diff --git a/week3/lectures/Lecture07_TrainingIII.ipynb b/week3/lectures/Lecture07_TrainingIII.ipynb new file mode 100644 index 0000000..94d3ec9 --- /dev/null +++ b/week3/lectures/Lecture07_TrainingIII.ipynb @@ -0,0 +1,1213 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# Lecture 7: Training III" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "skip" + } + }, + "source": [ + "![](https://www.tensorflow.org/images/colab_logo_32px.png)\n", + "[Run in colab](https://colab.research.google.com/drive/151rKfOzxrWMK7fiViIGsosquddN07yJg )" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:44.467687Z", + "iopub.status.busy": "2024-01-10T00:19:44.467138Z", + "iopub.status.idle": "2024-01-10T00:19:44.475581Z", + "shell.execute_reply": "2024-01-10T00:19:44.475048Z" + }, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Last executed: 2024-01-10 00:19:44\n" + ] + } + ], + "source": [ + "import datetime\n", + "now = datetime.datetime.now()\n", + "print(\"Last executed: \" + now.strftime(\"%Y-%m-%d %H:%M:%S\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Polynomial regression" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "So far we have considered only linear regression. Polynomial regression can also be performed with a model that is linear (in the parameters)." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:44.516067Z", + "iopub.status.busy": "2024-01-10T00:19:44.515424Z", + "iopub.status.idle": "2024-01-10T00:19:44.928255Z", + "shell.execute_reply": "2024-01-10T00:19:44.927538Z" + } + }, + "outputs": [], + "source": [ + "# Common imports\n", + "import os\n", + "import numpy as np\n", + "np.random.seed(42) # To make this notebook's output stable across runs\n", + "\n", + "# To plot pretty figures\n", + "%matplotlib inline\n", + "import matplotlib\n", + "import matplotlib.pyplot as plt\n", + "plt.rcParams['axes.labelsize'] = 14\n", + "plt.rcParams['xtick.labelsize'] = 12\n", + "plt.rcParams['ytick.labelsize'] = 12" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Example data" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:44.931698Z", + "iopub.status.busy": "2024-01-10T00:19:44.931400Z", + "iopub.status.idle": "2024-01-10T00:19:44.935887Z", + "shell.execute_reply": "2024-01-10T00:19:44.935221Z" + } + }, + "outputs": [], + "source": [ + "import numpy.random as rnd\n", + "np.random.seed(42)\n", + "m = 100\n", + "X = 6 * np.random.rand(m, 1) - 3\n", + "y = 0.5 * X**2 + X + 2 + np.random.randn(m, 1)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:44.938729Z", + "iopub.status.busy": "2024-01-10T00:19:44.938267Z", + "iopub.status.idle": "2024-01-10T00:19:45.153988Z", + "shell.execute_reply": "2024-01-10T00:19:45.153313Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10,5))\n", + "plt.plot(X, y, \"b.\")\n", + "plt.xlabel(\"$x_1$\", fontsize=18)\n", + "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", + "plt.axis([-3, 3, 0, 10]);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Clearly a straight line will not fit the data well." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Construct new features\n", + "\n", + "Can use a linear model by constructing additional features that are powers of existing features:\n", + "\n", + "$$\\hat{y} = \\theta_0 + \\theta_1 x_1 + \\theta_2 x_1^2 + \\theta_3 x_2 + \\theta_4 x_2^2 + \\theta_5 x_1 x_2 + ... $$\n", + "\n", + "Model remains linear in the parameters $\\theta_j$.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Generate polynomial features" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:45.157478Z", + "iopub.status.busy": "2024-01-10T00:19:45.157015Z", + "iopub.status.idle": "2024-01-10T00:19:45.487951Z", + "shell.execute_reply": "2024-01-10T00:19:45.487213Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([-0.75275929]), array([-0.75275929, 0.56664654]))" + ] + }, + "execution_count": 5, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.preprocessing import PolynomialFeatures\n", + "poly_features = PolynomialFeatures(degree=2, include_bias=False)\n", + "X_poly = poly_features.fit_transform(X)\n", + "X[0], X_poly[0]" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:45.491035Z", + "iopub.status.busy": "2024-01-10T00:19:45.490576Z", + "iopub.status.idle": "2024-01-10T00:19:45.495240Z", + "shell.execute_reply": "2024-01-10T00:19:45.494597Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "((100, 1), (100, 2))" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "X.shape, X_poly.shape" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Fit model" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:45.498108Z", + "iopub.status.busy": "2024-01-10T00:19:45.497659Z", + "iopub.status.idle": "2024-01-10T00:19:45.555973Z", + "shell.execute_reply": "2024-01-10T00:19:45.555227Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([1.78134581]), array([[0.93366893, 0.56456263]]))" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn.linear_model import LinearRegression\n", + "lin_reg = LinearRegression()\n", + "lin_reg.fit(X_poly, y)\n", + "lin_reg.intercept_, lin_reg.coef_" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Parameters are close to the model used to generate the data (2, 1 and 0.5 respectively)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Predictions" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:45.559266Z", + "iopub.status.busy": "2024-01-10T00:19:45.558700Z", + "iopub.status.idle": "2024-01-10T00:19:45.735843Z", + "shell.execute_reply": "2024-01-10T00:19:45.735234Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "X_new = np.linspace(-3, 3, 100).reshape(100, 1)\n", + "X_new_poly = poly_features.transform(X_new)\n", + "y_new = lin_reg.predict(X_new_poly)\n", + "plt.figure(figsize=(10,5))\n", + "plt.plot(X, y, \"b.\")\n", + "plt.plot(X_new, y_new, \"r-\", linewidth=2, label=\"Predictions\")\n", + "plt.xlabel(\"$x_1$\", fontsize=18)\n", + "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", + "plt.legend(loc=\"upper left\", fontsize=14)\n", + "plt.axis([-3, 3, 0, 10]);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [ + "exercise_pointer" + ] + }, + "source": [ + "**Exercises:** *You can now complete Exercise 1 in the exercises associated with this lecture.*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Learning curves" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "How determine whether overfitting or underfitting?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Overfitting with high degree polynomials" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:45.739185Z", + "iopub.status.busy": "2024-01-10T00:19:45.738769Z", + "iopub.status.idle": "2024-01-10T00:19:45.934670Z", + "shell.execute_reply": "2024-01-10T00:19:45.934005Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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z2kK9Zdeu5Vxz7Vr2fa2/vbGx+R2dJRMnTuTYsWPs2bOncA4oCIIgCBkkpCXg024VYXNf4MwZFSGzVyw5mr5c/ZUffBDOs0Ydz2lh0SLHBNTixZn1b1otvPUWzJgBRoNKhxoMGiZMgB498if4iguXFGWnT5/m5ZdfZs+ePURHR1OjRg1GjBjBs88+i7e3d5E+t78/VKuW+3q9MR2j0UiVKu451lWpYrlvuiEdFSmz3Nbfv+DjnDRpEj/88AO7d+8m1JU/YYIgCEKJJD41nvjUeEJDHRcyZkd/rc5m+jIiAl6cVhmMJgGFWUDZg7UJCTNmZD42YW89nDNxOVF28eJF2rZtS0BAAJMmTaJixYrs27ePWbNmcejQITZs2FCkz28rtRh+K5KEtAQaV2mcY132dObZ6HD0Rj0NKjUotPEZjUYmT57M+vXr2blzJ7Vr1y60YwuCIAiCifjUeBLS8jezP2v6MlWfmue2p0+rSJbF/hkCijyCJCZOncopwAwG0Ggs2yjZWw/nTFxOlH311VfcunWLPXv20KRJEwDGjx+PwWBg+fLl3Lx5kwoVKjh5lM5j4sSJrFy5kg0bNuDn58fly5cBCAgIwMvLy8mjEwRBEEoLCakJJKTmT5RlLfRPSU/Jc9v69dXsyKzCzCSgjibl/TxGI6xdm3O5TgdvvAEzZhgxZonAbdni2nVlLjf7Mjaj4Kpq1aoWy4ODg9FqtXh4eDhjWC7DZ599RkxMDJ06dSI4ONh8+/bbb509NEEQBKEUEZ8aT2JaYr7MX/VGPcRU4+Z/LUiKrpTntqGhMHf+NdCkA/ZPKDAaYfp0+Owzy+Wm/R98EIvEqdFov8+as3C5SFmnTp146623GDt2LLNnz6ZSpUr8/vvvfPbZZ0yZMgUfHx9nD9GpOL1dhSAIglDqMRqNxKfGY8RIUloSPh6OnXt3fFcHPgjnN6MONHoW++UdoRr2cBwvhLXi/TabGHpPS7sE2dNPwwcfZC57801o1y5zQsKOHZjr1Ey4el2Zy4mynj17MmfOHObNm8fGLEVaL774InPnzs11v5SUFFJSMkOksYU1xVEQBEEQyhip+lTzDMqEtASHRFlEBCyb2wGMGck4o86+mY8BkbS485ZdgmzqVPjoI/VYo1GzNceNs9yufn3QaI3mGZjg+nVlLpe+BKhVqxYdO3Zk0aJFrFu3jjFjxjBv3jwWLFiQ6z5vvPEGAQEB5lv16tWLccSCIAiCUHqIT403/+1oXdnp02A0WMoLc+F+ATEYYMoUS0H25Zc5BRkoATjh1UMOp0WdictFylatWsX48eM5deqU2eph0KBBGAwGZsyYwYMPPkilSjnz0zNnzuTpLNMmY2NjRZgJgiAIQj6wEGUOzsBUESqDhTArUIQqphp7d3vQoQVUqgRHjqjFGg38738wenTuu3YdHMbnNweyqecJWjT2dWlBBi4YKfv0009p2bJlDu+t/v37k5iYyOHDh63u5+npib+/v8VNEARBEATHySrEsgo0ewgNhQdn7jRHqNDq8x2h2rImFD4IZ3i/KtSsCStXwo8/QocOsHRp3oLMTEAkd3dMt/n80Ve84Xwnp04EcLlI2ZUrV6xaXqSlpQGQnp5e3EMSBEEQhDJFQdKXAO36HWNd6ng6+Y/jern9jB37fZ7bWzOYjYiAj15uatVUdvduFX0rLBYvhunjh4JhOLW/MjrcUaCwcLlIWYMGDTh8+DCnTp2yWP7NN9+g1Wpp3ry5k0YmCIIgCGWDgqQvQfmUuZW/TEizU3hUuGr3fhpNZlG+qk2zPnuyMAWZqSOAKd1qasnkjIiZy0XKpk+fzk8//cQ999zDpEmTqFSpEj/88AM//fQT48aNIyQkxNlDFARBEIRSTdboWH4iZXqDHq1Gi1ajzZfPGUCNGqCcxop29qTqKGC5zFnWGS4nyjp27Mjvv//Oq6++yqeffsqNGzeoXbs2r7/+Os8995yzhycIgiAIpZ6skTJHa8pARcp0Wh0aNDZ7X1ojMREmToSsgkyrLZrZk6qjgKUwc5Z1hsuJMoC2bduyefNmZw9DEARBEMok8anxaNBQzq1cvtKXeqOKlGk0GodNz+PioG9fVTcGgFsiL7+axvhRAUUSuQoNVT5n48cbMBi06HRGFi7UOGWmpsvVlAmCIAiC4FwS0hLwdvfG18M33+lLncbxSFlcjBvdumUKMm/fNHikOxMmxxepSBo7Ft7+cQ2M6sS580an9ccUUVbC2L17N/369SMkJASNRsP333/v7CEJgiAIpYz41Hh8PXyVKMtnob9Oq3Ospiy+CtMebMEff6iHFSvCvGV/QM29Dj9/fqhYNRFq73Kql5mIssIgKgpefVXdFzEJCQncfvvtfPLJJ0X+XIIgCELZxCTKfDx88lVT5mj6MuqSFpbu4uxxXwCqVoWdO6FBs7LVMtEla8pKHFFRMHs29O8PwcFF+lS9evWiV69eRfocgiAIQtkmIVX1u/Ry88pX+tJgNDiUvly9PACuq249oaGwbRs0aAARpx1+6hKNRMoEQRAEQbAgPi0zUpavQn8HLTEmTY+GZl8TUiOJ335TgqwsIpGyrNxxB1y+nOcm1Yx6FYo1apSRCUBGtwG6dgV3d/W3TkdNTcb1gdbG2xwUBAcPFmjogiAIglBYmNKXBZl9qdPq7E5farXAwNEs6FebWrU65GPEpQMRZVm5fBkiI/PcJM837NYt+7cVBEEQBBclITUBH3cfyrmVIyre8XppW+nLnTvB3x9atcqyUJdOxSpp+R90KUB0Q1aCgmxukp4RKXPPHim7dQvKl7eIlKVnRMrc7YmUCYIgCIKLEJ8aT2XvynjqPAvk6G8tUrZpEwwdCn5+8Ntv0KhRYY265COiLCt2pBAjb4WTkJZA4yqNMxf+9Re0bq0qE7PI/vDos6Qb0mlYuWFRjFYQBEEQigRT+tJD51Golhhffw2jR0N6OqSkwHvvwRdfFOLASzgiykoY8fHxnDlzxvz4/PnzHDlyhIoVK1JDNQoTBEEQhAKRkKbSl55u+YyUmSwxsqQvP/oInnoqc5sHH4RPP1V/56cVU2lERFlhEBwMs2YVuR0GwMGDB+ncubP58dNPPw3AqFGjWLp0aZE/vyAIglD6yRopy5dPmcnRX6PBYDDyyiswZ07m+scfhwULVI/JrGg0GsoyIsoKg+BgZR5bDHTq1MnhPmKCIAiC4AgmUeaucy9Q+hKDjivfvsKcLKb8r7yiTpllXH9ZRUSZIAiCIAhmjEaj2TzWXetOcnqyinxpdbZ3zkBv1EO6Jz+8OYKYvbebl3/4IUyZUhSjLh2IKBMEQRAEwUyKPgW9Ua8iZVrlKJCYloifp5/dxzAYDSScasvJXUqQubnB0qXw0ENFMeLSgzj6C4IgCIJgxlRDZnL0z7rMXvRGPRWb/UHnx35C457M99+LILMHEWWCIAiCIJgxzbb0cffBx12JMkfrykzpzjuH7SFkRnf69Cn0YZZKRJQJgiAIgmAma6TM18MXwC5bjL/+glWr1N8mR3+tVoNbpQs295UJbIoyXVNW1B+C0jK1V74sgiAIZYesosxU3G8rUrZtGwwcCElJEBBg3afMHjQU/3kzIgJOn4boFO9if+7slElRlobqrZWYmIiXl5eTR+P6pKamAqDLbigjCIIguCwmsVG/PoSG2r+fSYD5ePig06jf/bxqyr75BkaNUh0HAT74AALGWXf0dzUWL4bx48FgAI12KPTd6tTxlElRpkdP+fLluXr1KgDe3t52R7XSU9MxpBtITk62/TypegwG+7Z1VQwGA9euXcPb2xs3tzL5cREEQShxZBUbWi0sWgRjx9q3b9ZImVajqpyspS+NRnj3XXjuucxl/furFOYjm3LvfekqRERkvkcARoMWNi0kIgJqVHfOmMrsWTYoowm4SZjZS3RSNCnpKehibEeNriVew2AwwK38jNB10Gq11KhRo9SkYwVBEEoz2cWGwQATJkCPHvZFzKyKsmzpS70epk2Djz/OXPbYY6ptkpubSl/qNDqL9GV+I3dFxenTme+RGaMbZ84YRJQVNxqNhuDgYAIDA0kzxVzt4KudX3H4ymHWD19vc9sFWxdwI/EGSwcuLcBInY+HhwdarcwJEQRBKAlYExt6PZw5Y58YSkhNQIMGLzdV3qPVaC0iZUlJ8PDD8N13mfvMmQMvvpjp0p+9IXlBIndFRf36aiwW75UmnXr1nHe+K7OizIROp3OoVipGH8Pl5MuUK1fO5rbRadFcS71m17aCIAiCUBhYExs6HdSrZ9/+8anx+Hj4mLMjPu4+5ujZjRswYADszWib5OYGX3wBo0dbHsNkiaHRaEi/GcT45/IfuYOiaVgeGqrE4YQJSrRqtQYMfScQGvpFoT+XvUj4QxAEQRBKESaxYYo36HSwcKH9AsjU99KEj4ePOX158SIcOaKW+/rCDz/kFGSQaYmhQUP69dq5Ru5M5Ca6irpsZuxYCAuDHTvg7R/XQKv/Fenz2aLMR8oEQRAEobQxdqyKRJ05oyJkjs6+NJnGgqotM6UvW7SAb79V0aWNG6FVK+vHMFtiaDRoK521O3LnjNrl0FB1O384sdifOzsiygRBEAShFGISG46SI1Lm7mNR6N+nD5w6Bd552HqZ0pdajRZNQKRFmtDRyF1ZQtKXRYyrTgUWBEEQBGuYRJnRCPPnw9W1LxCXYulTlpcgA8v0pRGjRZowLMz5Rf6uikTKihBnOBMLgiAIQkFISEvAS+fHlCmwYAHAMI5US4T77T9G1vSlKTiR38hdWUIiZYIgCIJQgvnsz8/ourwrhy4dKpTj3YrRc/TDuRmCTJEY71gMJ7slhmAfIsoEQRAEoQTz8R8f81v4b7T5og2TNk/iVvKtfB/rwgX4ffY7XDncGlCWF+0nLySkn2M2EXpD/npflnVElAmCIAhCCeXUjVMcv36cbwZ/w/s93mfZ38touKAhX/39lcM1zX/+CW3bQmJEXQAqVICtW6F598N59r60htnR3842S1J/rRBRJgiCIAgllA0nNuDl5kWv+r2YeudUTkw8QedanRn5/Ug6L+tMXEqcXcdZtw7uvReuXFGPy4dcZ98+6Nw5Y/alld6XeZG10N+R9GVZr8V2WVH2119/0b9/fypWrIi3tzdNmzblo48+cvawBEEQBMFl2HByA/fVvQ9vdzUdspp/NVYNWcWPI35kV/gutpzdYvMYK1fCkCGqfRKAR+39jP90CQ0bqse+Hr45el/awpS+1Gq0ZSt9eflygXZ3SVG2detW2rdvz9WrV3n55Zf58MMP6du3LxEREc4emiAIgiC4BFcTrvL7xd8Z2HBgjnW96vXCXevO1YSrNo9z331Qq5b6e+RI8BzTj8AqmfLAx0NFyiIilKWFPadiU6G/venLEkdUFLz6qrrPSgFFmctZYsTGxjJy5Ej69OnD2rVrpRG2IAiCIFhh08lNaDQa+jbom2OdRqMh0CeQK/FXbB6nShXYtAl+/BGmTzeyYm50DvPY2H1DqPmC/Q3FzZYYpaDQv0pMOl2W7YbboiA4WC2MioLZs6F/f7UsORkOH4bVqwv0XC6neFauXMmVK1d4/fXX0Wq1JCQkYMjeNEsQBEEQ7MCR6E5JY8PJDdxV/S6q+FSxuj7QJ9BqpOyff1Rj8aw0bQozZkCKPhmD0WAhylJuVkG/8bMcDcXzek/1BlXoX5IsMbyu3WLWDnJEvwJj9XRZ/lvmcqMRwsPV32+9BbffDn5+0KEDfPJJgcbgcqLs119/xd/fn8jISBo2bIivry/+/v488cQTJCcnO3t4DlPSrxAEQRBKKosXQ82a0KWLul+82NkjKjwSUhP45dwv3FvhoVxFZ6BPIFcSLCNl338P7durGrLUVCvHzagd8/HI7H0Ze6kqGHUW22VvKJ6dkpi+9L4ew6u7yCHK/JIzROX8+Up4lS8PgwapZatXK5Wbnl4oY3A5UXb69GnS09MZMGAAPXr0YN26dYwZM4bPP/+cRx99NNf9UlJSiI2Ntbg5G2c0VhUEQRCUSBk/HoeiOyWJrWe3kvzHCOYNHp+r6KzqW9UcKTMaYe5cuP9+SEyEnTuVxsiOyfoia6Ssbj0DaPQW2+XWUNyEo+nLYg9g5FYTBvDvv/D669C7N9SowapPM6KNK1bAvn2Qm76oXx+GDSvQsFyupiw+Pp7ExEQef/xx82zLQYMGkZqaysKFC3nttdeoX79+jv3eeOMNZs+eXdzDFQRBEFyQ06czBZkJU3SnNLT6Wbl3N2xahMGoLv5NorNHj8zXF+gdyO8XfychAR59FNasydx/xAh46qmcx7UmymrW0EG/8Wh//BKDXmNXQ3GzJYbGQUuMQg5mlLt2k1k7QDPyMtQun7nCVBNWuzZcugTHjtFp1y8AaEeNtn3gwEC4ehWmTYMBA1T6MjhYffAKUFfmcqLMy8sLgAcffNBi+YgRI1i4cCH79u2zKspmzpzJ008/bX4cGxtL9erVi3awgiAIgktSv74qSM8qzGxFd0oK6YZ0tvx5LteUokksVfWtyuUIT+66C/7+Wy3TaFQQ6Pnn1d/ZMfmR+bhnpi993H2g1f/44ZWpeMU1o14928LWwhKjuNKXUVFKLU6YYC7IL3ftJq/ugrjLV6BisHLI3b9fueICjB5t3t3f2jE1GsIraKkZrYfHHoN+/SAkBK5fh5494eGHoVWrzO1Pny7QS3A4fXnlyhU0Gg0ajYYtW/L2P5k0aRIajYYOHTrY/U8JCQkBoGrVqhbLAwMDAbh586bV/Tw9PfH397e4CYIgCGWT0FA1Q1CXoVvsie6UFPZe2EuczyG0WsvzanbRGX2iKfELdpgFmZ8fbNwIM2daF2RgPVJm+tu38i06dbLvPdQb9aqmrChmX+aWejRFv6KiVI3X4cNU27ofAO8Ro1Qt2H33wcsvw2+/5Xp4Y7u2MH06LF8O58/z5OiMiRSPP65EWevWasqqNYKCCvTSHBZlVatWpU6dOgAcOHAg1+3+/vtvPv/8c7RaLR9//LHdIcnWrVW/rcjISIvlly5dAqBKbm+EIAiCIGRh7FgIC1OzL8PC8rZwKElsOLmBkFAjny805io6P/sM3p7QHRLVObNePThwAPrmdM+wwJooMxX9O2IgmzV9Cflvo+R5NZpZO0B7OcuEhaziy0REBGzbpv4eNUop0FatuO2L9QDowsJtPtfpPu3VWD/5BN5+Gx55RBXrWSM4GGbNyrTIMFHcogzgrrvuAvIWZZMnT0av1zNu3Diz0LKHYRlFcouzVSx++eWXuLm50alTJ8cHLAiCIJRJQkOxO7pTEjAajXx/4nv6N+jPY+O0uYrOI0dAn65O8XfeG8Mff8Btt9k+vkl4ZfcpAxzqf5k1fQn5L+T3vBbNq7tAdzmLtUdiorpfulQV41epAtWrw3PPqeXHjinfsNzo1EnNegD44gs4dAgOHeJcr/ZWN7/qr2P7yHssBVhwsIrWZRdlBSRfNWUdOnTgq6++ylWUrVixgt9++40KFSrw+uuvO3Tsli1bMmbMGP73v/+Rnp7Ovffey86dO1mzZg0zZ840pzcFQRAEobQTEaHKlOrXV8Ly2NVjnL91noGNBgJqmTXB+dFHcOhIKod0HzHz08ZUqNDbrueLT41Hg4ZybuXMy8yRMgf6X5otMcgSKcsjYeZ25RqzdoB7n+uQtRxcr2Z9en37HcxfpATX2bNq3ccf2xxHTN1QAs5GkPjBO3jf00UtDA5WUbaXXlL1YBk1YTev7+LVe+GVbELrWoAb20d1pEshCzBr5EuUmSJlN27c4MyZM9TLksSOi4vjuQy1OmfOHCpXruzw8T///HNq1KjBkiVLWL9+PTVr1mT+/PlMnTo1P8MVBEEQhBLH4sWZth4mF/2o+hvw8/CjU61OFtvGxEBAQOZjT0/YsV2D/7vTuZHyP7ufMz41Hl8PX4uSIw+dB+5ad4fSl2ZLDFP6MmukzEpBvu7yVV7dBf+ePAdHl6iar6NHafePKojz//TLvJ8wJARatIDNm+G991Q0DPj70Hd0HP86+rZtLAvyrVhhJFUpz+zOOUVZcZIvUdakSRMCAgKIiYnhwIEDFqJs9uzZREVF0bx5cx5//PF8Dcrd3Z1Zs2Yxa9asfO0vCIIgCCWZ3HzWGr/+O73q98LTzRNQ/mOffAKvvKJ0TJMmmcfw83GnolfFHAayeZGQmmCRujRh6n9pL3qDHv8bCbRcsYEgXyxtMUw1Yd27w7lzcOAAgRvWAtDk4WkWx7GcX5qBnx/ExamZk336qMad1aqp427erARZhgBLPfer9QHmVhPmZPJVU6bVamnXrh0A+/fvNy8/fvy42VtswYIF6HRW384yRUlxMhYEQRBch9x81o4e9KFx/EQiIlRp1ciRMHky3LwJAweqiFlWcmu1lBvxqfEWbv4mfNx98q4pyzYj0mA04H8zgdsXfk9wHBj1ejh5EpYtgzfeUPvccw/cfTc88wx+u/dZPWyanxpL4oDeqv5rz55Mw7XJk1VrgjvuyFVcJVepwKv3giHI0tGhqGrCCkq+Hf2tFftPmTKFtLQ0RowYwT333FPw0ZVwNHkl0AVBEASXwBX7Y5p81izQGGDdal59tCM1a0LDhspk3sT994NPNj1V1aeqQ5EyU/oyOz4ePpnpS2uWFNlmRJaPT6faP2EALNgMHlWCoFEjFd1aq6JiOVRndqZN48+v3gQg7ulJMG4c3HVX7nYUVqJfyVUqMLszGIMLNiuyuMi3KOvQoQOgrC9SUlJYt24dv/76K76+vrzzzjuFNkBBEARBKCpctT9m5aBkBk7fDBrVU1GjNagL/SwO/iYR6eurgkdvvw1u2YqSAn0CuXDRYLfoTEjLkr7MIr58PXwz05fZLSlSUuDoUfX3M89A9epcmJdE5/nKjqJDBGhstD5MaK9cGs6+9bx5NiTTp1vfOLfUo4tGvxwh36LszjvvRKfTkZqayt69e3nmmWcAeOmll2SGpCAIguDyuGp/zLiUOLot78ZGnwGMXTaXDT/HsuobLUZjzuxL9erwxx8qi2eNG3sGsGfaCrtFZ3xqfKabfxbx5eOeESkzGuHiRbX+tdegaVOlCk3O+Dt35v0GtmkDpu47Weworj01HoCEpg0zZ0QGB5NSpSKv3gv6oMDMY5QC8ZUb+W6z5OvrS7NmzThy5Ahjx44lPDyc+vXrM23aNNs7C4IgCIKTccX+mDHJMfT6uhf/XfuPPY/uoV2oqt8+ciTnthqN6hbUqJH1Y0VEwI4FD4JRxV+s9cc0kzEj0qPyDXwDK1mu27ePyZsv0uTsvzCmIty6pZZv2JD3awmpTMCl68zoBrPm7MbbwyfTjuL99y3sKPTRZ60eIyWwIrM7w7jsNWGllHxHyiCzriwsLAyADz/8EA8PjwIPShAEQRCKGmt1W87sj3kr+RY9VvTg+PXj/DryV7MgA4iPt2yNpNEoi4zcBBko0Wk0WL5AvR7OvLQ01