diff --git a/doc/pub/week37/ipynb/week37.ipynb b/doc/pub/week37/ipynb/week37.ipynb index 70763a9b5..827038481 100644 --- a/doc/pub/week37/ipynb/week37.ipynb +++ b/doc/pub/week37/ipynb/week37.ipynb @@ -3,9 +3,7 @@ { "cell_type": "markdown", "id": "53365fbb", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "\n", @@ -15,9 +13,7 @@ { "cell_type": "markdown", "id": "809960d9", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "# Week 37: Statistical interpretations and Resampling Methods\n", "**Morten Hjorth-Jensen**, Department of Physics, University of Oslo, Norway\n", @@ -30,9 +26,7 @@ { "cell_type": "markdown", "id": "0cac33e9", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Plans for week 37, lecture Monday\n", "\n", @@ -61,9 +55,7 @@ { "cell_type": "markdown", "id": "d5ba8d48", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Plans for week 37, lab sessions\n", "\n", @@ -83,9 +75,7 @@ { "cell_type": "markdown", "id": "560073ae", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Material for lecture Monday September 9" ] @@ -93,9 +83,7 @@ { "cell_type": "markdown", "id": "58ff8482", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Deriving OLS from a probability distribution\n", "\n", @@ -116,9 +104,7 @@ { "cell_type": "markdown", "id": "c9ed29f5", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "y_i\\sim \\mathcal{N}(\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta}, \\sigma^2)=\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}.\n", @@ -128,9 +114,7 @@ { "cell_type": "markdown", "id": "f3e177df", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Independent and Identically Distrubuted (iid)\n", "\n", @@ -141,9 +125,7 @@ { "cell_type": "markdown", "id": "943d3101", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(y_i, \\boldsymbol{X}\\vert\\boldsymbol{\\beta})=\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]},\n", @@ -153,9 +135,7 @@ { "cell_type": "markdown", "id": "bddef09d", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "which reads as finding the likelihood of an event $y_i$ with the input variables $\\boldsymbol{X}$ given the parameters (to be determined) $\\boldsymbol{\\beta}$.\n", "\n", @@ -165,9 +145,7 @@ { "cell_type": "markdown", "id": "8d119a52", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(\\boldsymbol{y},\\boldsymbol{X}\\vert\\boldsymbol{\\beta})=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}=\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\beta}).\n", @@ -177,9 +155,7 @@ { "cell_type": "markdown", "id": "b67e829d", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "We will write this in a more compact form reserving $\\boldsymbol{D}$ for the domain of events, including the ouputs (targets) and the inputs. That is\n", "in case we have a simple one-dimensional input and output case" @@ -188,9 +164,7 @@ { "cell_type": "markdown", "id": "3a76ed1c", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{D}=[(x_0,y_0), (x_1,y_1),\\dots, (x_{n-1},y_{n-1})].\n", @@ -200,9 +174,7 @@ { "cell_type": "markdown", "id": "58863d67", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "In the more general case the various inputs should be replaced by the possible features represented by the input data set $\\boldsymbol{X}$. \n", "We can now rewrite the above probability as" @@ -211,9 +183,7 @@ { "cell_type": "markdown", "id": "f3c19d2c", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(\\boldsymbol{D}\\vert\\boldsymbol{\\beta})=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}.\n", @@ -223,9 +193,7 @@ { "cell_type": "markdown", "id": "fe7606c4", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "It is a conditional probability (see below) and reads as the likelihood of a domain of events $\\boldsymbol{D}$ given a set of parameters $\\boldsymbol{\\beta}$." ] @@ -233,9 +201,7 @@ { "cell_type": "markdown", "id": "e1d5e31c", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Maximum Likelihood Estimation (MLE)\n", "\n", @@ -264,9 +230,7 @@ { "cell_type": "markdown", "id": "097eb026", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## A new Cost Function\n", "\n", @@ -276,9 +240,7 @@ { "cell_type": "markdown", "id": "46e9c4fd", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "C(\\boldsymbol{\\beta}=-\\log{\\prod_{i=0}^{n-1}p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\beta})}=-\\sum_{i=0}^{n-1}\\log{p(y_i,\\boldsymbol{X}\\vert\\boldsymbol{\\beta})},\n", @@ -288,9 +250,7 @@ { "cell_type": "markdown", "id": "20ca4ccb", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "which becomes" ] @@ -298,9 +258,7 @@ { "cell_type": "markdown", "id": "651adbb5", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "C(\\boldsymbol{\\beta}=\\frac{n}{2}\\log{2\\pi\\sigma^2}+\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}.\n", @@ -310,9 +268,7 @@ { "cell_type": "markdown", "id": "a0d30507", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "Taking the derivative of the *new* cost function with respect to the parameters $\\beta$ we recognize our familiar OLS equation, namely" ] @@ -320,9 +276,7 @@ { "cell_type": "markdown", "id": "f3269fe5", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{X}^T\\left(\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta}\\right) =0,\n", @@ -332,9 +286,7 @@ { "cell_type": "markdown", "id": "f7096467", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "which leads to the well-known OLS equation for the optimal paramters $\\beta$" ] @@ -342,9 +294,7 @@ { "cell_type": "markdown", "id": "e35c1080", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\hat{\\boldsymbol{\\beta}}^{\\mathrm{OLS}}=\\left(\\boldsymbol{X}^T\\boldsymbol{X}\\right)^{-1}\\boldsymbol{X}^T\\boldsymbol{y}!\n", @@ -354,9 +304,7 @@ { "cell_type": "markdown", "id": "6392c0ea", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "Before we make a similar analysis for Ridge and Lasso regression, we need a short reminder on statistics." ] @@ -364,9 +312,7 @@ { "cell_type": "markdown", "id": "ac50371f", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## More basic Statistics and Bayes' theorem\n", "\n", @@ -384,9 +330,7 @@ { "cell_type": "markdown", "id": "b73c9d79", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(X \\cup Y)= p(X)+p(Y)-p(X \\cap Y).\n", @@ -396,9 +340,7 @@ { "cell_type": "markdown", "id": "ab4c6470", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "**The product rule (aka joint probability) is given by.**" ] @@ -406,9 +348,7 @@ { "cell_type": "markdown", "id": "08a17057", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(X \\cup Y)= p(X,Y)= p(X\\vert Y)p(Y)=p(Y\\vert X)p(X),\n", @@ -418,9 +358,7 @@ { "cell_type": "markdown", "id": "248c56c1", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "where we read $p(X\\vert Y)$ as the likelihood of obtaining $X$ given $Y$.\n", "\n", @@ -430,9 +368,7 @@ { "cell_type": "markdown", "id": "7d49c8f2", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Marginal Probability\n", "\n", @@ -442,9 +378,7 @@ { "cell_type": "markdown", "id": "8b7ebd86", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(X)=\\sum_{i=0}^{n-1}p(X,Y=y_i)=\\sum_{i=0}^{n-1}p(X\\vert Y=y_i)p(Y=y_i)=\\sum_{i=0}^{n-1}p(X\\vert y_i)p(y_i).\n", @@ -454,9 +388,7 @@ { "cell_type": "markdown", "id": "ec8cf10c", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Conditional Probability\n", "\n", @@ -466,9 +398,7 @@ { "cell_type": "markdown", "id": "7572b3bd", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(X\\vert Y)= \\frac{p(X,Y)}{p(Y)}=\\frac{p(X,Y)}{\\sum_{i=0}^{n-1}p(Y\\vert X=x_i)p(x_i)}.\n", @@ -478,9 +408,7 @@ { "cell_type": "markdown", "id": "93806e54", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Bayes' Theorem\n", "\n", @@ -490,9 +418,7 @@ { "cell_type": "markdown", "id": "3a541b25", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(X\\vert Y)= \\frac{p(X,Y)}{p(Y)},\n", @@ -502,9 +428,7 @@ { "cell_type": "markdown", "id": "3ad6731a", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "which we can rewrite as" ] @@ -512,9 +436,7 @@ { "cell_type": "markdown", "id": "0b97ba97", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(X\\vert Y)= \\frac{p(X,Y)}{\\sum_{i=0}^{n-1}p(Y\\vert X=x_i)p(x_i)}=\\frac{p(Y\\vert X)p(X)}{\\sum_{i=0}^{n-1}p(Y\\vert X=x_i)p(x_i)},\n", @@ -524,9 +446,7 @@ { "cell_type": "markdown", "id": "f96a2bd1", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "which is Bayes' theorem. It allows us to evaluate the uncertainty in in $X$ after we have observed $Y$. We can easily interchange $X$ with $Y$." ] @@ -534,9 +454,7 @@ { "cell_type": "markdown", "id": "90c7d471", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Interpretations of Bayes' Theorem\n", "\n", @@ -553,9 +471,7 @@ { "cell_type": "markdown", "id": "2f5cdb57", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Example of Usage of Bayes' theorem\n", "\n", @@ -574,9 +490,7 @@ { "cell_type": "markdown", "id": "55d2bfb6", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(X=1\\vert Y=1) =0.8.\n", @@ -586,9 +500,7 @@ { "cell_type": "markdown", "id": "2a1ea166", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "This obviously sounds scary since many would conclude that if the test is positive, there is a likelihood of $80\\%$ for having cancer.\n", "It is however not correct, as the following Bayesian analysis shows." @@ -597,9 +509,7 @@ { "cell_type": "markdown", "id": "3a4cea04", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Doing it correctly\n", "\n", @@ -610,9 +520,7 @@ { "cell_type": "markdown", "id": "848763b6", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(Y=1) =0.004.\n", @@ -622,9 +530,7 @@ { "cell_type": "markdown", "id": "cb8668ac", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "We need also to account for the fact that the test may produce a false positive result (false alarm). Let us here assume that we have" ] @@ -632,9 +538,7 @@ { "cell_type": "markdown", "id": "196d47ff", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(X=1\\vert Y=0) =0.1.\n", @@ -644,9 +548,7 @@ { "cell_type": "markdown", "id": "38c54891", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "Using Bayes' theorem we can then find the posterior probability that the person has breast cancer in case of a positive test, that is we can compute" ] @@ -654,9 +556,7 @@ { "cell_type": "markdown", "id": "5fb29180", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(Y=1\\vert X=1)=\\frac{p(X=1\\vert Y=1)p(Y=1)}{p(X=1\\vert Y=1)p(Y=1)+p(X=1\\vert Y=0)p(Y=0)}=\\frac{0.8\\times 0.004}{0.8\\times 0.004+0.1\\times 0.996}=0.031.\n", @@ -666,9 +566,7 @@ { "cell_type": "markdown", "id": "bd303a51", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "That is, in case of a positive test, there is only a $3\\%$ chance of having breast cancer!" ] @@ -676,9 +574,7 @@ { "cell_type": "markdown", "id": "3bee4680", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Bayes' Theorem and Ridge and Lasso Regression\n", "\n", @@ -690,9 +586,7 @@ { "cell_type": "markdown", "id": "0c46bb57", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{D}=[(x_0,y_0), (x_1,y_1),\\dots, (x_{n-1},y_{n-1})],\n", @@ -702,9 +596,7 @@ { "cell_type": "markdown", "id": "32f47be0", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "is given by" ] @@ -712,9 +604,7 @@ { "cell_type": "markdown", "id": "fd925a78", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(\\boldsymbol{D}\\vert\\boldsymbol{\\beta})=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}.\n", @@ -724,9 +614,7 @@ { "cell_type": "markdown", "id": "006647eb", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "In Bayes' theorem this function plays the role of the so-called likelihood. We could now ask the question what is the posterior probability of a parameter set $\\boldsymbol{\\beta}$ given a domain of events $\\boldsymbol{D}$? That is, how can we define the posterior probability" ] @@ -734,9 +622,7 @@ { "cell_type": "markdown", "id": "1d2ac696", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(\\boldsymbol{\\beta}\\vert\\boldsymbol{D}).\n", @@ -746,9 +632,7 @@ { "cell_type": "markdown", "id": "9e1f59a5", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "Bayes' theorem comes to our rescue here since (omitting the normalization constant)" ] @@ -756,9 +640,7 @@ { "cell_type": "markdown", "id": "a8fe3b56", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(\\boldsymbol{\\beta}\\vert\\boldsymbol{D})\\propto p(\\boldsymbol{D}\\vert\\boldsymbol{\\beta})p(\\boldsymbol{\\beta}).\n", @@ -768,9 +650,7 @@ { "cell_type": "markdown", "id": "85db28a7", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "We have a model for $p(\\boldsymbol{D}\\vert\\boldsymbol{\\beta})$ but need one for the **prior** $p(\\boldsymbol{\\beta})$!" ] @@ -778,9 +658,7 @@ { "cell_type": "markdown", "id": "e6b6b507", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Ridge and Bayes\n", "\n", @@ -794,9 +672,7 @@ { "cell_type": "markdown", "id": "00f26321", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(\\boldsymbol{\\beta})=\\prod_{j=0}^{p-1}\\exp{\\left(-\\frac{\\beta_j^2}{2\\tau^2}\\right)}.\n", @@ -806,9 +682,7 @@ { "cell_type": "markdown", "id": "868f5e5a", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "Our posterior probability becomes then (omitting the normalization factor which is just a constant)" ] @@ -816,9 +690,7 @@ { "cell_type": "markdown", "id": "4e29d1a9", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(\\boldsymbol{\\beta\\vert\\boldsymbol{D})}=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}\\prod_{j=0}^{p-1}\\exp{\\left(-\\frac{\\beta_j^2}{2\\tau^2}\\right)}.\n", @@ -828,9 +700,7 @@ { "cell_type": "markdown", "id": "8d1ea123", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "We can now optimize this quantity with respect to $\\boldsymbol{\\beta}$. As we\n", "did for OLS, this is most conveniently done by taking the negative\n", @@ -841,9 +711,7 @@ { "cell_type": "markdown", "id": "ee32ea7d", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "C(\\boldsymbol{\\beta})=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\frac{1}{2\\tau^2}\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_2^2,\n", @@ -853,9 +721,7 @@ { "cell_type": "markdown", "id": "e05c6359", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "and replacing $1/2\\tau^2$ with $\\lambda$ we have" ] @@ -863,9 +729,7 @@ { "cell_type": "markdown", "id": "b2ffe0c0", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "C(\\boldsymbol{\\beta})=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\lambda\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_2^2,\n", @@ -875,9 +739,7 @@ { "cell_type": "markdown", "id": "7fccf482", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "which is our Ridge cost function! Nice, isn't it?" ] @@ -885,9 +747,7 @@ { "cell_type": "markdown", "id": "00a435ee", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Lasso and Bayes\n", "\n", @@ -897,9 +757,7 @@ { "cell_type": "markdown", "id": "6ed0d41e", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(\\boldsymbol{\\beta})=\\prod_{j=0}^{p-1}\\exp{\\left(-\\frac{\\vert\\beta_j\\vert}{\\tau}\\right)}.