{ "cells": [ { "cell_type": "markdown", "id": "467ffb11", "metadata": {}, "source": [ "# Goal: To Show the Effect that Overfitting and Unfitting have on Variance and Bias" ] }, { "cell_type": "code", "execution_count": 1, "id": "74ccf009", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "%matplotlib inline \n", "import matplotlib.pyplot as plt\n", "from sklearn.model_selection import train_test_split\n", "from sklearn.linear_model import LinearRegression\n", "from sklearn.preprocessing import PolynomialFeatures" ] }, { "cell_type": "markdown", "id": "c6432b7c", "metadata": {}, "source": [ "The Sine function was chosen as the model which we would like to predict" ] }, { "cell_type": "code", "execution_count": 2, "id": "e4bebf48", "metadata": {}, "outputs": [], "source": [ "def f(x):\n", " return np.sin(2 * np.pi * x)" ] }, { "cell_type": "markdown", "id": "8ec48847", "metadata": {}, "source": [ "1 million points were generated around the Sine function. Then a random number generator was used to randomly select 50 points. A visual representation of this can be seen below in Fig 1.0 and Fig 1.1. \n", "\n", "Linear Regression was chosen as the predictor of the Sine function as this will clearly underfit the data. This predictor function f(x) was run for 1000 iterations each with newly selected test data of 50 points. The result of these 1000 liner predictions f(x) where x = {0,1,2....,999} are shown in Fig 1.2. " ] }, { "cell_type": "code", "execution_count": 3, "id": "5dabbbab", "metadata": {}, "outputs": [], "source": [ "np.random.seed(56)\n", "n_samples = 1000000\n", "x_plot = np.linspace(0, 1, 100)\n", "X = np.random.uniform(0, 1, size=n_samples)[:, np.newaxis] \n", "y = f(X) + np.random.normal(scale=0.3, size=n_samples)[:, np.newaxis] \n", "y_intercept_list = []\n", "slope_list = []\n", "g_x_list = []\n", "y_pred_list = []\n", "y_train_list = []\n", "\n", "for i in range(1000):\n", " X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.99995)\n", " model = LinearRegression().fit(X_train, y_train)\n", " y_intercept = model.intercept_[0]\n", " slope = model.coef_[0]\n", " y_intercept_list.append(y_intercept)\n", " slope_list.append(slope)\n", " g_x = slope * x_plot + y_intercept\n", " g_x_list.append(g_x)\n", " y_pred = model.predict(X_train)\n", " y_pred_list.append(y_pred)\n", " y_train_list.append(y_train)\n", " " ] }, { "cell_type": "code", "execution_count": 4, "id": "895c20ae", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_plot = np.linspace(0, 1, 100)\n", "ax = plt.gca()\n", "ax.plot(x_plot, f(x_plot), color='red')\n", "ax.scatter(X_train, y_train, s=10)\n", "ax.set_ylim((-2, 2))\n", "ax.set_xlim((0, 1))\n", "ax.set_ylabel('y')\n", "ax.set_xlabel('x')\n", "ax.set_title('Fig 1.0 - 50 randomly selected points')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 5, "id": "0a623fc5", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "x_plot = np.linspace(0, 1, 100)\n", "ax = plt.gca()\n", "ax.plot(x_plot, f(x_plot), color='red')\n", "ax.scatter(X_test, y_test, s=10)\n", "ax.set_ylim((-3, 3))\n", "ax.set_xlim((0, 1))\n", "ax.set_ylabel('y')\n", "ax.set_xlabel('x')\n", "ax.set_title('Fig 1.1- 1 million points to chosen test data from')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 6, "id": "c16c0d68", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = plt.gca()\n", "for i in g_x_list:\n", " ax.plot(x_plot,i, color='green')\n", " \n", "ax.scatter(X_train, y_train, s=10)\n", "ax.plot(x_plot, f(x_plot), color='red')\n", "\n", "\n", "ax.set_ylim((-2, 2))\n", "ax.set_xlim((0, 1))\n", "ax.set_ylabel('y')\n", "ax.set_xlabel('x')\n", "ax.set_title('Fig 1.2 1000 Linear Regression Predictor Models')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 7, "id": "dde72306", "metadata": {}, "outputs": [], "source": [ "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.99995)" ] }, { "cell_type": "markdown", "id": "34db5412", "metadata": {}, "source": [ "A polynomial of degree 10 was chosen as the preditor to overfit the data. The graph of these 1000 models are shown in Fig 1.3" ] }, { "cell_type": "code", "execution_count": 8, "id": "8d88eaf0", "metadata": {}, "outputs": [], "source": [ "y_intercept_polynomial_list = []\n", "coefs_polynomial_list = []\n", "g_x_polynomial_list = []\n", "y_pred_polynomial_list = []\n", "y_train_polynomial_list = []\n", "x_train_polynomial_list = []\n", "degree = 10\n", "\n", "for j in range(1000):\n", " X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.99995)\n", " x_ = PolynomialFeatures(degree, include_bias=False).fit_transform(X_train)\n", " model = LinearRegression().fit(x_, y_train)\n", " y_intercept = model.intercept_[0]\n", " coefs = model.coef_\n", " y_pred = model.predict(x_)\n", " y_intercept_polynomial_list.append(y_intercept)\n", " coefs_polynomial_list.append(coefs)\n", " y_pred_polynomial_list.append(y_pred)\n", " y_train_polynomial_list.append(y_train)\n", " x_train_polynomial_list.append(X_train)\n" ] }, { "cell_type": "code", "execution_count": 9, "id": "d31e3191", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from matplotlib import pyplot as plt\n", "\n", "def PolyCoefficients(x, coeffs, degree):\n", " y = 0\n", " for i in range(degree):\n", " y += coeffs[i]*x**i\n", " return y\n", "\n", "y_all_list = []\n", "for m in range(100):\n", " y_list = []\n", " for l in range(100):\n", " x_p = x_plot[l]\n", " y_values = PolyCoefficients(x_p, coefs_polynomial_list[m][0], degree)\n", " y_list.append(y_values)\n", " y_all_list.append(y_list)\n" ] }, { "cell_type": "code", "execution_count": 