diff --git a/doc/pub/week42/ipynb/week42.ipynb b/doc/pub/week42/ipynb/week42.ipynb index 7364bd9ab..d1e603313 100644 --- a/doc/pub/week42/ipynb/week42.ipynb +++ b/doc/pub/week42/ipynb/week42.ipynb @@ -1862,10 +1862,40 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 1, "id": "b1fb7c4b", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/homebrew/lib/python3.9/site-packages/numpy/core/_asarray.py:102: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n", + " return array(a, dtype, copy=False, order=order)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial cost: 457.256\n", + "Final cost: 0.00310113\n", + "The max absolute difference between the solutions is: 0.000464088\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad, elementwise_grad\n", @@ -2188,10 +2218,53 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 2, "id": "4f67bd3c", "metadata": {}, - "outputs": [], + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/homebrew/lib/python3.9/site-packages/numpy/core/_asarray.py:102: VisibleDeprecationWarning: Creating an ndarray from ragged nested sequences (which is a list-or-tuple of lists-or-tuples-or ndarrays with different lengths or shapes) is deprecated. If you meant to do this, you must specify 'dtype=object' when creating the ndarray.\n", + " return array(a, dtype, copy=False, order=order)\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Initial cost: 457.256\n", + "Final cost: 0.00310113\n", + "The max absolute difference between the analytical solution and DNN Autograd: 0.000464088\n", + "The max absolute difference between the analytical solution and numerical scheme: 0.00266858\n" + ] + }, + { + "data": { + "image/png": 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EY0wU3qJXhXeZNbacQ2+bD/W4WroeBCyVsCPkWxnOwPsVWAHeTx4/pWXP7R/w/qXJSrx/6bjUd15b5NuPd0P3Et430Yvxfqptrp/4Mi3C+7XCX/CO7Wr247bWVuMtXTPw7l17GO+YoHWte1Tfuu06vG8Yo/D+ccIevG+OnXxXeRbvX25mA+/jHaB6qNtbg3e8zFd4NwLD8Y5hagv/wPvcv2+M2Y93MP1E3/2W4/srWt/XE5N8v/Mp3o3lZwc5DUew/lhrP8A7cHy2MWZME1cZDywwxpT6st9ird1irS3E+7zfjvdrsDuA06y1TX41Z61dgPeTby+8bwotZq19B7gf79ebm/A+f+DdyDe+7pGu941v7794x8H9GO/jXYN3TOjRvufigMm+56oEb2HuCIy31n7d6Cb3mW8fJ+y2g9z1ZXjHeq3DO2btVl+eD/GW0Ffx7l3qC1zY2seHdw/rXrx7GP6Dd6D6gdfnD4E7fevsb/A+pwdlrX0d73biReP9mmsV3tc+vvXjPODPeJ/H/hz69XWgCBYaY5b6fr4I7/igfLxfa//W93w05QlgiO819cahcvvyLcb7h00P4n0+NuEdn9WU94B3gQ14vwqrpJlfrbZyO/O073qNv4r8E94PCPuMMT9p4veaXIfwju3rgHebOd/3WJrrZGC1b13/B95xrxXW2vV4vy59wHe7p+M9tFN1E7dxuG3z4R5XS9aDgGW8H/JERIKLMWYw3jf4GOv4GHPBzLdn+jlrbUv23ks78+3Beg7v4T70xh0itCdMRIKGMeYsY0yM8R4g9S94j/2kAiYhzffV3i3Av1TAQotKmIgEk+vxfqWyGe9flv7AbRwR//Lt8d2H9y9x/+40jLQ5fR0pIiIi4oD2hImIiIg4EHAHLjucrl272szMTNcxRERERA5ryZIle6y1KU1dFnQlLDMzk8WLF7uOISIiInJYxpjGs4t8Q19HioiIiDigEiYiIiLigEqYiIiIiANBNyZMREREjlxNTQ15eXlUVla6jhISYmNjSUtLIyoqqtm/oxImIiIShvLy8khMTCQzMxNjjOs4Qc1aS2FhIXl5eWRlZTX79/R1pIiISBiqrKykS5cuKmBtwBhDly5dWrxXUSVMREQkTKmAtZ3WPJcqYSIiIiIOqISJiIhIUHvqqae46aabDnud/Pz8b05fe+21rFmzpsX3NXfuXE477bQW/15TVMJEREQk5DUuYf/6178YMmSIw0QqYSIiIuLQmWeeydixYxk6dCiPPfYYAAkJCfzyl79k5MiRTJo0iV27dgEwe/ZsJk6cyOjRo5k+ffo35x+wf/9+srKyqKmpAaCkpISsrCxefvllFi9ezCWXXMKoUaOoqKhg6tSp30yD+O677zJmzBhGjhzJCSecAMDChQuZPHkyo0eP5qijjmL9+vVt/th1iAoREZEw9/vZq1mTX9KmtzmkV0d+e/rQw17vySefJDk5mYqKCsaPH88555xDWVkZkyZN4o9//CN33HEHjz/+OL/61a+YMmUK8+fPxxjDv/71L+6++27uueeeb24rMTGRqVOn8vbbb3PmmWfy4osvcvbZZ3Peeefx0EMP8be//Y1x48Z96/4LCgr4/ve/z2effUZWVhZFRUUADBo0iM8//5zIyEg+/PBDfvGLX/Dqq6+26XOkEiYiIiLO3H///bz++usA5ObmsnHjRqKjo78ZdzV27Fg++OADwHtsswsuuIAdO3ZQXV3d5DG5rr32Wu6++27OPPNM/v3vf/P4448f8v7nz5/Pscce+81tJScnA1BcXMwVV1zBxo0bMcZ8s3etLamEiYiIhLnm7LHyh7lz5/Lhhx/y1VdfERcXx9SpU6msrCQqKuqbQz5ERERQW1sLwI9+9CNuu+02Zs6cydy5c/nd7373nds8+uijyc7OZu7cudTV1TFs2LBWZfv1r3/N8ccfz+uvv052djZTp05t7cM8KI0JExERESeKi4vp3LkzcXFxrFu3jvnz5x/2+qmpqQA8/fTTB73e5ZdfzsUXX8xVV131zXmJiYns37//O9edNGkSn332GVu3bgX45uvIhvf11FNPtehxNZdKmIiIiDhx8sknU1tby+DBg/nZz37GpEmTDnn93/3ud5x33nmMHTuWrl27HvR6l1xyCXv37uWiiy765rwrr7ySG2644ZuB+QekpKTw2GOPcfbZZzNy5EguuOACAO644w5+/vOfM3r06G/2xLU1Y631yw37y7hx4+yBv2YQERGR1lm7di2DBw92HcMvXnnlFd58802effbZdr3fpp5TY8wSa+24pq6vMWEiIiISMn70ox/xzjvvMGfOHNdRDkslTERERELGAw884DpCs2lMmIiIiIgDKmEiIiIiDqiEiYiIiDigMWEiIuJVXwc1Fdiacqoryigv209leSmVFaVUl5dSU1VKTWUZdZVl1FaVU19djq0uh5oKTK33X0RtBZF1FVggYtqvGDX5BNePSiRgqYSJiASDuhqoLoOaCqgp9/3v/dnWlFNTWUZ1hfdfTWUptVVl1FWVUe8rSweua2or8dT5ylJ9JdH1lUTVVxJjq4jGOy2LAWJ8/w6n1nqoMLFUE0OVJ4YaTyy1nliSqndi3r2CjUlv03