\n", @@ -909,9 +767,7 @@ { "cell_type": "markdown", "id": "2c7c149d", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "Our posterior probability becomes then (omitting the normalization factor which is just a constant)" ] @@ -919,9 +775,7 @@ { "cell_type": "markdown", "id": "77f01008", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "p(\\boldsymbol{\\beta}\\vert\\boldsymbol{D})=\\prod_{i=0}^{n-1}\\frac{1}{\\sqrt{2\\pi\\sigma^2}}\\exp{\\left[-\\frac{(y_i-\\boldsymbol{X}_{i,*}\\boldsymbol{\\beta})^2}{2\\sigma^2}\\right]}\\prod_{j=0}^{p-1}\\exp{\\left(-\\frac{\\vert\\beta_j\\vert}{\\tau}\\right)}.\n", @@ -931,9 +785,7 @@ { "cell_type": "markdown", "id": "793671d5", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "Taking the negative\n", "logarithm of the posterior probability and leaving out the\n", @@ -943,9 +795,7 @@ { "cell_type": "markdown", "id": "4e57ea79", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "C(\\boldsymbol{\\beta})=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\frac{1}{\\tau}\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_1,\n", @@ -955,9 +805,7 @@ { "cell_type": "markdown", "id": "12f8f838", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "and replacing $1/\\tau$ with $\\lambda$ we have" ] @@ -965,9 +813,7 @@ { "cell_type": "markdown", "id": "9cc2459b", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "C(\\boldsymbol{\\beta})=\\frac{\\vert\\vert (\\boldsymbol{y}-\\boldsymbol{X}\\boldsymbol{\\beta})\\vert\\vert_2^2}{2\\sigma^2}+\\lambda\\vert\\vert\\boldsymbol{\\beta}\\vert\\vert_1,\n", @@ -977,9 +823,7 @@ { "cell_type": "markdown", "id": "6c040408", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "which is our Lasso cost function!" ] @@ -987,9 +831,7 @@ { "cell_type": "markdown", "id": "86c5648e", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Why resampling methods\n", "\n", @@ -1006,9 +848,7 @@ { "cell_type": "markdown", "id": "ef10be44", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Resampling methods\n", "Resampling methods are an indispensable tool in modern\n", @@ -1034,9 +874,7 @@ { "cell_type": "markdown", "id": "f1c760d9", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Resampling approaches can be computationally expensive\n", "\n", @@ -1060,9 +898,7 @@ { "cell_type": "markdown", "id": "7cab5213", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Why resampling methods ?\n", "**Statistical analysis.**\n", @@ -1077,9 +913,7 @@ { "cell_type": "markdown", "id": "abd16598", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Statistical analysis\n", "\n", @@ -1097,9 +931,7 @@ { "cell_type": "markdown", "id": "dc17b500", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Resampling methods\n", "\n", @@ -1126,9 +958,7 @@ { "cell_type": "markdown", "id": "ac9620af", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Resampling methods: Bootstrap\n", "Bootstrapping is a [non-parametric approach](https://en.wikipedia.org/wiki/Nonparametric_statistics) to statistical inference\n", @@ -1151,9 +981,7 @@ { "cell_type": "markdown", "id": "b8ddd5cf", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## The Central Limit Theorem\n", "\n", @@ -1171,9 +999,7 @@ { "cell_type": "markdown", "id": "465046b4", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "z=\\frac{x_1+x_2+\\dots+x_m}{m},\n", @@ -1183,9 +1009,7 @@ { "cell_type": "markdown", "id": "c7370cfe", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "the question we pose is which is the PDF of the new variable $z$." ] @@ -1193,9 +1017,7 @@ { "cell_type": "markdown", "id": "b20b0422", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Finding the Limit\n", "\n", @@ -1208,9 +1030,7 @@ { "cell_type": "markdown", "id": "cbcf72bb", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\tilde{p}(z)=\\int dx_1p(x_1)\\int dx_2p(x_2)\\dots\\int dx_mp(x_m)\n", @@ -1221,9 +1041,7 @@ { "cell_type": "markdown", "id": "61c187d3", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "where the $\\delta$-function enbodies the constraint that the mean is $z$.\n", "All measurements that lead to each individual $x_i$ are expected to\n", @@ -1234,9 +1052,7 @@ { "cell_type": "markdown", "id": "67ac3e7e", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Rewriting the $\\delta$-function\n", "\n", @@ -1246,9 +1062,7 @@ { "cell_type": "markdown", "id": "8aff1a0f", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\delta(z-\\frac{x_1+x_2+\\dots+x_m}{m})=\\frac{1}{2\\pi}\\int_{-\\infty}^{\\infty}\n", @@ -1259,9 +1073,7 @@ { "cell_type": "markdown", "id": "0f67bf9e", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "and inserting $e^{i\\mu q-i\\mu q}$ where $\\mu$ is the mean value\n", "we arrive at" @@ -1270,9 +1082,7 @@ { "cell_type": "markdown", "id": "0462459a", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\tilde{p}(z)=\\frac{1}{2\\pi}\\int_{-\\infty}^{\\infty}\n", @@ -1284,9 +1094,7 @@ { "cell_type": "markdown", "id": "81bef4b0", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "with the integral over $x$ resulting in" ] @@ -1294,9 +1102,7 @@ { "cell_type": "markdown", "id": "fa89dce4", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\int_{-\\infty}^{\\infty}dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}=\n", @@ -1308,9 +1114,7 @@ { "cell_type": "markdown", "id": "9967e011", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Identifying Terms\n", "\n", @@ -1321,9 +1125,7 @@ { "cell_type": "markdown", "id": "d5bb8edf", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\int_{-\\infty}^{\\infty}dxp(x)e^{\\left(iq(\\mu-x)/m\\right)}=\n", @@ -1334,9 +1136,7 @@ { "cell_type": "markdown", "id": "99cce110", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "resulting in" ] @@ -1344,9 +1144,7 @@ { "cell_type": "markdown", "id": "d6daa176", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\left[\\int_{-\\infty}^{\\infty}dxp(x)\\exp{\\left(iq(\\mu-x)/m\\right)}\\right]^m\\approx\n", @@ -1357,9 +1155,7 @@ { "cell_type": "markdown", "id": "9f2c47a4", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "and in the limit $m\\rightarrow \\infty$ we obtain" ] @@ -1367,9 +1163,7 @@ { "cell_type": "markdown", "id": "fed9dff9", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\tilde{p}(z)=\\frac{1}{\\sqrt{2\\pi}(\\sigma/\\sqrt{m})}\n", @@ -1380,9 +1174,7 @@ { "cell_type": "markdown", "id": "ec9e1b49", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "which is the normal distribution with variance\n", "$\\sigma^2_m=\\sigma^2/m$, where $\\sigma$ is the variance of the PDF $p(x)$\n", @@ -1392,9 +1184,7 @@ { "cell_type": "markdown", "id": "1b2affcf", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Wrapping it up\n", "\n", @@ -1411,9 +1201,7 @@ { "cell_type": "markdown", "id": "5aeac1b9", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\sigma_m=\n", @@ -1424,9 +1212,7 @@ { "cell_type": "markdown", "id": "ea0b2510", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "The latter is true only if the average value is known exactly. This is obtained in the limit\n", "$m\\rightarrow \\infty$ only. Because the mean and the variance are measured quantities we obtain \n", @@ -1436,9 +1222,7 @@ { "cell_type": "markdown", "id": "08f2490e", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\sigma_m\\approx \n", @@ -1449,9 +1233,7 @@ { "cell_type": "markdown", "id": "7fc63b37", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "In many cases however the above estimate for the standard deviation,\n", "in particular if correlations are strong, may be too simplistic. Keep\n", @@ -1469,9 +1251,7 @@ { "cell_type": "markdown", "id": "73764f86", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Confidence Intervals\n", "\n", @@ -1492,9 +1272,7 @@ { "cell_type": "markdown", "id": "28bc2214", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Standard Approach based on the Normal Distribution\n", "\n", @@ -1507,9 +1285,7 @@ { "cell_type": "markdown", "id": "6f066b73", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\left(\\mu_{\\beta}\\pm \\frac{z\\sigma_{\\beta}}{\\sqrt{n}}\\right),\n", @@ -1519,9 +1295,7 @@ { "cell_type": "markdown", "id": "8d8212d1", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "where $z$ defines the level of certainty (or confidence). For a normal\n", "distribution typical parameters are $z=2.576$ which corresponds to a\n", @@ -1539,9 +1313,7 @@ { "cell_type": "markdown", "id": "f21712ad", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Resampling methods: Bootstrap background\n", "\n", @@ -1559,9 +1331,7 @@ { "cell_type": "markdown", "id": "370f65c8", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Resampling methods: More Bootstrap background\n", "\n", @@ -1583,9 +1353,7 @@ { "cell_type": "markdown", "id": "e8f5ddca", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Resampling methods: Bootstrap approach\n", "\n", @@ -1604,9 +1372,7 @@ { "cell_type": "markdown", "id": "fedb9fdb", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Resampling methods: Bootstrap steps\n", "\n", @@ -1634,9 +1400,7 @@ { "cell_type": "markdown", "id": "177746a6", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Code example for the Bootstrap method\n", "\n", @@ -1658,10 +1422,7 @@ "cell_type": "code", "execution_count": 1, "id": "c1874811", - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "%matplotlib inline\n", @@ -1697,9 +1458,7 @@ { "cell_type": "markdown", "id": "6dad6de5", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "We see that our new variance and from that the standard deviation, agrees with the central limit theorem." ] @@ -1707,9 +1466,7 @@ { "cell_type": "markdown", "id": "0342164e", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Plotting the Histogram" ] @@ -1718,10 +1475,7 @@ "cell_type": "code", "execution_count": 2, "id": "0c0490cc", - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "# the histogram of the bootstrapped data (normalized data if density = True)\n", @@ -1738,9 +1492,7 @@ { "cell_type": "markdown", "id": "0adf2510", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## The bias-variance tradeoff\n", "\n", @@ -1756,9 +1508,7 @@ { "cell_type": "markdown", "id": "df226e05", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{y}=f(\\boldsymbol{x}) + \\boldsymbol{\\epsilon}\n", @@ -1768,9 +1518,7 @@ { "cell_type": "markdown", "id": "1c89ed73", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "where $\\epsilon$ is normally distributed with mean zero and standard deviation $\\sigma^2$.\n", "\n", @@ -1785,9 +1533,7 @@ { "cell_type": "markdown", "id": "615aae51", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "C(\\boldsymbol{X},\\boldsymbol{\\beta}) =\\frac{1}{n}\\sum_{i=0}^{n-1}(y_i-\\tilde{y}_i)^2=\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right].\n", @@ -1797,9 +1543,7 @@ { "cell_type": "markdown", "id": "09df2f76", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "We can rewrite this as" ] @@ -1807,9 +1551,7 @@ { "cell_type": "markdown", "id": "bc115459", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\frac{1}{n}\\sum_i(f_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2+\\frac{1}{n}\\sum_i(\\tilde{y}_i-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2+\\sigma^2.\n", @@ -1819,9 +1561,7 @@ { "cell_type": "markdown", "id": "a897d31c", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "The three terms represent the square of the bias of the learning\n", "method, which can be thought of as the error caused by the simplifying\n", @@ -1836,9 +1576,7 @@ { "cell_type": "markdown", "id": "f35ccec2", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{f}+\\boldsymbol{\\epsilon}-\\boldsymbol{\\tilde{y}})^2\\right],\n", @@ -1848,9 +1586,7 @@ { "cell_type": "markdown", "id": "f78963d0", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "and adding and subtracting $\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]$ we get" ] @@ -1858,9 +1594,7 @@ { "cell_type": "markdown", "id": "5da42dc1", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{f}+\\boldsymbol{\\epsilon}-\\boldsymbol{\\tilde{y}}+\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right]-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2\\right],\n", @@ -1870,9 +1604,7 @@ { "cell_type": "markdown", "id": "681e6f51", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "which, using the abovementioned expectation values can be rewritten as" ] @@ -1880,9 +1612,7 @@ { "cell_type": "markdown", "id": "0cfeef23", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\mathbb{E}\\left[(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2\\right]=\\mathbb{E}\\left[(\\boldsymbol{y}-\\mathbb{E}\\left[\\boldsymbol{\\tilde{y}}\\right])^2\\right]+\\mathrm{Var}\\left[\\boldsymbol{\\tilde{y}}\\right]+\\sigma^2,\n", @@ -1892,9 +1622,7 @@ { "cell_type": "markdown", "id": "543454fe", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "that is the rewriting in terms of the so-called bias, the variance of the model $\\boldsymbol{\\tilde{y}}$ and the variance of $\\boldsymbol{\\epsilon}$." ] @@ -1902,9 +1630,7 @@ { "cell_type": "markdown", "id": "9b876527", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## A way to Read the Bias-Variance Tradeoff\n", "\n", @@ -1918,9 +1644,7 @@ { "cell_type": "markdown", "id": "3c700f4e", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Example code for Bias-Variance tradeoff" ] @@ -1929,10 +1653,7 @@ "cell_type": "code", "execution_count": 3, "id": "99d2acd5", - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", @@ -1994,9 +1715,7 @@ { "cell_type": "markdown", "id": "b41ce01c", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Understanding what happens" ] @@ -2005,10 +1724,7 @@ "cell_type": "code", "execution_count": 4, "id": "7c40879d", - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", @@ -2046,7 +1762,7 @@ " error[degree] = np.mean( np.mean((y_test - y_pred)**2, axis=1, keepdims=True) )\n", " bias[degree] = np.mean( (y_test - np.mean(y_pred, axis=1, keepdims=True))**2 )\n", " variance[degree] = np.mean( np.var(y_pred, axis=1, keepdims=True) )\n", - " print('Polynomial degree:', degree)\n", + "# print('Polynomial degree:', degree)\n", " print('Error:', error[degree])\n", " print('Bias^2:', bias[degree])\n", " print('Var:', variance[degree])\n", @@ -2062,9 +1778,7 @@ { "cell_type": "markdown", "id": "494b741b", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Summing up\n", "\n", @@ -2100,9 +1814,7 @@ { "cell_type": "markdown", "id": "68d67d77", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Another Example from Scikit-Learn's Repository\n", "\n", @@ -2127,11 +1839,19 @@ "cell_type": "code", "execution_count": 5, "id": "0b42fc93", - "metadata": { - "collapsed": false, - "editable": true - }, - "outputs": [], + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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lFi1aZJ599lljsVjM66+/nm4/V56fMcb06NHDdO3aNVdj7d+/v2nbtm22jh0wYIDx9fXN8DO2bt06l8/1xBNPmPLlyxvAvP322+keO3bsmClRooSpXLmymThxolm4cKEZM2aMCQgIMA0bNjSpqanZij87EhISTL169UyFChXMN998Y+bPn2+6d+9uPDw80n3mMMaYfv36GavVap577jmzYMECM23aNNO4cWPj4eFh/v7773T7tm3b1vTv3z/fnocrVJA5n1QHDx5sfH19MyTRvn37mmbNmpm6deumS9xfffWVAczChQszPe/FP7iOa/z777958hyyIzk52TRs2NCMGDHCtG7dOssfzJ966inj6emZ7oNZTEyMKVmypLnjjjuc26Kiogxgnn/++XTHL1++/LJJMLtSUlJMuXLlzM0335xu+7fffmsAM3v2bOe2tLQ0k5aWZowx5vjx41f8hT45OdmEh4ebZ5999qoxtG7d2gwYMCBL8Xbp0sX07t07S/teTnZfv6NHj2bY9u+//xrAvPrqq+m2R0ZG5vqbUmby6vUzxph69eqZIUOG5EncUngp77uWNzJz+vRp4+npafr16+fcFh0dbZKSkjLs+9BDDxnA7Nu3L9vXu5QreSOzvHf27FlTpkwZ0759+3TbC3Lev9jEiRMNYL744our7lvY37ddef2MUd4v7opbfr84LsfnOVcKMi1atDCRkZHpzpOWlmZq1apl6tevf9XjP/74YwNkWtzOjpdeeslERkZecZ+NGzcai8Vi3njjjXTbhwwZYnx9fc3Jkyed21x5fps3bzaAmTt37lXjzOr3OSkpyYSEhJgPP/zwqvtmZsCAAcbf3z9bx17s77//Nl5eXmbatGmZFmQ+//xzA5g//vgj3fY33njDAGbNmjU5jsGYrL1vfvTRRwYwy5cvd25LTk42derUMddff71zW0JCgrHZbBkKr4cOHTKAGTFiRLrt06dPNzabLVc/i+SWYj9lyeHuu+8G7EOzHWJiYpgxYwaDBg3KsL9j+Fa5cuUyPZ/VWrC/taNHjyY6OprXX3/dpeN++ukn2rVrR2RkpHNbUFAQvXr14tdffyUlJQUAT09PAIKDg9MdHxISAoCPj0+67VFRUfTp04fSpUvj7e1N7dq1+eijj7IU08qVKzl8+DD33ntvuu233347AQEB6YaIO4b6ZcUvv/zCwYMH6devX5b2z4ozZ87wxx9/cNttt+XoPNl9/UqXLp1hW+PGjbHZbOzfvz/b8RTE1w+gX79+TJkyhbNnz2b5GCk+lPezLzAwEB8fHzw8PJzbQkNDnbn/Ytdffz1gH1p/sfzKG5nlvYCAAOrUqZMh7xXkvH+xL7/8koCAAO68886r7lvY37ddef1AeV/sikt+z2lcnp6eBAQEpDuPxWIhKCgow//5zJQqVQog3XsB5Cw/XM3MmTMxxmTIH/feey/nzp1j7ty5zm2uPL9PPvmEsmXL0qFDh1yJE+xTZWJiYujZs2eundNVSUlJDBo0iIceeojrrrsu031czf9//PEH7du3JygoCD8/P1q0aJHplKLs+Omnn6hZsybNmjVzbvPw8KBv3778888/zmlHVqsVq9WaIeagoCCsVmuGmG+55RYCAgL4/PPPcyXO3FQws4sbBAUF0bt3b7766ivntqlTp2K1WjP9wOP4Ienfvz8zZ87M0vy61NRUUlJS0t2yMq8+LS0tw3GZ3bI6R3/z5s289tprfPLJJwQEBGTpGLDPPdy5cyf169fP8Fj9+vU5d+4cu3btAiAyMpLu3bvz3nvvsWjRImJjY9m6dSsjRoygYsWK3HXXXeniadKkCRs3bmTMmDHMmjWLrl27MmLECF5++eWrxrVx40ZnDBfz9PSkVq1azsdd9dtvv1G6dGnq1KmTreMz8+uvv2KxWOjatWu2z5Hd1+9ylixZQmpqKnXr1s3w2NKlSwkMDMTT05M6deowZsyYDD9nBfX1A3vvhbi4OLf265CCS3nfNampqSQnJ7Nnzx6GDRuGMYaHHnroqsctXLgQDw8PatSokS4ed+aNmJgY1qxZkyHvFdS8f7GoqCj+/PNP7rrrrqu+lkX1fftyrx8o74tdccrvOfHwww+zZcsWXn/9dY4fP86JEyd45513WL16NU8++WSmx6SkpBAXF8dff/3FCy+8QMuWLWnRooXz8Zzmh6vZuHEjpUqVomzZsum2O/LJxfnDlef322+/0apVq1wtvs2YMYNmzZpRvnz5bJ/j3LlzlC1bFpvNRoUKFRg+fDjR0dFZPv6VV14hLi6OV1999bL79OjRg4oVK/LEE0+wadMmYmNjWbp0KaNHj+aWW26hdu3azn2/+eYbbr75ZoKCgpg0aRI//PADYWFhdOzYMVeKMhs3brzsexbg7Gnm6enJgw8+yKRJk5g5cyZnzpxhz549DBkyhODgYIYMGZLueC8vL5o3b85vv/2W4xhznbuH6LjbxcMOHfNKN27caIwxpkmTJmbgwIHGGJNhaKMxxrzyyivGy8vLAAYwlStXNg888IBZv359ptfI7Gaz2a4a40svvXTZ4y++XW2InzH2oY1NmzY1d999t3NbVoeuHzx40ADmf//7X4bHpkyZkmF4WVJSkhkyZEi6GOvXr292796d7tiOHTuaChUqZBhWOnz4cOPj42Oio6OvGNfrr79uAHP48OEMj918882mRo0amR53tSkvtWvXNp06dcqwPS0tzSQnJ6e7tWrVyvTv3z/D9kv16NHD3HLLLVd8PleSk9cvM2fOnDG1a9c2ERER5uzZs+kee/DBB81XX31llixZYmbOnGnuueceA2QYGlhQXz9j7D+DFovFPPPMM1eMQYoX5f3s5Y2aNWs6r1uuXDmzbNmyqx4zb948Y7VazWOPPZZuu7vyhsM999xjPDw8zKpVq9JtL4h5/1LPPPOMAcyKFSuuum9Re992uNzr53gOyvvFV3HL7xfLzpQlY4yZOXOmCQ4Odl7X19fXfPPNN5nuu2LFinQxdunSxZw5cybdPq7kh0vz5wsvvGAiIyMzbHdMVzfGmA4dOpiaNWtmGp+Xl5e5//77XX5+R48eNYAZPXp0hnOmpqZmiAcwX375ZbptKSkp6Y5LSUkxJUuWNGPGjMk01qx49913zbvvvmvmz59v5s+fb5577jnj5+dnatWqleFze2bWrl1rPD09ndOwdu/enemUJWPsU32aNWuW7vW9/fbbTUJCgnOfuLg4ExYWluE9LTU11TRo0CDdlKLsvm96enqaoUOHZojPMX12ypQp6a7x4osvGqvV6oy5YsWKZu3atZl+P5577jljtVpztUdcbkg/vqyYa926NVWrVuWrr75i4MCB/Pvvv4wZM+ay+7/wwgvcf//9zJ49m7///pvly5czfvx4vvjiC77++mvncEmHr7/+Ol2FEcjS9Iv777+fbt26XXU/b2/vq+7z7rvvEhUVxS+//HLVfS/nSjFf/NiwYcP46aefeO+997j22ms5cuQIb7/9Nu3atWPRokVERkaSkJDAggULGDZsGH5+fs6h0wBdunThww8/ZOXKlXTu3JnU1FSMMc7HHUPVrhaXK1NcLnbo0CGaNGmSYfuSJUto27Zthu1Lly7l66+/Trdt9+7dVKpUCYC4uDjmzZvHJ5984nw8LS2NtLS0dLHabLbLxpQbr59DQkICvXr1Yu/evSxcuDDDX1ovHVravXt3QkND+fDDD3n88cdp1KhRgX79wF49DwkJKbhd1cXtlPezbsaMGcTFxbFv3z7Gjx9P586d+eWXXzKsVOKwZs0a7rjjDm644Qb+97//Obe7O2+88MILfPvtt4wbN47GjRune6wg5v2LpaSkMGnSJOrWrcsNN9yQpWMc18jKY4XhfftKrx8o78sFxSG/59TcuXPp27cvt99+O3fccQceHh788ssvDBw4kKSkpAzTgq655hr+/fdf4uPjWbduHaNHj6ZDhw4sXLgQPz8/l/IDkOk018y2T5gwgYEDBzq/zmpOy+rzO3ToEJD5FMlXXnkl05E99913H/fdd5/z68jISPbs2eP8esmSJZw4cYJevXo5t10tJ17qscceS/d1hw4daNSoEb179+bzzz/P8PjFUlJSGDRoEHfeeScdO3a87H4Ap06donv37sTHx/Ptt98SERHBxo0befXVV7n11lv57bff8PDwYPny5URHRzNgwIB0ry1Ap06deOutt4iLi8Pf3z/b75uQ9df39ddf55133mHUqFHceOONnDlzhg8//JAOHTowf/58GjVqlO7Y0qVLk5aWxpEjR6hateoVvyf5yq3loALg0sZcr732mildurR58MEH0/2FJrNKemaWLFli/Pz8TKlSpS57DVdlVpnN7HZpZfZSe/fuNb6+vub99983p06dct5atGhhateubU6dOnXFFSDi4+ONxWIxTz31VIbHPvzwQwOYbdu2GWOMmTNnjgHMtGnT0u136tQpExwc7PwLxYEDB676F4Kvv/7aGGNvMnvxdsfIiPHjxxvAbNq0KUNc1113nWnWrFmmz+dqIywyq7IbYx9V8u+//6a7XXvttaZbt24Ztl/cdf777783Hh4e6f4yMGDAgHTP6Uo/Yzl9/S6WkJBgOnXqZHx8fDI08LqSlStXGsB8/PHHxpiC/fo5lCtXztx2221Zfo5S9CnvZy9vXCw5OdnUq1fvsk0f16xZY8LCwsx1111nTp8+ne4xd+aNUaNGGSDDShwOBS3vX+rnn382gHnvvfeytH9Re9++2uvnoLxffBWn/H4pV0fIpKWlmXLlypkuXbpkeKx///7G39//qiMJHJ8LHU2/XckPjpgvvg0ZMsSUK1cuw/YTJ044j7nrrrvSvR4OsbGxBjAjR450+fllNvrC4eDBgxniceSzi7dt2LAh3XHDhg0zjRs3TrftcjnRFampqcbf3z9dU/bMvP322yY4ONhERUU53/vXr19vwL6Qx6lTp5w/Y88884zx9PQ0hw4dSneOhQsXGsBMnDjRGHNhdbwr3RxNc7P7vlm2bFlz++23Z3g+s2bNMoCZN2+eMcbehNlisWQY7ZOUlGSqVatm2rRpk+Ecn376qQHMf//9d7Vvc77SCJlLDBw4kBdffJHx48dnq/Fhq1atuPnmm5k5cybHjh3LtNLqqstVZi91aWX2Urt27eLcuXM88sgjPPLIIxkeDw0N5ZFHHmHs2LGZHu/r60u1atX477//Mjz233//4evrS5UqVQBYt24dQIa/NIaEhFCtWjXn/M7Q0FBsNhv9+vW7bC+CypUrA/Z5+ImJic7tjvmY11xzjTOGi+f9p6SksHXr1gx/0ciqkiVLZjpHMzAwMENTrMDAQEqUKHHZZllg/+tyu3btCA0NdW4bNWoUw4cPT3eey8np6+eQmJhIjx49WLRoET///DPt27e/4v4XM+er+o5qfkF+/RxOnTpFyZIlc3QOKdqU96+eNy7l4eHBtddeyw8//JDhsbVr13LTTTcRGRnJ/PnzMzTcc1feePnllxk1ahSjRo3i//7v/zK9bkHL+5f68ssv8fLyynLT4aL0vp2V189BeV8cinJ+z6mjR49y+PBhhg4dmuGxJk2a8PXXX7Nnz55MezU5XHfddVitVrZv3w64lh8cx19s1qxZeHl5XTGvXnPNNXz33XccOXIkXR8ZR56rV6+ey8/PkS8yy//ly5fPtAdMpUqVLhtnWloaP/30EyNGjEi3/XI50VXGmKv2utm4cSMxMTFUr149w2MvvPACL7zwAmvXrqVhw4asW7eO8PDwDE2tHe8Hjvzv+D6NGzfusqM0y5QpA2T/ffOaa6657HsWXHh9169fjzEmw3uWp6cnDRo0YMmSJRnO4Xh9C9r7gwoylwgPD+epp55i69atDBgw4LL7HT16lFKlSmX4z5CamkpUVBR+fn7OztQ5lVtDGxs2bMiiRYsybH/00UeJiYlhwoQJVKhQ4Yrn6NmzJ2PHjmX//v1EREQAcPbsWX788UduvfVWZ5d1R4JZuXJlupUdTp48yfbt251FAD8/P9q2bcvatWupX78+Xl5el7224wPcpZo2bUq5cuWYOHFiukZt06dPJzY2Nt1QQVfUqlWLnTt3ZuvYSyUkJDB79uwMQ2UrVaqUbojeleTG65eYmEjPnj1ZuHAhP/7441WHMF7KMcTQkYQL8usH9iGoCQkJudqgU4oe5f0r543MJCQksHLlSqpVq5Zu+7p167jpppuoUKECv//+e7pChIM78sarr77KqFGjeP7553nppZcue72ClvcvduTIEWbPnk2vXr0oUaJElo8rCu/bWX39QHlf0ivK+T2nQkND8fHxYeXKlRkeW7FiBVar9bKrTjksWbKEtLQ053uBK/khu7p3787zzz/PpEmTeOaZZ5zbJ06ciK+vL506dQJce36RkZH4+vrmWv5fvnw5R44cybC63uVyoiumT59OfHz8VaetPvvss+mmeYH9feTuu+/mgQce4M4773S+buXLl2fBggUcPHiQ8PBw5/4rVqwAcH5OaNGiBSEhIWzevDndHxZyU8+ePXnwwQf5+++/adq0KWAv1n/zzTc0bdrU+V518XtW69atnccnJiayZs2aTD/b7Nq1ixIlSjiLRgWFCjKZGD169FX3mTx5Mp9++il9+vShSZMmBAcHc+DAAb744gs2bdrEiy++mCEJbdy4McN8O4CqVas6l43LzOUqs64KCQnJdK5/SEgIKSkpGR5r3749S5YsSRfzk08+yeTJk+natSuvvPIK3t7ejB49moSEBEaNGuXcr1evXrz44osMGzaMAwcOcO2113L48GHefvtt4uPj0/2l9v3336dly5bceOONDBs2jEqVKnH27Fl27NjBr7/+ysKFC6/4vGw2G2+99Rb9+vVj6NCh3H333URFRfH000/ToUMHZ2J2mDNnDnFxcc4lMTdv3sz06dMB+/xWPz8/wL5SwyuvvEJ8fLxzW3bNnTuX+Ph4evToke1z5Mbr17t3b+bMmcNzzz1HiRIl0r1JBQUFOT/ATpkyhR9//JGuXbsSGRnJ6dOnmTZtGt999x0DBw6kQYMGzuMK6usHOJ9fZnNYRS6mvG+XWd5o3rw5t956K7Vr1yY4OJg9e/bwySefsHPnznTLE2/bto2bbroJsM/rjoqKIioqyvn4xc85P/PGmDFjePHFF+nUqRNdu3bN8OH84g+1BS3vX2zSpEmkpKQwePDgy+5TFN+3XXn9QHlfMiqq+d3B8RnIsWLaqlWrnH0Be/fu7dzv0vzg7e3Ngw8+yLvvvkv//v258847sdlszJw5kylTpnDfffcRFhYG2EeufP7559x6661ERkaSnJzMqlWrGDt2LNWqVUuXl3KaH66mbt263Hfffbz00kvYbDaaNGnC/Pnz+eyzz3jttdecMbvy/Ly8vGjWrFmmxZvsmD59OvXq1Uu3uqCr9u7dS58+fbjrrruoVq0aFouFJUuWMHbsWOrWrZvhvcDDw4PWrVs7VzqqVasWtWrVSrePY8RV1apV073/P/TQQ3z77bd06NCBZ5991tlD5rXXXqNMmTLcc889AAQEBDBu3DgGDBhAdHQ0vXv3pnTp0hw/fpz169dz/PjxdD3TsmPQoEF89NFH3H777YwePZrSpUvz8ccfs23bNv744w/nfi1btqRJkyaMGjWK+Ph4WrVqRUxMDOPGjWP37t1Mnjw5w7kdxZuc9KfME26eMuV2WZ0Heulc082bN5snnnjCXHfddaZUqVLGw8PDhIaGmtatW5vJkydneo3L3T7//PO8eGpZdrnVNlq3bm0y+xHZsWOH6dGjhwkKCjJ+fn6mffv2ZvXq1Rn2O3z4sBk+fLipVq2a8fHxMeXLlzddu3bNdGWI3bt3m0GDBpnw8HDj6elpSpUqZZo3b25ee+21LD+PKVOmmPr16xsvLy9TtmxZM2LEiEw7kF86f/Pi28UrSezYscNYLBbzww8/XPXarVu3NgMGDLjs43379nWpT4ArXHn9rvRzeHF8K1asMO3btzdly5Y1np6exs/PzzRp0sR8/PHHJjU1NcO1CuLrZ4wx/fr1M9dcc02WY5DiQXnftbzxxBNPmAYNGpjg4GDj4eFhypYta3r27Gn++uuvdPtd7Tlf2tcgv/KG4zld7naxgpz3a9SoYSpVqpRutZHMYipq79uuvH7GKO8Xd8Uxv2f1/0dm+SE1NdV8/vnn5rrrrjMhISEmKCjINGrUyHz44YcmKSnJud+WLVtM7969TWRkpPHx8TE+Pj6mVq1a5qmnnjInT57MEFN288NLL72UpdWlkpKSzEsvvWQqVqxovLy8TI0aNcwHH3yQYb+sPj9jjPnyyy+NzWbL0EclM5m9p10sIiIiW/1hLhYdHW169uxpKlWqZHx9fY2Xl5epXr26efrppzP0ZnPEdLX3nCutsrRmzRrTs2dPU6FCBePt7W2qVKliBg8e7OwJc7ElS5aYrl27mrCwMOPp6WnCw8NN165dM/Qgu9TV3jcdjhw5Yvr372/CwsKMj4+PueGGG8zvv/+eYb/Tp0+b5557ztSuXdv4+fmZ0qVLmzZt2pjZs2dn2HfHjh0GMDNmzLjq9fObxZiLWj2LSDq33HILKSkpzJkzJ9vnSEpKonTp0rz66qs8/PDDuRidXMmZM2coX7487733HkOGDHF3OCJSSCjvF17K+yKSXQkJCVSsWJEnnngi3VQoV/3zzz80bdqUDRs25MoUJckdL7zwAl9//TU7d+50TtUtKFSQEbmCjRs30qhRI5YvX57pUqhScL388st8//33bNiwocAlXhEpuJT3Cy/lfRHJiU8++YRRo0axa9cu/P393R2O5JLTp09TpUoVxo0b55x+VZDo3UrkCurVq8eECRM4cuSIu0MRFwUFBTFx4kR9KBcRlyjvF17K+yKSE/fffz+nT59m165dGt1ShOzevZuRI0fSp08fd4eSKY2QERERERERERHJZ1dewFxERERERERERHKdCjIiIiIiIiIiIvnMLZNs09LSOHToEIGBgQVvHXARkTxijOHs2bOUL18eq7V41cOV90WkuFLuV+4XkeInq7nfLQWZQ4cOERER4Y5Li4i43f79+6lQoYK7w8hXyvsiUtwp94uIFD9Xy/1uKcgEBgYC9uCCgoLcEYKISL47c+YMERERzhxYnCjvi0hxpdyfMfd/umQn4xbu4LZrw3m5ez13hScikmeymvvdUpBxDFkMCgrSB3MRKXaK47Bt5X0RKe6U+y/kfr+AQKzefnj5Bug9QUSKtKvl/uI1kVVERERERAoEg3F3CCIibqWCjIiIiIiI5BvHH4yN6jEiUsypICMiIiIiIvnGgr0io3qMiBR3bukhI1IYpaamkpyc7O4wpADz9PTEZrO5OwwRyUXK/XI1yv2u0wgZKeiU++Vqciv3qyAjchXGGI4cOcLp06fdHYoUAiEhIZQtW7ZYNm8UKUqU+8UVyv2ucXyX1ENGChrlfnFFbuR+FWRErsKRlEuXLo2fn58+bEmmjDHEx8dz7NgxAMqVK+fmiEQkJ5T7JSuU+7PHcqEiI1KgKPdLVuRm7ldBRuQKUlNTnUm5RIkS7g5HCjhfX18Ajh07RunSpTWEXaSQUu4XVyj3u049ZKQgUu4XV+RW7ldTX5ErcMwd9fPzc3MkUlg4flY071ik8FLuF1cp97vmQg8ZlWSk4FDuF1flRu5XQUYkCzRcUbJKPysiRYf+P0tW6Wcle1SOkYJI/58lq3LjZ0UFGRERERERyTeOX2I0QEZEijsVZEQkWxYvXozFYnGpC32lSpUYO3ZsnsUkIiJ5S7lfcoN6+ooULsr9eUcFGZEiauDAgVgsFh544IEMjz344INYLBYGDhyY/4GJiEieUe6XwkA9ZERyl3J/4aWCjEgRFhERwXfffce5c+ec2xISEpg6dSoVK1Z0Y2QiIpJXlPuloNMIGZHcp9xfOKkgI1KEXXvttVSsWJEff/zRue3HH38kIiKCRo0aObclJiYyYsQISpcujY+PDy1btuTff/9Nd67Zs2dTo0YNfH19adu2LXv27MlwveXLl9OqVSt8fX2JiIhgxIgRxMXF5dnzExGRjJT7paBzNsJURUYk1yj3F04qyIi4yBhDfFJKvt+yO6z33nvvZcKECc6vv/rqKwYNGpRun6effpoZM2YwadIk1qxZQ7Vq1ejYsSPR0dEA7N+/n169etGlSxfWrVvH4MGDefbZZ9Od47///qNjx4706tWLDRs28P3337Ns2TKGDx+erbhFRAoKd+V95X4pqrSIjRQGyv3K/fnBw90BiBQ255JTqfPivHy/7uZXOuLn5fp/2X79+jFy5Ej27NmDxWLhr7/+4rvvvmPx4sUAxMXF8cknnzBx4kQ6d+4MwOeff87vv//Ol19+yVNPPcUnn3xClSpVeO+997BYLNSsWZP//vuPN99803mdt99+mz59+vDoo48CUL16dT744ANat27NJ598go+PT46/ByIi7uCuvA/K/VK0GQ2RkQJMuV+5Pz+oICNSxJUsWZKuXbsyadIkjDF07dqVkiVLOh/fuXMnycnJtGjRwrnN09OT66+/ni1btgCwZcsWbrjhhgtDjIFmzZqlu87q1avZsWMH3377rXObMYa0tDR2795N7dq18+opiojIJZT7pSBz9pBRPUYkVyn3Fz4qyIi4yNfTxuZXOrrlutk1aNAg5xDCjz76KN1jjiGRlkvGDxtjnNuyMmwyLS2NoUOHMmLEiAyPqZGYiBRm7sr7jmtnl3K/FFjOnzE3xyFyBcr9l6fcn3tUkBFxkcViydYQQnfq1KkTSUlJAHTsmP6NpVq1anh5ebFs2TL69OkDQHJyMqtWrXIOQ6xTpw4zZ85Md9zKlSvTfX3ttdeyadMmqlWrljdPQkTETQpj3gflfim4LqyypIqMFFzK/Rco9+cdNfUVKQZsNhtbtmxhy5Yt2GzpK+7+/v4MGzaMp556irlz57J582aGDBlCfHw89913HwAPPPAAO3fu5PHHH2fbtm1MmTKFiRMnpjvPM888w4oVK3jooYdYt24dUVFR/PLLLzz88MP59TRFROQiyv1SUDkXWVI9RiTXKfcXLirIiBQTQUFBBAUFZfrY6NGjue222+jXrx/XXnstO3bsYN68eYSGhgL2oYczZszg119/pUGDBowfP5433ngj3Tnq16/PkiVLiIqK4sYbb6RRo0a88MILlCtXLs+fm4iIZE65Xwoiy/kxMqrHiOQN5f7Cw2Kyu6ZWDpw5c4bg4GBiYmIu+4MiUhAkJCSwe/duKleurG7hkiVX+pkpzrmvOD93KXyU+8VVyv2Zu9xzn/rPPkb++B831S7DFwOuc2OEIhco94urciP3a4SMiIiIiIjkmwvtRDVGRkSKNxVkREREREQk36iHjIiInQoyIiIiIiKSb9RDRkTETgUZERERERHJP84RMirJiEjxpoKMiIiIiIjkG0cPGZVjRKS4U0FGRERERETyjeV8ExkNkBGR4k4FGRERERERyTcaISMiYqeCjIiIiIiI5BuLesiIiAAqyIiIiIiISD5yFGRERIo7FWREJM8YY7j//vsJCwvDYrGwbt06t8WyZ88et8cgIlIcKPfL1TiXvdYAGZEiQ7k/e1SQESliLBbLFW8DBw7Mt1jmzp3LxIkTmTVrFocPH6ZevXr5ct2BAwfSo0ePdNsiIiLyNQYRkfyk3K/cX5hohIxI7lDuL/y538PdAYhI7jp8+LDz/vfff8+LL77Itm3bnNt8fX3T7Z+cnIynp2eexLJz507KlStH8+bN8+T8rrDZbJQtW9bdYYiI5Anl/swp9xdsRm19RXJEuT9zhSn3a4SMSBFTtmxZ5y04OBiLxeL8OiEhgZCQEH744QfatGmDj48P33zzDaNGjaJhw4bpzjN27FgqVaqUbtuECROoXbs2Pj4+1KpVi48//viycQwcOJCHH36Yffv2YbFYnOeqVKkSY8eOTbdvw4YNGTVqlPNri8XCF198Qc+ePfHz86N69er88ssv6Y7ZtGkTXbt2JSgoiMDAQG688UZ27tzJqFGjmDRpEj///LPzrwOLFy/OdOjikiVLuP766/H29qZcuXI8++yzpKSkOB9v06YNI0aM4OmnnyYsLIyyZcumi1NEpKBQ7lfuL4w0ZUkkZ5T7C3/uV0FGxFXGQFJc/t9y8VPLM888w4gRI9iyZQsdO3bM0jGff/45zz33HK+//jpbtmzhjTfe4IUXXmDSpEmZ7v/+++/zyiuvUKFCBQ4fPsy///7rUowvv/wyd9xxBxs2bKBLly7cc889REdHA3Dw4EFatWqFj48PCxcuZPXq1QwaNIiUlBSefPJJ7rjjDjp16sThw4c5fPhwppX6gwcP0qVLF5o0acL69ev55JNP+PLLL3nttdfS7Tdp0iT8/f35+++/eeutt3jllVf4/fffXXouIlLIuSvvK/cr9xdRFot6yEghoNyv3J8PuV9TlkRclRwPb5TP/+v+3yHw8s+VUz366KP06tXLpWNeffVVxowZ4zyucuXKbN68mU8//ZQBAwZk2D84OJjAwMBsDxkcOHAgd999NwBvvPEG48aN459//qFTp0589NFHBAcH89133zmHXdaoUcN5rK+vL4mJiVe87scff0xERAQffvghFouFWrVqcejQIZ555hlefPFFrFZ7vbp+/fq89NJLAFSvXp0PP/yQBQsW0KFDB5efk4gUUu7K+6Dcr9xfJDlayGjKkhRoyv3K/fmQ+1WQESmGrrvuOpf2P378OPv37+e+++5jyJAhzu0pKSkEBwfndniAPSE6+Pv7ExgYyLFjxwBYt24dN954Y47mwG7ZsoVmzZo5/0oH0KJFC2JjYzlw4AAVK1bMEAdAuXLlnHGIiBQmyv3K/QWF49tf1EfIHDubwLKoE1QrHUD9CiHuDkeKKeX+gp37VZARcZWnn71q7Y7r5hJ///QVd6vVirnkU1FycrLzflpaGmAfvti0adN0+9lsNpeufbVrOVyadC0WizOOSxuUZYcxJl1SdmxzXCsrcYhIMeGuvO+4di5R7lfuLyicy167OY68YIxh8sq9zFx7kLX7T2MMBHh78Nez7Qj2zZtmqpJHlPuV+/Mh96sgI+IqiyXXhhAWFKVKleLIkSPpktXFTbDKlClDeHg4u3bt4p577snxtS7uCH/mzBl2797t0jnq16/PpEmTLtsp3svLi9TU1Cueo06dOsyYMSPdc16+fDmBgYGEh4e7FI+IFHFFMO+Dcr9yv/tYLsxZKnJ+WLWfF3/e5Pzax9NKbGIK3/2zj6Gtq7oxMnGZcr9yfz5QU18RoU2bNhw/fpy33nqLnTt38tFHHzFnzpx0+4waNYr//e9/vP/++2zfvp3//vuPCRMm8O6777p0rXbt2jF58mT+/PNPNm7cyIABA1yutg8fPpwzZ85w1113sWrVKqKiopg8ebJzmb9KlSqxYcMGtm3bxokTJzKtxD/44