{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Modelos lineares de classificação" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import pandas as pd\n", "from mpl_toolkits.mplot3d import Axes3D \n", "from scipy.stats import t as t_dis\n", "from sklearn.linear_model import LinearRegression\n", "from sklearn.linear_model import LogisticRegression\n", "from scipy.optimize import minimize" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gerando os dados" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "np.random.seed(42)\n", "\n", "n_dogs, n_cats = 500, 500\n", "n = n_dogs + n_cats # quantidade de exemplos\n", "\n", "cov_dogs = 0\n", "cov_cats = 0\n", "\n", "dogs = np.random.multivariate_normal(\n", " [35, 13],\n", " [\n", " [4, cov_dogs],\n", " [cov_dogs, 3]\n", " ],\n", " size=n_dogs\n", ")\n", "\n", "cats = np.random.multivariate_normal(\n", " [24, 6],\n", " [\n", " [4, cov_cats],\n", " [cov_cats, 3]\n", " ],\n", " size=n_cats\n", ")" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(dogs[:, 0], dogs[:, 1], label='Cachorros')\n", "plt.scatter(cats[:, 0], cats[:, 1], label='Gatos')\n", "plt.xlabel('Altura ($x_1$)')\n", "plt.ylabel('Peso ($x_2$)')\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.add_subplot(111, projection='3d')\n", "ax.scatter(\n", " dogs[:, 0], dogs[:, 1], np.ones_like(dogs[:, 1]), \n", " label='Cachorros'\n", ")\n", "ax.scatter(\n", " cats[:, 0], cats[:, 1], -1 * np.ones_like(cats[:, 1]), \n", " label='Gatos'\n", ")\n", "\n", "ax.set_xlabel('$x_1$')\n", "ax.set_ylabel('$x_2$')\n", "ax.set_zlabel('$y$')\n", "ax.set_zticks([-1, 0, 1])\n", "ax.set_yticks([2, 7, 12, 17])\n", "ax.dist = 11\n", "plt.legend()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Classificação usando Regressão Linear" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0.11426327 0.08685168] -4.212013204016229\n" ] } ], "source": [ "X = np.vstack([dogs, cats])\n", "y = np.append(\n", " np.ones(n_dogs),\n", " -1 * np.ones(n_cats)\n", ")\n", "\n", "lr = LinearRegression().fit(X, y)\n", "print(lr.coef_, lr.intercept_)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(dogs[:, 0], dogs[:, 1], label='Cachorros')\n", "plt.scatter(cats[:, 0], cats[:, 1], label='Gatos')\n", "\n", "x1 = (-1 * lr.intercept_) / lr.coef_[0]\n", "x2 = (-1 * lr.intercept_) / lr.coef_[1]\n", "\n", "plt.plot([0, x1], [x2, 0])\n", "plt.xlabel('Altura ($x_1$)')\n", "plt.ylabel('Peso ($x_2$)')\n", "plt.ylim([0, 20])\n", "plt.xlim([17, 42])\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y_hat = lr.predict(X)\n", "plt.scatter(X[:, 0], X[:, 1], c=y_hat)\n", "\n", "x1 = (-1 * lr.intercept_) / lr.coef_[0]\n", "x2 = (-1 * lr.intercept_) / lr.coef_[1]\n", "\n", "plt.plot([0, x1], [x2, 0])\n", "plt.xlabel('Altura ($x_1$)')\n", "plt.ylabel('Peso ($x_2$)')\n", "plt.ylim([0, 20])\n", "plt.xlim([17, 42])\n", "plt.colorbar()" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.add_subplot(111, projection='3d')\n", "ax.scatter(\n", " dogs[:, 0], dogs[:, 1], np.ones_like(dogs[:, 1]), \n", " label='Cachorros'\n", ")\n", "ax.scatter(\n", " cats[:, 0], cats[:, 1], -1 * np.ones_like(cats[:, 1]), \n", " label='Gatos'\n", ")\n", "\n", "xx, yy = np.meshgrid(range(15, 41), range(2, 21))\n", "\n", "# calculate corresponding z\n", "z = lr.coef_[0] * xx + lr.coef_[1] * yy + lr.intercept_\n", "\n", "ax.plot_surface(xx, yy, z, alpha=0.2)\n", "\n", "ax.set_xlabel('$x_1$')\n", "ax.set_ylabel('$x_2$')\n", "ax.set_zlabel('$y$')\n", "ax.set_zticks([-1, 0, 1])\n", "ax.set_yticks([2, 7, 12, 17])\n", "ax.dist = 11\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure()\n", "ax = fig.add_subplot(111, projection='3d')\n", "ax.scatter(\n", " X[:, 0], X[:, 1], y, c=y_hat\n", ")\n", "\n", "xx, yy = np.meshgrid(range(15, 41), range(2, 21))\n", "\n", "# calculate corresponding z\n", "z = lr.coef_[0] * xx + lr.coef_[1] * yy + lr.intercept_\n", "\n", "ax.plot_surface(xx, yy, z, alpha=0.2)\n", "\n", "ax.set_xlabel('$x_1$')\n", "ax.set_ylabel('$x_2$')\n", "ax.set_zlabel('$y$')\n", "ax.set_zticks([-1, 0, 1])\n", "ax.set_yticks([2, 7, 12, 17])\n", "ax.dist = 11" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Análise de discriminante linear" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "def fit_LDA(X, y):\n", " K = len(np.unique(y))\n", " N = X.shape[0]\n", " pi, mu = np.zeros(K), np.zeros((K, X.shape[1]))\n", " Sigma = np.zeros((X.shape[1], X.shape[1]))\n", " for k in range(K):\n", " pi[k] = np.sum(y == k) / N\n", " Xk = X[y == k]\n", " mu[k] = np.mean(Xk, axis=0)\n", " Sigma += (Xk - mu[k]).T @ (Xk - mu[k])\n", " Sigma = Sigma / (N - K)\n", " return pi, mu, Sigma\n", "\n", "def predict_LDA(X, params):\n", " (pi, mu, Sigma) = params\n", " inv = np.linalg.inv(Sigma)\n", " first_term = np.log(pi[1]/pi[0])\n", " second_term = -1/2 * (mu[1] + mu[0]) @ inv @ (mu[1] - mu[0]).T\n", " third_term = X @ inv @ (mu[1] - mu[0]).T\n", " logit = first_term + second_term + third_term\n", " return 1. / (1. + np.exp(-logit))\n", "\n", "def boundary_LDA(params):\n", " (pi, mu, Sigma) = params\n", " inv = np.linalg.inv(Sigma)\n", " first_term = np.log(pi[1]/pi[0])\n", " second_term = -1/2 * (mu[1] + mu[0]) @ inv @ (mu[1] - mu[0]).T\n", " def fun1(x1, args):\n", " if args[1]:\n", " X = np.array([[args[0], x1[0]]])\n", " else:\n", " X = np.array([[x1[0], args[0]]])\n", " third_term = X @ inv @ (mu[1] - mu[0]).T\n", " return (first_term + second_term + third_term) ** 2\n", " root1 = minimize(fun1, 0, [100, True]).x[0] \n", " root2 = minimize(fun1, 0, [100, False]).x[0] \n", " \n", " return (100, root1), (root2, 100)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(array([0.5, 0.5]),\n", " array([[24.12554218, 6.13666121],\n", " [35.0072024 , 13.06073074]]),\n", " array([[3.69892204, 0.00649467],\n", " [0.00649467, 3.09207942]]))" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "params = fit_LDA(X, (y + 1)/2)\n", "params" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "((100, -83.06475782461128), (-39.14779205683636, 