xZFrQ9cYNS3J1U7oT591LpJkxi6OYzGJ6MzBVl2qlVT9y+9BAcO0Go87J05AoBf6oC+ZQtz9MsaaVUr8+q9kJpdEJYxCiTKTHVlAP369aNXr14FHpAgCIIgFAeu1B/zZtJN7vvqPk7dOMW2kdu4I+QOi/V3360mLVapAvPnw4ULqu49L+r7X0GrsQwF6rRG6i17CS5dgvBwWL1a1YGNGQPAMyvO0e+7Y/DDD3D5cs6DenpCs2bq76eeUjMkDh3KzIvefz+GNndwOARSK2Qap1lYYlipCUuvWoXZnSE9qGy3Usx3+hLAy8sLUM3A58+fXygDEgRBEITiYuxYlc47c0ZFyJwhyKKTornvq/sIvxXO9lHbaRHUgthYVaqVNZI3fboabw5PditmrAChmkgWGV9gnGYhGN3QaY0svHcloTsilUdYdHTeA9NqVc6zSxc2hsSz3e8qH7y0V4m11q2VH4fJkPWvv8y7mQRYSmBF/ntyKFFeayzNY001YUIO8h0p0+v1vJrxpk6fPp26desW1pgEQRAEodhwZn9MvUFP96+6cyHmglmQHTwILVvCW29ZbqvVQuU023YU6PXwzz/w3XeM5X/s8a3FdjoRZqjO2B0Pq21sCTLILN5/5x32jLyXH29zU8751sgS/dIbVGuklMCKHJ84nMt+4tlpL/kWZR999BH//PMPtWrVYubMmYU5JkEQBEEoE+y9uJdDUYdYPWQ1zQKb8+GH0KGDMrp/6SWVHbQguwADuHZN3X/0kdrZ1xduvx0yek/fFRdJZ3YRSqT1QfTooQrvgUn3e7JiyTSVkhw2zLyJj3sWR39rlhRZZkTqjUqU6TQ6c5sli/SlkCv5Sl9+8803zJgxA41GwxdffIG3t3dhj6vUYBGyFQRBEIQsrPtvHdX8qtE84F4GDYLvv1fLg4jitaCF1PedAGQRP0lJ6v7TT+H8edWg+2qGY/+yZbafsEULNZVz4ULlhA+ZMyKBfVVSaN6skUpLRkWZxZdvsm+meayN9KNJgOm0OrQaFfuRc6F92C3KfvzxRyZOnMjNmzeJzTCBe/nll+nWrVuRDa6kk7WhqyAIgiBkxWA08N2J7+gdN5av6rzG/phMAfbcw1E8tmI2XGgGey6o9kLHjqkplWDbcKxWLSW61q7lpcEVCOo2kEltJ6moWs+eap2VBt1GyDSPzSK+fCJVpMxoNNo8t5nSl1qN1tzZRtKX9mG3KNu7dy/h4eF4e3vTsmVLJk6cyNixY4tybIIgCIJQeshWkH/g4p9E/DScw9v7sUjfhk3cTWffg7za+wANTv2i9snNFTYrlSrBjRvw5JPQv7+aommKfq1dy4XbQrgcolUiLEtBvgXBwSTMfJao1HczzWOz4OPug96oJ0WfQjm3cnkOxxwpy5K+tBUpE9GmsFuUzZs3j3nz5hXlWAQbRESoi6T69Z1nbCgIgiDYgbUZkaZ6sP79iTZW4J3u53nqZCg9eRGAbdwH8cDqPI4bEqLsLEaOhN69oU4dVbTfs6eammkl+lXRqyLnTE3J82hRdHX6k1z+6N1ce18CJKQm2BRlppoyrUZrTl/aW1NW1ntGF8inTCg+XLU/myAIQmnj63++pv3i9vwW/pvtja015zYtNxXkG43qinrzZrXu4YepUNOP704+yAdMoydb7RvY88/Dpk3q76eeguHDVdsiGw26dSGhmU3J82hRZKoZsybKTMvMdWV5YEpf6rQ6SV86iIiyEoCr9mdzRYxGI4lpic4ehiAIJZTt57czesNozt88T8elHZn440TiUuLUSmsCzNpsyOho+P139ff48VC+PDRoAC+/rJYdP44mPT3vgZjqtbP0h2TKFOvb2mjQ7Vm9FldNkbI8iE+NBzKjYlkxpTTNMzDzID/pS0EhoqwEkFd/NsGSb459g/8b/ozZMIYz0fIGCYJgPyeun2Dw6sF0qd2F8KnhfNTzI5b9vYymnzVly5kt1gVYWpq6//ZbGDwYatRQNV6TJ6vlhw5BxuQ4a+g7dMgUa1kF2LPPqmWm/pCmFkU27CisUdWnKlfir9iMVplEWV7pS9M2eZE1fWmKlIklhn2IKCsBuFp/NldmV9guKnpV5KczP9FoQSNGfT+Kk9dPOntYgiC4ONcSrtH7695U86vGmrs+wnPuG0yuMYRjTx6jQaUG9Py6J69szxBPa9bAQw9B8+aq/xHA22/Dd9/BxYu5Psd5jwYAGD/4gEHP1eTV9/qhW7sWBg5UG2QVYHmlJPMQYNYI9AkkKT3JZurRFAWzKspMkTIH05dmSwxJX9qFiLISgCv1Z3N1/rr8F73r9+bclHPM7zGfX8/9SuNPG/PQdw9xPfG6s4cnCC5FRIQyJy3TpRBRUaS9/CJjPu9FYloiP474Ef+bCSoiduoUtbYcYOu++lza0IBnX8yoCXvzTVi5Eo4eBWtpyCpVoGtXAFY0nkcrDtKKQ0xI/QiAc01CWO8dTu07nmLHiWAirrjnPEZuKcl8UNW3KgBX4q/kuZ05fWll9qW5pkzSl0WKiLISwtixEBamfkDDwtRjwZI0fRpHrxylZVBLvNy9mNxuMmennGVBrwVsPLmR+fukP6sgmChzk4dyKcg3XIrEfe48bp4+yq/N36Xmtz9nGqN26gQPPIDms88IPnwK/1QrxzWZpz/wACxfDvv3w99/c2Dw2wC8/18PDtOaw7Si4yAV/dp2fhvl/pnImM5d1PvftymL+33vUErSEQJ9AgFs1pXFp8aj1Witzq40z760J1KWj/SliDZFgRqSC7YpzJBtaKi6paSnkJimx9tdOilk5cT1E6ToU2gZ3NK8rJxbOZ5o8wQ/nfmJQ1GHnDg6QXAdcps81KNHKYnA27CjIDhYvQkHDnBk4WwCqcarixtRfuHzkFsrIsDg7YU2MYkzd91GveFPQJMmqqasZ0/VLbxVK5KT4YUXYOf8KEyOYJUqwZdfwsB2wdBsFkvP7SR5/XYwZggWg4YJmwfQQw9F8fZX9cmIlCXkHSlLSEvA18PXqjmsKXpmT01ZVkd/09/2ngvLuum6RMqKkKLyW5n681RGrBtRJMcuyRy+fBiAFkEtcqxrHdyaQ1GHpK5BEChFk4fssaMASEhQxfOgCuiDgqB6dRgyhMO/tKEm4dyX/is1CWcxY6w/16RJaHcri4wp7aJJn/iECjNmqf06fBhat4b58yGKYF5lFg3vDeaffzLKxoKDOT35IfZFacBoefotyve/oldFtBqtXZEya6lLUALLU+dpV/rSwtFf0pcOIaKsBHL06lGOXz/u7GG4HIejDlOvYj38Pf1zrGsV3Irride5GJt7Ea4glBVKzeQha7Mh9Xo4e1b9/dJL6sX6+anQIKgakCsqYhRBNcazCAOqYNeAjgksJOKOgWrbrLMhX3gBMgTG5fgrrPtvndomo/brmlswHTrAf/+pxTc9gyk//1W+3h5MSEjm8NYdX0e5qhFotZYipSjff51WRxXvKnbVlFkr8jfh6+HrUPpSpxGfMkcRUVYCCY8J51LcJWcPw+X46/JftAxqaXVd65DWapuoXFqMCEIZokROHsotKgawc6fy8GrbFvz9Ydgwtfynn1T4KRdBsLPq7WZBZkKPG2eGzlQPcrGjqNO4A/P3Z9SoZtR+pVQMNndEatlS6bipU3OK37X/raXvHS1YtEhTrO9/oE+gzUhZQmpCnqLMx8PHsUJ/bWahv1hi2IfUlJUw0vRpXIq7hMFoIC4lDj9PP2cPySUwGA0cuXyE5+963ur6EL8QgnyDOHTpEAMbDSzewQmCCzJ2rKohO3NGRWhcRpBZqwczLZ89W4muiAjVnNuUknzmGdvHrVEDLlzg5vNTeSBxOYF+QbzS9xO0dxkxGDJLTXQ6qNfMy/oxMgTYqJOt6b9yAHvC9nF3rfYsXpxZo6fRqKE3aZJz97BbYRyKOsT0DtMZ3rR43/+qvlVt1pTFp8VbNY414ePuY59PWZb0pdkSQ9KXdiGirIQRGRdpvuK4FHeJhp4NnTwi1+D8zfPEpsRaFPlnp1VwKyn2F4QsmCYPOY28CvL79lWmqwcOqNuOHWq9LQHm7Q0NG6oCr2efhQED1LJr16BnT8YZv+d0nQC+GreDQJ9AFr0YzoQ51dDjhlar3C5CW1TO046iWbk+eK3awxOnwvjpnfYWkyaMRpg4Efr0sXxvIyJg3nf78IivQ+/6vYHiff8DfQKJjM19EgPYTl/6ePjYlb60sMSQ9KVDiCgrYYTfCjf/fSnuEg0riyiDzCL/3NKXoIr9Fx5aiNFoLPMzfAShWLEV/erfH9zd4Y8/4Pvv1brOnSE+76iM3k2HLl3P3sZ+nGtdG33j2/BqfScNUv1o2Xcc/3VrQVwtd/TGZMpFXaQVEJ0UzU8P/WG2iRj7hAfR+7YxY1t3DAYNM2ZAhQrBjDXZYmTBaIT//Q+mTdOSFNeBY2fv4Ov21zEYKluOK6No3yS4VCTNiMHwIBrNcFY30ha7rVFVn6o2yzfiU+Ot1uSacLSmLGuhv01LDBFtgIiyIiMiAi4fvY0UH9sfYEe4EHPB/HdkXN5XPWWJw1GHCfYNNpskWqN1cGuuJlzlUtwlqvlXK8bRCUIZwh47ipQUOHIE1q5V6/v2zVkrZkOQAaxoqWXUn3p2PNaN7RVucTp6LxG/f0vLS/AX8PB3D3N4v9o2KA4mdtbx5sPLLC5mI/TBPL892Fx2lps9SGSkSlGaeooDaHyv8fv1X9BqR1vMZs1atJ9pP2KKGGmdYj9ib01ZsG/uvmg+7vbVlFl19LczfVlUrgUlBRFlRUBmfcFM0OhZXL7wzF7DY8Kp4l2FVH2qFPtn4a/Lf9EquFWe25jWH4o6JKJMEAqKPdGv4GAVXjK1DHjnHTh5MqcTvrXi/az07q28wKZMgS++wNCyBU/++CQxkWcZ9Wc0L3V8iZdaqe93UloSF04cINLna5aNHIoxOAidRmeegVjJu5LFofOyBwkNVcNfsgSefhpiYjK3efRR8O+/iKUnPuSjTx/gqYnl0OtzFu3bOn5xUdWnKtFJ0aTp03DXWekggH3pyxuJN2w+l6Qv84+IskImuykjRl2hXhWF3wqnRkANEtMSRZRl4XDUYR5r9Vie24T6h1LFuwqHLh2if8P+xTQyQSilZBdfJuLi1P0HH8D586og/9YttWzVKtvHbdUK/vpLTQ9trWZNExycKdxateKDlJ0sNP7JrkdXQfBxi+f3cvfCp0InTvXrRP3KEJp78BzItAexFukKD1e/51u3Zq4LClJOGX37wsWYcSz453UMLb4gLGyy1aJ9X19AY7DwJXOG/YgpXXst8RohfiFWt7Epytx9uJB2Idf1JqylL6XQ3z7EEsMOHOkPV9SmjBdiL1CzfE1C/EJElGUQFRfFlYQreRb5g3KKbh3Smr8uiy2GIDhEXnYUx4/DG28olVKrlmpNBPDVV7BnT6Ygy069ejAiwwT7888z/cDmzVPLWre2tKPI4NT1U8zcNpOn73yajncOz9GKyNH2UbnZg0REQNOmloJs1Cj491/1UgGqB1RnaJOhvLvvXbwq3qBTJ0tBtngx3HmnMUOQGS2OX9wTLOzpf5mQlpCreSxk1JQ5aolhZ5slQSGRMtSX7/RpdcWU/YuSdaqzVgsdJ7WHxr/neqy8rroKg/Bb4fSu35vr7tc5d/Nc4Ry0hGNPkb+JVkGtWHJkSVEPSRBKLnnVhNWtC5cuqfTj/oxirYcftn3MKlXU7MennlKzIQMCMqNfK1dCmzZKfIGKklkjOJi0l15g/KFZNKrciHld5+XYJL/to6zZgyQnQ7VqKtsaGqrekt69c+47t/Nc2i9uT5+Vfdg2cpvZUiJ7LRlo0Gph3z71cosbe/pf2hMps6vQ35olhqQv7aLMR8ryuqqy9gXfteBBUm8G5nq87FddaPWFdlVkNBq5EHOBGgE1qOZXTSJlGRyOOkz5cuWpVb6WzW1bh7QmKj6KqDgbNSyCUNqx1aLozBmVInjzzUwbipEj4fnn4euvM13zs6LRqGgZKKXz/fdw8KCKmpn279w5R/TLggyD1hzrg4N5tkM8+/XhrBy0Ek83zxy7FiRTUa0aFpGucuXUTMvHHlMZWGuCDKBuxbpsfmgz/177l6FrhpKmT8t1LAaD6vjkDGyJMqPRaJd5rF0+ZVkd/SV96RAlQpS9/vrraDQamjZtWqjHze2qypSmtPalMhp0pFytnudxx46FsDDoPucN2rw9tNCK/K8nXicpPYmaAZnpy5J09eFIGtgRDl8+TMuglnbZXLQOFmd/oQxiTYBlbVGk18M//6hiqddeU+s7dlRXqzNnKsf83GjTRom2pUuVUFuX0X7oySdVVKx1a4v+kBZYE2AZBq3ZRdmWM1v46I+PePu+t2kSaMWZlfy3jzp4ENq1y2yRZKJDB3WRHRCQ9/53hNzB+uHr+fXcr4zdOBaD0UD9+qDRWp5AnNnKqpxbOfw9/XM1kE1KT8KI0aZ5bFGlL0W0KVxelEVERDBv3jx8fHL/oOQXW1dV1r7gGq0ez0Db/RNDQyGo6Qk8K14rpNGqmZcANQJqEOIXQoo+heik6EI7flHiaJ2HI/wVlXt7pezUCKhBRa+KYiIrlE7sbdB96RJs367+Hj9e9Ya8/Xb194YN9j3XI4+o+88/h3ffVQVXtWtb3zaP6Jc1AWaNqVum0q1ONya1nZTrNo62j0pIUP6y7drBn3/CuHHqHJAfutXpxlf3f8WKf1bw3C/PUSUohfJDngNNRipP6/xWVnnZYpgiYLZ6XyamJdoMBhQkfVnWPSRdvqbs2Wef5c4770Sv13P9+nWH94+JUV05rGGr/sv0BZ8wAfNU53smfsOtCnl7vRQVJo+ymuVrkqpPBZSBbPYp3q5Gfus87OFW8i3O3zpvs8jfhEajoXVwaxFlQunE2ozIxMTMOq2nnoJTp+Bqlt+wQ3Z8Fzp1UtGyL77IrP26di0zLZmVvKJf+eTk9ZOcuH6Ct7u9bT7J54a97aN++AEmTVIzLE0kJqqXFRSUv3EObzqcqwlXmfLzFA5eOsjN5HpoNVoMLhIEquqTe6sle0SZj4cPRowkpSfh7e6d63YWlhiSvnQIl46U7d69m7Vr1/LBBx/k+xh33AGffKIuCrOnzey5qjKlInfsUPeNu+/L91gKSvitcLzdvankVck8pbkk1JUV5YzUI5ePAPYV+ZtoFdxK0pdCycdaVMz0Rdu4UdVvNWyoomCPZdjF7NljKciy064dPPec+vuLLzJnRD6f0VM2a4Pu5s0LHP2yl02nNlHOrRxd63S1a/vQUHLMhDQRGQlDhkC/fpmCzNNTTSD988/8CzITk9tN5sV7XmTXP2dg0yJzoX/28hhnkFekzJSWzGv2pWmdrboyC0sMmX3pEC4bKdPr9UyePJlx48bRrFkzm9unpKSQkpJifhwbGwuo359JGdFurRa0/UdD98z97LmqsuhP9nc+X1AhEB6jPMo0Gg1BvuqXoySIsqKckXo46jDl3Mo51G6qdXBr3tr7FlcTrpqLXwXBZbFl0qrRwMWLakbk0aNq3ezZto9bt66qAXvnHVVXAJkzIt9+O1N8gfUZkQWMfjnCplOb6FanW57RGVvo9fDpp/Dii5lWagBdu8Jnn6nfqcJiTuc56M915E2jZdzDGaaxWanqU5UDkQesrrM3UgYZAi6PiiKrjv4lqP7ZmbhspOzzzz8nPDycOXPm2LX9G2+8QUBAgPlWvXrOYnyDAdK//5RrEX4Wy/O6qnIlLsRcoGZATQA83Typ7F25RIgyR+s8HOHw5cM0r9ocN6391xetQ1Sx/6FLksIUXIy8CvLDw5UNxYcfKn+v/hkGyK++qoo0//gDkpJyHrN8ebj7bvX3rFlqu0OHVAoBlCCz4gdmQW41YcVAdFI0ey/spV+DfgU6ztixqiGASZBVqQIrVsAvvxSuIANVJjGxZ/d8TTooSgqjpgywaYsh6cv845Ki7MaNG7zyyiu8/PLLVMlt1k42Zs6cSUxMjPl28WJuxfhaPnpikIUhYEkhPCbcLMqAEmWLkT0NXFgzUv+K+otWQXm3V8pO7fK1KV+uvNSVCc7DVkH+pUsqpLJiBbz1llp3zz3Qvj1MnQrffKPycNnxy7jgHDRIFeDv3q2mFH74oVrev3+mJ1ghzIgsDn46/RN6o56+DfoW6Djjx2f+/dhjcOIEPPSQCjQWBUV5MZpfqvpW5WrCVatRK5PQsjX7ErA5A9Na+lIiZfbhkunLl156iYoVKzJ58mS79/H09MTTM6dvjUYD2T8Lt6760aMHDB4M778PNWoUdMS5U5gfxPBb4QxqNMj8OMQvpEQ1JbdIAxcCSWlJnLh+gintpji0n0ajkboyofiwp0F3dLSKYK1fr9Z37myZYwPLXpG58cADqhbsxRczU4+m58uOrRmRLsIPp3+gdXDrXFsDWcNggBs3LHVnhw4wZw7ce6/St8WBvZMOiotAn0DSDGncSr5FBa8KFuscSV/aqimzsMTQ2GmJIaINcMFI2enTp1m0aBFTpkzh0qVLhIWFERYWRnJyMmlpaYSFhREdbb8NxEcfZV6paLVAxUzDw3Xr1IVoUVGY3e4TUhO4kXSDmuUzI2VlvdXS0atH0Rv1DhX5m5AZmEKhY68dRWpqpiHWyy+r2q5KlaBXLxVagZyCLDumSBhYFuQPHmx9exeLftlLmj6Nn07/5FCU7PBhJbr69Mlpb/HSS8UnyEy4UnlMVZ+MVktWZmDGp8aj0+jw1OUMbpgwR8pspC+tWmLYmb4szPNmScTlRFlkZCQGg4EpU6ZQu3Zt8+3AgQOcOnWK2rVr85rJ3NAORo7MTJuFh4PHU015+JVfCQxUVy4mo2pXx2SHUSMgM6xX1kXZ4ajD6DQ6mlW1PREkO62CW3Eh5gLXEx23WREEq2QXX6DC9JcyvqNz5yovMD+/TI+vzZvhnI12ae3aqfus4mvBgsxePU6aEVkc7Lmwh5iUGLvqya5fh8cfV161v/+uZlJ++WUxDNIGRWWanR/ycvVPSE3Ax8MnT58wc02ZnelLnUYn6UsHcbn0ZdOmTVlvCuFn4aWXXiIuLo4PP/yQunXrOnTMrGkzjdZIu54n+HhaNy5eVFOhs7JkibqScmYxpjVMxrFZa8pC/EK4HH8ZvUGPTqvLbddSy+HLh7mtym2Ucyvn8L5Znf271+1uY2tByEZuMyIBDhyA1auVMjh2DG7eVMut/K5Z0LSpqhn74gsVMWutPqNcuwY9e1rOhjSNITsulnosKJtObSLEL4RWwbnXjaanq3/Fyy9nvtUADRqomzPJ3jt50aLCq6fND3k1JbfV9xLAy90LcKDQ34H0paBwOVFWuXJlBg4cmGO5yavM2rr8UL68umXl+HH1BdJqYdo0VZbh52dt7+LnQswFtBot1fyrmZeF+IWgN+q5lnjNbJFRlvgr6q88f6zzom7Fuvh7+nPo0iERZULu2LKjqFpVhUCOHlW9ekC1F7JFSIiKoL3wgjLM8vDItKP44gslyOxo0O2sGZHFgdFoZNOpTfSt3zfX6M3u3TB5suoQZcLXF155RfnkengU02CtUJSm2fklwDMAD52H1UiZPaJMq9Hi7e5t26csI32pQeNw+rKs43LpS2fy+uvqqis1VU14athQGVZnNz51BuG3wqnmV83C+qGanxJoZTGFaTQa+e/afzQLdDx1CerHpWVQS6krEzKx1R8yMlIVoj73nOrHA0qAzZsHmzZZj1x5eECTjD6NU6bAr78Ssfkfdjz1PRFUUzVgd96Z7wbdJTElaS8nb5zkTPQZ+jXMmboMD4ehQ1XRflZB9sgjqmHB9OnOFWRQtKbZ+UWj0RDoE2i1piwhLSFP41gTvh6+NtOXBqNBzbzUaCR96SAuFynLjZ15NcQtJD77DKpXVzMyU1PVb+zIkWqywPz5mVY/RUFyejKp+lT8Pa33hAqPCbco8gfMs5EiYyPzHTEqqUTFR5GQlkD9ivk3GGod3JrvTnxXiKMSSgS2ol/9+6vebAcPwncZn4+ePVUaMS9MU707dVLeX02bqnqwy5dV5GvUKBYfbpWZziKcRd9HMDbrV7cIWhQVBsevHcfTzZM6FeoU23NuOrkJLzcvGrp3ZccO5SVmijDFxGT+a0Bp2o8/VjMsQUWpTp+23Ke4KUrT7IKQm1eZPZEyyGhKbqvQ36g3R8jEp8wxJFKWBT8/mDhR1QHcd1/m8oMHVZ3ZsGEQe7lo+ky+uO1Fun+Vexotq3GsiUCfQLQabZmMlJ2+cRqA+pXyL8paBLUg7FYYsSmxhTUswdWwFf0Cddb899/MRtyDB6sfg06d1BUZ2BZkAI8+qu7fe08VON1/v0pTZhBxxd0ynYWOCfNqWBaAu1j063x4GqPnL6PZW73ouaKnOS1VHGw6tYkG4W/RqJ4XXbpAzZrqtxnUfIZx41T2+MsvlZuISZAtXqy2zb5PceOKPmWQe/9Lu0WZh4/tQn+DHp1GvXB72yyJaFOIKMuC6cv8yCOwbZuqK2vaNHP9mjWw8vGXSTjnWMrMntk3EXERHIg8wOX4y1bXm1osZUWn1RHkG1Q2RVn0aTRoCnTl3jRQ/XP/u/ZfYQ1LcDWszYi8cUPdf/KJCn/7+akvumlWd1hYTnPDrHTvDu++q/7OOiNy2DDr22dEv04nhFhJZ2mcms7Ki9fmR1KntpZlT4/C8P45Tv96D6v/XV0sz30j8QZ7joXxz+KJOWqyTL+jb76pUpVjx2YKn9zquJw187GoTLMLQqh/KEcuHyElPcVieUJaQp7GsSZ83H3s8ikzTT5ztM1SXrM/ywIiyjKw9mX+6CNVKrJwIQRmtEgsH3IN75r2n8Sv/NbHrqu2uBTlS/TL2V9yrEs3pBMZG5kjUgZl1xbj9I3T1Aioka+ZlyYaVW6EVqPl2NVjhTgywSnk5hGWnKzuP/9ciangYHUP8L//wd69kJiY+3Fvv13dL1yYKb6WLlXmruCQHUX9Oyu5XNsda+gNel5c/xmzngkCozqxGo1a+GERszZ+USyz6H468xPG0/dhNFjvHQlQoYLKMmfFFeu4XMmnDGBKuylcjLnI/P3zLZbbGynz9fCV9GURIqIsg9y+zGFhSqydPg3PPw8dxq1Do1MhfFMEbONG6xfWCdcrcGbZc3ZdtZlSaFvObsmx7lLcJfRGfY5IGWSIsvgyKMqiTxcodQlqene9ivVElJU08kpJ7tunrqaGDYPGjTOdQr/4QjU5vGw9Ek2tWpnGqwsWZAowU4ujO+6wrz9kHqlHV01nZSUhNYFOyzoxb8MasyAzY9Bx+rSB744XbR1mZCS8PLUabPoixzpbItZUx+XIPmWNpoFNmXrnVObsnmP2v4QMUeZuZ/rSDksMR9OXgkJEWQa2vsz+/vDGG1Cj1QnAsm5hwABlyr17t+X+cZeDcvyw5XbVFpeqImVbz27N8eENv5XhUVbeSqTMt4xGyqJPF6jI30TTwKYiylwVWw75x48r89VZs1QxKChh9dRTqtbg+HHrU6crVlT3jz+u9j90SHmKvfCCWt6+faYAc6Q/pB24YjorK5tObWLPhT18O36u1d/Du1sGM2f3nCI5wd68qS5869UzErajM9lPT/aI2JIgfF2BWffOony58kzbMs28zGQeawsfd/tqykyRMkfTl2UdEWUZOPJlTr0ZaJHqBDh/Xk3P7t0bjhxRy/yDr4DGsjA2t6u22JRY2oe251riNY5cPmKxzpqbv4lq/tWIjC05/S8LA4PRwJnoM4UjyqqIKHMJbBXkp6aqau6PP1a9cgC6dlW9dF57Dfbvt35ck2h6+GFYuVIZu65cqZY99phqbVTMdhSuls7Kyg+nfuD2qrczrEMHq7+H8wY+yT9X/mHTyU2F9pxJSfD221CnjgpMJieryIpfQDrvvKOyFI6IWFcXvq6An6cf73V/j++Of8fPZ34GHJt9adOnzJhpaC7pS8cQUZYFe7/MKVdr5Opd9tNP0LIlPPgg6NPcqTvqbbuEXlxKHD3r9cTXw5etZ7darAuPCaeiV0WrX5gQvxCuRXmw9dc0l2jjURxExkaSnJ5c4PQlQJPAJlxJuCLtlooLe/pDGo2q9dDP6mTBqFHKEbRdO+X19dNP9j3XjBnwww/q72nT1JeybVvHol8uNhuyKEk3pLP59GZzSyNrv4f31LyHe2vey5zdcwot8nHlipqseuuWeqxzT8e74+ecO6Pj2WfVRayjItaVha+rMLzJcDrX6szknyaTkp5SqDVlRZG+LCuRNhFl2bDny+wZeCFHaF+rtZj9zqpVsH7S68SHNWLfPttCLzYllkpelehcq3OOurLwW+FWi/wBjv7cBj4Ip8d97k6d/l2cnI7OsMMopPQlwL9X/y3wsYRs2GNHAepsvG+f+vuJJ1R6sW5d1VIDVKuitLS8n6trV3WfdTbkU09Z37aMmrHmRUQELPj2X25e8bZo/m3t9/Dlji9zKOqQOcJSUGrVUv92jQZGj4b6r/Zh6LT9VK5ctmfhFTUajYYFvRcQdiuMt/e+TWJaol3msfZaYuQo9LchqnJbX9YalIsoywceFa7mCO0vWqQu7j/4ACpXVsuNejeu7Lyfe+5RszdzE3op6SmkGdLw8/Sje93u7L2w1yI8fCH2gtV6sogI+Oilpua6tewTCVypEW5hcvrGabQaLbUr1C7wsepXrI+71l1SmEWBNQGWnq7u16xRxfi1a6tpdJMmqeV//JEZMrFGhw6ZYi2rAJs+XS3LOhsyOLjMR7/swVQfO23E7fBBOP/83CbP7bvU7kL70Pa8tvs1h6IXRiN8/z106wYJ2c7pL72knPnnfRTFibSt9KjbIx+vRHCUxlUaM+3Oacz9bS5GjIVmHmvVEsPO9GVZE2HZEVGWT6yF9j091cX5uXPqN9+tXBKgZtXfdlvuxzIV+ft5+NGjbg/SDGnsOL/DvD78Vjg1/HPWk6kZo5YfYNNEAlcxUCwKTkefplb5WnjoCt5HxV3nTqPKjUSUFYTcUpKmE/a6dcr8r2XLzLYYb76phFlYWO7HNXWT/uCDTPG1di0MGqSWZxVgeaUkRYDlSnYrIIw6nnhcm+eFnEaj4ZV7X2F/xH62nd9m8zmMRpWJbtdO+elu26ZKA7NSubKyitt6disaNNxX9z7rBxMKnVfufYUq3ur7Y695rD01ZeZImbRZcggRZQUgt1Snn5+6OB+y6DlCen7N66+rad5Zo1ZffAHR0epvkx2Gv6c/9SrWo3b52ua6MqPRaLXFEphmjFp+0HU68PFxLQPFwqawZl6aaBrYlGPXXE+UuWSkM6+U5JkzSjRNnqx8vEwpxXnzYMUKNQPGWhqycuVM36+5c1ULjUOHMt3077nHPjuKUtycu6jIr69Xj7o9uCPkDubsnpPrNkYjbNmigpu9esGff2auyz5T3cSWs1toHdKayt6V7XwFQkHx9fBlfg/lWVbRq6Jd2yenJ+fZ3cHC0V8jlhiOIKKsCCnnH0+toZ8SHm4ZtZo+XYmmWrVUJuZilDKv9PP0Q6PR0KNuD3NdWXRSNIlpiVZnXqoZoxrQqJSQaSJBfLzrGSgWJqdvnKZBpQaFdjyTLYYrXck5PdJpqyA/IgKOHlU9buZknJjvvVd1iV6wAHbuVA0Ks+Plpe6HD4clS5QVxT//ZDrk9+ql+kQ6akchEbF8kV9fL41Gw8sdX2Z3+G4OXjposS6rGOvZ03JibPPmytfxxx9zHlNv0LP1rKQuncGQxkP4Y9wftK/e3ua2prqzxLTcTZcLkr4s64goK2JSoqvkiFqZzj9xcSqI0POORvDrPPTxFQDoXrc7p6NPc/7mecJjMjzKcin0HzsWWr89hO5z3jCnUUuzgaLeoOfszbOFHim7lXzLZfzeir1VjD0F+VFRqiDIlHfq2FGdYR97TC2HnA7K5TK6LfTpA/PnK/PW9evVsueeU1Xd7dsXqx2FYInJCgitino44uvVp34fqvpU5Zuj35iXnThhXYw1baqy1YcPQ79+qqg/O39F/cWNpBsiypyARqOhTbU2ZgGVFyYvs7zqyiR9mX9ElBUxSVdCrdpnZK0xS05ygz0z6da6Ls88A7d5dkWn0bHl7BazR5m19KWJ2jXdMdTcbv4hLc0GihdjL5KqTy0UOwwTphmYxV1Xllt6skhbxdgjwBIT1dkTlHiqVk1NLb7/ftViCDLbF+XGk0/Cb7+pv197DaZOVRXeEv1yOYY8FINuWl2e+ux7h3y9dFodw5oM49t/vzWnpqpUUQFUEyYx9vffMGRIzovFrGw5uwU/Dz/uDL0z/y9GKHJMkbK86sosLDEkfekQIsqKEA0aygVezPFDpNEos/HsJCZoef99uP02f6rsWMv3B/4i/FY45dzKmQsxrWHN1d/VDBQLqz7q9I3Cs8MwUat8LbzdvYtVlOWVnizSSGd2AWYwKOdjUGZRjRqposhx49Sybdvgko0IYocO6j7rbMiXXrJ+BpbolxlXqRnccnYLer9wpj3Q0qELt/R0aKUZQ2RcJHsu7AGgUiWlxx0RY1nH0bVOV9x17vl8JUJxYJoMkJcthoUlhilSZiN9KelNhYiyIsaz4jWLqFVeP07u7upDmZoKl3cO5LejYZy9eZYaATXMVxvWyK0puasYKBZmfdTp6NO4ad3yjBw6ilajpXGVxvx7rXi8ymylJwsl0plbTdjNm+r+3XfhzjshIECdNUG1HDp50nprIlDTiJ94Qv2dVYC98opaJnYUduP0msEsbDq1ieZVm9v9nUpMhE8+UZNjpwy7nVD3ZhYpzNmzHRNjADHJMey7uE9SlyUAL3dVF5qUnpTrNlkd/R1ts5TXua4sIKKsGMgatfrmG+vNy0HPgQMaZsxQgYpWd8aSGPwL646vMxf5R0db3zfEL4RbybfyLLx0FoVdH3X6xmnqVKiDm9at8AZJ8fbAtCc96VCkM6+U5NatKn3Ys6dSdd26qfXffKNaDsXnkoKoXl3dz5qlvMMOHVJO+qYImthR5JuICHhsvNElZkdnd/HPi+hoNTm2Vi1lK3f+PMTFaah58l3WHl9Lml7NrPXysl+Mmdh+fjt6o15EWQnA9NubbkjPdRtr6UuJhNlH4Z7ZhFwJDVW3iAj1g2V5Ujbi1/d1WrZ8hZYtVXeYK1d9uGtDRS7FXaJXvV4YjcphwNNTlfkMGJAZSQnxU60EouKiqFuxbrG/trzIS4DkJ4JX2HYYJppWacrqf1djMBrsKnYtCKb0ZNb3xVp60vSZMRMVpUJmEyZYCh2TAGvZUoms/fth+3a1bvRo2wOqWlX1unnmGfXB8vGBa9eUkOvfXwmvrM+VHbGjsBuj0cic9d9iNDxgsbwg34mCsD9iP9FJ0XmKsvBw+PBDFb3NbvravTsMv78WY/++zvbz2+lRL3+iasvZLdSvWL9QDKGFosVdq9LLJhFuDWvpS6kpsw+JlBUz2VNTWi3cM3YT1Xpmhv8rVIBGDXXcV0cZKNYMqMmvvyqbpwMHYPBgNVHg00/Vj2Q1/2oARMa5XmPy3LzU8lsfVWSiLLApiWmJhN0KK/RjZ8eu9KStgvybN5XvwGuvqX6QAAMHqsbbCxbAf//lfGIPj8w3fsIE1Rfy4EFYtkwtGzEi0xNMCvILnZT0FMZsHMOi88+i0VqeoJw1O3rTyU0E+gTSplpOF//Dh+GBB1THq/nzMwWZVquW//WX+gg+OqA+DSs15Jtj3+Q4hj0YjUa2nN0iUbISgt2RsnymL8s6IsqcQNbUVHg4NOy/CT8Pvxzbda/bHSCjpgyaNctcd/o0TJyoskyL3qoNsdbrypzNseSfod+EfE25z066IZ1zN88V6sxLE8U9A9P8GVh7g7Ap7zO2dx4NulNTlXhavVqtu/9+1R+yZ08lkPbute9Jn3sOvv1W/T1+vLKqaN3augCTgvxC5VrCNbp91Y1vjn7DitFv8cUiLVqdOklptAanzY7edGoTfer3sRod3r5dfVz0GR6h5cqpIv7Tp1X2u2VLtVyj0fBA0wdYf2I9yek2ZuVa4dSNU4TdCqNnvZ4FeSlCMWGaiJFmyCNSZrTS+1LSl3YhosxJZC3Cj02Nxd/TP8c2vev3Jtg3mNYhrenWTRXP/vyzKg42cfMmzH/XEz4I451nbufgwRyHcRr7I/YzePVgAu/ZhG5aXb7/KaZAM0HDb4WTbkgvkkhZiF8I5cuVL1pRli36FRoKnWqHEzr/mcyImNGo1NpW1dGBhx8GX19o0wbeekstu3DB9nP1zDjBZS3If/JJ69tK9KtIOXb1GG2/bMupG6fYMWoHDzV/iLFjITxMw4SPVsHUWjTv+aftAxUyZ6PPcvz6cfo16EdMDFy9arl+3DhV31qlivooXLigCvzr1Ml5rAeaPkBsSmy+mpRvObsFD50HnWp1ytfrEIoXeyJlemMWR39JXzqEiDIXIC4lDj/PnJGyIN8gLj1zyRzF0WigRw/lUnD4MIwaBe6m2eMGd/7aehsffliMA8+D49eO02dlH1oFt2L/2P3gH8HlyqsKFA04HZ1hh1EEkTKNRlP0xf7WGnSbCu0XL1b/3MqVVZPumTPV8uPHrbcmMtG5s3IgBksBNnWqWiYzIp1KXEocHZd0xN/TP4djemgoLJg4hBYNKjNu07g8a3SKgh9O/YB7dFN+/qgP1aqpj0BWAgLUtUF4uPrI5JbRBmhUuREtglrkK4W55ewW7q5xt9mUVHBt7Kkpy0/6UtKbChFlLkBsivVIWV60aKF8PMPDlSWUm69qaTN5suV2SUnWa7OLkosxF+m+ojvV/Kqx8YGN1Cxfk651urLy2MoCHff0jdN46Dyo7l+9kEZqSdMqhSTKcrOjSM+4sly2TBXU162rWhOBKhDcujWzIao1mjTJ3NYkvr7+Wok5kBmRLsjqf1dzK/kWPzz4g1XLCTetG1/2/5J/r/7Lu7+/W+jPb80LTa+HTZtg7oS7SPvoKIs+9yAhQX0sb92y3P/OOzM7Y9nigSYPsOnkJpvNqrOO62xYCjvDdko9WQnClL7MM1JmyH/60hRZK6uIKCti7PkgxqXGWa0ps4fgYNV68P6FT9F44iu0bWu5fuVKqFFDtSTcvj03O47C40biDbqv6I6b1o2fH/6ZCl6qddSDTR/kt/DfuBhzMd/HPh19mroV6pqvwAqbpoFNOXH9hGMRi7wK8v/+W0XARo1StVv33KPWf/SRagB47pz1Y4aGQt++6u/3388UYO+9p5a1aycNuksI/zvyP+6rex/VA3K/kGgV3Ipn2j/D7F2zzebIhUF2L7T581VQtW5dNan2+j93mLf19lYf05SU/D/f8KbDSUpPYuPJjXaPq0FdDxIPPCCirARhSl/mVVNmYYkh6UuHEFFWhNir+ONS4hyOlGWnRuXKpDVcZbHMaFStCtPTYe1aZanRqJH6cc4ekCkMd/HEtET6rOzDjcQbbH14q9mqA+D+RvfjofPg23+/zffxT0efLpLUpYkmgU1IM6RxJtpKPyNbDbrPnYNdu+Dtt+HZZ9W6Xr1UYc7y5WqqWmpqzuP6Z/zfH30U1q2DP/9UvmCzZ6vl995rX/RLUpIux8nrJ/n94u+MaTHG5razOs0i1D+UxzY9VignL2v+gE8/DS++qKLrJoJDk3n3XbX9p58qd5T8Uqt8LdqHtmfVsVW5bpNzXBrYtJCKac3z/8RCsWKXJYa1Qn9JT9qFiDIXIDYlNt+RMhPV/KoRGRdp8cFPS1MT7AIDM7c7dUr9OFerBiNHwu7d8OWX9rmL2xJuH+z/gMOXD/PTQz/lEE8B5QLo06BPvqfNg0pfFkWRv4kKqc3gfCf27/wrbzsKgwH+/Rf+9z94/XW1/p571MyNGTPUm2SNihXV/dCh6k3euzdzRuWkSTBoENxxhzToLiUsPbKU8uXKM6DRAJvbert7s6jfInaF7+L7E98X+Lmt+QOa0GjgtvbncH/kfs6c0fDMM8qGpzB4oOkD/HzmZ24m3bR/XEY3zp4t2ymrkoRJbNlKX5oyGva2WRIUIspcgLjUgkfKQvxCSExLJDYl1rzMw0NphosX1dT2zp0zt09Ohq++UoGYxx6z7bhvqy1MXEoc7+17j8daPUbrkNZWxzii6Qj+ivqLk9dPOvz60vRphN0KK1xRliX6tXgxtLqtEizbwdjhD7J49sVMUXblioqCATz+uIpuNW2qppF+951abusq8Jln4Jdf1N/PPw9jxqiekRL9KpWkG9JZ/s9yRjQdQTm3cnbt06V2F1oFt8p3NNlggF9/VdcO1vqnguqSdfYsNHzqGe7qegtvT898PVduDGsyDL1Rz3fHv7O63npfV6NTPNqE/KHRaHDXutufvpRImUOIKHMyKekppOpTrc6+dARTqvDro18Tfivc4gvg4QHDhqmasuPH4amn8r4yzt7yx55WSZ/8+QnxqfE8f/fzuR63d/3e+Hn45YiW2ZM6PX/rPHqjvnDTlxnRr4gj1y1en9GoZQILiXhynhJAQUEqvAgqvZjd1jw7puL9rLMhn3nG+rYS/SqVbD27lUtxlxjT0nbqMiuDGg3ix1M/kpSWe1/B7Jw9q9qP1q4N992nPjYJCTkNij/7TKUoa9Yy8Fv4b3Ss0dGhsVkj+3c3yDeI++rcx+u/vU50Us5JKybjZEuPNo3T+/MKjuGmdbNpiZHV+06DRmrK7EREmZOJS40DKHD6snGVxtSvWJ+JmydS68NaBL8XTP9v+jN97Yes3Bhl/tFs1Ag++AAuXVKTADp0yHksnU7Nzpo2TXURsNWrMT41nnd/f5exLccS6p/7r6uXuxeDbhvEN8e+MYtGexozR0TAuh+jIaZa/iNl1mrCMsZwevXhnK8PN84cuA6XL+d+zDZtMuvHsgowk51FAe0oCqPOT3AOS44soVlgM1oFt7K9cRYGNx5MQloCv5z7Jc/t4uPV7Ot771WdAObMsbSv++qrnP1TH39crTt+7Tg3km7QsWbBRFlu393P+35OTEoMD333EHqDPsd+j44x0OKNgdSYMooz59Lz7VsoOA93nbvdlhigUp620peS3lSIKHMypnRjQdOXlbwrcWryKaKeiWLjAxt5rNVjnN3WiXeHTeKhAcHUrGm0EDzlysGDD6qypoULLa+oP/lE1aZ/8IFy7Z44UdWhZCVrW5jP/vyM2JTYPKNkJh5s+iCnbpzi8OXDdkXgTD/8L4y6Ez4I5+c11fJ+AlsF+V9+qZ60QwfoqE5K9Ze+gBbLk4eOdOqRJVxYN6On6NtvZ4qvDRvUmwiFbkdhj1gVcseZgvZG4g02ntzIoy0eNadu7KVR5UY0rtKYdcfXWV3/yy/w0EOqIP/RR1VNqAmtFnr3hjVrVOQMLE2qTewO342b1o07Q+908JVlktd3t1b5WqwavIqtZ7cye9fsHPsu/msxfyVu5Kunx1Knpke+xyA4D5uRMkO2SJlGY3f60tHvTGlDRJmTiUvJiJQVMH1pIsg3iH4N+zGhwRxOLHkajEptGQwaq7VioH5cs15Rt2wJsZmlaRw/blkypdWqGZyhoZCQmsA7v7/Doy0epUZADZvj61qnK1W8q7Dy6EqbEbjsP/wYdTzxuDbzNeRlR3HhgprF+PHHyhV/QEax9SuvqKjWvn2QmAhAKJEsYjw61I+MlnQWMoHQl8eoZqOHDimlCmoKaxHbUdgjVoXccbagXXl0JQajgYebP5yv/QffNpiNJzeSqs85W/fjj1WEO+OjC0DDhvDmm6p29McfYcgQVbKQG7vCd9EmpE2BzFptfXfvq3sfr3d5nTm751hYZFxNuMqMX2cwusXoAkfqBOdhq6Ysq6M/SPrSEUSUOZnCipRlx9aPZnayXlG3bauydp99piyxsmMwwPTpqjH6+9uXcjP5JjPvmWlXdMJN68awJsP49t9vqVvPYKXoNzMCZ/M1mATYpUvKkuKbb+DdDAPOe+5Rg58yRRmsWhuUT8ZJaeBAxn56B2Gr/+THby5y24hajOV/qsF327bFbkfh6P9OyMQVBO3/jvyPfg36UcUnDwv8PBjUaDC3wkN59KmLOXzDHnlE3VeooNKRv/+uLppmzICQkJzHyo7RaGR3+O4CCyLrBfuWTdVn3DWD+xvdzyPrHzFP7pn+y3Q0Gg1vd3u7QM8vOBdbkbLs6UuNRiPpSTtxOVH2559/MmnSJJo0aYKPjw81atRg2LBhnDp1ytlDKxIKq6YsOwWd5WT60d+/H06eVLoj674pKbD/gIGP/5nDqNtHsW1dLbujEw82fZCI2AjCDHtyFCMvfOsWoV++ClFRuf/wV4lReZwvv1QLu3RR6cURI5Qwg7xbE5kYMULdv/wyPPEEoUPb0/uB6jSs7p5z22IsyLfnhCdYx9mC9sjlIxy5fIRHWzzq8L4nTqjasIe6NYfPjrLyk7ps2WK5Td++sH595kVT+/Y5Swvy4uzNs0TFRxVYlJkK9i2+u9maqms0GpYOXEqIXwiDVg9i08lNLP97OW93ezvfglVwDWzVlGVPX2o1Wpl9aScuJ8reeust1q1bR9euXfnwww8ZP348u3fvplWrVhw7VoR9CfOBPZEhWx/EooqUZf/RRJPO0Bnb8jXLqUEDpTtOnVLZvClTlPdZvbuPEJ18nUfrvJwjOjF+vBJz1mhfvT13UI3YmU8ztneURep0bOdzZj+w0FBY9JkenVYdWIeehZVmEtq0PHTvrs5KYJlrtcb992dum7Ugf/Bg66+3yb181LOC0+wo7DnhCdZxlqA1/RZ89Mt3VPWpSq/6vWzuYzTCP/8ord+kCdx2m8qu//dfpsr65htLhenlpQK4eaUn82J3+G40aLir+l35O0AWsk8ksFaw7+/pz/rh67kYc5EBqwZwV/W7eLSl44JVcC0cscQAlb6USJl9uDl7ANl5+umnWblyJR5ZfnWGDx9Os2bNePPNN1mxYoUTR5fJ4sWZaRKtVp1Es/8o2VOwaKopK4pmvGPHqraIZ87AOycm8o9hD0bjsXwXUmo0KpvXti3MfTOJeu8PZ2TTkaReq5kjOmEwQLNmytS+UyeoU0d1GgoNVVdNjwR2o++ry0ibdoHQNsFKcBiN8E/GbMd58+DcOcYeP04PQyXOUI96nCH0amTeg2zXTinHL75QaUdQQspUd2aqBwO1zEr0q80d/Rl8bhkDvdOwXSVXNGT939WrV7YEWUSEinjVr+/46zYJ2gkTVISsOARt1t8CNLPoMbWZuRVNbixYoLptnc6lq1LzNnH8U3kmQ58eAViZIp1PdofvpkVQCwLKBRTK8UJDbb+3jSo3Yvn9y5m0eRKf9/3cIoIilEwctsTQSE2ZvbicKOtgxaOhfv36NGnShOPHjzthRDlJvRnI+Bdz1q306OH4j7/Jzb+ofqhMP5rpNYZy31eL2HtxL3fXuLtAx4xLiePd/e9yQ3+eF+/5Gc9EJUyzC7O0NNXiceNGI6ABjAwbpmHuXOhVrxewjOM/Laf5+g2q8P7YMbh+Xe28LnP2WSiRhJJNjDVurHI3ixers3DrDMPaa9egZ09L8QXWu7Kbol/ZuLfmvWjQsP38dka3GO3gu1N42HPCK6nkJrzsudixRXEKWmuTUX75aAgRT2c+b0oKZPdovXw5pyDr0EEFb4cMgdDqPtT8YAM7r2sZVIiibPvfp2hTbgwREcX72RrYaCADGg4o8zPrSgv2pC+zRsrsSV9KelNRIi5ZjEYjV65coXLlys4eCgApV2sUWt1KXGpcoc28zIsutbtQp0IdFh1a5PC+UXFRrPl3DU/99BStF7Wm/FvleW33a0xoPYG6FetmSbepL5VWa6RTp6y18Rrz/ZrVBnY2GEfdUcpMtfmsT+GNN2DnzkxBlo3oil4AGGfMUJXNhw4p6/Inn1QbtG6dv/6QuVDJuxItglqw/fx222+O4DC5zY4szCJ9a1YQRYG1GjaDXsPvv6sI3YABqrtW9t+G/v2V6OzUSc2ojIhQ9jRPPw01aqiT2KBGg/ju+HeFFmF45+NoLs7+je+en+SUWakiyEoPDhf6O5C+tLdndGmlRIiyr7/+msjISIYPH57rNikpKcTGxlrcigrPwAuFVrcSmxJb6PVk1tBqtIxvNZ7V/6626rSdG4sOLSJ0fijD1g7jx9M/0iywGQv7LuTU4F0s+KOyOQI1diyEbTrGDjoR/sMxdqyM4puJe3Icz4iW+pxBG5UzDanXuZFW/zb1YNIk+OUXEvf/xuh+6qSkGTZMRcfyY0fhYE1Yl9pd2H5+u1y9FTJ5CS9nF+nnh9zaGQ0fribKbNyo7Cs2bLBcf8cdKlq2Y4f6qFezYr83uPFgIuMi+SPyjwKPMyICZkytkMUiR2xWhPxjjyWGpC/zh8uLshMnTjBx4kTat2/PqFGjct3ujTfeICAgwHyrXr16kY3Jo8LVQivEjkuJK/SZl7nxaMtHMRgNLP97uV3bL/97Oa9+M4ENJ1pyecRhdg46w6iApfQMHEf9VF80r72mRFliIuzZQ+jW/9GJXYSO6Q4hITR89YHcTVkzrpp31oTD4wfwqN9aquvDaHda1Qy+f/NRfk7vxnL9eSI9U3KMDSjS/pBda3clMi6S09G5FP0I+SIv4VUSZ53+8otqg0oeUYCqVXO+Zq0296Cuibuq30WgTyDr/rNuJOsIp0+D0WAZgXB1wSu4LnZFyrIX+ssFrl24tCi7fPkyffr0ISAggLVr16LT6XLddubMmcTExJhvFy9eLNKx2TPzyB4Koxm5vQT6BHL/bfez8NBC61+QLGasq/9dzaMbHuWJagPp+80hfviqQpaUk5HFszMusYcNAz8/5Qv2wQdqWUZrouymrDqTKSuRMHo0ACtGt+SJaqEsjRtMFJnhghVfq0kCT947nMTtW/mtyywORgZbOl0U4YzIu2vcjZvWrVSkMF2pXVNewsvVZ53euJFz2ebNagYl2VIutWurScR//qls9KZPd/z5dFod9ze6n3XH1xX4hFa/PqDJdoHk4oJXcF3cdTYiZdYsMWT2pV24rCiLiYmhV69e3Lp1i59//pkQG86Inp6e+Pv7W9yKmsKoW4lNiS2WmjITE1pP4MT1E+y5kDO1aDJj3fn7Nzz03UM82PRBXmj2JBFUY/zc6llSThombOxNBNVUN+TsYYAsjL3vImEvfskOOhH21mrGHpqoasIyUtG96/fmD8NCfth2g1degaq3BzObWUShhJYx3YMTZ+6j4/ZXadM/OFebjcLGz9OPttXasu38tly3KW6xk5iWSEp6LlHDXCgOd/ufz/zMsDXD+PjAx1yOz6NXKLaFV2Fd7BQGERHK9u7xx5UtTEiIpZM+KGcWheUJ58IFGDNGpSmtpTftZfBtgzl/6zx/X/k7/wdBRffpNx6tyV7GxQSvULKwZ/ZldvNYSV/ah8vNvgRITk6mX79+nDp1il9//ZXGjRs7e0hFRlxqXLEaKXaq1Yn2ulpce24ifLDFMsqUqtq6nHzrWQ6kBtJy4U40kV9zmk4YjJZnFj1unKGe5azI5s1V2ODzz1WzboDgYEKjogh9/Qno9n4OO4ou7Yfjfv4dTnt/xezZU2F2MNHRr9JkO7y+9A/+2VcFQ3RtACpXVpMus/LGG6rm/6674O674c47obD0eJdaXfjs4GcYjIYcs2MLY5ZgXlxPvM6hS4eUGekVZUh66sYpAn0CWXH/CrrW6WrzGLnVb+VnlrA1LsdfZurPU/n2329pVLkR60+sZ+qWqXSq1YkHmjzAoNsGUcm7Uo79bM2OdMasU4NB+fD99lvmLSws53a//w7dumU+HjQIdoXt5Ot5nSy2M6UGC/o6OtXqRIVyFVj33zpaBLXI93F+C/8NWv2P/W/OJeFKcJmzWREKF3etHQ3JJX2ZL1xOlOn1eoYPH86+ffvYsGED7du3d/aQihSTJUaRERWlLoknTIDgYLQaLRNC+jPo5Y94r9ZwQmIMND4ZTUjYDSpduIYWmPCnEbhiPkR9TqNFj4HML5lOo6ee8YwyW7orw4jSZEfRpo3ddhTlUdGyr49+zdQ7pwJqttrAQek8deF+JjwxgGcafcqOHZCQkDPqsHWrmri5PSPLqNUqbXjnnerWrp2KcuQnWtG1Tlfm/jaXo1eOcnvQ7eblRS121vy7hofXP0yqPhU/Dz9aBLWgW+1uPNP+GVYdW8V9X93Hi/e8yKxOs/L0w8qrfqsg4zQYDXz515fM+HUGblo3lg9czsPNH+Zm8k3WH1/Pqn9X8fiPj/Pk5ieZ3HYy73Z/N4eodSW7j+RkqF4918m/ALi5qc9TdipVgrOVPgHNPeYieiic1KCa/OBOt8qjWf3fal7r/Fq+ZzDuDt9NnQp1aHNbMNxWsHEJQlGkLyW9qXA5UfbMM8+wceNG+vXrR3R0dA6z2Icfzl+TX2dh64MWl1KINWUZAiyi3xOcjq2qPKCuZvSH7NRJRbEOHGDEzwcAeObt32wfs0IFQm9Gsqjj10zY8zB6gxadzsjCFyIInROpBJlJgP31l/Vj2LCjeKjZQwxdM5RTN07RoFIDALae3cqluEuMaTmGuiGqi1J2jEZz+ZoZgwGOHFG3zz9Xy8qXVxG1xx+3/XKzcmfonZRzK8f289stRFlRiR2AJYeXMG7TOIY3Gc7cLnOpVb6WxY/boy0e5c09b/LKzlfYFb6LlYNXEupv/UlN9VtZx2pNLDhi1nri+gnGbRzH3ot7ebTFo7xz3zvmaFhFr4qMbTWWsa3GciX+CosPL+al7S8RnRTNl/2/tGmoWlQkJsLff8PBg6rGq1o19XkwUa6cKsbPKso8PZWgv+cedbv77sxWqVmJjI3kQNw6Hn15P8tfv6vQDGstI7HvYegbw/4B+2lfPX8XqbsvFLzfpSCYcNO6kZiWmOt6q70v7YyUlXXrFJcTZUeOHAFg06ZNbNq0Kcf6kiTK7PFbyVekLFv0K+vyxbMvMn5OoPox1xhY1PQ3xgJ07mzezEpnRwCMVauiuXJF9YTs3VudpW/ehJ49GTu/KT0CtRkpJw2hV2/AnGwHsGVHkQt9G/TF39Ofr//5mtmdZwOw5MgSmgU2o3Vw61z302hUM+YLF5TH05496nb0qBJsJm7dUr08sxIWpt6+Vq3g9tvVrX59FRExUc6tHHdVv4tt57cxrf0083J7xY418hJAHx34iKd+forxrcbzaZ9PLX7UzM+j1fFixxe5t9a9PLjuQW7//HaWDlhKv4b9cmxrj7u9I2nYiNgIOi3tREC5AHaM2kGnWp1yfZ1Vfavywj0vULt8bR5Z/wiJaYmsGLQCD10++wPZyfXrSoCZbocPw3//qddvomFDS1EG6uNep44ycL3nHlULlt3w1Rpr/luDu86d+TOa8tpjhWNYmzMSq4FNC/l44Au0f9RxURadFM3fl/9mStsp+R+UIGTBVvoyhyUGUlNmLy4nynbu3OnsIRQrNmdfWhNgGQX59O8PQUFKlRw4QMSqPYxnkfoRBwxGLROOTqQH7+R0xM/Oc8+hGT5cGbE+84zV6JdFykmXhx2Fg5RzK8eQ24aw4ugKXu30KjeSbrDhxAbevu9tu66aatRQtwcfVI9jY1VU5MABddu/P2fq6c8/Vepz69bMZZ6eqgfh7bcrm4PGjaGl10A+Oz2TNH0a7jp38/uQl9hx1K3eaDQy77d5vLTjJZ5t/6xdr/vuGndzZMIRRm8YTf9V/Vk+cDmP3P5Iju3yqt9yJA2bnJ7MoG8H4aHz4LdHfyPQJzDP8Zl4sNmDeLt7M2ztMAZ9O4i1w9ZSzq2cXfvmRUICuLtb9oD88kt47DHb+4aFqf2zRr7efjt/41h1bBW96/cmoFwAAYWUkrUWicXoxve/HyPx4US83b0dHqNWo6VnvZ4FH5wgYEehfzZHf41Gel/ai8uJsrJESnqKqhvy9Mshvswn9uTrhJoEWHCwUhx/ZJhJTpumwgAZeZfTdLKo+4JcCvK7dFFFWLn1h8xKPqNfjvJQ84f435H/cSDyAAciDmDEyEPNHsrXsfz91Uvs0kU9thY1//ffnMtSUpQGzZqFrVBpAgmTJ3Mo6hB3hipl9+ef0LKl6gp1+bKl2MlNeOUmgLp3N7LgxPO8/fvbzOk8hxfvedHu8H0l70psfGAjYzaO4bFNj9GociPaVGuTY7vc6rfsTcMajUae/PFJjl49yp5H99gtyEwMaDSATQ9uYuCqgfRZ2YcND2zA18PX5n4Gg3rfTp1Sze1Pnsz8OywMtm3L/B+Dqh3Mjk6nxHWbNir61aaN6slqTxTMFudunuNA5AFWDV5V8INlwVokVqszkuT3D+uPr+eh5vZ/L4xGI1/89QX9GvYj2K/wrWOEsomtmrLs6Ut72iwJChFlTiQuVTUj9/Pws4h+Ld4cnHli1zRlEWMYO3OmOoueP595gN27LY5ntSAfvTJrzSrArl1Toix7f0gotOiXo9xb816q6lvz5lcHOMkP9G/Yv9BmpVrTOLNmKbF05IhKc/3zj7qdOmUp4po2ceOIhx/bz283i7Jnn81864OCVL1b7dqq6PujjzL3zxp5yk0APfftIlYlvM0HPT7gqTufysdr0/BZn8/479p/3P/t/Rwcf5Ag3yC79rU3Dfvpn5+y5MgSlg9cTuuQ3NPJedG9bne2PLyFPiv70P2r7mx4YAOVvauQlATe2QI/w4apFPT580oo58a//1qKsttvV6nHFi0yb40bq5qxouDbY9/i7e5N3wZ9C/W41iOxGr7S1WPJkSUOibJDUWoG79zOcwt1jELZxk3jYENySV/ajYgyZ5ARFUsYrtIJ/p7+kKRWRXz3B+PntTBbUBiMGiawkB5ba+WdgmzZktC772bRx+OZoP1CFeRrjSyccpzQDyItBVheBfnFIMCssXSJjquv/8EGgxY0k+g+x0ooqxDRaNSMu+rVoV+WcqzERHWy/+8/Va9Ws6aGgPL3su38Nl645wXAspH05cvqtnev9efJ7lafVQBptAZWnf6cdx/JnyAzUc6tHOuHr+eORXcwZPUQto/ablftlj01Z7vDdzN1y1SeaveU1fRobiQkqI/55cvqXt3u4Z4z5/jl738JmRmLW1wlunTR8uOPlvsePw4nTuR+bH9/aNQIAgLU41R9Kr+e+5X/rv3HwnV9uK1K8UwvXPXvKgY0HICPh5UZAAXEWtpZd2Q0YzaMIfxWODXL17TrOF8c+oJQ/1BJXQqFiq2G5DksMSR9aTciyoqQgOhExm2MgD5ROQrymT0bN0Ms87fCHb88D/+dBeD0699iwHKaYI4UZM2aEB4Oc+YoCwqt1px+HPtxa3r8MJUzXs0yCvJT4YNsA3OgOXdxYErtGQ0ZV1ZGHZ/Masb0UcVvm+DtrVJcbbJkAZP3dWHmtpkkpyfjqSvHlCkqonb6tLq/ejX342V1q3/pJXjttcx1RoMWFh3m2UXwegUVaatcWd1/9ZXl5IR//lFpO39/NUYfH3Uz/R3gGcLqQevpsqIjkzdPZmG/hXa93qwn/7p1lUg1cebqRe7/+GWaez9GL+27bNgA8fEQE6MmT5huN2+qei6TSAJ47z31EctJZeBeANKBo6djgACLLerWVZ7EdeqoW4MGqjjfdAsMhHRDGtvPb2fshtWsP7Gem8k38dB5MP2X6dxe9XZGNBvBA00foEZADbveB0f579p//HPlH+Z0zj7bpfDInnYe0ngIkzZPYvnfy3n53pdt7h+fGs/KYyt5+s6nrU4aEYT8Yk9NWQ5LDBvpS0lvKkSUFRZWCvIDbiby2KZL8EqkOnOZqs537ACg2pz5TAXgoPkw1lOQ6dR7ojs8PE/lYkx+YL17W/UDC62aRqhpcSEW5BcV1lN7mkKxmCgMutbpSsrWFPZd3Efn2p15/nnL9QkJqsbp/HnlAP/NNyqFqdVaRp6s+VyZuHlT3Uy9CLPXPH37LcybZ2uk7Wh0x3kWGarRMrglj9+hxP3ddyvxqNWqCKFen/OWlqa6ZE2cqI6UlJbE/YumEv3eLqIBW3GWN9+0FGW2+jr6+BjRVYjkott+Xtp+hNc6v2b+EV+xQglNa2nnf678w6s/fsaa/9ZwI+kG9SrW48k2TzK8yXDqV6rPz2d+ZuXRlczaOYsZv87grup38Va3t7irxl223jyHWHVsFQGeAfSo26NQj5sXvh6+DGsyjKV/L+XFji/m8H7LzrfHviUhNYExLccU0wiFsoI9DcktLDGwP1Jmj2tBaUZEmYP4RycwYVMU9Lce/aJ/fxUeOXCATpv/U+s6dVJn7rzw8IDUVEJ7NWeR3zYmrL0PvUGjUpCGCYSOm5g/PzAXE2DWKIjFRHHQNLAplb0rs/38djrX7pxjvY+PmrXZpAn07QtvvWV9tmOrVrDi2yRmrJ9PfLQv/auN59b1cly5ovoq3rihIk9eXjnrrGJi7BtrzUoh3Nd2MpN/mkzjKo3pWLMj0dFKx9vCVL+VnJ7MwG8HciburH1Pihp3Vpo2VbNhAwNVe6Lg4MxbSAiUL68BqvHO7+eYsW4Z27YbmP/gk7RtHIKvr6XYSNWnsu6/dXzy5yfsvbiXEL8QxrVSXm4tglpYTIwY2GggAxsNJC4lju9PfM9Hf3xEz6978ssjv5hrAgvKhYsGFn93jh4txuLpVggzBhxgdIvRLDmyhN/Cf+PeWvfmue2Xh7+ke93udqc6BcFe3LRuDqcvpabMPkSU5YW16Fd0Io//eEWtCw5WduB//QXr1ql9evUy57PuMR3HliADGDlS5YDmzmVsq1b0iMg4sScdI7T3/4CJmdsW04zI4sKe2iZncilSS5P4Sfxw8CBzutjePrfZjlUCDXzHw8Q038rvY36nWdWcFejp6TkFDsDgwSprHRen6t4SEizvU1PVrWlTeKP7exy7eoy+K/uyfvh6atToSkqKEr2xsRAdnXnc4GCVLnV3V/cp6SkMXj2Y3eG7WTfyZ9ZdB19fy5ufn0qtli+fecvemtZkupo3GiqdeA7Nh9PZb9DQfp4e9wETadh9D/Ur1qdeRaXKl/29jKsJV+lcqzNrhq5hQMMBZnuS3PDz9OOR2x9h0G2D6Pl1T3qu6Mn2UdtpFdwqz/1ssXgxPDYejIYVrNUaWUzx9ue8p8Y91K1Ql6V/L81TlB27eoz9EftZO3Rt8Q1OKDO469wLPX0pKESUQZ5mrGS1ozAaqXBNzZjkrbdUNfJ//6kzqYm8CoxAhVJ69IDJk9n90iNMvfoVB8f/ifb6DSXKMjCf2KMql8jol6PY6ofoLDItLmaBRs/4pP0smpW/iMurO19l/fH1fP/A9zSr2szqNm5uqq4sO507W/j/2sCdjQ9uZMjqIfT6uhfL3lnGg80eJCJCCbusXL2qHFZCQyFNn8bQNcPZdm4bGx/cSPe699K7CBqYm8isJcyIdBl1pG/8hFYDXyYq9U/W/LeG2JRYRjQdwRNtnqBxFcd74Pp4+PDjiB/ptrwb3b/qzq7Ru2gS2KQA4zWaax8NBk2htteyB41Gw+gWo3lzz5t83OvjXK1Fvjj0BYE+gRamwo50bhCEvLCVvszh6O9A+rKsI6IMcoovE6ac0fz5qvL433+ZEBurlq1ebfOwYXUrU+vsdRUGap1hJZDFD+xC3cqc8fZD2/oOc4Pu0hL9yg+u1A8RcnqLYdTxxew7GDs0knaNqzl0rPd+f485u+fwRtc36N+wf+EPNhu+Hr5senAT4zaNY8R3I4iKj6Jl8tO5+pIFhaQz4rsR/HTmJ9YPX0/3ut2LfIzWagmNBi2P1nydTp0K73n8Pf35+eGf6bKsC12Xd2X3o7vN7bxM2CNY1Hgt610Kq72WI4y8fSSv7HiFNf+u4dGWj+ZYn5yezFf/fMVjrR4zz8J1pHODINjCZqF/dksMSV/aTT7aNJdsguKMtP1is3Wj1H//hddfVwX0NWpkmiCtWAH79qncjzXq14eHMryDPv8cDh2CQ4f4/pGMKXytW2daUmQRXQmpCco4FjLFl4vMiBRyd1afsPwd9Aa91X2s8cZvb/DsL8/y4j0vMuOuGYU7yDxw17mzdMBSZt49k2e2PsM3ka+h1Vperep0ULuOnpHrR/L9ie9ZM3QNvev3LpbxmWoJs4+nKGoJK3pVZOsjW6noVZGuy7sSdivMvG7xYhVB7NJF3S/OJTroWeUCaCz/786ofawRUIOudbqy9O+lVtev+28dN5NvMraVUl25GRdHRBTTgIVShy1LjByO/tjf+7KsU/pFWbaO1UFxRtp++ZPqr/PGG0pMDR2qVo4cqXwLfvoJLl60erjYAC/1x7RpsHOnEmC7dsHTT6vlbdqYBVh8QC6ulRk1YVG+FF4zcqHQsSYatDojf6eu4/1979t1jNd2vcYL219gdqfZzO0yt9ib7Wo0GuZ1ncfHvT7my7Ov0uKxz9Bo1dlZo9XTYNS73LfhNlb/u5pVg1cVSxTPhKmWUJfx213UtYSBPoH8OvJXPHWedFnWhQsxFxwSLB8cf5aAoc+h0xmLZbx5Mfr20ewO383Cgwu5kXjDYt2Xh7/k3pr3mqOBeXVuEIT8YCtSZtXR30b6UtKbitKfvrx8GapWVb1xDhzg7c0ZH6TRo/PeT6uFWrXg3DnVUK9fPwgJYdnmV5n8yg/w8MNW7SiyElPBmy/6hvBYLinJyI2P4ZfgYDNyodjIzVn9ZI0HeXH7i9xX9z5aBLWwuq/RaOSVHa8w97e5vN7ldbPxrLOY1HYSQb5BjN80nvLPf45/QiuCayZQo7qWQO8e9GvYr1hSltkp7lrCEL8Qto3cRudlnbl36b3Mq7MPg8GyA4K1lORv4b+x5r81LHthGV3e0zi99nHQbYPofaw3T/z4BBM3T6RTrU4Mvm0wTQObsjNsJyvuX2He1tVnNwslj7xqyoxGI0aM+U5fFveFq6tR+kXZI4+oht0ZdMxr23bt4N571RS2jh2VR0Hr1vD442YBlrDHy/q+VmZExlT05ov+1XKKsgxsNiMXnI410ZCSPodfzv3CQ989xMHHDuLlbvmZMBqNPP+r6mf5zn3v8GyHZ500ekuGNB7CkMZDnD2MHBR3LWHN8jXZNXoXnZd15tlDA9Bq91vUimUXLAajgalbptImpA0PN38Yrcb5tY9e7l78OOJHrsRf4fsT37P2+Fom/zQZvVFPhXIVGNx4sHlbV5/dLJQ88rLEMIkvSV/mj9IvyrIIslwZORKWL4dPP7WMft24kWPTmIrefN6nKo8XQkF+bEpsZk2Z4LJkFw2ebp58PehrWi9qzYxfZ/DOfe9w9OpRDl46yMFLB/kj8g+OXj2a736WQtFTPaC6WZgFDJlOzLp3MOg1VgXL8r+X81fUX+wds9emYWtxU9W3KhPumMCEOyZwI/EGm05tIsg3iHJulqUTrjq7WSiZuOvc0Rv1GI3GHJEtvVHVXeawxJD0pF2UflGWlU6dmKX7jdnb9DkbdC9fnnN7K9Gv2Io+LOwXnFOU5YO41LhCa7otFC+NqzTm7W5vM+XnKXx+8HPSDGnoNDqaVW1Gu2rtmNtlbrHWZwmOU82/GrtG76KLtgvuDXbwzh3r6dK6hoVguZ54nZnbZvJA0wfoUL2D8wZrB5W8KzG6xehc17va7Gah5OKmVdIh3ZCewzPQNAnKwhJDI5Eyeyn9ouy99zDPrw8OZsucmkqUZW3Q7SQ7itiUWPw8JFJWUpnUdhLJ6cl4uXvRJqQNzas2z5HKFFybYL9gdo7aSZflXXjudFv6afoRsSuCizEXiYiNICYlBi83L97s+qazhyoILoO7Vgkxa6Ist/SlWGLYR+kXZXfcYZmStIaTvMDiUqSmrCSj0WiYftd0u7cX807XpKpvVXaM2sHQxdPYvUtL7brV6FyrHqH+oVQPqE6bkDbSqkgQsmCKlKUZ0vDC8kLUWvpSoxHzWHsp/aIsG5f9NPwxrhdti8kPLK8PokTKyg4l2byzLIjJTasC2TPtawwGOKOFoYtgbPHYtRUbZeH/KBQPpuiYNVsMc6QsuyWGjfSlpDcVrlW1WhQEWU53v+yn4Y/HeheLSautbvcy+7JsUJLNO+01Vi3JFOT/ExEBO3a4/v+yLPwfheLDlL60NgPTVFNmESlzIH1p67xZ2ilzosxVSElPIVWfKrMvywAl1byzJItJR8jv/6ekCJ2y8n8Uio+shf7ZMaUvLWrKJH1pN6VflLkocamqsbmkL0s/xdlOqDApqWLSUfLz/ylJQqes/B+F4sOUvrRmIJvf9KWgEFHmJGJTVB9NSV+Wfoq7nVBhUVLFpKPk5/9TkoROWfk/CsWHudDfgfSlRMrsQ0SZk4hLyYiUuVD6sqTUx5RExo6FsDD1/oaFqceu/n6XVDGZH6z9f/KiJAmdsvR/FIqHrJYY2bFqieFAm6WyjogyJ2FKX7pKpMzZ9TGuLlAKg9BQZZkXGur899teHBUrJZms/x97ti1JQqcs/R+FoierJUZ2rFpiSJsluxFR5iRM6UtXqClzdn1MSREohYWz329HcUSslCVKmtCR/6NQWORliWHN0d+eNkuS3lSIKHMSpvSlK0TKnFkfU9IESmFQkuqRhLwRoSOURfKqKSto+jJ7L82yhogyJ2GKlPl4+Dh5JM6tjymLAqUk1SMJgiBkJ6+aslzTlxIJswsRZUVMbnn0uNQ4/Dz8LD64zsKZ9TFlUaCUtHokV6Qs1CAKgquSV02ZWGIUDOcrglJMXmHY2JRYl5p56az6mLIqUBx9v/MrQkqjeClrNYiC4GrYU1OWvfelzL60DxFlTsIVm5E7qz6mpBVMFxb2vt/5FSGlUbyUxRpEQXA18myzZM3RX9KXdiOizElIM3JLpGDaOvkVIaVVvJTFGkRBcDUcTV9qNGKJYS8iypyENCMX7CG/IqS0ipeyWIMoCK6Go+lLuywxRLQBLirKUlJSmDFjBiEhIXh5edGuXTt++eUXZw+rUHG1mjLBNcmvCCmt4qWs1iAKgivhsCUGDlhiIJYYLsfo0aN5//33eeihh/jwww/R6XT07t2bPXv2OHtohYZEykonhV1Yn18RUprFS1mtQRQEV8FhSwxJX9qNm7MHkJ0//viDVatW8c477/Dss88CMHLkSJo2bcpzzz3H77//7uQRFg5SU1b6WLw4s45Lq1WiqDAEw9ix0KOHSj3Wq2e/sMrvfiWB0NDS9XoEoSSRZ5ulfDr6CwqXi5StXbsWnU7H+PHjzcvKlSvH2LFj2bdvHxcvXnTi6AoPV5x9KeSfoi6sz+9ECJlAIQhCYWMSZXY3JHcgfVnWcTlRdvjwYRo0aIC/v6Vgadu2LQBHjhxxwqgKH4mUlS5Ka2G9IAhCdjQaDTqNLk9LDElf5g+XS19GRUURHBycY7lp2aVLl6zul5KSQkpKivlxTEwMALGxsRbbGZONJMUn5VhuL6mJqeiT9Hbtn5qYSnpSutVtY2NjcUtzy/c4BNciKAg0Gsj6u6PVQtWqIP9iQRBKG25pbsTFxeU4h8XFxkEyJMYnEuum1umT9KTqUvM83yXEJUAyxMfFE+sRm2N5bGwssRrHf0wT4xPN+2tT845DJcUnZW6bRVQakg2kJKTYdb42bZNvEWp0MerUqWPs1atXjuVnz541Asb58+db3W/WrFlGQG5yk5vc5CY3ucnNqbezZ8/mSwO5XKTMy8vLIuJlIjk52bzeGjNnzuTpp582P7516xY1a9bkwoULBAQEFM1gBUBdGVSvXp2LFy/mSDsLhYe8z8WHvNfFg7zPxYO8z8VHTEwMNWrUoGLFivna3+VEWXBwMJGRkTmWR0VFARASEmJ1P09PTzw9PXMsDwgIkA9hMeHv7y/vdTEg73PxIe918SDvc/Eg73Pxoc1uFGnvfoU8jgLTokULTp06lSN3e+DAAfN6QRAEQRCE0obLibIhQ4ag1+tZtGiReVlKSgpLliyhXbt2VK9e3YmjEwRBEARBKBpcLn3Zrl07hg4dysyZM7l69Sr16tVj2bJlhIWFsXjxYruP4+npyaxZs6ymNIXCRd7r4kHe5+JD3uviQd7n4kHe5+KjoO+1xmh0PfOQ5ORkXn75ZVasWMHNmzdp3rw5c+bMoUePHs4emiAIgiAIQpHgkqJMEARBEAShrOFyNWWCIAiCIAhlERFlgiAIgiAILoCIMkEQBEEQBBegzIiy3bt3079/f6pXr065cuUICgqiZ8+e7N2719lDK1Vs27aNMWPG0KBBA7y9valTpw7jxo0zm/8KhUdUVBTPP/88nTt3xs/PD41Gw86dO509rBJLSkoKM2bMICQkBC8vL9q1a8cvv/zi7GGVOuLj45k1axY9e/akYsWKaDQali5d6uxhlTr+/PNPJk2aRJMmTfDx8aFGjRoMGzaMU6dOOXtopY5///2XoUOHUqdOHby9valcuTIdO3Zk06ZNDh+rzIiyU6dOodVqefzxx/nkk0949tlnuXz5Mh07duTnn3929vBKDTNmzGDnzp3cf//9fPTRRzzwwAOsXr2ali1bcvnyZWcPr1Rx8uRJ3nrrLSIjI2nWrJmzh1PiGT16NO+//z4PPfQQH374ITqdjt69e7Nnzx5nD61Ucf36dV577TWOHz/O7bff7uzhlFreeust1q1bR9euXfnwww8ZP348u3fvplWrVhw7dszZwytVhIeHExcXx6hRo/jwww95+eWXAejfv7+F56pd5KtjZikhISHBWLVqVWOPHj2cPZRSw65du4x6vT7HMsD44osvOmlUpZPY2FjjjRs3jEaj0bhmzRojYNyxY4dzB1VCOXDggBEwvvPOO+ZlSUlJxrp16xrbt2/vxJGVPpKTk41RUVFGo9Fo/PPPP42AccmSJc4dVClk7969xpSUFItlp06dMnp6ehofeughJ42q7JCenm68/fbbjQ0bNnRovzITKbOGt7c3VapU4datW84eSqmhY8eOOXp+dezYkYoVK3L8+HEnjap04ufnl++mt4Ila9euRafTMX78ePOycuXKMXbsWPbt28fFixedOLrShaenJ0FBQc4eRqmnQ4cOeHh4WCyrX78+TZo0kd/iYkCn01G9enWH9YXLOfoXNbGxsaSmpnL9+nWWL1/OsWPHeOGFF5w9rFJNfHw88fHxVK5c2dlDEQSrHD58mAYNGuRo1ty2bVsAjhw5Ii3ehBKP0WjkypUrNGnSxNlDKZUkJCSQlJRETEwMGzdu5KeffmL48OEOHaPMibJhw4axZcsWADw8PJgwYYI5/ysUDR988AGpqakOfzgFobiIiooiODg4x3LTskuXLhX3kASh0Pn666+JjIzktddec/ZQSiXPPPMMCxcuBECr1TJo0CAWLFjg0DFKpCgzGAykpqbata2npycajcb8+M033+SZZ57h4sWLLFu2jNTUVNLT04tqqCWagrzPJnbv3s3s2bMZNmwYXbp0KewhlhoK470W8k9SUpLVXnXlypUzrxeEksyJEyeYOHEi7du3Z9SoUc4eTqlk6tSpDBkyhEuXLrF69Wr0er3dv+smSqQo2717N507d7Zr2+PHj9OoUSPz4xYtWpj/fvjhh2nVqhWjR49m7dq1hT3MEk9B3mdQPwL3338/TZs25csvvyyKIZYaCvpeCwXDy8uLlJSUHMuTk5PN6wWhpHL58mX69OlDQECAuX5SKHwaNWpk/m0eOXIk3bt3p1+/fhw4cMDuC+kSKcoaNWrEkiVL7NrWWkrChIeHB/379+fNN98kKSlJfnizUZD3+eLFi3Tv3p2AgAA2b96Mn59fUQyx1FBYn2khfwQHBxMZGZljuclfLyQkpLiHJAiFQkxMDL169eLWrVv89ttv8lkuRoYMGcKECRM4deoUDRs2tGufEinKgoKCGD16dKEcKykpCaPRSFxcnIiybOT3fb5x4wbdu3cnJSWFbdu2iYiwg8L8TAuO06JFC3bs2EFsbKxFsf+BAwfM6wWhpJGcnEy/fv04deoUv/76K40bN3b2kMoUprKHmJgYu/cpM5YYV69ezbHs1q1brFu3jurVqxMYGOiEUZU+EhIS6N27N5GRkWzevJn69es7e0iCYJMhQ4ag1+stjB5TUlJYsmQJ7dq1k5mXQolDr9czfPhw9u3bx5o1a2jfvr2zh1RqsaYv0tLSWL58OV5eXg6J4RIZKcsPvXr1IjQ0lHbt2hEYGMiFCxdYsmQJly5d4ttvv3X28EoNDz30EH/88Qdjxozh+PHjFn44vr6+DBw40HmDK4XMnTsXUG0+AL766iuzA/1LL73ktHGVNNq1a8fQoUOZOXMmV69epV69eixbtoywsDAWL17s7OGVOhYsWMCtW7fMs1o3bdpEREQEAJMnTyYgIMCZwysVPPPMM2zcuJF+/foRHR3NihUrLNY//PDDThpZ6WPChAnExsbSsWNHqlWrxuXLl/n66685ceIE7733Hr6+vnYfS2M0Go1FOFaX4ZNPPmHVqlWcOHGCW7duUaFCBe68806mT5/OPffc4+zhlRpq1apFeHi41XU1a9YkLCyseAdUysmreLSMfLULjeTkZF5++WVWrFjBzZs3ad68OXPmzKFHjx7OHlqpI6/fifPnz1OrVq3iHVAppFOnTuzatSvX9fL7UHisWrWKxYsXc/ToUW7cuIGfnx+tW7dm8uTJ9O/f36FjlRlRJgiCIAiC4MqUmZoyQRAEQRAEV0ZEmSAIgiAIggsgokwQBEEQBMEFEFEmCIIgCILgAogoEwRBEARBcAFElAmCIAiCILgAIsoEQRAEQRBcABFlgiAIgiAILoCIMkEQBEEQBBdARJkgCIIgCIILIKJMEARBEATBBRBRJghCmWHv3r1oNBo0Gg2rV6+2us2BAwfw9fVFo9Ewffr0Yh6hIAhlGWlILghCmWLAgAFs3LiRRo0acezYMXQ6nXndyZMnueuuu7hx4wajRo1iyZIlaDQaJ45WEISyhETKBEEoU7zxxhvodDpOnDjBihUrzMsvXbpEjx49uHHjBn379uXLL78UQSYIQrEikTJBEMoc48aNY/HixdSuXZuTJ0+SkJBAx44dOXr0KHfffTdbt27Fy8vL2cMUBKGMIaJMEIQyR2RkJPXr1ycpKYn58+ezfv16du/eTbNmzdi9ezfly5d39hAFQSiDSPpSEIQyR7Vq1ZgyZQoA06ZNY/fu3dSqVYstW7ZYFWTx8fG8+uqr9O3bl6CgIDQaDaNHjy7eQQuCUOoRUSYIQplkypQpaLXqJ7BixYps3bqV4OBgq9tev36d2bNn89dff3HHHXcU5zAFQShDuDl7AIIgCMVNeno6EyZMwGAwAJCYmJhnDVlwcDARERFUq1aN5ORkqTcTBKFIkEiZIAhlCqPRyLhx4/jhhx+oUqUKtWvXJjk5mVmzZuW6j6enJ9WqVSvGUQqCUBYRUSYIQpniueeeY9myZfj6+vLjjz/y+uuvA7Bs2TL+++8/J49OEISyjIgyQRDKDO+++y7vvvsu7u7ufPfdd7Rp04YHHniA5s2bo9frmTlzprOHKAhCGUZEmSAIZYLly5fz3HPPodFoWLp0Kffddx8AGo2GOXPmALBx40b27t3rzGEKglCGEVEmCEKpZ/PmzYwdOxaj0cj777/PiBEjLNb379+fdu3aATBjxgxnDFEQBEFEmSAIpZt9+/YxdOhQ0tPTmTFjBlOnTrW6nam2bO/evWzYsKEYRygIgqAQSwxBEEo17du3JyEhweZ2Xbt2RRqcCILgTCRSJgiCIAiC4AJIpEwQBMEOFixYwK1bt0hPTwfgn3/+Ye7cuQB07NiRjh07OnN4giCUAqQhuSAIgh3UqlWL8PBwq+tmzZrFq6++WrwDEgSh1CGiTBAEQRAEwQWQmjJBEARBEAQXQESZIAiCIAiCCyCiTBAEQRAEwQUQUSYIgiAIguACiCgTBEEQBEFwAUSUCYIgCIIguAAiygRBEARBEFwAEWWCIAiCIAgugIgyQRAEQRAEF0BEmSAIgiAIggsgokwQBEEQBMEFEFEmCIIgCILgAvwfwXD9+skllBsAAAAASUVORK5CYII=", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.preprocessing import StandardScaler\n", + "from sklearn.pipeline import Pipeline\n", + "\n", + "plt.figure(figsize=(7,3))\n", + "for style, width, degree in ((\"g-\", 1, 300), (\"b--\", 2, 2), (\"r-+\", 2, 1)):\n", + " polybig_features = PolynomialFeatures(degree=degree, include_bias=False)\n", + " std_scaler = StandardScaler()\n", + " lin_reg = LinearRegression()\n", + " polynomial_regression = Pipeline(\n", + " ((\"poly_features\", polybig_features), (\"std_scaler\", std_scaler), (\"lin_reg\", lin_reg)) )\n", + " polynomial_regression.fit(X, y)\n", + " y_newbig = polynomial_regression.predict(X_new)\n", + " plt.plot(X_new, y_newbig, style, label=str(degree), linewidth=width)\n", + "\n", + "plt.plot(X, y, \"b.\", linewidth=3)\n", + "plt.legend(loc=\"upper left\")\n", + "plt.xlabel(\"$x_1$\", fontsize=18)\n", + "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", + "plt.axis([-3, 3, 0, 10]);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Training data is underfitted for degree 1, fitted well for degree 2, and overfitted for degree 300." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Learning curves provide another way to determine whether model underfitted or overfitted." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Consider performance on training and validation set *as size of the training set increases*." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Plotting learning curves" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:45.938531Z", + "iopub.status.busy": "2024-01-10T00:19:45.937877Z", + "iopub.status.idle": "2024-01-10T00:19:45.944402Z", + "shell.execute_reply": "2024-01-10T00:19:45.943841Z" + } + }, + "outputs": [], + "source": [ + "from sklearn.metrics import mean_squared_error\n", + "from sklearn.model_selection import train_test_split\n", + "\n", + "def plot_learning_curves(model, X, y):\n", + " X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=10)\n", + " train_errors, val_errors = [], []\n", + " for m in range(1, len(X_train)):\n", + " model.fit(X_train[:m], y_train[:m])\n", + " y_train_predict = model.predict(X_train[:m])\n", + " y_val_predict = model.predict(X_val)\n", + " train_errors.append(mean_squared_error(y_train_predict, y_train[:m]))\n", + " val_errors.append(mean_squared_error(y_val_predict, y_val))\n", + "\n", + " plt.figure(figsize=(8,4))\n", + " plt.plot(np.sqrt(train_errors), \"r-+\", linewidth=2, label=\"Training set\")\n", + " plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"Validation set\")\n", + " plt.legend(loc=\"upper right\", fontsize=14) \n", + " plt.xlabel(\"Training set size\", fontsize=14) \n", + " plt.ylabel(\"RMSE\", fontsize=14) " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Underfitted learning curves" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Learning curve for linear model" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:45.947504Z", + "iopub.status.busy": "2024-01-10T00:19:45.946932Z", + "iopub.status.idle": "2024-01-10T00:19:46.221925Z", + "shell.execute_reply": "2024-01-10T00:19:46.221338Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "lin_reg = LinearRegression()\n", + "plot_learning_curves(lin_reg, X, y)\n", + "plt.axis([0, 80, 0, 3]);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- RMSE on training set small for small training set size since model can fit data well for very few data points (perfect for one or two points).\n", + "\n", + "- RMSE performance on training and validation eventually similar but high since linear model cannot fit the data well (recall data generated by quadratic)." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Overfitted learning curves " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Learning curve for poynomial model of degree 10" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:46.225436Z", + "iopub.status.busy": "2024-01-10T00:19:46.224761Z", + "iopub.status.idle": "2024-01-10T00:19:46.559315Z", + "shell.execute_reply": "2024-01-10T00:19:46.558734Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.pipeline import Pipeline\n", + "polynomial_regression = Pipeline((\n", + " (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n", + " (\"lin_reg\", LinearRegression()),\n", + " ))\n", + "plot_learning_curves(polynomial_regression, X, y)\n", + "plt.axis([0, 80, 0, 3]); " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "- RMSE now much smaller.\n", + "- But training and validation set errors remain quite different.\n", + "\n", + "Model performs much better on training set than validation set, suggesting overfitting." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Well-fitted learning curves " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Learning curve for poynomial model of degree 2" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:46.562771Z", + "iopub.status.busy": "2024-01-10T00:19:46.562122Z", + "iopub.status.idle": "2024-01-10T00:19:46.882864Z", + "shell.execute_reply": "2024-01-10T00:19:46.882258Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.pipeline import Pipeline\n", + "polynomial_regression = Pipeline((\n", + " (\"poly_features\", PolynomialFeatures(degree=2, include_bias=False)),\n", + " (\"lin_reg\", LinearRegression()),\n", + " ))\n", + "plot_learning_curves(polynomial_regression, X, y)\n", + "plt.axis([0, 80, 0, 3]); " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Bias-variance tradeoff" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Bias-variance tradeoff refers to the problem of simultaneously reducing the two types of errors that prevents supervised learning algorithms from generalising to other data.\n", + "\n", + "- **Bias**: Expected difference between data and prediction.\n", + "\n", + "- **Variance**: Expected ability of the model to fluctuate." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "One seeks a model that accurately fits the training data, while also generalising to unseen data.\n", + "\n", + "Typically impossible to do both simultaneously.\n", + "\n", + "- On one hand, high-variance models may fit training data well but typically overfit to noise or unrepresentative training data.\n", + "\n", + "- On the other hand, low-complexity models with a high bias typically underfit training data.\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Contributions to the mean square error " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Consider underlying (true) model:\n", + "$ y = f(x) + \\epsilon,$\n", + "\n", + "where\n", + "- $y$ is the target and $x$ features.\n", + "- $f$ is the true model, that we will approximate by $h$.\n", + "- $\\epsilon$ is the noise, with zero mean and variance $\\sigma^2$.\n", + "\n", + "\n", + "Approximate $f$ by $h$, which is fitted by a learning algorithm and training data." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Expected value of the mean square error is given by\n", + "\n", + "$$\\text{E} \\left[ \\left(y - h(x)\\right)^2 \\right]\n", + "= \n", + "\\text{Bias}^2\\left[ h(x) \\right]\n", + "+\n", + "\\text{Var}\\left[ h(x) \\right]\n", + "+\n", + "\\sigma^2$$\n", + "\n", + "Three contributions to the error:\n", + " \n", + "1. Bias: $\\text{Bias}\\left[ h(x) \\right] = \\text{E} \\left[ h(x) - f(x) \\right].$\n", + "\n", + "2. Variance: $\\text{Var}\\left[ h(x) \\right] = \\text{E} \\left[ h^2(x)\\right] - \\text{E} \\left[ h(x)\\right]^2. $\n", + "\n", + "3. Irreducible error $\\sigma^2$ due to noise in observations." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Tradeoff \n", + "\n", + "By choosing a complex model, the bias can be made small but the variance will be large.\n", + "\n", + "By choosing a simple model, the variance can be made small but the bias will be large.\n", + "\n", + " \n", + "\n", + "[Image source](http://francescopochetti.com/bias-v-s-variance-tradeoff/)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Regularization" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "One approach to mitigate the bias-variance tradeoff is by *regularization*.\n", + "\n", + "Consider a complex model but place additional constraints to reduce its variance.\n", + "\n", + "As a consequence the bias is increased but can introduce a regularisation parameter to control the tradeoff." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Add regularization term $R(\\theta)$ to the cost function:\n", + "\n", + "$$C_\\lambda(\\theta) = C(\\theta) + \\lambda\\ R(\\theta).$$\n", + "\n", + "The regularization parameter $\\lambda$ controls the amount of regularization." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Regularization should only be added when training. When using fitted model to make predictions, should evaluate cost without regularization term." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Tikhonov regularization \n", + "\n", + "*Tikhonov* regularization adopts $\\ell_2$ regularising term (also called *Ridge regression*):\n", + "\n", + "$$ R(\\theta) = \\frac{1}{2} \\sum_{j=1}^n \\theta_j^2 = \\frac{1}{2} \\theta^{\\rm T}\\theta.$$\n", + "\n", + "\n", + "\n", + "Acts to keep parameters small.\n", + "\n", + "Note that the bias term $\\theta_0$ is not regularized (i.e. sum starts from 1 not 0)." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:46.887064Z", + "iopub.status.busy": "2024-01-10T00:19:46.886396Z", + "iopub.status.idle": "2024-01-10T00:19:46.893828Z", + "shell.execute_reply": "2024-01-10T00:19:46.893284Z" + }, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [], + "source": [ + "from sklearn.linear_model import Ridge\n", + "\n", + "np.random.seed(42)\n", + "m = 20\n", + "X = 3 * np.random.rand(m, 1)\n", + "y = 1 + 0.5 * X + np.random.randn(m, 1) / 1.5\n", + "X_new = np.linspace(0, 3, 100).reshape(100, 1)\n", + "\n", + "def plot_model(model_class, polynomial, alphas, **model_kargs): \n", + " # Use alpha for regularization parameter (lambda used already)\n", + " for alpha, style in zip(alphas, (\"b-\", \"g--\", \"r:\")):\n", + " model = model_class(alpha, **model_kargs) if alpha > 0 else LinearRegression()\n", + " if polynomial:\n", + " model = Pipeline((\n", + " (\"poly_features\", PolynomialFeatures(degree=10, include_bias=False)),\n", + " (\"std_scaler\", StandardScaler()),\n", + " (\"regul_reg\", model),\n", + " ))\n", + " model.fit(X, y)\n", + " y_new_regul = model.predict(X_new)\n", + " lw = 2 if alpha > 0 else 1\n", + " plt.plot(X_new, y_new_regul, style, linewidth=lw, label=r\"$\\lambda = {}$\".format(alpha))\n", + " plt.plot(X, y, \"b.