10, "id": "eb886610", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = plt.gca()\n", "for n in y_all_list:\n", " ax.plot(x_plot, n, color='green')\n", " \n", "ax.plot(x_plot, f(x_plot), color='red')\n", "ax.scatter(X_train, y_train, s=15, color='blue')\n", "\n", "ax.set_ylim((-5, 20))\n", "ax.set_xlim((0, 1))\n", "ax.set_ylabel('y')\n", "ax.set_xlabel('x')\n", "ax.set_title('Fig 1.3 1000 models of the polynomial predictor of degree 10')\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "fc4a1594", "metadata": {}, "source": [ "The sun squared error, the variance and the bias are computed below for the linear regression models and the polynomial of order 10 models. The results of which can be seen below." ] }, { "cell_type": "code", "execution_count": 11, "id": "3717931f", "metadata": {}, "outputs": [], "source": [ "SSE_list = []\n", "Variance_list = []\n", "Bias_list = []\n", "for i in range(1000):\n", " SSE = np.mean((np.mean(y_pred_list[i]) - y_train_list[i])** 2) \n", " Variance = np.var(y_pred_list[i]) \n", " Bias = SSE - Variance\n", " SSE_list.append(SSE)\n", " Variance_list.append(Variance)\n", " Bias_list.append(Bias)\n", " " ] }, { "cell_type": "code", "execution_count": 12, "id": "c89cb4f3", "metadata": {}, "outputs": [], "source": [ "SSE_polynomial_list = []\n", "Variance_polynomial_list = []\n", "Bias_polynomial_list = []\n", "for i in range(1000):\n", " SSE = np.mean((np.mean(y_pred_polynomial_list[i]) - y_train_polynomial_list[i])** 2) \n", " Variance = np.var(y_pred_polynomial_list[i]) \n", " Bias = SSE - Variance\n", " SSE_polynomial_list.append(SSE)\n", " Variance_polynomial_list.append(Variance)\n", " Bias_polynomial_list.append(Bias)" ] }, { "cell_type": "markdown", "id": "6f9c0d93", "metadata": {}, "source": [ "The bias measures the distortion of an estimate. The linear regression model is represented by the blue dots and the polynomial of order 10 is represented by the red dots.\n", "\n", "It is clear that a linear regression cannot capture the complexity of the Sine function and underfits the data. This gives it a high bias in comparision to the polynomial of order 10 which has little bias as it greatly overfits the data." ] }, { "cell_type": "code", "execution_count": 13, "id": "e0648d81", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The mean bias of the linear regression is 0.27586501344444864 \n", " while the mean bias of the polynomial of order 10 is 0.06967369931498046\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.title('Bias Comparision')\n", "plt.plot(Bias_list,'.', color='blue'); \n", "plt.plot(Bias_polynomial_list, '.',color='red', ); \n", "plt.xlabel(\"Iteration Number\")\n", "plt.ylabel(\"Bias\")\n", "\n", "print('The mean bias of the linear regression is ',np.mean(Bias_list), '\\n while the mean bias of the polynomial of order 10 is ', np.mean(Bias_polynomial_list))" ] }, { "cell_type": "markdown", "id": "44b39d65", "metadata": {}, "source": [ "It can also be seen that overfitting the data causes a high variance while underfitting the data causes a lower variance as seen below." ] }, { "cell_type": "code", "execution_count": 14, "id": "aaa72bb0", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The mean variance of the linear regression is 0.30599270842377924 \n", " while the mean variance of the polynomial of order 10 is 0.5058681103237923\n" ] }, { "data": { "image/png": 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4lvyiSD/4ZH4eePOb7b2AJTx8gEeRKx5o/p3DWmiyXB/RkYsqRtCbjMTxLfSqUrRGLEdt1nBw/eKY3J13Wr/KM58JXH55fC4Nox0NC1CVi0t9wMdItXU5qp3Wxph1dT372c82jaPTMWbLFmOKwv7tdPTvZ2aM2bXLmB07jCGyJ9oWhTGzs/6yZ2e79wLGjI93y3e/F0VaWby+s7O95VRBnXc2jdQ28PvkeMzN9ZYxaL8MAu3dVesTmoejapdWt7Gx7nwG0tdCk+3w9dVqFdfw+3vKHdJYA9hvPHR15IS96jUURmCMPgCcYLZaloi3Wr2LYHIyPGhzc733z8z0v7fKhGpiAg5rEvPyQ5M59f3yvna7fzyG1YZRYS0QfQ18Lcir1ao3DoO0ta4w43mnK+5kdMyFNGv2tCN1WgvCVEWEGEE2DTlopg2uzhJVP9QcsCYHdxpRqwUceWT/e6vY15uwtUqziFP3mzDtpJi6Utuwd2/32MmFBfudNh4PP2zvXS/O+xBW05ZdpQ/kWnCmTgB429vsvK66b2MQ82QdU1PgnTt3AqcW8/jI0gswYRZA100AZwXqtFZMdk3BxyHW6jU0jcAHJ0HMzVmJx2kErdbqSfCx8upKVsPQDFIkpZT3djrGTEz0a158PLTfZRlavwxTI1otib7Ke3xmq6p9wMuZm7Nm0rm5evXn84TIantVUbWvI3PzvvasWaIKUr58/1rV5kogm4YaAidCVQZ80EXjq4dmN68yCYeh3lYx+4T6MIVQtNt++3SoHsNS6wcZi6qEPfU9vnuHadpIaYuP0dcpq0q9Qv026PgNwlhXASNjBABeBOAuAHcDuMBzz04AdwD4AoCPx8ocKSNIRVOEOgWDLOi17PBK1RrqEPthtXsQu7XTNsfG4gJDqtY1O9vrV+H31u2Dpvw/xoQZuTG2H5xfrqlxSql/nblbdeyHTRcUjIQRACgA3APgqQAmAHwOwPHiniMBfBHAtvLzj8fKXfOMIOTgHIZTadAJVWdhdDq2Xe32yvdDEW5SNKm65p86FW6SCHLMzvYGIcjIsqrv4b9PTFhp2/3PxqxyH6S0rwpBDJXX6fRGJ7Vaa9shW3XsR+BsHhUjmAJwI/u8G8Bucc+bAPyPKuU2zgiapmBygNvtZkwlIQxLxdQmt6LSH5jrNC/cNCExraZZYZB31iF6ofdoc7Dd7jKEuhpAU/6flHZozJGbZOswsWGbYYZl3msIo2IErwBwDfv8GgBXiHsuA/AeAPsA3AbgLE9Z5wLYD2D/tm3bmuuZYQyGj3gOQ5IcNjQ7vdwXAZjbtrebF25k6O6uXXEpeZgLfdj7PZo0g2jzKWaG0ertAiT4vo1hCzXuece4nLlsZkbXckYRsFEXsl9WgzkxjIoRvFJhBJeLe64A8A8AfgzA4wB8BcBPhcptVCNIWRzDMCFIVLH5ruYk7nQsceIOPRmtA5il8Ulz2kRnOBpBSpTWamgPdSTdUToPeVmKFpfUzrGxbv+7edlUHVNMetyUxTUEonSmZkzcX9QEcQ49xxnbsEy4CVjLpqELAFzCPr8fwCtD5TbGCObmejfI+MIPV0OSqGLzXU2JptPp7SNnspibM+boo7vfF4W5rz3bPJ/qdKwmIImRxKD21ipmH+Eb8UIzz4QIxWppM7FQTamJpW7aa8os4htLuTFzbCxdM/FpMrIeqRqPbG+oPe43rkWPKKhjVIxgDMC9AJ7CnMVPF/ccB+Dm8t5HAvg8gJ8NldsII5A2WW1xpBKhuu/XHLC+0NSmHEsh56tWJ5+d1iepD4OgpSyCQRdKav9qhMMn1XIJMGTKWGvaTGob65ZvTHpEl9QIJDENMeSUdkimd+yxaetdlh0KCOHvcLRGOu1jqGLWC2CU4aOnA/jHMnroovK7NoA2u+e/lZFDnwdwfqzMRhhBLEqjilmiKlKkB/kbtx9XnUQOUqLizEB7LydmPKzRZ7vnfZYSAin7ZNCQvkGYUCohS5GWNULWbvfOJR+hGLY2U0Vib9K0qZlfQnWemzNm+/be/p2b63eoh7SsKo5tbnJyZYfWWZWAEDkfpqer+zdSzXoR5A1lEp2O7VA3+DL/j1Sljz22+mYw32LiTCiFKPDJWhT18