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Created November 25, 2021 12:28
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# XOR Problem\n",
"\n",
"One of the interview questions in the Math&ML section of AI Labs is the XOR problem (see document [here](https://blueprism.sharepoint.com/:w:/r/sites/AiLabs/_layouts/15/Doc.aspx?sourcedoc=%7B9D604D79-9190-48DE-BBBF-5A3DF2EEA502%7D&file=Math%20and%20ML.docx&action=default&mobileredirect=true&DefaultItemOpen=1)). We reproduce the details of the question below.\n",
"\n",
"> We define a neural network as a sequence of layers. Each layer is an affine (linear + bias) transformation followed by an optional point-wise non-linear function. \n",
"> Design a minimal neural network classifier that can be thresholded at 0 for the above problem.\n",
"\n",
"In the first part, we define a neural network in a standard manner. Note that the non-linear function is allowed to be arbitrary, rather than, say, fixed to be something standard (ReLU, Sigmoid, Softmax), or even have some restrictions on the non-linearity (monotone?).\n",
"\n",
"> Four points live in 2D space as shown above. They belong to two different classes: ”red triangle” and ”blue circle” as indicated. \n",
"\n",
"This is then followed by the classical XOR problem, which takes the diagonal points of a square to be in the same class.\n",
"\n",
"> Please design a minimal neural network that can classify the points. Exact weights are not needed, just the architecture.\n",
"\n",
"Finally, the question is, what is the *minimal* neural network that can classify these (fixed) points. The solution says that one hidden layer is needed to solve this problem. Below, we present a counter-example."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.collections.PathCollection at 0x7fe4a5b539a0>"
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# define the data\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
"\n",
"x = np.array([[1,0], [1,1], [0,1], [0,0]])\n",
"y = np.array([1,0,1,0])\n",
"\n",
"plt.scatter(x[:,0], x[:,1], c=y)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For simplicity, let's consider the canonical XOR example using the corners of a unit square.\n",
"\n",
"In order to construct a neural network with just one layer (i.e. no hidden layer) that is able to classify these points, let's abuse the fact that we can have an arbitrary non-linear function. The first step, the linear layer with one node, adds the two coordinates (i.e. weight of 1) and has a bias of -1 (because I want the points (1,0) and (0,1) to be 0)."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x1 = np.arange(0, 1, 0.1)\n",
"x2 = np.arange(0, 1, 0.1)\n",
"\n",
"X1, X2 = np.meshgrid(x1, x2)\n",
"Y = X1 + X2 - 1\n",
"\n",
"fig = plt.figure()\n",
"ax = Axes3D(fig, auto_add_to_figure=False)\n",
"fig.add_axes(ax)\n",
"ax.plot_surface(X1, X2, Y)\n",
"plt.xlabel('x1')\n",
"plt.ylabel('x2')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now, I just need a non-linear function that gets me what I want -- I tried using `cosine`, and that works."
]
},
{
"cell_type": "code",
"execution_count": 21,
"metadata": {},
"outputs": [],
"source": [
"# given (x_1, x_2), take the sum (and minus -1 to center it around the diagonal)\n",
"def f(x):\n",
" return x[0] + x[1] - 1\n",
"# now the non-linear function is just a cosine function (plus some factor to get it amenable)\n",
"def sigma(x, a = 3):\n",
" return np.cos(x * a)\n",
"def nn(x):\n",
" return 1 * (sigma(f(x)) > 0)"
]
},
{
"cell_type": "code",
"execution_count": 25,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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I8djwTMHXZYLDLNNbDoNDN7mynQg5f6ST68PDhEI7s9NTwG+8apQvvOd/cfZYD/X19QghCIfDuN3uZGeGw+FIkmGiGPnxCk3TMlquRqOR6urq5AM0Id+1vr7O5ORkVvmuIhkWhiL5FYj0pEY4HKa/v5+6ujrOnTu37xssFosxODiIxWLZpeySi/wemXJzY15/qUpXhYmBpUD+E1MQb3ubLuiaTEj0+g4MDfPwWGjHa5dvTtHW2IIaDjCzsNOt9gdD/N5f/j1fev/fcrynA0mSsNlsNDU1JTszUouRQ6HQjvq7OznaUw/0DpE3mUzU1NQkBS8S8l2rq6tMTExkle8qkmFuFMmvAKS3qC0vLzM9Pc3Ro0eTmb1MSJBWvpvN6/UyNDREV1cX9fX1u17P1OGRwEd/rJ+UOqqsDC/nL4UxGSQ6qksotZuxm2RWvAH6zp7GKAkkoaLEYkSiUYKhMFv+IJ4tP1FFzbpeuc1Ah0PlxuDAjl7fdMwsrWG3muk7dZxLN3Ymbzb9AV70P97GV/7339HTvlPUNVMxcqL+bmRkhGg0uiOWVsgAqMcTssl3JUIB2eS7NE0jFAol70O/3091dfUTlgyL5KcT6fLyo6OjKIpCX19f3hY1SZLQNC1rplIIgcvlYmVlhTNnzmC327Ouk4n8+uc3eWRKX6mKhABNRc2wjs1koM4hU+60sxlSWNiKMb4RweKN4DBobAQz9elut79ZnEg1dVRZDJRZTTjMMlYjGCWQhILBv8LPfvIjHgnlLrZOIBiOcnV8jvvOn+VK/wDRlJ7iDe8Wv/P6t/CVD7yF9qbdD4nkZ5WkXeMzE4mFRMlJOBxmfX09mWW9kzgosrFYLNTX1ycfmAn5rvn5+R3yXQkyTNSLjo2N7YiTPtFUrovklwfpbm4gEGBgYIDW1laampp03SCyLGclv2g0yuDgIDabLaOAaSoSJJqOj/5Ev9V3ptnJle2avlKribZqBxaTEU8oxqw7zIxfMOPf6Yr2Vlu4saCvaNofUfFHUqw/ITheGubK2BqNRy7QYNO4fv1azmLnVFwcnqSrvYPApoeFlbXk8eV1Dy/487fwlQ/8Hc11mfUP0yHLcpIEIP5Au3jxIl6vN5llTU8s3E4UIkxbCKxWKw0NDclBVwn5rtnZWfx+PzabLVmQnSC5dMUhIFlw/Ysq31UkvxxIr92bm5tjYWGBkydP7mopy4Vs7qrH42F4eJienp6kC5MLmSy/iVU/3x9Zy3LFTlQ7jMiSxLmOKtb8MeY9YQaXc5NQa4WVoSX93SLpOF2p8NhwvMd40e1nkXix85m6EqbHhllYyt//Ozm/gtNu4+yJI1wduKVSM7+8xgv//K185QN/R22VPmWcVCRKRLq7u4HsiYXKysqf27IauCXf1djYiBCCUCjE2toakUiEixcvZpXvUlUVRVEQQiDL8i+cynWR/DIgU+3e8PBwMglRqEWQbrEJIZienmZtbY2zZ88mVUH0rJNOfh/9iYt8BoTdLHOssRSE4NJMAf27QmCRNRRtbxZKtgSJPxzj8owH2dpI35OPElxfZOjmSM61fMEQNyZD3N93lovXbqBsxxan5pf4nde/lX97/5upKi/d0z4TSE8spMfSMrmP+8HdII+EfFdtbS1bW1scP35ct3xXggwT6/y8C7sWyS8NiYzh/Pw87e3teL1ehoeH6e7upq6ubk9rJtxeiLu5AwMDlJSUFFwEnboOwJw7yL/3Zy80NhkkTreUM74aYHQlQCxHMiITzjQ7uTpTeNsbQLctwKODuSXwNSEYmPMANjpO3Ue9TXDt2jXCkexxwceGJuk9dIj11RVW1+N7G52e43f/4m186X1/S2nJwfUDp8fS0t3HTBbTzwsSZTb55LsSGfNM8l2pPew/j2RYJL8UJGr3FEVhfX0dTdPY2NgoyDrLhARpud3u5MCcbHM6ciHV8lMUhXd8/QpqBqNMliROt5Sx4A1zacYLQF9bGZdcXt3v5bQamFzdm7t7okrm6lD2TpRMWNoMs7QJZV1nOF9tZfzmICtr6xnPHXUtUuF0cOrIIW7cHANgYGya33vDP/CFd/81Dvve/1a5kO4+pltMhZTV3K54n16oqprxwZstY+71enfIdyXIMPE5fx5Vrovkx255eUVR2NzcpLy8nPPnzx9IrCdhLZw7d27P9WYJ8vP5fPz08g1+OLvbQjrZXIYnGOPq3C331maSGV0urKC5u9LK1dnCuz8OVxq4fnMUbY9f7s1ghMuzEYzONu49corN5Tlujo3tOs/jC7AZCHJ/31kevXINTRNcGRzj9//nO/jsP/4VVkv+Mpb9EFAmiymh8Zcoq0kouVRUVOwqq9Fb43e7kKv6IBWpGfPW1tYd8l3pnzMh3wU7yfAHP/gBN2/e5E1vetPt/lgF4QlPfum1e2tra4yNjWGxWOjp2b+wZiQSwe12J+d07IdIE3M/BgYGuBqoIKbesq6O1DuJaYL+ha1d1x1vLOWSSz+RdVZZuLYH4ussNzA2Po6iFtYrnAmKpnF91k21o5yn9J1CRAJxUVBZRhOgahpRRWPdu8V9584wMj7BhneLn10d4o/++l186h/egLkAlez9QpIknE4nTqczSRIJJZeFhYWkkkuCJO62JZTN8suHvch3bW5u6nrQvPzlL+db3/oWtbW1DA7uFueQ4r+w9wHPBoLA7wshrm6/9mvbrxmATwghHsr3fk9o8ktvURsdHSUYDNLX18eVK1f2vf7GxgYjIyOUlpbS3Ny8L+JTVZXh4WFUVaX3xBle+/5HAOiqdmAxGbIWLZsMElNr+js5JASxmFKwnE+L08DCzBShaOaZHYWi1CSok32MjrqYV1QcNiuHmqu4fG33l2IMaGmo5XBHM4/eGOEHj17jT/7ufXz0716f07q5ndZXqqxVR0dHUsklETNMVBK43e47UlaTDr2WXz7kk+963/veRyAQoLm5GY/Hk3Neze///u/z2te+lpe+9KXZTnkW0LP93z3Ah4F7JEkyAB8EfhmYBy5JkvQNIcRwzr0X9lF/MZAwyRPqGKFQiEuXLmGz2Th79uyB9OZOTEwwNTXFuXPncDgcGevz9MLv93Px4kXKy8uxWq18/vIi5XYTp1rKmNwI5uzWONVUmnWORyb0VsjMukP5T0xBnV3GuzzDVlBfAXMuVDmMnK5U8boGGRidTHaMBEJhro0vcP7UcUym3c/suaVVFtfc9LY3crynjW//6DFe9/cfzPl7v5OuZ0LJpauri3PnznHs2DFMJhPr6+tcvXqVq1evMj09jdfr3de9ohfZ+or3i0R5UGdnJ2fPnuUDH/gA3d3dLC8v89znPpd7772Xzc3MFQdPecpTqKyszLX8bwCfEXE8CpRLktQAXAAmhBBTQogo8IXtc3PiCWf5pdbuSZLE0tJScmZswpTfD8LhMAMDA8l4YWJOw17jS0tLS0xPT3P8+HFKS0uZdM1yZdbL8maUBW9uspElWPSGc56TiiqHkWmPPuIrMRtpq3bgsBrRYlG08h56NBVFiT9U/MEQm74AXl8AVUepTJkZOp0aVweus5BjQty18TlaGpvwbXrY8O508afnl+lpa2JpcZHTvR08emOY/++dH+Od/98rM5Lc3Yy7ybKMxWLh0KFDQLwKwOPxsLy8zNjY2I4WNafTeeD7VFX1jlibTqeTqqoqnvzkJ/PCF74Qv9+fFOrYA5qA1Jmq89vHMh2/J99iTxjyS6/dSwz3ht1Tz/aK9fV1RkdHOXz4cFKeCHaXqOiBpmmMjIwQiUR2tNA9uqTy8JS+eNypplKuzemv62tymrmxmbnoubrETFOlA6PBwEYgxpwnxPBqiHPNJVyeS7c8zfH/7GWYHVBmM1FqNWA3yVgMIAsNoanEohHCoSBG7xzXBoZ5JMuYy3TMrXkpddg53lvL4OjEjtfGZxY43NnCyNQsqqoxPbvAWz/0Wf7mNbtdqbtJfumWl9lspq6uLllOldqi5vP5Drys5nZZfpkQCASSTQGFNAdkQKYPLXIcz4knBPmlt6htbW0xNDSUcerZXqBpGhMTE2xubmaUtCqU/ILBIP39/TQ0NHDkyJEdN/oP5/TH1LzB/DN2E+ipMnNj3gvE76SWSjs1pVZUIbG0FWHVF2UjbdpbvdPMwPY12aAJ8ARjeDLsxWowUKtFWIrZOX7qDK7JMdxefWS9FQjhC4a5v+8sj129jpqSZBmZmqOruY7ZhRUevjbI+Mw8VWUlvObF/33HGneT/PK9d2qLWqIrw+127yhETpXuKhSapt2xXuaE1NgBYB5oSfm5GVgk/rTNdDwnfuHJL71FbWZmZpdO3n6QkLSqqqrKOgUslxpLOlZXVxkfH+fYsWO7lGKGl7aY3tJHoscbnAwu7s78ZoJRArOkcrjaQkjR2IjIzG0pzG3lLo+ptMksefYWnzJI0GLcZNC1AYDbD5aaHu4/VcrKzCSTrvyagUIIHhua5Mjhw6wsLbLm9iZfm5xf4UhnC6NTs6y5vbztQ5/FKMPL/vuzd9SmPV4sv1xIHaqeXlaTa3RmLtwptxd2Wn77xDeA10qS9AXibu2mEGJJkqQ1oEeSpA5gAXgh8Lv5FvuFJb9MtXsDAwPY7XbuueeeAzH5E2UxR44cyRmozSZIkApN0xgbGyMQCNDX15dRbukLl3N3TKRi058/wytLcLKpFLvJwMPTCVdaQs/oluMNju3ujD1ACI6UhLkyvrOvNxJTuTrjASo5c38XUtDN9f4baHlihjenF6gqc3Kit5qBFDf45tQcZ48e4trwKJqq8faPfoHKEitt9dWUlZVRUlJy14qNE/2ye0GmsppE7d3w8DCKouwoq8mkOnS33N5ceNGLXsQPf/hD1tfXaW5uZmFh4Q+JywYhhPgI8G3iZS4TxEtd/mD7NUWSpNcC/0m81OVTQojsw2G28Qs5wCi9ds/tdjMyMqJbQADgkUceyUqSmqYllZtPnjyZVxdudnYWSZJoaWnJ+Ho4HObGjRvU1NTQ0dGR0RrxRxSe/K6fEIzmb1FrdkjM+3OT7cmmUtzBGEubYaodZlZ8+jO1ZgOUmmDNv7dxl3E1aH1KNI0VDhpsgus38ivByLJE35EOHrl8fQep9R3v5VL/MEIImupq+M4n/xGjHLeyl5eXsdvtyY6FxMyM242EGGki4XGQSC2r8Xq9CCF2fb6xsTFqampylp4cFJ7//OfziU98Iuv9nwPFAUaFIL12b3JyEq/XW3BnRSJOl05+oVCI/v5+ampqdCs354r5JZIk+azHb/Uv6yI+gNISO/gzu6zHGpwEoir9i/EkxakmJzfm9bnHCRyqLFwFOoFC1aAXPQEWPeBoPs7pegeusZtZlWA0TfDY0BSnThzH5XLh3Yp/xkuDo9xz+hiPXhtkYWWNV//te/jCe/8Wi8VCJBLhyJEjyZkZU1NTd0TN5XZaXomymsT9lGkmiKqqOByOpAz+7URiOPvjDb8w5Jee1Eh0QuSKxeVCJsJKxOOOHj1a0BMzk9ubqAX0er265n588Yo+l7e9ysZwhla23voSNE0wlPqaEHgC+pMiAM3lFm6uFD77A+BUtcSjAxP5T8yAQCTGlRnvthLMMcLuJQaGMtewDkzMUltZQX1tFSMTLgAe6x/hvrMneOTqAD+9MsDbPvRZ3vCHL0j2oKbOzIhGo7jd7l1DkiorKw9MwOBOxhszfb7BwcFk94nJZKKysvK2ldUEg8GDSngcKH4hyE8IgcfjScrvJGYbFEpSqUglPz3xOL1rQbzlrb+/f0ctYC70z28yrFNTr8JmwpXyc1eNA6vJkFGT73ijk8HFwsQLHEb2JHF1tErmytBowdelI64E4wYsHO57CtXCw5bXQzSmEonGCEWiBMJR1jybeAwG7j9/mocvXwfg0Rs3uf/sCR6+OsBHPv91Dnc0c7yjYdd7mM3mpJpLItPq8XiYnp5Oxq8SZLHXPu07GXNLh9lsxmQy0dnZid1u31VWY7PZDnQi3p3MLBeCx9+OCkRCVuf69evcc889yezXXkgqFQaDAU3TkmUndXV19Pb27ulGSM32JpRdChlvqTfR0VRuTQ4xaq20UW43Z+z1TSAcKyxTe7KxhBuzhUtcNdtiDN506Sp21oujNRZ8q5P8dGaBc0c6GRnfOfFNkiQsNguT0zM86exxZpdWmF1a45EbN5MW4P9898d5//98JceOHcv6PqmZ1sSQJL/fn4wjp84FqaioyDvSIIG7SX6J90/ENjOV1SRmCO93Il764PXHE35uyS/dzdU0jUuXLtHU1LSrNm4vkGWZ1dVVFhYWMpadFIJEjGVycpKNjY2C4o++sMK3B/OrHQPUl1rQNI36Mhs35jeZ9WTv7jhU62CsAPfVYZb3NOqyxWlgZc5FLJP21h5wqNpCzLPI1UuzyWNXbk7R2tCMFgkmJ74JIQgEwwSCYVY2PNx36ggN1ZWMuuZ59MZN7j1znEevDfK3H/q/POneC5SX6ivFSM20ps8FmZubSyYXKisrc/bs3m1Vl1ySVulkn6rvFw6HCy6rSaz7eMPPJfml1+4tLCwQCoW47777DiSwmlCqCIfDXLhwQffTPNd6S0tL1NfXF6zs8vUbS4R0WGh1ThMSEmv+GEtb+bOwxgKNjt5aG1cKUIYxyBId1XaMwQ1MJhNyOLZnmSuAzkoLhsAq/ZenMr4+u7yedeIbELf4Th1BVWLce7KXK8PjnDvey5XBUV7zd//EZ9/5pj2rnKTOBUkkFxJS+JnGSsLjy/LLhXR9P03Tkpbv8PAwsVgsr+X7eCQ++Dkjv/QWNU3TGBoawmAwUFJSciBB1YSbazKZ6O7u3jfxJUQgS0pK6O3tLfj6L16ez3vOsQYnpVYjj0zrI6f2SivDS/qtuPYKK9e3RVGzwWkx0lrtwG424YuozHhCWI0GBv1WcDRhc0qU2UyUWQ3YTBJmGWShoqoxgoEgmz4/gXB0Vy9wc6kRp7LJtavX8u4z18Q3uEWAD18doKWhFkVROd7Tzg8euco7P/EF3viKvHWxeZGeXEiVwt/a2sJms1FZWUkkErmrc4QTZWCFQpblpL5fe3t7Rss3tcZQVVXd4afvfOc7vO51r0NVVf7oj/6IBx98cMfrkiS9Afi97R+NwBGgRgjhliTJBfgAFVCEEOfzvd/PTZ1fQolFVdUdLWodHR00NDTw2GOPce7cuX0FVpeXl5mamuLYsWMsLS1RU1Ozo0e30P3OzMywvLxMe3s7brebo0ePFrTGlVkvv/vJy1lfN0hwtrWca7NeKhxm3XV3pxqd3MgRC9wBIeiusjC+upMsm8tt1JTF4z9r/hgL3vCOm+V4vYOB+cKLoGUp3gvstMhUKeuszk4yMjpWsNXY1VxPYNO9Y+JbAveePMwj29JYPW2NlDqdXB0a41NvfyO/9pS8/fB7Rmo8bWFhgVgslrSYKisr960mVAguXrzIhQsXDnzdhBCwx+Pha1/7Gl/+8pfRNI0PfvCD3HfffVkJX1VVDh06xHe/+12am5vp6+ujv7//WDZZKkmSngO8XgjxjO2fXcB5IURm+e8M+LmQtNI0jUgkgqrG69xcLhc3b97k9OnTyfF8BoMh+XqhUFWVoaEhlpaW6OvrS8Zq9iotlEjABINBLly4gM1m29Nauay+WqeFrhoHl2a8HGl06ia+eqdJd9sbxOd4zLqDHKpzcr6jihMtlZSX2Fnwq1xf8HNt3sd8GvFZDBKrW/pGU6Yj0QtcJYd5dGyJqbCdttMPcM8992Cz6beUJueXCWoGzhw/suu1R/tHuOd0PMkxPrPI4NgUZ48d4s/e+n4mZvR30RSKRDytqamJuro6urq6aG5uJhqNMjw8zMWLFxkdHWVtbS3p3dzOvdwOGI1Gqqqq6O7u5i//8i/50Ic+hNPp5Mtf/jIPPPAA3/jGNzJed/HiRbq7u+ns7MRsNvPCF74QcstSvQj4/L72up+LbzfSkxqxWIzBwUFKSkp2zbjdK/kFAgH6+/tpamqipaUleVPIsryn9ba2thgcHKSzszM5+GYvqi7eYIzvDK1kfO14QwmznjBj210ZQui/kUsNCss6jChZgtPNZfgjMTTZxPhGBDb0dYEcb3Bw2bW3wUcAJ6slHh24JV2/5AmwBJS0neRsrQPX+DALS5l/N6nYCoTonwptix/c2PH3vDQ4xpljPVwbGicSjTG/vMqRrjb+4MG38x+feCcljtszBySBRMwvdah6QgjU7XYzOzuLECJpGd4NwdODgNVqpaOjgw984ANA9tEBCwsLOzpAmpubIS5VtQuSJNmBXwNem3JYAP8lSZIAPiqE+Fi+vT1uyS+9RW1jY4PR0dGsw3/2YqktLi7icrmSWnmpKJSwhBDJub7pogl70fP79I9HiCg7rzHK0F1hZDAlXldXamF4SZ8lV2k34drKbVFIEhyrs+MJa0gSjK0WZsHVl5rpn/MWdE0qjlTKXBvaPbMD4iMvr8x6ka1N9D35OMGNBYaGc4+8hPjEt8OHe1lbXmJ1I+6KCyEYGJvhWHc7QxMuVtY91FSUU1lWyp++9X186u1vvK2B+ky9vYnOkkTyJH2OcCJ5kug82c/+7lT5SSAQwG63J3/Otucs+8m2yecAPxNCpD5hHxBCLEqSVAt8V5KkESHEj3Pt7XFJfomkRqJGaGJigq2trZydEIVYagktP1VVs2r5FUJ+iqIkEy+Z5voWslZCx+9rAztDFw1lFuwmAyPrO8mordLGypY+i6yjysaV2ezucXeFgc2wxuBKCIMkiCqFu+qVVpkl997CBR1lBkbHx1HyiUAkC51tHL3wVJyEuHbtGtEcruLI9AIVpQ5OHK5mYGQciM8BGZtd4vSRHq7fHGdwfJp7Tx/Fu+njfZ/+N/789397T59DD/Rke7PNEd6vxt+drLvz+/26RA2am5uZm7ulRzo/Pw/ZZaleSJrLK4RY3P7/qiRJXyWu7vzzQ37pbm5CFVlPH61et9fv9zMwMEBzczPNzc1Z19RLWD6fj4GBgZzagHrXSvQNr4hSFv23PsvpljLGV/0sbe4kOYMEk2v6LDOnxcDNLBPcjjc68UdUJlLk63uqzIysFSZcsNckB0C1RWNlfrbgGSBTq3Grt7r3PJ0VZoYHb+D2eDOe69kKsOkLcvb4Ea4Pj6BpAkVVGXHNc6K3k4HRKR69Psz547385HI/Jw938Yx7z+7p8+TDXur8UucIp4/ODIVCSY2/fMmTO1lmo5f8+vr6GB8fZ3p6mqamJr7whS9AXMJqByRJKgOeCrw45ZgDkIUQvu1//wrwlnzv+bghv3R5+ZWVFSYnJ3UXGOshv4WFBWZmZjhx4kTeekCDwUA0mvvLr3c9PXp+CXmso0eP8sXvxRMdFqPEicYyLs96M15zvLFUd9b2cL1z1wS3o/UlRFSxw40GQAgCSmFfDotBYjWLCnQ+lJkh6l7A49cvuZ8Otz+M2x/GXNXN/SezawJqQnBjapFD3d0szM/jC4aIRGNMzq9wuLuNkYkZhiZcNFRX8IkvfovO5gbam3e3wO0X+yWgTKMzfT5fsv4uVdaqoqJih3dzUMOL9CAhvJoPRqORD3zgA/zqr/4qqqry8pe/nBs3bgxJkvQqSEpaATwP+C8hRKqyRh3w1e2HiRH4nBDiO3nfs9APc9DIVLs3MjKCoigFFRjnsq4URWF4OJ4x1ytZn8uN1uM2pyKXnl9Cecbj8XD+/HkCisR/3VylpcKGLJGV+AAUne6LxSjtKFXprXMgkBheyazMcrjWyshqYUR0rN7GlTy1gJlgM0rYQ8u4tgobmpQNUSWuCVjnrOepfWVEg1tEozEMsowkySCBEPGscnlvF+sbbiZmFwmFI8wurtHaUMPs0hrhaIwrgyP8w0c+y3v/+nXYrQdbhnLQ1lfqfN329vYdslYzMzNIkpTsPLFarXdUy09v/e2zn/1snv3sZ+84lkJ6iZ//GfjntGNTwKlC93ZXyS+9ds/v9zM4OJjXJc2EbJZfwi1tbW2lqalJ95rZyDRbdngva0WjUfr7+yktLU0KHHz2kosTTaUML/ly9t7Wl1oY1ilKcLKxlEszXnpqHBgMEiNZSC+BcKywmFCtXebGHpIcBgmaDF6GVvXPGcmHMpuRTnuUKzeuMKMoVJaVUF9q2yFymgq71cLT+k4yMbvI/Mo6WyETLfU1zC2v0d1Sz7d+8DBmg8x7/9efH2hz/u1ub0uXtUokT1ZXV/F6vUSjUWZmZm6bkksCfr8/WfXweMNdI79U3T0gmSk9fvz4nlrU0slPCMHCwgJzc3OcPHmyYBntTISVWgRdyKS3TG7v5uYmg4ODOwRWhRA8Ou3h6mx+MmitsLGsI9FhkOIqLMcbSxnUoQzTXm7C5SlsBGVViZmVrQJdViE44gxzZSx/yYoe2E0yh8sFNwYHeCR0ay/uTT9eX4AH+s7wcJrIKUAwHOH66BRVpQ7uPdnLzak5QjGVloZaJuaW6TvRy5f/6yfUVTh59pPPJ2NqpaWl+7Ke7nR7W2ryxO/3Mz09jdls3pU8qaysLFi8IBf0ur13A3ec/BKBWkVRsFgsqKrK4OAgZrM5Y6ZULwwGQ9J1TmRfZVne85rpklaZJqnpRWqpS6IkZnFxkTNnzuwoA7gy6+UnExt51zNIMKFjELnNJHOho4IfjeVfMwE57AXs+U5L4kSDg/4C5OxLLQZaqkuosUl4t3ycPtzB5lYAr8/PViBUsPKLUZY4WWNkZOQmD49nJndNEzw6NMXpE8eZcrnY3Np5nnfLj0GWiURjCFWlp7OVuZV1GmqruDw4zpljh/jU177Hb/36r1BS4kiOl7RYLEnrqlCdv7s9P8RkMu1QckkkTyYmJgiFQpSWlhYsXpAJBzi/48BxR8kvUbu3sLCQVMcYHh6mq6tr36ZxgqwSRcb7ncyWLmlVX1+/b7WYRCeJLMv09fXtIuWvXl/Stc7hOjtDy7mTCx3VdqKKxqrOMhiA+tgCU6JR9/lWo8SyN/s+DLJEa6WdyhILmpBY2gqz4ouxuhliZDFKXOjFBJRDSTkWp0S53Uip1YjDJGGSQRIqaixKOBzBHwzGLTl/EBCcrLMwPz3Bw1P6yL1/Ypa6ygoaaqoYmXTteG3Du0VdVQV2u5VHrg3SVFdNT1sLqqox5pqnrrqCP33Le/n2J9+VtNQTE9USOn8JtRM9rWp3U9ggfXhRevIkXbwgkTyprKykvLy8IPf/ACe3HTjuGPmlurkGg4GVlRWWlpY4e/bsnkbvpUOWZdxuNysrK3tyczOtFwgEuHbt2r4lrSB+w128eJGWlpZE9foOhGNq1o6OdARDuQmtr62c6/Ob1DotjGQpb8kEp/ChTzwrjmP1Ozs5KuxmmivtWE3GpLiByxvD5d1Zf1fttGRsx1OFYCMQYyOjuvT2LGBnOWUVMr02P1rQiz/P7yIdK+5N3EYD9507xSNXbux8bcNDU201tVUVLKyss7CyztHudjRNIJCYXVzhrR/8Z972+j8GwGaz0dTUlJR+Ss+2ps7NSCeMu0l++d47XbwgNXnicrmQJGlH50mutZ7Qll967V4i0Go0Gunr6zuQG0BRFGZmZohGo9x33337TuNrmsbMzAyBQIAHHnhgX6KoEI8VhkIh7r333l2dJAl89+Ya/kj+OsVKC7g2M59XZjPSWmHn0nbWtbHMyoJXXyyuUl1j0tit61yAWsmHZyPE2ZYyhGxhaSvCii+KN49FWqibnAk9jhAXR+LlQLaGIzxw1snc5Aiz83lHtQIQU1Qu3nRx6tgRxqemCabECBdW12ltrKVSUXFvbjE84eLM0R6WVjfo6WjlU1/6Nk+/5wzPvH+naEimbKvX600SRkL6KtGdcTfd3mxaftmQKXni8XiSYx3MZnPys5WUlOz4XE/YmF967d76+jpjY2M0NDQQi8UOhPg2NzcZGhqitraWaDS6b+JLzOEtKyujtLR0X8SXkL9PzDDIRnwAX7uu74tb7zThjuy2jA7Xl7DujzKwLVpglNmlxJILNeoablN+ZWkLUTpiE6jCwLjohVAU0FcMbTVKLOVwk/XgdKXKY0O36vdCUYUrMx4kUx3nn3SYqGeF/qG8UwsBGJxepKG6lnpJY2r2lojE7OIqnS0NcYvHH+Da8DhP6TvF9PwS954+xuve9n5+8Nn3UVuVfUSCwWCgqqoqqQqUOhdka2uLSCTC0tISVVVVB5pg0IP91vmZTCZqa2uT7n9CBn92dha/359MnmxubuLz+XSRnw45q6cBXwcS06++IoR4y/Zrvwa8j/jYyk8IIR7S8zlum6SVEIJwOJz89/j4OIFAgOPHjxMMBllaWipY4il9/dnZWRYXFzl58iSqqiYLjveKxCS1w4cPU1JSwsDAAOfP55UFy4gEiVZXV9PR0cEjjzzC/fffn/Hcla0IT3vPT8gX6zfK8azmVuRWFlqW4HxrOZdnvTuuP9Xo4MaivglrJdomEazEpOxEbyZKlzbDnFSPWYvglSvQpMK+QOebS7i0D8GDHkeYwYnZvOe115RSLoe5dvUqER3qKFaziWMdDVy8NrDj+KH2ZuYXlwmEwkiSxL2njrKy4cFpt1JWWsIX3vvmPZGWEIKLFy/S2NiIx+NJqiMn5oLs19PIh8XFRTRNyxh+2S8SyZOZmRne8IY3MDIywq/+6q/yrGc9i2c+85nU1dXtuiaTnNXnP/95jh49mvzlbpPfXwoh/lvqtZIkGYAx4JeBeeAS8KJsUlipuG1BB0mSkGWZcDjMpUuXsFgsnD17FovFgtFo3LP8FNySjAoEAly4cAGHw7EvSasEOU9PT3P+/Hmqqqr2JWnldru5cuUKXV1ddHZ25v2CfKN/KS/xARxvKttBfHWlFrprHFyc8e66fnMps+JxJjTH5rMSn0lEOGqYwyoi3DQcwi+XUqOuFUx8dZYY1/fh7h6plBmZyi/sCuBa2+L6SpTK3vM86SlPpbKiPOf54WiMK6Oz3Hv+DBbLrd/DmGue9pYmrBbzthDCFBaTAQ2YnJnnI5/72p4+S+K70dLSwsmTJzl//jyNjY0Eg0EGBwe5fPkyExMTuN3ufX1PsiE94XGQSCRPjh49yr//+7/T2NjIq171Kqanp/nkJz+Z8ZpMclZf//rX9b7lBWBCCDElhIgCXyC3FFYSt9XtXVpaYnp6elddnMFgQFEK6+FMwOv1MjQ0tCtDvFfyyzZJbS+SVkIIXC4Xq6urBc3p+JrOLG8kdms/p5pLmVoLZhQ1qFFXcRl2P2EzwaoFmTG27zpuFFG6lQmWLO0Ma63Jx6RT3WTK1KVr7VTYN6dYNnYUfB1Ae5mBsYmJvIIH6fD4w1zW0fKWwKXhKTpa24j4t5jblswanpzhxKFORiam8AdDhCIxgt4tetpbeN8/f4kHzp/kZG/hv49UyLJMWVkZZWVldHR0ZJTCT8Tc0mNqe8GdTrbcf//9PPDAA1lfzyRn9dhjj2U69T5Jkm4QFzz4SyHEEHHZq7mUc+YBXYq0t+03IIQgEolw4cKFXQXBeyGqBLGMjIxw5syZXaUxe9HMc7vdXL58mfb2dnp6enbcVIXKUCWs0XA4TF9fX0biy7TewMKWrpq9pnIrN5f9mGU4UW/jxvwWvkjmB0iVulu9OBvatXlC8q26PqOI0hsdxk6YEfMxNsXOMoUmJbuVmA2dkVGm9kh8tXaZ9QUXwQxxTr1ItLwtUMmZB57B2dMnsxLI9MIqWzE4d/JWSGZgbIpjvd0YDAZcC8s0N9RxbXiU8yeP8Cd/864dCZODQEIK/9ChQ/T19XH06FHMZjNzc3NcvHiRwcHB5NyavaDQhMdeoXdyW6ZzMvx9rgJtQohTwP8GvpY4NdOSevZ32yw/SZLo7OzMSEiFur2JIcs2m22XiGkChRCqEILp6WnW1tayWmiFPF0TLXSpAqbpSHR5pK+rN9HRWGbFIEsoisLAcvab3iiizBlbda1pFFEWpbhckhGFQ9ICC6KcUUvmUY4WLcissU3X2sn30KJ4jdV7ih47zRJsLbHhO5i+X4CbCx5sJiNP7jtNyLtGMBTCYrEgSxKSLCf/PpIk8fR7z3JlYIStQJDrNyc4f6yXy4MjXB0a477TR/nppRvcc/oob3r3x/inv/6zA9tjOiwWy46C5MQ0tcSY1kJHZ95JYQPI/13KJGfV2Liz3lQIsZXy729LkvQhSZKqiVt6LSmnNpNdCmsH7kp7WyEupcfjYXh4mO7u7ozB0tQ19Vh+0WiUgYEBHA7HgZTaLCwsMDs7m7e2MCFukPp+UUXjW4P5a/tMBgmDLLG6FSGcR2OvIzbFuPmwrr13xSaYNHZxOHaTJUMDw4b2nL5AR2yKEXP2GbeZ0GtYYjBWuCqKUQtTsjyMK3JwZRIGSeJoFYyNjPDj8SAGWeZwSzWX+m9mveaBs8dQFZUrw+NcHhrjwskjXLwxzGP9IxzvbuPhq4Mc7WnnG9/7Kc/9pScd2F6zIdM0tdQBQsCO0ZmZ7u875fbqLefJJGf1uc99bsc5kiTVAytCCCFJ0gXid+oG4AV6JEnqABaIa/3pmkR1V8hPzy8kNX6mpxBaz5qJeGE+ItUDVVWT6jN9fX15q94zkfOPxtfxBnO7c0YZ7u+s5Efj+roYIpK+OKMkFMxahBIRYMScP+tuEApLxsKyg1VsMhqtyuyY5IKm0rRxkTHl4Brij9VaWJub4tLl1eQxVdMYmlnl+JFeJqenCYV3l+z87OoQ9506QnWZk8a6ai4OjHLPmWM8enWQmaVVaqsqWF338L5Pf4kzxw7R0lB7YHvWg/TRmakCBokavES80OFwJGdI3wnLLxKJ6GqNyyRndezYMdLkrJ4PvFqSJAUIAS8UcX9ZkSTptcB/Ei91+dR2LDD/++7xc+nCXgOzB22dJcpilpaWdvXT7gWJlreGhgZaW1v3rOySr52t1GqgsdzGRkBfHV2NssKsqT3veZXKGk3KPAPWM7rWBeiKjTNm0mdRJlAWXmTdqD8ZYBEh6rQ1qiILeExWWuQtfIqJLc2CtsfwdEeFBdm3zJWLrqzn3JxZprmhGYMSYWpu9wCjR27c5N5TR3jk6gA97c0EAiHuP3uCh68OUF1RxsLyKi0NtbzxHz/MZ9/113d11ka6+nNiWpzL5Up2W4RCoT0nHAuB3+8/MDkrIcQHgA9kulYI8W3g24Xu767r+aXD7XZz8+bNHWon+4GiKDuEE/ZLpAnR0UJb3tKVXTb8YX40lj0x0VBmwSBJrG1F8Ib03ahV2jpr5LZoe6IjzBnbCBgKcCeFhkfOXtCbCR2RMSZzEJ8kNOq0VcrwgSSxJZezaqwjpvi4brsHYb/1d7IIFafYokT1YdWCGNQIaDEUVSOsyvhVA1uqjYi4dU1tiZE62c/l67uVXDJhfmUDq9nEhTMndtX7ATx64yanj3Rx/eYkACcPd/G0e07zw8euc/5EL5f6b/LM+8/x/k//G69/+e/kfK87KSNvs9mw2Ww0NjYihMDv9zM8PMzU1BSapu25Z1cP9Ko43y3cdT2/hNUkhGBqaor19fUD6/dNiBwkZvvuZ4+JWSKbm5v09fUVXIiaKmgaiUT4yLcvky1811PrYM0XxRuK0ddWnmxXywUjCvM5rD6bFqBZmWfcfJgy1cNMAdnXrtgEk6Ye3ecbRYwtaedNX6Z5qRZuzCgEZQcrhnpWTK2kRzyNahhh3PmA0iQDm1IFm3kIuFLz49S2qPWPE/BHuDbrLYhoUuv9rg0MEYnstLj7x2c52dtJ/+gU/SOTyJLEfWeO8ci1Ie49c5yHrw4iNI3Hbgxzz6nsoYS71dqWEBOxWCwcPXoUg8HA5uYmbrc72bObcJGdTue+DYXHc2sb3EXyS7iBBoOBSCTCwMAApaWl+3ZzEzf7/Pw88/Pz+xI5SJBeLBZLtrzlmyWSDYnPm4g7PraaeY0zzWUMLfmIqnFm1DuPtyM6ybi5N+NrzcoMQcmRfL1BXWTEoD9xEdYZR0zgUGQYv+ykzrhATLawppbgNdayRW5LvjsyzHgB/cXpCMglVIVcXA3VomKgutVHfcTFxLqCv4BKmUz1fhC/t4am5jh/8giX+2+iCcGlgRHO9HZwqX+ErtZ6XAsrfPTzX+dwZytlzsz33d0UNUh9//Se3Wg0isfjYWlpidHRUaxWa7Jnt1DJLtg9ue3xhrsW80uUpni9XkZGRrKOpCwEsiwTi8UYGRlBkqR96QMm1vN4PAeyP0mSWFpaYmNjg9LmXkb/6/quc/rayrk8401WhXRU2Zje0NcLG5F2B5YloXJUnuemseVWzExorFpadZeetMammc1QBJ0JVcoqddoqU+ZDhOVty11DV8LDogZZkfb3968Lu5jbEqjE/+ZenHgtJ7A0K5yOTbK84WM5pO9+mF5YpcRu5dzJo1zpv9UppWmCGyNTnDnWy7WhURRFZWHdwz2nDjM8OYskNOYWFvlf7/kIb/7Tl2ect3s3RQ0ge52f2Wymrq6Ouro6hBDJeOHU1BTBYDDZgldZWanL8ym6vVlgMBiYnJzE5/MV1A2RC0IILl26RFtb2777FhPag2NjY/tOkiRI3m63c+HCBd79/Z2tZ0YZTjXvdm8rrVKyizsXMiU6ytUNnJqPobTjnYY1pjT9mW6DyF+SVK2sUiE8TJp6qImu3SK+AtAem2DEWFhCJRWlsTW2PG7C7P6yRYSREWMvUp3gmDZLZHOdic38lpc/GOb6xAL3953l4rUbKEr8d6GoKsOTM5w80k3/zQlWN7xUV5RxqL2ZLX+QsZkFDAYjX/jmdzl/pGNXxvVuW35A3veXJAm73Y7dbt8l2TU4OIiqqsmSmvLy8oxGxuNZzgpuY4dHLkQiEbxeL6qqcv78+QMhvsXFRQKBAIcOHdo38SmKQn9/P6qqcvLkyX0RXygUSvY2t7e3gyTzjf5bWV6nxUBPrZMraYOKZGBsfhU9qNJ2zvjtjo4SlazMZYgBSmF9094gLm46naOVrUZboyc2ittYzbj5MDIqC8aWrOdnXUdZZdyoP6aYDosawOSexJuB+FIhkJiU25ivOEdHezMnasAo5a8NfWxokkM9h6irrkwei8YUxmcWOdYTj50OT8wgyzJ2q4Wzx3uZW1nn3/7rp1TXN9Hb24vRaMTlcnHx4kXGxsaIRqN5pwM+npCQ7Gpvb+fs2bOcPXuWyspK3G43V69e5dq1a7hcLra2tpKhJ73k953vfIfe3l66u7t56KHdgiySJP2eJEn92/89LEnSqZTXXJIkDUiSdF2SpMsFfabbpeoCtyStUpFQTrFarXR1dR2ISOjNmzdRFAVN0+jt7d2Xcmxirm9raytra2v09PTseb3EZz127BgrKytUV1cz5Bb88b9cB+JDiEwGmTnP7g6GztgEU6b88S+jiGIRUQJyCWYtTLsyzZj5SMZzS1UPAdmJKukz+HuiI4ybdscR6yUPztg6E8ZuhHTr+dkbHWbUlPm9c6FDmyvIGk2FrMVoXH+USXVv15fipzHiYnI9jC+W2yWucDpoqizhxs2x5DGHzUpTbSWjU3G1mb4TvUQiUex2G8FQCKMs89WPvB3zdueFEIK1tTWmp6cxmUxomrajKPlOlMlcunSJvr6+A10zMVDd7Xbj8/n46le/yubmJp2dnbzlLdlH6OZQdIHtgIkkSfcDN4UQHkmSngW8WQhxz/ZrLuC8EGI923tkwx2z/DRN26GcUlJSsm/FimAwyMWLFyktLeXUqVOYTKZ9rbm8vEx/fz/Hjx+nqalpT/3CcCtzPTU1xfnz5ykvL09mexMiBj01DiKKlpH4IC5VpQcdsSkCcgmNsTnKxFZW4gNoVBd1E1+l2NyV4a1TljhkWGJFlDNuOrSD+BAaG3J+PcB0dEuLeyY+gA73w3smPoAtShixHIemU5xqdtBoz37/eHwBhmdXuHC4BXn7DxQIhVne8NLVGh+Z0D86RTAcYcvnJxqNYTGbecdH/iW5RsKddDqdnD17ltOnT1NeXs76+jpXrlzh+vXrSV28O1kSs18kBqofPXqUCxcu8KIXvYhIJMI3v/lNTp8+zStf+cqMlq4eRRchxMNCiIQk0KPEW9j2jTsS80to21VWViaVU/YjQQWZJ6ntdU1N0xgdHU2KEiT6I/cia6UoCgMDA9hsNs6fP5+MrciyzFYoxvdG1jjdXMrNZT+RLLUuds2Py6CvhzYsWTgcHWbcdCg3sQmNVZ1KLwA10QXc20TaoC5RYpaYkBpY0aSMCYzu2AQTBZTDAJhElI2otOdHcM/mo3tqncuEGCZGjYeQagXHlSlYn0QzOVDD8WFHQkgIKf5/7+I658rCjAfseKMGtvzxVrm2pnpmFpYJhCKsezapqSxjemGJdc8mT7/vLE86H/fWEuK+cEvEoLo6/uAIh8PJ0pPEXJBCkgyPB0iSxKlTpzh06BAveMEL+M3f/E2uXbuWcf8FKLok8IfAf6T8LID/kiRJAB8VQnxM7z5ve7Y3URR8+PDhpKot7F3WKkFUoVBo1yS1vZBVOBzmxo0b1NbWcvjw4R1ZuEItP7/fT39/f8a6QlmW+cGEl5NNpTsyupnQoswxmsOCS6BWWURG6GpPa49N4zLr67Yo0baYNnXSoMxjI8y0sQuh5WaooFR4kqMrMsLNPSY5On1XGAoWVnitB13BARY9QbaUag5pKwxvZvtcJlosAdocYSZCZXi2/EhRPw1lNpbWNjhxqIOh8WmOdrcTDIX5/97xIb79yXdTXlqCECJrwsFqtdLY2JgsSk5PMiRKT/bqIt9JazKR7TWZTFy4cEH3frJlwiVJejpx8ktton5ACLEoSVIt8F1JkkaEED/Ws7/bSn7hcJi5uTnOnz+/q8dvL1ZaKBSiv78/I1FB4Rp8GxsbjIyMcOTIkWSt017XS1iiJ06cyDh3WJIkLs/7uTSTP+EQkPLHGBtZo9qi0K926tqfQUdgP4GO6AQBQ6mumCNAO8u4Cuz7rVDWmTTsTeaqOTjCuN+GKLhpODsaoy5U9zyDYQcQv1eHo/UcrdhgelMipO0mmrmIA4MkMIsoHfYtxoKlOE0RqkwqA2PTnGm0cG1siqeeP044pvGGhz7Ax//hQd3Z3vS5IOk6fyaTaVffbj7cyUyznoSHHkUXAEmSTgKfAJ4lhEg2ugshFrf/vypJ0leJi5veffKzWq2cPXs28xsbjQVluxIW5NGjR5NN3OnQS6gJSav19fWcZTZ6LL/UOR25Zvqu+FX+32R+4qtWVpg35Zak6oqNs2BoIqCaQMfDv1T14NLR0WEQMQ7FRnCZu/HJ2eeNpEOKBuITKAtAhbKGu4C+3wSqI/Msb0ZR2H+FAECZ4qZqc5ibPjuC3Q+d0UgVtSVBqmI+5kO739MVLqHL5mPEX0KJIUq9KcIGVspElGuLcLRC4adX+jlbI5hdK+PTn/oov/7ffmNPdX4H4SLfKS0/0Ed+OhVdWoGvAC8RQoylHHcAshDCt/3vXwGyZ1fScFeLnPW4vZqmMTExwdbWVt62Mj3kF4vFGBgYwG6374jJZUI+8kuoQFdWVnLmzJmcn/f7U5kHaqejWltnPUd/7uHoEKOmI7TFXLjM+qy+Rh0dHTXKMkZUYlgKIr54OYy+fSTQHp3I2febgCRU6rS1eP8vEj5DKRgkHHWt1BtiWCJuDEoI1BgxVRBSZXyKCa8OIQSTFqHDd40xr4EVkdvSXlXsmGULx8rWGMrgBk+GnPSUbDHpt+LxmakzhzlUJjHiVZnaMlBnjuDySjRa5vnfn/k36q++l+ae46yffTbO3qdiqS3s95fAXlzkO6nllyiMzoVsii4f+chHePWrX/2qbXGDvwGqgA9tf8cUIcR5oA746vYxI/A5IcR39O7vtpa6QJwgMmF9fZ2NjQ16ezO3ZMGtRElVVZWuWRjz8/NomkZra2bLKdHrm0t0NBUulwuz2ZzRDE+0qfX29iafxLnwjHf/iIWtPD1WQqNC8+AxVO16SRYK3bHxZDa3JzqatZ0tfc0qOcCGyH4THo4OM2XqIipZaFdndCdb4vvIXA6TDQahUC3cLGvlO45LQqNKuKnQvBglQUAuYcVYTzSlc+VQeIhRHfWA8g4hhEBcCCFJkBKmzTmWPEE2ogWaq8ARyzpjXpmo2E0gh+1bjPhuueOdNj9rUQs2g0YgJtFuC2I2aERUmXceHcGwfTubq1px9j6VksNPxXnoyRhs+h8+2ZBwkd1uN16vN1lobbfbWVpa2tegL7143vOex2c/+9k999VTuBhaYYvfbvJLDCpPh9frZXFxMesEt0Q8Lj1RkguLi4tEIhE6Ona7ePPz88zNzXHy5EnddXuzs7PIsryjaFoIwdzcXHJqnJ4C6GtzXl74ifz1l22xaWZMu/du1/zUqGvJ1yxaECEZdhBDNrRHp7JaiE51k2ptjent2F6V8OCmbGcJSw5UqutsSmW6y2cAesMDjBh7KdO81BpDWIwSAdXAqignKGf/u9hUP7IawS/ntiTyoXvzIlNBK22xaebXA6xHCreCmkx+wuEQq5HdXsjxCoXBdZEkwBMlmyxEbFSZokwEbJwq2UKSBEedfl7SnEFwWDZgbz2D8/DTcB5+Kva2M0jy/i21hIu8urrK1tYW1dXVtz2L/Mu//Mt873vf20+Xx20lv7va3pbJ7RVCMDk5idvtLrjtLZPbmyiC1jRNl+hoKtITHqqqMjwc7/Ps6+vT7T589Ur+cYsAFrHbSq5SVpEldpBimzKTs54vFQYpc2ihIzbOurGeacOtpEaNssKGSX8GtVZZwW3W92BCaPTExlAMFsqkIFvmWrbgVu9vntu8VZ1lRN676AFAa2CIkaATFQMjpiPIDRonVBc+rxuXTz/BLMRKsJksHLZsMLK10w0e9Bg5XuplYCv+hR/wl3G21MN82MZxp5/RQAlttgCPeMo4V7bJUWfa/BZNJei6TNB1Ge/1byKiQWzNJ3AeeRrOw0/DXFl4Bw3ccpEdDgdLS0s0NjYeaBY5E8Lh8IGoM90u3FXySyeqaDRKf38/paWleeNxetYMBoPcuHGDpqYmWlpaCg4yJ4QSEmv19/fT2NhY0Fq+pQn+/ZoLyG0hWogwkzYfozU2zYahhoC888kZNpXrem+n6sVl3Gn1mUSEztgko2nlMbJQWDTpz9g6tC1dU9xkodCtTOAxVGJAY7xAQVSAOm2NcXlvmeEEaiKzLGypqCmZGQ2ZcUMnVHXSU7mE0b/E6IbQJZwa0kyMa/WcrFhlyGtCTdESHAyUc6LUw8BW3Ert95XRY/PhiZlptYUIaUbsUoz3T7XxnuMj2A2748q2lpOEl8cRsRBR9xyb/XGtTnNNZ9IqLOl5AIOlsO6jhIrzQWeRs+Fu9zDnwm0nv2xT0NKHGCVmdexHPSW1zi8h4338+PFd0+P0IpHwSG1TK6Qdzzvwn3zhsx/Fb/uTvOe2RacZS5m90auMM2Hs2OVSVgovc3kESxNoUhd2JDoaYvOokmkX8QF0xKaZNOsvUm6Jzeac52EQMbqUCdYNtYyZj2AUUULGvWVobZoflb39DQFKFA8hzypBssfS5qQGcDbQ4PRSHZphdD1GWM1vAQ1FammvieHxbOKO3SLWwUAFJ0s99G85UYTMUtSGTY6hIhNWZUrNEuUGhQ+52vjLrp3yFfb284TmbiDU3THi6NoUG2tTbPzkU0gGE/aO8zh7n4rz8FOxtZzKS1SZEh56s8gVFRW6ZOlB/+S2u4m7bvkVOqsjF2RZRlEUxsbG8Pl8exIdTV9vY2MDt9udsVYxG4QQLP77O1n89j/y49L/oeuapCSV0Dgcu5mVWGpjC7jN5To2kdLRsb3muKk3a3xO1RnnAzCLMPNZJsTFLcsplo0NjKWQbFd0Qlfhdjq6omNMyO0FX5fcjxbCvnGTOaGv9W6DcjZs5dhbwhyOTTO37mcjkvtr4vKbKLVX0iM2GN+6db8NpBCgVzFTbouxFDTT7Qwy7rfTYAkT0yR+vFHBU6ri3VuOrnsJTD0GekY+qjECE48QmHiE5X9/CIOjEmfvU5JkaCrfnWjQU+eXLYs8NDRUsIt8N6W78uG2JzxisVjGchEhBA8//HBSZru3t3ffJrLb7eb69eu0trbS1dW1r198LBbjypUraJrGvffeq3tvamiLqf/zarwD38EvOXht9UdRpNxZxXLVzaZcjokoLcosk6ZDWc+twcsa5Xn30RabZMbURbnqplTbZDZDIiWBSnUdj1ypO9FxODbCiHFnhtdChI7YJAvGlt2lMkKjWl1n3VCYRW/UojiVDdyyzrhiOjSVto2f7WsQkgGVTnWGTY+bWX/uL7qM4JjTT/+KipYSxDxu9zDgi7vAx0s2GfE7OFu6xXjAjoxGnSXK/+yepP3oeQKTj+x5r+koPfEszFUtcRe56z5ks42lpSUURdnRUlYIUrPIm5ubWV1kTdN46lOfyvXr13Ou953vfIfXve51qKrKH/3RH/Hggw+mvixJ8QXfBzwbCAK/L4S4uv3ir22/ZgA+IYTYLQmTA3fE7c2Era0tAoHAgUxSg7jbPDQ0hN1up7t7f4HxxBze2tpaotGobuILLY0y8ZGXEF6Nz3l4xPpAXuIDqFeXEEg4RCAn8TUrM8zrnJtrRKU7OsqisTkn8QHUqiu4DfosI0morEq3zrWLIB2GdVyiLqu1WqgMfgLd0b23vwH0bD3G4D4nwKkY4nHB6k4OVS1i8C0z6mYHuSWgITHgc9Jd4WHJp+JT4l+voWA5x8uDDHotDPrLOObY5PJWKaecWwRVIwHVyMfXTvPgxCO6BS3ywdZ6Bt/N7yOUKOs//BiSyYqj4wJaw2nMHffBHslPj4sshMBoNOb14lRV5TWvec0ORZfnPve56RUgzwJ6tv+7B/gwcI8kSQbgg8AvE5/de0mSpG8IIYbRiTvu9qaWitjt9n0TnxCCmZkZlpeXOXnyJOPj4/tab2lpienpaU6ePImqqjtab3LBfe2bTH/mtWhhf/LYz6xP1nVt4ou0mKdFzKHpU3V2qm5koema3ysJlSVDk651Abpj44ybenFoPtoMbqapY0jkJuRCZfAByvfR/gbQvXWRwVDhKjO5MCs1IpfW88KaK7T7ryeT1BICSUr5NyBXq/xgo4ofuGvRkLjps3O0PMyw18RYqJRmS4gbW2X0lAQotZkJ+Lx8dbmO32rIP8c5H+wdFwjOXAHtVkxdxML4x34MYz8m+KP34/9KbdJFLjn8NEzOvf2uMrnI3//+93nve9/L3Nwcb3jDG/iVX/kVnvSkJ+0iw1RFFyCp6JJGfr8BfGZ7TOWjkiSVS5LUALQDE0KIKQBJkr6wfe7jk/wSk9RMJhN9fX351Bt0r5eYzKZp2p6VYjK1qfl8vrztbULTWPjm29ka/TH2pmOEViZR/essG+qZyGHFJdATGWbG1ElEzk0QRhFlTodQaJW6TovRw3WDPoupQ5liqgCrTMVAb2wYl/kQw7TnLVFpEwvM7EHgtEpZxbPHeR6tgWFGAvurB8yEo9YNXm78Du3KNOhY/ozTzW/XzfMvS6381FvNmM9Cr2OL0UAJAc1IiRnWVSelUpRoxEL/VgmnSn10O/Q95DJBb8xQ2VrFc+nf8Fz6N5AkrI3HcB5+Ks7ep+LouoBs1BffTkWiF/l5z3sep06d4k1vehPPeMYz+Pa3v43VauXJT95pDOhUdGkCUi2Q+e1jmY7fU8h+75jbm3Al29vbd3RM7HWeQUJBJXW9xEDmQhGJRLhx4wZVVVU72tTyqcQoAS9Tn3oFm8PfTzkqQVkLjzmfD3lalw9Hh0ESeYkPoD3mYsKcm0zjpTHVLMccuv+yesUBZKFwLNrPiPk4MUl/EkmOBQvu+22NTjGxR+KrjsyxsKWgHlDvL0A5Pv6wcZr7N/8DoRQwCQlotYX4q85RJoLzfGaxjeu+crrtPiaCDrqcMaZ9glp7GJPFzFyskq9slfP6iklMUW/B+3R03be3mKEQhBcGCS8Msvb9DyKbbTi67qP6KS+n9OgzC1+PeF9vWVkZz3rWs3jWs56V5W11KbpkukFFjuO6cUcsv9TuitRq79QJboUg4ZqmK6jshURztanlUnUJzg8x8dGXEll3pb0iEJtz/NDYkV10YDv7OmbqxS4yi5mmQ8uTjDgUvRmfoaGssmza3Y6XCeWqe1cdYCbUKCuYiBGSnQURX52ypGv9VEiaQkQUfltKQqNGXcEcWCKqxyzTASMqzzZc5GWHIgjXz/ZVutFtD/CW7mGG/U4+t9ZNpxxl0mfmeMkmgz4n50s9WA1hlt0SX1Ad/NH5OowllSgBD5HlMRC5PRBH170HlizRoiHUoBd7+7k9rxEIBPJ2UulUdJkHUl2HZmARMGc5rhu3nfwWFxdxu90ZuysStX56yU/TNEZGRohEIly4cGFfQ5ZTY4/ZSmyyCRtsXPoyrn/5c7RoZvdk1HSYtSzCoSZidBrXGZGO0Rkb1+VylmibzGSZoCYJld7YaFLTr1x4WEYf+TVIG3il3VJeSQiN3tgI06YuTMRYpbDkQanmZcVQ2DWHDQsMa7l7QSWhUS02KBdbGFEJyg5WDXVUSlFGKi9gFBoVYgunuoVVC2BUIwg1RkSFkCKzqZrwaZacVu9pyyKvbnbRXibjG7ukq/RED8501nG0eorrq4JPzbUw6C/jSMkm/f5Sjpf4CGsyA1sOHh5Z5Fz5KACytRRrXTcYTEQ3XCibqXFBGbX6EIHJRw9kfwCO7vvoeMVnCy6gToWeyW16FF2AbwCv3Y7p3QNsCiGWJElaA3okSeoAFoAXAr9byB5vO/k1NjZSU1OT0SpLtLjpqcVLiI7W1dVx5MiRfZWxqKrK0NAQkiTlbFNLJz+hqcx95c2sfP9DOdfPluhwaD4qVDejxBMEBoO+X3+TspCxMNmqBWlQl5LEJwuFBZ26epJQWRLZS0jKVA8Vmjv5vp3qDCOG/DHMBMpVN1MFuq4OdQuXWrpD2VlCUK1tUC68GNAIbRPdutzEOrcSNU2sMKq2gARCktmSytmSy7O+l13EKNO8OFQfFi2IpEbRVBUtFubXxY+51ziN3XQC3/AVJJMVa8tJZLONqGeRmFtfEiwd1qbjRNenIRLgdCm84/BN/m68l2F/CTXmMCtRC7WmMMsRC59bbKTTPkmFWUELbxGcuZpcx1zViqm8ESUaQjaYCLkKmtuTE84jz6D95Z9ANu+vLU2PnFUuRReAV73qVQDfJl7mMkG81OUPAIQQiiRJrwX+k7iP9SkhxFAhe7wjMb9sRKVXfy/RYZFNdLQQJFrempubaW5uzkmiqeQX828w+Yk/xDf6k5zrRzHxmOXeXcerlFUkCeZNceKzaX5csr5EwJa8u7uhSl3DINQd09Xa1Dmmdej2AXQo01nFSrujoyyZWnAZbq3tFoV1WNQrS3jNhSktN8Vm2JCraFKXMKIlLbp1YyPreaxZKRJAGPS/nyKZ2DDUsJFSe2gRYf7G9zba5XW0kiaCritAPFMamutPnmcqb8Rc2YKmROItaNHArvXTYW8/S2h+EKHcCgTbDBpvOTTCQ5M9jAcdhGISFcYYzdYIG1ET/9vVxt8cmty1VnRjlphvA0tNO+GlEWzNJ5AtJcQ2l+PkukeUnXw2rS/7MLJx/0IHeie3PfvZz+bZz372jmPbpAfAdpb3NZmuFUJ8mzg57gl3rcMDdre4pSMxCKjQDotsSAii6m1Tk2UZIQSBmetMfOxlRN3zea+5ZjlHMK0Xt1mZwStX7lAkaTd5uanmt9Ia2GDJuLMUJZHYCBh2xraM+ywSs2l+mpWFXVJZLcoMczrrCxPr6BFPTaBSXaNJWWDCfIiQbGdDp9ueQHfkJuOG/H3GuSAJjT8JfIRuexjZWk90bSrruTHvIjFvPLwkGUxYG49hsJUS21rJeJ2j8x4C05cyxu3MsuBN3WO819WJK2hnyO/kkN1PmUnBpxj58tLu8hfZXo7JWUN4IW7ohOYHkq8ZS2uxVLUjhEZ4ZRwttKnr81f0PZ+W333vgSjIgL6Y393GXSW/XJZfLBajv7+fkpISzp07p7vQODElLfX8/ZCoNP0Tbn7xA4gs8b10/DTN5e2OjjFjat+VKPCHFV1Z0LLoMkspyimHtQnGje272tRsIohL0kcaZRmUndtiU2zK5Rk1Aq2avqTMrbVmdM0VqVMWcQo/U6ZuarR1QnLh85HNWoR1Y92+e5FeGPpX7ivbQESlnMSXDqHGCC/e8raMzhrM1e0gNMIrE9gaj+ZNRBgk+B/tU3xsrg2rrDITsuKQY1hkje+uVXPU6edISdy6NJbWIZusRFYy17MqW6soW9vzniUZS/0hjCVVORMn5pPPo/y5fw8FtDjmQyAQ0KVzeTdx1zo8ILus1ebmJoODg3vq/kgQaoL8EsrNDoejIBLV1BhzX3oTxp9+Etlejq35GNFYjMjyOFIss5uzJTnpN59O/pxQXU5vG6tU17P2xqZCEiqL2wXI6YmNdLTE9MtcNaiLbG67iEYRpSs2wZjpcMb2Nrvmx1WAUrNRRFk05ibhZmUWMzGmjZ2sSHJ8YFKBWeEEOqJju1rtCsVTIz/i+VXTxDxeVJ2WUjYovjUU3xog4ei6ByXgxtF1H0rAHSefLCwtSfDK1hk+v9hITJNQhIQvasBq0Hj3ZAf/dOwmlTWNoClEN2b0bUZoRJbHSAilyVYnakkjDmcZUfcsyuYylU/5Y4z3v5q5ublkkiLRrrYfTysYDBYtv1xIt/yEEMzPzzM/P8/p06f39MtLrJkoUh4YGNCt3JxAbGuViY/9Af7tDJoa9OKfugSAJBuwNR3DYC8j5l0isnYrxvKo9YG4RbadJc0qTqCznSwuVd+1K7GRCRFrdVwbLx+ElszANsQW0CQ5YzIlgRZlNufr6egS84xmkZ9qj02hSQZmTe07jjfH5nRZiunYzxCkBI7EbvLa6utEFqcQSmbV8YIhGTE2HElmYBOrGmxlWOq68QdCmEKrqP7dc7Zf1LhImTHGl5bqqbXGSJDlexaO85byeVT/xq5r9EIL+5DCowS337bhN/6G2me8Ov7vhgaEEPj9fjY2NnaJGJSXlxfUe68n23u38biJ+SWEQoUQXLhwYc+CiokkRWqbWiF/BP/UJSY+9vvENpczn6CphBZuuTmm8gYs1e1osTA/9T0VswjTrMzlJAy9Df4mlIyJjXRUqWvMiipdurcdyjTTxg4OR4eYMB3K23vslQtIWggNt2bfUd8oodFjWCGgyBlHZ8YVYvbWZ1qprOLeYzE0QJ26zF/VPEzUdS1vHZ1eSGYHpqo2oosDu15TQ5sEXVeQARUw13RgKq1HDW8RXhoDLV5A/ezaNUqNCu+fbqfMFKPBacQdiPGv40Z+62DGFNP4m39LzdNfteOYJEk4nU6cTucOnb+1tTUmJiawWCxUVlZSVVWFzWbL6dXpTXjcTdx1tzcSiRAIBOjv79eVgc0HWZaZmJhAVdWCawFXf/JpZv/1wR0ZuXyIeZeIeZdYNDSyVlFFrezLWbvXpMyyoMPltWpBFAyEJeuuxEY6atTVHVnLXLBpAVqUuZxafIXuNYGu2CST2xlkAypdsXG8ciVjUmPWweSd0ck9WX376QIBsIsA/8P2nzgNUZTaTiIrE3teKwGDowJjSTWRJX3tpdG1aaLbnoNsdmCpP4ZsshLdmOVJLCJLGp9Y7GHKE6PZFuUry3UcKfHvVn8uAEKSafntt1P1wEvznpsuYhAKhdjY2GBiYoJwOExpaSlVVVVUVFTs+p4VyS8PDAYDm5ubLC4u7kt0NIFIJILb7aa2tpYTJ07oJlFNiTL7xTey9tPP7Pm9r5jPYRIx5kVuEirR/DlfT6A7OspNywld8zHWDLW61jzEDFOWw4TRV8rg0Ar7kkUkMyYRpZt5lkV53hikJDTWLc0FJyskTck4QEgvDELhjc7v0jz3fQLbiVSDoxJLbVe81Wt1HC1YWOzPVNYABmPWREQ+aNEAodnrt9araOZXjx1h46qbH07F8Csm2iwh3j7RxYdODOE07qGHXTag3vtnuogvE2w2W9JA0TSNzc1N3G43MzMzyLJMRUUFVVVVlJSU6Jrclgq3283v/M7v4HK5aG9v51//9V93jaiVJKkF+AxQTzzI8zEhxPu2X3sz8MfA2vbpf7VdCpMVd0RjOhMJJVzTzc1N+vr69k18Xq+Xy5cvU1ZWRn19vW7ii3oXGXnPc/ZFfBoS37f/St44niwUFsx5YlRC43B0iC1DhS7ia4nN5Lf6tteUo37dxGfVggUlOpqjLkpNGlYpyk25K+MEunR0xcZZF4VPKjsUG2HJsHf/74+sP6B77is7jqkBN8HpSwRdl9FCPiz1vTi678NSf4h88QRzdQdCU/Zc/JwJpoomfMPf5zmWK3TYw1isNgyOcpqc8K6pzoIbTiSDmfbf/xha59MPZH8Jsuvq6uL8+fMcP34cm83GxMQEZ8+eZWJigm9+85ssLurrOHvooYd45jOfyfj4OM985jN56KGM0nwK8BdCiCPAvcBrJElKdRv+SQhxevu/vPV/d0VgPxKJcOXKFUwmE9XV1ftSWxZCMDs7y8jICGfPnqWkpCSvEksCvvFHGHr7MwlM769CftB8knUd1le7Mo2f7JXzRhGlOzbBiqGOOZ3upk3kLsExa2G6lAlGzMfYzNHxkI42xaVrOhxAZ2ycEquRYTrwSfqf9iGp8NIWu+pnXto78f26/ChPWf6X3CcJjcjyKIGJR4gsj2Gwl2NvP4+94zwG+84ie2vjERT/xnaG94BQf5Lg1GPJOOSrW6coZ5NZTwSiYebCdr4R68PedhbZmv/hIZmstP/xP1N26tl5z90rzGYz9fX1nD17lqtXr2K32/H7/bzsZS/jL//yL/Ne//Wvf52XvexlALzsZS/ja1/72q5zhBBLCSFTIYQPuAno12NLwx13exOzOnp7e7FYLExP770iPdGmJstysk1Nb9fI6k/+mY1Hv4ga1ueG5sIPrfqeplIO/85JkHI5wIT5EIejQ3h0ZIONIpqzZKZCXcciokyaDlGnLO4qls4Fn6U+rztq1YK0KjMsmtsIq6aCBg22xqaZzdKvnAstsek9l7acETd54caHC75ODXoIJlrIJAlLXQ9GZzUgE5y9prsGVA8yKbMYJPgfnVO8c7KLuaCFWkuQ/3PDQE9klKNlYawNhzHYK1B860RWd7rdsqWEjld8hpLu+3QbBftFYpzEgw8+yJve9CZdghArKyvJ+b4NDQ2srq7mPF+SpHbgDJCqgfVaSZJeClwmbiF6cq1xR8gvUXg8MzPDyspKUkggGAzuWX8vtU0tVRMsH/lpsTCuz/0FG49+Ib43oxlTw1EiqoQ54kbZXCpoHz6phKuWvrzn2TR/VnGCGmUZVTIyt+2+uk36ynLaYi4ms8hctcRceAyVSRKt0Lys6OycaFTm8wqrtsWm2JLjcb3D0SFdCZRUGEXmkZq5UKssMm7Ql+So0Ny0KzO0qy56SmI0B4aoCu39QZuEEERWxjE4Kgi6LmKwlGBpPweSgcja5D5KUSQcnReyFkQ7DBqvapvhg642wqrM0RIfb5/s4kPHh2BpJHmewV4Rj11KEopvlbaXfhh72xkg8/Ci2wVJkpKlMYkQ1C/90i+xvLy7iuLv//7vC127BPgy8OdCiK3twx8G3kr8kf1W4N3Ay3Otc0fIL1FobDab6evrS/5S8rW3ZUOuNrVsSiwAEfc8Ex99KcHZG8ljQokSWxpGJh5QsFS3Y6poRA14CS2N5C2BuFT3fBQt/6+xVZnLOMCnLTbFmqEuObC7MTbHoklf6Ue2mRsJeatEzFASKkuWNt2JhRLNl/U1k4jSY1jlpqkjqYrilgur5K9VlvZU1GxXfKjGne8lIaiTt+iQFmnxD9GhTNOmuigT8c9gazlFZGU8qwLPXpBqnSXKV+KbkbDUdmEsrUUNeuPlK0LH/S2bsLeejIuQ5kC9JcrvNi7yAVcbBkmizBDjXVOdvLlnnESIO2GlGkuq6fyTL2JruhUS0zO86CCQbXLb9773vazX1NXVsbS0RENDA0tLS9TWZg4jSZJkIk58/1cIkQzcCiFWUs75OPCtfPu8I+Q3NjZGXV1d0qxNIFuHRzaktqllm8xmMBiSs3ZTsTX6EyY/8YcoeZ7MkXVXUqPPYC9HK23CYrYQXZ1AC2/tOLek+z6+5z6m67cYzBDfSicpgAqrxKKO74tT29plScpCoSc2tqvGsF1eZVroi5NZtFBWC7VJmSUqWRiWblmFbawwYyysC6dc87JaoNRVZ2SMaUMrzerctkUXt+ralBnshIF4B4O1qQcMR4isTmGt6SQwcxW0wq3MbMipmycEkdVJItszXGSrE2tdDxiMRNdcKL7drpxksmKtP3SLQPPgiDPA7zUt8vHZZiQJQiED/7Zcz283pFhUjhpKf/djyNU76yoLkY87CBRSsvbc5z6XT3/60zz44IN8+tOf5jd+4zcyrScBnwRuCiHek/ZagxAi4bY9DxjM9553hPyOHTuW0RrLZaWlQ2+bmsFgIBwO7zi2/L0PMvfVv9sx00AP1KAXgl7CgCQbsTUdw2grI+xZxFLRwIBrmdnK/ImJSnVtZyFvlvGUMiqzsVJdaagmZX5HfZxD81GtrmUsrjZGNsGsj/zaFNeuEhVZKByKjTJmOowm7fzyWKIeMOsnvzLVw5RRvwiBUcR4IPwTnhH6Li3qPGayKylrYV9S+snRfR/K1hqOjj6UoD5B0JyQDNjbzxakm5e6H4gPHDeV1uJzryBvziGb7ZgrmnYoxujB/ZVeViNmfrBRhYbEt1dqOFbi56jTj7m6nbqXfQqfsDM0NISmackuDaPReEcsv71YmA8++CAveMEL+OQnP0lraytf+tKXAJAkqZH4ZLZnAw8ALwEGJEm6vn1poqTlHyVJOk3cv3EBr8z3nncs5lfI8XQU0qaWKj2vRoO4PvvnuC9/ubANZ4DQFEILQxgcVZjL6wmtufhh5e/purZWXcW9Hc8ziigdsemMMbK22DTTWWSm0rGZInNVqyyhGSzMZChNsWghZvJMb0tFIE2Rpk5ZREZk3K9N8+MqYG2ABmVBV3zQpgV5Rvh7/FroP6jQcsatd0KScXT0EZiIW2eR1Xjxcry1rAckicjKJGrQrX9NgwWtrIXg9CX912RAdG2K6NoUMvE6PnNVK2gqxrK6NIHS/PjNhlWmgjYWIlZKLQofnmnlnU9WOPpnX8RUVk8l0NbWhqIoeDweVldXcbvdaJrGwsIClZWV+5qRnQvBYBC7vbBMflVVFd///vd3HRdCLBLX80MI8VOypNWEEC8pdJ93tchZDwptU0tIz4fXXEx89KU7WtH2C2tdD2rYR2hhiCgmHqk+ostKS7SzJcRMMymnABj1xIdgR+a2MzbBoqGJsJT5Rm5niVFJX3ytPrbAQiLeuG2d5mqBa1NmC+rOsIoIMzna9CBuGf5q6D/4pfB3dUv8J2G0YGs6mjF2Fo/N3crYmmu7iMoOLERyCg7ItjJM5fVElkYL20sOCFsVSBKBiYeTx8xVbZjKG1DDAcJLI8lWt1x4bccsbxo5xFLEQkOZiU9G7uNC6U4r3Gg0UlNTQ01NDR6Ph8XFRTRNY3R0lFgsRnl5ebJ396BcYr/f/7gXNYC7bPnlQuIPFA6HC2pTMxgMRKceYfjjb4u7rQcER8cFgvP9iFjcpb5subBLty8TmpVZ5o2t1CgraJKcFDNNh1ULMpPW8J8NicxtNtWYVIRVSXc1Z5nYZJkmqpRVbCKU10LzFlA3CNAem2DElJks65Qlfj30LZ4c/hEmCo/RybYyzOUNhGau5T9ZCKLbcbkI8diupbYbJCmugbd93xhL65DNtgMlPlNlK9GQb1dBdHRjJqnWIpvtO1rdEtqB6TDLgge7p/jH+VMsqBWIVS8f/+I3ecULn5vxfCEEFouFlpYWWlpaUFU1OYB8amoKs9msu3c3F34eWtvgcWL5pU9wS0xTq66u5vDhwwX9Ebw//jjRG9/BUlaPGtxk30JvSJjbzhGYvrjj6I9s+mr7SqQo7fIqa8YyAjkmirUq+iSpJKGyZqimJzqal5zK1Q1mdYqQmkWYOWMbvdGbuIwdbMi5i7YblTkWCxAkkIXCsrw7ZNGpTPEc4yXusbswsEosXDjxGcvqkY3muMW0B6hBb4pVuK2BV96IiPgJTutLROiBpa6H2NYaUsib8zwtGtzZ6lbZgrmiCS0SJLQ8CinqM23HLvD3r/wb3vHJL+HZ8vFv//H/OHvsEOdP7B5dmir1BnFDoaqqiqqqeDdOKBTC7XYne3fLysqorKzM2LubC0Xy04lEjC5hcieKoA8fPpz8o+iBGvYz/enX4Lkez3CHAdlegeJowG4zE1keK7gYVbaWIpc3EZ3Z2QGyJtcwbMoft5KFgqyEmJN3i4+mI6JzsHd7bJqIbM3qOqeiXl3Gq6PNDKBTWiSsiIzlOJng1NmjnEB3dIKxlD0fj/bz34Lf4HgsnpTTtv8zVTRj2v6i63H/zLVdaKEtohuzBe0nK4QGSIRnr6MGvfvu+U3AUHuImHcBLVK4KEHMPZe0FOPzRE4hm20YS2tp/b33IZus/M6vb/Dhz30NZ4mDf/jwZ/nEP7yRyvKd3R/56vxsNhtNTU00NTUle3c3NjZwuVw7iNLhcORVdCk05nc3cNfd3lTx0dnZWZaWlrJOU8uG8MoE4x99KeE090QLepCDnni21mjB3no67sasTRHLE2A2V7eBphFdvrnrtR/bnpbT1YS4hXYicoMb1vzj/yrY1GWhNcbmtkVA9SVF9NbftcWmCCIxq7OX16KFcBXYneEzVyELlQuRx/j10DfoUFwZz4t55ol54uMCZLMdc90xZKM5PrVsa2epSHwgkAstsv8unQRsLSeJrEwk6wLjPb/byRFJxlLfGx8p6VvTrQRjbjpJdHkEVP1qQdkQnydyg7LTz6HtJR9AMsTjsb/1a0/HNb/Mx//1m7Q21PHgOz/CR9/2hh3fvUKysIne3YS4QEI0xOVyEQgEKC0tTYqemkw7Y8I/D1p+8Dix/CKRCCMjIzva1PTC2/8dpv751aihrZznCSVCMMWVsNZ2YyqrJebf2EWajrazhJbHMn6pNCR+bH1qzvcq0TapUt34DPrEGuqi83jyuLBd0TFWjXWsS/oUXPS6pYejQ6zLNWzoaKdLIFM5TC70SIu0hYb5y8A3qNP0ZzW1aJDw3PXkz+bqDoyldaihTSSzg8h8P+IACCUBe8d5QrM3EGoWa3O75zcpTlpShaWmM24VroyhZbgH7R19BGeuHWitYcWFF9Dyovfsmrfx+pf/DqtuL9/6fz9jad3NP3z4s7zpT24puOynzs9isdDQ0JAUPd3a2mJjY4P5+fiDKhErdDqdBbu9ehRdACRJcgE+4nKIihDi/PbxSuCLQDvxMpcX5Gttg8cB+QkhuHHjBu3t7TQ36xu7mLhu8d//kcVvv3NPM1XDqxOEt8sgjM5qrLXdaEoEg6UE3/hPs645ZD6RU0WlWZnBJ5Xikcvxy/oUS9xybtc0kdjojo0xbt4dy8kEZ44uDYiX3HTGphgxH4sToFEfqcLucphcOGNw8fur76BKLaC0JAui69NE16exdd5DZHkUS/NxZEkmvDaJFiigHCYDHF33xrPEBdxLqn+DYKJoXjZgbTiCwV6O4lslsjq5pzXzoepJv0/T8/8hozclyzJ/9eqXMLe0wuqGhw/936/S2ljHS37zV4G45befWdcJSJJEWVlZUokpFovhdruZn5/nne98J8vLy7S2trKysqJrDEVC0eXBBx/koYce4qGHHuId73hHttOfLoRIl8B+EPi+EOIhSZIe3P75jXk/R56m4wP5q2malrHrYm1tjf7+fnp7ewsiPiW0xfT/eTXege8cxPYAkMx27I1HCM4Popa2Yi8tR3HP7HK1PlD6Oh613p9xjd7oMBOmQ6iSUXe/a31sgWVTZsEBg4jF52tsW1kdLDKtoz9XFgp2EdoxLS4V5aobhwiwsG0ZVqurulRp4vtdZNmUfw82LcjLbT/jvrlP6FpXLzI1/iPJmGu7MDqqUAMbBWvqZVxznyg59BRELIwQCqHlcUQ498NID2qe+Roan/vXec+bml3gBa/7G1ob6rjUP8pn3vXXPP3eM0xPT+NwOLK2jh0ENE3jH/7hHxgdHWVzc5NIJMIPf/jDnMpNvb29/PCHP0y2tj3taU9jdHQU0mr6ti2/8+nkJ0nSKPC07WHmDcAPhRB5g+J3hPyEEESj0R0/T05O4vF4kn8MvZOeQksjTHzkpYRXd88z3SvMFU1IRguRDFO7jNWdCEsZJtXP+soif1r9kV2T2MwiTFvMtcMqq9HWWdMRc8tGkg7NR5W6kZx3UaZ62JLL8sYaIS4xlU1NuiXmwmuowLddJN2szDOvc9A5xAk+30yP47FB/rTkxzjmfqR73bwwmLC3niKoQ37M4KjCXNMRn6C2PI6IZCMeCXtnH8Gpi1le3xviLXApnSCyEWv9IQz2MiLuRRS3zgFEKVBP/R7lT/sTqqqqKC0tzVsB8cNHr/LSN7yNw11tTM8t8/WPvh2LpFJeXl5QInEveM973kNXVxcvfvGLdRU8l5eX4/V6kz9XVFTg8XhgN/lNAx7ivPRRIcTHto97hRDlKed5hBB55y/ccbc3dSTl+fPnmZyc1C1u4L76DaY/89o9Zcyywd5yksjGLKpnIePrynqcEFXg0Yrn7yK+amUFA9oO4mthmbkMZR3pkISaUT2lRllBSNKOQT9NsptNSd88jWzSWamWaQIOKZzx3EwwiUjO+b1WLcRL5P/iv9Utooa2CJlsiFiBhcoZIFlKsNa06yI+ADWwQSiQcEeNWBqOYLCVEdtcJrbhih83mJGqug6W+CQZe8f53S1wmkJ48Za0vWSvwl7fjVBjhJbHEHkSNo2/+WbKn/TyZJHyyMhIcspaVVVVRqvqafee5a2v/yP+8eOfw2o185K/eCv/+69eTWVlZYZ3OFgEg8FkzC9BfAek6PKAEGJRkqRa4LuSJI0IIX68133eUfJLtKl1dXUlYwF69fc0JUpk3YW96Rj+6csHMnCmpOd+/JOP6e75/X+c3/Fzj7TAvLGaEDtFP22xTdAhS9Uem2bavDNzm67ykoBbc+wYDJQNDsK72txkodAdG99lsRlEjHlJf19uR2yasSwxx6PRAV5t+Ca10TV8I9sDvY0WLI3HCCoCc9iDulWYXBjE5+AabE5C83n71DNDU4gs3crYG0vrMdd0oiITce2vXW0HDGZszcd0kakIbhCYipOzZDBhbTqGwVpKzLtENEHOAJJM8wveQdX9LwagtraW2traHVPWBgcH0TQtSYSpVuHL/vuz2fQF+Mb3f8rNyVne+J5P8q/v/7uD+8xZkGlg+UEoumy3uiGEWJUk6avABeDHwEpC2GDb7c0tBriNO1bqsri4iMvl2tWmZjQadSm7yEYzDb/yZzT8yp8xNz7I/CNfocI3QmD8p4VbgkYLJW2n8I8/nP/cbbiM7cke2fgM3cyjKS1EmDHoU2E2pnUy9EZvMpGm8gLx7odloz5hgubo1A6SKyVAmebJmJ1tV6aZNGXWA8yEUIZaRIsW5oWB/8tzyueJbS4SS+mqEUqEyOIQBranlVW1Ya5oRAn5CC/ezCv3ZKpqAyVCZFX/EPF8EJqCsrUcH0xuMGFtPoFstm+X2GS2/vNBMtux1HTq6y5J348aI5zSgmksrcNS3YamKtQ85eVUnP+t3e+XNmUtFotltQr/7GW/jS8QpLTEwSPXhnn9P3yQ//uev7mt6i6FlrroVHRxALIQwrf9718B3rL98jeAlwEPbf//63re946Qn6qqbG1tZWxTS5S66IGmaYyNjREKxej73b/CaDSixcJsjfwYb/938A58J2/9nrGsDqO9HP9kYe7Oj7bVmhNlLNmSGW3RKV1lIDsEB7KovCRQoblZQR/5BaRbN12jMk9QsjNnyBbT0985U6OsMJfWfnc4Oswrtj5MR2srwfnJvHNvd7RwWZ3Y6ntBlgmvTKAGdmaDrY1HiHmXDrRF0VzZjNC0OPEBqDHC87dGTJoqWjBVNKJFAvHyJx39tbK9DJOzjvDCHi3TNChbK6hBL20v+zBlJ5+l6xqTyZTTKnzRrz2ZDbeX9Q0PP7p4gze95+M89IZX5V94jyi01EWnoksd8NVtq9YIfE4Ikch4PgT8qyRJfwjMAr+t533vSMIDIBqNZhQ4XFlZwefz0d2du3A3Go1y48YNKisr6ezszBjwFUIQmLnG8H98Ett6/444C4Ct8SixrZW8mn7piGHktdUfpULbwCeVsmnIHntrUWZyxsUSOBS9yZj5CBYtRJM6n33cpdAo0zZzvmcCVcoqG9slKz3REVymzl0xygQchIhgQtH5/EtNzFhEmN/2f4FfDf0H9o4LhFyX9lfOIclY63swOqqI+VaRrU7CC8MHN0QcsNR1o/jdu0g2G+IF1oeQjSYi6y7UDDM6DM4aDBYH0W39x4OAbLbR/oefwnn4aQeyXsIqXFtb4+0f+zxXR6bxbAX4q1e/mD996fMP5D3S8cIXvpAPfvCDtLe373epvc+w1YG7XuenR815a2uLgYEBDh06RE1N9ho7SZIoaT+L3KfRe/IkwreCt/8/8PZ/B6Eq+Kcu7ako9rLlAs3K7K5kQTqqlRVdxAcQM5dSrrqxinDOOb9tiiujVFUm1GhruEUVvbHRvGorzdHpvFnbBAwilpwVcig6wit8H6ZeW8XUcpbQ9AEkDISWLDR3dN1LZG0ae9tphBIjtDSy7xkZtuYTRNamCgqP7CqwrumMKzQHPERWxjGVN4DQDpb4rM74vI2uew9szVSr8HUv/g0+/58P88Vv/5C3f+Rf0KIhnvOMB3RnkPUiU8zv8Yg7Rn6SJGW0/PKpOS8uLjIzM8Pp06d1/0ITsla2qhbqnv4K6p7+CjbXlxj+r89Q6h0iMvmzgtypK+ZzuoiiWltnnfwJhDLVQ1SoaAYTy1Lu7JtF6LR+hMaWVEqrMqNLZqqQQuWO2BQzpg5+1/dZfi307xhMVmzNp3YIdR4ESrrvx78t86RsxcMXksGMreUkssVBbGOWaIFxOXv7OULzAwUNos+EhBYfgKXxGLLFAZqKGg0lVWD2A4O9gs5Xfw576+l9r5UNkiTx1v/xCjQkvvjvP+C9//JNjvX2JDus8mWQ9SIQCBQ0s/du4a5bftmyvamSVn19fQVVpqevubKywuTkNCee8yc4nU6EquCbeCQeJ+z/TlK2PhMWDE08antS3veUhMqiQd90tNaYi1HL0byjIc0inFVSPh3tsSm2DOUsGvK3tFUrKzmnvqWjwRrjld6/pSE8hcFRiclZHW/ZOihIBhwd55PElwqhRncoHZurWjFXNKGEfYQXR3K2jcU7LC4eSGVAApb6wyieedTQtsCBJGOpO4ShpBLFt050VV+/byqMzpr4vI1G/S2De4EQArvNyt//xSuYX17lZ1cGef3bP8y3Pv4ODh8+rCuDrAexWAyLRd/Y07uJxyX5JeJ7VVVVBUtapa6ZKKb2er309fUlG7Alg5HS3idT2vtkWn/77wktjuDZdo8Drqs7viz/adcXdG5X8qswJ+TgV4wNumbidhjcjGr5uym6YuOYiOLS2Z+r10IFeE7ga/x24PMYjBYch56EJJsILx+cvp1ksmFr6M07vCeB6MZsUsFFtpZgre9Fkg27kiapVuRBIV30AIj3+66MwXaezVBShbm6M17btzKet4bPVN5I12u+hKW28IFOe4EkSThsVv7PO/6KB9/5Ub7ynz/ixX/xNr75sYcoL9WXQd6PVfh4wl0nv/RSl83NTQYHB/PG93JBlmVisRjXr1/HZrNx9uzZnGoWtsbD2BoP0/hrrye2tYp34L/w9v8Hi6NX+Jn1yfreM09uqFx1U6L58MlOVo36hvdEIyHILKKcxOHoEJOmbkx6R0EKjVVDfuKzaiFe4fsQFyLxmJ6ltovQ/GAyXGCubkcqqSHkWUXemtuTdSUsTuSS6h2CE4VAC/t3TE6z1vdiKKlCNtnw3dwtib4f2NvPEZobyBszVv0bhBIJNYMJS+NRDFbndoH1zs4Oc3UHXa/5IuZK/bqIBwWnw84H3/x6nnHfWf7qXR/l5Q++nS+8782Ytw2EfBnkbFZhtsltj0fcsWyvoigZ3VtVVbl06RL33nsvCwsLzM7OcurUqX3pgQ0ODuLxeOjq6qKxUd+s2kx41zev8vHL+bODJdoWIcmeNRnSHp1k3ViLX3bSG72pSzPPqW4SkEt2DQxKwIhCp+pizNBNV3Qs6/zedLTEXLtKVtJRryzy+s130aTG42v2jvPxL36W7KvBXh6fUiZEXA0nnFthB+IthUJAzLu32rrMGzHhaD1FYPoywlqOrb4bWWj7Tpo4Ou8h4Lpc8ACsdBjLGtAcNchCxSjLdL7ys5jKCpt8tx9cunSJvr7dM6bnllZ47d+9l+b6Wj745tfnXSdhFW5sbLC1tUVJSQlVVVVJeasnP/nJ3LhxI+86kFfRRQKQJKmXuGpLAp3A3wgh3itJ0puBPwYS6fjEQKO8uP2jnPJtYDs5cfPmTdbW1ujr69sX8W1sbLC6ukpzc/OeiU8IwfDNEb4y5NV1fpMyl5n4hMbh6BAzpg78snM7hqcvG9yoLmQlPqe6Sb2yyNj2AG/Zqk89BsCWZy7Gmchl3uL5qyTxObrvI+i6krPsRA16CUxfIuC6jBYNYms6Rkn3fZiqMscVLXWH0GLhAyU+yWzH1niYwHYLnBT2EnZdjidlVAVbywlKuu/DXKm/jxni40kDU/q7gHJB2VxCW+xHlqD1Ff8C9kpUVdU9