: 'ArrayBox' object does not support item assignment
+
    +
    +
    +
    +

    Here, Autograd tells us that an ‘ArrayBox’ does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible.

    +
    +
    +
    import autograd.numpy as np
+from autograd import grad
+def f9(a): # Assume a is an array with 2 elements
+    b = np.array([1.0,2.0])
+    return a.dot(b)
+
+f9_grad = grad(f9)
+
+x = np.array([1.0,0.0])
+
+print("The derivative of f9 is:",f9_grad(x))
    @@ -2114,7 +2185,192 @@ which also computed the dot product can be used:

    -

    More examples will be added, in particular how to compare autograd with own codes for the gradients.

    + +
    +

    7.11. Using Autograd with OLS

    +

    We conclude the part on optmization by showing how we can make codes +for linear regression and logistic regression using autograd. The +first example shows results with ordinary leats squares.

    +
    +
    +
    # Using Autograd to calculate gradients for OLS
+from random import random, seed
+import numpy as np
+import autograd.numpy as np
+import matplotlib.pyplot as plt
+from autograd import grad
+
+def CostOLS(beta):
+    return (1.0/n)*np.sum((y-X @ beta)**2)
+
+n = 100
+x = 2*np.random.rand(n,1)
+y = 4+3*x+np.random.randn(n,1)
+
+X = np.c_[np.ones((n,1)), x]
+XT_X = X.T @ X
+theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)
+print("Own inversion")
+print(theta_linreg)
+# Hessian matrix
+H = (2.0/n)* XT_X
+EigValues, EigVectors = np.linalg.eig(H)
+print(f"Eigenvalues of Hessian Matrix:{EigValues}")
+
+theta = np.random.randn(2,1)
+eta = 1.0/np.max(EigValues)
+Niterations = 1000
+# define the gradient
+training_gradient = grad(CostOLS)
+
+for iter in range(Niterations):
+    gradients = training_gradient(theta)
+    theta -= eta*gradients
+print("theta from own gd")
+print(theta)
+
+xnew = np.array([[0],[2]])
+Xnew = np.c_[np.ones((2,1)), xnew]
+ypredict = Xnew.dot(theta)
+ypredict2 = Xnew.dot(theta_linreg)
+
+plt.plot(xnew, ypredict, "r-")
+plt.plot(xnew, ypredict2, "b-")
+plt.plot(x, y ,'ro')
+plt.axis([0,2.0,0, 15.0])
+plt.xlabel(r'$x$')
+plt.ylabel(r'$y$')
+plt.title(r'Random numbers ')
+plt.show()
+
    +
    +
    +
    +
    +

    7.11.1. Including Stochastic Gradient Descent with Autograd

    +

    In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using autograd.

    +
    +
    +
    # Using Autograd to calculate gradients using SGD
+# OLS example
+from random import random, seed
+import numpy as np
+import autograd.numpy as np
+import matplotlib.pyplot as plt
+from autograd import grad
+
+# Note change from previous example
+def CostOLS(y,X,theta):
+    return np.sum((y-X @ theta)**2)
+
+n = 100
+x = 2*np.random.rand(n,1)
+y = 4+3*x+np.random.randn(n,1)
+
+X = np.c_[np.ones((n,1)), x]
+XT_X = X.T @ X
+theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)
+print("Own inversion")
+print(theta_linreg)
+# Hessian matrix
+H = (2.0/n)* XT_X
+EigValues, EigVectors = np.linalg.eig(H)
+print(f"Eigenvalues of Hessian Matrix:{EigValues}")
+
+theta = np.random.randn(2,1)
+eta = 1.0/np.max(EigValues)
+Niterations = 1000
+
+# Note that we request the derivative wrt third argument (theta, 2 here)
+training_gradient = grad(CostOLS,2)
+
+for iter in range(Niterations):
+    gradients = (1.0/n)*training_gradient(y, X, theta)
+    theta -= eta*gradients
+print("theta from own gd")
+print(theta)
+
+xnew = np.array([[0],[2]])
+Xnew = np.c_[np.ones((2,1)), xnew]
+ypredict = Xnew.dot(theta)
+ypredict2 = Xnew.dot(theta_linreg)
+
+plt.plot(xnew, ypredict, "r-")
+plt.plot(xnew, ypredict2, "b-")
+plt.plot(x, y ,'ro')
+plt.axis([0,2.0,0, 15.0])
+plt.xlabel(r'$x$')
+plt.ylabel(r'$y$')
+plt.title(r'Random numbers ')
+plt.show()
+
+n_epochs = 50
+M = 5   #size of each minibatch
+m = int(n/M) #number of minibatches
+t0, t1 = 5, 50
+def learning_schedule(t):
+    return t0/(t+t1)
+
+theta = np.random.randn(2,1)
+
+for epoch in range(n_epochs):
+# Can you figure out a better way of setting up the contributions to each batch?
+    for i in range(m):
+        random_index = M*np.random.randint(m)
+        xi = X[random_index:random_index+M]
+        yi = y[random_index:random_index+M]
+        gradients = (1.0/M)*training_gradient(yi, xi, theta)
+        eta = learning_schedule(epoch*m+i)
+        theta = theta - eta*gradients
+print("theta from own sdg")
+print(theta)
+
    +
    +
    +
    +
    +
    +

    7.11.2. And Logistic Regression

    +
    +
    +
    import autograd.numpy as np
+from autograd import grad
+
+def sigmoid(x):
+    return 0.5 * (np.tanh(x / 2.) + 1)
+
+def logistic_predictions(weights, inputs):
+    # Outputs probability of a label being true according to logistic model.
+    return sigmoid(np.dot(inputs, weights))
+
+def training_loss(weights):
+    # Training loss is the negative log-likelihood of the training labels.
+    preds = logistic_predictions(weights, inputs)
+    label_probabilities = preds * targets + (1 - preds) * (1 - targets)
+    return -np.sum(np.log(label_probabilities))
+
+# Build a toy dataset.
+inputs = np.array([[0.52, 1.12,  0.77],
+                   [0.88, -1.08, 0.15],
+                   [0.52, 0.06, -1.30],
+                   [0.74, -2.49, 1.39]])
+targets = np.array([True, True, False, True])
+
+# Define a function that returns gradients of training loss using Autograd.
+training_gradient_fun = grad(training_loss)
+
+# Optimize weights using gradient descent.
+weights = np.array([0.0, 0.0, 0.0])
+print("Initial loss:", training_loss(weights))
+for i in range(100):
+    weights -= training_gradient_fun(weights) * 0.01
+
+print("Trained loss:", training_loss(weights))
+
    +
    +
    +
    +
    diff --git a/doc/LectureNotes/_build/html/clustering.html b/doc/LectureNotes/_build/html/clustering.html new file mode 100644 index 000000000..41cdce5da --- /dev/null +++ b/doc/LectureNotes/_build/html/clustering.html @@ -0,0 +1,828 @@ + + + + + + + + 12. Clustering and Unsupervised Learning — Applied Data Analysis and Machine Learning + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
    +
    + + + + + + + + +
    + +
    +
    +
    +
    + + + + +
    + + +
    + + + + + + +
    +
    + + + + + + + + + +
    + + +
    + +
    + Contents +
    + +
    +
    +
    +
    +
    + +
    + +
    +

    12. Clustering and Unsupervised Learning

    +

    In general terms cluster analysis, or clustering, is the task of grouping a +data-set into different distinct categories based on some measure of equality of +the data. This measure is often referred to as a metric or similarity +measure in the literature (note: sometimes we deal with a dissimilarity +measure instead). Usually, these metrics are formulated as some kind of +distance function between points in a high-dimensional space.

    +

    The simplest, and also the most +common is the Euclidean distance.

    +

    The simplest of all clustering algorithms is the k-means algorithm +, sometimes also referred to as Lloyds algorithm. It is the simplest and also +the most common. From its simplicity it obtains both strengths and weaknesses. +These will be discussed in more detail later. The \(k\)-means algorithm is a +centroid based clustering algorithm.

    +

    Assume, we are given \(n\) data points and we wish to split the data into \(K < n\) +different categories, or clusters. We label each cluster by an integer

    +
    +\[ +k\in\{1, \cdots, K \}. +\]
    +

    In the basic k-means algorithm each point is assigned to only +one cluster \(k\), and these assignments are non-injective i.e. many-to-one. We +can think of these mappings as an encoder \(k = C(i)\), which assigns the \(i\)-th +data-point \(\bf x_i\) to the \(k\)-th cluster.

    +

    \(k\)-means algorithm in words:

    +
      +

    1. We start with guesses / random initializations of our \(k\) cluster centers/centroids

      2. +

    2. For each centroid the points that are most similar are identified

      3. +

    3. Then we move / replace each centroid with a coordinate average of all the points that were assigned to that centroid.

      4. +

    4. Iterate 2-3 until the centroids no longer move (to some tolerance)

      5. +
    +

    We assume we have \(n\) data-points

    + +
    +
    +\[ +\begin{equation}\label{eq:kmeanspoints} \tag{1} + \boldsymbol{x_i} = \{x_{i, 1}, \cdots, x_{i, p}\}\in\mathbb{R}^p. +\end{equation} +\]
    +

    which we wish to group into \(K < n\) clusters. For our dissimilarity measure we +use the squared Euclidean distance

    + +
    +
    +\[ +\begin{equation}\label{eq:squaredeuclidean} \tag{2} + d(\boldsymbol{x_i}, \boldsymbol{x_i'}) = \sum_{j=1}^p(x_{ij} - x_{i'j})^2 + = ||\boldsymbol{x_i} - \boldsymbol{x_{i'}}||^2 +\end{equation} +\]
    +

    We define the so called within-cluster point scatter which gives us a +measure of how close each data point assigned to the same cluster tends to be to +the all the others.

    + +
    +
    +\[ +\begin{equation}\label{eq:withincluster} \tag{3} + W(C) = \frac{1}{2}\sum_{k=1}^K\sum_{C(i)=k} + \sum_{C(i')=k}d(\boldsymbol{x_i}, \boldsymbol{x_{i'}}) = + \sum_{k=1}^KN_k\sum_{C(i)=k}||\boldsymbol{x_i} - \boldsymbol{\overline{x_k}}||^2 +\end{equation} +\]
    +

    where \(\boldsymbol{\overline{x_k}}\) is the mean vector associated with the \(k\)-th +cluster, and \(N_k = \sum_{i=1}^nI(C(i) = k)\), where the \(I()\) notation is +similar to the Kronecker delta (Commonly used in statistics, it just means that +when \(i = k\) we have the encoder \(C(i)\)). In other words, the within-cluster +scatter measures the compactness of each cluster with respect to the data points +assigned to each cluster. This is the quantity that the \(k\)-means algorithm aims +to minimize. We refer to this quantity \(W(C)\) as the within cluster scatter +because of its relation to the total scatter.

    +

    We have

    + +
    +
    +\[ +\begin{equation}\label{eq:totalscatter} \tag{4} + T = W(C) + B(C) = \frac{1}{2}\sum_{i=1}^n + \sum_{i'=1}^nd(\boldsymbol{x_i}, \boldsymbol{x_{i'}}) + = \frac{1}{2}\sum_{k=1}^K\sum_{C(i)=k} + \Big(\sum_{C(i') = k}d(\boldsymbol{x_i}, \boldsymbol{x_{i'}}) + + \sum_{C(i')\neq k}d(\boldsymbol{x_i}, \boldsymbol{x_{i'}})\Big). +\end{equation} +\]
    +

    This is a quantity that is conserved throughout the \(k\)-means algorithm. It can +be thought of as the total amount of information in the data, and it is composed +of the aforementioned within-cluster scatter and the between-cluster scatter +\(B(C)\). In methods such as principle component analysis the total scatter is not +conserved.

    +

    Given a cluster mean \(\boldsymbol{m_k}\) we define the total cluster variance

    + +
    +
    +\[ +\begin{equation}\label{eq:totalclustervariance} \tag{5} + \min_{C, \{\boldsymbol{m_k}\}_1^K}\sum_{k=1}^KN_k\sum||\boldsymbol{x_i} - \boldsymbol{m_k}||^2 +\end{equation} +\]
    +

    Now we have all the pieces necessary to formally revisit the \(k\)-means algorithm.

    +

    The \(k\)-means clustering algorithm goes as follows

    +
      +

    1. For a given cluster assignment \(C\), and \(k\) cluster means \(\left\{m_1, \cdots, m_k\right\}\). We minimize the total cluster variance with respect to the cluster means \(\{m_k\}\) yielding the means of the currently assigned clusters.

      2. +

    2. Given a current set of \(k\) means \(\{m_k\}\) the total cluster variance is minimized by assigning each observation to the closest (current) cluster mean. That is $\(C(i) = \underset{1\leq k\leq K}{\mathrm{argmin}} ||\boldsymbol{x_i} - \boldsymbol{m_k}||^2\)$

      3. +

    3. Steps 1 and 2 are repeated until the assignments do not change.

      4. +
    +
    +

    12.1. Codes and Approaches

    +
      +

    1. Before we start we specify a number \(k\) which is the number of clusters we want to try to separate our data into.

      2. +

    2. We initially choose \(k\) random data points in our data as our initial centroids, or means (this is where the name comes from).

      3. +

    3. Assign each data point to their closest centroid, based on the squared Euclidean distance.

      4. +

    4. For each of the \(k\) cluster we update the centroid by calculating new mean values for all the data points in the cluster.

      5. +

    5. Iteratively minimize the within cluster scatter by performing steps (3, 4) until the new assignments stop changing (can be to some tolerance) or until a maximum number of iterations have passed.

      6. +
    +

    Let us now program the most basic version of the algorithm using nothing but +Python with numpy arrays. This code is kept intentionally simple to gradually +progress our understanding. There is no vectorization of any kind, and even most +helper functions are not utilized.

    +

    We need first a dataset to do our cluster analysis on. In our case +this is a plain vanilla data set using random numbers using a +Gaussian distribution.

    +
    +
    +
    %matplotlib inline
+
+import time
+import numpy as np
+import tensorflow as tf
+from matplotlib import image
+import matplotlib.pyplot as plt
+from sklearn.cluster import KMeans
+from IPython.display import display
+
+np.random.seed(2021)
+
    +
    +
    +
    +

    Next we define functions, for ease of use later, to generate Gaussians and to +set up our toy data set.

    +
    +
    +
    def gaussian_points(dim=2, n_points=1000, mean_vector=np.array([0, 0]),
+                    sample_variance=1):
+    """
+    Very simple custom function to generate gaussian distributed point clusters
+    with variable dimension, number of points, means in each direction
+    (must match dim) and sample variance.
+
+    Inputs:
+        dim (int)
+        n_points (int)
+        mean_vector (np.array) (where index 0 is x, index 1 is y etc.)
+        sample_variance (float)
+
+    Returns:
+        data (np.array): with dimensions (dim x n_points)
+    """
+
+    mean_matrix = np.zeros(dim) + mean_vector
+    covariance_matrix = np.eye(dim) * sample_variance
+    data = np.random.multivariate_normal(mean_matrix, covariance_matrix,
+                                    n_points)
+    return data
+
+
+
+def generate_simple_clustering_dataset(dim=2, n_points=1000, plotting=True,
+                                    return_data=True):
+    """
+    Toy model to illustrate k-means clustering
+    """
+
+    data1 = gaussian_points(mean_vector=np.array([5, 5]))
+    data2 = gaussian_points()
+    data3 = gaussian_points(mean_vector=np.array([1, 4.5]))
+    data4 = gaussian_points(mean_vector=np.array([5, 1]))
+    data = np.concatenate((data1, data2, data3, data4), axis=0)
+
+    if plotting:
+        fig, ax = plt.subplots()
+        ax.scatter(data[:, 0], data[:, 1], alpha=0.2)
+        ax.set_title('Toy Model Dataset')
+        plt.show()
+
+
+    if return_data:
+        return data
+
+
+data = generate_simple_clustering_dataset()
+
    +
    +
    +
    +_images/clustering_17_0.png +
    +
    +

    With the above dataset we start +implementing the \(k\)-means algorithm.

    +
    +
    +
    n_samples, dimensions = data.shape
+n_clusters = 4
+
+# we randomly initialize our centroids
+np.random.seed(2021)
+centroids = data[np.random.choice(n_samples, n_clusters, replace=False), :]
+distances = np.zeros((n_samples, n_clusters))
+
+# first we need to calculate the distance to each centroid from our data
+for k in range(n_clusters):
+    for n in range(n_samples):
+        dist = 0
+        for d in range(dimensions):
+            dist += np.abs(data[n, d] - centroids[k, d])**2
+            distances[n, k] = dist
+
+# we initialize an array to keep track of to which cluster each point belongs
+# the way we set it up here the index tracks which point and the value which
+# cluster the point belongs to
+cluster_labels = np.zeros(n_samples, dtype='int')
+
+# next we loop through our samples and for every point assign it to the cluster
+# to which it has the smallest distance to
+for n in range(n_samples):
+    # tracking variables (all of this is basically just an argmin)
+    smallest = 1e10
+    smallest_row_index = 1e10
+    for k in range(n_clusters):
+        if distances[n, k] < smallest:
+            smallest = distances[n, k]
+            smallest_row_index = k
+
+    cluster_labels[n] = smallest_row_index
+
    +
    +
    +
    +
    +
    +
    fig = plt.figure()
+ax = fig.add_subplot()
+unique_cluster_labels = np.unique(cluster_labels)
+for i in unique_cluster_labels:
+    ax.scatter(data[cluster_labels == i, 0],
+               data[cluster_labels == i, 1],
+               label = i,
+               alpha = 0.2)
+    ax.scatter(centroids[:, 0], centroids[:, 1], c='black')
+
+ax.set_title("First Grouping of Points to Centroids")
+
+plt.show()
+
    +
    +
    +
    +_images/clustering_20_0.png +
    +
    +

    So what do we have so far? We have ‘picked’ \(k\) centroids at random from our +data points. There are other ways of more intelligently choosing their +initializations, however for our purposes randomly is fine. Then we have +initialized an array ‘distances’ which holds the information of the distance, +or dissimilarity, of every point to of our centroids. Finally, we have +initialized an array ‘cluster_labels’ which according to our distances array +holds the information of to which centroid every point is assigned. This was the +first pass of our algorithm. Essentially, all we need to do now is repeat the +distance and assignment steps above until we have reached a desired convergence +or a maximum amount of iterations.

    +
    +
    +
    max_iterations = 100
+tolerance = 1e-8
+
+for iteration in range(max_iterations):
+    prev_centroids = centroids.copy()
+    for k in range(n_clusters):
+        # this array will be used to update our centroid positions
+        vector_mean = np.zeros(dimensions)
+        mean_divisor = 0
+        for n in range(n_samples):
+            if cluster_labels[n] == k:
+                vector_mean += data[n, :]
+                mean_divisor += 1
+
+        # update according to the k means
+        centroids[k, :] = vector_mean / mean_divisor
+
+    # we find the dissimilarity
+    for k in range(n_clusters):
+        for n in range(n_samples):
+            dist = 0
+            for d in range(dimensions):
+                dist += np.abs(data[n, d] - centroids[k, d])**2
+                distances[n, k] = dist
+
+    # assign each point
+    for n in range(n_samples):
+        smallest = 1e10
+        smallest_row_index = 1e10
+        for k in range(n_clusters):
+            if distances[n, k] < smallest:
+                smallest = distances[n, k]
+                smallest_row_index = k
+
+        cluster_labels[n] = smallest_row_index
+
+    # convergence criteria
+    centroid_difference = np.sum(np.abs(centroids - prev_centroids))
+    if centroid_difference < tolerance:
+        print(f'Converged at iteration {iteration}')
+        break
+
+    elif iteration == max_iterations:
+        print(f'Did not converge in {max_iterations} iterations')
+
    +
    +
    +
    +
    Converged at iteration 5
+
    +
    +
    +
    +

    We now have a simple , un-optimized \(k\)-means +clustering implementation. Lets plot the final result

    +
    +
    +
    fig = plt.figure()
+ax = fig.add_subplot()
+unique_cluster_labels = np.unique(cluster_labels)
+for i in unique_cluster_labels:
+    ax.scatter(data[cluster_labels == i, 0],
+               data[cluster_labels == i, 1],
+               label = i,
+               alpha = 0.2)
+    ax.scatter(centroids[:, 0], centroids[:, 1], c='black')
+
+ax.set_title("Final Result of K-means Clustering")
+
+plt.show()
+
    +
    +
    +
    +_images/clustering_24_0.png +
    +
    +
    +
    +
    def naive_kmeans(data, n_clusters=4, max_iterations=100, tolerance=1e-8):
+    start_time = time.time()
+
+    n_samples, dimensions = data.shape
+    n_clusters = 4
+    #np.random.seed(2021)
+    centroids = data[np.random.choice(n_samples, n_clusters, replace=False), :]
+    distances = np.zeros((n_samples, n_clusters))
+
+    for k in range(n_clusters):
+        for n in range(n_samples):
+            dist = 0
+            for d in range(dimensions):
+                dist += np.abs(data[n, d] - centroids[k, d])**2
+                distances[n, k] = dist
+
+    cluster_labels = np.zeros(n_samples, dtype='int')
+
+    for n in range(n_samples):
+        smallest = 1e10
+        smallest_row_index = 1e10
+        for k in range(n_clusters):
+            if distances[n, k] < smallest:
+                smallest = distances[n, k]
+                smallest_row_index = k
+
+        cluster_labels[n] = smallest_row_index
+
+    for iteration in range(max_iterations):
+        prev_centroids = centroids.copy()
+        for k in range(n_clusters):
+            vector_mean = np.zeros(dimensions)
+            mean_divisor = 0
+            for n in range(n_samples):
+                if cluster_labels[n] == k:
+                    vector_mean += data[n, :]
+                    mean_divisor += 1
+
+            centroids[k, :] = vector_mean / mean_divisor
+
+        for k in range(n_clusters):
+            for n in range(n_samples):
+                dist = 0
+                for d in range(dimensions):
+                    dist += np.abs(data[n, d] - centroids[k, d])**2
+                    distances[n, k] = dist
+
+        for n in range(n_samples):
+            smallest = 1e10
+            smallest_row_index = 1e10
+            for k in range(n_clusters):
+                if distances[n, k] < smallest:
+                    smallest = distances[n, k]
+                    smallest_row_index = k
+
+            cluster_labels[n] = smallest_row_index
+
+        centroid_difference = np.sum(np.abs(centroids - prev_centroids))
+        if centroid_difference < tolerance:
+            print(f'Converged at iteration {iteration}')
+            print(f'Runtime: {time.time() - start_time} seconds')
+
+            return cluster_labels, centroids
+
+    print(f'Did not converge in {max_iterations} iterations')
+    print(f'Runtime: {time.time() - start_time} seconds')
+
+    return cluster_labels, centroids
+
    +
    +
    +
    +
    +
    + + + + +
    + + + + + + +
    + + + + +
    + +
    +
    +
    +
    +

    + + By Morten Hjorth-Jensen
    + + © Copyright 2021.
    +

    +
    +
    +
    + + +
    +
    + + + + + + \ No newline at end of file diff --git a/doc/LectureNotes/_build/html/genindex.html b/doc/LectureNotes/_build/html/genindex.html index 5ce5d1fab..6b34d9aaa 100644 --- a/doc/LectureNotes/_build/html/genindex.html +++ b/doc/LectureNotes/_build/html/genindex.html @@ -188,6 +188,11 @@ 11. Basic ideas of the Principal Component Analysis (PCA) +
  • + + 12. Clustering and Unsupervised Learning + +

    • @@ -197,17 +202,27 @@

    diff --git a/doc/LectureNotes/_build/html/intro.html b/doc/LectureNotes/_build/html/intro.html index 32cd03a9c..9b986280a 100644 --- a/doc/LectureNotes/_build/html/intro.html +++ b/doc/LectureNotes/_build/html/intro.html @@ -196,6 +196,11 @@ 11. Basic ideas of the Principal Component Analysis (PCA) +
  • + + 12. Clustering and Unsupervised Learning + +

    • @@ -205,17 +210,27 @@

    diff --git a/doc/LectureNotes/_build/html/objects.inv b/doc/LectureNotes/_build/html/objects.inv index 7b981a738edb2cb89e24111b525b52ec20300612..70bca6a162826681a827f621532136c892b7cba6 100644 GIT binary patch delta 744 zcmVs2X<;Wa>b=gIxQ`kFzw6lFGTq)s3C_)1dlpC^EXqEKm`!Udd zKwZ{CW;5LM}gsi(%N`IpaNQT=nJ^t zl0lOeUiVheOV1Y*)aiK;Sx$f|gB!F~M-m>>GDxvlR?@q>C0FQdh~PK^I_@f~b77rG zBd(?q)U+!{U4K>DIQU7a(*|zQM@e=9dK5E?a!_y*;W`Oib4rDG3(nBLC{803r-9;H zSt>V@`nWG(VRXrDw_*}DubCN~W}T{OUu>J>>sNMJ5?pG{DNy-@@#Mf21mEixsGr`a z@+_j_tZR3)oJWxnS`YLzOCwY&D)gOJR$BQ!nQ^N%R)1Ldu)Lam?0L^4yyt=UZnv>| zgsz+@#h-QpBH;0H;JF`JCat`b^?2$Ext1*1r>CpsFh_tg=Th^0l}RdV%hcXFb~sqO zp?bUJv;3%RU6I)e%PU}*&Ybv>(Q8X2aYNEm_0~Z2&HqgVYt& z;!NhWF*t#*?6;jhrkNRoO;A#5!;R2z7b#wY=xQFbq|{j?{HodO4}yzZoz>iiArYg~ z|G+wLJ7}90)V_|Q>1_eECJa+ITy3{1hxBay^kJ0ftBNwQkA9Y}ISXMfSx+Pz5=6cZa z2){8bo-N#BT1Y?K1o)XO+OU!ut8%O0WQ6M^a?L4K zAuV`I|Dre@p?^4y6xYU4xzW_$`vMl0OKI{-NF=-#X7DUJP17!1TjT3jNm&wHGD`_e zJ`p^5@CCuwx&`v%+fts5s5tA)g-+_IGC~)Cfo5ryNmV7zxZ<*6BQ}AVLESjz;N9|S z_P*ymAK^WZyq!5sH0M?cS6-Fsck8zi@Nhfw+z%p?R)1b9dIEKY(o2yX%G337>smma zORL4rWs;LbGJ0*(Y21(w3HxZw@+JIDlo0b!RU3#WW|f#!hHs7@|5hV3rW2ST3Se(FT$=i;M z(9EpGCVwg^*-G~sX}yt`0(~vBk(8W`T)%4e`i+?4ma|&C6ALle{SU0mwu5$QLG5yI zn?4p%Yr;4x+oSEnBUgHI!SW@F7vyP59EG9U)evLdNXPvp=9D-uCJC>C+ey5Qc2lQi zc#Ln&zO=l-jnbhZ>w?%eZ5dZRL`=5R?!*V((jviOf<895SvV1hK3NR!w!mKfhWY6Y Pt_$|SZkhZ6$uBy*<9=E? diff --git a/doc/LectureNotes/_build/html/search.html b/doc/LectureNotes/_build/html/search.html index 315741fbb..2f6153900 100644 --- a/doc/LectureNotes/_build/html/search.html +++ b/doc/LectureNotes/_build/html/search.html @@ -194,6 +194,11 @@ 11. Basic ideas of the Principal Component Analysis (PCA) +
  • + + 12. Clustering and Unsupervised Learning + +

    • @@ -203,17 +208,27 @@

    diff --git a/doc/LectureNotes/_build/html/searchindex.js b/doc/LectureNotes/_build/html/searchindex.js index cf2f29151..2acf2f68e 100644 --- a/doc/LectureNotes/_build/html/searchindex.js +++ b/doc/LectureNotes/_build/html/searchindex.js @@ -1 +1 @@ -Search.setIndex({docnames:["chapter1","chapter10","chapter11","chapter2","chapter3","chapter4","chapter5","chapter6","chapter7","chapter8","chapter9","chapteroptimization","intro","linalg","schedule","statistics","teachers","textbooks"],envversion:{"sphinx.domains.c":2,"sphinx.domains.changeset":1,"sphinx.domains.citation":1,"sphinx.domains.cpp":4,"sphinx.domains.index":1,"sphinx.domains.javascript":2,"sphinx.domains.math":2,"sphinx.domains.python":3,"sphinx.domains.rst":2,"sphinx.domains.std":2,"sphinx.ext.intersphinx":1,sphinx:56},filenames:["chapter1.ipynb","chapter10.ipynb","chapter11.ipynb","chapter2.ipynb","chapter3.ipynb","chapter4.ipynb","chapter5.ipynb","chapter6.ipynb","chapter7.ipynb","chapter8.ipynb","chapter9.ipynb","chapteroptimization.ipynb","intro.md","linalg.ipynb","schedule.md","statistics.ipynb","teachers.md","textbooks.md"],objects:{},objnames:{},objtypes:{},terms:{"0":[0,1,2,3,4,5,6,7,8,9,10,11,13,15,16],"00":[0,1,3,4,7,9],"000":1,"0000":7,"00000":7,"000000":[0,3,9],"00000000e":3,"0001":1,"000148":0,"00019998":3,"00024087":3,"00028369228101198006":7,"00029012":3,"0003153514830958081":4,"0003153514830958126":4,"00034944":3,"00042089":3,"00050694":3,"00058016":4,"000599":0,"00060705":4,"00061058":3,"00062595":4,"00066668":4,"00068734":4,"00069103":4,"00073541":3,"00076495":4,"00076925":4,"0007698473260556334":4,"0007698473260556339":4,"00079123":4,"00079968":3,"00084705":4,"00085884":4,"00087697":4,"00088573":3,"00092646":4,"00096314":3,"001":[1,2,6,11],"00100519":4,"0010479245355337968":4,"00105081":4,"00106677":3,"00107405":4,"00111756":4,"0011526":4,"00115999":3,"00118527":4,"001263":0,"00128479":3,"001323":4,"00137835":4,"00139705":3,"00149311":4,"00149956":4,"00152117":4,"00154733":3,"00156379":4,"00168251":3,"00174276":4,"00175331":4,"00186347":3,"001988":9,"00198806":9,"00200":6,"00202624":3,"00202756":4,"00217499":4,"00224413":3,"00228741":4,"0023548":4,"002381316302584885":4,"0023813163025848865":4,"00242999":4,"00243186":4,"0024401":3,"00249435":4,"002526":0,"00270244":3,"00274989":4,"00289724":4,"00293838":3,"002948":0,"0030828":9,"003083":9,"00312361":4,"00315593":4,"003215318065760509":4,"00323332":4,"0032542":3,"003301":4,"0033955154592040944":4,"00353823":3,"0036237":4,"0036367":4,"00369758":4,"003704":0,"003717":0,"003759":0,"003774":0,"003788":0,"0038335":4,"003909404072811231":4,"00391839":3,"0039987":4,"004":3,"0040919407077539514":4,"00410387":4,"00410478":4,"0041136346174431284":4,"004113634617443135":4,"00411363461744314":4,"004113634617443141":4,"004155986345861374":4,"00415763":11,"00424967":4,"00426027":3,"00433417":9,"00440346":4,"00443743":4,"00445655":9,"004579219539673836":4,"00458878":4,"004610275230656294":4,"00462287":4,"00471782":3,"00472199":4,"00472512":4,"0049544":4,"004999999999999994":0,"00512927":3,"00517114":4,"00526348":4,"0053018":4,"00554552":4,"00556826":4,"0056799":3,"00579953":4,"00588657":4,"00607783":4,"006162":4,"00617499":3,"00630331":4,"00642221":4,"00660427":4,"00672607":4,"00673407":4,"00676387":4,"0068011":4,"00683748":3,"00683964":4,"007012403613997257":0,"007024126888936694":4,"00719176":4,"00727646693":0,"007315":0,"0074331":3,"00759119":4,"00784393":4,"00803064":4,"0080866254785146":15,"00813803":4,"00817631":4,"00823002":3,"00827728":4,"00831018":4,"00834567":4,"00848904":4,"0086649156":0,"008675369724976501":3,"00894639":3,"00905423":4,"009163470508352211":3,"009164545680330616":4,"00917248":4,"00934499":4,"009450756365829578":0,"0096208":4,"00990475":3,"00992331":4,"00996754":4,"01":[0,1,2,3,4,7,9,17],"010018312644139347":4,"0100706":4,"01033172130665515":4,"010516485576652856":4,"01066519":4,"01076611":3,"0110":15,"011076219011339788":4,"0113104":4,"01179792":4,"01191824":3,"012073649439965807":4,"01219292":4,"01223198":4,"01231917":4,"01290947":4,"01295356":3,"013121573975499602":4,"013121573975499604":4,"01318643":4,"01347916":4,"01348565":4,"01367553":4,"01397146":4,"01405935":4,"01416528":4,"014209325470380275":0,"01433809":3,"014436800088969727":4,"01449782":4,"01458337":4,"0146081":4,"01463049":4,"015072388895177088":4,"015072388895177109":4,"01530715721129232":15,"01531845":4,"01538461538462":7,"01549377":4,"01558197":3,"016285782696075054":4,"01633913":4,"01640891":4,"01655318":4,"016587414993037307":4,"01691985":4,"01708781":4,"01708852":4,"01713366":4,"01724499":3,"01735584819559184":4,"017355848195591845":4,"01756972":13,"018232":0,"01831130e":4,"01831200e":4,"01866537":4,"01873344":9,"01873869":3,"01898855":4,"01905883":4,"01908936":4,"019587":0,"01963611":4,"01969145":4,"01975416527179247":4,"01975848":4,"02":[0,4,5,10],"02024962":4,"02054837e":4,"02068067":4,"02073509":3,"02098261":4,"02123176":4,"02159270458799264":4,"021592704587992645":4,"02198702e":4,"022022882954618364":0,"02208512":4,"02228115":4,"02229529":4,"02252765":3,"02299949826036602":4,"02348765":4,"02365049":4,"0245528":4,"02492265":3,"02498832":4,"02503753":4,"02511518":4,"02522069":4,"025709":[0,9],"02586427":4,"0260906":4,"02625193":6,"026408391362671896":15,"026605727637176654":4,"02707227":3,"02723445":4,"027609773491022314":4,"02926396":15,"029733":0,"02976145":4,"02994311":3,"02f":4,"03":[1,4],"03032441e":4,"03056589":3,"030566":3,"03076923076924":7,"03099776":3,"031":3,"03187339273559067":15,"03196357":4,"03251863":3,"03256632e":1,"03267527":4,"03278964":9,"032790":9,"03279636":4,"0330308045180234":4,"0330308045183163":4,"033657685071527485":4,"03447512":4,"03562355":4,"03568439":4,"0358909447132981":9,"0359565":3,"03630548":4,"03707133":9,"03781367141738885":4,"03781367141738886":4,"03814292":4,"03815288":4,"038300":[0,9],"039039":3,"0399676689527968":4,"0399676689527975":4,"04":[1,4,9],"04010697":4,"04063602":4,"041":7,"0411487294305246":4,"0411487294305746":4,"04220758":4,"043":7,"04315108":3,"0433816":13,"04346721":3,"04355837":4,"04362":7,"0437499":2,"04389027":4,"043927769551648":15,"04423486":4,"044334":0,"044613":4,"04483457":15,"04537385":4,"04543942":4,"04566964":4,"0458":7,"04615384615386":7,"04621521":11,"04648335":3,"04683565":3,"04784395":4,"04818727730430296":4,"04892055":4,"04909093":4,"04912436":4,"0495569966278269":4,"0495569966278315":4,"04it":4,"05":[0,1,4,11],"05009826":4,"05087958":13,"05100875":4,"051649":[0,9],"0517473":3,"05227921801205691":4,"05227921801205692":4,"05263":7,"05302":7,"05364854":6,"05383795":4,"05447415":4,"054585":9,"054785":9,"054963":9,"055137":9,"055320":9,"05533":7,"055676":0,"05614483":3,"05623":7,"05648":7,"05651951":4,"05667":7,"057088709963182":0,"05716368155351588":4,"0572":4,"05756733":4,"05785343":4,"05789007":4,"05796251":4,"05807125":4,"05883":7,"05884":7,"059783":9,"05999":7,"06":4,"060080":0,"060183":9,"06020587":4,"06021285":3,"060213":3,"06043581":4,"060507":9,"060655":9,"060781":9,"060841":9,"061025":9,"061048":9,"061321":9,"061390":9,"061509":9,"061604":9,"06160438":9,"061701":9,"061745":9,"061898":9,"061917":9,"06200174":3,"06208238634231953":4,"062142":9,"062294":9,"062391":9,"062435":0,"062451":9,"062534":9,"062834":9,"062884":9,"063078":9,"063250":9,"063343":9,"063513":9,"063657":9,"063872":9,"06388888888888888":1,"064052":9,"064108":9,"064184":9,"064384":9,"06444":7,"064469":9,"06453579006728315":4,"064648":9,"064681":9,"06491736":4,"064918":9,"064964":9,"065106":9,"06547790180152357":4,"06547790180152363":4,"065514":9,"065557":9,"065575":9,"065892":9,"066110":9,"066194":9,"066309":9,"06637":7,"066609":9,"0666807":2,"066753":9,"066837":[0,9],"066954":9,"067079":9,"067236":9,"06724062":3,"067544":9,"067675":9,"067714":9,"068094":9,"068103":9,"068120":9,"06844519414009438":4,"068659":9,"068809":9,"068831":9,"068937":9,"069091":9,"069455":9,"069584":0,"069672":9,"069754":9,"069912":9,"07":4,"070028":9,"070043":0,"070071":9,"07016":7,"07017":7,"070379":9,"07039":7,"070576":9,"070612":9,"07062318":4,"070635":9,"070889":[0,9],"070911":9,"07099747918547346":7,"071086":9,"07115":7,"0713":0,"071387":9,"07145103":9,"07160048164248561":4,"071698":9,"071705":9,"071935":9,"07201957":15,"072242":9,"072348":9,"072492":3,"072530":3,"072617":3,"072620":9,"072750":3,"0728785":11,"072928":3,"073016":9,"073225":9,"073362":3,"073368":3,"073423":3,"07345504":0,"073531":3,"073598":[0,9],"073695":3,"073907":9,"074067":[0,9],"07421084":3,"074336":9,"074488":9,"07456491":3,"074666":9,"07490892":4,"074945":9,"075573":9,"075820":9,"076204":9,"0764924":4,"07678":7,"076938":[0,9],"077022":9,"077467":9,"07777777777777778":1,"07820":7,"078253":9,"078548":9,"07864":7,"078667":3,"07871":7,"078911":9,"078992":3,"079347":3,"079406":3,"07944154":13,"07968918676726029":4,"079729":3,"079839":9,"079847":3,"079893":3,"07989327":3,"07999999999998":7,"08":[7,15],"080106":9,"080137":3,"080256":9,"080312":3,"080334":3,"080347":3,"080370":3,"080406":3,"080410":9,"08041015":9,"08043851":3,"080517":3,"080801":3,"080916":3,"081140":3,"08131003":4,"081431":3,"081483":3,"081540":3,"08156108":4,"081773":3,"082174":3,"082183":3,"082451":9,"08251519":4,"082900":3,"08299273e":4,"083053":3,"08318298e":1,"083220":3,"083227":3,"083404":3,"083441":3,"083506":3,"083527":0,"083600":3,"083692":3,"08376632":4,"0837663229239016":4,"0837663229239025":4,"083799":3,"083829":3,"083977":3,"084000":3,"084101":3,"084184":3,"084224":3,"084226":3,"08426840630693411":4,"08426840630693413":4,"084282":3,"084364":3,"084400":3,"084408":3,"084444":3,"084536":3,"084549":3,"08455":7,"084570":3,"084604":3,"084629":3,"084670":3,"084683":3,"08474":7,"084777":3,"084965":3,"085044":3,"085167":3,"085184":3,"085185":9,"085361":3,"085416":3,"08551306":4,"085764":3,"08576932":4,"08593216":4,"08611111111111111":1,"086303":3,"08630331":3,"086567":3,"08673755293381497":3,"08690":7,"087501":3,"08758":7,"08759":15,"087834":3,"08816688":15,"088176":3,"0881981":3,"088611":3,"088631":3,"08871404":3,"088809":3,"088816":3,"088825":3,"088853":3,"08888888888888889":1,"088926":3,"08902":7,"089059":3,"089212":3,"089329":3,"089425":3,"089614":3,"08996":7,"09":1,"090028":3,"090229":3,"090929":3,"091060":3,"09117221":15,"091224":3,"091236":3,"091340":3,"091349":3,"091363":3,"091414":3,"091416":3,"091426":3,"09149881":4,"091630":3,"09166666666666666":1,"0917":7,"091891":3,"09251":7,"09297039":9,"093247":0,"0934597075922044":3,"0940821989624095e":4,"0940821989673748e":4,"095510":3,"095702":3,"095871":3,"09609807":3,"096173":3,"096623":3,"09672929714683368":1,"097360":3,"09744":7,"09780":7,"09791":7,"099":4,"09903804":6,"099191989493334":4,"0n":0,"0x7fad10f9a280":11,"0x7fad20f69be0":11,"1":[0,1,2,3,4,5,6,7,8,9,10,11,13,15,16,17],"10":[0,1,2,3,4,5,6,7,8,9,10,11,13,15],"100":[0,1,2,3,4,5,6,7,8,9,11,13,15,16],"1000":[0,1,2,3,6,9,11,12,15],"10000":[2,3,4,8,9,15],"100000":6,"10001":8,"1001":[7,15],"1002":15,"1003":15,"10030":7,"10044225464078282":9,"1005":15,"10077114273548984":4,"1009":15,"1011":15,"1013":15,"1013904243":15,"10141413e":4,"1015":15,"102":0,"1022233262115424":15,"10222333":15,"1023":15,"10230":7,"1026":15,"1027":15,"103":[1,7],"1030":15,"10340":7,"1037":15,"10378326e":1,"1038":15,"10391807":4,"10398646080125035":4,"1040":15,"10405456":9,"10430":7,"104411":0,"1047":15,"10520":7,"10555555555555556":1,"10589577":3,"106095":[0,9],"108":[0,4,7],"109":4,"10913":4,"10931453":4,"10960":7,"10th":7,"10x":0,"11":[0,2,3,4,5,6,7,8,9,10,11,13,15,17],"110":0,"1100":15,"1101":15,"11022302e":3,"111":[1,5,10],"11100":7,"112383":[0,9],"1124":7,"11297834":15,"11362930e":3,"11388888888888889":1,"11390":7,"11462415":3,"11482289e":4,"11507992e":1,"11547777218940905":4,"11547777218940906":4,"115822":4,"11590":7,"11660":7,"11666666666666667":1,"117":6,"11744554e":4,"11780":7,"11790868":15,"117986":0,"118318":0,"11840":7,"11890":7,"119":2,"1199":6,"119999999999976":7,"12":[0,1,2,3,4,6,7,9,10,11,13,15,17],"120":2,"1203":7,"1203284":6,"121":[2,6,7,8],"12182967":4,"12196674":13,"122":[2,6,7,8],"12222222222222222":1,"122439":3,"1224392":3,"123":2,"12318726e":4,"12333649":4,"123459876":15,"123711":4,"12380":7,"124":0,"12400":7,"125":1,"125000":0,"12552073e":4,"126":7,"1261":7,"12618549":3,"1265":7,"1270":4,"127043":4,"127773":15,"12777777777777777":1,"12790":7,"128":7,"12945452":4,"1297":7,"1298":7,"13":[0,2,3,4,7,9,10,11,13,15],"130":7,"13003291":4,"13055555555555556":1,"131":7,"1314":4,"132":7,"13220608e":4,"132360":3,"1323603":3,"1326":7,"13280":7,"133":5,"13333333333333333":1,"135":7,"13519106":0,"13535942":4,"13646574":3,"13661243e":4,"13679863":4,"13740":7,"137400784702911":0,"137652":[0,9],"1378":4,"13865173":3,"138775":[0,9],"13890":7,"1392559581788775e":4,"1392559584983597e":4,"14":[0,2,3,4,6,7,8,9,10,11,13,15,17],"140":7,"14021063":4,"1404":0,"14042769":3,"140428":3,"141":7,"14100":7,"1416398":4,"14174745":4,"1418":7,"142":7,"14250":7,"142857":0,"143":5,"14360598":15,"1437":1,"144":2,"14400":7,"1440501043841336":1,"14440":7,"145":2,"146":2,"147":2,"14710":7,"14722222222222223":1,"147400":[0,9],"14741468":11,"147420":[0,9],"1479":7,"148":2,"14812206":4,"14818":4,"1484256":11,"148768":4,"14932651":15,"14988578":9,"149886":9,"14g":4,"15":[0,2,3,4,5,6,7,10,11,15],"150":[6,7],"15005476":3,"15098090e":4,"15130074e":4,"151986":4,"152":7,"15200":7,"15258907":11,"1527777777777778":1,"153036":0,"153106":0,"153760":0,"15384615384616":7,"154":7,"15454301":11,"154720":0,"154911":0,"155":7,"155491":0,"155687":0,"155883":0,"156":0,"15629539":11,"157":0,"1575":7,"158":[0,7],"1586300629904382":9,"1587":7,"159":0,"1590":7,"15990":7,"15g":4,"15it":4,"16":[1,2,3,4,6,7,8,11,14,15],"160":0,"16111111111111112":1,"16211139":3,"16220":7,"1625":7,"1628":7,"163":7,"1630775253":1,"16342407":3,"16343471":4,"16500":7,"166":7,"16660817":4,"166667":0,"167":7,"168":7,"16805821e":4,"16807":15,"17":[0,1,2,3,4,6,7,11,15],"17084902":11,"1709":7,"17174962e":1,"1726":7,"17300":7,"1731":7,"17339342":4,"17446471":4,"1752":7,"175300":0,"17641709":4,"176880142835407":9,"17777777777777778":1,"17801022":3,"17861098":4,"17917768":3,"17949575":3,"17953942":9,"1797":1,"18":[2,4,5,6,7,8,11,15],"180":7,"18029127":3,"1809":7,"181":7,"1812":7,"1821":7,"18327677":15,"18333333333333332":1,"184":7,"184519":0,"184895":4,"18526":4,"185278747229417":3,"1860":7,"18611111111111112":1,"18613217e":4,"18660":7,"18673098":9,"189496":0,"189622":0,"18it":4,"19":[2,4,7,11,15],"191262820314401":9,"19207979":3,"19220":7,"193":7,"19394283":15,"1940":0,"194042826653172e":4,"194042826815498e":4,"1943":10,"19444444444444445":1,"1950915150":4,"1954":4,"1956":7,"19569961":4,"1970":13,"1973":7,"197370":[0,9],"19740":7,"1979":4,"19800":7,"1989":15,"199":7,"19937":15,"1_1":10,"1_2":10,"1_3":10,"1cm":[0,6,8,15],"1d":[1,2],"1e":[1,2],"1e4":4,"1f":1,"1k":13,"1n":0,"1x":0,"2":[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17],"20":[0,1,2,4,5,6,7,11,15],"200":[0,2,6,7,8,15],"2000":0,"200000":0,"20015436":4,"2004":11,"2006":17,"2010":1,"2011":1,"2015":1,"2016":0,"2018":[0,4],"2019":7,"2021":[4,14],"2027":7,"20277777777777778":1,"20320502":4,"20500":7,"206":7,"2060":7,"20661216":15,"2069":7,"207545":[0,9],"20756638":15,"20833333333333334":1,"20867052175109335":4,"20980":7,"21":[0,1,2,3,4,5,7,10,11,13],"210340":[0,9],"21058097":3,"21130":7,"21169159e":4,"213103":[0,9],"213743":[0,9],"2147483647":15,"21596432":4,"216290":[0,9],"216683":[0,9],"21944444444444444":1,"22":[0,1,2,3,4,7,10,11,13,15],"22044605e":3,"221":6,"221180":0,"2216":7,"2218":7,"222400":0,"226124657522696":15,"22612466":15,"22690428":3,"22842468702288576":4,"22842468702288582":4,"22847924":3,"23":[1,2,4,5,7,10,11,13],"23002365e":4,"231":7,"23103285":15,"2315033":15,"23167717":3,"232435":0,"23333333333333334":1,"234":4,"23522201":11,"2357089093":1,"2361111111111111":1,"2364":7,"2397":7,"24":[0,1,2,4,7,11,13],"24140":7,"2416":7,"24175744e":4,"2419":7,"2430":7,"24390":7,"24444444444444444":1,"244858":9,"24485843":9,"246":2,"2470":4,"24829908":3,"24906604e":4,"25":[2,3,4,5,6,7,9,11],"250":[2,5,7],"25000":0,"250000":0,"250154":0,"251879":0,"252436":0,"252866":3,"25286618":3,"253775":0,"255001":0,"25617654e":4,"25617657e":4,"256962":0,"257":7,"2572":7,"2572495066":8,"2575":7,"259153":[0,9],"2597":7,"25976336":15,"26":[2,4,7,11],"26153846153846":7,"2619":0,"26290036":15,"26294938":15,"2629493813057833":15,"26301436":3,"26306244":15,"264":0,"2640931530791003":4,"2640931530791005":4,"265":0,"2650":7,"2654":7,"266":0,"26610075":15,"26666667":11,"26710969":3,"26780278":3,"268":7,"268227":3,"26822717":3,"269":0,"27":[0,1,2,4,11],"270":0,"2750":7,"275341":0,"276263":[0,9],"27692307692308":7,"27700":7,"2775623201":13,"27760":7,"27n_":15,"28":[1,4,7],"280647":[0,9],"282727":[0,9],"283":7,"28336218e":4,"2836":15,"28390":7,"28475098":6,"28590743":4,"2861":15,"2871":7,"2873":7,"2882":15,"2886":15,"2890":0,"2892":15,"29":[4,5,7],"29149329":15,"2915":15,"29167186":3,"2923076923077":7,"29592539":15,"296247":0,"2971492148":2,"29822833":4,"298273":0,"298375":0,"299748":0,"2_":[10,15],"2_1":10,"2_2":10,"2_3":10,"2_i":10,"2_m":[4,15],"2_t":11,"2_x":15,"2b":15,"2cm":6,"2d":[1,9,10,12],"2e":4,"2f":[0,5,7,8,9,10],"2g":2,"2g_i":2,"2m":4,"2n":[0,2],"2nd":7,"2p":15,"2x":[0,6,11],"2x_ix_jy_iy_j":6,"2x_j":6,"2y_i":8,"2y_j":6,"3":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15,16],"30":[0,1,4,5,7,8,11],"30000":0,"30010":7,"30119421":6,"301927":0,"303":4,"30466214e":4,"30535506":13,"30559547":15,"30787294":4,"309":7,"30940":7,"31":[0,10,13,15],"3123314713548606":4,"31276579e":4,"31318084":3,"31457796":3,"315":4,"3155":[3,4],"31718909":9,"317367":9,"31896852":6,"32":[4,7,10,13,15],"3200":1,"32047562":0,"3214960170351912":4,"3215":7,"324":2,"32458459":3,"3250":1,"32512":7,"326238":0,"32903042":11,"3297":0,"32992274":9,"329923":9,"33":[7,10,13],"3303":0,"33066907e":3,"3310":0,"33166055e":3,"331939":0,"332331":0,"333":5,"3331":0,"33327369":9,"333274":9,"33333333":11,"3337":0,"33611111111111114":1,"3384":4,"34":[7,13],"3403":7,"340782":[0,9],"34114547":3,"342680":0,"34305928":15,"3436":0,"3437":0,"34569596":3,"34740615":15,"35":[4,7],"35140":7,"351636":[0,9],"35182854":3,"3528556":3,"352856":3,"3530606977":3,"3544313922":4,"35470445e":3,"35533774":4,"356399":0,"357508":0,"359":3,"359999999999985":7,"36":[0,3,4,7,15],"360":1,"360688":0,"3613":7,"361556":0,"3621311":3,"363295916414895e":4,"3632959170548605e":4,"3655222":3,"36689784":9,"366898":9,"367":2,"369139":[0,9],"36it":4,"37":[2,7],"37396662":4,"376559":3,"37655936":3,"37732":11,"3777801602":4,"37835429e":3,"37900111":4,"37992857":4,"38":[2,7,15],"380":7,"38135733e":4,"3817475779":4,"38246359":15,"386":7,"38629436":13,"38901478":9,"38916861e":4,"38962192e":4,"39":[0,2,7,16],"39095416":4,"391602":15,"3925515884752442":3,"39579407":3,"39706038":3,"397700":[0,9],"3980313467":4,"399836":0,"3d":[2,4,11],"3f":[1,7],"3n":13,"3x":[2,6],"3x_i":2,"3y":6,"4":[0,1,2,3,4,5,6,7,8,9,10,11,13,15],"40":[1,2,4,7,16],"4000":[7,17],"40116777":3,"401168":3,"401842":[0,9],"4022":4,"4034668048":6,"404":0,"405890":[0,9],"4087":7,"40927184e":4,"41":[0,2,7,13],"4107":7,"41433969":3,"41511965e":1,"4155":2,"4162706317":4,"418506":[0,9],"41882037e":4,"4192423635":7,"41990268":15,"42":[1,2,6,7,8,13],"42441033":3,"42450":7,"4258989918":15,"426":[4,5],"42631342":4,"43":[1,2,5,7,13],"43054282":3,"43330971e":4,"435163":0,"43579948e":4,"43761347":4,"43766686":9,"438060758":4,"438136":0,"439230":4,"44":[0,1,2,13],"44089210e":3,"442600":[0,9],"443217":0,"444":7,"44970586e":1,"45":[7,16],"450":7,"450257":[0,9],"4504":7,"4557763":9,"455947":0,"456":7,"456418966187335":7,"457770268480242":0,"458027":0,"458078":[0,9],"45960079":3,"46":[7,16],"4601":7,"461":15,"462":5,"46383925e":4,"464424":9,"4644244":9,"466":15,"46602982":15,"46932688":15,"46984697e":4,"469868":3,"46986815":3,"47":[7,16],"47042744":3,"470714":0,"47075725":4,"47116868e":4,"47125748":3,"47132891":3,"47400238":15,"47432993":3,"47478057":15,"475311":9,"47531107":9,"47610036":4,"47815203":9,"48":7,"48089797":9,"481979":4,"48257387":16,"483257001":11,"48420165":15,"48476997":9,"486873":9,"48687342":9,"48994188":3,"49":[3,4,7,9],"4940954":0,"495916150936654e":4,"495916150938325e":4,"49636583":13,"4990":15,"4992":15,"4997":15,"4c4c7f":[7,8],"4f":4,"4y":6,"4y_i":8,"5":[0,1,2,3,4,5,6,7,8,9,10,11,13,15],"50":[1,2,4,5,6,7,8,11],"500":[1,4,7,8,11,15],"500000":0,"50000455":3,"50000553":3,"50000718":3,"50000855":3,"50000969":3,"50001063":3,"50001142":3,"50001207":3,"50001261":3,"50001306":3,"50001343":3,"50001374":3,"500014":3,"50001414":3,"50001422":3,"50001439":3,"50001454":3,"50001466":3,"50001476":3,"50001485":3,"50001492":3,"50001498":3,"50001502":3,"50001506":3,"5000151":3,"50001512":3,"50001515":3,"50001517":3,"50001518":3,"50001519":3,"50001521":3,"50001522":3,"50001523":3,"50001524":3,"50001525":3,"5018":15,"50227564e":4,"50321091":3,"504167":9,"50416731":9,"506":0,"50769230769231":7,"507d50":[7,8],"50846112e":4,"50j":11,"50x10":1,"51":[7,8],"510":1,"512132":0,"514219":0,"519842":0,"5222222222222223":1,"522758":0,"52307692307693":7,"5260627":15,"526744":[0,9],"52874252":3,"52911941":9,"52945798e":3,"53":7,"5303329":9,"5305555555555556":1,"531280":0,"53189647":4,"53697476":4,"53703498":4,"5378811":9,"53846153846155":7,"539261":[0,9],"54":[4,7,15],"540":7,"54039921":3,"541605":0,"544439":0,"546166676":11,"54780216":15,"54it":4,"55":[1,7],"550321":0,"5555555555555556":1,"55578041":15,"5566":4,"557795":[0,9],"55854694":9,"56":[1,7],"56033697":3,"56198284":3,"564":7,"564374":[0,9],"565":7,"56536":0,"566":7,"56636616e":4,"567":7,"568":7,"569":[1,7],"56912044e":4,"56939714":3,"56992937":15,"57":[0,2,6,7,16],"570":7,"571":3,"571105947979395e":4,"571105947979439e":4,"57201944e":4,"57266138":15,"574465":[0,9],"57it":4,"58":[2,7,8,16],"583595":0,"584804":0,"5888888888888889":1,"59":[2,7],"5944444444444444":1,"59591979":9,"595920":9,"598392":3,"59839245":3,"5cm":15,"5f":6,"5x":6,"5y":6,"6":[0,1,2,3,4,5,6,7,8,9,10,11,13,15],"60":[1,2,4,7],"60293962":3,"60420593":3,"606439":0,"60673226":9,"61":[2,5],"6111111111111112":1,"612939":0,"613579":0,"614808":[0,9],"618":0,"61808351":15,"618982":0,"6199381169260247":15,"62364974":3,"62373464":9,"625":5,"626635268":4,"62894215":3,"629961":0,"63":[0,1,4,5],"6300745149331701":0,"63025821e":4,"63249532e":4,"63498144":3,"63675140":4,"6371293350711955":0,"63it":4,"64":[1,5,13],"64012627":3,"645":4,"64615384615385":7,"646283":[0,9],"64742912e":4,"647473":[0,9],"649382":[0,9],"64x50":1,"65":[1,5,6,7],"65885453":3,"659306":0,"66204648":4,"66247212":15,"6628996975186953":0,"6638":7,"66410989":11,"66560":7,"667":7,"668172":0,"668186":9,"66818635":9,"67":[2,7],"67047975e":4,"671089":0,"672721":0,"67588315":15,"67838309":15,"68":2,"68192193":3,"68534263e":4,"68542204":3,"68545647e":3,"6869":7,"68929213e":4,"689519":[0,9],"69":[2,5,7,15],"690":7,"690569639355314":0,"690617":0,"69069n_":15,"692":[0,1],"69295955":13,"69504801":4,"69634577e":4,"69695259":3,"69985355":15,"6999536":9,"69it":4,"6n_":15,"7":[0,1,2,3,4,5,6,7,9,10,11,13,14,15,17],"70":[1,2,4,5,7],"70179437":15,"70710678":3,"70769586":13,"70832814":3,"71":[1,2],"7119":7,"712018":[0,9],"7134":4,"7151":4,"72174172":9,"72271878e":4,"7236674":3,"72373129":9,"72522848":11,"72859758":3,"7293182":11,"72981762":6,"73":4,"731000":0,"73174557":15,"733096":0,"74":4,"740":7,"74081822":6,"74840212":3,"749765":0,"75":[3,4,6,7,9],"7501749450963715":9,"750445":0,"751699":[0,9],"75170092":3,"753846153846155":7,"756352":0,"75838233":15,"75it":4,"76":[7,16],"76060096":15,"765":5,"76923076923077":7,"76936315":3,"77":[7,16],"77034458":3,"770345":3,"77152076":3,"7718":7,"774300":0,"775":1,"77636e":11,"77714169":6,"78011544":15,"78184120e":4,"7846153846154":7,"78941903":3,"79111643":3,"793167":0,"794282":[0,9],"79754246":15,"797e":4,"7d7d58":[7,8],"8":[0,1,2,3,4,5,6,7,8,9,10,11,13,15],"80":[0,1,3,4,6,7],"800":5,"80354994":4,"80469739":3,"8055555555555556":1,"80561191":15,"80609615e":4,"80734875":9,"807349":9,"80847477e":4,"81":1,"81048318e":4,"81160425":3,"81333805":4,"814":[5,9],"815563":11,"81633628":9,"816454":0,"816847":0,"8219235992494145":15,"8219236":15,"82198978":3,"82650876":3,"826509":3,"8265786":3,"82747653":3,"827477":3,"83":[0,2],"8305555555555556":1,"83512277":3,"83999999999999":7,"84062065":15,"84228957e":3,"842436":0,"84292394":3,"84355903e":1,"84443254e":1,"84780262":4,"84854738":9,"84923989e":4,"84994524":3,"85":[1,7],"85263220":4,"8527777777777777":1,"853241":9,"85324115":9,"85601992":3,"858":7,"8608479":3,"860848":3,"861":0,"86117291":3,"86134827":3,"86145244":9,"8638888888888889":1,"86546962":0,"86630":7,"8666666666666667":1,"86810":7,"87":[0,7],"871":4,"8722222222222222":1,"87381451":3,"875":1,"8759":11,"87625493":15,"878297":9,"88":11,"88046261":3,"8805555555555555":1,"88168312e":4,"88336879":3,"88477619":15,"88529063e":4,"88679947":15,"8888888888888888":1,"8916666666666667":1,"89288636":9,"89410423":3,"8944444444444445":1,"8962476":9,"896248":9,"8f":4,"8g":4,"8n":13,"8x8":1,"9":[0,1,2,3,4,5,6,7,9,10,11,13,14,15],"90":[1,4,7],"900449":3,"90054363":0,"90075537":3,"9011":4,"90220243":3,"90266948":3,"90268858":13,"903824":3,"90382431":3,"9040":7,"90475506e":4,"9055555555555556":1,"9083333333333333":1,"91":[15,16],"910":7,"9111111111111111":1,"91128596":3,"91379157":15,"913791573406831":15,"91416375":15,"91492986e":4,"91549644":0,"9166666666666666":1,"91760278":3,"91812702":3,"918992":0,"92":[4,7,16],"92343595":11,"924018":0,"924e":4,"925":1,"92507116e":1,"92578916":3,"92754397":9,"927544":9,"92857143":5,"931":0,"93155188":3,"93158979":3,"933":3,"93492130e":4,"9361111111111111":1,"937":15,"937082":0,"93799826":3,"938":15,"9387":7,"939":[0,15],"94":15,"94226022e":4,"94284104":3,"94320205":3,"9444444444444444":1,"94548496":4,"94591015":13,"94639099":9,"9472222222222222":1,"94735055":11,"947903":9,"94790323":9,"9482527":3,"95":[0,1,5,7,9],"95008046":4,"95231424":3,"9527777777777777":1,"95284275":3,"953065564":1,"95351665":3,"954":15,"9549351910143222":0,"9555555555555556":1,"956563":[0,9],"95684892":3,"95714723":15,"957147232685324":15,"95it":4,"96":[4,5,9],"960":15,"960130485007934e":4,"9601304850213484e":4,"96024953":3,"96084663":3,"961":15,"962":15,"9637117593816477":4,"9640435":3,"965548":0,"96653373":13,"96688672":3,"9674916":3,"967809":[0,9],"96863851":15,"97":5,"97005689":3,"97108e":11,"9722222222222222":1,"97230501":11,"97243128":3,"97300836":3,"97497404e":4,"975":1,"97507735":3,"9760832":15,"97705827":3,"97758848":3,"9777777777777777":1,"977880":3,"97788031":3,"9780387310732":17,"9780387848570":17,"9781492032632":17,"97898392":4,"97926491":3,"98":[0,1,5,7],"980":7,"98036405":0,"9805555555555555":1,"98091621":3,"981321":0,"98139097":3,"98275501":3,"983310":0,"98346748":15,"98413059":3,"98454786":3,"985":15,"98566191":3,"986":15,"9861111111111112":1,"98680716":3,"98716878":3,"98808176":3,"98822371":4,"9888888888888889":1,"989":15,"9890348":3,"9893149172528393":0,"9893447":3,"9898ff":[7,8],"99":[4,5,7,9,11],"990":7,"99009525":3,"99088801":3,"991":15,"99115119":3,"99176998":3,"992":15,"99242921":3,"99265097":3,"993":15,"99316252":3,"99353454":9,"993535":9,"99371056":3,"99389612":3,"993972":9,"99397245":9,"9943201":3,"9947756":3,"99492986":3,"99528218":3,"99539415":3,"9955282554647219":0,"99566069":3,"99578809":3,"996":3,"99608161":3,"9963961":3,"99650061":3,"9967458":3,"99700706":3,"99709215":3,"99729756":3,"99751458":3,"99758326":3,"99775587":3,"99793613":3,"99799099":3,"99813653":3,"99828624":3,"9983295":3,"99845267":3,"998577":3,"99861053":3,"99871521":3,"99881845":3,"99884384":3,"99893323":3,"999":[7,15],"99901896":3,"99903755":3,"99911427":3,"99918546":3,"99919837":3,"99926459":3,"9993237":3,"99933188":3,"99938942":3,"9994385":3,"99944272":3,"99949306":3,"99953381":3,"99953475":3,"99957911":3,"99961294":3,"99965056":3,"99967865":3,"99970988":3,"9997332":3,"99975913":3,"99977416":0,"99977849":3,"99980002":3,"9998161":3,"99984732":3,"99987324":3,"99989476":3,"99991263":3,"99992746":3,"99993978":3,"99995":3,"9999555851685968":4,"999955585168597":4,"9999840939906267":0,"9999858320366368":0,"9x":4,"9y":4,"\u00f8yvind":[4,16],"abstract":1,"break":[0,4,9],"byte":13,"case":[0,1,2,3,4,5,9,10,11,12,13,14],"catch":0,"char":15,"class":[0,1,4,5,6,7,9,10,11,15],"const":15,"default":[0,1,2,4,5,11,13],"do":[0,2,3,4,6,7,8,9,10,11,13,15],"ekstr\u00f8m":16,"export":7,"f\u00f8470":16,"final":[0,1,2,3,4,5,6,7,8,9,11,14,15,16],"float":[0,3,7,9,11,13,15],"function":[2,3,7,12,13],"import":[0,1,2,4,5,6,7,8,9,10,11],"int":[0,1,2,3,4,9,11,13,15],"long":[0,1,10,11,15],"m\u00f8svatn":4,"new":[0,1,2,3,4,5,6,7,8,9,11,13,15],"null":15,"public":[0,12],"return":[0,1,2,3,4,5,6,7,9,11,13,15],"s\u00f8rli":16,"sch\u00f8yen":[4,16],"short":3,"steinsv\u00e5g":16,"super":3,"switch":0,"throw":[4,15],"true":[0,1,2,3,4,5,6,7,8,10,11,13,15],"try":[0,1,2,3,4,5,6,7,8,9,11,12,13,15],"var":[1,2,3,4,6,7,8,9,11,13,15],"while":[0,1,3,4,5,6,7,9,10,11,15],A:[2,3,4,5,8,9,10,11,12,13,14,15,16,17],AND:2,And:[0,3,4,7,11,12,15],As:[0,1,2,3,4,6,8,10,11,13,15],At:[0,4,11],BE:0,Be:[0,2,12],Being:11,But:[0,1,2,3,4,7,8,15],By:[0,3,4,10,11,13],For:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17],IF:4,IN:17,If:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15],In:[0,1,2,3,4,5,6,7,8,9,10,11,13,15,17],Is:9,Ising:[3,10],It:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15],Its:[1,2,9],NO:[5,9],No:[3,4,6,7],Not:[0,1,3,4,14],OR:15,Of:15,On:[0,14,15,17],One:[0,1,3,4,5,6,9,10,11,15],Or:[0,1,4],Such:[4,10,15],That:[0,3,5,8,9,10,15],The:[8,11,13,14,16,17],Then:[0,1,3,4,6,7,8,9,10,11,13,15],There:[0,3,4,6,7,9,10,13,14,15,16],These:[0,3,6,7,8,9,10,11,13,15],To:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],With:[0,3,4,6,7,8,9,10,13,15],_0:[3,6,8,9,11],_1:[2,3,4,6,8,9,10,11,13],_2:[2,3,6,9,10,11,13],_3:13,_4:13,_9:11,_:[0,1,2,3,4,5,6,7,8,9,10,11,13],__class__:8,__doc__:4,__future__:[6,7],__init__:1,__main__:2,__mosek:3,__name__:[2,8],_asarrai:2,_auto10:[4,10],_auto12:4,_auto1:[2,3,4,5,10,11,13,15],_auto2:[2,3,4,10,11,13,15],_auto3:[3,4,10,11,13],_auto4:[4,10,11,13],_auto5:[4,10,11,13],_auto6:[4,10,13],_auto7:[4,10,13],_auto8:[4,10],_auto9:[4,10],_base:6,_build:[12,17],_c:1,_check_optimize_result:[5,9],_compon:9,_coordinate_desc:4,_depth:7,_fraction:7,_i:[0,1,2,3,4,6,9,10,11,15],_j:[0,1,2,3,4,6,11],_k:11,_l:10,_lambda:4,_leaf:7,_logist:[5,9],_m:8,_make_vjp:[2,11],_multilayer_perceptron:[0,1],_n:[2,3,6,9,11],_node:[2,7,11],_p:[3,6],_ratio:9,_sampl:7,_split:[4,7],_t:11,_test:4,_trace:[2,11],_valu:[2,11],_varianc:9,_weight:7,a0faa0:[7,8],a1:0,a2:0,a3:0,a4:0,a_0:0,a_1a:0,a_2a:0,a_3:0,a_3a:0,a_4:0,a_4a:0,a_:[0,1,13],a_h:1,a_i:[0,1,2,10],a_j:[1,10],a_k:[1,10],aaron:17,ab:[0,2,3,11],ab_channel:12,abandon:1,abbrevi:14,abid:15,abil:[0,8],abl:[1,3,4,5,8,10,11,15],abort:15,about:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,17],abov:[0,1,3,4,5,6,7,8,9,10,11,13,15],abovement:4,abscissa:11,absolut:[0,2,3,4,11],acceler:11,accept:[0,4,7],access:[0,9,15],accid:4,accmod:3,accompani:0,accomplish:[6,7,11],accord:[0,1,2,3,4,7,10,11,15],accordingli:9,account:[0,3,11,15],accumul:[10,15],accur:[0,4,8,11,15],accuraci:[0,1,3,4,5,7,8,9,10],accuracy_scor:[0,1,8],accuracy_score_numpi:1,achiev:[0,1,3,4,6,10,13],aco:15,acquaint:12,acquir:[1,12],acr:0,across:[1,4,7,12],act:[1,13],action:15,activ:[0,2,7,14],actual:[0,1,3,4,6,9,13],ad:[0,1,3,6,11,13],ada_clf:8,adaboostclassifi:8,adadelta:11,adagrad:11,adam:1,adapt:[0,4,11,17],add:[0,1,2,3,4,6,8,9,10,15],add_subplot:[1,5,10],addendum:3,addit:[0,2,3,4,5,6,7,8,10,11,12,13,15,16,17],addition:[10,11],address:[1,7,9,11,17],adjac:10,adjoint:3,adjust:[0,3,10,11],admir:0,advanc:[4,10,17],advantag:[1,3,4,8,11,13],affin:[0,6,9],african:0,after:[0,1,2,3,4,7,9,10,11,12,13,15],afterward:0,ag:[0,5,14],ag_0:2,again:[0,1,3,4,5,6,8,9,10,11,15],against:[1,5,8],agegroup:5,agegroupmean:5,aggreg:[7,8],agorithm:8,agre:[3,4,15],ahead:7,ai:[0,17],aid:9,aim:[0,1,4,5,9,12,13],ainv:3,aka:3,al:[0,2,14,17],alarm:3,algebra:[0,3,11,12,14],algo:15,algorithm:[0,1,2,3,4,5,6,11,12,13,14,15,17],align:[0,2,3,4,5,6,11,15],all:[0,1,2,3,4,5,7,8,9,10,11,12,13,14,15,16,17],allevi:[1,11],alloc:13,allow:[0,1,2,3,4,6,8,11,12,13],almost:[0,1,4,6,9,11,15],alon:[2,7],along:[2,3,4,7,8,9,12,13],alpha:[0,1,2,3,4,5,6,7,8,11,15],alpha_:8,alpha_i:11,alpha_k:11,alpha_m:8,alpha_opt:11,alreadi:[2,3,4,8,10,12,13,15],also:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17],alter:[1,15],altern:[0,1,3,4,5,6,7,9,11,13],although:[1,3,4,6,8,11],alwai:[0,3,4,10,11,15],am:[0,15],ame2016:0,american:0,among:[0,3,7,8,10],amongst:3,amount:[0,1,4,6,8,12],an:[1,2,3,4,5,6,7,9,10,11,12,13,15,16,17],an_:15,anaconda3:[0,1,2,4,5,6,9,11],anaconda:[0,1,12],analog:11,analys:[4,15],analysi:[1,5,13,14,17],analyt:[0,2,3,4,5,10,11,12],analyz:[0,1,3,4,15],andrew:1,angl:[0,7,15],ani:[0,1,2,3,4,5,6,7,8,10,15],anim:10,ann:10,annot:[0,1,5,6],anoth:[0,1,3,4,5,6,8,9,10,11,13,15],ansatz:0,answer:[0,1,3,4,13],antialias:[2,4],anymor:[1,6],anyon:6,anyth:[1,15],anytim:16,apach:1,apart:[9,11],api:[1,12],appar:2,appear:[0,1,11,13,15],append:[1,6,7,11,15],appendcon:3,appendvar:3,appli:[0,1,2,4,5,6,7,8,9,10,11,15,17],applic:[0,1,3,4,5,7,10,11,14,15,17],approach:[1,2,3,4,7,8,9,10,11,12,15,17],appropri:[2,4,7,10,11,12,15],approx:[0,2,4,8,9,11,15],approxim:[0,1,2,3,4,5,8,9,11,15],apt:[0,12],aq:15,ar:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],arang:[1,4,5,7,8,10],arbitrari:[1,4,6,10,11,15],arbitrarili:[0,1,9],arc:4,architectur:[10,17],area:[0,4,7,17],arg:[2,11],argc:15,argmax:[1,9],argmin:8,argnum:[2,11],argsort:9,argu:[1,11],argument:[0,2,3,4,9,10,11,15],argv:15,argval:2,aris:[0,4,10,11,15],arithmet:[0,11,13],arm:4,arma:15,armadillo:[13,15],around:[0,1,3,4,9,15],arrai:[0,1,2,3,4,5,6,7,9,10,11,12,15],arraybox:11,arriv:[0,4,7,9,13,15],arrow:10,arrowprop:6,art3d:11,art:[0,1,12],articl:[0,4,8,15],artifici:[0,2,5,10,17],artificialneuron:10,arug:11,as_fram:0,asarrai:[0,4,7],asc:3,ascii:15,ask:[3,4,9,10],aspect:[0,4,12],assembl:0,assess:[0,4],assign:[0,5,6,7,10,11,14,17],associ:[0,4,7,10,15],assum:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],assumpt:[0,3,4,7,9,15],ast:[0,3,4],astyp:[7,8],asymmetri:0,asymptot:4,atoi:15,atom:0,attempt:[0,4,5,6,8],attend:14,attent:[0,13],attract:[0,8],attribut:[0,7,11],attributeerror:11,audi:0,aurelien:[0,14,17],austfjel:4,author:[0,1,8,15],authour:0,auto:[7,8,15],autocor:15,autocorrelation_tim:15,autocorrelform:15,autocovari:15,autoencod:12,autoencond:12,autograd:[11,12],autom:[0,12],automac:13,automat:[0,1,2,9,12,13,14],autonom:17,avail:[0,1,4,8,9,12,13,14,17],averag:[0,1,4,7,8,11,15,16],avg:15,avoid:[0,3,4,7,9,11,13],awai:[2,4,15],awar:[2,8],award:16,ax:[0,1,2,4,5,6,7,8,9,10,11,13],axes3d:[2,4,11],axes_grid1:4,axessubplot:0,axhlin:6,axi:[0,1,2,4,5,6,7,8,9,10,11,13,15],axiom:3,axlabel:0,axvlin:6,b1:6,b2:6,b3:6,b:[0,1,3,4,6,7,8,10,11,15,16],b_1:[2,10,11],b_2:11,b_5:11,b_:[1,13],b_group:7,b_i:[0,1,2,10],b_ia_:0,b_index:7,b_j:[1,10],b_k:[1,10,11],b_m:10,b_score:7,b_valu:7,bachelor:14,back:[0,3,4,6,7,8,13,14,15],backbon:13,backend:1,background:[14,17],backpropag:1,backtrack:7,backup:13,backward:[1,2,10,13],bad:[4,15],badli:15,bag:[7,12,14],bag_clf:8,baggingboot:8,baggingclassifi:8,baggingtre:8,balanc:4,band:13,bandwidth:13,bar:[0,4,9],barber:17,bare:8,base:[0,1,3,5,6,7,8,12,15,16,17],basi:[3,5,6,8,9,10,11,13],basic:[4,6,10,11,12,14,15],batch:[9,10,11],batch_siz:1,bay:5,bayesian:[3,12,17],becaus:[0,1,2,3,4,6,7,10,11],becom:[0,1,2,3,4,5,7,10,11,15],been:[0,1,2,3,4,9,10,11,12,13],befor:[0,1,2,3,4,5,6,10,11,13,15],beforehand:[0,15],begin:[0,1,2,3,4,5,6,7,9,10,11,13,15],behav:[1,4,11],behavior:[0,1,11],behaviour:10,behind:[0,1,4,6,11],being:[0,1,2,3,5,6,8,9,10,11,15],believ:[7,13],belong:[3,5,6,7,11],below:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],benchmark:8,bendik:16,benefici:[1,11],benefit:[0,1,9,11,12],bengio:[1,14,17],benign:[1,5,7],besid:3,bessel:3,best:[0,1,2,3,4,5,6,7,8,10,11,15,16],beta:[0,1,3,4,5,8,9,11],beta_0:[0,1,3,4,5,11],beta_0x_:0,beta_1:[0,1,3,4,5,8,11],beta_1x_0:0,beta_1x_1:[0,5],beta_1x_2:0,beta_1x_:0,beta_1x_i:[5,11],beta_2:[0,11],beta_2x_0:0,beta_2x_1:0,beta_2x_2:[0,5],beta_2x_:0,beta_:[0,4,5,11],beta_i:[0,3],beta_j:[0,3,4,11],beta_k:11,beta_linreg:11,beta_m:8,beta_mg_m:8,beta_p:5,beta_px_p:5,betavalu:3,better:[0,1,2,4,7,8,9,10,11],between:[0,1,2,3,4,5,6,7,9,10,11,15],beyond:[0,1,3,4,6,11],bf:[11,13,15],bia:[0,1,2,3,6,7,8,10,11,14,15],bias:[1,2,3,4,7,10],big:[0,1,2,3,4],bigger:[1,4],bigr:10,bike:7,bilek:16,billion:[10,12],bin:[0,5,15],binari:[0,3,5,7,8,10,14,15],bind:0,binomi:12,binsboot:4,bioinformat:0,biolog:[1,10,17],bios1100:12,bird:0,bishop:[14,17],bit:[1,13,15],bitwis:15,bivari:2,bk:[0,11],bla:[3,13],black:[6,7],block:[4,8,12,13],blockingavg:15,blockingstd:15,blockingvar:15,blocksiz:15,blocksizemax:15,blocksizemin:15,blue:0,bmatrix:[0,1,3,5,6,9,11,13],bmi:1,bodi:[0,1,10],bold:1,boldfac:[0,3],boldsymbol:[0,1,2,3,4,5,6,8,9,11],boltzmann:[10,12],book:17,boost:[1,7,12,14],boostrap:8,bootavg:15,bootstd:15,bootstrap:[1,12,14],bootvar:15,bootvec:15,boston_dataset:0,bot:6,both:[0,1,3,4,6,7,8,11,12,13,15,16],bottl:5,bound:[0,3,6,10],boundari:[2,6,9,10],boundkei:3,box:[2,7],boxed_arg:2,boyd:[6,11],bracket:15,brain:[1,5,10],branch:7,breast:[3,5,9],breviti:11,brew:[0,12],brg:6,briefli:0,bring:[0,3,4,8],broad:0,brute:[3,9],bs:[6,7,8],build:[0,3,4,8,13,15],built:[0,1,4],bunch:9,busi:0,bx:3,bzl:3,c1:[6,9],c2:[6,9],c:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15,16,17],c_0:15,c_1:10,c_2:10,c_3:10,c_4:10,c_:[0,6,7,8,11,15],c_i:[10,11],c_k:15,ca:1,cach:8,cal:[0,6,8,10,11],calcul:[0,1,2,3,4,6,7,8,9,10,11,13],california:0,call:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15,17],calor:0,cambridg:[11,17],can:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15,17],cancel:[0,11],cancer:[3,8],cancerpd:5,candid:[6,7,8],cannot:[0,1,3,4,5,6,7,14,15],canopi:[0,12],cap:3,capabl:[0,1,6,11,12],capac:2,capita:0,captur:[9,10],card:[0,5],cardin:1,care:9,carefulli:11,carlo:[0,4,12,15,17],carri:[2,4,5],cart:8,casella:17,cast:1,categor:[0,1,7,9],categori:[0,1,5,8,10,14],categorical_crossentropi:1,caus:[0,3,4,15],causal:0,causat:0,cax:1,cb:4,cbar:1,cc:[0,1,3,11],ccc:[3,10],cd_fast:4,cdf:15,cdot:[0,2,4,10,11,13,15],celebr:11,center:[0,1,4,5,6,7,9,15],centr:17,central:[0,3,4,6,13],centroid:15,certain:[0,4,5,7,15],cg:11,cha:0,chain:[1,11,12,15],chanc:[1,3,11,15],chang:[0,1,2,3,4,6,7,9,10,11,13,15],chapter:[0,4,8,9,13,14,17],charact:[0,3,15],character:[6,7,8,10,15],characterist:[0,1,8,11],charg:0,charl:0,chd:5,chddata:5,cheap:3,cheaper:[1,11],check:[0,1,3,4,9,11,13],chemic:15,chen:8,chiaramont:2,choic:[0,1,2,4,7,10,11,13,15],choleski:[3,13],choos:[2,4,7,8,9,11,15],chosen:[0,1,2,4,6,7,8,11,15],chosen_datapoint:1,christian:17,christoph:[14,17],cin:15,circ:[1,10],circl:[0,6,10],circumfer:7,circumv:[1,3,11],clariti:15,class_nam:7,class_val:7,class_valu:7,classic:[5,7,11],classif:[0,3,4,5,6,9,10,12,14,17],classifi:[0,1,5,7,8,9],classificaton:1,classifii:8,clean:1,clear:[1,3,8,10,11],clearli:[0,3,4,5,6,15],clever:[1,8],clf3:0,clf:[0,4,6,7,8],clf_lasso:4,clf_ridg:4,clip:15,close:[0,1,2,4,6,7,9,10,11,15,17],closer:[3,11],closest:[6,9,11],closur:12,cloud:12,cluster:[0,1,4,9,12,14],cm:[1,2,4,6,7,11],cmap:[0,1,2,4,6,7,8],cmap_arg:4,cmath:15,cmb:14,cmd:7,cmu:0,cn_:15,cnn:[10,14],cntk:12,co:[0,2,4,7,11],code:[4,5,6,11,12,13,14,17],coef0:6,coef:0,coef_:[0,3,4,6,7,11],coeff:3,coeffici:[0,3,4,5,6,7,11,13],coerc:[0,4],coin:[8,15],coin_toss:8,col:[0,9],colab:12,cold:7,colinear:0,collaps:6,collect:[0,2,4,8,9,12,15,17],collinear:3,color:[0,4,6,7,8,15],color_cod:4,colorbar:[1,4],colsample_bytre:8,colsaobject:8,column:[0,1,2,3,4,5,6,7,9,10,13],columntransform:7,com:[4,12,16,17],combin:[1,2,3,4,5,8,15],come:[0,1,3,10,11,14],command:[0,1,7,15],comment:[0,3,4],commerci:[0,12],commod:0,common:[0,1,3,4,5,7,9,15],commonli:[0,1,4,5,7,11],commun:[0,10],compact:[0,1,3,4,5,7,9,10,11],compar:[0,3,4,9,11,13],comparison:[2,11],compat:5,compet:0,competit:8,compil:[0,1,12,13,15],complet:[0,2,7,10],completenn:10,complex:[1,3,6,7,9,10,11],complic:[0,1,7,11],compon:[0,1,3,4,5,7,12,14],components_:9,compos:[7,10],compphys:[4,12,14,17],compress:0,compris:4,compromis:3,compulsori:12,comput:[0,1,2,3,4,5,6,8,9,10,11,12,13,14,17],computation:[0,4,7,11,15],con:3,concaten:[2,4],concav:[1,7,11],concentr:[0,8],concept:[0,2,12],conceptu:[10,11],concern:[0,1,5],conclud:[0,3],conclus:1,cond:2,conda:[0,1,12],condit:[0,2,3,4,6,7,9,11,15],conduct:12,condwav:2,coneqp:3,confid:[0,3,4,5,6],confirm:[3,10],confus:[3,4,8,13],confusion_matrix:7,congruenti:15,conjug:6,conjugaci:11,connect:[0,1,7,9,10,11,13],consequ:[3,4,6,8,10,11],conserv:3,consid:[0,1,2,3,4,5,6,7,8,10,11,13,15],consider:[0,1,3,11],consist:[0,1,2,4,10,11,15],constant:[0,2,3,4,6,10,11,15],constitu:0,constitut:[2,4],constrain:[1,3,5,9],constraint:[3,4,6,11],construct:[0,1,2,3,4,5,6,7,8,9,13,15,17],contact:0,contain:[0,2,3,4,5,6,7,9,10,11,13,15,17],contemporari:17,content:[1,12,13],context:[4,8,11],contigu:13,continu:[0,1,2,3,4,5,6,7,8,10,11,13],contour:[7,8,11],contourf:[6,7,8],contrast:[1,7,8,10],contribut:[0,3,15],contributor:0,control:[0,1,7,11,12],conveni:[0,3,4,10,11,13],convent:10,converg:[0,1,2,3,4,5,6,9,11],convergencewarn:[0,1,4,5,6,9],convert:[0,1,3,7,9,11,13],convex:[3,5],convinc:11,convolut:[1,12,14],cool:7,coolwarm:4,coordin:[3,10],coorel:0,copi:[0,1,2],core:[2,8,11],corel:0,coronari:5,corr:[0,3,5,9],correalt:[9,12],correct:[0,1,2,3,11,13,15],correctli:[1,2,4,8],correl:[0,1,3,4,5,8,10,11,12],correlation_matrix:[0,3,5,9],correspond:[0,3,4,6,7,9,10,12,13,15],cortex:10,cosin:4,cost:[0,2,3,4,5,6,7,10,11,15],cost_deep_grad:2,cost_funct:2,cost_function_deep:2,cost_function_deep_grad:2,cost_function_grad:2,cost_grad:2,cost_sum:2,could:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],coulomb:0,count:[0,7,14,15,16],countor:11,coupl:[3,4],cours:[0,1,3,9,14,15],courvil:[14,17],cout:15,cov:[3,4,9,13,15],cov_xi:[3,9],cov_xx:[3,9],cov_yi:[3,9],covari:[0,5,12,13],covariance_matrix:[3,9],cover:[0,3,12,14,17],covert:0,covxi:15,covxx:15,covxz:15,covyi:15,covyz:15,covzz:15,cpu:1,creat:[1,2,3,4,7,8,9,10,11,12],create_biases_and_weight:1,create_neural_network_kera:1,create_x:[3,9],credit:[0,5],crim:0,crime:0,criteria:[0,7,8,15],criterion:[7,8,11],critic:4,cross:[0,1,5,7,8,11,12,14,15],cross_val_scor:4,cross_valid:[5,8],crossvalid:4,crucial:[1,15],cs:14,csr_matrix:13,cstdlib:15,csv:[0,4,5,7],ctnk:1,cubic:0,cumbersom:3,cumsum:[8,9],cumul:8,cumulative_heads_ratio:8,cup:3,current:[1,2,4,11],curs:0,curv:[4,5,8,10],curvatur:11,custom:[3,4],custom_cmap2:[7,8],custom_cmap:[7,8],cutpoint:7,cv:[4,5,8],cvxbook:11,cvxopt:[3,6],cyber:17,cycl:[1,10,15],d1:3,d2:3,d2_g_t:2,d3:3,d:[1,2,3,4,5,6,7,8,9,11,13,15,16],d_f:11,d_g_t:2,d_net_out:2,dagger:[3,13],dai:[1,7,12],dalen:16,darget:7,darkr:15,dat:0,dat_id:[0,4,5,7],data:[2,3,6,8,10,11,13,17],data_id:[0,4,5,7],data_indic:1,data_modul:0,data_path:[0,4,5,7],data_url:0,databas:1,datafil:[0,4,5,7],datafram:[0,3,5,7,9],datapoint:[1,3,4,5,9,11],dataset:[0,4,5,6,7,8,9,11],date:0,daughter:8,david:17,dbh:1,dbo:1,dcomposit:13,ddot:2,dead:1,deadlin:14,deal:[0,1,3,4,6,9,11,13,15],debt:5,debug:[3,4],decad:0,decai:[0,11,15],decemb:14,decent:8,decid:[0,2,3,4,7],decim:0,decis:[0,1,6,9,12,14,17],decision_funct:6,decision_tre:7,decisiontreeclassifi:[7,8],decisiontreeregressor:[0,7,8],declar:[0,13],decompos:[3,4,13],decomposit:[0,4,10,14],decompost:3,decorrel:[8,11],decreas:[1,2,3,4,8,9,11],deduc:0,deep:[5,10,11,12,14,17],deep_neural_network:2,deep_param:2,deep_tree_clf1:7,deep_tree_clf2:7,deep_tree_clf:[7,8],deepen:[3,12],deeper:0,deeplearningbook:17,def:[0,1,2,3,4,5,6,7,8,9,11,15],def_covari:15,defect:3,defici:3,defin:[0,2,3,4,5,6,7,8,9,10,11,13,15],definit:[1,2,3,4,6,8,9,10,11,13],defint:15,degre:[3,4,6,7,8,9,15],del:1,delet:[4,15],deliv:14,delta:[0,2,4,6,10,11,15],delta_:[1,13],delta_h:[0,1],delta_j:10,delta_k:10,delta_l:1,delta_n:0,delug:12,delv:0,demand:11,demonstr:[0,3,4,5,9,10,12],denomin:[1,3],denot:[1,2,4,5,11,15],dens:1,densiti:[0,2,4,15],depart:16,depend:[0,1,2,3,4,5,6,9,10,11,12,15],depict:15,deploy:[0,12],deprec:[0,2,4,11],depth:[0,7,8,13],deriv:[0,1,2,4,5,6,8,9,11,12],descend:[3,7,9],descent:[0,1,5,6,10,14],descr:0,describ:[0,2,3,4,6,8,9,10,11,13],descript:[0,6,7],design:[0,1,3,4,5,8,9,10,11],designmatrix:0,desir:[0,2,3,11],despit:[1,10],destroi:13,det:[3,13],detail:[0,4,9,11,13],detect:[6,10],determin:[0,2,3,4,6,7,8,9,10,11,13,15],determinist:[5,11,15],dev:[1,15],develop:[0,3,6,8,9,10,12,13,14],deviat:[0,1,2,3,4],devis:10,df:[6,9,11],di:[0,3],diag:[3,6],diagnost:[1,8],diagon:[0,3,5,11,13,15],diagonaliz:3,diagram:8,diagsvd:4,dice:4,dict:[4,6],dict_kei:0,dictionari:0,did:[0,1,3,4,5,8,9],die:1,diff1:2,diff2:2,diff:2,diff_ag:2,diffeent:6,differ:[0,1,2,3,4,7,8,9,10,11,12,13,15,17],differenti:[12,13,14],differential_oper:[2,11],difficult:[0,1,4,8,11,15],difficulti:[0,1,11],diffonedim:2,digit:[0,1,4,14,16],dilemma:11,dilut:1,dim:[9,13],dimens:[0,1,2,3,6,7,9,13],dimension:[0,3,4,7,9,11,12,13],dimensionless:0,diment:13,direct:[0,1,2,9,10,11],directli:[1,3,4,15],directori:7,disadvantag:0,disappear:4,discard:[4,9],disciplin:[0,10],disclaim:15,discourag:[0,11],discov:0,discover:3,discret:[1,3,5,11],discrimin:[5,8,9],discuss:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17],diseas:5,disguis:4,disord:[1,5],displai:[0,1,3,4,5,6,7,8,9,10,15],displaystyl:[0,3],displot:0,disregard:0,dissimilar:9,distanc:[0,6,7,9,15],distance_list:7,distinct:[5,6,7,8],distinctli:6,distinguish:[0,5,6,15],distplot:0,distribut:[0,1,4,5,8,9,11,12,13],distrubut:[0,12],div:3,dive:[0,6],diverg:[1,11],divid:[0,1,3,4,6,7,9,10,15],divis:[4,6,7,11,13,15],dna:5,dnn:[0,1,2,10],dnn_kera:1,dnn_model:1,dnn_numpi:1,dnn_scikit:[0,1],doc:[4,12,14,17],document:[0,5,9,11],doe:[0,1,2,3,4,6,8,9,10,11,13,15],doesn:[7,10],dog:1,domain:[3,6,11],domin:0,don:[0,1,3,4,6,9,11,12,15],done:[0,2,3,4,7,8,9,11,13,15],dot:[0,2,3,4,5,6,7,8,9,10,11,13,15],doubl:[13,15],doubli:1,down:[0,4,7,9,10,11],download:[0,1,3,4,13,17],dozen:1,dq:4,drag:11,dramat:9,draw:[4,8,11],drawback:[0,1,11],drawn:[1,4,5,9,15],drop:[0,1,3,4,9,11,15],dropna:[0,4],ds:[0,3],dt:[2,11,15],dtype:[0,1,2,13],dualiti:4,dub:0,due:[1,2,3,4,6,8,10,11],dummi:0,dure:[0,1,6,7,9,12],dwell:0,dwh:1,dwo:1,dx:[2,6,15],dx_1:15,dx_1p:4,dx_2p:4,dx_mp:4,dx_n:15,dxp:4,dy:[1,6,15],dz:6,e:[0,1,2,3,4,5,6,7,8,9,10,11,15,16],e_:[0,2],each:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],eapprox:0,earli:[1,11],earlier:[0,3,5,6,7,9,10,11],earthexplor:4,eas:[4,7],easi:[0,3,4,5,6,7,8,9,10,11,12,13],easier:[3,4,6,7,11,15],easiest:11,easili:[0,1,2,3,4,5,6,7,8,9,10,11,13],eastern:16,ebind:0,eblock:7,economi:3,ecosystem:12,ect:14,edgecolor:4,edu:[0,11],educ:0,eff:15,effect:[1,8,11,15],effic:1,effici:[0,8,11,12,13,15],efron:[4,15],egrad:11,eig:[3,9,11,13,15],eigen:15,eigenpair:[3,9],eigenvalu:[0,3,6,9,11,13],eigenvector:[3,9,11],eight:13,eigval:[13,15],eigvalu:[9,11],eigvec:[13,15],eigvector:[9,11],eispack:13,either:[0,1,3,4,5,6,7,8,9,11,15],ekstrom:16,elabor:15,electr:[0,10],electur:17,eleg:9,element:[1,2,3,4,5,6,9,10,11,12,13,14,17],elementari:[8,11,13],elementwis:11,elementwise_grad:[2,11],elim:13,elimin:[3,6],els:[1,2,5,7,10,11,13,15],elu:1,elus:0,email:[14,16],embed:[0,9],embodi:4,emit:15,emner:[14,17],emphas:[0,8,12],emphasi:[0,12,17],empir:[1,9,15],emploi:[0,1,3,4,9,11,15],employ:0,empti:[4,8],emul:10,en:[12,17],enabl:9,enbodi:4,encod:[0,3,7,9],encompass:[0,15],encount:[0,1,3,4,5,11,15],end:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],end_box:[2,11],end_nod:[2,11],end_valu:[2,11],endl:15,endpoint:[4,15],energi:[0,4],enet_coordinate_desc:4,enforc:10,eng:17,engin:[0,1,12,15],english:17,enough:[0,4,11],ensembl:[1,7,14,15],ensur:[0,1,2,3,4,9,11,15],enter:[3,4,15],enthought:[0,12],entir:[1,5,7,12,15],entiti:[7,10,13],entri:[0,3,6,9,10,13],entropi:[1,5,8,11],enumer:[0,1,2,4,6],env:[3,15],environ:[2,12,17],eo:[0,4],eol:0,eosfit:0,epoch:[0,1,10,11],epsilon:[0,3,4,5,11],epsilon_0:0,epsilon_1:0,epsilon_2:0,epsilon_:0,epsilon_i:0,eq:[11,13,15],eqnarrai:[3,4],equal:[0,1,2,3,4,6,7,9,10,11,13,15],equat:[1,3,4,5,6,7,8,9,11,13,14,15],equilibrium:[2,10],equiv:[11,13,15],equival:[0,1,3,6,9,11,12,13],erf:15,err:[0,8],err_:4,err_sqr:2,errat:11,errno:7,erron:2,error:[1,2,3,4,5,7,9,10,11,12,13,15],error_estimate_corr_tim:15,error_hidden:1,error_output:1,escap:11,especi:[1,7,10,11],essenti:[0,3,4,7,8,10,14,15],establish:[0,4,8,9],estim:[0,1,3,4,5,8,9,11,12,15],estimated_mse_fold:4,estimated_mse_kfold:4,estimated_mse_sklearn:4,et:[0,2,14,17],eta0:[6,11],eta:[0,1,6,10,11],eta_:11,eta_t:11,eta_v:[0,1],etc:[0,1,3,5,6,7,9,10,11,12,13,15],ethic:[0,12],etsim:4,euclidean:0,evalu:[0,2,3,4,7,11,15],evalut:11,even:[0,1,3,4,6,7,8,9,10,11,12,13,15],event:[3,5,8],eventu:[3,4,9,10,11,16],everi:[0,1,2,3,4,7,8,9,10,11,12,15],everyth:10,everywher:11,evolv:0,exact:[0,3,9,10,11,13,15],exactli:[0,4,10,12],examin:4,exampl:[3,9,10,11,12,13,14,17],exce:[1,10,11],excel:[0,1,3,8,17],except:[3,4,6,7,13,15],excess:0,excit:0,exclud:[1,4,10],exclus:[0,1,4,15],execut:[2,3,11],exemplifi:11,exercis:[3,12,14],exhaust:4,exhibit:[0,3,4,6],exist:[0,1,2,3,4,5,6,7,11,13,17],exit:[3,13,15],exp:[0,1,2,3,4,5,6,8,9,10,11,15],exp_term:1,expand:[3,5,9,11],expans:[0,3,6,8,10,11],expect:[0,1,3,4,5,9,10,11,12],expectation_value_of_h_wrt_p:15,expens:[4,8,11,15],experi:[0,1,4,6,11,12],experiment:[0,4,7,15],expert:[1,7],explain:[0,4,7,8,9,11,15],explained_variance_ratio_:9,explanatori:0,explicit:[0,4,11,13],explicitli:0,explod:1,exploit:[0,10,11],explor:[1,4,6,11,12],expon:1,exponenti:[0,1,3,4,8,11],export_graphviz:7,export_text:7,exporttext:7,expos:12,express:[0,2,3,4,5,8,10,11,13,15],exptmean:15,exptvari:15,extend:[2,3,5,9,11,12],extens:[0,10,12],extent:[0,1,4,17],extern:[4,7],extra:[1,3],extract:[0,3,4,5,6,9,11,13],extrapol:0,extrem:[0,1,3,4,5,6,7,11,13],extremum:11,extrins:9,ey:[0,3,4,11,13],f11:0,f12:0,f13:0,f1:11,f1_grad:11,f1d:11,f2:11,f2_grad_x1:11,f2_grad_x1_analyt:11,f2_grad_x2:11,f2_grad_x2_analyt:11,f3:11,f3_grad:11,f3_grad_analyt:11,f4:11,f4_grad:11,f4_grad_analyt:11,f5:11,f5_grad:11,f6:11,f6_grad_analyt:11,f7:11,f7_grad:11,f7_grad_analyt:11,f8:11,f8_grad:11,f9:[0,11],f9_altern:11,f9_alternative_grad:11,f9_grad:11,f:[0,1,2,3,4,5,6,8,10,11,13,15,16],f_0:8,f_1:[8,11],f_2:[10,11],f_3:10,f_:8,f_d:15,f_grad:11,f_grad_analyt:11,f_i:[4,10],f_m:8,f_vec:2,f_wrap:2,face:11,facecolor:[4,6,15],facil:[0,12],facilit:10,fact:[0,1,3,7,9,10,11],factor:[0,1,3,4,7,8,9,11,13,15],factori:11,fade:4,fafab0:[7,8],fail:[0,4,5,6,9,11,16],failur:5,fairli:[1,2,15],fall:[6,7,14],fals:[0,1,2,3,4,5,7,8,13],famili:[0,5,6,15],familiar:[0,3,4,6,12,13,15],famou:[4,10,13],far:[0,3,4,6,9,10,11,15],fashion:[0,7,8],fast:[1,4,8,10,11,12,15],faster:[1,9],fastest:[11,13],favor:5,favorit:15,featur:[0,1,3,4,5,6,8,9,10,11,12,15],feature_nam:[0,1,5,7],feautur:7,fed:1,feed:[0,2,9,12,14],feed_forward:1,feed_forward_out:1,feed_forward_train:1,feedforward:[1,10],feel:[0,3,4,9,11,12,16],feet:0,fetch:[0,4],fetch_california_h:0,fetch_openml:0,few:[1,3,7,15],fewer:[0,7,9],ffnn:[1,10],field:[0,4,10,12],fifth:[0,4],fig:[0,1,2,4,5,10,11],fig_id:[0,4,5,7],figaxi:15,figsiz:[0,1,2,4,5,6,7,8],figur:[0,1,2,3,4,5,6,7,8,10,11,12],figure_id:[0,4,5,7],figurefil:[0,4,5,7],file:[0,1,3,4,5,7,13,15],filenam:[0,15],filenotfounderror:7,fileout:15,fill:[3,7],financ:0,find:[0,1,2,3,4,5,6,7,8,9,10,11,12,15],fine:0,finish:2,finit:[3,4,10,11,15],first:[0,1,2,3,4,5,6,7,8,9,11,13,14,15,17],firsteigvector:9,fit:[1,3,4,5,6,7,9,10,11,15],fit_beta:4,fit_intercept:[0,3,4],fit_mod:7,fit_transform:[0,4,6,7,9],fiti:0,five:[0,7],fix:[0,4,8,9,10,11],fixedformatt:4,fixedloc:4,fkkt:3,flat:[10,11],flatten:[1,3,13],flexibl:[0,1,4,6,8,10],float32:7,float64:[0,13],flop:[3,13],flow:[1,10],fluctuat:3,fly:9,flyvbjerg:15,fm:0,fmesh:11,focu:[0,3,4,12,17],focus:[1,4,5,13],fold:[4,7],folder:[0,1,2,3,4,6,7,8,11,13,15],follow:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],font:[0,5,15],fontdict:15,fontsiz:[1,4,6,7,8,15],fontweight:1,foral:6,forc:[0,3,4,8,9],forecast:10,forelesningsvideo:14,forest:[0,1,7,12,14],forget:9,form:[0,3,4,5,6,7,9,10,11,12,13,15],formal:15,format:[0,1,4,5,6,7,8,9,12,15,17],formatstrformatt:[4,11],formul:[4,9],formula:[11,15],forth:10,fortran2003:12,fortran90:15,fortran:[0,12,13],fortun:[0,9],forward:[0,4,12,13,14],found:[1,2,3,4,7,10,11],foundat:12,four:[3,4,6,10,13,14],fourier:0,fourth:10,fr:3,frac:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],fractal:7,fraction:7,frame:5,framework:[1,6,8,15],frank:[3,9],frankefunct:[3,4,9],free:[0,4,9,11,12,13,15,16,17],freecodecamp:12,freedom:3,freeli:0,frequenc:[4,5,15],frequent:[0,6,7,11],frequentist:12,fresh:8,fridai:14,friedman:[4,14,17],from:[0,1,2,4,5,6,7,9,11,12,13,14,15,16,17],from_cod:7,front:[0,3],fstream:15,fulfil:[2,3,10],full:[0,1,3,5,7,8,11,15],full_matric:3,fulli:[4,10,14,15],fun:[2,11,12],func:[0,2],functionali:9,fundament:[0,4,12],funtion:2,further:[0,2,7],furthermor:[0,3,4,5,9,10,11,12],futur:[0,6,7],futurewarn:0,fx:3,fy:[14,16],g0:2,g42mrgv128v34gnnhxwk9nrc0000gp:[1,2,3,4,6,7,8,11,13,15],g:[0,1,2,3,4,6,7,8,9,11,15],g_0:2,g_1:[2,8],g_2:[2,8],g_:[2,7,8],g_analyt:2,g_dnn_ag:2,g_euler:2,g_i:2,g_m:8,g_re:2,g_t:2,g_t_d2t:2,g_t_d2x:2,g_t_dt:2,g_t_hessian:2,g_t_hessian_func:2,g_t_jacobian:2,g_t_jacobian_func:2,g_trial:2,g_trial_deep:2,g_vec:2,gain:[1,3,7,8,11],galleri:0,gamma1:6,gamma2:6,gamma:[0,2,6,7,8,9,11],gamma_0:8,gamma_1:8,gamma_1x:8,gamma_:0,gamma_i:[0,6,15],gamma_j:11,gamma_k:11,gamma_m:8,gamma_x:0,gap:[4,6],gate:10,gather:[0,1,10],gaug:10,gaussbacksub:13,gaussian:[3,4,6],gaussian_rbf:6,gave:11,gbc:14,gca:[2,4,6,11],gd:1,gd_clf:8,gdclassiffiercgain:8,gdclassiffierconfus:8,gdclassiffierroc:8,gdm:11,gdregress:8,ge:[1,3,5,15],gemv:3,gen:15,gender:0,gener:[0,1,2,3,4,6,8,9,10,11,13,17],generallay:10,genexpr:2,genom:12,geodes:9,geometr:[0,11],geometri:3,georg:17,geotif:4,geq:[2,3,6,7,11],geron:[0,14,17],get:[0,1,2,3,4,5,7,8,9,11,12,13,15],get_dummi:7,get_paramet:2,get_split:7,get_yaxi:6,get_yticklabel:4,getsolutionslic:3,gg:15,gibb:12,gini:8,gini_index:7,git:[0,12],github:[0,4,12,14,17],gitlab:[0,12],give:[0,1,2,3,4,5,6,7,8,10,11,12,14,15,17],given:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],global:[4,5,11,15],glorot:1,gmail:16,go:[0,1,3,4,6,7,9,10,11],goal:[0,5,7],goe:[0,1,2,3,4,11,13],golden:11,gone:3,gong:1,good:[1,3,4,7,8,9,11,12,14,15,17],goodfellow:[14,17],googl:[1,12],got:[1,4],gov:4,gp:17,gpu:1,grad:[2,11],grad_analyt:11,grade:14,gradient:[0,5,6,7,10,12,14],gradientboostingclassifi:8,gradientboostingregressor:8,gradual:1,grai:4,graph:[1,7,9,10,11],graph_from_dot_data:7,graphic:[0,1,7],grasp:0,gray_r:1,great:[3,11],greater:[1,5,15],greatli:11,greedi:7,green:[0,7,15],grid:[1,4,5,6,10,15],grossli:11,ground:0,group:[0,4,5,7,12,14],groupbi:0,grow:[1,7,8],growth:0,guarante:[0,11,15],guess:[1,8,11],guestrin:8,guid:1,h1:2,h21:14,h:[0,1,3,4,6,11,15,17],h_1:[2,11],h_2:[2,11],h_:[0,11],h_m:8,ha:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],habit:0,had:[0,1,4,5,11],hadamard:[1,10],half:[1,6,7],halv:8,hand:[0,1,2,3,9,10,11,12,13,14,15,17],handl:[0,1,2,3,7,9,12],handle_unknown:7,handsid:10,handwrit:10,handwritten:[1,3],happen:[1,2,3,4,8,11,15],hard:[1,5,6,8,11],hardcopi:12,harder:[0,1],hasn:[0,1],hassl:[0,12],hast:12,hasti:[0,4,14,17],hat:[1,3,4,5,7,8,9,10,11,13,15],have:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15],haven:1,he:[0,5],head:[0,8,15],header:0,heads_proba:8,health:0,hear:0,heart:[0,5],heatmap:[0,1,5],heavili:0,heavisid:1,height:[1,4],held:11,help:[0,1,10,11],henc:[0,3,4,6,7,8,10,11],her:5,here:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17],hereaft:[0,6,10],hermitian:13,hessenberg:13,hessian:[0,2,3,11],heterogen:[7,8],hi:5,hidden:[1,10],hidden_bia:1,hidden_bias_gradi:1,hidden_layer_s:[0,1],hidden_weight:1,hidden_weights_gradi:1,hierarch:3,high:[0,1,2,3,4,7,8,9,11,12,13],higher:[0,1,3,4,6,11],highest:[1,2],highli:[0,8,12,13,15,17],highwai:0,hing:6,hint:11,hip:12,hire:0,hist:[4,5,15],histogram:[0,4,5,15],histor:[5,9],histori:10,histplot:0,hitherto:3,hjorth:16,hobbi:15,hoc:3,hoff:17,hold:[1,4,11,15],holder:0,home:0,homework:[4,11],homogen:[1,7,8,11],honchar:2,hopefulli:[0,9,15],horizont:9,hors:5,hot:[1,7],hour:[1,12,14,15,16],house_pric:0,how:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,17],howev:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15],hs:0,hspace:[0,6,8,15],hstack:[0,1],htf:14,html:[5,9,12,14,17],http:[0,4,5,9,11,12,13,14,17],huang:0,huber:0,huge:[1,12],human:[0,1,4,7,10],humid:7,hundr:1,hungri:1,hybrid:14,hydrogen:0,hyperbol:[1,10],hyperparam:6,hyperparamet:[3,4,7],hyperplan:9,i0:0,i1:[0,4,6,10],i2:[0,6,10],i3:[0,10],i5:0,i:[0,2,3,4,5,6,7,8,9,10,11,13],i_1:[3,4],i_2:[3,4],i_:11,ian:17,ic:1,id:[5,11],idea:[0,1,2,4,7,8,10,11,13,15],ideal:[0,2,4,6,11,15],idem:4,ident:[3,4,10,11,13],identical:3,identifi:[0,1,5,7,9,10,11],idum:15,ieor:15,ifi:17,ifs:12,ignor:[0,1,7],ii:[13,15],iii:13,ij:[0,1,4,6,10,13,15],ik:[0,13],illustr:[3,5,8,10,11,12],im:4,imag:[1,4,7,9,10,17],image_path:[0,4,5,7],imageio:4,imagin:1,immedi:[0,4,12],implement:[0,2,3,4,6,7,8,9,10,11],impli:[3,4,5,11,13],implicitli:[9,15],impos:[0,4,9,10],imposs:[0,3],impress:[0,10],improv:[0,3,7,8,9,11],impur:7,imread:4,imshow:[1,4],in3050:17,in4080:17,in4300:17,in5400:17,inaccur:11,inact:10,inadequ:0,inch:4,includ:[0,1,2,3,4,5,9,10,11,12,15,16,17],include_bia:[4,7],incom:10,incorrect:1,incoveni:6,increas:[0,1,3,4,5,6,7,9,10,11,15],increasingli:15,ind:4,inde:[0,2,3,4],indent:15,indentationerror:15,independ:[0,3,4,5,6,10,11,15],index:[0,1,8,12,13,15,17],index_col:0,indic:[0,1,3,4,7,8,9,11],indispens:4,individu:[1,4,5,8,10,15],indu:0,indx1:2,indx2:2,indx3:2,indx:13,ineffici:11,inequ:6,inequaltii:11,inertia:11,inf1000:12,inf1100:12,inf1100l:12,inf1110:12,inf3000:17,inf4490:17,inf5860:17,infeas:7,infer:[0,1,4,17],inferenc:1,infil:[0,4,5,7],infin:[3,4,5,9],infinitesim:15,influenc:[4,8],influenti:1,inform:[0,1,4,7,9,10,11,13,17],infti:[4,11,15],ingeni:11,ingredi:[0,7],inher:4,inherit:13,initi:[0,1,2,4,8,11,13,15],initialis:15,inlin:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],inner:11,innov:17,inplac:11,input:[0,1,3,4,5,6,10,11,15],input_dim:1,inputs:1,inputs_shuffl:[0,1],insert:[3,4,6,8,15],insid:[0,5],insight:[0,1,3,12,17],insist:[4,11],inspir:[0,1,10,17],instabl:2,instal:[0,1,3,4,7],instanc:[0,1,2,4,7,9,11],instanti:8,instead:[0,1,2,3,4,6,7,9,11,13,15],institut:1,instruct:[0,1],int32:8,int64:0,int_0:15,int_:[4,15],int_a:15,intak:0,integ:[1,2,11,13,15],integer_vector:1,integr:[4,15],intellig:[0,17],intend:8,intens:1,interact:[0,4,7,10,12],intercept:[0,4,6,9,11],intercept_:[0,4,6,7,11],interchang:[3,10,13],interconnect:1,interest:[0,1,2,3,4,5,6,7,10,12,14,15],interfac:[0,1,13],interior:[0,7],intermedi:13,intern:[1,8,10],interpol:[1,4,10],interpr:3,interpret:[0,1,4,7,8,10,11,13,15],interv:[0,3,4,5,11,15],intial:11,intract:0,intrins:[9,13,15],intro:[12,17],introduc:[0,1,3,4,6,8,10,11,13,15],introduct:[1,2,11,14,17],introductori:[0,13,17],intuit:[0,3,4,6,10,11],inv:[0,3,11],invalid:[1,13],invalu:[0,11,12],invari:1,invd:3,inver:6,invers:[0,4,11],invers_period:15,inverse_transform:6,invert:[0,3,5,8],invok:[0,6],involv:[0,2,4,5,9,10],io:[12,14,15,17],iomanip:15,iostream:15,ip:[0,6,15],ipca:9,ipykernel_42331:1,ipykernel_42376:2,ipykernel_42449:3,ipykernel_42456:4,ipykernel_42530:6,ipykernel_42541:7,ipykernel_42553:8,ipykernel_42573:11,ipykernel_42580:13,ipykernel_42586:15,ipynb:12,ipython:[0,3,5,7,9,12],iq:4,iri:[6,7],irreduc:4,irrelev:3,irrespect:0,isbox:[2,11],isinst:[2,11],isn:3,isnul:0,isomap:9,issu:[0,1,7,13],it_arrai:11,item:[0,11],items:13,iter:[0,1,2,4,5,6,9,11,15],itr:3,its:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,17],itself:[3,4,10,15],ix:15,j1:13,j:[0,1,2,3,4,6,7,9,10,11,13,15,17],j_:4,j_lasso_sk:4,j_ridge_sk:4,j_sk:4,jackknavg:15,jackknif:[4,12],jackknstd:15,jackknvar:15,jackknvec:15,jacobian:[2,11],jargon:15,jensen:16,jerom:17,ji:[10,13],jj:[0,3,4],jk:[0,1,4,10,13],jl:0,jm:13,job:[2,6,8],join:[0,4,5,7],joint:3,journal:15,judg:11,judgement:4,julia:[12,13],jump:15,jupyt:[0,12,17],just:[0,1,2,3,4,5,6,7,8,9,10,11,15],justif:0,justifi:8,jy:[1,2,3,4,6,7,8,11,13,15],k0:5,k1:5,k:[0,1,3,4,5,6,7,8,9,10,11,12,13,15,16],kaggl:4,kappa_d:15,karim:16,karlsen:16,karush:6,keep:[0,1,3,4,9,11,13],keepdim:[1,4,8,13],kei:[0,1,4,10,17],kept:4,kera:[0,12],kernel:[0,1,12],kernel_regular:1,kernelpca:9,kev:0,kevin:17,keyboardinterrupt:2,keyword:[4,11,13],kfold:4,kg:1,ki:13,kick:[1,11],kiener:2,kilomet:4,kind:[0,2,6,10,11],kj:[4,10,13],kjm:12,kkt:[3,6],kktsolver:3,kl:15,km:10,know:[0,1,2,3,4,6,11,12,15],knowledg:[0,12],known:[1,3,4,5,6,7,10,13,15,17],kondev:0,kp:15,kpca:9,kuhn:6,kwarg:[2,11],kwown:0,l0:5,l1:[0,1,3,5],l1_l2:1,l1regl:3,l1regls_mosek2:3,l1regls_mosek:3,l2:1,l:[0,1,2,3,4,5,6,8,9,10,11,13,15],l_1:5,l_2:[5,11],l_:13,l_j:10,la:11,la_i:10,la_k:10,lab:[12,14],label:[0,1,2,3,4,5,6,7,8,10,11,12,13,15],labelencod:[5,8],labels:[4,6,7],labels_shuffl:[0,1],laboratori:14,lack:0,lagari:2,lagrang:[6,9],lambda:[0,1,2,3,4,5,6,8,10,11,15],lambda_0:9,lambda_1:[3,6,9],lambda_2:[6,9],lambda_:9,lambda_i:[6,9],lambda_iy_i:6,lambda_jy_iy_j:6,lambda_k:6,lambda_n:[3,6],lamda:1,lamdbda:3,land:[0,6],landmark:6,landscap:11,langl:[0,4,9,15],languag:[0,1,6,12,13,17],lapack:[3,13],laplac:3,laptop:12,larg:[0,1,2,3,4,6,7,8,9,11,12,13,15,17],larger:[0,3,4,6,8,9,11,15],largest:[6,9],lasso:[0,5,12,14],lasso_sk:4,last:[0,1,2,3,4,5,6,7,8,10,11,13,14,15],later:[0,1,4,5,6,10,11,12,15],latter:[0,3,4,5,6,9,11,13,14,15],lattic:10,law:0,layer:[0,11],lbfg:[5,7,8,9],lcc:[3,4],lda:9,ldot:[0,4,9,15],le:[3,5,8,11,15],lead:[0,1,3,4,5,6,7,8,9,10,11,13,15],leaf:7,leaki:1,lear:11,learn:[3,4,5,6,7,8,10,13,14,17],learner:8,learning_r:[6,8],learning_rate_init:[0,1],learning_schedul:11,least:[0,5,6,8,9,12,13,14,15],leav:[0,1,3,4,7,9],lectur:[0,1,3,8,9,10,11,12,13,14,17],lecturenot:[12,17],lecturenovember11:14,lecturenovember12:14,lecturenovember19:14,lecturenovember25:14,lecturenovember26:14,lecturenovember4:14,lecturenovember5:14,lectureoctober14:14,lectureoctober15:14,lectureoctober1:14,lectureoctober21:14,lectureoctober22:14,lectureoctober28:14,lectureoctober29:14,lectureoctober7:14,lectureoctober8:14,lectureseptember10:14,lectureseptember16firstpart:14,lectureseptember16secondpart:14,lectureseptember17:14,lectureseptember23:14,lectureseptember24:14,lectureseptember2:14,lectureseptember30:14,lectureseptember3:14,lectureseptember9:14,lecturethursdayaugust26:14,lecturethursdayaugust27:14,left:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],leftarrow:[6,10],legend:[0,2,3,4,5,6,7,8,11],len:[0,1,2,3,4,6,7,8,9,10,13,15],length:[0,1,2,6,7,11,12,15],leq:[0,3,5,6,11,15],less:[0,1,3,4,6,7,15],lessen:1,let:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],letter:[0,13,15],level:[0,1,3,4,7,12,13,14],li:[0,6,9],lib:[0,1,2,4,5,6,9,11],liblinear:[6,8],librari:[0,1,2,3,4,7,8,9,13,15,17],licens:[0,1,12],lie:[0,4,9,15],life:[0,1,6,10],lifetim:11,like:[0,1,2,3,4,5,7,8,9,10,11,12,13,15],likelihood:[0,1,3,7],lim_:15,limit:[0,3,4,5,6,9,10,13],lin_clf:6,lin_model:0,lin_reg:7,linalg:[0,2,3,4,6,9,11,13,15],line1:6,line2:6,line2d:11,line3:6,line:[0,1,4,6,9,11,13,15],linear:[1,3,4,5,7,8,9,10,12,14,15],linear_model:[0,3,4,5,6,7,8,9,11],linear_regress:4,linearli:3,linearloc:[4,11],linearregress:[0,4,5,7],linearsvc:6,liner:1,linerar:8,linewidth:[0,2,4,6,7,8],link:[0,7,10,12],linlag:3,linpack:13,linreg:0,linspac:[0,2,4,6,7,8,11,13,15],linu:16,linuek:16,linux:[0,1,12],liquid:0,list:[0,1,2,3,7,12],listedcolormap:[7,8],literatur:[1,5,17],littl:[1,7,10],live:6,ll:[0,15],lle:0,lmb:[2,3,4],lmbd:[0,1],lmbd_val:[0,1],lmbda:11,ln:[1,11],lo:3,load:[0,1,4,5,7,8],load_boston:0,load_breast_canc:[1,5,7,8,9],load_digit:1,load_iri:[6,7],loc:[0,4,5,6,7,8],local:[0,1,5,10,11],locat:[2,6],log10:[3,4],log:[0,1,2,3,4,5,7,8,9,11,13],log_:0,log_clf:8,logarithm:[0,3,5,13],logic:[0,1,7],logist:[0,1,2,6,7,8,9,10,11,12,14],logisticregress:[5,7,8,9],logit:5,logreg:[5,7,8,9],logspac:[0,1,3,4],longer:[2,6,8,13,15],loocv:4,look:[0,1,2,3,4,5,6,7,8,9,11,13,15],loop:[1,4,8,10,12,13,15],lose:1,loss:[0,1,3,4,5,6,8,9,11,13],lot:[0,1,4],low:[0,4,7,8,9,15],lower:[0,1,4,7,8,13],lowercas:13,lowest:[7,11,15],lr:[1,8],lstat:0,lstsq:0,lt:4,lu:[0,3],lubksb:13,luckili:2,ludcmp:13,lux:13,lvert:1,lw:0,m:[0,1,2,3,4,6,7,8,9,10,11,13,14,15,17],m_:[7,10],m_h:0,m_l:10,m_n:0,m_p:0,m_t:11,ma:9,machin:[1,3,4,5,7,8,9,10,13,14,17],machinelearn:[4,12,14,17],mackai:17,made:[0,1,3,4,5,7,9,10],mae:0,magnitud:[1,4,5,11],mai:[0,1,2,3,4,5,6,7,9,10,11,12,13,15],mail:14,main:[0,1,3,4,5,7,13,17],mainli:[0,3,4,5,7],maintain:[0,4],major:[1,4,7,8,11,13],make:[1,2,3,4,5,6,9,10,11,12,13,15,17],make_axes_locat:4,make_moon:[6,7,8],make_pipelin:[0,4,8],make_vjp:[2,11],makedir:[0,4,5,7],makeplot:0,malcondit:13,malign:[1,5,7],mammographi:3,manag:[0,2,12],mani:[0,1,3,4,5,6,7,9,11,12,13,15,17],manifold:9,manual:4,map:[0,1,2,4,5,6,9,10,15],margin:[0,3,6],marit:0,marker:[0,5,13],markov:12,marsaglia:15,mask:15,mass:[0,1,3,11],massag:0,masses2016:0,masses2016ol:0,masses2016tre:0,masseval2016:0,master:[4,14],mat1100:12,mat1110:12,mat1120:12,mat3155:14,mat4155:14,mat:12,match:[1,3,11],materi:[3,5,13],math:[5,10,11,13,15,17],mathbb:[0,3,4,5,6,9,10,11,13,15],mathbf:[0,3,4,5,6,11,13,15],mathcal:[1,3,4,5,11],mathemat:[0,4,9,10,11,12,13,14,15,17],mathrm:[0,1,3,4,5,6,7,8,9,10,11,15],matmul:[1,2,3],matnat:[14,16,17],matplotlib:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15],matplotlibdeprecationwarn:[4,11],matric:[0,1,4,5,6,9,11,12,13],matrix:[0,2,4,5,6,8,11],matshow:1,matter:[2,11],max:[0,1,2,7,8,10,11],max_depth:[0,7,8],max_diff1:2,max_diff2:2,max_diff:2,max_it:[0,1,5,6,9,11],max_leaf_nod:8,max_sampl:8,maxdegre:[0,4,8],maxdepth:8,maxim:[1,3,5,6,9],maximum:[0,1,2,3,5,6,7,8,11],maxpolydegre:[3,4],mbox:[3,4],mc:15,mcculloch:10,mcint:15,mcintsqr2:15,md:9,mean:[1,2,3,4,5,7,8,9,10,11,12,13],mean_absolute_error:0,mean_i:15,mean_squared_error:[0,4,5,8],mean_squared_log_error:0,mean_x:15,meaning:[0,5],meansquarederror:0,meant:[2,5,8,11],meantempvec:15,meanvec:15,measur:[0,1,2,3,4,7,9,10,15],mechan:[0,15],median:0,medicin:10,medium:[6,11],medv:0,meet:[0,16],mehta:0,memori:[9,10,11,13],mention:[0,10,11,15],mere:0,mersienn:15,meshgrid:[2,3,4,6,7,8,9],messag:[3,11],messi:2,met:[0,6],meteorolog:7,meter:4,method:[0,1,2,3,5,6,9,10,12,13,14,17],metion:4,metric:[0,1,4,5,7,8],metropoli:12,mev:[0,15],mglearn:12,mgrid:11,mi:8,microsoft:17,mid:1,midpoint:7,might:[0,1,2,4,7,11],mild:7,miller:15,millimet:4,million:0,mimic:10,min:[0,2,3,6,7],min_:[0,2,3],min_samples_leaf:7,mind:[0,4,11],mine:12,mini:[1,9,10,11],minibatch:[1,9,11],minibathc:11,minim:[0,1,2,3,4,5,6,7,8,9,10,11,15],minima:[0,1,5,11],minimum:[0,1,2,4,6,7,9,11],minmaxscal:0,minor:[4,11,15],minst:1,minu:5,mirror:7,misc:4,misclassif:[6,7,8],misclassifi:[6,8],miser:0,mismatch:1,miss:[0,8],mit:17,mix:[1,2],mixtur:11,mk:[7,13],mkdir:[0,4,5,7],ml:[0,1,8,11,13],mlab:15,mle:[3,5],mlp:1,mlpclassifi:1,mlpregressor:0,mm:13,mn:[10,15,17],mnist:[1,9],mod:15,mode:[14,15],model:[2,3,5,6,7,8,9,11,12,15,17],model_select:[0,1,3,4,5,7,8,9],moder:8,modern:[0,4,5,12],modif:[2,10,11],modifi:[0,1,3,5,6,8,10,11],modul:[0,2,3,4,5,6,7,8,9,11,13],modular:15,modulenotfounderror:[3,6],modulo:15,moe:[3,9],moment:[3,4,11],monitor:11,monoton:[3,10,15],mont:[0,4,12,15,17],montecarlocycl:15,moor:[3,4],more:[0,1,2,3,5,6,7,8,9,10,11,12,14,15],moreov:0,morten:16,mortenimac:[0,1,2,4,5,6,9],mosek:3,most:[0,1,2,3,4,5,6,7,8,9,10,11,12,14,15],mostli:[1,9],motion:[0,11],motiv:1,move:[0,3,4,5,7,10,11,15],mp4:14,mpl:[0,5],mpl_toolkit:[2,4,11],mplot3d:[2,4,11],mplregressor:1,mse:[0,3,4,7,8],mse_simpletre:8,mselassopredict:3,mselassotrain:3,mseownridgepredict:4,msepredict:3,mseridgepredict:[3,4],msetrain:3,msg:0,msle:0,mt19937_64:15,mt:[5,10],mu0:15,mu1:15,mu2:15,mu:[0,4,9,11,15],mu_:[4,15],mu_i:4,mu_n:9,mu_x:15,much:[0,1,2,3,4,6,7,8,9,10,11,13,15],mul:3,multi:[0,1,5,12],multiclass:[1,5],multidimension:[9,10],multilay:1,multinomi:5,multipl:[2,3,4,5,10,11,15],multipli:[3,4,9,11,13,15],multiplum:6,multivari:[0,2,8,9,12,15],multivariate_norm:9,murphi:[9,17],must:[1,2,3,4,6,8,10,11,15],mutat:5,mutual:[1,4,11],mx_:15,myriad:[0,12],mz1:15,mz2:15,n1:13,n2:13,n:[0,1,2,3,4,5,6,8,9,10,11,13,15],n_0:[10,15],n_:[1,2,6,10,15],n_b:15,n_boostrap:[4,8],n_bootstrap:4,n_categori:1,n_compon:9,n_epoch:11,n_estim:8,n_featur:1,n_hidden:2,n_hidden_neuron:[0,1],n_i:15,n_input:[0,1],n_instanc:7,n_iter_i:[5,9],n_job:8,n_l:[10,15],n_layer:1,n_m:7,n_neuron:1,n_neurons_layer1:1,n_neurons_layer2:1,n_sampl:[4,6,7,8],n_split:4,n_t:2,n_x:2,nabla:[1,11],nabla_:[2,11],nabla_w:11,nag:11,naimi:0,naiv:5,nall:0,name:[0,1,3,4,5,6,7,8,10,11,12,13,16],nameerror:[4,8],namespac:15,narrow:11,nary_f:[2,11],nary_op_arg:[2,11],nary_op_kwarg:[2,11],nary_oper:[2,11],nation:[1,3],nativ:12,natur:[0,1,6,7,10,11,15,17],navier:10,nb:15,nb_:13,nboot:15,ndarrai:[2,4],ne:[7,8,13,15],nearest:[1,4,9],nearli:11,neccesari:4,necess:2,necessari:[0,1,6],necessarili:[0,9,15],necesserali:3,neck:5,need:[0,1,2,3,4,6,7,8,9,10,11,13,15],neg:[0,1,3,4,5,8,11,13,15],neg_mean_squared_error:4,neglect:15,neglig:15,neighbor:[4,9],neither:11,neq:[11,15],nervou:10,nest:[2,7,10],nesterov:11,net:[2,10],netlib:13,network:[0,7,11,12,14,17],neural:[0,5,11,12,14,17],neural_network:[0,1,2],neuralnetwork:1,neuron:[1,2,10],neutral:0,neutron:0,never:[1,4,7,15],new_box:[2,11],new_root:[2,11],new_trac:[2,11],newaxi:[0,4,7],newli:0,newton:[1,5,6,11,15],next:[0,1,2,3,4,6,7,11,15],next_guess:11,ng:1,ngini:7,nian:16,nice:[0,1,3,9],nichola:16,nicholaskarlsen1102:16,niter:11,nitric:0,nlambda:[3,4],nm:15,nm_n:0,nmse:4,nn:[2,3,4,10,13],nn_model:1,nnmin:2,node:[1,7,8,10],node_constructor:2,nois:[0,3,4,6,7,8,11],noisi:[1,4],non:[0,1,3,4,5,7,8,9,10,11,13,15],none:[0,1,2,3,7,8,11,15],nonlinear:[4,6,7,9,10],nonneg:[4,7,11],nonparametr:4,nonsens:15,nonsingular:13,nonumb:[5,6,11,13],nor:[1,11],norm:[0,1,3,4,6,9,11],normal:[3,4,5,6,7,8,9,10,11,12,13],normali:13,norwai:4,notat:[0,2,3,4,11,15],note:[0,1,2,3,4,5,6,9,10,11,12,13,14,15,17],notebook:[0,1,7,12],noth:[1,2,3,6,10,15],notic:[3,10,11,13,15],notrace_primit:2,novel:[4,8],novemb:1,now:[0,2,3,4,5,6,8,9,10,11,13,15],nowadai:[0,1,7,12],nox:0,np:[0,1,2,3,4,5,6,7,8,9,11,13,15],npr:2,nsampl:[4,7],nspin:15,nt:2,nthi:0,ntrained_model:4,nu:15,nuclear:3,nuclei:[0,15],nucleon:0,nucleu:0,num_coordin:2,num_hidden_neuron:2,num_it:2,num_neuron:2,num_neurons_hidden:2,num_point:2,num_tre:8,num_valu:2,number:[1,3,4,5,6,7,8,9,10,11,13,14,16],numberid:5,numer:[0,3,4,7,8,9,10,11,12,13,17],numpi:[0,1,2,3,4,5,6,7,8,9,10,11,12,15],nunmpi:3,nvalu:7,nx:2,nx_test:4,nx_train:4,nx_train_mean:4,ny:15,ny_pr:4,ny_train:4,ny_train_mean:4,o:[0,4,5,6,7,9,11,13,17],obei:[4,9,11],object:[0,1,2,3,4,6,8,11,13],objsens:3,obliqu:3,observ:[1,3,4,5,6,7,8,9,10,11],obtain:[0,1,3,4,5,6,7,8,10,11,13,15],obviou:[3,4,9,15],obviouli:0,obvious:[0,3,4,13],oc:3,occupi:0,occur:[0,4,6,7,13,15],od:0,odd:[0,5],odenum:2,odesi:2,oen:0,off:[1,3,7,11,15],offer:[4,9,12,13,14],offic:16,offici:14,ofil:15,ofstream:15,often:[0,1,3,4,5,6,7,8,9,10,11,12,13,15],ofter:13,ol:0,old:[1,3,8,11],ols_sk:4,ols_svd:4,olsbeta:3,omega:[2,4],omit:[0,3],onc:[1,4,7,9,11,15],one:[0,1,3,4,5,6,7,8,9,11,12,13,15],onehot:1,onehot_vector:1,onehotencod:7,ones:[0,2,3,4,6,7,8,9,11,13,14],onli:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],onlin:[9,14],onto:[3,9],open:[0,1,4,5,7,12,14,15],oper:[0,1,3,4,8,9,10,11,12,15],operation:15,oplu:15,opmiz:11,opportun:0,oppos:[4,11],opposit:[1,3,6],opt:[1,3],optim:[0,2,3,4,5,7,8,9,14],optimis:1,option:[0,1,3,4,5,6,9,13],optmiz:[1,6],orang:0,order:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],ordinari:[0,2,5,9,11,12,14],oreilli:17,org:[5,9,12,13,17],organ:[4,5,8,13],orient:[1,3,15],origin:[0,3,4,6,9,10,11,13,15],orthogn:3,orthogon:[0,3,4,6,9,11,13],orthonorm:3,os:[0,1,3,4,5,6,7],oscar:1,oscil:11,oslo:[0,14,16],osx:[0,12],other:[0,1,2,3,4,5,6,8,11,12,14,17],otherwis:[0,1,5,11,13],ouput:[3,5,10],our:[1,2,4,5,6,7,8,10,12,13,14],ourmodel:0,ourselv:[0,3,4,6,9,11],out:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15],out_fil:7,outcom:[0,5,7,8,10,15],outdoor:7,outer:[4,10],outfilenam:15,outlier:[0,6],outlin:[4,8,9],outlook:7,outperform:8,output:[0,1,3,4,5,6,7,8,10,11,13],output_bia:1,output_bias_gradi:1,output_weight:1,output_weights_gradi:1,outputlayer1:10,outputlayer2:10,over1:11,over:[0,1,3,4,7,8,10,11,13,15],overal:[1,8],overcast:7,overcom:[10,11],overdetermin:0,overfit:[0,1,4,7,8,11],overflow:[1,3],overhead:10,overlap:[5,6,7],overlin:[0,3,4,7,8,9,13],overst:0,overview:17,own:[3,4,6,10,11,12,13],owner:0,ownridgebeta:4,oxid:0,oyvinssc:16,p0:2,p1:2,p:[0,1,2,3,4,5,6,7,8,9,11,13,15,16],p_:[2,6,7],p_hidden:2,p_i:[3,15],p_j:15,p_n:15,p_output:2,p_x:15,pack:0,packag:[0,1,2,3,4,5,6,9,11,12,15],page:[0,12],pai:[0,1,7,11],pair:[0,2,7,12,15],panda:[0,3,4,5,7,9,12],paper:1,paradigm:0,parallel:[8,13],param:2,paramat:2,paramet:[0,1,2,3,4,5,6,7,8,10,11,15],parameter:[0,4,8],parametr:[0,4],paramt:3,parent:2,park:15,part:[0,1,3,4,8,13,14,15,17],partial:[0,1,3,4,5,6,8,9,10,11,15],particip:[12,14],particl:[0,11,15],particular:[0,1,2,3,4,7,8,9,10,11,15,17],particularli:[3,4,6,9,11,15],partit:[1,7],partli:4,pass:[2,10,15],past:[8,15],patch:[4,15],path:[0,4,5,7,12],patient:5,pattern:[0,10,14,17],pauli:0,pc:[9,12],pca:[0,5,12,14],pd:[0,3,4,5,7,9],pde:2,pdf:[0,3,4,7,17],pedagog:0,penal:4,penalti:[4,11],penros:[3,4],pentagon:11,peopl:[0,1,7,12],per:[0,1,4,14],percentag:[0,8,9],perceptron:[0,1,5],perfect:[0,1],perfectli:4,perform:[0,2,3,4,6,8,9,10,11,12,13,15],perhap:[0,3,11],perimet:[1,7],period:1,permut:9,persist:11,person:[3,4,5,14,16],perspect:17,pertin:10,petal:[6,7],peter:17,petersen:15,phantom:15,phase:[4,10],phenomena:15,phi:6,phi_k:6,philip:16,philosophi:11,phone:16,phrase:0,physic:[0,1,5,10,11,15,16,17],pi:[2,3,4,5,7,10,11,15],pick:[1,7,8,9,11,15],pickl:1,pictur:0,pie:12,piec:9,pillow:[0,12],pinv:[3,4],pip3:[0,1],pip:[0,1,12],pipelin:[0,4,6,8],pitfal:4,pitt:10,pixel:1,pixel_height:1,pixel_width:1,place:[0,4,6,11,13],plai:[0,3,4,6,9,12],plain:[6,8,10,11],plan:[4,7,16,17],plane:[6,7],plateau:[3,15],platform:12,plausibl:10,pleas:[0,5,9,11],plenti:1,plethora:10,plot:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15],plot_confusion_matrix:[5,8],plot_count:4,plot_cumulative_gain:[5,8],plot_data:1,plot_dataset:6,plot_decision_boundari:[7,8],plot_import:8,plot_predict:6,plot_regression_predict:7,plot_roc:[5,8],plot_surfac:[2,4,11],plot_train:7,plot_tre:[7,8],plt:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],plu:[0,3,5],pm:[6,15],pmatrix:2,png:[0,4,5,7],point:[0,1,2,3,4,5,6,7,8,9,11,13,15,16],poisson:12,poli:[4,6],poly100_kernel_svm_clf:6,poly3:0,poly3_plot:0,poly3dcollect:11,poly_featur:[6,7],poly_features10:7,poly_fit10:7,poly_fit:7,poly_kernel_svm_clf:6,polydegre:[0,3,4,8],polygon:11,polym:10,polynomi:[0,3,4,5,6,7,8,9],polynomial_featur:4,polynomial_svm_clf:6,polynomialfeatur:[0,4,6,7],polytrop:[0,4],poor:[1,11],poorli:0,popul:[0,3],popular:[0,1,4,5,6,7,9,10,12,13,15],popularli:0,portabl:8,portion:[9,11],pose:[0,3,4,9,15],posit:[0,1,2,3,5,6,8,9,11,13,15],possibl:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15,16],posterior:3,postpon:0,postul:3,potenti:[0,3,4,10,11],potr:3,potrf:3,pott:10,power:[0,1,3,4,6,7,10],pp:[3,4],practic:[0,3,4,5,6,14,15],practition:[0,1],preced:[1,9,10,15],preceq:6,precis:[0,2,3,9,11,13,15],pred:4,predicit:0,predict:[0,1,3,4,5,6,7,8,12,17],predict_prob:1,predict_proba:[5,8],predictor:[0,3,4,5,7,8,9],prefer:[0,1,4,6,7,9,12],prepar:[0,4,13],preprocess:[0,4,5,6,7,8,9],prerequisit:0,presenc:11,present:[0,3,4,7,10,11,14,15],preserv:[9,13],press:[11,17],pretrain:1,pretti:[0,6,7,12],prevent:[11,15],previou:[0,1,2,3,4,6,8,9,10,11,13,15],previous:[2,7,8,15],price:[0,7,11],primal:6,primari:[0,5],prime:15,princip:[0,3,5,12,14],principl:[0,4,5,6],print:[0,1,2,3,4,5,6,7,8,9,11,13,15],print_funct:[6,7],printout:0,prior:[0,3,4],privat:0,prob:[1,15],probabilist:[0,17],probabl:[0,1,4,5,8,11,12,14],problem:[0,3,4,5,6,7,8,9,10,12,13,14,15],proce:[0,3,4,6,7,8,9,11,13],procedur:[2,3,4,6,8,9,11],proceed:13,process:[0,2,4,7,8,10,11,12,13,15,17],prod:17,prod_:[1,3,5],produc:[0,3,4,7,8,9,10,11,12,13,15],product:[0,1,3,4,5,6,10,11,12,13],profess:0,program:[0,1,3,4,6,10,12,13,14,15],programm:13,progress:1,prohibit:4,project1:4,project:[0,1,2,3,9,11,12,14,15,16],project_root_dir:[0,4,5,7],promin:10,promis:6,prone:7,pronounc:[11,12],proof:[0,9,10,11],propag:[2,14],proper:[0,2,4],properli:[1,4,6,8,11],properti:[0,1,10,11,13],proport:[0,1,3,7,9,11,15],propos:[1,4,8],propto:[3,11],proton:0,prove:11,provid:[0,1,3,4,6,7,8,10,11,12,13,15,17],proxi:[1,11],prune:7,pseudoinv:3,pseudoinvers:[3,4],pseudorandom:[4,15],psycholog:0,pt:11,ptratio:0,punish:[0,1],pure:[7,15],purest:7,puriti:7,purpos:[0,8,10],put:1,putarow:3,putboundslic:3,putclist:3,putobjsens:3,putqobj:3,py:[0,1,2,3,4,5,6,7,8,9,11,13,15],pydata:12,pydot:7,pylab:[0,5],pypi:12,pyplot:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],pythagora:3,python2:0,python3:[0,1,2,4,5,6,9,11,12],python:[1,2,3,4,6,9,10,11,14],pytorch:[0,12],q:[3,4,6,9,15],qp:6,qquad:[2,9,11,13],qr:[3,4,13],quad:[1,11,13],quadrat:[0,3,6,7,11],qualit:[7,15],qualiti:[0,7,12],quantifi:1,quantil:8,quantit:[0,4,7],quantiti:[0,2,3,4,5,7,8,9,10,13,15],quantum:10,quartil:0,quench:3,queri:7,question:[0,3,4,7,9,10,11],quick:15,quickli:[1,7,9,11],quit:[1,3,4,7,8,10],quot:15,r2:[0,3,4],r2_score:0,r2score:0,r:[0,2,3,4,5,6,7,8,9,10,11,12,13,15],r_1:7,r_2:7,r_j:7,r_m:7,rad:0,radial:[0,6,10],radioact:15,radiu:[0,1,7],rag:2,rain:7,rais:[2,11],ramp:1,ran1:15,ran2:15,ran3:15,rand:[0,3,4,7,8,11,13,15],rand_max:15,randint:[4,7,11],randn:[0,1,2,3,4,7,9,11],random:[0,1,2,3,4,6,7,11,12,13,14],random_devic:15,random_forest_model:8,random_index:11,random_indic:1,random_st:[0,5,6,7,8,9],randomforestclassifi:8,randomli:[1,4,7,11,15],randomnumbergener:15,rang:[0,1,2,3,4,5,7,8,9,10,11,13,15],rangl:[0,4,9,15],rangle_x:15,rank:3,raphson:[1,6,11],rapidli:0,rare:1,rate:[0,1,2,6,7,8,10,11],rather:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],ratio:[5,7,8,9],rational:0,ravel:[3,4,5,6,7,8,9,11,13],raw:15,raw_df:0,rbf:[6,9,10],rbf_kernel_svm_clf:6,rbf_pca:9,rc:[0,15],rcond:0,rcparam:[0,1,5,6,7,8,15],rd:15,re:[2,11],reach:[0,1,3,4,5,7,8,9,10,11,15],read:[0,2,3,4,5,6,9,10,13,14,15,17],read_csv:[0,4,5,7],read_fwf:0,reader:[0,4,13,15],readi:[0,1,3,4,6,8,9,10,13],readili:1,real:[0,1,2,5,8,9,10,11,13],realist:6,realiti:15,realiz:[1,10],realli:[0,1],rearrang:11,reason:[0,1,8,11,17],reassign:1,recal:[3,4,7,8,9,10,13,15],recalcul:15,receiv:[1,8,10,15],recent:[0,2,3,4,6,7,8,11],recept:10,recip:[0,4,5,13],reciproc:3,recogn:[0,3,8],recognit:[0,1,10,14,17],recommend:[0,2,3,4,6,11,12,13,14,15,17],reconsid:7,reconstruct:9,record:[8,14],recreat:15,rectangl:[7,11],rectangular:3,rectifi:[1,10],recur:[0,12],recurr:[0,1,12,14],recurs:[7,12,13],recycl:15,red:[0,4,6,7],redefin:[0,8],reduc:[1,3,4,7,8,9,11],reduct:[0,8,9,12,15],refer:[0,1,2,3,4,5,9,10,11,13,17],referenc:2,refin:10,refit:4,reflect:[0,1,3,15],refresh:[12,14],reg:[8,9],regard:[1,7,11],regardless:10,region:[4,7,10],regist:[4,15],reglasso:3,regr_1:[0,7],regr_2:[0,7],regr_3:[0,7],regress:[1,6,9,10,12,14],regressor:[0,5,8],regridg:[3,4],regular:[0,3,4,5,7,11],regularis:4,reilli:[0,17],reinforc:[0,6,12],reiter:1,rel:[0,4,5,7,10,11,15],relat:[0,1,3,9,11,13,15],relationship:[0,7],relativeerror:0,releas:[1,4,11,12],relev:[0,1,3,5,9,12,14,15],reli:[0,4,6],reliabl:[5,15],remain:[1,2,4,10,13,15],remaind:15,reman:2,remark:1,rememb:[0,6,11,13],remind:[0,3,9,11,13,15],remov:[0,3,4],render:0,reorder:[3,5],reorgan:0,repeat:[0,1,3,4,7,8,9,11,13,15],repeated:0,repeatedli:[4,8,11,15],repetit:[4,14],rephras:11,replac:[0,1,3,4,8,10,11],replica:4,repositori:0,repres:[0,1,2,3,4,5,6,7,8,10,11,15],represent:[0,1,4,15],reproduc:[0,3,4,7,10,12,15],repuls:0,request:0,requir:[0,1,3,4,6,7,9,10,11,13],res1:2,res2:2,res3:2,res_analyt:2,res_analytical1:2,res_analytical2:2,res_analytical3:2,resaml:4,resampl:[0,5,8,12,14,15],rescal:[0,9,10],rescu:3,reseach:4,research:[0,12,17],resembl:[4,15],reserv:[1,3,4,15],reset:15,reshap:[0,1,2,4,6,7,8,13],residenti:0,residu:[0,3,11],resiz:3,respect:[0,1,2,3,4,5,6,8,9,10,11,15],respond:10,respons:[0,5,7,10],rest:[0,3],restat:[0,10],restrict:[0,7,10],result:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15],retail:0,retain:[3,4],return_x_i:7,reus:[1,4],reveal:[0,10],revers:[1,13],review:[12,13,14],reward:0,rewrit:[0,3,4,5,6,8,9,10,11,13,15],rewritten:[2,4,6,8,15],rewrot:11,rf:8,rgoj5yh7evk:12,rh:[3,4],rho:[0,8],rho_1:8,rho_2:8,rho_m:8,rich:0,ride:7,rideclass:7,ridedata:7,ridg:[0,5,9,11,12,14],ridge_sk:4,ridgebeta:3,right:[0,1,2,3,4,5,6,7,8,10,11,13,15],right_sid:2,rightarrow:[0,1,3,4,6,9,10,11,15],rigor:0,ring:4,rise:0,risk:[0,11],river:0,rm:[0,15],rmse:0,rmsporp:11,rmsprop:[1,11],rnd_clf:8,rnn:[10,14],rntrick1:15,rntrick2:15,rntrick3:15,rntrick4:15,ro:[0,11],robert:17,robust:0,robustscal:0,roc:8,role:[0,2,3,4,6,12],roll:4,room:[0,16],root:[0,3,7,11,15],rotat:[1,6,7,8],rotation_matrix:7,roughli:1,round:[0,5,7,11],routin:[11,13],row:[0,1,2,3,4,5,7,9,13],rr:3,rrr:3,rthe:3,rug:11,rule:[0,1,3,4,11],run:[0,1,2,3,4,6,7,9,11,12],runtim:[1,4],runtimewarn:[1,4],rust:[0,12,13],rvert:1,rvert_2:1,s:[0,1,2,3,4,5,7,9,10,11,12,13,14,16],s_1:4,s_:4,s_i:[4,5],s_j:4,s_k:4,saddl:11,safe:15,sai:[0,1,2,3,4,5,6,7,8,9,10,13,15],said:[4,7,11],sake:[0,3,5,9],sale:0,same:[0,1,2,3,4,6,7,9,10,11,13,15],samm:8,sampl:[0,1,2,3,4,5,6,7,8,11,12,13],sampleexptvari:15,sastri:9,satisfactori:0,satisfi:[1,2,4,6,11,13,15],satur:[1,4],save:[0,4,5,7],save_fig:[0,4,5,7,8],savefig:[0,4,5,7,15],saw:3,scalabl:8,scalar:[2,3,4,8,11],scale:[0,1,3,4,5,6,7,8,9,10,11,12,13,16],scaler:[0,5,6,7,8,9],scan:[3,5],scari:3,scatter:[0,1,4,5,6,7],scenario:[4,11],schedul:11,scheme:[1,11],schrage:15,scienc:[0,1,8,10,11,12,14,15,17],scientif:[0,12],scientist:0,scikit:[3,4,5,6,7,8,11,12,13,14,17],scikitplot:[5,8],scipi:[0,3,4,11,12,13],scl:4,score:[0,1,4,5,7,8,9,16],scores_kfold:4,scratch:1,sdg:11,seaborn:[0,1,4,5],seamless:[0,12],search:[0,1,3,7,11],sec:4,second:[0,2,3,4,5,6,7,9,10,11,12,13,14,15],secondeigvector:9,secondli:10,section:[9,13,14,15],sector:0,see:[0,1,2,3,4,5,6,8,9,10,11,12,13,14,15],seed:[0,1,2,3,4,6,7,9,11,15],seek:[1,2,6],seem:1,seemingli:0,seen:[0,1,3,8,10,15],segment:11,seismic:4,seldomli:0,select:[1,3,4,6,7,8,9,14,17],self:[1,3,15,17],semest:[5,14],semi:[6,11],semilogx:4,send:[3,10,11,16],senior:14,sens:[0,4,6],sensit:[0,3,4,7,11],sent:2,sentenc:10,sep:0,separ:[0,1,2,4,6,7,10,12,15],sequenc:[2,5,7,8,10,11,12,13,15],sequenti:[1,8,10,15],seri:[0,1,2,3,4,8,9,10,11,13,14],serif:[0,5,15],serv:[0,1,2,3,5,11,17],session:[1,14],set:[1,3,4,5,6,8,9,11,12,13,15],set_major_formatt:4,set_major_loc:4,set_stream:3,set_tick:[1,6],set_ticklabel:1,set_titl:[0,1,2,5,10],set_xlabel:[0,1,2,5,10],set_xlim:[5,10],set_xticklabel:1,set_ylabel:[0,1,2,5],set_ylim:[5,10],set_ytick:5,set_yticklabel:[1,4],set_zlim:4,setiosflag:15,setminu:4,setosa:[6,7],setosa_or_versicolor:6,setp:4,setprecis:15,setse:3,setup:[1,3,4,6,12],setw:15,sever:[0,3,4,5,6,7,9,10,11,12,13,14,15],sgd:[1,11],sgd_clf:6,sgdclassifi:6,sgdreg:11,sgdregressor:11,sgn:3,sh:7,shallow:11,shape:[0,1,2,3,4,5,6,7,8,9,11,13],share:1,she:5,shift:[1,4,10,15],shortcom:11,shorter:15,shortli:13,should:[0,2,3,4,6,7,9,10,11,13],show:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],shown:[0,3,5,6,9,10,11,15],showpoint:15,shrink:[3,4,6,9],shrinkag:[3,4],shrunk:9,shuffl:[0,1,4,11],side:[0,2,3,6,10,11,13],sigh:12,sigma0:15,sigma1:15,sigma2:15,sigma:[0,1,3,4,5,8,9,10,11,13,15],sigma_0:3,sigma_1:3,sigma_2:3,sigma_:[3,13,15],sigma_fn:[5,10],sigma_i:[0,3],sigma_j:3,sigma_m:[4,15],sigma_n:[9,15],sigma_t:11,sigma_x:15,sigmoid:[1,2,5,6,8,10],sigmundson:[4,16],sign:[1,2,5,6,8,15],signal:[1,8,10],signific:1,significantli:[1,11,15],sim:[3,4,11,15],similar:[0,1,2,3,4,5,6,7,8,9,11,12,13],similarli:[0,1,3,6,8,15],simpl:[1,2,3,4,5,6,8,9,10,12,13],simplepredict:8,simpler:[0,1,3,4,11,12],simplest:[0,1,7,8,10],simpletre:8,simpli:[0,1,2,3,4,6,7,8,9,10,12,13,15],simplic:[2,3,4,5,6,7,8,9,10],simplicti:3,simplifi:[0,4,7,12],simplist:[4,15],simul:[4,15],simultan:4,sin:[0,1,2,7,10,11,13],sinc:[0,1,2,3,4,5,6,7,8,9,11,13,15,17],sine:10,singl:[0,1,2,3,4,5,6,7,10,11,13,15],singular:[0,4,11,13,14],site:[0,1,2,4,5,6,9,11,14],situat:[0,3,5,11],six:15,size:[0,1,2,3,4,6,7,8,9,11,13,15],sketch:8,ski:7,skill:0,skip:9,skiprow:0,skl:[0,4],sklearn:[0,1,3,4,5,6,7,8,9,11],skplt:[5,8],sl:4,slack:6,slice:[2,13],slide:[0,15],slight:[4,11],slightli:[1,2,3,4,5,8,15],slope:[6,9,10],slow:[0,2,6,11],slower:[3,13],slowest:13,slowli:10,slp:1,small:[0,1,2,3,4,6,7,8,9,10,11,12,13,15],smaller:[0,1,2,3,4,6,7,9,11,15],smallest:0,smooth:[0,4,7,11],sn:[0,1,4,5],sne:9,so:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15],soar:4,social:0,soft:[1,5,8,10],soften:6,softmax:5,softwar:[0,6,12,13,14],sol:6,sole:[0,4],solid:[0,5],solitem:3,soltyp:3,solut:[0,1,2,3,4,6,8,9,11,13,15],solutionsummari:3,soluton:2,solv:[0,1,3,4,6,8,9,10,11,13,14],solve_expdec:2,solve_ode_deep_neural_network:2,solve_ode_neural_network:2,solve_pde_deep_neural_network:2,solveod:2,solveode_popul:2,solver:[2,3,5,6,7,8,9,13],some:[0,1,2,3,4,5,6,7,8,9,10,13,14,15],some_model:4,someth:[0,1,5,7,9,15],sometim:[0,1,9,10,11],soon:13,sophist:0,sopt:11,sort:[3,4,7,9,15],sound:3,sourc:[0,1,4,12,13,15],space:[0,1,3,6,7,9,10,11,15],span:[0,3,7,9,13],spare:1,spars:[3,4,13],sparse_mtx:13,sparsiti:8,spatial:[1,2,10],spdiag:3,speak:15,special:[0,4,5,8,10,11,13,15],specif:[0,1,2,3,4,5,6,7,9,10,12,13,15],specifi:[0,3,4,5,7,9,11,15],specifici:[0,8],spectral:1,speech:[0,1,10],speed:[1,2,11],spend:15,sphere:0,spin:4,spite:0,spline:6,split:[1,3,4,6,7,8,9,15],splite:0,splitter:[1,8],spmatrix:3,spontan:15,spread:[0,9,15],springer:17,spuriou:11,sqquar:3,sqrt:[0,3,4,6,8,9,11,15],squar:[1,2,5,6,7,9,11,12,13,14,15],squarederror:8,squash:10,srand:15,srtm:4,srtm_data_norway_1:4,stabil:3,stabl:[0,3,4,5,7,9,12],stage:[3,11],stai:[0,2,3,9],stand:[0,3,7,10],standard:[0,1,3,4,5,6,8,10,13],standardscal:[0,4,5,6,7,8,9],stanford:11,start:[0,1,2,3,4,6,7,8,9,10,11,13,14,15],start_box:[2,11],start_nod:[2,11],startpoint:15,stat:[0,4],state:[1,2,3,4,5,6,8,9,10,11,12,15],statement:[0,5,13],statist:[0,1,5,7,8,9,10,11,13,14,17],statu:[0,5,9],stavang:4,std:[0,4,15],stdev:15,stdout:3,steep:11,step:[0,1,2,4,5,7,8,9,10,11,13,15],step_fn:[5,10],step_length:11,steps_list:7,stian:16,still:[2,3,4,9,11,15],stimuli:10,stk2100:17,stk3155:14,stk4021:17,stk4051:17,stk4155:14,stk5000:17,stk:17,stochast:[0,1,3,4,6,9,10,14],stoke:10,stone:[0,5],stop:[1,5,7,9,11,15],storag:3,store:[0,1,2,4,9,11,15],str:1,straight:[0,4,6,11],straightforward:[0,2,3,4,6,7,8,11,13],strategi:[0,1,7],stratifi:4,streamtyp:3,strength:[0,3],stretch:9,strict:[6,11],strictli:[6,11],stride:13,strike:4,string:[1,15],stroke:5,strong:[4,7,8,10,15],strongli:[0,6,12,13],stronli:0,structur:[0,1,2,4,7,8,10,12],stuck:[1,11],student:[0,14,16,17],studi:[0,3,4,5,6,9,10,11,12,17],studier:[14,17],style:[0,5,7,13],sub:[7,10],subarg:[2,11],subdivid:[0,13],subfield:0,subject:[3,4,6,15],subplot:[0,1,4,5,6,7,8,11],subplots_adjust:[6,15],subprogram:13,subract:0,subroutin:0,subscript:1,subsequ:[1,3,4,10,13,15],subset:[1,4,7,10,11,12],subspac:[0,6,9],substanti:[7,8],substep:9,substitut:[4,10,13],subsubset:7,subtask:4,subtl:1,subtract:[0,3,4,9,11,13,15],subtre:7,subval:[2,11],succeed:0,success:[5,7,11,15],successfulli:7,sucess:15,sudo:[0,12],suffer:[0,1,2,3,8],suffici:[1,4,6,9,11],suggest:[1,11,17],suit:[6,10],suitabl:[0,15],sum:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],sum_:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],sum_i:[2,3,4,6,11],sum_j:4,sum_k:[4,6,10,13],summar:[3,4,7],summari:[1,8,14],sunni:7,superscript:[1,10],supervis:[0,3,4,5,7,10,12],supplement:5,support:[0,1,7,8,9,11,12,14],suppos:[0,3,4,5,6,8,9,10,11,13],suppress:[3,11],sure:[1,4],surf:4,surfac:[0,4],surpass:4,surpris:0,surround:12,survei:[0,3,4],svc:[6,7,8],svd:[0,4,9,14],svdinv:3,svm:[6,7,8,9],svm_clf:[6,8],swath:3,sy:[3,11],symbol:[1,3,9,11,12,15],symmeteri:1,symmetr:[0,3,6,9,10,11,13],symmetri:[4,7],sympi:[0,12],synonim:15,syntax:[1,11,13],syntaxerror:[1,13],syrk:3,system:[0,1,3,4,5,7,8,10,11,12,13,17],systemat:[4,15],t0:[4,11],t1:[2,11],t2:2,t3:2,t:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15],t_0:[2,7,11],t_1:11,t_:2,t_b:8,t_i:[1,2,10],t_j:[3,10],t_k:7,tabl:[7,15,16],tabul:0,tag:[2,3,4,5,10,11,13,15],taht:0,tail:15,tailor:[2,6,9],taiwan:0,take:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15],taken:[0,1,4,8,11,13],tangent:[1,10,11],tanh:[1,5,6,10],target:[0,1,3,4,5,6,7,8,9,10],target_nam:7,task:[0,1,3,4,7,9,10],tau:[3,15],tax:0,taylor:[2,11],taylornr:11,tc:6,team:1,teaser:0,technic:[0,3,4],techniqu:[0,1,6,8,11,12,14,15,17],technolog:[0,1],tek5040:17,tell:[0,4,8,9,11,15],temp1:1,temp2:1,temp:1,temperatur:[0,7],temporarili:1,tend:[3,4,6,7,8,10,11],tendenc:0,tension:4,tensorflow:[0,2,6,12,13,14,17],term1:[3,4,9],term2:[3,4,9],term3:[3,4,9],term4:[3,4,9],term:[0,1,2,3,4,5,6,7,8,9,10,11,15],termin:[0,3,7,8,11],terrain1:4,terrain:4,test:[3,4,5,6,7,8,11,13,15],test_accuraci:1,test_error:4,test_ind:4,test_pr:1,test_predict:1,test_scor:[5,8],test_siz:[0,1,3,4,8],test_split:7,testerror:[0,4],text:[0,1,2,3,6,7,9,11,13,14,15,17],textual:7,textur:[1,7],tf:[1,11],th:[0,1,2,3,4,5,7,10,11,13,15],than:[0,1,2,3,4,5,7,8,9,10,11,12,15],thank:4,theano:[1,12],thei:[0,1,2,3,4,5,6,7,9,10,11,13,15],them:[0,1,4,6,7,8,9,10,11,13],theme:0,themselv:[0,15],thenc:4,theorem:[2,4,5],theoret:[0,8],theori:[0,1,6,7,10,11,12,14,17],thereaft:[0,3,4,9,10,13],therebi:[0,3,5,9,15],therefor:[0,1,2,4,5,6,9,11,15],therein:9,thereof:[0,4,11],theta:[1,11,15],theta_:[1,11],theta_i:1,theta_k:15,theta_linreg:11,theta_t:11,thi:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17],thing:[0,1,2,3,5,7,15],think:[0,1,4,7,10,11,15],third:[0,4,11],thirti:5,those:[3,4,6,7,8,9,13,14],though:[1,2,13,15],thought:[4,15],thousand:[0,1],three:[0,1,3,4,6,7,10,13,14,16],threshold:[1,7,8,9,10,11],through:[0,1,2,3,4,6,9,10,11,12,13,15],throughout:[0,3,12,13,15],thu:[0,1,2,3,4,5,6,8,9,10,11,15,16],thumb:[0,4],thursdai:14,tibshirani:[4,14,17],tick_param:4,ticker:[4,11,15],tif:4,tight_layout:[1,5],tightli:9,tild:[0,3,4,9,15],till:[0,5,6,7,8,10,13],time:[0,1,2,3,4,5,6,7,8,9,10,11,13,14,15],timefunct:15,tini:1,titl:[0,1,2,4,5,6,7,8,11,15],tmp:11,tn:2,to_categor:1,to_categorical_numpi:1,to_numer:[0,4],to_str:15,togeth:[0,4,6,9],told:11,toler:[2,4],tomographi:10,too:[0,2,3,4,7,9,11,15,17],took:6,tool:[0,1,4,11,12,15],toolbox:6,top:[0,3,4,7,8,12],topic:[0,3,4,5,6,12,14,17],topolog:[1,10],toss:8,total:[0,1,2,4,5,6,8,9,10,11,13,15,16],totalvari:15,toward:[1,2,5,10,11],town:0,tpng:7,tqdm:4,trace:[2,11],trace_stack:[2,11],traceback:[2,3,4,6,7,8,11],tracer:[2,11],track:[11,13],tract:0,tractabl:0,trade:[3,7],tradeoff:[0,3,14],tradit:[0,1,4],train:[2,3,4,6,7,8,9,10,11],train_accuraci:[0,1],train_end:[0,1],train_error:4,train_ind:4,train_pr:1,train_siz:[0,1],train_test_split:[0,1,3,4,5,7,8,9],train_test_split_numpi:[0,1],trained_model:4,trainerror:0,trainingerror:4,trait:0,tran:3,transfer:7,transform:[0,3,4,5,6,7,8,9,10,11,12,13],transit:[4,10],translat:[1,4,8],transpos:[1,3,9,13],travers:[0,3],treat:[0,1,4,10,11,15],tree:[0,1,4,12,14],tree_clf:[7,8],tree_clf_:7,tree_clf_sr:7,tree_reg1:7,tree_reg2:7,tree_reg:7,trend:15,trevor:17,tri:[2,7,11],triain:0,trial:[0,2,4,11,15],triangl:11,triangular:13,trick:[6,9,11,15],trickier:15,tridiagon:13,trillion:12,trivial:[0,1,3,9,15],troubl:[0,6,10],true_beta:4,true_divid:1,true_fun:4,tucker:6,tumor:[5,7],tumour:5,tunabl:1,tune:[7,11,13],tupl:[2,11],turn:[0,1,3,4,5,6,7,8,9,10,11,13,15],tutori:1,tv:2,tveito:2,tweak:[1,8,15],twice:11,twist:9,twister:15,two:[0,1,2,3,4,5,7,8,9,10,11,13,14,15,17],tx:11,tx_1:11,ty:11,type:[0,1,4,6,8,11,13,15],typeerror:[2,11],typic:[0,1,2,3,5,7,8,10,11,15],u:[0,2,3,4,8,9,10,13],u_:13,u_i:10,u_m:8,ua:0,ubuntu:[0,12],uci:0,uio:[14,16,17],unari:13,unary_f:[2,11],unary_oper:[2,11],unbalanc:[4,7],unbias:[0,3,4,15],uncent:4,uncertainti:[0,3],uncertitud:15,unchang:1,uncorrel:8,undefin:3,under:[0,1,3,4,8,11,12],underdetermin:0,underfit:[1,4],underflowproblem:3,undergo:3,undergradu:14,underli:[0,1,7,11,15],understand:[0,1,3,4,8,11,12],understood:[6,11],undesir:6,undetermin:[3,6],unexpect:[4,15],unexpected:15,unfair:4,unfortun:[1,6,7,8],unicode_liter:[6,7],uniform:[0,1,3,4,9,11],uniform_real_distribut:15,uniformli:[11,15],unifrompdf:15,unimport:11,union:[3,4],uniqu:[0,2,4,11,13],unit:[0,1,3,8,10,15],unitari:[3,4,13],unitarili:13,uniti:15,univari:15,univers:[0,1,2,11,14,16],unix:1,unknow:[0,13],unknown:[0,1,3,4,6,8,13],unknowwn:10,unlabel:1,unless:[0,4,9,11],unlik:[1,6,11,15],unnecessarili:7,unravel:1,unrol:9,unseen:[0,5,7],unstabl:1,unsupervis:[0,1,10,12,14],unsymmetr:13,until:[1,2,7,10,11,15],untouch:0,unusu:10,up:[1,3,4,6,8,9,11,12,13,14,15],updat:[1,2,8,10,11],upload:[12,17],upon:[1,4,9,13],upper:[0,6,7,13],uppercas:[13,15],us:[3,4,6,7,8,9,10,13,14,17],usag:[0,6,12,15],usd10000:0,usd:0,usecol:0,useless:1,user:[0,1,2,4,5,6,9,12,13],userwarn:4,usetex:15,usg:4,usr:15,usual:[0,5,10,11],ut:3,util:[0,1,4,5,8],ux:13,v0:15,v1:15,v2:15,v:[2,3,4,9,11,12],v_0:9,va:1,vale:2,valid:[0,1,5,7,8,11,12,14,15],valu:[0,1,2,4,5,6,7,8,10,11,12,13,14],valuat:7,van:0,vandenbergh:[6,11],vandermond:0,vanilla:[0,4,9],vanish:[1,11,15],var_x:15,varabl:6,varepsilon:[3,4],varepsilon_:[3,4],varepsilon_i:[3,4],vari:[0,1,3,4,8],variabl:[0,1,2,3,4,5,6,8,9,10,11,13],varianc:[0,1,3,5,7,8,9,11,12,13,14],variance_i:[3,9],variance_x:[3,9],variant:[0,1,4,6,10,11],variat:9,varieti:[0,10,12],variou:[1,3,4,5,6,7,9,10,11,12,13,15],vartempvec:15,varvec:15,vaue:1,vault:0,vdot:[2,11],vec:[4,15],vector:[0,1,2,3,4,5,7,8,9,11,12,14],ventur:[0,6,12],verbos:1,veri:[0,1,2,3,4,5,6,7,8,9,10,11,15,17],verifi:[9,13],versatil:6,versicolor:[6,7],version:[0,8,11,12,13,15],versu:1,vert:[0,1,3,4,5,6,7,9,11],vert_1:[3,4],vert_2:[3,4,9],via:[0,3,4,5,6,7,8,9,10,12,13,14,15],vidal:9,video:[0,1,10,12,14],view:[1,3,4,10,11,14,15,17],violat:6,virginica:7,viridi:[0,1,2],virtual:1,viscos:11,viscou:11,visibledeprecationwarn:2,vision:0,visual:[0,9,10,12],visualis:1,viz:[4,6,15],vjp:[2,11],vjpnode:[2,11],vmax:[1,4],vmc:15,vmin:[1,4],volum:0,vote:8,voting_clf:8,votingclassifi:8,votingsimpl:8,vrtx:14,vs:[0,4],vspace:[2,11],vstack:[3,9,13,15],vt:3,w1:6,w2:[6,9],w3:6,w:[0,1,2,3,4,5,6,8,9,10,11,13,15],w_1:[6,13],w_1x_1:6,w_1x_:6,w_2:[6,13],w_2x_2:6,w_2x_:6,w_3:13,w_4:13,w_:[1,10],w_hidden:2,w_i:[1,2,8],w_ix_i:10,w_j:13,w_m:13,w_output:2,w_px_:6,w_px_p:6,wa:[0,1,3,4,5,8,9,10,11,13],wai:[0,1,2,3,4,5,6,8,9,10,11,13,15],walk:7,walker:15,wang:0,want:[0,1,2,3,4,6,7,8,9,10,11,12,15],warn:[0,1,6],warrant:4,watch:12,wavelet:6,we:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17],weak:[7,8],weather:[1,10],web:[12,14],webpag:14,websit:[4,13,14],wedg:[6,15],wednesdai:14,wee:9,week:[3,4,5],weekli:[12,17],weight:[0,1,2,4,5,7,8,10,11,15],weigth:2,welcom:[6,12],well:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,15,17],went:6,were:[0,1,3,4,5,6,8,9,10,15],wessel:0,what:[1,2,3,4,5,6,7,8,9,10,11,12,13,14],when:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],whenev:[11,15],where:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15,16],wherea:[4,15],wherein:[1,10],whether:[0,3,5,7,15],which:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,16],whichev:1,white:7,who:[0,14],whole:[1,3,7,9],whose:[0,4,8,15],whow:[3,9],why:[0,1,4,11],wide:[0,1,4,5,10,12,13],widehat:4,width:[0,6,7],wieringen:0,win:8,wind:7,wing:16,winther:2,wiothout:4,wiscons:5,wisconsin:8,wisdom:4,wise:[0,1,3,10,11],wish:[0,2,3,5,6,9,11,13],with_std:0,wither:4,within:[0,2,5,7,10,11,15,17],without:[0,1,3,4,6,7,9,10,11],won:0,wonder:6,word:[0,1,3,4,15],work:[0,1,4,5,6,7,11,12,14,15],workshop:14,world:[0,6],worldwid:0,wors:[0,1,4],worst:7,worth:7,would:[0,1,3,4,5,6,7,8,9,10,11,13,15],wrap:[4,13,14],wrap_util:[2,11],write:[0,1,2,3,4,5,6,10,11,13,15],written:[0,2,3,9,10,11,12,13,15],wrong:[1,6],wrongli:[8,15],wrote:[3,9],wrt:8,wth:8,www:[12,13,14,17],wx_1:6,x0:6,x1:[6,7,8,11],x1_exampl:6,x1d:6,x2:[6,7,8,11],x2d:[6,9],x2d_train:9,x2dsl:9,x3:6,x:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],x_0:[0,3,9,13],x_1:[0,2,3,4,5,6,7,8,9,11,13,15],x_2:[0,2,3,4,5,6,7,8,9,11,13,15],x_3:[6,13,15],x_4:13,x_:[0,2,3,4,6,8,9,11,13,15],x_center:9,x_data:1,x_data_ful:1,x_hidden:2,x_i:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],x_input:2,x_ix_:0,x_iy_i:6,x_j:[0,2,6,7,10,15],x_jy_j:6,x_k:[10,13,15],x_l:15,x_m:[4,10,13,15],x_n:[0,2,4,6,9,10,11,13,15],x_new:[7,8],x_offset:4,x_output:2,x_p:[5,7],x_poli:7,x_poly10:7,x_prev:2,x_reduc:9,x_scale:6,x_test:[0,1,3,4,5,7,8,9],x_test_own:4,x_test_scal:[0,4,5,7,8,9],x_train:[0,1,3,4,5,7,8,9],x_train_mean:4,x_train_own:4,x_train_scal:[0,4,5,7,8,9],x_val:1,xarrai:12,xavier:1,xbnew:11,xcode:[0,12],xdclassiffierconfus:8,xdclassiffierroc:8,xg_clf:8,xgb:8,xgbclassifi:8,xgboost:7,xgboot:8,xgbregressor:8,xgparam:8,xgtree:8,xi:[6,11],xi_1:6,xi_:6,xi_i:6,xk:6,xlabel:[0,1,2,3,4,5,6,7,8,11,15],xlim:[4,8],xm:7,xmesh:11,xnew:[0,11],xp:15,xpanda:0,xpd:[3,9],xplot:0,xs:7,xscale:0,xsr:7,xt_x:11,xtest:4,xtick:[4,6,7],xtrain:4,xu:0,xx:[0,3,13],xy:[0,4,6,13],xytext:6,xz:13,y:[0,1,3,4,5,6,7,8,9,10,11,13,15],y_0:[0,3,9,13],y_1:[0,3,6,7,9,11,13],y_1y_1:6,y_1y_1k:6,y_1y_2:6,y_1y_2k:6,y_1y_n:6,y_1y_nk:6,y_2:[0,3,6,7,9,13],y_2y_1:6,y_2y_1k:6,y_2y_2:6,y_2y_2k:6,y_3:[0,7,13],y_4:13,y_:[0,1,3,4,8,9,13],y_data:[0,1,3,4],y_data_ful:1,y_decis:6,y_fit:0,y_i:[0,1,3,4,5,6,7,8,9,10,11,13],y_if_:8,y_ix_:0,y_ix_i:[5,6,11],y_iy_jk:6,y_j:[4,6,10],y_k:10,y_m:13,y_model:[0,3,4],y_n:[6,11],y_ny_1:6,y_ny_1k:6,y_ny_2:6,y_ny_2k:6,y_ny_n:6,y_ny_nk:6,y_offset:4,y_plot:7,y_pred1:7,y_pred2:7,y_pred:[0,1,4,5,6,7,8],y_pred_rf:8,y_pred_tre:8,y_proba:[5,8],y_scaler:4,y_test:[0,1,3,4,5,7,8,9],y_test_onehot:1,y_test_predict:0,y_train:[0,1,3,4,5,7,8,9],y_train_mean:4,y_train_onehot:1,y_train_predict:0,y_train_scal:4,y_val:1,ye:[4,5],year:[0,12],yet:[0,1,4,6,9,11],yi:11,yield:[0,2,3,4,6,8,10,11,13,15],yk:6,ylabel:[0,1,2,3,4,5,6,7,8,11,15],ylim:4,ym:7,ymesh:11,yn:0,yo:[6,7,8],yoshua:[1,17],you:[0,1,2,3,4,6,7,8,9,11,12,13,15,17],young:0,your:[1,2,3,4,6,9,11,12,13,15],yourself:[9,11],youtub:12,ypred:4,ypredict2:11,ypredict:[0,11],ypredictlasso:3,ypredictol:3,ypredictown:4,ypredictownridg:4,ypredictridg:[3,4],ypredictskl:4,ys:7,ytest:4,ytick:[4,6,7],ytild:[0,4],ytildelasso:3,ytildenp:0,ytildeol:3,ytildeownridg:4,ytilderidg:[3,4],ytrain:4,yx:13,yy:13,yz:13,z:[0,1,2,3,4,5,6,7,9,10,11,13,15],z_0:13,z_1:13,z_2:13,z_:[1,2,10,13],z_c:1,z_h:1,z_hidden:2,z_i:[1,10],z_j:[1,10],z_k:10,z_m:1,z_mod:7,z_o:1,z_output:2,zaman:15,zaxi:4,zero:[0,1,2,3,4,5,6,7,8,9,10,11,13,15],zip:[2,4,11],zl:3,zm_h:0,zn:0,zone:0,zx:13,zy:13,zz:13},titles:["3. Linear Regression","13. Building a Feed Forward Neural Network","14. Solving Differential Equations with Deep Learning","4. Ridge and Lasso Regression","5. Resampling Methods","6. Logistic Regression","8. Support Vector Machines, overarching aims","9. Decision trees, overarching aims","10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","11. Basic ideas of the Principal Component Analysis (PCA)","12. Neural networks","7. Optimization, the central part of any Machine Learning algortithm","Applied Data Analysis and Machine Learning, FYS-STK3155/4155 at the University of Oslo, Norway","2. Linear Algebra, Handling of Arrays and more Python Features","Teaching schedule with links to material","1. Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks"],titleterms:{"1":14,"10":14,"11":14,"12":14,"13":14,"15":14,"17":14,"18":14,"19":14,"2":0,"20":14,"2021":16,"22":14,"23":14,"24":14,"25":14,"26":14,"27":14,"29":14,"3":14,"30":14,"34":14,"35":14,"36":14,"37":14,"38":14,"39":14,"4":14,"40":14,"41":14,"4155":12,"42":14,"43":14,"44":14,"45":14,"46":14,"47":14,"5":14,"6":14,"8":14,"case":[6,8,15],"do":1,"final":10,"function":[0,1,4,5,6,8,9,10,11,15],"import":[3,13,15],A:[0,1,6,7],Ising:4,The:[0,1,2,3,4,5,6,7,9,10,12,15],activ:[1,10],actual:15,ad:4,adaboost:8,adam:11,adapt:8,adjust:1,again:7,aim:[6,7],algebra:13,algorithm:[7,8,9,10],algortithm:11,all:6,an:[0,8],analys:3,analysi:[0,3,4,9,12,15],ani:11,anoth:7,appli:12,approach:[0,6],approxim:10,architectur:1,arrai:13,assist:16,august:14,autocorrel:15,autograd:2,automat:11,back:[1,9,10],background:12,bag:8,base:11,basic:[0,3,5,7,8,9,13],batch:1,bay:3,befor:9,better:[6,15],bia:4,binari:1,binomi:15,bird:8,block:15,boost:8,bootstrap:[4,8,15],boston:0,breast:1,bring:10,build:[1,7],calcul:15,cancer:[1,5,7,9],cart:7,central:[11,12,15],chain:10,chang:8,chi:0,choos:1,classic:9,classif:[1,7,8],classifi:6,clip:1,code:[0,1,2,3,7,9,10,15],collect:1,compar:[2,8],complex:[0,4],complic:4,compon:9,comput:[7,15],con:7,concept:15,conjug:11,continu:15,convex:[6,11],convolut:10,correl:[9,15],cost:[1,8],cours:[12,17],covari:[3,9,15],cross:4,cumul:15,data:[0,1,4,5,7,9,12,15],dataset:1,decai:2,decis:[7,8],decomposit:[3,9,13],deep:[1,2],defin:1,definit:15,degre:0,demonstr:15,dens:0,deriv:[3,10],descent:[2,8,11],develop:1,deviat:15,diagon:9,dice:15,differ:6,differenti:[2,11],diffus:2,dimension:[2,6],disadvantag:7,discret:15,disguis:15,distribut:[3,15],domain:15,down:1,dropout:1,element:[0,15],elimin:13,ensembl:8,entropi:7,environ:0,equat:[0,2,10],error:[0,8],euler:2,evalu:1,event:15,exampl:[0,1,2,4,5,6,7,8,15],exercis:[0,4],expect:15,experi:15,explor:0,exponenti:[2,15],extrem:8,ey:8,fall:16,famili:1,famou:15,featur:[7,13],feed:[1,10],fine:1,first:10,fit:[0,8],forest:8,forward:[1,2,10],frank:4,freedom:0,frequentist:0,from:[3,8,10],full:2,further:3,fy:12,gaussian:[13,15],gd:11,gener:[7,15],geometr:9,gini:7,good:0,grade:16,gradient:[1,2,8,11],growth:2,ha:12,handl:13,hidden:2,hous:0,how:15,hyperparamet:1,hyperplan:6,i:[1,15],id3:7,idea:9,implement:[1,15],implic:3,improv:1,increment:9,index:7,inform:16,input:2,instal:12,instructor:16,interpret:[3,9],introduc:9,introduct:[0,4,12,13],invers:[3,13],iter:8,its:15,jackknif:15,jungl:8,kera:1,kernel:[6,9],lagrangian:6,lasso:[3,4],later:3,layer:[1,2,10],learn:[0,1,2,9,11,12],least:[3,4],level:8,librari:12,likelihood:5,limit:[1,11,15],linear:[0,6,11,13],link:[3,9,14,17],logist:5,lu:13,machin:[0,6,11,12],main:15,make:[0,7,8],mani:[8,10],materi:14,math:3,mathemat:[3,6],matric:3,matrix:[1,3,9,10,13,15],matter:0,mean:[0,15],meet:[3,8,15],mercer:6,mersenn:15,method:[4,7,8,11,15],mlp:10,model:[0,1,4,10],moment:15,momentum:11,moon:[6,7],more:[4,13],multilay:10,multipl:1,multipli:6,name:15,network:[1,2,5,10],neural:[1,2,10],non:6,normal:[0,1,15],norwai:12,notat:10,novemb:14,now:[1,7],nuclear:0,nueral:5,number:[0,2,15],numer:[2,15],numpi:13,observ:15,obtain:9,octob:14,od:2,off:4,ol:[3,4],one:[2,10],oper:13,optim:[1,6,11,12],ordinari:[3,4],organ:0,oslo:[12,17],other:[7,9,10,13,15],our:[0,3,9,11,15],outcom:12,output:[2,15],overarch:[0,6,7],overview:8,own:[0,8,9],packag:13,part:[11,12],partial:2,pass:1,pca:9,pdf:15,perceptron:10,perform:[1,7],period:15,perspect:1,poisson:[2,15],popul:2,practic:11,pre:1,prerequisit:12,princip:9,pro:7,probabl:[3,15],problem:[1,2,11],procedur:7,process:1,program:[2,11],project:4,prop:11,propag:[1,10],properti:[3,15],pseudo:15,python:[0,7,12,13,15],quick:6,ran0:15,random:[8,9,15],read:7,real:4,recip:15,recurr:10,reduc:0,reformul:2,regress:[0,3,4,5,7,8,11],regular:1,relev:17,relu:1,remind:[4,6],requir:[2,12],resampl:4,rescal:4,resourc:2,revisit:11,ridg:[3,4],rm:11,rng:15,rule:10,s:[6,8,15],sampl:[9,15],schedul:14,schemat:7,scheme:2,scikit:[0,1,9],select:15,semest:16,septemb:14,set:[0,2,7,10],should:[1,15],simpl:[0,7,11,15],singl:8,singular:[3,9],situat:15,soft:6,softmax:1,solv:2,solver:11,some:11,specifi:2,split:0,squar:[0,3,4,8],standard:[11,15],state:0,statist:[3,4,12,15],steepest:[8,11],stk3155:12,stochast:[11,15],supervis:1,support:6,svd:3,teach:[14,16],teacher:16,techniqu:[4,9],technolog:12,tensorflow:1,test:[0,1],textbook:17,theorem:[3,6,9,10,15],theori:15,three:15,tip:11,togeth:10,top:1,toss:15,toward:9,trade:4,tradeoff:4,train:[0,1],tree:[7,8],tune:1,two:[6,12],type:[2,10],uncorrel:15,uniform:15,univers:[10,12,17],up:[0,2,7,10],us:[0,1,2,5,11,12,15],valid:4,valu:[3,9,15],variabl:15,varianc:[4,15],variou:0,vector:[6,10,13],view:[0,8],visual:[1,7],wai:7,wave:2,week:14,weekli:14,what:[0,15],which:[1,15],why:15,wisconsin:5,write:9,xgboost:8,your:[0,8]}}) \ No newline at end of file +Search.setIndex({docnames:["chapter1","chapter10","chapter11","chapter12","chapter13","chapter2","chapter3","chapter4","chapter5","chapter6","chapter7","chapter8","chapter9","chapteroptimization","clustering","intro","linalg","schedule","statistics","teachers","textbooks"],envversion:{"sphinx.domains.c":2,"sphinx.domains.changeset":1,"sphinx.domains.citation":1,"sphinx.domains.cpp":4,"sphinx.domains.index":1,"sphinx.domains.javascript":2,"sphinx.domains.math":2,"sphinx.domains.python":3,"sphinx.domains.rst":2,"sphinx.domains.std":2,"sphinx.ext.intersphinx":1,sphinx:56},filenames:["chapter1.ipynb","chapter10.ipynb","chapter11.ipynb","chapter12.ipynb","chapter13.ipynb","chapter2.ipynb","chapter3.ipynb","chapter4.ipynb","chapter5.ipynb","chapter6.ipynb","chapter7.ipynb","chapter8.ipynb","chapter9.ipynb","chapteroptimization.ipynb","clustering.ipynb","intro.md","linalg.ipynb","schedule.md","statistics.ipynb","teachers.md","textbooks.md"],objects:{},objnames:{},objtypes:{},terms:{"0":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18,19],"00":[0,1,5,6,9,11],"000":[1,3],"0000":9,"00000":9,"000000":[0,5,11],"00000000e":5,"0001":[1,3],"000148":0,"00019998":5,"00024087":5,"00028369228101198006":9,"00029012":5,"0003153514830958081":6,"0003153514830958126":6,"00034944":5,"000417932":2,"00042089":5,"000464088":2,"00050694":5,"00058016":6,"000599":0,"00060705":6,"00061058":5,"00062595":6,"00066668":6,"00068734":6,"00069103":6,"00073541":5,"00076495":6,"00076925":6,"0007698473260556334":6,"0007698473260556339":6,"00079123":6,"00079968":5,"00084705":6,"00085884":6,"00087697":6,"00088573":5,"00092646":6,"00096314":5,"001":[1,2,3,8,13],"00100519":6,"0010479245355337968":6,"00105081":6,"00106677":5,"00107405":6,"00111756":6,"0011526":6,"00115999":5,"00118527":6,"001263":0,"00128479":5,"001323":6,"00137835":6,"00139705":5,"00149311":6,"00149956":6,"00152117":6,"00154733":5,"00156379":6,"00168251":5,"00174276":6,"00175331":6,"00186347":5,"001988":11,"00198806":11,"00200":8,"00202624":5,"00202756":6,"00217499":6,"00224413":5,"00228741":6,"0023548":6,"002381316302584885":6,"0023813163025848865":6,"00242999":6,"00243186":6,"0024401":5,"00249435":6,"002526":0,"00266858":2,"00270244":5,"00274989":6,"00275135":13,"00289724":6,"00293838":5,"002948":0,"0030828":11,"003083":11,"00310113":2,"00312361":6,"00315593":6,"003215318065760509":6,"00323332":6,"0032542":5,"003301":6,"0033955154592040944":6,"00353823":5,"0036237":6,"0036367":6,"00369758":6,"003704":0,"003717":0,"003759":0,"003774":0,"003788":0,"0038335":6,"003909404072811231":6,"00391839":5,"0039987":6,"004":5,"0040919407077539514":6,"00410387":6,"00410478":6,"0041136346174431284":6,"004113634617443135":6,"00411363461744314":6,"004113634617443141":6,"004155986345861374":6,"00415763":[],"00424909":2,"00424967":6,"00426027":5,"00433417":11,"00440346":6,"00443743":6,"00445655":11,"004579219539673836":6,"00458878":6,"004610275230656294":6,"00462287":6,"00471782":5,"00472199":6,"00472512":6,"0049544":6,"004999999999999994":0,"00512927":5,"00517114":6,"00526348":6,"0053018":6,"00554552":6,"00556826":6,"0056799":5,"00579953":6,"00588657":6,"00607783":6,"006162":6,"00617499":5,"00630331":6,"00642221":6,"00660427":6,"00672607":6,"00673407":6,"00676387":6,"0068011":6,"00683748":5,"00683964":6,"007012403613997257":0,"007024126888936694":6,"00719176":6,"00727646693":0,"007315":0,"0074331":5,"00759119":6,"00784393":6,"00803064":6,"0080866254785146":18,"00813803":6,"00817631":6,"00823002":5,"00827728":6,"00831018":6,"00834567":6,"00848904":6,"0086649156":0,"008675369724976501":5,"00894639":5,"00905423":6,"009163470508352211":5,"009164545680330616":6,"00917248":6,"00934499":6,"009450756365829578":0,"0096208":6,"00990475":5,"00992331":6,"00996754":6,"01":[0,1,2,3,5,6,9,11,13,20],"010018312644139347":6,"0100706":6,"01033172130665515":6,"010516485576652856":6,"01066519":6,"01076611":5,"0110":18,"011076219011339788":6,"011225":2,"0113104":6,"01179792":6,"01191824":5,"012073649439965807":6,"01219292":6,"01223198":6,"01231917":6,"01290947":6,"01295356":5,"013121573975499602":6,"013121573975499604":6,"01318643":6,"01347916":6,"01348565":6,"01367553":6,"01397146":6,"01405935":6,"01416528":6,"014209325470380275":0,"01433809":5,"014436800088969727":6,"01449782":6,"01458337":6,"0146081":6,"01463049":6,"015072388895177088":6,"015072388895177109":6,"01530715721129232":18,"01531845":6,"01538461538462":9,"01549377":6,"01558197":5,"016285782696075054":6,"01633913":6,"01640891":6,"01655318":6,"016587414993037307":6,"01691985":6,"01708781":6,"01708852":6,"01713366":6,"01724499":5,"01735584819559184":6,"017355848195591845":6,"01756972":16,"018232":0,"01831130e":6,"01831200e":6,"01866537":6,"01873344":11,"01873869":5,"01898855":6,"01905883":6,"01908936":6,"019587":0,"01963611":6,"01969145":6,"01975416527179247":6,"01975848":6,"02":[0,4,6,7,12],"02024962":6,"02054837e":6,"02068067":6,"02073509":5,"02098261":6,"02123176":6,"02159270458799264":6,"021592704587992645":6,"02198702e":6,"022022882954618364":0,"02208512":6,"02228115":6,"02229529":6,"02252765":5,"02299949826036602":6,"02348765":6,"02365049":6,"0245528":6,"02492265":5,"02493054":13,"02498832":6,"02503753":6,"02511518":6,"02522069":6,"025709":[0,11],"02586427":6,"0260906":6,"02625193":8,"026408391362671896":18,"026605727637176654":6,"02707227":5,"02723445":6,"027609773491022314":6,"02857":4,"02926396":18,"029733":0,"02976145":6,"02994311":5,"02f":6,"03":[1,3,6],"03032441e":6,"03056589":5,"030566":5,"03076923076924":9,"03077640549":4,"03099776":5,"031":5,"03187339273559067":18,"03196357":6,"03251863":5,"03256632e":1,"03267527":6,"03278964":11,"032790":11,"03279636":6,"0330308045180234":6,"0330308045183163":6,"033657685071527485":6,"03447512":6,"03562355":6,"03568439":6,"0358909447132981":11,"0359565":5,"03630548":6,"03707133":11,"03781367141738885":6,"03781367141738886":6,"03814292":6,"03815288":6,"038300":[0,11],"039039":5,"0399676689527968":6,"0399676689527975":6,"04":[1,3,6,11],"04010697":6,"04063602":6,"041":9,"0411487294305246":6,"0411487294305746":6,"04220758":6,"043":9,"04315108":5,"0433816":16,"04346721":5,"04355837":6,"04362":9,"0437499":2,"04389027":6,"043927769551648":18,"04423486":6,"044334":0,"044613":6,"04483457":18,"04537385":6,"04543942":6,"04566964":6,"0458":9,"04615384615386":9,"04621521":[],"04648335":5,"0466":3,"04683565":5,"04784395":6,"04818727730430296":6,"04892055":6,"04909093":6,"04912436":6,"0495569966278269":6,"0495569966278315":6,"04it":6,"05":[0,1,3,4,6,13],"05009826":6,"05087958":16,"05100875":6,"051649":[0,11],"0517473":5,"05227921801205691":6,"05227921801205692":6,"05263":9,"05302":9,"05364854":8,"05383795":6,"05447415":6,"054585":11,"054785":11,"054963":11,"05505310046362":2,"055137":11,"055320":11,"05533":9,"055676":0,"05614483":5,"05623":9,"05648":9,"05651951":6,"05667":9,"057088709963182":0,"05716368155351588":6,"0572":6,"05756733":6,"05785343":6,"05789007":6,"05796251":6,"05807125":6,"05883":9,"05884":9,"059783":11,"05999":9,"06":[3,4,6,13],"060080":0,"060183":11,"06020587":6,"06021285":5,"060213":5,"06043581":6,"060507":11,"060655":11,"060781":11,"060841":11,"061025":11,"061048":11,"061321":11,"061390":11,"061509":11,"061604":11,"06160438":11,"061701":11,"061745":11,"061898":11,"061917":11,"06200174":5,"06208238634231953":6,"062142":11,"062292565":4,"062294":11,"062391":11,"062435":0,"062451":11,"062534":11,"062834":11,"062884":11,"063078":11,"063250":11,"063343":11,"063513":11,"063657":11,"063872":11,"06388888888888888":1,"064052":11,"064108":11,"064184":11,"064384":11,"06444":9,"064469":11,"06453579006728315":6,"064648":11,"064681":11,"06491736":6,"064918":11,"064964":11,"065106":11,"06547790180152357":6,"06547790180152363":6,"065514":11,"065557":11,"065575":11,"065892":11,"066110":11,"066194":11,"066309":11,"06637":9,"066609":11,"0666807":2,"066753":11,"066837":[0,11],"066954":11,"067079":11,"067236":11,"06724062":5,"067544":11,"067675":11,"067714":11,"068094":11,"068103":11,"068120":11,"06844519414009438":6,"06858699":13,"068659":11,"068809":11,"068831":11,"068937":11,"069091":11,"069455":11,"069584":0,"069672":11,"069754":11,"069912":11,"07":6,"070028":11,"070043":0,"070071":11,"07016":9,"07017":9,"070379":11,"07039":9,"070576":11,"070612":11,"07062318":6,"070635":11,"070889":[0,11],"070911":11,"07099747918547346":9,"071086":11,"07115":9,"0713":0,"071387":11,"07145103":11,"07160048164248561":6,"071698":11,"071705":11,"071935":11,"07201957":18,"072242":11,"072348":11,"072492":5,"072530":5,"072617":5,"072620":11,"072750":5,"07285":3,"0728785":[],"072928":5,"073016":11,"073225":11,"073362":5,"073368":5,"073423":5,"07345504":0,"073531":5,"073598":[0,11],"073695":5,"073907":11,"074067":[0,11],"07421084":5,"074336":11,"074488":11,"07456491":5,"074666":11,"07490892":6,"074945":11,"075573":11,"075820":11,"076204":11,"0764924":6,"07656896":13,"07678":9,"076938":[0,11],"077022":11,"077467":11,"07777777777777778":1,"07820":9,"078253":11,"078548":11,"07864":9,"078667":5,"07871":9,"078911":11,"078992":5,"079347":5,"079406":5,"07944154":16,"07968918676726029":6,"079729":5,"079839":11,"079847":5,"079893":5,"07989327":5,"07999999999998":9,"08":[3,4,9,13,18],"080106":11,"080137":5,"080256":11,"080312":5,"080334":5,"080347":5,"080370":5,"080406":5,"080410":11,"08041015":11,"08043851":5,"080517":5,"080801":5,"080916":5,"081140":5,"08131003":6,"081431":5,"081483":5,"081540":5,"08156108":6,"081773":5,"082174":5,"082183":5,"082451":11,"08251519":6,"082900":5,"08299273e":6,"083053":5,"08318298e":1,"083220":5,"083227":5,"08336233266":4,"083404":5,"083441":5,"083506":5,"083527":0,"083600":5,"083692":5,"08376632":6,"0837663229239016":6,"0837663229239025":6,"083799":5,"083829":5,"083977":5,"084000":5,"084101":5,"084184":5,"084224":5,"084226":5,"08426840630693411":6,"08426840630693413":6,"084282":5,"084364":5,"084400":5,"084408":5,"084444":5,"084536":5,"084549":5,"08455":9,"084570":5,"084604":5,"084629":5,"084670":5,"084683":5,"08474":9,"084777":5,"084965":5,"085044":5,"085167":5,"085184":5,"085185":11,"085361":5,"085416":5,"08551306":6,"085764":5,"08576932":6,"08593216":6,"08611111111111111":1,"086303":5,"08630331":5,"086567":5,"08673755293381497":5,"08690":9,"087501":5,"08758":9,"08759":18,"087834":5,"08816688":18,"088176":5,"0881981":5,"088611":5,"088631":5,"08871404":5,"088809":5,"088816":5,"088825":5,"088853":5,"08888888888888889":1,"088926":5,"08902":9,"089059":5,"089212":5,"089329":5,"089425":5,"089614":5,"08996":9,"09":1,"090028":5,"090229":5,"090929":5,"091060":5,"09117221":18,"091224":5,"091236":5,"091340":5,"091349":5,"091363":5,"091414":5,"091416":5,"091426":5,"09149881":6,"091630":5,"09166666666666666":1,"0917":9,"091891":5,"0923":3,"09251":9,"09297039":11,"093247":0,"0934597075922044":5,"0938":3,"0940821989624095e":6,"0940821989673748e":6,"095510":5,"095702":5,"095871":5,"09609807":5,"096173":5,"096623":5,"09672929714683368":1,"097360":5,"09744":9,"09780":9,"09791":9,"099":6,"09903804":8,"099191989493334":6,"0n":0,"0s":[3,4],"0x7fad10f9a280":[],"0x7fad20f69be0":[],"0x7fd098df3280":13,"0x7fd0a9063be0":13,"1":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18,19,20],"10":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,16,18],"100":[0,1,2,3,4,5,6,7,8,9,10,11,13,14,16,18,19],"1000":[0,1,2,4,5,8,11,13,14,15,18],"10000":[2,5,6,10,11,18],"100000":8,"10001":10,"1001":[9,18],"1002":18,"1003":18,"10030":9,"10044225464078282":11,"1005":18,"10077114273548984":6,"1009":18,"1011":18,"1013":18,"1013904243":18,"10141413e":6,"1015":18,"102":0,"1022233262115424":18,"10222333":18,"1023":18,"10230":9,"1024":3,"1026":18,"1027":18,"1028":3,"103":[1,3,9],"1030":18,"10340":9,"1037":18,"10378326e":1,"1038":18,"10391807":6,"10398646080125035":6,"1040":18,"10405456":11,"10430":9,"104411":0,"1047":18,"10520":9,"10555555555555556":1,"1056":3,"10589577":5,"106":3,"106095":[0,11],"108":[0,6,9],"109":6,"10913":6,"10931453":6,"10960":9,"10th":9,"10x":0,"11":[0,2,4,5,6,7,8,9,10,11,12,13,16,18,20],"110":0,"1100":18,"1101":18,"11022302e":5,"111":[1,7,12],"11100":9,"1122558214":13,"112383":[0,11],"1124":9,"11297834":18,"11362930e":5,"11388888888888889":1,"11390":9,"114437":3,"11462415":5,"11482289e":6,"11507992e":1,"11547777218940905":6,"11547777218940906":6,"115822":6,"11590":9,"11660":9,"11666666666666667":1,"117":8,"11744554e":6,"11780":9,"11790868":18,"117986":0,"118":2,"1182":3,"1183":3,"118318":0,"1184":[3,4],"11840":9,"1185":3,"1186":3,"11890":9,"119":2,"1199":8,"119936":2,"119999999999976":9,"12":[0,1,2,3,4,5,6,8,9,11,12,13,16,18,20],"120":[2,3],"1203":9,"1203284":8,"121":[2,8,9,10],"12182967":6,"12196674":16,"122":[2,8,9,10],"12222222222222222":1,"122439":5,"1224392":5,"123":[],"12318726e":6,"12333649":6,"123459876":18,"123711":6,"12380":9,"124":0,"12400":9,"125":1,"1250":3,"125000":0,"12552073e":6,"126":9,"1261":9,"12618549":5,"1265":9,"127":4,"1270":6,"127043":6,"127773":18,"12777777777777777":1,"12790":9,"128":[3,4,9,13],"12945452":6,"1297":9,"1298":9,"13":[0,2,4,5,6,9,11,12,13,16,18],"130":9,"13003291":6,"13055555555555556":1,"131":9,"1314":6,"132":9,"13220608e":6,"132360":5,"1323603":5,"1326":9,"13280":9,"133":7,"13333333333333333":1,"135":9,"13519106":0,"13535942":6,"136":3,"1360":4,"1361":[3,4],"1362":4,"1363":4,"1364":4,"13646574":5,"13661243e":6,"13679863":6,"13740":9,"137400784702911":0,"137652":[0,11],"1378":6,"13865173":5,"138775":[0,11],"13890":9,"1392559581788775e":6,"1392559584983597e":6,"14":[0,2,4,5,6,8,9,10,11,12,13,16,18,20],"140":9,"14021063":6,"1404":0,"14042769":5,"140428":5,"141":[2,9],"14100":9,"1416398":6,"14174745":6,"1418":9,"142":[2,3,4,9],"14250":9,"142857":0,"143":[2,7],"14360598":18,"1437":1,"144":2,"14400":9,"1440501043841336":1,"14440":9,"1446729567":4,"145":2,"146":2,"147":2,"14710":9,"14722222222222223":1,"147400":[0,11],"14741468":[],"147420":[0,11],"1479":9,"148":2,"14812206":6,"14818":6,"1484256":[],"148768":6,"149":2,"14932651":18,"14988578":11,"149886":11,"14g":6,"15":[0,2,4,5,6,7,8,9,12,13,18],"150":[2,4,8,9],"15005476":5,"15098090e":6,"15130074e":6,"151986":6,"152":9,"15200":9,"15258907":[],"1527777777777778":1,"153036":0,"153106":0,"1533795":13,"153760":0,"15384615384616":9,"154":9,"15454301":[],"154720":0,"154911":0,"155":9,"155491":0,"155687":0,"155883":0,"156":0,"1562":3,"15629539":[],"157":0,"1575":9,"158":[0,9],"1586300629904382":11,"1587":9,"159":0,"1590":9,"15990":9,"15g":6,"15it":6,"16":[1,2,3,4,5,6,8,9,10,13,17,18],"160":0,"1603":[3,4],"1604":4,"1605":4,"160539":4,"1606":4,"1607":4,"16111111111111112":1,"1612":3,"16211139":5,"16220":9,"16231451":4,"1625":9,"1628":9,"163":9,"1630775253":1,"16342407":5,"16343471":6,"16384":3,"16500":9,"166":9,"16660817":6,"166667":0,"167":9,"168":9,"16805821e":6,"16807":18,"17":[0,1,2,4,5,6,8,9,13,18],"17084902":[],"1709":9,"17174962e":1,"1726":9,"17300":9,"1731":9,"17339342":6,"17446471":6,"1752":9,"175300":0,"17641709":6,"176880142835407":11,"17777777777777778":1,"17801022":5,"17861098":6,"17917768":5,"17949575":5,"17953942":11,"1797":[1,3],"18":[2,4,6,7,8,9,10,13,18],"180":9,"18029127":5,"1807":4,"1809":9,"181":9,"1812":9,"1821":9,"18276924":13,"18327677":18,"18333333333333332":1,"184":9,"184519":0,"184895":6,"185":[3,4],"18526":6,"185278747229417":5,"186":3,"1860":9,"1861":3,"18611111111111112":1,"18613217e":6,"18660":9,"18673098":11,"189496":0,"189622":0,"18it":6,"19":[2,4,6,9,13,18],"191262820314401":11,"19207979":5,"19220":9,"193":9,"19394283":18,"194":3,"1940":0,"194042826653172e":6,"194042826815498e":6,"1943":12,"1944":3,"19444444444444445":1,"1950915150":6,"1954":6,"1956":9,"19569961":6,"1961":3,"1962":3,"1963":3,"1964":3,"1965":3,"1970":16,"1973":9,"197370":[0,11],"19740":9,"1979":6,"19800":9,"1989":18,"199":9,"19937":18,"1_1":12,"1_2":12,"1_3":12,"1cm":[0,8,10,18],"1d":[1,2,3],"1e":[1,2,3,4,14],"1e10":14,"1e4":6,"1f":1,"1k":16,"1n":0,"1s":[3,4],"1x":0,"2":[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20],"20":[0,1,2,4,6,7,8,9,13,18],"200":[0,2,3,4,8,9,10,18],"2000":0,"200000":0,"20015436":6,"2004":13,"2006":20,"2010":1,"2011":1,"2014":4,"2015":1,"2016":0,"2018":[0,6],"2018906331":3,"2019":9,"2021":[3,4,6,14,17],"2027":9,"20277777777777778":1,"20320502":6,"20500":9,"206":9,"2060":9,"20661216":18,"2069":9,"207545":[0,11],"20756638":18,"20833333333333334":1,"20867052175109335":6,"20980":9,"21":[0,1,2,4,5,6,7,9,12,13,16],"210340":[0,11],"21058097":5,"21130":9,"2116753732":4,"21169159e":6,"21265216":13,"213103":[0,11],"213743":[0,11],"2147483647":18,"21596432":6,"216290":[0,11],"216683":[0,11],"2188":3,"21944444444444444":1,"22":[0,1,2,4,5,6,9,12,13,16,18],"22044605e":5,"221":8,"221180":0,"2216":9,"2218":9,"221805":2,"222400":0,"225":4,"2259440937":1,"226124657522696":18,"22612466":18,"22690428":5,"22842468702288576":6,"22842468702288582":6,"22847924":5,"23":[1,2,4,6,7,9,12,13,16],"23002365e":6,"231":9,"23103285":18,"2315033":18,"23167717":5,"232435":0,"23333333333333334":1,"234":6,"23522201":[],"2357089093":[],"2361111111111111":1,"2364":9,"2397":9,"24":[0,1,2,4,6,9,13,16],"24140":9,"2416":9,"24175744e":6,"2419":9,"2430":9,"24390":9,"24444444444444444":1,"244858":11,"24485843":11,"246":2,"2470":6,"24829908":5,"24906604e":6,"2495":3,"25":[2,3,4,5,6,7,8,9,11,13],"250":[2,4,7,9],"2500":3,"25000":0,"250000":0,"250154":0,"2517560119":4,"251879":0,"252436":0,"252866":5,"25286618":5,"253775":0,"255":3,"255001":0,"256":[2,4],"25617654e":6,"25617657e":6,"256962":0,"257":9,"2572":9,"2572495066":10,"2575":9,"259153":[0,11],"2597":[3,9],"25976336":18,"26":[2,4,6,9,13],"26153846153846":9,"2619":0,"26290036":18,"26294938":18,"2629493813057833":18,"26301436":5,"26306244":18,"264":[0,4],"2640931530791003":6,"2640931530791005":6,"265":0,"2650":9,"265109911":4,"2654":9,"266":0,"26610075":18,"26666667":13,"26710969":5,"26780278":5,"268":9,"268227":5,"26822717":5,"269":0,"27":[0,1,2,4,6,13],"270":0,"2750":9,"275341":0,"276263":[0,11],"27692307692308":9,"27700":9,"2775623201":16,"27760":9,"27n_":18,"28":[1,3,4,6,9],"28001319":13,"280647":[0,11],"2812":3,"282727":[0,11],"283":9,"2830637392":4,"28336218e":6,"2836":18,"28390":9,"28475098":8,"28590743":6,"2861":18,"2871":9,"2873":9,"2882":18,"2886":18,"2890":0,"2892":18,"29":[4,6,7,9],"29149329":18,"2915":18,"29167186":5,"2923076923077":9,"29592539":18,"296247":0,"297":3,"2971492148":[],"2972":3,"29822833":6,"298273":0,"298375":0,"299748":0,"2_":[12,18],"2_1":12,"2_2":12,"2_3":12,"2_i":12,"2_m":[6,18],"2_t":13,"2_x":18,"2b":18,"2cm":8,"2d":[1,3,11,12,15],"2e":6,"2f":[0,7,9,10,11,12],"2g":2,"2g_i":2,"2k":3,"2m":6,"2n":[0,2,3],"2nd":9,"2p":18,"2pt":4,"2x":[0,3,8,13],"2x_ix_jy_iy_j":8,"2x_j":8,"2y_i":10,"2y_j":8,"3":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19],"30":[0,1,4,6,7,9,10,13],"30000":0,"30010":9,"30119421":8,"3017":4,"3018":4,"3019":4,"301927":0,"3020":4,"3021":4,"303":6,"3037":3,"3038":3,"3039":3,"3040":3,"3041":3,"30466214e":6,"30535506":16,"30559547":18,"3063":3,"3072":3,"30787294":6,"309":9,"30940":9,"31":[0,4,12,16,18],"3123314713548606":6,"31276579e":6,"313":4,"31318084":5,"314":4,"31457796":5,"315":[4,6],"3155":[5,6],"316":4,"317":4,"31718909":11,"317367":11,"31896852":8,"32":[3,4,6,9,12,13,16,18],"3200":1,"32047562":0,"3214960170351912":6,"3215":9,"324":2,"32458459":5,"3250":1,"32512":9,"326238":0,"32903042":[],"3297":0,"32992274":11,"329923":11,"33":[4,9,12,16],"3303":0,"33066907e":5,"3310":0,"33166055e":5,"331939":0,"332331":0,"333":7,"3331":0,"33327369":11,"333274":11,"33333333":13,"3337":0,"33611111111111114":1,"3384":6,"34":[2,4,9,16],"3403":9,"340782":[0,11],"34114547":5,"342680":0,"34305928":18,"3436":0,"3437":0,"3456":4,"34569596":5,"3457":4,"3458":4,"3459":4,"3460":4,"346810":4,"3469819128513336":4,"34740615":18,"3498":4,"35":[2,4,6,9],"3514":4,"35140":9,"351636":[0,11],"35182854":5,"3522":4,"3525":4,"3528556":5,"352856":5,"3529":4,"3530606977":5,"3538":4,"3543":4,"3544313922":6,"3546":4,"35470445e":5,"3548":4,"355":3,"3551":4,"35533774":6,"3556":4,"3558":4,"3560":4,"356399":0,"3567":4,"3572":4,"3575":4,"357508":0,"3576":4,"3577":4,"3581341341":4,"3585":4,"3587":4,"359":5,"3593":4,"3595":4,"3598":4,"359999999999985":9,"36":[0,2,4,5,6,9,18],"360":1,"3604":4,"3605":4,"3606":4,"360688":0,"3609":4,"36102113":13,"3613":9,"3615":4,"361556":0,"3617":4,"3621311":5,"3624":4,"3627":4,"3628":4,"363295916414895e":6,"3632959170548605e":6,"3643":4,"3645":4,"3646":4,"3647":4,"3655":4,"3655222":5,"3659":4,"3668":4,"36689784":11,"366898":11,"3669":4,"367":2,"3672":4,"3673":4,"3674":4,"3679":4,"3684":4,"3687":4,"3688":4,"369139":[0,11],"36it":6,"37":[2,4,9],"3704":4,"370782966":4,"3711":4,"3713":4,"3718":4,"3721":4,"3722":4,"3725":4,"3729":4,"3739":4,"37396662":6,"3748":4,"3749":4,"3753":4,"3759":4,"3760":4,"3765":4,"376559":5,"37655936":5,"3772":4,"3773":4,"37732":[],"3776":4,"3777801602":6,"3779":4,"37835429e":5,"3784":4,"37900111":6,"3791":4,"3794":4,"37992857":6,"38":[2,4,9,18],"380":9,"3802":4,"3803":4,"3804":4,"3805":4,"3811":4,"38135733e":6,"3817475779":6,"3818":4,"3819":4,"3820":4,"38246359":18,"3827":4,"3833":4,"3842":4,"3850":4,"3854":4,"386":[4,9],"38629436":16,"3867":4,"387":4,"3871":4,"3876":4,"388":4,"3882":4,"3885":4,"389":4,"38901478":11,"38916861e":6,"38962192e":6,"3898":4,"39":[0,4,9,13,19],"390":4,"39095416":6,"3914":4,"391602":18,"3925515884752442":5,"3931":4,"39579407":5,"3958":4,"39706038":5,"397700":[0,11],"3980313467":6,"399836":0,"3d":[2,3,4,6,13],"3f":[1,3,9],"3n":16,"3x":[2,8],"3x_i":2,"3y":8,"4":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18],"40":[1,4,6,9,19],"400":4,"4000":[9,20],"40116777":5,"401168":5,"401842":[0,11],"4022":6,"4030":4,"4034668048":8,"404":0,"405890":[0,11],"4077":3,"408":2,"4087":9,"409":2,"40927184e":6,"41":[0,2,4,9,16],"410":2,"4107":9,"411":2,"412":2,"41433969":5,"41511965e":1,"4155":2,"4162706317":6,"418506":[0,11],"41882037e":6,"4192423635":9,"41990268":18,"42":[1,4,8,9,10,16],"420":2,"421":2,"422":2,"423":2,"424":2,"42441033":5,"42450":9,"425":2,"4255":4,"4258989918":18,"426":[6,7],"42631342":6,"43":[1,2,4,7,9,16],"43054282":5,"43330971e":6,"435163":0,"43579948e":6,"436462435":4,"43761347":6,"43766686":11,"438060758":6,"438136":0,"439230":6,"44":[0,1,2,4,16],"44089210e":5,"4410":3,"4411":3,"442600":[0,11],"443217":0,"444":9,"44970586e":1,"45":[2,4,9,19],"450":9,"450257":[0,11],"4504":9,"4557763":11,"455947":0,"456":9,"456418966187335":9,"457":[2,4],"457770268480242":0,"458027":0,"458078":[0,11],"45960079":5,"46":[2,4,9,19],"4601":9,"461":18,"462":7,"46383925e":6,"464424":11,"4644244":11,"466":18,"46602982":18,"469":3,"46932688":18,"4694":3,"46984697e":6,"469868":5,"46986815":5,"47":[2,4,9,19],"47042744":5,"470714":0,"47075725":6,"47116868e":6,"47125748":5,"47132891":5,"47400238":18,"47432993":5,"4744":3,"47478057":18,"475311":11,"47531107":11,"47610036":6,"47815203":11,"479465113":4,"48":[4,9],"48089797":11,"481979":6,"48257387":19,"483257001":13,"4837":3,"48420165":18,"48476997":11,"486873":11,"48687342":11,"489":4,"48994188":5,"49":[4,5,6,9,11,13],"490":4,"491":4,"49152":3,"492":4,"493":4,"4940954":0,"495916150936654e":6,"495916150938325e":6,"49636583":16,"4990":18,"4992":18,"4997":18,"4c4c7f":[9,10],"4d":3,"4f":6,"4y":8,"4y_i":10,"5":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18],"50":[1,2,3,4,6,7,8,9,10,13],"500":[1,3,4,6,9,10,13,18],"500000":0,"50000455":5,"50000553":5,"50000718":5,"50000855":5,"50000969":5,"50001063":5,"50001142":5,"50001207":5,"50001261":5,"50001306":5,"50001343":5,"50001374":5,"500014":5,"50001414":5,"50001422":5,"50001439":5,"50001454":5,"50001466":5,"50001476":5,"50001485":5,"50001492":5,"50001498":5,"50001502":5,"50001506":5,"5000151":5,"50001512":5,"50001515":5,"50001517":5,"50001518":5,"50001519":5,"50001521":5,"50001522":5,"50001523":5,"50001524":5,"50001525":5,"5018":18,"50227564e":6,"50321091":5,"504167":11,"50416731":11,"506":0,"50769230769231":9,"507d50":[9,10],"50846112e":6,"50j":13,"50x10":1,"51":[4,9,10],"510":1,"512132":0,"5138":3,"514219":0,"5177783846":4,"519842":0,"52":[4,13],"5222222222222223":1,"522758":0,"52307692307693":9,"5260627":18,"526744":[0,11],"52874252":5,"529":3,"52911941":11,"52945798e":5,"53":[4,9],"5303329":11,"5305555555555556":1,"5312":3,"531280":0,"53189647":6,"53697476":6,"53703498":6,"5378811":11,"53846153846155":9,"539261":[0,11],"54":[4,6,9,18],"540":9,"54039921":5,"541605":0,"544439":0,"546166676":[],"54780216":18,"54it":6,"55":[1,4,9],"550321":0,"5539":3,"5555555555555556":1,"55578041":18,"5566":6,"557795":[0,11],"55854694":11,"56":[1,4,9],"56033697":5,"561":3,"5611":3,"5615":3,"56198284":5,"5625":3,"5639":3,"564":[3,9],"564374":[0,11],"565":9,"56536":0,"566":9,"56636616e":6,"567":9,"568":9,"569":[1,9],"56912044e":6,"56939714":5,"56992937":18,"57":[0,3,4,8,9,19],"570":9,"5700":3,"571":5,"571105947979395e":6,"571105947979439e":6,"57201944e":6,"57266138":18,"574465":[0,11],"57it":6,"58":[3,4,9,10,19],"583595":0,"584804":0,"5888888888888889":1,"589":3,"59":[2,3,4,9],"590":3,"591":3,"591317992":4,"592":3,"593":3,"5944444444444444":1,"59591979":11,"595920":11,"598392":5,"59839245":5,"5cm":18,"5f":8,"5x":8,"5y":8,"6":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,16,18],"60":[1,2,3,4,6,9],"60000":4,"6019067271":4,"60293962":5,"60420593":5,"606439":0,"60673226":11,"61":[2,3,4,7],"6111111111111112":1,"612939":0,"613579":0,"614808":[0,11],"618":0,"61808351":18,"618982":0,"6199381169260247":18,"62":[2,4],"62364974":5,"62373464":11,"625":7,"626635268":6,"62894215":5,"629961":0,"63":[0,1,2,4,6,7],"6300745149331701":0,"630224":3,"63025821e":6,"63249532e":6,"63498144":5,"63675140":6,"6371293350711955":0,"63it":6,"64":[1,3,4,7,13,16],"64012627":5,"645":6,"64615384615385":9,"646283":[0,11],"64742912e":6,"647473":[0,11],"649382":[0,11],"64x50":1,"65":[1,2,4,7,8,9],"6562":3,"65885453":5,"659306":0,"66":[2,4],"66204648":6,"66247212":18,"6628996975186953":0,"6638":9,"66410989":[],"66560":9,"667":9,"668172":0,"668186":11,"66818635":11,"67":[2,4,9],"67047975e":6,"671089":0,"672721":0,"67588315":18,"67838309":18,"68":[2,4],"68192193":5,"68534263e":6,"68542204":5,"68545647e":5,"6869":9,"6887363571":4,"68929213e":6,"689519":[0,11],"69":[2,4,7,9,18],"690":9,"690569639355314":0,"690617":0,"69069n_":18,"692":[0,1],"69295955":16,"69504801":6,"69634577e":6,"69695259":5,"69985355":18,"6999536":11,"69it":6,"6n_":18,"7":[0,1,2,3,4,5,6,7,8,9,11,12,13,16,17,18,20],"70":[1,4,6,7,9],"70179437":18,"7050":3,"70653767":4,"70710678":5,"70769586":16,"70832814":5,"71":[1,4],"7119":9,"712018":[0,11],"7134":6,"7151":6,"72":4,"72174172":11,"72271878e":6,"7236674":5,"72373129":11,"724":3,"72522848":[],"72859758":5,"7293182":[],"72981762":8,"73":[4,6],"731000":0,"73174557":18,"733096":0,"73752910":2,"74":[4,6,13],"740":9,"74081822":8,"743u":3,"74840212":5,"749765":0,"75":[2,4,5,6,8,9,11],"7501749450963715":11,"750445":0,"750u":3,"751699":[0,11],"75170092":5,"753846153846155":9,"756352":0,"75838233":18,"75it":6,"76":[2,4,9,19],"76060096":18,"763u":3,"765":7,"76923076923077":9,"76936315":5,"77":[2,4,9,13,19],"77034458":5,"770345":5,"77152076":5,"7718":9,"774300":0,"775":1,"77636e":13,"77714169":8,"7782028952":4,"78":[2,4],"78011544":18,"78184120e":6,"7846153846154":9,"78941903":5,"79":[2,4],"79111643":5,"793167":0,"794282":[0,11],"79754246":18,"797e":6,"7d7d58":[9,10],"8":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18],"80":[0,1,2,4,5,6,8,9],"800":[4,7],"80354994":6,"80469739":5,"8055555555555556":1,"80561191":18,"80609615e":6,"8064":3,"80734875":11,"807349":11,"80847477e":6,"81":[1,2,4],"81048318e":6,"81160425":5,"81333805":6,"814":[7,11],"815563":[],"81633628":11,"816454":0,"816847":0,"8175":3,"82":[2,4],"8219235992494145":18,"8219236":18,"82198978":5,"82650876":5,"826509":5,"8265786":5,"82747653":5,"827477":5,"83":[0,2,4],"8305555555555556":1,"83512277":5,"83999999999999":9,"84":4,"84062065":18,"84228957e":5,"842436":0,"84292394":5,"842u":3,"84355903e":1,"84443254e":1,"84780262":6,"84854738":11,"84923989e":6,"84994524":5,"85":[1,4,9],"85263220":6,"8527777777777777":1,"853241":11,"85324115":11,"853u":3,"85601992":5,"858":9,"86":[2,4],"8608479":5,"860848":5,"861":0,"86117291":5,"86134827":5,"86145244":11,"8638888888888889":1,"86546962":0,"86630":9,"8666666666666667":1,"86810":9,"87":[0,2,4,9],"8702784034":4,"871":6,"8722222222222222":1,"87381451":5,"875":1,"8759":13,"87625493":18,"8768":3,"878297":11,"88":[2,4,13],"88046261":5,"8805555555555555":1,"88168312e":6,"883":3,"88336879":5,"884":3,"88477619":18,"885":3,"88529063e":6,"886":3,"88679947":18,"887":3,"8888888888888888":1,"89":[2,4],"8916666666666667":1,"89288636":11,"89410423":5,"8944444444444445":1,"8962476":11,"896248":11,"8f":6,"8g":6,"8n":16,"8x8":1,"9":[0,1,2,3,4,5,6,7,8,9,11,12,13,16,17,18],"90":[1,2,4,6,9],"900449":5,"90054363":0,"90075537":5,"9011":6,"90220243":5,"90266948":5,"90268858":16,"903824":5,"90382431":5,"9040":9,"90475506e":6,"9055555555555556":1,"9083333333333333":1,"91":[3,4,18,19],"910":9,"9111111111111111":1,"91128596":5,"912u":3,"91379157":18,"913791573406831":18,"91416375":18,"91492986e":6,"915":3,"91549644":0,"916":3,"9166666666666666":1,"917":3,"91760278":5,"918":3,"91812702":5,"918992":0,"919":3,"92":[3,4,6,9,19],"922u":3,"92343595":[],"924018":0,"924e":6,"925":1,"92507116e":1,"92578916":5,"92754397":11,"927544":11,"92819235":13,"92857143":7,"93":4,"931":0,"93155188":5,"93158979":5,"932u":3,"933":5,"93492130e":6,"935u":3,"9361111111111111":1,"937":18,"937082":0,"93799826":5,"938":18,"9387":9,"939":[0,18],"94":[4,18],"9400":3,"94226022e":6,"94284104":5,"94320205":5,"9444444444444444":1,"94548496":6,"94591015":16,"94639099":11,"94659383":13,"9472222222222222":1,"94735055":[],"947903":11,"94790323":11,"9482527":5,"95":[0,1,4,7,9,11],"95008046":6,"95231424":5,"9527777777777777":1,"95284275":5,"953065564":1,"95351665":5,"954":18,"9549351910143222":0,"954u":3,"9555555555555556":1,"955820c21e8b":4,"956563":[0,11],"95684892":5,"95703":13,"95714723":18,"957147232685324":18,"95it":6,"96":[4,6,7,11],"960":18,"960130485007934e":6,"9601304850213484e":6,"96024953":5,"96084663":5,"961":18,"962":18,"9637117593816477":6,"9640435":5,"96489434":13,"9649652536":4,"965548":0,"96653373":16,"96688672":5,"9674916":5,"967809":[0,11],"96863851":18,"96987657":13,"97":[4,7],"97005689":5,"97065296":13,"97108e":13,"9722222222222222":1,"97230501":[],"97243128":5,"97300836":5,"97497404e":6,"975":1,"97507735":5,"9760832":18,"97705827":5,"97758848":5,"9777777777777777":1,"977880":5,"97788031":5,"9780387310732":20,"9780387848570":20,"9781492032632":20,"97898392":6,"97926491":5,"98":[0,1,4,7,9],"980":9,"98036405":0,"9805555555555555":1,"98091621":5,"981321":0,"98139097":5,"98275501":5,"983310":0,"98346748":18,"98399675":13,"98413059":5,"98454786":5,"985":18,"98566191":5,"986":18,"9861111111111112":1,"98680716":5,"98716878":5,"98808176":5,"98822371":6,"9888888888888889":1,"989":18,"9890348":5,"9893149172528393":0,"9893447":5,"9898ff":[9,10],"99":[4,6,7,9,11,13],"990":9,"99009525":5,"99088801":5,"991":18,"99115119":5,"99176998":5,"992":18,"99242921":5,"99265097":5,"993":18,"99316252":5,"99353454":11,"993535":11,"99371056":5,"99389612":5,"993972":11,"99397245":11,"9943201":5,"9947756":5,"99492986":5,"99528218":5,"99539415":5,"9955282554647219":0,"99566069":5,"99578809":5,"996":5,"99608161":5,"9963961":5,"99650061":5,"9967458":5,"99700706":5,"99709215":5,"99724883":13,"99729756":5,"99751458":5,"99758326":5,"99775587":5,"99775949":13,"99793613":5,"99799099":5,"99813653":5,"99828624":5,"99829953":13,"9983295":5,"99845267":5,"998577":5,"99861053":5,"99871521":5,"99881845":5,"99884384":5,"99893323":5,"999":[9,18],"99901896":5,"99903755":5,"99911427":5,"99918546":5,"99919837":5,"99926459":5,"9993237":5,"99933188":5,"99938942":5,"9994385":5,"99944272":5,"99949306":5,"99953381":5,"99953475":5,"99957911":5,"99961294":5,"99965056":5,"99967865":5,"99970988":5,"9997332":5,"99975913":5,"99977416":0,"99977849":5,"99980002":5,"9998161":5,"99984732":5,"99987324":5,"99989476":5,"99991263":5,"99992746":5,"99993978":5,"99995":5,"9999555851685968":6,"999955585168597":6,"9999840939906267":0,"9999858320366368":0,"9x":6,"9y":6,"\u00f8yvind":[6,19],"abstract":1,"boolean":4,"break":[0,4,6,11,14],"byte":16,"case":[0,1,2,3,4,5,6,7,11,12,13,14,15,16,17],"catch":0,"char":18,"class":[0,1,3,4,6,7,8,9,11,12,13,18],"const":18,"default":[0,1,2,4,6,7,13,16],"do":[0,2,3,4,5,6,8,9,10,11,12,13,14,16,18],"ekstr\u00f8m":[4,19],"export":9,"f\u00f8470":19,"final":[0,1,2,3,4,5,6,7,8,9,10,11,13,14,17,18,19],"float":[0,3,4,5,9,11,13,14,16,18],"function":[2,3,4,5,9,14,15,16],"import":[0,1,2,3,4,6,7,8,9,10,11,12,13,14],"int":[0,1,2,3,4,5,6,11,13,14,16,18],"long":[0,1,3,4,12,13,18],"m\u00f8svatn":6,"new":[0,1,2,3,5,6,7,8,9,10,11,13,14,16,18],"null":18,"public":[0,15],"return":[0,1,2,3,4,5,6,7,8,9,11,13,14,16,18],"s\u00f8rli":19,"sch\u00f8yen":[6,19],"short":[4,5],"steinsv\u00e5g":19,"super":[4,5],"switch":0,"throw":[3,6,18],"true":[0,1,2,3,4,5,6,7,8,9,10,12,13,14,16,18],"try":[0,1,2,3,4,5,6,7,8,9,10,11,13,14,15,16,18],"var":[1,2,3,4,5,6,8,9,10,11,13,16,18],"while":[0,1,3,4,5,6,7,8,9,11,12,13,18],A:[2,3,5,6,7,10,11,12,13,15,16,17,18,19,20],AND:2,And:[0,3,4,5,6,9,15,18],As:[0,1,2,3,4,5,6,8,10,12,13,16,18],At:[0,4,6,13],BE:0,Be:[0,2,15],Being:13,But:[0,1,2,3,5,6,9,10,18],By:[0,3,5,6,12,13,16],For:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20],IF:6,IN:20,If:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15,16,18],In:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18,20],Is:11,Ising:[5,12],It:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18],Its:[1,2,4,11],NO:[7,11],No:[3,5,6,8,9],Not:[0,1,5,6,17],OR:18,Of:18,On:[0,3,17,18,20],One:[0,1,3,4,5,6,7,8,11,12,13,18],Or:[0,1,6],Such:[6,12,18],That:[0,5,7,10,11,12,14,18],The:[4,10,13,14,16,17,19,20],Then:[0,1,5,6,8,9,10,11,12,13,14,16,18],There:[0,3,4,5,6,8,9,11,12,14,16,17,18,19],These:[0,3,4,5,8,9,10,11,12,13,14,16,18],To:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,16,18],With:[0,5,6,8,9,10,11,12,14,16,18],_0:[5,8,10,11,13],_1:[2,5,6,8,10,11,12,13,14,16],_2:[2,5,8,11,12,13,16],_3:16,_4:16,_9:13,_:[0,1,2,4,5,6,7,8,9,10,11,12,13,16],_________________________________________________________________:4,__call__:[3,4],__class__:10,__doc__:6,__future__:[8,9],__getitem__:4,__init__:[1,2,4],__main__:2,__mosek:5,__name__:[2,10],_asarrai:2,_auto10:[6,12],_auto12:6,_auto1:[2,3,4,5,6,7,12,13,16,18],_auto2:[2,3,4,5,6,12,13,16,18],_auto3:[3,4,5,6,12,13,16],_auto4:[4,6,12,13,16],_auto5:[4,6,12,13,16],_auto6:[4,6,12,16],_auto7:[4,6,12,16],_auto8:[6,12],_auto9:[6,12],_ax:4,_base:[4,8],_build:[15,20],_build_call_output:3,_c:1,_call:3,_call_flat:3,_check_1d:4,_check_optimize_result:[7,11],_compon:11,_coordinate_desc:6,_copy_docstring_and_deprec:4,_depth:9,_fraction:9,_get_lin:4,_getitem_multilevel:4,_handl:3,_i:[0,1,2,5,6,8,11,12,13,18],_inference_funct:3,_interpolatefunctionerror:3,_is_primit:2,_j:[0,1,2,3,5,6,8,13],_jit_compil:3,_k:13,_l:12,_lambda:6,_leaf:9,_logist:[7,11],_m:10,_make_vjp:[2,13],_maybe_define_funct:3,_multilayer_perceptron:[0,1],_n:[2,5,8,11,13],_node:[2,9,13],_notokstatusexcept:3,_np:2,_num_output:3,_p:[5,8],_plot_arg:4,_r:3,_ratio:11,_sampl:9,_select_forward_and_backward_funct:3,_split:[6,9],_stateful_fn:3,_stateless_fn:3,_t:13,_test:6,_trace:[2,13],_valu:[2,13],_varianc:11,_weight:9,a0:3,a0faa0:[9,10],a1:0,a2:0,a3:0,a4:0,a_0:0,a_1a:0,a_2a:0,a_3:0,a_3a:0,a_4:0,a_4a:0,a_:[0,1,16],a_h:1,a_i:[0,1,2,12],a_j:[1,12],a_k:[1,12],a_ndim:2,aaron:20,ab:[0,2,5,13,14],ab_channel:15,abandon:1,abbrevi:17,abid:18,abil:[0,10],abl:[1,4,5,6,7,10,12,13,18],abort:18,about:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15,16,20],abov:[0,1,3,4,5,6,7,8,9,10,11,12,13,14,16,18],abovement:6,abscissa:13,absolut:[0,2,5,6,13],acceler:13,accept:[0,3,6,9],access:[0,3,11,18],accid:[4,6],accmod:5,accompani:0,accomplish:[8,9,13],accord:[0,1,2,5,6,9,12,13,14,18],accordingli:11,account:[0,3,5,13,18],accumul:[12,18],accur:[0,3,4,6,10,13,18],accuraci:[0,1,3,4,5,6,7,9,10,11,12],accuracy_scor:[0,1,10],accuracy_score_numpi:1,achiev:[0,1,5,6,8,12,16],aco:18,acquaint:15,acquir:[1,15],acr:0,across:[1,3,6,9,15],act:[1,3,16],action:18,activ:[0,2,3,4,9,17],actual:[0,1,4,5,6,8,11,16],ad:[0,1,3,4,5,8,13,16],ada_clf:10,adaboostclassifi:10,adadelta:13,adagrad:13,adam:[1,3,4],adapt:[0,4,6,13,20],add:[0,1,2,3,4,5,6,8,10,11,12,18],add_lin:4,add_outgrad:2,add_subplot:[1,7,12,14],addendum:5,addit:[0,2,3,5,6,7,8,9,10,12,13,15,16,18,19,20],addition:[12,13],address:[1,9,11,13,20],adjac:[3,12],adjoint:5,adjust:[0,5,12,13],admir:0,advanc:[4,6,12,20],advantag:[1,3,5,6,10,13,16],affect:3,affin:[0,3,8,11],afford:3,aforement:14,african:0,after:[0,1,2,4,5,6,9,11,12,13,15,16,18],afterward:0,ag:[0,7,17],ag_0:2,again:[0,1,4,5,6,7,8,10,11,12,13,18],against:[1,4,7,10],agegroup:7,agegroupmean:7,aggreg:[9,10],agorithm:10,agre:[5,6,18],ahead:9,ai:[0,20],aid:11,aim:[0,1,4,6,7,11,14,15,16],ainv:5,airplan:3,aka:5,al:[0,2,4,17,20],alarm:5,algebra:[0,3,5,13,15,17],algo:18,algorithm:[0,1,2,4,5,6,7,8,13,14,15,16,17,18,20],align:[0,2,5,6,7,8,13,18],all:[0,1,2,3,4,5,6,7,9,10,11,12,13,14,15,16,17,18,19,20],allevi:[1,13],alloc:[3,16],allow:[0,1,2,3,5,6,8,10,13,15,16],almost:[0,1,6,8,11,13,18],alon:[2,9],along:[2,3,4,5,6,9,10,11,15,16],alpha:[0,1,2,3,4,5,6,7,8,9,10,13,14,18],alpha_0:3,alpha_1:3,alpha_2:3,alpha_:10,alpha_i:[3,13],alpha_k:13,alpha_m:10,alpha_n:3,alpha_opt:13,alreadi:[2,3,4,5,6,10,12,15,16,18],also:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20],alter:[1,18],altern:[0,1,4,5,6,7,8,9,11,13,16],although:[1,5,6,8,10,13],alwai:[0,3,5,6,12,13,18],am:[0,4,18],ame2016:0,american:0,among:[0,3,5,9,10,12],amongst:5,amount:[0,1,3,4,6,8,10,14,15],an:[1,2,3,5,6,7,8,9,11,12,13,14,15,16,18,19,20],an_:18,anaconda3:[0,1,2,3,4,6,7,8,11,13],anaconda:[0,1,15],analog:13,analys:[6,18],analysi:[1,3,4,7,14,16,17,20],analyt:[0,2,3,5,6,7,12,13,15],analyz:[0,1,3,4,5,6,18],andrew:1,angl:[0,3,9,18],anharmon:3,ani:[0,1,2,3,4,5,6,7,8,9,10,12,14,18],anim:[4,12],ann:12,annot:[0,1,3,7,8],anoth:[0,1,3,4,5,6,7,8,10,11,12,13,16,18],anp:2,ans_vspac:2,ansatz:0,answer:[0,1,3,5,6,16],antialias:[2,6],anticip:4,anymor:[1,8],anyon:[4,8],anyth:[1,18],anytim:19,apach:1,apart:[11,13],api:[1,15],appar:2,appear:[0,1,3,13,16,18],append:[1,3,4,8,9,13,18],appendcon:5,appendvar:5,appli:[0,1,2,3,4,6,7,8,9,10,11,12,13,18,20],applic:[0,1,3,4,5,6,7,9,12,13,17,18,20],apply_gradi:4,approach:[1,2,4,5,6,9,10,11,12,13,15,18,20],appropri:[2,3,4,6,9,12,13,15,18],approx:[0,2,3,6,10,11,13,18],approxim:[0,1,2,3,4,5,6,7,10,11,13,18],apt:[0,15],aq:18,ar:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],arang:[1,3,4,6,7,9,10,12],arbitrari:[1,4,6,8,12,13,18],arbitrarili:[0,1,11],arc:6,architectur:[3,4,12,20],area:[0,3,6,9,20],arg:[2,3,4,13],argc:18,argmax:[1,11],argmin:[4,10,14],argnum:[2,13],argnum_0:2,argnum_1:2,argsort:11,argu:[1,13],argument:[0,2,3,5,6,11,12,13,18],argv:18,argval:2,aris:[0,6,12,13,18],arithmet:[0,13,16],arm:6,arma:18,armadillo:[16,18],around:[0,1,4,5,6,11,18],arr:2,arrai:[0,1,2,3,4,5,6,7,8,9,11,12,13,14,15,18],arrang:3,arraybox:13,arriv:[0,6,9,11,16,18],arrow:12,arrowprop:8,art3d:13,art:[0,1,15],articl:[0,3,4,6,10,18],artifici:[0,2,7,12,20],artificialneuron:12,arug:13,arxiv:[3,4],as_fram:0,asarrai:[0,6,9],asc:5,ascii:18,ask:[5,6,11,12],aspect:[0,6,15],assembl:[0,3],assert:4,assess:[0,6],assici:4,assign:[0,7,8,9,12,13,14,17,20],associ:[0,6,9,12,14,18],assum:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18],assumpt:[0,3,5,6,9,11,18],ast:[0,5,6],astyp:[4,9,10],asymmetri:0,asymptot:[4,6],async_wait:3,atoi:18,atom:0,attempt:[0,4,6,7,8,10],attend:17,attent:[0,16],attr:3,attract:[0,10],attribut:[0,9],attributeerror:[],audi:0,audio:[3,4],aurelien:[0,17,20],austfjel:6,author:[0,1,10,18],authour:0,auto:[9,10,18],autocor:18,autocorrelation_tim:18,autocorrelform:18,autocovari:18,autoencod:[4,15],autoencond:15,autograd:15,autom:[0,15],automac:16,automat:[0,1,2,3,4,11,15,16,17],automobil:3,autonom:[4,20],avail:[0,1,4,6,10,11,15,16,17,20],averag:[0,1,3,6,9,10,13,14,18,19],avg:18,avoid:[0,4,5,6,9,11,13,16],avx2:[3,4],avx:[3,4],awai:[2,3,6,18],awar:[2,10],award:19,ax:[0,1,2,3,4,6,7,8,9,10,11,12,13,14,16],axes3d:[2,6,13],axes_grid1:6,axessubplot:0,axhlin:8,axi:[0,1,2,3,4,6,7,8,9,10,11,12,13,14,16,18],axiom:5,axlabel:0,axvlin:[4,8],axvspan:4,b1:8,b2:8,b3:8,b:[0,1,2,3,4,5,6,8,9,10,12,13,14,18,19],b_1:[2,12,13],b_2:13,b_5:13,b_:[1,16],b_group:9,b_i:[0,1,2,12],b_ia_:0,b_index:9,b_is_vec:2,b_j:[1,12],b_k:[1,12,13],b_m:12,b_meta:2,b_score:9,b_valu:9,bachelor:17,back:[0,3,4,5,6,8,9,10,16,17,18],backbon:16,backend:[1,4],background:[17,20],backpropag:1,backtrack:9,backup:16,backward:[1,2,4,12,16],backward_pass:2,bad:[6,18],badli:18,bag:[9,15,17],bag_clf:10,baggingboot:10,baggingclassifi:10,baggingtre:10,balanc:6,band:16,bandwidth:16,bar:[0,6,11],barber:20,bare:[4,10],base:[0,1,3,4,5,7,8,9,10,14,15,18,19,20],basi:[5,7,8,10,11,12,13,16],basic:[6,8,12,13,14,15,17,18],batch:[3,4,11,12,13],batch_shap:4,batch_siz:[1,3,4],batchnorm:4,bay:7,bayesian:[5,15,20],becaus:[0,1,2,3,4,5,6,8,9,12,13,14],becom:[0,1,2,5,6,7,9,12,13,18],been:[0,1,2,3,4,5,6,11,12,13,15,16],befor:[0,1,2,3,4,5,6,7,8,12,13,14,16,18],beforehand:[0,18],begin:[0,1,2,3,4,5,6,7,8,9,11,12,13,14,16,18],behav:[1,6,13],behavior:[0,1,13],behaviour:12,behind:[0,1,6,8,13],being:[0,1,2,3,4,5,7,8,10,11,12,13,18],believ:[9,16],belong:[5,7,8,9,13,14],below:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,16,18],benchmark:10,bendik:19,benefici:[1,13],benefit:[0,1,4,11,13,15],bengio:[1,17,20],benign:[1,7,9],besid:[4,5],bessel:5,best:[0,1,2,3,4,5,6,7,8,9,10,12,13,18,19],beta:[0,1,3,5,6,7,10,11,13],beta_0:[0,1,3,5,6,7,13],beta_0x_:0,beta_1:[0,1,3,5,6,7,10,13],beta_1x_0:0,beta_1x_1:[0,7],beta_1x_2:0,beta_1x_:0,beta_1x_i:[7,13],beta_2:[0,3,13],beta_2x_0:0,beta_2x_1:0,beta_2x_2:[0,7],beta_2x_:0,beta_3:3,beta_:[0,3,6,7,13],beta_i:[0,3,5],beta_j:[0,5,6,13],beta_k:13,beta_linreg:13,beta_m:10,beta_mg_m:10,beta_n:3,beta_p:7,beta_px_p:7,betavalu:5,better:[0,1,2,3,4,6,9,10,11,12,13],between:[0,1,2,3,4,5,6,7,8,9,11,12,13,14,18],beyond:[0,1,5,6,8,13],bf:[13,14,16,18],bgd:13,bia:[0,1,2,3,5,8,9,10,12,13,17,18],bias:[1,2,3,5,6,9,12],big:[0,1,2,5,6,14],bigger:[1,6],bigr:12,bike:9,bilek:19,billion:[3,12,15],bin:[0,7,18],binari:[0,3,4,5,7,9,10,12,17,18],binarycrossentropi:4,bind:0,binomi:15,binsboot:6,bioinformat:0,biolog:[1,12,20],bios1100:15,bird:[0,3],bishop:[17,20],bit:[1,4,16,18],bitwis:18,bivari:2,bk:[0,13],bla:[5,16],black:[8,9,14],block:[6,10,15,16],blockingavg:18,blockingstd:18,blockingvar:18,blocksiz:18,blocksizemax:18,blocksizemin:18,blogpost:4,blue:[0,3],bmatrix:[0,1,3,5,7,8,11,13,16],bmi:1,bodi:[0,1,4,12],bold:1,boldfac:[0,5],boldsymbol:[0,1,2,3,5,6,7,8,10,11,13,14],boltzmann:[12,15],book:20,boost:[1,9,15,17],boostrap:10,bootavg:18,bootstd:18,bootstrap:[1,13,15,17],bootvar:18,bootvec:18,boston_dataset:0,bot:8,both:[0,1,4,5,6,8,9,10,13,14,15,16,18,19],bottl:7,bound:[0,5,8,12],boundari:[2,4,8,11,12],boundkei:5,box:[4,9],boxed_arg:2,boyd:[8,13],bracket:[4,18],brain:[1,7,12],branch:9,breast:[5,7,11],breviti:13,brew:[0,15],brg:8,briefli:0,bring:[0,5,6,10],broad:0,brownle:4,brute:[3,5,11],bs:[8,9,10],buffer_s:4,bui:4,build:[0,4,5,6,10,13,16,18],built:[0,1,3,4,6],bunch:11,busi:0,bx:5,bzl:5,c1:[8,11],c2:[8,11],c:[0,1,2,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19,20],c_0:18,c_1:12,c_2:12,c_3:12,c_4:12,c_:[0,8,9,10,13,18],c_i:[12,13],c_k:18,ca:1,cach:10,cal:[0,8,10,12,13],calcul:[0,1,2,4,5,6,8,9,10,11,12,13,14,16],california:0,call:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20],callabl:3,callback:3,calor:0,cambridg:[13,20],can:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,20],cancel:[0,13],cancellation_manag:3,cancer:[5,10],cancerpd:7,candid:[8,9,10],cannot:[0,1,4,5,6,7,8,9,17,18],canopi:[0,15],cap:5,capabl:[0,1,8,13,15],capac:2,capita:0,captur:[4,11,12],captured_input:3,car:[3,4],card:[0,7],cardin:1,care:11,carefulli:13,carlo:[0,6,15,18,20],carri:[2,6,7],cart:10,casella:20,cast:[1,4],cat:[3,4],categor:[0,1,3,9,11],categori:[0,1,3,7,10,12,14,17],categorical_crossentropi:[1,3],caus:[0,5,6,18],causal:0,causat:0,cax:1,cb:6,cbar:1,cbook:4,cc:[0,1,3,4,5,13],ccc:[5,12],cd_fast:6,cdf:18,cdot:[0,2,6,12,13,14,16,18],celebr:13,cell:4,center:[0,1,6,7,8,9,11,14,18],centr:20,central:[0,3,5,6,8,16],centroid:[14,18],centroid_differ:14,centuri:3,certain:[0,3,6,7,9,18],cg:13,cha:0,chain:[1,13,15,18],chanc:[1,5,13,18],chang:[0,1,2,3,4,5,6,8,9,11,12,13,14,16,18],channel:3,chapter:[0,6,10,11,16,17,20],charact:[0,3,5,18],character:[8,9,10,12,18],characterist:[0,1,3,10,13],charg:0,charl:0,chase:4,chd:7,chddata:7,cheap:5,cheaper:[1,13],check:[0,1,3,4,5,6,11,13,16],checkmark:3,checkpoint:4,checkpoint_dir:4,checkpoint_prefix:4,chemic:18,chen:10,chiaramont:2,choic:[0,1,2,3,4,6,9,12,13,14,16,18],choleski:[5,16],choos:[2,3,6,9,10,11,13,14,18],chosen:[0,1,2,6,8,9,10,13,18],chosen_datapoint:1,christian:20,christoph:[17,20],cifar10:3,cifar:3,cin:18,circ:[1,12],circl:[0,8,12],circuit:3,circumfer:9,circumv:[1,5,13],ckpt:4,clariti:18,class_nam:[3,9],class_val:9,class_valu:9,class_weight:3,classic:[7,9,13],classif:[0,3,5,6,7,8,11,12,15,17,20],classifi:[0,1,4,7,9,10,11],classificaton:1,classifii:10,clean:1,clear:[1,5,10,12,13],clearli:[0,3,5,6,7,8,18],clever:[1,10],clf3:0,clf:[0,6,8,9,10],clf_lasso:6,clf_ridg:6,clip:[3,18],close:[0,1,2,4,6,8,9,11,12,13,14,18,20],closer:[3,5,13],closest:[8,11,13,14],closur:15,cloud:15,cluster:[0,1,4,6,11,15,17],cluster_label:14,cm:[1,2,3,6,8,9,13],cmap:[0,1,2,3,4,6,8,9,10],cmap_arg:6,cmath:18,cmb:17,cmd:9,cmu:0,cn_:18,cnn:[12,17],cnn_kera:3,cntk:15,co:[0,2,3,6,9,13],code:[3,4,6,7,8,13,15,16,17,20],coef0:8,coef:0,coef_:[0,5,6,8,9,13],coeff:5,coeffici:[0,3,5,6,7,8,9,13,16],coerc:[0,6],coin:[10,18],coin_toss:10,col:[0,11],colab:15,cold:9,colinear:0,collaps:8,collect:[0,2,6,10,11,15,18,20],collinear:5,color:[0,3,4,6,8,9,10,18],color_channel:3,color_cod:6,colorbar:[1,6],colsample_bytre:10,colsaobject:10,column:[0,1,2,4,5,6,7,8,9,11,12,16],columntransform:9,com:[4,6,15,19,20],combin:[1,2,5,6,7,10,18],come:[0,1,3,4,5,12,13,14,17],command:[0,1,9,18],comment:[0,4,5,6],commerci:[0,15],commod:0,common:[0,1,3,5,6,7,9,11,13,14,18],commonli:[0,1,4,6,7,9,13,14],commun:[0,12],commut:3,commutatitav:3,compact:[0,1,3,5,6,7,9,11,12,13,14],compar:[0,3,4,5,6,11,13,16],comparison:[2,4,13],compat:7,compet:0,competit:10,compil:[0,1,3,4,15,16,18],complet:[0,2,3,4,9,12],completenn:12,complex:[1,5,8,9,11,12,13],complic:[0,1,9,13],compon:[0,1,3,4,5,6,7,9,14,15,17],components_:11,compos:[9,12,14],compphys:[6,15,17,20],compress:0,compris:6,compromis:5,compulsori:15,comput:[0,1,2,3,4,5,6,7,8,10,11,12,13,15,16,17,20],computation:[0,3,6,9,13,18],con:5,concaten:[2,4,6,14],concav:[1,9,13],concentr:[0,10],concept:[0,2,15],conceptu:[12,13],concern:[0,1,4,7],conclud:[0,5,13],conclus:1,cond:2,conda:[0,1,15],condit:[0,2,4,5,6,8,9,11,13,18],conduct:15,condwav:2,coneqp:5,confid:[0,5,6,7,8],configur:3,confirm:[5,12],confus:[5,6,10,16],confusion_matrix:9,congruenti:18,conjug:[4,8],conjugaci:13,conjunct:3,connect:[0,1,3,4,9,11,12,13,16],consequ:[5,6,8,10,12,13],conserv:[5,14],consid:[0,1,2,3,5,6,7,8,9,10,12,13,16,18],consider:[0,1,5,13],consist:[0,1,2,3,4,6,12,13,18],constant:[0,2,4,5,6,8,12,13,18],constitu:0,constitut:[2,6],constrain:[1,3,5,7,11],constraint:[5,6,8,13],construct:[0,1,2,3,5,6,7,8,9,10,11,16,18,20],contact:0,contain:[0,2,3,4,5,6,7,8,9,11,12,13,16,18,20],contemporari:20,content:[1,15,16],context:[3,6,10,13],contigu:16,continu:[0,1,2,3,4,5,6,7,8,9,10,12,13,16],contour:[9,10,13],contourf:[8,9,10],contrast:[1,4,9,10,12],contribut:[0,3,5,13,18],contributor:0,control:[0,1,3,9,13,15],conv2d:[3,4],conv2dtranspos:4,conv:[3,4],conveni:[0,5,6,12,13,16],convent:12,converg:[0,1,2,4,5,6,7,8,11,13,14],convergencewarn:[0,1,6,7,8,11],convert:[0,1,4,5,9,11,13,16],converttomatrix:4,convex:[4,5,7],convinc:13,convolut:[1,4,15,17],cool:[4,9],coolwarm:6,coordin:[5,12,14],coorel:0,copi:[0,1,2,14],core:[2,3,4,10,13],corel:0,coronari:7,corr:[0,5,7,11],correalt:[11,15],correct:[0,1,2,3,4,5,13,16,18],correctli:[1,2,6,10],correl:[0,1,3,5,6,7,10,12,13,15],correlation_matrix:[0,5,7,11],correspond:[0,3,5,6,8,9,11,12,15,16,18],cortex:12,cosin:[3,6],cost:[0,2,3,5,6,7,8,9,12,13,18],cost_deep_grad:2,cost_funct:2,cost_function_deep:2,cost_function_deep_grad:2,cost_function_grad:2,cost_grad:2,cost_sum:2,costol:13,could:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,16,18],coulomb:0,count:[0,9,17,18,19],countor:13,coupl:[4,5,6],cours:[0,1,3,5,11,17,18],courvil:[17,20],cout:18,cov:[5,6,11,16,18],cov_xi:[5,11],cov_xx:[5,11],cov_yi:[5,11],covari:[0,7,15,16],covariance_matrix:[5,11,14],cover:[0,5,15,17,20],covert:0,covxi:18,covxx:18,covxz:18,covyi:18,covyz:18,covzz:18,cpu:[1,3,4],cpu_feature_guard:[3,4],craft:3,creat:[1,2,3,4,5,6,9,10,11,12,13,15],create_biases_and_weight:1,create_convolutional_neural_network_kera:3,create_neural_network_kera:1,create_x:[5,11],credit:[0,7],crim:0,crime:0,criteria:[0,4,9,10,14,18],criterion:[9,10,13],critic:[3,4,6],cross:[0,1,3,7,9,10,13,15,17,18],cross_entropi:4,cross_val_scor:6,cross_valid:[7,10],crossvalid:6,crucial:[1,18],cs231:3,cs:17,csr_matrix:16,cstdlib:18,csv:[0,4,6,7,9],ctnk:1,ctx:3,cubic:0,cumbersom:5,cumsum:[10,11],cumul:10,cumulative_heads_ratio:10,cup:5,current:[1,2,3,4,6,13,14],curs:0,curv:[6,7,10,12],curvatur:13,custom:[5,6,14],custom_cmap2:[9,10],custom_cmap:[9,10],cutpoint:9,cv:[6,7,10],cvxbook:13,cvxopt:[5,8],cyber:20,cycl:[1,12,18],d1:5,d2:5,d2_g_t:2,d3:5,d:[1,2,3,4,5,6,7,8,9,10,11,13,14,16,18,19],d_f:13,d_g_t:2,d_net_out:2,da:3,dagger:[5,16],dai:[1,9,15],dalen:19,damp:3,darget:9,darkr:18,dat:0,dat_id:[0,6,7,9],data1:14,data2:14,data3:14,data4:14,data:[2,4,5,8,10,12,13,14,16,20],data_handl:3,data_id:[0,6,7,9],data_indic:1,data_modul:0,data_path:[0,6,7,9],data_url:0,databas:1,datafil:[0,6,7,9],datafram:[0,4,5,7,9,11],datapoint:[1,5,6,7,11,13],dataset:[0,4,6,7,8,9,10,11,13,14],datatyp:4,date:0,daughter:10,david:20,dbh:1,dbo:1,dcomposit:16,ddot:2,dead:1,deadlin:17,deal:[0,1,3,5,6,8,11,13,14,16,18],debt:7,debug:[5,6],decad:[0,3],decai:[0,13,18],decemb:17,decent:10,decid:[0,2,3,5,6,9],decim:0,decis:[0,1,8,11,15,17,20],decision_funct:8,decision_tre:9,decisiontreeclassifi:[9,10],decisiontreeregressor:[0,9,10],declar:[0,4,16],decompos:[5,6,16],decomposit:[0,6,12,17],decompost:5,deconvolut:3,decorrel:[10,13],decreas:[1,2,4,5,6,10,11,13],deduc:0,deep:[3,4,7,12,13,15,17,20],deep_neural_network:2,deep_param:2,deep_tree_clf1:9,deep_tree_clf2:9,deep_tree_clf:[9,10],deepen:[5,15],deeper:[0,3,4],deeplearningbook:20,deer:3,def:[0,1,2,3,4,5,6,7,8,9,10,11,13,14,18],def_covari:18,def_funct:3,default_tim:4,defect:5,defici:5,defin:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18],definit:[1,2,4,5,6,8,10,11,12,13,16],defint:18,defun:3,defvjp:2,degre:[3,5,6,8,9,10,11,18],del:1,delet:[6,18],delimit:4,deliv:17,delta:[0,2,3,6,8,12,13,14,18],delta_0:3,delta_1:3,delta_2:3,delta_3:3,delta_4:3,delta_5:3,delta_:[1,16],delta_h:[0,1],delta_j:[3,12],delta_k:12,delta_l:[1,3],delta_n:[0,3],delug:15,delv:0,demand:13,demonstr:[0,3,5,6,7,11,12,15],den:4,denomin:[1,5],denot:[1,2,6,7,13,18],dens:[1,3,4],dense_1:4,densiti:[0,2,6,18],depart:19,depend:[0,1,2,4,5,6,7,8,11,12,13,15,18],depict:18,deploy:[0,15],deprec:[0,2,3,6,13],depth:[0,3,9,10,16],deriv:[0,1,2,6,7,8,10,11,13,15],derivati:13,descend:[5,9,11],descent:[0,1,3,7,8,12,17],descr:0,describ:[0,2,4,5,6,8,10,11,12,13,16],descript:[0,8,9],design:[0,1,3,4,5,6,7,10,11,12,13],designmatrix:0,desir:[0,2,4,5,13,14],despit:[1,12],destroi:16,det:[5,16],detail:[0,6,11,13,14,16],detect:[3,8,12],determin:[0,2,3,4,5,6,8,9,10,11,12,13,16,18],determinist:[7,13,18],dev:[1,18],develop:[0,3,5,8,10,11,12,15,16,17],deviat:[0,1,2,4,5,6],device_nam:3,devis:12,df:[4,8,11,13],di:[0,5],diag:[5,8],diagnost:[1,10],diagon:[0,5,7,13,16,18],diagonaliz:5,diagram:10,diagsvd:6,dice:6,dict:[6,8],dict_kei:0,dictionari:0,did:[0,1,5,6,7,10,11,14],die:1,diff1:2,diff2:2,diff:2,diff_ag:2,diffeent:8,differ:[0,1,2,3,4,5,6,9,10,11,12,13,14,15,16,18,20],differenti:[3,15,16,17],differential_oper:[2,13],difficult:[0,1,6,10,13,18],difficulti:[0,1,13],diffonedim:2,digit:[0,1,3,4,6,17,19],dilemma:13,dilut:1,dim:[4,11,14,16],dimens:[0,1,2,3,4,5,8,9,11,14,16],dimension:[0,4,5,6,9,11,13,14,15,16],dimensionless:[0,3],diment:16,dimnsion:4,diod:3,direct:[0,1,2,4,11,12,13,14],directli:[1,4,5,6,18],directori:9,disabl:3,disadvantag:0,disappear:[3,6],disc_loss:4,disc_tap:4,discard:[6,11],disciplin:[0,3,12],disclaim:18,discourag:[0,13],discov:0,discover:5,discret:[1,3,5,7,13],discrimin:[4,7,10,11],discriminator_loss:4,discriminator_loss_list:4,discriminator_model:4,discriminator_optim:4,discuss:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20],diseas:7,disguis:6,disord:[1,7],displai:[0,1,3,4,5,6,7,8,9,10,11,12,14,18],displaystyl:[0,5],displot:0,disregard:0,dissimilar:[11,14],dist:14,distanc:[0,8,9,11,14,18],distance_list:9,distinct:[3,7,8,9,10,14],distinctli:8,distinguish:[0,4,7,8,18],distplot:0,distribut:[0,1,4,6,7,10,11,13,14,15,16],distrubut:[0,15],div:5,dive:[0,8],diverg:[1,13],divid:[0,1,3,5,6,8,9,11,12,18],divis:[6,8,9,13,16,18],dna:7,dnn1:4,dnn2_gru2:4,dnn:[0,1,2,4,12],dnn_kera:1,dnn_model:1,dnn_numpi:1,dnn_scikit:[0,1],doc:[6,15,17,20],document:[0,4,7,11,13],doe:[0,1,2,3,4,5,6,8,10,11,12,13,16,18],doesn:[3,9,12],dog:[1,3,4],domain:[5,8,13],domin:0,don:[0,1,3,5,6,8,11,13,15,18],done:[0,2,3,4,5,6,9,10,11,13,16,18],dot:[0,2,3,5,6,7,8,9,10,11,12,13,16,18],doubl:[3,4,16,18],doubli:1,down:[0,3,6,9,11,12,13],download:[0,1,3,5,6,16,20],downsampl:3,dozen:1,dq:6,drag:13,dramat:11,drastic:4,draw:[4,6,10,13],drawback:[0,1,3,13],drawn:[1,4,6,7,11,18],drive:[3,4],driven:3,drop:[0,1,5,6,11,13,18],dropna:[0,6],dropout:4,ds:[0,5],dt:[2,3,13,18],dtype:[0,1,2,3,4,14,16],dualiti:6,dub:0,due:[1,2,5,6,8,10,12,13],dummi:0,dure:[0,1,3,4,8,9,11,15],dwell:0,dwh:1,dwo:1,dx:[2,3,8,18],dx_1:18,dx_1p:6,dx_2p:6,dx_mp:6,dx_n:18,dxp:6,dy:[1,8,18],dynam:4,dz:8,e:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,18,19],e_:[0,2],each:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],eager:3,eapprox:0,earli:[1,3,13],earlier:[0,5,7,8,9,11,12,13],earthexplor:6,eas:[6,9,14],easi:[0,5,6,7,8,9,10,11,12,13,15,16],easier:[5,6,8,9,13,18],easiest:13,easili:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,16],eastern:19,ebind:0,eblock:9,economi:5,ecosystem:15,ect:17,edg:3,edgecolor:6,edu:[0,13],educ:0,eff:18,effect:[1,4,10,13,18],effic:1,effici:[0,3,10,13,15,16,18],efron:[6,18],egrad:13,eig:[5,11,13,16,18],eigen:18,eigenpair:[5,11],eigenvalu:[0,5,8,11,13,16],eigenvector:[5,11,13],eight:16,eigval:[16,18],eigvalu:[11,13],eigvec:[16,18],eigvector:[11,13],eispack:16,either:[0,1,5,6,7,8,9,10,11,13,18],ekstrom:19,elabor:18,elarn:3,electr:[0,3,12],electur:20,eleg:11,element:[1,2,3,4,5,6,7,8,11,12,13,15,16,17,20],elementari:[10,13,16],elementwis:[3,13],elementwise_grad:[2,13],elif:[2,3,14],elim:16,elimin:[3,5,8],els:[1,2,3,4,7,9,12,13,16,18],elu:1,elus:0,email:[17,19],embed:[0,11],embodi:6,emit:18,emner:[17,20],emphas:[0,10,15],emphasi:[0,15,20],empir:[1,11,18],emploi:[0,1,5,6,11,13,18],employ:0,empti:[6,10],emul:12,en:[15,20],enabl:[3,4,11],enbodi:6,encod:[0,3,5,9,11,14],encompass:[0,18],encount:[0,1,5,6,7,13,18],end:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18],end_box:[2,13],end_nod:[2,13],end_valu:[2,13],endl:18,endpoint:[3,6,18],energi:[0,4,6],enet_coordinate_desc:6,enforc:12,eng:20,engin:[0,1,3,4,15,18],english:20,enorm:3,enough:[0,6,13],ensembl:[1,9,17,18],ensur:[0,1,2,3,5,6,11,13,18],ensure_initi:3,enter:[5,6,18],enthought:[0,15],entir:[1,3,7,9,15,18],entiti:[9,12,16],entri:[0,5,8,11,12,16],entropi:[1,3,7,10,13],enumer:[0,1,2,3,4,6,8],env:[5,18],environ:[2,15,20],eo:[0,6],eol:0,eosfit:0,epoch:[0,1,3,4,12,13],epsilon:[0,5,6,7,13],epsilon_0:0,epsilon_1:0,epsilon_2:0,epsilon_:0,epsilon_i:0,eq:[3,13,14,16,18],eqnarrai:[3,5,6],equal:[0,1,2,3,4,5,6,8,9,11,12,13,14,16,18],equat:[1,3,4,5,6,7,8,9,10,11,13,14,16,17,18],equilibrium:[2,12],equiv:[3,13,16,18],equival:[0,1,5,8,11,13,15,16],erf:18,err:[0,4,10],err_:6,err_sqr:2,errat:13,errno:9,erron:2,error:[1,2,4,5,6,7,9,11,12,13,15,16,18],error_estimate_corr_tim:18,error_hidden:1,error_output:1,escap:13,especi:[1,3,9,12,13],essenti:[0,5,6,9,10,12,14,17,18],establish:[0,6,10,11],estim:[0,1,5,6,7,10,11,13,15,18],estimated_mse_fold:6,estimated_mse_kfold:6,estimated_mse_sklearn:6,et:[0,2,4,17,20],eta0:[8,13],eta:[0,1,3,8,12,13],eta_:13,eta_t:13,eta_v:[0,1,3],etc:[0,1,3,5,7,8,9,11,12,13,14,15,16,18],ethic:[0,15],etsim:6,euclidean:[0,14],evalu:[0,2,3,4,5,6,9,13,18],evalut:13,even:[0,1,3,4,5,6,8,9,10,11,12,13,14,15,16,18],evenli:4,event:[5,7,10],eventu:[5,6,11,12,13,19],everi:[0,1,2,3,4,5,6,9,10,11,12,13,14,15,18],everyth:[4,12],everywher:[4,13],evolv:0,exact:[0,2,5,11,12,13,16,18],exactli:[0,3,4,6,12,15],examin:6,exampl:[5,11,12,13,15,16,17,20],exce:[1,12,13],excel:[0,1,4,5,10,20],except:[3,4,5,6,8,9,16,18],excess:0,excit:0,exclud:[1,6,12],exclus:[0,1,3,6,18],execut:[2,3,5,13],executing_eagerli:3,exemplifi:13,exercis:[5,15,17],exhaust:6,exhibit:[0,5,6,8],exist:[0,1,2,3,5,6,7,8,9,13,16,20],exit:[5,16,18],exp:[0,1,2,5,6,7,8,10,11,12,13,18],exp_term:1,expand:[5,7,11,13],expans:[0,3,5,8,10,12,13],expect:[0,1,5,6,7,11,12,13,15],expectation_value_of_h_wrt_p:18,expens:[6,10,13,18],experi:[0,1,6,8,13,15],experiment:[0,4,6,9,18],experimental_get_tracing_count:3,expert:[1,9],explain:[0,6,9,10,11,13,18],explained_variance_ratio_:11,explanatori:0,explicit:[0,3,6,13,16],explicitli:[0,4],explod:1,exploit:[0,3,12,13],explor:[1,4,6,8,13,15],expon:1,exponenti:[0,1,5,6,10,13],export_graphviz:9,export_text:9,exporttext:9,expos:15,express:[0,2,3,5,6,7,10,12,13,16,18],exptmean:18,exptvari:18,extend:[2,5,7,11,13,15],extens:[0,12,15],extent:[0,1,6,20],extern:[3,6,9],extra:[1,3,5],extract:[0,3,5,6,7,8,11,13,16],extrapol:0,extrem:[0,1,4,5,6,7,8,9,13,16],extremum:13,extrins:11,ey:[0,5,6,13,14,16],f11:0,f12:0,f13:0,f1:13,f1_grad:13,f1d:13,f2:13,f2_grad_x1:13,f2_grad_x1_analyt:13,f2_grad_x2:13,f2_grad_x2_analyt:13,f3:13,f3_grad:13,f3_grad_analyt:13,f4:13,f4_grad:13,f4_grad_analyt:13,f5:13,f5_grad:13,f6:13,f6_for:13,f6_for_grad:13,f6_grad_analyt:13,f6_while:13,f6_while_grad:13,f7:13,f7_grad:13,f7_grad_analyt:13,f8:13,f8_grad:13,f9:[0,13],f9_altern:13,f9_alternative_grad:13,f9_grad:13,f:[0,1,2,3,4,5,6,7,8,10,12,13,14,16,18,19],f_0:[3,10],f_1:[10,13],f_2:[12,13],f_3:12,f_:10,f_d:18,f_grad:13,f_grad_analyt:13,f_i:[6,12],f_m:[3,10],f_n:3,f_raw:2,f_vec:2,f_wrap:2,face:13,facecolor:[6,8,18],facil:[0,15],facilit:12,fact:[0,1,3,5,9,11,12,13],factor:[0,1,3,5,6,9,10,11,13,16,18],factori:13,fade:6,fafab0:[9,10],fail:[0,6,7,8,11,13,19],failur:7,fairli:[1,2,18],fake:4,fake_loss:4,fake_output:4,fall:[8,9,17],fals:[0,1,2,3,4,5,6,7,9,10,13,14,16],famili:[0,7,8,18],familiar:[0,3,5,6,8,15,16,18],famou:[6,12,16],far:[0,3,4,5,6,8,11,12,13,14,18],fashion:[0,9,10],fast:[1,3,6,10,12,13,15,18],faster:[1,11,13],fastest:[13,16],favor:7,favorit:18,fc:3,featur:[0,1,3,5,6,7,8,10,11,12,13,15,18],feature_nam:[0,1,7,9],feautur:9,fed:1,feed:[0,2,3,11,15,17],feed_forward:1,feed_forward_out:1,feed_forward_train:1,feedback:4,feeddorward:4,feedforward:[1,4,12],feel:[0,5,6,11,13,15,19],feet:0,fetch:[0,6],fetch_california_h:0,fetch_openml:0,few:[1,3,4,5,9,18],fewer:[0,9,11],ffnn:[1,12],field:[0,3,6,12,15],fifth:[0,6],fig:[0,1,2,3,4,6,7,12,13,14],fig_id:[0,6,7,9],figaxi:18,figsiz:[0,1,2,3,4,6,7,8,9,10],figur:[0,1,2,3,4,5,6,7,8,9,10,12,13,14,15],figure_id:[0,6,7,9],figurefil:[0,6,7,9],file:[0,1,2,4,5,6,7,9,16,18],file_prefix:4,filenam:[0,18],filenotfounderror:9,fileout:18,fill:[5,9],filter:[3,4],filtered_flat_arg:3,financ:0,find:[0,1,2,3,5,6,7,8,9,10,11,12,13,14,15,18],fine:[0,14],finish:2,finit:[3,5,6,12,13,18],first:[0,1,2,3,5,6,7,8,9,10,11,13,14,16,17,18,20],firsteigvector:11,fit:[1,3,4,5,6,7,8,9,11,12,13,18],fit_beta:6,fit_intercept:[0,5,6],fit_mod:9,fit_transform:[0,6,8,9,11],fiti:0,five:[0,9],fix:[0,3,4,6,10,11,12,13],fixedformatt:6,fixedloc:6,fkkt:5,flag:[3,4],flat:[12,13],flatten:[1,3,4,5,16],flexibl:[0,1,6,8,10,12],float32:[4,9],float64:[0,4,16],flop:[5,16],flow:[1,4,12],fluctuat:5,fly:11,flyvbjerg:18,fm:0,fma:[3,4],fmax:3,fmesh:13,focu:[0,3,4,5,6,15,20],focus:[1,6,7,16],fold:[6,9],folder:[0,1,2,3,4,5,6,8,9,10,13,16,18],follow:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],font:[0,7,18],fontdict:18,fontsiz:[1,6,8,9,10,18],fontweight:1,footprint:3,foral:8,forc:[0,5,6,10,11],forcast:4,forecast:[4,12],forelesningsvideo:17,forest:[0,1,9,15,17],forget:11,form:[0,3,4,5,6,7,8,9,11,12,13,15,16,18],formal:[3,4,14,18],format:[0,1,2,3,4,6,7,8,9,10,11,15,18,20],format_data:4,formatstrformatt:[6,13],formul:[4,6,11,14],formula:[3,13,18],forth:[4,12],fortran2003:15,fortran90:18,fortran:[0,15,16],fortun:[0,11],forward:[0,3,6,15,16,17],forward_backward:3,found:[1,2,4,5,6,9,12,13],foundat:15,four:[4,5,6,8,12,16,17],fourier:0,fourierdef1:3,fourierdef2:3,fourierseriessign:3,fourth:12,fr:5,frac:[0,1,2,3,5,6,7,8,9,10,11,12,13,14,16,18],fractal:9,fraction:9,frame:[4,7],framework:[1,8,10,18],frank:[5,11],frankefunct:[5,6,11],free:[0,6,11,13,15,16,18,19,20],freecodecamp:15,freedom:5,freeli:0,frequenc:[3,6,7,18],frequent:[0,8,9,13],frequentist:15,fresh:10,fridai:17,friedman:[6,17,20],friendli:4,frog:3,from:[0,1,2,3,4,6,7,8,9,11,13,14,15,16,17,18,19,20],from_cod:9,from_logit:[3,4],from_tensor_slic:4,front:[0,4,5],fstream:18,fulfil:[2,5,12],full:[0,1,3,5,7,9,10,13,18],full_matric:5,fulli:[3,6,12,17,18],fun:[2,13,15],fun_nam:2,func:[0,2],functionali:11,fundament:[0,6,15],funtion:2,further:[0,2,9],furthermor:[0,3,5,6,7,11,12,13,15],futur:[0,4,8,9],futurewarn:0,fx:5,fy:[17,19],g0:2,g42mrgv128v34gnnhxwk9nrc0000gp:[1,2,3,4,5,6,8,9,10,13,16,18],g:[0,1,2,3,4,5,6,8,9,10,11,13,18],g_0:2,g_1:[2,10],g_2:[2,10],g_:[2,9,10],g_analyt:2,g_dnn_ag:2,g_euler:2,g_i:2,g_m:[3,10],g_n:3,g_re:2,g_t:2,g_t_d2t:2,g_t_d2x:2,g_t_dt:2,g_t_hessian:2,g_t_hessian_func:2,g_t_jacobian:2,g_t_jacobian_func:2,g_trial:2,g_trial_deep:2,g_vec:2,gain:[1,5,9,10,13],galleri:0,game:4,gamma1:8,gamma2:8,gamma:[0,2,8,9,10,11,13],gamma_0:10,gamma_1:10,gamma_1x:10,gamma_:0,gamma_i:[0,8,18],gamma_j:13,gamma_k:13,gamma_m:10,gamma_x:0,gap:[6,8],gate:[4,12],gather:[0,1,12],gaug:12,gaussbacksub:16,gaussian:[4,5,6,8,14],gaussian_point:14,gaussian_rbf:8,gave:13,gbc:17,gca:[2,4,6,8,13],gd:1,gd_clf:10,gdclassiffiercgain:10,gdclassiffierconfus:10,gdclassiffierroc:10,gdm:13,gdregress:10,ge:[1,5,7,18],gemv:5,gen:18,gen_loss:4,gen_tap:4,gender:0,genener:4,gener:[0,1,2,3,5,6,8,10,11,12,13,14,16,20],generallay:12,generate_and_save_imag:4,generate_imag:4,generate_latent_point:4,generate_simple_clustering_dataset:14,generated_imag:4,generator_loss:4,generator_loss_list:4,generator_model:4,generator_optim:4,genexpr:[],genom:15,geodes:11,geometr:[0,13],geometri:5,georg:20,geotif:6,geq:[2,5,8,9,13],geron:[0,17,20],get:[0,1,2,3,4,5,6,7,9,10,11,13,15,16,18],get_dummi:9,get_loc:4,get_next_color:4,get_paramet:2,get_split:9,get_yaxi:8,get_yticklabel:6,getsolutionslic:5,getval:2,gg:18,gibb:15,gif:4,gini:10,gini_index:9,git:[0,15],github:[0,6,15,17,20],gitlab:[0,15],give:[0,1,2,3,5,6,7,8,9,10,12,13,14,15,17,18,20],given:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18],global:[6,7,13,18],glorot:1,gmail:19,go:[0,1,3,5,6,8,9,11,12,13],goal:[0,7,9],goe:[0,1,2,5,6,13,14,16],golden:13,gone:5,gong:1,good:[1,3,4,5,6,9,10,11,13,15,17,18,20],goodfellow:[4,17,20],googl:[1,4,15],got:[1,6],gov:6,gp:20,gpu:1,grad:[2,13],grad_analyt:13,grade:17,gradient:[0,3,4,7,8,9,12,15,17],gradientboostingclassifi:10,gradientboostingregressor:10,gradients_of_discrimin:4,gradients_of_gener:4,gradienttap:4,gradual:[1,14],grai:[4,6],graph:[1,9,11,12,13],graph_from_dot_data:9,graph_funct:3,graphic:[0,1,9],grasp:0,gray_r:[1,3],grayscal:3,great:[5,13],greater:[1,7,18],greatli:13,greedi:9,green:[0,3,9,18],grei:4,grid:[1,3,6,7,8,12,18],grossli:13,ground:0,group:[0,6,7,9,14,15,17],groupbi:0,grow:[1,3,9,10],growth:0,gru:4,guarante:[0,3,4,13,18],guess:[1,4,10,13,14],guestrin:10,guid:1,h1:2,h21:17,h:[0,1,5,6,8,13,18,20],h_1:[2,13],h_2:[2,13],h_:[0,13],h_m:10,ha:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18],habit:0,had:[0,1,6,7,13],hadamard:[1,12],half:[1,8,9],halv:10,hand:[0,1,2,3,5,11,12,13,15,16,17,18,20],handi:3,handl:[0,1,2,5,9,11,15],handle_unknown:9,handsid:12,handwrit:12,handwritten:[1,5],happen:[1,2,3,4,5,6,10,13,18],hard:[1,7,8,10,13],hardcopi:15,harder:[0,1],harmon:3,hasn:[0,1],hassl:[0,15],hast:15,hasti:[0,6,17,20],hat:[1,5,6,7,9,10,11,12,13,16,18],have:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18],haven:1,he:[0,7],head:[0,4,10,18],header:0,heads_proba:10,health:0,hear:[0,13],heart:[0,7],heatmap:[0,1,3,7],heavili:0,heavisid:1,height:[1,3,6],held:13,help:[0,1,4,12,13],helper:[4,14],henc:[0,5,6,8,9,10,12,13],her:7,here:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20],hereaft:[0,8,12],hermitian:16,hessenberg:16,hessian:[0,2,5,13],heterogen:[9,10],hi:7,hidden:[1,3,4,12],hidden_bia:1,hidden_bias_gradi:1,hidden_layer_s:[0,1],hidden_neuron:4,hidden_weight:1,hidden_weights_gradi:1,hierarch:5,high:[0,1,2,3,4,5,6,9,10,11,13,14,15,16],higher:[0,1,3,5,6,8,13],highest:[1,2],highli:[0,3,4,10,15,16,18,20],highwai:0,hing:8,hint:13,hip:15,hire:0,hist:[4,6,7,18],histogram:[0,6,7,18],histor:[7,11],histori:[3,4,12],histplot:0,hit:4,hitherto:5,hjorth:19,hobbi:18,hoc:5,hoff:20,hold:[1,3,6,13,14,18],holder:0,home:0,homework:[6,13],homogen:[1,3,9,10,13],honchar:2,hopefulli:[0,11,18],horizont:11,hors:[3,7],hot:[1,9],hour:[1,15,17,18,19],house_pric:0,how:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,20],howev:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18],hs:0,hspace:[0,4,8,10,18],hstack:[0,1],htf:17,html:[7,11,15,17,20],http:[0,3,4,6,7,11,13,15,16,17,20],huang:0,huber:0,huge:[1,3,4,15],human:[0,1,3,6,9,12],humid:9,hundr:1,hungri:1,hybrid:17,hydrogen:0,hyperbol:[1,4,12],hyperparam:8,hyperparamet:[3,4,5,6,9,13],hyperplan:11,i0:0,i1:[0,6,8,12],i2:[0,8,12],i3:[0,12],i5:0,i:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,16],i_1:[5,6],i_2:[5,6],i_:13,ian:20,ic:1,id:[7,13],idea:[0,1,2,3,4,6,9,10,12,13,16,18],ideal:[0,2,6,8,13,18],idem:6,ident:[5,6,12,13,16],identical:5,identifi:[0,1,7,9,11,12,13,14],idum:18,ieor:18,ifi:20,ifs:15,ignor:[0,1,3,9],ii:[16,18],iii:16,ij:[0,1,3,6,8,12,14,16,18],ik:[0,16],illustr:[5,7,10,12,13,14,15],im:6,imag:[1,3,4,6,9,11,12,14,20],image_at_epoch_:4,image_batch:4,image_height:3,image_path:[0,6,7,9],image_width:3,imageio:6,images_from_seed_imag:4,imagin:1,immedi:[0,3,4,6,15],implement:[0,2,3,4,5,6,8,9,10,11,12,13,14],impli:[3,5,6,7,13,16],implicit:3,implicitli:[11,18],importantli:3,impos:[0,6,11,12],imposs:[0,5],impress:[0,12],improv:[0,4,5,9,10,11,13],impur:9,imread:6,imshow:[1,3,4,6],in3050:20,in4080:20,in4300:20,in5400:[3,20],in_out_neuron:4,inaccur:13,inact:12,inadequ:0,inch:6,includ:[0,1,2,3,4,5,6,7,11,12,15,18,19,20],include_bia:[6,9],incom:12,incorrect:1,incoveni:8,increas:[0,1,3,4,5,6,7,8,9,11,12,13,18],increasingli:18,ind:6,inde:[0,2,4,5,6],indefinit:4,indent:18,indentationerror:18,independ:[0,5,6,7,8,12,13,18],index:[0,1,3,4,10,14,15,16,18,20],index_col:0,index_of:4,indic:[0,1,3,4,5,6,9,10,11,13],indispens:6,individu:[1,6,7,10,12,18],indu:0,indx1:2,indx2:2,indx3:2,indx:16,ineffici:[3,13],inequ:8,inequaltii:13,inertia:13,inf1000:15,inf1100:15,inf1100l:15,inf1110:15,inf3000:20,inf4490:20,inf5860:20,infeas:9,infer:[0,1,4,6,20],inferenc:1,infil:[0,6,7,9],infin:[5,6,7,11],infinit:3,infinitesim:18,influenc:[6,10],influenti:1,inform:[0,1,3,4,6,9,11,12,13,14,16,20],infti:[3,6,13,18],ingeni:13,ingrad:2,ingredi:[0,9],inher:6,inherit:16,initi:[0,1,2,6,10,13,14,16,18],initial_epoch:3,initialis:18,initialize_root:2,inject:14,inlin:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18],inner:13,innov:20,inp:4,inplac:13,input:[0,1,3,4,5,6,7,8,12,13,14,18],input_dim:1,input_shap:[3,4],inputs:1,inputs_shuffl:[0,1],insert:[3,5,6,8,10,18],insid:[0,4,7],insight:[0,1,5,15,20],insist:[6,13],inspir:[0,1,12,20],instabl:2,instal:[0,1,5,6,9],instanc:[0,1,2,4,6,9,11,13],instanti:10,instead:[0,1,2,3,4,5,6,8,9,11,13,14,16,18],institut:1,instruct:[0,1,3,4],int32:10,int64:0,int_0:18,int_:[3,6,18],int_a:18,intak:0,integ:[1,2,13,14,16,18],integer_vector:1,integr:[3,6,18],intellig:[0,14,20],intend:10,intens:1,intention:14,interact:[0,6,9,12,15],intercept:[0,6,8,11,13],intercept_:[0,6,8,9,13],interchang:[5,12,16],interconnect:1,interest:[0,1,2,3,4,5,6,7,8,9,12,15,17,18],interfac:[0,1,16],interior:[0,9],intermedi:16,intern:[1,10,12],interpol:[1,3,4,6,12],interpr:5,interpret:[0,1,6,9,10,12,13,16,18],interv:[0,3,5,6,7,13,18],intial:13,intract:[0,4],intrins:[3,11,16,18],intro:[15,20],introduc:[0,1,5,6,8,10,12,13,16,18],introduct:[1,2,4,13,17,20],introductori:[0,4,16,20],intuit:[0,5,6,8,12,13],inv:[0,5,13],invalid:[1,16],invalu:[0,13,15],invari:1,invd:5,inver:8,invers:[0,3,6,13],invers_period:18,inverse_transform:8,invert:[0,5,7,10],invok:[0,8],involv:[0,2,6,7,11,12],io:[15,17,18,20],iomanip:18,iostream:18,ip:[0,8,18],ipca:11,ipykernel_42331:[],ipykernel_42376:[],ipykernel_42449:5,ipykernel_42456:6,ipykernel_42530:8,ipykernel_42541:9,ipykernel_42553:10,ipykernel_42573:[],ipykernel_42580:16,ipykernel_42586:18,ipykernel_47411:1,ipykernel_47448:2,ipykernel_47647:3,ipykernel_47724:4,ipykernel_47735:13,ipynb:15,ipython:[0,5,7,9,11,14,15],iq:6,iri:[8,9],irreduc:6,irrelev:5,irrespect:0,is_integ:4,isbox:[2,13],iscomplexobj:2,isinst:[2,13],isn:5,isnul:0,isomap:11,issu:[0,1,9,16],it_arrai:13,item:[0,13],items:16,iter:[0,1,2,3,4,6,7,8,11,13,14,18],itr:5,its:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,20],itself:[5,6,12,18],ix:18,j1:16,j:[0,1,2,3,4,5,6,8,9,11,12,13,14,16,18,20],j_:6,j_lasso_sk:6,j_ridge_sk:6,j_sk:6,jackknavg:18,jackknif:[6,15],jackknstd:18,jackknvar:18,jackknvec:18,jacobian:[2,13],jacobian_shap:2,jargon:18,jason:4,jensen:19,jerom:20,ji:[12,16],jj:[0,5,6],jk:[0,1,6,12,16],jl:0,jm:16,job:[2,8,10],join:[0,4,6,7,9],joint:[4,5],journal:18,judg:13,judgement:6,julia:[15,16],jump:18,junk:4,jupyt:[0,15,20],just:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,18],justif:0,justifi:[3,10],jy:[1,2,3,4,5,6,8,9,10,13,16,18],k0:7,k1:7,k:[0,1,3,5,6,7,8,9,10,11,12,13,14,15,16,18,19],kaggl:6,kappa_d:18,karim:19,karlsen:19,karush:8,keep:[0,1,4,5,6,11,13,14,16],keepdim:[1,6,10,16],kei:[0,1,3,4,6,12,20],kept:[4,6,14],kera:[0,4,15],kernel:[0,1,3,15],kernel_regular:[1,3],kernel_s:4,kernelpca:11,kev:0,kevin:20,keyboardinterrupt:[2,3],keyerror:4,keyword:[6,13,16],kfold:6,kg:1,ki:16,kick:[1,13],kiener:2,kilomet:6,kind:[0,2,3,4,8,12,13,14],kj:[6,12,16],kjm:15,kkt:[5,8],kktsolver:5,kl:18,km:12,kmean:14,kmeanspoint:14,kn_k:14,know:[0,1,2,5,6,8,13,15,18],knowledg:[0,15],known:[1,3,4,5,6,7,8,9,12,16,18,20],kondev:0,kp:18,kpca:11,kroneck:14,kuhn:8,kwarg:[2,3,4,13],kwd:3,kwown:0,l0:7,l1:[0,1,3,5,7],l1_l2:[1,3],l1regl:5,l1regls_mosek2:5,l1regls_mosek:5,l2:[1,3],l:[0,1,2,3,5,6,7,8,10,11,12,13,16,18],l_1:7,l_2:[7,13],l_:16,l_j:12,la:13,la_i:12,la_k:12,lab:[15,17],label:[0,1,2,3,4,5,6,7,8,9,10,12,13,14,15,16,18],label_prob:13,labelencod:[7,10],labels:[6,8,9],labels_shuffl:[0,1],laboratori:17,lack:0,lagari:2,lagrang:[8,11],lambda:[0,1,2,3,5,6,7,8,10,12,13,18],lambda_0:11,lambda_1:[5,8,11],lambda_2:[8,11],lambda_:11,lambda_i:[8,11],lambda_iy_i:8,lambda_jy_iy_j:8,lambda_k:8,lambda_n:[5,8],lamda:1,lamdbda:5,land:[0,8],landmark:8,landscap:13,langl:[0,6,11,18],languag:[0,1,4,8,15,16,20],lapack:[5,16],laplac:5,laptop:15,larg:[0,1,2,4,5,6,8,9,10,11,13,15,16,18,20],larger:[0,3,5,6,8,10,11,13,18],largest:[4,8,11],lasso:[0,7,15,17],lasso_sk:6,last:[0,1,2,3,4,5,6,7,8,9,10,12,13,16,17,18],latent:4,latent_dim:4,latent_point:4,latent_space_value_rang:4,later:[0,1,4,6,7,8,12,13,14,15,18],latest:4,latest_checkpoint:4,latter:[0,3,5,6,7,8,11,13,16,17,18],lattic:12,law:0,layer:[0,4,13],lbfg:[7,9,10,11],lcc:[5,6],lda:11,ldot:[0,6,11,18],le:[5,7,10,13,18],lead:[0,1,3,5,6,7,8,9,10,11,12,13,16,18],leaf:9,leaki:1,leakyrelu:4,lear:13,learn:[3,4,5,6,7,8,9,10,12,16,17,20],learnabl:3,learner:10,learning_r:[3,8,10],learning_rate_init:[0,1],learning_schedul:13,least:[0,2,7,8,10,11,15,16,17,18],leat:13,leav:[0,1,3,5,6,9,11],lectur:[0,1,5,10,11,12,13,15,16,17,20],lecturenot:[15,20],lecturenovember11:17,lecturenovember12:17,lecturenovember19:17,lecturenovember25:17,lecturenovember26:17,lecturenovember4:17,lecturenovember5:17,lectureoctober14:17,lectureoctober15:17,lectureoctober1:17,lectureoctober21:17,lectureoctober22:17,lectureoctober28:17,lectureoctober29:17,lectureoctober7:17,lectureoctober8:17,lectureseptember10:17,lectureseptember16firstpart:17,lectureseptember16secondpart:17,lectureseptember17:17,lectureseptember23:17,lectureseptember24:17,lectureseptember2:17,lectureseptember30:17,lectureseptember3:17,lectureseptember9:17,lecturethursdayaugust26:17,lecturethursdayaugust27:17,left:[0,1,2,3,5,6,7,8,9,10,11,12,13,14,16,18],leftarrow:[8,12],legend:[0,2,3,4,5,6,7,8,9,10,13],len:[0,1,2,3,4,5,6,8,9,10,11,12,16,18],length:[0,1,2,3,4,8,9,13,15,18],length_of_sequ:4,leq:[0,5,7,8,13,14,18],less:[0,1,3,4,5,6,8,9,13,18],lessen:1,let:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18],letter:[0,16,18],level:[0,1,5,6,9,15,16,17],li:[0,8,11],lib:[0,1,2,3,4,6,7,8,11,13],liblinear:[8,10],librari:[0,1,2,3,4,5,6,9,10,11,16,18,20],licens:[0,1,15],lie:[0,6,11,18],life:[0,1,8,12],lifetim:13,like:[0,1,2,3,4,5,6,7,9,10,11,12,13,15,16,18],likelihood:[0,1,5,9,13],lim_:18,limit:[0,5,6,7,8,11,12,16],lin_clf:8,lin_model:0,lin_reg:9,linalg:[0,2,5,6,8,11,13,16,18],line1:8,line2:8,line2d:[4,13],line3:8,line:[0,1,3,4,6,8,11,13,16,18],linear:[1,3,5,6,7,9,10,11,12,15,17,18],linear_model:[0,5,6,7,8,9,10,11,13],linear_regress:6,linearli:5,linearloc:[6,13],linearregress:[0,6,7,9],linearsvc:8,liner:[1,3],linerar:10,linewidth:[0,2,4,6,8,9,10],link:[0,4,9,12,15],linlag:5,linpack:16,linreg:0,linspac:[0,2,3,4,6,8,9,10,13,16,18],linu:[4,19],linuek:19,linux:[0,1,15],liquid:0,list:[0,1,2,3,4,5,9,15],listcomp:2,listedcolormap:[9,10],literatur:[1,7,14,20],littl:[1,3,9,12],live:8,ll:[0,18],lle:0,lloyd:[4,14],lmb:[2,5,6],lmbd:[0,1,3],lmbd_val:[0,1,3],lmbda:13,ln:[1,13],lo:5,load:[0,1,4,6,7,9,10],load_boston:0,load_breast_canc:[1,7,9,10,11],load_data:[3,4],load_digit:[1,3],load_iri:[8,9],loc:[0,3,6,7,8,9,10],local:[0,1,3,7,12,13],locat:[2,3,8],lock:3,log10:[5,6],log:[0,1,2,4,5,6,7,9,10,11,13,16],log_:0,log_clf:10,logarithm:[0,5,7,16],logic:[0,1,9],logist:[0,1,2,8,9,10,11,12,15,17],logistic_predict:13,logisticregress:[7,9,10,11],logit:7,logreg:[7,9,10,11],logspac:[0,1,3,5,6],longer:[2,3,8,10,14,16,18],loocv:6,look:[0,1,2,3,4,5,6,7,8,9,10,11,13,16,18],loop:[1,4,6,10,12,14,15,16,18],lose:1,loss:[0,1,3,4,5,6,7,8,10,11,13,16],loss_fil:4,lossfil:4,lost:4,lot:[0,1,4,6],low:[0,6,9,10,11,18],lower:[0,1,3,6,9,10,16],lowercas:16,lowest:[9,13,18],lr:[1,3,4,10],lstat:0,lstm:4,lstm_2layer:4,lstsq:0,lt:6,lu:[0,5],lubksb:16,luckili:2,ludcmp:16,lux:16,lvert:1,lw:0,m:[0,1,2,3,5,6,8,9,10,11,12,13,16,17,18,20],m_1:14,m_:[9,12],m_h:0,m_k:14,m_l:12,m_n:0,m_p:0,m_t:13,ma:11,machin:[1,3,4,5,6,7,9,10,11,12,16,17,20],machinelearn:[6,15,17,20],mackai:20,made:[0,1,3,4,5,6,7,9,11,12],mae:0,magic:4,magnitud:[1,6,7,13],mai:[0,1,2,3,5,6,7,8,9,11,12,13,15,16,18],mail:17,main:[0,1,3,4,5,6,7,9,16,20],mainli:[0,5,6,7,9],maintain:[0,6],major:[1,6,9,10,13,16],make:[1,2,3,4,5,6,7,8,11,12,13,15,16,18,20],make_axes_locat:6,make_moon:[8,9,10],make_pipelin:[0,6,10],make_vjp:[2,13],makedir:[0,6,7,9],makeplot:0,malcondit:16,malign:[1,7,9],mammographi:5,manag:[0,2,3,15],mani:[0,1,3,4,5,6,7,8,9,11,13,14,15,16,18,20],manifold:11,manner:3,manual:6,map:[0,1,2,6,7,8,11,12,14,18],margin:[0,5,8],marit:0,marker:[0,7,16],markov:15,marsaglia:18,mask:18,mass:[0,1,5,13],massag:0,masses2016:0,masses2016ol:0,masses2016tre:0,masseval2016:0,master:[6,17],mat1100:15,mat1110:15,mat1120:15,mat3155:17,mat4155:17,mat:15,match:[1,4,5,13,14],materi:[4,5,7,13,16],math:[3,7,12,13,16,18,20],mathbb:[0,4,5,6,7,8,11,12,13,14,16,18],mathbf:[0,5,6,7,8,13,16,18],mathcal:[1,5,6,7,13],matheemat:3,mathemat:[0,6,11,12,13,15,16,17,18,20],mathrm:[0,1,3,4,5,6,7,8,9,10,11,12,13,14,18],matmul:[1,2,5],matmul_adjoint_1:2,matmul_vjp_0:2,matmul_vjp_1:2,matnat:[17,19,20],matplotlib:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18],matplotlibdeprecationwarn:[6,13],matric:[0,1,3,4,6,7,8,11,13,15,16],matrix:[0,2,3,4,6,7,8,10,13],matshow:1,matter:[2,3,13],max:[0,1,2,3,4,9,10,12,13],max_depth:[0,9,10],max_diff1:2,max_diff2:2,max_diff:2,max_it:[0,1,7,8,11,13],max_iter:14,max_leaf_nod:10,max_queue_s:3,max_sampl:10,maxdegre:[0,6,10],maxdepth:10,maxim:[1,4,5,7,8,11],maximum:[0,1,2,3,5,7,8,9,10,13,14],maxpolydegre:[5,6],maxpooling2d:3,mbox:[5,6],mc:18,mcculloch:12,mcint:18,mcintsqr2:18,md:11,mdoel:4,mean:[1,2,3,4,5,6,7,9,10,11,12,13,14,15,16],mean_absolute_error:0,mean_divisor:14,mean_i:18,mean_matrix:14,mean_squared_error:[0,4,6,7,10],mean_squared_log_error:0,mean_vector:14,mean_x:18,meaning:[0,4,7],meansquarederror:0,meant:[2,3,7,10,13],meantempvec:18,meanvec:18,measur:[0,1,2,5,6,9,11,12,14,18],mechan:[0,4,18],median:0,medicin:12,medium:[4,8,13],medv:0,meet:[0,19],mehta:0,memori:[3,4,11,12,13,16],mention:[0,12,13,18],mere:0,mersienn:18,meshgrid:[2,5,6,8,9,10,11],messag:[4,5,13],messi:2,met:[0,3,8],metadata:2,meteorolog:9,meter:6,method:[0,1,2,3,4,5,7,8,11,12,14,15,16,17,20],metion:6,metric:[0,1,3,6,7,9,10,14],metropoli:15,mev:[0,18],mgd:13,mglearn:15,mgrid:13,mi:10,microsoft:20,mid:1,midel:4,midpoint:9,might:[0,1,2,4,6,9,13],mild:9,miller:18,millimet:6,million:0,mimic:12,min:[0,2,5,8,9],min_:[0,2,5,14],min_samples_leaf:9,mind:[0,6,13],mindboard:4,mine:15,mini:[1,11,12,13],minibatch:[1,11,13],minibathc:13,minim:[0,1,2,3,5,6,7,8,9,10,11,12,13,14,18],minima:[0,1,7,13],minimum:[0,1,2,6,8,9,11,13],minmaxscal:0,minor:[6,13,18],minst:1,minu:7,mirror:9,misc:6,misclassif:[8,9,10],misclassifi:[8,10],miser:0,mismatch:1,miss:[0,10],mistak:4,mit:20,mix:[1,2],mixtur:13,mk:[9,16],mkdir:[0,6,7,9],ml:[0,1,10,13,16],mlab:18,mle:[5,7],mline:4,mlir:[3,4],mlir_graph_optimization_pass:[3,4],mlp:1,mlpclassifi:1,mlpregressor:0,mm:16,mn:[12,18,20],mnist:[1,11],mod:18,mode:[17,18],model:[2,3,5,7,8,9,10,11,13,14,15,18,20],model_select:[0,1,3,5,6,7,9,10,11],moder:10,modern:[0,6,7,15],modif:[2,12,13],modifi:[0,1,3,5,7,8,10,12,13],modul:[0,2,3,4,5,6,7,8,9,10,11,13,16],modular:18,modulenotfounderror:[5,8],modulo:18,moe:[5,11],moment:[5,6,13],monitor:13,monoton:[5,12,18],mont:[0,6,15,18,20],montecarlocycl:18,moor:[5,6],more:[0,1,2,4,5,7,8,9,10,11,12,13,14,15,17,18],moreov:[0,3],morten:19,mortenimac:[0,1,2,3,6,7,8,11],mosek:5,most:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,18],mostli:[1,11],motion:[0,13],motiv:[1,4],move:[0,4,5,6,7,9,12,13,14,18],mp4:17,mpl:[0,7],mpl_toolkit:[2,6,13],mplot3d:[2,6,13],mplregressor:1,mse:[0,4,5,6,9,10],mse_simpletre:10,mselassopredict:5,mselassotrain:5,mseownridgepredict:6,msepredict:5,mseridgepredict:[5,6],msetrain:5,msg:0,msle:0,mt19937_64:18,mt:[7,12],mu0:18,mu1:18,mu2:18,mu:[0,6,11,13,18],mu_:[6,18],mu_i:6,mu_n:11,mu_x:18,much:[0,1,2,3,4,5,6,8,9,10,11,12,13,16,18],mul:5,multi:[0,1,3,4,7,15],multiclass:[1,7],multidimension:[11,12],multilay:1,multinomi:7,multipl:[2,4,5,6,7,12,13,18],multipli:[3,5,6,11,13,16,18],multiplum:8,multivari:[0,2,10,11,15,18],multivariate_norm:[11,14],murphi:[11,20],must:[1,2,5,6,8,10,12,13,14,18],mutat:7,mutual:[1,3,6,13],mx_:18,myriad:[0,15],mz1:18,mz2:18,n1:16,n2:16,n:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,16,18],n_0:[12,18],n_:[1,2,3,8,12,18],n_b:18,n_boostrap:[6,10],n_bootstrap:6,n_categori:[1,3],n_cluster:14,n_compon:11,n_epoch:13,n_estim:10,n_examples_to_gener:4,n_featur:1,n_filter:3,n_hidden:2,n_hidden_neuron:[0,1],n_i:18,n_input:[0,1,3],n_instanc:9,n_iter_i:[7,11],n_job:10,n_k:14,n_l:[12,18],n_layer:1,n_m:9,n_neuron:1,n_neurons_connect:3,n_neurons_layer1:1,n_neurons_layer2:1,n_point:14,n_sampl:[6,8,9,10,14],n_split:6,n_step:4,n_t:2,n_x:2,nabla:[1,13],nabla_:[2,13],nabla_w:13,nag:13,naimi:0,naiv:7,naive_kmean:14,nall:0,name:[0,1,3,4,5,6,7,8,9,10,12,13,14,15,16,19],nameerror:[6,10],namespac:18,narrow:13,nary_f:[2,13],nary_op_arg:[2,13],nary_op_kwarg:[2,13],nary_oper:[2,13],nation:[1,5],nativ:15,natur:[0,1,4,8,9,12,13,18,20],navier:12,nb:18,nb_:16,nboot:18,nd:14,ndarrai:[2,6],ndim:[2,4],ne:[9,10,16,18],nearest:[1,3,6,11],nearli:13,neccesari:6,necess:2,necessari:[0,1,3,4,8,14],necessarili:[0,4,11,18],necesserali:5,neck:7,need:[0,1,2,3,4,5,6,8,9,10,11,12,13,14,16,18],neg:[0,1,3,5,6,7,10,13,16,18],neg_mean_squared_error:6,neglect:18,neglig:18,neighbor:[3,6,11],neither:[4,13],neq:[13,14,18],nervou:12,nest:[2,9,12],nesterov:13,net:[2,4,12],netlib:16,network:[0,9,13,15,17,20],neural:[0,7,13,15,17,20],neural_network:[0,1,2],neuralnetwork:1,neuron:[1,2,3,4,12],neutral:0,neutron:0,never:[1,3,4,6,9,18],new_box:[2,13],new_root:[2,13],new_trac:[2,13],new_tracing_count:3,newaxi:[0,3,6,9],newli:0,newton:[1,7,8,13,18],next:[0,1,2,3,4,5,6,8,9,13,14,18],next_guess:13,next_input:4,ng:1,ngini:9,ni:14,nian:19,nice:[0,1,5,11],nichola:19,nicholaskarlsen1102:19,niter:13,nitric:0,nlambda:[5,6],nlevel:4,nm:18,nm_n:0,nmse:6,nn:[2,5,6,12,16],nn_model:1,nnmin:2,node:[1,2,3,9,10,12],node_constructor:2,nois:[0,4,5,6,8,9,10,13],noise_dimens:4,noisi:[1,6],non:[0,1,3,4,5,6,7,9,10,11,12,13,14,16,18],none:[0,1,2,3,4,5,9,10,13,18],nonlinear:[3,6,8,9,11,12],nonneg:[6,9,13],nonparametr:6,nonsens:18,nonsingular:16,nonumb:[3,7,8,13,16],nor:[1,4,13],norm:[0,1,5,6,8,11,13],normal:[3,4,5,6,7,8,9,10,11,12,13,15,16],normali:16,normalize_kwarg:4,norwai:6,notat:[0,2,5,6,13,14,18],note:[0,1,2,3,4,5,6,7,8,11,12,13,14,15,16,17,18,20],notebook:[0,1,3,9,15],noth:[1,2,5,8,12,14,18],notic:[4,5,12,13,16,18],notimplementederror:2,notion:3,notrace_primit:2,novel:[3,6,10],novemb:1,now:[0,2,4,5,6,7,8,10,11,12,13,14,16,18],nowadai:[0,1,3,9,15],nox:0,np:[0,1,2,3,4,5,6,7,8,9,10,11,13,14,16,18],npr:2,nsampl:[6,9],nspin:18,nt:2,nthi:0,ntrained_model:6,nu:18,nuclear:5,nuclei:[0,18],nucleon:0,nucleu:0,num:4,num_coordin:2,num_hidden_neuron:2,num_it:2,num_neuron:2,num_neurons_hidden:2,num_output:3,num_point:2,num_tre:10,num_valu:2,number:[1,3,4,5,6,7,8,9,10,11,12,13,14,16,17,19],numberid:7,numberparamet:3,numer:[0,5,6,9,10,11,12,13,15,16,20],numpi:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,18],numpy_vjp:2,numpy_wrapp:2,nunmpi:5,nvalu:9,nx:2,nx_test:6,nx_train:6,nx_train_mean:6,ny:18,ny_pr:6,ny_train:6,ny_train_mean:6,o:[0,6,7,8,9,11,16,20],obei:[6,11,13],object:[0,1,2,4,5,6,8,10,13,16],objsens:5,obliqu:5,observ:[1,3,5,6,7,8,9,10,11,12,13,14],obtain:[0,1,5,6,7,8,9,10,12,13,14,16,18],obviou:[5,6,11,18],obviouli:0,obvious:[0,4,5,6,16],oc:5,occupi:0,occur:[0,6,8,9,16,18],od:0,odd:[0,3,7],odenum:2,odesi:2,oen:0,off:[1,3,4,5,9,13,18],offer:[6,11,15,16,17],offic:19,offici:17,ofil:18,ofstream:18,often:[0,1,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18],ofter:16,ol:0,old:[1,5,10,13],ols_sk:6,ols_svd:6,olsbeta:5,omega:[2,3,6],omega_0:3,omit:[0,5],on_train_batch_begin:3,onc:[1,6,9,11,13,18],one:[0,1,3,4,5,6,7,8,9,10,11,13,14,15,16,18],oneapi:[3,4],onednn:[3,4],onehot:1,onehot_vector:1,onehotencod:9,ones:[0,2,5,6,8,9,10,11,13,16,17],ones_lik:4,onl:3,onli:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18],onlin:[11,17],onto:[5,11],op_nam:3,open:[0,1,4,6,7,9,15,17,18],oper:[0,1,3,4,5,6,10,11,12,13,15,18],operation:18,oplu:18,opmiz:13,opportun:0,oppos:[6,13],opposit:[1,5,8],opt:[1,5],optim:[0,2,3,4,5,6,7,9,10,11,14,17],optimis:[1,3],optimizer_v2:3,option:[0,1,3,5,6,7,8,11,16],optionalxlacontext:3,optmiz:[1,8,13],orang:0,order:[0,1,2,3,5,6,7,8,9,10,11,12,13,16,18],ordinari:[0,2,3,7,11,13,15,17],oreilli:20,org:[3,4,7,11,15,16,20],organ:[6,7,10,16],orient:[1,5,18],origin:[0,3,5,6,8,11,12,13,16,18],orthogn:5,orthogon:[0,5,6,8,11,13,16],orthonorm:5,os:[0,1,4,5,6,7,8,9],oscar:1,oscil:[3,13],oslo:[0,17,19],osx:[0,15],other:[0,1,2,3,5,6,7,8,10,13,14,15,17,20],otherwis:[0,1,4,7,13,16],ouput:[5,7,12],our:[1,2,3,6,7,8,9,10,12,14,15,16,17],ourmodel:0,ourselv:[0,5,6,8,11,13],out:[0,1,2,4,5,6,7,8,9,10,11,12,13,15,16,18],out_fil:9,outcom:[0,7,9,10,12,18],outdoor:9,outer:[6,12],outfil:4,outfilenam:18,outgrad:2,outlier:[0,8],outlin:[6,10,11],outlook:9,outperform:10,output:[0,1,3,4,5,6,7,8,9,10,12,13,16],output_bia:1,output_bias_gradi:1,output_shap:4,output_weight:1,output_weights_gradi:1,outputlayer1:12,outputlayer2:12,outsid:4,over1:13,over:[0,1,3,4,5,6,9,10,12,13,16,18],overal:[1,10],overcast:9,overcom:[12,13],overdetermin:0,overfit:[0,1,3,6,9,10,13],overflow:[1,5],overhead:12,overlap:[3,7,8,9],overlin:[0,5,6,9,10,11,14,16],overst:0,overtrain:4,overview:[3,20],own:[4,5,6,8,12,13,15,16],owner:0,ownridgebeta:6,oxid:0,oyvinssc:19,p0:2,p1:2,p:[0,1,2,3,4,5,6,7,8,9,10,11,13,14,16,18,19],p_:[2,4,8,9],p_hidden:2,p_i:[5,18],p_j:18,p_n:18,p_output:2,p_x:18,pack:0,packag:[0,1,2,3,4,5,6,7,8,11,13,15,18],pad:[3,4],page:[0,15],pai:[0,1,9,13],pair:[0,2,3,9,15,18],panda:[0,4,5,6,7,9,11,15],paper:1,paradigm:0,parallel:[10,16],param:[2,4],paramat:2,paramet:[0,1,2,3,4,5,6,7,8,9,10,12,13,18],parameter:[0,6,10],parametr:[0,6],paramt:[3,5],parent:2,parent_argnum:2,park:18,part:[0,1,3,5,6,10,16,17,18,20],partial:[0,1,5,6,7,8,10,11,12,13,18],particip:[15,17],particl:[0,4,13,18],particular:[0,1,2,3,5,6,9,10,11,12,13,18,20],particularli:[5,6,8,11,13,18],partit:[1,4,9],partli:6,pass:[2,3,4,12,14,18],past:[10,18],patch:[6,18],path:[0,4,6,7,9,15],patient:7,patter:4,pattern:[0,3,4,12,17,20],pauli:0,pc:[11,15],pca:[0,7,15,17],pd:[0,4,5,6,7,9,11],pde:2,pdf:[0,3,4,5,6,9,20],pedagog:0,penal:6,penalti:[6,13],penros:[5,6],pentagon:13,peopl:[0,1,9,13,15],per:[0,1,6,17],percentag:[0,10,11],perceptron:[0,1,7],perfect:[0,1],perfectli:[4,6],perform:[0,2,3,4,5,6,8,10,11,12,13,14,15,16,18],performac:4,perhap:[0,5,13],perimet:[1,9],period:[1,4],permut:11,persist:13,person:[5,6,7,17,19],perspect:20,pertin:12,petal:[8,9],peter:20,petersen:18,phantom:18,phase:[6,12],phenomena:18,phi:8,phi_k:8,philip:19,philosophi:13,phone:19,photo:4,phrase:0,physic:[0,1,4,7,12,13,18,19,20],pi:[2,3,5,6,7,9,12,13,18],pick:[1,9,10,11,13,14,18],pickl:1,pictur:0,pie:15,piec:[11,14],pillow:[0,15],pinv:[5,6,13],pip3:[0,1],pip:[0,1,15],pipelin:[0,6,8,10],pit:4,pitfal:6,pitt:12,pixel:[1,3,4],pixel_height:[1,3],pixel_width:[1,3],place:[0,4,6,8,13,16],plai:[0,3,4,5,6,8,11,15],plain:[8,10,12,13,14],plan:[6,9,19,20],plane:[8,9],plateau:[5,18],platform:[3,4,15],plausibl:12,pleas:[0,7,11,13],plenti:1,plethora:[3,12],plot:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18],plot_confusion_matrix:[7,10],plot_count:6,plot_cumulative_gain:[7,10],plot_data:1,plot_dataset:8,plot_decision_boundari:[9,10],plot_import:10,plot_max:4,plot_min:4,plot_model:4,plot_numb:4,plot_predict:8,plot_regression_predict:9,plot_result:4,plot_roc:[7,10],plot_surfac:[2,6,13],plot_train:9,plot_tre:[9,10],plt:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18],plu:[0,3,5,7],pm:[8,18],pmatrix:2,pn:3,png:[0,4,6,7,9],point:[0,1,2,3,5,6,7,8,9,10,11,13,14,16,18,19],point_1:4,point_2:4,poisson:15,poli:[6,8],poly100_kernel_svm_clf:8,poly3:0,poly3_plot:0,poly3dcollect:13,poly_featur:[8,9],poly_features10:9,poly_fit10:9,poly_fit:9,poly_kernel_svm_clf:8,polydegre:[0,5,6,10],polygon:13,polym:12,polynomi:[0,5,6,7,8,9,10,11],polynomial_featur:6,polynomial_svm_clf:8,polynomialfeatur:[0,6,8,9],polytrop:[0,6],pool:3,pool_siz:3,poor:[1,13],poorli:0,pop:2,popul:[0,5],popular:[0,1,3,6,7,8,9,11,12,15,16,18],popularli:0,portabl:10,portion:[11,13],pose:[0,4,5,6,11,18],posit:[0,1,2,3,5,7,8,10,11,13,14,16,18],possibl:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15,16,18,19],posterior:5,postpon:0,postul:5,potenti:[0,3,5,6,12,13],potr:5,potrf:5,pott:12,power:[0,1,5,6,8,9,12,13],pp:[5,6],practic:[0,5,6,7,8,17,18],practition:[0,1,3],preced:[1,11,12,18],preceed:4,preceq:8,precis:[0,2,5,11,13,16,18],pred:[6,13],predicit:0,predict:[0,1,5,6,7,8,9,10,15,20],predict_prob:1,predict_proba:[7,10],predictor:[0,5,6,7,9,10,11],prefer:[0,1,6,8,9,11,15],prepar:[0,6,16],preprocess:[0,4,6,7,8,9,10,11],prerequisit:0,presenc:13,present:[0,5,6,9,12,13,17,18],preserv:[3,11,16],press:[13,20],pretrain:[1,4],pretti:[0,4,8,9,15],prev_centroid:14,prevent:[13,18],previou:[0,1,2,3,4,5,6,8,10,11,12,13,16,18],previous:[2,3,9,10,18],price:[0,4,9,13],primal:8,primari:[0,7],prime:18,primit:2,princip:[0,5,7,15,17],principl:[0,6,7,8,14],print:[0,1,2,3,4,5,6,7,8,9,10,11,13,14,16,18],print_funct:[8,9],printout:0,prior:[0,5,6],privat:0,prob:[1,18],probabilist:[0,20],probabl:[0,1,3,4,6,7,10,13,15,17],problem:[0,3,4,5,6,7,8,9,10,11,12,15,16,17,18],proce:[0,5,6,8,9,10,11,13,16],procedur:[2,4,5,6,8,10,11,13],proceed:16,process:[0,2,4,6,9,10,12,13,15,16,18,20],prod:20,prod_:[1,5,7],produc:[0,3,4,5,6,9,10,11,12,13,15,16,18],product:[0,1,3,5,6,7,8,12,13,15,16],profess:0,program:[0,1,4,5,6,8,12,14,15,16,17,18],programm:16,progress:[1,4,14],prohibit:6,project1:6,project:[0,1,2,3,5,11,13,15,17,18,19],project_root_dir:[0,6,7,9],promin:12,promis:8,prone:9,pronounc:[13,15],proof:[0,11,12,13],propag:[2,3,13,17],proper:[0,2,6],properli:[1,6,8,10,13],properti:[0,1,3,12,13,16],proport:[0,1,5,9,11,13,18],propos:[1,4,6,10],propto:[5,13],protect:3,proton:0,prove:[3,13],provid:[0,1,3,4,5,6,8,9,10,12,13,15,16,18,20],proxi:[1,13],prune:9,pseudoinv:5,pseudoinvers:[5,6],pseudorandom:[6,18],psycholog:0,pt:13,ptratio:0,punish:[0,1],pure:[3,9,18],purest:9,puriti:9,purpos:[0,3,10,12,14],put:1,putarow:5,putboundslic:5,putclist:5,putobjsens:5,putqobj:5,py:[0,1,2,3,4,5,6,7,8,9,10,11,13,16,18],pydata:15,pydot:9,pylab:[0,7],pylint:3,pypi:15,pyplot:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18],pythagora:5,python2:0,python3:[0,1,2,3,4,6,7,8,11,13,15],python:[1,2,3,5,6,8,11,12,13,14,17],pytorch:[0,15],pywrap_tf:3,q:[5,6,8,11,18],qp:8,qquad:[2,11,13,16],qr:[5,6,16],quad:[1,13,16],quadrat:[0,5,8,9,13],qualit:[4,9,18],qualiti:[0,9,15],quantifi:1,quantil:10,quantit:[0,6,9],quantiti:[0,2,5,6,7,9,10,11,12,14,16,18],quantum:[4,12],quartil:0,quench:5,queri:9,question:[0,5,6,9,11,12,13],qugan:4,quick:[4,18],quick_execut:3,quickli:[1,3,9,11,13],quit:[1,5,6,9,10,12],quot:[4,18],r2:[0,5,6],r2_score:0,r2score:0,r:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18],r_1:9,r_2:9,r_j:9,r_m:9,rad:0,radial:[0,8,12],radioact:18,radiu:[0,1,9],rag:2,rain:9,rais:[2,4,13],ramp:1,ran1:18,ran2:18,ran3:18,rand:[0,4,5,6,9,10,13,16,18],rand_max:18,randint:[6,9,13],randn:[0,1,2,5,6,9,11,13],random:[0,1,2,3,4,5,6,8,9,13,14,15,16,17],random_devic:18,random_forest_model:10,random_index:13,random_indic:[1,3],random_st:[0,7,8,9,10,11],randomforestclassifi:10,randomli:[1,6,9,13,14,18],randomnumbergener:18,rang:[0,1,2,3,4,5,6,7,9,10,11,12,13,14,16,18],rangl:[0,6,11,18],rangle_x:18,rank:5,rankdir:4,raphson:[1,8,13],rapidli:0,rare:[1,13],rate:[0,1,2,3,4,8,9,10,12,13],rather:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,16,18],ratio:[4,7,9,10,11],rational:0,ravel:[5,6,7,8,9,10,11,13,16],raw:[3,18],raw_df:0,rbf:[8,11,12],rbf_kernel_svm_clf:8,rbf_pca:11,rc:[0,18],rcond:0,rcparam:[0,1,3,7,8,9,10,18],rd:18,re:[2,4,13],reach:[0,1,4,5,6,7,9,10,11,12,13,14,18],read:[0,2,3,4,5,6,7,8,11,12,16,17,18,20],read_csv:[0,6,7,9],read_fwf:0,reader:[0,6,16,18],readi:[0,1,5,6,8,10,11,12,16],readili:1,real:[0,1,2,4,7,10,11,12,13,16],real_loss:4,real_output:4,realist:8,realiti:18,realiz:[1,12],realli:[0,1],rearrang:13,reason:[0,1,3,4,10,13,20],reassign:1,rebuild:[3,4],recal:[5,6,9,10,11,12,16,18],recalcul:18,recast:3,receiv:[1,3,10,12,18],recent:[0,2,3,4,5,6,8,9,10,13],recept:[3,12],receptive_field:3,recip:[0,6,7,16],reciproc:5,recogn:[0,4,5,10],recognit:[0,1,3,12,17,20],recommend:[0,2,3,4,5,6,8,13,15,16,17,18,20],reconsid:9,reconstruct:11,record:[10,17],recreat:18,rectangl:[9,13],rectangular:5,rectifi:[1,3,12],recur:[0,15],recurr:[0,1,15,17],recurs:[9,15,16],recycl:18,red:[0,3,4,6,8,9],redefin:[0,10],reduc:[1,3,5,6,9,10,11,13],reduct:[0,10,11,15,18],refer:[0,1,2,3,5,6,7,11,12,13,14,16,20],referenc:2,refin:12,refit:6,reflect:[0,1,4,5,18],refresh:[15,17],reg:[10,11],regard:[1,9,13],regardless:12,region:[3,4,6,9,12],regist:[3,4,6,18],reglasso:5,regr_1:[0,9],regr_2:[0,9],regr_3:[0,9],regress:[1,8,11,12,15,17],regressor:[0,7,10],regridg:[5,6],regular:[0,3,4,5,6,7,9,13],regularis:6,reilli:[0,20],reinforc:[0,8,15],reiter:1,rel:[0,4,6,7,9,12,13,18],relat:[0,1,3,4,5,11,13,14,16,18],relationship:[0,4,9],relativeerror:0,releas:[1,3,6,13,15],relev:[0,1,5,7,11,15,17,18],reli:[0,6,8],reliabl:[7,18],relu:[3,4],remain:[1,2,4,6,12,16,18],remaind:18,reman:2,remark:1,rememb:[0,8,13,16],remind:[0,5,11,13,16,18],remov:[0,4,5,6],render:0,reorder:[5,7],reorgan:0,repeat:[0,1,3,4,5,6,9,10,11,13,14,16,18],repeated:0,repeatedli:[6,10,13,18],repet:3,repetit:[6,17],rephras:13,replac:[0,1,3,4,5,6,10,12,13,14],replica:6,repositori:[0,4],repres:[0,1,2,3,4,5,6,7,8,9,10,12,13,18],represent:[0,1,3,6,18],representd:3,reproduc:[0,5,6,9,12,15,18],repuls:0,request:[0,13],requir:[0,1,3,4,5,6,8,9,11,12,13,16],res1:2,res2:2,res3:2,res_analyt:2,res_analytical1:2,res_analytical2:2,res_analytical3:2,resaml:6,resampl:[0,7,10,15,17,18],rescal:[0,11,12],rescu:5,reseach:6,research:[0,4,15,20],resembl:[6,18],reserv:[1,5,6,18],reset:18,reshap:[0,1,2,3,4,6,8,9,10,16],residenti:0,residu:[0,5,13],resiz:5,respect:[0,1,2,3,5,6,7,8,10,11,12,13,14,18],respond:12,respons:[0,7,9,12],rest:[0,5],restat:[0,12],restor:4,restored_discrimin:4,restored_gener:4,restrict:[0,3,9,12],result:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18],result_typ:2,retail:0,retain:[5,6],return_data:14,return_kwarg:4,return_sequ:4,return_x_i:9,reus:[1,3,6],reveal:[0,12],revers:[1,16],review:[15,16,17],revisit:14,reward:[0,4],rewrit:[0,3,5,6,7,8,10,11,12,13,16,18],rewritten:[2,6,8,10,18],rewrot:13,rf:10,rgb:3,rgoj5yh7evk:15,rh:[5,6],rho:[0,10],rho_1:10,rho_2:10,rho_m:10,rich:0,ride:9,rideclass:9,ridedata:9,ridg:[0,7,11,13,15,17],ridge_sk:6,ridgebeta:5,right:[0,1,2,3,5,6,7,8,9,10,12,13,14,16,18],right_sid:2,rightarrow:[0,1,5,6,8,11,12,13,18],rigor:0,ring:6,rise:0,risk:[0,13],rival:4,river:0,rm:[0,18],rmse:0,rmsporp:13,rmsprop:[1,3,4,13],rnd_clf:10,rnn1:4,rnn2:4,rnn:[4,12,17],rnn_2layer:4,rnn_input:4,rnn_output:4,rnn_train:4,rntrick1:18,rntrick2:18,rntrick3:18,rntrick4:18,ro:[0,13],robert:20,robust:0,robustscal:0,roc:10,role:[0,2,5,6,8,15],roll:6,room:[0,19],root:[0,5,9,13,18],rotat:[1,8,9,10],rotation_matrix:9,roughli:[1,3],round:[0,7,9,13],routin:[13,16],row:[0,1,2,5,6,7,9,11,16],rr:5,rrr:5,rthe:5,rug:13,rule:[0,1,5,6,13],run:[0,1,2,3,4,5,6,8,9,11,13,15],runtim:[1,6,14],runtimewarn:[1,6],rust:[0,15,16],rvert:1,rvert_2:1,s:[0,1,2,3,4,5,6,7,9,11,12,13,15,16,17,19],s_1:6,s_:[3,6],s_i:[6,7],s_j:6,s_k:6,saddl:13,safe:18,sai:[0,1,2,3,4,5,6,7,8,9,10,11,12,16,18],said:[6,9,13],sake:[0,5,7,11],sale:0,same:[0,1,2,3,4,5,6,8,9,11,12,13,14,16,18],samm:10,sampl:[0,1,2,3,4,5,6,7,8,9,10,13,14,15,16],sample_vari:14,sample_weight:3,sampleexptvari:18,sastri:11,satisfactori:0,satisfi:[1,2,3,6,8,13,16,18],satur:[1,6],save:[0,4,6,7,9],save_fig:[0,6,7,9,10],savefig:[0,4,6,7,9,18],savetxt:4,saw:5,scalabl:10,scalar:[2,5,6,10,13],scale:[0,1,3,5,6,7,8,9,10,11,12,13,15,16,19],scale_mean:4,scale_std:4,scalei:4,scaler:[0,7,8,9,10,11],scalex:4,scan:[5,7],scari:5,scatter:[0,1,6,7,8,9,14],scenario:[6,13],schedul:13,scheme:[1,13],schrage:18,scienc:[0,1,10,12,13,15,17,18,20],scientif:[0,15],scientist:0,scikit:[3,5,6,7,8,9,10,13,15,16,17,20],scikitplot:[7,10],scipi:[0,3,5,6,13,15,16],scl:6,score:[0,1,3,6,7,9,10,11,19],scores_kfold:6,scratch:1,sdg:13,seaborn:[0,1,3,6,7],seamless:[0,15],search:[0,1,3,5,9,13],sec:6,second:[0,2,3,4,5,6,7,8,9,11,12,13,14,15,16,17,18],secondeigvector:11,secondli:12,section:[4,11,16,17,18],sector:0,see:[0,1,2,3,4,5,6,7,8,10,11,12,13,15,16,17,18],seed:[0,1,2,3,4,5,6,8,9,11,13,14,18],seed_imag:4,seek:[1,2,8],seem:[1,3,4],seemingli:0,seen:[0,1,3,5,10,12,18],segment:13,seismic:6,seldomli:0,select:[1,5,6,8,9,10,11,17,20],self:[1,2,3,4,5,18,20],sell:4,semest:[7,17],semi:[8,13],semilogx:6,send:[5,12,13,19],senior:17,sens:[0,4,6,8],sensibl:3,sensit:[0,5,6,9,13],sent:2,sentenc:[4,12],sep:0,separ:[0,1,2,4,6,8,9,12,14,15,18],sequenc:[2,3,4,7,9,10,12,13,15,16,18],sequenti:[1,3,4,10,12,18],seri:[0,1,2,3,4,5,6,10,11,12,13,16,17],serif:[0,7,18],serv:[0,1,2,3,5,7,13,20],session:[1,17],set:[1,4,5,6,7,8,10,11,13,14,15,16,18],set_major_formatt:6,set_major_loc:6,set_stream:5,set_tick:[1,8],set_ticklabel:1,set_titl:[0,1,2,3,7,12,14],set_xlabel:[0,1,2,3,7,12],set_xlim:[7,12],set_xticklabel:1,set_ylabel:[0,1,2,3,7],set_ylim:[7,12],set_ytick:7,set_yticklabel:[1,6],set_zlim:6,seth:4,setiosflag:18,setminu:6,setosa:[8,9],setosa_or_versicolor:8,setp:6,setprecis:18,setse:5,setup:[1,4,5,6,8,15],setw:18,sever:[0,3,5,6,7,8,9,11,12,13,15,16,17,18],sgd:[1,3],sgd_clf:8,sgdclassifi:8,sgdreg:13,sgdregressor:13,sgn:5,sh:9,shallow:13,shape:[0,1,2,3,4,5,6,7,8,9,10,11,13,14,16],share:[1,3],she:7,shift:[1,6,12,18],ship:3,shortcom:13,shorten:4,shorter:18,shortli:16,should:[0,2,3,5,6,8,9,11,12,13,16],should_sync:3,show:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18],show_shap:4,shown:[0,4,5,7,8,11,12,13,18],showpoint:18,shrink:[3,5,6,8,11],shrinkag:[5,6],shrunk:11,shuffl:[0,1,3,4,6,13],side:[0,2,5,8,12,13,16],sigh:15,sigma0:18,sigma1:18,sigma2:18,sigma:[0,1,5,6,7,10,11,12,13,16,18],sigma_0:5,sigma_1:5,sigma_2:5,sigma_:[5,16,18],sigma_fn:[7,12],sigma_i:[0,5],sigma_j:5,sigma_m:[6,18],sigma_n:[11,18],sigma_t:13,sigma_x:18,sigmoid:[1,2,4,7,8,10,12,13],sigmundson:[6,19],sign:[1,2,7,8,10,18],signal:[1,3,10,12],signatur:3,signifi:4,signific:1,significantli:[1,13,18],sim:[4,5,6,13,18],similar:[0,1,2,3,4,5,6,7,8,9,10,11,13,14,15,16],similarli:[0,1,3,5,8,10,18],simpl:[1,2,3,5,6,7,8,10,11,12,14,15,16],simple_rnn:4,simplepredict:10,simpler:[0,1,5,6,13,15],simplernn:4,simplest:[0,1,3,4,9,10,12,14],simpletre:10,simpli:[0,1,2,4,5,6,8,9,10,11,12,15,16,18],simplic:[2,5,6,7,8,9,10,11,12,14],simplicti:5,simplifi:[0,6,9,15],simplist:[3,6,18],simul:[6,18],simultan:6,sin:[0,1,2,3,4,9,12,13,16],sinc:[0,1,2,3,5,6,7,8,9,10,11,13,16,18,20],sine:[3,12],singl:[0,1,2,3,5,6,7,8,9,12,13,16,18],singular:[0,6,13,16,17],sinusoid:3,site:[0,1,2,3,4,6,7,8,11,13,17],situat:[0,4,5,7,13],six:[3,18],size:[0,1,2,3,4,5,6,8,9,10,11,13,16,18],sketch:10,ski:9,skill:0,skip:[3,11],skiprow:0,skl:[0,6],sklearn:[0,1,3,5,6,7,8,9,10,11,13,14],skplt:[7,10],sl:6,slack:8,slice:[2,4,16],slide:[0,3,18],slight:[6,13],slightli:[1,2,3,5,6,7,10,18],slope:[8,11,12],slow:[0,2,8,13],slower:[5,16],slowest:16,slowli:12,slp:1,small:[0,1,2,3,5,6,8,9,10,11,12,13,15,16,18],smaller:[0,1,2,5,6,8,9,11,13,18],smallest:[0,4,14],smallest_row_index:14,smooth:[0,3,6,9,13],sn:[0,1,3,6,7],sne:11,so:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18],soar:6,social:0,soft:[1,7,10,12],soften:8,softmax:[3,7],softwar:[0,8,15,16,17],sol:8,sole:[0,6],solid:[0,7],solitem:5,soltyp:5,solut:[0,1,2,3,5,6,8,10,11,13,16,18],solutionsummari:5,soluton:2,solv:[0,1,3,5,6,8,10,11,12,13,16,17],solve_expdec:2,solve_ode_deep_neural_network:2,solve_ode_neural_network:2,solve_pde_deep_neural_network:2,solveod:2,solveode_popul:2,solver:[2,5,7,8,9,10,11,16],some:[0,1,2,3,4,5,6,7,8,9,10,11,12,14,16,17,18],some_model:6,somehow:4,someth:[0,1,3,4,7,9,11,18],sometim:[0,1,11,12,13,14],soon:16,sophist:0,sopt:13,sort:[5,6,9,11,18],sound:[3,5],sourc:[0,1,3,6,15,16,18],space:[0,1,4,5,8,9,11,12,13,14,18],span:[0,3,5,9,11,16],spare:1,spars:[3,5,6,16],sparse_mtx:16,sparsecategoricalcrossentropi:3,sparsiti:10,spatial:[1,2,3,12],spdiag:5,speak:18,special:[0,6,7,10,12,13,16,18],specif:[0,1,2,3,4,5,6,7,8,9,11,12,15,16,18],specifi:[0,3,5,6,7,9,11,13,14,18],specifici:[0,10],spectacular:3,spectral:1,speech:[0,1,3,4,12],speed:[1,2,4,13],spend:18,sphere:0,spin:6,spite:0,spline:8,split:[1,3,4,5,6,8,9,10,11,14,18],splite:0,splitter:[1,10],spmatrix:5,spontan:18,spot:3,spread:[0,11,18],springer:20,spuriou:13,sqquar:5,sqrsignal:3,sqrt:[0,3,4,5,6,8,10,11,13,18],squar:[1,2,3,4,7,8,9,11,13,14,15,16,17,18],squarederror:10,squaredeuclidean:14,squash:12,squeez:2,srand:18,srtm:6,srtm_data_norway_1:6,sse4:[3,4],stabil:5,stabl:[0,4,5,6,7,9,11,15],stack:[2,3,4],stage:[5,13],stai:[0,2,4,5,11],stand:[0,5,9,12],standard:[0,1,4,5,6,7,8,10,12,16],standard_basi:2,standardscal:[0,6,7,8,9,10,11],stanford:13,start:[0,1,2,3,4,5,6,8,9,10,11,12,13,14,16,17,18],start_box:[2,13],start_nod:[2,13],start_tim:14,startpoint:18,stat:[0,6],state:[1,2,4,5,6,7,8,10,11,12,13,15,18],statement:[0,7,16],statist:[0,1,3,4,7,9,10,11,12,13,14,16,17,20],statu:[0,7,11],stavang:6,std:[0,4,6,18],stdev:18,stdout:5,steep:13,step:[0,1,2,3,4,6,7,9,10,11,12,13,14,16,18],step_fn:[7,12],step_length:13,steps_list:9,steps_per_epoch:3,stereo:3,stian:19,still:[2,3,5,6,11,13,18],stimuli:12,stk2100:20,stk3155:17,stk4021:20,stk4051:20,stk4155:17,stk5000:20,stk:20,stochast:[0,1,5,6,8,11,12,17],stock:4,stoke:12,stone:[0,7],stop:[1,4,7,9,11,13,14,18],storag:5,store:[0,1,2,3,6,11,13,18],str:[1,3,4],straight:[0,6,8,13],straightforward:[0,2,3,5,6,8,9,10,13,16],strategi:[0,1,9],stratifi:6,streamtyp:5,strength:[0,5,14],stretch:11,strict:[8,13],strictli:[8,13],stride:[4,16],strike:6,string:[1,18],stroke:7,strong:[3,6,9,10,12,18],strongli:[0,8,15,16],stronli:0,structur:[0,1,2,3,6,9,10,12,15],stuck:[1,13],student:[0,17,19,20],studi:[0,3,4,5,6,7,8,11,12,13,15,20],studier:[17,20],style:[0,7,9,16],sub:[9,12],subarg:[2,13],subdivid:[0,16],subfield:0,subject:[5,6,8,18],subplot:[0,1,3,4,6,7,8,9,10,13,14],subplots_adjust:[8,18],subprogram:16,subract:0,subroutin:0,subscript:1,subsequ:[1,4,5,6,12,16,18],subset:[1,6,9,12,13,15],subspac:[0,8,11],substanti:[9,10],substep:11,substitut:[3,6,12,16],subsubset:9,subtask:6,subtl:1,subtract:[0,4,5,6,11,13,16,18],subtre:9,subval:[2,13],succeed:[0,4],success:[3,7,9,13,18],successfulli:[4,9],sucess:18,sudo:[0,15],suffer:[0,1,2,5,10],suffici:[1,6,8,11,13],suggest:[1,13,20],suit:[8,12],suitabl:[0,18],sum:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18],sum_:[0,1,2,3,5,6,7,8,9,10,11,12,13,14,16,18],sum_i:[2,5,6,8,13],sum_j:6,sum_k:[6,8,12,16],sum_m:3,sum_n:3,sum_nx_:3,summar:[5,6,9],summari:[1,3,4,10,17],summat:3,sunni:9,superfici:3,superscript:[1,12],supervis:[0,5,6,7,9,12,15],supplement:7,support:[0,1,4,9,10,11,13,15,17],suppos:[0,5,6,7,8,10,11,12,13,16],suppress:[5,13],sure:[1,4,6],surf:6,surfac:[0,6],surpass:6,surpris:0,surround:[3,15],survei:[0,5,6],svc:[8,9,10],svd:[0,6,11,17],svdinv:5,svm:[8,9,10,11],svm_clf:[8,10],swap:2,swapax:2,swath:5,sy:[5,13],symbol:[1,5,11,13,15,18],symmeteri:1,symmetr:[0,5,8,11,12,13,16],symmetri:[6,9],sympi:[0,15],synonim:18,syntax:[1,13,16],syntaxerror:[1,16],syrk:5,system:[0,1,3,4,5,6,7,9,10,12,13,15,16,20],systemat:[4,6,18],t0:[3,6,13],t1:[2,13],t2:2,t3:2,t:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18],t_0:[2,9,13],t_1:13,t_:2,t_b:10,t_i:[1,2,12],t_j:[5,12],t_k:9,tabl:[9,18,19],tabul:0,tackl:4,tag:[2,3,4,5,6,7,12,13,14,16,18],taht:0,tail:18,tailor:[2,8,11],taiwan:0,take:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,15,16,18],taken:[0,1,3,6,10,13,16],tan:3,tangent:[1,4,12,13],tanh:[1,4,7,8,12,13],tape:3,target:[0,1,3,4,5,6,7,8,9,10,11,12,13],target_nam:9,task:[0,1,3,5,6,9,11,12,14],tau:[3,5,18],tax:0,taylor:[2,13],taylornr:13,tc:8,team:1,teaser:0,technic:[0,5,6,13],techniqu:[0,1,8,10,13,15,17,18,20],technolog:[0,1],tek5040:20,tell:[0,4,6,10,11,13,18],temp1:1,temp2:1,temp:1,temperatur:[0,9],temporarili:1,ten:3,tend:[3,5,6,8,9,10,12,13,14],tendenc:0,tension:6,tensor:3,tensorflow:[0,2,4,8,14,15,16,17,20],term1:[5,6,11],term2:[5,6,11],term3:[5,6,11],term4:[5,6,11],term:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,18],termin:[0,4,5,9,10,13],terrain1:6,terrain:6,test:[3,4,5,6,7,8,9,10,13,16,18],test_acc:3,test_accuraci:[1,3],test_error:6,test_imag:[3,4],test_ind:6,test_input:4,test_label:[3,4],test_loss:3,test_pr:1,test_predict:1,test_rnn:4,test_scor:[7,10],test_siz:[0,1,3,5,6,10],test_split:9,testerror:[0,6],testi:4,testpredict:4,testx:4,text:[0,1,2,4,5,8,9,11,13,16,17,18,20],textual:9,textur:[1,9],tf:[1,3,4,13,14],tfe_py_execut:3,th:[0,1,2,5,6,7,9,12,13,14,16,18],than:[0,1,2,3,4,5,6,7,9,10,11,12,13,15,18],thank:[4,6],theano:[1,15],thei:[0,1,2,3,4,5,6,7,8,9,11,12,13,16,18],them:[0,1,3,4,6,8,9,10,11,12,13,16],theme:0,themselv:[0,18],thenc:6,theorem:[2,6,7],theoret:[0,4,10],theori:[0,1,3,8,9,12,13,15,17,20],thereaft:[0,5,6,11,12,16],therebi:[0,5,7,11,18],therefor:[0,1,2,3,4,6,7,8,11,13,18],therein:11,thereof:[0,6,13],theta:[1,4,13,18],theta_:[1,13],theta_i:1,theta_k:18,theta_linreg:13,theta_t:13,thi:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20],thing:[0,1,2,4,5,7,9,18],think:[0,1,3,4,6,9,12,13,14,18],third:[0,3,6,13],thirti:7,those:[3,5,6,8,9,10,11,16,17],though:[1,2,3,4,13,16,18],thought:[6,14,18],thousand:[0,1],thread:3,three:[0,1,3,5,6,8,9,12,16,17,19],threshold:[1,3,9,10,11,12,13],through:[0,1,2,3,4,5,6,8,11,12,13,14,15,16,18],throughout:[0,4,5,14,15,16,18],thu:[0,1,2,5,6,7,8,10,11,12,13,18,19],thumb:[0,6],thursdai:17,tibshirani:[6,17,20],tick_param:6,ticker:[6,13,18],tif:6,tight_layout:[1,7],tightli:11,tild:[0,5,6,11,18],till:[0,4,7,8,9,10,12,16],time:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,17,18],timefunct:18,timeit:4,timer:4,tini:1,tip:3,titl:[0,1,2,3,4,6,7,8,9,10,13,18],tmp:13,tmp_log:3,tn:[2,3],to_categor:[1,3,4],to_categorical_numpi:1,to_numer:[0,6],to_str:18,todai:3,togeth:[0,3,6,8,11],toi:[13,14],told:13,toler:[2,4,6,14],tolist:4,tomographi:12,too:[0,2,4,5,6,9,11,13,18,20],took:8,tool:[0,1,3,6,13,15,18],toolbox:8,top:[0,3,5,6,9,10,15],topic:[0,5,6,7,8,15,17,20],topolog:[1,3,12],toposort:2,toss:10,total:[0,1,2,3,4,6,7,8,10,11,12,13,14,16,18,19],total_loss:4,totalclustervari:14,totalscatt:14,totalvari:18,toward:[1,2,7,12,13],town:0,tp:4,tpng:9,tqdm:6,trace:[2,13],trace_stack:[2,13],traceback:[2,3,4,5,6,8,9,10,13],tracer:[2,13],track:[3,13,14,16],tract:0,tractabl:0,trade:[5,9],tradeoff:[0,5,17],tradit:[0,1,4,6],train:[2,3,5,6,8,9,10,11,12,13],train_accuraci:[0,1,3],train_dataset:4,train_end:[0,1],train_error:6,train_funct:3,train_imag:[3,4],train_ind:6,train_label:[3,4],train_pr:1,train_siz:[0,1,3],train_step:4,train_test_split:[0,1,3,5,6,7,9,10,11],train_test_split_numpi:[0,1],trainabl:4,trainable_vari:4,trained_model:6,trainerror:0,traini:4,training_checkpoint:4,training_dataset:4,training_gradi:13,training_gradient_fun:13,training_loss:13,trainingerror:6,trainpredict:4,trainscor:4,trainx:4,trait:0,trajectori:4,tran:5,transfer:9,transform:[0,5,6,7,8,9,10,11,12,13,15,16],transit:[6,12],translat:[1,4,6,10],transpos:[1,5,11,16],travers:[0,5],treat:[0,1,3,6,12,13,18],tree:[0,1,6,15,17],tree_clf:[9,10],tree_clf_:9,tree_clf_sr:9,tree_reg1:9,tree_reg2:9,tree_reg:9,trend:18,trevor:20,tri:[2,3,4,9,13],triain:0,trial:[0,2,4,6,13,18],triangl:13,triangular:16,trick:[3,4,8,11,13,18],trickier:18,tridiagon:16,trillion:15,trivial:[0,1,5,11,18],troubl:[0,8,12],truck:3,true_beta:6,true_divid:1,true_fun:6,tucker:8,tumor:[7,9],tumour:7,tunabl:1,tune:[4,9,13,16],tup:4,tupl:[2,13],turn:[0,1,5,6,7,8,9,10,11,12,13,16,18],tutori:[1,4],tv:2,tveito:2,tweak:[1,4,10,18],twice:13,twist:11,twister:18,two:[0,1,2,4,5,6,7,9,10,11,12,13,16,17,18,20],tx:13,tx_1:13,txt:4,ty:13,type:[0,1,3,6,8,10,13,16,18],typeerror:[2,13],typic:[0,1,2,3,4,5,7,9,10,12,13,18],u:[0,2,5,6,10,11,12,16],u_:16,u_i:12,u_m:10,ua:0,ubuntu:[0,15],uci:0,uio:[17,19,20],un:14,unari:16,unary_f:[2,13],unary_oper:[2,13],unary_to_nari:2,unbalanc:[6,9],unbias:[0,5,6,18],uncent:6,uncertainti:[0,5],uncertitud:18,unchang:[1,3],uncorrel:10,undefin:5,under:[0,1,5,6,10,13,15],underdetermin:0,underfit:[1,6],underflowproblem:5,undergo:5,undergradu:17,underli:[0,1,9,13,18],underset:[4,14],understand:[0,1,3,5,6,10,13,14,15],understood:[8,13],undesir:8,undetermin:[5,8],undo:4,unexpect:[6,18],unexpected:18,unfair:6,unfortun:[1,8,9,10],unicode_liter:[8,9],uniform:[0,1,5,6,11,13],uniform_real_distribut:18,uniformli:[13,18],unifrompdf:18,unimport:13,union:[5,6],uniqu:[0,2,6,13,14,16],unique_cluster_label:14,unit:[0,1,3,4,5,10,12,18],unitari:[5,6,16],unitarili:16,uniti:18,univari:18,univers:[0,1,2,13,17,19],unix:1,unknow:[0,16],unknown:[0,1,3,4,5,6,8,10,16],unknowwn:12,unlabel:1,unless:[0,3,6,11,13],unlik:[1,3,8,13,18],unnecessarili:9,unord:3,unravel:1,unrol:[3,11],unseen:[0,7,9],unstabl:1,unsupervis:[0,1,4,12,15,17],unsymmetr:16,until:[1,2,4,9,12,13,14,18],untouch:0,unusu:12,up:[1,3,4,5,6,8,10,11,13,14,15,16,17,18],updat:[1,2,10,12,13,14],upload:[15,20],upon:[1,6,11,16],upper:[0,8,9,16],uppercas:[16,18],upsampl:4,upscal:4,us:[4,5,6,8,9,10,11,12,14,16,17,20],usag:[0,8,15,18],usd10000:0,usd:0,use_bia:4,use_multiprocess:3,usecol:0,useless:1,user:[0,1,2,3,4,6,7,8,11,15,16],userwarn:[3,6],usetex:18,usg:6,usr:18,usual:[0,3,4,7,12,13,14],ut:5,util:[0,1,3,4,6,7,10,14],ux:16,v0:18,v1:18,v2:18,v:[2,4,5,6,11,13,15],v_0:11,va:1,val:13,val_accuraci:3,val_loss:4,vale:2,valid:[0,1,4,7,9,10,13,15,17,18],validation_batch_s:3,validation_data:3,validation_freq:3,validation_split:[3,4],validation_step:3,valu:[0,1,2,3,4,6,7,8,9,10,12,13,14,15,16,17],valuat:9,valueerror:[2,4],valy:4,van:0,vandenbergh:[8,13],vandermond:0,vanilla:[0,6,11,14],vanish:[1,4,13,18],var_x:18,varabl:8,varepsilon:[5,6],varepsilon_:[5,6],varepsilon_i:[5,6],vari:[0,1,3,5,6,10],variabl:[0,1,2,3,5,6,7,8,10,11,12,13,14,16],varianc:[0,1,5,7,9,10,11,13,14,15,16,17],variance_i:[5,11],variance_x:[5,11],variant:[0,1,6,8,12,13],variat:[3,4,11],varieti:[0,3,12,15],variou:[1,3,5,6,7,8,9,11,12,13,15,16,18],vartempvec:18,varvec:18,varydimens:4,vastli:3,vaue:1,vault:0,vdot:[2,13],vec:[6,18],vector:[0,1,2,3,4,5,6,7,9,10,11,13,14,15,17],vector_mean:14,ventur:[0,8,15],verbos:[1,3,4],veri:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,18,20],verifi:[3,11,16],versatil:8,versicolor:[8,9],version:[0,3,10,13,14,15,16,18],versu:1,vert:[0,1,5,6,7,8,9,11,13],vert_1:[5,6],vert_2:[5,6,11],via:[0,5,6,7,8,9,10,11,12,15,16,17,18],vidal:11,video:[0,1,12,15,17],view:[1,3,5,6,12,13,17,18,20],violat:8,virginica:9,viridi:[0,1,2,3],virtual:1,viscos:13,viscou:13,visibledeprecationwarn:2,vision:[0,3],visual:[0,3,11,12,15],visualis:1,viz:[6,8,18],vjp:[2,13],vjp_0:2,vjp_0_fun:2,vjp_1:2,vjp_1_fun:2,vjp_argnum:2,vjpfun:2,vjpmaker:2,vjpnode:[2,13],vmax:[1,6],vmc:18,vmin:[1,6],voic:3,volum:[0,3],vote:10,voting_clf:10,votingclassifi:10,votingsimpl:10,vrtx:17,vs:[0,4,6],vspace:[2,13],vstack:[5,11,16,18],vt:5,w1:8,w2:[8,11],w3:8,w:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,16,18],w_1:[8,16],w_1x_1:8,w_1x_:8,w_2:[8,16],w_2x_2:8,w_2x_:8,w_3:16,w_4:16,w_:[1,12],w_hidden:2,w_i:[1,2,10],w_ix_i:12,w_j:16,w_m:16,w_output:2,w_px_:8,w_px_p:8,wa:[0,1,3,4,5,6,7,10,11,12,13,14,16],wai:[0,1,2,3,4,5,6,7,8,10,11,12,13,14,16,18],walk:9,walker:18,wang:0,want:[0,1,2,3,4,5,6,8,9,10,11,12,13,14,15,18],warn:[0,1,3,4,8],warrant:6,wast:3,watch:[3,15],wave:3,wavelet:8,we:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,20],weak:[9,10,14],weather:[1,12],web:[15,17],webpag:17,websit:[6,16,17],wedg:[8,18],wednesdai:17,wee:11,week:[5,6,7],weekli:[15,20],weight:[0,1,2,3,6,7,9,10,12,13,18],weigth:2,welcom:[8,15],well:[0,1,2,3,4,5,6,7,8,9,10,12,13,15,16,17,18,20],went:8,were:[0,1,3,4,5,6,7,8,10,11,12,14,18],wessel:0,what:[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],whatev:3,when:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18],whenev:[13,18],where:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,18,19],wherea:[6,18],wherein:[1,12],whether:[0,3,5,7,9,18],which:[0,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,19],whichev:[1,3],white:9,who:[0,17],whole:[1,3,4,5,9,11,13],whose:[0,6,10,18],whow:[5,11],why:[0,1,3,6,13],wide:[0,1,3,6,7,12,15,16],widehat:6,width:[0,3,8,9],wieringen:0,win:10,wind:9,wing:19,winther:2,wiothout:6,wiscons:7,wisconsin:10,wisdom:6,wise:[0,1,5,12,13],wish:[0,2,5,7,8,11,13,14,16],with_std:0,wither:6,within:[0,2,3,4,7,9,12,13,14,18,20],withinclust:14,without:[0,1,5,6,8,9,11,12,13],won:0,wonder:8,word:[0,1,3,4,5,6,14,18],work:[0,1,4,6,7,8,9,13,15,17,18],worker:3,workshop:17,world:[0,8],worldwid:0,wors:[0,1,3,4,6],worst:9,worth:9,would:[0,1,3,5,6,7,8,9,10,11,12,13,16,18],wrap:[6,16,17],wrap_util:[2,13],write:[0,1,2,3,5,6,7,8,12,13,16,18],written:[0,2,3,5,11,12,13,15,16,18],wrong:[1,8],wrongli:[10,18],wrote:[5,11],wrt:[2,10,13],wth:10,www:[15,16,17,20],wx_1:8,x0:8,x1:[4,8,9,10,13],x1_exampl:8,x1d:8,x2:[8,9,10,13],x2d:[8,11],x2d_train:11,x2dsl:11,x3:8,x:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18],x_0:[0,5,11,16],x_1:[0,2,5,6,7,8,9,10,11,13,16,18],x_2:[0,2,5,6,7,8,9,10,11,13,16,18],x_3:[8,16,18],x_4:16,x_:[0,2,3,5,6,8,10,11,13,14,16,18],x_center:11,x_data:1,x_data_ful:1,x_hidden:2,x_i:[0,1,2,5,6,7,8,9,10,11,12,13,14,16,18],x_input:2,x_ix_:0,x_iy_i:8,x_j:[0,2,8,9,12,18],x_jy_j:8,x_k:[12,14,16,18],x_l:18,x_m:[6,12,16,18],x_n:[0,2,3,6,8,11,12,13,16,18],x_new:[9,10],x_offset:6,x_output:2,x_p:[3,7,9],x_poli:9,x_poly10:9,x_pred:4,x_prev:2,x_reduc:11,x_scale:8,x_test:[0,1,3,5,6,7,9,10,11],x_test_own:6,x_test_scal:[0,6,7,9,10,11],x_tot:4,x_train:[0,1,3,4,5,6,7,9,10,11],x_train_mean:6,x_train_own:6,x_train_scal:[0,6,7,9,10,11],x_val:1,xarrai:15,xavier:1,xbnew:13,xcode:[0,15],xdclassiffierconfus:10,xdclassiffierroc:10,xg_clf:10,xgb:10,xgbclassifi:10,xgboost:9,xgboot:10,xgbregressor:10,xgparam:10,xgtree:10,xi:[8,13],xi_1:8,xi_:8,xi_i:8,xk:8,xlabel:[0,1,2,3,4,5,6,7,8,9,10,13,18],xlim:[6,10],xm:9,xmesh:13,xnew:[0,13],xp:18,xpanda:0,xpd:[5,11],xplot:0,xs:9,xscale:0,xsr:9,xt_x:13,xtest:6,xtick:[3,6,8,9],xtrain:6,xu:0,xx:[0,5,16],xy:[0,4,6,8,16],xytext:8,xz:16,y1:4,y2:4,y3:4,y:[0,1,3,4,5,6,7,8,9,10,11,12,13,14,16,18],y_0:[0,5,11,16],y_1:[0,5,8,9,11,13,16],y_1y_1:8,y_1y_1k:8,y_1y_2:8,y_1y_2k:8,y_1y_n:8,y_1y_nk:8,y_2:[0,5,8,9,11,16],y_2y_1:8,y_2y_1k:8,y_2y_2:8,y_2y_2k:8,y_3:[0,9,16],y_4:16,y_:[0,1,5,6,10,11,16],y_data:[0,1,5,6],y_data_ful:1,y_decis:8,y_fit:0,y_i:[0,1,5,6,7,8,9,10,11,12,13,16],y_if_:10,y_ix_:0,y_ix_i:[7,8,13],y_iy_jk:8,y_j:[6,8,12],y_k:12,y_m:16,y_model:[0,4,5,6],y_n:[8,13],y_ny_1:8,y_ny_1k:8,y_ny_2:8,y_ny_2k:8,y_ny_n:8,y_ny_nk:8,y_offset:6,y_plot:9,y_pred1:9,y_pred2:9,y_pred:[0,1,4,6,7,8,9,10],y_pred_rf:10,y_pred_tre:10,y_proba:[7,10],y_scaler:6,y_test:[0,1,3,4,5,6,7,9,10,11],y_test_onehot:1,y_test_predict:0,y_tot:4,y_train:[0,1,3,4,5,6,7,9,10,11],y_train_mean:6,y_train_onehot:1,y_train_predict:0,y_train_scal:6,y_val:1,ye:[3,6,7],year:[0,15],yet:[0,1,6,8,11,13],yi:13,yield:[0,2,4,5,6,8,10,12,13,14,16,18],yk:8,ylabel:[0,1,2,3,4,5,6,7,8,9,10,13,18],ylim:[3,6],ym:9,ymesh:13,yn:0,yo:[8,9,10],yoshua:[1,20],you:[0,1,2,3,4,5,6,8,9,10,11,13,15,16,18,20],young:0,your:[1,2,4,5,6,8,11,13,15,16,18],yourself:[11,13],youtub:15,ypred:6,ypredict2:13,ypredict:[0,13],ypredictlasso:5,ypredictol:5,ypredictown:6,ypredictownridg:6,ypredictridg:[5,6],ypredictskl:6,ys:9,ytest:6,ytick:[3,6,8,9],ytild:[0,6],ytildelasso:5,ytildenp:0,ytildeol:5,ytildeownridg:6,ytilderidg:[5,6],ytrain:6,yx:16,yy:16,yz:16,z:[0,1,2,3,4,5,6,7,8,9,11,12,13,16,18],z_0:16,z_1:16,z_2:16,z_:[1,2,12,16],z_c:1,z_h:1,z_hidden:2,z_i:[1,12],z_j:[1,12],z_k:12,z_m:1,z_mod:9,z_o:1,z_output:2,zaman:18,zaxi:6,zero:[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,16,18],zeros_lik:4,zfill:4,zip:[2,4,6,13],zl:5,zm_h:0,zn:0,zone:0,zx:16,zy:16,zz:16},titles:["3. Linear Regression","14. Building a Feed Forward Neural Network","15. Solving Differential Equations with Deep Learning","16. Convolutional Neural Networks","17. Recurrent neural networks: Overarching view","4. Ridge and Lasso Regression","5. Resampling Methods","6. Logistic Regression","8. Support Vector Machines, overarching aims","9. Decision trees, overarching aims","10. Ensemble Methods: From a Single Tree to Many Trees and Extreme Boosting, Meet the Jungle of Methods","11. Basic ideas of the Principal Component Analysis (PCA)","13. Neural networks","7. Optimization, the central part of any Machine Learning algortithm","12. Clustering and Unsupervised Learning","Applied Data Analysis and Machine Learning, FYS-STK3155/4155 at the University of Oslo, Norway","2. Linear Algebra, Handling of Arrays and more Python Features","Teaching schedule with links to material","1. Elements of Probability Theory and Statistical Data Analysis","Teachers and Grading","Textbooks"],titleterms:{"1":17,"10":17,"11":17,"12":17,"13":17,"15":17,"17":17,"18":17,"19":17,"2":0,"20":17,"2021":19,"22":17,"23":17,"24":17,"25":17,"26":17,"27":17,"29":17,"3":17,"30":17,"34":17,"35":17,"36":17,"37":17,"38":17,"39":17,"4":17,"40":17,"41":17,"4155":15,"42":17,"43":17,"44":17,"45":17,"46":17,"47":17,"5":17,"6":17,"8":17,"case":[8,10,18],"do":1,"final":12,"function":[0,1,6,7,8,10,11,12,13,18],"import":[5,16,18],"new":4,A:[0,1,4,8,9],And:13,Ising:6,The:[0,1,2,3,5,6,7,8,9,11,12,15,18],With:4,activ:[1,12],actual:18,ad:6,adaboost:10,adam:13,adapt:10,adjust:1,adversari:4,again:[3,9],aim:[8,9],algebra:16,algorithm:[9,10,11,12],algortithm:13,all:8,an:[0,4,10],analys:5,analysi:[0,5,6,11,15,18],ani:13,anoth:9,appli:15,approach:[0,8,14],approxim:12,architectur:1,arrai:16,assist:19,august:17,autocorrel:18,autograd:[2,13],automat:13,back:[1,11,12],background:15,bag:10,base:13,basic:[0,5,7,9,10,11,16],batch:1,bay:5,befor:11,better:[8,18],bia:6,binari:1,binomi:18,bird:10,block:18,boost:10,bootstrap:[6,10,18],boston:0,breast:1,bring:12,build:[1,3,9],calcul:18,cancer:[1,7,9,11],cart:9,central:[13,15,18],chain:12,chang:10,chi:0,choos:1,cifar01:3,classic:11,classif:[1,9,10],classifi:8,clip:1,cluster:14,cnn:3,code:[0,1,2,5,9,11,12,14,18],collect:[1,3],compar:[2,10],complex:[0,6],complic:6,compon:11,comput:[9,18],con:9,concept:18,conjug:13,continu:18,convex:[8,13],convolut:[3,12],correl:[11,18],cost:[1,10],cours:[15,20],covari:[5,11,18],cross:6,cumul:18,data:[0,1,3,6,7,9,11,15,18],dataset:[1,3],decai:2,decis:[9,10],decomposit:[5,11,16],deep:[1,2],defin:1,definit:18,degre:0,demonstr:18,dens:0,deriv:[5,12],descent:[2,10,13],detail:3,develop:1,deviat:18,diagon:11,dice:18,differ:8,differenti:[2,13],diffus:2,dimension:[2,3,8],disadvantag:9,discret:18,disguis:18,distribut:[5,18],domain:18,down:1,dropout:1,element:[0,18],elimin:16,ensembl:10,entropi:9,environ:0,equat:[0,2,12],error:[0,10],euler:2,evalu:1,event:18,exampl:[0,1,2,3,4,6,7,8,9,10,18],exercis:[0,6],expect:18,experi:18,explor:0,exponenti:[2,18],extrapol:4,extrem:10,ey:10,fall:19,famili:1,famou:18,featur:[9,16],feed:[1,12],fine:1,first:[4,12],fit:[0,10],forc:3,forest:10,forward:[1,2,12],fourier:3,frank:6,freedom:0,frequentist:0,from:[5,10,12],full:2,further:[3,5],fy:15,gan:4,gaussian:[16,18],gd:13,gener:[4,9,18],geometr:11,gini:9,good:0,grade:19,gradient:[1,2,10,13],growth:2,ha:15,handl:16,hidden:2,hous:0,how:18,hyperparamet:1,hyperplan:8,i:[1,18],id3:9,idea:11,implement:[1,18],implic:5,improv:1,includ:13,increment:11,index:9,inform:19,input:2,instal:15,instructor:19,interpret:[5,11],introduc:11,introduct:[0,6,15,16],invers:[5,16],iter:10,its:18,jackknif:18,jungl:10,kera:[1,3],kernel:[8,11],lagrangian:8,lasso:[5,6],later:5,layer:[1,2,3,12],learn:[0,1,2,11,13,14,15],least:[5,6],level:10,librari:15,likelihood:7,limit:[1,13,18],linear:[0,8,13,16],link:[5,11,17,20],logist:[7,13],lu:16,machin:[0,8,13,15],main:18,make:[0,9,10],mani:[10,12],materi:17,math:5,mathemat:[3,5,8],matric:5,matrix:[1,5,11,12,16,18],matter:0,mean:[0,18],meet:[5,10,18],mercer:8,mersenn:18,method:[6,9,10,13,18],mlp:12,mnist:[3,4],model:[0,1,4,6,12],moment:18,momentum:13,moon:[8,9],more:[3,6,16],multilay:12,multipl:[1,3],multipli:8,name:18,network:[1,2,3,4,7,12],neural:[1,2,3,4,12],non:8,normal:[0,1,18],norwai:15,notat:12,novemb:17,now:[1,9],nuclear:0,nueral:7,number:[0,2,18],numer:[2,18],numpi:16,object:3,observ:18,obtain:11,octob:17,od:2,off:6,ol:[5,6,13],one:[2,12],oper:16,optim:[1,8,13,15],ordinari:[5,6],organ:0,oslo:[15,20],other:[4,9,11,12,16,18],our:[0,4,5,11,13,18],outcom:15,output:[2,18],overarch:[0,4,8,9],overview:10,own:[0,10,11],packag:16,part:[13,15],partial:2,pass:1,pca:11,pdf:18,perceptron:12,perform:[1,9],period:[3,18],perspect:1,point:4,poisson:[2,18],polynomi:3,popul:2,practic:13,pre:[1,3],predict:4,prerequisit:[3,15],princip:11,principl:3,pro:9,probabl:[5,18],problem:[1,2,13],procedur:9,process:[1,3],program:[2,13],project:6,prop:13,propag:[1,12],properti:[5,18],pseudo:18,python:[0,9,15,16,18],quick:8,ran0:18,random:[10,11,18],read:9,real:6,recip:18,recurr:[4,12],reduc:0,reduct:3,reformul:2,regress:[0,5,6,7,9,10,13],regular:1,relev:20,relu:1,remark:3,remind:[6,8],requir:[2,15],resampl:6,rescal:6,resourc:2,revisit:13,ridg:[5,6],rm:13,rng:18,rule:12,s:[8,10,18],sampl:[11,18],schedul:17,schemat:9,scheme:2,scikit:[0,1,11],select:18,semest:19,septemb:17,set:[0,2,3,9,12],sgd:13,should:[1,18],simpl:[0,4,9,13,18],singl:10,singular:[5,11],situat:18,soft:8,softmax:1,solv:2,solver:13,some:13,specifi:2,split:0,squar:[0,5,6,10],standard:[13,18],state:0,statist:[5,6,15,18],steepest:[10,13],stk3155:15,stochast:[13,18],superposit:3,supervis:1,support:8,svd:5,systemat:3,teach:[17,19],teacher:19,techniqu:[6,11],technolog:15,tensorflow:[1,3],test:[0,1],textbook:20,theorem:[5,8,11,12,18],theori:18,three:18,tip:13,togeth:12,top:1,toss:18,toward:11,trade:6,tradeoff:6,train:[0,1,4],transform:3,tree:[9,10],tune:1,two:[3,8,15],type:[2,4,12],uncorrel:18,uniform:18,univers:[12,15,20],unsupervis:14,up:[0,2,9,12],us:[0,1,2,3,7,13,15,18],valid:6,valu:[5,11,18],variabl:18,varianc:[6,18],variou:0,vector:[8,12,16],view:[0,4,10],visual:[1,9],vs:3,wai:9,wave:2,week:17,weekli:17,what:[0,18],which:[1,18],why:18,wisconsin:7,write:[4,11],xgboost:10,your:[0,10]}}) \ No newline at end of file diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb index 0c8ec17f0..3b986144d 100644 --- a/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb +++ b/doc/LectureNotes/_build/jupyter_execute/chapter10.ipynb @@ -2,7 +2,21 @@ "cells": [ { "cell_type": "markdown", - "metadata": {}, + "id": "7e3af66b", + "metadata": { + "editable": true + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "id": "64b4469b", + "metadata": { + "editable": true + }, "source": [ "# Building a Feed Forward Neural Network\n", "\n", @@ -27,7 +41,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a27e39fb", + "metadata": { + "editable": true + }, "source": [ "$$\n", "P(y = 0 \\mid \\hat{x}, \\hat{\\theta}) = \\frac{1}{1 + \\exp{(- \\hat{x}})} ,\n", @@ -36,14 +53,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6332f4a5", + "metadata": { + "editable": true + }, "source": [ "and" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "5d2a5fe5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "P(y = 1 \\mid \\hat{x}, \\hat{\\theta}) = 1 - P(y = 0 \\mid \\hat{x}, \\hat{\\theta}) ,\n", @@ -52,13 +75,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "62bf3ae6", + "metadata": { + "editable": true + }, "source": [ "where $y \\in \\{0, 1\\}$ and $\\hat{\\theta}$ represents the weights and biases\n", - "of our network.\n", - "\n", - "\n", - "\n", + "of our network." + ] + }, + { + "cell_type": "markdown", + "id": "5fdb1150", + "metadata": { + "editable": true + }, + "source": [ "## Defining the cost function\n", "\n", "Our cost function is given as (see the Logistic regression lectures)" @@ -66,7 +98,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "64cfe441", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathcal{C}(\\hat{\\theta}) = - \\ln P(\\mathcal{D} \\mid \\hat{\\theta}) = - \\sum_{i=1}^n\n", @@ -76,7 +111,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "dbd78c70", + "metadata": { + "editable": true + }, "source": [ "This last equality means that we can interpret our *cost* function as a sum over the *loss* function\n", "for each point in the dataset $\\mathcal{L}_i(\\hat{\\theta})$. \n", @@ -87,10 +125,8 @@ "\n", "$y = 5 \\quad \\rightarrow \\quad \\hat{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$ and\n", "\n", - "\n", "$y = 1 \\quad \\rightarrow \\quad \\hat{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$ \n", "\n", - "\n", "i.e. a binary bit string of length $C$, where $C = 10$ is the number of classes in the MNIST dataset (numbers from $0$ to $9$).. \n", "\n", "If $\\hat{x}_i$ is the $i$-th input (image), $y_{ic}$ refers to the $c$-th component of the $i$-th\n", @@ -100,7 +136,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "67834a87", + "metadata": { + "editable": true + }, "source": [ "$$\n", "P(y_{ic} = 1 \\mid \\hat{x}_i, \\hat{\\theta}) = \\frac{\\exp{((\\hat{a}_i^{hidden})^T \\hat{w}_c)}}\n", @@ -110,7 +149,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "0521db23", + "metadata": { + "editable": true + }, "source": [ "which reduces to the logistic function in the binary case. \n", "The likelihood of this $C$-class classifier\n", @@ -119,7 +161,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "12a92031", + "metadata": { + "editable": true + }, "source": [ "$$\n", "P(\\mathcal{D} \\mid \\hat{\\theta}) = \\prod_{i=1}^n \\prod_{c=0}^{C-1} [P(y_{ic} = 1)]^{y_{ic}} .\n", @@ -128,14 +173,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e03ffaa9", + "metadata": { + "editable": true + }, "source": [ "Again we take the negative log-likelihood to define our cost function:" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "cfab4fa3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathcal{C}(\\hat{\\theta}) = - \\log{P(\\mathcal{D} \\mid \\hat{\\theta})}.\n", @@ -144,13 +195,23 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "864840d8", + "metadata": { + "editable": true + }, "source": [ "See the logistic regression lectures for a full definition of the cost function.\n", "\n", - "The back propagation equations need now only a small change, namely the definition of a new cost function. We are thus ready to use the same equations as before!\n", - "\n", - "\n", + "The back propagation equations need now only a small change, namely the definition of a new cost function. We are thus ready to use the same equations as before!" + ] + }, + { + "cell_type": "markdown", + "id": "496bdba3", + "metadata": { + "editable": true + }, + "source": [ "### Example: binary classification problem\n", "\n", "As an example of the above, relevant for project 2 as well, let us consider a binary class. As discussed in our logistic regression lectures, we defined a cost function in terms of the parameters $\\beta$ as" @@ -158,7 +219,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "8646c18f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathcal{C}(\\hat{\\beta}) = - \\sum_{i=1}^n \\left(y_i\\log{p(y_i \\vert x_i,\\hat{\\beta})}+(1-y_i)\\log{1-p(y_i \\vert x_i,\\hat{\\beta})}\\right),\n", @@ -167,14 +231,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "2dbfda71", + "metadata": { + "editable": true + }, "source": [ "where we had defined the logistic (sigmoid) function" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "5cd0a375", + "metadata": { + "editable": true + }, "source": [ "$$\n", "p(y_i =1\\vert x_i,\\hat{\\beta})=\\frac{\\exp{(\\beta_0+\\beta_1 x_i)}}{1+\\exp{(\\beta_0+\\beta_1 x_i)}},\n", @@ -183,14 +253,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "020de545", + "metadata": { + "editable": true + }, "source": [ "and" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "2efde2f5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "p(y_i =0\\vert x_i,\\hat{\\beta})=1-p(y_i =1\\vert x_i,\\hat{\\beta}).\n", @@ -199,7 +275,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "bf9a596d", + "metadata": { + "editable": true + }, "source": [ "The parameters $\\hat{\\beta}$ were defined using a minimization method like gradient descent or Newton-Raphson's method. \n", "\n", @@ -209,7 +288,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "0b392cc5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "a_i^l = y_i = \\frac{\\exp{(z_i^l)}}{1+\\exp{(z_i^l)}},\n", @@ -218,14 +300,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "5169434f", + "metadata": { + "editable": true + }, "source": [ "with" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "dcc8ed0a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "z_i^l = \\sum_{j}w_{ij}^l a_j^{l-1}+b_i^l,\n", @@ -234,7 +322,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "4010628a", + "metadata": { + "editable": true + }, "source": [ "where the superscript $l-1$ indicates that these are the outputs from layer $l-1$.\n", "Our cost function at the final layer $l=L$ is now" @@ -242,7 +333,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "7bf89431", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathcal{C}(\\hat{W}) = - \\sum_{i=1}^n \\left(t_i\\log{a_i^L}+(1-t_i)\\log{(1-a_i^L)}\\right),\n", @@ -251,14 +345,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "79bb56ee", + "metadata": { + "editable": true + }, "source": [ "where we have defined the targets $t_i$. The derivatives of the cost function with respect to the output $a_i^L$ are then easily calculated and we get" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "a27a06b5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial \\mathcal{C}(\\hat{W})}{\\partial a_i^L} = \\frac{a_i^L-t_i}{a_i^L(1-a_i^L)}.\n", @@ -267,12 +367,21 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "cd6acfaf", + "metadata": { + "editable": true + }, + "source": [ + "In case we use another activation function than the logistic one, we need to evaluate other derivatives." + ] + }, + { + "cell_type": "markdown", + "id": "b9e59acd", + "metadata": { + "editable": true + }, "source": [ - "In case we use another activation function than the logistic one, we need to evaluate other derivatives. \n", - "\n", - "\n", - "\n", "### The Softmax function\n", "\n", "In case we employ the more general case given by the Softmax equation, we need to evaluate the derivative of the activation function with respect to the activation $z_i^l$, that is we need" @@ -280,7 +389,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "eceaf7eb", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial f(z_i^l)}{\\partial w_{jk}^l} =\n", @@ -290,14 +402,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "bbc77522", + "metadata": { + "editable": true + }, "source": [ "For the Softmax function we have" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "88d4c18b", + "metadata": { + "editable": true + }, "source": [ "$$\n", "f(z_i^l) = \\frac{\\exp{(z_i^l)}}{\\sum_{m=1}^K\\exp{(z_m^l)}}.\n", @@ -306,14 +424,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b47f4092", + "metadata": { + "editable": true + }, "source": [ "Its derivative with respect to $z_j^l$ gives" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "65ec4336", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial f(z_i^l)}{\\partial z_j^l}= f(z_i^l)\\left(\\delta_{ij}-f(z_j^l)\\right),\n", @@ -322,14 +446,23 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "38f54e19", + "metadata": { + "editable": true + }, + "source": [ + "which in case of the simply binary model reduces to having $i=j$." + ] + }, + { + "cell_type": "markdown", + "id": "c0d8bc5e", + "metadata": { + "editable": true + }, "source": [ - "which in case of the simply binary model reduces to having $i=j$. \n", - "\n", - "\n", "## Developing a code for doing neural networks with back propagation\n", "\n", - "\n", "One can identify a set of key steps when using neural networks to solve supervised learning problems: \n", "\n", "1. Collect and pre-process data \n", @@ -342,8 +475,16 @@ "\n", "5. Evaluate model performance on test data \n", "\n", - "6. Adjust hyperparameters (if necessary, network architecture)\n", - "\n", + "6. Adjust hyperparameters (if necessary, network architecture)" + ] + }, + { + "cell_type": "markdown", + "id": "e3810222", + "metadata": { + "editable": true + }, + "source": [ "### Collect and pre-process data\n", "\n", "Here we will be using the MNIST dataset, which is readily available through the **scikit-learn**\n", @@ -389,6 +530,7 @@ { "cell_type": "code", "execution_count": 1, + "id": "5e7205ac", "metadata": { "collapsed": false, "editable": true @@ -412,7 +554,7 @@ }, "metadata": { "filenames": { - "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_33_1.png" + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_39_1.png" }, "needs_background": "light" }, @@ -468,7 +610,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "78721970", + "metadata": { + "editable": true + }, "source": [ "### Train and test datasets\n", "\n", @@ -486,6 +631,7 @@ { "cell_type": "code", "execution_count": 2, + "id": "dcc066a0", "metadata": { "collapsed": false, "editable": true @@ -532,7 +678,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "95cf3f87", + "metadata": { + "editable": true + }, "source": [ "### Define model and architecture\n", "\n", @@ -568,8 +717,16 @@ "\n", "$$ f(x) = \\sigma(x) = \\frac{1}{1 + e^{-x}} ,$$\n", "\n", - "which is inspired by probability theory (see logistic regression) and was most commonly used until about 2011. See the discussion below concerning other activation functions.\n", - "\n", + "which is inspired by probability theory (see logistic regression) and was most commonly used until about 2011. See the discussion below concerning other activation functions." + ] + }, + { + "cell_type": "markdown", + "id": "25c0cbe6", + "metadata": { + "editable": true + }, + "source": [ "### Layers\n", "\n", "* Input \n", @@ -602,7 +759,6 @@ "Since each neuron in the output layer is connected to the 50 inputs from the hidden layer we have 50x10 = 500\n", "weights to the output layer.\n", "\n", - "\n", "Typically weights are initialized with small values distributed around zero, drawn from a uniform\n", "or normal distribution. Setting all weights to zero means all neurons give the same output, making the network useless. \n", "\n", @@ -617,6 +773,7 @@ { "cell_type": "code", "execution_count": 3, + "id": "9f415ea2", "metadata": { "collapsed": false, "editable": true @@ -642,7 +799,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "afbff46b", + "metadata": { + "editable": true + }, "source": [ "### Feed-forward pass\n", "\n", @@ -664,7 +824,6 @@ "$$ a_{j}^{L} = \\frac{\\exp{(z_j^{L})}}\n", "{\\sum_{c=0}^{C-1} \\exp{(z_c^{L})}} .$$ \n", "\n", - "\n", "Since our data has the dimensions $X = (n_{inputs}, n_{features})$ and our weights to the hidden\n", "layer have the dimensions \n", "$W_{hidden} = (n_{features}, n_{hidden})$,\n", @@ -695,6 +854,7 @@ { "cell_type": "code", "execution_count": 4, + "id": "e05b2147", "metadata": { "collapsed": false, "editable": true @@ -757,7 +917,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6c8100ba", + "metadata": { + "editable": true + }, "source": [ "### Choose cost function and optimizer\n", "\n", @@ -770,10 +933,8 @@ "\n", "$$ y = 5 \\quad \\rightarrow \\quad \\hat{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$ \n", "\n", - "\n", "$$ y = 1 \\quad \\rightarrow \\quad \\hat{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$ \n", "\n", - "\n", "i.e. a binary bit string of length $C$, where $C = 10$ is the number of classes in the MNIST dataset. \n", "\n", "Let $y_{ic}$ denote the $c$-th component of the $i$-th one-hot vector. \n", @@ -782,10 +943,16 @@ "In the one-hot representation only one of the terms in the loss function is non-zero, namely the\n", "probability of the correct category $c'$ \n", "(i.e. the category $c'$ such that $y_{ic'} = 1$). This means that the cross entropy loss only punishes you for how wrong\n", - "you got the correct label. The probability of category $c$ is given by the softmax function. The vector $\\hat{\\theta}$ represents the parameters of our network, i.e. all the weights and biases. \n", - "\n", - "\n", - "\n", + "you got the correct label. The probability of category $c$ is given by the softmax function. The vector $\\hat{\\theta}$ represents the parameters of our network, i.e. all the weights and biases." + ] + }, + { + "cell_type": "markdown", + "id": "720d19fd", + "metadata": { + "editable": true + }, + "source": [ "### Optimizing the cost function\n", "\n", "The network is trained by finding the weights and biases that minimize the cost function. One of the most widely used classes of methods is *gradient descent* and its generalizations. The idea behind gradient descent\n", @@ -814,9 +981,16 @@ "\n", "2. It significantly speeds up the calculation, since we do not have to use the entire dataset to calculate the gradient. \n", "\n", - "The various optmization methods, with codes and algorithms, are discussed in our lectures on [Gradient descent approaches](https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html).\n", - "\n", - "\n", + "The various optmization methods, with codes and algorithms, are discussed in our lectures on [Gradient descent approaches](https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html)." + ] + }, + { + "cell_type": "markdown", + "id": "d0b1f84a", + "metadata": { + "editable": true + }, + "source": [ "### Regularization\n", "\n", "It is common to add an extra term to the cost function, proportional\n", @@ -834,7 +1008,6 @@ "\n", "i.e. we sum up all the weights squared. The factor $\\lambda$ is known as a regularization parameter.\n", "\n", - "\n", "In order to train the model, we need to calculate the derivative of\n", "the cost function with respect to every bias and weight in the\n", "network. In total our network has $(64 + 1)\\times 50=3250$ weights in\n", @@ -842,9 +1015,16 @@ "layer ($+1$ for the bias), and the gradient must be calculated for\n", "every parameter. We use the *backpropagation* algorithm discussed\n", "above. This is a clever use of the chain rule that allows us to\n", - "calculate the gradient efficently. \n", - "\n", - "\n", + "calculate the gradient efficently." + ] + }, + { + "cell_type": "markdown", + "id": "96417f62", + "metadata": { + "editable": true + }, + "source": [ "### Matrix multiplication\n", "\n", "To more efficently train our network these equations are implemented using matrix operations. \n", @@ -881,6 +1061,7 @@ { "cell_type": "code", "execution_count": 5, + "id": "c692ab5f", "metadata": { "collapsed": false, "editable": true @@ -897,7 +1078,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n" ] }, @@ -982,7 +1163,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9d0ad486", + "metadata": { + "editable": true + }, "source": [ "## Improving performance\n", "\n", @@ -997,7 +1181,6 @@ "If this does not improve network performance, you may want to consider altering the network architecture, adding more neurons or hidden layers. \n", "Andrew Ng goes through some of these considerations in this [video](https://youtu.be/F1ka6a13S9I). You can find a summary of the video [here](https://kevinzakka.github.io/2016/09/26/applying-deep-learning/). \n", "\n", - "\n", "It is very natural to think of the network as an object, with specific instances of the network\n", "being realizations of this object with different hyperparameters. An implementation using Python classes provides a clean structure and interface, and the full implementation of our neural network is given below." ] @@ -1005,6 +1188,7 @@ { "cell_type": "code", "execution_count": 6, + "id": "84088dcb", "metadata": { "collapsed": false, "editable": true @@ -1114,7 +1298,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "61dae78a", + "metadata": { + "editable": true + }, "source": [ "## Evaluate model performance on test data\n", "\n", @@ -1130,6 +1317,7 @@ { "cell_type": "code", "execution_count": 7, + "id": "999a01b6", "metadata": { "collapsed": false, "editable": true @@ -1164,7 +1352,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "12b8be76", + "metadata": { + "editable": true + }, "source": [ "## Adjust hyperparameters\n", "\n", @@ -1175,6 +1366,7 @@ { "cell_type": "code", "execution_count": 8, + "id": "f022ba3c", "metadata": { "collapsed": false, "editable": true @@ -1464,7 +1656,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n" ] }, @@ -1482,7 +1674,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n" ] }, @@ -1500,7 +1692,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n" ] }, @@ -1518,7 +1710,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n" ] }, @@ -1536,7 +1728,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n" ] }, @@ -1554,7 +1746,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n" ] }, @@ -1572,7 +1764,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n" ] }, @@ -1590,11 +1782,11 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", " exp_term = np.exp(self.z_o)\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", " self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n" ] }, @@ -1612,11 +1804,11 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", " exp_term = np.exp(self.z_o)\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", " self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n" ] }, @@ -1634,11 +1826,11 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", " exp_term = np.exp(self.z_o)\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", " self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n" ] }, @@ -1656,11 +1848,11 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", " exp_term = np.exp(self.z_o)\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", " self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n" ] }, @@ -1678,11 +1870,11 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", " exp_term = np.exp(self.z_o)\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", " self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n" ] }, @@ -1700,7 +1892,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n" ] }, @@ -1718,11 +1910,11 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", " exp_term = np.exp(self.z_o)\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", " self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n" ] }, @@ -1740,11 +1932,11 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", " exp_term = np.exp(self.z_o)\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", " self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n" ] }, @@ -1762,11 +1954,11 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", " exp_term = np.exp(self.z_o)\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", " self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n" ] }, @@ -1784,11 +1976,11 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", " exp_term = np.exp(self.z_o)\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", " self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n" ] }, @@ -1806,11 +1998,11 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", " exp_term = np.exp(self.z_o)\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", " self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n" ] }, @@ -1828,11 +2020,11 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", " exp_term = np.exp(self.z_o)\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", " self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n" ] }, @@ -1850,11 +2042,11 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", " exp_term = np.exp(self.z_o)\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", " self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n" ] }, @@ -1872,11 +2064,11 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:43: RuntimeWarning: overflow encountered in exp\n", " exp_term = np.exp(self.z_o)\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/1630775253.py:44: RuntimeWarning: invalid value encountered in true_divide\n", " self.probabilities = exp_term / np.sum(exp_term, axis=1, keepdims=True)\n" ] }, @@ -1916,7 +2108,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "118ee392", + "metadata": { + "editable": true + }, "source": [ "## Visualization" ] @@ -1924,6 +2119,7 @@ { "cell_type": "code", "execution_count": 9, + "id": "01cd7236", "metadata": { "collapsed": false, "editable": true @@ -1933,15 +2129,15 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n", - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/953065564.py:4: RuntimeWarning: overflow encountered in exp\n", " return 1/(1 + np.exp(-x))\n" ] }, @@ -1954,7 +2150,7 @@ }, "metadata": { "filenames": { - "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_49_1.png" + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_59_1.png" } }, "output_type": "display_data" @@ -1968,7 +2164,7 @@ }, "metadata": { "filenames": { - "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_49_2.png" + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_59_2.png" } }, "output_type": "display_data" @@ -2012,7 +2208,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "1cef52ca", + "metadata": { + "editable": true + }, "source": [ "## scikit-learn implementation\n", "\n", @@ -2032,6 +2231,7 @@ { "cell_type": "code", "execution_count": 10, + "id": "08650740", "metadata": { "collapsed": false, "editable": true @@ -2606,6 +2806,10 @@ "Learning rate = 10.0\n", "Lambda = 0.001\n", "Accuracy score on test set: 0.10555555555555556\n", + "\n", + "Learning rate = 10.0\n", + "Lambda = 0.01\n", + "Accuracy score on test set: 0.06388888888888888\n", "\n" ] }, @@ -2613,10 +2817,6 @@ "name": "stdout", "output_type": "stream", "text": [ - "Learning rate = 10.0\n", - "Lambda = 0.01\n", - "Accuracy score on test set: 0.06388888888888888\n", - "\n", "Learning rate = 10.0\n", "Lambda = 0.1\n", "Accuracy score on test set: 0.08888888888888889\n", @@ -2659,7 +2859,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9a5819b0", + "metadata": { + "editable": true + }, "source": [ "## Visualization" ] @@ -2667,6 +2870,7 @@ { "cell_type": "code", "execution_count": 11, + "id": "c76390e1", "metadata": { "collapsed": false, "editable": true @@ -2681,7 +2885,7 @@ }, "metadata": { "filenames": { - "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_53_0.png" + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_63_0.png" } }, "output_type": "display_data" @@ -2695,7 +2899,7 @@ }, "metadata": { "filenames": { - "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_53_1.png" + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter10_63_1.png" } }, "output_type": "display_data" @@ -2740,7 +2944,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6b973f8c", + "metadata": { + "editable": true + }, "source": [ "## Building neural networks in Tensorflow and Keras\n", "\n", @@ -2752,7 +2959,6 @@ "clear how to build one using an arbitrary number of hidden layers, using data structures such as Python lists or\n", "NumPy arrays.\n", "\n", - "\n", "Tensorflow is an open source library machine learning library\n", "developed by the Google Brain team for internal use. It was released\n", "under the Apache 2.0 open source license in November 9, 2015.\n", @@ -2775,12 +2981,15 @@ "Then we will build (effectively) the same graph in Keras, to see just\n", "how simple solving a machine learning problem can be.\n", "\n", - "To install tensorflow on Unix/Linux systems, use pip as" + "To install tensorflow on Unix/Linux systems, use pip as **pip3 install tensorflow**\n", + "and/or if you use **anaconda**, just write (or install from the graphical user interface)\n", + "(current release of CPU-only TensorFlow)" ] }, { "cell_type": "code", "execution_count": 12, + "id": "cb71108d", "metadata": { "collapsed": false, "editable": true @@ -2788,33 +2997,13 @@ "outputs": [ { "ename": "SyntaxError", - "evalue": "invalid syntax (2357089093.py, line 1)", + "evalue": "invalid syntax (2259440937.py, line 1)", "output_type": "error", "traceback": [ - "\u001b[0;36m File \u001b[0;32m\"/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42331/2357089093.py\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m pip3 install tensorflow\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n" + "\u001b[0;36m File \u001b[0;32m\"/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47411/2259440937.py\"\u001b[0;36m, line \u001b[0;32m1\u001b[0m\n\u001b[0;31m conda create -n tf tensorflow\u001b[0m\n\u001b[0m ^\u001b[0m\n\u001b[0;31mSyntaxError\u001b[0m\u001b[0;31m:\u001b[0m invalid syntax\n" ] } ], - "source": [ - "pip3 install tensorflow" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "and/or if you use **anaconda**, just write (or install from the graphical user interface)\n", - "(current release of CPU-only TensorFlow)" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], "source": [ "conda create -n tf tensorflow\n", "conda activate tf" @@ -2822,14 +3011,18 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "8cf89ee7", + "metadata": { + "editable": true + }, "source": [ "To install the current release of GPU TensorFlow" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 13, + "id": "ace3d31e", "metadata": { "collapsed": false, "editable": true @@ -2842,7 +3035,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f5d7454d", + "metadata": { + "editable": true + }, "source": [ "Keras is a high level [neural network](https://en.wikipedia.org/wiki/Application_programming_interface)\n", "that supports Tensorflow, CTNK and Theano as backends. \n", @@ -2851,7 +3047,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 14, + "id": "024068e3", "metadata": { "collapsed": false, "editable": true @@ -2863,19 +3060,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e36b74d0", + "metadata": { + "editable": true + }, "source": [ "You can look up the [instructions here](https://keras.io/) for more information.\n", "\n", "We will to a large extent use **keras** in this course. \n", "\n", - "\n", "Let us look again at the MINST data set." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 15, + "id": "42dbd743", "metadata": { "collapsed": false, "editable": true @@ -2929,7 +3129,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 16, + "id": "eba6a34d", "metadata": { "collapsed": false, "editable": true @@ -2957,7 +3158,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 17, + "id": "da80e8b6", "metadata": { "collapsed": false, "editable": true @@ -2986,7 +3188,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 18, + "id": "87273539", "metadata": { "collapsed": false, "editable": true @@ -3012,7 +3215,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 19, + "id": "8cd653a0", "metadata": { "collapsed": false, "editable": true @@ -3054,14 +3258,18 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "31009a5d", + "metadata": { + "editable": true + }, "source": [ "## The Breast Cancer Data, now with Keras" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 20, + "id": "991bf288", "metadata": { "collapsed": false, "editable": true @@ -3238,7 +3446,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d197746e", + "metadata": { + "editable": true + }, "source": [ "## Fine-tuning neural network hyperparameters\n", "\n", @@ -3256,7 +3467,6 @@ "training a neural network on a large dataset takes a lot of time, you\n", "will only be able to explore a tiny part of the hyperparameter space.\n", "\n", - "\n", "* You can use randomized search.\n", "\n", "* Or use tools like [Oscar](http://oscar.calldesk.ai/), which implements more complex algorithms to help you find a good set of hyperparameters quickly. \n", @@ -3272,12 +3482,16 @@ "as large image classification or speech recognition, typically require networks with dozens of layers\n", "and they need a huge amount\n", "of training data. However, you will rarely have to train such networks from scratch: it is much more\n", - "common to reuse parts of a pretrained state-of-the-art network that performs a similar task.\n", - "\n", - "\n", - "\n", - "\n", - "\n", + "common to reuse parts of a pretrained state-of-the-art network that performs a similar task." + ] + }, + { + "cell_type": "markdown", + "id": "3614fe93", + "metadata": { + "editable": true + }, + "source": [ "## Which activation function should I use?\n", "\n", "The Back propagation algorithm we derived above works by going from\n", @@ -3286,7 +3500,6 @@ "function with regards to each parameter in the network, it uses these\n", "gradients to update each parameter with a Gradient Descent (GD) step.\n", "\n", - "\n", "Unfortunately for us, the gradients often get smaller and smaller as the\n", "algorithm progresses down to the first hidden layers. As a result, the\n", "GD update leaves the lower layer connection weights\n", @@ -3302,9 +3515,6 @@ "neural networks suffer from unstable gradients, different layers may\n", "learn at widely different speeds\n", "\n", - "\n", - "\n", - "\n", "Although this unfortunate behavior has been empirically observed for\n", "quite a while (it was one of the reasons why deep neural networks were\n", "mostly abandoned for a long time), it is only around 2010 that\n", @@ -3327,8 +3537,6 @@ "(the hyperbolic tangent function has a mean of 0 and behaves slightly\n", "better than the logistic function in deep networks).\n", "\n", - "\n", - "\n", "Looking at the logistic activation function, when inputs become large\n", "(negative or positive), the function saturates at 0 or 1, with a\n", "derivative extremely close to 0. Thus when backpropagation kicks in,\n", @@ -3347,8 +3555,6 @@ "its inputs, and we also need the gradients to have equal variance\n", "before and after flowing through a layer in the reverse direction.\n", "\n", - "\n", - "\n", "One of the insights in the 2010 paper by Glorot and Bengio was that\n", "the vanishing/exploding gradients problems were in part due to a poor\n", "choice of activation function. Until then most people had assumed that\n", @@ -3357,9 +3563,16 @@ "that other activation functions behave much better in deep neural\n", "networks, in particular the ReLU activation function, mostly because\n", "it does not saturate for positive values (and also because it is quite\n", - "fast to compute).\n", - "\n", - "\n", + "fast to compute)." + ] + }, + { + "cell_type": "markdown", + "id": "0816093d", + "metadata": { + "editable": true + }, + "source": [ "## The RELU function family\n", "\n", "The ReLU activation function suffers from a problem known as the dying\n", @@ -3380,7 +3593,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d979c7db", + "metadata": { + "editable": true + }, "source": [ "$$\n", "ELU(z) = \\left\\{\\begin{array}{cc} \\alpha\\left( \\exp{(z)}-1\\right) & z < 0,\\\\ z & z \\ge 0.\\end{array}\\right.\n", @@ -3389,7 +3605,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "eadc7692", + "metadata": { + "editable": true + }, "source": [ "In general it seems that the ELU activation function is better than\n", "the leaky ReLU function (and its variants), which is better than\n", @@ -3404,8 +3623,6 @@ "spare time and computing power, you can use cross-validation or\n", "bootstrap to evaluate other activation functions.\n", "\n", - "\n", - "\n", "In most cases you can use the ReLU activation function in the hidden layers (or one of its variants).\n", "\n", "It is a bit faster to compute than other activation functions, and the gradient descent optimization does in general not get stuck.\n", @@ -3414,8 +3631,16 @@ "\n", "* For classification the softmax activation function is generally a good choice for classification tasks (when the classes are mutually exclusive).\n", "\n", - "* For regression tasks, you can simply use no activation function at all.\n", - "\n", + "* For regression tasks, you can simply use no activation function at all." + ] + }, + { + "cell_type": "markdown", + "id": "a78e9091", + "metadata": { + "editable": true + }, + "source": [ "## Batch Normalization\n", "\n", "Batch Normalization\n", @@ -3428,8 +3653,16 @@ "learn the optimal scale and mean of the inputs for each layer.\n", "In order to zero-center and normalize the inputs, the algorithm needs to estimate the inputs’ mean and\n", "standard deviation. It does so by evaluating the mean and standard deviation of the inputs over the current\n", - "mini-batch, from this the name batch normalization.\n", - "\n", + "mini-batch, from this the name batch normalization." + ] + }, + { + "cell_type": "markdown", + "id": "04e309c6", + "metadata": { + "editable": true + }, + "source": [ "## Dropout\n", "\n", "It is a fairly simple algorithm: at every training step, every neuron (including the input neurons but\n", @@ -3438,8 +3671,16 @@ "\n", "The\n", "hyperparameter $p$ is called the dropout rate, and it is typically set to 50%. After training, the neurons are not dropped anymore.\n", - " It is viewed as one of the most popular regularization techniques.\n", - "\n", + " It is viewed as one of the most popular regularization techniques." + ] + }, + { + "cell_type": "markdown", + "id": "f9eb2036", + "metadata": { + "editable": true + }, + "source": [ "## Gradient Clipping\n", "\n", "A popular technique to lessen the exploding gradients problem is to simply clip the gradients during\n", @@ -3449,12 +3690,18 @@ "This technique is called Gradient Clipping.\n", "\n", "In general however, Batch\n", - "Normalization is preferred.\n", - "\n", - "\n", + "Normalization is preferred." + ] + }, + { + "cell_type": "markdown", + "id": "95301882", + "metadata": { + "editable": true + }, + "source": [ "## A top-down perspective on Neural networks\n", "\n", - "\n", "The first thing we would like to do is divide the data into two or three\n", "parts. A training set, a validation or dev (development) set, and a\n", "test set. The test set is the data on which we want to make\n", @@ -3465,7 +3712,6 @@ "do not use any of the test data to train the algorithm. This is a\n", "cardinal sin in ML. Then:\n", "\n", - "\n", "* Estimate optimal error rate\n", "\n", "* Minimize underfitting (bias) on training data set.\n", @@ -3489,9 +3735,16 @@ "the test data. The difference between the performance of the algorithm\n", "on these two validation sets quantifies the train-test mismatch. This\n", "can serve as another important diagnostic when using DNNs for\n", - "supervised learning.\n", - "\n", - "\n", + "supervised learning." + ] + }, + { + "cell_type": "markdown", + "id": "e1da8c6e", + "metadata": { + "editable": true + }, + "source": [ "## Limitations of supervised learning with deep networks\n", "\n", "Like all statistical methods, supervised learning using neural\n", @@ -3504,8 +3757,6 @@ "\n", "Here we list some of the important limitations of supervised neural network based models. \n", "\n", - "\n", - "\n", "* **Need labeled data**. All supervised learning methods, DNNs for supervised learning require labeled data. Often, labeled data is harder to acquire than unlabeled data (e.g. one must pay for human experts to label images).\n", "\n", "* **Supervised neural networks are extremely data intensive.** DNNs are data hungry. They perform best when data is plentiful. This is doubly so for supervised methods where the data must also be labeled. The utility of DNNs is extremely limited if data is hard to acquire or the datasets are small (hundreds to a few thousand samples). In this case, the performance of other methods that utilize hand-engineered features can exceed that of DNNs.\n", @@ -3533,5 +3784,5 @@ } }, "nbformat": 4, - "nbformat_minor": 4 + "nbformat_minor": 5 } \ No newline at end of file diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter10.py b/doc/LectureNotes/_build/jupyter_execute/chapter10.py index fe19214e6..cc472478c 100644 --- a/doc/LectureNotes/_build/jupyter_execute/chapter10.py +++ b/doc/LectureNotes/_build/jupyter_execute/chapter10.py @@ -1,6 +1,9 @@ #!/usr/bin/env python # coding: utf-8 +# + # # Building a Feed Forward Neural Network # # We are now gong to develop an example based on the MNIST data @@ -33,9 +36,7 @@ # where $y \in \{0, 1\}$ and $\hat{\theta}$ represents the weights and biases # of our network. -# -# -# + # ## Defining the cost function # # Our cost function is given as (see the Logistic regression lectures) @@ -54,10 +55,8 @@ # # $y = 5 \quad \rightarrow \quad \hat{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$ and # -# # $y = 1 \quad \rightarrow \quad \hat{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$ # -# # i.e. a binary bit string of length $C$, where $C = 10$ is the number of classes in the MNIST dataset (numbers from $0$ to $9$).. # # If $\hat{x}_i$ is the $i$-th input (image), $y_{ic}$ refers to the $c$-th component of the $i$-th @@ -86,8 +85,7 @@ # See the logistic regression lectures for a full definition of the cost function. # # The back propagation equations need now only a small change, namely the definition of a new cost function. We are thus ready to use the same equations as before! -# -# + # ### Example: binary classification problem # # As an example of the above, relevant for project 2 as well, let us consider a binary class. As discussed in our logistic regression lectures, we defined a cost function in terms of the parameters $\beta$ as @@ -136,10 +134,8 @@ # \frac{\partial \mathcal{C}(\hat{W})}{\partial a_i^L} = \frac{a_i^L-t_i}{a_i^L(1-a_i^L)}. # $$ -# In case we use another activation function than the logistic one, we need to evaluate other derivatives. -# -# -# +# In case we use another activation function than the logistic one, we need to evaluate other derivatives. + # ### The Softmax function # # In case we employ the more general case given by the Softmax equation, we need to evaluate the derivative of the activation function with respect to the activation $z_i^l$, that is we need @@ -161,12 +157,10 @@ # \frac{\partial f(z_i^l)}{\partial z_j^l}= f(z_i^l)\left(\delta_{ij}-f(z_j^l)\right), # $$ -# which in case of the simply binary model reduces to having $i=j$. -# -# +# which in case of the simply binary model reduces to having $i=j$. + # ## Developing a code for doing neural networks with back propagation # -# # One can identify a set of key steps when using neural networks to solve supervised learning problems: # # 1. Collect and pre-process data @@ -180,7 +174,7 @@ # 5. Evaluate model performance on test data # # 6. Adjust hyperparameters (if necessary, network architecture) -# + # ### Collect and pre-process data # # Here we will be using the MNIST dataset, which is readily available through the **scikit-learn** @@ -350,7 +344,7 @@ print("Number of test images: " + str(len(X_test))) # $$ f(x) = \sigma(x) = \frac{1}{1 + e^{-x}} ,$$ # # which is inspired by probability theory (see logistic regression) and was most commonly used until about 2011. See the discussion below concerning other activation functions. -# + # ### Layers # # * Input @@ -383,7 +377,6 @@ print("Number of test images: " + str(len(X_test))) # Since each neuron in the output layer is connected to the 50 inputs from the hidden layer we have 50x10 = 500 # weights to the output layer. # -# # Typically weights are initialized with small values distributed around zero, drawn from a uniform # or normal distribution. Setting all weights to zero means all neurons give the same output, making the network useless. # @@ -434,7 +427,6 @@ output_bias = np.zeros(n_categories) + 0.01 # $$ a_{j}^{L} = \frac{\exp{(z_j^{L})}} # {\sum_{c=0}^{C-1} \exp{(z_c^{L})}} .$$ # -# # Since our data has the dimensions $X = (n_{inputs}, n_{features})$ and our weights to the hidden # layer have the dimensions # $W_{hidden} = (n_{features}, n_{hidden})$, @@ -512,10 +504,8 @@ print("correct label for image 0: " + str(Y_train[0])) # # $$ y = 5 \quad \rightarrow \quad \hat{y} = (0, 0, 0, 0, 0, 1, 0, 0, 0, 0) ,$$ # -# # $$ y = 1 \quad \rightarrow \quad \hat{y} = (0, 1, 0, 0, 0, 0, 0, 0, 0, 0) ,$$ # -# # i.e. a binary bit string of length $C$, where $C = 10$ is the number of classes in the MNIST dataset. # # Let $y_{ic}$ denote the $c$-th component of the $i$-th one-hot vector. @@ -524,10 +514,8 @@ print("correct label for image 0: " + str(Y_train[0])) # In the one-hot representation only one of the terms in the loss function is non-zero, namely the # probability of the correct category $c'$ # (i.e. the category $c'$ such that $y_{ic'} = 1$). This means that the cross entropy loss only punishes you for how wrong -# you got the correct label. The probability of category $c$ is given by the softmax function. The vector $\hat{\theta}$ represents the parameters of our network, i.e. all the weights and biases. -# -# -# +# you got the correct label. The probability of category $c$ is given by the softmax function. The vector $\hat{\theta}$ represents the parameters of our network, i.e. all the weights and biases. + # ### Optimizing the cost function # # The network is trained by finding the weights and biases that minimize the cost function. One of the most widely used classes of methods is *gradient descent* and its generalizations. The idea behind gradient descent @@ -557,8 +545,7 @@ print("correct label for image 0: " + str(Y_train[0])) # 2. It significantly speeds up the calculation, since we do not have to use the entire dataset to calculate the gradient. # # The various optmization methods, with codes and algorithms, are discussed in our lectures on [Gradient descent approaches](https://compphysics.github.io/MachineLearning/doc/pub/Splines/html/Splines-bs.html). -# -# + # ### Regularization # # It is common to add an extra term to the cost function, proportional @@ -576,7 +563,6 @@ print("correct label for image 0: " + str(Y_train[0])) # # i.e. we sum up all the weights squared. The factor $\lambda$ is known as a regularization parameter. # -# # In order to train the model, we need to calculate the derivative of # the cost function with respect to every bias and weight in the # network. In total our network has $(64 + 1)\times 50=3250$ weights in @@ -584,9 +570,8 @@ print("correct label for image 0: " + str(Y_train[0])) # layer ($+1$ for the bias), and the gradient must be calculated for # every parameter. We use the *backpropagation* algorithm discussed # above. This is a clever use of the chain rule that allows us to -# calculate the gradient efficently. -# -# +# calculate the gradient efficently. + # ### Matrix multiplication # # To more efficently train our network these equations are implemented using matrix operations. @@ -705,7 +690,6 @@ print("New accuracy on training data: " + str(accuracy_score(predict(X_train), Y # If this does not improve network performance, you may want to consider altering the network architecture, adding more neurons or hidden layers. # Andrew Ng goes through some of these considerations in this [video](https://youtu.be/F1ka6a13S9I). You can find a summary of the video [here](https://kevinzakka.github.io/2016/09/26/applying-deep-learning/). # -# # It is very natural to think of the network as an object, with specific instances of the network # being realizations of this object with different hyperparameters. An implementation using Python classes provides a clean structure and interface, and the full implementation of our neural network is given below. @@ -1000,7 +984,6 @@ plt.show() # clear how to build one using an arbitrary number of hidden layers, using data structures such as Python lists or # NumPy arrays. # -# # Tensorflow is an open source library machine learning library # developed by the Google Brain team for internal use. It was released # under the Apache 2.0 open source license in November 9, 2015. @@ -1023,18 +1006,11 @@ plt.show() # Then we will build (effectively) the same graph in Keras, to see just # how simple solving a machine learning problem can be. # -# To install tensorflow on Unix/Linux systems, use pip as - -# In[12]: - - -pip3 install tensorflow - - +# To install tensorflow on Unix/Linux systems, use pip as **pip3 install tensorflow** # and/or if you use **anaconda**, just write (or install from the graphical user interface) # (current release of CPU-only TensorFlow) -# In[ ]: +# In[12]: conda create -n tf tensorflow @@ -1043,7 +1019,7 @@ conda activate tf # To install the current release of GPU TensorFlow -# In[ ]: +# In[13]: conda create -n tf-gpu tensorflow-gpu @@ -1054,7 +1030,7 @@ conda activate tf-gpu # that supports Tensorflow, CTNK and Theano as backends. # If you have Anaconda installed you may run the following command -# In[ ]: +# In[14]: conda install keras @@ -1064,10 +1040,9 @@ conda install keras # # We will to a large extent use **keras** in this course. # -# # Let us look again at the MINST data set. -# In[ ]: +# In[15]: # import necessary packages @@ -1115,7 +1090,7 @@ for i, image in enumerate(digits.images[random_indices]): plt.show() -# In[ ]: +# In[16]: from tensorflow.keras.layers import Input @@ -1137,7 +1112,7 @@ X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=t test_size=test_size) -# In[ ]: +# In[17]: @@ -1160,7 +1135,7 @@ def create_neural_network_keras(n_neurons_layer1, n_neurons_layer2, n_categories return model -# In[ ]: +# In[18]: DNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object) @@ -1180,7 +1155,7 @@ for i, eta in enumerate(eta_vals): print() -# In[ ]: +# In[19]: # optional @@ -1218,7 +1193,7 @@ plt.show() # ## The Breast Cancer Data, now with Keras -# In[ ]: +# In[20]: @@ -1405,7 +1380,6 @@ plot_data(eta,n_neuron,Test_accuracy, 'testing') # training a neural network on a large dataset takes a lot of time, you # will only be able to explore a tiny part of the hyperparameter space. # -# # * You can use randomized search. # # * Or use tools like [Oscar](http://oscar.calldesk.ai/), which implements more complex algorithms to help you find a good set of hyperparameters quickly. @@ -1422,11 +1396,7 @@ plot_data(eta,n_neuron,Test_accuracy, 'testing') # and they need a huge amount # of training data. However, you will rarely have to train such networks from scratch: it is much more # common to reuse parts of a pretrained state-of-the-art network that performs a similar task. -# -# -# -# -# + # ## Which activation function should I use? # # The Back propagation algorithm we derived above works by going from @@ -1435,7 +1405,6 @@ plot_data(eta,n_neuron,Test_accuracy, 'testing') # function with regards to each parameter in the network, it uses these # gradients to update each parameter with a Gradient Descent (GD) step. # -# # Unfortunately for us, the gradients often get smaller and smaller as the # algorithm progresses down to the first hidden layers. As a result, the # GD update leaves the lower layer connection weights @@ -1451,9 +1420,6 @@ plot_data(eta,n_neuron,Test_accuracy, 'testing') # neural networks suffer from unstable gradients, different layers may # learn at widely different speeds # -# -# -# # Although this unfortunate behavior has been empirically observed for # quite a while (it was one of the reasons why deep neural networks were # mostly abandoned for a long time), it is only around 2010 that @@ -1476,8 +1442,6 @@ plot_data(eta,n_neuron,Test_accuracy, 'testing') # (the hyperbolic tangent function has a mean of 0 and behaves slightly # better than the logistic function in deep networks). # -# -# # Looking at the logistic activation function, when inputs become large # (negative or positive), the function saturates at 0 or 1, with a # derivative extremely close to 0. Thus when backpropagation kicks in, @@ -1496,8 +1460,6 @@ plot_data(eta,n_neuron,Test_accuracy, 'testing') # its inputs, and we also need the gradients to have equal variance # before and after flowing through a layer in the reverse direction. # -# -# # One of the insights in the 2010 paper by Glorot and Bengio was that # the vanishing/exploding gradients problems were in part due to a poor # choice of activation function. Until then most people had assumed that @@ -1507,8 +1469,7 @@ plot_data(eta,n_neuron,Test_accuracy, 'testing') # networks, in particular the ReLU activation function, mostly because # it does not saturate for positive values (and also because it is quite # fast to compute). -# -# + # ## The RELU function family # # The ReLU activation function suffers from a problem known as the dying @@ -1543,8 +1504,6 @@ plot_data(eta,n_neuron,Test_accuracy, 'testing') # spare time and computing power, you can use cross-validation or # bootstrap to evaluate other activation functions. # -# -# # In most cases you can use the ReLU activation function in the hidden layers (or one of its variants). # # It is a bit faster to compute than other activation functions, and the gradient descent optimization does in general not get stuck. @@ -1554,7 +1513,7 @@ plot_data(eta,n_neuron,Test_accuracy, 'testing') # * For classification the softmax activation function is generally a good choice for classification tasks (when the classes are mutually exclusive). # # * For regression tasks, you can simply use no activation function at all. -# + # ## Batch Normalization # # Batch Normalization @@ -1568,7 +1527,7 @@ plot_data(eta,n_neuron,Test_accuracy, 'testing') # In order to zero-center and normalize the inputs, the algorithm needs to estimate the inputs’ mean and # standard deviation. It does so by evaluating the mean and standard deviation of the inputs over the current # mini-batch, from this the name batch normalization. -# + # ## Dropout # # It is a fairly simple algorithm: at every training step, every neuron (including the input neurons but @@ -1578,7 +1537,7 @@ plot_data(eta,n_neuron,Test_accuracy, 'testing') # The # hyperparameter $p$ is called the dropout rate, and it is typically set to 50%. After training, the neurons are not dropped anymore. # It is viewed as one of the most popular regularization techniques. -# + # ## Gradient Clipping # # A popular technique to lessen the exploding gradients problem is to simply clip the gradients during @@ -1589,11 +1548,9 @@ plot_data(eta,n_neuron,Test_accuracy, 'testing') # # In general however, Batch # Normalization is preferred. -# -# + # ## A top-down perspective on Neural networks # -# # The first thing we would like to do is divide the data into two or three # parts. A training set, a validation or dev (development) set, and a # test set. The test set is the data on which we want to make @@ -1604,7 +1561,6 @@ plot_data(eta,n_neuron,Test_accuracy, 'testing') # do not use any of the test data to train the algorithm. This is a # cardinal sin in ML. Then: # -# # * Estimate optimal error rate # # * Minimize underfitting (bias) on training data set. @@ -1629,8 +1585,7 @@ plot_data(eta,n_neuron,Test_accuracy, 'testing') # on these two validation sets quantifies the train-test mismatch. This # can serve as another important diagnostic when using DNNs for # supervised learning. -# -# + # ## Limitations of supervised learning with deep networks # # Like all statistical methods, supervised learning using neural @@ -1643,8 +1598,6 @@ plot_data(eta,n_neuron,Test_accuracy, 'testing') # # Here we list some of the important limitations of supervised neural network based models. # -# -# # * **Need labeled data**. All supervised learning methods, DNNs for supervised learning require labeled data. Often, labeled data is harder to acquire than unlabeled data (e.g. one must pay for human experts to label images). # # * **Supervised neural networks are extremely data intensive.** DNNs are data hungry. They perform best when data is plentiful. This is doubly so for supervised methods where the data must also be labeled. The utility of DNNs is extremely limited if data is hard to acquire or the datasets are small (hundreds to a few thousand samples). In this case, the performance of other methods that utilize hand-engineered features can exceed that of DNNs. diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter10_39_1.png b/doc/LectureNotes/_build/jupyter_execute/chapter10_39_1.png new file mode 100644 index 0000000000000000000000000000000000000000..91a4496c5e66ab2c962e8d247a1291c2d93fd1c3 GIT binary patch literal 2976 zcmb_e3s6&68ji)<)sqdZ zKouffjDd=j@`?=@LV`)KfDscwq)AFlK*0!vS2Yj_2<)Yu+0Jy`+1XBK?&I8xiQg!FsKQ;>Qq!(ESv6ZGMCvQ6@Ue@RD==xZ+3BAuDc1)2V{L;$lor=629_N*ZZ+^dZtozI2 zn*S`PL$i^dda6 zr>*`)QiAyOtj2(b(lHoGT;BvkQ(9#5z?_*gr+Wk0JArI3fPDd!ae=)Z-%ySHK0XQf&ek&VX*#$nx09OJnyTb`i!t5@RrfOen}SC(oQ1 zGguDJ#oOPLOMDoIxkXU0UES(Md8QKv1*Lmpq@7inIrvO5&se2YV;zR)9fqM{ZYj6m z>63*r@rM9A54`eGVdrG2RZwk7)X4_X0AcA4cXcrVpV>m$lhDhO-+?UaU2wT24#NlV zUbe{9tw;$~rMk7Lzpi}92D!Q!DX~RfgodnKx!x*A%i$(NvDdkb0r ze3UfNVYnSK!KeVh*{`GA!V8;FUE=OOEdUo7_!ozD|17m>`oW)uafD1ZuutG)0Uim6IBl{YX<&;6gswLRXcD9uSs}k*03DqN_oKeD(~a z^LWP3NmDt|q#QdW5d_PHe&siADi1dBZfFwUU)_$(u|+0#q--fK1g#S(m&}!YtnF#; zfOkKEbT+5}a&=^d1vkMHzvwGu_-sK+tdOr^-2FFTP)(;{90_6{Ob!|&VL_{J_d9N? ztn^$gz!qk$=s-FEh%w*ZNM-vld|kWb{`ky2fVlem;yG~P8<4&m7_>&J9EQ;t!}7T} zmpI$*uB&riR{a(e7)9J(`-F2v`Y*x(fIuSVj|b0tdp>cK7q~^UU2q_Ff>n zg=gf+V+uf(15lXN9V+$C@c>pl0Wq?FU3wMI*tNBOWB^=fSE_w%mopqO*tkV+C0hPy z!MtC_(mXqWzojHBJuolqN?KEzA0-%x!DpU$OIme@C2xyr{b3QGAfEY23JYQ^U3op5 zGW(uxF5|~6FHE_+P;Ht(K9fqbUG&u$0}5jh`AN4Ajdb5fJ+pMlvYORGCbs;AsZ@Mm zQThOK#rIMv(l?RZ4=dOMdto~HO_v~_wAqzTx%^F+<%z}tYZT8Je40o$xC+Z-O?gR{; zA1`-iH~>#i`xfM4P}EC>dW)Gk!P%UXipzmj%iJ8xLFE1L)O9_^v+Y)b?#I#NRBBTg|JJRT>GbgjRUz8WJZl*)EiDb! z)+;3A9uNl0F+VTE*>j`P_dLB`7W&m>oI*scSn4_N_Q4mJ(2j1#YIL98P+HxTm|#Luq!G$+EHOK5L#QCaR{F!%5w`| z8G8PlQbQ(@>NHKlw6_MNcJC^1=`^^h;ap^4&{+J|cO?)jLnStH!QrnR~!w+Mv<4lYosQU$J==p%IxDLjDMD3K7! zZgz!%wA|cW9s96CwCh@S4%*3ynQ<^TYnIq=C}W0}7X_9$Gf8#f;o$)^1r%EW+gjR5 z_wt@&e`J^2H^6pttP)TNJm1B(8K`nUXg#zv|drCV~ccujri@{_ge-0u^@Gd lCgsJNArP99|CI*D93~?k>=eh%z^7$|zi$wpbKtWt{{>fyiKGAk literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter10_59_1.png b/doc/LectureNotes/_build/jupyter_execute/chapter10_59_1.png new file mode 100644 index 0000000000000000000000000000000000000000..6d146702945cbe319dd1eaa069902b9573ea2737 GIT binary patch literal 22294 zcmb5WcUV(P+b@i|?E<52tI?~xi6>AeLACAuvrDoB?a>77XLL`6V) z4M>*~N@!97B#^9cg8Dq}_q^YAo%06?S#@UCteN{)?s=)Dq0D%Q{SX5K10(FtO&tb? z-Adr^-hq8!i)HN*dGICee(SEgu9Ky^=Y3ZT2KD>y&h}33_BIdBA}w6qY@8g$gvEu$ zE}gY@cXxJ^5fO3t&jG?tu2v!~2{+rpMGiXOF?3^KILt!-+r`R zg<(&xY;|AWdA%nk#~*#(OYfNtqIlBEjg_V$jZG8 z4EL@ho%Vy0d>1Y_Tm~fbcbhySC&o!^ph}1*JzD;`ZOPl9huE$SZ_ujwW?!m+_}YrH;9WSOqft zsT9=s%L`Q;e=`i7(0H@U^R1|P{Y<|VM!z{yh}0yAotbP5BX%YSaH6+eB*1mzWjwkv zb<=rL8Ix$66U+_+MKBH-cP*ShwI@yebg^}(l5weH1W)z)fL+X0mn5D{U-AmOnB{93 z_nG(48Bg2RzdjYplir(-an<=_;X-->N=48h z=j&UA-EXTeAKkrpSvi;!U*)|j{@}|2KZv@KbvHlBvOOUe<4=L@+O^B*!@W=X?fv=Y z0SVqyr&=+Jh+qXu#_c!k9{RD9lMe~4vGjX)UBLJzfofjl=ZCpXx8d93WsAL*AGF3u zs454Yfl1}{^ysxliz(+C73g8x>n4Y3io-S_xo%t;=v;Zt$luBs9d+Rvol8Cr^J7AY=5!CpaH^n`5Dh_n5KfZ zj!r0jBfW$;>Uu2wffd_y-v*_L;Nej4y}O^8Q}4+>M#oGphP!**o<5RQs|#c$%*C#E z&3C1~DzWcRY7DzD_x;n8fl5!TfL?|(-VJn`l&(}&)zGGJ{$%gfsnp7a08Z4MP`wg+ zL*5G)1Qis_vf)^Rx!zpD(vk=awY}UxBK08g;_1Ux?K9B}Z+k+p5~ z=8v%f@Z30k=0)|fW~P~$nJP|3qXd>52T9`!2OjTzvXZgtp_9l;`6qc${$RJr@%DG3 zH(tJcX**PwpHg&4S558p`r@!47Z+E%BxKc|Am3+#sPb~DtpE?cc7=d@qMvPG^W*y` z6lFG@)NzA3(`$L$sLVN$r?IcE?*la>Q?6-kpJAA4t8~s6%SEu_Zq&b4SjF>wYiHPt1{OmBjhxhdKxM#!mGo9%Gt&p`; zv!x*j&+BQ55G+P680qI4>4UdPA6(a>u)oN0SO(Sw`X0DulwF=@xk*!$2!`GhU|pbh zVNZ=#c+B;@zrM#~{+l+TDWW@&RZtH11Uw$wkt%Q3auXE|4FimVpB#LWegx>Kx;Jk= z{rvg!l{L?OXSeR1{cGqGYJEQQe(m#2i{?n;NOdK6hB>tX%vLiBoPKNCw{G6dP>+=) zb|gMI!_=T3Ro5OTt;?*q{b8|YYcYG=_`|)&!X{)(HeI{Jc_y#ow&_yP-6dWXOD>V*Eohbbn)Q796TH=s7L zH`h2D+%pS~O-O%$2bHU9Xvn@1z;ueT1>SIHvfMovyS_X;=zl#G9(FLB4e6DQ4LBIX zs?PK;^p`lq?gMwNd&P$EKru1UK=--lazP`m!wy@W7Is0iiQt;4m#Kr=S}0{betdGF zgH{YmX16-k$}V9WE?|%|v*64y^y%b*T?`D(4}y*|FnqYQ56o{L3w~~D3YF6H<#B>L z1$>t%F_Et3_y=A-F;4&L-##lZGWJ2gLdh z`LqSWVXBYE5|~!Z!g&S3rO&RGxl=`Mx7``Z`|9Nb(RbXq1*VvjSBIzcpH|5qO+5b> z1H+}}!9Ai349)>AjWP(C>+}Qeo?xZVLHDNg%|~wkvEjSBm@?RXb}*TK;*m1jBcS}d zf0lo|2h5_Eon7hM&TjoY;N2xgaG70t^f_*qlpZ+e1A_p)&L3qEp&z<__VCRWz^i3zPTC5@ur2Q=TtH(R72qq{7hCOUi?Ryv) z9-{T03TO3}RVDb(iArz#dfc;0xlJOgEKjp^J8Z33waGl={KdjU=fwrL2Muzyz2&LB$u?974(=W8xJW>RU) zO^G$;6&cnqo%`n{bKjL;cT;S9K!u#8<*B#linbwztl%vT-R);~lMu`bobs-Qqx5s3 zV{hAinNuG1h1&~Of@`auI7`&fsZ`<(i#KGPICX#=yciw{O)Gl$whoXJH8^GG3~5M{ z-bS45lPf3+e#)kNNhU3LtG!~~4*gJ>W5`2o)IVP(bZyE?GxJ{l?gUH#TVuMS3?roN11az+ zq7fwGs0nZLiO5#V?mR_qiS^p0h`4ZKs{IwFuv8&FPnrqJX1*JRU9}<_IXp^Ys+*a; z9&C!wo1yNNaR1bt)twc1-!DpPU}iF3jA&r@mLj)SVvzhgJK82wuxyo2u_!`ZbF&<+Em1@jE`$r8h0sFG+#7G4O&~$rh zl)_@l1}6Ufv@I@qB0z&UyUQWZ7G89-?78piKenYA5APy2N3`Mw6K=kYmIh=9_J*lV`@mbhGU~8L*Bbd zEAJ&y*im~AKl|4~$_brf)m)NA{H~t<9)9`xBlFZ^l>4@c7#}UE^tPNZ3^g8Iv9g?> zZ5-f2>>U#$lVy9xW@Se1>@9u#_-#rPW3z30$rG7%%_5%Jt(Vz7AN)w!1I6 zpOYrcFdl}`bQ_9_z!t4<``>9`GMR_?aT%YI^|7{n%N^Y39lrs-Y*)tJ&;kqTf_uNaDoCiJ7&=!=WkiXb#j;_})abFjZ z%>-9FXz}8+6D{UQ_UO<2u{O+3VhcUrz6oG)+uQ%+gH{0u!&3!GXTx zI#)3df)ds*HJp)6j{EfZ(2+xz<2cFl_*0=N0*p;&#f(wisqh9*{RIR4BHGsI@$wC? zsr?Dp4;^pHe%IVYxsco@VCBrTcWOl{{A&ZF+Exm@+!0p0`f7+JOMWlYTs5|mAAQ%6 zTJDYGV=}W=nLl+d#o4UxOtrhwbPRPAot84U2Kv6)Jmg@Ag+!X6$$W@}el)h$Q6@EY zCsd$M#KEg3I5^lJQK%ZWuRRKj4IYW^y#dBm3Fs9jg7x^taAna3;bui5I~nIK3ZdYW zOLl!rxcRP>PlqQ#)5;<|;oHx0LeP(uyjk7)KN24Hl&>MSp45c7lk6aLjGUQiy2ck< zYM0^_iILYQ{*E-h5R6&9)Nr#wz$%Yn@6_5x9H;Ct4}%NBTO8C;RrMkll4EL`3~8{Q znm|e%E610ZGrr-h`dYLZBC3{oKpmrCDpI``x&t)?j3pP|JpBIgag4Z4=&5riQLT<) zvhk-@G^TThANqcS{4$}Tjii58CiNQN#+F*{(IN}ob9fxXw7UOXLU65e1Tnnl?P3@{ zoqS*~;b4z0RMg@aDz9g={FI339Wq8rHb&1|wLqcYHG~0BG1ursIs5(!xbcwp>3~IF&%FyccWhW&pKN;~$J!Cui#j418-O|CR z@IqLUL{zhb*ut1Y+L5Pe8u3|%g_fBBv)GQ-R1cIoVL9bd)>AFfAgl}mZ2(uBv>`CJ zFBl4IT?}r+ywuh4T~U|EsnixUc`lP*y16)5@I*GGMLdW;?oj{grCjRvn73T>-b0qxAmyQmQ;C*= z*%au+s?)c;n7|0(dBc)^dlmIY85TlvaDs*+6e~yTUJ;ozEa9J<+bD~o&X-)k6FpVN`kXs7my<5WZV}06KvQ$O?QkoJQcH4ISp^(E} z|5dCXOaMVOb3ovv#6CB>8%r(1GgofuWmqe~bXJl2#rH{$H)78`_Gee1@#mV7OP^OQ zzZnbsK=fFI2m7m&Q0-XKYG{s!(U05jxWhjIK#(TsFpy!{8guC2!H`xbh3{)gsSLO8H@OL-IAZH@fn`hJb78UTG^v( zdTulXz_snzDRj+vMSFQzoUF(7WV3`ssRl(ML_ly7Q+(Hpnr^-GNf~A*d#_h>p7I}_ z7D=cuC|{ZEdAEcJ8E#1PL*FJgZ%oCq`0o3$2Em6X=ccnW_K32N_&qR!f)|q#NRCO6 zA_c2}*eKz#p>7O{Lj|hYOYYMeW*r%9xZYTVLKJeFE3os$h^}7JXH(Su$uJ`6$J;pt zH0A3Oe&R`kgd?7Tyh*WcO&TqFNRbIk!ud^Wn1YkjXIn)o(n!#!lW%6kB!r-2npyDV z)00pqGf{NY<;@nkwP>5osXKIbPCbyezEd|!YftP%LdCa@3lih0rv$WXGR!uAxR7im z$Da>g)Vp-^!gD#KOMdzSBl=?M=jRzg|?>E>=7}wsC3&p=0_RZ7`d|_3T=%anS7z+aYFVI3OEXPnJ>(mC}_)4aj671SLB>wK*yYB{yY|MKXL7eXR zLRJ+7;!kA9Y=sM*Z``7DSvvsWQ@pc8lwrnC{BssyflIG+L16#!<7|mW{1=&Mz<`-N z{s{mKGc+E=tAVIK?`O~tuo*xQd$o>%WA>Ry06y>+sCfKJ8o&vLey$y$@V!Xu-xvCx z1%M61;rBaeWixN*2f(I(+0o(5q4ADW* z$K5+s*(2yTYa4myzyiA;ru4=ScF3d=fVJ$c-){he?N@o)-&gJO8yJR{qYoMlJ-4Y!e>X!HMTD%n_4~SLDw=@ybZOt z*1e+nVkEQo&UJs9YlR8QeBy7aH|6Q{^xi#B#Ic4}5~kuXtI)q&G{#DL4vQp4HA{wL zhLtPZZ_T|KJs}{Be+N-NC9-Rc9os9tO>nIw^_DCZuiA(6*qE=v-Q~{pb|c3}NJj3H zn!0Xf9E^w9H0RKmS5zFW!JUG8G?F=T=QbX#BEH}gZt$&NV-<5}AKe^lJl ztj9WYWBja>qppxWiBBUtURiKP)-GmO=U-UsT{@iCguAJgVJ0#<|9~c3UFjD>lVM8@ zVcu5uB(zN1z^`7$mc+?qD8yRD#Mk21lWn+_%@8?gUHSZz-nW0ut2&|f8WY>RkIZX1%YChZ-39~u64JZviNS;t-qI(CeG?^{E)q56yBTmZ9Jh}%UXu;P*Op0N1%DJi1#DeJ-7YP@woTk{^!fSgLyORzb+Q4HG7|9}-x~mPTp%Ybxem4*#kW`tq z&$jkU*mFtQsd)TL982pFj#DoH>XLc3*cqg&E#pOd&0{mL=wR!odFn=N1=yN+*s6#) zqZpb(P+rfPCXz!_I?j~$lvyA2FcTf@DHBs!_%KeHm>1;;RNdNhdG+Io;!8#&9aEn= zd^{#UpQ5@x!0^nbXUL;mx}`!>RLHNs5|B2i;q;;(iI8r)j)z6Nk|(eF95hi+6EW-U zNOMf|ai7`lZ>FFzs64Z?vk#zAeWiGKi>TC(BRYlG4pKc9GlITgLV5h$yuxBmWZkpY zP5$T?_*ya5L)3={mYob4K%?CPoT;vCz03{%QL2uq74b%=3yqndMTtqh9Mlq=G+U7K zQ40{^gbJBySyQ*p=h?dPEEe_NT#DeK`udid^~>~i)b~v#e~K6&)+(ZVUVgc2vDZLx zJ($Lc-OallQK@C*k-o znmE$Fh2La^+@A3?Hdyvi-tA#0Piw9e4@x8&D4X7ab%j%7t3umz1;WMdXuCv>lqHR~ z3w~>d0%`5By-;yXmix%jI=%}wUwidKh1a1hve^qc^QU_!dzZhcQn}(!W}5^t5Y|Wl z?NkU_?TS~cdH%6BR&cU#|9G{E_nrbp28~1a!38pcX-1CU+LArt25RHpxpFnlJ)2Ge z_+V;TmxK>}yLDho&TxZX)Dn#O40 z>tCk#JiJ$i6l!LFGMeMqnRJU?$}vtySC`IG%abR=o@17P2;o#siqz53(fe@kIwO~Y z$)`_!Tq!8@MdbbujeMm;@LW%`^~{fbj_@a+H*BXyM)AY|{+I&0>>5-?_4d4ir(oW2ZbyaBc;(Z14&Fc zwT{<&V%H2w7YJoJkSr@UaoNXT^xXJsbCUTepvtPpix&z!>$?L&iyhid$*;q-DDOUE{ORl;Z89w=As z9hN{rAa!a zHFEq)igLxO-*TJMpGzX>U%A@T-OCrNQ`m8OEWhmTGs0Jbp++ghk~a_e^`}9> z7ZUV$L8_Q{O50C7gr&`1Mv>5J4|14HUUXun&-13nv#;j&>t9t?Agqx3W`FR6;B+TK2Ai>ZZb0-=qjJ|s$IrJLNKa}_D^X?57{)JBYZuZg-V0!F%dlSTJPUU#>?Ha9Xj=i z*x)}F_&9JREXA#%Yo9;8xrgz)868&GHu{$1U#eV<6@bYUNo$lV`LUYu1<3e%m(pj< zlH|Y)y|A;xtM`QQv!@=QI1Nqh?Q_m^b7N6o>e)4=ZYwJb@=SIuNr{W=0paCxk@rGz zpZL9x3_#U0p6kQH1DH4*%h0++Z!xPjy@ntT3G0rt`k6X)uT4inbzd$MOKCoDvil5} zDoq1~Y}vjvXTQ6JnK42MIq$w)m4{Y6Q8*L};fKe?eu7>pel>iuNhTuLPCEWL zwy#vU=K_8ZjJTa+Wnx5}MNJcdKVw6%R4+Dy#r+DuhP+fu@B6^k@Y;sNhwv@Kd5!c2+LK;aexVy&f zbBx6Xb9$M8(JtsqeDCSOsZ6y+B~>MgdDn{_W9|-zF}OeA9-z4t;oEAsWn~}zEr(2;^371ttau+ zQSIJIj3BxGO+kLjDvb`sRsxKClq_9U)?;6}2m%CF<&tclrHt37?=urxP0rl%xj)E~ zwlG)i(}2*YhNOJ|ey{fCG*Gc^fOUXf&g%ouEKp?WuP)ZCnkV&**ogm@1F%?lhNf(8 zdf~J5RdEn)%VWc701@%x#Q`8~4wV5M^g|$Ou*xno@5~PqRiNgJTeh5xSMW2EcAe}f zuxLI~7g4!XW84tT)u#w;Cj-%SE*;~q1I!rM!aDI@nip`16g>U#;WBAq5FRhXRLeE&-;_lcywCe zCo_=vO44x+|3!ov5qgPLWU;H6`ggckdVXuw(ix-6qnb2Ym#JrY&(^cQ_U=!o+JD*| z;J-bh+1RM_aw{H1j<`uCM`Idr#Wu-UKJ+X${P=9bxG>3&K-^|)akC!tRV16X;H)sJ zrcV7dMVRfTbJojKL!8+g5cag6I6)Pin(|FAr%YF*Dm3Gx;0i*#J+W?; zIyt>$&{=6h9J!!Y^YPs_$GRpy#Y#kMMbQQFGIL(E*#i& z=`aU`v;Sbz!lt02k)L_frF6t!LccuktKXC-vNdL!8?9IxIJ(d~Cn6Ied)HMaH8I(* z$irvAia3BbB@Pbr8=ny1yG#9sJK>mNEo#+1ApYR)qkYx!@3Cq1nfJ~`)oh>t*fF)? zpb#V9jHp$vx7%iO$uf}FPgZC;2QylIg+0--+Wp~}3&m9@E;Q7hvL2hWD(tnMqs|?$ z-}?LD!I-PO8e@A+W7Y_Ga(grZo5(#b;iwdsWuS?lc}3=uegM~cYdpdC#hcTRpnfe0 zYL73TofzANqAvXP2KNm@_{}<57n;Wg*F+Q2KY?>Cm8v*160$_OQmH}bgTI9f-eDIz zH?sOw#py3l__fX-42)i~*AZqd=oQumXdRSWwi$8b_LsSC!64}Cs|F~YWn3;e$8{T{ zAjnARfOC(iZQCjPQI{ta$vinHLX$1SN#6Nz$rB~{RMW%YN_)JVr%0TNDjFN z-9s?`76;4ecq=FYu={-Y-k+Nsw2_ zGU3%f$EHjxo=dTw*oR0>xzija+mq*4@Xr(8N>fz6QxXVhmv0L|O-{zXdIc%E&qSt1 zlk^J=%tD}%YK1I4a>2G;x^;IwP{9XgxhsR$x(+`k_DZCusguIGXWyvNI4GmayebuX zWp|7mTa8k!@vP*fK|6R|lZGZf*q2?QeURnd(a4sD2HPOs;kA&DO66D0T1+7d# z)2Gis%xP}hxD}=M6`rk`vxXNTM%;jYNw~2m8_d{ov?-Gd{*AF5DjrND>YE%otZwX| z5u}!p->%Zxr{X#Glb{2)6Hm~4t;i|I!8`^7iG(=5LV$bo| zwuXU8_W`~90^KDh^^T6<3DO`qJz?px>>KpL!`H)NA47x*Xu>j%S}=i*K8MbHV39t; z#f}~0YM3n*sxf+ZD+prg)Y-Hs4|sNmZQMSv^3ukN#Sq0K*0dogT}WiJGY?d%tzIRU z(}n+PR8Lv_4Q9nDt4xOKKHaPce0G&~mLQm#Ag%~CFnE9g&se=o|{kJl=z$RiuOuZ9)dUSBuso1-3f zfs&5vlzrQr>fS!PWfB6RWqD_ZOLyb5eKh(VbhO^8G9fYzSAlUZKI73DojjAS^e@hb06OjywwBt;k>T0^H^nNdOovB-V%(gWugg}&X+9V`7R)@(^N7GCTBp)Wy zJj+wo7CENfZqYQ6DqTLHWbGCWI4riO$U6{ag4`}`RcgRB`%U!u6AqNpu&;p9zoy?X z?PpP_TK;6%byH;`eeso6W~(!|i~< zYK277PuGZFYY}S)ekV;}T8h|W%6Rqcc?D@>G)iXT;cNBl*BuF8T{6{utBz}*(^rp8 z^&0S%=tq3|B+kq(scQ@1TTKeWo_mVFdNDo-!R*LNQm?;=osCdy@9@yp<3x_O8lVPHv_q{>fkpE zw$s(u;aVSxT+6YG{EJ=kpuytzZlO2SIU#l7W;C&G0!jzt4}rX88M1x&xeD40Ij@Wf z{|9?@ePTRSfYroyP)-QPBHCpY<{K`1mom#1Yv%KbKj4Pz)s#qe6Qlfrytd%VydgYC zBe6lD>)jQ1&&uHf(=$jmK?AjkhTuM6JOnN{zIK#T*2=Xk8f{QHB*X?6bnDf&UUsBQ zP(x-IvU*4=eSEwtGF@{6Ub`=|pg%>%L$?T3d;|oUk`Sh;I0CLb$#CJp9NQ(YYE9mL2%T^ z%waTn#`@ua-EzP!CVYlP+z)R`xH=YhJY(|}m;=VrD;RYj7QzCUzDZC86*VCdv+r8* z6ho`e)&wv{b9G76G!ZV_?G@vj5Cyz#ox2tBt>+uity#hgo6TuALTs8xFRf`)_rH1a z?p>Hp9~(!7v*?CMI(a7Kxp2R|&g|B((Yo8fk`S-HQT0gPiz|laM|oW45y24xN|L1q zd86~q8*Hf*5(*}Wd^UQ<@ z8U2%#G*7X<$@B&~zrcDKop9qY+h!vnv?;lc$Ebok0xM}k3sgAOPHe``^OC3pj{aq_l3J7sTU=H|l zbGBP_*8nLhSSMa5z9JJv=}%EBf7*K?%uLKM6=D&a4X($=b_t);m_wJEReXamua9)R zJ7~kgccRsEW@|4~xv69Xe^i#EU#J`vBEMr;pf%^|rK=aurDd!ZHb!?tO>t}=r_^gG z#DWPZ;uTd9^^nOAwY-VAI+|F=wuQ5oPN%=LXyo#yrh?5 z+S5Vg0;b9(Tu9bebIEG4A!RqdwCc=uN?Tt4s^27?2CQ5gIIOXEQ`M?H)l>mzhc!iV zm1e<_bE%6qtVyp=%(lcGvNMogS3NErxqP}hXyx$!=n|}=QMLI%O_zDowL77b_TS!j zbZ8CxELA6XXlrZJy$K_}tF6WZ29`&j76i7iAFyDJmN?oZaK-LyxczJ9D_ z5MsC|G3WFAW3B$ZPO&A}_}tb(I7&@67Rddr*}bfn?*53}e;tH|r=HoEg0TBLQ&~`> zxZ$*nG6+VG?AZBE4jqKMML(mi>|yZl8$Z`DxMn z=@k6EqbGf({X`0X#_l_(oZT`%3$FT0{d?3r4dB2p&21;JeM{Be(fNk{01ezb zSNRP${)~%voRrtrqd*k@%=>ACNsi6rVXIehY4x(ed$nE>6BfUyrZ|;<|tniXi(H$@a=}y$Yk?^CeW&6|G6`>4Zm$k)bMI`vG8v+2f_9$gCaMJ z=9{|udI3qv^(@k-PoEAkF|A+10?V?5ZI4!hoHq|lJx07UlvlMU8!ocr&1F4#G6SgY zDxu&bauJFBLQfCyY7OVt6-Um0%kJGE;#GmYfBlj&ofzTyQh0`)Jqu8QUXjdP3OT#? z9-4V0HPSJPhH?SAv;*!JsUgK3c=B)@Ztp(Zbqly>t8J+S{8<j=n7#%ADt z9;oszOjD0dTOl;hO$00Ub|l`AaG&XzTg1>c$saL-nvYFYy}ZhR7ku0>=;cdoYwHXv zX&#=Nz>`}FV5ta0k`ju0$??!7On)!AAo; zC~W|jNwet~+mDZSsoc4v1&Rc+36S8X^n8ljo->TB#wGTdkwV7oy?)DeYzYuNL+kn| zc*%qu!gj>xpKz9&1SwFrMRq(15w-^4INWo(^e_wy|DiIP=qj-{v2oCduPQ|zVaeM zGmA{M)OE+waENvW_1^BCFST%Lxe`Y$u{!&1#^8R(szKqf-eg)yij zXC#~XKr%$K_u~&k6fcw%$y(}mzSTsl#;#I+yBeM9htT!e*_y5b{7BFjUxPN&^U!=8 zdc0iEf&Fx<4E0cU-MjH7)~SxA?gvL4bizyqE>qqStBmfdD~}|9W}fVFV$r-4N~5fY z4{4Of_`3(w|Kec6RMIfNQ;O?g8^*(KK-tlQ!@Ap;WuXb7WpuUQE9hZ6vecl(BYQ(D z)(mRNE6{g{k(RMbP;QKu(h{lO$QYTEy1(zl?;?X~c z$gt2wyHMqT-Y-oHHEUCgNSLcC|FSSl$2Lh7scf{DCq?ajQ;Fc&*kQiPV0G_T`!6m& z44n0T_|y~!^BfgO2IPu4V^CQl^Yyf z==auZU`l5+!C|UljIr>`MKG8KzTwH#>{{b0@FmIy3phPC0fD4;&D*nh+q<`&kXudj z9b)mV4kNXLj$XF*T`4ejS!7O}Mmk8S$k|%LA$V0I_2@}7Ah#v^PRMzw;^Zg$nFT;v z%Av!DyNAl%ihVX5_47;&!BAPbz|(T&M_m!R&tcj2q}hGK5bsKR8@U0arhji&fR*%R z+zn9YRK7Bxo}H1N&!V8mjA-@e$ot7(39i|l-z#}xdj+S~cgj;^@@M;jGBp+TknsnpL*#0f4IJy=3C5xg z?cR~*8easgv>xqtqxfh9$6rMnTnLIM6_IiNtwqbzrYhORls{r9<_3_G6{ z_uuvcDMM<S7$gzc z_GBc2JPj~f-x>Aa%4Irp^?ic8kEO|N2Is@VSfojtB~E;rFrRpnD!q{s^QK1m`k4O! zm1>jA;jb6``VwEPQ10+7^`(*6B^}JktyN?Pu3<-GmC;cr;UhnKvZLdZ0OX*Kqo~V+o#yGi_Z` zXAXcQ4OJjy0AD5+CRwcD9+i*0baypd}FS&*yFpOoSH?w#1J$cXCyOynl<> zF>u#`JYJUN&ZwI&Q?A~AE_sqMglVy&$agX2_&e1V=CZZ4cPEz&ULMHo<+j0L3NH*B z$>}$pdWbA46`9&Jj0n6)G!#C{p0heV9ua;|uJ{yqmP@Y}Qfi?u8Bie$Fp%3KGrr!G zisN3}UTwEq94hbI_6|9J3*@9cnRBcqxHbY@^z1NOuUNYrH>gZ|dz{9!(9^>Vr?T(W z#mSUkxIP`ss~Wm4ESvmU|IHGS{+d}@RsG$TR=taJ*w;+@2FD8XI=&OpZa4RZB}?&x zbtLCsFr8Ten>~p$$u|0-5~G#+HEH>+<+@!n@L`n~s&<9$k;cqDQR!DABkWCanyKdl zvpP&|rq^Pi^cczQ?b1Z`plgbZu|xWE2HUBL*fz_f;f%u{&WpRxXr-p4Sc8{_ZueD* z63zvaJpHYbst&7vb9xR3QL%KlCg^&qp~!`S)Lnb_Wq{-*NCCxAroOA(Pe0k}dM<~H zUY=g5>oZxsWY2T)15xi=CxWtPzxo_EQ%F}SZo@`6aYPRH@!?DqvIZ3${3lB?ZQ$=5 zI6a37Ti@zPuYGhgbV|_D;*6zjg^DlxmFnmY3utK(huYI__zcA?=Nn_umhijUvFuc3 z_T?mF$0*~C$cTZB7SxloFd0u74KBuQgFOl;r5Yx#TO884V@|%we_I@ytMeSlvf9eG zCEa8MZs%kp<_PWFfF`emEu+4dGHBsXuR5&?Wbgf5XlTD^7k?Hv^JA=bpxUQ&I^V8O z7(^;+w*rrMg1j*&lroM+$<8v!B^uJEF=+S6ug3rsUW$Bz^`jjl!o_v3WPuX{0DVMm;ev{(PW3bzFfxQ=x%*tk)FeH>1PQ1pDCIi zUC^oT|M;%5>;FsDx>~g^1#e0H!PUOrp>^LGZ4y+nZC6Kz(m+1T9`o2{COjjhHAN_>0h*s(_JC_Ypjy z`@keA(w|g#;2AaixzR=QK6%1YmuxU&-+*^)tHv^-@N+)q6jcN!VWg*x z!=m`7e!$w1lwOXEr-xsrO>HgmzV`bfQVs1A@4L~4-D&PeRwX!l_3*s zf!WUO*eE~z*IWcle$BD+7%FY;aG;E{Qah91O4^|NR>rHp$N$C`+apMs>7#nh!vEjPGslPypou2K)9w!f^ zCaWYLSQsflG^}$(@d$C^Oc*g4e)^RL!?80BFvYnjC#h(T2WeSdW&f<(_hXaURuOAt zSNR^%_-!BY-rz6;+g7R5txTfbcN3Sg#e+H$5F&G8dhs%Y*rpc_sQitrx$>y9!=%)Ay%CTM&vn0P;ACei>{DaQ!a;&Yx|@kc6#0|a<6(N91L6_u zN~zLlI%x?%C(^!*a;V42-GZc&3hSwoYF0rQypv!_wpwdwf~1A*2zKb)C;D@=e2U4; zah|ubgmB%CPtzCLJSvOasE+zJ#}iW#xlJ?TSK?SHoU_eqfpqX%1k%eR1oTya7^(~M zu8*HQIYWlxFHU`h5k%hg6`FwZ*Co`v|FX#=a@!(dhWkPU?ybZsD3mf+jZ09U9m~lx z86sx!Y17)r>QXUyN;vZ#&cgSX*@4&|}m%spPp|zrAE? z+Ep>d%p>=n)!=wfWF4@eT+2X1G|EhJ@EVABGPDwvYzIqnL7H%GiNjzPfV)y7kJ#)@ zYi^`wkESbaJW~xdl7l`-UK$uDWV94|^fN`|nJGPkq9913>-n?ZucL?ja31~0h&&fV z2x*tYc-X&sR#K=^LMO_TD~gA3ur)WWUEyH{?PiZqvV$Vk=C;78U#0v^zFACMeqoEK zdh~rHuuiXFz>nh5xWs3H^vUVixP#%3YVQLn?R1U+L^Sl~laBXXzwoqBG@reb&ojR%AJB~D*nNbU9bxb{t zL$vw@pkI7-mwbhoA(s5`Wqq|lb)B}?-GJwBT$ts^Vs+CXA@CUgo{qz+R zq?(m5<+<`-fT|o>PbWf74rO{qniW}x&~wH?9AyXShCcgJ(2`(5f*)xmjh;ZEek42c zlI4Q9ZO=uzUca)sstY_KdetZo`eF&skry-*dIGroy}Ace=|tC}7u`hyoLAu&G&%R~ z+m{85K1Kx(8}%3HnZH0cA6`Rd($#BjmJ6y4|C7u4A1utt1ThbyUIf4HZB_xjvRSGa zosuvUvuHa0hC>!mK-DOc&eBM=d^5;?mmEwr&L|sptX%<+qR77giXRCNm+{{&bNsm& z#Jwp-)=Kx;&_yYA6EnuplpjBw9r|5o9Y;k)MGrADk}ioD7Tg5?qvrD)!b3xoW@fDE zY1zO(R<=kxMK3Y7eC7DJ;vV2tFt2~zIoq8c!L7_BWL%;KtP=^-({wHcq;vDYLPA1_ zL*=WC`>+2Umb#1KW5nV|5mUy)hjmA5{P5*&R`mRHA)_KKV922JTvYI=AsPK{+yicI zAfWfw!R^6UWIf#eZe%|qU%Nck8}IDKL(5JXYV0fik_j&{uX;K8Ks%;Ebi%_OEA zc1#2oI~)ELReg*kE#|CZcXs?@VGRG18vLiw{x7QVUs1y!yyU;br$0Hw|Aci-4|W2g zM{NDRzJN-s`ns@&{A;9kRKaa0sQP93=Pvb7QTkctf5kBmZ9t&(Guhx@_j=q)SUAwK zlX?9svHHuOyw7(9z&rg81ea5@!H-}041cn!zpwabG;^6wt^F>PV+MFBesib49Q`|t z)(bk-`P;q!r?G)M>Ob|+K34JER$Xv5`V+_G54V|*Tmhuc)d^O#!nxrRDxXK+W5uAE zSnXHpL04AqN}~m*g+p+xE5CxBrZB`YHHmY#3Zh`%-pO zh)T2)I$3!$R4@4!D`_h$>H!mG%|6{}__0daTWec?D3X;zOWS#_7v(|pF&iOLIXeu! z?kXgh>GV9dmf!ls0#am+vfe%yI{jWI*kD5`Ji4KYY%J~hay$1edU5wBl!Xp+^`PU^ z1b*s2NlbAag*Px&vy#IK#H6QXH$8*~;eNI?nYO`tI;5!xUYLb#M2{3VTb41wA9&Pv zB9jn>eM++#T^E%qOXvIY{Tg^-uNp+)wHIs=_&og$K8j0MJB2W)ZW-_{Gbaug;T8pE z1~S~{Orkt)v9I%$v@m=h4{*mwO4`AVashhhh-0!pJ@ZS8?$E%3#Qw>3|fl zw#K_-pM?(chayBn(&d`LN4S{h``u4mPd25{gAkp8!xv@qU1@Y?4J|myrBn3i!FiGR z3Kfxtx#Ip}Zw%+6o~CTyLS*e|;y`fkTQOe!(BmM;FlaN$mKb%^>))?BJ50tBA%U8t zFlEiy*hw6iQI#nmi;|ID{7$I2AI078$EW@D)S<___pbFCJK2DAAIqoCs`f~q3PjbM zYefrl{o(&M&EP`G=_#*j$q7Wl`SM}*jls*+Vpxp7alR>kBLLW*18+KFoTOAjk$Hou z@pGP5(Yv0|g9$NG&$l>fH*qj-%9DC@QN+x2aPKu)*R#jnCR0|}TIN8qB1n_fL})$m z4P{Hd5*)Ew>bm$h+4vkZQ!CX5LYv)B_K@nbyVrcbG!sWRK z*GC;2``_JtGearg*S44~;`v%H-__Gb35V5BQgL}Rc%^4>%tA(R+KEoYl`7G!%pXXM zN4JYRFE+=NxrHzCdq&mcuIO*T`SaS*r$LHisJPo#Io6ADnk>lIJwGt}Y?|Kp4-{J9 zKr`$sCTlGq98(X<-p(3LNnjtkAO1iye#5dtsuhG3f;r-b15?OYcoYR7_2Z{cXM?pt zY{AMdGH6;ASgi%!JZLjN^LF{uu8$mT3oY#F(N~_dHZ%ati7yB@Ok2cW4`Wsz>}yxu z0@~HuJJgLj0LXo42*6m0d4fs8v6n+DQ?xl=>N;2;=_AiiDE?u1*M9}8ol)(p(nd%M zebW8~&Hpry-R|W-urq1&{-o}IA>yCVbn&UvGpWNnkoDIZOFyBZD19*for7iXOSf+Q z9yI?v|8(r7skE=pn0D3n`~Cj&crf^UkN5R@y`Moy{plIZnmuOhi*GKd*qqA5 z+^x{JH30yps|&epLRHH452x-W*;|CfBa*ey3KXc=o({lVIXxpEbFhv~GmMiHS0!t@ zIzsh?CPfO3=)F(dzOC41MDOaT5@mnk0uM1o0XCp8==H)T^N2t zQbC~<<yUBB1ql|NYlthr14o^tDVb&whg&T!Ce z&a?V?=^3;%yAVOIExZ~%XV{IYtZG$bVU2K7aJ??e8yk{S&qs=IsWp_9H(~5bcsZnk zdiJQxl9)g-WmX0N3k`ua)OL-0*khRc>(+B=f_{^V@|>ew2Hu8sZH_xqc^C7PnR>gK z^ihSK(2{3}E`ANNtrvxIl4#rVV^f!z3TywJ$QWJG3o!E^@=>4Ii0YGBWtD}{viR-+ zbvOBrR0!j@O}d-u^c&Hs+UjdnTlD$Q&vb7enYyr6hj-O~=yeH^s_wD-$rs5wi>xh2 z=a_{LwXwoq&~qks)qXD(qUhEh^`zNlBrZk$oLAeY1=n+W8W#E8f0w_Wa#=`Z#@kuk zurIZJ6qDlBzg4P=Xp5ro_q!)l9eBM@|6ulWml3xRcJ}hsZ;F|X{l4gRu88V^*4sQ% z7!>L4j_*KU;GDH_-n{wqgJ6v%e5WfZT171i5m$>BvE2T8@^##Cqamo5M!9Ee#g{Hi zA}j+V0X@>I;#`%CL#X$Ahl${gMq7XDN>ZYN(Kgsnwt}K%GCk=-lwPzJ87bP#QXs}| zBTyf|#<<7qfqym1EmHTnRD-( z4KA6cpTL@Lx_B|yWU#nAhoNHrnb?nMfv#6HonG`+dD^23^y$tQc7bW%tGiVdq(@B! zR)!)UOqb9+N8?>*yvxNjcAhTe=ry8>fA*uhMyR>_MhGA9!~ET8a_Wx6RUm33-V53_ zSxSGz`dT5>NJKb#H@6kOIG?g+n-CTY8;A<}tfko#le0H$_XU%sWz!2Y+qX3{#)BDa zgT;R}NQfGP_WPlACBaIFH+OX3Ycxo#eIF1g>OemB4c@$eNNYI~-d)XJAMh~x`GcoM z!3rZ95Vk5BC~=SAzApkYs|aRy+4Z|lahr7dA9m&dwx_4h9&iWM>UpT4$M_&;`EYd~ zMi0yK1lW5yZNM%iEG>k)TaA%*T!wBBBGxlZT?!#vghM@Sph)O0WAefi?amrzAzD9z z)jcsIBZE{k!#za;Fuuk^1M>cbPm|6XDq}cJs*7X|0^mZ3_pQ9yT^+Pli`nRocKj*% zSy&PXZ2-APU0>gYxHZs0I|H)D=Ikhhnil}yTp{yfBbT8At9~!B7ml~n+xq&#*BN|2-TqPcq4o^scHTFg_&0!hGiGyQzu36xp~}ZI)__FYy5Rd)$!C!ihDRK1WR@(+ z?(>MSjf#reXDH8mF%W@9TZhf@I}NKyAhv>_xDtXG9&^|?9*&gRggpO`D_Q31=Y@=i zs^+~y(X`5{-Dv!TTlLOdT(2;yQZP9uIT8E|@)8_q7P%<;570Dy6$J|)zs*HEk7#iq zg~4D{W8*>F!nYL1BR+Sv&Dk*z-U8Uy{T+R}AXU#lTt{h~DvyC}>uTaBQV6@Z_}H;y zVYF3F4bOVN9_Dj@$j;8L$DQ}~@o}l#VY^V?&_PX24LyG)Fp>(!lXs2|NL-V`lq8{P z(1FY9ms+|s7ZFQjHHRMPK zXXhjUNA8a7vC+e&hcn3mq{WF)RgcZ*9hHd!Yi4Ffz;k4=0eVjaO|#1|&5rax%MU&| zOxTJLiO7u|kXV4_*$!LMf`GN>PgPO5l#qYCnADx5O_%^8u?X|M0f`ppS1%s-!SteK zb>-wr4we#&q3uRc)yH2yY5I~xSOU4UH+gAJ;CSGtRZJlsdX?-kX;v$Ssl~|_s|x*e5at^;>|G0G*F~<{}~edjH{-pX@g;z%Y*A_ z$r%4YL{w8!`kC+b(_EBu&d5};5|m-rzAVOk&PQfMim>*9!5Qzp}V| zz8S_A2gLIsgZ&Sh>4(9}fV=>OUvo&5B(=7CR93fHKsYXo=(Az&YzF(qg`! zksk<}c-TompSS^vR_ZQ=Qj&R}_{w1l<4&$$m2c}3a_7=RP`KqO%~j-=)z;2MSF%lN mc8BrdxqrvI&i+R4Tk-Ojzf784E|bEw6tmi7XI{F|^T=-=B1vxm literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter10_59_2.png b/doc/LectureNotes/_build/jupyter_execute/chapter10_59_2.png new file mode 100644 index 0000000000000000000000000000000000000000..b7c47b451d2004ef6e10feb36f91a8b9a80a8c27 GIT binary patch literal 28628 zcmbrm2UJsCw>AnQO+ZAX3kZlvk*f4A2uM>wnslUhf^>*VFM^2l4oZLS8_ zmtTbMhMlLU8%R<>!1WSAClAv^ zox7o%P3nm}PhD2fWVC$dhue!9nUZ^H2XTz|qN;8CwoYu6yAf9c*eVDP6=JfN}7Z!9w5J zP&%KTUNOxHNzf9xkdRPMwp{l51f)9P&}00oGnu@fpX7Y!oB43opk@Rj`qxm2h{Mm@ zrFyIPMzk{}6REkh#7ndjZfSb(AFPcfWHjv^j{!3iB@cGM z#$!E4d#i>uc2uCHo|ft9?ChYU$gVEcBz}|b4{8a^gN2mN6JM>5_tyikho~B-v3Cl= zM3n)D+vI9jn&&#AxgY0U{HUH>pi`*TlOZvfO46Gtm0b1=QsslT3En}+5Aka3242(NF~a*^>uyCWV5(85m5Es?%%;ERpnD5z$<97fsHA!`y>en5 z=qWz;ez;^ZH8nNqrAv9hH@R#7BP1J)P5t6HBJ8{UJn7CeuPJBe(a*0;pkC+!6;>gu zPIA0}fPfSU&@EuR{et?-qm@>p>-($a5CcAAiFLs{cY1&F-?-6yh*M$l4FP8QV2%QT z5yYhzXg1P<-pAM1qS7E^oxIH)9?Ps-^yn2Z(NgqHeF;A~Y)sa$Yh*`{cmj^z4`0)1q`;g>hx|Nj` zhOhTrkjIuS83&$k!8;oaoosjNKI!*M+* z>{Pw?nTHnZPNF$$`x|h#`6rU0yuuqu7~q;CCW?Oh=3Am|FKF1jx!C^<$itic7T~hI z>7}xE@~QtdN)2P*;S^}`AD8~SRiR3TG>$VD|8D;L{accb8fRaD;5OA&px3yMxkA7{ zp-OwZv$t=ebbfzdjk|_Mzt8$JhWebmvmp^bI{#D}#ijrB_w|$oQD={plx0appc8f$ z`9Hn-YALAxeu*|dA7W%5BQ?+w8t=~`MKoYE;lIQGJ>)S(4GnVOfs(5nP1}S%G)?heR%BCZzgbl{WaO+g;B%U;4d=d(dgsU1o5*&;^=0#pdUj#j z?EGp6(nKXPD3BD@SCBS-*V!c0CGIC2kKa^vz7efH_GLX{2mAK3{4FhT43~d^e0T8< zf9wpbc&g!2-~-Q2u4FNP2+OUbRKpA@Q0Bbc;bS;DyXtDK=gIW1vySvAT%PK2%k7%r*IDCCsHO!L{g@xd5t1!%2{8?~*kqhIMa(8;%X zu>PdP!uLq&i(5NPb=xw0XRm`vXdwnmQS<6*Qa6_G9$&^qCi_ILF z+1n%s(9;9glJSGYkJ<~T7>rM~_rc>lvu7EzzTazJT%7WoingGSJ!o+UOmYXQDbpue zp1~*MILvoTJ1fH?@cHwb+H$8gAPFI%__uGbpgipCZo9j?_bp!KeE9b5+vffCiQ-4O z7u1va7XcqHHVNZVlz;R}nmqO7cD_HXfBwY-kLS}uM-3%^G{)6=(Jqjgw6n%m`+KylfGG+k|PajU({vaDM^Q^^ul zax3F-n3K2_-Q`?`lB8ne^D!y(}jTPu)qNkDHsQB=!&_^8Dm}0}?EGnij)0 z+w6Ws?wXxzQYmcFAmMuB;7hTCk=X~`+lAU$994Vbs5?@e3JQlFA`5T$8)SX>Psbl5 zxCy4p-Z!$b(=XK}aRp}8vC*Wn(R9uI7g6tTcO@`STbrYB`Q0*{brp+K3@l)-OWoP& zY_2k0tJ=K;-*xMf{N4nvrQ(PeV-g)#`za-l2UbLB_q_wSE@2e(Ttm{U>y z&8@_-!(-XGgPRw&dUsjv#>=$Ayw+JATdTB(tGp@?HG@EFT1$;P6k!(T5T>yPqX?7dE2q+o)-;RT!yx!!et+VS(&oqL&)74WwKC**iikdA~3d6tI8vIT*Z zaKAUaTXQ+uCdh+{+y@B{*G{Z(i}P|;6q-;|6b5`m?U-yFc;YSO+DZcl?V!kF^*n)f22bJjjJlQ&PA8d-)W{o*}lQqSS=Z)@ZsEq)DrR zix(;Ev!W+TFvCVY9lK51^yH1-$1$}2$>Kqa065>?5j2;a4Q3D?9-i?2{erR9!-wp5@9uhJJBzlqwWR{Pd9%Ph z8eqTq!JyJoEN001z7-gEDuzfF;9_ILFBy6WEK>@`yEzXNdBlR;Xvw(W#eHbw%0Q^0 zxw@F?<>gJ~2De82`}+xUY!bQ);I2le$ve1Q<()y_=F*KAuFM%Z_BTn#K_y9T_jZa9P>$hfP_r)z% z;Hk`catgTef=_CKSFB)Xrq{RKpPx)6Ns3tkY;? z--J;S$iF$V)`-Ko4BTR@DQ)E{37=ndwjS(GN8jK{lt z{gcKcO8ajDj$UuGvSh+9RHp+NM8y8b&36e2=z{~>jwqTK7MXEhSche<>vYo@WCE6x zO<#sux+nv0hCWD5*{&}`0@&PNe980l)1$g7j(BdTTilQkQHvUtejv-Pn(qc(~_}*j~!frvG_p zvQ2cjv;1~VgfD=zq{E|3uHzn#w(carXQd4HxYi&jPX!fo&{8r+5sh$3rJ<#LpsRbW z(Qhvgz*;qqBe4+?B!JoAz&5?osH|as+))~fnXhpeifV3_XYpUFWO5ndq{$ttwyg%X z94DuznybgVEB8@-nJW{J3f_8m6SeSIom?9=lt+tVONOj_QZ(ubZt=0r8*7QOqSkXTnoWxoct~ zeRnrTJBf^r|G5LZj^0G=kpR!6PE_m1>sD`^kMFX3t+1vB1!N{sNgvvHo335WT$jCw zFN)n3quJnpIBOZ}d&e0%d4DZ#=|>azrNDfFY`1m^WM@g;Y_W(A*Es}!oV!E=#|=Ca z$6B#0bhuDgFQTV+=P&c<3MkB8CB(Pe>1u2*AAPq1Prhvyk=6gT#o^0LIwE|(k!j1S zXVY+KYQhCrnnhP0XS8}tEbV>q{VZBp^40nX4aG@nw5fxB0T1Y(&QIdk!7M%RnvgE( z!y7q@U*@hgt^TOod>l8r`PJqKEq7;1BUqFQv*Zy_SUz&%;^orEQfcNqF96ob?WWlb zHgTka+JqOs*$H$T5=91}5!d%*eeUV^QF(|Z>xK}K)5`;xw+O%`Y;0@>e6&}osSg*E z%_5?rJb=YGRBTn4dPO3bN`!c3eYH2fQ7y)Q+p1d+8r`zFzf}C7;&gTXxN(?*kCq7L z?;Cb(2HUXd{#<7`wKp;MGZNIWGj91Hc0CLdN2hW*(|nSbjQd&TmB$>Cf?Ko2o)|M{ z#kSyDh#KLBvxjeN*A9U#NHRT>2mD0`t|emeUE_hq=B7CI_#M5NTm3vnYSW55cd9y!@ zJ05}eN1Apv519CZ7k7Mo{VVs=FD;bFsa0Vq-83z?I)g;@Ex4F@Vr@y_E@*F zkBz4-J8PGZ(Pm=7o71pYz_8a>Z?Abtfls!@%(QR=%8fWzEzWGtqeB57dk<}uHR4#2 zpk>?ljnLcuF)I(Ahl64CQzM|^crNjmYSF}2UyMc@_XJrR8Rqkl)24u{S8S@{VGI8TomwyRhAX8syY3$E6 zkn^XB-v7diu<6V1-Nu?6Xr@tBfhN(2K1MPC_5vQNd^{7tTU`_@-9G@lW$7Ve3$pe; zhi5)~PeaZ?+k%#OI^wDBAAF~Dj$gw%&pv9m@zKg`2eH!tP^>PB=M1x1S{~#`MxvB> zfY%;0=Pf7|_D2J~_~89Hw0(0%7XCeKFPAvGkX<7CPXjyuy@7vUp#-~khFRzE|FDif zzNegl#!+&UM~{JF-Gu)^ot_HHz`&>|bIw8K=!@US@fq6ZsB+-?8BqS`?2oyX1zK5bDL8`gFK)9pRL^e z-Do?(A299pPba_e=q*t`e&|$8N(%jWjs1Oqqe&65)e1X?xJ*4v<~LdXo=b3ge89!Y zxfnK~`}+d#hJ2N{tIW*3lXajoh7q8oB%t1#qF;RH--yxQwY#F8#FzX0+q*L&M{Kfu z={J!P$%`WS_~CD{K-_qK1sJ6a8GqWB z02M=h?V4xXDev!@1WCQ;NSnZ=-S=5mSomFGcF=fTMoJ36Cq;lH?%sW0TPr?j6-LRb zHQf}*AYwy~#bN`{9drQR`pujO)s59j;gkX1YXul}*q**#aP#B!N(24_gdq9gb|@L0 z&&tQ-Gd>P5cTb8?Fe)3IWj|POx{6KwJ^l$}nTuXBv$L~Kqn}&qGTy&eva>4!`2vsK zh3-V)W{}{q1Z*iF0}rN{T=Ww@Dk~{1#Oed|?b(Xd(pow>+$lAvd>ux?B)JJ&Er$Z* zHt)}p!3)5h9_SW70c`v9oZ8rEC*uhV4W*)?QLZp;R8?2ccN{4PZszw2GdUs(#xs8S zjCW>`_7McAs~mZJfFB06t@E7ODBkH0TY;?E00>l1EbMXqgS!qtmkYiY|6Ya~PTuCq zw@ZAqKAf!|{m18BuJKC;BB%bY*Yl}w7kfsl{6n~`g`MBU1)o3kNpJA4n_1Mwz$sn8 zO0WO$&4iOd4}#xhYU(7H)xJ}r=XUGP(9flh{!9Y}o)TIn4S3C2)Laq9=zG3_fxabb z>JL$fxFO5glJ#eYGY8X?RGoJmpVZ#HUn1(>4i=7|g$1;wdV)>_^jsgL&(Vmd`f+35 z&yyedQYkbA#gq?4Jv?j`PtNL0_Mb~>1hswf0>K@C%iBKP^J)jP$D_c9qW4b(hU^}$ z&e8C*;s)WqM}-|150B7(>q*J;IH_1eDY1Hvm}kS{4dnfL_OC0F#iX=Y7CR`+Y$IUC z<|G38uF9s_#-rp?9AZI;;RMpY=KEIAhUjas^K&C$cxcgJYnMwfyNe&NLZ?yF=lCM)`@r>$7Jh>K&8yi8g9d^1f2ANHYar*57Emknv#LWfQvy$q?4@IdkZ;! zjv*J2?{$a+E(~;X^i9plo`~=v=7)F{UK9QjV++!(4?WS4V8Hj5w<7TY0ofJZF1Rl) z^@As^bhbPsGIWb_*W(3=VQaz?2{+Y+?c+m{a(mu-{uFqV4i|%I1%CgCV{;cPOzcYu zgK0{ken4A6h|k~=+lvj(*)@A2{Gf_w7elNuw!x(0&Xit&2RF8pyaXAN42JSxUn?{04$hII<4S$yYzKeXVfVuOFqBy` z9iQ69ZU#-`bq+i92bb7Z;d)5J^z6GqPt&%$HxU`mCk+j$1D}ZnTrg?(NWp`pZW74i z!AL!X9A3_#$y0jWI;vUhtBp(ZNs9+NsCApN<^7NId$@p8BJz^ym&qe3X1IH;WFmHk zog?7qWs*M6?$l&Skpb+pXS67JL!syZtQ=%b54j1;mYZk%ny21ly#F!dxldUbdBxCM zs?{bDzt?{5>iAYuN?jUQJF6D@uGD$d?ABGCYJoCc7e>0R2 zJGj#8_L}T?3sFjaB7A(2g7})-S2dU&>Ui18GujR=h5Kj>eiKG5bXTKvJ5YZtv6A*avM4!oF|t8i{U=p;FCW3A?+O@aHOT?=9o#j6yaLw?{!w{y&lJa& zyIWxx{gHBSu5mco47W>C|A0dqV7Y{P3pD9*$E8f0UJ6-9a{ zA$q1Y_LtU2J>Rj@c|-Cxx35BLFY$|Q*YQ4NL*^Ifi;^-lwQQ#=PdXW8C-8UY_+74<1!>P&C87!(C8QCWWAZ`FTyDWu_M`bdt**Pa(*F{6P_MO zR}u2OP1oM2jmE>pEw=p(>Dlfp*aSuVSJx$y=Zv+)lNC+P^?`3Tu@3e1@yue3f<<(?<W;9eJrmm2gEN#!)rY#&@ zC61K6Dv&W-JSs5eeQRtn5XO9Ikz%211yO+uacsoyEZ9ut5;RaBQp+AWCthQ62l;{Ez=te-3@ zb-||}26OFHyZKzGKE7^=fD{%_NYTHXJZ!X=kbXbIF01cqR7J(9__E^y(Sxu((YB2f zT<#$E?x7!>R6-nq;Q9f@HOfnQ%QVv`c}>qA?yYQ6t)bu|Uw&B!!d?$wHU7NQ=orU(>z4MCib*Nq|nFnP=8H&)@MU| z>V&C-AecLei^R2rjw0&)Oz~57JD8oQLfr|yUwC0vgk#D;g9O zMa)H0FcOpZbD6e13i3|lX?{kRje)TjNG$oLA{vdx`GFvq!9r3*;2~3hPnL8>gIm_l zN-~#}-t9+k`}8T24L`qifed~gH3=bFAeu2YVpR8XE(H9}h$mK5JYeH}@oTE3?BoQx zeh@Ng$ylFFJVcALr;U^L#*_CR_!3*5?@4pp>Vy5cAeI-J;8 z3fsq7!HP?VRTK<~u?~QSYz>+vdXkviv!#@arW4_EZxf1_Fx0@D+#G~sM8?p5r-0J{ z9xojp#L#*u#H7Fs;LOlR5Q%pmy{r*CYK7$ujV^aKox50etnlXgvu>^Z@TZga*=R_% zgw54u%Z2>;Mm7-l-ARU|^@(q(HM&36ylB_4(TusFCc`)!k9I_|y-WYtyr{=w<=njY zVLtlIMO369BqZuRRvT`zs?N9C`-iQo?JvAjDgxuMXVLX68UO7rj<^&T8UKCHGx$6n zd|X7U7jadg1y9+E19Ms8~V{ih+m-@?WxU>~K_Iwn$cM<=W03p33Pvl2RI z#CwkYE&SxpEwdBP=K@1y*K(DR0l@WNiKdx_llRw&V(JSefC-7er8>swB$uk%dN{ay z`&njDL>S(+T|_UgTi5zqQ&~C1oScFGSp%lAFqN@irP4KspPerBF`s;KPtjZw^Q?0* zaxaP1^?{SuM6~A$^ZkqTa!9-v-P>`GiWvjIqX8!)*T*ymCR=nbUnb7cYnh`bx-RYi zV`!>zeVAobWp4{`2`t|F){9v&6}ZO~>5{ziak|Cb`&O|d;OeU%>4!dZH`0PT-epdh zOr7Eu;P;P44)n3(q5Z?3`(j^6xfj(>lE^ZoR#a2=PyJ#W za*+~CYl8UEv#*bksUo(^1Np>295>IVHx1|O&sop_V)C;d#+1L4Han0FC^cQvmiYE| zGwHFkU<4%XYfdjJ8}ECuv2s@FVlS?b+@z#jpWPQ1_w$N%OW0G{O|N zk;aL_b*Bk9c1|(P?`0iNYBXN$*(bc!9gsX~T#%tZ|!=5@Wh+}QFw$~(8POMgI za@T*X;Cb>qPQ_1Lm6!)(lU*~>+C|e@(CsBqJM3PPvf(ut#C4dw?%pMV-s-1mbN(wB zN)uR$rSG=TQr1^bgF~tr)u606yD%7pve=8M0@w8V4V*IVYjw#4iGx587eXsrTYC%U zp8xDSU>Nce@X8+e*UkQN;|J)R8=a!g3KRYOjaY>Kb9qhps@!Z3LlzE+KEh$+WiK8c zy6^Tdp!P*sBKzHj$JWgcV5d(bZYirvYGogIG#n_G9VX5B2K$sK@Q(9k5Xz&36Mcm9 zL{0U0Rr<1QM&l3>a{i1Z9j${yzXqCgeM@P1pT)8+c4P~i`ptOJ2W)mvG-?W2LG=TwK)e?-auLiWtx1jf6aKOc+!$MOFhR3FfGIsjb!`lDiFO z97&b$cS;3QbrEp-85;s$w*?doaUO+wA(obwJ^(US)7CEZ-b6~DY_;_re|4Vd+?s96 zM11@9?IIx|dT#{S@rhPj|K=pJ7J>Dwq@q%7-f{uZC#?Y5mKVQ%=4zx0Dp(RMh&|_6H9iUIKJX48z1kL|5tQmyJy!F3c}hhdIT?>Ho&# z**Q2wq`iLqEdKfFX*8f9LWLdc|L)gC3VKYOD3!f*}4fv9et?9$;4_N^MWfqXc6w1H4kUD-&V7RB3gg2LSNlRx? zFo}vM0~!Jn3X0zE8-Um?A9%*3B4M`Kui1d68AgA{6`uZ2+(X(peOL=1I4Cx4^ecdr z{JvWoJ{A@hO3KOuCHexAFMcUOz1D#_lLJU@oRAF+ZW+Rx^Yi!1jq8LPO@KJ~1HBiL zC45Mo-YJtSVgoNiJek?F3sy;d%ip$!o7BT>O2TWM%%;UsXUcrq{Cf7Kdmyq!qgPp!MXRp)hO8HhQWpRZ(hEtsJ|P6 zdyc3eQn#W1P^b|9?mI{KYuwX*oE%sbvqVi0J>-7E>es2LYN3+OYDGSLM?_UUbk6#E z+yT0mMf)YIC7U1PhXRGeCtF85Z&9DDa4Y(PwrrTi*H1buo?p92EV+>mz0!0-#BUnX zy*RsPF|)dQB$GAzib}`!7Aq<-a4B|ifm{=!B zNyRV@^@o}__Sge&~Wrtn9y9={BV{j%}yZH{05R*=|sJg1d(vPu34| zQOIVRZ(&r)1i(%o<=G5`+XAQ(e?}8kBSn`FszT|I)gIo=WM)m9b~|uwBF7|pX_?_x zb)7pO3R-`KZbU3Bab|}kceXDshcT8A1??|~{?QF=59x-cdZWu$|Hty;>9`r~ZcRHGime>jKImq1U zIa!w8`!(uw%q)i|o3^2@8j-1OlYweG=&!V^qv2rR? zUZy8a<6-U{G#}Tz;4r#ANvx)f>rCLvvwkdW&7f=x38G8gS|HTxQ)_cU$m-{B?_wY> zRgdzdLulOj#9VB*R(YaVUR&bY!Pt!X>1b379JL)tCm{ZbdnMTgIkwD%{;GL)wrLd1 zLdpOJOlGE(`Gb8SS1uU}n>XPu1UJA%>h(d-oTe{&CkB6Kk6nN$JR^gZweFsXVIy%r zc5rit2)NJb0Z}i@=eJT7ge60Y2ZeWjx-8Aza2e=_wM^0EC_RR6-)Ej(-Ryw}t!fqN zQ@08*4=zzy>`AH++JE!#*;P<^(d7`TpA~xfjxj5|>}Xxgl_v?JQ(D9^)5kn$aM%dp z#;!}1P3jCju#2#=&L>(qxxT7w#3;Sv$)hckdZ`)xoXp<-t(5n^@8+>s*lc||v~JDu z*n2t<9?zj-_p^u!c-DBA<4$(^eYaYOO@`h$O1|j1aeKjo@J3NiC>d&IPGSqH%ig=_ zI{QkMwSc@%RX%6_jr)vLtm|bjruW4*A2rQbomK<`b$NpDMHxN&Se{a8$H_^MZqqfK zIP}n6K=n&tiE!kUhlgz(+DtKTs@_Rea0t=Mw!||}O-!1%#nFbzI(66tci+n~GVxaO zaMZe~(DXVvIr#oetAud-^t?SiYp4hobt?t3vm;E>O*ypj!UWKZP^-nJ;M~hFpu=a& z*t;6^mRH`6G=FY;OBy?(F=rtjc&VV_IqIkT?LaY4KWTq*-kUcSb9vtlf4(9P8g3l} zg@Jtd^75?g*4!>!BMlE#XS>te`t4e9AaU+P!ey~*SK}0VNqk&h`dik~s3h=(gqa4d zhlkK-$T-eUN@TQICGw7AJYG?flG3)eQ8bw>-8V`L)#0YSL@T(p|9S-3)j{dlVE_F_ z=3K|dOKq<@ZvJADH>`45fb{A;pwL5qzfV~SNRv^4*@641y!BfZeD237g}bG6vB;W1+X;5|fxdgYoE z(X8WSLLj~d(cV6(owb_4u9?#TJ#vDi00%bL&n+SSYcc6os5N^7to1(TMu_@QIa52> zM<76o*ffjC3Z+mIejOBCej*BSV5?b)Uj%>=d9Y(2N*M0?*)z5U@B%TZjvuYP$yncr z0#f;Bl1|glzaJ=*wcRol_hz)Tv5BK>1M_6+SDT{0xoJP8$J~~dxlk`Vivd(kj2NH$ zMv|oycmoy9C-!bUgtvkgqOzu0!cHaO*eFcNgVB`<-b6aH{rO5P)_{-b)hi-dWO5uD zAz-qw+F>h^X=$;v=A?TWOBV*nX?mxO-;tCVR)@vO9z_6CSlG7jIuOP%0hHpGQV{(c zSFby;aUOceJ&9$&pzzIL2x2?b113%$!_0)>Rmcvz1+1m++9)PaQf1#XNJWTztDB|c ziaZ)c8L9&pfctIJUtAFCTJ)~#9j2h|))ghWvu5Bjj-1&F5>L309`x1CjEumQm86Se zFP&)(Gk7Yn(c{q$_8p^=E5P8!@jmiM-BKaA>q3b>o^^_{I-GI&Ja#?dLv?xp+Y&}w zVjdPi4skx=3WC>%>9@1$;(bD{rWmiUTjlEMkoiOEB%_|`+$Mil9&x%XMAGeeWd`g! zH3oWA!o!ClY04n#-2jzRUJm*GIySdTx~^q}cpUOl4pJ`~hGXaJnHjA_zz+@Hg*Nz7 zoK!^MCMAmWdOLURQHMUid>JQKG4JT;Nnqs%9JoR!d{iRX&EH=I1S16mu zU2_~{KE! zTtk|uk+>~YeJ5WQb8%c0bbU4Hjro`Z{HA@|%gqtVrR&yoUp6Z%U!*4nhhNv8R2GuG zTPrs8b7@qFOq+5awe}HX8~6)xsyX=CzBLkEUOS^drCL2K)i{uB3jMXL_^XPIg>r2SolgdWZIf@?{!Pw!4L7zQ?b27R1^(% zLleibs@uZ6(Dv+UzooCP)HhsY_)=UrWtbJo6sB{%VmX^j?RfK%-Zvvkk_-&Kw7-Tx ztgM*&uExn?qawpuG5ornUJg{|2}hJ z3z%_ToQZrUob$6yWd3-vlz=qm+BN>!T36(A_(@JF3u85d;m(xv>XCY3zgZM) zws|s=NT2~Vib~@olIx`R@t5Lf-GaTMy_ERb9KyhtPMjWe_w&ScHJt+m25lIOIqh&7 zOF4EACJumn^74_dYduwZ!VIIE$)S)_Bs4u01LS z_D;r~gPX45^ZV5haK8MSfN8*1uE5F)ZPc}|B6Fc+?W~o;UdH@3L7prxD`<~Co5xdn z5wLH36~F@9){Rz=ps(AHHg{UZ6{Lj?yCehn!4>xar<}-{4`A_L=1KoD z3V?yctE{XH2@88t?`e;!=TM0i3_S8Q^;`LvKCY*CQ}Lb5^QY|ZP5zHR%6|`QC8<6& zU}%!p9UWCh)>n;;MHBJ?)Wa|gsIiv|5^exMIDUeYNz?vJilARh&}Zer&|fZc7FJjJ zqXyUrsjf3tK39?d72f~BCug$#b69XDVyC8*^f&#t+Wg=6xF`4)>Az+1|A|Qch~#&; zf5U9*w$HU|ULpWsv>Pm-08(Yl0a+Zw#&oqUCBPqk01|4X_eZTV0J!#liOG8*UFnIm zWe;zj9_?9ud&hZ(g@LH{lpFLMZ}ofzRP1W2!)5s{Q}q{#iK(w#kw+xmG5qS3x`PGM zeXat>ZDADn^n&JilyWCq6p)f{XS$C$Q2;Rm86(dPSpP)x|C{`ofcWyG&*loI0cd3a zxj!g=@)3~oEl?a({0=bJ_Ldq}+YOf*hD`u3G}Zy_3@u{u(mMeW^g z?B?D(~@0K!tda1M2 zk5q*7u z`QYB#jHW@?;@3DY$iP?MeYIj5m@OQqQ<})ldiXYt$XcBthCVHg4ckxWgYIB=^*B`g z23;ffztzitlM8EFQ&+_gw&?#*SH1&LXzjfAwNEBWrdMmmB*16O#wMauWvVVv1;*lO08fg6uWEHM^bdU^-HMpSr+#e$$_Jzm&ZmLxUKOWXG-1y;1v0lD zMHpJl4xvpoe0n>P1Xr$+?8xLHcX*lHQd$@B;R7}Zzl|SpD?Yw`u-L9Yg z_OFCjB8x2O-&#?kK z^aW{_v6w=Z(};z6+oGoxFRmhqL=_rB1ESF0KWXp&V0v6#5LU4Og)F88i^89O~z3J zCP&WoC*?J0O5RGCp>NLpeRU%0d98#BPdwjCix+a9M_;&Z?0>bb)=SwHHFwj4&{wC* z7axxt`f5Fo`C0udnci5Lspek^GM^Nr#KySw`W~uM!BrGaf3plOQBy%H$IYSDu`lTQ zgZn==*iM@f>G5j#@+W#{X;^n;c&>e2(;+Q0gkF>S+CdGz&G52<&MC(p0o8Q=@nkSE zXvgtgTsFS>$iB}uO;<1klGqErZoU!og`Q}1oe1iE>k4fUimN%*Lde(~1Yyz(DbUXD zTlkhxIp%bY`$>q$V)x^w0N?Ip0qr`E#oIu(Ux62p+Rsgw{~pO3)=%EWUoYQ?_|h?gM4xxat7Ctm9}%q&$<~j{Co)D)dcRhF2VKp z)}?nsGIu>A0$QRc@%8+?s?BWUylKxSH>+mV6<4)R}4zmdU{>k^YXa7^HFz=!SIQi=e`X3ZLBy@c(9iSQSl~L3- zCbv+>nbu8l zLptcBLuQ_NvmThzR^9=%s%!m2~9jFa_tx6R^52 zkN3@VbMMPQ$5Nrq5BpsVk$V%0==lLOlUMDqCv64qTm_3op;?6|;B%vgF04N*q`qcn zUfCR7ad>r4mywXHw!9yb=-%5F*OBJF-n99S+f(~ST^m0op>uk+YPr1Ycz^-bvrjDo zz^<3~R%F%sePL;=meptl^)b!ibbO~SrBS)zVfBPa`OePHY+XDv2`R-wM^RnDad#4>?axtMC8lH=vxhP< z95zed&f!&`7NqJ<;G%rPB-RP2)`4^hhv8EDdffNi`+XtHerHx{I^BN;81?}`++zTJ zc2^=V9iXf{lMT9Phg=F}bV7O^n#iH)FD~69*#bE0HHq57Pb~z_%pY<2YJ%4Fi8=D{ zfcWi?6y1qlHTTH3`eZ?bG_Y_uE3M7v#VAa|J3ipbEf^1$acIrc$)DG-hh#%F zR_8{t^BksI4FXFI0$AKdHy4AvQTwNtX>$t=~zDfMfoR+K$fjZ7MY&lO(1=F$GFx!Xd^6y zaC^LV zWaDFBFnK|l&CJZAu5l{@Leg)EyvaMV6U>6Cd8T)QYhiqAatj7ou=a-u{=L&A0HrnE zg3NHwpl=P&HnN}k8QXCIdSH|yJVlmH0dTebv_|%0cm2tuU(OxuVpfq>RtQmE;>!}U z%S}<}yxGR35$hj9WCTPgk50K$9af{eU#K3B^@*7oKi^P^eU^NA<*utGLR9UFyunaI z#^{SI5tZv|NF>d-Yo8L`?RfWM-c*y)eKSJ_NSe5*fiG8p$TLR=DPo;e*}!!#OE)pj zkIKUmPbb!IGJ8pzfe(itEcz|Qg|b_hu8ldNc1hummg=RMCl+s|x?1A{i4by?77&IH zCU-Fsoeze>#!%0iJNLjk=neL3{AsK&y)qrI9?xIaVZz~=b!xA4^vgNf_8`bK)E-S8 zcMA)C;uMe;QBiv&Y9mxG#!G@~Z;Y)AU$^9mSdS}C=66g9^&}Mh5 zY=pP_VFsz&xs>)Rk7_=*@CtnJz(jBFI8E7IAEm-k^2joyg`_U8a!8Iwy z$lcNC!okR6@vH=Y0rN^l)kJCC6^7U$)P8ofhig_QBrttqcmm^9K=DlS+U@7Fxu^z- zpmuXCbfvGlB`CHM4T_-+CR;-^PBu!C}%xaBfCJc zJMZ(u9(7cfPATkrQZ<3>r>W#{Jr>1j7DrM8kXt7BEOa;G(WbNvBxmMj*LM07yr#vnV=8NiKuGF>oJ-;Ki#~ zOS}z09%Qve8{kWxJh_^io7=YtBr>0+mXDO1;H%^2bCms*qa z%!O2UTdcuzAh{hdW~2QSP_<(D1Pm|^_G49xn$9|Z$d*5dFX(rv001BU4z;tW|JD;& zdQ{7WrDgsb^PV#{{~*bKCp`Qoko+AY{s*Jx0R=LEAL*C>uCQTaIXINkMT$Tn_JTOZL@!JRQ|EVzigH_hypSa{t1tt zN7nxr(ER_u_k}(nSL{Ae;{qUB2!Z-DbuLiWAj~UZFKy$H{`=l`F>n5FdW`}vprXk< zka6ApcWF{blewmTaha0*HC(3d<|c@bkAEhqJKI3oiCMOjoQX3UP0sldXP~Bns+!uj z&$2+4Fpw~b^02gI2lChY7J;qP+}xZ-T&j$}D8LNmIShRQL=)%9A)wjkD~8oJLO=x% z@>LEF4&S4d!b}9P6^LH+p!jx{Akvp9b+$A_Z2N8ktqmR@EGrdxr87#477)wU1&lI5 zvb|Zr*`UIH+fTh+0$CqbQ{8N#Tkmq)%MPQHr5csdQOc2N8 zMrxK!3BQ)jub)dmq&GghOvNmb2`UsYu3oQZmF{aQ3&%M8Sgd-!aRb~b5crBzThn%A z^Vs<3>N9=li+e{+$SJDLrC<#oOQX(taHgnUNoXN*{k~G$CA?CzBVyLe*<|uV4-$Rm z*2B@;`|OJtds&|i>iu?RH{SrUe6MJpUEew~*(T)LlwZWMg2-8=gjGZn>@s?2f#(0I z?9Ah#-rN7Lv`2d(Tc=1Odt@6YC8>}U3Q0m#cE+xavL_X?Wyz8c*-Y58C8NBC3)Xmt9z=rGKb*Co7M7OpVb<5f7SM7MugFgC~u}d+r(f^o&NZA zl6%GO{)tITN}Gnan)R!iJ{(W}({Am=C?&;&J_sH3$|gEcYF)z^{avGUu>?$)@!AD; zMR7~KQ_IOqIYw3EMjh;+yfTi$8%piM{g+)N)vp&_dANd!Key6;M*e1%G z&?Ajbes!w2C0Xmlvb>m zo1Ea%^FHJ)!EU?3`g4=4yA5TRxA%DGIN#xw6H-^41dq*lhF4t+|N4O`G#4`b5I_!2 z{@gg)`JFBqHW$pYJhpc+D8fOH);gbyVnr^Dow5u+O}Hw6^ID@hy?3H5`ko9at$h!t zBtJcgBV!gn*~YFiLyZ*TKVfz06_dCpxrXnS_J!)P7y2t#g-ziDT zB=-@g{6@^zMb!&ng0s$Zw33#yvx|bqA3$sgJPl#-z|c@(Ma38d`~$3@o$}X*@P2@? z5;rS}gG@dE#^ltG9I=mHaci}R`a$EPuP3ntMLbat73|@+vd&Yk;G29Gs*59*r<$%O ztEJ?^$CefK7(eU84%zd>=JlE9`Rn}*QqEht*>#+p@77#K8|*tLH)f!41UIcKXVE?? zcpf*T&@>muP9cx^3OeoXd317)Zq{;Lpfrrr>psEdIw4_>Ut6$9q3H%5|B^OP@2@K% z=M9siSFUf2Dd^aH)lF&I&&<)p@bgp>U4~TYILeUWqr)up`OzmM3o&X~THZX6h~9W6V+Z z&Q5{mg)k{dg@J;9hSIZMTl5K#y-2NszM4&x8LJ}g_F>^!Uy3e-ZNAyaf01O|p$lY$ z!W>aP7Rv}2C;W6czs_KDPSf3O2fn@^a(esvwN!F)@=!|_7npO&0Mvqe4JnS3x9{?< zA-dMIHUryB2J(RD(GJm6qr(q3@HTm{UHP8e`KmoRh{Et~*H97>OU- ztKnN-Fs?~`_tkC1y;ahKNmobZalyNB2mjERh;-T4UKr;>D}QdpICVs5T$RkdJfrK1M_FbHCqG9_TL2C zh$j|S&PIO;KUk`U5hVJO28zDgr7KU}4gw5bI%qP|T;b9;4{!sTk|iWkVmhpzh^R~A zzpDqhA~dmP(JE|}LbtbU7S2H%a3Xy>SI>RCD=d4Xh{Nur3oEnUGSLJTLK6>i^hx_Z zq7a*5lrD}rz*8UA&6F?B>9P?wSYLVYc0Q?RZRe|8qgM(lZ&_akBO*)>xr+O*4&Lyt zwL8kNgik%H^ajng7mNSwy4>d?T`)X+taLD+IBW64;In>Hp43xTrBgh)FpQB;RFTOQ zOAm`5EZxoEuVQAAhhz#45WkEkpU#x3k4NdAP0`yX!C$GIW!CeZvcl~~N38#5k`ml~ z`OEX$?I~?hf&1z|oM*p3OI!T~ga2Van0=|P+>1oWkC~q5n+qK)^&*s%2BxI9O)+-t zH$6vXbUTlIn>u^)n2S3-EKyQef_vwBVBvv9{7l_{U30c+Y)Aez$j5!1C*Xtx4jsFt zJ`0?N;C>O|Sq`px(^{9<&n+ju4vcAZJ|)E6IMHPqVzR7|_Jdb*tp^ck)tg;zRC|S%y~%pQOrzq8spvA?)(`yK{(SB^ zz_#z~{*d0sLAmr9uOilX13C#!)IR@hQ;%;+|FH9xY4wcm~lEUb+QfX@#c@58X3QUYwcMEKu=8Dr?Pww{?LpgZkP&8=kFDE|V;G7=p5gAEQ9V}g zw?oj(zL$miNGul7&$bc`@TLi|+j11!#rkbKV0{0sPhi?uf~sqnp#XQ)yFj1sKPD@l z*jZd=W%9KF_Jp-M!VsBki@TtE7vsJ@!KZQ&8`%=h{`e!)5w2p-yNn`>aSU z(U5V4#}SFDeJXGJ=1O$icM9{!QkT-80g=UkKw;oJR&2r`yxD5whIUBU*SLykf3ogd=;J{@V^y4kn>XrRDoU zG@ANWDdy38T9w+RezG38)msVVeSLGMlCFb=88f#+w@Y?@VN5sqi1F#3zPj;4VT@rI z(RVEy#>MAeItwE?mQWy=)$%b;q2w|-K$XHVV}^`7WNkJ1xk?xK85I#eS|NV6do8ne zkYfT>1Fuh15>QO4Ar4GncdN^~9{@E@zt$Q;&OgWZ-f#$^{vU?gSYM#kM79yw!fTPYGtUC)Gz0j z(kc7eq*Uw>!js^oe`}&pZW|vUeC^O0YDoxlYcF9&ZyQ+PM>OmNkpVBM$ir^;9^gDw zO#)(}>f!>IpufJj^A&^@3j9UtHlJBYwEw~#?p%QO$u7nY`n?z90{@^N{5J=9QP=JA z1wlRhEM%`;%=A{zE)`w`_b3Yg@muAERf7JerH6=GiU=$|#MVVt#7~OC|H&!;huY&W zZ~swUTYa1(nyWnYdb&;_ZvAdMb6ss$G?z-y?@oU0_qc}-mTE?RPrzSY$bbLW`H@Jf z4*b7Q@b@hH-l7G4zz6=ld-n#&-{|<1tg(KuHYT!%`B=>GbBT`^&}?g<>_SUhySPVw zG3XUzj;Kcd3;U1-aVvycgg_J!h)16l#PC zs_9(1^cD0b3rhZldWpYDPOhG~0wIRAYu7qT+zSZU!o_9n84@185dvi9K*I&WkW)91 z7#vuO3x-(xTa2yV4r>AM)S3YE=qIek481+Rj30(iW3CUK$;Sn0WjQZ$K$za00`_S6^z+wQSDN>-(uO`FlCW=g*&qI`YLJ zxHdJ?8V-P7z2_&k9}5@IW-%F%7zQ?EfFV%M0*LwCmD+JQw|iIZ#(**cTPY5GYdP#i zVyd7T1+XJ6C+OZ$6wF~VRf5>s;ondQf!^c=@Fvx0adqd7Dj2!c{9cOAqNm?@T96RnhJAyy1(MdAm7$^V&p{u2IH_ z)Yin=yUx}UNSq|nD{ma*UgBvl%vR!yQu$$k{&-IER>fuWsx-h)GG)(5rWVTFjZN!I zTnjsUqEpb66MXo4#(OupcCXnmuJe_ev#~F+HBn2~$3_1J+eecA(STapj!B;noKNmfZrE403E~Dp8zU1U} z9JPF0D|P%sJ&jDY_&7OvYAon6r}bB3Qs(Itp~MnKzU=1VAL^^Y?zev5ln27bA-Yds zcjN~V`-;vlzVFBAjV+^|^QMfHtk4epSgy~jS-0q#Y1ab+%5nyI8Y`6j=&@j>u-*Sx z2ejWk=|b_#{<X=HFf{6h9qgX|?U!sU*rLp8)16N^%2tvvyGOg|OFba^EJDvS zzcsuJZNGAXAneAKs7>2ZCiR-g$?Woe@agib>E{{a=Y5HaJIY)Y(9YGLjG#acmL(em zj&rT*c0zpGrVFnK;a*n_E}1o=1`kq?Q~^uxURb2^KIA#-x7b*9yzzV~TGbah>(S_G zjnj${l%~+3y0U;D444p)eRE-R$2fwzBl~9h+YVFBGA~7V3-P0ROi(-gZg<{duIQ)A za)uYH&C9ac%4J^hoKF*ctH^?+nOgju!T>9vwz~HsOF@b0bP(88fahKL4iLoL0D=Kz z%QkVN2T^9eF(4Li-fsHgoo&9!WR)w%`?FP=HuwiIla+>l_clJI(AW}gOvyBOe@c9i zjK!uh%tU<~Lc1d^R#*55XSF!hnekx3?g zhB^C)L>RC8_}hx=m@1Rs-z=`xb0&%H&63UeME_rG&QH{+timf{ry+z3>FiYqbUK7z z`AJ)wQDrEvCisLVjs6@ud!I{{jC+N|vBV)XSULgQOWz=Ta8yk;HVWmt z+}=zQqHUMw^<_nk^A9zg8r8ZIslfa}4JUN046b-DyVXmnm66Z1@A6{iy`;g+8}9l;rM*q)ti`IWLmvI_K>+Fx*6r zedAqYNxx7$?-7N_PdyJ;099O(WtL~9ZAd}j#xgZ`_Nxnc@h>o?!kK}bu%W6yIIWJW z8`!^iZ&fWGsI@9Xx7&XEpHu%xaQw|?S*(9c`<;;0t3^O9>Mnor_ZJncR!_wbfL`w} zMI2-31z1bJG6TQTAB+0E|D-BwEY{s2nmL$K`9Ey2rpE{fX+cqk{PpNhD%U~{WN*&W zGc4Xfg?Z)W<)F9Wh1gsv>|L2o7BG(+k;Io`uw>xu=*j##kS9^LYK;%X3zx5wlln@NGg zEzsIF0yUbKVzyxXET~?AU+xs}14dF|Of}V8;z(f?mmMW|0X559=qxatnVtc_;CN+p z2^e8Z@GQxUHb87$+ba&>DmDO|w!b#No@*_3C(vQykiOeeW zTr=u9+=^)c>G2^0A@I*jIfja=o@{17GyFrH|w(e^*lft0440 zED%5(zcce=_}5ukz&zPH!OFr@D|uN(P#oHMtFh}(=W7aRG!#LXTN-qbLB#s%MVL!_ z$rFa+TxDqPq6vHX3By(h3pIa8HFEg#f0c$x;B(*nB8mTAk}2kQx$Gabs=o|s1T}8u zwy+qFI;kuz%Ky1Weuj%)|ZaQn8fE1gJZ*WtV&j*^Np* zT`60WI&Rp0Z;KY7^-q}FclvgD%=RcfBsmC;D|AJ6-xGs#E4x z2K|_WJ9>F|xDPiA&phQhoDyrxewvc-8Lz@RpS&|f=-Vg9N{pxfn_q4qr~SGwF*H?W z-|7!Q-vvF=bI7@^ShWg4r9&z%18Ry*i(DMfah*~R+78bvO?LX6)YrdZ-L732Lf+A* zG4ihju6?A^uJ~Sj)75Twre8CJ?z?Rxhn=Rw)lC)xK_w|An{V~b^e@_oh^VpQ&4L*V z1x>}UD6bRWh7Ju~g$@wM!CaZ?_EQrx%)SCG4??)5-)|>Ls#0%=vXN~{tNHr& z=uG0U$#nHV+5LuO?pEt{1mC>CAlHu*9S?g(X=CF+n3;@|){cp0eci_VYlh(eoor0j_|~2$@?*HA55Rl9 zAmIZZugoDNDpE2o?ZnIj82wh(j9wQ-HOA@SN$LJF5y*rMxf177uC}WSjh>XdF#}l& z{KUIMt8_;1U=k(Yy6|qL>kfQKNXgzn{mZ;UmJ9P#o^?~9HujxmdV`>f`-AZkdKeH0 zE%Ms;8NJ@6{ZtOB+Q0=CSL#1X&ud2)ucK<}Qi!1Jd))f{FP5_DiwcUS1rFq| zGooqb_P^h9wb_e`g8w*v7AyZRw~hS=Zn55#2%?LSmFst0v0dyh&>w~doM&=MN{ljE z0@P`}lMQOtGZYd}2M4#*%>^~i&k_zP6Ld`~)IRB9?M!dqxwCf7nrD#26gPfb+l=`1 zus9pxmOEv?NF^-)|7XZOfZMnX3>=HJ8O(z0q0(IKVr7=!}diZV{gEE@|wcfMft`OWW!298ZClbJpWam{3|%%=bM%^zPLaN?RQ)3 zK=CU;wS+BLEZYfxzN8ZQT}txLKPJU)`b{3;h(?=GKm?1xpP{s;5GN*~09|8{jR%L7 z2Yn1nBJoFg&5+PwPH-Y^dw}@}O+twHA76|)1W}zNl0zW?hCaW&VGJUuB}oXrQ?h?G=a(>*ZHX?U2&6wO<*BI*PQx~kHx^>E5zXjw~Vx6$lzOWr#b)e&^zVg9INX4YnKyMMzg93$LkSW5i4c;S-M%x69JRpTdA{{6URgo+vXaoiZ-o1PGP}GqlM*@R`oh`ym zMnV<39H4|J?RtA|J!_nZ4TttgGSEavVfw=l=ommFu;^-_Le~L52dKQx=qQt6Q0wm9 zzdr~R&js+#qrkHOWG@0dx3RIA8g2=GD16dsym+PvcTFM(njyirAaz)pVSGuBeU%&n zDs3dvL*nu6NvCoVc*qWNF383#t7k!vrGZdT<*#!KpLpZ|tIG}&+Tf}?^?%rmfJo5j zDofD4>L#iC1Kv3ShwI$|QaJJ$wtKIA7rwtCF%g>bAbvga8$x3n2w;Wq$Obg1vEl%; zx@a4%Wto(UZT4wcqzm0~ zCdpL|4dKwGp*!UmyUMLCNvHlbx(08_@fQ51-{As7y7Rz38lg}MI-%tXH>_$X2~AB) zn}7~r`rwKoGqkFWE`^?Bb)Zt@0eY==to%R)mzfJ1YcdEya74mxf_IMq>CbD29`$fV zJ+^0Bk$aIH0ouPydF@6xw*wF>bwgwOcmOYUKx4~S zqL?%bq|+4i0f`?0L1O)pjjH{X7YlV@Dc=tcM)1ne*ayp#8 z6h8jX#%pk^B3;>zr@gTwJq1v0?zL74G+N_m|64t{{bDBI{LqJz<|mS76iPOz0OjHA z6Vk`y@fqjy(li-gU)=Bao_i&|x%v?(9lyh3N;Vq+L;5J(nbnWL4g(p5qQh4<>xKlF z1l-E&;eniv5TIojJiH||=jyMEHQbt}Ayjo5#$ye`>%h}`gYk32Sx}j%pQOGLq{0-6 zUEuxB9WZpiSuu3AI-6w>3i?mB)9`2Q=p7M!N5EMyF$8-LM1_6GYs}6v%1MU9{h@^s rNBnYd4|WTjSdtn3-w*FEEcP288R7Dp_uQbv9-Eei&e3f3OSk_YJgk{0 literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter10_63_0.png b/doc/LectureNotes/_build/jupyter_execute/chapter10_63_0.png new file mode 100644 index 0000000000000000000000000000000000000000..59f332230a14b7ff2beb4e1adb4c808af1a8b277 GIT binary patch literal 26114 zcmb5W1z40_+ci9j0@9(H%x&-jo5EC8v z#k>(m1o#kek=Ali1Dm_J8#$SQ6pdUQY{4$JR>rh$W=_slV0$h$ZZ<9!T1yuf2WLTc zcDsL0U;{f@uy>_P!GN3Ga(Jfg3<6;jqyAn4C8v^tKxSZBDRFg=)XhoH)QCl7>+Z1c zQrA1Ocdjj8AHE~CF>R;rP>Q`x=VvfV_b6^9C6*xUZcrN$)UD&Woau8bRkt`g6LV4= zF7qXpFEiJd=`=x`-E)K>b=iNJs>nR+k+a4IDgStu8_%*yUrdyWpJm*~bOd zUF=~$kc*|&{HhCL(XZi$BZvFT!3OD`OJw$S@FV8o;ra>rYf0-k&H zGpkbYg8}7@k>bFwdexjhCk}!xD^F5*?M5n{8A11-zBBw)s11^mmVWHIre5W?DL0U# zs9oW355$%bu4&*Kx73|7@L7#f-)C34%6&WC$VWb&CDVSg%4K8Zz32Xt9X1% z{Nl??$7$c=>|yptkHRc6eBCq4rJS5Ne^?LAl~4Q0Pal1X6768j@QHcU z`b^5{u4|B#J*Pk7l#%&Gq2XLpSfNgNr1emKvB$2lDEvUpX|ba@U!#D{y9em-%49Vk zv*y<HOH-X-)3NAi);=j+3%B~=_@voG4Dye^)m$wm9@5JqVYW-1lqPx zy$zku&G7pu8H&fES9Lo;3~>_J7>YlTB@3Yt#G{*|;g)%}z@YZ!CC`SN^1#MuDdV)? zIji$h*X+)0Bc-rMG|*f9qtv*cz)*qJaTJ6>#pQR%#lZg_sQDSWD9*BWYL_iP??XIKbcbIv*-Wktoqn!{RZ>|kJ;5oV2hmi@nvDA7Uegxh~EUQlZ zP=O|zVfi@gcvM)}Jz&koK2i(8y2G@ynwwGLw)rxiMLWhQO-hQJo56{Ayv&Y5#QP`< zcr~|~)Zc85m(M#@a=Ow)kn*6uwf=ee*KA z@uy#2{z&8lQ=4_hH*?@XFZSd?Zrf9euym24im6REwQq*verKzUpkH70yqix@$CJ6O zB+Bh4^K>gYGko@B&umo6?e&0{`D%QVft57^m|D38?}xwW@U=wID915rJba$@EC*^% z7vr3FpWca>g2NCr-x`%`H(n-;IGG>JQw;=bMhuROGXUjPrtf)@d^Pyqj(Q|M_12-ASl*AzC zv5rkIw(ifm)!yFjvN^`1X24F^uI+MK^Ckl|!i>u4S-$5-0n4H?_4V~QG@=u&@8Lqz z{z#GgGLfd6V?PpbVPS7Bq^a%^ijh!IbiN_H&+j;Q!@fMFt?e0VXWCopUSID;6kDWw zh7{EylG`DSsO4f1dY_K(F|b`oNzsqGjg38+-BC&tEcSz++1RTcU&f9MSp^09$B%bQ4vmbAf`Ws! ze??FU9lae73lA^V^(CjKR zE0+2Jg7CcD1mc6dv z)=f8^uLL}b`&C~_yW_7KP3Cp9A=?^B#jb-qw(b3KoAqVv$;rvVA`n4L`Gbz!uYzE3 zN&%9?$-Ki7b0g!S>c<Sge3FWlvocjk@MPmbT3<#dE$ig`k>g`7~nc+dZ4#SKMj5q zrb)-f)Pc8$V3lX)`;2M4psHQOt=SQ-7*6_fWTR0{A<4}{D-7e!8m|iA=m}YJV zK^otEaZ%Fx6uSSAah}N2;$V*@lHYmgvtGPtEjb}6>Cd9NW-g<>R(eLAY2-0?Er2Vw z8n_joKTlKeJtxMa6vlgU&O2n~3cm9?5KX{gho6|i|6Swkp0ozy$Jk+KpUsR&x^sQK z7DJS_ueOe*m%*JXm!eQB3G26k<&1t^^|h@&w|657CQF!V_17c}RcPzrK0)p9>HDX) z9jtv#0ggo)_=QSW;`_`iexN5ho&F z@^{YOrQeRk+;=-czJy-S6c)%KHVI+NQm*EEBjEK`U-G5?i?8ZQ4lT9ADd^qII=`Z* z%HCYl%X$2vlRKxT;;^k2 &w9owBou1BbtG;9d zc1*tcVvW0vjt73L_3LZ{g*v`+@$66Q#$dZ1Y44>bsbm8qe}F1JDG4C>7ER8Eeec1y z&9`nWGDicwbz53wyxUtoL?20`_+j{)H#@UtzAb-I&uZf&YvD4~tDCuRYqm;w-1{zk z3@Wbj^@-p?&A862JcFtXW}c^}_R+RLOY!|%phCSPR>kdzl2}LnR0Znl_#ntKh`-{P z^d{C~y?wdrHwWr9p8TJsfg~OxM_nqP^ab!X5D*i84`}ljotnU$F9pC`+LUzFs=LrB zvp*AP+#K1whC?x)v|8lb6gI-8P3~---}m7=8>8U+GZ3Y6u*dgUiKgpu(5uBHhU^N@8W5`IAmsTIuQO zuYE)Qbi}&b7BOl6saYgWt7OBbCtb0g+o(ThrDkI8i!yQ%$-uzf( z*`G6Jwm9Ze&>4dCZTy8Rru~c0Ml)@38@xD?w4a#M{+&d##PjfY3R9%BlB4Em*+!p& z{CqLNVC0(-T5A+dt9dD~w*uG__s!e4RY#CgEsys;O|5ztGm%m9^zP}pK}&dYG}Pe{ z0+O~}&74TG{?|p&k*I-HhS??oeJ}IR!}C2Xv(o#7{ueQ4tqd_jU^WS744vmq;JUf? zy}?3Fw#Lox8|sjt6R9%r6y(P>i;{-sJz^SXLEqD+U9JT@?0ekG-^@HVie|r(<96tz z8*tFQ^ZO*kS+eZ%(zReYE|E*k!$W^gi9UzDwKd~`@|K~5WMF@2tFZ}jSVXN>4$?ol z1YRJ?pJp!?|M1zXi^ny*W!S-3OS8EdQJnBvSgl@!0--)V4I|s<rzL2j zrAH2A%T2vZL=#&y>UyVt`)yk%ObDOLX0CPWmOf{MCZ`1UU6z@4#*7=ZOiXX(;)JJp z4LoLVn#0mJBM82Bd?QOF>xy=_*eP(Xbh^p8H`H^RT{~KK)beE68mIAR*UU|aO7I55 zI#uk-p7u>W#;p;dgH*Tg{E;C)&%nnq^w!ifoC`ywb|(Uxxyfsbc;u)q08 zwFX4Y;H`AxRvnSdW4~BuqS*)T)dhfBvq>$vx$B5_!~RRt1O18`)*H)M3#X2H5B2kD zA+3c+Pd$CeW7pC4QFeUxU=E@`5;r>k+X%XOP6mCv`*!GjbCxDcm% zljjLLbVds4L)hh=-8+c=XH^ZRV;c;J6Duq|&hpO=Qlu6zdWhGQW1NNd;d*+`jOmZJ-(HopO&3-)P_ZCbV+_%#7jF+j*dw!c$BN}>toXc*KNGG6F>*B>JD_H6H0;RdyQ7o(tx}CaLUIQR{gdiF2u0F z(`q1IK2k4y0<>%HCVz@Up^w;}i)$6shDA|NGQ0j8eya->0?R^^Rm`8zj0DCQ+=XQ1bP6SjS{&2madjkuOq6WG%|baDA9;+_ig=Lp@o{{wvulKLSMa_4U3W6ui`TjI}*WaK99%*l0V zu(Uv6<%V?X)(!E{!H)#gPmpmW zJ;!V%Qgthm2JCkxfv{w<;W9BjCJ82?_OY+XsuSeMW9GCi2@7E`F5T z1LijBZ5V_mW-DdLnqREb>`s#i8kS=?uq@p!Qqqz+b&@6%JwN6?(dN=m27z ziSZKX--VXkho5-QWw}! zVMQp-X{eLqU~}rA=)B=hC#dGUO9H@~J>Jt1jhjyU@MUi;K~F0C^7e3ig-qo7>1 zF5FWU#tjhqFrX+?xln1?sOETU?9{b3bePBF3Z*-ZL6J zR73I+=mbPadPnX~*)Z4Kt~I^e*kwt}kKNSLLPSNSsH;l}u-lK);m?6r`S$iBr^az> z)$?qYHyqyI(qLqbj!1wPE+Id(%RO2I*VHc1i!;K{PfGc`&Gonfzqs5o2%S-*+4dbO zI6q&C(y1*gdYO&yZD&BXJEmbG{q}Yykk6PJO9R+Y8_#M_KZ+$ea_M$2vQ}k&1b#eW zy&^Aj<`v1EI#;abpX4WQ1S&%s+r&*M}$jw0!9RE*ObZTYK z^MA6dmHfy5^J@jqCD*23R=eV2x_+^YyBW!Efd^bfT+yw}f|mcuzA~rDiGe%pqWw