/wSH8+MyJBSyVMRKS97V5H3bLnqKkopa6ylDrfHqUDe5WorcBTW0FEXQWRdZVE1lUSQd1Bb84A0b5/DVXZKMqJoYJoKmwMlURTSQw1nhhqPJ2pi+hAXVQs9ZEdqI/sAFFxmOg4THQHPNFxRMbGExkTT1RsPNEd4onpkEBsXCKx8YnExSUSF59AVHQMiU1kKsheQ9RTJxHz3wvYcf1H9OyZ2oZPoEhoUAkTEWlHddlfUfPsuXhqKyglnkpfQaogmgpiqLTRlJNEBd2ptNFUmRjqImKpi+yAjeyAjeqAiYrz/ouJJzImjsiYeCJj44mOjSO6QwKxcQnEdkggvkMMCTGRxMdE0CUmkrjoSKIj22cocErmELLPeJqeb1zAxn+dS/yP36djQlN1TcJZdnY2M2bMYMqUKcybN4/U1FTefPNNZsyYwcSJE/nkk0/Yt28fTzzxBMccc4zruG1OJUxEpJ3UrHsX+9/L2V6XzIsDn6RX5gDiYyJ9RSmShJgIukX/73R8TAQxkRGuY7da5ugTWLvnbwz78ha+evhSxt32KlGRetsJSO/8DHZ+3ba32WM4zPjzYa+2ceNGXnjhBR5//HHOP/98Xn31VQBqa2tZuHAhc+bM4fe//z0ffvhh2+YLAHo1iIi0g8olLxA5+0bW1fdm+bFP8MvpTc5iEnIGn3glKwuzmbzuPj565Bam3fggxhjXsSSAZGVlMWrUKADGjh1LdnY2AGefffZ3zgs1KmEiIn5W9vlDxH/0C+bXD2HnKf/mskmDXEdqVyMu+C0rH8nmhF3P8dF/Mjjh0jtcR5LGmrHHyl9iYv73JyARERHfTK594PyIiAi/TaDtmo4TJiLiL9ZS8s7vif/oF3xQP57y8/7LmWFWwAAwhuHXPc7a+Akct/FPfPHOi64TiQQElTAREX+or2ffq7fQccG9vM5UOl3xPNOGp7tO5YyJiKLvD18hLzqTUfNvZfmiz11HEnHOWGtdZ2iRcePG2cWLF7uOISJycLXVFD1/DclbZvGsZybjrn2Qwb06uU4VEEp2baPqkeOpt5ayy96jT98BriOFrbVr1zJ48GDXMUJKU8+pMWaJtbbJQaDaEyYi0paqyyh64hySt8zikajLOe7GR1XAGujYPYP6i18ingrqnjuPgj17XEcScUYlTESkrZQXUfTIKXTK/5y/x/2Is2/+K+ld4lynCjjd+49jz8mPkVWfw7ZHz6esotJ1JBEnVMJERNpCyQ72Pnwi8YWr+HvnX3L1zb+lW2Ks61QBK3PSTDZNuJNxNUtY9NDV1NYefEYA8Z9gG5IUyFrzXKqEiYgcIVu4meKHphG1P48He/2ZG2+8jY6xUa5jBbxBp/6IVX2uYWrp23zwxC9VCNpZbGwshYWFet7bgLWWwsJCYmNb9sFLxwkTETkCdfkrKH/yTOpqqnm67z+45ZLziYzQ59vmGnbp31jzUA4zdvyT91/O4KTzf+A6UthIS0sjLy+PgoIC11FCQmxsLGlpaS36Hf11pIhIK9Vs/pza/1zA3roYZo98mOvOOllHg2+F+uoKtt53Imnl61h03FNMmXaa60gibUZ/HSki0sYqV72Ffe5s8ms78snRz3L92TNUwFrJE92BtB+8TmFkN4Z+egMrVixxHUmkXaiEiYi0UOmCZ4l65TLW1aWx+uSXuOSkKa4jBb2YjikkXP0axmNIev1itmzLcR1JxO9UwkREWmDfx/8g4Z2bWFg/mMJzXmHmUSNcRwoZHVMHUXnOf+hBIWVPn0fB3mLXkUT8SiVMRKQ5rKVo9q9J+uw3fMAEIi9/leNH9nWdKuT0GHYs+dP+wfD6dax/5BIqqmpcRxLxG5UwEZHDqa9jz4s/JHnJ/bxhppN67UuM79fTdaqQlXXsJawfcQdTqj5n7sM3UVcfXH9AJtJcKmEiIodSW83upy6l6/rneS7qHMbc+AxD0jq7ThXyBp71C9alnceM4heZ8+//p2NZSUhSCRMROZiqUnY/dibdcubwrw5Xc9LND5PeNd51qvBgDIOueoSNnY5iRs7feO+NZ10nEmlzKmEiIk0pL6Lg4ZPpsmseD3e6jfNvuVvTELW3iEj6/uAl8mP6MGX5T/ni849dJxJpUyphIiKN2OLtFD4wjY771vHP7r/j6pt+pWmIHPHEJtLthjepjEig/4dXs3LNGteRRNqMSpiISAN1BRvZ9+A0ost38u+sv3LD9TcTGxXhOlZYi01OI/KyV0gwlcS+dCHb8ne6jiTSJlTCRER8anKXUf7IdOqqy3l5+D+5/oorNQ9kgEjKGk3JzCfJIo9dT1xIUUmZ60giR0xbFxERoGLDXGqfPIXi2kg+mvw0V597lqYhCjA9x5zC9qP/yIS6ZSz559VUVte6jiRyRFTCRCTs7V/+JhHPn0tefWeWT3+RC06e5jqSHETmiT9g48AbOLHiXd599GfU6xhiEsRUwkQkrO398t/EvXEla2062898jdOOGe86khxG/wv/zMbuMziz8HFm/ecB13FEWk0lTETC1p73/0bnD25lAcOoueRNpo4e5DqSNIcx9Lv2KbLjRzJj0+95d85rrhOJtIpKmIiEH2vZ+drP6DrvLj4wk+l8zWuMG9DbdSppARMVS+8fvkFRdE8mLvgR8xbMdx1JpMVUwkQkvNTXseO56+mx8p+8Gfk9Bv7wZQb3TnGdSlohIj6ZpGvfwHgiSJ1zOas3bnYdSaRFVMJEJHzUVpH/rwvpufm/vBB7AZNvfpr0lETXqeQIdOjej/oLn6eH2Uvtfy4ib3eh60gizaYSJiLhoWo/Ox4+nV757/N04nWceutDdOvYwXUqaQPJA6dQ9L0HGc4GNj92KcVlVa4jiTSLX0uYMeZkY8x6Y8wmY8zPDnG9c4wx1hgzzp95RCQ82bI97HzgJFIKF/FE1//jgpv/rGmIQkzPyReQM+4XHFc7j08f/iFVtXWuI4kclt9KmDEmAngImAEMAS4yxgxp4nqJwC3AAn9lEZHwVbc3lz33TyNp/0aeyfgjV/zgZ5qGKERlnvpTtmRdzMyyV3jz8bt0DDEJeP7cEzYB2GSt3WKtrQZeBM5o4np3AX8BKv2YRUTCUPXOdRQ/NI2Yyt28Mvh+rrrqB5qGKJQZQ5/LHmRrl2M5Z+ffee2lJ10nEjkkf26NUoHcBqfzfOd9wxgzBuhtrX37UDdkjLnOGLPYGLO4oKCg7ZOKSMipyF5E5WMnUVdTyfvjn+DSCy/WNEThwBNB5nUvsCNuADPW/px3P3jPdSKRg3L2kdAY4wHuBW4/3HWttY9Za8dZa8elpOhPyUXk0ErWfARPn05xXTSLj3+Bc0871XUkaUcmJoHu179BRWQnRn9xHV8tXeE6kkiT/FnCtgMNj36Y5jvvgERgGDDXGJMNTAJmaXC+iByJwsWvEPvS+eTWd2HrzNeYMXWK60jiQFRSL+Kuep0EU02XNy9hbXbu4X9JpJ35s4QtAvobY7KMMdHAhcCsAxdaa4uttV2ttZnW2kxgPjDTWrvYj5lEJITtmvsYSW99n7U2i5ILZ3Hs2BGuI4lDcWnDqD73afqYfEqevoT8whLXkUS+xW8lzFpbC9wEvAesBV6y1q42xtxpjJnpr/sVkfC0/a0/0X3uT1lgRhB99VuMG9zXdSQJAJ2HnUTB1LuZaFew8pGrKamodh1J5BvG2uD6E95x48bZxYu1s0xEfKwl96Wf0nvt43wUMYX+1/+H9G5JrlNJgMl59Vekf/0AL3W8krNuuY8o/ZWstBNjzBJrbZNDrbQWikjwqqsl56mr6b32cWbHnMrwm19SAZMmpZ99F9mpp3N+yVO89OQ9BNsOCAlNKmEiEpxqKsl59DzSt73Gy/GXcOwtT9GtU7zrVBKojCHzqifJ7TiWc/P+zKuv/dd1IhGVMBEJPraymJwHTyV998e8kHwjp9/6AJ3iol3HkkAXGU3aDa+yL6YX01fexntzP3OdSMKcSpiIBJW6/QXk/+NEeu5bxvOpv+K8G/+gaYik2UxcZzp/fxYmIorBn1zDwlXrXEeSMKYSJiJBo7pwG3vuP54u5Vt4feDdXHTtTzQNkbRYdEoWEZe8RDezj5iXL2VD7m7XkSRMaeslIkGhfPtq9j88jQ7Vhbw35hHOv/haTUMkrZbQdyJlpz3KcLOJ/H9fyq59Za4jSRhSCRORgFe8aT61/zqZ+toavjruWc4441zXkSQEdBl3Nrsm/4ap9Qv48pEfUlpV6zqShBmVMBEJaHtWvkf0c2dQXB/L+lNf5XvTpruOJCGk5/duI3fA5Zxd+QavP/IbauvqXUeSMKISJiIBa8dXL9DxtYvJtd0oOG8WUyaMdx1JQlDvC/9OXrepXFz0MP959lEdQ0