IPs37+fhx9+mK1bt/Lzzz/z0ksv8fjjjzvnkYqIFGXK/cr97lKUe8hMW3UAgD5NK7JyZHte6V4PgInL95CcqlFW4n7K/QUr9+udR0SoXbs2H3/8MR999BENGjTgn3/+4cknn0y3z+DBg/niiy+YOHEi11xzDa1bt2bixIlUrlzZpWuNHDmSVq1a0a1bN7p06UKPHj2oWtW1vxiVKFGChQsXEhsbS+vWrWncuDGff/65s2o+ZMgQatasyXXXXUepUqX466+/MpwjPDyc2bNn888//9CgQQMeeOAB7rvvPp5//nmXYhERKayU+5X73aWo9pDZezKOVXtPYbXAI+2rUzbYh+4Ny1MywJvDMQnM/u/w1U8ikseU+wtW7reYSyd15YMzZ84QHBxMTEwMQUFB+X15kSxLSEhg9+7dVK5cGR8fH3eHI4XAlX5minPuK87PXQof5X5xlXJ/5i733OduPMID36ymcWQoM4ZlXKK2sBr7x3bG/hHFjdVLMvm+C703xi2IYszv26kXHsSvw1tm6GUhBYNyv7gqN3K/RsiIiIiIiEi+uTBCpugMkTHG8NPagwD0bJS+J8U9N0Ti42ll48Ez/L072h3hiUgBpYKMiIiIiIjkm6LY03fNvtPsPRmPn5eNjnXLpnsszN+L266tAMAXf+5yR3giUkCpICMiIiIiIvnGMWWnCA2Q4ae19ma+neqWxd8740K2g1rae2/8seUYB0+fy9fYRKTgUkFGRERERETyTVEbIZOYksqv6+0Ne3tem/kSulVLBdCgQjAAq/Zo2pKI2KkgIyIiIiIi+cbZ07aIDJFZtPU4MeeSKRPkTfOqJS+7X6OKoQCs3Xc6nyITkYJOBRkREREREck3zqa+7g0j1/yx5SgAt9Qvj816+RWUGlUMAWDt/tP5EJWIFAYqyIiIiIiISL6xULSWfV53vsDSrGqJK+537fkRMpsPxZCQnJrXYYlIIaCCjIiIiIiI5LuiMGPpTEIyO4/HAtAgIuSK+1YI9aWEvxfJqYZNh87kQ3QiUtCpICMiIiIiIvnHOWWp8FdkNh6IwRh7saVkgPcV97VYLBemLe07lQ/RiUhBp4KMiOQ7i8XCzJkz3R2GiIjkI+V+cShKPX0d/WCuNjrGwdnYV31kpJhQ7r8yFWREiqhjx44xdOhQKlasiLe3N2XLlqVjx46sWLHC3aGJiEgeUe6XwsByvqtvUSjIrD9fWGlYISRL+zc6X7hZp5WWJBcp9xdeHu4OQETyxm233UZycjKTJk2iSpUqHD16lAULFhAdHe3u0EREJI8o90th4Bwh49Yocsf6A6cBaHh+KtLV1I8IwWKBg6fPcfRMAmWCfPIuOCk2lPsLL42QEckn27fDnDkQFZX31zp9+jTLli3jzTffpG3btkRGRnL99dczcuRIunbtCsC7777LNddcg7+/PxERETz44IPExsY6zzFx4kRCQkKYNWsWNWvWxM/Pj969exMXF8ekSZOoVKkSoaGhPPzww6SmXlgpoFKlSrz66qv06dOHgIAAypcvz7hx464Y78GDB7nzzjsJDQ2lRIkSdO/enT179jgfX7x4Mddffz3+/v6EhITQokUL9u7dm7vfNBGRPKDcf3nK/cWXc9nrQj5E5nDMOY6eScRmtVC3fFCWjgnw9qBmmUAA1mqUTJGl3H95yv3pqSAjkseio6FTZ0PNmtClC9SoYf/6VB72cgsICCAgIICZM2eSmJiY6T5Wq5UPPviAjRs3MmnSJBYuXMjTTz+dbp/4+Hg++OADvvvuO+bOncvixYvp1asXs2fPZvbs2UyePJnPPvuM6dOnpzvu7bffpn79+qxZs4aRI0fy2GOP8fvvv2caR3x8PG3btiUgIIClS5eybNkyAgIC6NSpE0lJSaSkpNCjRw9at27Nhg0bWLFiBffff79zuLOISEGk3K/cL5dXVJa9dkxXqlEmED+vrE88cDT2Xac+MkWOcr9yv8uMG8TExBjAxMTEuOPyIll27tw5s3nzZnPu3Llsn6NjpzTj6ZdkSnRbY8KH/WFKdFtjPP2STMdOabkYaUbTp083oaGhxsfHxzRv3tyMHDnSrF+//rL7//DDD6ZEiRLOrydMmGAAs2PHDue2oUOHGj8/P3P27Fnnto4dO5qhQ4c6v46MjDSdOnVKd+4777zTdO7c2fk1YH766SdjjDFffvmlqVmzpklLu/D9SExMNL6+vmbevHnm5MmTBjCLFy92/ZvgBlf6mSnOua84P3cpfJT7lftdpdyfucs992VRx03kM7PMze8ucVNkueN/s7eYyGdmmWdnbHDpuO//2Wcin5ll7hi/PI8ik+xQ7lfud1Vu5H6NkBHJQ9u3w7y5FoLabSSg7iE8ghIIqHuIoHabmDfXkqfDGG+77TYOHTrEL7/8QseOHVm8eDHXXnstEydOBGDRokV06NCB8PBwAgMD6d+/PydPniQuLs55Dj8/P6pWrer8ukyZMlSqVImAgIB0244dO5bu2s2aNcvw9ZYtWzKNc/Xq1ezYsYPAwEBnhT8sLIyEhAR27txJWFgYAwcOpGPHjtxyyy28//77HD58OKffHhGRPKPcf+Fr5X7JzIUeMoV7ytK6/fZhDw0jgl06zjFCZsOBGFJS03I7LHET5f4LXyv3Z50KMiJ5aOdO+78+EekbavlEnARgx468vb6Pjw8dOnTgxRdfZPny5QwcOJCXXnqJvXv30qVLF+rVq8eMGTNYvXo1H330EQDJycnO4z09PdOdz2KxZLotLe3qHyYuN9QwLS2Nxo0bs27dunS37du306dPHwAmTJjAihUraN68Od9//z01atRg5cqVLn0vRETyi3J/+v0yo9xfzDl7yLg3jJxITTP8dyAGyPqS1w5VSwUQ6O3BueRUth09mwfRiTso96ffLzPK/RmpICOShxxF5oT9Yem2J+wvAUC1avkbT506dYiLi2PVqlWkpKQwZswYbrjhBmrUqMGhQ4dy7TqXJs2VK1dSq1atTPe99tpriYqKonTp0lSrVi3dLTj4wl+cGjVqxMiRI1m+fDn16tVjypQpuRaviEhuUu6/8LVyv2TG0UOmENdj2Hk8lrikVPy8bFQvHejSsVarxVnEWb8/Jg+iE3dQ7r/wtXJ/1qkgI5KHatSAjp0MZxbWI3ZTOClnfIjdFM6ZhXXp2MlQvXreXPfkyZO0a9eOb775hg0bNrB7926mTZvGW2+9Rffu3alatSopKSmMGzeOXbt2MXnyZMaPH59r1//rr79466232L59Ox999BHTpk3jkUceyXTfe+65h5IlS9K9e3f+/PNPdu/ezZIlS3jkkUc4cOAAu3fvZuTIkaxYsYK9e/cyf/58tm/fTu3atXMtXhGR3KTcr9wvV1YUVllad36FpGvCg7FZXW84WuP8Sks7j8deZU8pLJT7lfuzI+vtwEUkW6ZOsXB3Hw/mzWro3Naxk2HqlLzrFh4QEEDTpk1577332LlzJ8nJyURERDBkyBD+7//+D19fX959913efPNNRo4cSatWrfjf//5H//79c+X6TzzxBKtXr+bll18mMDCQMWPG0LFjx0z39fPzY+nSpTzzzDP06tWLs2fPEh4eTvv27QkKCuLcuXNs3bqVSZMmcfLkScqVK8fw4cMZOnRorsQqIpIXlPuV++XyLvSQKbzWHTgNQEMXpys5VCnlD8AuFWSKFOV+5X5XWYwbStNnzpwhODiYmJgYgoKC8vvyIlmWkJDA7t27qVy5Mj4+Pjk6V1SUfe5otWrkWYW8IKhUqRKPPvoojz76qLtDcYsr/cwU59xXnJ+7FD7K/a5T7lfuz8zlnvs/u6O549MVVCnpz8In27gvwBzoNu5PNh48w8f3XEuXa8q5fPyKnSe5+/OVVAzzY+nTbfMgQnGVcr/rlPtznvs1QkYkn1SvXrQTsoiIZKTcL5KRc8qSe8PIttQ0Q9RR+8iWOuWyV2Sren6EzIFT8SQkp+Ljacu1+MT9lPslq9RDRkRERERE8o1zylIh7SGzLzqexJQ0vD2sRIT5ZescpQK9CfT2IM3A3pPxuRyhiBQWGiEjIrlqz5497g5BRETymXK/uKKwj5DZfn6p6uplArLV0BfsywJXKR3A+v2n2XU8lpplXVupSaQgUO7POY2QERERERGRfJR3DU7zw/Yj9oKMY6Wk7Kpa0j5tSSstiRRfKsiIiIiIiEi+K6Qzlth2NJcKMqUDANh1PC7HMYlI4aSCjEgWpKWluTsEKST0syJSdOj/s2SVflZcc2HKUuGsyDga+tbMYUGmikbIFEj6/yxZlRs/K+ohI3IFXl5eWK1WDh06RKlSpfDy8sJiKdzDbCVvGGNISkri+PHjWK1WvLy83B2SiGSTcr9klXJ/9lxo6uvWMLIlOTWNXSfsBZTqZQJydK6LR8gYY5Rn3Ey5X7IqN3O/CjIiV2C1WqlcuTKHDx/m0KFD7g5HCgE/Pz8qVqyI1aoBiCKFlXK/uEq53zWOX3ILY0Fmz4k4klMN/l42wkN8c3SuyBJ+WC1wNjGF42cTKR3kk0tRSnYo94urciP3qyAjchVeXl5UrFiRlJQUUlNT3R2OFGA2mw0PDw/9NUWkCFDul6xS7nddYf5OOfvHlA3M8Wvu7WEjIsyPvSfj2Xk8TgWZAkC5X7Iqt3K/CjIiWWCxWPD09MTT09PdoYiISD5R7hfJG84eMoVwiIxzhaXSubNMdZWS/ucLMrE0q1oiV84pOaPcL/lJ4ypFRERERCTfWM6PkSl85RjYfr6hb42yuVOQqVpKKy2JFGcqyIiIiIiISL65MELGvXFkx3bnktc5a+jrUOV8QUYrLYkUT0V+ytL27bBzJ1SrBtWruzsaERHJD8r9IiIFX24ve53XuT8hOZU9J+0jWXK65LVD1VJa+lqkOCuyI2Sio6FTZ0PNmtClC9SoYf/61Cl3RyYiInlFuV9EpODL7REy+ZX7dx6PJc1AiJ8npQK9c+WcjhEyB0+fIyFZTWRFipsiO0Kmzz2GhUtTKNFtIz4R0STsD2Phwnrc3ceDuXMKc293ERG5HOV+EZGCL7d7yORX7ndOVyqd8xWWHEoGeBHk48GZhBR2n4ijdrmgXDmviBQORXKEzPbtMG+uhaB2GwmoewiPoAQC6h4iqN0m5s21EBXl7ghFRCS3KfeLiBQOuTlCJj9z/4WGvrnTPwbsK/pUUWNfkWKrSBZkdu60/+sTEZ1uu0/ESQB27MjviEREJK8p94uIFA4XBpfkvCJzIfefTLc9L3K/c8nrXOof41BVjX1Fiq0iWZCpWtX+b8L+sHTbE/aXAOyNvkREpGhR7hcRKRycU5ZyYYRM1aoQetNGbAGJ6bbnRe7fdjRvCjJVzjf23X1CI2REipsCVZDZvh3mzCHHQwtr1ICOnQxnFtYjdlM4KWd8iN0UzpmFdenYyWjFDRGRAkS5X0SkeHGMkElMyp3cH1b/CJZLfqtJPhiaq7k/LjGFA6fO2a+ZywWZimF+AOyPjs/V84pIwVcgCjJ50Rl96hQL7Vp5cHJWQw5+0p6TsxrSrpUHU6eoqaOISEGg3C8iUvxER8PQofahMTExJse5PyE5lRRP++iYU4tqkXgoBICKTU7mau7fccw+nahkgDdh/l65dl6ACEdB5pQKMiLFTYFYZSkvOqOHhsLcOfZGXjt22IcrVq+uD+QiIgWFcr+ISPHT5x7D3/+lUroWWH2SKdFtbY5y/6HT9lErfl425k+uwuxVwYzd8DeBlU4RGpp7cV+YrpR7DX0dIkJ9ATh6JpGE5FR8PG25fg0RKZjcXpBxdEYv0c3eGR04/6+FebMaEhVFjoYaVq+es+NFRCT3KfeLiBQ/jtxfspe9067FmvPcv//8NKKIUD9q1LAQHhnCuI0WDsUkcOj0OcqH+OZK7FF51D8GIMzfCz8vG/FJqRw8fc7Z5FdEij63T1nSqhgiIsWPcr+ISPHjyP3eZU+n256T3H/g/DSfCudHmfh7e1C7nL1osmZfDubAXsKx5HX1PBghY7FYiAhVHxmR4sjtBRmtiiEiUvwo94uIFD+O3J94OCTd9pzk/v3R50fInO/DAtC4on2u0uq9uVeQycsRMgARYfaCkmPEj4gUD24vyGhVDBGR4ke5X0Sk+HHk/ti/agL2Za9zmvsvHSEDcG2kvSCzZt/pHMcMcDYhmUMxCQDUKJ03BZkK50fIHNAIGZFixe09ZMC+KsbdfTyYN6uhc1vHTkarYoiIFDGTV+whHi+i45Ko1Q+OhMO+vR7EbqxA6hlfru96ijdH+2OMHxaL3gNERIqaqVMs9O7vyU6ANAsnZzXM0ed+x4gSR0ED4NrzI2Q2HYzJlSa5UedXWCod6E2wn2eOznU5WmlJpHgqEAUZrYohIlI8vDl3G1bvCx+aKQlBJS98eQDo/hkE+3pSv0IwjSqG0rpGKRpGhGCz6n1BRKSwCw21F2Wufx2sNsP27Tn73H/wfAHDMeUH7KNlSgd6c+xsIhsOxHB95bDLHZ4leT1dCS6stOSYgiUixUOBKMg4aFUMEZGirWPdMpQvFUaYvzceNgspqYaUtDROxSdx6LR9RYxdJ+KIOZfMn1En+DPqBB8siKJkgBdta5ame8NwmlctgVXFGRGRQst2fgSkAapVM0D2cnp8UgonYpOA9CNkLBYLjSNDmbPxCKv3nspxQcbR0DdPCzIaISNSLLm3ILNzIYSEgV8JCCwHvqGgIeoiIkXWmAaHCQpJBA8f8C8JgWXBJyRd7k9OTWPbkbOs23+albtOsmTbcU7EJjFt9QGmrT5AhVBf7rwugjubRFA6yMd9T0ZERLJm2xwIKQGePuBfCptHCezlGAupaQYPW/Y+/x88P10pyMeDYN/0U4kuLsjk1HbnCJm8W47aUZA5HZ/M2YRkAn3yZmqUiBQs7i3I/NAfvC9KwDZvCKkIpWtBqdpQpi5ENIWgcu6LUUREcs+PQ9LnfbAXZ0Iinbnfs2w96kU0pV54JH1viCQpJY1/90Qz+7/D/LL+EAdOnWPM79sZt3AHtzWuwAOtqxBZwt89z0dERK7uktwfAmz29mafKY1lxjQoUwfK1LN/7vcvkeXT7nc29PXL8Fij831k1u47hTEmR33JHAWZ6nk4QibA24NQP09OxSezP/ocdcqrICNSHLi3IFOmHngkQ9wJOBcNqYlwMsp+2/Lrhf1CK0HF5lD9Jqh2E/gEuy1kERHJgfDr7Hk/+RzEHYeE05CSACe22W/8fGHfsKoQ2Ryv6h1oUbUdLapdw/Nd6zBn42G+/Xsfq/eeYuo/+/j+333c2qA8T9xcM92ypyIiUkCUbwyeKZAcfz73x+BnSaSWZT9s3g+bf7qwb8maENkMqneEKm3A6/J5/cApx5LXvhkeqxcehJfNysm4JPaejKdSyewV7mPOJXP0TCIA1fNwhAzYR8mcio9h/6l46pQPytNriUjB4N6CzKC5EHQ+2SQnQOwRiN4Fx7bCsc1weB0c2Qin9thv66eA1QMim0Pdnvabb6gbn4CIiLik/8wLeR/shZmzh+HkLji+xZ7/D621vwdE77Tf1k4GmxdUuhHfer3oVedWel3bnH92R/Px4h0s3nacmesOMfu/IwxoHsnwttXzbBUMERHJhgE/p8v9CfFn6fjqD1S2HObTjn54R2+Hg2suFOdPbIPVE+0jKCu3hnq3Qe1u4JW+qLI/+vIjZLw9bFxTIZjVe0+xeu+pbBdkHA19ywX7EJTH04giQv3YcCDG+bxEpOgrOE19PX3sI2FCK0HVdhe2J8TA/n9h9xLYPhdObIfdS+23Oc9Czc7QqJ/9GKvVXdGLiEh2ePpCWBX7rfpNF7afOwX7/4FdS2DbbDi1G3YusN9+exJqd+P6a/tz/cAb2XjoDKPnbGXZjhN8/udupq0+wMjOtbjjuggtnS0iUgBZvfzZa8qy15Ql4fqb8Xb0f4k7CftXwq7FsG0uxOyDqHn2228BUKc7XNvfPrXJYnGuSORYoehSjSNDWb33FKv2nuK2xhWyFaujoW9eTldyqHB+pI9j5I+IFH0FpyBzOT7B9g/p1W+Cm1+Fkzth6yxY/539L6ibZ9pvJapD06HQ4G7wztvhhCIiksd8Q6FGR/ut4+v2YvyWX+25/2QU/DfNfitdl3pNhzK5/+0s2R3LG7O3sP1oLM/M+I8Zaw7yRs9rqFZa7wkiIgWJ7aKV8tLSzIUH/EtAra72W+e3zn/W/wU2fGcfLb/uW/utXENo+gBHTpUBMh8hA9AoIgSADQdOZztWZ0PffHgviTj/PDRCRqT4KHxDSkpUhRaPwLDlMHQpXD8UvIPsH9BnPwnv1YHFb9pH1oiISOFnsUCpmtDqSRj+LwxeCNcNAk8/OLYJfh2BZWw92hyfwuwHGvF819r4etr4Z3c0Xd7/k48W7SD14g/8IiLiVhfVY0g1l8nPFot9gY+2I2HEOrh3LjTsa5/GdHgdzHyAz6IHca9tDhWDMh8NWS/c3ndy+9GzJKakZivWqGPnCzJl836EjJa+Fil+Cl9BxsFigXINoMtb8Phm6Py2vQFkQgwsfgPeuwYWj4bEs+6OVEREcovFAhUaQ7f34PEtcPNr9tX54k/CHy/hMa4hgy0/88fD19GuVmmSUtN4e9427vpshf7iKCJSQFgsFmdRJi0rBXOLxd7ot8dH8NhmaP8iaYHlKM0pXvKcTLWpLWHFx5CSmO6wCqG+hPh5kpxq2H4kNluxOqYs1ciHKUuOqVf7o89hLleoEpEipfAWZC7mHQhN77f/5bT3V1CqFiTGwOL/wQfXwqoJkJri7ihFRCQ3+YZA84fh4bXQ4xN7H5r4k/DHKMK/acWXDaN4p/c1BHh78O+eU3R+/09+WnvA3VGLiAgXpi1ddoTM5fiXgBufYOsdyxiZfB+HKYk17ijMGwkfNoFNP8H5c1osFuqVt4+S+e+g66PnT8cncfzs+RWW8mHKUnioLxYLnEtOJTouKc+vJyLuVzQKMg5Wm70L+7AV0HuCfcRM3DGY9SiMb2lvDikiIkWLzQMa9oGH/oUe4yG4Ipw5iGXmMHqv7suCO3xoUimU2MQUHvt+PSN//I+E5OwNXRcRkdxhPd90PbtTSg+cSWFqanseKvEFdBsLAWXh9F6YNhC+6giH1gEXpi1tPOR6QWbrEftI+/AQX/y98771preHjTKBPgDsV2NfkWKhSBVktm+HOXMgaqcV6vWCB1dCp9H25pDHt8DXt8KP90PscXeHKiIiucSZ+3d5QMO77aMlbxpl7y92eD1lpt3K9+W/55nWpbFYYOo/++g9frmmMImIuJFzhEw2CzJrttsLFgFewXDdvTBiDbQZae8vtv9v+LwtzB1Jw9I2ADZmY4TMfwfsx9QLD7rKnrknIswxbUnvUSLFQZEoyERHQ6fOhpo1oUsXqFHD/vWps15wwzAYsRaaDAEssOF7+PA6WDPZOZxRREQKn8vm/lgfaPmYPfc36guAdc1Ehv13F7+1PUaorwcbD56h27hlLN9xws3PQkSkeMpuQcaR+9/6yF6w+PU7X3vuj/OHNs/Cw2vsI+ZNGqz8mJsW3sJN1tVsPXyWpJQ0l661/vzqTPUrhLh0XE44V1pSY1+RYqFIFGT63GNYuDSFEt3WEj5sASW6rWXh0hTu7nM+wfuGQtd3YPACKHsNJJyGX4bDlDvh7BG3xi4iItlz1dzvXxK6fwQDZ0PJmhB/gjrLH2V5tcm0DLcQcy6Z/l/9wzcr97r3iYiIFEOOgkyai38gdeR+vxr2z/DeESfT5/6gcvaekn1/hNDKeMQd5guvMbxu+ZidBw66dC1HQaZBPhZkKjhWWorWlCWR4qDQF2S2b4d5cy0EtdtIQN1DeAQlEFD3EEHtNjFvroWoqIt2rtAYhiyGDq+AzQui5sFHTWHjDHeFLyIi2eBS7q/UAh5YZh/KbvXAN+pXJieM4Lmqe0hJMzw/cyMv/byRlFTX/nIqIiLZZ3P2kMn6MRfnfo+gBAB8ysdknvurtYcHV0CLR0jDwu0eS4n8rj3sXJSla0XHJTmLItdUCM56kDnkWGnpgEbIiBQLhb4gs3On/V+fiOh0230iTgKwY8clB9g8oMUjMHSpfdnshNMwfRD8PBySlPhERAoDl3O/h5d9KPvgP6BULSxxxxly8P/4ueoveJHMpBV7eeCbNZxLUrNfEZH8YM3GlKULuf9kuu2Xzf2evtDhFb6pPZ49aWXwSzgKk3vCHy9fdQVWx+iYKiX9Cfb1zHKMORXhHCGj30tEioNCX5CpWtX+b8L+sHTbE/aXAKBatcscWLq2fQpTq6cAC6ydbG/+dWxL3gUrIiK5Itu5v3wjuH8JNBsOQIOD3/Fv2beo7nGMP7Ycpc8XK7XUqIhIPnCMkHFlypIz9x8MTbf9ark/pFYrOif9j7k+nQEDy96FiV0h5sBlr7Vhv72hb4OIkCzHlxvCQ+wjZA7FJJCWzYbHIlJ4FPqCTI0a0LGT4czCesRuCifljA+xm8I5s7AuHTsZqle/wsE2T2j3PPT/GQLKwPGt8Flb2DAt3+IXERHX5Sj3e/pAx9ehzw/gG0bw6U3M9X2eHj5rWbvvNL0/0QpMIiJ5LTtNfR25P3ZFDcC+PkfspvJXzf3XhAdzDh8eiR1A6m0T7Kvw7V8J41vCzoWZHnOhoW/+TVcCKBvsg9UCSSlpnIhLzNdri0j+K/QFGYCpUyy0a+XByVkNOfhJe07Oaki7Vh5MnWLJ2gmqtIYH/oKq7SDlHPw4GOb+31WHMoqIiPvkOPfX6GjvLVOxObbkWMbyNi/5/8TuE2e549MV7Dwem7dPQESkGLOe/y0k1cWmvlOnWGjW3H4/LcGTk7MaXTX3R4b5EejtQWJKGttL3mRvXVC+EZw7Bd/cBsvGplt91RjDBjessATgabNSJsgHgIOn1NhXpKgrEgWZ0FCYO8fC9u0we7a94dfcORZCQ69+rFNAKbhnOtz4pP3rlR/B5B4QZ5+Tun07zJlD+mZhIiLiNrmS+4PDYcAv0HQYAPemTmNqwFhiY6K5Y/wK5qw4o9wvIpIHnFOWXJyWExoK742z9/sqFeKRpdxvtVqoGx4EwMaDMRBWGe6dC4362pfH/uMlmH4vJMUB8NfaBE7EJmGzWKhbPigbzy5nnNOWTifk+7VFJH8ViYKMQ/Xq0LkzVx6qfiVWG7R/Ae6YDF4BsOdPUj9tx+Ce26hZE7p0sQ+V7NTZcOpUroYuIiLZlOPcb/OEzqOh52fg4cMNKauY5fcKvvEHuP/7FfQYfEq5X0Qkl2Wnqa9DXKJ9FHupEI8s5/565e1TjzYetPeGwdMHbv0Qur4LVk/Y9BMpn3emz62H6NjnNADxhwPpcas133N/+fMFmYOnNX1WpKgrUgWZXFPnVnvD39BK2M7s4e2aHehx9xeED1tAiW5rWbg0hbv7qMmWiEiR0uBOGDQPAssTmbaPmR4v0cR3M2X7LqfU7X8r94uI5CLnstcuTlkCOJtgL8gE+Hhk+RjH0tX/OQoyABYLNLkPBs4Cv5J4HF/PW9Xb0bztXACsXiluyf3h55e+1pQlkaJPBZnLKV2LnW0X8Ne+poT6xPBD9ae5O3QuAXUPEdRuE/PmWjSEXUSkqCnfkF3tF7DmcH1K2mKY6vU63Wwr8atygpCua5X7RURyiaOpb1qa68c6Rsj4e7tQkAk/P0Lm0Bniky7pE1nxBnbf9Aebj9ekQuBhZpZ+hrbWtXiGxbvlc/+FETKasiRS1KkgcwXbD5ak/de/MDPhRjwtqbzt+RkP2mbiE3ECgB073BygiIjkum2Hy9NqwhzmJTbB25LMOM9xDLDNw7fycbzKn1LuFxHJBdYcjJCJPV+QCXShIFO5pD8RYb4kpaSxLOpEhse3Hq1M8y/n82fSNfhbEvnccwy9bUvwibD3k8zP3F/BWZDRCBmRok4FmSuoWhUSU30YvOkVPkq5FYCnPX/gRb7FQhrVqrk5QBERyXVVq0JccgD9No5mUkoHrBbDy56TeMrze8rc8TcmJObqJxERkSu6MEIm+wUZf29blo+xWCy0r1UGgD+2HM3weNWqEJMYwh3b32JG6o14WNJ4x/NThiTNA0y+fu53TFk6pIKMSJGngswV1KgBHTsZziy8hpfWP8FLZwcBcH/pH1k4/D6qV0l2c4QiIpLbHLn/9MIGPLH+Od6KvRuA4R4/86b/eF6Yv5ztR8+6OUoRkcItJ019HQWZAG9Pl47rUMdekFm49ViGQpAj98fvLs8TyQ/wSdItALxU4VNm3P9/VK+Wf31kHFOWYs4lO5+riBRNKshcxdQpFtq18uDkrIa88u573DX9S5LTPGlT4kf4vh8ka26niEhRcyH3N+KZMeMZ/MsHpBord3ss4sWUDxjw+V/sORHn7jBFRAotm70ek70pS46mvi6MkAG4vnIYgT4enIhNYt2B0xkenzrFQoWmxwAL//fX8zw27w0AepX7GH59BNJSXY41OwK8PQj2tReb1NhXpGhTQea87dthzhwyNOwKDYW5cyxs3w6zZ8OrP/XGs99U8PCB7XNg6p2QpA/lIiKFUVZz/zPfD8B2xwSM1YPutuW8nPgWAz9fxpEYFeVFRLIjJ1OWHE19XVllCcDTZqVNzdIAfPrr0Qy5P8F6jnPBxwF4b0QFHvz6Iej+MVissGYS/PQApObPiJXwEE1bEikOin1BJjoaOnU21KwJXbrYhyt26mw4dSr9ftWrQ+fO9n+p3gHumQ6e/rBrMXxzGyRq+LqISGGRrdxftweWu6ZgbN7cbFvNy/GvMfjLpZyOT3LLcxARKcwcTX1TslGQOZuNVZbAnvtX/2IvyPy65miG3P/DvwdIM9C0chgDbwuw5/5G98BtX4DVA/77AaYPhNS8b1vgmLZ0QAUZkSKt2Bdk+txjWLg0hRLd1hI+bAEluq1l4dIU7u5zlTeHyjdC/5/BOxj2rYBveqsoIyJSSGQ799foiOWeaaR5+tHatoGnT73CAxOWcS4pf4axi4gUFc4RMtmYsuQcIeNiQabPPYbV80IxBrxKxVKy57/O3J+aZvhh1X4A7ro+Iv2B9W6DO78Bmxds+RWmDczzokyF8419NWVJpGgr1gWZ7dth3lwLQe02ElD3EB5BCQTUPURQu03Mm2vJMIwxg4gmMOBn8AmG/Svh29tVlBERKeBynPurtMbadwZpHn60sv3HsCMvMeKbFSSnpuVL/CIiRYEtV5r6Zr0g48j9gS22cX5wDv41jjlz//dLTnDw9DmCfDzoXK9cxhPU7Ax3TwWbN2ydBdPvzdOiTPkQH0BTlkSKumJdkNm50/6vT0R0uu0+EScB2LEjCycp3wj6zbwwUubb2yExNncDFRGRXJMruT+yOda+00n18KW1bQN9d4/kxemrMNn4S6+ISHGU3wWZq+X+6av3AdDr2gr4eF6mWXC1m+Cuby+MlJk+KM+KMuEhfgAcVEFGpEgr1gWZqlXt/ybsD0u3PWF/CQCqVcviicKvhf4/XSjKfHe3Vl8SESmgci33V2qBre90Um32oky7jc8w7vctuRipiEjRZbNkf8qSY5UlV3rIXC73pyV54B0ezYboowDc2STi0kPTq94B7nQUZX6BmcPyZPWlcE1ZEikWinVBpkYN6NjJcGZhPWI3hZNyxofYTeGcWViXjp2MvZFXVoU3hn4/glcA7F4KP/SHFDV6FBEpaHI191dqia3vD6RYvelgW0OlPx9n2r978ip0EZEiw+ocIeP6sY4eMoEurLJ0ae5PS7b/GuRVMpayfVeQkmZoEBFC7XJBWTjZzXDH1+cb/U6DWY9BLo+QdExZOno2QVNiRYqwYl2QAZg6xUK7Vh6cnNWQg5+05+SshrRr5cHUKRbXT1bhOujzvX1J7Kh58NP9eVIxFxGRnMnV3F+5FR53fUOqxYNbbSswvzzK0m1Hcz9oEZEixDFCJtXFQkZamiHufCN1V5v6Xpz797/XkWMzrsP/TCkcmb//DZFZP1nNztDrswtLYs97LleLMiX9vfHysGIMHInRyHuRosq1LFYEhYbC3Dn2Jo47dtiHqlevno0P5A6VWtqHMU69Czb9ZB8xc+s4nN3DRETE7XI999e4GWvvL0mbdi932Bbx9ZTHKDtsPDXKZuEvrSIixZBzlSUXe8jEJaU477u67HX63G+lWrUyVK9ehgOn4tkffY4bqoRd/SQXq3cbJMXDL8Nh5UfgEwRtnnXtHJdhtVooH+zDnpPxHDh1jogwv1w5r4gULMV+hIxD9erQuTOuDVW/7Mlugt5f2SvmayfDgldy4aQiIpLbcjP3W+r2IPWWcQD0t/zGgi/+jxOxiTk/sYhIEWTNZlNfR0NfT5sFb4/s/Spzae6vEOpHs6olsGTnD6jX9oNOb9rvL/4f/PtltmLKjKOPjFZaEim6VJDJK3VuhW5j7feXvQsrPnZrOCIikvc8G/clvo29CD8sZTJTP32DhGRNXRURuZTtfO3D1aa+jv4x/t4e2Sug5IUbHoBWT9vv//YEbJqZK6cNDznf2FcFGZEiSwWZvNR4ALR7wX5/3kjY8IN74xERkTzn1+YRTjV6EIBhZz5g0sRPtBy2iMglsjtC5myC60te54u2/weN7wUM/DgEdi3J8SnLh2iEjEhRp4JMXrvxCWg6zH5/5jDYtdit4YiISN4LvfUNjlbtjYcljf4HXmb6zzPdHZKISIGS3aa+cYnZa+ib5ywW6DoGat8KqUnwfV84uilHp9QIGZGiTwWZvGaxQMc3oG4vSEuB7/vlODmLiEgBZ7FQps+nHCx1I76WJNqtfZilK/92d1QiIgVGdpv6xiYmAwWwIANgtcFtX0BkC0g8A9/0hpiD2T6dsyBzSgUZkaJKBZn8YLVCj08uJOdvb89RchYRkULA5kH44O846FuTEpazRM7pz/Zdu90dlYhIgXBhypJrx8WeHyHj6gpL+cbDG+76FkrWhLOH7J/7E2KydSpHU9+Dp89p6qtIEaWCTH7x9IE7v4GSNeDMQZhyBySccXdUIiKSl7wDKPPAzxy3lSHScoSkyXcQfTp7H8xFRIqS7E5Zik04P0LGp4AWZAB8Q6HvdAgoA8c22UfIpya7fJpywb5YLJCYksbJuKQ8CFRE3E0FmfzkFwb3TAf/0nB0I8y4D1JT3B2ViIjkIY/gcngP/JEzBFDPbGfr+H6kpCj3i0jxlv0pS+eb+noV4IIMQEhF6PMDePrD7iX21ZdcLD55eVgpFeANaNqSSFGlgkx+C42Eu78DDx+Img/zn3N3RCIikseCIuoRc+uXJBsbzROWsPzLJ90dkoiIW1mzO0LG0dS3II+QcSjfEHp/CVhgzSRY8aHLp7h42pKIFD0qyLhDhcbQ81P7/b/Hw9+fuTceERHJcxHXdmJrk1cAaHV4Av/O/MjNEYmIuI/t/G8hri577WjqW2B7yFyqZmf7Ah8A81+ALbNcOlyNfUWKNrcWZBKSU915efeq2wPav2S/P/cZ2PGHW8MREZG8d0234fwTPgCABmtfYOcq5X4RKZ4uNPXN3rLXgYWlIANwwzC47j7AwI9D4PD6LB+qETIiRZtbCzKdxy7liz93EZ9UTOfSt3wMGt4DJg2mDYITUe6OSERE8th1g95jtV9LvCyphM4axOnDu9wdkohIvvPIZkHmbIL994ZCM0IGwGKBzm9B1XaQHA9T+0DssSwdWiFEBRmRosytBZnjsUm89tsWbnxzER8v3sHZBNe7jxdqFgt0ew8imkJiDEy9C86ddndUIiKSh6w2G9WGfssOayXCiOH0V71JTYh1d1giIvnKscpSmos9ZOIcTX0LQw+Zi9k8oPdXUKIanDkA3/eFlMSrHuYcIaMpSyJFklsLMqNuqUPFMD9OxiXx1txttBi9kPd+387p+GK0rJuHt3057KAKcHIHTB+klZdERIq44OAQuHsqJ00QlZJ3EvVZP0hLc3dYIiL5JrtTlpyrLHnbcj2mPOcbal/cwzsY9v8Nvz1+1ZWXwkP8AI2QESmq3FqQ6X1dBAufaM17dzagail/ziSk8P6CKFq+uYg3527lROzVq8ZFQkBpuHsqePrBzgXwx0vujkhERPJYtep12NL6E5KMjVrRC4maodwvIsVHjkfIeHvmekz5omR1uP0rsFhh7Tfw96dX3L18iA8AMeeSncUoESk63L7KkofNSs9GFZj/WGs+6nMttcoGEpuYwieLd9LyzYW88utmjsQkuDvMvFeuPvT4xH5/xYewYZp74xERkTzXsl035lZ6BoCqG8dx9N+f3ByRiEj+yO4ImbOJjh4yhXCEjEO1m6DDq/b78/4Pdv952V0DfTwJOj89S9OWRIoetxdkHGxWC13rl2POIzfyRf/raFAhmITkNL76azet3lrE8zP/48CpeHeHmbfq9oAbn7Df/2W4Sx3YRUSkcOrc/ynm+nbDajEE/PYgCYe3ujskEZE8Z3MWZFw7zjFCJrCwjpBxaPYQXHMHmFSYNgBO77vsruGhjmlLRfx3IZFiqMAUZBwsFgs31SnDzIda8PWg62lSKZSk1DS+WbmPNm8v5qlp69l9Is7dYeadts9BtQ6QkgDf9YW4k+6OSERE8pCnzUrDIZ+whtr4E0/MhNsxCTHuDktEJE9lZ8pSapohPsm+7HWhHiED9sU9bnkfytaH+JP2Jr/JmY+ACQ9RY1+RoqrAFWQcLBYLrWqUYtoDzfnu/htoWa0kKWmGaasP0H7MYh75bi3bj551d5i5z2qD276AsCoQsw+mD1STXxGRIq5sWBCpvSdyyIRRJmkfBycMUJNfESnSsjNlKS7pwmfiQrfKUma8/OCub8GvhH1k/K+PZtrkt4JjpaXTxaCNg0gxU2ALMhe7oUoJvhnclB8fbE77WqVJM/DzukPc/N5SHpi8mo0Hi9hfEn1D4K4p4OkPu5fCwlfdHZGIiOSxJvVq8de1Y0k0HlQ4uoijc/7n7pBERPKMzV6PIdWFETKxCfaCjKfNgrdHIR8h4xBSEW6fCBYbbPgO/v0iwy7OETJaaUmkyCkUBRmHayuG8uXAJsx6uCWd65UFYO6mI3Qbt4xBE/9lzb5Tbo4wF5WuDd0/tN//ayxs/sWt4YiISN677ZZbmVJyBAAl/32H+C2/uzkiEZG84eghk+bKCBnnCktFYHTMxSq3gptG2e/PHQn7/0n3cLhjhExR76cpUgwVqoKMQ73wYD7p25j5j7Wie8PyWC2wcOsxen28nL5f/M3KXScxLi6hVyDV6wXNhtvvz3wQjm93bzwiIpKnrFYLPQaN5FfbTdhII23aIMypve4OS0Qk12VnytKFFZaKWEEGoPnDUKc7pCXDD/0h9pjzIY2QESm6CmVBxqFGmUDev6sRC59owx3XVcDDamHZjhPc9dlK7vh0BUu2Hy/8hZmbXobIlpB0Fn7oB4mx7o5IRETyUKi/FxXu+ZD/0ioTkHaGkxPuhpREd4clIpKrstPUt8iOkAF7k9/uH0HJmnD2MEwf5Owj6Rghc+xsIkkp6i8mUpQU6oKMQ6WS/rzVuwGLn2pDvxsi8bJZ+XfPKQZ89Q89PvqL3zcfLbyFGZsH3D4BAsrC8a0w67FMm32JiEjR0ahKOTbf+BGnTAAlz2zi5I9PujskEZFclZ0RMo4eMkWyIAPgHQh3fgNeAbDnT1j0OgAl/L3w9rBiDByO0SgZkaKkSBRkHCqE+vFqj3r8+Uxb7mtZGR9PK+sPxDDk61V0fv9PZm045FLSLzACStuLMhYb/PcDrPrK3RGJiEgeu+Om5kwu938AlNj8NedWT3VzRCIiuccxQibVhY/msY4RMkVhhaXLKVUDbv3Afn/Zu7BtLhaLRdOWRIqoIlWQcSgT5MML3erw1zPteLBNVQK8Pdh65CzDp6ylw3tLmLH6ACmphWy4X2Tzi5p9PQsH17g1HBERyVsWi4UB/e9nosftAFhnPYo5ttXNUYmI5I7sNPWNLco9ZC5W7za4fqj9/k9D4dTeixr7qiAjUpQUyYKMQ4kAb57uVItlz7Tl0ZuqE+Tjwa7jcTwxbT1txyxm6j/7SExJdXeYWdf8YajVDVKT4IcBcK4IrSolIiIZBPt50qDvaJan1cXbJBAz6W5IinN3WCIiOeaYspSSlvU/kjqmLAUW9YIMwM2vQfh1kHAapg2gYpB9mW+NkBEpWop0QcYhxM+LR2+qwV/PtuPpTjUJ8/dif/Q5Rv74H23eXszEv3aTkFwICjOOZl+hlSFmH8x8SP1kRESKuEaVSrKr9QccMaGExO3i9LSHlftFpNBzNvV1YdB6bFIR7yFzMQ8vuH0i+IbCobXcceozQCNkRIqaYlGQcQj08eTBNtX465l2vNCtDmWCvDkck8CoXzfT8s1FfLZ0p7N7e4HlG2JPzjYv2PYbrPzE3RGJiEgeu6ddYyaVe4FUYyEkagaJq752d0giIjliO/9bSKoLBWbHCJkiP2XJISQCen4KQIND39PJ+o9GyIgUMcWqIOPg62XjvpaVWfJUW17rUY/wEF9OxCbyxuyttHxzIR8ujOJMQrK7w7y88g2h4xv2+7+/CAdWuzUcERHJWxaLhSH9+vGZx932r2c/BUc3uzkqEZHss1ntv4a4suCG4w+ngUW5qe+lanSEFo8A8Jbnp6RF73ZzQCKSm4plQcbBx9NG3xsiWfxUG97qXZ9KJfw4FZ/MO/O302L0Qt6dv41TcUnuDjNzTQZDnR6QlgzTBkJ8tLsjEhGRPBTm70Xje15lSVp9vEwiZybfA4mx7g5LRCRbHCNk0lwZIVNcmvpeqt0LJJZrQpDlHM/FvUVaUoK7IxKRXFKsCzIOnjYrd1wXwR+Pt+b9uxpSvXQAZxNS+GDhDlq8uZD/zd7CsbMFLPFZLPYl8Rz9ZH5RTwERkaLu+iol2d5sDEdMKEGxuzjz06PuDklEJFusjmWvs7HKUrHoIXMxmye2278i2gRwjXUXCXOec3dEIpJLVJC5iIfNSveG4cx7tBXj+15LnXJBxCel8unSXdz45iJG/bKJQwVp3qZPsL2fjNUTts6Cfz53d0QiIpLHBnVswqclnyPVWAjaOo3kNVPcHZKIiMscy16rIJM1HmEVecNzBAB+a7+Arb+5OSIRyQ0qyGTCarXQqV45fhvRkq8GXkfDiBASU9KYuHwPrd9exMgf/2PfyXh3h2lXviHc/Kr9/vzn4PB6t4YjIiJ5y2a1MLR/Pz6z3g6AmfU4nIhyc1QiIq5xrrLkwgjvuET7qqgBxamHzEX2lWzF5yld7F/MfBBO73dvQCKSYyrIXIHFYqFdrTL89GBzvh3clKaVw0hONUz9Zx9txyzm8R/WsfN4AZi/3/QBqNkFUpNg2r2QeNbdEYmISB4qG+xDjd4vszy1Dl5p5zj7TV9ILmBTa0VErsCajREyZx2rLHkVz4JMRJgfb6XcxdHAupBwGmbcB6kFeCESEbkqFWSywGKx0KJaSb4f2owfhjbjxuolSU0z/LjmIDe9u4SHp65l65Ez7gwQun8EQeEQvRN+e8J9sYiISL5oX7c8Kxr+jxMmiMDTW4mbNdLdIYmIZJljypIL9ZjiucrSRSLCfEnGg0nlXwTvINj/Nyz+n7vDEpEcUEHGRddXDmPyfU35+aEW3FS7DMbAr+sP0Wnsnwz5ehUbDpx2T2B+YXDbl2CxwobvYd1U98QhIiL5Znj3G/kg0F6E91//Fambf3VzRCIiWeNqU9+U1DTOJdunLBW7VZbOiwj1A2BdbAjc8r5945/vwq4l7gtKRHJEBZlsahARwhcDrmP2iBvpWr8cFgv8vvkot374FwO++odVe9ywDHVkM2hz/i+kvz0BJ3bkfwwiIpJvvD1sDBwwmAmmGwDJPz4IMQfcHJWIyNW52tQ3LinVed/f25YnMRV0FUvYCzL7T8VDvV5wbX/AwI/3Q9wJ9wYnItmigkwO1SkfxEd9ruX3x1rT69pwbFYLS7Yfp/f4Fdz12QqW7ziByc/lqG98AirdCMlxMGMQpCTm37VFRCTfVSkVQGDXV1mfVgWflDOcnXovpKVe/UARETdytamvY4UlL5sVb4/iWZBxjJA5dDqBlNQ06PQmlKwJsUfsTX7z83cOEckVKsjkkmqlA3j3joYsfKI1d18fgafNwspd0fT54m96fbKchVuP5k9hxmqDXp+Bb6h9xaU/Xs77a4qIiFvd1qQyM6u+QqzxIfDIPyQsHO3ukERErsh6/reQLI+QcSx5XUz7xwCUDvTGy8NKaprhcEwCePlB76/A5g1R8+Dv8e4OUURcpIJMLoss4c//etVnyVNtGdi8Et4eVtbuO82giavoNm4ZczceJs2V7mXZEVQeun9sv7/yI4j6I2+vJyIibmWxWHjszk686zUUAK9l72D2rnBzVCIil3ehqW/WPhc7V1gqptOVwL4yVYVQXwD2RcfbN5atBx1ft9///UU48p+bohOR7FBBJo+UD/Fl1K11+fOZttzfqgp+XjY2HTrDA9+sodP7S/l53UGXlvlzWa0ucP399vszH4DYY3l3LRERcbsgH0+69n2Mn1JvxEoa8d8NgnOn3R2WiEimbC429Y1PKt5LXjtUDDvfR8ZRkAFoMhhqdoHUJJh+HyTFX+ZoESloVJDJY6UDffi/LrVZ9kw7hretRqC3B9uPxvLId+u46d0lTFu1n+TUtLy5eIdXoHQdiDtun1ealkfXERGRAqFxZChHW77K3rTS+J87RNyPD6ungIgUSFYXm/qeO9/U18ez+I6QgQt9ZPafuqjoYrHArR9CQFk4sQ3m/Z+bohMRV6kgk0/C/L14smNNlj3bjsc71CDEz5PdJ+J4avoG2ry9mG9W7iUxJZebMHr62pfCtnnDjt/hn09z9/wiIlLgDOnQkE9L/R8pxop/1C+krP3W3SGJiGTg6giZhBT7HxZ9PIv3ry+OETL7os+lf8C/BPT6FLDA6gmw5df8D05EXFa8M5obBPt6MqJ9dZY9046RnWtRMsCLg6fP8fzMjbR6axFfLtvt/AtArihTR/NKRUSKEZvVwvB+d/Gx5U4A0mY9CSd3ujkqEZH0nMteZ3EUX2KyRsgARITZe8ikm7LkUKUNtBhhv//zcIg5mH+BiUi2qCDjJgHeHgxtXZVlz7Rj1C11KBvkw9Ezibw6azMt31zIJ4t3Opf3y7Emg6FGZ/u80hmDIfnc1Y8REZFCq3yIL9V7Pc+K1Dp4pZ3j7JSBkJrs7rBERJwcU5ayOqPeOUKmmC557RCRWQ+Zi7V9Hso3goTT9j6SalkgUqCpIONmPp42BraozJKn2/BGz2uoEOrLybgk3py7lRajF/L+H1HExOfwQ7TFAt0/hIAycHwrzH8hd4IXEZECq3P9Ciyp+wqnjT+BJzdw7vfX3B2SiIiTc8qSiyNkvIv5lCVHQeZkXJJzKfB0PLyg1xfg6Qe7l8KKcfkcoYi4onhntALE28NGn6YVWfRkG965vQFVSvoTcy6Z9/7YTos3F/LW3K2cjE3M/gX8S0KP80th//s5bJubO4GLiEiBNaJXW973fQgA75XvY/Ysc3NEIiJ2Nheb+iY4piwV8xEyQT6ehPh5Apc09r1YyWrQ+U37/QWvwqF1+ROciLhMBZkCxtNmpXfjCvz+eGvG3d2ImmUCiU1M4ePFO2n55iJem7WZY2cSsnfyajfBDQ/a7//8kJbCFhEp4vy8PLit33Cmp7XGiiH+u/vg3Cl3hyUi4izIAKRloSiTkKymvg7OlZYubex7sUb9oPYtkJYMM+6DpLh8ik5EXKGMVkDZrBZuaVCeOY/cyKf9GnNNeDDnklP5YtluWr61iBdmbuTg6Wz0gmn/EpSpB/En7EthazlUEZEirV54MGfbvMHutDL4Jxzh7IwRyv0i4naOKUuQtWlLCWrq6+Ro7Lvvcn1kwN6y4JYPILA8nNwB857Lp+hExBUqyBRwVquFjnXL8svwFky8twmNI0NJSklj8sq9tH5rEc9M38CeEy5UvD194LYvwMPn/FLYn+dd8CIiUiAMaFOXiWWfI8VYCdzxC8lrp7o7JBEp5qwX/RaSlWlLCSmOHjIqyFy1sa+DXxj0HI9zKeytv+V9cCLiEhVkCgmLxUKbmqWZ/kAzpgxpSotqJUhJM3y/aj/txizm0e/WEnX0bNZOVro2dHjFfv/3F+DYlrwLXERE3M5qtfBQ3zv51HoHAGmznoBTe9wblIgUa+mmLGVphIymLDlcmLJ0lYIMQJXW0Hy4/f4vD8PZI3kYmYi4ShmtkLFYLDSvWpJvB9/AjGHNaVuzFGkGZq47xM1jl/Lgt6vZdCjm6ie6/n57T5mUBPtS2Ck5aBgsIiIFXukgH2re9hL/ptXAOy2emG/vhdRMVugQEckH1ounLGVhhEyilr12qugYIXO5pr6XavcClL0G4k/aWxZoKWyRAkMFmUKscWQoE+69nlkPt6Rj3TIYA7P/O0LXD5Zx38R/WbvvCo0bLRbo/jH4lYCjG2HBK/kXuIiIuMVN9cqztO7rnDW+BJ9YQ9zCt9wdkogUU+mb+l59f/WQueDClKVzmKz0BPPwti+F7eEDOxfAP5/lcYQiklUqyBQB9cKD+bTfdcx7tBW3NiiP1QILth6j58fL6fvF3/y962TmBwaWgVs/tN9f8SHsWpxvMYuIiHs81Ks9H/s+AIDPX29jDqxyc0QiUhxlv6mvfn0JD/HFYoFzyamciE3K2kGla0GHV+33f39RLQtECghltCKkZtlAPri7EX883prejStgs1pYtuMEd362kjvGr2Dp9uMZq+i1ukDjgfb7Pw2D+Oh8j1tERPKPj6eNW/s/xm9pzbCRxtkp90JirLvDEpFixmp1ccrS+R4y3pqyhJeHlXJBPsBVVlq61PVDoFoHSE1UywKRAkIFmSKoSqkA3rm9AYufbMM9TSviZbPyz55o+n/1Dz0+Xs4fm4+mL8x0fANKVIOzh2DWY1oOVUSkiKtdPpjT7d7koClBUPw+Ts98yt0hiUgx5Ji2lKWmvikaIXMxx7SlA1ntIwPnWxZ8dKFlwcJX8yg6EckqZbQiLCLMj9d7XsPSp9tyb4tK+HhaWb//NIO/XkWXD5Yx+7/DpKUZ8PKHXp+D1QM2z4T137k7dBERyWN9WtdnctlnSTMWQrZMIWnjL+4OSaRIik1U8+zLcUxbytKy1+ohk46jILPvpAsFGUjfsmD5h7BrSS5HJiKuUEGmGCgb7MNLt9Tlz6fb8UDrqvh72dhy+AwPfruGm8cu5ae1B0gp2xDaPGs/YPZTWg5VRKSIs1gsDO43gG+stwKQ/NNwLYcqkss2HDhN+zGL3R1GgWU9/5tI1goyWvb6YpVL+gOw+0Sc6wc7WxYY+OkBOHeFhUBEJE8poxUjpQK9ebZzLf56th2PtK9OkI8HO47F8tj362n/7hJ+8OlNWoWmkHQWfhwKaanuDllERPJQyQBvIm9/nU1pkfinxnByymBNWxXJRe/9vp24RH2euhzHCJksTVk6P0JGPWTsqpwvyOzMTkEG7C0LwqqqZYGIm7lckBk4cCBLly7Ni1gkn4T4efFYhxose7YdT3WsSZi/F3tPxvP0j5u5/dhAkmz+sH8lLHvX3aGKSAGh3F90ta4TwdJr/keC8aTE4T85u/Rjd4ckUiSs2XeKRduOp1veubDJ69zvaOybkpWmvimOETIqyIC9ZyTArmOxWVv6+lJe/nDb52CxwaafYMP3uRyhiGSFywWZs2fPcvPNN1O9enXeeOMNDh48mBdxST4I8vHkobbVWPZMW57vWpvSgd6sPhPMs+f6AZC2aDQJe/5xc5QiRUghnqet3F+0DerZiQl+gwDwXjyKtKNaDlUkp977fTsAj1U95OZIsi+vc7+zqa9LPWQ0wB8gsoQfVgucTUzheGw2V0sKbwxtRtrv//YknNqbewGKFGfGwM7FWdrV5Yw2Y8YMDh48yPDhw5k2bRqVKlWic+fOTJ8+neTkZFdPJwWAn5cHg2+swtKn2/Jq97qsDOjArNSmWE0KRyYO4NM//uNMgl5bkRzZPg++v8fdUWSbcn/R5u1h46YBz7PUNMDLJBE9eQCkJLk7LJFC69890fwZdYKeHssZuP95d4eTbXmd+51Nfa8ywsMYoxEyl/DxtFEh1N7Yd9fxbE5bArjxcYi4wd6y4Ce1LBDJFau+gh/6ZmnXbJWYS5QowSOPPMLatWv5559/qFatGv369aN8+fI89thjREVFZee04mY+njb6NavE4qfbkdLpXY5ZSlCJQ/gvfokWoxfy7vxtnI7XB3QRl8Ueh58fcncUOabcX7RVLxvE8XbvEm0CKBm7jeO/vujukEQKrXfnb6c8J3jDa6K7Q8mxvMz9jilLV2vq6yjGAHh7aISMQ5VS9j4yOSrIWG3Q61PwCoR9K+CvsbkTnEhxdSIK5j2X5d1zlNEOHz7M/PnzmT9/PjabjS5durBp0ybq1KnDe++9l5NTixt5eVjp0aIeJe75EoC+HgtokvQPHyzcQYvRC/nfnC0cP5vNoZEixY0x8MtwiDsOJWu6O5pcodxfdPVq1Zjvyz4FQIn14zm3fbF7AxIphJbvPMHfu47zntcn+KbFQrlG7g4pV+RF7nc29U278n6O6UqgETIXq1LyfB+Z47E5O1FoJejylv3+ojfg4JqcnU+kuEpJghmDIeUcVGqZpUNcLsgkJyczY8YMunXrRmRkJNOmTeOxxx7j8OHDTJo0ifnz5zN58mReeeUVl+OXgsVWrS00Gw7AJ4Ff0axMKnFJqXy6ZBct31zIqF82cTjmnJujFClYtm+HOXPA+QfD1RNg+1yweUH3D90aW04o9xcPFouFu/o/yC/W9lgxJEwbAudOuzsskQLPkfu3bze8O387Q2y/0dS6BTz94db33R1etuV17nf0kLnalCXHktc2qwVPm0bIOFQtfX6lpZwWZAAa3A11ukNaCvw4BJJyMOpGpJjI8Ll/yWg4vA58Q6Hr2Cydw8PVi5YrV460tDTuvvtu/vnnHxo2bJhhn44dOxISEuLqqaUgavcC7FyE97FNTKn4DQs7fsAHi3ayfv9pJi7fw5S/99H7ugoMa12ViDA/d0cr4jbR0dDnHsO8uRdW0xjUI4ovGv8fFoCbRkHp2u4KL8eU+4uPUH8vytwxlj1Tb6JS8lEOfvsg4YOnuDsskQLp0tzvU+U47e5YyxNeP9h36PwmhFVxY4Q5k9e535bFKUvOhr6arpSOc4RMdpe+vpjFAt3Gwv5/4OQOmP88dNOoV5HMZPa5//Hey3mn3nv2z/3dxkJQ2Sydy+WCzHvvvcftt9+Oj4/PZfcJDQ1l9+7drp5aCiJPH/uSeJ+1xRI1j/Y1ZtHuwfv4a8dJPlgYxT+7o5ny9z6+/3c/PRuF82Cbqs5l+ESKkz73GBYuTaFEt434RESTsj+IYaWfxJJyDiq3hqbDIDYX/oLlJsr9xUvTWhX59po3qPDfEMIP/MbJFd9QolnWmtOJFCfpc/9JfD3jGev5EV6WVKjVDRr1hbNn3R1mtuV17neusnS1ETIpjhWWNF3pYlXP95DZHx1PYkoq3h45/P74hUGPT2ByD3tT0uodoWannAcqUsRc+rnf86AXD1cYhsWkQcN7oG4POHMmS+dyuczcr1+/KyZlKYLK1LX/dR9g3vNYTkTRsnpJfhjajO/vv4Ebq5ckNc0wffUBbnp3CSOmrmXbkcL74UPEVdu3w7y5FoLabSSg7iE8ghJ4rsGHXFduHdHnQtjd8BOwFu6/6in3Fz939OzFtIC7AfCZ/zQpJ/e4NyCRAiZj7k/kucDJVLce5HBsaXbW/cA+6qAQy+vcf74ek4URMlphKTOlAr0J8PYgzcC+k/G5c9KqbeGG8wsR/PwQxB7LnfOKFBGZfe5/p/5oKgXvZ9epSHbWGO3S+Qr3bwiSf5o+AFXa2BsU/TjYuRxq0yolmHxfU356sDk31S5NmoFf1h+i49ilDJ28iv8OxLg3bpF8sHOn/V+fiGgArrNs5UHbzwAMnTWWrYfC3RWaSLZ52qy0vHc06011/E0cRyYN1HKoIhe5NPe3sa5joMd8AAbO/ITtB0q4K7RCwzlC5mqrLJ2fsuTtqV9dLmaxWJyjZHKlj4xD+xehdF2IPwE/D7cvUCAiwMW5/yQA3awruM22jFRjpd9Pn7F9b5BL51NWk6yxWqHHeHuDosPrYfEb6R5uVDGULwY04bcRLelyTVksFpi36Si3fLiMeyf8w+q9p9wUuEjeq1rV/m/C/jACiWes18fYLIapJzoxfXNPqlVzb3wi2RVRMogTN39InPGmwpm17P31f+4OSaTAuDj3lyCGtz0/BeDTY72Yv/Mm5f4ssFqy2NT3/LLXPjmdklMEOVoF7MzJ0teXcrQssHlB1DxY9WXunVukkHPk/tR4b8pxktc97f8/3jvcl+X7b3A596sgI1kXVA5uOb9SwLKxsGdZhl3qlg/m43saM//RVvRsFI7VAou2Hee2T5bT5/OVLN95AqMquxQxNWpAx06GMwvr8XzcD1SwnGBPYjmGf/sJHTsZqld3d4Qi2de+xQ38Fv4oAOFr3+XMzn/dG5BIAeHM/Utq8T/bl5SyxLA1KZKnvn1fuT+LXG7qqxEyGVQpaR8hsys3CzKQoWUBx7fn7vlFCqkaNeDmTml4+iQwxvMTgi3xrEmqzotT38xW7ldWE9fU6Q4N+wIGfhx62eVQq5cJ5L07G7LwiTbc1SQCT5uF5TtP0ufzv7l9/AoWbzumwowUKVOnWHi5x8/cWWI+qWlW7vl2Ik1uCGXqlMLdP0AEoGv/p1hqa4YHqcR9dy9Gy6GKAPbcP6rfB9zsuYpE48GdEyfTvHmgcn8WZbmpr2PKkkbIZOAYIbPrRB4sHNB0WKYtC0SKu4dfO8GwEjNobttMvPHm4ZNP0Kqlb7Zyvwoy4rrOoyG0Mpw5AL89ccVdK5X0Z/Rt9Vn8VFsGNIvEy8PKqr2nGDjhX7p/9BfzNh256rxhkcIg1LKfkfUeB2B3xJNMXHADc+dYCA11c2AiucDfx5NSfcZz1IRSLnk/279+xN0hiRQIHrGbeazUOwAsCnuM6UsaKPe7wDllKe3K+yU6m/rqV5dLVS19vofMsdjc/2PnpS0LFr2eu+cXKaRWr/qDJzx+AODllP4cCg1i2k8p2cr9ymriOu9A6PU5WGywcTps+OGqh4SH+PJy93ose7otg1tWxtfTxoYDMQydvJouH/zJr+sPXXW4qkiBlZYKPw2FxBgIv45qg57WUHUpcmpXrcTaxvYeMjUPTGPviulujkjEzVKSiJ06EF+SWGtrQIfhI5X7XZTlKUta9vqyKpXwx2KBMwkpnIzLgxEsQeXg1nH2+3+9D7v/zP1riBQiB46eoO/BV/CypBJXpTN/BXbGABuyuZiNCjKSPRFNoPUz9vu/PQGn9mbpsNJBPjzfrQ7LnmnLQ22rEuDtwdYjZ3l46lo6vLuE6asPkHy1P5OIFDR/vQ97/wJPf+j1Gdg83R2RSJ7oeMtdzA/qDUDQ/MeJiz7k5ohE3Ofs3FcoF7+NUyaAuK7jsNlULHCVzeLalCUVZDLy8bQRHuIL5EEfGYfat0CjfoCBnx6Ac1qsQ4qvYzOepqr1MKesYfj3/phGkWEArN2Xvf8XKshI9t34BEQ0hcQz8OP9kJqS5UNLBHjzVMda/PVMOx67qQbBvp7sOhHHk9PW027MYqb8vY/EFC2vKoXAwTUXhvB2eQtKVHVvPCJ5yGKx0OS+sURZIgk1Mez7cqCWQ5Xiafef+K/6EICvQh+lRaP6bg6ocLKe/00k5apNfTVl6UqcfWRyc+nrS3UaDWFV7C0LZj2m3C/FUtKm37j22AwAdrZ8B/zCaBgRAsC6/aezdU5lNck+m4d9NIBXIOxfCcvedfkUwX6ePHJTdf56th3Pdq5FyQAv9kef4/9++o/Wby1mwl+7OZekwowUUElxMGMwpKVA7Vuh4T3ujkgkz4UGB3Lulk9JMJ7Ujvub9TPedHdIIvnr3CmSpw/BiuH7lDa06zUYi0VNfLPD2dT3KgUZxx/p1NQ3c1VLnV9p6UQeNlz3DoDbvgCrB2z6CdZPzbtriRREZ4/CLw8BMMXajYatewLQqGIIAGv3nc5WHycVZCRnQitB1zH2+4tHw/7sLYca4O3BA62r8ufT7XixWx3KBHlz5EwCL/+6mRvfWsinS3YSm5j1ETgi+WLusxC9E4LC7UvC6wO5FBP1r23GiqqPAVDrv3fYv1VLYUsxYQzm10fxjDvMrrSy/F3zaRpVVAff7LrQ1DerI2RUkMmMY4TMjmN5OEIGILwxtBlpvz/7KYjelbfXEyko0tJg5jC8Ek+xOS2SLXUfx8NmL6XULR+El83Kybgk9kefc/nUKshIzjW4E665HUyqfUm8hDPZPpWvl41BLSuz9Om2vNajHuEhvpyITeJ/c7bS8s2FfLAgiphzybkYvEg2bf4F1nwNWKDnp+AX5u6IRPJVq3tGstq7Kd6WZFJ+uI+E+Dz+RUCkIFg3BcvmmSQbG0+lPcyjXRq5O6JCzdnUN8s9ZPSrS2ZqlQ0EYMvh7H8Gz7KWj0FkS0iKhRlDIFWfy6UY+OdT2LmARLwYkfwQrWpXcD7k7WGjdvkgANbud72PjLKa5I6uYyCkIpzaA3OedunQ7dthzhyIirqwzdvDRt8bIln8VBve7l2fKiX9OR2fzLu/b6fl/7d333FV1u8fx19nsJeC4kBw4d4j9yTL2TQrNS3bpe1d377Vr2+7bKdZmaVp2bBhzsS991bcWxyA7HE45/fHDQgJggoc4Lyfj0cP4czPIb247+u+ruvzdiTvz91NTElMkhcpivjj8NejxtfdHoe63Z26HBFnsFjMhI76hjNUoq79EBsnXtpW2PnFfpEy7ew+HFnHOGNtQ2jX5WrCgrydvKjyLWeobxErZNSylL8mNfwxmeDEuVTOJKaV7JuZLXDzl+AZAMfWweJLa1tV7Jdy5+Q2mP9fAF7PGM5hcxhd6gfleUibrDkyGw/HXfLLKyEjxcMzIGsrbLPRU7rl50KfEhMD/fo7