    v>x!Q4|E8z*E<=|@G&1*h9{KlBGRTLc2L0OApi78Vp)UW2O_uw)XrOxb zXN<1W6HWLJFK>R=e)6v&JnPc{diLLXYI*r+fc#!wbrBze8r>!dNVYWa`47c?e)&57 zdE`WukN*Fy32M$kz+ovT;onq$QO1)9`S~-@skZ5d_g(70Qhl?H#LY#Mi+?2(T6L@4 zj&*;PDX_Z$_x0-!T2>HyG=;q&Js;tFc=}|?HdrSNF7fE)|B75wsA@7KrvpcY^k`u)V}eDH3i>6pL-mgFmx%bWJqBU91#o!$>i$+_=c`=y}W2 z)_aw0cdWl4(>Ikw(=wJm`%?$vDc?}bOT;bjG~E>Xd~pQ94%qv#F>$U%5c1x43R`T0 zLrYKy6x#SfoeUzXEXZzyq|h8YF?9uri!(IKryP*3&?%EXAr@t z!o)ffm*%X82`RjQJ$4lQAVs#qJ6KV;=@0E#2*X za5l|-s(#g_ztlpR+V8}ua~{Yqn*&KcASM0w4s%P;En-Y;?COSJ!m)(cd(uM$ipE!v zuTzRkCxS?Lw0XzR7)FlK3Jr`oY*SPEwkyK&Z_+4Kp6uC8n{pr?QRFI5rGnEb9FM-Y zzm~Q4sxvfMC2BBfwFy;h(bTyk)h1+5Z=5l>E zB0{>*ybiG#mlo601$AmKQ4&e>r5r<53X0{dmmU1i72}njWsbM$;-ub{ThO~!=sm2q z6xyvc7nO|TB^3J#9PD($NK##HmT|_I9+E`7i9^0cyM=N}SB7c-^36ciQrp{1 z=mkZ+M;H-Y9!GW*an@uk$;SFd;iI8-X~!j>Mn<$4l+(K!g0ZzLogRdfurKvy0`S44 zHPUQnroK?WHks3`g9CV7HujoS_Y9BS(aT>1&^-|Dj2KVc7_l|f???9&vs5XrlC5`u zIYm?}`b}I@!blapH7!GdXP^c~3ks_^C#>gFI%0__903G1+IW@D9gr?7%JT<$Whf@a*JbEcDhqF>&?^g}mCb zo|b}auc04334Hs*ZeuJSn6?;o&d)#AL^P1B8C1K{iuoa3m@y~buI)vnlsOXCj+$E`L-EPg^S6}1NcUgv`*1w8Tr?)BN~_`S z;BNFXP{pDfgt&OBNXC5Rm}04dZ2_yY!pm&RjIUm@4E!F&FQi=dE@{t`3!UquGs2p|Fe=+Ui!{bd*gsF~RO z(vUQHA|ZU6#b-A{mzJ`Jks^y8l1|M|Y_+$_M8RmHh;`=`J0B@O75XyKJ^y>898Bjv zJ9?d~C%|kCxR{NOdAE32!P7qzu3=APtcZ2@@knuB(_%oDRGVg-%qyg1u5#i6eqBXs z(YM^MpWCC?C42)VakgkIE!H4-PNANn7Z}j3)9-cJuj}12svbIrE(baeC$L>FQI(ic zsF8&>kVLs_83hiSDqFB?=2_@Dyb-T{Ro_MGmfp*OR!)Hc8)Jfawu(!=Qy{w{F%H!; zM{C!lrs8~+SQ+Ot4Nsbn3^)Rh{B^S0TjH*zzHwEp!1O8Zi=RS#+NwF3ATIu9<(N4N=?S=Vu7h@&)~e=V>b5PD&Y$azXL5m!sQGi z!^7_jU(8W()6u;Kvf>Rp|ra;npNg(4iR+gQCkj<1cr`3nRZ`W0zRS}KeB``jz zfuMIe`y*`aBs9qGW(({AQelx;iDp}=A~}=3k=y7B*hc#e+!BpAPg&X`xNz^jlQkOO zeLRgvs&HDA<~>%Or_Xp!iImsd z{ZWy{I-x&00}VB5k!J|$&e{qtqlw1-Gbh>DdkEKnDjSuMTa7Jzdikhg(!O&-a)6t) z^Ugygnj(GNc#9(=Vr^>xSHsN_^#0MxPuUVO3{#*R@0% zrJX)nl-Q=UZUpHka-6P)_8d5kiX$8XKP3!`?FPv{qsFYtLWDw{RnH=UeSM#DyL#-# zUSAh?46zZ+jl}NkrV&2(Hw=kG^K_iP$+Q~%IR7ja{)>`rV?E`xfC*2<*OF}U0vR~( zH72;LV31Qq{%f5}=+Vm!=kNlUZCBdeC&$;=)_A(1qejZ(brn9@Wd>id2CK6+i_&Du z#7NG7IA%_C_pV#_t!|KX_}#^EaGjz-WK_gC^jWh z%pjl3@43ecvq3D9lNfw;Bs2`|t?4bUOZ!+p@=TUjo4c<)%!DDa_n;nR&D)(E`Q&X9 zkH86hnt$}bkDM)6w*DjUmOm3ouJJ^n2Upyy0b$}`=u1dTHAvVYsE^w3vgOVyP^599X2Sf4YzkTahwRNy&*NNC9vWQf-_^6< zMY;-Ye-|F+E3)#ZaM!DWD$M;4x<#S&?~5E(FL~mBNX(xLF6)=OI^>rm5F6eU0<`A8 zRr3C!I{#~(@9(2D|00Bc9lheWf0Is2%d2vuY3DnYNnL2<&xC#-ssQCthcm$&H1fNy zAkn)k>mZ*Fqa5Ie41vX?<724%6&IYtC^5TiR!O9vu_VBq{^4_1CCz`>-zB5^hnQtv zlInjt{HIx0mD1qPmq&p*=fCOY6@UEa0ask^zkU7d@!gm8*j=>WPguGv$^K!g4cxv| zua5tEwMDQiGJ9EdZvtCgjuFd$=y)$Kr=rJ}M&O=VrlzJ?6_fz^Rmfuvxly13WjWYd zTeqxHK7=J5BI(8qJGwyqlq%4|cK-~w_l)H~x*8UF?|%9Ao*A=a!g%k3faJ7cMuDzI zSRlYR6i32IJoJ3RWqsjDQ5uoCQgl6WSDz!2JFvt|Pnb(Mc*4H`S+e-5P>W2;;hXGg zzkP`4dkL+?<>EU9*R{*pq6fM2RHnKIl(PwLFTlM_d4Y5S=Rv2@ipXF~4l80G{WM%` zm`eC?o98yK{jMuLH1lk^>x?lqghU_PuwP#3m(NU=sUw8XTubaO6ftFZBtgMt;9lYq z4?%aGxNtWHf##>NXt{5^fNq=Ck1LgJa*ULSoTuJb%HSpC6D2Xx7lvJU%HC$*GC%7w zluz1*;v4pbiYs`DBx!R&K07Bs!XQr9cA81t;)^g%`SK9Z;bjY711aLQ_DeIU|_|J`}NkCC^t z``~DUFHdbC%QDEKQX37z+J}x8x?IfLJ$d8C6GK|=LX#3J`J+><)1`3`9dpGa?S8e{ zqfJVmJ*yAd2n@WDJnaE#sR|3TMs%eznQ=#c!$t-nd^bmeyXd?WI26fp;Y)Z1>JJ8z za*h!`-8S1J%A%)1_@XB$eN$tJAApjkux1S?1e&rG_fux_P6L1uo(aC!n^RfzX@_b^ z%;Fc)BUQX_Cw#N&8Goug=QBB|7Q-4Iq^ORM-)*9_X3c~GFSLGDD$gmjeN2&;Qt6pe zh@t^$>a!iE2Z-PbehNZDlF+?|M#Y#IoEY}c{>^Xgq35Cj^Q|IDU!#UG<{U`r8OSLG ztmg-<0%u`Cy#>k-otMzxGe#lP8B3XqT!I*sQriF>lYq|&2foMwLBWeJa{e2Q_+kf7 zG3n^``0R-}tH9}-G0Gvy8VYBJE{_*(3h5!)L5=9A4GPycIW`q@VsjObE2b(1g5A+~=JNKtJQ$Ojqymr4 zZ(7v!*|u=w7Qs)GHK$5+%506A-`)XqT7VQ!X?v>n78ceV^n9zahHTFm*iZAcg4&h6 z+5Og9(*nNLFl62%>7;+qn5Lm9_`~fw0R=v|yX-wXPGoC61TIXRd(FJ3T(wH-NFbLa z%%RkMyE&?!co*GsKRHPEIdZ`?@8yu}`it~?MJFDCqt35yVFxw@PjJ_aCy7>8NjqaW zFE74}j27FKd)mgWh|@T*UVZpWCrQ*-5XFN5ZOQ7ov{X~|+Aq%0AFVUTpVAkz3+%W* zgE!ln(gLO=H&W&ISYWB(d1#J34qAL++3qh}SZiDR4J~NT(*o}jWtqHRX>3OuxHBuN zu;t!0o>zlK%Rm~!vB9vdS0#pR5E*z=oZDvZC&vd>NyZGjVo35@(t3$&N?IEh8(8zc z{E6DrHUN)%Z`UROy1r6CU3gnRC$c7w^Mqt zZDW9tN#&<$)6VUuwWJcqGLol<&a?A!z8ubr|AF{>ecrYp=i|G z30O};kMOn%XFr1LRH}}h#Q)Tex||D2}*femZ#^x?1CwNx2p))C?$v)cc59YpUwx3iJ=gpl;>IQ&7&i zA69m*>%VGk^@@#~?JI~;vX~g{lD-Q+R1Ov0zbaDpGH}n8UxkwJlv!&wu*e?kF`o=DMUyg6b2owvM70{+P%F3LcHu5MbFeU%FSE2b)3#g_KdtFy5G z9ctn(v%i2&=C=a(cO(8Cyk1;|r3Ihg;mJPlA<)u4v6K1gj+K>#+NB|Y)D)=h0mV=) zhtc^u#2GU{BXR)(j1thM0yHjpT>Ua5%Ax?&2&WI>pE9o4b9&YuWWYkG&D`nbuC)V-wy7buxg6 zgHW^<>$X8S8*iEnB8eY34jV%ugq`e=PMj??uWhtfP{2sXXjw? z%^OU&&9OM>MJtWJN`-?_y7!g3&XyP23{wbnBN6YxlLk@C-IBpwTafwbHN*gghkHtM?lt|cwTM~_|V9g zdZ&5pzCJNrQ&!X{lCe7m<@}iW7&ZTY!^i?#z843uD_r∓o=hfVOS@d;Xf%t+yiu zt|mM9>h!-RVBFVBT>8(Hmi(O;7rnYj?y|b@52)?G0=0il@fXP~tf&$ET{QUn34fNw zRdFPnf(cbC`DX!S3P=FgUaHH0596zahZ4SBqOK#2hX!}O+z(y3rxszZ7()gqTrf?9 z3-0>%eradWu8YflZ=oz+`&*acELPx*;X|D<(*+gCg^`0GVT%IihT0igreWWhHb>Y#lcnCW807nshkjDlDi1=mkK^a!l1 zRKC`P8~uh@ZDOcaoh))3kYiDlp9m6d?=M#ct`+^pRqy9*YaX|BSDo6+-Q`Q-p7a_$ zh}<^(MHi?InPACS%rT5dgi@vUSCs!w<|`g8fW%5Mf2LkT+Y7NH|Iv1T^Ml?>nj5|i{5&A(R4410958@WHI!XwnbTCu69&5 zD~FurJi|+TGy(;yX605U$Y1gvxzbN9|7Xk)5#o!_DzdXIDs8+Wt{J3>3G}W^31|HU&}@!)*I-+a0JT5QqGM^jlokllFp?rQF<_%j-Q zf+rElN)3%7%-i-eGX<7Hco?>0x1TMuSp@~Z>PD9g$?2`BY$VZWcL`ao6*H(_>Ky?> zLK3eXIiS)9^w=s;A5SLrye9zJduRX^ejp!T^OcH9)F&}IngFOCHuPu9kJkB%@mLRj z0K5dqDx#^q1_D@}f#3Q7hfhPsI$nO=+V&}5?vNM*-rJ|T7xYX-c*_84ijk$EE_mK& zir}PZjZC@Cj>Rm>>%foGL+?ecQ`+~zD^~U;x$T&-VY#GRk`)Ds#r?UMv(V5KdPXvO zMu@2Ji{g*rcbH$l5wTav%4-ife8o?R9u|f!6E()~J7(C#m6`j%bP_4PEXs>T66EEc?1OYZYR62{Tq)9fiOgeS^E!BDc95rH%WLUrK zqH^5dd^H8OX`h2WnN)tq*SvOPJ42cVgp`yDDE-MqWhpAoiK-N0Zj9ONXreQ2-3VIb zxrJM)#qfx1tI*oX-$prU#3NB~oYo+b@za5+7_cnUTg`n8RjN#n+R(2_NhNMfdhenk zrE0{dY8dVTIX?lie05hR17;boq~qlq#COe~=S8FAQO^;sc$ z-j}ehxd1o$SGk+%oYIq`d%QglJmYiy4SVyG!i;{#XrK?6dkYdV5*dyP2L9?sp}M6s zrK7D&R3|f=%p*QnV39WOycZNl<1jtK4bO4BCpUL zrWG#M>PqvcmO!imG9G32lX5^lJ5Q^a?hcbW?Lt4>KF@c{zSlC;os<*{WiEeH^w zx3;~%U%3rEM|d6ph&}2K6No*^fy*=&Rf~)Z&`fvU-xnq2sc+fSw(p1yX{|~U9)yLA z2a&5X!0>ln+|EReIgJY=j-tF6wD33Vh&1|Ic6-F8n+_Zww0GN0Hf;>S9j^TZhMtB1&Wvn!B#_gg z6mSZ98bLnk(7QFi2tE;@qZ>`5CeU@nBoC$2}z-<@5DD$%51ee;#s{V#|eP2$iDOGU9VVGl!~S0 z!=ZeQ&IJ`zZMQ~VtoR-S3D|B{Cq=(!`cOC`Vv1f>K>bHlhy^CZ6L2TmOfoSMq~6RiDnNq`|- zaQX|b{xvXv&b}Ix-=X}EB;ns3D!f7_?WcpkjcJ#FrnvV?T>k%Z&2PN@Z_zsQRier1 zH&l`MH<fSxHw=8iL2hK3I_@Ulh3!B!iZ~*#%zXb^<0D4PS%)( zN~f?}-lLm!R*~^u2v<7mbQWq+x8=u)-@uRr(mCiNj_KbxU?v4GZtm??(f0R$(Dfu~ zOqaX&uWz6P*dVUkISxQo8nn3eePFNH5a<3meS-UDfSI!`piU^k5f&U&Y@3cm<`&@a z7V%>0i%JsghHea!*-r3ZeN0 z)3iJI$RPiF%C$fkE4?4=k(m zGXqhue}~UyPaaS&05!q^1N^xWLbL%~+>~m|+_H=>V}5QWzUOX$@kbJIaeB>iwB*71 zaFGQ-KjNKG1{~lYHHfqI;U9Xq5!Z5+DHJF(!u#0Mm*GIhig|0PHmQ=u%f0ioMuW` zsCs=5*7w-cQw)lNyW?a$qH(td)bdovn-BPeT`zXvPq6Ordit7U6)DLZ4ZIY>I5N#B zf6-6I$2|QkbKUu#@ZHuj|`pWI?4;@egTK_I3W?vTxV2# zsy}7|ACW}u9x0;FXOuXenI4^kP}rqENcWx3uJCrZ;z!HJe9lv)Wk{Mje8bhy`WnH< zN#*ABs_SfwYHZ(;pJZ$ox^4D;y~{eN+vvX~CyYD5i2m3`ogA{1MWou*{ju%`d{S&g ztCT-_xiy#5-iv9-raH+pbCcauEc$h@B14zL;-b}O+m{p{$}%Fx5JRLuHjRjwSitLG z#mqk}EG#~8Zf*_}A79xZ^35AsUfy5N&4C?$!m*V~{maY4s`X^wsbX!*{}Xj4CS;-G zQ(}I2s>nD?0zI6Z{8_Kr=SGP)^8HbCk6u3}Hd+d92#z8kRt{y)-;27a;0hS;sDAXK zU#Vy5kc}fLsx-* zedf0AZFZ6;nMBt>gVt0{Utv^<2{j;lm`>mzJ*?{cZA_f16RnqT!v+8$L`AA0OcZYD z=5OI(bMxWzhSG_Oi1x_tki`?EU+)KFSIBFU9&w&6-c!fWTxhOx!*L(Fq`srK*onf< zB(OH-B+kJDY!NWTF9bd{&IhlE@Xb2JB%Yhkq7~BH4Z{#SAU7RzaaXibn}Z!Qp_7EC z(y`hNUF9gIY`W%4IJ+3`w?TM$ATN`qyXs0qagl3z_%?LU6yN*EeW&e#-SlVFdO>s> zZ%tHk+x*%nsRO)^FFPtH?d8k5xfMJ2UZG)(R5;!T)Wmg}@N-j3TL7=TBYoUJQr)AX zn;P-vO*r^s#{sfHAGl!JKQMoXxe9T5NbU4V17|6waDootb z4nbE{WjjL{blf>|+ZP}Mt314z3)RYWfb6%UFGFON-zS8-?C)X;?G~fYN-Ky?8@8@; z@TXwj#1el3su5s&LuGJ7r2rZ}_n;KkzN1i+;xkJ^p>`=vcqW2hDIv1{S`udrudTT& zHwF`z%b_|Gb^{i!22X$D26pBsZq=T!uc)m`YpcG_H8!O9=pHrJU8qM5P_I5U4U9Df zgz_Cy$v#ybE$vzm3F(_~yGm-+$8-x@# zDp_yZTX0{IOd-+PNYo2vKe}h!PGuv7>psk^%$$c?iRSkm?th1eyRs*WkJpLxcc0yP zwQA?z84}PrhWPII$_FkDa?jtiC@AyS&=-D(vS$K0$AmBV*x02kB!HIRbv7yYhThzmuv*T3+G_?)xg=5+jOULG93!t^e!SozFuW$v@x^0MuIdD#TpYe-uorbi-WdhZxwS6ZWXI`GRQ<+OQ1w{ z0J-J~k+{bsWB%dZ18ph81Bh*#O%NM&SjbJuWa#Y&+de|hqEDMLPb(|ysv)xM=tiWy zC;H1~cK$P%7>|_s6ECJ|fwPdl0nT_`F+SyV@MTxy9Dqq8k+UwJlc|@zY*!B)wB;>>%M+!r^!o3aSiL~&m{Rsiax48wj1}jjb`{YM(?K13 z{lul5mwK@EIH98QPu)I*gbcS5%8NPP)I|-j zxH;{@?UM~*4Bd6Tu4VAI8WS~VN=!vHX&q?^-{CZM#qS*&)YvpJ2W{r&zKubL*WW)- zU`OcX(n-JNa9L3SqJcQz?X?`p!PUrD&jb>W7l7#>S&^@ei1b}bvPk5%B0|~C0VjGc zuviv46QTekuX!TYesHq8;Ak~pz$Y0I_SP##)@`0DY-BRhJ3$YyIT9Ak94lhRkZZW) zf+Hmlq6gJsvOAr2ZcOTJq7j+aiX<4v=mgG#11Ef6eyA0EL>Ue)Fj{W&BVj}yG+lJdSV{dV&Jlb&P5pB=BQ;fM zk?i`|c^u@rG>+49sp>`<$PK(-W1y=9@fAvqeTPF^ou@vqkl;&jo@;Ts@A}kBW|pWnlOtU_<1TJ$^Gb~8M>lqsgO8AX$+T;TFL1`x@4E*Ol5u1xcA(Y7 z;66g^A|(QU3cqFX^`N>|Dbt&fh*BBe?{cVajrETs7;VrhxB|<>mSW24jE!gylPfrI zPS(Of@i2S^l-lanhnO*_JM*l?SeacX@Shxv0=6e0U3t@RsVfP{S88{}0d8`@5Ner#oo zIbh+{17g;^QR1aRV9%!>>Gasr0js`##;N}GskjfqllGEPnzum`4E$2ah;+60HTJ8i zc<*-OHLM2EH7lZvrpej9i*RSW`Pit+0y=OO=f+!DHqU#nq$H&kJ%{i%j_k7GQY>vG z<&jVHVE*>pD{4G>FM-kxdFJF(iko;o^M(Tx>biIjwYr|>8r@43+%g}E-9N~P#|WUZ z85k*MhzNLs*>2Liw5uyMLG;AwV~Xo`7Quc2MI*Xdffrlm4-9iZ_RI>ndJdS_@c)y7 zBoM)Sy*Jkk1WBkU+1NWJI?7@h-5M6!s6lF;vo9@u22?T~>-TDS8cShA%xK!)nQ+bg zjgQFSql}pAVCC*+sK~Vn-QEwGko2f*b6LjS??U^nbam54^NpiGAgMzRST(hfcBS5K zs#r~*h2t`#jZ}>7o8?NF@ztUW0x!Mr(X05f>B>+p`7uQOceh{6?2GZO6~!Vb2Q{QI$brW%02 zqAfpC#qIr_KLU$jK?&{F^^APIDwj<81h%QEFF>TyE!uG2ovw@bHUEJU*qd@9sVxAG z{l1g*4{cn#GDQEDykAw;|Iui3Yrp&-GJ^km+W0R`{a@^kGzXdWSLxoAc@_N_c z-;G!ac?%>3{!w!Lo29b+TdMw7n}Yv$0?)2v9)u{8#RnV=T;|WBQ9L`y`X-8C-?`ZR zj`|w=vCRA)VGDk~_(JV$RBSHa}_6xwiyotWJ%2QF9i@=EFI&F^A{EAFeq7)_VEb%nBZdgio z;9rKT$^*VRlVXSA0q#c!2d6(;(`1!IvbhtR;?MNHC$15;xi9<3DxOns>vIcSvA{6d zfqRR)sB5a}bLldxnLfo}{K9!Ow9>Bhp_6kLI1c z7{aqbg7mnf!M@s_YU%h;E&G!a?ShK(a=r~%RO3@5s3??>$~8o z13c;tACg3dN1v5)p!>JZ@u@LB_@=CVhn8d2i@&1ecS+rai1obKL_YtKBGYH1&It21 zf~hj#r_1k+#^QA1c^8m`9wPvs07WgO+0y5s1w1d2$uYHQ-&T+LBz##>_uym1`XqnN zHfg81pWmp-{pro-_7SccE-%l!G8+#N5Q67VF=-86O$eV_lju_)T=U&dYumkl>%eOb z+Sw6T#rj%v`Dk$~UN!#k@TK}kz2h_C^A&}&AIVaeo@VQrFF@yfZUSlK?8tXyWp6|` za|!mBA9;!NU6eRwcLZ_So3oR17ny2L7b^0goS&^i%Ab&EVAbrUF9~s#NsBOw25jG# zoW^V9Rqs49#O7ffGq0*y&FH`pGqc_{dn1YXo-3!Glwl&>{#!-hM+3D(Y3j@d4Jnxx zZ!aHPM@70n7<#a}!|+(9$mIf?%f96kcSWn0Et2a(|9Q;7Nu81!S-&rX`;=bf7;c9* z^95iUhZ3ZFmfZQ&QkW%^am;_$IT^V=)b>0_z5VsU`an>w3|l5F;P}+A&rRPe^F9c7 zEg@H}IvIzeI8g?3HKuk_z@2MC|kXj5NEURpvTJs5Bak04p^JlRUnI{bu+)M&8o~J zHETjeP3dITgSBaBV#xMlF(Qyw`GQSyS-zKcWtpB$so$wmnf=9R$<$rLXlDB8pR_`+ zUb$_&a_jF;)ejTln$S4CdvxKIdcQdLnpWAV%+?p3zUSuCv;15B=6JHp1DIGiv^7tt zds3?taq|haW2#ikOD?$9z3&U!D5#zj3y)-^Xw*K;Q04*_%A z@_?(@oLdTi8XI)fi&n=q$Y$taBNVOmbbsU#=ta?ax_9!+d3V4C?=f#eL=*!W@t@(p ziM`NbU*1=u{UDwNnOwU3oI^2@+ZByMY|?ksuOyIMk;!r9ypi&p2QR?&|EcWE@@am z495K4AIkT>y6^A(xbJ`QaXz2(IiGXR`~7~so+lUbb>T%~BINmO;WrEu5d+<^S=Xny zbk#@Ocw1Z^oBL@qWx1||pRmEW4`pg%i&`gpbnWQFm9_lO(w)Kmem=+kBe>tmQ9GJE zF@(Xegls6cUr7!aD(B|oBLe9ut9=Z7xY6m?#Tg&w-mlrVh1YD`U!tDXcYJ)+^U%%c z1`AqNEBvUttts2ynz9J0ht6Sv=W%W;pWjTO+z%~i>@qrmn#$&+piof}ru1%a7e1zw zlrAgxm6YqSw5gvRw3x^DN@V2^62((94hyBk*EI_ZF0?uo9zcCFSSm zrJgapZWUa*hnBkf4|+qdxmK!p+*6se<5{~@W;Pi-sa)Y6PjATb8KAKo{4^|Gc<`WS zUHrE)my+GN7K(U_$EsNVogW|}iyjEmJ$&QcVSp(i2BNw+rEYLNhY_tT7A_TuQRian zm`68U!|Mj>#_4_dzLfe>+W0V*twcJvtWNTYsl~$CGO_`~Z|P)DU78^O?P+f8y9nhj zuLJjfToDgRs*^ocR(1EZeA1!=ZJhJQ4lh5PNTT~pn%1T^W;AW8S;J^S<`7BH@_v^7 z2gHG1!Z0MeEn91}J+S#?fKvQ2T+Kd3*DbZkph@U@Fp3Pr@pb!ntDceaQ_p2@M20id zs4I_K^FLvn#`+bQ%|szl2eC!@w&NLPUv@ts&f~kbx4s~PLtg2TIm2y(E6>3cSL@H0 zL?BR9yOD#!YrQhcv0$AUBqk|8+{koqyaNY<=b5U5ShUph+HyWQP2Z!*jp5rlS^Gvu zEUuE|GAT4xM}NESS?9(4A!0^pYWo8#{oS^IJyr64QuX@fNUiU|X{Y(RIdZ9Yt{mF4 zLpEBA^NX{XqCTD3O&VW5?cRFux|e*9Xqdf7Bw>_m{^EgwmpvsfIcP^h#Y0i-{LCgq zP9>?{2CHkLI*)hv(DqLUS!<~$col%v-iMiazno`?o5(bKMP;;b&U8hA=18T|z+xcg z*0@QRr}@F5-3n)Y*%h0E%+<84)ZgeI5K{~e2(D;?2l#TSw{_<4zi&`b9I@fLEA2SY zu2ctE|B=kjh&}BdC{BKs6T|Yf!b? zYy)A>gPKOl$6P}|{o>=}(@5UJ!eW|B^NwtEYiHY~|MoJ0nXiv-hWH4lai zuEu;09&L9Kykth)Cg&}yG0+}xCH;aolkCa2HJsh3oX{iDO48y~2Tg)}0nJolqcDQ@*gJl+H zXNO8|uNB96oX8yUOIZiUs(0MDzAZ2Fb9h5@A8PmRa-P1T?73Rz;uH3HmTVob?kw3f z9)B7Cr}k25k-hso>gkjbi)6zW()=!WYyE)m7fkUkc-3>5zzUs zEPtAEAU)X9UGQUuleFm5V?Hs|$=Lbf_zp$1r_>f#)XddcM%Rc`b@8c@gDY}5%n#?8 z0xP0>!&oV=FJ~Su^Xs@2w_&0w+i+*VxyKFhMl#%Ai%zReR&$_oZjVtP59~Dk{57^^ z;|@0dfPpbwD`lP)BjemF8nXF|Y5x*EYfGy??N}@;mXvri&tSh~@*!sK5`c0^eZz$e zMaX+`kV4|On>ScMe}f}E}-qkHqf*?v0_e|8oZWx6{zf4`L~^C$g&vN1+TLLwNU z6FLuReTh|w>N-=%K@GzQ&pfIXt_zB{<*fO*JAL0IqEwo!Y(naZR|5tS{Zbf(a+WL> zdX~%79f^MKd!ci5spP*0Y>nE<);wNIxbbf?DwefI#UvGCWb4w(9whvDg|d9?rF2FO z2?f<=_wXRGi0PW?dR=!^gQM2h{UliZ)cyS~zGDdf3;-Exv7w&Ls-%1!p|#M2CyD$l z{{2gmFQU0x82*m}YR$~NUK;*)5cSvUc6pVw8NL=bnXZWh*Bkm(Y5W<373Lziu_~e^ zG4kZQ+us8IICdk;%_P;6mLRS_be~$)r2~NU% zbA~QHMa6fUMvUxSWc&5iP|e<>J>MY}U~c`8zO1jm{8Po(gmOF0`mlIT2 zK!1{1V7MkY{NHtel@%2nz{?}>a&UYECM7H`dk-ta0<__Ry1MD-=Un$Dy6BNhx@*p2E`Ytk$*?jx zUPeDtX&OX$-P3*Z4*bu+Jl~7p2L7w053wLY{{FjD0m2Jn0;#1HfJ${c?LmvUrU_Jc zc-`{;jsc|CZ1ts`2Q`=y6B9u{*uB$1XRSWpy_RzjweMH;YmHeQMZeUnztyz=uM&Yb z_Kk9vtXclgxq`SBL>RHIU|4NrJ=7ogYt1bGlRWSrHNonS*DLjFRrlX-X$=ne>vIul z8l!A2R$a@q82mfaGO`L%SpSHplWK>)aTNNr5tD{brtf)p#?`ysIkfuG&`YmVLI8p5 z`cctSg2}OKQx#Xkxvxgphi>dbNON1vaPl53)#_AZ^QXiMkPO&_eJh8Z_` z5^ulSuo~A-%*`1+Q^@^h&v71qh3XkdA5YTYUtS5r(%Va9iid8!mz&Qs`1US({qaiq0pT`G8EtCys)W6)uj*+Y18Mq@}2hYZ2LBQCKPwb z_~GSP-X?zuZLvh{q9f(Jz!nSoBRovxx^T4P#9YdmnTxOHh;7%B`rr1*do!*ry5UsA zBJ+*@5-ytLT{3z;GIi?yZLHuR747kYz(4|UPVz4-)Psrja3kcU?%Z=o+eB-;TBtRLbx>JeGdh7X<*#&bTIlKR2cNeEnANVOU-Ms@C|z!UkM|8fth^kT+8Ex4 zjS+CuLr_}!SNk25a<@K+)XX7E$CqvwkHjwYaq>8N*$EWP3<{iZ%Mv=jGM{0);k7>1 zwRT4O?PB2OV@D+zA*rlev!)DZ54hU3PQ-kd(ntIIlrwNa1g{En#;nSpp8QLbSAG4J zJOu8`tPHC=4Q&@X;c#KGp8O3cfX31EZr? za`Yby@-s3=)qHwdqIRddEUt}^N@UECm2;H9_VV7L`wJ{UtnBR8prX?~I4 z}I)WAuZqy0Pe*%U66WuIfz7UP-9F`XaX4X0j%aDY}kofHM3ihNnou4ka z20@X+b=$D&^t-v&mK!#0+eZv1-24aqMQ+{^6CHm!dn1Gym-Y%u^za_3P9t9*?9bM* zGsu3_pF89z8|{^2BC?MX3V5rWfHndnkG`O^XZc5ju{4pR=4OG@KySY~Y5zUYg{y06 zZT=3XAgp$fzEjf}*5H`AStK~S5fvt2hW2~b%s!GnGsJ}&8crgj(#jRu2UNEJ0wE2jd zfBUnI^(n^N6Ls%9cUltk{?JSko7-BmZ<8{eE${T?n7GlKGtF1psip5rXL1$JH5d0s zC`IOC3vPZ9DGA!Zyt%%>+4@Gly(Z``N4iSnz^!2kNZi?xrb?uzr4D_OwE51fO6X?y z42p^9?!`?mh}K*$@;#vAAsOFriNGeI6Qh2?tZ{oS7tKR=^x=kbUUidCGqs1^)Eu7_ zw*+rsFLwDhq>W;5Fvr@~)?L^B?pi=It;CDQ2JX=~nc!+AE93nwrYmi>P zb*uik6gMw%BjC1sLbMfosNI;#0jDeAY(O~3fH$^B8&Llkjbh=j+9TxLA`~h8qsq}( z?YmB<)XII!i^?m@uwTw!E})}etFcKjZ{@LDsa=Pz-2?LcoMYWLxek4zZ6BBn!V-1y zMr*vIWgY2{9efTAt4!B&hfXi4Fd*NQ|J(=vE~s;|U9~T+Q-w5|F!rxsujkp3UG~M_ zH2%`p_QGCaeMQgzX$hG6x&HrVdih1p`Q;G!_0Rt0p8UPIVEJQhFTne=7I6IE6s6yG zAiq~(er>_IQfwAU%JIm4T4?R&))7xXTmMxt`MJaYxgYs&X#Dz}dO$n};x$mKz-E*6 zf!u@cgxxh#lUBp>&$%2nlD^Y+0vYR+=C@$oD8`pf6&}$^S=9;V+Y@2a?!^~KLR5c< zVuoyrHU!hZO=sarz;35PRdpF8vIMs33{Y!mz@Gdc5cZ;J1L61i0xcxz!#`YpnRbA| z9UuQEu3Mi0%Sd5AcGO@l zNwLhHT8e!Rdb#6(%?6(Q#RL`KVW3EWX)obQk}82sQ_^2jg=_wYH$1AOfNtvZvAV z?z_Wl&)>TB8ZJ+7O4XKfpSFPA`Vi%E@i;`DEb(p=UGHqkfwY;SrPBfv;L_QHydMzI zZ`!lG!96r%>Iy0VL4(N4-v>o8f(D@-7ntCdbA1EFH5|z9lNk&^V0$f3 zRf^ttSLMgyZfs)mCkT^;bFE2(U7i!k7lH+lmjlw|3gF>@GHnXFCp;qJLT8~1;!e7I znip(6kARJHxzzi!Xw#(w0e!Tyi1Pv1D-eb23VrE5Zx|I3_j|#B zeCN;|i<~V0b$_H0q)8g^;r#;xwTw?`HsJ@i?Gw8hQRqUs3IKTIv;qZcN1txeh81PL z1j;qMkpc`c^$Qn}6%6EK!O-xctmu>v^bvCK00?8@o5({x9?%g;f*Y!_u@MOWeNEa* z$yUTjWQ>6NpbXRq`hau?AV3P}Zsn;R&d6^d1yQ>&)u*nhIRIR70quA(ypbw#FxF)=vV4o#H7Ki-N7dt%CF$@{qAWnD@cLHWXeUamnGMV zC~)#*82BBM@f6_7gH1MwJ!v`?20=DhE|HTal$Du|-FP=y%a%}z0N@cEJviyWw$TI> z`*dCWI3=q%1@a@X;`xCxtLN_N*T$uauo9Fa?OQ~^EG4@YW>gO2`c;hg!mq@o|81s5 g3fJr1NLRAMUS;yM{A&=-V_{N1uXQd{#l+`-06857Qvd(} literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter10_63_1.png b/doc/LectureNotes/_build/jupyter_execute/chapter10_63_1.png new file mode 100644 index 0000000000000000000000000000000000000000..10b90707a29331afc5f626165be5c8003070e6a7 GIT binary patch literal 28453 zcmbTe1yodD`vnY&w4@T!f*^u)*9Zn6rJ!`DNH<6fNH+*bGoq9tQYzggT}pQi2n@|I zOnn#e=l}J$-uGMI`dEv(%*^H7=bm%#xqI(tKPU2$y5eQxYs5G>IG2@`?rGxSTu=ah zO$qUVPpsQWWr2;P`+Z$^EhlStFEdvw95pj{XL~1ids}l>Pb*h9TPH_hJ`p})Ue;&s z?#^yf{QM4ocHnbzwc+o}xi<(jLgcKZ=Z1qrLVfm&i<6N>hlAtzO8K7r6Ys3;S)Z)f zBV^a!xc|VGg|)q~MKSMHDus}(s4W$4?x+NNJb+}vP4xM_cMoE{cUuVF z8`XLK+z%z8b$o6xUFB2=#$t5Ph)+g!Hw~)=s5w=uf0W(7Cv@d5gq_0`TKxDO{yW9^ z0`I*g?8csn|IyXnRDK)O$(}97uQ?ExgM*{Yc9c{5lVKzTGG7wHbN!Xs`VV!Eiy6{h zd?tQ-m-tenKk8MEl$wBuuik23>(8W@a=*!!N)niA5|B=Hu zmpfy5b;|9%98T&Lq=zGwCY{Xio6P>U%X^BBqfpNo&t(lr6Nw>8}b)F8jp4&b9 ztG%T+U*gd487g5=2<|6E6tN8AYX^fMjoTsC{TUrBU{p(MC7+tQ!NQ^e?B?&`13*QBhZUMu0)ybaXo2nv_8wj^c>ePb5&XKiCD@dGz54_t+;R72xV2BqqLK z`n~8ej{Eu$TmO+oXH3mnBXhvX;`g0!GNzt*5awI8%ko4M7^JMM%)!Z7;jyU=tJ{%d z_FllnIg74D{|io$cF8poTE0A&!7eq1BG11^09~2S z*VW!mK}jhOjK+K81}P90C2TkL(QIp?oY&y%)`#h-dLLom#*-xy;2vxz z2ceojJT2D!^86}rJuOc=HLZS2WPeihDCmaD>x8VVnBLW;?W*~;&C;gEpQrYd6?7Lcq>7hRM8oul$k6ocQO++7ICb+3&efijcUHZx>B17%P7k1imDc^&&c@!|T?F`sy@Wxlt*y;=zEM^! zLxhckBV>L3*~3)6e&7aF3njivC+8>ORKJH09GO?ILcn$9+xIRphpFUzl~m0(@$xh7_>G+XP@z!Vo@d7)N>^E!R&T!ZiXN4Xa!E3B3yxpH`Qw#|Gp)iqy(nr#KYy*)pCEI zI`-vlbTlwqd&f#C0LM396pz@RHqf)ZG`TY>!iv{Msh)}K6PGI+YLZI`1Q%K6c z54`mYJdYul{K=KGSaE+6{@Qy7)%)~($ME;RBA_{CJnJQ(+4G}F_!qL}od?4AyG5^G z2Rgy|9arSyHigWCzx#G$Bn^l~x7r<94{Vjz3gd?Euil#1*!&c~%(BpBQWr0{zkP{= zlOtd9EA&kPk7(NOcxKhio<3m z@6Iy!(l7LF*`&Q6yeYO1y&|m<2JU6{$)j+X)@}ne4`9%Oq%2>P+uJRB)4G^>I!6a( zUfL>Xz6vh4XtaXEEM5ybHH{`GaSaNty}O!2ihV7s*+{|vr8KUoNg7K&k3Ee-*~uBl z6lSJs^kbLfwaa|R1r_dI+(5jLh1E(Eh-J1!Sxu)ObiClVay{r7<9)C>cX^k*-Wvwb z@;Gt>e?MTHaA|)515ccVSw2bHn3=gZfUfuvHFWx=_Jm*pVK@HxL4#y!yPJ;BHgbWU zY)h)MUKy14DYIeEL7h=Lsa9sE@`qp3da8T8bc1ch=lIBPGz#%SYINTZNT$TD^$)id z+M<6h>%`O*-{H8+^|fGsxr2ApZVVjZhj82P(X!Y$IqXWlnS_lJ^r|rE$F3TCR41gV zA~{)xw-H1#sC9I5v1?OdYm*h_WaW@WyBnz^DBbhv{OSaV%NA`N%+opR;Uu!tzoDA{ zf?RK`>gUsVYQ<&m)$&~T67j4Tw^{O)Hc&Z47_o>5!h-S5BX8t(srOze5u+@X;54avQG6O<0S5Q(h3x9@oYs#zF_##` zc|ozR*APvbN#ef!1$U>F`?8LOoycEM1=5;)P_Va`+1A&{8|~G4HdG{XKYI1(!7cIa zks45>=Tm&QtsUymu+iNp7q3}{eqR&Mn$sGS1KHX!CiMpGl$)-5m(3nfB+4c;?||AC z)JLD`*wJ-iB=2t;dz8|7>Ezy=%ftw!hSsagE?y|nKU9^%?ng*zL> z@CqcnjS&I8f@1=%NxbHvVl4Pc{=k(N`JBW~8|A3yRLOvM2?^W?;Z02}0hj;|u0n5) z-%QGJc+-!me`Lz|byT17 zYg;2|H+3s5Gp*3on1eKlXSg_%@7ngrciH#sr*?{V?vaBG6O8KOTu*jwacFLzhGvMe zl*PDkNF$t2G}W^o;+Voey|Wz5xdZ~iRg}74d1-w$l&9ez@CM`cB;Rg^WvA|&)I0Nt zVm&ZYjOq{kcE8-f+S49jPu@AvV>ce+R6xJI1P8JZ>1^Dbv2{evl(z2c*^SD<3HWgM zq~XiL12rbKBj~NUfCP3h1jn@dqsJ2`-Jek|N08EQ`~2c%Ynj`xkI0i72~tNp%J_{J zlWxd98%7A)f9)Gqb}{$f>YbMHw6&ja^yf8c%(Cc;Gpn48h>Cjay4nL^yBRGu!>5*? z2+iY7o;!3h$8(ABMkEZ~>0Qm$m_uF*6uL^R$Bf->H7P=!1oxeMrS+_fE!jM-SPVBh zyAG>=puEtY5gA7;OYsiag`J(Qckx%-(w7cZcdO(FWb`6sU8Ot_?ZXlZZNWs{RF*aO zc5UaexQ}WdCh~k;bgf-KdaQEmhkwME-mh-Y=JyWCQDTuX#Oz|6avqXmVmZ8eFA0f= zlp18*Q780qCZ2Ki`w!K|N@njqjEZKItQdNKU~w2=L3YGoh)`Tnr@eYry{~DX9PNea z8gNEc^s+EX$#&L4W)T;wvp5^(pDU$&xPP)yXv8SxJyNNRQj|QftZQ)t^Wo$d(=?bf zz}%Xyru?+3cLUkLKDIN*su;<+Y?0=gwS-s_eKur99%f&{N&fU?V&A(C66;_G7x00nLHGC+5HLq=;!t+gU-=q-}Eio5pEMmXm4NLNay1G~ID z=8$D5O~$8E(CT$yqVH80)vpt#;^`M2JuP71wDV=v@3yafhYGNjCkRbk!m+yBAho<8z4+SwFJ zsm>G+RWKJSrghBKoDCo0nsBF}rq)P&>!X?K_8^Rs1)M`d`>_jj>sD6Fj$8)_49T;J z*8`@K-R6rv-PzJSrS+QBfm@Sz%O~yePNosNZB8;7UEr&3DAN1^W8x&(xVq#x7ej)`zQ*^ z*GO_qzWeTBu%;avqwWht#T$?EaU%`9h7)|^U35#b4@WUWohbs(j+lvJU-T__v?3c`v>Znrq zOjgA$#Icf$NouIt#p2eJqC1wB9ARd_CDC?zw7D_YP{*ZET_9XYMK_G)IVA(rfWXp< z6*3PGdGpFF#cqa!!kFS-_HG++t6(4^%iDiM}5~&ZgdS6V|eIS!pC0) zQC;q|iinGQqnVF<|72r?DX761`SK(>yE*0-A77%`-P9qlsTO<>t=Uv0J)~pW~ zGc!%8zjYZEx_4i3_t|Qzj6PySCUM-i&wPf9XJhOg8Fk_3iwjWEx|5&a%=(l8HA%O9 zMt0x6l@cO;BPqB^HcSp4UiHSU1YU|biM$9MwOSYUtKC;ySgOHJJ}18y;F~3x()>-l zaiygE_ACPH_G+=g+HF1<;q9R$EG5q9)8947cyODEKxAz+U$z`Mse91x`MQ5{J$HT8 zQ&3g7WRk6Fes8%;ugZ~0P*AYikPmoR-3Q1GaGs4D4ziCcOr-AJqz`i0?>i!}GVg{% zk39*Ett9-{mmNnJn&3rMcXx9ZSe+CXp3ZMEtqr3cPPv-8j-MXGE;3K+=*xJH>jGp7 zP!f*6!_Hv-Clv_qZGc74c(u+N=Da;e_mKQ^>^?)}<>nLh3-~WpKKTXs2S@S+0d!yP zoY6SSwU@1W#tks{e}VUMXT&2&yO+>a;Clq^Z>(Q6c*bD#c-n0p=GWbL`z2{O(Crmwb7ZWe`?EGFK!ADO?+1S! zx*PR71ln3V)w2*rwf+kI-~0+(dv^N&7dU3)1JK+V13Dvpy3c-Xfb%~;55se|mDs28 zdkB6)K1BihSqA*>zO`SY_NV{dLVyqeGWT2XJEOe7*k}B@1pXYe@YiVk->8fLlo|N> zXOwc!2hA(3BbrvL%F*adN$5)#E{LCmwgbcsgd#VO)#;i=R~nrMCRDz zT^tK&0MIPbMeS%vXn0KrvLv@=>&AuFX1(U~?Z!Xx>VJ;7aEVyJb|i1pQ7825jA!=F z1SCMo>&_76VPj+a{>dm4Pzdxofm;Jmws0iC7#Vqa`SICL=cgJv8tnh-ObO#R3k?sa zW@gT*Wu&IQYiViu)Ah-dD}ZQOB~#$FGxyncG>q+T7zH550dk_xEV}rY>RFmD<#7u@ ziVf!efR3>-lCSc!qIb1bfY0cmu-a&a-(u^fxfh$a<*+EXhsifvlDW0Kmt)1#1k74R z;iU@eZygv&*VMl*JJZcPZO(Iuzw+{KiG?n~Q6oArLZaZc(y53(iv;Jf zm0m&4aCkZ%UJLsd(hp)ix;jQ)4ytAy&~6DP&f!b;A{#XK9z}>^LE{Bwt`CI5F2Ag# z6A2JaV61WQ+k^S2GmC09*XwsYT%g2VX-soE1BHt znv4l`fi0u6D8f@6SQC27vV*h`IYS<7ZG`Sl?`mEZNyjP^BLmzZ*!#UxMe}2hh-LRe zqJE^Gn;K(-g`UohLoKrfY$3e*E)vVCkpaZ@M*tQUkB*Twa$+eVB;(o{X zBN60pw>+DJ$&yRo%fYi*R<(|E9xi~yHYRPYd~+!Cj(fs@m)1@?`dF zH=Qfw!&!?LCn9|*M{R#dXJyf4ois0=X1o0}F4?(rr8rSp2B}Rk%Nh1cHZ}ID)+=5M zMrBU7aHBW(=UJuVFXw(^_iSW_G9PRiw74@fC_u~EL}1sH9u>)>v#Lk8j}RPKn=PJ>;2*i*18_F3IAl$;Jo`a_5%yP~6Ra%VZ@ zG)TD)gYOhzzTBcnih;lP?W>ROYTUsK9)CcOs+nA=B6Z!`;aFT;Trz{F!$U16u5>(*s{vO*n8rmV>bYXUe29z$;4Yz*iNTcMR;W@Y=uPDfO*+ z;Lo+GJt@F14I$qWys6!D|2R68izVQD2R{R;CZqEyhrOQNyK!H#K>{$t*35HPIGQ45 z+^GHO2b(gVlt`aR{$}?eqAagLdG-yN6N2g{P<2K6-<0>_v%=Z?LukQF>Q|Mk^+lDa0OpU-Cpv0I-9@b4_ya(%i&NZ2po zMCgY=%{Tn$FoI7<02+_ZM<;0Nj?uUboPTh3_2mjl!jdysQtOkS@l3a;W2i5m^l{22 zy}f>iM|^|H&+;zUt!S$^7GPOEduC+qoy76rM6H^oV zm;rb;*2Cv~-8aW#@h@K!aGH||Bc*qp-Tpa3=PX21p=d1SQ>oaBxED+knP<$*^Q7If zQ0qw5dDdF(h0mD*o{P0Lz@jYuCH zJ5yd;3vgK%YxTb{uQg#h`Y`Eb#|(d16UN@Ws_;vp^k}+nQbbnjKKY<+Lh^b*3kk7H zDG90AvkA!rBH2M|D#ry^dF0}liiv@C9>wdn&Wl%t$3|~0h9vPy@-vn3N^Wy-Wk?KU z;u+S1DcaygT4hc~EcKS3l z-5L$~j4A0`)mUc-r}Jjoj@Z=4wp4C?f9@z?n}E!=SU$$5+m+{{rJi?rT%DYl8^AB_ zii$_Ct|0Zg-I-Wg8H5$yAIE@9>U~@G2VAyMmLEh1??jqd)+!yGFr==6_wNW9tYs~x z3;H}0y}^>7dB1E4t*e3&t%I&~*m}7vevH0tlB0}mcA^IQN=+x@y@laxTv%=H znv;O#>)5IO%W@1WFgmds@2zl8q4eE2TcRCCMk7Zi zhj96W>%G>->{PPO4QkkRuH6c86qGtwiHP>;W;L?CP`$bSy=O&;kJQvOzX1p1gwF=~ zR5~@qt4kMx`OxZ~_JZ8HeX{ZtZ(J`1mvW|YwBL255_xV%acvFLTVwu}$HVYJg6PP? z&?gl{7es()-~w*yYLi!SQXNZK5_^?&m*P)krMtOMkD5GR&HHWy5|Tl_A8e%`#-XwL$~Xly1Jn}Ymwn{OXv$`0+wVlHvA8OGy^+}oYjr&TlF zYa5(5!jVCxWp9IOijMQTv=ACIU6>KqsV-(>8up_!ZCjiJ&V(0R3{|3pm))@T2>T?Z z9gJiWwi(bN&QhgQU+hLJtW=GFpr<)*0%vAkKA3#qwjF6=vRu{F0lW4wZ}IjN1&xFyJ+6^ z3Y>(aQxaFAj4iS3Cg^3`_7;*msK0U$$Zx5KcQ-<)ziBODj#k z-&)Ot4q;i4q9&PFN==#E#v97Kq~CX8#(U$?8YY>3{*&b5L%h;=c@SRVvVYT0 zu&09oQeDRg;&UyxE{~iY^hY{Z#)-K?#j6vZ3Hhf*Q!CDttaU*IZyE^uKi@iW?*We& zTxmqh(Az{Q9~+A0_}z{eRW$0u-i#cun57OK<5#zCqayGG1uqB$pO)fL_{Sr?Do>U< zDlEl|F!pz9+u>NU8&IXxZA=3~hQTJQGu@mjrx$Xqbd43`O$>^WRjzyttEz6|m+jqA zSuRJ?<5`zKe(&#DG0${oM3NQ+JSpCTXF{I@DJtAV+T(?7A7kacS=Wag<~c314nULj zXf+fQLpCpZCQ|s4>x!87u_y>YsOi#Dq0B6GgHQ;qG{UD`SQO65g#P9c9~a>wdWs7JilED za5JThEZcxGg|**FG2Y)3xbGh-DB4X(bWT{efOlh$%2u@8TIHF z#Ci%P7L6x8om&Xc3l~+1=PdTE#knXKclE&_jHI9KOriz8)x(S!=2uIT9F8p|D?9G3 zL&Kh5Q9nNw^T;l}Me?Y}kRFCDb$Q^wWx?B^lZ`a6N_I3vd zCu(S42EVao^2R9dteidD_TWcQOxRI?DuS0H{37uc_hIyxgAfc4HuM0k_n9>?@J=<- zkv6+Fhf8Kg%6cKtv;r!yF>~}1`cgyj^v-=2w_9ZR^*dd=LEOAqFjf=hq+#l<*MgY= zf@wm%10m#0ev;gw4_DRjFMEwAwhkoCkGf2H>#OI%glWZ6|Y_fIjb+fm>hjL!Ai7#2m^}Q_@Xq#uYDUJLPcwX+U>ZyM z%57R{lL0cz_1$}N*$H>%GHWsFm?U?f||=CCwK6(;cXxB;qyLI3>f%LCe( zSv*Cdyu3T6fzX4K(lG}i@7)R%#Btr+_8KCU-=ctdJR_z5J1QI7GoNTqkr1?x^`Vy0 z#oIUO!%jXZTan%*_<$~FxRuN%itQ?{j?T6WN7}?b51J*z#XS0Q;p0imfe%Wj(GTU1 zu4(e9%x(?MUg?KkcoWcOsaQTG$LWr1sae6z_MeZ2eKJp)ChHc+GWA2vy%Ugl8FdPMM_1*AIpsi z>@F~|XOvtsHa>~H9NxythZ#vjs5snP6L|j^K_*cl4rD`}PC}x0c^_?ZgPDCtAa(l+ zKceWNUe3Io)ww8fjCo!<_#KyOYh|;A2IBFuG6>dVr+NGCDtQe*&&+5~)4j)DI_tX~ zC@A>ubIgsX*4C>FNA3aQBB4;EKeq`#ZNnS*f z!!$}FU}knhzj1~Ih)r&8VTCAI14OnID+euqUy@+vvodsmeQ28Tz%U!77OmJZR9>6NTx?Iq7*g!241X=LbuGbT>I|1 zH%l(2FYA`lROXd7^O&<~yZW#Pjzxr{c(CCr86qXn9HfT~ja-gB`*p@fgs&i z*Jvkj*5FGGE~fD6}0zBSn^dw-bg5G>yvwuD=5yc68jCxF9omJ8cv z5i+#clKu00y69$7wlx1Lcqv5wwLsFF-hB<#kfj@1-fur4N5&&{gWqdikbLpIbNHQD zC-`TMmiuXPQ17L<71r9O*OHv7NaFZpSb?p%A#WX^cnqHGE&IS{y(Y`d?*4q?^x@H1 z$1&(KMsCFzGk;zB2Q#3?S!mpucEn_U9QRXlgRUKJdWxqP-#y)jlHcT!#0+HA8mvymnq~P>;}pvu+$B zaS4mO_H+DD_oS*XHNL471n-r}Y8?P=Gs>+DEN*t-J}G*Zz3H}}7d!47^2%8d%Wr*2 zv*ZCW`4u-Iw_{0Qu4^u&rYah5mQQ)konAn=4`dw7Uc9++W)(Zrdw1p_;Pqm1$Fvto>6hk!FA^vgKiKk21zrO?Q1`=#TlP0wy_t5G+NrW zRw=}SE3F%l$F|`YVE|xvWZ?>rqpO$g8<>ekfcH{jCrRw9Rc{*2tn~Npvj|NM49Mbp zO3P?Y`6Jz5tn4`DX;8z%j{sE4L{`niPr7|EJnl}D8LX}y$2#Cr<(iuyczwLzpT}R} zdi@?B%6~$3uN>_*RHj`U64|B-sS_0L+4FKintT%Oal=*%`xD2+GN95>daT^s3DQ;3 z#tnmRTSc*nEcgc-cwR@9&OxAPT71*mHxt3?QXUO=Oy77&j~3#)uEiueRt-W2y+n+@ z`igeYUf!K(46r+i>pD)MiNB(NvpH76e(P40LMU z`2gB9TqLWG@3s&c@Q*t~n^o!O5YdHerhk?D9E}ZX{*AtVgo zCFKHYZ5Aft7Jvfzy~H3@|I2ehx3xZ=fJQ)?)c8Uql|i@SiylY)v$A?4Onob{pHyBX7H z@v91FNLf^?P~8f!mFj%lnW+&rs&!X3ii?b76A}{gkOZ!P?dhsQJ}h8qUFl0tlJh?; zv*;otrr}j;3P684Q&@o}%on@CwWoh6?SNU7t~0+{b@VfDVP0OD%kl&3zBGBDPv}LT zU%4AjW(CABKGSrbV9EfST&T-1tZ^*|46ff-Cnj{?zJ05i%FfPS1I_WhX_gaN#`5hkZk4o9(cxP_nGaD&z*0^UTSinzO z2lM>#%QGo$45T$@>%0m9iA{o$Ea$~fZXiD+U+1~KKJ|qM$W%d><3R;Z^Nm>`a1IdA zUJC(>p;uj)t#v*2=8}|WQ`KDx%Dw6X>sLS~FQbz0ETQ+o&?ny89gHY!*eUmCdUh0c zb_*H(%11)-RRG)Zb@PZZ^*~fI7Pbc z?&jA;$1w`uG#cqBVk0BB*_$shaI$H&36gkqnV80X|3N9q8L{v&K?sB8ae{(4z2>*y zB8zDW$-S^2&6XcsXXpQ-kpW8TTaM577PwgR^d}*1;nG4$uD}ZlKjDk}t3l*l23__O z#1Ma6tq090z2l1*X3Qbeth8`gd4nCit-o6j=Jm~BQc~b z>!z4P%l$P$df}E+jQ1$Nm>guatC~D1U6wmtu~(X2W`-ru>>^WN&WiDTX=*U9-W#u~ z7%jYx4ti2FYlOTL#HRBz-u{YtG+RlEk8l&KuQ))AzSn7t1QZ9ClRbT7(^E< zFC(X#sw!HOGI_6v;zGb29yv`A3Nh0=DE9Kke2~wi=m^O3Zm19d`x{W+SK-k{6>aFs z2Va^U!*Rex`ncMt1%wQS2Z%kT$!V?0F)7ykzTr&vV77f_n0g~(z_HuEi!WHQr#hlB z&9}dYFTl{I%|)+a+4&9@j`As~WIyssrnH~3FH|z4Mewc77v%=;XrCJF&o@jzNEcFn z%jfC;;fcE0wv-paHXO7yVb7Uua=E}`nnDgj6F9mNtLg}9JDf?aGOD7;kns@$9N7hc zef(@1b)2o;+bD!oJpXYE@TR!8NlQ5|-~h8Gfhq7NRc&JdrSFgD-HqzCIA zBY$X>>hbn^KaVST7ne3OpxkA}97fVqUbu$A((rzvPH)S5V3itvy-C*G-2UEuqbNzC z5e~K%*1ZZ;G>u335v_DrTn#^NKxN-Krf=R5xv4ePU6u<)JbQ9IQw*{9!w;-c$X2yp z>lV@(&oW5B;&%tgwMcmHvetR+SdV`)LY*wfZ%tMb1R`N|@%(_V|HJeN>R>Qk&R+^B zb^$6r+z!_tGlNksK(R}g2^f99P(9nxpv<*LFu@(L*V2d zLM|6t;J{|%S#%W2{nljgk)Pm5XHF0{6(zQm^Z zZoJ~VHtuF}5E&V&!G)xB5uDHVCCyU5dGM(7CqC{y#hQuo3i>*JyXX|GW{(Co|PMMLpP>^dO)X|x* zr9s9~>U;410$n9JT)oh z()z{#PC>=D2J*MY5iOP$AU)X(jO~WhK`-67(So{!c~bg%Ps*ZkKtSyvLn{TS=?HCG zd;@Hr0EHiK??-D^JDa`a=T9%SI9wmLpQ%m+yo_d5)3_5gZd^c(NIn33++j0_f|s65 zb=ZQ=`3M#OjYB*n7CzMrd?sgk8P^84l)D3w#|VDf zYOcqiCo>%kr3Do3d+06Scc_Ry$C0m3PaEIMZa#$cs%>Ji$A~N6GQ09Lb`BUNpIc1q zvT~}qYtWoNZv-9Co?6tBM$u~I8jN#XxCpp7=#Cy!fMI2cugo8ndP?xw`^kgnq|O$Oxg+dQ|&Z--zIP!<4krJR0ogQ~|dN-8w^A#{P?%R7LnQ!V+n zftZI6P&CFUmzyn3JFPRq+n+`458Y7Tb+*->VJth!`Y3o{BO3=Ij{9lA?CyY>k9{GN=; z!8G7>YF|=6d2?4|nClm48r1xyXns7068{4o{L6gR(-(-n4+ow9r{C+}u=pQC*53x9 zzok&^zac~D-(u&(U&8VqN78xwe~ee>8aALt{|5iRJU%D9=dgz7A9VA#*X*oh2l$a= zz3Ul5CjCn=mQ17C0t#(@zG43b)MNq*8<<||gigIW+hn_kor%hlt9?sn`_OCbJo+6I zKhOfuha60QV<4Jyl=YAD`~UC!{$?|O``-RP_Q`)6M3TRC?mv{|ztfoCL`CMrLzsr& zSQRi-yay`Kglz`ue^&n}*3kkA@ffBGeht_+rX4_Xh+&j`RoZwO6&Q$hhEb&+*&mUGa{^VJR1 z$e>1N^MVeVPJ%DAjBv0MTo>n8K_}I4?A(1HMKbA00Z6r7*uBEXe@)c9Kd%L8%W^0qoZbPbp*B0io=P7V`w z1o&q{!cATz0=0zy$?6Q4g&n3u&I%_VzUK95L+U6JMnntKVdN<;&dCizN2$JLcXilM z2lHBdMVs3UY~2a-Py2QfNtEo%5t_*U5?A6RKDNv`X^)y(vq?yk@(K$A)rj-pB^q~iJ&7F`4UWCvsmd|2SMaTb+BMRo%6 zx%fxY`1xOorAHA7XCaf*?7{PO=tdY6PNjIMkbhJOl z#p#2rhW8Tf#A_@C? zO{d*8E-}F8wE%|HcJ(nhQPJV~bJ5j{^(+kbb2d4AlYko`Pu;Nkq@!*o00GYjYISw| z)Uu_1P$m5`5;kSK%}ykeW4sUCO*{@A(Z}s%)>?d6Uo!FgL-%i|S$C zJmbO>pNV?`ooPmge}JnxHEAGtzQYZ>zy^4*}3;6E@G| zWDrKi^bimr8_G9DI@%{9qH5ij6dz=8aME#bzIx&F@!4ap11NzrDox&Z(_QHKtZNASg`_;;E&rW=5 z5?`Py*8fFi&K0N89JMjM3cwR$jQ^qeal$>RI3hKN{!a!8 zs%?DqrMDdc+Z6LyFZRu>3F9>xr~SP<3}Lt_LZf?LM%WWtZrD=yYwj3tX`Hse=Nfql zt0st@c?W@|ZJg)g4|ClSF^}ntk7k;-CRi}NE1Bt>PO)BtB>D}_E0yw`4WJ;-?aON# zBJ@+;95M`7_^fuv<6=fB_m7|f52%@#)Br21?T-&v$-;vH-V_Bad@uymU;|48JOorX z?5O8x14R$ujRySGZvg%6{ndG(o`YNGli`b<)3E#Z)3+vEHYS~~kFoOhaY&quq_y9> z`B*4a%7f{>g&c%R$-BC{iU-C0R8y zDs(-%aAIvv6}iWmONp-tmvoU-+ov78;}p){!+Z(6Epmdb3UuLO<%sr$bz$og*7?GC zK#R<7r+B<+&n=^tA?!VtJ62Haduse#GfsJ|6gK*`^Wz5fkq$utxEr_v$Wm;>Jvrm| z3O#HH;>W&8%nsWp0+mnstHMB|BzVT2u$_qum!g5kDZKX9Wz#u4r3f#LD^4?GtRj8r z%GFA>>j&NW_V^zc-V6J~X#qbF@^ny8DP8T-S8K_3ZfXkZRqBpx$gJ5&yqFTM22TM&z=M7`IYjWlb1?IBhW zur!#tbHl3WI^mmV^j>UN+$Q|%$Nd~M>tA~G8NplUwkg0Si)SI$A#!nmf(I#}@~z$dSOM!5nb9!36+U6r{>y*BLfV zmp&a9T{T#kcLyfJH@EJe^G?wrhK{-KBoe06bm`1VAb^uf!psZHQyC}0!v~hb5LkQ1 z>bX_6tQvIdsn)XtP0d^eg)2q^(*(^wS(XQ8p zifP|=)p*-jng)_)e}ZdS}J3*fZ>4!#jlibluyF_8H=WG!G5JEaTCMJZ*_|om1k@uvCJZ&E*Pc z^`Yhqupq5N?Hoq@E?0K$IE#A{X2N^#j3TEq=pPA5xLmQ074kWthO;19Xwp&D6YYcK z3atwpariX{42DV~>0*5x#}P;&tr8p3o*$}^mkY_lDz*0F?_}VR8ZWI{N9;WFPoWVD zyDV{T%=L!<^77{kh0sT*dnc-|0hBcSQBPQ7 zM;qX0j^CN26mQC|UnB?KwA)y{@y$H@gPQaox%)i7QR!}bR#EfueDjB5ise>-!)m|yvaN#q%lxFLNGrEg#m|F#SZYK>T z?2PWFx8=-2epB*)%v0``r|K%dC&kX& z{wHA&D);Lj|8)0hVeuJR|5vflKfbI#YQW!Y`R_F*^3SW#{*f{MNB8`$8T(z0^v?lY z5&w6hKM9SVe6<$Thuek#MdsjbiM}FcVddZJJ5;SS$FcV@R8a*6vVx^9`-CA?W`RXb zwx(VL#v}XK5HH)3xMyCSt)NibMGZrFFMqO#*h_3G*NBYUo zNb6NX!hM^aop8DzP_P7}x<)9lI>c?gz_|WflnXXCJ1x|tIiFvKkaWKm>}U3k;Id0@ z7Fm3x%6OL(+`CZ;y=^hKGZHvajTfe2vf91tq*wD0K3scX0jx^1H$De&^y=LYUDz*P z8P29VE*NqD+c;*6E$%**a+h`nJ3>i-uDiGq#JFA6SzjxeM^`$y5rpg!}--VsmpP@qu#^(Ln6U&s=Fn51IW&rlh~zCY{Ps7Uo512S z3w1RN>Bw%c98wVag{z+4^ zmH&Z`oy9@raCs+%)R=cFFnl>1n!Q?!^A!>Hxrg5WPh;mD)x_4daRe1Bh|;B8K}Dq~ zy@S$K1SyJ&fOL^AA=D5B1nB}wFCrp>NR{41N`L^NNs-<=A+!+Ez7x3Ry?4F$UEd!r zSU5A8%$##(_OqY;+j(q$m719&XX>S)Ym8q_zPNzBkEvotd!hQ-M#F_QW?#+3>~NPH zYosFST-8sVn%17`dneCC5=62yYu1(&FUVU7w|l}nCI&s?vALlkRETdt;ZU_-WQ~PMJH2LJ>y7tGNVe z5BTtL{aoA&OCnM}b==!bWF;{yW9WFQPRS&Q1aLl-vBJZnG{2<=8(me5U@;7vn~#+G zRg&kx7LCqb{)WCAJ(`D_ohgZq6DC@Za_xMyY!huq>QyxurJNut1~s#(p`7j6Hiub% z#jLg$)SB6dt}UG9+F0*oPEvGxxlLbtvviT>GT!|tm&b?mR75MN>29S-SAiLPR|5AY zHc;Vqic%LB3ZtfKfl`WKKna%-&;Po|w(PTl{tv=Mnr?NVz>?usHX}i-0 z8N}jmd|0={YAly3FWkZw;7k2DaQO37w`(3~Zv|xJvKo-fj|rq!28km}4Ey@+9tY%I zBsZ6f&I#X%E+EboJ)5{6(cmL1w>~aUC?~VhMj#GcbNrbnr<3;CvaN$gSPs|3c)Ek{ z%(x?;h#_-FQf2SSD@NzJnS$r$zM#L>CWgL;yi!`;-8iC7mqPudg)E_yt`)@JB<@|o zfn>IuL7++bIkkBj4)=wKO#3*Erqu1b3nq=-$;%UkhX#r_E(Ox39)8mG;cKsVPMl?E z{ls*=sfo*?J~b7XUKhN!1$J=dCQ7#zAd;3yCJW35S#s4?qp2HE`$1GB3~}JW`rwsk zaz+yYh+%^(iu~4juH24+(P2nK5O zafx~Egg$QQb9eX&Dji&5Pnppce{hEE!;WFVxbVCP7#9Vi{sD&=PP0E{!!CS(l|$-3 ze&BiyLAoV@_qd;eZ9QK|1?F)-LW%`W0>G5)`DN3FBpDEiyDSPkRH8n5@>qVTi;R)J zpwa6KyhD1~P6{zO&MXI|ivqeg$`?1!Vo&CtkgB^TBIA1oA;d`@h;vsedh9_^Bt5x2 zb``%8j6f5J*Tk1%8dj}&FG;<)B_0wbZ~dSG0jpF|dv)gQ*;Go*uN@4*APW;z=ubwucZ4~ORP392WvZSg1AMErp`5h-e|wTnfg zLfJ&+KzYWXU5Qv;piFXZ;;)YC3#(=WzN-Q$>%3=c@k9yLSdyItZ#!9R88Y&K1XYyH zxH5|H%Io;J6m5PaPO zayiCX8~a%uS(FyRA>x-G{gzM_$pG;xxk4q)qXghe z)Wnr4S)3v2;yQODhpciW?M8;sTMKG)L9pFHf6U1&|;XjQ~; zY8(+*ALA(&ahAztjZu|L=xs%ksJ28$ii~=_(eGr=8Id2^@BaDKk{(4Thh-9 zcvrc{)lrz0vP=!GihkAx3|!0o(id_Q@fUob!y&o#%cSBN1KqORkE|)oV+~EKtsjE= z*@hz3KelqdU765q1(ibpn)q0V1-Oka{5GyzDgE1T-$%kQgsNQs1Ws8e89o3?OVTvn1xoQGI{zj0z(tr8J z_4k#zxoZ!Ep=9VKBeOg7XMJS9`@MSZVgR{MmC$#oC8Bn@IJ6~R{B0fQ5`%MrB}t`` zXIT*vwc-`t`5vJH-oE_i@Tl=G=+cdqrV+MJN2mu1eYjPF=Xg;@s~+}SDOZpc+|ZG= zsU=0+wXZT|d@R=OT&-uqZf_6^Lq!dqZG5VAAAeajT`d)xaihLFhv-pisp;fI#U1V$ zE^Z4Ib|0sXy2{+L$MQ(!LL%+?Fwci>3K(x5|58id2p9CFD#_UmIj9 z&&-T{$?ASDhT3v+dqJQfeAcaH9P$~B7Am;4i_uWO1Vk|XFZWNrxZ!tL7&3pCvS#O- z*1Jz0MVlz?F)1qB$G-;IV~(#)&A)sQ;FjD3yMUhkIf3fJVX(Qlof2ZA8SC2O+MI4b zvD}6`brUC2tz0YEk#y_HbfSxgZQI5U4)45~8hru|qr=L_#Ttykf;+<0Og1pLt#Wy9 zs~j<(bps=?0E?>k-X1+ouL@t%N|i^wN8P{n&4q?Qu;U1qt{*xRqay|vb1e2q0{7&} z&}zMRjXTZMs5g6NkE-2c>T0#Co6z~v#`vD2-a8%CyRfwrJ|t*3mrP?mX`?*vDOUy7 zRs+F21x|QSuWxPl{io2>9)|jBaT2RuP_jpZa@SZzS(%E0JNziksLf&rx!ERw?qM78 zl}lHVfxNMUY*5pk)>E9EH!@mZW$BkYEt-36#i@E9PN1iCy0|UC4c!U#5tXSlL2o0j zYB2R0s=Cm7Tag7<0yG0V`R&*Zst~db; z&^D+!`u&&X(8C=H5hR7Q>VLB>#VqdA+^z{8iw3Eilt3=e*Mf#6PTR|az0?a$ zt6zxPF%unIJ5c~EndvV6z`+-{3yT-AlqGr!bZQpMBhf$5WW^-(A&x-dKRdydJ_-^0V z_h-DAwokbDW5@e{KhFJ{o>RZ4q+|CJkEZ*v^S{~Gb}ekcHv;MAy-e~0)=vusd5Hz? z7_-H`ueSj+6cBP}nH0$YCHl1YGsDTV5+6azB?X! zgaMBy#|uC{1)Pb4z-#&!uEJyD70c7^k1b3~fQ%`K1a#c`Yr3&_fIE|1TV##u&eG!x zX1p9V3k8JCJ%ETuJ})B|myc>!bPRay_)lM^fVr8OnLBW>UIH#t*zRU|8qvC0so7)w z8&DwFc^#)Iz?nf7GzEY%6B@EX`N6_LNyE3s$R|>^>0gkdP%!WRi_Q`?3-Afi?|_ikqdhR z8qkgRT*d!e7W#*JGx9Q3Aldj2A?WXp;lG#H{X^N|-yg#~@hShXSNtP;zb`la-IQ?u zA7~d5BOn2p|JRdvw{KhiLongzu7HgKxAt>at`F_wvmlhf^gGhBb@@;SS);}}<9v!t zE@-FC_d1uas~5o9=?;q#-&BUoW(@J!AMH5(+UCc{Qmdkwp_LRZbj(|?O@&8pJ}1aj zvhWq@j^-O78k!n~p;Q#)Gua~jz&X2H;!4$oP=U#7fWV zP{a#*y8!qLML5ytO(dsc<)pibeQ3K?r;Q4Ku)!7T@1K}zMG8=MRJZP5zEz1$XTJ;Gj0hPTyJKMuT;MAsE!Qc6}RMZrX&eNKZ-wDA|uH%oxq7)66PZ zQ&bds^r>Ayof~ta*35<6oje zCo^bGrsho$9t$J0l5$peH@d2HOX&07uGBZvr8)}{|pmxuv4S*rVt+w14GT@&3Dg;QW!%|jvNRg!a z6pU^|=|vuOX3tPqK22%$Ey)6C6o2hc|XxjrT~( z&Ca9=O2JpDSGawm9e&d4Zevc%t^4D#-Hui)pK9?;oc!CFj?wfU9`i*pl5K3kHlC|U zq)3O!+)z&2)P;d!4@LEDE}ADTJLu1t<#b8;Ce)Z#UJEBH_7}vAKAHNvRcYh}!%I}> z9{S#_8P`BV9KLkV94}Zx)pJPCcUS{CLN8s*8Of?%7_H;S?7TQFO$FYE{OzO*$LFlE z?p3APkS()i(hQaQHiBwxYx-yJ)9q%aDfTM;WXqoZe5(m&e_jxQAw@N(53X z5=8kX<==L-UpCtKOSTYkW)e@ya;i7ClQ?_h+)J>$OmWW#f*Ie!!Z9uQHpG8NrQ|E= z%nQHD2r&8ORJqIh_hpM?ZN=Uj26qVB`gj2lmxSD8aOlm06_La$0m2 zvLH~4ft^7~nLuE*L<92?q*=ByPt^xUrTp~!e=g`_Kc zLc~=fLr7Q8NAL5 z{RgNNh&VR29y!MOufCNf33-M&w3In|6~TzcbSoh@QEwa{TGT8jNqJXK!MB8EC0Ej| zHi8F;%LiW_*3Igw2Zv=+kMf)85vo4-xu=4??xF8Mfpe<*dc{gFLq+u{3~L08(b~GY zr-2d8tm}j7uot=-lnj*uqxS$Hgx2K`b`yvu#`(j|ai8+~O#8ex^kTuP;bCiK5KzjA za5+@jS=4mhn7DI+XT!4gD<+dKvHiOyud_9KamMA)fQ=-W6b zW0?ia_HC6T2CwDaeK|Y|KMBpXB_{9a%>m#tq~83PJcJ%v31A_s8l2I!4-~-aJCMK0 zLIrggMvlR`K4_H7mdcYHg%KTZctr$UrL8Sktx-vQ3ntq0&GSdp?)V&yMNV(grA9jm zt+X_{Re%B6;yhTnom5`*d>cZ2GpJ?s_!Z7Zf{QOl`PJg39vN(&`0R9K4?zr01Kuy9 zCp9K2<83cJBKdGR-h20E?TH$hAT(7%$E%*QyqSWz!o)7O+(pRco9(=5>)=u7yxl8} z#DL4KepbFM*hVpG(kY4+p5katRB5?F|AZAdW`x!}ldxo_UD&^Eb*g510E@5@1>%6DSkt2=S*y;KlylEzoAT+4zn`)c2$I#=| z3S?gCg$`K1m%L#OIhu!_<-B&?C91{Z+|~-m5)aAGkZ+cad5nT^ZVxiKYV~f2>v74E zwK(utPk&YveDL5Qs#nzp%%_Ysdn`H)Rkv{901%mAi2X{i|@% z1hJjLo`c_wJ&S3wxxKtC*W2-NvU3K>zy7n>c_oZm#i{}MiJBZUd6H?D;G>u1I z`3PboxvgG3(843a8@EoW90u6Z@08{lLnZbAV#73PHpMpTAV;*SrMz%b7P|+D+U0qW z1D>Id2!2caW7jq^(#ugOoXlxE=5_w>hu(yv!qO*tW?r{))}{XpUVmErAu9rwKBeE0 zQeMP&n=}NpdA2T(V=zVZ3lne};(fF}*p~*@Y@dfjJ{NVLlixf0 zQoC2CBzEva(yoLPXgSeeiCM<|@zHavgD%XDVU8<4xnx+>#E7+%Nl>NxmftMI$83Ni zV{}qiRAI$ZefrP70C?&mr*8U`BSb|P?jh8?WO@-ESECqUy29sVl0|@!%T9tfq1r{( z7lYhF6I($mY_%Ap6ZKDijpLR_cUe@COdoDVKj#>Ry^S2(x-&BN(Z{6Fawd!=*6oDB zY!dq$=6cN~C3hK0jm#Jf%LyFEk|4?h@wslbrz@!7bM6_+X6oeO+nr$&7Zs_aJlfx-dX)$3~KVmgcYgG#nT_n{NLCI?OWWkcI+lVU* z=(Vy>KAo6Sp8IG0D(esb{(p@( z|B);2-YYhZY(s(mKyE?@DcsP<|LDW;S1TZ3srdIkL4W^GhaaE^PnKb+Q1P>$W+25e zN{5)DAd)~0kThieO{p@b4D=1r%`=t<9eEI-N@{$?NzMTjn^5Y(Jhv8wEn68K1E<8% zwPb~AFYGpym8&02ez37Rcx|A_IFz(isq#ALu5!QYn~mOLZ&v+yogZl9F>D3=2a@yu zYHVLx>6DuUZCf%xB`AlK)Ayk?_hBG1;6MdhoFZHyz_hc(-mr$aZAdA?atxehI4kL3 z0nVEOCIx~xMN|5jeGimryf0PW`0TpWCk!WfgOZQgmAi7SVt42`q`qUv;1Q{*XkrUx zOoJ>BrH&0$0Q<2RyT9c2*?9@J_LLPXzXKjFH-PIg11xP8?FsMRygBu(Kerv&QmZ&) z5Z(Zv3cB08`26{jW8kE7WMt$fC>sVQeFBk4X$7Pn&VhkG;L^)|EDai`1OP-fpLR;a z0t66ICs*?20RA{Ul2^SuO_`RmJ5U{I-``1;pmgQ|$O(689@OskkR#<5fsQ~w#>P^? z#=3L|YDX5I_e<=~~i3MoSyG7o|Nn0hbt421=SK;Av1`>?FnU z?b**@z(5PV6fOsU||Fz*;@dW?fPmcxpzV`N|Mbp&rMm?77J|>Vk}z- zKsHrQl(2UvZuPgMD%O_PW6D4aszQemnQ$)oR)9QP00YX3a@{+U6G87NcUi`~OZT!F zxxLp8n3|e`h6TwKCndNWbwj2ep*;%}@+2h@2V}uL>=P;#y^=pIp?ePEN5L=K+1V{V zx3kO9Homxi4LGmv^{@hR z8Bk0_!`Q_q(<2njz`y~Y(EvWN4V3o*z_StM`zVMTT(a&+qIB^Am4Rm%85_(a0QM%i5tMKsDZZ??D8=zHDH=t62L=$+o zeXpOTJ4%N%2UQC%$@7c~$3zz2!^w?jAC2v9|!$c~99RU#7>Ud=ETO yL{8TC3jRiUfTjOKBK*CQ>-Wdm|6I_C+<8@qXF{QfHPEt->ZYoeO0Loq-~R(6BY" + ] + }, + { + "cell_type": "markdown", + "id": "7174820b", + "metadata": { + "editable": true + }, "source": [ "# Solving Differential Equations with Deep Learning\n", "\n", @@ -10,7 +24,6 @@ "approximate any function at a single hidden layer along with one input\n", "and output layer to any given precision. \n", "\n", - "\n", "An ordinary differential equation (ODE) is an equation involving functions having one variable.\n", "\n", "In general, an ordinary differential equation looks like" @@ -18,7 +31,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ac838a12", + "metadata": { + "editable": true + }, "source": [ "\n", "