ut0OrYNnBEce2z3eVknPrG1kENt0oeYa8x+OmyzV1OMhNdVs58bo49hVSZcpU3DDk9OrUtV4cbX307okdL/9LQxxx1n+9wJG0XhF9KqMEiu+bdalgmFiLXm2I/N8VDkVejZKma9CDIjkJCmofFxndjV1QhCk7AqUZAToaqK6MoUkT6GqPsOWafp6WoSnmsXZwSOycUWZNXoIF8bh8FotHLdd6l2Z3e/j/nH6u+rF2dIIYJYF1XrNDNjhYuQUBWbs3Jdunkqv9uxQ/dd1W2D1GZD81/eOzPjN+mG3pXql2hQUMqMgMNJACHC6Mwi27fX8xGEJn8VosDNMzFbs68MyUge+9h+ZhLSCKpEyHDVWmNkPqZSlenKPkplNFXGMGUB+ghNVVNIVUi7s3Oe1k1hEqpviikyVbiJlSW1Smd22b69t3xuy9dMu6G2hdrAza++daaZB+vkHwtpCPK+qiltPMiMwEESHXlJe1+deGUuLWr28ioqq7aAYhM7JnFoEohWpyoSYUiqTzENSPW8KUedu39y0jIpbl+V7x+Wg57XIzXiKKUc1yY+d10dq4xdTAuVQpKGXbt619GuXf46xxirEyhara52oaVyT/FHVWHAmt3fx+Q186A2DikIrY+GTaYhRrC50lDL4wxPOgl44hOBj360e9oY0E2RDABveAOwbVs8xa48jvItbwHe/W77+fzzgRNO6KYYTkk7zVM1A7YO/GSjWBu109bc+044of/9N99sUzk7yBOpQu8MnQ6mtVc7GvSRj7TpjVPPGnbtA3pPjrv/fls+r68xvX/5+4uim1aZpybmR1kS2XTddeBSPW/d2j19as+etLTLofOLiwI444zeueuOIK2S3jl0KppLAW5MOF34y18O3HRT72cOdz7v4mI49fjUlJ0Lbh1dfjkwPQ2ce679/frrbdnnnmu/b/J4TDmHzzpLv1emcD///PRzsjX46MFqH+3p4xBr9WpEI4hJp1U5sbRtOql4ECdPXYlA2jBTzQVSA6kT3VBXg+DSZ1HEcwuFIpzk95qmkeJ36XS6tuK69nef9BjTeHw+iBRHY1VNJrQmqmyCcpE+09NhaT9WVpOaWNU1VGUOy2caMt/0lLuKGsHICXvVqxEfQdOhiO12r3ro4u1DYV9V6lEn7XXVdAWa3TlV3a3aX5JAchMHURrxiplynImPhwY6xiiZHid2c3Nx00tqmzV7coppxMc4Ukx4dQWZlIiXWBl1fSpVy6mCJtpWtdw6z2nfN8xkMiNoGlKD4AS/1epKtL6NIFUme52FUUeq4vZZnxN90PppdvmUA2ZSIOvBfQfO5uwL95NSeKwPUgiydp+2oPlzKYwjRXsdhMDVRdOS/LDrP4jGLTWlVELtE9BCdWmQMYYYwebyEdQFt9UCvTbYs8/uPbaPyNrgAWtndHZhbr/22f+0owOr2grn54HPfMb+n2qzdO+97DLg9tuB666zbSoK4JxzbDsA4NJL+22yqfVztutDh2y93vMeYPdu+9sJJ3T9E5ptltvZDx7U7cLS1gp0+57I2nCXl7t13L27t4ypKdu+hYWuL4EIGB/v9oFvTPbu7b6L2+W1Ojmfi2vXzp3A4cP2PZdf3munvuyy/vbyoyxdfVfLjqyBj01TRzfK4zqHcaxoHRv8/DzwH/6DncMOhw5Zn8byst8nMz9v58j73tf1+R061H1nqC7yuNZhjbGPQ6zVa9U0Ap+tVkaptNvhFMI+CSIlcsc9X0XiltqJz2broO1alhJOExKLFhrok6Rlm1LDSzUzSSjmXz7H7wuFOkrTUkqYsRsbl2LAzQuuefB0CqkmndR55OujWB9WeX/TdnLtHU2VHZvTWjvkeLnx9o09X/tSy3SWA40+8Pnb0K5iY8IawcgJe9WrNiOoO8GlrVaLsY/Z5Ad18qXaVmP7I7Rn5GYdF5PuNspIk4UWphjKucPNGNIHMT0dX+Sa7yK04KoSwLrEjKdBSGFSGtHXvqsKmT+KM1xNKAn1d1XfUuhdTaHpMF4OTXAIzSONEfjmsM/Uytel79AgV6/p6e7zA+4qNiYzgupSRcxW67MHa9JoipRWp47as6H9EdoCmp31T1RO2DSJOkY0tPZMT/eWv317nEFKqchJRo5ga3b9KgSjKX8KUXhXtE/6L6XFpfFJs6fdqSbwaX0c2twVEzaqHo6jvStVaBlE6xkGtDGN9ZGT0LlA5Bg8txxwws+1Ry1izbeWB9QGjAkzgs3hI6hqD5QxxdJWOz/f/wy3a2qx3Jdd1o2D5vdx26e0J2s2+VD7QvsjNJvtzp3WD8B9HBzLy9aWKfciAMCb39x9jts7ZZ14n8/M2Dq5fnnd64A77+x+3rrV2mDd51tusWWefjrwwQ92y37uc238Nrf/G2bX5+2N2ZflWKfYtrnd1sGYbvw8Hzf3/hNPtPtLZJz6Lbfga3v34exrd+Lv3zeFicQtBn19/PDDtl7bttk54ObCwYNpdvx9++wzDkUR74uDB3vfdfvt3XFx896V7dtDcvPNdg7wPQIcqftuUhCaC64vtXnEn/vEJ/z+rJ07u3tbxse7fTM2Zue687Vpe1icD3Hv3u5adiACXvvavI+AX41rBE4dlPbgOqYEp6bLXCWaOSnV7p6yxd9XltRKtPZwyd7lrZGagYzrl/Z+bYu/r5+41CTr5TOVyO+lVOU0ttQEeXKMq9i2NQ3FSdBynLVd3cp7als/ZF2Kovckr1AdfH6g0P4TTVsL+Uq0eS8bK7XEumkyQvWUdY1psNJME+sXY3Ttuih6fULuPXL+a2lktLDnAYFNbxoyxj85qjpj+ETmYYnS1s7NSTKU0W1f961+aRePhXD62sd/C4U7cjuz9DX48iGlLA5OaPkik6mtHXyMgJlQzOSkJXb8vmc+U2eW0sQnU19oqSdikGNTFP5AAr6pMEDhB7J+yD5zAQLc8ayZ36qGnYae4enK3XydnNTTf8hytDxCPoY9iCkphdtq75FCDw8Pl89KpiydyD5zqqybYxQuuV5DCQUzI/BBcvHUzUwhezyXWn17DZyNO7awBjnViNdX7q6N5VNK9WmkLE75fk1qcpFK7XY3BfHEhCX4nEFxH4IsJ3TCnObMreuo1TQdt3BljikpnQcIXBVa11eG1OJkZllJfGJE0UcQUwUXoDt+Uip2fe+YlWTq7tmqWp37vom9O7xsaev3acD8ftcu3u/aeQq+ug3q9/IgMwIf6mgE7jkZoSMZg5QatAkaU7WrpnlwZUgntSSEMhrBt3Cqmk20usj3T0zo5if+u0YgeH/KlNchJq4xwtnZwSJ2tD52YyalOM0EkxLSKt8TgjSvuP7YsaPLWLn2FSKKIck/9owUqvjn0Ol2MzPGHHWUPh4xB7ckoIPs5veNq9z9HnOkaxpzyJwqzUV1LAIJyIwgBM1mF7Oru+fkYMeOgowt/JQwU1mmj5FIU4UzjcjFMj4+vGMUOfPjUTXa4SNS8vFltNSIToyJa+1wQoC04VaFJg1rUhzX9Bxx4VqSdlRqqp9ICjQ+Jsvnk4/BxwhvaC5KE5FkTJwhyz4KmQV9c1CaaXkUWtVwy9Dacb6MlNBan+Ch0Qtf+6qMfQVkRiDhm9ByAGLSeIjwV3mv9v4Un0DMERdz1rnF4qvXIDHcnU6/30Sm45aEI6YRyEXWatnFn7JQtDZWtcf4ytAYE9ArIEjGJ5PtSUZWVSp0/Xn88XpduEQe00JS/D+hPpJM3M0fOaacqPpCUbkZSVuvjAEuFePmcDFpllsVCahGvH37hULr3Y2z1j73nlSTW9W5mYDMCDiqSBih08Ca4tqaVO9jUvz7VCdgSGtIkTRD5oDQRNXs+Fofcvt6zEfgs/cPG1Ka1/qC1905kN3/mhlLM9FxCVaT8vk9mibL+4eX6yTa2NkNrtwmsq5KIcARV14/7rznphMXgeUz8/C5x7TOBRTmSrTN1UXbLI0nmlQ98+rAXMfsaXfMfe3ZXi02tG9GO11Nntjme39drbsCMiPgkBPOZ3OMaQTS5lfHjpdCuEP3VY38cJib6z3/NUTkQ/WJhRr6Nt84KU/2b8huH4oAGiY0id8nGDgHv2MCPnMRJ94hm7YvpcHMTP9zPjOgNEeFCLzW1ro7WqUfhyi8k1wzzcg+dGmulXQti1SYH2KLORkdcyHNmiUk7nhW5tWBuc5KVU6b6JhvTAuHsVampAfaePuQsmYb0BBGxggAvAjAXQDuBnCB8vtOAN8HcEd5/XaszIEZQWjnpTFxIugrR0rmKYMmNRDfQmlSfdQkzVAEg8YguGTnzA4aUZmc7NbZSfW+GHzNTrx9u67JrJYmYEy6iYYTLsdgNVMRT90hn/M5Q7U8NRqxjs0dXg9uo+ZzVvN3yB20qX0/N9dv/goFH8i1F/N7sPV2X3vWnDbRMUVhzBvH5sxylTUu+s11w8nomB9ii1mC6P/QvhmfADDIzuCG5n6IEQxtZzERFQDeA+A/AngQwK1E9NfGmC+KWz9pjHnpsOrRB7kb8uDB3t9l5kPfbr7bb+/97HYibt2afkKU29m7tGSny4c+ZP/yLJmA3XE4Vg6Vtvv1zjvTd17u22ezXXLwXaR8t+qhQ/a0sUsusb+57KFEvc8vLek7i/mO5YMH9XcDtr1bt9o6XHddN7vj/v32na4P6+wwrZO5kj8jTyp72cvsDmmZHfPaa+3YAXZX6Vvf2j2hbmzMZjA98cT+nbc8Q60cW9fmd70L+Ku/6pZvjJ27LpPlxIQt24HveJWnjbnn3Y5jeVKc23kMdHdsLy76M6yG+vrcc+06mZvrlnPwYDfrrIRce/v22fd+9rPArbd26w/YsXC7cQE8+crduPzEeRy8/lKc8PBnQJ+kbj/xNa7tbBa75l99/6W4sdiJU5b3YcIsoAX2XgB41av6T+7j8/N737Njz+f6oUO2Lb4swxL8ntU4rczHIQa9AEwBuJF93g1gt7hnJ4APVyl3qD6ClGddxAU3e4yPhzfw+MoRNs6+vEahbJiaTTgl+kVKWk5al/0jbfFSC3DOziq5hmIagesP7vCs6qTmCOV/j0WDSSdhalJBaceP+XW0+zSJlc8RNzfk/gXfnJaSuZuvvg1fWnhrzL8QMlUOKs3KeTM+7jURRXP0JIajLk5uMf9nes4sTno0spj/ZG6u/zk3VlpIb6gvU5z8CcCIcg0dBeAB9vlBAM9V7psios8B+AaAtxljviBvIKJzAZwLANu2batfI553X+Z5j3Fpnjve5bdZacEUcOWV3c++fC4uL7nL9++ksEc8Qs9rxCUB2/j+nPiuHsZ0c+PHpIVzzgEeegh4whP0/P9nn22lsP37u9oJ0NWkHPh5zgDwxjfav65MfrYrl2727rXv57mQnCblzn91GBurl9t+fl7PhwTo+YwcNOkL6D/PQOaYkefdAv0Sru8c5FCeqrPP7ubAabWAF76w90xoIHwuwfy8zePDpemlJSult1r2Mz+3gtfFnW29dauV7ENaqU+TbCJXkMvZ73L8nHiibdPhw3ZMHn4YeP/703L0hM6iZjmkCizg9O0HgZmbu2vWvc+9Q8ux5XDwoC3f9XtR2HrzObm42F0zPMeSnIO3327nAeA/S3lQ+DjEoBeAVwK4hn1+DYDLxT1HAHhU+f/pAL4SK3egFBM+riq5tLTjGqM77rhULW3pMuwt5HT0haXF7PWaTTLk2PNJ6b7NUdKZOzOjS0Mhp2eKz8Fnn67rqOx0+jf8ufBJmdIgFL8fc8zL51Ls5zzEsNXqjyqJhQD7TjkLSeNcu9N8AD6fgSzDRR+FNKlBorpS/HPyPXx8ZSgyHz8eYaVpeKE57N6rzKkDcx192Hk9fZvKfD6H2DqsCQziLAbwEwDeD+Cj5efjAbwu4bmoaUh55j4AjwvdU5sRhNRyLSe/nMiSEYR2GmqTSktLG1P75AR23/HFwsMWuYkqpQ/kJhmp/rucSJKRSQImQ0X5Ll8t2idEzGS+mpSJrzEzmbTLpXuQ4zw93V8XyZi1cahSJzkGknlrpjmNWXvmSqdjzJ52Gd3C66j1/Y4duiDj2/Qk6+tzlHKBRm6mSu0vznB85ztLMxxvg5uvfH51Or2x/ePj+kFCUhDhgQpaHcfGzN0zc2H5wMdUNVOTZmpzARQxU3MiBmUEHwXwKgCfKz+PAbgz4bkxAPcCeAqACQCfA/B0cc8TAFD5/3YA97vPvqtxjcDHpTWGIROf+Wx9GmGU+X1iPoVUWzXXPmKSg5Q0ZEicL/JE6ye5RZ5v7OG59TXC7CP0krGl+jx8tmweZqppHEURz7OUmEE0aa653+R843WUhD/kY2i3V6JlTmnZCJflVkST0QQa32/j4/2bwLT9DnxdzM3VT+bnC7+sG+JtTFiTl+soptEIgWB21phTWh1zAWbNKa1OGo12YytzEfn6KUUbTcSgjODW8u/t7Ls7Ys+V950O4B8B3APgovK7NoB2+f95AL5QMol/APC8WJkDOYs1Kc11tDZRfIQqpGK6+zQ1M/R+GZOvmQjGxlbC4pYl4eb5UEKx01zS0Ai7T/oVmtMSyEqgom++Od1eCeNb6RKnVmsLXZpmqjrbY1qOlMY4Q3LObp9kWBS9GUSlM1/T0lLaIImrlpzOpxkIIrhUxs+/F21zGImOaEeouQYpHcqckYbSeUhCOz3tT90hGZyU3H2n5cmkg77/NfgYAZHNdCq1MZ9Go4zHgTnLfA/DjsGBuYpEWhsbnzlswD0ExgzOCPYB2Args+XnkwF8PPbcsK7GGYH7XtsWPz3df59P+pTpGmTe/RB8kr541zLZCboMmEMYN9+cFu8vf1sGzN0zc73v8KmpKblPWD2XWsXKO36ESTv5WZtv2WWloz4a6GO4KTZ6Xv9Qhs9Qims+zlzq006f0zQC5xvhzNaZj+r4FLj5SYs6ikUYsbnndtSqGoFvvkuBRhJ7R8hdEj2flK7t/QhpuFIzlGkm5NkYLu1IXTs5F8rceEuzYcw0Z4w+HrOztr8B+3d2th7NduMho6AaIP4cgzKCZwH4FOzGr0+VEv4zYs8N6xqKs9j9Lid8TFqV2+BDCdxCSAk/7HTMwvgWcxgts4DC/CWmzf+ZZkRobMwslxtfDqNlLh6b7b4+Rlx5PSPS7G3b22YR3S39t21v99g9l4nMjzBhrqS2ef5Yx7TbxjILzhxjph9ZL0kgNCdwux0+RN4tNi3sUNPStPdzs1b5d4mou3kpJInLeki/j5amPGRiYWO6OLnF7Gl3uv0cYkaS6ExM9GtqrVZXs+Lf+bQhrgH4fF6aaU7rN8cg+eFOsXQvMUgNQgskCI2/6G/VnMR8Bqe0Oubisdk0DcGVIX2OPh/JABiIEdjnMQbg6QB+FsB4yjPDugZyFnNJQItGcepxwuLrsavGUjpLaCqyRgjEZDww1zFXF23zI0yawyjM4vhENzJpbm6FURzCmDmX5syedr/0GI3E8U34si53z8yZQxg3h9EyP8QWq5UIQrJcmo5+iC3mXJpLl1R99eEmA+es5p/djmyffVcS2phTXUI6XY89tk8DW4b1jQSZrEbwuYmFzx0nZFRhmL46S2ew9F9pmrDPz5ViuggR0pBGwOdeTCMYxFwi51QsDUWov5mQsjDene+HUZiF8QQirjFIrnmSNcE2oRwMqhG8GcCR7PNjALwp9tywrtqMQKaECB0uEep1n4kl5LySEomQoBfGt5h/2jHt31jW6R5c8unpWbNEbOIwZx8n0j/CRDfx1sREr3QXc+Jp9WXtW6aWWWxZCahvUbFrAYX5KHb12K7va89Wm9Sak9qFsWrETCYzc2VIglclV1Gn0+8QZf4aA5glwGpHck5IqZjVY5lHV8lnqjBvX51lHSTRcaYRn6+ozlkdsTr5fASufyRR9PkIpBaSYmvn4FpmKPlirCxW5+VWYW5qdee7MxcFy5DMTxGqfoRJc0qrY06bYEnwamBQRnCH8t3tseeGdQ2kEfhCHKvAJ+34nFfS/s+ctI6QHEbLXF207S5GOSFK4unmymkTnf7djkxac0yiJz9KUVizibRvp0woabbSNB5uOikKY8bHzXKr6NMIFie39DuSU/pb+jI6Hb+ZAdB9A1p+pdRKSMLT6fj9JbLPhLlocXxCf8a9RxI7PoZVM9zGhBZnJvPtEXAab10imXJvQEjyatbSL1EUKyayld3AKZPMtW+Q8zjEPXfPWM18RQOucgCRFtpbClTvLX1AS1TfXDQoIzjAQzoBFAC+EHtuWNdAPoJBJZyUiSHv1yJ9mAS9XDKCHlOOsA/vaXd66Mqedqdra2ftuXvGqaWtFWKz0lbf6VApbUgJ11OYodts42zXsh3JfFgSEaklSALvizSK+RF8CBD2b0y3zW3b2/0E3RNyuqfdMVeibd6Ldm/IoSYtH3dcb9t4qGddIsz/j/iDomWGQmR9DEiL5JImnxBxNsYbCXQYLfM3QgONtem+NtOwpY8ndU+E1t6qfawJN0WxIlBdSZ6osAoIMYKUFBM3AvgzIroKgCnDP/8m4bm1BblNvc5WbV/6Ad/2+X37YBaXQLAdd3i5wANHnIh//9KXAh/6EEyZOoJg8G5zPm464mZcit14KeZxgmW6wNISdj20F6cWwN9jChMTwNPOYmkAWEKvB+44iLNbN+O3li/BC/ExjKHcCv9zP2fTBdx8s932/7GP9adL8KXYkCkCfO1VkvWdAOAEAJgHsM/usPdl3+iBrIu75udtOoWtW4HJyW4iNbeVv9Wy32sF8zJ4CoeU9BWB1BA/ecMUflJ7F0+vwRLNnXjZzXjulitXXv97O9Gtk0yvIWFMN41ILAEc70uZZI0nfUsaEAW+RGja+3z3at/v3m1/O+ssfZ7Nz9u/4+M2RUOZfM8AKLCMb+HxWMAEiBZQRNo0Pw/svnYnPmImMI4FtMYmUOzc2T8eROFUJzzti/vM6+xLaSH70615wKakeO97QQcP4p6tO/HI2wG6bg+wWGOsUuDjEO4C0ALwRgB/AeB6AL8GoIg9N6yriRPKqghTfQ9qoYUeyeXumbkeZ+JenGkdSE66Pv74lUifpVZhLh6bNUVhzMVj3bA0Jwm6yJCVVyiSk8ujvrK5iDzb7SuGO9buL6XPvFvyfX3skx6lndlnd/a9w2fK8yHlYBKtHEUi7Ls1FFGjmbOq7DaNSaSeescsoKrJzve+lDFV7PR9ddDuZ0725dKMckNr2gYxhEK4O52VUOfXY878DXaZdx83Z2/TxiO0uTFmKYjNHV6GL/Q5MFapQD6Ypouq1p2eByWhCSyyA3Od0nHUDem8qbWrS+BF3pfDxeRK/P25NGcWW+N+W2lgAblqHZgLqLaaqcXTjsr9VaFs9TkfkUspx9cvIft0qnkj9P5YObGwZcfQfTtrXdZKzYHvq/fcnLmvPVvNZh6o8oE5GxJ5SqvTLcY57aXJKhSqrDl2FVOQWoyPyQhT67Lz5fgCJMrCl1uF+REmVqLwfgjrwzow10nzVTjE5ib/PeSfG5DQxzAQIwBwCoC/hd0/cC+ArwK4N/bcsK5BGUEts2gVG2f5vQvldD6AH7WsI2nl/qLoCxHrk+ZLx6safZISUcIm/MK4svORL04PYanUXzW0jb7nQpFXsXK0qJiQXyNg+6/UjppSt8q4QqlL+HO+3d+lVLkMmMUyxPeNY3OVok1kc/a03Xy2xPKUlvV1eEMwY/ULzeey/9Qu9T1/5pldJsDHXvpXFKFimWglsGIBhbmQZrvvivkqHGISv9yHUjVQoSHmMCgj+DKAFwP4cdgdxlsBbI09N6yrCY3gtAl7nN1pE51g/7oxuK8dkQYVTcFJ/k4TWCHCboIp0kqnY8wtu5hZqChsJIeWAE2TdpRJc8NMx1xFbXMl2r3tlYvKY1KppBGECGtoMsvnUuPVtQGTklxob0cFwhR8f1W1Kab9hNqZyJAcQVxAYXbTbOVoWf6K+9rdObkAa8K8rz0bzj2lMVK5q9tVSiGkvIiesEmtb3bt6gZkwIbyHi4mohqBY8BL45NmgWkEPf2UOudCu9nd79rO9BgBqmW+0DEoI/h07J7VvJo4mGZx0oZhLU76bb0H5jorDOONYxH1WiOqIUlcSq6+IxmlNMsTVXGNwhFPMWk6HWNOLXrzoexpR4id3mX+tcB/rDBxe8pscsJLSU72YUrMeWxxRxsUua+cG4dbY5bAVpEQU0xUra4m6s7xrZoVWhufnvkc6iONsbt7ubTON4spqU6STVtzvb64W7DDnFqUJp6Aj4DP2/vas70+uGCHRMaD3yvMQkvFuFksLQXRQallvvAjxAhSooZuIaLfA/CXAA4xJ/NnB/JSjwr79qFYXLByw6I4xOPqq4HzzgOWlnAcjeFvlghjWMTiYoG7n3Y6fvo0z0EuMvrh4EHg5ptB+/ZhfOdOnCDv51Eoy8v+Ixnvvx943/u6h338/u93o0pcJMPysi0L6DsY5CtPvQTPX96HCSxgDEswWMBp2Adgqv8wFS0KoYzemdq5E1O7PYf1+I79c4fRAH391f/YFKYGPbzEwUVs8KgTQI3gWelv+b6pKXtA0JveZPvz13/dRl2x+/qCrLRyNOzbB3NoAbS8hAKAAWCKMbQuuyzt+dC4TU3hzstuxsHr94EevxX//JWD+NAPduIzd015z9Txobc5U33z+c6r53H4hLPxxCcCT5gRa0LWEegeGtNqAU99KnDvvfazO87RlNFf7AjNJy8s4MnuEChfA+bn8bXbD+KbTzsTz/nKBwAYbMetWF4GPnxwCjgROPz+vXjiQ3vxhBff2XsgFSvnyVNTOIuVuTJfDh70z5uyrUtjE8DyAjA2gUIeVcuO/1wam8Bbli7DGbgeL8THUMQGJWWNNgUfh3AXgFuU6+9izw3rGtpRlZ1Or9OJaCWnjpU0yM+960i0UlX22ZZduTLHjjMbyYNvmOq9OGntwz/EFrOAwhyWW96rmCA009HsbK+qH7Kxm97HGhR00hGT3jhkrDrzwwykwHQ65nAx0WPPXqKKKQ4iZjw+JLF8bamKDIdMM3LDjBIJ5tEU+zZ9aRWUzlVf3p1Suz+Mwiyg6LH1Xzw2a26Y6ZgfYaJHW4hGfWn7bcQGTxlMwU3N35xu95siy7LdPpqTYbX0xZTNYXUGyAPkqCEBbUFxolYO4lIx3uuASknvXGXAUiiKNkF9TmSFuTj1+rvbd6WZOBxSFqNM2xEKIazY7KHAY8JTK6IxAragK+ehZ/jmdNssMpv24dZ4bxbXmsKGtDimuFwqj0OnYxZb3U2Sh9EyF7Vm42WU5he3s5zb/Q/Mdcxt220Kc9XE6AsJnu1uBuPE/nAxuVLmEusMNTmg7AglzUOIGfE+P6VlmbzqlxCvGTRdRB0MzAgAvATADIDfdlfKc8O4GmMEWtpXafPUDupoeuAiUp56byiOvAqxU4pe+dm3OPj7fBpBQh6XPht0KhOtwXC974rZ2z1ZNRfHe0MOvWkiAhVanNxiFssEge/AjLm6aNvcUD6/RIIapWkEjZugZ2f70qE/j5S044nvcxK182Ot+O0q9SP1OIvN9u3GzM31pPNYubRO4fPYndPAP3uSQPI+Lwqx/8cTzdeggF8ZAzECAFcB2At7EP3vALgTwPtjzw3raso0tKylD5ajxFdWqtOwDlI2nChtSNL3KxAQb4SGj5lo9eB95tNcfC+Pxf7XEGGDj9TtRyIbqw6WWKxq/Tp2Q5PLxcSJmSp0JJZdVa6oLKG69QMyS9Qyn901E69WWSm34VFagS6k2ZX0CYtU0VbYsWk+DheTPRsol4oxa3Kz3kDzadpuzqU5PT201GxnZlYi85aJzEJrwrxz2u9Idu1Y2X+w6qpuGgZlBAfE30cBuCn23LCugRkBC+20sdakRw85OO0hIeFXLW7f6fSnWdbCymQ9Ii+rMjkdjXO2SzWxle998ntBMKNpuXn6ZfeMz7CdYHLS3Bhcdb9ll8JcKkT7rGhIhRLt46uf5x3dTYe9SQi980ATVLgdvoao2enYfQK+yBy1WCG4BHeLCwYm7+UawQI8kXyJbfju9l0rkrxNxz5uFlCYhZY9H+P1mDMX0mw3cs5B02xne0NmL8BsWnqyUYr8EQzKCD5d/v0HAE8EMAngK7HnhnU1oREsjNtJ5w5Q6ZsY4v5USayWMMAm4Yr6Sr3x1HvaNmullBZDtJkrMjfM+Cen4y+Tk72SWSUvriRIvvBXraIyK2iIgQQ62feT2xErs6B6QwVDC5l3lqYlBjSkvlBi9z21uiYLx2BiG494PVL6OQYPA/N2tzw7QcwTd7bMDTOdpMRtbo7XsZlLrWZx0jphf4gt5vWYM1eibRZakyubOxdBZqnoHzf3HDdNOTrhQnBrJSxeQ4xhUEZwMYAjAbwcwEMAvgng7bHnhnU14SNQt8uX6Bu3RENq7UgYRhAOo9WNVGp1009fSLMr37vrm+VOZG3tS7936OgFTrPfOe2XDGP17yN+TnsJ2SiEdmaKIk7YPAtLSv63be+eRrbcKqyDszQVuB2kSaaikMbji/QS98vNWJ2OKIdvLuoEiCdnAKmb5lLGryxTMiu1qZJ5CzHZWVlWtEswW3soX49SrRT6KevoGIpzSnO7vc/05rQSucn0wFzHXFTMmpPR0Zoar2xt6XA4aCxqqNQGHl3lmaavRpzFRphOykFUx23YGkH5MLcXL5SnG/FwswUUPRP5tu3tvgXA25FyAJO60PlZur5Ok1xH8wAmdIY7/NtJXXfPMKZRUZJyrzyl1Q0Z1CI/nLR4Mjr9NFO2RdmkV3mghWTpoowOzHV689ZLZud7r+9sYa4dpJ5bwN6zOD5hbmhNmyupvZJvhxPUlSrKE/mEQ9Qd/X0BmHbpYRpadUIuqUgT+txXPaZRLRKoHPxYzIB2suhK2Z40FAfmOuaeY3f1Jn70mXw1X9gQtIhajADAz5d/f0G7fM8N+2rEWSzMGE4Seue0J19+4sAkjamnLE7Iri5sKB13rr1xzB6E4hY+/23lsBo2GW+Y6ZiLWrPmedSv9ch3useC/gSfQ1tbiYnqkTc3f010OsbcsH2291AeR7DKCKpvTLfNXKttptDpp0tSRfKdXcApVoLfxGmgz6OOGRuzvkg31t6zbUOaCGcA3GeUmhvHlc80j8XSpn64NJkeLmw5PWa0iDZgjKIRhBK3sTbyrg+E7at9E12e7ga+M5/1T5S3K/VcyQkmD4CatfsXes4F8Zn65HxzGvSQtIi6jOB3y7/XKde1vudEGS8CcBeAuwFcELjvOQCWALwiVuZAjECOeLvdo7ZfVMwOZGqNve7uGQ8xZfdLx12Pc01ZAM5JthLS1+pKst4UFww9CkDI2RlSMeRK9Em04h63GUjN8eIrO9Lfp030biLqOZ9YvPP5Y8o7OUENxWGGRFHle85HY4RObbKQ3vsOwzGm19TW8jPgFQGI+SeWijGzCMcUulFRPRWUgQCeZIc9PgIfcxL9xA8tCu0hS9LIQnNGm6uzs36Ht6eeVuMRWsak3b9wYaurDR1Gyxx87LHx8GvXp77J0YCWUNs0BHsWwatC9wSeLQDcA+CpACYAfA7A8Z77/g7AR4bOCBTVX6rtvs03K0gZkPIePrlPadmNOLXsNT5Vw9l2qTe3zDen0/LVJ2sEvv0Uob7gHCaiNSyS9YfIuoWiWbThcEWejI75S0ybB4/e3pcDx21A6sk0GRoDn0rP7lluFeaWXYrtn/W9LDKwWdZP5zr95hqulEhTm08AuK89a8M0yzlzI+0yd8/MdR2m4zYR26LMxyUrJzQi73TQfhBMix/HqhStj42PiwYYRU9VOp3es6i1eSze5+p5SqtjDoGdW10yxtlZY55HislTq5MMW/VNjhTml4BBncWfiN3jeW4KwI3s824Au5X7zgfwZgB/sOoaQacTdBynPB+6h5/Re/FYdyOOdFYF36Gpiu4epnYfRst8FLu6KYITJo5G77jPZKU+8uxcH3H3tUHbAOd5ngvkfVFMjEvz+2RXrajt0v5eagTeTJM1xtkdJejMPjfM9I6/M6tEaOgKgZqeDvt9NYbiTEzvnI7veHZakyNUP8KEeS/a5p3TXcbOEy56s3GKeantEQhBY1pJQm9sbAKMQj76Tzume4mw1HC0Sdbp1lPT8F3/vhdtcxW17Xzg/SaYYZ9GoEwOe5ymsnGzIpqIGnobgCcBeKy7Ep57BYBr2OfXALhC3HMUgI+XWoGXEQA4F8B+APu3bdtWqxNWoAxIstaVYvtWJIg+p1Vsc5om5rJ39pyzWtognUazsjYCKq9cy8GdqD5zQKgvNKerJnmJjpf8rScnC8tSuVSMmTeOzannhnQ6Sirv2e6pYM4JGsw0qdTNd88tu2ZXdtY6/u5ztPqKdO2W/kxtQysnZmNjXenzMApzqNjS79wV4FrTe9Eud0i3zGHqzskkF4+46ZZdsylKaE+/nUtzUaYl276nbTeQeR3ijEFLsyiv8imtzopWpDIC3tEhB7xSyWB2Y/ZIjwbu2UzZ6Vj/YE++pJobWwdlBF9VrujBNABeqTCCy8U9fw7g5PL/4WsEgyJFUgztEk7mOP53OmltZQPOuJ1Ad8/MmVt29Toetepqkmkw1NvX5tD3mqjO0zWI9rtu4YqD4zsrO17b7b7UBi6sjx+Q5euzJGm1xvh0Orr7JImYlpB+YHft2OHvYsfILx7rak3OxOJtQqfLoFqtXjv3ij+l44mek40OHJPqdYC7Z5km5dvt6xRRnuFDTUWhwKfl83b1aehF0S+tJ3M2hshzsm9VDVz4JKxm3HXqj0QjqHulmIZKpnJfef0rgG8DmA6VOwxGkKqSugRubuNL33NctKuZkkKtC/uSS3QruyQ9K1ebk9p30dRAIVHWN4l5QYnqeigK8sBcr032MFrmQpr1C2tKnwXXdAqT90Drv6ohkJOT/Yxg+/Z4vYNhqJ72OZPVDTO9CeSWW60VX4d3TQQk5aS6cN8Ktcxia1y9X7qltm9PT0URGu8+aVysVVVarzIfIvMoOhcVi8KgO68dBmYEAH4WwKsAnOWuhGfGYI+2fApzFj89cP9INIKk9d/pj3BRF3pdKaJEir9Cra/nvakagVsPRRFPDRSEr/2BTtasSBoBmp21Zzm79MeHisDu4IQ+6yN0nPLI9A4JkoJPEUpRMJz0y18v8tyFzUspkoxvbEouttxq9ZsXq5QT+42rMdy25VFFJSOYnk5PRZGk0bi6KKbJorDvipqgfH0e+C1YN20SdbrZBQbNVjqoaeh3YM8g+FYZOvoQgL+IPVc+ezrsWcf3ALio/K4NoK3cu2qMgI9Tqj1URpvs2qU8N4BUaTq958I+jzrpZ1w7kVKJftCEdr5BRvqrpM3d+05fxwr7bI+EJRadpAspAm3U9BComnu9qp5z+4503CnOX63sUFLYEPgclEFKoXpXogmhhzvWZn9KKyGLqKccR6zUKC9N+ogMPteSiqIbn8AJoroOZj2/JfQD17a9ObdifZk4FCozl5pWqiSRiEEZwZ2wYaSfKz//BIAPxZ4b1tXEmcW8v8ssBL1jqlDPw+O90SbeOeyZgVFCOtuf5Cr5eEEnUkZs8Fqdb5ixUSbO3s4dla4YfvZ2zOLFtZrUc+irSM7uvtAG6FgZ0idyy67Z/h277kfG8bXUFHI+1dmHkkpXBlQ4K0uqUmjwlSMl6T7JNUVTUOoUc7f1MfOUTgzkSXJlRnNuDTwQCjTVeABmo2FQRnBr+fc2AEcAIABfiD03rGtQRiAdc3KDprYiOh07wXfTrDm16KxIJ4lJSdMWOpOmf9Ta4s3xrq6biA3ehQKeWnR6COCedq8Wwp2v7bZ9+L62fU7SR0coZF14VTht5VFvg64j33k4MbhxkFFSB+Y6/cnv3I8l9/Slpkg1baXULfZcpVDnGpDax/PHukJCKDtEdDxrStCh3HbynTdsZ5F0vknV6UR3Rgc1mwHbE4Qss656GUAtRgDgCgCnAHgPbNK5NoCvALgdwHW+54Z9NaUReHe+K7M6lVn7FnMy4SsL8EW5eOdfYGLuafceXn9q0Q0v5GGoUgtxEtYS9TIJbrON1VFaW9i55MF1FCOKLp8NdySmQDKpY49lTIRzdiVmk4eDyki/pmmCCiYoxHaLNwE5b6bQDUOWY5Ms6FTgkD6arWm3ExPG7BhP8B/ICeDZGZ1U34rtSYLkxGtBIwDwVgDzAL4G4J0AngngGADP8D2zGldTPgLuk+k7jKVccIeKLeY3d3T6zEeSWTv6EUqYWYVx+H4LzmPPCv3u9l0rqQMWUJhPT7Pwwk5vQrQpML8Ee5ljEqkRLa4q7bZ+gFmo7Y4AhJJVSo3Axe6nOHSdRnAyrIbn3VTmeV4b52HQhD4MwxwRwH3trnlkAYW5qDXbsw5ktFZfHwzYKdpcl+vI8Wu3Hnsi6TTUIK6yGU2OtaT7tYIAKmBQ09CTAfxmqQl8CfaoyqfFnhvW1aSzeG6uVw3kYXU8/awjNpoU6OzCodxa/J1R6T5S74hm23tzSfWWYQ9Il5JSp2NTT/9WoZgbWAUPj29ZcSS6vkhx8tZpoxY2qD03Pd2955SWZWgpL+p0jHnr9l5p953T6QttlelxFwmdmSpYJNGXTjdH/8OtLWbHeEdNfKr6eBqQZrUifH1fScNMaLymdYi4gYGFdI2GaIJiqvk5BY3tIwBwYskQlqo81+RVlxH4Bve+dq/keyHNmrExPdsvt/9yqVf6HGKTpNNJOq9DRbttzBQSDk4PhaKY/okYisXnOZO4JpJCUKoKNZIRaP0pJfOes2ITOlNKu79VzFbSCoZhHtakzpmZXof4gblO36ZBh1THaiWHtjL+8lLzJgmKfV97thZB42s2EmQU1DCrjBe/X0a3qpGCkff7IDUenqDUjfn4eKLQl4hBNYJxAC8D8Edl6OifxjZ9DfOqwwhCg+vy8nBnoIupl+aHUASMe2Z6Ok4YuVQfON+977nZWcNS3IYTi8VWQBXJtpLEFah7qtYjN1f5pD/Xb7GIEc1scajoPyMgVKcq5oGq7dWkTimIuNTVPiKoJof1MHLpgE1pD+9zbiJStwKwBxYnbZbXKgRNai+83ZI5xlDVmS/lJ87kqhzdrbUl1Kcy2a2kP7VORxOo6yP4jwCuLfcPfAjAmQB+zHf/al11GIE2uD3x6B09q2O7POTKSTM+AVtKY6FwSCnxHndcXELj5V881nXwBlMNG6PPwvK7qknCUid0T/SV5z0xVV1K/Lx+XgbmqaBPUk6NwAlJ2r5+qtKvMjKGS538OuKI3vs4QZud7T+RjjNHnvxQagRJ5o5Of34mqWH3baZnTEgephaSpGX/8XVHZN9TZSx8J3r6hC+NMceEAJ/vrooA1en0Wgk0zWtQE1FdRnALgDcgIcHcal6DagRbtlipWtsKH6CbfQnauDMzJEXIgZOM4Oij47npubT3PEq3h8c6InjouPIoV+9du335gZzfZYH5FxwBc1WQB+poB5tz04AmIbrvNNODV1L2tElrc+ykNzlnJKPiJ8dJzM319p1LMqdpBCHtVCXGinlG8xFENcMEzhYzS/n8WlrRmgTP15001fqgCSjcqRwKi62i0YXaWNWfxOvMNa0YTUnFSHINDesa1EfQ6ZieEerJJS/u11IGbN/eOyFdtGGVQ0e0vDI+KUdKe0Xhj5CJTmDWbu0MAF8ZcqLziak5yy+kXq3l4rHZlXv5oV+++2JqN99MphFTTpRDZzfHaFyV57UcQ9rJcfxZzmSkJNlu26RzRx/dP1e0iK2+cUtUTaK3JVAznzuKM3KN4WpE3xeVtWtXP3Osureh0+lNXOdMwSGGkgqu2bmxrKNNOiuEMxWNjdnPVRiKD5kRSJSz32VA9GUp1CKBtBwoXBoL2XIdZmb6zx53hE0jwtxplHqMgcbY9rT7d0inEMbZWb+Eqi1gTdJvt3vb0WqFNQc32SWR2b69V70P2VI5AyuKfrsyX7yntKwjVhJr1exh+uvGtURnTuSBCHIFh5iMlAxlf+/YYf9GCUyiaBu8ja0V3/4F3k9unFKc0pKRhsw2UhgJMkHjn8syUOACzNZmBPy9sn7j4935rs29UF9IYbKpTcaZEWjo+POryAXOpQ8n0bu0Pr4zV3wLS0qCbtKEHFG8LpUOomfvdGWfWtj4ee3wdl8Z2iJ0hE/W1Wf794aFlvfFNtFxkxx/v6wTHyfOfNxi5FKqa5PLLaNlwVTHsvzyhpnOSuoNXoeTYUNyvSdTiXZxJuOk35CtmBPCmqnpVfjmrTxzmb+T9yevt+aU1t7j/o9tpJWatNj4rRJJ39jxw4nU40oT+0q+V2oFfNyOOy5s44+ZlxN5ehCZEXjgkxo04sM3N8mJHHIuSWjS9cyMP7qBb8pK1QjGxiyhdQs21YcR0io6na6KKiOdUiapZASaFOYrRyOObkycCl0Utn7ODCHNVa5ftWiX3ege3RjVvYU2+TyyDNUxBMdU3EExoQkh2yvnnWQAMqzZaT9NEInQ2Pu0F23uaxI+D77waTMxjdZnfqpqh3cvc87vOnnd5HzkAqDbDOlj5D7mzZ91mWcHHVOJECMYwybG1BRw883Avn3Azp32M//+kkuAj30MWF4GlpbsfVNT3cvBlbF1K3D++cDCAjAxYb/n9wH2PUUBLC7az0TAkUfaZ1stO12KArjuOntPUdhredn+/pKXhNvyrncBH/wg8JnP2Mu9c2KiW6/LLgMOHuxts9YfAHDppd37brgBmJ/v7a/5eeAFLwi3GQDOOgu49lrg8GFgfNx+TsXUlB2Lffvs80UBvP713TJ4fV/wAuDhh20/Siwv23oaY/uyKGz/d4qdAE0Ai7YRd27diQ9f2t8/Ky9bWAAtL2EcC9hh9uHTmMLrXgcsfHwer/zSJZjAIYxhGYtLC9h3/UFMXrK7pxzeh7t39xWN5eX+up90EvC61wFveYu9B7D9vXVrWv/HsG8fcOiQffehQ+Vch63oS7fuxG+3plbq5dYCYN+7tGT/HjzYP3/cuuD1dlh5z5R/LTrIOXzJJd17+PfuvSHMYwr7tk3he98D3n2erf/kZG/fyXm+8mw53098eB4zZh8+QTuxv5jC/fcDd95p5xPQXbeHD/e+e2kJOO884IQT+tvoniXSfx8qfBxirV6rcTCNNB+E0h3wZ2dnTfTMWGOsBsClhDPP7DUTcOeQjCmO2YVlHp5jj+2V2n2OO61dwbDPElUkspjJLObjqHLOuJOYx8Z6tRjveQHMRBXyK7jDV5aEf+nAnDuzwu7kPgw9v39M6/JFDEmTl/NDaGccx/pZ+02m7eBnL5stW1bMYHz+xcaMj4vWJp9264Nru+Y/qBL9pmld3OQa047cmdiHUZh/I6sVEnXnGdfqpW9MM+/6NIymgWwa8iOm3jqV3xdmJsNSZeoCH8GSmTn5JJie1qOQuHrpmyhyQQNdJ7aclLJNkqlJU5VmApP9VXeRhvwTKTZkOR68LjzKiDNErV7azmaZLM/tQblhhoW78ogstMznj9614n9KPerZvUMzbck+0YgZDz/ViFgoioWbf4hsNs+V9pQRZp1O/wEpKePrzB4pJpIQUhlPCJr/TzKlmL+NHw8q83AVRX/95uZ6x0oLoQ2eG94QMiMIQA4639DDHV5a3LLcDMQPTddy1zt0Ov2hg85u7yRYJ826KCSfv4KX6Rbk3JzVBORk19Jm+KQgSVDkhjq549IX9peycDnx485TSdhTUiNIQq/liwklCJSMwBGJlLOdXW6excktPZpFyK7ua8eBuY65YbtNAS7HXCNmPAWKj6HG9lTw+u4Y740wO7Xo9GkJvsprzEFqMsk2cFZYLX+AKCa0c1v2hW+tOa1wUcnMOz0d1polHfH5PmL9WQeZEQSQohHwxcwdpHITidvN6ctdz6HtRpabs9xidYtIaidycksiKqOTfOYGY/xx15pTXNsroT2fsnBludyRqGV5TVkQvn0dzokXShDY6fSr8o5Rh6S2Tqd77oMLy+WJ8YAKOZrc8ZHUWskKK6VIKWHzOaFpRT6HL4cUbN66vRthBth9HzGnegqj0+5R+0TcWHU3vO99jqlrApG7P2aGNB2rGfH0GVVCu+XaDZlEmwgdNSYzgh6EpBUtCoYvDjdpJJHq4fKd/nQV0jzhq0tosYZMNTKaxD3HTxZzBIzHuft27Ia23/smr2+yxyaxlJZkGgUtxDI0ttpOZ07EJYHXTtRyRNynGR57bDfSK8RIUyKltEYsFd0D5Q+jZS7AbB/d1TYw8fHRNkPG+lIjmFyYcBFRoZz/KaYvqVm12x4JXCmsjnSs1Sl0uFFMKJLtSfFb+ISqWKThIFqQRGYEJXyEKUSw3G9Sioxt8uADn3KilmYeuWGmW4isozTVcEInHV+aTdxHuENmE1/7fN9p5gC5aCQD4lrP3FxvyGqsPprK78w6ckd4UdgU3KGTqM48s59x8L8xx6lPsgwRM7vhyQ7mMmAOYVzNh6RplL75IRlFiIjKe6Qw4cv57xMSNGFDalZSc+rZY1JDHJZzXhNcuNClmclCZlKvBuN5Xt7jJe5loW4DptypnjWChhiBbwBCk8IYP4GMLSz3uyRCu3b13yelcS2jpmQunBDMzFTbzh7qiyoSSEhSkr4Nn1mKL1wnGY6N9TtMQ/llNLs5N5NxU8qKozLQ2E6nX4t47GPDjnsfI/QxPm2cuieDtcwhjJk/3DGnMlwp3WsaY/LZFRHEBASfhBvzMzl7uOagX3kHI44pmoCP2aQIQrIcrglwpjo93a/B+O73aUV8/M4805rhDo9396c4c5wTiLKPoEFG4Bv8FIndPe8dEPajXDi+Ixsd1IkTIVKamp/KmELqaRUJJLSYpJlLM8vIBeIzE0kJP5Y1Upq2vM460QBObDSnsXTch5iur29izsG5ue7ub9/paT7ThXwfNx9VcUSGmLtm7vBFdMm28vQgUiOPpR6PhXFrfcM15EGcsFKQkPNaHtuasoacIOfKuAB6JFIT6acdRsYIALwIwF0A7gZwgfL7GQAOALgDwH4Ap8bKHIaPIFUj4D6EHkmPrUKX8lcSvR07/HnUVaKhfMkXHpe0t2+P7/LV3pGizoegSaE+c1hKwjBJzB3RKArdT5O6sIPSX/kQj5OXQQJE3agS945YXnwfH/dJrJw587xVVcZSah+ajyhmEg3NE58WEDphS2qFRaGf2RHSOnxOdw3ynXwMU8798CGUPiIpCaCAZFjc/yI1gkE1AYeRMAIABYB7ADwVwASAzwE4XtzzKABU/v8MAF+OlTusDWU+W650PvJkUm6geHKxw8r5vikDqk4coWVw57AmZXOiKR2CIcJUdzNLiBhIZuWIZmgzm4/humyMoWifWJ+GFman0x/OGwobTiHEIeYj+9xJrKEQ3RDT0+YvZwI8UipmBtSYu9YOGWHki+hybdWCGWJj5j5LCT8WfeXGYscOPWS6ihDhwE2xmi+rqh1fahmOGexGN0rLd0xrXYyKEUwBuJF93g1gd+T+L8XKHRYj4LZp7qTxZd3kE8udeyy5uU/VrQNp3gjVSVtw2mYin3TqCLZz8oYWrSN+WqhniBDGJEzpKJMnYw1itpL3SUJVFOH3aCYPbaNejPnIvufMVAvR9TE2acbasaM/L5PGVGIagUwbzuuh7ZEIjUUo5XZMcpaJ9jij84XyhtauNBXF5orU1Fz6c64RxsZa+01GJO7Y0ZxjWMOoGMErAFzDPr8GwBXKff8FwJcBfBfAlKesc0vT0f5t27Y10il8cKSa5hiCL/mXtuj3tHtjrlOkEK0uvu9TNAKtrtx+LH0Kmr2aZ+UMLXS5eFIjK3yLLjYGrn6pRxWmOL0104VvoXNIk4smdU5Px8OFNW3MSdaauc6nfUnTiS9yKjU9AzfTaCYsSZxbrXC4sSPcfHxTJWlt7krGIs25ksD61gZvT2iuaNpPHT+aNE35GHETjmENo2IEr1QYweWB+3cA+Fis3CY0Ajk4munBEXw54XmGSzmoPgJ97LFhB7Q2qUKTRPMRyDbwie5zGmrvmJ3VF5E0j/gcljFTjI/5aGkV5Bj4bN2p/SrrJJmPU8VDz/J4fLk5jdebf3bEy2d+TNGcfI50R5icRqsxJblLO0XaDDm1tbkuhR1NYpcENXQYvBxLOW6+/TZSW3HmUqdx+TQcTVDSyvOlnk/pR95PPDjD/Q2ZTZvAujANlfd8FcDjQvcMGjUkoxzc4HCGIJ11sbQEDj5JMUS4fNKIN9LFhJkHn1ydjg1Dvajo1VSkeUhKqRpDS7GTh37TCKnsI2n+cZ/54uULvKqPQKuTZuII2cl9Rwi6uvIkcJzBaCfbuTqmEAApvGihzFxAcNeOHeHInpT3aeO7Y0f/HOGEVZPYU7RIbex8ddMIt7ZuYvPAGL/pVKY/d47uqhqBJuDwfggd59mUhjAqRjAG4F4AT2HO4qeLe45lzuJnAfi6++y7Bjmq0k2eougl2HzB+zYwxdRHSYSjuWlEvTSiHooDT5ogHZsThR/LpzkNJaTN2dllJXzmk5jDUfaNRkg44+XnDqRqBBK+8dMiUuSYhJy4MsJK06hkygrfe2LtiWlcvnfLPkzZpe0bX42wSY0gJrHzNvCNUzFizevgY551n9XmrHakbMj/4/uOBzw4YUJq6DIqTmOcgzKDUYaPng7gH8vooYvK79oA2uX/vwngC2X46Pwww0c1p5OUPlMyPoak3FTzjmZWijmTajmbZ3uT4F1UzCbvGg6pylKy1+7h7falStYc1T7Gy23nvsUWc2xrY+RLAxGSIkPhtZxQtlrdg1j4O1wsfIofQ/Z7TPrUTDZ8vvPIl9Ac9PWXZurw2b5DYbC8/FiOKd4vKcTRxzBDQpfU+KWAENNEtTkiy3TzRqahn5nRhb4q8yMFeUOZCaurPnNRSF2VE9kn+XMiNTPT7zDTJJZUySip0Vt6z5tNVTWlhqO1ORQSyJ+Pqb0+4h6T7ELlp0psjWwmDNzL25HiLPSVl0r8+A5zLaRXm+NyV3pImw21J1afEEPh6zLkjK3KPHldQ/4B2R5NK/aZYiXRdlqjNAfxU9XkviWfgLghNIJhXIP4CFJCzhyR40c9atAGPmQv1yKQfFkPXZk7dvSHcPoIkpdQKT9UYQYhE4kMUdR2b4Z8HbH6h9rqY0guYkez9/qc16HNhE0g1N8pY5FilvRpLBpTkgRK9l8s02oooopjbq4/2MIxbxdyq5myOh3/O6poZ77ooVDEENc85dGRoX0i3CoQijiM+UZkW5t0IGdGwBBblClOYXdvyoT0ST5OeuUTzKeOaimGYyaoUPt9Jh2JmK3fSXshp3inE04P4Ovz0DhJJsz71zHkkITpS4TmzCehMW/CcVe1nNj4aowixES5H0zbgStDdlPt95LpSDPV+Hi/WWTHDv3c6VB7HZNwKT98dZFh0FIyl33rO2fZafNcuNDMVz4tVUZ5hcYndczrIDMCBSEJsY7dNia9+sJQ5YTRGIHTHHzSi2aD9yHkyNPa5/OL8IUUcoo7LUeGTRrTH2XlYzghjUAuWBk543IThbQ3LcY99s5U6V5KdXUXOCcyMTNaLBrHaQVauKnc1BRKHBfyoclxcGk65FGqPPFcaDOd1lbffXJO+kw7fB7u2mXXEWeCbh5KZhkzXxnTH7Id2iWuoWn/gDFhRrApD6+XB67zw9zlIdmhw7Ddodu+A9zdAdiXXQbcfjvw/vfbA+nHx4GZme5h7A7G2IOrjel9T6tlDwA/4YRu3dwB9+4wdoexsXCdd+605cmDyLWDskMHirvDy93B8p/8pN5n+/bZNhtj/7p3zc8Db3qTfb8DkX0e6D0UXdYvVK/5eWDPHnsweqsFXHGF7bc9e2xZRLZcd5C9awc/MF57pztY3lcnbQ64/naHtl93HfDa14bL8cHdo80z2R+hurpD6uUcA+ycesc7uvdpZQH6+pD3PfSQLY/36+WX20Psb7qp+93LX27r5uaJmw9EdvyKArj/ftu/7j73Hve7mzc7d3bH4dAh++5Wyx5Mz9e4HLfzz+/ODVff5WXgi1+03/M2uH466yx7uX4CgEsv7Z37ExO2TZLGyPdr87gKHWoCm5IR8Ml06BBw3nl2sN3i8hGZUHlu4h061CUufNGefbb9nRNER5Q5MTzjDOAJT7AL6bvfBT71KfvM+ed367Z3L/DZzwK33tq7oIksoQnVeWoKeM97bJuXluwiqTLJfEzP12e+Cb13b2+7AeCoo4BXvxqYnu4Sbt8i4ISNf/bVxX23dWt34fOyx8e7hM4xXg6tHXwRa8QX6GX0IUKaghCBdwzBgb9j69YukZKCgMPYmJ0XvDytLEkA3X1bt9pyjbGE8qMf7RJrJ0svLABHHgnMzQHXX2+ZwAkn2Lpt3WrLf/jhXn14eRl43/vsfLj55v5xkAT20ku7xLvVAl74Qiuo+NYEX7tEvb996lO2X1w9iGzbrriit5/4mnCMaXHR/v+GN9j+0t7vW0uu3Kp0aCD4VIW1ejW9s1iql77kWb5yXHIrPn19+eG3bOkefH5gzr7AmSU0G7rP9utzPsdyvsi6p4QjSvW3jsqqOb1kVIbsv2HaUH0mHGcaCPkz3HMy8MCXYsN3bnElh3+gzbGyZJjvmWcac9xxXf+AFvmjmf9S/GruHfx0t5RACm6G0s7a1kw/ofpEj5lkkFFjWuqMkEnOF3GYQk9S1lJTfiljwqahkRP2qlfTPoJQDpcYkfQ5o2RYmivLHXq93Op9Qcy/4CPE0o8gD+AedAKFGJEvlE5unffZxfmClXZqeXCP1h7fIhqk3b49BVpdQqHIvO2c0YcIUypjk36p2DPSJ8Sv44+PR+WkCAohHw8/GjXFHycJMz97Opa3SYv2ic0DGTWmRZyF2u7a6Dvn2peeW9IejUnKTZWDRg+FGMGmNA0Bvar0CSdYFez++60ammK/lfZ9h/HxrirXp9rt2wcsLwDLvS+Qaj3H2Wfbv1y95Co0x+WXW7MK4Fc5q0Azh2jtknZZ5+dw9tmzz+43aezcac1YAHDEEcC73tV978tf3lsPXn6rZU0YvG7Ojnz11V2zT1EA55zjV8sHwb59vaaVouhV36VJEOj3kWhlSvOiz5a8e7f9zplBQvPVZwoCrA38/PPt/Hd1uP9+vUz+fn4v9zc4W70zH+3da/0iH/pQ93tZN2nCOnjQ+s/uuKM7D5wZk9dV+viknd+YsP+L12FyslvWzEzXfxcyyezd27sGn/3sXlOtKc1Jmj+K1/0tb+m21b3r6qttm51vDbDlzM11TWSNm4p8HGKtXsNIQ+1QVRqSGkEoTr7qC0K3cmlB2wmdar5JNQ9ViXPXVHpf2CmXukKx6b5Ip1C0ibtS0ym4tqaYFbh5LnbuQ2qmytDGtpAWllq2lubCJ8Frobza7zI8VIbepuwhiUnH2lyW3/HkdXUidKqYwtzvchOjlrZeq0ts/5HUNkMmsqpANg2lI3WzjDFdu7KLyU6aeIm2i1T7oS8GPyXUsU44pK9J3G+h7Svgsd+hFMK+8n3PaAvLt0kpBVqbU74LEbSQ6Y+blHwb20Jzwc2BlKR1s7O2/91mLl9IqLRrS4LOkyrysZbjqBFMH7H1MQ2N6cq5q6XsrivgxNZFp9Mbmirr6ksroTFvLfxV29HszFWpfg8fMiNIRBWNQD7XlEOnTl1SiRdHTFqr2hfSPl43NYUPvl3hGlGQzrtBdgzHNDON+KcSoqqx/yl5nerMWUew+cFM2vulRqBtwJLt1vJlaXUOMQ1fZtAqUnyo731ajG8PQyz5YYpG4Zs3MoW2Y3xV/B4+ZEZQogpxrBIR04R5pcnnUssOZTeNLYiUia5Je05qr5IFM/Ze7ftQOpEqCDmlYxubqpYb6teUNMmxyBMfg+p0ejNt+naIc8Yh/6+SeNHXp74ki00HBqQQex+T4KbH1KMkQ/WUWqEmnNWhSxoyIzC93NypW1XUQp/UHYqgkdJwHZvlMJmBT1qrurB5nX2mEZ/EHDLFOVU7JVqijlaUAl97Y7beGDhhT4kIke/bvj0tNXdMipXMpK4tOkVw4Npi1bklJeIqjF7THmLmH23eaBFNKfMyNZw11P46Wp9EZgTGDqy0HTsnT0zFTCEGPrV3kANBUsJZByF2GoHWzCycSMXazKXj2Nm0MQdpSGMJtaMpphmSpEPMLVYmj7svijQmIgm6L7OlhJZ4TY5byLdTpa9ixDWlv3zrjxPTubl0P1OK4JK6fiQNkUkjNUib//R0NW069n0VZEZg+okOn0SxiZ9iHvCpvalRI9q7tGRVHE0QQJ9q6qt7rM0yCVwo1bY8tYvvH6iy6JpSnWUdY07fqovTETTe5tgYy+el9B46D1syU0nk5bjFzoSOtTf0+yBjJJ+VfRCSzLU21pW0qwgnDinprFcLmREYXSOQC6SqVOF+i6md3PyRsphSNYJB7Pi+d3PJK5RgLNRmnkVV9qvUHgbRCLhU14RGEGKKqRuNQpBEwZk6Ujcxujry+REyKUmhQkqjIY1QbgQbVOhIfT5FIw8diuR7r2Ya0wSfFH9fldTQbh4T2XdU9SU1icwITO+EKAq7q7JK9EoVaZD/JheuCwMLef/l86H31LHj+94r011UIbC87JDJRyOwMR+BtjO1rmkmVGdfyoiJiV4tJ7ZfRCMWnU6/BuScjXU0i1QzVGz8fMxPmlCrmDhTzBspBJ/fl2LCDdVHc6pXEbqqvlN7rimBpS4yIyihEei60SupA+pbXEBk81mNNmnv9PkutEUaSptQZdLy6IqQRlBVAuYEv6rvJVSuJPSy7TKlcsgsoGkyXILlmkDThMBHXFMEFt4n2nnEqSbOVOajaTWDmlVjfRMSjmLzaVCNiJeTOh6pv6UiMwIP6nSuT7oI3c+JQNOMwPdOGWURs9Fy4p2iIcn3NRGVof0mbbzyMPa6C1OaTfi4aMduSgLpG3fNtyF3vvocu4NgUAbLx67d7t2JHDr+UyLFFyCFI+fnSD37wNeeFLNOyPkfiu4J+QkHJdDGhKOgmmJCmRE0BEnUY/HW/Ltdu/oJybBUQ21SpxDnKhpSTN2ty2RDzulYptiq5gJpFgi13RHIFPOBTyMYxL4eM49UdcbG7nftrZrorIpGoDFWTWuPlZV6qmCofprwFHuuSS0hFAXVVDDEyBgBgBcBuAvA3QAuUH4/E8CB8uoA+LlYmaNkBFxq1s7oDU2MqoR20HpqEyeWPiNVqko9TaqpeseYjrun6qKURCfV7l7HoVhXcvQJH1qobxMaQUp9UiXvKvOojl2+iqbm4JtjKcQ2pK2mzn1tzmmn6m0YjQBAAeAeAE8FMAHgcwCOF/c8D8Bjyv9fDODTsXJHyQhCTlBj0qSsKjbcupATx+0HiKUDSC03lliriXr7ImJ8/RXaHDcszWs1oPmYiqLX3FS3vXXub9rZOcgY+UxMdTWCOoJEXearpeqQQmIdQSWEUTGCKQA3ss+7AewO3P8YAF+PlTtKRhDLVz/IxGg6ikBK0ZJ4u+igKkmstIUXyjdft95VVH33TF1zTFMSbkq7hqkRrAazCwUBrDbkPEnZne0zscnfpRYXEpqqCHfSohA6wGYYtCHECIZ5HsFRAB5gnx8E8NzA/a8D8FHtByI6F8C5ALBt27am6tc4qh4vFzsHd9C68KP7LK+1+drdub2AzSe/d2/ae+UZAKefbo8k9OWbr1tvfn5tSr/s29d71u1rX2vz2sf6NnbWtMu9HzvbwXfubOw92n2yHD6nXL5+97s7R2NVjjKEfT8/01ce51kXsf7T7udHQ4aOg9Se8Y0BPxfEd/axfE6eJRJ6D+8/Y+zZJe6IXFn/YdIGDcNkBKR8Z9Qbif4DLCM4VfvdGHM1gKsB4KSTTlLLWA2cdRZw7bX2QJrxcZ3whQ6ZkRj2AdXz8/bwkLFylN1hLQ89BHzwg9XL0w5J/9CHmp+sVftF3u/GJVaG75xhebBM1UPrZR+kLGpZjjyLV+vXKnOtCRw82D3kptWynwdFKpPk4P0JAE42dGcfa4fEVyWs7n7O+Ko8p71H9t/rXmfrrh1oz9ftej+8/kEAT2KfjwbwDXkTET0DwDUAXmyMaWBqDQ9OWm1KChvmAdUhqWl+HvjIR8IMzSelhQ5Jlwe6121P1X4JHVi/d6+/TRrDkQtZayNHCoFJYWy8nEOH7AlVTlocyolUNSBP82qCONWRfKVm+pnPAL/7u3Y++6T3OsLF2FiX2bRa9YQSfr/sP02LqaPtNAKfzWjQC5bJ3AvgKeg6i58u7tkGG1H0vNRyR+kjGCaadmzWcVzz31J37UqH1ih3Tmp1i+0c1ezCvt2tKX3luycWisnLaTISq2k0OU/r+IO0Z7XUMVXnvFZ+6IyG2LNVNvENGomUCowwfPR0AP8IGz10UfldG0C7/P8aAP8M4I7y8lbUXRuREQwrGqNumb5NXCm7qNeKM9HVh28aq5LcranomyrjIB38a4WhDgMpEWIxaBFVvv09VTFMguzgEzqGNfYh+jrUw+uNMR8B8BHx3VXs/9cDeP0w61AFTZg16mAYjqFBzE5cvXWO5RQb6bCciXUhTQhE1gkdU/Gr2t5D91cZW17OajuCVxuanb9qO+X4nnMOcOKJuo+gKobtvwP0ubF79/DMxSEMlRGsJ8ScdcNEE5POF3FSp+4yUuX88/W6yXemOBObZrah8iQzBFZ/gdUd29V2BK82mpjzdYSd1Pk3bP+dW1taH4xk7H2qwlq9hmUaqmsOaQqD2F6HbZv3xUpXVWubrmdoc9Ba2ki21uqzVrDa/bIWfFhV/G9NA6MyDa0n1DWHNIVBpIBhxxxrdauj1jZdz5Twz7UQcbPRpfu6WO1+We3Y/JQ6HDxo182okRlBiVRzyFrEatgzU98ZWtxN1zMl/HMUi30zYFT+tEEwinXCMYr9AakgqzGsH5x00klm//79jZQVmszrbaKPor513tlEPeXOX15e1Q1KVeqz3uaEwzD8MmtN63JI2eU9ijGU+wPOOWeV9gcwENFtxpiT1B99NqO1ejXlI1gL9sKM6kiN20/NJFoltHM9zpdh1Hs1QivrYC2P0VroMwR8BK3V40drCz77csbaRsq4TU1Zu2uVVAWxOdDUfJmft6kQ5ufrPV8Vw5jnzsRSFHok2aWXAldfvbrtBNb2mg712VrApvURjNpemFEPTY6bVpbPdNBUiK80qQDDNVUMY577QitTE7UNC2t5TQ8zHLUJbFpGsNYHJkNHk+Om7TPYubObg4k7mpt4r5RY9+4F9uwZrq19WPM8FElWNVFbU1jra3rQKKmh+jd8NqO1em3EFBMZawOx8yYcBj1boM6ZvOsBvrMT1pKtfr2iCf8H8j6CjIxmMEjEjKaBcI1gLZky6kCGYK/WzvzNgGGHRWdGkJFR4qyzgOuu6z/XgGPQBSnNA2vZlFEH623zXNPhzMNq+7D9H5kRZGSUmJoCbrklvKibXpDrjXBuJDSxH2K19lQM2/+RGUFGBkOMMK91h2RGOpowt6zmTvZhCg2ZEWRkVESW4jcGmtDu1nLIahVkRrCOsFrb49drKoVUbPT2ZaShCe1uo2iImzrX0HrCatki13IemSaw0duXkeFDKNfQpk0xsd6wWtvn1/I2/Saw0duXkVEHmRGsE6xWrpK1nhNlUGz09mVk1EH2EawTrJYtcqPYPH3Y6O3LyKiD7CPIyMhoDNkRv3YxMh8BEb2IiO4ioruJ6ALl958honkiOkREbxtmXTIyMoYL54i/+GL7dzVTUGcMhqExAiIqALwHwIsBHA/gl4noeHHbdwH8OoDfH1Y9MjLqYrXPDljvyI749Yth+gi2A7jbGHMvABDRnwA4A8AX3Q3GmG8D+DYRvWSI9cjIqIwcZlodG2Vz1WbEME1DRwF4gH1+sPyuMojoXCLaT0T7v/Od7zRSuYyMELJ0Wx3OEf/2t2fGud4wTI2AlO9qeaaNMVcDuBqwzuJBKpWRkYIs3dZDTr+xPjFMRvAggCexz0cD+MYQ35eR0RhymGnGZsIwGcGtAJ5GRE8B8HUAvwTg1UN8X0ZGo8jSbcZmwdAYgTFmkYjOA3AjgALAtcaYLxBRu/z9KiJ6AoD9AI4AsExE5wM43hjzL8OqV0ZGRkZGL4a6s9gY8xEAHxHfXcX+fwjWZJSRkZGRMSLkXEMZGRkZmxyZEWRkZGRscmRGkJGRkbHJkRlBRkZGxibHuss+SkTfAfC1mo8/DsA/NVid9YDc5s2B3ObNgUHa/GRjzOO1H9YdIxgERLTfl4Z1oyK3eXMgt3lzYFhtzqahjIyMjE2OzAgyMjIyNjk2GyO4etQVGAFymzcHcps3B4bS5k3lI8jIyMjI6Mdm0wgyMjIyMgQyI8jIyMjY5Ng0jICIXkREdxHR3UR0wajr0xSI6ElEdAsRfYmIvkBEby2/fywR/S0RfaX8+xj2zO6yH+4iov80utrXBxEVRHQ7EX24/LzR23skEf0FEX25HOupTdDm3yjn9OeJ6ANE9IiN1mYiupaIvk1En2ffVW4jET2biO4sf/v/iUg7GMwPY8yGv2DTYN8D4KkAJgB8Djbd9cjr1kDbfhLAs8r//x2AfwRwPIB3Abig/P4CAO8s/z++bP8kgKeU/VKMuh012v1fAfwxgA+Xnzd6e/cAeH35/wSAIzdym2GPtf0qgC3l5z8D8Ksbrc0AdgB4FoDPs+8qtxHAZwBMwZ4M+VEAL65Sj82iEWwHcLcx5l5jzAKAPwFwxojr1AiMMd80xny2/P8HAL4Eu4jOgCUeKP9Ol/+fAeBPjDGHjDFfBXA3bP+sGxDR0QBeAuAa9vVGbu8RsATj/QBgjFkwxnwPG7jNJcYAbCGiMQCPhD3hcEO12RjzCQDfFV9XaiMR/SSAI4wx88Zyhb3smSRsFkZwFIAH2OcHy+82FIjoGAAnAvg0gJ8wxnwTsMwCwI+Xt22EvrgMwAyAZfbdRm7vUwF8B8B1pTnsGiL6MWzgNhtjvg7g9wHcD+CbAL5vjLkJG7jNDFXbeFT5v/w+GZuFEWj2sg0VN0tEjwJwPYDzTfiEt3XdF0T0UgDfNsbclvqI8t26aW+JMVjzwZXGmBMB/BDWZODDum9zaRc/A9YE8kQAP0ZEvxJ6RPluXbU5Ab42Dtz2zcIIHgTwJPb5aFg1c0OAiMZhmcAfGWP+svz6W6XKiPLvt8vv13tfnALgPxPRfbAmvp8nov+NjdtewLbhQWPMp8vPfwHLGDZym18I4KvGmO8YYw4D+EsAz8PGbrND1TY+iN6THiu3fbMwglsBPI2InkJEEwB+CcBfj7hOjaCMDng/gC8ZY/4X++mvAZxd/n82gL9i3/8SEU0S0VMAPA3W0bQuYIzZbYw52hhzDOw4/p0x5lewQdsLrBzp+gAR/XT51QsAfBEbuM2wJqGTieiR5Rx/Aaz/ayO32aFSG0vz0Q+I6OSyr85iz6Rh1F7zVfTOnw4bUXMPgItGXZ8G23UqrBp4AMAd5XU6gK0AbgbwlfLvY9kzF5X9cBcqRhespQvATnSjhjZ0ewE8E8D+cpw/COAxm6DNvwvgywA+D+APYaNlNlSbAXwA1gdyGFayf12dNgI4qeynewBcgTJrROqVU0xkZGRkbHJsFtNQRkZGRoYHmRFkZGRkbHJkRpCRkZGxyZEZQUZGRsYmR2YEGRkZGZscmRFkrAsQ0b+Wf48holc3XPaF4nOnoXL/gIi+TkST5efHlRvhmih7p8u8mpExKDIjyFhvOAZAJUZAREXklh5GYIx5XsU6hbAE4JwGy2sECX2SsYmQGUHGesM7ADyfiO4o89UXRPR7RHQrER0gol8DViTmW4jojwHcWX73QSK6rcxxf2753TtgM1zeQUR/VH7ntA8qy/58mev9F1nZ+6h7PsAfBfK/XwbgN8oMmiuQEj0RXUFEv1r+fx8RzRLRPBHtJ6JnEdGNRHQPEbVZMUcQ0Q1E9EUiuoqIWuXzu8pnP0tEf17moXLl/jYR/T2AVw4wBhkbDGPxWzIy1hQuAPA2Y8xLAaAk6N83xjynNMF8iohuKu/dDuBnjU3ZCwDnGGO+S0RbANxKRNcbYy4govOMMc9U3vULsDt6fw7A48pnPlH+diKAp8PmdPkUbA6kv1fKuL/8/jUAPlShnQ8YY6aI6N0A/qAs/xEAvgDgKta+4wF8DcDfAPgFItoH4LcAvNAY80Mi+k3Ysxv+e/nMw8aYUyvUI2MTIDOCjPWOXQCeQUSvKD8/GjYHywJsHpavsnt/nYj+S/n/k8r7DgbKPhXAB4wxS7CJwD4O4DkA/qUs+0EAIKI7YE1WGiMAgFnYPDH/p0K7XC6sOwE8ytizJn5ARA8T0ZHlb58xxtxb1uEDZX0fhmUOnyqVlAkA86zcP61Qh4xNgswIMtY7CMBbjDE39nxJtBM2XTP//EIAU8aYfysl50cklO3DIfb/EgJryRhzd8ksXsW+XkSvaVbWxZW/LN61zN4l88O4lMR/a4z5ZU91fuj5PmMTI/sIMtYbfgB7JKfDjQDeSDYVN4jop8ge2iLxaAD/XDKBnwFwMvvtsHte4BMAfrH0Qzwe9pSwuhkt/yeAt7HPXwNwfJlJ8tGw2TWrYnuZUbcF4BdhNZJ/AHAKER0LAGX2zp+qWeeMTYLMCDLWGw4AWCSizxHRb8AeV/lFAJ8lewD4HHTp/G8AjBHRAQBvhyWYDlcDOOCcxQw3lO/7HIC/AzBjbEroyjDGfAHAZ9nnB2DP4T0A4I8A3F6j2HlY5/nnYc/3vcEY8x3Ys30/ULb1HwD8TJ06Z2we5OyjGRkZGZscWSPIyMjI2OTIjCAjIyNjkyMzgoyMjIxNjswIMjIyMjY5MiPIyMjI2OTIjCAjIyNjkyMzgoyMjIxNjv8LB74UTjK0TREAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.title('Variance Comparision')\n", "\n", "plt.plot(Variance_list, '.',color='blue');\n", "plt.plot(Variance_polynomial_list, '.' ,color='red');\n", "plt.xlabel(\"Iteration Number\")\n", "plt.ylabel(\"Variance\")\n", "print('The mean variance of the linear regression is ',np.mean(Variance_list), '\\n while the mean variance of the polynomial of order 10 is ', np.mean(Variance_polynomial_list))" ] }, { "cell_type": "code", "execution_count": null, "id": "9695699d", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.12" } }, "nbformat": 4, "nbformat_minor": 5 }