zajUqYiASknPcfovt7P2AN/ai/8m3GDBvsOpKEKk8Eadc+z+6EQZy39be88tZbrhNJmFAJE5GAs2XWn0if9wsWekaTfMNbDMpKdx1JQl10PN2vf4OKqCSOW3wT789b6DqRhAGVMBEJKLvXfE7mkr/wedTR9Ll5Fuk9UlxHkjDh6diDxGteJ95TQ+Z7V7F43VbXkSTEqYSJSMCwNZXUvPZDdpFM1tX/pltSoutIEmaiew7Fnv8sWWYndS9eyqYdRa4jSQhTCRORgLH2v78htTaHNWPvIq1nd9dxJEwlDD6BkhPvYSKrWP+vaygoqXQdSUKUSpiIBIQ9GxczYNPjzO0wneNPu9h1HAlzXY6+kp2jf8ypdR/z/iO3U16tY4hJ21MJExHnbG01ZS9fz16bSJ9L/oHHoyPhi3s9Zv6W/MyzuKT8OZ5//K/U1evQFdK2VMJExLk1r/6RjOpNrBjxa9LT0lzHEfEyhl6XPsaO5AlcvvuvPPP8szqGmLQplTARcaow+2v6rX2IeTFTOP6sa13HEfm2yGh6fv9lijukc/bG/+PV9z5ynUhCiEqYiDhj62rZ++L1lNsYel70IBH6GlICUYckulz3JkTGMvGrG/ho0deuE0mIUAkTEWdWv3kP/SpXs3TwHWRlZrmOI3JQnuQMYi9/mRRTQspbV7B0c77rSBICVMJExIm9eevpu/IeFkeN47hzb3IdR+SwYjLGUX3WvxhqtrLv2cvZurvEdSQJciphItL+rGX38zdQZz10vuBhIiMjXCcSaZaOI2ey79g7mcYilj3zU9dxJMiphIlIu1v11oMMLF/Kwv630rffQNdxRFqky7QfsTHlJKbvn0Xubh1RX1pPJUxE2lXxrm1kLvl/rIgczjEX/sR1HJFW6XzM9+loyln18X9dR5EgphImIu3HWnKfvYEIW0uHcx4iKjLSdSKRVuk67AQKPV1J2viqjh0mraYSJiLtZvX7TzKsdB4Lsn7AgMEjXccRaT1PBLszT2dc7VJWbdziOo0EKZUwEWkX+wvzSf3qt6yNGMDki3/lOo7IEet9/NVEmTpyP3vGdRQJUiphItIutjxzIx1sBeaMh4iJjnYdR+SIJfQeQW5MP9Lz3qKmrt51HAlCKmEi4nerP36ekcUfM7/31QwaMcF1HJE2UzH4PIaxiUWLFriOIkFIJUxE/Kq0uJDun/2CTZ4sJl56l+s4Im0q6/grqMND8YLnXEeRIKQSJiJ+tf7pm0myxVSfej+xsbGu44i0qahOPdnScQLDi96luLzKdRwJMiphIuI3a794g7FFbzG/5yUMGXus6zgifhE95iLSzB4Wf/qW6ygSZFTCRMQvKkqLSfroJ2wzqYy5/M+u44j4TfpR51FOLKzUgVulZVTCRMQvvn7mNrrX72H/SfcRF5fgOo6I35joeLZ1n8748s/I213oOo4EEZUwEWlz6xa+x4TdrzA/5RyGTf6e6zgiftflqMvpaCpY9Yn2hknzqYSJSJuqLC8l/p1byTfdGHHFPa7jiLSLbsOnU+jpSqcNr2kaI2k2lTARaVPLnv05vW0+e47/KwmJSa7jiLQPTwS7MmcyrnYpqzWNkTSTSpiItJkNyz5nfP5zLOx8KiOOPdN1HJF21XuqdxqjnM+edR1FgoRKmIi0iaqqCiJm30SRSWLQFfe7jiPS7hLTh5MT05/0vNmaxkiaRSVMRNrEkud+Q9/6bHYe80c6JnV1HUfEicpB5zKMTSxePN91FAkCKmEicsQ2rVrIuJwnWNrxBEaccLHrOCLOZE3zTmNUommMpBlUwkTkiNTU1FD3+o2UmXj6Xv6g6zgiTkV16smWxAkMK3yPkgpNYySHphImIkdkwfN/YGDdBrZN/B2duvZyHUfEuagxF5Fq9rDk07ddR5EApxImIq22dcNKxm15iJXxRzHq5KtdxxEJCBlHe6cxsitfdB1FApxKmIi0Sm1tLaUv/ZAaE0XaZY+AMa4jiQQEEx1PdvcTGVf2Gdv3FLmOIwFMJUxEWuWrl/7G8Nqv2Tz65yT3yHAdRySgdD0wjdFH2hsmB6cSJiIttm3Lekavv481HcYw8vSbXMcRCTjdhk9nj6crHTdqGiM5OJUwEWmRurp6Cl/8IR5j6XbJoxiPNiMi3+HxsCtzJuNrlrB2k6YxkqZp6ykiLfLlqw8ypnoxG4bdTte0Aa7jiASs9KlXE2nq2fbZM66jSIBSCRORZsvN2cqI1X9mQ8xQRp79E9dxRAKadxqjfqTnzqZW0xhJE1TCRKRZ6ust+c/fRAeqSbrwUYwnwnUkkYBXPug8hrKZJUsWuI4iAUglTESa5fNZ/2Ji5ResG/RDumUNdx1HJCj0Of4KavGwb76mMZLvUgkTkcPKz89j6LK72BLVnxHn/9p1HJGgEZ10YBqjd9mvaYykEZUwETkkay1bnruFTpQSf94/MRFRriOJBJUD0xgt/kzTGMm3qYSJyCF9Puc/TCn/kLV9r6H7gPGu44gEncyjz6OMDtgV/3UdRQKMSpiIHNSu3QUMWPgbciPTGXbhXa7jiAQlEx3Ptm7TGVf2KfmaxkgaUAkTkSZZa1nz7K2kUETkWQ/jiY51HUkkaHU5MI3Rx5rGSP5HJUxEmvT5B69z/P63WJNxKT2HHuM6jkhQ6z7CN43Rhlc1jZF8QyVMRL5jd1ERmfN+xo6Ingy55C+u44gEP980RuNqlrJus6YxEi+VMBH5FmstK57+Kensou60B4iIiXcdSSQkfDON0afPuo4iAUIlTES+5ctP32XavldZ3etc0kaf6DqOSMhITB/Otuj+9M6dpWmMBFAJE5EGCveV0HPuTyiK6MrAS+9xHUck5JQPPpehbGbpkvmuo0gAUAkTkW8sfOYX9CWPqpPvITIuyXUckZBzYBqj4gWaxkhUwkTE58sv5jK98HnWdTuFtAlnuI4jEpJiknqyOXECQ/a8R2lltes44phKmIiwr7Sc5A9/zH5PIn0vf9B1HJGQdmAaoyWfvuU6ijimEiYifPHMbxnMFkpP+DNRCV1cxxEJaVnfTGOkA7eGO5UwkTA3f+FXnLjr32xInkb6lItcxxEJeSY6nuxuJzCm7DN2FGoao3CmEiYSxkoqqujwzq1UeWLIuPwh13FEwkaXo67wTmP0kfaGhTOVMJEwNveZPzLSrmPfMXcSk9TLdRyRsNFjxHQKPCmaxijMqYSJhKmFy5YyPf8RNneaRPrxV7uOIxJePB52ZcxkbM1S1m/RNEbhSiVMJAyVVtZgZt8KxpB62WNgjOtIImGn99SrvNMYzX3GdRRxRCVMJAx98J+/Mb5+BQWTf0Vs1wzXcUTCUqcM3zRGebM1jVGYUgkTCTOLv17DCTn3k50wmowTb3QdRySslQ8+lyF2M8uWLnAdRRxQCRMJI+VVNVS+cQvRppYelz4OHm0CRFw6MI3RvvnPuo4iDmgLLBJG3nnxYabULWTn2J8Q26O/6zgiYe/ANEZD97xHmaYxCjsqYSJhYsX6jUzd8ldy44aQeepPXMcREZ/I0RfTy+xhsaYxCjsqYSJhoLKmjsKXf0xHU0GXix8HT4TrSCLi02eKdxojVurAreFGJUwkDMx++V9Mq/2c7SNuIi5tmOs4ItKAiY5ja7fpjCn9jF2Fe13HkXakEiYS4r7etI1j1/8/dsT2JfOMX7mOIyJN6HLU5SSaClZ9/ILrKNKOVMJEQlhVbR15/72dLqaExAsfhYgo15FEpAk9fdMYJa5/1XUUaUcqYSIhbPZr/2FGzQdsH3wtCZnjXccRkYPxeNiZcTpjapayYfNm12mknaiEiYSotdvymbT69+yO7k3G2Xe6jiMih9F76tXeaYw+1THDwoVKmEgIqqmrZ8Pzd9DLFNLh3IchqoPrSCJyGEkZw8mOHkBa7izq6q3rONIOVMJEQtCbb77K6ZVvkdvvUhIHHOs6jog0U/mgcxlsN7Ns6XzXUaQdqISJhJgNeQWMXvEbiqK6k3Hen13HEZEW6DPNN43RV/pKMhyohImEkNq6elb+5+f0NflEn3k/xCS4jiQiLRCb1INNiRMYuuddyqs0jVGoUwkTCSFvvPM2Z5a/Sk7G2XQc9j3XcUSkFSJHX0xPU8iST2e7jiJ+phImEiI27Shi2KJfUBrZmd4X3us6joi0Up+jvdMY1a/4r+so4mcqYSIhoK7esui5XzPI5MBp92A6dHYdSURayRPzv2mMdhcWuY4jfqQSJhIC3nj/Q84pfYHc1BkkjT7LdRwROULJky8j0VTw9cea1DuUqYSJBLltBSX0/epnVEUkkHbRA67jiEgb6DXyRE1jFAZUwkSCWH295dNn7mSU2UTd9/6MSUhxHUlE2oLHw46MmYypWcrGLZrGKFSphIkEsVkff855JU+zvdtUkiZc5DqOiLSh9OO90xhlz9Uxw0KVSphIkMotLKXX5/+H9UTS65KHwRjXkUSkDSWlDyM7egC9c9/UNEYhSiVMJAhZa/nwub8wwayhctqdmE6priOJiB+UDTqXQXYLKzSNUUhSCRMJQrM/X8S5RY+zo8tEkqdc6zqOiPhJX980Rns1jVFIUgkTCTK7iyvo/NEdRHnq6X7xo/oaUiSEHZjGaMied6moqnEdR9qYSphIkPng9Sc5xiyjbMov8XTJch1HRPwsYtRF9DSFLP1M0xiFGpUwkSCSU7CfCVseYndMBl2m3ug6joi0g75TzqeUOOqW68CtoUYlTCSIfPHaQ/T3bCf6xF9DRKTrOCLSDjwxcWxJOYHRpZ+xu0jTGIUSlTCRILEhv5Bj8v/FjriBJI05x3UcEWlHXY66nERTwaqPtDcslKiEiQSJJa/dR29TQMIpd4JHL12RcJI6cjq7PSkkbnjFdRRpQ9qSiwSBr7fkM73gGfI6jiFx6PdcxxGR9ubxsCP9dEZXL2Pz1i2u00gbUQkTCQJr3vwrKaaY5DP+qENSiISpA9MYbf3kaddRpI2ohIkEuAVrNnPyvhfJ6XoscX2Pch1HRBzpnDGc7OgBpOXOol7TGIUElTCRAGatJfetv9DJlNP9zD+4jiMijpUOPEfTGIUQv5YwY8zJxpj1xphNxpifNXH5DcaYr40xy40xXxhjhvgzj0iw+WLZak4pe4PsnjOISRvpOo6IONbvhCuptR6K5msao1DgtxJmjIkAHgJmAEOAi5ooWc9ba4dba0cBdwP3+iuPSLCpr7cUvfsnYkwNqWdrL5iIeKcx2thxIkMKNI1RKPDnnrAJwCZr7RZrbTXwInBGwytYa0sanIwH9CW3iM+HXy1iRtU75GaeQ1RKP9dxRCRA/G8ao1muo8gR8mcJSwVyG5zO8533LcaYG40xm/HuCbu5qRsyxlxnjFlsjFlcUFDgl7AigaSmrp76T/4fGA/pZ/7edRwRCSD9ppxHKXHUaxqjoOd8YL619iFrbV/g/4BfHeQ6j1lrx1lrx6WkpLRvQBEH3p/7KSfWzGXHgMvwJH3ns4uIhLGG0xgVFO11HUeOgD9L2Hagd4PTab7zDuZF4Ew/5hEJCpU1dcR98WeqPLGkn/FL13FEJAB1OeoyEkwlqz5+wXUUOQL+LGGLgP7GmCxjTDRwIfCtL7CNMf0bnDwV2OjHPCJB4d3353C8nc+e4ddh4ru6jiMiASh15IneaYzWv+o6ihwBv5Uwa20tcBPwHrAWeMlau9oYc6cxZqbvajcZY1YbY5YDtwFX+CuPSDAoraql+6K7KfF0Iv3Un7qOIyKByjeN0ajqpWzN1jRGwcqvY8KstXOstQOstX2ttX/0nfcba+0s38+3WGuHWmtHWWuPt9au9mcekUD3/lsvM5mV7B9/M8Qkuo4jIgHswDRGWzSNUdByPjBfRLz2llbRd+U9FEWkkDr9JtdxRCTAdc4YztboAaTmaBqjYKUSJhIgPpz1FCPNRqqn/BSiYl3HEZEgcGAao5XLNI1RMFIJEwkAu4rLGbn+AXZHp9Hj2GtcxxGRINFvmncao71fPeM6irSCSphIAPjs1X8ywORijv8lRES6jiMiQaJD5x5sSJzI4IL3qKzWNEbBRiVMxLGc3cVM3PYI+bH9SZl4oes4IhJkIkZdSA9TyNLPZruOIi2kEibi2ILX/k662U3syb8Dj16SItIy/Y85X9MYBSlt8UUc2pi3m2N3PEluwkiSR57qOo6IBCFPTBybU6Yzav+n7NmraYyCiUqYiEMrX/sr3c0+Op1+FxjjOo6IBKnkA9MYfaRpjIKJSpiII19vzmFa4fNs7XwUHQce5zqOiASx3iOns9uTQoKmMQoqKmEijmx68890NqV0O+MPrqOISLDzeMhPn8no6iWaxiiIqISJOLBo1XpOKn6Fzd1OIj5zrOs4IhICek+9ighj2appjIKGSphIO7PWsnPO/yPG1JB2tvaCiUjb6JI5nC2axiioqISJtLN5S5dzUtlbZKedQUyPga7jiEgIKRt4DgPtFr5ermmMgoFKmEg7qq+3lL73R4yBjLPvdB1HRELMgWmMiuY96zqKNINKmEg7mjtvHtOrPiSnz8VEJae7jiMiIaZD5x6sT5zE4IJ3NY1REFAJE2kntXX1eOb+kSoTS9ZZv3EdR0RCVMRo7zRGyzSNUcBTCRNpJx9/8j5Ta79kx5CriUhMcR1HREJU/ynn+aYx0oFbA51KmEg7qKypI/HLP1NiEulz+h2u44hICIuIiWNTygmM3P8ZhZrGKKCphIm0g4/efZ3JdhmFo2/EdEhyHUdEQlzy5MtJMJWs/lh7wwKZSpiIn5VV1pC65K8UebqQNeNW13FEJAykj5rOLk8K8etecR1FDkElTMTPPp79HKNYR+mk2yCqg+s4IhIOPB7ye89kVPVSsjWNUcBSCRPxo31llfRffR+7I3uRfsL1ruOISBhJP943jdFcTWMUqFTCRPzos9cfYxDbqD3uZxAR5TqOiISRLpnD2Rw9kF7bNI1RoFIJE/GT3Xv3M2LjQ+TH9KHX0Ze5jiMiYajUN43Rak1jFJBUwkT85KvXHiDT7CRi+m/Ao5eaiLS//tOuoMZGUPTVM66jSBP0ziDiB3m7C5mY8zjb4obRfdyZruOISJiK69yDDYkTGFTwLpVV1a7jSCMqYSJ+sOTVe+hhikg49S4wxnUcEQljnlEX0p0iVnzxluso0ohKmEgb25ybzzE7n2Zzx4l0GTrNdRwRCXMDjjmfUuKoXaYDtwYalTCRNrb29T+TbErpesYfXUcREfnWNEZF+/a5jiMNqISJtKHVm7ZwXOFLbOwyjU59x7uOIyICQOdJl3mnMfroeddRpAGVMJE2lPPmH4gzlfQ66w+uo4iIfCNj9InsMt2I0zRGAUUlTKSNLP16FdNKZrGpx2nEpw11HUdE5H88Hrann86o6qVs0zRGAUMlTKQNWGspnHMXxlgyztVeMBEJPOnHX+2bxugp11HERyVMpA0sWLyI48vfZ0vG+cR2zXQdR0TkO7pmDvtmGiNrNY1RIFAJEzlC9fWWyvfvotpE0+es37qOIyJyUPsHnMMAu1XTGAUIlTCRI/T5F58wteYzcgZcTnRSD9dxREQOqv8J3mmMCudpGqNAoBImcgRq6+qJ/vSPlJgE+p/5C9dxREQOKb7BNEZV1ZrGyDWVMJEj8OmHs5lct5idw64nIq6z6zgiIoc36iLvNEafaxoj11TCRFqpqqaWLvP/TJHpTP/Tb3cdR0SkWQYecx77NY1RQFAJE2mlT+e8yCi7hqJxt2Ki413HERFplsiYODZ1nc7I/Z+yd+9e13HCmkqYSCuUVVaTvuxv7IroQd/v/cB1HBGRFkmafBnxporVn2hvmEsqYSKt8PmsJxjEVsqPugMTGeM6johIi2SOPoGdphvxmsbIKZUwkRYqLq1g4Jr72R6VSdbxV7qOIyLSYsYTwfb00xlRtZTcbZrGyBWVMJEWmvfaA2SRT/20X4EnwnUcEZFW6T31KiKMZcsnT7uOErZUwkRaYPfefYzc/AjZsYPpPelc13FERFqtW9ZwNkcNoFfOm5rGyBGVMJEWWPLqvfQyhcSc/HswxnUcEZEjUjLwXPrXb2XNCk1j5IJKmEgzbd+1mwm5/2ZTwlh6jvqe6zgiIkes/wlXeqcx+lLTGLmgEibSTKte+TNdTAmdTrvLdRQRkTaR0Lk76xInMqjgHU1j5IBKmEgzbMnJ4ajdz7Mu6VhSBh3tOo6ISJvxjLyQbuxlpaYxancqYSLNsPn1PxBPJT3O/IPrKCIibWrgsQemMXredZSwoxImchjrNqznmKLXWNttBkmZI13HERFpU5ExcWzsOp0R+z9j3z5NY9SeVMJEDiN/1p1EmHrSz9FYMBEJTUmTvNMYrfpY0xi1J5UwkUNYsWIZx+x/h/Wp55DYo5/rOCIifpE1RtMYuaASJnIQ1lqK3/k9dSaCvuf8znUcERG/MZ4I8tJnMqJqKXk5W13HCRsqYSIHsWjhF0ypmMumrMvokJzqOo6IiF+lH39gGqOnXEcJGyphIk2or7fUf3gXZaYDA87+les4IiJ+1y1zGJuiBtJr2xuaxqidqISJNOGrT99hUs0CcgZ9n+jEZNdxRETaRcmAc+hXn81aTWPULlTCRBqpra0j7os/std0YtCZd7iOIyLSbgaccIV3GqN5msaoPaiEiTTy5QevMLpuFTtG/oiI2ATXcURE2k1Ccg/WJUxk4O53qK6ucR0n5KmEiTRQVVNLt4V3s8vTjcGn/sh1HBGRdmcOTGP0xWzXUUKeSphIA