    \n", @@ -32,7 +48,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ccee4286", + "metadata": { + "editable": true + }, "source": [ "where $g(x)$ is the function to find, and $g^{(n)}(x)$ is the $n$-th derivative of $g(x)$.\n", "\n", @@ -42,14 +61,15 @@ "Along with ([1](#ode)), some additional conditions of the function $g(x)$ are typically given\n", "for the solution to be unique.\n", "\n", - "\n", - "\n", "Let the trial solution $g_t(x)$ be" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "39d7dabd", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -64,7 +84,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "74f33170", + "metadata": { + "editable": true + }, "source": [ "where $h_1(x)$ is a function that makes $g_t(x)$ satisfy a given set\n", "of conditions, $N(x,P)$ a neural network with weights and biases\n", @@ -77,11 +100,8 @@ "\n", "But what about the network $N(x,P)$?\n", "\n", - "\n", "As described previously, an optimization method could be used to minimize the parameters of a neural network, that being its weights and biases, through backward propagation.\n", "\n", - "\n", - "\n", "For the minimization to be defined, we need to have a cost function at hand to minimize.\n", "\n", "It is given that $f\\left(x, \\, g(x), \\, g'(x), \\, g''(x), \\, \\dots \\, , \\, g^{(n)}(x)\\right)$ should be equal to zero in ([1](#ode)).\n", @@ -92,7 +112,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "2565ab16", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C\\left(x, P\\right) = \\big(f\\left(x, \\, g(x), \\, g'(x), \\, g''(x), \\, \\dots \\, , \\, g^{(n)}(x)\\right)\\big)^2\n", @@ -101,7 +124,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "83d4ee25", + "metadata": { + "editable": true + }, "source": [ "If $N$ inputs are given as a vector $\\boldsymbol{x}$ with elements $x_i$ for $i = 1,\\dots,N$,\n", "the cost function becomes" @@ -109,7 +135,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a7a3a709", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -123,20 +152,28 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d3ca8026", + "metadata": { + "editable": true + }, "source": [ "The neural net should then find the parameters $P$ that minimizes the cost function in\n", "([3](#cost)) for a set of $N$ training samples $x_i$.\n", "\n", - "\n", - "\n", "To perform the minimization using gradient descent, the gradient of $C\\left(\\boldsymbol{x}, P\\right)$ is needed.\n", "It might happen so that finding an analytical expression of the gradient of $C(\\boldsymbol{x}, P)$ from ([3](#cost)) gets too messy, depending on which cost function one desires to use.\n", "\n", "Luckily, there exists libraries that makes the job for us through automatic differentiation.\n", - "Automatic differentiation is a method of finding the derivatives numerically with very high precision.\n", - "\n", - "\n", + "Automatic differentiation is a method of finding the derivatives numerically with very high precision." + ] + }, + { + "cell_type": "markdown", + "id": "9bde4bd4", + "metadata": { + "editable": true + }, + "source": [ "### Example: Exponential decay\n", "\n", "An exponential decay of a quantity $g(x)$ is described by the equation" @@ -144,7 +181,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e74337c3", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -158,7 +198,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "273549a4", + "metadata": { + "editable": true + }, "source": [ "with $g(0) = g_0$ for some chosen initial value $g_0$.\n", "\n", @@ -167,7 +210,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "db3c6623", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -182,18 +228,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "8547e3c8", + "metadata": { + "editable": true + }, "source": [ "Having an analytical solution at hand, it is possible to use it to compare how well a neural network finds a solution of ([4](#solve_expdec)).\n", "\n", - "\n", - "\n", "The program will use a neural network to solve" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "48341fc6", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -207,19 +257,24 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d25b1e02", + "metadata": { + "editable": true + }, "source": [ "where $g(0) = g_0$ with $\\gamma$ and $g_0$ being some chosen values.\n", "\n", "In this example, $\\gamma = 2$ and $g_0 = 10$.\n", "\n", - "\n", "To begin with, a trial solution $g_t(t)$ must be chosen. A general trial solution for ordinary differential equations could be" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "7c5dd91e", + "metadata": { + "editable": true + }, "source": [ "$$\n", "g_t(x, P) = h_1(x) + h_2(x, N(x, P))\n", @@ -228,12 +283,13 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "24223062", + "metadata": { + "editable": true + }, "source": [ "with $h_1(x)$ ensuring that $g_t(x)$ satisfies some conditions and $h_2(x,N(x, P))$ an expression involving $x$ and the output from the neural network $N(x,P)$ with $P $ being the collection of the weights and biases for each layer. For now, it is assumed that the network consists of one input layer, one hidden layer, and one output layer.\n", "\n", - "\n", - "\n", "In this network, there are no weights and bias at the input layer, so $P = \\{ P_{\\text{hidden}}, P_{\\text{output}} \\}$.\n", "If there are $N_{\\text{hidden} }$ neurons in the hidden layer, then $P_{\\text{hidden}}$ is a $N_{\\text{hidden} } \\times (1 + N_{\\text{input}})$ matrix, given that there are $N_{\\text{input}}$ neurons in the input layer.\n", "\n", @@ -247,7 +303,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ebf04383", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -261,7 +320,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ea4a0013", + "metadata": { + "editable": true + }, "source": [ "### Reformulating the problem\n", "\n", @@ -277,7 +339,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "2351b84f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "g_t(x, P) = g_0 + x \\cdot N(x, P)\n", @@ -286,14 +351,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f6cc00e4", + "metadata": { + "editable": true + }, "source": [ "has been chosen such that it already solves the condition $g(0) = g_0$. What remains, is to find $P$ such that" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "84e066a1", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -307,11 +378,13 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "feff9ab3", + "metadata": { + "editable": true + }, "source": [ "is fulfilled as *best as possible*.\n", "\n", - "\n", "The left hand side and right hand side of ([8](#nnmin)) must be computed separately, and then the neural network must choose weights and biases, contained in $P$, such that the sides are equal as best as possible.\n", "This means that the absolute or squared difference between the sides must be as close to zero, ideally equal to zero.\n", "In this case, the difference squared shows to be an appropriate measurement of how erroneous the trial solution is with respect to $P$ of the neural network.\n", @@ -321,7 +394,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "0c6f0e79", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\min_{P}\\Big\\{ \\big(g_t'(x, P) - ( -\\gamma g_t(x, P) \\big)^2 \\Big\\}\n", @@ -330,7 +406,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9302a1dd", + "metadata": { + "editable": true + }, "source": [ "(the notation $\\min_{P}\\{ f(x, P) \\}$ means that we desire to find $P$ that yields the minimum of $f(x, P)$)\n", "\n", @@ -339,7 +418,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f7f204bb", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\min_{P_{\\text{hidden} }, \\ P_{\\text{output} }}\\Big\\{ \\big(g_t'(x, \\{ P_{\\text{hidden} }, P_{\\text{output} }\\}) - ( -\\gamma g_t(x, \\{ P_{\\text{hidden} }, P_{\\text{output} }\\}) \\big)^2 \\Big\\}\n", @@ -348,18 +430,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "8d61d75f", + "metadata": { + "editable": true + }, "source": [ "for an input value $x$.\n", "\n", - "\n", - "\n", "If the neural network evaluates $g_t(x, P)$ at more values for $x$, say $N$ values $x_i$ for $i = 1, \\dots, N$, then the *total* error to minimize becomes" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "10d3aec9", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -373,14 +459,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "5e296388", + "metadata": { + "editable": true + }, "source": [ "Letting $\\boldsymbol{x}$ be a vector with elements $x_i$ and $C(\\boldsymbol{x}, P) = \\frac{1}{N} \\sum_i \\big(g_t'(x_i, P) - ( -\\gamma g_t(x_i, P) \\big)^2$ denote the cost function, the minimization problem that our network must solve, becomes" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "fe010d79", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\min_{P} C(\\boldsymbol{x}, P)\n", @@ -389,7 +481,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "add715f9", + "metadata": { + "editable": true + }, "source": [ "In terms of $P_{\\text{hidden} }$ and $P_{\\text{output} }$, this could also be expressed as\n", "\n", @@ -397,20 +492,21 @@ "\\min_{P_{\\text{hidden} }, \\ P_{\\text{output} }} C(\\boldsymbol{x}, \\{P_{\\text{hidden} }, P_{\\text{output} }\\})\n", "$$\n", "\n", - "\n", "For simplicity, it is assumed that the input is an array $\\boldsymbol{x} = (x_1, \\dots, x_N)$ with $N$ elements. It is at these points the neural network should find $P$ such that it fulfills ([9](#min)).\n", "\n", "First, the neural network must feed forward the inputs.\n", "This means that $\\boldsymbol{x}s$ must be passed through an input layer, a hidden layer and a output layer. The input layer in this case, does not need to process the data any further.\n", "The input layer will consist of $N_{\\text{input} }$ neurons, passing its element to each neuron in the hidden layer. The number of neurons in the hidden layer will be $N_{\\text{hidden} }$.\n", "\n", - "\n", "For the $i$-th in the hidden layer with weight $w_i^{\\text{hidden} }$ and bias $b_i^{\\text{hidden} }$, the weighting from the $j$-th neuron at the input layer is:" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "cb9b22eb", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{aligned}\n", @@ -429,14 +525,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "49f3c493", + "metadata": { + "editable": true + }, "source": [ "The result after weighting the inputs at the $i$-th hidden neuron can be written as a vector:" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "a352bd61", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{aligned}\n", @@ -456,7 +558,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e5636ad7", + "metadata": { + "editable": true + }, "source": [ "The vector $\\boldsymbol{p}_{i, \\text{hidden}}^T$ constitutes each row in $P_{\\text{hidden} }$, which contains the weights for the neural network to minimize according to ([9](#min)).\n", "\n", @@ -467,7 +572,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "68bb8b9c", + "metadata": { + "editable": true + }, "source": [ "$$\n", "f(z) = \\frac{1}{1 + \\exp{(-z)}}\n", @@ -476,7 +584,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ff6e6536", + "metadata": { + "editable": true + }, "source": [ "It is possible to use other activations functions for the hidden layer also.\n", "\n", @@ -494,14 +605,15 @@ "and biases $b_i^{\\text{output}}$. In this case,\n", "it is assumes that the number of neurons in the output layer is one.\n", "\n", - "\n", - "\n", "The procedure of weighting the output neuron $j$ in the hidden layer to the $i$-th neuron in the output layer is similar as for the hidden layer described previously." ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "6fb4c55b", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{aligned}\n", @@ -519,14 +631,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "09c31d8d", + "metadata": { + "editable": true + }, "source": [ "Expressing $z_{1,j}^{\\text{output}}$ as a vector gives the following way of weighting the inputs from the hidden layer:" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "f81fe361", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{z}_{1}^{\\text{output}} =\n", @@ -542,11 +660,13 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "c309a4ce", + "metadata": { + "editable": true + }, "source": [ "In this case we seek a continuous range of values since we are approximating a function. This means that after computing $\\boldsymbol{z}_{1}^{\\text{output}}$ the neural network has finished its feed forward step, and $\\boldsymbol{z}_{1}^{\\text{output}}$ is the final output of the network.\n", "\n", - "\n", "The next step is to decide how the parameters should be changed such that they minimize the cost function.\n", "\n", "The chosen cost function for this problem is" @@ -554,7 +674,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ea47ae29", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C(\\boldsymbol{x}, P) = \\frac{1}{N} \\sum_i \\big(g_t'(x_i, P) - ( -\\gamma g_t(x_i, P) \\big)^2\n", @@ -563,12 +686,23 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9dd83767", + "metadata": { + "editable": true + }, "source": [ "In order to minimize the cost function, an optimization method must be chosen.\n", "\n", - "Here, gradient descent with a constant step size has been chosen.\n", - "\n", + "Here, gradient descent with a constant step size has been chosen." + ] + }, + { + "cell_type": "markdown", + "id": "531a7b4f", + "metadata": { + "editable": true + }, + "source": [ "### Gradient descent\n", "\n", "The idea of the gradient descent algorithm is to update parameters in\n", @@ -581,7 +715,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e10c204a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\omega}_{\\text{new} } = \\boldsymbol{\\omega} - \\lambda \\nabla_{\\boldsymbol{\\omega}} C(\\boldsymbol{x}, \\boldsymbol{\\omega})\n", @@ -590,7 +727,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9f4fa48e", + "metadata": { + "editable": true + }, "source": [ "for a number of iterations or until $ \\big|\\big| \\boldsymbol{\\omega}_{\\text{new} } - \\boldsymbol{\\omega} \\big|\\big|$ becomes smaller than some given tolerance.\n", "\n", @@ -609,7 +749,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "4652fc79", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{aligned}\n", @@ -621,7 +764,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "41ae0626", + "metadata": { + "editable": true + }, "source": [ "### The code for solving the ODE" ] @@ -629,6 +775,7 @@ { "cell_type": "code", "execution_count": 1, + "id": "af7c165f", "metadata": { "collapsed": false, "editable": true @@ -658,7 +805,7 @@ }, "metadata": { "filenames": { - "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_47_2.png" + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_50_2.png" }, "needs_background": "light" }, @@ -816,7 +963,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "875a0c0b", + "metadata": { + "editable": true + }, "source": [ "## The network with one input layer, specified number of hidden layers, and one output layer\n", "\n", @@ -828,6 +978,7 @@ { "cell_type": "code", "execution_count": 2, + "id": "00684827", "metadata": { "collapsed": false, "editable": true @@ -849,27 +1000,26 @@ ] }, { - "ename": "KeyboardInterrupt", - "evalue": "", - "output_type": "error", - "traceback": [ - "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42376/2971492148.py\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 144\u001b[0m \u001b[0mlmb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0.001\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 145\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 146\u001b[0;31m \u001b[0mP\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msolve_ode_deep_neural_network\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnum_hidden_neurons\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnum_iter\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlmb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 147\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 148\u001b[0m \u001b[0mres\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mg_trial_deep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mP\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42376/2971492148.py\u001b[0m in \u001b[0;36msolve_ode_deep_neural_network\u001b[0;34m(x, num_neurons, num_iter, lmb)\u001b[0m\n\u001b[1;32m 119\u001b[0m \u001b[0;31m# The cost_grad consist now of N_hidden + 1 arrays; the gradient w.r.t the weights and biases\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 120\u001b[0m \u001b[0;31m# in the hidden layers and output layers evaluated at x.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 121\u001b[0;31m \u001b[0mcost_deep_grad\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcost_function_deep_grad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mP\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 122\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 123\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ml\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN_hidden\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/wrap_util.py\u001b[0m in \u001b[0;36mnary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 19\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtuple\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0margnum\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0munary_operator\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0munary_f\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mnary_op_args\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mnary_op_kwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 21\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mnary_f\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 22\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mnary_operator\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/differential_operators.py\u001b[0m in \u001b[0;36mgrad\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 23\u001b[0m \u001b[0marguments\u001b[0m \u001b[0;32mas\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m`\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbut\u001b[0m \u001b[0mreturns\u001b[0m \u001b[0mthe\u001b[0m \u001b[0mgradient\u001b[0m \u001b[0minstead\u001b[0m\u001b[0;34m.\u001b[0m \u001b[0mThe\u001b[0m \u001b[0mfunction\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m`\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 24\u001b[0m should be scalar-valued. The gradient has the same type as the argument.\"\"\"\n\u001b[0;32m---> 25\u001b[0;31m \u001b[0mvjp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mans\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_make_vjp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 26\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mvspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mans\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msize\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 27\u001b[0m raise TypeError(\"Grad only applies to real scalar-output functions. \"\n", - "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/core.py\u001b[0m in \u001b[0;36mmake_vjp\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mmake_vjp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0mstart_node\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mVJPNode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnew_root\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0mend_value\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mend_node\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtrace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstart_node\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 11\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mend_node\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 12\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mvjp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mvspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/tracer.py\u001b[0m in \u001b[0;36mtrace\u001b[0;34m(start_node, fun, x)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mwith\u001b[0m \u001b[0mtrace_stack\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnew_trace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0mstart_box\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnew_box\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstart_node\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0mend_box\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstart_box\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 11\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misbox\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mend_box\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mend_box\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_trace\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mstart_box\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_trace\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 12\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mend_box\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_value\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mend_box\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_node\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/wrap_util.py\u001b[0m in \u001b[0;36munary_f\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m 13\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 14\u001b[0m \u001b[0msubargs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msubvals\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margnum\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 15\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0msubargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 16\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margnum\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 17\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0margnum\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42376/2971492148.py\u001b[0m in \u001b[0;36mcost_function_deep\u001b[0;34m(P, x)\u001b[0m\n\u001b[1;32m 67\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 68\u001b[0m \u001b[0;31m# Evaluate the trial function with the current parameters P\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 69\u001b[0;31m \u001b[0mg_t\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mg_trial_deep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mP\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 70\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 71\u001b[0m \u001b[0;31m# Find the derivative w.r.t x of the neural network\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42376/2971492148.py\u001b[0m in \u001b[0;36mg_trial_deep\u001b[0;34m(x, params, g0)\u001b[0m\n\u001b[1;32m 57\u001b[0m \u001b[0;31m# The trial solution using the deep neural network:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 58\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mg_trial_deep\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m10\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 59\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mg0\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mdeep_neural_network\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparams\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 60\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 61\u001b[0m \u001b[0;31m# The right side of the ODE:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42376/2971492148.py\u001b[0m in \u001b[0;36mdeep_neural_network\u001b[0;34m(deep_params, x)\u001b[0m\n\u001b[1;32m 37\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 38\u001b[0m \u001b[0mz_hidden\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mw_hidden\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx_prev\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 39\u001b[0;31m \u001b[0mx_hidden\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msigmoid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mz_hidden\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 40\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 41\u001b[0m \u001b[0;31m# Update x_prev such that next layer can use the output from this layer\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42376/2971492148.py\u001b[0m in \u001b[0;36msigmoid\u001b[0;34m(z)\u001b[0m\n\u001b[1;32m 5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0msigmoid\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mz\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mz\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 8\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0;31m# The neural network with one input layer and one output layer,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/tracer.py\u001b[0m in \u001b[0;36mf_wrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 40\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mf_wrapped\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mnotrace_primitives\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnode_constructor\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 41\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mf_wrapped\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margvals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 42\u001b[0;31m \u001b[0mparents\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtuple\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbox\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_node\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0m_\u001b[0m \u001b[0;34m,\u001b[0m \u001b[0mbox\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mboxed_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 43\u001b[0m \u001b[0margnums\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtuple\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margnum\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0margnum\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mboxed_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 44\u001b[0m \u001b[0mans\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mf_wrapped\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margvals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/tracer.py\u001b[0m in \u001b[0;36m\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m 40\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mf_wrapped\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mnotrace_primitives\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnode_constructor\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 41\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mf_wrapped\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margvals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 42\u001b[0;31m \u001b[0mparents\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtuple\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbox\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_node\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0m_\u001b[0m \u001b[0;34m,\u001b[0m \u001b[0mbox\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mboxed_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 43\u001b[0m \u001b[0margnums\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtuple\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margnum\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0margnum\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mboxed_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 44\u001b[0m \u001b[0mans\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mf_wrapped\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margvals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;31mKeyboardInterrupt\u001b[0m: " + "name": "stdout", + "output_type": "stream", + "text": [ + "Final cost: 0.119936\n" ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_52_3.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" } ], "source": [ @@ -1035,7 +1185,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "5420c490", + "metadata": { + "editable": true + }, "source": [ "### Example: Population growth\n", "\n", @@ -1045,7 +1198,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "1436ed3c", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -1059,7 +1215,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a590bdb6", + "metadata": { + "editable": true + }, "source": [ "where $g(t)$ is the population density at time $t$, $\\alpha > 0$ the growth rate and $A > 0$ is the maximum population number in the environment.\n", "Also, at $t = 0$ the population has the size $g(0) = g_0$, where $g_0$ is some chosen constant.\n", @@ -1069,15 +1228,16 @@ "using a library like TensorFlow is recommended.\n", "Here, we stay with a more simple approach and implement for comparison, the simple forward Euler method.\n", "\n", - "\n", - "\n", "Here, we will model a population $g(t)$ in an environment having carrying capacity $A$.\n", "The population follows the model" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "48d788d6", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -1091,13 +1251,15 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "169c6c25", + "metadata": { + "editable": true + }, "source": [ "where $g(0) = g_0$.\n", "\n", "In this example, we let $\\alpha = 2$, $A = 1$, and $g_0 = 1.2$.\n", "\n", - "\n", "We will get a slightly different trial solution, as the boundary conditions are different\n", "compared to the case for exponential decay.\n", "\n", @@ -1115,19 +1277,57 @@ "g(t) = \\frac{Ag_0}{g_0 + (A - g_0)\\exp(-\\alpha A t)}\n", "$$\n", "\n", - "\n", - "\n", "The network will be the similar as for the exponential decay example, but with some small modifications for our problem." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, + "id": "6d2e33bf", "metadata": { "collapsed": false, "editable": true }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial cost: 0.221805\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/MortenImac/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n", + " return array(a, dtype, copy=False, order=order)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Final cost: 0.000417932\n", + "The max absolute difference between the solutions is: 0.00424909\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_58_3.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad, elementwise_grad\n", @@ -1296,7 +1496,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e31ec549", + "metadata": { + "editable": true + }, "source": [ "## Using forward Euler to solve the ODE\n", "\n", @@ -1313,7 +1516,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "2e9ee105", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{aligned}\n", @@ -1325,7 +1531,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e876da16", + "metadata": { + "editable": true + }, "source": [ "along with the condition that $g(0) = g_0$.\n", "\n", @@ -1336,7 +1545,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b79a3def", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{aligned}\n", @@ -1349,14 +1561,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9d99cb4e", + "metadata": { + "editable": true + }, "source": [ "Now, if $g_i = g(t_i)$ then" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "3b9dcc24", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -1375,7 +1593,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "65ce688e", + "metadata": { + "editable": true + }, "source": [ "for $i \\geq 1$ and $g_0 = g(t_0) = g(0) = g_0$.\n", "\n", @@ -1385,12 +1606,69 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, + "id": "d5497948", "metadata": { "collapsed": false, "editable": true }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial cost: 0.221805\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/MortenImac/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n", + " return array(a, dtype, copy=False, order=order)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Final cost: 0.000417932\n", + "The max absolute difference between the solutions is: 0.00424909\n", + "Max absolute difference between Euler method and analytical: 0.011225\n", + "Max absolute difference between deep neural network and analytical: 0.00424909\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_66_3.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_66_4.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "# Assume that all function definitions from the example program using Autograd\n", "# are located here.\n", @@ -1461,7 +1739,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "fa8f0bb4", + "metadata": { + "editable": true + }, "source": [ "## Solving the one dimensional Poisson equation\n", "\n", @@ -1470,7 +1751,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f765b0ba", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -1484,7 +1768,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "bd63b92e", + "metadata": { + "editable": true + }, "source": [ "where $f(x)$ is a given function for $x \\in (0,1)$.\n", "\n", @@ -1493,7 +1780,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "c0a7face", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -1505,19 +1795,24 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f71c3cb9", + "metadata": { + "editable": true + }, "source": [ "This equation can be solved numerically using programs where e.g Autograd and TensorFlow are used.\n", "The results from the networks can then be compared to the analytical solution.\n", "In addition, it could be interesting to see how a typical method for numerically solving second order ODEs compares to the neural networks.\n", "\n", - "\n", "Here, the function $g(x)$ to solve for follows the equation" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "35aa6a37", + "metadata": { + "editable": true + }, "source": [ "$$\n", "-g''(x) = f(x),\\qquad x \\in (0,1)\n", @@ -1526,14 +1821,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f8b35111", + "metadata": { + "editable": true + }, "source": [ "where $f(x)$ is a given function, along with the chosen conditions" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "33813514", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -1547,7 +1848,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "c70aadd4", + "metadata": { + "editable": true + }, "source": [ "In this example, we consider the case when $f(x) = (3x + x^2)\\exp(x)$.\n", "\n", @@ -1556,7 +1860,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d5719dee", + "metadata": { + "editable": true + }, "source": [ "$$\n", "g_t(x) = x \\cdot (1-x) \\cdot N(P,x)\n", @@ -1565,14 +1872,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a683041b", + "metadata": { + "editable": true + }, "source": [ "The analytical solution for this problem is" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "672cdaff", + "metadata": { + "editable": true + }, "source": [ "$$\n", "g(x) = x(1 - x)\\exp(x)\n", @@ -1581,12 +1894,52 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, + "id": "66e6bebb", "metadata": { "collapsed": false, "editable": true }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/MortenImac/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n", + " return array(a, dtype, copy=False, order=order)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial cost: 457.256\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Final cost: 0.00310113\n", + "The max absolute difference between the solutions is: 0.000464088\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_79_3.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad, elementwise_grad\n", @@ -1742,7 +2095,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d425cba5", + "metadata": { + "editable": true + }, "source": [ "### Comparing with a numerical scheme\n", "\n", @@ -1761,7 +2117,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a2efa110", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -1775,14 +2134,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "5011ee25", + "metadata": { + "editable": true + }, "source": [ "If $x_i = i \\Delta x = x_{i-1} + \\Delta x$ and $g_i = g(x_i)$ for $i = 1,\\dots N_x - 2$ with $N_x$ being the number of values for $x$, ([15](#approx)) becomes" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "705ee300", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{aligned}\n", @@ -1794,14 +2159,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b390796d", + "metadata": { + "editable": true + }, "source": [ "Since we know from our problem that" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "19c9ece4", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{aligned}\n", @@ -1813,7 +2184,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6ade1a7a", + "metadata": { + "editable": true + }, "source": [ "along with the conditions $g(0) = g(1) = 0$,\n", "the following scheme can be used to find an approximate solution for $g(x)$ numerically:" @@ -1821,7 +2195,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "78b16d02", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -1838,7 +2215,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f2bfcca4", + "metadata": { + "editable": true + }, "source": [ "for $i = 1, \\dots, N_x - 2$ where $g_0 = g_{N_x - 1} = 0$ and $f(x_i) = (3x_i + x_i^2)\\exp(x_i)$, which is given for our specific problem.\n", "\n", @@ -1847,7 +2227,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a6191528", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{aligned}\n", @@ -1881,22 +2264,80 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "aefef707", + "metadata": { + "editable": true + }, "source": [ "which makes it possible to solve for the vector $\\boldsymbol{g}$.\n", "\n", - "\n", "We can then compare the result from this numerical scheme with the output from our network using Autograd:" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, + "id": "471664cd", "metadata": { "collapsed": false, "editable": true }, - "outputs": [], + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial cost: 457.256\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/MortenImac/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n", + " return array(a, dtype, copy=False, order=order)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Final cost: 0.00310113\n", + "The max absolute difference between the analytical solution and DNN Autograd: 0.000464088\n", + "The max absolute difference between the analytical solution and numerical scheme: 0.00266858\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_91_3.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter11_91_4.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad, elementwise_grad\n", @@ -2092,7 +2533,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6f02e86d", + "metadata": { + "editable": true + }, "source": [ "## Partial Differential Equations\n", "\n", @@ -2106,7 +2550,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ad5c63e8", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -2120,10 +2567,21 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "c7b98797", + "metadata": { + "editable": true + }, + "source": [ + "where $f$ is an expression involving all kinds of possible mixed derivatives of $g(x_1,\\dots,x_N)$ up to an order $n$. In order for the solution to be unique, some additional conditions must also be given." + ] + }, + { + "cell_type": "markdown", + "id": "52f9394e", + "metadata": { + "editable": true + }, "source": [ - "where $f$ is an expression involving all kinds of possible mixed derivatives of $g(x_1,\\dots,x_N)$ up to an order $n$. In order for the solution to be unique, some additional conditions must also be given.\n", - "\n", "### Type of problem\n", "\n", "The problem our network must solve for, is similar to the ODE case.\n", @@ -2134,7 +2592,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "4d489854", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -2145,15 +2606,24 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "82311538", + "metadata": { + "editable": true + }, "source": [ "where $h_1(x_1,\\dots,x_N)$ is a function that ensures $g_t(x_1,\\dots,x_N)$ satisfies some given conditions.\n", "The neural network $N(x_1,\\dots,x_N,P)$ has weights and biases described by $P$ and $h_2(x_1,\\dots,x_N,N(x_1,\\dots,x_N,P))$ is an expression using the output from the neural network in some way.\n", "\n", - "The role of the function $h_2(x_1,\\dots,x_N,N(x_1,\\dots,x_N,P))$, is to ensure that the output of $N(x_1,\\dots,x_N,P)$ is zero when $g_t(x_1,\\dots,x_N)$ is evaluated at the values of $x_1,\\dots,x_N$ where the given conditions must be satisfied. The function $h_1(x_1,\\dots,x_N)$ should alone make $g_t(x_1,\\dots,x_N)$ satisfy the conditions.\n", - "\n", - "\n", - "\n", + "The role of the function $h_2(x_1,\\dots,x_N,N(x_1,\\dots,x_N,P))$, is to ensure that the output of $N(x_1,\\dots,x_N,P)$ is zero when $g_t(x_1,\\dots,x_N)$ is evaluated at the values of $x_1,\\dots,x_N$ where the given conditions must be satisfied. The function $h_1(x_1,\\dots,x_N)$ should alone make $g_t(x_1,\\dots,x_N)$ satisfy the conditions." + ] + }, + { + "cell_type": "markdown", + "id": "9d134db4", + "metadata": { + "editable": true + }, + "source": [ "### Network requirements\n", "\n", "The network tries then the minimize the cost function following the\n", @@ -2169,7 +2639,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "5a463498", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C\\left(x_1, \\dots, x_N, P\\right) = \\left( f\\left(x_1, \\, \\dots \\, , x_N, \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_1}, \\dots , \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_N}, \\frac{\\partial g(x_1,\\dots,x_N) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(x_1,\\dots,x_N) }{\\partial x_N^n} \\right) \\right)^2\n", @@ -2178,14 +2651,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "c40d8997", + "metadata": { + "editable": true + }, "source": [ "If we let $\\boldsymbol{x} = \\big( x_1, \\dots, x_N \\big)$ be an array containing the values for $x_1, \\dots, x_N$ respectively, the cost function can be reformulated into the following:" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "cc033de6", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C\\left(\\boldsymbol{x}, P\\right) = f\\left( \\left( \\boldsymbol{x}, \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_1}, \\dots , \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_N}, \\frac{\\partial g(\\boldsymbol{x}) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(\\boldsymbol{x}) }{\\partial x_N^n} \\right) \\right)^2\n", @@ -2194,14 +2673,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ae18b4f4", + "metadata": { + "editable": true + }, "source": [ "If we also have $M$ different sets of values for $x_1, \\dots, x_N$, that is $\\boldsymbol{x}_i = \\big(x_1^{(i)}, \\dots, x_N^{(i)}\\big)$ for $i = 1,\\dots,M$ being the rows in matrix $X$, the cost function can be generalized into" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "44ca21bd", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C\\left(X, P \\right) = \\sum_{i=1}^M f\\left( \\left( \\boldsymbol{x}_i, \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_1}, \\dots , \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_N}, \\frac{\\partial g(\\boldsymbol{x}_i) }{\\partial x_1\\partial x_2}, \\, \\dots \\, , \\frac{\\partial^n g(\\boldsymbol{x}_i) }{\\partial x_N^n} \\right) \\right)^2.\n", @@ -2210,7 +2695,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "fe94451e", + "metadata": { + "editable": true + }, "source": [ "## Example: The diffusion equation\n", "\n", @@ -2219,7 +2707,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "30a42273", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial g(x,t)}{\\partial t} = \\frac{\\partial^2 g(x,t)}{\\partial x^2}\n", @@ -2228,14 +2719,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "fd4077e7", + "metadata": { + "editable": true + }, "source": [ "where a possible choice of conditions are" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "dbbf2e4b", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -2248,18 +2745,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "83653db9", + "metadata": { + "editable": true + }, "source": [ "with $u(x)$ being some given function.\n", "\n", - "\n", - "\n", "For this case, we want to find $g(x,t)$ such that" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "d2c2ef4f", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -2273,14 +2774,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "8fb27bdb", + "metadata": { + "editable": true + }, "source": [ "and" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "dc9297ab", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -2293,7 +2800,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ab90784f", + "metadata": { + "editable": true + }, "source": [ "with $u(x) = \\sin(\\pi x)$.\n", "\n", @@ -2301,9 +2811,6 @@ "The deep neural network will follow the same structure as discussed in the examples solving the ODEs.\n", "First, we will look into how Autograd could be used in a network tailored to solve for bivariate functions.\n", "\n", - "\n", - "\n", - "\n", "The only change to do here, is to extend our network such that\n", "functions of multiple parameters are correctly handled. In this case\n", "we have two variables in our function to solve for, that is time $t$\n", @@ -2315,7 +2822,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, + "id": "b07e858c", "metadata": { "collapsed": false, "editable": true @@ -2370,7 +2878,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9a167ec1", + "metadata": { + "editable": true + }, "source": [ "The cost function must then iterate through the given arrays\n", "containing values for $x$ and $t$, defines a point $(x,t)$ the deep\n", @@ -2392,8 +2903,6 @@ "$$\n", "since $(0) = u(1) = 0$ and $u(x) = \\sin(\\pi x)$.\n", "\n", - "\n", - "\n", "The Jacobian is used because the program must find the derivative of\n", "the trial solution with respect to $x$ and $t$.\n", "\n", @@ -2415,7 +2924,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 8, + "id": "921e5969", "metadata": { "collapsed": false, "editable": true @@ -2462,7 +2972,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "0bc00b69", + "metadata": { + "editable": true + }, "source": [ "### Setting up the network using Autograd; The full program\n", "\n", @@ -2478,19 +2991,70 @@ "Be aware, though, that it is fairly slow for the parameters used.\n", "A better result is possible, but requires more iterations, and thus longer time to complete.\n", "\n", - "\n", "Indeed, the program below is not optimal in its implementation, but rather serves as an example on how to implement and use a neural network to solve a PDE.\n", "Using TensorFlow results in a much better execution time. Try it!" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 9, + "id": "20734418", "metadata": { "collapsed": false, "editable": true }, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/Users/MortenImac/anaconda3/lib/python3.8/site-packages/numpy/core/_asarray.py:83: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray\n", + " return array(a, dtype, copy=False, order=order)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial cost: 41.05505310046362\n" + ] + }, + { + "ename": "KeyboardInterrupt", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47448/73752910.py\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 141\u001b[0m \u001b[0mlmb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0.01\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 142\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 143\u001b[0;31m \u001b[0mP\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msolve_pde_deep_neural_network\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnum_hidden_neurons\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnum_iter\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlmb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 144\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 145\u001b[0m \u001b[0;31m## Store the results\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47448/73752910.py\u001b[0m in \u001b[0;36msolve_pde_deep_neural_network\u001b[0;34m(x, t, num_neurons, num_iter, lmb)\u001b[0m\n\u001b[1;32m 118\u001b[0m \u001b[0;31m# Let the update be done num_iter times\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 119\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnum_iter\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 120\u001b[0;31m \u001b[0mcost_grad\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcost_function_grad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mP\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 121\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 122\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0ml\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mN_hidden\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/wrap_util.py\u001b[0m in \u001b[0;36mnary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 19\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtuple\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0margnum\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0munary_operator\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0munary_f\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mnary_op_args\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mnary_op_kwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 21\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mnary_f\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 22\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mnary_operator\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/differential_operators.py\u001b[0m in \u001b[0;36mgrad\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 23\u001b[0m \u001b[0marguments\u001b[0m \u001b[0;32mas\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m`\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbut\u001b[0m \u001b[0mreturns\u001b[0m \u001b[0mthe\u001b[0m \u001b[0mgradient\u001b[0m \u001b[0minstead\u001b[0m\u001b[0;34m.\u001b[0m \u001b[0mThe\u001b[0m \u001b[0mfunction\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m`\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 24\u001b[0m should be scalar-valued. The gradient has the same type as the argument.\"\"\"\n\u001b[0;32m---> 25\u001b[0;31m \u001b[0mvjp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mans\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_make_vjp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 26\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mvspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mans\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msize\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 27\u001b[0m raise TypeError(\"Grad only applies to real scalar-output functions. \"\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/core.py\u001b[0m in \u001b[0;36mmake_vjp\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mmake_vjp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0mstart_node\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mVJPNode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnew_root\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0mend_value\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mend_node\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtrace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstart_node\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 11\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mend_node\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 12\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mvjp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mvspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/tracer.py\u001b[0m in \u001b[0;36mtrace\u001b[0;34m(start_node, fun, x)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mwith\u001b[0m \u001b[0mtrace_stack\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnew_trace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0mstart_box\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnew_box\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstart_node\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0mend_box\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstart_box\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 11\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misbox\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mend_box\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mend_box\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_trace\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mstart_box\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_trace\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 12\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mend_box\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_value\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mend_box\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_node\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/wrap_util.py\u001b[0m in \u001b[0;36munary_f\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m 13\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 14\u001b[0m \u001b[0msubargs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msubvals\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margnum\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 15\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0msubargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 16\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margnum\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 17\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0margnum\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47448/73752910.py\u001b[0m in \u001b[0;36mcost_function\u001b[0;34m(P, x, t)\u001b[0m\n\u001b[1;32m 78\u001b[0m \u001b[0mg_t\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mg_trial\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpoint\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mP\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 79\u001b[0m \u001b[0mg_t_jacobian\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mg_t_jacobian_func\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpoint\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mP\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 80\u001b[0;31m \u001b[0mg_t_hessian\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mg_t_hessian_func\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mpoint\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mP\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 81\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 82\u001b[0m \u001b[0mg_t_dt\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mg_t_jacobian\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/wrap_util.py\u001b[0m in \u001b[0;36mnary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 19\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtuple\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0margnum\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0munary_operator\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0munary_f\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mnary_op_args\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mnary_op_kwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 21\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mnary_f\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 22\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mnary_operator\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/differential_operators.py\u001b[0m in \u001b[0;36mhessian\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 76\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mhessian\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 77\u001b[0m \u001b[0;34m\"Returns a function that computes the exact Hessian.\"\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 78\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mjacobian\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mjacobian\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 79\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 80\u001b[0m \u001b[0;34m@\u001b[0m\u001b[0munary_to_nary\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/wrap_util.py\u001b[0m in \u001b[0;36mnary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 19\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtuple\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0margnum\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0munary_operator\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0munary_f\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mnary_op_args\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mnary_op_kwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 21\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mnary_f\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 22\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mnary_operator\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/differential_operators.py\u001b[0m in \u001b[0;36mjacobian\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 59\u001b[0m \u001b[0mjacobian_shape\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mans_vspace\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mvspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 60\u001b[0m \u001b[0mgrads\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvjp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mans_vspace\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstandard_basis\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 61\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mreshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstack\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgrads\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mjacobian_shape\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 62\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 63\u001b[0m \u001b[0;34m@\u001b[0m\u001b[0munary_to_nary\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/numpy/numpy_wrapper.py\u001b[0m in \u001b[0;36mstack\u001b[0;34m(arrays, axis)\u001b[0m\n\u001b[1;32m 86\u001b[0m \u001b[0;31m# primitives defined in this file\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 87\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 88\u001b[0;31m \u001b[0marrays\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marr\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0marr\u001b[0m \u001b[0;32min\u001b[0m \u001b[0marrays\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 89\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0marrays\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 90\u001b[0m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'need at least one array to stack'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/numpy/numpy_wrapper.py\u001b[0m in \u001b[0;36m\u001b[0;34m(.0)\u001b[0m\n\u001b[1;32m 86\u001b[0m \u001b[0;31m# primitives defined in this file\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 87\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 88\u001b[0;31m \u001b[0marrays\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0marr\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0marr\u001b[0m \u001b[0;32min\u001b[0m \u001b[0marrays\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 89\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0marrays\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 90\u001b[0m \u001b[0;32mraise\u001b[0m \u001b[0mValueError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'need at least one array to stack'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/core.py\u001b[0m in \u001b[0;36mvjp\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m 12\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mvjp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mvspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 13\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 14\u001b[0;31m \u001b[0;32mdef\u001b[0m \u001b[0mvjp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mbackward_pass\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mend_node\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 15\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mvjp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mend_value\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 16\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/core.py\u001b[0m in \u001b[0;36mbackward_pass\u001b[0;34m(g, end_node)\u001b[0m\n\u001b[1;32m 19\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mnode\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mtoposort\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mend_node\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 20\u001b[0m \u001b[0moutgrad\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0moutgrads\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnode\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 21\u001b[0;31m \u001b[0mingrads\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvjp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moutgrad\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 22\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mparent\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mingrad\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mparents\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mingrads\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 23\u001b[0m \u001b[0moutgrads\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mparent\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0madd_outgrads\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0moutgrads\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparent\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mingrad\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/core.py\u001b[0m in \u001b[0;36m\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m 65\u001b[0m \"VJP of {} wrt argnum 0 not defined\".format(fun.__name__))\n\u001b[1;32m 66\u001b[0m \u001b[0mvjp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvjpfun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mans\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 67\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mvjp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 68\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0mL\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 69\u001b[0m \u001b[0margnum_0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margnum_1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0margnums\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/numpy/numpy_vjps.py\u001b[0m in \u001b[0;36m\u001b[0;34m(g)\u001b[0m\n\u001b[1;32m 421\u001b[0m \u001b[0mA_ndim\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0manp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 422\u001b[0m \u001b[0mB_meta\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0manp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmetadata\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mB\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 423\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mmatmul_adjoint_1\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mA_ndim\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mB_meta\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 424\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 425\u001b[0m \u001b[0mdefvjp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0manp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmatmul_vjp_0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmatmul_vjp_1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/numpy/numpy_vjps.py\u001b[0m in \u001b[0;36mmatmul_adjoint_1\u001b[0;34m(A, G, A_ndim, B_meta)\u001b[0m\n\u001b[1;32m 408\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# We need to swap the last two axes of A\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 409\u001b[0m \u001b[0mA\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0manp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mswapaxes\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mA_ndim\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mA_ndim\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 410\u001b[0;31m \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0manp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmatmul\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mG\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 411\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mB_is_vec\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 412\u001b[0m \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0manp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqueeze\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0manp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mG\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/tracer.py\u001b[0m in \u001b[0;36mf_wrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 43\u001b[0m \u001b[0margnums\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtuple\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margnum\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0margnum\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mboxed_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 44\u001b[0m \u001b[0mans\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mf_wrapped\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margvals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 45\u001b[0;31m \u001b[0mnode\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnode_constructor\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mans\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mf_wrapped\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margvals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margnums\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mparents\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 46\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mnew_box\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mans\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtrace\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnode\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 47\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/core.py\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, value, fun, args, kwargs, parent_argnums, parents)\u001b[0m\n\u001b[1;32m 34\u001b[0m raise NotImplementedError(\"VJP of {} wrt argnums {} not defined\"\n\u001b[1;32m 35\u001b[0m .format(fun_name, parent_argnums))\n\u001b[0;32m---> 36\u001b[0;31m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvjp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvjpmaker\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mparent_argnums\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 37\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 38\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0minitialize_root\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/core.py\u001b[0m in \u001b[0;36mvjp_argnums\u001b[0;34m(argnums, ans, args, kwargs)\u001b[0m\n\u001b[1;32m 75\u001b[0m \"VJP of {} wrt argnums 0, 1 not defined\".format(fun.__name__))\n\u001b[1;32m 76\u001b[0m \u001b[0mvjp_0\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvjp_0_fun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mans\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 77\u001b[0;31m \u001b[0mvjp_1\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvjp_1_fun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mans\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 78\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0mvjp_0\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvjp_1\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 79\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/numpy/numpy_vjps.py\u001b[0m in \u001b[0;36mmatmul_vjp_1\u001b[0;34m(ans, A, B)\u001b[0m\n\u001b[1;32m 420\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mmatmul_vjp_1\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mans\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mA\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mB\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 421\u001b[0m \u001b[0mA_ndim\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0manp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 422\u001b[0;31m \u001b[0mB_meta\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0manp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmetadata\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mB\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 423\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0;32mlambda\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mmatmul_adjoint_1\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mg\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mA_ndim\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mB_meta\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 424\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/tracer.py\u001b[0m in \u001b[0;36mf_wrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 59\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mf_wrapped\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 60\u001b[0m \u001b[0margvals\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgetval\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 61\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mf_raw\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margvals\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 62\u001b[0m \u001b[0mf_wrapped\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_is_primitive\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 63\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mf_wrapped\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/numpy/numpy_wrapper.py\u001b[0m in \u001b[0;36mmetadata\u001b[0;34m(A)\u001b[0m\n\u001b[1;32m 146\u001b[0m \u001b[0;34m@\u001b[0m\u001b[0mnotrace_primitive\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 147\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mmetadata\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 148\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0m_np\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_np\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_np\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mresult_type\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0m_np\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0miscomplexobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mA\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 149\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 150\u001b[0m \u001b[0;34m@\u001b[0m\u001b[0mnotrace_primitive\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mKeyboardInterrupt\u001b[0m: " + ] + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import jacobian,hessian,grad\n", @@ -2719,7 +3283,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "143f1c80", + "metadata": { + "editable": true + }, "source": [ "## Solving the wave equation with Neural Networks\n", "\n", @@ -2728,7 +3295,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "190bd4f2", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial^2 g(x,t)}{\\partial t^2} = c^2\\frac{\\partial^2 g(x,t)}{\\partial x^2}\n", @@ -2737,7 +3307,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9719cfc5", + "metadata": { + "editable": true + }, "source": [ "with $c$ being the specified wave speed.\n", "\n", @@ -2746,7 +3319,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f69ec7fd", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -2760,17 +3336,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6ce8c5a8", + "metadata": { + "editable": true + }, "source": [ "where $\\frac{\\partial g(x,t)}{\\partial t} \\Big |_{t = 0}$ means the derivative of $g(x,t)$ with respect to $t$ is evaluated at $t = 0$, and $u(x)$ and $v(x)$ being given functions.\n", "\n", - "\n", "The wave equation to solve for, is" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "4be700d7", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -2784,7 +3365,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "993f93ba", + "metadata": { + "editable": true + }, "source": [ "where $c$ is the given wave speed.\n", "The chosen conditions for this equation are" @@ -2792,7 +3376,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "2cb2a80f", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -2809,12 +3396,13 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "3f1dcfd4", + "metadata": { + "editable": true + }, "source": [ "In this example, let $c = 1$ and $u(x) = \\sin(\\pi x)$ and $v(x) = -\\pi\\sin(\\pi x)$.\n", "\n", - "\n", - "\n", "Setting up the network is done in similar matter as for the example of solving the diffusion equation.\n", "The only things we have to change, is the trial solution such that it satisfies the conditions from ([20](#condwave)) and the cost function.\n", "\n", @@ -2832,7 +3420,6 @@ "\n", "Note that this trial solution satisfies the conditions only if $u(0) = v(0) = u(1) = v(1) = 0$, which is the case in this example.\n", "\n", - "\n", "The analytical solution for our specific problem, is\n", "\n", "$$\n", @@ -2842,7 +3429,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 10, + "id": "230a9aef", "metadata": { "collapsed": false, "editable": true @@ -3073,7 +3661,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a23bd19a", + "metadata": { + "editable": true + }, "source": [ "## Resources on differential equations and deep learning\n", "\n", @@ -3102,5 +3693,5 @@ } }, "nbformat": 4, - "nbformat_minor": 4 + "nbformat_minor": 5 } \ No newline at end of file diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter11.py b/doc/LectureNotes/_build/jupyter_execute/chapter11.py index e46d52a1f..ad19dc1c9 100644 --- a/doc/LectureNotes/_build/jupyter_execute/chapter11.py +++ b/doc/LectureNotes/_build/jupyter_execute/chapter11.py @@ -1,13 +1,15 @@ #!/usr/bin/env python # coding: utf-8 +# + # # Solving Differential Equations with Deep Learning # # The Universal Approximation Theorem states that a neural network can # approximate any function at a single hidden layer along with one input # and output layer to any given precision. # -# # An ordinary differential equation (ODE) is an equation involving functions having one variable. # # In general, an ordinary differential equation looks like @@ -29,8 +31,6 @@ # Along with ([1](#ode)), some additional conditions of the function $g(x)$ are typically given # for the solution to be unique. # -# -# # Let the trial solution $g_t(x)$ be # @@ -54,11 +54,8 @@ # # But what about the network $N(x,P)$? # -# # As described previously, an optimization method could be used to minimize the parameters of a neural network, that being its weights and biases, through backward propagation. # -# -# # For the minimization to be defined, we need to have a cost function at hand to minimize. # # It is given that $f\left(x, \, g(x), \, g'(x), \, g''(x), \, \dots \, , \, g^{(n)}(x)\right)$ should be equal to zero in ([1](#ode)). @@ -85,15 +82,12 @@ # The neural net should then find the parameters $P$ that minimizes the cost function in # ([3](#cost)) for a set of $N$ training samples $x_i$. # -# -# # To perform the minimization using gradient descent, the gradient of $C\left(\boldsymbol{x}, P\right)$ is needed. # It might happen so that finding an analytical expression of the gradient of $C(\boldsymbol{x}, P)$ from ([3](#cost)) gets too messy, depending on which cost function one desires to use. # # Luckily, there exists libraries that makes the job for us through automatic differentiation. # Automatic differentiation is a method of finding the derivatives numerically with very high precision. -# -# + # ### Example: Exponential decay # # An exponential decay of a quantity $g(x)$ is described by the equation @@ -123,8 +117,6 @@ # Having an analytical solution at hand, it is possible to use it to compare how well a neural network finds a solution of ([4](#solve_expdec)). # -# -# # The program will use a neural network to solve # @@ -140,7 +132,6 @@ # # In this example, $\gamma = 2$ and $g_0 = 10$. # -# # To begin with, a trial solution $g_t(t)$ must be chosen. A general trial solution for ordinary differential equations could be # $$ @@ -149,8 +140,6 @@ # with $h_1(x)$ ensuring that $g_t(x)$ satisfies some conditions and $h_2(x,N(x, P))$ an expression involving $x$ and the output from the neural network $N(x,P)$ with $P $ being the collection of the weights and biases for each layer. For now, it is assumed that the network consists of one input layer, one hidden layer, and one output layer. # -# -# # In this network, there are no weights and bias at the input layer, so $P = \{ P_{\text{hidden}}, P_{\text{output}} \}$. # If there are $N_{\text{hidden} }$ neurons in the hidden layer, then $P_{\text{hidden}}$ is a $N_{\text{hidden} } \times (1 + N_{\text{input}})$ matrix, given that there are $N_{\text{input}}$ neurons in the input layer. # @@ -198,7 +187,6 @@ # is fulfilled as *best as possible*. # -# # The left hand side and right hand side of ([8](#nnmin)) must be computed separately, and then the neural network must choose weights and biases, contained in $P$, such that the sides are equal as best as possible. # This means that the absolute or squared difference between the sides must be as close to zero, ideally equal to zero. # In this case, the difference squared shows to be an appropriate measurement of how erroneous the trial solution is with respect to $P$ of the neural network. @@ -219,8 +207,6 @@ # for an input value $x$. # -# -# # If the neural network evaluates $g_t(x, P)$ at more values for $x$, say $N$ values $x_i$ for $i = 1, \dots, N$, then the *total* error to minimize becomes # @@ -244,14 +230,12 @@ # \min_{P_{\text{hidden} }, \ P_{\text{output} }} C(\boldsymbol{x}, \{P_{\text{hidden} }, P_{\text{output} }\}) # $$ # -# # For simplicity, it is assumed that the input is an array $\boldsymbol{x} = (x_1, \dots, x_N)$ with $N$ elements. It is at these points the neural network should find $P$ such that it fulfills ([9](#min)). # # First, the neural network must feed forward the inputs. # This means that $\boldsymbol{x}s$ must be passed through an input layer, a hidden layer and a output layer. The input layer in this case, does not need to process the data any further. # The input layer will consist of $N_{\text{input} }$ neurons, passing its element to each neuron in the hidden layer. The number of neurons in the hidden layer will be $N_{\text{hidden} }$. # -# # For the $i$-th in the hidden layer with weight $w_i^{\text{hidden} }$ and bias $b_i^{\text{hidden} }$, the weighting from the $j$-th neuron at the input layer is: # $$ @@ -311,8 +295,6 @@ # and biases $b_i^{\text{output}}$. In this case, # it is assumes that the number of neurons in the output layer is one. # -# -# # The procedure of weighting the output neuron $j$ in the hidden layer to the $i$-th neuron in the output layer is similar as for the hidden layer described previously. # $$ @@ -343,7 +325,6 @@ # In this case we seek a continuous range of values since we are approximating a function. This means that after computing $\boldsymbol{z}_{1}^{\text{output}}$ the neural network has finished its feed forward step, and $\boldsymbol{z}_{1}^{\text{output}}$ is the final output of the network. # -# # The next step is to decide how the parameters should be changed such that they minimize the cost function. # # The chosen cost function for this problem is @@ -355,7 +336,7 @@ # In order to minimize the cost function, an optimization method must be chosen. # # Here, gradient descent with a constant step size has been chosen. -# + # ### Gradient descent # # The idea of the gradient descent algorithm is to update parameters in @@ -734,8 +715,6 @@ if __name__ == '__main__': # using a library like TensorFlow is recommended. # Here, we stay with a more simple approach and implement for comparison, the simple forward Euler method. # -# -# # Here, we will model a population $g(t)$ in an environment having carrying capacity $A$. # The population follows the model @@ -752,7 +731,6 @@ if __name__ == '__main__': # # In this example, we let $\alpha = 2$, $A = 1$, and $g_0 = 1.2$. # -# # We will get a slightly different trial solution, as the boundary conditions are different # compared to the case for exponential decay. # @@ -770,11 +748,9 @@ if __name__ == '__main__': # g(t) = \frac{Ag_0}{g_0 + (A - g_0)\exp(-\alpha A t)} # $$ # -# -# # The network will be the similar as for the exponential decay example, but with some small modifications for our problem. -# In[ ]: +# In[3]: import autograd.numpy as np @@ -996,7 +972,7 @@ if __name__ == '__main__': # Equation ([12](#odenum)) could be implemented in the following way, # extending the program that uses the network using Autograd: -# In[ ]: +# In[4]: # Assume that all function definitions from the example program using Autograd @@ -1094,7 +1070,6 @@ if __name__ == '__main__': # The results from the networks can then be compared to the analytical solution. # In addition, it could be interesting to see how a typical method for numerically solving second order ODEs compares to the neural networks. # -# # Here, the function $g(x)$ to solve for follows the equation # $$ @@ -1126,7 +1101,7 @@ if __name__ == '__main__': # g(x) = x(1 - x)\exp(x) # $$ -# In[ ]: +# In[5]: import autograd.numpy as np @@ -1372,10 +1347,9 @@ if __name__ == '__main__': # which makes it possible to solve for the vector $\boldsymbol{g}$. # -# # We can then compare the result from this numerical scheme with the output from our network using Autograd: -# In[ ]: +# In[6]: import autograd.numpy as np @@ -1589,7 +1563,7 @@ if __name__ == '__main__': # $$ # where $f$ is an expression involving all kinds of possible mixed derivatives of $g(x_1,\dots,x_N)$ up to an order $n$. In order for the solution to be unique, some additional conditions must also be given. -# + # ### Type of problem # # The problem our network must solve for, is similar to the ODE case. @@ -1607,9 +1581,7 @@ if __name__ == '__main__': # The neural network $N(x_1,\dots,x_N,P)$ has weights and biases described by $P$ and $h_2(x_1,\dots,x_N,N(x_1,\dots,x_N,P))$ is an expression using the output from the neural network in some way. # # The role of the function $h_2(x_1,\dots,x_N,N(x_1,\dots,x_N,P))$, is to ensure that the output of $N(x_1,\dots,x_N,P)$ is zero when $g_t(x_1,\dots,x_N)$ is evaluated at the values of $x_1,\dots,x_N$ where the given conditions must be satisfied. The function $h_1(x_1,\dots,x_N)$ should alone make $g_t(x_1,\dots,x_N)$ satisfy the conditions. -# -# -# + # ### Network requirements # # The network tries then the minimize the cost function following the @@ -1658,8 +1630,6 @@ if __name__ == '__main__': # with $u(x)$ being some given function. # -# -# # For this case, we want to find $g(x,t)$ such that # @@ -1687,9 +1657,6 @@ if __name__ == '__main__': # The deep neural network will follow the same structure as discussed in the examples solving the ODEs. # First, we will look into how Autograd could be used in a network tailored to solve for bivariate functions. # -# -# -# # The only change to do here, is to extend our network such that # functions of multiple parameters are correctly handled. In this case # we have two variables in our function to solve for, that is time $t$ @@ -1698,7 +1665,7 @@ if __name__ == '__main__': # network at each possible pair $(x,t)$, given an array for the desired # $x$-values and $t$-values to approximate the solution at. -# In[ ]: +# In[7]: def sigmoid(z): @@ -1767,8 +1734,6 @@ def deep_neural_network(deep_params, x): # $$ # since $(0) = u(1) = 0$ and $u(x) = \sin(\pi x)$. # -# -# # The Jacobian is used because the program must find the derivative of # the trial solution with respect to $x$ and $t$. # @@ -1787,7 +1752,7 @@ def deep_neural_network(deep_params, x): # matrix, which is the matrix containing all the possible second order # mixed derivatives of $g(x,t)$. -# In[ ]: +# In[8]: # Set up the trial function: @@ -1842,11 +1807,10 @@ def cost_function(P, x, t): # Be aware, though, that it is fairly slow for the parameters used. # A better result is possible, but requires more iterations, and thus longer time to complete. # -# # Indeed, the program below is not optimal in its implementation, but rather serves as an example on how to implement and use a neural network to solve a PDE. # Using TensorFlow results in a much better execution time. Try it! -# In[ ]: +# In[9]: import autograd.numpy as np @@ -2097,7 +2061,6 @@ if __name__ == '__main__': # where $\frac{\partial g(x,t)}{\partial t} \Big |_{t = 0}$ means the derivative of $g(x,t)$ with respect to $t$ is evaluated at $t = 0$, and $u(x)$ and $v(x)$ being given functions. # -# # The wave equation to solve for, is # @@ -2126,8 +2089,6 @@ if __name__ == '__main__': # In this example, let $c = 1$ and $u(x) = \sin(\pi x)$ and $v(x) = -\pi\sin(\pi x)$. # -# -# # Setting up the network is done in similar matter as for the example of solving the diffusion equation. # The only things we have to change, is the trial solution such that it satisfies the conditions from ([20](#condwave)) and the cost function. # @@ -2145,14 +2106,13 @@ if __name__ == '__main__': # # Note that this trial solution satisfies the conditions only if $u(0) = v(0) = u(1) = v(1) = 0$, which is the case in this example. # -# # The analytical solution for our specific problem, is # # $$ # g(x,t) = \sin(\pi x)\cos(\pi t) - \sin(\pi x)\sin(\pi t) # $$ -# In[ ]: +# In[10]: import autograd.numpy as np diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter11_50_2.png b/doc/LectureNotes/_build/jupyter_execute/chapter11_50_2.png new file mode 100644 index 0000000000000000000000000000000000000000..5742598bc953ff52ab6e2705d212b69739b562a3 GIT binary patch literal 23393 zcmZ5{1yodD^ez^lC?F|PBAp{3C8Z$ZfPf&~pmcXLs3RyK=+LcnNH+{2A<`w?L$?DG zL(MxgzxDsW_1;>rSloN=K6~%;?Qie1@425|sw&>ParXuR0l_Wk^QRgF1ecA$uOTrZ zxWcub{~7#|a97ZEf8}K9?q%j`L7-yh?riVmZf|3L&(p%y&Bn=5Sm2?6FyB3EcXwyE zM-Yg^{|*pva~95V9!#&z#L&FJL2nVF)>jl|8Oow}-e&wHXYo@V!Mgx(ga8PFj_*;N@hPrSePaBJ{uIFd02)by$AlP>mtFw8f_?cC?fhk z4FrnFq$>4>BG|G%wksppxE1(}xhdqVspO7@;3eX4XV|n4ibgK?uAH|lyyOA=ukWRhLJtY%k-PwGny&@*-zfhH=owqD~T-*C^ut?F%<(7UG^I~~GluNBJ zD3T;-nf-{#`s$ys^fh=*Ya0uE;1Qhs1Gy`z522(^6#&L~x~y`2CU5!50%u`?XR*L* zS>SPU#JyoEvXbzZ@zaWY*ICXIr`7BYwuB1C_7M~?&URs)b$+dt_t4)ga+ zB_8m>2ddgs9KZTg=$#+wPxLEHxSb+IUs5St6fTp+UuDqT`q$7*)QR;XY`jE6AWL8r zW>h5m*J<94LUO_Qu}sMgT{-hrLppDQ_|!8$g4|?eppGezv-AT>@7p!h-qJn>VQbT@N zip>LGQ?^f>Lk#nT^Q%h%pRYx5dt%DpzO_r}7=3&-`P$htbItt~^WpN)nZxNNsSy>` zQ+}Tr_Rc2hsBWaZ>&bfOx+I5M8W}R`3>)ky%O3ZWx)WpH80<57_s$o?Be$TjP?gQg z{&C5Nj00J1p0GfnsmtFSN^NdEm!i2_WD#JPWXMeNb}WdeJ=;XloIWKLc}_g;%fIzs-sx7x|H!2R%ACtAVVUjaHYi+@jlSOGts|v%g5$ndXQJo#qU? zF#4OGC5;wos<2X`=c`Q=^e@7eLeFRi!rP+O7T7%7h&a{6xT??>&rsB^q+jZTZ|$Tt z-=k1_3Vb_`)v|xhN3g?zX44j_RWBqUh0d;!u-)kB?VM^NIIbMuW`1IxLmzY=WbqjI z8QZ_)L8hi!9F=@w?aGvRX@V`)p10VkQJJrPdg;m{$2SV+$9q3Zj7o{1#U6a8Bl~{d zLaiyy-{e& zRJtz7S^d`NxzwO1L{Jt&FaotVnSn~pdOdffhh1re8aK*(;@n(}+TV{`3Mk&bexa?j zMgN?tvg5gZWIck5l&EO=q+fjtZ4&D6L;BPGMxsvvy?UM9I>z1GX{3LY`&LERs``00 zr<@#q2L?awOdx$jZ4lfY^o%_%X|&>V>7hd|lQYAo4hfv zv$u6q&#+9*PV53O*1uc&u?LAv)2l^RGm!*!>{yuSCd9biM1=H`s_F%dp*{6p5C@y_ z*VU30ln2vaGkGGwBZbOIJ~o4)Sc{aW@{?{r4uKgJ!%rpM|3L?A8~bj@EVRs%?q zjqK}9jF6<41GznGi{A>5mCC3>JWrVBKP_R?F75D%I@pb>BSk&yOmO_2U7Z(j|*Mhdbel{-d1oS67w_XtzT$L(bwr%eNHvSX5;p3vMWVET;Tj$ z^X_zlTw{A*r}@}Qz7C=wY;1fQf0zpPqdDss+aYWBa|R7(4j3Qv+cs;1yinRtw9h|0 z?loVXxh_>5yD8g|7&bOpRoVe09T?oUh@D@; zLav-d$ES(VM0+^M+tpx=-eTHSk4!pzF^IOXh!gg{rfX|P<}+%n7)RoyJnup$$?*XT z=GC+g??RI!uF$HF>A6}|3USZWE0Wv#mf++q??zy3o_|zAjhwoC9jm!P9vI=^>^I%TTjhw~%MtG*Fr=L5e4EPJLFUL}{aB=907WrJ zpt1bQP>&ZHlSHAQuKvl#zACu8sJDj#lg}2(X>;u%|JOwh3Zl)pQRY!K;)NdamXGGu zW3jRV#kYFvPUP@M|$rCVRz%|187D5?Y2 z{^*8YHgRQE-*ZR%q%bQC4w>h`=7JHM+hOE##>8eUpUU+1&@cUsDlRkeRi*T^mfjM{ zXnPb+(I2`wB}+3F-6o`Gcz-i^OWAZLa?nm`OHKc8N5}B49Pt>O{1?0I*M^|B#j@iv zy{SMu`6J=}s5?finBB0fq~1y=c^0@W3!GD)I7*&4?0Iw^zY-?z=l=6>$IoOe{T^CdwF8}dCZx<2{QLa&^xrPpv$*&StN0Yzj)}4^pB^bJnB>`uWxON zho+}J-+EAV4=p-mP9YgZ0!7|6HhLpwd77Yx(v7tOi&Mz⩔>4!BuxJG(Ednq4_ln zyl~7ptzh>EHfkee19ElwZ$0_wS7V-9qcMHpA8?G?4Z zP2Hu(qM{$#(C+Qk`}v^uls9L*Xq=TJe(Ui=@xp5=Mb$jv58qc0hy8}{r+wUPvow&@ z27M}p;%KBPu^BT3E0z;+M}6{Lo8arsnO~yjvcn{6G;-F8DE?`$P!)qQsUkc2I>K?% zan{gu{pQAk#X<;-N`W$i>(Pg{gV~7m?>dQW);i6bbQ-|b z#NQo=&5oA--ELlBf!B3@%_tak^BaLm&F>S)5wCvnX0MZwx^yO4JIr3&SkIob{MB38 zw3}j#?y>o*)IFa%*r(x=uTyGN3g>T!pNF?>mu7dv$yK?kR9B;PML)19^;EIIU&#|o zu%JDNB@yC}y;O`jTo}4-I@?DllK2SO*C9JSM({mkN+%rj^0^= zqVD8lW09(^lJ=Bx-tlb)T-6S3=Y99kRWkr1k2*X0HaI)tpnPFQQIQ>zK|cZFCO_&K zZdZ}ZWxe?>j%X8<{UYveW=y5PD@UC2JbKl`=W>l8yoB;G@prJ*@vu23ALoWU+q?c- zxG{QWZe6MOcyk0Yna-6chr07iGU_zh=y`Y}vLa$L&i_SW_p9diPW47|xm+eW@$@#z zGg}cTQXz>5@aBc8xgXc(Ta*1y)gQ*R5$PIVoqf?bRW_-=>LNY$QiXywjYN*v<1H*& zNRkCUEKht3(SMr+VMUAZ4rjV8C;kBbMLB)Ckgc>&>F&?Equ$NL;#)JML$U34tZZUI zj%>5DU99LEi^cZid&rbF&Zo~1$8gl&C7&eLIS^9Svuvs2YV7EZ%8DWt%ae#U146GT zaqWUX`-}>MJQQi}65(xJldst#&~!~MZU-S#0&MCiPj>XB_Y!QWKvW;J}sIwvZI^l650fzNv-eMV$X9};O%UrALm$on!29{o`_&Zfk!mC1U9L3Iulb(cMprlNWO4^z_Q8JN*ra zZu3g8!?3;m31LVw4%kec-O=^Q@#2xUQA2FK%=@-dgGDIAdrvJPHCc*|VI2r!K1#8|uG@K3j6lJI0G_vP2H(jzosPIDOj;{!Z&jB9PB;OaQ1!longX)L#(n;Q z-18nf(^w)DBRMam=X$kHhf0B7NU4}gIYRT`KKfE<`hk&g!q3|fs14W-zu4O@dBpZi zYqr`w52@Vf;Ke>LJfzhKx&>MFVb773=fa;}D+zoOi_ok>u-212_kVZzR=3ryNxl+Fjph%MsJcBr>Yx-LJ!c!umiJD#)co4P#z?ul z10l=Rjgf-tpBW*z?gtOK^4LnbVE54fZHPp>r26eh2-I(t9T;1l{9A8Ilfj5Dmj>; zNJe1$C--Ns*xZYH&+WD8TH$ib-pljnM{`z@(ubziGoFjz-jkl3pN-H!j9&nifA{wj znGU8aR5;Egj+wwxzRQQWPTJ&@ZWh&-`D0w`Jhx9y)yMa;{bE%%&lP>dbi7r2Q z^P9ZReZ9r8e*0ORfKmJdvlh!VuO?MFMCOgPs-unvo+s(OzDbgzh3&EtlQs=;ek%!9 zxdzn&-Ek1BqZzN&n#G9M>qA-YJJSg;?CG4L*NlhM!Jk)W+fK08yA4N{1K*y&$=4>z zIgh5@$d2Y<*xhQaa!VDUPFDzX;Pa!M8J~j@9f_TqMezkVrT4!<#oFD*)3x!^Mdlq@ z2qcn3pe6{?bcPUhn0(+gD@9N>7wFe`wx{gs>Uz9Y-e0qxo#egWD<-xnR0h^HGun6U zdx-bxcJ-xrA&VQ7oT`}`SxQaJiX-3UiB1l;N!S|wwlbqs&3}c{{m`$p{XCc8ae-NN z>z6(nXz=q&4LH~^@`q3 zu<#n!G!wt(l?^n(U^1s$!j0#L2KibA&&G<3^Z;yXYipZe((<03qSvlnBQOlaEE@(K zj4%ZJ8~nFBmuBG9Z~$|3D{eS6AIgN@yz?NarA2PC%AvmRraDz2y5OE;?J~{b91J!a zcKTvh(HBt#Y!1%`ubBWmU=Thb#SQ{a}v0 zQy;6e08v^KfAlWVSn=q$Cs%y`t^F+RU{VIi6<^PcBBztcNnBGe(2O_Sm+kZ z&9L;`#YBN!L1WNx%rF8D^#^eIw?53d!?kIFiz>S9g%IWlNx3{991CcKM(d$LcaTyp zo>A_O(H63f1>VR4|I`WFj2<}$#FLd&#(?%E6|ZRX5hFNH=b9v3i<3&Bxv{6y&iDku z7UO22jRf62ig+E=mSghZ{nCKV{Incb9{2(#fUC1k`L-P2nO^)T!~|%UBam z^o_s#B}SmjOS~XO@nLhGyyfZq{L*^G?K)#MX_^OnDMYA<`%sPAk!%%u&lwLLf=BLa z&6&_B0`bG~*Vt9$UUttj;QdDy{86NQ1*g-RlG{FaGES>scQgBOC^p!(F@kU}Qx63J zs8Q>>Jcmt7NjX0y(=C>fm6S|+_wJo;SxjYxbd3xt%hmMrq8u5LI|sAxT{^x3@(ph< zfL9rjTDk8CRM5@6kLiwUV+5-b!+P=D^E%7b8%GThC+DiG^8M^R3pk~qSC22vB9 z^vRJ4<Hk7IYY%8tH<_st}TF8Y<&wwKi`K1XD_wxB9O&bV<{ z8*$QOmD%A7)a`9URnlx9${+@79c)CZh%mg2V3A|U)T!DTzfX_HTiBrW!@k5QT+G6< zF74mJ%*x~RwTaTo)A&&9wyNJK`kpH^UeZfID_?Ws+oq56`J=76{=smJEvJ6?_LGY) z-rt3W{5#JPYz`GGy-C6z8=8B2d#DHv0ZkwQTyYxk;4|JNFDuh69W${JpSKTg!V+&s zHVORq%=EP3WQ7f-SNM(I>bqkZ=YcbKqRLr&JEWfc>{`aVj;;q)$;84Nwrq5v)M_n| zA>+-qBM!pxy&h8OyZqQrc<1a}%M50(KOnpu9){^~!+-F_dep`S4;ns$9a~SkfUpcM z^N!I7De4ds_47*%_f2lm;zdQULJ>k=+6$t~%F1=iRx2Ndt~}Ui?f9STc30e|vEsih zofMo4`c*9UfpnEGqB9Bj^7S*av80Jn(- zwcA~>u(B%sHazk$bnnjoAmx81fknCfh|!&5v8?L*!chcnp@z!69pGDAd@EjciO&Y@ ze+8bs`A_u{Z->m04C8|)7(D$<>%ZrlQI%g^UCR>2(2$1$iS0FN_{iO~LQh`xJ6nJA z%gRBeVS$X2S{$dvXfLYrI&SpvLVjEBSch6W4tZG;VPhPVi(g*RrBzaU1j{bv0{+tH z1Q)w{J2{HawH|UOb{?zw{lX6x3>&i?zzht>lUKb7`%ZS7dZhz@of};Lk`&eZ<4|WX z)0&VHuZNu(dh*31X5UAYEwO)?PQGOT_O$uTXPgAhnzpyx@?}@KVfFX*oE6^HLtonM zgeUj^4r2r>zK?p5;Z?o}0T=U=lUo0I>I`H$KcYO9ruSk1S;!JdnMhSk?u`5{B0?yM zGwVuh(otKxd%B`7Wg_Oa{LupLLO4kKCokAaL08zKr(E8Y6k9L zp!sWH>L2>cN@sP$X*T)~KA1FZQR8%?Vhz)|;V!Wu6__m%)7Uttjw|;bfNPq?8lTcU zkA-{pIEB{>;udk3H8)2qeQk(P4fkCpMbd_b;=O2Y3NGH&;@uxUj2qyC2{qkv2a08e z{zk>f8AZsXnOHwN)WO-Md0P*uk!xAW^J095B5_#_Rb6cI38$=*V3ksWw#$-y<-vD}s#2S_$1 z-y~i%*9-41P%E1cWleoJyDP%70jtJAL5rNGINn}8gXeX1?Z=gZK(mv1F}x8P%_!;& zff)gFjX&`83ol#;^{MCX2`G*MUC@>GHg|190a$y%ASq{%=iXZ;TJ55WV5OKyWrRy(LOmO0# z!uEmK)gg0?_)7Tkz5iqa33;kB*q%SRGTo;aQ@G{mx*n#JXscZ;DzBfc9A>c?f7BX+ z_fOK>cHYn1v)lbI!ZynPy~3fAhYT3-L*YIDo#`_MeLnhb`Y#zDZV-I{nX+`;3>{ezOh^$OjyD`CF^nD7c*0t#4HJL)_T&TnmryjaIEA6*+N=53YZXb^-x zRW+=gRafXD44+gr%DgRdJ!gtcwJWae%bw^=s{?>=1AYH^_R7 zetT&9hNYsxgQiFv(k(6n^`{yYSQ~R;Jp44bUU$MT@XN4ihVF8f^s4Xrp9fpF$IEV~ zjY-DPkc5=|>$vpaC{r{K(Iiseh7K_4AF?r(xIRbuWgS@g|7?3S*UI@Bwo9SN#8z z`x~VdQ8ATImo_4iK(kL&ezsbSXB#CjR(OiphuSS&pJ@}s!CjC_h3g$=!W#{epYLPd z>teda@EWuOy8Z4Dc}C)vk+_6MfPSfWj67qNO&@2aS|$eRq=)IQ#t((k6ua6cu@)(X z`(myuLJ>p3?FGq`0rj!|8k<)W`_F@8q6qP83XB@7dW3@XgxP*MYQ(uT>q?l8#HdX@ zjlbqTZfIgmR4}fR%De%IMN!KgD-)Z&AU1O+UWg%=ixGE?_F}mT1n{gVik!j0-reTj zayu`4;AYL`HBbZ_+@lwl7?I!!m9BD9NK5P(_V3gAktijOiz_W_mxht}E1I`hmIy|I z)&-Zjj^v0dB&5*v5hSxnLLBb`Abg0~Ls2UXKAe}C7c(U+c@Uberfe(#cQzw7vj#uL z#>V-tV|o2{1`?|`jh?nDWa$3e7RLD?uO)P`@YkcqV&85JP~p074NJ?QGQSNfbFR=w zqSgcVMg+TK$S;Q^`%=qiZ2#WyqUTGZ#g)lCnV>NvMSLt0nvUcO-FsUdBp|qy`%-_T z_-7=eV}{ZKMRtRaJdVfmzo58`n=Ylu6OYIdUlJ$3Ln|L~W3{Fg+a?(kk=fbbaPE5@ z8tclW_=?_#CHddPp0IBe2XH?M_9-L8P)6q2LnA5yDw$ z#Tz`i=0D&wrheIws1;wn%c#kt-T% zPjCd3=?eC!1doz0AlXlEbzyEhVwqrkjR!BQ#=nc9*JGijI zTP((Bte+u`b-yp4ztek2>G!~@3;v%^Q)3XXqg-RAYE`EIQwM4L?k5 z{}_kG)2UEmyYl9U=PoOq_U64wHJ{W@*$903L)VSU(y$5Wg6UDaCSX^zo+{vTG&idr zQj_N(vEt3yVO;5Em)XsoeSe$@UC(JCG5V*A#j9hcnC zMGyVz?8=@jC3~56E!+q5ES)P<5+Ki}AC>ia)cLd_eqieksqV4pod2l>&Ilzx8i)g; zP^~sDOK&7^_Q*H3=r`U7n_g6w3c{dVX1{*Ar)W@I#_!-KZhfLh`HUyu6p|r7&gE~n z88^xNt}%h(>nt1KKb5!`g%nDrbXDCJNb$^b^{+&e%7_XMFb9pul=~Zvq$mk@Oo;#V z(IQ?}ERbbiC50x9eKVFlQC5zj!{S7X$*rA-TL0YWj^FQ7`SJTmv4S0{56tK-axG6us6C%x zNS%xGlJOS9KXEH8uIuUk>x<6xY2OM)v|3<7W4%w%-nwm9zKNt2|(o zs?l%T@y3lXlq#TYK0afmPx+Ewti^*e$#p+y8=CG=;7S8?Gqi>+{P8&@bEXp4w^1GJ zo5{=g$dj5#5phl? zp;t0;gta{D`7d7B`HVvqQ?#jeJVZh)Zhb%E?N`@ainLZnbjgOrnZK&sG|@F|5V7ik z!N-WOR5&xblG~Nhop~=lzrIjT`k~i@Su$SX)1&hOML}0|yK?Cb1LkH_VZ;)0jX%}< zbRSO>*%T9^@TV|wRXL0si6c3fdd#% zQtM~*Ye?U~4L!spb&eUw%fj6to2b>4UAd(HX8HClWE#{h_E!pMQS|nqvi=QPGRHc> z7--=~K1-j~KHhJdQbuTk27a`5K9dX4lJ-Kb4R-mQIUAoxdcpGk(9eaL!xKwrC7w{9UOAv&y2Gle?!faRI6V0@$iF4!a3QtkK81< zl^?PME9`4qON5b3>%vF`c%wecP*Kse<8)K8L~BfTN&ho>T00`)HrpzN?ajoQQ_%^` zF&Wv6a{DX0hLDa$2c%j2YFT#S1O5R|fTP0L?&?&!%1t!}QyKX7xI{si7Tn9@KjB8=2Ho7Q)xRIPM*Cd30us*f@^WLIE(T$ z`HZ_>)F(eT3lo@*Kjk?>9^5Lpadz7Qs&P{8%`N=l@!{8_SHgU&@M~)Oe{`DKaLzs` z^X7IFnf&^rFV0!1kM`!;SV*T^93CSc;8wXu!`qgP&$S|_HjaUIS3d++$FXsL2A-SX z8Dl#wk(>~GVcrcbM!#(Ogm-EoP{Ci4QNCjNV%l(B9q}+RF>^ zoVl8n9MT0+Ju1b4-G4CMC{=do5VpiS&p&q}-uY~}B0Ss0O`S|&TO>T@+6R{$1lu~; z8u7?hO-BwKa75g^Vk5claDi!@vxPvFARt#kP7SXZFt^F_HZ*@^x#B&{JQT~8bsO+n z+z&qSY@!Jf`oAwKLuxluo`k2>a_wj$*e-#m6h}61t9qvf4>IiZ`XH2z8GfZxV{o%| zqOx4`6*yadV$;bMh_}$uTaUM<$C|CBz7t71D7IiAFguR!jFWHG(Xt{ za^OylYXGF}E#HFnul?tanuUXf zGek8T{%#w%oAt8_p274cT& zmk+O{5`Ij#28WJFG*aYGW-h@(wEbMXmQ!CO9ZQqJE?(inbXk*u)!5*&Pjfj7d{>@W z8kFS9#^AWZ|J^5Syvj%Y?t8nK#!|1O;ydCW&2$b56vb)@=+FwSBD(9+F4ft!V|(4K~(Y( zovrxVsOY=jXE=jADm)7gbCX>GP|-!+m&F0;rWG17n!V3n(mH5JcaVN@wp+XN`Rhe| z6`qhYE3aRwla|XJ4z;qC`ZYf&yZ5iz1Shr&aHWk={-0pV)EwWRa=s%zq4lzNyT6#M z;?_R;JD>5;$-{{c&c_W~HU4+RMvjBJjhXtk+IewI(e;=HlJ{^j?fSOr!j@L?kZ1b? z0T{*)Ur~U&53&TnA+AR(@Dw>>gJ5z#`+QxwAl4nuhvTUo1u{P~O<<^5HO@BNJZ7VM z-{goZ<%z{UkUzWhK8W+}Z1WO%%O(r_{MBs@C6bu@)=!X^30g?)BWNnqU)Hqn1UfGs zs0N|l-0uwypMN3TBFXogrDKyUSZs4RO+K$XNO(p z_=i?DI0(?)w=%*V(D7y*4!+bX>UW=eX4_xt?2x}Ba4ZT^UbTWU*77+WYRJ{+mfU%R z$b6`i|GH8s!uA91qz;xV>A41>_!6mg9sSX=R9~5%EV|n3+39jVU~!)9CwoM}+(*o!$=hnE zVL86@V0=@F)Nt=ojy8P{dqZ%!=|ny*;)gVC=4}0$YXHi^z`@^7&0ZFxu z3$bfZTY-y&0%Q6o>R&tjKDO^T$@diwskAHl_OJ zufOvC7nX)we{x zL%ENCLU@xN{YU`*SA}?Cmj%uW&g;k#p9Yin-C{u!`x9uYJW=I7cbJGN!K%0${)sEF zh4oSw`}bE|>&Agqi4`|r6P$d5pyLWB!RNQj&EoT)xI!BRPCsf8POR!5JCN&~O-8-_ zz>nEi9$60LdYx5f&*8rZx|B0UrW8gVyGiJn0ZsHfhqYf!-#gz(!npt z-dS~&w^v&Q-qDYN>!iPd7m8!g)ZK3l+_omz0%uX5O=R|rq*F4SsZ|;LWyjhNq|whZ zv`3cHbbx87%7rxOgZzn;Th7$A5` zhAy-hn}SG!t~JZeqd>2M4jgIZ3RUH8_1Ca0(4bfKf7`{oy04vKg|YtgFcssgfy0=f z-s%{XidJFpfvGN?<=3tpj{4?>qXE=8ug|wmPs16`B+p*E;Zl#8nkewTx(7mw(D;6? zSJK_dAcDPCHOhOFA&jk zG!Skr9<30{G|n97YfdAu(A~g<_VWN3j()j6@EL3Hh>Vj)1b#f(Z(2>DVMcpn)7B+D zwQ*{4gJT>T4)_E)A+}51=ky@9z%SBtZ#oO-tgN7R<eR=ONcR$Fl3d@+2aNT`}j2?%k>5@oW5eCO@*4cPTA_78RHpq}!N#t#Znj#DHA*(%B!MMXMI24H@fOIP@ zTfp>R8vL0W=%tiD8;YN=|9p{LDUPGy&!#}WQIygAU%$K)@KK24{@vQ|A7A;Au8c`2 zFRF4tCqX{qrgRr40kygaC-P^GL6d^I8B30|$Vcw|*!Gkchzii>*2o?|DlXae_``(d z38;ppvGeXrRIc7@GSxx|flWXc+v(g@KO^W&DP+hgM=id|of-&;p9s@w0|GQ}fGMKj z1Vl50DUht6@m6c~`>Q>=HOa$%q?WToS}r+JY=t2}%0rfB7O&==)!{e)qWtSNA9M5@ z{i0JNvs@@Us~H9r_)iqOMLPL>iQo70go--{#LT;*ADONASAJN9l)SNcGQG|Q1^sJ; zkd`(L1Lj_Zl+OJ2^Qmrq z9;}+$@d0x4wL+j7P7FKn`-`}kTOCr@B^gwv)V=neb-3I-vmwP5d0N*La4J&+Om@BB zG6dz)_~C=e$P?OP&$F-n9sMhzI*mEs2KLyY>n$ku7+Q&#`Lg04jT2X6QD2| zCjy|XtDs9{;hz}sXRn206UUXq6w5uZiP}qRl>G(Ph=(sMPBT?2@0Jx(!Ma2`N2T#o zl2?3tYZ|sK!{m(0O9*s<0StU}DoK;kq~CY6lVz7Vie^P4K|TMtzc}!dWCEL(I8ft$ zt}$7ke_V-zvOt=TFl^RWpc*C~K}!VsmtX`J7?GYkNYLjS`7-17*vd>B#-ML8*6Z1@ z-&!;Pw8jUpemsc8&kH|}u8(ZE>?4yT8b&S`!Q9w(BjRarYLEjp6kgTqrTc3YwKvh6 ze_l-FU)q?J{fl0sbK#82bnQp6Ydtlnc!AuGfAzsH_B^GP99#2}1PeN&l5tAZf+IORWhYb33AB~;X<_)_Fb&S(U7$0T3D2%?S$B#m_h%~Bs(r5=6X*PE_&vsD6ouCUxZ)o+ z(JN?p?w;5Bi`gH6w71G=+%{gl$FMs=r#sp53`@MBCmFFR3l+1P`VT)G+07{zrYj_m zx;=Qc!XE~-z%^kru_L}t;>*-LkmC%79YbHr1_TQCmK`D@kgAw@6J{SQS zuF%b@^9ASW;Xl7mQv+3)tPYWwWb{9B8i8({H!K){9tTr-k_`K7l~!a6VJp(d4u?{G z{+`5PI=YQ)HuB&oWK5p`=i_R{Jjs3fMr+JN%ADSX>D9*96Z!9O-T=K-C{Kft+J_9L zZ$HB?`Oj|n1jZ+KVEV}{a53A-#?1<3IK-1$wJsbDdOwquaheHZY3czrX{)ZDDFzgo zfX64DQv`zKcfMi5)i6JLdHp5KXyTgAq%j{9aL}o+L?bF(4$p)c+<6OgjuxW${f51^ zZWisFU-_V*j+?__xsCC$2I15x3;hA#l^jKB zx9Tl$Lp*U(bO33dlT$6bwf)Y~osbGCIDNc4&DS?w?tvSkjT>U3E$Z%f^M*zJ9E#-Q%k~}wwEV{qoj=Td z%fw5Cvwrc-JmX=_KydJPB?K!>y;+xWCwqmP- zJDCP4P{TiVcRv(lx>MUb?N$X>fO|9;Q#mhjp~lzM|=iWMTjPig9ZkRB>Zmx@xuEWq324h zTGc_X{9285O83LXz#Ds(JxkTBDOQuyPm18cSTd`z&gDgOBn-OF!Anotcq_s$v5w@| zUxh-0iN-Z6Rd195Y))OHmRuRME*=s^5cvLb!6JsH`#M^E(q3|NCRwE$)a3TP6!5VT zCp$=5dvb&j(l=x^CLbm%c3XC6 zOR&>AbOTGb2_q7Je^LwV?)kvv4&mN!6GT~Imcn9(}N=E#| zOrMY8m)L=0$i$-f$=A1M5AbD#&HGHGw}QI+Ybu4_3@+PS$v6F(6b9Ep6N9_8LYA^` zU0y_c&vO~(YvpZ%h|#q1X+V*`#hoMA zqqphzaRyzO^Bb#E9Ym(D{T3H~-u0j|v1KB_bZl7MY+V^SHxEt4_*20GeZ;%9soPRi z5u=^AAKpEURN!S}O00itvoGlC$KPha9#`XO+#OMYi_Zk^t84y(3*psyuPTDn z?535%eCC}0v6={(gIgJfg!HeQ}V>L z{;DJT2R^k!j9U%!Ms>16Uv@cqLF&r9(T8Hs^UrU(WjGM|qmXRL>EBY-j~wySyy7)! zcO{^#7U;r2mvv$$ox6BT`b8M@{&G9%G==%i9V4b>?36@F^R-PITW@^^}n}7?^Etl&#`z&e} zGo8z7uwUKp!CN?BPBSnE)!Fy9b?2R9WGVgP`m60-66(z_~s919s}4v<=1#h zes=Cte3*OJyLh9p=kC9|t5QddBym0i4Vh)2BG4=q*?nA7A{&#q)3O-D^rjyg>9Un! zf>xeIfHcVy0+>s)Trm0k(v~M-oMlt1Z0u~`dgP(Se47MFahiQ#g|FYs5n?!hz!1oM z`sTdZPEX8jvwZh&OLY|B*E|N0C5LQT9_Nq{TQw^0cky}`@A3Oz1VSzj`?&U`*NlfO z!ImNup}(tAlPjx5@6cNwvy%Z1+_{Yozt=0V*8)ppAs!aTR@h0ye|yv61-BD8}ea|bfz<-Pv0& zXQzlaT5kaWc%*S7v>OV4*L`Ewn__BlsO=vPY~xP`?+<#6%7j3=0LN{V5u#6H^x;t^ z!RJM*ZONC;JXS`MPk*1jh+hZ9H45rUC_N7^$zjuVRsXLkZaKql?UmCfM>2N4Oc*e zOSM)Oy^HL|Y_>Mskqp39Cb;(nY!0g1svM_CHS3qGah%#SkNY`y78eJF!Ty?C1+2S` zo84%tQk*|jd)Nr0Hv0bTWTR5*5OWof5>5dj^$eDnzVk2dX8KkT$ww0lVI;?P#l^b+ zt!evj;0ExiGKItp6Wb$H(^isjB5&ZMNcvq^bmQyuMo`xSdeNXGsZUcrlwcmr^%P-( zAY+hm5L9p+!#RTIK2R`Au3I|SA9L@<5%OJ>8=><^q}AX4)1B2QK_+jA78?j?rI_jb zH_UsGGJ&-YnuELOwDfx2gAKjuf2h?SlZ~}F&D+2b?vcdGoUSYr_3;Bs(r&t6m9i;6 z&yTQSk&3+^L97XZGA>hmN%MaFrpJ<@&=;Q1Rm+FzA-}f+Zd4=xUf&1Wbnydi+Vd6; zHS3RsZ(!XyPgf!qPty8Pou^KyMfG7^B;3T!LTKVn+N!yQ@uVKh?>~?RGSaum^^|GcXb6^9Sqz9-@>u!=uQ5uRC+Z z6f-CVCS9o!+E6GLi$q0O`3iRoLbw+JLbw@6Y~^~(jWhn%SWVRJ$z43cn9nw1DNg)l zxp7hem4QY9@ta+LzL5)|aEmF%)@y@F_WOqm(^LD`6q_<{f=x@NyH24%rCLB@%PZp? zml3(51lMb6(_W$h!76N_>7YoPBmh3{BA=K#|CFdhW--`j<$5<@95d7EovTQ;Mca(ZX&T@J`sb`Py0 z%n2A}rNTSXyuaWo4n~!sM>yxbTGsxqS}i&MuD>&X;-j+F`TN^PUaN~wWW`U|v%s5e zHjA1q%X)Pz#6;LDl76l0yi#n^le768g@@e|FmTr6Q{< zGretCrj`y9GM9hKN}z276P16PbxamLGRwa3g2|lk@dDSy1OMkGcNI+~uEc>eJ6EvXqGmj&2a>^J z%*bH9ecBF2mHZN%E~y_Lw+8fOO_~G?HVg(bG|k(rNY{|11Cdio(c>zzGAw&-fd^frdSjRauTJ*jbJN+04~*d~+S(dKtfyW`5OdNS?#Xoh46I=H zg}@M&u(9#tY~6z4pOS}&es6c{uStw&V6bK$ZIUMtxA*W1sqNiU4_w zeo7CP?@LG<3s4D064-%5LE^(QiJ`lPmsC7zg02{cyxWx6L#&q}U(-Qq!+_($MTZms zu%C4w-?%KlB_d$-Jt1sj(RO^qM`9w2*+o4{93Z124dB}5PVH9*x2BTrF24Om5+?hs zTvw}cmr&iwgT|o;%6pol$)al?pbOK@ls1CsY7rpN^ zD`|bQw2Ij~k)2roY`2iRYi9aG=Huq^$_y01;9Nre5aOrVRM_RFyUNjIe2pP}A#>UU zx22=yxrHWBU@omuy&yLiNkk<|J<=L{U}@a;=Aq?~h@vsVNDE?adVm z?(jxOnv4vX6}qftitAUa88Rr%%QeEr)~x&5vrFx{pP+YHloWCFn(sqHk*U$HUut zzcEpg@9}AgMaS+xpPaWZ<-^$_r4aQlNhe+Sn5Gdte_~~^99xW=f^+)0^Xe~-MD1kk zpE1Hn0V@)|(w}P<^e79h9GX`@u@EaAS?bRAWK<^A^3VsN>Bn&fEANo;ciIB$1x{|a z#nbs8-G!W`DH3JuA@5pFomgATXf1YasRT;lg1D(jv;~~~6Y-i$Rs*sxys|bqBoh_h zBnwtAyLGz>#c!E|wbg?xMV!P?kkq#?8jkptSvaG=VV`*0E1dA^$C_rLNKkB75Hghr zvVj1+Hdi!J&h0hgMlV|;nl`|C?o-s$i7=p+66v`?R?wIP5S061ip z+7x#f@_?Sxa_>rQ1w~rZXi|S`-z~w9!{O0j|0<~ac+Kkl8< zmR6qIFo^8S!201(4VBklbK`&S0TTeQJCKAd9g-@L zIryQ@;iC0)v;cQ8RIpzC(~E_KRg$6K$vl$5Yw@2fygW#ckbgUS^<)hUSXaKkUHYmudnUbe^bYcp1}!3RT-sp5BNtxZ@}c?Kmr!EH`2Fg6CZtskeujho=Y6>TNa z-?K{$^L*BfU26JMcetTxQf3PI@lp7cP0zwl>hBXT71u{MWLsFvGk*_fkXuqfNC}hAiO*&(caFUOM|5&z$X`_j{qnh?i@L$_HK+q~ zzcoQR&KfBAFXpCcEOvWlcDnUoq|Wh%&;gT z92CIW8ctom|CV+JV1!@He}qDNbeBLUy6MerGyw#Q-XO93Oz}Q5UhPtqLV{~wxl5}) z{+;=X<59^Vg1skgx&VTH2He=cmECQHe2YfYm~FW^&hm}IBx=*LKMl^G)>eki`t28| zj~%=KplXY+HT=QEhb-p;u>R@*6;WN@4jFX9Mf~}fAqiiIez%LJYbqSh{Emnl3cxIM zWlZ_AGvz*F#@>ucCtd+>JkSt#eMkt;78CEm|Cs-Jd+ZgYR;s-01{K&TZtAbHiLXzv z+wZRh|7oF#)s1l|_}I5vRDY*x#RI%L$E|jNInSn|KXL$g3C!m|=3f9#qE&%2b9VeQ+7Bd`E3gEWfj@k9!wMgb6fnR{uu?Tl%;j;=8zYvvZ~Va zfxUj8_kMWQ(${mBZPXrV#x8mDIx)zF|73KttNE+sBl3)Z#$_hA*8)-!Jp6sPX~S}O z>buTv(GnJ=(ttV2z^=>>ZauK8XlJ{4KsfwF4ErZ|Fi zM^tT~9{O&>$c|s-7d>IA(2Kd+8~X8ouJa5YPFI+zbfn$UmAXI2dvk>PYSvWOUK3AY z%xkNoz#6& zss5&$t$32RmZO{a5RVH-*}QZp5*-MgNOGPF3kg{@P1m;Z?6NKxowmb7w}1KglrZXV zT!I-=7!Nc407Z=420vb8bWJxeVPrTwo6|__eQ#I(!>9b!+@5r@RaGvnB3Q_?g96>` z#6EOq5D#`RoKdaxoXhR8StS$9ak^RP&y^D~P+B>1y}I!^PHn>{ko4KR=yR^_tKd}-PUx)5>d7@sif6H9fMOZEtV&-1vD1zw z?`Efc2StyIPKiSI2DY6OcAkhPYVW#WD< zk__iVU5UkL2T)=Jr?E7G^84^Vt;07&`y2=C$auC=L~hIS+}@cog|LxLS-jk}yp|Mk zDM(8OQgmwxa_cH=r+s4vye#j8!aBmrt!@^4m?R=2!hCqN3UXod73Z%2Mdfs;=EaI* zmXVjaMw6u0>fej+Xa#X1a=UIAj4a%gTPSAi&x<~ECRG4~&5Xv!idwBo7wRv6<|3jc z1Gw?=XRq1eYG34x%-YC3`IZ8&`tH(tnFV?W)+9o+mlp4~xb=Dx5xq-&BqQU>PEJoc zd2GT)u52hlL)KI*YZwPDmhctUj=fM}YD)p^u(_nAqCY_hA^))3S(`D-Wjbnx*e5k< zW9M-a3fGy$QpbUCt-U$b-2H8aP@{b{zv#}NMW-apxOMWb3ieu88`;=lMwisg!0PJl z;?EoDaJ3N&(V3gwOS*+tY$61Ux~{o~N=G2#m~q6?JQf){>ZJr)_cg-eecuP zL6epJc}cY7nP=9jLkPmAKl$5&=jNEN9p^y4-fywLquxtUO4w0Br$3(LB3sHuGzuYv zenb%VAK9c)hr|1-(Z(wz;Xa>O&;Y8EVnmjm1mLOT@d~MdDrno*9_NU$Z14PHZV($# zu+MW{`Yo19zg`2U(Bs678QUJxy#pVQLnp@nAUXxVh0q_My#PuV{dWcu$dvvEH|qb# zUjjfuqpJvPRPt7?9AnzPRyrJGucVUaFYQVBcku6B*$8?gRf%%ht?cXN-!Ps z284JcDzt(80TcQOh3Da&awqxSPxFV+LTqaEx1O}%vsw3we((ousn9B29Bh|$nasbX zOxqp6Wc!Lqtq|jl>)z01HH=p}$Fm!tk;3al-%r5 zGV0(EF^KZckGmJQ$2~*M&4*oFr5KZ1No)-!Z!xRxpDW$sw(9jh#3enejyiNc(m@Sx zPN|hYq}n^W;NSBgfp^HwSCwmJj)uaj+9L|cIF6!^eT=EplKvSeWX)6rxNA|lFO1I3 z-xUOOUM#9Tl*zUm*VkC>@?UGLnNU@7d$Po*kRHPf90uBQ8q5Jf(Qzi#i1~MaVr*+~ zUhia5KH~UB2z@Lk)U^1f?)s&msT!$bg+XKDct3r--k){yq!*Vrhm#`L$C~a7D{xiJ zgWCB^phr&Txaax6DtJk+yixhFxd5i!S4=Mf)KJUxBR)@Zeu~-Zgq0kEu2LLNAds8- z%$hbW(xUK4)CKF)(=imq&|V9*q}w@hSX%3+XPO@@iECdJ8u9izQmKe1G&Y^`iYe~R zkK%qy{rKD+*tS#v0x((dwaZx?GfLcWr9~W-Ir5EehD&)Hjwh&MlC>YOLn;zM>-)1c z>qrBp2OAa9jLs~Bc4R=&sjnQRTBdR)i>a}&VYA^4`6ihY2w~YX>PTVuCJ^vdAmGkP z84l0FCd?>xmzLjnx&+kV$C1Ne=AVyE0sMPMovG}$NeY;OYBWK}5l{!s3*pVEosYzs zeIyw;Y+5cI-3wrH1zcdy6rQ;VcbWD?+tvcIS=LA<_Z=>ua?0~+00Q4+ZZW8?D=Aq16$VOpu(u+2 zlmZa2?GtZKttbudMFHXwl&~HU8@MMv6bi=>x$^%RKwuhxV~wft3uv@tQr=){1im>` z>4wTZOF3$Yg6Yuy@_0)Z#21+g*s@Z@)Byn!IG7vCw2hJX7)+?#g9zD(-?t*+v>+-N zF!vvGJaP>c0;=a4GN9nnc#^;7L=7F0D)FYSyJ<%R=oy!FIq@dbfQ~=;Br7mtS6Y6q zZGnKt*I8B5T2r+3cBcP^P`u|qEG*C!;D4u%hNN44dXXZk;(F;64$xg6L8>@y>0!+ZY%aca)XnwJ|WTOu;{mTX^7! z%`pKZ_$B74pzo>UV&my!;cktgZsF2ugSyrH`9HOBCe6&t7)d76vQ$`6Sn=3jXd;)PwOueC6-1;xN2Cd_q_GUH z^ww#d!+lL{AI`l?^;yVVHJRTQLJ;vID8zdk8kj{fD9T5q)89g{|MJMv=7d*OS4>*4 z9m`b>8#)jgIEXZ4-s3=|`6JS1;Vv(cu@IdY2#=s~@JpzlWP80+F=V+%?Ksix(r0}~ za8~BtwQY<&G-lk5xTd+6Mo^GX@HC^iC#I^psmlACYQkQ4vs76qpQ$NhN!6Rsd|AS| zJi)qhH{VdMmX`rkvt0D6xm4qYSj9CX`Spx!|ItF*rUu?;zw%5U^g*Q2wQ!r`KD)z7 z5`%Tck1&R?If{geDoGDd8i%+fyHLbu~3f=yyoyE%L*v(~ufJhx4hN{u0nQH`Y- zmM$9x%krTbDl7FdWWaoZIT|n+GA+TQ4If&V;dTzdfJwbR|@MrZ)u3QgBMR!0(ipe^!F$sV&?opGZu7lyfe~oc=rY30J#kBVk(l+7-B-a|@ua4cAkFrV$7_efF4}w~r?)WuhE(uD_Du&)^N#V|a{BUO< zF8OYSJa&IVbhRIj!MV^_3_mU>_G3P8BB}|vLxa4$me0}4KR3afO6tEjVW4@tPnUr| z{L{6eDAa4l{v4P8&T4u;Ty*QlcF+`lfl-V<8%v?9Nj&tRc-BN8i-9jiDSx zhi1eZJ^XXHuu*-<@3#sU8;kRNf*B64CIyBzHq>F(o1*-9oR}A(6~=rR-)ufo#m^TH z5ziGTYA%&vUM!j55&Q1s>gQWu8NjTs*!~+>Gduqa-{)Z}NDKCUY0!NzMTmqm{b?MW z7ab5t-4d66cW6cSez|cg!I&571+OEX=XR*cvblow9^KX3pv@8d&N;LoO>hxi(Z#VK z?5ehG9W%uDggJouJni^GwZi|7?Jisu3);AU{2%|l_Pq~FM-SR7Lj()FJb1J9oU0EF zG|nqdB{t~Kdd>2q^tvTHuHIF+iQTH~8ZR_klQQ9I@3EqPHrpWk)C!g`vjNBK!&Sk~ zb2YuV?&lZO4!icVHN@O$OU5zYY8>1N;}K=Qhh_V^ntkY99-et?8wjdqc^E2eI0eE(%fwrwaymIlzXN(W4@T8-OY5$A+)Qa z&RJ?lZgwJL|H;n2gwPJtvBpO9Om8z@gdbmTKYWVdQHw$A70hJYSZ%aP6!$I_XG}$c zA4dVTPXuMF)*PA3fZfi5&_R}Sc*XC{B)>PlAFTtV2k=-&B!ZX^Oh+he*quBPxuTVX-UJGxj4mVsOL9oPtt@ zt{krdO_TP{1|@dm7K#IFki~GqIk*EIY^}Z-TS}lm(NJYt4W9!W!u>4XO%s}E>wV*3Tz}izYk7fUUpL`O>UnrASs21#s>?pxCx4&s zut`*sc7Q(Oc>2$pDfjqd2m?)WzjfK135%a5^?^pS4&fCYoZfI}&0Unf?Vs^LuaBVd zi@|_d3xh?`X-^^1d(UZS%T4>P<2R=i2KcsjJkp*9g~h|K%TxwBH{ys2&N0mVuCLkC zh5r-XDdg*Qos8)$!W(etcwO-!0AuIrE!#(%1UuKwxMx zj{bWzc*!IX(`PN(Or|l<37d!egodT3K7oz?BFKq8J}_$WDM)9&6f_=T(%-lY@iEtk z=p`C>D$t8e9zvnh3tEk99LdyvC!OxkN%Jvr`mi4fOFzPN)OcK#BTfTfqOx0)Ba;uK z>l3P#S%SVn&l!ffQlhdlYC+>8On#R3wYZi)YD376LrFlPa;cxo)j{1hQm-qv zeS6QZ&qUcJxZ3x{OdfZ;)ArnNw}4M_YM8-iTE=3`Nagp@;D7#CK-Pgs4%oZ2^;9Xyx z-wbW`tha-cfBuR-%e#%McaUYt9n9u{7)V!Wjo{MtC^S>tqC_fee?SPjtwk$P);dm; z+P&n_Bg$8UgbQ}_s(KGqQ4H9%ePq5plrLlQ1?z^_)8#{ki-0p* z(=u!6%+orXV5t;*P{;`*h`?$G8eJ?G0pd3Btu@p0rLguHFJ(lRIJsEKg2#eq*>6HY z>m9tL{&kH3ivZXBjr7MYTL_xhI`ttxMzZ>rJo=q!+i3Q`Kx|@?aw_U+zp9;WFFbx(~s7BQM~}y>8X|DvMUJ^Y4>s@J}xI*>GV*s z-tntz462TSXo)s-%yfwj9pX7h z`E^@g*yj(O}U{9@@mDg-$mQ*WZA<{+O_7L)(`k1I|t@r=jYIAp_AwYblOIw|qUD8e~ix zJ8ZdH1PPxs^`VMy$SfYEO&|4ewb=+OwhETYGIVKrU2*YfPoqoXSN~-?4J=M(SM^rBLRcnfsWDI&4Wf#1v z^Sy&9P6sU&MugKsKQ}USNKf|&RamsBBGR-GX&*!zdiT~Flvv%4YIg9oVls)ux11hx|sho_UYlk0mP;)VDYP6zB>U{5eW$6U5(M;7DYtbpBVHg#*$<*Zml%7?m?#9T^q{f@>^F=J+J`Ipupa)4#P`>^#wZQ+HjttBnduRdfh6ho zqa5l1H=(&rIe!Y<$gAN>y4zD*L2+85_ayd7iWn3^K>L#}{qBKCyIAt~mxlPx0}lqmnA4us1Cm zh%_ar+C$i(p7#+JdkjQD5ax4#HE#pdPSMbGk&!Jgy zRgtT(^Aoq3uT0C?4c^iSzpD@$DAJAC6aFh;a!RtGRrGxKcy2Qyh&y$VrNY)NqH%@J zR_~`33|qN;q_k^%OcQZ>VCdX5v|=%LXUD@I*ETp?&|ymsM&b|{A;=?wWLRw(3Z8&Kl-3+u$}coi$OCs*~>|y0l>cRU70k)ut*4 zWo{o&mW;hNtMlpY=gZ5gu&XI@T>taQw~`k+D-rX7bv)Vhn`C)pTPkY+z(!N5I53=5*!QH@0W_ zlT3%f)m2M6{wy+37I}AIbsuDu*yj^6wZ{CLD za+z%Z62X3_R9H`At7pwN;G^TU7tCtNW=9J}y3Sa6x{D~U{waM*3VxV>|L-?Jq)9Bh zYD(qvq8DBg5s{IRN^w*?hMp~k8B3`y`0~5o46C>Zsd+vBHx>gKzlwh4EffuAot7JEJMVl%I!A==OpB} z;;`MVAD@vZ79T(G*j=A(mN{Ji>j6nXi*ce~ppj`eQcQceF}jlB(uA4w?2{b)1o`ff z^Hkb9-ulSKfMYCvn?4#|_&>P;nd`ubDu?6a(}Iq!E}arXA#H7K3{me*8X%H&MH6Pal*!4+$?b>o`)6eyi@G7@KMFgkEFfa-C#!id_E!cAtb0>nAy=oBj^iJ^ zHb$0CJw`{BfilB$M!SkF4@;qb{@I5;)boGi4n5#AKC?lJj*i?>QBjq4zh40+)5$qB zTz@N2?~WL`?Dh!`{wgz*G4)?#H>`TuIaTKYLHueC2{}7hYsY5}{C6Bg$!nY@>@>me zJS8gbwchb>zP;{rIb&_APB1&XV#JFu-#D;Hy|DM*4|*zvA_z~0V6;YT3{#24j6 zjFpD2de61C?db+(4UK_4i38|H)M(5q2C4g)HxARl>iZY)AIWT~HvIIbS2QXR$jmUC@>o0)bT84@G?W!UimR zb>$!N{X4(5jt-{p!EZ%BWE4m3)!9b6xEEJh7IAD{6l$58h@$P73 zv;uF}dknwW>opEOU5cR-imt5{ov5_;7#I{0WJEi)w8z1!Rx~xAhMF1?@Gk4^sX8&! zX1O=FF^K3MaZYY{?aXABnl!i{Py1X4na;PpiHeWE9`)jDI;Z`UTOHfC3*y+%zWPv%~SFdK)ceAUi7S(U(ZOpiBj6wQ5Tp!v8stdfG=Fa_%T~t5yLOnRn_YO{Jx95yUOZLcwVN3SRP%w)S z`}o!^U^}wKy%JvohXU-k0+~VBuIs9zc$k@c8@q!Y7h2inD_aq4StrLnL4fzjMM^W~ zh35#v2KttBm$l7OyO_FJnu=dE6|UD;m#1{!Tu%*kD+Bb8Hr}3|i2~Aln!x&Wz{8s+ zA%O@NlG2)yU}%YxbBUAbH{Gv+LB;jdru{vI_lGC`@hB6}9iqg$nBPEFjne24x18@t zGs^^5t7WWkwrZusp8ee7M1jawNzKe>@2!bShtW6?yqLf8)#jtqEf=dcDOb|h{3 z(lAA3ragw#Mcn#@MxPbE;K}k^rWMJ}7BmZqA9ax>nKRjG&JDUa8UGftTUDI)C;TIQ z6Z?aC8Tl>>Z;1~8jIYxFF>D$n)EpaBvlyRm+n4>Y`^_3b!aVSST~$e4Jr8*CBZm>9 z(BWa-<-zR1lidZs%fr!hNk0J$)l^>V?howp3JO{c-cC$G2U=Xuza`a-2eHXCYgp3o z;}<%`j9bLiQ5U$H*vE`x7_Uif$xKKp62yJC^faqU1X{+)qZPDqU5FI{81^KARRI-A z*G-%G8O~Ta1{F3Pot>9K!IRZa4-6|gfB*hHT%;FYVpMY`?w!?LL(1piH0sFvGQ%w1 zuawR>@J?@m@Tar-E0|g!tPl&O;e@-%?LT#c1rSz#!MeH>7#0>5U-I*>HZF>J2_FRq zxHi(qKwQ%W*Q){#x}3W}(jpKC)NO_fwb<_8Cu3$FOoKqD;udwdOw%7Z`rYZhN3Y}L zB%^Vk$wwj%sP38lMCAhz4xf}0?@tBp_Z$1K>Oz|R@5=Ksr;brT-a?tDm(pwTwWq&xh>!Jr_|_D?}k(c|CT>cwy-y~Md&f5S#<&DUf zKkH@6f6D=XtnS3RaCh^Vd8^)n2Non1FE()o~DlIe+dZvm%0NrnF=$Nyf)Lnf>8OiZ=>_#TmDbSh-u9reF~FJOQvp5@b$ zPEzGt{Ss&+P}d?i;5dwsuQ|-x;tppsQuU9}Ix1V+Ds^rU`ASBdyvzC=F4ghT?Iu12 zbCF&Vyv~zRd0=*fF-o(n?l!vcfoEx5t`}__fc0{3_)`>Rwqx+PO+jy}ML;u1g>R@3 zg;$GN(W3^pNJth|-)L(8VX~YKADq6CMy_*%yUGy|&N@pnJQEXEK-2ypNLf}v!Ni0} zAcW_dF5K`Yrn4)KpIW)mp{*&U!gDTnGxHv0na6*mOo(|Z&1bBacj@m3uX!^758n0Q zGF>VBn=Dd3Jbcf)+xA9~A?;mpMbdc-2FG0-_92oVyFRi0z)ng>y70Z0JiVC?0iD#b z&TI>v4>#Hl2HGZ(e;Quid>X=;5d2;}#BLaMI`spXN0GO2-6rK@J%!o9*BjAQxlH}o zxL9F9{V=UEo{+$$8%~~p$Awis!$qr~HCYb7p#8ODu+Vqu)9O#xqpaBsvNim%Vzgb@ z$SKPty~l+z4PLH4^ZbM+yO<4_)AzIzZOD++h&sUTP(Pd4LLn^@9Fgrk&TtT~ND`+o zJt@DL?ZRbxnj@<#+VJrpUw#6!T4Mxl0#PtmIm1DsB58uc_+J!yE)EDK5r`J)rrlJ= z2mAB!qfrsG&ydRGAd};Hn~z@D4m)JUp&*)+vMlg9zxXSsSf*V0iQww%zk@eC2!H`^ zg>zo+1xd^0!@sDtlp=L@du-o)zBe}Ui}r8=lGl7AvI3W>w5uPOx+HnKZ;SA2_swFd zg}$e<^H>QTLcTF%_UB__&%01I3Fo5ZW3EHi^K$1>;VvKikFxgeUIHsF>$vWYmgUe< zxx+U!cLXTX!$q_q3K5WH*zM_$4?J6d!gVe@+2)fHNI-= zS8`r8l~x7XxyWAX!UK!-TRDY?gTlv#8#gmQX`#yBXP=Qvue=$ZZPQDXPq@*(5>7_R zM@_*;(OF-QBAXf{*z9pb78J*-Fip`Bw!r1LXm=wZ9}x;r91$DT3=>u1B&r*eDIugY6_SGvIE7E%*ejMjSy(KAC6vc9<`Q10%tgQhP0LVhyN=euMhUf&7EAMG2LKb7t5)lA}f5t=8&Jd8Hye>%H+_qN1m zT7MkS@h=3SwSdC{$Z9wF67{~6ly%&5j_W&}xgpyH$f`|l>{$8vd;KYJK!pq27%*}A z?M|q^@g=5ZqK}*Bw)qXiOn~7hP7?l#jrolQHrLJ!& zTpjS9W1Wjd4dlx899q9(id?3_+tC}DT4lpugC3z^kZcafV0`%JO}f#VbaeJqx7&@( zk0{G9Tu%?D4H8U~lfLdeHvEQm>_zUczPOp@{p8wUncXk6-P@w2zJN6DS!x+xJ)s>sCR7_tCgwjQQWM?3RcrDFxIls ztxdI5mQd1v)Q8rvdjufcXU*s@nrj-;Sad@+7fETp{+zR?(*5`uw>^H;yBiLaz|>#X zi~--d8gFx4-&7(q zOg$;@*ka@Pjdq2*&vtK{mw>mF#Ya$vy<6yu`yG+|Zr?V&;Xz7mW}<4aC)&doWji0X zRISg&__L#J)v*I~RGa_YGF^9_H=5mfVNn|`42>j7bFE?dud$ zg^Wn7Cx1rim$dmalF}*$Vmv$(P(1pj2CZBa{JwftWSB>*vq>Dy=E(jWosoip>Tc0O zYyZ_Z=qH*+k)svW;Q|!(bz~*k#PTiYL)b2uQDMKRHH}cPX6p<_t*4M zoYtJeeQBXw81b0>B~^Dq`R9bqR&G)14fFICvQBflTN2uxLwXPcdDM`PuR2tecyZqQ-g9_M31k_T-j&W?!v=C+<}tiYyf{OL>z{#A(7sDV z+8glS`SH%NS6`01^`$$}!|{y5M0{nCchJ_7OQCO|dxtH8@i%l&_A#`NF}=*Tx zIb}Er*Zr#96i2HY1DOiiP$yD#P+k0d_1*T(WCBR8av#8plbA-uRp%vD4_f$SRjJ*> zlfP~T$kD-HReZoD8suI1p-Q;Xmfzw;N3ub7@S5o>dGWs?rz@;wC!dShP z^7VI#)LKSG5EoX3zHf5&I&Z%pS;i%vU}a!DO(U+P22}~jqyPOa@p^(sv8i0%-m7fL z{|g<|EWqUQZ{GUV{!ryx&KqU9jMtm*c#JM0aiqXI-oeTG%OieaKZh3>==MLO75pkI zS}(GpNGBk|uQYdTV*ZPh5gO7Ga`KUs$Y_N8f0I{~N8^?Zw5Ob33hEe@0b_PweF?TQ zMlI!|@E^E2-r21lqjdu`{R`BLE`XO(FuQ|z#&^!N6oEw9gMCZ*bk2_U=Ebh|K%^ZnOIz7;c z@n=A#Hc-Bk{nLfB869$^TD&MJc;F!r$4D-N&c{kEI=df+)_$IK+n@dnPXG5<9Xa=d;D#@Kz}Gz} zQNK$_vZzr?Qn}{ib>$l~vQhGNC#&Q^4aQd$dh$2T7s_^SoaOFUU*%Gh=`~`Ta5J^e zpD%5Qm78PYl}mj>7U>p-e~EiKOW1)#wc^py2_PjUpEd z?*nUC%_ru!KE>!VNlEtE?uQD?m`_tBJBgOfqb`E-D)-Um?M{#<3uk^Ee5?qj5GrZ_R!9eeWY0GoBG3>x%X`o5}kdU zfr3|x*YX(C^iEXhT+XvH=~Ej}qI9?btz;FB96r$?Yn@MMEMHqgD|iGq+-(Ar)72{IDmKMCcCj+h_GUoVk2eHSPj@9qV}a1uYd^&$*DBLG=d(qYQ4Dn z2m8P08SaO?7SHSG?SoFJsroX}E=M{Ft*5D@%Yk|}z6kDyaca^tPk z+p3W*c@XcV&vwbOIZboLGQLeAk~t82D`tu4utwgdh~oGY_nzFA{M7v53OQ`3~;^d`ggG>%Un?tPQ3164Xz1AA#yyiSu? z?}tq{OKL_3%NqfB2X*p^aaeThn4hUnsnjVx6cO)+E*ij|DC*(2sROgPH(lBR^F@v_ z|Lvenn+@3Yk*8+4{8m%wQqAvW#~f4xHX7kLlzeXLo47UQMf!xLGGo~f-n~E@kZty> zZ&X0cr(vgTGUx|onrqfB&2_~}u znpfxAKUqBCc7x2PPdinosGmnh9$n{_+R|6Ny^OE)WVGXBWo=dNRK1XEy)W{k=78N( z>`JOx!wl_;34x!G>{qQcDzj$Z z+85E!AC~J$b^R`MH>Nz6t{B=m@TNb#qSLXPW_Vf=!O_AASRJ; zDB=43V#!lREQTed?|(08?UFU?B2(fc|LOM(1|;&}Yut#b2~->sUGj9VGk$1BFx8?R ze+{h{PVjt|%kwmm;o-9=-g9Y-O{6HAF&NlC?3$7Orr11S5t3{e7cV7IB-ftOK(#|O zfa%NL{B4TPeO@*{Q<-o;FYy-*Dl6d9=7s5RjUDoB$Rqt-nG{EfO*EcXfN;Mm(`Wx< zB-1ZsK}d5rB&$92XBtiI1@P~?@+K1*3va%;4VLrKNtKO^tpalUz%=Y10Sh(S+NA_tlUvT=(O6URh{DtdVgoFkCDI_Nz{iZhp zky7#za4Ymcc|)?iEmThyQZd=s3hFbJKz1AjEX;-11g3>suI$>m%QT%p^Uy4~t9Pnm zY3k!ZGNnI%7Lz@IHx*Bk@1Qv_205)ow~CTuW2WuW0(#=vA^&IS@ZJQdPOkwubA_r9 z`nKFUui35`{n~!CdO%b6L(B78qIoB?&t7A(cuNVmTdu&mkV-1 zo#9}Q46u=aDR1E3W`w5Qwt-@WdiLH@rMfc*=mnhOgE8JaF0I1NsrYSO<&JwKeG|Sd zXkZBeK%WBz>s9`UJ-v%`m|+x8kWvKL0@lLSTn*2TT;Dmrk=&p(Rbm&%u>r%}!OhC;ioFy;<`q-`C_z=n!*tMrc-8 zl)zAz^`K>u3Bo7=n-=1Y^{$4|8>Q-S8lV-%EdIX!OM>_Z1Jnu3`v>pS86<=MZ0Um9 zLk<|Cl7cICWh6}3idpl15MrS{^?g3`5EVEg1hW6q$z#vodRTefmv@%(DNxd{5iOxS z(3#!KQ<@`qk)PNee!hD8&!nnzbojBz0$vikUauWcX0a}vz$-KDNW{Wfl@x2$fZoJtUGrw;7@r4ekJ?L2STnnG$ee2C{4^;vV^|oOXG= zrml}We`$u<7rOZpg)&P2c{p@zK+Qi_RTKZB(O=LeCas;5E)2OhC?8|Ka4~!8_nR0! z@BN-1IFq2jG{m08(sxKKsZtEge6r|*knPgsFModetz{+fWP@mAQ+nB(3v`&}oMU{S z;~!yT$3RqLAeXTaTtTyL8jog(%_oS>{MF@oP`0+5swZh*$*j&)qU`LyK|ia1fpP44 zH{!+6cRpmWyB%m>BE>9#%}g zL$tCJB$vRB0dw>F$iRLUQ1*L7&wqLBs^g=Vt248y-vbgbEuQ? z<8O@MWnt%;Mo*tR=s#o~w|5n+tc?$lgg&U=@|igg%0&A{3rJb8fxj+~Pxntn>zT=I z`Yez=)2I+dwU61|#pktt`Q81UU_lgl8bhtfZPgn_jtaE|(1c+BkcfN^$!z*;GjTsl z@U^eqPgb(TLnuHk_hoQi=ANq&V0TKBnJ&L|N$%%1d^@P_8)#>j8&mT^)xfR!AgG!b zH0E|jcvf|p?9w|wzIBNdp3K2tr;}*c#9Xe#?V-^brrCc5vBBl1KA}4y7<(B*3(i2M zs96*)NytVyPe4YnEVQ$Ko(XF4z$WDM~JIOn7WZa6hewo)=Jac|&4&Q&NU>CjxN_BAmt zxg>89m&OoZGU7^*wIrH4VbA)!M5BA+@pRCjdo@pDS_5=bf;kKLo;l%~mq?|Y3OH=x zLDfiiT8~&imB_lSN=CBUzdbFr3(30nqun@0+(@aWanDqQ9%@4mHH9FIZDZSP;%ItbKcRBFu=<9wSVw$#_O_hER!9t_Gt4M- zK-Sgb zQgbnWf;0jKjCC65$3+M61X(DN=LHS9QKk!FQ1=C;0}cPf0aP3zIotzWg9PUu=P*2D zs%5srJ^(kV5@mkNW9jNz)E)*{{?X*G9TR~|1XB_&5Z9qiDC_)Ak09r3)zJfotwdRm z9Ex9bwGXp@MB$VQ970BeWHZ0y!S(;?G11niVRvbw(~5D*B=R|}(txWtZlPs~I!>h! zX?M@*^xTESYJ$M4h$uo|&s8$*p@XGw;5!%Ynob8!{!yC!Z^vEbwwUeU>Ir6$(HAA} z(jXF*(UtwxvdBqz770g*4=TOXa@I8eJu#b;p1b8r;rq+*Jfi9dd~0GPy-ZHvm;iCz zIF?V>4UV~t4%Qik_#K*}y-L+x0{N!OJE7_b>fmJNu+?@!#7?HGG7`Qaljq*XHS_RD z@cPvL!6fm0bo3d&-vH<#|uC14zDs<`+%lp4b-YNYrYoPk(k!8k*_mfM* z>?%ZM`}!TIyx5jpM-PLFjMS_s=#KH9jA{;qhtUB8)0G88kz8jA<(ASpNOokzL({Mx z9=|s(kzzl>I6@3n{Oi3?nQRf1r=%j`Z`yfgNvRCp&v!OkjeK+p6bed2qe3=-$l5$5 zvD!Kr1x-hbXKNPl>vKaJ7x6jN!rh?t%j*2iO)S5E-`LfWtTB3Ex!gi^%;OOnt5F?t z`KggJ`$9L|_=1B1mA$9_cTCixQ6b32iK5)U5SDQ^AN8R1_)W9<^hhRL!lDGdE;A^n zPhP)b|Fn;B`~K!)*N-PB-pe)!p4lz*x=^t0)#p8hU)w_KjOjfO*$a02ep)+D`Angl z^}}1R?uBx%;-@38smyb{41yMt!+KrCMgw<+!_>B+gzZd)Ox zei5G@B`Eo%B$> z3ad#Al*{}?T{zg)>)&~UC*m>mJIq+e6+8aods<@`+G)eoI#oN&Xt5b(5FI0P?cX({ zl%~42E|=ZsPLyjB!RrR7*KM`l%#Z9uDTxiFxnqw7uw_Y{4K66j{g~{&IeCmaX%INf zX;-8emxyovM#8ZzD>>bqF+B3ua|2WebDH|9rBl<^`nVmZ9ofFP*-ZC zQYhHl5Kxpbz3t7)4V>brAq1A7!cBp9OzusLPDR`u7h?sdH?JeTmO zVVJvWeJ7g!ZI7Lm>=sZkRutsdwpZ;O=1b?REVsjafuPG^U|u;D!}`fJkWlb}p283` zwaX@U6Pf-QXOM5L-1kdndKYAP*?CN4c-UBxgKg8qcUf&)7s7~xSPt1%_^x3VcUafz z;ka7!Of$`S5GJs({S+B#1zJ*U&-~ivBKYnevQd{^MPeRiFKu`J$4H7W%A_-o=>ePB zW|UY~7W1w;GD=e2OB>f+)Q6^v^M3zPZqFwZAL=%NtP&Fk=6KF0fV8gL408}^?#K5U z6*Par5EN|own}_iRlXw|cplE{NV{4m&io$sDT-sWnQx76_zIknL(L$WsmaR=fXy@k z6@ZL$SG70!Q%#pbro~m60B2S*)-t9v?z6I*0?}L9zVUm~M?KJq&uTE8kNVi)8*pKW z*B|F0kscWdB9bidHpOd+kj|vS*4zNI`T3Uteup*BiL#sfx2!HLQ2Osyahn-7c_jxHly{zn3^rx+D`e`C?`^) zRz9)3OE0%*M){f?=$|QZa%y4MUq^K1?^>@r7&8RG&YR4BPW9tY14+rWfg{K%tckm> zl=*6F{L5Uq^N~V*ZYGRSAHMY+O(FtC;=$;xZ3YE>q(y{0yweYte06s^5RG0aE>OyN z$@S>9^SxU#O&QsiSBiOs^4k~QOdCfX4Jc7pfvDl1xu~CvTF5huw-vJPkkY3p)m(Xu zS6&?e7b}8O|3w;%!pc zRPW!z)=@?a1b{sGZYnx z1G=rG-C2-dS3!2}_;*BtyMN;CpFj^yvrg=3?bk-OJi%28jw$fTDRM=UsrHIoN&U-d zPdx3PIs0vWJP^KTQ&YF%yJ|C^$+MXQp_B$dskbot-v7f3huPea%aygdTc7VqUK~f@ z(c}V1`9MGMmy@-QoC>oh5MQY5%T~V6Y2}PKKwU(}!iaf^w?uU0B1(UYroI%Ov@u`3 zA23#5q)K~<>~Hn)z^}W+Q9h3Y8d{`cf~2@P8?I`dgsbpFp_#(Q-P&`5F&pxh}KxRd;VsT#NEHKk6mK>SWX)Oiu(+|uu&6Z=+g6eB0>C`LqZRpsJm z`QP;ZyZA(1SJA_gb!jb@o4W0Z!hl(TR|y_^wSdSSaub+HTw`B9W!zqeW^Y=pdkxBv z7buTfjI~ULC6xWMJ7a^(o&V_a^&BJ1FP>gOa|+sItbQETbbv&BSbU<{(huz}Kl7ig zHqN4R=m{XUSpABI{eA^K%BoBZ%)G**Mr7rz922HBFTF>tVT^JozcRI;+I_t?4JK&l ziaH&Y^4vD&zQK>12u5{BSx<8V$!no(^BhMI?sb!I)M}r*eD)3M_6yN8a#1r1{^0)F z;%JL^T3LAUk0GjnzTdO72ZQb#T7o8&#czb{-TN#vPkT3kA%Kc{gdOrG~c_pcUE zIcFF2^+>xzgeKccX34$G*%wrURdoGXr_TnV=bv!UDg`Zv$djjA4)e=b6k`pMGCje{ z6WuuVM;X1_xlw2upq)p$n|UT8S5U@T>mZ!?@Q8zjCCvG9xtveB8)Z0Yl){?+))IPd zswOb%oL2N4Gl+V_Q0etoloe`~MF|v*MjM~jsvyp$EuX7m>6k72%ssD1ES)F{r=Te- zKjk)$4RW7KXY5j$;l1(79U74kp^RE=4ir*+Z~;isAqDcQ@Su)!FP~bGOdR&Evges4 zRfWh}4Wj~^C~(2Z2HpTF-Zk~{LmB?uZO$I5gI|}Erx*M#MJSE#f#ySGZ7+@8v3O;0 zL|f5YNcC!fv5^$mg_bN<&Av$Zn6m9HN17nHUKXBV^{N^+zqyB8qT-YzO1OK+;{2JI)aS_brQ;uI`ZRKIt{- zn+|+W-<+10O+%KDGp7Ow>*ADRpEc~Bup+y9M8eJsSUd*`IrFyL*ON2C(QS2x_LW9oeK z2lXX8{d_zl-}$%sGo`aT5kb4o1>~gNLP7DVkvI`#LOCmJg}+nsA71qq<3W|wRFH^4 zTS2dBX%vDkMi+r|Ux~klldb(ktYosE-^q#0evQ5TTIisS@qL%8xiO~gw=QV7&-Dm>3w zoKFJpZyc`!tL@5wGKFmHcIul3#N&n1VUu%O4+r9~MI7fdOW}}`=?#>1LO`*T&_Ydm zC$lNMXy)_DNYusiO{b645(AB|srLF0)X^-VfEfoLnq$pZ8-zo;D?#&qkErq6&cfEN zgP+Z!yGDL~9Y_SI{}aJ0wGwaF+3Yl|PG8I8p@X9452WwBT@|nW7(_v%&y$r538IJX zB&irz>bgVMp+7le#zv*lt$4=mJ-u{B=Y&+(lm-VY3n-)IU+IKd{&K=Go_hB(BgEW! zi7!%FqNm@i&*sldMo&K0Z4~EoO9ZcrW?yNTY5DHR-S2>_WQ@I@lJR9RQ=2Y)y{*sz z4qw1(LTk5uVmTyvq6W#b=IdT&tO>d?YF<^we4#)QYC^%=r%&31E4?pNN03)0e1ern zYQY9SUYA}j|3D!NV4D?1$dlp$iH~N>Blw#Xqh@pOe&)!@piqtMe#^h5xxjG}{zJj> zC-%=6Q^O<^jZaS*$G2wvHz5$sQqhqRP-VCR_44!ywQs??wscx$)=YaU%DCOsDC173{Pk{f ztWr^}-(G7k6G8|$k9*e#O1*9DLIutu4_GQ8O@H-B(D;B~-J96jG`Vc7!G%O5Q1~6C z1bPZ+W0R7Ges`^1W~{vuRN2lRthBt&6PH-MICMntj6ObQ{U8EFmlt^H&oL#GQdmh& zG>^N@T^^?x!MmKRyrHa#n&a+_o>LS^IweD?8AS(oT@;cok&KPMHXh7vPkEnK42-e3 ziNZyzJUfNj0M`6q4)N{tkIK&@{;l+scwYGnH^kqs&(x5|LZtyEZ&v7B3Z`pk@9=~~ z*s1mGO2^gK)W31=6lWPEa9aXdAU$gVl&CWJwllp-0=b(S*8!cnB>mdnA;VL?={3|G ze$<>gtrhWFAF}y`-+`HDx8qavm3HP;{jQI_P=1X%wUB44=^1`~USP>(B3qWbBUp%Z z34~Znkz9U{B-SrB*G!(Ps(J1EX*zpOZ6r>M5ra16b{iHb$Y9n1m(|6L`gbC>n@JPBW6W|* zKdFzo*9Qxxno;ezf~w)<0m@_^T8CsHuq`?t?wjs~_7d?< zgcVsP&u7g-yu^Q9>dOT4iiBehjr?nwd&7V>S{O=;rjcAYnfQ-0R_wifu>^YqTY9`U z>Xv%P9c7Z{fQEL-Q5y2=TnG~$Y%O{HAo+Wgy@FZ6SOO&q`U#Ps&!ZuK0j}Z!N<}_W zQ|I_v30g#V0$$U%+j;~v*AZnj-*NDo0`)&iu5J=*`nF4*f4YtcRSucO_AxWR-BjxX zhRXMis1loll@}C5q}_bDs%@Fgaup40G}rfrdO}(wVmE5{+U+mkc5k0H%cCwOMk)p0 zjt`Fu`qZwdD_$M`6*ntSZ{A)~$dcfg*zjjoF5M*=0XvHIre7CKzP`j+D*bgbS02kr zm!Z=cDQ-)OLp0^C4JcyafLLT%#|sZ{shNMc)``{p(nvp3&PORLioDBNVT6y)*vYU^ zt{d1*Bic+aDZs2#AY~FCGI;U9g{;}H2}J`XeeOQk-v4sOzCg!Ctk-9$Otx{^!f^GE`1{@*dM}*4UWR0N6o2G zp!SkJ^&J(xO&z)1@V(}QEnmjvN;0DXkK25d6g7~y65Zp$=D8jbyR7PP+BaFbXCtJ>`@eM~Hbj`ghhHcOn{N}oRrQB5eN?yV-1nOv zif7K9L2hV;*d3^{$)cS5qygl^E}Ggao%N3;YP|m>S6modyqGUL`B5x`lYi0#S#zRC zTXAbuq2DJ)|ApJqG(Uy+z1M0+Gb0L{0~Jj-E_$9esETQcOd_7KpNT?0n|QNYGU3UzR{f2E$bSJt}PJ$lJ0l&sKM87bg82Wxo98 zBMm`)f<;Eedb=gr#eDnxon_v`e_mE*+Y?s;J_n5b@9T^Jysf52%79cuN^pNE!+bjf zYs)m(lU+@{nU^*WfM>K*|3A%KX*iVa+eh^%iN_Yo zl0mk@pzKRR$d;0AG%=PeS;oF(Df^nrmYqu3myjjKl5Ol{XJV{1lRZY{f8Epn)BApT zKfa&lnB%zb>prh@xvq2hoo7ogK4jS&zjiGHmijz1TVXLm1& z?H)znsDfB{7NR%z^5yd*YwoK`ucN=fNJ<3H)=uRXMdWe!*fZei3NVgBd{#Buy&kG8 zLGAA*Rv)fEALQ>hT(BNNn^CQvkA#t+E1&O``uTRm(fO?3mzm59IkF=@>vu=dZ(xj> zBIR?2#1b2!cnfBb%g#Wr+xcKqVqD|O{LvFd(!on6w?X@w4St z+I}}LZAMM96toVMs%4N>M2VksxqPsx{${KpEkYsx(e6rIyW+UUG@SF?G<5oEm^Iz0gHt`z^BhS+0o?Y!q8xO(tfNhwaZb^Z)xP? z<2iDWug8bWEcIEt3biVfSS1O~5*=H)%-ci0OS__aWX$3mJ6DywCB46xfm`kq6hWzN zg+-NUgmK|i%fbjn9_Pjd;@%B)jUE1Kc~U%6J_+cB5H<{n0W9|`|1t8TyG+cLC5VnE z({1v;ms_;D9B?RZUgP2|pB1SO*>R-4TJndRanuosKDaAh$qs#ABfZZ-D3&nFNee+UC41mI2SgGKH zk~6#9$4QD70#((Tl4k3K2+}78cWNbl)kDi#eAFWO40bb`oVxmGf6-*YISZ4Vs)1nM zJJroCWxY9Qtfi%}43<+MFBh2W(3ULaYYTIfJM3BRl9RH)rQnYpF@=dPF9Nqhr#IEM z$XC&RQhlG;%HfJY#rs)(C%Q7dqoj4W#aTZmjw59!^i%L$e-va2`V8Tg7B9 z80|d!Gj9h!vWBdqH-AZE@Mr9d~ckq60JI}VYEF?IFM`q#$x9A~C88-m_TeXauo1Zi%)QCJ}@#2iw7^468*wTGC zB_VXj1FT6weo*c8{ivnx&a8*X+U`c9RbMa8+a253&m715RD?pL5vJXdPf4(KsPkMk@SrsU{>K^w$K#y7F>7*Hs$YJ`Fi zwWp@qW^&4X38=os8#9?(ya3~)B|I6t>LsR1bTq>74M6&-*>zh}&*ocioKv<^DmCGB z;p@+QDb7094JkQeNx~0b*g+#nxBc~%Cr74yXoRBj-EM-wTZANRs)^#-RAF#8 z=-&Yv+-Qr$JexznD`R0W)IEENIY6e7^vL%p_5v#%lonPv2b6C;s$0*ke(8mJC(mt7{V*RH+)7 zxunkqO;OYEFQ)>HK(BjJ@Ont4irfa6Cx9QB1?V=g@vn)Y)`4c9GS^p}-mWHIn=yV! zGY)?ixx@EydC%Ut@$6b zhJ+hcc#|eKkxX9OEtL?VS9){*oU+PY%N!&)N0uym-RrgkH2h(~qz+;1#-_9;EdZ1i z7*BWj=S|wzOr2se-h(oprxIAQdcwNh;nz9uR&gR+xksI-v&3ujwUsueL9XQkjSlq% z6UPLbdP3m0z~G)F5$WlA&!Y7c01K7zEI&#p7V+`f`bvAEhby%r>fOk-LophD?%=$n zT+-~|M|tKeYk-cMfu?{LVZrto^RX$Up0`CDr017z>(}a-H)n@b;Zv&vrN_g?mMdT* z?~}?;w!$(|7_%LZCUzuJi(%ui6rk*3!4;VGu_=1@`X=a9I~k+IN9nG+&wP z&XIK^Oa?u7hHrl=!ysQNRZ!+d%iyTT79I#1O%vav!w*Y*s;O)#L|mKnsJ@+YB<>TO zp?DhBBCI$ofx=UQDh;Zq{7=?f^eheEN)lg~k@$X;zN@XWTe!X5{g zYcJ08PPD%V+$NMl4lZKH5n2>R*=2?$=u)%G$j1Z4HT*)rhe^2CDa?Dr^ti^>ZyrFg z9{``!9vM)9OqR|5Qz9RKR*oG3{WCs8r<)hc1N-N~+(PWrBu9eR=yNEs3uEMCd^xi3 z`Jw6}nwaGyDqNnqqTQc2G_Snz=KCJc5flZ2j?juR2^TC6*fxI8$X~GcOqN)4=taZJ z2Hz&mA1S?wA=~QHiGJRwe&;UIv`ofxofJlMpErZd!o>9GiZz2D+IGx3&Gc*JcoD{P zNr*oVmrS%8B*@$+%4w9W<~JgoDX%8P@gBB65WLU+8h2s^_W>8t3zd&St*hM(+gcI< zZ97V2?^}hC!X0~Fi#~4VX?f#j`ZTgPuckVhm9GWTqars~9^=17S(ipCc8&1c-L+dc z>FxG8QnFSe-|uJK1n!Qo)donPu+KdgDGA|eb>$AVv3xWAkN`&lipXNa<^+Y+ZrDe5|p(*FRbl|)<)lEI_9(83s})M67!@n`F!zGePlz(3G&4r zX)PjqE%S_sx1`lP9Vnlx)Q8>YPuSKZSiR=V)La~rIh_zLH!iEJfA0u=`mDEn4Gy|K zK_zyQJLp9ec+HmNe7>Et)eIZ=*2`Ug-gi`9Dy{rYn?d<3sL%ch zz^YjDiu4MscZKyd159)2=kSj@MThG~bp4n&1uAQPbNCkLFxb*;Jb{%g+{FwK@?$=+ zG_Y4Wu@-r8=Cf@o82ZUd``8*DbV*=TcCi^2iJo$yJH~g(Ow-JoY&@31C$HP~ZdnxL z{4>61&F%RW8qkDxYwjJ9fxd>(fsYY+Af6) z{Gu4t-CU=ek37=vw$r4z$)lUdf?>#(-Q_Pqr4VgrqAlKVOb^5*y4O`<5QSNYm}^`* zaUvP`7Khr1F1A|U6|ylgxT*Wq+uWGp=@7;B?X!Rutnx5(Ub_)ltLqgX{3{Z};Jc;X zUh4PlPjMwoCk~`R<`Vfy6x=Lz>GW{hNzp)LU5s3}$SR|3jHBXqq@F(J{D)xs(Jw-l zZyg#q_ln8aY$Q@kPuFg_<0#gmCVj1_*3GR)pU`JwH6@tFv-$MCp@R^M?|wU5(o?ogr^934D7 zvPsJ01XORO1p(2V8n3hRZe#M*@+JF3^$n>{3?o1o9*H znh~x)pZ2XRFm>$Z$)ZP=(W1Ir+qFF6Aq*-(2)V05!IgMqfXM3 zO^tZ5qp;*o0rv{KYh0+wfHmrSF4K}o?%%*|Q9yE=f=8haIF^OnqIAqxU6a}s`vWl( zDr``mdRlVn@?Sg5x!>Sq>EP`YM|Ax#eTQr_d{S)OTo1E3j}Lo{fyfds{guQ5*_#HX zroZD`{@?ul>*=ziew{GiCRu7zQE!ppi@o+u``mp@$8SgrK~nmMFU6K`vp7EfP%L^n za$)H#XipoPT6SJ}9yA=Vsr*{tkJk2=<40Nh0<|kK|7)(!QM1bo-6hli@ucxe41iof z8qEOt2Ox4G`;=f3PbdNum=LH~Q!s<$QLL|M3>JWBnbw!UkM3+2yEYoGU+=r}1&!); zLg}ES(c!N%mT!mus21;d!;W&^v}rPUmF{Z=4f{0(BM)q1)0Th4<_fa@D9`Iig?FUd z%#qNw7iDio!I$Mxy-KLw9w$+67ju`Ab7{(#XeUnIqlSgpsC?ELx2M;kpmk*sA0W=O z9HwA>hZzNb9vxSM-NKO)h;^}t3a&BJb7k7>At7JrDa@ck16r(G~1j%yHwf z*eMPw*la&nZ;*;(j!?NoI@V%(EMh8h{1isRk!b7qSVElR6VHgJGeuKve4Pp$r6Y@^ zKF1^5&*VsSawJ-=ch{+?bKB9X*ZG!ED9{|z61HtV{hO5TiUenK3u7xUN&i>${>;u=iPJ-HO-QWlUZ@@i?h8qH-e!zTF^MD}bWvvzB$#?H%FI~9wEtmRazk4tp-bQQY8 z9j6amkqVLAaMO$w(r+oWJ7>3iUDjMjD%LI9xF|rE?|B1hnAK;@EPc5#F(n{5-ItM0 z>ckY)sbJZT)Vi^$T@t5gD4-W{?#iiB3I~dpv2e-a>dr0MbnAiY$4}m~lyR!Or7aLy zXgnc1@^R-m$e6)&n7D1fl zV_6h>Y^Zl9;wV|l4qv8|(9#>Fo^+y9k76gOMk$wnU(T~`fxba>Kv0Z=0;Xh#8dWW2 zvrT=!i;DNU0GB8gXu$OTE%)ejw_6q)O87)Gh4=T&hJi&HFq`aaakWuNwNXeSrcKy_ zBrN@-YzXtVBh?k9L+i>@-q9(0Qx~uc%x%<+h1&#AVQjPCz3N2(VUI?pRA2wfHga~K zbLFKV4orY#M{(^u_`}j)P&IYpV#vu1Z{ZjEXj%OSl-d+XpIgR;B{9ucxM|R`$o2@d zq<(R=V=SC0WJyJC5C`V_bguEcEN)eAAs^-d^l!gtsa;7mHR3EMRV=(M__~S~s+aDY z(Iu)G+}IC+XW;l!3*a05YmcAEp78%+_BZ*h#bXL#A1Q;J0(T;qTTY>+uBTS2`ta$0 E0LgD~`2YX_ literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter11_58_3.png b/doc/LectureNotes/_build/jupyter_execute/chapter11_58_3.png new file mode 100644 index 0000000000000000000000000000000000000000..6d89cdf1ed3793fe53f5101867d7685dc83523f8 GIT binary patch literal 29238 zcmZ_02Rzh&{5WpQ&Ww-}Niym(&MrjBs3fw(*&|2Jb_hjQh083fGPC7y2+27@_RP4< zvqxwAU&rVB|NXv?$N%q950A(D{k-Svx##P=)YsKyqCZPdMn=YTM@#(y85xBu_-}fO z20T$cd$|Jqf_iEgc|LT5d3sxU*plg3dAd8hc{)2hJ^$R+1McAF3X!-W0l9kK-qX_^ zE-xwR^8W%zxOvz~V$;>T01`TPEn_$t83Q}%KRMa^RBke|XIXdDZyF#{m&d#j9JBvg z*9dQJU;aRKi>Yqs%J~PJ9Gv9$3oZ|y_LJ09>Yx5K-8J4qBf~*$z)?%_ann3|pqtH? zDI49O0*gP*ek#u9`5PkKtR^AN`}sC1ZD>g0;rKN?pCI^Q+i%*JP*n#%9=98Hz%L>7 z%hfLgTmW7Bp!mK-; z^H2dR-b$L*uu!aX!h}~UBV^GLM(4ACcDi$Em@j&u9h*2~E6z6R@vUg)&tjoW*~;FQ zugD*pN(jub6T6*kynClVZn0z5W}Gx&w?0U2?EnRG5$ zL!!F6m49G+C`KZcV3k)&(mo|wrK)xK=;dZa9iZ|jVX)ZuLz*IM`&O{+jL`zoK^tZ@ zTulY8h7DJ9LuFCknA)rU`a|~)KRgtFm#i@OVQ@qYzI~34@(X3uDBWhVscOSuKBaaV z{Bt1JebtGPiyYxTSO(bh3#)XiZ2HXhjC^F5P{t_6EL~>ji+9P#kO!E15T^u(gd9qX zTM>cE9mJX+eoq?IW8T1ZReUxn3uwOCA@+kXvdD%J${-4b;2PBd#_89z=~Rc9k;ovb zY%*G;5`uR}5EF$7$8<%h#$z^WDd;c(m`jstllLb#Fy+rFH;}%VhG2C|es@^-*&>QV z`siA=YGt*N5Aze8h?U!uUl^A)koaI}jIJe{{-)7JS_^SNYSny+jEkalr4=UVdY4=7tgnC+3n5C5qFTU+6;Y^x z+2d&ypt|=HcFu{6nfp{h%Siq|%kb?I#@_L>$$5jSBf}W@4ppEo6B=JgxlBp1{F)-R zn7W>EKLEX`H@7p{kMVD{yQb$AOoy~>px(WzW6%QHmA zi}j(av9**P)*`Dsr_(+hn4`Ts)hz!pe|pooE;qHM-0OL@$pidIha1?7$)`|V$8V(Dxz=RatV&!)&hiN$SSBcL+xWVwhtCI) zjdJe#T^_%E7|!V8ojUn%W5vcGdNPBNw zt`uICBtGIrDf!(Q=L!|DuH6tfFS*SAsZ85)cOG#e|B+=){jKvisE7H-lb+mRCh+f5 z6E^PCOI~Kg0y7dwHavs&st*j`&P94<@{FJHnz*;IL9Wl|cCZk&X0nc*;1L%WTKK4TQMe|zRYN@HB1&}i(uIy=e!;yYg-W$e;{wbRZT`H;|Q&SOm;B# z@&vt|z0OlDxav)p88AukMeh9t{_97%c*|h!2}F{&bexONrM}dRC1z`!wl|hQ%`uaK zxm!+4Xo!?Xa^_whPmgASye3jc$iAAU+t*D0ptM0>OCcxHJY5$28`)6%=b$ZlO{GZ_ znQ>iFSyJBwG5PGCCADN)C)%HGG|}oG5qe!p=+Cka14FrV*VD6_X@q;t3R5oKP1hND zZ%(RsdvJ{g;#R9!OH@|96)atH*N&*s8J&J z6G8D)3^bp@sx;4s6oigQV+MHA{lr%tCfCj~N5oB=1%0DfT&w>iLY@QK8DlfZ#~Jqz&aE1RSIYAVSEv2;&1l(> zr!g0ikE*F00c`VgoS|@Q=aP?O1-sg884iv60LEA=RmYNlW|J;pXlnk$`lGJQu zA_x@RIDe_RBrn)%NHK`pn6_%E|Euh&{oXep0_cz>Z$iDC6_CrqnnSL(8>3L0vb09x z{?4iW0Em=C@4gL>drT#>?b<)_;ANh3u_`}3P?0-&+BNr@kC>vdV+SDjjK68@MaytDyO?y#>49$gyRbpT0O<416T!0FG(%M z3E@pWa`Dc%)tx}gCQRXh3lq z_ocqs!^s6Lro!h@b6@XrO~dRS=KlLgiSIR_y<+!enj9U)@39a$YYlt+ekhf(*QqI< z04(44uVCT=CYiDKfWdA0jaeakurADymC(@I72Jz0pcyxR14XXs+8l_!_P#tXiXX*g zVLR#&7Dc^S=MN~ev`(jUzGDT6^Tn$7Ax?I%-)r^fTlr?C%lwY6z-LP37w`*0{X}df zRiIsk>*Jr@>1kIG5%B9*&I~5<{o50Z!at&}gyJjhem(zAB&3dnR<$Wi6El2x0`F-vIx zA@pTPic0^~vd_?f8+x)~Yb5U~*N!+|nHZNE0<^r}pD zTPd}hH+=c(u*da@2xqb{G!j_3?6c!RPeq*g$E~KKy}rxgadhQ`76lG>t(L2~Ydb{V zQ(SJ-2aio;Rs+S)+Yuh?Iw~nVEc}J5*|PZ>od)k%laZ_X!%s8vy6W25=$(n(59j>_ z7rUOL;Xa_Q>n#-i2PNJ(BIfy>vkSSkM}bz0(}XLp66w$@^5^@pcaK%&25VVk4oLfJ z_vN1D*$5lc2<1kFr6<3kkLeL_g6d;=2EKYB@a!XV_mo^07I(eO9TFu|oKdiAt-Mjficy1c*}-O4aRc&G+LMr%O$u(p zbXwA7Wk?8o{X6E&iXUbJW(buE%A=|0h_$QF`xBr=kS^1LEWYwa?DW1#S0L!mNI+`4 z(1(*vodqvZX>9fxl&RLRuSliGRRY$&Eo(B|cYxz^jt4c>OzBLvV{WHl)>qi=wVM>O z?~C=qFHO3Picp=4?b_tlbw7B9drd3RHo`C{k^c-^5EO3vjh|3=rt22hU0`&j7`w10XN(zj;@!rlEDmrVwqozyCGX){gNd+(}tyob_;Qxs;||K zHlg_bskG)j1Iv_NMmIuNo2F0TTvy*OG!rA;lI;zMm@5nqqdyh#eUksFE`=a=$qK!7 zK_tdWVLDYCQ%m+&&C+1fzU#seZu(mP2X3@du>$rg7eXka!Wu@2y(+QF|MjAj91{WJ zTZBrpg2f}IR>{V%cQ`X^PW)fGRz6jr8nDXTB|LQy0cUBeQalXxet}a&i>cdDhtJ*) zs9lqZxwux3kZdLrpm{6IeK+_CacxJdxJMmp{t9^JKV}Y|GUMjxfi>K-C;m_2Uf;`m zS8rJ|pc!sdP6m8Pq>o;|FwR+=j}%yAmOba<8?}l%LPb|i*}wAEHFQPL5$cXW2RCh| z-z~BFjd;p5fKSe|M|m}s4#7M4a!4`!jZsi4TxH5EV6OsIfqVM)Ven^IrHDS!1y}P3 zS5t_vSn;0X|5$tG?`&$vddUa)iaw$^dPl=!G!;HUE=k!imA0w~?e;t$^-S-1U6*2A z*D7wYmeP&iB+NTz(E+*hC+;C7;kN`j&Wug21uCo3E95;Ge^5P!>eRMCdan#WMZ;HJ zS^72@#`n~-R=1!2rjdaD+G`$pQ_JtB*V={Is9S$rzJT!o+D-R_`B{?wA&$-Yz3ywf)fG@)`V}^$EHMb z*u$O&PP&`(pzGwVIft_|8Tg)~nGl*E3N7!uv&V<5_@dP|#8z>iYZ@m!)YlCyyVjY} zV#yYp72NG!@&;Fqd-w9Tlh&Tftj)vcgK3RN(e2k~1CuU*mmc>ZcDT_$sZkwY3iYX~ z&PqE3m^4Ur%AH`5lLa; z7hz#k32)vUNaUzS#>8AwR!;x%;|HIL=J8CyL+HWK4-riwv}uuYiI18}&=eTX>s(Yh_> z9_l(ZWID}zd@R4qbQvMD@6IG=7ts|G6b#7-Iz-W)Lj>Q?x;?w# zmwh}Ex-dJNWC6n_Un46psfq#mV&&xA+VQa|G^v`)%Lt@E*W)GXcc03*j{ay2r7c^6 zEDt*s&jQLmxJ}ffj}D3GgY6N`fCJHox!pBzd_x{5FE0ZIm!`lY=YGB;QM?&@I3AUh za;&SF>RFpEBXe$*Kt+|KeaIUTy$|hkxw|&)v-wN&=vrs5uEOiz`Hvx1O;kNSJ@!4>?f0GBakfM6+8T}y+`f4&wkBV* zHmdWLHmiNEG{4t*4^NtcY5f?ifs5GweER{McGVo63~1$p?_YWJg-ptSch$MAcKxSV z&1R2w&BB-b!*g8h?9D4|2pG4$JVH9*=$wpw_xW%} zp7os;x`^*BE!RB%>i^qX)C5*qv->BCyc*cb-ax})i$h-8?I%x$@8BHzvCt$DcIHbi z!{yH+iYQ3qJob$Ni=ba6R%#6$KiDn&*QhN5wm1a>cdhE{T@4AJQJtQ+igri;v}4D9 zF)Us++T=YE&{q9ydS7BT`B)d(`hK(T9`8$BX!DFoIgSfI%E0)HfHMAw6918V-~mZF zv%A-eeGkSG4lr%3a}8=N!wOM=I+KJn{X0HIr9F~n9 zF`zs2MmFS=EnY7drV1xFaL2h&o!Xbk7^CWRE^l`_1 z-lume9h@3j+}MeIPfj2UNQIkFhO!5L;kg|}D?@cS?hJcJ(N#z#H21hr)7r|)*)5R& zcQ1Rg${|BT2VhyW#IV?0r#YOdX64(W{b=iA zY09f-&a+tZh61(tEY=dOdiO`uU@f`s+r4dkE<>fZ(cITUswM(cq9ndWf)GF+_x}CQ za)(}SSy#STrEPBDlJJ%OGgRxP3URC$o6LHYaPp8eOy)Z_oa(j@_hkmOD-4cxrU`~i za8~o|lJ7Eb&!?JjBXGT{ED#f#%~OiZ^!GJhm3-_cJ1dafyg;qlFjWZTm0JB?+NlRb zRI(>kuAK|N^U41X6i=vxbKdZ&Z0m%2&tDrZrY`Etb>Ul$CF)W!=cUJsQO_Z7YS%gzVY>o!5R&-#6^H2h&cxKzRL}(3VfX6ls`~>5ds(x3i&Xu%w-UT< zsnr|yl?Qf}E~d-J(s+QmTs>QQMTsC3?P=&w44KFQWNDFSrC{-;XT8o|t3zlmi1_QS zkGH*)F#kzN0M!+5~X*b#Rg$hXwne6q{WIwFZ8Q)mZY0xIw zGKG4hILi&Ei8PHVrcb*Ae%0k6J|5ZNj2RW`Dn(0}v)ePJcfGP-5lwc1Nf$wmbV^lN zN#VI8qdQY);NEeuu!~QXVwNuB-}__AW?udMYhUR)_GLAZArPc+(dhmL{kH<&7_SYH2Ne!>4ccrV$BVA5tqBPU#l3wy<1I>k%hU4)c+j@R2hQ)C zL8lCE_3%0$?NO6bFP%?(e0*PlaWCOIy)^%oPBmNWj_YDYEU&%yTX9Ss2NIg34MA#% z$+`UJ+x*$=tzX!n(K$lv_>*3wkLW%{c&{+gtV3ai8`-EVmjvMfh<`T^?W9a+rNIz+xr>fIcYD66$a? zyR+Z;&N-c!H8D#v$5Z<58}~cl#UkzRp5lua;vNI$V{{rjH90#HpZbnc_l-!Sl;{{v z)Dw~#lG5e4iGF8u=1xyEfq$c^}ZnO-Dx>74E+!KcBA-@z7-#cpBbx+|4z_}I&YGm z-Y9&Sw$|eNAYghYdwKLfk*fnl`d@Lf>?=J+N-G*C3OfIBk}FKU!ln89>T?65f7kd% z7f%!VoM-f^EDgd7V0cW&k+*Y_`pV(l~4QJ=o~F}LUchiCU5 zp#L}2=~S)heVM?c)MNjS>;lx7M#=x)%^8FmjBH+<9~t;}eC#d|*$)(tu>3?MyktdT z%-HA;of$1>`$=I?h*uDM_5fUJpcgK+#<~+8X2us31 zPb|SdcarOtP4}m7f9bF6zuNdJ8MM z^=I!ZU}|VzY~IB1gsGW};9P6ichCBGgEOt+0_i&^NHhVGPejqqy=w*R&pI@l4wp~J z-viNJFc*O`5%3VuAN0w&*qh-jNQ@`!BB-9@KtFCv!cSsoM9Uj z5l=g8cGMxf&M*kp`Sybc55^7W-we-M?_OMC`$;hS**H6W;^XT^-88b0C<**@q%D|FzJgoK2o_ST~VNb!aCcQze*3ul3tKyNubNt4Qi^}x9( z-@rhthM-AvsoJ#TG{gT4&En)L%x&w%hNFJIWPkQD>c5lprD&_P+dY%}uvcsm2<5n0 z&iofIQTM;}o=z|mN(uCDJW&A4tgZL?i^1)x0T6AeGBCc3L^08oKfX~$HK{xK0V5|& z>CzH>4)gckn}AmAT*{DQCa=3DP{du|N~fmklA^a}*UoOco_JpSMOGhaEBt6qoBagU zce~z7mdhzEt70B`-$HV<)aCq4%=G%O8H4hNUO&@`B@@D=I{w_LIkg-QKHPjiYNE&F zfz7sGT*67clR(QcN*`G&{Hg@Kt$H`x)vhaA?>}{c{6XF`TfktHY@SBh(D3m%4$+^d zuA;~`Z%Noc=Y7p~r*LMnN8m&j9w-3c`-ym7rslfy(fogb#WZ))5aa2nk8=CimDQA} z@+@WUB(2N{0z|FY$mJW!0Y#_os2m5^_z?BRLNfV0vy1i23TcC!7L6-9C$?QfdhsfT z(axe{@f6%)DS7q3C@OK^T`Uu~*dL!^#`_W0z(Tw8pS@B5{8uD$PiZ?bWg87kZ0j8T zI8nx#%hjBgcBw-t(D@3e-25Xgy%WEJ-l2D;HfsKvvs*W+@pil+v9ASG{iK|(n*dlF z$R=_MReLP$YM6zRlCC_!U!)!S)1QAV#lysIvcKyjC_w1|8dIa>`<1;FOV2fiw#&A^ z0Ud;0r>?q{={-Ud{S|V#Zh?0YbrO#~KsKgFe!M@mRAXw}FRy z;}sVjS7_ZWtB%vg4?2B!F`+AOqhZE{NcB8|u+Om6Nz`G_oHUHw{QHc#w`cLqdfVdv zgfEX&a6N7|4NOBx(1aa#YHuKmXu zkj0M*`8t)3p8OJG)tScsB6AiH-VDz90qWYXI?)Pi)`Ikz;}Gw`0eCh=B;P+QM>;lLV3g%181{N9Sva{pb)a@8Hmf<0th+dq_yi{_-e97hhFAm#q`P z@F3v?)AjrAZyG9!%)=+1O6LA;bjj}Goj)ct0c+?1|N#C0;@o9D8L*H0kM5 z?mO;B*(}1(#X~t8c8~L-P3Gh!&B#+MS$`ZT2bb=a+3jne2#Du$b-T)@+v610A`xM> zOHFecC(p_0UDsK1UfuS{Y&pMOBe<0Dsg5-5YP{8`Q|fsq2^M{qaBt@0{Sv>jW1XF% zcTIS`U>jAI-AdMEdPVf%_=)mwHtNKD+?h|?gBEf+^p3v>B_4ZHcK1W~H_mAfvKSlQ z)>2niN_!vOZuVlwnf$vVmJQ{RNeA@e;h$M z1>SKu*yI zikx1zEN)eNAIS9i^XJvEx?@2<_yiR2?DK& zUiBdtYjT`y9iwco-9JJ2zord!NR*CD871twcW&ixn9KxrE_o=LvDvzFNd#iTwQF{% zcp+&?Lo<9sp8y-JIC31UV+}lrJz4z?yL;pE@<^}=(yq*bFqi5ymFo1yYVZIf ziL3dBkwmur35A?B%)D3kkY@__U5A&R4sya5rlV|fE;S|c46f8k&l9IZ`yj@;G$42i z*$_b)pjWL5bzsRDNIuf8OEzP*wOVo^1tXGTsGpRiPtOGlbUNpvm~c|)5V-3_)k*KY zrAwBu&`#%YRHxS6yFaHr81mlFzJeR$TSsf%$ehzz9-8me3XwWSaih=?2V9LIW(cDL z>)%6&Os4WKq&iKfIW=DU{(iCkb%iPiVaL8NZ4C2g8rL%{r|geAO3}FguQ|Z5*n49Ncac?n z%hUu_YRd#vCv`6Qggm~U<=(bKW&}!{(wFL7R2Me7?ca^LWlANj%TEOAYX!F5c51JZ z*lshuAXo4^SBF>Dx;5H5_Oi(A+SjOLnZ3uYTzj(pj^|T%J|1f|j1Q86`m9jiKt1;1 z0i9XZ&Zmytr&~O{W3;e(7N@*jvjk8MAU{rCs>!wS6x!Kx#vF`vS-btZYd+!nnf5?J z8`vyH-~ElL*Ufyy!sGlOl(aNAd!FuYfPx*g%c4>oqe72gyx@u5acvqPrj&ld&Pz=l zSuWBybdX-32CoOCUrV;+xa2?Enq#=b5F6s=`gnpALuynTb=JQt+4b86#mj|r@}J7T z)HJGhY)(Qm!1dBEKU92G+x4X@NT$lp&zWI&ihQv4H=z_H;9J1eXHXr(hFMlQJ)>y9 z^D7vM-T8@QZ(-{JXLf}}0FoTA0<~gN6+N?3cxyrlX=tB%np(E~p^M}9o?=_hB9j0b z(Huw2;K&8xp%c6b0B;Sk%QZMEaxUjDujL5+?g8|eQ#w!$B;bE0MbA}27S zamz*r5I2l8RaU8CeR1mTkNm|rly zUpm-VX{t)Zs_n@!g0-}e6sok`wVdjiw~mY{=lfCM5SMXv+|*TsQk#um2h9?=7%2G3D(5oUfk5 zp_g&(!i_Hm2_p3-KM&Kpn#YB9XP+I*ckMMezi?G*dQJKDP&EWKz}2Q&dqHYi$w;=7 z&;vZsADHCLLY>z}I5*=LAJ`w4<__`em)^~EtKv9jpxqltVDr%HIi+Cp>$X5sO1v_| z%c#jNP#KXdZvxQYEoO23{YdS=^gzqY{e*G)v)kcxU6{&u#~Ml~1{x9~CEwv^Ek64x z8baPjl3^N6vfiKE!01hsq(C8cjj%O)LTka$w^;AFOKLlsma~Xt*`8wp*8vA%(YjvK za^{WNOr?*PM{c~6$N zMa=Jmdi)XVgKqbuYesReQ8~b^c}dqR-$r#=xNQ6C&RNBC{c96Z4!7)LHzmKg-pBpeQArK->d3vIqa% z9}R#h9h!c9N8oY}VXnGms>bat%QrZEa*$A0ND8XX4)zjOc|K*E1|~CvWlkO%;|YH( zT{eMTl7yJp!>VlU{ra%|DMP84E~w9=hOqjM;YWG*a}xIPDH==KEE}#76>$FjZHr_7 zgI@UG)f|LLk9x%eCrvd>DT^}BVqBI4gBq&9)>&BNgA!7*+;YH%r?sOGN9aHGpL=3K z{cs|f34W|JuxvDThvRg!Q14S-~S|@LGz{2{K1Y@!;1O_>j`X|2@Yk z?s#|Ju-@iIl~-|xWEA_J*BZ>;U%5|-J@9~K$q0WeZz$JWfJ<=g)<_$!=2t|x0$xS| z-vjR8VMbI<8XVttU;m`0q)utBmZB{=4`g3LEkw0xJ0Nv! zlUtfgAae z(NU%PuD|=a)V(0uex03Tp0hwgxn<`L3W?X^KQCHH3JHtz>js^=YZzYa8a89rmL3d> zD?Q*--7ind3FE}-2$oC5NWp9FhbARn)X_EPNVU*?5CgR7T_0Tbax+RV+L}hJ<>d&i z=!U;f%fvq{vEjS7n=vs9eB9;^a2sLBG$>4f0;Yo|#Mfvl`5DC}BIxv*Evyg3!A3)f z0U)yf{YtE{BF*udqag)kz?l*vx8p+yd2vnc{F-EgHrTa5K}*fyDC?cC){^i`aeeDn zPY=KP?dBGNn>N>WH?I#ij1kzt%>OWV^3sbZYru;Uu4-Hb6D^SrPIX9OF~2F7Hu>E@ zXSMV;sp_ zYy{~q8|*H?2IaaY1U1x2T{1h}U;SD>Qhi>vA-fKYYaA1Kx%w~VWiEycb7sG)T@$b- z<8TD`LwFchOruD)(&rt8`sR@@TcYkmc=|#qWoqMQT;d<6*PydSfZEH(61Hz~1T&B{ ziB3^Qb?Yb89VqPY#x-cXiq!f5B6`9dFxhZpvhS=9{XDw6c9l7oX2ooH zpUpmq{aye&ENICs{-jraY4gGL1$TN)2@g;NzG3?M=*Amq&ac7$C zk~qWY%?nrgBoMTBA4kMLZo+LHa*2Yj5i~1W%qSi`i|)7IX05BYdWQ-ozD_t@esWfV zpIo$k{9UdnF`)1v;93HlJgtBAN{B2?xuCFg8n4Rxc4Xg;;tNH}o4oYAFuwpa|F=7J zpkt7D;LZ-!t@v|ybxETWl~VGityMyPw0n~8?>{muKl#J))nj>=0H$>@#;?UZ)CPwA zuX~AKv@1{;?cO_Q-`!E0G5>R|{;EBC_` z{i1XJ%BL!ex69Ol5G_6UMzICaC~29pC$L+zFGGnGMzo$DxZmD5FK{j68SWAFA?@b1 zGN*O)-T3qU9~~Xe&5uRWX}>|tC)q~uE_g<)#5R4DwCZ69d`DtZ>-(>>X>g^O9vRBy z_(jf_VVR(TwB8=(M{jmqfB#s#WuEB@f{EYt#p?~=$RBR8fAY?4cmXu6)$yyw5w@+Z z8~&2R5Y`&>Pv!$iyQ7EmeEqIt-k->Q8~%*F4eYBZv8_3QSLlbj{(^Bayk#&=Je@^eN+^#?9{>6ZO_D#w6zl4|Z5+B|;+BTGkPW|6?8p}8 zUgpiooevqs!2|1+H{!b=7CK)uM`u$9xeT|2T60Y@o4wWlc6L*M*(9ksc@b2C$DbAA zm#&85&4GxhR-WU2gWrt%H@tCm@Aaf#g}rs%>VPlKd+|t%AwlJ(G^$_5zUfb&7#&J? zv_Uc!I^#BZgJD(-bmy+jvT$d?9dnLLY(HHUvLwtF+eig2s_r>)D!elEL(8nxl*6u5 z!Lc7`$@hQgVZbiwLHq`>IO(!VSpN{VNT!Sh=@$HPPd`sf3zS*r=xS=tySL%fZDoVs z@WBI?G)4|}WVf{F%z!d1ip`=!@SH!mz1(OQ^N&O01(0#ChgF>i;@g^7{; z%9I!7b?(3PXcySdoQ{Jawc3%)qnZLU>2dCc5W*Q}`BD8s{#4@Cf?euBA8Z2!NpCYZ zs^3vRf#QMW$EeH6{{-VOnTlU@vN4Dm^z9q5k}YEyUADG8>CH@qv^P_nCS#K<56>LC z--io%jfH33rJAQXGQYuHRou@HHvy+*UB`pORSSDmSHGPTCQ1RFJSHOdNh1ydlIkejW&b$DX@|%D@ZT#kL*=T zQ(jW@xcDI#xC?nxOcUH4+M#miFQFWyV|<2F0=M@UQ)?Aj7THDhK`@A^#T9f7z-6VD zx_(FS-hI1MbYm=qDuX4YoTK3`2*2kOdzD<}@GzQ{>{YPByKT-T{2*?uJ4Z(8?4!wc zx1*>37F;5Dzm$h;n1}psXpUvsdz={=Nma;4E6du>Z)MdAKO-$tfA7BQK7#9IZ32s| zOas;M1l7ZdupxoH#~`Iq34@y!0&k;ZW;(^5l!-v!rKq5E?mh`m!R;XU9G@fIR)VRP zN4Z$zn?a=W@5y|6C%ryXwAavWdY-@~;Cd=H_^|nWuAsjR*>kt;!rQ>gB|wf;Ug-Tu z4?_3k*qwZC1@Gpm@TXth+fQkY(_JhMHrVK$3EoYOmc1&S5W7Qdu=`5crM#bvy!2TeMR zY1QlQYDRLKe!M^Xf=M}rYQhl!29W^co#gvxMswfoPV7YO!F|F_EI7rPKs*5{#pUaR zZK7dTWaKWmaw-&=%yU#*!UM8}dq?Du^C;>cPENx?5g9lO~4_J5gn>v`2e$ z#TR)M#+aCVeRd#b(D9^y>gwMGfOKvyfE`42JzQKlwKV)b1Y#O@nu`YCKsUS4h!3?S zIv(2)*p6Rf`@RCrS6+5%S;r*rT^%jia94}xuAZ@WpC50b2T6ov3NySQJD%raJ=ZFh zRQd7V*UPTE_FM`(wtrKroL#C{m9$K$EXF@Yae_RGRAg|4ZKtDz-w%a25A!Au*+3L5 z!9``q|KA&Uje=k`NU988E9}7Aen7MH>`vKxeFHNEt6xb{^VBDlCM5ZdhLbDB_S7>~ zb0TD>RUr(t=9D;^v*bzdjk8oY{?D9TklK84!4^^d_+p@0>W};eah1}q&4t}Fx4?wO z=wFr!se-5nqx=6oGrulfL7k|8H*l~p%D>d!f9z1-bRPCBI8Vj^OA!rhIX>7|JR!QdDhD? zM#yvnUN$H21-C2FQ)aPpSz(m>5w^DM7J|y(mj_&oDAorzTOf_xqgSJ>+5-A3;I5zG zMX%vSI;N(k5^sh7G=L2y8k#BXFdxIKoPNjSZaB_I`*G-Dv(=&pH(V(@kN6nm{h61R zjIMO5zZqkvkxa-2*%V{pU<~2Af0532Z|R?$_!m)6N-Pf~&h0r)#lMzTxY?Cw*)Es7 zT7E2^bh_3_nd8fPomc6rsdnYNxBr{AiwP{SubJ)K=B%FGl=qjh=FiYI@w2fWY3zPV zc5hc;U%Eeo6q5DSXMTruI#YFXUbchLVJ@l)1;bZ#Ao-`TWOpg%Vb2x1e?Y4`u&y+L zWKGDORCvU5F-4~68)Z(x6{<(*FBU?BW8-z_;Qh;!Q^j08B@ga^B4JrNxv{3}W{-sw z?9|&r%30ojPx1ku%Ox1R{&%Heg+q7k=gnz~6M(ej_dAqR+LB4Fm59UKXIysZus)^jk%J^M>U7MNU~ zxFVZ`zraEo)5JJ6Bx27n56s%-fWJ~?gEgo5w`^f;8NwX$+6MH`mo?D1*vs|JlY>dw zkO1)*l$!*at6e9zvSc26t!!Xp>aDb<%xw;2luF1Gv#I2-%m89azyHt2d(U-{-mO;BCDsM?h= zr>%=>*vcdM#5EGy0@982-^HR2AG=JW1QPe*VW7|5JEQ-ZI-2j4cF>QVv%viDAS2ON zZWFm#6qtCVs8mvSByR*>3TDR>z&UWQ5e17Q3{~ZS55ag-+pG!FlBVQ zgb(@vaEp_mg#;C&@sf@=8w?*I4)bypk9vD95{k(51(}QX&w_qGRx-@1cVE;Hw9Fu@ zWyjI6Kn@8_bEbWl(vyOWTgy}=_UsT*pUEiOZoOPz{Y4!o)tm8DLwyEph6P{fBa+uV z8(^lxl~;-nDns%bEcUxr4NDWwjK4}m#^NHF;QpTbOC0F=qaHhr*QZ8>H->A2gBnMSZaMjl znBqDGasO^w8OilLBUV=>K~b|$%%=vip5E=NbX{}q)cw_)ZdyP8 zNH79%kn~3dnf?Ih^$19M;(xRYH}(X5g`f}V5<8hBdTgSM z9PAo9!Q`MOXj8H0dPJ3nS6$Jqo?i57rF2xS6lmMhNncWFK=F8I7-x*&K6U)yp&Q+3 z84U`rT4zElxqYU!M7Rys4<|j*P^Z5LDj#SF>X~M&@90q0xh%UvJT4xtrK7Flkxl;^ zt#FlZl(HEY%I`!HLv|bq^VKom+h(LpYSB4_amnbsAPh(3_c0djvn6=@M(B7K?d0gP z#y6=0f=j&~R>>>6>r&RIRmGcVVh`;Q`J-$_+?2%1##QqYrz{oF`fz|-eS#hap$Y?Y z6Ln|T#zJ&PH%Su!7`@wCp%v!x;G4h8J|lHQ8Mgqv_&~J_rWIj#dnly+v9cQQEetN2rKs*$Ql-Q`dd|)Lzv|lG1Baz{zVU@L z>N89cui=x^3{x0aivF?#xrU>aJs8VC$?< z2c;B)KOp>mwQmN%kazq<=5tW6HOM5Sl=!lN^qnn4eE11`KM8nIyy-L8^ea-L)|OeG zTldZ_4RFg{?caa;cjIgUA4`TA^JiNB&kxmw-jZZo1kJLd4mTfqZ~M}(dUILSdF+j7 zY6Y4P=SP=##CWkdtS{7Jv%GK5&?mS^p>WAo6dZoauoE*4Ja&S zZ1^Ug;(ZCeX7XmJ8h#Xi(X*Q8n+pAgN<^{i0|YxOlm*{n-YOe z^mHSTt?B+X=D*vg!OXxZGN^7FBB)V`UQ55Y}L;G!% z7Hojr2vqoeQ3G|MA0(;O+uyIakzqQLu0;Ew#s;wH-04ZoFFFc|@ovKISdA*ty9o*! zllb!Qy;0ARVLA{KK>M&}w@|cTIN<^s)yTu57GYxfZv?DbNT4WSYg+Y=rZptc^iYR+ z)BS!ML!o8ps6CBRdhl~u%-eyfya>*5b@l7VSO-99avOkp;;RADt0QQldlnC9?R9II z5B+%p18z;}s0)FSq`LoouzAT~c8%pRz3xe`En`dXW~V|~NZUy0YTV5W$Om?iO!{*- zZVPXBnoQKIpUsavG%B|mm})JNlG~xShmu`VWMV(+Y5?vY0(MG~yI-E0(kb)$U(pb3 zs$NPHy=v63;cjijow{@VMlBVXxZm^rRV5FAktE=v+ckguWp)i-X==C+jXX?FDwzhr za$rpN-jqy5h2o9HMxib%YXeEB`kxFdxdEwqpP$B?9^wpO#bbfh*RJy61n6J?LyU#p z3+NzG;ZL%}n^~a7Q0Di)^0g(a`p=jH*0gNd-5NnPYr z-NGzatGvXf1Kj#yW9ZNLQT5gDmmW0upz@@V3_n--u_mG|+ z76mBC%3PPVL2MV=uoNb8KPET$&gAQ9eQL>nycdweG96Jp0)o{Fn7S~!FKsPuhS0*&jL{3=wJJo}C!F4(n?YOXlVxN&TSe=&5-=VbcP@i>MT;FpFD? zgX!j_pxF(C9fcCV29Q)_c>((-f6Uk(&C@^Y?>jpM-x&JcilPMiTH`1ek{h=wV8++Bpt(iQu%J)%*CYbQpSp}D2+ zOO|OSlkJWhkAmQkbNMG#DuXMeZ;dG?k0{g0l+-@^Hiw5!p+Jm=tq7|xO^@s*+o^Z| zK#2cVoNf#xOZ!Cp*M+k9e>4RMrve%+gSxF32acACa5T@?E$Adh^MlRYc8tO1Syuw? zSx-v(4JcBYTv|1Fe$Ewp#sx}5mV`w_w8y?s;gSLwXfgbJ>6ZeX;6eH14y02rC*u0# zx@nh`YCp}&mLGlH9;BLu*Wu;d1ln-fS7c)N1x$avAZ}>%>BaxVp$5Hj9w@)i0JtJm z)!zAm9>I3@)DF{Mm_Xo^+MVe;pve5#c$0CS;UP@x!VdFLEolLjf#Cqh?>Th4eIrGD z)ST$E4^Cs)V_-^|BE;+-ZMEd=dFfxmEyKo`X^{7@XD+-fWJq7I+fdcsSmxTeee`1E z>JbG4E#j7YKl^ub6S2Fa7&^=%3!K%=T!}C}l1PWJeQhgcIAOfve@9Lhfu*HcJdj$U zvR2v-rgxi2QW?UxS_2@MjUx>RfHdL2Fu{GJ5KWN)qN)P{UF9jR1Oeg$_L65mzjY*B zX<89e=Ay~Wk_kSnjXK&lJq>~Cd(-(Ax;ay*OLu(9z711OvwE;^$AxbLPY#tXTAYZj zka$=!hdmA6KwuEFQsu9iXsf|b+lu_&#`^)NpMC6zZoWQ`1w)5QpAQN^?9dm0 zA>g|^(8J$eR`&e8%cj_nj3tMwuYCLg864fGlOTs*tZQhqVa8c1?Mh zx=ohc2%wb>pC@#qnD(y8yK9d2(|uiE6!3qfyxcEkaBLKsfB*o})@y;V7 z$7eLn*S{kvrQWbeIkPaIIT#5pps63y9BZmATCs4QKS#S34>ZJiH$ab_E?&@_e)~$C zS>F8&V+|q^U>nsp;Ikf_K>u-J{9LhqLhX1VU1cu7QU#<&<=~LD6{DAKPKp9LJWJC< z@w{sb6CEKpEj%t#?U6>gx{upT6CZ^GZ50eXfggAqW{X1XklF<9RKroN@oh`J%0Ata zeAge>Z$H_|=ESfq+kN_Lx6+VhmQnYjyf+X=T1Me3EC>Z;97Wf5t z9)KMHSf7?}YOf?5mz$)S{@@2W+ zYRktTfS4s>^ex6ST4x*`K=E>X!1$e)5{UHhYf-k*+^}5@Xm~WB6zp!rX*lN~Q(EdC ze!Y{5F>`gK007vv(d(17t3R7oH-#$i#Dz`?fDNMrWB3_b2a%;S#!n^3LV}VIE3vl( z2Z|_R5sf4(*KnRDTOmficKc=fh6N`MJFH(6Ua+E-MB7*L)K`rKS9eHuDXTC5*zkjk zQb$6%lJp~U)cVLBXgsLG0kzg$rRIX8BLiU);%)XT+3rIJy9QgFw*zM4>tl`GB|rG$ zsB{lPMl-`zPi28Kiz1p)QaLoriJW!Kr>vtUU# z8eq=j?B@hz3wijqr!4CL6c$}D>@Y^Jra6_{H`7Qa0F z&Zl+TC!P;R0jB+yZ6=W3U<>Eoj--0ZRz{whV|qjEB8g z02^CuY&fU-&pv6l2pe_QFg1KMEQ3NZQTJvYj~cv8aa#%{((AORglAc+ zo=o$Km~lSz!M;&R`EaXvlsjA%3a@F`?ztsE;W$;@M&QGH5a*a0b>iWFB#V|qo@uYFKK?2)6`3bk5_q`49P*%=P(!@ zF(kV$l>d?4g$L2DS-cJnrL6ruj^wvl=Z7=o-Q&Tdp&~ahP!;5S03ID$R$$Q)p5N+> z_Lh#&Q#d8yyT1IT$RPz9`1*KY7eIUebO43Tq95sWnBCE`Y1GKQ@&foY3P!-fL!<~! z=p>1A08bx2A53k~Tfjnt+W$f3^m%(p{f`rNQy!9$&TBtq^phSYwV(6ok(U^GQ zXALiwXus%+`CaMZsLxL&u|t!t*R4V$A=egm@ttM_KmIuqSzuutP!%Vh<~jhk=F>TM z!w?Gb0IvWLK>k3nfNJPvZNVtOZ5~h3m!>tWWmu9JX};N9P%p%^wB)V7Sp~gw4iLc7 zp1$&uKmPI5Cg77b=ezM`ir_fi0)<+~f>UwHM{ypY$Ce7$YiK`#7vPilxHY^7l2HSZ zPd2OKb=rKL9rRdzf*&?;S`~h7YoxxXpKLm> zKZb^$4590^d<644q2uXR0}c(DeGcwZl=$aGv|g?vWWlL4Rg$}gDWOwzkVFzTVx+R3 zam&|L(G+WV288@9xai%($yGP>>Q|8QJ~WK*c-RNPD&O9){;pjn*YHStY}1NGt-pxHo`LI9_J(BatZK40m>waMAO8cNAmhNp~5u~F}axv;|MK0;?qAqt<2 z{GeU2Q=1lPdniFh{o(9>zx!?9BU@@V)#G0RB|8ApQ3SU2V1F~@Vsrw-&*b~P)g9qS zE@tzQ&maz53lx`UoDC~{fV#hO_(CPCM%inR^lju)^D2__(Qq%QOW=Va0LcNSMJ_&n zC3IFlt4OXCK~yH&85QrbK2x5%U&D%SyQxZ$sx=IJ2;yb{gNByt;8iMpb>4I1R>l^XS z)M~e6C*aq>ju5U|76oObk&fY`^x@~#{>8w1O5{SM5a2HGH z?XtHY4f-j?-2n_g`+rnfR6;4=O0gc(t}^>?O;-oS{pUWtw$}*b9@^YB*sBvyBw29X zGfY!W8^aZa$=v?PkBzyqB{OIK6Rpjha@B zH0R3KWGAI$CmXbr&BVln#s?7OBQhM-%Y9&IN1;t5^;4}y-}0;{ESEmyrwvrCGz|{!?8#>Syf}@3ql>p!~KD>mF{7U^DBsitfEIY{wc0Hhb1@A{D^gf$`MAWKx z*iiYD-r?-$1dr*6bpRx8crVeI=MOKt#==OVQX7`6#@gz8GMD_5u@x`Pb%roz1eiQ2 zd!C{TO-`hwhaBWyv7;&xp{j~C#bd#(clVw7HGCp9BjlR&z4=k)GKoHgN3Au+m?!Ni zL_SD9t#`UcF4-35m;4G85hn0e^0TMM(4IdrRBrSuZ9l#1L0c$ha~(=M5mrUw)i9^! z*7~dMgqQp+>p|lVr)3L9MS`w>$~RsDk>_nhBp|4O*>6n$?Yl);U7mJv<&K^TxWTTQ z*)4usJz?a?zBCxZ)Eo}q{OC}gFS-$!5AI47O{rkWkG_WBhg}nnI$w4rUmq65jmF!g zU2A6ISQt(KVDg?}rfQdrp8d}{1(4R3Y3uO^UMzOIaftTU;e??4Yzj7sNUvB15gQSr zFgDv`KDBp~eQ<_{WA$EUgWK9%Y4tX|>v`=df1aO&rFy%YEP z&m%aXTO1|%Uj6!L-@7CG-?c0w^U9mrscYC+8#lYVtbnSA1ldr4MBf5*MjxaA9i6iS z#0IJ{WQDRS({^_Yc{hAwr(mC|WuDO&;w!2ASgU%+K`_K;#MOv1Q^9BEs?h_DiH}dA z1_b_8joAxPQgDKj1fWN>sIgD( zs6LzTGbCLzmQw2qXSLBF3|ODpp~sh7z<;1j4Ss##?{oR6((~I4%z`NE#}-(9{?yLq z>78}$%lfQ)HD|Q-P8G>I&?xa1m|zw+Gh}9a^5{UY`oT0aN}f?D3N+a~p7pcs^y>7P zqNi}@3cyEOcHtwm9;!&)=E^d?t~-Ol#qR=#Im@^F6uK^55!`am?;J#5L`;Ae_^wDZGi6x1j0 zrt6Kz*$;I@=Td@+Jl}O_cWs`!?6bp>mGf*aQokrnvZc`E$2Y?Vg3KKNXmNa2Wf^l9 z3DY9Dd>mi}#?|PX;_riUf>8cbhAROe%nQw~yXk zz>z}5C_S;E#BwK7UpyL>NLZ!1?aK;_xQ44r8$KJlgLAi$+0I)15hGrG)M8n>h)`VL z(HiP1fe15P24J6WPL7q&tyFNmlIG!_TujdRuypRVLSOU|sSy&EZq6<0JfYTWJ$y6Y zu^B2qz?FTxjtX7H7aC4oK9MDgg6XHjZQw;7Sf)&81Ed~s&!;+03+NX4 zFit-Tx4+Z!7V`bB{6Os*l&kjsom=|lL4r7&k7u_`%zz^S`p_;k=gssi7ICOs8!O2p zhy%IJu&`HS;afcw^IzV6ZO#@r&P6~zz<7}_*=@W+!d{#!RzFK7?cmN?=H#XOGu(?~ z`KJY#%S@n($qhU9&M|BWh?Lw8dxWBZH+VetvkM9EJOvL))sO)kua(kkAEq2V|Nc?P z6GBeY&3WFuO~Llx5pYn7AGn(HzCf7^P+%Z0|Gb6(uiHVLjS)eQ#^#=HZufk)=B=Sv zjHhqj%p{-HZ|@7S8ZPZuGSqFPf9W7$|6DhU!i}p52N&^soWGMGRR!k=j*5M?_r8_zW zF^&!7rKbTub;rA(!7NzCH!lvEb9Th5=KHyJ8r@#>7Jaz6J@Ac z@KADC=E&xND*G23)`P+l{rq~gUa7le`qRRvn7mEvf!N!(or!Be!Sf3pZ41MiNMVc1 z87Ir;l0=Y!_^Uv1IF{h$p5p74wA(Mwy*1FQeAL#K50wIKQ%ZbVF<}A8)E|Y~^w84v z`qM|_)F~MLo)jh7cEc31Mt-dOe%isyt~udQVfV)9A7`kuI2-4Sy`iV?XQHmKkFl1S*CQlskkO3builHND!Djv}?)gx{Pb@XJrCZ)9EnJ z&~Wnfo9Pq=T^}iu=fBZ1`*`8{Zdu$t5o>&r50BRoL0%Fe{oCuEN7p;BymAk5Y?Qq# zW+2a6n^NU(<4L1cpnSe237KY`%YU`NKnvGIf8pfCM;W67f*y@!-88}J0ZOyXQNHz( zL86zMp7gmmt}7nT2^B=trcCstHwC_e_0#W_=3OTlo|OmXrI7AW^-=E!mBb;Vsi0)5 zYuRH3UuO2HVv9~@J9D)Ie7k>(z75Ps0fpS4j+!W`@`&(;Y zzO%Y;PIUiK=w-r}ogux*YdxiJB0?mQHvR1h4^Ky?)TDrXEFT9wq`aUr80ZsJPp~ba z2bG(U;C;1AVr=|UW_pOTx2K7*BL>{i;)pbhIRnqc4d<4PoOi0tl#LOE1dvuPiayBoM(zx1~WhH?lTK>cya{%gF7< zQ=mL!W&ts>Yab!83=(ErG?kw2dA+Y7$8fv}ehEx4vww{} zpJ&?j=qAtc_v+L0>X{!h;m>v%fQjy;p_FvEAfBu@9ey-iqUyywY}ropcd8`_poJeN ztjSxyB||k+uLR|GOZROzE@^0tSM4T2VwjU#daA2dM-VLC>3MYcSLFpA{asMs1!7?3 z>#;_HpdDXRsv1j^brYwWQI^TNS~Ss)0>RjB0s`xvix}^_pK@H8N}leZ9;#4;x6|J6`E3#N}@C5`$X5qi~0)t{6ACNWlM6P zYa=U@oPdADX&J!Qk?s?^33TABmdLB_=3fd!t$#1#3oJrcfzrH|jPi!3=QzLkc7dwR z0B88usn&L3&7qFjhemxcR#%>L=3O84m@CCEYnJUzKhx#AF&x3hdvY20Zb!K`R-;CS znI%NXf%u5p3mde{y0-#BMhCJ-8l%74sYfN$`S23ZtKWbG$Z#PZ_eFa8@;znAT7|zF zi7yfzunDJ0rHrrS%W*O;pj&?!$ z*0(1hr2!o%Mb&`}^)_XE`Puhs0BYUTzFVP^QtJ$~0$j)LDLzWsM?dO&cZVlIHiLfT zPu3Wy`f{L;U)?#wwuf%kshv5sds08xbq|feW zMyx>7Ct%5dFnr(PzIEHMBsS*i&D$t)>E6w)Z!YQEruo1YGO3eA`vM9XP)>_dyMEE>;e@51-lKC+ClK+S5!ESTru!bdmx_{klsNn7Xu>>|!3mOPi4qc)4U z`6JT^NJ9&K0sz)1Y?J-v>dE?v%bfi5S6}GMjB(=(WZ=2P4=4i5nM`=P`VeK8&kk)# z;Zo#M^dKdwtkGC&6Ve%^u1BS!2DBe2U!*@;qfZq9cyfW0g)m zBDJ#LCv_V@Nb;@jFpkONh9YlwrjlQEz%Ee`mtCtDHX*f-ce3@AD3oJjqPm-}SJG<* z+RfH5gQ7mZ#VwnFid2t_w(WG6wJ2Cp$mm&=4CF2&In{Lhi|}FbJ^`7mzpLuz{G*;U zIbb_r?q3nQGW}Hvrn{OW&1XUYK^3sp&N3ot+DHfut%X9rr#k)6>h4agFy9{q=R1!t zv$XzEw=!mL`NrjtHLpQvP$|=#;j|YK9;81G-LjGsp*N-~Z%++6RBhGUJfyg#PUI^B zI-pR$emZXCCV*U79jS2KtbW62D5j}?`*-c@HT7zJhl5XE0{i#7FVoT92pM>CG{TA$ z?;XYZ28fp@Qx0LqBhDE;$CjKiu#sl_J%g^2`{~5bE=`8TEE9mX^1=umcF2anro8qD0<9~ubJ^b{Vju}nV9!%C{T9)KCP4l-9p0>pjbW2CiIGX7Vu>n ze=nhj;62)1&+@*)T(z47hW?KA=3}%M=s-=3`Gt2i6dPX`sHgaGL*QFZ+RX-p0?*6c&e+1i~taW3T`dlc|pwmMK7_w4_lxJ{<9E}w3 zuDXq@yt8Is5w$WnX!4wE>-GQso)`belPLL!gTgUH`p6qVN$63r!^gPg>=Uc5O!4Yq zux5QmEVv?ryXeuGawW0_DmA1G+svW-q8?3nGe=)L0;gNu3f=*zWBVH4I_Na^iecz_ zx)Rjf8l?n?nICOxQX{pZYMf?XkvprK_9(AlX+q8mxK52!C?RX(!aM)SO2a`Xj;O17 zF=dPzQxG!<)O=B)ei$h@(z9?PWaZ90&)eMUwt46%^;?LIs8vQxw$AOs*C*uz;sx?C zIf-_|@oW(%v#d?W&+7l&&vBg@AMbZD{yd|Zpdi+?eyMtu0m&&nMA$QcJCY@a68<3G zd`!wcQJu=d{@S{|U_UCx`|uYFl&}U#rH3fGyA_$+=al~(k(z-&z#Ok1YYOG-C#(A( z-Mc|UBcMqB@1OfRY4Hp2dWdfSPwVghualjyyM{_B@M12LI~;Yl5hm&!b-`>3Lh)ni zPw3EJ3|_pByJg?@dRl83!5FWtltym5+ki0#t#)?|L)dP$bMIIr67&8YjW-hhr|0>< zcCWw8Jnwociu=F+;2)QYSvH`!p)Z^rs|DD_e{YJN7yj?U36-kE{&xQ@ck|x1*V2^H zY=Y74MD1oNi3iWjI}Wmoix9nzt)e4*=5glcj5ANYgYId>g(bR(7bDC|yD&Uct}lb` zQJ0!#VyyELJI)Bk=i;-AMX&s;8R7DvYt4&62hn2tG4V0$ceM67iQ;Wn2mX?eUU~_A ze$zTG_K?Kc0V__FqR5M%sbCY1SDHMa*}3Q|An4`z`8Fo+>Z)|tAfk_HHg(j6K>~r# z8zL42weMt=gq?{GAJj7F?NC9DmWRt$JV?qWe=_JUqxI*|GUQ$q8?9G0ILC-^iG(o{ z#cI2T78e~cPbSd&KM`eetM(LUQ#-{OZXkB^2!;qF3F+30%dhkEwoi$fd~vcB@^jK? z=U$n9Tp@Mg8;0ugDQhCF^)gH&=;lwm;*EV}H@Zn-+mc05B-}I^SYI^Be$%mYt#-7J zV08MK3L!#Q*j$H1iqj3wxxkNc{PQq}Eapn_nz_VJOaZ2Bo}v&f7?1Q1t|v8-w@-2s zmh)|kw%*w?L6zMMXPsZBOkSNEF+;HRL}^(cyYiJpBh|pXwysF^Ib0 zF38)?MQCvbed;_3Pg4JR+)#J5aKYL3R!0P70uh?}7pad}@hGUR|5Gl}nsTyQ-c#9c z#~oxxd=*<{UQMO2)r^|=Qn`^y4I;|KQ!NEBj-L$%2vSL}>m$b4;OZ_|??e%L26@D= zj}0(zBwKI$mEQpbDb5v)D~0@Y0-JD7BS=KfbDU{_Sj>42xDku>y*%40qIf0L!$yXo6aJ`T01`TPEn_$t83Q}%KRMa^RBke|XIXdDZyF#{m&d#j9JBvg z*9dQJU;aRKi>Yqs%J~PJ9Gv9$3oZ|y_LJ09>Yx5K-8J4qBf~*$z)?%_ann3|pqtH? zDI49O0*gP*ek#u9`5PkKtR^AN`}sC1ZD>g0;rKN?pCI^Q+i%*JP*n#%9=98Hz%L>7 z%hfLgTmW7Bp!mK-; z^H2dR-b$L*uu!aX!h}~UBV^GLM(4ACcDi$Em@j&u9h*2~E6z6R@vUg)&tjoW*~;FQ zugD*pN(jub6T6*kynClVZn0z5W}Gx&w?0U2?EnRG5$ zL!!F6m49G+C`KZcV3k)&(mo|wrK)xK=;dZa9iZ|jVX)ZuLz*IM`&O{+jL`zoK^tZ@ zTulY8h7DJ9LuFCknA)rU`a|~)KRgtFm#i@OVQ@qYzI~34@(X3uDBWhVscOSuKBaaV z{Bt1JebtGPiyYxTSO(bh3#)XiZ2HXhjC^F5P{t_6EL~>ji+9P#kO!E15T^u(gd9qX zTM>cE9mJX+eoq?IW8T1ZReUxn3uwOCA@+kXvdD%J${-4b;2PBd#_89z=~Rc9k;ovb zY%*G;5`uR}5EF$7$8<%h#$z^WDd;c(m`jstllLb#Fy+rFH;}%VhG2C|es@^-*&>QV z`siA=YGt*N5Aze8h?U!uUl^A)koaI}jIJe{{-)7JS_^SNYSny+jEkalr4=UVdY4=7tgnC+3n5C5qFTU+6;Y^x z+2d&ypt|=HcFu{6nfp{h%Siq|%kb?I#@_L>$$5jSBf}W@4ppEo6B=JgxlBp1{F)-R zn7W>EKLEX`H@7p{kMVD{yQb$AOoy~>px(WzW6%QHmA zi}j(av9**P)*`Dsr_(+hn4`Ts)hz!pe|pooE;qHM-0OL@$pidIha1?7$)`|V$8V(Dxz=RatV&!)&hiN$SSBcL+xWVwhtCI) zjdJe#T^_%E7|!V8ojUn%W5vcGdNPBNw zt`uICBtGIrDf!(Q=L!|DuH6tfFS*SAsZ85)cOG#e|B+=){jKvisE7H-lb+mRCh+f5 z6E^PCOI~Kg0y7dwHavs&st*j`&P94<@{FJHnz*;IL9Wl|cCZk&X0nc*;1L%WTKK4TQMe|zRYN@HB1&}i(uIy=e!;yYg-W$e;{wbRZT`H;|Q&SOm;B# z@&vt|z0OlDxav)p88AukMeh9t{_97%c*|h!2}F{&bexONrM}dRC1z`!wl|hQ%`uaK zxm!+4Xo!?Xa^_whPmgASye3jc$iAAU+t*D0ptM0>OCcxHJY5$28`)6%=b$ZlO{GZ_ znQ>iFSyJBwG5PGCCADN)C)%HGG|}oG5qe!p=+Cka14FrV*VD6_X@q;t3R5oKP1hND zZ%(RsdvJ{g;#R9!OH@|96)atH*N&*s8J&J z6G8D)3^bp@sx;4s6oigQV+MHA{lr%tCfCj~N5oB=1%0DfT&w>iLY@QK8DlfZ#~Jqz&aE1RSIYAVSEv2;&1l(> zr!g0ikE*F00c`VgoS|@Q=aP?O1-sg884iv60LEA=RmYNlW|J;pXlnk$`lGJQu zA_x@RIDe_RBrn)%NHK`pn6_%E|Euh&{oXep0_cz>Z$iDC6_CrqnnSL(8>3L0vb09x z{?4iW0Em=C@4gL>drT#>?b<)_;ANh3u_`}3P?0-&+BNr@kC>vdV+SDjjK68@MaytDyO?y#>49$gyRbpT0O<416T!0FG(%M z3E@pWa`Dc%)tx}gCQRXh3lq z_ocqs!^s6Lro!h@b6@XrO~dRS=KlLgiSIR_y<+!enj9U)@39a$YYlt+ekhf(*QqI< z04(44uVCT=CYiDKfWdA0jaeakurADymC(@I72Jz0pcyxR14XXs+8l_!_P#tXiXX*g zVLR#&7Dc^S=MN~ev`(jUzGDT6^Tn$7Ax?I%-)r^fTlr?C%lwY6z-LP37w`*0{X}df zRiIsk>*Jr@>1kIG5%B9*&I~5<{o50Z!at&}gyJjhem(zAB&3dnR<$Wi6El2x0`F-vIx zA@pTPic0^~vd_?f8+x)~Yb5U~*N!+|nHZNE0<^r}pD zTPd}hH+=c(u*da@2xqb{G!j_3?6c!RPeq*g$E~KKy}rxgadhQ`76lG>t(L2~Ydb{V zQ(SJ-2aio;Rs+S)+Yuh?Iw~nVEc}J5*|PZ>od)k%laZ_X!%s8vy6W25=$(n(59j>_ z7rUOL;Xa_Q>n#-i2PNJ(BIfy>vkSSkM}bz0(}XLp66w$@^5^@pcaK%&25VVk4oLfJ z_vN1D*$5lc2<1kFr6<3kkLeL_g6d;=2EKYB@a!XV_mo^07I(eO9TFu|oKdiAt-Mjficy1c*}-O4aRc&G+LMr%O$u(p zbXwA7Wk?8o{X6E&iXUbJW(buE%A=|0h_$QF`xBr=kS^1LEWYwa?DW1#S0L!mNI+`4 z(1(*vodqvZX>9fxl&RLRuSliGRRY$&Eo(B|cYxz^jt4c>OzBLvV{WHl)>qi=wVM>O z?~C=qFHO3Picp=4?b_tlbw7B9drd3RHo`C{k^c-^5EO3vjh|3=rt22hU0`&j7`w10XN(zj;@!rlEDmrVwqozyCGX){gNd+(}tyob_;Qxs;||K zHlg_bskG)j1Iv_NMmIuNo2F0TTvy*OG!rA;lI;zMm@5nqqdyh#eUksFE`=a=$qK!7 zK_tdWVLDYCQ%m+&&C+1fzU#seZu(mP2X3@du>$rg7eXka!Wu@2y(+QF|MjAj91{WJ zTZBrpg2f}IR>{V%cQ`X^PW)fGRz6jr8nDXTB|LQy0cUBeQalXxet}a&i>cdDhtJ*) zs9lqZxwux3kZdLrpm{6IeK+_CacxJdxJMmp{t9^JKV}Y|GUMjxfi>K-C;m_2Uf;`m zS8rJ|pc!sdP6m8Pq>o;|FwR+=j}%yAmOba<8?}l%LPb|i*}wAEHFQPL5$cXW2RCh| z-z~BFjd;p5fKSe|M|m}s4#7M4a!4`!jZsi4TxH5EV6OsIfqVM)Ven^IrHDS!1y}P3 zS5t_vSn;0X|5$tG?`&$vddUa)iaw$^dPl=!G!;HUE=k!imA0w~?e;t$^-S-1U6*2A z*D7wYmeP&iB+NTz(E+*hC+;C7;kN`j&Wug21uCo3E95;Ge^5P!>eRMCdan#WMZ;HJ zS^72@#`n~-R=1!2rjdaD+G`$pQ_JtB*V={Is9S$rzJT!o+D-R_`B{?wA&$-Yz3ywf)fG@)`V}^$EHMb z*u$O&PP&`(pzGwVIft_|8Tg)~nGl*E3N7!uv&V<5_@dP|#8z>iYZ@m!)YlCyyVjY} zV#yYp72NG!@&;Fqd-w9Tlh&Tftj)vcgK3RN(e2k~1CuU*mmc>ZcDT_$sZkwY3iYX~ z&PqE3m^4Ur%AH`5lLa; z7hz#k32)vUNaUzS#>8AwR!;x%;|HIL=J8CyL+HWK4-riwv}uuYiI18}&=eTX>s(Yh_> z9_l(ZWID}zd@R4qbQvMD@6IG=7ts|G6b#7-Iz-W)Lj>Q?x;?w# zmwh}Ex-dJNWC6n_Un46psfq#mV&&xA+VQa|G^v`)%Lt@E*W)GXcc03*j{ay2r7c^6 zEDt*s&jQLmxJ}ffj}D3GgY6N`fCJHox!pBzd_x{5FE0ZIm!`lY=YGB;QM?&@I3AUh za;&SF>RFpEBXe$*Kt+|KeaIUTy$|hkxw|&)v-wN&=vrs5uEOiz`Hvx1O;kNSJ@!4>?f0GBakfM6+8T}y+`f4&wkBV* zHmdWLHmiNEG{4t*4^NtcY5f?ifs5GweER{McGVo63~1$p?_YWJg-ptSch$MAcKxSV z&1R2w&BB-b!*g8h?9D4|2pG4$JVH9*=$wpw_xW%} zp7os;x`^*BE!RB%>i^qX)C5*qv->BCyc*cb-ax})i$h-8?I%x$@8BHzvCt$DcIHbi z!{yH+iYQ3qJob$Ni=ba6R%#6$KiDn&*QhN5wm1a>cdhE{T@4AJQJtQ+igri;v}4D9 zF)Us++T=YE&{q9ydS7BT`B)d(`hK(T9`8$BX!DFoIgSfI%E0)HfHMAw6918V-~mZF zv%A-eeGkSG4lr%3a}8=N!wOM=I+KJn{X0HIr9F~n9 zF`zs2MmFS=EnY7drV1xFaL2h&o!Xbk7^CWRE^l`_1 z-lume9h@3j+}MeIPfj2UNQIkFhO!5L;kg|}D?@cS?hJcJ(N#z#H21hr)7r|)*)5R& zcQ1Rg${|BT2VhyW#IV?0r#YOdX64(W{b=iA zY09f-&a+tZh61(tEY=dOdiO`uU@f`s+r4dkE<>fZ(cITUswM(cq9ndWf)GF+_x}CQ za)(}SSy#STrEPBDlJJ%OGgRxP3URC$o6LHYaPp8eOy)Z_oa(j@_hkmOD-4cxrU`~i za8~o|lJ7Eb&!?JjBXGT{ED#f#%~OiZ^!GJhm3-_cJ1dafyg;qlFjWZTm0JB?+NlRb zRI(>kuAK|N^U41X6i=vxbKdZ&Z0m%2&tDrZrY`Etb>Ul$CF)W!=cUJsQO_Z7YS%gzVY>o!5R&-#6^H2h&cxKzRL}(3VfX6ls`~>5ds(x3i&Xu%w-UT< zsnr|yl?Qf}E~d-J(s+QmTs>QQMTsC3?P=&w44KFQWNDFSrC{-;XT8o|t3zlmi1_QS zkGH*)F#kzN0M!+5~X*b#Rg$hXwne6q{WIwFZ8Q)mZY0xIw zGKG4hILi&Ei8PHVrcb*Ae%0k6J|5ZNj2RW`Dn(0}v)ePJcfGP-5lwc1Nf$wmbV^lN zN#VI8qdQY);NEeuu!~QXVwNuB-}__AW?udMYhUR)_GLAZArPc+(dhmL{kH<&7_SYH2Ne!>4ccrV$BVA5tqBPU#l3wy<1I>k%hU4)c+j@R2hQ)C zL8lCE_3%0$?NO6bFP%?(e0*PlaWCOIy)^%oPBmNWj_YDYEU&%yTX9Ss2NIg34MA#% z$+`UJ+x*$=tzX!n(K$lv_>*3wkLW%{c&{+gtV3ai8`-EVmjvMfh<`T^?W9a+rNIz+xr>fIcYD66$a? zyR+Z;&N-c!H8D#v$5Z<58}~cl#UkzRp5lua;vNI$V{{rjH90#HpZbnc_l-!Sl;{{v z)Dw~#lG5e4iGF8u=1xyEfq$c^}ZnO-Dx>74E+!KcBA-@z7-#cpBbx+|4z_}I&YGm z-Y9&Sw$|eNAYghYdwKLfk*fnl`d@Lf>?=J+N-G*C3OfIBk}FKU!ln89>T?65f7kd% z7f%!VoM-f^EDgd7V0cW&k+*Y_`pV(l~4QJ=o~F}LUchiCU5 zp#L}2=~S)heVM?c)MNjS>;lx7M#=x)%^8FmjBH+<9~t;}eC#d|*$)(tu>3?MyktdT z%-HA;of$1>`$=I?h*uDM_5fUJpcgK+#<~+8X2us31 zPb|SdcarOtP4}m7f9bF6zuNdJ8MM z^=I!ZU}|VzY~IB1gsGW};9P6ichCBGgEOt+0_i&^NHhVGPejqqy=w*R&pI@l4wp~J z-viNJFc*O`5%3VuAN0w&*qh-jNQ@`!BB-9@KtFCv!cSsoM9Uj z5l=g8cGMxf&M*kp`Sybc55^7W-we-M?_OMC`$;hS**H6W;^XT^-88b0C<**@q%D|FzJgoK2o_ST~VNb!aCcQze*3ul3tKyNubNt4Qi^}x9( z-@rhthM-AvsoJ#TG{gT4&En)L%x&w%hNFJIWPkQD>c5lprD&_P+dY%}uvcsm2<5n0 z&iofIQTM;}o=z|mN(uCDJW&A4tgZL?i^1)x0T6AeGBCc3L^08oKfX~$HK{xK0V5|& z>CzH>4)gckn}AmAT*{DQCa=3DP{du|N~fmklA^a}*UoOco_JpSMOGhaEBt6qoBagU zce~z7mdhzEt70B`-$HV<)aCq4%=G%O8H4hNUO&@`B@@D=I{w_LIkg-QKHPjiYNE&F zfz7sGT*67clR(QcN*`G&{Hg@Kt$H`x)vhaA?>}{c{6XF`TfktHY@SBh(D3m%4$+^d zuA;~`Z%Noc=Y7p~r*LMnN8m&j9w-3c`-ym7rslfy(fogb#WZ))5aa2nk8=CimDQA} z@+@WUB(2N{0z|FY$mJW!0Y#_os2m5^_z?BRLNfV0vy1i23TcC!7L6-9C$?QfdhsfT z(axe{@f6%)DS7q3C@OK^T`Uu~*dL!^#`_W0z(Tw8pS@B5{8uD$PiZ?bWg87kZ0j8T zI8nx#%hjBgcBw-t(D@3e-25Xgy%WEJ-l2D;HfsKvvs*W+@pil+v9ASG{iK|(n*dlF z$R=_MReLP$YM6zRlCC_!U!)!S)1QAV#lysIvcKyjC_w1|8dIa>`<1;FOV2fiw#&A^ z0Ud;0r>?q{={-Ud{S|V#Zh?0YbrO#~KsKgFe!M@mRAXw}FRy z;}sVjS7_ZWtB%vg4?2B!F`+AOqhZE{NcB8|u+Om6Nz`G_oHUHw{QHc#w`cLqdfVdv zgfEX&a6N7|4NOBx(1aa#YHuKmXu zkj0M*`8t)3p8OJG)tScsB6AiH-VDz90qWYXI?)Pi)`Ikz;}Gw`0eCh=B;P+QM>;lLV3g%181{N9Sva{pb)a@8Hmf<0th+dq_yi{_-e97hhFAm#q`P z@F3v?)AjrAZyG9!%)=+1O6LA;bjj}Goj)ct0c+?1|N#C0;@o9D8L*H0kM5 z?mO;B*(}1(#X~t8c8~L-P3Gh!&B#+MS$`ZT2bb=a+3jne2#Du$b-T)@+v610A`xM> zOHFecC(p_0UDsK1UfuS{Y&pMOBe<0Dsg5-5YP{8`Q|fsq2^M{qaBt@0{Sv>jW1XF% zcTIS`U>jAI-AdMEdPVf%_=)mwHtNKD+?h|?gBEf+^p3v>B_4ZHcK1W~H_mAfvKSlQ z)>2niN_!vOZuVlwnf$vVmJQ{RNeA@e;h$M z1>SKu*yI zikx1zEN)eNAIS9i^XJvEx?@2<_yiR2?DK& zUiBdtYjT`y9iwco-9JJ2zord!NR*CD871twcW&ixn9KxrE_o=LvDvzFNd#iTwQF{% zcp+&?Lo<9sp8y-JIC31UV+}lrJz4z?yL;pE@<^}=(yq*bFqi5ymFo1yYVZIf ziL3dBkwmur35A?B%)D3kkY@__U5A&R4sya5rlV|fE;S|c46f8k&l9IZ`yj@;G$42i z*$_b)pjWL5bzsRDNIuf8OEzP*wOVo^1tXGTsGpRiPtOGlbUNpvm~c|)5V-3_)k*KY zrAwBu&`#%YRHxS6yFaHr81mlFzJeR$TSsf%$ehzz9-8me3XwWSaih=?2V9LIW(cDL z>)%6&Os4WKq&iKfIW=DU{(iCkb%iPiVaL8NZ4C2g8rL%{r|geAO3}FguQ|Z5*n49Ncac?n z%hUu_YRd#vCv`6Qggm~U<=(bKW&}!{(wFL7R2Me7?ca^LWlANj%TEOAYX!F5c51JZ z*lshuAXo4^SBF>Dx;5H5_Oi(A+SjOLnZ3uYTzj(pj^|T%J|1f|j1Q86`m9jiKt1;1 z0i9XZ&Zmytr&~O{W3;e(7N@*jvjk8MAU{rCs>!wS6x!Kx#vF`vS-btZYd+!nnf5?J z8`vyH-~ElL*Ufyy!sGlOl(aNAd!FuYfPx*g%c4>oqe72gyx@u5acvqPrj&ld&Pz=l zSuWBybdX-32CoOCUrV;+xa2?Enq#=b5F6s=`gnpALuynTb=JQt+4b86#mj|r@}J7T z)HJGhY)(Qm!1dBEKU92G+x4X@NT$lp&zWI&ihQv4H=z_H;9J1eXHXr(hFMlQJ)>y9 z^D7vM-T8@QZ(-{JXLf}}0FoTA0<~gN6+N?3cxyrlX=tB%np(E~p^M}9o?=_hB9j0b z(Huw2;K&8xp%c6b0B;Sk%QZMEaxUjDujL5+?g8|eQ#w!$B;bE0MbA}27S zamz*r5I2l8RaU8CeR1mTkNm|rly zUpm-VX{t)Zs_n@!g0-}e6sok`wVdjiw~mY{=lfCM5SMXv+|*TsQk#um2h9?=7%2G3D(5oUfk5 zp_g&(!i_Hm2_p3-KM&Kpn#YB9XP+I*ckMMezi?G*dQJKDP&EWKz}2Q&dqHYi$w;=7 z&;vZsADHCLLY>z}I5*=LAJ`w4<__`em)^~EtKv9jpxqltVDr%HIi+Cp>$X5sO1v_| z%c#jNP#KXdZvxQYEoO23{YdS=^gzqY{e*G)v)kcxU6{&u#~Ml~1{x9~CEwv^Ek64x z8baPjl3^N6vfiKE!01hsq(C8cjj%O)LTka$w^;AFOKLlsma~Xt*`8wp*8vA%(YjvK za^{WNOr?*PM{c~6$N zMa=Jmdi)XVgKqbuYesReQ8~b^c}dqR-$r#=xNQ6C&RNBC{c96Z4!7)LHzmKg-pBpeQArK->d3vIqa% z9}R#h9h!c9N8oY}VXnGms>bat%QrZEa*$A0ND8XX4)zjOc|K*E1|~CvWlkO%;|YH( zT{eMTl7yJp!>VlU{ra%|DMP84E~w9=hOqjM;YWG*a}xIPDH==KEE}#76>$FjZHr_7 zgI@UG)f|LLk9x%eCrvd>DT^}BVqBI4gBq&9)>&BNgA!7*+;YH%r?sOGN9aHGpL=3K z{cs|f34W|JuxvDThvRg!Q14S-~S|@LGz{2{K1Y@!;1O_>j`X|2@Yk z?s#|Ju-@iIl~-|xWEA_J*BZ>;U%5|-J@9~K$q0WeZz$JWfJ<=g)<_$!=2t|x0$xS| z-vjR8VMbI<8XVttU;m`0q)utBmZB{=4`g3LEkw0xJ0Nv! zlUtfgAae z(NU%PuD|=a)V(0uex03Tp0hwgxn<`L3W?X^KQCHH3JHtz>js^=YZzYa8a89rmL3d> zD?Q*--7ind3FE}-2$oC5NWp9FhbARn)X_EPNVU*?5CgR7T_0Tbax+RV+L}hJ<>d&i z=!U;f%fvq{vEjS7n=vs9eB9;^a2sLBG$>4f0;Yo|#Mfvl`5DC}BIxv*Evyg3!A3)f z0U)yf{YtE{BF*udqag)kz?l*vx8p+yd2vnc{F-EgHrTa5K}*fyDC?cC){^i`aeeDn zPY=KP?dBGNn>N>WH?I#ij1kzt%>OWV^3sbZYru;Uu4-Hb6D^SrPIX9OF~2F7Hu>E@ zXSMV;sp_ zYy{~q8|*H?2IaaY1U1x2T{1h}U;SD>Qhi>vA-fKYYaA1Kx%w~VWiEycb7sG)T@$b- z<8TD`LwFchOruD)(&rt8`sR@@TcYkmc=|#qWoqMQT;d<6*PydSfZEH(61Hz~1T&B{ ziB3^Qb?Yb89VqPY#x-cXiq!f5B6`9dFxhZpvhS=9{XDw6c9l7oX2ooH zpUpmq{aye&ENICs{-jraY4gGL1$TN)2@g;NzG3?M=*Amq&ac7$C zk~qWY%?nrgBoMTBA4kMLZo+LHa*2Yj5i~1W%qSi`i|)7IX05BYdWQ-ozD_t@esWfV zpIo$k{9UdnF`)1v;93HlJgtBAN{B2?xuCFg8n4Rxc4Xg;;tNH}o4oYAFuwpa|F=7J zpkt7D;LZ-!t@v|ybxETWl~VGityMyPw0n~8?>{muKl#J))nj>=0H$>@#;?UZ)CPwA zuX~AKv@1{;?cO_Q-`!E0G5>R|{;EBC_` z{i1XJ%BL!ex69Ol5G_6UMzICaC~29pC$L+zFGGnGMzo$DxZmD5FK{j68SWAFA?@b1 zGN*O)-T3qU9~~Xe&5uRWX}>|tC)q~uE_g<)#5R4DwCZ69d`DtZ>-(>>X>g^O9vRBy z_(jf_VVR(TwB8=(M{jmqfB#s#WuEB@f{EYt#p?~=$RBR8fAY?4cmXu6)$yyw5w@+Z z8~&2R5Y`&>Pv!$iyQ7EmeEqIt-k->Q8~%*F4eYBZv8_3QSLlbj{(^Bayk#&=Je@^eN+^#?9{>6ZO_D#w6zl4|Z5+B|;+BTGkPW|6?8p}8 zUgpiooevqs!2|1+H{!b=7CK)uM`u$9xeT|2T60Y@o4wWlc6L*M*(9ksc@b2C$DbAA zm#&85&4GxhR-WU2gWrt%H@tCm@Aaf#g}rs%>VPlKd+|t%AwlJ(G^$_5zUfb&7#&J? zv_Uc!I^#BZgJD(-bmy+jvT$d?9dnLLY(HHUvLwtF+eig2s_r>)D!elEL(8nxl*6u5 z!Lc7`$@hQgVZbiwLHq`>IO(!VSpN{VNT!Sh=@$HPPd`sf3zS*r=xS=tySL%fZDoVs z@WBI?G)4|}WVf{F%z!d1ip`=!@SH!mz1(OQ^N&O01(0#ChgF>i;@g^7{; z%9I!7b?(3PXcySdoQ{Jawc3%)qnZLU>2dCc5W*Q}`BD8s{#4@Cf?euBA8Z2!NpCYZ zs^3vRf#QMW$EeH6{{-VOnTlU@vN4Dm^z9q5k}YEyUADG8>CH@qv^P_nCS#K<56>LC z--io%jfH33rJAQXGQYuHRou@HHvy+*UB`pORSSDmSHGPTCQ1RFJSHOdNh1ydlIkejW&b$DX@|%D@ZT#kL*=T zQ(jW@xcDI#xC?nxOcUH4+M#miFQFWyV|<2F0=M@UQ)?Aj7THDhK`@A^#T9f7z-6VD zx_(FS-hI1MbYm=qDuX4YoTK3`2*2kOdzD<}@GzQ{>{YPByKT-T{2*?uJ4Z(8?4!wc zx1*>37F;5Dzm$h;n1}psXpUvsdz={=Nma;4E6du>Z)MdAKO-$tfA7BQK7#9IZ32s| zOas;M1l7ZdupxoH#~`Iq34@y!0&k;ZW;(^5l!-v!rKq5E?mh`m!R;XU9G@fIR)VRP zN4Z$zn?a=W@5y|6C%ryXwAavWdY-@~;Cd=H_^|nWuAsjR*>kt;!rQ>gB|wf;Ug-Tu z4?_3k*qwZC1@Gpm@TXth+fQkY(_JhMHrVK$3EoYOmc1&S5W7Qdu=`5crM#bvy!2TeMR zY1QlQYDRLKe!M^Xf=M}rYQhl!29W^co#gvxMswfoPV7YO!F|F_EI7rPKs*5{#pUaR zZK7dTWaKWmaw-&=%yU#*!UM8}dq?Du^C;>cPENx?5g9lO~4_J5gn>v`2e$ z#TR)M#+aCVeRd#b(D9^y>gwMGfOKvyfE`42JzQKlwKV)b1Y#O@nu`YCKsUS4h!3?S zIv(2)*p6Rf`@RCrS6+5%S;r*rT^%jia94}xuAZ@WpC50b2T6ov3NySQJD%raJ=ZFh zRQd7V*UPTE_FM`(wtrKroL#C{m9$K$EXF@Yae_RGRAg|4ZKtDz-w%a25A!Au*+3L5 z!9``q|KA&Uje=k`NU988E9}7Aen7MH>`vKxeFHNEt6xb{^VBDlCM5ZdhLbDB_S7>~ zb0TD>RUr(t=9D;^v*bzdjk8oY{?D9TklK84!4^^d_+p@0>W};eah1}q&4t}Fx4?wO z=wFr!se-5nqx=6oGrulfL7k|8H*l~p%D>d!f9z1-bRPCBI8Vj^OA!rhIX>7|JR!QdDhD? zM#yvnUN$H21-C2FQ)aPpSz(m>5w^DM7J|y(mj_&oDAorzTOf_xqgSJ>+5-A3;I5zG zMX%vSI;N(k5^sh7G=L2y8k#BXFdxIKoPNjSZaB_I`*G-Dv(=&pH(V(@kN6nm{h61R zjIMO5zZqkvkxa-2*%V{pU<~2Af0532Z|R?$_!m)6N-Pf~&h0r)#lMzTxY?Cw*)Es7 zT7E2^bh_3_nd8fPomc6rsdnYNxBr{AiwP{SubJ)K=B%FGl=qjh=FiYI@w2fWY3zPV zc5hc;U%Eeo6q5DSXMTruI#YFXUbchLVJ@l)1;bZ#Ao-`TWOpg%Vb2x1e?Y4`u&y+L zWKGDORCvU5F-4~68)Z(x6{<(*FBU?BW8-z_;Qh;!Q^j08B@ga^B4JrNxv{3}W{-sw z?9|&r%30ojPx1ku%Ox1R{&%Heg+q7k=gnz~6M(ej_dAqR+LB4Fm59UKXIysZus)^jk%J^M>U7MNU~ zxFVZ`zraEo)5JJ6Bx27n56s%-fWJ~?gEgo5w`^f;8NwX$+6MH`mo?D1*vs|JlY>dw zkO1)*l$!*at6e9zvSc26t!!Xp>aDb<%xw;2luF1Gv#I2-%m89azyHt2d(U-{-mO;BCDsM?h= zr>%=>*vcdM#5EGy0@982-^HR2AG=JW1QPe*VW7|5JEQ-ZI-2j4cF>QVv%viDAS2ON zZWFm#6qtCVs8mvSByR*>3TDR>z&UWQ5e17Q3{~ZS55ag-+pG!FlBVQ zgb(@vaEp_mg#;C&@sf@=8w?*I4)bypk9vD95{k(51(}QX&w_qGRx-@1cVE;Hw9Fu@ zWyjI6Kn@8_bEbWl(vyOWTgy}=_UsT*pUEiOZoOPz{Y4!o)tm8DLwyEph6P{fBa+uV z8(^lxl~;-nDns%bEcUxr4NDWwjK4}m#^NHF;QpTbOC0F=qaHhr*QZ8>H->A2gBnMSZaMjl znBqDGasO^w8OilLBUV=>K~b|$%%=vip5E=NbX{}q)cw_)ZdyP8 zNH79%kn~3dnf?Ih^$19M;(xRYH}(X5g`f}V5<8hBdTgSM z9PAo9!Q`MOXj8H0dPJ3nS6$Jqo?i57rF2xS6lmMhNncWFK=F8I7-x*&K6U)yp&Q+3 z84U`rT4zElxqYU!M7Rys4<|j*P^Z5LDj#SF>X~M&@90q0xh%UvJT4xtrK7Flkxl;^ zt#FlZl(HEY%I`!HLv|bq^VKom+h(LpYSB4_amnbsAPh(3_c0djvn6=@M(B7K?d0gP z#y6=0f=j&~R>>>6>r&RIRmGcVVh`;Q`J-$_+?2%1##QqYrz{oF`fz|-eS#hap$Y?Y z6Ln|T#zJ&PH%Su!7`@wCp%v!x;G4h8J|lHQ8Mgqv_&~J_rWIj#dnly+v9cQQEetN2rKs*$Ql-Q`dd|)Lzv|lG1Baz{zVU@L z>N89cui=x^3{x0aivF?#xrU>aJs8VC$?< z2c;B)KOp>mwQmN%kazq<=5tW6HOM5Sl=!lN^qnn4eE11`KM8nIyy-L8^ea-L)|OeG zTldZ_4RFg{?caa;cjIgUA4`TA^JiNB&kxmw-jZZo1kJLd4mTfqZ~M}(dUILSdF+j7 zY6Y4P=SP=##CWkdtS{7Jv%GK5&?mS^p>WAo6dZoauoE*4Ja&S zZ1^Ug;(ZCeX7XmJ8h#Xi(X*Q8n+pAgN<^{i0|YxOlm*{n-YOe z^mHSTt?B+X=D*vg!OXxZGN^7FBB)V`UQ55Y}L;G!% z7Hojr2vqoeQ3G|MA0(;O+uyIakzqQLu0;Ew#s;wH-04ZoFFFc|@ovKISdA*ty9o*! zllb!Qy;0ARVLA{KK>M&}w@|cTIN<^s)yTu57GYxfZv?DbNT4WSYg+Y=rZptc^iYR+ z)BS!ML!o8ps6CBRdhl~u%-eyfya>*5b@l7VSO-99avOkp;;RADt0QQldlnC9?R9II z5B+%p18z;}s0)FSq`LoouzAT~c8%pRz3xe`En`dXW~V|~NZUy0YTV5W$Om?iO!{*- zZVPXBnoQKIpUsavG%B|mm})JNlG~xShmu`VWMV(+Y5?vY0(MG~yI-E0(kb)$U(pb3 zs$NPHy=v63;cjijow{@VMlBVXxZm^rRV5FAktE=v+ckguWp)i-X==C+jXX?FDwzhr za$rpN-jqy5h2o9HMxib%YXeEB`kxFdxdEwqpP$B?9^wpO#bbfh*RJy61n6J?LyU#p z3+NzG;ZL%}n^~a7Q0Di)^0g(a`p=jH*0gNd-5NnPYr z-NGzatGvXf1Kj#yW9ZNLQT5gDmmW0upz@@V3_n--u_mG|+ z76mBC%3PPVL2MV=uoNb8KPET$&gAQ9eQL>nycdweG96Jp0)o{Fn7S~!FKsPuhS0*&jL{3=wJJo}C!F4(n?YOXlVxN&TSe=&5-=VbcP@i>MT;FpFD? zgX!j_pxF(C9fcCV29Q)_c>((-f6Uk(&C@^Y?>jpM-x&JcilPMiTH`1ek{h=wV8++Bpt(iQu%J)%*CYbQpSp}D2+ zOO|OSlkJWhkAmQkbNMG#DuXMeZ;dG?k0{g0l+-@^Hiw5!p+Jm=tq7|xO^@s*+o^Z| zK#2cVoNf#xOZ!Cp*M+k9e>4RMrve%+gSxF32acACa5T@?E$Adh^MlRYc8tO1Syuw? zSx-v(4JcBYTv|1Fe$Ewp#sx}5mV`w_w8y?s;gSLwXfgbJ>6ZeX;6eH14y02rC*u0# zx@nh`YCp}&mLGlH9;BLu*Wu;d1ln-fS7c)N1x$avAZ}>%>BaxVp$5Hj9w@)i0JtJm z)!zAm9>I3@)DF{Mm_Xo^+MVe;pve5#c$0CS;UP@x!VdFLEolLjf#Cqh?>Th4eIrGD z)ST$E4^Cs)V_-^|BE;+-ZMEd=dFfxmEyKo`X^{7@XD+-fWJq7I+fdcsSmxTeee`1E z>JbG4E#j7YKl^ub6S2Fa7&^=%3!K%=T!}C}l1PWJeQhgcIAOfve@9Lhfu*HcJdj$U zvR2v-rgxi2QW?UxS_2@MjUx>RfHdL2Fu{GJ5KWN)qN)P{UF9jR1Oeg$_L65mzjY*B zX<89e=Ay~Wk_kSnjXK&lJq>~Cd(-(Ax;ay*OLu(9z711OvwE;^$AxbLPY#tXTAYZj zka$=!hdmA6KwuEFQsu9iXsf|b+lu_&#`^)NpMC6zZoWQ`1w)5QpAQN^?9dm0 zA>g|^(8J$eR`&e8%cj_nj3tMwuYCLg864fGlOTs*tZQhqVa8c1?Mh zx=ohc2%wb>pC@#qnD(y8yK9d2(|uiE6!3qfyxcEkaBLKsfB*o})@y;V7 z$7eLn*S{kvrQWbeIkPaIIT#5pps63y9BZmATCs4QKS#S34>ZJiH$ab_E?&@_e)~$C zS>F8&V+|q^U>nsp;Ikf_K>u-J{9LhqLhX1VU1cu7QU#<&<=~LD6{DAKPKp9LJWJC< z@w{sb6CEKpEj%t#?U6>gx{upT6CZ^GZ50eXfggAqW{X1XklF<9RKroN@oh`J%0Ata zeAge>Z$H_|=ESfq+kN_Lx6+VhmQnYjyf+X=T1Me3EC>Z;97Wf5t z9)KMHSf7?}YOf?5mz$)S{@@2W+ zYRktTfS4s>^ex6ST4x*`K=E>X!1$e)5{UHhYf-k*+^}5@Xm~WB6zp!rX*lN~Q(EdC ze!Y{5F>`gK007vv(d(17t3R7oH-#$i#Dz`?fDNMrWB3_b2a%;S#!n^3LV}VIE3vl( z2Z|_R5sf4(*KnRDTOmficKc=fh6N`MJFH(6Ua+E-MB7*L)K`rKS9eHuDXTC5*zkjk zQb$6%lJp~U)cVLBXgsLG0kzg$rRIX8BLiU);%)XT+3rIJy9QgFw*zM4>tl`GB|rG$ zsB{lPMl-`zPi28Kiz1p)QaLoriJW!Kr>vtUU# z8eq=j?B@hz3wijqr!4CL6c$}D>@Y^Jra6_{H`7Qa0F z&Zl+TC!P;R0jB+yZ6=W3U<>Eoj--0ZRz{whV|qjEB8g z02^CuY&fU-&pv6l2pe_QFg1KMEQ3NZQTJvYj~cv8aa#%{((AORglAc+ zo=o$Km~lSz!M;&R`EaXvlsjA%3a@F`?ztsE;W$;@M&QGH5a*a0b>iWFB#V|qo@uYFKK?2)6`3bk5_q`49P*%=P(!@ zF(kV$l>d?4g$L2DS-cJnrL6ruj^wvl=Z7=o-Q&Tdp&~ahP!;5S03ID$R$$Q)p5N+> z_Lh#&Q#d8yyT1IT$RPz9`1*KY7eIUebO43Tq95sWnBCE`Y1GKQ@&foY3P!-fL!<~! z=p>1A08bx2A53k~Tfjnt+W$f3^m%(p{f`rNQy!9$&TBtq^phSYwV(6ok(U^GQ zXALiwXus%+`CaMZsLxL&u|t!t*R4V$A=egm@ttM_KmIuqSzuutP!%Vh<~jhk=F>TM z!w?Gb0IvWLK>k3nfNJPvZNVtOZ5~h3m!>tWWmu9JX};N9P%p%^wB)V7Sp~gw4iLc7 zp1$&uKmPI5Cg77b=ezM`ir_fi0)<+~f>UwHM{ypY$Ce7$YiK`#7vPilxHY^7l2HSZ zPd2OKb=rKL9rRdzf*&?;S`~h7YoxxXpKLm> zKZb^$4590^d<644q2uXR0}c(DeGcwZl=$aGv|g?vWWlL4Rg$}gDWOwzkVFzTVx+R3 zam&|L(G+WV288@9xai%($yGP>>Q|8QJ~WK*c-RNPD&O9){;pjn*YHStY}1NGt-pxHo`LI9_J(BatZK40m>waMAO8cNAmhNp~5u~F}axv;|MK0;?qAqt<2 z{GeU2Q=1lPdniFh{o(9>zx!?9BU@@V)#G0RB|8ApQ3SU2V1F~@Vsrw-&*b~P)g9qS zE@tzQ&maz53lx`UoDC~{fV#hO_(CPCM%inR^lju)^D2__(Qq%QOW=Va0LcNSMJ_&n zC3IFlt4OXCK~yH&85QrbK2x5%U&D%SyQxZ$sx=IJ2;yb{gNByt;8iMpb>4I1R>l^XS z)M~e6C*aq>ju5U|76oObk&fY`^x@~#{>8w1O5{SM5a2HGH z?XtHY4f-j?-2n_g`+rnfR6;4=O0gc(t}^>?O;-oS{pUWtw$}*b9@^YB*sBvyBw29X zGfY!W8^aZa$=v?PkBzyqB{OIK6Rpjha@B zH0R3KWGAI$CmXbr&BVln#s?7OBQhM-%Y9&IN1;t5^;4}y-}0;{ESEmyrwvrCGz|{!?8#>Syf}@3ql>p!~KD>mF{7U^DBsitfEIY{wc0Hhb1@A{D^gf$`MAWKx z*iiYD-r?-$1dr*6bpRx8crVeI=MOKt#==OVQX7`6#@gz8GMD_5u@x`Pb%roz1eiQ2 zd!C{TO-`hwhaBWyv7;&xp{j~C#bd#(clVw7HGCp9BjlR&z4=k)GKoHgN3Au+m?!Ni zL_SD9t#`UcF4-35m;4G85hn0e^0TMM(4IdrRBrSuZ9l#1L0c$ha~(=M5mrUw)i9^! z*7~dMgqQp+>p|lVr)3L9MS`w>$~RsDk>_nhBp|4O*>6n$?Yl);U7mJv<&K^TxWTTQ z*)4usJz?a?zBCxZ)Eo}q{OC}gFS-$!5AI47O{rkWkG_WBhg}nnI$w4rUmq65jmF!g zU2A6ISQt(KVDg?}rfQdrp8d}{1(4R3Y3uO^UMzOIaftTU;e??4Yzj7sNUvB15gQSr zFgDv`KDBp~eQ<_{WA$EUgWK9%Y4tX|>v`=df1aO&rFy%YEP z&m%aXTO1|%Uj6!L-@7CG-?c0w^U9mrscYC+8#lYVtbnSA1ldr4MBf5*MjxaA9i6iS z#0IJ{WQDRS({^_Yc{hAwr(mC|WuDO&;w!2ASgU%+K`_K;#MOv1Q^9BEs?h_DiH}dA z1_b_8joAxPQgDKj1fWN>sIgD( zs6LzTGbCLzmQw2qXSLBF3|ODpp~sh7z<;1j4Ss##?{oR6((~I4%z`NE#}-(9{?yLq z>78}$%lfQ)HD|Q-P8G>I&?xa1m|zw+Gh}9a^5{UY`oT0aN}f?D3N+a~p7pcs^y>7P zqNi}@3cyEOcHtwm9;!&)=E^d?t~-Ol#qR=#Im@^F6uK^55!`am?;J#5L`;Ae_^wDZGi6x1j0 zrt6Kz*$;I@=Td@+Jl}O_cWs`!?6bp>mGf*aQokrnvZc`E$2Y?Vg3KKNXmNa2Wf^l9 z3DY9Dd>mi}#?|PX;_riUf>8cbhAROe%nQw~yXk zz>z}5C_S;E#BwK7UpyL>NLZ!1?aK;_xQ44r8$KJlgLAi$+0I)15hGrG)M8n>h)`VL z(HiP1fe15P24J6WPL7q&tyFNmlIG!_TujdRuypRVLSOU|sSy&EZq6<0JfYTWJ$y6Y zu^B2qz?FTxjtX7H7aC4oK9MDgg6XHjZQw;7Sf)&81Ed~s&!;+03+NX4 zFit-Tx4+Z!7V`bB{6Os*l&kjsom=|lL4r7&k7u_`%zz^S`p_;k=gssi7ICOs8!O2p zhy%IJu&`HS;afcw^IzV6ZO#@r&P6~zz<7}_*=@W+!d{#!RzFK7?cmN?=H#XOGu(?~ z`KJY#%S@n($qhU9&M|BWh?Lw8dxWBZH+VetvkM9EJOvL))sO)kua(kkAEq2V|Nc?P z6GBeY&3WFuO~Llx5pYn7AGn(HzCf7^P+%Z0|Gb6(uiHVLjS)eQ#^#=HZufk)=B=Sv zjHhqj%p{-HZ|@7S8ZPZuGSqFPf9W7$|6DhU!i}p52N&^soWGMGRR!k=j*5M?_r8_zW zF^&!7rKbTub;rA(!7NzCH!lvEb9Th5=KHyJ8r@#>7Jaz6J@Ac z@KADC=E&xND*G23)`P+l{rq~gUa7le`qRRvn7mEvf!N!(or!Be!Sf3pZ41MiNMVc1 z87Ir;l0=Y!_^Uv1IF{h$p5p74wA(Mwy*1FQeAL#K50wIKQ%ZbVF<}A8)E|Y~^w84v z`qM|_)F~MLo)jh7cEc31Mt-dOe%isyt~udQVfV)9A7`kuI2-4Sy`iV?XQHmKkFl1S*CQlskkO3builHND!Djv}?)gx{Pb@XJrCZ)9EnJ z&~Wnfo9Pq=T^}iu=fBZ1`*`8{Zdu$t5o>&r50BRoL0%Fe{oCuEN7p;BymAk5Y?Qq# zW+2a6n^NU(<4L1cpnSe237KY`%YU`NKnvGIf8pfCM;W67f*y@!-88}J0ZOyXQNHz( zL86zMp7gmmt}7nT2^B=trcCstHwC_e_0#W_=3OTlo|OmXrI7AW^-=E!mBb;Vsi0)5 zYuRH3UuO2HVv9~@J9D)Ie7k>(z75Ps0fpS4j+!W`@`&(;Y zzO%Y;PIUiK=w-r}ogux*YdxiJB0?mQHvR1h4^Ky?)TDrXEFT9wq`aUr80ZsJPp~ba z2bG(U;C;1AVr=|UW_pOTx2K7*BL>{i;)pbhIRnqc4d<4PoOi0tl#LOE1dvuPiayBoM(zx1~WhH?lTK>cya{%gF7< zQ=mL!W&ts>Yab!83=(ErG?kw2dA+Y7$8fv}ehEx4vww{} zpJ&?j=qAtc_v+L0>X{!h;m>v%fQjy;p_FvEAfBu@9ey-iqUyywY}ropcd8`_poJeN ztjSxyB||k+uLR|GOZROzE@^0tSM4T2VwjU#daA2dM-VLC>3MYcSLFpA{asMs1!7?3 z>#;_HpdDXRsv1j^brYwWQI^TNS~Ss)0>RjB0s`xvix}^_pK@H8N}leZ9;#4;x6|J6`E3#N}@C5`$X5qi~0)t{6ACNWlM6P zYa=U@oPdADX&J!Qk?s?^33TABmdLB_=3fd!t$#1#3oJrcfzrH|jPi!3=QzLkc7dwR z0B88usn&L3&7qFjhemxcR#%>L=3O84m@CCEYnJUzKhx#AF&x3hdvY20Zb!K`R-;CS znI%NXf%u5p3mde{y0-#BMhCJ-8l%74sYfN$`S23ZtKWbG$Z#PZ_eFa8@;znAT7|zF zi7yfzunDJ0rHrrS%W*O;pj&?!$ z*0(1hr2!o%Mb&`}^)_XE`Puhs0BYUTzFVP^QtJ$~0$j)LDLzWsM?dO&cZVlIHiLfT zPu3Wy`f{L;U)?#wwuf%kshv5sds08xbq|feW zMyx>7Ct%5dFnr(PzIEHMBsS*i&D$t)>E6w)Z!YQEruo1YGO3eA`vM9XP)>_dyMEE>;e@51-lKC+ClK+S5!ESTru!bdmx_{klsNn7Xu>>|!3mOPi4qc)4U z`6JT^NJ9&K0sz)1Y?J-v>dE?v%bfi5S6}GMjB(=(WZ=2P4=4i5nM`=P`VeK8&kk)# z;Zo#M^dKdwtkGC&6Ve%^u1BS!2DBe2U!*@;qfZq9cyfW0g)m zBDJ#LCv_V@Nb;@jFpkONh9YlwrjlQEz%Ee`mtCtDHX*f-ce3@AD3oJjqPm-}SJG<* z+RfH5gQ7mZ#VwnFid2t_w(WG6wJ2Cp$mm&=4CF2&In{Lhi|}FbJ^`7mzpLuz{G*;U zIbb_r?q3nQGW}Hvrn{OW&1XUYK^3sp&N3ot+DHfut%X9rr#k)6>h4agFy9{q=R1!t zv$XzEw=!mL`NrjtHLpQvP$|=#;j|YK9;81G-LjGsp*N-~Z%++6RBhGUJfyg#PUI^B zI-pR$emZXCCV*U79jS2KtbW62D5j}?`*-c@HT7zJhl5XE0{i#7FVoT92pM>CG{TA$ z?;XYZ28fp@Qx0LqBhDE;$CjKiu#sl_J%g^2`{~5bE=`8TEE9mX^1=umcF2anro8qD0<9~ubJ^b{Vju}nV9!%C{T9)KCP4l-9p0>pjbW2CiIGX7Vu>n ze=nhj;62)1&+@*)T(z47hW?KA=3}%M=s-=3`Gt2i6dPX`sHgaGL*QFZ+RX-p0?*6c&e+1i~taW3T`dlc|pwmMK7_w4_lxJ{<9E}w3 zuDXq@yt8Is5w$WnX!4wE>-GQso)`belPLL!gTgUH`p6qVN$63r!^gPg>=Uc5O!4Yq zux5QmEVv?ryXeuGawW0_DmA1G+svW-q8?3nGe=)L0;gNu3f=*zWBVH4I_Na^iecz_ zx)Rjf8l?n?nICOxQX{pZYMf?XkvprK_9(AlX+q8mxK52!C?RX(!aM)SO2a`Xj;O17 zF=dPzQxG!<)O=B)ei$h@(z9?PWaZ90&)eMUwt46%^;?LIs8vQxw$AOs*C*uz;sx?C zIf-_|@oW(%v#d?W&+7l&&vBg@AMbZD{yd|Zpdi+?eyMtu0m&&nMA$QcJCY@a68<3G zd`!wcQJu=d{@S{|U_UCx`|uYFl&}U#rH3fGyA_$+=al~(k(z-&z#Ok1YYOG-C#(A( z-Mc|UBcMqB@1OfRY4Hp2dWdfSPwVghualjyyM{_B@M12LI~;Yl5hm&!b-`>3Lh)ni zPw3EJ3|_pByJg?@dRl83!5FWtltym5+ki0#t#)?|L)dP$bMIIr67&8YjW-hhr|0>< zcCWw8Jnwociu=F+;2)QYSvH`!p)Z^rs|DD_e{YJN7yj?U36-kE{&xQ@ck|x1*V2^H zY=Y74MD1oNi3iWjI}Wmoix9nzt)e4*=5glcj5ANYgYId>g(bR(7bDC|yD&Uct}lb` zQJ0!#VyyELJI)Bk=i;-AMX&s;8R7DvYt4&62hn2tG4V0$ceM67iQ;Wn2mX?eUU~_A ze$zTG_K?Kc0V__FqR5M%sbCY1SDHMa*}3Q|An4`z`8Fo+>Z)|tAfk_HHg(j6K>~r# z8zL42weMt=gq?{GAJj7F?NC9DmWRt$JV?qWe=_JUqxI*|GUQ$q8?9G0ILC-^iG(o{ z#cI2T78e~cPbSd&KM`eetM(LUQ#-{OZXkB^2!;qF3F+30%dhkEwoi$fd~vcB@^jK? z=U$n9Tp@Mg8;0ugDQhCF^)gH&=;lwm;*EV}H@Zn-+mc05B-}I^SYI^Be$%mYt#-7J zV08MK3L!#Q*j$H1iqj3wxxkNc{PQq}Eapn_nz_VJOaZ2Bo}v&f7?1Q1t|v8-w@-2s zmh)|kw%*w?L6zMMXPsZBOkSNEF+;HRL}^(cyYiJpBh|pXwysF^Ib0 zF38)?MQCvbed;_3Pg4JR+)#J5aKYL3R!0P70uh?}7pad}@hGUR|5Gl}nsTyQ-c#9c z#~oxxd=*<{UQMO2)r^|=Qn`^y4I;|KQ!NEBj-L$%2vSL}>m$b4;OZ_|??e%L26@D= zj}0(zBwKI$mEQpbDb5v)D~0@Y0-JD7BS=KfbDU{_Sj>42xDku>y*%40qIf0L!$yXo6aJ`L@%NDD}pgdoiUDME&EDL_-Pp+tLBZI?;jO*PTPu?%Ze~u-R`zz>?9bV`S)W+CxHve!;NYs(YmEE?Br|{Q4fW;-1I&DUiq- zDLZfxz4aoW_KAYJ*yBp0gAH0{&5rl2h|EaLPo7B=;N^xadSkND1kmRu`TD1Q%u*L% z+@enzCBcf-FNnJFbzf|~cr&P-81xbRX%OMFKzoFThZkd$v&ukAOB*X!*boXHtm8A= zf&bDr28N}A|4OrG|L3s>zo3}nGtJUuLNc;HyCm>;w7&Y?T~8#Mq3By1wmq}U&d!#Q zkl+^#2H*8*kV0_`?J^A#!v4P&jp1l>Bml(8lQJ?CO-<>Un3zVQVi_+lFCS4*L=+Tk z@nrsEYl@zW3*X=0|CP8nq=#QnvD{pT2m*mfyne0P=5u8uqEsO(DIu}`IX5>~xz(Jbwln25VMXwPI) z%h#J|>1gzf3*+>E2p zV)<05!Hah)d{YgpkoLQC@|~%Q0^`nL1bRkBwHA+~5`&xhM(0w!##j;G>$IiB&!4^S zx4=Iee5{cF?O&30&}1y@Wy}5b4zVpYpWXabCI?UVYfVj}APhp2iF}2m7P|l>l-N`LZ*e(4)$WUavs*l~#-G?N#T2d}j`rJF@SbwcYi#q;jP%ZJ`?M<7!5LBt zb|Im8fGr0%EPx|D+pUpw^%BkD8OU+G+?^m#PiZ|X%dKkfPU!ze@qd9FhsCZZxgr9h z(vxhPG$T4jQuFj?R2C|qj(P41>DlG&+2!sLa{hKs+mkHWliWJvPwb}d2LObpwbsXI z7x#``Yuf*jrLB&p?K0sqHv%+5@Q`MVun-4}vqybYWQ%l}Z?O9NyQOM>VmRuEDKzI< z2j8G}85qN42dhU+VNGNYNA4T(Do3kJkrU1G5GUSI&D?k)#MSs`V9i?}%)>Oi-u(H6 zix0kTL@Ym!oKs$&+RYq9km8soPHDx?3N+JUM5u z!$EiMrZC=GJGnA!DB^j@qMU>TeS7oSq^{Li79x-J&*hp?5#%hRZ|{X*w)`c+OKRoEmwhD2pJMI;SvyHio>U?@ptV)A+IXLvEg`h=^*et6k{hY4X^!Tns^A#5%Bh(Qc`39J}Q#GRhP<% zWO*KS6I%iQUSmGII+iV7Yc;VM4D*Eb8+Wsb{u#TJoP667$-(PW3U}C^b38(%&VdaL z{20XS5t*6P&2D=pXMcWa3Af3U&aFR=V^nI}b#z~FB}PWYS_bAM)IPkllo=Qp=ubIU zYo$izv5bgAB_w@yyb&51nFqu|ykIk)D+61}-2am%Qv94_Te%tI7r}d-wZy(Q@peJM zDBxE!Ci3KnxwyCr^_zJ)+Ae7oK0j|53(MeqA| zXKJoCQ|+Bj+mf!`ts`{obu=&YqNYkz1)IyvFzbAEKcWOMdYqmr%03=Ug&_j3+0XJi zilV=w{eGau6L#IQxba(~C_RDY4T5OJOYM&O!Pf%tO@Gwu4n!xIuD7R7V9|1Oi!V`i zbbhC((5!Zo#wXgf_k`w0RS7RV=-g+oZX%@H#M857V}{xVQzz{d!6Ug>@meX;$2ui`p8HiH^SozFeFXId3*Ni>arSnA6NE97BBS-@e z7Sx-c>&9NI(b9!i)D^=suj$TY2((Z&4}Mx3PG=kRVu@k9@pE;f{~H$XuFrt`iv+%g z%Xw3NvP{?A&+zqYRGX>tjRp55v(w){w(9L?YeTmu3Tj+;H1m}*M}RG-<1Mh)I=%mJ zW<&D5b;rK5{m_GI%_ekgYy#X{tnv1A*+hWkrGR51Ib=DJz{Jf=|P_e~0Sg z{MMMeX-^7H*r)RKbycgSCT_b2?Bs!(e8yDQYKXK(es$OjfP5*42lVWu-Ovh1+3 zvZ5&=5vay3BxFmca^r8}okEJmvKWZg?7Q+)2{tiKT9f9A$!SEaicB zn5mY%BIFtNFWo&X#MM@Qp=T>AQeU9gfhJUN-f$H%99M`(C0vGbY_ z%lLPc+Wd-s2rhShmHDXB^P=&InJTz%W#;Ek?(35V8A3YcQ>DYBBN~4G%cc>)tZ^9& znhIA($X-A4vp@G(ag*%@aBtWM953U>V3NCAgpWdntaEZmGr8~g4=LUq>1~S}Ix$q8 z`)fAolpqO^a6%;HWBg4{^(ql1!%zHZc)()Y+nrq7{HVT>*zCR$ zIgQ`D?=N3n-9-%oGO*V)6oRSpA3k|kzO%pg>HjOqe~)_qJbkvi)gJ-y2058om%d&Ip!tF*Z^wHC`UI|5Xv2mne7yRwi`d(P9Y-a zZW#}fj9bTMO|*xbbP<)ugieD6L#tD;eNYf{jm3oRPqZhi8S4*PJOaw+auc}QUCq? zwneBR&(3PoPFQj6HHR_--3J+RQKx_0y=1my&+_klq&i-c?A;eBh^c7|?a|?-)Y<&E zITQ7HJ+U&b0Cg6^j#F2u-!o2+15#4t^-hBS!@r87Ghz=3>T?X^xhfAFZNlFNDrrju z(GHyENi{j}9b$qv@Pz-wf1B%!wAzW{%sPtm&>;e5xB8F5D?mXaE0b}-I>F?;XYDe` zEng}T*V&}r;RR%1<_FMgmtA(@MSV z;YK*2(REW!e2Hj0&Nk=X^Z|W7;|syhfP)4ELOx=Xh-|~oN0U@xW`^<@A6U*AzG)BX zU1a=+M`cH6Nb3&T+KTz5$m+ANsiH4G{KRToyrA3G0g{B5xQh9!nYG%joLt z_K{=!5No)ILPoxrCQ+QG)hh$w+izvNhl9@SNxmO7JWkw;>=7;H_T}=`@o*!Kag<8? zw;K?^f?NwV-+w`ANp3rTM$*~gbpfrsG(WTXk3_OoH@~+C&Hr9_lH4t*gqQwFw!g`J zoDJJNUAuoKzGftf5ilzNgwlP6jY~r}Xwnlb?Qmi0u;E8f9=^S^=;-zwFxw9dguPt# z=>2mHw(kI9RjlEa`O#xsPty-@hG?GBb_OghLlv8{D4v^`hbfwRDMC zn{U&9|CLJY2laWU0K2cUD+hbuYF(ueAKG6D@u*ECxA@|x=%gqr{^h3I7^LVY2@r+> zlA1lPn-VgpCMi@k5~8G6*%}5hpFr_njf6y-9(ebYIPbpqU7$!w z*y}|Hs!LtPt_j&EsHW|8CXKzf25qeq(R0mH5c12vVyilE=)}D=Fq@9``i#vu$uF1z zz`l;41?wpjP}5*}}?yTC0&Iw}pvl(`b4&?F-Cc@Gv( zPXuRAMBk#}IH+TUP+LCv%8Q+gh-T4oo=_+G4wBUTBB?>K#1#5dcw5fgqG!yEN@(PD zzN0!X+*mTZXKH-3H#^uSKm;6^}nGfD`)Nr6b^9tQ_pJmkFH;c&j@2rkU zsgG+dz<=q&*w{_>}qgZZe!Xg!0>Bb@m*KJ1&o=)b`9K&l_(3 zT!O8>_1@u3LB2GgJpPC;`-HSIb+Z(&VnL)ka+OAB*|UZEzgB3bnV__$G@Tzz<)K(#6xe?@KH46ph!ph-ssYIhJs(IHHiQ-y8p>XB%DGA6 z5oVgq{oe2I_~X7B)otp#1N?QY1;~vMfxq~aVs^9^+;=kfo@}9aSjOu1abw_gyf$M# z9JAhFA>;vK7O}Ns$>g^EXF57FC-qkkI1BaoRI8HfjtI6;;R0w@b{wR;=EGQVkjF2< z?MYkG%-&F|m60|7vq&v7BJF1K0=!g(Mp!TO#b#Lb!KH^@Z7dRE9;s?6o<*69-|SKP z$#-}t)CWA_iDc}bmTCnX)~Bz(Rh_-sJ9{G}mmaU)ws`%NREJbi{uvMhpKLc9?lusW z6{*h9tjF#xuUavYxX&P7N=(POZ1&$IQy7Ju){w155pPsfg%jz%!y6k#cVb@leQ zG~dIBO=p|JiIZ{P@~17zY!3-m#m0p)rpLoKc+Uc8_K}FU2h+S2a!OoaB)DH(A?Qfo zuHQsgl(qZd|8f?Wg2iNuAH< z{QiEQ<~5sft_gPMIv|b)GQe7?PWP9<$49LmihS>4zmlwK#Z0914=r58sZ|4Q_niT= z>71X(y8AA!-6$H|2?-_Mvl-uID$dV`IIc;798OUd&i|A+;Hqlx; zl;RK9jjXW-qwZI7;eO3Y7zni?HbA7dOf`*~mbSmIWx4+|#KrpbS>6P9GRaZY2@+^$ z_VECcXxDtqa_X;`+Yh4JESsgu<{DUjRnn|HN&UhrzzA2R9yejVPnK=Mldv0a?mKGd zrj>n}(OGfyz9G}`>x(o3xaiA)f<%^A_Iqrx-|JMfgvB{B5$~PYc;MaqU zA3^`iyhJx!=5J7+uwwe@`5!$&@j)V0-qsXi3-2cvby4I8h-hSBw!4yO{DNYsS@mp! zE-E&`Oux25yGH7_BYUVo2(iMLd$Btk_|hdaf(G z9f_?#xE?``J}C8K>X{6Us8asD^HY>8z3>9d%=n?xg$Zd{C8t+#TWkdC@#*TFNY6MM zsC2ktG9iFfy|(IqgT?;nwT~tlx4ZvA+B>*hB>`*l0AIOg<`A2;D*wHbiCdXJ1-XZ3 ziK8;3vhM#@!w0M7TlXXU34UyH-9)E7+5O>h;dB&DJ}2Y&nvRDoDCocag-L}hDJpzzeS(-f${!6gPSXo7flzB;$yybogD}=X2CTX3$*mB z!uVnTcFJwbRag7DXArKLkqKFeNqrTIThhPP^1y0puHqOfUvptk4U<+0q%$iQFU`y# zDuYIVS_2l?-M~L9i;95u9$otH;aZ+Q^2LwUesqP_J4)&P>aSrlg7-=-TDd$t8;*Rt ze)u0?VQof@mvL$mExo;>-RgvM-VSI%gKk@Xzp0_;=97qx&A6(#dzvb$SnnJb9s?T2E&NjIKuxoJ9Tt6^<<%)wX9FVb_p7 z)en!~4Gd>yNvd+G)hW^PaPx#rz)1!H(-7d}6JI)fq)Gj8V|lyFpIRAMkUX9VckHF# z)M*+n9H?7G4d}jP57ze0fuqO&@HisdcumSOBYr3l`@kx&2uKqo-ss)PK9*Wv`9;g4 z>4mv>3~v<5<}MAr5c}lUHWG5a2E$*AD{MeVxFZjCxYlC^!ROAqAcQ!tIcj5NT3a(s zyPpHium1{;tuLz#y#Fa_t!y}ir2{IXPB|75XN$I5zMf;7sF^tP!gUB{3X%Ux+AFBi z^WISg!()<*a{I&M6bbwZd=KazxxnA(sXo8n0&00vox`>3J~`?~B=X%vN)87p+_zqb zT8WbEgEMfVSD-zVMy%QeGXL&>0WFF2-PpR{{t>HWp1gJC&>;fYw0qy*9IBs$!0~^NJMM3bp=bDy&re!T)9n1wZC~y&w~~-#_5mxMaj+I2 zK>;A>@1?lvvc(_Uz_@`1guJUtnpv8xE^SIQ3o@+S`#**tg2(3$1zLATMEm?QLyat~ zj=#1EUo)61qvF0UqsZHUSAkCNI>S=UbOtLEY6kbBK~I|UlOJW$9-{ony(gE$jz7+` zq+kDPaBe<|=G&Jj;cHX-lK1Y%{2{BjN86i9&g?)L(jpthOAR_5ub@L-(4k7qx}-|h zod;s)OWo3e^dx)!Urjp2|~k#);kjRAOd zam)Dsn_wd-BVA6A)R1ap4t-^{@q^C>UXVf0ktl2YiP5%~I0NHPSvTLl@Y_JX3p0Ar z_8l_@?Xa?%q}BQ~p*`|%r0)7(sdg0$RiSf=v&p-2z6`~3$^Yp^H0H=OvQX<;AUx&u z8P2i5J(is$Gv7;R zOAuIfbq_b)5URXxSL}%fF&`#bRjoMwtO1X>p}-t9a*ibn2~4nr|PXdtU2mY)K_*W4QuvJ>q;`=313p~D#MhSX|wF*jmPn9OZrq@ zDHsnb=Ltsd>B&G2zDK+f2s+YH@;f!8wwJ&czoQR?3<& zdTKG6A}l}8`=jcwoje0-vvcQVlCo40HAroaix?^`$y6?6t@Vp_^G^IxWJxJ9bBm6) zT5jx83;?Vr0d|<06hc1gQr5Fr=qw-I5S&+u@Hq+y#q+#_$Vb?RwAJak&LmH~2tb8^ zQn$i=+z5~C*t6P)2duN=uLgL0YBpC;7J5`!&pDNdN=JeVv3=TaynE3IfkzVuZdw%5 zbNF517r!riq|*Jgzb&JNB{q+JPH+Cqb2iNo_sRCo{;s$vY`A(t3LE-sL8|!`)0jU7o@oo0AYan`ff7`ba{MJri>z%QT zJm^uWt_%GC+SG^k7o6Dub&CLXe7W*8hQW2uMoS}mr|~_{XBDkIIN}StJ0eBZN~B#E zwQo=@R7d!q7l8K-vcUVhZM=j`nq%Qw{*65{o(sau`9}?m6c)9*GWg>J9yXu_^%qZr z08iK_7f0(cI0-u5&k|AQl=SChXd<%~(*w(3iQdff10Vnzd#*e6qQd2|p+4Wm4*J0~ zr5-OAFI^d}NT>KkbwhqE?~S&4YpT&yB5_psrF5N2{CgdgD_!hD^9vs3-aI(n^hbMt zI;Y%J1HOzIKQ{=`;%f4cQ+%4S+KPQ3z*`77X9ouy+$Qp!9}H?;xVgY_^-HzA|Lm*`Rk|fGD#0^#CqVw z$ZomEJKRoP4b#QRI0=fd*19+!r0fY2{g+y9vP7?#T4)mk>7 zM%$69wYg8vvO_jSTjok0SeJV^Uhk1Va`#raHGxU6fd8Lt0A6rbwl=;Iq!(9S{nqhY zbh@2Y05g59>cw!t-UeWaSnL*3Inr=*u1ZIpHeK&PUlnw)JY?)lp>H7T`+!nI#fUGfP|K&KsM~+aWe2X#sjG9Z z^YFxF>&$Zs!ek$FJa+6jEfW4sWTQ~E0RyTTO(Vj#==c(>uLqK)^^adrT0OJ$pZd)a zc8B>+9hJSQ3CWU{6xtH){M|E35QpD+`SBp$uK3xR%6r{*5?_Bv#Q(GkQ zX3&+fOEfS^vrR(wby#OLi02Kogna$rEDyWn!Y2^NDpPZ7BWy&g26vV>0}j5!AjSPK z{#b{=XkP#IhAaSPFey-QiiZRf+ZVqE)nO)^pu-*`YJ4#7XvZST^Qh=-Ep3jr#d{t> z6E}YLQs61WRUG3ern2<#nx>e$3;ZdT)o)!}_TLI2g=vKtW^Pu^(mmT%ONQG^M#6pr z++Ns$Z%td>X4mK+swSy-xcHj6zK_1pD?YD+q~+gp5}9eCwad<6pSk;wA^6*0-l~YA z^04&c?$FIR-oDs0W0`vVXC8-zaqJsMAdZ>f;Zc6Hz+?A5V;#5>;20YIVB7id^vraq zg;INxM-dlk?8xl!_(Nm#iC&Jy(fQ$Ko(4yZnVG=fJzy$35)`1Ho~*B&8<$QKcOEq7 zl;3r|e>vv&nBtA%Sb&)j-u;6erLwJFVbK@=^99*-0|gi-EPwTE?(1ubVl>A_72o!% zTo&*`t`r*LRCR~dR-oM@mKivN!OrNXQ`;*G-k9cQxaen+rz0draR!KO$LrG|aM>mOt-ZRf5d z`Dw1wf0MEOxwNZ95%~Cm^RJt}hCb zVT7mVL-RXn@%0j}mR_Q7FUbzpQb`xyKJO)n<~Ck?&>IAg9AGN2s*2&|eW=|#P%7vW zd^K0@tXMZW`p(}f`G({y{8zqVf}i}1K+y1yR7wIcT%`{ILK@sAr;^{mNAZN-vyXF? zLsbn9-j8j#@;4Gr`hKH3qt0$HbToK#g}M3mfDSQ3<%=Pkp_p|cBv3!T zo?X!0=j##j`PP;c0qKo^q*lXRoYnmt+lrqe!y7X8n$)Xf+g$)C-8stqk2i&1;zhp~ z`gO=uCt+_qyKjZl562?G|1QB`(;0|Dps?V{LO*;5$-hRqS*l_!u{+Q7JjY@!-}(`i zaOC8^7HR0NzZ9C$Hg;yq--@Q`+o3>c_eC;=sHJ{II4WImGa2p;a5gJf&2=WZ-frwV z-Q<7+Y-qVK=neW{HLocw4Pp1e06%jXK|Ye8Ie*G}X)so48}jX}zdbtWx9eXE;DNcH&f z`sLWFvhYqqHkjuuer^wsKi#1qon1$KritR`i+>TJ{+f?mLDdW2zSOr9VhkK0Mb}1H zDx?R&5J`}2kPH^>o5z0nmC>OeuO#-Op^-G>Kr?;Kk;&(3>)VdtOy^+T!@C)}!z~YH zqT;^F+0JBtOA)zfc2@~Kz-frXy2}%_01YuhsC+KOybxj@2r-v9zmM%nmR^P|2kk5VZHsxe$=o~}!??c+&2VkgF1&-DBC$tF9dp5~wxTVW4_nt{rz>xN& z0+gQI9+Q}w9lc$%D56wP-GcdKq(fjUgdi?U<0ymelz5k^{^Zd8ScQ4Jja2Uxv(p>e_wR;gL__-L80Q4aKp)Q^B$SN?(s-i5&vDJb?5mDCy7?Zn z){_V$@tpwft2eX=bk@;X&XyKE71X2EeP(WothBVpON9+G84mt)vX75JPB5Q71@oF< zM6kPi_{II(F50(h&YnZr6RpBGxy(vz-eJBL=K>53fS4-~q7cp4RGiccb@PpTlEmGx zrh80vYur5;+MLBK(HAsO2zs_J++2EHayj)&kL0FRIa>p9?0|FMo;`b!gQ_%z2+++v zc$@H=W9$~M@CSh(Irfboa+Ya8EL{HZ9@^V&Xs$*69AE8!k?fpUh_qYWBke_C-0L z0e_Ddn;Hn$N>z74dr>DJ2<^%}xW#R7HbR6&Ic+bV3o-z3HM%j|#TJl2L4NK!LZ5fE zasYD_dkIop3tEYTz!_YzbAq~%KcW(;%e*b%JeDSUE;LbOCx=K<%EYMPi1* zUrReiQ=@B+`ux*+I!PMLkm3swx%Y#U?+_l`pmDbid(aZldj5$n=<915LD>h0zNZ8B zQxjZYF8!&Uui`#Q#uIitWrVVZI)VD?j{w4Vx!{vmam3n=J}7InJu{H6KnWW~04^FG zb02yIHO)Z>?zU-f-M?LVMY+M2Hf<5R=0H?bJKKF@ab9H)r)}Yi4K!0~mEdN;0tZZ) zlE*_0x$Beb3eXekyFDN-o+f(Hh9zj;nYlJKqg17z5X3Bvo(nxHY# zrvVJ9O}Q~p^o}fXWA0aoz$4%N9(K)!G+VQviRP7pn-N@1OU))yC0?J{JgFou2jlkgU^o| zh!Yb|4R8Hm_|BH4%AuDDbnY9EFnN6utj~g;LXAd|I_fn4I7epCwMg*iXhxXGohFjE zM+5K23skNJ8XHR6V$?lD3o@FM{%P?S96cSw2QT~IaIP%^a}Zh(CS5WYdg=F4==P>F zO}-^SU>$VW*nuaz3X3ifRB|hVw*zl$`*GCVJ+5XnH61SAS=DD!mnu&ea8lRayvseM zr@Fs0j^&QEzcm0^(g9FL+eD5csWlqf@%j4&`htay+!lW(b)swe_Y>a6lMnl-D{LYSgV`W&ZkMC z*<}?XiZ>kvx*}gkTS3OSr0N*wQ{))*#RU`!(MkJ^%rxC1#I{bF14^AOH$#u^ROxi$RB+dy>mKte4f6 zy_YK?n`lt^xioN!?jhlO3@52LCwW8nKrofvbyiU_oEyN{!`!E}V+(d>OpDnZaCpN z|E!Rp2nx$%BwvQPe6&WR%2$vj6M0L%05CqHy1K&~=dw3iQ2)DGZE!W>kEPBeAIP*? zyV@QOR#R26?#PAY5ja+UM``gW^d<4%4K<(1u)NW4@R9p{OSYSVIk+g&-uUK+b<6Cn z2CtO8Ip}Kqb+uC)pW8IJdv4v><|LeQ1XB}p-r|YA9-dKrCEIkzKJUT*lN3SD@WVoT z#?m}fEy2Z9Yo@@>7N_Tp>CFOsgDoY#Yn#vrCZxxMRB6ieH%iZxUr6DH@h8`Z2-+`c zrqWf(2%W7F-3X&_quP0)$^HsT>3rffdZqurBilb6cxrjC@=|Eyst@1aREX9D;8Kz+ z&~H62SB|%6Qs0=eWxO)EdU>NiJ;CQ~hElQn4a4!BZSFS9uwk}!OtH|{U8eK&8H;xB zFmSZn^{f5-VhwAF&>^__LC8ADoOxFeWu`;DuKYTN!cl4P*riM-mT&XGBvP0t8zyJO zd76%8f%AQ61vnWH0FV8eFOJR*&DLXM(qsgn|JHQ*s+Grvz&iNZA>|ISC;4;KLx$Li z2uO>ouI&Kf(b~5n^3bsQiLMreY__)_2+waZ{98QzococUdRFXtOFWf4njY_!9<5#D z15?r1ExkPrD|_gWEOZDK0a=KIL`Fc$A|USM&^AOrL?7oT1=3N6pz9bXNbbP?^aEPk zoS2t+;vM^)o79{U^5zNA%H-Pdf9AQB@6#B)J&%g zR3lpeZvur*=>Chp^}}65Mh-VCns?n-;KosI?``Jw%_u09WpQZiv-p+cXtewS&o94= z$Dl*LQ9Ka@T%%WO<{$%X+(K{Xa}M@9JTa!X6YsE)XAv^Vp&3r{ z&+)cEvFQ3Ifvqb}^sTw!Pk|eK{z|OVJF*dqY6XH=VeN0j4M(p__?}T~XY|56(mIbq z_S}_#MG%yKZ6HMXqnmgJR2_}HBKBwugJd`BEv@3l#!8PA^3K}Y_K5FNIU|Ip(~p>A z3ahCF(R;IVd}`F5eOc!n`X0lwv5?1MJzA(zc>NMMjZZ(-Jh`e#)Zk#;?UI#drqeH0 zyr34^@KH6Otwl78>LzFOXlSVHoRWX+kgCudjnx~|?cT@Fxze9=Z7zb5izc?<-Xko6 zRgma4;O-aT&KIqewy58foGo|F)wOU z^an2Nx8Xme?t~xFwwUsBJogMB?A79AH%YtOX979qEDs^LDP@4Tk1~Sf*a2+cppKR0 zM|Eic&Jg1&{=SWV47^PFGoM~6N@3HE>3uD>WdD|hRlb=rb~Iz@SF@A-exVx}k=-Ve zdYe!GRfvuL4gnv4M`mm6_vS=1Nq(;Qk0p-I+z~svAzVSejs63uikUTQ#7O?wn*83E zU%p`=M2Cnf){GB(xDJ<;ihf=E3lqKV&*7=ke#F0b`g@Vd9eA12W0q{`J2T==5^YfR zmjYWcjkayJ_`DlD58Za^(b-9ca@s`)s+@aw|7y_{T%Ri!KO0Ak*wzULCm~4cEk}PT zHBhaHXD_B#?%Ga6wr)2ODi9cIQ^kT4zV$t&laW`dJ@AFA3$(l%73+B(Zl3p;U3qN# z5!s1awPS+d_9#PG+j#3rKRX~h!d5sD*#h@)=-8sKdiSyxI4>t`LcSQ-vOk|jft$mV zX#e&U@q)d}2Sc6Y*S^S$C^cv-X#(vfI@{(#Glw#XRQdyfkp%yk4!T zblnn=ZkL(B|E(?Kzq?}+F=HDsV-exG`F>9_0umkp@vecf?-t(DP7MqXAKJAyJ-G6A z2Hl@f1^MP{nW=%!xw`7_Pf=Oane{^J-?Vm@PwTfdtV-Ur6@v~~()xeh6{N-#dJxg- zkOS$VynOTrSTwTh!T)(>{nN|+QWtsCo-c5vB!LJyk=(w?}Am+W@ zU}MMkqwxA+6f{Xw=2`nKhn2tfol?DzHQb4Rl>2u(inPwjt?^DJ(X0%499C8Gf4f&W zH3lTE>F|VON%g~qx6;X?iJ;PmZXExE;K1U9LSp^t4X@!kZB~^grzyoGOX(5t2@p`pI0cA_S_Gy3m{| zne$dKk$lpCck3dWHtXkCQ{T*Y@YOdOm=4wT9gQMmW*yvUx}G+eIEFuX#eOMF!k=+> z!UUCPdbiu2!|skZSS?b+$^r)Zhgn%qLV^gd7~w!~%t1t;YtvVfZK7n{5^k@4_0G2P z)%cPj-QyFsow<^QR-k zj!o5)cOC_X`k>~u__@2MCA#8unN*ul-vH%YTm6RdUlsOKFHDXKFC97sNr__;DMd6c zLTwavNRI>=G?)zfngsgV^nk-EBJ=?jvO%8+Lq~Nf*78du#7ct8#p=@b`_u#MtQ?3r z#~9?s9WUu;+Z%MMx4NO*cv2~CBf#i_pI5UyG<^17!=ECUZ*;b2BZ$Z#s4E)5vdGnIL@eJ+^DxUiX6-yQ$|Ew;Ub~n%TJpc_o zMNoOJ8cAY!9IbR*r-do4{Mb(ItKM2~p)we|usK8zv_j?}D_!1M8NAtB?49aNijjNm z#IP|$$PTVuH3o#GO5+r2)p5d_8&Scjxy=ttd$*^9?GH|Gi0~CVqTR*Kd#?1KV#cqx z)*XPO#@$dkYC5)w5v5xo6e-XQUjHOWmXrrhMzz#<;0~Tod)j?lc9=5?LT-oIRKD8F znvJj%`TS80PpIisC4mpj{y>FB51P0hWfpA3@rPS0R^*{V(5-&Yoh6hNapR4f%Cp{Z zw*~bT27|Z9w1c!sM|}s;mQnC8Wxo4~;Bu&V65#dQ0=J%)|72< zWkHzNyy68-%3;u5^|b64&o#}RzPJbaYj`#B~Mon(emH`FYp0_{fqzQrx>Wmo27n_}PJI=fETuQf-e;pJ+I#U*q&p$ zd%(9~&-)0Zko1`Wq53OB+5VJHa^1Ql6DC+YisftHo-*6h(v|}qcA)_6*SOmL8JMI+b&U1}_rf9b!-V#mUx_NJXsnShU~cX3y@Gijfg?>q z81Z`9+@H#oJ{^P9`iXnKXF3GIw-|Q&oJHgmOP3YmO-uEEzXUgU z2pk~`Hc2Ly;m7iCJU`B)-U}x$2cu{N)0}h+QZp5E zfriALGraKy7xGIm$d&CJ`!2){W${*gIt@dWWbRmKe--fLGM|y+a?LQrg=r~>?@ep= zF$3)?xDzCy_o<+noO<3M6KRnu;?hkRoyjdDjra-Y^!aS9vOw}U+Bxg(6pj9?=0o!m zz8U=1AiVI`4(xkre`$h)ump}OPmz2sm(RT@qGVRLNp&k(LA=6THvG?XLI zd{-g{RnLt0r8?3;;{Slew={GWJ!2Jav_h!TgNUISxs3rCdO{iRzZ~ z0k0BliUzpIBapkz_<0F-65}$`3?o+9OG>O4!&#qiWn&r3do5!Cb0xOH>EhpHXbV~% z(NQiZ9U{ZQBY?R|_c~FM&Uvv4DjpbheZhm{LJ_nlR#!mFhEo+59e@@uJU@#pK`oS&%39NbTBHJ63g&;8aU$IYYG|-a$uCzk8PI!lgz%lFV1eF#tk!b9)-p9R-E4ww@8#s$jH@|uClL-EJI{!t zC%Dro1oAk&^+_+Yh7v0Q5ktREKyLi|ulK3OP6+;HWSE#4H(H)Hx^-*^wVojh7H-^c zV*s|K6+yb%Z)Wh@Al=Ih^JpD6b%uJcqex(Wer59_`{<$eUCdr{eQCJik2-X#&Su+1 zvxAh@`Q}3d;79S$fRg*ozzw8JOC#SF;RVv8VK00&ZVGp9Xx1S4*eXO@6y1*uF@<=k z!d2R4(e{S@W@KLtu42&OkI^es&*C6J{R#Cy705_$`~`_Sx$h?V&51GFilCd{87=;V zZtsiu82n-K*~% za31I7<8~+KjTod#qd$nY}p#rMCcyyYhyDL>D4JmJ@`Jud|`el}W!Z2`&Ha z@@b=b@6z*IySa}O;)5%x2A`ac_-uyIFo`*B&=y~)Fz7oi-Xcps`yvp+4_oSJAifVL<41XPUPM2k7V z3pjxbT@uHiRQR<1ry?P!@Ov+;{ua}HC@@g1?$~W}415`H?bOzStbEFedfwpqG+^gD>`A3_RZ z6&)|$H;2lGH4Oy;yUT=&=o!F-pzjVoyq&7X`zSTp?JRCLPuf%0lSP}NZ5tge(V({Z zWhko8_zD4-N;G(XTS$`?N^qV51sDX*bE(7sQ`=icRkej}!-SNSbb}zGbV;{@fFK|U zNTZZUgRtq877&n<5^0fE*mQSF#|Abn-CgfodY&izh=`lBZl1e(AisxX1W zaMLeDN*iv!_?r$OVKks9o)Mj64C+>{T%^UI4Bvd5&NXFF>?$F-b;_C>tLg;CE|Qe^ z{+cx$UgH=Nm zLm^YFx(!C`xv)*X>{bA?0Srm=L2WBV1;v4?xfnNTiRQ<co0r>jRC5=8dvc+i+Y9|)n z2+8yx3(|*GDK%9!Scr3+5r$hm9Zi=O+-!CN;iF3jD(NKY^1f4Z4A0aC}rtP*(*}ZW5J`1^YX8yU?{z zL>wdl~g^RtN+1G@zT|rNQIpV9UD;JB4Y!{lzW)B0OGq zvmT_+X%@Z}sQ+__(M8pTr^6!)JbEdh9adqQtm=W>qFyq(=G0Hf@#gI>=TrK?!kL2Ovd@hwndT|+ zlc~RKX??deVH5; zy$$I-c^{@kjwvxg7^fKzl%yVErydn7J(ww#Z$$lMB80Eh2%B^xM3_M!}e#wbv z+qmBx+;+rZ@>LxF3N-2T&PoTMgHbEuLotRyvMj2<+|RS?A?$?B;v4{Pc(72Y59c#- zxsFk0kIldh`d%BVP>%#aj*n;Elq6;!CtZ@R+9?m}dCk*#&BJ+fypNCB+7q8sT!sQD zN=)6(eUsi&Ac6#NC`6@u?_nmMbJcinU&e#}#cH<5bXRwG)4o;)K0*YyU#_W@>&^vC z2A7?-Jt5V4c?*oVd`Fo;ii{M1e1aba223{HXm2672_(lN*nkgWdWB^FDX!yR& z#$y<(bqC|#J!LB*Oz;r>-kH8#-GMKN=`!(HZMv0wD!tCm-tHVC(uj>aki1l5v8Bz1RS?x;y?0$?*u#T5c=sCAD$+gaNCMwM3OSZ$G&4PBbc2lgn{Qf0pEL z=4#&+pgb!nVqvrf@~=A<-iun8aQigB&P^MNbwcHueuS(7-7b3`@c#hTz+z`D{1j$ zPy%{ALDKiNc+8PYU~&Dyq*5sl{6ZUK%v}=5-R}oAm*Q8HiQ^v>H(~TyHMQyOX5O3yXuA>D9=nWYe z8J9>drb;2M9&o)9JDlR7H@s?@%%b(I))XE&Ug~T3U=uTY)sQ~7Y>sgKx{Y2tb8Z84 zLf$kYP&YqLCPDWVZD&%O4S~J(@t+|UX;6)(C@SXn^{HjK>JYM*@KcI>MHZd%JJXg* zlKxeCYRBT*&E&gpB?M-Sw*ga#?0={Y#)(O3?MQ zTrdUipK+NKW$`4ZGeF%1cc$!Sj(L)F4xyEQvY&T);Txr;NpR~Vi~aN((?Y5*Aj6OE z@Di2Hfu1A0W@QHI)`6zP+KrMA=&-=P_4vHSBsLQ4I2r zGG%>*U|zq1q>h(%^}{d%jFEV6rEa_Q2C3>b?M1A@w83%TsrHedS#Wl{9$2Mf;7#lO zL7SrRN_I&KBuhlW52^mN9L_(_SNn1IMA@(d5YdXfV|Zc>bvC_93P>t;2Up+{?djg zhJ+k|=pdv8$oU`(n(%>8g)sN^Pl$t%e!%$AFXyCX5W^UOEa2K*t@#v(Asws!JaNj4 zP0lln$Md&+{oIvTzXj>v_=>0tVkvui%A-TlB0}CXZ4($ZspVlZNtiruL|)e5kVpCN zoJ)VRVLUHGHA@<@x&8c^(0trz@$UM%HlR%ooP7i=4p5Y15@`p3my`4HOe0rphRgb> z-%>kw*?Vx7`ySjmR}R`cUBl-3OHNXnb{Cs;2QTay_Adws;GebJ> zgIOs=I)d8Z?;3KL5cfbX8Th5L zX=og|LI25EkDx$4o8EKujGcIxgi6@%E-1r^JjnbDKp=9s4cxW!_vUhg0zOy|4wPPe ze*fUP|Hc+!on!z#!(-E1o(S6GD@ z=e!k1ueJ-E7@Up==AqyKkZung!xZWv>*dO@s56$Vt&^ONZ2Nt4FbYt8>$N(?*IDqq$H0(g8YiI2F9x_gXMd6+^Pq?pN-?_$pg{9G8u;njPx>By?ab&OFvKcb$m zuP85hu)W>zb~wVdlN-7h@#!u0=G*Ynq!J;{dg@D%ih)qeK}Yl1`9aHW&Z(Ol53+m| zP&Ehv zUGjWmmARfpoGt5uEXT!#d3V=erMP)(?#U(Zbipv^+%OxQOr!dF696ODP$2p?y~_U% zff5>mTQ=?)pO>pfH`$TNpDb*0TUfMqbevdAh*ZW)xZQr5rX$_pbaUK;L<;-D920)wlrEl6EvkXwk?&Rx*wkx$y}kx!lr^C zC<<+3z@5mM+nOzG_7IQaD5#|da3hS2m-piEQiML;+vAGSmUVL2m^5;z!*raEq_ZGZzduZAK`;D9b4(b-B>}jYspSM-#22b!Md*Tc|JUd-)8)g zMK0;zT04-?;3gEB-7$)qroMGBYv)1556j*7EF=V*7P1TQ_B$j!{f5q1v%;UfQTd2_ zIEB}${XZ87b5SSiGJ_U!eBU0nSUCHOYUC%a(WTp`i(G4@wK~wYyW;#=wKZxPD9E#e zbNl)|!;X+!5~Dy6kJrijrySHxkb(|055W5YJujf-m0+9S1gLpsZ#!74Yim;CE>y(C z#^!F52BHqz9Mo@JlbsAq@4o8N`e?};6!C(FiU)>rF|ZADc}CQA|L;Kf+j+h@%bCy2 z(Ms9DY;WG+o2+c#6=;zI>{qAq!k_jhXeGYIqE0>eEuN!mN}#s>KYmXvJ7ftBoUa&* zk=q1I3DKOC6L5}nZmG^fh9c9ba*DhLHG8;C;c&Ns@jUK`!KLW%l$Wy3P1#?c2bg-! z^~2zRL!QPhEIk3s#C>cbyrwx6G-_6GeE2NeWX4%#>jN|9Dj`7muGsyC?Y1oHli#KK z@(|V&Ad^%fy)2Eezi9nv@%$%8#JxUQWFU=N&Q6E%xGso(BUVqL>uINaD~=b$g{BIw znzgo98vYj>h>ig)@0Gs}Z!+-jFraJ6O$#6fjqq(ddnDeKoJ->w%o_B6qsvX9+px>t zXfBcZ`c$=d#{_QIgVruY)i%rT0mU&ct(*2PkBJ<3p_Ry`G6AK|hYcUCWx7xpwy#9} zEi7#BvvRgf{MQ;pae(rw)RS>R2s77IYSJf zwt($`B&~?Lgdps2g`PkTVmNW>P}$wJ_WMoQF zWprnz2M@&eI!HiMTSP1)L^uhuEHSW(Cf6;6fAq_lK@X$PcRXBbWiDszt}eS7Tc$RUAkk{n83uK7eqrZQ1bIm^W^zTzj!hBx+B!Jx~?)MU69_% z%;VUsDmfdV(cgZ#;<+Lz+={vYK@KRI<1P6TT^kY@oR#6GQ)IC6hk z9}4vl<=wL7%dTrjckhh5zwHjE#gQMSMMv4*VPJCmleuEnlsj$kU;J(@4?bR5oH$Gm zRPuszJ`N3nRt31+Tf6o!6VnSGZ`$9as<0N{0quj8OM@&kc<0;xbqV7ocjcarwR#JY zasr0zG>g~mKd4$l+U^M_xeh^tz)HN_Z5V+>Eki=EEjsQ*>of5R1SI&(HXVj!j&P7P zf`sQqzN?Hy$GP67%&Swhu_B|>dRLwHGmnM&?G~r!X_+2p+mt3LscHbH{Xby$+y_8R z`$i3*RfX&d`X0a@-Q8E_6MFutzp{X^rk}lwX*uJDwAY|~O2cnq(7;0*!12ugBK8&fcBcRf*;K}s&wp6-}H;Sbtht4i` zUwWO|!b^eJh93Jda_#AW+F(zh;XzoZ<{I=kzP%GaV&e!8xRF!{O#}c(BCsm^=;Uf#seDW+m z=MnPReE{MV5wWqhXD>SribTXm*6y*S^Sh>rwawseuk@J>M8`xgY`*_jK$a~E0FX}* z@}+{fnn_Y5HI1PV87p-hyUezc>TmP={GHGX*r{$kATKf*khJ+GK&OWTn(JOuOx9DdDc9P2 z#B0MesgH9Sk;8WdQnlHS9>ACRk!y=UO6@ES(p_Id0W4PfjaNwwPalD{$i*64J163~ zdrtTdn7iK_zh&3r9Z$pj3!a*~x;3v;EOXDzu}6_&JxL zk7+yLyyV!av)A55mPiI#I!9Tp_%;e3dgK;H4eRD=+k~X^TTKxl7RkkWk3E39(!1+H zvQ$n926wu+Ot}AY#s*DA;Fer#M#}#8k^iMH7s0#YWzs8Y(o1fle1&^V_pfRISY1GF zE`--Sn%CU!crK7G&PcX34M+vG=xQ$IVts-7-v&m7Wd|paTIJz zQLpkh+JRyKYJ=Gg7gLPY$V0l$fqQy9aGi%F+O*#~u-GTum}bG$@fBkE_C=JH*`)SB3udflGMYFr)I5vvREI@~F02LO^W zr@VJjju!7rYU3ovu0oy|BZYm3C9YB`HGMwUwfSSV4iAMRD1nwd%w>H&bdfQZ5o2e`G~@k5*w|-~U&Nyxd6?P*XBr z;<0spy!hhalN@$gA{k@5!)>t`&EFsCtQhEd8)|a96^!c9J`;X6muRNEcFd%+tk+_f zIiJ~HazMeEe*cXHL2^eQB|q6)bW(H`)Jzmr6abszZKp({Ti;WS^<@M&N&rST_UOh$ zqIz2Bj3sVbkz>?jb)(7qO2(TRIP2Q=EwV6G^?gC-g{mGZ?YX;ZH9Yih^@s>z<0{#zvmL&{?BKo*)A;*_^$RznVa&0V{%fNuK@ZLkYQ!w$h*xCP)ywU<>$hQYZLweL5KzBM?fBSUO6gbY7-iT<@!((IFjW9e*dJqI}kbUj_ zp#Ue0zk z&}pMJu)4V3I>mgbj`~Fs#n~2%TgpP7+yQh7q3L1`@s%Z3Y-8`-R74H0s;|AQyQS(< z1cl!g@->|R4CD&P8Y$02+W^+P3djVwQo|-hXtZkW*zN1(zW%No+%Q+Z}6%Yhqzyvuv&~4aXWchCN zqE;?-5vdY$Ux;g>8%7_jD?U)6zlJ=mMW) z_Wv1T^noC~NQ>S9tbAP>uPM;WtyaU#HeUl1MgayX!JZ00*}Fh-MmW|zD47k>`s9fI z8z_ePFno@~5%UR(+i591s_?_Z-|>6e@(8^2*59c|hrfz%+po)YbGqgNaLU|wiau$Z z`hhN*;We$a_BfU}p1-!(p>u}<(`ty#5C~Qu-0)X)=fsWtQ9%ZuIcS`rS-%$e#MrCY zC1(rNv_OK=c^{Z0lvX(4!kiwmga%~;^H7av3NPJQ@!b~4=L^t)u+>D7e@bI0Q(d$6GI zgskocEK&bGJ51xuBAl_I?1T`^B1Nh1tHlhT_*5w$qg=|(UW1tqN4S1F{Af{_67~t; zsUhtHfw0ljlO{{W63g2^&hPZoerV1BBX+jKDn=7YGgxx}d%{EX6Ur4WJ@-3MS&D=e z;>~zV97O1?wL^hMXDVI9#~*mpC_#M;M9IWTC%0$Z@@Ag^()IZqmW5e!k&!jYIej?F zTyw=JCG`w0M)<0yYqZtZzgEAWp7K#?zHaV#->dZn$YkNUW*9(EfZm5;pdfwI7}VGI zMk|U>-8;s?j?#_pAk%bDkUP$y_v<-uBa8gvNQ}qz?N9tguWVH3{n?-w1Ckzal|)sH zfR(`OJx>o5uVtdq48;d4h|y^h+B$~M<|0y+#Vu(XOKvP~yHUK6O(i2zqL)iu{hEJX z)qNOV^)2TJU+#$K=XyhnwLqZO;Odoz?c=X2^NY(zU6llTU&B7y4*X}DO zUx>!PJ()-aZnAod*@R+qrEyIby6c7wz7N44zp#+M2SU^&4~zZz972Hp$+kKx64$?Z z-A&5jbQW92XEWDO=*hq|ZboQ&Y9)sWEHWkY?}jY!P$lVH!X;yX{M53k=WUzsxAsg| z*+94m6qbRS_7oQr$AsN}6^rjMAm<)9+m7JVPvFdi zv}9*l@VPBB0=Je9UwRMD^%nq@%F%zZ+F&c5L}-<6I=;xom3 zqQ{4luTmvGG2X*qgZ=Wt(k@B@Q*QY;<)uXMB1yf9bnY8*g{L`fzE91lChLjYuDnv{ zA`D7vC~0`(1s;s4jWuvUJ*;E1X``#@+ScKcZQNHERLpJCYv+TPjCt<-aE~Qr*Dj%d ze$7$;rRVJ(?#Z5?zvQ8oHApk@tPK269{lxdKJ*u{;2cgcRHnPPZS2XOk^r)t*HP?n zjPb$C>FPW%adDKR?LleGQksAJoGbEPG}XrlobM_G^SF-_wztgmW2e=N265?ahx<2AZE9-cDpnI^eci@;SKQn}w z&7=M0pDGk>XReiFgVK^i2*~nZ`ZH49;MXl5PJ_XV%gT%giYw4yruU8S{tPT^)Z9U> z52PhCa%BDc;%NP*G7drcc3!ii*Faz?1xVWghNz=QW*I`g@{zY;zuRcy=QLB`Z@h?s zl03rj$R%i$-en8;8)6TXife4WoF~1K)8Fyp#HKMHeQ-u2wClJ;S19`S_dLdIwBFC< zw|c@nS18e(rm?zva*Tu^mURv~-{Y#gV>Ahf0U901^O=s#>YRF<@z);PpKEVLCDe=` z8FZE*PoGZgOIRnPhQ2_OV2|4Uii4LuZ|bYcv}tqu&-6Ka%0h%agLcMfUvH0*WSN=1 z0Ghm*f?V<^Q`sqe3mV5s(+Q7mb!SQUxXpagy?1)*45y>Hwhm;#iak zfOC%Ed~YF{S5>QYow@OD`YAghFmTM~d_!Eqmm$lUH#4rag!XKjvj)!fZ^^~m$~d&> zLgvAXUzJ=jgU>2JAtHG3ntD0&EWOAHDHlI`EX2zMS~A~aGuK`f-HRIY`TWUugR;?{ zb@kip3uV1fu?l(~wfgKWR{dYeHpN=^RsTlW;1h2u=}ODNAqqf4DiQFtNm-F{>6lFr zhGp=LNTv5%Ajc64Q#N0y2+gv{9&UK%6Ese*!kGS8$a^pGszN(oub~p(-u@(r&A{e< zkvi5cyx(rK6>zyhpd7N~rlUjdvn|&5Ss+-amOl*0@{`AfIRFcP|HBY%fL2$RU6gf7 z(D(Hm$8A?~W7n;DygX6lITnw8nAv1n{gpr-PU{KTczh z6_9a1gA$3oI9K3ZAG`A)tl@^&I*-FnmlcBQEROlSuUxOij~|%bj-QV{j~W#DS$?Gz z)TtbN)i9mbymg7e7h@B9Iks+f!J=Z7y`uYX7thqqo+`5rE!SiC+4a*j^sgk)&!gX}*jgtTjum?Y&kVX-5(CIrThnYSBvjLl^7MJsac z1v~c)>rZF}Aedr*pdX1o)c-WYkd)imR_(bNru1fVVLyiXgd_-4KO z9`u=o;ng8*uFW2BEv=EzD?9iwfJt!jN8FcB;BgvI)=GU9*fdzH?BpJNl;dn~CBCKe z9SUTANd!&{lEj!a75|wFp!TPErxpMJ_fQ-Y&92bX`DQ*c*0XX2oBgB%IdA^wW#%mq z%4AvweuImgvg(^YW|rEz2-UeT2gDRPqI9OiyorFc*AgJGpRE__Q3$wdm`rQkO2eXJ zRTDnkk-=|k-t>^F0*Mw>UUZBgkWDvPpSlNS{pE^lAIOhPq=D}OSlw?JbT!zX=2|T5 zk;TRsQGXI^ z_0NYfjkDgDh&`KD;WO)dJw_)QkWfQo@Gjoec(Lpen^CLxu)BWy+R`wj1Og%!N8xK8 zpoBD3_Za3Lc=QdFqmCP1U*b%E4dNW0Un1w(R?CRk(tJ0%jZ8gI3R~9xZyM;wDbJ9= zA3#^fhtGIyWZa!w5#2*I-aLNZkynj#WgKJax&ys+{5r0#jQL6VFWJ>20R7~TRt62K zA?k61

    Figure 1: A regular 3-layer Neural Network.