aNQIBgyAhg2N72NzJRbdLGaGtA9l/pM9+WRoGxpW8yUhzcZnC/fS7Z1I3vh7B6cSUkvwg4n8iz3TGGKdEgs120CvF529IhGnCa4eyvFexvywzmd+Ye28wmcKFCX2i5Q5tnT49R5M6YmszGzKdPcbGd073NmrKvfMRa2QsalC5mJ8PazUrWLMkdl+vBSqZAJqGa3aAEveh4PLCn2KYr+US+nJ8Os9kJnOoSo9mJLZh471AvHxsOZ5WPYcmcsZ7KuoJsUnrFOurbCfNKplLmLYcAeRS2wEDdpIyEMLCBq0kcglNoYOu/CXssVs4vpWNZnzWA/G39GO5iH+JKdn8tXSA3R7ZyGv/LGN43GX3rMncsmWfwQHlxpbXA/+Bqzuzl6RiFO17DWYtdWHAlB/+TMcPXzxmQKXEvtFyoyFb8DxjZzDlycyHuKRPo0J8HJz9qrKPWtRh/pq2+tCNa8ZAMC2Y+dK5w2b3QRt7gAc5y9UZXE4HMSnZpCYZiM53YYt067YL+XTvJfg9C7wrc6b1jGAid6Ngi94WJtQY5bYjuPxl7xTsLXwh4hcgu5Pw76FcGQVKVPuZXG92dRv6EaDBnkfFhUFc+eYCBq0Dd9mxwGy/jQxd2Zr9uzhgueAcSWlX/Pq9G1WjUVRp/l0wR42HI7ju5WHmLrmMIPb1uKhXvWpHeRT8p9VXM/RdRCZvcX1e9riWiRLm1EfcuC91dS17Wf/pLvZ0HY+TRoVX+wXcar9i2C5UQ3wbPq9eFcJY3in2s5dUwWRUyGjba+vWPMQf/7cfLz0EjIA/d6BQyshZh8JUx9lWY3vsVZJ5OPVm9h27HyljofVwomzDfGPiMO32QlAsV/KgZ1/wbqJACQP+pzIyca4jN6NL0zIhAZ6EeTjztmkdLYfj6ftJQx7V1ST4mWxEnf1VyTa/PE6u5a1H7yTb0nivn3Gn56hMXme7hl6FoC9ey/+NiaTkZ389aEuTL23I53rBZGR6eDHtUfo/f4invhpE3tPJRTnJxNXlxpvlCw6MqHZzdB6mPqgRbJYPbzIHDSJFIc77e0bWfvzqyUS+0VKXdJZ+O0BwMGPmVcz196Bu1o34Z95ZsX+YpA9QyazkCKJnKG+miFToOYhWRUyx0sxIePhy7lrvyHD7obfkT/5e8KH3PPTsjzJGDC2LQ+M2Il3w+g8tyv2S5l17hj8+YjxdZdHWWJrRkamg2AvH2yxF174N5lMNM0a7Hupu50pISPF7vaHQrl/ljFT4KXu73P97RMvKEmsn1VYkHok7840STtrAmAtYu2WyWSiS3gVpt3fiV8e7EzPhlWxO2DGxmNc8+ESRv+woXQmzkvFN+tpow0vIIzYbh/SbwDqgxbJZcwLLXl2/UsAvFxnHNeMmlRisV+kVDgc8MdoSDzJCbcwXs24A5/4Ktx5TbBifzGxFLVlyaZtrwvTLKtl6UhMCueSS2/no9ueaM3LS42tsN9r9RYN3I+QeiiI+jt6s+v1fuz4v7482qU5DpsZs5s9z3MV+6VMsmfCjAeMNrwarYlp8zLPfXwKgL1LqxYY+/09jTbW7ARyUSkhI8Uquxx9Xkg4P9l6YTY5GN/wdWpfs4K5c0w5V5MaNoS+/RzERzYncXsI6ad8Of5tN+IWNQHg2msv/SCnfZ1Avru7A3+O6cq1TavhcMDfW0/Q/+Ol3PvdOjZfxpAlEYATc6bBlp9wmCww+CuG3h2gPmiRXLJj/zRTD2ZldsDdlMmXtd6k5oCVJR77RUrKqZkTIGo2mSY37kl8kFSHJwf+bEjQoE2K/cXEbLq0ba891LJUoAAvN8ICjV2/tpdSlUx27J9cvw1LM5vjZUrnM7dPsSRB5F/eHDlowdvdypPX16buvi7YYo31OTJNnJjSSbFfyqQzv4+Fg0uxW415kUNHWonxOA2AT5NjBcb+7IRxcroSMuJEucvRX7WNZJ+9BjVMMXzW5HXAkackcdpUExE9rJyd2ZoTk3pgO+ddLCe4LWtVYsLI9sx5vDvXtaqJyQT/7Izmhs+XM+Kb1aw9GFP4i4hg7Ahwz0178FvyFAAvL3iB7nd0ZO4cE/4RxgwMq38qvs2O4x+xPc+Jp4grOR/7Y3k+416OOqpQ1xzNBw3fxWTNLJXYL1JcYmLgocFbCFj9HwBeiRnFDkcd4tfVwbvNQcX+YmTJOhMpdIaMTUN9i6J5iNEyUVptS/v2gVf9aNyqpPBkxkOccfjTxHyY/zX+CMjbijRjYgBNjnbFFueFyeLAr+0hxX4pU2Ji4MkhK6m06S0A7vr5A7rfXJ+FGxKw+BrbyVt8MgqM/d7uRnxKUUJGnCl3OXoKnjyS8QhpDit9PdYy+qqvCM+1Q2TlyjBntom5cwGHicBrivcEt3F1fz4d2oZ/nuzJzW1DsJhNLN1zhiHjV3LblytZtucMjkKuyIhru/OOVEZXuxtf9yRWpDdnQkBvVq7JOijUDAyRHLljfzy+PJY+mkyHicFuS3ngtg9KNfaLXKlRIxJ5vOYoPKzpzE9vxxSvnmQmu3FueQPF/mJW1JalnKG+miFzUdltS1uPlU67vl+1FIIGbgbgNJV5KuMhAEZ5z+a6hrMuiP3z/3bnhYjWOOzg2/SEYr+UKfePjOWxWvdiNWfya2pPZoU1ZuWaTHyaHbvgsfnFfq+shIxalsSp/l2OvuVcY149YgTnsf3+QwO/rRc8JzPr72xJHeTUr+rL2Ftbs/CpXgztEIabxcTqAzHc8c1qbh63gshd0UrMyAWioqBX5uu0rb6FWIcvT9gfxLtZNH6djSOFf8/ASD0SBJDn4EPEVfw79q8+14r3zowA4L36H7D/+PILnlPSsV/kckRFwXWW52kUtJeTjso8a78PMJEeHYA9zU2xv5ipZal4ZQ/23V4KOy1lZNoZu2oDFq8M0qP9SdxRkwVxHfn85G0ATLnlYRoEX3giW88vkPhVF/6DUewXZ4ra7eA2r8eoHXCUg/ZqvMIIfJsdx6/LbnxbHL3g8fnFfrUsSZmRuxz92Lirefvb11kV2xd3cxr8PArS8k6eLmjIY3Ef5IQFefPWzS1Y8mxv7upSBw+rmY2H47h70joGfrKM2VtPFHqFRlxH/Lo5PNX5MwCeyXiAaIy/nz5NjoPJwbkFxomnLd6TxO0hxEc2o28/h7ZtFJf179j/0riPWJ/aFl9TKrUiH2b3sdN5Hl9asV/kUiSv/pl7207G7jDxRMbDxGK0gLgFJSj2l4AiD/XN0FDfomietcvL/jNJJKSW7GDf71YcZMPhOHw9rDSOacvZv9pwbNzVPPHVZ0QltsbfLRZ+vRcybXmeV78+xC1vQGaKW57bFfvFmdJXTmRIsz9Id1h5NGMMiRjzjnxbHMPilZEV82teNPbntCypQkacLbscPSoKZs2CqCgTnd4cB3414eweY7eaXP59ZbWkD3JqBHjx6vXNWPpcbx7oUQ9vdws7TsTz0A8b6PvREn7feAxbpr3wF5KK69wx2hx8EIDx0YP5x94u567UI0HgMNH5qvMnnmdntiaih5VpU03OWrGI0/079u/abaHN81OINwfQzHSQ7ZMeIz7XCUJpx36RQp3dR8tDjwMw9swwVtqb5dyVeqSKYn8JKEqFTKbdQXpmdsuSTl0uJsjXg5oBngDsPJFQYu8Tm5TOJwuMiuH/DmpK5B8+ObF/+y53Gr74Lbj7weEVsPjtPM9t2BD6XmvizC8dyP7fnnygimK/OM/JrTQ9bOwU9vrR+9niqH/+vqy/o0FxYZyd2eaisd/LTQkZKWMaNID+/Y0/8QmCW74Bkxk2T4NN0/I89t9XVkvjICfYz5MXBjRh+XMRPBoRjp+nlT2nEnn8p030GbuY6WuPkG5TYsblZNrg13uxpMeyJ6kVT//wSb4ni0sW5046GieilSs7e/Eizpc79psrhWC6aRwAN2f8zQ+TvsjTIuqM2C+SL1sa/DIKsy2RLfFd+CR1CAD2dItifwnKrpC52HWwNNv5kxtVyBSuWVbb0rYSbFv6eMEe4lNtNKnhz+B2tYB/HfcH1oPrPjIevOR92L8oz/OnTTXRs2UAiZvDADCbHYr94hxpifDzKMz2NFbH9uWdH1/LOe5P3lcVi3cGOEzM/zK00Nifk5BRy5KUWbW7QC8j+8jfT8HpqJy7LqyqKb2DnMo+7jx5bSOWPRfB09c2pLK3GwfPJvPsr1vo/f4iJq86dMnDmaQcW/yOcUXH3Y/gh7+lW1efAk8W8xx8iEi+/FoM5FTz+wAYduJtfpx3fp6MM2O/SB7z/wsnNoNXIBuvfgVz1WQyU9w4Nj5Csb8EnU/IFJyRyR7oC0rIFEXzrMG+JbXT0v7TiUxZdQiA/wxskvP/8AItboG2IwEH/HY/JJ7KuSs79v/5VjgWkwnP2md55bMYxX4pfbOeMTo4/GrS6LlxRPRwyznuz0zwAuDaJtUJ9vMsNPZ7aZclKRe6PwV1e0BGEvx8F2Sk5LnbmQc5AV5ujIlowLLnInhxQGOq+HpwLC6Fl3/fRo93F/L10v0kp9sKfyEpv/YthCXvGV9f9xEBdevrZFGkGATf+CZnApoTYEqm0fLHWbXnZJ77dYIrTrXzL1g9HoDYvp/w3hrjRPaJqxsx81d3xf4SlNOyVIQKGTeLqeCTf8mRs/V1CVXIvDV7Fza7g6sbB9M1vMrFH9zvHajaBBKj4bf7wJ73RLVrGy+GdgwF4MN/orTJhpSujT/A5qlGB8fgr6lUMyjnuP/XPzOo2t4YSj2qe+0ivZxalqR8MFvg5q/Apyqc2g6zn3P2ii7g42Hl/h71WfZcb167vhk1Ajw5lZDG//7eSbd3FvL5wr0lPihNnCDhpHGwgMO4otPilpy7dLIocoWs7gTdOYUUsy9tzXuImvoMJ86lFP48kZIWexB+H2183XkML22vSWKajdahlXhsUJhifwmzZJ2J2C9yIq4try9Ni1pGhcyeU4nEJKUX62uv3HeW+TuisZhNvDCgSeFPcPeGIZPAzdtoW1o69oKHjO4djrvFzJoDMazcd7ZY1ytSoFM7jY4NMDo46nTNuatBA4ipdIRUWybhwb50qhdYwIvkpQoZKT/8qhtJGUyw4TvYMt3ZK8qXp5uFO7vUYfEzvXnr5haEBXoTk5TOe3N30/XtSD6cH0VccvH+ohMnyZobQ9JpCG4G/d919opEKhxTYF3MN30BwEjHn0ycOE5zusS5bGlGtW7aOah1FQtDH2LW1pNYzCbevKmFqjFKgSWnQuZiCZnsLa+VkCmKYD9PGlf3w+GApXtOF/6EInI4HLw3dxcAwzuGER7sW8QFNYaBHxhfL3oTDizJc3eNAC+GdjCqZMbOV5WMlIL0rE4NWwrU6210cOSy+Ugc787dDcCdXepgMhXtd4GXdlmScqV+b+j5rPH1X4/nmSdT1rhbzQztEEbkUz358LZW1K/qQ3yqjY8X7KHbOwt5Z84uziSmOXuZciUWvwMHl4KbD9z6Hbh5OXtFIhWSR4sbiG91LwCj497nk98WOHlF4tLm/xeObwTPSqTc8DX/+dM4FrmnW12aZm0fLCXLnD1D5qIVMlkJGe2wVGQ9G1UFYHFU8SVkFkedZsPhODzdzIyJuMS9qVsPg9bDwWE3LoDlmicD8HDvcNytZtYdimXD4bhiW7NIvv5+Gk7vAt+sIgHz+WTvqYRUHpi8nnSbnT5NghneIazIL6uWJSl/ej4HdbpnzZO5E9KTnb2ii7JazNzUphbznujJ58Pa0ri6H4lpNsYt2ke3dyL5v792EB2f6uxlyr9ERcHs2bBnTwEP2Lsg19yYj6GKatNFSpL/dW8RH9iSSqYk+mx7jp9X73P2kqQCKjT27/gjZ24MN33JR2tTOBaXQkglLx7vo98DpSW7QsZ+0QqZrJYlN522FFXPhkZCZknU6Yv+bIvK4XDw4XwjYTmiU22C/Twv/UUGvAdVGxvzZH69J888mWr+nlzfqiYA3688eMXrFddVaOzfMPn83JhbvgHfqjl3pdvsPDxlAyfjUwkP9uXD21rnJI2LQrssSfljtsDgb8AnGE7tgL+fhHJQpmgxmxjYsgazHu3OhBHtaFkrgNQMOxOXH6D7uwt5+fdtHI0t28klVxATA/36O2jUCAYMgIYNje9jY3M96NxR40oNDmh3F7Qc4qTVirgQqzv+I6aQavWjtXkfyTNfZOPh2MKfJ1IERYr9Z/ednxvT5VG2+Xbm62UHAPi/G5rh7W4t/YW7qJwKmYslZLKG+mqHpaJrXzsQH3cLZxLT2XEi/opfb+HuU2w+eg4vNwsP9Kx/eS/i7gNDvjPmyRxYAoveznP3XV3qADBr6wlOJegCp1yaIsX+k1th1tPG171fhDrdcu46cCaJB6esZ92hWPw8rUwY0Q4/T7dLWoN3rpalS2m9U0JGnMuvGtwy0chSbp4GG7539oqKzGw2cW2z6vwxuivf3d2B9rUrk26zM3nVIXq9t4hnf9nMwTNJzl6myxo23EHkEhtBgzYS8tACggZtJHKJjaHDsgKkLR1+HgUpMVC9pbETgIiUjsq1cR88AYA7LXP45btPdQAuxaLQ2J+eDNNHQnoChHUho9d/ePaXLWTaHQxsUYOrm1Rz7gdwMdYitCylZSghc6ncrWa6ZO2AtGj3qUIefXEOh4OxWdUxI7vUpoqvx+W/WHBjuO4T4+sl78Ke+Tl3NQ8JoG1YJTIyHfy45siVLFlcUKGxP/WcEfttqRB+DXQz5sYci0vh+V+30GfsYiJ3ncJiNvHJ0DbUq1rEGUm5eGYlZDLtDjIylZCR8qRud4h42fh61jNwYrNz13OJTCYTPRtW5ecHO/Pj/Z3oGh6Eze5g+rqjRHywiMd/3Mie6ARnL9OlREXB3Dkm/CO24dvsOFb/VHybHcc/Yjtz55iMMsZ/XoGja8AjAG79Htwuo/xWRC6buckA0js/BsALts/536Q/NeRXrkiRYv+sZyB6m7Hb4y0TmbD8CDtOxFPJ241Xr2/m7I/gcrIHJ6tlqfhlty1d6RyZ+Tui2XYsHh93Cw/0uMzqmNxaDoH29xhf/3YfxJ1PvtyZVSXzw+pDZFxsL3SRXAqN/VEO+GM0xOyHgFDSrh/HzG0nuXPiGrq/E8mPa4+QaXcQ0TiYP8d0pXej4Mtah1eupPGltC0psknZ0PVxaNgPMtOM7GVK+StfN5lMdKoXxA/3duLXh7oQ0TgYuwN+33Scaz5cwkNT1rPt2DlnL9Ml7MsaSeEZGpPnds9QYzvFxNUzYJWx2ws3jYfAuqW5PBHJ4t7nv6TU7IyvKZXRp1/jf7+v1Q4bctkKi/2pK76HTVOyZgdMZG+qHx//Ywwa+O+gplT1u4Ir/3JZzNm7LF3kn31adsuStr2+JNkJmQ2H4ziXknFZr5FpP18dc2eXOgT6uBfP4vq9BTXbGMf7P99p7HgG9G9egyq+HkTHpzFve3TxvJdUeIXFftuyz2HnXzjMbvzT/F06f7yJMVM3sjjqNHYHdA0P4teHOjPxrqtoVjPgstfhZjHjZjFi2qUM9lVCRsoGsxluHAeVwiD2IPz2ANjthQ9mKqPa1a7MxLuuYuYj3ejfvDoAs7edZNCny7h70lo2aF5CiaqfdQEn9UhgnttTjwTRuMpuWh08PzuAxgNKeXUiksNixWvod6R5VqWR+SjtNr/K5JUHy23sF+e6WOxvV2MDzQ5lzw54CXvt7jz36xbSM+30alSVm9qElPJqBS61QkYJmUsRGuhN/ao+ZNodLN975rJe449Nx9h1MgE/Tyv396hXfIuzesCQSeBZCY6thznPA3Bwv5kOgcYW2N9puK8U0cVif4/ay2h85L8ATPS9j3sXOIhJSqdGgCdjeoez6Ole/HBvJ9rVDvz3y14Wz8vYaUkJGSk7vAPh1slg9YQ9c/n+/ncvPpipHGgeEsC4O9ox/4ke3Ni6JmYTRO46xc1frOCOr1ezav9ZXQ0uAQ0bQt9+DuIjm5O4PQRbvCeJ20NwLAtj3t3DMduSjB2+rn7F2UsVEb9qeAz9nkyTlRssKzgwcywtrzlTrmO/OEdBsd9tZXX+vnMEZnsaNBoA3Z5k4vIDrD8Ui4+7hTduaoHJVPSdNKT4FGmob/a212pZumQ9GxqtF4t3X3rbUmpGJh/MM6pjHu4VTiXvYqqOyVa5Dgz+GjDBuol8MGIKjRrBhOdq47CbWHMghtW7r3wgsVR8BcV+3zWB/D78LkyOTH63d+P1U13xcrPw4oDGLHm2N0/3bUSdKj7FupbstqXkdFuRn6Mx8lK21GwNA8fCHw9zR8jb/D2sEssDGpB6JJDIyOYMHWZlzuzyd9DUoJofH93ehsf6NOSLhXuZsfEYy/aeYdneM1xVpzJjIhrQo0EVHRAWo2lTTQwdZmXuzNZZtzhY+sgIQr32gH8I3PItWBQCRcqE2l0wX/s6zH2BF91+YOttdVmV1ILUw1XKdeyX0vfv2G82ZbLmscFU8zgKgfXgpvHsO5vMe3N3A/DCgCaEVPJy4opdm8VU+FBfVchcvp6NqjJx+QEWR53G4XBc0nHmlFWHOBaXQnV/T0Z1rVMyC2xwDfR6ARa9ycNhTzFziDt7qgSRmeCBNSCVB989zMZvmpfMe0uF8u/Y72ZOZ8njA6nsdpqd9jCeT7+HXo2Cef2G5oQGepfYOrJ3WjISyUU7z1CqWcqcKJ/hjF83CrPJwZfh/0fdgEMXDuUrp+pW8eG9Ia1Y9EwvRnSqjbvFzNqDsdw5cQ03fr6c+TuiVTFTTCpXhjmzTURFwaxZcHrGx3QL/AvMbsYQX9+qzl6iiOSyJ/Ahpm2/GTdTJl94fUxNv+gKE/ul9FwQ+396g3YBC42tdm+bgs3Nj6embybNZqd7gyoM7xjm7CW7NEvWmchFW5ayZsh4WHXacqk61g3E083MyfhU1h0qeqlhfGoGny/cC8AT1zQo0WRYVI1n+DvqWrzcUvm+8YtU8T+NNcDYde+M73G27yx664e4rn/H/lOTX6Sp3xriHd48kPEEN14VzsQ7ryrRZAzkallKL/pQakU2KXP27YPH5rzDxowGVDIlMcFtLF6k5gxm2rvXyQssBrUqe/P6jc1Z+lxv7ulWFy83C5uPnuO+79fR/+OlzNxy/KLlu1J0DRpA/wYLqLL5NeOG/u9ArfbOXZSIXGDffhP3/fEpu2yhBJviGO/+Ie5k4BlqzD6oCLFfSk+DBtC/9h8Ebv/AuOG6T6BaM75csp9NR+Lw87DyzuCWqkx1MnORKmS07fXl8nSzcGNrYz7SJwuKntWesHg/sckZhAf7MrhtrZJaHgD79pu5Y8YEDmZWI9R8mk/cPsNCJg47WLwy+HXNyRJ9f6lYGjSA/tWnUCnqKwAez3iY9m3a8uZNLXJaJEuSl/ultywpISNlTv36kJ7pwcidb3Da4U8T8xHec5uQM6gpPNzJCyxG1fw9eXlQU5Y915uHe9XH18PKrpMJjJm6kWs/XMxvG45i07Z/VyZmP/xyNzjs0GYEtL+7wIdqkKiI89SvD0kZvozY9RbnHN60Ne/lVesk7BlGyW9Fiv1SCqJ3wIyHjK87j4GWQ9h1Mp6P/jFmYrxyfTNqZrUqKfY7j6VIM2SyWpa0y9JlGd07HKvZxNI9Z1h3MKbQx++JTuCrpfsBeLZvI6yWkj1drF8f4lIrM2LXWyQ7POhh2cqz1h/JOOMHwMZzRwp5BZFcjq7HMfMJAMZm3IJPi0G8d0urfJMxJRH7s1uWNNRXyrXswUy750Zw1+43yHBYGGRZxX2JkfTt56BBA2evsPgF+XrwbL/GLHuuN4/3aYC/p5V9p5N4cvpmIj5YzI9rDpNuU2LmkqUlwo93QGochLSHgR9APldDY2KMwaHlfYi0SHmWHfs3z+7HfXtfxe4wMcy6kLuC/6TD8IMVMvZLCUmJhR+HQUYS1O0JfV4jNSOTx6ZtIiPTQZ8mwQxuG6LYXwbk7LJ0kQqZtJwKGZ22XI7QQG+GtDeqXD7MSkgWJDUjk0embSTNZqdHw6pc07Raia8vO/avnnU9Y/a/AMAD1r+5JuogOGDj8bMcPptc4uuQCiAhGsdPd2DKTGduZnuWVL+Tsbe2yokz2Uoy9mcP9U1VQkbKu2lTTUT0sDLrp5E8OutdAN7o8To/v7kgz+Mq2lWtSt7uPN6nIcufj+C5fo0J8nHncEwyz/+2lV7vLeS7FQcv6R+4S3M44I+H4dR28K0Gt002tlnMx7DhDiKX2AgatJGQhxYQNGgjkUtsDB2mtjGR0pQd+3+e+gAvLjC2qXzVOonaYb+xaPepnMdVtNgvxcieCb/cA7EHICAsZ4D7u3N2szs6gSq+7rx1s9GqpNjvfNktS7bMwmfIqGXp8o3uHY6bxcTyvWdZc6DgKpm3Z+9i10nj38n7Q0qvpS879n875QneWmZUN3zZ+1mG1ooD4Of1RpWMYr8UyJYO00diSjjOXntNXjaN5qOh7XDLp8KrJGO/Z84uS0rISDmXezDT9a/dw7n6IzGbHPjNuRvO7KnwV7X8PN14qFd9lj7Xm5cHNSXYz4Pj51J55c/tdH93IV8t2U9SWtF7E13S4ndhxx/nh/j618z3YVFRMHeOCf+Ibfg2O47VP1WDREWcJHfs7/niEySE3YS7KZMv3D7kjanzWL07vkLHfikG8/8L+xaA1Qtu/wF8glgSdZqJyw8A8N4trajq56HYX0YUrUIme5clnbZcrlqVvRnSPhSAD+fnXyUTuSuaSSsOAsa/k2A/z9JaXp7Y3/rJl0mq0QdPSwr/TX6dKpzjpzVH6dvfrtgv+XM44O8n4cgqEhxe3J/xJM/e0CHfLa1LOvarZUkqnAYNoP8AEwFD34fQTpB2Dqbexv0jY13iqpa3u5V7utVlybO9ef3G5oRU8uJ0QhpvzNpJt3ci+SxyD/GpGc5eZtmz4w9Y9Kbx9aCxENapwIfu22f86Rma94pRRRoiLVLeZMd+vzs+x16tBVVM8XzseJf7vlzCovWJFT72y2Xa+AOs/Mz4+qZxUKMlMUnpPPXzZgBGdKpN78bBgGJ/WZEz1LcIuyypQubKZFfJrNx/lo/+icqpuHY4HMzZdpKnphv/TkZ1rZPz76S0GbHfgs/IbyCoAV4pJ/jG80PiEhNYcfikYr/kb/V42DiZTMyMyXiUpi3aMbhtSL4PLenYn9OypAoZqXCsHnDbFAgIhZh93F95FJUjNrnMVS1PNwsjOtVm4dO9eHdwS+oEeRObnMH786Lo+nYkY+ftJjYp3dnLLBtObIEZDxpfd3wI2o686MPr1zf+zB4anS31SBCgQaIiTuXug3noNOzeVWlqPsQ7Ph8RPHS5y8R+uQSHV8HMx42vez4HzW7C4XDw7C9bOJ2QRniwLy8OaJLzcMX+siFnqO9Fzquzh/p6aKjvFQmp5MXdXesC8NE/e7j2wyVMXX2Y2yas4sEp64lNzqB5iD/P92/s5JUCXpVg6I/gGUAronjD+g0BPXco9suF9i6AuS8C8GbGUHb5duCNm1oU2G5X0rHf010tS1KR+VaF26diM3tzbf2FvNnkwzx3u8JVLXermVuvCuWfJ3vy8e2taRDsS0KqjU8i99L1nUjemrWTUwmpzl6m8yREZw1yTIZ6veHa/xX6lOxhcvGRzUncHoIt3pPE7SHERzarsEOkRcqVSqGYb/+BTJM7/S1recrvxzx3u0Lsl0LEHoKf7oDMdGhyPfR8HoBvlx/kn53RuFvMfHx765ztSEGxv6zIHu9gv+guS8aJjYdalq7Y8/0b8/Htranm78HhmGRenLGVNQdi8HQz80hEOD/d37nsJL6qhMMt32LHzBDrEh6s/FueuxX7hdNR8PMocNj5xd6TbzIH8Op1zQjwcivwKSUd+73djJ0hL6VlyXplbylSymq05FTXL6m5dAT3eP/NwYyqTM68FnCtq1pWi5kbWodwXcuazN1+ks8W7mX78Xi+XLKfSSsOMrRDGA/0rEeNAC9nL7X0ZKTAj0Ph3BEIrA9DjEGORTFtqomhw6zMndk657a+/RxMm1o6w+xEpBBhHTnd8SOqr3qYx6wzOGCvwe/2boBrxX7JR2o8TLsdkk5D9RZw03gwm9lyNI63Zu8E4D+DmtCsZsAFT1Xsd74itSxl77JUVhIF5ZjJZOKG1iH0aVKNzxfuZeqaw0Q0Cubpvo1ytoEvU8Kv5kzbNwne8DwvWqdyyFGN+fb2gGK/y0s6C1OHQNo5drs15cWEu4loXI1+zasX+tSSjP1e7kbiWDNkpEKrefX1fHske/eN7+mWusNlr2qZzSb6t6jBzEe6MfGu9rQOrUSazc6kFQfp8e5CXvhtq2tsFWi3G21Kx9aDV2UY/rPxZxHlHiY3a5Yx8GvObBOVi/4SIlLCqvcbzk/HHwfgHbcJtDftIv2Un0vGfsmSaYNfRsGpHeBbHYb+BO4+xKdmMGbqRjIyHfRrVp0RnWrn+3TFfucrylDfVA31LXY+Hlae7deYTf+9lrG3tS6byZgswdc9yG9xQzCbHHzs9jmNk4+57HG/ZLGlwU/DIfYgid61GJrwKGY3D167vlmRdgYrydifPUMmRS1LUtHd+N6TzDs9DIvJzhdeH1N9tTsRPawue1XLZDIR0bgaMx7uwg/3dqRj3UAyMh1MW3OY3h8s4qnpm9l3OtHZyyw5C9+AHb8bOyrdNgWC6l/WyzRoAP37o1/uImXUtW+/wrKY6/Aw2ZjgPpbwantpc9Mxl439Lm/O87D3H2NHpWE/QkAIDoeDF37dyuGYZGpV9uKdWwrfulex33ksRaiQSdNQX9dmMnHVM5+wxNYSb1Ma33i8j8fiYJc+7ndpDgf8+QgcXondw587U54kBn8e79OQ0EDvS3qpkoj9Xu6X3rKkhIyUS5UDTVz78cckB3fD3yOBjU8PYc5PJ13+qpbJZKJreBV+eqAz0x/oTI+GVcm0O/h1w1H6jF3MmKkb2HUy3tnLLF4bJsPS942vr/8E6nRz7npEpMRUDjTT7f0JpAa2IdCUyLdu75IeuorlR447e2lS2lZ+AWu/Mr6+eQLUbAPAxOUH+XvrCaxmE58ObXPRWQLifOeH+halQkYJGVcVGuLNvOZvE2UPIcQnmv2v38qc3xNd/rjfJS1+B7b8BCYLE2u+xvqU6jSq5sc93eo6e2WAKmTE1Vjd8b5rMgSF45Z8NKuPMMHZqyozOtQN5Pu7O/DH6K5c07QaDgfM3HKCfh8t5f7v17HlaJyzl3jl9v4Dfz1mfN39KWg9zLnrEZGS5+6N56gfcQTUor75BF+5fcDzP61h+d4zzl6ZlJbtv+fsqkGf16Dp9QCsORDDm7OMuTEvD2pKmzCdrZV1OS1LRaqQ0WmLK7uhUxPuzniGM44APGK3wvSRkJnh7GVJado4BRa9BcChzq/zv53VAPjfTc1xs5SN+KAZMuJ6vANh+C/gUxVOKjjnp1VoJb4a2Z7Zj3VnYMsamEwwb0c013+2nDsnrmH9oZgSff+oKJg9m+LflvDEZph+JzgyoeVtEPFyMb+BiJRZftUxDf8Fh4c/7c1RvGv+nAe/X8PGw7HOXplkKbHYf2gl/HY/4ICr7oWuRlL+VHwqo6duINPu4IbWNRnZOf+5MVK2mAupkMm0O8jI2hNbQ31dW/valXGvUpdR6c9gs3jBvkjjotxFqquk9JVY7N/7D/z5KAD2rk/y0M6WANzSrhZX1Qm82DNLlVf2LkuqkBGXElgXhv0Ebt5ZwflxBed8NKnhz+fD2jL/iZ7c3DYEi9nE4qjTDB63kqETVrFi7xkcxfhzi4mBfv0dNGoEAwYY28z16+8gtjjOl+IOww9DID0R6vaA6z+DIgzxEpEKJLgJptun4rC4M8Cyhsft33PXxDUVry2znCnR2H9mj7GbXmYaNBoA/d8Fk4l0m50xUzdyOiGNRtX8eOvmFkUa7CjOlz1Dxm7P//7UXFeZ1bLk2kwmE7e2D2Wrox5v+TwLJjNs+gEWve3spQklHPtPbMlzEfY7rxHsOBFPgJcbL/RvXAxvUHy83LNallQhIy4npB3c8m1WcJ4Cka87e0VlVniwL2NvbU3kUz0Z2iEUN4uJlfvPMuzr1dwyfiULd58qlsTMsOEOIpfYCBq0kZCHFhA0aCORS2wMHXaFr510FibfDInRENzMGOJrdb/i9YpIOVS3O6YbxwFwj3U2t2fM4I6v13DwTJKTF+a6Siz2xx+HyTdBSiyEtIfB34DZOPB97a/trDkYg5+HlfEj2uGdNVRRyr6cGTIFtCzlTsh4WHXa4upuaVcLN4uJb0414miX/xk3Ln4b1n7j3IVJycX+mP0wZXDORdhTvd/ng/lG+c2z/RoR5OtRDKsvPpohI66tUT8Y9JHx9dIPYNU4py6nrKsd5MNbN7dk8TO9uatLHTysZtYfimXUt2u57rNlzNl28qI93RcTFQVz55jwj9iGb7PjWP1T8W12HP+I7cydY7r8Msa0RPjhFji7B/xrGdtbewZc5ouJSIXQ4ha41jgwf8FtGr1T5jL869Uci