1/OforBdhP7JtyOiYp1HUdEpN0NOu7ANEY6cKu/qYSJ+JRXVpG58j7yItMZcOK1ruOIiDgRGRPHhq7TGV7yKfv3F7uOE9JUwkR85r3+MH3Io+qYn2MiIl3HERFxJmbIqcSbKrK//sp1lJCmEiYCFJeUMnj9Q2yNHkDfYy9yHUdExKm0oUcDULJloeMkoU0lTARY9Np9pFKAZ/pvwRjXcUREnErq3pvdpgtRu5a7jhLSVMIk7BUUFTFy6+Ns6DCKjPGnuo4jIhIQ8uMG07N0jesYIU0lTMLeylf+TIopJv6UO7UXTETEp7r7SHrbHRTt2e06SshSCZOwtn1HPuO3P8uaxCmkDj/OdRwRkYCRkDUBgJzV8xwnCV0qYRLW1r/6BxKooOsZd7mOIiISUNKHewfnl21d5DhJ6FIJk7CVnb2FyQUvs6rLSXTrN8Z1HBGRgJKQlMJ204OY3StcRwlZKmEStra9/nsiqSPt7DtdRxERCUi7E4eQWr7WdYyQpRImYWn92q+ZvG82q3ucQXLaINdxREQCUm33UfRkD7t35LqOEpJUwiQs7Xnr99QbD33O+b3rKCIiAatjv4kA5Gpwvl+ohEnY+XrZfCaXfsja3hfRsVu66zgiIgErY+gk6q2hMluD8/1BJUzCirWW8nd/T7npwMBzfu06johIQItNSCI3ojdxe1a6jhKSVMIkrCz76iMmVs1jY78riUvq5jqOiEjA29NxCL0r12Hr611HCTkqYRI2rLWYT+5iLx0ZetbPXMcREQkKttdoulJMfu4W11FCjkqYhI2FH7/B6JrlbBv6A6LjO7mOIyISFDr3nwRA/povHScJPSphEhbq6urp+OUf2W26MvyMH7uOIyISNNKHTKDGRlCds8R1lJCjEiZhYf67zzG4fiO7xvyYiOgOruOIiASNqJg4cqIySSj82nWUkKMSJiGvqrqanovvJs+TxrBTrncdR0Qk6BR1GkZm1Xrq6jQ4vy2phEnIWzj7MfrYXIqPugMTEeU6johI0PGkjqaTKSNvyyrXUUJKs0uYMaazMWaoMaaPMUblTYJCeUU5WV//gy2RfRky7VLXcUREglLXgZMB2Ll2vuMkoSXyUBcaYzoBNwIXAdFAARALdDfGzAcettZ+4veUIq20+LV/cCy7WT/1bownwnUcEZGglDZgDJU2iro8Dc5vS4csYcArwDPAMdbafQ0vMMaMBS4zxvSx1j7hp3wirVZcUszgjY+wLmY4g44+03UcEZGgFREVzebovnTaq68j29IhS5i19sRDXLYEUCWWgLXilb9wLPvYf9ITYIzrOCIiQW1f5+EM3TWLmpoaoqI0vrYtNGtslzHmmkanI4wxv/VPJJEjt6dgNyO3PcWq+En0GTvddRwRkaAX2XsM8aaKbeuXuY4SMpo7wP4EY8wcY0xPY8xQYD6Q6MdcIkdkzat/oJMpI+nU37uOIiISEroPPAqAPRsWOE4SOg43JgwAa+3FxpgLgK+BMuBia63mL5CAtGN7DmN3vMjypBMYNWSS6zgiIiGhV7/hlBGL3b7UdZSQ0dyvI/sDtwCvAtvwDsiP82cwkdba/PofiKGGHmfe5TqKiEjIMJ4IcmIGkLxPg/PbSnO/jpwN/Npaez1wHLARWOS3VCKtVLArnzEFb7Ay+SR6ZA11HUdEJKTsTx5OZu1WKisrXEcJCc0tYROstR8BWK97gLP8F0ukddbNuoc4U0X3GT9zHUVEJOREp48jxtSQvWax6ygh4ZAlzBgzBcBaW9L4MmvtBmNMR2PMMH+FE2mJkpK9DM97kRXxR5M6YLTrOCIiIafnEO/g/KJNGpzfFg43MP8cY8zdwLt4jwl24Ij5/YDjgQzgdr8mFGmmlW8+wBRTSuEJP3UdRUQkJHXrPYB9JODJ12Eq2sLhDtb6Y2NMMnAOcB7QA6gA1gKPWmu/8H9EkcOrrKyg3+anWBszgsFjjncdR0QkJBmPh7zYgaSUrHYdJSQcdkyYtbYI6AisBD4AvgD2AAONMaP8mk6kmZa+9Tg9KMRO+bHrKCIiIa0sZSQZddsoLd3vOkrQa+7A/LHADUBPoBdwPXAy8Lgx5g4/ZRNpltraWlJXP8qWyD4M1hyRIiJ+FZcxnkhTz7bV811HCXrNLWFpwBhr7U+stbfjLWXdgGOBK/2UTaRZln7wPBk2j5KxP8J4mrtKi4hIa6QO9Q7OL9bg/CPW3HesbkBVg9M1QHdrbUWj80Xala2vp9PiB9huejDixMtcxxERCXnJPTPZQ2cid61wHSXoNWvaIuA/wAJjzJu+06cDzxtj4oE1fkkm0gwrv3yLkXUbWDzsN6RGRrmOIyISFrbHD6b7fr39H6lm7Qmz1t4FXAfs8/27wVp7p7W2zFp7if/iiRzGF/dRSBLDT7vBdRIRkbBRmTKC3vXb2be30HWUoNbsATTW2sXW2n/4/ulQueLc2qWfM7JqKZv7Xk5MbLzrOCIiYSOhzwQ8xpKzep7rKEFNo5glaJV+9Df204EhM3VYChGR9tR76NEAlG7RNNJHQiVMgtK2DSsYU/opa1IvIKFTsus4IiJhpWOXHuww3YjW4PwjohImQWnHO3+llkj6z/yJ6ygiImFpZ8IQepatdR0jqPm1hBljTjbGrDfGbDLG/KyJy28zxqwxxqw0xnxkjMnwZx4JDTu3ZzOm6B1WpJxGcvferuOIiISlmu4jSWUXBbu2u44StPxWwowxEcBDwAxgCHCRMWZIo6stA8ZZa0cArwB3+yuPhI4ts/9KBHWknfp/rqOIiIStjn0nApC3+ivHSYKXP/eETQA2WWu3WGurgReBMxpewVr7ibW23HdyPt4j84scVHFRASN2vMryTtPolTXYdRwRkbCVPmwyAOXZGpzfWv4sYalAboPTeb7zDuYa4J2mLjDGXGeMWWyMWVxQUNCGESXYrH7zXhJMBcknacpSERGX4hKTyfWkElegwfmtFRAD840xlwLjgL82dbm19jFr7Thr7biUlJT2DScBo7xsP4O2PcfKDhPIGjbJdRwRkbC3O3EoqRXrsda6jhKU/FnCtgMNR02n+c77FmPMdOCXwExrreahlINaMfshkikh6rjbXEcRERGgvucoulHEjrytrqMEJX+WsEVAf2NMljEmGrgQmNXwCsaY0cCjeAvYbj9mkSBXU1NNxvonWBc1hMETT3YdR0REgKR+3sH5O9ZocH5r+K2EWWtrgZuA94C1wEvW2tXGmDuNMTN9V/srkAC8bIxZboyZdZCbkzC37J0n6WV3UzXxZjDGdRwREQHSh06k1nqo3KbB+a0R6c8bt9bOAeY0Ou83DX6e7s/7l9BQX1dP1+UPk+1JZ/jx57uOIyIiPjEdEtkamUFC4UrXUYJSQAzMFzmUlXNfok/9NvaM+gGeiAjXcUREpIHCTkNJr9pAfV296yhBRyVMAl7M/PvZSQojT77GdRQREWms12g6s5+87HWukwQdlTAJaGsXvMfgmtVkD7yaqOgY13FERKSRLgO8hwzatW6e4yTBRyVMAlrV3HvZS0dGzvyR6ygiItKE3oPGUW0jqclZ6jpK0FEJk4C1dfUCRlXMZ13GxXSIT3QdR0REmhAZHcu2qD50LPradZSgoxImAavwvb9SZmMZcsbtrqOIiMgh7Os8jMzqjdTW1rqOElRUwiQg5WevZ1TxR6zscRadkru5jiMiIofgSRtDgqkgZ6MOVdESKmESkHLf+gv1GPrM1ETdIiKBrtvAyQAUrNeR81tCJUwCTuGuPEYWzGJZ55PpntrHdRwRETmM1H6jKLcx1OVpcH5LqIRJwNk4+29EU0uPGdoLJiISDDyRkWyL6U/nfatcRwkqKmESUEpLihiS9xLLEqaQMXCU6zgiItJM+5OHkVWzmaqqStdRgoZKmASU1bPupyNlJEz7iesoIiLSAlG9xxFrati2Tl9JNpdKmASMqspy+mx6iq+jRzFw7FTXcUREpAV6DPYOzi/aMN9xkuChEiYBY+Xbj5LCXuqn3OY6ioiItFCPzCGUEA/5y1xHCRoqYRIQ6mtr6bHqMTZE9GfElNNdxxERkRYyHg85sQPpUrLadZSgoRImAWHFh8/S2+ZTMvYmjEerpYhIMCrvMpzM2mwqystcRwkKercT52x9PYmLHyTH9GLUiZe4jiMiIq0UkzGOKFNH9uoFrqMEBZUwcW7Nl7PoV7uJ/KHXERkV5TqOiIi0UurQowHYt0klrDlUwsS9L+5jN8mMOvV610lEROQIdO3VhyI6EbFDg/ObQyVMnNq87FOGVi1nY9/Lie0Q5zqOiIgcCWPIixtESula10mCgkqYOFXy0V8ptvEMn3mL6ygiItIGKruOIL0ul5KSva6jBDyVMHFm+8