    \n", + "\n", + "\n", + "Convolutional Neural Networks take advantage of the fact that the\n", + "input consists of images and they constrain the architecture in a more\n", + "sensible way. \n", + "\n", + "In particular, unlike a regular Neural Network, the\n", + "layers of a CNN have neurons arranged in 3 dimensions: width,\n", + "height, depth. (Note that the word depth here refers to the third\n", + "dimension of an activation volume, not to the depth of a full Neural\n", + "Network, which can refer to the total number of layers in a network.)\n", + "\n", + "To understand it better, the above example of an image \n", + "with an input volume of\n", + "activations has dimensions $32\\times 32\\times 3$ (width, height,\n", + "depth respectively). \n", + "\n", + "The neurons in a layer will\n", + "only be connected to a small region of the layer before it, instead of\n", + "all of the neurons in a fully-connected manner. Moreover, the final\n", + "output layer could for this specific image have dimensions $1\\times 1 \\times 10$, \n", + "because by the\n", + "end of the CNN architecture we will reduce the full image into a\n", + "single vector of class scores, arranged along the depth\n", + "dimension. \n", + "\n", + "\n", + "\n", + "\n", + "

    Figure 1: A CNN arranges its neurons in three dimensions (width, height, depth), as visualized in one of the layers. Every layer of a CNN transforms the 3D input volume to a 3D output volume of neuron activations. In this example, the red input layer holds the image, so its width and height would be the dimensions of the image, and the depth would be 3 (Red, Green, Blue channels).

    \n", + "" + ] + }, + { + "cell_type": "markdown", + "id": "a142cd5d", + "metadata": { + "editable": true + }, + "source": [ + "## Layers used to build CNNs\n", + "\n", + "A simple CNN is a sequence of layers, and every layer of a CNN\n", + "transforms one volume of activations to another through a\n", + "differentiable function. We use three main types of layers to build\n", + "CNN architectures: Convolutional Layer, Pooling Layer, and\n", + "Fully-Connected Layer (exactly as seen in regular Neural Networks). We\n", + "will stack these layers to form a full CNN architecture.\n", + "\n", + "A simple CNN for image classification could have the architecture:\n", + "\n", + "* **INPUT** ($32\\times 32 \\times 3$) will hold the raw pixel values of the image, in this case an image of width 32, height 32, and with three color channels R,G,B.\n", + "\n", + "* **CONV** (convolutional )layer will compute the output of neurons that are connected to local regions in the input, each computing a dot product between their weights and a small region they are connected to in the input volume. This may result in volume such as $[32\\times 32\\times 12]$ if we decided to use 12 filters.\n", + "\n", + "* **RELU** layer will apply an elementwise activation function, such as the $max(0,x)$ thresholding at zero. This leaves the size of the volume unchanged ($[32\\times 32\\times 12]$).\n", + "\n", + "* **POOL** (pooling) layer will perform a downsampling operation along the spatial dimensions (width, height), resulting in volume such as $[16\\times 16\\times 12]$.\n", + "\n", + "* **FC** (i.e. fully-connected) layer will compute the class scores, resulting in volume of size $[1\\times 1\\times 10]$, where each of the 10 numbers correspond to a class score, such as among the 10 categories of the MNIST images we considered above . As with ordinary Neural Networks and as the name implies, each neuron in this layer will be connected to all the numbers in the previous volume.\n", + "\n", + "CNNs transform the original image layer by layer from the original\n", + "pixel values to the final class scores. \n", + "\n", + "Observe that some layers contain\n", + "parameters and other don’t. In particular, the CNN layers perform\n", + "transformations that are a function of not only the activations in the\n", + "input volume, but also of the parameters (the weights and biases of\n", + "the neurons). On the other hand, the RELU/POOL layers will implement a\n", + "fixed function. The parameters in the CONV/FC layers will be trained\n", + "with gradient descent so that the class scores that the CNN computes\n", + "are consistent with the labels in the training set for each image.\n", + "\n", + "In summary:\n", + "\n", + "* A CNN architecture is in the simplest case a list of Layers that transform the image volume into an output volume (e.g. holding the class scores)\n", + "\n", + "* There are a few distinct types of Layers (e.g. CONV/FC/RELU/POOL are by far the most popular)\n", + "\n", + "* Each Layer accepts an input 3D volume and transforms it to an output 3D volume through a differentiable function\n", + "\n", + "* Each Layer may or may not have parameters (e.g. CONV/FC do, RELU/POOL don’t)\n", + "\n", + "* Each Layer may or may not have additional hyperparameters (e.g. CONV/FC/POOL do, RELU doesn’t)\n", + "\n", + "A dense neural network is representd by an affine operation (like matrix-matrix multiplication) where all parameters are included.\n", + "\n", + "The key idea in CNNs for say imaging is that in images neighbor pixels tend to be related! So we connect\n", + "only neighboring neurons in the input instead of connecting all with the first hidden layer.\n", + "\n", + "We say we perform a filtering (convolution is the mathematical operation)." + ] + }, + { + "cell_type": "markdown", + "id": "bb1e3617", + "metadata": { + "editable": true + }, + "source": [ + "## Mathematics of CNNs\n", + "\n", + "The mathematics of CNNs is based on the mathematical operation of\n", + "**convolution**. In mathematics (in particular in functional analysis),\n", + "convolution is represented by matheematical operation (integration,\n", + "summation etc) on two function in order to produce a third function\n", + "that expresses how the shape of one gets modified by the other.\n", + "Convolution has a plethora of applications in a variety of disciplines, spanning from statistics to signal processing, computer vision, solutions of differential equations,linear algebra, engineering, and yes, machine learning.\n", + "\n", + "Mathematically, convolution is defined as follows (one-dimensional example):\n", + "Let us define a continuous function $y(t)$ given by" + ] + }, + { + "cell_type": "markdown", + "id": "051485e5", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "y(t) = \\int x(a) w(t-a) da,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "799b8e5f", + "metadata": { + "editable": true + }, + "source": [ + "where $x(a)$ represents a so-called input and $w(t-a)$ is normally called the weight function or kernel.\n", + "\n", + "The above integral is written in a more compact form as" + ] + }, + { + "cell_type": "markdown", + "id": "3353345f", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "y(t) = \\left(x * w\\right)(t).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "ef341ee6", + "metadata": { + "editable": true + }, + "source": [ + "The discretized version reads" + ] + }, + { + "cell_type": "markdown", + "id": "ca8f7582", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "y(t) = \\sum_{a=-\\infty}^{a=\\infty}x(a)w(t-a).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "216e011f", + "metadata": { + "editable": true + }, + "source": [ + "Computing the inverse of the above convolution operations is known as deconvolution.\n", + "\n", + "How can we use this? And what does it mean? Let us study some familiar examples first." + ] + }, + { + "cell_type": "markdown", + "id": "5545738c", + "metadata": { + "editable": true + }, + "source": [ + "### Convolution Examples: Polynomial multiplication\n", + "\n", + "We have already met such an example in project 1 when we tried to set\n", + "up the design matrix for a two-dimensional function. This was an\n", + "example of polynomial multiplication. Let us recast such a problem in terms of the convolution operation.\n", + "Let us look a the following polynomials to second and third order, respectively:" + ] + }, + { + "cell_type": "markdown", + "id": "9f317908", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "p(t) = \\alpha_0+\\alpha_1 t+\\alpha_2 t^2,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "eb6f1070", + "metadata": { + "editable": true + }, + "source": [ + "and" + ] + }, + { + "cell_type": "markdown", + "id": "9fe61b3c", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "s(t) = \\beta_0+\\beta_1 t+\\beta_2 t^2+\\beta_3 t^3.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "38c68ea7", + "metadata": { + "editable": true + }, + "source": [ + "The polynomial multiplication gives us a new polynomial of degree $5$" + ] + }, + { + "cell_type": "markdown", + "id": "3e91a9f1", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "z(t) = \\delta_0+\\delta_1 t+\\delta_2 t^2+\\delta_3 t^3+\\delta_4 t^4+\\delta_5 t^5.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "5e24ac44", + "metadata": { + "editable": true + }, + "source": [ + "Computing polynomial products can be implemented efficiently if we rewrite the more brute force multiplications using convolution.\n", + "We note first that the new coefficients are given as" + ] + }, + { + "cell_type": "markdown", + "id": "ac215eb9", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\begin{split}\n", + "\\delta_0=&\\alpha_0\\beta_0\\\\\n", + "\\delta_1=&\\alpha_1\\beta_0+\\alpha_1\\beta_0\\\\\n", + "\\delta_2=&\\alpha_0\\beta_2+\\alpha_1\\beta_1+\\alpha_2\\beta_0\\\\\n", + "\\delta_3=&\\alpha_1\\beta_2+\\alpha_2\\beta_1+\\alpha_0\\beta_3\\\\\n", + "\\delta_4=&\\alpha_2\\beta_2+\\alpha_1\\beta_3\\\\\n", + "\\delta_5=&\\alpha_2\\beta_3.\\\\\n", + "\\end{split}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "eca51025", + "metadata": { + "editable": true + }, + "source": [ + "We note that $\\alpha_i=0$ except for $i\\in \\left\\{0,1,2\\right\\}$ and $\\beta_i=0$ except for $i\\in\\left\\{0,1,2,3\\right\\}$.\n", + "\n", + "We can then rewrite the coefficients $\\delta_j$ using a discrete convolution as" + ] + }, + { + "cell_type": "markdown", + "id": "0d517816", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\delta_j = \\sum_{i=-\\infty}^{i=\\infty}\\alpha_i\\beta_{j-i}=(\\alpha * \\beta)_j,\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "8cf1037e", + "metadata": { + "editable": true + }, + "source": [ + "or as a double sum with restriction $l=i+j$" + ] + }, + { + "cell_type": "markdown", + "id": "efe18d99", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\delta_l = \\sum_{ij}\\alpha_i\\beta_{j}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "14ae41db", + "metadata": { + "editable": true + }, + "source": [ + "Do you see a potential drawback with these equations?\n", + "\n", + "Since we only have a finite number of $\\alpha$ and $\\beta$ values\n", + "which are non-zero, we can rewrite the above convolution expressions\n", + "as a matrix-vector multiplication" + ] + }, + { + "cell_type": "markdown", + "id": "046e108b", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\boldsymbol{\\delta}=\\begin{bmatrix}\\alpha_0 & 0 & 0 & 0 \\\\\n", + " \\alpha_1 & \\alpha_0 & 0 & 0 \\\\\n", + "\t\t\t \\alpha_2 & \\alpha_1 & \\alpha_0 & 0 \\\\\n", + "\t\t\t 0 & \\alpha_2 & \\alpha_1 & \\alpha_0 \\\\\n", + "\t\t\t 0 & 0 & \\alpha_2 & \\alpha_1 \\\\\n", + "\t\t\t 0 & 0 & 0 & \\alpha_2\n", + "\t\t\t \\end{bmatrix}\\begin{bmatrix} \\beta_0 \\\\ \\beta_1 \\\\ \\beta_2 \\\\ \\beta_3\\end{bmatrix}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "0c73a726", + "metadata": { + "editable": true + }, + "source": [ + "The process is commutative and we can easily see that we can rewrite the multiplication in terms of a matrix holding $\\beta$ and a vector holding $\\alpha$.\n", + "In this case we have" + ] + }, + { + "cell_type": "markdown", + "id": "81bc84d0", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\boldsymbol{\\delta}=\\begin{bmatrix}\\beta_0 & 0 & 0 \\\\\n", + " \\beta_1 & \\beta_0 & 0 \\\\\n", + "\t\t\t \\beta_2 & \\beta_1 & \\beta_0 \\\\\n", + "\t\t\t \\beta_3 & \\beta_2 & \\beta_1 \\\\\n", + "\t\t\t 0 & \\beta_3 & \\beta_2 \\\\\n", + "\t\t\t 0 & 0 & \\beta_3\n", + "\t\t\t \\end{bmatrix}\\begin{bmatrix} \\alpha_0 \\\\ \\alpha_1 \\\\ \\alpha_2\\end{bmatrix}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "6f314582", + "metadata": { + "editable": true + }, + "source": [ + "Note that the use of these matrices is for mathematical purposes only and not implementation purposes.\n", + "When implementing the above equation we do not encode (and allocate memory) the matrices explicitely.\n", + "We rather code the convolutions in the minimal memory footprint that they require.\n", + "\n", + "Does the number of floating point operations change here when we use the commutative property?" + ] + }, + { + "cell_type": "markdown", + "id": "e01eb276", + "metadata": { + "editable": true + }, + "source": [ + "### Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms)\n", + "\n", + "For problems with so-called harmonic oscillations, given by for example the following differential equation" + ] + }, + { + "cell_type": "markdown", + "id": "1016b422", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "m\\frac{d^2x}{dt^2}+\\eta\\frac{dx}{dt}+x(t)=F(t),\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "c237cb74", + "metadata": { + "editable": true + }, + "source": [ + "where $F(t)$ is an applied external force acting on the system (often called a driving force), one can use the theory of Fourier transformations to find the solutions of this type of equations.\n", + "\n", + "If one has several driving forces, $F(t)=\\sum_n F_n(t)$, one can find\n", + "the particular solution to each $F_n$, $x_{pn}(t)$, and the particular\n", + "solution for the entire driving force is then given by a series like" + ] + }, + { + "cell_type": "markdown", + "id": "4f2f2089", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + "x_p(t)=\\sum_nx_{pn}(t).\n", + "\\label{_auto1} \\tag{1}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "a32fa928", + "metadata": { + "editable": true + }, + "source": [ + "This is known as the principle of superposition. It only applies when\n", + "the homogenous equation is linear. If there were an anharmonic term\n", + "such as $x^3$ in the homogenous equation, then when one summed various\n", + "solutions, $x=(\\sum_n x_n)^2$, one would get cross\n", + "terms. Superposition is especially useful when $F(t)$ can be written\n", + "as a sum of sinusoidal terms, because the solutions for each\n", + "sinusoidal (sine or cosine) term is analytic. \n", + "\n", + "Driving forces are often periodic, even when they are not\n", + "sinusoidal. Periodicity implies that for some time $\\tau$" + ] + }, + { + "cell_type": "markdown", + "id": "0b6ca2c5", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\begin{eqnarray}\n", + "F(t+\\tau)=F(t). \n", + "\\end{eqnarray}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "789cd636", + "metadata": { + "editable": true + }, + "source": [ + "One example of a non-sinusoidal periodic force is a square wave. Many\n", + "components in electric circuits are non-linear, e.g. diodes, which\n", + "makes many wave forms non-sinusoidal even when the circuits are being\n", + "driven by purely sinusoidal sources.\n", + "\n", + "The code here shows a typical example of such a square wave generated using the functionality included in the **scipy** Python package. We have used a period of $\\tau=0.2$." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "2c90eb89", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter12_35_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "\n", + "import numpy as np\n", + "import math\n", + "from scipy import signal\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# number of points \n", + "n = 500\n", + "# start and final times \n", + "t0 = 0.0\n", + "tn = 1.0\n", + "# Period \n", + "t = np.linspace(t0, tn, n, endpoint=False)\n", + "SqrSignal = np.zeros(n)\n", + "SqrSignal = 1.0+signal.square(2*np.pi*5*t)\n", + "plt.plot(t, SqrSignal)\n", + "plt.ylim(-0.5, 2.5)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "8e7b8f5c", + "metadata": { + "editable": true + }, + "source": [ + "For the sinusoidal example the\n", + "period is $\\tau=2\\pi/\\omega$. However, higher harmonics can also\n", + "satisfy the periodicity requirement. In general, any force that\n", + "satisfies the periodicity requirement can be expressed as a sum over\n", + "harmonics," + ] + }, + { + "cell_type": "markdown", + "id": "4453c025", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + "F(t)=\\frac{f_0}{2}+\\sum_{n>0} f_n\\cos(2n\\pi t/\\tau)+g_n\\sin(2n\\pi t/\\tau).\n", + "\\label{_auto2} \\tag{2}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "32d5f410", + "metadata": { + "editable": true + }, + "source": [ + "We can write down the answer for\n", + "$x_{pn}(t)$, by substituting $f_n/m$ or $g_n/m$ for $F_0/m$. By\n", + "writing each factor $2n\\pi t/\\tau$ as $n\\omega t$, with $\\omega\\equiv\n", + "2\\pi/\\tau$," + ] + }, + { + "cell_type": "markdown", + "id": "4a58698d", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + "\\label{eq:fourierdef1} \\tag{3}\n", + "F(t)=\\frac{f_0}{2}+\\sum_{n>0}f_n\\cos(n\\omega t)+g_n\\sin(n\\omega t).\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "5664f63d", + "metadata": { + "editable": true + }, + "source": [ + "The solutions for $x(t)$ then come from replacing $\\omega$ with\n", + "$n\\omega$ for each term in the particular solution," + ] + }, + { + "cell_type": "markdown", + "id": "0d9a2811", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\begin{eqnarray}\n", + "x_p(t)&=&\\frac{f_0}{2k}+\\sum_{n>0} \\alpha_n\\cos(n\\omega t-\\delta_n)+\\beta_n\\sin(n\\omega t-\\delta_n),\\\\\n", + "\\nonumber\n", + "\\alpha_n&=&\\frac{f_n/m}{\\sqrt{((n\\omega)^2-\\omega_0^2)+4\\beta^2n^2\\omega^2}},\\\\\n", + "\\nonumber\n", + "\\beta_n&=&\\frac{g_n/m}{\\sqrt{((n\\omega)^2-\\omega_0^2)+4\\beta^2n^2\\omega^2}},\\\\\n", + "\\nonumber\n", + "\\delta_n&=&\\tan^{-1}\\left(\\frac{2\\beta n\\omega}{\\omega_0^2-n^2\\omega^2}\\right).\n", + "\\end{eqnarray}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "ac8b5fff", + "metadata": { + "editable": true + }, + "source": [ + "Because the forces have been applied for a long time, any non-zero\n", + "damping eliminates the homogenous parts of the solution, so one need\n", + "only consider the particular solution for each $n$.\n", + "\n", + "The problem is considered solved if one can find expressions for the\n", + "coefficients $f_n$ and $g_n$, even though the solutions are expressed\n", + "as an infinite sum. The coefficients can be extracted from the\n", + "function $F(t)$ by" + ] + }, + { + "cell_type": "markdown", + "id": "5bb70ae9", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{eqnarray}\n", + "\\label{eq:fourierdef2} \\tag{4}\n", + "f_n&=&\\frac{2}{\\tau}\\int_{-\\tau/2}^{\\tau/2} dt~F(t)\\cos(2n\\pi t/\\tau),\\\\\n", + "\\nonumber\n", + "g_n&=&\\frac{2}{\\tau}\\int_{-\\tau/2}^{\\tau/2} dt~F(t)\\sin(2n\\pi t/\\tau).\n", + "\\end{eqnarray}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "4f64082e", + "metadata": { + "editable": true + }, + "source": [ + "To check the consistency of these expressions and to verify\n", + "Eq. ([4](#eq:fourierdef2)), one can insert the expansion of $F(t)$ in\n", + "Eq. ([3](#eq:fourierdef1)) into the expression for the coefficients in\n", + "Eq. ([4](#eq:fourierdef2)) and see whether" + ] + }, + { + "cell_type": "markdown", + "id": "bdd9e4e8", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\begin{eqnarray}\n", + "f_n&=?&\\frac{2}{\\tau}\\int_{-\\tau/2}^{\\tau/2} dt~\\left\\{\n", + "\\frac{f_0}{2}+\\sum_{m>0}f_m\\cos(m\\omega t)+g_m\\sin(m\\omega t)\n", + "\\right\\}\\cos(n\\omega t).\n", + "\\end{eqnarray}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "e64a4a4c", + "metadata": { + "editable": true + }, + "source": [ + "Immediately, one can throw away all the terms with $g_m$ because they\n", + "convolute an even and an odd function. The term with $f_0/2$\n", + "disappears because $\\cos(n\\omega t)$ is equally positive and negative\n", + "over the interval and will integrate to zero. For all the terms\n", + "$f_m\\cos(m\\omega t)$ appearing in the sum, one can use angle addition\n", + "formulas to see that $\\cos(m\\omega t)\\cos(n\\omega\n", + "t)=(1/2)(\\cos[(m+n)\\omega t]+\\cos[(m-n)\\omega t]$. This will integrate\n", + "to zero unless $m=n$. In that case the $m=n$ term gives" + ] + }, + { + "cell_type": "markdown", + "id": "d51a4f59", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + "\\int_{-\\tau/2}^{\\tau/2}dt~\\cos^2(m\\omega t)=\\frac{\\tau}{2},\n", + "\\label{_auto3} \\tag{5}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "44804e35", + "metadata": { + "editable": true + }, + "source": [ + "and" + ] + }, + { + "cell_type": "markdown", + "id": "7de0dbe5", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\begin{eqnarray}\n", + "f_n&=?&\\frac{2}{\\tau}\\int_{-\\tau/2}^{\\tau/2} dt~f_n/2\\\\\n", + "\\nonumber\n", + "&=&f_n~\\checkmark.\n", + "\\end{eqnarray}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "4d1a02e0", + "metadata": { + "editable": true + }, + "source": [ + "The same method can be used to check for the consistency of $g_n$.\n", + "\n", + "The code here uses the Fourier series applied to a \n", + "square wave signal. The code here\n", + "visualizes the various approximations given by Fourier series compared\n", + "with a square wave with period $T=0.2$ (dimensionless time), width $0.1$ and max value of the force $F=2$. We\n", + "see that when we increase the number of components in the Fourier\n", + "series, the Fourier series approximation gets closer and closer to the\n", + "square wave signal." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "4ae0ec42", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter12_51_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import numpy as np\n", + "import math\n", + "from scipy import signal\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# number of points \n", + "n = 500\n", + "# start and final times \n", + "t0 = 0.0\n", + "tn = 1.0\n", + "# Period \n", + "T =0.2\n", + "# Max value of square signal \n", + "Fmax= 2.0\n", + "# Width of signal \n", + "Width = 0.1\n", + "t = np.linspace(t0, tn, n, endpoint=False)\n", + "SqrSignal = np.zeros(n)\n", + "FourierSeriesSignal = np.zeros(n)\n", + "SqrSignal = 1.0+signal.square(2*np.pi*5*t+np.pi*Width/T)\n", + "a0 = Fmax*Width/T\n", + "FourierSeriesSignal = a0\n", + "Factor = 2.0*Fmax/np.pi\n", + "for i in range(1,500):\n", + " FourierSeriesSignal += Factor/(i)*np.sin(np.pi*i*Width/T)*np.cos(i*t*2*np.pi/T)\n", + "plt.plot(t, SqrSignal)\n", + "plt.plot(t, FourierSeriesSignal)\n", + "plt.ylim(-0.5, 2.5)\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "acd75ab0", + "metadata": { + "editable": true + }, + "source": [ + "## Two-dimensional Objects\n", + "\n", + "We often use convolutions over more than one dimension at a time. If\n", + "we have a two-dimensional image $I$ as input, we can have a **filter**\n", + "defined by a two-dimensional **kernel** $K$. This leads to an output $S$" + ] + }, + { + "cell_type": "markdown", + "id": "0cdf3af8", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "S_(i,j)=(I * K)(i,j) = \\sum_m\\sum_n I(m,n)K(i-m,j-n).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "1640aae2", + "metadata": { + "editable": true + }, + "source": [ + "Convolution is a commutatitave process, which means we can rewrite this equation as" + ] + }, + { + "cell_type": "markdown", + "id": "11491f4c", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "S_(i,j)=(I * K)(i,j) = \\sum_m\\sum_n I(i-m,j-n)K(m,n).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "a1e3ef9d", + "metadata": { + "editable": true + }, + "source": [ + "Normally the latter is more straightforward to implement in a machine elarning library since there is less variation in the range of values of $m$ and $n$.\n", + "\n", + "Many deep learning libraries implement cross-correlation instead of convolution" + ] + }, + { + "cell_type": "markdown", + "id": "919fb5e9", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "S_(i,j)=(I * K)(i,j) = \\sum_m\\sum_n I(i+m,j-+)K(m,n).\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "c42d55ac", + "metadata": { + "editable": true + }, + "source": [ + "## More on Dimensionalities\n", + "\n", + "In fields like signal processing (and imaging as well), one designs\n", + "so-called filters. These filters are defined by the convolutions and\n", + "are often hand-crafted. One may specify filters for smoothing, edge\n", + "detection, frequency reshaping, and similar operations. However with\n", + "neural networks the idea is to automatically learn the filters and use\n", + "many of them in conjunction with non-linear operations (activation\n", + "functions).\n", + "\n", + "As an example consider a neural network operating on sound sequence\n", + "data. Assume that we an input vector $\\boldsymbol{x}$ of length $d=10^6$. We\n", + "construct then a neural network with onle hidden layer only with\n", + "$10^4$ nodes. This means that we will have a weight matrix with\n", + "$10^4\\times 10^6=10^{10}$ weights to be determined, together with $10^4$ biases.\n", + "\n", + "Assume furthermore that we have an output layer which is meant to train whether the sound sequence represents a human voice (true) or something else (false).\n", + "It means that we have only one output node. But since this output node connects to $10^4$ nodes in the hidden layer, there are in total $10^4$ weights to be determined for the output layer, plus one bias. In total we have" + ] + }, + { + "cell_type": "markdown", + "id": "4ebd8c85", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "\\mathrm{NumberParameters}=10^{10}+10^4+10^4+1 \\approx 10^{10},\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "6d886fa7", + "metadata": { + "editable": true + }, + "source": [ + "that is ten billion parameters to determine." + ] + }, + { + "cell_type": "markdown", + "id": "cd3b731e", + "metadata": { + "editable": true + }, + "source": [ + "## Further Dimensionality Remarks\n", + "\n", + "In today’s architecture one can train such neural networks, however\n", + "this is a huge number of parameters for the task at hand. In general,\n", + "it is a very wasteful and inefficient use of dense matrices as\n", + "parameters. Just as importantly, such trained network parameters are\n", + "very specific for the type of input data on which they were trained\n", + "and the network is not likely to generalize easily to variations in\n", + "the input.\n", + "\n", + "The main principles that justify convolutions is locality of\n", + "information and repetion of patterns within the signal. Sound samples\n", + "of the input in adjacent spots are much more likely to affect each\n", + "other than those that are very far away. Similarly, sounds are\n", + "repeated in multiple times in the signal. While slightly simplistic,\n", + "reasoning about such a sound example demonstrates this. The same\n", + "principles then apply to images and other similar data." + ] + }, + { + "cell_type": "markdown", + "id": "fc38055c", + "metadata": { + "editable": true + }, + "source": [ + "## CNNs in more detail, building convolutional neural networks in Tensorflow and Keras\n", + "\n", + "As discussed above, CNNs are neural networks built from the assumption that the inputs\n", + "to the network are 2D images. This is important because the number of features or pixels in images\n", + "grows very fast with the image size, and an enormous number of weights and biases are needed in order to build an accurate network. \n", + "\n", + "As before, we still have our input, a hidden layer and an output. What's novel about convolutional networks\n", + "are the **convolutional** and **pooling** layers stacked in pairs between the input and the hidden layer.\n", + "In addition, the data is no longer represented as a 2D feature matrix, instead each input is a number of 2D\n", + "matrices, typically 1 for each color dimension (Red, Green, Blue). \n", + "\n", + "It means that to represent the entire\n", + "dataset of images, we require a 4D matrix or **tensor**. This tensor has the dimensions:" + ] + }, + { + "cell_type": "markdown", + "id": "c153f6eb", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "(n_{inputs},\\, n_{pixels, width},\\, n_{pixels, height},\\, depth) .\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "f45ab21d", + "metadata": { + "editable": true + }, + "source": [ + "### The MNIST dataset again\n", + "\n", + "The MNIST dataset consists of grayscale images with a pixel size of\n", + "$28\\times 28$, meaning we require $28 \\times 28 = 724$ weights to each\n", + "neuron in the first hidden layer.\n", + "\n", + "If we were to analyze images of size $128\\times 128$ we would require\n", + "$128 \\times 128 = 16384$ weights to each neuron. Even worse if we were\n", + "dealing with color images, as most images are, we have an image matrix\n", + "of size $128\\times 128$ for each color dimension (Red, Green, Blue),\n", + "meaning 3 times the number of weights $= 49152$ are required for every\n", + "single neuron in the first hidden layer.\n", + "\n", + "Images typically have strong local correlations, meaning that a small\n", + "part of the image varies little from its neighboring regions. If for\n", + "example we have an image of a blue car, we can roughly assume that a\n", + "small blue part of the image is surrounded by other blue regions.\n", + "\n", + "Therefore, instead of connecting every single pixel to a neuron in the\n", + "first hidden layer, as we have previously done with deep neural\n", + "networks, we can instead connect each neuron to a small part of the\n", + "image (in all 3 RGB depth dimensions). The size of each small area is\n", + "fixed, and known as a [receptive](https://en.wikipedia.org/wiki/Receptive_field).\n", + "\n", + "The layers of a convolutional neural network arrange neurons in 3D: width, height and depth. \n", + "The input image is typically a square matrix of depth 3. \n", + "\n", + "A **convolution** is performed on the image which outputs\n", + "a 3D volume of neurons. The weights to the input are arranged in a number of 2D matrices, known as **filters**.\n", + "\n", + "Each filter slides along the input image, taking the dot product\n", + "between each small part of the image and the filter, in all depth\n", + "dimensions. This is then passed through a non-linear function,\n", + "typically the **Rectified Linear (ReLu)** function, which serves as the\n", + "activation of the neurons in the first convolutional layer. This is\n", + "further passed through a **pooling layer**, which reduces the size of the\n", + "convolutional layer, e.g. by taking the maximum or average across some\n", + "small regions, and this serves as input to the next convolutional\n", + "layer." + ] + }, + { + "cell_type": "markdown", + "id": "4af74ca7", + "metadata": { + "editable": true + }, + "source": [ + "### Systematic reduction\n", + "\n", + "By systematically reducing the size of the input volume, through\n", + "convolution and pooling, the network should create representations of\n", + "small parts of the input, and then from them assemble representations\n", + "of larger areas. The final pooling layer is flattened to serve as\n", + "input to a hidden layer, such that each neuron in the final pooling\n", + "layer is connected to every single neuron in the hidden layer. This\n", + "then serves as input to the output layer, e.g. a softmax output for\n", + "classification." + ] + }, + { + "cell_type": "markdown", + "id": "2b435dc0", + "metadata": { + "editable": true + }, + "source": [ + "### Prerequisites: Collect and pre-process data" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "ffb4904f", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "inputs = (n_inputs, pixel_width, pixel_height, depth) = (1797, 8, 8, 1)\n", + "labels = (n_inputs) = (1797,)\n" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter12_67_1.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# import necessary packages\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from sklearn import datasets\n", + "\n", + "\n", + "# ensure the same random numbers appear every time\n", + "np.random.seed(0)\n", + "\n", + "# display images in notebook\n", + "%matplotlib inline\n", + "plt.rcParams['figure.figsize'] = (12,12)\n", + "\n", + "\n", + "# download MNIST dataset\n", + "digits = datasets.load_digits()\n", + "\n", + "# define inputs and labels\n", + "inputs = digits.images\n", + "labels = digits.target\n", + "\n", + "# RGB images have a depth of 3\n", + "# our images are grayscale so they should have a depth of 1\n", + "inputs = inputs[:,:,:,np.newaxis]\n", + "\n", + "print(\"inputs = (n_inputs, pixel_width, pixel_height, depth) = \" + str(inputs.shape))\n", + "print(\"labels = (n_inputs) = \" + str(labels.shape))\n", + "\n", + "\n", + "# choose some random images to display\n", + "n_inputs = len(inputs)\n", + "indices = np.arange(n_inputs)\n", + "random_indices = np.random.choice(indices, size=5)\n", + "\n", + "for i, image in enumerate(digits.images[random_indices]):\n", + " plt.subplot(1, 5, i+1)\n", + " plt.axis('off')\n", + " plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest')\n", + " plt.title(\"Label: %d\" % digits.target[random_indices[i]])\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "bb2db46c", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "from tensorflow.keras import datasets, layers, models\n", + "from tensorflow.keras.layers import Input\n", + "from tensorflow.keras.models import Sequential #This allows appending layers to existing models\n", + "from tensorflow.keras.layers import Dense #This allows defining the characteristics of a particular layer\n", + "from tensorflow.keras import optimizers #This allows using whichever optimiser we want (sgd,adam,RMSprop)\n", + "from tensorflow.keras import regularizers #This allows using whichever regularizer we want (l1,l2,l1_l2)\n", + "from tensorflow.keras.utils import to_categorical #This allows using categorical cross entropy as the cost function\n", + "#from tensorflow.keras import Conv2D\n", + "#from tensorflow.keras import MaxPooling2D\n", + "#from tensorflow.keras import Flatten\n", + "\n", + "from sklearn.model_selection import train_test_split\n", + "\n", + "# representation of labels\n", + "labels = to_categorical(labels)\n", + "\n", + "# split into train and test data\n", + "# one-liner from scikit-learn library\n", + "train_size = 0.8\n", + "test_size = 1 - train_size\n", + "X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size,\n", + " test_size=test_size)" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "100a8d6d", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def create_convolutional_neural_network_keras(input_shape, receptive_field,\n", + " n_filters, n_neurons_connected, n_categories,\n", + " eta, lmbd):\n", + " model = Sequential()\n", + " model.add(layers.Conv2D(n_filters, (receptive_field, receptive_field), input_shape=input_shape, padding='same',\n", + " activation='relu', kernel_regularizer=regularizers.l2(lmbd)))\n", + " model.add(layers.MaxPooling2D(pool_size=(2, 2)))\n", + " model.add(layers.Flatten())\n", + " model.add(layers.Dense(n_neurons_connected, activation='relu', kernel_regularizer=regularizers.l2(lmbd)))\n", + " model.add(layers.Dense(n_categories, activation='softmax', kernel_regularizer=regularizers.l2(lmbd)))\n", + " \n", + " sgd = optimizers.SGD(lr=eta)\n", + " model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy'])\n", + " \n", + " return model\n", + "\n", + "epochs = 100\n", + "batch_size = 100\n", + "input_shape = X_train.shape[1:4]\n", + "receptive_field = 3\n", + "n_filters = 10\n", + "n_neurons_connected = 50\n", + "n_categories = 10\n", + "\n", + "eta_vals = np.logspace(-5, 1, 7)\n", + "lmbd_vals = np.logspace(-5, 1, 7)" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "635da5a7", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "2021-12-08 06:58:03.630224: I tensorflow/core/platform/cpu_feature_guard.cc:142] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations: SSE4.1 SSE4.2 AVX AVX2 FMA\n", + "To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.\n", + "/Users/MortenImac/anaconda3/lib/python3.8/site-packages/keras/optimizer_v2/optimizer_v2.py:355: UserWarning: The `lr` argument is deprecated, use `learning_rate` instead.\n", + " warnings.warn(\n" + ] + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "2021-12-08 06:58:04.114437: I tensorflow/compiler/mlir/mlir_graph_optimization_pass.cc:185] None of the MLIR Optimization Passes are enabled (registered 2)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\r", + " 1/12 [=>............................] - ETA: 1s - loss: 2.4411 - accuracy: 0.2500" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", + "12/12 [==============================] - 0s 853us/step - loss: 2.4410 - accuracy: 0.1944\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Learning rate = 1e-05\n", + "Lambda = 1e-05\n", + "Test accuracy: 0.194\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\r", + " 1/12 [=>............................] - ETA: 0s - loss: 4.2597 - accuracy: 0.0938" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", + "12/12 [==============================] - 0s 842us/step - loss: 3.4744 - accuracy: 0.1361\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Learning rate = 1e-05\n", + "Lambda = 0.0001\n", + "Test accuracy: 0.136\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\r", + " 1/12 [=>............................] - ETA: 1s - loss: 3.0466 - accuracy: 0.1562" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", + "12/12 [==============================] - 0s 743us/step - loss: 2.9400 - accuracy: 0.1028\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Learning rate = 1e-05\n", + "Lambda = 0.001\n", + "Test accuracy: 0.103\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\r", + " 1/12 [=>............................] - ETA: 1s - loss: 3.8064 - accuracy: 0.1250" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", + "12/12 [==============================] - 0s 912us/step - loss: 3.8175 - accuracy: 0.1056\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Learning rate = 1e-05\n", + "Lambda = 0.01\n", + "Test accuracy: 0.106\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\r", + " 1/12 [=>............................] - ETA: 1s - loss: 12.1612 - accuracy: 0.0938" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", + "12/12 [==============================] - 0s 763us/step - loss: 12.3063 - accuracy: 0.1361\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Learning rate = 1e-05\n", + "Lambda = 0.1\n", + "Test accuracy: 0.136\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\r", + " 1/12 [=>............................] - ETA: 0s - loss: 91.8768 - accuracy: 0.2812" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", + "12/12 [==============================] - 0s 922us/step - loss: 92.0923 - accuracy: 0.2972\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Learning rate = 1e-05\n", + "Lambda = 1.0\n", + "Test accuracy: 0.297\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\r", + " 1/12 [=>............................] - ETA: 0s - loss: 529.5700 - accuracy: 0.2188" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", + "12/12 [==============================] - 0s 935us/step - loss: 529.7050 - accuracy: 0.1861\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Learning rate = 1e-05\n", + "Lambda = 10.0\n", + "Test accuracy: 0.186\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\r", + " 1/12 [=>............................] - ETA: 1s - loss: 1.2495 - accuracy: 0.5312" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", + "12/12 [==============================] - 0s 750us/step - loss: 1.5138 - accuracy: 0.4694\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Learning rate = 0.0001\n", + "Lambda = 1e-05\n", + "Test accuracy: 0.469\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\r", + " 1/12 [=>............................] - ETA: 0s - loss: 1.4077 - accuracy: 0.6562" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", + "12/12 [==============================] - 0s 954us/step - loss: 1.4837 - accuracy: 0.5611\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Learning rate = 0.0001\n", + "Lambda = 0.0001\n", + "Test accuracy: 0.561\n", + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\r", + " 1/12 [=>............................] - ETA: 0s - loss: 1.5539 - accuracy: 0.5625" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\b\r", + "12/12 [==============================] - 0s 932us/step - loss: 1.5615 - accuracy: 0.5639\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Learning rate = 0.0001\n", + "Lambda = 0.001\n", + "Test accuracy: 0.564\n", + "\n" + ] + }, + { + "ename": "KeyboardInterrupt", + "evalue": "", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47647/2018906331.py\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0mn_filters\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_neurons_connected\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn_categories\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m eta, lmbd)\n\u001b[0;32m----> 8\u001b[0;31m \u001b[0mCNN\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfit\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_train\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mY_train\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mepochs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mepochs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbatch_size\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mbatch_size\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mverbose\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 9\u001b[0m \u001b[0mscores\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mCNN\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mevaluate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX_test\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mY_test\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/keras/engine/training.py\u001b[0m in \u001b[0;36mfit\u001b[0;34m(self, x, y, batch_size, epochs, verbose, callbacks, validation_split, validation_data, shuffle, class_weight, sample_weight, initial_epoch, steps_per_epoch, validation_steps, validation_batch_size, validation_freq, max_queue_size, workers, use_multiprocessing)\u001b[0m\n\u001b[1;32m 1182\u001b[0m _r=1):\n\u001b[1;32m 1183\u001b[0m \u001b[0mcallbacks\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mon_train_batch_begin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1184\u001b[0;31m \u001b[0mtmp_logs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtrain_function\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0miterator\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1185\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mdata_handler\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshould_sync\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1186\u001b[0m \u001b[0mcontext\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0masync_wait\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/tensorflow/python/eager/def_function.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, *args, **kwds)\u001b[0m\n\u001b[1;32m 883\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 884\u001b[0m \u001b[0;32mwith\u001b[0m \u001b[0mOptionalXlaContext\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_jit_compile\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 885\u001b[0;31m \u001b[0mresult\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_call\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 886\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 887\u001b[0m \u001b[0mnew_tracing_count\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mexperimental_get_tracing_count\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/tensorflow/python/eager/def_function.py\u001b[0m in \u001b[0;36m_call\u001b[0;34m(self, *args, **kwds)\u001b[0m\n\u001b[1;32m 915\u001b[0m \u001b[0;31m# In this case we have created variables on the first call, so we run the\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 916\u001b[0m \u001b[0;31m# defunned version which is guaranteed to never create variables.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 917\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_stateless_fn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwds\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m# pylint: disable=not-callable\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 918\u001b[0m \u001b[0;32melif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_stateful_fn\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 919\u001b[0m \u001b[0;31m# Release the lock early so that multiple threads can perform the call\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/tensorflow/python/eager/function.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, *args, **kwargs)\u001b[0m\n\u001b[1;32m 3037\u001b[0m (graph_function,\n\u001b[1;32m 3038\u001b[0m filtered_flat_args) = self._maybe_define_function(args, kwargs)\n\u001b[0;32m-> 3039\u001b[0;31m return graph_function._call_flat(\n\u001b[0m\u001b[1;32m 3040\u001b[0m filtered_flat_args, captured_inputs=graph_function.captured_inputs) # pylint: disable=protected-access\n\u001b[1;32m 3041\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/tensorflow/python/eager/function.py\u001b[0m in \u001b[0;36m_call_flat\u001b[0;34m(self, args, captured_inputs, cancellation_manager)\u001b[0m\n\u001b[1;32m 1961\u001b[0m and executing_eagerly):\n\u001b[1;32m 1962\u001b[0m \u001b[0;31m# No tape is watching; skip to running the function.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1963\u001b[0;31m return self._build_call_outputs(self._inference_function.call(\n\u001b[0m\u001b[1;32m 1964\u001b[0m ctx, args, cancellation_manager=cancellation_manager))\n\u001b[1;32m 1965\u001b[0m forward_backward = self._select_forward_and_backward_functions(\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/tensorflow/python/eager/function.py\u001b[0m in \u001b[0;36mcall\u001b[0;34m(self, ctx, args, cancellation_manager)\u001b[0m\n\u001b[1;32m 589\u001b[0m \u001b[0;32mwith\u001b[0m \u001b[0m_InterpolateFunctionError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 590\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mcancellation_manager\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 591\u001b[0;31m outputs = execute.execute(\n\u001b[0m\u001b[1;32m 592\u001b[0m \u001b[0mstr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msignature\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 593\u001b[0m \u001b[0mnum_outputs\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_num_outputs\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/tensorflow/python/eager/execute.py\u001b[0m in \u001b[0;36mquick_execute\u001b[0;34m(op_name, num_outputs, inputs, attrs, ctx, name)\u001b[0m\n\u001b[1;32m 57\u001b[0m \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 58\u001b[0m \u001b[0mctx\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mensure_initialized\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 59\u001b[0;31m tensors = pywrap_tfe.TFE_Py_Execute(ctx._handle, device_name, op_name,\n\u001b[0m\u001b[1;32m 60\u001b[0m inputs, attrs, num_outputs)\n\u001b[1;32m 61\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0mcore\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_NotOkStatusException\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mKeyboardInterrupt\u001b[0m: " + ] + } + ], + "source": [ + "CNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object)\n", + " \n", + "for i, eta in enumerate(eta_vals):\n", + " for j, lmbd in enumerate(lmbd_vals):\n", + " CNN = create_convolutional_neural_network_keras(input_shape, receptive_field,\n", + " n_filters, n_neurons_connected, n_categories,\n", + " eta, lmbd)\n", + " CNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0)\n", + " scores = CNN.evaluate(X_test, Y_test)\n", + " \n", + " CNN_keras[i][j] = CNN\n", + " \n", + " print(\"Learning rate = \", eta)\n", + " print(\"Lambda = \", lmbd)\n", + " print(\"Test accuracy: %.3f\" % scores[1])\n", + " print()" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "df145244", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# visual representation of grid search\n", + "# uses seaborn heatmap, could probably do this in matplotlib\n", + "import seaborn as sns\n", + "\n", + "sns.set()\n", + "\n", + "train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n", + "test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals)))\n", + "\n", + "for i in range(len(eta_vals)):\n", + " for j in range(len(lmbd_vals)):\n", + " CNN = CNN_keras[i][j]\n", + "\n", + " train_accuracy[i][j] = CNN.evaluate(X_train, Y_train)[1]\n", + " test_accuracy[i][j] = CNN.evaluate(X_test, Y_test)[1]\n", + "\n", + " \n", + "fig, ax = plt.subplots(figsize = (10, 10))\n", + "sns.heatmap(train_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n", + "ax.set_title(\"Training Accuracy\")\n", + "ax.set_ylabel(\"$\\eta$\")\n", + "ax.set_xlabel(\"$\\lambda$\")\n", + "plt.show()\n", + "\n", + "fig, ax = plt.subplots(figsize = (10, 10))\n", + "sns.heatmap(test_accuracy, annot=True, ax=ax, cmap=\"viridis\")\n", + "ax.set_title(\"Test Accuracy\")\n", + "ax.set_ylabel(\"$\\eta$\")\n", + "ax.set_xlabel(\"$\\lambda$\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "a6724f1c", + "metadata": { + "editable": true + }, + "source": [ + "## The CIFAR01 data set\n", + "\n", + "The CIFAR10 dataset contains 60,000 color images in 10 classes, with\n", + "6,000 images in each class. The dataset is divided into 50,000\n", + "training images and 10,000 testing images. The classes are mutually\n", + "exclusive and there is no overlap between them." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "90c28005", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "import tensorflow as tf\n", + "\n", + "from tensorflow.keras import datasets, layers, models\n", + "import matplotlib.pyplot as plt\n", + "\n", + "# We import the data set\n", + "(train_images, train_labels), (test_images, test_labels) = datasets.cifar10.load_data()\n", + "\n", + "# Normalize pixel values to be between 0 and 1 by dividing by 255. \n", + "train_images, test_images = train_images / 255.0, test_images / 255.0" + ] + }, + { + "cell_type": "markdown", + "id": "759ea77a", + "metadata": { + "editable": true + }, + "source": [ + "To verify that the dataset looks correct, let's plot the first 25 images from the training set and display the class name below each image." + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "494edadd", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "class_names = ['airplane', 'automobile', 'bird', 'cat', 'deer',\n", + " 'dog', 'frog', 'horse', 'ship', 'truck']\n", + "​\n", + "plt.figure(figsize=(10,10))\n", + "for i in range(25):\n", + " plt.subplot(5,5,i+1)\n", + " plt.xticks([])\n", + " plt.yticks([])\n", + " plt.grid(False)\n", + " plt.imshow(train_images[i], cmap=plt.cm.binary)\n", + " # The CIFAR labels happen to be arrays, \n", + " # which is why you need the extra index\n", + " plt.xlabel(class_names[train_labels[i][0]])\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "46d2ea5d", + "metadata": { + "editable": true + }, + "source": [ + "The six lines of code below define the convolutional base using a common pattern: a stack of Conv2D and MaxPooling2D layers.\n", + "\n", + "As input, a CNN takes tensors of shape (image_height, image_width, color_channels), ignoring the batch size. If you are new to these dimensions, color_channels refers to (R,G,B). In this example, you will configure our CNN to process inputs of shape (32, 32, 3), which is the format of CIFAR images. You can do this by passing the argument input_shape to our first layer." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "044310ec", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "model = models.Sequential()\n", + "model.add(layers.Conv2D(32, (3, 3), activation='relu', input_shape=(32, 32, 3)))\n", + "model.add(layers.MaxPooling2D((2, 2)))\n", + "model.add(layers.Conv2D(64, (3, 3), activation='relu'))\n", + "model.add(layers.MaxPooling2D((2, 2)))\n", + "model.add(layers.Conv2D(64, (3, 3), activation='relu'))\n", + "\n", + "# Let's display the architecture of our model so far.\n", + "\n", + "model.summary()" + ] + }, + { + "cell_type": "markdown", + "id": "738f34a7", + "metadata": { + "editable": true + }, + "source": [ + "You can see that the output of every Conv2D and MaxPooling2D layer is a 3D tensor of shape (height, width, channels). The width and height dimensions tend to shrink as you go deeper in the network. The number of output channels for each Conv2D layer is controlled by the first argument (e.g., 32 or 64). Typically, as the width and height shrink, you can afford (computationally) to add more output channels in each Conv2D layer.\n", + "\n", + "To complete our model, you will feed the last output tensor from the\n", + "convolutional base (of shape (4, 4, 64)) into one or more Dense layers\n", + "to perform classification. Dense layers take vectors as input (which\n", + "are 1D), while the current output is a 3D tensor. First, you will\n", + "flatten (or unroll) the 3D output to 1D, then add one or more Dense\n", + "layers on top. CIFAR has 10 output classes, so you use a final Dense\n", + "layer with 10 outputs and a softmax activation." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "e0fea435", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "model.add(layers.Flatten())\n", + "model.add(layers.Dense(64, activation='relu'))\n", + "model.add(layers.Dense(10))\n", + "Here's the complete architecture of our model.\n", + "\n", + "model.summary()" + ] + }, + { + "cell_type": "markdown", + "id": "62f1e50d", + "metadata": { + "editable": true + }, + "source": [ + "As you can see, our (4, 4, 64) outputs were flattened into vectors of shape (1024) before going through two Dense layers." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "e2d8f4f2", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "model.compile(optimizer='adam',\n", + " loss=tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True),\n", + " metrics=['accuracy'])\n", + "​\n", + "history = model.fit(train_images, train_labels, epochs=10, \n", + " validation_data=(test_images, test_labels))" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "d2965f40", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "plt.plot(history.history['accuracy'], label='accuracy')\n", + "plt.plot(history.history['val_accuracy'], label = 'val_accuracy')\n", + "plt.xlabel('Epoch')\n", + "plt.ylabel('Accuracy')\n", + "plt.ylim([0.5, 1])\n", + "plt.legend(loc='lower right')\n", + "\n", + "test_loss, test_acc = model.evaluate(test_images, test_labels, verbose=2)\n", + "\n", + "print(test_acc)" + ] + } + ], + "metadata": { + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter12.py b/doc/LectureNotes/_build/jupyter_execute/chapter12.py new file mode 100644 index 000000000..f6700ecd8 --- /dev/null +++ b/doc/LectureNotes/_build/jupyter_execute/chapter12.py @@ -0,0 +1,921 @@ +#!/usr/bin/env python +# coding: utf-8 + +# + +# # Convolutional Neural Networks +# +# Convolutional neural networks (CNNs) were developed during the last +# decade of the previous century, with a focus on character recognition +# tasks. Nowadays, CNNs are a central element in the spectacular success +# of deep learning methods. The success in for example image +# classifications have made them a central tool for most machine +# learning practitioners. +# +# CNNs are very similar to ordinary Neural Networks. +# They are made up of neurons that have learnable weights and +# biases. Each neuron receives some inputs, performs a dot product and +# optionally follows it with a non-linearity. The whole network still +# expresses a single differentiable score function: from the raw image +# pixels on one end to class scores at the other. And they still have a +# loss function (for example Softmax) on the last (fully-connected) layer +# and all the tips/tricks we developed for learning regular Neural +# Networks still apply (back propagation, gradient descent etc etc). +# +# **CNN architectures make the explicit assumption that +# the inputs are images, which allows us to encode certain properties +# into the architecture. These then make the forward function more +# efficient to implement and vastly reduce the amount of parameters in +# the network.** +# +# Here we provide only a superficial overview, for the more interested, we recommend highly the course +# [IN5400 – Machine Learning for Image Analysis](https://www.uio.no/studier/emner/matnat/ifi/IN5400/index-eng.html) +# and the slides of [CS231](http://cs231n.github.io/convolutional-networks/). +# +# Another good read is the article here . + +# ## Neural Networks vs CNNs +# +# Neural networks are defined as **affine transformations**, that is +# a vector is received as input and is multiplied with a matrix of so-called weights (our unknown paramters) to produce an +# output (to which a bias vector is usually added before passing the result +# through a nonlinear activation function). This is applicable to any type of input, be it an +# image, a sound clip or an unordered collection of features: whatever their +# dimensionality, their representation can always be flattened into a vector +# before the transformation. +# +# However, when we consider images, sound clips and many other similar kinds of data, these data have an intrinsic +# structure. More formally, they share these important properties: +# * They are stored as multi-dimensional arrays (think of the pixels of a figure) . +# +# * They feature one or more axes for which ordering matters (e.g., width and height axes for an image, time axis for a sound clip). +# +# * One axis, called the channel axis, is used to access different views of the data (e.g., the red, green and blue channels of a color image, or the left and right channels of a stereo audio track). +# +# These properties are not exploited when an affine transformation is applied; in +# fact, all the axes are treated in the same way and the topological information +# is not taken into account. Still, taking advantage of the implicit structure of +# the data may prove very handy in solving some tasks, like computer vision and +# speech recognition, and in these cases it would be best to preserve it. This is +# where discrete convolutions come into play. +# +# A discrete convolution is a linear transformation that preserves this notion of +# ordering. It is sparse (only a few input units contribute to a given output +# unit) and reuses parameters (the same weights are applied to multiple locations +# in the input). +# +# As an example, consider +# an image of size $32\times 32\times 3$ (32 wide, 32 high, 3 color channels), so a +# single fully-connected neuron in a first hidden layer of a regular +# Neural Network would have $32\times 32\times 3 = 3072$ weights. This amount still +# seems manageable, but clearly this fully-connected structure does not +# scale to larger images. For example, an image of more respectable +# size, say $200\times 200\times 3$, would lead to neurons that have +# $200\times 200\times 3 = 120,000$ weights. +# +# We could have +# several such neurons, and the parameters would add up quickly! Clearly, +# this full connectivity is wasteful and the huge number of parameters +# would quickly lead to possible overfitting. +# +# +# +# +#

    Figure 1: A regular 3-layer Neural Network.

    +# +# +# Convolutional Neural Networks take advantage of the fact that the +# input consists of images and they constrain the architecture in a more +# sensible way. +# +# In particular, unlike a regular Neural Network, the +# layers of a CNN have neurons arranged in 3 dimensions: width, +# height, depth. (Note that the word depth here refers to the third +# dimension of an activation volume, not to the depth of a full Neural +# Network, which can refer to the total number of layers in a network.) +# +# To understand it better, the above example of an image +# with an input volume of +# activations has dimensions $32\times 32\times 3$ (width, height, +# depth respectively). +# +# The neurons in a layer will +# only be connected to a small region of the layer before it, instead of +# all of the neurons in a fully-connected manner. Moreover, the final +# output layer could for this specific image have dimensions $1\times 1 \times 10$, +# because by the +# end of the CNN architecture we will reduce the full image into a +# single vector of class scores, arranged along the depth +# dimension. +# +# +# +# +#

    Figure 1: A CNN arranges its neurons in three dimensions (width, height, depth), as visualized in one of the layers. Every layer of a CNN transforms the 3D input volume to a 3D output volume of neuron activations. In this example, the red input layer holds the image, so its width and height would be the dimensions of the image, and the depth would be 3 (Red, Green, Blue channels).

    +# + +# ## Layers used to build CNNs +# +# A simple CNN is a sequence of layers, and every layer of a CNN +# transforms one volume of activations to another through a +# differentiable function. We use three main types of layers to build +# CNN architectures: Convolutional Layer, Pooling Layer, and +# Fully-Connected Layer (exactly as seen in regular Neural Networks). We +# will stack these layers to form a full CNN architecture. +# +# A simple CNN for image classification could have the architecture: +# +# * **INPUT** ($32\times 32 \times 3$) will hold the raw pixel values of the image, in this case an image of width 32, height 32, and with three color channels R,G,B. +# +# * **CONV** (convolutional )layer will compute the output of neurons that are connected to local regions in the input, each computing a dot product between their weights and a small region they are connected to in the input volume. This may result in volume such as $[32\times 32\times 12]$ if we decided to use 12 filters. +# +# * **RELU** layer will apply an elementwise activation function, such as the $max(0,x)$ thresholding at zero. This leaves the size of the volume unchanged ($[32\times 32\times 12]$). +# +# * **POOL** (pooling) layer will perform a downsampling operation along the spatial dimensions (width, height), resulting in volume such as $[16\times 16\times 12]$. +# +# * **FC** (i.e. fully-connected) layer will compute the class scores, resulting in volume of size $[1\times 1\times 10]$, where each of the 10 numbers correspond to a class score, such as among the 10 categories of the MNIST images we considered above . As with ordinary Neural Networks and as the name implies, each neuron in this layer will be connected to all the numbers in the previous volume. +# +# CNNs transform the original image layer by layer from the original +# pixel values to the final class scores. +# +# Observe that some layers contain +# parameters and other don’t. In particular, the CNN layers perform +# transformations that are a function of not only the activations in the +# input volume, but also of the parameters (the weights and biases of +# the neurons). On the other hand, the RELU/POOL layers will implement a +# fixed function. The parameters in the CONV/FC layers will be trained +# with gradient descent so that the class scores that the CNN computes +# are consistent with the labels in the training set for each image. +# +# In summary: +# +# * A CNN architecture is in the simplest case a list of Layers that transform the image volume into an output volume (e.g. holding the class scores) +# +# * There are a few distinct types of Layers (e.g. CONV/FC/RELU/POOL are by far the most popular) +# +# * Each Layer accepts an input 3D volume and transforms it to an output 3D volume through a differentiable function +# +# * Each Layer may or may not have parameters (e.g. CONV/FC do, RELU/POOL don’t) +# +# * Each Layer may or may not have additional hyperparameters (e.g. CONV/FC/POOL do, RELU doesn’t) +# +# A dense neural network is representd by an affine operation (like matrix-matrix multiplication) where all parameters are included. +# +# The key idea in CNNs for say imaging is that in images neighbor pixels tend to be related! So we connect +# only neighboring neurons in the input instead of connecting all with the first hidden layer. +# +# We say we perform a filtering (convolution is the mathematical operation). + +# ## Mathematics of CNNs +# +# The mathematics of CNNs is based on the mathematical operation of +# **convolution**. In mathematics (in particular in functional analysis), +# convolution is represented by matheematical operation (integration, +# summation etc) on two function in order to produce a third function +# that expresses how the shape of one gets modified by the other. +# Convolution has a plethora of applications in a variety of disciplines, spanning from statistics to signal processing, computer vision, solutions of differential equations,linear algebra, engineering, and yes, machine learning. +# +# Mathematically, convolution is defined as follows (one-dimensional example): +# Let us define a continuous function $y(t)$ given by + +# $$ +# y(t) = \int x(a) w(t-a) da, +# $$ + +# where $x(a)$ represents a so-called input and $w(t-a)$ is normally called the weight function or kernel. +# +# The above integral is written in a more compact form as + +# $$ +# y(t) = \left(x * w\right)(t). +# $$ + +# The discretized version reads + +# $$ +# y(t) = \sum_{a=-\infty}^{a=\infty}x(a)w(t-a). +# $$ + +# Computing the inverse of the above convolution operations is known as deconvolution. +# +# How can we use this? And what does it mean? Let us study some familiar examples first. + +# ### Convolution Examples: Polynomial multiplication +# +# We have already met such an example in project 1 when we tried to set +# up the design matrix for a two-dimensional function. This was an +# example of polynomial multiplication. Let us recast such a problem in terms of the convolution operation. +# Let us look a the following polynomials to second and third order, respectively: + +# $$ +# p(t) = \alpha_0+\alpha_1 t+\alpha_2 t^2, +# $$ + +# and + +# $$ +# s(t) = \beta_0+\beta_1 t+\beta_2 t^2+\beta_3 t^3. +# $$ + +# The polynomial multiplication gives us a new polynomial of degree $5$ + +# $$ +# z(t) = \delta_0+\delta_1 t+\delta_2 t^2+\delta_3 t^3+\delta_4 t^4+\delta_5 t^5. +# $$ + +# Computing polynomial products can be implemented efficiently if we rewrite the more brute force multiplications using convolution. +# We note first that the new coefficients are given as + +# $$ +# \begin{split} +# \delta_0=&\alpha_0\beta_0\\ +# \delta_1=&\alpha_1\beta_0+\alpha_1\beta_0\\ +# \delta_2=&\alpha_0\beta_2+\alpha_1\beta_1+\alpha_2\beta_0\\ +# \delta_3=&\alpha_1\beta_2+\alpha_2\beta_1+\alpha_0\beta_3\\ +# \delta_4=&\alpha_2\beta_2+\alpha_1\beta_3\\ +# \delta_5=&\alpha_2\beta_3.\\ +# \end{split} +# $$ + +# We note that $\alpha_i=0$ except for $i\in \left\{0,1,2\right\}$ and $\beta_i=0$ except for $i\in\left\{0,1,2,3\right\}$. +# +# We can then rewrite the coefficients $\delta_j$ using a discrete convolution as + +# $$ +# \delta_j = \sum_{i=-\infty}^{i=\infty}\alpha_i\beta_{j-i}=(\alpha * \beta)_j, +# $$ + +# or as a double sum with restriction $l=i+j$ + +# $$ +# \delta_l = \sum_{ij}\alpha_i\beta_{j}. +# $$ + +# Do you see a potential drawback with these equations? +# +# Since we only have a finite number of $\alpha$ and $\beta$ values +# which are non-zero, we can rewrite the above convolution expressions +# as a matrix-vector multiplication + +# $$ +# \boldsymbol{\delta}=\begin{bmatrix}\alpha_0 & 0 & 0 & 0 \\ +# \alpha_1 & \alpha_0 & 0 & 0 \\ +# \alpha_2 & \alpha_1 & \alpha_0 & 0 \\ +# 0 & \alpha_2 & \alpha_1 & \alpha_0 \\ +# 0 & 0 & \alpha_2 & \alpha_1 \\ +# 0 & 0 & 0 & \alpha_2 +# \end{bmatrix}\begin{bmatrix} \beta_0 \\ \beta_1 \\ \beta_2 \\ \beta_3\end{bmatrix}. +# $$ + +# The process is commutative and we can easily see that we can rewrite the multiplication in terms of a matrix holding $\beta$ and a vector holding $\alpha$. +# In this case we have + +# $$ +# \boldsymbol{\delta}=\begin{bmatrix}\beta_0 & 0 & 0 \\ +# \beta_1 & \beta_0 & 0 \\ +# \beta_2 & \beta_1 & \beta_0 \\ +# \beta_3 & \beta_2 & \beta_1 \\ +# 0 & \beta_3 & \beta_2 \\ +# 0 & 0 & \beta_3 +# \end{bmatrix}\begin{bmatrix} \alpha_0 \\ \alpha_1 \\ \alpha_2\end{bmatrix}. +# $$ + +# Note that the use of these matrices is for mathematical purposes only and not implementation purposes. +# When implementing the above equation we do not encode (and allocate memory) the matrices explicitely. +# We rather code the convolutions in the minimal memory footprint that they require. +# +# Does the number of floating point operations change here when we use the commutative property? + +# ### Convolution Examples: Principle of Superposition and Periodic Forces (Fourier Transforms) +# +# For problems with so-called harmonic oscillations, given by for example the following differential equation + +# $$ +# m\frac{d^2x}{dt^2}+\eta\frac{dx}{dt}+x(t)=F(t), +# $$ + +# where $F(t)$ is an applied external force acting on the system (often called a driving force), one can use the theory of Fourier transformations to find the solutions of this type of equations. +# +# If one has several driving forces, $F(t)=\sum_n F_n(t)$, one can find +# the particular solution to each $F_n$, $x_{pn}(t)$, and the particular +# solution for the entire driving force is then given by a series like + +# +#
    +# +# $$ +# \begin{equation} +# x_p(t)=\sum_nx_{pn}(t). +# \label{_auto1} \tag{1} +# \end{equation} +# $$ + +# This is known as the principle of superposition. It only applies when +# the homogenous equation is linear. If there were an anharmonic term +# such as $x^3$ in the homogenous equation, then when one summed various +# solutions, $x=(\sum_n x_n)^2$, one would get cross +# terms. Superposition is especially useful when $F(t)$ can be written +# as a sum of sinusoidal terms, because the solutions for each +# sinusoidal (sine or cosine) term is analytic. +# +# Driving forces are often periodic, even when they are not +# sinusoidal. Periodicity implies that for some time $\tau$ + +# $$ +# \begin{eqnarray} +# F(t+\tau)=F(t). +# \end{eqnarray} +# $$ + +# One example of a non-sinusoidal periodic force is a square wave. Many +# components in electric circuits are non-linear, e.g. diodes, which +# makes many wave forms non-sinusoidal even when the circuits are being +# driven by purely sinusoidal sources. +# +# The code here shows a typical example of such a square wave generated using the functionality included in the **scipy** Python package. We have used a period of $\tau=0.2$. + +# In[1]: + + +get_ipython().run_line_magic('matplotlib', 'inline') + +import numpy as np +import math +from scipy import signal +import matplotlib.pyplot as plt + +# number of points +n = 500 +# start and final times +t0 = 0.0 +tn = 1.0 +# Period +t = np.linspace(t0, tn, n, endpoint=False) +SqrSignal = np.zeros(n) +SqrSignal = 1.0+signal.square(2*np.pi*5*t) +plt.plot(t, SqrSignal) +plt.ylim(-0.5, 2.5) +plt.show() + + +# For the sinusoidal example the +# period is $\tau=2\pi/\omega$. However, higher harmonics can also +# satisfy the periodicity requirement. In general, any force that +# satisfies the periodicity requirement can be expressed as a sum over +# harmonics, + +# +#
    +# +# $$ +# \begin{equation} +# F(t)=\frac{f_0}{2}+\sum_{n>0} f_n\cos(2n\pi t/\tau)+g_n\sin(2n\pi t/\tau). +# \label{_auto2} \tag{2} +# \end{equation} +# $$ + +# We can write down the answer for +# $x_{pn}(t)$, by substituting $f_n/m$ or $g_n/m$ for $F_0/m$. By +# writing each factor $2n\pi t/\tau$ as $n\omega t$, with $\omega\equiv +# 2\pi/\tau$, + +# +#
    +# +# $$ +# \begin{equation} +# \label{eq:fourierdef1} \tag{3} +# F(t)=\frac{f_0}{2}+\sum_{n>0}f_n\cos(n\omega t)+g_n\sin(n\omega t). +# \end{equation} +# $$ + +# The solutions for $x(t)$ then come from replacing $\omega$ with +# $n\omega$ for each term in the particular solution, + +# $$ +# \begin{eqnarray} +# x_p(t)&=&\frac{f_0}{2k}+\sum_{n>0} \alpha_n\cos(n\omega t-\delta_n)+\beta_n\sin(n\omega t-\delta_n),\\ +# \nonumber +# \alpha_n&=&\frac{f_n/m}{\sqrt{((n\omega)^2-\omega_0^2)+4\beta^2n^2\omega^2}},\\ +# \nonumber +# \beta_n&=&\frac{g_n/m}{\sqrt{((n\omega)^2-\omega_0^2)+4\beta^2n^2\omega^2}},\\ +# \nonumber +# \delta_n&=&\tan^{-1}\left(\frac{2\beta n\omega}{\omega_0^2-n^2\omega^2}\right). +# \end{eqnarray} +# $$ + +# Because the forces have been applied for a long time, any non-zero +# damping eliminates the homogenous parts of the solution, so one need +# only consider the particular solution for each $n$. +# +# The problem is considered solved if one can find expressions for the +# coefficients $f_n$ and $g_n$, even though the solutions are expressed +# as an infinite sum. The coefficients can be extracted from the +# function $F(t)$ by + +# +#
    +# +# $$ +# \begin{eqnarray} +# \label{eq:fourierdef2} \tag{4} +# f_n&=&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~F(t)\cos(2n\pi t/\tau),\\ +# \nonumber +# g_n&=&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~F(t)\sin(2n\pi t/\tau). +# \end{eqnarray} +# $$ + +# To check the consistency of these expressions and to verify +# Eq. ([4](#eq:fourierdef2)), one can insert the expansion of $F(t)$ in +# Eq. ([3](#eq:fourierdef1)) into the expression for the coefficients in +# Eq. ([4](#eq:fourierdef2)) and see whether + +# $$ +# \begin{eqnarray} +# f_n&=?&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~\left\{ +# \frac{f_0}{2}+\sum_{m>0}f_m\cos(m\omega t)+g_m\sin(m\omega t) +# \right\}\cos(n\omega t). +# \end{eqnarray} +# $$ + +# Immediately, one can throw away all the terms with $g_m$ because they +# convolute an even and an odd function. The term with $f_0/2$ +# disappears because $\cos(n\omega t)$ is equally positive and negative +# over the interval and will integrate to zero. For all the terms +# $f_m\cos(m\omega t)$ appearing in the sum, one can use angle addition +# formulas to see that $\cos(m\omega t)\cos(n\omega +# t)=(1/2)(\cos[(m+n)\omega t]+\cos[(m-n)\omega t]$. This will integrate +# to zero unless $m=n$. In that case the $m=n$ term gives + +# +#
    +# +# $$ +# \begin{equation} +# \int_{-\tau/2}^{\tau/2}dt~\cos^2(m\omega t)=\frac{\tau}{2}, +# \label{_auto3} \tag{5} +# \end{equation} +# $$ + +# and + +# $$ +# \begin{eqnarray} +# f_n&=?&\frac{2}{\tau}\int_{-\tau/2}^{\tau/2} dt~f_n/2\\ +# \nonumber +# &=&f_n~\checkmark. +# \end{eqnarray} +# $$ + +# The same method can be used to check for the consistency of $g_n$. +# +# The code here uses the Fourier series applied to a +# square wave signal. The code here +# visualizes the various approximations given by Fourier series compared +# with a square wave with period $T=0.2$ (dimensionless time), width $0.1$ and max value of the force $F=2$. We +# see that when we increase the number of components in the Fourier +# series, the Fourier series approximation gets closer and closer to the +# square wave signal. + +# In[2]: + + +import numpy as np +import math +from scipy import signal +import matplotlib.pyplot as plt + +# number of points +n = 500 +# start and final times +t0 = 0.0 +tn = 1.0 +# Period +T =0.2 +# Max value of square signal +Fmax= 2.0 +# Width of signal +Width = 0.1 +t = np.linspace(t0, tn, n, endpoint=False) +SqrSignal = np.zeros(n) +FourierSeriesSignal = np.zeros(n) +SqrSignal = 1.0+signal.square(2*np.pi*5*t+np.pi*Width/T) +a0 = Fmax*Width/T +FourierSeriesSignal = a0 +Factor = 2.0*Fmax/np.pi +for i in range(1,500): + FourierSeriesSignal += Factor/(i)*np.sin(np.pi*i*Width/T)*np.cos(i*t*2*np.pi/T) +plt.plot(t, SqrSignal) +plt.plot(t, FourierSeriesSignal) +plt.ylim(-0.5, 2.5) +plt.show() + + +# ## Two-dimensional Objects +# +# We often use convolutions over more than one dimension at a time. If +# we have a two-dimensional image $I$ as input, we can have a **filter** +# defined by a two-dimensional **kernel** $K$. This leads to an output $S$ + +# $$ +# S_(i,j)=(I * K)(i,j) = \sum_m\sum_n I(m,n)K(i-m,j-n). +# $$ + +# Convolution is a commutatitave process, which means we can rewrite this equation as + +# $$ +# S_(i,j)=(I * K)(i,j) = \sum_m\sum_n I(i-m,j-n)K(m,n). +# $$ + +# Normally the latter is more straightforward to implement in a machine elarning library since there is less variation in the range of values of $m$ and $n$. +# +# Many deep learning libraries implement cross-correlation instead of convolution + +# $$ +# S_(i,j)=(I * K)(i,j) = \sum_m\sum_n I(i+m,j-+)K(m,n). +# $$ + +# ## More on Dimensionalities +# +# In fields like signal processing (and imaging as well), one designs +# so-called filters. These filters are defined by the convolutions and +# are often hand-crafted. One may specify filters for smoothing, edge +# detection, frequency reshaping, and similar operations. However with +# neural networks the idea is to automatically learn the filters and use +# many of them in conjunction with non-linear operations (activation +# functions). +# +# As an example consider a neural network operating on sound sequence +# data. Assume that we an input vector $\boldsymbol{x}$ of length $d=10^6$. We +# construct then a neural network with onle hidden layer only with +# $10^4$ nodes. This means that we will have a weight matrix with +# $10^4\times 10^6=10^{10}$ weights to be determined, together with $10^4$ biases. +# +# Assume furthermore that we have an output layer which is meant to train whether the sound sequence represents a human voice (true) or something else (false). +# It means that we have only one output node. But since this output node connects to $10^4$ nodes in the hidden layer, there are in total $10^4$ weights to be determined for the output layer, plus one bias. In total we have + +# $$ +# \mathrm{NumberParameters}=10^{10}+10^4+10^4+1 \approx 10^{10}, +# $$ + +# that is ten billion parameters to determine. + +# ## Further Dimensionality Remarks +# +# In today’s architecture one can train such neural networks, however +# this is a huge number of parameters for the task at hand. In general, +# it is a very wasteful and inefficient use of dense matrices as +# parameters. Just as importantly, such trained network parameters are +# very specific for the type of input data on which they were trained +# and the network is not likely to generalize easily to variations in +# the input. +# +# The main principles that justify convolutions is locality of +# information and repetion of patterns within the signal. Sound samples +# of the input in adjacent spots are much more likely to affect each +# other than those that are very far away. Similarly, sounds are +# repeated in multiple times in the signal. While slightly simplistic, +# reasoning about such a sound example demonstrates this. The same +# principles then apply to images and other similar data. + +# ## CNNs in more detail, building convolutional neural networks in Tensorflow and Keras +# +# As discussed above, CNNs are neural networks built from the assumption that the inputs +# to the network are 2D images. This is important because the number of features or pixels in images +# grows very fast with the image size, and an enormous number of weights and biases are needed in order to build an accurate network. +# +# As before, we still have our input, a hidden layer and an output. What's novel about convolutional networks +# are the **convolutional** and **pooling** layers stacked in pairs between the input and the hidden layer. +# In addition, the data is no longer represented as a 2D feature matrix, instead each input is a number of 2D +# matrices, typically 1 for each color dimension (Red, Green, Blue). +# +# It means that to represent the entire +# dataset of images, we require a 4D matrix or **tensor**. This tensor has the dimensions: + +# $$ +# (n_{inputs},\, n_{pixels, width},\, n_{pixels, height},\, depth) . +# $$ + +# ### The MNIST dataset again +# +# The MNIST dataset consists of grayscale images with a pixel size of +# $28\times 28$, meaning we require $28 \times 28 = 724$ weights to each +# neuron in the first hidden layer. +# +# If we were to analyze images of size $128\times 128$ we would require +# $128 \times 128 = 16384$ weights to each neuron. Even worse if we were +# dealing with color images, as most images are, we have an image matrix +# of size $128\times 128$ for each color dimension (Red, Green, Blue), +# meaning 3 times the number of weights $= 49152$ are required for every +# single neuron in the first hidden layer. +# +# Images typically have strong local correlations, meaning that a small +# part of the image varies little from its neighboring regions. If for +# example we have an image of a blue car, we can roughly assume that a +# small blue part of the image is surrounded by other blue regions. +# +# Therefore, instead of connecting every single pixel to a neuron in the +# first hidden layer, as we have previously done with deep neural +# networks, we can instead connect each neuron to a small part of the +# image (in all 3 RGB depth dimensions). The size of each small area is +# fixed, and known as a [receptive](https://en.wikipedia.org/wiki/Receptive_field). +# +# The layers of a convolutional neural network arrange neurons in 3D: width, height and depth. +# The input image is typically a square matrix of depth 3. +# +# A **convolution** is performed on the image which outputs +# a 3D volume of neurons. The weights to the input are arranged in a number of 2D matrices, known as **filters**. +# +# Each filter slides along the input image, taking the dot product +# between each small part of the image and the filter, in all depth +# dimensions. This is then passed through a non-linear function, +# typically the **Rectified Linear (ReLu)** function, which serves as the +# activation of the neurons in the first convolutional layer. This is +# further passed through a **pooling layer**, which reduces the size of the +# convolutional layer, e.g. by taking the maximum or average across some +# small regions, and this serves as input to the next convolutional +# layer. + +# ### Systematic reduction +# +# By systematically reducing the size of the input volume, through +# convolution and pooling, the network should create representations of +# small parts of the input, and then from them assemble representations +# of larger areas. The final pooling layer is flattened to serve as +# input to a hidden layer, such that each neuron in the final pooling +# layer is connected to every single neuron in the hidden layer. This +# then serves as input to the output layer, e.g. a softmax output for +# classification. + +# ### Prerequisites: Collect and pre-process data + +# In[3]: + + +# import necessary packages +import numpy as np +import matplotlib.pyplot as plt +from sklearn import datasets + + +# ensure the same random numbers appear every time +np.random.seed(0) + +# display images in notebook +get_ipython().run_line_magic('matplotlib', 'inline') +plt.rcParams['figure.figsize'] = (12,12) + + +# download MNIST dataset +digits = datasets.load_digits() + +# define inputs and labels +inputs = digits.images +labels = digits.target + +# RGB images have a depth of 3 +# our images are grayscale so they should have a depth of 1 +inputs = inputs[:,:,:,np.newaxis] + +print("inputs = (n_inputs, pixel_width, pixel_height, depth) = " + str(inputs.shape)) +print("labels = (n_inputs) = " + str(labels.shape)) + + +# choose some random images to display +n_inputs = len(inputs) +indices = np.arange(n_inputs) +random_indices = np.random.choice(indices, size=5) + +for i, image in enumerate(digits.images[random_indices]): + plt.subplot(1, 5, i+1) + plt.axis('off') + plt.imshow(image, cmap=plt.cm.gray_r, interpolation='nearest') + plt.title("Label: %d" % digits.target[random_indices[i]]) +plt.show() + + +# In[4]: + + +from tensorflow.keras import datasets, layers, models +from tensorflow.keras.layers import Input +from tensorflow.keras.models import Sequential #This allows appending layers to existing models +from tensorflow.keras.layers import Dense #This allows defining the characteristics of a particular layer +from tensorflow.keras import optimizers #This allows using whichever optimiser we want (sgd,adam,RMSprop) +from tensorflow.keras import regularizers #This allows using whichever regularizer we want (l1,l2,l1_l2) +from tensorflow.keras.utils import to_categorical #This allows using categorical cross entropy as the cost function +#from tensorflow.keras import Conv2D +#from tensorflow.keras import MaxPooling2D +#from tensorflow.keras import Flatten + +from sklearn.model_selection import train_test_split + +# representation of labels +labels = to_categorical(labels) + +# split into train and test data +# one-liner from scikit-learn library +train_size = 0.8 +test_size = 1 - train_size +X_train, X_test, Y_train, Y_test = train_test_split(inputs, labels, train_size=train_size, + test_size=test_size) + + +# In[5]: + + +def create_convolutional_neural_network_keras(input_shape, receptive_field, + n_filters, n_neurons_connected, n_categories, + eta, lmbd): + model = Sequential() + model.add(layers.Conv2D(n_filters, (receptive_field, receptive_field), input_shape=input_shape, padding='same', + activation='relu', kernel_regularizer=regularizers.l2(lmbd))) + model.add(layers.MaxPooling2D(pool_size=(2, 2))) + model.add(layers.Flatten()) + model.add(layers.Dense(n_neurons_connected, activation='relu', kernel_regularizer=regularizers.l2(lmbd))) + model.add(layers.Dense(n_categories, activation='softmax', kernel_regularizer=regularizers.l2(lmbd))) + + sgd = optimizers.SGD(lr=eta) + model.compile(loss='categorical_crossentropy', optimizer=sgd, metrics=['accuracy']) + + return model + +epochs = 100 +batch_size = 100 +input_shape = X_train.shape[1:4] +receptive_field = 3 +n_filters = 10 +n_neurons_connected = 50 +n_categories = 10 + +eta_vals = np.logspace(-5, 1, 7) +lmbd_vals = np.logspace(-5, 1, 7) + + +# In[6]: + + +CNN_keras = np.zeros((len(eta_vals), len(lmbd_vals)), dtype=object) + +for i, eta in enumerate(eta_vals): + for j, lmbd in enumerate(lmbd_vals): + CNN = create_convolutional_neural_network_keras(input_shape, receptive_field, + n_filters, n_neurons_connected, n_categories, + eta, lmbd) + CNN.fit(X_train, Y_train, epochs=epochs, batch_size=batch_size, verbose=0) + scores = CNN.evaluate(X_test, Y_test) + + CNN_keras[i][j] = CNN + + print("Learning rate = ", eta) + print("Lambda = ", lmbd) + print("Test accuracy: %.3f" % scores[1]) + print() + + +# In[7]: + + +# visual representation of grid search +# uses seaborn heatmap, could probably do this in matplotlib +import seaborn as sns + +sns.set() + +train_accuracy = np.zeros((len(eta_vals), len(lmbd_vals))) +test_accuracy = np.zeros((len(eta_vals), len(lmbd_vals))) + +for i in range(len(eta_vals)): + for j in range(len(lmbd_vals)): + CNN = CNN_keras[i][j] + + train_accuracy[i][j] = CNN.evaluate(X_train, Y_train)[1] + test_accuracy[i][j] = CNN.evaluate(X_test, Y_test)[1] + + +fig, ax = plt.subplots(figsize = (10, 10)) +sns.heatmap(train_accuracy, annot=True, ax=ax, cmap="viridis") +ax.set_title("Training Accuracy") +ax.set_ylabel("$\eta$") +ax.set_xlabel("$\lambda$") +plt.show() + +fig, ax = plt.subplots(figsize = (10, 10)) +sns.heatmap(test_accuracy, annot=True, ax=ax, cmap="viridis") +ax.set_title("Test Accuracy") +ax.set_ylabel("$\eta$") +ax.set_xlabel("$\lambda$") +plt.show() + + +# ## The CIFAR01 data set +# +# The CIFAR10 dataset contains 60,000 color images in 10 classes, with +# 6,000 images in each class. The dataset is divided into 50,000 +# training images and 10,000 testing images. The classes are mutually +# exclusive and there is no overlap between them. + +# In[8]: + + +import tensorflow as tf + +from tensorflow.keras import datasets, layers, models +import matplotlib.pyplot as plt + +# We import the data set +(train_images, train_labels), (test_images, test_labels) = datasets.cifar10.load_data() + +# Normalize pixel values to be between 0 and 1 by dividing by 255. +train_images, test_images = train_images / 255.0, test_images / 255.0 + + +# To verify that the dataset looks correct, let's plot the first 25 images from the training set and display the class name below each image. + +# In[9]: + + +class_names = ['airplane', 'automobile', 'bird', 'cat', 'deer', + 'dog', 'frog', 'horse', 'ship', 'truck'] +​ +plt.figure(figsize=(10,10)) +for i in range(25): + plt.subplot(5,5,i+1) + plt.xticks([]) + plt.yticks([]) + plt.grid(False) + plt.imshow(train_images[i], cmap=plt.cm.binary) + # The CIFAR labels happen to be arrays, + # which is why you need the extra index + plt.xlabel(class_names[train_labels[i][0]]) +plt.show() + + +# The six lines of code below define the convolutional base using a common pattern: a stack of Conv2D and MaxPooling2D layers. +# +# As input, a CNN takes tensors of shape (image_height, image_width, color_channels), ignoring the batch size. If you are new to these dimensions, color_channels refers to (R,G,B). In this example, you will configure our CNN to process inputs of shape (32, 32, 3), which is the format of CIFAR images. You can do this by passing the argument input_shape to our first layer. + +# In[10]: + + +model = models.Sequential() +model.add(layers.Conv2D(32, (3, 3), activation='relu', input_shape=(32, 32, 3))) +model.add(layers.MaxPooling2D((2, 2))) +model.add(layers.Conv2D(64, (3, 3), activation='relu')) +model.add(layers.MaxPooling2D((2, 2))) +model.add(layers.Conv2D(64, (3, 3), activation='relu')) + +# Let's display the architecture of our model so far. + +model.summary() + + +# You can see that the output of every Conv2D and MaxPooling2D layer is a 3D tensor of shape (height, width, channels). The width and height dimensions tend to shrink as you go deeper in the network. The number of output channels for each Conv2D layer is controlled by the first argument (e.g., 32 or 64). Typically, as the width and height shrink, you can afford (computationally) to add more output channels in each Conv2D layer. +# +# To complete our model, you will feed the last output tensor from the +# convolutional base (of shape (4, 4, 64)) into one or more Dense layers +# to perform classification. Dense layers take vectors as input (which +# are 1D), while the current output is a 3D tensor. First, you will +# flatten (or unroll) the 3D output to 1D, then add one or more Dense +# layers on top. CIFAR has 10 output classes, so you use a final Dense +# layer with 10 outputs and a softmax activation. + +# In[11]: + + +model.add(layers.Flatten()) +model.add(layers.Dense(64, activation='relu')) +model.add(layers.Dense(10)) +Here's the complete architecture of our model. + +model.summary() + + +# As you can see, our (4, 4, 64) outputs were flattened into vectors of shape (1024) before going through two Dense layers. + +# In[12]: + + +model.compile(optimizer='adam', + loss=tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True), + metrics=['accuracy']) +​ +history = model.fit(train_images, train_labels, epochs=10, + validation_data=(test_images, test_labels)) + + +# In[13]: + + +plt.plot(history.history['accuracy'], label='accuracy') +plt.plot(history.history['val_accuracy'], label = 'val_accuracy') +plt.xlabel('Epoch') +plt.ylabel('Accuracy') +plt.ylim([0.5, 1]) +plt.legend(loc='lower right') + +test_loss, test_acc = model.evaluate(test_images, test_labels, verbose=2) + +print(test_acc) + diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter12_35_0.png b/doc/LectureNotes/_build/jupyter_execute/chapter12_35_0.png new file mode 100644 index 0000000000000000000000000000000000000000..282fbd25e708eacf218db601f47abf2805ca21ae GIT binary patch literal 7811 zcmc(Ec{r4B`?q~f3|XQG)ns2LM4@FuS+fffWea29$5LYKm7>W=lx;9$%g&H3HB9zp z3`3TpVWeR!>Am$l$MbyO<9EF8pYQv}%-nO__jTRZd7an!IX~y;Ofoak=iw6NVqjq4 zxnTe`XJBBA0=TTtlTfcp%_cZ2-AVL{%WE~i572LyV; zd?AYG6(RDcJc5G!0=1NseE#!*A}qjN3I7^O04Cw|Gq4L}VBi)w{4g@SLWwXioTT1> zUa<^AQF47!9c_XW^3)DupTwVa&SdF5n;&rFvJ@Yiz)kzY$InmmysN!+qr^bas``!D zt)!c8sI<3e=pOS;uVk@74k;_M(kD;QMbFJ&#SfXG&Pjww-Ojd7Tdei>_Ubi3_`A`1 zwL_O&+LI(-*h#c98_lO-$?f%!AyIMyV=2sk#CyY$C3yrH@!=MO;NY z9>P*p(wsXqdS2>PlEqw&q;08bDn%e61v;ooN2={OC7j(kEtZrgnc4)WLXgF&OTArd-E4b6~EG}9LFDilkK_?-KaD>B?^d-nzz zsTpVx<(@NPftDQ+-gx zwdYmjdh2!)-r*wA{T90RDip;w&AETqEqdoA;We+({iS?F13%r;&G*ubCKwD3+}omD zpK?!CQQ!k@yDcqv=Lt?03V_ODl^A2f%O{xcEp^~8jkM0Nl_w+A&UlNtrrL>|3Hi=K z6>gVC?j&iZYc^j@M@)=NlIm@VJtD3`CP^X(VzHr2yw|&alL)>n>J0amtjVHe63G8p zm}rB#W6`jPE4tdFgMf!I`lDRy80>`}d=_!V_kA_8cTM$V;cipuIsfqgy4&*f9+6=V zp{W0-kKY}9C;X{dKj}CQ=R7`mKAEa_|$pz7WGZCafE)upXvn(^?&!r?l6Vdr46Q z&k(hHQg~Aidr9A=nKzj;8aQ52ob*=wrLZ5pHT$2+uTc>bN4(i4D(`mQc)yr|4L@V? zLZ6hFA{T%3rp z4b0suK#=vjWZ7K)WFvPL?T$|JluLxiC|0`H1>RrkZ|`Tw%*+HAPN}gve~c@R?n
  • jEC5UUcy8 z_gU6y84Uc@_Z@d!ZaY_H2#&=ui1*=5@%|Gh+i4`!nO|66k-%jI)^EnM&?3u7>N^a76y0}&aO^3@^3H*_FU=)nV-x8fj!_{)@q*rZQs zX54Xl`)=N4C9M{El!e_7$hyZOT&BssPx0l7(Zg_|9;(%R@w+Cv@hp*cTx)D9CY07n z5*FIOTB3htD6B5v#5>U)&ZcsH9ACm(!r2E{`%_0rw8yMCzD}`#n-``k6r-<#H58&> zP!jyk7W3;CX6AT(>7yk94?t4Fxg`0L^1k%(_@IT9)!^2DuZd=pm$=?9+|&YGtJ`ei4O)3wLa(-2Aog4c(`TRJSkFl%JrjpH8v_>(MHCOj=~)SaGL7 zw|?6-DVw`qf8r?@7;tS5-L1CBR8(@Qx*+-q#^8>748DghwEqyn)@;6Eq1lK+`v$y1 z)OEq$F{);wZ)>4f>fv`glnmn4-@U!Oyl}peT^Ti6D;<3;X9$UE-+IINweWB_OMas+ z)Z%xXF>T=8F4O~4W4?bcUHfsmV-Rc`@bu|?QYHq(R7IE3Yc4^d%=ZgQD@xu3{&k{3 zER^%P1ss_v&{HEV>QI(n5ykyQvr(stEc~wfLNUINhhpeLFBrsF?$<7!K6Yn7Itrrn zh??M6OEg1SXqOFM&@7}UjTf^No$S=u99pt;T3C3uDkLSzmz?JdM?;jF>sN^s0q*E4 z3&=VqqAa+08hIWh3)Z+S*lB|?9aRJ~endIs0UKFB#DLQSt?SVy>K01Q>c^S{2n+vm z0_P~gIpUb*?63GweKOs=74+|zK>I#70npc?ZK3^VCDyd!_<1lvo9{)Y$M<|C<%W8} z`)u!m3qH`O?q{TYlMubqF1;u6oc@#X&-_qSyDCH!OqN)o>cQ_73KmgP__6WhcIUH> zH(w{dcs#JF>CEl7dZ~9h7il9{U4Qy1?AEafYx!3X8*UfLCt#bu02X-Rnv4^J+`y1^ zrmgG?;{iqeUPzCdS4}yKcRh-BZ}wsW19HO$6Ii-iNnkZsIyM6V5RNj?MsnlPWJEux zN?WRKozz_KvMH2NK7(iyZ~GZ@Rj?BavsR4edfpslX@W8J;yi%28>((fkxk=>%Ua41 z*Z{r{k8)@Z@hMz-apfdoEXm3Kt)t_^-0Env$mXDXXONNalF9D>WCd#8lI5hs zcqcZw#pJoS##k87Mi~c?98QvA+@RhoKi10bHY=`BB6!X$l$4#TtFwO8ARc|K&kb&V zFWUqf#n^DnRshr-m%&)Zpc*LW$3tC1T;RIIOe0R+ATI5hMWxT!uS5Nd0fX^EdAJ*C_ z)O6^4MmYp$4uAU~Hjgg(T6pN%Z{n%>Cc0SPx<2-LX@`!v==6k-GM*{Ke@*)X3@aXOI1dgD5Q>5b@1A}a z;+0@Jena@avlmwn55-19AvAzXqgeLH1Q>|Fj}qTVUrg9M7Y+FO7oN|LlNC?)C_Dr( z@Mg-qJJ^P|kbdPYjoNFpp+ILHbeA5huMpB5wREyO4i)Uo#(Tvh>)r$hz@0mk5Wc<1 ze&`Gx=GrD>(egy4vaC|a5^+dtJvkeCaQYpa1l!QU>tDM?!THT|!9wR=Kz#c5&)f6j zD!B52JY)II*TYFQG8otZUUb(bPgG3@t5I&|>W_NM)22J*kPK>n)WRt;OpWA98%RHv@1O<4)`4acwT9&QY075)AD*vY}? znPO4nmwvJOG*q{F?raftD#^mo-wen4KboTA>}G4*#M{~fYBDaA!|H4RkoQy^R=4bv z`BWPHh%*GSCx5$MMB@@>FFdCEKC{fU%joftf5$^7zThKHYFtAXG)aoNaqzhQwa642_5P}b_*_n- znK1tYFSM=;PF-@Uy5N|u+4zv>^32*H{shtV9Aq2L?%vj-jC4xOI0*3k3+A9suy;B? zBk1U-PQhhHVm`7#8nxJ)Euw$35wtb9qBKJKFF5D_-Ys#ZEBqam4Rzpk+Pb_hB&^ID z;>e3rOrIlMfll*-GW5IBHFYu&4Kh+8*Sj8p{QWtb4by~H=RO|-FJCY9dX1>(Ms1cG zR@>Yw{*Na4XSfcIX<`EI!=_{LaqZbv9ZCi4wi7SzIv8A8VbWs$Yl=o)K6QvOgusuZ z?G>72adIl+LUBB$FupwOwtL{!$`@DaA`5PS$0uPW0q+9#DDnDqaK9FL@acAQbKY+j zP?e@soqpF=Yvi`Ir-RH$N?moq?S2Y?Gy++dk&JVXv-bO14VT{`DG~j<#dv%UBv2Is z9>+Km18Y7F-Q(wf6(K!U8lA&E%H?)7v|!bNf-^zFM z!aYk*2j!K^`#(d_nfzob&q{?bOE6nA0(HrMIaWNWFu|MaTv{MnAiy$mNFiG7C9)YU zgzh!mNa2WfyAz5c2!xq(+8ZJ{3_3nyfy~t+9vwJ8?xDTEF%;=Ol?4^J7eRi(?l52s48SsV%E0w3w~)MJvfa15Xv4t0;W5J(m-1mKb#G+e#Xu8{1?> z<8Z1qt2pvKHGkfo$~`<)Tkp8>z>l$}%`W`0SueF874Lz-o?uOz!g|&0%{-?k={FAz z&5kNWW~XZ&MXy8*+aF`K3A}now&4tT-0J!Z%XIIm+eJl$L-K`an?cA9lybn%b=s~Z zwsEAsZK@v)F6c4*31H0AQL(2znxk`RyImg4vZ}6Cxe;{8mRd-!;hF;d`d|iiRbX(* zdPHWat??vN zk>6llcLY6o^+)2%obX#pKRxDAXp-2~jm+^Er5V7sUo%x-Jq$SL>doEKXxA!7k`bn6 z#_XF(4s5PV4#NAW`x3x`&JD<1b~4m|=_$uWk`YoC{9}6U(g%&r0<4C)#Lm_C9%$_4 zMniV1{?m=FSXjNOJYZF}zHiB4qKpnalYf7Y99&~#^$l})XRy0w^nPGjj!(6CTTrcG z3is$Cmhe@dl*|2{Rfkc#Fq*w?{2}JY@F6$I0_$$0NpYLZ&TI1hW z2#%VA7cA@1m_lhx;_T2hrv*ZUh|(cq-Q!#Keqb7bcz#)PR3C`=!o;?Zu5_kOZNM1@ zIn6;M(ot4vFIL>#^_pqMtEg$j@2Qfpg+uJ*`)$Hzbv0da(nydn_Ny^cvMkGPR&jXT zZrJnwyp04veTKZXqZaG%MImQp>SvQf-*9>ZsW9V^6G_aC>s!O1GSMEnsDUbOSNb!O z?a}Y}n@|UF&}<6A5wy`^r-M5$brcGe^W*x46OI8N(dSl<;cjeX+N76fG-aiG#q0Ve z*~ke;K1A3uMu|2Ync#`ikXrkQPt4H#wT5r;s@lp@Rq!1j)@=0L93AXm7$L%5Nbj!{ zIr7FFRcCBg-P}Wlv(Tmdg5x$7FOG0(qA3wv&*#B`0g$CKf$GGzpe->j672?OhZFlH zt)J1M+cmD?aOfpIkW(7M1|M9Fm^c9I5G)d}HYc4>G~j%$k2Q zIgSa^-nTJdsOSBB(uvVvhDi<_5a+A;O1W^| zhE}ebEKPRDmu^HAU82^{2=26W^(}bDTHKFZtYDo#^#R1;~p*W=gpH%0 zTL?Rn?Dd@=`zm=ZC1t^r9YVq1**iSxJ0DG-i%d+H>n$!MY?axM!Ei4Y#ZxEwW)Gu4 z@nruwgU!q91JUqdT{j%sc+o?cCV)lf9Ac_zO>@vn&I?l-fXo-BtaOL1mln`D6v4y7 zp^CIy^f)DaMU|O$D?Nmr$85rKEg`_57vI?xkDftb@Ui8|1rca$>fC2^!5DZ@^Fm?} zzU8Any_yxj8}fc0%>U4+f}Z3;N2_*s&}G_yis+|E+sfTjqDsXAy1AJa*8}hI!X<;@ z;<|sCmb%oJqFgUkWed6J+J{}CP zZ|$hjYhOosx4$z3tG!3lGuNh!c7+5>N4?0j$Or*E$bZMv&mQGZ^4}89it8$In|cISD6CoA&)aIJYPH+HaLdY&*8TJ5J9h?5V8O@ zU^|5CUj?!RAl#*_o$-NU3>%Yk?sWa?UY*$}LKvYnmSet;bTbwEe#w z-}x1|{Q6P(om*Hye3E!N*2zB6xXe)IwcYsYy@b0*=;2LN$$0YbPdcW5bR|mK(klb5 z`*lnblwxL>mTmunr3ST$^+e545xEZCU>cdQvzoUP5=?a0{nI$=!-Q&zU}eBesE?ry|8XE~HM%G7PLqf*k~xm>z$Ef0QFp&+ zepx}1Uenm-3ckXv>E`F$<;HebLfw0!vLVZAiGp<`>x-izZ14P+58kZ` zNdpvlkuz7d?k%aa73l2NR7hk0GC)AUH96`&CHf!j|Nn~`{eNmi{9`fkFH&|E5n+r} zoA&Vb7)IPvr0&bbhCfWNSzfcI15&@s4^h`tO@E<_AO4)8rs1bKqTWX83gccPvDFiR z&Y#fDbuik#+&rGg9v%F283IV|0x4YI8QkwLxiTPkY@sb4>0kNjdk6zE0kXN&Xd(j2 ziR&j3uYopNGrftTu&kv~Vt^-beA)~Lk^W~uoR#05BAlz!j2SBi3I z?-e0Ax&*so3L=JGadk!jq?C^EA*r}C&L$(+V`Eqk)FFR-pN0s3K&`U4rv7X3$JRIf zU4fQ^YY+23{hsw6keU|(YY`KIAl;{nV$8lPIx)&piq^F?r@6mv!b0G1WvRB4AYqv) zyJuf%;R_ApdR;Xjf8+iwTF2Gh6QFFpuHT?4h}2p+sb@%@JabTrpywdM09BqRIV9`! zzm=u2H2H2dc}Vu6a3vF+mt5HHMP?)~0;l>6)#_BNVeEPd(J`N(%Z-|BZ7X=JlW}4@ zqg|aW8r&@BundV!jN>8g36~x|qQMk1(t3yc2fK9{vF&5@A0|JQO4oEkiq}Md_#BKW zovlz@uTiu?jeVLKHMqzvZ<9`3#_xv=9II?*zfd0_W?1uN^$4}OJ^Q7! z@I7SJ6CE5gJ;3ci<4AymY<<;v?(cz2#rjZ&Vimsqx4}7fStm}vS<72~QXpD~VvRXT z{q}K>L?W2{db!w@w6$D+JoRW6q?Zy1EoYu#^RAe{=-7P>J~&RsBk0A51`R0;cC0Dd z)*!E*L6|8rHZgYl{*qIy0G&8z zf{%r{WoK3md7W)6qeVA6ZdrHGHA{ed#T44YPnY+*?zUDoQr8Bo2OOsq;(}vqP?Z9L ziDGrz_Vwc#qUpV*yJSD;G^+!PyiJFbK^}}j=k+7<76w5#B{Q*c=6=0-i^qOIGIyOx zOnQDFVawz2`OQe@xlo4jP&raI1ABGZTBDJsZ=SRZGxa_>_j6dS#wY(h6mr>pDI6It zP91Mwmv^m7d`u!bF-Gf1S?hIe#*Q;)So*r(5E@$k) z3(3&yij2dm*v{e3KtlDpnwtpqsuNZIhwX*r4vxE%)$KYl$HFA3?j%I0o$g)lIJmeR zFdIJVwA8`TFus>eIyuPCb$X*r*i8wByc9&DNW7NL6XfTndjbEOcK1etC(x4>=*q<} so)}W;5ea1aS9kOup!7f6d(=PYV&gRSi_VS%4Pk~G*G-_9tIiMq7wcwOLI3~& literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter12_51_0.png b/doc/LectureNotes/_build/jupyter_execute/chapter12_51_0.png new file mode 100644 index 0000000000000000000000000000000000000000..cd49564e7f1028f093d19f8db6a6ed3fd039a271 GIT binary patch literal 9850 zcmd6NXIRru*CtiEB2}8GNbiJR|DtrHL+GGDkdE{kny7T8hpHeo^w3dy5l8^(A%xy* zkQM}F!}ILEyL;`sd+oQ~4=Iz(Z|1bQ=bm#WMo&kLikz7o4-bz@L;ZyT9v*%O?)w$# z9o)OmBlcq4hm4PksgI!t$jAScmjm9*S3aJu9zL#4uOIn2czHW{xC4a5g#ZGN-uU=< zddmt6yZuK8ArCJ{VR+t)QQRP8p6X`acz6`Fw=aCWtegjUc$}LWFP<3%0s$i@^Vp)!^RN z9wMTCWVwRhWb4SxqaRC3%xp*c;FG0U|FoVxi(MbVaK}@vI?ls|lCb&U#Za@ugSPPn zg~iK*Kt+HY*nbgvp0gUfcqp@Z;R{ETMLr@;SB!2Yd`3<5j9D2I^@vpLF_98!SH7uqbW200!Ip&HI=)vrOU?I%w zr4NAb*9L$#!T@Tlf`5lg`sgf?D}nUIT8ePs-{bs65F<{|ba6Sqy?|Nt4B{lO!PvYD zu7lrBc*X61GgN<`N1S>9{t1^PVD~?#cptif#Ws5^w*N@`OZ<#_EgZ7%d42?0aN*P( zfT!cz+-aA#+QXl}{?f)?ZsS3i4nfXI&fUdHw4uhLFMH=orUr#pk{p(BoSJzB%9!3) ztQ%{@%^!I&@t*3YDZGimKMOhX$Ag_f60iA^VTr0!4&h1=K-1h`sO^X|s{w-m_TaBV z=X*;S)9m-LM%=)WwA^BD|7TnO@4fK<CNf+?E08y32+*AYqu8yrWkZ6drdX?`Wc29cE|Cqj+sn96BH<<+VuYSSXYU(kI(B3 zDKtKbaF-T*c*nz<;B@z|G!;8*H8N*^LwaM1Kcm+DGKS@ar_T z+|z3fDK1`5^2ECMfh)R)b`t*So5#q(84M$P0LSi3PW=O`?6iEPkj&wm6NV}Q@Xy`g z#nq5Y&e6J_oL+sM4c?#)?ki*w3nxNXVq;)e^pG!q;4}qzq@;*d9Z{6n&pZsqiU6;+ z1ziQ)SABnU>?Q@$tC^+Q!ox1QT%>m=>uJ#nm-mi--~48iWN142v#|KKec!Hu&Fn;U zQC~6XM)rcaJp|1nb8O}`@O|^^^Y1Hmi_89h&SlVAxb#vjp#~ z#0Rcuq$`BhJUkZsUeTOFNFv3>cr}p7y6PW`!Wz|yvfEz&Qo|zD+?Usf4_A~}|7edN z5y%H&oo>yrv7Wz%DL-YEKE?LC4g+ib?*EyJUCKs^@zvfGw1qjm*E%EEyn6+{i&@gn zUq6^3oFR-)O3ELbyve@#ea-!QboR7C@H=LJ-F9^Kyz@OkcMG6H=igi~J2){sQ?nD= zW-8GruhG`_ccvt8`E0j&^C-Wk#c6G5YuFvLayMFLeYU*U zt}1`uKom5NG!z4O~1pN)->|F4i}%TjZHmXH;HVL`dA(hhM}ODF%R zf%>U#0#Ajz&2bSA{DbT`%A?6|NrOwK8crQEFfR|R3TTW_7To{`7sTY!1&pZ@@(qYn2e(K>mBu&YepJf=x@Sl;l)7zAn@#Ft@`PsWDQ)3>!27E1p&q6+DE2l3fnG zS47Wm*h@M_#m{9D1mqxB2cE&XDfWhuE9gNEPyN0T-` zg5c!Ak_~~+PhA=Lyo*+l50#sO3j0s|Mou=Ua+#n;NLV!O<>ZjA_(o2i+XRGP%R^fh zUAO#U>E4nu3)oCe?5UIoX>Op{kqehh1QT>G$;@t4h&Uxj`zq_qo@*|-O2f4&h@<}< zKS3Hc@GFbAQV>TiAxvp-Fei}wSd{~;+z~w#Uxb+w-+!-B(sRO=dEpk!`B|f?*1L69 z#zuuJhBcF>LxnzKV~}lXh_v1rm=XeiPTIx(VyE6%rg7&Z{kpSM3-u(_>Q`@-=Sa5C zYasDcqfuks`rv*2^Dt55VKY~mCnLyF*Pve zZffDmZ%`_`aKl;55eUv#Qdw1{{rl4LO{jzd?JSJK%I~f50})qjZa=wI!Fz$bHqN7d z8V%ZIREsQ+sbxeQUO^y8%%yL^6U~yI(mvgqZpL&IOuK?y1D5QX;mz()v-Xt_vX6#E z@m0^E;!rRDXDo!Q=|}mP#IlaN=9Tycm6gF)_vDE=OdDq{PNU5BTtjU5H~+cmyV?=d zsZWjo7vwgc`E5(}2!V-dI*sUmS=v+(mg>ME3AM^CG&ctQlj8A}H<`OKomck!3uMh` z{WIs{=3^hIlyhnk{Xd3+hI^fp(#Q42bl!3O2JCN3#kXIq7-#6apY|0+a%!j-41NBi zZ4p5Tdpn|)Bn{^|Dj#X8`8d8UG+v{PWXjx$d@FmDl1@H?o1bSQ&Za|Q`Jlm$28CMy z+uh_H>OZ=x_mSgM?y7wgZ*(q(MxC-3^sN+t(WMW;UwOzB-r>Bx_KQXK_`SFQ0J=r> zmZzNONOPrAfVsp?)zRqQSBoF_?S^Ex#U4|0XRn*kFn`8s_*c)t;^?`pPf=7|haxg@ zHYQLjhxTaID{WKYo!%HA(}nZ&66~}# z;ZbvWxmYdz(!SC0xO`qjns4+Nc-EUQ>p08dvqt3j;;s2R-`qXP`&2K?OD_vsUVe z^k0xh1cA`1HYy_v$p$*}1q64wGD47C0F*ljb$+;*UlVMFJS(=oKMAIIg|yUC7$m#r z?vYq`(t7})&EF{Y961NLspz0`0B#;6Bi`q6;kpDix%$VsE?^t!7XkYH9jxo6GF} zqd3!Fa^)$9&Z&vc;>xycrRfm6Vz(Khjx-)NKpR;ztEmepI3kH)7;iq50&{067bJ-< zPiDC)B=goz2X33J4B8ZzZ&6^0Cll@^X)4KI)08R;?4ix}ssGEHk*;PkJGKJbhX&nlU&r3cYkK2*Q#-=Aq<@PO(f% zChO8qPju3jeZzJ33bzDbQ+iU;PElse`hAUk@HsVQ>|4H6ilqsp@d0P_n`9`0uS|favO}=oJ7&mWV{Vni8f~Rwr*Kc`>w7RlY{M? zAhIhi{UCf|5db6C`~fZV_aYDWgQd`5osHrke{URrk=wlP@o3l8sx{v*cr^s!uJN9R zzU*VD`G&X7r@mBwI`{K)PCGWHUjX?d-7r^O+bMd>bYKTrml*Bve(9bb(vL#_4(PZ@ z4~NsxN6)s*%fz-%xc#Q8R1GDGj8=f^+Ok8A!9us%Ue{>HXbmq)c)AuQi5-4jW3f~pftS44hmL>n~R%9~6im!Lu7W43l(qaM9v_-1E0 zgV}psL>WV(_uir0Y zV=SS1Uv&pmT@b9Cq7#;EXg^o}#Kf7U9qv=&X(VOG@Xld~O9s)a7>{#fJX5nv_vs%u zauaOT+|-vC?PMLV(@-6^R{lSdA$_n)e)vT?ANlyE;#GRmq>>wbacIz8B z&e)KE@@b0eW#-s`u4J_06KN-cY) ztT+uG`jibTWX9dvM-sQ+%<&CzxHxZb`AM|$u+bi@896GH*2R70&D)54rIxC*35m6* zW|*Ss`{wc_<%PqY(%j>29yYDLP8_9SF5(dJF!jw(sXmHs%WA=)^0%;d7gfotyHBk- zg}Hy(=YmXhlsBOFIkTTRjBk^fV7Uay6c}$ggVUX2^{cILCjM*k4vI7m74B?}#6zR$ zp2L`(174Iik6s;aK z5hRVg9h~Y+uzt%@g9Cc^!hOkYZfml3x^jB(tL_5xA`o;j#*3ydH^=szkM9Anp)6*6 zP(i?30n^!e7`)q|KnOtDgK+7A%fHu`DLz$;k_iA^{|6s6NyXckt%@rTdih_K*&;(t zKy$IKSb|WF?oL-)thryyzI+-bJ|S7|AS639RW%fWT%1z( zt5!aO6`O-rf(7S(+~qL#_;05++k(c;mnptk#z*1~3L$1)(qFMLack>zvE(nEh*em@ z3;b7=oejSABMzPT{)-u<`+*ZVPEdsh&wWm;bXI1fQxHV!Pq`eT@uMM)FH;k7Bxy#> z&0=s>3YHx{9MJ%3WW@5+PH@O8*>?U3Wpvx+ll1h zrl1M@$qz3|O`c_G=os2MJ9B4@_FDUVp==y^U;PsoHSA>NB0?&ui3j+DPHS zWA70uH_a8yujs`Q71F=r_KtIBcHns<#4JhKRf$`Nly_ zP^+P4$Y<)>KLq!YqECld9_^m}ixs~l(UWORzAlt75^8bp>Dad4@PBfZ()k9Z^uN1~y@OFr{);@fQx&BebthkbUGOZn|={ z{B=4kDLOl#=*3MOw&lOy*^+CSknExEo9B{2!UWNSQ#vT=2?o-xusf~NAz!g(V7uvD zCn#?B*O#5+xC=eQ1qNBkzWSGPse**@vcv)P#TscY1vxcea0;t$vD=Qh>}MyrC#3~G zlfDk(MUhi08NkP)Quam@(h{B1u-kY0^>R^3OF4Io96brtGEgs+pL#Ms?y6SJ96W2 z@qH5g=!iit^uf>S)5rIBg0NE*X;`uzj}#@8@)5s}zJCf^>WoQ{J*Zj|mY;=u2)JCL zJhX8Kk-%LYua7@V&RJ0w=LDA1M-&GzKN9!&nEdI^7#>KGskkCw;b@qHXZyqh03Q zU=f2-{+vFiY73MX);3zSr#Py@VmMaR`Ov>(2Aza2MF?!dw9wdZP%RTap_m!gyDH`O zBQ}hK-~v$WX!p>1Le8zNx!a>q?LQKjvceKDIr!c#=qwVc2!~5TkbVGEd)UoihF1TO z(quzDcl>A#b-p9REGbK$d|&>M478*DAgHwuZdre{h7d2`*7}HwIG(?LvXs&Zbi5S# zAC3=#K8IL6Ft0t->Q%2MI3>pmSUCS9_Q3nsi|ubVZ~^14MT#6b%%x0cR1{>Y_k>WFvQBNJv|i>E1{ShIQWZ%H_e?1j>p8GWcZ5V> z#|T#$PpTSU3;{rHxWe23f-LfFOR699yDWW&mrH#jgOFBI0up-FO!b3@vwJ%fYjLEcvBtE&(R+*U0hKx-uvbBm9v ziHVi001@w#sni0ri$l*0S9X!kcfQom8s1|+9>xsnlcq9dBB#dn)5m^_#C<0l*0vV( zCd*K>Hqb`G3{ieP-%{v)El;a3x?;O*Kzh}u%rQtw zeE-lGFeN{XkEU9c$oSe7mv-u~N~kjj`Ta5-iusWrkS1NN+G>}di}O>w5R1Mki*=y- zI|0oS4P_eAh@X%QI|i9@Q3{T+TT3SwnqO?QTC^H;b$crrLmElrN_b&EjZZOv`N4lh zgpp*(KBO@#^-|ef(9l%=<-^+KQCKBKM?x?3{xeRnjOzB5Yg@U7j%;n*0qi$YGA%~3 zz(+O8z{KMPFL;Q+uzW4`s#lk}_KEkLbBM(KBES7%THTay`dc2yuL}x5fJ(zfkELQ9S!2%8|cDBzZ;Y!u8nO z=zK@f-o8I8iu!8XKHwyGkTtX0&EsqK+KF6C$dHEVSF=u>O^x(aJ#e_)>P6FP7~!MF zy7PKGEhT3MkIuNx?43g*k!)~djcb*75J$Brzu`g2$k9t1dgF9oKEN-bS0$B@A9HZ9 zGbk9o7X`Rwv@w6Ktw4TnS@wnQ483Eu;%h9`Y1Q@XjDWODhPcN7$EC0OzZH7U38}EO z8{b*d#m7-u0uM15MTwQ)ZK(-HhJ`Dmti+j9M%HS-Ardc$WJy41_Z?BdQ z%gWy`4vo%G<~o~Ar7D4E6}h4tCN)M1_eV1B;0^#m2A?xpm$CY5s)c*0P^6trl5 zg^8hJOba2Wi4H+xS_<93-Ep};(){dbMBqB%p5>93wE)X8OlBVy*4q{AC-5h8AW^YD zR?QFgb$Ozwa^&`s8C16&^5z+MbQ&e!H@Jc2(Polyv_T!fIMeoa4pi}?6T&~)l zkIwZ**xJ%4IMp7`&yGaMtVivcwtUtivO6=JKH|6OiEdLGDU`Yq_?3CM!MZqbmIl=5 zmuGY%{Ts9t5wUnqAPgCh*o_z=`x{HoA9!qdxcQvcW<{l~W5~=eKp&NjiL~*OwaE#g zQj%L0wER(8iGat_Lj#6!9b03vlM@2-m9lTF+tY(z*jcx)JYD!bdFYMq&1mN7%FI7| z*l{v(;j!-0a;}ZY95Bi0%_g>MuMH7A&piSmV4>r@mce_3mOyX}BNyv2;}Gg{Xt7x;rU?0=^dlu()eU=$h+?Fj<d#fqId_&ZBEbIlq+kV(Wf9~$!b-?tA&m4R4xqW1j*M!dzUu>1u6`D>NOXE@U_ zGw@-7gf^u%VfX=P0wrPG6$jI&4EE#rBR=P$cn9sH@R7`QS(3j^5E+b_e+Rhno;d7f zXYrqz=b*C*+C7x{(lYH;Q=w+O%)Qs}K+gg@MUO@)IC}Fc19T?1RKc|HM+8IcZv*h$ zw>tpOQRW}9`iIrzQMZ$QA3%HLI&SKc0#JF`7d-trB%&MgrtzZptZ4FAeL z;@>(CDih!6h6A&Zqv62m4qO>q6y|m+;YhFufXRik9ltVB>Z0NL_xx`{ z;m_UvHU9Xc|LG=zsyPO+Hw8K~yv-?${`}n#t2=pkD27YyU%RFR#$O;#P5mLrbHv^g z6(yAYY$i$7B{xXY3FM)U?C7&qw3CDlBV0=$Xa~@u26~_oG5`xLhg>&6(E3Ri`?280 z7zo-HbPs}zj}WMI$!tqnyEjI7fS*SqKyrX5l;ej`UD^%D&%jqQI+yFp#H|za>pw%R z{qmmZ8~jFm4?Wzkq1J@+RIa6AO3%@UM0S6vG5NbQyWwgP>pShjp7R}4mXufa>E{+x zHTu@eHspJ6&x6s|4?F?JWgnhZ-ElvOMTJZFws)3_`M?kUhUW9x`m=cItSB}jLJk0( z!QsLHEuo(uMe{{(gfR5}H^fFVLNS-KlE+LiLMQ?rZdgi$KauMgP!I0u$G4rXK=;?9&*MKXxp!n^ODkjbig@=H)NKMQQvf%8^ z5o9#;h7udzrfU+{@!3()?jfNNzV+Q4qN`50yZ8A`(`>HA(+$7|5MM4L?CureQa0$! z%3rDZXQ<(L`TK;rr9>^C|s*8|L|bc z_k5EejO?oIK0|QkBJ3L2IShA&!%gso@%^|D9JAp#;Qcc9%NFEFa6{TG{Yfm39U zeDS}M`cnBTspd;7&{^W2YeA#?EG!WUo%hS>yMKy}iiQydNMg2w`sBvB;}PC)t=Nlr zB-%e4xro;mPJ_*9OL9#p4_w$(B2x4K`5QoF6_*Y;ti+ITcLE`j=`5u6QemfjJhm)M&xI@WT5T0XeDUwC*LDmpK!lx-vb3l08Ui~s-t literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter12_67_1.png b/doc/LectureNotes/_build/jupyter_execute/chapter12_67_1.png new file mode 100644 index 0000000000000000000000000000000000000000..91a4496c5e66ab2c962e8d247a1291c2d93fd1c3 GIT binary patch literal 2976 zcmb_e3s6&68ji)<)sqdZ zKouffjDd=j@`?=@LV`)KfDscwq)AFlK*0!vS2Yj_2<)Yu+0Jy`+1XBK?&I8xiQg!FsKQ;>Qq!(ESv6ZGMCvQ6@Ue@RD==xZ+3BAuDc1)2V{L;$lor=629_N*ZZ+^dZtozI2 zn*S`PL$i^dda6 zr>*`)QiAyOtj2(b(lHoGT;BvkQ(9#5z?_*gr+Wk0JArI3fPDd!ae=)Z-%ySHK0XQf&ek&VX*#$nx09OJnyTb`i!t5@RrfOen}SC(oQ1 zGguDJ#oOPLOMDoIxkXU0UES(Md8QKv1*Lmpq@7inIrvO5&se2YV;zR)9fqM{ZYj6m z>63*r@rM9A54`eGVdrG2RZwk7)X4_X0AcA4cXcrVpV>m$lhDhO-+?UaU2wT24#NlV zUbe{9tw;$~rMk7Lzpi}92D!Q!DX~RfgodnKx!x*A%i$(NvDdkb0r ze3UfNVYnSK!KeVh*{`GA!V8;FUE=OOEdUo7_!ozD|17m>`oW)uafD1ZuutG)0Uim6IBl{YX<&;6gswLRXcD9uSs}k*03DqN_oKeD(~a z^LWP3NmDt|q#QdW5d_PHe&siADi1dBZfFwUU)_$(u|+0#q--fK1g#S(m&}!YtnF#; zfOkKEbT+5}a&=^d1vkMHzvwGu_-sK+tdOr^-2FFTP)(;{90_6{Ob!|&VL_{J_d9N? ztn^$gz!qk$=s-FEh%w*ZNM-vld|kWb{`ky2fVlem;yG~P8<4&m7_>&J9EQ;t!}7T} zmpI$*uB&riR{a(e7)9J(`-F2v`Y*x(fIuSVj|b0tdp>cK7q~^UU2q_Ff>n zg=gf+V+uf(15lXN9V+$C@c>pl0Wq?FU3wMI*tNBOWB^=fSE_w%mopqO*tkV+C0hPy z!MtC_(mXqWzojHBJuolqN?KEzA0-%x!DpU$OIme@C2xyr{b3QGAfEY23JYQ^U3op5 zGW(uxF5|~6FHE_+P;Ht(K9fqbUG&u$0}5jh`AN4Ajdb5fJ+pMlvYORGCbs;AsZ@Mm zQThOK#rIMv(l?RZ4=dOMdto~HO_v~_wAqzTx%^F+<%z}tYZT8Je40o$xC+Z-O?gR{; zA1`-iH~>#i`xfM4P}EC>dW)Gk!P%UXipzmj%iJ8xLFE1L)O9_^v+Y)b?#I#NRBBTg|JJRT>GbgjRUz8WJZl*)EiDb! z)+;3A9uNl0F+VTE*>j`P_dLB`7W&m>oI*scSn4_N_Q4mJ(2j1#YIL98P+HxTm|#Luq!G$+EHOK5L#QCaR{F!%5w`| z8G8PlQbQ(@>NHKlw6_MNcJC^1=`^^h;ap^4&{+J|cO?)jLnStH!QrnR~!w+Mv<4lYosQU$J==p%IxDLjDMD3K7! zZgz!%wA|cW9s96CwCh@S4%*3ynQ<^TYnIq=C}W0}7X_9$Gf8#f;o$)^1r%EW+gjR5 z_wt@&e`J^2H^6pttP)TNJm1B(8K`nUXg#zv|drCV~ccujri@{_ge-0u^@Gd lCgsJNArP99|CI*D93~?k>=eh%z^7$|zi$wpbKtWt{{>fyiKGAk literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter13.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter13.ipynb new file mode 100644 index 000000000..87a579b19 --- /dev/null +++ b/doc/LectureNotes/_build/jupyter_execute/chapter13.ipynb @@ -0,0 +1,3294 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "6d2db899", + "metadata": { + "editable": true + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "id": "f4908a97", + "metadata": { + "editable": true + }, + "source": [ + "# Recurrent neural networks: Overarching view\n", + "\n", + "Till now our focus has been, including convolutional neural networks\n", + "as well, on feedforward neural networks. The output or the activations\n", + "flow only in one direction, from the input layer to the output layer.\n", + "\n", + "A recurrent neural network (RNN) looks very much like a feedforward\n", + "neural network, except that it also has connections pointing\n", + "backward. \n", + "\n", + "RNNs are used to analyze time series data such as stock prices, and\n", + "tell you when to buy or sell. In autonomous driving systems, they can\n", + "anticipate car trajectories and help avoid accidents. More generally,\n", + "they can work on sequences of arbitrary lengths, rather than on\n", + "fixed-sized inputs like all the nets we have discussed so far. For\n", + "example, they can take sentences, documents, or audio samples as\n", + "input, making them extremely useful for natural language processing\n", + "systems such as automatic translation and speech-to-text.\n", + "\n", + "More to text to be added" + ] + }, + { + "cell_type": "markdown", + "id": "43cb4913", + "metadata": { + "editable": true + }, + "source": [ + "## A simple example" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "cf6b9dab", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter13_3_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "2021-12-08 06:58:41.160539: I tensorflow/core/platform/cpu_feature_guard.cc:142] This TensorFlow binary is optimized with oneAPI Deep Neural Network Library (oneDNN) to use the following CPU instructions in performance-critical operations: SSE4.1 SSE4.2 AVX AVX2 FMA\n", + "To enable them in other operations, rebuild TensorFlow with the appropriate compiler flags.\n", + "2021-12-08 06:58:41.346810: I tensorflow/compiler/mlir/mlir_graph_optimization_pass.cc:185] None of the MLIR Optimization Passes are enabled (registered 2)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Model: \"sequential\"\n", + "_________________________________________________________________\n", + "Layer (type) Output Shape Param # \n", + "=================================================================\n", + "simple_rnn (SimpleRNN) (None, 32) 1184 \n", + "_________________________________________________________________\n", + "dense (Dense) (None, 8) 264 \n", + "_________________________________________________________________\n", + "dense_1 (Dense) (None, 1) 9 \n", + "=================================================================\n", + "Total params: 1,457\n", + "Trainable params: 1,457\n", + "Non-trainable params: 0\n", + "_________________________________________________________________\n", + "Epoch 1/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 1s - loss: 0.4255\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 2/100\n", + "50/50 - 0s - loss: 0.4030\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 3/100\n", + "50/50 - 0s - loss: 0.3958\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 4/100\n", + "50/50 - 0s - loss: 0.3931\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 5/100\n", + "50/50 - 0s - loss: 0.3914\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 6/100\n", + "50/50 - 0s - loss: 0.3898\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 7/100\n", + "50/50 - 0s - loss: 0.3882\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 8/100\n", + "50/50 - 0s - loss: 0.3885\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 9/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3871\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 10/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3876\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 11/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3867\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 12/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3850\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 13/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3854\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 14/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3802\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 15/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3842\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 16/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3820\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 17/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3842\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 18/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3827\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 19/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3819\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 20/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3818\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 21/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3803\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 22/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3833\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 23/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3804\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 24/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3811\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 25/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3805\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 26/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3779\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 27/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3791\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 28/100\n", + "50/50 - 0s - loss: 0.3805\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 29/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3794\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 30/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3776\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 31/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3784\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 32/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3748\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 33/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3773\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 34/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3759\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 35/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3765\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 36/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3772\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 37/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3760\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 38/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3753\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 39/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3739\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 40/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3753\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 41/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3729\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 42/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3748\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 43/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3749\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 44/100\n", + "50/50 - 0s - loss: 0.3725\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 45/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3713\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 46/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3722\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 47/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3721\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 48/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3711\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 49/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3688\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 50/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3718\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 51/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3679\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 52/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3704\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 53/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3687\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 54/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3672\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 55/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3674\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 56/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3669\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 57/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3684\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 58/100" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3668\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 59/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3673\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 60/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3655\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 61/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3659\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 62/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3647\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 63/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3646\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 64/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3628\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 65/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3646\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 66/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3643\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 67/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3645\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 68/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3627\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 69/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3624\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 70/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3615\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 71/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3605\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 72/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3609\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 73/100\n", + "50/50 - 0s - loss: 0.3617\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 74/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3604\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 75/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3606\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 76/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3598\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 77/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3595\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 78/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3593\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 79/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3585\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 80/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3587\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 81/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3572\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 82/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3567\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 83/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3576\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 84/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3577\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 85/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3548\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 86/100\n", + "50/50 - 0s - loss: 0.3575\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 87/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3551\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 88/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3556\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 89/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3546\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 90/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3560\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 91/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3558\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 92/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3538\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 93/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3525\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 94/100\n", + "50/50 - 0s - loss: 0.3525\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 95/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3543\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 96/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3514\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 97/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3529\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 98/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3522\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 99/100\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "50/50 - 0s - loss: 0.3522\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Epoch 100/100\n", + "50/50 - 0s - loss: 0.3498\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "0.3469819128513336\n" + ] + }, + { + "ename": "KeyError", + "evalue": "(slice(None, None, None), None)", + "output_type": "error", + "traceback": [ + "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", + "\u001b[0;31mKeyError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47724/2517560119.py\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 65\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 66\u001b[0m \u001b[0mindex\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 67\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mdf\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 68\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mpredicted\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 69\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maxvline\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mTp\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mc\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m\"r\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/matplotlib/pyplot.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(scalex, scaley, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m 3017\u001b[0m \u001b[0;34m@\u001b[0m\u001b[0m_copy_docstring_and_deprecators\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mAxes\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3018\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscalex\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscaley\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mTrue\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3019\u001b[0;31m return gca().plot(\n\u001b[0m\u001b[1;32m 3020\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscalex\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mscalex\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mscaley\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mscaley\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3021\u001b[0m **({\"data\": data} if data is not None else {}), **kwargs)\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/matplotlib/axes/_axes.py\u001b[0m in \u001b[0;36mplot\u001b[0;34m(self, scalex, scaley, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m 1603\u001b[0m \"\"\"\n\u001b[1;32m 1604\u001b[0m \u001b[0mkwargs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcbook\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnormalize_kwargs\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmlines\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mLine2D\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1605\u001b[0;31m \u001b[0mlines\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_lines\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1606\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mline\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mlines\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1607\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0madd_line\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mline\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/matplotlib/axes/_base.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, data, *args, **kwargs)\u001b[0m\n\u001b[1;32m 313\u001b[0m \u001b[0mthis\u001b[0m \u001b[0;34m+=\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 314\u001b[0m \u001b[0margs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 315\u001b[0;31m \u001b[0;32myield\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_plot_args\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mthis\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 316\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 317\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mget_next_color\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/matplotlib/axes/_base.py\u001b[0m in \u001b[0;36m_plot_args\u001b[0;34m(self, tup, kwargs, return_kwargs)\u001b[0m\n\u001b[1;32m 489\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxy\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 490\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_check_1d\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxy\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 491\u001b[0;31m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_check_1d\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxy\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 492\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 493\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mindex_of\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mxy\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/matplotlib/cbook/__init__.py\u001b[0m in \u001b[0;36m_check_1d\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m 1360\u001b[0m message='Support for multi-dimensional indexing')\n\u001b[1;32m 1361\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1362\u001b[0;31m \u001b[0mndim\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 1363\u001b[0m \u001b[0;31m# we have definitely hit a pandas index or series object\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 1364\u001b[0m \u001b[0;31m# cast to a numpy array.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/pandas/core/frame.py\u001b[0m in \u001b[0;36m__getitem__\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m 3456\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcolumns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnlevels\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3457\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_getitem_multilevel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 3458\u001b[0;31m \u001b[0mindexer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcolumns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_loc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 3459\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mis_integer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mindexer\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3460\u001b[0m \u001b[0mindexer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mindexer\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/pandas/core/indexes/range.py\u001b[0m in \u001b[0;36mget_loc\u001b[0;34m(self, key, method, tolerance)\u001b[0m\n\u001b[1;32m 386\u001b[0m \u001b[0;32mexcept\u001b[0m \u001b[0mValueError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0merr\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 387\u001b[0m \u001b[0;32mraise\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0merr\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 388\u001b[0;31m \u001b[0;32mraise\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 389\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0msuper\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_loc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mmethod\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtolerance\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mtolerance\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 390\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mKeyError\u001b[0m: (slice(None, None, None), None)" + ] + }, + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapter13_3_192.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "%matplotlib inline\n", + "\n", + "# Start importing packages\n", + "import pandas as pd\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import tensorflow as tf\n", + "from tensorflow.keras import datasets, layers, models\n", + "from tensorflow.keras.layers import Input\n", + "from tensorflow.keras.models import Model, Sequential \n", + "from tensorflow.keras.layers import Dense, SimpleRNN, LSTM, GRU\n", + "from tensorflow.keras import optimizers \n", + "from tensorflow.keras import regularizers \n", + "from tensorflow.keras.utils import to_categorical \n", + "\n", + "\n", + "\n", + "# convert into dataset matrix\n", + "def convertToMatrix(data, step):\n", + " X, Y =[], []\n", + " for i in range(len(data)-step):\n", + " d=i+step \n", + " X.append(data[i:d,])\n", + " Y.append(data[d,])\n", + " return np.array(X), np.array(Y)\n", + "\n", + "step = 4\n", + "N = 1000 \n", + "Tp = 800 \n", + "\n", + "t=np.arange(0,N)\n", + "x=np.sin(0.02*t)+2*np.random.rand(N)\n", + "df = pd.DataFrame(x)\n", + "df.head()\n", + "\n", + "plt.plot(df)\n", + "plt.show()\n", + "\n", + "values=df.values\n", + "train,test = values[0:Tp,:], values[Tp:N,:]\n", + "\n", + "# add step elements into train and test\n", + "test = np.append(test,np.repeat(test[-1,],step))\n", + "train = np.append(train,np.repeat(train[-1,],step))\n", + " \n", + "trainX,trainY =convertToMatrix(train,step)\n", + "testX,testY =convertToMatrix(test,step)\n", + "trainX = np.reshape(trainX, (trainX.shape[0], 1, trainX.shape[1]))\n", + "testX = np.reshape(testX, (testX.shape[0], 1, testX.shape[1]))\n", + "\n", + "model = Sequential()\n", + "model.add(SimpleRNN(units=32, input_shape=(1,step), activation=\"relu\"))\n", + "model.add(Dense(8, activation=\"relu\")) \n", + "model.add(Dense(1))\n", + "model.compile(loss='mean_squared_error', optimizer='rmsprop')\n", + "model.summary()\n", + "\n", + "model.fit(trainX,trainY, epochs=100, batch_size=16, verbose=2)\n", + "trainPredict = model.predict(trainX)\n", + "testPredict= model.predict(testX)\n", + "predicted=np.concatenate((trainPredict,testPredict),axis=0)\n", + "\n", + "trainScore = model.evaluate(trainX, trainY, verbose=0)\n", + "print(trainScore)\n", + "\n", + "index = df.index.values\n", + "plt.plot(index,df)\n", + "plt.plot(index,predicted)\n", + "plt.axvline(df.index[Tp], c=\"r\")\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "897a47c7", + "metadata": { + "editable": true + }, + "source": [ + "## An extrapolation example\n", + "\n", + "The following code provides an example of how recurrent neural\n", + "networks can be used to extrapolate to unknown values of physics data\n", + "sets. Specifically, the data sets used in this program come from\n", + "a quantum mechanical many-body calculation of energies as functions of the number of particles." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "6776ae2a", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "\n", + "# For matrices and calculations\n", + "import numpy as np\n", + "# For machine learning (backend for keras)\n", + "import tensorflow as tf\n", + "# User-friendly machine learning library\n", + "# Front end for TensorFlow\n", + "import tensorflow.keras\n", + "# Different methods from Keras needed to create an RNN\n", + "# This is not necessary but it shortened function calls \n", + "# that need to be used in the code.\n", + "from tensorflow.keras import datasets, layers, models\n", + "from tensorflow.keras.layers import Input\n", + "from tensorflow.keras import regularizers\n", + "from tensorflow.keras.models import Model, Sequential\n", + "from tensorflow.keras.layers import Dense, SimpleRNN, LSTM, GRU\n", + "# For timing the code\n", + "from timeit import default_timer as timer\n", + "# For plotting\n", + "import matplotlib.pyplot as plt\n", + "\n", + "\n", + "# The data set\n", + "datatype='VaryDimension'\n", + "X_tot = np.arange(2, 42, 2)\n", + "y_tot = np.array([-0.03077640549, -0.08336233266, -0.1446729567, -0.2116753732, -0.2830637392, -0.3581341341, -0.436462435, -0.5177783846,\n", + "\t-0.6019067271, -0.6887363571, -0.7782028952, -0.8702784034, -0.9649652536, -1.062292565, -1.16231451, \n", + "\t-1.265109911, -1.370782966, -1.479465113, -1.591317992, -1.70653767])" + ] + }, + { + "cell_type": "markdown", + "id": "35227d36", + "metadata": { + "editable": true + }, + "source": [ + "The way the recurrent neural networks are trained in this program\n", + "differs from how machine learning algorithms are usually trained.\n", + "Typically a machine learning algorithm is trained by learning the\n", + "relationship between the x data and the y data. In this program, the\n", + "recurrent neural network will be trained to recognize the relationship\n", + "in a sequence of y values. This is type of data formatting is\n", + "typically used time series forcasting, but it can also be used in any\n", + "extrapolation (time series forecasting is just a specific type of\n", + "extrapolation along the time axis). This method of data formatting\n", + "does not use the x data and assumes that the y data are evenly spaced.\n", + "\n", + "For a standard machine learning algorithm, the training data has the\n", + "form of (x,y) so the machine learning algorithm learns to assiciate a\n", + "y value with a given x value. This is useful when the test data has x\n", + "values within the same range as the training data. However, for this\n", + "application, the x values of the test data are outside of the x values\n", + "of the training data and the traditional method of training a machine\n", + "learning algorithm does not work as well. For this reason, the\n", + "recurrent neural network is trained on sequences of y values of the\n", + "form ((y1, y2), y3), so that the network is concerned with learning\n", + "the pattern of the y data and not the relation between the x and y\n", + "data. As long as the pattern of y data outside of the training region\n", + "stays relatively stable compared to what was inside the training\n", + "region, this method of training can produce accurate extrapolations to\n", + "y values far removed from the training data set." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "7dc577d1", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# FORMAT_DATA\n", + "def format_data(data, length_of_sequence = 2): \n", + " \"\"\"\n", + " Inputs:\n", + " data(a numpy array): the data that will be the inputs to the recurrent neural\n", + " network\n", + " length_of_sequence (an int): the number of elements in one iteration of the\n", + " sequence patter. For a function approximator use length_of_sequence = 2.\n", + " Returns:\n", + " rnn_input (a 3D numpy array): the input data for the recurrent neural network. Its\n", + " dimensions are length of data - length of sequence, length of sequence, \n", + " dimnsion of data\n", + " rnn_output (a numpy array): the training data for the neural network\n", + " Formats data to be used in a recurrent neural network.\n", + " \"\"\"\n", + "\n", + " X, Y = [], []\n", + " for i in range(len(data)-length_of_sequence):\n", + " # Get the next length_of_sequence elements\n", + " a = data[i:i+length_of_sequence]\n", + " # Get the element that immediately follows that\n", + " b = data[i+length_of_sequence]\n", + " # Reshape so that each data point is contained in its own array\n", + " a = np.reshape (a, (len(a), 1))\n", + " X.append(a)\n", + " Y.append(b)\n", + " rnn_input = np.array(X)\n", + " rnn_output = np.array(Y)\n", + "\n", + " return rnn_input, rnn_output\n", + "\n", + "\n", + "# ## Defining the Recurrent Neural Network Using Keras\n", + "# \n", + "# The following method defines a simple recurrent neural network in keras consisting of one input layer, one hidden layer, and one output layer.\n", + "\n", + "def rnn(length_of_sequences, batch_size = None, stateful = False):\n", + " \"\"\"\n", + " Inputs:\n", + " length_of_sequences (an int): the number of y values in \"x data\". This is determined\n", + " when the data is formatted\n", + " batch_size (an int): Default value is None. See Keras documentation of SimpleRNN.\n", + " stateful (a boolean): Default value is False. See Keras documentation of SimpleRNN.\n", + " Returns:\n", + " model (a Keras model): The recurrent neural network that is built and compiled by this\n", + " method\n", + " Builds and compiles a recurrent neural network with one hidden layer and returns the model.\n", + " \"\"\"\n", + " # Number of neurons in the input and output layers\n", + " in_out_neurons = 1\n", + " # Number of neurons in the hidden layer\n", + " hidden_neurons = 200\n", + " # Define the input layer\n", + " inp = Input(batch_shape=(batch_size, \n", + " length_of_sequences, \n", + " in_out_neurons)) \n", + " # Define the hidden layer as a simple RNN layer with a set number of neurons and add it to \n", + " # the network immediately after the input layer\n", + " rnn = SimpleRNN(hidden_neurons, \n", + " return_sequences=False,\n", + " stateful = stateful,\n", + " name=\"RNN\")(inp)\n", + " # Define the output layer as a dense neural network layer (standard neural network layer)\n", + " #and add it to the network immediately after the hidden layer.\n", + " dens = Dense(in_out_neurons,name=\"dense\")(rnn)\n", + " # Create the machine learning model starting with the input layer and ending with the \n", + " # output layer\n", + " model = Model(inputs=[inp],outputs=[dens])\n", + " # Compile the machine learning model using the mean squared error function as the loss \n", + " # function and an Adams optimizer.\n", + " model.compile(loss=\"mean_squared_error\", optimizer=\"adam\") \n", + " return model" + ] + }, + { + "cell_type": "markdown", + "id": "1978b6a1", + "metadata": { + "editable": true + }, + "source": [ + "## Predicting New Points With A Trained Recurrent Neural Network" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "d4ad417a", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def test_rnn (x1, y_test, plot_min, plot_max):\n", + " \"\"\"\n", + " Inputs:\n", + " x1 (a list or numpy array): The complete x component of the data set\n", + " y_test (a list or numpy array): The complete y component of the data set\n", + " plot_min (an int or float): the smallest x value used in the training data\n", + " plot_max (an int or float): the largest x valye used in the training data\n", + " Returns:\n", + " None.\n", + " Uses a trained recurrent neural network model to predict future points in the \n", + " series. Computes the MSE of the predicted data set from the true data set, saves\n", + " the predicted data set to a csv file, and plots the predicted and true data sets w\n", + " while also displaying the data range used for training.\n", + " \"\"\"\n", + " # Add the training data as the first dim points in the predicted data array as these\n", + " # are known values.\n", + " y_pred = y_test[:dim].tolist()\n", + " # Generate the first input to the trained recurrent neural network using the last two \n", + " # points of the training data. Based on how the network was trained this means that it\n", + " # will predict the first point in the data set after the training data. All of the \n", + " # brackets are necessary for Tensorflow.\n", + " next_input = np.array([[[y_test[dim-2]], [y_test[dim-1]]]])\n", + " # Save the very last point in the training data set. This will be used later.\n", + " last = [y_test[dim-1]]\n", + "\n", + " # Iterate until the complete data set is created.\n", + " for i in range (dim, len(y_test)):\n", + " # Predict the next point in the data set using the previous two points.\n", + " next = model.predict(next_input)\n", + " # Append just the number of the predicted data set\n", + " y_pred.append(next[0][0])\n", + " # Create the input that will be used to predict the next data point in the data set.\n", + " next_input = np.array([[last, next[0]]], dtype=np.float64)\n", + " last = next\n", + "\n", + " # Print the mean squared error between the known data set and the predicted data set.\n", + " print('MSE: ', np.square(np.subtract(y_test, y_pred)).mean())\n", + " # Save the predicted data set as a csv file for later use\n", + " name = datatype + 'Predicted'+str(dim)+'.csv'\n", + " np.savetxt(name, y_pred, delimiter=',')\n", + " # Plot the known data set and the predicted data set. The red box represents the region that was used\n", + " # for the training data.\n", + " fig, ax = plt.subplots()\n", + " ax.plot(x1, y_test, label=\"true\", linewidth=3)\n", + " ax.plot(x1, y_pred, 'g-.',label=\"predicted\", linewidth=4)\n", + " ax.legend()\n", + " # Created a red region to represent the points used in the training data.\n", + " ax.axvspan(plot_min, plot_max, alpha=0.25, color='red')\n", + " plt.show()\n", + "\n", + "# Check to make sure the data set is complete\n", + "assert len(X_tot) == len(y_tot)\n", + "\n", + "# This is the number of points that will be used in as the training data\n", + "dim=12\n", + "\n", + "# Separate the training data from the whole data set\n", + "X_train = X_tot[:dim]\n", + "y_train = y_tot[:dim]\n", + "\n", + "\n", + "# Generate the training data for the RNN, using a sequence of 2\n", + "rnn_input, rnn_training = format_data(y_train, 2)\n", + "\n", + "\n", + "# Create a recurrent neural network in Keras and produce a summary of the \n", + "# machine learning model\n", + "model = rnn(length_of_sequences = rnn_input.shape[1])\n", + "model.summary()\n", + "\n", + "# Start the timer. Want to time training+testing\n", + "start = timer()\n", + "# Fit the model using the training data genenerated above using 150 training iterations and a 5%\n", + "# validation split. Setting verbose to True prints information about each training iteration.\n", + "hist = model.fit(rnn_input, rnn_training, batch_size=None, epochs=150, \n", + " verbose=True,validation_split=0.05)\n", + "\n", + "for label in [\"loss\",\"val_loss\"]:\n", + " plt.plot(hist.history[label],label=label)\n", + "\n", + "plt.ylabel(\"loss\")\n", + "plt.xlabel(\"epoch\")\n", + "plt.title(\"The final validation loss: {}\".format(hist.history[\"val_loss\"][-1]))\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "# Use the trained neural network to predict more points of the data set\n", + "test_rnn(X_tot, y_tot, X_tot[0], X_tot[dim-1])\n", + "# Stop the timer and calculate the total time needed.\n", + "end = timer()\n", + "print('Time: ', end-start)" + ] + }, + { + "cell_type": "markdown", + "id": "e2cad4fc", + "metadata": { + "editable": true + }, + "source": [ + "Changing the size of the recurrent neural network and its parameters\n", + "can drastically change the results you get from the model. The below\n", + "code takes the simple recurrent neural network from above and adds a\n", + "second hidden layer, changes the number of neurons in the hidden\n", + "layer, and explicitly declares the activation function of the hidden\n", + "layers to be a sigmoid function. The loss function and optimizer can\n", + "also be changed but are kept the same as the above network. These\n", + "parameters can be tuned to provide the optimal result from the\n", + "network. For some ideas on how to improve the performance of a\n", + "[recurrent neural network](https://danijar.com/tips-for-training-recurrent-neural-networks)." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "c39f1516", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def rnn_2layers(length_of_sequences, batch_size = None, stateful = False):\n", + " \"\"\"\n", + " Inputs:\n", + " length_of_sequences (an int): the number of y values in \"x data\". This is determined\n", + " when the data is formatted\n", + " batch_size (an int): Default value is None. See Keras documentation of SimpleRNN.\n", + " stateful (a boolean): Default value is False. See Keras documentation of SimpleRNN.\n", + " Returns:\n", + " model (a Keras model): The recurrent neural network that is built and compiled by this\n", + " method\n", + " Builds and compiles a recurrent neural network with two hidden layers and returns the model.\n", + " \"\"\"\n", + " # Number of neurons in the input and output layers\n", + " in_out_neurons = 1\n", + " # Number of neurons in the hidden layer, increased from the first network\n", + " hidden_neurons = 500\n", + " # Define the input layer\n", + " inp = Input(batch_shape=(batch_size, \n", + " length_of_sequences, \n", + " in_out_neurons)) \n", + " # Create two hidden layers instead of one hidden layer. Explicitly set the activation\n", + " # function to be the sigmoid function (the default value is hyperbolic tangent)\n", + " rnn1 = SimpleRNN(hidden_neurons, \n", + " return_sequences=True, # This needs to be True if another hidden layer is to follow\n", + " stateful = stateful, activation = 'sigmoid',\n", + " name=\"RNN1\")(inp)\n", + " rnn2 = SimpleRNN(hidden_neurons, \n", + " return_sequences=False, activation = 'sigmoid',\n", + " stateful = stateful,\n", + " name=\"RNN2\")(rnn1)\n", + " # Define the output layer as a dense neural network layer (standard neural network layer)\n", + " #and add it to the network immediately after the hidden layer.\n", + " dens = Dense(in_out_neurons,name=\"dense\")(rnn2)\n", + " # Create the machine learning model starting with the input layer and ending with the \n", + " # output layer\n", + " model = Model(inputs=[inp],outputs=[dens])\n", + " # Compile the machine learning model using the mean squared error function as the loss \n", + " # function and an Adams optimizer.\n", + " model.compile(loss=\"mean_squared_error\", optimizer=\"adam\") \n", + " return model\n", + "\n", + "# Check to make sure the data set is complete\n", + "assert len(X_tot) == len(y_tot)\n", + "\n", + "# This is the number of points that will be used in as the training data\n", + "dim=12\n", + "\n", + "# Separate the training data from the whole data set\n", + "X_train = X_tot[:dim]\n", + "y_train = y_tot[:dim]\n", + "\n", + "\n", + "# Generate the training data for the RNN, using a sequence of 2\n", + "rnn_input, rnn_training = format_data(y_train, 2)\n", + "\n", + "\n", + "# Create a recurrent neural network in Keras and produce a summary of the \n", + "# machine learning model\n", + "model = rnn_2layers(length_of_sequences = 2)\n", + "model.summary()\n", + "\n", + "# Start the timer. Want to time training+testing\n", + "start = timer()\n", + "# Fit the model using the training data genenerated above using 150 training iterations and a 5%\n", + "# validation split. Setting verbose to True prints information about each training iteration.\n", + "hist = model.fit(rnn_input, rnn_training, batch_size=None, epochs=150, \n", + " verbose=True,validation_split=0.05)\n", + "\n", + "\n", + "# This section plots the training loss and the validation loss as a function of training iteration.\n", + "# This is not required for analyzing the couple cluster data but can help determine if the network is\n", + "# being overtrained.\n", + "for label in [\"loss\",\"val_loss\"]:\n", + " plt.plot(hist.history[label],label=label)\n", + "\n", + "plt.ylabel(\"loss\")\n", + "plt.xlabel(\"epoch\")\n", + "plt.title(\"The final validation loss: {}\".format(hist.history[\"val_loss\"][-1]))\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "# Use the trained neural network to predict more points of the data set\n", + "test_rnn(X_tot, y_tot, X_tot[0], X_tot[dim-1])\n", + "# Stop the timer and calculate the total time needed.\n", + "end = timer()\n", + "print('Time: ', end-start)" + ] + }, + { + "cell_type": "markdown", + "id": "842c7602", + "metadata": { + "editable": true + }, + "source": [ + "## Other Types of Recurrent Neural Networks\n", + "\n", + "Besides a simple recurrent neural network layer, there are two other\n", + "commonly used types of recurrent neural network layers: Long Short\n", + "Term Memory (LSTM) and Gated Recurrent Unit (GRU). For a short\n", + "introduction to these layers see \n", + "and .\n", + "\n", + "The first network created below is similar to the previous network,\n", + "but it replaces the SimpleRNN layers with LSTM layers. The second\n", + "network below has two hidden layers made up of GRUs, which are\n", + "preceeded by two dense (feeddorward) neural network layers. These\n", + "dense layers \"preprocess\" the data before it reaches the recurrent\n", + "layers. This architecture has been shown to improve the performance\n", + "of recurrent neural networks (see the link above and also\n", + "." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "6f0e9b62", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def lstm_2layers(length_of_sequences, batch_size = None, stateful = False):\n", + " \"\"\"\n", + " Inputs:\n", + " length_of_sequences (an int): the number of y values in \"x data\". This is determined\n", + " when the data is formatted\n", + " batch_size (an int): Default value is None. See Keras documentation of SimpleRNN.\n", + " stateful (a boolean): Default value is False. See Keras documentation of SimpleRNN.\n", + " Returns:\n", + " model (a Keras model): The recurrent neural network that is built and compiled by this\n", + " method\n", + " Builds and compiles a recurrent neural network with two LSTM hidden layers and returns the model.\n", + " \"\"\"\n", + " # Number of neurons on the input/output layer and the number of neurons in the hidden layer\n", + " in_out_neurons = 1\n", + " hidden_neurons = 250\n", + " # Input Layer\n", + " inp = Input(batch_shape=(batch_size, \n", + " length_of_sequences, \n", + " in_out_neurons)) \n", + " # Hidden layers (in this case they are LSTM layers instead if SimpleRNN layers)\n", + " rnn= LSTM(hidden_neurons, \n", + " return_sequences=True,\n", + " stateful = stateful,\n", + " name=\"RNN\", use_bias=True, activation='tanh')(inp)\n", + " rnn1 = LSTM(hidden_neurons, \n", + " return_sequences=False,\n", + " stateful = stateful,\n", + " name=\"RNN1\", use_bias=True, activation='tanh')(rnn)\n", + " # Output layer\n", + " dens = Dense(in_out_neurons,name=\"dense\")(rnn1)\n", + " # Define the midel\n", + " model = Model(inputs=[inp],outputs=[dens])\n", + " # Compile the model\n", + " model.compile(loss='mean_squared_error', optimizer='adam') \n", + " # Return the model\n", + " return model\n", + "\n", + "def dnn2_gru2(length_of_sequences, batch_size = None, stateful = False):\n", + " \"\"\"\n", + " Inputs:\n", + " length_of_sequences (an int): the number of y values in \"x data\". This is determined\n", + " when the data is formatted\n", + " batch_size (an int): Default value is None. See Keras documentation of SimpleRNN.\n", + " stateful (a boolean): Default value is False. See Keras documentation of SimpleRNN.\n", + " Returns:\n", + " model (a Keras model): The recurrent neural network that is built and compiled by this\n", + " method\n", + " Builds and compiles a recurrent neural network with four hidden layers (two dense followed by\n", + " two GRU layers) and returns the model.\n", + " \"\"\" \n", + " # Number of neurons on the input/output layers and hidden layers\n", + " in_out_neurons = 1\n", + " hidden_neurons = 250\n", + " # Input layer\n", + " inp = Input(batch_shape=(batch_size, \n", + " length_of_sequences, \n", + " in_out_neurons)) \n", + " # Hidden Dense (feedforward) layers\n", + " dnn = Dense(hidden_neurons/2, activation='relu', name='dnn')(inp)\n", + " dnn1 = Dense(hidden_neurons/2, activation='relu', name='dnn1')(dnn)\n", + " # Hidden GRU layers\n", + " rnn1 = GRU(hidden_neurons, \n", + " return_sequences=True,\n", + " stateful = stateful,\n", + " name=\"RNN1\", use_bias=True)(dnn1)\n", + " rnn = GRU(hidden_neurons, \n", + " return_sequences=False,\n", + " stateful = stateful,\n", + " name=\"RNN\", use_bias=True)(rnn1)\n", + " # Output layer\n", + " dens = Dense(in_out_neurons,name=\"dense\")(rnn)\n", + " # Define the model\n", + " model = Model(inputs=[inp],outputs=[dens])\n", + " # Compile the mdoel\n", + " model.compile(loss='mean_squared_error', optimizer='adam') \n", + " # Return the model\n", + " return model\n", + "\n", + "# Check to make sure the data set is complete\n", + "assert len(X_tot) == len(y_tot)\n", + "\n", + "# This is the number of points that will be used in as the training data\n", + "dim=12\n", + "\n", + "# Separate the training data from the whole data set\n", + "X_train = X_tot[:dim]\n", + "y_train = y_tot[:dim]\n", + "\n", + "\n", + "# Generate the training data for the RNN, using a sequence of 2\n", + "rnn_input, rnn_training = format_data(y_train, 2)\n", + "\n", + "\n", + "# Create a recurrent neural network in Keras and produce a summary of the \n", + "# machine learning model\n", + "# Change the method name to reflect which network you want to use\n", + "model = dnn2_gru2(length_of_sequences = 2)\n", + "model.summary()\n", + "\n", + "# Start the timer. Want to time training+testing\n", + "start = timer()\n", + "# Fit the model using the training data genenerated above using 150 training iterations and a 5%\n", + "# validation split. Setting verbose to True prints information about each training iteration.\n", + "hist = model.fit(rnn_input, rnn_training, batch_size=None, epochs=150, \n", + " verbose=True,validation_split=0.05)\n", + "\n", + "\n", + "# This section plots the training loss and the validation loss as a function of training iteration.\n", + "# This is not required for analyzing the couple cluster data but can help determine if the network is\n", + "# being overtrained.\n", + "for label in [\"loss\",\"val_loss\"]:\n", + " plt.plot(hist.history[label],label=label)\n", + "\n", + "plt.ylabel(\"loss\")\n", + "plt.xlabel(\"epoch\")\n", + "plt.title(\"The final validation loss: {}\".format(hist.history[\"val_loss\"][-1]))\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "# Use the trained neural network to predict more points of the data set\n", + "test_rnn(X_tot, y_tot, X_tot[0], X_tot[dim-1])\n", + "# Stop the timer and calculate the total time needed.\n", + "end = timer()\n", + "print('Time: ', end-start)\n", + "\n", + "\n", + "# ### Training Recurrent Neural Networks in the Standard Way (i.e. learning the relationship between the X and Y data)\n", + "# \n", + "# Finally, comparing the performace of a recurrent neural network using the standard data formatting to the performance of the network with time sequence data formatting shows the benefit of this type of data formatting with extrapolation.\n", + "\n", + "# Check to make sure the data set is complete\n", + "assert len(X_tot) == len(y_tot)\n", + "\n", + "# This is the number of points that will be used in as the training data\n", + "dim=12\n", + "\n", + "# Separate the training data from the whole data set\n", + "X_train = X_tot[:dim]\n", + "y_train = y_tot[:dim]\n", + "\n", + "# Reshape the data for Keras specifications\n", + "X_train = X_train.reshape((dim, 1))\n", + "y_train = y_train.reshape((dim, 1))\n", + "\n", + "\n", + "# Create a recurrent neural network in Keras and produce a summary of the \n", + "# machine learning model\n", + "# Set the sequence length to 1 for regular data formatting \n", + "model = rnn(length_of_sequences = 1)\n", + "model.summary()\n", + "\n", + "# Start the timer. Want to time training+testing\n", + "start = timer()\n", + "# Fit the model using the training data genenerated above using 150 training iterations and a 5%\n", + "# validation split. Setting verbose to True prints information about each training iteration.\n", + "hist = model.fit(X_train, y_train, batch_size=None, epochs=150, \n", + " verbose=True,validation_split=0.05)\n", + "\n", + "\n", + "# This section plots the training loss and the validation loss as a function of training iteration.\n", + "# This is not required for analyzing the couple cluster data but can help determine if the network is\n", + "# being overtrained.\n", + "for label in [\"loss\",\"val_loss\"]:\n", + " plt.plot(hist.history[label],label=label)\n", + "\n", + "plt.ylabel(\"loss\")\n", + "plt.xlabel(\"epoch\")\n", + "plt.title(\"The final validation loss: {}\".format(hist.history[\"val_loss\"][-1]))\n", + "plt.legend()\n", + "plt.show()\n", + "\n", + "# Use the trained neural network to predict the remaining data points\n", + "X_pred = X_tot[dim:]\n", + "X_pred = X_pred.reshape((len(X_pred), 1))\n", + "y_model = model.predict(X_pred)\n", + "y_pred = np.concatenate((y_tot[:dim], y_model.flatten()))\n", + "\n", + "# Plot the known data set and the predicted data set. The red box represents the region that was used\n", + "# for the training data.\n", + "fig, ax = plt.subplots()\n", + "ax.plot(X_tot, y_tot, label=\"true\", linewidth=3)\n", + "ax.plot(X_tot, y_pred, 'g-.',label=\"predicted\", linewidth=4)\n", + "ax.legend()\n", + "# Created a red region to represent the points used in the training data.\n", + "ax.axvspan(X_tot[0], X_tot[dim], alpha=0.25, color='red')\n", + "plt.show()\n", + "\n", + "# Stop the timer and calculate the total time needed.\n", + "end = timer()\n", + "print('Time: ', end-start)" + ] + }, + { + "cell_type": "markdown", + "id": "0752ba7f", + "metadata": { + "editable": true + }, + "source": [ + "# Generative Models\n", + "\n", + "**Generative models** describe a class of statistical models that are a contrast\n", + "to **discriminative models**. Informally we say that generative models can\n", + "generate new data instances while discriminative models discriminate between\n", + "different kinds of data instances. A generative model could generate new photos\n", + "of animals that look like 'real' animals while a discriminative model could tell\n", + "a dog from a cat. More formally, given a data set $x$ and a set of labels /\n", + "targets $y$. Generative models capture the joint probability $p(x, y)$, or\n", + "just $p(x)$ if there are no labels, while discriminative models capture the\n", + "conditional probability $p(y | x)$. Discriminative models generally try to draw\n", + "boundaries in the data space (often high dimensional), while generative models\n", + "try to model how data is placed throughout the space.\n", + "\n", + "**Note**: this material is thanks to Linus Ekstrøm." + ] + }, + { + "cell_type": "markdown", + "id": "784138f8", + "metadata": { + "editable": true + }, + "source": [ + "## Generative Adversarial Networks\n", + "\n", + "**Generative Adversarial Networks** are a type of unsupervised machine learning\n", + "algorithm proposed by [Goodfellow et. al](https://arxiv.org/pdf/1406.2661.pdf)\n", + "in 2014 (short and good article).\n", + "\n", + "The simplest formulation of\n", + "the model is based on a game theoretic approach, *zero sum game*, where we pit\n", + "two neural networks against one another. We define two rival networks, one\n", + "generator $g$, and one discriminator $d$. The generator directly produces\n", + "samples" + ] + }, + { + "cell_type": "markdown", + "id": "a42f89ee", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " x = g(z; \\theta^{(g)})\n", + "\\label{_auto1} \\tag{1}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "abe7212f", + "metadata": { + "editable": true + }, + "source": [ + "The discriminator attempts to distinguish between samples drawn from the\n", + "training data and samples drawn from the generator. In other words, it tries to\n", + "tell the difference between the fake data produced by $g$ and the actual data\n", + "samples we want to do prediction on. The discriminator outputs a probability\n", + "value given by" + ] + }, + { + "cell_type": "markdown", + "id": "0821eaee", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " d(x; \\theta^{(d)})\n", + "\\label{_auto2} \\tag{2}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "55e0ccf6", + "metadata": { + "editable": true + }, + "source": [ + "indicating the probability that $x$ is a real training example rather than a\n", + "fake sample the generator has generated. The simplest way to formulate the\n", + "learning process in a generative adversarial network is a zero-sum game, in\n", + "which a function" + ] + }, + { + "cell_type": "markdown", + "id": "f37ece14", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " v(\\theta^{(g)}, \\theta^{(d)})\n", + "\\label{_auto3} \\tag{3}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "d6d6d5fa", + "metadata": { + "editable": true + }, + "source": [ + "determines the reward for the discriminator, while the generator gets the\n", + "conjugate reward" + ] + }, + { + "cell_type": "markdown", + "id": "3c74b45c", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " -v(\\theta^{(g)}, \\theta^{(d)})\n", + "\\label{_auto4} \\tag{4}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "605ac8c9", + "metadata": { + "editable": true + }, + "source": [ + "During learning both of the networks maximize their own reward function, so that\n", + "the generator gets better and better at tricking the discriminator, while the\n", + "discriminator gets better and better at telling the difference between the fake\n", + "and real data. The generator and discriminator alternate on which one trains at\n", + "one time (i.e. for one epoch). In other words, we keep the generator constant\n", + "and train the discriminator, then we keep the discriminator constant to train\n", + "the generator and repeat. It is this back and forth dynamic which lets GANs\n", + "tackle otherwise intractable generative problems. As the generator improves with\n", + " training, the discriminator's performance gets worse because it cannot easily\n", + " tell the difference between real and fake. If the generator ends up succeeding\n", + " perfectly, the the discriminator will do no better than random guessing i.e.\n", + " 50\\%. This progression in the training poses a problem for the convergence\n", + " criteria for GANs. The discriminator feedback gets less meaningful over time,\n", + " if we continue training after this point then the generator is effectively\n", + " training on junk data which can undo the learning up to that point. Therefore,\n", + " we stop training when the discriminator starts outputting $1/2$ everywhere.\n", + "\n", + "At convergence we have" + ] + }, + { + "cell_type": "markdown", + "id": "cfec7462", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " g^* = \\underset{g}{\\mathrm{argmin}}\\hspace{2pt}\n", + " \\underset{d}{\\mathrm{max}}v(\\theta^{(g)}, \\theta^{(d)})\n", + "\\label{_auto5} \\tag{5}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "37c65d4c", + "metadata": { + "editable": true + }, + "source": [ + "The default choice for $v$ is" + ] + }, + { + "cell_type": "markdown", + "id": "c868a092", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " v(\\theta^{(g)}, \\theta^{(d)}) = \\mathbb{E}_{x\\sim p_\\mathrm{data}}\\log d(x)\n", + " + \\mathbb{E}_{x\\sim p_\\mathrm{model}}\n", + " \\log (1 - d(x))\n", + "\\label{_auto6} \\tag{6}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "ad465af3", + "metadata": { + "editable": true + }, + "source": [ + "The main motivation for the design of GANs is that the learning process requires\n", + "neither approximate inference (variational autoencoders for example) nor\n", + "approximation of a partition function. In the case where" + ] + }, + { + "cell_type": "markdown", + "id": "27858a4e", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\n", + " \\underset{d}{\\mathrm{max}}v(\\theta^{(g)}, \\theta^{(d)})\n", + "\\label{_auto7} \\tag{7}\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "86006023", + "metadata": { + "editable": true + }, + "source": [ + "is convex in $\\theta^{(g)} then the procedure is guaranteed to converge and is\n", + "asymptotically consistent\n", + "( [Seth Lloyd on QuGANs](https://arxiv.org/pdf/1804.09139.pdf) ).\n", + "\n", + "This is in\n", + "general not the case and it is possible to get situations where the training\n", + "process never converges because the generator and discriminator chase one\n", + "another around in the parameter space indefinitely. A much deeper discussion on\n", + "the currently open research problem of GAN convergence is available\n", + "[here](https://www.deeplearningbook.org/contents/generative_models.html). To\n", + "anyone interested in learning more about GANs it is a highly recommended read.\n", + "Direct quote: \"In this best-performing formulation, the generator aims to\n", + "increase the log probability that the discriminator makes a mistake, rather than\n", + "aiming to decrease the log probability that the discriminator makes the correct\n", + "prediction.\" [Another interesting read](https://arxiv.org/abs/1701.00160)" + ] + }, + { + "cell_type": "markdown", + "id": "2fee38bd", + "metadata": { + "editable": true + }, + "source": [ + "## Writing Our First Generative Adversarial Network\n", + "Let us now move on to actually implementing a GAN in tensorflow. We will study\n", + "the performance of our GAN on the MNIST dataset. This code is based on and\n", + "adapted from the\n", + "[google tutorial](https://www.tensorflow.org/tutorials/generative/dcgan)\n", + "\n", + "First we import our libraries" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "004a0b53", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "import os\n", + "import time\n", + "import numpy as np\n", + "import tensorflow as tf\n", + "import matplotlib.pyplot as plt\n", + "from tensorflow.keras import layers\n", + "from tensorflow.keras.utils import plot_model" + ] + }, + { + "cell_type": "markdown", + "id": "353af161", + "metadata": { + "editable": true + }, + "source": [ + "Next we define our hyperparameters and import our data the usual way" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "id": "8cbaf16a", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "BUFFER_SIZE = 60000\n", + "BATCH_SIZE = 256\n", + "EPOCHS = 30\n", + "\n", + "data = tf.keras.datasets.mnist.load_data()\n", + "(train_images, train_labels), (test_images, test_labels) = data\n", + "train_images = np.reshape(train_images, (train_images.shape[0],\n", + " 28,\n", + " 28,\n", + " 1)).astype('float32')\n", + "\n", + "# we normalize between -1 and 1\n", + "train_images = (train_images - 127.5) / 127.5\n", + "training_dataset = tf.data.Dataset.from_tensor_slices(\n", + " train_images).shuffle(BUFFER_SIZE).batch(BATCH_SIZE)" + ] + }, + { + "cell_type": "markdown", + "id": "822b8cc7", + "metadata": { + "editable": true + }, + "source": [ + "### MNIST and GANs\n", + "\n", + "Let's have a quick look" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "id": "52b5965c", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "plt.imshow(train_images[0], cmap='Greys')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "21c5199c", + "metadata": { + "editable": true + }, + "source": [ + "Now we define our two models. This is where the 'magic' happens. There are a\n", + "huge amount of possible formulations for both models. A lot of engineering and\n", + "trial and error can be done here to try to produce better performing models. For\n", + "more advanced GANs this is by far the step where you can 'make or break' a\n", + "model.\n", + "\n", + "We start with the generator. As stated in the introductory text the generator\n", + "$g$ upsamples from a random sample to the shape of what we want to predict. In\n", + "our case we are trying to predict MNIST images ($28\\times 28$ pixels)." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "id": "356759c7", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def generator_model():\n", + " \"\"\"\n", + " The generator uses upsampling layers tf.keras.layers.Conv2DTranspose() to\n", + " produce an image from a random seed. We start with a Dense layer taking this\n", + " random sample as an input and subsequently upsample through multiple\n", + " convolutional layers.\n", + " \"\"\"\n", + "\n", + " # we define our model\n", + " model = tf.keras.Sequential()\n", + "\n", + "\n", + " # adding our input layer. Dense means that every neuron is connected and\n", + " # the input shape is the shape of our random noise. The units need to match\n", + " # in some sense the upsampling strides to reach our desired output shape.\n", + " # we are using 100 random numbers as our seed\n", + " model.add(layers.Dense(units=7*7*BATCH_SIZE,\n", + " use_bias=False,\n", + " input_shape=(100, )))\n", + " # we normalize the output form the Dense layer\n", + " model.add(layers.BatchNormalization())\n", + " # and add an activation function to our 'layer'. LeakyReLU avoids vanishing\n", + " # gradient problem\n", + " model.add(layers.LeakyReLU())\n", + " model.add(layers.Reshape((7, 7, BATCH_SIZE)))\n", + " assert model.output_shape == (None, 7, 7, BATCH_SIZE)\n", + " # even though we just added four keras layers we think of everything above\n", + " # as 'one' layer\n", + "\n", + " # next we add our upscaling convolutional layers\n", + " model.add(layers.Conv2DTranspose(filters=128,\n", + " kernel_size=(5, 5),\n", + " strides=(1, 1),\n", + " padding='same',\n", + " use_bias=False))\n", + " model.add(layers.BatchNormalization())\n", + " model.add(layers.LeakyReLU())\n", + " assert model.output_shape == (None, 7, 7, 128)\n", + "\n", + " model.add(layers.Conv2DTranspose(filters=64,\n", + " kernel_size=(5, 5),\n", + " strides=(2, 2),\n", + " padding='same',\n", + " use_bias=False))\n", + " model.add(layers.BatchNormalization())\n", + " model.add(layers.LeakyReLU())\n", + " assert model.output_shape == (None, 14, 14, 64)\n", + "\n", + " model.add(layers.Conv2DTranspose(filters=1,\n", + " kernel_size=(5, 5),\n", + " strides=(2, 2),\n", + " padding='same',\n", + " use_bias=False,\n", + " activation='tanh'))\n", + " assert model.output_shape == (None, 28, 28, 1)\n", + "\n", + " return model" + ] + }, + { + "cell_type": "markdown", + "id": "854bcd6b", + "metadata": { + "editable": true + }, + "source": [ + "And there we have our 'simple' generator model. Now we move on to defining our\n", + "discriminator model $d$, which is a convolutional neural network based image\n", + "classifier." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "41473304", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def discriminator_model():\n", + " \"\"\"\n", + " The discriminator is a convolutional neural network based image classifier\n", + " \"\"\"\n", + "\n", + " # we define our model\n", + " model = tf.keras.Sequential()\n", + " model.add(layers.Conv2D(filters=64,\n", + " kernel_size=(5, 5),\n", + " strides=(2, 2),\n", + " padding='same',\n", + " input_shape=[28, 28, 1]))\n", + " model.add(layers.LeakyReLU())\n", + " # adding a dropout layer as you do in conv-nets\n", + " model.add(layers.Dropout(0.3))\n", + "\n", + "\n", + " model.add(layers.Conv2D(filters=128,\n", + " kernel_size=(5, 5),\n", + " strides=(2, 2),\n", + " padding='same'))\n", + " model.add(layers.LeakyReLU())\n", + " # adding a dropout layer as you do in conv-nets\n", + " model.add(layers.Dropout(0.3))\n", + "\n", + " model.add(layers.Flatten())\n", + " model.add(layers.Dense(1))\n", + "\n", + " return model" + ] + }, + { + "cell_type": "markdown", + "id": "353af567", + "metadata": { + "editable": true + }, + "source": [ + "Let us take a look at our models." + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "f899d4e3", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "generator = generator_model()\n", + "plot_model(generator, show_shapes=True, rankdir='LR')" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "87ef384b", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "discriminator = discriminator_model()\n", + "plot_model(discriminator, show_shapes=True, rankdir='LR')" + ] + }, + { + "cell_type": "markdown", + "id": "b2bef82d", + "metadata": { + "editable": true + }, + "source": [ + "Next we need a few helper objects we will use in training" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "e397847a", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "cross_entropy = tf.keras.losses.BinaryCrossentropy(from_logits=True)\n", + "generator_optimizer = tf.keras.optimizers.Adam(1e-4)\n", + "discriminator_optimizer = tf.keras.optimizers.Adam(1e-4)" + ] + }, + { + "cell_type": "markdown", + "id": "db3396cc", + "metadata": { + "editable": true + }, + "source": [ + "The first object, *cross_entropy* is our loss function and the two others are\n", + "our optimizers. Notice we use the same learning rate for both $g$ and $d$. This\n", + "is because they need to improve their accuracy at approximately equal speeds to\n", + "get convergence (not necessarily exactly equal). Now we define our loss\n", + "functions" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "931eaced", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def generator_loss(fake_output):\n", + " loss = cross_entropy(tf.ones_like(fake_output), fake_output)\n", + "\n", + " return loss" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "id": "0c4a44bb", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def discriminator_loss(real_output, fake_output):\n", + " real_loss = cross_entropy(tf.ones_like(real_output), real_output)\n", + " fake_loss = cross_entropy(tf.zeros_liks(fake_output), fake_output)\n", + " total_loss = real_loss + fake_loss\n", + "\n", + " return total_loss" + ] + }, + { + "cell_type": "markdown", + "id": "fcf8f066", + "metadata": { + "editable": true + }, + "source": [ + "Next we define a kind of seed to help us compare the learning process over\n", + "multiple training epochs." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "id": "eea2bbee", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "noise_dimension = 100\n", + "n_examples_to_generate = 16\n", + "seed_images = tf.random.normal([n_examples_to_generate, noise_dimension])" + ] + }, + { + "cell_type": "markdown", + "id": "94a6e341", + "metadata": { + "editable": true + }, + "source": [ + "Now we have everything we need to define our training step, which we will apply\n", + "for every step in our training loop. Notice the @tf.function flag signifying\n", + "that the function is tensorflow 'compiled'. Removing this flag doubles the\n", + "computation time." + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "id": "8d48470b", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "@tf.function\n", + "def train_step(images):\n", + " noise = tf.random.normal([BATCH_SIZE, noise_dimension])\n", + "\n", + " with tf.GradientTape() as gen_tape, tf.GradientTape() as disc_tape:\n", + " generated_images = generator(noise, training=True)\n", + "\n", + " real_output = discriminator(images, training=True)\n", + " fake_output = discriminator(generated_images, training=True)\n", + "\n", + " gen_loss = generator_loss(fake_output)\n", + " disc_loss = discriminator_loss(real_output, fake_output)\n", + "\n", + " gradients_of_generator = gen_tape.gradient(gen_loss,\n", + " generator.trainable_variables)\n", + " gradients_of_discriminator = disc_tape.gradient(disc_loss,\n", + " discriminator.trainable_variables)\n", + " generator_optimizer.apply_gradients(zip(gradients_of_generator,\n", + " generator.trainable_variables))\n", + " discriminator_optimizer.apply_gradients(zip(gradients_of_discriminator,\n", + " discriminator.trainable_variables))\n", + "\n", + " return gen_loss, disc_loss" + ] + }, + { + "cell_type": "markdown", + "id": "62015b88", + "metadata": { + "editable": true + }, + "source": [ + "Next we define a helper function to produce an output over our training epochs\n", + "to see the predictive progression of our generator model. **Note**: I am including\n", + "this code here, but comment it out in the training loop." + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "id": "b189ed96", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def generate_and_save_images(model, epoch, test_input):\n", + " # we're making inferences here\n", + " predictions = model(test_input, training=False)\n", + "\n", + " fig = plt.figure(figsize=(4, 4))\n", + "\n", + " for i in range(predictions.shape[0]):\n", + " plt.subplot(4, 4, i+1)\n", + " plt.imshow(predictions[i, :, :, 0] * 127.5 + 127.5, cmap='gray')\n", + " plt.axis('off')\n", + "\n", + " plt.savefig(f'./images_from_seed_images/image_at_epoch_{str(epoch).zfill(3)}.png')\n", + " plt.close()\n", + " #plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "ba2c82d5", + "metadata": { + "editable": true + }, + "source": [ + "Setting up checkpoints to periodically save our model during training so that\n", + "everything is not lost even if the program were to somehow terminate while\n", + "training." + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "a0e2fc8a", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# Setting up checkpoints to save model during training\n", + "checkpoint_dir = './training_checkpoints'\n", + "checkpoint_prefix = os.path.join(checkpoint_dir, 'ckpt')\n", + "checkpoint = tf.train.Checkpoint(generator_optimizer=generator_optimizer,\n", + " discriminator_optimizer=discriminator_optimizer,\n", + " generator=generator,\n", + " discriminator=discriminator)" + ] + }, + { + "cell_type": "markdown", + "id": "4d93a0f7", + "metadata": { + "editable": true + }, + "source": [ + "Now we define our training loop" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "id": "a1275556", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def train(dataset, epochs):\n", + " generator_loss_list = []\n", + " discriminator_loss_list = []\n", + "\n", + " for epoch in range(epochs):\n", + " start = time.time()\n", + "\n", + " for image_batch in dataset:\n", + " gen_loss, disc_loss = train_step(image_batch)\n", + " generator_loss_list.append(gen_loss.numpy())\n", + " discriminator_loss_list.append(disc_loss.numpy())\n", + "\n", + " #generate_and_save_images(generator, epoch + 1, seed_images)\n", + "\n", + " if (epoch + 1) % 15 == 0:\n", + " checkpoint.save(file_prefix=checkpoint_prefix)\n", + "\n", + " print(f'Time for epoch {epoch} is {time.time() - start}')\n", + "\n", + " #generate_and_save_images(generator, epochs, seed_images)\n", + "\n", + " loss_file = './data/lossfile.txt'\n", + " with open(loss_file, 'w') as outfile:\n", + " outfile.write(str(generator_loss_list))\n", + " outfile.write('\\n')\n", + " outfile.write('\\n')\n", + " outfile.write(str(discriminator_loss_list))\n", + " outfile.write('\\n')\n", + " outfile.write('\\n')" + ] + }, + { + "cell_type": "markdown", + "id": "6ff3a75a", + "metadata": { + "editable": true + }, + "source": [ + "To train simply call this function. **Warning**: this might take a long time so\n", + "there is a folder of a pretrained network already included in the repository." + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "id": "371ed41a", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "train(train_dataset, EPOCHS)" + ] + }, + { + "cell_type": "markdown", + "id": "654399f1", + "metadata": { + "editable": true + }, + "source": [ + "Now to avoid having to train and everything, which will take a while depending\n", + "on your computer setup we now load in the model which produced the above gif." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "dec4b560", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "checkpoint.restore(tf.train.latest_checkpoint(checkpoint_dir))\n", + "restored_generator = checkpoint.generator\n", + "restored_discriminator = checkpoint.discriminator\n", + "\n", + "print(restored_generator)\n", + "print(restored_discriminator)" + ] + }, + { + "cell_type": "markdown", + "id": "296bfa5c", + "metadata": { + "editable": true + }, + "source": [ + "We have successfully loaded in our latest model. Let us now play around a bit\n", + "and see what kind of things we can learn about this model. Our generator takes\n", + "an array of 100 numbers. One idea can be to try to systematically change our\n", + "input. Let us try and see what we get" + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "id": "eecfbb1f", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def generate_latent_points(number=100, scale_means=1, scale_stds=1):\n", + " latent_dim = 100\n", + " means = scale_means * tf.linspace(-1, 1, num=latent_dim)\n", + " stds = scale_stds * tf.linspace(-1, 1, num=latent_dim)\n", + " latent_space_value_range = tf.random.normal([number, latent_dim],\n", + " means,\n", + " stds,\n", + " dtype=tf.float64)\n", + "\n", + " return latent_space_value_range\n", + "\n", + "def generate_images(latent_points):\n", + " # notice we set training to false because we are making inferences\n", + " generated_images = restored_generator.predict(latent_points)\n", + "\n", + " return generated_images" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "id": "333a593d", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def plot_result(generated_images, number=100):\n", + " # obviously this assumes sqrt number is an int\n", + " fig, axs = plt.subplots(int(np.sqrt(number)), int(np.sqrt(number)),\n", + " figsize=(10, 10))\n", + "\n", + " for i in range(int(np.sqrt(number))):\n", + " for j in range(int(np.sqrt(number))):\n", + " axs[i, j].imshow(generated_images[i*j], cmap='Greys')\n", + " axs[i, j].axis('off')\n", + "\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "2f5f0154", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "generated_images = generate_images(generate_latent_points())\n", + "plot_result(generated_images)" + ] + }, + { + "cell_type": "markdown", + "id": "ff581bf2", + "metadata": { + "editable": true + }, + "source": [ + "We see that the generator generates images that look like MNIST\n", + "numbers: $1, 4, 7, 9$. Let's try to tweak it a bit more to see if we are able\n", + "to generate a similar plot where we generate every MNIST number. Let us now try\n", + "to 'move' a bit around in the latent space. **Note**: decrease the plot number if\n", + "these following cells take too long to run on your computer." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "d3617ad8", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "plot_number = 225\n", + "\n", + "generated_images = generate_images(generate_latent_points(number=plot_number,\n", + " scale_means=5,\n", + " scale_stds=1))\n", + "plot_result(generated_images, number=plot_number)\n", + "\n", + "generated_images = generate_images(generate_latent_points(number=plot_number,\n", + " scale_means=-5,\n", + " scale_stds=1))\n", + "plot_result(generated_images, number=plot_number)\n", + "\n", + "generated_images = generate_images(generate_latent_points(number=plot_number,\n", + " scale_means=1,\n", + " scale_stds=5))\n", + "plot_result(generated_images, number=plot_number)" + ] + }, + { + "cell_type": "markdown", + "id": "1a074f93", + "metadata": { + "editable": true + }, + "source": [ + "Again, we have found something interesting. *Moving* around using our means\n", + "takes us from digit to digit, while *moving* around using our standard\n", + "deviations seem to increase the number of different digits! In the last image\n", + "above, we can barely make out every MNIST digit. Let us make on last plot using\n", + "this information by upping the standard deviation of our Gaussian noises." + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "4ef8937d", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "plot_number = 400\n", + "generated_images = generate_images(generate_latent_points(number=plot_number,\n", + " scale_means=1,\n", + " scale_stds=10))\n", + "plot_result(generated_images, number=plot_number)" + ] + }, + { + "cell_type": "markdown", + "id": "385a2d0a", + "metadata": { + "editable": true + }, + "source": [ + "A pretty cool result! We see that our generator indeed has learned a\n", + "distribution which qualitatively looks a whole lot like the MNIST dataset.\n", + "\n", + "Another interesting way to explore the latent space of our generator model is by\n", + "interpolating between the MNIST digits. This section is largely based on\n", + "[this excellent blogpost](https://machinelearningmastery.com/how-to-interpolate-and-perform-vector-arithmetic-with-faces-using-a-generative-adversarial-network/)\n", + "by Jason Brownlee.\n", + "\n", + "So let us start by defining a function to interpolate between two points in the\n", + "latent space." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "id": "57de87b8", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def interpolation(point_1, point_2, n_steps=10):\n", + " ratios = np.linspace(0, 1, num=n_steps)\n", + " vectors = []\n", + " for i, ratio in enumerate(ratios):\n", + " vectors.append(((1.0 - ratio) * point_1 + ratio * point_2))\n", + "\n", + " return tf.stack(vectors)" + ] + }, + { + "cell_type": "markdown", + "id": "cfb76bb6", + "metadata": { + "editable": true + }, + "source": [ + "Now we have all we need to do our interpolation analysis." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "id": "e25decef", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "plot_number = 100\n", + "latent_points = generate_latent_points(number=plot_number)\n", + "results = None\n", + "for i in range(0, 2*np.sqrt(plot_number), 2):\n", + " interpolated = interpolation(latent_points[i], latent_points[i+1])\n", + " generated_images = generate_images(interpolated)\n", + "\n", + " if results is None:\n", + " results = generated_images\n", + " else:\n", + " results = tf.stack((results, generated_images))\n", + "\n", + "plot_results(results, plot_number)" + ] + } + ], + "metadata": { + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter13.py b/doc/LectureNotes/_build/jupyter_execute/chapter13.py new file mode 100644 index 000000000..97cd2c4bd --- /dev/null +++ b/doc/LectureNotes/_build/jupyter_execute/chapter13.py @@ -0,0 +1,1306 @@ +#!/usr/bin/env python +# coding: utf-8 + +# + +# # Recurrent neural networks: Overarching view +# +# Till now our focus has been, including convolutional neural networks +# as well, on feedforward neural networks. The output or the activations +# flow only in one direction, from the input layer to the output layer. +# +# A recurrent neural network (RNN) looks very much like a feedforward +# neural network, except that it also has connections pointing +# backward. +# +# RNNs are used to analyze time series data such as stock prices, and +# tell you when to buy or sell. In autonomous driving systems, they can +# anticipate car trajectories and help avoid accidents. More generally, +# they can work on sequences of arbitrary lengths, rather than on +# fixed-sized inputs like all the nets we have discussed so far. For +# example, they can take sentences, documents, or audio samples as +# input, making them extremely useful for natural language processing +# systems such as automatic translation and speech-to-text. +# +# More to text to be added + +# ## A simple example + +# In[1]: + + +get_ipython().run_line_magic('matplotlib', 'inline') + +# Start importing packages +import pandas as pd +import numpy as np +import matplotlib.pyplot as plt +import tensorflow as tf +from tensorflow.keras import datasets, layers, models +from tensorflow.keras.layers import Input +from tensorflow.keras.models import Model, Sequential +from tensorflow.keras.layers import Dense, SimpleRNN, LSTM, GRU +from tensorflow.keras import optimizers +from tensorflow.keras import regularizers +from tensorflow.keras.utils import to_categorical + + + +# convert into dataset matrix +def convertToMatrix(data, step): + X, Y =[], [] + for i in range(len(data)-step): + d=i+step + X.append(data[i:d,]) + Y.append(data[d,]) + return np.array(X), np.array(Y) + +step = 4 +N = 1000 +Tp = 800 + +t=np.arange(0,N) +x=np.sin(0.02*t)+2*np.random.rand(N) +df = pd.DataFrame(x) +df.head() + +plt.plot(df) +plt.show() + +values=df.values +train,test = values[0:Tp,:], values[Tp:N,:] + +# add step elements into train and test +test = np.append(test,np.repeat(test[-1,],step)) +train = np.append(train,np.repeat(train[-1,],step)) + +trainX,trainY =convertToMatrix(train,step) +testX,testY =convertToMatrix(test,step) +trainX = np.reshape(trainX, (trainX.shape[0], 1, trainX.shape[1])) +testX = np.reshape(testX, (testX.shape[0], 1, testX.shape[1])) + +model = Sequential() +model.add(SimpleRNN(units=32, input_shape=(1,step), activation="relu")) +model.add(Dense(8, activation="relu")) +model.add(Dense(1)) +model.compile(loss='mean_squared_error', optimizer='rmsprop') +model.summary() + +model.fit(trainX,trainY, epochs=100, batch_size=16, verbose=2) +trainPredict = model.predict(trainX) +testPredict= model.predict(testX) +predicted=np.concatenate((trainPredict,testPredict),axis=0) + +trainScore = model.evaluate(trainX, trainY, verbose=0) +print(trainScore) + +index = df.index.values +plt.plot(index,df) +plt.plot(index,predicted) +plt.axvline(df.index[Tp], c="r") +plt.show() + + +# ## An extrapolation example +# +# The following code provides an example of how recurrent neural +# networks can be used to extrapolate to unknown values of physics data +# sets. Specifically, the data sets used in this program come from +# a quantum mechanical many-body calculation of energies as functions of the number of particles. + +# In[2]: + + + +# For matrices and calculations +import numpy as np +# For machine learning (backend for keras) +import tensorflow as tf +# User-friendly machine learning library +# Front end for TensorFlow +import tensorflow.keras +# Different methods from Keras needed to create an RNN +# This is not necessary but it shortened function calls +# that need to be used in the code. +from tensorflow.keras import datasets, layers, models +from tensorflow.keras.layers import Input +from tensorflow.keras import regularizers +from tensorflow.keras.models import Model, Sequential +from tensorflow.keras.layers import Dense, SimpleRNN, LSTM, GRU +# For timing the code +from timeit import default_timer as timer +# For plotting +import matplotlib.pyplot as plt + + +# The data set +datatype='VaryDimension' +X_tot = np.arange(2, 42, 2) +y_tot = np.array([-0.03077640549, -0.08336233266, -0.1446729567, -0.2116753732, -0.2830637392, -0.3581341341, -0.436462435, -0.5177783846, + -0.6019067271, -0.6887363571, -0.7782028952, -0.8702784034, -0.9649652536, -1.062292565, -1.16231451, + -1.265109911, -1.370782966, -1.479465113, -1.591317992, -1.70653767]) + + +# The way the recurrent neural networks are trained in this program +# differs from how machine learning algorithms are usually trained. +# Typically a machine learning algorithm is trained by learning the +# relationship between the x data and the y data. In this program, the +# recurrent neural network will be trained to recognize the relationship +# in a sequence of y values. This is type of data formatting is +# typically used time series forcasting, but it can also be used in any +# extrapolation (time series forecasting is just a specific type of +# extrapolation along the time axis). This method of data formatting +# does not use the x data and assumes that the y data are evenly spaced. +# +# For a standard machine learning algorithm, the training data has the +# form of (x,y) so the machine learning algorithm learns to assiciate a +# y value with a given x value. This is useful when the test data has x +# values within the same range as the training data. However, for this +# application, the x values of the test data are outside of the x values +# of the training data and the traditional method of training a machine +# learning algorithm does not work as well. For this reason, the +# recurrent neural network is trained on sequences of y values of the +# form ((y1, y2), y3), so that the network is concerned with learning +# the pattern of the y data and not the relation between the x and y +# data. As long as the pattern of y data outside of the training region +# stays relatively stable compared to what was inside the training +# region, this method of training can produce accurate extrapolations to +# y values far removed from the training data set. + +# In[3]: + + +# FORMAT_DATA +def format_data(data, length_of_sequence = 2): + """ + Inputs: + data(a numpy array): the data that will be the inputs to the recurrent neural + network + length_of_sequence (an int): the number of elements in one iteration of the + sequence patter. For a function approximator use length_of_sequence = 2. + Returns: + rnn_input (a 3D numpy array): the input data for the recurrent neural network. Its + dimensions are length of data - length of sequence, length of sequence, + dimnsion of data + rnn_output (a numpy array): the training data for the neural network + Formats data to be used in a recurrent neural network. + """ + + X, Y = [], [] + for i in range(len(data)-length_of_sequence): + # Get the next length_of_sequence elements + a = data[i:i+length_of_sequence] + # Get the element that immediately follows that + b = data[i+length_of_sequence] + # Reshape so that each data point is contained in its own array + a = np.reshape (a, (len(a), 1)) + X.append(a) + Y.append(b) + rnn_input = np.array(X) + rnn_output = np.array(Y) + + return rnn_input, rnn_output + + +# ## Defining the Recurrent Neural Network Using Keras +# +# The following method defines a simple recurrent neural network in keras consisting of one input layer, one hidden layer, and one output layer. + +def rnn(length_of_sequences, batch_size = None, stateful = False): + """ + Inputs: + length_of_sequences (an int): the number of y values in "x data". This is determined + when the data is formatted + batch_size (an int): Default value is None. See Keras documentation of SimpleRNN. + stateful (a boolean): Default value is False. See Keras documentation of SimpleRNN. + Returns: + model (a Keras model): The recurrent neural network that is built and compiled by this + method + Builds and compiles a recurrent neural network with one hidden layer and returns the model. + """ + # Number of neurons in the input and output layers + in_out_neurons = 1 + # Number of neurons in the hidden layer + hidden_neurons = 200 + # Define the input layer + inp = Input(batch_shape=(batch_size, + length_of_sequences, + in_out_neurons)) + # Define the hidden layer as a simple RNN layer with a set number of neurons and add it to + # the network immediately after the input layer + rnn = SimpleRNN(hidden_neurons, + return_sequences=False, + stateful = stateful, + name="RNN")(inp) + # Define the output layer as a dense neural network layer (standard neural network layer) + #and add it to the network immediately after the hidden layer. + dens = Dense(in_out_neurons,name="dense")(rnn) + # Create the machine learning model starting with the input layer and ending with the + # output layer + model = Model(inputs=[inp],outputs=[dens]) + # Compile the machine learning model using the mean squared error function as the loss + # function and an Adams optimizer. + model.compile(loss="mean_squared_error", optimizer="adam") + return model + + +# ## Predicting New Points With A Trained Recurrent Neural Network + +# In[4]: + + +def test_rnn (x1, y_test, plot_min, plot_max): + """ + Inputs: + x1 (a list or numpy array): The complete x component of the data set + y_test (a list or numpy array): The complete y component of the data set + plot_min (an int or float): the smallest x value used in the training data + plot_max (an int or float): the largest x valye used in the training data + Returns: + None. + Uses a trained recurrent neural network model to predict future points in the + series. Computes the MSE of the predicted data set from the true data set, saves + the predicted data set to a csv file, and plots the predicted and true data sets w + while also displaying the data range used for training. + """ + # Add the training data as the first dim points in the predicted data array as these + # are known values. + y_pred = y_test[:dim].tolist() + # Generate the first input to the trained recurrent neural network using the last two + # points of the training data. Based on how the network was trained this means that it + # will predict the first point in the data set after the training data. All of the + # brackets are necessary for Tensorflow. + next_input = np.array([[[y_test[dim-2]], [y_test[dim-1]]]]) + # Save the very last point in the training data set. This will be used later. + last = [y_test[dim-1]] + + # Iterate until the complete data set is created. + for i in range (dim, len(y_test)): + # Predict the next point in the data set using the previous two points. + next = model.predict(next_input) + # Append just the number of the predicted data set + y_pred.append(next[0][0]) + # Create the input that will be used to predict the next data point in the data set. + next_input = np.array([[last, next[0]]], dtype=np.float64) + last = next + + # Print the mean squared error between the known data set and the predicted data set. + print('MSE: ', np.square(np.subtract(y_test, y_pred)).mean()) + # Save the predicted data set as a csv file for later use + name = datatype + 'Predicted'+str(dim)+'.csv' + np.savetxt(name, y_pred, delimiter=',') + # Plot the known data set and the predicted data set. The red box represents the region that was used + # for the training data. + fig, ax = plt.subplots() + ax.plot(x1, y_test, label="true", linewidth=3) + ax.plot(x1, y_pred, 'g-.',label="predicted", linewidth=4) + ax.legend() + # Created a red region to represent the points used in the training data. + ax.axvspan(plot_min, plot_max, alpha=0.25, color='red') + plt.show() + +# Check to make sure the data set is complete +assert len(X_tot) == len(y_tot) + +# This is the number of points that will be used in as the training data +dim=12 + +# Separate the training data from the whole data set +X_train = X_tot[:dim] +y_train = y_tot[:dim] + + +# Generate the training data for the RNN, using a sequence of 2 +rnn_input, rnn_training = format_data(y_train, 2) + + +# Create a recurrent neural network in Keras and produce a summary of the +# machine learning model +model = rnn(length_of_sequences = rnn_input.shape[1]) +model.summary() + +# Start the timer. Want to time training+testing +start = timer() +# Fit the model using the training data genenerated above using 150 training iterations and a 5% +# validation split. Setting verbose to True prints information about each training iteration. +hist = model.fit(rnn_input, rnn_training, batch_size=None, epochs=150, + verbose=True,validation_split=0.05) + +for label in ["loss","val_loss"]: + plt.plot(hist.history[label],label=label) + +plt.ylabel("loss") +plt.xlabel("epoch") +plt.title("The final validation loss: {}".format(hist.history["val_loss"][-1])) +plt.legend() +plt.show() + +# Use the trained neural network to predict more points of the data set +test_rnn(X_tot, y_tot, X_tot[0], X_tot[dim-1]) +# Stop the timer and calculate the total time needed. +end = timer() +print('Time: ', end-start) + + +# Changing the size of the recurrent neural network and its parameters +# can drastically change the results you get from the model. The below +# code takes the simple recurrent neural network from above and adds a +# second hidden layer, changes the number of neurons in the hidden +# layer, and explicitly declares the activation function of the hidden +# layers to be a sigmoid function. The loss function and optimizer can +# also be changed but are kept the same as the above network. These +# parameters can be tuned to provide the optimal result from the +# network. For some ideas on how to improve the performance of a +# [recurrent neural network](https://danijar.com/tips-for-training-recurrent-neural-networks). + +# In[5]: + + +def rnn_2layers(length_of_sequences, batch_size = None, stateful = False): + """ + Inputs: + length_of_sequences (an int): the number of y values in "x data". This is determined + when the data is formatted + batch_size (an int): Default value is None. See Keras documentation of SimpleRNN. + stateful (a boolean): Default value is False. See Keras documentation of SimpleRNN. + Returns: + model (a Keras model): The recurrent neural network that is built and compiled by this + method + Builds and compiles a recurrent neural network with two hidden layers and returns the model. + """ + # Number of neurons in the input and output layers + in_out_neurons = 1 + # Number of neurons in the hidden layer, increased from the first network + hidden_neurons = 500 + # Define the input layer + inp = Input(batch_shape=(batch_size, + length_of_sequences, + in_out_neurons)) + # Create two hidden layers instead of one hidden layer. Explicitly set the activation + # function to be the sigmoid function (the default value is hyperbolic tangent) + rnn1 = SimpleRNN(hidden_neurons, + return_sequences=True, # This needs to be True if another hidden layer is to follow + stateful = stateful, activation = 'sigmoid', + name="RNN1")(inp) + rnn2 = SimpleRNN(hidden_neurons, + return_sequences=False, activation = 'sigmoid', + stateful = stateful, + name="RNN2")(rnn1) + # Define the output layer as a dense neural network layer (standard neural network layer) + #and add it to the network immediately after the hidden layer. + dens = Dense(in_out_neurons,name="dense")(rnn2) + # Create the machine learning model starting with the input layer and ending with the + # output layer + model = Model(inputs=[inp],outputs=[dens]) + # Compile the machine learning model using the mean squared error function as the loss + # function and an Adams optimizer. + model.compile(loss="mean_squared_error", optimizer="adam") + return model + +# Check to make sure the data set is complete +assert len(X_tot) == len(y_tot) + +# This is the number of points that will be used in as the training data +dim=12 + +# Separate the training data from the whole data set +X_train = X_tot[:dim] +y_train = y_tot[:dim] + + +# Generate the training data for the RNN, using a sequence of 2 +rnn_input, rnn_training = format_data(y_train, 2) + + +# Create a recurrent neural network in Keras and produce a summary of the +# machine learning model +model = rnn_2layers(length_of_sequences = 2) +model.summary() + +# Start the timer. Want to time training+testing +start = timer() +# Fit the model using the training data genenerated above using 150 training iterations and a 5% +# validation split. Setting verbose to True prints information about each training iteration. +hist = model.fit(rnn_input, rnn_training, batch_size=None, epochs=150, + verbose=True,validation_split=0.05) + + +# This section plots the training loss and the validation loss as a function of training iteration. +# This is not required for analyzing the couple cluster data but can help determine if the network is +# being overtrained. +for label in ["loss","val_loss"]: + plt.plot(hist.history[label],label=label) + +plt.ylabel("loss") +plt.xlabel("epoch") +plt.title("The final validation loss: {}".format(hist.history["val_loss"][-1])) +plt.legend() +plt.show() + +# Use the trained neural network to predict more points of the data set +test_rnn(X_tot, y_tot, X_tot[0], X_tot[dim-1]) +# Stop the timer and calculate the total time needed. +end = timer() +print('Time: ', end-start) + + +# ## Other Types of Recurrent Neural Networks +# +# Besides a simple recurrent neural network layer, there are two other +# commonly used types of recurrent neural network layers: Long Short +# Term Memory (LSTM) and Gated Recurrent Unit (GRU). For a short +# introduction to these layers see +# and . +# +# The first network created below is similar to the previous network, +# but it replaces the SimpleRNN layers with LSTM layers. The second +# network below has two hidden layers made up of GRUs, which are +# preceeded by two dense (feeddorward) neural network layers. These +# dense layers "preprocess" the data before it reaches the recurrent +# layers. This architecture has been shown to improve the performance +# of recurrent neural networks (see the link above and also +# . + +# In[6]: + + +def lstm_2layers(length_of_sequences, batch_size = None, stateful = False): + """ + Inputs: + length_of_sequences (an int): the number of y values in "x data". This is determined + when the data is formatted + batch_size (an int): Default value is None. See Keras documentation of SimpleRNN. + stateful (a boolean): Default value is False. See Keras documentation of SimpleRNN. + Returns: + model (a Keras model): The recurrent neural network that is built and compiled by this + method + Builds and compiles a recurrent neural network with two LSTM hidden layers and returns the model. + """ + # Number of neurons on the input/output layer and the number of neurons in the hidden layer + in_out_neurons = 1 + hidden_neurons = 250 + # Input Layer + inp = Input(batch_shape=(batch_size, + length_of_sequences, + in_out_neurons)) + # Hidden layers (in this case they are LSTM layers instead if SimpleRNN layers) + rnn= LSTM(hidden_neurons, + return_sequences=True, + stateful = stateful, + name="RNN", use_bias=True, activation='tanh')(inp) + rnn1 = LSTM(hidden_neurons, + return_sequences=False, + stateful = stateful, + name="RNN1", use_bias=True, activation='tanh')(rnn) + # Output layer + dens = Dense(in_out_neurons,name="dense")(rnn1) + # Define the midel + model = Model(inputs=[inp],outputs=[dens]) + # Compile the model + model.compile(loss='mean_squared_error', optimizer='adam') + # Return the model + return model + +def dnn2_gru2(length_of_sequences, batch_size = None, stateful = False): + """ + Inputs: + length_of_sequences (an int): the number of y values in "x data". This is determined + when the data is formatted + batch_size (an int): Default value is None. See Keras documentation of SimpleRNN. + stateful (a boolean): Default value is False. See Keras documentation of SimpleRNN. + Returns: + model (a Keras model): The recurrent neural network that is built and compiled by this + method + Builds and compiles a recurrent neural network with four hidden layers (two dense followed by + two GRU layers) and returns the model. + """ + # Number of neurons on the input/output layers and hidden layers + in_out_neurons = 1 + hidden_neurons = 250 + # Input layer + inp = Input(batch_shape=(batch_size, + length_of_sequences, + in_out_neurons)) + # Hidden Dense (feedforward) layers + dnn = Dense(hidden_neurons/2, activation='relu', name='dnn')(inp) + dnn1 = Dense(hidden_neurons/2, activation='relu', name='dnn1')(dnn) + # Hidden GRU layers + rnn1 = GRU(hidden_neurons, + return_sequences=True, + stateful = stateful, + name="RNN1", use_bias=True)(dnn1) + rnn = GRU(hidden_neurons, + return_sequences=False, + stateful = stateful, + name="RNN", use_bias=True)(rnn1) + # Output layer + dens = Dense(in_out_neurons,name="dense")(rnn) + # Define the model + model = Model(inputs=[inp],outputs=[dens]) + # Compile the mdoel + model.compile(loss='mean_squared_error', optimizer='adam') + # Return the model + return model + +# Check to make sure the data set is complete +assert len(X_tot) == len(y_tot) + +# This is the number of points that will be used in as the training data +dim=12 + +# Separate the training data from the whole data set +X_train = X_tot[:dim] +y_train = y_tot[:dim] + + +# Generate the training data for the RNN, using a sequence of 2 +rnn_input, rnn_training = format_data(y_train, 2) + + +# Create a recurrent neural network in Keras and produce a summary of the +# machine learning model +# Change the method name to reflect which network you want to use +model = dnn2_gru2(length_of_sequences = 2) +model.summary() + +# Start the timer. Want to time training+testing +start = timer() +# Fit the model using the training data genenerated above using 150 training iterations and a 5% +# validation split. Setting verbose to True prints information about each training iteration. +hist = model.fit(rnn_input, rnn_training, batch_size=None, epochs=150, + verbose=True,validation_split=0.05) + + +# This section plots the training loss and the validation loss as a function of training iteration. +# This is not required for analyzing the couple cluster data but can help determine if the network is +# being overtrained. +for label in ["loss","val_loss"]: + plt.plot(hist.history[label],label=label) + +plt.ylabel("loss") +plt.xlabel("epoch") +plt.title("The final validation loss: {}".format(hist.history["val_loss"][-1])) +plt.legend() +plt.show() + +# Use the trained neural network to predict more points of the data set +test_rnn(X_tot, y_tot, X_tot[0], X_tot[dim-1]) +# Stop the timer and calculate the total time needed. +end = timer() +print('Time: ', end-start) + + +# ### Training Recurrent Neural Networks in the Standard Way (i.e. learning the relationship between the X and Y data) +# +# Finally, comparing the performace of a recurrent neural network using the standard data formatting to the performance of the network with time sequence data formatting shows the benefit of this type of data formatting with extrapolation. + +# Check to make sure the data set is complete +assert len(X_tot) == len(y_tot) + +# This is the number of points that will be used in as the training data +dim=12 + +# Separate the training data from the whole data set +X_train = X_tot[:dim] +y_train = y_tot[:dim] + +# Reshape the data for Keras specifications +X_train = X_train.reshape((dim, 1)) +y_train = y_train.reshape((dim, 1)) + + +# Create a recurrent neural network in Keras and produce a summary of the +# machine learning model +# Set the sequence length to 1 for regular data formatting +model = rnn(length_of_sequences = 1) +model.summary() + +# Start the timer. Want to time training+testing +start = timer() +# Fit the model using the training data genenerated above using 150 training iterations and a 5% +# validation split. Setting verbose to True prints information about each training iteration. +hist = model.fit(X_train, y_train, batch_size=None, epochs=150, + verbose=True,validation_split=0.05) + + +# This section plots the training loss and the validation loss as a function of training iteration. +# This is not required for analyzing the couple cluster data but can help determine if the network is +# being overtrained. +for label in ["loss","val_loss"]: + plt.plot(hist.history[label],label=label) + +plt.ylabel("loss") +plt.xlabel("epoch") +plt.title("The final validation loss: {}".format(hist.history["val_loss"][-1])) +plt.legend() +plt.show() + +# Use the trained neural network to predict the remaining data points +X_pred = X_tot[dim:] +X_pred = X_pred.reshape((len(X_pred), 1)) +y_model = model.predict(X_pred) +y_pred = np.concatenate((y_tot[:dim], y_model.flatten())) + +# Plot the known data set and the predicted data set. The red box represents the region that was used +# for the training data. +fig, ax = plt.subplots() +ax.plot(X_tot, y_tot, label="true", linewidth=3) +ax.plot(X_tot, y_pred, 'g-.',label="predicted", linewidth=4) +ax.legend() +# Created a red region to represent the points used in the training data. +ax.axvspan(X_tot[0], X_tot[dim], alpha=0.25, color='red') +plt.show() + +# Stop the timer and calculate the total time needed. +end = timer() +print('Time: ', end-start) + + +# # Generative Models +# +# **Generative models** describe a class of statistical models that are a contrast +# to **discriminative models**. Informally we say that generative models can +# generate new data instances while discriminative models discriminate between +# different kinds of data instances. A generative model could generate new photos +# of animals that look like 'real' animals while a discriminative model could tell +# a dog from a cat. More formally, given a data set $x$ and a set of labels / +# targets $y$. Generative models capture the joint probability $p(x, y)$, or +# just $p(x)$ if there are no labels, while discriminative models capture the +# conditional probability $p(y | x)$. Discriminative models generally try to draw +# boundaries in the data space (often high dimensional), while generative models +# try to model how data is placed throughout the space. +# +# **Note**: this material is thanks to Linus Ekstrøm. + +# ## Generative Adversarial Networks +# +# **Generative Adversarial Networks** are a type of unsupervised machine learning +# algorithm proposed by [Goodfellow et. al](https://arxiv.org/pdf/1406.2661.pdf) +# in 2014 (short and good article). +# +# The simplest formulation of +# the model is based on a game theoretic approach, *zero sum game*, where we pit +# two neural networks against one another. We define two rival networks, one +# generator $g$, and one discriminator $d$. The generator directly produces +# samples + +# +#
    +# +# $$ +# \begin{equation} +# x = g(z; \theta^{(g)}) +# \label{_auto1} \tag{1} +# \end{equation} +# $$ + +# The discriminator attempts to distinguish between samples drawn from the +# training data and samples drawn from the generator. In other words, it tries to +# tell the difference between the fake data produced by $g$ and the actual data +# samples we want to do prediction on. The discriminator outputs a probability +# value given by + +# +#
    +# +# $$ +# \begin{equation} +# d(x; \theta^{(d)}) +# \label{_auto2} \tag{2} +# \end{equation} +# $$ + +# indicating the probability that $x$ is a real training example rather than a +# fake sample the generator has generated. The simplest way to formulate the +# learning process in a generative adversarial network is a zero-sum game, in +# which a function + +# +#
    +# +# $$ +# \begin{equation} +# v(\theta^{(g)}, \theta^{(d)}) +# \label{_auto3} \tag{3} +# \end{equation} +# $$ + +# determines the reward for the discriminator, while the generator gets the +# conjugate reward + +# +#
    +# +# $$ +# \begin{equation} +# -v(\theta^{(g)}, \theta^{(d)}) +# \label{_auto4} \tag{4} +# \end{equation} +# $$ + +# During learning both of the networks maximize their own reward function, so that +# the generator gets better and better at tricking the discriminator, while the +# discriminator gets better and better at telling the difference between the fake +# and real data. The generator and discriminator alternate on which one trains at +# one time (i.e. for one epoch). In other words, we keep the generator constant +# and train the discriminator, then we keep the discriminator constant to train +# the generator and repeat. It is this back and forth dynamic which lets GANs +# tackle otherwise intractable generative problems. As the generator improves with +# training, the discriminator's performance gets worse because it cannot easily +# tell the difference between real and fake. If the generator ends up succeeding +# perfectly, the the discriminator will do no better than random guessing i.e. +# 50\%. This progression in the training poses a problem for the convergence +# criteria for GANs. The discriminator feedback gets less meaningful over time, +# if we continue training after this point then the generator is effectively +# training on junk data which can undo the learning up to that point. Therefore, +# we stop training when the discriminator starts outputting $1/2$ everywhere. +# +# At convergence we have + +# +#
    +# +# $$ +# \begin{equation} +# g^* = \underset{g}{\mathrm{argmin}}\hspace{2pt} +# \underset{d}{\mathrm{max}}v(\theta^{(g)}, \theta^{(d)}) +# \label{_auto5} \tag{5} +# \end{equation} +# $$ + +# The default choice for $v$ is + +# +#
    +# +# $$ +# \begin{equation} +# v(\theta^{(g)}, \theta^{(d)}) = \mathbb{E}_{x\sim p_\mathrm{data}}\log d(x) +# + \mathbb{E}_{x\sim p_\mathrm{model}} +# \log (1 - d(x)) +# \label{_auto6} \tag{6} +# \end{equation} +# $$ + +# The main motivation for the design of GANs is that the learning process requires +# neither approximate inference (variational autoencoders for example) nor +# approximation of a partition function. In the case where + +# +#
    +# +# $$ +# \begin{equation} +# \underset{d}{\mathrm{max}}v(\theta^{(g)}, \theta^{(d)}) +# \label{_auto7} \tag{7} +# \end{equation} +# $$ + +# is convex in $\theta^{(g)} then the procedure is guaranteed to converge and is +# asymptotically consistent +# ( [Seth Lloyd on QuGANs](https://arxiv.org/pdf/1804.09139.pdf) ). +# +# This is in +# general not the case and it is possible to get situations where the training +# process never converges because the generator and discriminator chase one +# another around in the parameter space indefinitely. A much deeper discussion on +# the currently open research problem of GAN convergence is available +# [here](https://www.deeplearningbook.org/contents/generative_models.html). To +# anyone interested in learning more about GANs it is a highly recommended read. +# Direct quote: "In this best-performing formulation, the generator aims to +# increase the log probability that the discriminator makes a mistake, rather than +# aiming to decrease the log probability that the discriminator makes the correct +# prediction." [Another interesting read](https://arxiv.org/abs/1701.00160) + +# ## Writing Our First Generative Adversarial Network +# Let us now move on to actually implementing a GAN in tensorflow. We will study +# the performance of our GAN on the MNIST dataset. This code is based on and +# adapted from the +# [google tutorial](https://www.tensorflow.org/tutorials/generative/dcgan) +# +# First we import our libraries + +# In[7]: + + +import os +import time +import numpy as np +import tensorflow as tf +import matplotlib.pyplot as plt +from tensorflow.keras import layers +from tensorflow.keras.utils import plot_model + + +# Next we define our hyperparameters and import our data the usual way + +# In[8]: + + +BUFFER_SIZE = 60000 +BATCH_SIZE = 256 +EPOCHS = 30 + +data = tf.keras.datasets.mnist.load_data() +(train_images, train_labels), (test_images, test_labels) = data +train_images = np.reshape(train_images, (train_images.shape[0], + 28, + 28, + 1)).astype('float32') + +# we normalize between -1 and 1 +train_images = (train_images - 127.5) / 127.5 +training_dataset = tf.data.Dataset.from_tensor_slices( + train_images).shuffle(BUFFER_SIZE).batch(BATCH_SIZE) + + +# ### MNIST and GANs +# +# Let's have a quick look + +# In[9]: + + +plt.imshow(train_images[0], cmap='Greys') +plt.show() + + +# Now we define our two models. This is where the 'magic' happens. There are a +# huge amount of possible formulations for both models. A lot of engineering and +# trial and error can be done here to try to produce better performing models. For +# more advanced GANs this is by far the step where you can 'make or break' a +# model. +# +# We start with the generator. As stated in the introductory text the generator +# $g$ upsamples from a random sample to the shape of what we want to predict. In +# our case we are trying to predict MNIST images ($28\times 28$ pixels). + +# In[10]: + + +def generator_model(): + """ + The generator uses upsampling layers tf.keras.layers.Conv2DTranspose() to + produce an image from a random seed. We start with a Dense layer taking this + random sample as an input and subsequently upsample through multiple + convolutional layers. + """ + + # we define our model + model = tf.keras.Sequential() + + + # adding our input layer. Dense means that every neuron is connected and + # the input shape is the shape of our random noise. The units need to match + # in some sense the upsampling strides to reach our desired output shape. + # we are using 100 random numbers as our seed + model.add(layers.Dense(units=7*7*BATCH_SIZE, + use_bias=False, + input_shape=(100, ))) + # we normalize the output form the Dense layer + model.add(layers.BatchNormalization()) + # and add an activation function to our 'layer'. LeakyReLU avoids vanishing + # gradient problem + model.add(layers.LeakyReLU()) + model.add(layers.Reshape((7, 7, BATCH_SIZE))) + assert model.output_shape == (None, 7, 7, BATCH_SIZE) + # even though we just added four keras layers we think of everything above + # as 'one' layer + + # next we add our upscaling convolutional layers + model.add(layers.Conv2DTranspose(filters=128, + kernel_size=(5, 5), + strides=(1, 1), + padding='same', + use_bias=False)) + model.add(layers.BatchNormalization()) + model.add(layers.LeakyReLU()) + assert model.output_shape == (None, 7, 7, 128) + + model.add(layers.Conv2DTranspose(filters=64, + kernel_size=(5, 5), + strides=(2, 2), + padding='same', + use_bias=False)) + model.add(layers.BatchNormalization()) + model.add(layers.LeakyReLU()) + assert model.output_shape == (None, 14, 14, 64) + + model.add(layers.Conv2DTranspose(filters=1, + kernel_size=(5, 5), + strides=(2, 2), + padding='same', + use_bias=False, + activation='tanh')) + assert model.output_shape == (None, 28, 28, 1) + + return model + + +# And there we have our 'simple' generator model. Now we move on to defining our +# discriminator model $d$, which is a convolutional neural network based image +# classifier. + +# In[11]: + + +def discriminator_model(): + """ + The discriminator is a convolutional neural network based image classifier + """ + + # we define our model + model = tf.keras.Sequential() + model.add(layers.Conv2D(filters=64, + kernel_size=(5, 5), + strides=(2, 2), + padding='same', + input_shape=[28, 28, 1])) + model.add(layers.LeakyReLU()) + # adding a dropout layer as you do in conv-nets + model.add(layers.Dropout(0.3)) + + + model.add(layers.Conv2D(filters=128, + kernel_size=(5, 5), + strides=(2, 2), + padding='same')) + model.add(layers.LeakyReLU()) + # adding a dropout layer as you do in conv-nets + model.add(layers.Dropout(0.3)) + + model.add(layers.Flatten()) + model.add(layers.Dense(1)) + + return model + + +# Let us take a look at our models. + +# In[12]: + + +generator = generator_model() +plot_model(generator, show_shapes=True, rankdir='LR') + + +# In[13]: + + +discriminator = discriminator_model() +plot_model(discriminator, show_shapes=True, rankdir='LR') + + +# Next we need a few helper objects we will use in training + +# In[14]: + + +cross_entropy = tf.keras.losses.BinaryCrossentropy(from_logits=True) +generator_optimizer = tf.keras.optimizers.Adam(1e-4) +discriminator_optimizer = tf.keras.optimizers.Adam(1e-4) + + +# The first object, *cross_entropy* is our loss function and the two others are +# our optimizers. Notice we use the same learning rate for both $g$ and $d$. This +# is because they need to improve their accuracy at approximately equal speeds to +# get convergence (not necessarily exactly equal). Now we define our loss +# functions + +# In[15]: + + +def generator_loss(fake_output): + loss = cross_entropy(tf.ones_like(fake_output), fake_output) + + return loss + + +# In[16]: + + +def discriminator_loss(real_output, fake_output): + real_loss = cross_entropy(tf.ones_like(real_output), real_output) + fake_loss = cross_entropy(tf.zeros_liks(fake_output), fake_output) + total_loss = real_loss + fake_loss + + return total_loss + + +# Next we define a kind of seed to help us compare the learning process over +# multiple training epochs. + +# In[17]: + + +noise_dimension = 100 +n_examples_to_generate = 16 +seed_images = tf.random.normal([n_examples_to_generate, noise_dimension]) + + +# Now we have everything we need to define our training step, which we will apply +# for every step in our training loop. Notice the @tf.function flag signifying +# that the function is tensorflow 'compiled'. Removing this flag doubles the +# computation time. + +# In[18]: + + +@tf.function +def train_step(images): + noise = tf.random.normal([BATCH_SIZE, noise_dimension]) + + with tf.GradientTape() as gen_tape, tf.GradientTape() as disc_tape: + generated_images = generator(noise, training=True) + + real_output = discriminator(images, training=True) + fake_output = discriminator(generated_images, training=True) + + gen_loss = generator_loss(fake_output) + disc_loss = discriminator_loss(real_output, fake_output) + + gradients_of_generator = gen_tape.gradient(gen_loss, + generator.trainable_variables) + gradients_of_discriminator = disc_tape.gradient(disc_loss, + discriminator.trainable_variables) + generator_optimizer.apply_gradients(zip(gradients_of_generator, + generator.trainable_variables)) + discriminator_optimizer.apply_gradients(zip(gradients_of_discriminator, + discriminator.trainable_variables)) + + return gen_loss, disc_loss + + +# Next we define a helper function to produce an output over our training epochs +# to see the predictive progression of our generator model. **Note**: I am including +# this code here, but comment it out in the training loop. + +# In[19]: + + +def generate_and_save_images(model, epoch, test_input): + # we're making inferences here + predictions = model(test_input, training=False) + + fig = plt.figure(figsize=(4, 4)) + + for i in range(predictions.shape[0]): + plt.subplot(4, 4, i+1) + plt.imshow(predictions[i, :, :, 0] * 127.5 + 127.5, cmap='gray') + plt.axis('off') + + plt.savefig(f'./images_from_seed_images/image_at_epoch_{str(epoch).zfill(3)}.png') + plt.close() + #plt.show() + + +# Setting up checkpoints to periodically save our model during training so that +# everything is not lost even if the program were to somehow terminate while +# training. + +# In[20]: + + +# Setting up checkpoints to save model during training +checkpoint_dir = './training_checkpoints' +checkpoint_prefix = os.path.join(checkpoint_dir, 'ckpt') +checkpoint = tf.train.Checkpoint(generator_optimizer=generator_optimizer, + discriminator_optimizer=discriminator_optimizer, + generator=generator, + discriminator=discriminator) + + +# Now we define our training loop + +# In[21]: + + +def train(dataset, epochs): + generator_loss_list = [] + discriminator_loss_list = [] + + for epoch in range(epochs): + start = time.time() + + for image_batch in dataset: + gen_loss, disc_loss = train_step(image_batch) + generator_loss_list.append(gen_loss.numpy()) + discriminator_loss_list.append(disc_loss.numpy()) + + #generate_and_save_images(generator, epoch + 1, seed_images) + + if (epoch + 1) % 15 == 0: + checkpoint.save(file_prefix=checkpoint_prefix) + + print(f'Time for epoch {epoch} is {time.time() - start}') + + #generate_and_save_images(generator, epochs, seed_images) + + loss_file = './data/lossfile.txt' + with open(loss_file, 'w') as outfile: + outfile.write(str(generator_loss_list)) + outfile.write('\n') + outfile.write('\n') + outfile.write(str(discriminator_loss_list)) + outfile.write('\n') + outfile.write('\n') + + +# To train simply call this function. **Warning**: this might take a long time so +# there is a folder of a pretrained network already included in the repository. + +# In[22]: + + +train(train_dataset, EPOCHS) + + +# Now to avoid having to train and everything, which will take a while depending +# on your computer setup we now load in the model which produced the above gif. + +# In[23]: + + +checkpoint.restore(tf.train.latest_checkpoint(checkpoint_dir)) +restored_generator = checkpoint.generator +restored_discriminator = checkpoint.discriminator + +print(restored_generator) +print(restored_discriminator) + + +# We have successfully loaded in our latest model. Let us now play around a bit +# and see what kind of things we can learn about this model. Our generator takes +# an array of 100 numbers. One idea can be to try to systematically change our +# input. Let us try and see what we get + +# In[24]: + + +def generate_latent_points(number=100, scale_means=1, scale_stds=1): + latent_dim = 100 + means = scale_means * tf.linspace(-1, 1, num=latent_dim) + stds = scale_stds * tf.linspace(-1, 1, num=latent_dim) + latent_space_value_range = tf.random.normal([number, latent_dim], + means, + stds, + dtype=tf.float64) + + return latent_space_value_range + +def generate_images(latent_points): + # notice we set training to false because we are making inferences + generated_images = restored_generator.predict(latent_points) + + return generated_images + + +# In[25]: + + +def plot_result(generated_images, number=100): + # obviously this assumes sqrt number is an int + fig, axs = plt.subplots(int(np.sqrt(number)), int(np.sqrt(number)), + figsize=(10, 10)) + + for i in range(int(np.sqrt(number))): + for j in range(int(np.sqrt(number))): + axs[i, j].imshow(generated_images[i*j], cmap='Greys') + axs[i, j].axis('off') + + plt.show() + + +# In[26]: + + +generated_images = generate_images(generate_latent_points()) +plot_result(generated_images) + + +# We see that the generator generates images that look like MNIST +# numbers: $1, 4, 7, 9$. Let's try to tweak it a bit more to see if we are able +# to generate a similar plot where we generate every MNIST number. Let us now try +# to 'move' a bit around in the latent space. **Note**: decrease the plot number if +# these following cells take too long to run on your computer. + +# In[27]: + + +plot_number = 225 + +generated_images = generate_images(generate_latent_points(number=plot_number, + scale_means=5, + scale_stds=1)) +plot_result(generated_images, number=plot_number) + +generated_images = generate_images(generate_latent_points(number=plot_number, + scale_means=-5, + scale_stds=1)) +plot_result(generated_images, number=plot_number) + +generated_images = generate_images(generate_latent_points(number=plot_number, + scale_means=1, + scale_stds=5)) +plot_result(generated_images, number=plot_number) + + +# Again, we have found something interesting. *Moving* around using our means +# takes us from digit to digit, while *moving* around using our standard +# deviations seem to increase the number of different digits! In the last image +# above, we can barely make out every MNIST digit. Let us make on last plot using +# this information by upping the standard deviation of our Gaussian noises. + +# In[28]: + + +plot_number = 400 +generated_images = generate_images(generate_latent_points(number=plot_number, + scale_means=1, + scale_stds=10)) +plot_result(generated_images, number=plot_number) + + +# A pretty cool result! We see that our generator indeed has learned a +# distribution which qualitatively looks a whole lot like the MNIST dataset. +# +# Another interesting way to explore the latent space of our generator model is by +# interpolating between the MNIST digits. This section is largely based on +# [this excellent blogpost](https://machinelearningmastery.com/how-to-interpolate-and-perform-vector-arithmetic-with-faces-using-a-generative-adversarial-network/) +# by Jason Brownlee. +# +# So let us start by defining a function to interpolate between two points in the +# latent space. + +# In[29]: + + +def interpolation(point_1, point_2, n_steps=10): + ratios = np.linspace(0, 1, num=n_steps) + vectors = [] + for i, ratio in enumerate(ratios): + vectors.append(((1.0 - ratio) * point_1 + ratio * point_2)) + + return tf.stack(vectors) + + +# Now we have all we need to do our interpolation analysis. + +# In[30]: + + +plot_number = 100 +latent_points = generate_latent_points(number=plot_number) +results = None +for i in range(0, 2*np.sqrt(plot_number), 2): + interpolated = interpolation(latent_points[i], latent_points[i+1]) + generated_images = generate_images(interpolated) + + if results is None: + results = generated_images + else: + results = tf.stack((results, generated_images)) + +plot_results(results, plot_number) + diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter13_3_0.png b/doc/LectureNotes/_build/jupyter_execute/chapter13_3_0.png new file mode 100644 index 0000000000000000000000000000000000000000..2619cfba803df616e52c284fe277e5d50ec2f1cc GIT binary patch literal 19939 zcmZ6yWl$Vl)HOP|1q%*Af(;TvaEIV-!QF$qyCt|wa0u@14jEj7yA19O!3MwcykFh> z)^~sO^mJF(>0PH!@4ePut0PsEq%qM+(E$JermT#_Hvj<65B495iVXX`tT(8G?fBdz zwcXSlzq@&wxL5!bP28O99Np}!O{qLATwJXk9XLL7e&+Z@W##7PoAmxSht336|_U-z6*g*C1IAp@O`#3Y-0KR~U?=dX1 z1jmTRSqHuu4Y8h8WRYbl5pv_>P{ z2tP$eZ1`--F(llA6U}p}?5QC(oP5pw+iOhv+i%2_Fyt`2S18--O|QmrP1FD~ERW-KV8^^F1OVrVdUo*MR|`zQb`IUzoIYM8`JS8}9>tTJP|HQ_fGY-1 z{-y*dM#W7@cZ{|^`{l^8e!9Urbo2tW00=7h6T-P9VT!^CQDm^gH%Pmi<~zNDZS58< zl!AoU?-O;)w6U}n28H#w&VTt!UmcxY_U{SFF#5(b!1re0Lol2+ALuryg-vIPGCe~Ma!mJpu2(4=fH!?<@>?~)$8fiobanLEj_1|IU|x6 zb!r@q(HRlS_m&?j%ZKycT1iC$9_5Xu@s47&j_E~!ufnuBakc2gEST@gs>(r0EGUVv z80s#n{cFv%%WF86AWN6RA&%UG&0Y)H9{aA3Wfbpwq503KuiaL*9hJD~C#hI9nc**D z=ze%j^rYR$c;GTl%ouP(Y44v3a#i2Arbuxok1Y?Y?7UrDAy9-NXlV^H*;PVY4*oMN zGCV_iotQpAam%Rtl|hl8w8G}}YAUHA-CD|4N{J9U+FM(08-eBvfG&`2fj6-=A5|Cr zs%hBPfR|*0Sw9S=?`Pt%d|Qq#6qYbV+7M*!+zpY@D<5GI+oT z)#qNk3FIg#5!+jb^~Zy6g2JAm)n;;v^W;8cuRnmjGSJV8{5u(q9y|c!bawZ#Mu}E0p|_*=>6z0D@A?+jZv(R1qtw5h}E)|!~JG$7sZ2RRgs(TI(MYd=`APp>+wJoP<(<9tPFs* z<7T?_PLFuM#K)i$eW#|OoIXYY6-I+(gMyrR7HGcBTB9pz@h+^^-h66a&-cc98IJ> zd6x>Xw`6-VyRt;C(?#C~I;Em$X@f6CQ*m1LbM}R@W~iHTq^{e;x**+c-D|6ib@7nU z0bjS&PP9^A_b2XE2tM?~JTlMR)Hzn?i5lk<1^2uPnywObcVgMHd#wa_?e3{lT}WYo z%kRFB+Iq%WI;1a+G{EL>ZOOjkFM(UB1kxUk`Gb9HsP0EcX%NbL8V9+FQB}gUHs|*% z-Vv7rPGt?;2QTz&^k#^{xb7bdyd|2#A~bPlssCB>4xf6f!6`=rll=wv z_6j)Wtd|AKl^U+XZzT(45ZbHzUPWldk?eZbC18~b6M(8+r{=qs4-S6otzU+KU0kcdUV z5u$PPl38g~yY2n<@pM3h|J(QL0J{~>dAIh)jYt9#_7&mP`^o@tDn;eXmD$+c{n%+H zz&fvXE4tth{EfBI2n+KD`$nSGELuw#WoSec+&j2F3?1I2h+nuf3e+c#E;0XGb~LAP zXaoctXEmGI*1CbSVV79UWZeNKzi=CFyYs&{eQQ5?kmS9uN3yO^^jdZ=Lzm|K4AKqm zbvLrG3of<#fd(t2$lLaS-tRHTbK)#;e`DFWQTuiQn;iUDW_J8$RX^A?zp1O!R`|q? zPDVN@@>gI6&d~d!aTj53k#mJ``b7%4@Xi2Q&ub+{jfCCZKCG;rv+d;bwcV6^o%vR0 zxBY9EBz{s3G^`MVJ=pz^OlL-BG2Mk*)5HQ3!~z9=xo}kR5vx(WtwuO8&k%B-<0E|v zO$U)552trt<+@fgEmf&sTWvvUgvh@5PT%n5(li5A6uE6ZH3nLa72~B0l?`#h#o~Zm zl)5msyE4&?J2^g_nJ@cYPhGis_=5Q=TYXS^^6=qBTj-(4D_@Pjb3LfgoKh3M`&-xn zK@@jyXxdMa7|BV3_hxa;MOWH z99G-w^A^y!Y_=xHBe!cjwTxdbqGH&O%{gx|W0+G&%$`$Qu)=$0vDbx=yoWX#-Nxbc zhPRtv3mXe?$zNgwa;=xyj;)LmG~rLaT2#m2+Xk(EBG7R6vY*jhzgwJ58I7!xH=QB| z2`d_ZF3eXKy54%sij@sHIU$3*IJ`O;QI0dPN_Po2SZvLtXE113@3X^I-)AJAIq#r9 z4c}{yX-tLDayvDK=v&WTMZf8FvGlhtTX9t<9$czR$&&*Udna|no#zNmLAmJT4efmJ zn-LvkPODo7!-QQUT<@KmNMA(`tA;xa2xMR0l(EDWr*#?y?jHJPNZZl1M7Pd$xu=vf zvPbxXYk837c_3U5R$Dg?vx)CT5-(dQ5CJJ#w9=sYt;qF=^b7B*5(*-r2PD`EO{p^& z;)_ZyJY80vlAl_6zVKWlCs$kR5WmQaUE=&m+Cb7>UMacTmD2sLQE9u?E;|jf@waHM z&ko4PR#?*0KU?^*Qe`!Tf%N)y`c03Z5%cs((DAnPdXDYWh6j#(EBSywC4HD@k_qe1 z5fOgW7oL;LQhg_4$*oh;!^5J9tWQsf0mvxNz4=>+dvpy0JgM|^8Bq&=m#*IS;4kfq4#b(ic)T|b;Xxjes~6L|T` zW?WN-|4?2!>nC?)jrRu@EZgWT&_SY(jp&}GeuQDCw{N2J`7!*>ayx6Y=9ly(JE&TT zb>zMr&N;j#2*~~2@MeX%2@P{xY{=T`XVxhN^GqrG4g2?)usZm=T7PRtCR~t_aDT%7 zMYkrBGqgWyexnmljqiCqu10U!dakUXpUd1QA70;PTh-HEOc{_(3&&bud!p`hF7pVR zh^q-p_P6S>oXaYiQSSz&?bD~LP>w~X@j-f5q!sQ)f8NS)1_yB-mtK5}*+?|Mjg2(! zXI|NtOz+Fa@v-;7Q48DByed5Cqf%+CZ1w(bYG)s@yl%qIP#8Akr~KW~z27{}h}1=z z4@W2&aSW1Hi*iZrsxvCalC-PR5tpCHA7#tVSu@T8<^8WBPl!D=OC*B^fyd*Me#uHL z^46j_s%LcRj=#atjo@oVey&?gFW8Loud9Wi7 zZw_9A{w7LDRaTSx>@l%+Lucmli8;%UHp~r~x@c`L0?fqzEiJ8S$ZCPr>(0NZiXya^ zFHU3g?YwSPgjuC=o;RJal4N|Ldn|RFx>D)6Yixn}nfdrV>Pn(JX%AlH^ct5|{H^@KGN;dTw$_`TeCA3^N{|z!*Y8Cje|Q2hVkfyoDp6L_`?z;cpByk}w(*AZ5jxYg7JdVCfU5hb`Y z$ke(@65`#tODsx{S_s2MG~YHW-7}hfTD|*mep50^-q4dzIsQOY<|q%<9C_(YBitRc zBwA6bO0v#=7_lsQnj;tz$bw%c>0W1_lrP2Vb0jhIhl>F?ap2z0rSf5aW!>M31?0YW zGSuSL{WHOK9P#0i)I0tMZedsd*CxdWdh$TBuzNr*WH|n6vgD;FmnWjgls|M0r9lRS z{ik!XvClH*+&qRwRagt4jqp3UW*HGsTgPC8U?nR--j%zCsq{#MAm8vb_JjUTyL8CdUEFO~uKIVX8!Q#jN|IBO^|fxW#QJ4PFED&;%o$ zGR(aH0TOjGt(AB|_L-L!G69T5h|&%jA20(q`FqkrD?5tbUY~~AtTCLYLHJL$g-v`{cNY$yoG?uGzY#QOy3D$r=W(U zHT=*Yi}5ZPRF+-4nVfPnlJGj_#e`ZEIm-rLV%t>FR%?-7c4a&>=tBk$+n`29PWMRQ zh99VY)MMi6%e_OyzTs*`@4gaE-cJEMAaR4lSyRN!CNZh_1O$;~hC5f}zqZs=S-P+U zd)9oY=niF(JP6Oe44LW%BJ5&p35F-P;9?MnSSup!u3cpj5(Aa7nVT79kQ-mN+2(n^ ztiR^98Tk-zi1J)k?m6)Il$N*@vHp<{2MA&tW15|*hMH0W+H|iLN#M3|%wi zV7UL#-_m;ZS;DvQCBoo6?akOd_2d9UXu7OkX}xC*MN^4R8JMzCHr8_%MosYu1AkhZ z+y0!1NLoUq+t7XZhJs7_$_Su`<4unE#q>6WJ7Z3rS(TCjXG{}>3CKlqN)Ec_KTr(S zo<9~7$gZxa9zK8532UUt$m>Bz3o2!s)~?6%?CxYYS)0$WH48o^B@VQ@oDXxn4Uy56 zuvDp$4QS(f<`TeTsd2x>ER$8GYM0Eq1OBKRp=Tv8l;6L7IhA(5FUHE%AQ@UdtkeE9 zRPb&4d+nhd0gX@7&=T2;=j5C%^zDKB8m|b_l$vE^^oMor_mm05of5WIN-wHa8^8UF zr~beo%jz%Bb&K=b$AS(l;G)M93CnXfGIisZ|qG zrDOdR7~Q&a)jk@T;eBMl_I9flxEM)?{_OM#3buwyWybQ4+TiPoHihM>vxc4{8sCF$ z1n-W0q=(1xU8sLpyY4LgVsgd8Ij3CZELeTJ35)s6(Qe-$eI zso;bPe9M5{Pi{XS)AF>IZQg6fr(%j&J4RSwn!T%K-O2iL?SdLV^(uVV%`OR_$FRCL ziO1;|rmS^2G;5Ed_AT7a)NWRGbFo3Tht++gXN8fBb{sR1wr4Tn>im~EYmR#-)8BH9 z-56&)L0yA1oV+3Qg)k#kjp6efC7?-84^<5P%%21wmxD2bFpLrUH-VV}O&yRjyt(9$ z?Cx!}K4v3(*=5bGJ|_@!F<_hbhwI1U4u zt(^*(CI+>~v-H78|JCBO^rISF|4r{bo)&AV-j;rpQFegetVb!M{l=#*bY`XZ9c|dRekWu>!4n^kZbUY?NzJ;PM z+Q{zUVy-v)<%7xh_&(2XzrGcMv#K4`6=?#(QL)ek!C>{EP8}}-!aMTvA-(9(y*pR(o$wb@Z>( zL%cjL_${Wp}lY#XyHF9St-SIq8=%1?I%DE^m+vbOocj znY*hw%-VL%%fI3Hu7RIaWrC+gw^m+eA(QHU=U;sH@5EoTMZQLSIo2jvYUSRwLr4Oi zbHKg0^RlHv6!;6Ie@T%BXp1pJ9t|-jeGsIF|JA=)#P-!X{f?#0a$C=94IDlQd*VJ9 zvT0L(!lCfkc1|pZ956k{6`S4sS)eHCDj>aH)IkZA=kZZoiKKG3oplbG85j7(?MJ~v z)`<`O2D%^Gq?w{Nr1w7d^4iT5;tj8iF%nx1|DxfnG%NcV7!$JlQ;Tr_HemK$-Mc`c ztCiZTH$(kw=S^BA#2&rmIJ}!-+Z3YitySL!8|i~Mb8q$n=iJV8g<1Jwnoev1gOX2E z^26t$YNZ*IE)D67R?7q_UC+%*Ya1s>`L(0{a<3z@zA2O`ds{QKEdAZsj}_hv5XmR> zqr<)HRLoVIxV*de<>V5aO|y%ZRvA|Ec;05bs2h;ysiuw^Q7y;xP$r`w_pqTLX^re~ zxn2pVq$RmdU&wsA^ZU-ly=LYwMK0fX_1%fy>EWS&G-#}aBK~z_s%_^f%MkZ_b`hS6 zm(S46a9U~Wpe0?0TLc)9Kx3ut?)0&ZCu(@o#vv|uCwaav4a~)K&TldAE_U~a7&GLgGKByBPPcIHpZlC9x zW9(my=aBWImlm?WU+|ny@0hv#uqO;U*Eln{vAee+4bagmiGq+jy3{B;2?uZ2EAHp# z1;;B`PISIsGuWBNDBNyMQ;Nl8;T;*LvPlU@%)^uI-~|?n<%)q@wn+0S*?1?v6S{e6 z0$S&U16Cp8l=6oiX>#OmQd^r{lA<2qm6CInQg75yyV(_QhRjm8dz04zFPbboEy45k z@;dj`**gXPAHR`JRE)Hdyc3H^`7`dlp}X#~YySjqyeS@WLyvGJI>3gp@>y~75Ve@i z!O3XuoxA=Sn_G7{La1h$xF@sMRd3E}Vl^jC_sVg4aNiOIa3s2J{sTG^Ut*E1Ys2iX za4SsxKxTivwWQCyX}br6_ymO8o`-i=hLi{rbZmja5qCJao|@4SO27i~O#F!Z2;N$w zBSnS>iYD^b2US}T|Mf-C(X@H?p zL)fLeXtGsf$fgACsyV*IgsBBdJ+y|6c&0EGyE&42tmyiE5D?I1`tAEivok-@!)te znZoL7l(n%rsLzD4*IzCMu)ILS+0#CFO3QoxNS2C*PQ?AbfHbNUffupsVi>~?mPG-nuZ7WojZpm)VC?f$iU|je$>fsTp_dlf>4Lh zcS&qk>Gd<>ND9CM|8=RxKux=wccEh{{qUP2ux-h_iCd?ep0p@N!G_DyX=erD>zv=c z!NjqJF2NFpWG;zp;P34wH}(q8$(_lkWPLzR2V%#hj|I^S)yf5buE=f<0S*w%6+5HBQ46cQ#3{IJA&EK zY)9m{?!c*29sA7pJf;5`^(gQXSWnQTnX@rowg{Wn*pjoMTQr~FP0??+bW^@|CZ-79 zRW9NP;+l*DD-5mB?rb!Du>)n0hCVk^~)C|JP+;)e^fCdpR<9-NzT7X9!RT5kS z<^QAN?0o|;6Og@f0<`J?(gm|ipW++OL>_oX)8_huYCa?N+&Mi`86D$8$6Lq|0bRXz zD7kuVGee|s_pLe$=xf}Khl%FZ;57k9apZKjJMwB=Ql5>PcH8I3XZ4?&?=Cm_!A~zl zm`?85b8o_wJY73}Y{hwP1QteH-h`Pva_6gBA1%#d6q}ac5DOf#7zfW||Mu3OSE28r zB_j{5WB5&4cK2b2;5=GADET${l@@!36Itl^Pp`U1H|yfsFKNJpg?P;ce*TBDV-H~XTI zJ@P70umJXeX8iUy58-nV``G+nqJRewK=IsJ9snCW!aPUlw`kJJSk_*h`j8? zBjXBm>*lZD%(*_by1IXcN8*=CR9kO)2~uJK6a_>v%)@V;iyIfQTs38p^zswL8?X(i zfIP{*YwCp;az78M{Zu<&OpcFpVd@SG+$g(P|EJ0A*Lg|N7+{7^`&px_;!2jMQ@8Z| z^$_DJ>%wvE6QyVDX;$5NRgY@0NK2rv^dYs&Onitf+?_c{`8Jw$4}PmyHoUND>gC+p z>xl>mwAXrKxzso04_Q%0Siet(a9US#)&yV;G9)Jy%MQ1s#W}ZADgLEPce}ZD(N;7> zO<*m_CVBGf{~ZTiIif%dr<0J@S61d9ooO$C-_m)3pFflJD%Y!+Y|JNs4%?hK&mnQw4D)DisW2?z-yj1xJ(wZ(o7w{Ql!&uJX=Wa;JniskcRc_My93fs&1A>|0AGAd(l%VN zX0S`K8*lwN*gYAka%N9+5=;;~cX2HFl@!yH2KUeE)9}tK zT4c26j|?}&4>TK)%$Ku(i*<%44=ajJqK9@|edBFH4BESRES4App`7nss{z~Ef9|PJ z{Ror`m+|Fcx|_Q`UsolIKy@bmpw(5h;S*w2cs(C(6gds5A-{CxsUWM_{XxHRSFNg{ zQqtc#_Tw`lQ`RasoYhTc!H=|ZY3lKlr_)ks+s$7N)>E7hX!7X%-awtq+2nn6&9|7p zDo48+;AZ8eaU3}JU~{nBAFbSUJLHg3%5Cr*RxU#3Y3eKJbQLMvTi?SumFH4N zk_xBTBbT5?XJwJ)FSAXYKnA)ny-Xea1`lU4eFVAQP@eZPYCqYW$FMvx!vUl}NDR-@ z{IQsv;$YkF!u!&Z=FWS5$E}%?xdy2|r4BLUy7juwsut@Gkywc~)0y%bZp;UtMxlX& z;}?J5Z*chIK2~~s7;1S*U9LMs_3Yg+|11a-zD2#fmCoMHOf<E zO>!mLmyvmDjf>Uk)|ZFbzFK9DW6=wz=X>@eL@)+MZ7zC@daiO#cjZ`f0LIcXusQIV zi{iV3L0xdMGU?AWh9+FPzwt8;(vzmtGzvuB&K{cT3k6$3dE0Ek&K~n0P{ZRR<#k!* zKyM2=-H?M=8kKMB{MLCw$r)avL<5II5k$2ws%MQJ^KbEa@BY24f7^DgvjoMX`x#Q( znI*?Pu(@*fy3PiNHWABUBfNE-FFU=|Ij%-_9nZ744)-$w`eF!no_7||j`$P3Rgt(X z9h4AZ%?H`#l1;NsMtUsQi@xn&3K63viu|?q$gIa-$Fo$Ib6+#ME(Vf}N32~pfe z`+xN(ySS4@)p(JYbU#ALZ?4ony!$qlX}E>Wlm|QTp*$CGP{j4+!DV`Lfw6n9?{07&*`}mfB)1?JGWXv;Xv2#BDT^ zx7bqe-Nh{Xs{pYtD}Z~Q9o8v$5?W?m>+WfR0ad3~Q7=OpVl%X*;@M&iv$MkqajWC` z2DYAbmy%-%+hM}kFCDEfL?IeMTzx*p=dF5J+r!HKk+m0sc;vdAL-}KEeXP0va6c2z z$zK5?7>j0Z~3Y|R7n(J zg^lZ63@4fK|Jq~rQ}ITp1Cne_!Nd zB|G()A-&HgtpCx*q7r~uDlAB}Pp|;kA${GrtRCRB za4-h@#N)LIkKqAL`Zfk;>*W(BvzS(yY%IhKN>Kd(tZ>A(4R3;g?vy|tcrUrX-k9}r z6L0`LWY2*)Elf$1LVdUSDs*+n5$B(=Dhak1Yt^tPh>6&#;lZGR_kCievHTpUCEST> z`Rv~lYP2>yS!9G@woYVlT5>l_*fDstk!cGHeK0_SxRNyEgruOiR{)E?28(O=VVcKe z?bQsbJxWkT@Eg_*q5yn3esHv-j1SMNY+dNF1tPk;&1%LBzzhz3om;7cM4wilH>Sjg z>&$IAImIM3>_d{&4OL?`1hCM`DY5Ozn>W}93_S|IefUgOV46(*pWSG${v|U)_q{60 zP&(^O-lkENj?Cow|pIs3HT#+>KBJSJZ( zC7IF}Xu27;jEcG~!t)frNG0}loL-gAY~JXwKml!`&ilkmpY6rAYSoz-CL5ptvTsNH zKGal1`xC{s1X`yus3q~Xzq+0gg3Q!P zwF}BqcX=aFG070E2ZS9vR!c3iVH(Yx#b$0rDyXf=-0m-}^g|*-M zyj!FP9QIxoSZU*(#+WPK^EiEWKKidQ-Lq1EY0=RpSeZg_l2^6*^FGaC7|gW$Gt9_t z`SkaY-}`K;Z+0N%g(8;AJD1uxHg57hHvj`8qw@m1ARI@LEwkQ!3O~bB&h6MMxt{Su z-jr-+S*N)bFhxsUPuNL`(~rfM`D`%4IjZa)^>T33b~P{0qsvllTFWyx@?VsV{_BJm z0LWqPKpRqHKY=%{hgt1vO2Jt{0>go>rtoT$K_?t}rM8VQ1=IFPTMEjk95HfNMk~Uz zBe%_3SC2Y5E`NSl8(^z*ke^|zPbngWY6sO!f&2Si;^>`mxTwzbGQqsm;Jk+?$Jw5@ zg`m%aahK1F)A-g9Vh<)+kH;I5vfst;u&Ky!UZ>LC>wsZfJzPBR|58fd6w6hkny=IS z8pm<^CCtjBkt8J%$LXiBEghdx*a*~I@@XALv=F`)NtQ-;8&?oiQmIKyYwVZ1!aWYL zm8d{`MFG@kcDYLdc=ys?C~zz(J+gwjIs0z zm0~X;+gi>p>VlM;z`orYYboiHt7gYW3Z_lHH+SVm@y9>ad|E^=J${NIzS1-<(%Cn5 zh}9<7dq~@N&BS%E%&>4YbNhXyC#Uv7=sO0izE>p)@`c-j1DKsz12_ON2z78@>4M&X zJ6%$|vCY+`byP$I3+_8RnMc(|dMl`AOb)ZkyLNE%&f~ zDO;8AzXpHYkD^%SMVNVP+%u*k2u_U=t}Fev zmOhui)FAuVPd`}CTRU-4r1$0o!rD?@8Mf)4{&2qMf`4Ec1U~rLj=f{3OzT}f!ntT%8iV@Re6qx(Qh+f%#NCA?UP=ssg5v@dq(^2D4)?f)B$)T%aP{4a9{ZVO_kW z1yFmvptmytYs?jlYujZZAaC$s^g{37UkI0CM|&*WEOGuq4|W_cGIK6ZOvmgMWxRY9 zUD*0QRDjWX@#N(G#{>6n!_5||E5WGt_yhwamKk*epTl{BPtP>7h(4%j6g9QxI|p>V zk~Ge8TNUw_2O0Pfa&c_b5_oC0zE;LQAoC@(=KxTn@7f+fJFS_x077c52`rnrS* zpwDsHQbnNQt>vT7t}wpx18NpmwBOD7_=hc;?L7g1Qxi_+7Y-}()yk+t*K zz_C&1tG$V6!}XALRHw(%qBCp#F8VHpu)s>h-btzo`m_3QddoPSxBwVhP!jfpmsF0p zeXO9rzJJz=7A(#xO%X;;xhixM`QaM=$Pgpke*O>kV9ty z2$Ia&VYPj6TqL7i!N~`sj26+LZ_-V=d|4_&?%A#Pv2;P^>l8{U1;5$3Vf*pzE8NWN znX4cmdf3h(;vthAq7zEWAO(D(6UH@3pkLOV4VXNn63krX=S?NhwO^`{&!@aUUw=KH zsaAZZTWk5tZymm16=oS0`KtK3v1RG+Xdp{AzZh8u#we5NgZL;Sym87aNV?&>tT$e} zQp-LN{|6fmZ*0St9Efw@k4wPrwR2Ap$PW}E0GrH;;=%BqP|n_;B0SdK4eFAZlg8|* zCAWL-A(~GF%xV=KMmgrTe_yyl(n$Y0R94_^8=~q8Z_Yh=Vf&sJ88ysLuFx+ZXn0YW zDq^^>y_~#vbFk9B5hd%NY3zM5Lg(*p;yDO`bL<0V^op>EbD~7~}yav`T<*_`&L><-W|(MZ|(Sy7~1>zU^>SuJF0;hNV~%S5DIu1}W;cn&NmZx(7x zlU=*|0c-RNn-qgf=afZ?vD=c-SQ`B&9!6-b;J0F6Erdv0sZ}E3RV4Prh((sUR|Z*w z`Q)+Jzm*0JL64VviRG0+SR#3#9Y#tz772VI>q*yc^%<02-`hu%xFp60Nd}~VAQt`- zF>SZz98~KUP#-Y}W?X~=1U{MP>}mvwavVoUtPwuN&u^DeYiDyNb|f%q{Cj;=-Ebam z2h!SWC5M=Q9%5;ezFeVgtDn4R)of=RiQS$z+!RWZz!{@G2yOvqwS`62v=oACf*tt) zpH`bFQ@Ms@Kei3;+RXuPiRasq=-(Y2^rLY)rv4ffHhNeuShnPm-&M2FqS)-_`sWh* zq~AuDlic$CUa4}uh=`Jy{HK& zx(rA?8{stMtcGeL&-jvu&mQA&|9MZ>pZdqVbPP=V*Oq0`9q)XpDCjfNcDdhaOA73v zedsj!d;ayea_13yfY?7*)!FLQ&QSEdlf=Q?0LPN~qx%T2&GQZ>TYKoSi|;dQ@iQq_x<1}r5Vq^o}BF-gIR7+@^1@g&CJHh3j7_z`{?1pMPVNH8BHueF)zOz z96zW$o40Lfm`+bn1461S*ahxQk)K>o>WRPB5y@Vu*q-C?8cpwxOawIgU9R5Vp1S~} zB2dVUv`ENe|}v` ztG93G`+!3%A)dBa`(`9b!vqk1xqs41;H z3I}FW7`_1&mDnruRZ2o{d=F;eZc?bH0F*C@TOj+-|T9>FzQzLxXfv$dUjDXmyzj+d}l z1Domg4+#=GREmwHlZ6%g4HHlSvHv9Fc_+wm&k|tLjm&Fd2NS}9E4QeIgG9Pp7~FCn z@fs>X;)Xs54R8Z5VnM7J5C9!l)i(5C7;Kg;Dysu{=50;SIIbgW%y~GSTWUPXtUEsI z@jwn#LmqJeedXOz|G{@yjbyMm^s|&D3AkQlHyPfwPVMT{wxcn%;`e&2NOpobJfI$a zJVL7zjl-YLcvuy!aBx&Bl>jZ)J!y<oTmpg5`I8iEq6mIr>SS@&PhNU{8q^^ z=Qx{QZ<r7Dn=j`MYUV!gRZ;zArBEt#GvY@*lMaP~50Ity%`FH$sb;yRtZpMUza3S#E^^WsK zbDd-Qc#C4VxL>Cq3%B4$pPOO(!B0oXh3A!|i^D{U!*II^A=CoUVb$Y_Tqmv<#O9IC z<{|MQi13vHx0%4n;d3$J)kJ8N6{b=2LcwpC_MQpxpEG>g#1?E~-3VE?;yGRC=aQxP z6J`)ReF{uO%@3FSyicVHr1Gr&MW=^l(}Uzm=T?DZ0y28{n+Vq(rH;Ih08leeNL6qL z@ZcCC#>EuBk=#`#ym&XHoI}-514Q!IW`@A}d~w4-tbP*Uhr_o>`}c@1;|}C!Hqmgz zOER8WG)VQ{73K)k?DITNr%0%t*{8(HX80BI!73{A6!nUk{Ma^ z$w2ShrOWgohE2Fuee%g)$1`**R{9);5X3det^UIq^{LoLV0w@EN>qN>B{{HV#`|>L zTiROIatf{!zg6}!JLE`qO#vu2`r7(%W#&ta($BKcjC#Pdck*#pp9BV2Jp?PfhN~72`sanOy9?%Z;gDauVz;L%d(l zB>Lr-%ED2hs?N;WYrXy*l}SPK5QHCzn$NrWIe%vd5U=i7rFJr8ff*Ef0_uj4?sjBH zdPI=K?sGQn+|+HR)1-YCfpOBXRowUG)M;VB|`92(z>U zBYKA@p9tED_~mfB5IHg)s@VxJ0|q|@$WwpK}F>#>`?Bb1xNmUgp7x6 zwdlaDwvDLco8OT3thRV`8D}r2o&Rzx0Ozgs3UwfHl9u4!8*u`J;-jbh%ciR`NX8?1 zX2*@}@6>sK6K@;GvV2q_Qe{X1C00--4?%pdWp99uALlWmJM@Hbfj}it$78PsPvFrn z>y-RVdG$MevXmRBw3iPPpi;{~|9$CfpeUJ%1k&m1Q`ly&=4P`(3`j^LQP?^gRI^url!mG(tsd;-*qo9Wwg+f;RPIE;x^)E>$$t9m zMR1<(CPA_xf1ou#LP*F={D#+^B^0d+>&dEEe}z04eybQnJpr zbL^t}UUd9%y+*L1EXj@=tSbxz?UGw6q^gaEO{5!dBtfu`0#uYXU~dT-tQ!|4^;K*$y3ZgL%! zV6+AKQl-*n>*jmgcY@`!*0X2@_fe=fOO!=KEA209X6G+vGo}6}9hIgSAL0KmI1?FB z!uXViH=}}km?|Obd5@hZEA0r1FG%H(`m=!TD$e~=b33010+)1e9FwnVcu-|`_X!fo zfYO%?m_qoA-6uhPQp)T>5o9>lO9m&nf7`V(WB^MI;WM=QnG^sn4bx@B*b4B{i5*n8 z-)xWRIQ&+dY@~pNhqFaCl&kS$zv{FB2P{wXDK_-=Fo z#`s0vUrLyJlMdC8CSx}qa|@bYn3B#S6jT~z%UA(Pq&@aXlh(ly>P`&~cTc8nmVc)8=+4MKn4)R*ru;N#1w$F(G^y|1LrI8g3VfKS&c3RObnc_{wl>ylMps# zK4TVk>`F*(pIBTgmQr3m=*J~h{J`mcPhNEK%bK42K0*%(#NW4&p!u;w?S2|ui@O^%kh)$Xy{IH)@x2Zg%y4gP9NvR8rdi+<)=OGI z)al#Os{;!3G8d&Qyw=RJxLqH*f5y7ZG|2k>SyX-G$+D=lIX$Q394MRiNPf=V+hd5b zsWqad72`x2{hmXS9bT?Po*UFSmnKm#8Y2>hb3B`w!NWjE0Yy);2gEdakP|*wJT89i>i<44N=gt9#PeEoO z*pfpxId1jUXD+U#>hRiIM8b-AzL*Z(#nnmolDf$%`*C4km)$vq87Uy_TW#6SBbpG< zKViwlmvFF|Uc>8(zNBI1-tdWAy;h`Wo2g?1+d@z#A8{6Lj?>RSNR!`U$378W1T@1s z=3E4Jjf$Ijr#gw18tlKpab@g$Wi8H?R17Yv29zgci4(6E7a#8a2%hsn0rqGn{NY@a z?6COGP%$Fg0Pf@s!~LFVL2tujsCvi)`?4I4QaP02wX2;k@yBkiNFBoG5A(PhA1=$k z6tp}!PG7`kO&w)yjxoGDninJ-hPfqRG03)n*WRi%bXC;A#HypF?L{hqTB3}M-H*`OvyFqRlNF~z~ zl`t0`zu+w*Lkf#XT=l6cV0Li^F;7xQ!}ffk28So^jso$MLRs{-i%cyT_)9G-ohWGP zvo{~^jRTPZ&Qh229p)G?&qL4$pKCC^C-QSbL7Jeoc#8H+ceQB8Ob`tW!if2i^-ShT ziU=?;%f|Q{*1AT=dhe1!!H4@Df%7h|sQ3DRv1_-!d;m5%UOe(<$o*HrFC3MnPfJXt zxTRR5Fi_~E%l5BeUZ=j1-8Iy5`3l$r6pyrpns&Q29Z6$gT=IhM>Om1q4Ac^3YKT3g zcYR~nThU>8WRbtAcu;_r+q5RI4q2G-4R4GdnpqdOV?$y`VMDYlG2f%N~haqiJjZhaizgHduF znOw^Kp29FLgWTqc#+^h($SoPS5OSSFMs6LK2&pDTL{#Lw#1xGhA;J(L8Zs&qoeV1P z(0G-ydN;FO&Y zts1l+XlJs1n>&B4JeXsSJr&9T$on?RTiq8H&h3P4;|pYV*~5fe_$(U0es-X?8eGf& z=FuwkYwqqWX4bt*C8Xzj&{eBFcXQ+E*ruyBZ-m-5J_P(y4vKq{uMXz4Y4M1XTZslU z0<=*d+R@DJC>s$*d%<#2aN46`G9ybix!Jcew7Yb#y7YC{mD8Kf#PNM+B3*VQn$}RY zLX=eQ2%%CizFxfb)q2ksi|hdV!SY%F5I<*9(WQb}qwLf^ey(fZ9!B2+V=}r!jPo7m zf<~L#M-x5_?~3;A40pL~*fc^v-|C}}66eg^Q8>4>qTPEl4$b*2;b)96UrQ*r!14O* zLM7Qk2Bp%M|JlX0R*yajQJTd4J{E^fiv0wl&TBEBB*nPE)MU#Lyx3Trk?nUp*Ve(Ecmu$@Kyk>6roKuFrsiW#X{3x5AHmTC4UF0$p zruIVEx7Bk05%yx`<^&7;aQjt<=Z@Hg5+diy&Ni3n@jz&G1muf<82#GG&1V?j%1}f8E`$dLw#wy=?un{C;VLt=Jd3%${rJ~L^*CnYq z;1+KZJ`%Ngkel6Agpcr@?-II?o@oo<__MEOz|#X4*D95GIeZ!0rFxc#ej~xZCq6zp zeB5=^zp_h)=k9wC44UczMIRv50Zne8z}h~Iqm3GZ&!DY#JH->+htUn+<0kJ_owm^I zlPzfz^MrFBS_`RRp`~#CnX}|h)RGoP7Xq?lO~SD_<;L#kc%%0-^4DHhCCRgPOE^>* zF}`BrlDs-f4-|aeLRf5o^5 zoGwxkw#Rd*x^xZqvetsR-9~_7$$~5BD&UJUi&~L6Y533Tk9A9I$M{`{miEvXPKyL(+y!&bx6dJlVfUwq5C=(*ffe!R2czv`*E1 zEwcjmHhMPFWs* zEdfcE&PvVk#Y3r(v+Qi@#Gba8&WObIvNr&-=E*_ASLK1hi$@A_hvqN9M+4*8Q&m>; z4&QE#jiy?Gy0W?1iC=TI1G<7+1K!L2Ln?XUonOPZiibO!Pak}(eqfw3f2Q|Gz1N8I z)Q$KBCDY)?6~p}Y$aJ0;F|Ho11JfTyE z{n6aJ!#B_%bF+Hcr1ZL><^&;_li#3VZv?xd0dr|;GPa`J9Ujve%u%Ve{!IdWqpKyoR(-qR{l9+6xb1#|ejsk6 zWI9MWgB?1k+Z)7c+I_LA*67$vIP%z4U?xp}R~$O4iM!M9^1$^e0k`TkD$5O@-{7f| zQ?-Q4o%kIV#`NC}({~s(g=DX6i=i@=PYCq*k7KW>!i90g2+mGYJGh9U*$C2ekZebQ zBL_Y!Wii`C33pz@mI>@LaDyN0=@u+QrIq7LzsfhIDztb>cU|oEUHzxjTEZ!1lC4kv z<#KW)FyWgv0Y8DA5+zxtU*pV6v>9s$`1qz?yBDTcxb)zQ%gIrNK0!4M*Ah$F@u$Q~ zoqD7Ig^ZIxU+u1t1r*Lz0(_c^qiiQI$v)e%WerWY=sSb-I=^^D%d{R_qpH@u>dNT* zkNqXA_HzaUpejAw4-Aza*)(E_sQHViu08jkB12cTf8HMlOtQrL6pBiMwY7V z%%FX!Iz@^ggjIg`2MYOL@C*9)5eQpG9??kgIGr3-H7K-5{y6b%cyc#Xh=-<70~z#H zCvRO;lM-c9bl^BMIqy{}vE6=wp^^DfP$5{XnW#efGXPdM6cUw~14WCX>YTpYD`pj5 z;M1mAt_Tk(Etr9i2sv4*4){5ELd$|Nf}lDvqvT0Ts9w|$ZIU|uyE^z)llY~|GX+8V zV$=Gea>K~eYa<-A2~Fdf3Dx%{sXZXf$#kAONOF#7h2@@90XaoW;fNOf5QcycmUI)i z1vlf`t-zF=)Xfs`iYKDtol%;7XCAXZAbS`%t;`3SzyKrIvZc@OfbjOQmfzOB+%7#4 zm{wq}@PKd~T8*S%83-|dl%%smfhFK$LYl{x;S+kHp*_w|*(N}n7A)bn4K+h_dx3mi zLXJdWEwBWa>iVmgWjGGHPt0nZaRsiZ8%}eO#|| zG0i*4?P6e0l^DORhY9br5D+X4J=s1d1L%mh>XOC^MarG+U-fip&D3d?HXOSE2#(nbBl(~#EJppRW~4z+;hxko!CHb%ZU8jkC*N>Rhn z8C-FfF#0@HXDDOc%KwL+M$94~xm44LE64_Nzxp%n;r?6oW4u<3j|*=*RoM7zX2s-X z5%l-_7}}(>{*v3pb56g$I5%h9-0y&hkVl1D4VlEMpnmRt-#(`U0F>Sv5cn*DT!eoDR0&P@}NUUs9kUaKjH$XQ;K z0!zeZZwm+s4N048L8=Kluu}xjPhWPUFSNw;q>UcgzN)vx)sRD8S1aq|YLJp|4}|P- zisb6d!Tx^B=-j=p824sAN}(S*B2hU`Z&|^;;r9ruubPB)-_MHt;j@OIo>-{Qqb^FN ze|#N^Bi*KVoB?k^3AfLa<;P8P2C?d&8-#=cmoIRHsSD(Ug|zijgaEHo&BWp=ctlSn z{?a8i0XMEVwDVG-(+ORYfylL6)dyV4sieg literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter13_3_192.png b/doc/LectureNotes/_build/jupyter_execute/chapter13_3_192.png new file mode 100644 index 0000000000000000000000000000000000000000..8e81d8d7844d86a5a99340fcfb76fd34b8871d1d GIT binary patch literal 3541 zcmd56mWzklYP!^TPAX*d(h%ANhEFz2uSY!|hi|l2m5Viy%(TdOF0uuq1 zC9P~SD2oD-B``<}&0}j(RwKk3K@mbgfglJS_1JgX({tXR?H{xJanHTKx!?W1`^~u{ zPIgN2YVrU8C_(lITmXQOjK8m}lg01U?b}N5hdI^Ooq9AXh??LV69_o^QlrD8sNo@g z+v5XcVnd=LjrI5H8}Hu!6_pwtYhhpz@q2)NR7|izSHXc^JjwcK`{S_yprHKrA^_L& zRPl;mKnM1_Cgx4^eg0ECf3jnCv9$4HHP*p%tPD{_0A=6`_vh=%+QlJ`Ho0E(YU!pU zHbtAyY|+LOX_!i^Ig#KfJ}aXff}?gPmBp28oscRk^o+5yddYiz(MOoGd zx%Qa^dGJkZPSFmk=%$G4dJbW!T zH}_o-vNGXe9k13>d-67$`MM|d}g=c6Mc1TUV+sQ+^ zyp4=ph90sT7?UCcN8q!JCs;RTDW(W|=GEMgn)q_r7BrIbG@0O&J8}RiihHaVp;Na0 zv;pL(nhb^B`^(<=ivNxfzawJSl*8N?$P&0%5xuGnr69sGuoU5&zxh%JV!4}0pgO`v zV42CqBA^9*%7TfY9&J#$yIyh@%sHIo2K7m&c|INkx{mcfM`;RX@*3`SC5(-_>&03E zB>~@6Hw$zOuoou)mAlQoRjunDyunJD#+Wf?icaP~W$)y*g0awePk~iqd!`N)W(Z1- zKd$zOU$GTHf<>mal*oCGKJ)rJv<)_)z;}#|jY(!G7_!OcRLeW4SifYgxFkqjdhnB_ zcvJK|_26aDu`NTu1{T0!tJO2oMK@qLsW(i4t^a8^~rdcNB}ra!>oC#+Qwnjnz-_mYR3W{ zS(P=22vC*>w3H``b#1fJEU0 z!7Nkg4qI^ox&yJ(STjm9=XDH(ctd?^I0st@S1Qr_@VrX&X0xjB?rBULo;Uh8%-#3M z5T6INO)Hw1p2I~_`=vc`TcVQ?wyybA;l(WSm&j>o9O=rpqQ^%lJ0Jr%=6CM-*G?sV z9&IH)hLM;p4l(_W2 z)!Pt7yyQf;hx&wnW~J|=LFP88O2@CsP~T<6^{XF*bJYjY#BvxmGxO&Vjl)Jc0ivnl zJ0y#8Fht7c6no3o^1zNU0!|3d*b8O2|1o;)7CLQ$yTuE4&_3=;*cLZ{<%rg7&$ zmy{g~@Fei_gr4x5uheXCWK2PcF2f3nC$7ox<@wFj{qXc^%OcBCafMZ#QO+mPw*<9(B z@@GNlzL8LVO}a{#CjxT-j#NjszI}|2c%3*4rG5R{ABVB_FA26zvP1l(pcMor(9rld z?b)E$4cA)|>Pkaye*Ufc`g+Hu5#&`$mQd(naN}h0Ezsnj!l$=RWn4S!V8Wf*fEKn0~$cHkG3WS=dx!RR#! zz}CQ|g;OPu8Y%$qu_-P6O`;$Fwdj{guYPtk>8{)tW${p- zitu+UbCWLS?rFPDpwB*?-D;UH#0NgIJx|@Ymg|07WDJcu#dIF*;bf*w*&?}!g8& zcVo_`@E$&$L^pv%f^E4-~4h8jc z&(UW&7^h>V7l;CK!WX7qRFP8UJ>@Lv1uw%U$7w!~>6A3va*^!^sMeT%z16VIX5spKV{@?8np5px(Sp*>|FRfQew$8iEt%ta z_h%DI>zNd`Pv9$4iCfL2H#kg4UT;>zjEzXsvL+oP1-NF~($8_wbbA`Cn-pIjw0^Ka!ZbOl!H-k0cY|ng_hb?YZL>KJcJ>enT@S(0%W- z<-;F{U%UTKM2!~RP(eepV^v--4o;wxcIrlt+dp|7ESyJa%8AB2f2;2bM!XQ1a_->k082*a|K(z>Nf*tpVt5Y literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.ipynb index db15b1b80..0e8e35acd 100644 --- a/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.ipynb +++ b/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.ipynb @@ -2,7 +2,21 @@ "cells": [ { "cell_type": "markdown", - "metadata": {}, + "id": "4d72e1df", + "metadata": { + "editable": true + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "id": "fb6e8fcd", + "metadata": { + "editable": true + }, "source": [ "# Optimization, the central part of any Machine Learning algortithm\n", "\n", @@ -15,9 +29,6 @@ "analytically, however this is not possible in general and we must use\n", "some approximative/numerical method to compute the minimum.\n", "\n", - "\n", - "\n", - "\n", "In our discussion on Logistic Regression we studied the \n", "case of\n", "two classes, with $y_i$ either\n", @@ -28,7 +39,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a507b82a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{align*}\n", @@ -40,12 +54,13 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "4071429e", + "metadata": { + "editable": true + }, "source": [ "where $\\boldsymbol{\\beta}$ are the weights we wish to extract from data, in our case $\\beta_0$ and $\\beta_1$. \n", "\n", - "\n", - "\n", "Our compact equations used a definition of a vector $\\boldsymbol{y}$ with $n$\n", "elements $y_i$, an $n\\times p$ matrix $\\boldsymbol{X}$ which contains the\n", "$x_i$ values and a vector $\\boldsymbol{p}$ of fitted probabilities\n", @@ -55,7 +70,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a3cca0b2", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}} = -\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{p}\\right).\n", @@ -64,7 +82,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "12a4ad28", + "metadata": { + "editable": true + }, "source": [ "If we in addition define a diagonal matrix $\\boldsymbol{W}$ with elements \n", "$p(y_i\\vert x_i,\\boldsymbol{\\beta})(1-p(y_i\\vert x_i,\\boldsymbol{\\beta})$, we can obtain a compact expression of the second derivative as" @@ -72,7 +93,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "5d6e7796", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T} = \\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X}.\n", @@ -81,12 +105,13 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b324ae78", + "metadata": { + "editable": true + }, "source": [ "This defines what is called the Hessian matrix.\n", "\n", - "\n", - "\n", "If we can set up these equations, Newton-Raphson's iterative method is normally the method of choice. It requires however that we can compute in an efficient way the matrices that define the first and second derivatives. \n", "\n", "Our iterative scheme is then given by" @@ -94,7 +119,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "7c39cc3f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\frac{\\partial^2 \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}\\partial \\boldsymbol{\\beta}^T}\\right)^{-1}_{\\boldsymbol{\\beta}^{\\mathrm{old}}}\\times \\left(\\frac{\\partial \\mathcal{C}(\\boldsymbol{\\beta})}{\\partial \\boldsymbol{\\beta}}\\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}},\n", @@ -103,14 +131,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "10749f5d", + "metadata": { + "editable": true + }, "source": [ "or in matrix form as" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "3ec50136", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\beta}^{\\mathrm{new}} = \\boldsymbol{\\beta}^{\\mathrm{old}}-\\left(\\boldsymbol{X}^T\\boldsymbol{W}\\boldsymbol{X} \\right)^{-1}\\times \\left(-\\boldsymbol{X}^T(\\boldsymbol{y}-\\boldsymbol{p}) \\right)_{\\boldsymbol{\\beta}^{\\mathrm{old}}}.\n", @@ -119,13 +153,15 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "0145d9eb", + "metadata": { + "editable": true + }, "source": [ "The right-hand side is computed with the old values of $\\beta$. \n", "\n", "If we can compute these matrices, in particular the Hessian, the above is often the easiest method to implement. \n", "\n", - "\n", "Let us quickly remind ourselves how we derive the above method.\n", "\n", "Perhaps the most celebrated of all one-dimensional root-finding\n", @@ -136,8 +172,6 @@ "numerically and/or your function is not of the smooth type, we\n", "normally discourage the use of this method.\n", "\n", - "\n", - "\n", "The Newton-Raphson formula consists geometrically of extending the\n", "tangent line at a current point until it crosses zero, then setting\n", "the next guess to the abscissa of that zero-crossing. The mathematics\n", @@ -147,7 +181,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "43c17534", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -160,7 +197,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "32ef04f0", + "metadata": { + "editable": true + }, "source": [ "For small enough values of the function and for well-behaved\n", "functions, the terms beyond linear are unimportant, hence we obtain" @@ -168,7 +208,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6700017c", + "metadata": { + "editable": true + }, "source": [ "$$\n", "f(x)+(s-x)f'(x)\\approx 0,\n", @@ -177,14 +220,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "8791dec4", + "metadata": { + "editable": true + }, "source": [ "yielding" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "69008872", + "metadata": { + "editable": true + }, "source": [ "$$\n", "s\\approx x-\\frac{f(x)}{f'(x)}.\n", @@ -193,14 +242,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "fce4ef1f", + "metadata": { + "editable": true + }, "source": [ "Having in mind an iterative procedure, it is natural to start iterating with" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "e64aef7e", + "metadata": { + "editable": true + }, "source": [ "$$\n", "x_{n+1}=x_n-\\frac{f(x_n)}{f'(x_n)}.\n", @@ -209,7 +264,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9acecc44", + "metadata": { + "editable": true + }, "source": [ "The above is Newton-Raphson's method. It has a simple geometric\n", "interpretation, namely $x_{n+1}$ is the point where the tangent from\n", @@ -223,16 +281,16 @@ "guess near such a local extremum, so that the first derivative nearly\n", "vanishes, then Newton-Raphson may fail totally\n", "\n", - "\n", - "\n", - "\n", "Newton's method can be generalized to systems of several non-linear equations\n", "and variables. Consider the case with two equations" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "18bc9fd6", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{array}{cc} f_1(x_1,x_2) &=0\\\\\n", @@ -242,14 +300,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "7dcad370", + "metadata": { + "editable": true + }, "source": [ "which we Taylor expand to obtain" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "f1724121", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\begin{array}{cc} 0=f_1(x_1+h_1,x_2+h_2)=&f_1(x_1,x_2)+h_1\n", @@ -264,14 +328,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d04bfa9f", + "metadata": { + "editable": true + }, "source": [ "Defining the Jacobian matrix $\\boldsymbol{J}$ we have" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "a4d3a9e3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{J}=\\left( \\begin{array}{cc}\n", @@ -283,14 +353,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d9d6ff69", + "metadata": { + "editable": true + }, "source": [ "we can rephrase Newton's method as" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "362a86a3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\left(\\begin{array}{c} x_1^{n+1} \\\\ x_2^{n+1} \\end{array} \\right)=\n", @@ -301,14 +377,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "4b8c2937", + "metadata": { + "editable": true + }, "source": [ "where we have defined" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "7580aa9a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\left(\\begin{array}{c} h_1^{n} \\\\ h_2^{n} \\end{array} \\right)=\n", @@ -319,18 +401,26 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a2e3adc3", + "metadata": { + "editable": true + }, "source": [ "We need thus to compute the inverse of the Jacobian matrix and it\n", "is to understand that difficulties may\n", "arise in case $\\boldsymbol{J}$ is nearly singular.\n", "\n", "It is rather straightforward to extend the above scheme to systems of\n", - "more than two non-linear equations. In our case, the Jacobian matrix is given by the Hessian that represents the second derivative of cost function. \n", - "\n", - "\n", - "\n", - "\n", + "more than two non-linear equations. In our case, the Jacobian matrix is given by the Hessian that represents the second derivative of cost function." + ] + }, + { + "cell_type": "markdown", + "id": "83a585c9", + "metadata": { + "editable": true + }, + "source": [ "## Steepest descent\n", "\n", "The basic idea of gradient descent is\n", @@ -343,7 +433,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e127ea11", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k),\n", @@ -352,7 +445,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "bce435bc", + "metadata": { + "editable": true + }, "source": [ "with $\\gamma_k > 0$.\n", "\n", @@ -360,7 +456,6 @@ "F(\\mathbf{x}_k)$. This means that for a sufficiently small $\\gamma_k$\n", "we are always moving towards smaller function values, i.e a minimum.\n", "\n", - "\n", "The previous observation is the basis of the method of steepest\n", "descent, which is also referred to as just gradient descent (GD). One\n", "starts with an initial guess $\\mathbf{x}_0$ for a minimum of $F$ and\n", @@ -369,7 +464,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "2691da5f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathbf{x}_{k+1} = \\mathbf{x}_k - \\gamma_k \\nabla F(\\mathbf{x}_k), \\ \\ k \\geq 0.\n", @@ -378,12 +476,14 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e7ae7322", + "metadata": { + "editable": true + }, "source": [ "The parameter $\\gamma_k$ is often referred to as the step length or\n", "the learning rate within the context of Machine Learning.\n", "\n", - "\n", "Ideally the sequence $\\{\\mathbf{x}_k \\}_{k=0}$ converges to a global\n", "minimum of the function $F$. In general we do not know if we are in a\n", "global or local minimum. In the special case when $F$ is a convex\n", @@ -402,9 +502,6 @@ "Note that the gradient is a function of $\\mathbf{x} =\n", "(x_1,\\cdots,x_n)$ which makes it expensive to compute numerically.\n", "\n", - "\n", - "\n", - "\n", "The gradient descent method \n", "is sensitive to the choice of learning rate $\\gamma_k$. This is due\n", "to the fact that we are only guaranteed that $F(\\mathbf{x}_{k+1}) \\leq\n", @@ -415,10 +512,16 @@ "\n", "Many of these shortcomings can be alleviated by introducing\n", "randomness. One such method is that of Stochastic Gradient Descent\n", - "(SGD), see below.\n", - "\n", - "\n", - "\n", + "(SGD), see below." + ] + }, + { + "cell_type": "markdown", + "id": "a6a44ea7", + "metadata": { + "editable": true + }, + "source": [ "## Convex functions\n", "\n", "Ideally we want our cost/loss function to be convex(concave).\n", @@ -433,11 +536,8 @@ "$\\mathbb{R}$. Examples of convex sets of $\\mathbb{R}^2$ are the\n", "regular polygons (triangles, rectangles, pentagons, etc...).\n", "\n", - "\n", - "\n", "**Convex function**: Let $X \\subset \\mathbb{R}^n$ be a convex set. Assume that the function $f: X \\rightarrow \\mathbb{R}$ is continuous, then $f$ is said to be convex if $$f(tx_1 + (1-t)x_2) \\leq tf(x_1) + (1-t)f(x_2) $$ for all $x_1, x_2 \\in X$ and for all $t \\in [0,1]$. If $\\leq$ is replaced with a strict inequaltiy in the definition, we demand $x_1 \\neq x_2$ and $t\\in(0,1)$ then $f$ is said to be strictly convex. For a single variable function, convexity means that if you draw a straight line connecting $f(x_1)$ and $f(x_2)$, the value of the function on the interval $[x_1,x_2]$ is always below the line as illustrated below.\n", "\n", - "\n", "In the following we state first and second-order conditions which\n", "ensures convexity of a function $f$. We write $D_f$ to denote the\n", "domain of $f$, i.e the subset of $R^n$ where $f$ is defined. For more\n", @@ -454,8 +554,6 @@ "make a drawing of $f(x) = x^2+1$ and draw the tangent line to $f(x)$ and\n", "note that it is always below the graph.\n", "\n", - "\n", - "\n", "**Second order condition.**\n", "\n", "Assume that $f$ is twice\n", @@ -465,12 +563,8 @@ "single-variable function this reduces to $f''(x) \\geq 0$. Geometrically this means that $f$ has nonnegative curvature\n", "everywhere.\n", "\n", - "\n", - "\n", "This condition is particularly useful since it gives us an procedure for determining if the function under consideration is convex, apart from using the definition.\n", "\n", - "\n", - "\n", "The next result is of great importance to us and the reason why we are\n", "going on about convex functions. In machine learning we frequently\n", "have to minimize a loss/cost function in order to find the best\n", @@ -487,11 +581,16 @@ "is minimal, where $f$ is convex and differentiable. Then, any point\n", "$x^*$ that satisfies $\\nabla f(x^*) = 0$ is a global minimum.\n", "\n", - "\n", - "\n", - "This result means that if we know that the cost/loss function is convex and we are able to find a minimum, we are guaranteed that it is a global minimum.\n", - "\n", - "\n", + "This result means that if we know that the cost/loss function is convex and we are able to find a minimum, we are guaranteed that it is a global minimum." + ] + }, + { + "cell_type": "markdown", + "id": "809f8f01", + "metadata": { + "editable": true + }, + "source": [ "### Some simple problems\n", "\n", "1. Show that $f(x)=x^2$ is convex for $x \\in \\mathbb{R}$ using the definition of convexity. Hint: If you re-write the definition, $f$ is convex if the following holds for all $x,y \\in D_f$ and any $\\lambda \\in [0,1]$ $\\lambda f(x)+(1-\\lambda)f(y)-f(\\lambda x + (1-\\lambda) y ) \\geq 0$.\n", @@ -502,7 +601,6 @@ "\n", " * $g(x) = -\\ln(x)$ is convex for $x \\in (0,\\infty)$.\n", "\n", - "\n", "3. Let $f(x) = x^2$ and $g(x) = e^x$. Show that $f(g(x))$ and $g(f(x))$ is convex for $x \\in \\mathbb{R}$. Also show that if $f(x)$ is any convex function than $h(x) = e^{f(x)}$ is convex.\n", "\n", "4. A norm is any function that satisfy the following properties\n", @@ -513,13 +611,18 @@ "\n", " * $f(x) \\leq 0$ for all $x \\in \\mathbb{R}^n$ with equality if and only if $x = 0$\n", "\n", - "\n", - "Using the definition of convexity, try to show that a function satisfying the properties above is convex (the third condition is not needed to show this).\n", - "\n", - "\n", + "Using the definition of convexity, try to show that a function satisfying the properties above is convex (the third condition is not needed to show this)." + ] + }, + { + "cell_type": "markdown", + "id": "f3b91277", + "metadata": { + "editable": true + }, + "source": [ "## Standard steepest descent\n", "\n", - "\n", "Before we proceed, we would like to discuss the approach called the\n", "**standard Steepest descent** (different from the above steepest descent discussion), which again leads to us having to be able\n", "to compute a matrix. It belongs to the class of Conjugate Gradient methods (CG).\n", @@ -533,7 +636,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ec752109", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{x} = \\boldsymbol{b}.\n", @@ -542,14 +648,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "eb64c8e7", + "metadata": { + "editable": true + }, "source": [ "In the iterative process we end up with a problem like" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "7e99eb7f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{r}= \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x},\n", @@ -558,20 +670,24 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "3a3f6414", + "metadata": { + "editable": true + }, "source": [ "where $\\boldsymbol{r}$ is the so-called residual or error in the iterative process.\n", "\n", "When we have found the exact solution, $\\boldsymbol{r}=0$.\n", "\n", - "\n", - "\n", "The residual is zero when we reach the minimum of the quadratic equation" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "a88175a4", + "metadata": { + "editable": true + }, "source": [ "$$\n", "P(\\boldsymbol{x})=\\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T\\boldsymbol{b},\n", @@ -580,19 +696,24 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6992cc4f", + "metadata": { + "editable": true + }, "source": [ "with the constraint that the matrix $\\boldsymbol{A}$ is positive definite and\n", "symmetric. This defines also the Hessian and we want it to be positive definite. \n", "\n", - "\n", "We denote the initial guess for $\\boldsymbol{x}$ as $\\boldsymbol{x}_0$. \n", "We can assume without loss of generality that" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "00e22e2b", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{x}_0=0,\n", @@ -601,14 +722,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "faab896d", + "metadata": { + "editable": true + }, "source": [ "or consider the system" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "02cb8061", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n", @@ -617,17 +744,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "fe52c448", + "metadata": { + "editable": true + }, "source": [ "instead.\n", "\n", - "\n", "One can show that the solution $\\boldsymbol{x}$ is also the unique minimizer of the quadratic form" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "f698b7fe", + "metadata": { + "editable": true + }, "source": [ "$$\n", "f(\\boldsymbol{x}) = \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T \\boldsymbol{x} , \\quad \\boldsymbol{x}\\in\\mathbf{R}^n.\n", @@ -636,7 +768,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "022bda7f", + "metadata": { + "editable": true + }, "source": [ "This suggests taking the first basis vector $\\boldsymbol{r}_1$ (see below for definition) \n", "to be the gradient of $f$ at $\\boldsymbol{x}=\\boldsymbol{x}_0$, \n", @@ -645,7 +780,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b64077bc", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n", @@ -654,18 +792,23 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "dec06904", + "metadata": { + "editable": true + }, "source": [ "and \n", "$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$.\n", "\n", - "\n", "We can compute the residual iteratively as" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "b566de75", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n", @@ -674,14 +817,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "2c2d16e7", + "metadata": { + "editable": true + }, "source": [ "which equals" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "6c97f03d", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{r}_k),\n", @@ -690,14 +839,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "2b40818b", + "metadata": { + "editable": true + }, "source": [ "or" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "6619d064", + "metadata": { + "editable": true + }, "source": [ "$$\n", "(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{r}_k,\n", @@ -706,14 +861,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "467c71be", + "metadata": { + "editable": true + }, "source": [ "which gives" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "d58fd1af", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\alpha_k = \\frac{\\boldsymbol{r}_k^T\\boldsymbol{r}_k}{\\boldsymbol{r}_k^T\\boldsymbol{A}\\boldsymbol{r}_k}\n", @@ -722,14 +883,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "38e32957", + "metadata": { + "editable": true + }, "source": [ "leading to the iterative scheme" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "98043fd6", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{x}_{k+1}=\\boldsymbol{x}_k-\\alpha_k\\boldsymbol{r}_{k},\n", @@ -739,6 +906,7 @@ { "cell_type": "code", "execution_count": 1, + "id": "8c7efe84", "metadata": { "collapsed": false, "editable": true @@ -748,14 +916,14 @@ "name": "stderr", "output_type": "stream", "text": [ - "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42573/483257001.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n", + "/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47735/483257001.py:18: MatplotlibDeprecationWarning: Calling gca() with keyword arguments was deprecated in Matplotlib 3.4. Starting two minor releases later, gca() will take no keyword arguments. The gca() function should only be used to get the current axes, or if no axes exist, create new axes with default keyword arguments. To create a new axes with non-default arguments, use plt.axes() or plt.subplot().\n", " ax = fig.gca(projection=\"3d\")\n" ] }, { "data": { "text/plain": [ - "" + "" ] }, "execution_count": 1, @@ -771,7 +939,7 @@ }, "metadata": { "filenames": { - "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_56_2.png" + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_61_2.png" }, "needs_background": "light" }, @@ -805,7 +973,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "3bdeb3c1", + "metadata": { + "editable": true + }, "source": [ "And then as countor plot" ] @@ -813,6 +984,7 @@ { "cell_type": "code", "execution_count": 2, + "id": "e6e460db", "metadata": { "collapsed": false, "editable": true @@ -827,7 +999,7 @@ }, "metadata": { "filenames": { - "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_58_0.png" + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_63_0.png" }, "needs_background": "light" }, @@ -842,7 +1014,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d165add7", + "metadata": { + "editable": true + }, "source": [ "Find guesses" ] @@ -850,6 +1025,7 @@ { "cell_type": "code", "execution_count": 3, + "id": "236615ae", "metadata": { "collapsed": false, "editable": true @@ -862,7 +1038,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "4b90442c", + "metadata": { + "editable": true + }, "source": [ "Run it!" ] @@ -870,6 +1049,7 @@ { "cell_type": "code", "execution_count": 4, + "id": "0346fd1d", "metadata": { "collapsed": false, "editable": true @@ -895,7 +1075,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ecff8b5b", + "metadata": { + "editable": true + }, "source": [ "What happened?" ] @@ -903,6 +1086,7 @@ { "cell_type": "code", "execution_count": 5, + "id": "0d9b7732", "metadata": { "collapsed": false, "editable": true @@ -911,7 +1095,7 @@ { "data": { "text/plain": [ - "[]" + "[]" ] }, "execution_count": 5, @@ -927,7 +1111,7 @@ }, "metadata": { "filenames": { - "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_64_1.png" + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_69_1.png" }, "needs_background": "light" }, @@ -943,7 +1127,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b0f8920b", + "metadata": { + "editable": true + }, "source": [ "## Conjugate gradient method\n", "In the CG method we define so-called conjugate directions and two vectors \n", @@ -954,7 +1141,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "67b215c6", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{s}^T\\boldsymbol{A}\\boldsymbol{t}= 0.\n", @@ -963,7 +1153,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "efc1c192", + "metadata": { + "editable": true + }, "source": [ "The philosophy of the CG method is to perform searches in various conjugate directions\n", "of our vectors $\\boldsymbol{x}_i$ obeying the above criterion, namely" @@ -971,7 +1164,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "eb4e1832", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{x}_i^T\\boldsymbol{A}\\boldsymbol{x}_j= 0.\n", @@ -980,7 +1176,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "775cf999", + "metadata": { + "editable": true + }, "source": [ "Two vectors are conjugate if they are orthogonal with respect to \n", "this inner product. Being conjugate is a symmetric relation: if $\\boldsymbol{s}$ is conjugate to $\\boldsymbol{t}$, then $\\boldsymbol{t}$ is conjugate to $\\boldsymbol{s}$.\n", @@ -990,7 +1189,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "95893950", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{v}_i^T\\boldsymbol{A}\\boldsymbol{v}_j= \\lambda\\boldsymbol{v}_i^T\\boldsymbol{v}_j,\n", @@ -999,7 +1201,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "16bfad5c", + "metadata": { + "editable": true + }, "source": [ "which is zero unless $i=j$. \n", "\n", @@ -1009,7 +1214,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e2577f1c", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{x}_{i+1}=\\boldsymbol{x}_{i}+\\alpha_i\\boldsymbol{p}_{i}.\n", @@ -1018,7 +1226,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e4defaaf", + "metadata": { + "editable": true + }, "source": [ "We assume that $\\boldsymbol{p}_{i}$ is a sequence of $n$ mutually conjugate directions. \n", "Then the $\\boldsymbol{p}_{i}$ form a basis of $R^n$ and we can expand the solution \n", @@ -1027,7 +1238,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b4632612", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{x} = \\sum^{n}_{i=1} \\alpha_i \\boldsymbol{p}_i.\n", @@ -1036,14 +1250,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a0a06bf2", + "metadata": { + "editable": true + }, "source": [ "The coefficients are given by" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "1db7cc6a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathbf{A}\\mathbf{x} = \\sum^{n}_{i=1} \\alpha_i \\mathbf{A} \\mathbf{p}_i = \\mathbf{b}.\n", @@ -1052,14 +1272,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e7aa5384", + "metadata": { + "editable": true + }, "source": [ "Multiplying with $\\boldsymbol{p}_k^T$ from the left gives" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "884580b0", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{x} = \\sum^{n}_{i=1} \\alpha_i\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{p}_i= \\boldsymbol{p}_k^T \\boldsymbol{b},\n", @@ -1068,14 +1294,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "934990e4", + "metadata": { + "editable": true + }, "source": [ "and we can define the coefficients $\\alpha_k$ as" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "8be96384", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\alpha_k = \\frac{\\boldsymbol{p}_k^T \\boldsymbol{b}}{\\boldsymbol{p}_k^T \\boldsymbol{A} \\boldsymbol{p}_k}\n", @@ -1084,7 +1316,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "44f4d8d5", + "metadata": { + "editable": true + }, "source": [ "If we choose the conjugate vectors $\\boldsymbol{p}_k$ carefully, \n", "then we may not need all of them to obtain a good approximation to the solution \n", @@ -1099,7 +1334,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a8739d7d", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{x}_0=0,\n", @@ -1108,14 +1346,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d871e171", + "metadata": { + "editable": true + }, "source": [ "or consider the system" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "7ed84e84", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{z} = \\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_0,\n", @@ -1124,7 +1368,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b690f75b", + "metadata": { + "editable": true + }, "source": [ "instead.\n", "\n", @@ -1133,7 +1380,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "86ce9e8a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "f(\\boldsymbol{x}) = \\frac{1}{2}\\boldsymbol{x}^T\\boldsymbol{A}\\boldsymbol{x} - \\boldsymbol{x}^T \\boldsymbol{x} , \\quad \\boldsymbol{x}\\in\\mathbf{R}^n.\n", @@ -1142,7 +1392,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "7968787f", + "metadata": { + "editable": true + }, "source": [ "This suggests taking the first basis vector $\\boldsymbol{p}_1$ \n", "to be the gradient of $f$ at $\\boldsymbol{x}=\\boldsymbol{x}_0$, \n", @@ -1151,7 +1404,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "0d510b11", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{A}\\boldsymbol{x}_0-\\boldsymbol{b},\n", @@ -1160,7 +1416,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "c7c47a8e", + "metadata": { + "editable": true + }, "source": [ "and \n", "$\\boldsymbol{x}_0=0$ it is equal $-\\boldsymbol{b}$.\n", @@ -1172,7 +1431,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "5dc0e4ac", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{r}_k=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k.\n", @@ -1181,7 +1443,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "0aecb4b3", + "metadata": { + "editable": true + }, "source": [ "Note that $\\boldsymbol{r}_k$ is the negative gradient of $f$ at \n", "$\\boldsymbol{x}=\\boldsymbol{x}_k$, \n", @@ -1194,7 +1459,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f3dfc701", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{p}_{k+1}=\\boldsymbol{r}_k-\\frac{\\boldsymbol{p}_k^T \\boldsymbol{A}\\boldsymbol{r}_k}{\\boldsymbol{p}_k^T\\boldsymbol{A}\\boldsymbol{p}_k} \\boldsymbol{p}_k.\n", @@ -1203,14 +1471,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "12e92892", + "metadata": { + "editable": true + }, "source": [ "We can also compute the residual iteratively as" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "1514b03f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{r}_{k+1}=\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_{k+1},\n", @@ -1219,14 +1493,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "7b09db3d", + "metadata": { + "editable": true + }, "source": [ "which equals" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "4a0638f8", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{b}-\\boldsymbol{A}(\\boldsymbol{x}_k+\\alpha_k\\boldsymbol{p}_k),\n", @@ -1235,14 +1515,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "298f5e46", + "metadata": { + "editable": true + }, "source": [ "or" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "acd35abb", + "metadata": { + "editable": true + }, "source": [ "$$\n", "(\\boldsymbol{b}-\\boldsymbol{A}\\boldsymbol{x}_k)-\\alpha_k\\boldsymbol{A}\\boldsymbol{p}_k,\n", @@ -1251,14 +1537,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "79625f01", + "metadata": { + "editable": true + }, "source": [ "which gives" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "dc5888e2", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{r}_{k+1}=\\boldsymbol{r}_k-\\boldsymbol{A}\\boldsymbol{p}_{k},\n", @@ -1267,7 +1559,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d11b96a9", + "metadata": { + "editable": true + }, "source": [ "## Revisiting our Linear Regression Solvers\n", "\n", @@ -1288,6 +1583,7 @@ { "cell_type": "code", "execution_count": 6, + "id": "cf7c349e", "metadata": { "collapsed": false, "editable": true @@ -1301,7 +1597,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "adf34219", + "metadata": { + "editable": true + }, "source": [ "with $x_i \\in [0,1] $ is chosen randomly using a uniform distribution. Additionally we have a stochastic noise chosen according to a normal distribution $\\cal {N}(0,1)$. \n", "The linear regression model is given by" @@ -1309,7 +1608,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d28eb4e0", + "metadata": { + "editable": true + }, "source": [ "$$\n", "h_\\beta(x) = \\boldsymbol{y} = \\beta_0 + \\beta_1 x,\n", @@ -1318,14 +1620,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "60060fcb", + "metadata": { + "editable": true + }, "source": [ "such that" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "82983f16", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{y}_i = \\beta_0 + \\beta_1 x_i.\n", @@ -1334,7 +1642,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "60fc4bc0", + "metadata": { + "editable": true + }, "source": [ "Let $\\mathbf{y} = (y_1,\\cdots,y_n)^T$, $\\mathbf{\\boldsymbol{y}} = (\\boldsymbol{y}_1,\\cdots,\\boldsymbol{y}_n)^T$ and $\\beta = (\\beta_0, \\beta_1)^T$\n", "\n", @@ -1343,7 +1654,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "0c5dac72", + "metadata": { + "editable": true + }, "source": [ "$$\n", "X \\equiv \\begin{bmatrix}\n", @@ -1356,14 +1670,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "002d8c9b", + "metadata": { + "editable": true + }, "source": [ "The cost/loss/risk function is given by (" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "b91d8b5a", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C(\\beta) = \\frac{1}{n}||X\\beta-\\mathbf{y}||_{2}^{2} = \\frac{1}{n}\\sum_{i=1}^{100}\\left[ (\\beta_0 + \\beta_1 x_i)^2 - 2 y_i (\\beta_0 + \\beta_1 x_i) + y_i^2\\right]\n", @@ -1372,17 +1692,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "d0fc6c20", + "metadata": { + "editable": true + }, "source": [ "and we want to find $\\beta$ such that $C(\\beta)$ is minimized.\n", "\n", - "\n", "Computing $\\partial C(\\beta) / \\partial \\beta_0$ and $\\partial C(\\beta) / \\partial \\beta_1$ we can show that the gradient can be written as" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "3f99dab5", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\nabla_{\\beta} C(\\beta) = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n", @@ -1393,17 +1718,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e1305a22", + "metadata": { + "editable": true + }, "source": [ "where $X$ is the design matrix defined above.\n", "\n", - "\n", "The Hessian matrix of $C(\\beta)$ is given by" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "ef62073f", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{H} \\equiv \\begin{bmatrix}\n", @@ -1415,18 +1745,22 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "dfb78235", + "metadata": { + "editable": true + }, "source": [ "This result implies that $C(\\beta)$ is a convex function since the matrix $X^T X$ always is positive semi-definite.\n", "\n", - "\n", - "\n", "We can now write a program that minimizes $C(\\beta)$ using the gradient descent method with a constant learning rate $\\gamma$ according to" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "56cee86c", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\beta_{k+1} = \\beta_k - \\gamma \\nabla_\\beta C(\\beta_k), \\ k=0,1,\\cdots\n", @@ -1435,7 +1769,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6cc71454", + "metadata": { + "editable": true + }, "source": [ "We can use the expression we computed for the gradient and let use a\n", "$\\beta_0$ be chosen randomly and let $\\gamma = 0.001$. Stop iterating\n", @@ -1444,14 +1781,13 @@ "And finally we can compare our solution for $\\beta$ with the analytic result given by \n", "$\\beta= (X^TX)^{-1} X^T \\mathbf{y}$.\n", "\n", - "\n", - "\n", "Here is our simple example" ] }, { "cell_type": "code", "execution_count": 7, + "id": "90fab6b7", "metadata": { "collapsed": false, "editable": true @@ -1461,29 +1797,23 @@ "name": "stdout", "output_type": "stream", "text": [ - "[0.32903042 4.1484256 ]\n", - "[[4.04621521]\n", - " [3.00415763]]\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ - "[[4.04621521]\n", - " [3.00415763]]\n" + "[0.28001319 4.21265216]\n", + "[[3.96987657]\n", + " [3.02493054]]\n", + "[[3.96987657]\n", + " [3.02493054]]\n" ] }, { "data": { - "image/png": "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\n", + "image/png": "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\n", "text/plain": [ "
    " ] }, "metadata": { "filenames": { - "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_118_2.png" + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_123_1.png" }, "needs_background": "light" }, @@ -1541,7 +1871,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "48ba87fe", + "metadata": { + "editable": true + }, "source": [ "Alternatively, we can use **Scikit-Learn** as done here" ] @@ -1549,6 +1882,7 @@ { "cell_type": "code", "execution_count": 8, + "id": "7522775d", "metadata": { "collapsed": false, "editable": true @@ -1558,9 +1892,9 @@ "name": "stdout", "output_type": "stream", "text": [ - "[[3.97230501]\n", - " [3.14741468]]\n", - "[3.94735055] [3.17084902]\n" + "[[4.00275135]\n", + " [2.99724883]]\n", + "[3.97065296] [3.07656896]\n" ] } ], @@ -1585,14 +1919,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "90552e2f", + "metadata": { + "editable": true + }, "source": [ "We have also discussed Ridge regression where the loss function contains a regularized term given by the $L_2$ norm of $\\beta$," ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "5d7c032c", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C_{\\text{ridge}}(\\beta) = \\frac{1}{n}||X\\beta -\\mathbf{y}||^2 + \\lambda ||\\beta||^2, \\ \\lambda \\geq 0.\n", @@ -1601,14 +1941,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ed86f1ba", + "metadata": { + "editable": true + }, "source": [ "In order to minimize $C_{\\text{ridge}}(\\beta)$ using GD we only have adjust the gradient as follows" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "0386e23c", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\nabla_\\beta C_{\\text{ridge}}(\\beta) = \\frac{2}{n}\\begin{bmatrix} \\sum_{i=1}^{100} \\left(\\beta_0+\\beta_1x_i-y_i\\right) \\\\\n", @@ -1619,14 +1965,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b65523fc", + "metadata": { + "editable": true + }, "source": [ "We can easily extend our program to minimize $C_{\\text{ridge}}(\\beta)$ using gradient descent and compare with the analytical solution given by" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "c62584ee", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\beta_{\\text{ridge}} = \\left(X^T X + \\lambda I_{2 \\times 2} \\right)^{-1} X^T \\mathbf{y}.\n", @@ -1636,6 +1988,7 @@ { "cell_type": "code", "execution_count": 9, + "id": "e8d43667", "metadata": { "collapsed": false, "editable": true @@ -1645,22 +1998,22 @@ "name": "stdout", "output_type": "stream", "text": [ - "[[3.92343595]\n", - " [3.15258907]]\n", - "[[3.815563 ]\n", - " [3.23522201]]\n" + "[[4.1533795 ]\n", + " [2.92819235]]\n", + "[[4.06858699]\n", + " [2.99829953]]\n" ] }, { "data": { - "image/png": "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\n", + "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYwAAAEWCAYAAAB1xKBvAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/MnkTPAAAACXBIWXMAAAsTAAALEwEAmpwYAAAoIUlEQVR4nO3de5gkdX3v8fd3dpfLLCgwu3JZ2Bkv0QSIQRgFL4kkakCE4PGJkXUhaNA9rLngOSSKbIJ42USjJ0o8x0NWRDQzQDwoRjlqxBiiKKCDokLWGHAvbLjtLte9CO7uN39U9U51T1X3r3uquqp6Pq/n6We66/rr6pr61u9a5u6IiIh0MlR2AkREpB4UMEREJIgChoiIBFHAEBGRIAoYIiISRAFDRESCKGDMcWa23sxeGb+/2MyuKCkdJ5vZpjL2PVckf+se1l1pZg+a2TYzG8k7bSn7u9zM/qLNfDez5xSdDmmmgFFhZnaWmd1mZtvN7KH4/dvMzIrYn7v/pbu/ZbbbMbOx+B96fh7pKpuZXWVm7y87HWUxswXA3wC/7e4HuPvWHLa53sx2xgHogfgYH9CY7+7nu/v7ZrsfyZcCRkWZ2YXAZcCHgMOAQ4HzgZcC+2SsM69vCZS55FBgP+Cuble0SNZ15gx3PwA4DngB8K6eUyh9oYBRQWb2dOC9wNvc/Tp3f8IjP3D35e7+ZLzcVWb2f83sy2a2HfhNM3uNmf3AzB43s3vN7NKWbZ9jZhvMbKuZrWqZd6mZTSQ+n2Rm3zGzR83sh2Z2cmLeTWb2PjP7tpk9YWZfM7NF8exvxn8fje8gX5zyHfeP0/+Imf0b8MKW+UeY2efMbLOZrTOzP0nMe5GZTcXf8UEz+5vEvJcl0nyvmb0pnr6vmX3YzDbG61xuZvvH8042s01mdmGck7vfzN4cz1sBLAfeEX+XL2X8Zr9sZjea2cNm9u9m9nvx9GfH045PfK8tjWNpZm82s7XxMfyZmf33xDYb6XpHIl2vNbPTzOyn8XYvbvn9rjOzf4i3930z+7WM9A6Z2UVmdk98LnzWzA5JWe65wL8nfs9vxNNfYmbfM7PH4r8vSaxzk5mtNrNvAzuAZ6WlocHdHwD+iShwNLbRlKszsz+Lv/99ZvYHLWkcMbMvxefD98zs/WZ2c6ffRnrg7npV7AWcCuwC5ndY7irgMaJcxxDRXeDJwK/Gn58PPAi8Nl7+aGAb8BvAvkTFDLuAV8bzLwUm4vdLgK3AafG2XhV/XhzPvwm4B3gusH/8+QPxvDHA26Uf+ADwLeAQ4CjgTmBTPG8IuB24hCg39SzgZ8Ap8fxbgHPi9wcAJ8XvlwJPAMuABcAIcFw876PAF+P9HQh8CfireN7J8XF4b7zeaUQXuoMTx/n9bb7LQuBe4M3AfOB4YAtwTDz/rcBaYJjowvjhxLqvAZ4NGPDyeL/Ht6TrkjhdbwU2A1fH3+EY4OfAsxK/3y+A342X/1NgHbAgnr8+8Vu/HbgVOJLoXPg74JqM79f0e8bH8BHgnPj7Los/jyTOjY1x+uY39t+yzWRajgR+DFzWcm6/P/H/8CBwbHysr47T85x4/rXxa5joHL8XuDnkt9Gry2tT2QnQK+VHgbOBB1qmfQd4FNgJ/EY87SrgMx229VHgI/H7S4BrE/MWAk+RHjDeCfx9y7b+CTg3fn8T8OeJeW8Dvhq/b7rAZKTrZ8Cpic8rmA4YJwIbW5Z/F/Cp+P03gfcAi1KWuT5lXwZsB56dmPZiYF38/uT4uM5PzH+I6UC09+KV8V3eAHyrZdrfAe9OfP5ifFH8EbBvm219AbigJV3z4s8Hxsf1xMTytzN9Q3ApcGti3hBwP/Dr8ef1id96LfCKxLKHEwWbGb9Z6+9JFCi+27LMLcCbEufGezucl+uJbl6eiLf9z8BBifl7jzlwJfHNSPz5ufE6zwHmxel+XmL++5kOGB1/G73CXyqSqqatwCJLVBq7+0vc/aB4XvJ3uze5opmdaGb/EhflPEZU79EoKjoiuby7b4+3l2YUeH1ctPOomT0KvIzowtLwQOL9DqK7/VBNaQE2tOz7iJZ9X0xUlg5wHtFF4ydxEcTp8fSjiHI9rRYT3X3entjeV+PpDVvdfVeP32cUOLElvcuJ6p4aPkF0h/wxj4sUAczs1WZ2a1xc8ihR7mZRYr2t7r47fr8z/vtgYv7OlnQmf989wCaiY52W5usT6V0L7Gb6GLdzBM2/F/HnJWnpaOO17n4gUWD8ZZq/d+v+ss6VxUQ5h+T85PuQ30YCKWBU0y3Ak8CZAcu2Djd8NdHd7FHu/nTgcqI7bIjuNo9qLGhmw0TFNmnuJcphHJR4LXT3D/SQpjRNaSEqTkrue13Lvg9099MA3P0/3H0Z8Azgg8B1ZtYoenh2yr62EF1Yj0ls7+keVbiG6PR97gX+tSW9B7j7SgCLWv98FPgkcGmjrsDM9gU+B3wYODS+Ifgy079XL5K/7xBRcc99GWl+dUua93P3/wzYx31EF+KkpUBy3eBhsN39X4lyFB/OWKTdubKZqNjuyMS05LJtfxvpjgJGBbn7o0RFLh83s981swPiSsrjiIqR2jkQeNjdf25mLwLemJh3HXB6XDG8D1GZfdY5MAGcYWanmNk8M9svroQ9MmP5pM3AHtpXdn4WeJeZHRxv848T874LPG5m77SocnyemR1rZi8EMLOzzWxxfAf9aLzObmASeKWZ/Z6ZzY8rQ4+Ll/sE8BEze0a8jSVmdkrAd4Hojr7dd7kBeK5FDQoWxK8XmtmvxPMvA273qMny/ycK4hDVz+xLfNEzs1cDvx2YpiwnmNnr4tzp24luPG5NWe5yYLWZjQKY2WIzC7lBgSioPdfM3hgf5zcQ1R3cMIt0fxR4VXyOt/os8CYzOzq+yXl3Y0ac+/o8USAeNrNfBn4/sW6n30a6oIBRUe7+18D/BN5BVJ7+IFHZ6zuJ6jOyvA14r5k9QVRn8dnENu8C/pAoF3I/UUVlamc5d7+XKIdzMdEF7V7gzwg4Z9x9B7Aa+HZcDHBSymLvISpaWAd8Dfj7xPq7gTOIWs2sI8ohXAE8PV7kVOAuM9tGdDE+y91/7u4biYp0LgQeBu4AGq2E3gncDdxqZo8DXwee1+m7xD4JHB1/ly+kfN8niC70ZxHdfT9AlPPZN74In0pUNAjRb3q8mS2P1/sTot/oEaLg/sXANGX5R6Jy+0al9Ovc/Rcpy10W7+tr8blyK1HdUUce9cM4neg4byU6R0939y29JtrdNwOfAWZ01nP3rxAFlG8Q/YbfaFnkj4jOjQeIzqNriAJl29+m17TOZeauByiJDAKLmlA/x93PLjstZTKzDwKHufu5Zadl0CiHISK1FvezeL5FXkTUKOL6stM1iAZi6AYRmdMOJCqGOoKo+PZ/ERXNSc5UJCUiIkFUJCUiIkFqVSS1aNEiHxsbKzsZIiK1cvvtt29x98Wdl2yvVgFjbGyMqampspMhIlIrZtbaM78nKpISEZEgChgiIhJEAUNERIIoYIiISBAFDBERCaKAISIiQRQwREQkiAKGiIgEUcAQEZEgChgiIhKk8IBhZlea2UNmdmfKvD81MzezrIe/i4hIRfQjh3EV0SMqm5jZUcCrgI19SIOIiMxS4QHD3b9J9HzlVh8hehawHsghIlIDpdRhmNnvAP/p7j8MWHaFmU2Z2dTmzZv7kDoREUnT94BhZsPAKuCSkOXdfY27j7v7+OLFsx7OXUREelRGDuPZwDOBH5rZeuBI4PtmdlgJaRERkUB9f4CSu/8YeEbjcxw0xt19S7/TIiIi4frRrPYa4BbgeWa2yczOK3qfIiKSv8JzGO6+rMP8saLTICIis6ee3iIiEkQBQ0REgihgiIhIEAUMEREJooAhIiJBFDBERCSIAoaIiARRwBARkSAKGCIiEkQBQ0REgihgiIhIEAUMEREJooAhIiJBFDBERCSIAoaIiARRwBARkSAKGCIiEkQBQ0REgihgiIhIEAUMEREJUnjAMLMrzewhM7szMe1DZvYTM/uRmV1vZgcVnQ4REZmdfuQwrgJObZl2I3Csuz8f+Cnwrj6kQ0REZqHwgOHu3wQebpn2NXffFX+8FTiy6HSIiMjsVKEO4w+Ar2TNNLMVZjZlZlObN2/uY7JERCSp1IBhZquAXcBk1jLuvsbdx919fPHixf1LnIiINJlf1o7N7FzgdOAV7u5lpUNERMKUEjDM7FTgncDL3X1HGWkQEZHu9KNZ7TXALcDzzGyTmZ0H/G/gQOBGM7vDzC4vOh0iIjI7hecw3H1ZyuRPFr1fERHJVxVaSYmISA0oYIiISBAFDBERCaKAISIiQRQwREQkiAKGiIgEUcAQEZEgChgiIhJEAUNEJMTkJIyNwdBQ9Hcyc8zUamy3AKUNPigiUhuTk7BiBeyIh77bsCH6DLB8efW2WxDlMEREOlm1avqi3rBjRzS9yO1WLPehHIaISCcbN3Y3PY/tVjD3oRyGiEgnS5d2Nz2P7RaVq5kFBQwRkU5Wr4bh4eZpw8PR9KK2u2FD+jpZ0/tAAUNEpJPly2HNGhgdBbPo75o1sy8aarfdefPS18ma3gdWp6ejjo+P+9TUVNnJEBEpnln2vC6v22Z2u7uPzzJFymGIiFTS6Gh30/tAAUNEpIqKqjeZBQUMkaqrWFt86ZNG/cbIyPS0/fcvLz2oH4ZItVWwLb702c6d0++3bi319y88h2FmV5rZQ2Z2Z2LaIWZ2o5n9R/z34KLTIVJLVWuLr9xOd2Z7vCr2+/ejSOoq4NSWaRcB/+zuvwT8c/xZRFoV1cO4F43czoYNUSudRm5HQSNdHserSr8/fQgY7v5N4OGWyWcCn47ffxp4bdHpEKmlonoY96Jid7uV1+54heY8qvT7U16l96Hufj9A/PcZWQua2QozmzKzqc2bN/ctgSKVUKWWMhW72628rOPSyGkkcx7nnBP1u2gNHlX6/alBKyl3X+Pu4+4+vnjx4rKTI4OkDuXxRfUw7kXF7nYrL+u4zJs3M+fR6IjXWmzV+P2XLi3/96e8gPGgmR0OEP99qKR0yFxVp/L45cth/XrYsyf6W1brqIrd7eaqiJuHrOO1e3f79XbsgIsvjgKEGY+dvZKHNu6kEqNyuHvhL2AMuDPx+UPARfH7i4C/DtnOCSec4CK5GB11j0JF82t0tOyUVdvERHSMzKK/ExNlp2j2Jibch4ebz4Ph4Xy+W9rxyjr3Eq/dmIP7MiZ8G7NPGzDleVzL89hI2x3ANcD9wC+ATcB5wAhR66j/iP8eErItBQzJjVn6P6tZ2SmrhkEMDFlGRnq/eejlOKUFqJbXOkYd3NcxmsuNTW0CRp4vBQzJjXIY2Yq8466aiYnsC3enm4duj9PChe7gWznYlzHh6xj13XFuIrmNbQz7Mib8hBM8txsbBQyR2ZhLF8VuzaVg2q54qNP37XSc3vAGd/Ad7Ne2BGo6eKTkUnL6LfIKGJVvJSVSiCq1PipatxW6c6n5bLvv1KkyP2Nd37Ahqq/+h2sxnGF2pi4H0dX/al/OmK9nyFMaNVSsoYEChsxdVWl9VKReWoNlNQc95JBi0limrO86MtL5fFiyJHXyBrKHH9+9uzmr0FHFbmwUMEQGWS+9s1evhgULZk5/4olqNjuejaw7+Msum7ms+96mrmbwxk0fYDvN625nmIuZvvvfvr05QAz1csWt0I2NAobIIOuleGn5cnja02ZOf+qpwRsGpNMdfCJA2JBhOEaUNbiG5byVNaxnlD0Y6xll18fXcLUv3xsgWmPRXnXoNJpCj2gVGWRjY1ExVKvR0ehuNcvQUHqZiVl0pzuo4seiNoJCJ3feCccc0+U+WoeshyiyFFjUpEe0ikhnvVaazpVhQJI5CKMpB5Hm619vLmLqOlhArQdxVMAQGWS9VppWrHVObl73uq4CxJVXNgeIV7wihzTUuBWaAobIoOul0jTv1jllldl/9avNAeL6z7cNEBde2Bwg3vzmAtJU49ybAoaIpMurdU4/B3p87LHmAPHqU9sGiFNOaQ4QH/5wTulIBshFi6JXI1iedlptc2+q9BaRYvVa8R7KLLiSep994MknZ7/LttIqtZOGh+Hcc+HLX46KoZYujYJFgc1lVektIvXQ7kFCvRRPmXGE3ddUD9FOMgdReLCA9ErtpB07omBRkb4V3VDAEJH2Zlv/0K5svvG0ube9LXsZM86wLzUFiPs5InPx1oGX+i6k8nrDhtr1wQAFDBFpJ4/6h7QWV0nucPnl09s04132V00B4gbOyF59YhIfHcNtCB8d65y2oivgQyuvi67PKUIeIxj266XRaitiLj0rYa7La+TagAcHNZ4B0ek1Y7vdjDrcj1GKA5530e+RgMlptFpVekt3SuilKiXKu8d3VgU4sAeYl1If0fYS1W2FetEV8A2Tk1FdxsaN04M2Pvxw9pcpuAe9Kr2lHDXupdo3NR0nKFUefQZ27OA2OzEasG/DavZgGQsay5jsrg6i205w/eo0l2ySvGVL9NqzJwpMaWrQBwMUMKRbNe6l2hf97HPQD2n1DwsWwLZtbQPiRls6XQexcJiTuA2IBuz7OOentmsawrl6tMsbj24DWtmd5uregz6Pcq1+vVSHUQFz6WlsvRjE45OssxoZcd9nnxl1ADtZEFxc7+7ZM7t9pnoV6zBC0tznOkD0iFYpRRX+4aosp2cwt9WvC07afjICYrsK6z17UradZ2Dt9njMwUYbAxEwgP8B3AXcCVwD7NdueQWMipiD/3DBur0Q9nKx60fATtnPNoZ9d0ZU2I3t/fjzn/e2fd14FKf2AQNYAqwD9o8/fxZ4U7t1FDCk8rq5EPZy0exXkdf++6fu5xfM633/rcFx5UrdePTJoASMe4FDgPnADcBvt1tHAUNqITTX0MvFP7TIq9ucyy23NG1uN+n72Q2+e78ecgbKUZSq9gEj+g5cAGwDNgOTGcusAKaAqaVLl+Z6EEVK1Ut9R0iQCbk479qVWecA7utos59eiiQHsTFAjeQVMEprVmtmBwNnAs8EjgAWmtnZrcu5+xp3H3f38cWLF/c7mVJnVe8P0UsTz5BmmRl9ZdafvWq6qev8eZm7+PM/h7GJNvvpZdhzNcceDHlEnV5ewOuBTyY+/z7w8XbrqEhKgtWhCKTXNHa6w8/IuSQrppOvU165q7f9dEM5jFJR9yIp4ESiFlLDgAGfBv643ToKGAOiH62s6nKByvFYdCpOajR93W+fjABRpDoE8AGWV8AorUjK3W8DrgO+D/yYqNf5mrLSI33Sr57QdSkC6aZ4p6WI7Y02GQ23YZOstzF2M8Q6xriB09jOzOKksYnVuMPOJ7OLowqT9yNfpRx5RJ1+vZTDGAD9uvOvSw4jqV1uY2LCtzGzX8THWJk6vZZNVtW/pzD0q0gK+Drwa3nsbLYvBYwB0I+e0O71KwLJ6Ci3jIm2xUyz6hdRJXX7vWomr4ARUiT1DuAjZvYpMzu8wMyOzAX9Gvyt1yKQslpWpbRsWsgO/pJoML6lpBelzWd3+vaqVvTWiUZBroWOAcPdv+/uv0XUse6rZvZuM9u/+KTJQOrnaJ3dNv/s80izZ57J3mauezakX+AbgWJoNCOgzsuoj2gXgPMOinlsry51TnNdSDaEqBXTscD5wBZgE3BOHlmcbl4qkhoQVS2rLrje4z3vSd98245yIyPRyllFNitXljtaa17bq2OdU43QxzqMm4H7gBuB9wGnA88BPgasySMRoS8FDCnMxET21bzH+pV//MfpTSxjwtcx6rsxX8fo3rqJxsvf8paZw4aD+4IF0xffrEDbTQDO+8Kc5yNcVYdRmH4GjGMhepRryry1eSQi9KWAIYXo9AzmwIvf976XvvoyZrZwcph5MRwZyfdinibvRgd5bq+qOc8BkFfACKnDuDPeYZrX9FgSJpKt3xXPaRWuDW3qV+67b7oOwgxe+ML0Tfwlq1hIyvZbK3Qffjh9A3mW4+fd6CDP7fUy5Ij01aw67rn7z/JKiAjQn4rn1oC0YUP2somWVTt3NgeIJUuyV3Ns7+32mAVW6OZ9MU8LvHk3Oqj7I0elO3lkU/r1UpHUHFB05Wda8VNGscqepaOZpVStrz0w+++UZzl+u23lXfSjoqTKo+5jSfXyUsDoQd3+mYvu2Jd18W7Zb7LTXNprB/tlPHs0RbcPVcrj91KrI0lQwJDOym550s3Fr83zonO90GWO5ErbVkybOML9nnt6+269LD9b/epRL7WggCGdtbvLzOMC1mHso1k9qrSgINdpJNfGa4rj3S+5JH0jK1fOvCBXpQlovwKv1IoChnSWdZfZuMDN5oLXKSB0UyTS6QKXw5DfjVdaE9dtDPu3OSn+dwj43lnHteyLcR8Dr9SLAkYd9btYIutCPC+HAes6BYRuikRyLD7Jula2Bo2tHNxbQGoX3PpZ3JN2LhUYeHNVt3q1AaCAUTdl1Cdk7TOPC16ni3weOYyAABYSIMD9FdzoQTmIXr93Mr1FXxCL/F2LVna92hylgFE33V4U87rodHMnmmcOI+TCkExLYJ1AaIA4gk35BIjQ72023WS16AtikTnHoqn1VikUMOqmm2KXoi86eWy/m4AQWineOEaJZbMCQtrYTA7uu3YVe4efle6VK6P5/bggFlk3VTS13iqFAkbdtLsrbP2H7sdFp+hWUp1kfMfW1kpZwWLG2EzJTmlFXzTbfe9+XBCLbv1WJOUwSqGAUTftWrC0XtDaXS0HRWZ/CMv+6uB+/vntLzplX5D6FeyrnpPIUue015gCRh1NTLgPDXW+oGSVRc+bV1rS83L66dFXCekPkRkk293Fl13k0a8LYtVzEu3UOe01lVfAmNXgg7NlZgeZ2XVm9hMzW2tmLy4zPX2xZ0/69ORAdLszHruZNb2Tsh47SjQga3LAvhtuiKZfzGq2Mzxj+TE27L3STr9p0W6Qvn49AjZLr4+G7WU/dR3Ztc5pn+vyiDq9voBPA2+J3+8DHNRu+drnMEJ74OZZrNHnIoDPfCb7K6YWMTXu/ru50+w0sJ6KPKSOCsx5UfciKeBpwDoyHs6U9qp9wGjXuqXXYTU6KbhM/Vvf6iFATEw0PyxoZGT6u4X+03RqgaUiD6mTgm90BiFgHAd8F7gK+AFwBbAwZbkVwBQwtXTp0lwOXmmyLt6N5zYn5XXRy7lM/6c/7SFA7NjR/L2yHkXa7fOpRQZFwTd2eQUMi7bVf2Y2DtwKvNTdbzOzy4DH3f0vstYZHx/3qampvqUxd42HAyWf7jY8XEwZd0PWA4JGR6Py4w4eeQQOOSRsV45Fb266CV7+8u7SAzBvXno9TWBaRWpraCi9vs4su96zC2Z2u7uPz3Y7ZVZ6bwI2uftt8efrgONLTE/x0ipEzz03qhkuqkK6yyeiPfVUcyV1u2DhWPR64/LoXG/cF2UFC2j/uNGsSv08H1GalxIbEsgAKruxRqg8sim9voBvAc+L318KfKjd8ic0smiDUkRRgSaYe/aEFzHtJlG81at2Ff91GNrCXRXrkj/VYQTXY0wBPwK+ABzcbvkTBu2fs6ROZqEBoqk3dV4GoQ6j7M6BMphq0EqqtDqMXoyb+d4ajEEo1y643DK5uRCbWMIS7os+FHleTE7CBRfA1q3R55ERuOyyqMhucjIqotu4McqOr15dvXb6ffrdRPIyCHUYs1PFcu1u5VFumVKWnqyDaBcsfsBx0/UQDkv8P6fvl4u0fDls2TK9ry1bpoNCslPX6tXF1u/0qi7lzSI5q2/AGIR/zi4rpGdotLrasCG68G7YwPazV7CM9AvrVzh1OkBsfZjj/I7+BIhepHw3VqyoRtCY7e8mUld5lGv16zVwdRjuPZVbNg5Dp/GYPsF509Ovv77gL5KzqtcTqHOg1Ahztg5jdLT4cu20cnQorWw9q1hpN0MMkfH7nXEGfPGLxSWqaKonEMlNXnUY9QoY/ei4l9a5bsGC6EL11FPT0wrscBdaSf0Az+BQNs+cMQgNAmbZ4VBEpqnSuyirVjUHC4Bf/KI5WEC0zKpVuewytJL6MO6froPAOHTiI4Nblq56ApHKUcBo1U3rqx5bah17bFiAAJoCxP1+eHOJfruhtOveE7lfw4SLSDAVSbVqN9ZRq8Dikbe+Fa64ImyTe8djgqisPrR8KqmMMatEpLJUJFWUtKKQBQtgn32ap7UpHvngB5tzEO2CRTIH4fc/0JyD6CVYQHqxWo5FaCIyNylgtEorCvnUp+DKKzOLR669tjlAXHRR9uabAsRn/19zgDjssHy+Q1ZR2SB0dhSR0ihgpEl7hGRi2s0T67Gzl+8NEMuWZW+qKUAQB5uJiShAvP71xaRfPZGz1b1uR6REczdgdHHhuPvu5hzEr/969mZnBIiJieYirn70WFYLo3RV7j0uUgd59P7r12tWj2hN9swdGZk5Ymqi9/jWremdjNNeMye0KKvHsnoiz1T13uMiBWFO9vTutZVUWquhFOsZ5Zmsb7tMUysm6DwOk3osV0dWIwL9FjLg1EqqG2mthlIsZWal8Iwipl27mu9PO25U9QmVMDmZHTD0W4gEmRsBI7B10EaWspuh5gCxfn1zgJg3r7t9qz6hGlatys7p6bcQCTKwAePww6crqTd7mwdTJ4yxgaHPXdccIEZHZ5cQ9ViuhqybhkaPeRHpaGACxvnnN7dkeuCBaPoyJnkaT7RfOdnU9XWvyz9xac10pb+yip1me0MgMofUNmDcfHNzgHj87yZZxxi7GWIdY3sfIvT3nMO+PDVzAyMj07kIXcQHn4oGRWatVq2kDjts3B98cGYrqWVM8glWsJDOFdt7qWXM3FOH54WLFGBgWkmZ2Twz+4GZ3dBp2QcfbP78Mr7FIxzE1ZydHixGR7OLHKrYMka9kIulokGRWZlfdgKAC4C1wNM6LXg0d/E9hhlm5/TEZz0L1j2e3gKmMeqsWfP8KhZFtPYVafRCBl3YRKQSSs1hmNmRwGuAoMG/9z/8YIav+Fj0MKNG/cM993TOLSRHfq1qKyWNMCsiFVd2kdRHgXcAmZUJZrbCzKbMbGrzggVw3nnRcONJaRWarRpNZKtaFKERZoul4j6RWSstYJjZ6cBD7n57u+XcfY27j7v7+OLFi9MXau3rkKXKF1/1CC+OBh0UyUWZOYyXAr9jZuuBa4HfMrOJnreWrNCsU0V3g5p9FkfFfSK5KC1guPu73P1Idx8DzgK+4e5n57LxrKfmbdtW3SIJ9Qgvjor7RHJRdh1G79qVSbdefEdGor9bt1a7SELNPouh4j6RXFQiYLj7Te5+evAKIWXSyYvvAQdELauSVCQxd6i4TyQXlQgYXeu2TFpFEnObivtEclGFjnvd6zYALF063YmvdbrMDY3nsotIz+qZw+i2TLpdkYTa54uIBKlnwOi2TDqrSALUPl9EJFCtRqtteqZ3HiOPjo2lF1U1eoSLiAyAvEarrW/AyMPQUPZjOzX0uYgMiIEZ3rxUap8vIhJsbgcMtc8XEQk2twOG2ueLiASrZz+MPKl9vohIkMHPYaifRTF0XEXmnMHOYeixp8XQcRWZkwa7Wa36WRRDx1WkVtSsNoQGHSyGjqvInDTYAUP9LIqh4yoyJ9UzYIRWuKqfRTF0XEXmpPoFjJCHJzWon0UxdFxF5qT6VXpv2aIKVxGRLszdSm9VuIqIlKJ+AUMVriIipSgtYJjZUWb2L2a21szuMrMLglZUhauISCnKzGHsAi50918BTgL+0MyO7riWKlxFREpR2tAg7n4/cH/8/gkzWwssAf6t48oaMFBEpO8qUYdhZmPAC4DbUuatMLMpM5vavHlz39MmIiKR0gOGmR0AfA54u7s/3jrf3de4+7i7jy9evLj/CRQREaDkgGFmC4iCxaS7f77MtIiISHtltpIy4JPAWnf/m7LSISIiYcrMYbwUOAf4LTO7I36dVmJ6RESkjTJbSd0MWFn7FxGR7pRe6S0iIvWggCEiIkEUMEREJIgChoiIBFHAEBGRIAoYIiISRAFDRESCKGCIiEgQBQwREQmigCEiIkEUMEREJIgChoiIBFHAEBGRIAoYIiISRAFDRESCKGCIiEgQBQwREQmigCEiIkEUMEREJIgChoiIBCk1YJjZqWb272Z2t5ldVGZaRESkvdIChpnNA/4P8GrgaGCZmR1dVnpERKS9MnMYLwLudvefuftTwLXAmSWmR0RE2phf4r6XAPcmPm8CTmxdyMxWACvij0+a2Z19SNtsLQK2lJ2IAEpnfuqQRlA681aXdD4vj42UGTAsZZrPmOC+BlgDYGZT7j5edMJmS+nMVx3SWYc0gtKZtzqlM4/tlFkktQk4KvH5SOC+ktIiIiIdlBkwvgf8kpk908z2Ac4CvlhiekREpI3SiqTcfZeZ/RHwT8A84Ep3v6vDamuKT1kulM581SGddUgjKJ15m1PpNPcZ1QYiIiIzqKe3iIgEUcAQEZEglQgYnYYIscjfxvN/ZGbHh67b53Quj9P3IzP7jpn9WmLeejP7sZndkVcTt1mk82QzeyxOyx1mdknoun1O558l0ninme02s0PieX05nmZ2pZk9lNX/p0LnZqd0VuXc7JTOqpybndJZhXPzKDP7FzNba2Z3mdkFKcvke366e6kvogrve4BnAfsAPwSOblnmNOArRH03TgJuC123z+l8CXBw/P7VjXTGn9cDiypyPE8Gbuhl3X6ms2X5M4BvlHA8fwM4HrgzY37p52ZgOks/NwPTWfq5GZLOipybhwPHx+8PBH5a9LWzCjmMkCFCzgQ+45FbgYPM7PDAdfuWTnf/jrs/En+8lahvSb/N5phU6ni2WAZcU1BaMrn7N4GH2yxShXOzYzorcm6GHM8slTqeLco6N+939+/H758A1hKNoJGU6/lZhYCRNkRI65fOWiZk3bx0u6/ziCJ7gwNfM7PbLRrupCih6Xyxmf3QzL5iZsd0uW4egvdlZsPAqcDnEpP7dTw7qcK52a2yzs1QZZ+bwapybprZGPAC4LaWWbmen2UODdIQMkRI1jJBw4vkJHhfZvabRP+UL0tMfqm732dmzwBuNLOfxHcxZaTz+8Cou28zs9OALwC/FLhuXrrZ1xnAt909ecfXr+PZSRXOzWAln5shqnBudqP0c9PMDiAKWG9398dbZ6es0vP5WYUcRsgQIVnL9HN4kaB9mdnzgSuAM919a2O6u98X/30IuJ4oS1hKOt39cXffFr//MrDAzBaFrNvPdCacRUuWv4/Hs5MqnJtBKnBudlSRc7MbpZ6bZraAKFhMuvvnUxbJ9/wsumImoOJmPvAz4JlMV74c07LMa2iuuPlu6Lp9TudS4G7gJS3TFwIHJt5/Bzi1xHQexnSnzRcBG+NjW6njGS/3dKKy5IVlHM94H2NkV9KWfm4GprP0czMwnaWfmyHprMK5GR+XzwAfbbNMrudn6UVSnjFEiJmdH8+/HPgyUW3/3cAO4M3t1i0xnZcAI8DHzQxgl0cjWR4KXB9Pmw9c7e5fLTGdvwusNLNdwE7gLI/OoqodT4D/BnzN3bcnVu/b8TSza4ha7iwys03Au4EFiTSWfm4GprP0czMwnaWfm4HphJLPTeClwDnAj83sjnjaxUQ3B4WcnxoaREREglShDkNERGpAAUNERIIoYIiISBAFDBERCaKAISIiQRQwREQkiAKGiIgEUcAQmYX4eQSvit+/38z+tuw0iRSl9J7eIjX3buC98UBzLwB+p+T0iBRGPb1FZsnM/hU4ADjZo+cSiAwkFUmJzIKZ/SrRk8+eVLCQQaeAIdKj+Mllk0RPKttuZqeUnCSRQilgiPQgftLa54EL3X0t8D7g0lITJVIw1WGIiEgQ5TBERCSIAoaIiARRwBARkSAKGCIiEkQBQ0REgihgiIhIEAUMEREJ8l/Q+Hs0O9UNZwAAAABJRU5ErkJggg==\n", "text/plain": [ "
    " ] }, "metadata": { "filenames": { - "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_127_1.png" + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_132_1.png" }, "needs_background": "light" }, @@ -1715,7 +2068,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "1ca83847", + "metadata": { + "editable": true + }, "source": [ "## Using gradient descent methods, limitations\n", "\n", @@ -1729,9 +2085,39 @@ "\n", "* **GD treats all directions in parameter space uniformly.** Another major drawback of GD is that unlike Newton's method, the learning rate for GD is the same in all directions in parameter space. For this reason, the maximum learning rate is set by the behavior of the steepest direction and this can significantly slow down training. Ideally, we would like to take large steps in flat directions and small steps in steep directions. Since we are exploring rugged landscapes where curvatures change, this requires us to keep track of not only the gradient but second derivatives. The ideal scenario would be to calculate the Hessian but this proves to be too computationally expensive. \n", "\n", - "* GD can take exponential time to escape saddle points, even with random initialization. As we mentioned, GD is extremely sensitive to initial condition since it determines the particular local minimum GD would eventually reach. However, even with a good initialization scheme, through the introduction of randomness, GD can still take exponential time to escape saddle points.\n", + "* GD can take exponential time to escape saddle points, even with random initialization. As we mentioned, GD is extremely sensitive to initial condition since it determines the particular local minimum GD would eventually reach. However, even with a good initialization scheme, through the introduction of randomness, GD can still take exponential time to escape saddle points." + ] + }, + { + "cell_type": "markdown", + "id": "dcf3e808", + "metadata": { + "editable": true + }, + "source": [ + "## Stochastic Gradient Descent (SGD)\n", "\n", - "## Stochastic Gradient Descent\n", + "In stochastic gradient descent, the extreme case is the case where we\n", + "have only one batch, that is we include the whole data set.\n", + "\n", + "This process is called Stochastic Gradient\n", + "Descent (SGD) (or also sometimes on-line gradient descent). This is\n", + "relatively less common to see because in practice due to vectorized\n", + "code optimizations it can be computationally much more efficient to\n", + "evaluate the gradient for 100 examples, than the gradient for one\n", + "example 100 times. Even though SGD technically refers to using a\n", + "single example at a time to evaluate the gradient, you will hear\n", + "people use the term SGD even when referring to mini-batch gradient\n", + "descent (i.e. mentions of MGD for “Minibatch Gradient Descent”, or BGD\n", + "for “Batch gradient descent” are rare to see), where it is usually\n", + "assumed that mini-batches are used. The size of the mini-batch is a\n", + "hyperparameter but it is not very common to cross-validate or bootstrap it. It is\n", + "usually based on memory constraints (if any), or set to some value,\n", + "e.g. 32, 64 or 128. We use powers of 2 in practice because many\n", + "vectorized operation implementations work faster when their inputs are\n", + "sized in powers of 2.\n", + "\n", + "In our notes with SGD we mean stochastic gradient descent with mini-batches.\n", "\n", "Stochastic gradient descent (SGD) and variants thereof address some of\n", "the shortcomings of the Gradient descent method discussed above.\n", @@ -1743,7 +2129,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "473b1af6", + "metadata": { + "editable": true + }, "source": [ "$$\n", "C(\\mathbf{\\beta}) = \\sum_{i=1}^n c_i(\\mathbf{x}_i,\n", @@ -1753,7 +2142,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "3353fe2a", + "metadata": { + "editable": true + }, "source": [ "This in turn means that the gradient can be\n", "computed as a sum over $i$-gradients" @@ -1761,7 +2153,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6e8e47c3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\nabla_\\beta C(\\mathbf{\\beta}) = \\sum_i^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n", @@ -1771,7 +2166,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "a2eeb6ad", + "metadata": { + "editable": true + }, "source": [ "Stochasticity/randomness is introduced by only taking the\n", "gradient on a subset of the data called minibatches. If there are $n$\n", @@ -1779,8 +2177,6 @@ "minibatches. We denote these minibatches by $B_k$ where\n", "$k=1,\\cdots,n/M$.\n", "\n", - "\n", - "\n", "As an example, suppose we have $10$ data points $(\\mathbf{x}_1,\\cdots, \\mathbf{x}_{10})$ \n", "and we choose to have $M=5$ minibathces,\n", "then each minibatch contains two data points. In particular we have\n", @@ -1797,7 +2193,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "5a7a0f8b", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\nabla_{\\beta}\n", @@ -1809,14 +2208,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "b7b5884f", + "metadata": { + "editable": true + }, "source": [ "Thus a gradient descent step now looks like" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "6492d660", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\beta_{j+1} = \\beta_j - \\gamma_j \\sum_{i \\in B_k}^n \\nabla_\\beta c_i(\\mathbf{x}_i,\n", @@ -1826,7 +2231,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "584164f4", + "metadata": { + "editable": true + }, "source": [ "where $k$ is picked at random with equal\n", "probability from $[1,n/M]$. An iteration over the number of\n", @@ -1838,6 +2246,7 @@ { "cell_type": "code", "execution_count": 10, + "id": "42d97cf8", "metadata": { "collapsed": false, "editable": true @@ -1847,7 +2256,7 @@ "import numpy as np \n", "\n", "n = 100 #100 datapoints \n", - "M = 5 #size of each minibatch\n", + "M = 5 #size of each mini-batche\n", "m = int(n/M) #number of minibatches\n", "n_epochs = 10 #number of epochs\n", "\n", @@ -1862,7 +2271,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ca9c6c58", + "metadata": { + "editable": true + }, "source": [ "Taking the gradient only on a subset of the data has two important\n", "benefits. First, it introduces randomness which decreases the chance\n", @@ -1872,8 +2284,6 @@ "cheaper since we sum over the datapoints in the $k-th$ minibatch and not\n", "all $n$ datapoints.\n", "\n", - "\n", - "\n", "A natural question is when do we stop the search for a new minimum?\n", "One possibility is to compute the full gradient after a given number\n", "of epochs and check if the norm of the gradient is smaller than some\n", @@ -1885,8 +2295,6 @@ "compare the values of the cost function and keep the $\\beta$ that\n", "gave the lowest value.\n", "\n", - "\n", - "\n", "Another approach is to let the step length $\\gamma_j$ depend on the\n", "number of epochs in such a way that it becomes very small after a\n", "reasonable time such that we do not move at all.\n", @@ -1903,6 +2311,7 @@ { "cell_type": "code", "execution_count": 11, + "id": "d2921658", "metadata": { "collapsed": false, "editable": true @@ -1945,7 +2354,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "84469eb8", + "metadata": { + "editable": true + }, + "source": [ + "We note that we have defined several hyperparameters. These are now the number of epochs, the number of mini-batches and the parameters $t_0$ and $t_1$." + ] + }, + { + "cell_type": "markdown", + "id": "b4b94e7a", + "metadata": { + "editable": true + }, "source": [ "### Program for stochastic gradient" ] @@ -1953,6 +2375,7 @@ { "cell_type": "code", "execution_count": 12, + "id": "71dcdb35", "metadata": { "collapsed": false, "editable": true @@ -1963,34 +2386,27 @@ "output_type": "stream", "text": [ "Own inversion\n", - "[[4.15629539]\n", - " [2.7293182 ]]\n", - "sgdreg from scikit\n", - "[4.0728785] [2.66410989]\n", + "[[3.99775949]\n", + " [2.94659383]]\n", + "Eigenvalues of Hessian Matrix:[0.36102113 4.18276924]\n", "theta from own gd\n", - "[[4.15629539]\n", - " [2.7293182 ]]\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ + "[[3.99775949]\n", + " [2.94659383]]\n", "theta from own sdg\n", - "[[4.15454301]\n", - " [2.72522848]]\n" + "[[3.96489434]\n", + " [2.98399675]]\n" ] }, { "data": { - "image/png": "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\n", + "image/png": "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\n", "text/plain": [ "
    " ] }, "metadata": { "filenames": { - "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_141_2.png" + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_148_1.png" }, "needs_background": "light" }, @@ -1998,34 +2414,34 @@ } ], "source": [ + "# Importing various packages\n", "# Importing various packages\n", "from math import exp, sqrt\n", "from random import random, seed\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", - "from sklearn.linear_model import SGDRegressor\n", "\n", - "m = 100\n", - "x = 2*np.random.rand(m,1)\n", - "y = 4+3*x+np.random.randn(m,1)\n", + "n = 100\n", + "x = 2*np.random.rand(n,1)\n", + "y = 4+3*x+np.random.randn(n,1)\n", "\n", - "X = np.c_[np.ones((m,1)), x]\n", + "X = np.c_[np.ones((n,1)), x]\n", + "XT_X = X.T @ X\n", "theta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y)\n", "print(\"Own inversion\")\n", "print(theta_linreg)\n", - "sgdreg = SGDRegressor(max_iter = 50, penalty=None, eta0=0.1)\n", - "sgdreg.fit(x,y.ravel())\n", - "print(\"sgdreg from scikit\")\n", - "print(sgdreg.intercept_, sgdreg.coef_)\n", - "\n", + "# Hessian matrix\n", + "H = (2.0/n)* XT_X\n", + "EigValues, EigVectors = np.linalg.eig(H)\n", + "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n", "\n", "theta = np.random.randn(2,1)\n", - "eta = 0.1\n", + "eta = 1.0/np.max(EigValues)\n", "Niterations = 1000\n", "\n", "\n", "for iter in range(Niterations):\n", - " gradients = 2.0/m*X.T @ ((X @ theta)-y)\n", + " gradients = 2.0/n*X.T @ ((X @ theta)-y)\n", " theta -= eta*gradients\n", "print(\"theta from own gd\")\n", "print(theta)\n", @@ -2035,8 +2451,9 @@ "ypredict = Xnew.dot(theta)\n", "ypredict2 = Xnew.dot(theta_linreg)\n", "\n", - "\n", "n_epochs = 50\n", + "M = 5 #size of each minibatch\n", + "m = int(n/M) #number of minibatches\n", "t0, t1 = 5, 50\n", "def learning_schedule(t):\n", " return t0/(t+t1)\n", @@ -2044,16 +2461,20 @@ "theta = np.random.randn(2,1)\n", "\n", "for epoch in range(n_epochs):\n", + "# Can you figure out a better way of setting up the contributions to each batch?\n", " for i in range(m):\n", - " random_index = np.random.randint(m)\n", - " xi = X[random_index:random_index+1]\n", - " yi = y[random_index:random_index+1]\n", - " gradients = 2 * xi.T @ ((xi @ theta)-yi)\n", + " random_index = M*np.random.randint(m)\n", + " xi = X[random_index:random_index+M]\n", + " yi = y[random_index:random_index+M]\n", + " gradients = (2.0/M)* xi.T @ ((xi @ theta)-yi)\n", " eta = learning_schedule(epoch*m+i)\n", " theta = theta - eta*gradients\n", "print(\"theta from own sdg\")\n", "print(theta)\n", "\n", + "\n", + "\n", + "\n", "plt.plot(xnew, ypredict, \"r-\")\n", "plt.plot(xnew, ypredict2, \"b-\")\n", "plt.plot(x, y ,'ro')\n", @@ -2066,7 +2487,23 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6231b86f", + "metadata": { + "editable": true + }, + "source": [ + "In the above code, we have use replacement in setting up the\n", + "mini-batches. The discussion\n", + "[here](https://sebastianraschka.com/faq/docs/sgd-methods.html) may be\n", + "useful. More material will be added later." + ] + }, + { + "cell_type": "markdown", + "id": "8d50214c", + "metadata": { + "editable": true + }, "source": [ "## Momentum based GD\n", "\n", @@ -2078,7 +2515,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "45d43ca3", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t) \\nonumber\n", @@ -2087,7 +2527,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "dcdd91bf", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -2102,7 +2545,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "c7519d1e", + "metadata": { + "editable": true + }, "source": [ "where we have introduced a momentum parameter $\\gamma$, with\n", "$0\\le\\gamma\\le 1$, and for brevity we dropped the explicit notation to\n", @@ -2118,7 +2564,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "f4d4340d", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\Delta \\boldsymbol{\\theta}_{t+1} = \\gamma \\Delta \\boldsymbol{\\theta}_t -\\ \\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t),\n", @@ -2127,12 +2576,13 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "41ad532a", + "metadata": { + "editable": true + }, "source": [ "where we have defined $\\Delta \\boldsymbol{\\theta}_{t}= \\boldsymbol{\\theta}_t-\\boldsymbol{\\theta}_{t-1}$.\n", "\n", - "\n", - "\n", "Let us try to get more intuition from these equations. It is helpful\n", "to consider a simple physical analogy with a particle of mass $m$\n", "moving in a viscous medium with drag coefficient $\\mu$ and potential\n", @@ -2142,7 +2592,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "eef8ae92", + "metadata": { + "editable": true + }, "source": [ "$$\n", "m {d^2 \\mathbf{w} \\over dt^2} + \\mu {d \\mathbf{w} \\over dt }= -\\nabla_w E(\\mathbf{w}).\n", @@ -2151,14 +2604,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "80481a6d", + "metadata": { + "editable": true + }, "source": [ "We can discretize this equation in the usual way to get" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "6aab8db7", + "metadata": { + "editable": true + }, "source": [ "$$\n", "m { \\mathbf{w}_{t+\\Delta t}-2 \\mathbf{w}_{t} +\\mathbf{w}_{t-\\Delta t} \\over (\\Delta t)^2}+\\mu {\\mathbf{w}_{t+\\Delta t}- \\mathbf{w}_{t} \\over \\Delta t} = -\\nabla_w E(\\mathbf{w}).\n", @@ -2167,14 +2626,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "dd6414d2", + "metadata": { + "editable": true + }, "source": [ "Rearranging this equation, we can rewrite this as" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "b76a8372", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\Delta \\mathbf{w}_{t +\\Delta t}= - { (\\Delta t)^2 \\over m +\\mu \\Delta t} \\nabla_w E(\\mathbf{w})+ {m \\over m +\\mu \\Delta t} \\Delta \\mathbf{w}_t.\n", @@ -2183,7 +2648,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "07bbe6db", + "metadata": { + "editable": true + }, "source": [ "Notice that this equation is identical to previous one if we identify\n", "the position of the particle, $\\mathbf{w}$, with the parameters\n", @@ -2194,7 +2662,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "7a9a2ecf", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\gamma= {m \\over m +\\mu \\Delta t }, \\qquad \\eta = {(\\Delta t)^2 \\over m +\\mu \\Delta t}.\n", @@ -2203,7 +2674,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "fe5a2bbc", + "metadata": { + "editable": true + }, "source": [ "Thus, as the name suggests, the momentum parameter is proportional to\n", "the mass of the particle and effectively provides inertia.\n", @@ -2233,7 +2707,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "04540023", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathbf{v}_{t}=\\gamma \\mathbf{v}_{t-1}+\\eta_{t}\\nabla_\\theta E(\\boldsymbol{\\theta}_t +\\gamma \\mathbf{v}_{t-1}) \\nonumber\n", @@ -2242,7 +2719,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "dfbf53a5", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -2257,12 +2737,13 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "32ac3869", + "metadata": { + "editable": true + }, "source": [ "One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of $\\gamma$.\n", "\n", - "\n", - "\n", "In stochastic gradient descent, with and without momentum, we still\n", "have to specify a schedule for tuning the learning rates $\\eta_t$\n", "as a function of time. As discussed in the context of Newton's\n", @@ -2281,10 +2762,17 @@ "\n", "Recently, a number of methods have been introduced that accomplish\n", "this by tracking not only the gradient, but also the second moment of\n", - "the gradient. These methods include AdaGrad, AdaDelta, RMS-Prop, and\n", - "ADAM.\n", - "\n", - "\n", + "the gradient. These methods include AdaGrad, AdaDelta, Root Mean Squared Propagation (RMS-Prop), and\n", + "ADAM." + ] + }, + { + "cell_type": "markdown", + "id": "6f575b16", + "metadata": { + "editable": true + }, + "source": [ "### RMS prop\n", "\n", "In RMS prop, in addition to keeping a running average of the first\n", @@ -2295,7 +2783,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "274604c4", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -2310,7 +2801,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "cd679323", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathbf{s}_t =\\beta \\mathbf{s}_{t-1} +(1-\\beta)\\mathbf{g}_t^2 \\nonumber\n", @@ -2319,7 +2813,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "0a7f8e9d", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\mathbf{g}_t \\over \\sqrt{\\mathbf{s}_t +\\epsilon}}, \\nonumber\n", @@ -2328,7 +2825,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "48ba8fff", + "metadata": { + "editable": true + }, "source": [ "where $\\beta$ controls the averaging time of the second moment and is\n", "typically taken to be about $\\beta=0.9$, $\\eta_t$ is a learning rate\n", @@ -2338,8 +2838,16 @@ "is clear from this formula that the learning rate is reduced in\n", "directions where the norm of the gradient is consistently large. This\n", "greatly speeds up the convergence by allowing us to use a larger\n", - "learning rate for flat directions.\n", - "\n", + "learning rate for flat directions." + ] + }, + { + "cell_type": "markdown", + "id": "83140ab2", + "metadata": { + "editable": true + }, + "source": [ "### ADAM optimizer\n", "\n", "A related algorithm is the ADAM optimizer. In ADAM, we keep a running\n", @@ -2358,7 +2866,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "61874dc3", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -2373,7 +2884,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "24e19d86", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathbf{m}_t = \\beta_1 \\mathbf{m}_{t-1} + (1-\\beta_1) \\mathbf{g}_t \\nonumber\n", @@ -2382,7 +2896,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "506f78ea", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\mathbf{s}_t =\\beta_2 \\mathbf{s}_{t-1} +(1-\\beta_2)\\mathbf{g}_t^2 \\nonumber\n", @@ -2391,7 +2908,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "cb4b8585", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\mathbf{m}}_t={\\mathbf{m}_t \\over 1-\\beta_1^t} \\nonumber\n", @@ -2400,7 +2920,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9b5b11b1", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\mathbf{s}}_t ={\\mathbf{s}_t \\over1-\\beta_2^t} \\nonumber\n", @@ -2409,7 +2932,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "92292a73", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\boldsymbol{\\theta}_{t+1}=\\boldsymbol{\\theta}_t - \\eta_t { \\boldsymbol{\\mathbf{m}}_t \\over \\sqrt{\\boldsymbol{\\mathbf{s}}_t} +\\epsilon}, \\nonumber\n", @@ -2418,7 +2944,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "1a264832", + "metadata": { + "editable": true + }, "source": [ "\n", "
    \n", @@ -2432,7 +2961,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "6a307202", + "metadata": { + "editable": true + }, "source": [ "where $\\beta_1$ and $\\beta_2$ set the memory lifetime of the first and\n", "second moment and are typically taken to be $0.9$ and $0.99$\n", @@ -2448,7 +2980,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "3285f010", + "metadata": { + "editable": true + }, "source": [ "$$\n", "\\Delta \\theta_{t+1}= -\\eta_t { \\boldsymbol{m}_t \\over \\sqrt{\\sigma_t^2 + m_t^2 }+\\epsilon}.\n", @@ -2457,7 +2992,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "657349da", + "metadata": { + "editable": true + }, "source": [ "## Practical tips\n", "\n", @@ -2467,8 +3005,16 @@ "\n", "* **Monitor the out-of-sample performance.** Always monitor the performance of your model on a validation set (a small portion of the training data that is held out of the training process to serve as a proxy for the test set. If the validation error starts increasing, then the model is beginning to overfit. Terminate the learning process. This *early stopping* significantly improves performance in many settings.\n", "\n", - "* **Adaptive optimization methods don't always have good generalization.** Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications.\n", - "\n", + "* **Adaptive optimization methods don't always have good generalization.** Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications." + ] + }, + { + "cell_type": "markdown", + "id": "65044ac7", + "metadata": { + "editable": true + }, + "source": [ "## Automatic differentiation\n", "\n", "[Automatic differentiation (AD)](https://en.wikipedia.org/wiki/Automatic_differentiation), \n", @@ -2496,15 +3042,16 @@ "while numerical differentiation can introduce round-off errors in the\n", "discretization process and cancellation\n", "\n", - "\n", - "\n", "Python has tools for so-called **automatic differentiation**.\n", "Consider the following example" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "dacf05cf", + "metadata": { + "editable": true + }, "source": [ "$$\n", "f(x) = \\sin\\left(2\\pi x + x^2\\right)\n", @@ -2513,14 +3060,20 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "da4ad36e", + "metadata": { + "editable": true + }, "source": [ "which has the following derivative" ] }, { "cell_type": "markdown", - "metadata": {}, + "id": "f4c3e6c4", + "metadata": { + "editable": true + }, "source": [ "$$\n", "f'(x) = \\cos\\left(2\\pi x + x^2\\right)\\left(2\\pi + 2x\\right)\n", @@ -2529,7 +3082,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "1c8bfd4a", + "metadata": { + "editable": true + }, "source": [ "Using **autograd** we have" ] @@ -2537,6 +3093,7 @@ { "cell_type": "code", "execution_count": 13, + "id": "e1d91b8b", "metadata": { "collapsed": false, "editable": true @@ -2551,7 +3108,7 @@ }, "metadata": { "filenames": { - "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_177_0.png" + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_188_0.png" }, "needs_background": "light" }, @@ -2604,7 +3161,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "cd1158a5", + "metadata": { + "editable": true + }, "source": [ "Here we\n", "experiment with what kind of functions Autograd is capable\n", @@ -2616,6 +3176,7 @@ { "cell_type": "code", "execution_count": 14, + "id": "e2e9faff", "metadata": { "collapsed": false, "editable": true @@ -2652,7 +3213,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e4a83059", + "metadata": { + "editable": true + }, "source": [ "To differentiate with respect to two (or more) arguments of a Python\n", "function, Autograd need to know at which variable the function if\n", @@ -2662,6 +3226,7 @@ { "cell_type": "code", "execution_count": 15, + "id": "f65983d8", "metadata": { "collapsed": false, "editable": true @@ -2719,7 +3284,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "1d369f97", + "metadata": { + "editable": true + }, "source": [ "Note that the grad function will not produce the true gradient of the function. The true gradient of a function with two or more variables will produce a vector, where each element is the function differentiated w.r.t a variable." ] @@ -2727,6 +3295,7 @@ { "cell_type": "code", "execution_count": 16, + "id": "46ea0652", "metadata": { "collapsed": false, "editable": true @@ -2763,7 +3332,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "9cc6674a", + "metadata": { + "editable": true + }, "source": [ "Note that in this case, when sending an array as input argument, the\n", "output from Autograd is another array. This is the true gradient of\n", @@ -2776,6 +3348,7 @@ { "cell_type": "code", "execution_count": 17, + "id": "17813055", "metadata": { "collapsed": false, "editable": true @@ -2813,6 +3386,7 @@ { "cell_type": "code", "execution_count": 18, + "id": "6da49540", "metadata": { "collapsed": false, "editable": true @@ -2843,40 +3417,10 @@ "print(\"The computed derivative of f5 at x = %g is: %g\"%(x,f5_grad(x)))" ] }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "1\n", - "8\n", - " \n", - "<\n", - "<\n", - "<\n", - "!\n", - "!\n", - "C\n", - "O\n", - "D\n", - "E\n", - "_\n", - "B\n", - "L\n", - "O\n", - "C\n", - "K\n", - " \n", - " \n", - "p\n", - "y\n", - "c\n", - "o\n", - "d" - ] - }, { "cell_type": "code", "execution_count": 19, + "id": "a8ff2c17", "metadata": { "collapsed": false, "editable": true @@ -2886,7 +3430,52 @@ "name": "stdout", "output_type": "stream", "text": [ - "The analytical derivative of f6 at x = 2.7 is: 37732.5\n" + "The computed derivative of f6_for at x = 0.5 is: 3.95703\n", + "The computed derivative of f6_while at x = 0.5 is: 3.95703\n" + ] + } + ], + "source": [ + "import autograd.numpy as np\n", + "from autograd import grad\n", + "def f6_for(x):\n", + " val = 0\n", + " for i in range(10):\n", + " val = val + x**i\n", + " return val\n", + "\n", + "def f6_while(x):\n", + " val = 0\n", + " i = 0\n", + " while i < 10:\n", + " val = val + x**i\n", + " i = i + 1\n", + " return val\n", + "\n", + "f6_for_grad = grad(f6_for)\n", + "f6_while_grad = grad(f6_while)\n", + "\n", + "x = 0.5\n", + "\n", + "# Print the computed derivaties of f6_for and f6_while\n", + "print(\"The computed derivative of f6_for at x = %g is: %g\"%(x,f6_for_grad(x)))\n", + "print(\"The computed derivative of f6_while at x = %g is: %g\"%(x,f6_while_grad(x)))" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "id": "ec67d4a3", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "The analytical derivative of f6 at x = 0.5 is: 3.95703\n" ] } ], @@ -2904,7 +3493,8 @@ }, { "cell_type": "code", - "execution_count": 20, + "execution_count": 21, + "id": "742a2d68", "metadata": { "collapsed": false, "editable": true @@ -2951,71 +3541,78 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "e7be6348", + "metadata": { + "editable": true + }, "source": [ "Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input.\n", "\n", + "Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd.\n", "\n", - "Autograd supports many features. However, there are some functions that are not supported (yet) by Autograd.\n", - "\n", - "Assigning a value to the variable being differentiated with respect to is an example thereof." - ] - }, - { - "cell_type": "code", - "execution_count": 21, - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], - "source": [ - "#import autograd.numpy as np\n", - "#from autograd import grad\n", - "#def f8(x): # Assume x is an array\n", - "# x[2] = 3\n", - "# return x*2\n", - "\n", - "#f8_grad = grad(f8)\n", - "\n", - "#x = 8.4\n", - "\n", - "#print(\"The derivative of f8 is:\",f8_grad(x))" - ] - }, - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible." + "Assigning a value to the variable being differentiated with respect to" ] }, { "cell_type": "code", "execution_count": 22, + "id": "c551058c", "metadata": { "collapsed": false, "editable": true }, "outputs": [ { - "ename": "AttributeError", - "evalue": "'ArrayBox' object has no attribute 'dot'", + "ename": "TypeError", + "evalue": "'ArrayBox' object does not support item assignment", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", - "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", - "\u001b[0;32m/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42573/546166676.py\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1.0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m0.0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"The derivative of f9 is:\"\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mf9_grad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", + "\u001b[0;31mTypeError\u001b[0m Traceback (most recent call last)", + "\u001b[0;32m/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47735/1122558214.py\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m8.4\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 10\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 11\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"The derivative of f8 is:\"\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mf8_grad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/wrap_util.py\u001b[0m in \u001b[0;36mnary_f\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m 18\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 19\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtuple\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m \u001b[0;32min\u001b[0m \u001b[0margnum\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 20\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0munary_operator\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0munary_f\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mnary_op_args\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mnary_op_kwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 21\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mnary_f\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 22\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mnary_operator\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/differential_operators.py\u001b[0m in \u001b[0;36mgrad\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 23\u001b[0m \u001b[0marguments\u001b[0m \u001b[0;32mas\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m`\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbut\u001b[0m \u001b[0mreturns\u001b[0m \u001b[0mthe\u001b[0m \u001b[0mgradient\u001b[0m \u001b[0minstead\u001b[0m\u001b[0;34m.\u001b[0m \u001b[0mThe\u001b[0m \u001b[0mfunction\u001b[0m\u001b[0;31m \u001b[0m\u001b[0;31m`\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;31m`\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 24\u001b[0m should be scalar-valued. The gradient has the same type as the argument.\"\"\"\n\u001b[0;32m---> 25\u001b[0;31m \u001b[0mvjp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mans\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_make_vjp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 26\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mvspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mans\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msize\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 27\u001b[0m raise TypeError(\"Grad only applies to real scalar-output functions. \"\n", "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/core.py\u001b[0m in \u001b[0;36mmake_vjp\u001b[0;34m(fun, x)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mmake_vjp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0mstart_node\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mVJPNode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnew_root\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0mend_value\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mend_node\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtrace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstart_node\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 11\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0mend_node\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 12\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mvjp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mvspace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mzeros\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/tracer.py\u001b[0m in \u001b[0;36mtrace\u001b[0;34m(start_node, fun, x)\u001b[0m\n\u001b[1;32m 8\u001b[0m \u001b[0;32mwith\u001b[0m \u001b[0mtrace_stack\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnew_trace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 9\u001b[0m \u001b[0mstart_box\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnew_box\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstart_node\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 10\u001b[0;31m \u001b[0mend_box\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstart_box\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 11\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misbox\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mend_box\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mend_box\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_trace\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0mstart_box\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_trace\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 12\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mend_box\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_value\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mend_box\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_node\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;32m~/anaconda3/lib/python3.8/site-packages/autograd/wrap_util.py\u001b[0m in \u001b[0;36munary_f\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m 13\u001b[0m \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 14\u001b[0m \u001b[0msubargs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msubvals\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margnum\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 15\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mfun\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0msubargs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 16\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0margnum\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mint\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 17\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0margs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0margnum\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;32m/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_42573/546166676.py\u001b[0m in \u001b[0;36mf9\u001b[0;34m(a)\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mf9\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# Assume a is an array with 2 elements\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0mb\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1.0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;36m2.0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mb\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 7\u001b[0m \u001b[0mf9_grad\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgrad\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf9\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", - "\u001b[0;31mAttributeError\u001b[0m: 'ArrayBox' object has no attribute 'dot'" + "\u001b[0;32m/var/folders/jy/g42mrgv128v34gnnhxwk9nrc0000gp/T/ipykernel_47735/1122558214.py\u001b[0m in \u001b[0;36mf8\u001b[0;34m(x)\u001b[0m\n\u001b[1;32m 2\u001b[0m \u001b[0;32mfrom\u001b[0m \u001b[0mautograd\u001b[0m \u001b[0;32mimport\u001b[0m \u001b[0mgrad\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mf8\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0;31m# Assume x is an array\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mx\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 5\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n", + "\u001b[0;31mTypeError\u001b[0m: 'ArrayBox' object does not support item assignment" ] } ], + "source": [ + "import autograd.numpy as np\n", + "from autograd import grad\n", + "def f8(x): # Assume x is an array\n", + " x[2] = 3\n", + " return x*2\n", + "\n", + "f8_grad = grad(f8)\n", + "\n", + "x = 8.4\n", + "\n", + "print(\"The derivative of f8 is:\",f8_grad(x))" + ] + }, + { + "cell_type": "markdown", + "id": "7a13b21d", + "metadata": { + "editable": true + }, + "source": [ + "Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible." + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "id": "19c7502b", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], "source": [ "import autograd.numpy as np\n", "from autograd import grad\n", @@ -3032,7 +3629,10 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "4450885d", + "metadata": { + "editable": true + }, "source": [ "Here we are told that the 'dot' function does not belong to Autograd's\n", "version of a Numpy array. To overcome this, an alternative syntax\n", @@ -3041,7 +3641,8 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 24, + "id": "013fc7f8", "metadata": { "collapsed": false, "editable": true @@ -3066,14 +3667,18 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "8d360f7d", + "metadata": { + "editable": true + }, "source": [ "The documentation recommends to avoid inplace operations such as" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 25, + "id": "e29a24eb", "metadata": { "collapsed": false, "editable": true @@ -3088,9 +3693,229 @@ }, { "cell_type": "markdown", - "metadata": {}, + "id": "ad8fbbb7", + "metadata": { + "editable": true + }, "source": [ - "More examples will be added, in particular how to compare autograd with own codes for the gradients." + "## Using Autograd with OLS\n", + "\n", + "We conclude the part on optmization by showing how we can make codes\n", + "for linear regression and logistic regression using **autograd**. The\n", + "first example shows results with ordinary leats squares." + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "id": "904f65dc", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# Using Autograd to calculate gradients for OLS\n", + "from random import random, seed\n", + "import numpy as np\n", + "import autograd.numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from autograd import grad\n", + "\n", + "def CostOLS(beta):\n", + " return (1.0/n)*np.sum((y-X @ beta)**2)\n", + "\n", + "n = 100\n", + "x = 2*np.random.rand(n,1)\n", + "y = 4+3*x+np.random.randn(n,1)\n", + "\n", + "X = np.c_[np.ones((n,1)), x]\n", + "XT_X = X.T @ X\n", + "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n", + "print(\"Own inversion\")\n", + "print(theta_linreg)\n", + "# Hessian matrix\n", + "H = (2.0/n)* XT_X\n", + "EigValues, EigVectors = np.linalg.eig(H)\n", + "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n", + "\n", + "theta = np.random.randn(2,1)\n", + "eta = 1.0/np.max(EigValues)\n", + "Niterations = 1000\n", + "# define the gradient\n", + "training_gradient = grad(CostOLS)\n", + "\n", + "for iter in range(Niterations):\n", + " gradients = training_gradient(theta)\n", + " theta -= eta*gradients\n", + "print(\"theta from own gd\")\n", + "print(theta)\n", + "\n", + "xnew = np.array([[0],[2]])\n", + "Xnew = np.c_[np.ones((2,1)), xnew]\n", + "ypredict = Xnew.dot(theta)\n", + "ypredict2 = Xnew.dot(theta_linreg)\n", + "\n", + "plt.plot(xnew, ypredict, \"r-\")\n", + "plt.plot(xnew, ypredict2, \"b-\")\n", + "plt.plot(x, y ,'ro')\n", + "plt.axis([0,2.0,0, 15.0])\n", + "plt.xlabel(r'$x$')\n", + "plt.ylabel(r'$y$')\n", + "plt.title(r'Random numbers ')\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "ce338980", + "metadata": { + "editable": true + }, + "source": [ + "### Including Stochastic Gradient Descent with Autograd\n", + "\n", + "In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**." + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "id": "de261f10", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "# Using Autograd to calculate gradients using SGD\n", + "# OLS example\n", + "from random import random, seed\n", + "import numpy as np\n", + "import autograd.numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from autograd import grad\n", + "\n", + "# Note change from previous example\n", + "def CostOLS(y,X,theta):\n", + " return np.sum((y-X @ theta)**2)\n", + "\n", + "n = 100\n", + "x = 2*np.random.rand(n,1)\n", + "y = 4+3*x+np.random.randn(n,1)\n", + "\n", + "X = np.c_[np.ones((n,1)), x]\n", + "XT_X = X.T @ X\n", + "theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y)\n", + "print(\"Own inversion\")\n", + "print(theta_linreg)\n", + "# Hessian matrix\n", + "H = (2.0/n)* XT_X\n", + "EigValues, EigVectors = np.linalg.eig(H)\n", + "print(f\"Eigenvalues of Hessian Matrix:{EigValues}\")\n", + "\n", + "theta = np.random.randn(2,1)\n", + "eta = 1.0/np.max(EigValues)\n", + "Niterations = 1000\n", + "\n", + "# Note that we request the derivative wrt third argument (theta, 2 here)\n", + "training_gradient = grad(CostOLS,2)\n", + "\n", + "for iter in range(Niterations):\n", + " gradients = (1.0/n)*training_gradient(y, X, theta)\n", + " theta -= eta*gradients\n", + "print(\"theta from own gd\")\n", + "print(theta)\n", + "\n", + "xnew = np.array([[0],[2]])\n", + "Xnew = np.c_[np.ones((2,1)), xnew]\n", + "ypredict = Xnew.dot(theta)\n", + "ypredict2 = Xnew.dot(theta_linreg)\n", + "\n", + "plt.plot(xnew, ypredict, \"r-\")\n", + "plt.plot(xnew, ypredict2, \"b-\")\n", + "plt.plot(x, y ,'ro')\n", + "plt.axis([0,2.0,0, 15.0])\n", + "plt.xlabel(r'$x$')\n", + "plt.ylabel(r'$y$')\n", + "plt.title(r'Random numbers ')\n", + "plt.show()\n", + "\n", + "n_epochs = 50\n", + "M = 5 #size of each minibatch\n", + "m = int(n/M) #number of minibatches\n", + "t0, t1 = 5, 50\n", + "def learning_schedule(t):\n", + " return t0/(t+t1)\n", + "\n", + "theta = np.random.randn(2,1)\n", + "\n", + "for epoch in range(n_epochs):\n", + "# Can you figure out a better way of setting up the contributions to each batch?\n", + " for i in range(m):\n", + " random_index = M*np.random.randint(m)\n", + " xi = X[random_index:random_index+M]\n", + " yi = y[random_index:random_index+M]\n", + " gradients = (1.0/M)*training_gradient(yi, xi, theta)\n", + " eta = learning_schedule(epoch*m+i)\n", + " theta = theta - eta*gradients\n", + "print(\"theta from own sdg\")\n", + "print(theta)" + ] + }, + { + "cell_type": "markdown", + "id": "ccd8829e", + "metadata": { + "editable": true + }, + "source": [ + "### And Logistic Regression" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "id": "cc5811d1", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "import autograd.numpy as np\n", + "from autograd import grad\n", + "\n", + "def sigmoid(x):\n", + " return 0.5 * (np.tanh(x / 2.) + 1)\n", + "\n", + "def logistic_predictions(weights, inputs):\n", + " # Outputs probability of a label being true according to logistic model.\n", + " return sigmoid(np.dot(inputs, weights))\n", + "\n", + "def training_loss(weights):\n", + " # Training loss is the negative log-likelihood of the training labels.\n", + " preds = logistic_predictions(weights, inputs)\n", + " label_probabilities = preds * targets + (1 - preds) * (1 - targets)\n", + " return -np.sum(np.log(label_probabilities))\n", + "\n", + "# Build a toy dataset.\n", + "inputs = np.array([[0.52, 1.12, 0.77],\n", + " [0.88, -1.08, 0.15],\n", + " [0.52, 0.06, -1.30],\n", + " [0.74, -2.49, 1.39]])\n", + "targets = np.array([True, True, False, True])\n", + "\n", + "# Define a function that returns gradients of training loss using Autograd.\n", + "training_gradient_fun = grad(training_loss)\n", + "\n", + "# Optimize weights using gradient descent.\n", + "weights = np.array([0.0, 0.0, 0.0])\n", + "print(\"Initial loss:\", training_loss(weights))\n", + "for i in range(100):\n", + " weights -= training_gradient_fun(weights) * 0.01\n", + "\n", + "print(\"Trained loss:\", training_loss(weights))" ] } ], @@ -3109,5 +3934,5 @@ } }, "nbformat": 4, - "nbformat_minor": 4 + "nbformat_minor": 5 } \ No newline at end of file diff --git a/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.py b/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.py index e368e574f..cb4459c01 100644 --- a/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.py +++ b/doc/LectureNotes/_build/jupyter_execute/chapteroptimization.py @@ -1,6 +1,9 @@ #!/usr/bin/env python # coding: utf-8 +# + # # Optimization, the central part of any Machine Learning algortithm # # Almost every problem in machine learning and data science starts with @@ -12,9 +15,6 @@ # analytically, however this is not possible in general and we must use # some approximative/numerical method to compute the minimum. # -# -# -# # In our discussion on Logistic Regression we studied the # case of # two classes, with $y_i$ either @@ -31,8 +31,6 @@ # where $\boldsymbol{\beta}$ are the weights we wish to extract from data, in our case $\beta_0$ and $\beta_1$. # -# -# # Our compact equations used a definition of a vector $\boldsymbol{y}$ with $n$ # elements $y_i$, an $n\times p$ matrix $\boldsymbol{X}$ which contains the # $x_i$ values and a vector $\boldsymbol{p}$ of fitted probabilities @@ -52,8 +50,6 @@ # This defines what is called the Hessian matrix. # -# -# # If we can set up these equations, Newton-Raphson's iterative method is normally the method of choice. It requires however that we can compute in an efficient way the matrices that define the first and second derivatives. # # Our iterative scheme is then given by @@ -72,7 +68,6 @@ # # If we can compute these matrices, in particular the Hessian, the above is often the easiest method to implement. # -# # Let us quickly remind ourselves how we derive the above method. # # Perhaps the most celebrated of all one-dimensional root-finding @@ -83,8 +78,6 @@ # numerically and/or your function is not of the smooth type, we # normally discourage the use of this method. # -# -# # The Newton-Raphson formula consists geometrically of extending the # tangent line at a current point until it crosses zero, then setting # the next guess to the abscissa of that zero-crossing. The mathematics @@ -130,9 +123,6 @@ # guess near such a local extremum, so that the first derivative nearly # vanishes, then Newton-Raphson may fail totally # -# -# -# # Newton's method can be generalized to systems of several non-linear equations # and variables. Consider the case with two equations @@ -183,11 +173,8 @@ # arise in case $\boldsymbol{J}$ is nearly singular. # # It is rather straightforward to extend the above scheme to systems of -# more than two non-linear equations. In our case, the Jacobian matrix is given by the Hessian that represents the second derivative of cost function. -# -# -# -# +# more than two non-linear equations. In our case, the Jacobian matrix is given by the Hessian that represents the second derivative of cost function. + # ## Steepest descent # # The basic idea of gradient descent is @@ -207,7 +194,6 @@ # F(\mathbf{x}_k)$. This means that for a sufficiently small $\gamma_k$ # we are always moving towards smaller function values, i.e a minimum. # -# # The previous observation is the basis of the method of steepest # descent, which is also referred to as just gradient descent (GD). One # starts with an initial guess $\mathbf{x}_0$ for a minimum of $F$ and @@ -220,7 +206,6 @@ # The parameter $\gamma_k$ is often referred to as the step length or # the learning rate within the context of Machine Learning. # -# # Ideally the sequence $\{\mathbf{x}_k \}_{k=0}$ converges to a global # minimum of the function $F$. In general we do not know if we are in a # global or local minimum. In the special case when $F$ is a convex @@ -239,9 +224,6 @@ # Note that the gradient is a function of $\mathbf{x} = # (x_1,\cdots,x_n)$ which makes it expensive to compute numerically. # -# -# -# # The gradient descent method # is sensitive to the choice of learning rate $\gamma_k$. This is due # to the fact that we are only guaranteed that $F(\mathbf{x}_{k+1}) \leq @@ -253,9 +235,7 @@ # Many of these shortcomings can be alleviated by introducing # randomness. One such method is that of Stochastic Gradient Descent # (SGD), see below. -# -# -# + # ## Convex functions # # Ideally we want our cost/loss function to be convex(concave). @@ -270,11 +250,8 @@ # $\mathbb{R}$. Examples of convex sets of $\mathbb{R}^2$ are the # regular polygons (triangles, rectangles, pentagons, etc...). # -# -# # **Convex function**: Let $X \subset \mathbb{R}^n$ be a convex set. Assume that the function $f: X \rightarrow \mathbb{R}$ is continuous, then $f$ is said to be convex if $$f(tx_1 + (1-t)x_2) \leq tf(x_1) + (1-t)f(x_2) $$ for all $x_1, x_2 \in X$ and for all $t \in [0,1]$. If $\leq$ is replaced with a strict inequaltiy in the definition, we demand $x_1 \neq x_2$ and $t\in(0,1)$ then $f$ is said to be strictly convex. For a single variable function, convexity means that if you draw a straight line connecting $f(x_1)$ and $f(x_2)$, the value of the function on the interval $[x_1,x_2]$ is always below the line as illustrated below. # -# # In the following we state first and second-order conditions which # ensures convexity of a function $f$. We write $D_f$ to denote the # domain of $f$, i.e the subset of $R^n$ where $f$ is defined. For more @@ -291,8 +268,6 @@ # make a drawing of $f(x) = x^2+1$ and draw the tangent line to $f(x)$ and # note that it is always below the graph. # -# -# # **Second order condition.** # # Assume that $f$ is twice @@ -302,12 +277,8 @@ # single-variable function this reduces to $f''(x) \geq 0$. Geometrically this means that $f$ has nonnegative curvature # everywhere. # -# -# # This condition is particularly useful since it gives us an procedure for determining if the function under consideration is convex, apart from using the definition. # -# -# # The next result is of great importance to us and the reason why we are # going on about convex functions. In machine learning we frequently # have to minimize a loss/cost function in order to find the best @@ -324,11 +295,8 @@ # is minimal, where $f$ is convex and differentiable. Then, any point # $x^*$ that satisfies $\nabla f(x^*) = 0$ is a global minimum. # -# -# # This result means that if we know that the cost/loss function is convex and we are able to find a minimum, we are guaranteed that it is a global minimum. -# -# + # ### Some simple problems # # 1. Show that $f(x)=x^2$ is convex for $x \in \mathbb{R}$ using the definition of convexity. Hint: If you re-write the definition, $f$ is convex if the following holds for all $x,y \in D_f$ and any $\lambda \in [0,1]$ $\lambda f(x)+(1-\lambda)f(y)-f(\lambda x + (1-\lambda) y ) \geq 0$. @@ -339,7 +307,6 @@ # # * $g(x) = -\ln(x)$ is convex for $x \in (0,\infty)$. # -# # 3. Let $f(x) = x^2$ and $g(x) = e^x$. Show that $f(g(x))$ and $g(f(x))$ is convex for $x \in \mathbb{R}$. Also show that if $f(x)$ is any convex function than $h(x) = e^{f(x)}$ is convex. # # 4. A norm is any function that satisfy the following properties @@ -350,13 +317,10 @@ # # * $f(x) \leq 0$ for all $x \in \mathbb{R}^n$ with equality if and only if $x = 0$ # -# # Using the definition of convexity, try to show that a function satisfying the properties above is convex (the third condition is not needed to show this). -# -# + # ## Standard steepest descent # -# # Before we proceed, we would like to discuss the approach called the # **standard Steepest descent** (different from the above steepest descent discussion), which again leads to us having to be able # to compute a matrix. It belongs to the class of Conjugate Gradient methods (CG). @@ -381,8 +345,6 @@ # # When we have found the exact solution, $\boldsymbol{r}=0$. # -# -# # The residual is zero when we reach the minimum of the quadratic equation # $$ @@ -392,7 +354,6 @@ # with the constraint that the matrix $\boldsymbol{A}$ is positive definite and # symmetric. This defines also the Hessian and we want it to be positive definite. # -# # We denote the initial guess for $\boldsymbol{x}$ as $\boldsymbol{x}_0$. # We can assume without loss of generality that @@ -408,7 +369,6 @@ # instead. # -# # One can show that the solution $\boldsymbol{x}$ is also the unique minimizer of the quadratic form # $$ @@ -426,7 +386,6 @@ # and # $\boldsymbol{x}_0=0$ it is equal $-\boldsymbol{b}$. # -# # We can compute the residual iteratively as # $$ @@ -728,7 +687,6 @@ y = 4+3*x+np.random.randn(m,1) # and we want to find $\beta$ such that $C(\beta)$ is minimized. # -# # Computing $\partial C(\beta) / \partial \beta_0$ and $\partial C(\beta) / \partial \beta_1$ we can show that the gradient can be written as # $$ @@ -739,7 +697,6 @@ y = 4+3*x+np.random.randn(m,1) # where $X$ is the design matrix defined above. # -# # The Hessian matrix of $C(\beta)$ is given by # $$ @@ -751,8 +708,6 @@ y = 4+3*x+np.random.randn(m,1) # This result implies that $C(\beta)$ is a convex function since the matrix $X^T X$ always is positive semi-definite. # -# -# # We can now write a program that minimizes $C(\beta)$ using the gradient descent method with a constant learning rate $\gamma$ according to # $$ @@ -766,8 +721,6 @@ y = 4+3*x+np.random.randn(m,1) # And finally we can compare our solution for $\beta$ with the analytic result given by # $\beta= (X^TX)^{-1} X^T \mathbf{y}$. # -# -# # Here is our simple example # In[7]: @@ -925,8 +878,30 @@ plt.show() # * **GD treats all directions in parameter space uniformly.** Another major drawback of GD is that unlike Newton's method, the learning rate for GD is the same in all directions in parameter space. For this reason, the maximum learning rate is set by the behavior of the steepest direction and this can significantly slow down training. Ideally, we would like to take large steps in flat directions and small steps in steep directions. Since we are exploring rugged landscapes where curvatures change, this requires us to keep track of not only the gradient but second derivatives. The ideal scenario would be to calculate the Hessian but this proves to be too computationally expensive. # # * GD can take exponential time to escape saddle points, even with random initialization. As we mentioned, GD is extremely sensitive to initial condition since it determines the particular local minimum GD would eventually reach. However, even with a good initialization scheme, through the introduction of randomness, GD can still take exponential time to escape saddle points. + +# ## Stochastic Gradient Descent (SGD) # -# ## Stochastic Gradient Descent +# In stochastic gradient descent, the extreme case is the case where we +# have only one batch, that is we include the whole data set. +# +# This process is called Stochastic Gradient +# Descent (SGD) (or also sometimes on-line gradient descent). This is +# relatively less common to see because in practice due to vectorized +# code optimizations it can be computationally much more efficient to +# evaluate the gradient for 100 examples, than the gradient for one +# example 100 times. Even though SGD technically refers to using a +# single example at a time to evaluate the gradient, you will hear +# people use the term SGD even when referring to mini-batch gradient +# descent (i.e. mentions of MGD for “Minibatch Gradient Descent”, or BGD +# for “Batch gradient descent” are rare to see), where it is usually +# assumed that mini-batches are used. The size of the mini-batch is a +# hyperparameter but it is not very common to cross-validate or bootstrap it. It is +# usually based on memory constraints (if any), or set to some value, +# e.g. 32, 64 or 128. We use powers of 2 in practice because many +# vectorized operation implementations work faster when their inputs are +# sized in powers of 2. +# +# In our notes with SGD we mean stochastic gradient descent with mini-batches. # # Stochastic gradient descent (SGD) and variants thereof address some of # the shortcomings of the Gradient descent method discussed above. @@ -954,8 +929,6 @@ plt.show() # minibatches. We denote these minibatches by $B_k$ where # $k=1,\cdots,n/M$. # -# -# # As an example, suppose we have $10$ data points $(\mathbf{x}_1,\cdots, \mathbf{x}_{10})$ # and we choose to have $M=5$ minibathces, # then each minibatch contains two data points. In particular we have @@ -995,7 +968,7 @@ plt.show() import numpy as np n = 100 #100 datapoints -M = 5 #size of each minibatch +M = 5 #size of each mini-batche m = int(n/M) #number of minibatches n_epochs = 10 #number of epochs @@ -1016,8 +989,6 @@ for epoch in range(1,n_epochs+1): # cheaper since we sum over the datapoints in the $k-th$ minibatch and not # all $n$ datapoints. # -# -# # A natural question is when do we stop the search for a new minimum? # One possibility is to compute the full gradient after a given number # of epochs and check if the norm of the gradient is smaller than some @@ -1029,8 +1000,6 @@ for epoch in range(1,n_epochs+1): # compare the values of the cost function and keep the $\beta$ that # gave the lowest value. # -# -# # Another approach is to let the step length $\gamma_j$ depend on the # number of epochs in such a way that it becomes very small after a # reasonable time such that we do not move at all. @@ -1072,39 +1041,41 @@ for epoch in range(1,n_epochs+1): print("gamma_j after %d epochs: %g" % (n_epochs,gamma_j)) +# We note that we have defined several hyperparameters. These are now the number of epochs, the number of mini-batches and the parameters $t_0$ and $t_1$. + # ### Program for stochastic gradient # In[12]: +# Importing various packages # Importing various packages from math import exp, sqrt from random import random, seed import numpy as np import matplotlib.pyplot as plt -from sklearn.linear_model import SGDRegressor -m = 100 -x = 2*np.random.rand(m,1) -y = 4+3*x+np.random.randn(m,1) +n = 100 +x = 2*np.random.rand(n,1) +y = 4+3*x+np.random.randn(n,1) -X = np.c_[np.ones((m,1)), x] +X = np.c_[np.ones((n,1)), x] +XT_X = X.T @ X theta_linreg = np.linalg.inv(X.T @ X) @ (X.T @ y) print("Own inversion") print(theta_linreg) -sgdreg = SGDRegressor(max_iter = 50, penalty=None, eta0=0.1) -sgdreg.fit(x,y.ravel()) -print("sgdreg from scikit") -print(sgdreg.intercept_, sgdreg.coef_) - +# Hessian matrix +H = (2.0/n)* XT_X +EigValues, EigVectors = np.linalg.eig(H) +print(f"Eigenvalues of Hessian Matrix:{EigValues}") theta = np.random.randn(2,1) -eta = 0.1 +eta = 1.0/np.max(EigValues) Niterations = 1000 for iter in range(Niterations): - gradients = 2.0/m*X.T @ ((X @ theta)-y) + gradients = 2.0/n*X.T @ ((X @ theta)-y) theta -= eta*gradients print("theta from own gd") print(theta) @@ -1114,8 +1085,9 @@ Xnew = np.c_[np.ones((2,1)), xnew] ypredict = Xnew.dot(theta) ypredict2 = Xnew.dot(theta_linreg) - n_epochs = 50 +M = 5 #size of each minibatch +m = int(n/M) #number of minibatches t0, t1 = 5, 50 def learning_schedule(t): return t0/(t+t1) @@ -1123,16 +1095,20 @@ def learning_schedule(t): theta = np.random.randn(2,1) for epoch in range(n_epochs): +# Can you figure out a better way of setting up the contributions to each batch? for i in range(m): - random_index = np.random.randint(m) - xi = X[random_index:random_index+1] - yi = y[random_index:random_index+1] - gradients = 2 * xi.T @ ((xi @ theta)-yi) + random_index = M*np.random.randint(m) + xi = X[random_index:random_index+M] + yi = y[random_index:random_index+M] + gradients = (2.0/M)* xi.T @ ((xi @ theta)-yi) eta = learning_schedule(epoch*m+i) theta = theta - eta*gradients print("theta from own sdg") print(theta) + + + plt.plot(xnew, ypredict, "r-") plt.plot(xnew, ypredict2, "b-") plt.plot(x, y ,'ro') @@ -1143,6 +1119,11 @@ plt.title(r'Random numbers ') plt.show() +# In the above code, we have use replacement in setting up the +# mini-batches. The discussion +# [here](https://sebastianraschka.com/faq/docs/sgd-methods.html) may be +# useful. More material will be added later. + # ## Momentum based GD # # The stochastic gradient descent (SGD) is almost always used with a @@ -1181,8 +1162,6 @@ plt.show() # where we have defined $\Delta \boldsymbol{\theta}_{t}= \boldsymbol{\theta}_t-\boldsymbol{\theta}_{t-1}$. # -# -# # Let us try to get more intuition from these equations. It is helpful # to consider a simple physical analogy with a particle of mass $m$ # moving in a viscous medium with drag coefficient $\mu$ and potential @@ -1256,8 +1235,6 @@ plt.show() # One of the major advantages of NAG is that it allows for the use of a larger learning rate than GDM for the same choice of $\gamma$. # -# -# # In stochastic gradient descent, with and without momentum, we still # have to specify a schedule for tuning the learning rates $\eta_t$ # as a function of time. As discussed in the context of Newton's @@ -1276,10 +1253,9 @@ plt.show() # # Recently, a number of methods have been introduced that accomplish # this by tracking not only the gradient, but also the second moment of -# the gradient. These methods include AdaGrad, AdaDelta, RMS-Prop, and +# the gradient. These methods include AdaGrad, AdaDelta, Root Mean Squared Propagation (RMS-Prop), and # ADAM. -# -# + # ### RMS prop # # In RMS prop, in addition to keeping a running average of the first @@ -1314,7 +1290,7 @@ plt.show() # directions where the norm of the gradient is consistently large. This # greatly speeds up the convergence by allowing us to use a larger # learning rate for flat directions. -# + # ### ADAM optimizer # # A related algorithm is the ADAM optimizer. In ADAM, we keep a running @@ -1393,7 +1369,7 @@ plt.show() # * **Monitor the out-of-sample performance.** Always monitor the performance of your model on a validation set (a small portion of the training data that is held out of the training process to serve as a proxy for the test set. If the validation error starts increasing, then the model is beginning to overfit. Terminate the learning process. This *early stopping* significantly improves performance in many settings. # # * **Adaptive optimization methods don't always have good generalization.** Recent studies have shown that adaptive methods such as ADAM, RMSPorp, and AdaGrad tend to have poor generalization compared to SGD or SGD with momentum, particularly in the high-dimensional limit (i.e. the number of parameters exceeds the number of data points). Although it is not clear at this stage why these methods perform so well in training deep neural networks, simpler procedures like properly-tuned SGD may work as well or better in these applications. -# + # ## Automatic differentiation # # [Automatic differentiation (AD)](https://en.wikipedia.org/wiki/Automatic_differentiation), @@ -1421,8 +1397,6 @@ plt.show() # while numerical differentiation can introduce round-off errors in the # discretization process and cancellation # -# -# # Python has tools for so-called **automatic differentiation**. # Consider the following example @@ -1619,35 +1593,38 @@ x = 2.7 print("The computed derivative of f5 at x = %g is: %g"%(x,f5_grad(x))) -# 1 -# 8 -# -# < -# < -# < -# ! -# ! -# C -# O -# D -# E -# _ -# B -# L -# O -# C -# K -# -# -# p -# y -# c -# o -# d - # In[19]: +import autograd.numpy as np +from autograd import grad +def f6_for(x): + val = 0 + for i in range(10): + val = val + x**i + return val + +def f6_while(x): + val = 0 + i = 0 + while i < 10: + val = val + x**i + i = i + 1 + return val + +f6_for_grad = grad(f6_for) +f6_while_grad = grad(f6_while) + +x = 0.5 + +# Print the computed derivaties of f6_for and f6_while +print("The computed derivative of f6_for at x = %g is: %g"%(x,f6_for_grad(x))) +print("The computed derivative of f6_while at x = %g is: %g"%(x,f6_while_grad(x))) + + +# In[20]: + + import autograd.numpy as np from autograd import grad # Both of the functions are implementation of the sum: sum(x**i) for i = 0, ..., 9 @@ -1659,7 +1636,7 @@ for i in range(10): print("The analytical derivative of f6 at x = %g is: %g"%(x,f6_grad_analytical)) -# In[20]: +# In[21]: import autograd.numpy as np @@ -1693,30 +1670,29 @@ print("The analytical derivative of f7 at n = %d is: %g"%(n,f7_grad_analytical)) # Note that if n is equal to zero or one, Autograd will give an error message. This message appears when the output is independent on input. # +# Autograd supports many features. However, there are some functions that is not supported (yet) by Autograd. # -# Autograd supports many features. However, there are some functions that are not supported (yet) by Autograd. -# -# Assigning a value to the variable being differentiated with respect to is an example thereof. +# Assigning a value to the variable being differentiated with respect to -# In[21]: +# In[22]: -#import autograd.numpy as np -#from autograd import grad -#def f8(x): # Assume x is an array -# x[2] = 3 -# return x*2 +import autograd.numpy as np +from autograd import grad +def f8(x): # Assume x is an array + x[2] = 3 + return x*2 -#f8_grad = grad(f8) +f8_grad = grad(f8) -#x = 8.4 +x = 8.4 -#print("The derivative of f8 is:",f8_grad(x)) +print("The derivative of f8 is:",f8_grad(x)) # Here, Autograd tells us that an 'ArrayBox' does not support item assignment. The item assignment is done when the program tries to assign x[2] to the value 3. However, Autograd has implemented the computation of the derivative such that this assignment is not possible. -# In[22]: +# In[23]: import autograd.numpy as np @@ -1736,7 +1712,7 @@ print("The derivative of f9 is:",f9_grad(x)) # version of a Numpy array. To overcome this, an alternative syntax # which also computed the dot product can be used: -# In[ ]: +# In[24]: import autograd.numpy as np @@ -1757,7 +1733,7 @@ print("The gradient of f9 is:",f9_alternative_grad(x)) # The documentation recommends to avoid inplace operations such as -# In[ ]: +# In[25]: a += b @@ -1766,4 +1742,184 @@ a*= b a /=b -# More examples will be added, in particular how to compare autograd with own codes for the gradients. +# ## Using Autograd with OLS +# +# We conclude the part on optmization by showing how we can make codes +# for linear regression and logistic regression using **autograd**. The +# first example shows results with ordinary leats squares. + +# In[26]: + + +# Using Autograd to calculate gradients for OLS +from random import random, seed +import numpy as np +import autograd.numpy as np +import matplotlib.pyplot as plt +from autograd import grad + +def CostOLS(beta): + return (1.0/n)*np.sum((y-X @ beta)**2) + +n = 100 +x = 2*np.random.rand(n,1) +y = 4+3*x+np.random.randn(n,1) + +X = np.c_[np.ones((n,1)), x] +XT_X = X.T @ X +theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y) +print("Own inversion") +print(theta_linreg) +# Hessian matrix +H = (2.0/n)* XT_X +EigValues, EigVectors = np.linalg.eig(H) +print(f"Eigenvalues of Hessian Matrix:{EigValues}") + +theta = np.random.randn(2,1) +eta = 1.0/np.max(EigValues) +Niterations = 1000 +# define the gradient +training_gradient = grad(CostOLS) + +for iter in range(Niterations): + gradients = training_gradient(theta) + theta -= eta*gradients +print("theta from own gd") +print(theta) + +xnew = np.array([[0],[2]]) +Xnew = np.c_[np.ones((2,1)), xnew] +ypredict = Xnew.dot(theta) +ypredict2 = Xnew.dot(theta_linreg) + +plt.plot(xnew, ypredict, "r-") +plt.plot(xnew, ypredict2, "b-") +plt.plot(x, y ,'ro') +plt.axis([0,2.0,0, 15.0]) +plt.xlabel(r'$x$') +plt.ylabel(r'$y$') +plt.title(r'Random numbers ') +plt.show() + + +# ### Including Stochastic Gradient Descent with Autograd +# +# In this code we include the stochastic gradient descent approach discussed above. Note here that we specify which argument we are taking the derivative with respect to when using **autograd**. + +# In[27]: + + +# Using Autograd to calculate gradients using SGD +# OLS example +from random import random, seed +import numpy as np +import autograd.numpy as np +import matplotlib.pyplot as plt +from autograd import grad + +# Note change from previous example +def CostOLS(y,X,theta): + return np.sum((y-X @ theta)**2) + +n = 100 +x = 2*np.random.rand(n,1) +y = 4+3*x+np.random.randn(n,1) + +X = np.c_[np.ones((n,1)), x] +XT_X = X.T @ X +theta_linreg = np.linalg.pinv(XT_X) @ (X.T @ y) +print("Own inversion") +print(theta_linreg) +# Hessian matrix +H = (2.0/n)* XT_X +EigValues, EigVectors = np.linalg.eig(H) +print(f"Eigenvalues of Hessian Matrix:{EigValues}") + +theta = np.random.randn(2,1) +eta = 1.0/np.max(EigValues) +Niterations = 1000 + +# Note that we request the derivative wrt third argument (theta, 2 here) +training_gradient = grad(CostOLS,2) + +for iter in range(Niterations): + gradients = (1.0/n)*training_gradient(y, X, theta) + theta -= eta*gradients +print("theta from own gd") +print(theta) + +xnew = np.array([[0],[2]]) +Xnew = np.c_[np.ones((2,1)), xnew] +ypredict = Xnew.dot(theta) +ypredict2 = Xnew.dot(theta_linreg) + +plt.plot(xnew, ypredict, "r-") +plt.plot(xnew, ypredict2, "b-") +plt.plot(x, y ,'ro') +plt.axis([0,2.0,0, 15.0]) +plt.xlabel(r'$x$') +plt.ylabel(r'$y$') +plt.title(r'Random numbers ') +plt.show() + +n_epochs = 50 +M = 5 #size of each minibatch +m = int(n/M) #number of minibatches +t0, t1 = 5, 50 +def learning_schedule(t): + return t0/(t+t1) + +theta = np.random.randn(2,1) + +for epoch in range(n_epochs): +# Can you figure out a better way of setting up the contributions to each batch? + for i in range(m): + random_index = M*np.random.randint(m) + xi = X[random_index:random_index+M] + yi = y[random_index:random_index+M] + gradients = (1.0/M)*training_gradient(yi, xi, theta) + eta = learning_schedule(epoch*m+i) + theta = theta - eta*gradients +print("theta from own sdg") +print(theta) + + +# ### And Logistic Regression + +# In[28]: + + +import autograd.numpy as np +from autograd import grad + +def sigmoid(x): + return 0.5 * (np.tanh(x / 2.) + 1) + +def logistic_predictions(weights, inputs): + # Outputs probability of a label being true according to logistic model. + return sigmoid(np.dot(inputs, weights)) + +def training_loss(weights): + # Training loss is the negative log-likelihood of the training labels. + preds = logistic_predictions(weights, inputs) + label_probabilities = preds * targets + (1 - preds) * (1 - targets) + return -np.sum(np.log(label_probabilities)) + +# Build a toy dataset. +inputs = np.array([[0.52, 1.12, 0.77], + [0.88, -1.08, 0.15], + [0.52, 0.06, -1.30], + [0.74, -2.49, 1.39]]) +targets = np.array([True, True, False, True]) + +# Define a function that returns gradients of training loss using Autograd. +training_gradient_fun = grad(training_loss) + +# Optimize weights using gradient descent. +weights = np.array([0.0, 0.0, 0.0]) +print("Initial loss:", training_loss(weights)) +for i in range(100): + weights -= training_gradient_fun(weights) * 0.01 + +print("Trained loss:", training_loss(weights)) + diff --git a/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_123_1.png b/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_123_1.png new file mode 100644 index 0000000000000000000000000000000000000000..fcf4c6806bc9b6341be72e93bceb25da03f4f055 GIT binary patch literal 11310 zcmb_?cQl-DwFbIhjhCvW@ z^ub{62-E+=bcb$9Ix_`WD*4poW_Uw1}{p=mDtF1~-%1DZbhexiirlgODho6Xh z=PiZR0eO3fz-(sw zcJv`iR{fE*CfzMUVXCk9=pyflnI=*=J-feN6~~~f7hlq#DtqU>9-Sy_YiX5g%%?j! z-%<$Py{~$cckelMA0hQalHiwj*fH9fV9a%?Q>u1l);4&%X1`#0v*R*nt7f~Vv!-^Z zzOtaQK-gbZNvSNmqlw@iRmyfzG&=`J%46Gi@6@<77&thn-~UJHW!K7(aJAanTc=>c{E49>6%+`qB($NH#l z+JO|u;A0SHX3z35_`VPnRmKvh_K2Hoehgku7)E+^PlADgFoaHmrfT9C42Zw|n4?<1 z?;al9B^+rE+g!Y6^_L<{^K?iS(3ur5cnU6-GcOG6lyhFn z%9*DIn%jZapo5m~pfus7LN^c)?$QMw148v4tX1U9w~p=V0T*6_D8cg)9w$u)s372i z3&`QO$xwmq)ehVR-$P^OTybpI3TSQ*N`UXm3lHWyfyP#(>P4Vz4vEryoE!F_vv`jH ze;_6WEI=;rod!N78~Pv&T?hHuo1~iCg0f=P2J!78Yx{jKybDmfZ-AIMaGfZ06TZv2 za=_Vd%PBnL?7Pq+0v(0B*tU^di$Nz|!=VE8wZPTO2ynhTXd>?TI%o#%pA5d1%Uh-a z`8_WP*n#glgU4~YY^PcqEL#Blt2?#Egz_+QAr@G#5Mw255xP8%uGo=%qDkE zZrxB^Jzj&NZYL3v1q8P(Qki;MG7b7lej+`$Y@-;u<&LNNIwV{=k}~E;_-zwHpSweX zUmTCX>&0;#^Qf@RU60p;pMVj{E7;P$yzYBQg5 zBX@+Cup|MD0i=JdY^=}(*6{bWn&;i_ZI(Kt**$}<J(-8tmv5ohRcG&So1`}HDvr5?4t@d< za#Kg>P^A+Uh(eWNx3hL|S%%hBI9)9vXrCkv*$1czcSMyf8P{xQKjjMa4S7K|| z0)*;zd2w0y@!`8NNU67}W|j<_KTJKFqp|LHvGs6<9s#~_II2~2(VAk6=9mo*5w$b9 zt6(|L*KTa^1Q#}%z$7lj0K$C%VOKx;p&o)8Vu=aFvJjLhvZW)27Ix4=G6tdVwa>N4 zq)Hb82nw9!JzZ~ni^P+c50U3`o=;f3uF3=YhvPHYfqY@gFj>%y{MBN$q+DYT5*7sM zY~8dmaS6@Dr|iUZdVLUq$`NvREkx|#oYvpk8H6C|UQWgj_d(}_{Nxpcog4arndYh< z!&}obPs67WYzw&GI7G)pJ&>cJS;P^oCf|#S%+I9;;J;Fjbs{BMMNDt*dKgH2sUvJ7oukbZTVi=y5uz;y zP2hhsb;bRbCfQW7qLU=s21Jer68jDZ>>?Yv6*L$cb33tk=Q>EIw>w*WB=rg58AWoO zg%kM8!cZ+jUpjvWxVPLv;9LD~q&6%ck3o|D)+)Mv7gD|Wt`9tDsm=`imq}mXv67qf z1L4dq z@5q*y&#iA;5rV+;D#$|Er&l}F9pn;^EV3}(5Y(f$1lI$E4#y4n%fuaV#4D48S|#k~ z+N#;}a|hm7g#(s4PPP5;_Y4Md;apV)ropAd9mY}XeU{Aj4HAsd`KA7N2QOO-N`qC~Pr@pedge*jKFymXsi>md;p)mBj> z51D_V$^m4}MV>vtuZi^=j*Hv+)%`+HG(kff=F6QQNkAwF=xo*OWOQpX{+${io`(#$ zb32i^{)2E=r;ZOgWnaz<38V1e1aNTdrK^yvsUfvsGC*@OW+E9|5OL+b1Y90ZKPO0E zymmwuwV-XM7`FCn(~^{xlu9&9O!q8dFKn{G0^(4ej9@S>@%J=l2`z@cNI6s-Wr=$C z&L?mGgzkSJf&ZDj{txzhu*`#4ikOZLB zDgCnFnwpB8{e&xR{P9YmvDX9=mDqdl~q{zg6?rHvZi`Ll>RAJLKdx zbXWNjpMMwy5M*~|g|mYcBZ(KU+aN1zktr}`R`!o6oT@?I-rj+4?^9Llfy9Oos(wCl z)uOec&}0I7ybpS*G4I}$@nuBYf=VMBZn^uT>jo<5sZvh3Cn0A5n@2)$cxLW=Wds)g z@)lMI+79wFXkWwGXcBKQj{TwE3?b(2S$rHEhc(eJ^*M0X^j~b3i`QsLtD{4lo=W{W zxldX>uFg}Vb}GvC!C7|-*Ux9-TYu|6^{Pm>sSKRer|J?Q%J^_~Ay+X`hq^HzFI7re zB8#~Z2}kZI|C1uG;k#_0v*+h%nAZ@_F;ZKCxib0j(XwbY zpVhK|Jj%vr=2HW{!Q%B}8;x@-r7|zWd0FcAfZF5TD8V7Io`2kn2r|YP!tUX4j?IS= z|D#c>c7UuA4$(DJzWc4TVBz>sQr@^N!piPEIQgCHlH;^3nHQQCZ)G{^Nb3z~4Gx)y z=NQ+SWtc>8OesuzUCS?*SB71C=~&yM)gYmcENCmyvAwaWm#c%%{l-Hi-o+=2}Y* zjh+Y^9nVA*;^)XF*#$BKc{@Ia(hPdT*jKP|coWLtWa?P8jBoz;+}@~3H->`OlcpgE z;?oihwJPbB-Gi;3yiM^hrNa~RSasB(A2Hg^1?_znKII;unx=zYms$R7uevlakRimM zZ5#-m*G1y{%L78NiZ&lQ!zbX~L?_bCVQU3o#O=geMA`FRNGW763;{ahwc$Nj`D+&>jKW-K{HI$x z*fbvEx|~b^d8VvwU$^+MR`w@<`Ze8~eaR!kyjFneNbjk$$$Ec;?U(We4uI^LI^)F7 zV3lY8pYWd^HUSr_PfGqqfT7%tg<{)AjmUuyChfGDJ33{Es@lpQlD)j7Y(!*ujLe%|soF${~E&SC)R- zroQ3?S^TC=BVGOe2i2`+RMiyaOM#YyLHFH#3or{D6^ow}d4F{NIQcaRLEA;xNz`NR zhHQMD7qR-D<_%yQyirU-9UN(-mhOY@h$gQyLrTeb&>A5}TZU3mWp9r%(lIa_Jrn4pumlkQRlZoRkRgN% zPe)IFHY@9wa7A&g^50jTi45A@^S>+=mtC*>om5N9_iJ5cIQ234hRNWaH-`*Ky-wWR z`g>D)6GY%*GJ8NoE+oP zj$w8~M8oyXv~+@?)9wi_CwgwOls4{b=69d%qH<>$8Q%ggV`Hzxp&6RpuRU%qf?Ed8 z4-XELvqZ8p-3VV?o+_8v-Qohw1 zik%J42{~gq4xK%-yvVY4l3733?(~TdUAT|Cbf8wALO=eBpnhB*WySbvj;^x>bu@&^ zLoG8QextT$cV*{Skyb+h`8xEEo6}a&i=G<{$#RRE`N?`#hhTcCuW=uy9A`K8)t5`} zp^r+KPeuZGOBH{87BDk63th3cI>KHY7-Es^!0Tt`ofx|zzwjmOT6FczP{YL0spd>; z_=ROh`paMZvvTP+!^R|vT<^YiT-{W3J<4| z$5U;0rN#-o7JV7krOwyQH<|lqzqHMux|~45mTq59Ez9POjmbt|_T7swAsVN!bLBQl zA~bu=%rwvJ);GMlDrYmcz_PI z*=*>?o=_}LSAjV5V&`YX#FBfxwR{cl4M4m^t;Re_0^OWV9b!SEXc_g+=aK!Ng8rTD zw@cZLO|KGnB?|}bjHd!@*~VGL^OlHD-DZVf>Fw96YlL#x+|B$hSsM0e%RSs>eHTDCh?wkFAzT}Qu*(N0|LfF8mf|2R<`R@JYJgZ zXCY>K0pAImrDr|Wp$wi|{^>isujQ?VAjJ+uxL=L~5Pade8J+k_x0f3fnrCgJN$ehc zPe$r}ro=-5P9AWR@pftiv?u{cX8W6b+YigrDlQLY3l_Q_oH=w^2ORKYFXAdL-^%y2 zRdO4M{-nvkye@i+nytEwrh*Vy6N(YkMhpj5JRlY!7*mWT;|)}dZwo$Qv*eaB=P*~L z@NwNC5AG=a_W35JWATlQM^ZQ%p>;F2H*r4hDm~ixKAzX%RV{MLahit=`3z|ddsf8c zA@8AHJb~*yxQAs-Ks;~ZY+f5a7gp+7Lc)|Tdwc#>Fj?lhuAmFe!i%t8fOy5#W1TFf zJ$|&6`R{KZ*RF z1Q3^MWTo{QM9hE95Yl&k=?tpGZzZV2TZoYE%eV~eo~SadQ_5^0v3~?DYF01aS`DK% zyRY{uu4GK%SkxaO%WAj&Wme+6jyQwW?taDr*E4*lBGbA~d7?!E8GIR*LE)!$0cC?q zj!z_Cs~v8cnWt&d-4i%t*0P-yFq;T9o>)B|l7~+stU>YgZb6RZiode>OT?tdTUj+T zf4V`}&FEF1a#v>o)YV@PY;*krd@wXaC>PH`gG>c}t`7zhIA92PlF*r#tcO-0zI9=P z?$gJHg`AC{o6BAWy4F)5?Flny^aZ3w6&(#rEAPsgLWDk5ON)wZl&; zDzD5@E+Y%;gPc9tn+xKu%fVJuX6ni>HGWJ!UsmAe+R)}2j(+;KNc2ZTq~fZ{o8Z3` z`9F|;uOfM}ALYdSNb6{ZUGd8_T>OOjxBPB!6xv?V171F$v)vBs5pEpDUhWNr9*>L- z4;VQ?*LG1wU9{&@?4I0--!hg!XYR0OSSXBgG1Po_cIdrsxqk*&M)D7x?bZ}B$X9c; z`$yF+AHjqQ0lN{`1h8=PU96ek{RYf4yrk`xcY~#wlM)?FsPkQ+OSWmjd^~Bhl)Co^ zhF^`gSn3#V5it{o(3z0)69YbQ+GQNo{GnEfY3b3{vd~g=w&(_kQ`85K4N>Ipw_1yh zWx-7f{IY|6n#xS}Q!B#aBvX*w)myMyn0$mguBC7%3Zrw^XDXHIGV}S&vkiytj7|$EZ;D^jKCfq`L+M-aHEkMwCMneqmJl$? zQ@(U+m(hjPmw)T6XfB^F3_ak+4)o}pCQ#&W5&!yyV3V!D+`Wlu)jq{EfY*2E8j^Wt z+9-D~a=NWNm4`O-o6Ig)G9z(}RA)xnJ@v#QYgXXREaLkD;a5gI$49DHcB(R~Q9D)$ z*{zSbi@CrBX=r2 z)(cfVS9>TE1WliLMA`W@;>~^LWH7FGkk-k*#}(@ZH+Rxu9!M{iRf(0nJIeR0twDM--p&rC5O(-c_4;9OC>km5Z~nXR!Of@T z>-7iS+w;>b=5D!X5S`)?bjzOc{!qg9ukbNkk@8!qj?7)BJn%Dc^Nji1(bvhh89k#P z&N2xf;e(yZ0``9G zo=&LB>l|RtRiS+Ln)$4Yt2J}^lb@&Ri_6Js#JsjYYhDp|cr99FfwD*gJ1XAXcCQ-^ zJ+K@vKJ;s!WF2rj=X2PqNUc8l!hyprdF*g`L9u_0X~o9noUtseC{)mX5#@{BMGMFV zy&P1iGC^oM$h>)}0d<;J)#4&U;vrd)rZ(&zD#csQa<)p6KPFB~Aq~r|F6E<2yo;>^y$n_W;yz#=D|L6Bf6-90q4zL5 zzo~?^-VLqT&}7)(ljeMJ828JpXv?{?WAVFv!Fib{M=`2_1J^_A?<_6CDTqMrnC}PI z^RU^)>#hsA(*3c!*|^Lx?Xxvilr>30GjaskHM(nj+>l$~@B@3Das2WsM=>xaFEoF~ zE9=iR$FleIv}<4`jWK$oTGn?7VGV@ZgT&y7LITFf+l~VUr-MlXns4V$wjWh!g=F%E zFZHG0jyw3t)X&hr+@680pkMF`ud37ZQJ?+D-d^Zi>^54Sudm5aEQpsj24M|&(8j+W zAl0?U)C%00y$kk21y#WJhIY03=LdLwHp$0jJn(783q~@$>q{`dWQI$Mi(Sf@cqgMt zgxr{25FHNLsqH?`YH+>uCiPEyH4QWWW?|eN#o@#-AFdmvOom9ty5^~|2qf-yeXJc1 zNFSu!A6k$T%`3Q8A!Mrw7C^({J`ZYAo4EG~0Y(~|MLhey!b{sSShVt$6I?{jXYK{j zOvC1H&Di7Vo}^b78wBSk=4_ic&a8H0t79@P7ZTmlcK1IRe<*V3DF_DXCsp>)20ypz zKFm0Z?$HqSbNTqy+&rpBgKmn-^JgB<>Gu7)vJqs4B;S>IVc=K!u-}|vCRxUQ;+c|P zM!kA=alPr*`>mVpvhY_0&1t+sX7BS?*;PODy1RTRTe%s_0*kF zk{7J>Fdl!B$9^yADkRr)^8O}~t3&5}Q(a&?s;On`Y-K^h*^E0@3~Fw7HSheeMME#N zexvmw@bV$9kWPHr@jXEx4`_q`q0+V3bGJ9|V5L=eR&>bd+i;q>0)tLP8 zhY8g&l~PSiXO_~}X~;{GQtI>o%7J=uze$-b(~7GwQLM{S;e(xITVll4h_?2!JN^fr zy3#{MVy|C3u?EYP-RDPf6k~`h;p$-C_X6_E=K#y1a&GKqSzA+2u(}eC%hS;pBXo*5Q#dOKOpQ#bqE zR8rRrzUZ5A`o{rJ$SZ4;a zUWA?Kg`elIz~)%ZU9JeShfSuxm!VUad za2JuvTlhTr?uQ`9;u*oNCRK-ai&9kg2Cpqwar&khy`=O)w_~UL6|_BUPf{xkv>dpU z!9ua$^LkM(nH|CNl=jCYwF+a+%0nYav>y4+!&ME2808CgRdB`6GwcK6^vrw#IftoR z*xn1Rn}VCqpO2cZ5=33S=pe4wwr3L+9cz zo$Jq=x%J=iEm` z-t5O|CLmK;Oou!8p>4mvs%xA$3m_mTGa}+DEah%KE0QHI)y70^O>X=x^ zW9)%}Wb;G_5%XkLLYRkCp>-I!{LZnj*a>qq!BV;AL1Zk^wp-`z&a!7&q!*b8G0M@P zFw5di`X=9NEslX{o_Bx%P?z3WwV|F`a$!lz^P z*4ROZrK6_s&BaIIL-;xY{w?hI=Hh-?2jgkU#^wQjO@9RAiNB?96#Z4@H; z>vH&1TOa?*8h0?YvM=x{dEUaQE#vZ+=)pKjGeI8SZ3%594qR)XR7+RC zu`f7*1ol@>c5wN}ct;7W59E_CemP*4J4$OcQf-U~s4q3PD{p^S#xd;>l-0j6D+b)# zh+!!c9Ut zvggx4XU~G=dhCuVDy~CVXS+h5IP9VC6SGd`qpiY8d$PTyu7h0Gr8l+hHv}d=fy~`0 zF2|BJq&XX6p{OJoXyDa(7h4`dFXnJPUl!?22E9IOj@w~sIhkVKj9o)$f`XN#=4wNQqqshj*s_eAZeRCOh+K=#)9Wg@@!wxR9-Y~c14WiF%emW#?M8sZ8 z)9Ka^8G&lcN$rht5`0KKje;sI``W1582{wD-vTlbCldS_JWLEdzDfj$ClMwk3g%d3 zy=k1Dnny>Iv=?qdawn9y;(k)cf-UjB?C*QST@1Uo7DG9NsNRB_d)(wYLll(NiKfjI z3N%&u#+1tp)S=Oyj}F3s(rkb5cO5`!i`S_?IT(e@Jcc5g1I}dqAk@+Clv2(3c>Q|@ z5tQEOV%PwzM_-HXBc?mHr8}RI(PmYN#X`C4hensFtMUVBF*QLX~1t<@{0K@N&M>t%xS&i7tkubPmY*gdO~c zNQ$cZR&${cX?|DbAzq0EiH45*zc9Yf2Tx_aJ>sr9o|yfypj5Ux9oF~Q=d9qQyeNcZ zyO$X4nqN-pPE{@R_qZ&OV@p#ZhT2dyD4&)}{n;K*q6PY8Q-0SFj;elD{d1)nlRX}? zZ{cTFkHP7RQzRNnTq=&}m$}_s7=3+*a1Q-}nucgS610|2^!5{_G7TeR61zP!*(ft5 zF79cgzJPUF-(q%-)YNSa25GsX6_J=@nNqZYCC&YnlcY5P@ER&IX!ZQBkF= zPC-tVZd+{a>tvf++a!Un`w{eI3~9K5Qi>U_0x@pG(5zr{BVu64rd1qz-;)xGet7IH z9{l8W2Jvxt&KM+cy2dDe=n)4;dv_mQ{s1>uy`Kr<<0Wt-pzFXS|9FoZ7nl5FH6FYN+Q3|Gwp)~Mb!Wv--D6ZN0=tNt%*SO4F@)sM)4Os=2_@O%R3tXahFuOM*s z9%$zF`E3tY4>F-ac#=BbUuOBos0XWI3HvvVohZB;`Zl3~0Nk2bL_IGcSm+b~+O-$5 zX*VA3!Yl*`=|sQ_)E~AaG2%hArQhAT?+{YMuA-agS(_;lH}Et~geG>KVFN?vQF!MC zp%4`0&t|$0lhW`UtYut<#4;#&4%X$YCfdn4TBVv%Fc%!&2qCA_|7w(D>IFkGfhu@D z7Y<=mZ>e~1$Vezj$)7uphZhK=YUu#8whgodRgYw?G_{;ZpKSQ9Hz`_F&x7<%Sl ztMyCjIOigyZ=L1sf7$BAz=JWzvM zFgrc@T#r0=0tzy$e1pLF!SySfXE81ldN6{$3zt++kQP=BY0c|0;T=H*0|pLOcDt)2 z0#8GMukxxJp zP|I^ay525s^__2G)m3|7domAW@T=j`zoYKEFZ4+;ph*e7*UO2Gvd4d4bJvA>$8^e5 z-Sm){sC|!8sW3rLXs9u?cib7a+6wuhbm3y5VL4NIM>v>?m{k}mN$2CQ571ka>4$HC z=dH(f=cwhG;=YXvL#<$MkV}cZ>aG*7p4cw)8<}B1hK{J*6r+)DN8C_6En=uqWuPOx zVqR1&_pxR4@7zcFXpX1xU-*H+#J$N!ki=ex4ooe`@7@6=Fj!0`L7j7)CxXa-*#)#o zfF@8?zQQqLI)jN&MaUi}3Rdr#zTn=?O)3B4uA+zgCSLtz@i7RcLf>U-r#qZAe~oi* zN&a6#3i-h`-=$V&51u!VG>^QC2-RBf@DCTg!blwuzvZxf;@N>w@n2@X!9M&x1}DOO zF-{w8*$|HKw+qm0oR&GOBSN87r1RpMDciVjLEK3lc!h)qjjmlwPoVU+15J|modb@87RX9hWcLH?1fEJI!)EVpyW_E;jbocDpHpz` zk3Ag^fp&k!1)#;C?ve3S#eY?LbSQ8U(1Y*BFQf&*IBaK?$>`9tgU;qXuC!oLgw5B2 zx6C6)Nkhd3BpPmC67+}wBP>}@UQ6CNSCoM89Z36Q&EI>5-D&HC`{6G{B*@MsJaG-a z6>=}&8>01fh|K3bN02{N)8Ydg&}igNgxiCs|Cs@*wdi!T7V-sBAL)n-a1yfeiA@7H8-Yad$?2Z4krQY;o1vHAD1l}5NvrMr}C7JXr@eMuYI zx0VXMWH{_gaWJWGa8{yAyi%C}K%|=16gO`Qg%EU&q#&fla`?GZK5on-9is!teQ{9M zC;&PuNLQrh<-<*5{O%Ms`LTJFcM1}AlUo!z>2latNd2?G^Z&#jZsp}h-nK~R*SHec S4!66Dr>?B6RR7%O?f(KlMKw?W literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_132_1.png b/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_132_1.png new file mode 100644 index 0000000000000000000000000000000000000000..bca109752117934179cce4328a79c468821f9ea9 GIT binary patch literal 10420 zcmbt)cT`hP*KP;`B8s3OAWe$WYv^62iGtF5mrxA|p%Vxe2wen$P!&NsD4_>P6cB;X zo0LElr3eI&5+DR_e((3)ciq13y7!NhtT|_9&z^nG%slfvJK>Ru!KDk=F8~05OZNV$JWa@S8JU#VJaQ9n(>Ypl9&jxDl4~B-i26_ODU7-Pf{!l+}w;LfIfkEE>5RkNj zG)VG>7Ze&0q$VTtg zHlzDq#7Lv}u9dC=NJm3dU)86Zvsm=)^Wr;GoB=X^Et}HQ9p{Netx|KE0w)NxnKe@+KTXxGt1Ofq-w+I31>Xz`a$?EC~BY<%T#5q$e3v2p~3!H+2 zS9EFa>gqldb-_IaH!a|txGIx3YLgK;TxxtNhhm<)SF7bO2`m7X<@o1WpLw!2rkBH`5 z6VF3BdVsfN)OkJRP;}Tu0A`cO&_bT#X=+`-g?y!1jXmV#AIaGwuAs?eFq*$F8>p{` zoOy}$z{bP7;CEwpW3z$e$JL-Zf5yz#Uyoe03AGUG2E(b~<%^-(02Ssin(f*`b5Ynk zxan>10hG{zotvkqg~ogl(heZ~CZ0ZSpSJ`b#0+i>fSY&^jX{wqND3Cmr;Lgm+!)Jx zQsfTi#`#qtYkZKQ6-Z-Yt)j=^MLCqg;6^++B+zZa7<`}wA~zv5UBS*El-|yU|JNA) zl&u@i`G0vyY2#-IB!zqXOV*J=&ddtV4~47&p|tPeBGZw^J&QZHLFByd_UxNuQFX`; zvBJ(eBFc@!1WfMTHBmwtgF{^NGti5;1)gDh8cBu))|hM=j}tJ)53HO!(*-`* z0v|-~?0NQ%r#_6TlS*;-2Ky_a8h7MQkVp!tTZwxu!a&fmP7yVZ+bG)!k%1ghYC)(N zL^BBnA~z=QF(YU6z#$K#q@$*A%=c`Gtyqjm^ss;TxU(C05rpdfiIKTi9h8BrQ9}9C zs>3}?OW%FQ^8-#3L<1C>Ml-9ZgGs`i!N3O$QrE)s5o0uBi(Thxyr5F;!% z=<+XY0GC5;h~fmfVuxOqQAa`_w(e_D(PfSE?MhCkUM}3*+}KXto{MO>_19e)x?4X< z_u(~I@0}(m_82FgVGLsnLzwi(n3E&gopw3wTq*w{U|Wj7LJ%dGxR`7BpKsx9c_FI2 zFG=vkitU`(!-Ia37yu$YTiL*efB`ri_I!YY#@2f*#}bA2d=%qhRoFt`&eJge_62WU zj<)AldygnjItT6$oCt&1C_@#y0-j6p5F;W&1V=#Bz_yjqGB2BKEN2l*uFEK=xc0>6F|I8`=$h;9rAs+@73LF zz=!F4vI~qSuz{viMiu4gn5)|>3E}>>p>z>$(gkgysW=;_xw|!O&$9Bab zMLCuPNHWW6)$(wr_hTq5$T@IxaXdNwb=WfW5Ep}3(`g|6e6!=Y0Envcm|djVGKo5M zi!wc7{pg?f1V+>H_NL?R&tZnIz5CtWf15$Dy8&VWzHSRF0ovQ^J1hGMixE=WiQV<_ zSLyP&Ft+Pk_t-=`=jw4%*t{z%UnAA?v)2!q7|fwzw;ZW?p*?x^%h1M}3!k@zHTDPI` zCvs^?Y&5uyNpOg-gTr4@QzF>Zt)qt6sUD31oswPLPKUCfw_+AGvA2rd3$m8iudX>V zZGewCn}f~`VmNkIZhEhIEj1FOZb%odC3(_t8wcXaUmTv8C} z?Be%cm@dc9l2V;OJi+xNp5mMk$i_cpQ-W`;N0xsle(P@dRsST0do2~HPuEI*ud64` zuZ&t$MA7~<>R&=6rq8Ofgnh@yK)^DB(D=1RGJ>@1i#0VQ2yPDdG4{fChtJS-7;aYbcNA65r z_pS^rgjC-5_e|u%PnOByjr&ofAe1#NhBxPfq)5)p`p@~bxdey?#MqV?=+cNx0p`rO zftXrv$BLF~PU99h`B#)#CVA&&lb|tdVU|&;&Bv14w?OJ@oqge5b8qN_7-kReX-NnvvUi#EecO>n9i)LC;S1`w_ggYLu%f(@Z6c{R@wrdz7pjK z)Hc=g@bOd)#bk@d2g!}nZ8{N#&#QRO!x%nZKMZlW7+}`#wk05LXTuP6>5$xgjE)5% z>;|ia`UMNUj)!&Zt=r(!;r^vErV#nMPO3yBkf-Nu(Z0A zhdk;sFus-C>QUw~A{s9s*m#YE3hUH!(wz|fd0aoPh@f{{rDsKsGYgBysXZ${Jcwas zAG|kYA$(I%@b-WF`dA7#dW{P5b8}0ma|sGI29h_M{hyM03bOs`tZ3Z*{E{mwD(W)? z1kEJCQ?nq9i1_O(|06y^APiaPF0!&R7Q+RohX2=Ks$?7P3bxLjxeE^Q>~Ggr1SzAc z<1tAHL%ltr_^0fnLgINjGp5)ocnZw$IRb$*`$5x%$K2bC`fbH85OM7z-#4lcw51cS zIWt>;vo)gjMVpY9NMq#8#PVPs`IQ%DOjwTmvSIN|lH-*{LGIt@)e{Mm!z8*Q~tkIHVebb zq9g`41VCtz+~!^I!Br4B9qH%~W?(O1W@SYdME{bl1)4lTh6n{zqqX@D#kOm;N~kCn z{B9fmgSdE(4}v^U3|(Z8X=hidUxgwN-!?4XF)v+)*F7FoK(T|BJiz98%Kk+6dMY5U zn4re93hsz~JS9);{EF|z!=iS6_E7HUBM=Hm=c&}e4F>|0z)mE3lv4Znl6gfIw_!mj zzz*PH23+1$98KJNZ@a08mBQ}g{4$UQ3@82s9fCdx-G!5uQR5X9lvjVbB0CSW?f>=g zT8A?$Yo9f{-Ms{a;U!U*|LXt=cmEPjPWe3YXfISg2sh#5*9<7Vq$Mh7#+{Mz(T#2c z5#KrYQQ-LE$EfiACVQ6ORH(0J+vsy#yztT8K%wK?rj;b=9Zwv>P=s4KL|HR!(@OR~ z%lEVYRlfG73Q0%(zSB*t>f(O^yLc88QRrhV#B^kd5TnDdn^3tJJ zw{jIxGS_{Y@!`8;(|x%M3|3`j?^Dy#$P*J5Gkq+qVuiK`?b3B~;1D!AZCGBf-xYzd z7+duU{ZCVgiIvL#^p{>)Wn&+;mZ4Ai`t93Z1BE0bqgl=$XV_@@QL1xqW~g9%s~IA- zPmhHA92D&mNy5@*#;4F z?j-2MR@aVwva5w7Wqv5`lBq<2KE&X*kRxAjl@Uf8cAk@XYE1Z%)#nK;N?nY(9`=ufCGffP8xvWvSM>cmVCA}j?YwMhlxNMnnXD)#9qyk@Xr4@9%j#naex^Tqd;ZdX}qsozH7(_X@=3sGau)noI1~M=GPT1s^7%|<8Y3a z-Y|<2C%fk!iVT{+Ub&6ge5l@1lOH>ZvZ)si{!3pU&%fA#R;?N_?Sc4Fw*-1ynGTe7 zT^t<~*d*p>f{&7VVM?|7;ed2rYc+Y{LoImwt1-We`rtamGbahzNnY&iP}RA(AJ|hf zl9B?9`*vf!G|c-bFl=_5+Wt?)XKwnEao#9Fo$s$)RrE6zTjGAVzfr9A%+%yu=kl2D zoepS}S>(Q9=RWEbysD6UC(VnU>#@7LshmaC=;$g$abV<81Tw)ETBct9v$t63*&UJ4 z1;$>U@!wi@@zwF7^=vj1B?b+NhMpZ(xkGPUbzZBUe=o+6zP#@2FYWe6%|@q&;i(0d zh3hf(xm9(r3B-xiRtxNYW39x1ux=NOSD0vF&!xKkcD-~=VQWg&#*Dc5AM-&!2Aoq9-(^Xs zJkyIE^sro$65Jml-oDep_7M5>1%BG%@~DYCgK5}D_@2>b39ovwi)nf%JN^-tCH(+w ze>PI<*SXWs+T0-($psqvD5FS+Agc-n?M%gHA4`|~jp&M--Tw@rE{EPCX~*#m*R1am z1CD-=&nYZ99#|XG{G=cH<^*%Q!q40FM9g`q>dqm)OHSURh$$SWdh z$p@nk*&ryX%U%EI-{o`Q!o_rbAZMeNxp>YbfbvHn+wXO|$Njxol*ok#-aaD?v~02^ z_W!izplk$v zJl#B_1MS8%B%CfeG3WVNz~{COmV>}g>jqepnPH_kSg5|m_moY_;cgMB35E}2D?6Z} zwEKxqGvRDA7)_qim_E?Yxa%p3V^uog(`AN6lVA&r<3xFUDn9g z$`{N)>j@k_mkPL+J2O)=&`Q1@${$MF=}F=ssUyuiEw?U@-oHBh3XJ4}c}x{`__S55 zpM)dPhr8PGpAwYFYaZW&6nptDhU*qMIbqjhAKubB)7st%SuZycOmZ+WErpdC#iq;tRfo$q!u!kwA@G41NWC44OU2PquAkIQ3%;tivnp-yv-`$; z`r1pjv$TYxbkH;O_@L5iZz@6mcJ0g5f3Wrz5u-QpiC6_bfPm&Ohb4VFe^$H-@JeSJ zyM`#w!oCG?ZKP6(Gl4tS%}YV(?a)AZnimIrmpL)quTDDHB*@WF=|wsF_$TZU_L|Gp z024mje2A0y>+39*QdQC|3rm_?_ZFk(QUisAM*D5`lq9UP)a`to=BnHa%u_~s)spjK z$#Cvi5=|NHFpU;{b)OLHJL(=NhU?Znm~8JoeiL)jyJjru{$*P34_eN-cXgpH;p@QS z-z;QT+;j3Xx^a%hYMnV_z!3RM{)&);WxQ!lG<~wWKt!f*e|uxNu;5-PT;S#E-o<5X z(juudyYpBc+!PR)6E4TY)kktGytSpz5DuxUR2`;yWsN;w(bWQ4aLt|Gv$=BXb^e<}VkW4!`UfpWLjnG3-CEmw@s|tH5Z(vzAuyt2c%>_vL>f_9m;< zh^^$|zeb4jBSncTQ}71Yy9f0NS(fUd)IH+n{d(&lzpc%K96GDjWtiMUruJ}UwQ{nM zL8*H9WAo#Ev-Am`N6_D%c01dIwZC2DSu358sEYN3L4P^xFz6}>&AOq&B}(iH>SOX zr@#6pF5zWbg<(Px)!?m1v|L>Y+CFF)LeLM4Vc~aYB9yy z?&>rZo;0h9ora!2T(IqJ+(>%LPg^&U1k~rsH8p>hPu9up#uH$iDkPGw0^e5%QCz_lwkuoU+B z)!V8FCrqe(hn_P_(ure|RY=DyPbswl-id9uZ50|MlIzJV^y|y32lrhHbiCjy&y0`G zAx5^IDB&MBt}?l$tM(RG>|2Sk$^Q9}=ayY8qZaOm$%C`li7lw;CwQQMcV@poU?!qN z*dybM-VonNyg#C}+_+||Y^l(=ApR1lk8eOr_)+4Cy?SMM7so0TG&!=vr zaKkqc+sO?t;e-lLFLoza>=rTcYhaho36!Mrn#L*7N}e-UaO zo$!aW{t1g)v^*1#quCYNJCTHC+v?F3LHKagEwaRiYjTRjQ*`V2hQi0fM2(Wv3%Kxq zEx6uTHF>_F%!5i8)@!=0blO!>O|0bs#eVURfX;&l3fhuhj~^eSU!IObePT-mFIQwd z^M}$4xbQGUakN}GqzRz=DC^P6j%AZ=gszP_FgtnIOE09XD2eZiE)`AJlYqq9^l zG$o$)W)V?I!{Gr}=-nyWXZi;3|1L4}g`Zw^M3`t9rczQLo&3+VU+lG9{9-yp0Chsw=TdM@C>G;8NmQGSn z&mo*jqLi(w%k@WcHn(n>S%+u(?yoBb1alHK-`FcL-!0q8(fS-dK3<3EB*?r*RZd?m z4|+RsKB$S=9oldhxY-a06|M2ptg`V|zI!o!hg|TKK58ea=Vql>r3g!(u~RVT{sm6T zYD@N1E9CRD)jRtW=HufRHUc>8?oj~4ghxul`Eutk0l_mr9_fCl7(9C(4Ruj?Xzklfa(3FSg%Rr^(sDlAKpkm8#o{r*iDHJ z3rdJaziU`uxZ3L6^&-homi=C%kMfjh74~O(b0>Rki=badWUu?P@@lPyDDjG9xhma~ zdJAF8%!cAubWAQqu-vjnF}@=LLtYTe<}*Ech94yDk^JYYH*ItxKG~(}c?rrZi@7uy zNnALZC?oVsfRYSqJDOB=9H6EL%Xz?V&ok#BxXQ-IsLs1qrZYF7A#CYmqAn%(B40dq zn;pEm{t1=6b%|vl%fr7?OoxRbFCjrxr~P!lr^Hz^9W~hjF(}auQg(qp{n0`uF7tHP zokbjgJmH>(jngX2RuMtsr^a z2_(`WTGd-0AvkQYzpx}o=W24WM{Im!VORBzZJp~kvf3a0z+B?iss?jLgrv2Bl@O3} zO`b4eRLSjK6K5vr0WRH67X09d&fR*b4zbv0d?Txh#%FFc(Sw6#H)2ahm6bzJX^p z%f3x*Ty(PpG^Wz9Ytk<#pt?=s)8=O^VCia8t2DG1g4?;^Z^@#=G z$h$Y><0q6{=A(jw;9)0Qw`_Yk(Oho4?veb0d!+oXP7TE%S|OqF*7J_t3`L3bdf*zX zni6Jpzj^+s0I)=b$AiC&Rv%vtvClQU%)4+Z-7eTsr)Xl-|;G`wD@+qEz&sz2xo#fV#n2_!W2SxG~>9yD|_9Z znoLugg$uwBa(}9AcTdEx=`|d%d+*($cl@qfa>Zzn%B-eiec^9EV@TR3E^&2-HhZ$~ z^(kGNByY#bgV<02@(m-n=?m@y&d+D}8C}3a_-Me=J#Y5h zn(M}otL)g`v4WFIe`=-MN=Uin%&cMW5~Cy0zvur=%qER<_-wAfD(&ZR-ajvsO3%yI zr-xKc&IV%K!RxWUv5WGkgu>>m>XB-5z0l{muxkcAFu_()DVG+i%uX>3<)m8AmB09m$XI0pet4N+Co?^w7lh^FvpwooQ~^F5A5`=1m*q9*vr&N{JIiA(oqec zP#4^WyOgq0pJX`v2idjS^q|c#{l)A`65?EiCze`Nt1<*mXgTW&KdRBMdJ^#=lusxv zHKmlpQZeF165=AfUB9ZvAN#FqB&JI^p^8K54o;>D(e|}%8tySN88pM+p^v5wJfok zs8)JG&np?1TJ=4|@SiEZ zV9lB?jl&!HTec)3GK-^W?y}bk3YJnMPG#o72QuKMDI8HA#q`X|;$;=WP^=&4x&f4i zlALKwfTtt4RANh(xPzXqk?HKn4JsQL5OZ?M2(o9Aq&clw>c1}gNVjB5+>}aIx?`E( zb7spmvM4c7-fVk#(Bk+lLBaGf+BhUHAc{E*jn-aJTf|SdkXz7cGEVI+XN+vDtZ#o& z*=Q!jvz`)kOed~^$`40+G`*H5WMJ(=&+_WWsM3Qg)uVPc6^2785Lzg@z{)Lxn%t2h zZ+{Pe(Z-g{LFJ<}ov3t(;64@K{%?hf|38NQf097N6sggx_$Nsrq#5aG0k)&M)G-E( zLk`lOUf%X0c)1{vypC4?c-kQ!#3=(LhLDO{$>!KbEb`_D16|$O9Os{%*#OclEq|bi zpW`>26+q%=+QZzL0+`{PpA@huvj71w@{IoTO8=4Cu2nWvOC~KPlS@|8BX>B5&`EDY z>jE|>YB@o_fbXy2ta-<5;}xEbA)D1oL1~+rw!)2!D&jjwhJ?=7V^rOPm)f$E;p8<^ za~yX-L!DqY{}IHo#FBYfHj=`+{Sd1`Fbc&~b@})vKD3q29EzG0CJ)O#CBPMAfXFW zHUUDI9Gi#Nq8I}LPEIFNpkIroX_LeQH6GGKRz2|1A5b1gAh>^KfJO|h3SSGzJ$h{g z?4ovGTbXv;_PCYn^-yAdUOa7Y@7CpW(RO={s0*seuLSN4ozq%Mw~u{}+t|hile0`h z&r;FaS7O@Vl>6Vq3@+zb{0VEap?5HUWGCNBR*sFIlQer7gmPDt2!zD(3`@RIE0pS2 zQ{DKhPRZZyO8O-n<_tc_(>=?Sx&I)#0=?)79tJ=ZP(|ILavmkSWNbN_ z3Z2K{G5`!)3&g2yW||AzjMohBovvG&xyL><=yJ0tPoOdY67qg8XdK6U*SnvEN$W*ri09|s7N^>`NDo4Bmlo!Mo8Y2058B8p=GXd2Cz5S$ zx8D8)Yi)xF$OqP)Jmd8^U$5GhBgntLBr^hpa8qiW1ITb|A%;Pvu^Y`%sE&^G=KaAlylsA2HhQ~4!1~;dq}j#v|dWZF=1CGSJ{8GY0szFEX-Yi>sY<%_T*O3I^*vFKR31cm?Jf!MVduZN8Z zrC3#L+TccN*ldrkGQ-RKqU+anscC9d8IP*L`TV0s{gboyf0WOVFAu}d)g>-s7ICLd z8wv?*rF&E*Q;`HAbnNH^$pE6ue(fRH^ff#5zODP_Y!c=kQDLJ zjNw9ykFRc*!3D$c=bf+fihri3L4W1u6*4k1dM!;=12Qu5 zB+_&JGBs%=p!*$|^dsZ1X6A1Q2KhtmUpSNL+WY%>g8e<+9Bu_VzwmPddjo~Vg@F%l zx%&J2_{oZhc>Vhe!r&J!BB%mYG)V}pkEXdF8QE2qi-(--Z5{_1nNWw8s-O zic9;KY7~bfgOphI%@Aod4pz2Hs>`pTWND7lD@UiqKRlkXitfb~%}p*?bZ;Rq%70?F z?Cm09?Zn0zmjZ)nN;*HMxdi}xRHju?Ri${|d5tOUafYa>D&IAJIwmGs)qfj)%`kw% zi6PgX_cGlDa)LpeA5v6g1^DUi-ve5DfCz)0HE=I6r0rYt?b0RYw9O1rzAL89Q1JYN z`K^xp;n-0bxOsM|^J-9+bC77?)OiGd!#lWx{`WKo67~Miq!5F`z?E z;KsN+!d48q72hCmw{=dzH+(#I$^=M&!w)>!ROg*jGL_h zWhxnhikc#VocOE!7Exf{VBTroeZHo{lzB#ok|@!&K&RC$PuIY9SF00O0P2jBeF4(i2KC!fV2 z3ES62MKQOZ2hE}m$!aKPB5UeG=W(fxgu4)MAYLQNxT86J+ieYRbc+TrlzXDHNji-eeu8HG>22$sJtt=8y<1hLIxTmQ7fe z9_3B|1nh%vCxb?b-N*uO&EVQ*FxlkVQ39AV2}s17phfrA?X0Cds?!@stE!7F+(&uM z+x~ckj&sUteT$kKNA3=ov-pNM3gh_6)rPw{Z^SRmW*dTcjNI)oOD|7BZQcRZ@jX}j zoOo2fv0VP~;X|bcXxL&ew!^oB6W1o)zfe5Jygs?9dBlE_;KY zE?#GGW>+LWVx|{W9*LktPzYjLMRvh6Ss<1^Ny;-+rRfOtPI@?2wdH1PcUw|W0J`Up zSJ{pLV_$w4yWG%f)Z0iqsVCo+R%N7f^PNx#?m6 zo+j$}Hn+xI?MTKP^H=cXyV#zzimauUYYkU|9{5h|`^^(Tl9xMBvG6J9HAx4MDSYaW zDg}mKoZkkZ@x1f3W+Rk)M|4;AI6LZ`y5P1AzaO<|4Sg;_bXR>hzk5cFM{gSabY6X4 zqq{xcR<{MZ{r(!mo!o88I2iA!N=Fh`eLYoB^pW*5R*pP1s>JDn{{0Dw6L_dkY`iwN`7{ckNfCH2vdv^#|iDyl_A4{Tb3 znwuF>ZB8KmOi}d|E-f!FuV3~sSOzQ5GCQnn(}}vJatG4dxPB|x zHxN7*(PrLT1d<1as8_-?X<8@~nI(&{vR&rKzcDQX6;>XUE7MQTeu%v3oy7LlVMHNelhEKh|?7+m77I}q8#t(_0 z<@og%3UEvE!*9JxQBzfYDWqCItr6)GDF&+hhVmZ7E2^pTg$B2G`QSM}hblgr6C)`A zCq82NzYEs?ix~d@HO#k7+lAs0zlf^hYpvTkQ&)h{VHD906t>452ZJpaUxRS8UlIl% zU=2Iga74*@w)vkF-K4{j`2p?p!B2JkG}%^I!zIVtvXgcF+Z2vzQAO%g2}~SFvJd4x zSXozHT^(s357Ydt$r204P>E9jM;WQwX5`Kwt)#tLdKHg5=*f+cbd!op6^C_Wjy#e-)X zd~GZ(IRi-3AE>7!3B-?=m)mVkKhYQse;6+!bHm7}<5!ue@1o^)X6APmM-R}@Y+m3V zsBRL|`}<}w$+L?5t8C}$@QKDla&b&|3~CU#v)A|SVVY|R4P;(O|1mvfmbr}kyK<>c zY;3#utB*;!{HbX-m20k(JGd|F$bxxLS4tUO@XY*1O>B9&Y}2%0DrxscLCzkR3#7$t z>`aW+3?l2airq_e;%fpvOx02zZpXQeE^djxk~e{fz$d0$5Lpv#kLNjE$+V63;enXM9^HIkc}bbe;97 z#v1w9ht}TFp9Rk~gv&{%z+4O?9PxfE+>dl0#vWz?+$T*tucb9O2)#=zeMhGTov}