\", linewidth=3)\n", + " plt.legend(loc=\"upper left\", fontsize=15)\n", + " plt.xlabel(\"$x_1$\", fontsize=18)\n", + " plt.axis([0, 3, 0, 4])" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:46.896773Z", + "iopub.status.busy": "2024-01-10T00:19:46.896231Z", + "iopub.status.idle": "2024-01-10T00:19:47.338341Z", + "shell.execute_reply": "2024-01-10T00:19:47.337595Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10,5))\n", + "plt.subplot(121)\n", + "plot_model(Ridge, polynomial=False, alphas=(0, 10, 100), random_state=42)\n", + "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", + "plt.subplot(122)\n", + "plot_model(Ridge, polynomial=True, alphas=(0, 10**-5, 1), random_state=42)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [ + "exercise_pointer" + ] + }, + "source": [ + "**Exercises:** *You can now complete Exercises 2 and 3 in the exercises associated with this lecture.*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Lasso regularization\n", + "\n", + "\n", + "*Lasso* regularization adopts $\\ell_1$ regularising term:\n", + "\n", + "$$ R(\\theta) =\\sum_{j=1}^n \\left\\vert \\theta_j \\right\\vert .$$\n", + "\n", + "Acts to promote sparsity.\n", + "\n", + "Again, note that the bias term $\\theta_0$ is not regularized (i.e. sum starts from 1 not 0).\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:47.341641Z", + "iopub.status.busy": "2024-01-10T00:19:47.341174Z", + "iopub.status.idle": "2024-01-10T00:19:47.722342Z", + "shell.execute_reply": "2024-01-10T00:19:47.721671Z" + }, + "slideshow": { + "slide_type": "subslide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.linear_model import Lasso\n", + "\n", + "plt.figure(figsize=(10,5))\n", + "plt.subplot(121)\n", + "plot_model(Lasso, polynomial=False, alphas=(0, 0.1, 1), random_state=42)\n", + "plt.ylabel(\"$y$\", rotation=0, fontsize=18)\n", + "plt.subplot(122)\n", + "plot_model(Lasso, polynomial=True, alphas=(0, 10**-7, 1), tol=1, random_state=42)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Differentiability\n", + "\n", + "Note that the Lasso penality is non-differentiable at zero.\n", + "\n", + "Gradient descent can still be used but with gradients replaced by [sub-gradients](https://en.wikipedia.org/wiki/Subderivative) when any $\\theta_j=0$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Elastic Net regularization\n", + "\n", + "\n", + "Provides a mix of Tikhonov and Lasso regularization, controlled by mix ratio $r$:\n", + "\n", + "$$R(\\theta)\n", + "= \n", + "r\\sum_{j=1}^n \\left\\vert \\theta_j \\right\\vert\n", + "+\n", + "\\frac{1-r}{2} \\sum_{j=1}^n \\theta_j^2.$$\n", + "\n", + "- For $r=0$, corresponds to Tikhonov regularization.\n", + "- For $r=1$, corresponds to Lasso regularization." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Stopping early\n", + "\n", + "Compute RMSE on validation set as train and stop when starts to increase." + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:47.725983Z", + "iopub.status.busy": "2024-01-10T00:19:47.725495Z", + "iopub.status.idle": "2024-01-10T00:19:47.734570Z", + "shell.execute_reply": "2024-01-10T00:19:47.733897Z" + } + }, + "outputs": [], + "source": [ + "from sklearn.linear_model import SGDRegressor\n", + "np.random.seed(42)\n", + "m = 100\n", + "X = 6 * np.random.rand(m, 1) - 3\n", + "y = 2 + X + 0.5 * X**2 + np.random.randn(m, 1)\n", + "\n", + "X_train, X_val, y_train, y_val = train_test_split(X[:50], y[:50].ravel(), test_size=0.5, random_state=10)\n", + "\n", + "poly_scaler = Pipeline((\n", + " (\"poly_features\", PolynomialFeatures(degree=90, include_bias=False)),\n", + " (\"std_scaler\", StandardScaler()),\n", + " ))\n", + "\n", + "X_train_poly_scaled = poly_scaler.fit_transform(X_train)\n", + "X_val_poly_scaled = poly_scaler.transform(X_val)\n", + "\n", + "sgd_reg = SGDRegressor(max_iter=1,\n", + " penalty=None,\n", + " eta0=0.0005,\n", + " warm_start=True,\n", + " learning_rate=\"constant\",\n", + " random_state=42)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:47.737763Z", + "iopub.status.busy": "2024-01-10T00:19:47.737190Z", + "iopub.status.idle": "2024-01-10T00:19:48.426308Z", + "shell.execute_reply": "2024-01-10T00:19:48.425611Z" + } + }, + "outputs": [], + "source": [ + "import warnings\n", + "warnings.filterwarnings(action='ignore')\n", + "n_epochs = 500\n", + "train_errors, val_errors = [], []\n", + "for epoch in range(n_epochs):\n", + " sgd_reg.fit(X_train_poly_scaled, y_train)\n", + " y_train_predict = sgd_reg.predict(X_train_poly_scaled)\n", + " y_val_predict = sgd_reg.predict(X_val_poly_scaled)\n", + " train_errors.append(mean_squared_error(y_train_predict, y_train))\n", + " val_errors.append(mean_squared_error(y_val_predict, y_val))\n", + "\n", + "best_epoch = np.argmin(val_errors)\n", + "best_val_rmse = np.sqrt(val_errors[best_epoch])" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:48.429987Z", + "iopub.status.busy": "2024-01-10T00:19:48.429495Z", + "iopub.status.idle": "2024-01-10T00:19:48.654702Z", + "shell.execute_reply": "2024-01-10T00:19:48.653840Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10,5))\n", + "plt.annotate('Best model',\n", + " xy=(best_epoch, best_val_rmse),\n", + " xytext=(best_epoch, best_val_rmse + 1),\n", + " ha=\"center\",\n", + " arrowprops=dict(facecolor='black', shrink=0.05),\n", + " fontsize=16,\n", + " )\n", + "\n", + "best_val_rmse -= 0.03 # just to make the graph look better\n", + "plt.plot([0, n_epochs], [best_val_rmse, best_val_rmse], \"k:\", linewidth=2)\n", + "plt.plot(np.sqrt(val_errors), \"b-\", linewidth=3, label=\"Validation set\")\n", + "plt.plot(np.sqrt(train_errors), \"r--\", linewidth=2, label=\"Training set\")\n", + "plt.legend(loc=\"upper right\", fontsize=14)\n", + "plt.xlabel(\"Epoch\", fontsize=14)\n", + "plt.ylabel(\"RMSE\", fontsize=14);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Note that for stochastic or mini-batch gradient descent the RMSE is noisy and may be difficult to know when reach minimum (can employ simple strategies to deal with that)." + ] + } + ], + "metadata": { + "celltoolbar": "Tags", + "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": "3.13.1" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/week3/lectures/Lecture08_LogisticRegression.ipynb b/week3/lectures/Lecture08_LogisticRegression.ipynb new file mode 100644 index 0000000..503782a --- /dev/null +++ b/week3/lectures/Lecture08_LogisticRegression.ipynb @@ -0,0 +1,1208 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# Lecture 8: Logistic regression" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "skip" + } + }, + "source": [ + "![](https://www.tensorflow.org/images/colab_logo_32px.png)\n", + "[Run in colab](https://colab.research.google.com/drive/1NSiPlX-azox9No8o7PgcF4o70bwMUH3A )" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:56.779513Z", + "iopub.status.busy": "2024-01-10T00:19:56.779124Z", + "iopub.status.idle": "2024-01-10T00:19:56.787591Z", + "shell.execute_reply": "2024-01-10T00:19:56.787055Z" + }, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Last executed: 2024-01-10 00:19:56\n" + ] + } + ], + "source": [ + "import datetime\n", + "now = datetime.datetime.now()\n", + "print(\"Last executed: \" + now.strftime(\"%Y-%m-%d %H:%M:%S\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Estimating probabilities\n", + "\n", + "Estimate the probability of an instance belonging to a particular class.\n", + "\n", + "Can adapt linear regression algorithm for this purpose to perform *logistic regression*." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Sigmoid function\n", + "\n", + "Consider linear weighted sum of inputs $\\theta^{\\rm T} x$ again but then apply sigmoid function $\\sigma$:\n", + "\n", + "$$\\hat{p} = h_\\theta(x) = \\sigma(\\theta^{\\rm T} x), $$\n", + "\n", + "where\n", + "\n", + "$$\\sigma(t) = \\frac{1}{1+\\exp{(-t)}}. $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + }, + "tags": [ + "inclass_exercise" + ] + }, + "source": [ + "#### Plot the sigmoid function" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:56.827687Z", + "iopub.status.busy": "2024-01-10T00:19:56.827194Z", + "iopub.status.idle": "2024-01-10T00:19:57.238220Z", + "shell.execute_reply": "2024-01-10T00:19:57.237523Z" + }, + "tags": [ + "solution", + "inclass_exercise" + ] + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "%matplotlib inline\n", + "import matplotlib\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:57.241818Z", + "iopub.status.busy": "2024-01-10T00:19:57.241170Z", + "iopub.status.idle": "2024-01-10T00:19:57.489933Z", + "shell.execute_reply": "2024-01-10T00:19:57.489276Z" + }, + "tags": [ + "solution", + "inclass_exercise" + ] + }, + "outputs": [ + { + "data": { + "image/png": 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jIDRUnszt4GAgKMhyatBAPstJVFfYXbz+9ddf6NWrlzJvvpNz5MiRWL16NS5dumRxB2+LFi2wefNmvPHGG/jkk0/QtGlTrFixwu5hsoiIiBxBQQFw8CDw55+l0/HjgD13kISFAS1bAs2bA+HhQLNm8hQeLk/16vEMKJEtdhevDz74oMXwRjez9vSsBx98sNzQOES3UlRUhA4dOuD06dPYuHEjnnzyySqva/z48fj8888xYsQIrFmzphqzJCJXl5kp3w2/cyewezdw6BBQZgQvmxo0ADp2lIdfat0aaNVKnlq2lL+iJ6KqqfFrXomq6pNPPsHp06fRsWPHcuMk2uudd97BihUr8K9//QuvvfYaunXrVk1ZEpGruXYN+O03uVjduVMuVivi4QFERspTx46lU0gIz54S1QQWr+SQcnJy8NFHHwEApk2bZnEH+c3y8vIQEBAAo9GIWbNmWb3ZqFmzZhg5ciSWL1+O6dOnl7uJkIjqtpMngR9/BH76Cdi16+bxK0tpNEC7dvKg93fdJU+dO8vXqBJR7WDxSg5pyZIluHr1Kpo1a4annnqqwtikpCRlbNWbnyJT1ptvvonly5fjl19+QVJSEs++EtVhJpP8VKgffpAL1hMnrMdptUDXrsCDDwK9egH33otaGQqIiGxj8UoOx2g0YtGiRQCAoUOH2hzX02zfvn0A5PEeu3fvbjOuTZs2+Mc//oH9+/fjs88+s3p9NhG5tuPH5UeWrl0rj69qTevWQL9+8qNG77tPvnmKiBwHi1dyONu2bcP5G8/ke+aZZ24Zby5eW7VqVe656Td75plnsH//fmzcuBGfffYZ/P39bztfInJsV64A69YBX30F/PVX+de1WuCee4ABA4D+/eUbrIjIcVV8SouoigoKCrBy5UoMGDAA4eHhymMbK5r+/PNPAMCGDRsAAK1bt0anTp1svkejRo2g0WiU+FOnTpVb583Fr/nGr7y8PPzwww818aMTkQMQAkhMBIYMkYeleu01y8LVzQ3o0wdYswa4fFkeTeCtt1i4EjkDnnmlanfw4EE8+eSTFg+zuBWtVouOHTsCAHbs2AEAuPvuu23GX7x4EZmZmbdcr3mdZs2bN0doaCjS09Pxyy+/4Nlnn610jq5sxYoV2LVrFwDg8OHDSt/OnTsBAPfeey/GjBmjVnpElVZUBHz3HbBwoTz+6s26dgWGDweGDpUH/Sci58PilarVmTNnEBMToxSWAwYMwIgRI9CiRQtcvnwZK1euxHfffafEP/LII/Dw8EBISAh8fHyQlpaGlJQUABXffFW/fn0cPnwYJ06cUMZ//fTTTy0eoAEATZs2Lbdsjx498OOPP+K333673R/XZezatavc+Le7d+/G7t27lXkWr+TIrl4FvvgCWLy4/FOtgoOB556Ti9ab/j9LRE6IxStVGyEEnn32WaVw/eKLL/DCCy9YxDz66KMYOnQo1q1bBwB4+eWXMXDgQOX1PXv2KO2uXbvafC8fHx907NgRBw4cUPr69u2LO+6445Z5duvWDT/++CMuXLiAjIwMhISEVOrnq2i4rspatWoVnnvuudteT3VbvXo1b2Ajp6TXA/Pny1NuruVrXboAr78OPP00h7IiciW85pWqzfr16/HHH38AkIelurlwNXv99deVtvlrabO0tDSlHRwcfMv3NBevAQEBaNmyZaXyLLves2fPVmoZInIseXnAnDny06ree6+0cNVogEGD5IcL7N8PjBzJwpXI1fDMK1WbxYsXAwAaNmyId99912Zc2TOqZYtVALhy5YrSrl+//i3f01y8du7cudJnRhs0aKC009PTK7UMUHot6O2wdhkDEVVeURGwfDnwwQdA2V9fd3dgzBhg4kS5oCUi18Xi9Ybu3S0PhK4oNNT6MDHVIT09XbnhZ9iwYZAkyWasp6cnNBoNhBDlxnC9du2a0q5M8Xrw4EEAFV9icLOy6zUYDJVe7uabv4iodm3eDLz6KpCcXNqn0cjXssbFsWglqitYvN6Qng5cuKB2Fs7r999/V9qPPPJIhbEZGRkQQgAAwsPDLV7z9vZW2vn5+RWOw3rhwgXl+touXbpUOtf8/Hyl7eHhUenliEgdaWnAhAnAv/9t2T94sHzJQPv26uRFROpg8XpDXRgypSZ/xiNHjijtyMjICmP/KnP69+YRBRo1aqS0r127VmHxWvZmLXuK17Jnd2/1UIOyyv6MVdW0aVO73pOoLispARYtAqZPt7wZ66GH5Otd+YRnorqJxesNNfV1el2RWuY5i40bN64wdvPmzQDksV1vHtqqbPF6/fp1NG/e3OZ6zMWrh4eHXV/pX79+XWk3a9as0stV9MCEyqrMaAPVMaqBKzGfpae6Zd8+4MUXAZ2utC84GFiwQB6jlb8mRHUXRxugamEymZR2YWGhzbjr16/jm2++ASAPbXXziAJlC8STJ09W+J7m613btWsHT0/PSudqXq+XlxdatWpV6eVqixCCU5mJ6pbiYmDyZODuuy0L13HjgOPHgWHDWLgS1XUsXqlalC1C/6rgNPbkyZOh1+sBAG+//Xa517t3765c9/qntcfjlHHixAkAQNu2be3K1bzerl272nXNa3UUYo44xiuRo0hOBu6/H5g9W368KwB07gzs2QMsXQpU4h5OIqoDWLxStbj33nuV9qxZs6yeMZs3bx6++OILAMDzzz+P++67r1yMp6cnoqKiAAD79u2r8D2zs7MBAMXFxZXOs7CwEIcOHQJw6xvLqHaNHTsWzz//vNppkEo2bJAfKnBjqGi4uwPx8fIlXdHRqqZGRA6GxStVi/79+6N169YAgP/85z/o27cvNm/ejP379+O7777DI488gokTJwIAHnjgAXz++ec212V+4ta+ffuQk5NjM878UIKff/4ZixYtQlJSEo4cOYIjR47YXO73339Xit3HH3/c/h+Uasy+ffvQvXt3tdOgWpaXB7zwAjBkCHDj/6No2RLYvRuYNAnggCBEVI5wAnq9XgAQer3eruXy8/PF33//LfLz82soMyrr0KFDomHDhgKAzWn06NG3/DwyMzOFl5eXACDWrFljM+6nn34SGo3G6vskJSVZXea5554TAESHDh1u62el6pOfny+0Wq3F5/f4449XaT3O8vuem5ur/Ky5ublqp6Oaw4eFaN9eCPkiAXkaOlQIOw/1ROQgqlqv2YtnXqnadOrUCUePHkVsbCzatm0LX19f+Pr64s4778S4ceOQlJSEFStWWIzlak3Dhg3xxBNPAIByc5c1jz32GH755Rc8/PDDqF+/vnKXvq3RBwoKCvDvGwNFvvzyy1X9MamaeXp64r///S8A+Wa6S5cuYfXq1eomRTXul1/kywH+/lue9/UFvvwS+PprICBA3dyIyLFphHD823mzs7MRGBgIvV6PADuOagUFBUhOTkaLFi1uWTCRY9m7dy/uvvtuuLm54cyZMxUOmVVZa9euxfDhw9GwYUOkpKRU+BQwR7B27Vr873//Q1JSEg4fPoyioqJKDbXljL755htMmTIFKSkpVV6HM/2+GwwGZf/Lzc2Fn5+fyhnVrs8/l5+UZR6kpHNnYP16wM57L4nIwVS1XrMXz7ySQ4qKisITTzwBo9GI+Pj4216fyWTCrFmzAAATJ050+MIVAKZNm4Zly5bh3Llztxw71xFNmjQJGo2mwsns0KFDt3y4BTk/oxF44w1g/PjSwnXwYCAxkYUrEVUei1dyWLNmzYK7uztWrVqFtLS021rXxo0bcezYMTRr1gyvvfZaNWVYs1asWIGUlBRcuXIFL774YrWs87nnnqu1hyC8+eabOHbsWIWT2cGDB1m8urjcXOCJJ4CFC0v73nlHHmXA11e1tIjICfEJW+Sw2rRpgy+//BJnzpxBamoqmjZtWuV1GY1GxMXF4aGHHoKPj081ZllzYmJi1E6hHKPRiDVr1mDNmjU4cOAACgsL0aFDB0ydOlW5TtmsUaNGFk9Mq8jhw4cxevTomkiZHMCFC0D//qUPHXB3B5YsAcaMUTcvInJOLF7JoQ0fPrxa1jNs2LBqWU9dVlBQgMceewwJCQno2rUrRo0ahcLCQnz33XcYPHgw1q5di2eeeaZK6y4uLsaxY8dw6dIlSJIEf3//as6e1HL6NPDQQ8D58/J8YCDw3XeAA/7fjIicBC8bIKJKef7555GQkIBPP/0U+/fvx8KFC7FkyRIcOnQIQUFBmDZtWpXX/eGHH+Lzzz9HWFhYhWMAk3M5fRp48MHSwjUiQn5aFgtXIrodLF6J6JYSEhLw7bffYty4cXj11VctXmvcuDH69u2rXJ9bFWPGjMGlS5cghMA777xTHSmTyk6dkgvXCxfk+Y4d5adntW+valpE5AJ42QCRi4qIiMC5c+esvmbtpq2KhuFatGgRAPma13fffbfc63/fGKzTZL6FnOq0kyeBXr2Aixfl+Y4dge3bgUpeAk1EVCEWr0Qu6vXXX0dWVpZF36ZNm3Dw4EHExcWVi+/SpYvNdZkfIrBixQqbMV5eXpW+QYtc18mT8hnXS5fk+U6dgIQEFq5EVH1YvBK5qNdff71cX0pKCg4ePGj17KktWVlZyM3NxcCBA7Fp06Zqy49cz4kT8hlXc+HaubNcuAYFqZsXEbkWXvNKRBUyP4QvMzNT5UzIkZ05Y1m4RkaycCWimsHilYgqVL9+fbRu3Rp//PEHtm/fXu71oqIiJCYmqpAZOYrMTKBPHxauRFQ7eNkAkYNasWIFdu3aBUAexN/ct3PnTgDAvffeizG1NMr7nDlzMHjwYDz88MPo27cv2rVrh7y8PKSlpWHXrl149NFHER0dXSu5kGPJzwcGDpRHFwDk0QQSEoCGDdXNi4hcF4tXIge1a9curFmzxqJv9+7d2L17tzJfW8XroEGDsGPHDsyZMweJiYnYunUrGjRogPDwcDz//PM2Rykg12YyASNHymO3AkBoKLBlCwtXIqpZGmG+oM2BZWdnIzAwEHq9HgEBAZVerqCgAMnJyWjRogW8vb1rMEMiUpsz/b4bDAZIkgQAyM3NhZ+fn8oZVc3EicC8eXLbzw/4/XfgH/9QNyciUk9V6zV78ZpXIiKy2+LFpYWrmxuwYQMLVyKqHSxeiYjILj/+CLz2Wun8558Dffuqlw8R1S0sXomIqNL++gt4+mn5elcAmDwZeOEFdXMiorqFxSsREVVKZibwxBPyCAMAMHQo8MEH6uZERHUPi1ciIroloxF49lng/Hl5/p57gFWrAC3/ihBRLavSYWfx4sWIiIiAt7c3oqKisG/fvgrjFy5ciDZt2sDHxwfh4eF44403UFBQUKWEiYio9n34IfDrr3I7OFi+QcvLS92ciKhusrt4Xb9+PWJjYxEXF4f9+/cjMjISvXv3xuXLl63Gf/PNN5g0aRLi4uJw7NgxrFy5EuvXr8eUKVNuO3kiIqp5//kP8O67clurBdatA8LCVE2JiOowu4vX+fPnY+zYsRg1ahTat2+PpUuXwtfXF19++aXV+D179uCee+7BsGHDEBERgUceeQRDhw695dna6uQEQ9kS0W3i73nNOH8eGDYMMG/eDz4AevVSNyciqtvsKl6LioqQlJSEmJiY0hVotYiJibH5bPOePXsiKSlJKVbPnj2LLVu2oG8F46oUFhYiOzvbYqoK7Y2LsUzm22KJyGWZf8+1vAiz2hQVAf/3f8DVq/J8v37AO++omxMRkV2Ph83MzITRaERISIhFf0hICI4fP251mWHDhiEzMxP33nsvhBAoKSnBiy++WOFlA/Hx8Zg5c6Y9qVnl7u4OrVaLgoICp32CDRFVTkFBAbRaLdzd+dTr6jJxIvDHH3I7IgL46iveoEVE6qvxw9DOnTsxa9YsfP7559i/fz/+/e9/Y/PmzXj//fdtLjN58mTo9XplOm++vdVOWq0Wvr6+yM3NrWr6ROQkcnNz4evryzOv1WTDBuDTT+W2pyewcSPQoIG6ORERAXaeeQ0KCoKbmxsyMjIs+jMyMhAaGmp1menTp2P48OEYM2YMAKBTp04wGAx44YUXMHXqVKt/aLy8vOBVTbexBgQE4OLFi7h+/Trq169fLeskIsdy/fp15OXlIYx3EVWL1FRg7NjS+U8+Abp3Vy8fIqKy7CpePT090a1bNyQkJGDQoEEA5OvMEhIS8Morr1hdJi8vr1yB6ubmBqB2brAIDAxEfn4+0tPTYTAYEBgYCHd3d2g0mhp/byKqOebLkPR6PXJyclC/fn0EBgaqnZbTM5mAUaMA860Gw4YB48apmxMRUVl2XxwWGxuLkSNHonv37ujRowcWLlwIg8GAUaNGAQBGjBiBJk2aID4+HgDQv39/zJ8/H127dkVUVBROnz6N6dOno3///koRW9NCQkLg6emJrKwspKWl1cp7ElHt8PLyQkhICL9ZqSaLFwPbt8vtpk3lef5fn4gcid3F65AhQ3DlyhXMmDED6enp6NKlC7Zu3arcxJWammpxpnXatGnQaDSYNm0aLly4gEaNGqF///748MMPq++nuAWNRoMGDRqgfv36KCkpgdForLX3JqKa4+bmxm9SqtHJk5ajCaxaBdSrp1o6RERWaYQTDI6YnZ2NwMBA6PV6BAQEqJ0OEdFtMRgMkCQJgHyjmSOMhlJSAtx7L7B3rzw/fjywaJG6ORGRc6mteo235RIREebMKS1cW7UCPvpI3XyIiGxh8UpEVMcdPGj5+NevvgIc4GQwEZFVLF6JiOqwwkJg+HCguFief/ttIDpa3ZyIiCrC4pWIqA57913g8GG53alT6RlYIiJHxeKViKiOSkqSr3UFAA8P+XKBano+DBFRjWHxSkRUBxmN8sMHTCZ5fsYMoEsXVVMiIqoUFq9ERHXQkiXymVcA6NDBcnxXIiJHxuKViKiOuXgRmDKldH7pUvmyASIiZ8DilYiojomNBXJy5Pbo0fLDCYiInAWLVyKiOuTXX4H16+V2w4Z8GAEROR8Wr0REdUR+PvDyy6Xz8+bJBSwRkTNh8UpEVEfMmgWcPSu3778fGDlS3XyIiKqCxSsRUR1w/HjpJQLu7vJoAxqNujkREVUFi1ciIhcnBPDSS6WPgJ04EWjfXt2ciIiqisUrEZGL++YbYOdOud2iBTBtmqrpEBHdFhavREQuLC8PmDSpdH7RIsDXV718iIhuF4tXIiIXNm8ekJYmt/v2lSciImfG4pWIyEVduFB6k5abm1zIEhE5OxavREQuaupU+bIBQL5hq107dfMhIqoOLF6JiFxQUhKwZo3crlcPePddNbMhIqo+LF6JiFyMEMAbb5TOz5jBJ2kRketg8UpE5GL+/W/gf/+T261bA+PHq5sPEVF1YvFKRORCCguBt98unZ87F/D0VC8fIqLqxuKViMiFfPopcPas3O7VCxgwQN18iIiqG4tXIiIXcfky8MEHclujARYskP8lInIlLF6JiFzEu+8C2dlye/RoIDJS1XSIiGoEi1ciIhdw+jSwfLncliTg/ffVzYeIqKaweCUicgEzZgAlJXL7zTeB0FB18yEiqiksXomInNyBA8C338rtoCAgNlbVdIiIahSLVyIiJzd1aml7yhQgIEC9XIiIahqLVyIiJ/a//wFbtsjt8HDgpZfUzYeIqKaxeCUiclJCAJMnl86/+y7g7a1aOkREtYLFKxGRk9qyBdi9W263bQuMGKFuPkREtYHFKxGREzKZ5OtbzT74AHB3Vy8fIqLawuKViMgJrVsHHDokt7t3B554Qt18iIhqC4tXIiInU1QETJ9eOh8fz8fAElHdweKViMjJrFwJnD0rtx96CIiJUTcfIqLaxOKViMiJ5OdbPvo1Pl69XIiI1MDilYjIiXzxBXDpktweNAjo0UPVdIiIah2LVyIiJ5GXB8yeXTo/c6Z6uRARqaVKxevixYsREREBb29vREVFYd++fRXGZ2VlYfz48WjcuDG8vLxw5513Yov5kTBERFQpS5cCGRly+8kngc6d1c2HiEgNdo8KuH79esTGxmLp0qWIiorCwoUL0bt3b5w4cQLBwcHl4ouKivDwww8jODgY3333HZo0aYJz586hXr161ZE/EVGdYDAAH30ktzUaIC5O3XyIiNRid/E6f/58jB07FqNGjQIALF26FJs3b8aXX36JSZMmlYv/8ssvce3aNezZswceHh4AgIiIiNvLmoiojlmyBLh8WW4/9RTQsaO6+RARqcWuywaKioqQlJSEmDLjsmi1WsTExCAxMdHqMj/++COio6Mxfvx4hISEoGPHjpg1axaMRqPN9yksLER2drbFRERUVxkMwJw5clujAWbMUDcfIiI12VW8ZmZmwmg0IiQkxKI/JCQE6enpVpc5e/YsvvvuOxiNRmzZsgXTp0/Hxx9/jA8++MDm+8THxyMwMFCZwsPD7UmTiMilLF4MXLkit//v/4AOHdTNh4hITTU+2oDJZEJwcDCWLVuGbt26YciQIZg6dSqWLl1qc5nJkydDr9cr0/nz52s6TSIih5SbC8ydK7d51pWIyM5rXoOCguDm5oYM8+2uN2RkZCA0NNTqMo0bN4aHhwfc3NyUvnbt2iE9PR1FRUXw9PQst4yXlxe8vLzsSY2IyCUtWgRkZsrtp58G2rdXNx8iIrXZdebV09MT3bp1Q0JCgtJnMpmQkJCA6Ohoq8vcc889OH36NEwmk9J38uRJNG7c2GrhSkREspwcYN48ua3V8qwrERFQhcsGYmNjsXz5cqxZswbHjh3DSy+9BIPBoIw+MGLECEyePFmJf+mll3Dt2jVMmDABJ0+exObNmzFr1iyMHz+++n4KIiIXtGgRcPWq3B46FGjbVt18iIgcgd1DZQ0ZMgRXrlzBjBkzkJ6eji5dumDr1q3KTVypqanQaktr4vDwcPz6669444030LlzZzRp0gQTJkzAO++8U30/BRGRi+FZVyIi6zRCCKF2EreSnZ2NwMBA6PV6BAQEqJ0OEdFtMRgMkCQJAJCbmws/P79yMbNnA+YvsYYPB776qjYzJCKyX23VazU+2gAREdnHYAA+/lhua7XAtGnq5kNE5EhYvBIROZgvvigdYWDIEODOO9XNh4jIkbB4JSJyIPn5peO6AsDUqerlQkTkiFi8EhE5kJUrAfMDCwcP5tO0iIhuxuKViMhBFBYCH31UOs9rXYmIymPxSkTkINasAdLS5PaAAUCXLqqmQ0TkkFi8EhE5gOJiID6+dH76dPVyISJyZCxeiYgcwNdfAykpcvvRR4Hu3VVNh4jIYbF4JSJSmdEIzJpVOs+zrkREtrF4JSJS2fr1wKlTcvuhh4CePdXNh4jIkbF4JSJSkckEfPhh6TzPuhIRVYzFKxGRin74wQ1//y23770XeOABdfMhInJ0LF6JiFQ0Z46H0p4+HdBoVEyGiMgJsHglIlJNPxw+7AYA6NEDePhhldMhInICLF6JiFRT+gitqVN51pWIqDJYvBIRqeKfAO4GAHTuDDz2mLrZEBE5CxavRESqmFramgpoeTQmIqoUd7UTsIfBYIC/vz80N75bKyoqQnFxMdzd3eHl5WURBwA+Pj7Q3viLUFxcjKKiIri5ucHb27tKsXl5eRBCwNvbG25u8nVqJSUlKCwshFarhY+PT5Vi8/PzYTKZ4OXlBXd3+SMxGo0oKCiwK1aj0cDX11eJLSgogNFohKenJzw8POyONZlMyM/PBwD4+fkpsYWFhSgpKYGHhwc8PT3tjhVCIC8vDwDg6+tb7vO0J7Yyn3117CfWPs/q2E/Mn+ft7ic3f563u5/Y+jxvdz8p+3ne7n5i6/Os6n5Sm8eIPXu0AHoBAFq3NmLwYB4jeIzgMeLmz7MuHyPsjXWUY4R5W9Q44QT0er0AIACIy5cvK/0ffPCBACDGjBljEe/r6ysAiOTkZKVvwYIFAoAYNmyYRWxQUJAAII4cOaL0LVu2TAAQAwcOtIht3ry5ACD27dun9K1du1YAEDExMRax7du3FwDEjh07lL7vv/9eABA9e/a0iO3evbsAIH7++Wel7z//+Y8AICIjIy1iH3jgAQFAbNiwQenbtWuXACBatWplEdu3b18BQKxatUrp0+l0AoAICwuziH3yyScFALFo0SKl7+TJkwKACAwMtIgdOXKkACDmzJmj9KWlpQkAwt3d3SL25ZdfFgBEXFyc0nf9+nXl8ywqKlL633rrLQFAvPXWW0pfUVGREnv9+nWlPy4uTgAQL7/8ssX7ubu7CwAiLS1N6ZszZ44AIEaOHGkRGxgYKACIkydPKn2LFi0SAMSTTz5pERsWFiYACJ1Op/StWrVKABB9+/a1iG3VqpUAIHbt2qX0bdiwQQAQDzzwgEVsZGSkACD+85//KH0///yzACC6d+9uEduzZ08BQHz//fdK344dOwQA0b59e4vYmJgYAUCsXbtW6du3b58AIJo3b24RO3DgQAFALFu2TOk7cuSIACCCgoIsYocNGyYAiAULFih9ycnJAoDw9fW1iB0zZowAID744AOl7/Lly8rnWdaECRMEADFlyhSlLzc3V4nNzc1V+qdMmSIAiAkTJlisw5mOEQ8/XCwAIQAhYmMPKv08Rsh4jCjFY4Ssrh0jhHDeOgKA0Ov1oibxiyoiolr011/Atm3mL72S8eCDF1XNh4jI2WiEEELtJG4lOzsbgYGBuHjxIkJDQ3m6n18J8itBfiXotF8JPv44sGmTeYlx0OvnIiAgwGpsZT5PHiN4jKjKZ89jhOMeI6oS6yjHiOvXryMsLAx6vV45rtUEpypea3pjEBHVpMOH5ZEFZBcAtERu7jWLP9JERM6qtuo1XjZARFRLZs0qOzcXQJFKmRAROS8Wr0REteDkSWD9erkt39+xXNV8iIicFYtXIqJaEB8vjy8AAK++WgwgT9V8iIicFYtXIqIalpwM/OtfcrtePWDs2GJV8yEicmYsXomIatjs2YDRKLcnTAB43ykRUdWxeCUiqkHnzwOrVsltf3+5eCUioqpj8UpEVIPmzAGKb1wl8MorQP366uZDROTsWLwSEdWQS5eA5TcGFfD1Bd54Q918iIhcAYtXIqIa8vHHQGGh3H7pJaBRI3XzISJyBSxeiYhqwJUrwJIlctvbG3jrLXXzISJyFSxeiYhqwIIFwI3HrmPsWCA0VN18iIhcBYtXIqJqdu0asGiR3Pb0BN5+W918iIhcCYtXIqJq9umnQE6O3B41CmjaVN18iIhcCYtXIqJqlJ0NfPKJ3HZ3ByZNUjcfIiJXw+KViKgaLVoEZGXJ7eHDgYgINbMhInI9LF6JiKpJTg4wf77c1mqBKVPUzYeIyBWxeCUiqiaLFwNXr8rtoUOBVq3UzYeIyBWxeCUiqgY5OcDcuXJbqwWmT1c3HyIiV1Wl4nXx4sWIiIiAt7c3oqKisG/fvkott27dOmg0GgwaNKgqb0tE5LA++0weIgsAhg0D2rRRNx8iIldld/G6fv16xMbGIi4uDvv370dkZCR69+6Ny5cvV7hcSkoK3nrrLdx3331VTpaIyBFlZwPz5sltnnUlIqpZdhev8+fPx9ixYzFq1Ci0b98eS5cuha+vL7788kubyxiNRjzzzDOYOXMmWrZseVsJExE5mk8/Ba5fl9vPPgvceae6+RARuTK7iteioiIkJSUhJiamdAVaLWJiYpCYmGhzuffeew/BwcEYPXp0pd6nsLAQ2dnZFhMRkSPS64GPP5bbbm4860pEVNPsKl4zMzNhNBoREhJi0R8SEoL09HSry+zatQsrV67E8uXLK/0+8fHxCAwMVKbw8HB70iQiqjWffGI5ritHGCAiqlk1OtpATk4Ohg8fjuXLlyMoKKjSy02ePBl6vV6Zzp8/X4NZEhFVTVZW6biubm7AtGmqpkNEVCe42xMcFBQENzc3ZGRkWPRnZGQgNDS0XPyZM2eQkpKC/v37K30mk0l+Y3d3nDhxAnfccUe55by8vODl5WVPakREtW7hQvmyAQAYORKwcjgjIqJqZteZV09PT3Tr1g0JCQlKn8lkQkJCAqKjo8vFt23bFocPH8aBAweUacCAAejVqxcOHDjAywGIyGldvw4sWCC33d151pWIqLbYdeYVAGJjYzFy5Eh0794dPXr0wMKFC2EwGDBq1CgAwIgRI9CkSRPEx8fD29sbHTt2tFi+Xr16AFCun4jImSxYIA+RBQDPPQe0aKFqOkREdYbdxeuQIUNw5coVzJgxA+np6ejSpQu2bt2q3MSVmpoKrZYP7iIi13XtmnyjFiCfdZ06Vd18iIjqEo0QQqidxK1kZ2cjMDAQer0eAQEBaqdDRHXcpEnARx/J7bFjgWXL7FveYDBAkiQAQG5uLvz8/Ko5QyKi2ldb9RpPkRIR2eHiRfmhBADg6clrXYmIahuLVyIiO7z/PpCfL7fHjweaNVM3HyKiuobFKxFRJZ0+DaxYIbclCZg8Wd18iIjqIhavRESVNGMGUFIit996C2jUSN18iIjqIhavRESVcOAA8O23cjsoCIiNVTUdIqI6i8UrEVEllB0Oa+pUwN9fvVyIiOoyFq9ERLewaxewZYvcDg8HXnxR3XyIiOoyFq9ERBUQQh7X1WzmTMDbW718iIjqOhavREQV2LIF2L1bbrdtCwwfrm4+RER1HYtXIiIbTCZgypTS+Q8/lB8HS0RE6mHxSkRkw7ffAocOye277gIef1zdfIiIiMUrEZFV+fmWDyGYNQvQaNTLh4iIZCxeiYismD8fOH9ebj/6KBATo24+REQkY/FKRHSTS5eA+Hi57eYGfPyxuvkQEVEpFq9ERDeZNg0wGOT2uHFA+/bq5kNERKVYvBIRlaHTAatWye3AQHlcVyIichwsXomIbhACeOMN+V8AmDEDCApSNyciIrLE4pWI6IZNm4DffpPbrVoBr7yiajpERGQFi1ciIgCFhcDEiaXzc+cCnp7q5UNERNaxeCUiArBoEXDmjNx+8EFg4EBV0yEiIhtYvBJRnXflCvD++3JbowEWLOADCYiIHBWLVyKq8+LiAL1ebo8aBXTpomo6RERUARavRFSn/fUXsHSp3PbzAz74QN18iIioYixeiajOMhrlhxCYh8aKiwMaN1Y3JyIiqhiLVyKqsz7/HNi/X2536gS8/rqq6RARUSWweCWiOuniRWDq1NL5pUsBDw/18iEiosph8UpEddIbbwA5OXJ77FigZ0918yEiosph8UpEdc7WrcCGDXI7KAiYPVvdfIiIqPJYvBJRnZKfD4wfXzr/8cdAgwbq5UNERPZh8UpEdcqsWcDZs3L7gQeA4cPVzYeIiOzD4pWI6ozjx4GPPpLbHh7AkiV8khYRkbNh8UpEdYLJBLz0ElBcLM+//TbQrp26ORERkf1YvBJRnbBkCbBzp9xu2dJymCwiInIeLF6JyOWdOgVMnFg6v3Qp4OOjXj5ERFR1LF6JyKUZjcDIkfIoA4B86cDDD6ubExERVR2LVyJyafPmAYmJcvuOO4C5c9XNh4iIbg+LVyJyWYcPAzNmyG2NBlizBvDzUzcnIiK6PSxeicglFRXJY7gWFcnzEycC99yjbk5ERHT7WLwSkUt67z3g4EG53bGjPE9ERM6PxSsRuZy9e4H4eLnt7g589RXg5aVuTkREVD1YvBKRS8nLA0aMkB9KAABxcUDXrurmRERE1adKxevixYsREREBb29vREVFYd++fTZjly9fjvvuuw/169dH/fr1ERMTU2E8EVFVCQG8/DJw8qQ836MHMGmSujkREVH1srt4Xb9+PWJjYxEXF4f9+/cjMjISvXv3xuXLl63G79y5E0OHDsWOHTuQmJiI8PBwPPLII7hw4cJtJ09EVNbKlfKIAoA8qsCaNfJlA0RE5Do0QghhzwJRUVG46667sGjRIgCAyWRCeHg4Xn31VUyqxCkOo9GI+vXrY9GiRRgxYkSl3jM7OxuBgYHQ6/UICAiwJ10iqiN0OiA6GigslOe//hoYNkzdnGwxGAyQJAkAkJubCz+O30VELqC26jW7zrwWFRUhKSkJMTExpSvQahETE4NE8yjgt5CXl4fi4mI0aNDAZkxhYSGys7MtJiIiW7KygCefLC1cX37ZcQtXIiK6PXYVr5mZmTAajQgJCbHoDwkJQXp6eqXW8c477yAsLMyiAL5ZfHw8AgMDlSk8PNyeNImoDjGZ5Me/nj0rz991FzB/vro5ERFRzanV0QZmz56NdevW4fvvv4e3t7fNuMmTJ0Ov1yvT+fPnazFLInIm8+YBP/4otxs0ADZu5LBYRESuzK5bGYKCguDm5oaMjAyL/oyMDISGhla47Lx58zB79mz897//RefOnSuM9fLyghf/+hDRLfz2GzB5stzWaIC1a4HmzdXNiYiIapZdZ149PT3RrVs3JCQkKH0mkwkJCQmIjo62udycOXPw/vvvY+vWrejevXvVsyUiuuHSJWDIkNLxXKdNA/r0UTcnIiKqeXYPIhMbG4uRI0eie/fu6NGjBxYuXAiDwYBRo0YBAEaMGIEmTZog/sbjbT766CPMmDED33zzDSIiIpRrYyVJUu62JSKyh8EADBwImL8EiomRH0ZARESuz+7idciQIbhy5QpmzJiB9PR0dOnSBVu3blVu4kpNTYVWW3pCd8mSJSgqKsKTTz5psZ64uDi8++67t5c9EdU5RqM8ksCff8rzTZvKw2K5uambFxER1Q67x3lVA8d5JSJAfoLWa68BN4aZhr8/sGsXcIvL6B0Ox3klIlfkkOO8EhGpacGC0sLV3R34f//P+QpXIiK6PSxeicgpfPcd8NZbpfPLlwMPP6xePkREpA4Wr0Tk8PbsAZ59Vr5sAJBvznruOVVTIiIilbB4JSKHduoUMGBA6aNfR47kyAJERHUZi1ciclgpKfKlAVevyvP//CewbJn8QAIiIqqbWLwSkUNKTgYeeAA4d06e79hRvkHL01PdvIiISF0sXonI4Zw9Czz4IJCaKs+3bQts2wYEBqqaFhEROQAWr0TkUG4uXNu1A3bsAEJDVU2LiIgcBItXInIYZ87Ihev58/I8C1ciIroZi1cicgg3F67t28uF640nTxMREQFg8UpEDuDAAeD++4G0NHm+QwcWrkREZB2LVyJS1ebNwL33AhcvyvMdOwLbtwPBwermRUREjonFKxGp5rPP5AcQGAzy/N13s3AlIqKKsXglolpnNAKvvSZPJpPc93//JxeujRqpmxsRETk2Fq9EVKtyc4FBg+SzrmZTpgDffgv4+KiWFhEROQl3tRMgorrj7Flg8GD5Bi0AcHeXH/c6apSqaRERkRPhmVciqhXffgt06VJauNarB/z6KwtXIiKyD4tXIqpRBgMwejQwbBiQkyP3tWoF7NkDPPSQurkREZHzYfFKRDXm4EGge3fgyy9L+559Fti/X356FhERkb1YvBJRtRMCWLQIiIoCjh+X+/z8gDVrgH/9C/D3Vzc/IiJyXrxhi4iq1cmTwMsvAwkJpX1duwLr1gF33qleXkRE5Bp45pWIqkVBATBzJtCpk2XhOmECkJjIwpWIiKoHz7wS0W1LSABeegk4daq0r3lzYMkSoE8f9fIiIiLXwzOvRFRl6enyDVgxMaWFq7s78M47wNGjLFyJiKj68cwrEdnt+nVg7lzgk0+AvLzS/p49gaVL5UsHiIiIagKLVyKqtNxcuWCdOxfQ60v769cH5swBnn8e0PL7HCIiqkEsXonolgoK5DOqs2YBV66U9nt6AuPGAdOmAcHB6uVHRER1B4tXIrLpyhXgiy+AxYvl61vNtFrgueeAGTPkG7OIiIhqC4tXIirn0CH58oCvvwYKCy1fGzJEHhKrTRt1ciMiorqNxSsRAQCKi4EtW4BPPwW2b7d8TasFBg0Cpk8HunRRIzsiIiIZi1eiOkwIIClJfmTrt99aXs8KAAEBwNixwCuvABERqqRIRERkgcUrUR2UmipfEvDVV8Dx4+Vfb9VKfjLWyJGAv3/t50dERGQLi1eiOkAI+TrWn34CfvwR+PPP8jFeXkD//vKNWH36cMgrIiJyTCxeiVxUQQHw++9ysfrTT/LZVmvuuw8YPhx46imgXr1aTZGIiMhuLF6JXERhIbB3L7BjB7BzJ5CYWH6kALPISGDwYPnRri1a1GqaREREt4XFK5GTysiQv/7/80/gf/+Ti9WCAuuxHh5Ar17AgAHAY49xbFYiInJeLF6JHJwQcqF6+LA8MoC5YD1/vuLlWrQAHnwQ6NsXeOQReeQAIiIiZ8filchBmIvUU6eAo0eBI0dKp6tXb718RIRcrJonnl0lIiJXxOKVqBbl58tnTFNTgZQU4PRpy8lgqNx6JAno1g246y55iopisUpERHUDi1eialBSAly+DFy6BKSny5O5nZZWWrBmZtq/7rAwoEMHoGNH+Uaru+6SH83q5lb9PwcREZGjq1LxunjxYsydOxfp6emIjIzEZ599hh49etiM37hxI6ZPn46UlBS0bt0aH330Efr27VvlpIlqgskkn/nMyQGys4Hr14GsLHkyt69flwvQm6esrNt7b3d3+RrVVq2AO+4A2reXi9UOHYAGDW7/ZyMiInIVdhev69evR2xsLJYuXYqoqCgsXLgQvXv3xokTJxAcHFwufs+ePRg6dCji4+Px2GOP4ZtvvsGgQYOwf/9+dOzYsVp+CHJNJhNQVFR+KiyUp4KC8u38fOuTwWB9ys0tLVZzc+XrTmuCmxvQpAkQHg40a1b6b6tW8tS8uVzAEhERUcU0Qtj35zoqKgp33XUXFi1aBAAwmUwIDw/Hq6++ikmTJpWLHzJkCAwGA37++Wel7+6770aXLl2wdOnSSr1ndnY2AgMDsXhxBnx8KnfLtK2fyna/xmbMrdZl619bbSGsL1NR++b1WE4aK33yZDJZnzeZ5HWVnRdCA5MJyiQEYDRazptM5j4NjEYokzmmtE+DkpLS14xG+at1edKUaQPFxUBxsbw+uS1PJlPpZ+Ko6tcXaNhQoEEDgeBgeQoNFQgJkafQ0NKJxSmZGQwGhISEAAAyMjLg5+enckZERLcvOzsbYWFh0Ov1CKjBIW7s+nNaVFSEpKQkTJ48WenTarWIiYlBYmKi1WUSExMRGxtr0de7d29s2rTJ5vsUFhaisMzo6tnZ2QCA8eO9AXjbkzJRBYwADACyAeRY+fc6gKwy/5rbmTema7h+3Yjr12s5bXIp5iKWiIgqx67iNTMzE0ajsdzBNiQkBMePH7e6THp6utX49PR0m+8THx+PmTNn2pMaOYUSG1Pxjals2zwVAiiyMhUCKLjxb9l2vo3JYGWy8fgpIiIiclgO+UXm5MmTLc7WZmdnIzw8HO+9Vwhvb8uCQ1PBN8u2XrO3/+bX7GlX9G/FfeKWy1Zl0moBrVZYzJf2l07m193cSpcp+7q5382tdNJohMW8u/vNrytbB4DHjYmo7uFlA0TkisyXDdQ0u4rXoKAguLm5ISMjw6I/IyMDoaGhVpcJDQ21Kx4AvLy84OXlVa5/wgQvBASU7yciclZ+fn4sXonIJRiNxlp5H609wZ6enujWrRsSEhKUPpPJhISEBERHR1tdJjo62iIeALZt22YznoiIiIjIFrsvG4iNjcXIkSPRvXt39OjRAwsXLoTBYMCoUaMAACNGjECTJk0QHx8PAJgwYQIeeOABfPzxx+jXrx/WrVuHv/76C8uWLaven4SIiIiIXJ7dxeuQIUNw5coVzJgxA+np6ejSpQu2bt2qXL+VmpoKrbb0hG7Pnj3xzTffYNq0aZgyZQpat26NTZs2cYxXIiIiIrKb3eO8qsE8zmtNjxtGRFQbDAYDJEkCAOTm5vKaVyJyCbVVr9l1zSsRERERkZpYvBIRERGR02DxSkREREROg8UrERERETkNFq9ERERE5DRYvBIRERGR02DxSkREREROg8UrERERETkNFq9ERERE5DRYvBIRERGR02DxSkREREROg8UrERERETkNFq9ERERE5DRYvBIRERGR02DxSkREREROg8UrERERETkNFq9ERERE5DRYvBIRERGR03BXO4HKEEIAALKzs1XOhIjo9hkMBqWdnZ0No9GoYjZERNXDXKeZ67aa4hTF69WrVwEA4eHhKmdCRFS9wsLC1E6BiKhaXb16FYGBgTW2fqcoXhs0aAAASE1NrdGN4Uqys7MRHh6O8+fPIyAgQO10nAa3m/24zaqG281+3GZVw+1mP26zqtHr9WjWrJlSt9UUpyhetVr50tzAwEDuRHYKCAjgNqsCbjf7cZtVDbeb/bjNqobbzX7cZlVjrttqbP01unYiIiIiomrE4pWIiIiInIZTFK9eXl6Ii4uDl5eX2qk4DW6zquF2sx+3WdVwu9mP26xquN3sx21WNbW13TSipsczICIiIiKqJk5x5pWIiIiICGDxSkREREROhMUrERERETkNFq9ERERE5DQconj98MMP0bNnT/j6+qJevXpWY1JTU9GvXz/4+voiODgYEydORElJSYXrvXbtGp555hkEBASgXr16GD16NHJzc2vgJ1Dfzp07odForE5//vmnzeUefPDBcvEvvvhiLWauroiIiHI//+zZsytcpqCgAOPHj0fDhg0hSRIGDx6MjIyMWspYfSkpKRg9ejRatGgBHx8f3HHHHYiLi0NRUVGFy9XFfW3x4sWIiIiAt7c3oqKisG/fvgrjN27ciLZt28Lb2xudOnXCli1bailT9cXHx+Ouu+6Cv78/goODMWjQIJw4caLCZVavXl1un/L29q6ljB3Du+++W24btG3btsJl6vJ+Blg/7ms0GowfP95qfF3dz37//Xf0798fYWFh0Gg02LRpk8XrQgjMmDEDjRs3ho+PD2JiYnDq1Klbrtfe46I1DlG8FhUV4amnnsJLL71k9XWj0Yh+/fqhqKgIe/bswZo1a7B69WrMmDGjwvU+88wzOHr0KLZt24aff/4Zv//+O1544YWa+BFU17NnT1y6dMliGjNmDFq0aIHu3btXuOzYsWMtlpszZ04tZe0Y3nvvPYuf/9VXX60w/o033sBPP/2EjRs34rfffsPFixfxxBNP1FK26jt+/DhMJhO++OILHD16FAsWLMDSpUsxZcqUWy5bl/a19evXIzY2FnFxcdi/fz8iIyPRu3dvXL582Wr8nj17MHToUIwePRo6nQ6DBg3CoEGDcOTIkVrOXB2//fYbxo8fjz/++APbtm1DcXExHnnkERgMhgqXCwgIsNinzp07V0sZO44OHTpYbINdu3bZjK3r+xkA/Pnnnxbba9u2bQCAp556yuYydXE/MxgMiIyMxOLFi62+PmfOHHz66adYunQp9u7dCz8/P/Tu3RsFBQU212nvcdEm4UBWrVolAgMDy/Vv2bJFaLVakZ6ervQtWbJEBAQEiMLCQqvr+vvvvwUA8eeffyp9v/zyi9BoNOLChQvVnrujKSoqEo0aNRLvvfdehXEPPPCAmDBhQu0k5YCaN28uFixYUOn4rKws4eHhITZu3Kj0HTt2TAAQiYmJNZChc5gzZ45o0aJFhTF1bV/r0aOHGD9+vDJvNBpFWFiYiI+Ptxr/f//3f6Jfv34WfVFRUWLcuHE1mqejunz5sgAgfvvtN5sxtv5m1CVxcXEiMjKy0vHcz8qbMGGCuOOOO4TJZLL6OvczIQCI77//Xpk3mUwiNDRUzJ07V+nLysoSXl5e4ttvv7W5HnuPi7Y4xJnXW0lMTESnTp0QEhKi9PXu3RvZ2dk4evSozWXq1atncdYxJiYGWq0We/furfGc1fbjjz/i6tWrGDVq1C1jv/76awQFBaFjx46YPHky8vLyaiFDxzF79mw0bNgQXbt2xdy5cyu8HCUpKQnFxcWIiYlR+tq2bYtmzZohMTGxNtJ1SHq9Hg0aNLhlXF3Z14qKipCUlGSxn2i1WsTExNjcTxITEy3iAfk4V1f3K71eDwC33K9yc3PRvHlzhIeHY+DAgTb/JriyU6dOISwsDC1btsQzzzyD1NRUm7HczywVFRVh7dq1eP7556HRaGzGcT+zlJycjPT0dIt9KTAwEFFRUTb3paocF21xr1ratSs9Pd2icAWgzKenp9tcJjg42KLP3d0dDRo0sLmMK1m5ciV69+6Npk2bVhg3bNgwNG/eHGFhYTh06BDeeecdnDhxAv/+979rKVN1vfbaa/jHP/6BBg0aYM+ePZg8eTIuXbqE+fPnW41PT0+Hp6dnuWuzQ0JC6sR+Zc3p06fx2WefYd68eRXG1aV9LTMzE0aj0epx6/jx41aXsXWcq4v7lclkwuuvv4577rkHHTt2tBnXpk0bfPnll+jcuTP0ej3mzZuHnj174ujRo7c89rmKqKgorF69Gm3atMGlS5cwc+ZM3HfffThy5Aj8/f3LxXM/s7Rp0yZkZWXhueeesxnD/aw88/5iz75UleOiLTVWvE6aNAkfffRRhTHHjh275YXldV1VtmNaWhp+/fVXbNiw4ZbrL3sNcKdOndC4cWP885//xJkzZ3DHHXdUPXEV2bPNYmNjlb7OnTvD09MT48aNQ3x8fJ17LGBV9rULFy7g0UcfxVNPPYWxY8dWuKwr7mtUM8aPH48jR45UeO0mAERHRyM6OlqZ79mzJ9q1a4cvvvgC77//fk2n6RD69OmjtDt37oyoqCg0b94cGzZswOjRo1XMzDmsXLkSffr0QVhYmM0Y7meOp8aK1zfffLPC/8kAQMuWLSu1rtDQ0HJ3o5nv7g4NDbW5zM0XAJeUlODatWs2l3FEVdmOq1atQsOGDTFgwAC73y8qKgqAfDbNWQuK29n3oqKiUFJSgpSUFLRp06bc66GhoSgqKkJWVpbF2deMjAyn2q+ssXe7Xbx4Eb169ULPnj2xbNkyu9/PFfY1W4KCguDm5lZuFIqK9pPQ0FC74l3VK6+8otxga+9ZLQ8PD3Tt2hWnT5+uoewcX7169XDnnXfa3Abcz0qdO3cO//3vf+3+9of7WWntlZGRgcaNGyv9GRkZ6NKli9VlqnJctKXGitdGjRqhUaNG1bKu6OhofPjhh7h8+bJyKcC2bdsQEBCA9u3b21wmKysLSUlJ6NatGwBg+/btMJlMyh9NZ2DvdhRCYNWqVRgxYgQ8PDzsfr8DBw4AgMXO6GxuZ987cOAAtFptuUtOzLp16wYPDw8kJCRg8ODBAIATJ04gNTXV4n/mzsie7XbhwgX06tUL3bp1w6pVq6DV2n/5vCvsa7Z4enqiW7duSEhIwKBBgwDIX4UnJCTglVdesbpMdHQ0EhIS8Prrryt927Ztc/r9qrKEEHj11Vfx/fffY+fOnWjRooXd6zAajTh8+DD69u1bAxk6h9zcXJw5cwbDhw+3+npd38/KWrVqFYKDg9GvXz+7luN+BrRo0QKhoaFISEhQitXs7Gzs3bvX5shRVTku2mTX7V015Ny5c0Kn04mZM2cKSZKETqcTOp1O5OTkCCGEKCkpER07dhSPPPKIOHDggNi6dato1KiRmDx5srKOvXv3ijZt2oi0tDSl79FHHxVdu3YVe/fuFbt27RKtW7cWQ4cOrfWfrzb997//FQDEsWPHyr2WlpYm2rRpI/bu3SuEEOL06dPivffeE3/99ZdITk4WP/zwg2jZsqW4//77azttVezZs0csWLBAHDhwQJw5c0asXbtWNGrUSIwYMUKJuXmbCSHEiy++KJo1aya2b98u/vrrLxEdHS2io6PV+BFUkZaWJlq1aiX++c9/irS0NHHp0iVlKhtT1/e1devWCS8vL7F69Wrx999/ixdeeEHUq1dPGTVl+PDhYtKkSUr87t27hbu7u5g3b544duyYiIuLEx4eHuLw4cNq/Qi16qWXXhKBgYFi586dFvtUXl6eEnPzNps5c6b49ddfxZkzZ0RSUpJ4+umnhbe3tzh69KgaP4Iq3nzzTbFz506RnJwsdu/eLWJiYkRQUJC4fPmyEIL7mS1Go1E0a9ZMvPPOO+Ve434my8nJUeoxAGL+/PlCp9OJc+fOCSGEmD17tqhXr5744YcfxKFDh8TAgQNFixYtRH5+vrKOhx56SHz22WfK/K2Oi5XlEMXryJEjBYBy044dO5SYlJQU0adPH+Hj4yOCgoLEm2++KYqLi5XXd+zYIQCI5ORkpe/q1ati6NChQpIkERAQIEaNGqUUxK5q6NChomfPnlZfS05Ottiuqamp4v777xcNGjQQXl5eolWrVmLixIlCr9fXYsbqSUpKElFRUSIwMFB4e3uLdu3aiVmzZomCggIl5uZtJoQQ+fn54uWXXxb169cXvr6+4vHHH7co3FzdqlWrrP6+lv2/MPc12WeffSaaNWsmPD09RY8ePcQff/yhvPbAAw+IkSNHWsRv2LBB3HnnncLT01N06NBBbN68uZYzVo+tfWrVqlVKzM3b7PXXX1e2b0hIiOjbt6/Yv39/7SevoiFDhojGjRsLT09P0aRJEzFkyBBx+vRp5XXuZ9b9+uuvAoA4ceJEude4n8nMddXNk3nbmEwmMX36dBESEiK8vLzEP//5z3Lbs3nz5iIuLs6ir6LjYmVphBDCvnO1RERERETqcIpxXomIiIiIABavREREROREWLwSERERkdNg8UpEREREToPFKxERERE5DRavREREROQ0WLwSERERkdNg8UpEREREToPFKxFRLXvwwQctni1PRESVx+KViIiIiJwGHw9LRFSLnnvuOaxZs8aiLzk5GREREeokRETkZFi8EhHVIr1ejz59+qBjx4547733AACNGjWCm5ubypkRETkHd7UTICKqSwIDA+Hp6QlfX1+EhoaqnQ4RkdPhNa9ERERE5DRYvBIRERGR02DxSkRUyzw9PWE0GtVOg4jIKbF4JSKqZREREdi7dy9SUlKQmZkJk8mkdkpERE6DxSsRUS1766234Obmhvbt26NRo0ZITU1VOyUiIqfBobKIiIiIyGnwzCsREREROQ0Wr0RERETkNFi8EhEREZHTYPFKRERERE6DxSsREREROQ0Wr0RERETkNFi8EhEREZHTYPFKRERERE6DxSsREREROQ0Wr0RERETkNFi8EhEREZHTYPFKRERERE7j/wPoGYUFNLq9XwAAAABJRU5ErkJggg==", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "t = np.linspace(-10, 10, 100)\n", + "sig = 1 / (1 + np.exp(-t))\n", + "plt.figure(figsize=(8, 4))\n", + "plt.plot([-10, 10], [0, 0], \"k-\")\n", + "plt.plot([-10, 10], [0.5, 0.5], \"k:\")\n", + "plt.plot([-10, 10], [1, 1], \"k:\")\n", + "plt.plot([0, 0], [-1.1, 1.1], \"k-\")\n", + "plt.plot(t, sig, \"b-\", linewidth=2, label=r\"$\\sigma(t) = \\frac{1}{1 + e^{-t}}$\")\n", + "plt.xlabel(\"t\")\n", + "plt.legend(loc=\"upper left\", fontsize=20)\n", + "plt.axis([-10, 10, -0.1, 1.1]);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Predictions\n", + "\n", + "Can then make class predictions depending on whether the predicted probability $\\hat{p}$ is greater than 0.5, i.e.\n", + "\n", + "$$ \\hat{y} = \\biggl \\{\n", + "\\begin{split}\n", + "0,\\ \\text{if}\\ \\hat{p} < 0.5\\\\\n", + "1,\\ \\text{if}\\ \\hat{p} \\geq 0.5\n", + "\\end{split}\n", + ",\n", + "$$\n", + "\n", + "where we recall \n", + "$\\hat{p} = h_\\theta(x) = \\sigma(\\theta^{\\rm T} x) \\quad \\text{and} \\quad \\sigma(t) = \\frac{1}{1+\\exp{(-t)}}.