wfB2oaWhjq988G10tTbynk99Me/5CavwyJEjXLhwgdbWVsLhMJ/97Ge57777iEQiPProo7o6txKKLuPj4zzzmc/koYce2nWOEGJUCHFaCHEaOAcEga+mnPJPidf1Eh88Diy/SCTCj3/8Y7q6uujo6Nhzul0IwczMDCsrK1RWVuJwOPZEfoqi0N/fzw23zEM/SVfOyYw6dZmVtDm0Ds1HjbqKK2VgT090RLckVaMyn7HvtyG2QEi24TVUJt8nItlQ8ihFQ1zGyiQUQvLuh4skNJ4X+DLPC/7b9uNWpqTzAv4CRjVmgrmyGXNlS3zw0+II9uZjhJcPdoi4wVGJqaSKsE41F3NlK6bKJrTtPWVLmtyOuKG17Rw9f/J5ZKsTTdN2fCckSUKW5dsyXlIIweXLlzNafqm4NjRGVFG455T+wVSpmJ6e5sUvfjHnz5/n8uXLvPvd7+aXf/mXs56fQ9EFMtT5SZL0K8DfCiEe2P75zYBfCPGuQvd6R0td0pGI71ksFjo79x7wVVWV4eFhJEmir6+Pubm5PT1Ng8FgUlvwH6/O67qmq8bB5NpO4mtWZvBLzh3EBxCzVsW12vOgRlnOSHxd0XHmjS1E5FttZi3yBiO069prW8yV0T22awFevfUBzkTjpSuSyYat8fC+iQ8g6p4n6o7/Lkt6HkCLhbE1HSe8ururYy8wlTduJzz0y1hF3bNE3elJE+N20mQDkHB03XPgxGfvfoCeV/8LBku8ZMtgMGAymZIkKIRAVdVkDNxgMCQJcb9In5OTDWeOHSKaQX5OL8xmM42NjXzqU59CCJFRyi4VKysrNDTEu5caGhpYXc3blvtC4PNpx14rSdJLgcvAX+gRMoW7mPBIxPfOnDnD9evX97xOOBzmxo0bNDQ00NLSgiRJusUSUrGxscHIyAjHjx9n1i9xbU7frIZy286MxPnWMq7Pt6GkkVw1m8yoVbpq1qu0DdbYSajZJrUFVIMuwQMAyVq6i3yblDlev/ku6tW44sZtKWUBHN334x//WcpmZKwNhzE4KlG2lvfUvyucjcQiIQjtXcg0PWliaTiCpbKZyHrhslO5UHLkmXS/4p+RTbuz/KnWnqZpSRJMzp9W1X1bhenDi3LBbMqTZcuB1NY2SZIwm80HpeiCJElm4LnA/0w5/GHgrcS91LcC7wZerme9O05+mqYxMjJCNBrdUb+n98mUCq/Xy9DQEEeOHNkh1WMwGHboB+ZDYnbIuXPnsFqtfOZ7+vo0LUaJ0ZW4VpzDLNNdW8Ll2cykWSdvsq7pkLUX2g4XOj7kfCpj32+Vus6cjro+iPckT4vqHeR7rzTMH3neiVXEXVBTVSuoCuHlMV1r6oNESSYrSmg7pq2ZyuoxV7ejRUOElkZ2TCjLBGvjUaKe+YzS8XuGwYLBZGFr6LtAXOHbUtOJUBVCy6OIPUqplZ76b3S9/KPJeRu5kCCohPBAwipM/D/xUJdluSCrMN/wooNCpr7eg1B02cazgKtCiGQDf+q/JUn6OPAtvXu9o25vYiRlTU0NR44cSZJd+gQ3PZifn2dubi7jsCPdMlnbRKwoCufPn8dgMLDmi/AfQ/rmTBxtKOXa3CZtlTYUTXBjPvMXUQLW7N3gz0/IrcoMs9uCB6WqB6fwZ40T1qorumdvNCkLyS4VSWi8IPB5nhP8BgZbKdb680gme3ywU5YZsXuC0YK9+Zgu9zm2uUxsM24dyGYb1tYzSEYzkbUplLS+WnvrGUJLN5MzlA8CkqUEa3XrjrIbxbeO4ovHfSWDGVvzCQzWEiIb88Q8c1lW2onyC79Dx4vfh7RHi02PVaiHCAsZXrQf+P3+ghKWehRdUvAi0lzehJTV9o/PA3QrTNwx8vP5fFy5coXe3t5dqs2JFjc95Jfo/IhEIly4cCHjNbIs5435JQqpq6uraW9vTxLx5y7NE1P15XnCMZVzLWUMLfkIp/u5KThSX8Lwsr4JY1YR/0I3xOYJyfak1HwmrOWYJZIO3/Y8kRLNx2s238eJWFzNRA1tIYDg1GMITcXWdDyun7c2g7q5dyKUbaWYK5oIugpvgdOiIYKz2263JGGp68bkrCHm38BgK49ncA9wIJDBUYmxpJLQwnDWc4QaJZSiAGOubMFc2ZxM5GTaT9WTX07rC95+YD2zuazC1ORJ4vVUstvP8KJCcFCKLouLizQ1NX17W9EFSZLswC8Dr0xb4h8lSTpN3O11ZXg9K+4Y+VmtVs6cOZPxqaDXUtPb+ZFvvYSoak9Pz45C6qii8cXL+sovGkot2M0GrmRxc1NhMup74ppQmTd30B0dY9bUlrMLpEmZZUFni1qtssSisZm22DSv23w3tdotS8rRfV9ceXg76x9KkWYyVbZiqWyKqzIv3tRdyGwqq0cyWeOaffuFEERWJoisTFDSfR+h5XG0qkNYTAaUtYl9K0Uby+qQjRbdYygTiLrniG7P0pUtJVgbepEMRoKLY4iQh9pf+lOaf/N/7Wtv+ZBuFaaTYKpVeKcsv2AwWFBfb1VVFd///u6C9MbGRhLEByCECAK79PeFEC/Z41bvHPnlaonRQ34+n4/+/n5dnR+51ltdXWViYmKXqCrAtwaW2Qjkd02PNzoptZp4eCp/ttJpNXBzSd/wmqPNFZgNMpdnrHlrjEoKGBpeqbnpDk/wR1sfxcx29k2ScXReIDCRfXBPzD1LbDsrarCXY63vAU0QWh5FyzKQx1LbiRryEztAtROI19v5t/cq+9eJsT2LeXuAd2RjtnCX3dlALBpByqMBmQ9aJCVpgkTjb72N+qe/Yl9rFopM7nEqIUYikTtCgj8vii7wOGhvg/xqzsvLy0xNTXHq1CldJnUmt1cIwfT0NBsbG5w/fz4jGX/m0dmc6zaVW6mwm5hY9WHWKbRwqLZEl3VoM8lYjTKPubx5z5WFktMdToVBKNwf/hnPCKc8XY1WpMr23bMmckANeglMxWXfJYMpGf+KpiitWJuPE12fyUqMe4JkwNFxLkl8qRBKhODcrU4CS3UHpvIGlKAnLpGVw1JN6vuF9l9uk7JZmn7rrdTdYeJLR7p7HAqFcLlcdHZ27itpogd+vz850vLxjscF+WWz1IQQTExMsLW1tUOYoND1VFVlaGgIo9HIuXPnMv6xL7o83MwSl7MY4FhDCQNLfha8Ic61lusiNAB3IH/NVFulDZtJ1r1mty3AWDj/DVaibfGnm+/lWOyWTHqilCW8PJLjytwQamxn/Ku6HWtdz//f3pnHN1Wm7f/K0jZp2iZdknQv3SktXahFwNFBXFiEtsiqoKKivgyMMI7j4OjLq864jdvoKL8ZR1zwIwq0gCDbKIgrUgS7QFfa0pYu2dosbbPn/P6o55CWpDlps1Hy/cvlNOdpenLlee7lumFU97h0uNRl0wN6noF6eSv08lYAl3eqhIWAbsROlRuXDb2iDRYd/d2z48UykXjXa4iatcp1r+kC9Ho9dWKKiIhwWykNycDAgFNjaL2Jz4of2WkREhKCadOmORU0tn496zrAxET7MTJ7u76ChDC0yjQ4e+nyh0eqoeexNymSi1bF6J0M0xL4qO3WICc2FCYLvUQLNyoBsJNZJok3teMx5SsQWS4XjbqnlAUIFMRAXfsVQBC/ik4GCMuvPbUOXE3sweTyESiIGbPpgfVOFUw2lcixEAS07ZUuzRSDycKke99BxHV3uu41XYBOp0NlZSUyMzOpfll7SRNSEMl/HmuBtbMJD2/i1Q4PahEj3JwHBgZQVVWF5ORkqvrbGUjxIztIRtYBjuRSnxbH6oeXU6REBYPNvLLYOUscgjoJvd1NRHAALipsB+Q5bCayYkJx9tfXl9AUVF4gE/UOMseFhrNYp/oHOFZGqJzYKTAqu1w6EwMYHosDSNEZ2qkxWAHgJkwFMygEBnkb7ZgcO0wMZiB3WB3guLCYoO08B15yEQbbfkGgIAYB4fEw6x17AjqEFYBJ9/8HEfkLHF/rQWwJny0cldKYTCbqGjpCODg46I/52YKOm7NMJkNjYyOmTp2KsDD6DfvWMJlM6PV61NbW2s0wW/NJRQfITRefy0aakIdfOpSwtRFjs+h9E7KZQEOP7d1ZQjgXAEEJa6owGM0yer2uGeIQ/NJhf9f3PzcmYf2s6dA0TIGq5ihU5/6LwKhJo7qyjAkmG9yEPJuxOBLCbIS24/LxOEiYjAB+DEwDvb/a1l/5BpMT21xpDw+QxqanAIIYnqnlhIIbnWE1SMmJbhE2B4ELnkeDNhy86moIhUKf8LsjhW/y5MkQCAS0f84VBdb+nZ+TsFgs6HQ6tLa2Us4uY32ACIJAU1MTjEYjbrjhBocO0AN6E8rOdoHJAKYlCtDQo8GZdqXNayOCGDhPM3ObGMJAi/rKD3dBQhjqevqhM14Oxo9skRsNrcF2EJ8bwMTzJVmYN2WoQl6QOx+C3PkgLBYMtJ2FqvoIVDVHXWJEyggKAZMfB23bGccXW6GXtUIv+zUmx4sAR5w+JJC/Wk4FxUyGSdXjht2pfYMCi06DAaq9bajljs0Lh0HVA8Ova7UFI5CH9PWfIiR1BuV3J5fLKSunqKgoCIVC8Hg8l9X50WGswmcLe6U0oxVYOzu20pv4hPgxmUx0dXUhIiIC11133ZiDrtZxQi6XS8v6fl9lN2IFHGgNJvzcNvq3frIoDGdG2XVZE8QNBtSXj8ccNgNZMaFX7NqCWAyHx1gSYUggGiRXXhvDD8LbK6YiK/rK+ioGk4mQ5OsQknwdYoufwoVfvkP/+S8RrKgZOp46eeRjh0SBFcyHXjo+ETUP9FLuzQx2EEKn3AKLUQe96sopaeNh6FhO06CAZssdgytA5u93Izgxb+jfreboJicnw2AwQC6Xo6WlBQMDAxAIBBAKhQgPD3drobFWq0VVVZVLhG8kI4UQgM0C6/7+/qtifgfgA8derVaLCxcuICgoCFOmjM1GB7jsyJKUlITY2FjI5Y7tqMwWAscbpKjvcbybCw5gop5mrC+KF4AG6eVrE8I5ABg2j6tTYkLxi4PkBUlSRDBkI1rkpiXw8ebyHETyRt8pk618DK4Q+aufA4PBgGlQCfX5r6CsOQp17XGHJSoBkUmA2QC9tJnWeukSnJCL/oZvQZiHMuNBohQEhEXDONAL/VjjfgwmeMlFox7LHWHdcscI4MISmQ6OQISUlS+CG2Pfmox0NomNjYXFYoFSqYRcLqeec6FQiKioKHA4Vw6BHyuk8GVlZbm91IQUwZG7wvb2dpw5c+aqcXL26s6vr68PtbW1SEpKglo99gb13t5e1NXVIScnx6k//L6qLnzfTK/Oa0pMmF3TgpFEBVkg/1X7ChL4qO/RQGu0fVy1999tIesfHrNbNi0GT8/PQICDOKTJZEJNTQ0EAsGwVj52sAARRUsRUbQUhNkITeMPVJyQjImRcGImw+iGI+nIDhMA0EtbKJcXdkgkgsRpQ2Msu+rodXSwAhCckEt7LggdCKMWbFM/Uld/DI6Qvv0ak8lEREQElXAbGBiAXC7H+fPnYTabERERAaFQOK7RkZ4UPlswmUxIJBLce++92LNnD5KS6Bn2ehuPmZkCQ/bX5Ja5o6MDnZ2dyM/Ph9FoRGtrK3Jzc51+zY6ODnR1dSEvL2/YN+mPP/6ImTNn2n2g9EYz5v7zR3Sr6JU8xPK56KJ5bUxYIBT9Bkzis9DYZ79zJTo0EBKNgdabnBTBRVvv0AefzWRg89w03F3kuJ6KNJNISEhwKnM+eOnckBDWHAUYTGi7al1bHgIgKKkI+rbTtK9nBASBG5MFRgAHelkrNd5y+DVccKLThiVaXAE7MgmTN+512gl6NEwmExQKBeRyOdRqNcLCwhAVFYXIyEja0woHBwdRXV2NKVOmjDlBOF4kEgmWLl2KV155BXPmzHHlS0+coeVke01dXR3MZjOKiorAYrGo9LozkMc4o9FIObJYw2QyR7XJ+qSig7bw5cSG4lwXvbhchoiHQYMZMQIuGntH36XER3DRo6FnvSUMDURbrxYCbgDeWJqN65Ptly+Q9Pf3U8OgRiv1sUVwfA6C43MQM/+PMCh7oDo3JISaxu/HL4IMJoISCpwSPgAgjPphdX9BojQEhIlg7JdD39M4ZKYgiHW58AWKM5C5sRwBYa6dt8FmsyEWiyEWi0EQBNRqNWQyGdra2sBisaikib1qBTLUk52d7TXhk8vlWLZsGV544QVXC5/b8aj46fV6nD17FkKhcNjxy9Hg8pFYGxxYW2NZQ9b62UqeaHRG/Pu7i7Tv54wpdDQ/CD+3qTBocCzmLRJ6mWMGgFb5INJFPLyzYiriw7kOf6avrw/19fWYOnXquLNvgYJoCH9zH4S/uQ9m/QA09SegrD4K9fmvYOqnZ/VPwQ5CcFw2Bp3MFNtCL70A/a9zcoPEaQjgx8CiHwAjgDtuwwOSoLgcZP6+DOwQ5748nIXBYIDP51PHVp1OB7lcjsbGRuh0OoSHh0MoFEIgEIDJZFLCl5OT47UEQ29vL5YtW4ZnnnkGc+fO9coaxoNHxa+zsxMpKSk2La3o7vz6+/tRXV2NtLS0UY0PycFItlri3vu+DUotPavueAGHlh1VUgQHEcEBqGhVjmpvRZIVzUNdD70ESlZ0CGL4HLy0OAu8QMd/sp6eHsol25VBdQBgBfEgyLsDgrw7hspoWk9DVXMUypqj0DuwkmdyQhEUmThkSeVCAsJjYTFo0d/4HQCAEcBBcGL+r8fjFpjUDq3RbcKddB0y1u8Ei+t5ceFwOIiPj0d8fDzMZjP6+voglUrR0NCAoKAg9Pf3e1X4VCoVli9fjs2bN2PhwoVeWcN48aj4kY3VI6HjvwcMFUA3NTVh6tSpDv/o9gRVqtHjo5/oW5SLwzi4pLRfHBzGYSNDxMMvHSqIQoNoCR8ABLHplTwwACycKsZ9MxIcBsTJIU69vb2YNm0a7bjRWGEwmQhJvR4hqdcjrnQLdNIWqGqG6gn7WyqGTTxjhUSCHSyAtvP8KK/oPIFRybDo+4cZnhJG3eXjMYOBIHH6kB+gRkrbuoqXfiPS130MZuDYJwm6CvIIHBUVhf7+flRWVkIkEqG5uRnNzc2IjIyEUChESEiIR2oKNRoNli9fjk2bNmHx4sVuv5+78HjMz5n/TkIQBC5evAi5XG7XkWUkpDv0SN450UI7wxoaxLJb1MxiAAWJfDRI+vFzuxIsBgNtdlrZRhISyKJV28cPYmBtTgBmReqgUqnA5/PtvlcEQaChoQFmsxn5+fke8W4bCUeUAs4tv4P4lt/BNNAH1fkvoao5Cm13Ayz6AZeXyLAiU2AaUMCiHSULTxDQS5qoXSk7TIQgYQosRt2QR6GNrpfQ7NuRunabzXkb3mRgYAA1NTXIz8+nQhkGgwEKhQKtra0YGBgAn8+HUChERESEW2oKBwYGsGLFCjzyyCNYvny5y1/fk3g022s9mWokP/74I2bNmmXzZ0hHlsmTJ9P+UNfW1iI2NnZYsedFxQDuePskbQOBokQBTtsob8mOCYFaZ0RH3+XAf25cGKo76cXwpiXycdZB2czM5HC8vHgKwrks9Pb2QiqVUhlBso2KfLjNZjPOnTuHkJAQpKSkeLSjgA5mox5N35ZB2/A12N1nYOwb/7zeoNhsGGQt44rtMQO54MRMBoMdiMHuJhCDveAXlCBlzf8Dg+UT9f8U/f39qKmpGTWGa7FYoFKpIJPJ0Nvbi6CgICpp4orwx+DgIFasWIHVq1fj/vvvH/fr0WDiZHudha4jiy3ImB8JQRB446sLtIWPCQba+4Z/sIb8/Ng413WlyOmcqNdTjRJvZDEYWD97Eh7+TRKYv4qYUCiEUCgEQRDUw93S0gIOh4OIiAh0d3cjPj4ecXFxtNfgKQiCQOOFFiB2GvLn3A0Gg4HBjhqoao5AWXMU2o5qp18zeNI0aC+dH3evssWgpabUEWBAeMt6JJT875jnbbgLOsIHDD3z4eHhlJHB4OAg5HI5amtrYTQaERkZiaioqFFPEPbQ6XRYtWoVli9fjjVr1ozn1/EZPLrzs1gsdud4jqzLIx1ZJk+ejMjIK9yrHdLU1AQ+nw+RSASCIFBzSYnl7/1M+xey3smFBDIxOSYUlR0qm+KZHBWMVjm9HUhCOBcdfbavjQ4Lwit3TkFhooDWa5HFsgEBAQgMDERUVBREIpFTA2TcicViwblz58Dj8ezuSA3KbqqeUNP4vUNB46VMH+rFtThXGuWIqJvWImHZ8z63a9ZoNDh37hxyc3PH5ZZiMpnQ29sLmUwGtVqN0NBQqqbQkU+mXq/H6tWrMW/ePGzYsMGT79G1sfMjExRsNhvd3d24ePEiLUeW0V7P2s77tWPNTim5ZlAHgBjy85MP4uc2pd1rh4wJ6ImfOCzQpvjdnBGJ50uyaJscqFQqNDU1oaCgAGFhYdDr9ZDJZNRwJ/K4M57OgfFgMplQVVUFkUiEhAT7rtOBghgIb1wD4Y1rYNb3Q113AqoasoxGMezakLSZQ5PgXNw+JbrtUcSXPO3S13QFrhI+YKimUCQSUZsBjUYDmUyG9vZ2MJnMYTWF1s+L0WjE/fffjzlz5nha+NyOz+z8fv75Z+Tk5KCjowMajQa5ubnjylZevHgRbDYb0dHRONnSi7WfVDn+oV+JCWEhiM0EwWRTXRX2CA9mY0BvgYHGxDcWAwjjBqBv8PJ7EMBi4I+3pOLeGfRs6YGhOSRkR8zIsZ3A5c4BmUwGjUZD7YAjIiI8kggxGAyorKxEYmIioqOjHf+ADYbKaCqg/HVXGBAqom9Q4AT8WzYhuWSzVxJEo+FK4XOEXq+HXC6HXC6HVqtFeHg4FAoFcnNz8bvf/Q6FhYXYvHmzN4TPrTf0qPgRBGF3mPiZM2dgsVgQFhaGjIyMcb/R7e3tUKvVSElJwT0fV9uM040kOICJmGACYcEc/NJNbydXlCTA6TZ6Pb9TY0NRY7WOhHAuXl+SjexY+rVaHR0dkEgkyMvLo2XrTzbWk0FwHo9HNdbTHQvgDGSfaXp6+pjCFfbQSZovl9G0nnbBsZeB8AVPwZA6F729vQgODqbeF2/78anVapw/fx55eXkeD2FYLBb09fXhueeew5EjRxAaGorHH38cd9xxB8Ri13a40GDii9/g4CBOnjyJSZMmITU1ddz3IKdVXbp0CYfP9WBrlf04koDLRkpUMLR6IxqlA4gOC0S3xmTTyHQkLAYD4cGBkNOY+AYMF7/52SI8uzATIUH0drfkPBOtVoucnJwx7VRI3zmZTAa5XA4Wi0UlU2ztIJ2FDMxPmTLFrQ32pv5eqoxGXfe183NDGCwk3v0aombeDWDofRkYGKDeFwCUEHraj0+tVqO2tha5ublei92azWb8/ve/R0xMDO655x4cPHgQdXV1eP/99z29lIktfqQjS3BwMCZNmjSq5Tad1yftdRgMBswEgUVbT11xdI3kspAYwcWAwYIL0gGYrd6DqfF8WrtEAMiP56OSph1VeHAANDoT2EwGnpyXjmXTYmn/XhaLBefPn0dQUBDS09Nd9mHU6XSQyWSQyWQwGo1U3Cc0NNTpeyiVStTV1XnkmGaNxaiHpumHX3eF/3Vslc9kY9J9WxFRWGr3EtKPTyaTUcdA69Yyd6FSqVBXV4e8vDyXfBmNBYvFgj/84Q8ICwvDK6+84u1wwMQRP2AovkBi7ezS1tZGpeLHwkjhYzAY2HmmE88eHDLdjBdwEB0WBJlGZ3euRoYoBE1yenbyAJAm5OECTfv56xL56NMa8fqSbKSL6PfaGo1GVFdXO0wcjBej0QiFQgGpVIqBgQHqAx8eHu7wA0CW3ox01vEGgx3VUP7qWm09YQ4AwA5C6oPbwJ96O+3XI1vLZDIZlEolQkJCqDpLV4YNfEX4/vznP4PJZOLNN9/0tvABE1H8LBYLGhoaYDAYkJOTAxaLhebmZoSEhIwprkC6wpAuLgwGA1qDCQ/vqAIDBLqVOlxSOnYiSQ4PxEUVPYOF1Cgemp0QygdmJWD9b5PBDaBfda/ValFdXY3k5ORR+5hdDRn3kclk6Ovroz7wUVFRVyShurq6qC8wd8QQx4Ohrwt9VYfRebIMDMUFpD30PkIzbxzz61lnSRUKBS3nFTr4ivD97//+L7RaLbZu3eoLwgdMNPEbGBhAZWUlIiIikJycTB2vLl68iICAAKcLdQmCoLpGrP9gLxxuwMenOuz92BVkx4ailqbRADBkUjraICGSdBEPf74tDbNSnXMFIbN9WVlZLrckdwbyAy+VSqFQKBAQEEDFCXt6etDX14fc3Fy32rOPFbLcJiYmBjHR0S4vXiadV2QyGfR6PdVj60wRsVKpRH19vVeFjyAIPPfcc5BKpXjvvfd86W85ccSPIAh8//33mDRp0hU7mY6ODhAE4VQnBzlDgNztkRyvl2H9Z/RLWxgAJgl5do/DI4kIDoBaZx61WySSF4jfz07GkoIYsJjO/Q0VCgWampq8GvS2h1arhVQqRXt7O8xmMxISEiAWiz2eGHCE0Wikym08kaU0m81UeRFdY1JS+PLz870WLiAIAi+99BJaW1vx0Ucf+ZLwARNJ/IChD4+tLXVXVxf0ej2Sk5Mdvoat+B5Jj0qHxf86RduyCgDyE/iootmXCwC50VxU99g+Rgexmbjn+ng88psk8Ghmcq0hj5F5eXleL7mwBWlGy2azkZycfEViQCQSQSAQeFUI9Xo9KisrkZKSAqFQ6PH7WxuTjtwtkyLX19eHhoYGrwvfG2+8gZqaGnzyySdudwEaAxNL/Kyt7K2RSqVQqVRIT08f9edHEz6zhcCaj86M2o0xEjaTARGfg24VvT5RNpMBXgATKv2Vv8P8bBEeuyUFcQLnjy8EQaClpQUajQZTp071tW9gAEO7m5qaGvD5/GFmtOT/I9unVCoVQkNDIRKJhhkweAJydONY3KvdhVarpbLqJpMJPB4PKpUK06ZN8+pR95133sHJkyexa9cun4vX/sq1IX7kkWHyZPtTsWwlNqz559fN2PqN/VmrtihMCsfZDnpFyoDtWF+qgIW7MgMwI10MkUjk9BGQ3E2xWCxkZmb61PGRxGg0UvEzR3FZawMGhUKBoKAgiEQiCIVCt+5myXkW7hjd6CpkMhnq6+sRFhaGwcFBt1tQ2YIgCPznP//BV199hfLycgQF+ZZ1lxXXVm+vPewlNkgqWnvxr2+dEz4Om4mLCvoZWwBQay9ng2P4QfjDnFTckSOCyWSCXC5Hc3MztFotIiMjIRKJHPbWkrOGIyIikJSU5JPCRw5BshWrtQWDwYBAIIBAIEB6ejpVQEwO9CaPgK6sByQLrL05z8IRvb29aGlpwfTp0xEUFDTMgqq5uRkcDofKqrtLkAiCwIcffogjR45g3759vix8bsfjOz+TyWRT5Pr7+9HS0mJzgpu9xAZJ36ABi//fKUg0zlkcFU0Kpz2OEgDShTw0yQYRHMjCQzckYs3MBJuOzGTwWyqVQqPRQCAQQCQSXVEzR4rKeHpg3Q1poOmqY6TBYKCOgDqdbkwZ0pGQ7WCumFfiLhQKBS5cuID8/Hy7gmPdZWKxWKgyGlc6NH/88cfYvXs39u/f73PJNBtMrGOvPfHTarWor69HQUHB5ZuPEt+zZt2OSpxodG6QThiHDYLBQL+efo9oQQIfKVE8PHpzMoQh9L4xyd5aqVSKvr4+KhYWFBSE2tpaZGZm+kxsaiSkqLhrVsTIDOlYjoBkxtQXM+MkpPAVFBTQPvYbjUYqmeRs0bk9du3ahQ8//BAHDx70aBfOOLh2jr3WLs+k8JET2OwJ30cn250WPgDIjA6lvevjc9mYnR6JNTMTkSl2TgSsh1aTWcD29nZIpVLw+XzodDoYjUafCzj39vaisbHRrc31LBZrmM0SacBw4cIFymhAKBTafW/IkiBvZkwdMRbhA4CAgICh+sSYmGFF542NjWMyYdi7dy/ef/99lwnfkSNHsHHjRpjNZqxduxabN28e9v9VKhVWr16N9vZ2mEwmPP74455yf6aNx3d+9qzsLRYLKioqMGPGDIeJDZLzXWrcte00jDTspKyJ4gViwGgZddhQnICDOZlRmJMhRGESH2wXFciSk9Vyc3NhMpmoIyApBK6yHB8PEokEbW1tyMvL80pMyNpogHxvSKNWMjsqk8nQ2tqK/Px8nywJAobMZltaWly6xpEmDAwGgzoe2xO1L774Av/4xz9w8ODBcfXOk5jNZmRkZODLL79EfHw8ioqK8Omnn2LKlCnUNS+88AJUKhVefvllyGQyZGZmoqenx9n34drY+ZEDzekK34DehMfKapwWPgBIiuLZzPBmRYfglkwh5mRGYXK0a4959iarhYSEIDk5GTqdDlKpFOfPn4fZbIZQKKQyx57k0qVLkEgkKCgo8NpulMFgICQkZNh7I5PJUFdXB6PRCA6Hg8HBQRQWFvqs8LlLnEe+N6QXX1NTk835vkePHsXrr7/uMuEDgIqKCqSlpSElJQUAsHLlSnz++efDxI/BYECj0VBOQhERET5XR+gzq2EwGFRGl8FgOIxrPHuwHu0OjEZtESfgoLpzqFSFzWSgKEmAOZlC3JwZhVi+e3ZcdCarcTgcJCYmIjExkXIVIR9oT7gyEwSB1tZWaDQa5Ofn+1SdIYfDQUJCAhISEtDe3o7Ozk7weDycOXPGbjLJm5DC54kvkKCgIMTFxSEuLo6qtZRIJLj//vthNBrR0dGB//73vy71Vuzs7BxmshEfH49Tp04Nu2bDhg0oLi5GbGwsNBoNdu7c6TN/HxKfED8yvhcSEoLTp09DKBRSLVO22FfZhQPVPWO6V3x4MHLjAzEnMwo3pUcijOPeh5MsDA4NDaVdwxcYGIjY2FjExsbCbDZDLpejvb0d/f39w7ooXPUwkeJssVgwdepUn3tISdrb26FQKDB9+nRqTIF1LIzH41GF1d7atXpS+EZi7c/4hz/8Ac899xwWL16MVatWITIyEgcOHHDJ39ZWqGzkc3306FHk5+fj+PHjaG5uxm233YYbb7zRp8qQPC5+I98k64xudnY2FQez3vWIxeJh6f5ZqZHYuzYPTY1NTnsAikIDEUhzYPh4MRgMqKqqQmxs7Jgnq7FYLIjFYojFYurDLpFI0NDQgLCwMMqefqw7NdIrkMvlIjU11SfrDAGgtbUVarUaeXl51AeYyWQiMjISkZGR1PFKKpWira3NZkuZuyHv7c2QATA0DOypp57CF198QT13CoXCZV9q8fHx6Oi4bBpy6dIlxMYO96f84IMPKOv7tLQ0JCcno76+HtOnT3fJGlyBxxMe1nM8HMX3yMJhqVSKwcFBqnDYYDCgubkZU6dO9dmUPdlt4Go7dxKyi0IqlaK3txdcLhcikcgpe3qywDoqKsrp0aCegnSw1uv1mDJlCu0PsHVLmdlsdkvNnDWk8Hnb2quiogKbNm3C/v373fY3NZlMyMjIwLFjxxAXF4eioiLs2LED2dnZ1DXr1q2DWCzGM888A4lEgmnTpqGqqspZv86JVedHih/dxAYJWRNGTqaPjo5GTEyM15vobUG6GrurPm4kZAZQKpVCLpdTk7qEQqHdbC25K42Pj0dMTIzb1zgWyOM4gHG1/Y2smYuIiHCpM7NEIkF7e7vXhe/s2bNYv3499u3bR8sgZDwcOnQImzZtgtlsxgMPPICnnnoK//rXvwAA//M//4Ouri6sWbMG3d3dIAgCmzdvxurVq529zcQSP4IgoNVqqf5eug+fxWJBY2MjTCYTJk+eTBUOq1Qq8Pl8iMVinwh6O5qs5glI2ymZTAaCIKjMMVmvRw4ZSktLG7Nztrsh+50DAwORlpbmsi84i8VCGTAolUqEhoZSzsxjyUaSwldQUODVbGZ1dTUefvhhlJeXOzQHuYqYWOK3f/9+VFdXo7S0dJiZ6WiYTCbU1NRAIBBc4SYysoOCjINFRkZ6XAg7OjoglUqRm5vrM0XLZDuZVCqFwWBAWFgYFAoFsrOzXVb64GrIYeehoaFu3cGMtJ4KDAyk4oR06ht7enpw6dIl5Ofne1X4amtr8cADD2DXrl2jGoNchUws8ZPL5SgrK8PevXvR19eHBQsWoKSkxO64StLKfdKkSQ5NKck4mEQiQW9vL0JCQqg4mDtLNwiCQFNTE/R6PbKzs72++7RHb28vzp07h5CQEOj1ekRERPiE/541ZrMZ1dXViIyM9HgccnBwkIoTEgRBFVbbiit3d3dT9v3eFL6Ghgbcd9992LFjB3Jycry2DjcxscTPGoVCgc8//xzl5eXo6enBvHnzUFpaiqysLDCZTLS0tEAikYxpFKK1/bpcLqcSAkKh0KUPK7lL4XK5Lj2euRq5XI4LFy5Qdunk8c86dEAe/7wl3qTtfHR09Jiz466CrLWUSqXQ6XTUFwWfz0dPTw+6urqQl5fnVeFrbm7GqlWrsH37duTn53ttHW5k4oqfNUqlEgcOHEB5eTna2tqQnp6OmpoaHDt2bNzebGRCQCKRQC6XIzAw0CX+cqTHnVgsdutktfHS3d2NS5cu2XWHJvtqycwxWS9na2CRuyBt5xMSEnzO4cbagEGhUAAYSsC4+0QxGm1tbVi5ciW2bduG6667zitr8ADXhvhRNyQIbNmyBQcPHkRqaioaGxsxZ84clJaWorCw0CW7EjIzat1TSzqt0MVbk9Wcpb29HXK5HLm5ubSEzLpejvyiIBMm7molMxgMqKyspO0X6C26urrQ1dWF5ORkKBQK9Pb2gsPhUF8Unmq1u3TpEpYvX45//etfmDFjhkfu6SWuLfE7efIkPvvsM7z22mtgs9kYHBzE4cOHsWfPHlRXV+O3v/0tSktLcf3117vkW9c6MwqA2hGOlqklrZ7Gchz3FARBoLm5GYODg8jJyRnzl8bg4CD1/jAYDEoIXZXJJm3n3VUP6So6OzshkUiQl5dHPXe2TAbIhIm7nHC6u7uxdOlSvPnmm7jpppvccg8f4toSv9HQ6XT48ssvUVZWhjNnzuCGG27A4sWLMWvWLJccz/R6PaRSKaRSKWUuIBaLhz3IZOzMl/3jCIJAXV0dmEymS23x9Xo9lTk2Go3DzBfGcg+y5MaXbeeBoZ2WVCodJny2IN8fcpSlq3uyJRIJlixZgldffRVz5swZ9+tdBfjFzxYGgwFff/01ysrKcPLkSVx//fUoKSnBTTfd5JLjx8gSEbIeTqFQ+LSNktlsHlYm4q4EDFk4LJVKodVqhyUE6NxzYGAA1dXVPm07D9AXvpGYTCYqTki6eZNGrWPZhcvlctx55514/vnnMXfuXKd//irFL36OMJlM+Pbbb7F792589913mDZtGkpKSjBnzhyX+NEZjUacP38earWa6hkViUQIDQ31qewumS0Vi8WIj4/32H1JNxGpVAq1Wu3QaYUcyO7LtvPAUN0mGS8dT4iFrEWVyWRUQok0I6VTD9rb24s777wTW7ZswcKFC8e8DmscmZECwIkTJ7Bp0yYYjUZERUXhm2++ccm9ncAvfs5gNpvxww8/oKysDF9//TWys7NRWlqKW2+9dUzH1JGT1SwWC+RyOSQSCQYGBqh+4/HMoHAF5DyQpKQkjwzptsfIovORtZZXg+08cFn4rI0UXAGZUCLjhNZOLLbiqEqlEkuWLMETTzyBxYsXu2QNdMxIlUolZs2ahSNHjiAxMRFSqdQbySi/+I0Vi8WCU6dOoaysDF999RXS0tKwePFi3H777bR2HI4mq43c8ZB2U+Hh4R4VQtJEwZdm1QJX1loymUzo9Xrk5+d7pOd5rLS3t6O3txe5ublur3kkjVplMhm1w4qMjERYWBj6+/uxdOlSPProo1i+fLnL7nny5Ek888wzOHr0KADgxRdfBAA8+eST1DVbt25FV1cX/va3v7nsvmPg2nBydgdMJhMzZ87EzJkzYbFY8Msvv6CsrAyvvfYaEhMTUVJSgvnz59vM2Op0OlRXV486Wc36W5u0m+rp6UFDQwP4fD5lN+XODxB5hPTF2BmDwUBYWBjCwsLA5/PR1NSEmJgY1NfXg8lkUuEDb9v2W+NJ4QOGG7UajUYoFAocPnwYL7zwAjgcDkpKSly24yOhY0ba2NgIo9GI2bNnQ6PRYOPGjbj33ntdug5vM6HFzxomk4nCwkIUFhbihRdewLlz57B7924sWrQIIpEIJSUluOOOOxAREYHq6mr09fUhNzeXdv/rSG85pVIJiUSCpqYmamJbZGSkS4ti+/r60NDQgNzcXJ+19gIuN/8XFRVRMS5yx2Nt209aTnmLtrY2KJVKjwnfSAICAhAdHY2SkhLs2LEDBQUFUKlUKCwsxJ/+9Cfcc889LrkPHTNSk8mEM2fO4NixY9BqtZg5cyZmzJiBjIwMl6zBF7hmxM8aBoOBqVOnYurUqXj22WdRX1+PsrIyLFmyBEwmEz09Pdi2bduYyy8YDAbCw8MRHh5ONc9LJBI0Nze7rHuCdI/x5cllwOXC4JGuJyN3POTgbmcGvruSixcvQqVSed3JWqfTYdWqVVixYgUeeugharzD4OCgy+5Bx4w0Pj4eUVFR4PF44PF4uOmmm1BVVTWhxG9Cx/yc5dNPP8Urr7yCBQsW4Pjx4+BwOFi0aBFKSkogFovH/UEkg91kmx3ZHTDaeEZbdHZ2oru7G3l5eT7jHmOLjo4OyGQyp8pERg58d8W8WkdcvHgRarV6XMXgrkCv12P16tWYN28eNmzY4Dbhp2NGWldXhw0bNuDo0aMwGAyYPn06PvvsM0+bJ/hjfp5Aq9Xi66+/xrfffouQkBBq2lp5eTnuu+8+AMCiRYtQWlqKuLi4MT2YDAYDoaGhCA0NRVpaGtVGdvbsWQQEBFBtdvZqCAmCoHYoBQUFPjVkaCSk7by9gU32sG43HDmjwx3hA3Jok7eFz2Aw4P7778ecOXPcKnwAwGaz8fbbb2Pu3LmUGWl2dvYwM9KsrCzMmzePCgGsXbt2wrnG+Hd+NCAIAl1dXSgvL8fevXuh1+uxcOFClJSUXOEvOFas28iYTOYVM3wJgqDMXEnXG1