    +X(b*aPvOUGV`e3wr%NJ+Jl5YxtmO4ubw{(ERrb!WZ-QKK!Hr3*n=i9`uZ&p zkx!$T^8r*F-M$}Q#CawwL@Qpi+5ZcVsh82C)}q-k$xq0!nF$I;{_yb2K@k@M^(xJ7 z?rS$%(EVW^4yS1*fXEPTo_>YIz*IfDVZR_8uO1j$r24s)U5{=t zCTw9p<;vh|=)9n6bAPt}gWdmHfN9tIii&sC~Lkv=2+9lJPJ#v0@ zrTS!A&X1v0&4|{q0!~k*dD{H&gS2W9@Sah0crk^N$oLC z5;ceWCBHtci^Y@C@5LSRI4pDt!Opw|YFAH0BPQ;171210`v%sq86iwG4#rx8@m`K= z3Ptz@-I%dI`FL8&D2>R$$CRJQ8`w%O5y>l`p3W%!s1rYa2a6G|q-96yGUs?b`Y!&4 zMbeR2HQ+$R_N&=^!*=oJPdUDdz;TP6FGa|2G>>ofbKHCz`b?Ei!(Oj}!zsPv25`~q z`o=^r=WK~iu!oWxPITPh`@QiO?s!wU&tLU&k?o(~>k&G?wazHxu8(uak}SmEhLXA) zAu?GHnQT_IK2W!unZ%3Vn!EzHrsm47cgS!z8rp{Ygt>nJO6~z@Z*x57NC+dm!+s zESOa^VX0qo51S@b))quHR-febORbmER=;KXmZ5~{j|*@0>-T3L#_rx=5%|2YOxw+4 zrt4V@+*^5G>2Z^R3;npFFyu(^u2nN>|UJ@?{jzC*l9x6O^70U8ZTN|{)UmAoqzB(FJTeIw3iB~Gun za-eZbuI}9x1q~C9Fu$t@BhqwfdVrZpn5W~-&gsIptvCy@)^4Ty8pB2j5$M@!0t`R3&m{4p;-vWiPd5dJFF93rfg29%^d+ZaDJb;X50$^II?(T5B> zS#E6e-CgOV$}EdSXPk~ynVR2NXOH^C96K$l`t*5|?B3rOL4V$VaCN0ml#;6%s}wjK z3UNU8!&<`uxw&y!>TTMeWB*j!lHUPxO%aBooPY8o~hU~d0~y1vi1eZ zq)-{dGzM%{<6~a~8E)~OzL#}#4iOG0@U;1yX&d%}r#>}*@K5zdscZxXZ|gZmes}tQ zi{FopQ*<0?_bXl-u|N5jx|>!X!K9*Y%{;Q)IvpV9spvzgI*dD@I6 zo-g?dMVru|#_JiPMQ5_pM$GxfPy*3K@K&@Z@bT>i=#uyOp2F3$xt{N*n+eWw0-GDk zt+pfJTKz`xmA!Mkn$nl;XP+Dge+fO9@MS#a8A#tg2alGxDDZLv?8y+6S)@);Ba#Q6 zW!iaJIjWqih-{iLC~Zi7!ztG-t8AOpoXLxrqwx|VSg!4RwseG}2- z@vdby?C6gUEaU6gVou%XCL$KjvoIo{A->>X=_+_xrOD6GJUA#VU7usuaUR%V^Nt}W4FuPE z{P3BaLpSW%PjE@GT#{YF!HkpHXC0xDpijf>#24@gLPCzMqTPGELuxePX8B0O!jDy% z{_)tfHKb@89oyb{E?HmYG7I$(V-79dr6!70N-2pess8I(mAvo z4d?@*B2&ZY7`SEso>f~fu(#h^H@A~gsDCwiRslcu2i8g$SGpyk4aJAnIg~by%jYm1 zF{yN`%LD3aKzrNrDXYYzQ0jEIx+y^LG!Ls!odpnj^XO%B`|FLLFG$feIJ=tcpR{_F zNAK=T*4T5ub3q4v$wz);yDcN6#M)MuxT|9FEDWoBcQ%OYBC$GK0}5Qe{6GX_yn&#O zWT|3eB@DzM?9>@Vvtw8O^C*6x262XvT z2RgrWI*1BqoZY|?{4kB0!#BhL0pGH`Z?4Nvx7te~OR8@jW`{V4FoODsV$!Q4Z$hw` z2pN{%iDzf;$@3I^A6SR9Am?|#YSp>5X-|dWKej>p#o2=6``?O^p-_>T9r{sViu&BC ze4OG##J70X*^K*XXRC9h0(Otb>>KKQM#XcD?D{sRHp})0IU4Dj?H4#1h$M^RBmxrV z^Z*lr$j1jgF;C-D8 z9w#Gd0=ehmG}$cBQ(cho8oE=#(d`|lwd;JIW0qmqieCBLT-=`b4Q(`0L1ivNIpCLM z5;K!YrqS!_nvyq~5AG{k@~E3uy%Pzj7>qX90+^RJsLZ0jDbR%dOtsyq(T4>G%&oS_ z5x8duT=yY|7VEaM0xJ=O6~G)aSl@MlJ=36dT$U`so{QS&35W8fu>1Bgm6J5~AKwUi zBae!L%d)({w=D(DwVR%o15CdVy62QNjWu=unl#oXJJ}5#_9_?KKT|#KL2)jhtym15bvkG zeZ+60_NJ2cBvl{I+qoB0N>8+s%R^&v$6uL@J(`AU#&ncJAQa5Bi_}h^=ZoE0hZPml7XEH|CUTH2_~I2# z@`h7{dDhh55y^<<(Y?@-Npr=fjkjI-?@wkJ&O3b3N2!WtOWM4)zXx>(ciFBS$iwOi z1`M`#?@}p?`ByyLuNW0ba=`UsvnYf*mnMn*4ChMKE8cr<#4kwhu4!Y&9L*2XTlk$(-1{PM{lhMM);p@2N4EMMoc+= zU$8!ONVPR-{BgeVH%H|3_apG++_licW4)lQ`=@gADhNJ#dw#lriid396+r-3c8ol4 zFZLl64n4o(5HUS~`WPKl9Zq-NS#x|H@51D`=DeWB{IfeXSN^naKzxOCB(6fQpXAoG!)1#N%4X2}o~~@f^gH}X2BKk2(BR;cC%1BS=46G0 zwCk_+y*9haC>gT#CHqWnJMox}l05_*$g8*v45{3YP(b$Zw);hGhi)a?5d;t9k{l8Z zpBltzay+)3ukS|G)N)CSjQ%AdnV&J-myTm|w=7+X!`MB>R4XRm@)WFy$k&ZT_*f^~ z$~i^hze+LiF6MYwg#C3xo=PEdw`XjsJda!e-#s{!>%0Fz0^nHBCM{f~Nhy*)Xloa7aJ5P(TS>*{<+oIFM6|SRumZ3cY zEB|blv~3<6=g6^Rnz%uHI|7<56|kK~Owp!q1_Z0ol&0ULsMI|an!SJkA z6H8JdjF-|cQY;>^P2Tp#?RbbqU1JN*{MWBC7kap_HZi+&9s){63_Jc_NDV>GTol>u zdu=%rdeA9OM#*9TkIskee^gIvLeT<10T74P7OF_9bb-4!`gp2 zF#aT$WTozs9Z3o1*?G$=zYVcv-MgA+xr1Jl-wRG-w{BcZpVk^x71CDpa ze$Gjy^~T;sVSS#;`yiN$%Ei->azz zP6-L|R5#)P6Z}|Kmh5g?M`NAG{t7Bs@ZWwrmG28%eZ=J>Fd$rbiO7-{b z7{Gs<@R1quXKJWnJxUtOrn1lG1kZo@EM59G&as{hmn8S&bg3 zYcmedY{&6(E6nf`kGO2x?Ho^%oo-%DD}Ridka67zj8=5Kv)SYJ)n1e4Lrj{!eJa|u zSJq>t1;>beGy|5kPhk|A@t2MvK~cxuX?|zKTo-}|a(p#hXYERNXjm5mwE6hKlVx&cHXy(sN`MQyi*0R^nAcM}%}eu-(lb z!_NNV!ioiK-Q14PAg#w#IS(gudn@c#MtO?rXM@fk^+t2TDqN03(*6w>paXH&5OmyU zZM(;rgM-R^zU8%!?aD1tldd1zU(*QmqTje5QB|L-{Y3Edx=NY@E2-3-z0*1)IQnD9 ziCkSw$}wXUCAPWpL0RZ%tiVG$Fd|{Cz2X9OpLGPM8Wq-c-P~1t!B=Ss*(Z1@U_aH} z8Hsu&G1Bap+T~jDZb@`~!;LtSFYk+g5*Wyx@ghw@fqHi{dSJ4#{iQ%%TcRVQr*>9pzWT7#3j3cAw+dpM3T5m!(zc?|KXK1<{JDy&^{w0^OmZ|Eh2o_r%8DEV#XZAF>ox zcocK&P0e$Hy8Mg7N@vP7v9B^kWo-%}P3l8NsCSJrzcom(mASklRc&t_OU2gUEO*H> zeUT*4&-KRib;EjtFlQ=utYoaBUjb}lqhto$bau&0Rli=R?PjQfUG}DE;C24WD}6Y;oSv zoxjQ9qqKgf7p?7EnHriIP}5n=6rr317_u2Y0Hh;Hp)RgGefpCtu$IOIxW{`3=9M!b z%gaEpdltscl0wqXtBTUL;7f%fWu5&g17UG+>bkFAE$-QlX>W}oS1o&sd%T(6U!E34 zRdSV5kuEijz04s4i8G~*=f)t#F-^~d%Qjvdv~(Zax13IgOpg|+D$3e?IZCVo049>6 zr}JIa8whE!lP5C9DksFV;qP|bU@%4K5&4a?>V)0LoK-2V6j^lS;4M-rmnP{pe)WAEsP?FX~omPIvJ&GeVN>#dlw zRpU$k!5rH>w}$J&gz@<(h>l{wsNk-PRTLDy_KpC3KhTM-Cj8DF{!m&a0;H1xhjQs)1#crVRbDw)&j>b9`QcX>B<})Z)_GaM4<;S`mw3 zXJpXQA+~iYTd3IkGXOv}Udy8Xy77$#b@|q0TCnBT+6y7TNRu>Z%18w1uVGIoB@53!+zx+rI zHZ7#8n!&g8v^nfTk1a zemX@8nFD_)MdAq^!b>l1**8CMtzj;Qe#0PuNXN+Upu>#jb}oAz03co63BrMEo5CQp zPg`ir80ZoOd6<~`D({he!jo?&aDIvvq5BAF0j#L1s1OSBBoPkSgF8i$*pBT;bQ1wL zj%X$rL3mejOVkWpW=CXds+VBW_7^mbK8M)mbH#o$5-|XI52|%zhwRfVrk&lGizGrP z1H!>hCPmJI^3+-kaE{p}-Ca|s1yls!8za@eMldnC<^JGoRZ}ez|9>Gm{NK?c{=?hM zZls+J40?Wqx4MIDQyyI>Y2v}>7<Kv&sn9~q{XBZ=;js8g(rH|gmE0ia*=>6RdWuT=+v-q+T{`XE0^WmIf{~qIBz&xi&=5+KCG`D9wE+yt>Tv1%jXHw_VA7VV zIsaF3X~i}CLPs&|;!GcW(BVjoe1r1LfCo@k(-1lA||_!!@7bH6hwv$N)nan z^MeZA!3d}K&+--oUrB4p%>Y)N~e!EYf2u zqF5rmJFa$=Rb@3Y9|`T&a;{RKsjcffdLC6(XBV+q`%7@Z zvccL9i>wRBuEQb~w8m%HTOREP5aYU=dRfUchi$GVts|P0!Vq?E zJ~T;2C!9>vRhm`n0y$}0xP$7(G~U}Fp6k(%0DiFEUdy5tZ`IVK*d9QY$DfykLPloT z8weyi;w5=!kP!2n!w1-&%)5RJ{_Rv|$5MwD`2@YTryoeV1)L6l6#@0kUJV z%~fXY`Z{%;q%6>QZcyh*W%IW8nQwyebXeH+E^hVL_n(YBH2krqMzJ-3!cxyNT5aIu zEU*x~ZhS;NdBm-7Z4Rxx3$7dfZaDGk&=`vPl6n1W-@A0zL#e)NvNYgUl@-jZAvybi?!un9$Xl-D z&8?r=bckswp=pFuMStFIk#OC!?l|dgd|18*H>+mcZCbW@o`>#MR8Mb9ll<>bUd$>t ze($g7PBh&>Oh}lz4gYVq;>%)4IcCH;-O<(EaiVEd$b6R0hC0V8<}v>c3y{)v|41h* zI!cKTyFqc z$M~IxLDIil9f!;E1gJy$_M!(%16c!YP#-Fb4@uM?qO+9|^kRx`QD2b67|mAWO4qa@-M@cPS=91q zr)itV4Mc&-@Txa6Gz-e;FPN~y-2aF4vU6U|rQDF8|9HJAlK0*hcnWprFXAY7vR7aAxngB%2U`&kz9TEjDAXU@Y@!+ZvQu$TGn z5jO3YVbM|A2anK6D~-F*SxJd8*_t_%{K_J2QFUA82C7wp8c#4)RW&L{o<90^M*0Rj z=oK?9z1O@X0u7#`#EVS0axrM)hRv;tu$Ec3v@o z_riMV%<%#s5ch~)0mn5Q2-rCy%xnr_5+6oRD7;HvSfv3`Vlh2eAZ)rNFSz>>=BqNk z?lVwTn;+&&2mT&&a8f}UXT-*H`;hRN#;-{m7Vs5>zLpiqWjR9!S!vnK+9g~i)o(Dt zkB})3TM6sk13SluX*6k5nELa;TuV2P#H(-e$9Q347EwiqScBP`(pXxsT0M{l$RLU* z+IESbHD%exLxQVp<)~jjRpqvid~BSYk0_>1=wXkXimbg^)HAy%uSuQyoD%bQI0Q^NMW|dy#r^sJJy}eUPPN6sK1Jw#{sv zL$)xf+R1s=p*(D^i+bf1y1-=#OX0l>eB7DyA(o1O7;SF$sxHtnP_fh9m{J8r<&N_u zNIkCsZI8xlkjkHnyK3q<8_N*tXoSIzOu@7Y<=B#qQ9}`AMysxb&^r{IDjS^$5PQ>o{(DvrU#Ahid|z_VGTY! zMbAbj{5504UO8reMMyoChONKnbZ4{p{_GUFYrErtTH-xBI0}6E0_&Vg=GfC;**GYD zi^v##Uk3X~;)k|g2S%;C(Vobe-`z7y%w40-cg9%z)K9jQmV3`9LFsb>t=NAt@>(to zSuJ(!RxQXM5`&`UY$89{2T*c97s6X?ziO#y##AyM__#skD%J zx-fU<)&_TOnf6m+g;vAQ>*m~1kJ&MHyKnFkcq3*qm;kxXHC1+!#$?wZJoLvQ@o4aA9iji_De9Y-v-c$17j#3LUM0 zLl#7J#ug`2A2rezM*+P$@T9ZMytQy09d~ZklyCnFymG?9C(0S+$OJX2lJF2fR5z1& zVmB->*O#6-p(F-Pr?@jDa!Lgbx8FM~#!7fR8!ibR=&3LtywVi9c_RR&p?1S8ToB^j zv1@4CBC{n!`mgnxnsh>6IbV?2H$p>7BW5TC7LM2f58%ecMGJM}F^`K|{xL zh3~BL>_mNNqF#y(7JYg?WU5V;fmu(Az_R00LVJYa{fB+UK;AmkT8K)W@(DhkD~;rk zpCOk=GZ(rf+0_dLw9O^g+|WRp!1`D0h+xrTZM_?0=ESQE^qHyz0@z4M&(Yg;rw%eD zIBL>Tp=>W%NhZ*e4Uv>J_V<}bn{4~{WOm{0qkrw`OrI()Z4!$A_ zshPFo{8rWh*IA1#)i(@R|Iq_=?{LHb&zUHLIvST7KuIccUB52y?A;0pH|F=Y@UH~9 z;r2BTG7^8>5$pL=L)Z5nW*`>nJf0iO2{>*Y=m>AOpZ)2~6rz%D6uo|$p~Uc@5f3ox zrIC5ePLAE{iGpqaMZ1hQ!;dY!F2Y7}9q5$~B0UP*9v8~M8!KF%SgEuIbT8NJ@sy1cGONv<#&qiJPNG>R^4#q19zC5q6{=nup0SS= zoXrr2UPd5x_vc?pHi+vk6aPfX>r5o0eH8z!_;8oGFuMHA6WOpx?9j!sRL0sUmY@xF zl90R#L=*Bu-a(Tx>Gn`NLIbWY9_O~5aPwn6X=>b_3*R;L9dScP3GUXX_Pb5a&aM)( zt?6h^d+Y=5%NC;5onknxtMl!6=lN4EMi|uWfB4fEOD|xF+}nzaEU{N3 zLYdmOu>{@W)II7!K4QCfWS-^Pp*nEW^TN)XUy|eu94ps#i|rApXFg)}PYb^gbZ-3o zX*#v1(Y{!J;<=5rXc2owHCO-Wh`b{ezHc|n;dFLOFD4TAl($rZm-3ux_qn$K?h7Zt=1VB*I~q<6Q>9@-%hNJ9Y1_HcD;n{>r*eVd^s^ zx`1b^G**yG?CQcIscr1)o=oV`6NdxnUg#q6WxTxC&P(GT(msxd8vI`Qyq9df#}4_9U(g z%qtCXZyE#kGSr|COVQ8Z82hvPwkL>S4pkP|F3sCAMva!>`bGuUIGM-71G^_}$&Q8E zYsgP1Brg>%gc5h4VgKV_3%{9zrQA@T2{u=#l9UCCMhuzadUz`aalj1J#0*QS1$<_2 z)%6-1dIH~3$7&XE#5|273K9^~%Uooqo0Fn1!by!ao3o2zVNGgyhNz~1Wv>q%xrfJw z_fmnY^&zK?_EZBj12$tHmXpUPIG{MT)=iNORqKaw_P0W*D>+vkr2-OZefE)2bYnzu zap13ORokx1$ZT=s1xp3ZkHKqn^BG&uQRyW{LUokp(nZ{E)laQg zV;{0Bs;<4fB;_EN5xvUbuMA)xD1H&~-hkX7E0_wh!bUjF2=)nr%X#h+(ty?@WnMyA z5TAcd;2>;^1`IKiLPxJR+B~ir>|+0v1@=*o8Q>EiuDi2u9C<(vE)PO@)&kR;!1jjV z2FDB)yP2$$?|{z{YO*$hN3jY`FG(ytHeY8LRGrLrXq!f@zpKSi7gh|5Jgx|2#{3ty_X}%`= z5z1cTI4z+TLHOc!ds%1=#jK0hf!)~QWl;a1BoGe}x!1vZakn|_iGH^h862KS6(9xr@C>_1GA*@WF0cHKhD$9Q3RrHq4cic0p^AVv&R}+yzdx zh=2R2@g3yrEXgN$U=u9mF-hj#Q!#chp#zgYH3A1)s0GUTG>-XfOLCILXWl)-6kEC# zZFZ%6H9YJ$VVsK;{lj$(9ndT**aYlMhzNfMUou^!0gu8ATKw?}hj3%ebHPu;)qCGz z$WjM1faqq+qNQHFKl2OwIqkMqjRfu}M@kVX7 zO-+aikzgh|tXq7W_$%U=DQgYQM{0$du!sZv4LmwD_ku+h50OliLI@6lL|y8L)JGXiV5V@H2TDfU7njR{ z(sPqt2KAv@(3!@Y0m!0thQZ$jA3V;Ip&BSYiT5e)ufn!rDn~KyIr8{r{NioE3R)MH zNaFM}iv4L2ulH=lJ}-Q9LGPz@a`zbQyr|TGNefw0P#cIkd0;O@9GT2Tk7=umeXi)- z2%Kn2KM9yVv56A?H0G7`a)-~!ozHS z{kjUbg|+_Ape-X}H!^+p;=y{YI*Sibc-}Utq2e?*0<8B&8WRi|qL6wdb+SzD)Ma z6raL0=}(3cH-)9wR*Xx5qmJATRus>|BBkWj2-P~gnsH^(SJqj!|%7K|H&m`EwlC;)HKNc_60Lahr(} zaDi%-vM$TqoR?1F_!rsl?z;OEpAY$UTqW}E#9r9m`~c4W+UYd$5N%g$0t=S1wi;F3 zssPD)@SMW*-84eY0J1`xL1bTEn<=F!NvIQf#NYp{zJ@vUHmO>T;Ypkl`0L+YEm3OA zvzwK}tilAYCvhf1ErA2G@j0yn9RYQ3i_(Zb*02?^AZS0`Ep7X2_7{ftDr8h}8E9^^ z`m&42q?zynjuL?BSB2`Ig!H5q46_F@vw=vS!ZYdru zKgE8Go3<-#^#CRM{NZoXxSm(U2!6{%wPILmE|?T~nQ|&}>1S^A%9Ek$%R<6Y_ZQeymro~uV5+)(nCfukn%0}Bb~zDyGl|H#LO6z} z9Wuyw>?r+BB^YD5a7ESR#;6YKbI3rJ0%beRU*YdR;~pVDdTouARZTJaQs7f9eF=QwuhVHA*x z0~KNnaNIAK()#gA*2`ZA&gCCA9yiz9VU6#{)l%5c^m;tJNcxV#$YSn-hzDGIwW+oi zaNx{es5SrOCFUeKA6d#Hb`a_E;MJDaTb6wE{wxEXQlC@y%k5Oec9P)eYWcIDg5_B* zuSFQM-(~7q*6>z~`i;VPugY3@q@>1q?N_N@yWlmj9+Q`=73aD;pa$C~k>9NUkdDR% zd|h#I{1G?VCz$}xegAI664@~5AoA6JQZn|_`9ys@bq`0XW1GAj%W9~*r9H#hiHo&% zW2WZE`SPj{xKC8szOJAoEF3<5J4X7(3h&M8nO5W%C*RXjA`gAs_vn3Qn_hAZn$6`1 z{&hbbejcERjr|Qd{Irn+2F6q9-XjpE$vw_awg-n1OJ0+mY%@7vVu zVjp2Y&Yw&n&?a|7?;FT^aZ?y>=wq+RuL}k26h}do(7M9#?c}xVsE_2kSaq%g@6W@P z+#=UIrUIYpz6}lX*y(3&p5PTP-4kRQB!f49O=6H2X~IJlbY8uR6VAT@tsnCf3Degt z)~IeHhpLjK5*2aF)#NlszZw-nuQ%6qo``>0uJD?1r+m)u2(N$5HJZ!)(R|r)xB~Zr z`JQLf#1?I^FF1(Oo1&bFiVgF%Oda6Qw+Hc=}8VJOw;Pj>J2h=Y!|2t{co|)qX+4*Bq z7B{Ssqd_)%cu}Q=y=YD4c-`^5VEix10Bg~hH~;QlT$vNt&C*aM{lQ9dlLY0&TDHDQ z@Rc^Y=xnTwvR~9#RB3qZp4!ZpNxi0|!qKYwHYpiyKiun{As1O{5Nd!yogdO?_NOow z6+?8~ZHM&;;v#v)HB!>?qLn#zKld%Mj8N!XTNh@rq_-m+UoP!`OqLUrwVZs{GE3NL zlq-6=JyR8;B!34V4TE@R3(mM_u*!>_d>CD8d!6jI+&6vU(INDZ>PPM3#HViGHwv^~ zCT`O-YLQP|QYyPY{+4Wvdv~?=wCRSMJ@mTBguQG$bymxAIQQ8{lcR%Yrk+_8?;&Pr*}V8OOQFGKi|x4AAEKUd zfeBwF@GutE9@yqCCegdx;0W9v(hf~3=K)$}I?;BS<#(m=Zb9C-W~c>~|ET=JAA3eu z|04abDCvViOQ_}AyIjMqo`@9x<7OAR==LPi*{>I8{$J&u#5H$<78OCJ3jR93CeqXD zHz0R$ci%2<wfk~4Dtkp6v*(mgjRUL|$VC$@8UaEAG=mn-sU9vm! zMNng{SMjb&qnv`3xJhR5Ui6UjO}0rA7J{zWfgrf9^F6FZG+H>Cvru`$%>AZ;i){^A zNu^j6SR-o7W-!^_l{@3N;Xe8VYdcsp5wB%|Ah1>6`7U_PICl2b~C>rq4-^i#0{D1imIcG@!czk>zt5QZQJLc ztryLQyXLRep#}{gng|(@FAvVgSq&$N5VV)|!t6z3$^LBF;FIY{H?kVF@fR*Va^AZs z3UVKhtjC)gc7*sj54uIC6b%jo_DeX2_b@fP_+fcXa7&_S9x`%McN9WH$8C#02ToDT|3k}+zTvw6XtxT09E0!=;* zpN_?YRBwW#j*5xds_VpM#|Qt#-R9mDo168)_@g9bri18LHGk9PLk;hpiy$dQPTF=S zd6ZM@ZsXBj?iUr_0&#OuIhEmH3Q$`8uFTJqg)dYyfm%jJzeX1drepFFjC!+9xv`3* z;3i#lZa$DVV-tDfl9AM+g>h}-J?=;G_R`Pq?tS(3#KsM6tsKy+fBVM(Q2uqF<7x=)J|Hh zf8EZoCMB;;GH(9(!v~6&)l~52UbF_agwrOR@Lj3d@_1IjrjjH@>ddPcH4A$X!`~=Vs#;UiR;cUgX<7zUSimm(H)GAic6?===se=n6rA(?6$>nux&dnWq^;QwiK1?91W&ee5%}* zl7KiHKI+^XqzNe55t7rXvxSp-+ua4%Hu71I7MoruKLW?qZB2Z_ZH7Es8Er7g1T2iz`zp@&vR+I=yNO~Pj<;z?w_=!-TJ7xAn)tNQBs4aTmTZeio zhDEEc$Gki7N*1b1ey)bi2>8+U|cwnt@HFT!tK(1Aa3&@@dq=DtBQjJ@_2f`_LF2ng(<{ zed$dHw_qt|rV7q)-UK)Bd1rq5G`zjpFwLc!5EYAu2|~y6wli%U?BJ5$D)PG zRKVnbh4^9DW8`DAhb$lNSSpqvtlNlOaaUU3L3 zEZ6K-Qc1DA2*W97)f;{G{)^ff-dDl4p){$E>6q`oc>q{0eWjTFg?c(viz*&~kvNY= zgKeWyt)qmIK-Dtl|9fCNj{Hq~tBwZ;TSt<_vfol)7p3HkJ8^ytPJeKT94TNu&zOW; zlE_*mCxDYIW*6Dv;LXFH!@{qjk}CRMyI3qK``lId$P`KMb%ZL_IllKD%^5&|(T#mx z-kI28nr0OVDcthQNc``HCJjHq>M#|k&;qa)tNEESms98O+yUXsmcIT5t1is|LOsc# zs9S=ua;P{$MxYQMzlbRx!1~< z#D&&vUlOa~vik4LCuF)%&2Yd@8GDRCFSg=&F7*cb*GVW5g+rIh+G=d!TA4m5Ku1Qv zZS!qrtHn2{V8hFcVx&p|lYnsjwde3y>p>;_v-U1P8*+KTEmQsf`6lV+ROpJ{nxY z%Knl)s=G^hB${dU~fQ)!O{pzDTAe8?(XOt3l9%E zu-+xT{EL(H&b6?on(V|QDe*m3+7Y8LWb7s?4lp!L695T`hs)UJFmX>h6L&Du(n2zh zgq*g`H<$?S)$$WzpDsIi6G9S=VB%#3YQcO~_P;pgVGxY?KvXo3k36}AE<_DN&%nku zaD{fGaFrLIO5;P?#wR(7JI+?2EqqN8bL&jU%xPM80*$Tlt#J0Sq zfb}VS66R*3OOR+0*1~+D z6S@?D9VgscqLnZQWUp@hP)-`4nXIa$-K+J=;tdtBjnqucca3~Z#V$?$ipgOfJ3MQp zk4?&(u_ixk8g^TpJ{emH%W&~lT;H3qeRnrq@2(FQM`V4aaX(PH`~ayzg|gk#8LRW$ z9ne3=7+3du`_MNS{?d#rr0ux)Reu0redBU(-Y^U8 zynbFCSsShlh=Kkoul*PP=Ge_|d3$Nq;(ox2Z6;4Xxo8tlhjMPsn;|)G4xYH#@d}pa zU3C#p)HjAz?mxN@KfD}`#qS{5SC2;4Km!t24Li*JNc-zs61?Fxg*LqGLr1{rqpc>} zXmCF$7h0~tx2LM-fx^1*kYIJhe}Ig=d@L5m5mN(rg()EXcuE18gxn)3yA;3!nfsMF zZvU7r^}YUDQ3u3b(}I5&*o#!<{E<5D&w>?bS_4imsbM=JYR3@dfWcY)->ZI{l1cug z1y5b%JFFJ>Pq%s#&f(`*eLMN}>2t`x9063!HX0w_4aqusk+hxO4Q|#N0gCcB8;E)@ zZ1={xf=Rvz^bNROqXStiL#P$L!X#gk=C2j1S!MW+QI*gdWGTJA8W7s%-$g+6QflSH zA&!qQ{nfe$WJ`bJzOy|dY0f`zBS*k~#{p{MFyd$AE>JKsXB^M~E=TjD=3E@eDF(`7 zNWk8Tqm@bZ37^q{o$6hFY!Z=B4Wz|<-$?5SW9U!EAbUc({!q5+rdoQV=^VH8|%+Flt%}quWBFfUM|!{><%i$x1r6NLCrJozA8BdlTi# z5#MKo@>l9YsEOj-wLTV^KGkW#r)Y`(rrzZ|YUyty8guv>>uh~gc*}OwRGF6ZTll>L zv1PM2f?(trb}n}~fkMW)VPcx&*3EhYY*J>?VY7OQs+tVPl!qSmGIX2Qr^J8*0tZ7= zbKcTWG=P??)OepwiZk!G*rW+j3n~m;2;7CGbfC2bnP_HMFz@qnlmA862clImOLcM1 zeweNq;~WA2LjQ4_gxI2nV?ThS%sD!+1dxtK-BDjK?oSMWibwFmd@Z7c@r(X__C4c)X-|t2=Bw&qqv33`Bq5pZ96{n=uJ$#wg~~xy@vr z#`wjGntha4CwWa(g2_OM(6mJ-(3yX>YZ?Fs{}&Y<>z4D=0vTdk!ehADiVwHLzXvd5 zx@yZd*lVKK>oxE0Q(^ReU$EX=IgzpH>s2&ULqQllh3QwKr%zj-un93_3V*HpW^diP zFO0uV1K5sEQi~j~T_=B_+Bc{pnYSQS4bK$rUFw1w3Y#yv6?%IWAdRs{$>^LyXt@CpZbQ@|3F zQgXpd@BMpchU;sUpWg!se#ZM^xBx_sp@5Zyk^S5>X-1J`7QhTW7y!p(H`?xraHlly z>&KKF0RV}pX!LM=zQ!xu;(QeOQ5{dgN1lRAo;6jJ7qP4Ofp5|~dgs~xN#RCG06&<& z-sP&OS%8e5ly2DpQRE$fUp3pM-@JJwd}H)8z9$!%T~8(LH4QMauE>iZh676?gZBXv z2ABdIjs49CKO|V3H#Np~;lslG9AH0Oy0<&FkbaXTtj#_()_ovsNzfh+VujHq|BBB7 z5TI8$0I>VgVs)NP#JPtv0cWcb4fwV1n@~dx9RMU52)4ts3@$&?bs0}*I9h8abY+#l zpN`2*cn_c-3A)pa&>sV6Nq)BgLC}wjkDx{x=Kl3x8wax6DhWWABCSwmTty>=Um7py z+;^rvh{hDZo<{M>%!n6u#E`_ag?MRv3M|);D>L#xW7lUA^y6yE%&j{JHf$MhGj0 zO309hlxAK7mA=Mf?ZYETTIvp^LNg3-pjNs2D*%$x{PjndjizPX|L~s04o9$fDatu4 z18dQ6HA4UyUF0Q^i9PBp;G(Y2fM^y*@yq{>6U^r4;G)gd%DWdj5fD25d4nCY`_s4M z!P_*Bt>foJLEz=9WFa8<1)P!t0qRf$I26memcOrYuxXFv=lUN%xDN~FSHz=R_%GV6 z*?{Q(pKE>z+Dqxi%WoteQT?MFq^Z9DT8Js+yejfrQUtVVey^i35q(!0uiqcm-!~_2 zApsWpaZ=kr^Op%%iCYC=rD}ldJhVQc5TFBU_R)!t%__ zH$sN}WMdYkeihygNg%m#L_ zvjCKU`zN_er#rQ#+dVPxZEImeqcY<-l?aG6=2MbeQm0R)8eD+0l6(DySbve>#lv$$ z$SA}tW9L=zruSp29#U&a=0etRnLbUO{g{pS%I#n^j7*KGAPcz5#itx*0EaF|@o+@( z$nIv}rj*d&#{Q79h}9D=hjLgibT|S$f7j=VY|NY!;k(KV2+IN?G3I;BtgQ7I3w0U3 zr8SASCa+&#D61IOND78>q8MwKEkMzF^$k?gEZIP=zQ_k~OSShMO#$anqmML7|xXlTpSB<@x7meK(=z`x}H zymC?YWmv`ea!v|2zAu=i0ti8Y$25{a#O`m;`VIi8{&gVK023y|B&B#;GF!ipF3^DT z9ii7;zPBZIbXnAvF|~j(Wq$`&;s*%M{o_#UUd~ZQ2@`ia1xL*AbTv6Rj`B-|s{Tihj zJi0a>DKm41E1z!oM!^mMqW^Q1)tqqZ@5Zj<8G*RL$3PDPTSTwJKjNOG>NU6zgEasQ z3>?{9l4gF>d+l2a5UJ(>pZ(R{PhR)B>8GHB36M@CzP^2l)!ww=o{&>{&;F#w%S1ktsi`*r%;!HB zF$i#Gk?csvrzH0;Wp~t4F)ear9#Zl+f0^Pto+?vY1$2O}gf#J}N_=30^iIj`euHvC zpXj=2sx>;Jj;zI#-2}KsP%AmLKV7P5*6-D3_0|lE$L>OTlK-XvtZT+@oHVDOVwT8eUKZ~N`LpeH zO3bkPg(sS1{*~AVf>^?#=>JBXh&!~cK!Hv$;WX$a7HOD_X}VXU#|Z$=*m^`p70iQo_=Pv%nas^b%`siFan#ZDwr{Eh;0f0UDzn~rS!u}@qf0U82Vy0ae zf15Ggb4YL^eagn>f#eh^f2Qnh=GdI|!;+CrlLXBOnkbU%H`|B-@y(?R36sMq)xH;k6 zM&(M!Hev>V)XD?eHJ=PoOkZ{HD0STw0QASw0aP=XRDjc;Vj|Vxlx8Q=9#b*PW7QHJ z>FC{7K7Gsg_IU=_XU^{ec^b8Jy!G?BG3`s#OO%uE=+}jU(W6esyoRQ%^MW!Ui1qIQ z4)(ePuBlut^_)<2`A+B`BFk3OR(Z8ULt{*VO>ZD_&t;(p0|M6COop4B<=l$Nq!g))&a=pPrzir7~@Sq z>7y-$y{<{X(=<8(j1z3Q9*2zMaQYPBhI}}V#2k%@3BVc(3V3CD4euZTZ_EZGudb=->+Q`^Ob7ZK*RrD< zJ*n9e;S%ZdAI$rkToojS-03UW*qL*zHg{HJ3`C+mVfVU-+2tzEYi$*K{?aPvS3M5o z)5FKl&$s7;VkV% zPhQ%-MGYTL0>t4g(D#j&zu9#2rasRM*@6EL(}Bs((fB$?1lQs9>(_M(@Z|A`DDd{z zhOn2Rz1}_#Fhh^*rHgq)`2D)OWP`r_VvQn+U8h@g zueGPvdaQR~!1V6+=6p1frQ{9+WR%*{ryXxT-U_zciK^A{NlBUcLg_LUB-}Wuq^(livE;_-=ekeS z9otSwi;9Z!^78h(ak;)^W*RJcGG#!~-+spXvr(AM$iWfqzB9w)ydsn3dnh|PHnuU} zCQ2ZA%?+B=cX_-Fi#9#op8oXt^R2Z=jU{qz&SPN}P7^@S%lox2o~Z_SZpr_0gK4*M z89$0Aub_a}r27FWr+)8xb^zk~;>fm@%0}(*LXfwi3-fs463u!cz)V!BF8yp;ot`R1 zQ5TM~9%&D~H}KXRoqUowy+EER7n^h=J#YOx9NR1%1=PZ>nS4tY z(5#W2M_aUG>-w=ooGC~XE2p7mB;iU zpdyQrT&d&j>G;;xR!P6rg6ah~eprHVt5T+jv}3^epHMS%^SHD$IbGf7(a-rsF1_2Y z>#~c(fT4vSY?9reP|3zmZNdzDvinR|E-sJmmb{(wI62C_^pJ8|{qn)9@uz}|*rtQD zAk#to0k4?8EODQ($VfU?)(8?dEpAH$CFnW7&CkQt0TxzPk>(TJCqzVV9m-uUnx>|- zmzI{!SCfrEo_9BA&xD{aoSd9~{`^UqIq?absNeVI^J9vq)YJ%N$(x@*&m4`M+ZYtj zq`bD+^>Jlwjn{4S_w&>MN86bKqI9HZv_(j&9l1xUQ8vUJ7~HyroxJ24G=o3mQt2?^ z1A1^c&%4y1q9CToUVXw;2C$zTh3fx8e{(OM55F?~PN#{9iNBw%94u6EODI{caFXGD^8C&H?r{X@Vxx|gH8+r(EeJw zBQM~emuGviJfEkgrk)xF{0t)mto=(y#$YIozf7T0Cg|^Y30bm%`!iWtSv(4XsCZ?G zrq6oaKFyh)61XjQkwBX}uk`>ZRf_F)rSBNM_Ra?F{pjYD#O`|+!4U}!Y$HZty?8lJ z*dKQ>s4@K?IAC0YvO)HW!hG2o8Fs*|-tF-epz@7bVeXh^k_N{GiQMm*w%HN~KZ)$- zniBzMXrD2HXQQA9w(lDa%S3Cgt?B;B3zniv`FY3;$Ygf8sp@eb{mlZ|Ct^_^rJ_wR zxCrPfp@e-EJ2PIIM?KS+;U>JG*l*G^UJsWcd_r)(##qWQR-m|i0H-O;$qCdd(>*|l z?oGw4xLij0hlJb>F&QwMQFSs-`;u+8`|@?gm;?({>4SPd4W?9=W-%ks3a7o@ zTd1OK<(TttN&IcSY%eWhgDhvSZ}%kKIecGz{ON9FXXP8vc_cXo(vutBhb^Yzm86Z* zn7;~p7arW}ZCAi3oED$CBl5-8YK@hjCzZUicX*a%bak3E%PP>u|2glqP6dm4roJnb znwl!TXB2RAqQ!Z#KJekg*4Qb{m~6CgqW_km@hvW0ucStk(Pc5`R`SsLaHG1lVP*Jg zVHDj)6kF+virfuANoW=)!=JyBCF>ppSKp+#s8Si>`^<)iSz&x z*TMLEBh?mn`}XTY`TMBwyGY$@B~H2*i7b5m@u4pei(cCN{`;Cw7ie2iUgVGlVWf zmabOwBsPl8S7MjGxt&ghQ;y3eXUH%mjc>%L94fFH*1|KOflf&Ua*AfB({F3J2rSJXv<# z+AyTV)u0dG-m-V58_8A0MK}kcy^JB0ATs;;&m=c_+m$+Cj6-Qn{pRnzcftt1Uu1R+ z%K%;?A=?0rmBOrt*viQ!uSbT3Ew&yZFmgQh=6!)63NkY@gHD?#R{^Ea;n5Kw&X7@o z$IZ#)(QkESr!GvgeLzt(925Dee3tka5AlRV%IK1J)ngdTL`L_sj8a4oteZIlvi3c& zcnc4>XN+7WA3x`pT-$KeX~-DlqRB&MZ2$#xZM@OU_Vo7JIOiM&mq-gVQ+OFt2_ma;qDkozK+c_BD%Opw!6+1)}z3uuf74L zxo*GhDX_nFEo}hi%BWJert4WlS~Vp{?BGaO-c(BNIvHzM>>W;W`MZL$ouL%9Vzt`E z%WpMEiFBuBSX@eq43O+&4YMj<5{Mr^N!EA99!lf?Zq(rq2-5!Z;9V4XSI6xM7iY)y z;rCbrzmxG<*D*zDfc@(_*Kk%D-0Z80j4aX+uJp zamu7r%e3ilg>uu~z8N5cAQR=LqUCBNxykEnsSbZwJB1NfLxKzYCzD2~n5P=Rc<6Wa z1-@^4sXzghZ<9i*kJ%Z?)ovvk3=9*$6qj$paTW9(w??t#2Pcxw%0)y)(Tj@e;YyQ` zoAx3QjJ&*~Kp6)xn{)a4vP0>DOmuV~OH0{Ns@G~}X7oepG*<+Y%=rl&Bf)yIfByVo zxK)b>hS4=i=kiPczn(7dc&Yi2un%28>tN%c6JZmzOyHXJ@gu?oDwO2qU>+s=1Hm2i z3fJK=VO)aol{H`H`eM!zC1tQvmTlU9N9FH_Kv`BXb)mM1t$GaY`~L%LyyZr?M30*O z=c)C-r2oCT z=q%k>9kaw?TXf(Muyd8*k!C~0U`1F47;Fu$)__=eiJH2VbUIV9fz_qV;zW^?Q@uKw zkQENX>3eeE88!4KSrbNnQ?f+!1g8{p2A!}IoFiZ5gg|RYd+--)ur3pYd*qA$WPP5R z67Oi6XFj%bvh!EH%jCX~K7sbbTGu_n+WSkyNIgf}GC|wuU^`1m*abD{7(FS0S1jj} z3l-2D;$s(sH9>AV@yzrv2)lFm!!jP`JYS6PD{(^WrJbDdAG2Npuxp2?>7DsZjPt9L zbJjx%j9GLAbazia{l`CguMN?Bf&V@*j>7)zCGaXL?9r2GbtrBtMUD3}Q-4@$?C1mC zJ9EGoOvmu1ww)w<{7S2r&*S?MNH-zd-rLeyFVZ-R&X7(auC-zo60cZMkQ10!9ik>> zmNz*%9u+ZoB>&3t1(7!1tVI;dp^}&_df8pITt%plUEU{nL;$iF46KHOj19|(P=_iP zk3je=;c3vJElKJEca9)bM1>-S1MCvTQ(_~c|G21EEE_Wqtq^S|a8GK5 z%ye-6Il@9c=fp_Mx=UQ(*(==Gt0AWee>Tw=$)e%wFc~m6HMw0>->F)Cnp&Kf(nH3^ zUjo!Z(h!^|9wSc%lau1V&TV7lH8fLPU`Y&dPyk0GN$R?7AXAhJ)FnEs6iWo{sFi3W z;?-71>8L?J+(Kg55Hb@c^MIQ&Ma?dQrBmk2uEW2R+H_FM5v%OoDxxN=_JIUe`Qb7L zwKDJ*PeJs57#eQE#%bk94h_4e+owW0kZuS)&R<;iGiSu6Mx59Dry8l)u$Sl}=v%F6 zqgVg*1SFLpo`P2p7--B1;p{s=UZVkVa1M>_5jH)cG=2;PS#nG}YC^MUK+i!Hje5SA zu-FO_wJtAwa*|Xd(?Ms#3sM=Zh`<9_%F_N_k?X$a}^woMzHe0ef?nR4Ip5tyci#Y z35R+Ymi+!gN#Ab?*@SV@fifA956#F;sT(L|Su}wew!}leUB?>))?pw~6i-MJ9ZNpz z{qrxY0h`PEAn}Km^6yzzv0QQAvq;i`)dR6#QRIa4SVXPL$Q9uXmteB2N<+-(5#z}c zPvcY;JqU$|$dA77*vS=DZ~Twfd*l5dKVk8IwV7L*Tq<;p6IL&FE+64R-Qy7vdG>72;-e^zrcoOY-r#{l7Qx zdU!kVjs8?X0Dt6>r?L?k3+u_V{~p*_8CjHASZ&2B3UayuS$ntsKkOiWvyVdKpi7y} zVodG<9)ipvTM)fcouMZ$A7Ou@cq+~5D>P1xw?i>Lg>&}XVP;(DLt6N>Ff4=B3ZF}r z5u2>`_a0W~?)G6F*R35U{7*lF zK~3Q6jr5DNP+YX1JNkTL4hqgeK||#C7odp!1({sGg9YFhIqyLJ2f%x^erJO)&}CHNIMq;e;d`_CR5FQ@+{ubt*7(|4=p+GTziDMkxs_kK`_t?Jof17P|{mf02K=;EsXTg}KZrojk|^ zVFoPys4I6RBO)To%ge_X7d7%H7*j{It7acP{M>6T09-sWGV<@=zZJ~&$J4<(9!oU* zcFeJ~v=#=7&Exo?%9=68w!XfurRdzl&ylRUaT@3irTr@Z(UAMCn%a{INAf0AY~?O| z-OkAG&i`O9hX7c04>nMCcvVG3O+$mCg#|-)b~cu9=GY6#%|Cz0OLU`*E8g;^zR@P{ zUafwHG~=Cp|2m6%MAP<#;_(8q<8qJrvKx-w5Z~!zrld_StYPEtpSr*AW^7`zy|aT8 zz$(uh#nff_-A7VGON+Rr@;x`j(5Cm^!9iXrXM*w_T?0$8 z3v5+~qR>-Zjj4C!4-~c2GBe+#*j-&;JBel@LfRM!erJSptMIi|azw>3<2q(+iC>?e zi)Iu_bi^w#VR1y^WPz@mYJn&+5$xg5ax~*0Ps`3Otg4D{Y!p4mV4Q@h;WiKCUX$Rl zf4aW}zE%eA$Ni7tz164Jsfzw8iQoFHftAKWi-4iDnVFfC;a&%OXdp;EdiItYDtF7P zs=&d)qsd$bwDs3^aA(Sg7J=d;9>JS3Ve1Z|pJdNrIidTrsVtEJQkqiq`06AGzw@&* zUpzTR>R7VqK7xoIj;QXTp+}qE>FR9jfA$htvO(AEgFxK9nR6O1N4g41OKWhDul2{$ zd|P{VvOJP?&0)Z3z>RxEe7ElbhB$w`KgBHFyc-oUN>O1UV1neX4u9Zo+)+Zy@R#(=N4>cHsGH=xB<83_q1FRz5vRjb6I4Sf1*LA1Fc z%Igkt$T9No)PI46;>4_lDQ9XT=OEP9Z z^@>?RyLZ!DBH)DhE;(8b7b#QaDWB-D-OgED`oN-kdK z*4-o7tJJ%P_b7{76&ZhU@I>U#z`@*MYjEX09prO2NCLca4_3X54z|+xh=fyL)~cw-#<9e;Y>aXkRp2RpyWq$E9-ymVG87d zP{v~GjBobsZOF{b3?&1D|NMKtI)mv2EV&%w5AVjcDs3eLp~mR2>(u*%{m;)r&$aFa zBqtfvFJ&K}21wO6HcrmZKYk4}XHOlesjGVfHSOO$lf*J(BoPO0@Lzc|NLy?*H#aZJ z&;NXR87Qo=zBQKFY+5N~wyp@TaFWDqr9eeRKUgJTgLJ&M$_d*2vv4i%#Ro8V7I#W_ zTNXD}7oV3y*DFFQ>oR6{3o9yOfrx(EeC04JOsJAbfQN&I z-wB|AZ0gm-R5mp=AyKIOva)D(wo~I@lc!m&ro43_X@!QB-eG>}h{fh_9FM=?=;IMz zh!4FO8_;(l=h6#3HV92x4!nPPkI1>=%N_`!ggmoUC&3GrVUWp*KR@>aZtqyTySuB) z`5fothxNTa>x3ZKLG`KY2l!TB4(M9R0Vq&7K-?`YEfwjP9hYc@L|O7*%+E^hFSJzF zH8(5E%p8+zH)-aT_C5O#bT_QjtsHh3=n zGFO8H?v?E8I?XwjnaOaatDWJBJM=P50roL~2NYPWrK8$^f+r$4;b#;FR1%=Up zWJPlXXoOvase$C%*kA#Y&yru6kt87BWgc!;Hr))t@Y2Uea2Zs-6B?~+5TPnu(oHi% zGFfm;rbn%wro9RiCTBF^zh2oa-QH`-Jsr4TyU*-6$K10v1g&54UHJ;ikq|um>;v@X z<2A(~2qbb~UDFACe-}bQK_M@J#9#G?z&jClnt4IF(s zIyN@3ysYKo!gbhjFVj-V4Eut6$Mg*Eqj5$5XMAEx8X9Jb==25flUE)Z{YY6jZnf9< zLZq&vh647t2e%v1&pRzKN4-J$TaeqyTc^2N7^5R zu9UMxQ`do2%Je?24A?HF>%dQnH~r@1;fH6NPaZt;j8^(|b9#SqeY3PbaI=te`|Kw7 zFc?jGCMFZz|F%WASk%zS*w-F5mmLh z0JP-)UJ?}zA6U1tvRW-!MpU|bLxLiY?=&ClE1b8C5&Vo&k{I2>uA^&g4C(Y=%CNMz zOVX9O4FtfiVIp^$9BzqU6}3S!rlpQ2g0Zyc75&trfS-SS&*~)Tk+* zJ%?y@-pbQk*~`skL@1(bU@#366V&^J zTN9(gEfY9Yt9W(VIeB~A3260HR8)c6FTzp=-HKNM!~irGbPxhW>54vZcC&K#eG-pS zbeU}XxXAmgepj6xxd3{&!eU|VhW-Ggv}Z{0_uF+^R0^13Giv5^w5qO5x^JzYsN;My zLdqPuN*s0|nUhWVIwePZ*h!-?e$vM*tPHl78rwAEEJ806eDNostjLMz#2rx^RwjPk z^aGru*@HPhpPQSr3=Uo(6%I&;ae4!D>hlMLQ>(*w?tfAoT0h- z9gv5mr8$Pl8Cq>%6!|1RG5z@L?7-;g)5XO_Tfy|%7WnD-$&12O1mwU8ZEm`3|Enw( zI_>5#DnuJBC@u(V(da~Xxp~d5Cy=;+t^*c$8;M8F{VOI4bStz=L@9R<^Kv=LT@SF| z)eiE?b-efxH&c+*y_{~kvU~@hy;$|=81i3k8DzM;JN(tqa0V6DF;SDIh?d~#nr(=m zg625zrbg>>Dsm>{1Z)QE)^$H$9_19taYW1fPYs2`y|*U|#jG==O~4)8gkdv3eGdkr zceyJMy}`lXBTl)tAk(AE{zXZnDPkpms7K4)Jx|w2@*J1mWmoWUdt{J?EmLzQup}Up zHQok+0??BL82gmD#z`N&DJ52eua+0<-Jln%W1EIh%c9%mCDzglc`ZkILg05(2u{ zLW}QiY!@9$4v`q%@fX@CZEpBx$~W#ru`=fT)Y9*(jf*miE8!P~PcoV(tiZR7uhWAv-vnD5HopQX%U%Chufx-TOdH@!mps zDX2v^(66mw!m+xwRZTLx{}2<_qpB0KmUS)sRXBA-Kvov9vch;4bo(Z^F^@y1Y#Kmr zL3aNW$M4l#uvqe~4%GPs<}+V991lF7j%jooqWtRp{ArreQh`p{)a*nQBY{sr5?kvS zf0poKdmCzV?RbqkHR77~ZKg(I&BsPvrr}&)@j2Hf*W6yj%~=Pc<4((BYjGt1ri9^& z7a!In+o2)4y}y6^TJ5oC79&}txbR~92y~g^Ds1L>rl;qPPRXD5oFaa<_ixkf?iD1O z=t|s%fjC+RfMWp69004be`573^pVTU4%XId$xat_e)CX0J)0n;Pq;TSrhMA?b9f%m zo3>*DuVD6XzpE;UO9{|8RCsIVw+`0g(ZE{HqAGJ!UA_lG!yJqPM{j4QTN$MZ^2dk}p} z%fL`qTf6qBwm5K&p%51J2*Y+>dprZcfc1g+9BL0~>5;qlvS;sa77(|z%*<6{PRtD8Uua$xuQLw!3CYl(C^ z=(8ioU`3?W&e=mH*mp#b0-CoUTSG=9cgfx1)3l{z@@>MmGWtAZLPd$X5a2v`_RY@^U5L4 z{l*_eD9wdY55KM)$(`g;UFZG2-ixauhRb?6Aw4|_Ny)X@x`C=Ebxlg-ax42c3IV}ziXSneQjSD*|>*#~89;?aLnT@<V(oFR2+BZZ;Dcny+#{2s|W2XG(Q_znkg3A=@P1! z$WiM=_xP*M*Zo_Y_VukViYm`(3)*yqrdE~5@c;z>NEAZ^^m$wB->D-#((rR=V+!5? zl!@2K+t|J^ifS{2{?r4BoayeK7meRC0LsCN!+pp72Zp;ie=3^4Th}rn*RnX0W#9bjAfWo&BZp6JD^y2kjSq ze1c+PN`HA&bWP4Ju43>%+b2Wmv`lxGa3}U*6EBe$FddzlO&Jl6Bna_%r8HrND29W#b|`CENTc6c zf^*b4;YEG=s3nlXl<(us$3u>3ca@^;KFciibDEVVv+C^mdvrM~UPJ19Rr$LQQy;cM zMFc*vq-#zf=eu{#Wh})JO;f?w-~YP0c@d@ZE$3{_-km~jwhRuue{dZsb)bb}&i#)| zMr>HDNzoohd;Zo>Bmo*p5(Jv?&Gv?>i)PyS`OT!`fnd}BxR+5VpM!PNj~E6xKdgDU z>h{3kvK_Iofxhq7%DTLa%3C?TZ1&rqH-TtbjYB?CI=2eG~JE!-0$w;ITp4Y(rwteQP0aoDEfF#P z4aMAkSzSADnL_7mlNS+zKm|!;scC^}sc{c$^AfM97bC4?sG_T({>oC+OfIlHD^Ucz zOTYpm-m`qk-q9T!-ScBuPsV?j>}7l}ra2^r@L&7Cl?I14NKjCgO0}!#^~crkj>1<9 zCx3gyn@XLz%iRQ<+PY@xHIFUr6B_nIGNR-ylt3;hh$-a(WJiL*e?*Ps3&Q~3eEW#F z&5z3>uY;*y=|xVXa5z)cTKcPkDsQ+!f{ytBbYxR7DJcoazln+C0;voOl(+MG+on%x zDJkItM~(iuYNlp;n5KbCV#(&?kxWRz8mYS(ZNGW?(sYKk`?M5?=3{%<-f=(xf0L?3 z(bwapr@Ig(%^wXYtD5R`CN?H3&GNvb+jS|LR{S=w(+?LLT)bQJ_5i;4fqm-%=LV!r zi625LNi}gS^(bf|PCh2&`?tKon|TVEoCy3nwVSo7JKl^^uvK-$NIvdA-$sE2l!}K^ z*=eXIsxHa0v@{Wc9{{3l^*LcGsAi14&v1+C&tdxt+&p2HdYc?fQ_z zx170g)n|2}F*b#oc>7-4bBK(lm2Drh_6i-E>;c<9&tW83j(_wkq}7UYx=!XWvm2^~ zsf_Mps;jF5SjzFGrO+*xwm}Jms;WepVb9VMJuqe>#@Oh`s&MQV+uFf@P5sdvBd-l; zQk8d~m0f z$}s6?RSVv{V=-?+N&HT%AsB#udY0@)B1jcq-3U|iFG}7#qYE}CzRlJ;5HYE|v^y^% z;w9+rz>>jdc_26UFqHlo9R{nz&FnO!hyO0qz-*Uh2`ZvtO0!A1eK(7_;rFApyVLlUr#r zmZ#fh0dHzZxu>2Qn_NefyYB-a8Y(1#0FrkhJEOQNKX$r8I*F2LMELpF)g>Z|nZ{;c zryrT9QzW*@~X^!KnTx|0TrR_g24JKg&DC2C(#cRer!`z#>)b z8pT>m;IHnvc#U`uzu`pd>z&1dxWcV&BGES&sY@Hi%heV9G{SX}cK{j^rY3Y>YP+0| zBSfIXWdn{r@XmxBtB?t}w3xV-C#P%=uFJEJ9ym{cBJ)INBmXp%Pzz-=gR!+?3O#@IO)jA?Xf>GJF&&MXSV+e|3-2QgrB5!>lvEd z4i`;K>5dFh53E2Q+p=sZze4SakT`O3HUxbh>eCY}5r@%L#GLtqBEH-jxYS_P>q@Ck zcqhVaP8q8u4y>O1*mc*kp?nB*T{}AE%lEIOUo$z|OPjg9LRZ%k6N649;~UIdrITMz z`P!=Zi2no4oRv|ev;7ql`l()qjMwVRqtKZ3tj)}8An(3&eGzdj;g(SZtH-NuKy@sg z6K?-k{*kUJ`T5Mo#>SMuFmE%ikjMfs`m?@UXf$$u{y#R_fvvF3apUyjBJCP;C?qa^ zG5IFX*rT?&=Cjr7cEio9ImXXsZt&PJ*TR_u%MXkBw42V^m5mg;PWg*xdR0iw(HKE%q)~aBk#AROA_q^I?4y996|6_m^q#QVt zS2VxvD^9)v|ARA<3HrgQ=Wa^bzw5V(3Cc3Fui#;`;i3HpEZo@lI$|Z0-kMhF*gR(f z9M?UWeZ%uE+pw*;84Bl_tqG0Yng`Lz>_!-cQHj6C6T)<<++L0X7n_m$Wf}3+^FKI=EZ)AZA2fGgcXp~wiR@z4Y$g)d z1=5dJP5z8oJ#F?HBEx=?dnnQOy6yp!X01KjN|W$X3rZ(zLv113d}V2rNkg$~-}@N8 zshv2%pT{vi;S7J@YP&sTWtGhMDOrY{o7&C6WEh8DQXcn+C^ zplGU&6w~~JsL$J$q)#0g`cz6$?YIjoi+bfbK_-@yq{8mx775-xp$yHzk2kRou11#} zp6EGU25yA*?+Ke~lLJZ@=5Sdlk;OrzGURi6iC&o=AWR^#!ew2Gnf>dK8+W(Ye_P-H zoQEs47|siN%zr?vzmst}dzc*b*<}4qT;2SXd1y3qXxdoPSZcH6{Gls$tnrl9vFAAU zl%}^L{U~ozoYMB8E6^N@O-0^oXNI{e%~pzn8v`-o1KC4?^4PL+9jS)me-)>&(VA&tFVScbJgyDD+G7rtGNh5iG2a@wrJ*0yq*#UgpPoV zqnB^qy!nU0FcW-A(&^Z4K%>#G$R7i}vrRy3A#UL^_-CvC;pFsm-}v}=`pB20yzMkt zx<2~*oa~S`r$LF>^QCl3HnPX!4SD;9`#g`Lk~xXD^a&mW_jb#n83(iGubi4DqLQh( zOdv7;{KmfH=W%~mIYaQ^<|)Q6v37D5Sh;sPT)slX z$Zo=y9f4SiZ$cf~{;h~BRV)>}t30}6PWqn6rw6b(R`ngx{=Bhdg!oi@2cEXM3kSt? zVvA&89a|JtS%X8Cl$E{e{x)8+bM}-P&0fX=oWy#SametC8Z+)fvv_x_L4Ty8d@qxn zsNZ>-k#WAMTWw3o>+z`Omt~@d?rJryb#H16ecGD<31-v#l7`7U%xvPsK~MPw1qGlK zG0gpX1+dhL2UCvCux|$%fGQBx#{>vr0Eyp5@!J8=?ioHI7@p=7 zDnkW3Tc;I{nZxdt+bmv4@4q_G}@oW|5$2dR-k(ZObHQTQ*ChKLkvX#TaZlf2=l^&fVT%CK3;K@5Sh0=MZ^0F2AL=hKDJ2&%R$Bz}%MTb{}Fu#@l?({zzOF z3yOayrZ1=64(C8&b6_UQPu$CaG_;>z68{ z-R^=0<+~uDd8|5kqYw!Q2Zf6+DY!H@N%8`syHFKi95v_>Ri2(%>#&GA-BRBJ4ZiVr z*CBV)WbaXKE@DFZ!FF?T&>FHE{ z{{A`CZnyj*O^gKhfM)$hj-*KImKy+W9#1}1+ulNo{+;fwEfh~30c~8#!4Ix^hDI{`R{bNb# zFhErJA1tgIgq;}#-rr&_NzUUx9ENQ<+~Xd#hFd+w>2SHdH<%yTSrB!!_ZZL0$jCF~ z_CDPjOVxyDO$%6rhj&DR4-XCmB_xLWqF<;KPkGQ@dT3>!-WosC9&UIDwf>qU9|;VS zf9rScdpvb^Ejtl6{n$Oybej7v%NO)zeA(Z^krGlsiXsWwB6ry)x`sbxPSP>z+TlZ97_GvhPFJ18js&l~^EutGf8#{Ctt2ibzu3-PhGl zb=ow8&O#<;l%AFep5?Z^#~nJL66A4yR4RqDw|d3m26)d+;AT$C);CuF+Qp{QP;7n*G#{4Fi2wXf--hHJ>Hmf9ksR#-V<;3wFK91m9nbBomPz&B$gD z*~?;z8KCStID5tV2!927;{PAB4mGvLZ69iFSmzQn6pzwlf-|4`Ub`vsAtHR z#8mETzV)0p$NL?bHwf4^nu9L|W$#aA5r_A8hv4=8SYoLILT)$8e) z#_+Fy#AY*g&H(nNU&VlEIeo+ahTAKl#Ns3YCHSS0V2lQ9tYW!qp0uJM#p;Q&>|(lb zsuDg&3MbHJ_UP!r*Ap?|G*jxpj5ceOkqUQc$G!R!J{ityldd!xO;fY(BND}_Gf)uhwInI)$|-<%#5>>nv+e&`ga1fZ#HlfP zD@|dgK>lFHpJ;GPZI3RCzphrJVrfG>wYZh1PuYS!r#i5|w!jP-Uc{~^7#Q<9n*dS4m1DCfOySh6grdXh8S14>^(F~Cu_t`B`Hm^XRqp!<{1EcRiBzU=momZG6Zmp|9V=F)EP&Awl zaKIRvn%V{g%pviPCC{bMp>&I$0Z=eaco)Fh_E{enn!JINLCdB&0q&{3sR^j7Lml^p zVYq1(ReXy%tMhXoz{>yp3bL^i*G&_EL92cJ>Vf8o;!Z5vE`@hl>DI1aJsVUS`r5!{ z5(?d0FK&f>-7X}2y25Xfr&IR6bcWzE#5U22s4md-B*`x&y9gzH2xL&hzVvxKSQy|t zYI^&+=qqE1*AiLvo6djEGq@Me`fbD-{y`ix3cG+HY$vXY+SiPUW`d_eChAXH(@YIn z0cc9D)5J|0|K&StWI{Wyv59rSf?&eC@7@jJY7|bQdM)$1Pt6?4t8mS<(vBs#_YA@=L~Nk^MU}yt$qHM_+7~erkFLBo^24^vx{2tYxWb zcayv;79eJjv9-1R0vHtl>J$FsQBi}*--}!1b00JI zBvq35G_en}>(*`qeqSULSp)^x*zEi{A|ad zfXAMokZhuniB8YFkP3T^NQw14`*{W;yg6y9mnIxFEe#_#J8a0{$ZMf!T^HX2b+|US z0Tk5G2>`Zu3jK7mMe9J9_@O?LMn88D<%kr$4~u6cQ0v4P-rpym>t_Sv-yh9% zx8lHOX51)OvJpT^kgY;wk8C#kAJPM<{*;KQ-FxHIE+Nd$u5UFR)mpe4TO@S0>6NLX zBSp4xw%`2kM_H>(^q?a|laAm5VZPs0qVH{F_8@-)6?Q_=@m`N*h^-4?Yt0o>A~ z9{zd20!0-*VMW=`M-}d6P1)~H6)xa-d(EA3X9{tF18e|p#{S{q>BX_l+qZ84*BOIx zvV0=T&e@eqtfLGt5;s{<0-i#^3N<)gWoFz0$r-GsNNDYSoYE#)96f`7}22FC=x9KO(NcScjgst8-oI zd>P$t z>nteIY%}z@;dZ(-p->EF23CuQ04JkJKuD+upf>^V?ZY%TGKu7a?@N3;I33kj1-zS8 z$pDYw_s>8tSt*`gyFwr8wcelpVnJG~JXe>~3jjNSxRV2lyJ}DZ)7n4DB3H#LXT|l) z{4M<)EpD-PTcU{nua=JCXZdvk%g3*=bTZ(5oT#s$td0H6k6XFlH5Jm0=PmvE$mRdK zYDj)b1o*2`eaSY5Gk;cv6oW%6fafnqle%2OdStC;~(?J1D*6Uy##8a z_|Wsfw(3u%B?LGCPf1=itHGA-W2_>oz2T$Ufr(j{2}BenDSg5|kKdzSJ_yOo={pEP z<^M-;zj=)m_oc+vjB-u#wa&#lR{l1U9|9;pUS7@di#;~_qW*^F%Uj1cf-fR|&ZvXj zsuF#!6g0mAu3A7YO-oDjG*+&XFCmWdz1x$$;oNLF`M8X9YM$NgL!ZL*0YN@8?=Mzx zMMXtSY-|We!zc{c^`au+x&SM+!?O4->}Ld-X3OhaU*#O!TYFkwVFPT_yOJ4Yg|Vr2 z5h`%M)c$s1P`(N`?Z$~`6>dFJ(<%wHP#aw(oneDs`2yfXK?=XOtXfKMAe>w)XTN?^ zUs|VMHt;-bnSb=~<|2fieW$@>zgkynZ8QQk0cY#z<=$gV(iH4y>AQ~KY8Go41azI! zQo;FU4N21VnO=ey5m$hY@=Zy8&mP`OYuPF-fLly4HsM$5-fZOXT zX~l}APF6M7eY(kvnDsQ}8zGtNi+=odttR)7)$&I4k z|0wfSot8x54**R;S!o#0e^eiNmxS>Ak-wx16`WTRCiiqUY^|6^CA^&$_E}t+xZy1H zPIlx_=B6z`d6R3C(5kvD;v}!l;6Ia2xhU0+Z} zV{bl|Pkn)cRGfC%=7w~R!Gfdl)FL#76id5&mS926D+|Cw<39hukCF2_-i*9cWUIIuc^jz z)eULldw>pcG)mFdJCleP<)Jt_g1?R$$dtJIyL@TZF5ZNB>v$18dLZFYXLJ*KAK|PG zu!JxO1}K?;%yC&*e7gQsgq;lK>uA9?wy_3~lj^ySGdbp|m(QD7BB!%)fk7GwfS`Hf zzx&Fd3FObyxNw|>Od~eh6HqkvsUif9x^dmM{gD)$5S~}t0#gEfNfmuDDFE}X+1mgh zNY9Fj%}DAI1Nu>ZSiL4}Vq>QF+j|_Jg8lZE<<(wPgHNHWWJottOno7lZh2zo!`eOi z&`z}7AxCu4wp5y#b*OI=-(tvU_K<{q%FKU5cjG(TP`hUuQ%3W1ZxdNkW}1dlhZi!9 zS0)z7FhyI?+kg~6E?cZEASNbqMBVRU~S-zj`xx2?1x%^=oe(_d1YLuZ&ONN3H9EQPk`ryci#C6SUi22c6*SV{QO`E zrdFYE6Bd?Jlne|Z%N!He%*8oB`=A{d>+n?{lGG*3j`9h2?BpQXD@d@S*$!FK zM-#>K&GEROXEV)E-12Q;k0pxwqIxqfYpH4T3s4v&eV!_5Oy32&M=ZPB`$|&@(E!SU z3u;R)=qRQ~#wgS=Gz^w5O0Dq#m|gl0uqQl8ss?~;w=r$y-wTdEXGwz*k8a8T+4Z%z zxBt%|t)`|1ID~&WQIFZ5s?+GetpN*x|0l*#f=~QBfNn{Gx7r~31PDx?krTCSlUd($ zF@r}f!ih7##9y`6dCsF?|M8TA{t<}S%7Htvd5~_DLb`< z|6nJ=zipF+c6vHwAC}@LDUp=Fa`uD@^mFi#DRLC30W>&G@b#k+tldu6Rp+ z-ZT%ITyAs)560zkj{3(C);5IaU2`a8T&WXYusOQL?_U$~LzNU@)KPay%uMYMz?_KF zRq!b14bC2Dd83c_@bO5sGOZ|^7u|z`f||WI9~)Gev(m>Wjci_=q;`z@hhhBRmrVy8 z!Z7B>aqYu+a)Vf5*v;-0C&?ceAlWX#W>Y6q1wUjjkxznsH`6>ARKTWjsA&S+8&bclm$wj8Te3=Eg}m@>K{o1!!tx-U)Je+?Ma>?O3rXz^{GOn9@9z=-l)} zo>=R#I$s6Y#hM_#;ha5$Gr2-Ux5%Jr`@qqryy{uJn&0c1#OH1x6d6Zp|7RrYd0ZWU zYXWs5ukG`IJ^77KyFt#Y z%XR0j@g|8ZWB?(KiyM3Z&RO@k-|vWBK18R6Zl_+P=Uk@0Fh|F*;mXL7*me@{wI3wO z>LjsjL)qu*7LI)0_MwAbSCp)#uu86BdndE`Dz00!cSI>woi>H~j0$Y~xK$UY9ZER)vm$)3rXcaOE5 zZzG!#QfB3L0Q}Fl-rHqOB?_6OA^@$n-}!2?C(;@okB9SLvj+|?uu@nxH%(y=y9&)- z(kB3=)x6;i?Sz|N8i9)mgu-Akc-aJ>9T*q;@mrmQGXWqF4gn1nXq1+#rTiA727cjV z#+nrMzCvGxJ?{cWZ@i}6GOzPHLsLyk9;)*ug;k3F1+Z_&fl@ITf3l}n&7v|2EaZ&Y zV-r7}S6BDQTHKEU+#eYwk|>huO^H_%8MfM3HvQ2o-aynDkQ(BA#Dc+KH*0)%Yid=e zoI+1+lt{ic1v(72G4$ra3j=JDMhvi!x0 zxbEUu?&4dhA=>D^GdS}p{t+}==1z?=Z4->ZmO<_j!gCwm6-r0qP?!& zV-i3}%DfVO+1F1>J0`q)Xj42~F_c!K^BDg6ZRI;_E4OIpimv?uu&xUskT!{2Dd{GQ z_5g;S-VY(t^xmVV_4+aPzG7NJYH0N|fcEFb#=_$|wcX(DC7U9H#x#?qmAg?Kqd`x6WaMpCtXNhbRF()Qnzis>#0T?VbOZ#Sj*89E)C_7|qkabl zUOo4J&)nDKhuhT|4I(=P7cZ)yyj zp?N$4QUU@*;uC(PK6~{3$s2_fbw2&Y4N?N58S77dxbAnZSvuK`M0r1jtxU-h}r(%7P-ztU;AD$ z%+JcPoWJRr5x*|CCjE9>jaS?DEHT3Adu93eUyrzzN>*a$vis*RqT_SUue$#E)oWLXeP`VsqJ>W9 zHz5qW4kk?Ss8LoAuz|o zwZuO9j(Q&rNIDlmz0I-a-|0Xh3rv6KI0SLPx3yGzl zU3Ad<{}%IHx7$d;65)ceH>Sf;X*abA4T*OKEPRq(uazFBa%a9?6e4l}$$Kbql@=M@ zu7(iBf%oWtdWPAPYLg5WkS%0UuJ-p?0kt%njLCy5&(J?(e?vN5zw|6z1nefcn)JML z>!W2AS#6{koAe*4w!KLHrsN9bYumY^%Ercb6=FxtW||OJK-p85j703NnyGclkv*_g z*?>g|U9|l)z$s=(eFvNuX!;n2D}`0WA98ls0T+?cK?CQafMZE70ej-aE(3I4qoz{F zK%|r~xf-Epz|=YEMc2bWo+A)FIK6bBk|b)p6v^E=w1PP-PC8ICZNN z_yQbzWaBm4TE4wA!;`bE9@){LdB|mQ?bsssX1ZBMM!9p>3Mn69lS{(L-_fYiFk|`q zT4jUsuQQm|I|Thbc9A(~ehTOp)~g?q9;05lLO8o_k#@t=)I-0AxSCMfewj6_6kbGW z-msyqu1B?~*a04}Q+4KyLhmS1ImV&scb>jUc~kz_%U^R;3KdJXKt&9K4FR(hi}tS) z4nXE6CAtX2oKTuKWddd@_Wh=kQfVsi);zfizlG5C)9){u#;=y*L;-r1mY^CI_ND9D zR^}oi?k#h(nIO*uKVTV*A@=dI`V|qmD)YEc5QML^keRU#Q#f(S-u&QfU&XC%@04YgS#{5e!bHflBH9AjZB&)LLTLE;_ z_E5o?U)C`TtT6%O$^W5}W-zgLZ-+vrD)ViAWF^ht3^|UKfkR)g*YDJs6mj4bgiL&@ zaeiEp^WX5UUQgLX76F;@&&%k|?st48woic*V8Z0Tj9pf|q2t2IfP6fiAyI2oG6M(z z3P$#UE~$X}AIJ|HQ1-wFi2p|0Pq6i8fM+mCV6GgR8XGw8NAa2`Su!bfRmmNo^JR$% z!xq2dEQ>6~&9agnLtm2wv;}rssux9masQCFO`E#=w5VsJY>V*uzvc_5MLQzwp6{SK zR5$3rS5ccK2LV1@k_HZxBNUiJ&M*Boc#~BD#2gQB{SNyR9?PLm(}p>PxJ(u@&5Eje z6h;-bE&Hrf1I>8PTrzX@`{-xdm;3*xV zG*G(ElD6tgY|vU*i}!Ct!903M|25&O?1g$+L_8wD;t@40(Xk70$SLX5^X?;SVnArS z{DIy&#sPQyoDS$`eu0OpPlZNyxy#)F@3*R`!N$ZM*;!HdzRIb@p>)Qoc&bCFTV@3e zut$hu&H4AM><@{kMNZFfctqwqwMd{svJ?{)D%)(yMjPv}oRTm= z)usz23*&-ZnLx81e&FOrc}0cS+0L|>b2>8N+9%sRXEL1Cj75!!S(?g4{Eg-AN*Zwd zw;z(T*FT&(EKHv4S~>X6fF}0?B4KOH&@D6HG-2qg?|(LGw+SkZ34E6bKT*WZJW;sS ze&Q&9>>$Z=~VDffmIoJ-z(2)-i-qb~=yr8_(w? zMr&&uwEhoIXBk#i7j0qb?rx-|Bo5tO(%m85AdMg(-65&eAq1qPL!_j;ySuvt;jZuA z=ed9P&$G{7bFMMRcqcmhDuR#d`;;H-4C(a^1P}k@=f5Q0$RnF z)j(zcf&8{MI!ctx+@tA^2sTqzA@ur4&w!L!G8Dvb9svP;G{1yvKXN!ts5#9po9PP0 zpj`n`U#yEq3$Sf@ac~u4>T5+bI>UyZ2zP?0Nu^kIRG__I7^7^y!N&H6*x_z6#fQZZ)Hqf=hQP{zXV#OR;3lgIu zW*9FqY~E3$?2cG|Z^%A?pYclpLBnZM3?MP^kCI~EQ;gL66%4dx(n|(XfizQg9ZAlx z;ga70IA4J1Yh~|70pBDzdp5lZZhYT8E#G3+Wt!g7=~YZ@|46XTG+ZiPR3kn)g3?o3 zm9%Edj}H@STtsfk^D>y(z)RTBMxhwVc1tkQdm$>8zu~vZqr0+Pr`2W3WNI2w8xm_{ z=x2ZLSCO9HBUWPsuzRnKV-|{VHLS1m2#mV{PwR|<# z{`XZ7=-+C3xIkG!_iPlxF*{=#I~>I!dK4t@>QCyaa#mv0UlQ6KR7>a%yKQ#LgaXs` z(L1(EymNnr9@=ZqtkKuV{CGCN=m~;E4VJMETc1JgMAC0?k!?+IhMo%nJyAlN2N+$U z?NeWHReESusum9dmZmIbmp{qRC0v8mRnd>dj)8nI0W-D+`Pj&VLvxm1VzPmu^ zc7?}2CY(=E;JES|u>C{RDV#*q(7f*Tb^J8=&Z9x2bmpQdXL|THu|H)8fzX#em7|A2 z?r#(S^4Rw(6FNdnT+I7S1HFyYZE|pDbUdNF9Nlpfrc9vScDveD2Ev7!b}9fE09kEl zbCU*m^NNfjR2>a4spx8csVF;e{{eo_hYPXuH=-h6pgf!J?Swhg^-iFr_+xp#qfi0j}cehc1j75ZqH5x9a zN2Ab(O<*+!Zd#CB1y;MRq76}?Zc0n4j{DfOH+rsL>rFuL&xHw>5ss?;6OpDgXb6=;t;{4Q=uQ^DqQBt`ZKZa3mj4IP&H#vd5k zQ^*mp(`3pm28OP!#>*{`aM1e=&gUt-;psSWcl%_Yqgc^9-Nk%in_zNviZ+^t@6q6X&(x3}4=wR}=-nAX^Fq2b{`$XES}sm8oZMk? z!FR&z8>5FfC+cD|vPm%~68JKmuMiDsmkot>9UKJPui8JwwcjJXy(r-GPb$*Qb$Wb! z1i=z8Cg}v@kq@dTac#81lvuzUSs0#GeDQpZ3l5VBo{=m*-g(hMx8%1MrAo9-R+*Wp z%4uw;KH#!#_aQxTO-YwIeC~wCc7*oMY7)pI@sRo^MPc$h?rcln_vzA*ZGLFBK_898 z>L+1U!x({bjmjDFI9LA;s7R_0jkJ$X*XahzNh!R)oc`~VMgFp~pPxK7rB};S5g&zB zwG64os&G;7v-{?2CvNSbuH$21nvm`EW_Pv$hoiu)trYv(_uO9u2zuahz3;4=6d4AD zBp_VTNl5ddSH@#x>UFy2>aThCwC&)y|(+=z8{`DuzEAyy%e(tu&emAVj zKxpRGC~rJ*-a=2OPK|fP~WTsb`~ySsLn>F>6|yO+4N^~T}`(+mre z@J{gc3JD1T#pE+!a!7_RRs~$J-|gufI4TJwS(mq`C{~P~l+tJ22wp_K`Q{Qsrek0H z_h7Hm)YV?&>-ogo#NhB^nsyaY z{Aa48Q??o34o`2t6f9&n_>F*p=hn8DVr3cdVdu~ipHEFq3<{;oB~|Qr^SWA(1uSXm zfx`a=;Tu9oTD|_CZ#kp9hsp^0xFAvpHE^i@T@PZ->|q+2rD59m+B==YG(C!`k5g!% z^|_ountI1xUenajbJ>d-=ALQMytyC0WZ(w3LIUDmbod;;Tj3j)Ft__9{~CV=|Ne?s zFxG~YW8*b);?*ja*abL9oP2zJSWg{T=Tl<;rl!j=yN|M{kEotIhhqwux1f95kgJXCd2!bMjwmCsEU&MpOdoz)&%AHPtwFC%N;IfT-o@ron8|Z3?+$q~61=Bu7 zSnGz+%|Z3G2J_4BQLn6M`!~%QNWsRU^K0hw7IQbAS@SZ?l%9X^o$O1qdzUgLk25`` zjWcyni)t3;RzFV8c@1!}>+fc>Y<;}lO~v~7{cX)2jJ+4?%ihaVE@P7X`Ak({D%C?0 zmB3VaH(EIsKkRcpH8K{0#J!9Jwn=N^iyqD06-`cA*?)KtN#wVS6d-kdjg8fGpaNgQ zEC{U9lsEZg=cz?-qI`>k>JzaaZw$h2ehq#{(mdWB)|@)?a{F|W@$8WyJ+92WZSC70 z$%^{z3+eF5?n7%kPdC;}#oD&Fjn}uoEnq+l7lWE}C-7h0ZS1E$@CgNe)A|)DIpR+s z+NeGCM#tWfYRBhp61gBCTV=%m%iEfU50PVAo4sKY@Gx>31F>GPwJe4pUhRIgnUWvg zSsA-^{>bRNJLeT8-DN~^WK-9;6;+-zgInY6cjMV`;p!aLTu;GVPkLrV>Iuy~`6gPm zbPzzq8o)~?Cf^HP&eh)rk}GgFM}|KE63dwhWdS|qYjTeIl@4K6N76D3{6)5^Ci-=b z@tOGIqtK9N%?jb#I;J$oIPNQ#oS$khIqz6NW*Zn$duSHsNh1F7{cOIdU~`jJ-|ljy zO7BB_IF1{V?uN0{-@e@{PSvT!$q z64&1BJWUi)R7qv+KIV;xEESWyM z?iK#xnOSU|XNzc({zuRM%g$$-WF|FT9tLkkkDdUJMtBnYm>PGzLi%khyY`OFz~I~$ zKJSOm?dM+|N!)M;u-KV>RxLu_KCL>@NQhCC@*B=Ne(m$M-G2KJIr0y0 z)&G~cFgcWm1jP9SY8Pu*FP^t)bY=f$XU!rGh5IcIq%$w)WPL9!i@o*4{i(Cs(D;WU z-nT(*w{saaUoDZ0D4h6owEDeV5A9U5h9L2zJ)EKn~1}cvhL( zSZ2>8V3Ay;!QjR4%o}?5iKSi;T)%+SPzwYjwQ?;KBse3|0~?TxR_bmuqCD|t%JF(x zI0#0{#WwDcK5}~94Tsk6V9+|5<>j&xz5mac1YesL_qx{KBV_GJVhRH6=^IymO@Zdb z3CCUZAXT5~ulYgih=)*z@4%VQt_r+AKf%$;@JFtZ%f^!I1`J2TCwC5kU0u^V8W##R z|0L3wvNAA$0?BthL&L4jo){ZMO3@c5xToXx-*SS~Np?}3?YepSwnnGX?k+dTQrHKI zGT0nMgHC(Q$Gc_A$1djMWW~#B8A}6OAEL-pNgXYZK3X#=yC_9U_Ybwr(Ed#cOiTD- z2^D?rdn>$66=;cFJ$CZ3VJc~f1O4~8{~3T!Srs-?Oe~}mSOtg;ZS{Em z6`HE6|6`XBAuvb?^Le1i(>{)&ksbZq-Y*EJ_zYO25n&_()c zE$|;KsP!P5zf!;o?5(AZ1Tq^N%c$Vp0-Tl^XP0Az8~6Ljh$r$LRB0&~o6WKbEj8`9 z221irC0T7A1|pp#=?OP?{~~pWrF9f26T3RR6-@RhnATUIp151p<@TXD0IhVJ=_|1Q zTUR=E+}-|da=dO&H{%GJ+p(~y zMru@oR?#Z=pIO;y(x=99);ERBZON)@L6jM@W2bDHdGO4jC8V3OtbWLa2${9gB6;C z$b^Lz;RnU+hRF0n)7~Sl_QZF>{VJ7;{YRTsFOPChqu0FMPU@mBnXmuY*q{1;_)%`y z+VQbwxS$9F7|3dW*$E!{d}74f)kS#-=(odDBRxGZGY=r+Kp?M-zbzT` z+sd=(o@@WT!7%Q%h$;XaT(!P_zUmOGO}x}zXEeEkr6MyB6#8!{D__j-qis?de{LmQ4v;*RpeP&p#T`M)~2lQ>n=A z8qVYCs29(dIAt&r?YUa>N}Y$FmrRqHke{xq*seaj?6SYC5Lw@^G{ecQT%~{73jk*y z^(%+g2;%U8>cbQHt*a)S@(G!ArOne}Q~)9PHj)E!AP@CUl*1LcDDc2~`+EPXrrLQm zlv3XspYnZ`Y`g*4HC3D|>65_n$nYF8G}Eoy&v!HCrkeVsnU z04f1MUZm8j1+>oajysJ8v|2^c58>22&?M~XmhfefTVENG04bv+AqtpIiu(gq8!|S7 zijMvK8kU?B7H}#??1eBq>NV?;-`obfx?a|$`3*-`|1)MNnN3r4^-1P#{;Shw%=$HV z?uc9SV*>p%Hkw#|8*i2}?oZ^UN4ZF-c)r%|Vwm}Afbw2o<`wVP5v=<2%gi}nOX6P7 zZVm?Y?t7eW4)?0S*{R#4f*mcZf}|yk~J}h&cv7zzoX>6pB9hS z>lhjKf{_R+SyTSKSoocOxO;?^NXUZjvq>~hSkf(1LL(Y+c<>n8Ml!r~MHJ?Bqil1V zyEM)I>toLe9IWc5^gjA1NAj<>$L9IH(<(`yu2&Jyp4L8vy&SA9Z=jiG?~EQZpT*v3 zmS^PU%${_Wq|W*H+5 z|8JG?YWh~i#X*wIT-_AOFUPfOuJMlZK99Lf1bxcft@E)}uw<4j6!!K~`ZGq1+-e=> zTF{NjFUri*2ExBW2F?7_eLG1oyxzA9iy~%uty?!Py+reTxI!4BUHwjP>r72e0q^V= zXYLZOgu~^^3VXZ*qLsEKH32l=-ZAIPfohn1_{WcS=DFT~4bPkDFH;$y)EsswVoh{O z#n$75x93F<0bJ%p6RyM(KJMJ1ZO*3^6jOvZ+{saHKes7@l7HEs)k(gV_W&P^4O>-xF3t-ScoM4nQGUz(<4-hrcen42CpNo=y z6IG)7<+RzutQ%^X`?B07O)rB+i4J$;@6CUR({|qWr@DpOjWrSMUF={B<<7k{!1C2F zE@HuvuEXc?=r%L2>PS6>&#KgPw1sG8YqTkNcd5=;uoMB*MHTtQK|Z8e@iUl;&PM6e z&Jx6xR=a6ub!#;m{y8A-Ep+8z7zynd%|F;K+d-dYpleyu{EuOf zOb@=laV`AXaFeCY!;DfG(a9wRUK2VTjDj-3fb5gVV`_>Au1J)Wbu ze&ZJ@H@vdSt}pG?42GqlV_N`awRQi`#Q9w;(A;d5diUiS0USY9t|d$;!KR``IEGb$ z+>lENsUbew@|jJ{bB6{9EUc`oAb<29W^C(%2odU19K~^u{H;}w_40f}Dm*;=Ticuq z7YU;EwJCs&f(Y1FFUILgYu`>KhpDl!B^a>IpjY0|>CX>+(6T?z%*O{^!ypDhIxCHB zBD&u=Bs=vp?q@fW0k&jxUjgPU_43lg;nVGh_zB+G_@V0}NnqhZ@ii`|OzYSE>cI$i zT^D-ZO23>eJ_{QSQAV0e5iGBiocc<~iES-|p!?&i-sD(zvwn*PO2k{y)wO}{2W{Ys z$sj)79h9e1mNED9#pCc_V_AwYB0KqBLEpP_KyO3NogG=zP&+pJj04QDM?{DeJYD%Y zn3N+G)TppZWJ178fV#ts#3=Cl-(UDgMgahgAnzC<^akU|z0PA?nA~)sl&k%gPI(tb z@DK2)FUlrdUmh&34S<(`T{xzh@AqXOunD+BPIy$n$R0@__k`1)$uM2m?)`)8&A4}P z;`rXlfhe8zwb`VMLmUIk*H&p-2{2%hr|;D>THD-Iqe`$zm#2rSNZ&pF(kkQm+q$?Q zG&pG=H@Fx>+`?^#sak`6>%q}jBf(5*<^O^W1Z*Sj+8<))*=w@i#WN&Gqt>C8z_(CU2w#L`q0qYSCf8*TI&f&}t)$G6;R-w{yePwlg21Z7dFiE3UuaVN3Pn+Cu zPfL$q>tz0gwz2QtUKUE47|;eb)M}S0hq0`nc-3foU1^K*B+{5x;=0FBw`Pi!pC5GM zd&w zISRXi`=o8qf6zjTqwhK{uHRUaS+a;b0O94XINgW8RdW1nXSQd9vEIi!JnV+;gH-=% zFv2xYrs)c}CBKG;0qyug^{cmE-;2$!j1~ygrq=yxc5psJz6Utg_1+yc^jK5L%WwfL zI_ZJ2#his~JH2^{7W#p|r#LH4Y=Gaje%F#cSAFL|Hp_miB|HdZBDfWbVKx_R)W2+- zu^Wz9^+!(r>qV_?sog2UpxFnm+>t#!q*RfPO;+Y=%*x2NMZT%t4TYS}987fdmPNyC z8Tb%tY-D(V)AjK3g4&V(KWiD}ZKY{~*Umn@vA&KYY+mylIl1r=O`QGZyv>^G1@m|IPi(5V8 zfSdm7)0FuU-RAbdcivp$%$x5EMFyXob0XJ9x}1Y6Qn*AL-+_u2IkOetgzh0lO>&*+ z6x|QoBtudEO=b%6lpIezuz!O}4V@iC4v8$uA_-xQk)QD5{o$;$;~WCVm&irrO5d79 z`-YPB40_<|Rzk+1?$>Iyn`X7E)7Zqrc}%_0BJ+>@;3QA2(jCyIinJ2{N@OCkLI#4Chwi`nm=1eeEecYyfhYrO+VKy zaPQxKFi26ad4T#dIXS*(9-{>3I*`KtZ6YVR25tOSu}H$cVj-h@pF|{BCPK%>&)*+M z#z#y+A(LhWxEvs_4UoESuC75);kKbuFp~?RmM6Tq7W;L;Bg%_Aq@V2%IOTD180^L^ z*TG_60b=zCHe$WITxtAH30k{G-oGYsHLu zcVi+j^VBji>>q4j4`ME*;sow(Qq)6pqZd%jhfj8-ez8a885VMHN)il<&8V+>m`Kg3 z!}EnO1v9C$5hboTKZz1)zdE|IC*(46C|l=T;!%F(9h6MHwvqU?9cDRTb7yw&ByKJ=nFO& z%kq10Lyj4+70!JaRauk7v1AA8Of5C%kWEg_O(ExZU*jv&RIx<@596ZoP_AVOCU%Mn z{h4Nd02lw3TPy!SIx!XSv3Y*@V1bX5J!=^|+JFxZ#q2i_7;uUyC4Sp!qKt`I1Msrd z4NmZFu~xX?ocmHRHX1s3J&xpDD$3Hr!@+PJ5CUUyI_pn=pLZ2Hd(YeC$}*mQTipS> z8xNUe>7yQEA(?Rvjg7!jEx^wYXrHNoU*6C-(#=O0vvK$MhA_s3+x-Pn{Kf5F`R)17 zM7>d(dP|3@1vJE*Ikd*2sDG4LpEmqu9~eyyUvH;nu8w^8(T<=z^)T24lis=saUifx zAT6X7U4#~QV--p|?y`VGP9f~qe{JMM1Jm7Hd=mV5k<=ep=S>)_AtV{UP0?a6RP;hA zGh`!MEbg|HZVrg6KPNhzDs^adB>SV96;|FRC+ReYxF$#WG==vosX1FzcJ%rv>eh)P zD`}TkZ$0hh<@ZaH6I#^2v&*4)BiW%kqlT+cbM=QX(R%jjVTY8ci>8UU?e(%js?ju^9u3#-T81*|oKSx^^63 zNif$7nj`?yTlKG>QcA*uj|s)izIL&xaTFl?!Chbd&c;8hVg>FhZ=U1m#HH2kq5kZ> z@>HT#raavyYlaqn7$9R+z5K1ZLTf)q1K>%GQhc$eZn0xCl`4l2YL8c+udCXdT_mzLY%|#d4a)t;-|5LlDnDADHXK$gp@H_%y{VP_4~i)VC*<7~ubFpHmt^8% zvfTu?V1BoFboemHG9T|07QaS?omvubzG=k1Xf5I8K{TNKXtfcPHy6f=0>4b7&Egr0 z^ox~>P+%}!eD0jolTN+ER!cqU9F-Zmgr-PAkeLOgMcmqt4ylA(9B6~@p>YCULfj?8 ziQSmTK~bpfL-VjaoiD5zF;fT`35EnVC#g0PzoraU7K^y{_0%K|7b!#6`X_95wI8@!Ev{myg?vHdN_GP=Wad=LkNQ8JHj&HA<0jh|IvBjh;Rr3U_4 zF50bWd}(+bhchPeSaJ0`G^_sU-{JOK9N-8pmbpN_0-&(e@UsEPmfSLCIoH_2-YxY} z^Gf)ezQqTd^v9{I=|fLvv7DlOi0{h;Bup{Wf9i^y+y=~V^Cz^v)pRiol@KDD%^fyG z51CahbhmR%?-kxwy&rQ3Yc^sBZzlKUY43si)9%=Lf!N;yd{l)0MMD1le(VDGB69m@ zm~63cclmAfGT=k~$9)3u%r0fRvDSDd)Q`{HpYh9-;}ty*qh;2- z!2B*RI<5u35I0-hG#;)0KBD}&cAe{mpiP2KiW@8D?-Uxm^pFCAx_jVUH74^i3_O|> zR~Eq$mP1_KptF%4Qk-W8a|oFP->2O)X-lb|v!r}?*c-0Cv|sb)vmUJef2MOd92)Iy zgRC41X9)T0cGCW~3_p9R%CR6gEDo{L&Q_4Fr0K*P*tz7+;87j(4zNzRj+>Wfdfuhn zP22L?snXj;$^G}~P~FGR5%R#8tf2mwu}8AtnFS11Z zR#Zd6cUP0{z}akS`l$jTa4gcFm< zQ}`D1yw`bTh;luG1t&Nja4O8GE#_*KZ({4^=J|)=iqAW;Q)v+wyRI8TqkLstA33HO zT8?|hJ%4o~D=$+I+RlW~798DXsOV@aGhW`0kku3`$Uh@nb;q##Ck99u*(0>+OO@{_ zM>LR+swvx)>;FB*=>Ano=kjWrA%vRWEPHIRL49hZy^X2W%~0j=L*^LX%C0{y-NG<+ zP!NHWl_@f-qxfXS{_#yFiENvAforV6sJe3*Q^-34tSn3)*n2#ukADyOCE61#S-UC; zWKLT1Rt!3Y#G31Qq_(8B|hu~NZjV5J7t=g;w_U?bIt>-$YRg`(O;eI1mxu&l?a4lF=x z!F*C$7XpK%m$rd0(d7Pr<)6jArY+Sjrz-9YqdgrT3H!@GQtG$3{AyKb$k!$1Vjot7 zo%QK-?c8m45>t#|DohxtkBB4p<4DV>HzXx45ib71F;%`YsE=Hu&*x)~%z0(2tkoGu zh9Tu%z{gB2Z+nA_4CWy;Nbm1|nb5h6!>@l46m3LnSMMH&Tq{x*Er|a}?cm_Zvfi$p z@)f#7W3TcJ5O>Imf2(KLv=7GeBdp?fdP|1zC~YRPvxiNoxPfiam5>R0D=jHrk!dp7 zFDvq$#4Rl6bg7M#-ZIx}c86emN*x6Y0-X7$=rweiAAQ@K)j(Ji7ZZ{AnA5H?Nv(ra z(w8RBcIdSLOJe!H7uLE=M;QZ`t>UBrl+c9=D!O(k_BNnrp!!L*mE^v$^c5d<1ZmAEp zBs;zdV2TC?6k1wZ`YlaK1&|rT}~l^3aa9`u88Xrk4Yy zCGtvtG=(uJOCWXUnf!SDu+lWHmY75zoV?M+_+vjru|8SO{V_=x7a3PnKM#g@c8_U} zv>%2l`gPDN_D{qZNet{-Qhfvpo4lkDc+hm=YH1Pt^1~wlHRmu+(7slJ2_LG)hKr2> z=6M#H5+1GRgQ(DL@Q4}(QCUXDoeUy_6)9MDELEYMB!YvU9!u9xjqC%Dfq-33YKRR_ z*A^V#_dp`9T^C7vVh6(hDUo)+?reK$zWS7C9RYKzCTl7Rx(6PBaZw$cpYba(6N1+= zm7_?5?CR@?ErH$4zbrR?_P(UgvOHChKyXPD7+}BC<5)R+;(-9z;;m>|agFykdQ;Y| z1}=i{V@^1Zf=h-ABElO>m8$%L=T!~>83@4+C`i&1P0Lz}-v$d2g#E4~FD@?Tyc~T( z(w2mpb#--{0i{OFCm`tJU95)G>wQnov?$!`mdurrB-F=Y6lP^Pko0B`)=nzKOr1Ril53~rEO8fFGW}J{ZR-Ys!;;FKBizh* z3h@p;#)(0m-Et)MZ$nwsHp+UJaO|;3(>8{n`p0&Q=TSn-YF&8m#(I#GzVH>nWI0~v zSE|%2p3u@;n3v$=@SMUAi{OrNJU+gtN78)9R?g8}J-qpsFoMw+1U*!y>oosutg>q< z7x0iUnzG`79@_VNn6|@Jq)d(-GwQz;lHV^&YvrrqwVczd$^100KtATTIkDJ%@z{&r ze-#4cy#C|$0&%BngU?|l3JPce!hug2vIYMkF0yf2+t1qyfL@KK#*1$4?H=3EmnfY` zA6#LCpgkAmM-M!O-@Y7fE71#D1hRY4XRHqV^wOijxyHuuAs+gZu`u{EyMnr9#6!3C zP+iLD6>J%l8o|PPNJ%r_giF)1K584otOOOKGcGoM9qqN>({$mh=;948g{Ca}Is+0a zPjT_uj;f%egQ^};e*A$5vwenjoyG2Y#guQMpZ?S)Sj-?~a3C&io)3f2k5u%I7U$dQN)pib9b2+mRRXsR}RDdx6@O;t@ z2Vkh32?^*1HBjnUE1arpevbT6JIh3p$*E5$-3@fOO_DnWMyY>~4Ci;yA~3m8p3>9T z&o3$po0ypRen^#T2sWFX!{g+lDd2+>M_m(=l{GqOo*6aD56=H7Ipx2}Fp|k#vL;1k zsK_DBJC^0Ny`TmwdLp#TN#f?KS7jDrm&(wJa z6T)UixvAkKY})BqQga<;1uz~xvA;qP&NCxI9)x6mPJFoH3Dumdbl44MMM1Q`Aa2x< zwVNJ4BFJhg`5{QZqTF0*5y=JZ8;b*sB%s-kMB%{0Yh08Rz&oTUI|>x6#(TwoKv+(* zgU?~U#ex`$2T1c;MX)+%p%+D_Ok@LuxL-bK_W)a?S*JYTFR(ld88y^A)Py~K87#8T5*A%m+2Si zD9LnfU|Us0jg?H{TfrMkq#9A9LX0G~^U&0}h`31=DV9a0$MDpLzU^9HOa!pUU2_BH z8^A8mnSvD{<67G62^hF22;k=>29Q-P8sG`c*DIrrhK(+Bx3he;U;uUq_%#V|DniJ& zS6Fu0PdsR3JI>yJu%Sw)``Pq6Z0yL~=H-?43}E*HL=nm15$v%Qma0MM+TDUT*y7U3 zfzF%?oUUmA`3+G9JBPqFu_$Spx9}q-2qiQ2^;jZ{PrN6zA5H-&otKY~g7jc`=(EAiI985Qp&Fh1Ivj?y-6T+LGl z6V>QQ!OZM@rbw#NgPuw2&`ey)j>hlF2R>C%N+wYTK+rJqG;|YxNeCOH+DpCOZtSOl z*eRNL6saiRQs=)$+Cnx+v2R11c14ohZ;9TFyJouGSbQ5(8}Vt}uDwVN*K zMwcIT>>fN@_@*UMDiG2g`wd2`EIdA+Igdvi-;Jag8{vkgWnWV35ZU={%@P_k6hG3O z$uldNsE|v00?DLg0|DocERL}|4mx5f9CYZjq09K6xG{%k4CzL!HWP_!M1JS2#^h{f zEDx(DAs#^J-UN0uDAW3#ACs;_?9ClV>#xy@p#tFy{q^1+b;>a|?)j(*RzyrE<<2U9J=R&4(k+LQrX(KG|&l;qJn}{CvIXPM> z8TnBdUW6;zHhLinDlRo~pn^D%=Dl|$2{-Y!`hzm}*%Ylu1$euYMZ+CGq7O1fej1r;MJ6*heF51YXk6|`M~Ki?mx ztdzO@Cv=1W!ZVA2JC4_b0v^YOA2k_C09$GbLpp(~kuGB{(TF&b*jX$YV?0X7Wr?A; zDWE?qvv^TM#&ek==aqc;LluoL1;f|b66)EQ=`2)g{zJBgcN$-NFv(6&0F)aC^*)C` zyN94L9iFZ{IOTPW!tB(m}g!7@g$u@1x|^FNU3*j>e0Qbm36_VncB zs%RKXIJJ5em52wth`9Uff2t@Yvf`JNhlZVLcZ`rk^ zRj~(7WKuuwXGODq?z0V|M^~%9jYNWF*o-^QcWk=2mqM=js;Decv3>4mS!aMUa3lxu zkWRo#pOD6;uN}kiVe1$&SvQ_i-ayrM6^Mm2A{3K^cyjxFCeE^lo)c*P>Ztx5*h%Ig z&wW$&K#I}*H=7!2xNcl(AopW?;s?T)F45$Cu=;Gg?e(^NG+H|Q*U}%<{PlGelJCbp zE^(;asfpfa^|YX|p{_v&ShdP&;$!>1BexG* zlT0R6WL14(tbk?wtzg2o=GV^=?~jLBwU>8R)(M|-R&fa9WCetU3-wsJ0Ksr{bX4=J znA2l5K&MN72e7JzMGRhAW?p(2?1b^7rpv6WZ@_(tIz(Le>ok4sPS}oG z*0GGN3`Qu_;KzXSrdrN2fjzz`nF`w##;9>R%od zOv=kG8lj+5hukIdWI5__Z}>U@th3moH5-RQvOGfyU5WyL{DJhnWvxCyh^yoG;CT8> zXvEDy2<~IT&4sbyU&AjG!EZETbo)5zzrTlq)=l3Zav0Bp4205W; zskNIozjg8M2R_|vV@C5BC3m=$b}E!cy(Web#DzmAr_t%)r2!+Y`OUQUubR-ZBY9|i zSt~YuB0RysD-;avTaCG_CRiNwA_W;IvnJ~8E4BJ>`mT@T9xwxBT{c>8=Il$dLiq6I zG|7l-$SO<_T;}P9f&|!^k&%<%NnL9E&`pHnJPZ#vLyinFlXa8$!|1@&B0kTU!j_Zw zL-~&%rMBidnRfIJDVHF7LVDg>Sh4OKduGuJN$`nqKvEWp?d4lkM$V}f1U1H$A_WP4 zHOXMLP}3r>Yp_6eUQvF+CaC?W#^PHj{^gf-plL{c?FZL)M`2*)Lgu90(qja0wv3;B z*Q+!m7CaJatz&q9Oiu20HOb^nImWd-*R$Ql1&TwM_J<1#R$Mw=CQk6I>yTmYZ7ks9 zdP3$vcK;n)1t;(P(DoBoTlNWX^5VvX>glb}WyfALdz%npMjDy3@-d;nJ&d!7R+ zPVPG?B=s-id{sv&`Ncy_EkR`@@Rk(Hb{1yI@6W?HAp|m0Ni(F$GlOLYR7==KK$K#4 zdDX+gGcE-UfkHSTsSLAuO4R7#!P{t=rOkY=6e*+<&rzbI^bFgs-KAtakxEIq+?j%f z7VWL!Ht3?uXd`g%VPWuf6KhVP%=fM`8r02+QYgU23Vj<&9-D<)42@LcQ$ikj)@*Hy zO!JGaScFFBFluQTBN+26Db_6MM_5k%5nOuLGdb~02`KhJ2`O)lV-#vX)KMBV;fC1G zjMDyF*+!+`oZvwFQ9PWYtoHLRoTuV(@W^fJ&i7!T4lvo>fVn2Wo_=)ar#b9%V}gZJ zvNTN+*i`pz?LKZTueFuTcz)1qzFNme%L|6Da?DnVNT@2K@LT3vInT(v_uxVOi1U`=L*i z(Vp3fhLV~DS@J$BH4CC#9wF>FMkb0p2vu_thE+oUcB{w2X#DJ$m_wL0XPEOGnqm<> zjrzj{ww#zS&SjWb5Z#%g3`4D@B-ki7C1fgq_XKCaow>ayqufATqk~2%G6y@nvH;b& zc9jsmnt!{c;v{^@=ntd+x4+Fsye~85Uf-x&$1Ada+b2mMhAcE9+0G6d{4PheKB?5Y zDAR_O#mJpQ$_O%V@lSNj4^>LbFf>7OEzEZesLfwx_gKkm7wYa*zyxB&Q?$Of%Sk3W zcaQtL?fk41AAMxsUwpl$D zqXCaUDBpj|dk){$qzicGtC{)vWr6%|x=O~sb-id8vZLLX3o1f>)@d~lI6&%#Nrx9r z|7xJwv&S3EC*^_Tfu?m>_6E7+4fS9XIvfHV0!mdOEh?96+q;<)32bz_h0m|$wX{+! z>>)$8iX-LvZ8)&(+z7fy+J!-6`k)7fp;Iql@DVQwd37V3oyVHb`_)#FqJ2!xSi3~Y znNC?E-MFb9Rr!h7o&q_K3>G&}(WI7=&??p*rjy9)+YBXzcH)G+3|;PYq3PDEgPkTi}U0HJD@ME9o=j=|+Vp*Mi z#qFHV$r-HDO5M8E%_3p5!O+drr^S_H>0ToFu@I;}@*HpJM zCXsvW!op;Zihw? za#c%bq36lM@<~s4d~+lfp=2oN*&kcX2$$(zZDY+8`keikz!BiiBbUI49KjljJs+>c zkWy4yle1PHR(aR;$_*TV`b(WRADM@g`WI9rbd}M+ ztn89WTffWxb8)M(JC-A%>rJIwZeqaXBtnGzy4Q$Y9mV;aqgqb!A^SrMF`i}G?qepf0mHV1`AQ zOAp1spkj&%mtUg1XHT=+%zxiXsjkEb{d+Bt_Xaz6Vp7o;~rT43l8X z^*D5ATR6BXA}U#ifR}6P^AXyUBdQE{b>U}dS(q#);-vP4yct1>4l$cSbcI}hKehsm z-UP82|sWYL564|~jSOtaA0dR3N=!Kj1ET8LUuNAcCq!-B-n91uRifdaE`ZA^V z@3cll#wU!aLpW^es65B+d5%1^9(1AxP4H4JO)XLO-?6RHg|g9+e~`(G6Hjz7>c&a7 z4388|#BmIK6Gua`XK8UklHg*DAdNOhbIKc#ma=S}fbLkjV;VrBe`G`&i7{hyb8L3GqltI<$FoDv=|#nlu0be^vV+1=S{$-Pkv*JY)cs7`muY0&*;&xXfgy5F zvVPz3N_xpHO15iSM;o+T_1Xl5lO$bf137RJQ8GX5=BN6+cG9 z24nQPBI17gq0e6Q1ovsOncpV%hklOA_k|j(q3Wk202KXhXKQOVTdw~u3t}fN=3is? zw#afP7M1torak3-mF~jAWDG5Q!yX>mL6eDi#TT}59s(%@-JnXALPxBjakV1VUaU|e zh)C?#U(0WfYAu-~!6ZFe!d%uUWhoLo=-)iBteMawJK%{#|4B+nSfqWS{YWK3*^`8u zPoign_!{21I6@C1$(+&|`DJ~ceOmoyRu^IO?y~m0oE`q1+S-YY~H03+D4&Yq^+pi48rU4S_L`@w^*pXPo^a{k8US7 zRGP-zQG^iUwofR@om8pJd}RLD&LS;(>8p7CquXD>^WXHw0{^s#njI03MML+nCkeDzBujoF;xNm+EoFGWRHDPLCW|nRF3nrwQ;T#9 zXqUDZ_AUO&CKXsi#O>h!wk#RhWpp|?IB5Pj$4G0sZn4CxYwS6rpP)Fx zQlj_<4d!KF*{`5t~xdxFAoj3nANG#k&|)^&>R1gaIg=QFCeZK zv}YMoV9;dE5P`#wOZEwsmLr;Cm>I9O5!19Un{V)^O0_Eb^>1*9!-L|r^hUy-Z!k2r zIId)1>z$}KLrOjrYB4`Yh80`-A4uC492%2_3R>FQ6Z7*vI&*lE)edt(j;eI-D%^<# zGM#t-x}-!?t3*G!ze!m6gz<8>_Gu_4!e1R94uPZ23_gkF6?)BIBCg1bCTB z1$ye6#gbVabVwb@62(+q66_S>8Jy?`7JD`OlRY2c%#lN5>}AFW^80?MVV9dUM9TN) z)wZTbPZEm+1V8J0n~GUo5VsU-sFQ+?IHZnq=CgIB9v(Lu`jp)bBG%K&l1Z))gY@(9 z-PdpG>l(bra|g#4R)+F-b#&Ns`fl5h^lI(jyy8AAb`_o&I63{#GC99rlv4E0_WkhiPf>3HRdx4#4=W)ENOyOMfN+rpi3?}ErjQV8}`8ulv87iC5Ld+OFMIDKlqvM-Ti!$%IlFfS7? zAdRS0!w=vlQ;*T-Xf8EQ7Jb0!t$IT6r*%})92ryo5f%(7x)45DM5 zAqjNd?S zsO@+bdS+#mtb`ng^RU6lV`qFq5C8bMl$smA2NtCi?QE3;m2Qg{JTt2T;PKmHvi zh17M0aW5ryEK!|hud|Ncd;JCg(Qt zcTfLHM@5@F)-5VaXt0El4wX)tB6C1=?BPc}&vu3cITTr@ zY~qrnPF}+s;g_RBDEzecl?k}G=cFBhVu)TobLbn z&AEB zj?>KnSkW%YPU!sKzp^SS6MJYXry^%N1+nR9{)nb-6W+JyJ0G(|C}x~?_V@FOi$jgL zLiZX6)A{27PQ>?K;)Fat9?IRU`#L{fhFbl)FdkJy_Im$KbnlwDB#e&!BwFFGv%h1C z*(xeBUQ|W)I(ia@fQd}!nU3m+lq+U|0W~>F1nT%%-!2YYXFIPUUq3tk&=1<2xHAGv zLByC--*^q^D8Y;RRwRPbujCrC_F)9)R?>e^*Q2{7otkXb(DkP(-^MUA2ZbrB($Y#R zD53w%l4TzKBEf@Q%>GLgx!96Wn6ziCqutVeivCLxssUbPz-Zsv_2*q&{cv9rhQ+Gj z6sNd3pL&u3$m|?3c3m}Sn+@&o-4XJTq6i(fR%c6rot+>#?Cl*3WdYz4r%>2nbRr}~ zll)1$J0@|R+~SDZh;(1jF<>+NU(EKt!EOBeo}JdFX=J+KtNnH-U9f$NN=itTjTx4e zG4Lh%P*7IMds&)03mbdL{;-M8B~e&Yev>n0r0<B|l(%dw}J zS(oGtgiV)W4;7+@2yLHKTPyIRa}p}fDS1(1d%Vx~l`%29{aL7|8k665KS?wyeV*r` z1fjWs>*ur4Dr|#aU!oz%^D0((ZP;sx(}r`<7dZN59$Hd`m8|9=An;%QMvC_xd;jSd z{?1?KM&BJ|_HUw!i6znlih1vO*u=Rw=R30%e_-UAhZr$=SK)OIteD2trv}pTRLLeU zJ>o|a((V)^BH*HZf>Oj;u(E_g8;o`kWOH!T-(&@PXK`cffyX6xLjfrZgGRa5P?Jqd z=FUW6wfPjQdbyswnHdXwYVS`6ESFm|K)3XDzG1Uv5)eTluO=Yi00m#9gtj)Bv9U4o z*~13v{nyu7kuQ4Qj0lr&1QP&7O}$LVO#x5h%*3_T(za+Qzo8)ooRG#tBF~QpVm8R% zNJo-`^k~U{{}q>&{X45GTPYhbIo6mFtcUP1Kkk$827=?W`*LJ<$b~Cf~f9L1LY!%!B~*l870$TWrHg|DJi#zJ@Y7bI1fjbkj`lJ zk|89Z({ut(9$liP2TvGO}HiC{Qs6?T|k)}eTm2I1}$!J>F|oa-l4 zKsqz-NVj46JG(pUt~qf#DvV>}sh@|!81C)%BK^!n8sHOtg;&ewyf64nM&QNZ&E$J> zTBDRnSX#$^ic0a%GHURTJ4{U$>Gc+>GDJN_4!UxE1h5@-3kwQ@Qd2*t+p;F)R9D9Z z1-*F2`ua6+>9mwlS*H}Ba~E*(;l=}rIN{w2ZY3U>(k?DnWSwlHWJX*hwN~>|US7g+ zOfZpytsuiCtfX0SR8lgs6QL-z|I}N`!b|h=0%BuhJIt2G#_asE9v`lBJF1&-@8@l< z#*);J1L@aqfd-%}t6VERIIi@~d!FeF^LB}X&-5#V2r0h4*Z+|+6iEDylMxac>WV{K zb!9305X(!YMB)Ta`@hsUu7n!5pUk?4A1u0)rTu|ANK> zVV{DqGbMT6{2FJb*;!+LL8HGy`Zhi~7#A~D8ef!H@9Wjok0ezTk^1-|_2i1dm~L9a zs5Kd1Gm>Ol`RNk`9BIhp_^0vS&cV{~>a7(6z%hq={HYm2%YH0Ok`f0)EP7P&k^c>r z=GOf5Pu=B5rP1Q^V5C?SW=j{2vl6^A&|*BG&~?p}rYFx4O`z4Ey;yCU$+&D$#1C{8 zQV^mnY;C3NwFA^>tuKZyPnktlP7WSU!H1$_jn|!XBD?M<>ch|a!cUkj*K6VALaxWn z<1qiX^jABmPOL1c&8L528RXD%m0-c#84H~ZwOelcvz7kiy(Ii@h; zWb?-i)v43y8O-y@cU}ZC1AzvYMFP(nyMY(M3L>mbh$_s=h|^8yABgit%#|IDIyS=> zO}p=R9k=Tkab|{CK#tL^|LM%+?^(L;Fx(7*B(q9LL;BFY)&#$8ULe$Amw&-CLTiGt z`e+5`qpsn|qlB152tGN?5$C(qY^?=V(oda^VK0=1FBe=oBcQ`Txa&^Mfli|*PVYP} zn?8hU-mZRi_jR)HD5(H>azXz_e_V=?8<#jLxNaY9L`_YND+ME*@D1syr1wG1%=JLq zz1-tt=$A!7=f2oSps3zGJ|UNj2P)k#L)&t0ibJ z!A9EfL2n(;&k27BrbI-SQZ^K$$; z_qs%?3pSC}pMyrF#(SJWzPY)HD%b0zlE+0t&qBM3UHoVb_S5#>K{p2U!%M0m)!!AU z=xOPclDmOw;!?8sIA1H!3yFB}q2UR+AE@-lP+3IgEOFI%W}COL=Tt=#&Fo8m`hQSM zpl@_f=FW|jkdAWLIfXX=tq4z1vEcVC%_y#!g6v!8(GwcpWj+8Y2I+Zig4`G+0lC_A zd~qHor~T!#ZM#zIc|TUvwbsAv5?1hpz#)Re+_Q~NuT=^a@yMOkTVM z8YDde5d{-Fs<-&(Phq?4!eTx_5-%^W{iT*PXgFcUm@F~NsrN01o?suA{#V)<3?wq@ zYufyHYGe{=>~a6}s=ZhEzSJjy!NulZ$Ga~Hgl42(b#p>7wJS&O$y;-9RD_Yx9*Q9) zB<v9JXb+HT1n-KHapGXPj{l8gaolCuqY+gkaQq1X^lKn3^(y{b{+_ zm>@~pt^yP8j)RHxgA(`Qi&{h4G=VY&@uj?4tF)msUcB&b%_^h*5YGgaluiHF!$FPe zAToPg9U6Cs5#%aZUdLs5-%Y)~S>{+8-m=z`GM>Cw;hFpfH8A(>ihcb|URsR+9|>pT zy{wpe>ULugDVkvjc}nSb->5RPAEZXQA6|rOLc+`g`tntL3sSd!7o?wF*$i8JZ0Ra6H8+x^pPJ(ImIh7iR9+)iTle>; zgo`=QaD@=hEhsJ#o96FS9*d&#@-3paYh`l0t3!eQeVk*CL|miw7-6tg2a zl)u5>B*mtFy_cFJ_?r40@eli3Jj;0rB`3(x`|u#edp7=ToUy8}i3&a?Sc3QxjU)hK z8+0?gcJi!?qBrntA`(`QWZ=FwM;#c69^#kTSqWtucM7d%DU~7CHIeye=_%-s6Zyqd zrHd!wF~T25xk3%GTVXXwE(A&^R+CO3EwS>N)V%PDo#@9Rm)$PN$)`wZH4_7sY z&@bfM8qD9N=W3g9ph|oKKNM3bzLum26bDU9GRYAQGK|g1FK&DqpJO|bNnSso_?V^K zDOY~*x&NO3el0Lb3t~gqM22Mt5=#xI@>`7Gl7~#-3hZh}pu}+1e4CG`{=+V~oG{8~ za6DgbXK#<}&E|wsZ*t1!&4eT8JDa7C@6wE?O4LjulV88OB5FIog{LZ~2$taDS&D&#% zd`-StuGwqVWwEb>iAi14hMKfw$>&@lI7RA6i-+A)x$Ql%{W!0*>zxTpQCpF+w`HIV z8~J@^O8Bd9XM{tJ_*CPQMyDoFl%t3F1AbylN7b!j38~CGGjoJbj7@d^>aQUeUg}9t znc%anPZ>~W?{?CaU4JXk=y7wI^vIEvZnE;*HhP9wv)*6cU8os)e#l$-`zN*N^{Nlq-RJf*&$EWBe@KtPj>$ zy)QQBZzctkxN3wV$}9rd5am_+>-~yI@@}{&yWSAc7lrw$zS4m}n%}2Pp}s@nn26%c z-ENE|ET^^9I=>;beivvCMGc1-P)q{#v?MsBZ-uEzF#{v9PZ<{-ucI9YZ6kKWlBkZu zmxf~hk^Q5n|ItkV^o4Frz@kWwEMdw)=W#WkIO0y6nz(DG#HW`rDiZa?*CkMy7fe+W zoGXeZce4|3%x0^z4m?P~){9XUkY3Nu)lB>V(-#GrC=di~`>T*8C1{pvO?Xt8rj9RP z&wvsJV8a~)+Ahz~+PuxU9rg;N&?XE z^hQ!h(&DJ9<>%#XIJH;A{Ag*(01OX4i9KT5g3kM&htv5@jUS^3Pw8TS)SAri@b4wr z7`Jws>$%Gv|9DE*g;(CQ`3ugP&k}=tA_ZkH#8_5yECkT}O3SH*iR5SA;)}hD>zMSH zhw*k6p>5;^Ia)#{B(KHtbY&Qbk-i2TPl)Xm$~a~Bu!jC&GZQBsZ-+|ADhB#bN=V*A zNO=7I75FEru#5_!WCw@DGC)z~Z>f<<5hg}fvq4d#ECCE1xtqfsBk%L`H}p+-s%r6Z z!~YcXK>r7WZGnd!w#Yq@iZXKGmtA}7?tWKX#>O-@Hw12cOAZnf*6PP-cbFXv=HgKn4l(*ip*3{GtW{H9p%u)+N zT*R$MDxW^dvJrwmqOe?QPRW&yiXAe6UF&FQ5W(lJKb8Sc7G$^F0Mbf^nBiVrT$ERH zTI*QPJnAdjx7%dheVavKX#{G?h2;|dV+xWN$f|^7v^y$C~Az{Dl4O2)$37? zBr)t!b$Q6L)Rg1G(mUF5#`)z?>nq@VzJB2W7X&aZ@$zL_Q0Iz z#)bEHd>2t7N5`kz6Dd4w1C2)7f1n-P4%o5EBE_*AT6^Cmn976U&VkIw+13bE?5vfQ)q>NEuIG`*GTG}dQ6xS48;3_nrl5&3 z6Mg}NmzOTz2q-;tjng{_rVTogk&&1niE=CyRZ_wlfbHnwQtf$j>acq!qOtKNxB+yK zVyO`#PD$^?%3SU~6O0_saJCf^5DQ|J9088?^u3tA+csy@OPZNU$n-q{R-!r$f>}tzXaeXr7OmCNV|%JS${z#8wo*T z;ou2d+r%!xERoVQ>BprFlP5)w-tLgfL8{q8fJpQ@=m>E~{xdl~=VV5^_{3|_l%`4l zQ6P=MQtOwCvtbHj(-p6hmY%G%25xN!a7E!l*yC+M3aI^F0~XlR0lw zloLwojx6V4-%0c5!*6@5vI!x(F?K>7LB1UHl&p=k6~cq!phjH$C9hxi z{pEkZ3Uc%v2H}a*NO9(@A%S%FXBwiNIX4c{AFX@s;4s<&)T}D==L7OCcv$b>_AuYJ z8AN8y_n#>rf{x}!qH=558KWqR9q?71tv$A^!>4osUn+^KO-H0q#egkRP*9v-U8$(6 zOF2355D*X;QmV?)<3f0ND#8A$PK+nT7`eK6@~%rVt)=+)RT?d{izwD{xO?)w+V3;O zKw^E?ZPyL*sG@8?gfhIM)ZLEuDY`D6q&%DV1t=ZHh=DA|Mc$aj+eK(AP1j+OS%(te zP8YEz-doxOF+>~UPhVsN4zBXwW_RY zu^`LC7AK$LOhW@- zjhFca1^<$L7J6uM@*TA?tNoJNyyX1KQAPQa6l+>12K1O9qiB$G&Zdx_wCBRJgC-nY z;KC{^=V~?Lz4XhHrgk0Jo|KP3XQ8Mo(~;{LL*Nm8T>t3Um>8f0z+(e*adNuYYitgZ z+iz_Zfg2sA=dqY|+ry=jPf%fdAk=!r3DiQhw2%urM*vEJb>q%o2jgpzJ-aUi0xpE>N0{({468!fL}8pN`_@u?{&m=$ni z^Z59*1GrN;-Vxl zbYwCFW~|9%F(04QwWDAH04KN0Exw5Rozur+61~s3%#Lm~b#)H=vu}aB09;-8=M5;A zaJy<+9`d?c?7dsMYE^P)?d%DZ298J}`qLki>ixy0t9a-$Iu-_D`wdiJe{8yqj+2A> z^R*x7ahW8SEX>VAq;d;&<-B*{`z(a}S?+g`*}FVk8~_j>oL*^eeBx{S$~U-VxJbUI z5Ie}{N=sZ34U-ngd>dQt}F;*jcEl1s6CvwNm-{ZgWaCOzN#cA^-5y@#P zRRiOh6xCkscwC1Ctr{!7!c#-VN6yQk_6ntDmRAo9FTvdIcrD8*q@*;eR#eVzuo^+C z&Ys+#%5avf?By(QRkl~iPg)+{yk(pQ`donpCy8^yAOaaP zAmG{dQR@vm-)vqo*1oH8IM&1peZ=T5r6~G^>bw2{0{!fPAb|{3vJ)nnKz+eyUP8EC z^MNG&UU}u_hebPMb}?G!(fWtcz~G#{ugX7|&8Z(EB(HJRkfE{|bi@OyBv@~Yg%lp* zWtV<^CbZEOrgFf4XF1~pM;*ZVdFp0ed_H@4ygOn_khPmq(>VEQ<7F}FG@6>0=Js^A z3N4SnOGR34wkcFxcYQHK9YN|HsqZtGLpfSjwL{uEl0*6&JhQRf$R-Tig-*Kg*giRm_wOe+4;ucZ%xC@+jaGDX@ASB=5bPOsP^wkk^AJA? z`S~M*G2jPCEdYHAoG}?18k(&YW{kO7g?|r#F?bSU`YI~;O_`2R+-sr{&&9S)#Ar8% zcja^%dV0@ODJ=)ZKko|2qg)xL{tM`#Sb=qAf=P=$3fpU3a9Q@!@w%Au{KuU|Qq8jk z6@IpM!iP@8zA;;A$Q0-Ck+aOk=neUC!<*S=B(I*E&cAY+=*5g3CyGMZ7To&w5 zmLCpXdJm#WRkH4kiWyiKI9ji1xlIOtG&bJ;D#(kE1?v&3P^bk|DXl52D8d(UX7yr1 z^R+wM+te{KD~;APrHk|oZ ztFl6Yjp*v?26P&jo123~B5N~J>ru7E4134wvD*p4(LzI~AcY64W_0wuyu7@@hBBr9!+BX*8QvGdT&wPl87}fK=rpb?z9=Ex zUp(*TmnnJo#AW+YM2??>wB_}oOPfbyly3coNP=s2e5|8@ya(uFm64HL@Bs=%283dA zYU-`i?xaJ*1wUO@Z5o&HpQ4|esxem}E^$vcHD|8P5;A^Ij)gUg;sT zA-}Igk6Vab#~5fk+}{3tb+`yF*)-M)WWm83t4)a-j>;ePkFQcZTUuO{hmgL}eCxkR zFkcH7c>WEh;AO%_wjvAV)11{~M{n-!X=A7}6jb!|M6kW68nQB(oUN=5qSMN;{n{S) z+89$lp88YWuQZd9bACgQT7at?)h0vmtuApp1n?_xs?qs!Nx0vo(3`wyW1bOLuS^z4 zCy7vwY~S~@Fik+vdB)({#!|Bzp2+N?UAnkZ-&ad6x0b8stjy(wp!GtKxKfsFy{su8 z`}_A#CzhyCc4Zo%wscqPQKG{z?^C?XgZW;b8J*6*H5Lu$<8m<0p|gg+;5{?B0^>Q* z<>_&+TVVic0t#%H!#6iJrc|Us74?0?vCoJLP`Qcmad8N#F-RM)*EVFJ-9(nmRhveI zGQ?%ACfIC~{DBdPkAfWmhhFy&api#Kc*g-n`*=GyNk*lP!NWln9abKmXJY7P+CYir*na_Eb& z<1A%!)+^}DT)Yi!#v;1mn&%EBi(sspv!p>ydCCB7X+X>iWbHPaD9E_n%8!Q=Q^URK zpZ6O~qAAB){1`g*8lOGhe)@t6VH8Gw5c2UB_Wet9>>#~%4S z-TiN;`8;m<^fdqY8gFYCO|~+i|Hw6v#IcpAZM{0v_Q(THMs5TW>8*gYJRW$sbubTm zA(UZ9cgQ(~$}I5QKF9$WHnJ>-#Lhsn`hJl`lq%c<3-GjdgZN3^{8&r*)!d6Hj_SNW zE2gDIQmMI*Br06q0X)32EKq<9GCdCY-&rs4Ws|zob#+S|sBG0scV`2 z`siq3W=0buqX?2Xy1EpA8{z#k#bUS81(IZPJ@QTJ6^NEAFtctIt5~lL>p9`5e5Al`%%aY&&maqiH@^zo-un)-WYxbl&kT<*`UuN`5j zoh*FWl4D_KfVE<>!e4 zc~H&=pKj~ModT5-Z7|mk8+|w+syX|KCh{7d8CPU07JcrCR6}FXXVOzrdTa35y5$x~ zZRF!4nz>bJyDAQX10$q@Io}8zg8(X`34l)#6M!<^Qz`{a+7+p<8i z5ghqa36YO50dY54xys|pT09#Y@OsMAYOu4&K`g@_5jq>JU}}sY4BN=0-k68-S}*j0 zaf|8eQ>heuT)kU<5&@q{#)=`c`f6%5E9IG1^zTHoc0EUR{eRGwgW@8B*XsE1%Euys z$8h_io#-URy9qZ#{hL1;v%kzH0z9Lj_At)8_yv!n7FAVMMScAdkW322_Ja?@X>VFd zLxYz#XUo1poTLiaKCRVnr8d``tAFe1;aql-!9Yh^aF52G5~JO==%uQEjp6{ zfJmD2pms;!e=Dp5nE2Lx!$!n!XYU77B?ER-JmZvixL?G;>VZ*98FU7{8cgH08JrewXO8t~j`_$q_sa|q_;2_L5gm_%8n8Hta_kL8GJfR3 z?!RoscN_IwSHUe3=yZXADE7#+INHw4yB5~Mlk?r;H&RhRk@&`q>jB7?=e7jZTA}E} zPW`qgj2dii8H~dZ;NJ>@XrQgtS`s{tX zElE@e+#OhEa6pEJG75{t&BoGls_N4Wjtt?Y8NHFVxugmKF;I=ED_RbC{0(Lw3Ntod>H*r5f$^Zc0 zj{W13k`jl@(6fT_qdPC#U%Ve{5a-~TIXG?!GfQkDfx6ww(i^)B6*y{@v$YFv)=@S*&nyRZIWWp= z-|+r^OOz>TAmciAL@x6j?2wl zocYaSU*8wfy+c}Foh()X?wlX=X2SA5_P6}|D|E#Bvf8jJQ$x=!5Ts!^EvDH%PHY@D z9Z_C9|F(tLqsDU>BTczl)^tcZq8*8T*!J|;A?Go~Gh+*0D|aFs&Bq9EXz^PA1`UK0 zlf_1-=7$3tQNyv|9A;2*_J4{gV}?SU3_TECEwYy$R9nqkC)k!9?OL$~(}ps~wrngc z*1;RBH7!4|!;9^c%XZ*&?rR0;|8;UYz!9}0%!H6DepuJ`aPX_9rseR-=V4FZ^x$tz z;M25I25_J*5NqJ2R5^YYnCUo8sli_$^lm0-z~dj>pM%hA03J=p=i#DrS1?j4cXDP% zMPDEGE{y>wk)U1(tZ8}+hcRiY&7H!me@Siko6sAE%$Fr4RVG8E;6RMZ_6L0s`$TQ&t~%Cd+1xWO$H%|6O?H9?VtVM`L96y`I~PA1&p!%8ziBNb94O}E=&C&S~!)p zT>iDw(gx@N(CEOnx?jK2i74E2zrV#Q5(c|m==e9{{bgNSKA?Cy94<;U%WAO@gcZH~)vY%+=7yaek@S;vzefX@9%#B?~l2r#$X&EDzE1+vT}FKZhcuyF}?Tcr&}W>RbcEC8+% zmi*m`_59+(u9w2)c*P&f9z00YPO3tnX{K8c%;$FEx^)CDngPq|w$tyV)=A!A|FS{6 z5cjwd2m7K$Shrx04mzV71OCMv#xh?o)G;Ags~K_UGGU;{UP!u9?vr00FcY z;4H2j%;M&K2QY#CMpe{zI(mBE!;+%z=gdH@GcDDH6;3qYEgt=Ay*pg@0tA46@r+hH zWKfNNCZ(D&~=tBS%U}2cAv)KYj&={2I1ZE$C0px=;j3kn9!oC9_a9UGM zTTMg5lR9xjCjXNSTdtM{z%20Qc<5{puvoa6S8hvgiD1v<&4dI+g& zIj{=MJV&8){RRTn{{k#HOIn)gsHRq2TAEi?g$o2mVPS9`H>foP9Aa{MI&-w&N#NJ7 zUl`%DAXf%VDM|3CIS$KfTf+3>j_56y4ur{tQbXVC0_tIp^}q1yy7m$t{{GI-!?r(A z?d<=G6KpWIuz+bDWzKxl2azy3?c4uJN}G*)W$STS_Zwtf6z(tZhfY`V2bz`og^58> zfrssNP^q*I%J;w{$6VTPZ3S)dOp0eK`fdZD0P0e?ap#?MMZoqt1^6Xp1ZY0cFIl8e zdn^>FeO5@j@Xq(|-@%_w{ihK%TQ?leKq=}?K5_>4gn&&JT1A6mN-Ur2P7vy2M|>X7 zz#mf*nXJp;;Dx&i4KKPZ4}mrSZXn>eo~11hg5Q)Vt6xJCxoQ|WSqtY_yL+rCBM9$C z4ekVr1t`A#esl*vQV2Zk=)yvT)qLOxP(OM_AMFU=e1cea=>a>3!)Y}&P+%eS?@Dml zZY+HvO7xKrjGqZ;EI&$1;h^cb?dh%!uch>i(BETR-{XJ>{-)MV2k*e=u!-7aaIv%f z{k5HXsivJDi-_iB1JJSHbmreb6O+N@cHY*L?{p76N7LUAp!SvjKXfslx_8;Je3_wf(^x8oN=q%U3=L`W5>k0tl z&cVSZ5Wm*1!tw18!kDf&Z7Eq@BG5gTx3YsN*MddwX+RcgjZ4DbinY9!n`5@{u%_o%PX0;XjJhGkJlzfE&5b zb+FHGJ91F|)(cbsDW_R6oUNcQtd_*Cxy&vYM8IFWUzk509z8~a7X!L^9Xa9t+V1e>1Y$x1?mjeeWk;3&u0}B7#?Ks9uko z|60E=hK~DA{yrcaz_F9}uEIf=+nG3#QrC{6P($!@a0SAa&!Z{)U;5eiBFUcOD|J;U zehef~>gvkX)P9s|2No|4a%SMTU&?kqzTNX&nZq+|Am^aCUCx;@xsyP3R+wY&gu2u; zba^bz)@j4|D8e?_b3(%Lq4q>}daG~*hEB-#864DHaGtk1zq|ye!q_$O`*pkA0$rNd zDfWTnb}(NDM<`&HvqSa9k;7>l!uiT=E2BIqVfg)Clxu+2uYwS43NRwj$WD$sv0&%1 zj7U*Jr>IAsTY}&*h}goQY|se7Ai+~mJ2WJ8IcsPWz?kteMvHZg7Jz_>Z%@w{pCerJ zvTR;4y2?{Md&IK+8PCNXW6=<;M1MsF9N5PfjB+gcD)yxM~A}V$z`b_iv%S|qIf5;rthSkd`oi~It zuh9ZZ0L8b9$@%}j37!(FlgAv}6hh0c41XdVB9{MuMU=XrVNX>2p*&BcBSXW_z{dxu Lf@GQaXTSdk9a)P_ literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_63_0.png b/doc/LectureNotes/_build/jupyter_execute/chapteroptimization_63_0.png new file mode 100644 index 0000000000000000000000000000000000000000..b1441ecf45660ca6870991f6ba7d6442d68619ff GIT binary patch literal 27781 zcmX`S1yoy27cNYT6pFh;@#5~*LV>0bDDLj=?q0mOTPg73?(Po73GOa|w7A^E_y6~1 zP3D}HH5u8n=h-?D-{ob{-;=zDgM&i{ef^>Y2lvJYcz;Aj0&15JltsWp&_znaMcLlW z#of@!6b@|Y;$UO%Vq#tEMv?94hYX_YGV|77-kr^%dyLXBCgEvkvz(?M2UnmlilSFG>Ti12n-?BV4KF z1Pf532_$9Dj#>W3DqB~0#H`~aX~V7-B5(q(Es=KwZ})eMrIfGJeWM*%7tC7c;65b3 z+0NOZBqU3~q5HP|lgQxwz;n_Wsk>*uo3nWXmUEK>qW~cXzJ5MG8J9M`L3;fxB1uBg z(a_LRP{KAziHL|;aM61BIXE~p=!t^t4Gavb=7A2`&-| zzl{@UpBCtrzXFd6T2OETEqMy9B`n#m@^yqB(!N^cq3?k&Od(6`poDiGpoHHtAy`A~ z7BKm|E~Q5J7mbqFVbLnF)laujsft3e9+>@$193mCjAe8X-nRbnd;^tDm~$%3wFPEj z0KL~l!}NaxN@xuPcSo^%m!K1MZC-xaYdMl7+tJ(9gG(K2Fa_Fif_a*$5i-7iL`9^+ z?({?qF+RbmY zbu2;Guq-ZczKE<|%un@yLdDXph^uwUUlRGUPnIVgPKeE86+@17(44fLGXx87Op$B!qorw5 zG?%m*an&4dlGIkv0)18rQ1~*kgdMfC97Zd=Y%K>2QPf35g1veyEe9p5<|`7I@{A^hhGD&pasF3Wg^!DqU{X4VV>S|^S!>W6 z0x=n6Nsp&PB^U`BFzKNl(ExMRf(ET>sWVM%=$ZKv(K8`Mi}a)zb?|MFur-?@vs%N1 zWA|*6k}Udy=$~xp>;kMMGn!X>!xE%rBXLuWIJvHLek)8q3vWag?Br&CO^TLy(t^A| z$Tk0zs)#q{a0*$z{f;#ML8$QaW6lRfq0gl*1mGk%QNH7b>)GQ@bl~q|*5YE;l(i6L z)3FVa$fBQW+$M8qmULh(aH3+J$^5BAHmmtaiJ;RSS&LInRz^V{KAS%j^$((kbmfmK zwq6331mN@zQXf&1lTnYm)W&UOs)mk~rig$-w%U@l7%5yA&}vNl~h0rsc5V z7vo2XLYC306*Cl+Hc0I3X}6)vgtMFPV(n&{(QlPOEl>-KkKt6?Y7sJ>~2J= zat+0f^uY(<3MCIE8DMyi%QU_BL!gvNmVRN=#MA&=Ua=K8zZ0g%#y6`@=HL(`p8R+v zrG8lyoNqxP3A81&gvUt<^cBCqmRMfxJ(f`n+12jU3OH)&2u#Rl5irQtv3a#J*ofn7an0E>&)DzKZMPf4#L?jyl%TD-)a~9Ncci^DC zddsxEQ=?)930~aRger*=tSP%@Wbi(DWK(*{053woBf@H$4CcO z0>`t^jil673502K?Iijln23M24#?yE8e9>GWDQTH4R5H8TnuRm@sHY}jb!+%=(r_t zx$UTupKHG4D9YdHS2L=nM;iTe5~p~|9rNwy?nZ*9)xi3Yb{19TboNPH#z{`?EYn7g zAsxrqmS1dF?3l$%a(qDxAAnKR^qJp46uOTY4A3_deNl4?sWzjcfb(U3wUy|bnk5Qz z!UIzk{{H$A1Z=Gb8L12BH1ZHzDv1RolCv0|n}n*OMv>aSHhvYJRl6rFD*kc|ojxI>AH-p_t{k8SoI zn>ti;KMF?Zd8n3{EUlgPll8a$?SYjwJbELNj@e?uUpVx20SRO-tFSwzBn!?_A4k25 zLs><$DCcqf{qOyE=?3(2z(g|6z&wyli$?zGZHs)!y4ImhNVXlZJ&?2t@NWts4 zk*CLj(1kHAdQG&`fww!TEMk>*=MH7C);M~9(BtFP zaIY6)G30Y6)E_07@GVekf{t3{RS(=LZ|$No-&`;uwIB3JmKJfP=b8uzkA9VRcc6$Bi4-dE_os*o z*HfR8csFx$+|zNFFH>|0NagGB!=(llFN-SZo##6ws1WEX!1tX~`cQ~RDAZaPDwt3x5}`z)+U}GMAJE4#3oN#_4P`|%#D=Zc4Kv0K6O4fw zgTW5Gh(YxJUF^(Pr?I%Sv>rNTPfZk9F#)GAthNtz54wwu@D?S4KnB&fQtw{G_ix*S zMGZeY1lG1dG|QC=r%!QD^04!6IN3RXqU+T8rlxmIHrE?*t+JAi(w-eP2I7+up%XM> zlLgczItfQU2}e2!={}LauD?;;Xp@K7oJW3aL4m9yFzZ?U*{3#e#ioHRl@&cg;Pasy1FN8_136YsfH>EO$9_>5sWdGp-3<}YfHr{MR^2y z2eQ;VPLMewQN_^zZ;RqybStunpr{YO+o<&U=bC}#2N2HI=u=8XeiXl;Vm;RmM8JI3 z`IS;~z?^gT23iciWr#J*gnUUA9%j zj-^<+E=x{YASG?TXJiKz0AE7u$BOcQP1Rz52Jb&HQ?+5c>)W99R5?0XMHECZVhqp= zkY(L!2HBO(WL4_~lazcR zHJO5(bGcGZ3>w=h%fdFahU(8?m;os%{8>4Ay#YVzRvxpVB7%Ox@2WQ!NM@l}Cv2DZ zY?}<-4tph(@2Q?WIK{kMIFn^-#f1g~mjvD!<7R!E{9d{0ap8ivL~v~8o0t4AkWcL) zGj$$Oi76F?AN4yDk*g2~q6DhK?_m3nNl=QamtBR-&ZeOiBLHxNH018zYnMUVzpsoZOX(4y^3@TCv+Pt43z)t>6HHgt znAsqaD`tJR4ciUN&?Os9?^e*_j%$)c;S}#;ocR$!*-)7l!1j-WCkH6 z-z)Ug-8H{rgv&BZNAGdtLt0)UI^6{Nd87SQ&Y{8^W5G7$!zRm<%aAdKJ#j*(_z{bJ z7qp8?``$BQfO^CzFzEhXtx9XcjEsQTTgu0lKsR~{rQU{*MqO<+1Dwz~Zzwg#-Y|Eq zW1fcsh@`4!)@0@*VxAbKmh!45y%e7k`KZ#*Ijc@XEzbR%iJ`u36i`-0oG4QaL^#+YlGodOE)*N5XPqF zAu;x>*R7gcNE70rmGJv~Kw!a18o3AZSETJA%)`+x%@^4l}>kEc~LTIE)u%l8kd?6yZ|R%wYr~h@xdC zU;8dnbwUHh~edvJY)@tF>V(Hjs>E>;5>0#m4W(o5EN{yx!%`ej0ww4Ch z0B!Aea8LWtkzKThf*rCSv9R7%4)IKZx1YL?O|1WmI@_{y3-dm5BW-bGGnwAsQb%|( zuiDyrflGrc`qS}boGQHUbP2u46&Ri6HeV9uudhBV?87(EmLyz}(6vEzojoqk7Wr!m zHfG8;V@Wm;NjG6hHxWrTpiVZTPNvS7>ev>gDo!+O3O7s5tR9nEI-)*x!gdlOY+pnQ zhmV_A(5#M_Ivs5`eVncfRy`|~IV9UQC0o3x z5I!YSyeLyVrBJsL;~C)+ohpgkqro@Xd8c?i8CT0M)T_dVa;Pln9^ws|uT5xbs;sOn zTnsDZ!1NdYLl-g(IN=ze#(6JF=yae~!e+v}x;mH=_&D|gy{rFdjzyTn8-jgqDASzE zm)f;#)ISt8plx@2W2n;B?(nT0b=rN;-p}0XYZ_o*#dSoUcifbGh{a zN_*kX_972e+P7i>(kMqhJ;oX$%v{kv_gHdGi-QITkp*%c6Q0orJTvge@lPLh{&^#s zjntb|)>zeP%yM-hp1zexpasMEBM-w#{P2G(hWr>t3u5~DPK+tV2`AU|lcK7ip!iV! zFq(`R4Ox1O10R8In%7~Y7BO;Yi}gGlGpR&*xrgKDaK|kcez}A%ZHqE(i$fD@qJ$lM zxnqv>LR0A)Ny^in@)J{+eYiuzOkSPjfGqK^4s?wHm)qMINh)*0=T~F*mf=WW)td%j z1x=d-!OzZ;MawyVZXXTicw-N9i$P8mMW}jGdGg z5F*_gK1I6>65AQK;;Z9Z9Ud$)Pww;43wggAIyrTeDAF%XrGcy4$Vad)~ zH|kxNTA)`jE31vIt+8%%$#H(3R^c(HPjH!RsfNkM9IbaT{SrU#Nc>k5Lq!Gq58ajL zdVEdwwIwZ~&j!Jc@bjA)G`d&>t#$evz2E0~6X_D3YXA7AK>`vLSumG z0KIEllWJ?NIB3TteNd0w+FJa8sA_mIM>`c0clmfrG<0A#9rB4UU1MWOrRD1~WOe3S zcTK(fXe&VyZ;VaNm&&}K%*n$9_)Y^jh*EU=N*|d@_2#%DORFMTOHAi#I~gj9P)0L4 z6RwrgCM$+{L1|MJa}9@#_$E=rnFG;lOvZ_ z>dU18eaM_h10T#V9~wPh4X0vxh5th7Q2uC5@~vf@w4{O~H99px_nIpB>smrw`i45Buiwic0{MqY`)8IXEYK(k(|NHmfz3*4KMtve#CZ zAOn$~{vgY$0p>r_NYXbEezDO+nm!R;u5mdv{lFDMh8Dq5a8*FhtCxX zBUcg9r%q@8Ig0b5HaDj+t1%M_#(+m~BZ*I;m- z1&Li*a+8~jqq93Eznk0iamm_gK%|x#SB{a7SkIDAP=rQ8iAE$)Mm!>2Iz1G<6KS!p zS}p#zB73iebg)V25mLn|-?)f+p|oZR*gCCwc}O7F4&cE33!X$9*oztwxKgT;g-{DdU^wBAzelH^be=Ez-*FCi<$V8B*yi3Fv3thnkr zIyul=FNV!mIdm)MFp~=b+@eSfUxbgH?pU$#`qxmK7WuB z8+YnB4yY&{WRezHoEBT07G0PYd6I4YSuj_1&L+VE#p4L$-QO9aye7`C`p!QB+8WPa z@Klq1XA?yPxyEs6B+&+3FZ@j;R#=TMna=kW-X`>MB&NO=}M41nv z^IGl{h(2&|AYHn|#;(9SeYv zQZOgZRp8>wH4w=#u@Rd*)Cr1j5xASVLmwp-k-yKB{M*1&T}n4zy1>Dl5v*aoYj)&7 zJ!vdy?&;(4!!0*eyzMO3D$@nbf#4rO6QXg|o64Fbz$rL(8KD`g@I`=^cL-_|U0d|x zN2ZqExgUlYcxY{x*HjWHU1dFzn;96374((5?~hG1H#aORJ;&UEeiV{^*!y3%5!dtz zo=G0-_;I83f*VgwX#;k#t>w_T^%jXX3lQh?ko;(suB_}#Mv=L7xP&G%L<8&#fl*(K z7=PJHZ@HDNiK_LFz(#3+8H}|Ivy~Qj1`9y)@{>+hRyo8bEgs&rj%@T<*V&t72Od^A6X0y`Lq)JR=&^)usPi)M<-nhV@ zG-lVo4)2uK4j{<}LQKMTaIs?*#+__LdZ#bbLmhG^j9%LbDt8EnNMvBcu&c5V9)bMRcnox+u9o$yQ7{6yDC&b?0@TWc=!U_6Im?4CDgZ7 zLyQq8@BH}oAfI{HTwDL$%7f6-@}iv!oH`1?41(zr@uI=FBK}rMqQN_8Q^$3IA{eAA zYV~!6P1z@{+8S#M8aJq(XqBvVs(ZKnEbqdLm-u;lWF-?(QMc|hNSD?(dM1-~ZFHw& zXU%@gYoMX^=$ir9Z@hz@BP`f^K5Gn+xu_fk*hAJ1TbqlM&HHBzwT7^mb|IuiyoPc| zBPTUV!yIDs7bq>F)PNCRO-)&7c3G>(SgD;_6EDe4$U1GSZk!H5yfPq{evDXO~du6f}= zpHRUw)y8@^0AS?-#)Tfnf6fu`N|7v>wUEGa5nl2OGGKN8MK;L=G8DoH8Z|kI-$>)ynHOd&JpD7 zg%!(y_TQ(0aWcJ@ml_&VR~Bxj3Cd$!ndW=39)*l-#Cn3?DO~>Pna#>sXhP6iTNs|O z_Go5{Tp@gqR_Ob2Mj|rTr>By7XrJ~1;g{@fj?KJMd1paQ%pX6;sES_mJ zzD(5?Ihxpn6~|%1b}y+WRs1fjmq}ZEcfQ$m*%eYfr@nfF&6!fRdxDESpnojoDje!=rT}GOZhf#FN!#FR%NA8!Wf(@ z#88PssFS#?N=g7ky?xjiYw zd@|l$=bF4g@f@Cqo?_9T>JhB?BbE!XBz}I~Bg&QM5KJ_15}Guj9Z{j}8MleFpnizF zx$VH{MW>K>L-_e6bRc5mr2oKi^F|2jbtIQ>s|z1ZGWQRuLzcD z4}dl)0C`M={HML?P)Od|W%TK3W%|_fK3G~`&939*bqvI9X!}24DSSy3aXI9{Bo~7@pAy*Wp4>aIejy4F8$9s@(8 zB1aR4!f%f{cSPKs@Kk3trtx-lGu2^};4%yQ|9lnnW)WuVKw*RX#OXh{gosUTxF(lW zqUElA8s!o}zZiG(8%7kImt1~a^mzfDZ}=xn-yzgO z#$(FbTC7hT2m!>Ie%o5tbc3$jTHkG=pB$mxmDz6dZe@hH z(1MPU{H~dTUZggGcz+X9oWh&75UklM*YUj%w-U(b_gyceUwB4XPt>7-XD5*L4Mk_z zPAHa~R05eW_r&F_GMPAc-{vq2os_=mk&6Z}iQioed zN2rqnN0?KfuOuJ2a5QE&Z)0RRxxz+cZ7?j*P3@XzVear`b&vx6SwZ+)~%PTpgc%J96DygolYgwk(Ns&<8IxJztAR|5Ku5pydm}K#|Ag_4iW_M&d zF{-vuX_H?}qf%!Wxc38M^Q)~R@cbIduFDfWFMMY*cEb7bFVE1Voa5hJys1-Sgl?;b z>Y}c6u(j|~ePeI~vv%s=rzGjzOle~zOu$4y(?bN~W>LgKd!G%j$w;TYGAzM03BrTPtH+f>f#vV3Tg_;JGSE++}CVr}t>=m?kgI4`8qTNRh%iI+++02nTF z(Y@Bv_8lqGa&&Xs8@MBzz&-|gK?j?xCz(M3(ef&6ly_^Z)h($_HfN?MVQis=pq9~6r1))F~7mMI$i&)C&VQU zV%%|qEcxm3^V^*7g@M@+`j ztNUBOO(7ZVWe$!?OP9TzLoN2a3gspf<&D7lGjq5zc=F(J(ufaiv|axudL^IxSzh-Ht7P`EJqKQwXWZJYO9fC&ESmATMNc1$%JY6r7D5kODf- zIr!}_4uCd)-4@P${DTW)u!6Yz>O|_ye=_I`Oh7&G0{)e0d9F;Vu3n|6hP)jF&kq1% z)bv};@7ML6`=5UF#*F)bP_8xIzv5PIvWU)XX^*0^@+H`G`0z^-&_^FI7N-DLIE1#w zR~hr7)s$Sgsr#8--3uJa1s44bcR$w}BX3(Ep|-F7O_crP z3dRt3xv4yq9%l;mCSR?wW_4d{44iBIz z<+(P0wW)7$&Ebdvs33*+nu2W0JdS(|;%m;B%F9=AwprO^zqwC(pXzhfRu}?!+sAk1 zf+)pZem+o&e`8Y4E8y+cwcqF_=da>5`$9BF3+(8-9Dz|_5Hl}6K=f>iHrZ~Tukg>{ zl~%FTsKZM_Pkz!cFx(Bs-9T46>(Xc=NSkh8&ns2Nv#l6A`zO}l)y8OX1rusmj#P5w z3V$mjUO}kubRvv8e=kZQsxs!XTcxM!vn3!9K%xhX7OWxBYi!2u8a2WdOXO-GVNDumM>+R=$S2i*82RN^AL)`MK5HKGd>fFp zw|VRJ-lA$FLi~_^>5yt}mu_{JX0<#u<@&=G0c9=rq=6aVNF0SwzXFBW7kc&G`;*qY zWXv;zzE9c>U~MNrFW5n*^0?eYe!1^hBNOD6lI$K}U-cEeXt5Q=Xlq#B*Hs?1N*`7U zx{UXv4?7^D%rSOi86E$Ub@%m{nlqI)!e9y9JR-w!+Ox4qkL9vs@34c~>Jqnd(!Dd= zVc#~}dPw2kQXW4=Kq!rUq!KH~r9hoRhdqWBXZH0=-IoKUaT%rl18&0X;1ODEtLy0* zg1m;Zz}OrP@-@R{Zwa2p+tf8=s!Zmqf^dwhvxn>WuX~X8%3%GwO$=ib?>AwaiytMB zuPI3Om^b`lcg%|{(L8T&A1V)Yo67ZPMoI~yOhm>YiL+?AIfl1#AzQQD(dZNTI@RQP z?3=$T+5#7@KTMo`&RBuxX+pHHxx_{Dte#uK6PHqqm?-=gKWdVd9w9KB$XPUGEEheV zD4(-&HfmM(r{Pz8PV&Uxzx=an8(%h#2}H&=*TJ3Nw>xDpU=z8gbR<)?j;_MFw@cap z0v9Y7sgeUp06!&%7;d-ubGM)opbQBLzq?>zkAunvS7Di!pX`p?e*}tSqn+<>@q&jK z(zE5++9}Yy56|s?6<0-6c1kaM_qw=*r-U}^e&xzB_3?;}i1(D9n&fh#?;TD@zO*pQ z2RmyAbn;gGt+F&VkbGCh?_y9f>%%vYFgiscI=<+COAVYP))V2Dn;cTjHmAG6TlAhP zDzkkhpDq2|-I29o6vVa1nRkt_bM3{&wfcIa&s(=WoER6R`_OemdGd6C@m$7ibcjt>;}6qPgb01G)Z$a0dJp-*&zmE5wVfKU&!DfR)z+W!laGY)rQ)b zW&CbN6?ND~HUB|(!Z9x|#Fr&S(s!;i7oenFF0-{dJ=Vy6=--u8I$^V^x2YFrNSlNk zUDLy^PAlk3$ycfWob+lVwpDOk@C7g(9=rZ)I$#bx{z+xBkj3mqz z8}Xq<{A6yQHX(e!R9_J1n%U;i0+?AYo$%h5AK+?{x=^I3%ukri`2wd>?sT$ zCdxFr8j9K4Um}hK{GaBBJh!?5wTH^@0Jq6$jVt1U6iA~`OyatE++XC#r1g6Me(oy* zG#MAE-^!kP9@_|0;(kF-ZSNQf@J=z9Gu^Li&MKH8wRLfW1pW;ZJaA_8M(y?9KSdRC z_cx==fmUSl%-U|(b+Cnbn=VVZ)M7VbV=6#aiH>dfoH=G;Fuz>A_<3rU3jo<%5!`&l z1ufIsb&mH+Ak!)3VvpTU_*3t59#d7C)zh6YU3i-=&j9q5<38(h^GL+dVDB)G%aX)) z=q|{}+0q0u{*S+6yRnV$bxPKDgR_F~r9$sC%pkk*TnHPRr5v1GQ&axcaWWSx3S2of zMAy(pVScCCvlES$#tOUb-Z6CWtbnISP%))YFD@n-J@FI{a!bq8IqT}>Gb>LMDQF^v z3&>e!A&LBT^=QoCvFYtCQ11>z<@;lG;ej?4HtRKSVO*_(jbz`Gxx8~lCxXS7hStp$ zXb^0cYl4Kun`6k^kfL91aQd-)f|=3^H&~gnvvbD>*_2D8D;Mh$l1pDt zs>uLkhW?4WhHYZra8iP>?XE9#;_MD$Z|nz7^z}}tQn(h46jp=*OJuxTJp?P)A9B(b zkPFwBTkiS~WVNe=1KeTtu4(OyIO#;0PP zg;x@;-b@e*G@B!rP4upuuMW%jJ<)3kla|`9*B+F<2Qq)nHhG|K25*;8edLfGAA|VX z0;Z6u)}N$fZIS){rDe-QFJ5j1;?~{a%E0^N?)Lkllxy-b3eC$!#4J?OlV5H}n%rQw zQyBTBrsp0TYUg*mE76Mj_@1mi`q3r0i}1k`Kk`SzeMvpo9Ugf%Osj!Fjg!vO^S0u}lfUaW*KSW+-z(u=XIH9>zgIw;zu`N|`+3qB zDHqx30Vq@)d6g>U_RHQS``eXJtlZYT3AW95hcp3pX5_iDlf~6KpM9_G%SrI?#kZ(g-AiffhcaOXUKntVEteI ziM87|b5^GYNg>L&cK+#``s^XMe-Ull1L*(%Xc@o6kLNM+733ow-w-U3n?uLWdv#1M zQEc;-80NeFi`CDIk%Ly5X5ag=LN!3Y|U8~-xYeU`P z{Aoj)JFaeT;6kuo4tUqO-`e0yjCU>6p!amOelb^m{73ne)-jb+WGzK=^W5ZKYkFY% zUX4{m?JWx{(SYBUZ$XZZ-Lk6-oKsD{|_>z9=Nh`Q~Qto^7?zZUmNuu2faUI zXh9R7z93W4f?6qV#s1K-!M4IS^+okOu4w)5#Qne45UKzy5nX z+{iiDcz)&-@ngunTYb0WBMEqBOSSc6p;aDw*;o>YVu&ILS#X`qAp-QE83sDgy-6YD zU0?x_zW?@_;P!B@e|_`#JIlw%r`+cx@%ssX2H>cpZrmxXK3!&qEs^T*nm~HP{mm0hHPwSV2`!|N4ARWEGqq9vYz= zFH_;s$+1YX1i&GE?V|ZE_MgwcDvIq)eXn23^z*EPx@|(co%S8wH_vy(>rY!JcT@gQ z3S-xTo`fOlOxK})qx}6Nwr#)K-)l|ZFisex`If? z)=qBwz>gKuIdrqSh}SO1O|pt9gp_QZkKam?TV>U1?R&pGqQR32Emc<(FYg1FTbNet z^`sUfr8{BC#nU_$%lmU802c@-hTI0fwwdw!qR(rFTeJfHHb}hZ(JMq#j9i%PUv%pTqGm!peH<%#StFIaaf% zbXMU9K{taWCkXP14ocX!Iga8u`ClJR7i^Cz8yS(1)RP-B+lGr!qe;r_tB?VeFsA&{u)#F5x9RdL!LmJoj_~(J>mC8NB>CzEy!Qn^9ev` zX|>-{n@c^MLh3vuWmf3NIYkR_TV|9)7(_w-bgvgQ5=@YuDLfdek#5syLDqT;r`ezU z3s+GecYqr^Z+<6wN`Tj`G7SwJz{tFwAO`1ozJem)%FT46fiK?(Ktc6N5y_^#(Yi#>pG0(rT^l>Br#I!*V?^CzQdc7|cIBA6ZjPS>?XUEOp7+lZk5iF3U zHiJS_WLYipmCk92e8DPHah4@)^8)dn4s;w(JM!KKuld5%_8i`?giHGX=>ua(nqJ71 z-U6D<;pS-x@l}ga1DKPexwOB47=YUHb%Wo}oj8>m&`>NUDB~v8CIVEKs-F{-AjSy5 zAoBzTTv)*8&9QF()|n~ZKL;DurZKqTgX|ki-FabxYU%!6Zc#P+yWcdDz~iA@1YA>jIETl5{L z70sr?Omj*>HCtui?h}awGDf>Yit5Qq{GQaMVk+w^GYW4sX4K>h#!`}%{f|RJQ*$Uy z08X@Tb2e@Omw3Krik*ABsI~hsY}}11&+`p*Zx^5Pz73cp0rDC<#i2^{m3^jg*-L@sXyK)o|NxzaBi-rk+{?uU#Q_vg#d*#ZN^)X;Nz`;HSLT@JsQ8xQGFOM{U z)-HCFZm-P51b}t-COCcy|8CX1GiJ>Apf2}?!>o=L&(cpxitivF!Xy zh^e+h1|Q5HjTO}Okob^B5_Q!Ev<^gaZvdCRf)BUd5^wiAzq^XZQ(^Y29e@AM*F9;c z>ioCI;Q44CejBRL856U3qqdUO+Lv~q5)O!{&g}FEqL;tsn0X&f#r~G@tF6!iBKr$+ zPuEM|j?Ye%g2PE$)lR{Sp*k>#EP%BbHN$3p7gJ)r;HIjbGXH;AFV{D5`NiB^92#E8 zRJSwwk6HFUmniF(ofD6fFMeIvOBglBZP!zM+6}C?U?u@m4diSQrvTR=G~scnwbEtIx#?Tvc!>o261l&ySVJvSxx3- z?YqBRgdd&SmN!}=jiu!)&-y&qZ2*>Jj{XaK6X{KQCHCNwB{7gb2`G2=d;U*rLlKij zw|`|`;sGUZ@y7|Nj&lgsw!0_VMy0-rFQPq}$VIFEH^J(pPF%dzy>CKsyv_?vRXka;zijlRDZfw3{M* zAFfqbqFW_rdHkSNQKk5#xb z@4E3F3_n=%9J3O;6n6i!4Eb(bhj#p`x?{wlRpI2ayoBBD0-@iA* zf>&;D?N@`u4@(;@$HIV4QK&**f`%NazHH*0g#`+H2w;Ct)%llXsQv%T9djN#JUq;7 zoZ5`xcCpIve_oMUdKkAPArbX?Ol*S2w(%P`rj^-d^x#MpJ|wn^OE)c37VZ=h9G%1|JqOF4m-_iY?pE`fxIuV5cKW|tQkgnxYT zdEZc;jHI}sF0f6!Gk9ga4yAZZ&2|Hg!b1wWes@*bDDAvo9sjW@`2sys; z@d+6^B=KX6-Ucv&Edh;ZcMHYuYGO?UHmq1*YXFNCTfgh6SapEG5kQb{Sl)f3OJ0l1 z-8|UX80!(09Ij2z+-M2BS$BqivR*E=&G{S(P#?Y9Jy6~N?e-@YH9bg)8H!KU4~X%9 zZ^cX72j2Q9BVV>GI{N^-Ofe0?!}RfI$9#g)?VBqjNZ8qRd80OU`J=L)^;l(^JK(1g zr5_vshHSyj83Xau^b%mFUTlmCi&x`!)qEaF*eOMMo*%?|ER@w`t-FD6KR!NqLmo~o zdBD|vviwb*2SRS^wMbO}4&$O%27F-|bB-h5nSQ`<0K84~brGa)=ne<(nrb|U-qRH9 z;Q$@c$ulW;@6^uQoI2al_Y~Za?@s4Z7&!4nj@TIOG*Z0c>~-cl3p?)tU!P#Q;W>>Y z!W^LyRE3<~Ls=S&j67#48higKdOOc4SDp~jdA>_9Rmg`#=50qv84v~O0S1t3DR;cM z@P*GE>al;hXLV^@u+sogH+@H0#7sHCqLlOVkRzA^*zx7x*qf?OOBj9 zJ6^A*0G?;R+s)6NS7+vo$)i4hD=S_-T|3p_(*%PDFp^=);9I)r#{#n{K?pvS$)OSPRkr9nyFb#|@O0n~2-SE{RH@t2La0^_0 z{kx^wy4(rjhb0eRb~bn45MdrLbeNmrHr(GkQiFQT+is=X|1p&G(lbS&^z|Cjk5>=m zSe3{iWLj{c%4!dn(wkX(!Ch^oTuKVLr+--Fot{7$>U5`Jf}<$dS+XF!bKVy4Cj$OH zW?$=N{%@PzFxrILVBC&P`Bm%qvI3kWTAzuz6rG;80J$%NT z>AwSRQ6rO_>AE_=9Odva3)`B-<|+|^qfh)|ZcpQDt)bESI46eF(<7^;J`yB_@^uD8#pYny>QZS51p%95X@~h|m7x2?ec{xd zHsk~G6el;fu^06q;5t8wAi^zx$)Qape#_dZAKa>+0sP2Qqh`Re4oNKv-Br2WWX?9= zy;vtb|GwNm5ej%&MFOG!uD?B`9*ZjrRP3U6Loq^r=+M?@m$} z2za?qL@sB3p5-y4-v$l}C&1yiP_msqm|W~65M*GtvaTBo$?yruY!Aus1W$|9b zz*!)Tq)P@OKD}Kp7MOJ~OCVr+HGT8Hu$j)a9+*nq$c(FV6MIT3p*3Lgkd9*FyIO;6 zr+TB7gZG($uG=XFaa&(xpXC4$C>b_0fkZ=oEzXSfB4}ymm71y)Mwg}lZq$Kx2`YW9 zk1cZXa!hf*lGyL=2%^$I4TGB@GR=^tKZ?9f?<|jyXXcKpyyKpn@MM|dM7rntUv~aSQwpzRfsMxzy}=?QgeUoR=M}(AijCpno7>+` zD~lxX0ZE*)AF z6G#xmsFzy1T0;(qHg)VcELRJg06`~;D)<}30m|}d9+K5&(Q8v)C2tzJDf+uh$?#i< zvCP*Z*k8A>=7Wxv=Ci?hjqx#a6PWaCde1aZ&$=Yd5>Ps&yHQG%7zF8|TUt5>P#Wp(29c6( z5D-wmh41;}oX=}t!;IIkS$pjjd#&fbe-C~jt&C>B$oUw_xu|Q1=q>r^n_$_`qd%`5 z^(fEF%gDi$g!w!MNBqqx{<*kckPef)SxW`u z6|>=-ghUC%zobGRz0O?!^C;5wa0Um3^Ax_5GeHMGr+t|!0G9pzaa*%c@wdm+cSZc- zlIzG--^YWZR@!wdmVKYG2x*bj1S+6LXOkpwlI35CLnv;RYJsb|lLQYCs4R84zkM4# zmL})e1Ymb}d0lL+iZoe8yXU`a=R&(FaSME}K+(Z}E*Y$&CGM1QCELe*yL#`rjU3-y z6j!dyT{##2V&fzJ`FnLRQSp5E%r(=E1P!Z5Zyki@GiKhT6c~$0GsVl-Ce2ng$I_J_ zta8q4k=&+E)uT2LLXYx;82s97Qy@eT9$93|e_^=bD=psOsM8z#WKXVVoy`QCj2TQx z#F=Spv!a0_=-1JOAsHj~9>#niPW`fb-3U*MpL?Ep8_(%xgzQ+lGu*=8L3s6EP*j9a z!pbiCvr$XHO=Y~YC_eJ3?*r%#XWbx@J5j?Y0~u&=2_2Q=&+#$+$^-XOy=OqI3=FK+ zHm5YwPS_t&j$W{@ARyW3ZXOOAfP%%1T5CtE2E_933OMfM6gM@K)^K{1t!LEU$NGb> zLu9}m^d(mqh$e0w3cRCvQ$9c3lCeq`U@S^n2=O6~1if5(_o;|tHY%x@b?qexxx&jF zt=c8%(j6pouytV8DJJGjeao@25HX&w{yD1you~F`k}a_y;64l5CirnQg{c3bw+0^0 zY$dRp@qO1dz{UrPMv$nHJ_+Lt>pqzjq-6m-WE<0NF20Qeck@Om5ZK*CC5!gIDO5Zvy}~fpj+uda!g+UqUtU$!b!~!tOBr(n*Kd3-5^3swt@M7H^qRd7 z4h<4i|MhO#_Lb;kmLTe)>fi7~qot~V7K5bF0s=2Xr8B$)C<64c&AmHE{;wUS@V{QX zNV}0K_}Zet53g4Tx)=kn(2OB9+3Qpqol%)*@;yDTt2$U&*`#w$(jXt4w|DP!t3Kls z5o?K7%r55aDWkj8Z7GTX4a(Z?Y&yJ^-8NYV{w#JlDcqTJtiJ|xl}aQ7qqarQ41wCm z-N)VBEh&!>H;VZF>vA{*I@aiPCA|3dx3FHIl8wpXQj!k@rd=$?^P>4hi10W>wM zr-vNUW^SM2*Ia?1Y4Z2r?p!76$#0;ovFp+gd@2_){OICqnEbEN46_n@f}FtA{3q;;vY@@frhIH$mRLHXz41bxt8~=_c@;M3xxr42D7yFQd zJ+T3|0yz?_G9ZNfmU`=pgS0q@_=zzW_9B^;;M=GvYt+Na=t^t zn5@`4)%LQ>msfjfS-RlYtkR&~+7xRsFZNM(&M)UPM=5-9o z%30s)cWe@=>&$-o*FyMzkjkAJ3+H1le)R`9W+wzClzalE`^$!)+%6t>;dQkqZwMKa zBJyb<$!4Cu8OukXxD;Ytc~eFEzI$y`@&v@#&48Oh53{oquGUCcC8}Ciq?PdP~1A zV!6;vdg1L7bT|Vd$!T}Wj|UWGwu?;`PX_<|sB!%~7vLn>V&lX9IMi?ajDfME5?n?d z!5^U@5(s^i^WQ&Y*VnB!rpXY;hIsv{(xtNe#gDu~C{omK+N5S8 z;Zu`35RvlTR6A;5AP?NSz5*Wk>Y_9Vel=E3?Ly2oSek>^~xcYW^7%Es34Eb90$i%-O5mm^t%Ye9wNE-m8G*r{_ty&_@QnfoIMvj^oCqC5??di`uZ;H<1k|6 zK(Dqg@}CqLvfjHYE#l)EWT5_awZdhmUJPhVnWxWRKS}#(Tb|mga#ING)%hbmA zDA?<44PU;?iUf;RMDV+GQZ9qaW{>~9NS>fhJwsmKv$ zOoxJplki_J5;jyL4i|dWjRg7RM2gEl7|xQe1jnZve4qZBun1o`yNvur%b}w23+rk~ zwaUsloJuvy1x||X&iyC&kLsfE$l#EsAH%!H=jDAb?+|_!h6#9bN_L2{)sR@fzYO}=b_0O1qFwCdxiKJEBYznKdYgV2Y4w7ooSrcjYA+i|pz)&`pS)GdeGv}guEr?S;u zwTJdCkJ?0r4>~)Wr!4D!3;djSGk5sXeRNW>01 z7#uzcCJ9KEN#WyDA5tFX6XY8Pzb73-t*HC=?L5bg?V-fR$<#rf4Cu&pM;A;6-WxL+ z)SUL&|h}GAk#Mfm`28-7|7|)+XZ%}b@SyeuP-gc~Qis8)GoL*MrW13np&o;@(K^Apm0y$1 zz<2b9lkrvAw&}+w0}}d4Luwyka_+L4KYoSs0B;e~uKTh6JXqo97NM)-ERuOsdk;^( z^7;Nglw7C+W}{a}wHZc^``h`WHT-U#{g&VQcbo{0_BnyA=b8D*ogo>Tw9%%vm^$iP z!3Ca6t-WDW99|H(Fs*MjZc{a$Z#5ox6{*H)J6|n$%~H?Eqhl}Y;|814dIDhH`X9Gc*o{}M zyRJkSPlYV^7#B>Dqskf9Z2bnp{RX_x3(*76F&Pxi?Y_=BBt(m_6qB11lbfE%PgqI} zRDpZ&bv5prC#j(|FSy)HygxjWfA3}M9u#}xhEeS;vM~0oAGnOZWHp)fMx>O(l!%i66rI?{ik2HuU2TF{KXjU!F!*^d98T9%O-|cO##9DUWlLd8sJMJ{gFyPz3+uFEmP`epJk& zqYSI9sdaJFzS~gmvw0Uj(fOX6ZV0bT9A|fi>cCu>L_*h6aKeyYg;WuV&ZEaOeUPNiB!|4UK2PaNB z5Pf9p!P0LWgT3TR=7h}0%t-qmPT%IWz|@W_J1VO;$!1!b{fX9safD5(jNog3ITZp$ zDU2Np;BBaAPAYc@B^f*nw_!3srPk!LPKCZjTKs5N-JHW`&TvKBCyiCq_>6*dQI$@% zzziC@o1Ow}>o~1eXg6sed5gGt+0Wu?7IulSo9IzdzKgG8f+)DW^b`}|jy(!!jxY&q z|C+z91^>Kh@y3jdShoyVvG6u}6BHql0~K#AQ$VwXq$Srco$r|2+0o7G&Ce`O4N0)r zmt6bN-%L~^K_;76cWwR-@IMR{#Gs4~^$#YYO9kWj#6VX*r4~+LQo(U&sj}3KX zLp}^R-?(^_ZB*qpM%ieqnMll^D~0h$HAw*l@p{Lx5b=OA=sYQbF*d~VmXvK0j1MGWp@A%d5Cbaq1e}L%wo*H}mUJm-6>cF5YoA7Y&uR5eBn?$Q)fjD(`OO`)y zk+Wk-dIw7CEijnLsBKtFJ&sp(fm5#98*p2hst?KJK*KiPJ|rT3R4i4Gu7EA{Tz0{< zaKcN9r%}bpddn<_eoJBHIeYU#Bq!PzULK(&+1rbeo#v(vMp{>3#){--I5C!_Q{6iZ1JD8pVKbebAB`xad_oZjAH@DCM@> zLx~Zqfl~o~XRE)8mw{kTv{2z6;jl<{tJn0pn|~O4Ee& zh^AfZU5hs#iDqB?mU)4Kj&8b+Z@RjfX`i>9{6`|-Iy?&|b5R`_KI$1+k_`*or6i;` z$~5v7n-ek86E&J^G6HV`${V+0m zvHRbeF>dU!bogWXG_#yP|LP;y-5$e-_GcM0GU>Cs=~qtl4?x&Xb3;$%f}*t@1tnMt zlM3NB%o#2vn8MTZ^t~j1`}UZ%+4-2&fRbIGw*HIQMCX(m;IwcmWn&8h=4ntmSDPx; z{QOfcZxzC1Qb*gWrsO`vdQoo4o#lBx=-<}a@f2yIMDMdvGb+(=YJIW2FHGE z4;^+CXp<`sfZ>EnW$1_v8^HSwxWLhE0GEcQS_r3G!eYUZm1~&R)@D{Sy8m;G%6=&! zV-Y!2_lV@<qBo$j?q;4|ECO_?LerRD_Yb`vUJJz{ z_%!e3Y`Le@*`HBl&Rflex;kbqGXs^H z)1UYH6T{s>$Ge=40(%ViOXKfpm6oZhu;UVU!DjB$uS&S50S?OT_~`N5&ywiczU|_l zyT18C7iFMNuv8XTET**K8t}KO_AQQi5XoDYy4wEV`FjS8?MkESXM<6IcQaIIjzi>6 z5USY>DN;i7#2DW5ShM>{+C1`b%WgAW}z6oXS;UrE3%FRuTk>eMAQ`vB}pm!VwCdz+E1@5+-oiPG(fJSy|D zVm~_AEXse;dZBs9jBv$-G0M~*pFeE9Psqs7xZsl5u+)+kuCWGw{dXnLnS8epBokV& z&4_w8*&8fDM;G8=k6&HMH4^+?@9#+plB8b1KzM_Q3PE|>Jbo;oAPwBU!oGl3N;WKg zwnWy1esVUZ5^L{2beiltQifBf20|2!Z)@0Pr4C*Upa^0SdYc?WuOXJ8ql3vTRrkOI zQiTgZKh-_JfuG2+TC3;MtF@p-=UD7J`l-_ny^8u#Pjc9QkKIy;G;>A47u9}*Ant}K zuw5!Y_}qCzHcF)vo`vk1NLSD&cIsJ#B~og;>8)SAYr$@lz!GE$`eKO6)mmbg3V8|? zL%4n~yuxrV@<~?Q$~QpVxCL&J1&CFv;MxN#35dHNQ7aB}<3BH8Z>4?9ZU^?e2&=2+ zro)|R+_AL7v`<5y%00U%ha1(rhT;m*7?%kFG#%3?Jm0AgiQ+JXewrKwwUfJnvDcrM^y*}2RM_;oW3 z`!9XISS{Dx6sm*2n`}HySynJU{Lp=EKx$VXp1kGpe)A-F>->hFWr=(w^Pb(>9S6?| zUzVLOA@l|jHhT)O(m>zI-=Ibe=itAoFO%iH;e2sUbSgTLfuRrZrZ~b#%xic=ZY)M6 zu5i)rE%PA0Eg`(;mz_fC;^MT?|DnD_8NC;X+>O<+;8ql+0-peCW+e~uFqx%&>ywdH z_ML(an*J`e&R-tXd#d7Z0M$$69T!n8zq`H+IjxKJXvL3=6zg*Il~{V)F}&Br%(rtM$hryOhN` z&Ea1?;X|HWLprc79W8E~AJ>X@-+1uHb_kBnrZBw$M$_?G4}LEP4|vqT5~1{h$UfgZ zKOO(E+hJO?*wV>4Pigvz3fv5s8v(ctuMVDS!u5(CR48RZrdB}| zpv(cp901K(zE6ZTyq9}Vm1*$3fuGYNhy<$W#e^h}@l8<>>vR|E1?6(*>U|;B>(1q+ ze#;e#i48M|W8OHt-7vmm~3aAT}+EWV}#%_vR>3 zFhiK&9Y^o!mxe93aucK-F8hKgPRZo=S$TLeRhtmEaj^DSpYjGud2L16k_^0tTakf} zBH}&?vr?B7&uJZCgb~DdU#6x;e^Z$$nHjqAB)` z050;h-h10XfF!e`7dlke~a-&VTGGQ7D+A=KdzC6;3tOm!w0q*hp_5%}- zmCwRQy7ZnFPsL^hqHj*?v;q26v-V={rE-6Xq+&{& zj-&loGn&3Te8yw35sC@`QVIyD<9oaL-IKEK(b%bV@WkHC95q0^bR%4}Y1DY6=mok9 zD345@s-{f&r@}=Kl9pk$P>byXh~ zjV-{Z#>V*(k`3*7ElQjCCq$aopW^jK`{MZHHFWcG<5_Lla5b|&ZiThpwm|yodQBn? zsZ0g*5BuVYowCT>Nh-F|myr*1Oe}KE`KHe#n$@@-C(v0zpSC%_ii_FBA4k#*aUu!l z+fM6z*dMMK38&L*5`}5e-N^moP?myE2h=Q+mUkbw&#G$_iADV~cr@~3H@ANlQBWMK zDu2sy*3hE3oD0lsfaIxu+x*2hx*--^R|{l`p21I9V?%w8V#2qXRJNi| z+PrwCjog;w7il)r182?Kn9>hK%wwDDr)-6_2Lw5I;jtx7wvH%(=%k`TQ$*RfKb&{b zwf|y42bx1oSLc;$ZXEw=or|2C*?;g>L+HNWto-LETaSmKBLH+2P-r2RW9W5y)Y?(9`&9TEV)3Z!xLXd){{qaf9dTTy%!?dJsDS~vP|lG#+RH~ z-@{s&Qc^86H?wK{tRW|Y*y+g5?~e(QLo>cj2k4DNd0Bf{57_$n$^j zS-`qY?t6B$)-R0pepV9Q6bjQPQ#q3ZoL>IfPA z;>Sn@C4={EcX0Ot(npoydXUnRlhUloMX6%x*Me=eBrvmYT{nsyivR@gsKLDhLV4_z zk&r}EWh(c(_QK-r$}fWfS<@(dZ@CQ;LyQgtAYyP-a4PpuGMN+Jt3~3^(pIE|%ff#u zR2rB!lUpn9_2C;lv($rd;+VHAKYjs3 zjENX0zkVk%(}~S1Dx-W=#OI;O))lxm6}Y+^`aYv}%qlO-1m$xd_uIQ9%(g+$ow{AF zWDo_2Uec;Baa5;t;1h)r%G|HC&<9sX`oD2XFtJ=QS|;CrGw1lC$A-_yVvW0!hjXNn z_C=#miNG|Ex>6(DnpIA2(BM=|w~C|+391eNhwGLw03{iJUaBYG?uyQjvoBkw%9BdHMA_Qm)!Q=}E8U!C*=yXPVhMMEvUwkR97>alg}H=TAV zBML0NxaHh>A9#(!N!dF?$eGd<(xJvf#w$r$*H!m3cR~9&>@^apx|O-xZg;d4BMQLe z3zPx?R*tT&rn=&I(wD6)HyEvs&W-1{d7=Wy*cxNG6M&2@D}{&wE3f!9+2uwz!NEwR zk91QR1Fby~;7iBH7~q%h8lo7fRagK~A8@flsG`WY8Hz)i6#s{cJqOdGH%k~IeNdo$ zkDcM6k)UFuXSnB)phZ?#o^I7Dx~#)VKjM4s?G}e8Mmrzu#7I5)$op`?Q18MlSwe11 zk}ShoclcUSrKK&fktA_8w11_`!excG!5MJOIaSjv0mmG>pfj``P}r-?1m<0m_GSi& z?O}9qG(~D}Ewpn>!&)lm69sER79QC=l^@h&a_4mJF!6h-8&Jt;!~SlC0~! zik-;kt+fg7-q5S|=e@Em6%V&b2AjJUV|^^4E1|ef%(@~-w$m`(wt(q+tV{>Ms?VFb ztV}M>3|JogXv;?PL|Ox(**Jd3=E?ITHNLgJSzO8fPXLb(Q1yNap@x z^?tBN-C*})aRG)Ou3Mo%`R1u~Z@4b68ERk?y~C^=?{&s~SDt`zWaM=hDL%md%Sn@2 zfLp3-{Ygr8assJ$kL|;Mz<((OyZV?SiAmqS1r)*O8p6*tVXw}g zQf7#6{JyCLis5Ls^dI)y4c03GTh8lpAYXxq>s@eFj&+1l3&{2{12okK;IMj};(+sM zFlNwICWIFx=cwkD%IDWBlviMHC+BiD8bHxU)g)SO=pX4_+4_+;ya3vou1fuY8BT$b zwZ@mrLX3UpaRg(1BwJ$@MsfGL#>Ay5W|6O8y}|nX9h|S1P)|?i#{BgiyIuhYV&T-VB+)lK%s z{E>-$fT`H3yQGaI3010Yz`mes4Q~eI{PHz7A|pBk?`q|%<;qw7I}U`ygp42wNiR!| zd0Zv#U3NoSOW4&N+6}WFQc43?c2y;xJV(P%=?Pl)>n4W56nD6yNN773$*5YZJw5+&Xi7`rG;#_sVu^wd+CFaq8 zt|5D0H+nc#&Zx~9%pK%;5%8WH<9?$IddD9`iPbujoUjjYx!5o8rinrQfV?VwtaC2VR`58^t%Itm0xg^>ws>u)-&y=AyC9Q*0~mg zB@`j-@wK1P|tE| zw|VmiL(SjGV4Eb-b6;~+0c=)b8hcadpEb>?;#KI4m}=dIGM1WOH4 zA!bg;CtNh!h1lCa8$bFD4+@sgY#F!%E^m(pomL11WHwFXb+SHFlEL~A0WoSj+-zHfdW$L!Dped&@E!{4Frmx z1u=G@HJ{N5vJaJmkL-xCQQP^dBn8w2Q2dhtXVj-_;!`9|Y*kU$))!({6L0!4R$c{tA7g+p0(Hsl=}F~WrB}-VE9X-|N_y~&1x--L)1?~Y zs^T;LshT_EfT5ts;lcG-XfNhMm&IuXrPbCoh7MBf#EkqRm&CNHUdvDj1tr3QFD*n4 za!>T`=A2``y%pq-yMgWWvopi*xkY?=A zF1DRu0*y`I-|F4N%@oYTE2)rMMOKq5;Q#QJj7Q&w!A`56yuD62D17oSC)Q(6w+RD< zZjcSDb!iX?0D*1oEALkl-YUA}vgEQnHIw*|67H@sW&w~D^oiA|64ccJ*Gq5|M#r|^flF4`D?h zbM=3_C&%WK+*IZ-5Ei~qhxqpYj>WXOAN3 z01nh2uJ{_4mHIG5hb9js*McB$r!>eF=nfnhPk=!P4 zAN_yll(we}T)nGY4#;@$SOxg&K*-_l_Dg56V5f@o2 zamt1toshB>1KGM`LkQ8BUK(>)PhawjQ_{b4mv5`@A9@~<#`m-xl2U`>x$F6txeP}c zh=Q%65AMc*D_>4I!}V%@mLFg<;zuS;}yxos!}Srp<}xo=IsEw0F{J6vrchm7w zUOiY*qzQX_`l$_cgwZ%b6Aby0_=Y27s~|wc_wU!oZ;U$6<`&-G*adF+pQ)M?2}a*1 zYY%3`zazFKiV)z&@pkKZUemWe>!(gya-ERGruAy{QVJvAg|45<%3Z;6dZkSif}tQy znb6psmWFHV<|Gn<3IkfTVcv+)<>3F%dc;VHzR(&rN^C zG(7Hk)8}NO1~k^;r3RCcqDXqEo6h;io?M~ma;MG~_( ze$fr#D$$gPJ%6sq+ZwHgrIe6d&$K(1>AVwG)rRBFG zO(&FJM!Q_}`jdn%V(`1mO9^yk) z#)u5hg$@n6te>q@R!}pc-^U1-j;E6ttXTVlqh8(xfaFp|FR-E;G*xNvj0ccSCjz>T z@d+QebXJIneJ#0xl&l6++B)3vWKmdU(hoiOBR8b`mpRbt9eN5s7Ax(fSYakf!BC-{ zLAVA3Ibk0SI=|dG*(>3&;q@F!L{8Z#j zcYTjm`Fd_}H74xBnw`lxwU&xR5}^{$`%2qDKLSYHsTAXp&wbcHdUv$VGmvqFV|6{) zs&jQ)n_fIBttZ8{V*Er^GKbaA*7aljCO~GV9&J=apE=3eD0ZH}Y)X@-P&O;u8cd@$ z*tba&1=L^`=b|Njm%J%O3B4>WL5SISacNH+9kKbzyT0S9W#kr(8S+C5-or-h0Cp~) zGY%WPWi%ApHedi0VrD=8bo9|;!`cxCyPKJY*{G4TVf?Il;ETw;p75>o7h-8A_A744WZW_ZwxSS_vL ziWuC+rSAGdip7?n8kfO!D-a8-fG>_qcRe36z-kR9aISx^eC;DkW?p_G+ zM)7Rv<9I1+6FAxvx_DID;-ht!72|OCWWz=HFr{*Wl`;3vOhdoUaf<)>tQovAzY?MJ zAVqY8se?%agY8QbCg<^Z(jC9~JmG^_nFE*YcR*-|q8}el2u_6MV`d|@%oqnNDd1jS z_23iL?-tq0;Nm|!F5LT|(R1i216Tor_YWMRr!v3X#gmf|P{Ug(Fercx<4vQ?dJ2cL z@D>Mr{s;KWWU{j6r?atwbX^WSs|I^y5~(E7XWl~(DW&sjD2IUB6Xd8D4{ZHO!x;T& z?-4^bn8ak0pe}>(u%6yyZQ*y}JEuA|kHD#V;(Z%rReE&32_JaMp7rJ@&`F|buv)Y# zI&Y~c@256QelE~c6K@~@LIZaddc<^4TkpW2DU^ESWvuk%BC$hB1|fW?m_s z$%qH6w!C?FmBMj5i{Nt^x1VgwdB7MWY+t%e6t0MZQZ)o*dYsP#e#bEpq~QQiiBsbS zsb89c`9m$;b-nK*B4rXp) zV28wpS-Wj6_oVMsQ#eHvP}~YTRlO}aplzvfQF&T=#&e`W5?CrSr;r^sUcs5e>3 z6c)f`N{wfVDR&t49`nX&q%s>7z15uP%O;ChUMFM8aIm=myWZ-52OKsLz4=9N;J zP&`DS(YA&wF_pGxMpJ$TFm-k_7FyXi4q-Nn7#0};iJ}*MLnX|fF;F@2J%#JM)uLLl zxeSVWx!&h5CWz1)DjI>20PwqFUM_fGsH*xyy3|wwlE9CnbBlPuo@1dTR*OwVhno=8 zt5?rz9WTRh;*mV%2W1=Z3aFvzdjVD(i8~!` zz~wcHD=DlNv9?x-o@Zck(c@wlp9a$Cb*0Rd$-Z>SDjcbJ9U+Rakh-fba~^(rphYi4 z$rsDhug`ank_{Bf;cHqDzhg$zbrcOFCbFCmLy>Av=tss0M~Z)@i&A;9jK}}G9uow5 z(_|djT+;rw?q0czrcn&0PEO-xLL-#ZjnINPUn8FA=H!$VoXV*;PMpfAQWWFn56y57 z+V<(Q3vUO4p}UTa>@QP^KmdH3=r!T?Cv&v(EAZ3d(jk<5p**_+a3ZcGcX6*vnyw$Q z|D+J$5_`=-0;hyh0D*4?d)&AH6t&rquD>2flv zjQcbz_^`i78i>??rz9<+R^B(~2@z59X&}F0C%xLcN5?oPJz;a9Dw8`zoJ>XP`pfl*h3rm zk?JyYBF%@M-ajfztw9`w;efp<#!LwE!0$a}c7UDEr6G#HhffT>uxUAv|7EL{yCRkjnxk%<&!53F zCs66ao_tY+nyRPRx{b{*-!Y%a3^G`ChrtVo2-ycX%|B@$*Hobcm#}CK3ZjU?A9a@& z64XhFbJF-r(#GuWJz^cNZ#xR}Y|)Pkow}ZZ=SWz&nY1L^m(#m8KX`K{n**?Bn(tzqkBt^JHBnPQPd!Sk6ABREcuZa zaEfk0DQ#q&;g|%|E6PVilRm8PS>$~NdpIRLKbTfGq9O+90vUS zIG8Tt7p?~Y_Es!@73M)kz~YO;@UbUU9XN)}dp3hf0sxo7U3l%0Sa3A;TIL@1)|EC!imcd^N9fz=uf+oEdXui*EJYV+;tugOOL6Zo> zUZxfWuoIY?hBDVATu+oKurlYE{N|aiF)8A_sA_J5-I?p z@ItKbGW42>kwJGhTAPWS@%6NeZEbV8}GYP0OjqnvGDW^O8CsM>)m3EPu`1bvfxt zkz~-KQJER%OKfHbmk%*kZWJLW@5up2@w67Mqo4l3VfbU=flysjBDBHHxo=j2&{RrE zW;z00hY+et!IV0taVKdteu!!O)hTW3-ZRE&9W+RxL=SV~Q`SmUOIk~50(g){V;l^m za*w}%x~m|lDP-2@jK$f!eM$uEcLq(Lv0j#17=!W@wS)$TiDnm5%&`tV%*>6- zSZno+*s@$>@+HznNF^?HTFcP@_&B6M0%!f0|9g#6it%4uns6L$^-MwDL3Q%C)j57z z0w()V1F6GJ%{+U`*3RPAsXNQ*kw-eqmzbBqBZ40%#A-U3Q2b!ajx2aV2XsI>o5ds> zietd1NJ$p)Mj+`zb_3?R@q?MKaDm3CEz44goF~ zAH3E{pfW1bo1(%^k;T!O-lQa1=2pZ($nJD$s%sZf)ORUZI)EN~!J?SJ?~FxJ_Y_$t zy-$jTyt3jg*JtnFz61I11?TKZI$dThK0Cb;dF7JYx>S77O3^||W#-0isk44YoKNu` zu*y@qp;>(gQe^Ewr;J&E^K@Ja;5-u^f*bTKyBAMZ^%NV=x{o z$Q}iWek(FG$b0phZq8D8)P5uTI8Q_421|#UCLmWGK0dywH^BCjR`}v~O6$@k(KJ(v z3B$%e(Y0r4+jPRq1RlC0!=KvD#)nYWP1QrAh+Ew!Ucu1$B`*}K^aOVNCY*t43^F%7 z^7D$V`80kHqj{oBLJKCXR$lYtac`N2s+^eUtu8EKC&5O~=u%9mP}6dgN8W)>zt)Rr z6z^Q&zu)W(ESJ4>OEplTw4eQL*yPNZuA?=CF@CBEx7{$Csv++c*n#rsPd$L7OA?E# z%;M}@S-IBTyqz-=a#T_i1VExcdtCF0!qTwZ?>1wG#K^=mwkABur)qvvDj7r|l}E59 zj76kMR_6*Tc$^);X%SG3Hqgq;%YcY*IAY`I7=pR$hlR=6Qj5}PtK3{X>Iq+2tHCEaWf{TWHCNi>1j}b_UvZ~B5KHH4aK1S2-r%TQa?k#g|()1L=7m||= zd`d+J33D8?rl6?l<~Y3yR_34UPsu`&%Mz7Ii>}FcU6WPrrkG&Uj!Cvs9ggT}IO98} zOPya=<`iKy;Ki;RgOyHk{*)x2246WYs#MuW-@Eh$0hJM>DdPsheUmj1)OXGD<(7x$ zGa^E$Qquu;Zvg#!4m(LGzHNp^VoQ}mf zJjvVuF$^;^hQ~^tteN%&o9b;cu3QqoU}C#e4%xb!3TXfVTeW0r&_T!N)J|-al+dXp z;m=!G^woPMEUiu(m5yPf)89S3s>^3g>uVjf=rrD;THGrsCRO&2i+t!=rf zn9I{6&%n$E2Scgo<~`!FQ;(^_**{FjGET<$6k`Z+@QT>+z+RHSB*E+02UE~O4L~y~ z!U=}xx8xGi@przcQ=k1c!iY&m{%y-Z zjhi$^Wh+U}f}{lFitS{lx}Hvm{l3;y_rp!ouZ2hGIBHbo z^|sPRi;r@XEYkJm3n*Hj)0UlvkIT@(rX#8_MrejOb&KgSJ~r(P{YWOiq%nQ-?%uhk z9Sv}u#<*Gs#BeMX)gnX5hg{R*-7|rmxORL?>6q`m=y7Or&WpqF*0OD56X=M`9L8T? zOnv!A*&$jwkR{!SYhlfSte(+YmXCJNXVvi2A=zZL{G+mJ*6z@9mOq`Y(p9GwGjo8N zKuY>B5xUFwNK<=17#Sc$-O@CLU^-S4^|ad>ls4KESz=`fL9w4}BUi&;{<{iIKG$u` zH-II-zg`Nsy*on=s9>Fhqzfm3#_C~4wJOu0Z*7bQE6kLN))VG9IYT=|oRA!LSS6jcaf{{iL(t?XQj6@7K`EI!P9G+7HEucH7NcTg|W~N z!;5WDygAT~9nNLjZCGr^rtEnKoyfg7f*5j1YB{^NYNTUnpQ+* zwAdlJ^7(Z%FkD2?$VSl1JS?JEZNaY)<1pTMck0V;N*KS03liVB@sBl1czs>MLu2ZT zwB?pST=EdRM1!2HJlC)QX?(`gW{;e~HiRkMtVGE?o`-(S=W;L6g;7lpIg>4=g_>q1 z7U3+{epnnprYAPc)FK%N+3s|6{;7~Tsr%>I=uIMMDK;=+pXm_feHn0itME9Wjo*I< zheZu%!I{O#>-xX7i?Ll)!L6mG)wHx%&&L|??j>-fa+qXF+S}SqXkm$zN5$qjTZ%uI zkNq)^Ys7$g@Q0+IdRi)zE{(qafLz?CD6?UU^UrCoAq{KTooK=DC3X^G{lq{GOL zqFM}%;0qCbzdP4lOK;qCtJ$J$5|5c>fEa@}GQk=vcNJQUJV7SS zm^?Vm=a7GBTSZ5qM(#DMj5O)&#hA@Im8VtgY}4GeY<;N6EC#RRRUgg?TkF2%<|qO= zV5%D;;9grN9;4SgsuDt|>GJ4bHR7XKSdq9&gRb!zX{9Tk&h{WteG8SBUpwqu&nh=CSGd~LK?E_Zl7^@aGd zMC4mTj4lx$SZzoXYhufaWv@~SWPL9kgfDhVs>totfRR|52>ha)$Wb;J=kEzJo&I%6 zTnCzXQnoAp+ETqvWm%f7{RE(v4SZ~j)#GDR!|L;Haf8ZVD=6&(-P?a^cc95-3hpBw z-1;`T^`p{pRTu*mDt>4+tCkFj-iGE&q0a~MXeQFxV%tO~Qhi3XZdQ*2sQk*0y^^epm2WU^Q;a`Ktyn&#gnpsCb1wuVcEVa)r&HHj8FF_y;Q zAg0e#%kCSh^0h`+y}v5O4EaTG3>z}yWfS^Q^mg}6jrUQiJwZ6gT3q%$P_zwd4;O~8 zta}qk@=Kz->(b9lgo2sWzV#2MCCZ7ja|V1FsE5UV@1_0#S03d}*;!y zpEK_pn#K;Mca}`2qXiBcPwWvc(J? z{PU6AMUr-q9O})K?N#W;Tj&t7e}XANM(|(#XTz1d!~_s|0sWKIT;z(K5*3WXA5ki+ zOAI=a4`~M3s511ch}_WS^lm)x4K~f&Bqy%hTD^$Ax}g8(U2*Ig_=dNXCJelE6TLrz z>3#vnK#UM^3!L$cMv3BPw3Qr`X0VAP(9G7wCyYwd2hr7qHaGty#H_R;`aiT;(OZ1) zdbLv@6SHN8as-%a(wl$$=2QD^imj#qyI})UscBeRRf(3tRP~QCr+ag3t-50YIS`5a zqx!LY2q$)U$j-cEjY4kkPs%DsXoj6g0beZ}1&ROfn0)=zs8>@r{=UX-z=s*!ORH5P&*^L54%04jXC({u%Tck@q! ztEo`>|G@R1%dO&!Mu6)*4x`$7-1ij83(f+ZnBmB+5p zUzPuowU72wf9dmLZA{wqpZcP(8$JM`FQ*WUs~2a*M%^cCewezioSXBCX|)n=qmW(h zii3A^#bS2H8V2@g10-uwnG*z!9i$6*%JJaqmWZvp3Hf?0h9E#?;$6VeHxdC>$~X*I zQ$Q%EMm1>e)88Q1WrsbPqO{4z?FF8*Yi_TnmL@R|gv9u8^0dzxfMHE?u^WmhHO$eM zr~0s~l7ehJb!V6@{m1*NiA#Z?MW2QbDk2KNY*WRa7*&?A8ZL0{FPvn4dlkboBO^2Q zjL-6aNfc|WUUL#`XDf$ulK-xuo{Ac7fT)3$)d8I0kk3)C!J}n%iF0hPSv&Xzn;S7G zXaR3IUX1AusIbUIUn0O2u*m;yHw|MWk`1oj8N^!c%>xsjxZcZUypzmRT?5fdvqcyo zL{EfI2HalbHENm55{2VqdIuv+_@b0UEKkkN<9#9o*_i3~ZvZm`b)xYwlGsCP`HGnd(GLC2sl= z7^o}FZfdSQG{aWfgd4h>AfI`ypP6Xw4PV4Dg{Pxp6Ec*jAQyFCzr7v#Rv}L;Y-wPs z#Uj9tu)#*{-aQ7!FDYj(>7S~4HMv5vwNZnrfnE2>5`fXIQuc4=-cVRcBJ706Cs|Jv#7KmaP&&!NMSG&*;QZ6_re&Q1uEGx_{ttDTHg!PAU~+ip01y zN;rF2y$;cntj`k=XB>U271sU4%B^0pNc^vJ+@?`Bu1fsRfGh2(FRypT$DmEcGy1}Q z{N(>@l-uKhH~0r%a}$cGgBJ#yvMSzc!Q5QFEd3x}(!9trp!rr>HdH|gR9vz8z8?Hh znhmzqOy*!{C+-YXq?5#hf1mzB7mrd~@n9SjFyJEAGX=D8>R09XrE&dI9CS#yoQe?D zAWZj2SYfo&M=4)lNRfYFPvsf+0Jw&1k-S8TF8S*Nb? zq1WT-eF$T)d*2{Cx!_msA|c1PFhbA6WD&4gEsrmjX4m6T6po&@i_G?o^O8dlkku$d z{yU(TE1={DCA(nhFX2+Jv~|k0I4WMN6?0&Me+|H#zoPhDH6s$0kzmjLbj*8zfHT+R zh16G6=6Mo341V%a5M?}<$H)KjElxXd9txI43{Q(Flo#1NKDLdDlAPzUZw30t)zsMr zNbmLrIh*jysmFb~KRkPuEOH&0EQ3{)CrqpnDEW23$FDc-kwQCDU+EurKA{007A9`W zq~`EKcaL4;JC}Y%c+c`hQtvpG*_c5f=0CFnmKGwgn8+1mRbL>lE__DJl7O(nfG+ZI z0c=L3m8>zrj^I*uve38gxvr-HHK)({mHdS=Yy{IwtRSMOJIespIqB)~kgv+oNv{lu zv9q>c_$1P7tV_#;P+{CXujM;hwQXhIN^?!HDk5by;d-KLOtzk0`e^^bagh4)3%Zqd zu8b`)FJRQ`ESleDEToI}gb9ibJ088w-WSJf75ksbrjqx@*nq9Nhu2ocoww^ICs3nw zTv_T2+8{?AJ}o*W;PfC`hnl`6_wYKls@yI~g~~zBe-J_OmM-2fmS1pS4fl%E5~EB3 zTrN2}|(#WD?V=ycG;>gbLu9cIpNFGxhz>2aX#sJDhBxVCv+(4?T9HuHJ1v zqMlIi2H@5Nvq9Cspv3#-<-!D#3Fm~TJ8W9&z>zjngvlA;+tnIqH}DEKpUim}Nq0+e zX7`qb?9;Tyhg-ju|44VopMGQ}`*eGA>2|tKa`xtY`Zn(Q5+@PMnp#Gx9U4*Ml+-@G zRH(T|<&TZuaUwu(^4}Z~-9B5b6Jn=;S$C~c)e;l6EbP+He3E|w@nlam7C{Xo@sq6B z;kj3`thDX3Zh3DF?AM$!CjI{SoASDMh}1R=*?;`{`w;bbBwIBu(nw_DziLh51k22m zxeY5BE1$7|n3tMPu%;mav5H9J{Kk~SYi`%J6&bX4>VU7Rt)$H%j{%Yx_bR;RWy<&~ zY!26-ztPSawt-ixuYOuj@xz8yc z1x)08vw=MoEP&KTshI@RS;1)KCyN!>8=q`Xwt>jsrIi`R@e2&Bq0r%kl4^lrts=MV zKGZ$hgd)Onq}U}p>o)+}KZWx9oWI+cP$%~#cLbl>mJ0b@lG+;G6$oW4M|QZYBNhY- zt<=>1E8De!{nmI*EdNqWji;6aMH60AmpX>FsY(!fAmCM@{s+u2=Ed2Of$)|ioWevK z=ye9$k`*kwm?1e;oQ6hCog#EU;Mgtxmt&8~JC)lk6}ldz_*XbgMS-PPZ>pkw*v4nf zwsscA6Pb^|nd)o__N_U3Wo<8Wym~+Dge0NU#>!?2iWd&2=ot$yTl-9H>XgG|rTyf; zmAXb^>GAiuracRvFLe$1XyYd=z8DQ|!@#o}FK$D+DiSr!6FsFQR6fOci%ER_*m;!= z+V;K0Ef!Lhf+I{xf=`(a-}qj}Ke{C)*w9pyNv1Fdo+D{Zy^d;T zx80tT+m`klb3tl_ek*;Nhqxa*#13Ax?wbAiqD_qW^aIzrR~>vvlb1TSz^-B3rD?%U zduAMx?LAKtUkRjC10NQ-WbYmO*Z3^*zuayvYr+mmT|7TxbP3;V`VU(GsgCJ{>t1g*Uhlu6m zhLxyQ`E1EK#kX$OWQla7SULq`bQFX1ZH|DuMRL*pn1uF186rTkOrA^PMnS);NC0=N z`MIL1uSJiI(U2LUUbeE*HS7GD(2m5VM_wp0y35q1AXi1W59SGK%WM{xhGY6vK^851i zh^(nn(y)@uNuI^?Li9B!fmkHI%&mQS+NTMr-K{}+eJPbd(SWhfVLVcEFZJZr&k1Gi z{l9AV27)$Kahsic_X57V8at`YX7NHqern}?WzlqIPdaFn-S+5eQ5^b|mOwTeCtnw1CdfGlZ9elHk$!bMra3O}%?d=m{XNL{+qul^FQg3s z5-Hw0Q>LSdp!-O6Wlu+zoac?CIO6DWClVGGmg{`~{v1625kG(P$LB`u)L*LLfr#Fi z!LeKJZf%gsrS%(3TGd|*&w?FO@=<{4L91W6pJa_C(%!FFRQpA|Z6{amHSNJ;02JtE zKKb4x%U&T{Ih`pgyT0W?06F`W}FdQ zP1RtlBT(c7d6gJZ76~TdtEotjRMNB|{F!3Y&ssa2jip>F%DP}(ACG*75*mU`4l$LY zvMQ#T?(js$E`-_|azyF)wk!h>?otqQx_k+L86QwP(C5_0oc{EjVPqaisohWedH0{c_Zx9%%}R6Mt}=;= zM&u;>pJ4C8d~2V^#BwSL;nF5etd-ByYVE)Y&VI$Bqi^~<6Qy?P%YVMr4MX1jYBxXl zZ}LHlvO#%!qrgK@!*B9K3p%pIWb=b{hSl4p-Q|_daH*GQ+QaaW_ToRT)&=vbEX&b% z^PvY)r-T6uVvFJQ_i43s&m{db`oG$zUoMTw4#GXep8bTks%lL)05e;3ayb%zL3p() zgfgj_GbZNiPh++kmJhr;&9&q}ZD#_Zud6$8VJ;^i%E1u!u53cV`G9xbGoO8`}eb3-!L}A8@!Pn2f<88F?6UKOd@vJJ+;AHYX7PrYF7RRLEzZ>hPk51KSL$kHzla-=!5v} z1M5#SLyorB*`jDjRj5;& z;hL!=HQjdl9JI3A0GaJm5EfPTD*qfAHIL4*kW)ueKPgMLj4qS4X_~YyS(IJXYmEAo zZBanjp}7vMI+yHJKD+t4DHvWWm5cN&(z6lDRy9PCCw=vA>#sElG5`=t+X4X-(=Qui z%&`S7p5>NXFUyla5%F9?)UjDZ7 z7ipxE%g$Y;mT)+)&eWB?QmmzTLsdbpOh>`8%?v%dTNg$QFasExE>(B)aNx$ zMTsyETMRNI1cb`g8G0%=(jKL?Xv%?>eWIQ?=AA5 zl}J9c@)w1btE|yoQt2m_uRE3)2~*Ga5_z)pgVJgil})f&ziX6%xH8g^l4ARbG~uh$=l2$V(zlnt%BMc( zrJff?SoTr}5`y*OSC~uw%*Nb(8?id3kuPNu+Ze|7#X5q+7jC55r#ck~8w>O^`kuMo zgMFBs%S|wMV00=F(jf#PQTa?l8g5%OCV@*WG?kjM7?=gFdbT~cJ&hIMpf z-S!Q;Q2raLKrR6iOQ2doB7%17)wFZIxcQ&RR5f@KDRLX{9F z`MhXjy0C@0*E_k;ud7)XR;*zQht`SbN7tGhtqMmiCB);zZt%?|AUcP)^; zr&D~{OYzYm2aTVJhGI(x*;rC3{r z9|QTeNo^sVAuzDct!yi|W?wRJJ)^JV#FM{j?i8mb6q`b*0N3*uZXh0rO7>A>d$Vsp zQ&6A2)sJwraOT+ia(?5NkozyYgq8Zi^l}xUCb^&F|DXZ#u@xP8dzM{zp7LO;d_;%( z9hdjz^LN)An^5Q>s_h-q#9yD+Nq~RnXXb5OZYJgu(xqPpig<^bpShk$se|{er8d0^{&efSO z(zbhV#=Le&yYhkf7L}R^6E(8bfY2u0_n*2@nR)Iulk;$4y(ESpJH2OuP*maFMw!J8HW*~I893r84+Tl1=Z9LhpSONKf4GH*}ce0;ux01Lzfy5 zqs^>YEI|@D1n?kvw&hRz5Y|^9h(pycT(PpU5ji}j`3okf0=C;m*^+0sE5iZcAY&|@ z{wVM<#T)Ng$x48_WK{2%Agww;(8tKk9+r=SrV_TeEF_(waRgcG*0{8G>w=~9BIoN) z{s+!~k60f>%8i@@`%yq`OoLqVb#QV(BJ?!(Yb;m~5-V{om#M{PFD_`LX1`+k-9`HS zizitLBJaZgIB>I@r{{^S+sOEgU-pjn{+uGs(|CHRN zcYiuL2rV2ILJYUeS>0Kq>Cl_sZax3~gXN)wkyH)p&j%TKjUi3ZX3o0Vst?cQ*G?ZX z5fGkT#`M%mmaBRndcd_enNTK!tPs*QDQhf$)%7Sd=Sz0NQ=w{952V^||40i$ZyC-wICzbzn zzdflTB$D?u)aSz9^OAxp8X2Wy*#H%X?ghtjS)FB8*jD_VZ!FYISWlGMSeu(k?!%YU z&QnnuluP}t84orIhYIHijkh3QPVZX0<3#om5#mGngUK4EKNXFtuOv6}e{r3fTc_2H zP>mwBy<3bv=`qu)2fa|7vu>KDR0PHUt;|;YIq8I4-mD!EIgmOz3J*!JKXfmA|9RPO zmGGxnf>d9ByYWvE<+w;_axbilEiW$Hw=k-U69TgCS7Fi2VS)i?U5tMy%=Mngqj=iQ zs}7Cq2wJXay>Q*LYKwPV%yl&zUUJ6S_R#DoqLa=b!l!bM()^FF1EIa?TG^$pv?>{F z^CG#m(rwkRUUz7ux3H;f1y&BeHwc9b6GmJ}YOZyXTkLcH*~d3{<9^0gQW35>{#>{z zTar>+B?BTiYAf0*yL~dBoH4LseWOt6l4dw0I;=Y&2wCrI@%Ra)Hy-UMNZ##8sL{hO zbDE*?(CY>@#kfDo2a^C>>wm6u7iaZxC;HcifND>`X6CZ{1QyVgRTiZmyip^5G!|NF z0~6C$Gu*7mHs2N&9<_Cpm5h$o@ziX2?29uLhOU1>O@2Wc5E2JNR1)vg_HKMn>-^5~ zob#(WSD*UtU_5ZvD1%zogi6+4+=)iJ|6dS$3C}5b>rGzO^FjM|Bf*B05r#>ofx2G* z^4`R7p@8d~jrM{EOujZ%aK3a19U-T29RT;5=J$zsdj6|MdX`#1D_xpv#oRgfJgfD= zF+bkC^pASbPn9FoH0}O(`1ef2+WV9Tf7ZSLotCWJr%D-gj~*9Ze+TV;AZU()D~dl) zW3jCo^ACQ%6hi~aJl>oBjLeoLG(ZRf;MXq8m(wn1 z${|7sIsLlBsVSN}VD;t3_kMco`CZ^Reo*|;)Uo9Kr+f@m!(+|wpSl0Jx%mWf5(?Q2 zOnREm@Zel7s>(`Mq;p@yr|KS;q&a`_zj5_)$ZitpV31~ru&D|YCac@BT@a~VjdAu->QcnbaE!6b<)z6rrxm5f?&?Q? z!cfkiH>(A_rV3xct|B#tvwHx%D^RlEG0#u0EAE7YCZunok$eJb^82L~jzSi^mT#uC zl;b*H=v=8yUH+gZk$aRUYUeml^CjjZDED}PWeJ1uL5bIMExmwekVT^8&~cSyhS^N- zQNqH_SUx$DfmW3kMbyVh+jo-=ZIe%A7Z^nI5lu#ejYfkQ-TpD-JEMS#d(p0vy%cXg z`WWfg4vBAR-4QX0`(i)oSoL|%(|63(v(wz6X(_wrIRfhIWgpknPvU85XSMjfYS#C5 z#R^Ugl}dE5w{N!)#EeO?uhSD8z_aN^@4p}vk8iPDf77G{&Xzp!C}sAf_5CDOWU!$2 z)}%MJg#gphpTiN@blZuKU(jQt!wPJlq2c5Q(I*-|V#e8${Jeb%eNIm6zsIZz zGW)%@&mdU0hkDMj)z9G|B;elwncOofzdG$_GS7r;2E|Dye+G9AeZ3aqsQrdgjE|MM zU#?{#a6en8JcW)%JNm1A?%ft>^*@$g+nzLWbVj@^3$=AxVIux>!ET*yfT+#8N!zw1 z+jmPP3mk`^o{DA0=p*9w?Ufn!S?)jLHj zpm>W1EyapUu;5Oy1b4R-mlU`E>GyZ@Uc3x*ZeS*J_Fm6g>yf=9?^K$3tOqU-*_@nNT=86KWCky&O23R+C=rM4YhI?&J{#9Xt^(aWC$HP6S3hmE;v z$1q*4h~E^`9_HVM&HpdJa{^I&w}?0KhlyJL+Bld z9EpI)i^7o%vF4U)SoiG5Zv40KVQjP~r>!*BpY3?kxwRNb9zqm=n0 z51JNB-@w}fIzs#23w1+Pqd2sQxz&?vYEi@fQO!M zqsiBmh4)?0!<_`hoIvwVlM5`rUMOL*Lm55cuLSThw-ViTL^6+iJWP!4_@-QP{Dq#? z`un^E|2@tudlbd_J(kj%kdOZa*naBI;Izw_d7iITMgDkddX#wbSHXB7eQeC*mS5lJ zamm*>62gA|{{5t9%}Gxdzs)OuODZYBKRcdyivx#RCxnVQCx9XG+)dTz@(&3Xo@lR@ z=sPw-(OzYck|eo;{+6AYMf|jzpnI8EIn5MqOnpLApCwzr)@CMlv2X$-pSKfWEodgw z#ecnF>A<0r^RjOmhA4mEaiUNn5e%1cp_y!io9E3-?aumFm~0L}vA`y}`@UAW` z1uZX#rA=xN+l-5g33V4Jzf{vTaBc8)21kgU@g4(xD4t>D$>KgIpQ%Op#I~4mhLcwp z$q-Ol%P}=sH_3fF1M>3&CpO@m1Emcu@y?ufH%R-{IGEP&RmePWc?B^272kgHM!urE zZk))fe{1T%d3kZ6^CT!Cy{`yG>gVnM0w2?bO2^O7GuoChT09Yn9`6zdpZYoVZ(Ii_ z&wzZGk5Us~W@qGV0Rqb>m%B`Rx_tQf=zvC*pmHv)GZCgO&S#pNq`2xQnK6PRbWyUn zTxlgw)yO`SSxMB$tGn*RrXf9XES}Sd$q&=FZY)W|#mDup;+udj87pX5U> zNB__h3Z)H1sDEV6v1LzWBvE3Es2@=;?U&E%m2d41zW8&iB+Z+OtkObw7G{FkQ{}%i zT^IH`ve8OH)Y?99HZd2GLO&86GU2;b^bAj8~7VviF71C9C1`ZPHt(&ut ziX?kFv)0=Bba`>PfLJ8igTE6S+tVbAJ&%oyZ!s4*To+r1pVo%-uQP%P<7|BCCD=4E0a&W+<4~899wk?Dl8>S|I+h* zC6l2JfnSNN{!+2=AjNJk_T5q5fr>3@|G#&F#>6a=KC{_#9$nVx(OUBKb3P24@BtK{ z%EI@W5OwxKg|Q&AHPXC?jqjevfjQ^Dt=pHZ8i?gD1Im|sKFg#%O+yqIvTqr%Z>4eN zM>?`gx{dC^^c+uq%v;08pu(zh2?pF-jl$aNCIyPj7GdLq^3jydx`$L$&tJ01pmv=g zEVk^bC@tS-i{)>8!Qh;mx~i)j&S$AbL*fEL-IjC_8v!j1Asvnx3zK;*<6fe@D$!_@ zY<8ew+;DO3XXEMlld8$6_!!#zoPCEVqZMam(Zs5pTK)lrEf;*&C3ipQ$rC)wb*XLh zzi~73o7NSe!xQM@4y`RjBMv3a%}w(}DCn>|VK9L}Z~Mp{>!=aE2-k8Kx4Zu)cTkpm zW=82K$dw^MNgsgNQp$zJS?p4r*K%v~i-O1zB(RxQ^Eg7@B`tOEAqNRB-V#oC_mUn$ zPi>QIZhY-G>8*6YA5B(7J^+iczvl(&h3pWZilR7EJ?s)xL!7FOoKHWr58Q>mDDNB_ zm8vM^O!nYR@!%wZ4R0~f%%XQ*_3hXDI|()IgPQjRn^-Qb9;torW_=+0MLhBHbbzeb zKsZ!uRRLm@BI9E>P9C!pr+Up0y*!#Pgf%7FT|M%(WBEVg2`HC!8b>~q z!#0h}`Zwb%Yqpq4A0vr+3TMzBHE7qluivggnjHZzrUw^cXBHDFQc$Fzs?A&>aUqrJ zbv~0(R`8^a$SbxAgx>E0%U7Hc#y4*&j%eJDe(<@Ip$4C48>eras*;-~`i|Khr>Hob=oh zaTJIr-~oHMIA84HQ;F~|e-kNbl|DFE-1Y3gZR|NW_NLCXSfh+HhiKq=;E!>Wwy&XY zV~ZxYW#CO8DS{#j6v-&wJ<6+=YZc3%Cf7U)i;q40W*gG8+D#uM67yFZ|5M?HMQskR z;Ci_7_-G_0JD*zbsE%b*R7sfU2G&njN#XriLT);p=kc5^qE3t6lS-&Rt&cv_Ue3lv z*ejs-jBpr+vSrV^-G3o=VuvF`cY~g}=0xof@xP4P5iW2_@Bk@^B<3f*&bxVw`J%A* z9k{~>I~vBsJ(2=|$?fhF#uW364^CrS&|86o+1;q&DL7lUQReok6S-P4T;KV0dYk*m z=}056OGoZ`!z84Jrbme=u!%*Vjom;;)-}B*%cJdIc|C4f``#C9a-Q2ng z7|eJ9#C17Y_916>ybnbV7WRUos8T#?t4kc-daiyff1Z1`-`tW z(;gq5OIB96sL@~6=Av)MsdzY%d^tm-6fu5atM~?xH?R<&zU8#@>u(oB$SV-KUrX7= zM!1CJ*QY)ajjYqA3qvO_|Qi7 zWXQ5MNkGY(jx5gEJHynQa;;`&-+gp9#|`UI3H?7QS7OV^Pm9x5WMR!G+)Uupk&~7U zI#wIX6{`88usTNzeI=i31SWdC|GS3V7^m>Sa-KWxW+V3cja=U-QOsAZs6C3vG_ikiUL0y9kO`49#-!uOS*IVXx1y2|0w$X+D9d#Kii2aAinrfQA55y+S??EzR)$^459l&1#dull@ap4KCG0wH^c4dcUBc2q7UK z7M#_lmO9qQl zNUs(L>BB2dPq&!?y5E9A$?q3JZdR_Vvp4#C|3?pdHx^yHxJQ*I+vnWDc)S@(=w43_ zaWOF&AM4X{49Y-PtLW+tOI9o%E+l#FZkgvCW3OL2qfPGWC1l&B>OnI{?NwP(%?OwsH>h4$31uuS* z&Itpy(x(Bjv?O|QK|$!I#~9hG90$YKb{lG2;khetwlCA3=(uXNWIRllPFRzRer z4Hi|I#NS}VvhoV2jrujwdjhMYtukSfUixDX%dw8c)ph^$ypQIN^|M%(+R5!86_R@- zL8H&mSI9wyg^aI@FL;DPBp_K9;g&+9!)Zwj4dD=!=t8T;| zn6?FnB!}KVGQ>19$wWn?^n8OYQdG81aRW8(85jPS)I~oW)1rTjt(#PLAWembCIlwR zri=p*5JAgxa~K~$8QW-Zs-M06tNRx#O%0OY70j~AkBbGO#anqp?ZpC*I!P)Q z7pxno<>esOnWTE#zAiR#Tb6MS;Es$^v6kwlZgqite?htJK@*50@S0gU^f@ur3x7`U z`yLB{aDA&*(iU&$!a5-UH30vU#>JPYVkLsJcf)mfI0>2aEN| z4{OSWIeJC-(h5tK&2l6RP9hAW%KxYHtkUgLG3qdjjIdtt*USW6vjXy#DzL+jM`{4mkO zX~?bAE#1*@j_UtL;(?^(`RaLaY~^B$*yAgp7AF;O!U+fzxO8l7&qvR1tCP8KBLUa1hobE#5PP{xc&T%A_SBA?kqmh2Xjm|%b2w`^zPx-8&=A_{$(kO z%z)<_ZX>UV{IR>;ew<(A{`J$tW8kB~xkQ6nxXj*XRJR`MW2Gsjh(1!4Od)i{6-7MsI!Gh;5wX7N?*Zx z1+^i9$tF=+pwAWTX(=i&v3z{F>sW8HgN6VrqgMQb<*#d(dD!KaO%(E%_>XA6R8_G5 zDTyhOC;UdGE=?eJHNG|(+Ryo43F7Rh!=dn^v$__K6S{m4|QF&L;8%)(7A z7VmZXvi#d}<45mqaN<-evyaa%i=>$Tu$z7EZ~+916s58`?p~i^>f)>mZ}aOI8DW6v z^HHPbPhV+N4xetW6LCMD5xVg6bdG44_GW>&fs3$Od|k3NGL8Ssi9+9>KVE5VAJ{8h zh@mD``|cNP6NfZ4*p7s-O;d2SeRK^yT3q>HH`ntf8JTUo4(86bU{75KoJjBk;_2Z` z2I28T?+{AZoSSZlKm(~BvUzfEU#;B{GJH^Z7rnB!ccBN=`mwj@+r74)@NkWI9{uP% zT4_OEOxL>yxn25K5OXAp(}c~ z6|g>7#o1|vr~8APJlR<&XtJTx!q!2Z#Ik=?cfj5aA*4^5ZAg1aK)jB>d+Uln<-pw$ z{fTnVBEMZ*%Ap3NKdAb4wJQ(`4NTW_?P)y_Ep2|S=aW%(_(uJc8+!#zJPTZ%0B%dL z$xX1TNTSPiti7>1-=i})m}=gi3D7YPDk+zoW_ZM(5%vCe&p;93<~W`3_P9I0Qm87w zyePi1AR*stC4y(~Y46u&`)V`o+`BPXyxpmMo=nH>t@#BLtwnf^=sB=G7tKqn6Rfqc0<)iQ)1O<+Wd+PV>UeyZ#+n*F+aIMJ;aPYioy< zEFGmxH{!)NqRKbo#n!FLrUoL;ld7LB{y0}sH&@|3D{NQoJ}T<24kS6rbM#JqSw#=sOY6=74KHiv+C zfNcsGF-*_cX}s6m5*(7zFyq5VO)8htST8)n!ozub3-t@H9~rs;`CcveMeg08Q}r$< zujGKiE}_GUle2|V!50iVhTGa;(#tCj6p$hN`F#up2%_Hz2H||x9(YFo&|8^R;`Psh zRIS`@``~vJAvyo0gaI>0r+s}m*|fYlL&u)_h?6VqA+HGLmBzY0p`)@fnz;AYk$|LJ z-S*mKn`K(m&984QPzGKczR3C>iRWfh(WOF4;&-wy9!`%w-=(QsS=c_PTT%-13oiUE z07m&94s&v7`_(&|E}JfG-PHxTIP0-c1&L&A?v4}brxrH0802OuRhjO21i%KD$|)}D z_x5R@hN*U~4m)A~2eyskR70_$68>T^XWTf0E{vV@#hhqs=ZZg)L0K|_w*=e^ar15i z*`L(~MrlbZG26d=)cRQoCXl~Gt=3V!L^(kjv-4W|c>i@*{sFF44I?vt8>15I3QLzy z>nI(S{H2uYkTqSGon#iTVv#gUvJyEE*fl%CSHHh+!2s_;_6~29CZ@RV#iUVC$;c?3 zUPjP4g~UAV?|4Q_3eRLtbTSn>nKODqgro?~NGLj`mveTf_b2lrz3dS5hgM7vR-meQ z#F+xGHLxg5%bnlxbc7AY#y)i^JJLAiYhw4bv5#`(5HJxF=vJj0xw~U_tvo#54yB&P z>H2OXJ>$DQ%!$m&LG2`y1M_DWhps0;P`VsVf6^qlF2;@yyk6(WF5q;nI65sCb8M+= zi{85d`iX6Bevlk^V0c=^X{?xI;K6nf(3~SuS}zd5zU@l(1Ty}>o6Z;RYFi=qJEXzC z99LPU{(++YKg`S4J)f(Ci^F3;sDO)&q$P)V%p{Pc+!b!4hv=!ji%Z1PYoJ9kIC{0% zYZJVEN}duW(iY&8=(=dI)jFaXnyJxuY3-F~lF8;CwDC#b#r1f8saz>OIk^~U#F(!_ zJkgoZK~L8r1f@@d-_1Su-k4f3JAW$4pouYbZ6Mhmfg~xe!)Uqq5Kp;>vA8V!WBKI{ z8Qq86gpJ!kC^ni2F_LPKJ~&31CO+%p7E+3sS5J(+V?H~_hcFBg2=oe~wc&W*1`TaF z=&};O+6&IhoI9A}?3$iaN|cO9*4gIB2fS?-3cmb6@WuF?w=2FwAWKkDK61g@gaLmh zQh`8C1{eNOM*qFFh*KOxho=nN7Two?Y}%@IdCy)-2JZ@`IE6c}bso2STNtIp`COoU9E9Haatl>tEVWdC}l^ zw+y1JG1eM*?gEaNq6r7j(_kG+_sW?yHU6I95ZDJbwfH+G>bp97 zfW=~d5rp?mfWdy(`>%kvwy8*4JC~1bIC4fK?o1DzXq5Iyiabor($~i=Au7=}DMjf0 z>88cGU+&<%!Gkk)$L0|w>9J8F#4xd8`T$HY5$rCCJXQT1DB5S%+CLo}J+edsP>nav z{Ju`}U#TDLN=&Z`qu2%^L`XP6}Er~N#2GTTY+6| zgwtWe?5r!Sdd51aq4(OwD&d2^b)*1Vj+83j0(1|guJU*_SMH|Smd zRJOCz5>kX5IURU64w%bX$ZBO$1)w`R(v(|vc<(H4I=hp?Ld=A9T8*8LXrPlY3 zBv#{>Lpr<}Hq|OQbuJgDh$RDTASPX_$r+R_9-g5yM^1b-Q~>!!Cfl1e)&9mNB{g6L z!`qsWdkqb~dxxM4pWSEgdJAo_)%2yjff*)5v_s zY#;Wv+GMTE66%R&8iX(!2RQ3BP?jAD8Z6k?v`tvIFH4O1fJ@SBEkygBM1~f1Qh+^! zdW7$2y^u@!1@hO~lW-W3Jlp;+=G^!xMfu|q#5Z-HzqvY5xg3my@|YDbvt&(h6YHz< z6jw&Ov(f2=KZ>zR=;=5-6pv&l5g5%j*TKAN7ZOq(Vto$__0b2uiNAxL=3~@YfGgkB zi==AFUX?3sv;0T(e2bqhOM94!l~jueTWRo$r~qIfk8}?{$bs+vOfwJ(`+8#gR9>^O ze``2UHC;UtBcS8TO(B8R;4u4Yud7J;i<8KeOl+8i?7Q%pY*I`2-~H z?OD9j9Ut{wTYr)hYzfscGx|AAd3=!J7>K^6@bQt+MQDlilV*!|r&eS!5YJrYQI_7` z2V68(Q|qNmRrB^Dr9Ni!NVvz<`6sRfp>WLG>jr1N(?$xel8bmwwu-nDA}NUyPNe#l zt`fmO*`3T7@7Zmi)HPRIKnS)WLE!Z*LHp@nrfjpcHRFbv%hraY=ouI1 z)4l^PmkQd|tH4tTU^zHhLA#;Y~v*N0p%Q2YXPAII568MlIst4yPG| z+WTT*U$1#zSBz@XUr?+&BF+>Q}s^t;lo*(QUz>3TkvD(M0d6dB-&v|BgOp zlJ2(>qiMZQQwMlVsBnUEBFcjhfT(T2+q^gVV-%wY@wD?1(%b_&Y$K{n-At6lcKJAl9@=@ zMV8yzyM0_;kC!qibrvj~e-}XbbK07QQQ0PRi7_YTl>gww?kb6iHk^PHnYVbS@R*4y z@FlL|F1I6RfP(zN5`}b!Cx>U?6*M| zz6&{hjNAX8<9j@xR-OgFBzqhpg88MPeZ^Y}=M(NRZu^O72|XI7kMOW+9z1ICi`G93 z3%rLaXY)vTM&^X*~=WOlf6{X$$;9Y1^Qs1@lC#0l9iz_AQ z^DOFRIIQ~&<0g?Zup)D9z!N6!7aU#+OdoK88`}+0)1g5wmB3QB_MN{AIBkxCGonaT z61Ro}Bj-HA{T(~z^+IE_m@}Hy>b)174(iBW#oN79BG8Fqvt>6dRJJc1B4;lU)Gqi2 z$mU}W6cY-$S; zwpV5x@sco^>95J6ZDeWVe3_ucknh2)k_o7$Wa@vZYTuAdti%aPSZskSMPoEtY~^Nxyl~UY z+~ey5uH_ck$iWEvyGH|Q2z2VU-_9TbkE!WTse0e5K2e?(1Jqp|FR3nq`D!tdBk+7c zz$A_1WH9UX{qfRGi$55GyqE+1zkgF_rq?(7II#!hLDgwdf1eC^pN`LftYT!9rNEAmX(H&OTe)7ObOTh z)`(r z^jBKCg_iv~I%<{3C~{hAdQdsy-7J-yTF$R8`xY*)w#9H8+X+2>Oh5#48f$*5=%@JJ zkBcw04U`^LqIYj7TRsK=7hvK)K_F6nuh*$G%+t2!;fAl&*6soVT7n!iE)EYpz~!QB zJC#IQCI&dgnb91?+?@J~EMC(->5Hc29zNxRcV`r(86W%lCxv?h6ME;w(STvG?dqQ^ z=A0;aCH=N;*~+!O+pKPA`CY_asEgv>WI(Mbu0}Mg$`>b)GMv~`09Zr6CJ$r$`dC-y+rKi z1f|qwe%L1y(7S@9LM>$hfn*DR_Mu^&aA+~-mKMdz#aw0hB;wpGqr4Sl+{{()ZOkIC z9NE|h?Il2^44N1eyPY^eAahTa?$g8^bq~w*;mu}S=SIo$L=eZ4;Vl7eaX*U`FgFt2 zb44C*1uV(IDPoCN(O~H%3m?!3Lz)?_CeEbz?hM$hhYwQv)cc+Fy;u>Wnd8yByqy4F zbqRn63M~KG64$nd!O{jHpf|G9h#<|8?B@{=`Hn`*nZfG@j@murQ(c``eQ7))ui8($ zZ0;AaQ|;pW0C+XuE{pltohxi6@&%t=aok>Mh<8f!-LObjO1(TUlHS3jOZl{Nhu86d z(IEuP-xrOcn>$dU|II%9at;R0OkqB`UwpWtg-z_A3IINC#ys!~3u)11-%aW5#Y*!) z2CnzFuvJ1*lFMXLZZy1f2q@fL4LUYl-8CGJ?Zzwic?EA5!*2IsD8Iu+&e8z2`_78&Vn#L?H=K z^1489yDlxR9~dtznpUn~J&po8*#%v7*f4Q-fW}a^zrpMKy3LC%?a1N z?|V@C2#m)DRPRM=-hQ_cJoq{|_VZrkq%qtgEdC@-p5OkPDn)+6 zi=Cu*qSOo-k%=RHe6NTf0gaop{@QsNqXW9L=}$(j8s#+G{5TF0I1WpM1GaMC)3OkJ zQi)bBp#CnC&jnXcRIr~DxMy{aT3QtiILJ0g%>F`u$OE}|H5IxA!-oqzCrm`7Mz%aB zRFlUi7oNH-ub{45C6?P8`m@fyRi@fRs&Eiz!^M#>eG=c(u2+Ryr-&?SvvxQT+pene zk5nf7B+n-KbNsGf=_A!)rhCU(7t@#j2%(Kcx>K5|pEO6JKQ&tnxvmp8bL4`?a9!G< zJd*riEkY#lGWZ@2@K3MGFwuD6ULQp}`kKqExgi$sI1)ShcAll;7&sPw+QZ3k(48u~luQn5h zTD+Vip<3ZUpf5MJ4NwZzHwL>NeGQcm8ktB%`E8Gj>m$_|l)i|S>Q=1GZQU&ZXlzhm zNl>O}>gpBHHWAi_iX+svx*~PG)5Q%ctDDTg&UuJFy+rxFU%eHDgTwNZ-HT3faMtx4 zC_?Ku(|5+t&dq}9PaW!Lri^&l^kYx+`A z`l}?Sg5wu{xo1n2a)P?8GmFx~*F7Io+Wwc+eYt4fykEhBSXo1E)>a|1$>q7F)-ZRh zt7j1D1Zhd7+;90hs_%h&jguybu-SBU`_O@aeg|NfdgF@j@7K>RJHlWKw&2R3pT$PS zX_kJu9l(_dupt`+XDT4K3}GJv+9k*%mxA3omg;t`Y0-1S`UvFlW`SXLi*Wzd7JnSd zU4r7E6%d65$K0o*IuJ)vTi^Rgx$O3)-|$|7g(;lMwswTiiZSXyOsp|mLo^pX;5Za` zT`UlII?vBAv~7G;cBKf+3 zC;aVyyX2gZ8x7{oz3ssV%r^&;0Bz<3tns(s53m5dL~%!#iee8byFs&z{6iepaZbpi zW-|4e&95#nTzN1}7<3TwqbB>CaKS;%+e5cCL{ znX#2>-ZD&@BccEk+jOj4T63&iu_&E~e!3;i5ksPKL_;_H18)v=+pe~sF1NJCqOO3! zh5toYumgm&f}0;iZ59v`s=s22I=c{JPR{)2yE4v;qhXI08=L#Zgc|%%+aMnrD%GDC zS5PVqleD$dEAooW99zG(uc)gs=Sld@>ZbtQ5TRe_tOU* zkx<5${;hlqVqD%A^K=EU6^n---S@$%dN*rVu8B$#&-yT_Jm)SMEfKcs`4fCvN}<;5 zF(taX!GBD`h=xxvS9(9j6Vzv;Xh+`r+Vv;a*M$94WceAOrY)^@k1 zLq?hFo7q{1sj+ z)%88-d%@EV>*F{opV*0iPYgv>avooSk*82F;=gBs8wVJ-YZ({5Xap!259mj&qRbnA zBinsH>nyHbth5XrwRvak?cFF!AFmfY4?alLzZ#yhSvFkRXfSK-q-}k8G=ug7imwl$ z8d3v1k^v_eEgT^=2kwtXew$$FiQB>qww)H)_$Pq*#jT(q*i zp|kwvrm-TP^ChBEr_tLlj)ezt+S5z!0evz~gQjN66*qb zTRHES|D%~uEbJx^jmu=i6+(Zu~whz?W3;uks)~ZlGz42q-=HbWCeQ?Az z-wxAT5Ft328`&lOSzw3>QI=$A$d;)3r?H}c+9i7GOcZz8anZcg{o>zAgbH?ku>PP) zt6+CxD#~~LloRgs#WsK}?$6==>0voFjnm}u-6LSY$0Il#RmpWa4&%r)E!Qmc+ZiUx z3ATl3NY-^-74R2s9rp!Lwwz8=RJOLN!vth88>_U|pe!W+i%PRhCj1%udW@EUpbVeo zmG!K>h5dcVE|sZvqnAZG2dQnNTYVSAQ(H&bJ`4}=J%>wDUsKpGXsI+yX&>t{6I$6< z|GqVmG_gewBenrRjS4=;%sbX|>;Q->^bQ9D!xWIkSpRtcR*lx>5LODwT3MhO!>?Fi znXmQYL{@Q&>PvM+=^uY0=w5D_mZZ}UW)(#b!Jsuhbm*fM>;;B^Y^kxeg=ze9E1E$m z1#iWJSKWj2!N~j-S^)})ra5DF8%@qa))cK=&r<7OvP$!VI^oiEBDrZmJ9G8N(78)= zRu;*^SWWdDa7=~WvQ%e0Q%bD&3Py~`$ymRIv(?NAzr(9CKk&GCmn?R10srWeBX)7l zlGg}<-#+BD!f@hu=jSh7*AEX}WHA}TR@L1iQnVmiKETgK3W<-;YkcX&r6p&tkPuZx zLjISvtryMCYeCuQe4C@7?M$fWa_hO#kx|Amo=}&}5+<&DZ`b12`ZyOY7`t%JdwDG* zHn`j_6}~YCp?v(YrBfIwe(vF)U57+dgKj7qlBvwj*kG{4(=n0FmUov%au6RHOYUcL zMy2+9OVfnAU`p-Jj)Q>YV#eIY7c%PgcR`+FHyfU_)EP<^Hc#cRn|fk!tWSD015KU2 z4sqMu?0Cg7lm5^wCL`S+7-Up-J)*ejEeb=(DFFyRmmbT7cN6w05`Jvlho*svU^qQb(|dzO>}(llFEl=CCpB97J31>sipl$XU+ zA5>pDJF8aLztJ5c58$*>QL!2xc|A5p{-+)t`(N_lcO_y8#){pS%QzL? zGh@^8%?f?RMMbe@$j#i!%IJE;XbCOcL`g*j+)k`yB_norw)?Uyw=H&l9+aMbjiLv( zd}H4!5*F=m>E*6#{P*w>lm;a~moz_neXy&mgZ!SMFC({gbZUqZ;Q8fA7UnBAde+gG zv^-*e|9X8JAl@XI{FeS+-NT5y7`o;4u{gBZj0Pl&bMYVlV(6#^_n*Bzt(8gj#VdMC zBr!pbmNYo^RgeTVefJ`{)L;Z3Lu<95(5|7yw!0vAgAas!fA9BSzQ?MOr`_{iX~SI( z=h=w$4<Ae5NQ}qVtFvWj z6xN)`vd21S`HC31FD2n~Qjqd*9v!=OPW6=nj*7{sJ4*)yK=<%DDv z3E1r=t#3GWj}KS?`1!%~-R;;3XCc1e`+I}f`g)R$?$$IRy0kGm8pQ&SxSp+=BOMYH zY!FY{SxJqSuw&9rYQKEsSB2x&<(x@e)(C@y!oj(FtpNCzm9|gLpOE6um->{jpX2@r zW)gxN9aSS+5iAIngaoy8XePPHVipjgfvpE)W79ti>Z1R~c#Mw^DGjl*2vs)Cn1_7U zyuG73zVPgsS-@dn2zn$cRzO5N_1-{J!NP*;A9#``Cl(bv{P?OxL=0C~KYR|&6FCnm zd%*rSlq`7h&DIk)5+w9-e0sjXd$0D_gSWThltR(`?tLZP>u>GUSwIXAm48|~xut{c zS16Rub~`-Hn9Rc7=4W<(S!{KcAPw(3r2-EJ2czN=hr+@p$lze%I~HjGi;EIY$H!Hj zLqj+`JjUYU&U}KCPk*$wW&p7FK$i>*7Viqt?E%<2LcO)C;^^!)!Nl?Co1Ae;iEQ~poW7e-hIgw<<6>6F+eT78QVfQ_US!=O^w)?1rQ-_)uP}MNrwL3A= zTm9gbcFGEZ`xUAKQ>~cSe-(doZ_I=$Wh!&Xs;ES>F$5Y)io~q7AvTkzU}uV0Hwf#A zIj-)Bx%B6Rp^@Z-U!jqYPl}oLCBAo_^gOZlc+QPO(i8LA`g-=!B31b>XSv7BvKHTzp0g=t<1`_ z*f}x++A*xGg2ct0+%Bp*mrR2i;f7X@;Asu&iRpPc8#zK<~4YF1GPqmB|)6pV$OotIh@;|n9@=^v|b5S9fjih#UrXT{R2j_l&{5}6R( zDP$S9hd(vhbtk9mwT$N9Dk%jW^%$DyXy|J^21P#0%;Y*jdv+j^_);Mlw|CS5ET6B# zK{dep{Vw~DD=#y1(IH8hnBb+a-#k9ew)~}=Pk2O=rFFiBPeW!>%s-C){_XEg338w_ z^A{#hpRB(C{p4$BXRgyI2NCidWHk&nplv{fXF@-ab^&-ZutNifRCUD$L=Q z&Mw1qwU)v2S-;_B{C_{zK}8310CxWcvv0_OoTX9BOroE=BcSXjt|%? zj5Lp-rK%1jhxty){%JKB9U05 z^NzVu2N3MW0Rm1=BUN>K?mK@ChEk??+qWgI&!ZbysjvpK%M2mX#ol|YN$IkpyH1NV zK5+<$GBjlM;^;78VsY`EwhV?^EVba9x(S07^&nH@qxbp?$^pg?Upz=iYPct8$&@{gt_XxA4bEdRKcMF$7RsYG~6$}=8UF=-jomoMF!7$=E` zvR^he8>@S(6BqB;FczhJ|8DqMweYR6ar8F}ZdnCCLWy|{eNv7`C62~l#q?#Jr0JB{ zm=tZWhE-pa(H`_~y5EOIH09=%%PILi?MDF01&X*`7p<*hl!XNFgOz!$*Q)KjZ%*;z_@KoZ924o#$3625<~m=vso zT^V2j!ZtoWrj`~@D1@Zxoy9{+{k?h6c27Qj=);qCTZ)#N7~|R~H2gjsiKEr*yzX)7 zr$K*Zb2e*40kiDGBvHlc9G?Ajn;;6>*RXsjb^-{f`)TICPbXvu8k-s`tg6kX#?YP% zp--$ociDGVg}$*T<4X+x2OGREwZm9AG((%SJ5)vsO?-UQ;6*!g=6Ez%HjUE1Nt892 zU29@cm^h<ivuYOh@#wGLv!6W|K2xU3NEa0jX$#xTCrC(C`SnZlCi3+w zFLIK7Rktea&z}*OS7IMr?gQvJ01e%wZ{jv8kxIc=@ND;4kUyT=xpA+hPm*aE#JL?VJzu3yKq`Q`F}dns)3`$H$h{ z6yhBe=D8H+t&+`Kf>yVr6%??8o-QqSk1A%_*-SEEzu|k+G2DeIfXy%*fTQ9_Smvb4 z3*sY7N)nxKF0OFcF-|1DMa(Z((i6Dn2!yI{0y1W5DcrG?So^ zPeP)plC3Qh`OcQLt=`{luEr)KK5;&u!*(?R5RSKEP8 zBV+F+V<z!@ z7JFcjMou7LPlhgntZzF(bP87$O}H~~856&o7sOe`;#&Ht3ezB_1?#+P4h$&va5IaF z>k=Q~22|t_cIIQ66Jarlse_L<+MZFBja*(=6Nl_x+!n2|uRV;sUmA^yg}lTnNXY7+ zxB?(F_1f82)Y$WGAJbMA<41WxFLYBncpbU;w?eMzP@@TU>!xQOxDq%`( z&Ho&g5GCR+nkoQB+dCgfYXEoocP~ZK9LW4-<#BQzc~qw%0x-_yrE~&LqkvS;wrj5R~fo7;lp|>L$+3xz5b9_-ewb`<_ zukYOYp?x&Gw?jFCANpl?klBGfy|~z+u)e9_!tR%2L3JDT+!sw}Q*pPIM&4I#roGUBPtQqcR6h6Aadp#aP7Dql{X9J_QBq@LcvFxxIay<- z|1CaVfm$k23w1x$4IQY zfxopUa zR}FM+ID_B|Jd%!hYQ$+FXZVm|r?%c_W7m4%b|<$-l`6adj!&JX6_-71akM5l4r3o1 zPvGSr&e}=*LMAm&%D^D8>A@6ro@X?$71J zU=A0}#B)sah>P69pv;YMb6OofIK0-DySVk1A4AF+hS) zk7GMKmto}$4zDX`n+6pc%%xje*pyXNTiM6#*syxvFMJy!uC4PL8(&mXNu1A`FsRhq z6r8MkZ@!>xs>X5lruWY5`th$OhZnzfSRerC;1O(xhx{P)zjol)XHD9))_1=Te5s_=Yn@*j zdj8@?(<@vb7XI<*KX$bH)WeTI9^W|y(iI^#JwR>WD!9pkIE$g(>)(ug97A>(7Z(RQ zpw^1Z8Q5B_R!x|gOy-QhXy$h`;w9|Awy^u50A$DkafPsr5A3>iTmVDyyBe`#gTpOc zt>l4iH^wcfx_ZkW%a!$yPewAo_rze!0_sYL!n$<#5r;zF%o?S;EtO%CsN-~Mnx}F+ z{+~B0Q0}c!XwUmu5Bc@M$0eIq&i50x>5>PCRv6i|6bUdK{-1-6I+y~#UlNa~=zPA7 z{_#+~uR03}kgf4b4yN`BL=e*KN6FIX{`i%mCYC51D2`pM`nkFE4Xp6FfRz^Bv>r1i z9pH;?k!?D0S-%U*TPd{(pZ3L`*^FO)GTT$deCO^i(I02)ekzN@#I(CwR$5B@J+I~K z*T3|f!{tIsiUkClw)zQp#&5MO@#n~iS&4Q#a+-^{-gR<6dm%Htj8r4#!d3+pJancpHcbcqk2KhgF)dk#Lh&IiWk^Qm!@GIi;cbXUB z{$yum%&H@kotE0348!Fyd@$aozh~^ag3}G}ji;n_EcTz?QsK90M5A-c9}F>xdSnCODuGwXuX#N_wyZ2g}XkUlx||9>o9Wl&sA(|r<> z0KwfM1ef40OCSVy4Z4BFHMqOGyL)hVcV}^z;K5xN`EK6&er*+1z}~q%-KWnvJ+u4{ z)y_yXA1^Pr{o>Z)@3Tisi$S^&SVUih{Nf@&<>uW=d)sj`%T!iK+*=#F+7Gh~m3{g8 zky&G#*D2b3e1-sxz-Flb$<8QXbK4UBtECPDEXt_nPJs|dbsV4Ykj+C0U3xE~uXm0x zK`J^~vuEC8I2}}k+9wx$x!V#D^X`%7a~uN?c3Q8s+eD1IQcy$yYw2E;{^qR0wS9dE zly({V@80n5DH9Dxho=#X76~Jr_q*9xMCl^5UVB#EhMPgXKOvjj4=2Az`Qt1n{L`;{a>;DQ)D#n6KVHfoO;Bh=AT&b-ZSAPUME__7^?}G6 z3ch7{8spLRBWv@M&#V>E_lxeBP~6GYvi0U6=B|(`j8lJPC&-Urq(Z^vb0iZh3mW$N z^s+j(n(2|@@%yzX3zPgHd2b5cj@u@exxjJl9|HjR{A#6aO5eptI65 z|4e5g6fNRb6tCDT*kr1~k@IE(fm}j@d3Vs#CViB#cYee_4OfiS%NF5Z-q=x_oF_Nb zZd%Ch?C(SbQV-dGKMK%Tp?3@6?jSl)#o+$al8+6?zURk0@4rAw84iDYn_HRxH!)lSg2&m?&ZDLcyg*&6vXN>%yv+eA|})@V?$+C8ZCD7kj7Ci`yE= z`thbr2ByEH{A4Y_j^v5g@YvI4T-VwD=j*2fJbv&6*4wI@#|&DtQY{`kwxk&vTM1bv z;R5XB6e3K5-SOY7pm5?{&aN|Etu+x%CDvj|s(hLR1>KUw{e!at9a)phM=wS6o5?!2qp+SVMVb<`%tE%Ro?E@up-i@_ zj;*_A`JEjDq`u$MD7d(J`H_od8usmD+UTQB0(}c#etT(f!@S(GR*Q+%advZcMq!|1 zDiNQ_Z{=3&)Wa3nnjg?zrIEh2$F*`+WHvOpE^cj^`eoz=3>>M_tHvkI#-(XU%89*S zI@rbDQOi>*fgbIdej7qS6X{t)Bsqw5K;s2}RffQa*t|bP6sU*>P?f!X9Rks2_afqp zXw+SQAvC$Ag-ebYx;M0mTvJ;bE%AwCEW&igH-&>Yn|nXEzCH{th<&l1CM9EUdei4I#<6BrIR$VAcZwx*__8&>hm}-togLH8=Fb z+jf$stJDjCc`E*r6pz{Qa>9|~qPn=0Tw^vxyC;Jv43-bNMWy4vrK+`o@e-!-o!`_z z`g0|yBUI1!ixp^jUHFnL`C}zynZ?22AiB7>Dco*6Zv=5Wm5R6Al~`f71-6Fky!n&7(dnlVg{_Xe_JJq42<1$jj)3%xb7Jf-BV z4!*JpNRML9FA=YYSmet8YT_r~Jbf3?vW4|0xTE{)tC_Si{QD(U>|HhGcmR)DaTWwP z48c@VIT|?zmU;r+`*7`jN!YNp|zp9)_@qK{5S-mLb>)vk-I0NN51YSPDjHOb)5e z8k-}rjN#htJHk{x1SEUC@p=d%*f zIN_BSFA5LdJT22E>Z{GM@uJJ4EE-rvA)>^`hPicoI7NU-X9?~*b6y;|pZnY7HUYVJg-M9DE`PEW^gyrr( z@M54JO8xxJ;EMO2G2tUsfD31SCIdAP_Oo{V_D;hbv@zxpzu^OMA z>y~@j+0nS&7S(tdW7a!ZF0Q0ho4g?GjT1!1#B{hixK#u@q-{wI(+GFP3Gn|d6$w#ZJOkB>+7@LpO?r~pc13~NMWuc!^u|{cl%7l2;>JngA&{pg$6?wh z590sorH!r{M7gXaf$uHVCxM2`9Q=uXy3|QhOF?0D0L6w_Fg8S~`19xKFpXM~5Yla! zn-5z+Xw#zmt%dyOO^Y}537>u?vtt!~VD+^9&+&GzeSyjU6GM4A7CbwT2S?cQA#PnA z<-5Qp7PjS}b46XV(bp}uH*2CE#RYC=*&sR8(+Xfk9p$33aq3Y??K!phz^Bnm!hJsWPB zJG$5eM;jgfH6d>v;{2o{l94{AETzGu{OKh2PKHpag@4z+!Rbzp(eg_M;qzmQE8ilo z#?O6=koHbvyM|z!RYm zK#aJiWEqqF#`_T{OgKQI+|jlG@e&A9ai@PF;HQd4oC(~-+nJ4GDWy;2v7rpZ60aE= zuMm;e61n~%w8u!?9V`L$lqy%Iv0G~7PRP&K2ex$zD}{f-sQAqX*90k?YMTd(b=Sz9 zS*5WtWQ}TjY^42wyB2@88U~F<-biKRD^_mKoj~(k4Hk3f%4@q7A8gNcLV0Cr8g`m@ zHiIZwRn;8A6$;ant3H0RUJG-bIRAqwDcaqS8T&(ikY@o{{Ojr3=tM#{-4a>J(|LRL*y$e{H@6f%GG{QUUKBj##K zYFxda*`sAkdW^c5K5;W=-3yN`TtHyxpG_DX9xYeZuxK%W!Z_j>1LsJrL+^}g&duUkB5n#&y1EbuER6y8YEA3HSE13 z6W9z|?7+`H{Ahm#M>~$1R#@j%S40dfa}kmK3HygtkyN#qstHRT)$;wOZFUjs_b5(V+(AicN)6PF(_tWX)_;?1OU9g*b z^3?7JL6&H4mDQHJ3S|+A7qbdcC&XY?wuT(NzB;Zj14H%8Ugn~ZFy_9oS#R^i@6{&V zL%LKyboEfOJe<<)hN*b?HGdtUU?p?RqXCp3u&J{e2d-8k-vQ`Hqg@|a+9==^YS{Fe z)g*QAW!IO%ywz?Ush~U8*GCIJZ8pV3bu?q(fjTx5=MCe-LBelX9e7TUcv^3uKz`gBuNp-tur4r)Az+SD@8bJ*kLv~Hv9C* zQU|L~++dAjv5Kgu3%hYQLhiuhwVNX0(F#u+cfz+;C7_G_4#fXGEi*L~S#K=g+mjwu z0ZU6tgxqG(Hkdy~)+2&1V`F?Y5n~GEFAhT&=<(=kLW-8$#Wqll&C(Utb>(#-z=_{m z$UU4YI66G|vj+)kjS^(iZQyZRyw>ddAm;ko4gUK|rbD7cFLg-AT$Yzh^HnER{hO(< z<(b)cEpa3#FuZ#Z?>5$P_!$eH02~Q?#=B*$RtbJ}86^vlWc7ne{BOU#TRB`&S>#V< zxkBU^nQ#M*^^P`=61d`M`7yBy`D#1&{4AEIzY51b9uz&sj3%V>ru3d#N~X)JXk7tG zu=zgqn+Cu`|@&877V<5c9`( zC*EA_?5q6)fn&f{1`A*oWiHcZXR2(;?b-g^cfo{QDbl@v(>)=RK{DWPD*WR|%5`g2 z!#vXj>G;+dup{)ZVjM?VS!N-9_++04A6RX}(HuQ|-94s$tVoF|v1&+C8Bis~W+_fd zTkWY0+<$2OLv$Q&>`jsB8OhV4^-8W9QKuyau{1xMn$MSWH8VfVt}phR;Bxq2p&k@p zackAmYCvlswNsP%Y`Oa}LRd>jki_18u7XU*gX9|J24MaNvy1o&s{vs;aUfZfP|rv& zJSD*fYSxPkq=##!&58r00BuP_Nx}Z+Icy`qU)EF zuUHerG>^BpuB9!;uKJ-bYlw=s;y=?y;%^kd{csnCW3yj#so(vySoUJG`VGkV-N=#0 zvQ*5aA4y2QmdKxn}Aj%#ZhfRw(cZ4lkbhxpgtjGD`hlxy4PtQ=mE;wcnU? zS;+6KfaNIOROqmUn&U+s>P!?G#$TPn!|0fbX=o=yIDz`m)~f zwbX=#2t6t2=o_=#jYjqq2ch)bjtUefc_Lh1i9E@f7I~7vYF*{!1##1WBpr5GOk0sx^5eO&ur1^^Q7!_4 z9DdDG%P}xC`&EZ`X7RsXQm>B84pcr@zQ2FXfMUbm6;!EI;_7g3Tl}_JMp(Tl{uGr! zhvX13Kd(M)zECb-$IrrEU(esK6i1G&yHSLZO|7hPgFPrbu54MSv8KBG+jAI zTRM$>=^^P?kDBXqyHEPQLKs+2h=iMw6@eQ-WuoEjh;G_mN*7F&h3F8qv@D0G{(;s# zY>Gx+5oJ5mk5q2{sW3o2lPqYihGQVY!qsI@<&_q@RerR$m*8#UPB=-!q-D13>z+zK zvLc0ECr_?Ff^3^(zroKuIOs6q;K<&?_6?63E1Ry>?ibY%* zzSJm&rP z9-PMKloov(qLmj5zoFon#;W{JJR*M2og{WB;^wA1$@6u--#o}Tq7h(Kh=i=;HVkRX06`%hRW zkbKjgl%K0F4qH7qCx)~ZH^N}5UUBgz=B7l&x3=i&$K5lXZ4JGRWBpd(98ldYe^l<4 z18eNel5y6-E9~Jx6i5BO=C)zDor+k6zI$q0!~J$wF*TL{2Zz_Y##NpU?kX+CxjtAH z88xUl_*{WIv&kCw)=^!o>h|sb94R6Q0Hv{4YaNxBm)HN?C=Xfg`$~yfZ}f0KObmLu zM*s39gHZ#&dz?G`sD7Zeb+-(*i%c{>n3I<`?oc{VWngMh`TdLkrxzIz*vrv>tB3FD zEpfByN&XvAu%^nO^+v|d-xrQLN=%?c8V;ARI$!5^gT1vY{)}xh-dcpyP~{+evHX%t z^B%pH#}{L29d4EKzvBq z&c*$Zl;boE;G}i^I7X2AcbjC#7o5x>Od*I!yy-JXB~f0hBQ>(*{x9O3DB}tr9qsMw z5s6O5lMlMX(+I*-K2XJrR8VfJFu}NJVt>)&k$)0cPFs?u2+71|`Exe`tZy|x=nv&PYZC7B^*;x;UM+gmRvle5b8$6Xy$r$wybzuc7@oAnn%c9&46zX1cc#b| z7%cfVJ733U`N%TA&h_5>Xv5QYN1n-% z7laH3h>QLl zv~FGG0;TVAQgqcpY`k_X86&YD>Ky72$hJrOc=bf(k)}-^7F4-wz05IT4U|gYnb2}S z-m8j`&qg-yjPMLq7gRWF4~p22*Bns`MEdhny0z`DoLAdDxjzAWF$V6y{dJestV9c+ zcO;C{Nv?Ykx_NgsTL<|6#d&N5h>VS;Pdl9W^2A&KtBrx$`2;+SmcGJxIsVgW2ZV4> zkiN3y&`8(Ai@BI!H$3ce6FAc<`-*HL|Al|+6(YZa{|D|X(Y+?Z#pCyrIPa6Micld- z43ReH;wxQ5f3)*GaoELG1Ejlbv)#ab=La>JyL)tn6)!hfC~{X?{H8?(u;4krwtMsq z;%pt5j<(;814L-~oqGhziTlNra3t|iS5Hsyk-GfPTi=)IIzaB}c)mw3iZX&2lnp-Z zDl&FhU3>E}PyzJx{oXs8+amHLh7kOt(Witw;Dg`0N|hc*vgmTL6%=_7S)$#MB3>&? z;h_l+vFkbid-WL{K5=Wcg=QS=A#26N8*w6*-?0EbKvW*(v(b0#-n@4B9|J&*0c!d252wVPdy(sFhhzc% zaGX+_KRfeYxu(CZAy-i2#dr2ola(juAg6&FThmpA)>h`J8x%vY(KqeQbUMYDuPn}(If9$6|y~L2snp{P%EDg z?*}ba^QY+f$O%0DIbPqv_6GO`=c92!047>>7z!ZaMjlhylF#DK(43tXY0(=m)#qtc zo5^&dhyWnE40ii2&5O?u08L@)VzuYXQ*a;C=F~W^u7KdJ+ZF&e?AQ+;UzY{Z&BG<3 zpGb%KMc=fb)z5=7@pyB3dX_yqF1;xNLd03Z?ho124^6!U>8lwcTh)v^Z10WK2K>Ln z&~ZJo3S*kV+MN43H_-MI6E&DzN2SDX?#Fys5y| zOye^#H7P3Sh}e7NN6E`r)R$fc{KvY^>-ytA+7WP!&Yy{yTUc+?tyg&8lmy*v#-%lb!w z&N4D6&1X{@;c57jD@<{8i*0m1S)Kv`IXR?Jf~<{M^;uwr(X_Kua^}v!UFpvnt*+Bv zZCukrZ(c2XqCRBeiHsdTywd#Vk6w9mz#dZS?N}b*3H=aY%$R^!A~~Ce{Z%%zXjx zxg#O&GDF#FO(GRLt05MV7Lq&1ImiY|yz{qv;b}M{_szXPwY6DFv~rWCNeKzqp~Q*H z(iGDL4y6|)vVmLV0jQT!Y6U!Nequojn_rEkurjz7151V^sJ5~|NG{rBU6N<8i3q=ag;Q;SSy)vUU%MN zlDH<|`4v+~M-~a(;pGjmnZN8Cb|%D)Sk2PGouGgR&bFINxl6m!6pk;!tz_W`#wU1q z3s;xYD?pWZe}m2_Aru;kn@UjH^SoOmJ*(e z>eERgmY^lR^n%PMmQ@c0^ELng`=xF1Hc*5l20D(Fg{SZ^r-xkiFsJPhnQKY#CP=$# zgHjL!;tkZv{l7{}`<7PvrQ(0nxj=O2rRYN3CTDYeoiH&!&8KXQZJSlPRF)o=rYmU6 zZn)DG^i3zgJ?O8ZCF>b@)ME{v=wN1we!bAy=dET)0UErrAun32YS?P{FwcHJOdU<-_mv+z5n z4+?d~6lG~lGMl@zf z8DhY7?t|WQr?lUp#P~$g8u##b#&2;c_2Tj>?BY1jPRN!r&S`zwucHGM*z{4qe{UpJ zWsoR=JYN5UITigO`ZEN9GIg~_sRHd4P-1+}0Kd3Y@z&!CP3`^i)brbP5d=B1k)5== zTSe7%(H&=@c>#Ps7%+_ET{8V)-pe!o+sXuaj6|}4PRnaPz`^q$?p<{btW9J8sRlhcSq#5mQ1DC)kvfpWSIqIXWn8)2X_e|KeP93guB zbtk-r{fZ0F=W%f=GGgv;2rk|mWHB77(z(2EMF*{ConO517lrAvNifFIOYo!)Z;m7O zk&TNMD`0R;`)M!?vUtkjKYmEXQ4Y{Zuy}gpp}Eb^EuhldtC3J!+I3;yYZiUzUMEwzHNlMUV21;4{l6L zAhzB~{%BnC4S=$MIk0u4E=UyAaBOkIl!~S@)fl`eVkeD}p>wS5-PFeFdzrd=c^Iph9`y68cy8G*zr02^4M{gkS)tFsa)yX#A z7iP;pDdG#t8tZ+W3sHJ=U$7oEo@G%^+8%ePm7qB6Y|CkGWLYcB3LhpFRz_e@YYL!o zI9+!v^Dw}r7(`AF0@STC*fon*Cx1v{B5ti(xc)&oR`p3<^=ViGAU1p0rIT!A<+s-( zISIiVm4_RR^u#15|-L+UOym~eEma*(n2oA8txt|}(O~*|dyPgmAq)I6*Np;z5F5lTzwL4lK*0wwOyWVhjYZ&9qgL9br z@K~D$jFN222n!bPepv-grFl`jtoT>@@tN@B{QgQ(r?a$RND(7J>`h4SA1y(d=Pm2q z+SC^W20*mgMtebkO($h>6iA>85KBWs5O;lo^dIRgfG+9$X`5(jdVXt3JrSL7eM2xV zLw7R9S7rsgJ-=nP=Hv*Z{?y7wz#YuMdKhr#*1%sb{c-kf5n5|>; zkbK9zE`(+7HlBJ0AIc6b~=Y z_8`DPJUC;BieJr4!Ps@Gzk%M$D+`~mppMgFaysuR#_<+fksv|&gJ1K{79^@Pi=x6a zvgv_;3uDJtqavkya*dAa3s+WLYb;MaLkd8)TBI{3xADX#9}R5nu(B+!1K??T0=Md5 zl!B6Yyk~4WdDltK@bm@(Uw>~-pL+kY=0UuY65bw0#9-G)c}m4Vo{M4LSc$67po6x1py=W?>tRmdo{!XO0k+G{g2qHF^qtie z>Nq;*?He6p{?z_U9L2JBOE%09fA;q`t2fe^l~5!Dqb3I9kB7}}Yc3#Nf(d+UqL+yK z*J#6u59{JzMxWFWE&zXDGs#zki)P@Hs0mKtKbDzOw|8dk>(eae1!K`1j`l zA{>Y=$>*WV#T?{ycT;#&Io!6(TTUKbgZi_L%s%nTvw@NM`2BTFpGGgQjj}qeiG{OM z$iB6WGd$1bJ<%v9z4c+K*8O$=NgwG*7sF&oYZh4I&v&fR_d_ka$1l6cM?!+4(%<+M zX98_{{c6t-uS8I}POmc!ZlCN!uWKJnj!an1G!c}OB0t+6RtXh=t<6tAF?4vh?OyxN@Iml+dD~_mYL=>l=&>zd@vgU zG}PiE#>&*1ReC-*E_?VYhlU=frq)M1tz2q0n*ve3KA zR3QX{?ANgj;py>8p6+gFk~DTz4cz;wtwrp1-)FP8m9{_L?*v!^!VH_~=`SlcGg4f< zkT?H*v@3Cbu11N+ov*$wv{`kA*1cKbHY!NCn9d^teE56a#&|5IV!t|Xr?*@)UGKS5 z371_C3;IRx5bx;|=s_>%{{f|!#z>784a9+DY58ShXQ6g)P_%+%cVPYs=hdtxs5C_V z6@SR!qpq_jgE8bv!)?VtP5TNqt%A^92!>wn4hA72+U-7YCqm|fkbxosZfniTAi}~2 zjl>n{>TrD`DCDUOTp(NdYU7C#RzcP~em9P9%Ka5plH@-f{@!%p&cc{E?+a zmNi=Uo#Mmw$!YAx+zM>5ot1Rs6Ah`G2QL%p^Kc_DCXoazjhGa{=)a|Ll0CV5;^b_& zy6!z1hL-Q0!b6f9oeetAu7iLBV`rj@05eteU{>-df6(Q_QPDA&Ff_R4JQ7-;jDe~l@;_|Ofxu+&)d(H4( zR9}ky3l^d_6T@`Tz4Ka?ozEW10qg12`KWYolf*}Ov(lG{AWtg6oZ!tV(CXFn)|(Ix zJcVS9?jU)KPc#MCXL=K5p0=P(2z+KOGyO;Nhli83^u?HWBIqPo1L;JASX>ilXjCMs z*t5Uvm5FU&N<-3WrA^4;H;CcapPj?Wy7N3PNKSpG46#XJ{JD7rap_n627P-mq-o-g z`sCA01ehW3USl%DBM~9f(~3MzXeWihP_5GU>1syD=U=}5-w6KgUl$w71wjrX7^Uv-sfPn^h2OhF=_~X5KL=k7sBy4B^GV_x%|>6pt9s7_vAeuJ zlmj#hsfz<0r10I1dD1A3`^yB#(NfC5ppF~bQUBHtR8atUuPZ^V2>^8rFz+_2b&g7% z7XV*-@vtw>LQEnNIQbnc9#+5IeoxhLT@vu>)DNUN5rlPj2siv~(ZvwNE;t17WZ`9d zVesK#C5};-HFV`PWu5tzY&Y zFOF{>Qg8&kR_*{`Xa}3QO6lMc$)hR)viaqWji<94ccGEk>eIb;AyXuNY}JYuAMhFk zj~`!n0Ip@M!;|>RDka!&Ww+Bl!*Y#yg?O+dOD;A|C0z6~ISVipbU+@SjO{OCBx~a*$0@AYKl54gU$}wS_d>yv4#5dm>Lz`mXn7rIUBy#lcvi_+8k% z+}<(_!oor7?yEu{e+(uY1onmSG8JT8`6{K>>^K`blnLIxKfKWa%=Q;gN!*(idcMC) ztu}Xo=wq(+g$HYo0n!cJ(PF z>HhjD=1?k%On?fs<-9#O{)-z`{vtMp>>_pibW%0|f;D7dv5SFdbe-?j0m}9f7{#T( z*iugGtNWYOchQ?7f^cJZx17ni`Lf7_@jPb5>iPn&KX_}`4w2hm2!TfKqPb+f8vGZc zk1p44w)q;RsJ<|8v*0nXSnVnBeC+FqtE?nKE)TjV(xX^)+08J2q;mjfn3#ncd=|HP z1@4dE8tEF4Ad=r-#PvQs?y^!3_@56kNW=eK4?wqgKBWYAR>N=nG|q$_4+xhs71Cf| zJ_-s=FE4gmLYWM19Uy_%0eD97R|j!KL&3~lUjFb-?JaLNKsTO&zJTp=tb&ru%hvnY zUj&ezldEWbm$+pqKlL1SZuzOx$8*fpO)AXEKpfanRAo69>Ze`w?5?z|UFU|mfy&&6Z zEH5_MdRXZ!0*o`QnOa@PAe-WUMvJz~bJwj%7XSq~JKaEZs=c($W9k1+JXwTJKK319f6-gKmBSLj%@=jR|?M>87g~4aOfBb7$@% z2pvEdOw`FgJocTU`EKbw9D;bU%0>Su|Kfu*BgFW_)p;5N%Vf3!AhlUMJ|PIT)#Aac zGi2W1i@84@3%Ro9>#%uxx^ZiD@c4!_V>Al1djqu?jQe2kB(d~5O4s1w7+kW&2M|pf zzhEkbI_w|fUMIs!R7z-Nz7%{aNWNU9AGs_k9x5#?sS>*q+Xn_DQVD;Wk@cRu=sU`OVcL9Jl))y8j8mf1{Oj*MmDd_bj%&{*9>% zA+N33TD5LU=dXPPJsnaXAHz!N<~=;p$v{FQU!3F(`(@$Eb54%*AC7O<#&kfTt(mDs z7gSGA2_zP;n;c=*1kgiqV{=MU@^@r{%`pJOz@}%#bJx+}K17mCXs+e_5(ou|9x9_< zd@C1M@xsI>1`*!E*$#$7v8uzX_b+Dsj^kj+Q)S?@@hJ+5vj;-Zb%5EzoE~`DG5o9b)~;7 zp@Wv@*8I5(=^tD6-;4{y02$)Pu=iB8n?PcO-~zO}hfnqwFNfa%F#6YJ&31Q`H8sy; zY{nkUYC4;B!>L=YKD2!d$8}MtI}vynBH{IJlRe z6vn#=4K+S{RHRLiituoJbye%T2hoGP3Ha1Ee~JGG$wNFq)_E*Jf<#np$`{X1nQZPBjr)=PRP_V9 z>1{Hg9$P2%;LzS9xsXs_vm6DJ7tfb8g&~|=#zrOL`-gmIyPN$jO{kk|<=KlQbMQFX zDNem1ir0gk3VnivKsu8ZvYSlbj|z+|!I#p%hkrYcFT@+EgI!MVLgye^csSqdlb*`t zGuJ5fSI_W{K&!yb#&?;EwEFI3IO0y33yb183Zddw51M09?z-5!s^$WNGj}hHdyy`Z z@wjt0FDvh}o)6{aLyM=FL&!Qoo=bO+)^OkM&tLcRL9;egn4XSC0m-blh8OEZt?+d~ zX{~mApxH_#untKqjC^wfct5uWk{kO=4y?^A@I-=l7TsBC&TTHP53K_!+rUDgPyfDF zmO$-6tU;D7pE%=%n}jyeW7Ciikp%F%4ON?LPIDH78s|I>FKMz1F}2yp}AJy)^KHroAr~@ zkm03njhC5u2{5v`m0;W$oP1Fkyp@T#Db)*%CIo#YR}ba4dX!?!f@K2z8R6v1xHx=& zcnmb8DGm;-nIJ`_+xCjb%Kt)*N9qCv3SudiLve3>3sE) z^+AV9yX!!3SifSWUH`-%@4JKPGu5dAifN;a`{QDZZYhZ3w33e67K#&kclId8SfxQ> zgkOf)_+5bf-;(`iEPIgNe+Fj*!S;0d$W_gEtjOB?GvS9pr<%L{#$7H;`89I}_k)32 zW&P{;Rhqvxb!VB)?t9Lyy(wtu`^>vAyFs>~w`sZc)gD6~c$3;2^rxx! zzR9N5n*Y|R(_jwIFg^rE)Bfq-@?0@mV^~){D;Z>t!?ZLny|C#Mr1CSza4R>ii<2Rq zwaI!_QUYvOIEtAldHLV>&sCN!GAwj8@8U(4a2cv7J}%>o}c)`3u`VC&CN5 z4r_-3>a-0koV)L43W|0R%h$l5@$Wm{qSX)r3c=Q?IS7Y)pl!`s>F-f3na%dy)=d!? z8h)utN#6;#CzV>|(=k}@zb6dj@AvBKFJLd_zQH|Z<+Yw%!x%UfRDjq_7mVp`+s$L) zBKRH4TlFOb7=uz<1AWh1F09oVvCbkPx2S6zFbl*xzjA|_m>>ShR8K^q+f}BIZ*y6= z`%mCyY5bd!iLSSH;h)_!5CwCyKTSt-#NVY}W?nI@Lk2<@vllJ*mm#RXJi!1SVrBJt zMM|=E?(wA%fzf;+W4jku)?lYp7cCj6=}0RR`~n)U|B^&n_9iYdd}~wQn*79`$-3w7_o+Yit@oQJ7@lIzj#00Z**1&6H z18Q{akyBpYKT;p}yTWAa{)OYKWp+n3bCJ4nC-q|FHvCL+`RS_;fIEIvarnmOx++1z z1ZlK7sQ=tZ@A$cB^erJ$*Y`d*CJj%RVSxI4mGm9e1bA?Zr&G!|ITe8W+f3lDflO|C zda*kK4K=<;=c}S4RjVi8cv%7@aCQmq>2}kT4eMj`Q9VwQDyc9+H|*}EtGSn8_3j15 zEA<#kBDW2s+!&0s(RQ-6v9L628H~V)2D3-2wG3cc^tla>u zrRks>9~ezox;oN`@W`cp+&;A&e5{nuR-uQ*JcnKRX}IffyzRcdv4I#O+=qG;(r|oMf`1prAjL6ALha@A_0iU@`5$#Gjiu(ts?Y{@J{py~8b; zH84dm*4)eMArSNkaw7o`|1+(_5evoph`z1m#E#-~;6N%?>3-Tx9dy&kxoC8FT_UrFeT#y^+;) zn6|>hWWq3_8NaB3`urxYlhsl9-5Hr1D&7VI1;m!t8QE^PH;$Rb))j$l;|?waUio#_ z#mdDKQIS>8{pLE*Gpz{i10ZL3ScCt~Pj|M}8V_{%9icH=fpV<6ph+juX_l}w z1b)z|$iyOxg(7((rsJ5_>_Ge$kHzbOmT$SBFJp{^#c`qs1F&Yu5f8WQwCf=L@0ksZ z)wT|;{OSYg6E%trfrGR*cloQ9vt{UMXv))v$VZT}gyN!rIjYQW`3Zw$!=ln!VZ%t` zsLSxP2e5tlJr+xsS;Hj0#pe^7Xo(-sJ<~#lF-~>%mj~a3HnC2-v4qwGasu%O5zbhV#|AO5bN9h?%Ikb^&JYHF6b*bsbdj(rx&Xe(pI)#fi&)3ZGd(9p5Bd^>!YG!Ay*23ngm z^&sX_a%%m%tIM7Ljxh29jxgfYNVtbLqux2bwtXw2%@J#8<@z2lx&DbEB^(?v{5Xvj z1{kvPs-NF(MHygnOk>SRM>`*PsHjNcZ11DWxGcQWXiR?=%KGej`^zHZReQ<%EOSM| z&JyX)%YBrL$?g}`S9x#}4AhZwxWzZ$4x~H-+NMW7bP!$i+6IYuG5!yE39JDq5^&TD zjUK{hfCsMw%ttBr6e)hUF%p!(@IkC?LpGSD$=cg7)(=B%_#qx=9u>c`JTC$qjkRP7 zhe*~XG#PR{ma`_W{t-xHulNr2hfU|Yz6~^8r)Lo?#`o6qvk**< zQxbD33a|Rxjo8@%94|EXQA`%GZKpnSHO1er6$O-2k#vmoOJD14dBn+>7JC)?{O%`y zP?ipu)aZqT{hTC+_mc+>Iv*&SfLrG0jGG(n1T9Q?Ke^H9<4uBW-$|#y!X%)a16J3$ zv?cAgd4=y{Tq=?q_9BI0fbV84w1$O_Q zPf254RLgw9aBZcN;1#0>n1*4+450+3qj#h!V+T3wfSKRnAi9r&O;LJ(Q;FVC7AlhSFF0!0`a0T)x81oj$_1p5-Q{*K%~$a|1Ae_SnnwFhG*e< zE>)zo3#IqXL4B$&{G^40dK#ftUDNC7L|IywMFU{Trkgo)7B=>s)_v~h;tNIgZ`BSB z`e%28%%z>c85xj$|F~bYBpQwGLmhe4@Ht8)JYHtmQO|D!qb@$oLXZ0mUbmip5@(cG zIk3<`&_fKr1|tD+)wAkT?d$#NrZpi+*+Jv()_MR;{XajI``fX%zTW0kn8W?YtVri4 zyz_6fp68&?joIzSSmq3+KHbxROm0pzKKF4&v!$w<%pGkJFeiu0q6FH{)p69p{c%Qg zG1RhymkRi(zR`V@4-S7Ep?>NSe633@Y-x%-r|V^5d)_8;0h_Yaa#0zS332v2c$u{| zL~?cXt`#5EZo&%w?CpEkX~`M8-9Co}-PqHIeg|M8QMg_!uG5?fb?}A-&D0x0eCv0U`(l=R{S1azRMmWNw(<6K`>W z*HtpR^|1@ADyJJVJt`E|`K0q4)oJ#I*i7A&5>|Q-{UaoNKk*ejsOJLhe4YaRCqWro z54?HB&oPwqbI-iyyYv-X^e-CdA__!16UA~i3CFKt_wwi+h2Y(-y7tk7yccou4r~!X zM*nPKY598DuhTC?Byw}Nmc38^!rt_!w(`z_YFfee|9{VucT&A!^R0H7PfI#Tos!AI zd~qE#+4*~8X1=hS8S$q{zPMJcQ5Ll~kXdyylv+3~S{K|RNp;*HI!Dn9E;+h#9{sy8 zXIaK@T4-hS@e5wBP*2)++C*+Nnu@OWcQ1)ngB=_s^smeED1Ys9XltQm;YDK`? zr@5?&kB_oSSj(JhHU~}A%d+Hyd7i${YX7cBC4G$YfeHq=og!9#y>0(U?193W&2)dm zS+8RXJgn#2KMXMv0#ukGq`y$AwsS%J-bAjme0e^&~e! zIlQKnpJo$$(+}U!?c$*mZ-yx4eBRc+$j%}I$z|lEIa~ad5w$bNdP^a|TMzp`p3Xa* z>i_@$l|l+3du1zoZz`hf@U}-0lD)^_96~lpNX97=viElEk#Wf0dyivt9M1VZeSX*V zyDoopxvs9`yq?e3W8NRP$K~g%3(Jd2t8PtRc7@90vaaKf5&NzmpLr%PTbdNau&S+f zs{tMmZ;ei#M?`A#6iB|mihzB2a>jx<0=a})bf|TZ{@2ZT_T`pQ-oXaPY zcXFg@mp`XzZE*KTmVrnU%uf>DA8j!51B3K{5#xVJ5J|+(z34Ai0lr~xh(L(;4R1V5 z5bvAd2ds*$@iYAKFP%`ERRr9(4}*#WWpG>TSd)bn%g~6tn^H!2>k0sUwUf@>P+&NH(a}`Om`_?#q!WS)LYy+OxU%;~Jt-;~^i)xpR5J z%}J%KZYWyv6wdkZSK@0k9pt%hvc6##bALPJn}|3GRU^);^jNr{hz!7YE}x68`@B2e zK!wGOq`7}dH;=8aX8c6Q2~R6fb=Xxey-3K1!zi$9(*7*%Oe`Vr2dyTA2dYR!06(C{ zt|LMpEEQ#(K4582tQJ8(8oV9_UU)h1C?zncg+JKl0sg02pj+A0Xs)9HBWJhod$UP- zxwI05r!gpfaKL^pVh(h5AFYIH?lpLn5$CFHX&Q-tw@O_KQ?H{X@@{aK0~hf+i%tG- z=s-1CHG8S89?>>2^V!701f4T5q&?b~Vz!=A`(cKo@Z_FksmR@HwY=5yu$}R#k!NGI zmdYB8V;JY}9;c6OkM7d0hQ=1HIcy#OvOFgC0HvaD#hE&J-LHxtxqS9dOzTsPiHI>^ zEwY)y5-%`sC;@B~Bi(V|TQa5*fFgQ5CHSL%qCF6}-85-QA3w-B4KtB2PhS29rV8Z7 zW(&yXVjY>kcRQx@(FzHDF0^2JQN)twa?pqwrGL+g*x`xX%H_3t;{y^RcS06PSk(>O18NUXPy7n%)$xCGV;WEQ zpDtPe5N#r*1|0=`vC_39{${7NvKJfgooD=a(YwpRFYCjq4wGku5<$rp3bhA@n7^5)J#kV(>m7=e zOR~=OP5)tUOT%;yh5N7)6yi>R>Br5L%2gYI02E~X||=@?A5M?wgSn~ApCTi|n(Q8*Xx%T`mdFCZKafh$Od z1DltyMl$Y`;ck2Q_;IfF;f`R;ZoLFoW`2&w*H4Y?r+e!7Z)VyRl6SA1uS+)c*Fi|& zBQ7t8R}2ePCGLW@JHMXBoHX6Eq*8ff^S1q>SS+V~y53L-^PQW-LGxF`OLubs+n}me zs1N^ss4O1f>d|e_2u}7}qSeHC&odoO(u^nb)b{44%H4(vbG6$h1I)N(>kpNcl{L8G z(U~i3%vOv7E1VU5o^3^f(`Vn&T8w?I^~IGlISgUk%ZM_?<$Ni!JYzpPP*k9h;`=5h zz}r|LWJ~(16s+XsZE_^~X(gJx(iG^)yq8n^GhN2q5cK(mUY_1bNlcqa_}fa~^;W8z z$ogu$tF%~UhYKWE(05@oU3PbQvn83y$sL^8iKG_ zx2-vd+3mGQc#SAEASMzR@B4b)G&Gx~F8_(Ta=CFc{L=3h^9Dm-TB&daS;>v{u$Tku z%QQi8f55Fh>|`lEsY*^-TCwg0?X9OK!`X$7ps=5TS#>h?XY_F$?ONfWwgCMzpcU$? zcceox`QpprnK8jnq%GtQc!W0xJx#G18+%_553c5qj$5mR%EdtnfyCMM%3rDT7Z+l0 z&AX6hT<)Fr{!yAT9Bze>UPc>~+>?+Of^|1pqs1I>d$&cB;#vhpJO|zGDl}9xQ@AT8 z0j(`sIwA5E*zWuGC{XDH{a1}Zs}()6huuRTcS`;BM(Wb zWuYG@p4s9PY)^dKHak(a$4f-KYQJtKLI><3^h&in(b>-G`boR`dlPL&ya+aL`_4uE zC?2fbb!7Ty;PmDf(h5GKt`nw^Vg;e;|kMicVVN)Zmfok5;>o@*qJ z^DVgm#-ze%PJk$|qq{s9pOek_{?`VI@mk=d{B84z*I4XR0>MA2QrH`Y8*ethM@ZHf z9?VhD6KIT;xmT@phS^fUBom6w=j4Aq>6GY;G08CQPHB96U5rVlY_IgHSQzCa{gGYR zaW!mVeOBFt{d(BhJP`;{Xh@;1mIW0kdaVJlz~E#JDu2JgFiZ2U?vX$Pak;?SlWe?3pfnID#C|#A zDyzL(wXQ)E7uixj-yce#e;Ltl3p&|o)>0j|Nr|z_gEd9O+x2%Xm)m0YI8tC<4?LK9 zol|}YEpA~zCO$LK5}8U+K5`S`!LR7CCUTwkgh#!|vUo_zaYBcLyB59dBldeP>vcu_ zyl4^V`amzc-4^Lcb=`@8&(C}J*w3ABJ|kOp$?@6x9;c*YGR}dy$D(AVQSM`TP;dFW zUZ;pOhKIpo*_LTJXkP5Yn93%$u+&f1v zZH7)D!{Rgp82M*?f`%MS=_lVMs}2f42NQPDkocl(dTqb4d1J#eMpJ&2vn(SH$?~ySryyUJ;@2G;-DKKh47Ld>r~Ep8wP)d9U?~mt2G`gMzuS$^NOy{MpM3>ZWqo zlRzaQ!W=B}RY2~tDw{t`h$KW>>$=;2dES3;)3J~*-Ey^{y5qYw^F6z2ho=w?>jXpL zQ)}1tN4w7nU0u{N!w&-V{Lgo&z|#~xef=bHX_o*-cKt{T=Nal(#84*Q#(iE*CNoke zl&?*Oe0s3d@>Uq?unzwmnReFk`VOF>An}t+j`~vIc7SG6h{_(Qj-tiSZ+|{5wsevz ze>I%|Gf=6PtQ9kFDBEJYu8>~Wj(NT7b^T9PiZf*q7Xs-fd3uq%7EDz4(ohehOi@%2 zn5^sMyt}n)x}nJF9ij1Eb5{qGB@PVYc+7m!bDrv8L)WC;9wK~Q9}bz#P8c5p(5PQ3Mc6BT-1vEcwDA-iU^Es zr90S9lkh9N`mWQTpP&GygZarxeuaBG<5YRQ8Z@r2*qZSSFBANz&JcI18K0`h{?M(T zCk;p1ZS59M2^W9{xYzrLuKg#}b!qdzM#Y+6m=A8xxdWZGiHqOP=PuZ++=81P7UlBQ zUnc5})jlt^oXE1YYi?uZ6Gwfyst)irz3vU{LG~rcj(5ys-U);}KtTNruM5!7tK*W+ zBVZd2Iw|Pe3rcccxS0lZ%A*hsiha>On!n%zw1Y|MuUTxO1B@ClQ%`$wsx8_f0w(o*~;rWeHKd!Lq~ z!*pk`8xB+-v<1K?n%8Y}EydZmBBP=rjO109J-dGqWmp_h_T(HI`l9X^HG1PuO$B2V z?}_~NJ-tA_civj~)U{UnrvF#34h;N%uYiDPXY+{=)t{D!W!zNrQh0HX`b}i8WT1`y zCC>Uwi9+I$%JAbJy>X6zB7+^1T{mr+2|z{4^}w@vZWf=1;2!Ao;{MreJ|_eXGP?q& z-~YeA%Z)7jEsKc!d-;9tTbOM)&tgI_EhUBW#(5yFyQvYKm+gS{QQ)fL%yiD}nleZd zxvqSEaRRj^@c_SYPtRrrWRO`1uEV&$8NRE7Cyf^9kLC?^w zy_B6cMUg8A#tE|sR(F;q^c=PMt`t(z72D1xtDp~-+e~5W4~yyp{sx}n$smsg?oAtc zUD1rqj4P1-0606yI5h5B6^fYobU<0R*r>!R#T61hIN^0o8O$wo?3kMR#hj86C9skg z24$0N4NeAHQcY&ojlHCU6*GnSbn_N>l&RuK4fe@x(DApAD_TEZRM%G!Ot7Z=Xgr%P zY+k$0MXt40wshJvX5<5t!Z=lmuyVtoGl-O@{> zzn5uO`qGQ}xg}|kBegbe)RLr9%AOh+*YV*_FN8BaLMw@X;=E`# zRmcE>mUf^%FB@>hz7vPb)drPa(sA}Nw=fp-c3Fn+%uYpenj_X#%DzMb2^X(D+~}pH zuZVZC4Dt`R1T>asbvbcS$=C2;)V_WKyKL7vK)5#KT}1oiknH*XQI5*_YE+hbx=b2@ zg|TdN4VcMt>$#`FiOq$8~>HH1^HE;x8J|~-g`T@K+LAU5t8Kdy@?Z)bDz5R)C)| zRrlJA{n_Z)&{q0=aF~LkLhb(s?%S)V{ZD66(L6SaPvD)33qOGh(f#>;EulHR^7#T3 z#Xt;hrEsvJJMwS^2aX+63E{FeV-%x0K$(QRhXLMKNx)*Gm&9RHa>2zWllRKuCct{b`vFmJb~ zCThB2hV_>eLa>=$R<>-9r}fW&K19jZ8~xA2VAq^tTBJcITs$DawC@n2K2yEIHl#f* zy-`WEt`}*N)5K}xEBmMk;y%vtADbED>{7i!RYYykSvUujG=k590jsD=VVA7VV9w0L zlu>wkfGjoRF>l%warLr@{M=h4d(v^|Wxe%M-yZwH<=?n=-ffc(^{COM(mT#k%O*>> z!L#Yv$CTR&GXhk8vjS_787?T)w)(S|9m(k#)GJxtAKOZG-Gi@jA2Z2p*gumTw(UCX z*u0z%IIT?7utXmsJ92B8Bh0of#WJ*j#NsStn$_l$EQfr6W3u)Wf+ucYmWbNZHmEyh z$6+i}V%#lF7b_*#l9cn^oFJh*z_RK1`l>imKwd$3CEzNx`9EgtJUuwpE@m?=KR>Br zMD54LHkiOoo{)tY>S}i%nDm*vto_rmH&y}kq_Y={d>V`mmy1t6KF1^{|Cgudf3Rj= zRUBn~@zG_^*RQGbSIUGUZNtG}F#wewP1KK*i?%8*S9*D?qIb}R3=~7X>x#QrRS#wa&T-UC?)Z3mMtll zo3UUU7e4l9j0`s7y`#hWWvMzjNw&L}mhdiLy5YokVXIX`OD7uGq^HY`I_Wy83YORy zX69c-Wf4OniZ#0(*^;J~Y?zU9G|-sYsJi8+crQzi$qF$yKGP5BDMdG+_nm?HltnK- zQI4grVcpsLda&niB3Y`CZts-d9Rmm{B}5vUyi1dq@x={?9ute1kdzm&djV|%rPnj~ zYy5OAjikse3Hdz-c`b#?h}@yMhW({4EX!IrPE*g#OT59Usg8g%tdfT3J%NUrkZyVU zXMpkzcFwW6+8)+kD}Q~q+o7ahj-DcMb67mUgPysXV6db*Eq={^ajw#M$>?(#vs&Xz z+^61$%w5Q?hh-L(rPT7MxGyUT1>-jj>}V}7=Sck18}AIMU7Wd`U|=vMC^ldXS(q78 zZ-O~;-PyDTcs-Hr3s)d-r^2vwn%%EeZ>eqDWSD)Z)!HHoTr^0KeMsC{B&U)WgrK)o zFqS9GhcUQfZHq~zsT5OT%cGZZ{aKP~j1J1HZLu=kgX=0ZH5h zn0T2osoQ5>Y~j=5t9hr91|SY#={a>N!M_sEvV}Q=WD22I?z2~5SgHvMB+TL*OFM7d zMBt`z^{8g0!q&7W<}e35>lY_8Zn)^1uAD5lr^mYvIv^NV*YdR(q*ME!I8yU$^6P>3 zs)9J%)~`=9{NKJ-c&^|n9F}Z8^C>5X5!Hks&+6sHTsmJ9$-{os)+VShV-x@V!_RPT2|!{)=j@-F;9$Hivwmc;y<}XGYhuOWJWiSB~5p%%j0) zpL-{#O*5tU7jTf_@%{lrKMD;9IHN*F3uvR&TNt))Jbp%3T%E7@w^JatWVJU7bOkMo zX!|SA)Vn?qD%69e3KRZS0iIvWF}gRyzmd0J4`qn)os*(#0ld%%(8<&Oa)MF=_*Y|# z4w#4c5364mnPHq4^lng`DRC3T>AvX1rh+OyIElB$w7!oyRydMBgI!9BT2l6Gx_Gz1 z&IfO-Vt z(Jv243|gbpb&V?gSTE?x{6imHgFI{n9CN^C1u%G6a=2%QXZai;M*s�=3&U(i$FS zVbmHvbQOH@&q<28sVYjbUYAC$1+HRYI)dE){ED&xyX2+G)Ni?1_RuG{}Hj`6}cS{`gsySPh@+Lzmx)PN!?XLJG9&DL&$n$^J^3 zF{SS6B(`iDT5=lUJ0ba=^YCKJ270xB10&IXO+jg(?<(Cn&HH9VvTKv~*!~T!PGkos zmel#3s(`UCrHVJQM@@Ng4|T56B>t4qpYJ6f$CZP;?|KwaK>o}`X4EPF{&YQJwY46Y zU(9yuG&WKDhg40b9QTcU}mv55GXaA$BA$|*NLOJ@w-Cvj~Tl{?>L(YJM{B9AH z6KWJuoUPCYj7jq_V&DHZW9cONU+{u9RuDHCD$RYMz7`k0ukj?Y%9TT_O( zo@ZXgGI-5tiB^WL;~u<@V)>>Y{?em&RvFtFds-zXQZVM`k=37KRIjIS&Qkc;)BbXN zu)IOqP(pYwABzN(dJzHnvW$j;Cq)QHavlS%jkEfSDv!e*EBfx2eCt(^-=!f zCjd70+3cs3ls-$IWt90mP%q%r)jkr)WnrSazmJ`61=Ba;IG67zP$tbzyi3|p6CQ7M zfs!DS`@Z9>xj&r~c0HF@SDzz<`&4>WR4MR8Z41466~Hi?6cSX*bX3IL^)Z#}{^RA_ zCrXqs?({|l_}WYdE4pPBV)pDNUpy~Dol zX+Cz0VXP3X8rGRt2IZiBPcX}IWepeCOuCMP0m~Ci+hw$w?vuD)sa@az>q2u+78&1v z@X+?Z%)+dW+`JYL4kyJYeB`ec&dvW|GcD0IdDTk`#&|@MVwR>LHg6=l&jfap%F(II z1-MIY&{rs^vz5N*%#iQ;F;eb(2Z4Y?R+ib{LeeflRHiN6qsK*ojzlXYA4PrY+U6e9m()g1hihciddN9p`YFusKRY~&hPs3rHX}dIqKFDL@xTIt;MgK@eB}#3k+ZUK z{8(H0*k+8=a5Ckjh<(Sju++N}tJV&^>8Qc@D{Wx)vd7_z)|&QY`TR2gD9}xcwY;1m z`(|OuY>=(fQM+ukW9FT7&PMwvUeFFI$%9IdD9?K6MPYZAS6) zQWbDo&=~j+xIsS%^W7Y`gG29yc!Q)R-`59~r&at-==}$fs*JY&;ZL^nb@&Ex^LX9Q z2~Qmqkn7A$?akV8)aDk-+TEyWS}%{6zL-L}G|3E&z5;C~|M&W+6);VCzK{_7^{e>) zsXfm{qasfKQsOR7(%PXXB7>kI%9C2_R8UV%93hrc!{JC#nL5{z`kX(I%Qzv{*Z{>N+@s zf7kfIp6ezaT9qO0vvR|PwcG@^e`Mzc!xdy&_hRnS&~28w?Xs^G zGt3GUfz_NVi|X$&Ba=bWtt@FR-BEsweSi-)0;H&51Pa>3-2pK4z zpWAO3^!?Y$Oin;*yMKzoln6?!bl6faqR#3`WrTiy9ygzT1rUVwdnp4ulW!YIE5Ve) z71H+nV4K3wknX72syu>j8caQ>7P(OZ^#JcLPX)4+=gj*-3f0-(PhM^2}xFX*S6O|0Mtg|ED<8W`!B6!F~iL^XKo-g!%-j zGO_rE3b%@i%J6Rwo53Yk(juijX7B_{WH5UVA!A)bvyZJte%(l#m5x|=iM$z5FP-gx z-n^fRP)1kXK|i8_vW0fb~^Z7rFWoE&^mezFoU9c9lB#p~)-IkAN%yi0)KVGVTUc8YFZ=atMayDdfwMR0LYgJoLxCOmCJJl+kqxko@3@l7cEfbjrr;#azog#sHhQvV(B0Z{tNqxRN^W%4 z@%lTx42_6bcc)Za_x@r5la2|^7P3cu|GTn@ zaF)KQtvlLBjoMp29&$*VEvQ*MeH;y!7W|Q%WY}KK%deb)Ay~ zn$y!7%#R4U?}LCa0X2Sn$IkleirzJ$$IeOYU(vjT&G^u8OUo#oiLDy1gF1xNot{Fy zFGf&Yq3ht^#a*q-cLP;Jzp!Ecop1J90c^F1osFP93LfMMccTY*uwaNTdTp2u zz&mT9C%2P|qxWW;l?YolhkgBzTW%T~OJ7f=Q}JQVi~-B12gA&~04R&faffSpU2Ep9 zU)0a(YdrYrj${Yj)h}+&JICx$m@yuzKO|*H8Yttk}D+P$&}|8cIewBa+}6 zpeIU8yV`*6bo$#%M=LQGCxc4+6u{i`4(xS8HI{}o>^$+uV=!`Gf2gcsih} zBh}V149gEA9-kA=cqMYNy#VqwxupI&fjB_B4FYx<5GvoziM^%^u4i-vPvL9#9Pz>R zVP^qGw<}aVjq&eB9+0vP@y1g;*G|*z=#hKO&WPj`D7+8WKIRmwExaWC2vz~mEk1i% zL%_KP<9(B_lXrbunI%aei}~Xhd-2D{Gq9>DrYJTjwaxw`2&9auHKLznZ7@wD{nOxX#3NBA(tQtsyNoxHltPL*sWhsoLOo-Q3@^TX*N+Aa(=<>N) z#J7jt=TdF1^dDEIP3pttzP239KEC!fs(G!$^YKPJ%0iAqFYk+~A7+PE?wpIoD#{ED z&vLN6ub~GsbCxTH^U$+L$vlz`GKup|3a|e2rI>?~%$zQ$w_eD`JtthUx_7=-&IZgT z`NO5wtGI#Aa%5E~C1s5N<4Dc>2G^dPfv9YK0afQaSPZ0pkC z)}op^LjE9;#uYMN& zxdWQ&%CTp*eaCN=G)Nf!9iravvhpKjr`LN8Lui(3h8kqXxydJWf0Y zN5=u9fEh4PqW$!VIMe}~S^_5K=jCYC#6e8n$aBI~~E`{Oazo+jN@(mF;}>-_C0SjpES zP57esF`=BJdIq4bbZIvwX6KiVz;@NiJ2J>v%gz7*e-Yb zTEObC?NU>k} zz_Ln-_25?3>HVRbV|Q81YtxRd88usB7ro3{CBC-gMFUB)CkqU>ARnuM%++%ndD!b* z3W)wL(_63lV()HOngitH`Oa`#nrwVRo!#^+fn95yz-?%)@oyN=!6fX;OB8 zM4WmA2;1fj?$J{KRwzVYA>%x>)>2UEOZ+#C^e_Ywcg^F&zo za>gAghr_^pnH3YTVfr*dF_O;yNBFi)kSO&(;l1{Y9Z0674kTmi;mv7VakCZ7e9b_< zMZL1L(Hn=dgko%`9SI||&qAfdxYgw%Dt-A9a%9LW4c%l;TUs?BsW6C(%It=q`j0GN zXL6bGyjlw7Ve^+=T5p}NATi1b1_)Rx?v!Btz3BJLsp7PidvLj#rgd-IDzpXmOd`Cq z+#f9xh6Y`Fnm_Q8sI6u4I4bk2==T2l)XOm3C4R)a3<204A>yKA*|7>ynYf^EHD)rC zK4oJW2Zx~*|{f@C;7wsfnht zQV>9VE)p=32O|?U*)du?rMk5750^IzZamm?ubXIg9SVd*6CP#7V># z{biIfXXERadV*#Yr&3f3K1&MZ{^};1?$sbi0)Ax8ycn47iRau+oemkbd!CKmyz#Ws zl#RCcOSH`^C1G|pqvxrvUgBV5efwQ!uJud@w!j4$EX7l$vxXQnG{`dLY%D0 z{K63T;MDcx8ds-ymq&M>qFe~N;Izx_<;%x0Ub4rY|9Wmw&!?>Rc{_{1yy;U+J4?Bg zeKwE6q+A+sidWIiHfbp6E}e6eU#e73z* zlxip(ZR@a1oW~8{^IwKY9Qg5GZo>{(DXf?sSFs4HuChb$%<LF5AeGdjd>T(-<=w@A&)aJk!cDJZ& zV)FA14_guJ(`7G-3O_OBD3WrGxS`Bsa4Ct68|l)Y#VF?_y`xKH2-T6kR~BY}eq!9n zhx;1&pK7S;Hg^ItsXIIJo$j5oyj!bFVe?VSIjz&n?bFN6)w-h*Nb(A-bh7VvW2 z9?R^TpR?RM<-AudF=?JaWtms0ddkSWFu3`a1kMC~e?u@{jq`;m)XnTP;B_+A~&%sTKsOiTXa8swj4Tc`QAT2~i-27!_*O1+R;h8U+3|n$>9q$+9 zZ(YW@iqdIdhY(oZK4m`K(l|V`mq#x8+Hw@)F8F)xUvnx4T$aPmAF>tZ1*bSfC|n)& z`maN(AH0ayYHEO6VE-OeHNla|=rIZB{eEXtF1UdEzBZ}FRW`-WEQEAqxs;(8dL&&O zfT5~2O__sI!?Bkv8U9WTy8*`TqG^kL_TIi2jQ7N(X6DcnsgpjY45;guo?toBZq7{Z zGTG|3P?2&|SrHW%-LhAw_iLms&IMI8NkxPgVY%5QIz>V-NCJ8~wQqLn-QoZh+Trev zLh~26+_)B3X1rzSg|hVinKXM)F(Af7g^ z)O^F&xphgxQ~oT;_G7^SLEhJ2o_9H;V&ku7qjym@J8vY~AoWajPwMpZfni9sU#F_Q zz_LykCf1o<@iRgEq7#riKbpVDN%nXm63M|j2P z{b}C#mMj2UmF$Wmtq1}Yh=aLl5&w012}6_EH-aC0_Of4@`>o!XWj36Xhj>R-BfP`h zZEYS?{h46EXMzDBSO&ALPaH~-RQCP>rrPm@C^RiXQH~+N zKO`#-?AfFqb`Vd26YbBL45!J6sB!+M*h}+xf4XaOoy#zE+WzrGNKx zlMUoy;azY#``-7!?H{dE0Sk<1J#?eV8SbWT^7)!LS@caNhO4dB+vE^hg;l?#| zvNhvq!1?&$1%n$K%zja%a0!(ca zmXh_^dk_>dYbf`;FNZ|-#^vaTbcy+IOZG6|L~ZUEr1R<#T%pw+sZ{~Foyjfi?wx9Y z@C}Ya31}Bfq)bfr^upzv^SG3m2kUuO=?nyTT~7<`ip&gu>)S6J7)hc>Xt>~X*4HOb zuFh|=G>|w-HNi_k{Hm?jl+lKh^hDUVCb>tku?7|{R{Gkxq>|3s>TzGErJ=MyXvE$x z=9+=Yx1GawUAyI~Ve^sYZ6EvX+V{kNioAzzscSuaaX3ldV;K96U5z)5ll&#wT~!qy znOCxx3xN{V^Qy?tIRVF2PtxN)Xo6FHFVi!-y{$fLXbZNu9=xXtBtawwbKy(5SOzw# zT*!~4Ig6+EX*jwsru*_YNoa}kN)^U}2&QMfOUlD?Kj_a-(<0Z?KHg%4Un+X?k!oVv zuvYBh-*r-vy7i3U9K(YB&Ta2&llp+fb{}2nzsl3)yEb{?)h3?uWIx#g@i%`Sp;0)t zFqw0&(}n$K3?yI%e5xUyAu{FzbJovc!~zmTiiTX3jaPh zUv$5Pbm-){1RQZ(P9ApyXT`LtN~~c|{iojjCUzLr*tTU89r0EGagdn6koK8Qf5;~m zcgjWWvpq|D-;Wr6)ee=%MBo`3H#aqrEyv+@$Ze5)KlFKgH$z{^ALZel2asD$TmNT) zoBEH6>N$-DT?WMIBei+jFH{p{eBQet<_2i;xJ6^XreJ7G?qVrOOQ0XVUWNHFe`|vy z6Kl@*WY_0XmIo@uwoW*`a^lt2a-0@I~zJbpSy@?y2xq1ky8dQD*I>Fx&&6T9_Y*OukF7YGT`6m z!+2TPUdE-o!Qnp5w}#c z)9|`3q^|myG-ZVjn_KHYR1Wmp+c)3_7?P0!uX*)1cdCvKc?f(?JMOBV6++F-WB1qS zy`_#$c|)IvM)YVl?T4~4)E7_9%tRg)8aN+}O%IQJAkOgpK#DjVUEW1GvnH;m&Np^c zThwc0>nyLXbD=R7zV}oA6DXvuZ5)7MqM~>Ulxe`0O#v7X&f#ZcN3W0*NQmrptPq~r zt#AcLeA3Kcg8Of>Cmm2yr_Mk{M*Wn)oZ{wfcTL24vSol^{EYjevVlPXc; z;~L@D*faP!Y~AA9N?uOa6y5{~X=JL!eK04F`O_^j4Re8~kaYbJo}d-&vfv`Hg<;C{ zFKSP8S2LBW?(XNwe|V4b_RWhhnF-jhxPUOoWO?on>CO>!sb{cfOiJ|mo$AD*OL3+cKdU?rN#R_hDC+TITXH!lV3)(`(Li> z{5%}|v^CEzDorUJT$gC-LDOd(&Bia8h+V6?{zc*E6U;lEAi z+$f{gIJ9znz=FjJ$SG^(m`%NM^oyDYx1o=BZ*WogfVAnD1_@_Ud7Ox=4A$$(kq+57}2$sjgV!{bLb`q+bETtjZwY)5*+Y zeWu>sR2regV(~2NwcGytAfoQX8#kg@UnxD)V~zvXcq1Z6JPYp?)ad*C;@GH|lZA;D z^h2s&V}v@tpyZPE(o+cvOg(M-u@$r%T9IuTIvV_^kKw8Wb1(doN1Mw7C#U z&FOoX_d1%-jw7Y-=)z>!A9o_7lxbwD$yV%tctb!=VG`>!zn0y!`N6fp-B%K~Skr3qjzRb@i}%|kXvvAS%wvvUn~Jlos>WPj8#r{GE|MYKaFu@Q3Ve=r;-39VtSHC1k$Te$4tXu8_s`)!NIo#>`1 zC*ICwKGWNTNs|G$1+;1+&*sv(5}*7S&zHJ7C)84q>s*;D5+?+P^0$+-+rbPgu(f1y ztG}cqt>j}FQ0v_hH!lc4PQnasL2cfR;cD@3b(KB;96lS{vj-LTc5Wzfu~9&kPtP}K zT>{=ils`91GQ2EpWMV5JvxUfYp8BON*ra*bvy3_Aim673)oVz~+U#huQKjCDGK(8^ zYPL*ZXUsCfRR3GKdd(8an&=h-d|es-uJyup8kh|VkM(*cS{5*-awx`&8^gYmaQ)+yk`rpasoje zZOVRDt#hSY`Qx&RlD0}U9#cfw-=#~EOhW$Zh-*`_b1b+Fk(qvEQ7lp84oMIJ6&M#N zSo<0|`*vXygc_Ge6vq{7TN0_P5>ACjSK}zR&A&vzxLjfC&>-A%S^CDlJ3_B9U}3&y zKVLgAV@Vin-p?bjx9kp=4xIh)WAb6GhkK&J`Gqx=K3ff=G88SM;=7sWI`ZVsPmrse zpHiAbVEBnTEe7WD-3Au&Az147>-qnyU`&oaVAK>5Pl$al+=T*GWL`lg*pzcW#rE`Y zG?{dp+;TquHdrSXrHOzUJ*r7GZthY3Q?> z9UzNa$sq8+j?dNfn%LTOuk)M-=x4xe(zxI>9qV8n3;0^o)#6M(fqeRmIazr0(r_viRmtf4EhA^z9#SH$hxL%4<`n@b$?Z`~>`T^I+wC zrL6ycj^=6GvlCn7ePuIvX}gF=2Q6or%fGcn{Gn3Wq-|a<5>145$V*?4rvbJkzb$as zs&iAQnj*2wIV)@U)3iPM<(2uv7hfV|r?-Ww#+D2CKN)6_mX^|G4}FGOq_#DK8=I8? z?c|iEWjK-_bfJ6^->m;-Qzmt$wz6k;d;8b$i`zFJN5E+oCL*3)gw5_-hJ zd%VR>u3;{E7kf~wE`jgjrmKfBC2$Ge{Ji_r^YtxL`V7U>eZ|mI8l-~!C!NP!4}15y z<{JmR=Tkw^O8)AY9dWvuHNop=nI{{e9u%Jum%(*>^zb@#Wr(p!Kwjm8(Dw2EUkZxL zL$xs1>6jfQkxOhf|Ir#+>cQ;{8KKr>3+Zm{xG3Yo784Zmz_!@j)}AY(KXW+&sebs^ z9pX9}?3W+rmHxK>@;{rbU zK)21KVr@0KSF8vGZ!?p3icF0_RR44I&jjp8YFija(*IXnEavp32FKA%O+b{qq7EjVWg1B8gNDP`Aia%Ftug;xzh9mj|NKf(pq$6aV&mv!7(^RB~*J z=8bPTYU4ih>E6iJ2{L6#a7ZCa895()GPE)BzCsmb$({PaK4&Ep#)+S116$79%oH=Z zzw~}3yraA0z%_Z7eR491J!3aUGW4=>(OJ1X>E~+!ye!81u|BkPM@tvYe`efjJHd+p zk{5T8n>IPOe(CCzRZbl2?kbF~5by>PdA@t(SeevhKTi zA1(`@)i?Fh#4kXdps?N_mu@FqOCDfG0u&f;Go-{KpYvOJakN`BK@)(VVIjN)_jmhf zaqUIC*knrY!;Y`E{c)GP(CSbHoCWkG{?`%VKJ22DR`oD!9x;%byhaw7tQmX2Bf$7O zzfF}pX;Hu&(Q`JJ3Kp`vz9~o$X!Hr}A~|Mx%g53aA)CX?1autCNNn;0l2Y9cWTOLe{AaO^NUXB^TC4tQ6Dy z9K!ebWj;RA&Ks!-uutGI(690GjCpBqVF=5KQ4I5&g#8F>1QuD^5!mcTTHCDwDiQDM zZ>b~?oF;`RiD<8anebI)@5guuO3pmff|v7AJni)*?=P!lvV|yGmVkHP>(;BKp&2~* zPyL+MRiWi6>mE?b3L~o@4hOmKhheL-4JMzfIK`0g)y~)?HHfJ*PIdJpWDp39R#DoM7lAcv@&&SYAqH<;&83Xc?Xz`XHZ& z>^t#h?b$^^w8r^$KHuKtbZJ&~I*)u8Ia6ESv1>vs_(BsFLqKGk+l zD{gqT`Ze%WKJFk$2uQZ~7JqO%NH>h&d?yMcB{=sg>+vD>#2R}TW1=pw`(ymi`G_us zKe{8hW=DDKmMeCna{F@O@Ro2&bTWvB^97hY*UK(foHx22G2O&=$^IRsqf7jvE!zuk zfP&anL9uXd;UF0A@^5b#EeiF>fct3n>^Hj8r21}``}qu&{Mn4WxqKr*!m~C__WrX0 z^`oi!VfNt{rX*}|AHR>u856->*1yf2T~5}dof{>3SMBrl?1`m;&k3-M&e4n+oODyV z?X6>4!!1`)&gc7k*m?PU2pY@G_{MT3&XhmlUEnVJxJk6L--lGU+E0&~7k-3Y5%_&e z+j-~TifdLse8-Axb@*JH^5~xXvn1-ahbGGriBF{D8Z|HQXO4+$Hg^AyrLT^P^83D~ zq`MoWTRMgiP=*u)ksOe2h7L)Q4<#K#4~T$BcXtjjba$tew3NP&-`~5|UHXs9HP5{# z_SyT~bJGZ;uY2FDx;LvyCRlJLu+eLf;S@!M3%~9qRk0B%j0l>;%*RYtidg*i%4G%s zMw4`+2eGtuAPU-8((Awo#pkao>=uP7YKWGFv-pi|+85>YhsB0>X<>8PJi1&vygQfH zxOc)~kPM9$6>*b*Pw;gnn`lD)2%0p+=hjzh77TKwx|6=;M5|GJaGt6TT5B(<;d_Vw z>S0`2M?ydOxshfwf`U8dp7HV3I4@Z(*RbT4of`T^JU_MiH2wo4usJr(a=rewK$G$> z6;vONT6Idr(lgigE@mkNKA2c@rhtjfEZUOa0VK@b!dw4i#DHG5<b!-jkGf4-J4Y zIO7Q}R+260m)1iS1z4#yfddlxhZv%CQHw^qICF9~$i_7`ywg=|qXW*4@z?zx;;!(U zMgq?J(c2z>OM+sPq@xx7{H{NOw6(?=6>f-VXLb_3+$;&bMu9^ATk4)iH zha44Gw=z&iH zfXSBQ4!=SK29g7bF+yZy6f+|OM^LtY)Gr#w3v(a1`7P=C&;DCz7*Fl=!BMYsjwI%r z-JM}{67$^TrAhk1!4jPDMDAO^&HVe6ffBcMpUU_45$!0;4Fi?%_++n{b3igM02{8U zR1DcY-eouScL|rSMa4jkV@fEQvBYA#a|;q1kqB~)5J{u@F-J?J+l+Fy4%yT)?d(2w zppMo?Qst~7_H)-F7Qb%Z_lS1_T-OyX#ozVdn_;b;KS3-1R}L?d-{nhGUKY8mv%z?U z*7i4f$LTi?(L;5Q2s$4A;0OQNd(#s|Z(5Y0pOe0kTy$gBcwh*L|25ip_G>QeSxG%8 z|B2C5Mrv4u6I_+)`QJC1HA!jY(b*VroHZciWP@b7$beqUnnt>MBURCy?c*?|wbrUG z0Cs=+!^nvsymq^K%j6Gks9+lTD2k=-rN1+DsEhp!J z#ihvL$mV4Ra1?5*hGh1@%_5Le>S?MLuMdnu4})}Pj$*}mU!*zeBKZkA*S>1I=#)zM zrbkxl4zd$;zJK=Pr7ruU9gQlv67C)D5P)Y&hOVvpXI=xC#5X>0iZ)OHn0UfIFV`+VZmiJn zSCl6p(>S* zP7M&yHAifC3Vq2ea1j%()(i$D8{HBeK3#4~UO?6bGSQ+_2IRYnxG_r>ccLm4laV<9 zd$Tpkyo*S*B4~Ufo@qrq0|Hy_`hC|@gv~o(uw7L%iLJ*w(A>O*lT%-@Ug5ZsK-%Q= zwwYa1Xx?)oOaFkYh5-?vS7A8>qxPStxQNKou{E{2wSb3qnsNbOk_xCw`y&T1TEt(h znu7d8j~eHiKl&sqR)0}^Zh7X*i6FW@{~h%lqDgkA7=~<|^Zh$a3c$#B#dFo^b=h*D z!OJ2eA>hI_RZlCN0)(nfdztA(B z?Ez`X{od?lwQi0}$4lVOwpQ{m?BH_g?qd4kt}jX`1^4a+#scu_-rog8=O35Ke4W9& z;dc)-7gEilwPW*Z?Y+B;1XjW{TBl4Kcv`2sT?x76u3yfw;d}L$wN@9_*?QvW$2D8ohV$D4;8g8yDAN73-#)lQkONch2;{+?ek6RgKegOHsQYdPjWx5g9oI z!m_oaBTfkr(mH&Pc50K+!FvVkF#3L*^e>DxdY!*H@h|?9;64qvhrL>)9)L~RKQ+Dmu0Q9LE z9roV}MZmVE)hihCRYQjgdadRx8V-!!NA0XtFXBs@3=qBN1Xut&QFX~|b6ZX&!2}j+ zjfSyetRSY=Re8X+JA%@5Rj*qQe%3TD`m-e3+DnZ*T14K3G3-&jA~$*>uQf#WF}@`8 ze~gKLprLgI)czqW^%eNy-rnjPU^mz%)UY)p5?QhQq=J6Lhx)fp9_qd(lN$SAyxDV2 z0UcMvJ3FS7jc20UiL!j95qAf0ija=lu?%E1q^Vx5SqHH#c=0$SWGX487C%1bC)j;E zHu`Iz@MBU2i+F9E7Qo8E5Qsz9^k(tSeu=TQ%@w#9iss45HgL?_2L@ENStNgs;l_5e zYJb){ACK2(o&Oa76aA ztu-(S;+YsXhFD+G)1E1EU~BMWG`l*7UC!$-*f&GLSTgj|6UcM)z?dt4Vhn@zFCI@f zm=aJIS6dGGdLv~HGU{WG>fmqDfn@NQ_l4@i7E_3z!wB`Snod*sD)so_- zBYVyJ8t`)Tp3t|M5tZ>eIq>N!hi?H6|M*fOyM!k|F?gpu?0izt?mC+#VC_dw86(0s=ZO zGVYigiyE6`+ed%;k!xeb8V&u4(j+`N+no5r*zzO}h$D9}!8B-v+wL5#`q31ogo!B~ zXZ)4N&tEA1;cYWN2`b*WxZf-Z??cNHUg%X(*UNZ$M%rq|RQW6@H@w|DDUEJ(bBkM? z6?AWoNq+FV>nnEC)VN9DPPtp_H|z)u$~5B(?f>em-$xjoVOS={GdM+Fa2*lNq=4jnk zbn@4JVo&Xwek}|@Tmbex7TlE7vQo6b{lc;wY;~#AV-hGZtwN z^x)b7;J-MM*>-_+76T?QD#wKb+G72L+H?}|DgqAhICdDuj=SnyBGQ@&<_RE~>w)%y zx20lBIQd59|IEj*$iNxSyW?S9(_F)LXvMBt^gBUH4mS)x0w|)O@ig&>7=&fw7=z8q zsei6k`x-O(7%?{6A|bFi4A&!TJ4hTm8<^$wi%is-(4qf4fv{=P;XOdhiZ_z+Rs5G> zvS4l_urRmzUQNm$9C)02VDJs^ln07m9*8w#|HK{y2Ej<A|PDqlv$n672tbCQ67g_t;iC2^dlM{o~WHOtZzaXa%H5M7Zzf z0XA761D`YaWV20yRFLeAwuqL=IxjjFKLpi|n&IxGY*-KT_7=MSK{)X6EjX}D`73ROm*rAB|qdip8^H^{OIk(riN!@%O!b_gi_~O_yi&hP2#ofRTVMY zGi6y#IR+kqghWmAQ@%K%mPAFcp4iGkuInVj*`l1M+h)?u*M$h6#{T_<3C|3>#!fpc z^VmHFdGMNNev9n?v3r$=nj-`1>z0LE;aQKZ8tp!1@vfvVf7f%_sQdZxW&sb-RY8KKenqmZ#AXl;@Vmv#i%UR-L4NhU&F1j3K8W-z*S;%?g=2VcSjz<@; zJta!n9v*y)eDMfhJId92WJ3)mw?pehe=Lna?O?`sH^cFz#73D9sf_$4d7E$gmkRZl zlJ-txM{uHxN#^tST$}Y7zmLz|ap-uDsk(xrNu!6@{un2od{K}w9qvHX;~9Okdc#E zGPfGOSOOcd1_>^3(89<6O*`8TK>-X+Pl)cl{1kzaZBt8FsuWQ;TQ++%OH?JJO!W zt`rjv`{CZg4The_>(h&JEdk=*-)Jhvo!p%LlCx@!tuC!GP{9u}^vlb=)$Q#uH?52K zg-x#hv3Ndn>86Q1s=3G!z`uRBHc%`B8NbgfW;a*&wMwK#+2R5qC}-hi*QIi}l<-vl z3^?-aL&p9{Ir|qFt!ZnNzUJ{J8DaqC_YI7uBk*IY9Y=g`!FDv~?M2oL`Ug7M(wDsF zWNDrl3X(`=^gnJJ>tDY84mj%kEB1-&%ip7Tzts;IU0B#f?&)<7W25Dlqw3QT<0UW$ zwv6~vZ&Cc&=8heakG{|EKeHd#n%gy+jSy#ompz*#rjjx-2#1~H6N+tLt?z7Vom#*qXs+4_qv@k*%|S-Fb7SLk&8N*I@||WM&}P@K!5|ZGElpC8>0wiZAJUO3tuYC0ICZ@Y&H9L zrH>^4jqKO>%seCw4#j+>{%+p>y|cY?zTP*TK>4Y}p#)?Y6ZfG?gi5bEYU2Fo$ERg~s#Vk5^ok=G}_ z5A9wLP8xCd>C`tuQa^k5tBF;2n#3Ac0Oo`+cupj5E^i%~-uyKF4=4{jf1g7yVzd z6hH=z(^Kz|DI=(lygj^aV$UEMn?I*0Q8>YVzgMDg;^I9MdG+102!dgV3tRD^rB8o9 zZamW_56-_{??j`gP&&^I>~nl#-C#lmCf+gtx5ggnIy>Y21FkzCr4l{k#_1XMYn2Cz zB{JLmyi)Zm$4HUnRX^+70(}3|qGv2bns2rjzc+0a9>4B)&ipo*us(zr5&rRXf|#Q` z+`~s-%EKcADMAN;LMJdo(e3ql-yc-Mc<;nv@@7|M3xihcI&k5}h8-v3_Qu__jjj_p z0u~&)&ftfRIJw(CSLxtFwJ$;p?^LC=_sVfZ1bX_FSzWU4rM?>B4@);86zZghegHV0 z!!vKeg(I7)`62oE=nhRRAa^KM_w0FpzAne0Gj_wN`mCzB>6sPsxlgej3RG<(jA=A! z(~---kqd5B(N$-9ox~dQz-SLOqC8vVL9ErgkO~a}PF1PqfQ*2SDa>^f<_bLrAXeQB z&ve=YLcgw>J+k+KELtzW$1Wu)ZjzauIaxKjzpQtvM1_yiq?Pu^EN#KmGm9vhL<9A) zsNKjuAdyN=SLDc-_ysUVr$|1D`?b=0`Yauu*5yx^4DP7`EwP4+G1WCBmiDs4OLOfM z%^acOlL|xtqK+Z(78Kv;{yJaPoSZ`XI7R3~g@%!zadZ6uegw*!t-;q4a7MhWJaT6jNgSm3 zcr?HQ*pnH5%4-2KN%5so&bT-?hnlom*Q7I(tnJt=JRl{uiIY{*Gi)a-4*)o5y$#gc zSUD;@v$@gvXM6mqd}Th~|1lQj1Mz<%pZ1>zU%3ECs@`kVP>%LjCyLBp)UKB-U$$QU z)pmKL3fcU3zogbN;OT;#ib{f5Nm6)Xh?6kp7x1RMNS1krhjnW0wBrmdL5qoA&hpE? z%ZG@n1JUf}`VqQ$s`SMKn+^OsxQyH)g3SNnTzUkOv$%5%rx4IAf5)Y-&AUraec|Dx zMT9{3|5}JyF-lmN-z|>4d39WMu=sMz_HR}06KfD?m2$3O+gV(qzV4OxykD`t$kM)f z)BLDPZq}rngg{o}ThZPvqyPG6fmtNxsS*}M2bY>zAp*H?KyBhJZ9qKIgAkHMvPf^@ zhrm-X91=C?R(h)O3yDTjQ3Ywl7Wnw35I_2zT6|Q>Ok)))yT9sNP83f%!0g0Iu)Kev zsq$9N{nRaueOT~M2DeB34hi{Hk9)FsuFuzI@<*i+eM;TDS1+kA%)Mz&5Nr z0H%WlsLV7PUJJiZNSY1IU4$Og@c_V0EjY=FRyIFfk|2tCmsK{pOVCY~93Kj7==|_S*mB`7dm(GbZLF?q72!No zuGUaBXvJ)c<|O@nV6COnqDmx6K;YxVrge7xCsJ^auMJ=*JA`bxWWd6j_G&vpNMS?KJaB#VkDu~pe)QB#* zF$BUf1gat8TeJVduWCDAKJ9)u;}GjT#ij3%GF;EJ$V`bLxSICEiBeX)lo5blv)>T* zX;uu4)BkCfvcR}WzgS21)%<5^s5praSaG*XrmN_se3+G}-NA*?;l)U!~E(oW2^KPCl z7h;{ix!P&aCI$qWXE|OPLvq(yauPeV0!^h6H=Z6AZE2HGDhd71kaW}io@3Ct25Pg0 z+22pOoHsXael@vP6@wYA$Tkn3FnJcB@y6BjNA&&;k(+y2M3$q1X={5|SQx?2SdMl9 zx?GUx@a03e0U_rPF*=!-LRa~W{khSBRo@;tNae z(~IC99m%-WuiIn~;NLSL+78zom8+TivCHagmrD4w6k4&jmyaFh;WFN1qh%g@r@|6? zXrh@c40^0uZwP<&y?)s)z?-%&@iEvTw)8TKoL5X2R|+fQQKq3NV%t*o$BuBtn6sM~ zG?@->*$S65`uKc7Qu27et11^gRE}pB(*1BFW7mkWiVCQ;w&L6^?EB}S* z^$-NqiZ$Iyq<6QRy42XMq~5<&Mp~BA?}_mK(cACIyQN+H5sC-2ppBX(nQ^@lOyVF` zBXO#}e@I4EAx-SH>9UvDsH1UPxLV-%!(ld#DBS&&h_p)j@7<5O@i2?9fDRT^w_>$o zNWMXZn)t90+@V~do(I+YQZCjsNk*=1cNYDPamIui^(|?H8haWWL%mMTCx;Y(W+@e`&M^tW)`C zgxw4-TB2x{wCWrh&Kx=p5OFbj>@)fCCw@@idrHw9xC>8}%(b+Mf1VWea5T5kQyi&K zjS9RyySh6*X1EZN+Ob|wAOdfBr7w1_`|K)P+is$T2IqB$*_MkOA!_Te5cJzNp7$P{F zb0J_-1Y@LHw@xHdC(#$wA34-@G?<1?ueh#+g3`Yx)8^w znIFh~wLV>lHPjct|9v=1Tw7{xqtA}Az<*uuz#ht9MSbEXGIP>*RznH5z`v_5wHqEUb)6+oy(uco%4F_zZp3L8Xyir7>E|%qUft%=NRaK z5XpB9@L!>M(F_!Cv(ebf_FUY^mVQ^Qv?&{(2FA2KF%-D7pO#@Xx7PFmhSi1C>FHab3OrV0a!!JIME)HTcduHnWtp&lsIZu`_qB2VM0KmW7bbBkaK5zqZ0?(Cio29n?DhF@ zw@}=T&o^zk%+x!(%~=HVpTpcXwPw@(-6(Uy>)*{yb={7QR86()1R~N4+uO}i3YtW> zHH>dA_TWluS%&#C*850Y|I{ZWZf zd|EO6{lbXTr7iI=cM641=AF@@uYw2(?`h7?iBBjHx9+qOF%>Kpa>g>XRG6 zrEQC*X@GLF36kx33@^A9a0YWX$}1KpOdr)xt{;A#cPv6U<|7rfLRtva=3rngs z&B<1loT`FJ-+h@5aL^X`F=Yr@86$AgRwJh!y3A*{t7xl?uNFq9euTePA5$&Bv+^KS zAKPQI=hWv)c0_f`Gho-}dRH+MRIqZ{$nY7(DE6o6mOVQYP?z=pa8?IV=2K?9j~^}T zb(niTh(TJ6cJ2u%LRvB=%&8+JQTve`9{*V^Hk3L@Tp3XW#fL#FV}VscNVjUr3v_V; zT2(BZEh~@hNE%14VcY4Lt+>&O6X4w5Hby5hO60dg2mE9YJk==0^G963>C2IV^)0Wy z&wda*5<8~5asx=jZu6Ib#Bo?J*r*4@AlxeY7<99l5+L~WpHD*LVmuT1QkrV2h6=;p zoK~Do*nKe|Fk)mn+a8Jv3V+gsmSIXtHx2*^3n=fwfWITKe9hO1l@~uxq#EAQq`1>? zV)^+71tgfKh2B!leSA7);Uy{lD7NQuezky76z(5sdy$=Cy1Vj7I~0HeL}CFjd# zQ~&%9DRwgt3XS%l<2z9y$~G+8ocNl{8VaYU{-w>O*VIA1ala)#ee}G={{~&Mk*5&yMh;03MuC{m7~RtYO0|{cS1v>n$lDDM%-Z<~0>)DJcmlFIc(UAXEu{Wjk}W6)Et4ey|}qQBUwtg3Q|8n?@PeB3%(;CZ)fn|B3}a`hUWVnx8pK9nTzrVIfY zEBQt8C`@Hntw2~wXL0KlFEvaj1YzE1Eittzy6KkwtC);U5x`p_{2m*XBJDYG(^m!}Ez2{q1rhJ0As8&LZMQDq^`52E5k z_yM6k6!P5F-aHu(k50oSf<&o`&P%4cDBgAeOOUQE+t^@#v5IlaW*f&_AQz1nq+@&9 z!`Ad?XM1f)^UJ3!t@epm3Pq}hbPC6=j3QedrB_T=pRZ2c5YSRs zu0jX=rPB}2Cr)Ze$9FPZggW}mxr`HM+O=_vD4tBQ0PA^@!$Oyn7AQ@Gbd1~XV)Td|weu$d=X2e8)J0B8zQc(*Z<;D|MFKJ*@V|m-r!{r#QJZ%T3k^v?C(sPH z{!i!ChlnuEQU^}%EJHO@y=2N#)ri%p5{D5`9W6zn8cYRXvNKqd65`;#;c$a+1D?O~ z(5VvGZ(|)ptq5Ifua9Nao(?_5^rhXtM=DjcF^%l98O#$W)xs;g7In*`Dvfxhst7P! z|A=2?My#MmR^rXIc>bx}w+)42T~{C0zEK!Tqh4si#Z-?}=jupeo@N}r*VKNs2vdx^ zy?t^i(wOa%9RqbhS~i>haPz>7>P{`pBbu(QvkJ@wPqsPodGPfcN5S%I8&S4+H1p0V zbzGjwdJ{lN_Cgc?yw81vwI6k_z zcw1_K-w9l zuAJZ2Wq2CI7>!`^+k|448{x133>0o*NdcUSmt5`rFf4PXseFdJQReq->L1f`RpnZ4 zF()6f`v?N9WYHjQp+PI*ney0i7_QV$%H{bVFuPgYI(~@+)1rZ|tL5UlKT_OZe>JE` z97-G9K^A!Ekg7M38Ui^fF_8^Ej8#IP!MsuRvykmjaMLUE95nhn+lF3GwqGq4h$g^_ zeVY_p<#~Mb0fi6KSz3YU4vy~)n)m^80#E_C~g7UB>tm`BEo}Q)HwT5Vfr6 z3-v|<6;AFpP*{D_m21qyij33>VzNVX>W*}ua$c&lN`Z|R^)>;~UA)N{ckPq+p1Y~O zp?A0c4bC2Lk)uWS z%4>leR>}wMPhU@xH?Z`nM6Zx*rH7qE*AT;OCGSYozm zv!BMz2aW`{z0!Y4vHhx{DSY2>=oFp2yu@$FQ;ngd0RU5qHzS`qH5sYm^#VEcIyB6oL6@nrq zEtd#5G#-{iNY~EbolS{;s2ElM_A?BQp&mkw457ZONg>`54p}4gmu@C{V6dCv(NlE$ zF43dm5^m5IkAL;i>GaW)NZPY?^WA5u3Q1x z9R5kUPbINL`hDJFYet1Ap6K@5d`VMVOTRy!;|QS6Y`ubFX~o}oSbU9k6&NSlOZymX z9qQg5H~n?LzxsI&?azK&p=s;-fF0Y%|GN>vnESW)r7bt*zUK#`as2Ci{U4H@E#1p_ zylm0z0NzFTfj(MPrO9Q%7R~+>xh&PdVh^1DK7X+wFA;z3vn@^oz-GzLs_v6fhM%Jx zYR%d0CX8`cUNw!S=-TAXwTxR!!;~V%BtPF2YtNrGR97O9Rz6s(guEF6QN^Rg?~b0^ zG_sz6%QVZa2KTKN_O1H%3lP?Yi{y*goQAl4hWLF3gab?S=nHQ^ek~jv zJ{LsoNALRMcj`KeJn9?)Jd3Uo%2Ojvt8gN?{B_ad8$q?J@_};G(w?vHEoVy4uIW4- zL}@A96~1zd52f-X<>c}w4N^whvduB6??)A0o`l~+vC*2!zyXA0azOfN4AV?|Rx}%_ z!9k4NS&aL>81sGM%Xi>Qmdk({?1cC9_;)7wKA=NyV}(!GDoOojG5zu}{qP0!^$1xL z#+w^&!O4^EAMa`@-w3x;?2UmVuYbJOA$O zD6kCx&v(7;G56UR(}sZWy17{=YZS+55HGCHc2DP{)AwvAnnqSV`v6)7M* zSVOaq&p6%-c-Yv(E|2KwuO5E)R>~OJKLFDkFx{YDaG%t9Uw`{BgS?gLcRxjw41-Be68spRu&Gb*NIy#b77Ze(2PcHeD5w`h;IZm=J?gB z^1Wlu9;r?qB#yDg?h|1%D*fQo3!R$Wt(iKhnOZjQJrm8>;~u2s1vZ8+Vyi5i)CqBB zXcucF_R18iH;5C6nR@xDkmepm!GRgQ^gH?gba+V&JZW#PeHWLf6)KlC%NNc3q(??$ znLWC(W4}iNT^M^F9tGp$zC~FrT<(q@5$dH`Wr#waY4Zs;_o|5e_8?IQ_C|E3AjTZ( zW9zB?=h@?zYs0kj4W9wXAp=GqCm{MYV)hc@-@$jY@NKGBt_Uwb5dYqVhMz5Jgx>c6L=lAQXD_cX`O&BC&{eVOxvP@#r(8G7!w=|zo z=Ky{Z00#<$gR+57#x2BkOl0HD!vNNDwSV--9bweYUd7yHaQw1b+VmG>!7F*@K$As0lO_nvps{*;{=2p!e1>==+32i$5}^hnHZMh!zjo?Hni1EaG0t}GAH zCOvcPz!vuzL@GwY3SHJ>8$Je0IJ34A<`bnPBvCfFPW?J%%D_s(*vh!EeL;o+$RU_Z zI4j|L`D__4YRJEcFhvS8#Wb)p!4$_L=Z9W5M#u&cakOWuh>ycZiG3Qp7h;M~-wy9; zc(zE*9NEqseN#;?Hv12#F-IcU6u-Uak(}Ay_x-?WLdYAU5sv4W1zE;^TQRRav`c?- zxN{!DxWa+%F-d*KS6NLAv&un@h%Lf;Slo82PSiZV8Rjve6#08c_TumA>PD``zZ?4> zAIIvC+8U|`opjyjV?b~jk%{pi(?fnT{jI!?D>&iAs70oT?WcD7qtn-MU85%qW94OJ zD(ZNS0XAfu_W*R0W%gTd*Gd&O(<#fYAFP{mTC>a;FTOyt1~kIi?q> zp^Zk+Zq(11n>8drlyAyu6qcj{LIem7K$v^fBqwd=dBU=T;^7MaR;WM(1q=cPeXwB7 zwBS!lp$?K+)ueCz8@_HnU@NihlYYKD+Qf$m6gw7VI(ICaR+?z_4{^F3zu*3CQxxd6 zn6MDD6FOw`cA2pUC;^?&y8dIJq@jh8HfzYs+l3Z?dcCDoy=bwoQ`@j;3YiTU1Q{>g zcW4j;vl>!x4{a5iv@U`6vp0!;wcLgxyh(MsWh(eDjmr}FQ;n6wJS$W{AE4^c+XxNf zDw_IR(!Bmp(-vKpA{Ih+Bp4wM?Fwvg)`SG=Kc~&Q?fVcN?j281;eRVf4U^LR#gX^hXgM84CjYE9loFd5 zMeR&etL@&695U1Qe*`-J&(_u23+TMdzYX_Zlg)r^A zJ!ZuJ?=tOQ*K_(^qgd6n2!oD6>C(~_+*4*W1~6;;s zF1Zg_h!*L?#zhrMb;vrltF>hoL@CKSJlmVl`!4;L-`gRpGNpGb3;2Q**o~;I2&i?> zna$K$cg3_e-+cOVlyEzPg%G(5dfb~z>%Jq4zN3P5>sLj(I(+j6_OQRmP08xxcFa7} z@^1i6K-d>9+xNSO5jdfUcP(Rv##e)K5*4e3$ijasrf`W;9R=1AQvYMB82?TiS6&Vb3&X$+p*sCT6;ML|r$~at zqi*Ij@y0>@(!pmTPo^*8y?iz&eqw*Gg)FYvaL~gbM7Yne9!&{-?p+VB``n*FozGl( zt6o+2H?`TYK0KLnv_bLJD54-C8D=T1A;jlx1?N1w!k7@k8($OrR)zyzHGoe?=3(IF zQ6m$5>1F`H42^&(G{S?@7#bHpK@x!Yy!fSPF_L{TrVyvFmZ-`-U++!PYRtGzkE7VM zx!5=TQsPg3?W&*;EZJiun!AyT45V#O$pJdN)LL3S*ONQ`4}dkXOzzZE@JKz8D2 z$1DW;_!9$~do+0vnmkBNVWc<9YN~~IFjnR4>-cH4c%&NeC7Su)1;lX*J<62G%3hN? z4V} zXOW8Prkiyj^z>WYKkI@{kPPiNcQEXDyDBGfJPU~;B>Lx_Rn(C?mynf}EvSJS3b;P= z-Rdd;vFwLmS70_aSJkT)n<^LSUK}P0{aH;Oe|*n0nmgnRTs*n_{n7=JxAMdCoui>D zo3D!{Tt&f;cmOV->3zL1Nr!D)_~K534egU^`JP=-?h}J)o%=JoA@cdgP`=lNvk|mm zp94Dx34eoJ>F~*i-`n(RL$SP<3Twc5W@Wwo|INQ?oc+v<`=5^Co}#vm&o?VIQvYNm zh984CSXL8rm2iYsEcUw!8{CpT$&5XdIboy@RT~fvjF_iR5*FI^ih&|XIbkHN zWJe8#wG+)mA*_&Osf!B?d&4h;{6PV#+ReOa;jC{9n)ugqEM-Q46856OWzY0m^WO0a zIj|ocKrdt7hG=o25fkTEI*q%$H_)W+7O@;pn3}WaM3ackd0?t4erTgGh z_p|Q!yoLI*#WgE7GSaDFO5<7YNLaqEaZSRwlSOA|Xf+`fZDEqD9AdPK(8s4omyQ6# zZ02N3r6^uAE5o9FV043U9u4(kmPc6OUy%2;X}WdDCba86eloaG~~$Bv`yvQvC2hgt4DRVbW>ZoGnf0&t`FJQSRuR>_U? zZ{$0C{acWw6_y0pm4BM)_@w4bGAI#GMt1D$FIn9Td#p)%JX9FqRn41+wyVW5<{lg2 z{wvM@nqBJ%T7dX| zFS4Z$)xuP28P%(4w6t4@K9LL4n3k$q{MI8gjmAmVTlL;0=Y7wTA(QBtqXOa#F>Ltt zHoPQjw_y_ODV0#l5bhM|CqKaVLTr+ zWA`kBxsIky?YS~{TE6b!TORTsK8zLVj z?R}A|N~KnSM>Ky4bC(jRWsJ~{2Q1H0XiJz5XjKNYw1-J_}7!80UnT*K{I@nkRB}i4W(Nne9<+f z`E82EkrBWJ^eYduA+`@?9B3)5g@#8_gv&lq4PQo?}e-qCUB|2 zY}5KjqACP18N7K$K@y4z6&MZNGY){}MCcz#f9dm&+EW?$=;IMGvLQF#G-9xU>37OYL3fr*Z>1N3yeCmFop6G;L@kYD@sr z*}J5k<8qQqzY+a4UQ*oY)RENAtMD6^Mc|0OaDL)TV zT1%-eME9kNUcC-=pg>z>%UgKMd&*iYpLi#Q=e;Dh^P@KO{W`O~eW}sAZhe;&zHY}J!%-j3MgnuF z@0@xNa+uY*m~yN>5H;{LasqQ#+ow!H7>ztW0e*E3Ni-1G;!0-C9wS5UGNE`T_z5!T zkpZk+P!>(ALWEKA*ASHw0}Iwf3)UP9*_``{c6!%E8c*qi8pDYaikUtR;~~+@L~6W5 zg9pDtje!JYchmfv_|?xwd2H_mgc!aEQs9!kP}wNg=UzNIF>{Hai_q38*0$v#-}4h( z!1Rru?5ZBq1ZQiK@B%7=P{ziTzR&ng);jHXlNt43Ec=pqL z>LgD<+|}+nz~1TtasL=R_rJRs+rShjkBTsKl&cKq>?^PBIoe3_3&_fvg&4nB4ZRTq zX8>u}{Lz~|OQ8yk#v%Q}h;oF*?%Rko##$IK-_e0(D0YJ|Zw~#NHdp$urVLkq*8|U) zpI&oY+}~d%HasKmaugQ+=`FnDX{K9TJbUzC?MF&hH_H5KtOdV_A(hT)aOZ0HtIAi; zleH`6qO2~Q*r&@7?@nerTg~5={xUW`UUN$Mr2KqHwjP`uP^>7L1&pdE8{3Jr#$!t2 z^6stU4YUIyapuk9*VKR;+zfm}WK^wVf{UoqPp_!<`OKt8o#J`+1ZeF8AYmti9reZp ze!O%dyIi$mP993Y`&_Vk#z7c{U$6K)*7)t9Hg;0*aeaq8;2r`*h3GEw{w)fPW?z8q*_$9#VM%4(8=)rP!#xL z6dbj=%-5vhr^^$zb2v_Apw4C(#lD;={YkUfYT?AJ@1)OqDnA7|q{{Ozzh*1wzHo$a5d?`woJ|Vg&VY>FB!X+=zz^VY|iT9Nn#jIbbJWp?c=$IeN zV#D*F@72Py34s8V?I+9Aob6r@7KB@i+%Av|m49LwhYEteQkb8RK;+daT!xUT1Xo-*<6>%+=znhqi3gzE=o%&qFw(F^d z?8Ue!+-WV670cBGlP!5OY(!u|8#xClYJLoQnDpW@He|Gg*$(-tb#KjtXl>bZz8WM~ zq~W0jdegBAU;zmWrl?tAWGc=AwVFSngtRi z1Fga)O56l4ReVIbgzF%yP=FL#x5mFpf$ne)LZ1;s(i)1>h*hK)zd*h?w38kS2F$^( zt^-fJJXJd_S)rAo)+ls=T$KXJhalqvTRJ;ac9qOdoK;QR)^1H4y&c*GMhNTl3ojSr z8yAa)=zf1%Vun2dJJH$yI$|i&r1Dk%Tjp0^*AnP?0Z0vOxu`yK;)@1-l3+oAkDhx- zZ#U#+z^umwiYy(0YKIJ0t%N*|yj$)=t+D_F0hb<8;o*1gFX=nGq zxznmO(-&%lD?U#vA;_43VjvUvQdx9%-%=@YE6n`d;n87HPcs6jVGa{M?FVebL4aVN zKXT0iXoG3T$vQScZF26}BepL}-ol1xhkSV&ry)U~fF$E0H0@lw(U>XdSkJYK1_Os0 z(}A|ww<4;81RWYzqp6xQC+tYm$+lAgg;=t(DZl!*GUKI7B=nnR+Wdog z1mk}A;`W<==Q2;TVu{}TcTGL8fr>f=zb)jUEBj%rkF-0d{{Ox8(=>T1M(VkMfO&<0 zh&)9|CF^BjMc>!;xK?;?})Q#?BSWq%s28i+3+4tZC_aF!-ae`9{Go1J+;lf!-f z`!#YU>mW()YL^gdQohA~*ZIUjryj|#7s*Gg#SKnJi<4!U^k$k+6I!o=13~zGco-!= zBZwp*Md^xHu9Ic6)}_nV5h};CZ0H=8C5}S1^*?-bWw6_D(V42j)~b|2i`YnooI&;c z#*YXoFM)+bUXh=4rC~n@e$G$|Q7QwFW5+h8w>4_ibAPL95O>6MMrIB>mqtp=qw9VRPIsOdET5_~5Rd3TNg%|Hq$NWb85+82;O9Yh7179WmXWSv8e z040mkwG`A}VCL88WLt}=yx38?#bdZS0;o_I;>%pGR2X+6`7%)jzy3z`G==;yZTX|i zG~z9^Pz9%8&F!^D^7G{L4FhfqIJgCn*cQju-|DPbGCW4!jGwct5J)px#x?Lindb=lfmx$-iU>A~T-~XeU$f9ea ztp^v-UA_Prn-4Z{$WyE4ObGo>OOj6>Ub>5XC)g1Q&ZL9q|L6T9BaW=6eP@QfZ0^L# zh0U_I01JmI9Nv739S^IPC*p`(XL;NCA7^UpY~3RD)>ywWh%lb2K%MSOo#2;-Wk<^* zcEn&v(ztVak$b@Rw``sYRl0*l@L{9&rmfW$PIbXA@``*3VU$&@}*)qJD~J1lmWy2dcqSK)YyrTZoAcxq1}tJ{%6@s!dz*%v$l7EFMoW;2`FUHR_kB zSbb1oQRd5dR*`@S+ZDX^B=-F3+VQyn9M#(2ZKX|M6Gb!cnI%^#-l=9)|0;pPg)$!! zxD$i?0gCaVvjkh;RP=Y>WCO2Im#e{7-dk&2s1XR1b1}G5%hO;`W!#xT-qs*3fX3cd zbHmAuRN>TH!4$PGA32dy6OXu!gDFB&VDBZ!6aMjL zKqEs(!lFM+$P~-gN#hFXyMX-h-{LcCAt$chG}xYv;XjwC5+~VnLNSNdRy7wLxY+l; zZ*hE488W3Bkuu-HT&RzKp~HrgwpEh0{S56@@Api4bdGE>4H~G5nmsaK+7l}QVKMHv zkf30&Hb3cjav~7x{~|;?1ji|L1p9G6&KVqczWnM}#=4OCL31J4-Svd&?6qtt8h7bZ)E+EGm*-s4*SrsT%qcK_9Go3OXES#CL7dBd#s>FSW-FP^S&VK|nEMy$Y#Rf@V^+nc|=z$B!T#hKOHzWpH8163$ygGX|be z>n-s^jfUMPjm+w_VaeCa_cJqdNBi*{aE5wgOu8iRe zUDPJ`8;K-ez)6w?^UBa}@xSd z1dSw4?z*kqyjqzoT?%F5s2?45)W|p+YVZfBfR( zfE^n}f_S^GAp<6jR&0Ebbd_OFL7;v;Zm_O&L*l-M5Hv(fS?CroK`+sesZ}+i!8PY+ zWbUmicWIyDo_M!;cOre{e-r9g)}6tG`^N;$!&ZNNe;F}|FU2|F6%bFXO;-Fah*`K| zONI?Mz)bRU+#bXMUuztvb4eDb!8uYm^S%3De+4I{BpI0QJ1-`MZsMCRbwd5%o_V*e zOo@tW+5GZ^c`6XFI;Oyah^lphs!jdX;HOxXt`TK|IXfn;K^sDyQdTy3#n#VD5am(S;aYbqp6BhKUg`Fq_`&4#ON?s$h0H@uOs1(M{g{&C8<@otJ?tK{p) zTy=)kU+YuG4+2HV9pEr&@+iA?yPNR*KPMH;ry}YMaddcL_~BIYMIkI>kOOC|Hr|6; zsDln-*ntqZsDeo`81a@T zHr!mW)HfU;D4dCU`D{EjMsseydig-B<|Iw8>k+(H^Br zl{;0j;fX`~SYXaeiN{Nr77uC}^JW;4(?~}x#W0No>!GG)9pK2xHGU#m#^D@BEYjc{ z%LTEUJ58I^vg(^o;)9(Zc(y}@2j?UEHHOGke!*yI>3i73+K(kc~xHagdhZ;8!V zwT)}EDw>~wzgo9Qtb`V7P^vT3Lo1DA=A^PDWQUVqKT&@D1RUip2bG#afHn?I8aYin zX#n8ICQupRFr-GmNMXVJ0m{1ta#8w463|p?GUG~mr!EbeA+~A2pE=Ak#b(=D-^2Zd zzhC1*&fFVqU|QeN-TZKL*8OT5^P8sQ{f`vs#np*ipsEmDo|t)+#L!Y+xcJUyC0hbA zp0{>9fI8fuis{nCQk{;#Pcs%N)f%BV$U)cqy^likdx7f7szn119RE1eYOETeyo8Yp zovKTRy9~weSTSiS2h`j0F=t#eN1oKmryLfEXGj5I3fxy#2aD3}TE{Q1RU9`s@$VlTVBd9d`khD}PenhzVTx&LF7}L%kCQ$@pB3F&WPKNjNW;Kh zP_ku!4F*RAJ133@G;GSzYH}Fe{#!`5;sSgOW|}QiY5U`96LnJSUQ_N2BBBrsX5t+7 zvPa007*3s!Qnrw0)>J87Sehu(mK|KJ&ciUh$*{Xgw@pnX#30u!tH~O#iC0qVtj=sM zZ@fvbbUuhWNMeA48)+0MQwtMQG7i5FOoDO0k@l9RRLUahQ2Thhh9&`-XMi64E~5NP zV(`)$X0vbrtjRwa#d;v_j)YY@?(*xD&Wo4jEv2~A}x32XlzNmJvlkjWJ?o`1aNKN zUqu1~jUuosCB)m~%@`WTF=a^KcQ069P3;c`nS75>-(eTubjVo4xBOmI7vJ*PUN-c6 zQ~DKBq3_f9xdsjfu1Ia~CD12^+fPI-IP%MMiU3nY)HFTk!_!hY>SgP+e&hizPS`IH8#%91mk=SST&4h97j>+^1gJ~EJB%945l2q0>Ug= zA0ng!^~)rn^Mjpse?0lv@@d8qGnGLeDSOVKowy%c@oKDb+brOZlAEeyff2u4GwLAX zmeskzUSQFSscGcz2I#p(kLLnE&Ma?bQ{z5(Pa$O2A9R~BB=nX;H4y64PB}oTnghmu}GxRbod}@`L zfQo|66f$d) zcxNaJf{d95;2g!@%oa3rT0+?EFRyK0OZ*P@pRch*)uHefM;`*Hjy3xF54E~z?X3eEF0a#{|Q;U)=Hl6$XL&roM2VSC|*eMMf{87be zsS8Mtlh|4d8-F7MGqB}E$Ck^X|B{GhH-t=?)#RsCl<}kk!r_xS+2ikp=j*EOEpxHlK?Y#TH3|%?#hvOVtB~Krgd+LNTjWYQ z{HdBZQYlp#q5j&ro)|CDsYb5KfXR$U68q^4J&nvz)uzU>0lGCui8`IiFfN_jX&iH? zeR!qffR5`Zw6@VfU+G)PO$f?R9Jv)p^2`E%yP90gK(pGBSWTu!Q+_U`m9p$8(c_Jg zps95#(p`VjjxJ6zg!+ICEnKpS%SVzY(VEGlrl)%j*oVT4>1YgSWqBDD8bhE$KuTF6 zbP5R^RY{~|$zbukF{rHY76n32K9`OLnMV$T#ASI$yO&*bpHt(*wSU6)EkLS}K1v}I zYf+`tr>}dBJ^!&`SUhSuP&Ew=mCAUI|BS+G)P=cz!=>V2vvu8^JAytghI53=gM#(@ zoQA3mJXzWwELi|6PNhB0nesWV3^*Soo@YL`)lPRHvZtKj{B@@#Wb^My)JAm@WG%J+{}o6&UPlPCe3@V?48{V8zb2e6%M zPmIW$lK@rd{#p~q@A)uqq*Wc`=H$|O`WE~|)GG0X#2pgjslzdfW`#4hb!p0VnGsVM z8Hk8C1ewmqUoCeTAoGMaEquq1e|*M<|+`@Y+g6gP_#bRh@cXUnp zMJwld(o+cRe#;)?=W+eM=jsU$)1liJI~)Tv%3ZRoNt3TpP3+v16QA&(4%9LEU`jO# zk5`8YaS3}p*kSmjXisd7&0$)|Xtn@Bk|^?u9IN1-HK{RCv&NK?)ntUbvf{Ze<54L$ zg?L8t2sF^3BBSLa2B#O^S6O`9IllJ?P$$e<)oe}^u+z_%nj#bC(*gOQV=j!7zq7xS z$JUoO{&x9vLKt>fu^aDYp}EMqU;}N%!78E{mP^yU{U_Nc_L03nE*MzUQ`%Z`S^>^w z#xI<2IrX(2U50JDb~t0MDnEZZ(wWHdx>B&2#rX%@H~Z(gG8MWzt^+k~3)x?t#703+ z@!!pr#%;9`H@<|G|E#boQcTlyDny@>9Y(S%(@wB>R?C_)Izd%b%W$8f*R>uZU}Y1 z;0RdN8Szibu`IkfMd<=_dcyR~pvf)zIhzxlI$PW`?wLdme&J7oEK!(I3Q`4+?+)kV zCT43h^_?4S3r_=t_wL1B4(RqKZ65}sg9=cid;co9b^{bX;sh{-65C=7QE5byN#yUs z{rH~fZ;AsQZbcr3E0fxTc@dHpS-a-5rr5T&b|2|g-eL1J(5UgIWuSiQGXWh7eC9Pq zU@xqxvwx;%;M3SyU7megwePd;=27g@-_Z|$pNy|bu}8G*&wGVgz}FW#;E}qBOS>EY z9I?E@)7(oY_d5xFNfGj-8W2}=46>8F-4~!>&iUIe6uD88VSYkI@JdHMpM@PQ^tnzXkSfnY!t0a&fX<%cxOU^toAF3~M=QgZ0s7`^@uA^V z#G+m&mZN~S2&d?gaXGQD3u%!pSBD`sB^3&srmfP<%l=1tMVT>a9MZFM2qS4cf#k7{ zQU!lb4r!%ma~O~JFTWw91sRmFm4L}fQg*w5v6REm7&QCuu{&hZ+eeu>210*asxLKs zyNNu$pJwvnd;fOJ5WV8=y5{e)VWn*fdXL}sd;W`lb$E#X@YoOg%Z)Cm`6}atR&bM> zc0MyFLsW}a;C_qTVK>B7pr9uCc@(9yhEF>Qp*9EAopGbYfdhQbPoLuL>)Y_gfznI# z__?|MDn|pE&{&S_M+w=#U(J17M6i~rzLVM;Wfvh4Rud$+VW-p zcLu2wDR#i>wEo_0Ph6Pgp>t8x&t3u@=h{Fg@>g)vm4|9NJXr6lXqS>^ZM%%ayTLD_ zqakDvqMLO&afL||gE=na)%@^uIr!ip(rTC8ME#Ni^Zu&rLzR(?>5#6X zz|=PL;Qf1yCgPjCuw^+0dchP0D;;a1!i3fYmCl)D#7T)l&=9sW$G3L5Eo*GBl(Txb zv`dz-dhAbsdF-GfNOC?J$E1`VL=|88>ou9&l00MpI6#LKOn?c{NX46>Kuds{hjR7BB#$!8i`PyvtF8bk+P0$ej&*yX{D-F%s^a zqMKyP(^@$XjG)!!(2V6+qs)9MI=g;V?%lI1=gJn^k&C=_kq|4ok#argmr$_PgV!Pu+S3r^ zi?5SsJ$qAd z;uomB=`-#H`dFc_lnz!pr(_Rb(n0yXz<8kV%J`M~8zOH#`}1(DF0H!+^{#f~rmth| z-BtB~bL{6OJF$J?-}zTEq-tNd z!dD=p*hZ5kR?+LtMb!JaS_vcAPOFK#zSvVj$B(#!&YT#YR#{X|;+%rC;@GL}n0;nk8e)uvm3;Il zeGJL7(AtPJadF_3Gy32!y^CBvlLh;o{65p6C|iXMDn9T;2Fe-k;4xCZ1;_f>9f1@< zbaK6CZ{U^X>r2KV3GXa>t=d=y{r%{3gUAkCr_s&r%fIT!3Ac`rYLx#Orf1Q6AW1U% zQrKshJ`dr2{T4^k6M)HGf@H%Vrj_)zex!PyrOgI9`=XG@d`t{v%`@i7)Fz^gzv6X$ zzCtvr^p*FSi}GhI%8L-pZoVU@)ab)QV(RdGJN^pfvy=qJvshU!sGI~Hb3lWL;Uho) z{IhD@EX@=ak1U`w5hY*?Rl~v!86W8=sT0rtT`E6uw2O_jacjdc&NuP}K;IGubjHbl zGfadNYPw#n_C9W`Pi#8W_}~)zy{c@}hX8|7v5FFc?NCU9%V59F5}s1EtRuSwCfwln zSV`CZ22o{Q1WpgKM`F1qko56UFJd|_0w$im$C%soSaI*?x3q4}y;*{{6cGZk{|I3dNbz*gk%!Lf~ zT|UC^f@^uC)O@5v??xW&(I+y+lUcSo*kwhB68 zE}uo8Lb4Zi?$k`=A6WU{CIm&h*LLweR7lvHD*&JYBhLuXtpNXC0#dbVsM+lI@(85n$Mp}afi6n@(KzugEa^{qT6|W zpOd_=8vrcMNljULmbdC)sT2EK2mFqZ92EuiwxmC^Dl0#GdCq~+a*alYYEP;PopRC@ zQ#>t1@OCmgqfJ}++8kvm$D98+22>~X)%)O`1Icx4>)?85){1ub@ zRZ5GDK|c;1X;;zXx~f|&X^7Pai4r8*M~zzL^SOevE=yaLPbDtcxFn%A-<$58uIn*s zyn3> z5!>+wmejdXH|iUZ4634>eSjXP1`S3_sZuWzPKUL3)52m_!6DaOqsc(XpQ>9Uzm@s( z3a_qskE*_rLs;?kX*nZ6wc9=zA2MtmaQL(nD&ba{piX=5Orf?k^>>v;dsS_vHNj0z z?%vshaUN69ae__muu@a<-`@qDa;1F!YJ7#G{&X(QA(t^<0Yl!2A;s^fK}ll6Py+eg zN;p3#=R}Fd*qMai)quM{o>%~>iyngiM@HZji+Y$wcFc4VP;eC#yaoq@aGBcYtWZVy z%ORWWK91l!5{|TUwK2b?H+2F##@p(hYs@~dw%>7Nc#Luxx=9v z`+xNH-u^7=1YVPrpJ-?H014+GQ6z$PPiT0<)RnAsl#Y=S%q1+aOj$(?zntbGCUiS; z|I5#+A|*{HZ@XlvMaCP~*14$3{Dq=M22k<3{G2v{!Bu3FI)@TH;*>6La0ZY%={NbL z8l%4s6JsHVN} zIh&0h)Rb4l9nrLtPhW*`g)9+z5aKw%CMVm*gR^PnGg`--#)C4E{$1G7Y+`YfywdSAh~<~8S`vh_L%a$b+_j_e zr0Uz3RVi-)Wvmar4`;M31}}n2MUMv<3K*+nX?1&PAkcOIdpk<1iShD?dGmLMuJdJ=-xA%M0YE-xUjT#k(i&m8g);f8Dg{7(V9Q zJ9TrI7O5p=IlU>#nj&^2o|Drw>ZVvn!$84{ly-FEYsR()nC52HlIL$)?HKV~P*a?J zZF}l);TaNIQ$A)gC}T9}8TiH;E*miTR(CoZs=xU8moA{Ezg}*lYDEA}yX2C&(N1e6 zyoh;mythiS95v9gotqb}EgchG zdkTF4+kJddUp{ZaKB-0zs4Y3Mq|3PL@+RvIOnS^6RHfJTmkL6fsAMtfz`9RsJ}AXedglbxxx z$jR{#g`cYpHUDcvA=f&G9bV=_iDrIB9szskz#oP_FDUT$Z!>{TzEY*K>LYw435O)o z6u;2nd1lRr3)6(fp*wnfk%ILUkQI}2PVsMKvKwz_{%x5IQl2jShC3T`C3eIxKo>}H z<78lURp~ZYb^4bdE!d9UR?6!5p1F=r^%$ZM8#czz^w&am{J+7|ypMPLEzH+kh!zRS1scew>Unh^KGp$hLkDtiJ!iX0yM}?p& zuB)pAx^T<4ZRWS+I%oW;f@!-{N?Ak#uC1`7HSLeFNZm@KK3}rH&QhwSFW`=?Al17{ zzO_s&N4d2zIE>C@v)e^4?yS#B4qS?qh1YZ%E(qm9Dvth!c0Ay=5$o>)uFbc3CvH-+`Ne>8W<)IM^|x{` zxg~=)`LAME6YMq?nIH>IEXxARn7@&1ShMb=$>-x9yxKw6meY|1dXTlj(l7f#Gw=bT z4#mo{a6YpZhMx)rB;|wd;Vh!;QhDTyPusmF)Mpgbd&!QVNpIQyFYJ2wvMi4?M94bq z&A3uJu7#di4nJ?XX&9)Ov2l&4KM32yYocKp^uuQQq~Ghui&Rag>3Vie1OD+f>e%N3%MdMsOxCn!nZ&j2fEw(z zT!)`@j-b0pk86MRq&~jZp79f+M`ioBn91MO)d>GHxPxbJ_B8X8xuHY(f^-BbEy>zm zaz=s0EOZd3K&_Y>{oa%c{+64fu)_>Viupkgt)+nLy+R%OUo-(MQ#{R~HK4kG6bW{8a!~zAGo$@w=6zZ?d3zMtz@lm%~L?yGcS?6zi zC!P>*tVOqR4`OnxMZLi>^)oVAelRelB)0LysVKqRZ9Ph-AN#vp1i z)W}c+-fr5{ESE|a&{#ol*VCRQiaCxDuk1{JY0&&Vj=z|WcaxvCZ_c3~gt z3y9I|ES)NQ7;;5|ED@^p+L4F4?OsjRz=ld&_)L=KPW$LSZcz5{kc)Jc2?g%cW?E76C{Tb)i z=m_;*x)thg^m4hk@_466QL9weUY>xBNLf(iHFc42Q7ae!&FyC&&d(mOyakr$+m?tG zv614=30hKo&4#JoUk&^o#uV@LQEZXksRv79IwQ1Sc_QxKz-_!7WIWAcYSx+@4kXhL zVxTqZ8B4?Pj;&S4GvX^PqgoS<%a5Js& z&$`YkppmK33wKBsdeX7yg^s9?t$Jv}){uV_AG-0^y$=J0V+B&)OwkKQx!Y^5pI1;3 z0|CWeg#wiEU#LHkpUmvEmt5v)l{IkBC(+$6o05cS%S&Y>`JaJFOKTXk&g17X%ZF&( z@i9n+u43BUHSQUP#NTRVde1+H+()ZVX4GueG*tC_${*_xF6v_286d>qDHeZI!-dyO z2oLD$vRTH^FDSaiO=8wwfj{MrYbPU*U)0`@o(Xl&bg zLQB%Av7}9r75+PH#8q5^@Mi>uxiO>OGG-A|(4B+Z@Jm#fdia#eD*fo)v?s-MK0!Jx z$E>7D?O8y+kN@DuY}wtLTkQD}e!xTmc3PG5ofKrwNE(xMHIRmim|0qcs%YAs?24d^;&OZpbiMa% zjE-jU2}iW3iZb0tmV|)w^_U>t{Xzj->4N^;;LYbtJGX3Vc|jcn{FKSK!^qCFxTC1d zZ6C>PWMnV#-KwKUY2%;Mp$fZz5t!r!sH8ZLZfkuz1Wpdgg`pwMkIQ0(S$a{#h@&EGU9TR~KzO}{A;H4BM zRa6&XLK2`;ErO#GwMY3U7P&eL8#t}q=IxPUOM|jWVh<8!Q3D3mR9E?fg}VR?!01Un0JA>drWQmB%vuq#iVqWv)?KE{ z>qVE;$VR2&mwStw$F$kfl3tqRzMBSYE}FmIENKiN?f28Nfl}dw+0k+4wjP#<0B_AXiop$ zD>Jo+i|q95f}fAGO63EkoZup{-!mAOM08&2u8iK%>ts3Kk!;LM@e#XsB|Ay{>7+PH zUf^AH_bWeJmpHA;HbCTA)S}KhEkXR55W)CHalBF6IKnCs@=VQG9=JNG^Fz-kveL z6yk1fSfWJ~mktZ5k1-Fbm*MmK{KnGR5i!jhcJrb3Nci^oUcC32!W;8ZWRv#;_k~lp z-)V+k`^+Pe>!*|I-me`@ev z#=Bu&31_x-lcD0!9U9$ypfDQk8_9CU{y~dNjvG41V*d3~$J$MLTB)Ytz@7sGHEdm~ z;sb_k=M{XgaDGEX^j2{8M+_`(su|dZLMXYv@__6|W+oQwti?ldgRI07N=f2IrWwSI zV1f&5h&CArH4!w!7+LtgX;h#MfgZGbWF-oXZ>*{P_4i>5kC!F)H+u~3`hKNn+npr1 zJY6Aa{83;yNcmak@vTUZGqN+ihtf>oUT>Db!3IoCD9o?69dEzykkLlCiC4#3Qm!D8^{2i~z9 zR9KMNGwH;{%97rM!w+d^vk?$b;s@@^4As?ou{U3(HP2sw9nTcdKI(YJraYK8&oO}w zI^;)3%KUD~MHHjWU}l9f(;%QL#O^$Q{&U*8QLbpv1N?%>pL&>Pm=g9qyttO&c-VH~ zfoG=+bWE=xNOR7s)C&uRibEzPUzDadO)|=Z(9T+T>In`CS#PFe8V7)!A`r zE9IODaCPdbsiM=4G{K8yn=#2ZTWB@>LbD=#9$C_j5tX^Z$5WFraf8MPczfZ#sM(u`5KsG9B-i1d9T?yc7Hklhc&fuyW@RYzUz(eLZ_Pl zB*TBw<6LwDZO`Gu2C`7Xg(#hD$VNovJ6hADmF@L6Ls6MXN<1m9hXTGv`EP#V#gANe z&pa!v(BU{Dg`#f;rRmLO={ZIAB7t_IAy?G=v5b6wpG8Ygk<6~0aK`uPGA3u2y!>e? z0fVH=&nSAZm8`Y4owCd8X3Kwz4m(ZRF&N#QF1!fL-q|DeNTi-a&7NcPeY)#>WUZ97 zd}^;_!JBN)%8%uj=O)Y9b+$3|wpzd-ze&0i_M{Hm<3PmF*3ehVK!fqc$j+#l@v@W1 zkqLUehh|q4hPH$J1?omdOI`8PWUezSPgj4KX&0&bMdFq>WuCXU(cg812RFC(;WZyd zXZ5u)D>5w=R|slXsHcUE=P6Z%jn^pEVbz4mrhTxuH@_ux4G2c~tz;GTwq29$Vhpj( zQ$l4S+NxOYHZ)F>woJYFY-%1esnnS>dqwL{{hQMofjeA*G**gt8R(0d)&jJ*kIxXy z#C;EauJ1wv@p;Lak!yIFP7_7O$0W#*QpBuFc#q>xzI{>oAzUCHm&!YoUv13$&TTra ziCOkR#$w}hroV6xP|mh9UFa2;YI+eXquR{%4dK%F)7>?hu)>X_!qYflnpONnZ{_hF z`HcK~Bu5uwmhZ=}?`qCBq@DZsyDkGx@+;v(=&*jPUhj(}&(998gpV7>Qd`kuRov6Ve*c-^@)*#u3cfq;vJ? z9s&aQ<8H7UTdzf^Tk0?Jn-x+!loVL7U0)x%HYShlYy0tZY%h1WeK18XUb|r)5Gbw^ zD6YC-Lx=1zA2DIheNem+F7AIc{~*0t_d8CyH~?7JU9GJ72mT1aul3fS3jUA&{sdCb&Q?8A@CyZ2preJA}Wa@O$< z%j&LmPIO+R*k6H&`6wU}(bt9eqI&+yxXQTw+JNM-OiuC6&xY_;e*c!zesC$o8al+h znSB373owOwvDxhMR$S-&;JNc>n%tg!h5{lyS?7A*WM=) zm3jnOT|tuwB8H8UigT~+jHI2AAav+Gg8}OweDN|BcbhkAc`klxJc+RPK;4GqPM%Ylpb_uK67TeR__M=}7s<%PbCaf@ysL$432 za2Y`wpBL|TJP0m-9Unz|H1puHQm>D?bkIE1tpwR#UWoyoy3s#u+@{K1$n|+Sblh)< zslast0qg3~Ui7?T9vXrn@()Da@31dn2HpRJc!fg#`-RTP`(yRNCdDDfP^FDG^37_m z^Y^m|l1Wy$_WON`tM?B%Fxlzue)N{y8L^tE zddAlX{?JA9yOWC9_mBX5*02}B9QHTp=X|(OcRqZ<$g``1?L>U}aQ@nXFIaw$j`>I& z3sbU|)17m%-gTAH9X{mu>E+vIiBX4k&pULD;_!LP_hB&~JvXbnJ@0d%s{dZ*<}*>wgIQ0L|w$|A$Hu jGH7lCin-c;1h{umvQ$1n5oL=w80ZTqr39#wFbw!V(cRb_ literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/jupyter_execute/clustering.ipynb b/doc/LectureNotes/_build/jupyter_execute/clustering.ipynb new file mode 100644 index 000000000..bf67f2669 --- /dev/null +++ b/doc/LectureNotes/_build/jupyter_execute/clustering.ipynb @@ -0,0 +1,718 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "c3edcae5", + "metadata": { + "editable": true + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "id": "4102577e", + "metadata": { + "editable": true + }, + "source": [ + "# Clustering and Unsupervised Learning\n", + "\n", + "In general terms cluster analysis, or clustering, is the task of grouping a\n", + "data-set into different distinct categories based on some measure of equality of\n", + "the data. This measure is often referred to as a **metric** or **similarity\n", + "measure** in the literature (note: sometimes we deal with a **dissimilarity\n", + "measure** instead). Usually, these metrics are formulated as some kind of\n", + "distance function between points in a high-dimensional space.\n", + "\n", + "The simplest, and also the most\n", + "common is the **Euclidean distance**.\n", + "\n", + "The simplest of all clustering algorithms is the **k-means algorithm**\n", + ", sometimes also referred to as *Lloyds algorithm*. It is the simplest and also\n", + "the most common. From its simplicity it obtains both strengths and weaknesses.\n", + "These will be discussed in more detail later. The $k$-means algorithm is a\n", + "**centroid based** clustering algorithm.\n", + "\n", + "Assume, we are given $n$ data points and we wish to split the data into $K < n$\n", + "different categories, or clusters. We label each cluster by an integer" + ] + }, + { + "cell_type": "markdown", + "id": "0deb3255", + "metadata": { + "editable": true + }, + "source": [ + "$$\n", + "k\\in\\{1, \\cdots, K \\}.\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "cfd8fe00", + "metadata": { + "editable": true + }, + "source": [ + "In the basic k-means algorithm each point is assigned to only\n", + "one cluster $k$, and these assignments are *non-injective* i.e. many-to-one. We\n", + "can think of these mappings as an encoder $k = C(i)$, which assigns the $i$-th\n", + "data-point $\\bf x_i$ to the $k$-th cluster.\n", + "\n", + "$k$-means algorithm in words:\n", + "1. We start with guesses / random initializations of our $k$ cluster centers/centroids\n", + "\n", + "2. For each centroid the points that are most similar are identified\n", + "\n", + "3. Then we move / replace each centroid with a coordinate average of all the points that were assigned to that centroid.\n", + "\n", + "4. Iterate 2-3 until the centroids no longer move (to some tolerance)\n", + "\n", + "We assume we have $n$ data-points" + ] + }, + { + "cell_type": "markdown", + "id": "a29b7459", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "

    \n", + "\n", + "$$\n", + "\\begin{equation}\\label{eq:kmeanspoints} \\tag{1}\n", + " \\boldsymbol{x_i} = \\{x_{i, 1}, \\cdots, x_{i, p}\\}\\in\\mathbb{R}^p.\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "98f9e37b", + "metadata": { + "editable": true + }, + "source": [ + "which we wish to group into $K < n$ clusters. For our dissimilarity measure we\n", + "use the *squared Euclidean distance*" + ] + }, + { + "cell_type": "markdown", + "id": "d3c32572", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\\label{eq:squaredeuclidean} \\tag{2}\n", + " d(\\boldsymbol{x_i}, \\boldsymbol{x_i'}) = \\sum_{j=1}^p(x_{ij} - x_{i'j})^2\n", + " = ||\\boldsymbol{x_i} - \\boldsymbol{x_{i'}}||^2\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "29d24648", + "metadata": { + "editable": true + }, + "source": [ + "We define the so called *within-cluster point scatter* which gives us a\n", + "measure of how close each data point assigned to the same cluster tends to be to\n", + "the all the others." + ] + }, + { + "cell_type": "markdown", + "id": "fce5c797", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\\label{eq:withincluster} \\tag{3}\n", + " W(C) = \\frac{1}{2}\\sum_{k=1}^K\\sum_{C(i)=k}\n", + " \\sum_{C(i')=k}d(\\boldsymbol{x_i}, \\boldsymbol{x_{i'}}) =\n", + " \\sum_{k=1}^KN_k\\sum_{C(i)=k}||\\boldsymbol{x_i} - \\boldsymbol{\\overline{x_k}}||^2\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "674a26b7", + "metadata": { + "editable": true + }, + "source": [ + "where $\\boldsymbol{\\overline{x_k}}$ is the mean vector associated with the $k$-th\n", + "cluster, and $N_k = \\sum_{i=1}^nI(C(i) = k)$, where the $I()$ notation is\n", + "similar to the Kronecker delta (*Commonly used in statistics, it just means that\n", + "when $i = k$ we have the encoder $C(i)$*). In other words, the within-cluster\n", + "scatter measures the compactness of each cluster with respect to the data points\n", + "assigned to each cluster. This is the quantity that the $k$-means algorithm aims\n", + "to minimize. We refer to this quantity $W(C)$ as the within cluster scatter\n", + "because of its relation to the *total scatter*.\n", + "\n", + "We have" + ] + }, + { + "cell_type": "markdown", + "id": "f200e7ff", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\\label{eq:totalscatter} \\tag{4}\n", + " T = W(C) + B(C) = \\frac{1}{2}\\sum_{i=1}^n\n", + " \\sum_{i'=1}^nd(\\boldsymbol{x_i}, \\boldsymbol{x_{i'}})\n", + " = \\frac{1}{2}\\sum_{k=1}^K\\sum_{C(i)=k}\n", + " \\Big(\\sum_{C(i') = k}d(\\boldsymbol{x_i}, \\boldsymbol{x_{i'}})\n", + " + \\sum_{C(i')\\neq k}d(\\boldsymbol{x_i}, \\boldsymbol{x_{i'}})\\Big).\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "5471a94d", + "metadata": { + "editable": true + }, + "source": [ + "This is a quantity that is conserved throughout the $k$-means algorithm. It can\n", + "be thought of as the total amount of information in the data, and it is composed\n", + "of the aforementioned within-cluster scatter and the *between-cluster scatter*\n", + "$B(C)$. In methods such as principle component analysis the total scatter is not\n", + "conserved.\n", + "\n", + "Given a cluster mean $\\boldsymbol{m_k}$ we define the **total cluster variance**" + ] + }, + { + "cell_type": "markdown", + "id": "299a99ce", + "metadata": { + "editable": true + }, + "source": [ + "\n", + "
    \n", + "\n", + "$$\n", + "\\begin{equation}\\label{eq:totalclustervariance} \\tag{5}\n", + " \\min_{C, \\{\\boldsymbol{m_k}\\}_1^K}\\sum_{k=1}^KN_k\\sum||\\boldsymbol{x_i} - \\boldsymbol{m_k}||^2\n", + "\\end{equation}\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "id": "bdfa54ee", + "metadata": { + "editable": true + }, + "source": [ + "Now we have all the pieces necessary to formally revisit the $k$-means algorithm.\n", + "\n", + "The $k$-means clustering algorithm goes as follows \n", + "\n", + "1. For a given cluster assignment $C$, and $k$ cluster means $\\left\\{m_1, \\cdots, m_k\\right\\}$. We minimize the total cluster variance with respect to the cluster means $\\{m_k\\}$ yielding the means of the currently assigned clusters.\n", + "\n", + "2. Given a current set of $k$ means $\\{m_k\\}$ the total cluster variance is minimized by assigning each observation to the closest (current) cluster mean. That is $$C(i) = \\underset{1\\leq k\\leq K}{\\mathrm{argmin}} ||\\boldsymbol{x_i} - \\boldsymbol{m_k}||^2$$\n", + "\n", + "3. Steps 1 and 2 are repeated until the assignments do not change." + ] + }, + { + "cell_type": "markdown", + "id": "f5def86c", + "metadata": { + "editable": true + }, + "source": [ + "## Codes and Approaches\n", + "\n", + "1. Before we start we specify a number $k$ which is the number of clusters we want to try to separate our data into.\n", + "\n", + "2. We initially choose $k$ random data points in our data as our initial centroids, *or means* (this is where the name comes from).\n", + "\n", + "3. Assign each data point to their closest centroid, based on the squared Euclidean distance.\n", + "\n", + "4. For each of the $k$ cluster we update the centroid by calculating new mean values for all the data points in the cluster.\n", + "\n", + "5. Iteratively minimize the within cluster scatter by performing steps (3, 4) until the new assignments stop changing (can be to some tolerance) or until a maximum number of iterations have passed.\n", + "\n", + "Let us now program the most basic version of the algorithm using nothing but\n", + "Python with numpy arrays. This code is kept intentionally simple to gradually\n", + "progress our understanding. There is no vectorization of any kind, and even most\n", + "helper functions are not utilized.\n", + "\n", + "We need first a dataset to do our cluster analysis on. In our case\n", + "this is a plain *vanilla* data set using random numbers using a\n", + "Gaussian distribution." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "b0260188", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "%matplotlib inline\n", + "\n", + "import time\n", + "import numpy as np\n", + "import tensorflow as tf\n", + "from matplotlib import image\n", + "import matplotlib.pyplot as plt\n", + "from sklearn.cluster import KMeans\n", + "from IPython.display import display\n", + "\n", + "np.random.seed(2021)" + ] + }, + { + "cell_type": "markdown", + "id": "fe680e35", + "metadata": { + "editable": true + }, + "source": [ + "Next we define functions, for ease of use later, to generate Gaussians and to\n", + "set up our toy data set." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "9db2bbce", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/clustering_17_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "def gaussian_points(dim=2, n_points=1000, mean_vector=np.array([0, 0]),\n", + " sample_variance=1):\n", + " \"\"\"\n", + " Very simple custom function to generate gaussian distributed point clusters\n", + " with variable dimension, number of points, means in each direction\n", + " (must match dim) and sample variance.\n", + "\n", + " Inputs:\n", + " dim (int)\n", + " n_points (int)\n", + " mean_vector (np.array) (where index 0 is x, index 1 is y etc.)\n", + " sample_variance (float)\n", + "\n", + " Returns:\n", + " data (np.array): with dimensions (dim x n_points)\n", + " \"\"\"\n", + "\n", + " mean_matrix = np.zeros(dim) + mean_vector\n", + " covariance_matrix = np.eye(dim) * sample_variance\n", + " data = np.random.multivariate_normal(mean_matrix, covariance_matrix,\n", + " n_points)\n", + " return data\n", + "\n", + "\n", + "\n", + "def generate_simple_clustering_dataset(dim=2, n_points=1000, plotting=True,\n", + " return_data=True):\n", + " \"\"\"\n", + " Toy model to illustrate k-means clustering\n", + " \"\"\"\n", + "\n", + " data1 = gaussian_points(mean_vector=np.array([5, 5]))\n", + " data2 = gaussian_points()\n", + " data3 = gaussian_points(mean_vector=np.array([1, 4.5]))\n", + " data4 = gaussian_points(mean_vector=np.array([5, 1]))\n", + " data = np.concatenate((data1, data2, data3, data4), axis=0)\n", + "\n", + " if plotting:\n", + " fig, ax = plt.subplots()\n", + " ax.scatter(data[:, 0], data[:, 1], alpha=0.2)\n", + " ax.set_title('Toy Model Dataset')\n", + " plt.show()\n", + "\n", + "\n", + " if return_data:\n", + " return data\n", + "\n", + "\n", + "data = generate_simple_clustering_dataset()" + ] + }, + { + "cell_type": "markdown", + "id": "c0bb8c76", + "metadata": { + "editable": true + }, + "source": [ + "With the above dataset we start\n", + "implementing the $k$-means algorithm." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "29a75065", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "\n", + "n_samples, dimensions = data.shape\n", + "n_clusters = 4\n", + "\n", + "# we randomly initialize our centroids\n", + "np.random.seed(2021)\n", + "centroids = data[np.random.choice(n_samples, n_clusters, replace=False), :]\n", + "distances = np.zeros((n_samples, n_clusters))\n", + "\n", + "# first we need to calculate the distance to each centroid from our data\n", + "for k in range(n_clusters):\n", + " for n in range(n_samples):\n", + " dist = 0\n", + " for d in range(dimensions):\n", + " dist += np.abs(data[n, d] - centroids[k, d])**2\n", + " distances[n, k] = dist\n", + "\n", + "# we initialize an array to keep track of to which cluster each point belongs\n", + "# the way we set it up here the index tracks which point and the value which\n", + "# cluster the point belongs to\n", + "cluster_labels = np.zeros(n_samples, dtype='int')\n", + "\n", + "# next we loop through our samples and for every point assign it to the cluster\n", + "# to which it has the smallest distance to\n", + "for n in range(n_samples):\n", + " # tracking variables (all of this is basically just an argmin)\n", + " smallest = 1e10\n", + " smallest_row_index = 1e10\n", + " for k in range(n_clusters):\n", + " if distances[n, k] < smallest:\n", + " smallest = distances[n, k]\n", + " smallest_row_index = k\n", + "\n", + " cluster_labels[n] = smallest_row_index" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "9fae7fc9", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/clustering_20_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "ax = fig.add_subplot()\n", + "unique_cluster_labels = np.unique(cluster_labels)\n", + "for i in unique_cluster_labels:\n", + " ax.scatter(data[cluster_labels == i, 0],\n", + " data[cluster_labels == i, 1],\n", + " label = i,\n", + " alpha = 0.2)\n", + " ax.scatter(centroids[:, 0], centroids[:, 1], c='black')\n", + "\n", + "ax.set_title(\"First Grouping of Points to Centroids\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "90d2a873", + "metadata": { + "editable": true + }, + "source": [ + "So what do we have so far? We have 'picked' $k$ centroids at random from our\n", + "data points. There are other ways of more intelligently choosing their\n", + "initializations, however for our purposes randomly is fine. Then we have\n", + "initialized an array 'distances' which holds the information of the distance,\n", + "*or dissimilarity*, of every point to of our centroids. Finally, we have\n", + "initialized an array 'cluster_labels' which according to our distances array\n", + "holds the information of to which centroid every point is assigned. This was the\n", + "first pass of our algorithm. Essentially, all we need to do now is repeat the\n", + "distance and assignment steps above until we have reached a desired convergence\n", + "or a maximum amount of iterations." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "378c29fc", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Converged at iteration 5\n" + ] + } + ], + "source": [ + "\n", + "max_iterations = 100\n", + "tolerance = 1e-8\n", + "\n", + "for iteration in range(max_iterations):\n", + " prev_centroids = centroids.copy()\n", + " for k in range(n_clusters):\n", + " # this array will be used to update our centroid positions\n", + " vector_mean = np.zeros(dimensions)\n", + " mean_divisor = 0\n", + " for n in range(n_samples):\n", + " if cluster_labels[n] == k:\n", + " vector_mean += data[n, :]\n", + " mean_divisor += 1\n", + "\n", + " # update according to the k means\n", + " centroids[k, :] = vector_mean / mean_divisor\n", + "\n", + " # we find the dissimilarity\n", + " for k in range(n_clusters):\n", + " for n in range(n_samples):\n", + " dist = 0\n", + " for d in range(dimensions):\n", + " dist += np.abs(data[n, d] - centroids[k, d])**2\n", + " distances[n, k] = dist\n", + "\n", + " # assign each point\n", + " for n in range(n_samples):\n", + " smallest = 1e10\n", + " smallest_row_index = 1e10\n", + " for k in range(n_clusters):\n", + " if distances[n, k] < smallest:\n", + " smallest = distances[n, k]\n", + " smallest_row_index = k\n", + "\n", + " cluster_labels[n] = smallest_row_index\n", + "\n", + " # convergence criteria\n", + " centroid_difference = np.sum(np.abs(centroids - prev_centroids))\n", + " if centroid_difference < tolerance:\n", + " print(f'Converged at iteration {iteration}')\n", + " break\n", + "\n", + " elif iteration == max_iterations:\n", + " print(f'Did not converge in {max_iterations} iterations')" + ] + }, + { + "cell_type": "markdown", + "id": "545a6742", + "metadata": { + "editable": true + }, + "source": [ + "We now have a simple , un-optimized $k$-means\n", + "clustering implementation. Lets plot the final result" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "d9d3973b", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [ + { + "data": { + "image/png": "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\n", + "text/plain": [ + "
    " + ] + }, + "metadata": { + "filenames": { + "image/png": "/Users/MortenImac/Teaching/MachineLearning/doc/LectureNotes/_build/jupyter_execute/clustering_24_0.png" + }, + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig = plt.figure()\n", + "ax = fig.add_subplot()\n", + "unique_cluster_labels = np.unique(cluster_labels)\n", + "for i in unique_cluster_labels:\n", + " ax.scatter(data[cluster_labels == i, 0],\n", + " data[cluster_labels == i, 1],\n", + " label = i,\n", + " alpha = 0.2)\n", + " ax.scatter(centroids[:, 0], centroids[:, 1], c='black')\n", + "\n", + "ax.set_title(\"Final Result of K-means Clustering\")\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "id": "ee6a145f", + "metadata": { + "collapsed": false, + "editable": true + }, + "outputs": [], + "source": [ + "def naive_kmeans(data, n_clusters=4, max_iterations=100, tolerance=1e-8):\n", + " start_time = time.time()\n", + "\n", + " n_samples, dimensions = data.shape\n", + " n_clusters = 4\n", + " #np.random.seed(2021)\n", + " centroids = data[np.random.choice(n_samples, n_clusters, replace=False), :]\n", + " distances = np.zeros((n_samples, n_clusters))\n", + "\n", + " for k in range(n_clusters):\n", + " for n in range(n_samples):\n", + " dist = 0\n", + " for d in range(dimensions):\n", + " dist += np.abs(data[n, d] - centroids[k, d])**2\n", + " distances[n, k] = dist\n", + "\n", + " cluster_labels = np.zeros(n_samples, dtype='int')\n", + "\n", + " for n in range(n_samples):\n", + " smallest = 1e10\n", + " smallest_row_index = 1e10\n", + " for k in range(n_clusters):\n", + " if distances[n, k] < smallest:\n", + " smallest = distances[n, k]\n", + " smallest_row_index = k\n", + "\n", + " cluster_labels[n] = smallest_row_index\n", + "\n", + " for iteration in range(max_iterations):\n", + " prev_centroids = centroids.copy()\n", + " for k in range(n_clusters):\n", + " vector_mean = np.zeros(dimensions)\n", + " mean_divisor = 0\n", + " for n in range(n_samples):\n", + " if cluster_labels[n] == k:\n", + " vector_mean += data[n, :]\n", + " mean_divisor += 1\n", + "\n", + " centroids[k, :] = vector_mean / mean_divisor\n", + "\n", + " for k in range(n_clusters):\n", + " for n in range(n_samples):\n", + " dist = 0\n", + " for d in range(dimensions):\n", + " dist += np.abs(data[n, d] - centroids[k, d])**2\n", + " distances[n, k] = dist\n", + "\n", + " for n in range(n_samples):\n", + " smallest = 1e10\n", + " smallest_row_index = 1e10\n", + " for k in range(n_clusters):\n", + " if distances[n, k] < smallest:\n", + " smallest = distances[n, k]\n", + " smallest_row_index = k\n", + "\n", + " cluster_labels[n] = smallest_row_index\n", + "\n", + " centroid_difference = np.sum(np.abs(centroids - prev_centroids))\n", + " if centroid_difference < tolerance:\n", + " print(f'Converged at iteration {iteration}')\n", + " print(f'Runtime: {time.time() - start_time} seconds')\n", + "\n", + " return cluster_labels, centroids\n", + "\n", + " print(f'Did not converge in {max_iterations} iterations')\n", + " print(f'Runtime: {time.time() - start_time} seconds')\n", + "\n", + " return cluster_labels, centroids" + ] + } + ], + "metadata": { + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.12" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} \ No newline at end of file diff --git a/doc/LectureNotes/_build/jupyter_execute/clustering.py b/doc/LectureNotes/_build/jupyter_execute/clustering.py new file mode 100644 index 000000000..ddd1ea383 --- /dev/null +++ b/doc/LectureNotes/_build/jupyter_execute/clustering.py @@ -0,0 +1,443 @@ +#!/usr/bin/env python +# coding: utf-8 + +# + +# # Clustering and Unsupervised Learning +# +# In general terms cluster analysis, or clustering, is the task of grouping a +# data-set into different distinct categories based on some measure of equality of +# the data. This measure is often referred to as a **metric** or **similarity +# measure** in the literature (note: sometimes we deal with a **dissimilarity +# measure** instead). Usually, these metrics are formulated as some kind of +# distance function between points in a high-dimensional space. +# +# The simplest, and also the most +# common is the **Euclidean distance**. +# +# The simplest of all clustering algorithms is the **k-means algorithm** +# , sometimes also referred to as *Lloyds algorithm*. It is the simplest and also +# the most common. From its simplicity it obtains both strengths and weaknesses. +# These will be discussed in more detail later. The $k$-means algorithm is a +# **centroid based** clustering algorithm. +# +# Assume, we are given $n$ data points and we wish to split the data into $K < n$ +# different categories, or clusters. We label each cluster by an integer + +# $$ +# k\in\{1, \cdots, K \}. +# $$ + +# In the basic k-means algorithm each point is assigned to only +# one cluster $k$, and these assignments are *non-injective* i.e. many-to-one. We +# can think of these mappings as an encoder $k = C(i)$, which assigns the $i$-th +# data-point $\bf x_i$ to the $k$-th cluster. +# +# $k$-means algorithm in words: +# 1. We start with guesses / random initializations of our $k$ cluster centers/centroids +# +# 2. For each centroid the points that are most similar are identified +# +# 3. Then we move / replace each centroid with a coordinate average of all the points that were assigned to that centroid. +# +# 4. Iterate 2-3 until the centroids no longer move (to some tolerance) +# +# We assume we have $n$ data-points + +# +#
    +# +# $$ +# \begin{equation}\label{eq:kmeanspoints} \tag{1} +# \boldsymbol{x_i} = \{x_{i, 1}, \cdots, x_{i, p}\}\in\mathbb{R}^p. +# \end{equation} +# $$ + +# which we wish to group into $K < n$ clusters. For our dissimilarity measure we +# use the *squared Euclidean distance* + +# +#
    +# +# $$ +# \begin{equation}\label{eq:squaredeuclidean} \tag{2} +# d(\boldsymbol{x_i}, \boldsymbol{x_i'}) = \sum_{j=1}^p(x_{ij} - x_{i'j})^2 +# = ||\boldsymbol{x_i} - \boldsymbol{x_{i'}}||^2 +# \end{equation} +# $$ + +# We define the so called *within-cluster point scatter* which gives us a +# measure of how close each data point assigned to the same cluster tends to be to +# the all the others. + +# +#
    +# +# $$ +# \begin{equation}\label{eq:withincluster} \tag{3} +# W(C) = \frac{1}{2}\sum_{k=1}^K\sum_{C(i)=k} +# \sum_{C(i')=k}d(\boldsymbol{x_i}, \boldsymbol{x_{i'}}) = +# \sum_{k=1}^KN_k\sum_{C(i)=k}||\boldsymbol{x_i} - \boldsymbol{\overline{x_k}}||^2 +# \end{equation} +# $$ + +# where $\boldsymbol{\overline{x_k}}$ is the mean vector associated with the $k$-th +# cluster, and $N_k = \sum_{i=1}^nI(C(i) = k)$, where the $I()$ notation is +# similar to the Kronecker delta (*Commonly used in statistics, it just means that +# when $i = k$ we have the encoder $C(i)$*). In other words, the within-cluster +# scatter measures the compactness of each cluster with respect to the data points +# assigned to each cluster. This is the quantity that the $k$-means algorithm aims +# to minimize. We refer to this quantity $W(C)$ as the within cluster scatter +# because of its relation to the *total scatter*. +# +# We have + +# +#
    +# +# $$ +# \begin{equation}\label{eq:totalscatter} \tag{4} +# T = W(C) + B(C) = \frac{1}{2}\sum_{i=1}^n +# \sum_{i'=1}^nd(\boldsymbol{x_i}, \boldsymbol{x_{i'}}) +# = \frac{1}{2}\sum_{k=1}^K\sum_{C(i)=k} +# \Big(\sum_{C(i') = k}d(\boldsymbol{x_i}, \boldsymbol{x_{i'}}) +# + \sum_{C(i')\neq k}d(\boldsymbol{x_i}, \boldsymbol{x_{i'}})\Big). +# \end{equation} +# $$ + +# This is a quantity that is conserved throughout the $k$-means algorithm. It can +# be thought of as the total amount of information in the data, and it is composed +# of the aforementioned within-cluster scatter and the *between-cluster scatter* +# $B(C)$. In methods such as principle component analysis the total scatter is not +# conserved. +# +# Given a cluster mean $\boldsymbol{m_k}$ we define the **total cluster variance** + +# +#
    +# +# $$ +# \begin{equation}\label{eq:totalclustervariance} \tag{5} +# \min_{C, \{\boldsymbol{m_k}\}_1^K}\sum_{k=1}^KN_k\sum||\boldsymbol{x_i} - \boldsymbol{m_k}||^2 +# \end{equation} +# $$ + +# Now we have all the pieces necessary to formally revisit the $k$-means algorithm. +# +# The $k$-means clustering algorithm goes as follows +# +# 1. For a given cluster assignment $C$, and $k$ cluster means $\left\{m_1, \cdots, m_k\right\}$. We minimize the total cluster variance with respect to the cluster means $\{m_k\}$ yielding the means of the currently assigned clusters. +# +# 2. Given a current set of $k$ means $\{m_k\}$ the total cluster variance is minimized by assigning each observation to the closest (current) cluster mean. That is $$C(i) = \underset{1\leq k\leq K}{\mathrm{argmin}} ||\boldsymbol{x_i} - \boldsymbol{m_k}||^2$$ +# +# 3. Steps 1 and 2 are repeated until the assignments do not change. + +# ## Codes and Approaches +# +# 1. Before we start we specify a number $k$ which is the number of clusters we want to try to separate our data into. +# +# 2. We initially choose $k$ random data points in our data as our initial centroids, *or means* (this is where the name comes from). +# +# 3. Assign each data point to their closest centroid, based on the squared Euclidean distance. +# +# 4. For each of the $k$ cluster we update the centroid by calculating new mean values for all the data points in the cluster. +# +# 5. Iteratively minimize the within cluster scatter by performing steps (3, 4) until the new assignments stop changing (can be to some tolerance) or until a maximum number of iterations have passed. +# +# Let us now program the most basic version of the algorithm using nothing but +# Python with numpy arrays. This code is kept intentionally simple to gradually +# progress our understanding. There is no vectorization of any kind, and even most +# helper functions are not utilized. +# +# We need first a dataset to do our cluster analysis on. In our case +# this is a plain *vanilla* data set using random numbers using a +# Gaussian distribution. + +# In[1]: + + +get_ipython().run_line_magic('matplotlib', 'inline') + +import time +import numpy as np +import tensorflow as tf +from matplotlib import image +import matplotlib.pyplot as plt +from sklearn.cluster import KMeans +from IPython.display import display + +np.random.seed(2021) + + +# Next we define functions, for ease of use later, to generate Gaussians and to +# set up our toy data set. + +# In[2]: + + +def gaussian_points(dim=2, n_points=1000, mean_vector=np.array([0, 0]), + sample_variance=1): + """ + Very simple custom function to generate gaussian distributed point clusters + with variable dimension, number of points, means in each direction + (must match dim) and sample variance. + + Inputs: + dim (int) + n_points (int) + mean_vector (np.array) (where index 0 is x, index 1 is y etc.) + sample_variance (float) + + Returns: + data (np.array): with dimensions (dim x n_points) + """ + + mean_matrix = np.zeros(dim) + mean_vector + covariance_matrix = np.eye(dim) * sample_variance + data = np.random.multivariate_normal(mean_matrix, covariance_matrix, + n_points) + return data + + + +def generate_simple_clustering_dataset(dim=2, n_points=1000, plotting=True, + return_data=True): + """ + Toy model to illustrate k-means clustering + """ + + data1 = gaussian_points(mean_vector=np.array([5, 5])) + data2 = gaussian_points() + data3 = gaussian_points(mean_vector=np.array([1, 4.5])) + data4 = gaussian_points(mean_vector=np.array([5, 1])) + data = np.concatenate((data1, data2, data3, data4), axis=0) + + if plotting: + fig, ax = plt.subplots() + ax.scatter(data[:, 0], data[:, 1], alpha=0.2) + ax.set_title('Toy Model Dataset') + plt.show() + + + if return_data: + return data + + +data = generate_simple_clustering_dataset() + + +# With the above dataset we start +# implementing the $k$-means algorithm. + +# In[3]: + + + +n_samples, dimensions = data.shape +n_clusters = 4 + +# we randomly initialize our centroids +np.random.seed(2021) +centroids = data[np.random.choice(n_samples, n_clusters, replace=False), :] +distances = np.zeros((n_samples, n_clusters)) + +# first we need to calculate the distance to each centroid from our data +for k in range(n_clusters): + for n in range(n_samples): + dist = 0 + for d in range(dimensions): + dist += np.abs(data[n, d] - centroids[k, d])**2 + distances[n, k] = dist + +# we initialize an array to keep track of to which cluster each point belongs +# the way we set it up here the index tracks which point and the value which +# cluster the point belongs to +cluster_labels = np.zeros(n_samples, dtype='int') + +# next we loop through our samples and for every point assign it to the cluster +# to which it has the smallest distance to +for n in range(n_samples): + # tracking variables (all of this is basically just an argmin) + smallest = 1e10 + smallest_row_index = 1e10 + for k in range(n_clusters): + if distances[n, k] < smallest: + smallest = distances[n, k] + smallest_row_index = k + + cluster_labels[n] = smallest_row_index + + +# In[4]: + + +fig = plt.figure() +ax = fig.add_subplot() +unique_cluster_labels = np.unique(cluster_labels) +for i in unique_cluster_labels: + ax.scatter(data[cluster_labels == i, 0], + data[cluster_labels == i, 1], + label = i, + alpha = 0.2) + ax.scatter(centroids[:, 0], centroids[:, 1], c='black') + +ax.set_title("First Grouping of Points to Centroids") + +plt.show() + + +# So what do we have so far? We have 'picked' $k$ centroids at random from our +# data points. There are other ways of more intelligently choosing their +# initializations, however for our purposes randomly is fine. Then we have +# initialized an array 'distances' which holds the information of the distance, +# *or dissimilarity*, of every point to of our centroids. Finally, we have +# initialized an array 'cluster_labels' which according to our distances array +# holds the information of to which centroid every point is assigned. This was the +# first pass of our algorithm. Essentially, all we need to do now is repeat the +# distance and assignment steps above until we have reached a desired convergence +# or a maximum amount of iterations. + +# In[5]: + + + +max_iterations = 100 +tolerance = 1e-8 + +for iteration in range(max_iterations): + prev_centroids = centroids.copy() + for k in range(n_clusters): + # this array will be used to update our centroid positions + vector_mean = np.zeros(dimensions) + mean_divisor = 0 + for n in range(n_samples): + if cluster_labels[n] == k: + vector_mean += data[n, :] + mean_divisor += 1 + + # update according to the k means + centroids[k, :] = vector_mean / mean_divisor + + # we find the dissimilarity + for k in range(n_clusters): + for n in range(n_samples): + dist = 0 + for d in range(dimensions): + dist += np.abs(data[n, d] - centroids[k, d])**2 + distances[n, k] = dist + + # assign each point + for n in range(n_samples): + smallest = 1e10 + smallest_row_index = 1e10 + for k in range(n_clusters): + if distances[n, k] < smallest: + smallest = distances[n, k] + smallest_row_index = k + + cluster_labels[n] = smallest_row_index + + # convergence criteria + centroid_difference = np.sum(np.abs(centroids - prev_centroids)) + if centroid_difference < tolerance: + print(f'Converged at iteration {iteration}') + break + + elif iteration == max_iterations: + print(f'Did not converge in {max_iterations} iterations') + + +# We now have a simple , un-optimized $k$-means +# clustering implementation. Lets plot the final result + +# In[6]: + + +fig = plt.figure() +ax = fig.add_subplot() +unique_cluster_labels = np.unique(cluster_labels) +for i in unique_cluster_labels: + ax.scatter(data[cluster_labels == i, 0], + data[cluster_labels == i, 1], + label = i, + alpha = 0.2) + ax.scatter(centroids[:, 0], centroids[:, 1], c='black') + +ax.set_title("Final Result of K-means Clustering") + +plt.show() + + +# In[7]: + + +def naive_kmeans(data, n_clusters=4, max_iterations=100, tolerance=1e-8): + start_time = time.time() + + n_samples, dimensions = data.shape + n_clusters = 4 + #np.random.seed(2021) + centroids = data[np.random.choice(n_samples, n_clusters, replace=False), :] + distances = np.zeros((n_samples, n_clusters)) + + for k in range(n_clusters): + for n in range(n_samples): + dist = 0 + for d in range(dimensions): + dist += np.abs(data[n, d] - centroids[k, d])**2 + distances[n, k] = dist + + cluster_labels = np.zeros(n_samples, dtype='int') + + for n in range(n_samples): + smallest = 1e10 + smallest_row_index = 1e10 + for k in range(n_clusters): + if distances[n, k] < smallest: + smallest = distances[n, k] + smallest_row_index = k + + cluster_labels[n] = smallest_row_index + + for iteration in range(max_iterations): + prev_centroids = centroids.copy() + for k in range(n_clusters): + vector_mean = np.zeros(dimensions) + mean_divisor = 0 + for n in range(n_samples): + if cluster_labels[n] == k: + vector_mean += data[n, :] + mean_divisor += 1 + + centroids[k, :] = vector_mean / mean_divisor + + for k in range(n_clusters): + for n in range(n_samples): + dist = 0 + for d in range(dimensions): + dist += np.abs(data[n, d] - centroids[k, d])**2 + distances[n, k] = dist + + for n in range(n_samples): + smallest = 1e10 + smallest_row_index = 1e10 + for k in range(n_clusters): + if distances[n, k] < smallest: + smallest = distances[n, k] + smallest_row_index = k + + cluster_labels[n] = smallest_row_index + + centroid_difference = np.sum(np.abs(centroids - prev_centroids)) + if centroid_difference < tolerance: + print(f'Converged at iteration {iteration}') + print(f'Runtime: {time.time() - start_time} seconds') + + return cluster_labels, centroids + + print(f'Did not converge in {max_iterations} iterations') + print(f'Runtime: {time.time() - start_time} seconds') + + return cluster_labels, centroids + diff --git a/doc/LectureNotes/_build/jupyter_execute/clustering_17_0.png b/doc/LectureNotes/_build/jupyter_execute/clustering_17_0.png new file mode 100644 index 0000000000000000000000000000000000000000..1e6a8c796726cad4240af4d925bc4bd8ab338a8c GIT binary patch literal 79050 zcmY&^b+&@CzKk=}3b%QuL3h@f_3UNQNb9Z-kd(Ow_@c&-G z>*Q+7HnU)m0-D6R)XyR1WDHpKa(sAqJTt-LL%#V)Zbr{3=?M8e>BA8F}~K)tEG%_&ag1H zsJG6dP>p`vU*2E%J!<*wyVO)e3D!h>wm>m0PnnaI#elsNM+}vi%(9V}n|DtW@Y_9C zTetI0CKl{#&Z-W{;YL&j=0Vt0Ual;%`{e(*Yk)|$ARD6ocR$aW8{-P&5qE7jd7R=C zv;VxXw+?UP-y;}W;#5Jtz@-KV{K2OQe5lqS()9r12-e{pur&E zN<<<{XvWI%ARf!K@%>$mR5AbfKE3Mx_X$I_@FvZBG_gQg*U`EAiosJ++-^QRmNciUg$D+&3jxN5 zoB;?=!-xH?hzQhUEbukZzUBYQuV zABCjrP#=bBw0nAl7Q9Bk`vI%Pp^#MJHkfq%M&XP0-Gf=nrVn)(>FT$JtyL_&gUk7R zYK7Y-()XO9mx-k77t()io8W2i1+gI6AY)I`ctcx2p)`+JOsN!Zk9oGQ8x+1U&#o?#E8K3ATr*sJ&d2t@t_5~kO7r%n zdlHim-3;5G>XPK|;T=0dYx#H~fcSSEyz_HD68Jwr@8OOF-3eonW0gXI8~s5VWrjA| z9YB10(QI|}z>KgqL3`*z2wo@WOTT&83kV+l_P~g6!eh~6UOSnvsQT5t+Ka8}JP8lL zH$j`g1fi(^&fVX1HwOh&0E;y~oAhP&+)w-K_D~Z>s(sgChU>pEhnoE7)E90Oh@mZdqbv?XA@U0%2!xvU@(n3imkr>xz z-;wMOQqKKGH|bTdRM>e9+96uNOFS2*OIn0%BYX>ZDaL)9vH!UidcdI3jb|ln!00Bs zo5cCi*kHdXZ^rv7>3aA*k-fwFs$8@O5DH9k+1{o7U}9Z$*M-4?^1a)C?4^WP2Rv(J z-*sbo%kW6b!T{?Sn~6g-aJTvP=JTCMC2X-<7Woj?_!168J8+P^p){CX*r$IV z|9r<1dI_9l^RD1e(m%%*5`WBa^DtM+)l~v62QMY4ym}FS3mmoGT9i#LL7U^(tJ|$m z3XI#Xpa9GZp9@L&LREzLmKn|p=6w=OluTi1|IV@B8*zv(DQAZFvzwulf_4=Ls2KWKIBTzpunZ*3?^2!Y7{-T>1ZKV-T$MOTQ zaRy%icRw`x=Le8o?ta4GkpOWpKhq}{W1=hN#86G z^~&9@P)%!Xr^SBKh~{<$+-{KZCf{U6PyXocal>A9rJ%HX{ipY znW15wmh{#EjSOe=ny}_#(-X8KelY z{!clM{8x^F0{uv8?O)XY&nL)r0*`Q`LM{Kdwkw@d8z6*2Ep(jsod?8uc7DiE>t~(P z^_2P8v>dDLMYfm2Q?Clu4w&73?pjf-`&3A%SJ7SpvnK%e;L*m5Ah;0FJTN4 zmLIo=bHuhJ_iNZPbN~71%NX;Vv>*5Tn$C4KG^LxR?n;lOK>zbh0r^cav~%AcQoi%! z{{MRhv96X}T&5C5V84HR2rMc8yqpI```>S6i`AjjJvVWIFE#uGgeNr&+@-Ee#b)|4 zs31$BaO>oJ@P}&q*JX{NeZ!#39yZmbR1fxvBEl5$6BQ}s%JPF25kTZSV|2qVhaPa8 z%;foR$ADAoL(<_L2O8jMV-O)&W=tjQ0rB6f zyu`V2BB?Ha(6*9(CArl`Jmtr_w+Dh4s7wQlH8(Te`8eVM_qQB=i@+xo3{-`@?7n>f zc89rQ<=$}kKo-1x#D;LG)w_SP^fH_Ti~ux)%N8D>y5MnyyyVCfm-0&Z zV>*A3JKrIiR%J2rtB=-9cJ;x)@Tg;Dm(4&7Bi^6&36Dt45)BG=ayQsHdI=dsmL&#| zT<&(0xXix5zwOuhyaX&9v4$!OdD(2!mPgUvDzeUZcaD1tZ@c+OGUM$bJFLcgsF{Gr z=37~L>7RLa*Jw@UiX9(5*lSb=zn4HvO2=6OOWJ0PH=>uJW&7?SZka&g{yu+u?oe9A z{jnUZuDwl+<(Lv&l|Vm;Z&)5F)o;Y{-Y4Vn6+vwy>qC&?(elI%@V-D~uDZn4)okUj zX?xP<+j5`&Con^AQt6o(#+Z3q^020opDMs{C=Nk5{$R{Bb(-AG-^9rrZ-aQL#}pbbdo73Cu=U4z3ybzp6yoo??XfR{Jy3_arsnIf9{uSmQZCa`i87E zCLYGRSzsR!#9AA}|6pAZQa=Bu-?z%~W2dWSU=oJ?zF)(-@uW{u>PM0{&kTnv%j`m< zU>@#sV@7BOwFb4lcWnd99<{`uQDJ5N~yf>DMO;s=VX#)ubEV|P9|I!zZJXpA1E z>ltsPuGyuLUj@fH{7NMQYr8$2Z?XM{4@4-HhnkOApmRoqjbC#@-YGnrZ*K|LFT!@X<(YkDsTX=gNti z@yc(y#}QF_h(wC4eTxxSa8CYcjZ~M%q5#vUi=%?w3vb5+UcqAyynLmBBYwk;?cuL` z$$L^vTlcwEJ>F37t7|lFUu5s&!qS5)|BL6PH$NXAdhix<%+uSFz;@eC@@hUk?Q}00 zJm9p>_&z-`5sl%;Xyo#xXb9Fzjrs>7RX*Ll0w(tdRkr$z)c0`%Vk>~p_R!zCM^=1+I82|v`?GLR%I%BUJI zXzAcw7fZ$~57RJ<`m8dQEQx0w9iR31mY(x(&)Q=FiNO|DQcsG@q{Sm<=y>@tUeH6C zHg~9KHf^p+3D4zba&q`ox6*)%i2p#iEp0M-4t=Jn5@M#<5|MtJLi|rX=vg z)mRI2sG`z676QIk$#^BzbzoU#jruZP6CV-{e%0x>8K`Zf^OkDTji}Dd|NO;TgYtN# z|Kk?@kn`lJ8>Ua&E;VjmCi6G^px?CCUKr0^86YhHeaxcL32|0D5Z-l|5@ zPsO~A?8FqqzGQWHd&>Uj{uj4kTOZ9L>xAi8sn7%~=+@Pls9KbA7GcMU=bw`-7g@Y$ zIbc;YyziFccYT5r&IRPSlkr7dFYbsStp zY|AJUzP#LG0&rApX_}p~jAT)YlbM7ZTJBWQbQ+M$Rn@sf_r=a#ZuiA=$EJpVa)ZjIry_lU z76Q zJ{XtA!ONmZ-5N3A(t8C}>fm%;)fvi--ue{+q7vZST%xPw38vPBp>MrVEaXTWk|4KD z%w44iPAU{J!}Ts_Y8FSeN4Ul=j5lM+FvM?Z8a;o*i-arRH^=^}tmv%jwYF|J#B{vN zgMU~eXUiApt*k_PAW+L9G16+5NoHPie`43=*l_hX6H6eq==a865_PS?hMXe9iP1S+ zJ4=IaxWPctfc~NyY>b9SmC2(4voQ=dOrC{@!9=N>3%?E(Em9X%1tY#-k96vn8AfhIza+rSniC zPsu@zeTcpwDe=8ZoAf#}|4i?B=VgRi=@H;FlU1@e*bOx?fw)4T{qdp^Cej%bgEuE? zZWgW55AFGz?+~T2icbO*TppV|GwiPr!`(<_*A4z_@=*98gCrVh*pohSO2dYoY%&w& zJHaC&kw@tUnNeQTU!5mqfU?_r3S%9n2FZL>I&V?ezNl#xGSl!>0#ToIf|wnMk3tI; zi8HLT=0qcIduPD$4)mX=UrXZ4b?01r?bU!Y?5$zw%%*I zzE=OSa!n1%V;U$s(JC^ek9M#jxUo$9SM1e9DyHVArXP_KR@`tM)kr7{PJy}c7e`lSO#xUvHSm#cMjv+6kOQ_R##69@N zlNDd)Ia7G`MQuuFyf9WQ)F(Z>pxeLXnd0HuRf%E08aO9FnwVmyosCC0v1TiJM!3T3 z>Y8juqhX0aVkQ~{TRW>_NnLAVDe6=0;Rk_WHYs*e5PUxpErO)4?-fDMRENc@S|k#r zn&CDXX%tWkd-0-5LWAFQMvX4BKkr?NoDiy-!YBh zU|(%@9pVSo!s}-VUe|A!Cy`%8*}{z|QmxbU8=(c$O)_F3FvRd;z@cM@6SA@Ro1B_< zmuEO>@NR@qQZM!i(Cg4-+}!Z3X0N_b|9`>&YhUm9o5#t*3_A zF$nwu0aA0=QDPcY9TpP7L?o{RGti-lL|I65kA9MA-*&nqE#BwfS*ObM!Ay$K%q?b3 z{u1a`CQMWnfD2r4wi1J?K}ktwK1Z{bR~qqAK7O5g8-71l1^I}A9;Ylg1Ar#eKV%$9 zt6Ck283s=yAui215UIt>3d-SoJY(|4?v?3>P*N;{q-p*M!S8jGVVhLcY1tI1TL4a| zgr9%3-~Up?Rw|fwaZy^Go~Ym6va;5uA1^)^k1y4~CakQ6PNf71E2VHcB%G%&&Dj~i zOMFVIyC4F&i4D}&c?v~@oe?Wq539Y>qpKfz&5o^IpzUFb&4k zV?-8E`e5Z*x$#>jq`K3|thP)IzHwcV6yIUyMwtVfsD;NI5q7k4AL_U<$LRaTS8?vT zy;*k6?Dkrs(`_@b$WUf7?Rnkgj%H|*)U4NSUtTgc>64`Z8Nuy~T9KVL5iGMshN-CA z#il7U$yM8wwA(G?Hakr9*g&Yw5YSSVe?LUp+FV@w0(08Qq+4&J9TvyMh-&M7Nb@9ka{g5IBS7Jgf5xw~gW0%&+vCj??zCpp1S)f9nWcUYH8Ns-E4E*yc3;e37BxiPYm z!sqCIl(Lb#3`%bQI-8KjuEitqj@c61em`(q3+Ck+Fe1+5Z39znCL{HV0#2L)NM}!v z!S)8p_bDGb{jBqyWME^|V&7Fj8I+X%>I@_!3tKanVg(UGcA9p_<)$m?LiLYSPbIji|KW$6+-Hf0E zd!$n3Ud4DcD~%I;U_#jWx%y)2tFjuw#5p~HaOHKLU~z&je~z=X6~#o4RxN%w@g#n_ z9DQ`$!kBUZL%cJwxcAn) zWuZUpR~YZbyG5xXZ<5rE>%V=Sreh~6JZz9q!B4RYND?f^bT44LK{9~4)01G1p#m7} zST#=Zat0-akvd7*MoAP|Y&D!PizI5c)D{aj|*{ z@+5y*6|Fu2apk?UPu9!2AhyXd7Q9tAlT{Ww_qO*LYvw(C1L@23k9iywa5^D_Y}^3b zeqLf2`^~&<1ywTcYc&n=pDCS98*L*8-s<{`${fZ8z*an9p3Q!u90aFnsIdaPkQp|JqfH^{Mwo`%E1?8oh4`9Z&mM6c z?yL4>8?)Z`WVZo*g<8uK7+v!-aIW}^kR17gSH@hX&sS};-U87t$uL2XkTj*QJK$;= z(8~t)K5}oH`2B8v4K~iw`Pg?y!_)DaUxNT+b-O>7DZ4K;yrvfJeCIq6D<5@;kD>LH z>>~*|fKhjzXN$m{ztg+9@gwcG(^@1lT*P^R>0_Q2ngaid&K%SeS;P415zuR*>M@{Y zF%~JQW3I1QUvEIs?Im(HH=req*au8XOrx=Zt0$)f%nai#{=&$!aRD^~j7eMm3WLKd z?tT^^D{t3@1b|uQ>hHXaSe#90UYlq|u2<(tyN56`ntnOLyOF94APr^Fr3fpK6LRZJ zm%Kj6N*fG=l%$uP>-{tDRu=P7lLuWNFtezu9M+T~g-i`mkjsTz^*K$)tWMM1*QliPbSD)s|)=;;#Ip>A>M9TF;D zZay(JScRp)_Wm45(ht`${;VwrK25+VQB*DGq3`&@mvew>V`g9>1A>z+j2S1O8Q1s(CsJ7~!rhYDk|-onNp%#?&jKcjl@kD~6+4fw zCd(JT$xY}}je{|Z3SJD*Zl}E`F2y$P!+K{}jKP8xa0#X-@vo)I060Zi946Sx-4ngR z<@!#2C&Ei$-k&(7w+eg4BT~l~i4p(HV+eP!!H4N&BIxYIay_O{8;GLHi&EE`cx(lw~80&tTqO%YNgx_05_iWkggIqtdTP^7?7V@AnU7U4;#^&QcM z_I2|l*1%qx&=ep673hr&*1zL_gUPGPvtcVlwZ1muI8M;1pC%k~9T(>l&$9M?SRgZm zLKK;((~JOq4c7{4(?QM34IpR~LlHXxK?L6`bkCap(F3PQtN+-dc}{>Yzw z)5tt-|7k!jivJS-=Fp$C0_kYDssqk(^Hz8G;yamYkW$91F?vzWR5$BBkH9zc?pVyq z&wuGEr9MpXii4O`VJZ@nxJ07c0l7S(?H8lppaa0J)DHYRz3zqzo^aKxM5V2Lfiv29eaN$HGO5C zv0;hOaR23{8XB)L<7&VBj_LeaRr{H$-m&B%bDeh%zs95Yt4Q4QFHWW=&raD6nKiDK z?Umb|zmLBGk6(#jA8=YiDP6xW7Ld0pZKvJ|7!TrW)rinqQ&OkVsen+>f~m2c$lc`( zW)tSxmB>E>O!kb;f&MNkD8WI~MZ)XBa#zl=}xFQb7eZN1JU z%!H|FzV)@H35~jxpiG=Vk1EfZY4D||5O+(wFnAo8ELZ&=zIa|d141z2aeXh48N?j4Xx^I!7#zk+$!^D~=0N8eYLiuXUyg zqz54KLa&(xT3XTte&9PXB4FcW0QLjL+EkGT!vKn9Wrg;rXN}_B?kBDKsE4hHYzD1m zX}S{Zxp-TZH8n=G#8UAL8glf;pF5|~n=pVwEr>Rn{I)8VxN^jjTGmv{H)#U8E z?3<7DRGKHG84!-YwjlZ#@75Gg9s?8h>xZU_E|+K-(Fp^`Ue;(4pu?~B$R=!S+9*4} ztx=r(BPBuTWWqq4SL-v_Z0a%^GWuxDwX33zRDw?Jkx)j@L}@MWb@%H_re<(IXTvx^-z8EgFxq- zIDN0TxW+n<<)0^Ic^EdBl=z6{bN2)0Xn<0^DQRLG5g?a75yk7 zHOr~Xr+Zu;gX$>@u!f;|!w|lY?kdMoUj==)N6@LLy#R`H)MEXQ&19A5<#Z;KlS91s z2dMWVBAySs>k3Xh&R;MGoNJiwnca0{`(CE$So6v<$Lpl-WD^5NU^?jiEcUfNJUaqp zSbh}BhN3W&UPN}>Mbf(-QO3%BEk@*a;M?91X?`k_puS3_$6S%jc>Fm@9UK>QvM^32 zyFdr55bQ(le?QITx2My{9N+0qIMen5Q8hDr&b}gHQZP*O zhpUj4(IEy-LvV+xQUR8k__BqbuCV<$r51sb;jsSXIht7J&GpuoT$cfzzF$R)g<{+A zt^jdGgA5z?nRW$yRlZ}|Vs@XI9Ca`gz@*6=V6Y1e=;$7NXX3z)NY3%^<2Yp-@3u^{ zPcueuL&iY#rsFWKV*{1Uf77us&`0yJ=T0f(iT}Do$)u)|4@LR*+vz>VWrD&9ODGNW z=cpB2@0`OEYT{>r0Ffn!0{GUs_{Vw1_AWcOkG-Mubk8_JOd~W% zEUm8!+sFYVSJmxv)I}vMzyyyBEq2g-X_CR8;Tg#VSI5#wjCc=#CXuSz@t=2FOV@|X zE?k8Qrl=e;#nOQpPB67G7+=;0g6&P6=go26DxuQSvao*bqM)OzQ6JS_A9F&WMd05k zvT?i;T2)A|V0btHv_Ls7Uo98$VPGWa?_oneDwRC3R7V%X#SbZ7*XWXmu8rKMs8@_H zDlMmHp$BY$=}jba>O?dE0S)@=*?_^yVm2^FIGOxu5E;8fIFF=HxL++?vF91uyIDJp z#XAyTU5ByX59y0;K})oaT+htaSW#YUy4iEh;l3At$yC?WlmUjKWyvZf^%gmLvllNk z!7U>GD>BkgaYH@k3@@c<0-t5e@b55UoDG~wNqKk>dnDbzqZw1W#J1(O%c$x3{=Ag7 zW{F`6FNY{wlB3_L%d?xaoV2%IQcWVm>UPC;4o|AbKKsRhs%jw-{JX&A*G8;7^H#E- zF%+@g$g4A|855z5O+2i@hL~~rD1q>$j4Vex!^4+*ua?+sjdXwHDFf72bc`Gb7%c#z z^G8r`GKM8LGXq=WQxdIUKFWqMZE9$!VM*PmrUQ_?wK;TiCRX}fnRaj{xGz#NJy%w|_9O-+pmy%jY$rWdVeP?4pZ)sP}IDR?shD4U|6hdF)ONENW1f)RBTT?^;Iw0o- z<}W}|gBHgqeoPS#k?px=B~3d{)N7q}a8K$T{!FDDOTy!l%q{0E7va%Nt1OQ_GF+ya zUJ>~9I4^*6+C#{fHx>^M8YDGnpJ6X3`~j`M=GRoa-|>k6PP|kvO9lL!u9&S=NmX9x zSoI{TO1_t$XJkBB+e)vfsg`BqDM<&UVK2Dyifh(B>0}rJ*s9Onj z!;-7<9x!4^wXJMv)W{2=Xr8f$S*=WcRF+Xw?ew>ZtjTM;lkvT{D_ZoxHIrD}2G~h& zOP>w8$UB_6QadaeL&LA1Uhb);I6r3wvdlK47LGqW^1;#A!@s4n@V|Zm*MlpL|Wu^Un zlwo0_&TFHPZ`37f#wqT4PEAu9LSipx0l4^~KXjys>^Z^SJ*TD7_pr`sDobZsV~B#8 zpc**bFiZsu%t}7KM;hsnl6g8pK#Y*lb>W7woKvb-CFt0%$YunF`Jep6K$Sw;j}3c} zLqmM%xZMGu&`U0qAj-B9)=XIzN*X|SIfJ%6nIAytbhCr7D5W`!kd)j5lpax{ZDYxU zzG9$Fvec~5)Xx%fg2(SUtr;$*V0+I1Y^EX6M)8KW@2J?^De0tVEv3GmyBRaj_z;0V zyvB_j=}B>tf(bu_b-_TVW96b}P|7B^4(3hujqc^rG9P6JL*OQ3ed^2>S4 zxswIi-TzWtCZ4y&2@?NB4C3lrY_qKYy5Veeyb#MWS`|2xOH(e~87hYlV6@ijYM2|{ z0-SSG>we7pe4sj!=GSyp)li>NJiv5|0|-DExk(b|y<-xusy6|NsH>5wmjpzD(l!Ag zn_F9^UlPncJ5GI4gH`&StdqjZTGbT4+tmd+Og-s7&s4$<>-}urj~aj{i0d|DkdUf? z{;7dDJG?i@95;0$M>^c7JtMkKwqxmqM6E(1z#O0%OFFv6$zCHo)Ba<<!BEy8eug&o&E6Wm{06=7bG@0W{yC{b#7}fH{jIz~P?OpHL

    j7XRk*9Z2>>H=kOw4ejdh zI6A;aDv7<%dP|u6n6154dL4Qq?a06p0|*yoUOOiFjZ;hF9tTJ2H z8Jz||2wMn1VdW~RBURnlQ4mcnusEc<0jdbBxHHQR@*msaKNt+>anFJsLnftm6=%60`(0 z0uYYEIxGqOa8Gk;pnfG*B8zh9GeCg%PjGIU$l};vWk!!uKsT9V8y0+KhL;BN?9p)Y z?Ee~>>$U6(sH)eGka8)4gsrWQFoGI^x*@L<$G671p4zb$UY~{ znx_G=vUtL#x^`bvu0k-{!`-Kw#Wn}v$DVcYj$KR;NsH3a$!_jVmay!e(3N*D5^p2B zy99Rb1Nh&b^Ckp1qBu`WB|*+1#RbOkWi_9^F5+l*Yj1E7dA~irhU3{2$wYC!{>Y?N z?jDk=*L`1HAQ-M%aun8`99+rYUN2EVkE^>-D>m{6Q0We1c0?EzYw2(H=DyGLL3+Yc zpE)_k+F?Z%Pi;V1Mte?7(1y6w)Aa2uL9z1mwiu*1OdY?sLy(#D1j8Z#cjE11`;wtd zBL4YIoOfZYMFth%!jLBbx{1nKS*i|RF`6Z!=I-Ft{g27KQu>=pSkaZHf||kMz~xA! zBL12h#VfNq5f$;SB{mS3|NV|NP`uE~8Z+ls)3arKkc9R;ouxFtGM7}RIzK%>$KvQ& zKO1KWIP-LRZ8tveAEH6ed-!T+VDK~>9o{=%ZJ$sA?MV(cEbmdMS$jj*cY_E^Rgbh<(-Bcsq-E2unLE6!VHW3)rYu@;FTPA<=Vp6V3A;deGQp>Gtp z8rst&?ibVQYw{|7B%ChOj#3E~^!n!hFU5nYWOMBN=OQ7>JE zM|Uq?=lmVmBh+zyRCp+$`bY|2vM6*&-%D*>9mue!AmO$brFPU;NlJex9&-S^FOI5^0iUdE!_ZcruynS*5G022j~1a1FaeEU{Fg!hrzH)@_}>$J2D>o5WS;hgic zbACl*G4qBMe0=HQO6NsKOCHI-lzoq=QY;8G5&lkc6Buv3F&u<}CiIk@p~(&YoQ%FB zuls1Fb!&MB~>lRYz1B0q#qIep9ia{9v}6h@aE_Hj85_X7mmJouM3={Gn&+%xc5?JQr=5q|boVqC?123nB{l%1 za&RWa#Mr&O+*!nlorM_FMlted_!PPBK!PrN#W+nB5mgupyRW#QtlQJ6FS5M_{(2{w z+w4i`OD>gN!%#rjBJ?YP$XCCM9HZlOeiQ_&oyOl0^SzG!vZ)uyft?*fVZVGa$s^MJ z9DA_HaP1GQ88IP<{2;lp<Wf%za-nLZ zOOP^TUKH0exs2y}e*}irjDAKC<%OtDObihjs;mk2><;3Zm^e-mNuNW}9PC7Vr+Zsd z^aqlx09X;IWBj$7bq)t=C7sJ*7tUlHk|Hc-m72Y=#AIV)B(kx9n!aMX@ga9kf^&ir zTP)bnQ&ORVIQCBna*mv=mkOeE%>P>CT%41`+cXV!%=f4;#XxjFtA%TbZ3&Z-G%0FD zRB8>LLBh~FYsmz`T$N#l2jTBrtGpdsV|%Qtfs%dL8SrDR@d=oS-fs?zNSfmtG!*be z4QkZ8-a9w5<^yB2VAnw|jsIpVOrrF`!uc5SfCyo=fefp0e5HI|mEOb6k@;c4C11V5 zaSBQgenv}Zi>=cV_*_Mu%RW*{zFZ`BYI}G4dN1aUQuz#vld|J$+Z^iO0+q8D?mig_ zl$544Q^eAmpA>+(d$rS5&QzV2PsFdJ)gmbsrWD`C(O|*~wQ8k(Qf!s5g{8wks-9Ii z__-m7LNoKVvA*#nxYX8P2UkR{49nUY-#3~Ai+n%0Gbwl`_lxw}Z%$<8OY=mXr_PUp ze-yyhoU>T4W2S=xT)p#c=N7!wSV%8B*=EC$^UJSPHAi9~w#-l@mcyPy z8{%d^Wi5Fg-ye=Lz-Wb?zeQxnBMr2kGKJl{+eUP(I``}?>A3N3e%`km0sLkQMxCDf zcn$@O5}A{mdfiGj@*FwO_!VaZse4qcz;|n|unYpRU@xGiA0Ukc!@1q%o zJL}oD1JxN49N&;+k1O=v>}RA@xT^df$lY2cn!vJ$90myt3_ncVjcONG(YAF`s-2EP zr69(0$;_nZipag)pT=KY*nDcTrD0=V9N$(r4ZxbEkSbUw7@A7hFZo47HDXEEH;Jr{bku9aN*D zpubCJoV)l^s|_5&fRb0~uHX?)D~U`|)jNWnNXLZlyNvwuvn5;uM^f^SJmQk-eCP@E zXO*MZ?;L`$fP?`B{9HG?!(~7m3<9g0LQJ&uv~?->yKR%Gb*BN~Y)}zm`NxOmjYJXN zlXEs5xx!^X_`p+ath}$^xPx5V$~0-FBBf#?f75bQdz;Xu)N+eqNNEX9yMA2k-gMrG0vdi-pW*@NsximJt^u{_EJ(X$Oic&1raYPlcOBVnpOrxb` z+A2rSMABW}u8MJ8)qnuAi9-T6nb7PzPm8E#MG;v`;?bRIcvE=0uvcEOa25dga?+)T zaR>2(l3p@Zda{N?6!r9qp`&FfPKi{-k9FYyO*{P*b4?Auw9PS#6ss_)((^s>0IgPy zCa#doU7-a5K}78Fj#WOc4N1PK;mF&n)}a$M~Td2 zW_sR433cEc?!{dxAMUNGU*t`I-_$L{(Xd}BH(G0IJi&4-1aqBqf82u?0FIFCB8a@6 zE`x^2Oluk8cDhkaeelEKp=l}Q_dw#_9qK-7DgX^y*^g z63h6sHk1uZ&YuFtDus)^`_DO9j{PbrH^QFrxoM^_Ln&y$sMI$?IaKUdbw!L^TBMw+ z)=zkrKgwG#Ymz=vgaBN-voMdrp^~G)pwaXQBJ;ZM(O(PJ5K+>w$7Xnq{M=%gq`}iP zb5oS!MF&%TZ<0bjD>Ra;K2zY&+dR!e&kji$O1Da785h~_-qz)NpQCFcsRo$ATJ~4i z!nRDh!a+Z^J(l$YGhFJbu#cv)1IYVyv@PD|T9{ceN(e!BtU zJ&Xm$rF~mIkH+d!ed7a`ap4d)ThEmDK_>KZNl|)#P5}FiypG@qS5^=pH!*%D>Jr77 zn1Vw-R5r0DP5(-Pi2!Fy;DDD}K<@K0?WlUn!Sel?8ND_vo3o ze1TMY&sEfrerO&-@{nmN(ytMHH6+zWPUuvibnN6Xk zU-b23d-f1EWn&b0NJFvk9i&)~q(E&6hLTRVKGY(Z<0g`7gyB8HYoKEdDWQx*b+ z_c$bsy1412?!S6c$}}Gg%<^CC$cC6PNcz;S z*iK6UpF80GvCc@-Xh?!84W09|qH=JpI0#zW#nu1;(AQbm5=O2=H)^NHuL@3aRYJQf zIn?mM+@=OWt$>RJU+IYVRB1A_7=7Gqnn-ReCQ}(9Fe;=slg*(5W=)_3rOs9I;y)?e z@iFI_S$dt4My=Jh_OsRsPND2^kAs`A#z}gffamFgAPU+F9 zMsbz#JHiLu>>W&(83gDk|6@en7`e{?lzKHucUpGdDf1kxitJu@ilz|Az^@{ZeN}?c z-5=KD^3vyIw%4(X;@izxpw$meEP-;Z{)*+m60qCN{48Pt4+fwl0;B0S@g)s~AUP$yIy5q5i#2>krr#YD=iPHE?yoA(6=OQ%~HFN?VLxJ7wU? zg$v!txWqfMZY-={Ve{|eW6}|c>1;{=ZB3)y?-;AJvWZ*a^;`xYltc60XQkq?;7QA8 zwTUhL>96!qQ1b3)11;Bq`zoDhiaH<12#xE^oZ0YJ3tu6e2i!`teEBo#e?Ed-$`ta= z(-oV`KQVL+=fpD9{^duy9q#V!DV3k&5E=z=lMvW2oPTXWzPJC^GuzK(H_3#n1B1X2ij%S5kE z1o-qU3VvsA#QY5e4CR6KEd`CT6QIUI<_K;POq;L)gBM12O@p+tuh&!u$M{8#I_R6= z{gIT1EMNFxb5JBZZdm-aX@yNWaW1%Yf8en4$pE&AQ$4nZ0xF=wf|mk5NdZjhe>X7h zBRtOq7G5P)H!1XL0y{+OlN_V^cLUcK3e@Uuqv)o%BSDp@s~;c#fP5!KUgc(Ftw+;K z`%gmO4j2v#S8z7ot3dYtw`}7{mBG&oV(v^=yBZhPnL9g10e765yg+&HEeTF1cbnOj+gCA1TOa}@HD$-7)N z#!}&BC*XJM_&s#T3)d3IVjCxtg>;}y4mg(C&gi6X7*abjf3diPJ zp)m+fRChW<>BNdd>rQeyU8vmp2>bTUD=y1AaRLOu*QaLTAk>4XG-Z{IJy$Vyvi!d@ zHHZxeyjuT$V3JpiIGdER!1~3MyQ?vrIjPlm{_69@oZ;tfJp1);KG;WW=*vEy~gH z0B!a5Gd=tA;cZpYqtZwKTXrX3xIjM(Cns}|Ma%i)9;8Xg{`aIES3Nz<+m^)D3?SGW zbfWR(dW-0hqDnmiw>mDV(bV3`;>)Qj={5ix;( z79XC^r+PVJJ+{!oLSKjlbrE@Qrt^ro_45^Ak}&7G>@U?fbckTkeCIH&Up?F;q?R}` zoJqHIZfd}(md=B({S_P%$3wKb?JHI?8;2`BOz^cE=`LpTN#cD96~iQfXXS{w^jqB5 zD9m_mJwYBd4EFBt{Uwz-JxUB-jeUW|m7MPVKZWxvWbXIgs0(8#>d`I~PNq+umi-O; z3n*@m#5SjNGIR0d{$7^dk9HY58-H$Yxr{h9>QyPqu6(Sm!{E%%_c_tu?0cPGjb(CmO&!)Q5zo_=Y(Ph+UaZD$H7n$wnTD1w zp#Y4NWP}U-&idH6fQ<84t-!Y|rf_y_{uu}DWs$fU{AgalT#W;iKpEaBJT`)%J^Iw% z9?y64?-I_p-j4i=WIVum)fDVeZ1CZVyZQZ|FebN85rIAS_O(E+xOpoj{}|V_g3!1K zp!O9qdbfXe>$VqDuKe@@aI7Bgx8duTvhC2#bFe4gsVa$`15??ZRv5{>A)<&62Te$$)>_>2Oigu}ew04dSb;{b~PC zr_C9qrxCK`2PeRmw!@$q)bKWw`FylbIJOo}Nky^rnN3v1q{0}bb5f(~jUJ!56by`l zdg+u!J}Tyc+ltwNvHZ;AN2NPa#i);Et>dv)Z~M8?n&4}8c`ns7`|pWDWkcXt(QrLd z^PnDKTYm5tOhs)tD-e~(%FOa9Bwu=1# zAvWc9@kdt@AXfdh(I`e*bC=HgGLdN!GOC5%56^%pw2 zFc0+uVLc4nux5#&*E)~AliHm-2tX$Aj~|R|`aFsHh3DEm#jO)48d>A(sfID)i`_A- z)ZwpcO_%feRa}+Id-|lyI6j~_t~V1)IV+5or&?-2Yjjz0lDg>{8xdx0%vcB8J!cp; z-in1pLEHYFWtGXJsYwcLtL18v4iuO)MB`KYwJ`#hBc*}`b==K4e||$n@_`dGlzi;B z`7yt_Nx7^9q0!az2K)*~$d)LAv=XLZx-9ikR&hxd-Nl9Ej+KV_z4d;feGe8nnoSJW5qIx z&D*d}j5ni%awHk>yt1RP4-Z}evU4II2v%rFFMp{s9gCSVZ3U~(qtEx0+G?N9`TG)< zorr|-HTyo-?iQZA6*4;@zhMH#!{Rc)uPUU=336;Gk<8l!e9%Re8_Oa1kEaG&vG7?g z*LR2kQ&O|%fK>C!mMtHzkj7{$`rw-IHsJ6FoMv{r6g29VW!!i>E$0gaT!s}G1STbp zPokD=I|Wn#Ga8Nk_8iNwNwSk?ijW3_qEiaw>04*P(+X#K6E(Zg>g}I+xx@X#Q?XSc zAEei0m0za|xt>^LD!TX#FmZ|fM!MTRnF%kRZG4e0=lAEM@WfKPjqLfZQHx|+=@T9R zqeG4Dp04gBt6NCqwFYrGaJwM>#3RQfv;bG1Bk>y?)d{6Z0X;xvsB!$B86<~)J|Iz% zo1nx)cMd!8Gi?=cj#Gkp?lz{G=;@$*oV1N@UDlA7@OyE1zt>g%vpS-xq(BCinqL8QGZis1Vx`l}=!HS&hHba=^U8-?J~jls@sfT9C@{!89ec z$4HED_S7VH$)MDohV#NR=n0B}M+8jNX?qltZ7HrvF!2Ych|N-0Ow@AqU4;C)e|pYW zXmYvuTl>^5U(0U&Ne_udC;kjdJch;cMZ6s`h5y6SS%yW~eQp01X$fg5MFHvVMwA*# zMyVkbkQjRCR-~k1fB`9`JBKc5q`N`78>B&>?f-qhaqt0{i)*jF;yix~h!~8TT&5rA z(5dtPT1Xy_xUYU;lJyBF0uRJ1{?;Dr@m1;SHZ5R0U8*X63cOJLaE%)CNtQ`7mY4YL z*XF6t-KUV#yWMUuYyx_Fk{i41gN}P({;c?4LnhrjynhzSigUF+5e(JT?eJ4%*5l8> z&IG|Vd3Un2@#&xJzA|Y_4M%zTa{B8AxE`6tz^ux+;42Dc&=7u=rR|xKy4;oh^kn`e z52CWld@0?kX&1%w)r=WE3J;00R#0L*I$Ce4*@nt)DW5=M<4_rPgZmLq%^&w4WiJ6` zMb&}A(sKpG>YuJQRyGd{H;9pV@y?lRfY7*}XAe-Fmoi!JN1v*w0edKzQulDMw9n!j zR#%S`=-DcUk0Gst(Q|ui=Uu=U2NG+hz!#97eAl0xJnp6z2JdtR{xGdS`GHo1y*<78 zSU|?t$5C>iG4r^-rzh1|eM?1d5kABEGzPlDwv17jTLu~dxG&|GdahR3vkLQ7*uZnh zG5?+?o~kY9h}5;-xv_YkgxZTjU*BOu>J8&r7Wm=|(2ktww%1lFaQmSyjYy82#k<~G z=(l1Q?G|N%2YF@zsU(39Q3_ji8&*rw7TT8LF^U`x&X9Ky)N1r@_nX`~qeDt5Hbag7 z6bt9+v*WOVkM1?p;m%S)Z+rG~_M{&cCeV}^ul+w)Uk?I0sMb~bxc{;h=U+hn!?d~3 zga?Ojq}9mSrR;UtcjmS#zQa7BY46zf(?BC->pTyEsc3J?C?TRH*?tiS$k0McKY_8@J#+V1HK<}^p* zA92W_+&s>r%9q#0pJX999)aam>_%o*2ZzC;R}H}r{!=zi@l11Q?UEXEqKA21{-hSmmd_JuR&Equ8{ zbkXX+)P^n3?_B{$wUE&q-H8)bf)f6wk7ohJ@xTMnmVDaGa=FBsO?9PvUq3Uv9UfA3 zH1)AIgwG|lVf^-JBYMh?NGv65un9+nPP96tYLK}bHvgW`g?>i#Zr_~C1{F^ML{IJT zE?zdit}+Q#O}W=`LBx?cYqQZ>*oQC8FxhuM3qn_vTfsZ$u8q_#DKP{yrWc}KGAtPz zy+$n2XRTS6M~f9kqLr>yc3M%tf}5ZHW{Ry`yIu}&S60`w0wU4(+DKHSC#dONeoOX1 zIX*N!L61ZoWvvCiu?6ZO#_U86mdFQc->AmG7@T0VAb6T34|^d&1OlEXq6K7SnefPJRMv1@ z{EKnZ*^BJ2cp|sygaHt~V)i&^m#x?wy)``WPJdPJfJtB^^Chl7x}VJ_$VhBWSY6lGP|4=n<$gwX(@mE>(bopQTrP@8+;7J?fG)EW%=#-#XTE&^ zW{Y>8u7O~T^F=slLjArU!#Asy7B$t!Ao9-8Pw9JG1UU}FYLp&2Npj%Ef3Sx} zYn32&*}hdeNas$%*fYzudDS_3uNC0;(@T5sb;e!&p^+-7l=Xvg3oa;^YVJ?IYXWS& zb<>GF1|fT>e9wyc?M(MxsjUr^%sFb$V3PDfy!oH&+MI^Z3{ye;9Qj28u9FmTIZP*X z6C;msrM_S&YibbSK+7ZskFppdCDo@KdlcazEDN=NMV)>$WV47R)-ME>Q_IPgQdi94 zUoBY%K})vb#VTc!vv#^$O?P;pn?94YVX6HZZW(0vXz&eE;c|88%@db`o9;k)hEfD{ zmsGC*erYid8L<5T%fqvG19#Yg(Wm=!Q-e4LGszCCqQ;4FziFj`=t1djzH`H&>$vEB zCe`WW;Fp0Ha`{|(#P;GrcJ`OL=Rj+u=6mgPtcmf1j>n zEw#uK{VncooWtr)MH&G)#6qlpO^nyw%EQ91G-DFiTXDbUDkTN9`YAjya1= zzcF#fQc_h<&vLINwJcuMOuqal7V%|F2K-DJvEv**2j-y;|h0>W6tvh7EgAY9Gp(wOlLT$5Y zrfie6Q~eVGRR}8ip7Q$deJA7L$#Iy(;H3#l#|bZRqI$hiOeA5Bd?t+d>VY$ zQmk^|+oH?a>;IDvG z$$0`=PRX+;`|(A}`IJxOrMwk(ZwGwEJ9DZ42fyPDQmr)P}Jw~Cjw8~LYSoJn){e}>q_=WGbhiO&_H<(XSg zQ>t{}^EVsWU5{R9*3oxymg?@-)?YBN@lBFmhay&X7RF%s=awj^Q_CN}Z)4_v8&{PEN{K*KFZ$EV~(^m51DRs`DgYu3i#cnL@zIqj7l3(GS_~|w>WB7Ju ztS`$$85-Arf^WhGTYK!dZ4BKQEQQ-DjDN<-h&I-RMptYmsSJABhTYMSE3}EoeMhavaz8p zH#q3}cH+;Z1Dp?`!P~;H&apl>>wjLnn#zh3}JS>*D$- zOyESc+;ugjLeaWq|4n_3bvUu>i3E5W>v@fY^eJ3v6A@S7LEdEfcyY(b&DlWYmCZHq zQ*-Ut!jscNo|L4qOmO9ZQPR|AE!)iKr?)#EGdnQAxZzVw5t_fFAmd_W`TX2^0Ff{(&FW8KsQSXOb z)$4H(mW8lfGiA4wR;fV^cv{||;ATpYscC)NU>idIU$c)Vh+g6iygpVLDgn2&eREa& zFQ#sqcHRjv52E^}$6T5^7Y0H93cC!<)dBus-~@dx(H^di8;qwq8rs`Z+FaHpU~Nm3 zL#-IwM*Un@*D9dHFJtQW_BeU3CM*V}{+qp!MPx4hL$+35(KWuFMjJNLGi9OtlR8ag zGt`EN?4je}Umgwj4)xDqLd;3Rq|er3Q1~=lHYeUiZ$V#XccyjKaMB=(+xB%upoXRTL4MkUH&_IpQ`xm5}^2IFU+Gx1<5H6#v#1DeoL0xeqxhD`%!YNf$*6G@GS9_rrta}Ive zT!N3ezucsKpTj+hcbH$AjtJ3bh$giagosjf8Av=%Mt+7HzfSuwk)W!g)<^uaAVn7M z`PbNr)D0|{^|^)EP-!Iz;kSxj(G)Fr{4B)1+bmx@#N3_1$J*8?tDILQT;TdoT>Hdf z{L~ml+txC|nEE~T>04BSJweJZ+@sc!I30VUVH(gw;AIn2!mmUKffi@CJLG7zPP)`S z0#~XBxRy(Q(e>|-b$vC@rWh`yxA(2Ki?nk#1;YWF=585pFC6C7PqDJ!{YulE8j2SX zT})$w7=eQjU}__eU*DxdxqB7^rw?1K!BBE8ORLrrCF1GRK2E45WWaX(C8BMP%I-p7 zfGdqukg%m=-aJc4@WEG&7ChSapTH%M}e(6pBFUc z7h)U3E>ZIMA(+qg)@dfv#}ufU#Pl>{Cb9bvO9BuBkK;aCLy-Q7712i^+w{oKSHJYu z?_Fg(`FLyet8lxil=*JYOaybsdu!)?mLUSZUoQ7D?)HWIcUBT6$arVkrvvMh{{hPk zQDfBjl#T?6&Up?nWoPeCT$8BNRBFL0tBc&8u^7VYLgY-b%2~EMrO|Do=Ak$+iPQ+| zZUOD2r$cF0F$olC1N5vT4NrD;KZGhPqMYtImhsZ@e7E)j)#>nR-4W=3?=P zxf3WY#MJUKRE`$kHqku4uL29RIYmDW&l+SCiSbJJa_gT`zJyVSwu#{_SR33j(Gu>Y zs+e)Li6-;=0iky$C*hE39rbs=cKC~Byc{$6B62x=(5N673*G!@C|}-#`iB+T3gh76 ztcDN!n}4@bd#DDjt+x_50!GMonCMv8me5ONBQOj4_kvTn2F?PO!FlzFJ(xv;3VU+) zDQ(lV+8_MOJD!x4s$|Ayud`@i;CZlXYe#1RybG`JtX}RC&%9j1Mzq2FyC&KU^Y8<&M^``I4gQ zVq#CS+(syzDrljBAypeLeNF+9g?ag4LneKQYD^P#bEDn&dDF>m0K&j7_XDBYJHEtt z=Vu^;d5?rU8Y1e`cH%~vU$aczO>Pp=F<&x$`gk_)FSZ(G^51Eeu_oh3%oNPicOJg` z)im=%GEM!gT-3~BU5^x$2Z2nrhWr#zF8&Pe&fOkVnVz#m8lC@!#fmy4jV}DmTqJnt z@(@_)(pk2JQghQEB2QKLfEAJY}xy~&@N3Z)OKJnw8>JB6wV zRHu#$ZwbNVBVcYy{VMSA65~hOjzAYyjNY=P;hfKUHwoG&OJMSX+GM7)-IkiF}sNw0T3Al)f^N{L-_02)Nk(S$DTK9{$q_ zFPM*==T#jH;cFfJV}pJq0HC9_D4#pfQY;sMfcD(Cy4sG5QhG)bQ1!pm)VdwKQ3UF( zf4<-!C-ZFDbAbM^I;GcNlvi6e{-KV7l)d%eZAT?CE9q9BGpYB|ET#Di^mDfM7Ye&j zyJ9jY-+aIFBT!$1ccU8~SwO2ftGn6CX1L0E!u+B*thh=ZvekW%E)M??*b6jS2v{_E zP=<;0i@dnLgHT8Vjy@hrzeIT!m%R8VknNZsO7#zKK6Ja?ZBKusoX+I|-|5#IvBk8@ zeeI@^O5j)gH&JZ0^Ma|psAFYXDxziP+gb8cjbcGPJ8a3S`S)Il{7U%TMWTvH0C|Rc zdGeKe_3f!nvs-FHDe)Jn5TT=}#hKOARJ@^5H>J?fzXw&e|EM0&`qrjYAW?ZR#@U>cxr(_x zn5>zs4}5s~;~T+$se(eFcKKW4@5SQyfW^01qriE;7?ke^{=wPogk&PaK(Xy^*EG-> z|NP_M2tyz+s3BSLzz-XPr)^L`@VSeHwmTjJ1cxk-w(Kh-EB@m0cn8yy{4sJpIClRD zNTPsk#Y)<<(@`KRZyp1<&w+yiM^ON9KblrM&V$jU*0#2C?;qCMoH@Y0$7K@Y%j&j@ z^6<&7h0V%Tu37#)Cpqr@oL^^C&yR}-6w-BP!tW$%IyM-d@^IJ@kSb0UayD-!Qe5Dx zQnGTA*X5fLTBQDEd z6DL`0^85*u2(!AgF;43q=EVaO{&)~bWDYeDUjp$J1lQc7?Lf3WDJj9w>KdVx%?0w5 zACFz(L63p;h~tLLj*gjih%gs)Fm*(5Quc*#arHrlR?Tp5Srv$JUH zc-WniUsKK-O+Gxk2zTv|fm-7m|5O=pK$#XL*S?i|7>q0ksGRg7j?b)li(QFuZ1dpy zY!=R(cbGsy`E(c7TzBW2x|d-vHmg>Wwi7V8)}|ZU>%kk?>q875o)vGpHCSbcLvS7g&~k86p&JwX?O-rWbcxLE6fI_7PgS#vC$ zvBqDN63zP~l@53J91ev6RDeGQVED#$N? zXrKO45(3HVKwMdpvKvlmH-Gn*2YbGyyR~EDQ{n7GUD}6T6%wj!RXO^nOB!x+DA1Qf zDq;RTN|j3T>n_UMl9%@HFgx&Cjq?>)s#%m+QY~#|$mg9k!LlKO0@lE22%U?Q)6(&T zlN9hCHYsDPR$-!us*+9z6?lx}(rh#_)&u;y&XXqf5>Kn6De`?IW(A7Fue? z@ti^!HF;Bw=kS8fH|;DJzsQEeCAm2}!=Z|Wl8GC3A}oe_y<%i~*a8W6aswe#pOrVv z@k;iGcH|l4a4n`AC-IaXY*skKtAze8igjMF3eTiT+D9hbAS&Pjzua#YhOewLn|bDqDL!!;eDm> zOdD9>K|NqNHy9f#v~Gtl3mRc>Eg#ys=BAi>a*@_?Oe`3CKb7-N1jCXIj=mLJW0J>QAwFxbTd`^J8LEL zIe=dAecTG$_1-o}h)1EvVufU+elz>}L}46$AbpFL={b&Hn|Z@!uD6`>T`t!YJ&$YH z(?;(SX81DWBdt^neZoVA2oNB#a+$)xgeg4)W_0-S+)pC6vQsZ;eD z;j(s}c!xmNFL>NbMSUgZz@i05#v90_X}$_cep!4(@SrsQsYk=VCX}_~cSq zq`vhSGn=_fe3{FZOLGY!I&e?LXr}Hx>OXU{g)-8IL8SV+;k-&0oPK#iB99#+IL{bD z{~LU_CcP2XHViT2kL;?;D3=qLP;- zPlJdTnhvuBrO+Ezxia;9Ywwf%0(}|Rc9z2zFArRNkH1m?Oi!sjAX_oHLmUuwog2K& zMBcEc;5J0Y4-#57ku7_L%GQ0FK_cUWhJb3T`Sh2x;kHERH|b+HXK_lFH{T%QT5?5W z1U&dJwe{jQ`&}N~*W8oj4)ptdZ)$UJTUH0KimtJ#X3)Q_wpq zgCFSm!4JsHa+uxmGeK&r(~rW=yV=rnw}d1|+lE8EyY%GWgw6`;O${{1TASd-b>P0# zuDeFZk#cbw6}!8VUTXBR*I0ov)if8poUh>l{2d zF07hJRkUd$&6!t=Qiut)CP`I7Vm{~O4p)6oXkimFl28rt?qMx{WFZC-r>%d@c1`%? z9UDqA*U+^1L6YWoT`Noib8aPj=YRHD5BOGxG-$55uW#_>HV~p{?wQB~)-y!nWYbPf zc{yAKn781VkB7eP9L-LCnG(hU7DHl<9dktekH%Q zx`^J7B>go*O*U1Lg$*z>W+*X>ufwN1=CKc8k;nf5z*`|fI?pC^tX#uv`A9$Q=Y{F+ z)A^xCtG}Da=A+jJnMA_Jn|M?SRp>wM*26VvWmvwN^6jY!RAU46o@GZx4pclR=zaK;OE>QO-z*P*P*gmFNvNt&!i<|Z54G9 zpDNFtrp^gy1`HFx%rjz4jH-QSV0%1n^qQ(xtDI2dg*;!;I%uYx5c+~) z!s=6!dC3Xohp}3AsHd-yzU`ZDS=L4&u|IWgM@m!IcQwSQ{lP3kKlJM5J4rQ`6R`!` zqjiCWI_>L8-qncxW!v8`-lyrgt$>|E%}L^c6y?i4=p%e`cz{ZQXS;@0onq__0F}u%kjkUPeLnLADGU5xyK*R9^j% zc3!qGFFUD3>Rq~|U`FkM3^?a#6SMS>M$H+ubdfFsdr0?+At?{J%kfB8mL=gGxo*l%U`I>1_ zlUl`P$BLRVAS?Lp^mDlvoJ+)$T9}Y{zDjetpxM|HFq`ct+F-wgBh)(}20w;_CTNlRE$Co}DRf zz9RD)s8!|mRnFpD>LuInr;nnp@>jGAMwLz1IvS26_CYcgK4xeU=iTdw40I z*v$9eT3rXWG3Nt7~I zfQyL<9~V1~wx+f^<%A_`VBuI$+WW+~t-FA*LiHB56ABPpfh{7qK8IO*c9?)7LHi~k zt>}sN)PIl7>K(cT&>xWNqec+sw7H-Z|(807naS&+sNE$2{A zbqYGq%0|b(mcyG6y)Y0;titT}J~HL8vjLsUE7uJ1S%Uk`?m3DQj(`3ejDeVjGZzXC zvgmbQWn-%p-%QoXaFA9;-H&39e(-b<J-}{z%=agkCM=KCx*^#mXQ!y6&SvnV&g?pPq|v>=xS{~>IbfBasy56>8%4{B#$s#- zL;#i(Q?p|>IfeKXYS_s{*=*gshhz1_+xzb-$UOlc#2D~+#v*)RF$H~$>Sx>>sWYFW z2k#X1S)A9|be{3b!s>zMhMaJ9XU1b&b!}yM`zJY#w}x01>+;SZ%$oh_$Ycg!5s;b7 z2Tn#VG|m&`RX#moR^ZiPDGE2vqyRa4UD^BxFpUO8%PBi?vOVo0Q8FRA*lwCK^~$2T zqpw+5h5J9LpDIl$0@vSrWVuXF4`d)ao)Tw_z|dkGw{N6&Z3PDKaj+^8Ga$jp5X`ZQ zrWpnO{MdLlU0a-2&E12%h^`qq5Wm}kz<(^ZwQWWdM}cSDo7WWf zHc^15f(aQ7^Nv>k15|=U94AuZF|-e@<)yXEu2vKhh>0xr)S#g9{RkX1J&<-V#_HR) z+k-%>@*P>u0asGvxW;G(xJgUA|B_=C8-nBG&AMrytlwa{nXE((To0)VA%%#@blZ`f+CwZ~K(d5R3qa zcG`wjI_4}>T854JN$ot)Ll*=9{Qf~!=01)r(mgePNoKK{@iohx$_{j!gXnN*9E8^o~ z^o$fS9AS|v)4BIM=BlJ>Q^Z(o!=CJXvPM8cjTo#Hsry7-_7b4h0i(pbCRIQ7??rp?UF@QbOI`v3*Lag+b}O=myZK0qER7`rOk9eky|m*kEW0 zt=EV6jr|2YWus?-OMzqb09rlB>V)#GiXEI9;z6X46ChK5URHyw=+V%!Gs`mto-T&O4Q2`dxEBBH=}i70P)%=lyl9GW@!NAq8nF!!v`VF51Kv(x zt9Gxt-+%=0fE0^SxiKQCXX_sb!(9r3)8gFIm)S#I33R=ow@+gY~!6 z+VBD=h1lFGKn9hP^al=Pv^W}P|0BlP1%{7C1E?2RuaJWJhYt8?X-~((p5BnwvVKkXiipic-?TF)@DyoCBiKH)5W?R&geji`p9uM6k83xPE zf~w9nq=HO8T7iHgu7qD-eyB@88p%>(?qg=(2Fl0c>D4|9FUf}UbpIQH+}Zzc74}~9 z`?JJq%-dH!S%>cMQ#7)|Hzkof0+ABv(29ycGhD57xuKu)jM@yS55mI=xw6P_W8H|S zX|lslN#Dsz;Iqck-LeXryFleOhV)wkbPEMw}vE zkDOwR8knlQ)I*yAO9Or@6W38(76mH?38_2s4z6y7&l&kkw2uRotZqGPvIA?NHPSm& zP<4#xK*V{aKVu^_(}Z;qw?p*NdckKh!p zhY7nebv8xXL&>JmH7Qdz3#{gffb!tD&xnnzFj_weduvYgs9vi_Z+k30&wo$p<+ZF; zN`zLkvgomx0{@X(L7oT_(BasWT@lfLq;KUtFV^gNZ-0l)MiF(uq39g5ZT4&)Ds8GA zkyq+%8czEdRlD$S&c z>}YgG8i>X!8NcPq<>~`VR1GfSn+j-V#Hu`TEGZ+WpYY|V7==fh8VhAtPj11i5;!d; z7I7;&-2ais_fevI^Pg*X@xikkCaLs{L5d-Xo-|LfI`0nA|CzV0$DvY~4Gzzm^`_h(thln(@B$STNbKP;-X$l3EEt>ctD zo!q^xJaTl@K`=E&i>BBR-AL~N94_F)&elh`8c_p-maLJLc*G~)b|0TiS^-tVZMM>s zx)TQ!8BS=td2nAtY=bb{p;osv-jUvV|9AbEZYam4YUIq{TCv?Qzwcg4gMQz&Q~9#w zI~7X(a+&N8Bb7PAlp&MiDDAC*x?-@c=un?b0)!|Pi-z05iI)m5Sy1D63xYYqDDAbP zYMOMgGUPJ&a1UXe-!oRI);K#OT`H)5pCv+~kf05}C0QdMP)wl?PyqW7`Q zUw6uxYKcXv@0CkI^sKP|#hficZ|t#@;nOcW^;?zWV2e_JgkFht1CQozkf>1GzVXKM zKY*Gps|UB?ShGYv^~)N?-DP!+kVUT9SvlGx-%Oq%YzY)Ya;UC2tK?{aX|m;U-X5=50s&YFUz@}*Ds6ai}|ZARcs6Xum0@l ztOA>=Y`J`9rD(#d&UR}V+N0#ZSog7Mj$%LgIF(6ICnhBLSJG?RGg_Cfc~?;|U+ z_Qm!}D#2bDbS*<6ru42mQEVkckM(3dz}F_4F+W0QZ7hgKB#DZu&AGvE9Jw?`KSxC} zPButmcNR+c*rj%*uz(z0IKD|Ue8C347dhZfmk=jp<1Dp9^JjmE`10V)1!E3rCpows z$ZetdLWFnakL4UNg_%yDzvwv=Q&!1V4z8#>#AjQ!f_n3h;6QT%xQ_M!hF235D#) zs4c=fg+Rk3Ew-CQEyE1=MY%n^?E5FqxJwU-9dO*aK3x=5@Ey-!9R!~ zjpMU%_NjojN%96or0EV{tFM}syf;!hZsv8UL-6O0ngp4F(+?Xtx8Zz%?Wf35mT%RX zM6VJwsec#!fa7WIX&n4{?6LY*v|=YT+$_AcCazYNX6u>~#TG1i zqt{>idlx;XyZ3A*!>Y_JofL*zIa>h2=s6~{ff)mJEM+4nkIUpKwT~pbIs2-Iu`Lu*eV?!y)&s-qRh-eREX@V&|yrCnS7u+ng@&1GHmU`9CkE?T9X zvbsVvEqBdq0QKad@cmh@%tx6^>s&oq25=7pJ!>B0tQUE8UTF@9Z25fS6kO}}s=zly zqw(923PxKj1h?Y6O8ch={?YAv5D^DlDe631XYbLB6;5{LUea!D8<)nQW5&=9w8GHydQd z#(@$k_;HjPk!YpQg6{YLRf64K2SecF2!zD4{CwppnRl2ijomlXv#shG@OwI@0C^=i9Um{(s;9PHNcKy;# zq-(YvIj6_=>l@+B91ij;eH6q^!&_&Zxr^{99?;{|#(rZsN@!bBT=Ug}0%dl(5lB?! zcc$LL#66RowO0}lzWO|syMyr!3td?^YujJ?|$`tO9N+TICS+!f0GVcS)nHjr@^ zOUo{D@y3`!`MuXWZ8N_h39cGy>v-G#r%5LCYV{&A(Sn(4s;itF>~akL+;=m3`2{{rhDy99l7ZzJ<-Lr-`0CpVA8dL zxguV#tdTXi8BQWNIBwT|>AKHABA3!Pk4t||n|*v1V+I$qFq)V~{XFHusx}kYtN-o& zWHE-;mX2y(oMLw>^~Fy;ra?bF#-Dn4QsI1b>Zd_Bwx%!IACkP=MOpCeU8ZzrlY@YU z-drt+(!-0NY&?Chu%$wmX2v!O89Sy|-xPyT_kyqJz|jOQuHNSYY91DgNAsQ*9xL^= zvy>Di+0)xN?vb6u_ED_t17Z4HHq5l$*%LsF)=5l7l?_Z+l?F4sTugYD#j8%DJ+)qx zd^U1PGLmVU<3XDu_2gO+`>ZEW$+bW-BlJk%--$k|d+m!0w6XC*9}h=A!P@77-^BS9 z`?6k@x(qN;6y3Oe(>Fzu=XGUnJo(Yssc{hXlYKy+`1y48$_^|z!sv@N$3ZGfZFL5# zb)JT$MQsp1neDVx*o{>p z#vfB04kgo{)Y}lt?ZDo=4f4=F*%VQi9{c+@_oCa9FjI8XKT}MmS!9LSXa+Wz=}Y$D zt`v#>qxJMJ*3|d)JgKsSTNo+Uk#0J_}=$A$#Ym<0d|tMk!LVr;9OV zA5=#0I%4aEGcbIN3%fbF5Vpz6C{5a)A{#7W#Wy5bAnoI57v7bMD$r~voRhvtdLO91 z#EWa__k8f#MhNDc{x^Jzp%usm}y#S z25^hZ4wXC5M=3-3hB*EN|EO<2uu9f(t*?!oW@W{)U0m*k1#eDC+^#EHcsuiN#-~08 zaaNZy>Q#VLh*1t}-J+;D(cGVkxkeuvJ~b6OefKje?Kzt>47OXf>qawwHs-qAT@JsP z-XsL{2#3d>&+bI`{?zmQz>3;mXLaC}vc$5vVAlBkuF=CURD;i{m;G-Y$O zEuJm9fH~`GeV;;oGthlp^jXN0N*_DA!7pHN{Pw**W!2<|z}jzT_cf18+A|@prw1vWmV_6I zcz)LCU&mjw9iQFkEH?hUv2L?iu8d&%|*gDyYturb=pr@8ClMo-{$|P_-TpGH2 zB-^XWIc%d^C`jIj{AP7g)3(<3A?A21`H1EAtoRLgQRU2*rz%ul!eQG}7yyIUh^@t; z4_;Lh=E2CsdDYU%-iEKx#dXdYoCu&RUrk|a2@7Lo=d8}93R!PBdMlHvyGu-zR8R$DAC)+{H>o6Y5>QxzdqON@HT$3JDZ}& zCgJ~||1itYYRZ6-?AE2^kCBZcgqi^pnx|0)me&69bXK@#=-CNGCWiVrYk9*{2b$!2 zF-rppk-3Y=6w_m)yH0&kxP4%@WiTEzj2?!O)e~hGD?!w@W^B%xXn(h|rc;R;ERv&e zJ{6MJbdw;s$GanpK4q_+VwZQPc8HZ8{02KlSW3;#%SX<><}f3Soc>B0QFgr0fBz}g zBl2*XK!O|m{`%&ZnmU$TLHhPakHAB%Yn*(}VU@PH_x<%eedj!_{Af=*W9OCEAw9xn zdfA!^n@$x z=dw@~0Zh8u6dbY+kHRs zPWNBcRYl@+z8rEw*o4&%2Sk1dZT5h-u(G?~t$aF*jIw0|`6-zh((1Ryzx{9I^O7MQ zt3HK&u0N`>)VY!K!CX ze29{n9WR5$z2#X-zumIg^I9KDCm(dMZL3!>&;Sm-pv}m5pERB_;N-hGOGCf7k$a(d zJ5cO2m=Uh0ZOqYW)y>EugcBQAY}7*A0307+f6)6h9S|NcC4bwT=fc~^@!@sPnzymI z{j2?i-?|HBZV$>tg}pCk<4oJs0+A`1T&TL&1tp z>KQ3T1wHt9G|gZgAvwibm3dRH*f%pebttSv&F_(l3&t@zF&oQ|(Hx3~NjANk+ka#2 z?$HposS8$RYzK3*pi_oxzGe%hbEpOptLLc3%8h$LykDPp@#EAsPHynnrHv9B0Onwx zujF$gF zm9TWS(yIqH3x_%d(MPE>0J5s}aqq#W!d-egMS`$D2ZN6yjE7H-e8MWUoqceIs;ONi zUA1ACX#?=L{FZeFM%E&9JK+~ZIk#CMr8Je`O|0VbJ-l)$v3D)=BaYg9B`?1;%c?(r zPfDLp9U?87=5!&M^Q1OKL5u}WU`k-S*mWAfwJafA+>*1YPtb5LdEt}M5>%*C?7>g= za+Nciu!+cS>xTQ+e!(wJROuB%6sx&{W$6wh}$&s_^Cu1VO<3N zxYyqfI1w(z175*z&byUYIoV!HPnodIjwm5Mp041(`%x>WXZ`EfH`00{5OYEPzp2>+ zf@7_RxM}gKW}J}QkcnNYLbz#<-2%-QV#<(Nipc^|B696zR!zyz=L@aE9!lIB{L2d#Ja>_#6 zZ+g&B%Z&At>p+U4{cF-+SA26$p=o71Qjw~``cf>4e6hGfmtg}5$B{=KWF z-QC}E33tk&BiLq41q0RZQ5cbJ=vO4ygMa?@yTgNwEHfj_Qdba7hu9FBn8l$FD5C?aDUo5;U<=#=&z?HG;k>1uy%bfj8$}+bnOt>P*ev z-nIrzx#4&_(;#*QF#;S#hYDDHyZlkk1x+p4<0cSSpUmKF0-Uk9zZ+-!>+>CUyk31! z1ATiZTQ%}3KkHR7{!gIai7yX@heF@TV>M|Ha?DA^RI#j-8o>u<8oxi8WeT);gr8(7 z6JgE4Ettl0+K7?49Uu$~qd#V1o7sENUm@_RXuMJqPhIOorpV35=E1MpvbLco;U2t^ zJ@{8epuKb9?wdJP`(opj2dF+W9E@yl8ogLGy_-#AbcE6^PA|UcuX6SxY^nn24%0fP zQJx)lM`K$a3Bk61CPa87(@DbofAp_ zmP0B~o0(Z&9kppEw8MMjt6T*-PH_#AJ&YXrORv0ibbj_F>4Ey??CQEx8m@N=YKGSk zhqHwjVT(R?UqC;x%wqV&eYNe=w}mI5mh$!f*w2J&HSLQn!x<`p&pF=LF&hY+paix7 zUE3?x`)Gszqw2fkss8@>KZ!)7>@7vey++wCN>O%{ajy}{xUP#E;o4Qb-ru2@36egZuvyF4Ez&w~pL5$b_^AFylTs3m z5?%UR5(Zv=sNRsRQ268GAOFsn!f@WE>*MwZXN#*o-aT7;$15w~?lYYkw|^tI^Ilwz zLimH$)3Hj&u+lP6uP>%28&in0D;{xRQufIb&$SUc-5V1qlmcXtT&itHgL$g4cHf&W zJe`L)!|0e|#0FZ;5b5s44}g}k!rLWJ@EP7!z%+S!NocYYVZ?)UIv+i2v4ZgQ#37b2 z&5B%U8>q{G6m$d9f@B&xZg=;m(Ky#3M{t^oHI`oI>oi#z`V+-CP<75QfB9^BUC^0T zoBUm)8~gf8Ix)Y%V3dLU2_wwd@F1F++t_Gts-QQUn@L#pP=6U;Vd%)xBxv+by5L_ySc$Uf@zi@O^2gE-{n2`(9#{!oaDW?GGxiswxjR%vFw~H; z2Ig!xqk{W|4YiAEg3_EgHwokC(34iBd>akZjv``}z>~33bu`!Tp$5|kh?a?= zRo7Y1kf;o{O3&!WT^tGCOn>HM?9wqo`q?jwhoaVrj^Kg1UN^G6C^RcEh&llU| zgqW${3}hXrkKOyT9x-6zni&VNT<*`0PeZPhBX^4#y_$LWtm&!(-+5gAoL2_RsGjk} zS?N-pLQy({-{H##bP9l)<)Z>q&t11YTM==o)^OUKb zyTilCRPZG8`{b(vS%J!!UqF^?m;dk?3<7P`j1XoLb6-NFlH@bXEo*Mj*7_~IL=HW# zV%ut}x*=0_PD8(M%MnrAq2liv+R-HA?>8HiaN(s%UKE~8=8a5R6znUT`n!5AQ(&JylhVToAM`*2GvNkxq2oE9PUf~-Qptc9$+D@TTcQ%- ztqUV8f0{2IXLz*r`>OaK()d2Fg|itu1lwC$){0^N2F0GVh-g?8W;Kyhe&y5`16uIW zggts_Ep!YlK7v^|Vpd*Nu}f1jIXt`)8y#C<$K)wvs+0zDm5VY;03%_1?`NDt;JfPl z4rh8Ww(8H!1L?LKf9>Yf0Dq`+EL#-m*iAqxQQ9mYMl z@GhMch-nmN{Cv-l>vl7#nMis5FL!8{Q~gTSc|W(^R3zeO^d%z%UXFJlSp|CHez_blPr=?E~y^R^8KPHJwpc8XlUP!nanG0@=Z92J*m@>CGO>ISWeA_D!Y#QY3&WyAgoIMe~`Hg<|!AqGwgD)v? z`1$Y*#&D#5zZ(U>b^IzdDhmV4++<>Ld^(#Kx6YIBTrg+wSEHY{u(Una%yfO@`}gj7 z`3_EN%F%V|%Sfwo4^~%fzD@^0J}N8aRBgZx>w5}Le}AR{kErVpge8aM*z1`OFjgJuH@Z*7lO#sjcMz0NdwSK?*#5yibP;VYi@P<3Oj zngG-a&%_890JiE@o)Q`#WZcTimsNA%ZR&$Lc`b@QIOYe~27%%VjMS{Na~e2f8}6nK zo(Um-OSd)5097s7MSF78#AIgLnG&1#B9=K|n(V~Q#3GG<6Za+lE+w?YYc%%19=Or% zKaZBw^_S-@A)+X;{I}~nU2*bYmq8lFNq5JC`ck&qxP@Vk?1+s+ zs>{0Qw?F^J_l`A+twso`u2Lbp01W$Vvff7XZ)C{da zfs?6xO{t@OC$?n9$6}*VHxb-v+r_H!=4 zKmjI{c{DJ<+l~gQ|8olsBQ=&XpDtz7*ZLuYPxmIS+HFVP1GRHC5&6usU-Kjh7O*IYH&zy?a8ljqi2$QMNt~IKpo0;0RMmqmskoezygCEy^ z6+;U0zJnWV9rw@(4sqbfM>YW0o|n6jn@|+R!}oL2+h#B?B6UW_AE~uBSh)B&$32;P z4~CmCcCE#leufQnN=a`sHp=E}E1Q~qMm|x`s7=Bcypux5=8RQ8Lll_ShLdS9DF+y0R>@Ma?X@JnG2Cr?11GN@(0}6ZfU9nqz}Aq(!rS zIBi;)Mp>DXgR+%*Wz9va z8tZ?XK6r_{*kf63&=Rd1N4AOHi;}DL(_EtYIS2~>fdk01%x46)J?F-Q+;=Lo2i0s% zZ!|U~@;jvP6KMqAH9C4AAWUx+wWyQq@CjoIN!tf4=SsQWd_4uC=b7-?Wm!4{_OWS` z=PE0RjkF1s8IQDQcFYk<-`0on%FJ>{ta|?K{an3TgS(%a@HBzHP@2s+D?mJUPS$JY zp6_ikl|nInc1TooC~EX*s#_jSUU-4K$|kMxxftT z#u>^L!-rQpe5N6{_Le-O7is3>%4>rzmyM0b3&GihsrDul;UEBq@h)^smu- zO5tB4Q=>++j7vYa%uiYd-Fefgl<8}|K&cPkWFL%Oknz_a_zp#kG0|I#YDqjWP#Jmi zwvHC_e5|7HBFvU~z8Z@R2Eg(=*K|)C#17BWSrQxZji()9Z5j@648Yj8py6%)|613C z_D1x)YXWhk?rU>1kTb~!u!a$V1GgoW#pe+}+LJXPt;T}`3O=6PKQAe@YIIMIDOeBD zZ1AYX8&?;PKI=6jVH&`R=%H)9If<-t0|Rey9UY@eNf>4pP`7Q!IcS*Yah_t(7TAWo z!Qgbo7{{`>EMUUkn$~!r;>OV;|D9~t85f>F?2ywp<7{7^OFY(QP5GNc6M%2wTJAUl z@#J#l^_C5_S5z?`{{W{Xr_>_#ZEwRQcl3T6L;QqL8tJI^Sn=Bd3{4lfmG}X6qQMTr`4p1 z7^-<^ZZ^8n-h1vop#XuWU845w)qasF>a$p#yFcukzTvyQbt@W;Ih2|i@d^do0z>Oo zl{k7A13@jHFB#cq7lYSJ#iTeAd=}sLEKu3}WcT#;e}mSrcO#W1EwTWPODvCw#a4B+ zL2_0{cT_`V-4ET)Cq|2}H#BY^|4uH_+R`jl(b)SUGIn;i{?MBDckTg;9ZR&$RWF%` zrJ$&*ePHW>J-n!Y8;O-UoDE7_k3t@b3Ei<0(TRPIEqpq%v1Js4H3}DjBVzkGqh>%N zfw=fmqRkWKy!Al&)Xw*2M4^_X|3S^(sMr;-eVtOQY@5+NduqJlX~#ED;URzxwgUjz zwKqfc{HPK~0Q3U{qmNmKWaLSWo~Pme?>-#WTjEryo`zfB7*qFN?y4Et+*?S9I3o{E zu#F8;EhWt3J=5SFYR9I2ti5}l58wRfvg$$lc~+ps_YjJq5fOm_eoFutI*a6-QV$N6 zd+@q$3#jr>)9P_1`;HtQ91ad@Y$a)fOTV=Jc#C#6J=Q*s7V$m|C*mjwKsOIM=Xv1?RPPO2R{tFzk z(Tl(sAXCZsaIff#9gbG&d+!$+afWF}{QE>{o@Wa@Hs}wZshm~r^Ph@a+3$CpDMp1D zrM%x&uBRE>V8I_QZEd;e2dOjuM$pKD@>r)P`1 z9ihrokpHS2BW2p&?0;gZI$DY?-4r~hQ4PMe<9eHEovkCUltJ-7TSDu6`cFd&oJ$AR zUT(k8g`;AtTaCgID2%aGY;3879B0{!M~86P&DoXBjH8c>&FY4zAwHok_O8b*nFCZ4_+T+y)o!d2K)dRV`D3B>Cy8Xr(sWudz$?X9dk-% zSZ7jTt+jJqhkVWx#Gzv!T?eQ}B}}*eOkLqJKiSHBatj^S5f11o1)Zt&auLdB0)919w@$%PPOx1b#~eQ0 z7`Drf5%bfPk$Ii#^YByLc!G#JtxF@rbx&X-kVtJST93H)6sFKA+yQ~A!m z-`+u$H*cI_av3D(T>oE=AhDeHp1r^Ymh;8I&vRGX;G1gk`OD@hx|Y`OF4kt`!u{=y ziuNM;CcYStQrtiOa{|aRa=#S-o_;GKxVk@QdrO$CG+%f3_f z0#DX5bxMvkF*FtmXTL9WB{KsYgW`^_RMMZip)bWZ+m0(ma0pW24CuJQR94~~L!Gz8 zv}t0fa5gUur3p8R&FM{OU;Lq+$f8EHOh_V8VU7j(2?o5+K?iMdhR@{u=r<-BA_r6A zTAxENgps`<&yG@$K8~v&IQJ~g+a8wxIr@hTy2pJ@MS-Pb0EfcJU2W|SPIxz2S9|hf z8z{ozns+WLh2wiR*J7S8B+)^|>FKdwvAdS-ZIJt1J)DNsJ4K5Os)z$5QtK^&H+FrN=%4i5As++!iJ^l6V=uDV zC4KQXHv7W2mSMB=s}n-CwI4KK9mPk}X{Me8hz|na`bPM7GB_H!b?+DxEd1jTNB=D+PD~$s_L{r1FYfDW_`|1au~V27}CcH6nFB@g0nYh7w2MyPKrg~|qhqo>Bk$AdXc zDxNkG0C*hZI;6y0c+_M!ih$y8z(dKkA5m<7nZ&{ z`U~_nprnd^viN_<_p?LJ{DqXhX<2?Ty^BHD+?U<^&~%Ixxx+wa%|*B_LTs7Y0Os5X zb6GH^>1-OMfs# zm<=*s3^f|%jYdnpy`-D_22wazs-b06$y>N~`NiX;L7-c1S7#U-0cY%wTw0q*lVNus zZY^C$q{VEd%y!=Mp}%r5n(>mU52<)2Z@QS>vId_5Ff#7OeAb?MlRyl$7UAw#@VqHQ znth;JD}-$GC@g%!)l?Pgx|a5kJNk){g0gWae_Z)oj<>ZRVC|%0DdtCJ3gp9GEyjMw z8YctoGHq`RY)5P}xqeFq1Ib9l*2&LEtI;NpRq@WF-yKf5e}R=tx=@HE{8*#ih`dPJ zRd@5Ta&_}re9L2NnAF<(dzPhA#!g>X)@ARc%lbDbespQ0QQf0$VlQqt2G^<)anu$k zJgZXcPgmbzYVH7SHT57fjo_o!huu<^3e|odWO_vNY6L%nom5dXK_G}}lF5cYeWF3IGWf-(IF;o+t^CZd8f`)EM=S?3~)@I zZcvhoD~JQ1^LXjUJsGR)zn#v->8rQ_LnNs*zOUjzfsLWgqz6!Yvj@0!no%%1b0AFS z_k|TcL#Uzd#~bFoqNq&o__T_Fb#b%^j`w6wZhg=*h(vygsRJHEn{Rd;gW+Jby z?(qdc@18#$Vc(wgogf{f&12YTvzr~Pv zhlmuJ80G`-bL(VPiKh6KFVjN1XVWHH9mci+1LzmGinYpa0YaI8c!iXsk}CDsZ)!kN zdp9S$pR0j&KmH+F{E`q4Ov4Q~TKsQ$a-5-dSobuvRNujjsQ)*;vWKiSRVAYJmOAC_LXHpif{n zRr?Niwuv(}w=ScZmgG07@8su|uSo)JNw(78prKf!tMe@Bc72!4wn}amO11x3l<&B8 z3;N5z6s{fqCM)mjb)B!$xdv`2^g@Mn$2|?Nnx|jJvX(Kumbrz-Y3SkJRQG0Oo0*=H z>nfTYNOq-*t~gfa;MP~nrBB_?jn_{@+ABT>ix`5B%eb1TIF(;RqXx|pBpCp*!k%V7 z7!O@|K^ImM-cM{=?PH%LAS+~~_=oH22CxDW^NHql^q&#W9z3)-cWP(dsTXfxK1I^} zy3S!eaY(^?`2D4lnXsRif2Zgu@b7iWCq2}$FXZk!ZAnp#ar=<7or*~X;szeA|5Vy} zHA*DqX`a6|b1!aNf>$wEm zD!wi1LbLrKhR(jCg^zwe9tvG$P?u~Xl8bIk++wJcd6y#4e(Q`y0CjY7X?7;<*P)kS zTz>BU)njtJYw?gNV6hHQwpjYPX>Kvh0qg@Ydp@x4zt3Q;8GR93;aZ~5r`Ekxdb{-& zM{5F56VxFyLE@$389T9B3d9FR%7Xjom$9m@R@Y7>^ev?6=tG6YlX6&U4>yr52CQtx zrgFqa58xNmFdF=nQ1rBQ<^p>qYYwJ6W)1&V$$6=F(_GWMWNja47?A^6*$>wGiMFD2 za`?9uhOx$1eA#wQZN4cE&^QRHUI>GD1!kI{plzLa-irl@N zQ_fljON?IM7?_C9`;yXpJtl)D`M;qh>K#+wUG=Nxle6tb(2)>zxI#EBkX`wK{fy|v zk2PdclQ$kz1otaWohgN*CN|msxd~>=(mOA79L{WS{qX17TTZJ2$%@Obn-=O8HNWn@ zHlO-l@b2`MOBo!&Sk5X;b08gn8Wm7eQ*leQ=+4=W%=!heyj}jbFqKPe*a#D)``*uS zSB2Mss+bkX44^r<%+u#PN zjN&P<)8hU1k6RNhp{`43htV~%58>e>6Ry2aM;iU`9=)VQtmKa?`y6xq=LOQ$y*#Fi zCuwui@PbX)Px@xHmeYTxY=HJ6*lduH@oyjQCwIzT&bcH1KK@l{h0L9_*7Qvj+jrc% zse1eTO!49vVVM%|#`r1JN0?j-X*^#Oi9 zaVHvgr^snwY1-?Eqv zycwX?7d|tCUk>48xNnjdsL{SDWz+LgL+f<_>o{@mOWBWa$$b^f-4UYDSXF@|py&ZU z_3EUX&jGXt(YM7jp_tlB!~I#KZ5X!LlzDN`$PB(BbvYV7%PYdqP=J!`YR)d=Do^b; zkh0`ZTN*Bp4z{_c?@&f8>S3o-gU7MRw1!>j@Nler-JwaE^-R99_$JhpcI5R?$4whG zi~DFg1ee2k=pco)J+(|M@r(WYT>AN@^@Ro`h%)$j+p;`AraJjv^k0TXBD~)2{l&ie? ziOdHFUn_9%_MbZunmTL)kY(^uWm>=E|K}1u53p8-Q;+&;pHicO> zMvVveP9Cb(xj|a8Z^}(?Ua$5XH>9trzbS&!wdH6xprc59EBQx{aiJne6xMZKvHcb# zd+EEt%$g&*sDed$yZQ=#9T@b!$TB=E1|5wS|rv#uhUK)Lq zm&e8Hv-zmL`O`eq?v9GL1SlP(F`o2*|8)dz$S0eB>?)}1gbyQ6Q&%pD%xQ|Si2#kw zy7Tl%4YuH4@VAV{-QZCoL3oA$ik&rWESpOA<94I>pG_#g@DQAfx)f;l+y>J71khGs zE%k+r96uE!HIT z*d({V`?jhmOxIU76C4E!isoP7-y4SfjqX6mep;2+j!XTrIpE2;csw51c0*QO+zpJ- z016n}4@>-=E?R|Jx_OJyRq^TczfSev3kyIL&5XV53#vxDVVI{(F3AoA!~9PZziUKr zTAL(${52H=mWBksC9%*Zy-G>8!m8Oz6aF%6xQFm2TfN>m$Bv9IQlnfAz1_Q;q-Dz3 zDUex#8dt&xOH8;ZcPK*nCU}cwHI_YP5|iPL!eT?bL2~Vlgcg)d`Wh_8^`y>!H-K+U z`GyP61*pc{*Qkb4I^aHWzxEC&JA2V|8hs@h1%l^9P!^*O9W6u_{d7T`UKKEo!bEHw zZ0Jxm|Cx$}8^jq(LnqU}+){s=o}0}?GTJLpi+yAz{ixYA`yNLiDguME0R;lbJ%UiW zSrbR+Z<GFWiAe9&eqADqg-@WPG-ic2q<NeiBMQ27&&G7NQ^^0B?@zxQgLP8ERBBmqGvxwY8jw*9}GG&cDaLmP8xZh_!$ zxg#4t+fp$G?-DDoK2FF|(^1*kFpsGICH&tFDx%C4HWo744Y%b-GP*vbAvocTOGuTy z?Yr!L$E?G42xBvqPrnjnjwyI`SQ7=8uh)Dv0y%CETtM`nz!H6pqRo65u@NGuup zbKtYm{!Umt;=uOQi9g1i(VzQWYfLJG zR7cZ8y%nN@r?oIg74RWcJI0GMflpxR$LYBZf656X&EvfNk<%9T?e)3<(g~q3N2f^f z^~P5oErr*>sWUB*{VQ3+Uhs&!p++h1}6 zydB2uu|t84>ot6fquc#T zbRzs_$^kcrcA6ShiqhuG(@^mO$qr531r8wSlwvOnmmu!wp={|F%#m+<&#RgJVkTI5 zTyaql$C#^ilzx4wW1AJx$~bhR@K$sVM@>C{z5~QY{}(4Imf!9xsC9T=vlz#ceD4MV zvEunaXX4wvqK#_i{mpWr-D5u~f)cnb#dQ_*no3oo zqP8F(|0TY~?Wq+RoiOhI@fRI5aJ&Q{UMz-IEULq#*H1w?%Z6wj^yiQ&i*TtUaI zzSh$p0Af;nhDJ;wz!SUO)|YcQvO~uESqp3c?jN@29$KSefrz2jK9U|_!Lxecl1?8Q z7oUl2eJC_Tz8!8;DxWm(Mj;9F^7Z(y$W7A>b(q=`YX|1UE;!z7lM1~1<(+qC&}+fK zrr?JieZYkMRP}@D1WER-sFUqHuJqEF5vlnx=P#m)1{qxg%9(h;>CjN?| zyC>32ZV5m~B+IsEODO(Wn67%0zOKVKA^!nn{L+v{Gb604xikj4Ar`+(He3Ocwzev})+9U`U;%+YudK`jYfHNZ#AR;WUR00js zROsr*yWvw^vtd{Z$%{4@xPJgo+9n8D%&72tDb$c z059;IvY$Si$=}m=MCY%7@;*>20Qc?!>l*s4@|(E3he{TpQmIn0%AaNOLMtmoUsMWp zhu;a;8vcY3i_6O3q8wr^Q%c;8S#aEKYJHsdf_u>n4s$U*zeu)PKGyCvo1i|QUvHH?&uGH}wmja%GT#&p zMDfHXXeh&5Uv=Q3f2tPMd^gbG!l2R1gHBLS`sG&CPfNv5^v!~Dn&q@CoYtQTbX-gB z$hFUaTX10gyhOKflocM=%rjl8#hfNc{;EAontgA)@byn-jv$5afY(Tkqv`J?h1IkD z9XOMQ5N@s!DHET{Yk%%Hlg&n#0AudCYp)(_Y)^+Ce2zCvZIK6A4M3qyla*oV^CR}> zS84+Kk|f{57G$XY->3!Sn<^tiwK zY*1O=BQQAcqEe@&3G(o)S;EZqcEnz&xKo%2BjYeDNQvjmrPyh2$5sw76PWROneOK1 zC;&gpv5b;$U4ijT*Vj0{FlYPdy?xoUozJ<1>Hd%B#GM>Ka%E$?hQ|5Nzcl+$FTjx# zR@0eN$*z^Jwb-nf(*<0t@wmKKzPbzYO+>8@kG(^3KH#7-KgW$NQ9ec73BS{d(M30Z zaAX9sTUN;FbxFoulv;N74KYHGj=nVKYdwnj_Nl^mQePBA z6LA%|HHjCHU?jT|etJ z<)*c&@9zh;-I1nxb`zYu${7&=Ht3%|$MG;lby*#$38~UEAA_x4A=8NUmcc3qzYcAv|f{|9u8VW)Sgc z3eEfg^ek*@Y2T%C49qSyKB%B;-YTNByxwSPMDWREI-jTGKVMt82FURv319}bN)@JY z6JnP=Uow%f`%U;&(>{Hg7c*}e%y0cbL1;Tt!@%>!}Zd z8noZ_Zh)+zr{DdefzUu@;135vGaoNm9&f{b!=YId<#&3Zu+G;Fobz;uwch`JC#)(H zEa)DB2-3m}{B31O*j6%b@iyu@IcxjXG6A*#Z|EoJHtDvr3kiaW8phJKE1#koOX}@u z$}h(kS(PB-jHD3}vLO_Z^BQ7J#*>C1W+2B@pfy_hLrdShl89(uKx+j(c-4fsD#2SO z886*I8hpg>KLj_2TRwi8;8cVS%x^As$rRm~1X^KUOK5e8RA1JoRV^VWczB%fqDLAR z1?;&tNL^NxUmpn%#^Nabek}hhy%3|<)R0E#JGuRnu`WLN$XJKQ3&&5Iw@Q&KWLJ|0 zZWk<}#a3l1A)gnQjl2KB*xd^dxnUrNk@2g!B4}^z-~EN8Fo#@Dy6dF{Weu*70cw7G zD;4cniumXFM3|i3-tzHPE}k}RSjwWA2{MjZT3>&&*F7;4u8T9yc(4OH3G#@70mdQ` zHTvyfvj>T)S~Nzg3y5-xf$ywF1;uVnD1X2xpzOU7t}9ZFuN+4T%|-QdID!SA{iSQs!SH59Yh7~av- zn&5f6VVf^XY#3pGu2sxh35IS^X9nfvRmhYre}`$(lS-e4=jzj^jb0aRhF`r>-gH}- zS>q<;Lw2byl*$~Qu>*0?NlmcNAfQ200r7bf(l}*KWu3 za)IFRH!$YVtJV?=nl@YcosXM8UuTB^?kmWrZ(RwePNH#tq|hYLD%oFxXV+Vn+BQ^up7 zzh?i`X@H%1hX2T$s!anCo5(^$TWOZ=JlQmhDEq~3 znQX+ZEugbBzbZDHH3cdJb}!ok$JDA{nBAz4i&W-7GPX(YG%sqm??N~EO_cJAHNIQ$ zxQ0)GvOvcmY$`WT3bd&J(|cdmT-T-ZypaZv&%A$8O(J&s-6?D;e$a2w7!{Db@gmvb zG{VV1&cGRI_kPIuwTFLBn6+x5vU?jO0TgT|&*zednN>Fcjreoh`~aHRq|qvj+s(T@ z#m*t)a9#~r6n~FPcqQiVD{1=K=DW$4@+HJxJaXVa-;r^F6jB*dQjl0q7zinmF`@T+ z-dQ3~om^1IF@hilJ71!%&82%4_vY6>?u8_FPk9{OV=~iKeyZpwYg6I#`cGhlb7%p$ z12c;mH_;QF1CrUd(4KYr4eD@$RG{hJsn1B{9Om4!_(3@tttUjaoMX#W$Z{dzq6-Q( zMVHI{`@0qs&)9Y0doguwnw!ljCy@62Z7v}o5ez6O7p`8${h_yh&}j)T8fTMfuA&Cf zKas$m*_M1>WO{|K3@{v;al7|icpSxCDbum+YY;!i)iM_xblsFlr9M5%>OD&t0LICy z=ngL(?A-spDSx$U1dC|jTUmkUU6( z$$w-6$G${(xJ~;(pV-_pDw+K~@X}quKQc8Ojzew79mZu(8!HwiaYu|!OF`|u#mMMK zn_r~qMwFw`(3+leAh4lfakb)h>3?s3nyw$r*+kihnvJS*-S1#R9su8GW08&_m#(dR zbhhWIOSm=s7bmMzi>CB-o_hT$1=h-6%zRvCGg2S7C@7E%@7d>8E;MxVWIx)9{no^~ z!V?2P9y{G@`s|m0#HxRj)#C%hJ6TX$!Y$$9l?88Cl8KAGG(2FDVD)<$V7<3mjaZ`v z<6HBDG2B+=?AOEumqtq<)gdxKu{Kf-&6NR4N@6IFOqFtGR=q1kiWBV!glwgmd#7a_ zZJ;&;(h^F#`Wn@DX)b=R6#Q_C!{5nchbW%YJ0kgMcE<|IWN~x;(+rV&dR}ok$hR3U zYSO~&KUtINhgdjKzxSL3j)fGX#!t_H;yY~gB>k$*P6mI)DQ zEEweu)r!idvvZB=rPp3_6RfsTKL|WFJ-IDq zip1)bMfv(D(WH$1_DJsf$HtK7*K3VelP{FU4}p}ke3Bg{9_shBH6ssLFWc?yi3 zpL&6N+vTheEsRlIlw2|2rM10#`4+5f;awxyY>e z>Yu8MjFQsDJw@?1bV6IBO*)ICOjFa5L z8nzvbp`g%{)Y9UOWct@ivt2d^D6qJSA5EtXuBaj6S+&m(Q5_XGtW6HNXmzuxYH1N&m}m5Q;VY(!n?nV5qM%#@!R2>k*}0~fQg3*)w-#1CuovB;xrBjr zgc(dTaiM|ZS6#oK{f3;s_(oU)ySgFbiP3d;&G2yC3Yc}dOvO81-(sM8KP5*{Eqi}6 zkS0@ju~G8}NP`nr;}ZTpL0eD91PT;mrC? zt~sfZ2zAJ(ffX05vaz&M_Rh<+8r4=!JsmVDP@81Dr)$)1S^8zij#jn=aShi}axRm9 z@WSNll3e-Jg)*gxo&^8i-hiuPzWn{hKU$}TEFCWL3|~Ru?=NZS+5=+WHwCxoV&O1Q zsoYecH@FKPgQkj`NLfQMD%OlrNBRO87gaj>#VP_+h4Z@!(s?B(R9E(y`neAdD5izo zG7CbfXfXc+BYHsQhy6zUKwcj3{~bPfLTouO+-UaaA#Z1k&OO^HK14ddG#b!?xnugo z2Y?woFf+DBqaBh^G?P1!=Ycr-)9|6J2iVB-{pydmgTC)R+)-t?qPyxfNWwS*1ED<{ zM8Ri12A*ZjqG|yWe5B7MRzL*zri=q^O}g;E_zr=5c2d#@)!@r&Hen^na&d1QP2VJZ zzSre7_>iN;|6uB!#Zu|;?tbC3u{pg7l?717Nnl+7W|JYJn~&eD#>6EUg)vBg4X0&k z5z+?U8HYIi=b>lao3SvXd6E4BI!48BJxqgXrh0hu3rYv^t65F0gOErp)+_ztTWx8V zy#Q1}huqU`PV-Vb5a?wp)W#EU$9-djFjrKr+O< z3Sl0l6sId2->sbBKchrKaFtws{z zju|DN*G+bOVn%-biJ~mhr9Bq$Pl5!RosS>{m?5H#UMG!4}{1SE`{(yCs{8-#frJ4QHb~e)!~pz#yksMl`V^% z^NBr#4f9Krgs)Kxs z_}2ej?_@0+uX0aes_(js;AXIs=rrXwqhmxnF_H$c?sdPwpJ+UKw0H8Mm%u?Z2ihMf zR>{12wirC4$Cb_SVXy3orV_dSKAP8rBzWPp1^L6PA z)YsI1yJGfLI{UU~t7YWQ^O3tYbb+{sMo)i5eMEj0MBR3A>@|~lQz}O)VO}v$1BnAr zi$T@`RYAx4beb3&VgAN%=yfLZf4dWkGrxBcMK~_>j^^4?wP~T#oKf0fJcnL5WpX4fHbJ@|KddB{AzD*RcHm2dEH;+8)1XcC57mtECg3#Kj8xC^ zH^mw$S5*@3OsFISDt*8H<9nPm9-7-+&1~{~Xmf)*1#x5geEaopw3l;0PzJC@S-*p# z$gMxkdWQxp&zZjN8sC24bPY-@``BX>ulX`MJInjcXIFI>!+7mOJ9zhI=fdf6lef>| z?<-_t@}&NbDuGkgv)Ys!lMwtNA{{gq(FP6_CLWrZlv3iLj0 zG^9FrcxfLPMaO&QM-VBp;suYTsWvc=L|vFcgA?C!x%%6?PXTTJm4I}lhJcqWirznd zhHEF>xhQh03v{$D!&d|tJeG4en=u2j(C*lNVzL^E7*Y0Tx1ig`64p? zi-X&&j7U;Rvhd*^oDNd;H+LYF#KALZ^^Hy9;ygYV7DgR z6Z}0^f19+gtN6W~_bwrs`3I-92V}X(vKwI0qJn)H@ z<-u3>=qOT+FQ=-&XGONUdf2Eof&8Ez0Z~{du4C3XCxsr>G$dP`2GI#SC5X*eLnB;dOcsQ zdI`3J2tf^(g|;WJ3aXs!1I)rag3576%WQ&mRPe2B;2)_vU(nUR1KY_3+L>nG-0mUk zja5hxELg_&&a7zy<^rH|9#liqt&JFDMlF{-2p*=Ys7AapS^WW*1Bbv>0&8tM<{HuDRLPLC=1(5~CbY$H($7xPgMhUQ?8U9Re_xbJ!v!ZZ*z zn2%%DqYh2_I8E=36mu59>Dm=@^NB7uTEgX0g86~($?%5Q`AASWmMSkO5YdoOse~lH zvtpX!8&LX9KfdM?+@R?RfP4hCkHs`5Lp z{oFLPP*L<$Zhao1J|SAF)|Y6mt z9zHti4Z58mpgz$;GPY@j%iwn*Qwja{;4q`l%_lJu+qYDc1k)L_d3ba4tCw&GrlB_l z?%|2*-a0wG*E6Pu&CT>qLIc*`_blLX-qZ|BF=G@fKXN8EW5mXIUkStFpF$%5$L42f8JZ1O*>B<-(Spgm3E^&3mY+aXN5Qn7anyqC zS4zZ}ltZJ}g%qN|8o4$XdvHk@{&h0+v+Kp5bZOV)kCIyDcvm)_4z8W!l<}4s@jCSP zSM%^zybqK7PKSxxf0k`3D;@^Xgj^)6&c$01Z@H!f3ZPNG8uhTlfGE$%nm<6c>lYI)Z!#IbuNLYuiE zzNOdIv>Sqbt2vbt>Co@>6ey-~qt=Bu2Z+?~6Aa}E2!qOZ#8WMww5wjRoh@~2Toj+f20kwxG8OE8;nZK&UlH<{5lwpbi`(WTfkS z#<$rrMk14{j6Cj=c=ExZNtyyW{s&iVjm9L*2mavw3)_FUgVFA~kjrw`0HT(h?o{t} z(;$f9+``M);EjxvVEd@U+TVPe#vb9;vgK51a)mPe%}3O6P9 z+djGYCB*d~Lx*tP+h>Q-csuTPJ>S&q>^;10FDNDElGZ-&S*v}}SZgFYMu${fXO2aN zS}vHsdgXQ}NCcgOh3pdNfJn+^N91;o=d8?w947zSD4Dh0(o;Y|pFBZ}? zfIvp+?1ZQ3MynHNhIU+ConvQ=RY+m9Nnc-8hbyJC9>C7#)NW27!i{!KalmE=fVf^! zgG~TYEBnRjT6}`={?e_!`h*O2K%BHXS0s_RIo>%gv8>yAK0bP-yswP)0!tB%z2n{= z?@L5lYNXas<0cQoBUU`@fwwAt((|8V#H!-(Czzhd!NJ_l^_JcO&x&1zi_oxW=FXR6 zt?!m~9a^i+_cY3@xC6%N3qLkQZ}?Ao-ut}F%J%c&LK|RL@7&m^k=7!6ScRwRzSa^q zbl1z%)A{fX=F%^dtwhO2uFw!75RQj7XTYnss$zWU!}%8Lc;>Ki4>?#=R`J z?f9fR40V5NQQ8L?xEyc2-+q2Ao*2UIkSQOLlLneosPnOvMVL?W{~wJ~Tl=%#FyqZ$ zs;5mQomEir4_t%Kh()})0int1Qd;WzcQ|qO!F&S|d%VK~i@|7hh!`Nq z=p{^Z-1b9_q|sI$irmPEFOnE}cwdNx-d8fe>Ur*q4MTenlZzy z9Y40gnt=7mKNu%|7-dOUad1ZP{O+tC=oxAj&MvmMbRRAvs7=UU#)sG!G4YN7RzUQ! zm}zW6v}W|$P*}d-H=@g$0@J@Yr>AVT`DJX~=b(%S+VJ5?v6{Tq9(FU=4n5IiLbENC zCUT;WFKxS^yrL=j5xM?=XgNJiy-{mUPm>pap$H+dHRQj6+c*3C-KK-XC@k3GMbbuz zRpj8$a@m~%XC+2e^b8)w<*fs7_n$G#*aS!}?HhX3sw`uC`HM$F`9TgXg={iI5OrN* z3pEbUgH~_HzcgmZ1EG?2qK;PaTfqk zft0aiCiVuzwKaj>MP@d;nw($L2s{uXzgfI@01{f2U-Kt0SS~m4z2%fIUHQV@8`g68 z_xB-k?XHIczzTvDlu6%?h8f{4=)3aFH|dhTzoL#yvQ1H7sSf_}8VDc#|pz?C&0}nRFSH#_d;qO0&oIIUVxCx z_O|Sd$J$y4i7b6KOQ2Luh2J&Fnp0PF98a>~umMQ%qqx^^LlWcJ-Rz)ZB-JxVp(p+= zLX-<*)ojlFb@tFc)AB9lK}~znaM$WRm}sFTKkM|X`kbw~hJ-p7n2 zLF?jP1jSnBYq%|cm@2+K4Y52gx%@9LUgnV?omIGqbQbNKcSlmQGQ;nDnPb2vfRu?Y zVMQ|PV%b}f)(nho)}{}lTeq1iSpGF5U>TKd%+3ZV7SDJ|U&JTgq_(u_1YOgp_uK%f zkAwdV2yw=b>1)!F&zPKsBXd0|;M>mBJJFKMrut`gsqNRhU@@s+G)28djzPpE zDKaN#9Z@LH<pavd1j}&sq6}Sctu(`dvs_>hx%$>L*0~&_*gaG9xOh4~)2ZxLta-y|3Y+PUT za#X%(hSf#=T;bWB#ONrix7cCS(AJqv_vktMX1vqsIQb{s$@ba>_Q9=Rn$J!m<2Y%o z224_;H7vhMCQqI{bhH0inbggu7YE%EI&{}nCcssAAvI0HHB{1j#3n|FH#h^)*_h1L zTrh4%mk0@5)KbOs>%{xq)IVT4wb2{UTu7iut>(te45@#Hxm4TQ0P96}Z%4H?K!8m@RBFpaS^Yap&pMJ25UKD_j}F{!%WyT|aLm`YG7%@TLI%YQ&Q8!9K(jnf3UgxbpIc9jQzzx)w7M~@32DOMN^t=yH} zG+8n4YQ?V4b;X>+wLH65JTP{j*UdH+7(DDpsA>>Ew+(f`BOkUlV}WKtauz7X zb-8hrEeNA8YjBt4?SEp7e;SU)Pd!#?u{tIBsHhqpG8x+ei-}j2Edz9#O(S zb9irHh8-YiME99nIRhV>IHzpgIOX_QkE{>&J(2>5P_6{?+WXIE#cyQa-J+%-F}aVHWaiEPLjv#s3szOxd)8gNqdPjc7e!6@FQ4jVMq$N3xG-Udkh;q4w4 z@%kQD5vG^($_Vl%5pT09Wo|Cn)mNg7(K%(wTWr=p4e7*Z6}X?R=1fGsSGkX$6PlKX zXV4l0EVU8q5ho4Cez7L>lKFbUSYDA@=WJL3$H;pcHMFk4$4r3=ldneD9$I?AgvUV3~z?S>QGf=#WwD{Bpa`O~aq)3m7XIqO>O@)EU;4JhDJ z9tMp{1j;&tRu*Qn(E6T8%tY!v8Io`Pg72#WM>ZTWZW>ch z`;To6%svpVNGsq1Lb0zNyu65FQWpdOk}u3|N~!^qV?^8*0OB83G|dOdKfoec)7|7g z<^q7?WWAl?+*~z*4>(VpCkDIjMA_)YQFf~JqageKsI_!0;$LeE=z89a(YR`4^<6t+ znQ(>GU5uO~uMlbO473|M$1+JN9t(lkA>=K3X1Z?LW@QWNgcI z5_(s-MRs;#y(`x|>VX%JvJOFM4~nD?6}dAwYFAM!`jTh?8^8#;UrHrhFL03&T8->8 zt=X@U8nO1QPci~XRUkdekr_X-x3uYjR`3yl{QyASYBGdw0BGvZ6grjhhlG*-JG0${ zZm|g$^`=&A<|zqC`g&jl18E=EziyHsr5CGCy#~K2`2B71rVuX zd-EiM)xa=Y{6JM1?^YH?n|aXnq_uozaJrN)rk=Y8Ou|-RK>P@-qTn?K?m>Ye0BX2d zG5{uAZ6IT|A6@TY?UA|f^`LK>`1!)WZy#>kfy&cm`}qrp_njaTIW~UU3m8NiY~42>Rh=TrBJ#)8f0$qFC|D2E}fOo`y8jTAJ$8H!zP_6wadT#<^h=z;JrET zBYawuW6~w`VMIPCmCFr98~Et&bT|X1&Ls99_h7QjJeT4B*!YWu_g}ZyPBgGQf=vnJ zk}D~EX$FWwSLonXTtxgn1F-ld5i#`D&40(k#rAMX{Nc5@AELN%?z=HNU3V6HXdeN; zIq!U5TqMNB?U=mt%tpMj2j*p>x-UlE?)NVJ@9;C8e~DWF{w>}HJkp{6wxM7U_jfHF z=Vou4rYD$y_t+UY5vms7IXHi1mxoKj4#9_9D7Ja$;Q>F8V-#)#H#9<8}(Bl>gCHnpPOfy z!)L1T{8~b}@&XLL&5XqrrghGBkSd$ z31P%Ky1#X|8pDNt?lB2>SXI*eWHotecW1Oi3m9f=rcV;3mu_Wnz4hRA0w|=vCoj)| z#eYzghqYO&BPgD_PUNAwK=p)XD!n41q$L;OCrFA(`+n&A!U^(3d>mXAWAVi*_+g0M zsjSfo-Op>ULX-W_Dc@M7;391HftcO-y9Mm$r_#BqPKFHn97Nm`H>{-zdvgYb{4hNi zYN{z(%SadXuWTf7avF}zcs{K=C)+(#83v9gUlAb((*N=PN*LQquW4|WefaaG(c*UF zY5f;wyS1VnUG;L(#E|lrZu5z$e9<5&8Y}}%GU9<~^7(r0g@wWElBjE&ZNX9hbSWES z5oI)+ItK^pULOY_{=>l1ZY0&8?Oxaf8y&EgdTo>%+Q=Fk)EY*2*=VfJyGf?j6fyG* zZoPlXEtHWvXFYJlKgfyfgL0TPd5Jq1KB4i3*-of9d>QtAFM^gP*nuteZ)caWHkEF` zX#>NTiII{+rm+~x5~DZ2qj~QVAjMqR8>#8xn3@HVuMD;_eK}>6_M=e7Uw01p&@MS; zd6fNWB@fc1c)2X$!|^8lss?`)H537?0uvrU{lQjyMwo2G3=CzJd5pF^M$KwPfL_pc zKRvkbdegHXq$pimhGa@5k?#m|aVG-$JOJlI2Q%mMc9m!Kq}(pg>V$oren%LsR!gZT zxPH)|`K=Zgt76OU&6fT2HnAt%_0!QJJP>*=6Edd#Wg-Q{fB+|9qCVn!X-P0@2hXDG zEvGG5U5Ef@Ken6zP-BPE*uO2)g7S+u!j82UJR4b<9Hs_y-5#MjC&r*sA-Dr1qTvze z=9QD(&x7b4fdo>x?gpgC6C-GMnbyaVo+WER!Z>P~5aw}XlVCX!tCXE8@DkoL846IqLvstB#z> z^Bk_E$cnHmKXBdp1F`ni>F%H&1 zgL}V=&EOf)=*yedVD=K#(A%%-Wo+rxro65>qwsXEVB zWp|4Wia%T5Pwz8X$Bn25SA|8I3IbNK6_%+4m2DaGDB@Jd+G5zEyxQ102qCaD&xF;I z40|9LV&WIx!xecJWz|q`ybusIx(va~PqxG}_~SJ1d;^3m^}L;BJ)|wGM7$B>%gd>; zl*0PK+(120UK2{pwRTMTbI8cxACtS(R^XYZw_j%fVM{Fsl!{P@T4d}<(yVR+1PnQI zTt*YKcO!;2jw```Em3Cv2&@?Iu@l0KYX1CnJXH5%6+5|Z8>R4&Q&^67_i)!|vWxAq z6-`Swv#LvYGrJIPt{g+-Z$6ZePeXh=ftvvzI&^iHq@NG^pZ{&?gq2q@BxSR<9pVbP zrzj6@8%qz-hb~I@Qq|9vrro#GofRd0kK`=%g_~2~QO0 z`QAN~STkCV0Ono~(s(8F(nk$YojijSRn90xt9O0Mi5wgxmzy{4O&qJAJ;k$ECuIuA z`)}8nI$zRA|3Co#o==#B&+5B$YHfA|5n|onGIp3Iain(`n@9JF2v%b9m}jF z28mt~A?kM_K+7u{?^Z%>V3A?bjN&IEZrTV8Dk(=76+E%%7~$&{o<Ww{rKJI=O z;YvXgQf`V@DGFGsspl5563PN@EJeSm!*z*Q_!|J#{gdCm>;e@7N4}SF-a5-`DS}tU zV(3yvuEU6mvMD+RjsQLj58AZ_{2lS>c^pamiWc|szF}X{xOqoX8EPNzZH>zYuClHd zzn(5qiR*gL$b`lE3k^-(ngp#C1Hh8Q7z}8s_NxTGM<`Yj5%I&E`jW1L#3c; z@m?&|;J(4ro;sb1rh|EsI7~_TMv6!)^V+Q~?5jHCSSn7Uktt`jaOWHWX$I^7U zHT+&ZOPDJE2V0wNWodTZsWdB2Z&Q`bpNO6uo860gqu>yw`1=g3{W6#3#4L33VpPqa zDe1BKEywYNXw3l?Va4*V@*GB-c__AIl!dQD@!+y(?md+$nQeHEQ6ah^(s}tz~Mjr2JwxSkba2W~-*Hnew65 zS+O+udAF$m-(6n1M@TdjQ%zCq+dDB$?eR*XpODo#h2{R&?=LYayf`b=ueO-^If%-t z+ZnnCjZ3!{af^@L?r%Ah_(vdnBg`zA&pJ_&VHwpDQS)@1lh|@;q1=u?>%>Do4T8NB zCbaowB1m5^+oCrQlO>ODy_4$;T@O6s&6F1xS}vS{rE8*HFO&JCYWD3g`;F!^s$m)Y|ej^LL`Rs zENYFjM)Qv6jD}U2LeoUVlQM?U6Gie$VN)2p*Id5`mXx)YQ|G@>ofzlf+L#msSJK}h z?GXJ^$?fi_%wm0cZ?s~nu~uqZfj4Ul5wQ`$JZic8-;%PwJp{FinB>ww#>1B9?)&GL zs5hI|JVV2an|%(WEqFpCzl%cQc@n5>tCmdUBw^+KR@NX!8Hc}mXpFXSchod9S_I#XdL*=wS zsYA7Qym&P~5SxHTtY!YdY|sCPs7dVhMS^sVX_asUhRI{PR|s>YhuNNDjI-?N9;1rO z-=i088X18UWU|i{D3Ej2xOFE6#rzysmd;46*iCi7Ll`Z9RA} zJR$rrH;W0vM9s*y6g^bdE2$sQj?Skr=M1GA6iU>Z%O+&&cqv%<@Ix-cW)KmhXcEMs z(x#{b?wB)j7XUdzKl4|)N5(fr7TDOGJ}HUHV%qGl7PZx?eul183t0O2;GLW@Hc(Z@ ztds^rmqAFiXzW+^m9Z2%fa+o!aq*()DG(iZ5ob%NYW{@PK%x?+(FQ}68z!YzMD9O{iN+GT95+ zy39(Mj)y0S(+qW}2@0^zUL97gx*P{=7@~{x{dXl%sGwzlIcKGl`JCU%pO9U%{7cDI z{$rV!W?j6n;#2XGz3UdO4=)@aDzd!B!7^Q)kghU#+{BQt&%S?+GdDLU8vNRuQl-kn zAmPvWa*}ddR(7!b-2j4IWOlFT2;uBT`JeZ#Ca-#1mGQH4xEm8b=p*`~R1=vOsYDBU z^IPA;%JjIUWBExaTre+PmSA8(Ih*x#XrSfRD7CeWnKyZst#~~L#D)Jv!`Ys3lKfTh zXOUX1W22^JDz*)I$UX1;uUGUbtDF9#60>(%lO+W{Pfd3cuL$hwaPu(c368u?TR9s{ zYNAIp?b-asN=x-us`bZBOiJRYQ<`fXMaT~rj8^-X*p6rBWf8jJwlcF1PZ4)Mz}pag zlE^Hlz^kO>nm@>($nmU+rOhmc25+$|RH|WOYpYJYIX5ZbzbbV**}?;2je0J@>2GV( z+M?QxMSqn~?#xcy&m1d%L0f=s54O!F{7_u_bwp!&+xDr!wdNyca>-A~t7X zZJ`=MFd5-xvYssdH1(0x(j$R4$6E8&AE_qE%}&?bgd@Zzk1kK7YC6iL)r=^0mhMZJ ze6&K*plGSmN5G50gPg^|eO0U*oy_WOKDb%kGDQXOp9rq(1_mCe(K3Qm!rQEp~8Gmr@nRhBl z2u>D_$7SzJjP1KkaM)Id3`yYDVVbxW33Fh!rIbOJbM11G94ob{Zx zj5|@2JyUqk1gC$8suCqZiuGV+^?6Y?V{UHsA^h}r0{3zg_AH4$*G*Hu%F;6+_)y5u z5H+YTw`|#tNvn1{qeSSOb1`@-a4Q!u;nguKU-&|8yzfP#dlV)3Gs?fjV%>2@ zpjY4T>Avkwmd|u9i%851RQ+u>qcZBG`TUrVTeSI=i7hQZ$%707taJT_l$NbU$%U&L zG#8{>t@y8$aymBx71Au0t5o}SNDh9 z6Az>VHRk<9++%Y-k7a+GH}{lIqVZ{wu&lB)+Z9)4nP=#U$iYwyqmP^J`z5C;|%^db7Ych+&j2UQX-&lz1B~8J~v<2I7Zv zD^{t-q@ncZ7!^pmNM;4*$Q}q~Z5XgN5>33aX%H;{vGhbP(weSna>*h>5dtIJdZ2vU zbW^mb5iij2ctDX)=Phf&WS5HXKD&;1#ymiTWyGazT0MWUu)$R-Ji?>2NiH$m(*V9$QajeewLEzbJ}m;ChI^}x83 zZ_v6>ETgz#n04NcR$QGSGQKI1zYM45wsSOXeZ&#o<7sB2=()W3?TyQ<@K zjTI53Gjm((+H)pIlUv!5nQCzBkjs#g(v(o^lXXrEYZC?sXD@tg@w4qVoz{~JK+C34 zUDQWq+xocY_UNlF&VRz5{+mD_Ovnoax94kD zS{IyjU8b0G5F=$J*bbGY)`~Z)@J?sSW2svsge)Q-Qa@+n+~k^Fd<_A0)^3T}ak?w< z^*(X)+xiiPRCTX>fg@u|L1it_Mdofz6wjxr`&f7ze41klatjD;g+ zN#Nt5f#X~|75Tx6>kuO}>g*msGJTvBOi20u%e1l1{5}!*N=tvkun{XKS-5eEOx!P< ziZ7;o;M?@v-0ER**87$ui|5PSg>AR|Dcy)j)T?;LaEC|}m6HVITGKeA;MGiS?63l& zz+5w%!H31B`%}ocD97AvlT`nb+?LJwf5nn` z!rukik(<8@5A+bP3MW2g-Slls?@{ zv*VCTX4MXlV?zFLDP^j9rq!jdY4UiVG%>G#elMt{-e{-uEUEOj+1Tegp;&<}MG6$w zoJhK7s#pR)J*5jZytc$$7ptK)(AV6&_lN>LJaueWode22uj8m}IWwk%2(j@db^E2g zyNWGch4%MkXd#%#S(W=dddJ`#qnOcLz%a^%d~Bn@0F1!nDI|_um#^*-xkfT0d&UP)gIF^Md>#RJ({)o^%NZmCZ{>!`Cj@zB&O_vh7;nx*y}-$MA6^#-?2 zNM(M_d$~OQIT0bAyz{gtT`G^w#OcRM_oP2R$7I9o*E?VQG`l0NNL7>=*ST z#9X@AbD8=+mXxuvK!iQR`j6{35Yl$mxvkMCm6bTOO)RzifOp|n(xftBLlFcO_K{kH z7y0MN+dGLRzXAe5rQ3kqSn+Ln8M_75v-f9}5Qsrwe`h+ix70q{cIzvYP_}$Ny4Cc0 znd?u8$~#Ys)($?kZ+F2w0QPRJn(6OM9ZxPKeg2@NecyyZJj0@L=9lHWlVw(u>^+F% z2^wL)-;^Z*n|;cSA#2RG%?lcgc;{TMpttE$`z#y96~M#SP)$==wVJ(8&*h$2V0GV0 z%+W|$m)4nAv*$I$dm-9^6dXjoJs$mg?AJe45(^x216=;Y;8kFsdD`fn{{1bj1}iem zDK7nBlcFpnTlvcUCo~qj7ip%WOs0op#gl!7@P-9_WZA62WR zt9t>;5f-~;!pOF2gv2_dZ^JOZVfI~Rg`SCqhSc>Gda9w-y^bW`m^BG;gFipV{7Q{* zVJRo4!_A|6OaDDIafNJ=){b6>I*B6)3TB0*-Q&nMGh2y=Jn^lYZ^Mu}Zh}ER4m=C!ZcF z7H;TYywzu$Ewa`s?v@NT(&`ZEl#8WCTeX4aK=4#B7t%F`o5C{o-Xxhp#9mKLqU3=^ z14cPaKZR14kvK+3GVwH_ug>8!>!7v1eF{~0fU+Wz*=HXJ-_TF4mN3`QFn-BD4y04BXKH z&fswYz4>bXwD@c@i%G2MH<1j(!TpmoA^l!`D~Xanaa*y|!Ck1XjRS^v8VOO+?S73Q zn#Cl0Jxqj5xiO2B@`jq^f#!KWA!RQ`Lzc!#>w;> zMG>vCRaOEV1Nqfcku_;4_D)UO9Udfag6WfswK+&zuQp=x`r#-EFwY1FH7gZg+GbLd z%V`a1)S;eo5^Vi4>ekxxlo6L%IJH|_%LrPak2mh-zDpSWC=)(d_qzr+>>616X z5-lxynRVJcc4Xi;tsUekU&Y7sBWge;$bM2#Y}{#{p$`x&NwOb8gUFMDS7(?X563%g zUz^6W@-~czgXvF{BTL|>rPSuN3zeqqii`@7iS&r@1qC}4NniH;Hba6UhRRd=69f2A z=_Lrp*N6C1OO$<6M|SCT!HO~4&}q!2o|IBQ+w}yoDpHJKR}ppoOqrO7V@yc-St#65 z@1k)>JZ%sE7dzpsH`s|kR&jl?%&>9q@d$<|=#JRQz4qDjH#?^*&?U0Jr+2*xSoqwe z^?0zLuUYZ-OHG`m_jm`F0>*Q)fWn*@sUrG)a4AT%&*}B7Pb?>C6I0Ek@+6Y6yY=yN zxre}##)(Z4*q*vSgwlwy%!r2N)Kyw>zw0e3FOyF2I}OuTE;WVNzSLHn6~dSH&$cD$ zOk&mk)h4sYjLW#vAvm3Pqto0A83`2>Hg0htH%5pfVn1#Vp3jd>k!vQRX^e`ZJ3gsF zbQV;M1}pG5`MT=j?VfPdUBI)wwz2k_n`l`FBDSpY!2c-j82*=5q>0)x((euZHu!P0 z%6+0N=`?CmhpkS>a9S^^=_olEJq<8ws@}I9(@@8!aoled`1Q~G1Or(6#*U!xdLc?D z{!1p^$vt~eO)(AK{cIXm=#0(?YUopAi`3dQ#i#ZSiJph&&H9hFZ!-mR*kFzHY3lFV zk>$c`zn%=8!X>u)X1yOqP&oX$BSPatpCPuNztgz6*AXZkV~X-eTadHSSta_QWnA(Z zoSJ@K^z0;BDvSI!VDk(UL45qiL^I8rsNQuD$!w` zBH5&)uP3@C;A}2!G5uLB$$7R%pJzY7d+U}Em$IC+&Tq3VyWK_n_M_Z=JDv-uUi_F9 zXIT5<`J1OahcD-lKfl@M$tf!&skj*)P_FBQt=(%c>x1=rtSt3;_rBJR`)_W#kItcMMYbWo+t6F&swJVzeLo%c5mnC$Tvap z!K%|RtW&P2{9{bfU0u=OY_E$L5H;#cF)YB{V*0Jc!}W9H7N;jn(^cK4Zxz{BX!;Gg zlo?~QXF_1g_Gm(gElxy8J^87Hyz)?-9GsuHNU7RiQlA~6EuoVvOK+a9&cSK%oR^RE zUBUHK5Phw3ao${zT-95Zoi+isDCIKKfjrHTAnipR;UbVDsRRDXCgkkbKYE_e(DO7E zI9G2x8QOiEP1sh|$ag~Y%srBow=!~3ElwIUai-RLbl|*i+1#0`@141u&h*G`dEe;1 ze+a5^3OT*gURmDBi5y}cc6oD`|3IZ1!da7{qOt7LAcnV86e7 zRVL=M|K$!C6__~ohZXd3?GMkpUo0qupF5JyG4&)htyekLN`mf_4wul;@bGBeu19M9 zc=_!Ne#<-=Z4e(^S5QI2ujoF7$TwAxM5TJ_D83b4WHAAv&p+-kA}V5ERl^(%1| zWx{_c&*GP+^Zl^3eb{nQ>iBFV-2Vrw0&dQ)(y@lZ747NiX( z@yFyDjs3!Wks2gIHRf3|w6qFCH)_nkWwR9NLMO_yzNMo0_KG^TEc*&K7P}icsYiK1 zE3F`BGot?dGtVM_L3Z98;|d6Z$+BV2(~?<+Nif(md9obY1qg9Dxv9gyqg3?FQaJe<_8{%Nb$vVAPQ;t13y=k4@GKW%ECV^%rUTccb$`9m(S?5bhI1^mnD_c~e~8HN39V{t^}1I8AojS`V5+#h|TUGRiz~ z0bblRL=l9+-?v}YmXmmb-)#>YWKv}NJH6)9Ys*{+_vIA&;7R_%N5bqMip_2^YA62X zzDh}(ayA_|qTA~up;3pc%>@F2LmaY?h$K~WV}ek42^kWq!ZbtVQ^#q(Nox}9PZ5ul zQ(Rq{$Ax0fnw@Q3xCu?OzS*7KA@r;H{bovaEx2e_#CiAOy&Hh$&cBFR# z@j=P0gvnjATtCURHPqXC#66m$Th&mC>*aSu(}={gyJ_&Bjc_Ad4&v#-Ng)K4 z_nD#nsjN_zAVrD>lBH_UrGQFQKR**ok6GXoZ9}Lc-VO3#wV2~>&5{9rMzcQGi?x^c8@8Ff#Kfz107QOBy zRz;;|Y{_k5_at`2TUwS^y$=t++=+i}=;-9>s5V(+iTBs2YyWPee!=?3u7(wy7wNg* zNpdF&^vznojg`zH=b3<8ywVLuFSeCtS9;@~K-2P0_JF=5s+wLDlzQ=X;!NKozy(&+ z$j-n`CaW(I1H-tOcn3n{pCx3UEHZun`PC&}e#O#?@@VZWbQn)pZL(!GcZt7=omP$` zM{OT&EBbX;;cbCJ(t8Iw^Tuxec!MnrzV{oLXN6yjMD`EJNtyC|=jC1)KCy0yGsfAr zXsXa8Ws>Z{X%6q}oN{!~7;b>`pu$ksgs=mtjE08~e*TW%u<()U-A>VAcrh@ff9d>A ze^*(=`=hVSUBI#0QHWl0?siqZDf@G|pb!^#K$LjaTa!ND!P+sUBigSg#X90*C!6V+ zAw_J&nHdbqkgmegsw?Tv=!(-y5dPNUP7-ejJQ@CStpmLP$H{?FPPC7ld*tu20!~;_~<03XLFh|$z<^v&$ z;~U0gqS<%vek+4m$#15(4wTv+dwE>WP6a%Zp zt3b0N(Pp8zuSBvWhIN*)l8QMkl>x{J&iti4des?QYWa*(>FRvfCT)wV?JuHhA;S^3 zG7OF{tv$N=Mnv^JE+#7~n6jx}6k)C$&Ifao*vdta8Lx}8i9s%R^hAVqI?<^>QqzAf zzVOp<#gE6H#S7bIs~UH+gRw_f3MUlb>EEZez6bWyq;9AVqrd2e+|Uy>mp6U?dsKe;d#jSSOQoNejh+ly&w#9$N*%zA#s)uV_K& zIc@M5u?uGc^Q^lT5n3S3P;s1=4Lxm2hrUxR!$8s-hK?x}#cy?vz=axWzx$%BvJ|Jo zIGuwMO&~hw9!7B1XUp8SOMfGO86TY+@i=iexEC>LQM~P9OP*sBJFO7ZQ?hVxMa<{x zUdUH^IlFqU7U$~c2Je`jKI(zmxMp`o8f68VPT=Z9ziIt8jGy9YxF3HWltTE6eeh!i z6T8rJhDFVBb6fTE{zLH=*9I3p7|XOe+0fX(XCBH`q^l;voryNn^dP~9-P7VD(7JL~ zNw6rJdG5k7zZW8etRptWN({P{L*^c_QU=LA!*w4uePG23m-e7^&4F>y@l`%2xY+)7 zFQs7Q_wh|&;tYMs7?E_6`KyhjaPKEuN$`4aAjQ>FI+i&e3==1A%f)2EdKF4@wk5-^ z(p&k~hD)FO7?3u(tA8=d^Y9*DzC4zQ@ID%Sw`iQJyLS8`hYt~aruMcNRMg2bFG#dS z7O6mOj02f{ZuqocaK?a2!K8#1Vlp^nOZsA&N!vrs_cGtY*R5{UvF%;l@SC8_=aVM+ z*?Qek*=Zz`YNm_gT9oBodv}KIB=4@p|KHoD;eb@XP{+iHd}66&fQwv z^!&iGitrF%(2UIe-bPsy(gQ97Vaf1JiP^PuhIcO(7+LPOG$5pMXs^K(-oxS7QnPLhR$jXV>#k_2{a5||VprK=#+^&Z5d;Z+*i#&8l!%lcHunx^ zFiQc8<&Fr+Z_xtOpSKAQAntwlO%P5^8?H4pF0DGPGY{)FuAGD9i)k_w2&L@#KIN~7v3y&=&rtUDdkDA+cn+hjf1`O@B(%Q7Yz6lf z*DEGb>(~W=3#mjuh0A0VLJ#xccDt=RYW}cLNHT7#2?$!iv~b{D>V+{m>y%_T+F~NT zh~dR3Yc`hlZn$vxfzcP4VVRt%xM$uJl6{}2aIM63ff@4woki>c>k}2?K+Tx~!L^U& zRpVOUKeoi^5Cv?dbn&S*2uFaXO?X!GX1bt*b$DEuF>jsyW!&6GnI=gJ5=YfjRh7^r z*0rX>M_>=z^Gw8`8$OcXO4!6BT7%rUb|GC60Yz_%cMX}$81VxhyO(p1a9e5@jLkYy zNsF4|E+{Ak8-6<-OWOoRnBYsHo57Gu|rCtMgZ)g{3r?k)U83o+@k$D{tNW_8$>c&_>n zSR2l<`WVV;<^jq>{a&#{N3yr}t=S6#CM9-?q>;l>qpYx!b|#~56WCXx!M%4s{ZCup z83H%jsXTn|hpc-}tM5vGUNRK&wSRH2Cjx>F!}c zE@R$kZ6l)&sP;?Qkpj^$!_QQ4p+)c@xSMnW`D9+04GsM#iy8$|P2K&YK{w&X@6k^1 z-NVg@)xIj*ix0aomM_F4n=co+H4PW0L@8#LgXfq-W8Vt@$v@N1_oRQawm9fXf4jS? zxd9aV9-J`bu!Cf?6DCP_OKoqc0Z+FmI?xjRj_`B{qP+ZdVhc>%zu$6I;^=2aBO-(5 zALneO06oCd7zy~!>k=V}CO`K;spHv4;AK<@MRMdWFUy1i6uQ2wP~?*pZ}gKWoyp90 z{Zuo1l0$_7p6B;RSk|5p8Njiv2E7_L3ei9B0$^Ui7&U8g($v~9vgOi9_r3;&O783< ztYBYg*mFb}c{B+ur4QaAb|O8)?l}G|3D0w=5+DD@P@mVAg<~!wrJ`RbMs0=v*`^rH z{=u*=D5>(hkWwu4B-=i^)p=|&bVZbK(7JTv;0lt?`-}u$1Z({XbS`U2MQQKqe*J)= z-sH=qQgKa4sPTB}hYf`P?9_e;=C;Ce=;6Swnnk_zr$YN>5i8pdd6i7zq~&FTQ*;WP z&6-8I=rBt#=%T9Xbp(!tECQOoTR@&|k_;4HKzvA!{p+XTclPg_)CddF zYe#>~)uSfMeGq<^HZ55w-%T%)V_q~PLr6t>UV5ujV0i2LCsudcy4&7`+bJFiSY1o= z62^Nv*|)4T;_W#Qq8p=p5W;o$TC17~`V6h&bKiI`bG{Po#s@4J3Ls2?dIZo%p3Rpx z*ulI{RQT1ZpQah^>lf8&zl(Ru+=xxGlW_|d!&zs-K&EbIR@fbxL!SADj_mSxLiW+p z$;roU2}&hKck@}LAurzy5kAm;%aFufJFnGvj)>9$>H=>52f(y=6*sUsV7eM7()`rAqJS1FJd4hJmf+{5SysQ8FkwVjrtbQ%?CL%1WrgKC4I z@{KBmqB(M%i!SY+=Tbe+e4n{>5AP=q^Gq8F`y?Iwxb4$eSTAJEIsqs}#v-qYGfkHd zG08yx=VetYsUnV$XZ<(1dyo`fPybKz+VRDb2d1n$x$6|B)h@;cp8PR)sPLDaA>KSI2E3?j5VZ z&vLbj33-!~IUZwy$Rp3jxpHT4n&rL6(AY-w1&!DdS+>EY0(T5Er&^>yF0* zbBT?J9v%5BeeY7YTd(@rCngF7goqhi4Ebz6ahw&xW=mTr9+ zT%QS0tgAswhn;mx2l(H`y4SJaqP3sS9fp00bIP}CEl?bT@bauHaMWuAMHtc$%@L5j zbA3Zp4UOJO?&R|IptiDwDxC=4jS{3|g9hH7W0GHv13PsfMhPrw$E_ugmE>o@W89ZLY2EH5h#g1V`2?|iNUN|Iu_ zQkFonk(v+^aa|nLA}^lCZmgT#;n41SAi?<#W|x|f5UFX9s;XY$n&)dhF*-#jS0ZE# zVp$Fr_O8bee#vQ?gG_&)f9Wvt2K@od>2)<|6Rf@ikUg{6kSCSO?y+Tfk>0I8Qy$Zx*jIvIgg%z%~_jB(b;pssNo>w`Fkqm3E`2#zv%^g`|r_hU!{K?87!o5FQ3UsDb@lK z^=UET0MA%0fWUvBek`)wA2tl`NR`bm()JSUT3#y4ju|s12qYsOGmbiQB-F`{$kMDP zd_#k!>!t$47N_!f^%(=7zH=r;?gOmL#B!pF?}UW06BaP#8dUsvO9c4Q zQHOXL2q4G|Gn5i&-lRCU7uR!U47?x=GY{f+U6MIT3x3Qtpq=Fok<7N=#AS*VG2|ZV zxizcX(K#x38U|sF)_9Z+s!*ojwD(ZS9YwvM%I2@Y@5ebLoPQswJ(-K3-FEl=hP-_L z)hW{;xwI$z$=-S52@Y_sV7H4Z@dwN*uBxFr>LWwa6o-1_6xh4(Nm{=IQRFE?DT@bK ztaurS;)Sn%9+tK0orQ6(mdZ}WwXwL+Xz(PfjV&Hxa<$3T`)dUZoBG9sE|x==M`c2( zbl(Dn&)~}Sfy#BET@Z1N0<~zGNlBlf-iW<(?FYx2r$&<0C^31C)QCcnw>C-3*j_|W z39(dNM5-4Ku49O6E2YeRNczQFjg>P=@11t>1subzKuD9nVPF-dy7>N}5xM(^PtboO zbfq#qnHN`E`0)5DZ(`lxKQq$Wdzm=6&2KE#{$MkL6)8L?pMCM=z1YCkR=%Nd9xeIY zIu1~lc4M1j|Ak2FDxR|8H8QPiO1Cs$dS+@S9PaQFSas%g8@8Fpv5O*$w+K~KS6(xy zSb!{gNqgW>jG(3Ber`w!yX|EXzCoGc^M$X>kfn_Cg`xmTctMwf|Czzn%-wOwhPsgQTS6SWPD!3i6h;=Q z_l+Pi<<`nTUElFuvsa!3frf6gI){(Een>2Xv==alK>IcdIf%C5Xii$w+w{Fu3ExZG`XLkzAx%j$&f!rm z8iXw=*F9?1Gu5Fnotw{7PxL0B2#+pF8WmeKFIf zSjb`7N?cA4@_!(eY_J$gFKEgmj~lC(O{G{S`>kR@Lu*g?HC?msl=nC1$oNC$9EVib z;JX~yVOaxfhAC&0`zmUBoLpn{kAoaZECGO>yfi}#!%r$7`PTmD&fDmYw<-Sokx(^{ zgmb8rhX0d69-X>Msm0*Z+k@rfz~n28eoooy*q)E)J4fuDG|Jie>ka)0UKrrT)0)tC z^3F6f7so}c@P_UV)P1r+Qs(`t8CozDGNZNvxj?r&MWd^*xKV6zboWzxH~+0*horX* zJCWxR?wxuqM1s6ugF9pnT?24 z-Bf0J?{!m-bn;;Xm3v{ss>+5pf@(kC)O4)}v-|*Qod5QL)wy4z%c>`@F9*T-B3(c# zo)@oXX~>+Wz)YU$G$Tu_?~ZnSjJv`%5sQj3%9@91kl>x(-238xGDt;|wb6%Ify;-j z$)?xScujuR=9Ct&6SF?1k9epwwJDb*Y{<23k;X?A$gA7WkS*1&Nm~qL-IuSi0I5hX zYeNoiPdOCHqs#4vsK-xNuVlvP9r@beo>R`43 z9{~43fdX+&cx_lGL9rm0ENbOM6xm!gsLQj^XYm=x@P;wek4psTiRAg9FJqVQD)m5( z>*jZ2EJ0n2?i>GIqi|$HZC8WPrE3w9e4)EUL)BHG(UQWKsQ_Bq@ZXPjb#fWQme5ST zt9s*fJq0D7^1o5GA)>|_is&X%DVqE%JA?-&H^V=nNGX)N5ET6D((M8x_Qm!=jHX)^ z-x{7a=Nm0V>P~8^>qC=+{c}a3N(7e z396-q_G#~Q5~Lt@>*O}rJmrD~b(BpG?_nP8)xmhd?27O+5KG+x`baHEu?wBknD(#}~|>Q^f{+v;iuT`{TLN>8lshs>>RuKc~gLaTk z=1az$5B&-T2$;VQLq~vNmRL#90(WQJ#@cu{&tt)=l zD0LV|d4{boD{_t=e^8q_KseMiey^!P)o?%J*;dt{s7{ocCWntN;Y4a(t>4+416UY# zB0E63ui(Q%)F~3x6lzJ0@caQVCXwH~fAEz+j8MzZsz#ANJNyv%;zIXOM;dYmI$Gd~ z0AQfu{b!WEgPXdOX5thJvrWfVTPxJckDXx|XG1ok;ZF_yE~yMrBoH6@zL=Wp)hfNQ zw4N&ZGmN>7*W8C%6G8Yw&6~RZ@TpV%Y9G(?ps#~*M*u~f64=Qb^3ZsM*G;;g?;Hd7 zW3^iHjYF5ISEZQ}B@#y@Z4yaI|L=efnu#Ayk({WHTl9`xxp;$~gB7lHHvy4qIZ6tJg< zv#lWR2#efXfYUR#^Sx$CGk$C(7W&MCTdch^AwI#!8?tS zOv@GxaORlcn?*I_Rr=zJ=Dtu;lT10~HIrIBX_G=RBPm?Zt>N2YWr+Fre@U*;hBp<% zOM6^D=p3qPCj?>blITVKmm_N%jt(haix{r`z8|^_a*J#sWFbI{-y6EaoWpMAM2?X7 zh)ySH0H8g9{}58qN(B24<3Vi;V!fjGGM*)JINkiNmBxGcv3U*QXRdgKMY#K+H-bgLD&#O0x zWoAaX4c!|kUWxC_f?1q~Vl{T=@K!3t$}N2lRY6-p0Z^&6__YzuAz8|+W;z;9@g?&s z{ys0=ic-bXqUhFs^FQ55gDz2$d1Wq*R13+|SjGB#p=~`gz$uOz$Dh?)T(ypI!;++U z2^1kqeUav~Np>qKXlvTf#{%A^HXSzbdBkP&4$Nl(0NqO^_SJ3oo|K;qjDdA3TfS z)hEnyJZ04nt2`DY{QOgrIyOn%MN4ZpWKOB4)cn<)rdS#_QmV2o1!uX*C1?jInn z@=&ct+py1^qsD>y*AF8ravNY-e34MeNe0fLF|4wS=mzy`UeDQ@7TC_?rN=qCg3*sd zC&NzhViLkTG{wvlJ%r4vhPiLuNGoZI?~gDLm$E)VsrTM6pPM|a$9b&d z#R4!K;rL%wP(W~-uisIg;C1aV1mG?ZRwh5D>5mL_U@!Dap1z+=ACX<@l{7G3&43c_ zdWJvWG?g!7eZW#pT(si82Ea6OpRb|QFk1q*0>{SbDFP`tutdS zoT?I@{V=W31d5yPB#SC>Tk|Wfi&5fW1qTB9@ItBrs+*`{H&E0U4>C^I0d9`sur9j; zddViH0fwi0hX`7EDf|p=x?QEk6pm$Lp9iX76SJVB-p#PUTz~wAUrhj)n3GtDsqf?k3TmBO!IzhRSVE&(L4`Iua+T_J=5Y3Hp(i7k7b;fc;Bf z+lV44YV%qd{p`*I8OsI{>V9d$W$CZ_1x1ERn4Z9)`g-{D&vBQ8qn+ZGW5BzYqp@X} z=smLg&9C)`ag{YS^^V^UiEQHv>rWI~6SZ0?5-as;zy!~x!r?cWHG+*to`4VtI8ET>@v${f#;uUPH{7S7NwK&wycHPt3o1?^Oa81I3hDry z=o6KWi80Tws!&G`s4s`y&9=ozwy7{5sAq``cL@4*OTewiEnO|9anRG4#aafuvl+}h z&C?qF>Xi1v=h)L~B2z_w_f;PE73haYbp*dFWjw{HpRpM?{tub6tM14w@Hf=VMH>5X z_dbi`{X0p%;bX%TJl**IM+!oocBQQoYBm4z_J%zNkO(Bvag%j}h5T{9Nb;+aaqX9- zHukm!7DTkgZueBRlw|F=MT|XQ&l(fTWCP;<7U-v$?32p;Ez|#`%s1w$;DXNDQzHXT zkkLSzXDqG3+D($(Rds(}7oAAM zKPY`M8$Qr*^{C80(-qkF0xX{diDeQ8ZMx%&d-b_XDi_sd-Wj}!1=dXKMx9m<@_g?A z`lEE0hamo3%kmS;%e-;o-i7U$Ik(Hs2%dz~%B#xJHD8<%W|)>80Rcp5WE+M(YgeD^ zf+$Kb98i!|oHfpSF8$8=-{X*ksuk`@MLmq5Cb43{AZ-ghN*`?9k-a;upEO|DyV5a6 z`^*$Rwk2b*AqnIZ@M>BwX0UnUs1YbL+eD0=y={Ykm})sxW9^!|l43YDob~c^kX`#6 z?_gqB%6LF~{s<*Z!xKLB|R>s2Mhg zjph?_#US#p2R=&*T{0UCaMgMkay6~LUKuQM@?G04r+SQ_x=3IUyRHi-HIR5Wzmikp zFSVs}H8LIMLr-rLbH#&o)76N9ll*V3W~Zr7K*6`X*B7toY_pGP_*}zQdd^|<qn=SuV8AwHPgjwB<;@BB}<@30xpmk?Ig?JJ$5 z7Xw#zB<%uf`kSkSBoB{b4tY<4LqG=d^~EjGf6_Z2phjuJ4{Ji%G%Gevb4U^}_oZXI z(%bYDa5nj=GE}AS3wNEd^KAQ6Ga>7S@;8%XuCM(x!^$$*LaxYbnn;#RZ})nf>jh{* z&I7(m9SH>reUM_2+QAA0Wrd*cQ@E6GNSmLq3i3+Ghne%8Ne)#z6Ltpts$6LLt^N7; z;y|&e4iL1y8u=r%%ILeL>f$n*${iZeP0IXiJ6BD)RNzDjTvLm zPm2|zZM=82AdLwSeZl)$q8^?>>JrurYpuRphEARRnHL@kc52)Nps3&`qyd>OudOc2 zc&*9nK%o}30A3dAFjR5{##r+WU9!(UaqYpq?f-kkmzwooyeFi_D^Obw`Q`zfQcMb!B_I2Fu=v zTLHR_$_26evQO^ZIk`1wpm8bv{3v(>O$pE^pu5c%L9sXV9_VL!dLrwlZ0O-toTp#@ zl-WJ+Lzz+Mz2nxlo}aAAVzH9;pl96R512~E_oyLG&FJViX^GHX`I37Q6RBWuJ?}sf z;1!Ua&}AC8w^w^mTasvsgAv_7g7z$U5^bR0CpmbNBE(M3gZ`*GzLe!=Cr7QH(RIeB(l{l3Z*_&3-n^eH~3cEID}uTN5| zi}KhMJgR9!!)2B+MouaLnvn?2h=n%kVva&N zmfl}kE1YEus`ek4N@U%^QmgS*F@73se{Y)z#GY?99M@*jA5Yfnrs{9tG6M|2OB1lo zxD(o3B&xVcTQ7LZ$M+vT*pZBE6)Oid6FMcS!+d+fs_;DG>wHa_X53C)7ja=CEso~; zq2V|_u6@l zb4@#@s=wW&y^K!|v!6fn-1|jT&#LcK|E{XhvToo^w0uK0;OC&k?w)t_Al1>{-obuh zN#fw0Oe*^oM9Ve1<5_B_=_HMFo|Yf`YG)($BjVx(KpugvEN-8ipGc}oP21}562d0_ zRNSMG_9HFycj-IeLYb5#dNE7M&nn^3$#FO#*TKqeV&EkHK5HAC>H$;la0ul9?!P~> zABYElEEE7YzpBQ+YgIF@^OrNIpyw~emgV@ObVmfNKgD@TXIMt(W5uXQrJ-73YXbhX z^S<>c#;g@TTKLrVA+h0u-pu>lkVW-MFiQ;#h&EpaiSghUokB6GwKj;qNi z5Fqv&dJWgc&sB(hLU;Gy26atM(N3VOFH94XU=7wolrWr%HO;nOKq5-I8-)?KGwj;1 z7Ve^Vq2~cN;%_&HjGcf^Rl$7UcJSF!=lvYyO%0rW%pdz?dLs+cn>PjlmJF2R*g{=MB76F3*<1_st#oXsL z_3w9>xyheQlGXqIQp?M;td4uc6!Pz||9)^`x&H45Mt4c+|9g&E)1ypq(^bzNKAz=& zSD{xISq=3C-z1|rx_-qDf^S^JSHL5IZ-9N!%RtW0Z=lSlABr_f0}VgWUe$I=biDA(WuU=Um4tegIgP|ROe}{rHTJ@ z!6O+-aErc!1XQolpPTu3$q$3LM@QcEyi(=)_e>{UE{0G4tbtpLWKj5~=>7K@2k-vB zXZ%_pOTdgtB3Z&>ZWojJc%zIv1RTmbG|NwO3~vc$sN9&nZ$vnI?GBFr3uc3^H- z4<*^dW5!I!OXi_MNMxvFemx062V@*q&{Ktw5Hh!ye;phH#~{6jyIkqPbtYCM&}Ae` zjCjmxY`1b0j z1=06pKDsT$UT;G6geJnSlvW0j2^V!GGY$7?b$N^Kr({`4W&91 z+y5FEfXO9ZBCWtNk~&_a6KBD8!e?&hSSW5G&e+eQr^47QG-F4y`O+(Zz-6NCb9NNaIs@8E#Q_54lDCVR&Dzf4BY%5-ZW05h7EdH$`y;Y!NaS>ZyT z1oT(13De^Y*$=#VfG*EXXk+sek0D@g&%EUhPjHgluoSVTZrN(Nc?7@W|@6-6wZmpbG4T z_DF!PG)}jWIG8gwZ|(5?zVbhN_n6yxumT>UWc)=A$ZeNGNUlRXm%o zN(>=$$jg)00i5uw%#7m$daB%n09i;KH(WgQq6~wy`TmgwK8sUEz&!9Z;Dn&%Qhh%* znqcAs7~fxq8CTd%X0o$3{&E-&^uI+|-A~H*-y)o`%`73Fn~*}XRDK63r#gBQm~hz0 z=BwWon2C*fu)rqsk@0K58B&?!W-4ARS40x~278~l7rW!h0*}NZ%IlpXM*vd@+HFCh zfO7k_Z|m}fO9bXW&OkcHfk{1Dr49F4=ORlW1zn$@@N z53eI*m7LzjJby)i`uwd(3#yx^yZa~03f)hLPXE|t&rZ)r(4!G|s_iGOPZrvK78Cr& zVUc$PiR1%`fjiwE)(UjpMkfa6mkB~pj(exx73v}G$*4}3ItJ1~ei zxHLYpc>-Ak6ML$@yi)FKA1{LJ9&x|}4vP$aZ$w!$JU#mgYbl4tl)Y_ysX5yXmPAN%%)&_KOI}t|J?~<>)B4Esz3QsddzJ&z4vQ6T`iK*Co)O z0bi7O>IJhK`m->?r@i6R6HB(8{TWqM(7d(@p{3cKi)v%vUMWI$_@gg;+UJ4}2?0NR zf`5Dn-EUfG(g5cMbXEm^IRo|O0&}FN4XDL6yOXx{T)Ymos05cDVRzu)3m?PyiqY=_ zzM|xH_S)tUxs1Le9SAmrj?Nf1>I(D=29X`-qdYmnrv>PTcBRbN;1)qhOxe}DI6k%2 zfndVppYNRRkNP`H-x2j^{F{ipM>oI<*cVQuUUj>8>Lj{v>UzRe4WdVXL^;OdMbip? zqWF%^_chr0qRubdKak*B{7PpwUl#4*iC_*rfY1v431tqe5+(3O^^b!m+~Y(CuZQSe zNzk7oW2{Gk)$A^mYi5&e?#0K8-D}2G?O+7;<-?KI021?YDtFwp;lO^@Ah(x#;t#TO z%r=lh2eDOSznX|Db=(xxu)E`k`gmZZU2!ChHU8=7fjnqcJ)itova2cRRW;82*kbvC zdR6;Ii$h&vKDyEJ6aG>4m}Xbir$F?bVCjHf*FgGf$Dk+pZB7TOgofmm{vS)R(wR%g zgM9MMkY?2TUTlfPeAEs@+CB21K-_zSizS-lk++?Cd)h~r9a75D^mk}dIMSZDvTY(? zh=S<9hkQUONAE20>A>@AynRv&ylj=IWDy!c=8Lp6Swn41?kgXjdVRV_#9@w;q}8g4tl~Jbo3-FJ2-0G_RTE| z-6=bJj4Xpn;@k_Z?scK@65SIX&pI|CcLg3%(1(3B=BkDHq%8R=qQq}pY&~n*{7#c zJ`1xr1pfVOSH54+)eTWRUlk>kMTzBM;7FF_K@vK;*q=dhZP|tQXCn~*S{v9Wlu-WF zr#OtbtFH@J*oJ4dkROQ{)tzw|b7x(h==Z?A)A%f?fvL_NJuOqzS;WnwKmH*&+VL0+ z{tYe_g^tcqoLyk+9EFzKk|{qs49iF1riMP|@fCl6?0*zJrQF{zrhsaP|7CR7V<2b4N2@-OqigL> z;;`bbHN=l^=dk)9{!Q|;Ayt{$h0q5I=_ZmI$BdTtrUOAiE0i>Gu*{KJ;dWtxLzAPSiBm9aj-dMTr@R(1UtiE3=S_@IoF(vWBNe3;deVZ*VUQ*}4)Ij+%BMjJSKMpm)d_ZZz&U#PSu57>w~tY> z>|20y(ZWA2Qlu~{)cF5fVc{)<*&xly1L>}T74Q5C)BAqujREp5A*V?CFX8~PISX96 z(Up(>sL?RQ(M6<{bu4_GzhWUGT>288E&h|LN`QPMiC!IR(7?E<#JEK+_N^pwB5^c5yn z4!g|;m+pL7U(CMJ{Y1I7ntG2AYC`>f1lR3dL}-rM zO`}g#>~9`(TWQWFUT0n@$lshwqdmzrOc=|-Fm{5{zc4s)JidZ3EWX8Ue0oH0Lq0Tg z8dYrMzt&xNHitF^Y$oiV6R(DoU87Dn7XLtr!o>ZII_bR(*@dtkg^yVs3K$PB7w(L- z`(^{BU1m=S;M32p-M>{oR`OY3+&czI2b&F18}NKwA$r7hN&3qHf4rt`L{wd9U3`%a zAzkxTI@mB?sve@;B!tFcJUo@~ZI4_b#*b{iTUVIGL}J3H(_f?xBmD>O>=|_TD50b9 zNW>9)@wG#jAY=Y|QW#_xSd4}kk;keps)wfotv>)fAoyRJm-ulVYT(Eq8v23g_u>G1 zaWg^j^zi@11Bz08z~M>829&QpGdo*=RXyh#L@4<`C+F7T=|&5D{iDd+>jC1y_c@^M zrjCn>#Er@Sg$`UWh_=JkHB2w_{|{5V2T+El#C8VODS$FQ#|+T?_Vxju_^g25++ZP- zH_lbBU}Oj(mYa3u%wrq#j^=k9fJf+FoEOEVS6vR`sx@sVz03j*|Gt|aXs>6dbN(MR zBk{VqUZ7xGbXo!%KHdGqbD%192v<9ag8m13)?ak58z(P!D%D?h!JIo$p~SGs{wXlOk*$L!Ateag>iU1pmAjP<{e=^aLH)_`S#`w2~~ z5o}GAEMIgc_lH(-Gb>%p{Rj37dbB5OGoQ<{u8Adw$5p_f&YnuV`B;bSbolfjMr|;y zBG!Ju3dI?Fmm(HI{Xc`Kp1fE!6~YjG`yDnMOvRsP3t+J8C|-M}TeA&x%gz3bPiCOQ zPbRb!6wrW+&_hq)a{>SnI*{N$ z+56uEUOLz@p%Ff|*9&+X``r~KFH67K^P)NC{m3DWWx(HWM-6pZHAX=O?kVGZr16BZO#<+9# z=a|H2ck%LfnV_ZCq`&I(hZXbwr37UU8L{FdQoiMP9kuJ?w6@YZvl5XGV~pb}MjZP}-TZh;x{r$Lkz}^AZ z%DB3I*{#aMLrIuf- zJCdu8u3vOne}DX#LW<4U|sBFoySOI|+0Ubr*#gr(9P%s4Du283JyuEk?~Kx;?8!>ploya~C= z+c`?nVaRR#3v3U@ut;ljUsgRicASij`Yz9~4kbLb-lj~)TN)c|uY_>LA_57-bRne@ zi(g6kwfY_%YaeZVm-_ghc`9ZJxxc6joDSgll6O^vYC9*~Jslcef2ce4HBUN9pMChY20WJlO6z*oV;nH#%>oGy3R|f^ECq44a>ldqoiS7L$rn`r+883S{^;CB%?28d>E5iK0h$r3+QC!un*0Xv40~6u@_m~bS^2Ezi@AtA1~g96DuaVgOL`)o|DEThYd+TL0Ol_`{Mpr0ZPPshrHE56 zIy~*iS8D+w=Nld>cLAX%*j&ZSj;p)V5?R3`S9!!O1uuO(+dwP!YMw=kK#aX)+q&=n zB9rqw+pMj2YKOzoULY>k*9hi#l{q2ePw2T zTDb-!zUc;;QM=`hMQvY^UxGwG0z318b-r-T2OJvx5^=Kqno|l-hGZCxWzp&SjQ)*u zfVA%BhMUTrjMY~npPds1%8dt$BVb9(T1kvrrZ#{nYa}CQv&4iFk*V!hMR6B0Aw^$b`g{xDzVDBM3J6(HT}k!3 zu$sZiooy6Fp=%C!;SK9B z@ho~T^^Cx+YSjnI00Hw~-&h=Xz$C6*o!jaK);8^O%X~?u3V(XqO|=0bE@L7W89oBG!P z)Vjm@5H>vc5Ei~d6%|9Q7d)aTy*>OZ!Y=>35N9?^fz3s!JZIL4Y{TWB5^)ZpTY%}Z~>!&LtSW+tU z1g*nw{G}@l+X0QXmW3Sz<1)1Y`OEm#hvhN9DPCZu1up%yZ#llicR9-54fb9b<5;dO z8%KUc4^TPZd$2wJCmm2dguNz0&xGENjN1>LWcAeBXrFQ2>w_XlPIFVG)Qod5o8GZk zRb1XouZ{a&q7r{I>S&3yT+GRGp6c(ZB$TawT(Mf40K@KeIF~vpO6{ zjC2A)>Oy98XdWxr*4f&#hj-|Nwy(kHCy4!edW{gTVzt;mNB^Iujog@Pb+yuINZ`q- zkOwQJ`+zBegm)+=)b2u&To!()Zoi+u*AOrYVz<~7I zc8dP|I!TddV6*bu-5IxA@Qd_rbIRh{3g#qpc{_d@`WPV-3C?awz~8l(j47ysWb(Zo zL{NwI!6WUdtGtj^aK45fudj;CG2l+dASu_0hh+jHO$FDIE6)n@Uy1xSdA+|J;=5|R zq5ev+mo$fAe*dCHX%@x4N~6uL10fs8$H%lleps2OIxF33#Bjk|S+>z*(jS8+{-XtiXcq)WZ75a zUoSVQp*?NzY}B>Gq(G1FDxe(n?$k(iv9|2->)lz3@roJH?PnNA*s-gR{%LNc-VhV6 z_<;Mhm&x+^4(USMj>JKrgKtV)X2d%!3aw<~cvF^h!b7Qq@o7Tb?5n*NP&iOu(3{Kq zI-Q8TI+V){J&=8RlXLq5r}`In2BdzA?RYOa{++mq^tZ%Isc(r_9RGaZ%Y2|-Xkvf% zW|Z*{yHClLh&t{z)noTYfu(@D>v}np(?MwLZxFlJzhUl;Z)S~auFWLL=~>#^ccfX_ zS#chUln-pIJStck(NIdi+3p%r4J}^F#kj&8Qv;_8OJ|P)W$E!Dmob|_StBdn>ID&) zp55oB2%NDl1=Jmph_JjdMd|I)&ndai!@NV$Qz3G>&j)I+7sSQSi}0cN0t7^h!}D}- zjLNZp;aIw+8Q(C~R5W14dfELHPUYF+kq-Au5zguwLFT2qb2wo3%6-)+ew=L{nmrT= z7k`{YF(3_T^e>D|wqluLhh$B%w%eY1O-78(ZXsV|4}|ikAX$BRpEi4Sdq+u})l!+{7qb!*fr`TxQ1bmW>gMt;)HwD(t*4y|$QC^A=Aa{h& zb|lZZej9Ae$Fxo7ASqm$^`YjDvaqzUJT+Y^?xQ%-=~B}V(~^6uuldwfYHOLsRA3M< zVR?i_22;HpkRJ#VCT50Wk{yi?_>AK%^{ue>71_gu4d$p+`1rWIEK2)kc@ACbsn!olqT~na2V47tLFOK3z zn_w9iOsfUe&3${(EU)Xl*cqzzmtTpWlQe#^+m%zxhr~x&y=?mwv0(`K{&(8_S)$@* z5x{aqJ$IDPYW$5F-NUu}2)gRGPIjI!46bYI|0OnUiFOiH^qT0`K1DXLxL+ZU(o;GN zWsaA?iHfT$Zg>xwP(v)|@v8P3nNri@Z9dH_L^BWsTj;$lJb>M2ZRv6xaG6Rb^d8N3 zH70ehs-q_QNJl<%d($tJ?GLbd0$?Y7nsw(J_p62O&b~~URhGYT4YGn&_*H>YJjZ%F z`!kL{Q1*-ujt~zte)kpTXnmpZ>flnpD6Cz%KRT0YquvCX@s*(bf>CzXlxt`ZSMDQh zAD;wmqTiisWuE42--UXh(aRP(%EmRQ5_OhCB0#{2SFgb-D4AzqcYHaMVVdLW)1ltF zy(TIw{W$s>*m6z65p4~8CePD>RLLb3_&LooeNiXvbMnjP@E%A6==bQffx)7M|Cj0| z93oDVV%*fb|HwwtIUdy(_oTzEn)`sN5Hq@NE6qo)&rY&Vwh$)_EAGLw2FgJarAU*s z)qVQrD}{9r+m`F>WP4~O_GLTXq)tet=B%-=oZMu^kCdH6kHf|D!A8<|Ekb$)Dm=p< zaP3r1a&7&Ev2a)|sj>THp2wfZ8y}0a8_`{k_KPbMy&rc5%)Fy7?1v3gI-j|H(OQ(j zx}AMZkk}B=lNru3U}=k=LNm~)a~L){E%~^ktu;?oY^D&sr$-8Z#f}?O`?FE7W3P59 z_QWo>LSyth?qr^QjgV>$X>(eitoU2o@CwqZN`kkP{mKdU`uOWPY#hK2ZkvvqievjD zh!)w^Fi!R$~n+%oc|v{0AZ!NAv+->?@gWXqIvKMOeg z$l30!*7AIT{ry9;c8*62$j;QB&_@`KO5FXP9tQnXvdI(N zDOoW)FZ;#BQ}8+QkPYnhYr8X18p&s)1s16_cn3}n@I+eJjX1f3FBdYZ z4*1Ngg_B+5Aal>0nmOFTQ#8A5Sz9dSaVD-(Z(-}oZVC?;c59<4e2E);^vLP*o8b8+_!IT}P{I)T#S7O#C!`=*> zR8hn@(iRz3_q2FbY26H=Z6aE91Ya6wN3JmI_+kYveo?Foy!p(fAa2FuyceJ+FD4gzYg#WDBp z8lojdwRdcf?9LYS@<$d)BBI%}7YYV!%lv^5>;1W7Jast=2(!Tck9FAkll3 z-?%9>^idJXQ-~&>oe}6w%YLfS&plf?1N}8|VZh#S;cwwAJOsI2MQh?Zxc$27MpS9y zsPE}*PR2%Bb=Z>I=T8mR~Xs_n6Fo zg{`yZ>35u6S;t%f$sI{V2RrIWKiz1Y9#L`H^!@6Ozgr`*9YJhD9ZPI-R6p@>Vd$&D zf50EPP=1}sitcq67=BaY7~n6KcHn_b>MyKj3~tkUnd5;B-@<2gk2+PrP&oOA(IbvsS+8;4Uy5Qv3sIF(lsp4!_thnrHH7k+eVf)j2$cE>& z6V<3N8W3ll?Rh@K$u(dReHL9V;;U2Y7;l&BaO`5cT&=?CymhAt4KEAhmaNoyrgaZk z=g1^nzYj5S&C$Wx7=BZk>rP8VmQM@vhJAWb&neUhf5sVJJKg=u>2lTdpQ$IAv;)8xWB1*ywH}%KxQp+?g*g&M$mLVlv3f$qE9*z8F|`Bq z8?(J-rhu@6=#ez<;FO*^8=6Av%g*haWUmmO<8E*mW>hT)SE-%y`94 zsBr8j#e4qyIa^(a3ZE^er-OgWM?g0cq3lM+)W?6Cnt=L09iRaSTOL;yDEN`j)%}uR z3d+8B*co8QswQn~=j&-C9qU?K0_OvnX>`VaTOYNu0%b@mGWyyX$rjkE>EU1G;1Aop zKMXh2x_o`>toT>VZ)E@UCZ+B=p%17zkZtuNnvq#K8D;eKMUMEy+f-7K3qpFqq+-Z< zs@fLvlb^D=G7u-f;s|qg1C^vynn9BEg;&UyDQM}-NkUpOJ*nK5k-8Bs7VDwT0QdNE zL3!&THjeq+pETBg2Epm=HOI(0_jEyyo7t)g%`~jV8qh+;uSD1S2nz<<;*N^B1c47R z)rEd8_D-C5`oVBczk%X&d>7%D&Jf-YF!}RflRz)JoJ(4{f=a#Cq$(nd-9aqzw2U+j+1`QMVCXemF z_J0*bb=mtSbDd*s7ysl&7EHUmOG?eU@lfJ8{*Dk%D55A4Eenle8`7m`+E-vdQzKH5 z;TgBaAnUv;#q2nW79FoRzd7pkNP1ecB?mQ44b+%eCZ8OX`2v8B&{K9h`w=}J=bmXS zuAPJqtXK)#MF}LoCUuFt0lE;Kcf6MmgKG~hs4HXVyB^cA2R&;OI6S$mv+WJ{+>GEV^A`JN&u%n0m4`#Obty^iz@K z+E!ik{#B1-NQl1MX07?-JH4_4pC-k<)VJ90=op^epaB|sTBq(095LkI9}0Zzdr3S@bdV}RwTs>Ii!XBnLiOLVv$4{m(y8K*Ee$=Qtiji#^bhL&!W zQzxn}DztMv4WWj0*KySgn}z4hwzEMkVN(@|>jZ^m*Nkt>bp(m=rahn`Yb?6utaoF- z%P(JF)^|5>>UG3Is^>Z$MYqB!%rGm*Op-}_2!S9^O>Po4t3A9vJdR=BEi15!yuGhM zHyr@j!sTi zRZ+v*^4NcnU}Q?dauC(B-cIf0MF`r~fHR-ZTIt zxDvAL{|K!;a?j}65KrNE7?piP^J1Y)J0cT~01yXBXhLgV61NBk+ZM!!TE@Dmv%7zR zABwERCFdw>0d1z|vo)gAxXyO}eoC}XuYce$v&}g^ZJ-l+-(NkHWf!osY>%Z842g)B z8NFm%!=B(=6^(J_@Q=_?*RqLA629gX@k;pINcMrq4q!@BR0#U5l^v4{KkTa!Yx(f$ z*+MEf5Cx{CFRMk9)yF{`&uAkBXYI^z^6Xvx8pkg|%;$DADg_N|rylZ*PEMRoT-nO6 zrxZp)lp&vg*e%z*439uWsEE7GQ8Deu3wS8jrd`O$H*MEVp5qwch&-zAqoG?pF;{)srpsRp3;( z-f*l6n_S|EDjsE-{cU6TP6npb7iDLj}(&oEEg@M~9&58dcY_f+J;e z&Ja+;#{=XQx`EHteYd{U<#-fF1GP0kmYZNZ@7%~sg+*U=rg(j)>cX0ftkPkt1}1olLD#_AL-8p zTPd4;-E*}7JFlpmP)iDsCjcu#a;Da($X-=R_;-dD2KVx`{VAT!I8|uo3OfY`wh%lb zuFtrlLu(=$;x}phcXl}w1)w(jU|W4sIMxJEy=s6> z+57x@p%vuOhIXcGxM~i9%38cJuD8lY&X2+=hsA}=6e~bQ3 z2gkUx#qL8C=_|zU&x6a}v{!+D`^}K&q1u{1(Kv5w_JnZog!vh&HUIVsh zewBGW-ul&*U5i_ai}J!u<@yL}+!pYnrRIaUC)vu4hza&v$bsX#+S6ZRG&e@PdT0n` zX7Ts8E;1+jlX|bm`O8nlH@7M8w`p_>yj`J6$y@tzuH%LW0*l9>Y22E9;#sr_t^0HO zYhr5cmG*yvhV4#yo##i70gvyW5(9?}dRf1h>r)4Z@(}`5v1!hKR4dRh^;)xv)JUcu zB$S)A@P!?p7tC}^We1NGcnmIP%K@#`8W=3vKtG8rrq3hDmOWX5m5bB_1XMWlz4id< zEI`m{qx0+kb_mhgI7il92Q2^gQQHw{0+e8LBdb0 zR0U0+n_)w6M`UHeqH^u@W&={aNDF5|6m08ZRLTiB4S~mo5G~CwKI>5a{H8Dj8sk%% z{RUapAyc%S@!=brEcn;T2A|X;@gnmsP_Ad;0^7l(RIItD6xnL<7D*Dugr7-b&pHpP zfnn**Y2mii_*hWVg)X3?UHBWbQiG@!H+9V*ZYH~!Gd{>>j!@8oO-p7&dI5)y z`(@QDM<08&oDlh9kao4MD<2Tg$gy8E1$Uy{!>L91`|l-=&rtH8?st&lV;9an2iJ#p zsZ1+Bd?+1bkXHrdKh2N(S8-3D9)*(76kA`@eylX>X$iY6Cl!sA4|%X6nUca6HlrPx zzqEKM)jrIDjN+I8sp2>VIcO1sm z5S?lx#e`piPu<84mH&zd8KQ;U+1qlIVO&&L6WZ}>73jVkRPY&ter=V?5i>XvtlxR< z+-J8rmG}N>k1~Z!9@`s%7MRDum4`#;*O@H?XYa%*(04=>u`f%UjewT&itFM5C`N0H z6^us}>^FZlWfHeG`Z<za@G;D4qzt^N%k3^gs~FBrt6v# zB0g0Yo60fnYN64&TqW#{6;Llq9`r>qbHPrsS=N|_>|Y%#^k`u-b7hWWfFf8t1t>82 zQUaBOFU!gi=Fw<?5ouv2x!?+d=g0A33!J#{o>Yh zzD-^?s#Stddse-0N8UOJ>h&^l@%8g2Xf6bg+1jE{wLN#`RQZJ~!Jf12ZC=MP;6W41 zmJ+CfTR2)RsXVEm3`?6fppNfu;7a22;bsV5XHD1hq@D5;mr!jQ8F)d&_@xSk0}v*D z?0kAnJSZ*d^;~(q0@CYMm3(&qMm_7VeE-GX{S~U`gE>2MYvtgJyL4vWSu&Ga9COqg zB^XyDx&qVQGqKYpFFC8U3K6s16FLk-iYo2#=+;R|ob0L)@@Fqom?5g}5;%Vq-oRpJ zOk7T+oBVa(gF=7%#!gm2Pu0?Pj914lPzx;S|9($_z{ue<=NoZNBJY+yXI#;#LVkgH z1VcmhEk{D&9#OWjx-f{W#Al)mRY4GRU-i8fm% zb?5;5V59EhsvIh<)7CPzL*C(?TFxmtRgnbCI?IMGtkEsEMDjU(i@^cO~jGqaih-!`F(cp;L)+)KC$McF~ zbBQ_(ObJh(Uj*koudDqw{kF2kfZE)QK1~B7Z;XwL&3%YTU{nM>;Cjfr zg}EXt)Sf*rqti9}k=0NjK-_QjtwY@W2e6?gSkgL9l<1!AxF6ei0UCyF-QD@=A~_*E ztyyDXCt|V_t@i?q*TMKPT0e4z7=MQ8t5~pG&;mEU)|R_gYDE*#h!l322`A2|gBt&y z*|Q>oUui^TcActQp5iauN3HPI?FS(mRUoMhS;2#UA8KzF%AGb^%4;uSlREgxue4Z* zyQh>w#~>pEo}4V1OCGjRouh$rAt=q=VbXnSnLj6ECo|}=5<{%N5=#&o6=}38Wq)Uo0>5&Pa5|$gapof@zw@&UkhATmtpp0wAlI04jCgjf{Fhn74AU z(@G;|!4cn(i(BaltwMp2Mv{Or5xYu!w<01Y0G9M}b=Y*SiJV7;ZTNxHxBwPzE@$9f zA%Yg!a>Sn?Fa^=13jOuv6*(Hzq;l(b1;Wi1wT^&j08)PbIWB1@aeTTfDs&(b{ zTRDc za1v9oSm7itJ3OOJ?vw3`jQ?{wuHfmvLu>-CGN>~HcL$rf{4(`|w+^>W!7Xb;K}aHg-9 z>p49XXz!BJnT3#Bb?;isiJ(|D*Iz`?t)~Gp%Ho+TL1LRAP{Jmccb!OPb@YB7vGo6P z3Ej$@$A#juD zmVP()WR_%EpvHLFwHC5~()sMA0Jb3;X^YBNQer?izK;Y??Vs{oEL#I2TDw!f=(%6D zb4Vf;9hgC+zYWdr(P+_sc3p-ky6J~e4<%0JGD&jUX3gJj%e*hDSHq5Y@oPfxRh{fq zL{5PIM|NHIH)#?{oXfUKBHw@Ylr|9!+0wk{ChS)tbHJZ7RcQVB+uFu>5HCI-}?R{Cd&r$8c|i0 z!_4?)3Q_<;v2hVfwA+sqmKQGj$$>7EwVb?J3pKC)Mi5$CN7aU8PQpKtJa(|*ZBt9d z9(+NhP54Ng`cnviaiv_#8PUH+@R2u}@rK#zQ(%S)7Im%ljYzf#B|`B0lhU%-IB;mP z1!C2Jz|+gb%7bsM@mfeXyPVC+hr39ys2X3uJu&Rzu>%mAWaD`Gw?azh87q-Ne9>OZ&wDtZB8^6nPlKH$~7 z8U)MrdS*H{1K6YT!WwIqmF$m1WMP<=Nu3ZFAe)NhrDjbbZ3B;&4pO3bot?=4+yKT$ z@4tL*hsJahQS(aQJfb3@os=F?K1q{pee7Ri`B#mf>XYU~hv1PX&p!VU*iT3W+8FwG>aOb;n%}> zwZwjSxQud=F%V6wP?=x2G-(T{8}()smir2#Rs}Acc)VX5Sa=E!V~tfHuqpO3(n@EmPFA8a90|{$x+%V>b zPOuDv0dBsnUG($w9e{4AI;2_q9Vrep8oURRnd@_@{phly&vabB&FQJ_KB5vv$G$voRkW^kZ3 zh}Y{P-c_S8+a{)TT#i4B3jYTERTu7$XscEG5dw00cu4V%olK8zY?9H9Hcx!YG>6n}Ps*|UD)Sp= z<-w|0Od;34D-T+Dw!+cardN4z5*Z8D17nvgjv{I2izDqig0 z+iS;972PL&bu=nWAkJW`9eq~vVsJ(OQMteyJu4Kt5Q zc~)C3zX|UkXqxbtCf2ht0+_~jRtLV*TQmYaP8~R&CX*dNaL2Yn$$&;iYq#&dCb>Rp zWNSkSis+M18rf%ATqed`b6Q6&y2!|H1C|o zkXpgG-!%3hUa~X$wI;5&^ZZFh$Wy+Mbw$1Rwm+Vaj&pHCHRu}fCbwFc-`N5o0Sxn~ed)OAZIr3mg0+nR+~ z1RmHz-R{$BYHzP> zNN*i%UT0yQ-gQ5GhaAEgJAa@3%5(eZ(DtUUZ|#TELWLXzLk+73YWYcfdqp855PZI2 z6{YfQ=bLp2C)1uftL#YzF{km&-nC0oRD;u^0-7#X3M#%xSh6)Y*!9=)b2oX7lz3BL z6mjw&{sX6)7GAl8-qQn3a#R~46ik>2e>M>&kw}Vg7e&#c6Uo+s?Oj$;;CJ z#L{BLYm08SE4~rzvl5x|iNTs@@jpT}f0eRyl4G^F=N~w~Ib*&0e5)a2M0UO&vdp&Q zG{6cr!zxi3vMocWSuA`xCttesVn0qZt3c&)~-b&2U;8`WX9dU}s>Q|L`dwmM@2a74;Hv_Deq8A1#oPxkB5zE^stfLq0Tk})Il$W zoVEPPRBUZ%f-bVgnU*~(CNpcSZiKeuXj%dgf8~&xncvXa>>I_)BGuI7f4>coZccx* zWkh+Go0l(2;P`}V*TF*R0b-m#_tL!H{>mOKP(_2!m+bG@VWdnn;8JB^k<7eEIGtvG zw_?6lyH{X9(TEK8Lg`ERJE>v9f1`~cJ};tk3g*fEan=xfON6W5C%2+*9U{EW;WT!I_vQ( zgKtyf$~j9h39XHYtu1zJJzeZ1_0LYxigXtS@~sxWO{CgR;6-#KJP!xmmwR)0N}sBss#79>gMyo(>QN>n$0ZbB*f*c}APVhhfIo z+n-hp=#yW*R*pMGqekfK9FvvbV@~$l)KA&%GlhaU94n&8_uXZ)OJ&3s&3S!C@d_u9Ga5oqIY3o*Y)~L~ z*cXT{6!51cS>U8e_EoViu;kF;or{Q+~ z%SFk2LbyturvjD~tkkR}UV$Ox*AILb3j3HJo0BDF&JNr#Mx4L#3Tso59JPrE0hbrw z$CTDwYq{cOJs84Oi;}W!It#VFi^(V9MYEe$4{JY-zUX+`5xH6Ryu)_9id4V#yOF*@ z!>`0K*CY+9B<1)N`F(ff?v0BqJx$qWX(n+Dnr+*Vol9n~R%pFDnx{vCOiqo+&>%RT zTd=>T3_&4ye1@^y!Q!+@p=msG>j_JYx9RXbwnw+a^khwCTHuSgQcW9}g# zh>;oIwc(WvV;}GEt~#QG)J;rtZ~v);3KN5vnvY^h1;g*%^+$#MweI+=xhY$Yz_tOs zp1Qjjphh=itOT`>H(yDcZ zWJ@-@WYt=WiH7i37LWh3 zVmbq?w@RKA@Hz~r&81=hVT(?-Amw@yicoy zCw6w5LnBz6boR6GI^7GO)KZ$KAb+k+YI|K1(dL^BkWSZ-kHn|L(*%bkuez{e6F%=y zZ5GSHHZonKh9Jwr{Bf5trcev3XSA_%wbl0Fwj97~3(m>FMjS@Bx+P>@Hncl zPVnm{&qf8*mctkfNHGdlPjk!H3oc0JVKDc;s*`=J?E{5jT3aPSeua^Url+#28ti4N zr^*{Tj=V90UQ2koi9T5{G|7U$eh!i>WXt?!B8vmF55(o|X{idlGKEFxZJvxts9`jG z66aQJv_$nQ7J^mNFVpc|!M*tEVFZ1Eh3AcD@9xB)mP<-;S)%?c!O=&kXQ-?Z5d;rV zit3i0(0Kc6QPhkyaMnWFMq?pu8iJ|NFdk1GJzImtRBA>1Is!gg@rKn}A@E>XwEP6^ zztjE&l-5enQib#9N_EHAMQa~o!XqX)IDEgs*K|ty3miTyOTzdYD+}ZO2BeFyKQVvW3#bs+qTu% zZPKRa`JHvvI{(1DnP=Vm-XB~${59=Jg**YHOq#~=^=%FbiBv*?2TDEaL+Wg<{0%j%`ga z39bhBZ=%~Y9;7@7AfSZU#^bp=(y}Cuc>$!CE|oP5xD&*aAD*8PQTR)0tI^aH?k)@P zIuB!cS0l2G?Cyo>tj|aJb1mj$IDmLRFcSe;v5@PaFWp|*>}ZK!L7hn2OuObQ^7s-r z+&5`syP9XpR0E0)0vO%TF<1=uj;I>1-=&-rp>SR@5aswdIM>PGOt!0QZj*5ECGU1R z;}0Fu_m8)X0#wVZws=5G)N40&g8_(1Jen)* z=|J<51a{kjsuRQDjucU@f+Ju}prWQ^8$;^_XWCX0&ZQY9N!6>Wp0JJelX5@I>Nucl zo*0TWPjFoV9l@@EW;*P+iuLM4tpHQNnh)XSV+qpp5p}m0MFj?SoKLSLm6Nrj;7+1* zEOy@?&bs$#%f{^#w-rZ2m}Y}S84`v02-!e%`k4M`%c()_0!}|&(+ieyAaNWewppuK zddXcfU*-+JU+=!I664LYhBXIJgY&)D%_i^<%lyA@>&p`tXOe#^89Ye<{>#NP!W9R~VZ*dg>$Qi;zI_54?}f zN*)O%A4YX?O>7z)}b_+^W{LF5%LX%_&|os~POWixKf10a&%1~5to~y}jsq>AYI%oJt;%Gh z3md-Is`;S*s!>k12aoP)y*_l)AG+vUV9=me3|O5__yP%(5}xlx5OGcy{i?1Bla3AG zvg-&;Eg%Ge9CpLF!JX$cZS9==c})P=*}Pzeq_^9=vY(=H@2q1Jk(ayNO3D?90nZZC}%DtI*s9|`={5o=EDC?9^k zJoLlvH)nDKnr?~ysUG)Uf4RKcioxUVxmd&fUFsZr#fH_fp_^=CeCW*zJhia=U_(8D z4NV|}&B$Lyf7OcEcI1`+pxXbnNIMpSfA=;VI}Le-DY#y^wI;?{lF5@T{2+2Ybvq^Y zG-O5erOfCYulI=O?g;lkZsl`$`SoZ2zg7{+){_D>KKcW&&#^f4VPzzp3%~X!01%ni z()XJI)-QWQX0E{a=_Oyca=`1QV;Kr>-dAh^x)>SG2&jkIih?OwBjb+f*aqJeIX$8{ z;vo9WJb|>fBlZ`Pe(K@#G=@d#y8-qod`##>!FYxrQkwP-R??e$JXC64Gy_(FV#NJ| zDHFSh!a<;*>)bQ)+W4fnD&NR7+kGBv6)4600xX{(PVY!H-jhQ zJJ+-MvTt1j{TYr`!ACgZzK7o*u9uWbL;5(v?CP zghzYmhljcqv0}x4BpsiY{I=RB1U1`{eP^9{N`qvjh*I`Df1!8#m)UgY+|9~}vl(%M zMPHjtTzVfD^Kt}}|J<9Kxrtz4!AEb)U*K@zmwaWYaJ~5giHY+q@OLnYu6h$W@--km z99d6$qv%fxw04zl)H7|T=Q3`J6Yc8b^fxIbaB%rf1B^7ZT`Ox1T;Z7Hb*ryD9QcbZ zmJMp6slRj3X02MzEp%(XI#+!HVkSU8F^IX5;ZrkgOE?nHcmjIL9|v>)_1}OG04L-| zm|qf#+txB{PPO+i+BwA=0G4(2@xnRWJDf?Lyy!=r^m$(Y;p@ixe| zTpl^Ds3z}tKrV5l!G(Evh2F|J85@7V-n!(6s@k4EUc4iz9PW#mw&13BPSbyt9WGGF zGOtea&Rb2~jUM1pG6`aP$uQ^}bEqKurDXHrpPLy+FU`9$TM>yUZYLf)eYMaRYF-0s z9oUsWt+@NxneH4E1(@QtT(7je8Q4g!*i{q&k3GI*Eu$E`MLM5V+|?sO&ZGdi^8Bp} zWpkN)Y=}a{C8qxAZnpkFf9e%>`forlAAjqvFQe98wY#|}qf+^IWZiIGL}HXsaeM@( z&~<_?0o_b@p)^`ldj8d3xwBtQ+X(U*ZccC7xrXn|j=g`4gStV$4z!O9H#=t0tUvA` zOI(O#B1%X2oOFYm3AxCITbM_rzhL=VQBC-gvW*{3*caFs|d%x^u7JQK_1=t-|oHNp;U=G%H|42+w> zJo3n;>&BzpmZ!0DPa0DZI)UUg3Xp|O)!-6}FoquT^OPis9U5RkS0WfvgI%Bt745(P zA^J851VF_aCIUYTJ~{xkcto)6^uH@_uktq@*-q~JR5N?%9I{c5hgE#7$y&iu=5HOe zFiO(2&|D9t>sTy6fYoXJ#ev%IK0JPR7OPlx(ZD-?>libwE~6p0zfx~>P=%pi2*T+Y zA{b_89jlCOUE1rUk*6(g;Zlf76_}Y|)J&Z$)rMRkpCPaoF0y(R|#D$n}^ArexvvP1YnJyaeMVUS#)SmKUw;31ax*>9evz zb4%6;X!%kpQAyClSPer$xA{ivnVVKnQ`?PPwDQP0R^tmqC2r*Q=vpLva9H_ z@sY}8$Fz3K-OW>)I;$j`K{`V>%(}q3<^Xpk&1cT_8swBP%LxeO?nFLKZFiRWn$}iJ zLs(C}gM2@;re~-ZU$m9e2YiswP>#H&XF{7+x-^^60g&GLrq|}VClxpp1FEv zda!`I-ITR&$g@oX)A}c@)_4nj_E?nUF6s$|gDT6?Yb=52+?Ci7{)kS`0NHwB6@66& z5&y!;C`PJ|q)*!~Yd-#(!9KRA#Dk#{#PPg#v6{9UzFzIq8{{Vk&!IU{>3mnQoJdga zggHQUDFNUFYcU)Fo3u>0@s94rh887sGR8I4#aFw*iw|fum(p;{V9cKMgGqQ3$;^AOy@s)&{=36aickjhojk#lKb zzQbd4dRJ_-MeCs=5zy{m@g6pznM9lTmN6$wJUH{C_VeV-+8E zj{z;p$s$gU)n#voCd{aVoDMEg)bhQeeAzq=CfrQplwu_(KV}B(Ok-@TTvO;JCbYwi zUMW8ksiTYlLREuSdpFs=8ub8*c}K0E`E|VQ4z6r2HgrGEY8a&2)m$IdAx&@ApASn| z*}F0cn{FLKt(+R7pS+`Kb_?)T=0SkEJd7iPO_Ulh87EsD)q6z&n1-w3P#O2^RJO! zh#>>x*81b0gg}bfCsO)AYej9Oj#Hk03&|Bq$-;HmL_W?1?5yRuVu}2KO&+ zlgb-$CVu8OJ@s=ac6yDaUPjSQGZGLFTOlp$U{7ujEhp zxOzktDeis|4*6Uor)wpUnpe!$B*y{$uR?J=l|>dx(_-XlL_|NL5!sZZ5S=b(*iG8! zAge_?foXv7=?Bb@8f4G}UImrSq`iagj;v7PDqcOD<7P_!RxjmjYpV3O#xG_d?XN8% zjDxj>p@t!^1q$d%<06wv(Zdh~8#nMzE2Z>aMF;M4eb3y5wDqi`M>=6Y!Ay!BctcJd!lH40@!yzMR4YXe%MA?loco*f6C6K ztEO$WmLAuj+k4APKLuL2izuEeZ%AllUX%pG@L}P*Z%Z&`_?Zp~*j}<3s7mbYnh!|A zSt{El+Vb=tUB$Cw&b2i>op=Ic+GQY(KR5IcXRr0Ot}erqFW_ZYTlCLm^Fs$fGE!nh zY8;kwUFuK-$Svu3PczR_fUd{y$Y`k#B@1n-I6^OqZbU9io;BdK!a!B`NP5?WU!G!rlv z4WLT_5%S5pZcEwS^3fXXx-Zu@PM&TmKDR(JG%a&5C(%01FaW5WIW}I(N;Cd41A0D8 zO@Dd*cOZP<$3-~*TDp2P^@p&)@arK;-bpscUib~tqlw9zK+KbL(tq*16j^gFSq>X+ z7qS_XRf=>_v#~=Kq_!4qNSg>>#vFmMp%$Yw^KM%mOQzE#rtF~5_o-D7R75wgN|$9ds)M=kMxKqvK6zCUp1>oZ0{FLq)?~3 zO%CIlC5~Ud*S7L#p6G`^CPt3EiRU(T(V;Zo*&X8g6<53aCyQ_&So3=>-bhEfu_g8npqb);y@&)wYfR3d6 zeKHV0r)L1#Rgh$N2rn%YYM!vjAT|mbQ2gYqxO7x>L=Uc%_+<+bPbOg2PEOmR7S>XT z&Y>r~WmiFqum17TO?*x+sZI02g_N)YP)PpLr`^jfJO13jc;$gmSUf5~(6=xvd-Y_> zN3@AnbsSKUD>9E9r&>`{8|pBaj2ux5*mmf<>1lxGyIr5#SvzWBERZoOOWOpt$VN?N zuIL6VU4{-bF*9oapnV(sRrQb1$?6jwfb5huGquaBeg8ua{{N~AXltKNy#24ez6G&n zTVyBL`m$skz{WOGxO;v7P@9)RevPnz(QPv@(@Pgj>G1_((I05REtw>7+~4xXSXnzWz!k7Oil*q+Wo*v+t94iAyx5AI(N( zbb%SS=MU%yoQ|JcN)g}Bb^HSVWUV_RypXS_ye#oizwAJi_{Zg59143Vi1o2ph>-Eb z;BU)vO!ogl{;KmVQ7Aal$BNq$YL?FVq=vPiagUm{T&u$XHN`3Q*oWY`7WLGF4JRd0 zR=&;XT6|u5w>=J&UsEV_p z_P_!xlAjYV9or2paPUcfh5{RCs$jtsy!I`XDvR6o#@AYtEwdg>prDXa>5o)f^H`4y z+yffAcF;d9L;@@yTXh|98xEiIQN3bcPl1?#iYG1@&DII96Hn2-`FOA!He%XWVt}w7 zPKgWyO_*VuIHskUU@DxOW>o6)us)g^?$C0T>TFAeK*Sa( zHkOatcq0lRJw*r>Y%vfjZ#SPS15qT!))SC|!a~EI+VZlk{_R%MOuuh$eLCWSaT{4* zo~WPm^sjCQM>14Pm+kI23%PLf8?iV%EQ+NcmrsY1Tj+}ywaOLfc?koL-xlsf$N9uMbhzNoRG7b4S{r!kZ4HwLZ_v=Ro$0px^I*QjE zefS@u<9ExGd`>ORz@cGr;`Fs+m;z^Y8%YDZ4InJ-!O%?0f@*8LXTWhb;C?i~ABp3C z2vp-DtmV;6>(7&HfxBycjjFAJar???L>_o=Dd4cw!CzFbcemx2|N4f=4A3x)_*zt5 z^k=9%Z*Mpbe?8lQ1AoTVY9E!&v0G}=xt{NZ`EZ`Gx9fo=$o#sIMEK61`fb}MM_goI zVa>F7l&d=Uu+iFvSTXoyoh)L!#_}nJMLk_jK^&AN=c23idOtkT8-P06OQvIjlZSJx z)hK*uhhVLp?_r0P__kVuuMncLJg@H=)bRmQCBG^IJ;d77{xyy1HJ$o&Q>g*fMyvWk zo#vFYV22sUHC{(f`YDnp(4#<2Cfdqes!&Zh8>N5~^J34abz=w2fQzp$B8yI&cmor00P208pM^(n>yp~i#dpY>-xVYLnq$uxi; z!amL~q6vWV#Pp`#+4s*Q|4p{65tSZ=nI%Rx06xS?)@N5p;NkinqqGhY3~aokSySoB2DL&G z)VsBdk?9}yXm~LWYz+WFiCRY>4hcQ>imP^IG-fVQs%DF|(ragDZ6axqXvB}Ao@)^E zGb{#;RX@HK{=@t9h*jXrwJIoTfvRkh`R$pO0Z(CMfG`6~>jm5(k(36nPhn+hHfYYP z@X0EdR)1W9jdENevtV+buzj-KsICWpHINQ6QACORhaKS4c=rR662vD=ou}}en}0_j zs4ru;!-(ywUeDynRQ?JUTGtxGPe{w2^se-WGjSJoD>1k7f)iTZJ5}An$Q9gCCykQFK z&hu=QEq@9zex8W2Mp~Y}vHWrp;|br{j2>SWo+A>hyW99YfwPu70M(|b(mr5YzRTl_ z3A}HFZdMli^Uo7sn7$2VWtwZimVm-Wjv$_QuKmkDV5*G8-MNlNYu<_7CTUPE)G8ZS zb1fWjW*vKD(qt~fNi%b$jqU5o3@+D#mQz_jj1q*L8i2PlZifOw)S<49&cQc&%uO&o zL9P)g4^JWWcE08O-E&6=&p-`wjg$`H6abx?H3g776%QcwOHg>hY|oX^qh$@kwb}u) z13FOR^=^>?Z^zY<+NuChncAvHzJ>DrO+0y>x}CJWOTlEMGKCZ47TAcOWDETTw>;ce z+9Kw*j1{$I_YNqEzHzFhLdprvU-@XB1y@@pnhbYVd_G669+vx53CVJrELA3K=4!ND zDg}a~Sj3bHalE%RXC|iR+pBn*oXQv$z^bs3)EPsi-Az5McloC&oyQY z!TYO6Tj=|=#I1yXd9KC{IvR&RAu{i-BdeONe)P4rj}2>6XZ0R{r2*g$*BRBK$Qu2h zU>7rTy!(Lf!|9D=pJjOZ^dzs7A$`}jGmY2e#OIAKwPMJ49Zq=5)V*P3Huvu?Kr+eR z3=Fxv*F|iEBgu1JIQ10nC%Ty%=k%*llo>DYDz<9pYGrc)`vNebyCo~8Yk{y5)fj6< zJb72`4^DFH7fH`<6H*qdLVr>RTCja{bg{LgSo@umucVb$SPF9`yACz*kSEo@cVU!& zF|Q*DyGMoQqkO8w%m?Fp*TgN`93T*$4~^=f9klKY6=NP3hlc3S@E3|lfRUziH$*C! z83r-v5aqK-c|v%Y#M9aXq|_`QgYk~f8)N?<6lpyeKEnvp<VeGkbAWt3@+y&0l9e#Lz3$yK=^mfw1C1T zd$*1>!F*h;|KX1g;QHpOeI4Slfc6TT@%nJ11JK`hc8mumJIZV$&`i5B8z7%7K`Ldp zT!t^)X9A!h**HxSu3pT~zK_J20nhbpWY8*oyOR=3l>b(BVv|XB@z8}P6_N+`HW1@1 z#TX>FUw-)V99D^?Wp2weuKbretTb(*r%c+wOfc$p2RaexHfQ?r5q;EJf>6ToTLW_; zH65=^Fwe=?>w6OYW(&#fls-e?Kq+?sv~-2>zLT)j2>Z=!eTUn(Tw#yfo(R_wMP0us zE+OWjck*#X0EmR-s6}e=rRAr{^WOXD$Q8z=XyW9+DEW9oUj|mf3Ot z8yqv{fp_GRz1v=I1g91xlV)@~6bx7j+HOAQzI^xa|H%kTza1rz&>OHm@0i&;hcK>|txMfMrDBfex(!lY`sqb?CMB3f+kd z;mRB}p&&b^K~aGS;Z~`h4tWqL(Ip1-{B)4KV9HF)dkfmwV?q;LaUAjp=u3)7!z}bx=gb9ROhnlQ6nSBX!c5oNwT>i8VW)qKG zcD=GH>c?)|X&4F&q_Lr^(KECy3!l@n&^*{junrcB5l_3xj*ML?a~N=cMA0J~8qyc9 zZJ6VhDS(~(~HBIXG=VVXI!CS7lZWe>xLvX zmAa2X`-_N&R)$)BPDyu=u#pukCGnPohU8(dKECf8!8dDP&8)##9q3Pe$AEr5Bt5=K zOf}z(51&f&3{$eg7Y+-rq@L;!r$N*+c^*cz+rBcYfj4b;T~>r6c&PRIUj^$NHPapG z$JJ#1`~rI*>?P->e5TI@o7KQ&3F%j0>o^zm1*&C019b^}m~XM_&CKeQ0I*a(k+9zA zX59bKn-lq;aY^bjcdl=i9j8xNlbDs=$Z0J<5$e8q8W|lq7&pk<%~J;(-yH91>kqi41n_0~gq7g?;nht)gqH0>*` zg?Ws9uN!v{>k-+aB>jK~K|PEM4 zP(o)6@i>SyDB0pw-T2hybleTGAYlh-Q!Gno{ntor=G{qsfs|`8Hv0Wf@WfZpr#pKWPlHWq<`$ue0%W*?dy zoKyj{Z2I7)A>vWJL5d+^D~oCN^!}+C5RvRJ=PsEtUxMCENIfn_8jY_N2DiBh`cW^aHoSM4Lu;ckJ&(+sMZ;vMk zp8uvIqkXd<|Irv7+fwQ9CbK-&gIO{>?Q~nf@(pZXkanPSm`|@*pzy3sf7nL8nhB7L z%onL<6z(bFa5R~B>xT|>>?bso8lj-JmazF!zgh*EM%zL5X+W9pxxnI+IE5Tx4hgpoSwMI$#J9>@qcni`e4^~zAM~}G$F14ARk{m$MbP0)WOk)r zfZ#@ttzcsOoMw*Z(zZaYQ}2XR1B#fSjXUt2nD|`a|2nwGKYukc-VMxYz9WKNEnDXw z{^|3*lz74W0=(WfQbK7qPrv07Kjv6hAvlB+>mFmhjehmpdjBA;|2a|zSAI5MGs34* zjE*7fj^e|nd!5ienfA2lLUxsj=_x{y9n?0Ql<$nbno`Pj)#;0G%>+Z7L;|fTs`Qu8 zdktuB7z4`wVRMhusO}cl)OW1$q4%v(KQwIVe4H9ZiWk2b;br zUWA;zJrkzZ2}`v}2u7$M=uU~Mo@pI`dtT49+jP;1LXwMha=oAmp%kHSdAUDNQCnZL z)JZFM>>X*A$~46cSDYBfpN^7>g7FfrQ!Q{55ZuQzuuYb53Syot)I#_eHT3pvm;Bqi z%q+BOPETz6;r0p(!f**Lu4vIP7k1`CmMrH^(XvS^;^YR%#+tvs6C{Hh1;+_#e~T}w znV}Xy3RtAK>lv6N*~0j^f!in&I7S@IuB73hI5PLU1%OxsxkS!*pH%`Xan4%@E4$C# zQE=zSUVRRWbkp3`bH^FScx)z{hiaW8O4E|l46IkNwg}h#O{MfqaxwS$?5{`WG47SH z0G;92<34)44eb{>nv`;6}t{T&gcdP+Ls&~}97uWnyexJ$>#dGFy_ zX%ZR*l_xB}Zk^iKAy4s@$T4jS?jDO7xC-h;a?O`_89aZ12Gb8fY1UWphCsg#ltWgq zhJ;n$t5=z*SSwW0V74#Dh16#UYgR#rAc0wmS(msG7B?9D`)LZRxx=GzY$1PYtI<3R zI6}r9iu0%OEXQ$RC8+EAZ}Ep_e0W<#9(f!V-ofXc0^l7FaAA({hOg4$^21U?q^0wK z2IrBI^;B~><@QCr5Mh0_(8LS~4}F$h-W_l#%RX_pw{cqWPOKA`0j7v80&8ax^vO(N z`$5mnp8%(1K0Dps#noCV8CNg$mk-kr>=r?tLsqFX=ePoxYLK3p=6$cnA_a<|Y8$X> zg^_k7!{_EmK9Tf|xInpx@qK0`Ff}u}SzJk-2ui~#QO`_L0?-z*bBGE~)wGngxOYz~ zPg~_;BpQOsUTyaKHl=JZ@q5_`9N7&xl@wv<{)5mz1r=yUrxjdq%nVsh*0TUGOY_Ov zQUu%gJ?r>e!yAVr?RS<@E4zUGA%|lt{lmqGO(0l-?5IaZt*4X6mYXe@_-P}xgP}3# zT`nR<&|+tUdUrp&OT>T#B=}vDT5QR+(&(J7%jj zDpKn;CvlL{7@bVhA%s%O&W>IGLu#1HeZ{6m(f6c2JN<==t4*~EJDxKZp8R;KbLfRc zro!AVnMl3!bA8@7>kO&?G_|KL1O23fTknOTSNSikg6x>%$1gIlhyGYwbeN$O6D=V5 z;7S~oqVQHPcse4N$0OV40fF{Y4Mnfv{Cw! zU$9xHk-L5|uH8|)=><9uHV(Be)I0mbD@Z)sM2?yZ>pgPUIF^Q++05oA(b6-yfx-4A za-fSE%j}{yKz7KX%Bf={kG38IxGPQ(KwJVv(BckzHC$c;a6fBG=wti6aatfLmYE$l ziMTZK%QYsSz)eZ1e$Bg0MKz1;xsHp7Bok7_iC)|{OAUz>cs-JPV@-MDG>T17%GJ!0 za8+ALHoVjE%reW|3Yx(jNB9^PQ1ygDh&ADe?Kcj*_>!o5m}<0XwQ#eD<-QYejIQFg z_bo{THCvq{@hkwu3~Q2z5dAe^7BJew@WXh66kBV%^_zX;5|G&kyq6P~GA~oK+qjrc zdYY$izr(p~guUA&*(RI}_qIm8Q)>R0SsnfRa7#Pq7y0%_&(#8Uu1A1|)f`4}Z+e?o zpRBfVNza^f<4Ecaj+}5MK)K^TqfKdhWvHx8kt<7@MjBu0;7=di-FyC4_jvqOlOcDZ zji9Vd!@)-3jV5&k*RH_qE1N7cky0u5sz4aS^;qwfdV5Uu$~c2p7{+spFaB8$fDZ+| zQIoMPF{vDLg(#BW#8K1x=fZ(4is40-`O`mH>0^Yi(xLLj!|7L3Am;0&YK>rbhhe**Kh{y*~EWm2~DoH>2CY z=>Gp$jfb*@qO6T9S2S?8Y4v+mKtvXF*z7c3sRv=7BjU;S>rSyxX*vbSx%h|kM}v!O zje}CAI78RdCFRHIjfy$9Xx4IFPBe`KrqQ1=2%~dIw_1&la%R+t+}%l>{g+s?i}WQ9 zt7Br5lgn~NCR^4sTN{zbUSHvtgwnL^nPGbz)p0nW{4Tf`unaCd6$1S#ndO*=QFg0^T7C0@{ zKYTUt`IeA;_ifVXS$w>$2Ts_n3XTB;i@2c2F1D8ABqhsGB(n>R)^cEi^(Su|gm?mg zg054JCV%WIqJRv9pVDo&a!%i!7QTx@#cH4eFn?~o_I~)&9#KCli^gkpR(YshgIep- z5SXkoXO@V{*Xy6F&Kfp-cy$PjB!oe107{nbu(#pX*|Mca%cAKgpHNv;38(Y5WvJHA zqU#$EQ4uQ26MRQAtExvXIg3VkP|Vhm13Y)Y=4o9HyO2ku!Cyo*i3^P9MN!04Hd6%H ziT>1p$?w|oL{4L+M)=2XSR}agtFRXA+Iu=Z37`%vY+b@mM@bCR<%_i^A{l+0%}u>4 zo}~-=&2XVnn>dwZM#WRV6(@bb2|pYGLDWs#Sxb#aow(+r^tu?U)gcV{=(Tp{Fzg6M zsXrL)c}Eg!Ym4Zxp?HDe!h#X=L`vF}q?!l!tO4#G%&J*8nYx{FsRPls z7?VamZj-XP+t=5xT}w7psr7FYsTzu!>Kf2k&30I@)5p;G;SF}HMIYMN9H z;I?+T3E+G6TF^%7)}Hmxr4M?Y3<)fTgd48!9yPLxwu4t!!W|Mcg*FSZ+f1YWif7wq zsQwgag27+a;etskWEbk(I=TN}B}1w8O_ z6ZO~}F9M`707XU&+yd?|-6HJ$F#!M&keH1Q+}S+-e~9wgnt6ojYi;ls;d`F!4i3qbX46C* zX?jD7iUA)bSy*hI5pcSNJ-)c)q#z(lGOtRX@>eAPE>|OB$*v2pXC_Ffx3->_7GJ+n zq`c<)LEc9lWx0fWse|qPn_Z_`X2+qB8HIH8hhL7HMTi?0mQ$CptUlhv%Uq{FR^Ru5 zisiXO5F}HAL^GVi3pZ4mapySorU=}AyRM)fKbpLLD)B@xne55Ts*WC!2*H_$D?&?! zm~j))&!!cYue8a=j|rrNUX#5`uH~TrH_ue-a2?D#6N?222rWM(Hgz}yWM@WJs)u;&J!NohuIl#f&^NR5hUxF4{QO~{0m?ld;qp& z9dw4&<7)d!Rvm3Nv2bJEDn-837M|zaIN|639uI-)zHY|F>l>v5rxHialR0{Gz|7Pt zAj1Lls>&$A=!PXOCj61AIlk0F+%eOW;zWstYMj4(*q(~gzX@a-gW}1)Xd_@TG zs9yno4ApjG=8ceB##2PO{=dF&V1_5`zEsc&P07-yU0XqmsaaUjPYW22;t6kNha)n1 zExT5{I{*^yOIDe6o=ib{<+N-27sAi<)jjT zHVg?;#}OR+DD|`;S=13GVhgarZwk$Wm#s3|(FyG;Qkn#@8U{=~UBxTfuyh zo^++wWK~p3mg{>8ypQul8h8?zaIL%i31hyQE;Nb^6I;SA&nPZ}csnZ+b^NA=LqA#A zUIB#CCS+-Ntsqp zVO}1~BNHp=r{=FlmY@3l&lR+@ir^xCenYxPl5px4D0S!?|WO)-GPr; z0oa1~k>V1>&lZ%|Hjr{A>4A?5(DvQsXa4KSx_Mi!w%QI4|ToG}7gUi3qt93P1 zho2%WQ)44J;l?2VZw-dhfYSjyAFsenV%W!mt68sw65jA@#u&dEh| zAeN!BY*yH~s@Pn>VJS0Tj{Obau&?GhEg!7IOfiVTPgFi&R9kfF_H`&diz?_5QCR_X zRXSTZCY3tUE6c?m<@7+B;|r>p6rMD}8WrZUdLtvmcQ zDYRhYs|V?8pe0TcTEs8!Yg4EqUkL}wGRc0QBpbuY$N$trtuk>gw0}y+)itX6Ey>>C z$n)~(v35$ykNmDuZTm~{*Gz16MxEC^yXy^edxH{zu*}QZ-R*_-o7wy#+7#c>i_<^u zT6~k!esIQxR-Her@x_%(XGi?a(b>nSfi)ILA`Ry_y^gv|xRWVjAl6y29)~R>(jxSo zuXIl@mMU)X!PjfU!mIN`3x!^#50@$`Px+r;?&_*XJx1=* zrD(f4f3bGVxq7BGXqFzg%2`S*m%H_P=P6m?RKX1T$jMTJ%ZAHU$nZ|{=Pj5mF6p(T z*Vz-@-RCZ*e|+@|M1N^s)dn%+)Vb#}E);=Q&NYYp-;fpLl|wI*pJ>_R%*dHznB}#; z#ZWe}OEoe-ajp)7^{Dyz#E59kJ+;kt)TK_|us6)A>U=50Y~)1yeyrB3WQ(CANXg3D zq)byQYFd&MoVw{%GPTwA#<$mrb+sl~Z5Cgl8x(vU;{d*!*#7_2>AzwiPEtBGiz|2* zuI-Ng&>8=7_+owYW#dXBvru=!QeA500+a0XKA0~7q)Yef2)nq(LZ{L)_;&c=g%P0Y(V)1;JpFw2y5W*s`Rlsq@0T4MJBR35=W+b*|b9t(Zxmy+O zYfw^Pf^50=+3QHXxhS=-9xc^L*EG+r-C=}}5B!J|ZS4!N(QvqNe}0*rkIW)LlXNh2 zW4vBS&!d_dSqo3+6Hq{ZQy6Co?c?A=Edb+=iYv^3>Y2s;N#>p`PEw$Y4-kPOf=P^M zMw_!WiNQJQaExEBGWL9wavBR-?L>GaA-}t(omS~`P)7!-4~s@g2lz_P^tFUM-`vJa zE@VAMD9j26zIPU3tS)3s;hs+2fEO$NeYFPd2JgNFJO!Z~l zPX`0a>5h6x5p>xIH5^z{zHYj~DE^R<2fCR_;dK8MC5n>$i)*p^`v5Y2CI0WdTi6aW z{BQZDxHcahH8k9;&}VONQ4@@p4nGQtnpW41SlMDrauN(v4RA?`?9g$-N%D_8b7g;{ zrXFcv4#P|sRbw`Q5Rv(*w+^6GUi_lef%ib*X{G+Wr1d(nkDp<0{rw+r2KwGa^(t&Sx-x@ zKR@^xe0+=?uT&py^0)y-a(TU4M`+44l+P~3-uXdI zm5-3dBZ8tnh0Xv>F>Ux5LQtHo{&3A3p2F7_o9&p~D2!?}_e6C~ie8TIKuwgEs<`DG zYZGVjDjr>Kf7v8^mZA*22W6Mf86BmW&Zbw)@F#}J|4%iiCyCJyrvMxc59Q3k$Y3g0 z;b`)tEL1e$)ogeuB8C6@u zi$gl6c3eIgoek+vy}RTU>K{G5UP##vg^`UZ#)V7ZKT*)?;7+QtpS*wx?AsEfc68UMW z z)gJ4lZx?BsIW{kc`vgX>UX?_T$Uh%bkrn@h%`DjE3R|twU%~WR!fo<#QNrD!;f`SX zL9WGH?(jbkBV6%aIy9K#8!92y{eLZS#^pa$+80N9gJ9j=v4KCg!71(R&SGkqCU#i5 z0m%c-4&x%5e|j%MG?YtHk7uUyrXX!nDuK-XG2tC^W*8-Xa*{eCqPPe&v);&OJ;QjS z$eKVBH-`f6X5t^S*DrbWF5-seQDsYX{rll8EZ8rgQvOc$-y{DPDS5XSTK6B1Z}TJ( zO`HAjE2_*?i(31C!~~Er<0QAO)lSkFAJ0<>5Fj`Xv7%RykO3 zG{p7zqIB}6XK$~^#3c3cW26M;_7e_iov|$32ir#ZpKqoFdJhlLW<|D^^1&e9vO2$A zx+{-4WfVtmd{!giI2sGau=gcAjon~xWTz%YJ^S+F-EWW5*hRce+*73@vBEdE;wt#hnN% zyHp&@CFZUhnpzb%$Pz2H(>M91gOVviXR<1NHISaVB)xGO7oYUY+dO12WkbYVCv(Qh ziJ~l!J(LHzpbCpTp797D@Y9eV|3s!d2~Ao=T&<)Rkk$9(79C||XUrBU>oG1;Kx$I0 zjTDFm#c~9U%>w7aDF0h?YLS1JRpHaX;9gOp^@=Z-n-lYx5n<6%lueWoNQJEb%^hA7 z_k8YFLo#WKy0x-y8}$DCCBlqLD=XL@gO*~AJzAz%W@0pgOw*N#=lM>jOKZo7|;iubJWq?K6jzNzu9&~cCD3`U) z{hAjLeBE(&oIJ2Lh_U@3M}+qDc?e`6qT1CR7kEz%EGy&vAKv4L)9F;rp_9M--_k29 zqdyc9>%}M{PMZJe|2W1sqNo3%AO-%z%EnLk!NsOcnrt!NOpM}gk<1G$;h?H?sqg~R zjBeq9(ap1FB3lfM?e-8Qtn3uJ+oH%RwF!OY)$xHuOZGmvm7Y8F2q*Y|MW1eENM~{l zi|pG_op%arvW7}Xa8U<}C2Mgx>9u}srYVO06+Wn+32=!F0-mq<$iBKu^{+@!Y8g$z zdWO@a%KRshVKr!ZN|r>}TqXPw6@Qv#p6%$i5Oh6HbzeW*=h9}c(^tKh9?Yj)j~b^i zV^v)d?nifW?^CLh45?ZcnwdKF4Q!rT&SCA$0Rg{6vuas>nOsV!PDuy{5^W27EFbor z_-~xUCPBi96!n)&<@EoyZ5bBc&e`22iGQ6(RbRBnz6@(OD0cC@5CP*Pd>)t{7S#>m ztR6!9)7LM|Bj^)Km8J|8f5#W(gM1$qMFjpJQXj>V9D2kuC>=$~vq{;0YQ@*vAboa)%$rCTm(sYDKlQVy1@Cd&D3NC74u9|IWw}jp($iW7IT)ofL2O!;B#@ z4AW1ZiV$tQr4@8~l9(Be3OiufI;W(GCf10$?TYao*|sxoisSMa(j@VLP&#yTlb{64 zPb7i;d+2<(%ZEmt!K&rkn=PFKTyo-ssLw)b6|>W5k=PCU7zgPN6*4&$N`r{o4;ZN> znyL%Su|d8EN4*}T999JbaPWE6vM$W$6LEHAmzlnbB|> zOl#xlE@|s}0}AzTeia$vh83yM3Fp5-!^Wnc_+ z%bE9m3t60~ZhMzjNkVG=xB!2?LAJ|@rOxH>tE+w1&nOzaN_-4|Wz%T(6>8Uvq>s(qzdCP$|wl{9I_GR0&) zatukHN3{3EHKVtvW=4$k_8vbVuy8_e)RJg)j8(w($hqC8lD1!h&pgCvHCT&@`3a~+ zDIOgJPXd`2=6PCb(I)~&y?1EbRZR}u4xUB|UtYZSs_O!jO)Lr%%(c zWeWE_W690`(XWf$JyI(1zW*7fMD}-mBxvb1EOHOW8I~Swvia+1xq28sQuq_Z#kfP3#}94pEZZA3XDr?vj|$f8V4i z3wl3if3d8cUyu%px0}-ZEVPmfxl2|}n($w1$<=?;j0nB*1of&FP%S{~Z+5;BSpN!gKf-ugCCa3MJ6|U!MuO;vZRfq> zTX#u0o|9O2#rfVL&2Lj&u6GjnDe(F?sEB0q!h=P9Jc6}rDzFL+;)+)K_4L$IKUYUN zs)@=^pHFV0y99Z7XSwi8-t&*eAWLJmbFF)vIZ&M5Lq@Udw*ste2sb^Yh0=}phTjA; zcgXZ`ibR{{@XS#)i}(sQ8*_)M-(4>x3d zs8w$d!s9WC_6SI}C4Lbm_pVP}U#o;`Vv@>LFP~IP$=j^=6Ni@pcZZBhF3w_`#e(@%BlGzrC5pi6=E z1icvjYqO;D>aLMTK*gWFzMBFPo-b1CBQtSNi)}GgOGt@7RIL4WD5N-wRRjj}Yqd%p zex}J##ZbB|kQ2vF>4!1NN1U&cpWUN}{+I>TcPh3wL@8I9I8=Ulx>TG(fJR!O;gnaI zQFD|?yzsZ@w2<&=6QzIb`bzMkIFUz79EXiznrT)YMMK@=s=gqQaE!Pj$%rGe0RL^Z z=pxKNpmK7j^AU$5;!>zJmQM4c^AQ%o-=X<(-6Q9PtE=qdg-)`Cg(6K;tly1r8}IzI z#(4JN<51}50j_Uo0$#z+mlR&UvAd=DM!Bs#u3M=gL^tZ_xPhBbt~V<136n_@=$E(0 z+_uz7C)m^B z@naTsNK$MH^!1`iJ+LDkFC~MK(c|~<(-Z$hhWSfr2wO--Y@KLUNUXIjqz`M|4VWdb>u9hoXf7ij{HI@|wPRaFXfRZ08U- z@6(G#ZC<{44KJ`Af6<<=XkB{kV!CUrY3pRz&Fl37mP7YpfW{&P7?a@}w9qYnjAVM| z@X|l+a)p%MOLFVXD+okN?F0e(S3o}gLxke`h$&)Lxhl2g9vdh~W2)e6R-3Wf7+G|+ zmt^8q7wI(mX3h2Hd&YL&8-33;+?fzri+|q3x&ViN^tTn6CV;)2_%lP^;;e~Gga|!t z@p)>tZsXdbIyh_+2C!EvXR?h4{5-*VFHI0KjTayzE9KoxTIam;5X}JKrZ~w)nZ_gZ*%=|1ZqySUvi?NUgl!N2zmp` zE$a-%$%7fL{-zD&-l;EWhP*gyu|~#tulh$*Gfk*XI zz$TyfoO9e(UFw<|5}iwAT~$n7+4MC!1UitAYf3MyaY0kxt~tnn4!|W^zZ441@y#fs zTL~_^1-D+k!}U;{of4QXESVC@=(g9W-o9xli;s~MXtvCvmrqndt40d%jJNle%WLTfM#?-58<25A8mJY*n9m~fyIhs49ZLsFUBXTzl7no zgFegn-&rbh=0v1L)3{V(($*^4G4z-31lT8qbR&5s?yzeUktYQ=&JOVSlgL~Bg9?Fh z5?%dPh>HL>Bi@kAlQG7zXKk8U9)S8}*88JAjCD7`I`HB<)hmew9@_b-Dbq*e57k_k zybDuQc+Re9pU#^`qpS5PSJuc8MQ=oN&$^x#xM>wBpThpQWE1r-9`u#|Sh)avJ!^V7u}6M10uF_#J3xea;jwQx4DQQtSH$Io~?b##U1gON`$lw9@0=Kb-s1A)@5K;jws@g$T$sywP&?R2NDDX8~ zY0Eespj>v7cR2VH7HTP7fa`({Dz-W^8)oA)UV{8=PnPN#7J;uh#gXCkmVN(VI8+QMNiXnJi4y2Q z(Sj5*7d+pi8z{KGSEXV&9JLjsXfWVKMOn2et=*3x^xR5&mD5jMLpOqg=)}LsB^r=g zr}tIiaKt*X=>5$OZ~MTpp((cRL&Ajw|7}epmy3@t9dl4lAdPZ)sT%-$>nmcqhJ&Lf zoSgeSS9&laaub}3m3zq}0GsFL^Ca|0!XX>Mh`lNkGSlrb@8~oC1mfLD>;JzhK-iDG zzTutMu|)!1AxweEKT}A0djz8|qW~Y#_f>B~eIlX38Efp5GQrj%N~$@#!obOmyR_LS zg5*;U|N2YXu~z3Vl5*o^mky+_x+4*?+3xWirv8nSbOedlI9OHR>H(JeMn_q72XB2i(FI=6E*-(DGrJ((Nv{d+l^+TuNw?36TmQUTqcvH8epnopbozb5 zT^a?2oon6+VD$^pbtY7ABXkf?4r>Ay*H%3Al-;U7ld1R zOMOLR_4M!3VKp?wzM3>nIl+*qke)n2H%IsUGAUyWT~t3h7ZRI~|DQ-_8}hZY`Bgwi zBq~yWtE2ed!~fhDX`GCbQcg6G%BZ7uV(m`fZH!nUHCbfA{dZ@t&$ryC`Usrjc=Ntz zZ~nzMF09mzfl@U*!&cGdb4)>xfY!!nes1Bsn!@H4;CV@J4C-mq5XY*KyXw~~gtg3x z)+_)_hBBQ|Wi&Bo+>&?zGbvY&I`JIwtpU9x?oiBVb?26!j#T-C8 zG7OPMMpVqx_!bt@gH$u_W4JY2({l42-`P6B4x|yOIN8hXEQt&sXCFS81^^N58pY+~ zvY0`(eDlnV#T_s(HB#zFmnnf zhiW0|ae}MaAUnOq^Evo4LX)r4ucaltvDEGTZ2PYxx7K<3QVSwUyKh%^ZdzGoOhv!W z=P()BiQIrcFuNjX4U*18?(x27J2*($h&vz;XqoYpIk_!AZo!jf#mOrS^P8XSI{c4Y zV60U9(*0CPouHTbC%D8KsgT^A&%F+rP=AI;S0IY?8F*QInC0?b@%{Ce!5{|C{hxb$ zTGMhj>_NxU7VPhmv2)uDekY%&ZnBtmal+G(R}I(ux&Qt2#`(-c#$ywIa>6j*r$;>g zJL326T23x>Z*O3e8Yf4J|M^2z#i?VkRT`X6AVUBHZiuL5s(kd!9!SWnCQbQoEX!hotp1jb0CQ@0z8$cDGmY?ZdaWLk!$!0D2H8kdn6QSgP?rAEpbYMQ zr;ZlIE}}YeWB+%}os|_`<15^X=-`sA3NE4$6twKds z?aI?zKq9+{<&-m^dOy+*9qQY`A#RxbAewlQfTnsGPLc{_6K}$!XEWvCrbcO>T7Vxo zkt;64jry1V&gf?y_r(M>NN&vuKu16+-D(Z|Fcukd-_)ES67W7uYg6c=zkO;C;67wH zfWBPwocM8x_k5xqoq}Be2&(q^+Bn5s&z5~vzpt`0kXS+vj9FMs=Z}jzND7qH+8>!H z*Vjc1b*N5Vz*3ZneC}#aSb^IcZ!5uZ$wtFnu88*BYUlP7sv4hq$uGC^Gv%#5*&2&L z+XsK7ILP1o9xe0+bUnn+W7;pMLS($$!E*M~W-8qxV9`s(w}(fC2MCUrJ&G?#^6WIB zm|j$~CM%;P@Gk)}^sPW)x^K!Y$FE^}@oR0NcaBP+i({y_Yx z2fV%0Z+RuFByl8$+;r=NmYK5~4gl^(Y!Vj$%LU%|(uHshI^>vbGAINwSjI zKAL4&S!*+Sv#fZ9?-eUVU;OF3_HLhqW~;cu+FVlTe=E2K)64G?-Gee=&s?dhAcY z1?2B+v?w(Gk;QpPmyLo`MOJEnz|m|Gm?R$CaHDAB6{N_NA1X41fH6U%l6fvOJ*u8n zty~+~$dPe1*613`MWS@cBYKcYFiJ=mE!2%^le(e{=!Q=7> zsnU^b=t2!+-nkAoz;>HDfw$J3ow<(*!}*%A8`+5%Mwj4Oa_-tTxsybXjcTeBQJ#X` z&**BB{S4^^Xirj^kcPbk>LKBPWFyE=C5s6iQ&c8H5x8`rGyq(soKhphBDHEo*DNHj zD&fQSSJ261U)DseLMtn4x9iQdf6>vdavT#c>0-ZVDZ7l&aDe4eecpu|evIvX=h#Ce z{SAOaxVf_Xj1RQdO==iP2gX%Zi7}GFs3fAP?71#;XCa7RN(UIzw$cM#eD)B!W3m{6 zACeT~MTA%FD8BPxpBS$IJK6b&qYYp;_`yIg-<$WA?D77=+xhdkt%GTm!_@o2JHhdd zHE`Ujla!YL^^`vE!6v0>NjwRIN%pZrihVso{zHK;_DR0C4cT!vZ%C;c+T%;qsZX5g zzeoPIozh)8`Z~oNs#UM(-0Rv6pPk~=zj=@N#Lk)7)jJVNdAHZBy-(%wUE5Dgn3WrQ zye#)=(!XI>DzWD+ltuuj0n4QR{vafdUJJUj>5}>C+P?Zy|YD z=7oZ=sr`qzLQ=cmsictmuSwz{Uy+YztrL62u*WKo%dLX`JJ6JeDCIB|OlGfIH}GJ6-GocvFUz2}wCOvwvnY9$+@J@x3$Bz6bySjj zHL?!Z1^S=oUB~vQ#V5RnQ|QuZ+nv*H4&j_lKUd8tbN@LHvi~u4vF?G`p+jj+R3^`x zM@vZmz_7gD?W8~EMf?n?+8z2gJ}Arw#?>`tlh$lX?{XFhnf8=O#Lqp@l_}UCnv@mD zfNHItHM=u7#O7hMlffbn_ut6{fc_y+e|8on@eOt#mW0*sn5M>}M&z0co(?OkMjbXGN9J>~3P`{QxmA=TJ{tQ^e4CDn3^CqKi6i<`o1UmWOak_51Syp1a8$9?dL zZiK%C6+PZNRXh=XaH97DY9+uV3^DbFo3bH+R(?>C6U4BEie2!#%n1MHi>%3}Dld#S z9s3T=oK|>q|F%u9vpHHTchIyDPx_kZVF{a2av1tUgKjfhDD0x$kPy}v5&+y9@-ad= zk2cD5yNY>Q0roy-p-w{+o|HbE+J@6o0-~c&9z_Wf8%(d+F=+q!v*PcshXa4XAZuZE zTLZTa28cC$VV#W2H4V5hqP4z&dpq}+TAAq5`alPXWLb1mD;Rk51#WJCko@1Aqiv9l zGl#lA99-Fcxo&KnA@_0210g>djn%UnkzahTUwKHN*`DQgScufmvKB z4&!w(oTqLP_jeIz>k`Q_0F%8{C{+~n0|EQUrEWgu{k7&fLyqfs2W_$8OM)eNy`j6s z6_@A#RIrXn<@sM#h-s{j*GXBd?XQ~JKpTIC=nkEJ-(z`DFO^SY2ygEk~#9Z)aJ6noy%{sc-BNqY$+f@nMcms_tU?Ejt zyDB?~f*E3>Z1MXne~2eLYSqfWIe z=*NUMNf9OmYx-trMrsU;xUA(`e|XdnXCPYkJ-M>0R!R@^d337=GDRiE%uIAOw;cil zfNsyzN(%02S;@jy$e>z0m>`G!Y(gFmP|HoZCF!=da0}GS8Y+N`=<)oYvEwzzo=`?xHIn*&XRUDMb6h?mjZ=p}5Irlhi3 zL@}{=w5A*xb@94ClRi6e2b-WD#lbg|P$of{I>8$+u_btZxf5AHzeYUFjq?3Rm1&;f z#)mhD&^P1cG3RIc2zrEj1mI)2GHP%z(EtlCZt8=wT(ZL^M$!cbskZwExpY z#+NTVzGugVw98B6E$*mF1qA2NVhw3kWujjQ84rX^x1X7>pgA`D5nz4QS)7(nIo=*j z(LM>}gs9;aQw!8eC=_(Yg-li7oSGjY!-eNwDp_#v$eXy|}ik^Vf| z1+=&c3Ew}0Qd2J+HZ(|hQo%0of{^vxOh6e101bJhL=WKtKG6Q-Kppa+3Z!Z3-I6K! zxTo8TTK|!sK1~G00*z3Axd!&!7jPcNZP9C|if`(uRSE(PU=~W~XD?9tTdI-ZBsYD$ zW%%bVBjjZxEPt=&&wrf!PA1Ojj?Ya+Ohp$4>8p15;1m+fNOag$FQm0GA+kKZJjs&KwamvG+?=%(p?I2!TbueW~1k_Dt=z2U- zBBNv(@fE(vNPLN+7#M4`pOfSCiuh}PyZrP+gcOZP5;Rj`l^Y^BiA2fcqD7c64dx+2pTXA*OxP~=ex@~YuI!2ml(jFmrW24L>gg^D8u?xK2) z;eu;!P5>i>R&y{gVpDsQG9Go%rPOkAUab3I;`a|xkplv?LJq~#ks>*Gc)%1;C~y9w zv42#~bnEFpS8XqB6*2=K6cR=%nrV{EcsN(S&6XxpGe(`eKDoTAMvfL6WU&GjM`Fy( zypxk53^Rxz!%4L1|6Ly$*EMJJOdlK1=?QdKHdD?mSjZsXrZ3(qzI=wZ(HY}N1i+kK zqYsZnCKMR;T=Vci|4b?**%rJI?k`dGp9YpU*YQ$#n+?Dl;$g-DO)^qXb@T+oRyzPuszIF$nM`= zC7K_A0ezD&|%1J>RoGxxzc z!2eJLzyDf$Zm7TBgiwCCY2}#?L!CY9bp@lKsG;4CAUry}ys6e;o}W|h;5F!JWfK|108Uml$5lv^nc{xzKz!LF#|C@5_;Q*LGq(}2!*$XiwJyE{bl-P z7%6}m&8l#mYQm;m#laHq#YsL&g(}L9gS)e-Zfd(Z@1ur^zyGtJw#q7GQ0yUOrct&y z!;%-PyeS+O0bj>km99-X3pMyxA!iKL07ErpL$nLOiUH#u#+hweo)65V-7L6a_@c(Y zQf_?RD+$O@yzdxpcU}&p$>cm{{f99R+70@o6sLo2$AMe&9`022pDdh`q+X>IUC+%nWZ^uT9*`F~FeO2rEiF z2IlBZa44Ei{z6s)J1Nclu%BWWg5H(};CBsZAvmm;pT~elKj_?_)L7T7Hvt2gnHA95 zo?iHuek!ioP{>d>k_mI80H%b?ok6O?{3j&X&qExNnl%Z?*k4uSD6uVn9V2v+pnwNV z%`gh_Y4&>p+fd|H=Mf9ZOG*;NN1SOrZr~PvQzIU9po`+%Oj>qiVzwrhq3B>Fqej-#@&BsdZQN$0z-O~AQ%e^DSIa`17m&1>e109gQsO1VGXTi zRIjB4cC*K<%=3e-eH;<$=--;1HavFdx28t92U*+Zk1iBhaT1i}KqQREiyBcyOKLP) ztwfjeIG4(w3snYupNU;Ja`g9x6D^9~w4hnCN)pQmX|#XIP9x1;)TxQzc`H?H8MOQq zSMB}JA3Yt=2n74PMJ%AJ0)~nihws0=?#c#fm#!oDW6!3pbOCYY{JazJ z{c*}>Wmo6YIP3v28`85EG%-9X4)W$iQ){Qswl&>%lUo-|@d7&~{_6EB`5Oa~{pUtTvn*vhrF@ z)efa`39MKEniR@+Z$nK`=jFrj-=u>O(is-7hlaeeL*ALb)m3rHOVyfZiitXbuFKUX z6hJifDl6q5iHlX+B8f|BvaOR|&eb9&B4W57h(wqQCl&nbyCc7s$3b8`YjgM*s3Jr{ zR4PxMC&ikgh7gx56DZX66G}%{x9^m*$2ET0Y{=^v=kSv;ADeQE#W>A(iYizvZ;OIu z`Am5>mteH?q`*8EUVuQLi%VhZ*D(~sv~ixd%W9lcsh#ZM&!h==yRZFClF-P-uXxD}uQjGA?i@ zL+X`M>q6_Gjj`+gSHE`exQ6uK8-C@7u;9O2hw;mLF+hAJ^&5JzqKaoCXv^!G*MYfR zqMI(>?GMrFQ+jbLW?ybB9^DRuamL~?VfrYeP5j>TqOGl>rxhL|;(t}mT%PYWQE*g= zEOPdz;^BYij=CPOw4_&v>$ij-OIxa+dI+9Wky4LveO@jH<1L1`C2Q0iSqy2sUedc! z{l$;Y-%E~0NL7a2!%(t|+=B}z95(ez(;dt)lH3_~& zO=}_1(#9NxG&6V2IsuvnD4rvikOOl0Bu8&4>?ZfQkj_1sxdKD~N5Odde&5^U9H^D%`c#uY3em{SYy8;>N0WEm4Lq|1WyF@q}KA2N- zGZpLjmPrvN1_UmEBZ}kt8WKEl7=#+H4YUe$TtkFho7)nAF{e<6+UEgntq!86XnfW| z(mD>nxQCeWnogt=ovxTz{*P~5DkE_qdBzW`Vy zXVZ9JfovMhm(a`jF78WQ{(nNB)E3rmvRndD0J|kZ5?xHodb>g*O?FjI|5v^58nJ*u zCeAzVadY!Cpql3+<`n3gxwptNsP2>A4e4^ig0tjt$mCNhSDn?jeeq0~SX6+{dBAHR z;>=vDp|wTYrOUPzdfZAh@pw&DwXZ5jI*A}O>#UdI>UHE1+*Ds)>X3x>+_)zBC0D`G z|7x*~gU{X~{J=@4D_n*?2+hsWWeaqf0 z^2OhgQ!^lJHFPMM6m7b{9&$Jj4Ee)Of7#+Yg@Q!t-Lm9L$;)Y|brjgGr!Uht_vP8- zicyF5;A`}=E+*AY5~3;0eVK}{zObgjkvf>}UZ)=)n`OcT#`Y$F`;3>c57=a6j!XmIY$4hk)auuudtm`sK|7_qgB_1DsQwXWKJn-Xf%S z$A~&A2eT_MjDu+&9yWI}zHIldi=DZgu^mhp6LNn2C0Wd6BxD)ya9>*NIh0bzs!!o{ z@nMN{6F^(4{WsbKiwzeN)7+ncyUty)b)3!x^X~$tn>#~Nudxig?fP?2mV@~!`C@w% z3d4)m26PPk@?T4HCozTAB}ez9v*i1pc*W75W?POkQr!MT*BIu}vz^8urywsMC+)Z4 zVc+)8F-0}b^$5PU!@9K;dmMe|rUFD())XM=vz;RVm{VqRn4;|XHH?SK{?RoUpxP(? z4mQtEkrCI8ggMgd6rbi+2^z2nDpKkzotqs4(8sizvfz)F1=Xb-(Vy}N_8^k7E^PX_ zVcN(cpS{bNk_!1&$OrvWJ#~G}N#Z2L^OQ7T#caMRlsGNl9;}+)Q7o8rGjO74lnOppR-`s;3fp65R8@KplErUx>KBr|oh+E@M00 zJp18Q)1#DgWk>jNgxT5n$F^-vS%ySvpf&w<6V(sy{CkHt=J__2rZ<}7(Z7oCRVF}* zw*TbtQOLV{@(puS=%bdQ;k$k3$w7VWb(gEW|HzCP0o>(rC18%VIHm#IOD5mY1K5y< z>!X2aSP@6@{ybXdW?^C6MV8<>OXp}tLM%!3$onBj37OMGM zMIh-Qp0P9zl$LG9r0-VA0`d82{=z<5W~l!y1Gu?@dqcBkyW@?wK+n$@ug8V@`B^+n zDw6ON*32{yxKte?4gIyIs{Gg*l>FD)HN=iTS6{Qe8PzFTyNW`VTK$k1_kG@;dh_TW ztjiqeeUBFUqoY${|Cy=^=Q}?IVTCjZN$hfz)=_%aN;q|#i2m2xsW^nm10Oz^Jj1@i zgt?d@v6aZ8SQL-A#{&uT5PAW65O|i>c;zb%a<4m{@#cUhqjEu&mU*V9bS~W84T~0F zy+#hCgB-8Cm(vN4cm2+f5n%I-wmST;9fl-Fqzvx)T?@)Jz;R(Zy7Np%CcF)Y{?99T zA)mkvJhBlZNI_PXxXwRFkCSQ?$e#hI)abHiE ze0y=2_EJ6&*z^CT&3g@Ul26M!drh{Dv1MgCteNiCJV9vIX|8pND$p-7!UjCjs(Y$> zwtBs@@&LK7)k7ge(I%3%-%I0vzq?`1-Yh-pKwfN?jzpgh4dhSdZ2;R_+td>2*=Gb@ zE>}$5X8LU2AYaS8?_4xQCjicO`K-)Am*_XlV%bo<9O9~^zEXMl-|PxgAAz@ zD^Ek!I(c9O%le5L5**uFUw&u>8zvJ>0d;pY!vOEM{mG+U731+!tNVuW#oM!$m9&^< z$PKgz)XZ_JHSeX$J(xg#E*~dSdWm**V-OD+-QcX4Wbw$cRPQZP!W?DJF7fmFd_17=fO3@uJ%l=h9{VIDJtXH$-CHQe5-&0wPuyN?3wr`VKrm&)BhdExSp6-TMUW+16DT9H> zu=I+hL9UVLM|0P6*!E;;LZ4ksKfKOTpe6bws6zuugfjgW3q(<7K*4Ffp3lTCD;kb! zW#T@Le<9E36*FmRlst=42>SZonG`cn08Jwgx92Yi-zrGL280=J5Mu)fSi9Zp?{+zUq?Y> zJgg%q#fi6R(DL^Xw~Oq5e8u0-+rI=UnD<4XX3Ncy;Bm7~@J^hf?9t4f6EV~R*< zv);bSxv4AYfv$%DGY3=vNPBRpK<;qTk{$kw%o75h_9^5}~!`*|*B@Dhnskr0_o9`&A$trJo{@1ck?tctQ+U=qVp{)PXkt8%RW%V`G`4IsP481f&Qd)*SWWU%DcoAAumtO1A9c&HtiPcJVIW|C)$3 zFVh^>26)g5uo3dK`{E3n>l(#@_)2}At9}X^Yw-7{l@&1>_JNUqvR#`%PLK+|I|w#X z0WZ`FlUowzV}VxRccOYWB^xbaH3k_sK>}k1nEdWSDY!Kyl*FL?ZI%1y;M3m(C?#bD zBm^)8I?8qK9AY(dYQKmFF{Al%`qr#%6l#A*dcW~IHAHCB#m5dJ1VTU(T+!;)zj7y& zz-7QKtT@`46Oka5@=s-op&gh@{7KmwF8W*Bh3IM{Lt&^>_F+Xc%0X)6Y`FWwzNgI7 zTW}p};`iUvM`fv!Y!{G%PBsG?*EGsRQ^Ac*A+0Up26-n+>@aa8NMeN^zOgP1a2~gw3@Q9F5*^raika-A5mDvEFiZkGMeQmdr$U!?On{jyhou3O&Gra*eD znLmzL5|h3S7z03r9C3FKUbashKyPi{D7oHv;i5X_1VS?3w9NuSL;a6A=a(~0BKZ*~ z`I7=Mi|HlHK!t2Jh>_}r*a-1OR=F}h?~SZ;H*FyYWmMUPV)Yi7$J-Ksml;dU5+mC2 zB{TOmkZ_Nqx9g2vvN*E!w}Ru|e`*;+6=L<5D zMDAl#YbF@{=b}{8YZXkFhP_s!quzeeEsTB2r0N)1UC|@Zy<}NC0;NkE3%*B{4k4q* zhVUzjm=~g7-k}ucy&*Xpe=Llbawe7(dW+~;+tEVidG>XEngZ2}+f#ifXv~>3WnwX6 zVHSX1A~sZgFts}b(2{Udq_1R-i$SQRKLO#MI`1hf2J>Zex6Y%j@beg-pUC`ZVgQbF zlpPiqP}2cc^QL!LSfS(tcWCdKV_K%>j>{eha6jwj=rZl%K3r^y1=G~J5=NL=*7n*M zrx*jrMT=CgL;M$KtQ?9$EAjNu=pA+u0wrhLRjc)%xOb(kUvWAl3P2`2&C#I)bR>XZ zwxw4vc#rMdum{(De0)}I3XNTH&XV?M ztO5x4&yfy#-22d`+FxAryf3F2eam7^bD;!7Hr{>vKi4dzBzMhx>`liH>p02m$sqW28S_||Rv9aN#0&0ZI$((cz+NGaE^Yze41)=l@b+kpIv5}~xD4W<7 zIT13<7a17=uaLx*JO^(E%GX~ZtMxziG!~N071!Z_{+2#iCX*m0At?zu|0*%fNv{2m ztm7;1U4K-OZ!tz{XIwM|wEkX7SX(qjzu=W`@Oed2qJ3AguS@%;7vM41Zv*|2_gI&` zJV~olM%$jtX6q7e?5j!6nXFWl{lu_D-C1{q%rdUOP3m`p%0oax4g%)WWbV*lfD>t` zw0qjQ6ced^d>+`fQ;oAYfo@+%PeSS!p$h~QlXv~J=Ev?k zRPJSX&(}WPWRx%{_cN2^NbWS&1UFun_dWk8Afi;DMsemALCOzIC#jI|co#f!3|3|W z3O!y5LeDi|@&qJ((`rFXq~h4ZK88ZbiGbgdvKA|jrJ8s~ao>1JpoATw=|5OMJKyEB ze<40s#|!WddbEPPeR^8LB!sO(-tyMX6{S&4JOIdq1i`{hQX(d2s5LeOX|q%aM~RBS z=jnxQPUH+bGeUqNOxt#qU%oZL0a4#BMXa()d09I2n38<$eN5w&9Wo^SZaSyRNc+SO z45c2tpxnqvvl^+X)4=3%)m(094w9tbD>i~t$MmW-z*{Jy*G?7a9w`P!e=*6j8xEK@ zSyM$U3%jUd-(Nn!BYhcOr;?X;b5A*~L4&$KH^o8-hJB7N0#d$Sz6Ql|-AF+TMcI#u zm=dh!q#fMohy6Lvm$w|8krs#l%s=CozE1?_;_2o1Ff(=v3YZbV4WuS2oDpTU@G^gpBc)!+LV*KJ zd4sj3xlR%-=%E_|=;eSKKu`!1$_7A>O0tI*-X^m6>9pkep!GF-S+=Z{GOz!R@;MkqSOmG?`^R2t*NR~ zuksRju(YU#z4QYUu2>=nk#A)1N3VzcUj?S=D2`mhN$ia$<^Zqi^ck9aTREN$f%dP@ z{RIRM7Wm-8A3QZG?up;hE@4R%pWb%cXn!M>@xBhz)AEC7Kd8dZeJxx?DYh0o`k4gf zTrEieWfnG)E&J5@L=*+BLJp8X$A9-6OCwu%_&s9{6z%DfZ1eO-sea;v>bZ04%%?B$ z)rLNe7v~rl^&H!+U7kN;*gEVehfJNJzr4Ars?OYo#W8FKW zi*!4-3urY{SUw3>5!)NL&@b}(WpX@*e3QC}4#xO6nuMB1AstJTiYbbao2*J44Nvb& zdmO|lGqc@seow|p+uH@YR%(Nat^se^^KqEOx@dp}0<`sol?Ckm+>jz|8QPO61YO|w z#2Ao_%q#%_f)ju4)_S2wA5hKx7A^6R6Ecek-L!|8Jod<_%0U=yYSlkn&Lr^p{=)w;K}HkxQ{YPTWsM&B^0H_H^VikPQY`bX zI7gzBB-(_et-Pk+q2B+nAUlK6fWN1}jj&LoS4%ILjcRF4q+u)#B}#31lFPyvK}BX2 zlXj@%ndR>B8t|Xm2PCT$A4Lzc?)rCG2~Yz!DqkA>iKg3y2Qsx$q98F#pVLg0A8vmb zK&GZaKoXk}Ing5N;?i{5Eei-hL^Rd?V3QLs4t(CvN{@!1$^)Rzk#j!Th=%m>X`0`)OZX=N z0d11oU&`0akTbI?6eXK5l4i ztzErA+J70d_&%%LFax?kG`u;60UzRnXpXOhZzsRvEyVfwA}4U65JCaB4j~G}_A6*c zP4DIsPq``)`3X)p!f_0U#4Rk4%L3CNs5~B&=$V~cX|JA+ng}EBQA-1D@er;8XvIb% z%9FWsUB<`WbZgY6h{7solz$aPpdwh8lL)aNi_*Cs0*;*a?zHk0I1`UFT8{{|fJ&%ZH*c&+>T|pS+eOQ5trOj@YK(3e)FX?RS|y0UrTZWDlQvxNeoU z@`ou#Y)K%|3`pPFT{RSAz<`l0;mguO>5%Wqqme>u-^8$ts~vzDwp;OlL7}{I0{knN zn23ya@je=bJ0EER!8>)F4EI*HSh4N?$k)ekjYaJ;1(>KP_izm6pnoBtx*FbeUiMYw zv-jxv?vzd23pqMg+`ZKijLT;GPDPhu@e7#y6dRO|^A3^D;ic)-Vjc(lekV;|PY`j@ zL}|e)J-S?wYftLhdZv1|K5fnNeZ{PVF>zyHAizD#kw2_-tfF2|nn)h^qg~O`&7iQ34f7kaA4|h%1idG_RO=zB9Ye0B@aCtSmc28p2>28pEm(Pdy2XFw#zV@}&9CM6wl)%Km;laIR3k-Ygcsk*3A=Ix5fQcJE_(bKg`iNQ%4|@-v z&n`XM-_$V~kT!7*+F$F?ZqmaI1*6|+cZc1_m&4}oi|dPLfwV7P=l}b_8{2ja-8#y8 z&ZPaq)et9Uj~=Ct;NDrkqg$l@x7Uds$STj-1Y_UZLTG|*xb`6Z7t7~3@GS+gR$8AA zn*biyV#KjGRxh;B&ml;1Lz0g~3=OS6zes$#wU6pnI!;Cc($ga5nELxnd#ONzhIRNt zSWVdU++y4UpXkKCt9*t*5J?#eCrY$|hib_hDXrBe*~RqHeK;60C=hjaKJ%QLFq{OO zGp4BvJ0$&GCc@5Cd+#P1>QTDuBaUb^49gLAOg*he0bk6n?RCpAFaN90nUF-eM8h}f z-N)W+?zO%siMVg%@bIT=s?f}8rB@Wo3l{ToLS5flWNP&voB1=qXK&T)$ZSA$omDYzQVC@oZ{wt=+eZP9q`yp=rp&REi_2LJT#-=LC&E-u2YQT6Vr7X7KG?Gu# z6E1iN%6u5eTDH^xOcGV?cRW|UE1^* z#6J3To0rW6I-&%@Os&Yux{O=-SyCDW5EUHt5(+7g#f)g8Biub8Z^awvRNiE05Q4GY z#7UWNK4eqQ&SVqz$L72N^nJA}=Ky_#>ZqV1=2IpQ1P=Pzm*l+ydQDh;od{s4bo{8| zw~O`ZgO3cj8~~}xp;OeUF7n^IG`quy*#R#TNpG6!#8Qd|cx3oY8TqxpXggPo2P;hy zJF0PAPENI#3X}Ed&WYI|&CmUI7w-AY-(gqRUW1|0@#I}Z_x}{4J=#tWT$lw5#m>nj zJD|x5UQBGe{RFT48PB!Oac}J~QkqTViieBSxZJi075j+xlXjp0;{`)==6@XwR(D7S z##+A=Jm-3xv&QrgsXf8W#;sM1*iVI@{i`xkL^OOm@T zS5KS6q?bY2q>etmnQA4R$hmPxCMkaj+!Lm?94Fz+(y5zfdu!CfZ{4937E5IjMB({D z7|plYejgr2XDoo^v0D5W^!=+V20f#0_9;CNbHYdVs1*w&ciel~-bAYKhy^LnHHX@0|awWphLFlj+;J;1j>rM0f<`(;kbaS-QJYu2)fiM{kO`ssxMa` zN?)_jFxP%ot0jlZDkS`@B?~QIA^9Xo1Fm-u{z&-+HyWDi18dghsK2k&^5tgI-;UeX zJy_X9Rw~UWG4o!ePuUU%*VJ83dE&;C&-@vR*wm`0R!Ay?$PVsIx_A|R@K;HreW-D6 zD5pKab@fsDVNi0Mad4%mg!j3`N>-e8bI_&*#VWG7A<%7iN(<0sP#5V!swK+ zmQikF^S`en^tSpuNu5Huq)Ja$p4lvVS5#k=6!bw4B1@(i&w+7z_s21Nr{5 z4Cb88O+3^Vvqnpn2A-AePpQ2s@wGj4Pb((>&B%Egb^ zXc=$k(na4L1ilB>v;q#{Gf=}AM4vCsntY)O!Z*hCk2y+*-n`Dg2sH3;`M~(+0#dNit`<=TAOce>G^d8TKnY|cWwy<;)URk zHyq!(7yaVah5fQ>3NuxItk4o8gCPMUR@~L|vw2|})65tdJhuO7T7_fW0F_wTa;ahz zmd}4i%XvuAvg(qP3izC=Mv3T$Y8$-6?&Na7Bn>jPdzVxZ402QQ(09{)rTizR0fr%x zaRZGg`Xf7rON(u(%=Cq|7K`+W+9P{?Sg(Qxdq|ptn+L(!hGs%X^!|l@L1d_`AwzT| zPT%}A=~=k^esA7&lRTHzCM9Tm;f?ve);8{JpYGD^QuRl3lGARt)Vb6pENBYKW69&3 zgH(3`CFRv%B`0rzmwqD+-Bf z8_56iEv=thSe4i>2zcJ@V&q8w=={L3G0cxxOS<0rB^uj|1s^%dLGHVJL;Jv|=sE=7U((@B;AhC9{$5h~{;^kVSIyBrrfU94(l z!Dl_-yZwGNF@};jX3*W8bwu_g^Tu1r-(p_9&zC}Lx<~?#<~Gw|D@R}?Dev^hEk8T* zLBQD~_`iVBA8&_!>dWxaEHXgLi9a!Fvd+&t8KN_>37rssOJhw<$w{~hFt}~b9XRqO zM|!BN0-Isr)mUDJ^a>x z;&^Fo^(26glYVP)Px+Wa8ONqm{2)qlG@ zmhr@$?cF>0vvti)I7#ZTxVt-b%?XPce8ZOLV(M!;sVpIBe!Q~S+8L;sUs;t{Cuj6O z@2IxkBZ&k1`_=%12xXfGTA_+4Y8bq}W@Nug#HP~Pz{8Sm#e!a^sITLB5o7k{4=}C& z_a4}j#QtDEQUbe*Ww{!_A_I&vKpu5v3n)dF?}_1wddttUpDe`n(9irr_$ax;X(69v z%c;`G3;E?XC*osW$-2nIPOo12o*Fv}ua80-oBrX|RpDVbw$O2(RW0-3DG)K<{+q=- z1CL2eY!N*Ni}KTHfI9*o#B@|wpU3x z!r>O$#+qNam}WqAD}EI~7Pt54>&=*d%NmV`1s<%h0oNCCW&dn#xeU`BK>quCGRz1%)6< zOoWU&I0(cA*ZfAFl^!mAP6bNR?uBT&PsYe_(XzOI$+}$hVOLD)*`p`*-+dh^ukkjH zsxZR`Q9zDY2RoIdETnfyvi8o{{0i>Oe zIV=XHO!`TE2k%o!|92^8HoR{9eL-0}xW_jCJIQfia*8RFNo}%=b6M4$A5qcSwy1=j zq{%2R9d0Q2jCfBiBi2Yq7MqJJE7D|cQE@*D2C9J-K><|^Xp%V-MxzszvlKmK_M9MY zMBVBUw|}usTP`$^5F|re7qv}?v+JtB9fj}aL@__$rYcYE#NTNqT*p@9y9wA>LXOC6?Bv;G2knp3hN%pX%Cj(drhg) zsO2T4gHiHl`?EgtZ|3n0I8O6?Bvsod-b6{uK;S|XBoU;s*aeaR2^z@^>auLC!|uc8 zIGWX4yFlJg6SK0iP1C>4+8sKF#-(S@U$x)+K_1| zH4~U>Ke>u5(l;uv$M< zN1!5u!QqriJa@2b#vBW{Nq)Wu(5ue4=Wj3QLb;T!9)?EKM>Z3iq5qr&^L^hPq4@C1 zPTeEXkj$J-lSd>VRjvI&Ut}Z7=Kvz&@A@-I@@v-z&z~Zr4_VN#qf#Cfzs?-C#4H|4%4N4C2iUnRG+14rH6w7g{G30E)@#t z7c3dN$Q(M6(uvX|C6y3lafGObXvbHP4u=7&#F?W^y;Pc{RpwY|r_pntb@5sa^%cEB zQ9*)y%}R+llCQA?5eN zd7-(GjL#({PuY2eCC?eL<(UQGRxgdf}$YL3dCR&CyeKf&$gTr6cK2sv)BeRGP>`l zSM@=boYN-fx=d6Mf+mZGIti48#Sg#qbf}`l;C=rW$0<^Ap}B2Pk(CN~rp%f*(Ck9$ zA=kz(RA;bsdeW;}sl~!$74oKyp_~R5fFLe%fIT4A+RqsC{Z@+!3|qVW zbee*AS|r~B1Eoc%RN27@9=^Q1JgfPtDB3rf<#;r)5Psq+6$Jcys&*edM#i*E+VE4b zPvg#Yotr5T=<6!A(HVRjRJuqu@HSs{cj%h0LEa8=AnFJDp#8hCD{Pt%5eCpXD|epA zE7uPtws`uQa0UQUPZaZMD@0f|Lb3V{4fIC^co5?T9#7lM)~Sy{H)3Bb9paeaC#5L? z`dFDM!L{w4)c3#82tJ-t^LG|GXkaI)MPZl(lQ*GbI4ovRhltlrCQE7Cqrrrpuk1cN z>T~sHG>bh8F)S^12snroQxwNdUk1J(VnW78$2L%)gLaj^Rxc$J$hv3Gy2iBx1M@V~}?vV{A2J@k<*-$=A>K+okeJo97VaoIju0iG+3=cAFAH`#OO|N>cF{9U57}kKh0Y?ABc2aTHBr%JiYdRD{=aXF@~h3banH zL%}WOXmDD4;}q>efpNlOzT1Ram6a8`XReOxo_?W;oeXk+qLTi**8X>1@I(><{Q+A_ z@r(Z?t-QEv{sh&1sQJf;ctYoHuT0nKW)E=nZtsI4I+ zh8=uyzar$ElA|xg##Ap4yUH~#5T8u{&lc>UqW5ZqRS;q#J_91vwV18 zz@##f%K%*!jZ9B1hRDf@i79meuXL3}+a?eENxUQzTJ)jzWLP(8PJ%Qk^_P%$Eq_plBWj*dP2Dx65nf}Kc3hOZ&A$;QT5{Sx(&vXY zxBMOcv0@RoHWe(#OuM#W-l5o1-?cxC6XKy+X+8KoAkTO;lKRi5&n~A`#$MQnc~-4^ z;}~aWY-_93R^O5{H?c9Hl709>AO$iVsYWvVB$fH6m+YqL-Mtl(|=ok5KNu*8b0umgM3`3 zEnG%*Rj8ye+8E8fF#T|>2p+#x9ygSYpMDpWfWUANb?$(UE@cLCB+3NniJ6Rooz@`i zMz2;8#YQX&lLoo*f_9SbNrbai$yyDkb#JUORtrhI|HN~hUbAOPbJ1e<-4B2XI?_O= zysYc)57mui@ASWAg?bj6oO{H&;mb3=4fPNvd%9DFXJmrvmgpVSbKS(ju$9zB`16!- zcAmJ&%7!lCx_4wHYF=TI7tksJQO16<*jRIc&UO-kAGrX^f7b*)1fp4m_)q&5F#AXS zBU9GSb;1QlN)es3ctr1STi5)VIGmB@T8%+GI? zl318P z$XRAcIqoq7GK-cDh5xn8&PNR!z;3g`uAC*BQRDT>s3;I5O1OQLW&7S<>8PBaZ}kSe zBUa>64P>XL<%(&)X;!MeUb5i(okKw?BS2DEExCIFxd%TA*7M-&!*|gmOPG>k^LUT5 z_!y~P;CIkxNmh44^zH5tN`C*nNnV2q_~$dcS&Ag~8SsS*xtX|DJ?08zBa_9-#H0S(c#UlQ^ z+osfZ`JE5eOJ2ZsJ{!l)2oJ=xWiQi(=Or%qbQ9-COG@+}vJMNRDW}^#ES_9CRFt<0 zIn^6pA^eHa6d(_f@Gp<3a%RX}`XX%2)imTY0Q1UiJv@^gp<3wV907dPcc(s$s_OiB z=qsH{K<1Ggp#rKb*!6SNK5T<=4Fq8Po-)7D_>1UYOF`e=%;Vf#B83+RcRv*{R5E8v<15#t$pB;m{R| zIJ)2Xl=-^??(RFq6A5%GX0w62jWfzMh&k>NuxYX*b(LQ>m2=gIbu6k9K88vdaWamI zVR81ONbSNe*VVH}u_CFLTBZ$3R0P(rJ!Y5Mrf@2-v6|QB7n%^>jtcY0iy0e`QHUZ$ zlzg}fmZrdp)j)L36i1z~6A>OLcTEJh01$_ctl`F^3k|Wt6!x!bU_w!)-i{vFziDGv zJ#+`uEzTaY#r0gbpF_&f`GoKTC9fwACQMADrVmQgWu2ef%&Myy?%JN8(aDX{h!gz zE&LImuZ9}13w6lti}q{6I_mSq*a0ME#LLnuvWW>+T3+DLN^!SWmOHbXNcD*?GWqSD zlODnBYpx2un?BC&fs0~TO5)?-5DmW>ZUm?L)A{yR{*XzL8U2L{dYR4GUasr*K!y()u0pL~CjkpMpu zWcB~h4oI9oti71(lCD^YB>*Q-4|w%^kz$lo8jXGcfJ#R;1W^Gy8X1P3vzBv#na zNGiU(t;mBeDuS{4TwN*CD#}adumeawTTB`u2CCVu5qwxz*F8TkiD@a*pIBHf(?Z*n zk|e3p4}XTxpsS1;T$wQ{n#ix3W?==-y-~1}aHEUZWdg@a0+ne{7uN1)GjbH@4n2xC zCsiD>3Cb~c*YyD{Jt}_QUre|V8v3(t*1AI%st)GGarF9t&wi&w-K^mrcY~m|?SsIx zSvTdpjY~XD@ZBkZR2?=~sN-aHU0pX?!2a7&ZM#cDzR}wIX4n;KR)VlB(Q032UXn*)nw|+pX|}v?3#)wvp--ie$t?BgkqWC+9ISdM!I`7qx3Xe- z{d`tApYuzR9U0VAO*J3~mn0O+W4YMj@Db5JhUuUHI*0;%)=a5IX$2T+n--}~Zp^os z@L`7Wsx*4Mwqr`$jzO6DUkA`2mc5YF0yp4ylL+?$76oDYzq<+&fXL|Y^#rPu4O5J( zCF!`}p#Zg1F{?Zfr-a-Hvq3}KXWZk-(RFYjCXQZ5mcn5lEIU7cKB_+AZ4+lu9ac`ucAv+Hi_jleE@&-B&UL%lz;%o@*8Rrj${+lgm_3q%Jb{;@vXhbzlN$BAIUa68T)=3*MFc4!&PC`>E zjS1MndKyW^D2Y%mCkyS_T`F$GzmSt%aDHcekfLW7;zLjt8tJS+ z=dz{TJa+B!Z(HkU0+Vq(q-5Ajjhvu0D6Y`{W;AElL{;{V`C&I@U;l z@;g2VEc`}92`(;Va|FbzqKO2$C%{FjISio>SM8$!0n#KXZ6wohBOme9iiJ@2Ufh8B+!cl%^icrFW+BR0%12tq{G(t20p3cqyBauF z3-fp*(D9eZirjYAQJP={_w&dKFX4av6$i6aMi~qxk_-nwUXk|ysldsH*P5LacFn9M zrA``(7$>Avivh!Zi|=ixBB#)~w3^S5 zqU@Sk!7Klk097>X`Q{6wF~6X4DZLuQH(d@D1|A?WMqv=}WUwhz5BHW65wc?ul}oolvA*k2+zqvl=SfmEnX3#uP(~=hAT{V!L!IND)OBaML%E`H| z`JnYzTBiYueXnus;WiRzfa1Vp#qla zQX>S2bvhs0!@HVoT4JIpMi;fakLJ~#h!{SE8T{$_a_Bh7C;u*Tds%X=CE0cDuF=tS zZuiIQV0awFs@|l9?18(^FnPnGT5akXB@>bn-k~3gxO$NtA%?Vs4G#vb z5++)jJfzfRxtCGH!(sQBNyd%0F7;nJ0e*gdN~apC^3SalQ57RapwB7M_`wY4wpKAS zUu=PEsP%?D^Lzh8kN%9@f!A}eEXw_C^hr_CXl!hY#6`z<>Rb%x@{x~JSoZA6KuUKk zFM`?C-{qR{Y0#p*eJof&l*6)NW>uLvBy>#21?4l9f@P=z4$;?JNCJ$U7H=d)g+5A^A zbD}HWSdK3$NfLjm1w-v8f#??z>ECVvHSlYii4$9h&4Gb5{lYbC>=y33Q)>A${QEr& zT>`1Huly}-Hz)26-(X`QQ;8Z#AVG7Ntl5AzU3X4!broccjk&fYlAA+w>nG8n*jf+e zB%#H;&BQ_(+*&)T!;%UZncc7F6jtA&l*>Qm3PrIZClvNbbJMq_)_*l%NC4f7|~%>e|cZS#uf6tDZHaj=I&kRM_A8a zD5=WfTmqG?+bJRD+6)|X4d{Nk*pq+#rddTs$_0K|+F*euyS_KmXBIsca2S60W9as; z-|W^mi_-oIr@=u^;H&k>Yvuu?wm8d8zj$01TNEi+8*unlSDrqW=`0q z7if{_&=bW9eEQa@@EG^11q+rBpmB9GM_A$F?fNVB39FXwfY*)swYNSsI>HwL85D2j z3o#t$Ru57Ck7rN*?^Cyt(~>U{&+Iw|G%S!lTtg&ffpi;B*Jp9eVID^w{ArYU+xod; zE93~*M$TTEL{w!21bOj9S* zw>1UtdIf_POBWaH&e!LGzm99GJPxmaXw&3Iu!-KjUYaee^y=tKx(lQ`C1Ga}_{YZN z3$$2g|GAPO55K!h&R^J~_`A@`plD*!3ox9w+zsz#^(m<`vDQ>K{8o4cO7e8$k7QL8DB?~2hEu3BYUKi9(FN|Ab#wg&9YW`` zS6-kn&+Hg>fi`8zd98G9d)v4!f5iOou{WmQ#OKEM>$yDQcl52=H?P!r(617*58%5s z;HS1y>#-K){WRXZPW}}Er(G$iYD^Ar)oX_pEyCzx%J|i9+k9lm@jdzv zf{9}TDZ!MkuL`Rc#dZ7ar`JPWTApu${ua0s#NZJ%zBFi;5P!3hQt0*%r)KhYLZf6; zLni!}R}sf+4V5G6%RNk8k1@JXfbi`DI+UKX<#^oS0;^SqF<#`1{{|`gNZOBNT3N~h zt;Ho&QpV(OlJbxQGA>BCbsv}z+q3nVd4*#)RqEQ*w!-Nn88U3~ei06Yiz)lP)yV)Z!6{4*sKmYh)I!QV8=(9J$sj zW)BPh8u}&H?6E0c0La|myriDmg3W;#W~4tP(z4py07;0K89d%~Yp5iiz5=S8$qKwri4={EnPqzB@tzhZ-h6 z)OoIFTAKNt-8vc3*cN&9N{yCAVTvg8lgGPss>m)17?7#L?kFjb%r7Yyfb9|SCiy*! zJ+v`fO&wu;jI1RONYph|d88yj{`(uPkXG>vnX*(ReKbU}Tft45=27^&#~KYN3LYCV zi>4^*)zMM;UIrcO>G(|WZ=meTSHY!4$T;#pL_IaTG4eVTV-BAD@=9xjVkp1<`^4F~@<2TkVuk4bg)YWYdbqTB zt#Vtgaxp?l6Y}(SD{ekCWHKE`yU(0#jT&cOm$W$Y+6Ub0yivB(rLA`^QH!>F^ zRq~AVqEOWv8H3Bq)8S631EzV!NzwT^DV#nG6`7Xy<@>L-WpVbgaZ2g?^&f@FDiduhW2E&!? zmj!#1@zITdON4Gtb?=FKwDYiHwdLSqvpzw7H7_CE7QqY+jrS!MnMF$?q++3jK~qHA{ng zm^`MLiJ(T8*9|B5djVJyZwJ$9LesVHi+(lH{V-uN;@@K?NMSzjc1>75;XYR4{`NMN zw6xX?N2{S1qse=&*9~yEVdGa;raOZ1so;h-KK0tqf5&kCTU%Tct#Q^+pDeK+bN%AkUCy1DkDF$PF zT;1&VIIZYSgSuYKBznE*aLsw4q>q29h^QNTMeqLW`6wcMhh9E6YvtgM`?&BHPlQDiUF5YNusRj9!2(ng zR`BsYA4|N?aN2g-&`>&2<;KE<3lCc+OH%`qD4|S)1RJessQzq#ok+Q`HtySB9RijD zSXTQ~Cm>lQ;-c>+>!y#nu1T0g1FGN*>kPeM$AC`d0eKPz<-Lb(lSk!QV>$}eeGT^C zvTWs?Hpadb=5KHKZxh~k{!Nx`nb`Zt-^gpGF@hu)v`Ax81+n z5R#7!{Y8jU<7zOra|$Vv}VyXbf)i=@ZjR&?wc*ZDihb_^7LAF65F)RKq5AV7)s3#1Op zw>VhB@iC@)RXz^=vXq0vi&&BW@g2&G@7Y3l5E3g#Jd%~=^*GpZR%a)Kb4RuEIPi?MG*Hn*w z$xSu>U20JSZg90-+mxzL$+Fr6%F_pVN@^EtzEL%56DfxJ%C{}CLBQOnqfpMv;#Z_a z6hZ;KZqHA9GURod8t9>l)3#H8{~%87!okgc6Dc{#MQuwE9v50oaWo4FUZ=eqU#5zIbE+(! zZ7&AbIlQGGAB`LIP~Ybc2z#LJ^&%8YpZi?T|Ly|)HC34Nhu8kkP*UUov&s14=|;i$ z6VKaSljhRPvL)%!Twj}y>iOr=aqQ;*KT;jS9G9vAZ^2Vk+(()dYg4}jxvU;0Qs!%{&g1T{M z`-F~73|$0hH=|QwO5lyTK#oh^Li`%7-o7$6AOZA(?L>Onj?iht1 zR}K{NSmdH3?;H)ZsaF=s%ZZJWWYah}fPE6ocP<6ZZcQqXdiD&3t!(1aa{8?fp*{p9 z>TdUVr$AQZQD^Nj+P{7PAfX&LQkeW&T!PshuR+>^s~^xF=^D zCsC(O-S@$TVolAW;MZkeFZdCG5l@}6gM!3Y=A(U$Pgk2IislA?!dr9+h+YyGUouxRyS z?`u#ll1rN-Nxlw)8|x>8X8R#%z>jG~K~#_Vy-T$hO1g}zLOn3)sXU}x0naaLq4=eH z&U{oYV{vJ8ohy=DBYXnr&n(!TpDYTs092q{GqV(D>Lnx4sB{oI>^Z`v$DkOJl%%+l zpL-24O?Ze!`~HWYzb4;VyoZWP<_)40R1c@+Z6;8{BOvn8<(U!@mxh^SZsud-zI;S{e7h~X*cFS6Y=$_~fH!+rP5HPpciw7xrlsV)|?%np* z!ote4DSET-elgzpCE$jD%xR(%vSfvIdQA3~Msa|z3utQLXtxoW3gB_7GdIVs1Pmc> zOk^eM{@!5O9nmpqm32*n19&&x+!2#8mb^t&@A7bPY~UrT%I4$s0iVcowL*~*ow8hY zXmeejL6`=TjlJU3lioW&Ys49+eZ#gQ9r^4QSvu?H$zikZ8!oPeSuP*~t!Nr_&AUw> z@l485A4ecu%Z4kEjSFd~4+pt(o|4Y4 zT)Sud9DuSOs-1)B1)nEyCWP*vGPbH@OUT{kxS z`@ErrOg3f}mjbF0O)xChos{q%-uNe(ciAuEsEB7WSl_IQ}122 z<050kp0zvsEMA>S19F^f8|hJcsG!bVtIIPg*Cp1s@@mMLLJA#sJ!lQEd(ij z$;Hw|KwcKS$|HPo25=klW=vXVVXBH!ILs zHl^Gzfq&c1HPPdB;ug5>EAQxnVq%ZGcZ~nzT^8XBuP2!Kilal&U;n!o$9_KVOjR-P zK1^N>30s_Biwe|omVNqk@D?0_Cv{`&BmV&i4bTTuqDGEyZo?D8*({g@Hr>V5&xuyM zxRNIejn#RlMrX12Oc|8T_@HtfVp0{RDCQ)RHw^p79##5%T0b#-^HOKIZ}DQ& z$eFxtiBm`zps)Y{z!&L(#Z}KiZ-7H^JZYkCYB6uE(t^l^-ht4MI1FD-R)2CU39pWe za7*Gw7;Mf%zqrwtl-tV7QCBVE?+E$X1UcHF6!i)}M;6RWVgPKO>+2Rvyir-G@6Uh% zk>MP@ze!6RK$nm>IM<{(F7>A}Twz}m!HqFcRw%`{ODF;W39cvm=1K$uK z5BkH8VZr2t^WX2?66QIRht-%9;hAoc zrh>)?%eLVU3M!x!cYx0Z1ao_D`ic26#ORRzBZuifX8I%8J%*Ank~%2|4Qt;Sck0!f zjS4}hQ{Vp#SEe~IbqO1NKyUVeP`Xzd+`!eDjdHziP|wb{?P50(gl_yKiL2&755TS$ z_;uy}KFrchjnI1&>)$c1{eIN?Cl9YbWg2E|`4LS7OEVWg`EA_g_L;0A#Tgs=e0X^2 zV6vZ3pSalU3Ij|`Ecb}gs;)p90XcF6zrwfsg`BJP6GVT%b;WK!;3)shRjIh~LGq<;w1}XxW zaoQzh=Uz|ygjNR4Sk`)e+j6ZS8jIz>p?&J@6#9V;S98FA8tu~Plql?%+y~!U5@n_{ z>*IFwxA*6gh-r5fPvw$Qs3gyR#Vnb=I2OT4D@vLFgW}vqJ85rl%Em`ICr+%}&& z1ik7Ecyt-5;CzV`DUIS1jy0%>pCy!q^Z(1q%Y6+EgIUe5NB}3RP)67r_V(Lb>(3nx zVy)l3CO)pVP7OvL%@q9vo0A8y_C@_mUXrf^E%JIfP&9^n`n_@Z;JoyMWNt=xPWIT} zUCY3izBo0qzM=wBIMRSnAsm5us|7%TiczWL}N%ttBkK>I3FLR^?QiR zE%IhRTtw~PvQ;YDsWfBYizuK$71}RX~X}f^4k9b2}}so zLJ0BCUo@lb$cuWl{a}5}lGkeeBYbXGh^w$#zsY)Nr8Q@jQoU5utd1$TO5coefk^Qp zwVt77=H15lvHj6D3!wqL+1|Fy`B}=@x_)oihju-^-RIT2gT9XAKiM2ESq!;vHZ*-Y z3oy9PABDjUM9k>R_a~y|Y&!#DAN7kyNcyP4zX07WE_~8EugQ(NuU7*+oCA!wLe zRN2+M$Wx$zF(LxfAHa*<8ew8evk?#g1p*wFSviG_>Ud2xjMU{3)>a^^-)TwC>t%C2G4#_@ z%#)MNpSJ}4Mb@R)wR(MCX6iUsGquLKyrQp5T+>tLcb<(10OqraSpZ2GKI>gfWAP!dAQx@t{ehN4=f z(Zs~p*V}L5+&mF+*0O0_+@Z&BCFUK_eR8&3Q->EHU5W0nHjxcqO|2rDR`Z_|bISw- zdL*RS2C-cVWRC`3y~!$Hug#wu{x}Mw8ib3zl-)MpC7kt?F0%u&E|{YFrYRa9w1Mo% z83;G?-D=55cX4vbj9Z8BzFw)vp>A=lmyPIUtT-T1V__@RrxPqs%NKCm66W5^8-b;` zR$K88g)Q{e$@*YxH+d~A-q0WuUM5`JWCl)zbL6<2TYhjNZRIcsD9e3=H^JfmIw*ng znUl_1lHV%K`{RVO1Z<%H$^e(XycK3iWI|fJY3Vf;g#BBu#-!N0wuax5faJ-q9A>|u zjv5{G(Vra+qTEAnfR0Qo}?|YNzptHBEmRO{#X=qLorCL7Y?&>;hf-h8& zj}HLz(i_1Ki>bTlR~ZdDV*{c(D5Oe;WhgbuQw+c1H#QbS*<`>`k2mxY@^LuBbrF>L ze#c9CUNooDHy011IUnJEhkZl|UuP&3v)h*T@9X-3s%8!zl%p!qMR>kst`nWtsulpg z`ytAttLwbDxA1MbYEk*$oMbBO&PV-VBZ_C?sZFSVrk-6;a=P=Ul+oW4JXO?fflTZy zKfG~_1j2z&@Dp(!_&iI|plLok`Vjv0OO`4kv@W#bRQp=1fe{;Jt`q64&6KxuDa*?t z9Bau9;NB4Qf;jc~YTWT*L$Q%};iV;I&jGLL1cIn*Ea@e{BXhIE#(^o2m*59ou)G+#jt>L7POxW+ht)b*E#-)ut=01tx@Du0Q1G;zs)Ky}oC3e#uMD>e9$dmzLnyj%rW-DBRYBqF710 zmch}2L#2Tjxa_+ZWD|2-BZ39FsBb4QoT8w~s{I7VK7%3FcF+cny0u(QZT!!F0KWP1 zw(~{p?CJi~mH)61=SjT|vv)nba`0;eyY)2DTl|4wz*+^`b!8n1LU+@wuSf-tkQFx| z$ID=j7E^DPEQx^G8yG*T1?Rz=B`bHp=ehaV&2ilq>moBQ0yHtOta8>fT=AAFVl?Yq zv*`WebAhw)N(cS5#bntzF-2tAZe;MLAO@MZt=GB0+QAu!Lq5@BgB+9EkAoCsJ zvTIn$ip_)Be3ED{WPHTJhF2v0b_Z4d-7J0Hll&tD~xlzO5}fL_!)Qq@`0zKsv6pAR!>Fbf?lF zAtl}2-QC?Fed+GJ^nIJ(d*gd!yuUvGa45<>hqKRKd#$;TLONd);$I|{ zTci$0`Kt$1`>h=lso+x1!F!0=X)3Wwy-dRxwTtl-ZJmu&fpih!E~H8T_*he^qsgXE z-grfmza_LD5`h;g$v#Rfu9 z52QWy2fB1L)6XVS7|a%zjSWc(D6(l(z9oH-9%jVj>}d7az*AbvxqZ0(EIUA8U;tP? zPR1kYu6#aw>Cyc`(a+bLPb}0rBOMYl)s$(cv@lmc;;GA1S=5ZZLt`r~#&C3ya!aXP zqRl6LrPJicCRF@FO)>M~g?De2h?o0&tDH$&zQR6fAH#4T3LC5kJs`c(1Dz9{cv1f8 z!-ReNml~{O|BCwjhoQEoH-nsuDfj4rUl>R8nHGX&X+dwxI<2~g^UT#=T)a|VPM^ho zN9PL5+=VDZON5-5>hl+M=$5xb?@5T-4EMckOzGd4aDIN7GXdmYEX80U?!QgyC&QsK zh(rNHl_DR&yO}ZP%JM6wzvEaG_f+!0Q}=yir-CspV<9+hu;V@*O-I*UJ^`Im!CcTV zMNoGC1N2?L$3!p5%m7->tjUj2j0Tf>i81E!-I{GbZ9oANZ|HS!{8INy#^hX;;ZK&v z{_So5(nrS%XyvGi<_H+@2a`CU!;w_lp<)5Vj_#DX=M%siqzC^4L<)V(0;7u9k)zGN znbF)n2stxC+LWNIRXP|-s=0z4RIjbG`-5wL{IOpkRh+>4!4{pz0FC!eBkb?s5A2%< zrXXqhsvzpg>0$T(K{2LWizDC0@L)GpVnw@aNP5x{mV2(eD>>a4_ns)b9#26zqOET< zRyXr_@rcr$oDeb7o!osi2zcFQT=WPJKZ|af)>UTHitbNJUVT|7-kf4n;&_sd`jgiW z$-VW$=CMRwZF0x^NYeAUq5{++E8Xul#Ps8kWfkc|RPA%6G6H~X40Ur@@(82F?JgrP z@a%*4<7Fu@y#@rZQ8_MGskt9s1?nQm8_OoMb`R?ifHsd7-~cQ47t_VS6S-jPxBiAK z73X+1>NVD1Up@{oVEz?Uv!rYhCH7^7PDu|#+RJ{I+O$N{Z4EJ9i{`>LAE|iH$uha8 zP)!wc2bx??xP40<0tUBRt)0{xL{8Rd0Ruq&- ztdZlW8%1O=i~TACDXLA$4m`|Dxg7NDogz z8nlUawhy}`j5NqJ%{Tcajr>eg?{|divowXFgb;avQ{T;QraY=Vxs-$&YC6^T$a(lV zOiD=oGTUKG5aKs1$E~%qvQ{WfMWe)Ceu3Kqj|a=3o$$x`MEuQX|?9^ezXumfgAy2bk2Mj z>!y(^)~~fxKFrHLoLC$jLfQp>Bcm5zTgqju4v0(}LaNF|uP>&LQt^cHqi%Hin`qf& z*^P~G8ziPHpiSt{K7;A&9fwyyk)uBT?IMgtTj^oW+l!yX2X(C)3(=y&{0Y~SLl`)c zqV&{8dJV4no{LX$qJPT~Gb0F)@$EdK+Oz+bnHvwNB_G+nAFf7k5h1=pztd6K zyIGGtFU&!L{wlus5EGpXUECzr_N@O!ffmh8)1#0b=h)aQN_mu;nzFyIQHr(I`v>)3 zjYmC9na_ZePpd`2&FSZ){eG5s^b}vL_rfCPFMgi!24iB)=AXB7d^hTV8#6k~;W)^7 zuC#M$q|Klo%s7|9_57Yu9q)PXS+b1!G3AOc{rbxe7xScY?cs9PNY0g3;a;Z&^*wbq zPVeh>0eX5qsu<^TU}eg$#T66{kOvmpg`Be*YIwW{i(1axd@#(w3xu0>py0|9Ltm# zqi5d?E?Zip4WiP2r97m%BQ8kN(FSqrzOe3Bi&L9SkK?q)P#5e@9W^cvZ0}uv_^W5= zJyEWmjSnm5`sYQ&9t~8bu#hHi?Ssmt+8CB;h29o?l#$^%q|AJivnBNj?r>xms5;T! zJTB3V0th3_gL(?`*oXUG*?J>`Usa~G#}+$!OpN`3_kyc4$`PY((?Qk=`U$m>^yN7A z*gx)-f3M3wtMrK%0b1^N8q8hoD=a+%FqF3lgHq*9mqC(0L06+iet-ReVQzFetn*OD z?|=O7y>v^MAph@DCZN$9+5O6>%%{3C;O_`U(A#gaDB}@EIJ0Jy8OZJ~MB$nJ?qynP zoNamZQ;eYo>G$qg%aitlZJUuVe$8=iZlV19H~QX^;>=-HsS5j=!^%j0F|Ci0!W7k+|9gds)~e1O(QKmL+*Rc!>Qq}{M10NARs*G#XcnLs>w=V#qLCnkm!xK6Bu;EOJ zYxyPj&$>iQ+jLHg0*gvl;jW6b6!HXCk5z9LpOR8G+JuSrJ68;9C22TLm+081%8!96 z=kklHD`VCv7L#w~#DFk`+KiHfj(6<)fznAt_D=qj)(oDe4u1M*CI$d_{#kIc-CvVJXe9&T$b^}c=n10eWi(;Pd31D$InAQs#0Z)6e@ z$UOHxT7%zAf4r#2UPDeZ!o*Qc_ZCYZk`E4KxVH2}yLo!@kj&uXZ7$2KGiVYMzegz$ zQ>ylSsYg?X1`4H_ndyv8{0Jl>ihE|39_DAcjJyXVNYhMXr%K7P@DrLDAXqU*<54SJ^uDdk zsMfEHMF0VwF61-QJ8T+?YQ2hy*{5G~D#WG=%AuM$t7_X4{hy^M0UiQa!-KI@JVZQJ zoc?bxV*5r$1K$JBxA;*yO>t14g13R4N1C4Ay4WRD_wXS?VkY%lOm82_MQXCI=nLr& z!iOA(p%wGoEW#Z{Oo~UvTITcn329<(dEW~Uh{as*@BO0H56+VJz z>%Ym!r!&i3CUC8q=<)%;(0bb-z~)_wGDGaF032qR`7={3$8!S}i1C9_BAE}I$a0~( z7ZAn4WoSpAWEP%Kphkoav+~uy8g|P^zv+>!KKJ_{cmY`Sh)CW~bL&cfmJT9Wg8EXr zMzXZ2sFQDl{iNIP6aywO-YmS$|HW)=?_#pFg#0U0N-Ho6pMlcMF44ljEQwdo6WE@~ zpg6B(%b+pfjxxz&2tGBper4|BS2^F27~dY7A~v#RS)x3#txJ^4cjgTId0*)T7{xOL zxLAamIL4Tmqa86?t|SV%_i&MU7P;axe|^Vdz)8%I`d)str)Tv0Ug)o_iCXODV2RIR z-Z9yKUdFxa*sgwqxhs%VoL3^O27O6AX!{FT`>gJ z>l+ozX8a44UHAA>O`VMl?=WyUutz5J$rb+XmjyyUvAN0?#Sv?x!qhTUQv;!s(oXMr z;6P)Yp35pHo+~W0jlWZP4O#6GO3LjhfqBYzV61;e+ra#bFjfogadoj(Y0DpXQfnD#fFOsvyR(-L*?(D-p`7_^`vr=>GwW z`f0^56ADWG??#PbZTZZdTBNTcWOZY1Uw zn771BZ{S6id0Zq6v?AutaVE-fjtHQ?6Dl@$5TT%eO-e@jJ;BP@zg_o1mLbvLN^|J~ zo_9ng@Y38!!dLBMcsV||-M%v8OLS(kW}y=!V!$8oY9_3uh@h$TIHwBE%VP;~+Nx-k zRqj19ss;$;U}L$(GkUej|26w`MAH&nvjrXf)9@BV(#K{O%21MG6`xb zlA)DU$J7N(F6AmVADME=RuJ+_6x^eQ=N~xUVvQFL9=X+Jy6JOrI)L#!QRBK=IojRP z(7FBASBa#bZDl3?UK_Lv4J z#N5qDQuiD2NIlaO`Hf=f6`@TjuM9o%7+f8sELU1iu&r@T=$KI21A4)Lxkdqnip0|J zVs>Bgj{W<)ia-AvfS%aJC5&nx8I#_lxx8$!U*lp=K)#dG;i%6#wf(jH53!T&a!0*|b2Vw?8H+rHKZN6p-)ia`Oegz&)hF0--^82oDx=`A zpXsovxRUa*IUqz{r`FPKW2%9HPnA-yn}b(9bNC&HmJPIHharhMq*Z*|WTlIXo28Dq zCP5;_Rn$gDw_&&E`cp>_V>gd6nD6{0pzYpRr>Kpl$DEIjmDv+RV60q`LCR^+ z5{?6T12dY0q#>s5*)Vq!F<)KKuPZ7Q=lG7D`4pic^-!SQLd`^es58u6ZfH=HnQ1ZI z1aC)Tv9Ks3js8`*N*h7w3hRM9qvBZW4Y$-Y!!dpW>K;?MB3&^``UFFvJa^HGrFE@~ z1ybCx%&|8Mi&W5gNz^GuNWA>uj%je8^teKTlO?&UY22M-vsi6)D11zkcWXE;Zd1@T z8|DCz&ba$Ly`#a*5{6^7YC)C~1%{XnErdcK?3*M0TD1BT_E0`) zIjaK((;76tUtmOlg=ty$3ad$}kIoS^v^IgAlmX5VCo3fRV{41hdqHc@)KF;5HQrJpr&yPX)E6y$-K2q^oh}JJkwatVpw-v6N%~y z`G@FPf1LyPU7fWY!wHd=`pD0PFRu^B9rJEw9-t`vV9QlhNHZvRCs_-82{Z>p9*x;;_j1>zpeAAf(F#U}Lncz@`cw_jsUKD6E@PtTY*u;1x% z_h>$|^(ejb-sgJxZ<;M%wf?9j42uYCWT5O=TJ3imT{GIlz?-9HrK^tZmhmaIrCP%3 zB1oU*+b`^zAK%9+bNasukkLHNoqx~|U!JRyWM0?sbUdI@nqafx!+RzukcD|Q*lr#0 z5>o|oyUS&$`iCX=lkXl6!R^Zj_rhyua5)IP9jP+}v981&!`A5a?Ib;@t3Y6`o$umA z$1AsfaOmwO&A9^tq|SuKZ+;)?HhEdhQ(FV;uK*z(RfOB)Pgz*+mMm`1ncZ@mmkz=m z>aS9?+H|y9;}hNr2~dZqj89m@VQYN(Fm5ha@5-YI=c63pA*iE6Q#>6le^_?x&*J@` zFs|KuSJS$1Mv2bY$nh^+P6#Lu{PbdPQ0 zVEkz-kfm{`w1q|lcq~Xx+kq|>n>l(1E8uJxvRR2DgZC|wDQTUKH+@%ic5feGkQU)R_~L;fP!DA4`pCj%gM4i&QP|$AUBG-cQUVhsV6q} z)4`jbzRwg&$mcQ$@bS0b62HECXOQ9%{UAx6H*uI+MQta4l5dZ3yB=7GFxFtTqKq)9 zqeg2dn4(TBRg^vRwz^26OG#fI!dMJDWnY9X(bn372HHylHxgTYr7YO~elA^o2361! zT&U?ce)Or*g2z-S{u0t6scER}NrR_`uhiroXsTYG2JYYZm5dEAL$8@q1@9zvgh(8f znPw1%R|pg zLfs~ywY+zzw;NQp8ZTp!l8GXU3ZlL70-^CBDV60qz;$L9m?o}GqfIq6)5k1RWs@Sb z+eb0*5-Fni{?f~JDLQsLJ3eUVTX4CO3QS~>Rs$cODj%hdb-FAS_J`WAG{Q{N{=n0~ z?;Vx5+tP?q?6}U6Y~=14 z(@B;<_|k~HqKvaYpE~WnRh>f|n{jadm!WS59sj(4dDk_nSFxGCtBl8<0gp=10AmRjbS@R%N6VW7F<@aaP=FY`8_Wm`5sZ>`Yw>WJgB{TmIpZ#n(oo3Z zm|I*bGX+cPRg>h5X1SBY_6hCFA^IPO2e$3NJMpoGn>|O=z+Tl?&MIfIK!d*b^$SqS_u&U(gqf6vB^ficVtE43`i%&u?Lhwh zl5Mvoa;|(9PDEf!`DDaH_REVCC@2i8dG!jXL2W}gVDi&uqzg<(~48Pz31_3_Zb{6sRC4NaB z`xC!iRhk$8$^3LWY}97Wd)_0ayx58NcoKyAOD~j2 z31fDhC|(Uh>uk?gsek7TVE<856S8-YHw7&)`Yv;Iyzb>2E}tzuC$dCgxRieUia8^? zHin9^F}HQ%bl zS~z#Yt7H-&5+<~s=-9zbT!i6617vEo^g=xrXoEYx*E%`e73%-`%xA%AQ3?`P(rRbN zOKt49(uqaAK|(RqJ_}>~pGlXP7pcR-Ee|7n8t?mTtm9l#m7IaWounf`8Nh%$T?m+C z2CWQEZ<=f)_6-HL$b^-myqYNES}cvF>rvs%SDXQnv6C_tWNyNT2Il>iSt*x!oB0fF zbY_5`gOl~jW8W446gmsaLd@A>wEL+jA#YT5IFOp2(rfC;UeC`s<7o;mAK@QRfS@5qe2$!fi{AoRgtN#Lx~DQ(UK)7| z^yqaE3OAyQCGX?X)!Rzk9#^3y!5|8&kv&^AH7U%O$UNK?Pfh16aH{80`kUQG`_x!s z`aJi(01c=`Xl>|q)RQ+^Hlp9F%J~t`7WkxA{hM`QW+%u!6sA?jI-d6&&PNiTobphw zJ8T5~3CcAdrfym&BVOTEL|p&AEep%iXkcan#tv97DFfp)xc2FAfVHBA-H<1l6 zA0o04v#LBog0$P%NFDeaD!pDK32r>+P><~xMF&lA1d;<7xGW_aO27+ttxgVhj>RW;ck-=D{?uh9`7?J2MFekE9joj^VK ziA5P+;v78<%LPCzJVTZsD`Jiyw8}7f+7)Kl2Fh&mx6^05pn}d@z%2=Gvgvv8;B-2A zuW)E^`1x{X>C27IWn)5-{OCfdH_A?55;i%A|ig7r`!7 z((J=c7oNRC0Sc&@e+VbKUb^F@f1e3Z!J?sXO%hz?&5mJEE&@speiq9+WFWJPFoLoy z<_;)0`h&0p29Jt&v`TbohIfg<8m zdbva_<6v5v;V;6uK%7Yrcf7Is?)`J1f)oC4H}ko0G?UiqE7Y~KpyL}R&G#_(;#=Hr zwnp*C{}3Pi`!fe(lf+Sfd9Ji8XLT)Ue?9O;05!25f#V#KaC_gi6S0I1W2CI66_}w-h|ufHecV=Xut)(J`Pk)AHD&2AK>MJfP{2>~V_N#a!@=Bk&v^E>*03CNB>Wd zcPyAe^@X7Tpb0LT&7|y_ln+t}Ke5tEf=ZW_jrq8Q0`fpjHZ*-#Ef0aKowpO>24I`> zRkG>5X=nR8RgjKqe##)Wt9X&_+x{%u$j15%=xo=~MtNf#G^ld7oFt z=GmzPNOj^xA9(AMQx%R?OJsmT{={M$F+JC6EPuC8&ZJdG&--msfpG&C(BnG%4vy8~ z=IPM6!A&r@4|R6oZ-xTya2&M`rL|p`TwJgGSJT(v%mT8q=QF05_hRTnt&>AcD%VxJ z=630rO}Ub@j0K~c)G8FO^!Uwffz77xFhZ87{10Yw?QCd??Tm2e7zxRQNM`>9s|=-F zhYEtmPXpfV_~fd9(3*0vYQH_kw@MuWWr(1?xA5hSbV}Clv$UnQv(umHQyRa2Q%m}X zX%Ptj7P?qlmY#n$(msh61q*cFR0Tbx%q1~f?R{lhY1aqkDyPsAmcxr=hNII8A_-xX zWOd?0=M@0*hsE#lbsoQ9L2t{?^4NTS-In7qJVpwXm4#2qZ)V;$bk?2Nl3Yt_2{i_r z=TbUqEjpE4Yz~ru6qS397?^+>Hpq45SxxdkOY4;8i+hg5Bv!{w6fe@o#JVGI1CC74 zD*9XOBXJ;w!Dm2-)A`i(ge==g>E*7B3rp5&XNFwGICU0YO;oF-l-y7zUNx_(P*>h5 zJ!n7YG;~z*4E6Yv0|qsi=mjX#QLku`i)#DlI$<4w#(<*v&+%P7I^L^Qg2OD0NlC4~ z*@|}$F!K4>-Lq|FVOfC!ew3!qo$(3YD*3(dWf6oj_8?QMe9c0$dxEOa4Sd7Y>q71k zd=!9^c}{9UKK+OWp+|jJJ(stJkTKhVztAbbW89dAr$fnlCoRlf>&DaL)J^S}+^`Ao zK0Tc_h1bW&-hwIKN%swi(76ktZTDkEh3p-qo%VY2*dPUG1E+tJd;eHkzK%%2b)v9l zTBO~~Fd78xhDB{m7o?f^5Y9{+4P36VZ;bq(Z4L^79*rjkUYw~)Nrr{BgNK(-p}$1*+-}N*mvu8Ipliz- zi_$Z)vgbtdg}%;jt%ctYMr@~K^OEYO{2dTf1V8)1`K`db)d(6ywHHw9`HrW5Vbx;Z zk0k!q_F)~(=Y%M;e6#RS{D!z)y>u8Sca7=r&tQfZ&Tho3o~)x9+K3y zAN(7%?(XmS_oec;79gjD{qu|p^Z^X~*!n&XOJTG|f^vm)&Q+Mj9hq_Wh?U2x07!za z*1mYkwK1@+$iE36#M=T$u9-(jUOO(}CTUF!MFdhu&|9LW1u|infZ+3kjwU230!(4g zzN^sElt32gQq&^`k5G;2t+6oFA|J_qSZxG47J6C`xo`Sf`K2@I5t>*}iyO+P@f-XV zpNqmn>d+JiHuOa09M*orRSB^?n%`afdp-2IJ=4ZRg8~lVd7PZzHiGBz95SGJ9n)&A z)X(#iu~pdZ=B=PB`fXhYE~)lJ9+JJ$Sp{fJoAB8T2pX)`XO78px_`9+WZ1&Qtw>yc9T z$wA|QKkmBg^^!?4>=Vt20J|O73tf6uKtXB5fIAv9MvLjUcsNboU&o_+>jteZWXi zFq2VSWZkS0Y%frkS&Qs@eu z$e)$t$f6Xha<>RmOQOK_QQ=N5ZG~uv;g77f)!fEtV*r^9l`K{)p4WD4A*DI)V2@pL zvrCsRL-oq8(w7)K)!f$_=8?n*-84(6XlTgll8!5#V<0v+_l1xX7Bk{Q(_<#rbx-^& z_`*?wXg~|no#4-|t}f%N%9q`xqo^NWYrm#RJ4GQ+OiZb4ZB0t(1RWFe3v*YKQG01Sj1@pfpkj7yNS8s<&wII0{*kihBTMGbnW z8KM+66B^{VORg771OFQ57r}@^uLi@<)e@$AJcoLI@S%ncgZvXmth$LUVx4v{Rt^03 zAhjfW+i*^=`lGA3^q*$K+7>ydTQhlt#B+E%0vNrC-vb&VZBqrG85u`m!WR{~nK}np zDZW^nhtJ|28v1kd=Z78+73WbP70tA!q>Cl~2fFn>e@BEbZeikt^&ZJsN~7cdPi2(uJOm(tsm72bE_iUM{H~Wr7n_ z#_O>x!)uZcR8^n+!kinw9@sg?4vZK!LKS9KT<+hKlX`Rls2X&NJ4Zu$TtXYBf%}X# zwk-fjJSKZ4f(YmX3Twh&<;el>sBvWC$`0<|zT#?(1&Ds!c;O;p}cD*l`m%MKO zDD#qX$_bf!cc<(56LwMJNe^wI^~G9^QR**QyobFM1UsVz{s-wH?B^0<(5<&oh3ZtVD& zN5k^G=FsEaY|c@JQu|_a_FVu?PwH8{9xQo}@8LafeMeS@tX)R&ZUr%=dCsKwje+)2 z(;svJaj$~u$qzl{A7mn2?n8ynVnXt)9B*6cVoqutqgJL2WcE@J!5(RvrWg9GD_Nq_ z%z3m_(LGVF_P}tQ^2AeG=6V~ubOfcRZj~`Qx-cmfEvcpKl!xrr&WS~>ACRHJLW1$~ zBne^>?=u|7WG}Kzc6Tf?-*?YTTSXn3#JE8SeUteqG}KfoV`*9D9+iCGv(*v5S$2&1 z6x5m;tv=*83#gWC(J7*lM9w^LsS+_J15~vYOvHgmoufs9e1s%*HQ?JV#s7m9eW5|Y zOcyj+nq1~LmLAN5s!sW8aL8)7Y)i--lnPdwum6z>!`NFqM~EQvRPd4~#8)xi^O?di zN)PurI#V3&C%?Wx`z!Q|z8(67ed%0*az9a3pY6hoV}2$A9Xzu>Fz8NX1M2|cI(H*M zFL87#dJ==ltXMAly_yFgbk@d+4wIWb#KJ~djb7&UgBx2W2=Bn4fG;mBp;74My}|Gd zRTC!Ytw(*d%b2IVGPZB(c-ge+Ji}NpD}8pj?2oU?dd^v^{z9g zz99AaZ87X{T91ZDjNi-vc`dGSxF;NeQh>Vu;P=<>T%#DTsjFeuo~WS|PY%gAwo0?C$Q*hSzppr&(_J?nDFn~7$c zW47D?or$kzG@$s8P<2^$Ir1R2lQ-t(8F15k02g&!JA8THG=~tTc`SLQuYdj^NJ`eP zdChd}T&5<3CP3G?+EfHnfjrD`Hj`G?{j2Q`91rZ#w^#_HV9&f1WFXEYr!1EO3knm*%b{DVHZxeQ`lYK}HqK+FsFd|CupE^Z}hsC5-H)WwV`KU}N~! z_ltch{C=a+b>n&A3_{Lm5!FX3(+XpxE|_k<25{bRXo}$isb^--g2|8LwGi^iULTMP zuBwds{KZg|L~!%G&Vpd7$;8Giwb5xI;3enpAajl}u<4?EcuSnt9&8x$DglXv~ znXy4?=~(9{8};#xDudkcAOL{ZhvpMHwnTooX&Lvtk|0<)>yRDNbcWU@ELzX-uLHsd z=;63I9j~}U#(*2RiT?qUaRsrxsh|9&jcwEcdr_+REVHm}KESb<7SSaM^n8qeD^kGG zt$|n1)U19})i4MEvv*8-M9`Ypl!9afZeiK@>`v1`ISW5i%lLeC!$HEe8ps1TUe0OU zr~5 z@wJ{xuQ2U`EEJwfu`z*3o5Dp#D`V;NO5(~5JiHW~WW&++vv&L+wuE{VQ{mZ20HHmd2*W(c3XFsl0 z!!Xu%WJt(Z;2ob{=KvY_++;in-~aQM6%BtKums4uI>D&dw(S*|P2eK0ni~l)_*1AP z8uuT6Mvbp_l;q&65>9R4ULRKsnT1!v*A0AyUns2Z0E@J|18kN703PK7gD zmzkm@Pxex7ah3uZtgaHLkHP0?v%Hp=zF1xUZ6z@L1c?LKP|g=MGK`nb+Z0&MeCu?c4P_Ou@x_U2XW6@y(Tj|9$Zo z1l>)X>;HV0?63d*t}Nzt(Ezv>@(D3Tr$6|UDzc&n)Z9f0nc^WIYZZs0lZ&Dge&$@V zrSSo|?2XS=8P=)+Mdw?JPS3l>>2oFupHW||me-q4;H+p?PysNe6%$3iol(&yT_FhzRj}kvl40gr6TP>>QXGLoZ zix2OuoBD+u)^oTc{RZJOaVvc1ZCx?NgTeCJR#Sj+FdX~pIsHaKtFw;R9**eXQ#k%I zCPZaeHWM(7vv}S$>_uS z-Ca=+{0HXa7QrKN0gBC^AqKjZrxCb~6h2r3tzTMo1-7yT81Gts!IAz5 zZP^RRCceP@3D+BCzo8WkSUA&}oDh|%L%73lefJf~LdC_YQ@H z1ui+@$o9l=NXn8-3hFAECv5y!#uv+Z8IE+Pn-x{G)s&nA5}2A_?(`chDd3jb(3cro zJsGpy(6*nk+%-xdD~c?xBtJ3wm58+pKXy~Mr`5U1<)Pnzk)OMR<$H0*eJpsr8nMgs z%hy16#^4ZE;fCpGg9FdbxJNnzm*j=kPF)l)AgbZjk3X?!4gd*yPJaj z92l{d9zm`7X^BkH*mkrIyYj-Y*1f^G7CY8`%6-f-b=#2wYMX~M?eR4+8A3FQho{H> zxq&yHELn}`i7^*U$M2Tm$Xd9fZmd@ga21*B+Yw7?DuEYp6nAdD%RcvIo9C- literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/jupyter_execute/clustering_24_0.png b/doc/LectureNotes/_build/jupyter_execute/clustering_24_0.png new file mode 100644 index 0000000000000000000000000000000000000000..e2dbae3dcb84b738c4d9e63a17113989842908d6 GIT binary patch literal 79456 zcmagFWmr_-7dA|aw6sVI$c%J%Dm6$A-QC??3L+q&IHW^6gh+QIT|wTV&&xg6@I&;q6XUE!W-RoZW#Av7~65>6>LqkI&R91QoMMFdP1U`=+KLUP{%M2?6 zzC^v{^}V&+Y`y&~JZ;caExg^G-MpP0EE#=mJiQ#;T=}^KxcE63?Y+I-y~Mb=UH;Dl zTyCCr+{0O~M}bao-IWZy(9rP7{(aEVGT=|q(9zJ8U(0Iy!}sq3U^W51)6t=!c2a%` zqI{ksKN`Q6d~YrhWG*%$4NM|gqn3OZ5&csLW2(#Cir`U7r3E#&H21s&kA!sh5xv5U zKILOf(wyREP3Gd}lBOo7k?(_|TdN}%Sy#793^#tv&#U=7iw1WGf3yXa>XUe&8rx6B zw_gW`-CQg#x7JS>^4Autx;SbD`6I83*m(ZCxG@*PKKbwGeiytAt*>*F1?QjU$@>e1 zfCmnk>cOAXfi_>~Ub$*9W&<~cYNHnlWbV;2ppHc_F+Yaht8y4rIz)QQTlx*yM*)mT zhK__hLwO)3haklf(A~u4L|$n%+ru+v;tq*>ICR%7Z1VI{1bBnAoEF4H6C(epfz6EF za4%!(dLlab5Tyr6-hyKyCb1Ed47WU^0dbkoyn>vHM-r-pkE3Ql*jS*MeS=30yo zI|qFP?&@t*?J?V?(}vUGkB+j@!c@R#m%_)l43lb@<;%zjNbxe>E!oQQwBbV+u@`ii zKnsGzXh)Ci@N+EP>mWwwT)9;gsioNuJ!mWN4f=|4g=rsM-`&f6O#>;;7B-zuO@?k0 z)7|JLL#LCWA&5y8phM5{?O&GdXf+Xb$c7Z?uCyM+L>qDdMuhf;<3NgKz-Pa<&dQ*> zC6Hp)(^WO(5x>HO6mzF%CqsA3)2{vwOZqE-&%Sh^uU<2n+y%RAKQL~m|W%;FBAr@48gU5 z-I8e;mEcd(wC5;{Fp@O%CG7i?+>16m3F2Xl2lk^d5aMkR^+Nc$8_pK;5-p7OlCI+d zom~d!l4h$ljMyH7Ekbl95pBE`uH|&M9btxfpEetFTWK`B$GZ}Sd2eNoeu=%34Ms?m zo^88c-_9$-cl*M#ABA>u=+;*+$N1MKrjOp?uZ%KX^vE6JLWfIZnI@w$^;VQ?xP5;y*} zIOB%hM%8#odDI*(S$d|94m^z-mb~Xhz_4%mS7>bSrO|HtAjJ$)0!xXQ(oVhCIEwJo zpzuEA_Cu$2#G`wa6#{pn0Lpfhl<{)k5^xU3=cRc~P4vKL>IouSz+2k$YDYeYecWbq zvo8%ZbZRZE9jTpqz+7Q|VDz(MhZJ*RbV}pgDwm!OZM8}h+y<1MeV-CTzh_@zgE=Sj zV|6f$8&VnWrPfT{1vTz8*DPb-woF|Em()kg%-WrPi(OB%v6mj*BTZ;;q#a7@Yo?s~ zpC8-&>+U*?=<=KB;RSkoPVGH#PK#^rSy$v&6wzy@q|0mD?0v<|utG^@L*8&;-X~3o z@y88)dS{n{t`0^#Gu%sS7z%P{8wwXY!pf>2J+u8H0Yu6RW+i4)!~Sbs)e!ooAh zy}apY$GFdhI+}pbmcfXHW{K_A89aBNlelB4a^|d+#knwamj1VYFrPMAlN#T*Mkg$a z{q^#WTV}hs6F3SJuR-%8AwEr`eo%x#+lyh2UoS#oG}!}L1~4|?%k+CSuUj3&BvmqW zIiTC;Ky~CoR@LdQq{B?n*VqVfAW(>4g2=5vFS>~LK^W0hbK1;Vv&eyF*e`bBkbBqO z>lDB#OLrGU5NpyIcZX~ZcCqVDsDhdsKC1bkvzYB{E~r~PLKhf>Vavy5YwhrFq4 zaJTrqO9x6gn+84kRTua2;iO;MoEQdexO?N{%xd5IY1^&S{C5e)2?U16& zotxcsM0?n;)?&xf2cv5JTW0Hv3hS%^ZuivD*G_jjrDutlaZ2vzb_pVXQzITqa>WjN zU2lwQrow>fIIK8CT3(I5a9b1@@mV=hod%rk!_MmJp{H7X72!&E?y`Dlcx9W7Gu{Sq z{qG3c8FX5})ycH%1qqe<;N22;nDKDmg@w2OfQb?2zzj7YcMVrp)sSL!5W+bp(HV(< z+E|X+ZUo+Zi7-VAT@xx?lxrBv-?t0@=gTpB*B{hLP}kF_#&VoPbl z+cfBIbTYIqX$5t`j!;9RmvcKnYlQA9J|VhJD1e;+`=tl|Euam}es>dCeV5o@eIFE^ zH4cQchayx*}M_T^H>Vf zUc%GBcOcbz>2Rt1oEvz<1)8vQStlU03k8rn37VLco~>LJIliqTwFu zrfBG0_29>3j4FnM9te{f{VH1H3?r1Y#4SsunB6S_4_ zZ5n*slejkdU!$=M=rf#IOGs{E&%@*@Nj7I;&Nk>8|!12*& z<<3VfiN3Wjg|-FXlZzL}594k%z-QTL4@?u1H##fCj-~52yyw6WORX`sv{tg_T4!<2 z`&A3~q={N`YC|7YL@eLQ_GSKWor@PU7t13VaULf_sWs52P`?`ft?yxHLCovrx$_7~ z&(gDJN6VPg;e!GBV z%HdjtY9V94)Bupl?S#m)QEH-6L?wioZ1+aCo-L%(CZ z?jT0{CFKeXT6o|^%xf}r+C#XKH>^IW+RqG@QR~``SR~076FhBeS<4?0MBj_u=FvL- zQ1v#o+~;zmIQ^z==(1t{Zl%AS;FjY^@O7X)y7bw9Yvb$ZTORW|y49o)+R`?)9(Hxc ze!Ev+Z-7#`S-N8!X{ZqGkhA!Ca}w*eZLnNcH(X=^do_@ zj@Ep=;F5slk?KQ5YJOoPulK>7Q^T}LZ+(^O-e&;06MtGvaBbjETc&GJL-WR1i`dJl zEnwJ&XO?&bxV`3df7&aWm9KP?^vi2)Q9bXuVGHk*vp~52_SZT zhp6BQEFrVDsh@S^hI{jYJ<;2eANZ%5N#2QA!M3!6zxD*WtBe|=+mG3gK|+OnOH6tX z4wvga!@YMuOTQ6v?V5}GRQP0M@S>J#^DJ?$*G2#CWy{Ub$(?N4FHBp%b>5{>Xq_T9 zLG61le8Hp^Yd6@FhS+4=j-JKUHbnwIt~DQhv4+{WS!$LSGIMO~kl?-oonwvuHILJ$ zseXzalbBiJqFwlQTmFX|1o&qw{fm8>|M&G%ZI4|kB)UY^+UmJO8%(b@9w< zNYe77P^~rxJd&4D)|IWA1h+tWsSj?**Nkl*HGE)2yadC-xRx(2*9ff^_72z8E>K3I zGGb@_3@_q>R^AJ@ZM{Faj<)fu#usVn0I@DFes8(wtQWF9Yo@#lUQ!Dw;=Otq2&I~6)*=!$%|se`~MAz`{%^3CzHAT7B#1vWYBzj1~$EcKxU_3qKH!yc;^BUDH$jfaa{w~C&)@ytH|hwA1Gt&%m5 zAJo8}dlKeuyW5rx8u!?=QdQ5!IbabPOaona?>_Cx|3->_wkSUgQ6h@LBiK97r> zdWI{KQ{-ayoz=_gs+=0`LHOH(eNw4GnQapEIpXK2=4taeO=#oIW~*Nxn5OlqqAc@Y z!0q6F#Z*J;rj;&U(Xy9*`aP27bt(vx-K`mm%tHEyk&J`>21x~p|8I=N;}bFVkBA@! z-3C9`hkTq>7PV}5kc@YwyB^B}Kqka9qo``Ka2s~J^x%YkfFqylNkf6e(G*(1H73UV z3|;%lJ^3!Ez4i3kNwZF!hfh!Yg zzk`OU7Vra{+a-0+L5my-eU>KSZ*$y}A#$U(tu*6_{NLMN_4pkIR$k^7rd%R~g=VQ= z4C@-Jjp~4X1`0=qp~S{Qfh6tcBSd)imqY=%e-eH*f0MOUKJ|QTPppVfU|CowN1%@0Ik^`@I7f-JW*e#^^q z`iC{Ay9xf=U1ze2y)rp5w00sS*+u<5L<9$QkB7y1M3ZNRGL2Th6&D^^zq9pS!mC() zXA`?*_j1?ua{g=MMY3+cux|5YNHIqPzmmU8=@5UP5sDfU>zirYRByG*2}*@)bO{+HZRc^v^4+PLX^0~Vo=gZ*=?7=zm^}z|K>{deSh=k zPTABwu&gbt6;-%2TptVMB^I@~{tA-%LAWPa#tg9-c_VjUSQUcY_XDo72wq={cqxST z9c^7e#a4LS^BE82T&@&4bkA|v<=wN3i{>3_+5UD03R~t=dH9wotQZmxb5d~|a`ug1lBhsN)VnO+^@9Py4cux^mZS{c-c)8H}LZKH~ zXFyj^wwWsJf zXIDc1uv<%b?V+Y=Piy2+Dw($>E>WewJ-e>T<$N{{f(RsXPowmGJRB{x7{kU6K(VAhhI0Mn!|qfH{jIDk5{O_*`pCXY2F-nJ71VKOW7zGyp^2-b!-W* zZ1^n%w9L=m6m!Y_J564C^(tQLTyz#cN>X+==8<*=!&}M?*6FCk`|RosrB) z!4ePI7+ayg=Y9-qcI-D1$mY@}5y5}lTfdNNyI$8~>x*ZH4LIwPV^Q`)nk#xeGz_S> zA=&f?i%JYAUHX9PZPP8!H(@$8$Bf~n0Xcl~iAfwp>+q|L_J_coS%NPgL7b0`gUm|# zK6;rpHTCgurIlRKxJqc0A4(L+I({BJLI0^-;Nrw{t^7d&9zmS!WZq*ds=S^07{XNH6=wP?&h1G6E90q^^a3#MYUAyyDe0-yE??kNN z8?;VQA}KwoOS1@ZwQ)m!qtlAgkD0P^D|3KB029tP%Bn z0gn=JLz$riAP`=B!epWz%Uy7SC&g9eTA@E zzY4PFAQy}53%oFe=5`AqsWuYnpMX5%`B_D7zauZ2;Bva9kXjnreQf&yN`fbEs`SaX zU~QbnPCsQWX7iCl8IW#>u*aMx1;a`Gg)|K7&{ZD(&ZE%uE+S(&WrcwmmH2HZ6+6H>J^ zI$U?r1&q4Mt&7Y|Eh74s58#t@q3uR$*S4dr9&(hd?OZq40~qeN*t1bBcla7GjZCs@ z#9bMO?xjSNp!aDZwpD-Vw^q4D+g(SP$lDpGzIV5iTrI(?DtRn8gn`DE2%VYC1K8f>uze38!0JT&p?j@mXw3&G-)~BLDujR&&aX$wO z6QnMXS=yPL$djCBX7 znUc@w#-N&h_&%4Iw+wp1%Y$|>OF4gsr4r#}z#)V=2(@7EDcO_M$gqH0%u}|4tl*R% zzrcThs9C`4-@Z|bV3i@y8FRfnsHUMHfrL$xLTaF~2B_5Exp;8!O%#xY?pS7mxc&X? zx(8;HmamGx2)s%ap1KJ>?i32p^bCH{tt-@iJtcGpTAy9#Eb~)vz93usku%21W<+88 zoy#D%u|jmE5-}GP>#cfl{@=Q0zkjk`=U<%fqQvZO{2_WJN>2GlJBQ4)7&EOGAGtYP z)XR!;>)SGECFkI-7glcCHfjp4M${cW*hohel;w{$yFlDMp-Sev2kkH@P;NlL&KsZvj75 zadWN^hy1KMGWpsvX*^HQ^MOB0Ojnq`d5oz1hp&fA4}ag+8&!s;b@EZ407pcRqu-mJ z+VQ51-NO$~nUAM6{Q)3l*(zQ@-$2X1Px6jK%Wdn<+!iJ6-{P-G0)fC%~3$s|~xmxJ9D+TMg_Z6~u{BFBBwN zPgZnBf98s`(ur9k?53nfUIz;;#>Qamkl{ylAARtv96# z58hW?5-+^}F6u_*yF`v^uR_Zls<`(NxmPCB-ef$w45ci}pJXAUP}`1$H&N$>Eo}~t zdi7dHIEhOB8B`*6BSt;>CbUmE12p3CFf~2=g>s>nK|U#nDFPBeTY;=&0u- zc#|T@SXugxouF@ews0!gGvh8K%JtkKl3s<7K?Qu$VxCWR8oy_fk*iXyBK8hre&UBu zU$=pBPc=1yIt5^Xe`Bzh0QQWxc?XSMKHncKeF!b^ zRRO^1O=Zw#GwR!J1H$fx6n-gWpY_&}rMxj0P1i*k?YxMW?X>w`2fgX}yFvIQe_~Ll zB)3Gs`u3Mx+WLzG_bCgN@D@u9wIEdIAe$S3by?WK;jasn_vnk4v~1*U%O!Dgg&a8? zQM%NwKmVXapR&Ov(L97dS#cVLW`itNP4$|GXMr4y;)hQ!mRfwHVaK`(VOf3O58vL6DBEKC ziV1>-7V$?pyR%qz@++bOa*01c_V2k4JRk)s^aekwrs69({de^UH?ZI5KWuMQi)=f=IGEhf(EB(@ z&2Xl9Pq2KK#554EF=ql*pvT(`WCrWVh+!b>arwd_puC*@Wo1J%Mw;x| z#@hDkWuc8n+Q-_nCJrIASq(mAP0}%Wd?i#1D>-!RNua}?Pr8+hGE3^SeRgU?)imAI?H(S9zt7WLVWdq&+`E#dBI3~~ed7h{ljNZw36CEm=~ug@T8w>Ud7;u)zvlN(?0?D`k!t&M($XS2XG2;n9z*TQ{ z6L1n#xkr>v-u9(r>>nu0_Xe(n>(=B)QmKtDjNREmLn_ziIE3YrT3AM6?+m&8X!hZ{ zYH*>H2EQQbJ22Zq#X9a&v8DKquo7JdATf{ZGQjm!Fu8IKs5mD4L*%_SzcKT>T!tRs zF7!;L;_iia`QuO9y#9i#bFyg7V)#2W+t$r_&pqU3LU4pk-;b9WTM1F}s6N6urK!)Y ze^mZpH4{u%!P02AzK1ateG}|k_V|I`r~935U9L+R?cWEuBsUt}1%doza#XGm_x0s& z5(k#1kuTw$j%c=7w6!+`sCm{TT8zZLBk_d6D z+-Fi2woGBi*MZsPrVeBxl%rYp9szd!BOnBsjXmUhTRfLVYj(vFy_Tcu?^;n|vqA%( zn5rZUeOIgv`GIpr1Qp`r#9Oa8pSHUNT4bzxl2cyIr*Dj-1t7sp4+TRd9&f+2mASgv z0Q*>|FS&ze)fj;T7CpsuuLpS-i&d$xEv=pNU(31m$f%}hL=KtFBu3n*WM#i!R`z!C zZ?3RymDI~-v!;Ib5))c{Uq!H4^OS9?_?ADrb?)J^Pc_k{IZ{rF%hyc86QPZNIp4wm zLH#evsWfao^y6K}>`mz-|K>McMw;Ap?DS4!Pt=2gSW4d9=BQ;`T-m#Egn?g z@iFr9U5dN%VD5XNuR2;obw>hD;S-O!?!UYL0v$U~n^ESNger*aN>I2NGMP8u{$OD| zXkqe3R&JZ`>7b8xMQ9I2;J3RoyX42clXpLF;b2J(#pW<83)_PGFCZz#L~F_iX_MKf zy>7pdvd@Hejj`*9j*ifbiLf?*S%0C?e66EUcNHrbC70|A%9X>%=JhdbE zLThADgORERs}y`AB8)of_9TP#R&x$QzicI)EYlb66Or1!k39K*=IeA4=MVj@~`UUht4j-NcP zPhwsdG7J7#7xkXn`R4>bjuktrl_K3|nk~`&7Q)lS{xe@>(C+~M-DN2d)>cEsQPE`L zY$GFD*vWiu{mVYuAR@I;1=0_`OGyo#18%9jFSNBLld(rit6FM0=bh$f^xB7q#vR(K z5V*#1)m}P*9=+S#ⅇFqEbc{#U!LnLJ>}yjyR)~f8bEZWtB{pC4#k∋3(x(w5m zqEnAOoCmstog05vD)gW8Y;Eq*z09hyXs+S^wl;fv-7NmMR}|tP6htEaE)5mpO){$4 zQZ0A8@;FqIssub=Aw8MR zofy;Mni*tbM9R8V>An7S|H83&SL9f=2Zy|YW7+=4Vr-%W>@pkvSotP<1D;s?n&T-t zqtB^4W?l~OiRN3=&UtM77`sHru&9e{ zm?58RnHZ>UI%LXVj%dsHx9DgX1G??<~&{r$KFB6`(F?C2|Yzhov6dKO$_TVrw_?1w|k1rk?xZ_^ectsRVC!`n;#1vj3fBVN)QtGovk$ zDl!C$4IitlNS?eZ3M8Ug{-`F%d zKaY9-9$bfA=JJ_})juOy_X8A91x)Ekzn57Fi$e+qm?r&60ibHt{&@8`+NEiRVVLnj zsQ<=xINi!a2`rGvANP{XaF6EkOT?r)hBU7G?qu!>OPsN z3I_-JW64{>|Pi(XyIr8V#iH{ZA&XdseCZd)K25N%U zisFyCoXx_YN2r*g)!SpKF~Vw{Ihvks66HSWc2~#y5(^Bb%fpLZc^90&RwwOiwe zN6Q|e3Ck@FeItyvx%5D6-WHM6Yn5G_qGtoL5ulR#ZhHn`uzwOu1$+#JYkIhxhaZFv zE-CRno$n$i^iPmaBah5dfu{iBS*|Z{@=0n&4agpg-XX=xh~CYG2n0cT@&grPOM|MX zR|!Z3ZU7BGHatzQ_WG8-rFT>Lrxk4D`brTaJd0V@gzzIYm+6tF0zCDyPPG89%6Q!$ zPvupC${?wNa>P`I1#FDK8K^gXwr(Wvt0Ir@_|oB!k`9UTbnOGEuaj0rJGi5-0~GS!&gTF%eBfn1CcYkjFS^)3^^>^Hh@gTd0_!4&$x4Z~({@2ekw3fr4$RU&mu zd8XjPd@)ZpCJNWa#8Kupcn%>YY$)?DTx7=>PL_Y_62tbDFtWUkuD_2jF^3gJC>&)w z8~SRCx|S&|V)cD7ya9*bj#d8;wp`D*O8?meHngv7a>X#j7^^%JZ6i&8+CiKr;UA@j zz4&RCCx2KJ z+qykp>PH4|)x#3qHyGnIZ=SOS8o|pl*C))WO1ItVzGfY7yvPX&Jd}AMT#2g>fT7K> zhe5%Kyp`@ZQ4Ij0D)^1MF1$>@?U6qlD1 zFP5|)!ZEGjK;1PF+fhx;A}Vjd0};eO3rB?oM{u{bB59gUu03S)*UXJ#Pw^EC|Adt| z^}5+GJngTY`U)xDgB17GPEmz3pe+^1uSTfKdN-ZVOJ4|HI9RHS92^aJp&MHCaF8eA5!fYXI=4s zIw}yPS6Nojy&n(BGm>6 zyE5pI2BYG}>yL{`E!Pt}5doHZ%@gdfzgo z)tBwKQ!jFUmcHVp4CmrkQbC`7{$;elD%ax0&kkGFaQ^tnSnxTPvmFCPxYV)3(-v@e zQH}q(u5XUVC@K0Wsln5U&;DJ1l(cybhXU%C-_P-`qHezOB@TWZdl|~H4;H@tt0Bb2(r<|-&R?->+SwFiJCCp<;O)=Q1%vn$Wvnc-Bp5ZN|td1^&ElaP6CvJ zHGD3H&$ASlR$iA}J2+K66K;{uFdp}fC_wVl>&(!kyc-^~Q((&j{ocU0MA{S={q!9# zffO_JAd@bsrQ6HdwuGzeoAndBZi9$DC9ww(xPl|D@q2U?hnVJDJFtSX!f!wQGTjQ8 z_6v?0_dR8<`%LyWf4e$V)AM_R;Fa*XRbgviw68EBrupFV25cpC$dwQL0l9GkRg z@ez?jg$Q2l6aqvX9?mpToj#nmdEX=<%U&ozbYxLV!)taLQ}veHbY|<;GBZGHq#kre z*m8Y98nv=hML^7)woJu1Z5T%9zpB<3;(TDr@-KpR8lYFF^Wz|l=TUTe#?d$BDj073o*$w?NBZ%;q$atF;Eaky`h!60zqrZJ08Te(xK@c!2k~iQ+L$ z9)SnOXTAbv>d~YedWcE|Z{kMFV9JB9iJXh9#BQmcye!l~Zi4)3rHB(AG?{Xxw-sqv zJUn1obth&Vrs>OsT<3FjF(~@F`W{R8*JqI5KH3&T>dL{0(U=H0My_?weYctAyy8sk zM+jloRVK>78OLM9kd2MbSp$~1Fis;*fTy!;@oD2mu+?QKkH@}VgG?<1wq-m^_v?G$ za3qm(E_I=3b*@VObI-<>euJVb4#8JjG*UE+Y4M@mj3ZYY#VG>eyNbqhDZNk1TyiP? zCc$W<%T50P@;eYDmpduX8cvCofCOrLb=SOiBFsaA%BGCG244k6i-Wk{v9Q()RO=+l zVf75kt(EU;JZ^Oo=6m}YRCTuPevx%TCmH_MXW zcAkChqKt%NA%JMf(Gegs4U8SJFPU;eluzo7SAWEj*RbEcqG87<@=6?#tGP@0sF(gO ziY;8u_jwcfC)Z4@LcDdl^k%0m$py>y8do=+t>zOryxK>OocrqoBsTVUVvL^~4ygov z{j!#k?UQYwC{>t8+IdZT(9)7G?E93Q-k_*j_)W|&c&4nZu00@Yopg>jg`W_&dnRXa zhch%0Wd}K?FE=zq@6BA+&25)BRWr%s8r^-!n*<6nR)pEEaDE7c%jJUFh819FmuScu zxD45oY8VGdUuNw;;!x3ajB-*D?6S!CTqEymFOD}_*RS${Z-$O#;~BWVgb4`<-4bSL z3OIx@m8ZrtK-?Y>uVcI~&e~AelS|4nDEW8mvfT)%wG9~E1RFVqI20GD>q!`R;(|qq ziP%XbHPlJ`t@e7wusc8*Mm{N-iqMq_gL?(I4HwVGYFi16+QKQ}@M4Wq*70os$lV{l z$35#nP&c8JF`BgU#`?f9_IMk9PW4)dg%XzIl<%o2AVE0VUz#;ZcI;4*c#B+G~wG>+|lGk4loywu3=XV?U<(aRPb?6Th30vG0vTae)xF4e3>gJ zHyM1Lf`ly_(N)Gr$#c4kh|;Wyo&vaNePZNO`uDzKY|+D$k+dcKKrJD5E;l#A5B$d| zb}ymfgY^^<+bgqq!xfyVKR~l|EY>yyZ+9BQz{+~(#7;Yp;9wKf!&_RUSp)T0cIDFt0(I7EHba7Sc>4EI8X6M?!6;a<{VK?x@Ac zF%+`ofj=$BFUG&zd?#>2SHD^s#`WjS!Az#8-q!yxBK+!nuj0gE$C%VdB_010tK{*g zT z+0tL2WGsuG9Ay$agx`h1R=l? zQ9uy<2C-Z*6nI6oT#Hb*GvG^L%?u0r^hAU*N*9_fpKi`9WB|Ssalw|)rG7z;5Taqm zZsWYI!v-0NO{l~7VpRV!$`h6GQBWl%aj2)4;#?*G$V&sVDjo~^OjcGSNBK;umBo%{ z#CpHQ8U{Hpa$>*s`04yRk3Bd15%QClpUc@DZ9D z81D!A1$en4Umm|y;GKvrBIg!LWKy-5BpW;ZUL~{N%Gn{hKzcSX!Ow@1Ai1YyCD#y( z%%tBp6|hn~(fLLiOnZO=jIq!c~QC$(?Off-9ZKd0;24^)Cffet*t+5mn^& zHl<}+f7n5 zK#@9m<_c;y_uzugL!Mmvrb)@K@u9;@j7)#&>Vne8Eu3m7-A7{O_#`-ETEp)oYPY-OqeOlfT)U?jUku?H&%a<- z;Q&M?xdByx;u*Aw5qeeXGAPHVOywvQ%Dgdg_@PvGm@(-Dv&_ZIvF`0uhFshlf?w@| z-!`PL*N4S^j?NB{R21qN25&cFUwicOj3~#gNlwmWl153XDZd7)Xf(}VUT&(<-)N#n zr7+wc*aw0+yaGn?vG;e`I~i~|*IlMQLCX@bj^Q$(_!fZ{Z*YyWjeG*im;}}EEF))4 zd<}cMIq#Jsu3`eIO&nLZ)^?r}@w)uL3 z@L!U&NvT9yDo4vDk{1`#8YDlJ`Aj!SU!Gy^AO`DkYGIFkR{k=_S#0KUm{gKeHJw5C zGq#P4{5A~*q?M;MF-~ru3q5s9|I}AAIh}24UA5|^C1!flyyf5&*Ug4vNmGr}gS*(6 zvyRQ<%}0BSN-rtrVi|%xV@iUU?=Q-Y*OBp34qQpy9w}DLHQfrrxx2IeW%A-l=dNBl zsVwX=V2(&GQ9&(MZoy}t(TD(+SXTqxSVa@0nkyfgO|@b``j`DpMunWA z=MYrXl>(<{$Yb?MS8R`@}eZ4|!E; z&iDFr)N3laKl)to2h&_u1#!>NAxibOddJX_&uB%Qwd2)T+InT|qmgBm&S{b_7{zBu zpY<0jt<=@Akakk9cK3F!ll+EO@~OyUG5@i1R*ZB0OJd^{-!q zo8ylgpMi|uSNCrXQEgEsOtu6@AFR&r<*z$>d(0P0+ivKP! z3(rvP=y|Z!mvGFnpSVmb$X?Cx)u*ShVXvm$15$u5vmqUZ8ZEq-y3dQlA2!&&`C^I9b%u z^s(M*N0!otb3o97NxLWCPvv}iozvj-l8y@>E&7!2Vc36Dzhbm)%d(JXx)rKPTO%!u=_FCAIt(uyju=gUc!{i?Z}7 z>-pPz1cvPC9ohWSW4G5Xb=0t4NzL9WEtXbCu6rGU1 z(p$B)TmiYj-)p=TMeA%xL?|IDc62J#9vZj~u5x&Y7Z3oQ(48Dkp(#e##9Ff&42ZCQ zsG>y(#+`-d_5b;3B@~2ff1yfDR+RS4FQ(iifttfOX<r zn(sE}cztuO|E{TOLan6c%uLzGYy#`HI`;3$5|lpiTD+5Qm}FNWDwL^gVa@)3?tB{6 z)j(E8Bk`qwdV>mt9f<8NFtT2P@l;!mAL*p{yW(;YL6#PFPG>wb-NeNeg$Ivl<3>bm z{L+qwk140ct?&o|;q(uVf!YNzMKE4zKc^Oj22)lbuB`cI3f5^cs}ve0L<(P%0h8=V ztX=i2%1(lO-gF#3hIkL`MW2GqLRHS1O4I+x(piQ@*@at}?od)fKyrYgyOB=mF6ow* zMp|hZhM~J#hHj+0C8fK&MbG=4bAH1`%o}^}^{jO-|Naz4(xgI)D%DPyuV~8OJ!*#a zw$6XwPL`4~AEf_X|MmGQ_IVxFM^z?*?Dh^@W!3xgBy2+NMgNM=R%*d@lN)9!4ISxl zWizlt(mP5rQktbw?9tM2kW$-80PMItAApmN@wuGm046J&MrEb9WoPGduZNSU5un`b z+dXKj0A}Ru^i3dHcxb2X0BB;IDusBl&diP7wdqi1uow;9%2G!jndP4<0No;$s& zv!B7i5haBl6Y~_BqkZp1PnT&+WflAKUIjihkBVDQ8xbe8bTMW-?U&otj;egdl*JUO zi77ex#V}psK|F=jZq2w6i{?~tr4WA3DF25S*9vkcVK2_LqzWy1l!{k=`g%Y%`X?YM zIjuSWlkA@O8AiT#)8_AcEXn;^H?oG{O0z_IChO7W25ZC}Of|DTsa}=Of`i#f&u%9| zQFJ&eN8%W+9HQ^AO}BI8(46Is;!OBWi_V^6B zQM!Pe5H#-FzPvFq@jcq5P91-V!UiYbliJDo+QbpVz?aBDt@@g}r>4Ikrhila0+7G80UPNd<-iNQ#1uFpn^Jka>rN3&>1#Hd1S?TC za;GDp_f{9UDKRrlQI$|~u-puAi4iX1n6%&nUI`5cqy@$a_oI+eNSV&xnFhScEIW6L zVkui_zWPITzQH9hPOX>6j9(H4LVcgnxq!2nT_n|@;X7DpjoI;UZtH(RD`7Kp7D`pW zKPox61Li`fm+ikHwt=i8)=mgP`E-+(&3`jyqMd)RQMKwNO6joX5T#UgF+Lq=75@y= zdacf`oW~8x_Sx-q7V6?2tn37dgj&(?_MrS$ViR@0j}8z&N^5kb!^Cr-! z2980j60C%hnJ9FtjOTxN=%hzlD)498B?OeQh6O;JH4k!JcB5U}gJ# zry~Z-t5QNd&Js|GX_ahub%vyFbkY$LaaCaOXisf2LWN~PNcs83^PRX@?)O28eTeva0*_LGB=Du=s!GL2POO~{ zc(^&Vb~R!Ak*E};Xq)HiP z)qZdK=A&UR;0B>{E%l`>@nnl>nc8>o2YIa|gUl&MA*l$o6~9kptr&n@g}G5Qu)~A5 zbH>&1C4lDz*RaxRBK|i>WtR{Ua~7|~ej4j@sg$xNXzTy|0!Va%SktN=*P*&DgjG-G z&!C$F0I#yx?CiOOoQP;sHa9`_Y2-PHC0xWMdZf_bMDpK{L#fuA%qKi8`*V0OK1Oq; zC{uU+1GF$#Kut;Y9G7QeX%g!}HJ#SGMmhTL-EqEDZ6G4&E?J8??LRjSBN7C@$9r%K z!<55#kisbDuKohy`Mf6FC1;4l5nJkhvGZafNqEP=V#1u7+y@CWJ~m4((xx_iTQ0_S zt&LqY=!>ejnF%DT&rbgAOEv~VO3@Vkh`4^Pv2?OF35r*=F}KNVt*1hCtGn?_^ANc} z=R3;B!li4ye~qFwTI<#hz0D85e9KF6N=n~uw>C(9@kS0M^Tc%QNL@9LoWH0uGb+lw z_-*iWq1xMb*Dq!DJ^iXbkN_)Ht%tD-8PY}Zy`gG>KCS314Aio1foqLOe1f+#NcMSRT|co>4<0##vask!lzv>hy{_Fim=H9!v876b2B7R`YP$$ zY=W?o1Z*_V0~ZFo!Dt!-zgAzjg@yC70#Vp34LNAk4JWJ2(SaaI9be9F8XyQD48naZ z$|mSyyuiw*dLK?oP_v!$phzY&F@#8B*X~U5%}{7+eS?>2`!8IV%0&)i*lElZW}aN*p)F7H9|Pq&gnJi zTp%#1mfBaKDfkDDLNL3uM!$N19{N}jMb7rbka^=;1CFXD(EToXp!#lqpo zcnO}}pM-na#}w9ob6_fC{c5HE$`8WTBJ$1GvCgIOVFu@?2b-Mz@UTJ3e5|rRbZdpg zC=4o?(xVrDN>J1?M9{#eL(bsj*#qldc6buux7xB0hIh90JkgE_40Z$Ay@P1}@9~z16eqCm1 z5PB}TVNhsbj#L>v9u#ZI+|#|Oe*j;NS&HGNRGxWxc6$#?v5N1XQ2$I?6t970sFM?s zKAGI{y0J>X@=@w~hatvGk;Kp2zgts`#uU6rQM7}q9Y|3WepdcK-I?>0%iEBO^w`Jv zr&$xdTjcU{SaEPQAr=DCv$Zi3L2p)5p^wfSSJf<)Q0Y7FLkpg@B;Ff9$yj0MzU=g7 zA8J0-pJOR-Hb8NrKGFQ^;b}5JcADB_jgiR_f=|EUaaaQftJ8aeZ2N3+pH?sXPmj$~WJ_CU z2jxv#vaRU%nfGLc4Nit9O5K#iMShdi{M~87Hi5+9k!XMKEZ#i%*;9e7#R>j8VvrXz zqSD>zopp5Ps4dUs;l|J)Fz|dYPeu6TW7g8y;2I)cCHZ>qAsKqB8C0W z^t$M>A2b}Ni9vFdJ{bS2)Q1FEe@DlI+k?|x>SnO+Gd|cAObQ7Z6@mFWEwvmHK~%{_ zkLC)f)F@)WZ%bR0@pWHhG`w88M(RoG88!f~?VtD>Al$JlF3nldc*>-A->!cT&e>HY zr3fZmw;35s#~B;RRL2kV@_8mTKW5v6#LN+OUiCM)2Ry0>qd=!#T}rmkEyF2|(q+iH zf)0@IW~pHaRitmczS)lKkdO4azgtUm#4tqvMKG$_-JpW%6b3UUq#Q!MmLXwSNy!R( zo0?m)*}*mlrj1aX^&a1Xj{43jtZ@(+WI_^+^%B4NMb4mnY=bPN-|YU4`yAo7}0(eMNcy>~B!a-SP)HMEh4zWjU0Xa+9xLsFwHkcutU z{n#@b^Y5&Mpwz=DBYIo&mU2XsYed#wlSN^aU`2D$As;dg_#uzl!1KsX6#2$UDGd8C zhs?~XkIaBeCST{$E zOGB;g1jZt1%M_Y5t>oo_i`Yf(b47l-LgW>(cRyX+Gg7YgyEXXkH+Wy8>U>e;Z!6j5 z_(a-){E|lGRL9}ae9AoQ3k2lcBFsLJQ8laGh^>>J;Qr7-?e!2*@s&#Pu8wb4E$!Nc zmH9MU?rC>$-O^YaaVZs{6-bk;PGMJ^KCp>u!6Kt-gxGHFB| z(W-kkt4*mjY1|dnaS<0M*%6Ai3q+JClqM@S4I*d^MDg>qNGz}Wiw5T8G#Ef}=ily4 zVCm845F1o-jYQDKrNo_9sV0xoXkfAuX1=BT2V)Y=bpGLwDj`Wk^g-rWu9&I>MY}-) z1*sNaCgK^Y_MLjIk2PN}!t5DR2!%;n<}>Yd1i1(`q2%ke4_CWDAPD{&18|&1pL0eR z@%u@P*d-7^Lm$h%t=uZ=u6x3~2gwXH+<~a(jZ)aTujeMr^e&8+_zx#QUmdsRx=UPB)ACOu$Y4Qfj+SCMlKK~D^U%9FQ_t)s^xUbr@?XZSOxasW$ZBM51{%JifTTY6N{E;xfvcuFt5PDy73- zq<@tWiy9laeOV&C#Ao~hCo@uBP5DK-OKD1&8UOnj{@uUzrPcWOlC;n-pRoImV$qR8 zw45cN2xBPe-Sw~QdX>Qp;KV#CIBsAc2_#vxjlY`tdLXYrkUn6^B8qyuM+&koo($q_ z0kI&hJ~F*~+8N{Pve~*!v&zef`S0&FPtetvnk3()l!3ol#uZ_~rJIHZD(&UYwpOCe z^WB_e`M#s($&7AkUb?=uFVEaTU3FvJe9h)q=qP=#Lez4z1BR~E#DlC*aUcYG$<2)x zbt#q>kS0)PQ7tqgV$O%7f$^q@U&%J}Rf$ld{SQh%_71lZCDt86R#o;>+$FxZaRc@t z6+}GdlGXkGL4S8}stfLzQ!-+V8d#{-uMc`mv>5*HS!MoC-3UCZ?Qf?RQc&i4NPKK} zA4*w6CjZ+_&Acbv`H1*~!F&+6uWca$#pJ7qy9yO%u29}ZXQTa9FbTenkfwY)oQ4>= zPQU%-DIZgF51ql$3$Y*`VR0sjd#_>rdpEP8UA)^0inO#=){pOKL`B2DRi26ubls=^ zsyd>$i`pxMu-%R+JE!aR*=UHcymFj*{Z{(5s-G(fGZAbF*RCZe8I`Q04cV6_W|V$$ zxrOCE@DMZ2>=;TkdSseJfLQ(IJH2+_OvupX@G4r{DV3U0MkPO$d5xxdrWFwT{GO5? z?Q$uWz>cuhQ8lLhMn(u&x?;R?fV_E8);rL{388Ykd&i)Q>9Tbm$$wrN$J10jy|zUx zz+|RDS=bv!zx5EW3L%ZePC?i=r)onukw%;`*CcoSMV|)fOW9&;TXRlBhD=+2OcoW? zNu&%)%$UDvy)>lM(#;p+86>O6ZR`l%{rVd1`YuW}Y2yUtU|fsvN&dZ+U!Y&3Y$kE6 z))E&^y|zMoyGZftRv`52giBD*Ue?MF?6v7!)5?5+JFIX>X#V1TRL|}bVb#lXkYFl? zW``@%#$;A|oz0&Q*3Q&6K)9)6QA6^}lmEuAoWz`$$Y7J-$u?*UX5rXfH1OUc+i(&C zA8nsYCvb4aMD+b{VN6AN$$DP*vk$_w1Z=y}9 zVKEcG8Bc!lkq`ENxi-&OuhFKY3zW}?+IJPmB`Q2QCqhWuoaQO_%1fCnG1*b%=45 z6O5vOvZ4_#T-78O;40VFq-FMcL+p7&>&ROOIbFtAOI-~%^bi;rtwAV{-B|0_R0ZY+ zjBt14)CmdS#%;Pt<5%IWhK>0M}*OcYlJCd%t>h@)s zB>d6PDw?NBSnF^bkJVfQ)kKfgC|za}u>Ll2nC$|T38_J;l#9ovMjuDZ?(I?B0s9FF zf9ovLniF#ah#+9E@bRx3++F2zslN9KY#6-b>}eq0uBY*2Grl(4Uz!;bWE(3UZM<-j z?Qgg=dHyV=DJgo*y8u!qB-IQ)zIJhb-HO*+|FOs*Ps7dC851_48>mH)+g-~>qRL~n zf;I@hpgiP7LF-P=2mh36x7?|*kkEQJsti~0{9VLe=3D(OSAB-$gR*R2`95SX8uVXA z+D-H03XmIDDR58(`8ie$R#b>ppTr3Yv9@Izp)%rotSXhg!fiSmWs)QZy1n+a-}B`>tYC9wHpJ<4pZfLr%M5Aw zY_?q;PZ_~iBQC_T8IUrz+cBU0vD6;xo1~Ok_QNMXc4?RGa+Ru^496DAHqW_mG|2<3@ufp zF00v!S~&4RnrIF0nUYRp^YCa7GvrQM#T+{JKUa{LEM=-6vC3<^Vn`L?SfHGXNXYT0 zY&r?4(m(4^tuVCB)8SU?OibeS2d){7`A70l|=V(^6PWw7&_UmVC~`gL@wgY^gj$?3VA1Q3y9CYdde=qXss8L&R;}gx>ifvTTgT2B&YGgKXb^!Vg*{X zXKQM_TbIDWZARE~9**a0-7qS$A`LDi-&JD$tq1oUIDFf2i~gSF!F-WuC;{Gfh~?R~ zy{s3WgQ}4-mMx+HtYL!p28sQ+{NdcGV%8+#@rrlMD05!#x>gw3I)_lf8m}m@3KXn= zcX*@f$KZVCNCl5;?rGad`9A0j8^#I4J${&g*tC8)(hz;+_Zp~;rTW8Pth_naWSVq* zeLT>6-_4I&eUsJhCK!x~vOe95JW=YR(^LXK7cRHnU6tnjs9Ge9R8 z+-yl=17>+fVX3zt`t)kfHVychY^Bzg$q`;zM9F_r^y)NCPu!h(=AI=8#xd@v8IFR4 z%7MngN`!OuH;5@gsTtXSKC#B$V^`a5FGt@A_BKTztIdWAE;KhnTa*33>E+B_A}Ssu zQi-uLMcd2&8BseAg{=%YW3e#%j>3u-HPmq_KTJm6&?f4f;SeS=7)mKC+S01p(ywv6 zQ4Pp@)2B(WadkHYMnY6l?A_~+l!q#%6nS7bymWnU2R%MDu-Eb7W6SD70ld@ogFEty zCa=_eb}}=*6z1}?xt7B&NF=kY3>v_pd|AK#VqNASc)92zKEZd`0?cIHvPNl5ROBJy z?pr)ITvM)pJ$gbWGm~;H<|5Yk5Oo<5B-y zYa{v5bf@6N$#5r2+H+%Ol5D-$ZX@Hb!Wq6BtjVT(kYl>Ww`t0oEWxFRBGDUkKaD1` zO5cWSewDLt(KDowTyR&*V6uMiY0T`VZp2&k>Fsr(CeJ|1s*?9am^x{;qo$1VwatGkN=tj!1TDQ&zpF)?#1%GKL-(9+Xy@B3Kciz7 zXdgMT7Ln0wDvOTub*Xn6~!N9I<=Rzm()6zOI-RoV<1rM)P;{xDt#P@fKj!TeG|4~N#-LQ7Vi zds^3T!3ApfCfEy!-6w^W&Zb08_yoo)Thm441%k57va8-@U)eo~bKrAOL;A1e-)2MG z=bB+adZV6&YMVFZgPh$_h^mHy=A?sdK(E>GZpUlDvIwBAAjW60Kq7aU?5w0;jXZ?1 zG3xA(&9mU)NQq<+bk*2W^h}vsX|AQ#RoDA=zG29AGP1hI70 z`{QW^Qt{{{#;aT1xN1PU>ENd863P4HtwsO?BV$Iud|?p^ujN=C%x)nv-kU|f&F#bkK@bQz}EU8Pl=Y@)_ObJl_E@<+?#i)vj|DV?PO z-W&<0A(L;V0q6NXPHCRk&+RovHyDo!7W;YZ5Iocrx(Sl)_a3^2U>k+KoOW18u~=7$ z*ktbTN_|Z~w=jah&h?|GYV9916{mQbOn!C>7}NejORDeFMarDWTQQ?e@Ff6cVF-&E z1-FCwvK`Y0y6$%dJ5cmrcSvasSL$8{Z^6bEP~E=^MWXnt-@c>qeDKFrE$UZw6ZEn4kYL#;Ezm*V(-DYje# zHw-cKl}39VF{wd|SNp(~yPB6vFzagWb#xRXIqI~(&=_nWwy#!s=_d&6e%h&@*zfqp$wh@E@79>-4gGs*Z<@v4jj8a1DG#9VBx6DNpg z@_6a25kGxAYe&fE(Wr95j)SB=Eyr_YdkGV%E!FfMo|Dvg_0*~H{vwR}XdYTP0@|$OozYtCVxs)${Q=;`L;f&Yz?693h3}VLA7+W|z;z6mWf_mMLi% z>c|jE?IOCH3X--4`9jSnEMK8~{mUb6x%<|Or&XPn6h*aQ|G%&8FGO2DSr5A%>UWEi z4P{1(pkqssC?ouG9D37IYSq&|Xt93`X3zt%<)FO=XlZkzF{Y61RuWdWX-J9h@EOS3 z`}-6{iIuG4uR5-B5v8i7Gi4*e!BBu0iOSx{oVmL~QZ^lB1Zxrd=04DXt7D;zFxN<& zhn(l^0LifZSV7To%gZr*4JqHB#xg0-lRgmfiC6vQ0StSMQ$W132HZ;Fp8!GL zQA!bZxCScV8BvIh6cHfHY_y!N^a-zy<4z`XE^2P4FlPqPH+sv`^CFgTxMW^xna@Kt zuXZ&W-Uz`|W`+NMmNg4TV6spU0|CsU`cC2O>s~?eDK$;@2|PBeTTy0f$qvy;^Zshp zygpX7oz!mv1Im8V3|_*kuTN`}5!_0H?tzU=#_r~!)dNAh_tYO=1pek) zQ!M53?~W(u$+!=rW!be?DdzH_o?`!a*12n=v#&#lyR&-dA>9(`NrRQFXe10Z-glKR zEnf2YamC#7FN|-o4XpIGhSBmyPc`ngb?CkAhm6m@STU7ZCW%o|5(In(9+!R)C#A3{(2I}v)mh=#G?ZYKi6o?3v$$NMPV6K zVJ*eJ^=C4tnG&? zWFNjGJb)kkvdmargb_$8v2dVSFbWCMd?knoQq}l?lts{vW0GRdBHKv0lE1YC<_p+! z5O>qP+RhRE*%f4)F*oM|0PHq-Z1)ai0fGv#xLf!mu zqd!MvdTZwFds8D?z|q`TqHLx3ht{iSv>hd83ZK{dvxff~pZU(@Z3LJQbPTsTPyq+| znR4AXS2=|Cz}M_w-p?_PPGWso>A=wpPzd`P8HD1j1{vPk8s_SG=s)| ziea)*jZq@DOj2IV&1ANuzPGFM@sW^GeHq3D3Hfs`6wfSDfogocB^e}m8Og^eXx}~W z9+x3-sf`!2q0;^93J;Q~fESv!jD+cXs>o5mrn-|7V z6}G{VFUyOEKH~_&Eu)vGkE@L#>J0zzBeiJv4o01Q(-G>=Ug<|rP4n*{<~6fD`aY)VSX z=^`swFmla$7B=4OA~HrHB_l!IVZl*mWmPfHA>8vb;pj@JA)C(nPY=p1@L;2}=!#9* z>luuy!UxaMzdr`3 zL&DoowQONSy1#BS$?Iwff7B3Mkm8;N_v9VF5(YCKK|O&~(|`a zN_sd|%AqogHkvH_4#r_=`nZ6^_?}Qo+C`r+E9kD$-dGe`yGKndd0dUfN5EV3*LNBE!D4g0;5WqCG%{TtGdhrfPMX~lM@>V zeF=P0x`xF3Pp=hq-2s*w=kR0SB>;`Wss_?4mQm>B&6>0RoktMIH%zEJI@Eg1ex{L9 zM|m>#@B15ul=A3BjizU3yh?Q3rWHn7&ws3w5{W5xG?hL}edCxH(;5{ia3uH=Ag|4q zZOQXt$2jkp)5t4tt{pD^v54#=BJm^xvoaXB(>ZZ}1}fxAOwkdZey+*m7P?Abw6%Q2 z^idI8P-6(>WTXM;ML^^S%NLLjx9Rs+S6>4OhW^M&Kz13Q3dAp6hRH&d-@&_yOUs|A z)TmuF@F|&hbjS^?%c4}{uHR<@uGb!?)4QW2^dgkgmmkkaJ4$7Q-Cd}EtT)uw61b=Z zMNaa(tFacu?n~)YV^@A$rcY-yq0EJ$<(mJ+d{YTu*RkEJM>z3O8*r7r%x-|;-6iee zH&~ZW#(d3YD%PmotTQoNPHyRR?Q4Byu(oubl+NxZZxY{z;;YL(9QEq|+JG@M?CzoEOoMnBW2 z6q54a480P>+yIT`Q)ZK8&h*P9#YrL+1(W<8S&=VG#PPp(dd< ztXe0EdYiJtx@9uu7q1m5M>gm4aw>r1DkPM2z3i8hWlp>FBLtfSa3zC??X5S2d67sL zbOD~7=mNlf+8O!J(A=lezuhF^4RG%s0n)0_JWd%po}%e13cu~I*@j#H0(|4rISe1^ zIRG@?Ak4vd@#y+SDdzZ;YtWX(>5i5t$&ZEo|7o%!e~rEvd+y$k(*65__=UWb+ACP| zh$$ooMbPVLE>QUNtCIi|N`%MN)5qRYSsWT%{=Qi@kH>`NAn8_wM?OS9rNq(O`F=X> zMs*e#c3nvXMZ71xX@QAvAY@v9=W4Yg zoqVgMOgTU9N*2?ObriahMcN&+ES1z;ZTIuKws73?eZjjTl=gCZUgp7@)yj-x$ImhSt&m>auEfK$2BUQW80i|Pb*e%ZB|s1? z76Ne7Y_6%^VDgaOGa74;SFd#gKk$kX)RhXu@+o#t@U(z*RJ2^j5f-kMa#l*ir|<%z zZF<|zJ)RHO6mYg2iC-6o1C#W%MkcQlDAlH3MIWMimh#9V1ODB1_VqM;Ex;U^OPsqvVBW!qG)Up7hhpOmH+N}G( zx^JRX+d{cUB@ee}m}r+6N|$H_l^Xz*I=+boI6ebco1Ozxbo}s{r7b>xtdI+CW#Etxww1$FP25S3NS8MR zv^BRXz;;fdB zkw~gbenBZj?_YBXOl@m;-c0-=aIuoCDS?F|DGfA486K|#jaz>YPWI-VHH_?%?9}X{ ze^w(5Oc>4Jf=V%mI7EY{egCwu6=Pmush*}I zIp*rBOKJ2`&6{mw!Ov<~R)?BABZb77mLh^MXL8{vrD71TqQ(@p?HqD~TRCvp8*uO+ zGZX-9V?ag1;#=$3q}VCqtb0F>0Zs1xs?JhH0NA+SqQ&!PN^2CrM)Zo@z9aQUyBQ!W z`f%YKlNAEx6BIDBEZ(}Dw*lCHer|HB-f#NI_|{wUDo->-`4w(^)1n6f>MMN`L2Hah z13LG|NAm@#e*j0P;cs1c4k{$oY)*^1>VvRJx1bK}hX~%WXc29$$ z?e0Ed4i~lf{n};DAFhWPv-hIDq+5vyXNT*w8wY4xI(SXie_W~V*fD}5 zKZqTr3a_X6Ou*=H_)o&W5k;MgJoT>)Vy7=yC8K)8*JZUJwQ@dhKrC(adAl7;$U|&XvBoC$ z1ISUCnw(zkD*K05t9n!qa1H}&IN$}ROx|47TY>IG_bs?Y>#BwL@ViAJ>&gUbZZzfmtf*^t&0W;~I-j=8MGx6yg})pL8*7!UZ^! zwK6ORix03K4e~+wH#nqY^P3=tN`7KK)qg(y`PSDF8XOG1!wc133h+?5e#>Ioni^i| z)4z`6FGpv5)6EhV(j(`_s&xNSqiRXuW;Z;8(;* z_t^=WofTnwVJtqE z@#E73hf+i5qx|loC(Ztui9oll<|UK;EsUc^HQl&=B6a>CvaV)Kv3v4v=Vh&2{r&l$ z=s6JCDaPsM1A52%3fl+^B}U%wtotn3h^K3<2P=H)87cRS4HoL~RJ#ItH&*oQe;=hk zGb~$$#(%cLOGdqHHDa{;WtMau=`l0l{G03NmWt^0;1`tY7mB)}v}aEH=_YTD5gL_j z`7b61wLI(2!U7$Lrg0-<_EaWhDELk)j znHxj{zHhn9Ii)09wfgv*?q#}57B*$im+C4X&oXwtj#)swv1G|sg{ExXI>fXJ{q^Db zm}#vo24td$Az)i?D8W910T9ok1hDCX%&9g0V+*;|wz;>RyysgJQ}to2Wl!unU7?mn zo&`|vrbzHyAa8VuUOK=_tQD9z7=)KrHp(yBXsE-WHpQI9+v{f(p$BlEkB{ z-kalJ*mL>sOA!peXodPUSOSQ0B}3oiSf6FRPWoF_C*{z@_sW7d8b*7Ezwq1rv%)@G zpBqk-eyWVXW89|S0 z*oHzazA_^CNrg81qI@PkNeg@8v+T6J6L$nXy`l7<2gj$N{H9Mu@*)vGz)0`VkML7vf~Q^ZeS zzUuIF7J;(`=L^YNfshQq@0R#8cE#4w6*SjTg?=}tl++&HZAB6fiMHV$r zqlFQ6m!uS$q4VB5)Mm_Y3X#^B4B1H=(RYf7df~~k0wZO9{4mt2?gE0voe0cnsVQ+EkN z%ddO9&0Zj$e=Z%7FidrVogRe{FEO*=ProRH?uPI0WXb&RLs4*6CA&{&_En?(@!M4q zwFZ;qCW2Iz76(l7UM-uws%m9tcvBWDGx-@WG(Bmi%40u*n%e1`-YIobi;oWT9;)Vb zKs{Ub*@+O@Yz{z|^iYKI$)a6m$2OS3bTgEq5~tpdoDf}=p9mV3^vB?lBh9o14?u$N zTu0|{y$cV~q`L{!TH#huUb@RtXSH-NwZCrrEg16g-0J6;MGJ?^KkO*2`iY_2VjI&X z{c2d;K`Mq0hMgAdp3I0@cEH0{vR`o$&kfXY)r^&X<=-bM$JwGBh5P=M ziIeIDqw9uoAwU7u_U2g!4rlMYzA2^hRn$#_= zDP03y#yFLPyvl(?EPyb^wbo`yqOta>9$>CoA{(fz?=f1N%s4f#Fnlm~oCoGHB5gYI zxj(EmuSiw6V=*z3kvhcg=6`8Es2Pnuczq*W+YKR@VkpI4C+x2SY z<1H(?W*2P=O6LBTgek#e4(d6#T7a^nVqUYHnP~mw9$(59GW_G6=bVpxFmD2CDQlf1 z^O{>?^nSI|lI;>sr9EvpU>2LOI{Xj;*~YJQe?}6ZH-h{&aaf)d5b+ z9-oyetL&idQu}PoV=L)+q&xCR*3a-Py2OC_S-jKur*02W{8rUzYZUOt7z&JQ{_7rS zlz+|&-gEqq-@)1@y{D42*VOb>7_kSq1MN*eibT`Tx>vVC9_;I@l7y6zdMi2f-)A{LTN+2CxtDl7xIyT#)eQdkd+=b$b(KyER;6$ z`x>~rSN9ae@Btg`Ex>*6n8l@cKky%vqUw7-NYP`QX5s8$#?u82{~edcs8J!5t9){XKlmunP(7BfQ5;K>Z_w! zWJQEy+P5t2$+9J0ydm_Z_-;MkQpVsAw)hg_VS zD--dykuqTD8@%dPd2;V;X4RHC#;IQ?R%`UtY`zwS?e!;FXg9`P;8u?r7!>cOGw{mp z!>1&$($?o4ZN9!HD>Ik%dAg)hAMy=N2fxay;MVIx451TAu$)vhYJZ}2>ikp)Rlxap z9~$uKtR1W{EJ-BTlJ_%OWg@GeyLdYTPb%+(rt?ZmQ_lR5(7mgGKd`+0RCJ=CWZytv z;c=#|4Vam4lqI8;*i`6~2oPDcCbz330!o%BgpI?+BGKcyFqZw8xY%{)0zh=|JuwzOb*UT%45uDHalY#@XKp z2IQd+vd`-{#_k?x@)fx7_MHdK2;e6VFJXyrM-3OWVcsB`5pj1e907Fr&o6LD!- zh++paj1Q$o_=9N$;dHHLjB`UqHVmJy|)4+rAb@vH%oJiI{qS6ACS%Wg=zvkQs8(Dkn+z&D(hJW+G;lR zVRNYW;1M{z=UZ+gt_dZei>T~f$NQS5L0+V<@+mUAh#M^ZMHAmOXlDld<${Zdcy!Xt zHVi%GF##|%z+0nX#&TK#dJq7f1HhGS=$IC#X)KpQ2Il4ggErNB?!X_i>a7ry35SLn zP3G9SwG+Ghbt+|&04Hkcyyh7yw+1mHHL6bt`@mI7s`KE>7MZr_px9jGAGBpH^!*8- zt4)Tl3-|4TMvrH%NI76T8GElh6_l#kg+2|mK?R-I{1vsslB6y+|0Hgs+2sG?h>it& z;!?~fJI5-Whas>@RwiGJ!RY!6uVl#iMLI8jZoj?rcilrK8@!@F@Vi>+>pi0|{quXD z-l+bC-KoRtyB*;vW>GG<*8sm?`m{>vmFr$5_>IPbRRkJmrJ_e#F?oC8|l^i#V&Vp{=Rk3Ud85a zDk`BLt@D17WJw$Bd7PAByqWr_dRD_OdrIJy8ze>YGuPs1F!hP`H0GvY7BJZL*yNbg zMlsp$m+usH7AaZKa%5a=_R56DZPzdEk1Vvk4sq1Fe5;NgG66t(`^nPa$sx!0N&P?uh*~9@s&L00;mI6Lu%u+&P?C=vwnf@9!7R`+I3P?IV61`C=acd>!!cH*~+dahmsgt&yH_)d2~Z z#V|J1K`$zNbmzHv*euy^{*P!Y1Xw_241QKPicL(cVoXHjNoU*f`UV)3GFS2adpbQe zf4`er^Uk36-+-Fgu{Pr|UE8-#?|6c(zd=+OL&!NGH5^ zg%UgC8d1aHwFrA-LYF<)+91euF+!ygDgmNH4I`Du-0L6pVo60yuUMo=35GmHrw!E} z0w>i4K7pbWP6bfkR4KlNCZdqCUUMf*?BfH1m&ieXnJVHBO*$_Vm7}h=qwT$sKI0_t zQCDdX71_N*vaHtaXeO7Xtw)I~WcX0lAAX_9fd%WILjQ!wY}@H#cIYH%-tUSM2j3s} z_~Uy=SO~qmrNu_os=A`sDx&r$*<#Q@)kx(=AG+-q`{oZqt*N}Vi=c|@emAUaYH)mc zqqGf6X#M|syIZn8Azuxp5`RJz<4Sa#?Eo|Xsu01X?X^`ZOHY61I#tX_( zUVm5MSPL}&Xa{^{O5pPic>FiHmV>GYvv~|$Ja2ox4UFQm92cvA!>Z4YveV9}5W@Dp z@w`HrQozWaE=4~?Y9-kg?B~bL z=iU8djJd$ASeI!I)x3WTg|JUf2yPy^r$t1|`x8kdq1yU>@Xseq>1VTi#fYLfki0v) zS4lIR%Hhw!HYp;ax6@I@|3Xu|CBpLsHh4^8M&iGm64zxISZOxzvnJTQR!y`eHzY*`*>xv( z;qL!M0~?bxj83y{LaRcp?uQk+{pMh(#U5&s0Y3EF7=HPFmyB$86IKW^vTO2Q2IL-B zH`-d+;e^@CNj$ReewPnsz%ly0{JtZ^Iqj7>&Kjho!j6EK8RtHD1Xlk%}m1 zX0f_^bPay8jYSlM5j{GE8O(l&4}R90KWcB#Wg2!DUp(DhAu%(k+SF%c>J4{XF*&2W zPh%D8Qyl1>|K>j^EnM(sgqJQ6tGRaZjg=mO-`~y>Wt!ltv z52xzHTma7O#?Q-C^Gr@X&nZJf#--RUi52h+8AG@tf7_&X{uUQ;Y(7z(4H2V7hGQD# zjZ~25eyTiE0TbgjFBV?gYH$KR8hu(ZK>l}1dim6?AtB=^M)BvOZ9k(fhq~*<7x|q7 z>Q{*XuPE)_OU^#-IYKW0v)!K}KA*x6l#%#_>asr6T9|*rliu>|T(VX4lD;+^UoOf; z**`y=ncw=Glq+qTFDxcrL_j8lOYnQ_=j{wB*7{E|B>kd&%Nnm7bzDS=CIlaNq-qk@uAa<=FS?h^C+Lj^xiVbBsRg!Ghh%F;f== zcK`mW8AWpa*Ty|Xm!0Y*+c9iBb$yViKeHxA<$kW8UZs019>y7XCU4BDP;7YV1fdLA z+1QdomA1e0L;UjR=}JY}iQMAB>P@uAwd}-r@>13mdprZ`(4C-M-kTC3H%JnmB}>FN zy%g4&dGUCSNZN4^!?4tH7w&lLpXw@38(#6wEV@kD9AO~TEUhb5`&XY;3^2;2>N3lQ zJ#%}k(6S)^xXeCt;rdtt4f3aWD_O72Gqvu(f4dewH~&yiYkn_>QxH3TNg^z1hThu9z6Zba!d6Q}Qnm=9k@7jW{S*gk+d~vqZ z=?}?}L_#WyesNL|-Y1OIls(kcy&45ZUmxk_BQQ*AeXC+7WU-l(?4NE5n47$N17rS+ z8Uh<7MoRmW4zu6di^s6jwmP}(#NSTvD=l3AJU2rpuTe-t{K_j;QvqD2Y&Pr7TQ8P? zm(4iLEUTd{A~h%M-=QZYjM4a+aDA+uODl^>GT#rh5uoT8xNE(5wr3n8A;)E2d$Aeu zl*E%l^@99A&z`DhI6^Y1l}7rEPD9+R#g*rf{B|hFc1D3Di5J@Maq7K8iG^#wwEkSQ zxWrNz@4CkZ;w^o6yWE>9x{#Se>X%2|cXE%^y8Y0StL}7`j0~q)WQH1(cBP?w0!Q`&;W< z>;3}^E|+=EJ!hZ2_j4XUKJ|?ADWlxx#9x%z@NkyRjTl@1|);0g5Y&;4d>r_AKL3_O!&qb98_yJVQjT+5b4@$vbKxH?Q>1McVoS=FY&(^ zQgC4eJQbf{U7Fa!N*~%;>Lt7sqryfIuxj!?rpyo7ijbagxyaQsf!Hun?~xygsz zCfZmA**G!Z^LS{NJD~5KJ{nZ^rt_ol;yOi{^;f908SvIO!lvXlBezf2VI-dN8Ogqj zwSEFGXp>G&7=EsX#hWX|VD*wad+~ogUR#HycvL?_iljX7iv-E~7c9?155h4qEgX-o z)fJS%zp{+dAl+rEh@eBy(v>F3=eh?%U;Kd`Xu)MF$w1HXe`C7UZz*LMi7Vc}d!LJY z>s!9aQigVGQ|}3-$Z_Tvp7*qa=r%{R)=N}uap}0KcMYN;pHSSSXDUr_V@Zo(qc>8y zO2&b&nfk=dO~x+oQrlQ)AuCh0@kPLKD0Sp|DmF5O5rWbU4GGZ_PW8 z66q5HJJr;#rZr>RjL`ZG-k{G_RD&$Z3?>h<)Ef&_j)kw)<4yu~)yT?XN zLgjxWi_V9+Q3jLeprk#Xd{fa!f^$L^UKF`rDvDJiviwf^JYgaH6;Vn_kAUg?^pTnY zCXE<&j^WOB3|{`cdZhT3PY0i!f2)WKoX$NXuiu?M-%GtMRH>5odF{E9y*De|lZtj6 zsZ~7+OAHP6v=Ju@z|tXN5;=D~x0M(L264EKRdb%wQ$(;@JYPuF86%#4^ihJO&>btv zRIF7ST$9M|6Bx~_wqA-*IhD^^3hf7e1qfmf;dO;w{1ECutgv5H3nm{P*AQcA%;uQ$ zAzai;11DbRcDv9@;Aj}$ZyME+brgeO^bIUKUXzoPaQl-Lm<>suuc1tXkHPBZA2XH9 z6V5$0ZGpPBzJ8Q_HFg2e%TY+ckB;6QgM_y{v@Os03CU{vz@Qg8JE7uI_Q%dg&03?} zwz_zmMJ_R1EA2=x&+q<*o?uOn39b=fw~l;YIb!C_Oc-jT zSWI5O{eB~EX)b_)SJFnkBX=qDF40NRuGKhXf*#SKm2DyDjY5k3ylbn4q&aEI>gNh- zOcGqCbVm-@zRq#aHSc6gC%#~}5nPLNJigVl==ArYvy2XQN(jqcnUoLlECACIp0@h> zc41M(681p2v#U!*sZp*otQ>tdfQ^8)N`HJ^Jri@?;Dfbl{yWxv*NQ8)ighE%mYRuR6{tjxrDFwC!QQji|&Dr2m12ZH+>+jAO0SNpX|sr z{KxZ}1Hz3el(xG?+DviZkrz&Xv2~8;Qn9&-8%DIqU`Bx^CVKqKvLPb1GW_9n8}Uf@ zMAa~8UqNz87J*r`o@Pe`uHIMCRUW{-M#~_#z3acd<0?8N?fv>Hdg{*~?nVt{AvWx>XyYBa9 zOYwEyM6D`2=^S9DT$*LSDE9Hl$R6YDqs=WW>2{ST=OVlc2L4Y%OcV}7J;`v|?(owM zdq=Z7(cv3D%a3;(XU_q{6VX&EoxR)F98o*QMwltIOO9kaT#c|Y6@GE2SPQ(O?GDu;X+`O{9GOYUDjx z=kqC2GHbnS$2mGR4?0f})I!w#NRwX><~S?f-j!#ww5u z67C0$*d^ND_3GsE;*Yi%9xYP4OiVvEW@QhbM+ zNE_~ec*2{3#gH?EnjE%6j+COV3f`Db{6%fUu;5D}M?cw91{VHZA$Jq>ScBl;5(s8) z=Jk2`B*#z(E66x!Qb@fhwNh~S=!r9|mSZJU;MI90TN@F0^^*BZ&0`^!S&=Al*3gFH zANI!n2JG57bvzb@)nmPl8tv8E>*}EyxVKgK)*8agg+-z^rk$y&r+sgtSUVe54Pty& zLnte;@$yy~v2?5{ne9%Up&%AChtoL`F4u!MdOH+?AVRXX02-L4v&@-t=M8X0ohQWg zYJNO+Qi~hBYj?Quj3YgztmdUkoS3U&kLHeIj;UtPEQ0jh1Srkq8PyIKqWALWyM4Ch zVBDZAjVEJm-u7g4ZkBa01PGkgHXOxPDH1|K{!PLfHVZbL8vsJ+H|=9bGs za-^Ys^v_eUp*p6#J--6MM$E*TaO86pmNEI+?2-~5#lkx+6%u!*D+RjvKj~QnN?>P^ zd?N_UnUFN1Cmg}g<74HYCB}tjfuiAuHX4O22}vPv=B|aQ0u7!JB-^$;p@fv^`BhNur-VhPLs@aqv5E=-iHhL0Ch5qrSUO9bs`0Sbh^Qz?F>(IJP zguaId@04yZ_vJA%Mwv&9FXg*K4Q6|Y+fy-3M(iL-(VODkgd!H}Siffqdy$P8j2ezg zwR^9QYddvH%c9RXy$d}UdA)db8a|~Doml7kG(ih@yg*TlE=??G^Y+c0_Tof@XsLIlJqVSr%vgOYUShZas~f8|tN2!uatMVJkc6b!I20v{Ds_S2>^dD%6;m zp0kS8B#Ws4xyk{9E0fOzU8FE8GCmr+m}sN~%t?CLOZ}Ql_1HEkA2xrP%9P=y*k#PJ zfKPG*+cK07oSo7irc;iHHQ(c_b7G(G>?wv6K`!(lFYh?e?XISmI zTnlf!=o?1G-F(9Tdiy1p_Q&qjD{5 z#DV(h7iqji3dKvrC{bX>5Ki_SKAfVOwqngMb1xxG7N0ngHhG*PqhVfj3bLz@SyQ*5&so7Ywuuf9Ve0&sP1Btvr(V^3~W}${2$MNY=_LzcO);fNO|$ z&W!_5vWxe)@-7C0V%`TSG;WEXNvzD4|EZp2GpDS26Lf{Y?}F)PfdX8GYQX|Bq#z%{ zgeza&KV%a-ps990l5Mb0Ob&jbpr`)><${5?^@@0_k z-B)|AuJXD3nSQ7-6LoCR@gz*Ikh$$X48gxK1X`-r~Fpvu`~`!Go`9sTQ}K~yHq)cYZ1+_LgsWE>34C6B5vPAGw zw6Q|3FJ6t1d$5DRC2H1_9jBMbMB97PrYZdAr7T|XxZ(4k?^PumJ}6+jz#K^2&}PKi z-}hrO$S)ODd2E?`>qI9zs8bU-!xMZm`N3XLW?ITH0XsY0SfNn)S)sdiTy8s$i}hgd zpj>}miMJTKp-2k@18j#`3Pc_`1S?IEV5RbHp6_On{sIhvcX(C~*tZuJ)0^~KH4#wO zb;I^3D2F)_#A=4*Hn59CTWd6qWVtWp?H?Wao7d~8EIO~L@ZI!TpCTC3PFrC#q(;#lm5=u zYoykeUB-X9Wi+!EPwYdX;2Byb}m0y7YGDqH@!uLrufsg9Oq6*2&`H6hS z6}{77@-By82{IfD(=hc$1djb@>Jdvv4v0dqZFrvp^=I`KX%MAJFO7wOJw z)`bWQgKCmD64#!(yL*OYAu3O!d`*xmdxFpMZ^2Z^ZMeT&Ba=~A)W>HBh|-6 z&L{4(eZ5VaF{<4r>)v1n#o(`jig_A!O+=HP;vFKav4SKcuV)e!-f>GoVS)HrJW zNS^s;eTTXYWZ5rsFZx8tgS3HH=-I_-mzUq#S75YUmWllUIxEv-Tv-ukdfmspaLx@S zF`F1Sg^!x(z2bLVGj10u^oh}UU1tDtY*6c^g)8m}^wG$f;EXr* zK6oZ~qP~y;UHx2j(f>+;Bd(PPc16Q)90+cq7K5M=!{N2uBGa8tr3pKyxh|1!Pbe~Q zi+MiF{9p|QjIKDzzt30MGo9GdqsIJ!m|MASR|Qma@l~6Pq8}R-(n1ZyIwr_3o!ThU z#IhIW_*KU%>XG2QbG#F;z5k*#or&Qyj;?T`)K5M(3-+|dhL!xM~hV|IXn+0QR zW6S^0i3;@jZNGJ=;PE{bfqqk9bk9%;?))-KHVucw)$H!(Hi@d9=9KHj0(r8@lM;9> zSLVB_k2wveF6LtYqkbs#pV<8u2OD3#DqeM}cT{s#z}i5x*yUBswK$Dmjrf-zu})6QFCm#~+@;C*$J%h8C{trkr){ zk+^I)<(rA>O=Z&=AGJ)nhqN~p;SaHVT;Wvfr@J41EngLGnnCgh16m?UB+We2_hT;f zL{9U98GsXAT&n^7<;>;LM^xPXM^NTQ*?*sIRhW#x3V%L16IUn*tq+lgW569P`)AMkwHUTE%VmG1kzW~CG$}ZWI z&Uo(5Csfbv5V1Db-Z8e-f4;j}W=rKBwK$^rAb5lM5l<-UtkQ^4SO8$8YFOWHY?{|T z1^g0pNqM97ZsSwhZdx)1kfbg1$L#L__bCS7ZOtG&*Y7wd8vVG~*1?i6D{ z{EO#qeG65uDCoiKz2w^6k)sl!qr?`syXZ!^$eOyw9STRD*2d(Cl>h4hx4{S!p-7Ay z+~XC8^4)9{WQA+Mo<#SpBPs}Ovhw_Mfw1wPvsgO*WU=Asi05=_LWH?zkYw+awA>cC zV4ryNuoWU|>4x(#Mv66uQnYo$AXCCJYoJ+stbp=z@Mpp5%w3&lVVUvtmh}0`$~%>F z-NCWv9#hpH^zw7?f2&lh2^#Bxf^g2hzeHr{`+*c+?z<M_ulR{tHj`HUB*<`d$%xSHJ)b@f5(Y`9l|%aDe7b&7+%qh^W5$6n1>P;a{3V= zx&qckUSxr|+&oG!*!#)(bOf)9V*+!WJDGr^og)}~I&G$d6G(h!jAd@jxk={9sjA9t zMgy&uBhl2WM9pTGp9$ZKPt>&CNko-XGW_0*7w@+1k zt;3ivrNzQlHiykS_=b7I=abvKg}$Kew~3qPSI!@1Z4=(HR;PqoZG_gOp~E%|5-?qxs^o-c=6iAT0OA;4S>rl;h;YohFA$=i` z@m^d+y~Mj5H31t{%Ima%^{pJig;DNvMLc&VHrCwJ*jQD^Ua=m4n4emhTiH9c;xT=JmHqlnxQWHcVUj27`aRqfqvW^+#>6D?z{ZgW7jJ6~ue<(QzuevGp1!st zi@?Cdv`5YlYgA*!Uug{wx+y=qL%*#YVQiZ-qCfOhN#=@2wDI+hP~kbc_nCeQh;b!N zF1GHa5rjykgIdJ8bW8m~J37XwniZ=gL&+L;T`!cn5;851^cB}Z&zV%Wqhuc&M*xUX z{bx19Vy`z^g zv+t1&QOBj5&F&<@c?I-7%DZ~$!OeU7G>Zcv@R)!Rctp{Y{^&ZHG?*W`pTluv!R}_p zX8B^#%Wja$>>*}&TN~B~ps^8}N1Kr#MU}~y`@5fbauNk>IUaNM(cq2Y#z3ieAaFQE z|5{S&?#{uHuM`c5lgGj3hWF%T(hEV-JQ4@=^>vHh*i`Y`6qn|sN!s{%iD;F6iK9!n zj+G&alN8#M%rGlvAwl(Nd`Baq-eyAbT_dudNkbYyCiQH!+R^o^Oz*C^0*ogJ)PAz> z5=ifHeRya6BKC|n=8NrS6Inh(tNJG2L54oxPl1tT#L<4}(2~?w;J-ZanVhObdzh9Z>wO7o`^UO({pF7}o``qwelv3?O_pDktcx3g1+=r~{!ePR)?wYy zkmg!YNyBrf#t*Ev68Jx!itF*owRz)_w9kTF*PDk1js`m_yEub|<{H_FhgqiJEvM`! zeaMm6D~3Zy6m}s~w8@KV>`Z~^=BXC(j3NVDqn<|pD3yfXbJ}>{c<V%{~SC&wp8o`8(+k5(hU?D1WpcukV=(q zydNM+)tEsAu%DYdL+fW^0a?psj;UcmU-{|J!NVir~Nq;RnE(VzF# zO7Pu+hX8kq1e-p4J1^ogZOMC4pik&EencwN?PDe6ik7Zr=;t70kR0D`;3o7*F-;kD z_C~K%ZF zd{?b{M?7mvgy@|~ff%RRtnHqFj1{SMY(rB7wCs(@-vQR->bbe$t|2N=hEPn~xh zz+>NR(DiZeSBJFLsCZ6)hDhF1ZFk;0UG(UTCu-Y@EGR5(!M_NfMZXi*iNdg<4VYB%rKzCwwPD-`tE1eBSY^=Y<%;H5N!O?Jqf?j57#^B z`(4O&=Wxcl0{@j9n3`YF?Ndwp)gaEvy z4WO{ZY>})wt8MW(Nl~gK3W_|QVPKdTu0=*IfeVFJgF;(FD70du-81>>P7WB6Z$9mc zQnnyPiu#SzCk5ZZX>{zsD86km`N#*U{#>_hw_#R;BG&xEWP`LyX$U;MY3`D)h0)6^ z?ZI z2zvN4!rL(BK|nxp$5VT_eHMx8d=O@Mcu2bS{|r18pa-Rle(}QD(v!wlU~x9YqKP&? z>X&A%>g0GI4MAS)2JSFJmxa||9@Hs%i5gRKu37GXJx^mFC*H3`w zW00)@4SmAxf6pB+{gjBRw&E}I1RnpE)Gji%LlLI&YOX5Dv$f#9BQU#%+{xs(ZNUkb z@=~l-_5)BeH+t!(WYB2u1!yR-OnK=JZ(U}!8ABkVGNh;{2N*!}c6+tcf<-=iEt1flYf;6j#DMu7Ne=Vf$kG@$$l1z$vC+bZlgg#Ut=Q!zh&q_!$ z$*sV6VWhf8wAgLSC-3Pgm1M-a4v&JF^7`a*+zbfyuRc+(cQYAypQ^sV{dqwxUaCjP zDtaWbs0;4v2+kBh_qB3=S(hOV$PpA}1|WxqUr^99cZzgdU37c>l~ngXomkG0(pf8D zz)IsC~mxP)_&4sjO&;@wc>%H2;Aa8R(%m;6szgV!exUD&{pNMGTJI#g|?Hi`kg4 zL`UhHwstC~h4N6n_+;Exe48XMGtO-f?>>p&i)-~R4!4s>GhSeEdy`ddvCxLE0wPfc z-_>e-iB*n@lY}e{#>)1E$-6vbuBP^(P3qfwSfIxR#r4RwEt z`@G$6E7)ykjKPg6DNY7Z6mI{1!~(|Re%Box?F$bFNDY$W*F|rjt=J0d<&}v)^^j~` zuza!N=-uT~h9`Yc3-JjtdUWh!7px<87I~RgE?&XKi((qnlEz@C;f({lD0H zuL86Ro8 z@CwoWVR5^mSY3S<4Z1m-6wnmv{nK1lo;;T`6)d*gy%6mSUf3Aa>z0*sN1&yRY+3vFaZzfx z*#h`NoNVlSO5oD2#4%FGHn8Y;mbBQ7-C1I?-K@XjA7ac9SBPy^oU)gE&0JW8EgZcZ zXRb10lDL_=Uq3aePI0(?ja^9V?3+DNC5ee=A>Jvidgj30HRH%ti(FAb!g#@A! z0p*~;?qsyALc_l?>PmIigxCQju8w$hmcn?4BTIshtUS;6t>66ozH6x8Io1!|q@;B7 za!R3pLd9rePtA+5t`I>kpet#=rA zok-L+6)$zGkMQU50pRG?&2w&3BCvuCJnIdR(KpyEzhcdwIPoZj8T>FdOT%jZ)6tJs zfeRD@uwP(`)e-is_q^XwCZ>~U!giImwjc#H(i#a)JZd}_yj#X1BxDLvoM=s0wBzP= z9p0Sl0+qdHJuq=d2f!OQ;SUDo##WD% z&LY+(?V%g-_lzohOIjdOGLw~s)MYDeAO%~g&RF4|)5YW-EW#Gm5XV@Y{o9i>zfvsC zl^+~nuHQ_v%*8=hvln0hdYXwHK9Gdb5)PGBB_18;&%Cm;xDE|kySV^=V_AQCpks=m z`~4+u$}~c~bj_Q}hk)8 zw8#24t^6;cL3=*N8I{D>gW1D4QY^LFnC1>|UjXe>8?)5_L>?ddSzTc(O#ZV*gh%jf z+O^Qa@N1ux@egDbC^X~pHD1$vswwitju}1C@iJ;v`P55;?jisqhfx~#slDmLd6`oJ zwrtuT49oog7)ClF^aN`v%puQ<>`3MG2Ly7=2tE&sEX^N1j z;a{ScLk8|kfg<}28fBsT3K~2e_4(rmoBog!Nr%2&{Bh^*-z#k=t6VEmBc7GsC4!MSHSUX9|6YcVni_G-5E#0jhuN1K; z3A*)e^DmZSmM)R?1*`gzFZxXKLpQiXSRwU#;%_l}nBrv^7KLL1FEjyUTJHLK+b<^Y z%6xq}Nh&JqspCi#PN!-?JGEH@dnkG{J56_UaiOI1?5?yQUt{scpcOS1^+bAMzb#_& znc@A&DD1B>19ZbGU+-Q~O8T)VV%Nhc4Ei7C6gz@i48G61MtqVRL0IU!T&#n5hPU!! zDs%kibcTrTXzvn57fG)Od*e!yHWf$9)bY%lHnfd!QPuJ*1^fX;iAMx5mo7Dg;r%Skf!^atRG322v7zmMldXEBI??dv{~_wkI+Btkon8T z6c3nJvvc2)MV~f8%S=DA0@5dN^~uUI;8I6`Em+Ba-`jsjPGPKkjY}15vr%4d5)+C# zU6=s-n-nUsD|j-3(Xx!%`}Kh-8sMZbw&IW*GO{#ta*ZNr1StI-7Wbw|L>8cU(i#lP zZvb(jhn(NpI3T%vHT96-6>wP8!4C$i1EDzeemWpLUwt})FENRj6`%925mg!$IbRjm)AEGCI=BD`kUtSF1k2s}!Z3kf>=^ zQ9I!8l5^8Ee%sio3YYfxSTBp2#s|s~P#r4yDyJib9%mk2;5r#qY92oTAcNb2%Ph$F zS3L8f{Q)b9)}m2qfkpH7;O?jDJ8N~1A7gKK)sh;X`XIC;^fJTNp0T}bga=!t%);C0 zqM|eD&d2K1gU^c^i-X@7-bz8a9ayK^sZ1L&^%RRCE*LNf$gZ(S^w(iz z>6{e5BaGB1C)agbueVQ|sOSsNB)Hjlclsz>943;LW4XasKdc3zf6nTdKN~Y&#t$eEc0~j zc0?IjF{&gb=KoxB1-;^8um;_S>YagkFkkn+FsKUXhzw5MMR4Kzn6G0iS(q`0TsB++ z?=x`IP;&v@ksdHxisI-On+PjEDIY2RgT!r83w;FF((1nRJ(AICXC<^5uKTqumg!P)1jtwHi|nO8O+vikQ7LTFEenwymH(CP=+JKFyplMc0{j51T1vLRO!>$FD`-xZ30#4s1)Z5Nqiv3nBGOCV)jtMWwN8iu58Ne( zxhVbJ#}ixX$+0V_i>Y6x-FHX9N~Sw?&(r7@bVJSF{Wdr_j|ui*I`$;(e4v8jDNXp9 zjeZ?IQB{4vZo`VA)cduZ)J6FB&wvc^5|$f-BsQ#J-2N;@G(}MSQzx-d^Ch2P-g#;b~kt#zMF$IPU6J~G?fv{cy(n;@Ab+DOV zwX)a&PfWOV(Y}l!QFJt%Vk$hhBFmzoUIDoI^$#FBcnN#$OHmd;dI0+%VCeHd5@8tE zJn=fce4ct(I$dE>l61^n+WB|xL4{3aO3qhkFZFfg5O)I+rM0X1KoIpjmHkQDQ3kl-d~`PRnAWk z{nS210iaVycwPATr8j^E&evUvj|#IWaks?vLxpNGV+ZHeFyWVy_!+$qB3MOf=@x*l z{4E;?uwI7a3r!Xwq!$+m=334tVHph8{9+fUp%G0MQ`t`$jQq_~txB9Zd= z)A*795sB*21!ask=kSXl6di7!TW*Z;OSr?p%tF!yY#R!j7{%b`r8cFnuXx)*r&JxI z?I$7|N>suTXz-;sz1DJK2T2F+Agh?^h~^CnD+Q}xdP&=)@;TMe<-Yd@o~XhmU2Xih z7%HC$j57UVlg?gE!e^fVE?u0=#N_K?R#sMvaS8PmH+B*i=6`=BEez;AD)K^|?%Cd^ z0^zva&GAqe5Z7ytp^Z3N{Q=Y1uo~04;(m6d@w?A^``%*8pUrBmA7<<>p0ZEtgqOAf z4vv}BlsQC9=vLO?yRrAizW|L#>swi^=PT)$^yQiF-c-} z7T)pESKRQlanQ(5>1a_Zb6zq)EDn38EO4_>2bej&TJ_yhuL81;(y;aGV{kNvdQms#}? zYSJ<4&dFtJ3D75tN3h2{-C!jBygol!1f?pm$QdeLg|BuJFW>6mf1}1N`t7H8*qGb# zgehC`I6&ZOL}&EPAl-6H^XYc`p9KK(nWMS5yzS1}KTBDo4?63Xv$<|=p*BzKhfU`t z9cGoe>BxJGpmhU`1+28G@5Y&Y^@1Dz$>{-p^rp4f@UJ*I;7D8Gvp)#TCa)l;z`|*o zZ;~4?b1Cr)kJ6+aLSBJff|NUl0VPEswgxM@>{4f6S|pI~nKTS+?W=t9^Ax;02^57c z4Wi}mied+sdAGqvzmvv9VymkoB7htgx`FhwHqvzpd|N1r){D&6yW#o-Uj9DnYmu#g ztPeyeK+OVV3n2LTa6EH&l^~rlz0ESVr1ds}#Gj7o4T7KAHM-N>--9X$+%rrjCpXJ0 zl5YIG0dARsYb{Ge(fxsMcz76#5Mj(Wd+IhQSdd?K<#ZIiP6pXc0FTmx!kn4$gDJ`M zE5gC~L-LJ#Fab4>`k#Oo`p3)w}mGt_l3f*_Nj>gRedexn1j{%-2Qe{e z?F(>GA3w`wp+13hGIT5tuq)ml=f&n@5k-U7pS2%|{0c=_Jwp|*6<-0vqD`VrAus@1 z$`r!s<^*kW0D6;(%9QR$A~OL(1KeM!a=%u1iIItE2+1={cR<_*Pz$|pJ__dZCLLUpUbCIOvP{%20-{p+0Q-(3g9aGH0BWLp4`I;#RadgKk`ny2 z^!05>H6S z)ykX)0UJFJ@+iB;{5dvva z%^Z#EVcTOCx{pjQUbnz5dh=oM4>=6F>cmoL+VVkTsJhiaz{{0xKU0AKfT?0sAsm(Eik2yN0Hmvi3F^UCzp`ni;xd-Vh*c8 zLdDa4Hi$pf@OY|ZBr}pmEDGcYM6NT__kR~g_$xe-4A^u30w9c|xlY+01Fe`~w}J7X zkuJ?4dXacezDJzb{>D*Dkj6Uq;ca()#OX?QY|3cif7V(IovI0th{ZCMiko9f`pe<3 z$RH};D^7~9L3%$Q%LXpNkAX|!y2WSS#e?$BJ>yB41sl#~z~^Y071KQ5Bw*(yMg^Rk zJHPEz{(_wm2&C!z^OgAjK3=kUL`g*r5Tu4Q?!-unBOH= zvEF|B4uQ2V1mNtc*cKpEfc9_U#3?DkrPSqh?7(|Nie4ad6!1z|L@_9G1tbBH8ZS&8 z^0|sLFuPXMGN?)QD@uJYUlp&hsaLfkTxMy1rJI|QFe*boQ=U`IW)#)FdVPVRicu_hLp+puwYxwLQFC!&Z_3jP;4y;i4Kh&?|Qjg3A)-p@s zHgaWRZ!C)d{3feK);1&H2R`a&ObiLw_l+sg9O?NfkBd`HOdJ{)NoUi+t(<`FyTW23 zit{_Z@we)x%Ubx%AOz>ehXdMT^Jcj-zWrxd>rd2TaaU(%R-!?C%6~J1nh{Z;Q7Kn+ zl7xXssi8CcS%H;@$(jDp(qBQ94O>e!)60}vgpC-=xL-~ivT zr=9rx)!R$8$z|r-1zOPNeXduLg!d&q;`#8Jl_ZNbujK)JQjzJ|r)`25XUMqz_&NDE zW_&*o1epX=Tp)P<#$PW_qMi%8V$se{N2NBAxKEgi0G zs-NQTlJ5fAg*e2-s=9Z@I$j)X(%v>9?<~<@aR#7F6Ee{0ai=U?S}U71H6s zB)P%1^Y{EcP{5KmFrth47tE%yr4ufIO(I@bf3sp7AK3Ql2N@$ZCm`~gpMiC!#Ntw9 z)JieCLn-fC|CfHKE3T%!c?c+f`Z^Ny9r9t3w;Q49Mo*X1Kn|$73`M?}^j&-^z!Fm^gboO>cPN`TH;rZA zP~L?3VHF^bsC^T%Xs8|mJQH;aW==K&1{0+P=Mip18gDe&kM{Ku-)-hxBk^yShSp>8EScnu-;dOY4MJ z`nwRYnpCuv0c+ApP818;cjB+BD-ziv5b;3BiPu z-4w3yiaLO|#=-$$0@FIexy4kE<6qLAJO5!8#EYd=DvZJrvBhZ!d+V2}Oduftvk(5A z*#A`ys9|!<)0Px?UP3&WV^j)R)Muq+0Iriepv56@o~~Yr8OCC8Zw(>;nqPP2K6pkl zKcW^N$y%)2$CmP|`;IUz>6Hjo;iv_v?v&^!$J5`37C$P}sk~Zx5#SnN6SIN@ok~n- zSY55edJQzkrZM{Eubt{q+y#xdqov)f?VVExZAw=!qD&3*Qj3i#Ax7Qmr%B2Gf8}!< zk8}7A+ms+UR2cn04&HzipZozhV@+3uN!T3*BQgc(L#=^Sg{w#0I!TTLMT zV!hyNRRJo>IxRgw_tJl=fRcAQJrI^7tI|73@F|4=F<_W~NXM8krzmKcqEJ-9~Ow0|h| z(PMD?I+Z#RaEwD~iX{l^L&(JY=7gjJ_z!(Xl_K>L6JohbI1m_hZKQI!F{+mRzklez zrSuW{W^Wi=t7Pln5M z-kc`1)^y*co{k2Gk1M<9B$1=;Jhl-s6{6Q^XM21h>iG8_2#~WKKs5I#$TkG_^p`L7y!aHu>+rHFwj<1CWMYh(6ySg(R6gukE9@s3l&Z@DBlO)KB?uACwrlO1gVzaxg{Z;RWV_LOdE#cXMym$Fdl=Tzf+3_zAA z$8w&V^;WVaaeer0<6?$u(!`O5s@+aYzgLWrVPl?T zI#k(pskRN?BE9#HfpToNgO=X=gw?V?mQ{%+*pxgxfY|`!ewzE_53~Ky^opSCA0z=H z6)Nd_U1FTscf038#sW0qOiV|QtmpM5cjGt8Jq*C4Pw9AR*mIcS(15 zN_V3)NOvRM9n#(JzMq+I=KIHSoYBD_o9jBywT`tm|B(JpW4 zmLMpnTQV~#6clN;=!=MNc^Xh223%iR^uIpiMU$@l%0()ZPa;7EN5OzKkyb2OAm40Q zBF%>}IvBe3bD~5bZ?7WE>d%NU=`t0dH0P=G*7xP?+3qu@4c8>eS*?iV-ovK6L1vX) zAr&SaM#?X^=N%T~yVNp(i0=2Ju1mn{ej57(PDrd)`6fLBV2Cwu@E)egEbV_dZE@H# zF@D290Eh}3R8Whw1;sNmrBO0n)bCr&s%TEE9sv2X}q2~`_4>K6X4s@lt6IQyi{8K!FtB(PUP}9tBIxVuCI8y!dhkiB&6Jvl-4qNkN-C~F# z0}^1oH8~7v(tdD& zJTk9D2oP5m+GXlW*%3Zx*sQd)d_dP8hi|l(XG=NU^q! zX8VS+P3{l7s^*1?g&!BYAW74wxqL#b`Ax3_h(pm*_u)DIX6C=Go*7JVgx%dr#YD4& zizn)nEH3tGY5N$~^lsCkS(#uu#zS^aMm#%CM!y~VWHC|3-sKUU{c8sU<9E|PPUYSa zfNO9~@x`WBa!Nd5r5Orknq~U=E4x&`D6KUY2?$W0F&)&piQ4tb+FhJBbHi5usX4$B zsye(BeuDxx-J2FQNOaNF@U8SUdc#clF{7rr?$frKc-Y4PbXP-Yz`;T*oy~eo-8Vvh zGER1ZAz^nh@=D%Ggz2A>Q+Vp|duUG1B7?kN{py^x(L+O1=153hGl2aIorXhCXwlgJ zX7^cMe#QzcwBQZrwT#{857x9uGmqh|J|oWq`ju43h2lTh@DcDYRoX`YNeufK z8<*N>jn6CQE@o{Xb?(*g*YHyHwddu1@;nUyBIgS12UwM&zYxJYGiRNY@)24X-03tZ z=LP(xPqc}Xzh0A8Dmv8sExKX}&&6+3X1}`V2iyHYHycR~g&ZWU>s5QTHDgP~lf@lY zx`Bp%eyY1A86#hO%g@OZYAw?0mhEI9Z&auG4TnHbK?1J0F(j9uRW*KFKB6o;gbs68 z;M$|W-iw#WHr+%)*bCt?0bZQc&8eR?g-l~Aie0pFzb%6$io0UIx-qqZ1|a-4p^5x1@+GCOOBW{} zg%%zl!G50_NS}-aKmB><$B^drW@;vF_NKX$SQpKQLpUy1V3pu#LIDGm;)_&WVC!lt zPH>lleOkgn;A(=dj5>TJJM|{~@46v1#uc~hjSNBPVm}*rXSBWeLR=ip(85Dz-1uXH z0Xw+*Sb$}4RQCfu1K6Be*-965y%wW1ga-J(n+W$Bcz^-=OCKeI3uMq%R5Mr8 zYV#NkLEIwlZ-e|_MI5$D>?SDYT!+&Nk6ursjkF8Ur!HrPv=P59m)OLQE7!2HPcA&i z)-#Y70OtWt5xbn%m!@k9h0tFZt~30Fha4sqE4Qu>t=O-pU(EJ$8g8;Z?15<+*mxEi z)7MK*0cgJDi4Ou^G&X13EaO{b!*wh+8TaG57cVHHb@}8<4zd-j>TV+Q@MqB(YfWn=?u$LaI;;|<$jMK9chDRD(5lOi8Xvgn z+8MEEKG@W}Z4^HRS3gDK1A@%_RBOw9p1Vnl-@^FAnJdg-zj(#zAPSY=E5CaHF7O_0 z2l=N9ZbC&5w|*xjOy_=KE`qVou0W61&Hphdx&)mMU7x!K>%-3 z$n)Opdb{J^)rxyKdf~`+Q;P^>3#%OK_>HQ#CF>`RQ<1>xns6RS69GW=cy_dg)3vvoB|2nDN_qZn*bP>J%d|!1MZQ=tfu_l8iDq ze;XKmvt#BZ8B?)%7f${$>t{pWP9m5~^ky^KVMiJkDs1cit{dhy{V}wU3z+JvcsMZk z66;H%^Ww9v=UOsqZWwK2VPcPCnh5~Ylb6>ei{v&r76M|gg>0fkuls0ulm>0p)UDh>q{7_3fbrJW!DX*Q>**7AQp&H`-!$RUwJ_n+%J+56J<|Fk;Aov#Ui zHAMmdkcA_GU%!G_2u;dhk6+U~NGDfVVhUVP!5WY6vRiRR&A?<>u*t^9y6|%UrQ=1C za=oijSFhok__*FGIcGUmcccaBI2@p0gs>CPm0%e=fROu^(fmNo?Es-b`#QrDH-i9y ze_)HPMgvDJgxd}?_%7Z=A^JzaOogw<*IMqG_TwoyD!qex#;H=ZKLrqFNC6cyT_x%) zIw?E%n%cJ`CO|_0WDP;oV2Eg>Oi;rNrQ4lujrG4~o>E;MFPEC$>b#E+d9o0X4d7I` zFVY&}V%cMDYgd(gMiL(@uT|9iX^!1zM~7$V$qBq?9t{Dm8A_p!llcQJ)6@hb1N$PU zVEPfavjc%6Tiv?djX)CQK_{vs6s`>SLe1bl61>nSeY`x!vD0rU?Nda~#nGh&Lom=0 zuX%o+SaHXh{#qN%ycnPV;x>;{E@wM=25U*B4zVE5{4~d!(ndc{O~m-3^`4hR5(`QH zf$guf(BVX|B2Ms+?+@>#|8(8^mBLP3d+3ztea<}?@CGw$yh`3TY-ScE8EIjz7_*){ z!rgCl2?neM*f%(onKX*Qt1T zy696b-d256E_#tZwK&2?A?4Au-C!+t{gA?kg&N`(F7QELx24i{u>M*Em6bWDXiz!j z>6zNWv>JbP)yv1nYQA_^c=K|xuh2>#(xYPQ#R{9aX;<{|;Vva*$nWjyf<;nmIM3uF zXLRi9thyqz>?;-TDXszvIs&wNmWZ&+M-^r+B=;;mh3w;})S!0~rD6_lG%>iyq>-jQ z8IYq6S_l{Rk#ri&MaaSd9c^brNK@9V(TrJxoMT-O`|WZ947ZKpW1GwDp7jZR^LX=e`v}mwG6x) z^Z^G|l{VQTSH*pt8#m!V%xfB1W3AO+nEg*ZzZOQKaAt(FO==JzCM2mPQ&Zn-{qcl7 zt7Tgto#&z6M#qvtG`0vf^N5^bAtjZj;X~BI@@ z{p0jJh<qzfH>-D12|<4olWiXzMxw&}I~}#C#R}`l`89 zoa5W){uZ^egD!}(OG+j8#F3vEue&1@Po9ykuF}gk_H3ETWF(GE#q81qJru`d{UC6M z4U&+9j+?!%uHwU7LkBkvlRShyoLL7~+`m{@>R7}3w9wIme<(3t5p&`_PYj^1-fgcI z&QN7p+!b2LH$8udzfNRzZ!__|)ahX#qW1YT>?~{rBInu+aPL@qqyN;%)+u5^ntAJ* z$7c~RY&+CHZy&~!71VYtB>%6 z>4wnUlYKhVZ94xq8ETvIn)B8?_~qD{)=R-fSznCte_qG77xypGtTOd!offPKjd7Km zGT>1c6W=r|cK)Hktrc1-Mt9*RBEHIsI^)k(gJq5zZxiO<01s`hf6A`M)`?sIcLSa^ z32F_}X2G$1)_-`*m1SG~9f|>6y7DoiMG)1Y5QZv~Qy0WrX!w0oUlkoWga9HB=rr6|lE!X^J;<{jy2H7<20Z8pYLCHRZ zS1ZIIZV=o!TKS883#+;^{O=Y_w8T2Eux+0Ai~tXIZj|q0_%8+b&@EeOqYp;S>p4E+ zs6Q?RFz)-D59VSH4*qK8hU!-Dlw#Funpg1flmS=ai>R4YFYDQJ+D=00_|jz+p@@oM(_?!_p9 zX`7pmgM&_3>qvz%ef{k_1;RMUkHrhx`}q>*lGcH{VoYt4k{2`yPYww!c_r0{rg zpntobj$ZGZwlj`NYEg+_4>?g04m4$C0JcZ{7u|fdCYXI{)8%G&mRL4BD~sG(*z7GE z#u*ZjVKF*iqZX^^@R8uoR>9iR`FR%)Xt{U8Non)X+aOK@azrRyl8qp#*3%dhbFuCw zT9Bgu8JrmCozC#9O{eq;E{%?%7+2rX%5erIDf8Y?OR~z=ndSg9kNP;17~=24jY~yi ze4b}DLMzm=B6xaG^G?7f8R_)8W>V75Wj#Das*erV&Bb?dpY;tal|Ay&eeT&7OtaQD zD~p$s>{a52G8M%oh>5{nBnLp&5Wp$oWvA+VhcV$J>Ikd+09&Emd< zg;=*^x>T%0-k~>i{^v54Vf8d6Uc>r2=`PwDJ>C6)Iat8rh1P`vSw0r21}OrN6=Ndk zh+p>NjvyKjrtR=qSs8IbjtzD@AZ^0qleqy7h_GH%|9-`c=&ov@IF#_*S<5rsk=&%&Ef?Wu5$%}Ar zoaFaUZpEfAO$Vt5#|<%z(SZ1E)rNr$se_Ifjh3so*V zpHMPArCV|Qmn!dAKk=OhB&3@tq)dxQaibi!W96?%`z!AX3bf@77yQ<#KNX2A<(PH0 zF%7E{KWJRKKd6-(fa>OE5kUeFR$A$-6(;IS1!)qy^FR%EyBFSzTh6IlPW3{vnKT%v z@b!BTq&x>=Q-^(kn=5v`rr(g=<<33M)tUh4fO(UV|8GPQfqbYw_9~fDz!(j8i7WfM zYv;tx_A9(DGv=*IKImmepeuJku=9_AnVx|rTuOAdf|NClSqBJmme4&-kOwzKhs zg#XAHdJJqgn^TS!1MJEM<1ypcl-M}HWLMFWZ-QMnUL_u$&z>Ta|4U#7J{W?t#MdF`|<6dc4~?gh6(-iL!4cuUtmw65MS8pQm)| z*g>&S(%gliQZNxQp}}G1t?%2qL3M@V^V0lzwGJtOuG+8A>-4aDuEJbhffH-|r*1!A z7LicAI3R}F=xQ;| zNitxlSjfnT?6?zfKY>3f$cOVZfK1x|Ml-$n!5ZXiF$D;Q#PUtiJ>79laNMvNM_trF zm6ukz_}uYWdc6})IE!X|*xg=+g7M-M*ejC|)SJZ`Zs2;HLCm%r78NY-umAt);ASY0 zLp1Gi8;nZ8r)Y*yPZSrk=+*WTnhyi8A(HLw3 zs%^%~mFz$LLvl5b(x%YzXT>nJ9j8GJ@_47}X^)Ek)NmpwEA?v-n~hRJE7?M+Awong zP@uM3T>92#kSsP%sg{lgBda9f$N6fr;EjR1lB^oj%nz)HKJjjLW8nU@!k&GkB8ADybJ^)^zBA9Ko1<@4fqE2kT}ZK3sE!BYyp5^meUkx^IPi6$eexvRQcF8DJ^eZnER z7*Bh9U|Se6{3S?8#ByVh=3lN{;-J;^P8vUzQCl6b{5x}x}8zQ=>!6r37k+zsqbKFA`n1q|BomHYGdpq^< zpHJSAztmR7kVh?(K)vNo4`kO#47}}{*dnKTdvrQh$V{TS*?zOu?{~lg1g$U@zXn^O z5>0$a5wp&rp)M611fMBRpDo7fEJCZ6Idp)D89e{3k}*6S$PFhy$2#5anYalE0U85@ z)PJaVyVz5gU}IIbr^Bcu6UG8T4sm@5D_)9)Nto6EU4Q!6ap_7aN2R!hVXC17TxixP z+I9m=$R5psreVzX6EWe*b3B}2;jyY(ww1WHpLoa^ud+5Jd2l-ws0YMIgV@-iS2~GU z&8GKPt_JMgdin!pe{tTnuy;7@R2xB{X`}5D!KF~7u3pr^ zi+}svIXi#AXjt&yKefsO?`sSW~x`#MSc6L(Gg36qR&j?8+Wy7XmWwxe6^2j z^Rkw<4kgdWT`Wf{wE9NN(b)fLm!m{B#&VqG+|Az0Lf9glg81t{&!xN3TUnXT7JB{K z0?Rm}Ix!tGb{{T=i-GZ-Y^Ro#)yuZ{Xz^RtQ6m2cv?_80`xkL^+i)tK{dfT@_8vE> zc<^8aDTCxstfTx`zVlYE# zDJ^bft-1nnCQjFsMZ8!_3ELv%M1k<0KWblk&gsK9208YVZ5AyIwAEH>!KFTbyQM6Y z{$T`*4RwUs)*n74-@7@y>XXU6cU0Mh`Ywu*rW6R8_#JcKQ zWTE;m+8LicyN{YCfT@50yO3il05*0Q!c>js+xS?RsBty*{3kd?&_hC>#)~oVZn`Q$ z20cCmRdIhDK+B;l3wCanuSrEa?b#(R?8faxz_TCkhq;);lIRptO3F0-JCzKF_FS%U z!Kh!9QpD;!bR{;8D~aZ4Alyxo&g4Lzvm$V_6p2a}S|)E1arnH&VY za8IAzq3iW#0o@ONzR)Nj0lBsJ;_jgo^D@=ZgrUud>WK;oP)og)gf299sbmxG;VwtY zFL(5)>z9Y`2@hl0Z3ffQ%+yZkO67420ZAe|(Way)<|@m!Pw}OoB#n|D18Z;y#0Wrj zLglrrQFhT`g)r^V$0?f(td|mn%%OwE{de40(VO2$E_>q{1X;)0hU7Z}teR7sX^dng z`E}b?^6_18#mOzGL|h1iSs)+W2DROzzC?WiruN#RcSzDSLe*isF+6ydVXcaHi~X}K z7G<=wjfy&g8CGVh2m!}s-*W#yQN*6NXm8HV`BY8TWEy3O=_K}n--x_kJNG)On(cXU zf~8!ouDxALax)Qq-d$qucvxM}s*Z-t^WF|-QZqT#T+Z6QvJWIQomYN2OPqClg5aMD zKBnmBag=D-jtur@h?%ed zS`@fx_k3Oo~Rt9=_LD~$FH_mlk-|7OC*u>-L zFlrE>|0^~uH=+?gTwXUl$MzL&X{6rX(DOtFJ-l?j_hZi-&{n$qLV@ zRRTInF2EJ;Zh|DfA6;L`hIaum9JB=O)9?f?QEYv0|GCPc%r*%rZXDX;bC1o>#Jo+e zrkQ5)7Q30;O)d~lyZU=IyMnjeW8+W%^IzhSW3Ar}1F?d;W>HYon1e-Ho$j9S8)Sf+ zU)C}ip%*=RPOwBm+?ZE?@hhE5S-&b3{7^+GFT-cvV9}{$^#^s5s(>O^vpPwrTnTH@ z@H}BWDd9Qxi$uw>@*#iDwPH(+TAK{{g)R;q1Q%iMJ9V?mybvy;Xmuu26>U3m{FkuQSsvminwx=J_VEF zxe^-Tz$}`JU2pstZ6k>4&F5E97NSY9pUBG4t!`Kr4MMvern7WR;2#M+TNTxy!*P%1 znd*)ZKP3g_xxu94doYXA8K7Jx#%T1xeX30%SZ&8X5-pgFZ`ASdG?OkI25RdS;%>{L zYlc3_j*F{r0nu*4)(``6!mB@qD?sZC(a$Ztc$IOyzyHfy)w5c}|I*MPAHVMh|E%9I z_ck!G)x?C)v^733l=^mY`X*Jx2D&fU6&CSNmF(#N90rVD5LX0)iS%V4&-Z9B(P~?y z>m?ZQ?@;g>jA!()zyBOHyFtVKU$IIs24OyXo^gtz3_SB92h5?L-ZVLi5y39A{D5W} zrO|?)WRIlg@W*gc>731xoM_tny&bS4n^Eb^pp0g{nTCv`@`+^NOy0W$R6kSeZ*p^E zd1@7l#Zyz18jsHy?LIby(T=b-t`Ww&)f{xi1?aj z(T|K&=9Bc$%@1s)t^>cf$Co$l78VZB1~g@o%kKi)O2*eP!q#~`GById$CsuFd%IC) zT!$(bTbJeSep6r#0%-=ED6k_Htru9QlyWDnd*L)1eDJv^l7}H!5S=nqOH^!+hNZt{#t~`tfbBghR-wfc@clpUo>p%q3%s$RK-Wgwu zDm;rm0TMSk$b0jhX?YM(*iv-2bYM(1#nXn3t1HpZtVPp*_V{g`c?I0RdPj=b7tx4V zfnK|`2;Qks$-C2df`17_jWv7wJN4%;X6c?C6@v7gEU}*oWjEg5KaR zJu8fYmr$8J=5qZZrGSS)i~%bK%6vI%^uWsD3Mq(`9&T$hikC}S_k*}uZ8Ys7<*;p< zJwH__l#Fdyo)U#@kCwUsGNRR7pM{}JJsLumRl~HHg;>$<#n-nntgJJk+lW-rCs>=c z`7_4{U+*-X{rhO4Pk#Q2oY4;8Ycyc*WjD!{nSNi%4&I{v6eL6F;Vw!9ACk^5qBj+5 zKNXJ$7MgUcR=g8K`7=6Xhl5&+obhGs3wIbh7GYFO$&+)MT)2eQn7;no@yf|s9}5BK zj{!qc<8q@}-x7D!ly<$IRt|^d!)>71JXL_(=PE~kiVe%Fqkl`!Wh^&qQnz=2%=irA zN8Myv@v;BT68`=B84mp~O72k4x=|_U9jHJ6t+~DrAEyFB7G!d8(zTbjS<4!J)xZ-KVU#$}oT(AmN=kx6>&BF=V-T_cO==mS~5 zNWsU`rKR2fcJvjn>I@JbzK_KUG~pEy*k)0DpcMG!%r~d2^Et(Qrdz-hD_@z?=N$AP z_b#vaajj>z-%ME1P3{xsh)cX8Z&b}a3i>G@`9i!ho;QQ$pQfvDa$G~9g9!{|@KH~h z)5${*IDlx;@SmU(g(2DtP~D+9oJaTz&}exo1(q5-M1)3K%IpnDkjcy`{WFlFZUxr;7zT^gmxCeKmsllf*kW2L>7x|{43Mi2V} zv2=hM_0j0_27?Ju2f$wdX4mkP5b-K@xRZI4%5wlPvCG_Zcft)6sFK19iK0bkVwTSBF57SN@ko zbF}$}%?0tm)w%DTE4Q%3b$&o3yMVCTxf+vCG^})$!?lWsv z6Ej1b^6k`>-_+td0R`)3*Y!CdWwUVQSQ6zNEOei1d^oe+$~b<6aJWWvdgcYSzrq73 zer6kdPe&+E6LE@cUTVS^xN3du7GtCB=I}gzIK^P$Ydgdqml_TANon3V{^6$Pwi(h4 zE5Qp~UpXf0B^(< z&(n354e2>Q#|W&CW!q)5Zv1V5{B`AQ1$)(Tq35@?Qtbkf%qNLOxS%{kkb6&oeSwYK zX3@5KhdGIVO%js#NlqedJdk+8A#J}D1Nw`XMzrJrPB7`~s#dU7D+O;Fvf+P+Vky$- zLZr5Ki0Uo3@VMR_n-shKPTM&OpPI`}I19re^={9d+bvWbk6lcRZM9iqV(FHlC+`5m zZ0$&xlVxcdO`R%2DxUIZ8Uuuhf^m)vZDMZ00gr{=@DQ$<(S`O95=iJ%D3o|Q_YbA6 z&M}HhuH8+Yhw2~cUmmTLgRCa6fuz?r*_5JnknP~bPrhi1WcKo^=`LvEJ6U^iHk`ZA zs0?Qxa~=v71#Jij`tA{NbAEYF7yb*&9z;vOhn8&)x7sdpOSp&sE24c}oS2l^1YNmx zvY=}4b)Zq&<+t#U*55Mh_Mc_9(S}Drzrr*>HLA#HSwB67-Ml*d_w{}P%%N?Z@~O{q zyj)lGJEn%XNbUlK1yr8?#Y%OJz9}tPt*1 zv{zq};`@IZq6x%F8`7v2zAGY)l1tdjr&Zg@6beBQ3Gci@22f|i`T#RSq$M-}tu@tl z0wBvYdufvFK+u%W6RTcN64t0YD;a-+Yn24}w72TOtni@v`-S=>Wlrd#zx) zq@VM!g<@}O=CMJ!^e!=d`y7}DSJ4yi2LC$RdhRJmTfM~i`My8DUH<--?rX^uUA%lp zI0Jm5+?_-_- zB)ic13wS7G3JHlBE=T%xBAq`K@PmIy$nyysF05mi;fEZD{s|ZvnkIp^ zALA5exdhOBM0_)JDeGnOj~74}eC8@Oh#-gs%23ADChQ3aW)QTk)ww`<0EqNea)9NN zk}YQtt{Maphsi*QSZ3aqe*-k#n3bFPGFX}{U6?ghA<2%j(qM%(x`K!UW};0#J18e# zD~te_Nf@7?1C#;iLuTGln-e|~mv)Hx+L&q*)sihBT+t-u;YO2wu9L5Wnq>-Z4X^rJ zAcz($hD!8}D}!b}j%@#e#l178zAn7oD>yF~j#z+f88bs;mzzwNKBabV|G)0{Vb8^- z_`HpPkh-RYE$o=>pRnEy#|W`zY3C=*_8b_<9)cg-e>VRPW|>OiJGROTI=fTKX41Jg z9xp{300oyNh2rOk-1r$awDU5whXFvc%yirjJzeQvUCC@FEIL8q4G)cp=__7wW}(B3 zKd}KU|B=g|I-KWwLV#%6GwG#1^naQ_ZzZ)4mSrn_6#B> z##9UXRxn`uRpz4My?uSl(CV75QxOZYk`?!Fw)(HXlH@*FC^>v-({tD56>uiwHSZxE zCIeY;m&yJ~7(mO$Lf31h{WVl;K|oGWqVNCOv8!@-)Qwy$+D%U}vpDMNRYu7bCk$W2 z+Skq$LG#swemM{O7WmBg8HpIn4brR@ABUZ&f;F^c%mdjHN*>SVb9M%)r|w;#RMJ2S zsCl^b;n!kfzJ-fduE!6_0Lgb%T7>JDg|$?oSh-<%Fm79(Wh!X`>AP%M9$j>U&oi3g z$(~oXCv;rvR}r@PK3;qu&75N%L|u;vam(@63@QAghkkZ-{>0 z6#X3azy*xknFvo%$7xd9BsN4lWK6ZK)z>}J%l-*`Lrv&V6CR3%{nSb!WPacDeH=f+ z3qCeb{{))Sj2P%;LJZ>#lVt*1`OHV+i;`XN!R-ONEv%V_CgR3E9Wl*Kp(pNvT(*Gx zE$I0nOLKI`V#%>p8KS(vjy!6L{x(hdZib@MmAGEJFDqxDVtxn~${(ML#{2jy+fSKg z!s%7ryez^r33eiMpJx_J`Y6j_6L<~5I7GVj0d|I5Du0OL#SgqRaDynQ_H$g!eolt? zvDP-gm}E^JzmpCTt&mAN-;M!SQ`9Q6OaNJ{j$?vy(}ZGe35=UbjB)p6V;tApTeH;FSO7>-qiFXg+Q4 z&U>wX-SO^g<86|$(nl_(qvY92b=Q6Yfo^@NV z1wj1Rel{eBXRT$sb&J2a*33SP^WeAqC8kXAbp_ywo~zz`#~H+Ho~Y$CjNzMtRXhUiO>(>33?0~>mw#l@lAiVVJS<2iEZ9N?NUJqLQ5v?y!%RCj{*6F0F3X4 zYLip;NRnD}!6BwK02Wd$2PC4=9jfsByG7yv^}`4$?i>ll;%^n z|1Mq}T4WK~y1kQ0P(ONUaiWrhMUfQKa=_FJLmt&08g|$x;LoiXp^3zv%aWE>aMB1` zBijba$=P~)7lJF3v%6)V2VW)!ICNOmgB{8${F9zOK6M$oo;&I^U}3JRsO0;NET^FJ z9{$;LAvs#Y|8Uu`P=1eIim`Xky>?l52~jJ{x~`NA8PK>(w zo+jMS(p?9~$$9G@g4$1j1G9BAKPfq!nxF5)$)&bmZDEefaWq}0mAASY7{;3FYE>2C z`1)>*scPHX1>492VgDcQ%6=yPD?7InX^L{NNN6Y2Gf}wDy+T2v2C8=*>^a5LQi#%r zEBS2wtT#3A*@7YF2QlDG6GY7T+i$mTO5!fEq!t(Sd~5q zf~#@Ph+fa#z%YN5vz@oy#$z-?Fw?ZCR6J2dk8V!9i|QZ>4yD=5ldQc|X9-HHkq!iW zOs#6$Gp%cQ+6vOhm`QTR$ROd+;g-dbUe;%rHdU`MA>B8X=Rq@e4jHb0f=XSUjrJ)) zEAP~*)9G6V9Jdt`Z-tOb!7J#~v+vt3*-FN?Mq3#jN%ko5HmU)zg8xhYsy{7)aLhT7CB*8lSHhVR-HNpAUNXb5~Z?oH$?>{kdDU$!cr zCD8?6%$On%7D|h8vl(`25eTHwmFX6hSAhy+b3?hP0rU=jG$=mIbfS zTkPzj7L|0uFtmt-Bw>=68NzQ1Os>*p^YD?5dcnwq7J%hu0n zZzoNE0(!dasHR7xl*EeF8q|+VvOCLr<-%hrxikfFv1>&ihWbS<5!|vVsS=74T3y}s zKO2@muV)LAx#3%qBPQQxNd@u33dhph6{^zSwMU({ONj(WsgCZ=3N?kIR4?^DJamOb1phAv;SeT`MrYt$!8T5JhQ@u&d<%t zx;tTzQf@x--X6~2`1#&3Y73Ewxa#h*tZ}U(d|y{uZL5l`*s@e>MvRUk&4=@Kh89TC z$g*AP%T6b=Z3GVnH8_cN7m}v{;*E7(vZ}v{@am2EI?xbRpUGk>@tnUyA>L3T%j|lI+1n4xU`Q8w2-AMWr(%T@?oZ7(!8?0x z?WlOYLbG9#LD`?#Xr|eL{Z;Lq>P0LlluWxMe#&{unv!Eg$JVE86qc@GL?$3S^PLV~ zyY-KZQ4rXS<|=EKbb#*n`tLcXaFgra?n)Ghn0dOYSrxVh2noUSf2J9BZ9YC81V>XQ zrkaB4G8O_bzcBKF2VY!>RTDi&N{!PO%sb7+FzuGY1!8kCR%KZvWC!hN^_9FMwFCmC zA3woxo<=KcLG_S=rZinBsgxMW4`?*qgJErK0hT|OPd2-M7WV64?fs0n!=D(~b$Zkg zrnpIrOygrR4A8%5W{&3ca_EBp$mQe0ahu>R@A9e*X5Eiy49m7eR%PiyhYzsUuD{X0 zyD56YiPC)8P;yO7i~~%wrY*gr?R7`q+p#1!A@ zc=HZ4AZr!y&$1~vGm=*TEnUMy3L4MnYn5Mz<*}HHi&PCd+|dpALPfHhz7zgzt=cL^ zeMbf1YlG||kR(xneY4g-0`eS?}vxhdmTN{o|7+pi9=gbp~7k4=-4HBE_Kamir zHQaUl^>N+R-E(jhv+u23s-z%27{0}9F-Tclp$9b=Vy6DBQLS+A6Aq>Or>W}SRY5>- zbV-W|s~WX+-U@=p1=UP~afNK&`FnF%8!|GT_KDOFe(&cUrUE6VXbq33stz409isZW z$!a5qG;zV?qY|W2(Kx4NQ}yv@Kc*CO;E$?9^YmcK*|y~few`Wd{*O$zA2XInkV3@@ zba0+#ySSs_+aN@7q)Wtcg5X3yh*>t|!J8yQd-4yNBx?4cm}i{SR1&e5)P_^d9t>h} z;_~%)8Du9tB1Gv0+?};gsG1_k&7_Wum5Sid;O%lzcc!@oWu&Ju2g86V2MCZZlk$RG zIT`!YbA=OQ<9Cdl#5b*E9~3worW|?T-nHb=#~OrowpU_=jujys$C1c>vCl7j z%$2+WuOJkqKpr6lO%1|49zprXuir_%iQoF=M$>Rt5cj88kM6i{maIbcb*NWX)#{yQ zdg;bDGI_-(%_m!(;P*#yGlQVpmK&4&oebj#?=UdyO5ddzO{lyH)bu4OH`5{HX2L6x z5!2tCfAB`d4kS5svXjrI(9xG%2YcY@G1l3=^o#?=>h{Au6P> z7GiWk$xJlE z#Idip%hG5u>2i58;?8Af{MXuoauG*AC*T5sMG-Psli?su9g z{=2@oCXti*^JON-aD0M%8}4`qzWcA|Fadp%@;>^zr|Z0Mb9};{?C&!jPPkTv@A4JJ zn3B#<8EHXT8n^NHJTPc`XjB_A(38y1C&}g!$CCPgXjhf-QQv%Qk%6I0nib{BP|H3! zK0a9dhqzgINx_dD^!)Sctej6n>w6`2kTZDWP>`3k)0s48dg)FvD&Lf8wusNEzL7t~ zDReQGu>4r3Fx%I(sF=K6Hg74~S#O82>69zfAO(MDRZYt!0{<&p2D*+tqVhEPl50w3 z$XeT+u5w@X0)zUBx)y1dmNlDbKSup6^zR;>-cIezGHEzDS*`>bbUB27Z@qDOt9bu# z?5{*F*+P{cnwXaJcJSh`*ysQrSRILw%lZGdU)^<#TY2=Sv^ zZi-t^4nEI7>!&lSAH(~SZYt(hs(_ zr6gO-z3J&9pRg`8l9N!wOu){}kGkDpNw-Dv({UF;sWBpZ=$o8;UX~C1{_}r(E{(Gx zV+apdglXBT=&beDY8$-BxABR5EzU}zXHn4idVNW=Ifn(_MyZI1M^DhCYbVQaxoGqF z;cqrtsR;>yaxUFkJ@K=kys&!z1HmektU`r447APgxqb+GXWy7_y3rE-v?LA^FuSp~ zwsaXk^ioQ|tsX?&DE5Wn>Uc`G4L4;78NcblX>UNMR=xY4jrk`pyc#Z5;G#E~YxD=5#SW2QUw3U^7*}f$Y5IeRAMWF} zSUlsDl|6C?ylk^kIfZ^smog`0 z#+y!xN&PV5!NCEYbGfRrY24A6trXTq2bMa9$DFG*8IhVBK6bs|Sm1|Mz!{2<4GXR| z-8CS{JLYY#DZUgLL(0BBH$+{o3G31H_AdTGiu4Y5!?VoItOBXMNwP~F5?z_DYtq~$ zQ85_sBEzz^vHIU;3FWvqQD6D75hGSg%W0axTT=(8y(UKeo4E*fhyN^yT}ltxhlNJ6Y_t@qbODg{tNQocH}zdd~U7 zoo=o200T@ShE|-vY9uJgStVdbYQR{4WKg4{Z`#@}wka0yBn^(0FPKk)8n`@5%%>grT?V~>F>t4Aed(D?8nU;_C(pZ- zd3vaxmIww~PE~s3C{Uw1L^eJs3<(lDmxI9{3&d}D>y#v6Ac2rZ7M}EEnETV*e|y_f zogn!A*RL{NrN^l+AqqS0N4YF)0YKB^-KhK?`!Lt|Aw3ve9NgFt=y+RU*bbLl5?d7J z`^4GJ9+rXZG$6r*#nJUZnuIg$spczl@epcrlRw_Jsu{+o2Ytd73Q7Eqf%FerP3pPX{~>?G8( zMivgh8UIoD{1i7AQ#=s16*@LfC0;xz;v)Wi7b5D^!)U=>ICa%CM-SZY>5a3>^}JG)N;LB?E%AG^h*> z5`uJ>bW4X0h;(-|Al*YrcZV=^N!{(e-*cb)_xejmICIX~d#(MhcfD(^<*!j=9UY1$ z%)>M9?C}}YL#Bs%t2`pLXSG+ilOy@87vXKlnqgSi61V6Hu{!QGc_L5|JfCnAoT666`VP;aPEv z^{DadE)n{`kBEefy;?T_=aGp+;sUhShOU(EJNLr0Z(qQHVAEzEdOyF?{4Be-j!Zw> z;goG&At}T|?ECR1Bq(3a(bE*6KqVG0z{4W5F!-%wo+i~|>G|_a5j60vIjMYcRL z{U*&SKpFt2MBfa}L-^ww%jJNiioU4z#p*y1F3sR5E?pC)#(G z_L03S6eU5aE}j#See z)*U?S4(SA1WEPNdi53Mgl2C>yJ9uT4=J`e_w*Oif9*iV|{aL29`uM5-0xe*8Ky+E+UVkwed6 zuAswJ9PIe51nPH$v}l&BiUmIOGum#t8DBqc>RAPcVndDtuLE!Sk9m}}gV%Wj zwhd~$PPe{S#@wIpnRznU#(uryFip2cS_5IXx9^tYx*YKRVE{I7!aJT^8Tyo%^JXo2 zDmsEe$r>A5~Sj~Qg@I*Cw&E?g>RKQgWSn3$cI<|`l=EWjf-hcbu)5MJ#>gkw)(GCrcaHBSnTQOtal%ovROex> zLo>;wCV2NmLR-bQpq*o|mB?hWq6!msr}D6B{<&QTh%&^dZv!IF(BrmyJ31_zxm6$- z7co2bW1ajW^VA?sQn~xesSOaVfTJ?aB2+m-lNC)Y-!br~N!JozA0N>!=kJuW4Sdcq zzhZ)7m@iXc|M-ub0-GcXbzpI--X^5c^f@E0(*C#qOVz9{7V(0o(K#~Xv3zG181k(a zAJO4&^^9lUtjhLDh<(Z?z-;O9Wz-SI%wC2axXd zmfMCyU)9H9EbRu8jml#Xf;Y?4@KTS;q|T1d790;fch?L%yG_|?PmBvzwa5Fc zgVt-%Y^9_;TJIQ|H_wE3-=s3IzTVGk)Iu4&~|4Pd0Be)C5-Qtn;5wV76H zB*5`fjSCN@i-S~I49=4ZRS`kryk7*wB5(F=l>or0*>89qMefE2MEbK1I)wcCZv zep)H#`2wd7__SJD8h69jBK@0o{+HKrS!>Ix4cT&oPFx&Y6+LE|nR)AQxyp0#7j>?m zecHyEkbqqA8gr3ii28Va(M`U(s{iB=Nrtx9tAFHaF#PFpo&{hTa(LCZQjv8c%AjpO zCZ%E>k>$jmV1fx^NDnzP9U!6iht=UZ*GbQ;Ti4j?zq~_JoH;LFuR?ax)+4rj@dzlG zuY`^s9@xoX?aC=43wZ=mWWXrP1ipQ%{sxX=7b_R6tP0QK6Sm*(0*V=10p%eHvUR?| zbT(y&Dp&XN3^3(ZT)dk-)0*J2QpTAGKTbzddz^@=XIrUiE~%-!`J)1G(CVB+AcziE z+{#l%7*|E~tP}RZXVXo? zHL!~{+T1Qlih8eD56-TeQVAL@<|a9fo~Nmum8Hr4-ZoHH%8<*yKvk!vGCtW5Hw%t1 zR@)r%vw+m5Zh3|M1k-rjS0A4!27UH;;;GMLcQ#naHFDjn^7}!ymI6v;&W4$0t8eI0 z(>lpd_hGvVkR2 zVevS_R{axaJ6sa)m~vjW{?XFaP8wa2!UeaBy{zHXR4~iH$kL3^-f){#m|a%nBeOB} zW2MlLEbJ~YsRqjh8XER@q87Hs8oqE#FB~DohQKD2YvnkwSXbXcyxi>DJag)FDn*)k z#0{3bBi?s(1{zH!^|*)}8PKT|LzbjTIE$3pEcYj@4kGair#y>QV`KieTQtzk8%2rb@Z!j4mqEy+IIXK%^ z=;7??5QUVU!)hp+hs_I$=zCXnOAj=&5kF`+$k}Q&urp{p8*(ldJB?O^u(+CCH^YD7 zX!g){teX8~k0iPMcp6>T;E_OJ9sm$;I|O~ctp9woMWy<^5-+n;M&-;q#zdZHNX(Mr z4!$RQkE?$vNQqb*|EWo(wPH%D;o|uQ*YrFrd(Eo(^N$M%3yhzX3_<=(-z*so7C<|`I^6+I1@;`3z`+8sE?Lfj8y{94fO*aB% zST*VQa{e{S`Rk&2$fTU-R#Wnw0;BOEYkX28r=!dqf%T#pU2bB1OvKcgMw6b1_392M z*jIPvhMVfJJyzlgTh`heM=6WSjvq0jEFMeqLfN|=Qs2?qhKZ-6wA`f4}tS} z5H?Y#p}(TFM_L-y+`#qLh#Q|QBsYfy)w#fp^$M{!w0>YS|MD}P%0{D$gp}n=V7;m| zl207-y~Ha&Q?>1V5*TZC!x^+2=G7%B_zzMSNN#L4+bD8ug4?_YYKJR8>hS&Uh?yJETre`!;z@A8GWdyZDkdc1$ zIY3)D;srL`)q}aQl`OxntFNu<*x0z{y{^6Wq5fxl(#oyg?0Zkzq_?HQtoDm{d~DJ` z-!Ya5mXRqlObXV?ay9(75%WFsq1=TRn(c9H$_yP2_S$}Vy8IFlAGzVVmt9kWz$?O$ zQEHK0bbR#`ZQP1mk&OsFOEJ@;)7(Ek^8L1l6CLljQk7>E`BJo4k0tZMlCyQ$>VCdA ztVDoGK^bz9LRys;-EZwIREc?3A{abRo8ab^h|qlYF8MwU`zw|xh#G_5Ct$6{CZG9( z^G}G0Qm_&%QqyxM3NsYo038lLCizYmFPzA#*s1CwqQ`!Mc`(1!G~^wBR$4q+}^{SD%nEM_bvXNbzbB|7sSSC7z+IT}PH6uJ}&d0T5e0g3335bLz_OqrtE;1KQj^Moh z>F$rpO&_g4;aS*w{{{^?&1Xqb&zxY+h2E(>w2tZGd|)&8A2W7?h-j$(7x{+N1RhPb~%&vmx{4Dk@_-oqu>GS#nLDDep@?`>;XN6zOyk` zoV9MXzWB{zQrj3_vW>-jWp>I0I2vy^R8oDj2OK~v3ck#N8s4~vs=u<~3RO2X*l>s{ zA$(&i3Jh#hG^?y+bJvxL$nKijwO;8K=l$wgbxNRAD#xRl^^qk1f~4l<`=9(@H?J0D5_@hg>#zy_L z0QeNx8Y8U&Yp)Om0GC-O#GsTpbPnsq%o9L8vhsBT6-(li{<*yQrR)`jf%Q#tm1sUd zFm4g2v&^{t9vZ|!056PpV2~WZtyHv~KUB_**JeGfkP+^or)EBshZM&qun^1`%jSeJ z=)mN@V@HnVYW6(5+Jl{1lLBpc>K#h2=n(6~h``vMQ0&`0v#n2ZvKhqh>__bH)bxFq zcBf(ff$ivRga+Uq|$8OfxKn(BOeT>L-hfmP91gG`W@lyQM!twEf zx8dL2UpPA2Y;Zz|hON8xwr{+~f{NpLKF7I))t@~jsu(Q2qs>RtVFw79ThWl7-g430qlwdjRR%m zwpon`DyL@@n-J|fjF+HG5qM#BB6z<}=l>K{PkiQQE^krV&d*w^Z#b$|-ev{y$$A&> zqugK8mS1eLWZ1(QNg!fxeP>eP|BcLrMP$2r$`)XoTI--N^K*kEr9!2UhaN~4IT^SrK-ED^{7j=n8V#1y(~lb++we?l2Q-|+bFQjp}4<3%Ysie4?i)Ux4MV#eaoXjLh6KK-4Rb7ao<` z+_5Wfs4%ITAo65qZCAJO0J;>`1a(A!5E|bo2$LUE>{4G<%wcx(x^`Np;FRWdS=dH_ zK0pDgZ>&3eahu7`$^_PHN5ehh$4nCph<{Vq$zZPd+Dxr~xTJ!YWqN*43{G4G`7T&d zlUa?(EZd6GWUq+ZYmbMcTB$heI6y6uN#xiwE&Te=$&sq4W2_eTujI;h`-TFsWR>caHZa9VwKeV{4C^ z1TIPM`IMbt0CxcLz1yJ{;)PyaHZDo_1rf!w*FXQ_P|6bqg@4Fo@1wq#n z361bK>VmzqZX3J~VdBghbsd8{N~mg$`>Jo=Odvy>${@r`{qZud~12;j{ka&*l;!EPAlar7@rSZ|NS2dE#&(k0I7o4is$&jk?p@O=cO#MV_W zbb7cBHrBrNBKCsjnR6~g!v}6z4t``1QKjh}<{4e&-PgY%yTfne4r%}T*)*_haAoqLy}pGvD^rsBK_8(+5TLdY5#AB!4Dqjt^P zi5Ghpbg{?8j(Eg$8+r4nhTNK*G7p$<#6X!8lS&pf>H2~qLmqjr0SCf>EA_IRcYFo~ zvMJ~#D5Gss9=nwr@Q6jVlPQWSK;{dg{=J<~*FCx0g3}*u4R)BKmburJS;J?VAMY(- zj67{9rmn$S@f{O3jpT;IWuz4D^C_>Xd@ghk2a$b~hHGei%Fi9`-glr2EIU?`5a#)n z1)+BoVKgO<4k%ISSFOX3ToXhh_2# zB)c0N-@T4L)%Pg<=~!497#~Y?NmQ4!W56*_A0d_M&3D=CCNc!vTQkqu;|k|Q=P9!e z3ZSm(2I`!_vz#N-Z4tbULD7a`-Tk6P7rqE%TtkCxtrZNS{$!m3suAa5GvFPyTyVHf z4(Ou^%pc0S01bwB!8xfl8M#TZyelcL+&>c=8HLzI}&00t*F^rnnbeCRjLM8wR+F%LFi;9E+Z_0C>q z%}V4QY;sTa%LsEi2PO^@T3Z_o4jOWC{!C$7MtEQ{Cw#6;Cn-qQXShP_$GmjGd!C-@ zvBw5a_X#;c_;+V@@*wLSJ_bq7S!Ph6gTJ!b+k|itb1BOHv*HHr++}wBxT1VD3-P%N z2-lIT*Y#;uVasftLRX(?jl-hIv-2qI(SOsrEe8MS9k;9%fx&@dM_=Q{Bz$`OL(d&>iCTtDK3(%q?Fk$2_@K^;<$f;` zt=+s*RCs{o_IW4M4#Zp)?{h%v%C>Y2FP^eIo{eXRO<-=R8hCCD_r1$GQNR&{^M+*G~D^H0UnI6A+_A3kK!@jY`VtfWGAnF^c%<%ln^GVRe^HYTjGux?oNF`82L z@W3jvtbrmLJyD2Pa9|cshlg=eEyc#jH zg*Kj3ZewPtDZ9ArgCzFKQD5|afMK6|yI4{<7baDqBNAk@(chUgYyHVXTP(3Z^IFr znEeCD$q$S5%44<_(+mH0N~siQqv`eAdI{Kc{g>j|&H4!|-M6H9nr` z>MeaA=P=V$0C3}PLjgX$`ptJcm zz>&|wKUojTP!c{QZ+kVV@#^TQ<8<^@Yj;B&v64b9$gHbxYrXkq0pzGp#-GR;jVuIa zlestX-QWT4c0tdLjO#2}UZwo2-kSv_ka$Z={dDwN6~E;p70D{749Hb4G#*5&x21{S01j4-Ml1|&Uo4Gsx_0EC#Dq=pCci|-A!{dl2$ji<9dh8Ss- z7=PjMkKsThm$Q#wd@R^2L*GeHOjq*AxjY*6a35^`29x9c%CyuAdOvVpURYr7EF9~` z#i_u-lJ9!AU^Z-NQwN(CUyFZ+$zQU4esFOWEHOG_%(a?9>`lJ*%=e%j0?@p?gK7^`!7hw2FFux?9JM5UkI>qEB#(<6o{rwQWZ5*g)=| z=g4j{$dRoP3YZXW85jt0K>kY#i3E+~P4+mBFWnrKrkA5~WB}ha@m{{lvA{K~2%c?{ z1QOoX?Pfq+IvrC<4F6eiOakOmWjY_$thYJrs0#N#nG3&v`OR?=Y)TW3xIk0E-O9 zUFJy;L$9AN*`f^$4pJ}IdWoV3YCVnJ;*~f`P;qT>5FZ$|-j^~0X^-Na=K+wpk_DMb zM=-$(!1pT}VhqUzqyrGK0r!_GsXmwk7frBvG$IH)eU=Vt@o zSj<5AT_3v-qwukehkxQC{ipnUVfx?h1b`WUvL-MovzDp3Q_;pOJ!HF;;&dT!-QNiQ zv)JU^qvclDYzDAb3484EYK#>@KSLLa78F;mX|88hA-G~#`T>xQ*87yTvwe95^UC5b z!**?k$a9X&OxeM*M(xs{ro6#v)jpbuCHhPO@zE|YQs^~#vTG0R%>&kT+w+zU+IzP5 ze00UPANdI`xJupbnoD>Dt%_5lzxG5_mk_>zXo#JL@1=5DJR1b3jLopvLDOlg5eTWw zU-H2Z+~0eLgGAZCjCpA!qU(bVr(CVuObTkjMj`@QqFFM6oFy8^}+{m7Ws1AKKik*F*$uEP>uyfaGz)e?}Q#nb^Bp-W5{H@ za`~i30Tauvy5)8SmSCvY1e7E&4)5Y*CfU&T3N3Hy3y)u1a;*5AXjidiN$kx!9~8T= zz-b!Ux#+s1yl2>H#3=}HcxY9E^2^p#?bVg7Th1-rPIe5#{(A$w-#+a7Dvch!$7GGq zG~QMJGhU~PXzhMadwes!A6Mz{VWIi^Lq*3M&i-58)f7Aa{1`b?JV#n6MQnA&6*-42 z;{*kH(%#J_McWeevaLCN(GDl5*;>@PM(<)-|7}qMm)rM)s?3z&!7|{&ep{99Up0`y zE$rikb|bE7(Ow)}-PFqY&}U!I28)jq81A<{H#XI&A|-NZH+O5iDKk=4W^J588+-k< zCz+x|y9A6v0w*S3^@%4XZi&n1;(H+f7h8K=^g>xb5!#2xDpKVpL@-RBl(5pslvQjvOmPDA>~>1|J)rXu&(?FdnE{Z`!?cd_lP}5 z?=<29ZM#BG9)iq7-{p}TJp~UO-bKt*{K_qC*U=g8)C)f>SkJav8vtWaU}iL5p_K>< zPx2RAN5-KVM3g{E0qj6^l`cc#s0n`|xc7u%@JA?J#IyP#kMhZ^KX&oMnYX(5hv0h> zMiH(A=X3SOf=nK1hi!GV;@RNfy9742(+9EcnxYBud+GjX`B&cGF(fY zFe9T!VS8#-;h`VI!8_*or!-E01vVx4?7Go5;Wy;)C8Pm4paaACrRwA<@0l8T&BPdv{h+Xjf{kn@E>k|6w!7L?4-7x9Z$N<9S+Y@BVa`AcCpZvQ{WY;!tBC zQkF*={dco}g(OfNEjFLdZl#uN493Vyr1l~~-Y_O2Ep+=(GyCsjo{sPc*>bI*z-vsN zx6!D_w#^`~6%n&+eYxw0V>(}WJXW2qcD~d1qo7i5g!L%0+;%wJ{lg*x3C>s``oTL% z1^F-lsFL2u$W^5>Rhfjo|zPx1Ey`QES+Srg8QE6|+ zDOXSm@+#oX3(QN$>O1#ixDNt(zr?%ik!Lt(lG|?WoSq?c&8g(1N6$L^qk{YoHvA;8 zs3Hhma=n9#QaWE)gN3e202)}pc_^Ca_9mxz;l}tkZAe-~M7NE}Y=h^5=+l6w3MsEO z5GP;2#mMZ~qjt%TAeJQd)yU_z;6rd_E&nKW)A5{tCx*CVb z$g?ivV=?)pPJYI2|zgImCn* z(C!SZZzT6AioFoM09=-O3hRmxQ-l<#N&q+k1=s4yv4F`7|6O8^&i?8{@-*NgCH^RKRlHl(*i~--WpTU9naBEVa3Y?|<%s?2-Ov z)c@RL;IIF^$BTDl_H-Tppbiw%P8ai#D*zI>Dn3>T#XS524N(b%)CNHA2JO-}S)K+Y zlR%r;1L`;f>evD<8oRx6G6Nt`GN>m*zy*9&ykAukQxyWe*1EeZ1ixAveWfUiM%Upp zeMfyQjd|FDL-(Eeu9yp7{|^-J|A6am&ouKd5Gcki^U@HSxnB!YfRIO1?n}aeUp|c4 zq7OWuT&U=O{X@C5e}6Li3L+bEM{seM6<>Of%nhwX1(WCT_2#c9YJJDPc-P~rV&mSP z#W?lxM~iP*+i!z??hjCHy5afN`o34|6H$|=y^!#wr9MucdexK!-p%?v*~cyG@R^*SMhdy`v0?zNC^3jr;ZDpygCn=1vDQ zMjRzYO{&)C@yiE;A^OUp7~}48B(3xkBd_-GZudgjoh2mL z6BW3efKA8y>+bP2nOa{LSd238o*`4QYTmAM=E6qgzXW~nbmcE!4x^`Cc|}5ghPVfN z+)utg3Jtlta8;?MmQz(^)x`lbihL68*?2!17kUaPaNYZnNKKG5>hWL;m<8?!yUPi()W?K_keKYI@v z;)Cajagp2YULfYWEOOK>2{z8J#RuL}^3%eoW2*bK_i_Uv%mENmOM+vr=u5@mAPDrw zM)72J{M`+BlDwzc*H>zN6s+s_cg#<1^?m81;_V;k5I~#e?tbI@T6Mc-Ww!Aie4-1O zy@Ow)>6bI2a28`E(C#qH{1&w(Xm6$EFKeUE->BfTnz963fYv=3FLv&v<=sw`qn(Id zF)mbm*`XoPSLs)_+3_tNp0boHSQkUSJ`=VqsCzAL1DnG9S@Cx;%)|G;hE$(TMPG#V zo(2=%{Kszf|NO_!!hvV{kDUQ$^#3yX)jN!Z@@@^@@_d