100))" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "boundary_LDA(params)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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l1wkZ4+nbCxNB2xg3SK8kx+qTA+JHCh9KIbOkkoQiDV+Gv02ctE1r0ODbzYwl+zD57NukLOF2wMJ4qpgw8CxwSILLdYv/3h1Y1lynjrF3SIjP7WLShNGowjnPzF7v/O/VroToLwmORI1xrd82sgAN/ButeQOtJ6NI/ikkXhRN1O3P2Kv2wi6/Ery7kzjPPRiD3PhYOLEnT32qboTw+wkOuMA9DHIPiadXqDXiPsALnu0hdwLkX4J0n4j0/hTxJswwbvBuS2IJKhfJbWSvrAISPwUIuApTv5+spEWVqnrV1t6Ib/WLMg0AltR7vTS+rz7XA8fGk0rOAM5pbnTOAq1DUjbs6ee2I7bkjOnfcttb87n6wMZPkl2ZFPMg8aB2AA1MhcA0oApwmQClChcUPYF4hiOufqj/RKh+nNQaPKDlECuHmmVArileElsC1Mtg6dkW8EDk0wQdRAAvRiNPRAQ0kmB/DKI/QfSH+Bgt814QKJyM5dsl9bgbIZKLdrs9vjBtm/GIH7y7xNci6uHZxuTz12oaGn0fkjuhRdfNBhRa4mmzOkU97UQzhMZ3xfHANFW9U0R2BJ4SkRGaog6lY+wdUrLfyH78Y8fBPDrrd7bfuCf7DOub6SF1CGLlod4djNdJA2nCB7mHoSVHQ/RX1hrjaF1qYS09HXp/aHLUFFyExlZC6C3q3CcRzGKpBTR2w4wBNeDZBul2LRqZa9r69oXg6xB4MMmIleSGvjnq3wRqbUUMyi5A+3zSYs8YK3cf1Ps2WvMq2BVIzu7gGdPEE0fEgqLHzQKtVmJcTSNQcCni3aqV7yVz1EbQtgFLgUH1Xg+kqUxzEjAOQFU/E5EcoBeQpNalI+M4pMGVB2zBiAHduPiF71hauv7o99J9oskPL3kY45wLnlHg2hiijWbd9bHL0cBkNDwHU2KwL2ZeVWtI3eYpIP8kmqYiBohB5EvEtxNW/hmId2tYcxgE7sR4uHQQGkUDT2NHfkLt8hadKq5+WPmnYXW7BPFum9DlEkDcf0F6f4AUPob0uBvp8ylW3rFtMfqM0EYpjr8CNhWRIWJKlh0NvNqozR/AXgAisgXmHzRlLVZnZu/QLLX6/YH3zeLsp2fz/Hrify+uPtDrbTO7jy0F9xbg2RKtuJrURjcIVQ+j8ihYAyG2iIaz7ohxkdQISRc0LfMEpbE1aOnxzVyvvaiGqn9BFSgu1Lcf0uMWzCSydaiqKYUYmGKye7o3R7pdiXiTKRqdB5PieN1n9qoaFZGzgbcxmtpUVf1RRG4AvlbVV4GLgEdE5ALMY93x2kxebMfYO6TF4J553HrElpw5/Vtuf3s+Vx2wfuj3Ii7w7dxgn1r9SK2PA4Tidep+JbEEGzLeKL7dIPRhw74kF8k/zVyr5r8tqDzVnsQg9AZaWgKFjyedqTeHVt0H1VPXxgNEfzAyTs/piGdkG443M7RVkjNVnYFZeK2/79p6v88Dkvi/JqbrT88c2oz9R/bj7zsO5pGPf+d/81ZmejgZQ/xHkP5XJ0ZiuccC90Ck+23xoiJeIxdJPuRfjvjiaYWjy2i9Ft/WKIQ/Rcsvb1VxFdUgBOoZ+jpCaOV9bTPEDGI0e6fguEMX4cr9jX5/0Qvf8WfZ+pn+VlwbQLdrSdutEkhcEvAfiJWHVTgJ6fMR0vMFpM/nWHnjUbWxqx6E0H9S9GkBeS0e/1oSlSpMg+AraOmpaPjblp0XWwkJnwg0nv+nc2O8cay0tkzQYVcVkakiUiwiP9Tbd72I/Ckic+JbwpDf5kKHHTqOHI/R721bOfvpb4nEOp//vcZWGN/4dZBHJPdAkqUMaIoPPKMxs3c/SCHS484GmSvFKjKLleI1Y6y8E6oeSjALbowNtKbgjBvyLwJfawqT2BD+EC05AbtqSvqnWb2TS1LuTVoxjuSo2mjN69glJ2CXnBiPgWjv/1VnZl/LNOKuQo24W1VHxbcZjQ+mGTrs0IEM7pnHxL9tyew/yrj97c4zI9PYGuw1E0wGypIj0eIdsWua/MulhUgO5J9DYm+axkSRvJOQ3u8hPV9E+nwK7iFo4HHsqqnYgUfRwFQ0atIMqwah+t80LWbSGJu6IuEtxmWSjq2TxlwDVfclzcDZBHsZieMN3Ej+2ajGULsc1RYmZmuEqqJl56IVV0H4k3jOnSvR8ovWqd90aKMI2nahwxZoVfUjEdmoFafWhQ4DiEht6PC8thudQ0s5YMt+fP7bYKZ89BvbDyliry2y3/9eS0+B6HyMT3x8Z/nlqHtDxDOixf1Z+aegrgFo4GGIrTKBUY1TAgAQQwMPYfV8DtXeaOVEqH6a+nq+4oLKu1H/PxD/0UZhacNUNg3JhdzDUdwQfjd5M2szsBNFEdcnhoY+QfyNo/kNapeigacg9DHYK0i4fiFeNDwbSk8zTzLiR/PPRvx/b91CcORbc736N0utgdB7aPi7dvPhbytvnPYiGzT7s+NZ26aKSKIY6XRChwEQkVNrw49XrUrpcurQBlx1wBYM79859HuNLGgUBFVLGA080ep+JXd/rF6vYPX9FHo8QFIdPxZf0A5/AdXPYmrB1h9LzOyrfgqNLUveT5tQAzXToeS4lK2kaDLS40GMC3eyeWEsfgM1aGgWdunZRj6pehJdfZBxs4x+V1d1qwkagap744ncIuamWXUXWv1ca94chD/HfL6NrxOOH2s/HBknOQ8CmwCjgOXAnQnapBM6bHaqTlHVMao6pnfv3m03SoeE1Or30ZhyTrbr93ZxktJ8NsSaySuTJuLbKR6A1RgL8GKv2A4tPYnU8kzQJEXLO5n0JKJ1wF6S8rAGZyA5eyF9ZoFvbPKGkR9NdxV3omVnQegdI59U3WI+92a9iSI0Mc5aA4FJzb6FhEh3jGtsY7zxql3tgyJE1UprywQZNfaqulJVY/F8Do9gJJvGpBM67JAhNuqVx8S/jeTbP8q4I5v1e88w0ASzPXxN/Ohbi4gXCi6joZG2WFsNqozEMk9jbPCfAr69ad8ZfjMEHjeLmpLXzIxY0NhykwOowYJyOjf/FAFayeryNkfu/om9fkSSFlxpC0xZQqfgeEJEpF+9l4cBPyRolk7osEMGOXDL/hy7w4Y8/NFvvDc/O/3vxSqMz5Ybe9Bo6llrC7H8RyGF95ukZa6B4Nq0hT3kQM44KD3WzJDbT7hvHi1DV26JFu+YPFc+Ajl7GHkq4ZNTMuJZNXP3B2tQ4iaujVo23toRWUVIj4fMDF/y4/ELPZDCKUg7zuzBkXEAEJFngM+AzUVkqYicBNwmIt+LyFxgD+CCeNv+IjIDTOgwUBs6/BMmYf+PHTVuh/S4+oBhDOvXjQuf/45l2arf546nqfGMQtmZ6+yWp3YAu/xG7JVj0LJzwdUHCp+KZ65sAe4hEFsBkV9IqDt3KPHkaprqiUSh8g6zJtKSQCvf3iamoPtEKLicpjP8HKTgslaNGkB8OyJ9PkUKH0YKHzG/p0rN3BakOavP1My+I71xxifY/ViStsuA/eu9bhI67JBd5HhcTDpmNAfdP4tznpnNs6fugMeV6SWhRgRfSLDTNguH4a/At32rulVVtPQEiMyjTp8OvmW2ltZ3jc6Dypto3u0ymwhD9RM0X/ykHhpArHwgniXTeiBef3cxuIYgBRci6yiviXji+fU7htriJdlKln0bHTozQ3rl8a/DR/LN4lLueCcL9fvoIpIuFjZX/CMVkW/jhU7q9x2jxYa+Fq1q/VgyRgSs/mm2tUCr0egfdXvEtyvS7XrIPQp8O8YLqXQ+snlm7xh7hzbloK36c8z2G/Lwh7/x/vykqbUzg2cMCT1c1AZ3y/3s64j+YvpYr1GwF6bZ1obIt+iag+L5+sGuuBkt+YdZ5A08hq45Crvq4fYbbjugQNS20toygWPsHdqcaw4cxhb9unHh83OySr+X3IPB6kFD9TIHfH9FPJu1qk9VRaNLyLy+ng20ZDE5amrNll+HRn6A6ucx0pURQ0ya6AfQ6NJ2GWl7UFu8xJnZO6w35HhcTD5mNOGozTnPzM4a/3ux/EivlyH3/8DqBdYAyD8L6XF/q/vUyjviqQ0y6DXTmYnOQ2veIunNMpSobm72ks3pEhxj79AuDOmVx7/+tiXfLC7lzneaC7nvOMQqwup+PVafT7H6vI+Vf5pZyGsFapdD9ZNAsG0H2WmwMFW3eqxDHwrhOSQ2RRa08m+TEdTR7B3WUw7eqj8Ttt+Qhz78lfd/zjL9vi2I/gKSKFJzfcEDhY8g3W+h+WjfFKYmOjvJcbtpkfIsxgmqclivubZWv39uDsvLs0e/bxOsfibfynpLGEIfIzl7Q8GlIAUkj/hNJeUpeHcFfCC5mJTNPuh+K+LqXF45jrF3WG8x+XO2Nvr907OJZol+3xaIeyB4x5A4D4uPhgvBuZhyol2M6AI0tgor7xikz+dQcC1NA6SaMzMW4tvWpIAuuBrpfi3S52Os3ITlLbIWRYjZVlpbJnCMvUO7s3HvfG45fCRfLy7lzpnZo9+3BNUwGv0DtRv6wEuP+8G3B8bge0xxEv+J0OcrI294tgH30HibrnOjMyiEv0RX7YkdmI6Ix5RszNkfE2CVB/jAKmqmH4GccYirN+I/Esk9HLHWZR0gczgLtA7rPYeMGsD47TbkwQ9+5YNOpt/bgelo8Q7o6oPQ4h2wy69E4/KNWPlI91tBijDpeatNQe1VO6DuEcbVM/p7vKh4V/TYCZmtciJ29X/Q4h1MTh/xAlEouBbJvyguzyTB/3fE1S/5cYgXNqlqVe3bjkKdBVoHB8N1Bw1j6AYFXPj8d51Gv9fgO1B5WzyqtQYIQ83raMUNa9uUXQC6otGJ1VByJIQ+wRjEQAeOOhNEoeJa0ID5rDSAuQlcjYa/MG6uyTJcVj+Fhr5IeMjU4p2MFo9Bi7dDV/0Vu/rFdnsX64qqpLVlAsfYO3QYtflzQpEY5z7TOfR7rXqQpnlqglDzCmrHywGGP0pycoCu6ZaZyFglSw2hEHwF7DXgP4PE6biCaOWtic8OPAhVD8c/y6jpp+JK7FX7YFc9tvZvkBU4QVUODnVsEtfvv1pUyl2dQb+3VyQ/Vpf2t6U5cATyzgO6kXhxN9tJZqySFXDX+JNRafIuoz9gV7/S8CyNQeBRmt5s1SRMq7rX1BLW7LihKjgLtA4O9TH6/SAmf/ArH/7SceUjNfo7duVt2GWXojVvoJpGIRHPKBIbtxBaeh52aG7LB+IehlVwFtL30/jCbfZmSmyKh9YtNEdMZlFJUayk4ho0Wi+/jgaacW0NQnQp1GRJeQs1un06WyZwjL1DRrjuoOEM3aCAC56bw4ry9p+Z2TVvo6sPgcA0CP4XrbgKLZlQt9CalJxDSGqMo3Og9Mg0rl4bBeoFyUO63wiA1rwJoffoVAu37mGtP9fqGS8gk+xpJoJW10tDLflx3/1U1KBZlFLB8cZxcGhErX4f7AD9XjUMFZdj9PO41KDVEPkZrf5P8vOiv8XPSzY2pXlD7QP/seDbE/JOQnq9Ce5Nscv/BRWXkF6Zwiwiug7Sm1YjeafHn2YSEQO7pO6ViAUFF5GydCGA1bf1Y2pDFGeB1sEhIZv0zueWw0by5aIS7v5fO+r3ke9IPDsPQvD1pKdp1cNJ6tamixu8o7G6XYFV+BBWwQWIawO09EyoeWId+s0k6+BFFZkDRJFuV5Fwdi9+E41bD8t/JNLjNpBeyfv17db6MbUpzgKtg0NSDt16AEdv2876veSSdHYu/uTnRX6g1QVIEMg5AOkxucFejSww9Vq7XIBVOkTRyHzEtQHknUTDfDq5RiLy7dXkLMkZl6KKmA9JWh+343E0e0BEpopIsYj8UG/f7SIyX0TmisjLIonT54nIonit2jki8nVHjdmhY7j+4OFs3rcd9Xv38CSZGXMRf6JqmbXn/YXUXxGLpk8MFnh2Qfp+j9XjdsTKqzuiqmjwbVp/A8k2LMx6RAFGanHR7GJz6d/R6B/mKadwsin27t0J6XYdUjQNSVa03DWQhGUPxZ09Mo6CbVtpbZmgI686DRjXaN9MYISqbgn8AlyR4vw9VHWUqo5pp/E5ZIgcj4sHJsT1+2fbXr8XEaRwiolylbz4bN4H/qONlp7svPzTaCo3NDLw0g0zQ80x/bo3Q8T1L00AACAASURBVArvQhplw9TYcnT1WAhMocsYe89opPf/sDb4Bun7FeZzaWbaqiE0YCpQiW8nrML7sYoeR/yHN/jMNPQB9ppjsVeNxS6/EXx709RH3wKrENq7kHgLyGYZpyMLjn8kIhs12vdOvZefA0d01Hgcsou/9Mnn5sNGcMFz33HP/xZw8djN27R/8WwGfT6G0CzQMvBuh7gGNHPOMCicglb8E2K/s9bwh6mrqKTVYPWBvFMQz6bgGYOIoHY5Wj3dXM/VHyI/QuwPupR8E/sTXTUWtQog92jSe28xiHyfsoUdmAaVd1O3PlCzxKytdJ8IlbeAXWGu5d4MKbzfLORmCVmczaHjjH0anAg8l+SYAu+IiAIPq+qURI1E5FTgVIANN9ywXQbp0H4ctvVAPv+1hEkfLGS7IUXsulnvNu1fxAM5yTxBkpzj2wHp/aZJhFb9IlROpKFRi4CWIe7BiHdbVEMmnL/idkyahChE0pjxdkbs5fGfQfPEIt3MjTQlVlweS4xqTUNDD5gShlUQmYP0/sgEVEmO0f6zjEx52qRDVhh7EbkK4xM3PUmTnVR1mYj0AWaKyHxVbRKjHr8JTAEYM2ZMF/x2dX2uP3g4c5aUccFzc5hx3i707daM2107otE/0MBjEJkHni3AriahN4pG0egCcG+Mrjky7j5YP5p0ffhXDIHGMJJWiOSzfB+Sd2rybqILQVwJPrIIhN410bJajvj2RXP2Ta7xZwAlc26V6ZDx5x8R+QdwIHCMJklpp6rL4j+LgZeB7BHpHNqUXK/xv6/JcP4cjcxD1xwMNS9A9DvzM/QWJk99Y0JQ+S901YFgryJ52oCuTrxQeCo5p/utiGdo8uNWL0gW2RxbCjXPQXAGWnElWnJ8elHQHUUbZr0UkXEi8rOILBSRy5O0+T8RmSciP4rI0831mVFjLyLjgMuAg1U1YUYjEckTMWF0IpIH7Av8kKitQ9fgL33yuenQEXzxewn3vrsgI2PQihuNHl9nuGMYrT5G4q+NApU0P4uvPTdzTyzth02z7z/8TcrD4uoH3tEk9LzBpu5GotXGNTb4divG2Y5omlsKRMQFTAL2A4YB40VkWKM2m2IcWnZS1eHA+c0NrSNdL58BPgM2F5GlInIS8ADGb2tm3K3yoXjb/iIyI35qX2CWiHwHfAm8oapvddS4HTLD4aMH8n9jBvLA+wv5eEHH5c+pIzInyYFo3Be8pfKB27iA5k4wHkCeUa3oowsQ+arZJtLjPvBujylTGC+AkvCJqhoNzkiwP3O0UQTtdsBCVf1NTT6PZ4FDGrU5BZikqqXmutpskYiO9MZJ5ND8WJK2y4D947//BmzVjkNzyFL+efAI5iwp4/xnM6DfS169rJYN91uFk9DAk2jlbZjZfjr4IP98rBwT7WmvOZb1Uu5xp/ay0thy0ABS+IhJZ2yXoLFiKD8vQTSzgNVc7pyOpY28cQYAS+q9Xgo0jirbDEBEPsEEOFzf3CS4xTP7uKzSBYtpOmQbuV4Xk48ZTXW4/fR7DX+DXX41dtllaOijtZWQ/BNoKrXkxF0MMUarRYuDASg7Bw1/GT9/MzpXtsu2QCD/ooRHNLYCe/UR6Kp90NWHmGIl4W8Qz1DE91cSJ0/LQXKPatcRt4QW5sbpJSJf19vqr1on+sdofBtxA5sCuwPjgUeTBaXW0qyxFxFLRCaIyBsiUgzMB5bHFwVuj2tHDp2AxT8t5YFzH+PaQ27llclvUVOV/dWi/tKnoE6/v6+N9Xu78h605ESz+Bp8GS07Fy2/BFVF8s+BnH0wmSoLAB/k7IkUXGBO9m4Hro1pWT76IFox0fwqPtYPL51a/FA4Fcvdp8kRVUVL/g7R7zFPShGT3rj8vHhtWzdS9JiJgpa8uLTjhfyzEe/ojn4jyVFAJb0NVqvqmHpbfXfypcCgeq8HAssaXW0p8IqqRlT1d+BnjPFPSjpTk/eB/2EWA35QVRtARIqAPYCJIvKyqv47jb66JCUrSpnx6Lssmf8nw/86lL2P2xV/QYqamxngs9e+5ubxdxMNR4lFbWa/+z0v3f06k766lfweec13kEH+ts1APv9tDfe/v5DthvRk501TJMVKE43+AYHHMG6CtTurITQTIl8j3m2RHneisUshugjcgxv4dYsIFD2JVt4FNa8AVaRlvKPzzc+al5pva20F9ncteFfZgmXyEflPBd/uiJWHuFPEvURmQ2wFCT+/ypvQ3AMQzwjo8wmEPwO7Cnw7IM0WMu94tG0ePr8CNhWRIcCfwNHAhEZt/ouZ0U8TkV4YWee3VJ2mI+Psrao3qurcWkMPoKolqvqiqv6N5MFQXZ4F3/7G8ZufxzO3vMR7T89iyqVPceKw8ylZkaIqTwcTi8a448TJhKrDxKLmTxisDrFqaQn/uTNLCj80ww2HjGDTPvmc/9xsiivaIH9O+GMSPi1rEA2+V/dSXH0R3/YJA3jEysfqfm08XcCP8fwtzRGfX2l5M+18oKvT6K8jsUAGNdNGoOBypM+XWAVnYHm3SG3oAexiUqaQCL5rehYP4tsVyd0/Kw09pCfhNLdAq6pR4GzgbeAn4HlV/VFEbhCRg+PN3gbWiMg8zIT8ElVdk6rfZo29puHImk6brsrtJ0yiprKGcNB8BKHqEGUry5l61TMZHtla/pj/J5FQ0z9RJBTh45cSF3rONnK9LiZNGE0gZPLnxGwzC/y9cjVv//kj88oaP+U2g+SS+N/f1SQTpkb/wK6YiF16JnbgCdSuatqduJHCJ9MothFGQ582u1BpUjEsb6ZNR+MDq1szbRTc20DwbezVh2MX74Fdfh0aS1He0bMVyY290ODpK9tpA9dLAFWdoaqbqeomqnpzfN+1qvpq/HdV1QtVdZiqjlTVZ5vrs8XeOCKyD/B/GLefOSJyarL0BV2dqrIAS+b/2WR/LBrjs1ezJzmnvyCXWDTxlymve4oUv1nGpn0LuPHQEVz8wnfc9b+f+aP7HD4pXojbsrBV+UtBH6b89Vi6edKQ0Hx7g/wzwRfPheQeXPdKQ5+hpadjPGciEPoEDUyFXi83mV2KeyDa+wuouBGCyW72Nlr9NNLtarTkJJIXJBeMr3k2GboIxJqrO+CFwL1o5CvQ2tw2L6DBt6DXG2AVQXiWiUp2DYKcfRBXP9S7F4RnJujPSlHsJMvQ7E6X0Bo/+zOBS4BjRWRPYFTbDqnz4PIkd0ry5iQKCskMfQf3ZqMRg7BcDf/cOXk+Dj17vwyNqnUcsc1AjthmIJPe+5UPf1lByI4SiIapiUWYX7GCf85JXoykPmJ1Q3pMMrP4ukU/H3T7J+IeDMQXDssvxaRIqH0yqgF7NVr1YMJ+LcuN1eOfqS9ul5s1gZ7PxLNu5tDwq5gLnl3IvipW8RteStxGV9fGuW0CaOARdM1hZiG86h604mp01R5odCn0uD/uW1/fWPog/1wTaNVZaKOZfXvQGmO/SlXLVPViTDTrtm08pk5Dbl4Oo/fZEpe7odH35no54NS9k5yVGa578RL6bdyX3Pwc/N1y8fg8jDtxT/YYv3Omh9ZibjhkOB5/iMpfNsIOr304jdgx3l0+n7Cdnv+6+HZG+nyGdL8N6X4L0ucTLP/haxvE/gQ7kbYegWCiWWj9zpt6ndSRs7/J8WL1QXpMRvp+i3T/F3h2AO/O0P0WiM0j+zJkpiMEuOKeRo0JQ81rEP01HplsG48bew1afhmWZSGFTyJF0yH3OPCfhPR8Dis/RR6drETS3Dqe1gRVvVH7i6peLiLntOF4Oh0XTz2LS/a6nuLFq81N27bZavcRHHXZoZkeWgP6DOrF4/PvZd5nv1CyvJQtdtiUXgN6ZnpYrcLvdVMwdBElc/5CaMEm5Az7GYl/f2yUqG3jTXMaI5Ibd7FMgOUnqcG1mvFgKrgIKmrz+9U/rz9E5qArb4n3bRlpw/dXpPs/EfcQ7OD7YGfPAv9akt1E3YAHXH2h2zVQemaCNhIPUmschGZDZDZqB0yhF+8YxNuJS1Zk2/25HmkbexG5B7hAVV+pv19V72/zUXUiCvt055G5d/HDrPmsWFTMX0ZtxJCRgzM9rISICMP/2rZ54jPF7kMGMaP8D4K/DiGytD/eQWaBdtOCPvjdLfF9T45YRahnFES+oeECYg64R2FX3GYkn5wDECu/wbmW/zBsbKi8DbQU8IB3J/MzOIMGWry9HGpeRmtmoL4dIfQRnSa6VnKh4HrEOwpcGyEi2J6Rxp2ywWemJghNk0Ucd4GYg1o/+yylJTJOFfCqiHFVEJF946G66z0iwshdtmCf43bLWkPf1bh4+D70GliNt88aIkv7IxXd8bu83LD1wc2f3AKkx93g2mitto/XpOANvgHVj6IVt6Cr9kSji5qca/n/hvR+10gziFmYDM8k8aKrDdRA6H061tC7wbUZuNPNSFJ/LSoXvLshuYci7iEm9gCMDJVoiqshmiY4s8CzZZObZWclm2vQpj2zV9WrRWQC8KGIhIAAkDD1poNDe9Pf34PX9zqbpzf8msn/LcP+dTOmnbUdw3u0ccETV2/oNQMi34G9HK2ZGU91XGuQa0BDaPnlSM+G3m8aW42WXxMvMJ7uYmu6lqCtCqK4kPxTIOdAdOVImr3R5J9nZu1qI/7DwLdvnZFXVYj+DMFXMYnLGnsaWWD1MJq9BgC/KULS/dY2eB9ZQhY/oLRExtkLk2ktAPQDTlLVn9trYA7tS7A6RHVFNYV9e6ydkWHcSd9/9hNW/1nCsB03Y8zYrXC51i0V0uplJfw+dzF9Bvdm8BbpBB6lRw+vnzOH78revSo5+IFZ3PzfX3nqpF64rLZ9lBYR8I4CRqHl19LUINoQmYva1YjlR6ML0bILzWJku3jU5Jhrpp2ELRUhiC1BxIV2vwXKL03ZWvxHIFbTRVON/IyWnB4PBIuQWLyOgDUEyT8eoj+ZILSccWbdpKuQxTJOSxZorwKuUdVZIjISeE5ELlTV95o70aFj+P37xbx0zxss/72YUXsM5+Azx9GtZ8Mgn2B1iHvPmMKHz38GAt0K8zl38in89ZBtWTj7dy7e43pi0RjB6hC5+TkMHj6IO967Dl9uIg+L1Ni2zX1nPsI7T3yIN8dNNBxj02025sZXL2/TFA2b9S3ghkNGcOl/5nL/ews4f+/N2qzvpqRQPsVC7QC6Znx8MbK9pnltEEFchw/cWwBg5R6K7R4Jaw5Lco3uaMWtqFYhOfvFDbXblGxccyzQXFQwEP0KPLchOdnlrdYmKEgWL9Cmrdmr6p6qOiv++/eYxPo3tdfAHFrGF298wzk7Xsk7T37Idx/8yNP/epmTR1zQJG3DxGPv46MXPiMSihAJRlizvJRbjrmHeZ//wo1H3UWgoppgtdGUa6qCLJz9O9cddjufvvpV0sCsZLz24Nv8798fEwlFCJTXEKoJM//Lhdx5UmIf9XXhyG0GcvjoAdz77gI+XdiOaQZyD6Fp8jMXeLdHJAeCb2EqLWXx83x9rIHg2x0A1Sji6gtFr9L0PQoQhOB/ITQTLb8cLd4Oe8VItHhXzAN/Oiha3WywZyclzSRoGZr9p5P1MuHIVHU5sFeqNg4dg23b3Hnyg4Sqw9jxNMCRYISKkiqm3/RiXbs1y0v58s3ZdakdagnXhHnyuudY82dJk76j4SjfvPMdE4+7j5OGnU/56gQ53htRsqKUVye/zZP/fIFQdcPFyGg4yhdvfNPmGTdFhJsOHcEmvfM599k5FFe25ey33nXyzzPpicUPeMyirdXH+MkD2MuAhEXXGuGF3H+0yxjTxjsW6fUcoNgVt6LF26DF20Lp0ZB3vklH7N0T/CeyNpq39iYWBq0y+7Rxzd1miP7Rxm8ki+jkQVXvi8g5ItIgm5GIeIEdReQJIMP/tes3KxetojqBcYtFYnz++toycKuXrsHja6rcqcLKxavW5nJPQE1lkBWLVzHpvKkpx/L+c59w3CZnM+WSJ6lYXZm4kQjBQNunAfB73UyaMJqqUIQLnptTlz+nLRErD+n5ItLjQaTgYqT77Ujv/61NlOYZ2SS3TvzM+E+P2XIOhIJzgAx5obi3xCq6H7G6oRU3QfX0eNRrzBjvwG1Q8yLS/UaTcTJhmcBW4u3CQfed3NiPwzjMPiMiy+IFbn8DFmBSbN6tqtPacYwOzeDvlosdSyyx5Beu1cYHbt6faLjpDMzldjFqjxFsMKQvqZ7RYpEYs176MunxijWV3HHCZMI1YUI1yRcPe/YrpEef7skvtA5svkEBNxw8gk8WruGB9xa2yzVEBPHtiOSdgOTsjUg9Q+jdJZ7nvv4ahw88W0LvT5Gip5E+HyP5J8OqvWmZm2UbVhGNLcQuvx674i6o+Q8JNfrYIrTszHg6ibZ6ePciuY0r7HUhOrOxV9Wgqk5W1Z2AwRjpZrSqDlbVU1Q1WbHOBojIVBEpFpEf6u0rEpGZIrIg/rMwybn/iLdZICId/hRRUVLJs7f+lyv3v5kHL5zGsl9TZPDLAN17dWPLXYfhbpSrJyfPx9/OP7DudV43P0dcdBA5eWsNkViCz+/lqMsO5ZrnL6SgKJ/c/OTl/1LN/r9441tc7uT/UpbLIsfv44JHTqc9lb8jxwzk8K0HcO+7v/Dprx2bJljEhRT9G/JOMtGy1gDIOwUpehLL1QvxbmWCtUrPxaQ5bk5uEpB84+vvP5Y2K1Su1VDzNFQ/SkqvnsjPqGtDTOW75qhtY2E0fx+QixlzDlCAFE5BrIRf885Py4qXdDgtSpcQT2Xc2ryr0zAFxp+st+9y4F1VnSgil8dfX1b/pHiRlOuAMZiP8xsRebW20G57s3pZCWducymBihrCNWG+ffd7Zkz5HzfPuJItdx3WfAftzHvPzOLJ655j1dI1uDxuxLLw5ngIhyIccMre7PP33Rq0P/6Go+m/8QY8f8crlK+qYMvdhnHiLcewwUYml8v0xQ/xyctf8szEl1kyfyl2bK1xd7ktdjxom6RjsW0bO0n1hl4Di9h+/9Ecdt4BKd0vS4vLeXf6R6xZVsqWuw5ju/23brHrp4hw46Ej+G5pGec9O4cZ5+5C74KWexO1FrH8SMH5UHB+wuMaWwaxJaSe4llg9UOKnmiQD15zDkQrb4fI9xgN3SJlLvg6w5vsptLck4WFUI0WPgQlx6Vonwv+Y5G84+O1AnLAtxuIB8KzzZOBZ+uGT0FdkGz2xunIguMfichGjXYfgqmhCPAE8AGNjD0wFpipqiUAIjITIy11SML4adc8S8WayrqiH7FIjFgkxh0nTuKJBQ+06wy1Od54ZCYPXvBEg0VQj8/NhCsPZ5+/70Zh36YlKUWEsSfswdgTEqeNzfH72OuYXdhqj+Gcu+OVVJUGqKkK4s3x4O/m5/S7jk86Hm+Ol1Cg6SzR5/dx7QsXs8X2qStY/vDJfK4YdzN2LEY4GOGNh2cyZOSG3P7udXhzWpYCIc/nZvIx23DIpFlc8Nwcnjhxuzb3v281aZUzssFeia4+CAonI76dzG7PlqYYt+Sa49X/hsjPcQObpN86//nWROaqWZAOTMfM3BP0IfmQdyKSdyYiFuQe3vC4r3Gt7DSuqgrhzyHyA7j6m1TI0jZpMNZX2lAEbBV94149td49iVIFJqq0PiBRZyJyam0B31WrVrXJAL9449s6Q1+f1X+WUFachl9xG2PbNi/fP4Njh5zJPadNaeLtEglF+filLxIa+vos+nEJ1x56K0ducDJnjLmUWS83LGLSq38R0365n/1P2Ru3142IEK4Jc8boS/nx06axdH/M/5M7T27qUikCB5y2d7OG3rZtbjrqLoKBYJ23UE1VkF/nLOLVyW+nPDcZm29QwD8PHs6shauZ9H776PetwjUAElS+Msa0/lcyCtSg5Zdh2zHswFS0eHvjNbPqr2hoFlbBxVhFj8Tz7jS+mQl4xmDlHphGUZUkFFyNiA+CL5M4zUMOFD2HlX+2MfRtgGoNWnIUWnYGWnV3PBXy7qaUZJYjmt6WCVr01xGRrUTk7PiWbjKNdSWdSutmp+qU2gK+vXu3Tdi8vyCxRqpqZqwdzZSLn+SxK55m5eLkN7PF85bW/b7k5z956KInuPGou3hr6nuEg2EWz1vCOTteyeevfUNZcTkLv/2dicfdz6uT32rQT9nKMl5/6B2i4SihmjDVlTVUrKnk8nE38vnrX7Nm+Vol7ZUH3iQabhot6s3xsteEXZp9X3/89CeB8qbumKGaMDOf+rDZ85Pxf2MGcdjWA7jnf7/w2a8pq7Z1GCKC9LjXzIiJR4+KH2PsE8zO7Uqouhcq743r/DGw10DFDdg1Jn+/dLsWpBtrF4Z9dTNuu+L2eDK2VLhouKhsQf4lWHlH1o462btBZN0irAE0uhi79Hzs4h3R4t3NjF6rqc2Fj12Cll+8ztdpd7JYs0/b2IvIecB0zOy7D/DvNkhvvFJE+sX77wcUJ2iTTqX1duPgs8Y1Mepur4sx+27V4UXFK0ureO2hd5rM5hvTd7ApyP3Za19zxjaX8t/73+SjFz5j0nlTOXPMZUy96mlC1aEGi62h6hBTr3qGSD2DPfOpD4nFmhqfYFWIm466m+M2OYs7Tp5MLBZj+W8rEz4BuTwuVi9t6r9fi6oy7/Nf+OGT+WgSeaNxvYCWUOt/v1GvPM59djarKjNb+UntKjQ8B6weSO8PkW5XQN6ZSI97zCJsQqJmMZXGN8MgVN0DgLgHI73fhvyzwLcv5BwK5ELZeVD9SDOj8kLRdCi40lTw8v8d6TUDK/+UtU1yjyDh4rCrF7iGpPPWk6KxZeiaw03OIXtN/MaUKCXFj6hdtk7XalfS9cTJ9kRowEnA9qoaABCRW4HPgHVJcfwqxkd/YvznKwnavA3cUs9TZ1/ginW4Zos49Jz9+HXOIj58/lPcXjd2zGbDLQZyyeNnddQQ6lj6y3LcPk+ToKj6+PxeTrhxPNFIlNuPf4BQ9VoNPRgIsfy3lRQvWYMm8EGPRqKsXLSKgZv1B6BiTVVCV02gzrXyg2c/YdBm/Rm150jmfjivictlqDpM+eoKwqEIXl/Dxbk/Fy7n8rE3Ub66AhESumvm+H0ccMq6hdYb/X40hzzwSUb1e7tqMlQ9FE/1GwHvNkiP+7EsI7Govxgqb6ahUXeBezhE5ybutF5tV7GKkPzTUbscXbV7PNlYM1h9oOfLWK7e4B0NeeMTNhP/eDT0gUn3rGHMU4ALco8yMou1AeL/G+Lqn8Yn0RCtmhL38U9zLSObyeLA6ZbIOELDZf8YLSi5IiLPYG4Om4vIUhE5CWPk9xGRBcA+8deIyBgReRQgvjB7I/BVfLuhdrG2I3C5XFw67Wym/nQvl047m7s/upFJX05sknOmI+g7uFfCwuG1+Pw+xowdxZCRG7LohyVEE6Q3CAcjSX3yQ9VhThl5IbdMuIeqsgDbjtuanLzUrn6h6jAv3/cmB5yyFwVF+U3cPxXloQunMX7gqfw2d/Ha/apcMe5mVi5aRU1lkOqKYN0XxZfrxePz4PN72WbsVow7ac+UY0iHoRt0q9PvJ2dAv9fgW1D1MBBcG3ka/hotWytNiP8IyD0AI8HkGWnHtSH0uA+sXok7dieYVQdnpLcI7B6B9H7PGPpmEPEghY+ZLf8C6HY5uAdC1WSoeQECD6GrxqGhVmQ9j3xN84vHAu7NmtT9zTbETm/LBC2Z2T8OfCEiL2OM/CHAY+merKqJpwzxlAuN2n4NnFzv9VQgdehmO9N3cG/6Dm7b9LnpUhMI8ul/v6KypIotd9mC7z+eTzi4dhYsluD2uglVh/jijW/4+q05nDTxmLrUCY3pN6Qvy39f2WDWX0s0EuPjl75g6YLl3P/5LQzd4S/89OkvKYOkSlaUgggPfnsbT9/8Eu89M4uK1ZWoKnbUrovuvfqgfzF90YOICL988xtlxeUJ/faHjNyQPcbvzIidh7LZNpu09ONKylHbDuLz39Zw9/9+YdshReywcftV6lK1ITofY6Q2RwOP0lSGCUP4E9QuMbNysZDut6B5Z0Jkrqn85BltCoLkXwIV19DQhTIHKbik6cXt1Qmu1RQpuKBFHi4m++cY8I5Bqx6D6O/1xhMBImjZRdDnk5bp+K4NIbqA5NPiXBAv0uP29PvMFFk8s29JPvu7ROQDoLZo6fHpBlQ5tJ6fvljAFeNuwo7ZJhGZCH0G92TlolXYMaWgKI+q8moicWknGo4RJcZjV0ynz+DeLP15WQPJJifPx7HXHEFNIMiUS56iuqK6idYeDUdZPG8JJ4+4kJWLilFbycnzobYmNvoK95w+hauePp8z7zmBxT8t5duZTWWHqtIAC2f/zqajNyZQFkCSSCk+v4/DzztgHT61xIgINx82krl/lnPuM7OZcd4u9Mpv+0V2Dc9Gy86Jz+AxnjDJZtriNnVu681YxT3QzJrrYfkPQa0ctPJuiC0D9xCTrsGXYPHbs415KtDUOXoSnlv7HiI/oRU3mNz1kgu5RyEFF669OQRfI7HvfsjktPekH4MieaeioVmN+vOCe3Pw7Yy4BkDO/llf4CSTnjbp0JIF2iOBBap6H9AduFZEtm63ka1HlBaX89qDb/PCna+x+Ke1njSxWIzrDr2VQHk1NVXGJTFcE2b10hIumXY2L66eyiZbDyEaavoIHKoOc9Dp+9J7YE9yC3LJLcipKzK+65E7suHQAWw0fFDSMPhwMMLSX5YRCUWJRmIEA6GkxllVmfXSF4TjElM4wRMDmCeQ2vWGodtvSjTSVE7y+b3sfHjL/bLTJc9n8ueU15j8OXYb589RuxwtPRHsYmNstRrslfFFx0SzXQ+4BiXY3xTJGYvV+y2sDeZi9XoFvDuh4Tlo6FNU683kvTuCeyQpo23dI5K/h9ifaMmEeDnGeGHw6ukmR3/dYJI8EahN4oLjKd6XdxR0vyMuVfkAL+TsixQ9hVVwAeL/v6w39HVksTdOS2Sca1T1BRHZGaOv3wk8BLTfN3M9tBuy5AAAIABJREFUYNbLX/CvY+9DBOyozbRrnuHQc/bjlFuP4+evfk0otQQDId6Z9gF7HLUTf/6S3DHpl69/5anfJjH3w3mUriynW898Zj75Icdvdg4rFq1KKvMACR9HVRWPz5Nw3UBVWTJ/Ka8/NJOVS1ZjuS3sRk8MIsJmYzYGwF+Qy+l3/p2HL36KcE0YVcXn99F/k76MO3HdNfpUbNGvG9cfPJwrXvqeyR8s5Ow9U8cAtIjgm0lm8W6M+hnFSB4C5EC3axFpeWyjRuajpafEnx7McpoW3IjlP9jILUWPmVTCgafA/oO1f1ABfEi3q5P3HXiCprViQxD6EI0uRdwDEf8EtOLn+MJqLWLiB1wbt/j9WLn7ojl7m5ukFJji452RLJ7Zt+S/rHYadgDwkKq+IiLXt/2Q1h8CFdVMPO4+wo2kkVcnv82OB29r5Jckk4BgIMiMx96l+I/kvuOr/yzBsixG7TGC7z/+iSv2u5lIMNzq2WyoOky/Tfqy4rfiJlp774E9uWCXawkHI03y3ru9LlwuF5c9eQ4e71qPnINOH8smo4bw6qS3KCsuZ6fDtmfff+zWqkIpLeXouH5/18xf2HajIrZvK/3eXkNieSMC/pOAKIQ/A9cAJO9kxDu6xZdQjaAlx0NjP4WKq1HvMOT/2zvv8CiqLg6/Z2sqSQi9JfTeexPBQrUXigURP1BA5ENs+GGhWEFUQAHFgoqKggqIiB3p0nvvvUP6brL3+2M3MWWTbGCT3ST3fZ55sjt7Z+ZMZvfMnXPP/R1TDUQsSPCDEPwgyr4dFTsNkveAqS4SMgQx183+APbtuK2wJRZIOegMMQXc6jyPhMWAAcTgLDEYMe2qZ5WLGLKZbFZ4KCpyCcdFZAbOXv3rImLF9zNwCzXrft7sVvclKd7Gb58vY8g7A9z+cEwWEzvX7GXvhgM59s5TB5TPHj3H6B4Tcs3Pzw2D0eCUQk7XfTGajZgtJkLCgzl1MOs0idCSIdw2tBtdB3RO099JT702tajXJj8rS7knNX6/9dhlhn+1kR+Heyl+b2npjHFnjpeLBQnojFiy1xbKCaUczkHeuFmgsss1t6Pi5yIlRmc8tLk+EvGe5wcz1wf7JrI4fGVLy6l3Dia/jgoeBLb1zhCMtWOR177JkaISswfuxZnz3lUpdQkoCbhJBdB4inI4MjjOdJ+QkuLAbDEzes4IrEHWNB16a5CFlGSnPo+7EE96fvvib4a1fpb7qw31in68I8XhDM24TBaD0OyGhszYNJFD24+63SbmQiz3j7kbh1K8/uAU7iw1gNsj+vPmgGlczEVuIiE2gYXTlzLpkff59q2FXLmQjT7+VRJiNTHtvmZcivdi/N7c0jlASvoJd4FgaQ3mvPfiU1Exb0LsNFfsP7uZOa6ZtdeIBPd3E5MPAOt1zsHj9G1N1Z0x9YAuxdvRp1JEJlUlAME4NezH4qxm4MfT2fyfFl2bZDNIaU2TGGjVvSmf7H6HXz9fxqWzV7h89gq/z1mezU0iI8m2ZHb/s9/rdqeiHIqLZy5ToXo5jCYDydnce0Z2GsPO1fsyhH5+++JvNv25jY92vO02bHPuxAWGtnyW+CvxJMYlYQ208MWEeby9fLxXi5bXLV+CF2+pz+jvtvL+X/sZ2rnGNe1PRCBiOip+PiR+AwgSeA8E3nnV4Q3liIP4z3GvTZOeQMR67eMdYqwIJedkysa5Fwl98pr3XeQpIj3794A2OJ09QAwwzesWFSMS4xIxuZECqNG0Ko06OVPXUgdFbxvWnUcn9ieyfITb2a++4uIp5/2+dOVsJv0I7FqzL0uMPyU5hSvnY1n2zWq3m80cNZtLZy6nPZEkJdiIuxTH24NmeM94F31bVebWxhWYtHQ3aw9e+3w9ETOG4N4YIr/FEPmNs+d7FYOwaThOOlM0czxoIJjrQMDNV3+c9Lsz18UQ+SWGcrswlN2IocRzWnXSA4qKEFprpdRQXKNPLj15ffWvga9f/yEtXTE9+zYdwpZoY/Nf23mo1nD6VBrMnZEDePnuiTS5oSGWwKz/dpPFSFS9PPZ4c7n6lkALgaGBhIQHE1Qiqw6QwSBpmv4d72ztPjVTkW14JDE2kR/eW8L8t3/MUhh99aL1WcYjlIIdq/e4/Z9dCyLCK3c2JCoymMe/3MD5WN/q52TBUA5UNpr1hlJgbouEPo+U/EyHUjTZkhdnbxfntDgFICKl8XuhCv9m/a9bSHETxjGIsG7pZp7v+Son9p8i2ZbsLNS9aD2fj/2GG+7rQECwFRGnw7UEmgkMCcx7Ba1crp4twUZIeBA33N8xi4MVgcDQQPqP7Q04BeMCM0krmMxGDMacv2K71+5j1ugveKD6UL4YP4/9mw+hlMJkcd+TFYNgyAddmxBX/v3FeDv/nbvZ6/n314IYQiCoLxnHAQACkIjpGCI/dT096L6XT1H+LZeQF2f/LvAdUEZEJgDLgVfyxaoihlKKnWv2sv6XzcTH/JuXnL4+bHqS7cms+H5tFslguy2ZfRsPcsfwnoxf+Bw9B9/MrUO7Ua1hFPFX4rG7mVx1rZw9ep4fpi7JMnFLjAae+mQoFWuUB5z695P+epnarWpgcMk3dLiztUeKlc7JYnY+eeErRnT4H4ObjKLjXa2xBGTspZrMRtrd2gKTOX9q7tSrUIIXb6nHsj1nef+v/BvruBok9BkIeRTEVbvXVMtZ4s/cyLeGaTJSFAZolVJfiMh6nFo2AtyulNqZb5YVEY7uPs5z3SZw5XwMYhBS7Ck88tp9rF2yib3rD2Rpb7aYaNSpHueOnncrGWwymzh9+CytezTDaDby2dhv2LXWB8JeDsXqhes5deA021ftIapeJXoOuompq1/FbrNjMBowGo18MWEecybMy1GpMz2JcUkc3nEMk8VErRbV2bfxoLPHZBDKRJXmzhE9Wf/LZqo3iSa8tPeLlvdrVYXVBy6k5d+3quofwlsiBiTkMQh5DKWUTyukaXLAfx4IsyA5FZAGEJEA4FGgBrAVmKWU8n4X0su0aNFCrVu3zqc2OBwO7q86hHPHzpP+32wwOn+o6eu7pq6v2bw6He5ozS+z/+TIzuNZ9mm2mvl07xT2rNvPq/e/k2v6ZX4iBsFoNJJsT8ZsNWOyGHnzt5eo3aI6F09f4uMxX7Fq4TpS7CnEXIzN0w/BEmDmg22TuXz2Cge3HCa8bBhzXpnPoW1HMJlN2JLs3Da0G4PeeMDrji8m0c6tU1eQYEvhx+EdiMwH/RyNfyEi65VSLa5lH4EVKqvoR0bm3hDYNW7kNR8vr3gSxvkUZ7HvrUB3YGK+WlSE2LFyN7GX4sh8P3WkqCyOHpwDkIe3H+Wj0V+4dfTgnKi44rs1TBn2oU8dPTh798l2533fnmQnISaRSY+8z7qlm7gvegg/ffgbl05fJuZCrLM6Ux6cstFsIu5SHHVb16THf25kwbQl7N94kKR4G3Eu4bdF05fy6+fLvH5eoQFmpvZryoV4GyP9LH6v8XO8FMYRkW4isltE9onIszm0u1tElIjkeuPwxNnXU0rdr5SaAdwNXOfBNhog5mJcnhyccigS45Ky3BzSY0uwM+2Jjzl/Ircyc77h0LYjjLnltSz6OanpoiaLicCQgFwHbg0G4eiu4zza7CnuKfcIG37bmmVOQmJcEvMmL/LuCbioXyGMF3rV4689Z5m+zL/i9xo/xcO0y9xSL12JMNNwdq7rAX1FJIuMqIiEAsOBNZk/c4cnzj7tV1sYwjf+RP32tbOt9FRUcfb23acJBoRYGTJ5AFNWv8J9z9+ZFs7KjMFooMXNjXlr8Az2bzrk1L3PpncdczHWa7Zn5r7WVejVqDyTlu7hn0MFVi9HU5hxeLjkTCtgn1LqgFLKBnyFs35IZsYBb+BejCkLnjj7xiJyxbXEAI1SX4vIFU8OUtixJdo4c/RchvqsnlCiZCgPvtwba1DxSIkzmgwYTTl8pRRUbxJFVL3KXHdPO0wW9znhBpOBZfNWk5SLxIPRbKRNz6vTmvEEEeHVOxtSOSKQx+ds5EKcb8NmGv8nDz37UiKyLt0yKN1uKgLp9UeOudb9exynvHxlpZTHj7a5ZuMopa69dHwhJSUlhY9Gz+GHaT8DYDQauGNETzr3bkelWhU8Sivs/dRt1GlVgwXTlrBt5W4unrqUpZdaunIkIeHBHNx6JF/Oo6CoUL0cpw6ddZtFBGCymqjeNJqPx3zJ4pm/kpKcgsEgWWLi7vT5M2MJMBMcFkS/5+/yiu3Z4YzfN+PO91cycu4mPurfMl/y/DVFBM+Hd87lMEDr7guWtmcRMQCTgYfyYprPVStFpLaIbEq3XBGREZnaXC8il9O1eaEgbPt87Lf8MO1nkuKTSIpPIj4mgS/GfctjzZ/hnnKP8Nc3q3A4HKxbupk5r8zn9zl/k5SQtTfauFN9xsx9kg82T6J0pZJZLmW9NrV4+tNhBJUIzHYyUWGgbtua1GldM9vevS3BzsiOL/LtW4u4dPYKKfaUPA9+lqwQQcOOdenz7B18uG0ykeUjct/oGmlQMYwxverx5+6zzFiWNV1WowE8H5zN/St/DEhf0aYSkL5wRSjQAPhTRA7hlLFZkNsgrc89i1JqN9AE0gYmjuOcvJWZv5VSvQrKLofDwby3F7mVBbYn2bEn2XnjoanMfulrzh49T1KCDWughff/+wmTl4+nUs3yWbYrERnqtoD3msUbaN2rOZ/uncKIDmM4vvdkvpxTfrN8/lo+3TuFZ24al6G4eCpJ8Uns3XjgqrV9rEFWRn/+BI2vr3+tpuaZ+1tXYfWB80xcupuW0RG0iPaP/HuNf+El3Zt/gJoiUhWnP+wD9Ev9UCl1GUgTo3KVix3lqt2dLT7v2WfiBmC/UiqrpyhgbIn2XFMbbQk2ju05SUJsIo4UBwmxiVw6d4Xne0zg9f5T+OCZzziWznEf23uS04fPZrmzJ8Yl8cmYrwgJD+byWe8Ng4hRsi1+kh+kZuCMmDHY7U0tr1SpWxGz1Yw10EJYqVBGfjDYJ44enPH71+5sSKWIQB7/UsfvNe7xhlyCKxFmGE5J+Z3AXKXUdhEZKyK3Xq1tPu/ZZ6IP8GU2n7UVkc04H2dGKaW255cRSikO7zhGaEQwl8/lrKGepXiIghP7T3Ni/2mMZiM/TF3CM58Np+OdrbEl2DAY3N9fzx49x0t3vklEuXBiL8XlaqMYJNcesnKTy5+fpCSnMKjRk0xZ82q2oZy89Oqf/PBRqjaMIuZiHJEVItwWeilIQgPMTOvXjDvfW8mTczcxS8fvNZnx0k9OKbUYWJxpndvwtVLqek/26Tc9e3GqON0KfOPm4w1AlFKqMTAF+D6bfQxKHd0+e/bsVdlx+vBZBtYbwajOL5J4jZWdUuwpJCXYmPjwNGxJdqLqV3KrWAnOCVWb/thGl37tCQjKOGNTDIIhnfMMCLZSqVaFXHPVCxpHiuLyuSu898THjPpoCEbztTnn7Sv2EBgSSJnKpXzu6FNxxu/r8sfus8z8W8fvNenwXsw+X/Anb9Ed2KCUOp35A6XUFaVUrOv1YsAsIlkE1JVSM5VSLZRSLUqXLp1nA5RS/K/Xqxzfe5LEuKS0MI4YBLPVnMG5msxGrMH/VpDKjT3r9mM0Gnn2s+E59npLlCxB+ztaIQZxqloaDVzfux1D33mY+u1q0/C6unR7uAtnDudSMNxHOFIUK3/4h9f7T3Wr6JkXls7+0ztGeZn720TRs2F53vx5N+sP6/x7jRPJw+IL/MnZ9yWbEI6IlBPXVFQRaYXT7muvv5aJwzuOcergmSwZIsqhaNqlAaO/eII6rWtSoXo5bhnSlQ82T6RK3UoEhjjj05LNJCFHiiPtCre4uTF3j7rV7YQio9nEtuU7WfH9WpRDoZTzBrR64XrWLdlI7VY1GP7ef/jz65UkJeRjzNgL38bEWI/meeRshp+KfYkIr97ljN8Pm7ORizp+r0nFj3v2fhGzF5EgnIXMB6db9yiAUmo6TpmGx0QkGWd5xD4qNwW3qyD2UlyGcEl6Lp+PodO97eh0b7sM66f98xrrlmxiz7oDXLkQw5KPfs9S7zUxLolRnV+iTc/mPDnrMe4a0YsFU5eQkM4hikEIDLby9/zVJNv+7RErhyIhNpFVC9djNBlYNH1plqpPuWEwGvL2FOAHUjDWIAtdB3T2tRnZUiJ9/P6bzXz4YAsdv9f4dcFxv3D2Sql4IDLTuunpXk8Fpua3HTWaVnXrFC0BZjrc0drtNkajkdY9m9O6Z3OUUhgMwsIZv2AwGDKkbabYU1izeAPPdZ/A9fe2I6x0CWdBEOV0xlUbVqbXozfz1n+muz0OQEqyI9sJS9lhDjBTtkppzhw9hy3R5heO3BPE9f+Lj0kgKDRrlSx/oEHFMP7Xqy4v/LCdD/4+wOBO1X1tksbX+F9kNQ1/CuP4nIAgK0PeGYA1yJoWQrAGWihduRS3PJZ7bU8R4YEX76XPs3cQWjIEyfTfTbYls3fdfj763xxOHTxDij0Fg1GoUqcC7656haM7T3jdGdsT7Zw6fAZbQuFx9OAMA3360lyGtnqWhLjsQ0Jnjp5jfJ/J3Bb2IPeUHchHz8/xetnCnHigTRQ9GpbjDR2/13hJCC2/8IuevT/R/eEbqNqgCt+9+xMXTl6kzS3N6fHIDQSG5N67PLbnBMPbPe/K0XefyeNwKByJ/8oB2JOSObH/NGsXb+TgtvyRS/BEfsAfcSQ7OH3oDEs/+YPbhnbP8nnspTiGtnyWK+djcKQ4iI9JYN7bP7Jv40FeWfx8gdgoIrx2VyO2HV/O43M28uPwjkQEFw8tJI0b/LhDpXv2bqjTqibPfT6cN397kbtG9PLI0QNM+s/7xF6My9bRZ0dCbCI7Vu6mcu0KV2NukcaelMzqRevdfvbTrN9IiEnIEHqzJdjY8teOfLtxuiM1fn8u1saT32j9++KMP/fstbP3EnabnR0r9+Q4eGqymNymXVqDLJSqFMltw7rlp4mFluz0b3at3ec2K8lgMnBgc8FOwm5YKYzne9bl911n+HC5zr8vtvhxNo529l5CRJDssjEEykaV5sGX7iEoLIjMGYVJ8Ta+fWsh+zcdolTFoq+5kjpvodfgm+jct0OubW8Z4rwJJiUkcfHMZRwOZ08+un7lLEXJwZnBVLFmOe8bngsPto2ie4NyvLFkN+sP+2dxGU3+onv2xQCT2USbns2zzBoVg1AuqgyDJ/WnzzN3MHnZOKrUrZSlh3/q4BneeGhqtrn6RQnlUNiT7Pzy2TIaXVeXqWtfy6GQibBv4wEmD5rOnZEDuC/qMfpWGsyyb1fRc9CNmMwZh51MFhOV61SkdssaBXEqGRARXr+7ERXCA3l8zgYu+bhspKaAUXireEm+oJ29FxkxYxDlq5UlIMSa5ryUQ3Hq0Bne6D+F1/tPJapuJT7cNpmwUiWybJ8Ub+PKufyrvORvJMUn8e2khdRuUZ3317/hdjJXit3BB09/zq9fLMOW6FQbvXDqEm88NJXje0/x1rKx1GpRHYPRgMlspN1tLXl96RifTcjKEL+fuznPcyI0hRdB9+yLDeGlw5i1fTIPT+iHIZOWS2JcEsvnr2HP+v04HA4unLrkdh95Hdwt7KSWFQyJCMEa4D6LJe5yPLaEjOmUSfE25rw6n+qNo5m29jUWXJnNwtjPGfP1SEIjQvLd7pxoWCmM0T3q8NuuM3z490Gf2qIpYHTMvvhgMBiIuxRPSnJWXZhkWzIbftmCwWCgZDaDjtnG/QsBYgCjxXPBMhFo3LkBAKUqliQ4PMhNo+xlKE7uO5X22hJgYd/Gg3z37mKWfbuqQHPt3dG/XTTd6pfj9SW72HBEx++LC6KUR4sv0M4+HwgJD8ZszTpwKAbh9y+XM6HvZLr06+C2Nm1wmBuHV0hQDkix5U387KGXewPOm+SI6YOxBlnSbngGg4ByL9VsMBqo27YWAMn2ZJ7v+SpPdXmZD575nIkD3+O+qEc5uvv4NZ7R1ZMavy8fHsDjczbq+H1xQKteFj869W6XJeMGnD37g1uP8OfXK1k0fSmNOjfIUsc2/kpCAVnpe8Rg4NCOf+sqt72