0tx8sJcT4nF/uQYIxF/7ggEhRtVse7GbhqTVx7kh9WHMZng46GtqVvFp/g+kJQ4s+niLUupNqN0xt1izmlvEtdVxdeDAS1qAPDJuW7Q41njjr+fMmZLiVOUWOxPiDZif9IpqNYCx62TeemvKBLTbLQKrcTtV4UV6+coDt6qkBGX1+5OiPiP8fWc52HLz85dTzlQs5IXr17fjKXP9eb+HvXwcrOw7Vg8D05ZT/+Pl/Ln5uMX3Y4yP/v2GX96huadT+MZehaAvXsvY6G2dPjpDji+AbwCYcQMCAi5jBcSkQqnyyPQxegtf9vtaxrHL2PYV6s4eS7VyQtzLSUS+9OTYdrtcHon+NWAO34DnyoArNh7hlf/2gHAc/0aE9G42mWvXZyjsKG+2RUyHhroK1lGdDLmQ/2x6TjnOj4D7e4CHPDbfbB/sVPX5qpKJPannoMfBkPsAahcB+74lT93JzF/RzRuFhNv39wiJ36UJdmtlSkZmUXuOFB0k4qn+9PQ8UHj698fhKh5zl1PORHs58mLA5qw/PkIHokIx8/Dyu7oBB6dtpFrxi7m53VHyMgsoMn7X+rXN/5MPZJ3yFbqkSAAwsMvcXH2TJjxAOxfCG4+xiDnqg0v8UVEpEK75v+g9XAs2PnC/VOqx6xn2FerOJWgpExpKfbYb0uHn++EI6uNasg7foXKxsnYwTNJPJw1xPemNiE80KPelS5fnCB7Y5QCK2QysndY0vwYMbSrXZkmNfxJs9n5ecNRGDgWmlwHmenw43A4tt7ZS3Q5xR7705Nh2jBjwxafYBgxg1ME8Mqf2wF4JKIBTWr4X+myS0T2DBmHA9JsRTtvUkJGKh6TCfq+BS2GgN0G00fAgSXOXlW5EejjzlPXNmLZ8xE80achlbzd2H8miWd+2ULv9xcxZdWhnC0oC9KwIfTt5yA+sjmJ20OwxXuSuD2E+Mhm9O3noEGDS1iQ3W5MVd/+G5jd4LbvoVa7PA8psYnuIlJ+mExw3SfQsD8epPOtx3v4nd3M8K9WcyYxzdmrcwnFGvszbcYV7z3zwOoFQ3+Cas0AiE1KZ9SktcQlZ1DHrxL3ttQQ3/Iqp2WpwAoZ44RGW15LNpPJlFMl88Pqw9gxw81fQ53ukJ5gzBuJ3u7kVbqWYo39tjTj3O3QMvDwhzt+wVG5Lv+ZsY245Aya1vCnT0j9Mnvc75UreVzUOTKKblIxmc1w4zhjFwZbKky9HY6sdfaqypUALzce69OAZc9F8EL/xlTxdedobAr/+X0bPd5dyMRlBy4aaKZNNRHRw8rZma05Nu5qzs5sTUQPK9OmXsJBs8NhtJ5tmmIMbL7lGwjvk3N3iU50F5Hyx2KFIZOgbg+8SeV7j3exnN7B0AmqlCktxRL77Xb48xHY8TtY3OH2KVC7M2BUTIyauI4DZ5KwnfNi6VvtaN7UothfThU21Df7ApC2vJbcbmhdEz8PKwfOJLF83xlw84Sh04yB3ymx8P2NcOZy+mTkchVL7M+0wa/3GFtcu3kbsyJrtOLPzceZtyMaq9lE8qKWNGtiLrPH/RazCfesAeSpRZwjo4SMVFwWN2PnpXq9ICPJ6EM8sdnZqyp3fD2sPNCzPkufjeDV65pS3d+T6Pg0/m/mDrq9E8m4RftITLNd8LzKlWHObBNRUTBrllHFMme2icqVi/jGDgcs+D9Y86Xx/Y3joOkNeR5SYhPdRaT8cvOE26dBrQ4EkMhUj7ewn97N7RNWER2vpExJK5bYP/tZ2DwVTBa4ZWJOIt5ud/D0z5vZdCwWe5qVtNO+1Bi5XLG/HCusQiYtp0JGCRk5z8fDyuB2tQD4fuUh40YPP7jjF6jWwhgC+/0NEHvIiat0LVcc++2Z8Mdo2PlXViJ+KoR1Iio6gRd+2wpApePhrJjnXeaP+7OrZJKVkBEh68B8KoR2MoZDfX+DsZe9XDIvdwt3da3L4md78eZNLahV2YuzSem8M2cXXd+O5KN/ojiXnHHB8xo0gP79ubRyRYcDFr4By8Ya3w8cC61uz/OQEpvoLiLln4evcWWtegsCOcdPHm/AmT3cPmEVJ85p96XScNmxf/ZzsPYrwAQ3jTdmQwAOh4O3Zu9k5pYTODJNpJ0IwCf8tGJ/OZcz1LfQGTI6ZZG87uhk7LCzYGc0B84kGTd6VTY2fQhqAPFH4btBEHfYiat0PZcV++2ZRlXklh+NRPyQ76B+b+JTM3hw8nqS0zNpVSOI9d+Hl4vj/uydltKUkBHJ4u4Dw6fnKmO83hgSJZfFw2phWMcwFj7diw+GtKJeFR/OpWTw0T976PZOJO/N3UVMUvrlv4HDAQvfhCXvGd/3fQuuuueCh5XIRHcRqTi8KsGIPyC4GVWIY7rHG3B2L0PGr+TQ2SRnr07+LbtFNbsq8vpPoeWtOXePX7yfr5YeAODs7Ja4Beb9f6jYXz4V1rKUatNQX8lfeLAfVzcOxu6A8Yv2nb/Dtyrc+ScE1jOSMZMGQdwR5y1ULi57VuSmH4xkzOCvofEA7HYHT03fzP4zSdQM8GR4nTbgMJeL436vXDstFYUSMuIaPANgxG8Q0s5IynynpMyVcrOYGdyuFvOf7MmnQ9vQqJofCWk2Pl+4j65vR/LG3zs4dantAQ4HLHoLlrwLwOm2b0Lnh/N9aLFPdBeRiscnyDgwD25KFWKZ7vkG1rj9DBm/kqjoBGevTrI5HDD3RVg9HoDojp9C2xE5d09bc5h35uwC4P4OTUjaXkuxv4LIblmyO8h3i9jsob4eVp2yyIUe7m38g/9t41GOx+WqfvSvCXfOhMp1Ie4QTBqopExZZLfDX4/ApinYsXCiy1fQ/GYAPo3cy/wd0bhbzIy7ox2tm3gA5eO4//zW19plSSQvzwC44zeo2RZSYuC76+DYBmevqtyzmE1c16omsx/rzoQR7WgREkBKRiZfLT1At3cX8vLv2zgWV4QWAYeDlJmvweJ3AHhy7hsE3zC6wGFdxTrRXUQqLp8qMPJPqNqEqo4YfvX8HwGJ+7j1y5VsPhLn7NWJ3U7qb0/Dqi8AuO+vj6k+YGRO7J+99QQvzTAuoDzUqz4v3lxPsb8Cya6QASMp82/ZLUseqpCRfLSrXZlO9QLJyHTw1dL9ee8MCIG7/j6flPl2AMTsz/+FpPRl2kib/hBsnEKm3cywXyZQ89rB9Ovv4JO5+/nwnygAXruhGa1CK5Wr4/7sliXtsiSSH69KRm9pdvvSd9fDoZVX/LLadhnMZhPXNqvOn2O6MmnUVbSrXZl0m53Jqw7R892FPPfLloLbBOx2mP0cXus/BODlIw8zvU2TQod1FctEdxGp+Hyrwp1/QXAzghyx/Or5P0JSohj21SqW7jl92S+r2H+FMm3wx2g8t36N3WHiiUNPM7tjaE7sH/TgSR6ZthG7A26/KpRn+zYCFPsrEkuu7crza1vK2fZauyxJAcb0Ns7Ep605zJnEtLx3BoTAXTMhsD6cO2wkZU7vvuL3VOy/QrZ0+GUUHrt+xGa38ODBl1jWozJBgzayOn4fYxfuBODRqxswtENYztPKS+z3ykrIpGZcuOlJfpSQEdfjVQlG/g61u0J6Aky5GfYtvKyX0rbLFzKZTPRqFMwvD3Zm6n0d6VI/CJvdwU/rjtD7/UU88dMm9p7K1SpgzzTKFbPmBjx96AkmV+1WpGFdVzzRXURch29V48C8Zlv8HfFM93yTRhk7GfXtWn7feOySXkqxvxhkZsBv98LmqdjsFkYffIEZ1drmxP7K16/naNgGbHYH17WqyRs3tcCUdfKu2F9xmHOdieQ32FdDfaUwXcODaFUrgNQMO98uP3DhAwJqwajZENwUEk7At/0ve4MPxf5ikJECPw2HnX+SZnNn1P7XmF+zSU7sD+huJMyGtw7niT55y17KS+xXy5JIUXj4wfBfoH4EZCTD1Fth+++X/DLadrlgJpOJLvWrMPW+Tvz6UGd6NaqK3QEzNh7jmg+X8PAP69lxOBp+vhM2TsGBmZEzxvOjV/c8r1OUYV2XNdFdRFyPdyCM/APCOuPjSGKa59t0YyOP/7SJLxfvy3eGRX4U+69QWiJMvQ22z8BucuPWnyfxl0/7PA/xDDuLyeKgbdUafHhrqzytLdkU+8s/a66MTL4VMhrqK4UwmUw5s2S+X3Eo3x0/8atmtC/VaAXJZ42ZMgeXXfJ7KfZfoZQ4mHwz7JlHptmL63+cxkL/phc8LG5FOF39G+Yk4f+trMd+75wKGbUsiVycuzcM/dHYUjMzHX6+C9Z8VeSna9vlomtXO5BJozrw15hu9G1WDYcDlm7dT/zXN8DOv7Cb3TnR7VsmbxlaLoZ1iUg55ukPd/wK9SPwcKTyjccH3Gxewluzd/Gf37dhy7z4FS3F/iuUdNbY7XDfAnDz5njPH5mx6/oLYr/JBMm7q/HGoNZYLTpcrahyV8hk5pMQTctuWVKFjFzENU2q5WwuMXZ+AS1J3oFG62pYZ0iLNxIDO/4s8nso9l+h+BNGy9jhFeDhz/GIX5m3rw9pJ/3zPCwt2p9zSxvSoEHZakO6FDm7LGmGjEgRWD2Mve7bjQIcMOtpiHzD2PGhENp2+dK1qBXAlyPaM/++hswOeItO5p0kOLwYnvoMzx2qQffBZ8vFsC4RKefcfWDoT9DiViyOTMa6j+cB61/8sPoQd3+3joTUfK6wZlHsvwKxh2DitXBsPXhVhpF/UqtXn5xBjalHKuf8+k3ZF0ybtDY0aaRD1Yos9wwZe74zZLIqZDRDRi7CbDbxynVGpcXkVYfYfvxc/g/0DDBmSTYaCJlpRpX2uolFeg/F/itwZg98cy2c2g6+1WDULGp17UKnoUfwCjN+ng47pBwM4uz0TvTtV3arX4oiu6JPFTIiRWW2wKAPodcLxvdL3oUZD4It7aJP07bLl+nkNhr8cSO10vZh86rKV/U/ZQ3NWbrnDIfDV1F/1DqStoVwbFxEmR3WJSIVgNUdbvoSOo8B4AXrNN5yn8TyqJPcMm4lR2KS832aYv9lOroOvr4azu4F/1pw9zwIvQowBjW2veEkHiGxmEyQtL0mrRPb8uMPOgmv6HK3ouU/1FctS1I0XcKrMLBlDewOeOWP7QW3oLp5wa3fQ9s7jSzAzCdg/n+NDSYuQrH/Mh1YCl/3MYYqB9aHe+Zx0FqP4V+v5kTYFsyeNtKOB3BsfASnfupUIY77c3ZZKuIMGWtJLkak3DCZoNfzRtb276dgy48QdxhumwI+QTkPi4oyMuTh4ee3XY6MbA6Y8Aw9S+qRoFwVHfkHk9yvUZ6zv5clah78MgrSEyEoHOvwn3kysB5DYpIZt3gfv6w7SopvDNVuW0Mdv0rc3SmcERHBFNBCKiJyZcxm6PsG+NWAef9hqHk+dbxOc3/0GK77bBmfD2tL1/Aqiv1XavuMrAsdqVCtBQz7ydj9BHA4HEzfsp+TYbswAd1qhPKfUS1o3EiB3xWYTCZMJqMwOb+WpVS1LMkl+M/AJizcdYp1h2L5bcMxBrerlf8DLVa47mMj9i9+G5Z/bGyJfdMEY6RBFsX+K7RxCvz1ONgzIKQ9qUN+YML6BD5fuIQ0mx0Pq5nH+zSkV426HBxqzvoZlf/Y7+V2abssKSEjklv7UVC5Nky/0+hx/PpqGPYTMZZGDBvuYO6c80Gibz8H474w8dDDVubObJ3n9vwyuzEx5Psa06aWvengxc7hgNVfwtwXjKsRdbrDbZONknUgNNCbN29qwSMR4Xy5eD/T1hzmYEIc/52/jmnb/HkkIpx+zapjzmeoo4jIFesyBirXgd/uo3PGJmb6vM4dyY8z8hsbQUcbs3ZKXcCIP4r9l8DhgKXvQ+T/jO8b9IVbvjEG62NURLw+cweTVhwE4N5udXlpYJMCBzlKxWQxmbA5HPkWKGQP9fVQhYwUQY0ALx69ugFvz97FW7N30adpNQK83PJ/sMkEvV+AoPrwx2jY+RecGwC3TyXGVlPH/VfCngmRr8OyD43vm91MZKNXeXXCTg5nVZ92C6/CGzc1p3aQDwBNGjlrscUve9vros6QMTmKuqVAMYqPjycgIIBz587h7+9f+BNEStupXTB1iFEl4+7La9vG88Yf/fCP2IZnaAypRwKJj2xORA8rc2Ybg7z27r149rtff2Mye0GvUWFlpBjloJunGd+3GQEDxxrtAgU4nZDG18v2M2XlIZKygll4sC+je9fnupY1y+2AR1eOfa782aUcOb4Jpt0OCSdINvvxQOpoltpbkhHnhclsz7oaqthfJGkJ8PvDsDNraGanh+Ha/xltwhitKI//uIk5208CxpXte7vXc9ZqS5Qrx7+ifPaG/5lNus3O8ucjCKnklee+2yesZNX+GD4Z2obrW9UsjSVLOZdus9P/4yXsO51EnybV+HJEu3x3acvj0EpjK+bks+ATzFNrJ/Hp3x0uety/bbeNaEs0J9JjOX4ulZPnUolPzaBBsC/NQwL4ZUIAa+YE4N9zp2vF/pRY+PVe2PsPAEkdn+CJUwOYt/M0ANX9PXlpYBMGtaxRYZPvP6w+xEszttG7ng+THuhdaOxXQkYkywUlhYmnjZ2XDhnb4r1/YgRfVO6LPWv0UuL2EM7ObE1UVOEliFFR0KgRBA3aiG+z4zm3X8prlEtxh+GnO+DEZjBZONX6/1jvNprwBqYifd7YpHS+XXGQb5cfICHVKPurHeTNw73qc1ObWrhby1dixpVjnyt/dinbLoj98ceNuHVsPZkOM+/abuXLzOvIrpBR7C+Cs/vgx2FweheY3Yhu/x4bTKNyfsYnz6Vy/+R1bDl6DneLmbG3tWJQy4p7su3K8a8on73Jy3NIychk6bO9CQ30znPfjZ8vZ9OROCaMaMe1zaqXxpKlAth4OJbbJqwi3WbngR71eGFAkwsec0HsjzlgxP7obWRkWnnp2GimB3cgb+xvxQ+RZ1h58ijzd5zMaakriD3dgtn9fJVEhY/90dvhx+EQewC7xYtfK7/Ka6fqkphuw81i4p5u9XgkIhwfj4rdpPPbhqM8OX0zHWt5Mf2RqwuN/eXrbEakBMTEGFcwGzWCAQOMHtF+/R3EZlSFkb9zoPrDADxdYzKT3N6hCsbk9kuZqu6Sk9mj5sKXPeHEZuyeQTy34zeq3TiGAQNN53/GsRd/ico+7jx5TUOWPx/BM30bUdnbjUNnk3nu1630fn8Rk1ceLPIEcxGR3AqM/Zk1YdRsjlQdgcVk5wW3H5ngNpYAEgHwqhcNOBT7C7J9BkzoBad3YfepzhNb/6b6wFE5P+Oeg2MY9Mkythw9R2VvN76/p0OFTsZI4bKrFzTUV4pLm7DKvHdLSwC+XLKf6euO5NxXYOw31YV75nE8aDBuFhvvhn3MR26f40MKAF51T1H9zmW8OHcNf20+TmqGnTpB3tzfox6v39icr0e2Z+p9HfnvoKZ0rBaCLcEjTzIGKnDsdzhg4w/G8N7YA5xIC6PPro945mgoiek2PJP9+eHObjzfv3GFT8bA+RkyaUU8R6n4PxGRQgwbbpSTBw06X5YYGdmcocOsTP3BjZFT36R2XGsm3PgIPSxbmWV+gcczHmbekb5A0aaq557MnvsqaYWczG5LhwWvwcrPjO9rtOKuWZP58Z+aBA3aeMHPuChlm/6ebozuHc6ornWYuvowXy7Zz7G4FF7+YzufRO7lgR71GNYxDG93hTQRKZqLx34Phv30Cc2S2/DxgOe41rKepuYXeTR9DBu8GlLlho0EhzYHCm69BBeL/RkpMOcFWP+t8X1oJ+74YxK/LKiSFfvPYkvw5GD1eExJDhpX9+Orke0vqIgQ15PdTWLLJyGTZsse6quEjFyaG1qHsP90Eh8v2MNLM7ZS1deD3o2DC4n9Ptz289d0sLXhnWv+y42WFbQy7WNMxqNs966LxTsDT6uF2zuEclObEFrWCrig7aZL/Sp0C4bGzTKpNnw5HtUTcu6zJXgCFSz2pyVkbYjyEwBr43swKvleEkOtOByQfsqP4z934L973Jkz28lrLSU5M2S07bVI4aKiYO4cE/4R2/Btdhyrfyq+zY7jH7GduXNM3HiTg9XrbUyP7kfHb/9hZ0pdgk1xTHF7i2cyZjCwf1qRSg6zJ7PHRzYncXsItnhPEreH5JrMXvKftVSc2QsT+55PxnR8kD095jP5z9oF/oz37Cn6y3u7W7m3ez2WPtub/7uhGTUDPDmdkMb//t5Jt3cW8vnCvSSkZpTMZxORCqNosT+TiUduoev3s9mfGkIt0xmmu/8fo82/49/4KKP/XMqKvWcu+j4uE/ujt8NXV2clY0zQ7Umius5k2l81cv2M0/AMOYfJ4iB5dzXevbaLkjECnK+Qsee7y1J2hYxOWeTSPd6nAYNa1iAj08GoSWt54vvtzPvHXmjs/3T/CPotnsQxexB1zdH85v4Ko5hDlei6rHghglevb0ar0EoFzkBp2BCu7WPm7M+dSdxVHXuG8ffXMySOdiOjCA8v9YkhJePYeqMicstPYDKzofYTDHE8TGIl4wKpyQQe1RLw773zko/5y7PsChklZESKoLBy8qVLjAP2akNXsc+9Ou3GrmDC+jsxmxw81+kjfh9wNZzcVqT3mjbVREQPK2dntubYuKs5O7M1ET2s+U5mL3fsdlg1HsZ3g+MbwLMS3D4V+r/D3oMeQPGW7Hu6WRjZuQ6LnunNO4NbEBboTUxSOu/N3U3XtyMZOz+KuOT0K/1UIlJBXUrs32GpTesPVzF16y1YTXaecZ/On16v452wn2Ffr+bl37eRmFbw1pYVO/ZnwtKxRnvqqe3gUxVG/AZ9XmHfAWNnE8/aeZNWmalWTv/ejmOHVNEoBrUsSUkxmUy8P6QVd3QKA2DGjoNUv3MZXnVP53lcduxfuS2JKrevoMady9nbycqA9LeYl9EeD5ONVzy/Z2XXZwlMP1Gk986J/X+048jYfpxbaZRMnqmxhxdnbMOez9/3csOWDpFvwNfXwNm94B/Cws6TGLz7KvCw47Dl/f1WYVu1CpBdIZNaxF2WlJARl5a7nDy37HJyMA7YLZ42goespfKo1bxov5tbpn9HujUQ65mtRmZ4yfuQefHKjMqVYc5sE1FRMGuWcYV2zuwKsPVdzAH4/nqY8xzYUqBeL3hoOTQeCBT+M76Ssk13q5nbrgoj8qmefHhbK+pX9SE+1cYnC/bQ9e1I3p69izOJaZf/BiJSIV1q7Pe7cz2Ppo5h5IzxZFgCaOaIYo7nS9xtmc0Pqw7Q98MlLN2T9wA/W4WN/aejjIrIBa+BPQMaDYAHl0P9CADq1nPgd9V+LN55k+Mp+6oBpopVsi9XxGy6WEImq2XJqoSMXB5PNwv/u7EF3466ikAvD9yrJGLxznvMbrJmUmvMfELuW4x71USyC19iUioxbOu7PDhzLDazD25Hl8K4LrDuW/Ldpz2XvLHfxJqvG/P6Dc0wm2DamsN8+E9USX3kknVyK3x9NSx5FxyZ0Hwwf3T6ibsXWnEACZtDSdqddwB3hWzTvQjv7ISMKmRECnexcvJu3Y0Dg9wH7G6ByWCGX3feyNHrVxsHoPYMiHwdvuwBh1cV+p4NGkD//hVgurot3UhEfdEJDi4FN28Y8D6M+B0CauU8rDRK9q0WMze1qcX8J3ry+bC2NKnhT1J6JuMX76PbO5G89td2Tp5LvfI3EpEK4fJiv4nJW4Zy9LoVUK837o40/us2mVler1D53HZGfLOGx3/cyKmE/GNNhYn9GSkQ+T/jpOToWvDwhxvHGVWRftUAOBKTzCuLVhEYsROTGWwJHtgSPCpmu5ZcsYJalhwOB6k2tSxJ8ejdKJh/nu5BpTNh2OI989xn8c7A4pOOw27CluBx/nYvGzgsfLn+Ho4OWgZhnSE9EWY+Dt/2h+gdhb5v7tg/onMd3h5sDBv+NHIvv64/WqyfsUSlJcLcl4yKyJNbwCsQhkzi5zqv8fhfh3E4YESn2rSnOfGRLSp2m24hsiv6kgvZhSub6kXF5U2bamLoMCtzZ7bOua1vP0fW7Q4iI5sDJjxDz5J6JCgnqNRrGQwtpsKW6TD3BTi1w7ha2HYkXP0K+FRx2mcqcQeWwqynjS1NAer2gEEfQVD9fB9+sZ9xcTKbTQxsWYMBLaqzYOcpPo3cw+aj5/h2+UF+WHWYIe1r8WDP+ppbICKXHfvrtq4FrWbA+kkw/xUap+3jT4//8r3tGsZuGsyCnad48tqGjOhUG6ulgp1E7vnHiP2xB4zvG/SFgR9ApVAAbJl2Jq04yNj5USSnZ+LlZiFgfxNWTw0je+vYkoj9Ur4VVCGTnmknO0fjoZYlKQaBPu4sfK8FQ4c5+GdFCp5hMZg9MmhR35P3XvXmlae9WLzIhH/E9gtif5229aD137B6vNGuc2QVfNkdOo+GHs+Ah1+R1nBr+1AOnknii0X7eP63LdSq7EXHekGFP9FZHA7YNRNmPw/xWQmkpjdA//f4+4CdZ3/dgMMBIzvX5rXrmxHX08TQYaYSP+Yvy7JnyKTbipaQMTkc+UzQKmHx8fEEBAQUuie3SGnas8fobQwPP38FMzYWhg5zMHfO+SCSHVTylJsnx8D8l2HjFON7D3/o/hR0fBDc8mbhy7Uze2H+f2H338b33lWg7xvQ8jYoYLBZbvn9jEuSw+Fg2d4zfLpgL2sOGrMirGYTN7YJYXTvcOpW8Sn5ReTiyrHPlT+7lG1XFPsTomHui7DtFwDiTX6MTb+JKZl9qBNciRcHNKZ3o+ACBz+WG9HbYd5/YF+k8b1fDej/DjS5Pif2bzwcy4sztrHzRDwAHeoE8v6QVoQFeZd67C9rXDn+FeWz93h3IYdjkvn1oc60q32+Mu1cSgatXpsHwO7/9cNDbUtSjK4o9scdgTnPG4kKAJ9g6P0itBkBlsLrHex2B2OmbWDW1pNU8nbjrzHdyubFwuMbjaqYQ8uN7yuFwYAPoOG1bDoSx21friTNZueOTmG8fkPzPL/rXDnup6Rn0uS/c7CnJXPko1sLjf1KyIgUQZGDyqEVMPs5o5QPICAMej1vJCyKEKDLrPjjxuDG9d+C3QYmC7S7CyL+A96BhT69LFi9/yyfLdzL0j3GgEmzCQa1rMno3uE0ql60qxpXypVjnyt/dim/ihz790XCnBfh9E4ADlGD99MH87e9Ex3rVeX5/o1pFVqpVNZcrGIPwZL3YNMP4LCD2Q06PgA9nwNP49/xsbgUPpi7mxmbjuFwQCVvN17o35gh7UIxm8t5IqqYuHL8K8pn7/3+Ig6cSWL6A53pUPf8McWp+FQ6vLkAkwn2vzmg/Cc2pdwocuzfNQvmvQQx+43vg5saiZlGA8F88QrJlPRMbp+wks1Hz9EmrBLTH+iMW1mpqjyzFxa/A1unG99bPaHzGONis7s3x+JSuOGz5ZxJTKNPk2C+HNE+p/VQjIRbvRdnKSEj4jR2u7H924L/g4Tjxm2V60D3p6HV7WBxc+ryLsm5o7DsQ9jwPWRmDWZs0BeufR2qNnLu2i7ThsOxfB65lwW7TuXc1rdZNR6JaEDzkIASfW9Xjn2u/NnFRWTaYOP3sPBNSDIG/O5z1OTjjJuYae9Mr8bVeezqBuUjMRNzAJZ+AJunGUl4MKphrnkNAusBcC45g/FL9vHNsgM5ZdmD29bixQGNCfL1KOiVXZIrx7+ifParP1jEvtNJTLuvE53rn2/dOHw2mR7vLcTLzcLO1/uV1pJFLo0tHdZ9A4vehtQ447ZqzaHns9D4uosmZo7GJtP/46UkpNoY0zucp/s6+dj6zB4jCb/1ZyMJD8ZF5YiXc1pTE9Ns3DJuBbtOJtCkhj+/PNgZH49yfNG5hDR+eTbJiYlFSsjopydS3MxmaD3U6K9c+xUs/wRiD8KfY2DRW3DVPdD2LvApw/2iR9fBqnGw4/fzB+O1uxrVPnV7OHVpV6ptWGW+uesqth07xxeL9jJ720nmbo9m7vZoejeqypiIBrSrXd63PxGRUmexQvu7ofktsPpLWPkZ9VOP84n75zzjmM53e65lxK5etG5Yh/u616VbeJWydcXf4YDDK43Yv2vm+YPxer2h1wsQ1hGAs4lpfLPsAN+vPJSz3XfHuoG8NLAJLWtVctLipTyzZp2w/nuorwb6SrlgdYdODxkXXVd8ZsT/6G0wfSQEhUOHB4zzgnxmzNSq7M1bN7dgzNSNfL5oL90aVKFTac+TcThg/yJjNk7UXCDr32HDfsZxf802uR7q4JmfN7PrZAJV/Tz45s72SsYUwNvdSnIRH6sKGZGSlp4Ea7+BFZ9CUlZVhtUTmg+GVkONREchZY2lIiUOts+AjZPh2Przt9fulpWI6e60pZWkPdEJfL5wL39uPk72PMGu4UGM6d2ATvUCi/WEyZVjnyt/dnFRqfGw5ktY+TmkxAKQ5PDgj8wu/JrZg8Sq7bi7e10Gtazp3APapLOw/TfY8J2xnWm2+lcbsT+0AwD7TicyeeUhflp7hJSsrTwbVfPj6b6N6NOkAszJKUGuHP+K8tn7f7yUnSfi+f7uDvRoWDXn9i1H47j+s+XUCPBk5QtXl9aSRa5Mcgys+sJIzKQZM7Xw8DcqTVoPhZptL5i7+MzPm/l5/VFqBHgy+7HuVPJ2L/l1Jp4yKmE2TM5ptwWMHWR7PpsnEZPt2+UHeO2vHbhZTEx/oDNtwnQBsyBd347kSPRZtSyJXI6oKNi3rwSGUNnSYNtvsHocnNh8/vaAUGgxBBoPMoJfaSZnUuNh3wLY/jvsng2ZacbtFnfjKm/HB6Bm69JbjxMdPJPEuEX7+HXDUWxZmZn2tSszJiKcng2rFsvJhivHPlf+7FI+lFjsT082DnpXjzd248ty0F6NP+xdWWq+ivCWXbm1QxhtQiuVTmIjJdbYMWnH78YVUXuGcbvVC1rdZlzRrdaUNFsmC3ed4ofVh3PmbwG0CAlgTEQ41zSppjkxReDK8a8on33Qp0vZdiyeb0ddRe9GwTm3rzkQw61frqRuFR8WPt2rlFYsrqbEYn9aotH2uXo8nN17/vYqDaHFrdB4gDFzxmQiKc3GdZ8uY/+ZJAa2rMHnw9oW40JySToLe+YaF2D3LgCHkVzH3RdaDzNif5XwfJ+6+Ugct4xfQUamg1eva8pdXeuWzBoriKs/WMSeo6eVkBG5FDExMGx4ESarXymHA46sMYYkbp9xPnsO4FsNGlwLdbpDWCdjmnlxHpzb0o1k0OGVxhDKg8vOH4iD8Yuh1VCj7NI3uODXuYgS+8VWSo7FpfDl4n38uPZIzlyE4jr5cOXY58qfXcq2Uo39B5fBpqk4dvyBKSMp567jjkAWZrZht1crqjTtSfd2rWhVq1LxJTtsaXBsw/nYf2jF+QNxgBqtoOXt0Op2MjwqseZADH9uOs6sbSdISDXakkwmuLpxNe7sUjvfdqvyHvtLkivHv6J89hs+W8bmo+f45s72XN2kWs7tS6JOM3LiGhpX92PO4+W7XVrKnlKL/XY77F9oJGd2zgRbyvn7AsKgYV+o05Udbk25btI+Mu0OPh/WloEta1z5e2ekGFXvh1bC3n/g6Jrz7agAta4yKnda3gqeBc9RPJecwcBPl3I0NoX+zavzxfC2Ob8DFPvzd92ny9i8/4QSMiKXol9/B5FLbPhHbMMzNIbUI4HERzYnooeVObNL6ApgRgrsngU7/jQy1ekJee/3qwk1WkLVxkayJLAu+FU3EjfWAoYmOhyQeg4SThpDhc/sMa7KntppJGNsqXkfH9QAGvUzqnSqt7zsBFCp/WIrJafiU5mwZD8/rD6cU57fuLofo3uHM6BFjcuaJu/Ksc+VP7uUbU6J/elJsHMmjp1/YN8biSX3ATpw1FGFvaa6pAU2IqB2C2qHN6V6SB1MvtWNeQX5cTiMgZIJJyH+GJyOMsrQo3cYrUjZFZDZqjaBRv1xtLiFg5Y6rDlwlkW7T7N0z5mc2TAANQI8uaF1CMM7huW7LWtFi/0lwZXjX1E++01fLGfj4TgmjGjHtc2q59w+b/tJ7p+8ntahlfh9dNfSWrK4CKfE/tR42Pkn7PzLmNvyr2PyOI+arEoO4bAljNsH9sW/RnjWcX9wwZuCOBxG1WPCCWNX1NO74NQu49j/5Na8F14Bqrcw2pJaDIEqhWdQHA4HD05Zz9zt0YQFejPz0W74e7op9hfi1vErWbX7qBIyIkUVFQWNGkHQoI34Njuec3vi9hDOzmxNVFQpZH1t6XBomZGYObwKTmw6P1A3P+5+4OZpzKMxW40roLYUozz+3wfeuXkFQlhnqN3FGNhVQGnipcr9i83il0LKvmqkbAnj6l4l+IutFJxNTGPi8gN8t+L8AMt6VX0Y3Suc61vXvKQtCl059rnyZ5eyq0zE/oxUOLgUW9R8kvYuwy92J2bsBT48zeKDw+KJyd0Tq8UNsz0Nky210Njv8KmKLaQjp4Pas82nM1uSKrPzRDwbj8QRk5Se57FBPu5c07QaN7QOoWPdwItW6lTU2F+cXDn+FeWz3zJuBesOxTL+jrb0a36+KuDPzcd5dNpGOtUL5