+EbKvT6XRO2c7TeV21Wg2pVAqFQgEul+twqLkjWlpaMDAw4HUbMpPJhAceeACFhYXU3As/APylLr4FQRCQSqXYu3cv9uzZA6VSiTvuuAMlJSVIT093yYNLzvCVSqWUE7NSqQSPx/Np2yxSoC0WCyZPnuzWdVqbL4xl4LsvCd8jjzyCyZMnY8uWLT77t/USfvHzZRQKBfbt24fy8nJIpdJhnoSueJC1Wi0qKythsViGdZf4WnaXIAjU1tYiICDAZV8CdLEeVmSxWKgdob33iEysZGdne1VszGYzNmzYgLi4ODz//PN+4bsSv/hdLSiVSuzfvx/l5eVob2/HbbfdhsWLF485g0h63MXFxSE2NpbKikokEqrfWCQSuW0iGV1IQ1cej4eUlBSvrmVkTzaZOSaLqltaWnxC+CwWCzZt2gSBQIC///3vPhvG8DJXv/g56iMkCAIbN27EoUOHEBwcjA8//BDTpk1zxa29hlqtxsGDB1FeXo6mpibccsstKC0txbRp02g96DqdDlVVVUhJSYFQKLzi/5NjPSUSidfKQ4DLQ9nDw8ORlJTksfvSgTQXkEql6O/vB5PJREBAgNNJGFdjsVjwxBNPgMVi4c033/QLn32ubvGj00d46NAh/POf/8ShQ4dw6tQpbNy48YqK86uZwcFBHDp0COXl5Th37hxmz56NkpISu56EAwMDqKmpQWZmJq0ia7I8RCKRoL+/32OzOcxmM6qqqiASiTxqpOAs5IyV/v5+cDgcqFQqlwx8HwsWiwVPP/00dDodtm7d6he+0bm6xY9OH+EjjzyC2bNn46677gIwZBF+4sQJn50nOx5IT8Ldu3fj7Nmz+M1vfoPS0lLKk/D8+fNUse1Y+l8tFgu126HjsDJWSAv/uLg4n/47kUPPjUYjFYcdOfA9ODjYKZeV8azl2WefhUwmw3vvvefTpUo+wtVd50enj9DWNZ2dnT79oRorZOH0okWLYDAYcPz4cezevRuPP/440tLSUFNTg0OHDo258Z/smbXuN5ZKpWhsbHTZWM+rxXae3PGZzeZhCSgGgwGBQACBQDDMtv+XX36hNfB9rGt56aWX0NXVhY8++sgvfD6A28WPTh8hnWsmIoGBgZg3bx7mzZuHTz/9FH/729/w29/+FkuWLMG0adNQWlqKm2++ecwfQlv9xlKpFBcuXEBISAjEYrHTBcNkLDI1NdVnB54D9MturAvPU1NTqbEGNTU1Nge+j3Utr7/+OhobG/HJJ5/4hc9HcLv40e0jdHTNREYul2PXrl346aefEBoaCrPZjO+//x5lZWX4v//7P+Tk5FCehGOdnWGr31gqlaKlpQVcLhdisdhhvzFpO083FuktSOEjCMLpekMul4ukpCQkJSXBYDBAKpWioaFhzNl1giDw9ttv4+zZs9i1a5fLpuHRMSMFgNOnT2PGjBnYuXMnli5d6pJ7TxTcHvOj00d48OBBvP3221TC49FHH0VFRcV4bz0hsFgs+OmnnyhPwoyMDCxevBi33XabSxxQbE1rE4vFV3ROkLbzvjy0CRj6fRoaGsBgMJCRkeGyEwSZXZdKpRgYGKCVVCIIAu+++y6OHz+OsrIylx2j6SQRyetuu+02cDgcPPDAA1ej+F3dMT86fYQLFizAoUOHkJaWhuDgYHzwwQfuXtZVA5PJxKxZszBr1ixYLBacPXsWZWVleOWVVzBp0iQUFxdjwYIFY/byG3nsI8d6Wse/goOD0dDQgJycHJ82IXWX8AFDz3F0dDSio6OppFJXVxfq6+ttejcSBIEPPvgAR48exb59+1waP6yoqEBaWhpSUlIAACtXrsTnn39+hfj985//xJIlS3D69GmX3Xsi4S9yvkohC4t3796NQ4cOITo6GsXFxVi4cKHLjqRarRZtbW3o7OxESEgIYmJifM58lIQgCNTX14PFYnm0w2TkwPfu7m4olUpYLBbs378f+/fvd7ldf1lZGY4cOYL33nsPAPDxxx/j1KlTePvtt6lrOjs7cffdd+P48eN48MEHsXDhQv/ObwR+V5erFCaTidzcXOTm5uK5555DXV0dysrKcOedd4LP56OkpAQLFy60WSBNF61WS81yYDAYlPko2UI23kSAqyBHdQYEBHi893lkLPX8+fN4+eWX8c0331A2UMXFxS5NDtFJEG7atAkvv/yyP7kyChO6wvLIkSPIzMxEWloaXnrppSv+/yeffEIJyKxZs1BVVeWFVY4fBoOBKVOmYMuWLfjpp5/wzjvvQK1W46677sLChQvx7rvvoqenx+aHxh5yuRxNTU0oKCgAl8ulzEcLCwuRl5cHNpuN+vp6nDp1Ci0tLejv73fjb2gfbwrfSBgMBhobGyGTydDa2oo333wTCoXC5fFrOgnCn3/+GStXrsSkSZNQVlaG3/3ud9i3b59L13G1M2GPvXSCwj/++COysrIQHh6Ow4cP45lnnplQnSXWnoR79+4Fk8mkPAljY2PtCoVEIkFbWxut+cRkv7FUKoVOp0NUVBTEYrFH+o1JM4WgoCCkpqZ6vTzqwIEDeOutt3Dw4EG3DmGnk0S0Zs2aNU4feysrK7Fu3Tqo1WqwWCw89dRTWLFihat+Bbr4j71jgU5QeNasWdQ/z5gxA5cuXfL4Ot0Jg8HApEmT8Mc//hGPPfYY5Un40EMPwWAwUC7V1pPpSJfogoICWt0OAQEBiI2NRWxsLJURbW1tpcZ6isVit/Qb+5rwHTlyBG+88YbbhQ+gl0QcL8HBwdi+fTvS09PR1dWFwsJCzJ071+2/myeZsDs/OkFha1599VXU19dT109kCIKARCKhPAnVajUWLFgAjUYDpVKJN954Y9yxIlt29GKx2CX9xmRsjcvlIjU1dVyv5QqOHTuG5557DocOHRpXjNVbnD59Gg8++CAqKipgNpsxffp07Ny5c5hzc15eHsrKypCenu7Jpfl3fmPBma6Rr7/+Gtu2bcP333/v7mX5BAwGA9HR0Vi3bh3WrVsHuVyOdevW4fTp0xCJRPj73/+OkpKScXkSjrSjJzOhZGmIWCweU7+xrwnft99+i2eeeQYHDx68KoUPAIqKilBcXIynn34aWq0Wq1evHiZ8FRUVMBgMPvF+u5IJK350u0aqq6uxdu1aHD58GJGRkZ5cos/w2WefITAwkHI+2b9/P/7617+ivb0dt99+OxYvXjyuGRdMJhNRUVGIioqCxWKhSkOs+43puKtYLBacP3+e8g30Nj/88AP+8pe/4MCBA3ZnO18tbNmyBUVFReBwOHjrrbeo/97d3Y177rkHH3300YRzoJmwx146QeH29nbMmTMH27dvHxb/u9aQSqU2e3zVajW++OIL7NmzB01NTbj11ltRUlJC25PQEdbuKgqFAjwej2qzG7kWsq4xNDQUycnJ4773eKmoqMCmTZtw4MCBYaYcVys9PT244YYbEBQUhNOnT4PH40GtVmP27Nl48sknsWzZMm8s6+q2tPImhw4dwqZNm6ig8FNPPTUsKLx27VqUl5dTJpxsNhs///yzN5fss/T39+Pw4cMoLy/H+fPncfPNN6OkpATTp093SS0ZQRDQaDRUmx2Xy6XmG7NYLJ8SvrNnz2L9+vXYt2+fT6zHFRQXF2PlypVobW1Fd3c3Xn/9dcyfPx+LFi3Cpk2bvLUsv/j58S10Oh3++9//Yvfu3fjll1+u8CQcLwRBYGBggJpvrNPpIBAIkJWV5bD0xt1UV1fj4YcfRnl5uaeD/25j+/bt2LdvH/bs2QOz2YxZs2Zh/fr1ePDBB4edlD788EPk5+d7cml+8fPjuxgMBhw7dgy7d+9GRUUFZsyYgdLSUtx4443jNga1WCyoqalBcHAw2Gw2ZDLZsESKK/tl6VBbW4sHHngAu3btwuTJkz1672sUv/hdjVyLlkNGoxHffPMNysrK8P3336OwsBClpaWYPXu200JlsVhQXV19xWwQclKbVCoFAKrNbqxWX3RpaGjAfffdhx07dky44d0+jF/8rjauIcshu5jNZnz33XcoLy/HiRMnMHXqVJSWluKWW25xKFSk8EVERCAxMdHudXq9nppvbDabIRQKIRaLXd5v3NzcjFWrVmH79u2ePvZd6/jF72qDztwSAPjHP/6BgIAAnD59+mp13aCF2WzGTz/9hPLycnz11VfIzMxEaWkpbr/99itm61osFlRVVSEqKsqpLOrIkZVkmx2PxxtXUXVbWxtWrlyJbdu24brrrhvz6/gZE24Vv4lVuOMj2JtJMvKavXv3uqQVyddhsVi44YYb8Prrr6OyshJPPPEEqqurcdttt2HVqlXYuXMn1Go1BgYGsHXrVqeFDxgaCRAXF4eCggIUFhYiODgYzc3NOHXqFJqamqBWq50ydgCGakPvuusu/Pvf/3ap8F0rhhu+zoQtcvYmfssh+zCZTBQVFaGoqAgvvvgiampqsHv3bsyfPx8ajQY33ngjVq1aNa57sNlsxMTEICYmBmazGXK5HG1tbdRYT7FYDD6fP+qOsLu7GytWrMBbb72FGTNmjGs91pjNZqxfv35YSKS4uHhYSCQ5ORnffPMNZbjx8MMPTyjDDV/BL35uwBnLIWDIPurQoUNgs9koLS315FK9CpPJRF5eHjIyMnDmzBmUlJSAwWBg8eLFCA8PpzwJx+OFx2KxIBaLIRaLKQfmzs5O1NXVITw8nLKity7alkgkWLZsGV577TXcdNNNrvhVKfyGG76DX/zcQFFREZqamtDa2oq4uDh89tln2LFjx7BrWltbqX8mLYeuJeGz5tSpU1i6dCkefPBBAEOtVk1NTSgrK8OKFSvA5XJRXFyM4uJiiMXiMcfwbI31lEgkaGhoQEhICJqamlBUVIRVq1bhxRdfxJw5c1z5awKgN8rVmm3btmH+/PkuX4cfv/i5BU9YDk0kZs+ejdmzZ1P/Ts7g+Mtf/oInn3wSFy9eRHl5Oe655x6wWCxanoSOGDnWs6OjAwcOHMBjjz2GnJwc6HQ6aLVal5fQ+A03fAd/ttfPVQNBEOjs7ER5eTn27NkDk8lE7ZgTExPHldVVKpVYsmQJnnjiCcTFxaG8vBwymQzvv/++C38D+pUA1dXVWLx4MQ4fPoyMjAyXruEqwl/q4sfPSEhPwj179mDPnj3QaDS44447UFJS4rSdvVqtxtKlS7Fx40a3N/D7DTecwi9+fvw4QiaTYd++fSgvL4dCocD8+fNRXFzs0JOwv78fy5Ytw8MPPzzuLDNd/IYbtPGLnx/nodNed+LECWzatAlGoxFRUVH45ptvvLBS19Pb24v9+/djz5496OjowNy5c1FaWnqFJ+Hg4CCWL1+Oe+65B/fff78XV+zHDn7x8+McdNrryJGUR44cQWJiIqRSKUQikRdX7R5UKhXlSXjhwgXceuutKC0tRVZWFu6++24sXboUDz30kNdngPixib/Dw49zWNeSBQYGUrVk1uzYsQN33nkn1Ts7EYUPAPh8PlatWoXy8nL88MMPmDFjBt5++21kZmZi9uzZfuG7hvGXukxA6NSSNTY2wmg0Yvbs2dBoNNi4cSPuvfdeTy/Vo4SEhGDZsmVYtmwZFAoFIiIi/MJ3DeMXvwkInVoyk8mEM2fO4NixY9BqtZg5cyZmzJhxzZRVXKvzWvxcxi9+ExA67XXx8fGIiooCj8cDj8fDTTfdhKqqqmtG/Pz48cf8PMy8efMgEAiwcOFCt93Dur3OYDDgs88+Q3Fx8bBrSkpK8N1338FkMmFwcBCnTp1CVlaW29bkx4+v4d/5eZg//elPGBwcxL///W+33YNOe11WVhbmzZuH3NxcMJlMrF271u9Q7Oeawl/q4iZOnz6NBx98EBUVFTCbzZg+fTp27tyJnJwcnDhxAq+++iq++OILby/Tjx9fxq3ZKP/Oz02QPm1PP/00tFotVq9e7d9Z+fHjQ/hjfm5ky5Yt+PLLL/Hzzz/jiSee8PZy/IwTRw7MBEHg0UcfRVpaGnJzc3H27FkvrNIPXfzi50Z6e3vR398PjUYDnU7n7eV4FEdCoVKpsGjRIuTl5SE7OxsffPCBF1ZJH9KB+fDhw6itrcWnn36K2traYdccPnwYTU1NaGpqwrvvvot169Z5abV+6OAXPzfy8MMP469//StWrVqFP//5z95ejsegIxTvvPMOpkyZgqqqKpw4cQJ//OMfYTAYvLRix9Dpmvn8889x7733gsFgYMaMGVAqleju7vbSiv04wi9+bmL79u1gs9m4++67sXnzZpw+fRrHjx/HjTfeiGXLluHYsWOIj4+nfN0mEnSEgsFgQKPRgCAIarYGm+27IWi6Q6kcXePHd/Ddp+0q595776XaxVgsFtVe5g5rdF+DTnvdhg0bUFxcjNjYWGg0GuzcuXOY44qvQadrxhmXZj/ex3efNj9XLXRE4OjRo8jPz0dXVxcqKyuxYcMGqNVqTy3Raeh2zTi6xo/v4Bc/Py6Hjgh88MEHuPPOO8FgMJCWlobk5GTU19d7eqm0odM1U1xcjO3bt4MgCPz000/g8/mIiYnx0or9OMIvfn5cDh2hSExMxLFjxwCAmqBGjnP0Ray7ZrKysrB8+XKqa4bsnFmwYAFSUlKQlpaGhx56CFu3bvXyqv2Mhr/Dw49bcGTV3tXVhTVr1qC7uxsEQWDz5s1YvXq1l1ftx8fwOzn78ePnmsTv5OzHjx8/rsZRqYs/T+/Hj58JiX/n58ePn2sSv/j58ePnmsQvfn78+Lkm8YufHz9+rkn84ufHj59rEr/4+fHj55rk/wM3WNQ+czFHawAAAABJRU5ErkJggg==",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"x1 = np.arange(0, 1, 0.1)\n",
"x2 = np.arange(0, 1, 0.1)\n",
"\n",
"X1, X2 = np.meshgrid(x1, x2)\n",
"Y = np.cos((X1 + X2 - 1) * 3)\n",
"Z = np.zeros(X1.shape)\n",
"\n",
"fig = plt.figure()\n",
"ax = Axes3D(fig, auto_add_to_figure=False)\n",
"fig.add_axes(ax)\n",
"ax.plot_surface(X1, X2, Y)\n",
"ax.plot_surface(X1, X2, Z)\n",
"plt.xlabel('x1')\n",
"plt.ylabel('x2')\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The plot of the function is in blue, and $z=0$ is in orange."
]
},
{
"cell_type": "code",
"execution_count": 23,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"1 1\n",
"0 0\n",
"1 1\n",
"0 0\n"
]
}
],
"source": [
"for i in range(4):\n",
" print(nn(x[i]), y[i])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Thus, if you allow arbitrary non-linear functions, then there exists a neural network that correctly classifies the XOR problem. However, if you restrict the non-linear function to be monotone, then I suspect you need a hidden layer to solve. This counter-example relies on the fact that the non-linear function is not injective.\n",
"\n",
"Also, if you were to ask for an arbitrary XOR problem (i.e. the points are the corners of an arbitrary unit square), and asked if a neural network were trainable, that would also be a separate problem."
]
}
],
"metadata": {
"interpreter": {
"hash": "64e5bd0976a8fcd691718d6bf1aeda9c2a2280bd7a5e750746c45186ee42e431"
},
"kernelspec": {
"display_name": "Python 3.8.12 64-bit ('base': conda)",
"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": "3.8.12"
},
"orig_nbformat": 4
},
"nbformat": 4,
"nbformat_minor": 2
}
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