lBZOXjeP63u2JblA5x6ccR4qDpPgkTuw7yQ9Tf2LLsu0kxidhT7KTEJPI5bMxjO89uSBOI1vCAp3x+zMxiYz6RsfviwPeKF6SX2hnnw9ElAnjpflPExwWRFCJQKxuNOwT45LYsHRzFolkR4oDS6CFkPDggjLXZzhSHMwYNZvPx3/LueNOEdOazaox+osnaNG1Cbn5xr/nreGhOk/w8Zivs1QVU0pxbM8Jzhw9l1/me0SjSuGM7lGXX3eeYdZyHb8v6ugB2kKOUoqzx85z4ZTnsdcWNzfmm9Mf8tL8p2jUqZ7bNiLO8oeZsSXYiI+Jv2p7CxNnDp9j9stz6V9rOJv//Lf4WGJckkdKncqhsh3UFhG3YycFzUPtoulavyyv/bSLjTp+X7TRYZzCy76NBxlYbwQP1Xqc+6sO5bEWT3N8n2cFwc0WM027NCS6QWW3M2cNRmOWME4qjgIuKehLVIrClmDjuW7j+fmTP4i7Ek/HO1sTEGzNfeMcKFk+gnLRZbxk5dUjIrxxd2PKhQUwTMfviy5+LoSmnX0OxFyMZVSXlzi6+0Rajvf+TYf4b8cx2G2eZ3t0e/iGLJN/AMwWk8eVrooDdlsy7zz2AX0rD8ZsNdGmV3MCXIVhciuoIgZJC5dZAi0EhQYyes4TflMAJWP8fouO3xdVdM++cPLbF3+TbMuoGKkcisR4G6sXuhfnckeVOhUZMWMQ1iALQSUCCSoRSEh4MDf3v56KNcp72+xCTeoA68hOL3L22HkGT3yQ7gO70GPgDf86fjcEhgTy1MdDuWtkLwa+2o/PDkyjTquaBWh57jSuHM5z3evy687TOn5fBPH3SVW6W5kDpw6ddSu0lZxk5+zRvFVFvPH+TrS/vRVb/trBwhlL2fDrVhZNX+q7gpQFjNFkBCFPdWm3r9jNwa1HmLXjbUpVKMltw7rzSr+3ObzjWIZ21iALj03u77aSmL8xoH00qw+c5/Ulu2gRXZImlcN9bZLGi4gfK57qnn0O1G9XO62+bHqMZiN1WnuuvXL68FlWLVzH6cPnUAo2/b4Ne6Iduy0Zuxut+YBgK5aAonMfDgkPZvDEB3l8ysA8zyOwJ9pZMG0JANUaRfHhtsnM2vE2tw7pSnSDyrTs3oQJi0bTbUCX/DDd64gIb97dmLIlAhj6xQYux/t28pfGi/h5nr1feBQROQTEAClAslKqRabPBXgH6AHEAw8ppTbkt13tbm1B+eplObrrBHbXjExLoIW6bWpRt02tDG2VUsRcjCUgOACLa0JVSnIKbzw0leXz12C2mkm2J2MJsGRJEwQwWYxUbRhFuejStL21BbNGz+H88aKRuRF7KY4GHetQrVEUddvUYty9kzh16GyWEJk77LZk9m3MGPKoUqcig958gMvnYogsH5HtILe/EhZkZmq/ZtwzfSWjvt3MzAea+83Yguba8FUOvSf4hbN30VkplV1SdHegpmtpDbzv+puvGE1G3v57HF+99j2/f7kco8lAtwFduGtkrww/ztWL1vPu0A+4ePoyBoNwU/9ODHn7YeZPXsSK79diS7SnpVi6c/TgDG/0H9ubNYvW8/bgmXmuNZuZMlGlOHPYtznm6RnS/BlMFhM33NeRaf+8xuVzMZw6eIaNv29l7psLcgzv1GxWLe11sj2Z6U9+yk+zfkdEMJmNPDyhL7cOKVy1AJpUDufZ7nUZt2gHH604xMAOVX1tksYb+G8Ux6+cfU7cBsxWzhSG1SISLiLllVKe5UBeA4EhgQwY35cB4/u6/XzH6j2M7/NWBif+y+xlxF9JZOuyHdk698woBQe3HOaX2X+5zb3PK3GX4jBbTW7DRL4i2ZbM0k/+5NjuE7y9fDzlq5alaZeGbF+xiy1/7XS/kcCtQ52OPNmezAu3v8GGXzan3QyTgJlPf05E2XA63tWmgM7EOzzsit+/9tNOmkdF6Ph9EcBXg6+e4C8xewUsFZH1IjLIzecVgaPp3h9zrfM5n708N4tDtyXYWD5/DfExnksfmCwm/vhqBYlx3lG9jLuc4HT0VxkdiCgX5hU7MqOUYvuq3Rza/m/ZwBY3N822fcP2dYgsH0HclXgebfoU//y0MctTT1J8Ep+P+zZf7M1PRISJdzemTGgAw+bo+H2hRzkHaD1ZfIG/OPv2SqlmOMM1Q0Xkukyfu3NZWf5jIjJIRNaJyLqzZ8/mh50ZcDgcGWZ9psdkMVK7VQ2nmFcuiAgVa5TjzJF8CLtc5ffq4qnL3rUjPQpWfLc27W2bW5pjsmR9yDRZTWmVrL58dT7H06lcZubssbxlR/kLYUFmpt3XjNNXEnnqW62fU+jx4wFav3D2SqkTrr9ngO+AVpmaHAMqp3tfCTjhZj8zlVItlFItSpcunV/mprHpj+3ZznS1Jdp57K2HCHajgJla2MRoMhIUGkhY6RK8OG8UCXl4EvAHDEa56icHU7r/SVipUCpUK4vB+O/X0Wg2ElEmjBsfcN73//hyRY4DurVbVL86Q/yAJpXDeaZbHZbuOM3HKw752hzNVeLvefY+d/YiEiwioamvgZuBbZmaLQAeFCdtgMsFEa/PjSM7jmXbc6/eKIqqDaowa8fb3D2yVwZHlnqDEIGHxvVhzpH3qVy7IoZClFVSvXEUX5/4gNuGdnOr8JkbsZfiANi+cjcP1RrOyYOnnVo44pQvdg7kvk5gSCBAjhk31kALD7/S76rOw18Y2KEqN9Yty6s/7WTzUfeFbTR+jlKeLz7A584eKAssF5HNwFrgR6XUEhF5VEQedbVZDBwA9gEfAEN8Y2pGqtSt6D78YDHRc9BNgFMBs0bTqliDsuq8OAXWzmG2OHu5zW5smFXW1+X8/I39mw+z+5/9DHt3YJY0VE/47p3F/LNkI6/e/w4JsYlHd4eGAAAfCklEQVT/DiQrZ6++dMWSRJT5d9yg68Od3eoLBZUI5O0V4zNk7BRGRISJ9zSiTGgAQ+ds4HKCjt8XRnTPPgeUUgeUUo1dS32l1ATX+ulKqemu10opNVQpVV0p1VAptc5X9tptdv76ZhWfvvg1509cpHTlSEzpiowbjAZCwoPp3Ld92rqE2ESUI2sqZUqyg/grCVy5EMPI619kw69bM8TzAkMCKFUxkv4v3+u20ImveeH211FK4biKAaek+CQ+Hz+PS6ezjg3YE+388dXKDOsiyoSh3Byn6Q0NqdGkaKQthgdZmNqvKacuJ/K0jt8XTvw4Zl9YUi/9gsvnrvB4m9FcOnOZhNhEAkMCsAZbad2jGWt+2ogjxUGLro0ZPu0/aeEHgOY3NXIr1xsQbKX97a0Y33syO1ftJjldrrnRbKTn4Jt4aFwf9m86hNFs4uP/zSHF7j+zNhzJDsb1eYsufdtzcOuRPNfPvXz2Co5sHFpmgbh5kxe5vamsXbyRxPgkAtw8ORVGmlaJ4NnudRj/404+WXmIAe2Lxo2sWKBA/FitVjv7PDBj1GzOHD2XNgEoITaRpAQbtqRkFifMAXA7E7JUxUj6PX8XX776HbYEG0opLEFmoupXxhJkYduKXRkcPTgnWe1cvYfR3SewZ91+km3J1zzRKq+YLSZCSoZwMZvi6AB/f7Oa5jc2pFqjKhzadpSE2ETEIG574ekxmY207tmMrct2sG/ToQztrUFWeg6+KUP7i26eAFKJvxJfZJw9OOP3qw+c55XFzvz7RpV0/n2hwX99ve/DOIWJ5fPXZJnp6UhxsOHXzThSHDlOeb/v+bt445cx3PjgdURWiMCRrDi66zjPdZ1Ait19lsmRHcfYtWYviXFJzptBpi9S6UqRNL+5cb6FeBQwa/tkt+MS6Zn94jdMXjaOpz4eSo//3Eir7k2xuKnOlYrJYiIkPJjeT9/GmLlPUrJceIZjBIcF0rJrkwzbuBOkA+dNI7xM/swJ8BXO+H1jHb8vhHgrZi8i3URkt4jsE5Fn3Xw+UkR2iMgWEflNRKJy26d29nnhGuVL6rWtTYnIUGIuxpJsSyb+SgL2JLvb9E2T2YjdlpztbFpLoJn/zR3Ja0v+R/mqZa/NsGwQnDezUR/nPB5+4fQljCYjHe9qw39nDCayQkls2Thna5CFG+/vyMwtkyhZLoLy1cpSu2VGUbmLpy8zvN3zXDrr7M2f2H8y2/0ppTAYit7XODzIwpR+TTl5KZFnvtX694UGL2TjiIgRmIZz3lE9oK+IZC53txFooZRqBHwLvJGbaUXvV5KPdLq3XZZertFkoGW3ph6Lcf304W/YcumpmSwmQiJCsuTnpyfZlsyWP7ezc83eHCcbXQslIkMpERlKlz4dqN++dvYNFdwW9iDj+0zm9OGzRNWr5LbuLji1gf74aiXnTzhF3o7tPcm6nzdlyKFPLTW4aPpSAPZtPJTtoTOHv4oSzapE8Ey3OizZfopPVx7ytTkaD/BSz74VsM+VvGIDvsIpGZOGUuoPpVRq7dLVOOce5Yh29nlg0BsPUKF6WQJDAzCaDASGBhBZsSRPTHen8OCe7LRyRITWvZpRvUk0dwzvwczNE7nu7rbZpl2arWZ2/7OP/143Jk2R05uICHePuhURQUSY9OfLOVbVio9JYNk3K3m06Sha9cg5jJMUn8R7Iz4G4NC2I27DRLZEOzvX7AWgcp2K2YbIykbl/+Q5X/JIx6rcWLcMryzexZZjOv/er/GexHFe5WEGAj/ltlPt7PNAaEQIM7dMYvQXI3hobB+e+mgon+6ZQqkKJT3eR8OOddxOQqrfvjbjFzzH9A1vMuiNB4goG86A8X0oVdH9vpPibSz/bm2eioHkBaUUM578lAdrDGPF92sxGo3c8UTPHENZSkHspXie6vIyL80fhTkg+yeTnav3AFCxRjm3RcFNFhPR9asAULVBFSpUzxqqEoGh7z6cxzMrXKTG70uHWnX83s8RnNk4nixAqVRpF9cyKNOuMuP2FiEi9wMtgDdzs087+zxiNBpp06s5fZ69g453tXFbWzYnhr47kMDQQMyu3qzJYiIwNJDHpz6SpW1YqRK88M2T1Gub90lLmbEEmK9KM/3kgdO8ev87rFzwD/c8eQsh4cG57ufciQtMHjyTiLLZD5ympqZWbRhFzWbVsjw1mC0mbhv2r2zxxD9fplqjKhjNBoxmI2armWFTB2YZyC2KhAdZeLevM37/7Dwdv/dnRCmPFuBcqrSLa5mZbjceycOIyI3A88CtSqlc85516mUBE12/MrO2T+aHaUvYs/4ANZpU5fbHu1O6UiQA546f5/2Rn7Lmx/Uk21NQDsdVTVoC5wSvFjc3onLdSlRvHM3Ux2cRfyXv+jtJ8TZmPTeHWdsnM2XVK0wb/hEbftvqdu4AAApOHzpLhztacfbo+axpmAJ3PNEj7e2EH0czZdiH/DV3JSnJDqo1juK/MwZTpnKptDalKpRkxqZJHNtzgivnY6jeJBprYO7plnabnQObDxMcFkSlWhXyfO7+QvOoCJ7uVptXFu9i9qrD9G8X7WuTNJnx3oSpf4CaIlIVOA70ATLogYhIU2AG0M2lKZYrUlR7CS1atFDr1vlsou1VER+TwIDaw7l09kr2jjSPNOhQh8nLxhF7KY5Nf27ntfvfQaUobHmM85ut5rS5BKn897oxbF+5O9uc+qDQAMJKl+D04XMZzqd1r2a8/N3TGI0ZB7VTklNItid75MQ94a+5K5k8eAbKoUhJSaFC9XKM/eEZykWX8cr+CxqHQ/Gf2ev4e+855j3WjoaVilbKqS8RkfWZK+TllRKhFVXL5kM9avv7X8/neDwR6QG8DRiBj5RSE0RkLLBOKbVARH4FGgKpGmFHlFK35nRM3bPPZ84dP8/8dxazZ91+qjWK4o4nerhNlXQ4HHz3zo/EXo73mqMHsCcl82jTpzi8wzneU7dtLZp2acjKBf+wP9NkppwoF106zc4fZ/7CD1OXEB+TQImSIVw+F+N2m4TYROq2rcVDY/uwdslGAoKs3P5497RYfGaMJqPXSgwe3HqYNx+elmFA/PD2ozx901g+3TOlUJYBNBic8fue7/7N0DkbWDS8AyVyGBfRFDze0r1RSi3GqQmWft0L6V7fmNd9amefjxzeeYzhbUdjS7STbEtm+4pd/PTR70z8/aUMkrx/fLWctwfPdGroePlJa/c/+zK8375iN+ePX2DGlkkMaf4MR3cdz3UflgAzAyY4nyInDnyPZd+s/lcaIZcB242/bePVn/5Hl34dUUpxdPcJ9m44QLVGUflaO/aHaT9nqdLlcCgunb7MjlV7qN8uh1RSPyYi2MKUfs3oPWMVz87bwrR+zQrljatI4udyCXqANh+Z/t9PSIhJSMshT7ankBibyLtD/h2LWTZvNa/0e4f4mASPHX1AsJWy0VeXcuhIcXD6yDk2/76NNrc092ibum1r0fHO1pw8cJq/vl6ZUQMnF5NTVTyP7TnBwHojGNLiGZ7s/CL3lHuENT+uv6pz8IRzx8+7fUISg3DpTD4WZikAmkdF8FTX2izeeorPVh/2tTma9GiJ4+LJ5r92uL2ue9cfTEs3nDxohkf7MltNmK0m7hjeg9d/eYFBbzxAYGjAVdmVYk/hy9e+4+jO3Hv1zmM7QwW71u7Ncy+yZLlwHm36FIMaPcmxPSdIik8iISaRmAuxjOv9Fif258+EsFbdm7mVlbYnJVO3Tc18OWZB8p+O1ehSpwzjF+1k2/HCffMqUvix6qV29vlIYIh7Z2y2mjAYDVy5EEPsxdgc9xFepgTNbmzI/WPu5rMD7zHk7QHUa1OLdre1JLx0GMb08somg8fOeNc/+4i7Ep9rO2uQhdY9mnFi/ymmPfFxtho12XHh5CUObDmM3Zac5caXYk9h8Ye/5ml/nnJT/06UrhSJJV1MOyDYyl0jelKyXES+HLMgMRiESfc0JjLEwtA5G7jihSL1mmsnD6mXBY529vnILY/dnEU2wBJg5uaHOiMibPxta47bi8ClM1fYsWoPh7YfpWS5f9UPTWYT766aQMtuTdNCJY5kB8rDboPJZKRJlwZue79pbSwmSleKpOuAzrxw+xtcOe9+INat7S6b3E2YSiXZnsK5Yxc83mdeCAwOYOraV7lvzN3UaBpNk871eWb244W+olV6IoKd+vfHLibw3LytOv/eH9BhnOLJ/WPupnWv5lgCzASHBWEJtNC4cwMenfQgAL9+tizH7VO/E4lxSaxasC7LzeG7KT+xZtH6jBk1rpeWADNGkyFr5SsXSfE2vn/3J4LDgrI9fnSDykxd+xrnT1zk1MHTHmfuIM66srkREGylRT5OigouEUS/5+7k/fVv8uZvL9HhjtZFbjCzeVRJnupamx+3nuRzHb/3LQpweLj4AJ2Nk4+YzCbGfD2SU4fOcGTncSrWLEfFGuXTPo/PQ4HxxLgkPhv7DTWaVqVEZCgbftvKtxMXuO3NmSwmGnWqR6Pr6lO+elkmDXyfpPjELB2KmAuxmK0mjCaj2x54WGQowSWCOHXwjOfKkgJd+nZAKfjzqxXZ9jYtgRYq1CjHdfe09Wy/mmwZ1LEaaw6cZ9yinTStEkGDijr/3hcICnFTkc5f8HnPXkQqi8gfIrJTRLaLyBNu2lwvIpdFZJNrecHdvvyVctFlaNW9aQZHD3B97/Z50qLfuXoP90U/xqY/trF45i/Zyh8n25IxW830fe4Orr+3He+uHE/L7s3ctrUnJbt19NYgC616OLeJrl85RwXODNsFWunxyI3cMbwHlsCM24gI1iArNZpG0//le3l7+XgsHu5Xkz0GgzDp3iZp8fsYHb/3HTqMkyPJwJNKqbpAG2CoG+1mgL+VUk1cy9iCNTF/6DqgM1UbRhEQ7IybG00GLIEWTBb3+ecpyQ4S45J4+e6JxOUge2CymKjb+t+Mk6oNo3hm9rBci5CkJ7JCSboP7OKyy8gzsx/HGmRNq7cbEGylfLUyBIcFEVQikMAQK+YAM/eMupXG19enbuuaPD7tEQJDAwgqEYg10ELN5lX5ZM+7vL/+Te4ddRuBwVeXTaTJSslgC1P6OuP3z87X8XufoMM4OaOUOolryq9SKkZEduKU89zhU8MKAIvVzORlY/l73hpWL1pHRNlwuj9yA+ePX+DFO97AlmhzW9jEkeKgZrNqbFu+k8S4rPpHQaEB9ByUsaxfSHgwwWFBXD57xSPbnv3s8Qx1dFt1b8rMzRNZ/MGvnDlyjhZdm3B973YA/LNkE3GX42l6Q8M0jR+Arv0707m3sz5taMkQKlQv59GxNVdHi+iSjLq5Nq8v2UWbapE80CbX4kUaL+OrTBtP8LmzT4+IRANNgTVuPm4rIptxqr+NUkptL0DT8g2T2UTnPu3p3Kd92rqoupWYe/IDHmkwkjNHzmXZJinBRr22Ndm+sjq71+0nKZ3Dr9WiOmPmjqREZMYBUoPBwH9ev58pw2Z5VBj8+J6T1G2dUW2zQvVyPPLa/Vnatr+9Vbb7sQRYslSi0uQfg6+rxpqD5xm3aAdNK4fr+H1Bo5197ohICDAPGKGUytz93ABEKaViXQJB3wNZZsa4NKEHAVSp4l5/pbCw/pctXDh10e1nKfYUPnnha6aueZVVC9ezcsE/hEWG0n1gF6LqVXa7DUDXhzoTGhHC7Je+5vSRc9gSbG7j/mIQKtUuvAqRxRmDQXjr3ib0eOdvhs3ZwMLHOxCq9XMKCN/F4z3BL1QvRcQMLAJ+Vkq95UH7QzjrL2bt9roojKqX6RlQ5wmO7ckiYZ1GYEgA4xY+S+NO9a/6GNtW7OS/HbOOdVeqVZ6Pdr5T5NIUixP/HLpAn5mr6d6gHFP6NtXXMhe8oXoZFlheta3mWTGdn3e8cs3Hyys+H6AV57dwFrAzO0cvIuVc7RCRVjjtPl9wVhY8Jw+ezvHzlBQHh7cfu6ZjNGhflwmLRxNWukRa+cGmNzbinRUTtHMo5LSMLsmTN9di0ZaTfLHmiK/NKTb48wxafwjjtAceALaKyCbXutFAFQCl1HTgbuAxEUkGEoA+yh8eSfKRclGlcywkbjQaqFzn2kMtrbo15dvTs7hyIQaz1awzZIoQj15XnTUHLjB20Q6aVgmnfgUdv893/Ngt+bxnr5RarpQSpVSjdKmVi5VS012OHqXUVKVUfaVUY6VUG6XUSl/bnd8MmNAv2xx8k9lI2ejSNL7+6kM4mSlRMlQ7+iKGM37fmJJBFobN2ajz7/MbBTiUZ4sP8Lmz17in0z1tefLDIZSNckoZm60mEGcO/XX3tGXSny97PqtVU2yJDLEypV9TjlyI5zmdf5/PeDihqhiHcTTZkJqSqZRCRNJ+qDqerskLLaNLMvKmWrz5827aVo/kvtY6/z7f8GO5BO3sCwGpzj0nJ58Qm8DC6b+w4rs1hESEcPvj3WmZjyJjmsLFY52qs+bgBV5euIOmlSOoV6GEr00qeqSGcfwUHQcoAiTGJzGs9XPMfvFrdqzaw9rFGxh790S+GP+tr03T+AkGgzD53sZEBJkZOmcDsZlKNmq8gQLl8GzxAdrZFwGWfvInpw+fzVBYJDEuiTmvzOfyOc/kETRFn8gQK1P6NuPw+ThG6/h9/uDHMXvt7IsAqxauIyk+awUpk8XEztV7fWCRxl9pVbUkT95cmwWbT/Dl2qO+NqdoobNxNPlNZPlwt0VKlENRwoMiIprixWOdqtOxZileWridHSf0k59X0T17TV65ciGGJR//wYL3fubUoTM5tr11aLcsuvBiEMLLhGWQOvY2R3Yd56W73uSu0g8zsP4Ifv7kDx0aKAQYDMLk3k2ICDIzTMfvvYhyZuN4svgAv9DGyQ8KszbO6kXrGd9nMiJOWQRHcgoNOtThoXF9qd+uttusnJ8/+YOpj8/CYDTgSHFQulIkE34cTflqZb1qm1KKUwfPcPH0JZ7rNoGE2MQ0Bx8QbKVNr+bs3XCQE/tPEVkhggdfvJfuA2/wqg0a77DmwHn6frCaXo0q8E6fJsU6pdcr2jjmMqpdqXs8arvk1HsFro2jnb2fEXclnt4VBrmVIbYEWGjTqznPfzXC7YSqpIQk9q4/QHBYENENqnj9x7tl2Q5ee+BdrpyPwZ5kd6u1nxlrkJXBEx/glke7etUWjXeY+vteJi7dw6t3NqRvq8KtFHsteM3ZR97tUdslp98vfkJomoysXbwRg9G9k7Yl2lj70wb+nudO7t9ZErBBh7pUbRjldUd/5ug5nu/5CmePnicp3n1RFXckxSfx6Qtf6/COnzLk+hrO+P2C7ew8qeP314yO2Ws8JSU5xTmqnw2JcUn8MvvPArMnlZ9m/ea2Vq0nxF6KI9GDgimagic1fh8WaGboFzp+f214mImjs3E0AC27NcnVqfpCE+fUwTPYc3ME2TxMBIcHExBk9b5RGq9QKsTKu32bcuh8HM9/p/PvrxoFSjk8WnyBdvZ+RlipEgx992HM2VQXCgi20nVA5wK2Chpf3yCtMHpmTGYTZquZpl0aYg3MqNRpDbLy4Iv3FOvBv8JAm2qR/PfGWvyw6QRf/6Pz76+aFIdniw/Qzt4P6fHIjczcPImbHuyEyWzEEmDGaDZiDbLQ6Z62tLutZYHb1LlPOyIrlHSqb7qwBlnpdG875hx5n+8ufMwbv7zAM7Mfd2YACZQsH8Fjk/tz65BuBW6vJu8M6eyM37+4YDu7Tun4fZ5ROvXSJxTWbJzMxFyM5e95a4i9GEuzmxpRo0lVn9kSeymOr17/jmXfrMIaaKXXYzfTa/BNGI3GLG1TlTo1hYtzsUn0eOdvQgJMLBzWgWBr8dBK9Eo2jrGUaht8i0dtf475RKdeeoui4uw1moJm1f7z3Pfham5rUpG37m1cLG7a3nL2bQJ7etR2adxsnXqp0Wh8S9vqkYy4sRbfbTzO3HU6fu85/l28RDt7jUaThaGda9ChRile+EHH7z1GASkpni0+wC+cvYh0E5HdIrJPRJ5187lVRL52fb5GRKIL3kqNpvhgdOXfl3Dl38fp/PtcUTjFBz1ZciM/fKLPnb2IGIFpQHegHtBXROplajYQuKiUqgFMBl4vWCs1muJH6VAr7/RpwsFzcfzv+206/z43lHeKl+SXT/S5swdaAfuUUgeUUjbgK+C2TG1uAz51vf4WuEGKw6iRRuNj2lUvlRa//2bdMV+b4/d4qWefLz7RH/KqKgLpR4GOAa2za6OUShaRy0AkcC59IxEZBAxyvY0Vkd35YrFnlCKTfUWEonheRfGcwMvn1ft16O2tnV0b+XG9rrkKewwXf/7VMbeUh80DRCR9uuBMpdRM12uv+cT0+IOzd3c3ynzr86QNrn/WTDdtCxwRWVfQqVUFQVE8r6J4TqDPq6BRSnlr9qDXfGJ6/CGMcwyonO59JeBEdm1ExASEARcKxDqNRqMpWPLFJ/qDs/8HqCkiVUXEAvQBFmRqswDo73p9N/C70qNFGo2maJIvPtHnYRxXvGkY8DNgBD5SSm0XkbHAOqXUAmAW8JmI7MN59+rjO4s9xi/CSflAUTyvonhOoM+rUJJfPrHIyiVoNBqN5l/8IYyj0Wg0mnxGO3uNRqMpBmhn7wVEpLKI/CEiO0Vku4g84VpfUkR+EZG9rr8RvrbVU3I4p5dE5LiIbHItPXxta14QkQARWSsim13n9bJrfVXXtPO9rmnoltz25S/kcE6fiMjBdNeqia9tvRpExCgiG0Vkket9ob1WvkTH7L2AiJQHyiulNohIKLAeuB14CLiglHrNpW8RoZR6xoemekwO53QvEKuUmuhTA68S1yzDYKVUrIiYgeXAE8BIYL5S6isRmQ5sVkq970tbPSWHc3oUWKSU+tanBl4jIjISaAGUUEr1EpG5FNJr5Ut0z94LKKVOKqU2uF7HADtxznBLP6X5U5zOslCQwzkVapSTWNdbs2tRQBec086h8F2r7M6p0CMilYCewIeu90Ihvla+RDt7L+NSn2sKrAHKKqVOgtN5AmV8Z9nVk+mcAIaJyBYR+agwhaZScYUFNgFngF+A/cAlpVSqtOMxCtmNLfM5KaVSr9UE17WaLCKFser728DTQKp6WCSF/Fr5Cu3svYiIhADzgBFKqSIhAu7mnN4HqgNNgJPAJB+ad1UopVKUUk1wzkxsBdR116xgrbo2Mp+TiDQAngPqAC2BkkChCCGmIiK9gDNKqfXpV7tpWqiula/Qzt5LuGKl84AvlFLzXatPu2LfqTHwM76y72pwd05KqdMux+IAPsDpLAslSqlLwJ9AGyDcNe0c3E9PLxSkO6durlCcUkolAR9T+K5Ve+BWETmEU/mxC86efpG4VgWNdvZewBVHnAXsVEq9le6j9FOa+wM/FLRtV0t255R683JxB7CtoG27FkSktIiEu14HAjfiHI/4A+e0cyh818rdOe1K19EQnHHtQnWtlFLPKaUqKaWicc4Q/V0pdR+F+Fr5Ep2N4wVEpAPwN7CVf2OLo3HGuOcCVYAjwD1KqUIh4JbDOfXFGcJRwCFgcOq4RGFARBrhHNQz4uzszFVKjRWRajh7jyWBjcD9rh6x35PDOf0OlMYZ+tgEPJpuILdQISLXA6Nc2TiF9lr5Eu3sNRqNphigwzgajUZTDNDOXqPRaIoB2