bljNz/BavSLqBjp2TXcUREpA10yJpAhLFsW6WDth6OSpg4s+Odu6kiigGn3+46ioiItJHeQ48CYP/mhY6TBD6VMHFiz/YtjCh8l2VdZ5LSI811HBERaSNJ3dLYZboStUuD8w9HJUyc2DL7bjxYep96h+soIiLSxvLjB9OjbJ3rGAFPJUza3f69uxi24zWWdDyB3n0Guo4jIiJtrLrbKHrbHRTt2eU6SkBTCZN2t/bNe4kzVSSfpL1gIiKhKLHPeAByVn3pOElgUwmTdlVZVsKA7P+wNHYS/YdPcB1HRET8IH2Y98j55dmLHScJbCph0q5WvfUgSewncqr+IlJEJFQlJHUlz9OT2N0rXEcJaCph0m5qq6vove4JVkUOY/jEE13HERERP9qdMIRe5euw1rqOErBUwqTdfP3uE3S3e6iceDPGGNdxRETEj2p7jKIHeyjYkes6SsBSCZN2Yevr6LL8YTZ7Mhkz7TzXcURExM869ZsIQN5qDc4/GJUwaRdr5v6X9Ppcdo/4IZ4IrXYiIqEuY+hk6qyhcpsG5x+M3g3F/6wl+qt/sJ3ujDnlStdpRESkHcTGdyQ3Ip24PStdRwlYKmHidxsXvkv/mnVsHXA1MdExruOIiEg72dNpCOmV67D19a6jBCSVMPG7qrn3UEgnRs280XUUERFpR7bnGJIpIT9nk+soAUklTPwqZ818hlUsYk36pSQkJLqOIyIi7Sh5wCQAdqyZ5zhJYFIJE78qeu9u9tsODD3jx66jiIhIO0sfPJ5qG0F1jgbnN0UlTPxm97Y1DN/3Mcu7n0NylxTXcUREpJ1FxXQgJyqLxKKvXUcJSCph4je5b/2FWiLpc/pPXEcRERFH9nYaSkbVBurq6lxHCTgqYeIXxbtzGL77LRZ3PpnU3lmu44iIiCMmbSwdTTl5m1e5jhJwVMLELzbO+hsR1NFjxk9dRxEREYdSBnoH5+9a+5XjJIFHJUzaXEXJXgbmvczi+OPoO3Ck6zgiIuJQ2oAxVNho6vKWuI4ScFTCpM2tmX0viZSTcILGgomIhLuIyCi2Rfej077VrqMEHJUwaVM1lWVkbnyGZdHjGDr2GNdxREQkABR3HkZm9SZqaqpdRwkoKmHSplbP+Sdd2EfdUbe6jiIiIgEiqvdY4kwV29Yvcx0loKiESZuxdTV0//ox1kQMZMwxp7qOIyIiAaL74MkA7Fk/33GSwKISJm1mzYfP0NPuonjMTXgitGqJiIhXrz7D2E8HyF/qOkpA0TultA1riV/0AFtNGuO+d7HrNCIiEkCMJ4LcmAF01uD8b1EJkzax4cvXyazdSt6Q64iKjHQdR0REAsz+5BFk1W6lsrLCdZSAoRImbcJ+fh876MLY077vOoqIiASg6IyxRJtastcsdB0lYKiEyRHbtvwTBlatZEPWlcR1iHMdR0REAlDqkKMA2LtxgeMkgUMlTI7Y/g//yl6byIiZP3IdRUREAlRKWn/20hHPDh2m4gCVMDkiOzcuZVjpl6xIvYDOnTu7jiMiIgHKeDzkdRhISokG5x+gEiZHZNc7f6HMxjBo5m2uo4iISIAr6zqCjLocSktLXEcJCCph0mp7t29iaOH7LOl6Bj16pLqOIyIiAS4uczwRxrJt1VeuowQElTBptezZf6EeQ+9TNVG3iIgcXurQowEo3rzIcZLAoBImrVK2dyeDdr7BosQTyeoz0HUcEREJAl16pLObLkTu1OB8UAmTVlr/5t+IsTV0Pkl7wUREpPny4wfRo3SN6xgBQSVMWqy6rJi+2S+wuMNkhowY7zqOiIgEkapuI0m3+ezbu8d1FOdUwqTF1rx1P50oJfLY211HERGRIJOQNQGAnFXzHCdxTyVMWqS+upK0dU+yPHIEoyef4DqOiIgEmd7DvEfOL92i6YtUwqRFVr/3OF1tERUTb8YY4zqOiIgEmY7J3dluehCze4XrKM6phEmz2bpakpf/k/WmD+OPP9t1HBERCVK7EgbTq2yt6xjOqYRJs2349EVS67aza+QPiYyMcB1HRESCVE2PUfSkgIJdea6jOKUSJs1jLVHz/0EOPZgw4wrXaUREJIh16usdnL99dXgPzlcJk2bZumgOfao3sHnANcTGRLuOIyIiQSx96GTqraF8a3gfOV8lTJqlau497LadGXP6D11HERGRIBeX2JnciDQ67FnpOopTKmFyWDvWzGNQ+RK+zriUTokJruOIiEgIKEgcQu+Kddj6etdRnFEJk8MqfO8vFNt4Rpx+i+soIiISIup7jaYr+9iZt8V1FGdUwuSQCretYsi+T1nS/RxSUlJcxxERkRDRud9EAPLXfOU4iTsqYXJIeW/9hWoi6XeaJuoWEZG2kz5kAjU2gqqcxa6jOKMSJge1vyCHIbvfZkHSqaSnZ7iOIyIiISSmQwI5kRkkFH7tOoozKmFyUJtn3Y3B0v1k7QUTEZG2V9RpKOlV66mvC8/B+Sph0qTKkj30z32ZBfFTGTR4uOs4IiISgkzqGJIoJW/rGtdRnFAJkyZtmH0v8VQSf7z2gomIiH8kD5gEwK518x0ncUMlTL6jrrKU9I3PsDBqAiPHHeU6joiIhKj0gWOpslHU5obn4HyVMPmOte88TBL7qTvqVowxruOIiEiIioyOYVt0HzoWhefgfJUw+RZbW023rx9jpWcIE447xXUcEREJcfuShpNZvYnamhrXUdqdSph8y4aPnqJbfQH7xtxIhEd7wURExL8i0sYQbyrJ2bjCdZR2pxIm/1NfT9yiB9lk0pn4vQtdpxERkTCQMmgyAAXrw29wvkqYfGPLV6/Ru3YbOYOvJyYq0nUcEREJA2l9R1BmY6nfvtR1lHanEiZe1mI/u4ftpDDh9GtdpxERkTDhiYwkJ6Y/yftWuY7S7lTCBIDtKz+ib9Ua1mZdSUKHWNdxREQkjJQkDyezZgtVVZWuo7QrlTABYP8Hf6XQdmTUzJtcRxERkTATnT6OGFPDtrXhdbwwlTBhz6YlDCqdz7JeF9K1c5LrOCIiEma6+wbnF21c4DhJ+9Loa2HnnD8RYzswaOZtrqOIiEgY6pk5iGISMPnLXEdpV9oTFuZK8jcwuPBDFnY5g7SePV3HERGRMGQ8HnJjB9ClZLXrKO1KJSzMZc/+C7VEkH7K7a6jiIhIGCvrMoKM2m1UlJW6jtJuVMLCWEXRDgbueJOvEk+if78BruOIiEgYi80cT5SpI3t1+IwLUwkLY5tm302kraXziT9xHUVERMJc6pCjANi3SSVMQlxN2V6ytr7I/NhjGDFijOs4IiIS5rr2ymIPSUTsXO46SrtRCQtTG96+nwTKiTz2xxijibpFRMQxY8iLG0y3/eEzOF8lLAzZmgp6rn2SxZGjGT/5eNdxREREAKhKGUF6/XZKiotcR2kXKmFhaMN7j5Fs91E+/kd4PNoLJiIigSEuawIeY8lZ9ZXrKO1CJSzc1NfRadk/WW36M/mEM12nERER+Ubvod7B+SWbFzpO0j5UwsLMli9eokfdDnYOu46oyAjXcURERL6RlNKLHSaFmN3LXUdpFyphYcbOe5A8ujHxlCtcRxEREfmOHfFD6FG21nWMdqESFkZ2rfmCvpWrWJt+CQkdYlzHERER+Y6a7iNJtbsoKtjhOorfqYSFkT0f3EuJjWP46Te6jiIiItKkxD4TAMhZPc9xEv9TCQsT+3duZlDRxyzqMpMeKSmu44iIiDQpfdjRAJRvXeQ4if+phIWJrW/fSz0eUk+61XUUERGRg0rolEyuJ5UOBStcR/E7lbAwUFu+j765r7Kgw7EMGjTYdRwREZFD2p04hF7l67DWuo7iVyphYWDdnIeJp4KoKTe5jiIiInJYtT1G0Z0iCvJzXEfxK5WwEGfraui25klWeIYy/qgTXMcRERE5rKR+EwHIW/OF4yT+5dcSZow52Riz3hizyRjzsyYuP9YYs9QYU2uMOdefWcLV5s9eoFt9AXtHXacpikREJChkDJ1EnTVUZi92HcWv/FbCjDERwEPADGAIcJExZkijq+UAVwLP+ytHWLOWiPkPkUMPJn7vEtdpREREmiU2LpGcyAziC1e6juJX/twTNgHYZK3dYq2tBl4Ezmh4BWtttrV2JVDvxxxhK3/VXLKq1rEh63I6xES5jiMiItJsezoOpXflemx96FYEf5awVCC3wek833ktZoy5zhiz2BizuKCgoE3ChYO9H97HPhvPiNNvcB1FRESkRWyvMSSzn+3bNriO4jdBMTDfWvuYtXactXZcig402iwl29czeN9nLEk5m27JXVzHERERaZHk/t4j5+9cG7pHzvdnCdsO9G5wOs13nrSD7Dn3UIuHjBk3u44iIiLSYhlDJlBtI6nOWeI6it/4s4QtAvobY7KMMdHAhcAsP96f+FTvL6Lf9jdZEH88/foOcB1HRESkxaKiY8mO6kPHoq9dR/Ebv5Uwa20tcBPwHrAWeMlau9oYc6cxZiaAMWa8MSYPOA941Biz2l95wsn6OQ8QRyUdjrvFdRQREZFW25c0lIyqDdTV1bmO4heR/rxxa+0cYE6j837T4OdFeL+mlDZia6vpse5plkaMZOyEY1zHERERaTWTOpbEPa+TvfFrMgeNch2nzQXFwHxpvo2fPEuKLaR0zPUYo4OziohI8Oo20Hvk/N3rv3KcxD9UwkKJtUQv+idbSWXiSee7TiMiInJE0gaMptzGUJcXmoPzVcJCSN7yD8is3siWflcSE6WDs4qISHCLiIxiW3Q/kvatch3FL1TCQkjJx3+nyCYy+rTrXUcRERFpEyXJw8is3kxNTbXrKG1OJSxEFOWsYcj+L1nW41ySkzq5jiMiItImInuPo4OpJnvtUtdR2pxKWIjInfM3qmwUfU/RYSlERCR09Bg8GYCijfMdJ2l7KmEhoLK4gIE7Z7MgcTqZGVmu44iIiLSZXllDKCEOtmtPmASg9W//g1iq6Xi89oKJiEhoMZ4IcmIGklwcesdzVwkLcvXVlaRtfI4lUWMYOWaS6zgiIiJtrqzLcDJqt1JZUe46SptSCQty6z96ii52L5XjfqiDs4qISEiKTh9HtKkje81C11HalEpYMLOW+KWPsMmkM+GEs12nERER8YteQ48CYN/GBY6TtC2VsCCWveht0mu2kjvwKqIiI1zHERER8YtuqX0poiOeHaE1OF8lLIhVfHY/e2wnxpxynesoIiIifmM8HvI6DCJl/1rXUdqUSliQ2rN1BYNLF7Cy1/l06pjgOo6IiIhflXcdSXpdDqX7i11HaTMqYUFq+zv3UGmjGHCqDkshIiKhLy5zHBHGsm3VPNdR2oxKWBAq37uDQbvnsLDTyaSl9XYdR0RExO9Sh3kH55dsXuQ4SdtRCQtCG976BzHUkDxde8FERCQ8dOmezi66ELVrmesobUYlLMjUVZWTsfl5FkVPYNiI8a7jiIiItJv8+MF0L13nOkabUQkLMmvff4LOFFM38Yeuo4iIiLSrqm6j6G3zKS4qcB2lTaiEBRNrSVr+KOtNH8YdN9N1GhERkXaV0Mf7DdC2VV86TtI2VMKCyOb5b5JWl8uOIdcQqYOziohImOk97GgAyraGxuB8lbAgUvP5/eyynRl36tWuo4iIiLS7Tp1TyDM9idm1wnWUNqESFiR2bVjMoPIlrOl9EQlxca7jiIiIOLErYTC9ykPjyPkqYUFi53v3Um5jGHTaza6jiIiIOFPbYzQ92EPBzhzXUY6YSlgQKN2Ty5A977Ko8yn07NHTdRwRERFnOvb1Ds7PC4Ej56uEBYGNb/2dCOrpfuKtrqOIiIg4lTFsMnXWULFtiesoR0wlLMDVVpbSJ/tFFsVOZtDQUa7jiIiIOBWXkERuRG/i9gT/4HyVsAC35t3H6EQpnqNuch1FREQkIOzpOITeFeuw9fWuoxwRlbAAZuvr6PL1v1jr6c/YKTNcxxEREQkIdT3H0IViduZtdh3liKiEBbCNX75Kat129gy/Fk+EFpWIiAhA5/4TAchfE9yD8/XOHsDslw+ST1fGzbjKdRQREZGAkTFkPDU2gupti11HOSIqYQEqf81XDKxcwYaMS+gQG+M6joiISMCIiY1nW2QmCUVfu45yRFTCAlTBB/dSamMZepoG5IuIiDRW1GkoGZUbqK8L3sH5KmEBqHhXNkOKPmJpl9NJSenmOo6IiEjAMalj6GjKyNuyynWUVlMJC0Cb37oXD/X0OvnHrqOIiIgEpC4DJwOwa918x0laTyUswFSXl9Av9xUWxx1DvwFDXccREREJSOkDRlNpo6jLDd4j56uEBZg1c/5JR8qImqKxYCIiIgcTGR3Dtuh+dNyrryOlDdi6WrqveZLVEYMYfdRJruOIiIgEtH2dh5FRvZHamhrXUVpFJSyArP/0v/Ss38m+kddhjHEdR0REJKBFpo0l3lSRs3GZ6yitohIWQDwLHiKPboz93mWuo4iIiAS8lEHewfl71i1wnKR1VMICRO7XnzKgajWbsy4jNibadRwREZGAl9Z3OKW2A/X5wTk4XyUsQBR9+HdKbBzDTr/RdRQREZGg4ImIYFtMf5L3rXYdpVVUwgLA3u2bGLpvLsu6nUmX5C6u44iIiASN/V2Gk1mzhaqqCtdRWkwlLABsefseLIaMk291HUVERCSoRKePI9rUkrM2+CbzVglzrLJ0LwPzX2dxwnFk9h3oOo6IiEhQ6THoKAAKNwTf4HyVMMfWvP0QCVQQd9yPXEcREREJOj0zBrCXRDw7lrqO0mIqYQ7Zuhp6rXuaryOHMWL88a7jiIiIBB3j8ZAXO5CuxcE3OF8lzKHVH/+HHnY3ZWOu18FZRUREWqms6wjS63IoLytxHaVFVMJcsZbYhQ+TSw/GnHix6zQiIiJBq0PGOCJNPdtWB9e4MJUwR7Yu+5h+NevZ2v9KoqMiXccREREJWqlDjwageJNKmDTD/k/+TrGNZ+SpP3AdRUREJKh17ZXJbpKJ2LncdZQWUQlzYE/OOoaVfM6KHufQKSnJdRwREZGglx83iO7717iO0SIqYQ5sm3MPtXjoc8qtrqOIiIiEhMqUEaTb7RTvK3IdpdlUwtpZefEeBu98kyWJJ5CW0dd1HBERkZAQnzUBgNxVXzpO0nwqYe1s7dsPEEcVHafd4jqKiIhIyOg91Hvk/P1bFjpO0nwqYe2orqaa9I3PsiJqFENGH+06joiISMhISulJvulO9O4VrqM0m0pYO1r9wVOk2EKqxt+gg7OKiIi0sR3xg+lZttZ1jGZTCWsv1pKw9FGyTSpjpp3nOo2IiEjIqek+kl52N0W7t7uO0iwqYe1k06L36FO7idyBVxMZqYOzioiItLWOfScCkLv6K8dJmkclrJ2Uf3Y/RTaRUade5zqKiIhISEofNpl6ayjfush1lGZRCWsHu7auYtj+eaxOPY/ExI6u44iIiISkhI7J5EakErsnOAbnq4S1g7w591BDJP1O/bHrKCIiIiFtd+IQ0srXYa11HeWwVML8bP/eXQzZ/RZLkk6kZ2q66zgiIiIhrb7HKFLYy+78ra6jHJZKmJ+tn/0POphqukzXXjARERF/S+rvHZy/ffU8x0kOTyXMj2qrKsjc8jzLo8cycPgE13FERERCXsaQSdRaD1XbFruOclgqYX606v1/05W91E660XUUERGRsBAbl8C2yAziC1e6jnJYKmF+Yuvr6bT8MbaYdEYfd5brOCIiImGjsNNQ0ivXY+vrXUc5JJUwP9kw/y2y6rayc+g1REToaRYREWk3PUeTRCn52etcJzkktQM/qfniAfbQiVGnfN91FBERkbCSPGASADvWBvaR81XC/CB/4zKGlS9kbe8LiYuLdx1HREQkrGQMHkeVjaImN7AH56uE+cGOd++l0kYx8LRbXEcREREJO1HRsWyLyqJj0deuoxySSlgbKynIZ9ied1iaPINu3VNdxxEREQlLe5OGkVm1kbq6OtdRDkolrI2tf/vvxJgaup14m+soIiIiYcuTNpZ4U0nuxsCdR1IlrA1VV5bTN/sFlsZOpN+Q0a7jiIiIhK1uA72D8wvWBe7gfJWwNrTq3cdIpgTPUTe5jiIiIhLW0vqPotzGULd9qesoB6US1kZsfT1dV/6LTZ4sRk45zXUcERGRsBYRGUl2TH+S9q5yHeWgVMLayNovXie9Ppc9w7+P8ehpFRERca2k83AyazZTU13lOkqT1BbaSP28h9hNMqNmXO06ioiIiACR6WOJNTVsW7fEdZQmqYS1gZw1CxlWuYSNGRcTG9vBdRwREREBeg6aDEDRhvmOkzRNJawN7P7gPsptDINPv9l1FBEREfHplTWEYuKx+ctcR2mSStgRKtqZw4ii91je9TSSu3Z3HUdERER8jMdDTsxAuhSvdh2lSSphR2jT2/cRST2pJ//YdRQRERFppKzrcDJqs6msKHMd5TtUwo5AZfl+BuS+xPL4o8joP9x1HBEREWkkOn08UaaO7NULXEf5DpWwI7BqzqMkUUrUFI0FExERCUSpQ72D84s3qYSFDFtfR/c1T7I+oj/DJp3kOo6IiIg0oVuvPhSShGdH4A3OVwlrpVVzX6J3/XaKR12ng7OKiIgEKOPxkNthECn717iO8h1qD60UseCf7KAro753pesoIiIicgiVKSNIr8ujtGSv6yjfohLWCltXfsmQqhVs6Xsp0dHRruOIiIjIIXTIHI/HWLatDqyDtqqEtULRR/dRZmMZdpoG5IuIiAS63kOPAmD/5sAanK8S1kJ7tm9hxL6PWdltJp06d3EdR0RERA4juXsaO0khatdy11G+RSWshTa/fR8e6ul9yu2uo4iIiEgz5ccPpnvpWtcxvkUlrAXKS/cxOP9VliUcS1rWINdxREREpJmqu40kze6kuHCX6yjfUAlrgVVv/5OOlBF/3C2uo4iIiEgLJPQZD0DOqi8dJ/kflbBmqq+tJXXdU6yNHMyg8dNcxxEREZEW6D3saADKti52nOR/VMKaaeXHL5Bqd1I29gaMMa7jiIiISAt06tyVXNOLmN3LXUf5hkpYM8Uuepjtpjujpl/iOoqIiIi0wq7EIfQqX+c6xjdUwpph49JPGFSzhpx+lxMZFeU6joiIiLRCbY9RdKeQPTtyXEcBVMKapeSTf1Bi4xh22g9dRxEREZFW6tR3AgB5qwNjcL5K2GHsytnAyJJPWd3zLBI7JbuOIyIiIq2UMXQSddZQsS0wBuerhB1G9px7sRiyTr3NdRQRERE5AnEJnciJSCeuYIXrKIBK2CGVlhQxdMcbLO94PD1693MdR0RERI5QQcehpFeux9bXu46iEnYoq2Y/SIKpoNPxOjiriIhIKLC9RtOZEnbmbnQdRSXsYGprqsnY9AxrooYzYMyxruOIiIhIG+jcbyIAO9bMc5xEJeygVn7wHD1tAZXjb3AdRURERNpIxpDxVNsIqnKWuI6iEtYka0lY+k/yTE9GnnCR6zQiIiLSRmJi49gW1YfEoq9dR/FvCTPGnGyMWW+M2WSM+VkTl8cYY/7ru3yBMSbTn3maa92iDxlQu4Htg64iIiLCdRwRERFpQ0WdhpJRuZ76ujqnOfxWwowxEcBDwAxgCHCRMWZIo6tdA+y11vYD7gP+4q88LVHx6T8oJp7hp+qrSBERkVDjSR1Doqlg+5ZVbnP48bYnAJustVustdXAi8AZja5zBvC07+dXgBOM49mx87esYWTpF6zpdR5xCZ1cRhERERE/6DpwEgC71n7lNIc/S1gqkNvgdJ7vvCavY62tBYqBLo1vyBhznTFmsTFmcUFBgZ/ieu3ZtoYCk0y/037s1/sRERERN3oPGE2e6UF9dbnTHJFO772ZrLWPAY8BjBs3zvrzvkYcfy51x5xJRGRQPDUiIiLSQpFR0aT9dj1pjnP4c0/YdqB3g9NpvvOavI4xJhLoBBT6MVOzqICJiIiIv/mzhC0C+htjsowx0cCFwKxG15kFXOH7+VzgY2utX/d0iYiIiAQCv+3ysdbWGmNuAt4DIoAnrbWrjTF3AouttbOAJ4BnjTGbgCK8RU1EREQk5Pn1ezdr7RxgTqPzftPg50rgPH9mEBEREQlEOmK+iIiIiAMqYSIiIiIOqISJiIiIOKASJiIiIuKASpiIiIiIAyphIiIiIg6ohImIiIg4oBImIiIi4oBKmIiIiIgDKmEiIiIiDqiEiYiIiDigEiYiIiLigEqYiIiIiAMqYSIiIiIOqISJiIiIOKASJiIiIuKASpiIiIiIAyphIiIiIg6ohImIiIg4YKy1rjO0iDGmANjm57vpCuzx831Iy2m5BB4tk8Ck5RJ4tEwCU3sslwxrbUpTFwRdCWsPxpjF1tpxrnPIt2m5BB4tk8Ck5RJ4tEwCk+vloq8jRURERBxQCRMRERFxQCWsaY+5DiBN0nIJPFomgUnLJfBomQQmp8tFY8JEREREHNCeMBEREREHVMJEREREHAjrEmaMOdkYs94Ys8kY87MmLo8xxvzXd/kCY0ymg5hhpxnL5TZjzBpjzEpjzEfGmAwXOcPJ4ZZJg+udY4yxxhj9Kb6fNWeZGGPO971WVhtjnm/vjOGoGduvdGPMJ8aYZb5t2CkucoYTY8yTxpjdxphVB7ncGGPu9y2zlcaYMe2VLWxLmDEmAngImAEMAS4yxgxpdLVrgL3W2n7AfcBf2jdl+GnmclkGjLPWjgBeAe5u35ThpZnLBGNMInALsKB9E4af5iwTY0x/4OfA0dbaocCt7Z0z3DTztfIr4CVr7WjgQuDh9k0Zlp4CTj7E5TOA/r5/1wH/bIdMQBiXMGACsMlau8VaWw28CJzR6DpnAE/7fn4FOMEYY9oxYzg67HKx1n5irS33nZwPpLVzxnDTnNcKwF14P6hUtme4MNWcZfJ94CFr7V4Aa+3uds4YjpqzXCzQ0fdzJyC/HfOFJWvtZ0DRIa5yBvCM9ZoPJBljerZHtnAuYalAboPTeb7zmryOtbYWKAa6tEu68NWc5dLQNcA7fk0kh10mvt33va21b7dnsDDWnNfJAGCAMeZLY8x8Y8yh9gRI22jOcvkdcKkxJg+YA/yofaLJIbT0fafNRLbHnYj4gzHmUmAccJzrLOHMGOMB7gWudBxFvi0S79crU/HuLf7MGDPcWrvPZSjhIuApa+09xpjJwLPGmGHW2nrXwaT9hfOesO1A7wan03znNXkdY0wk3l3Hhe2SLnw1Z7lgjJkO/BKYaa2taqds4epwyyQRGAbMNcZkA5OAWRqc71fNeZ3kAbOstTXW2q3ABrylTPynOcvlGuAlAGvtV0As3kmkxZ1mve/4QziXsEVAf2NMljEmGu8AyVmNrjMLuML387nAx1ZHt/W3wy4XY8xo4FG8BUzjXPzvkMvEWltsre1qrc201mbiHac301q72E3csNCc7dcbePeCYYzpivfryS3tmDEcNWe55AAnABhjBuMtYQXtmlIamwVc7vsryUlAsbV2R3vccdh+HWmtrTXG3AS8B0QAT1prVxtj7gQWW2tnAU/g3VW8Ce+gvgvdJQ4PzVwufwUSgJd9fyeRY62d6Sx0iGvmMpF21Mxl8h5wkjFmDVAH/NRaqz35ftTM5XI78Lgx5sd4B+lfqQ/3/mWMeQHvB5KuvrF4vwWiAKy1j+Adm3cKsAkoB65qt2xa9iIiIiLtL5y/jhQRERFxRiVMRERExAGVMBEREREHVMJEREREHFAJExEREXFAJUxERETEAZUwEREREQdUwkQkbBljxhtjVhpjYo0x8caY1caYYa5ziUh40MFaRSSsGWP+gHfqmA5AnrX2T44jiUiYUAkTkbDmm+NvEVAJHGWtrXMcSUTChL6OFJFw1wXvXKSJePeIiYi0C+0JE5GwZoyZBbwIZAE9rbU3OY4kImEi0nUAERFXjDGXAzXW2ueNMRHAPGPMNGvtx66ziUjo054wEREREQc0JkxERETEAZUwEREREQdUwkREREQcUAkTERERcUAlTERERMQBlTARERERB1TCRERERBz4//v4BSbiVUBJAAAAAElFTkSuQmCC\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], "source": [ "import autograd.numpy as np\n", "from autograd import grad, elementwise_grad\n", @@ -5219,13 +5292,7 @@ "45/45 [==============================] - 1s 16ms/step - loss: 2.4278 - accuracy: 0.0995\n", "12/12 [==============================] - 0s 15ms/step - loss: 2.4059 - accuracy: 0.0861\n", "45/45 [==============================] - 1s 15ms/step - loss: 2.4412 - accuracy: 0.1044\n", - "12/12 [==============================] - 0s 13ms/step - loss: 2.4813 - accuracy: 0.0889\n" - ] - }, - { - "name": "stdout", - "output_type": "stream", - "text": [ + "12/12 [==============================] - 0s 13ms/step - loss: 2.4813 - accuracy: 0.0889\n", "45/45 [==============================] - 1s 13ms/step - loss: nan - accuracy: 0.1044\n", "12/12 [==============================] - 0s 13ms/step - loss: nan - accuracy: 0.0778\n", "45/45 [==============================] - 1s 14ms/step - loss: nan - accuracy: 0.1044\n", @@ -5597,7 +5664,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.9.10" + "version": "3.9.16" } }, "nbformat": 4,