$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Note that $\\sigma(t) < 0.5$ when $t<0$ and $\\sigma(t) \\geq 0.5$ when $t \\geq 0$. \n", + "\n", + "That is, logistic regression predicts model 1 when $\\theta^{\\rm T} x$ is positive, and model 0 when it is negative. \n", + "\n", + "The decision boundary is defined by $\\theta^{\\rm T} x=0$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Cost functions" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Consider the cost function:\n", + "\n", + "$$ C(\\theta) = \\biggl \\{\n", + "\\begin{split}\n", + "-\\log(\\hat{p}),\\ \\text{if}\\ y=1\\\\\n", + "-\\log(1 - \\hat{p}),\\ \\text{if}\\ y=0\n", + "\\end{split}\n", + ".\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Exercise: Plot the cost function for $y=1$ as a function of $\\hat{p}$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "tags": [ + "inclass_exercise" + ] + }, + "source": [ + "Consider the cost function:\n", + "\n", + "$$ C(\\theta) = \\biggl \\{\n", + "\\begin{split}\n", + "-\\log(\\hat{p}),\\ \\text{if}\\ y=1\\\\\n", + "-\\log(1 - \\hat{p}),\\ \\text{if}\\ y=0\n", + "\\end{split}\n", + ".\n", + "$$" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:57.493545Z", + "iopub.status.busy": "2024-01-10T00:19:57.492986Z", + "iopub.status.idle": "2024-01-10T00:19:57.715480Z", + "shell.execute_reply": "2024-01-10T00:19:57.714807Z" + }, + "tags": [ + "solution", + "inclass_exercise" + ] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "ph = np.linspace(0.01, 0.99, 100)\n", + "cost_one = -np.log(ph)\n", + "plt.figure(figsize=(8, 4))\n", + "plt.plot([0, 0], [-1.1, 1.1], \"k-\")\n", + "plt.plot(ph, cost_one, \"b-\", linewidth=2, label=r\"$-\\log{(\\hat{p})}$\")\n", + "plt.xlabel(\"$\\hat{p}$\")\n", + "plt.legend(loc=\"upper right\", fontsize=20)\n", + "plt.axis([0, 1, 0, 4]);\n", + "plt.title('Cost for $y=1$');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + }, + "tags": [ + "inclass_exercise" + ] + }, + "source": [ + "What can you say intuitively about the cost function at the edges of the domain?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + }, + "tags": [ + "solution", + "inclass_exercise" + ] + }, + "source": [ + "- For $\\hat{p}=1$, $C(\\hat{p}) = 0$.\n", + "- For $\\hat{p}=0$, $C(\\hat{p}) \\rightarrow \\infty$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + }, + "tags": [ + "inclass_exercise" + ] + }, + "source": [ + "### Exercise: Plot the cost function for $y=0$ as a function of $\\hat{p}$." + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:57.718928Z", + "iopub.status.busy": "2024-01-10T00:19:57.718470Z", + "iopub.status.idle": "2024-01-10T00:19:57.934523Z", + "shell.execute_reply": "2024-01-10T00:19:57.933872Z" + }, + "tags": [ + "inclass_exercise", + "solution" + ] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "cost_zero = -np.log(1-ph)\n", + "plt.figure(figsize=(8, 4))\n", + "plt.plot([0, 0], [-1.1, 1.1], \"k-\")\n", + "plt.plot(ph, cost_zero, \"b-\", linewidth=2, label=r\"$-\\log{(1-\\hat{p})}$\")\n", + "plt.xlabel(\"$\\hat{p}$\")\n", + "plt.legend(loc=\"upper left\", fontsize=20)\n", + "plt.axis([0, 1, 0, 4]);\n", + "plt.title('Cost for $y=0$');" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + }, + "tags": [ + "inclass_exercise" + ] + }, + "source": [ + "What can you say intuitively about the cost function at the edges of the domain?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + }, + "tags": [ + "solution", + "inclass_exercise" + ] + }, + "source": [ + "- For $\\hat{p}=0$, $C(\\hat{p}) = 0$.\n", + "- For $\\hat{p}=1$, $C(\\hat{p}) \\rightarrow \\infty$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Log-loss function for logistic regression\n", + "\n", + "Cost function can be written by the single expression\n", + "\n", + "$$\n", + "C(\\theta) = -\\frac{1}{m} \\sum_{i=1}^m \n", + "\\left [ \n", + "y^{(i)} \\log(\\hat{p}^{(i)})\n", + "+\n", + "(1 - y^{(i)}) \\log(1 - \\hat{p}^{(i)})\n", + "\\right],\n", + "$$\n", + "\n", + "since $y^{(i)}$ is always 0 or 1 and we thus recover the separate cases considered above." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "#### Aside: statistical interpretation\n", + "\n", + "Interpret $p$ as probability of target $y$:\n", + "\n", + "$$\n", + "{\\rm P}(y \\: \\vert \\: p ) = p^{y} (1-p)^{1-y}\n", + "$$\n", + "\n", + "$$\n", + "{\\rm log}{\\rm P}(y \\: \\vert \\: p, x ) = y {\\rm log}(p) + (1-y) {\\rm log}(1-p)\n", + "$$\n", + "\n", + "See [MacKay](http://www.inference.org.uk/itila/book.html) [Chapter 41] for further details." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Minimising the cost function\n", + "\n", + "No closed form solution like linear regression.\n", + "\n", + "But since the cost function is convex guaranteed to find global minimum by gradient descent." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Derivative of the cost function\n", + "\n", + "\\begin{align*}\n", + "\\frac{\\partial C}{\\partial \\theta} \n", + "&=\n", + "\\frac{1}{m} \\sum_{i=1}^m \n", + "\\left[ \\sigma\\left(\\theta^{\\rm T} x^{(i)} \\right) - y^{(i)} \\right] \n", + "x^{(i)} \\\\\n", + "&=\n", + "\\frac{1}{m} \n", + "X^{\\rm T}\n", + "\\left[ \\sigma\\left(X \\theta \\right) - y \\right] \\\\\n", + "&=\n", + "\\frac{1}{m} \n", + "X^{\\rm T}\n", + "\\left[ h_\\theta\\left(X\\right) - y \\right]\n", + "\\end{align*}\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Similarity with linear regression\n", + "\n", + "Identical to linear regression (up to factor of 2 depending on conventions adopted) but with a different prediction function:\n", + "\n", + "$$h_\\theta(x) = \\sigma(\\theta^{\\rm T} x), $$\n", + "\n", + "instead of\n", + "\n", + "$$h_\\theta(x) = \\theta^{\\rm T} x. $$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Example of logistic regression" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Consider [Iris flower data](https://en.wikipedia.org/wiki/Iris_flower_data_set) again." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:57.939374Z", + "iopub.status.busy": "2024-01-10T00:19:57.937962Z", + "iopub.status.idle": "2024-01-10T00:19:58.295225Z", + "shell.execute_reply": "2024-01-10T00:19:58.294555Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "['data',\n", + " 'target',\n", + " 'frame',\n", + " 'target_names',\n", + " 'DESCR',\n", + " 'feature_names',\n", + " 'filename',\n", + " 'data_module']" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "from sklearn import datasets\n", + "iris = datasets.load_iris()\n", + "list(iris.keys())" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:58.299485Z", + "iopub.status.busy": "2024-01-10T00:19:58.298085Z", + "iopub.status.idle": "2024-01-10T00:19:58.303784Z", + "shell.execute_reply": "2024-01-10T00:19:58.303189Z" + } + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "%matplotlib inline\n", + "import matplotlib\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Train model\n", + "\n", + "Use petal width to classify whether Virginica or not." + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:58.307016Z", + "iopub.status.busy": "2024-01-10T00:19:58.306450Z", + "iopub.status.idle": "2024-01-10T00:19:58.311305Z", + "shell.execute_reply": "2024-01-10T00:19:58.310697Z" + } + }, + "outputs": [], + "source": [ + "# Set up training data\n", + "X_1d = iris[\"data\"][:, 3:] # petal width\n", + "y = (iris[\"target\"] == 2).astype(int) # 1 if Iris-Virginica, else 0" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:58.315162Z", + "iopub.status.busy": "2024-01-10T00:19:58.313802Z", + "iopub.status.idle": "2024-01-10T00:19:58.370892Z", + "shell.execute_reply": "2024-01-10T00:19:58.370148Z" + } + }, + "outputs": [], + "source": [ + "from sklearn.linear_model import LogisticRegression\n", + "log_reg = LogisticRegression(random_state=42)\n", + "log_reg.fit(X_1d, y);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Note that Scikit-Learn automatically adds $\\ell_2$ regularizer to cost function." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Prediction" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:58.375263Z", + "iopub.status.busy": "2024-01-10T00:19:58.373897Z", + "iopub.status.idle": "2024-01-10T00:19:58.555888Z", + "shell.execute_reply": "2024-01-10T00:19:58.555274Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "X_1d_new = np.linspace(0, 3, 1000).reshape(-1, 1)\n", + "y_1d_proba = log_reg.predict_proba(X_1d_new)\n", + "\n", + "plt.figure(figsize=(8,4))\n", + "plt.plot(X_1d_new, y_1d_proba[:, 1], \"g-\", linewidth=2, label=\"Iris-Virginica\")\n", + "plt.plot(X_1d_new, y_1d_proba[:, 0], \"b--\", linewidth=2, label=\"Not Iris-Virginica\")\n", + "plt.xlabel(\"Petal width (cm)\", fontsize=14)\n", + "plt.ylabel(\"Probability\", fontsize=14)\n", + "plt.legend(loc=\"center left\", fontsize=14);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Decision boundary" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "Recall the decision boundary is given by $\\hat{p}=0.5$ or, equivalently, $\\theta^{\\rm T} x=0$." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:58.559105Z", + "iopub.status.busy": "2024-01-10T00:19:58.558652Z", + "iopub.status.idle": "2024-01-10T00:19:58.565651Z", + "shell.execute_reply": "2024-01-10T00:19:58.565067Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1.66066066])" + ] + }, + "execution_count": 11, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "decision_boundary = X_1d_new[y_1d_proba[:, 1] >= 0.5][0]\n", + "decision_boundary" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Updating plot with decision boundary and training data" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:58.568895Z", + "iopub.status.busy": "2024-01-10T00:19:58.568352Z", + "iopub.status.idle": "2024-01-10T00:19:58.801548Z", + "shell.execute_reply": "2024-01-10T00:19:58.800895Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(8, 4))\n", + "plt.plot(X_1d[y==0], y[y==0], \"bs\")\n", + "plt.plot(X_1d[y==1], y[y==1], \"g^\")\n", + "plt.plot([decision_boundary, decision_boundary], [-1, 2], \"k:\", linewidth=2)\n", + "plt.plot(X_1d_new, y_1d_proba[:, 1], \"g-\", linewidth=2, label=\"Iris-Virginica\")\n", + "plt.plot(X_1d_new, y_1d_proba[:, 0], \"b--\", linewidth=2, label=\"Not Iris-Virginica\")\n", + "plt.text(decision_boundary+0.02, 0.15, \"Decision boundary\", fontsize=14, color=\"k\", ha=\"center\")\n", + "plt.arrow(decision_boundary[0], 0.08, -0.3, 0, head_width=0.05, head_length=0.1, fc='b', ec='b')\n", + "plt.arrow(decision_boundary[0], 0.92, 0.3, 0, head_width=0.05, head_length=0.1, fc='g', ec='g')\n", + "plt.xlabel(\"Petal width (cm)\", fontsize=14)\n", + "plt.ylabel(\"Probability\", fontsize=14)\n", + "plt.legend(loc=\"center left\", fontsize=14)\n", + "plt.axis([0, 3, -0.02, 1.02]);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Predictions depend on what side of decision boundary fall." + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:58.804779Z", + "iopub.status.busy": "2024-01-10T00:19:58.804533Z", + "iopub.status.idle": "2024-01-10T00:19:58.811352Z", + "shell.execute_reply": "2024-01-10T00:19:58.810755Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1, 0])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "log_reg.predict([[1.7], [1.5]])" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercises:** *You can now complete Exercise 1 in the exercises associated with this lecture.*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Extending to two features" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:58.814372Z", + "iopub.status.busy": "2024-01-10T00:19:58.813922Z", + "iopub.status.idle": "2024-01-10T00:19:58.827801Z", + "shell.execute_reply": "2024-01-10T00:19:58.827253Z" + } + }, + "outputs": [], + "source": [ + "from sklearn.linear_model import LogisticRegression\n", + "\n", + "X = iris[\"data\"][:, (2, 3)] # petal length, petal width\n", + "y = (iris[\"target\"] == 2).astype(int) # 1 if Iris-Virginica, else 0\n", + " \n", + "C = 1000 # inverse regularization (smaller values correspond to stronger regularization)\n", + "log_reg = LogisticRegression(C=C, random_state=42)\n", + "log_reg.fit(X, y)\n", + "\n", + "x0, x1 = np.meshgrid(\n", + " np.linspace(2.9, 7, 500).reshape(-1, 1),\n", + " np.linspace(0.8, 2.7, 200).reshape(-1, 1),\n", + " )\n", + "X_new = np.c_[x0.ravel(), x1.ravel()]\n", + "\n", + "y_proba = log_reg.predict_proba(X_new)" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:58.830821Z", + "iopub.status.busy": "2024-01-10T00:19:58.830145Z", + "iopub.status.idle": "2024-01-10T00:19:59.072590Z", + "shell.execute_reply": "2024-01-10T00:19:59.071979Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10, 5))\n", + "plt.plot(X[y==0, 0], X[y==0, 1], \"bs\")\n", + "plt.plot(X[y==1, 0], X[y==1, 1], \"g^\")\n", + "\n", + "zz = y_proba[:, 1].reshape(x0.shape)\n", + "contour = plt.contour(x0, x1, zz, cmap=plt.cm.brg)\n", + "\n", + "# Solve theta^T x = 0 to determine boundary\n", + "left_right = np.array([2.9, 7]) \n", + "boundary = -(log_reg.coef_[0][0] * left_right + log_reg.intercept_[0]) / log_reg.coef_[0][1]\n", + "\n", + "plt.clabel(contour, inline=1, fontsize=12)\n", + "plt.plot(left_right, boundary, \"k--\", linewidth=3)\n", + "plt.text(3.5, 1.5, \"Not Iris-Virginica\", fontsize=14, color=\"b\", ha=\"center\")\n", + "plt.text(6.5, 2.3, \"Iris-Virginica\", fontsize=14, color=\"g\", ha=\"center\")\n", + "plt.xlabel(\"Petal length\", fontsize=14)\n", + "plt.ylabel(\"Petal width\", fontsize=14)\n", + "plt.axis([2.9, 7, 0.8, 2.7]);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercises:** *You can now complete Exercise 2 in the exercises associated with this lecture.*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Softmax regression\n", + "\n", + "Can generalise logistic regression to classify multiple classes." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Softmax score\n", + "\n", + "Consider the softmax score function for class $k$:\n", + "\n", + "$$s_k(x) = \\left(\\theta^{(k)}\\right)^{\\rm T} x .$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "**Important note**: each class $k$ has its own score and set of parameters $\\theta^{(k)}$, for $K$ classes (i.e. $k=1,\\ldots,K$).\n", + "\n", + "Define:\n", + "- Parameter matrix: $\\Theta_{K \\times n} = [ \\theta^{(1)},\\ \\theta^{(2)},\\ ...,\\ \\theta^{(K)}]^{\\rm T}$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Softmax function\n", + "\n", + "Predictions are then given by the softmax function $\\sigma_k(s(x))$ for each $k$:\n", + "\n", + "$$ \n", + "\\hat{p}_k = \\sigma_k(s(x)) = \\frac{\\exp\\left(s_k(x)\\right)}{\\sum_{k^\\prime=1}^K \\exp\\left(s_{k^\\prime}(x)\\right)}\n", + ".\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Normalised such that\n", + "- $\\sum_k \\hat{p}_k = 1$\n", + "- $0 \\leq \\hat{p}_k \\leq 1$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Predictions\n", + "\n", + "Can then make class predictions based on which class has the highest predicted probability, i.e.\n", + "\n", + "$$ \n", + "\\hat{y}\n", + "= \\arg\\max_k \\hat{p}_k \n", + "= \\arg\\max_k s_k(x)\n", + "= \\arg\\max_k \\left(\\theta^{(k)}\\right)^{\\rm T} x\n", + ",\n", + "$$\n", + "\n", + "where we recall \n", + "$\\hat{p}_k = \\sigma_k(s(x)) = \\frac{\\exp\\left(s_k(x)\\right)}{\\sum_{k^\\prime=1}^K \\exp\\left(s_{k^\\prime}(x)\\right)}\n", + "\\quad \\text{and} \\quad \n", + "s_k(x) = \\left(\\theta^{(k)}\\right)^{\\rm T} x.$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Cost function\n", + "\n", + "Generalization of the logistic regression cost function is given by the *cross-entropy* (measure of similarity of probability distributions):\n", + "\n", + "$$\n", + "C(\\Theta) = -\\frac{1}{m} \\sum_{i=1}^m \\sum_{k=1}^K y_k^{(i)} \\log \\left(\\hat{p}_k^{(i)}\\right)\n", + ".\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "For the case $K=2$, the cost functions reduces to the standard cost function for logistic regression." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Minimising the cost function\n", + "\n", + "Can solve by gradient descent.\n", + "\n", + "Derivative of cost function given by\n", + "\n", + "$$\n", + "\\frac{\\partial C}{\\partial \\theta^{(k)}}\n", + "= \\frac{1}{m} \\sum_{i=1}^m \\left(\\hat{p}_k^{(i)} - y_k^{(i)} \\right) x^{(i)} .