tlrNBpNMUA7e41GoykGaGev0Wg0xQDt7DUajaYYoJ29xu8QkTtERIlInXTrYl1/w0VkSD4fP1BE/hIRYx62sYjIsnQzOzUav0I7e40/0henTK+7uprhQJ6cvTjJy3f9YZwSuimebqCUsgG/Ab3zYptGU1BoZ6/xK1zCa+2Bgbh39q8B1V3FON4UkWgR2ZZu+1GuAivRrsIr7wEbgMoi8r2IrHcV+BiUgxn3kW4KvjiLuNzkej1eRN7NZrvvXdtqNH6HfuTU+Bu3A0uUUntE5IKINEvV1XfxLNDApfCYKr+cHbWBAUqpIa62DyulLrj0Y/4RkXlKqfPpN3BVPaqmlDqUbvWLwFgRKYNT6vnWbI63DafCpEbjd+ievcbf6ItT9wTX377XsK/DSqnV6d4PF5HNwGqgMlDTzTalgEvpVyilluHUlxkJ9FFKpYhINRGZJSLfpmuXAthclb00Gr9C9+w1foOIROKUsW0gIgqnsJcSkadz2CyZjJ2WgHSv49Lt+3qcapBtlVLxIvJnprapJGReLyINgfLAOVfVLpRSB4CB6Z29CyuQmIO9Go1P0D17jT9xNzBbKRWllIpWSlUGDgId0rWJAdL3nE8DZUQk0lWJqVc2+w4DLrocfR2cGvZZUEpdBIwiEgBpks5f4CwxGSciXbMz3nWzOquUsntyshpNQaKdvcaf6At8l2ndPKBf6htXjH2FiGwTkTddjnUsTjnpRcCubPa9BDCJyBZgHM5QTnYsBTqISBAwH3hSKbXTtd1LOWzXGVicw+cajc/QEscaTSZEpCkwUin1QA5tIoEJwE3Ah0qpV0VkPvCcUmp3AZmq0XiMjtlrNJlQSm10pVsas8u1dz1hPJr63pXF87129Bp/RffsNRqNphigY/YajUZTDNDOXqPRaIoB2tlrNBpNMUA7e41GoykGaGev0Wg0xQDt7DUajaYYoJ29RqPRFAO0s9doNJpiwP8Bz2IVCBnNMM8AAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y_hat_LDA = predict_LDA(X, params)\n", "plt.scatter(X[:, 0], X[:, 1], c=y_hat_LDA)\n", "\n", "bound_LDA = boundary_LDA(params)\n", "\n", "plt.plot(\n", " [bound_LDA[0][0], bound_LDA[1][0]], \n", " [bound_LDA[0][1], bound_LDA[1][1]]\n", ")\n", "plt.xlabel('Altura ($x_1$)')\n", "plt.ylabel('Peso ($x_2$)')\n", "plt.ylim([0, 20])\n", "plt.xlim([17, 42])\n", "plt.colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Regressão Logística" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "def fit_log_reg(X, y):\n", " N = X.shape[0]\n", " x = np.hstack((np.ones((N, 1)), X))\n", " def fun(beta):\n", " pred = np.clip(\n", " 1. / (1. + np.exp(-(x @ beta.T))), \n", " 1e-16,\n", " 1 - 1e-16\n", " )\n", " return -np.sum(y * np.log(pred) + (1 - y) * np.log(1 - pred))\n", " beta_0 = np.random.normal(size=X.shape[1]+1)\n", " beta = minimize(fun, beta_0).x\n", " return beta\n", "\n", "def predict_log_reg(X, beta):\n", " N = X.shape[0]\n", " x = np.hstack((np.ones((N, 1)), X))\n", " pred = 1. / (1. + np.exp(-(x @ beta.T)))\n", " return pred" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-1829.71197232, 55.89210549, 22.37151795])" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.seed(7)\n", "params_log_reg = fit_log_reg(X, (y + 1)/2)\n", "params_log_reg" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 16, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y_hat_log_reg = predict_log_reg(X, params_log_reg)\n", "plt.scatter(X[:, 0], X[:, 1], c=y_hat_log_reg)\n", "\n", "inter = params_log_reg[0]\n", "b1 = params_log_reg[1]\n", "b2 = params_log_reg[2]\n", "\n", "x1_ = (-1 * inter) / b1\n", "x2_ = (-1 * inter) / b2\n", "\n", "plt.plot([0, x1_], [x2_, 0])\n", "plt.xlabel('Altura ($x_1$)')\n", "plt.ylabel('Peso ($x_2$)')\n", "plt.ylim([0, 20])\n", "plt.xlim([17, 42])\n", "plt.colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Regressão Logística Regularizada" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-52.25448716] [[1.39914425 1.17444506]]\n" ] } ], "source": [ "lr_L2 = LogisticRegression(penalty='l2').fit(X, y) # sklearn faz L2 por padrão\n", "print(lr_L2.intercept_, lr_L2.coef_)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y_hat_lr_L2 = lr_L2.predict_proba(X)[:,1]\n", "\n", "plt.scatter(X[:, 0], X[:, 1], c=y_hat_lr_L2)\n", "\n", "inter_L2 = lr_L2.intercept_\n", "b1_L2 = lr_L2.coef_[0, 0]\n", "b2_L2 = lr_L2.coef_[0, 1]\n", "\n", "x1_L2 = (-1 * inter_L2) / b1_L2\n", "x2_L2 = (-1 * inter_L2) / b2_L2\n", "\n", "plt.plot([0, x1_L2], [x2_L2, 0])\n", "plt.xlabel('Altura ($x_1$)')\n", "plt.ylabel('Peso ($x_2$)')\n", "plt.ylim([0, 20])\n", "plt.xlim([17, 42])\n", "plt.colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Perceptron" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "def get_instance(X, y):\n", " i = 0\n", " while True:\n", " yield (X[i], y[i])\n", " i += 1" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [], "source": [ "def fit_perceptron(X, y):\n", " rho = 1\n", " N = X.shape[0]\n", " \n", " idx = np.arange(N) # embaralhando os dados\n", " np.random.shuffle(idx)\n", " \n", " x = np.hstack((np.ones((N, 1)), X[idx]))\n", " y_ = y[idx]\n", " \n", " beta = np.random.normal(size=X.shape[1]+1)\n", " repeat = True\n", " while repeat:\n", " n_misclassified = 0\n", " for i in range(N):\n", " value = x[i] @ beta \n", " if np.sign(y_[i]) != np.sign(value):\n", " beta += rho * y_[i] * x[i]\n", " n_misclassified += 1\n", " repeat = (n_misclassified > 0)\n", " return beta.reshape(1, -1)\n", "\n", "def predict_perceptron(X, beta):\n", " N = X.shape[0]\n", " x = np.hstack((np.ones((N, 1)), X))\n", " values = x @ beta.T\n", " return values" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[-2289.19440607, 36.70080277, 122.0765935 ]])" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.random.seed(7)\n", "params_per = fit_perceptron(X, y)\n", "params_per" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "y_hat_per = predict_perceptron(X, params_per)\n", "plt.scatter(X[:, 0], X[:, 1], c=y_hat_per.flatten())\n", "\n", "inter_per = params_per[0, 0]\n", "b1_per = params_per[0, 1]\n", "b2_per = params_per[0, 2]\n", "\n", "x1_per = (-1 * inter_per) / b1_per\n", "x2_per = (-1 * inter_per) / b2_per\n", "\n", "plt.plot([0, x1_per], [x2_per, 0])\n", "plt.xlabel('Altura ($x_1$)')\n", "plt.ylabel('Peso ($x_2$)')\n", "plt.ylim([0, 20])\n", "plt.xlim([17, 42])\n", "plt.colorbar()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Todas as fronteiras" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.scatter(dogs[:, 0], dogs[:, 1])\n", "plt.scatter(cats[:, 0], cats[:, 1])\n", "\n", "x1 = (-1 * lr.intercept_) / lr.coef_[0]\n", "x2 = (-1 * lr.intercept_) / lr.coef_[1]\n", "\n", "plt.plot([0, x1], [x2, 0], label='Regressão Linear')\n", "\n", "plt.plot(\n", " [bound_LDA[0][0], bound_LDA[1][0]], \n", " [bound_LDA[0][1], bound_LDA[1][1]],\n", " label='LDA'\n", ")\n", "plt.plot([0, x1_], [x2_, 0], label='Regressão Logística')\n", "plt.plot([0, x1_L2], [x2_L2, 0], label='Logística L2')\n", "plt.plot([0, x1_per], [x2_per, 0], label='Perceptron')\n", "plt.xlabel('Altura ($x_1$)')\n", "plt.ylabel('Peso ($x_2$)')\n", "plt.ylim([0, 20])\n", "plt.xlim([17, 42])\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 4 }