Mf7O5fWksUFlInYn55sJGX2LzQqWKK3kTNQ9wImYyiwNfu432wc92ekQEby+Z1Q8+NbHWp3NmZWNuyXs1tSUf2w+hAvzdiGu8XMrw91oUUto5JGsf/iRk5cw6Kth7TLkkhR7dtn/OkZGpPnds/QswDs3VsKgdnqDvUjjP+AmOgk3npkA8kHd9Gs6k6aVd1FWMARavqdxMOablTT/LuiJs/iKxlZ9cD6ENzYuBpavYXRu1rMc2qiomDuHBOVr91J8o4QUvafb3eaO9fBunXQvn2xvmWpCfL14Jm+jbm/e30mrTjIxOUH2H86iad+3sxHC6J4qGc4g9uF4GG1OHupInKJykTsd/OEBtdgbXANAUDMyQTefmwdtrgNtAjbStPAKGp6RFPNFIu7KROPzCTITIICjr8TTH6cswZxwhLCIUsY+02hbMwIY8O5INLOZh/sn836z+BuNdMiJIBu4VWIaBxMi5CAIrVLVeTYL6Un++9a5r/ykKkZ2bss6ferFK8yEfvdvY05Mo0HABB74hzvPr6e9JiNXNVhKQ0sRwlOSaC65xncLDZjxEHuMQf/5h1kJF+qhBvH/MGNjXbUynUvu/p9T3QCr880Zp89269RTjJGsb9w3pcQt5SQEQHq1zf+TD0SmCdTnnrE2HouvHiKSC7JsLu8iVzSCXxbkrnVi8p9tuPpHUPq5spYV4TQv3si336ZalxdtWecz5q7eRmljW5epbbW7F9sybtqknHKn6BBG3PKP2PmN+fBh6ysW1u+s+UB3m481qcB93Svy+SVh/hm2X6OxKTw4oytfBq5hwd61OP2DmE6cBQpR8pk7B/lS+SSbuDblswlWbE/9CwZp33wjXajWdNoGreI41RMPPHJqaThRirupDrcOUMAaRS0O4eRjAn0cSe8qi/1g31pEOxLm7BKNK3pf1lJZVeI/VLyLFkni5n/KtpPy07I6IKHFLOyGPuH3u1P5JLu4NsOn/QBBHTej8MMKduq4rasFn27JjNxfKrR5mTPPF8l7+ZtHPcXNMrgMqVmZPLItI2kZtjp0bAqd+ca4qvYXzgvdyVkRC5Jw4ZG32NkZHPAhGfoWVKPBBEf2Yy+/Rw0aFC6QSU781yp1x7iFjXNU1Lp2+wEiZiZ9EdrXnyvbAzQyv7Flna4yr/WehwwsX5ma/bsKRtrvVK+HlYe6lWfu7rUYdqaw3y5ZB8nzqXy6l87+GzhPu7vUZfhHWs7dxtbESmS8hT7rf5pnEsN4a8vB/JBVjl9akYmZ5PSOZOQRkxSOmm2TNJsdtJsdtwsJjytFjzdLPh7uRHs50FVP49iTRq7UuyXkmPJqZDJWyKTmmF87+lWirtPikso67Hf0sHIeJhM4N3oNIk2N779ow0vlOJx/9uzd7HrZAJBPu68P6RlnqpJxf7CXcrvWp0xiGSZNtXE0GFW5s5snXNb9nCq0padebZ4GzXpTi2pLIKGDaFtOwcb1pvK/FqLi5e7hbu71WV4pzB+XneU8Yv3cTQ2hTdn7eKLRfu4p2tdRnapQ4BXAUPYRKRMKM+x39PNQkglL0IqlV5FZG6uGPul+BXWsnQpV5pFiqpsx/7YPPd71TsFlF48nb8jmkkrDgLw/pBWBPt55rlfsb9w3pcQt5RyFslSuTLMmW0iKgpmzTKy1XNmO2dSeHbmOTPZKD1PPRKY5/7iLKmMioLZs2HPnit7nfHjjF9gJbnWssjDauGOTrVZ+HQv3rulJXWr+BCXnMEH86Po9nYkH8zbfcHATBEpOxT7r+x1XDX2S/GxZJ3/2u15W5ZSbUZCRjPapCSUp9hvds/EGpBcKrH/WFwKT/+8GYBRXevQu3Fwvo9T7L84L1XIiFy+Bg2cn9HNKaVc0gC34HPE/tOM4i6pLO7t6q66qmyVf5Y2N4uZIe1DubltLf7eeoLPIvcQFZ3Ip5F7+WbZAe7oVJvbWgU5e5kiUgDFfsV+cY6clqV/zZA537KkhIyUnLId+89gsjiw+KQTfscm6tbrxOXWUxQl9mdk2nl02kbOpWTQslYAL/RvUuDrKfZfnGbIiFQAOaWUcwLA5OBsMZdUDhtubFcXNGhbziCuyMjmDB12+dvVlaXyT2exmE1c36omg1rUYN6OaD5buIdtx+KZsGQ/ExfucPbyRKSMU+wXV2POHur77wqZnF2WVNAvFV9Bsd8akEzofUtI8Y3lo3/28HTfRpf1+kWJ/R/Oj2L9oVj8PKx8NrQt7taL/9tT7C/YDa1r0iTIytUfFf5YJWREyqjsUso9e2DvXhNWK9hsRgnglWads4eHBQ3adsEgrrlXMIgr75qLZ63lldlsol/z6vRtVo1FUaf5dMEe1u05XvgTRcSlKfaLq8mukLGrQkZcWMGx35udyS15dNpGPlu4l3Z1KtO7Uf5tRAUpSuw/mBHNF4uMYTZvD25JWJD3Ja5ZsT+3WpW98bcEFv5AlJARKfNKopQye3hYSQ3iKgvln2WFyWSid6NgejWsyj+bDnLtR85ekYiUB4r94irOD/XNf4aMZyFX6UUqkvziaANqsvZADJNXHeLJnzbx96PdqXkJw9wLi/2LNsXz4daNAIzsXJuBLWtc8Zql6BThRFxQ9vAwDeIqPSaTiY71NUNGRJxHsV/KIksBLUtpOS1LqpAR+c+gJrQICSA2OYPRUzeQlpWwLIqLxX6zTyoTdq0lOT2TbuFVeHlQ0+JcthSBEjIiLih7eFh8ZHMSt4dgi/ckcXtIrkFczl6hiIgUN8V+KYvUsiRSOA+rhS+Gt8Xf08rGw3E8MnUjGf/eK74ABcb+xY1pMGodp5NSqVfVh8+Ht8XNovRAaVPLkoiL0iAuERHXo9gvZc35ob55b9dQX5G8QgO9GX9HO+6atJZ5O6J5+ufNjL21dU5S82L+HftN7jYa37uOZJ9zVPJ2Y+KdVxHg5VbCn0Dyo4SMiIvSIC4REdej2C9ljbWgCpmslgwPVciI5OgSXoVxw9vywOT1/LHpON7uFt68qQUm08XjeO7Yv2lnOl9FrSHqzDm83S1MGNGeOlV8SukTyL8pISPi4jSIS0TE9Sj2S1lR4FDf7JYlqxIyIrld3aQaH97Wmsd+3Mi0NUc4FZ/G24NbUtXPo9DnegYlM27PGvafSSLQx51v77qKVqGVSn7RUiDVAIqIiIiIiFNkj6y4MCGjliWRglzXqibv3dIKd4uZBbtO0e+jJfyzI7rAxyen2/hwfhTXfLiY/aeTqBngyfQHOisZUwaoQkZERERERJwie5clDfUVuTSD29WiaU1/Hv9xE7ujE7j3+3W0DatEr0bB9GpUFU83C/tPJ7H3VAKTVx0iOj4NgKvqVObj29tc0tbZUnKUkBEREREREacoqGVJ216LFK5JDX/+GNOVD+bt5utlB9hwOI4Nh+MYOz/qgseGBnrxQv8m9G9evdCZM1J6lJARERERERGnyK6QySxgqK9alkQuztPNwksDm3J3t7os2n2aRbtPsXzvWUxAvao+1K3iQ9valbm1fagSnGWQEjIiIiIiIuIU2Vv22nNVyGTaHWRkGt9rqK9I0dQI8GJohzCGdgjDkZXgVCVM2aeEjIiIiIiIOEV2y5ItV0Ime6AvqGVJ5HIoEVN+qAZQREREREScImeobwEJGQ+rTldEpOJShBMREREREafIGeqba4ZMqs3YYcndas65X0SkIlJCRkREREREnCJnqK/9/G3ZFTKeqo4RkQpOUU5ERERERJzCknU2kl/LkubHiEhFp4SMiIiIiIg4Rb4tSxlGuYwSMiJS0SkhIyIiIiIiTpHfUN+0nAoZnaqISMWmKCciIiIiIk5hyXeor1qWRMQ1KCEjIiIiIiJOYc4Z6ptPy5JVCRkRqdiUkBEREREREafIrpCxOy4c6uuhliURqeAU5URERERExClyhvrmVyGjliURqeCUkBEREREREaew5iRkzt+Wom2vRcRFKCEjIiIiIiJOkbPLUj4tS55WnaqISMWmKCciIiIiIk6RX8tSmipkRMRFKCEjIiIiIiJOYck6G8lTIWPLniGjUxURqdgU5URERERExCny3/ZaFTIi4hqUkBEREREREaew5LvLkhIyIuIalJARERERERGnsORbIWO0LHloqK+IVHCKciIiIiIi4hQ5Q33z22VJFTIiUsEpISMiIiIiIk6Rs+21Pb+hvkrIiEjFpoSMiIiIiIg4heWiFTI6VRGRik1RTkREREREnCKnZcl+/ra07ISMVRUyIlKxKSEjIiIiIiJOkW/LUoZalkTENSghIyIiIiIiTmHOOhvJ07JkU8uSiLgGRTkREREREXGK/CtktMuSiLgGJWRERERERMQp8h/qm92ypFMVEanYFOVERERERMQpzg/1vbBCxkNDfUWkglNCRkREREREnOLfLUsOh4M0m4b6iohrUEJGRERERESc4t8tS9nJGFDLkohUfIpyIiIiIiLiFDkJmaw8THa7EqhCRkQqPiVkRERERETEKbITMvasCpnsgb4Wswk3i05VRKRiU5QTERERERGnMJvyDvXN2fLaqtMUEan4FOlERERERMQpcipkshMytqyEjNqVRMQFKCEjIiIiIiJOkb3Lks2et2VJCRkRcQVKyIiIiIiIiFOYs85GMh15W5Y8tMOSiLgARToREREREXGKC1qWcmbIqEJGRCo+JWRERERERMQpsluWMh3/blnSaYqIVHyKdCIiIiIi4hTmrAoZhwMcDgdpGuorIi5ECRkREREREXGK7AoZMLa+zmlZUkJGRFyAEjIiIiIiIuIU2RUyYLQtqWVJRFyJIp2IiIiIiDiFJVdCxm7XUF8RcS1KyIiIiIiIiFPkaVnKVSHjoZYlEXEBSsiIiIiIiIhTmHOdjWTaHaTmDPXVaYqIVHyKdCIiIiIi4hS5K2TsGuorIi5GCRkREREREXEKS0FDfTVDRkRcgBIyIiIiIiLiFCaTiewiGbvdQVqGWpZExHUo0omIiIiIiNNYs6pkMh25Z8ioQkZEKj4lZERERERExGnMWSUy6w/FsvFwHKAKGRFxDVZnL0BERERERFxX9hyZMVM3AhDk407HukHOXJKISKlQQkZERERERJwm905LN7cN4eWBTans4+7EFYmIlA4lZERERERExGkGtKjB5qNxvDigCT0aVnX2ckRESo0SMiIiIiIi4jTv3NLS2UsQEXEKTcsSERERERERESllSsiIiIiIiIiIiJQyJWREREREREREREqZEjIiIiIiIiIiIqVMCRkRERERERERkVKmhIyIiIiIiIiISClTQkZEREREREREpJQpISMiIiIiIiIiUsqUkBERERERERERKWVKyIiIiIiIiIiIlDIlZERERERERERESpkSMiIiIiIiIiIipUwJGRERERERERGRUqaEjIiIiIiIiIhIKVNCRkRERERERESklCkhIyIiIiIiIiJSypSQEREREREREREpZUrIiIiIiIiIiIiUMiVkRERERERERERKmRIyIiIiIiIiIiKlTAkZEREREREREZFSpoSMiIiIiIiIiEgpU0JGRERERERERKSUKSEjIiIiIiIiIlLKrM54U4fDAUB8fLwz3l5ExCmyY152DHQlivsi4qoU+xX7RcT1FDX2OyUhk5CQAEBoaKgz3l5ExKkSEhIICAhw9jJKleK+iLg6xX4REddTWOw3OZyQrrfb7Rw/fhw/Pz9MJlNpv72IiFM4HA4SEhKoWbMmZrNrdYwq7ouIq1LsV+wXEddT1NjvlISMiIiIiIiIiIgrc600vYiIiIiIiIhIGaCEjIiIiIiIiIhIKVNCRkRERERERESklCkhIyIiIiIiIiJSypSQEREREREREREpZUrIiIiIiIiIiIiUMiVkpMI7ffo01atX580338y5bfXq1bi7uzNv3jwnrkxEREqKYr+IiOtR7JfyxuRwOBzOXoRISZs1axY33ngjK1asoHHjxrRp04aBAwfy0UcfOXtpIiJSQhT7RURcj2K/lCdKyIjLGD16NP/88w9XXXUVmzdvZu3atXh6ejp7WSIiUoIU+0VEXI9iv5QXSsiIy0hJSaF58+YcOXKEdevW0bJlS2cvSURESphiv4iI61Hsl/JCM2TEZezfv5/jx49jt9s5dOiQs5cjIiKlQLFfRMT1KPZLeaEKGXEJ6enpdOjQgdatW9O4cWPGjh3L1q1bqVatmrOXJiIiJUSxX0TE9Sj2S3mihIy4hGeeeYZffvmFzZs34+vrS+/evfHz82PmzJnOXpqIiJQQxX4REdej2C/liVqWpMJbtGgRH330EZMnT8bf3x+z2czkyZNZtmwZ48aNc/byRESkBCj2i4i4HsV+KW9UISMiIiIiIiIiUspUISMiIiIiIiIiUsqUkBERERERERERKWVKyIiIiIiIiIiIlDIlZERERERERERESpkSMiIiIiIiIiIipUwJGRERERERERGRUqaEjIiIiIiIiIhIKVNCRkRERERERESklCkhIyIiIiIiIiJSypSQEREREREREREpZUrIiIiIiIiIiIiUMiVkRERERERERERK2f8D3w/V/vYt1v8AAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "\n", "\n", @@ -2189,9 +1909,7 @@ { "cell_type": "markdown", "id": "d4adf4c3", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Various steps in cross-validation\n", "\n", @@ -2214,9 +1932,7 @@ { "cell_type": "markdown", "id": "6e6c3fd3", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Cross-validation in brief\n", "\n", @@ -2242,9 +1958,7 @@ { "cell_type": "markdown", "id": "f56b418c", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Code Example for Cross-validation and $k$-fold Cross-validation\n", "\n", @@ -2255,10 +1969,7 @@ "cell_type": "code", "execution_count": 6, "id": "64e72139", - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", @@ -2355,9 +2066,7 @@ { "cell_type": "markdown", "id": "92d3a119", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## More examples on bootstrap and cross-validation and errors" ] @@ -2366,10 +2075,7 @@ "cell_type": "code", "execution_count": 7, "id": "20a55cbd", - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "# Common imports\n", @@ -2455,9 +2161,7 @@ { "cell_type": "markdown", "id": "0b1ab15d", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "Note that we kept the intercept column in the fitting here. This means that we need to set the **intercept** in the call to the **Scikit-Learn** function as **False**. Alternatively, we could have set up the design matrix $X$ without the first column of ones." ] @@ -2465,9 +2169,7 @@ { "cell_type": "markdown", "id": "d04d7a1a", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## The same example but now with cross-validation\n", "\n", @@ -2478,10 +2180,7 @@ "cell_type": "code", "execution_count": 8, "id": "bbd6bfa9", - "metadata": { - "collapsed": false, - "editable": true - }, + "metadata": {}, "outputs": [], "source": [ "# Common imports\n", @@ -2556,9 +2255,7 @@ { "cell_type": "markdown", "id": "3d61d3cd", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Material for the lab sessions" ] @@ -2566,9 +2263,7 @@ { "cell_type": "markdown", "id": "33014e05", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Linking the regression analysis with a statistical interpretation\n", "\n", @@ -2595,9 +2290,7 @@ { "cell_type": "markdown", "id": "af8973e3", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\begin{align*} \n", @@ -2611,9 +2304,7 @@ { "cell_type": "markdown", "id": "95f08a4f", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "The randomness of $\\varepsilon_i$ implies that\n", "$\\mathbf{y}_i$ is also a random variable. In particular,\n", @@ -2630,9 +2321,7 @@ { "cell_type": "markdown", "id": "69a3772b", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Assumptions made\n", "\n", @@ -2644,9 +2333,7 @@ { "cell_type": "markdown", "id": "6f44e2d9", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{y} = f(\\boldsymbol{x})+\\boldsymbol{\\varepsilon}\n", @@ -2656,9 +2343,7 @@ { "cell_type": "markdown", "id": "9f820ddc", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "We approximate this function with our model from the solution of the linear regression equations, that is our\n", "function $f$ is approximated by $\\boldsymbol{\\tilde{y}}$ where we want to minimize $(\\boldsymbol{y}-\\boldsymbol{\\tilde{y}})^2$, our MSE, with" @@ -2667,9 +2352,7 @@ { "cell_type": "markdown", "id": "cab623c2", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\boldsymbol{\\tilde{y}} = \\boldsymbol{X}\\boldsymbol{\\beta}.\n", @@ -2679,9 +2362,7 @@ { "cell_type": "markdown", "id": "47218f25", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Expectation value and variance\n", "\n", @@ -2691,9 +2372,7 @@ { "cell_type": "markdown", "id": "9290dce4", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\begin{align*} \n", @@ -2707,9 +2386,7 @@ { "cell_type": "markdown", "id": "65a7ab7d", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "while\n", "its variance is" @@ -2718,9 +2395,7 @@ { "cell_type": "markdown", "id": "a35cbd7b", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\begin{align*} \\mbox{Var}(y_i) & = \\mathbb{E} \\{ [y_i\n", @@ -2741,9 +2416,7 @@ { "cell_type": "markdown", "id": "0b5e006f", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "Hence, $y_i \\sim \\mathcal{N}( \\mathbf{X}_{i, \\ast} \\, \\boldsymbol{\\beta}, \\sigma^2)$, that is $\\boldsymbol{y}$ follows a normal distribution with \n", "mean value $\\boldsymbol{X}\\boldsymbol{\\beta}$ and variance $\\sigma^2$ (not be confused with the singular values of the SVD)." @@ -2752,9 +2425,7 @@ { "cell_type": "markdown", "id": "77270968", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "## Expectation value and variance for $\\boldsymbol{\\beta}$\n", "\n", @@ -2764,9 +2435,7 @@ { "cell_type": "markdown", "id": "49715a2d", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\mathbb{E}(\\boldsymbol{\\hat{\\beta}}) = \\mathbb{E}[ (\\mathbf{X}^{\\top} \\mathbf{X})^{-1}\\mathbf{X}^{T} \\mathbf{Y}]=(\\mathbf{X}^{T} \\mathbf{X})^{-1}\\mathbf{X}^{T} \\mathbb{E}[ \\mathbf{Y}]=(\\mathbf{X}^{T} \\mathbf{X})^{-1} \\mathbf{X}^{T}\\mathbf{X}\\boldsymbol{\\beta}=\\boldsymbol{\\beta}.\n", @@ -2776,9 +2445,7 @@ { "cell_type": "markdown", "id": "fb6a34f4", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "This means that the estimator of the regression parameters is unbiased.\n", "\n", @@ -2790,9 +2457,7 @@ { "cell_type": "markdown", "id": "942e7e6a", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\begin{eqnarray*}\n", @@ -2821,9 +2486,7 @@ { "cell_type": "markdown", "id": "f127bfb2", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "where we have used that $\\mathbb{E} (\\mathbf{y} \\mathbf{y}^{T}) =\n", "\\mathbf{X} \\, \\boldsymbol{\\beta} \\, \\boldsymbol{\\beta}^{T} \\, \\mathbf{X}^{T} +\n", @@ -2843,9 +2506,7 @@ { "cell_type": "markdown", "id": "2def67b5", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\mathbb{E} \\big[ \\hat{\\boldsymbol{\\beta}}^{\\mathrm{Ridge}} \\big]=(\\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I}_{pp})^{-1} (\\mathbf{X}^{\\top} \\mathbf{X})\\boldsymbol{\\beta}.\n", @@ -2855,9 +2516,7 @@ { "cell_type": "markdown", "id": "d28e3d89", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "We see clearly that \n", "$\\mathbb{E} \\big[ \\hat{\\boldsymbol{\\beta}}^{\\mathrm{Ridge}} \\big] \\not= \\hat{\\boldsymbol{\\beta}}^{\\mathrm{OLS}}$ for any $\\lambda > 0$.\n", @@ -2868,9 +2527,7 @@ { "cell_type": "markdown", "id": "ab34b80c", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\mbox{Var}[\\hat{\\boldsymbol{\\beta}}^{\\mathrm{Ridge}}]=\\sigma^2[ \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1} \\mathbf{X}^{T} \\mathbf{X} \\{ [ \\mathbf{X}^{\\top} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}\\}^{T},\n", @@ -2880,9 +2537,7 @@ { "cell_type": "markdown", "id": "677844a3", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "and it is easy to see that if the parameter $\\lambda$ goes to infinity then the variance of Ridge parameters $\\boldsymbol{\\beta}$ goes to zero. \n", "\n", @@ -2892,9 +2547,7 @@ { "cell_type": "markdown", "id": "89529d82", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "$$\n", "\\mbox{Var}[\\hat{\\boldsymbol{\\beta}}^{\\mathrm{OLS}}]-\\mbox{Var}(\\hat{\\boldsymbol{\\beta}}^{\\mathrm{Ridge}})=\\sigma^2 [ \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}[ 2\\lambda\\mathbf{I} + \\lambda^2 (\\mathbf{X}^{T} \\mathbf{X})^{-1} ] \\{ [ \\mathbf{X}^{T} \\mathbf{X} + \\lambda \\mathbf{I} ]^{-1}\\}^{T}.\n", @@ -2904,9 +2557,7 @@ { "cell_type": "markdown", "id": "688cfbfa", - "metadata": { - "editable": true - }, + "metadata": {}, "source": [ "The difference is non-negative definite since each component of the\n", "matrix product is non-negative definite. \n", @@ -2916,7 +2567,25 @@ ] } ], - "metadata": {}, + "metadata": { + "kernelspec": { + "display_name": "Python 3 (ipykernel)", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.9.18" + } + }, "nbformat": 4, "nbformat_minor": 5 }