    • u@Q8=Zf5k$L(<#Cl$S6?6N*`Ji$NGtB z=DS#e3@HBG3|HimRo_!r{D7d>qv)ghcSQ1&uLU^NT&#%UVQLb|mnBTgb-*4L(3j50{YB6zsHh$dqsJ z-dBK_hql0NZ3Q4Irf+gs9ZF0h3tQ>VNlLyd3y)OeH;d-C&fNXCJPtfPWfR1f9=C-o z4jf{J`SUedK26gkEXRvxvm&=ncbW-W>5#c~QoJ5F)}S}RIFmW5@%jb8Gi@WRIQVbDr!?-&T!pA6^7k$Ui zj*xr`s%S9ohvRr`&OgbjzOtQjZL|Hi3pfCo03gB2I!+&qDpKxp-U|o56oB+q!1sTE zd^x3L8i8w^n;*aur=%lJWEXHi7O}7rCNwPeLx>DlWH-*-{Wh(R8N0&;`IAGg>Ep&b z(~f#^q7!3kM-Gj76Z-#LpKJ;T(4Wk%$$SN0BvpdRMJL9GrYDF2w*+#6TU+1BbL~;F zByd^;t9I5&3X;IKD@AfKf}mbh#u@T}AVk?aICPq*LlyQo+<^|Cf)a`lA-3fkcE{Ir z8M4nMBA)#9v9kKl-aTaj5Ze;hRaWwykOdIcZ`%g#0yQ7-L#f{rvaDZpkmZB#A$ZT; z@I&=6V}uO2d%l8{;gDeCdBisXTFF8jD$6@nV_FNxTtOOoHq*HAz1M<85DLFOkS@7J z?w=dLFFsa^*ciln(&B0RtO`7L*>sjIXEQlI7u@Adk&5}#0;k?#%x$RHm=$A_8}2!ta`RP4Xs zQs8o6W(k!OQ!Rblp$MGH6Z3evP!zCF<#F&Fvhani*Ec&0#6!fVN66w{gjnnr@ARJI z!8cGag(d}{^ay2wxSU=*;R?x%U+YZ5^}j1-iXXo0_0HBUr6aX()OY4;W`({JLuOBM z$4p17Pia%A(L-A3E)J!&&KRbNGWM>38gVBYpoVVLZ8{mEZDV{Z=RN?lJ1B~m19uxx zkKhlr1kzDqa$+ibAZm{p;$!`@C9~08v9mCx#k&3JekFu#gd8j2LW7}V?-4=@jJEl% zxNTRCfc)X~+a3vkO zbOoORZEsIhm(JfLUM2j2WecR2@J(2bvwRG~ne~>S%eoIMCp=q7yYP0@w%T|ES;D&j^9OavV< zAWo4^KbUJ1$X6rfCcN;>j8BW}-|t+8ObDdtv1Vq!;ie{#SM;hn1|lcZ%aY@LW!CIM zn+B#HOtAL?re?kgQZL_Lomh=NR$)sTZ_*5()<+)skXGhGk^)yAGDuK?H`C!SuZ%-c zK_}n6U7`IQX0$Tf;`hr#=&J+q^1=+(Sn{T}w}2H~`~86}^4GWgL9$?8n9!kI|p7B9mHr46|EX znxwAN9GNADDkSpO=k6Ej^Y7ZL|E@*T=Cn=l(tP)E@0K?zIS{S8b}znCb%zY*?8P&8 z7N2bisN#HTGtLSk4>Te`JJF-%q^qp#m4_oIdt@O}4Z%pz&cF=lJId?_ zm%MFPVH%QO#evp9#TyD^cG&&fpY1P0G<*F2%v8MienH+cANMH17g3E)xPOBDaKhR1?z6cdgsVs3))wbEA&w`Hw_;}+P?lEILQ!K@|{K7K-aj}&-a_i(89Po0x>O4}x%oevOj*fj|X1rxkIyA$P z+v8kGsp8b`p7MZ-(*h!Nr{>{;V_t!N9?EWGlvJYx`pKi81OdrS&ttN3@>9|mz(Qg@ zWuv9cw?8};9xhkBg{ZAc&TtHE0&l{4X1!)PsB5ESeYqgqve;%q@;h}{ysQfW4=AOu2uzv@4XF_xLsZm%(B9r1#2i3V@3?eery`g zMMi8+mlFA|CF#_=Ir?95W9W5+6|PrW%DZQ}IGr0&dtK!);!xVzXZ?jsnXjkF`caKE)Mc?N3w)0p1vyN>$ zGsRD_gn8ky<~7%?l_1vfZ|qwUs)h@L>~ZTq5cYxhIy#cRDR*5~%B zv(nSb{X6WKl`4D7An^aJ5){%?Q<*F*JVFsV{$XBHajOe#-HFj$Ul>d3gH^QJ7-q$T zAKUB3JJLsJn7-i9wZ)P+$!z-s8!i5}P(>Lm&k1k3HuSzIqQi?<;w+d1)*d5k69K0g zFW+cCx@=E1SXtrEc%zBo@pVTO`vY#p zm@I!D;5wMeJ^R4FCFjAu6%wklF5YSjx-Kc&aLp(f3xTRZ{B)Y zA@B!Gh95&ri1vbU5e!6o+P^NMWLpV;ed~8omsj;J91FikwD(dLF&id2-8Xvf*apuC zNem6SNY*hD`=0xN$U$3{HZo+DX(7~nd?Iq)m2e|8gj>F~{8zo_Pcr9<*bvu;Oe%7% zLbEH^@m^yz2y#XyQQroPZ44LG24bR`75o|sc>eKGa^sx9uTDV?3)LXM^v>Ry#@yZ7 z=%9jf?t~66>Qh}Oc5A7lLuMvH6hbtH{$4#_BWst`t(^Yx?j5uNiCPda z@}|e!b_>4HJJzwY*Gs8uEba9a;m`Gz_q|w&s3JTK{^3qNafe9ni@{r(s&}e<2l>6U z1y`q!2FI7Er(Z}ElljhJUE>Ik_JT-DLgGvl8J=`@TiSdop}ioN8|S^eEXs!OZJrqf z-?Wmsck24VrHk&rUn*=Y(7yDnb(wzC@pg^l`0Sc;cQiAPvzC8Bs9P!oBAOMP8%B2@R+&Xb*fd8yQSjtev`tr{7Lmcvx=x8s|{uIG^~F4)^WdS)BwH3k>P|W zG@mb{M>UahtvtH{jn^xm^DusHmd`%P4tGLp#nwX~bNJc`1~D9?g80NfIZer&r1jX(Ep2d7r;w zFt6j&dmE?r=P`gSQp2>s{%c2yiU>UE6CM&Ba(WhWS{@=yO%x?3t8Ifw3vvBcA#yR! z^rokF&h5eOYoy=QkJ-qT8?%_Oe&EHlE74Ey*fZ=#HTsyZ*fi2K2EUu%D)zhJcOu-q zv-?2%+P~K`Y+X=@ety zZ3@Ov;qs+f_bu#WvkGdkKP8nDIk3)&i@3(GU%W*bFk7kDB72xG;hOg{X10dHZ-eO# zgS6~>xmHfxkI5+2$+}5dR$;*X&Sv(eplxGG(h&`y1^bCnP@ZG&?uEFvhm$bZ(Qsig hLF?Q9fA6eMeRO80J5qid@t}Y|igGHlMURdB{}1!eGV%Zb literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter11_79_3.png b/doc/LectureNotes/_build/jupyter_execute/chapter11_79_3.png new file mode 100644 index 0000000000000000000000000000000000000000..4f89c99e972be14ce55273350dd90da75ce36d6f GIT binary patch literal 27834 zcmZs@cR1C5_&;t%5<-QnLNswm)1-r*aB&DXQ& zExcl31R04hnZmL^HaBFniF|eZWL0;#qy|^BP}#noTf175TacPtpg&UZy@2|G&()QB z-dkU;T)b7EG|eGY1tV8@#$(of;>yl0=zv$o#=9@|CrG$#z=m~Y!B@J~r)rv;oSdBW zA(}1FFIZnvGSJb{**&?f41Q`O{we@|qNDiVe{^VK8X9BT$%ZX{hb2=EcxMwGvPCpDc)3IRip=)~om$9$9c3belm*AL`-p8?m=O?pB`#yhNfJ-lC3ZHsPB@zv!4QYLcX|Afj-6;?uRE?`ab+ ze<4*u!TfGannWE?FZ^nZ^&s5wP{YM42teU#^_y`w}9Va`YZ`ogxJ)qzj zNwA^Wr1(n(XPGzi{qX(Lo#xUXVdUrJ^X`N*>Y#nBmtX|NDcR@+IO*ht(++n-3g53! z4F8%nvEO7AEjI|r^)1J`RuYYjBsedhd(YRetNvYe8$$TH`>r<;|8=;z|317na>>T$ zp!yEUf23yag@n+9>Yw{k93zkHCu)6SeY5Jrjf4equ)76Kxlf3Tu2q#|%d&i?MLg=L zV{mFd*N|9EE}s;Vg!)DcYFpL%qe2oX>0U%H*#q0#5q@SiON2iO?Em2#sOrP-wo5$h zaG#*ZH*R5F}O#_`amSk<2sQK1{I%Jsh0Sd&IZWHz>pvWXL4 z_PoiT9CucZwS3<6-EByHtM0luo2l#Mj6OSsPpnUz+Yr93G;GlwKTT3kTME~$!-`aK z%;{fud0ZuRS^L82z5n9RP@^<*9DYo(qM;>pFW^MObwQjo=9#qzayEAOox58aUw)(8rCsg!0`pIHu zbZnN0Wx|R)*f*tk+nebBR+(B>ek)5NW+&OO+H{{Lw{G2WD*)g3ns<&x%al38%4mqY zki&f>_&xkf8y24fVUM^DNpkHq&&gWflT{Uoi4*P5bqBET&A5~KG^>P!!z!9ucGmUk zgDmfUQnKzw^80Ec_-AKq5n)Tzdya6H1&z8`jryJb=2E*GK}*z9C6Qn8l}#jYn-|$g zgTuz$O5ew>RK zb-TtIIWlW{QNN!VyR`Z0?$l7M+cxTUn=#>62r+8s8 z>6|2a@80DgVjkB*wdT^923CwXviQJ0&<#RVN(#~WOT3f~309(ITYK5_Tw}8?a{6!5 z<7;Y>tQXs6#$Iw{`Kl1;Bh4F|OAl~GIP&CYB`3B$M|UQYbdWEem53}+ zVsTl2?<#ZE_3UvVsUloz+IPtRgb~)uPcC9`X_CnzXZKm)j0diG92p$v(dafr;XdMf z3yF0!dxV6mk!~S}3z?Ayc+xr?n%~D2dn7UII(Hs+ur;}HHWlbz+W47#f*hW)ZUo28 z3BYg9rngR>-(9UgPbdltZPMuOm>nC|TS<~W7C7)`{?&XU>g{iKh7uch&J~+rhJWJa zxR`su8bh4K(jX#S5oUMj^pn(v`E;jwXrt1d(d$97N@mc#Mb- z$M0H#eZ$dWBL&8wKmcF%BXqKZj>E+d7v5TGcPZCpiV8_c%{0Hg*6J2p>T8e3Abb-hSMRKT7Z(c95d%! zA?HO9cUPTCohi2L*!894l~aUmYHzgd$W{MhDjjFq znQA@lmuajlHaUh}u|P3fpjLd%5QJkoucevf#sUuq9kwker^`4`8TWdENQJdaw#b?7 z;FiZbbwhc4#r&_v^3cfwmLiO9ZDXYQH1a&Z{5Eo5cEtOf#hUAeK>K+lb{;1{FC zJ?*9PKhMd9vAQQqZabrClk!r@jD%ZL^&`T2`++8?V6;QsZ^Ny%22~Q%xv@L!eFpGa zM|WYt{JY^N5gy+Y4wNVZ9Xoay2aCJgcLprZSc8YhK|N5~TC@yJg#$7pGks9Hn_qjhWj48yj>qIlpKP(7 zY^TFaXJ<&>Sh(m|G@9kFU(%z6TcTE`I`Qyb_r`MNdND)vPUOOEWLO4#)V6_VGBvMma~UxW znNjrzb_!=s%dT(^E9cVT3JUg_2@K-Q=>a2V%Vlq5N84f@4)58-EtsNUtVUwn>rNsZ z7>B6Qo46Tv7l+EEYNV8SVTxqG?#Z)O=1^G2%#rM061e-fs7+Rc^KYlT3ls5XzANas zA4sW1&opcqmn51iUq+hbm>7{?zV0(e+b*H&Ww9=2vEGiP@vUM(w%49N(&MLnIE{|M z3{>=iK0vnNLae?mk}MOiBOh@cZif9T8vT4 z&WQD=5&eXrl}S~tx~c1JlGTU~m=QH@9MecVi=G4fK`he1*5w9*GZYrR<>7xk3zHVd zba=L-<5HL~N9dMNm>&w3RzDO=oW+7ruXF!mEzy0}KIgi{NW_FFK<_Yqut1U>`niyz zTwK)-RPQ(K6hFm~SH^!flaU;8cUAT4`PH)5p({aAbrplHE)MNOpu`%nf>Ys3)!FSD z?~iXF_+V&RCd}RIC0neM6LCvhtOxel2TL(X=BjZfp(ZAVz$H6&)z2d*0d?*c8%;Z` zhO_#ZL7$E-RtG2V)(PZD>jOlu^rlDecEa^jY!Xsx+it%of(s`d>eV5W0fOO7k_=` zNPET_-r+2KWcS7*chdu5dLy~sf_6@f=e>Rp`yY{w+UsgRSOS)MDBZW}#3~N@w=XB# zSX+~xe_rCM=bDQXil|g*q zM2}Svd!l!3?r!h8&%p5bSL%(DPLCb9ku!jE?Fcqx?}UhciFAI`GFe{|e_eI*11b9rQ6D>rfr-m%|4tCPY= zgcrVDJEHlv+(qA;2xC`xZFqbSDaCgdc;JO;arlsxBeya4equ3AvS2Zf!m9^)-pN2m z`2Zb9jKuy;%b#=Ty&#BBUNOrr?;CUHx9Y8>!0EsZ8-7ZRpVBjx@hZ!b08p{wbO+llC-PnNR+US6(scB8vEwEFt*HnsmFlLdjVr8k@^tGtBSNS@>!J2qL zP*70kD`v!vFurYJPu9DDa@Gfk17D=~jKEKvG-Q)7=r4ofIk~xAJw0iusVz=ld>9!R zWaQ+?BO@bK8bYBDC{(n{(T>`PG4MXA$G8L#u5l%3Vw!iv?MGj*d7n5?#(s=4+T7tVzv6l5j4<>-XxX8(g@TX42Umb!*UYs4*? z!v%itt}45^Fj0cO%T)W(QVPbdgH668jEz=e8iLgM*-7=`?B~XYjhx(q*#H*n!{eq? z8Sv?NF$W&tYCf4jnuQiBezJdvFq1xEX5dv#uc+8(;xL~>l@If}tldwO3oQw3=z|uB z4=bJ5b;&O?{S}wXbzk_Zg#-}QsF|IF^pp(0}#fwJYVM0QW_en z+A0@j$`@pR|99n;)>BRW+pj7|e9a4%rx#v*VNj_KO-*FF7nFMMLBO{n?hh@9pP{H9e4N*DXJ)Ch zH}8dQE+bpgW`lx)dGGNgcg7)8=jemNRBk@z^Q}5`ZoAD5Vo2p9jQdfiMu`pY345Y) z_(7o&qWi(|F2`WETB^cd4d54ZnTofP8R0313F_xVm*( zw!pyefR2}p?6|v1k;QSHqRN^Nj9zW|KX0dFkA9-5%oP2oNU936Db+ zqj_L9Soq-3kSoAY{9~&dh>oy@Xf>%HKYs>6xrNnb(ym~xLLBU-BOj~B*7}Edr^vVp zPsVPk36i63ONl2QE(aC%sCV4K5CRLr!!BAl+Ri-rb=Tp_M88)^fsH}ias2eH^L;{8 z+%Mad_`^^a?@P7+Rcv@>QU{oOOU*t2Nn-vJqrqP&4SuBJ`};@B@WS`Z%z#f+j1XYG zb`qvHX977YtRG855FI4{@YwTN-wvaOc61ZYk7Jf`Dd~l__S=};#ZFecOBM&`pPF~9 z&9JSpu;akOE6hJC*^g54@*V_GvyeA+Mskf+Sg{a+h})K5vl$N z>$?RSM@h~}?l0Z9l(^MjtP3q^6uA`Q6gX9XLLve}j4zobKYxLxfM0cBGn+hiadUp* znAC0Kv>_4jF*|&))LLSKy*^@a`_f3{v;V%c#mpD#Zo_lHXIXQjNcJT??yc`Xn6X*+ z>dmM;_buCp0eSVkc0!|%jzv%f2EDPg`Z6ji`8b7JygWPsEiKQk6(io|XA~7h#KkSv zZ#X3b6eHdq*krw5)M<-ZpXW&OZlxZ30DX|FtLxRPSF6J4H;s*rJ3Bky4_lRGT%j}nQ8Q(6*Y)&4OU?_|vX1&m`vnu( z032z+;tj{6`aDm8KywL>#m2(jzrS~EY}xLvD}O$tFs@H&wOwsH6zU7@RDp)w4I3=^{;Y^a!_v)sow> zt4vsyovR{xNM{8U>57ukt76CcEvNnG=~0pgZZZ6XZYOTKlz*8fV6f2O*4ihkG2Mya zcHa7?Yi5Z*5plYT$|tIA`e!$0$fFDz{qw8E3b=v~zkps%f#I6BRP<BX_Ly!>x%28c%@Wj!D;%)iewnRfS1oeGp*6p}#YC>bpL zjy%)Lx}xOG-r zt$J;@gvYQypxMRNV?j^qXzAha;T8CQ^d3+Fp~3AK!V}HnexoS%+z){U9 z>E63t$pgkbB?3(rV|`Oz*7>}6m_qKq!-JaS&Muvz`o>@`ds#{JJjQ#VR6}AU``KsM zE@30h@`Fg&P$l8h0oJ46i8J!Q3@F9CY$x7_dx*2`EN#ATIf&o#qfk%^0a6})l8jJaseuA1}t*Hj9HE-KXTNIUB$V%z$dOSgU?#XfRD9uz*)#){Q z6|qLeS&E?`})?Xrw&ojjo-zHcU@fpVy99FmXype-ZvTTgslrD7JPy z@_bD~dr>^96E<*NPWG9>Ld=n-)Z?!qt2azTPZ>w_Jbnb++SbsQOIF1CPYYG--@h(> zs(&x%gPuISISk04G|$ML?vRp9`uI(BQOzq^36q>@6m+V$m@QJAjdx1aJ?Fzq9Sf~G z(!eNRf*FFoB;o9cXL9xCS{P z@~C~UZGm;u=}y6kKvKqruC6qS+A!`uy6bX<__GA7Eg4bIAseL4KCXZv_)!8dlmB&# zv9o=f710AT543`DftR1%m`;I)B2`?cwxBgK=`1pdX=kC&V{0K6*y#~8P5Fn_h&wkp zvLwY$_S70hcU8??BR9*eR=wSEle3s>z0lKdvq(VD)UbI~;Rk-VgWuY+ZiB7GAEr_)Q)w5| z&Jb6x$T*XR1?nh_e+NuUIrq2-0}d`YPD;d38w($`oXd2MrilN;Z_AO(*o z5>Nb26hgwC*_1rK_xOMAWIGb#8S&`nrJYtbfl?o*{Ctn35yD4hc>Lk;_`Sc+--4y? z6iMBswJoFTbd*n>+G|I54x(4I%c8Odz56mmrZS9zKI(-F;om7Ow)fugj2GcJksMxS zHJ)ws&}kX;opg)csT=X^V~VCpB!%0jO9-O%z*f@|rK9)q<*(JJ&$$mZ@l!1g-iZp& zbolu9t7CHu>O+5CWFu$UMg3S>pe=c5Lcg?e%u-mt`vqjOz=fWN>WHjF>qFkIX`d8r zi|{JUsIJ72u0*%4#64l*^78Fqg@~NaH&0ij)i~>N;&fWs7q*oO2L)t*aKk^ck2H2} zj2a|X>}S;-%y{eb(wl$bSJGzxm5*Jxe6z6`p60_C3Y+l36Vb9DOb-R3gUG6*s8cj{ z3eCTaG%a;Vwq96DOfw3477?tPK16M!&K%iUgegFrms|tz@%YTIG|Krs9LCeb#Bf26 ztnRfpxrJ3s`Qsto1j;%Rk7?bL09v77g)0+{Yi!`@O`xPxa9+|rN58mh2u@-48Gnc_B~Geh_7q@VwVOWDSc(c>f+ZWsptHqex!s3|I-#@0J;WKlJx{GXcG9$$nVT1 zBYUcFe&U^mJ2fngvotP1#y^#;Wjm9jSKpS7R~)I9UYz==5sy4^DEl00&!+gyA7&a{ zUNO*kY47zdI!e9asFQL26>-8yFExu&_nu9zk78O)GLlWq&)Qh`kGCs6QX;z`-+@h0 z7UXymO?@^o3|6-Cn)gzDXY{grPwwv8;DFP;EyNV&gmj`dx%mP`^85lXenhOTO$-Vs zxbSOB?^F638?P{t*?zqsBt z`%0tdn~rYtjXg?=BlfFSLW-)t1Y`$g=?2oLH*Y*2&=+%UU$2us5E=>Q_6J)4g{GhP zr{uBIYFufyQv8k$eh${>p95}1nF`t6<@Uy_w6wG`Z*IBhRDGz&DbS~aGQxdRlX3m+ z!F1NI?00O1yQh+j1_UZ<8SaPIzm7+5Dj8;$-sL?0sx($5)5@qcF?3y7_SB%gAoQxF z=%==jq+a$@7rv@l9`J#V2R}wcU-X~y`i;qA8~Mx*d<91$x!a&t$55im>h6M&+O4`8 ze+&=2S!}vmv-OH%?ux*w#2Wj7l4{H`?2d@Tg0l)8#5l8#jt1JoR+14&(m8c`vztr2eVN zJNgd(hG5!7i$vqChY){`;S$^!F1y%B)?kxNa%f18H|h$*a03)SGQiU*8hvoCm=e|Q5$QxlO7X5XjO*6DoSvJje8>O;o|IKaezT$eGf+q()FEA7 zR)_@h8J>q_%=pE5bR`wcDFi7o*$PsqHiU2Gy_=dFdHGUrMm&n_7SO~Fqidhs;A{Iv zrfruZI5@;HNx`2cy1;m3b3(Lqp9||fPt%r&AtY+nnpC%a z-T}-V0h!zEvF9;8>49fcmVSZhVJBt5To9{)r65~@dvsCI9dv(Va`^Rp`y_>r(Ed*J zm7OhzV#=w1C{MJV)+rXKk#FC&ii<0Hu?1DHA#-7M(7e;shOU9 zBvB^lrmQ~f3Ay~rF7T<>*vRlSPQ{6GKBSKx4zwyJU8%*f-E*YZGKZXIF7&4HIO4|< z|Bh?77)t!yal}qGOmY1$)e6F1r|NA1?hgHTaF%oxO|38VNB#M0kFqZ}%o;#cI*VJe zuT;nuKBu^_Jtu)$*s|bjm@^crhHakXz$_|SL$8BQ%yfp5Z8QoVIYS|pUR3qliIwsR zrx;rI6IUmT-SuqW^j5_6S#>6*V9G6GCfLn&I(Ww}WWTUdPZHakaM^%hH zKtSJbnwlV~`I7g|S7h5mqYq#YPR}Kj0 zHUcQAwuM)JQOyi0T&$ZB41aD=^9~O|a zcLZLySI#S+ho5*FTVA7Ngg?_pR)M~0Lsm9=!s#C3-eU3VR;I33z+Rm&9nlj-xv!q+ zZLCPdfZ0zVvOj~(x(ziT?*-UuS0jo(8OH4r0G z^dI0f1KISmw#C@)Zhl$iZQ0}#ff>3;XxySe+*xy?;ral4)OTaVye<46<%8qDx6!eu zu?z89Lz3=!K&IF2onHcSDdtREVsJ=ch36;t6)F7EyuXXt==8%{hd$S{Z5k+{Cgq$}1zU!G1H8h83iHlszvHk#f% zz*PCO%c$7`W;T0?9%8R$UuGJi<^`ar>k6T{I$*MqG#}_>w7GCl6~;9?(lVzp8ucjB z=s8CT;cYxlbT;rGWz5-$YEALyZgX!gL7rx4$-yXntghZi+;BYaH1evA7Sb&G!O?6Z ztJa}lk3@>h@NzbYCo+F)gxO0=`e1O9WgWpq(t zmKjspwHs)KRS=Yst;e(RwaYdlr38Oz`XMQ>$BFd$D%LK68dy@R4de8Jx}_WCmMfg9 zqg$dDQ9MHy+a{1wWmRQTmceYY_@vUGc>syCKY;b8)eUr1Mkgv?nx}Tv%^HE&_}KEp z2z8zR@VC>|Ee4?b_Ctr1GcK9c;S%>2{kDvBP$=oIx+U8(1OGG}>Hv$XK}Z$J(<}ct zXU}ddGpl`^XrB*G_>_zD2WbM>@RcpgguDPz3uOSwYp;bh>%D}~OoRL>l<2B3ZhFnx zx>lx#0|Ig%K_LF#*`hjtl{kw@$PrM7s_~HKNgIeP4d9u<{~gAGyqZlMXTfD&h;|`kCk$xS`*CSv~4Fh)a|EVJ8 ziZa-9cb45t$5c0h+{Qf*#q__xk%u&Usba{Y-5l%w)3PiMjq5-eo1~dA7 zWW#Od9Ej?dyG?!P-LC`_r4)SB?|;#J>n`W5PkoBfOzOM0C|+~}Ttjz$pY?+Jz+AJY zwHDI*{ott40Z2?|yMbQL6)UU>t)@k!&VosS(mXH#7NWh! z0gwQ$5Jz6w-dG!n|8M{L8$o^^*Cwcs@P}gr(Qa#~+uKb3$m zl;w5P_Xr2ppZ#-Gl^ZPlI`5Bw+%0)PL-zZRPK?x!hTAuf-dzfT0WjDH2WfpE1g~9I z%bL3meDnd*ys4I>t|Okp&`1d_=Ex-22ZBBu1LC3R+t)mUTC~#*a~S~Sr+hYeVz<5% zN{ZI#&YE2>VEc5sc#VR68pLiH?#^HUVD&MsJm!KLA?n;zLU?GSy^RN~1~@|%6mYGJ zaZh(AkHP|Amu^A4*3Q%xZHIlAMq`|BWT#=A*yLryzPtUpu*(@M!Y+Di~z^y$v) z{24u2(wTw}!Zu>1z*Z=T^?6|zK*S4S)T>TVoG70S>n_62-UO6Hc1IHww2gBBZ0xT_ zQr@+E@vSZ5jKluBW-HSt5@6SxyUj~GaSeFN3KzKVZ_3!}FfL9N$M;NW87Xy(;vr>_ z?QfQ5RiWm?y_EH}$(TXqM1c-l_S?^n(G^yKVA(vkF{i8MP(FIvrrYD4(vUEam$~ad zeI@zJhImxaBR`O3vQhU4AM2880Vp`YKt##O;dyjzh>HC-zw6~B)x%`qr9qM;UVTMW zwrLVDh8x5!b@S~782&6sK|_8#Lue0{uHdu!=q>%x%!(sOrcc#?Clz|#Hi&tOzmPI` z$;oy+fNY zMcAD#Nc$hMs??HuAEvAQkQ$1s8R1X=MVmc}e(1R9uCsuoOM{G4C{XS{pd9hW-V(>m zJBgIDG#lO$2X9F7S4~>@v=E4;8|XXQkklfz*utgW$;J|i29BgG>ho5rQio!-XKn({XgME-|C;cw_)pauBP` zx||sO!gCa#DMv7)9V~LGLTFR7~C-!JXGYE^G$7PwuAPV|;Dmn-lh03ccr! zi=yCsZ5>dSV*pvs5O+BQThk^=ce6bA#Dq#HG(REg?3r9iPJzy#CqwACnhQy9_D`@4FZ%-I?{Ra zHB?{R&`wvyl0LZl>lSXdPgH(2Md)Aka1jf}GCSeWTr z$m>|hXJlqpSihi?E_?fjJd@4it5uRJPesQa2zV*TK-i7{YNPf*V0}L-@n0aGTGj6- z+NKpLE#KGp9t+D%1Iw#JNsEWIW@o|L8qY@@Sk7u?WuNIS1}D>oJwm;DyJJH6hHMvx ze#eYR_4({mxr%vkakGu|{ zo^;`LId@-U0)6z8a3QD_2_g$Jn9FkTk>&iaeht(BXf)?Q5~f7r-o+MqAF9NSzJoYD zff9#veD`LF>)LqfgcGYd4`?e#-b|wQ2=Uq2RLuUwL7yENmg|HVjI| zKPoAY6IZ#Cm_a*f|DRBH;cjy5N|yCPigzUd?Z1PFw)?sHR_sh`8iNhuOIND~%K$n` zS#(j>lGx>3{jLCN0EP$<(xQ)+_By&APyCde;k`l!g%R1$WQ_vy|I6jw(z)N|=~IE) z)Y4`6)+I=kPdRQd0bE4vngl&5NiaAamto!UO-U808D7GrmKI>oNFuFxPh!a~#8HbF zh(+jPj%bmm)-48m4lWVCgx{~0AcQ~tj``B_lRGNvIi@;{Qw7`ynQe+1*+|R1%RPgd z{s@Jn!j&LZ1tXc0;LGC&P)ff7(ubAh*}g~E^x30{@lYPuzrd}4ESSxSl1&-bvj~;l zN4_AXv%EPuo^pKD?ihFOKJrSIyL0!3v>zuurQuN&$T4IPqxVMv50%FV^a&EmJjEmb z?AVD6fPDiK4v9a+qT3Z0&K-BDCUJ)XVxiy(dcBSt=+0?ypt8v4_y2R~ZWbAxT(~?d zNDh_$r#Tk;vd;clLq=&~R68z^j3(V4>{ui3q;^fpi3DW6IA)or7zZZx+K^D(NR=v= zJb2tYNG@eq6%^ewZT2P{eFr@h*^GZ{0zIK5x5PT>q0a z6i1Qarj2b1wck=BrJH1V|55zJ95P=W2rB~fQzv+vBlxhXdHbGV?3B_|q?w>vE!dIJ zQNH5g49Pdog4J2FyIm7{YqAOx@m zbyE43)6MoJBj-s;k&?@gk3K+_YRhmBguMV0mKW$@)4zJ2kNfQkN)&0F)BX=)Uz%NZ zFEIt)AOCKIIt8d!xIeC=-4^sPJc3~;rC^Q^jKH#FK6!ViFTCx@A~+|?u7Xy~{P}0Y z`jpG1v2ochzW-_nQN-_Z5ga1m7Z=`&8Zi$I1-f1PNf%JlTV!t-0*1_&HGw*^4Ktt# zyMMjUj_rBfKay@Og0j4Z@`;dlVf|aqS(oEvWISm7`1c+vdV{ug@X}*T%*^4(rLj0i z*1KoC5ZbmM!k_|Ca^R_;Qyl=?rhtzAb_nOq?Q1WdvIC)Bmgc@`I!K*jkS_o@#N_Ue z#X|%^K?RQqjWeGZ+e@r^wFHJOZ4gMZnubT#u2_|Ku$XAw1 z5}`&JJ9mKI{lH_ae(gOmg4ORHvkYNwOXWk80;l{}@h;%`4)G_`!l3cEUNWqHx`8j^ zNzB{X0JD;8x}qStDmOpej~iGf5tx{&&v5fX^nEE)C5%$AVi#oMbaRxE+M;8??>ytu z0GK_1V)}*E)dx--XUT#LN_Ypa8KAO4={uF`8$NYvDfTSfZBQ^anK?`&)cZWP$@OI3 z8OuW^{&rieo)(uD2t2_CH#oUBUGg_kFN14hkw$c)st_`HmtNjKV^| zfPK3w?u7z5))(9Zrj)fUp^%l;O`rbKlU){hmEU97=}QDykPKc16Lb2*hQNN?p`@jlP<2kj>vfX#M!95UVCq z8d#*^MQ!9Z7NoGb{J0aSlQ{y^5pxrv6APL8bi&lIZuhu@`ZnUX&OZzBAx4wLlA48c zM@wF{GL_#3u1(Y4@1AlLeBP#Z@{nl`@<^@(5VA4pEul)U3jiHqX4d8!Ey9ziySMk&{^4v^V_|G*sCDD*pIJ~g{4WDR zt)pcoR1EtKz29iEe*HLr8X8%T90G7hQRG!`uv8cic@fuXWa&LuDXXD!EH+NX!`aNw z0~-UU@&?T<^i;&WZB;lo&hf9+uv5J135xjNp@M%##zq*^lz{zaId~EhDYxd?v7^$N zx8pS@9ulOGup$CQD1S{DJv}(i4egqD#L+JZJpmhx^eN-5keePeTxV`yEX%(9FbRYG zC<$)AN&-G^dF5XS2bG#}?~fA?pd2kbu9p?81rp1#b}Q4-H-JJ(s>Z`0%CCk+83%vb z%J9$xs*r$_dQV?%#LR8w(dYE#dltyjueHpA<96I>A`}P?-m8!SS+fjxt4TXs>9f_^ zPze-{TZO4P-wF)RKAmnBT#j@0gM@kg5H%5q|C5lNm*dEG`+c^*VrK$jQTcduot4#_ zmxr?(n2N6P${#CkupV8v*o#ar{OPZ#aR2W8tb^6YQppnDvrIi`whNkGp7e$jePUr0 zRiy_xkvsjN$2u`s8jg20`Uupsf?TH9)4h1pE~4=_P$$EMjZ)|2GmU`l9G7JXyDWxs z2^v~vwUo6*#b9U4wr|V9$-s@jXTw^BXP^2_rC()DT>z^sK;!a4;xbRE>HP&0lY%rd zfM-fYP+NiPZ zpVZKMMh&2d-{R%x4;-j9cx!UPup;=j?w@sX5pMkZ17Vx`;-b@x;863HZtIn8>Wbs2 zX|NXLoSjA)$*&Qq(-t@-ao+*PQy438m7JrRervKCpKeMGWz9DH*DRVJ@>VqM?azTC zY(U++M>dn6nxkBk!!CeZgCSLU1O6;M`>(~#Ei5!Bqa%u)|7fA^dxig5nZA{+qy~YI z!_O@fW{d0VYKr16ip1 zDLpm4_Z60ZK^M~^eWEy0RF>4)5~s((QI>Tqvd{jCu-^1t+d2Q2xO_DJnBSRNSKVKq zniGHV5^(u`@W-r_=~a1L-&upavT+Gy6Jp-trT0Yk|9Q`dD%zUcgDH)h1p(gfaJzxf z#B$&K{b!i&Y=vXgB8u6gpACvtvUF=d9^#iZCdG5y&9`S27(!v|z6m~`eeZlH3L+L~ zL0l)IePbcL<@zG>y6*0b5-MM(wd7V~Dnj|=KY4d=Wpha=-+*1{(UYgVC;z~x>3-8t zlil!m>M;Wf#^u`+3X{w)Cv3lxioBkioqcPer?!h$39+eD3E_bLmou;FP&x9#uQ*N4G?p^QU>Grl{+A$9}g zhEF_f6DFwY%;p7K1WL7n+bcJw263 zQC@j06M~QIKN6Fs_F-L5wb!TWisqD_!%}SlKZ!5LdHjIv^7Ix@gXBa@EnTI{ClD%W z*&Oow#9l;omn>Tyo`AP39D>V62S+w|L!b33Hj=Qx?}3VPX~Jx%-k7bTpdWMyq@#(P8Mb{OPf(LP70w0EiJfz{&r%1NgKE*Z#KcW3AFQsy4P}b0M6OOQC?~$Jhq#Wwh<>btNC@3D*7pcR2y#VB}JFM&P z@+-mr5#Wm_S|T-nB35)ADLWl;)!PWS`o8jzV?N;#d5Zm~eKJnchJGoU}?&Kec zqs1cZew%^U4>{gbEv)^GXf8KAY2#j(v^v1 z%v&2Qh$}W(eE7shIZ5P5TthNK9PQfyUPd|Q`KBP`VJH2G8#a$((dPxm`H+2vCM|NG z^5{?`G1O4frg-aLzE1=GI|iRuPwv^mZNG+>1V8E;&q#sg*;6LC>p#^*sT%Tf&MGl` z25J~_W&deD>d4E!ohR|~HQrwMSF7$D8qEr~dy%Ghjy4Nfxnq3IrZ=Ga_lqhVW$dnL zGtRg&*NOO(ZuHq_$rrpYDN-McAu$j@w~<!8#YZw@5O>$5rgWc#5@RL1bvH9B)8eRt|if9XEsZ4nmn`iltQ3xd!FK-S1-RHTW6Z%K=U!#*WWoF_R4KULKgDBiv5s1tC z_E1yvOKli^k%w*z3Z@YX!-c{UP%vq$cgGp%xNBJN9TZH)GhY6qjLyo_V;k=naM!ex z_0hl9FXAdFg0C_I@-41cLmd7C9A=tinjYO`sTyS(+H^?EZ=xI?ztx2IiErrUYDSDr z&<^>M$|h~fK%M-v|3-Wni0+IZX3TN>_Wb|trIuVfGRd@w-W>{rlliW$-gC<%Fygo< zetEC`8#$i+_d(7uM4@f%xA{HY?%3N8*gErF#4zqtGkTMn>Ho%Hj%X!u6&eD&a>`(p49Vv&=(xkF%r^1gLtD1n zH^D0FA;~clq67td)%3jS&7PS6+L6M5l&^Bwdei7SrR}h8>UDS%pE|QRxLyg+LZ-m+ zh|XuWkBW_#Qdxz);%9YUxiC5|!S}$|_AllCT)@JvgcCKAh=Xflm@P@+;qg}u-Q2$a zr?>Bpr~3W-7x|!~k5h>d9V-%!B90L`_KqSlkC9n~hLJKlviHc0>^+WF8=ODTYCkrnW1x=ln%LYcVaLk9-)6BUIzVT zyqC?-#6=~}V=^_kUY=*U^Ey~J)P-*e?F6|Cm`n4s5>GuA=%|hQ9zshT$1C2W&pfa^ z7;-*OOKXLxqOqEO--TIvu#8r!1MYF{y-#AnCghKccz182EjQskXt2*3NGhZ9otfDt zfulY#vP!JRXv)l41=6H}W)qJOl^X(;#c$t?0jZ_B3ceDp^ltlxzzRnc2a|lTM^a{)L%=b=^CEF_e;h$dXXl?6`NO-<=3smjQL zMm++!4+xlQ@9JyGjAX~!o>}RfRJ4RbA*8DIpgDckqNU|H-Jm9^FQ9DX1r|w}TkqA^ zGT)<2^dw|4q_TG(f2-f!wV4GWjL0S*mq+73f9R(jX-5?u-vq}Bhy#1hj8O!oH2Z2+ zxEBHSB*USy-yFw3p8l+pbDhFa{yE0`cvW|i-!x{EHARDB?p7rD81>%n!QvGk6U&Dy z(2+}}O!lNVGj-Js>=M8>(qNm0S@R^pOh@kbFAWq`Y~$f=NYe>V!c?eU=nHvkYJpcU zx_Y>J`JJ7(S659x{FEs)?ky(@Z4vZU;63h){RvL% zk-HmS)db`Xc&S}W@$P3MF+Fp()SB!_L@V-xX{+C&;-338p!g`kOZJU3>(f`RNJKe{ z`}cJ*Kz!MX8c7nzbz}#EMyyXkQ`_JzvpOG7$k0ax-0*<3Bd+ufE`YY_{V7LbzGuu| zRzT2k*s){bsVz63YBA1(nca`Z&IAx-ss&9k!{!v8Y=xKeU# zt3N?KBTOhi9P~E}tW}JS4hT-yweS+$__&$HASV}Tmxgqv9JARF(J1`}o(tf&lF?!W zdutpkA(sV;Zjg3Y`JSFJX%4H>TB732_y&z~SVrjh^{+6AWyUC8&~)*S zfAHF11Z7Z?Wovo02x;nsj4@EX1DK+Sn6?~DMhlEi&&T)y^mv@YTmY4sm! zD9wvu8e+KZS=v*UkKFtgs?d|Ia%o&*|E9QD=n*vmQe7Cq~R!CkuucPF+CMk6*Tn>5Vk*WciyUUU}>tZ z^*!b3K^{&d;Gw$b&@>m!42fOT#(n zz&n1I$yzjRs4t8HIA}@-I*hFm5p}?$Q4pXma zgyrNZr#m|+4Edp&18#L1+{!faqwMAgk<=f{6(V6)3hB?Oxx0ISIVVc&YXFgfqSmur z5Gf{yL-N~7F6(8inGK01M0;6XjWi%BbZFcYRhssKz`R2e|4cppLw|zZq^DRsa zh;z(`4ug0{Afl>KwJ$Fpe2ps1 z-uqaptN=l|pgi0uSQ8VghtD&ZM!(YnhcWXxs(x?E*fLr2_$kB^q`HHPR3zu^_In%< z<>1zer^*W~jJqF3IY|ch^}%i{yXVLBZHwDW0%D-v<_mYEfK}L!XUpmDC|@S*Vj;(v zy)L#;z!AF_uE#V&F_+`rrpe6PYBHJlY)5e6Oy#o`2r|W;e7zndv!MB2rmda~92n>s z`Lf+kR{`Cg^l@0tob(&Y4TVvZ4Fh?on=L5w!*hQ3^~1*KweW>o#)a?;unQJ*k!pPA zaH_qM1-2+XT-x)?c(cO|!H&p0E{;4g*LkU?{O`;%cR5sOa`43wml=~RG^Zc=2E|Xp z=ZM|kIdtNCKtTHfwAoSD#`3lb;!B^}XKF0$V@!Zwv zGBe*HX=Zxm3m?N9Q7lJR=-v-h)emS%-qAcadT=S_(T=LOj}<@YA}X!1_X371+SXuR z#1DwWd-3XXvS+Rw~alzG-iztzcKmp z0~;Icf3f1lOh^orWi}?=A_aCiZHkh{ztY@gcsc-8hu{=Ka?}{rE)wq+UK@0d5C#@| zBBXpD`|@7CiNU}<_9hr_LrUkn^8?rFMUKo0yo;|F%eYL6T}xrfV@HS!?nprhMv3pb zoxg#+)l+cVvNx*A^cuyU<_7#9WE^4G2thi92ydhQ#%jNEYEW|oqz~Newij<}nPTUk z4J<*5N`aDFp@TEk?HHaA224qEe(tfc)K3cDMS+BXd;`c_hyHzc(D@`Yx2X=~3XXun zV3NY6rK+qe@ynKvlI?-X*Kc!gCJm|OET!qvp*q*Ty_7c5b?ZUMbDnC~E!fuFQQ2NZ zX^%ePd3uKc-N)qD=&LI|10inN#5aC8g;DugRQfu!GL627|tXhQQ!+?IjKyT{{)g5Z;$K-g_kme@8Ay)Vx0>2xEb9~o0!1< z3zf;(pP=Lh;QukAA=&WB9=Q}2CD~!!`__Rg;TJj(gk+y^nU8>W`Y?8Q51f|)>{GVe zJExd4_GS6XEd&ECtd}We6}?(>M-)_@0bXc#hlBV01Lf)c+M>w(fZGSBAftsL!L`yW ze$HaI{3Qqo>#d|q*>12;GnOM6S-hmZ?+1fp0w84li)_dM2hT!zof zB{)|@iUnz;ydo5Hm(iroKZ+ zhaLZhc?bJnG)z#gAE%JoQ@NdrJJ|uj3u~faQPJVpt1txyiw0HLdNM^(oo2h0&cf`k z1I#dB?v&*GsEB($6TLybaO@)(%tya;u!!z zZ3Lnsn`6Y>VmY*z3^zopdF~hCTg;nU=W1!iL={cnc zc`F$m19rT4AV2HYsO02*W8VTt@5*YHAM&|@*wxqxP+AX0n6|C|`qR5R8JGHvzRs@elqv=FH!W zuy++p8-|0n%`pVHNl? zCHs*?*iwz(nA`iGk{I`$y|l!w5*B2l;|I<$*xyhnDO(xxNk~5z>I(UEHvsJ6?g=ne=ffk`=)4zUGe5}~gbvx^59pa$?vqqTfB?GD5+FSQXsGL~+pGKc zMlX^86qv#$KKZteKLGWjImV@?{XCCwr~7L)XYxgsm&_(;(Hvm7GJkh9DwJ0Zmvf2S zR@fNk<^kw#$?IY2eAl$`Z&j;qD%^Qr^crg2a7;b)w~qZsj2>^%ApOvpik!Ld9;kak zFQF@j#mpr)Uglf7vu#J^o0v?6<74LTNqvjmP%i&#u6|c?>>Q_E!F=kTU-{Y@QGy&S z0zry*_Rc#t^!Q!Z1$I*Xk-F~Rq9NspCuEa~(|Rk?($ipH)UkueZV_%+Lt~@w6m_jO z9YKe|ch*E-YG{oo9*dHmtii|=bWyOxE_gdDXC4#j59`KP+}9_}Od8I=+**W^h#-sj zXu=hO47^r4cEJ+UgIo%~)Hk2b**n9W*1t(F5_O4DZiWalA*JZZLRMp&?D^uu3En{Z z_SNndI4tS0Hl0GW`OT}{`3XEkJunI2Z{4G{-n5ZBO1?(HsAH-|H@J{3+%LMUuQP{M z%DGE*+Gzk$GEa*S>x$9hf07^v*cvE%X+es%3H-Qo80Z0}n{X{Xvi3N&V1g};jv?{RvT=4Ad6xDbb*5!S>nhB zMx20qUy3Xwx#y7V=}|RqVKUXWIUfqu?STBMk9h!VeMEQ_>UndhHq~hj!o&+t-RwuV zWL@ilo3!(h$V^d}$O?afr2pQ%kfMbLQJ5g()>Q}CgWq{5H}NxK_|b0{w;4bbO{&vU z1j(0SG%mLzQ)>&tOCS`KG8ktJVBs)gfg|(B{!DN3OE!wS>sQ~aK9f@y9fWn6uvWZa zOvi7~lcQ4+)WZX)(lH=gGH+NC`NIPs!pHVR;l1Cy@H={~PGXrd;D-x5CMVL}mM4a7 zMsMr~5RRo=3&h?n(iiQ4C#y&RmVlL9KPued56870{$zJkIJbke%eEPidgu3c|05vG zDL|OwUt_KyH@qn(lL311L%(Ai8e099mD^uWia?Z=idY_P^L#VRYkfO%bJHHaw}@ts zi9oE-Xy#RZXXcrhEN^lg^~!$WqijXd8DUrm;{BFUaSB>r@j|B!)_+O;cfC-4D%9J3yWHxK(J80Xe6G%h^6cOgf|izh zMZ|l#tRjMm*Abj`-eBz8y;p~4UBWwBdu!pOB+dx;^^)qRB3mP&3Fipx2gGcPi=A$V zXE8_af(weu;h(qm34qY#ai*b(5N)arY}I&eupncn=Z(j(q%}QGb6RfZLnA6&V+mJV zFdQA~%s<|Lt*c%s64`YE14E#yJWNx;VgQSjUYp(^DhS{wNh6!Y3CfJ1Qmx0w%)g@T za!JW|Oi}aaWgv(u935xx=|p^gy64Xu#H>ECm~zZ@2~CMulGX=XAdJ19ftYPmQDF+fbz*I@c}U*~Fb*)G7}0hmjsx?v6Y!(oc6o zI=aV{$Hc?p*IYrEW|h~Q`awiG#JV`9f#oLK$|%sfn)+pvZ^iQWtVF9CTF`o=AAX*l zGDy#2`N_qe0)C_gv@gbXy8Y4NwR8_w_6zib3ZTG+Ikt#Q@wHe8B+!%N=m=gsn3Pnq zJwx`b=fo~JhwmAF zIK%h~h6j-+KDrX=vu#B#j7EQg_Xx^+zlSg&xM<#7L__ILaNLs-^D!cLd5dm)qe*7y zQo1|QXG7(=X0mD!>C z_(DoOuGF*1fnSy>;~^h)B&@87_hrn(N`du0<%b{;r=_}N^7AJMvpII5FdO<1wcUe1 zwADF-C3!26|AKiC+B7cocPzH(c&>c~(GdcCN_)MHjHwXV=wHV+`i+|Qb|@zH628E2 z8m$zb>0K83W{E(rz0dHqw=30s@7N`IqZSQf?Zwee;Cid3A_nB}wXXa^-ra=FQ7G?9 zOQmEr_NOoj)36Q#?T?Du4I@%k-G;@_s@rsy)R5Kka2)~WO&ILX-e&eE`vroZLg7M} zf!ny$Fc&R*IHG6IjC5wYvpvGpt^|TPQJzQvmYlr&4}0mBx|c-*7Jov`qu^WCCD)Hx|w$ ztuw>n#v4O`VGhZhqOFRm406=wF_A2F=-%7R9mW_QtsqihnJ@L*|8(etoO8I$UPX;iWWNl1?CJXJ>~47KGr`4fzux zRliTSCOFA0h{mLF3SjTf`LckAj8su(`aG1n-eeM&b$ z<{wyo-uN@U$ zwksMX8=ST>c`SwAX}?QbFH zeoE8>N6|ryaD+1^O54_hFq=kMHRZxRcj8%MPvXxEP@V?Ut(?n&gki>}$k`c)nG!hf z;!t5k{mkhHgG)%$UsEsuNA<$lz_&LPNnHE^GGwXR4SH=|+bgLJay=^@EO7bBs&`I$pE2A}&=5P*`B)Kpxc`@X_+37;j3o@&!-BS&I^*Brf?0D zU=*{LP*SbhcI87NO%2Vt^b8QKH%)BP3%pZeR8;LU9n`Fm?fgkU^x|ys+w;Cj9&mjP zvIo}+qHI}W8XRT2`77z3p2^(}lfGb7gxWxSNX5cp5!!fF=@KTmJ+N;8BwE&~c}%XC z&Ux)|mvoyYeS|rBr=$>0w5&skmKjDs*5oHTG&014=o#j3>=iOxu#TIiL~k*kty_ka z(=HSd4&5YpATv`5eaE66n%X*lBjTSZyZu(Cw~&_Xu=JmqnvUWfs?GTuL-4&t->u>( z@$%bOvRZ2)EW{=~vg9&{AL2t0Xzv4zKx_43YFgUt{^OMF;vVM+kY^E+F|fOCWs_v= z{+#8nAPG3Y1FKq>+5Ck2r*pxeK_9TFF}s4lH_x8pOJhFl-hytJ5l?^u+OH;gZS=Fp zU77m&c34r~SGBt5_%puwv1B4r;udoN_N+-q3}E!{yGgsuoWc_;<6B$dnm|k%gNiP_ zX!k#bUq)I~HXjaH#?-R{O(tVO9S<;5$m<$C4j^BF*U|(TmQ%@y0d{gRyg=GK_P$f1 z+TJwHF}Iv<+N4)a%Q7F0<2R5$0e%4k0tKj2gO+Rw0z(|`_m#_njSYa^ydZg6}8?amT><^g#O=&c1m2Du(NUtXz-EYu!CB*;+?2tY0 z0G7!HDhM8}@MVbpuX=~@F=M=y6w692!SmH09`&cT@10rbWCj@ik!-yOrr)|rrt=f$ zZocK;_6|HD{J^GM*CxmF;_C(K*;pEJI|(`x#pW13$qpxNinEK@@A{}i0=Fe$_!|x2dd)ds`D#0i~}mV=u3v^OFkthC--{|l)H}Vy=z2R z-InFDyZ}s-+)^02m`{-Lw{^lSZuO`8d%66Q>oF7nQ!wVN%hXJ*5vms2x{MATd2K@# zygH)=@;*qut)tpWN%j98I77ZsDtZC><(4%eqo_hzDHg0s6pHiIC(7qJ_2Q3D=sd6G z5Ty|@&Kp~3RDoF2qu#R0?f2@AQvxFLXSP=xn#GRgC=zyo!nOFwTj(g zxqj{_ZD#6Ksmi{VK5z8pfswvu&XW(RY_5U26HslD|Fre!(SIxpC(L{ZW`kao3FP(x zMZquQEUsEq(y&f^Fo!n^kMck27F<(Ti}r_yTY?p?|29vS)`2xmIR<5sjk2glS%jlz zGXhm^HOJJtW)uiC2RsSA(Rb6N;^A+D%b>vws@^e}KEole&$%_rXcv$r)a;gVeZwa^ zo%bTP!wlOYi0uGldVb)$=&j=l53C;tycne~`B9~k?-F_=f*zYF(7cFh&P8`PS*~nd z(f^MEpMPg~yjAPpeN8jP7ewmy#7^!oqbK__;y$U+bUwSa>M_cBMpg9zUvmumq{*bM z&63pQKE8`VDQ-uvf=U;g$9ziVuVtZTOqtd9?;Ga@wkUfOst4cNQjz^fpW0s=Din$M z%cniT%<5=7%_Y;I%7?jS8@XkB)fX?4FxbVT`fkpYkv=)S%2Swez0s#Ioi|$9b1=6| zlw?5fI^%?OyI_&j2UIf&Rh?vVx*gV+&Soj&dE#871JRJB{l9C644%$~4)p(++rKnv zki;35%6AT{f__4?s=zpV%31YA-X?iiAnIuVN;v?fQ~IFtdtZe4I;#LlE5&_MFm!sL zOjTU;3?LP)-J0@#gw=GV?;PP#yLeA!+yq;3*b_j_m;UR+x(2-8)xakZMOftd;98{56tadV zKld9amU~|NJP}V%!BjY~Y)eSKGMoAJ3w)Plrf<8L6S0`hr<7sS3+gJC=*(3pjtzSzfTP=L{O*yd4B_gMzKHu*vW<*yj%D>Dd z4>c=cOs+v8Zl7njY4gW%5%AY8^J)ajf&+{I_b|;HBk(#=3N(NAoO_?i9Ef^RSMXZl z$&q1!i9e7<3=`$du~f!`3Zi4FJf1=gdf31}sCWH8ME1Y`NChy@Zcr-M97B&)`HZqC zLs^6n9wHI@PQ~|WsQ?T*L56z%S4CIJz+syMJ1x}-puZ67pMULNC*|=3<#Bo~p`h() z9-4iva020p5qE6@%3cjfJo_|&s!0t`7JKpyjJ#)-M}+?U_fNDZ4yW84bItRT&C*75 z%oF28l*PL;B6e^XplVj?AX5g0Uc+;3|Bv6=`hQ$(=M{%AAxQWM$`t&L7>S~+8Ycga H@tgkwaTP7+ literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter11_91_3.png b/doc/LectureNotes/_build/jupyter_execute/chapter11_91_3.png new file mode 100644 index 0000000000000000000000000000000000000000..4f89c99e972be14ce55273350dd90da75ce36d6f GIT binary patch literal 27834 zcmZs@cR1C5_&;t%5<-QnLNswm)1-r*aB&DXQ& zExcl31R04hnZmL^HaBFniF|eZWL0;#qy|^BP}#noTf175TacPtpg&UZy@2|G&()QB z-dkU;T)b7EG|eGY1tV8@#$(of;>yl0=zv$o#=9@|CrG$#z=m~Y!B@J~r)rv;oSdBW zA(}1FFIZnvGSJb{**&?f41Q`O{we@|qNDiVe{^VK8X9BT$%ZX{hb2=EcxMwGvPCpDc)3IRip=)~om$9$9c3belm*AL`-p8?m=O?pB`#yhNfJ-lC3ZHsPB@zv!4QYLcX|Afj-6;?uRE?`ab+ ze<4*u!TfGannWE?FZ^nZ^&s5wP{YM42teU#^_y`w}9Va`YZ`ogxJ)qzj zNwA^Wr1(n(XPGzi{qX(Lo#xUXVdUrJ^X`N*>Y#nBmtX|NDcR@+IO*ht(++n-3g53! z4F8%nvEO7AEjI|r^)1J`RuYYjBsedhd(YRetNvYe8$$TH`>r<;|8=;z|317na>>T$ zp!yEUf23yag@n+9>Yw{k93zkHCu)6SeY5Jrjf4equ)76Kxlf3Tu2q#|%d&i?MLg=L zV{mFd*N|9EE}s;Vg!)DcYFpL%qe2oX>0U%H*#q0#5q@SiON2iO?Em2#sOrP-wo5$h zaG#*ZH*R5F}O#_`amSk<2sQK1{I%Jsh0Sd&IZWHz>pvWXL4 z_PoiT9CucZwS3<6-EByHtM0luo2l#Mj6OSsPpnUz+Yr93G;GlwKTT3kTME~$!-`aK z%;{fud0ZuRS^L82z5n9RP@^<*9DYo(qM;>pFW^MObwQjo=9#qzayEAOox58aUw)(8rCsg!0`pIHu zbZnN0Wx|R)*f*tk+nebBR+(B>ek)5NW+&OO+H{{Lw{G2WD*)g3ns<&x%al38%4mqY zki&f>_&xkf8y24fVUM^DNpkHq&&gWflT{Uoi4*P5bqBET&A5~KG^>P!!z!9ucGmUk zgDmfUQnKzw^80Ec_-AKq5n)Tzdya6H1&z8`jryJb=2E*GK}*z9C6Qn8l}#jYn-|$g zgTuz$O5ew>RK zb-TtIIWlW{QNN!VyR`Z0?$l7M+cxTUn=#>62r+8s8 z>6|2a@80DgVjkB*wdT^923CwXviQJ0&<#RVN(#~WOT3f~309(ITYK5_Tw}8?a{6!5 z<7;Y>tQXs6#$Iw{`Kl1;Bh4F|OAl~GIP&CYB`3B$M|UQYbdWEem53}+ zVsTl2?<#ZE_3UvVsUloz+IPtRgb~)uPcC9`X_CnzXZKm)j0diG92p$v(dafr;XdMf z3yF0!dxV6mk!~S}3z?Ayc+xr?n%~D2dn7UII(Hs+ur;}HHWlbz+W47#f*hW)ZUo28 z3BYg9rngR>-(9UgPbdltZPMuOm>nC|TS<~W7C7)`{?&XU>g{iKh7uch&J~+rhJWJa zxR`su8bh4K(jX#S5oUMj^pn(v`E;jwXrt1d(d$97N@mc#Mb- z$M0H#eZ$dWBL&8wKmcF%BXqKZj>E+d7v5TGcPZCpiV8_c%{0Hg*6J2p>T8e3Abb-hSMRKT7Z(c95d%! zA?HO9cUPTCohi2L*!894l~aUmYHzgd$W{MhDjjFq znQA@lmuajlHaUh}u|P3fpjLd%5QJkoucevf#sUuq9kwker^`4`8TWdENQJdaw#b?7 z;FiZbbwhc4#r&_v^3cfwmLiO9ZDXYQH1a&Z{5Eo5cEtOf#hUAeK>K+lb{;1{FC zJ?*9PKhMd9vAQQqZabrClk!r@jD%ZL^&`T2`++8?V6;QsZ^Ny%22~Q%xv@L!eFpGa zM|WYt{JY^N5gy+Y4wNVZ9Xoay2aCJgcLprZSc8YhK|N5~TC@yJg#$7pGks9Hn_qjhWj48yj>qIlpKP(7 zY^TFaXJ<&>Sh(m|G@9kFU(%z6TcTE`I`Qyb_r`MNdND)vPUOOEWLO4#)V6_VGBvMma~UxW znNjrzb_!=s%dT(^E9cVT3JUg_2@K-Q=>a2V%Vlq5N84f@4)58-EtsNUtVUwn>rNsZ z7>B6Qo46Tv7l+EEYNV8SVTxqG?#Z)O=1^G2%#rM061e-fs7+Rc^KYlT3ls5XzANas zA4sW1&opcqmn51iUq+hbm>7{?zV0(e+b*H&Ww9=2vEGiP@vUM(w%49N(&MLnIE{|M z3{>=iK0vnNLae?mk}MOiBOh@cZif9T8vT4 z&WQD=5&eXrl}S~tx~c1JlGTU~m=QH@9MecVi=G4fK`he1*5w9*GZYrR<>7xk3zHVd zba=L-<5HL~N9dMNm>&w3RzDO=oW+7ruXF!mEzy0}KIgi{NW_FFK<_Yqut1U>`niyz zTwK)-RPQ(K6hFm~SH^!flaU;8cUAT4`PH)5p({aAbrplHE)MNOpu`%nf>Ys3)!FSD z?~iXF_+V&RCd}RIC0neM6LCvhtOxel2TL(X=BjZfp(ZAVz$H6&)z2d*0d?*c8%;Z` zhO_#ZL7$E-RtG2V)(PZD>jOlu^rlDecEa^jY!Xsx+it%of(s`d>eV5W0fOO7k_=` zNPET_-r+2KWcS7*chdu5dLy~sf_6@f=e>Rp`yY{w+UsgRSOS)MDBZW}#3~N@w=XB# zSX+~xe_rCM=bDQXil|g*q zM2}Svd!l!3?r!h8&%p5bSL%(DPLCb9ku!jE?Fcqx?}UhciFAI`GFe{|e_eI*11b9rQ6D>rfr-m%|4tCPY= zgcrVDJEHlv+(qA;2xC`xZFqbSDaCgdc;JO;arlsxBeya4equ3AvS2Zf!m9^)-pN2m z`2Zb9jKuy;%b#=Ty&#BBUNOrr?;CUHx9Y8>!0EsZ8-7ZRpVBjx@hZ!b08p{wbO+llC-PnNR+US6(scB8vEwEFt*HnsmFlLdjVr8k@^tGtBSNS@>!J2qL zP*70kD`v!vFurYJPu9DDa@Gfk17D=~jKEKvG-Q)7=r4ofIk~xAJw0iusVz=ld>9!R zWaQ+?BO@bK8bYBDC{(n{(T>`PG4MXA$G8L#u5l%3Vw!iv?MGj*d7n5?#(s=4+T7tVzv6l5j4<>-XxX8(g@TX42Umb!*UYs4*? z!v%itt}45^Fj0cO%T)W(QVPbdgH668jEz=e8iLgM*-7=`?B~XYjhx(q*#H*n!{eq? z8Sv?NF$W&tYCf4jnuQiBezJdvFq1xEX5dv#uc+8(;xL~>l@If}tldwO3oQw3=z|uB z4=bJ5b;&O?{S}wXbzk_Zg#-}QsF|IF^pp(0}#fwJYVM0QW_en z+A0@j$`@pR|99n;)>BRW+pj7|e9a4%rx#v*VNj_KO-*FF7nFMMLBO{n?hh@9pP{H9e4N*DXJ)Ch zH}8dQE+bpgW`lx)dGGNgcg7)8=jemNRBk@z^Q}5`ZoAD5Vo2p9jQdfiMu`pY345Y) z_(7o&qWi(|F2`WETB^cd4d54ZnTofP8R0313F_xVm*( zw!pyefR2}p?6|v1k;QSHqRN^Nj9zW|KX0dFkA9-5%oP2oNU936Db+ zqj_L9Soq-3kSoAY{9~&dh>oy@Xf>%HKYs>6xrNnb(ym~xLLBU-BOj~B*7}Edr^vVp zPsVPk36i63ONl2QE(aC%sCV4K5CRLr!!BAl+Ri-rb=Tp_M88)^fsH}ias2eH^L;{8 z+%Mad_`^^a?@P7+Rcv@>QU{oOOU*t2Nn-vJqrqP&4SuBJ`};@B@WS`Z%z#f+j1XYG zb`qvHX977YtRG855FI4{@YwTN-wvaOc61ZYk7Jf`Dd~l__S=};#ZFecOBM&`pPF~9 z&9JSpu;akOE6hJC*^g54@*V_GvyeA+Mskf+Sg{a+h})K5vl$N z>$?RSM@h~}?l0Z9l(^MjtP3q^6uA`Q6gX9XLLve}j4zobKYxLxfM0cBGn+hiadUp* znAC0Kv>_4jF*|&))LLSKy*^@a`_f3{v;V%c#mpD#Zo_lHXIXQjNcJT??yc`Xn6X*+ z>dmM;_buCp0eSVkc0!|%jzv%f2EDPg`Z6ji`8b7JygWPsEiKQk6(io|XA~7h#KkSv zZ#X3b6eHdq*krw5)M<-ZpXW&OZlxZ30DX|FtLxRPSF6J4H;s*rJ3Bky4_lRGT%j}nQ8Q(6*Y)&4OU?_|vX1&m`vnu( z032z+;tj{6`aDm8KywL>#m2(jzrS~EY}xLvD}O$tFs@H&wOwsH6zU7@RDp)w4I3=^{;Y^a!_v)sow> zt4vsyovR{xNM{8U>57ukt76CcEvNnG=~0pgZZZ6XZYOTKlz*8fV6f2O*4ihkG2Mya zcHa7?Yi5Z*5plYT$|tIA`e!$0$fFDz{qw8E3b=v~zkps%f#I6BRP<BX_Ly!>x%28c%@Wj!D;%)iewnRfS1oeGp*6p}#YC>bpL zjy%)Lx}xOG-r zt$J;@gvYQypxMRNV?j^qXzAha;T8CQ^d3+Fp~3AK!V}HnexoS%+z){U9 z>E63t$pgkbB?3(rV|`Oz*7>}6m_qKq!-JaS&Muvz`o>@`ds#{JJjQ#VR6}AU``KsM zE@30h@`Fg&P$l8h0oJ46i8J!Q3@F9CY$x7_dx*2`EN#ATIf&o#qfk%^0a6})l8jJaseuA1}t*Hj9HE-KXTNIUB$V%z$dOSgU?#XfRD9uz*)#){Q z6|qLeS&E?`})?Xrw&ojjo-zHcU@fpVy99FmXype-ZvTTgslrD7JPy z@_bD~dr>^96E<*NPWG9>Ld=n-)Z?!qt2azTPZ>w_Jbnb++SbsQOIF1CPYYG--@h(> zs(&x%gPuISISk04G|$ML?vRp9`uI(BQOzq^36q>@6m+V$m@QJAjdx1aJ?Fzq9Sf~G z(!eNRf*FFoB;o9cXL9xCS{P z@~C~UZGm;u=}y6kKvKqruC6qS+A!`uy6bX<__GA7Eg4bIAseL4KCXZv_)!8dlmB&# zv9o=f710AT543`DftR1%m`;I)B2`?cwxBgK=`1pdX=kC&V{0K6*y#~8P5Fn_h&wkp zvLwY$_S70hcU8??BR9*eR=wSEle3s>z0lKdvq(VD)UbI~;Rk-VgWuY+ZiB7GAEr_)Q)w5| z&Jb6x$T*XR1?nh_e+NuUIrq2-0}d`YPD;d38w($`oXd2MrilN;Z_AO(*o z5>Nb26hgwC*_1rK_xOMAWIGb#8S&`nrJYtbfl?o*{Ctn35yD4hc>Lk;_`Sc+--4y? z6iMBswJoFTbd*n>+G|I54x(4I%c8Odz56mmrZS9zKI(-F;om7Ow)fugj2GcJksMxS zHJ)ws&}kX;opg)csT=X^V~VCpB!%0jO9-O%z*f@|rK9)q<*(JJ&$$mZ@l!1g-iZp& zbolu9t7CHu>O+5CWFu$UMg3S>pe=c5Lcg?e%u-mt`vqjOz=fWN>WHjF>qFkIX`d8r zi|{JUsIJ72u0*%4#64l*^78Fqg@~NaH&0ij)i~>N;&fWs7q*oO2L)t*aKk^ck2H2} zj2a|X>}S;-%y{eb(wl$bSJGzxm5*Jxe6z6`p60_C3Y+l36Vb9DOb-R3gUG6*s8cj{ z3eCTaG%a;Vwq96DOfw3477?tPK16M!&K%iUgegFrms|tz@%YTIG|Krs9LCeb#Bf26 ztnRfpxrJ3s`Qsto1j;%Rk7?bL09v77g)0+{Yi!`@O`xPxa9+|rN58mh2u@-48Gnc_B~Geh_7q@VwVOWDSc(c>f+ZWsptHqex!s3|I-#@0J;WKlJx{GXcG9$$nVT1 zBYUcFe&U^mJ2fngvotP1#y^#;Wjm9jSKpS7R~)I9UYz==5sy4^DEl00&!+gyA7&a{ zUNO*kY47zdI!e9asFQL26>-8yFExu&_nu9zk78O)GLlWq&)Qh`kGCs6QX;z`-+@h0 z7UXymO?@^o3|6-Cn)gzDXY{grPwwv8;DFP;EyNV&gmj`dx%mP`^85lXenhOTO$-Vs zxbSOB?^F638?P{t*?zqsBt z`%0tdn~rYtjXg?=BlfFSLW-)t1Y`$g=?2oLH*Y*2&=+%UU$2us5E=>Q_6J)4g{GhP zr{uBIYFufyQv8k$eh${>p95}1nF`t6<@Uy_w6wG`Z*IBhRDGz&DbS~aGQxdRlX3m+ z!F1NI?00O1yQh+j1_UZ<8SaPIzm7+5Dj8;$-sL?0sx($5)5@qcF?3y7_SB%gAoQxF z=%==jq+a$@7rv@l9`J#V2R}wcU-X~y`i;qA8~Mx*d<91$x!a&t$55im>h6M&+O4`8 ze+&=2S!}vmv-OH%?ux*w#2Wj7l4{H`?2d@Tg0l)8#5l8#jt1JoR+14&(m8c`vztr2eVN zJNgd(hG5!7i$vqChY){`;S$^!F1y%B)?kxNa%f18H|h$*a03)SGQiU*8hvoCm=e|Q5$QxlO7X5XjO*6DoSvJje8>O;o|IKaezT$eGf+q()FEA7 zR)_@h8J>q_%=pE5bR`wcDFi7o*$PsqHiU2Gy_=dFdHGUrMm&n_7SO~Fqidhs;A{Iv zrfruZI5@;HNx`2cy1;m3b3(Lqp9||fPt%r&AtY+nnpC%a z-T}-V0h!zEvF9;8>49fcmVSZhVJBt5To9{)r65~@dvsCI9dv(Va`^Rp`y_>r(Ed*J zm7OhzV#=w1C{MJV)+rXKk#FC&ii<0Hu?1DHA#-7M(7e;shOU9 zBvB^lrmQ~f3Ay~rF7T<>*vRlSPQ{6GKBSKx4zwyJU8%*f-E*YZGKZXIF7&4HIO4|< z|Bh?77)t!yal}qGOmY1$)e6F1r|NA1?hgHTaF%oxO|38VNB#M0kFqZ}%o;#cI*VJe zuT;nuKBu^_Jtu)$*s|bjm@^crhHakXz$_|SL$8BQ%yfp5Z8QoVIYS|pUR3qliIwsR zrx;rI6IUmT-SuqW^j5_6S#>6*V9G6GCfLn&I(Ww}WWTUdPZHakaM^%hH zKtSJbnwlV~`I7g|S7h5mqYq#YPR}Kj0 zHUcQAwuM)JQOyi0T&$ZB41aD=^9~O|a zcLZLySI#S+ho5*FTVA7Ngg?_pR)M~0Lsm9=!s#C3-eU3VR;I33z+Rm&9nlj-xv!q+ zZLCPdfZ0zVvOj~(x(ziT?*-UuS0jo(8OH4r0G z^dI0f1KISmw#C@)Zhl$iZQ0}#ff>3;XxySe+*xy?;ral4)OTaVye<46<%8qDx6!eu zu?z89Lz3=!K&IF2onHcSDdtREVsJ=ch36;t6)F7EyuXXt==8%{hd$S{Z5k+{Cgq$}1zU!G1H8h83iHlszvHk#f% zz*PCO%c$7`W;T0?9%8R$UuGJi<^`ar>k6T{I$*MqG#}_>w7GCl6~;9?(lVzp8ucjB z=s8CT;cYxlbT;rGWz5-$YEALyZgX!gL7rx4$-yXntghZi+;BYaH1evA7Sb&G!O?6Z ztJa}lk3@>h@NzbYCo+F)gxO0=`e1O9WgWpq(t zmKjspwHs)KRS=Yst;e(RwaYdlr38Oz`XMQ>$BFd$D%LK68dy@R4de8Jx}_WCmMfg9 zqg$dDQ9MHy+a{1wWmRQTmceYY_@vUGc>syCKY;b8)eUr1Mkgv?nx}Tv%^HE&_}KEp z2z8zR@VC>|Ee4?b_Ctr1GcK9c;S%>2{kDvBP$=oIx+U8(1OGG}>Hv$XK}Z$J(<}ct zXU}ddGpl`^XrB*G_>_zD2WbM>@RcpgguDPz3uOSwYp;bh>%D}~OoRL>l<2B3ZhFnx zx>lx#0|Ig%K_LF#*`hjtl{kw@$PrM7s_~HKNgIeP4d9u<{~gAGyqZlMXTfD&h;|`kCk$xS`*CSv~4Fh)a|EVJ8 ziZa-9cb45t$5c0h+{Qf*#q__xk%u&Usba{Y-5l%w)3PiMjq5-eo1~dA7 zWW#Od9Ej?dyG?!P-LC`_r4)SB?|;#J>n`W5PkoBfOzOM0C|+~}Ttjz$pY?+Jz+AJY zwHDI*{ott40Z2?|yMbQL6)UU>t)@k!&VosS(mXH#7NWh! z0gwQ$5Jz6w-dG!n|8M{L8$o^^*Cwcs@P}gr(Qa#~+uKb3$m zl;w5P_Xr2ppZ#-Gl^ZPlI`5Bw+%0)PL-zZRPK?x!hTAuf-dzfT0WjDH2WfpE1g~9I z%bL3meDnd*ys4I>t|Okp&`1d_=Ex-22ZBBu1LC3R+t)mUTC~#*a~S~Sr+hYeVz<5% zN{ZI#&YE2>VEc5sc#VR68pLiH?#^HUVD&MsJm!KLA?n;zLU?GSy^RN~1~@|%6mYGJ zaZh(AkHP|Amu^A4*3Q%xZHIlAMq`|BWT#=A*yLryzPtUpu*(@M!Y+Di~z^y$v) z{24u2(wTw}!Zu>1z*Z=T^?6|zK*S4S)T>TVoG70S>n_62-UO6Hc1IHww2gBBZ0xT_ zQr@+E@vSZ5jKluBW-HSt5@6SxyUj~GaSeFN3KzKVZ_3!}FfL9N$M;NW87Xy(;vr>_ z?QfQ5RiWm?y_EH}$(TXqM1c-l_S?^n(G^yKVA(vkF{i8MP(FIvrrYD4(vUEam$~ad zeI@zJhImxaBR`O3vQhU4AM2880Vp`YKt##O;dyjzh>HC-zw6~B)x%`qr9qM;UVTMW zwrLVDh8x5!b@S~782&6sK|_8#Lue0{uHdu!=q>%x%!(sOrcc#?Clz|#Hi&tOzmPI` z$;oy+fNY zMcAD#Nc$hMs??HuAEvAQkQ$1s8R1X=MVmc}e(1R9uCsuoOM{G4C{XS{pd9hW-V(>m zJBgIDG#lO$2X9F7S4~>@v=E4;8|XXQkklfz*utgW$;J|i29BgG>ho5rQio!-XKn({XgME-|C;cw_)pauBP` zx||sO!gCa#DMv7)9V~LGLTFR7~C-!JXGYE^G$7PwuAPV|;Dmn-lh03ccr! zi=yCsZ5>dSV*pvs5O+BQThk^=ce6bA#Dq#HG(REg?3r9iPJzy#CqwACnhQy9_D`@4FZ%-I?{Ra zHB?{R&`wvyl0LZl>lSXdPgH(2Md)Aka1jf}GCSeWTr z$m>|hXJlqpSihi?E_?fjJd@4it5uRJPesQa2zV*TK-i7{YNPf*V0}L-@n0aGTGj6- z+NKpLE#KGp9t+D%1Iw#JNsEWIW@o|L8qY@@Sk7u?WuNIS1}D>oJwm;DyJJH6hHMvx ze#eYR_4({mxr%vkakGu|{ zo^;`LId@-U0)6z8a3QD_2_g$Jn9FkTk>&iaeht(BXf)?Q5~f7r-o+MqAF9NSzJoYD zff9#veD`LF>)LqfgcGYd4`?e#-b|wQ2=Uq2RLuUwL7yENmg|HVjI| zKPoAY6IZ#Cm_a*f|DRBH;cjy5N|yCPigzUd?Z1PFw)?sHR_sh`8iNhuOIND~%K$n` zS#(j>lGx>3{jLCN0EP$<(xQ)+_By&APyCde;k`l!g%R1$WQ_vy|I6jw(z)N|=~IE) z)Y4`6)+I=kPdRQd0bE4vngl&5NiaAamto!UO-U808D7GrmKI>oNFuFxPh!a~#8HbF zh(+jPj%bmm)-48m4lWVCgx{~0AcQ~tj``B_lRGNvIi@;{Qw7`ynQe+1*+|R1%RPgd z{s@Jn!j&LZ1tXc0;LGC&P)ff7(ubAh*}g~E^x30{@lYPuzrd}4ESSxSl1&-bvj~;l zN4_AXv%EPuo^pKD?ihFOKJrSIyL0!3v>zuurQuN&$T4IPqxVMv50%FV^a&EmJjEmb z?AVD6fPDiK4v9a+qT3Z0&K-BDCUJ)XVxiy(dcBSt=+0?ypt8v4_y2R~ZWbAxT(~?d zNDh_$r#Tk;vd;clLq=&~R68z^j3(V4>{ui3q;^fpi3DW6IA)or7zZZx+K^D(NR=v= zJb2tYNG@eq6%^ewZT2P{eFr@h*^GZ{0zIK5x5PT>q0a z6i1Qarj2b1wck=BrJH1V|55zJ95P=W2rB~fQzv+vBlxhXdHbGV?3B_|q?w>vE!dIJ zQNH5g49Pdog4J2FyIm7{YqAOx@m zbyE43)6MoJBj-s;k&?@gk3K+_YRhmBguMV0mKW$@)4zJ2kNfQkN)&0F)BX=)Uz%NZ zFEIt)AOCKIIt8d!xIeC=-4^sPJc3~;rC^Q^jKH#FK6!ViFTCx@A~+|?u7Xy~{P}0Y z`jpG1v2ochzW-_nQN-_Z5ga1m7Z=`&8Zi$I1-f1PNf%JlTV!t-0*1_&HGw*^4Ktt# zyMMjUj_rBfKay@Og0j4Z@`;dlVf|aqS(oEvWISm7`1c+vdV{ug@X}*T%*^4(rLj0i z*1KoC5ZbmM!k_|Ca^R_;Qyl=?rhtzAb_nOq?Q1WdvIC)Bmgc@`I!K*jkS_o@#N_Ue z#X|%^K?RQqjWeGZ+e@r^wFHJOZ4gMZnubT#u2_|Ku$XAw1 z5}`&JJ9mKI{lH_ae(gOmg4ORHvkYNwOXWk80;l{}@h;%`4)G_`!l3cEUNWqHx`8j^ zNzB{X0JD;8x}qStDmOpej~iGf5tx{&&v5fX^nEE)C5%$AVi#oMbaRxE+M;8??>ytu z0GK_1V)}*E)dx--XUT#LN_Ypa8KAO4={uF`8$NYvDfTSfZBQ^anK?`&)cZWP$@OI3 z8OuW^{&rieo)(uD2t2_CH#oUBUGg_kFN14hkw$c)st_`HmtNjKV^| zfPK3w?u7z5))(9Zrj)fUp^%l;O`rbKlU){hmEU97=}QDykPKc16Lb2*hQNN?p`@jlP<2kj>vfX#M!95UVCq z8d#*^MQ!9Z7NoGb{J0aSlQ{y^5pxrv6APL8bi&lIZuhu@`ZnUX&OZzBAx4wLlA48c zM@wF{GL_#3u1(Y4@1AlLeBP#Z@{nl`@<^@(5VA4pEul)U3jiHqX4d8!Ey9ziySMk&{^4v^V_|G*sCDD*pIJ~g{4WDR zt)pcoR1EtKz29iEe*HLr8X8%T90G7hQRG!`uv8cic@fuXWa&LuDXXD!EH+NX!`aNw z0~-UU@&?T<^i;&WZB;lo&hf9+uv5J135xjNp@M%##zq*^lz{zaId~EhDYxd?v7^$N zx8pS@9ulOGup$CQD1S{DJv}(i4egqD#L+JZJpmhx^eN-5keePeTxV`yEX%(9FbRYG zC<$)AN&-G^dF5XS2bG#}?~fA?pd2kbu9p?81rp1#b}Q4-H-JJ(s>Z`0%CCk+83%vb z%J9$xs*r$_dQV?%#LR8w(dYE#dltyjueHpA<96I>A`}P?-m8!SS+fjxt4TXs>9f_^ zPze-{TZO4P-wF)RKAmnBT#j@0gM@kg5H%5q|C5lNm*dEG`+c^*VrK$jQTcduot4#_ zmxr?(n2N6P${#CkupV8v*o#ar{OPZ#aR2W8tb^6YQppnDvrIi`whNkGp7e$jePUr0 zRiy_xkvsjN$2u`s8jg20`Uupsf?TH9)4h1pE~4=_P$$EMjZ)|2GmU`l9G7JXyDWxs z2^v~vwUo6*#b9U4wr|V9$-s@jXTw^BXP^2_rC()DT>z^sK;!a4;xbRE>HP&0lY%rd zfM-fYP+NiPZ zpVZKMMh&2d-{R%x4;-j9cx!UPup;=j?w@sX5pMkZ17Vx`;-b@x;863HZtIn8>Wbs2 zX|NXLoSjA)$*&Qq(-t@-ao+*PQy438m7JrRervKCpKeMGWz9DH*DRVJ@>VqM?azTC zY(U++M>dn6nxkBk!!CeZgCSLU1O6;M`>(~#Ei5!Bqa%u)|7fA^dxig5nZA{+qy~YI z!_O@fW{d0VYKr16ip1 zDLpm4_Z60ZK^M~^eWEy0RF>4)5~s((QI>Tqvd{jCu-^1t+d2Q2xO_DJnBSRNSKVKq zniGHV5^(u`@W-r_=~a1L-&upavT+Gy6Jp-trT0Yk|9Q`dD%zUcgDH)h1p(gfaJzxf z#B$&K{b!i&Y=vXgB8u6gpACvtvUF=d9^#iZCdG5y&9`S27(!v|z6m~`eeZlH3L+L~ zL0l)IePbcL<@zG>y6*0b5-MM(wd7V~Dnj|=KY4d=Wpha=-+*1{(UYgVC;z~x>3-8t zlil!m>M;Wf#^u`+3X{w)Cv3lxioBkioqcPer?!h$39+eD3E_bLmou;FP&x9#uQ*N4G?p^QU>Grl{+A$9}g zhEF_f6DFwY%;p7K1WL7n+bcJw263 zQC@j06M~QIKN6Fs_F-L5wb!TWisqD_!%}SlKZ!5LdHjIv^7Ix@gXBa@EnTI{ClD%W z*&Oow#9l;omn>Tyo`AP39D>V62S+w|L!b33Hj=Qx?}3VPX~Jx%-k7bTpdWMyq@#(P8Mb{OPf(LP70w0EiJfz{&r%1NgKE*Z#KcW3AFQsy4P}b0M6OOQC?~$Jhq#Wwh<>btNC@3D*7pcR2y#VB}JFM&P z@+-mr5#Wm_S|T-nB35)ADLWl;)!PWS`o8jzV?N;#d5Zm~eKJnchJGoU}?&Kec zqs1cZew%^U4>{gbEv)^GXf8KAY2#j(v^v1 z%v&2Qh$}W(eE7shIZ5P5TthNK9PQfyUPd|Q`KBP`VJH2G8#a$((dPxm`H+2vCM|NG z^5{?`G1O4frg-aLzE1=GI|iRuPwv^mZNG+>1V8E;&q#sg*;6LC>p#^*sT%Tf&MGl` z25J~_W&deD>d4E!ohR|~HQrwMSF7$D8qEr~dy%Ghjy4Nfxnq3IrZ=Ga_lqhVW$dnL zGtRg&*NOO(ZuHq_$rrpYDN-McAu$j@w~<!8#YZw@5O>$5rgWc#5@RL1bvH9B)8eRt|if9XEsZ4nmn`iltQ3xd!FK-S1-RHTW6Z%K=U!#*WWoF_R4KULKgDBiv5s1tC z_E1yvOKli^k%w*z3Z@YX!-c{UP%vq$cgGp%xNBJN9TZH)GhY6qjLyo_V;k=naM!ex z_0hl9FXAdFg0C_I@-41cLmd7C9A=tinjYO`sTyS(+H^?EZ=xI?ztx2IiErrUYDSDr z&<^>M$|h~fK%M-v|3-Wni0+IZX3TN>_Wb|trIuVfGRd@w-W>{rlliW$-gC<%Fygo< zetEC`8#$i+_d(7uM4@f%xA{HY?%3N8*gErF#4zqtGkTMn>Ho%Hj%X!u6&eD&a>`(p49Vv&=(xkF%r^1gLtD1n zH^D0FA;~clq67td)%3jS&7PS6+L6M5l&^Bwdei7SrR}h8>UDS%pE|QRxLyg+LZ-m+ zh|XuWkBW_#Qdxz);%9YUxiC5|!S}$|_AllCT)@JvgcCKAh=Xflm@P@+;qg}u-Q2$a zr?>Bpr~3W-7x|!~k5h>d9V-%!B90L`_KqSlkC9n~hLJKlviHc0>^+WF8=ODTYCkrnW1x=ln%LYcVaLk9-)6BUIzVT zyqC?-#6=~}V=^_kUY=*U^Ey~J)P-*e?F6|Cm`n4s5>GuA=%|hQ9zshT$1C2W&pfa^ z7;-*OOKXLxqOqEO--TIvu#8r!1MYF{y-#AnCghKccz182EjQskXt2*3NGhZ9otfDt zfulY#vP!JRXv)l41=6H}W)qJOl^X(;#c$t?0jZ_B3ceDp^ltlxzzRnc2a|lTM^a{)L%=b=^CEF_e;h$dXXl?6`NO-<=3smjQL zMm++!4+xlQ@9JyGjAX~!o>}RfRJ4RbA*8DIpgDckqNU|H-Jm9^FQ9DX1r|w}TkqA^ zGT)<2^dw|4q_TG(f2-f!wV4GWjL0S*mq+73f9R(jX-5?u-vq}Bhy#1hj8O!oH2Z2+ zxEBHSB*USy-yFw3p8l+pbDhFa{yE0`cvW|i-!x{EHARDB?p7rD81>%n!QvGk6U&Dy z(2+}}O!lNVGj-Js>=M8>(qNm0S@R^pOh@kbFAWq`Y~$f=NYe>V!c?eU=nHvkYJpcU zx_Y>J`JJ7(S659x{FEs)?ky(@Z4vZU;63h){RvL% zk-HmS)db`Xc&S}W@$P3MF+Fp()SB!_L@V-xX{+C&;-338p!g`kOZJU3>(f`RNJKe{ z`}cJ*Kz!MX8c7nzbz}#EMyyXkQ`_JzvpOG7$k0ax-0*<3Bd+ufE`YY_{V7LbzGuu| zRzT2k*s){bsVz63YBA1(nca`Z&IAx-ss&9k!{!v8Y=xKeU# zt3N?KBTOhi9P~E}tW}JS4hT-yweS+$__&$HASV}Tmxgqv9JARF(J1`}o(tf&lF?!W zdutpkA(sV;Zjg3Y`JSFJX%4H>TB732_y&z~SVrjh^{+6AWyUC8&~)*S zfAHF11Z7Z?Wovo02x;nsj4@EX1DK+Sn6?~DMhlEi&&T)y^mv@YTmY4sm! zD9wvu8e+KZS=v*UkKFtgs?d|Ia%o&*|E9QD=n*vmQe7Cq~R!CkuucPF+CMk6*Tn>5Vk*WciyUUU}>tZ z^*!b3K^{&d;Gw$b&@>m!42fOT#(n zz&n1I$yzjRs4t8HIA}@-I*hFm5p}?$Q4pXma zgyrNZr#m|+4Edp&18#L1+{!faqwMAgk<=f{6(V6)3hB?Oxx0ISIVVc&YXFgfqSmur z5Gf{yL-N~7F6(8inGK01M0;6XjWi%BbZFcYRhssKz`R2e|4cppLw|zZq^DRsa zh;z(`4ug0{Afl>KwJ$Fpe2ps1 z-uqaptN=l|pgi0uSQ8VghtD&ZM!(YnhcWXxs(x?E*fLr2_$kB^q`HHPR3zu^_In%< z<>1zer^*W~jJqF3IY|ch^}%i{yXVLBZHwDW0%D-v<_mYEfK}L!XUpmDC|@S*Vj;(v zy)L#;z!AF_uE#V&F_+`rrpe6PYBHJlY)5e6Oy#o`2r|W;e7zndv!MB2rmda~92n>s z`Lf+kR{`Cg^l@0tob(&Y4TVvZ4Fh?on=L5w!*hQ3^~1*KweW>o#)a?;unQJ*k!pPA zaH_qM1-2+XT-x)?c(cO|!H&p0E{;4g*LkU?{O`;%cR5sOa`43wml=~RG^Zc=2E|Xp z=ZM|kIdtNCKtTHfwAoSD#`3lb;!B^}XKF0$V@!Zwv zGBe*HX=Zxm3m?N9Q7lJR=-v-h)emS%-qAcadT=S_(T=LOj}<@YA}X!1_X371+SXuR z#1DwWd-3XXvS+Rw~alzG-iztzcKmp z0~;Icf3f1lOh^orWi}?=A_aCiZHkh{ztY@gcsc-8hu{=Ka?}{rE)wq+UK@0d5C#@| zBBXpD`|@7CiNU}<_9hr_LrUkn^8?rFMUKo0yo;|F%eYL6T}xrfV@HS!?nprhMv3pb zoxg#+)l+cVvNx*A^cuyU<_7#9WE^4G2thi92ydhQ#%jNEYEW|oqz~Newij<}nPTUk z4J<*5N`aDFp@TEk?HHaA224qEe(tfc)K3cDMS+BXd;`c_hyHzc(D@`Yx2X=~3XXun zV3NY6rK+qe@ynKvlI?-X*Kc!gCJm|OET!qvp*q*Ty_7c5b?ZUMbDnC~E!fuFQQ2NZ zX^%ePd3uKc-N)qD=&LI|10inN#5aC8g;DugRQfu!GL627|tXhQQ!+?IjKyT{{)g5Z;$K-g_kme@8Ay)Vx0>2xEb9~o0!1< z3zf;(pP=Lh;QukAA=&WB9=Q}2CD~!!`__Rg;TJj(gk+y^nU8>W`Y?8Q51f|)>{GVe zJExd4_GS6XEd&ECtd}We6}?(>M-)_@0bXc#hlBV01Lf)c+M>w(fZGSBAftsL!L`yW ze$HaI{3Qqo>#d|q*>12;GnOM6S-hmZ?+1fp0w84li)_dM2hT!zof zB{)|@iUnz;ydo5Hm(iroKZ+ zhaLZhc?bJnG)z#gAE%JoQ@NdrJJ|uj3u~faQPJVpt1txyiw0HLdNM^(oo2h0&cf`k z1I#dB?v&*GsEB($6TLybaO@)(%tya;u!!z zZ3Lnsn`6Y>VmY*z3^zopdF~hCTg;nU=W1!iL={cnc zc`F$m19rT4AV2HYsO02*W8VTt@5*YHAM&|@*wxqxP+AX0n6|C|`qR5R8JGHvzRs@elqv=FH!W zuy++p8-|0n%`pVHNl? zCHs*?*iwz(nA`iGk{I`$y|l!w5*B2l;|I<$*xyhnDO(xxNk~5z>I(UEHvsJ6?g=ne=ffk`=)4zUGe5}~gbvx^59pa$?vqqTfB?GD5+FSQXsGL~+pGKc zMlX^86qv#$KKZteKLGWjImV@?{XCCwr~7L)XYxgsm&_(;(Hvm7GJkh9DwJ0Zmvf2S zR@fNk<^kw#$?IY2eAl$`Z&j;qD%^Qr^crg2a7;b)w~qZsj2>^%ApOvpik!Ld9;kak zFQF@j#mpr)Uglf7vu#J^o0v?6<74LTNqvjmP%i&#u6|c?>>Q_E!F=kTU-{Y@QGy&S z0zry*_Rc#t^!Q!Z1$I*Xk-F~Rq9NspCuEa~(|Rk?($ipH)UkueZV_%+Lt~@w6m_jO z9YKe|ch*E-YG{oo9*dHmtii|=bWyOxE_gdDXC4#j59`KP+}9_}Od8I=+**W^h#-sj zXu=hO47^r4cEJ+UgIo%~)Hk2b**n9W*1t(F5_O4DZiWalA*JZZLRMp&?D^uu3En{Z z_SNndI4tS0Hl0GW`OT}{`3XEkJunI2Z{4G{-n5ZBO1?(HsAH-|H@J{3+%LMUuQP{M z%DGE*+Gzk$GEa*S>x$9hf07^v*cvE%X+es%3H-Qo80Z0}n{X{Xvi3N&V1g};jv?{RvT=4Ad6xDbb*5!S>nhB zMx20qUy3Xwx#y7V=}|RqVKUXWIUfqu?STBMk9h!VeMEQ_>UndhHq~hj!o&+t-RwuV zWL@ilo3!(h$V^d}$O?afr2pQ%kfMbLQJ5g()>Q}CgWq{5H}NxK_|b0{w;4bbO{&vU z1j(0SG%mLzQ)>&tOCS`KG8ktJVBs)gfg|(B{!DN3OE!wS>sQ~aK9f@y9fWn6uvWZa zOvi7~lcQ4+)WZX)(lH=gGH+NC`NIPs!pHVR;l1Cy@H={~PGXrd;D-x5CMVL}mM4a7 zMsMr~5RRo=3&h?n(iiQ4C#y&RmVlL9KPued56870{$zJkIJbke%eEPidgu3c|05vG zDL|OwUt_KyH@qn(lL311L%(Ai8e099mD^uWia?Z=idY_P^L#VRYkfO%bJHHaw}@ts zi9oE-Xy#RZXXcrhEN^lg^~!$WqijXd8DUrm;{BFUaSB>r@j|B!)_+O;cfC-4D%9J3yWHxK(J80Xe6G%h^6cOgf|izh zMZ|l#tRjMm*Abj`-eBz8y;p~4UBWwBdu!pOB+dx;^^)qRB3mP&3Fipx2gGcPi=A$V zXE8_af(weu;h(qm34qY#ai*b(5N)arY}I&eupncn=Z(j(q%}QGb6RfZLnA6&V+mJV zFdQA~%s<|Lt*c%s64`YE14E#yJWNx;VgQSjUYp(^DhS{wNh6!Y3CfJ1Qmx0w%)g@T za!JW|Oi}aaWgv(u935xx=|p^gy64Xu#H>ECm~zZ@2~CMulGX=XAdJ19ftYPmQDF+fbz*I@c}U*~Fb*)G7}0hmjsx?v6Y!(oc6o zI=aV{$Hc?p*IYrEW|h~Q`awiG#JV`9f#oLK$|%sfn)+pvZ^iQWtVF9CTF`o=AAX*l zGDy#2`N_qe0)C_gv@gbXy8Y4NwR8_w_6zib3ZTG+Ikt#Q@wHe8B+!%N=m=gsn3Pnq zJwx`b=fo~JhwmAF zIK%h~h6j-+KDrX=vu#B#j7EQg_Xx^+zlSg&xM<#7L__ILaNLs-^D!cLd5dm)qe*7y zQo1|QXG7(=X0mD!>C z_(DoOuGF*1fnSy>;~^h)B&@87_hrn(N`du0<%b{;r=_}N^7AJMvpII5FdO<1wcUe1 zwADF-C3!26|AKiC+B7cocPzH(c&>c~(GdcCN_)MHjHwXV=wHV+`i+|Qb|@zH628E2 z8m$zb>0K83W{E(rz0dHqw=30s@7N`IqZSQf?Zwee;Cid3A_nB}wXXa^-ra=FQ7G?9 zOQmEr_NOoj)36Q#?T?Du4I@%k-G;@_s@rsy)R5Kka2)~WO&ILX-e&eE`vroZLg7M} zf!ny$Fc&R*IHG6IjC5wYvpvGpt^|TPQJzQvmYlr&4}0mBx|c-*7Jov`qu^WCCD)Hx|w$ ztuw>n#v4O`VGhZhqOFRm406=wF_A2F=-%7R9mW_QtsqihnJ@L*|8(etoO8I$UPX;iWWNl1?CJXJ>~47KGr`4fzux zRliTSCOFA0h{mLF3SjTf`LckAj8su(`aG1n-eeM&b$ z<{wyo-uN@U$ zwksMX8=ST>c`SwAX}?QbFH zeoE8>N6|ryaD+1^O54_hFq=kMHRZxRcj8%MPvXxEP@V?Ut(?n&gki>}$k`c)nG!hf z;!t5k{mkhHgG)%$UsEsuNA<$lz_&LPNnHE^GGwXR4SH=|+bgLJay=^@EO7bBs&`I$pE2A}&=5P*`B)Kpxc`@X_+37;j3o@&!-BS&I^*Brf?0D zU=*{LP*SbhcI87NO%2Vt^b8QKH%)BP3%pZeR8;LU9n`Fm?fgkU^x|ys+w;Cj9&mjP zvIo}+qHI}W8XRT2`77z3p2^(}lfGb7gxWxSNX5cp5!!fF=@KTmJ+N;8BwE&~c}%XC z&Ux)|mvoyYeS|rBr=$>0w5&skmKjDs*5oHTG&014=o#j3>=iOxu#TIiL~k*kty_ka z(=HSd4&5YpATv`5eaE66n%X*lBjTSZyZu(Cw~&_Xu=JmqnvUWfs?GTuL-4&t->u>( z@$%bOvRZ2)EW{=~vg9&{AL2t0Xzv4zKx_43YFgUt{^OMF;vVM+kY^E+F|fOCWs_v= z{+#8nAPG3Y1FKq>+5Ck2r*pxeK_9TFF}s4lH_x8pOJhFl-hytJ5l?^u+OH;gZS=Fp zU77m&c34r~SGBt5_%puwv1B4r;udoN_N+-q3}E!{yGgsuoWc_;<6B$dnm|k%gNiP_ zX!k#bUq)I~HXjaH#?-R{O(tVO9S<;5$m<$C4j^BF*U|(TmQ%@y0d{gRyg=GK_P$f1 z+TJwHF}Iv<+N4)a%Q7F0<2R5$0e%4k0tKj2gO+Rw0z(|`_m#_njSYa^ydZg6}8?amT><^g#O=&c1m2Du(NUtXz-EYu!CB*;+?2tY0 z0G7!HDhM8}@MVbpuX=~@F=M=y6w692!SmH09`&cT@10rbWCj@ik!-yOrr)|rrt=f$ zZocK;_6|HD{J^GM*CxmF;_C(K*;pEJI|(`x#pW13$qpxNinEK@@A{}i0=Fe$_!|x2dd)ds`D#0i~}mV=u3v^OFkthC--{|l)H}Vy=z2R z-InFDyZ}s-+)^02m`{-Lw{^lSZuO`8d%66Q>oF7nQ!wVN%hXJ*5vms2x{MATd2K@# zygH)=@;*qut)tpWN%j98I77ZsDtZC><(4%eqo_hzDHg0s6pHiIC(7qJ_2Q3D=sd6G z5Ty|@&Kp~3RDoF2qu#R0?f2@AQvxFLXSP=xn#GRgC=zyo!nOFwTj(g zxqj{_ZD#6Ksmi{VK5z8pfswvu&XW(RY_5U26HslD|Fre!(SIxpC(L{ZW`kao3FP(x zMZquQEUsEq(y&f^Fo!n^kMck27F<(Ti}r_yTY?p?|29vS)`2xmIR<5sjk2glS%jlz zGXhm^HOJJtW)uiC2RsSA(Rb6N;^A+D%b>vws@^e}KEole&$%_rXcv$r)a;gVeZwa^ zo%bTP!wlOYi0uGldVb)$=&j=l53C;tycne~`B9~k?-F_=f*zYF(7cFh&P8`PS*~nd z(f^MEpMPg~yjAPpeN8jP7ewmy#7^!oqbK__;y$U+bUwSa>M_cBMpg9zUvmumq{*bM z&63pQKE8`VDQ-uvf=U;g$9ziVuVtZTOqtd9?;Ga@wkUfOst4cNQjz^fpW0s=Din$M z%cniT%<5=7%_Y;I%7?jS8@XkB)fX?4FxbVT`fkpYkv=)S%2Swez0s#Ioi|$9b1=6| zlw?5fI^%?OyI_&j2UIf&Rh?vVx*gV+&Soj&dE#871JRJB{l9C644%$~4)p(++rKnv zki;35%6AT{f__4?s=zpV%31YA-X?iiAnIuVN;v?fQ~IFtdtZe4I;#LlE5&_MFm!sL zOjTU;3?LP)-J0@#gw=GV?;PP#yLeA!+yq;3*b_j_m;UR+x(2-8)xakZMOftd;98{56tadV zKld9amU~|NJP}V%!BjY~Y)eSKGMoAJ3w)Plrf<8L6S0`hr<7sS3+gJC=*(3pjtzSzfTP=L{O*yd4B_gMzKHu*vW<*yj%D>Dd z4>c=cOs+v8Zl7njY4gW%5%AY8^J)ajf&+{I_b|;HBk(#=3N(NAoO_?i9Ef^RSMXZl z$&q1!i9e7<3=`$du~f!`3Zi4FJf1=gdf31}sCWH8ME1Y`NChy@Zcr-M97B&)`HZqC zLs^6n9wHI@PQ~|WsQ?T*L56z%S4CIJz+syMJ1x}-puZ67pMULNC*|=3<#Bo~p`h() z9-4iva020p5qE6@%3cjfJo_|&s!0t`7JKpyjJ#)-M}+?U_fNDZ4yW84bItRT&C*75 z%oF28l*PL;B6e^XplVj?AX5g0Uc+;3|Bv6=`hQ$(=M{%AAxQWM$`t&L7>S~+8Ycga H@tgkwaTP7+ literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter11_91_4.png b/doc/LectureNotes/_build/jupyter_execute/chapter11_91_4.png new file mode 100644 index 0000000000000000000000000000000000000000..5d106940e37126b360c8c18743918fbd1e1839a2 GIT binary patch literal 27519 zcmZ_01ys~s_%4b8D2NECG$<)3UD6+lbSNkt(%m)GAfSYlbc1w#lpxb-`lIuxJ0?dY(7-#=wsXl6W{|I2afhc+yhhN*EY-mBF{@11#{4vWr#^ z_`&b^LCsOw#@NwC&)x__UeD3i(#Fx!O#g+mk-dYNjWri5H!Ihh7p9JmwhjVpY*zpG z0#+M)6Sn>o@gcCuLt80z2Mi2cBJ}qijD#c-3=H!fX>qa7kfhyt7s$lg^34ItVX)^e zp~RH*3%w!syAJ{$lu>?rRJ}qqkzc7&q+3}v@wl=mL#3l}JLN6n-N*m@Ub!P1dj{2q zkodo-ncuyD^TVOq#H#fC(hIic_LuxUuECYh3BW&oUMkof8t`vK&Ok<7Ts-qGcQ*JT z&ivp1`K3p(i0$>oiIuZ+RRKO5_?(ip!+QU;UXhh;E{vaCd3t)fKSg+U!k-vy&ctWX zKcnlGOtnq~UgcqgFo7T8IKy#-|6ZCba?#V!5a!+W#vtdl{9REo?)39>`Rb}6Cl{Br zl+-KKtf^dJK)_YIA0D}syga?2Ah|&>f+CM$Qp0&~t_Qr^-P6N_n%&Y90o$g&Vqu{d z7S?{xJV;_7rKl*n{W^k78A#~=`{lFL&^0Iw{n+qSSJb@A`RwA2vz$$0a`HeZrC{i} zfnthKyt1P3N!(&n-IhDr0;`ffe_zl_h8nJRhZifS`xK)^5s%}sm>h2MbZ4#K;S_M* z=^jpd&&0%Z=WENiJJOz9`^&3qYj&*<8A}a&2r*b2_TO38EMs9krsy8vTLha3wei5T?zK!7 zY4Tqmk8O=+;cC}8>djP`VFXhNCp0t&p+#s9B*MQm!TIq{3$pyfaeF*)Fj?@Z#OoUO z+q2gy?2!Ghb&gx_P8X5_ntKpJhk&f5($*Jz`MQr8d zOr(N9536QXKlnf}Dc4Sm_r0RZNrgD}zbW>;OuQtIs32adx}KF_CD-6vc*`uduUNgw z5S2wyrJ&1R#iWL&mX@WU^Ny*@&XitJWtHpEy7T4fuIL5V0EpVhR6=JhNEhUS75J5E ziOwl-1Nt*cO8P-Rf9??LdgzUfj_zEXAgo?JEo*c~RVn8vR6?5oh>SVRI-NCS}Y@I=p4S~$#@<=h#rbud{UNR-smdpVXZZ*X;XfW44i zSh&+78b&QjRRX&#M_rz8q#n&V4Bc5eam&-L=f%JmIeTH#c=8+r0V^>%KU~Yq$)PSQ z`VjQIP^0oE@Bu6d*!dBqK$MTqU0&A76G8p`au{{ayS)iK7P-nf zk8z*B`P%*KWlK|mwtNCN|30s%(3@!>6Np;Kk`s$Y#aF;29w!s3{qbD>DZ=h|KPoA` zYxBbkJ43nA{ev#SD<-C`7E$-cg?so%=N=-h%j_*f(C@cP)dvtEY$);o@&L>Cdz;?& zcwU>!qNhuDm^v_qJxU(HSyA*lYHKVk*0VRL;{}&1%*~uUlbiuPY9G(JS_n zrVC~ic!O=>CdcdMD|rh&g+r_|8fwpqnEcJJn!lajR?hZz6PsDOZO zJ&G+HC8xf@L1Ta&wAwITuj||eUKW;+q$CO*_g$XOFzT?%7!X?{S+cQhP4mCSd?6r| zYi=$O4}ZLS`s~>s7o^ViWRYwL8IM|-;X^Lt{dv4A{&kd2^QDAv8k58Z+-*t0&4hUyZp`%pIU*PgpQ9dcGjjjd7;sr`qa~Mt|t7> zJuGx20`_XXr|O^Lb>m9qu`g!t;IK7Y%?1E{-hm2_i|a;|G!Fte$)O)JQ;G1l@nZ{n zOetUs({|x--24dElX4n%d)s_1d0>F@a`A9NjAZydE~e>O=?F4gY-&V2vRnO# zYUVHwt*q)wvo3j!=69NBzd1l2p;5Z?FJ}IKU%HJd5QLKuRq4t2W<_DizG8X(yTXu| zKCAu}%X~RfRb7Ps#zW=`GwLFU3GewQ!dD9@-ZUkd_eN2E*HPbn?^_1oYNU$Y5?MQ4 zcSRT+qdDIF)bi#U=|z3Y``-U?mf2V~hL+n_)|_n{p5x~5a<0haYENV>vgs0nY(z1S zQ&^!>YyKy83L$n486Wzn`?9C_sn=|;fgF}>Sy}E(!t4+nriV{Ik-f^MtGGQ)&CJg2XJbwaFk(YEw(ufA8Aka=Ddauwz0 z8#VPpEc7NYf~b(5-%|RIUPKW+y`^;3FH50uUY&@LFhiTWJt<_FkVvUhhRCE}?|znG z^*rQ}l9r?A|MR>@+Ki4dJ3K-wc6D`zjuA$mCE=;0v<;Un^yU!N)vG@(T$`&_fX~$4 zuKbvpHmoGkBK2}oQUFnH3^*VvCdPi=31)Y`7OPyK!cttnC$Qj-6joAFf@~zan2zTX zL^8;)fVW$bsK}I*K@gZy84@9n8%h8Rfyhy>vLt=@@ZsvlMr2}QUn6RvZ)dukA2sJ7 zEiJ8gal92w!r^ndS06?t?6yB5No|KHswTwwk*nJ*lInR%%4IURdVwg($;|v77416@+O1MF(`4BU!7m~vHKCUz_lAOOsuij>7ioLQm=Hk?U5!t*AKM3EE zrkhR_|H&6`sLR>Y^fZFVJR;&_WYj(19NwOuN@?lh_e%DZ9zB&W|2(Ig@M$0SyhX?g z=x2zMWaqw-TE5Z!U?k=oi#h%Ad8Ta_KHHJ9T2)MI*|7KQ)0msvY9?I2n$pWuh~1IZ z)piiV_2r3^IiIO2o>$x5{c&Z*PbE6SGBPro)8&i?U7=aIxd8y14xq?!7?bBaID>~d z%vx2Cl<0~Y_s4m2_%WtHeBAeH{k^W>)YuEE=H|@zupTX4qZUn$H%A(-4*Ssja{%u; z+Hb?BCQ-zmZSoY1)pjOT&X#-0$mp+K?|f&tSX(e#F5YKo0}hh*+N7q#UuKizr zCd{-&-J~g3#kQ6uV~1ou`H^+!XYaeGSL}YLw};qmYZphEbdbF0oeY(TumouxbNX{r z4aRs4X%XH%re$PgU(IeN;(RFkvetQ2T?o3KLpNEdJJQ^_d9ch%~@%>(xOQ{^fy5f1KFu%{6{QiQCEcol-#O403TThiiQtolhRz z@4Yn%6GMYeQm@mmq-L+YAdh^X>(9v7gychv8+PpC?Wa*#Oo!M^b4P8_srop5hbX+H z>yp>6@NOWFqIb#PcL{uhl8BKyDdk32AlG;zJu(?~FBg4p&%12k8OG_vsi;`5(t7SE zD?T~K_Cv8$P#E$N)!Zprbt9C_OVEWg#a@dt(tywP&`{+1SUFoURRLrg685hcSy@?h zbaWIDsY%2M;Ula&XD20I19*IME#2X?@j|YgE(@+3Lkk-RUDQJ$iJu+zv4MmIips50 zyvdpOB3JI0yVYE_OaCpnAy_60)!V+^xyO995n_y1cI|kp7gf7eusAlS+iAcuwA_}7 zTeC5E`)L(F8nJ6Z=jJ738R20#E}f~ORFsPMn;L6qNGD|n=!0LfLDJNBMMB32iHAU` z45;Hf-!D>hbKmu z6TssXZK%|V^?cF$f|aUFjp?UrTb`{W5fYtDlAYvH^e|0c4} z$@g;0Ci23&xrk5n`)S7@RtKcP{nP#Mtb!hoTl>x=w=@61)hRq`kt9iKXMEx;(U zp!COgzZ66^L;`q4hKGxRH_)=Yv~dBoxII9r9T1utGW~;Cr#o6z$90K(*lYN=*gXb? zr0zHlg9rX?+?G?n6h+RzCtBA9J|tq;AM(111Ql_f{Y}fKel_=FQFSF!x8qGclcAK| zRfC`aiV#MV#i485)YY>H&OL+!u}g{NkSrI>PG#uL9@+d>DSl)}1SUDkzSCf=Coffe z%&nU1b&daRg^+&}#~H=vAY!&`&;t~6<+r2rH;}#UXh;+(K(9}^eZ$w;|7Y^_?f5Pn z&h;&zo1=8{Ff6ay;kK2L^pjSnD3(Zn$dSh3Xup$|a4EePC=L?`pdN}Ft}`7WJD9fPiO zN-^EJ1W5MvN~^*dopvH3H}*PBKSX=L{%o2R$ry|8tz1c)D;}#sEin{zs^&xQu9Xw` zSrDCLuAO6cR#&PexcI!DdErem*z6|;L-lyvW$!jXrtKb?&JH{2x3hQdSO2M{SY%Gd z&aPZfKUR+4#yf<;6xy)hmk%lEZ_sLCB;xSeFKg1OYd6GWH^g&qqX^-t+CD=Dklmjm zjy5VVu#fbyD`d4nNQ0-a17418Z)~orQ|S&lE#mq+qWCkY23CEcEyI>+qk z=?^GGIe8{Ir0V|HRzauJoX=K7o>iw1tY+5pP{{L>BH-h=iq*SV^t@}-9ew9#aD;YF zM-n>BLCPI+@}uwpRdai#t7fxNtGmgQQ{n?h-P5!TM1jA0{MY^&L- zM^r*_pg6zF{z**(r|HL9%#2 zAk&Fj*BzCH(a{HT{<;TRTk2Q48Cgk_Sxkxwo6-Yx$yH7jp*CMqo5Kdy3Zi2sn{M04 z@S78yU%T^qA_Q2N2SBG2s|$^kTh{@g@4^`qBZkRrY{mo;<>e=Qbl$)w25$`J7)!JDxB+j`#s~ z&2>hfD|A;fNz=U6dg^u3xz4w9^3%h8{&}9v{BJ{u5%te0fE;a89so-Y1a=xaE8HDybB}iqB!~r8zWI(Wqo9&p7eoh{_ zC=!)jG_;crv7||)$HGdsWdVH`6Tu}4{PKjLV)&ED!==}?(FvVhB~4!6ieBGr2*_tD zp^?%*9oL-l&?cpKW|UGWYBbb#k4WpR^a_%Rh@z$o$8|U8*9qG>taA_9PoPiMcZX} z6TN#KLdiToha$cDD3PqjAM5>uT%_5|bLeUmg56_LHh(ca6OI;ZSxBP=ewGluacLGI zM6lTGHTCu@c$B#qLe|m z4@RM1!APoDIWvKtkufqp-u1IhMvlaj@Lbe#`mH^pzj>7N$Z{Ps6!Bv16C8_X_d%zG?oa4&%LVQD&COP&P{SdfM2xyM*%^(AJkB2v%{yVb zzq+OxGA^Omc8nlgQsRbv2i%FI-!wdg9~=}+dl{g%*|c*4qcm$fqd1IfIE?c+jDK*f z$F$8A=Ws9>29v6~2GY>n>b{^@nnW?~uVnWmAyFK9OBTVNPQ-$^eURk{_}e^fT3Dcc zR2^SI-#rs2cs*WT#bezzl~jKV(d%bMf-&_9L`<=?p-cwB#1ImaJB}EGyq%6`KW48f z&uYqOKZs+1HeT!Y^zFjpIVH@`oa5{}j1;vZ5bO;r-jNO4aVsWTBf&$C$B8D*cn`%G z4T~;oH7T-REzZIp5+fax8SKT^YB?ux)%1$Ajfzh0vE9pfY*(*)&jw?b`H!Ob{cl%g zjauiOW^x0%J-gX2i`;Hv%XQTxt~I0^phmhgyb4aqubw$BAMk5Azk6&mIAjFreIlap z;Gm^|_NCgofc$D{FIP6_w-fAZXxmLJ<=5aI3Vu3zyf=rwxbOTnIxU1WYTF}=jM9Hikklb)I;Wn0yoqxUIKR)JJX3HvwySSMs9utRta_t<)dV%=8 zXmU3ZYM)5e($^Ws)ADvnv@>o*)KhYDCUA0w3Vh*_alft7CkP~$t%eR^B9j!vN&~vM z6xRE`lb`qb_r1+>AWEq#Wvq;F40!)WMq!`xz(=TTdqV&8r-kWOUPs7mvtf@astzC| z^DsD1{XYu>xlj%Ug15L3)DpRxg+pQG^yG}?lGBpv*R6kFv(!fYi92L-$C^yZZYR?@q{hP0 zB)ib`12xh#o8GPFGK6C)LKyfDecls@F{yEL)G=^n)#H$~T0OULt3DWSs9s$V2So44 ztCiPg{AsX30Shj`u3Gi|;Yspq*q@K^uF(1Rs|T1M51^}BO+E5;HfrrbT7<|~$Cf@L z#)j52Rn*5F{DV=W#w}P~6GA-j3EyL@zO8xAIBpxdMk0*^jQX>s5Qk%m&nroQt=r;Mr3b#x>@0W)Qz_nU*4SsSk7)oYb|nhEO@S3=V$J@^ z@|#2C%EHY2)YOuQwWkZyy;6_%VTDU+Tuq19XB8Ocq> zUn1C7#hp=kOR>%fsdXBy{f@E*9A+m0P73ooMhD7kzK)VU{UH+{=fKOhCz85hTnH~C zvahl6ASP_MaHNw&exJlUo1N0iF6qtkC+%gF_Va4w#p%UCi!x%uMv!OkpmH4+B+^8p z`>F*_S-jR1{T^boUcFAKSZtQ=i43%|bZ}+O3?-?i;JUIDDImg8s`&z+rOF&V-y+jdRi6$Ow`EYG+ z53H7?vB1|y6YJ`{Wn@S;Gm6(bvlyLnl6fB95I(f%(T^(<~L zWN$_1(bjOcQ%d{q`z8MVL%Ry~5?gOHuPsJ}q_xV|<#~r(M*;BO0^sC10^pn-JcAUj zjfQ%yB*AbWsP`499xvBC-zq+$^P7-4JUIR#oEJI%%V(fDdn&P|q^U91=UHlBy9PJ8Jt(j@Rf2kX}$SC33th0Ry;=cm|ISE9i(O@rJ1OibK-J_m)_(e zw>;iOK|qCIbYRF-I-!{Nv~LK7@A@&uq`r4{lh>&)V^cpduThA6J6iXNnTT!k?{<-u znYyz8SA@sac{0}@Oikd-NB=%dC&nIrn>3q@l_!mU_K9`)pr?tW z-sv{H8;^QOQ+ofbfcCHMs(`#cy0-Y7fNvt)VtDI3cv`X2@ujHN&Qw!lvqj&|)G#)C zjx(K7mrXcYYb?g!qoV<}{q})B5cv_hnvnVP+Kbjp^NcRpcfU6wXmhggF)^yoE}6dd z*|nxE6lvL{<0!H#_kQm|vB_k8EP_8ba}-^zW}VIY$A0|!hNW%ekKnKNM!5aKcKiVS zT@r&D2SZ7$>Y=ZLqp!^@&F!y?w+a*Ns}bCR1YqK&q?hV-NkScCy(%{ryrJs6!sk0X zoUfOUcoTlFfvWAjiA#pVSazX~1D=i|O|!-gjbO9a2yic&7xR8yrSHz2TsNB$Rmf?$ zlWKEXI7~lugDBD{%B06KG9LdHlVQlxEdJ_0)K$576(7N)3@jTp2DHSfMfwI!8@);1 zA+=H;BmJGQ$wG2_$jkB^9m&fvFD%;i!buKq}af9i$7-^2rLW zz=Ifnpe`nz(%9IO{w$EA%GG+VtrosywB@2$KN$Wh3&gf$Rz=}A(f*ns2E9HQdCBkh zk=#(8(kx(jgHfSI1|Ex$HWQY}n5Jz3$#gVXQbbFNGz9acuzR-Vlr_B#aqrsLUKS2C zH#idb_2qLS{?+Wm?H7jpSQn38(X3V3o?i;po7|yobpn!jL3w`DQzlM21ASlSI9tnz zK}DU<8a%j;?!fp7e*k4OweH>!?wxJl<`P$VRG;I_@F=V$L~7Iz66Tf8@DQ3tx(Zaj zV>jEq)!LAHiiU>0>mj^AZT+F04`pj_tJ|DlF>auUCrUPh9#DtlB@Ii*J7bRn8{ox`zh_AcdW?E>J3Tgsqj;`(?s}XKv3GN zrTtD7Y-$J}FEyH;>@%BZkG8jQHjfV@qlv?0U>1)1wqcAY5S_1TBJTy++w=)+FpZKY7Ic725ipR zNh0AS9NHg2$FRoMbs?+8C>@37&G&BCV~d=#QFcmaZ=dg(^$Wx6ekJ|(N6}S>RM>GjpIS2K60P!nhXAMcd zp|SBu0ZAHkwSuwV6D4{W$nw>;hIVn!^6z5Tx)SZkhJY-%>Y)KMvDspm5vCGJ&Vn1Q z?t}RI-Y6LBfa-;rk{=#k9G1rq=kPabW`gju>)beD|9u^B>(vlkSsY2{VN&IKtKx)B(H)M2s|1xs6UV$+1RYpC} zk49~^_$8wr)KJY}_yYiU!W?7IqZcJu)m$%<+WM`M&u6Cw#{qBAh>m7DykmSLc28OS z8-Z*tF#iOxL!&Z4M@?DYg%s2=4gokx1(X>`djrUw0|njIY}+Vc)%Vb0xHrS=m`qQ2 z(CIvseEwN7LSl#Isbd5T>)|9pchW;2yN6Lj2zn*wW%!&uX1Lpy# zt>uBxN}u3|Gh>Chywqpa+Yr(_z;*f&C$Y90cLDTQJbSnWJh6Ob6o{+y<8`7PV zY9Uc6tPfbGOthCVK}$UCwvnm)lte7AtBsM1+BTUs6utUam`GD-Pty~tAa{aO!=sIn zWcE%#oPqpQVau7JjAO$#aTP{>p|ODuXi@ZGGbLw;Dloms*`KHzJBN3Na!XABgnThV z6Oi%w8%-4tU_5liABdTT;dObefg?mUS(MuH>#;n^bXFdMIXrGMUyqsLAQ+Cc(I^y;bOA)7UM8&XPHK_$YS7F`8oA&B?<>8U+RQ=Ood@mDpO3B9MiDvKiJ0VQr zrcWOqEcwU&=|Q~o8dFc267W56jV~?`Us1C6iJg0HvIU8M3o2>CAL|M?w6{DT9N$>T zH#OsWQDy)Mw8&tz{@Iuz@p2p=W}nv$hMS|88ueDOEr)(78ELtQYg!kw7R(ZsM`WTM zXCa&b%c6sn0hcKQmyOU-tcRo6^yGcQMp@u*)4nj6oc7ym(-WeCIUa3${QRF~pA1J- zz2Ky$qiKcw?lNwhK$Qoa+3pNx=PdDSxaCG`=%RuL?Nvf=?SdMEt)uZOohEfI@5R)) zl>Ry%Et9}*DF2DYio6IB!12Ju0q21@U3A6{t`GlA%a?Pn-I|?%wTvMOMW5LNr2YdvCR``0w90TM~u$=jC--_!{ zEwBK3`SLq=*pdGaBI!R=>xJ%ar6?42i@QqFp0)ECuH-pniuNalM3g1E2Ahxl|uIrpyM zzxP$^s0}KBAHoByDyx9znnl3w#=@)rv+_F*7-$Y6soE_X`ZXO0`0y+gov#xB>Q^5S zdQ#O@2qcdGTAQDsM*9sEHiUtNYbVmg9ItyMdqc$>`%M4-@GRF>4V2;!*$tPE^y%~v zBlt1<9F(8TXfJzL^?UkxUBDuVa=WsH-`AKVQ7sS!GR&84KY5TU7mo%q(j}Sp3pz2j zPPOh{*_{f15BC3H!M4(wwre`_I|lKFfFGxm1j|Jv+7H@RubGX2#FONJt@RcX9Utn_ zpG(b8qz=k!IM_8)z@%yHA1NSHq&1+p>u0T&>gR#r66`w=LM{rnO{yVR$KpyvKFE_y1qzDb>Ky!SIB`DtjmjWg;| z^q2l{BOfS?U+DwdE$ul-?Z1rDI@>#2^8S9iHJ{NAY>aeBTw>~;2ZUK(?2!2rBqZ@~ zjkt>|#Xdi{@h0@IPe08GHsOkt+?+fObOzax+syti@XGT>z&!Z@BAP)pDs{2$O?4r{ zI&2n`IxSAVvm@D`@)67gd350R$$w~npYfqB0h0d8)HteSW!@0~7+ z<@6vm+8K_FH}A`EaxJJc zQ>EsJw|kVSvOZ`D)X`4n50L;)PIPLJD;zPgA;32Ff@143UheO{4b?qCig#sKYBPf8 z3pQ#pRC>MDF`mc)_9X;q;4_zIX$Ur-hg|ZnSf$%7EuP=e2s(m1EWjzhBHXF~NuaNp zOjvGjG@Do}-A&uQu66z>sYKXV94Vfe5IiWDvJ-KCVLk(Hq#p?I!-IoV@A92(Vi1n| z1`A&8r&33+BLfp^5?wLY0wSR|38)4TTj&ksdi0nKvPt)K&Z9TVBG9At1;N6kHoz~AH zhc*mq4PzhRAF}Ly(ktrlWn)q$xH-*ocS*ppK^5K3Ox$O5Wp}YHxRg5HBP;wU0A8@ z9puf(T&ql%A8nn~M%(e)R7oRp$IX{yyeSRX&aQpqWVmtH6(Hk$7%kDER{S<*Vd-RX z+2n6gd`)QO%$D3X$^T))S$*j+5Dq%5k`E~@k_tknHtR3X)l>ko09^i(rYD~D?pQ;&8! zg$IcLPNO6b-)}qMJOYrc80GpM^x3e$mHTa2jiBJi0tkw>>^b(@ z*P|Jqp7)l$aLj@h(E;ip{OeXNk3j1{mgyF9^D`s;&L9+rHtPwEg%_RJeTYb>dIV6Se_LnP$ z%gvDTJOtc=;ViSjayoK|i+o~yv^}H^9u8{hy!)vh&RnvDo@dp`?Rf76el1NjYtYy` zZo_2K6_Oq9K#-c?>GH>y3Eq(rPx~k*K1bLUU zSE;*@&&S(}{GU28NlRHDCOhc-SdgH)$xQ>+yi?+NDp+;qVL8kBGtsZIjYK<|F#IPe ztel7+Y?co;qsU0dE00qv`&k(AS-|A+zxivVI33opsSYt5*=1egzg13UpG><3oMRuH zlInq5->AcDN!o?hUceGR;-YKw)bx_Boz;E$|-+cg5^0vP(Q0o0}P@pA?{k>K-YL>B?UG z&`qL(6pFRLu5<=*#<5+&N;>|!ds$OAP9A8T4l)nLkCR2wp~MtI&Qo4^KULRAg~CsC z?0j;vU{I>w10Af;N{z&0Ne~nbtuLukj@TNWPww%j>f)Jh)k%r#&uyk$n;ig%rTs=w zoMQqwtW{V}dY!e9|6bnX)tciAJJyg!tK5la3Hz3rt~GfEvJYr8X`+FXUBBNI;`XB9 zDb#Zqan*8r7mA=E2)rjP!p2e#^5gmk82=$I2;1J}`jXqh)%&^SyH_aGGc?;_aN|7Nj$5;UA5dK-J>#^(Z3ie09Axxm?7pl}3Q;lIah zNJEu$|5ZxiTI-J{5kw7W@j^)qHYW~fM&HF$J2uFP15oil(kzR`hBZmL4Zk0Dcn&|} zL?>?wvP3lg+5lR1v_QQI1@op=c9F{~)El||)~cH;XDLY!o$J@MG!rH2Zg>$y5-TW@ z8@{8|Vuw}6<7lx};_o=s2gB<<+>g(s@;E}31^Ccu&(2b9VT=0|6c6C(nV`=)$3%Kw zXsXadn5G53C;C-)!8!hknH(`2b?oyToz_~NLMcFvzxw2=Ugan?*`fQDY`XM?DOQEq z5ulTS=c1+m{~hoVvwj12Mr} zvu>!M3bZrmZ&Ago!lC`SI{+?QK+IK>U=9kHD;Q7Olt6}@LeXe#G0>e?Xd#*05eh?K zRe~uU&0$dI`r5A(5V!Rzb%TNKAZ}ayK9n5Q4KTXfD0iYZW#KbDz~JC)S|a(WIm51~ z&N?|I8$1Ejpp`l^0)k`Dh3}Q3%4v6*(>{asd z8}@S%>D?zg$BIi}G*`2P%<;43^vm?<6 zY!`a|zX-JLa?cv5W~!!K8v18(9aU0alPMF%7Bz5oy<0 zH+vRA8=;^}T+X^nw9DI2azB!&|M#i*!BcRjy(i1bhhKPA# zz!xF%+pfj8WSu{Fb9~AvB0%cL@nB=X%*(#n*9^4^fwJJ4E+S`F&s7*84{gZ1<=X^S z4oJ}YKI6>3ycN}9@X85|&9er}RPX-KbcG;3bM|>;=7i;VAuiA!V=nxp!I{?s5E7pU zH_A^0!bS6m)Ov@Auzi@7uszy8CCMmIq9G*rLs8U&hM`0|r=2o{DUh5Vz-Vf()-aZC zgxP@`9C-k0CCKA$6XZz~6T@ARW)5VKJz)AgH3;(ke)gGmJK;Gu3yPBL0(=_<|tzHYFPf1oaw4wpQLZG8p$FX;2-eaGpxGlM}9G68r^f3($xdP7-} zG`?QbzT;cUxZL4Chp4o3s|_hjJ=R>eycu+okpp_faT;x>o-bhM z2_DwisSyL_*VPhVQPpw22ZHhq%Em64aO^l*LSJG^x8Jv5A>FR!zYtu~g}gt2{Rncv zmD*fl8IvqNsbO#^%4lpRC*6OxAEc?i&UIErJtW^Is2_~Z4l7#MtB<4HgbKAz0)ft; zYvy?Qu`JP_&*NRp;``m>qb*o|6Piy0hG`65V3ezPtk=*vgWcpHi1Nih3mY#>o!I&C zY)U}f(_EgI!cr5`*pFP^I3^R8AItd>p2*j*gnjK}FS z-h@AUD5#aw{zf}KA{TX-!&f>0=4i8dSJrBRFn$^u0ze+JZZ!l29(q^cuJcAa9RQO# zrl9J6`<`nBt3tMBB1eT)61vi(Tj9=~4*bpWM*AQQ=#j}m|7o{&2->Gp;=eoFd6@Xu z3JoOj%*g@2yX+2Y#G$hKpcE7@(oSrK*QP(Kc%9qvjWuWVO{3pGWyi~R?ZzMfP%m{y zTLrxvBCv-~+5AzWbMgQ<`(FbJj*HfJF2HPTj=dpcw}~ErbwQ% zxGy@%^pC_v7P)hh;63=77@5jff5Hk z=Y6K#|DnqS3^EA*n;4z6wwIes`!%?C$fpJqv<->|&_ zSFEPDc+9k7T6^0Yi)v3s`U&9YJl>cfJIHE`@IE2_!?j4cyk{9PdkuyKe+(s%`MZSuxs=?T4Z%FI@*#m9z3Eh9A)kkjMon zSwH$2aw%M1cerd^R$>yAwRf@7()2f98~Z@cgwm+V2CuN_mfZq)hYrs?duFR0$_ehA4qDF`zy8;vvh_ z?n$ZB(HpQKDDi1Vv6YdAL9q9xFbpVH&A+N9ZnW_40Y<;hML0ZS3KS{?j1+jqfm?_Ve>*Hu${!!*{d6LtmY8PIk+*S`=hJbX7=oT9~FT8Sp(xG|o3CUq!& zpDbUULf}IX=ASIz_7nB#X4tii=587NyR`(o&@U~k@EiJ@^|g@E)W=~bg>gV)0i2h! zfp7Nx@~R7HRg*JQmxu`RnDHVsl$TCQq4S?%OrI2i{JliDDVf&na{BYHdj<;8Ns7+c zh)?9sxA?x>jT*WOKsW7b4VzBc@k*R7)vNj5$=U$S?G+8DZBjUzO^ci`Czz>>H zB0|D3F!LJ6pESv0`|s7qZ2`u7@KkY#+r|9Zn^k{C_KNqkXiBn66O+-D5u#ElzG-)o z`3%N;8&x*RU4ll50Q0d&ib4colIT#&e_s$RhS9HeS__ZZ1b8157F~P%u4Q4goOFVx z%_%fMYHo8{?*&h*-a0aFLx4Vii+s2v?@HLhwbGWK@~1gR#UdCp&!A{%CbB%o1Po*7 zOGm5c!4qG@R9XLD^RL>@IM+)rd9F^!ysOWFA4;IE8kdip<;}uqp6;{@x zZk@4ysn^C61}&T);)5~8K9aQcJGdO7yU?qkOA{OHLqbL-;UQb zTkZYfhUhjNEE$N~k)cM6+h(}?ok|OEqneN)P_}XAgr4Q8@pAD8@LwsYpyypsg?Xw& zzs^U7i*a@5#5!KJ9L7}~#;2#d7sl0)(*u}G`H02-u0TrPMKw5LrXj4>;FY7zcoP_% zru{!#U@a{n9}V8;y*`%cjMG|r_%*81c_VEhywW+nvdX`*O41h#FEmS4{~O*9i2X#p z;RQ>PhOR_Lg(14svg?C$WR88W6p@t@I|zW5h=5?J#@RKK?QuB-X%E0Ct;okRvE5S} z_EGRD!=Js9&8SbaAXWn~;+>RDl~jDAox>1OxgZ@*7z4+iN4&Fl=7ax?tV1_v;n%?& z<0!*Yk-r~nT&}|x|AT@`D}Nwz@hUmWHtxSsBZ^pM&@=@EP-L3z?qPUT8%6+VWPrW& z;hi>TuWEdq-N|ixq`M6I(^8t`#KpC?<}RLM7#Cg7*hwFQ9ASR2qw3X)L4SG|tI}c< zkc2oiU3E5;8%Hf>y#&-7PL5@TpKFuBpPm{YXb3#d^oKmM$NP|G|j)gtN9Z>shp8&+W?S&45OKu=UQdmiAVEZ z#ece%h+LYuT?2ng{zb)25o7(0>yVwaGaIs~{#7z7b}Qy+l|cZL@bkz}vCP zc{37=_(o_Quoy^}UpjSFTFNzZ#)_x%slVKFRbWZ#~Bu+YvCe-^@& z#~GP@6TYkCJ1zL@-;@DJCizj2-dn<(TO~oibP^CNsEC;fa4uZU=et&;-oXZAl?3U* ziGM&q)cbq7xXx!nmh=B85xwqUI`~p;<3~chyWQ497Bp{4@$*OgJshfn-kJGn;x zKTR|p+CQx`G6`SiD||J*BtUNtY?kG&e-k;5@0XWqhc_^0fey0pjE}S_GhS=Z|3BxyRhZd+W`OwAim7W*^XB@8BXM9 zl(_)6Jh*m2L(}#91N{Fg?kmHh?7qDTMMXkT6v;d*OUNn|-gn_HXrCdoC0GG24_0S4e*i z=t|H)H_wHBvHAMjvNel?c@f^~SxNX!Sqfkr@^fVFP^YdEg)pnA)F(<^6j)YupC38h zDHmlX$$P}2=`H}mL-IP_+p#Zt#t041t3$#GPFREmNIZc@XM90FE?L?u%>$A*uR(o_ z2AC|aj%_u33yI$bf#M|?tpli5|2HG1`ih5Wq0UjjYD_Q)9_XrF@a_iOTFN$$Df^jR zxo~i(srtBxmy8I3n(VZZOb2x*^$7*TW7gX&ubW>|__c z!k|htP`H^E0qS^Vo&C(NmrXBEC2u5D1i8Ds~|+1WAh4Zt0iz z+^wyB9t{$t5PG<@XQ)VX>BuWw$Jxd?;cs@uSFpT@eW*A+J^k^|8%>xta{dCtXhk2| zf>sa*NbzGhg{;POSPXYWF{H-jy81F8Y=d;I>e(w?p#fGXCtj+&+U1 zwrw$QUgw&h<$lbNdoN4ZE!%V3g5qMFH$dYHK-@Er7wc^!l!19Ob2_lk1Ms7fD;a7` zD|t+E88RXUQgg-5Pan?yo7hMZ4kXtVm*MayU;3?-ajG_+KjD6 z8WXB9YA`G4(0U>P6h7nyziq%76;Sfs)<@azJ!vPDgT!`gUH_GUL_}4I0ZTDP_;AN3 z8r%`ko%4G;K#!S!ihgwg$^<|HVil#G!#GC2zyk%mAVV1CFjYGAc$ERQ_QsdKvriXdptF}Nm{ zaegXw+2;ah14&w{0?;tISfiYyRu*K;q4x%iBlQ3$EW>QqodkjYSs$*z7SY7pZQS^G zG<9PB!7aL^_K5}xhy%Z5_xEy05a!eTowp;wPTtQDON)6`tiyF9L-mUq|A~~_BUy^R z4z=5A8&u+)Ovokuio{47MB!b1;LN34D0U5qimw`G2DFaYx--9bLVtv=`F!Nu z_K=`fqQ-aCmx8~AIbMKu5rtYJ0h~X@DrbhV3S_%b29b>>+g_F18R)?gNw0Iz8d2mL zPZYr3Xzg1l3V@*g#&Yl@E79=P)x#o-F_GPNGdW%vZJR$zkao@Jnw&fbjz=fh!2s4rA$8Kd& z0@t%(+;bUJEiDu;JiT4->bA&KcZERjHAJ9?3N691XVA$)M81}x63&dYH~6#PjOQHs zc}CpGdUd8vSm2Za#VR>JZw1^7b@l`bkZp6|&_D<(Z#Nad^%&98~+!w?*-`J*0pB{m>2hc$D zOY6>+xh^`};q<$`_F^R*U5ijsg6&zlWgk_H8->Di&tJkFLYO?kJwj5D_A2GDg^El6 z`tT40K&eRQ$=Af#YEa2TaVcw~-8=^!P0l>29B7P8kUQ8D0#BAT&x)i<_1R%>i(IQy zwpRwryefV)-xcsqz}vJ1a8$z5{4CotIl(0McDZn6o6}p+f@Qz5Sxc=ZL7(ncF!QX& zEFFdwXmVv33?98;e3<2-zbKf6qzk%Qe29Ht?JM9>{?X3J1-_lEgzR}*{y>6)gk3V2 z>`-TN_r%TQ(UA|AZdUOZMZ-2FU41dGjR;$I2>fmvOT~`&4-(C`-HaHM_p|woKZij2 zDoX6bsl5#KQ%-L|ACkSv zYB62I^M*hhLY1J)XOMdaJCX78DrrOM4r|BcUtxeEx4oXJ(no#m+e=ZP*B9`y-M6rA z`aEOX?*Ketk~Cn_?|a|689lCkX+%VBO7_DzK&C6Ksu5u;-1BE?UBJDyE2!DzOrUb< z7?fr}4IKKC^v?1-8Fxf)x&M5zTGAl)E$Qv!CkEeylZ&4QMyu3a0nfdGd{_ug6?iw| z09_jBInLQ{q1fS9({#Y+A^J{}H#m(s5tdH+;m=cHlotXUJ;ne+Ns)H`Y@x;6jtZ-BN@|{M7{bV zefA-Y3~I=`FWW?$cIe8FZn*CqGKYvyPXn_+*wS$U>FV-yi>lQt96O^A0+k5soSGi~ z{8LjQe19uJJ&=tJ$ptcC!;kK1dVmoZ!89aYMq!nxfGwL6$&Ifr4evo(7&4EvZ44YH z6{CyBoqHfU%1_3rhaEUiiroG1M$^Ml5Z~Spa|$=l|C_R9e49gvC(j#DW%aAqNA=+q zHjzc?l@VDeL}Ei0KktkLUTd>u_G*k(4wCM5TybJ|<%W&$x@G&>*9S141m7hlD@nJM zmYXF1XA#TE0gu(2HhxRbdl)natO^8wY`a^~DxzX*=ozW%`|~ux2hEPE&w8p>N7{Ix z9lyW30TUI@uWZ%DQxc?<*yNO~TEw6IqBmM?z2)MFN_`kqf`rrxm=uwdAZjxBlQJ8% z0z^R4`M3T+W~=GWXO)FQV-$?aq~&A}E(5f7scASMDvN{l?TrC1H%8(Q%B|Y3x^qF3 z4~UTzr`VM~Z!v1V#{e$H7AtlH`$y?F)HzbQJvC5fbq8&k04b6z5oz`xc?udq7UQ#% zaut9SO^IS{G+RWP!NwK$nq1hw{G~n|Qw?0zLY;k(E4Io&(vf!iXEl^AUvvn)*G8uQ z8i|7(^7g#y_Z%b}yRFnr@#?GqEgSun&E>ravBdzY_?E5u1iMWi%yd@86{lal(@lRN208xhpO zE$*1CdT(d+;aer$KeRoV)G>lJ{dj#c#0nZBVH0W+Biv8~bG$k=ChyMPM9oR|V}w*t z_`~R^B{*mzY1z~dd`C-FVKPoK&N&LCM*bd1#?@B)hI=GBXr8b@w=6|v5u+Juc6>%N zs2UvcDuddyl`c!43^PGR=j~N6LHh~P2%jVPvuV(t#w4Zz;Chm9>Q}y&d(frET7S^> z<}#;dfNk2GdAX{{>^^;y?iR@Nash}2r2O5Y*7_j#mGEDxZqD36mx|QLjOkD+6{jA< z$;17lXxg!hdyCg>$?cS$Je8bdV4UwxRZKX^#|~rP^4fYjJq%!xycsymnNba$K2kDY zjW6V`4=uX2UN1)-n1egCzP|{{P7DcW6JClTp zn16j8#RJ}Y5y16+ZxR#lU(KT!@Fd8HK2m<&ldH=&2;IJHZIvwE??IsD_ILYaRZ}o^ zEI_1v?nwOd#H+ikAW{5(yN^1zcz!7xciDXJGkmn)dZwS=IS{_DjG>G+NbBxb%|_*` zr63<%w6G5ALgH?bm=ohQt>X@V#OC>=PoO@_3SxdAJb-)yFx9hOBrz{NA<$!0cY8oz>O;lLLO2m3NXBxq>GoU-Mzmck*e$q#v)@_Wl zIsQIpngdBKjS#yMZNheuEmFj}@Pqdeh>f_CQ;5Z$0QbWE=QeOJC`5m1h7Cr)dK)bJ z%4+h5AW>7wejGR^un1{Qy2mUEqNbJHFS|;4?m^lxn5kmcVP8yaexI?~UQhKw_bwt; zy}7fQz+st&m=>P)e=gGrS@PA9!rRxqdl<$5DrxI@>HNlQ69=BBt-a#R?fiH-9FCDy zZvcI0c?UC^!dBY3qaF)FIW7`0A%b$lqp7fhy!V-*LBIeVC9qeS1P!#|`XC+lib0LW z%y!UO{Em*ifiasoB{QslGgT{XhR*qxEUGx@sS^0J*?M~nzsrSmzEeYqVuqsN3sHYN zTOZbnzPDY|>zu5*yhE>g=E9r9h6Ype7#BKD_NG4A35K9w=ulHx1fO6_YZ#H z&oz;Tch-N0n=Gv%tqOWT=p~2k^fmv=mx1xMBza&rZUEa^zeATmkfdO=3xzQwAO9@l zfkz`q=O!-*XQ^5$J`J8!_-+*N@X^#S=N;QrsLmsmIaJlNMBP#uz{>P9Zty9J>xp6# zfyn8JaX8*S5f&5dNXe8XXlP7da|Bv|3zK)g)NGr{tTgDGe_)cc-gB5D4Ymveu>^ux zA>~Ve@H}w-mRZB&$oA4Kg`QQ}on;;%Zxf^K*`OO*Meqv1kL6D6RGC;nBH^P6-SkB@ z!R<^n_;%Iv3KP~i_gu9;9y*S5#!92Q%NE6(U-L$!DNQ@({zse2#;#z+F8MAihy!N3 z@n7fe!7iDV=aBcbqmbL$fP7~v#y+#q*!qbTD=0!ZZ(?Kaf!%` z=kJKU+&tLCsN=x0ckjxVtXxjXIv3Cu0-UCz@BwBiprYnI;(vZsVMg|IagiRxg%9(EefGlp%YK(juQlrm#UBA=Z&*|0u!j1`INtlO%gA@G5*8W+Q zpw}*jd>ET=HsI+k;*DDR_J<8>eub=7(&yr-*bhigKD^jCCtWsD10#R*w4u?1Nv_+z*e_$T$3`->~j}}uq`5S94+y}}+}ueoCYKW&eE!k6roQDR zii&*KtkW;Om~tsGaj@WX3#bw*vV{{HY&4)uXF_IGK6V9=dOh#+?{3|F?!I zo=F7kv$J*0hkXXUlq4KgId=wTGfj@mVkFVs3Bfk|t};;S3D)>&7ySI8x8kZ1wgNW| zr-N^?Ia!PavJ>~LY%q*-b}By4&i~9&!D9M)U}$iMom*@a)*Vv3xOdkTO^a$iJ9Q($ z#j_3YxCTo5T|xyN4m!OBYEi03*5;EyY7k}OwU5d|>#dQ)>{`oxpSd6t@vV$UjHrHgkiftQ-m+lcmgbbvlgJWc*KME9h z-JYr=#}cYT~Ek0xiI~f_PT^cA*{x7BV&gW#0;pp$NFC-JB)yR1|3tsKThlX za_@)&YD0tIoG$&h_n1ggcLTW5897J|xhHA=*xDp2PO0{|<>-MvKp;E$J9uH*)T+Ca z$nn#!-NLK*`1Xl^-reO8djKO9A+u3i!&qTyTcz6gBJrgZ z-e4Ut?+0DQizhSRK8;WWX_uKtuEsckMPy?-1_ryrN~Fg961&Q$``o;Z3|Tmq8k=G+ zR_j(mt`tO`~VY}HF4&OX>2$WeLTrlpICkIrA;zp3J?t7BJwG9(l9)Own zLOHaq_Dq=Z*9I4Tc*QfFT5oo~MvvuZU*FgieT8B=nh>GssW74+Q=>qQfgahBX9<5g zST{-9>SumK47|m@Yc&(`H4RZf9#^N#c@2}7QCeek)9}q$)N{S)pPiI&v`!mMOY6yh z@m59nG$8mXYUPgN;gW#7Xy9?*{lP&b;Gf2ww)js6XA~ZPat2qPiPTW`GvZ{O8%Rfm z1n~udqyvP(>?%dP^k@2P&;7X7n43dbuAF#@`b1`N$&wKoC|3wGPzO(yLyYj5ejct6 zu87KKDy(WK^QP54MqE~|?}M+icXdcO;@}gaAXF2GF&ie&;m?b`ibBQngTuqgJC!=8 z`=lTP3ymnp+_wNwBXR0Nq9;cgBNqaMT$aEYz)k&D4x9d3k1@o;P4mKOcA?hH40RaiCoU?GL7rB!K| zIi4wH!0FMgsalVFYQLqo)dNyG~e#s{mR`XM7jlFqZuPg)_VuZsw#p_~uBaH15 z3wCZnQZ?F3FR7V(72OEJBPs>d%C$d79iDoJV#x{(VPeZ*)*Gy`=j7uIDiWt=6u9r4 zycNoy?fuD-b*76aHO=tAqTw`-v`_OI{!XMwIJU025tN2>IxoPqkX*z%_|3NV$H=Kc z57Fg##TZ%^*P&}xt4w&xpcb_8bEi`)+Gsg>B2kA^?v!Lrv)78eq^14M-<`Ve4`GGh z#9tFrYBa)LxVi2CtATyq)++7Ud$_&v;DY021woz>|H42FtOnW}3mJ+g z=C?~dr}f4;gEEo3msPxv9!9ms@u?hUK#l5o+cUXVwKACvd`<@ctfl0HrM zn9{rY=)$~*&dn`5%FF1S*o1&3b(z+(Jxus;%=3bBZD1ry-oZo=uFtOmc?Qv{=pi)_UiNd_w~ypPp?Upk3~R^~w_1eHh7VvBg|&ARe2ttrcU5kVvA^Nuya$ZbBfapv zfA6%MY&EBATu&03V}S9isx0K>xamP*IN&kh)J<$Jlx=W4Cl2KAV4Njv0HkSw6Ua6{ zQqgBe)TFx`FdKDppQm%Ae$^nu7}1-Rb36%I@L;BZl(lp37|1K?j6nMq=`R~arIaJC z&?pin{IZl)->K-&-Es9YNH`azHNZ2@d9HmLdw~CTE{}%FakI4fqcY%bBIfPDoS)fC2hjm=tF+|MPvo34Z!6+z@iRy16HnI9CG8drtS23H_=M;3irNX+*M z5-{!@!rWa1ulo{Kvjur3Ic#tv#f`eyZmYWZ(M*>`zf;uFJ6TOeyMIEU-vUiV{A=m@ z7mlVA5AsG9<({T?_(1BuovT^eh=AP`F^G~{Ub>C=P3_IQU*p^ay?&U&+hqEe)0R)X zBbsssPwLRJqE>1n@Ma4BKQnh|K;C^3utoN4mGuai;Z$2_0_{}dxRId5nJoK%dOLEC zKb?NYf7VfkxYTYK6l&}d+2V%>+HvdwOQ|EtbD398@8^P!sZ-{&e|iswMuCohm>q^} z!ypwfNbWFX4b!h(9R2o>zqLaXGlT4(6zQ3|)SQu!`Sm*v*Ll z^&(nVpEOa?{z)B^Yi5*4MAv>#lbP}hVy`xB{=8JEJr0xHSXEG1<^99dXhg+^kKDC?osTpZ6=td0RV1@E$qBjzE-QnnF$fdt<$Fr*q=?**;|c)g$ZwDLKl%{bd6Xg%{v?U~=mZ)B+6 zd3erja;nDmzRCtf6sW4~T5X^pZ_h-rK%ZZJfhA??$#m`DpBM^S~Ja z<~HlnG37JtB;bwgS#wkYFXft}0O=O)9Tuw|%L;^5ipl+G3$M=+v)Vm!_d^wuy^}ur zeA3y&9qfXO-^INXbwlv5eU-E0?HZN`l+drBPm&2DecLvlG9M*nx z@>)r^V>3O9j2_j*hr7#<^VFWkY-Tg1Hd`^G*sr6SW_(ih=F<66=us)WxR+qbpMdfD zzdE)>m=#0cYg!j7iD>=sepC{*eO)a{o6@DoLMJ1+e?GLhF;@GudN?7Cli}!I-(jl2b#Hw zn#sNsRcn~*F>wzZIZ$n6S2;8LR%z}ljdBfmz3@{F@F#+yA!HM-wMeiRxhVH;YA2iYtj%7*Onts0Dfy zPi}SHAN7>Kb2E=Tj4mUPW}n_@f<}D?N^kd3y85A`jsX zv6bgpPgTKR!4C~u%=p+TJh(G(^ow-M_wgfg#56r$n@)XU{_HPxxAkb_7MB*eM+!eK zqk7drs*kRw>%Jqzq5pbGupHlfC45gnwYGcL#U`xlYzmRI7TQHqO}7CYd5F~2?c`lP zb<)eQ3p(hT;<(m7>fZ;9MGC8)K8i$|k$*Y+1)I+>U#r4Ha%{HmRnZTISgk%VBP!f! z=PxCB6-5LD5zL5-Fi0UBR_e#yAJeJd7W9AkAI&V!FixP0ruC-N>=%OfLy_6nH`wi( zjxW~hFl~yLjV)-Q0r)3dR$EH=GxPP_#Df}1lZ?VPucNGpI*CIIYWY%P7R9wYo45n$ zQ4GY^ej1}XoD%cD(Ox5l??K-gJYHFW=Rl;CkMZ#1^lDFbBg*kPQOabRL><5X-Y3s{ z0?@WjG~{>kyP1}@QutA2cg(hUq?KmM-wvJn3Hogs1oe4R6)iM1VfLr0{rsWJ{6GsI z4omp$;ks;wUZXM}v~Qu`rbQ6t+J;RM9TLkD?HjJ{QY^t@dFdkcHY9X{pz8$u$N%ex iIKWWN{}kpE>e!!sX35C90Ptg2L~>7+rHY>z`TrmDXPKe^ literal 0 HcmV?d00001 diff --git a/doc/LectureNotes/_build/jupyter_execute/chapter12.ipynb b/doc/LectureNotes/_build/jupyter_execute/chapter12.ipynb new file mode 100644 index 000000000..b8432d08a --- /dev/null +++ b/doc/LectureNotes/_build/jupyter_execute/chapter12.ipynb @@ -0,0 +1,1942 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "b1ad0b52", + "metadata": { + "editable": true + }, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "id": "9548423d", + "metadata": { + "editable": true + }, + "source": [ + "# Convolutional Neural Networks\n", + "\n", + "Convolutional neural networks (CNNs) were developed during the last\n", + "decade of the previous century, with a focus on character recognition\n", + "tasks. Nowadays, CNNs are a central element in the spectacular success\n", + "of deep learning methods. The success in for example image\n", + "classifications have made them a central tool for most machine\n", + "learning practitioners.\n", + "\n", + "CNNs are very similar to ordinary Neural Networks.\n", + "They are made up of neurons that have learnable weights and\n", + "biases. Each neuron receives some inputs, performs a dot product and\n", + "optionally follows it with a non-linearity. The whole network still\n", + "expresses a single differentiable score function: from the raw image\n", + "pixels on one end to class scores at the other. And they still have a\n", + "loss function (for example Softmax) on the last (fully-connected) layer\n", + "and all the tips/tricks we developed for learning regular Neural\n", + "Networks still apply (back propagation, gradient descent etc etc).\n", + "\n", + "**CNN architectures make the explicit assumption that\n", + "the inputs are images, which allows us to encode certain properties\n", + "into the architecture. These then make the forward function more\n", + "efficient to implement and vastly reduce the amount of parameters in\n", + "the network.**\n", + "\n", + "Here we provide only a superficial overview, for the more interested, we recommend highly the course\n", + "[IN5400 – Machine Learning for Image Analysis](https://www.uio.no/studier/emner/matnat/ifi/IN5400/index-eng.html)\n", + "and the slides of [CS231](http://cs231n.github.io/convolutional-networks/).\n", + "\n", + "Another good read is the article here ." + ] + }, + { + "cell_type": "markdown", + "id": "315b8308", + "metadata": { + "editable": true + }, + "source": [ + "## Neural Networks vs CNNs\n", + "\n", + "Neural networks are defined as **affine transformations**, that is \n", + "a vector is received as input and is multiplied with a matrix of so-called weights (our unknown paramters) to produce an\n", + "output (to which a bias vector is usually added before passing the result\n", + "through a nonlinear activation function). This is applicable to any type of input, be it an\n", + "image, a sound clip or an unordered collection of features: whatever their\n", + "dimensionality, their representation can always be flattened into a vector\n", + "before the transformation.\n", + "\n", + "However, when we consider images, sound clips and many other similar kinds of data, these data have an intrinsic\n", + "structure. More formally, they share these important properties:\n", + "* They are stored as multi-dimensional arrays (think of the pixels of a figure) .\n", + "\n", + "* They feature one or more axes for which ordering matters (e.g., width and height axes for an image, time axis for a sound clip).\n", + "\n", + "* One axis, called the channel axis, is used to access different views of the data (e.g., the red, green and blue channels of a color image, or the left and right channels of a stereo audio track).\n", + "\n", + "These properties are not exploited when an affine transformation is applied; in\n", + "fact, all the axes are treated in the same way and the topological information\n", + "is not taken into account. Still, taking advantage of the implicit structure of\n", + "the data may prove very handy in solving some tasks, like computer vision and\n", + "speech recognition, and in these cases it would be best to preserve it. This is\n", + "where discrete convolutions come into play.\n", + "\n", + "A discrete convolution is a linear transformation that preserves this notion of\n", + "ordering. It is sparse (only a few input units contribute to a given output\n", + "unit) and reuses parameters (the same weights are applied to multiple locations\n", + "in the input).\n", + "\n", + "As an example, consider\n", + "an image of size $32\\times 32\\times 3$ (32 wide, 32 high, 3 color channels), so a\n", + "single fully-connected neuron in a first hidden layer of a regular\n", + "Neural Network would have $32\\times 32\\times 3 = 3072$ weights. This amount still\n", + "seems manageable, but clearly this fully-connected structure does not\n", + "scale to larger images. For example, an image of more respectable\n", + "size, say $200\\times 200\\times 3$, would lead to neurons that have \n", + "$200\\times 200\\times 3 = 120,000$ weights. \n", + "\n", + "We could have\n", + "several such neurons, and the parameters would add up quickly! Clearly,\n", + "this full connectivity is wasteful and the huge number of parameters\n", + "would quickly lead to possible overfitting.\n", + "\n", + "\n", + "\n", + "\n", + "