\n", + "$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Example of softmax regression" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:59.076992Z", + "iopub.status.busy": "2024-01-10T00:19:59.076312Z", + "iopub.status.idle": "2024-01-10T00:19:59.088101Z", + "shell.execute_reply": "2024-01-10T00:19:59.087548Z" + } + }, + "outputs": [], + "source": [ + "X = iris[\"data\"][:, (2, 3)] # petal length, petal width\n", + "y = iris[\"target\"] # consider all three target classes\n", + "\n", + "C = 10\n", + "softmax_reg = LogisticRegression(multi_class=\"multinomial\", solver=\"lbfgs\", C=C, random_state=42)\n", + "softmax_reg.fit(X, y);" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:59.091075Z", + "iopub.status.busy": "2024-01-10T00:19:59.090368Z", + "iopub.status.idle": "2024-01-10T00:19:59.115277Z", + "shell.execute_reply": "2024-01-10T00:19:59.114655Z" + } + }, + "outputs": [], + "source": [ + "x0, x1 = np.meshgrid(\n", + " np.linspace(0, 8, 500).reshape(-1, 1),\n", + " np.linspace(0, 3.5, 200).reshape(-1, 1),\n", + " )\n", + "X_new = np.c_[x0.ravel(), x1.ravel()]\n", + "\n", + "y_proba = softmax_reg.predict_proba(X_new)\n", + "y_predict = softmax_reg.predict(X_new)\n", + "\n", + "# Select contours to plot\n", + "# zz1 = y_proba[:, 0].reshape(x0.shape)\n", + "zz1 = y_proba[:, 1].reshape(x0.shape)\n", + "# zz1 = y_proba[:, 2].reshape(x0.shape)\n", + "zz = y_predict.reshape(x0.shape)" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:19:59.118315Z", + "iopub.status.busy": "2024-01-10T00:19:59.117863Z", + "iopub.status.idle": "2024-01-10T00:19:59.387990Z", + "shell.execute_reply": "2024-01-10T00:19:59.387264Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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JI2u/vKXpGELI580I29UB/WNxECajbLRguSWTyi5bcUwPfJCVMMBd8KLd0xVIWpWcP4zMSo1h58chKK6AnkoQBEEQzlsiuBIEod5x2tz7gnRBDK7s5U62fZEDQJdxzc9aA+CjyY30GN9oTPjujuj/kwARGpStViy3ZrozWTNKArpcUBsCqa9UMmhVETE97TgrZNY/YmZhvyhKNomCF4IgCIIggitBEOodh939qy6IW4MyfzmEvcxFRCsTTQbH+DWWP1ksAClai/HFRoTv6oD+2QQIl1E2WbBct4eqS3bgXFru1/yOF9nRyRVLiun6YRnacIXCVXrm9ohmw7gwnJaAnkoQBEEQzisiuBIEod45G8HVrql5ALS5IyGgWStfAywAKVKL8QV38Qv9E3EQIuFaXUnVgJ1UXrXL3aw4QCQZWt1jYeimQhpfa0V1SWx/O5Q5XWPIXxzEjW6CIAiCUIeJ4EoQhHrHWR1cabTB6XFlLXJwcGkxAMk3xQV+fD8CLAA5Rovx9caE7eiI7r4GoAXX3DIqe2zDMioLJdseoJmCKVHh4h9KueTnEkIauajYrWXxoGhW3mnGViDKtguCIAgXFhFcCYJQ77gc7l+DVSnwwMIiVAWi2oVibh4SlHP4G2AByPE6Qt5vQtim9mj/FQUqOKYWUdFhC9Znc1BLA1eJIvEqG0M2FtLq/iqQVPZ+F8Ks1Fj2fmckwFXiBUEQBKHOEsGVIAj1jsvp/lUOUo2FmqxV4yuig3OCav7uxaohJxsxfduC0BVt0VwaBlYV+//yqEjZgn3iYVRnYKIffYRK1/fKGfB3ERHtHdgKZFbeGcHSKyOpyBJvN4IgCEL9J97tBEGod1xO93I0TZCCq7zlpQA0ujgyOCc4iUBksjRdQzHNb03Izy2RWxtQC5xYH8qm8qKtOOeXBWCWbjHdnQxcVUTHlyqQDSp58w3M7hzL9ndMKM6AnUYQBEEQ6hwRXAmCUO/UZq40gR/bUemiKKMCgLieEYE/wWkEIoslSdXNiNPbY3wvCSnaXb69atguqobvxrXLGpC5avTQflwlQ9YX0rCvHVeVxIZnwpnfO5ridFG2XRAEQaifRHAlCEK9oyruX4MRXBVuKgcVTAl6TPFBLEd4GoHIYkk6Cf39DQnb1gH9ww1BC85ZpVR22or1mQMB248V3srFZXOL6f5ZKfooheINOub1jmbDM2E4KwNyCkEQBEGoM0RwJQhCvaNUxwVyEF7hijLcEUFManjgB/dCIAIsAClKi/GtJELT26MdbAaHiv2dfCrab8H+dSGq4v9+LEmGFqOsDNlYSNL11WXb3wlldpcY8hbqA3AVgiAIglA31Lng6pNPPiE1NRWz2YzZbKZXr17Mnj37tI/56aefaNu2LUajkY4dOzJr1qyzNFtBEOqiYGauire5g6vodqGBH9xLgQqwADRtjJj+aEXI78nIrQyoh5xYx+6lqu8OXOsCk2IKiVfoM62US34pxpTkojJLy5IhUawaa8ZWKMq2C4IgCOe/OhdcNW7cmDfeeIN169axdu1a+vfvzzXXXENGRsZJj1++fDm33HILY8aMIT09neHDhzN8+HC2bNlylmcuCEJdoVQHV1IQXuFKdrkb8Ua0MgV+cB8EqqJgDd2QCELT22GYkAhhMq5VlVT23o7l3n0oBYGpRpF4pZ0hGwppdZ+7bHvW1yHM6hjL3mmibLsgCIJwfpNUte6/lUVHR/O///2PMWPGnPB3N910E5WVlcyYMaP2ez179qRTp058+umnHo1fVlZGREQEBQVTMZvrxgcmQRB8t/R7mbdH6Ei9TOHVuY6Ajv19hxWU7Kziyjmdadzf91LskyZdc9q/15fk0yB9HhFZGwnN3YWuohiNrQpFa8AZEoYtKoGqhk2pTGxDWbOOVDROQdVoMY6e4vOcjqcctGN7NgfHd0Xub0RpML6ciG5sLJImMJmmgpU61txrpnSru8hFwhAbF31QRmhTJSDjC4IgCIK3LGUW7ou9j9LSUsxms1ePrdMlm1wuFz/99BOVlZX06tXrpMesWLGCxx577JjvDRo0iN9+++2U49psNmw2W+2fy8oCV4JYEIQ6oPqWkRTglWaqqlKe7a6mF97UGNjBq4VlZ9Diz/eJ2bIU6RT3vgxlhwnNzyJ6+/La7zkNJkqSL6Jo0aUc7nQF0hPz/Z6L3EhPyFfN0Y1tgPXhbJTNFqwPZWOfVEDIR03QdPN/aWRsTwcDVxey7X+hbJ0QSu5sA7M7xZD6agXJ91qCsrRTEARBEIKlTgZXmzdvplevXlitVsLCwvj1119p167dSY/Ny8sjLi7umO/FxcWRl5d3yvEnTJjASy+9FNA5C4JQBwU4uLIWOnBZ3RmVsMYBDq4UhZa/v02TeV/UBlUlLbpQ1OFSKhLbYItsiMtgQnba0VaWYSw+iCkvk7D924jI2oCuqozYjL+IzfiL1j++StnEjhQ+FE/Bv9rhiA/za2raPmGErkrB8dlhrC8cREmvovLi7ehGx2J4NRE5xr+3Eo0eOjxbSZPrray538zhZXrWP2pm3zQj3T4pJ7KjaI4lCIIgnB/qZHDVpk0bNmzYQGlpKdOnT2fkyJEsXbr0lAGWt8aNG3dMtqusrIykpKSAjC0IQv1VmePOeBsb6NAYArehS7ZbaP/l4zTYuACAvG5XknXlw1jimnk2gKIQdnAH0Vv/IXbTIiL2rMO8bzPmJzbT9KlFFLW/lMMvxlI8NBk0vs1b0rpLt2uvj8I27gCOb4twfFmA87diDK83RjcyBkn2L5o1t3XRf0Exe74IYcO4MApX65nbI5p2T1fS7plKNOem8r0gCIIgeKxOBld6vZ7k5GQAunbtypo1a3j//feZOHHiCcfGx8eTn59/zPfy8/OJj48/5fgGgwGDQbxLC4LgHUu+HYDQQPa3UlXaTX6aBhsXoGh1bLtjAvk9rvZuDFmmonEKFY1TyB44Fl1ZAQ3XzyF+1R9EZG0gdvNiYq8HW5KZvLu7kD+mM85Y3/aXynE6QiY1RzemAdYH96FkWLHesw/HVwUYP2yCJs2/fauSDMl3W2g0zMa6f4eT84eRjNfC2P+zkW6flNGgT2D30AmCIAhCINW5aoEnoyjKMXukjtarVy8WLlx4zPfmz59/yj1agiAIvrIccgdXIXGB683UeNHXNFw/B0WjY8PDX3kfWJ2EwxxLTr/bWff0j6x8cTb7BozBHhqJYX8ZTccvoWuLD2nxwCyMOwt9Poe2Txihq9theLOxu6rgykoqe27D+uR+1HL/GxCbEhUu/qmU3t+VYGjoomy7loWXRbP2wXAcZaJsuyAIglA31bngaty4cfz111/s3buXzZs3M27cOJYsWcJtt90GwIgRIxg3blzt8f/+97+ZM2cOb7/9Ntu3b+fFF19k7dq1PPjgg+fqEgRBqCsCXAvVUuDOmhhjdAEZz5SXSfIv/wVg1w3PUNK6e0DGPVpVfEv2XP80y9/4m62j3qSsSXs0Vifxn6fTueOntLnpZ0LXHfRpbEknYXg0jrDN7dFeHwUusL9/iIqOGTimF+NvMVpJgiY32hi2uZAWo90l8Hd/ZmJWWgw5f4rVB4IgCELdU+eCq0OHDjFixAjatGnD5Zdfzpo1a5g7dy4DBgwAIDs7m9zc3Nrje/fuzdSpU/nss89IS0tj+vTp/Pbbb3To0OFcXYIgCOdadWIj0I0mbEWBDa5a/P4usstBQYe+5PS7PSBjnoqiM5DX81rWjvuF9Y9/x+HU/kgqxPy6nbReX5Fy5TTCVxzwaWw5UY9pWgtC/khGaqFHPejAcmsmlmt2o2SdfNWBN/RRKt0/LeeyuUWEtXRiydHw9/WR/HNrBNb8Ovc2JgiCIFzA6tyeqy+//PK0f79kyZITvnfjjTdy4403BmlGgiCcrwIdXFmL3cGVIdL/l87QA9tpmD4XVZLZc91Tga8bfyqSREmrbpS06kbowV003/00DX7IIGpeJlHzMim5ojnZL/Slokei10PrBkegTW+P7c087G/l4ZxTRkWnDAz/SUD/aByS3r9AKO4yB4PXF5LxShjb3zWxf7qR/IV6Or1ZTvOR1rP2FAqCIAjCqYhbfoIg1DtyzStbgIMre4m7JLg+0v/MVdLirwE41HkQlY1a+T2eLyobtWLLpb+w4sX5HOxzA4pWJnJBFqmXTCblmu8xbTh1S4tTkUJkjC82InRtOzR9w8CiYht/kMpu23D+U+H3nLUhkPZ6BQOWFxHVyYG9WGb13REsGRpJRZZ4SxMEQRDOLfFOJAhCvSMFaVmgvbw6uIrwL3OlVNiIWz0DgAP9R/g9L39ZGzRh+x2vs/LF+eSPSkPVSETN3kOn7l/S+rZfMe4q8npMTVsjpnmtMU5qhtRAi7LNStVlO7Dcsxe1yP++VdGdnQxYXkTahHI0RpX8hQZmd4pl+zsmFNEWSxAEQThHRHAlCEK9I1W/sgU6uHJUV8HThWn8Gqdq5jY0DitVDZpS2rJLIKYWENbYJDJ6/kT6pns5fFN7VAlif9pK59RPafHgbHR53mWeJElCf3sMYZvboxsdC4Djq0IqOmZg/67Q74IXshZSHq9i0NpCGlxqx2WR2PBMOAsuiaZkU51b9S4IgiBcAERwJQhCvVOTuVL8rwh+DEeFe0B9uH/BleXPDAAOdRl09vZaeaHk70fZ9c1wNq4ZS9HQZCSXSvxn6+mS8jFJL/+FXGH3ajwpWkvIp00xLW6D3M6IetiJ9c69VA3ZhbLb6vd8za1d9J9fTLeJpegiFIrW6ZjbM5pN40Nx+T+8IAiCIHhMBFeCINQ7cnXsE+jMlbPSHVxpQ30PrlRFwbJwJwCFHfsFYlpBYZ00kqK1T7H9t5vYsuB2yrs3QlPpIOnVv+nS7mMaTkoHl+LVmO7eWCkYXm4ERgnXonIqOm/F9kYuqt27sY4nSdDyTitDNxbS+BorqlNi65thzOkaw6FlganuKAiCIAhnIoIrQRDqnZplgQHPXFVVB1cm34Mrx+Y8lMIqnIZQypqnBWpqQWOdNJJDu59nzZ2L2THtOqwtItHnVZJ87yzSun1JxIJMr8aT9DKGZxII29AezQAz2FRszweu4EVII3fz4T4/lGBMcFG+S8ui/tGseUA0HxYEQRCCTwRXgiDUO8GqFuiyuLMrWqPvL53WlXsBCLukEarmPMqoSBI5pW+Qvulesv53BY4oI6FbDtF+6DTaXvuj10Uv5BYGTDOSCZncDKnhUQUvHtiHWuJ/RYqka20M3XCk+fCez03M6hRDzky932MLgiAIwqmI4EoQhHonWJkrp9UdXGn8CK5sq7MBMHRvyujRvwdkXmeT5dvR5P67B+nb7ufgQ91QtDLRM3fRKW0izZ5agKbE801OkiShuzWGsE1HFbz4vICK1AwcPxX5XfCitvnw/Ormwwc0/H1tFP/cIpoPC4IgCMEh3l0EQah3JNn9oVzxbxvPCRSb/8GVfeNBAAxdvG/SW1dYJ43EGR3C3rcHsnH9XRQNTUZ2KjR6bxVd2n/i9X6s2oIX81sjtzag5jmx3JaF5do9KPtsfs83rq+DwesKaftYJZJGZf/PRmalxZD1rTHg+/IEQRCEC5sIrgRBqHdqCloEMnOlKiqK0/1JXKP37aVTdbpwbD8EgK5jo4DN7VywThqJddJILG1j2f7bTWz982aq2sSgO1xF8r2zSO3zFWErD3g1prZvOKHr2qF/LgF0Es5ZpVR02ortg3xUl39RkNYEnd6oYGBN8+EimVWjI1gyTDQfFgRBEAJHvKMIglDv1Oy5UgOYuXIdVc1OY/DtpdO5txjsLiSjFm3TyADN7ORkp5Xw3NU02PkzjTZ9TqNNnxO37Tui9i0kpHhXwCJP66SRAJQMasnG9XeR9b8rcJoNhK3PI/XSKSSP/sOr/liSQcb4fCNC16ag6RMGlQq2Jw5QefF2XBuq/J5vVGcnA/4pIvWVcmSDSv4CA7M7x7LjA1PAl5EKgiAIFx7RZVEQhHonGJkrxXEkcyLrfKs659hTAIC2ZSySHPh7Wxp7BXHbpxG37VsiDi5HVk5dGMKlNVIRm0ppo96UNO5LcZPLcBkifDpvTYAFkPtvDQW3dKDJc4uJm7yRht9uJvr3Hex//lLy7r8IVedZpUVNSgimha1xfFWA9ZkclHVVVPbahv6ROAzjGyGZfH/+ZB20e7qKpOtsrL7PzOG/9KQ/Ec6+H4x0n1hKZAcRZQmCIAi+EZkrQRDqnWAUtAhEcOXMclfU0zaPDsicaqkq8RlT6PVFC9rOv5uoA38hK07spoaUNOrD4RZXcbjFVRQ16U9ldAourRGN00pE3mqarH+P1D+u5ZL/i6Hzj5fReP2H6CvzfJ6KddJIHA1D2fPZlWz6ZxTlFyWgLbfT/MkFpHX7EvPSfR6PJckS+jENCNvUHu31UeAC+9v5VHTJwLmwzOc51ghv5aL/vGIu+r8ydGaFojU65vWIYfPLobj83+olCIIgXIBE5koQhHqnJnPlUgLX10h1HgmuJI2PwdW+YgC0zQIXXEkuO23n301CxhQAqiJbcrDj3RxqcyNWczN3d93jKS5CSjMx560hImcZUdkLCS3eSdT+JUTtX0KrJY9QnNSf3A6jOJx8LYrO5NWcrJNGYhw9hYpuiWxedicNJ2+g6bOLMW09TIcB33L45vbsffNyHAnhHo0nJ+gwTWuBY0YJ1oezUTPtVA3Zhe62aAz/S0KO9f2tTJIh+S4LjYbaWPdQODkzjGS8Gsb+n4x0/7yM2J4On8cWBEEQLjwicyUIQr0TlGWB1cGVJLtLiPvClVMKgLaxb8vvjic5baT+djUJGVNQJA17Ln6dVaO2kd39KawRzU8eWAHIGixRrchPuZWdV3zMqtE7WD5mD7v6vk1pQk8kVSE6ewHtZ91On4mNaLXo35gKt3s1t9qlgrLEodGdSc+4j7x7uqBK0OD7DDp3nEjCB6vB6fnGON2VkYRtaI/+gQYggeO7IipTM7B/V+h32XZTosLFP5fS+7sSjHEuynZoWdA3ivWPh+GoEM2HBUEQBM+I4EoQhHpHU53ICGi1wOpqdb5mrQCcB93BlSYhMMFV8l9PErN3Lk5dKJuu/ZN9Pcb53JjYGtmC/Rc9xrpbV7B8zB4ye72IxdwMna2UpPQP6Dk5hbTpg4jOmoOn9ctrKgrWlG7P/HAIm1aMprxbI7RlNpo/MZ+0Hl8SvsLzqoKSWYPx3SaY/m6L3N6IWuDEeudeqq7cjZLl31o+SYImN9oYuqmQ5iMsoErs/DCU2Z1iODhHNB8WBEEQzkwEV4Ig1DtyEPZcqYr/wZUrrxwAjYfL4U4ndvfvJKV/CEDGsO8paj7E7zFrWCNbsLf3C6wYu4cN18/hcMurUZGI2TePTr8MofuUDsRnTEFyeb9krrJLApv/HsXuT4biiA4hdPMhOvadQst7ZqAt8LwaoLZ7KKGrUjC81AgMEq75ZVR03ort3fxjlnD6Qh+l0uOLMvrOLCa0uZOqbA1/XR3FilFmbAUiiyUIgiCcmgiuBEGod2r3XJ26WJ7Xasq6S368aioFlQBoGoT5NRfZUUXrhQ8AsO+iJyhseaVf452SJFPUbBCbh//OijG7ye76KE59OGGFW2k3ZxS9vmxJ4/UfIjvOHBQdncVCljg0pjPpW+4lf1QaAHFfbaRzx09p+NUGUDwLjiS9jGFcAqHr2qG5NAyqFGxPB65se8IAO0PWF9LmkUqQVPZNDWFWaiz7vhfNhwVBEISTE8GVIAj1TlCWBdZkrmTfMheq04VSbAH8D64SN36CsSIHi7kpWb1f9mssT1kjW7C73zv8c/d+dl/yJrbQeIzl+2m9+GF3kLXuPWSHxbOxqvdjOWNN7PnsSjYvGUFlh4boCi0k3zOTDv2/xrTlkMdz07Q2YprXGuOnTSFSg7LeXbbd+p8DqBb/mp1pQ6HzfysY8HcREe0d2ApkVoyI4O9rI6nMFm+hgiAIwrHEO4MgCPVOMApa+Ju5UkqstXuV5OgQn+chuRwkrXsPgL09x6PofB/LFy5DBNndn2LF2Cx2XP4xFnNTDJV5tF7yKL2+bOHOZDmtZxzn6N5Y5b2T2LRqNHvfvBxXqA7z8gOkdv+SpuMWIVfaPZqXJEvoR8e6y7ZfF+ku2/5WPhVdtuJc7H/Z9pjuTgauKqLD8xXIOpWDswzM7hTD7s9CAtqsWhAEQTi/ieBKEIR6R6N1BzGn6aHrvZplYD5WClSK3cvUpHADktazRronE7vnd4wVB7CHNCA/5Tafx/GXojWS0+k+Vo7eyfYBnx0JshY/TM9JrUnY/CXSGf4Bjg6wVJ2Gg4/2JH3TvRRe0wbZqZD49go6p00kasZOj+clx+swfd+SkJ9bIjXWoe6xUTVoF5a796IW+/cDodFDh+cqGbSmkNhedpwVMmsfNLPoiijKtvv+byoIgiDUHyK4EgSh3qndcxXAzFXtJhsf6xkope5sjhzpX6YpPuNrAA52HIuiNfo1ViCoGj0HU+9yB1lXfIo1LBFj+X5S5o2l++QONNj582mrCx6zFwuwJ5nZ8dMNbPv1X1ibRmDILiPlup9oc+N09Ac8z0DprnKXbdfd2wAAx+RCKlIzcPxU5HfZ9oh2LvovKqbLO2VoTCqHl+mZc1EMGRNCUURbLEEQhAuaCK4EQah3avdcBTJz5SelrDq4Cjf4PIbGXk7MvrkA5zRrdTKqRs/BtHtYOXoXu/q+hd0YQ2jxDjr+eQNdp/Um4sDfZxzj6ExW8bBWbNhwNzmP90LVSMT8voPOqROJ/2gNuDxbhyeZNYR80ATT4jbIbYyo+U4st2VhuW4PygHPlhueiqyB1g9aGLKhgITBNhS7xOYXwpjXK5qidb43NRYEQRDObyK4EgSh3glGQQt/KeXuHkyy2fdsU+T+JcguO1WRLamMbR+gmQWWogth/0WPs2JsJlk9x+PUhRKRu5KuP1xKx9+GYyracdrHH53FUkL17JvQn42rxlDWMxFNhZ0Wj80jtc9XhK7P9XhO2j5hhK5NQf9sAugknDNLqUjLwD7xcG2hEl+FNVO49PcSek4uRR+tULJJx/w+0Wx4JgynZ/U9BEEQhHpEBFeCINQ7tQUtFKnOlMxWK9zBlRTqezPa6H3zAShqOiggcwoml8FMVp+XWTlmNzmp96BIGhrs+Z3uUzrQauFD6KoKTvv4o7NYValxbFkykj0fD8EZaSRsfR6pvb+i2ePzkMs9axwsGWSMLzQidHUKmh6hUK5gfSibqv47cG3zLwqSJGh2q5WhmwpocpMFVZHY/k4oc7rEkL/Yt6bOgiAIwvlJBFeCINQ7mqNWZQUse+VjIYsaqsW9GUcy+R5cRVYvrStO6ufXXM4me2g8OwZ8yuqRmylocSWy4iRpw0f0nJRM0tq3kVynXp53fG+s/LFdSN98D4dvao+kqDT6cA2dO31G1J+eF7zQtA/BtKQNxneTIFTGtbySym7bsL2ei2r3r+yfsaFK72/KuOTXYkISXVTs0bJ4UDSr7wvHXiqaDwuCIFwIRHAlCEK9Ix9VuM0Z6AIDPmbClOqS4rLJt0yGxl5BWMEmAEob9fZtEudQVUwKm679k/QbF1LeIA2drZRWS5+gx5QOxOz587RFL+BIJssRF8aub4azdcbNWJtHYthfRsr1P9HmX9PR53hW8ELSSOgfaEjYxvZoh5jBrmJ78SCVPbbhXFXh97UmDrMzdGMhyfe4K0RmfmlidloMB37zfb+dIAiCcH4QwZUgCPVOcDJX1b/6uM5Qtbqra/iauQo7vBFJVbCFNcIenujTGHVBcZP+rLl9HdsGfonNFIepeBdpv11Np58HYSrcetrHHr1UsGRgSzak382BJ6oLXvy2g06pE4n/ZK3HBS/kJnpCfksmZEpzpFgtSoaVqkt3YH1sP2qFfz84OrPKRR+W039BEWHJTiwHNSz7VyT/3ByBNV+89QqCINRX4hVeEIR6Rz4quHIFOHPl6x6u2mWBBt/6IYUd3ghAeYNOvk2gLpE15HYczcrRO9nX7WkUjZ7offPpPiWVVosfQWstOeVDjw6wFJOO7NfdBS/KuzdCW26nxb/n0rHvFEybD3k0FUmS0N0STeim9uhujwYV7B8doqLzVpzzSv29Uhpe6mDwukLaPV2BpFXZ/4uRWakxZE4x1pn9gIIgCELgiOBKEIR6JxiZK6nm1dLX4MpWnbky+rYsMLQgA4DK2A6+TaAOchnM7Ln0DVaN2srh5OHIqouk9e+7mxBv+gLUk2egjq4oCO6CF5uXjiTzvYE4w/WErz5Iao8vafLcYmSLZ9G1HKslZFJzTDOSkZrqUffZqbpyN5ZRWSgF/tX014ZA6iuVDPyniKhODuzFMqvvimDJ0EgqssTbsCAIQn0iXtUFQah3ZBkkyR0FuQLU60qqLmjhc7bB4Y7yJJ1vmStTsbtoQ1V0Wx8nUHdZIluy+Zpf2XD9XCqj26K3HCZl/l1cNLUn4bmrT/m4owMsNDJ593djw6Z7KLymDbJTofF/l5PW5XMiFmV5PBftwAjC0tuhf7ghSOCYWkRlagaOaf43H47q7GTA8iLSJpSjMarkLzQwu1Ms29811am2AYIgCILvRHAlCEK9FPBeV7WZKx/3XNmrozy9b8FVSGkmAFWRyT49/nxQ1Gwgq0dsYle/d3DqzZjz1tBtag/azh17ytLtx1QUBOyJZnb8dAPbf7oBW2I4IXuKaT94Kslj/kRbWOXRPKQwDca3kjD93Ra5vRG1wIllZBaWa/eg7Pez+bAWUh6vYvC6QhpcasdlkdjwdDgL+0ZRmuHbz4YgCIJQd4jgShCEeqlm31WgqgXWVGJXfQzWVLsfmSvFhaFsHwDWiOa+TcAPqlKJ6ipGdZWgnmKpXsDOpdGxv+ujrBy9g9x2dwDQaMuX9PyqNY02fnraaPnoTFbRNW3YsPEecu+/CFWCht9sonPHicRO3eJxgKztHkroqhQMLzYCvYRzVnXz4f875Hfz4fBWLvrPL6bbJ2XozAqFq/XM7R7D5hdDcXnWuksQBEGog0RwJQhCvVSTuQrYskC5elmgrx+qne6gxJfgSl+Zh6y6UCQNttAE387vIVVVUSoX48x9GMeerti3mXFsC8OxPRrH9igcW/XYdyTiyOqH8+ADuEqmoNo9X3bnKXtoPNuGfM26m5e5S7dbi2m74D4umtrD46WCLrOBrPcGsXnpSKraNUBXUEXrUb+TctX3GLJKPJqHpJcx/CeB0DUpaHqFQoWC9dH9VF0WmObDLcdYGLKxkMQrrSgOiYzXw5jbPYaCVaL5sCAIwvlIBFeCINRLtcGVIzDNWyVNdXDl8nFZYHVwhdb7l11DRQ4A9tCEY5t4BZhS9gfOPWk49/ZHKfoQ1boelPLjjnKB8yBq1VKU4o9x5YzCsasF9p0tceY+hFIxD1UNXInG0sQ+rL19LTsv+8C9VDB/HRdN7Umb+fegtRSd9DHHF7yo6NmYjavHsO+lvigGDVHzMunU+TMavbuyNug9E01KCKbFbTB+kARhMq4V1c2HXz3od/NhU6LCxT+X0mdaCYaGLsq2aVlwaRTrHwvHUSGaDwuCIJxPRHAlCEK9FOg9VzXVAn2uaVDzIV7jQ3BVmQuALayRjyc/PdVVhnP/zTj3X4Nq2wySCTlyLJrGP6BL3oqubRm6dnZ0KRZ0rXPQNl+FJvEb5JjHkEJ6AVpwZKIUfYRz3yAcO+Jw5oxBqfzL7yIQAKqs5UCXh1gxeie57UYgoZK46TN6ftWGhC1fnbaqYO0Yeg054y5mw7q7KO3bFE2Vg2ZPLyT14q8ITc/zaB6SLKG/tyFhG9qjHRrhbj78cq67+fDqSr+uUZIg6XobQzcW0ux2C6gSOz8yMbtzDLnzfOuNJgiCIJx9IrgSBKFe0gR6z5Vcs+kKnwIGtbqxbU0GzBv6SveHf7spzuvHnonqKse5bzBK2Q+ABjn2aXRtDqBN/BxNxL+QDClImnAkSYckG5F0jZBN3dFE3o42/m10LZaja1uEtskfyFF3gTYOXMUoJZNw7u2LY3drXAX/RXUe9nuujtA4tg2ZwvqbllIR0x69pYCUuaPp8kNfQg9vPuljji94YW0dQ8a829j92TCckUbC1ueR2nsSTZ9ZiFzlYdn2JnpCfm1JyDfNkRpUNx++ZDvWJ/ajVvoXzRtiVHpOKqPfrGJCm7mo2qdh6ZVRrBhlxlYosliCIAh1nQiuBEGol2oKWigBqr9wdFDkU00Hl++ZK53FXSnPYWrgw4lPTVVsOLOvQrWsAE0U2ub/oI17A0kT5dU4kiYcOfwqtI0+c2e2mi1BjhwNchjYd+PKfxrHzsY4D9yGYlnj97xLGl/KmjvS2X3pf3HqQonMWUa3bzrTcumTyI5TZ5BqM1mSxKFRnUjfdA8FN6QguVQS31lJp86fEbHQs/1jkiShuyma0I3t0d1a3Xz4g+rmwwvK/L7G+CvsDF5fSOuHKkFS2Tc1hFlpMWT/ZBDNhwVBEOowEVwJglAvHdlzFZjxpKNeLX3ad1VTCEP2PvtQG1yFxHp/3tNwHX4FtWopyGa0Tecim3r4PaYkaZBD+6JN/BJd61w0jb5ACukOqh2ldCrOzO44svqilP/pV+VBVaMju9uTrBq1jUPJ1yKrLpqufYueX7Ujdvfvp3zc0UsFHfFh7Jx6Hdt+uRFb43CMWSW0H+Jd2XY5VkvI5OaY/kxGaqJH3WunauguLKOzUAr9q6aiC1Pp8nYFV/xVjDnFie2QhuW3RfL3dZFU5Yi3b0EQhLpIvDoLglAvaTTuYCZge66OyVz5sCyw+jGSL8GV1V24wWGM9vqxp6JYNqAUvAGANnEScki3gI1dQ9KEoYkag67FKrQt1iJH3AFoUav+wpl9NY49HXCVfIOq+h6E2MxJbLnmFzZeOwOLuRnG8mxSfx9Ox1+vxlCWfdLHHNN8GCi+sjXpx5dtT51I7PcZnpdtHxRB2IZ26B+qbj78bRGVaRk4fvK/+XBsDweDVhfS/rkKZJ3KwZkGZqfFsPuLEN+yqIIgCELQiOBKEIR6KeB7ro4OrnwJ2Go+X0veB1daWwkATkOkDyc+OVf+k4ALyXw9svn6gI17KnJIV7SNv0bXei9y7NMgR4BtG66cETh2tcFV/IVfVQYLWwxj1agM9nYfhyJraZD5Jz0mtyNp7dtIyonB2/EVBZXw48q2H66i9YjfSBn+A/rsUo/mIIVpML5d3Xw4xYh6yInltiws1+1BOeBf82GNATo+X8mgNYXEdLfjKJNZe7+ZRQOiKNspmg8LgiDUFSK4EgShXtJUtwkKXJ+rI7/3aVlgTfbCh5oEWrt7D0+ggiulaiVq5QKQdGjj3grImJ6SdIlo495A1zobTcMJoIkFRyaug3fh2NUaV/EknzNZis5E5iWvs3rERkoSL0brqKTV0ie46NuumHNXnfQxx2exasq2Z7/YF0WvIWr2HjqnTST+/9Yc2Td3BtruoYSuTkH/XALoJJwzS6nolIH988N+Nx+OaOfi8qXFdP5fORqTyuG/9cy9KIZtb5k4SQwpCIIgnGUiuBIEoV7S1gRXAe5zBb73unIP5P18NLaa4Mrs+3mPohR/CoAccRuSvllAxvSWpDGjafAMutZ70cS97a4y6NiL6+AYHLvb4Sqd5vOerKqYdqy/aSnbBn6BwxhN+OFNdJ3ai9YLHkBjOzELdXxFQVWv4cB/Lmbj2rGU9UlCU+mgxaPz6Nh3CqYthzy7PoOM8flGhK5OQdMjFMoUrA9kUzVgJ66dVp+uq4asgTb/rmLIhgLirrDhskps/E8483tHU5yu9WtsQRAEwT8iuBIEoV6SA93n6qjgSvEruPL+IRpHBQAuXZjv562muspQSn8CQI662+/x/CXJoWhiH0PXKtMdZGliwb4L14Fbce7phFI+07c9S5JMbscxrLxze21vrMYbP6bnV21psOOnU+6lOjqTZWkby5aFd7Dn/4bgNBsIX32Q1B5fkvTiUiSrZ2kiTfsQTEvaYHi7MZhkXH9XUNl1K7Y3c1Ed/mWxwpop9JtZQvcvStFHKRRv0DGvdzQbnw3DafFraEEQBMFHdS64mjBhAt26dSM8PJyGDRsyfPhwduzYcdrHTJ48GUmSjvkyGo1nacaCINRFge9zdeT3fmWufKCtDa5C/R5LqZgJahXoWyOF9PR7vECRZNORIKvhqyBHoNo248y+Eufey1CqTr6s70wcpgZsGzKF9BsXUhnVGkNlHh1n/IvU367CWLr3pI85ZqmgLJF/Vxc2bLybwqtaIzsUkl5fRlq3Lwj/Z79n16aRMDwUR9iGdmgGmMGmYht/kMpe23Ct97/5cIsRVoZuKiTpOiuqS2Lb/0KZ2zWGQ8t0fo0tCOezjKwMxk0cR0ZWxnkzj7oyZ8E/dS64Wrp0KQ888AArV65k/vz5OBwOBg4cSGXl6d+AzGYzubm5tV/79u07SzMWBKEu0gQ6cyVJtdkrnwpa+EF2uMuCKwEIrtSyX91jmq9H8mGJYrBJmnA0DZ5F1yoTOeZJkAyoVUtxZvXEsf9GVPsen8YtbtKf1SM2kdXzeRSNntjMmfSY3P60BS+OZk80s2P6DeyYeh32uFBMOwrpeNnXtHhoNpoym0dzkJsZMM1IxjipGVK0BmWThco+27GOO4Bq8a/snzFOoc/3pVz8UwkhjVyU79ayqH80ax8Ox1FW9/6dBSGYVFVl+pLp5BbmMn3JdL8rdp6NedSVOQv+q3PB1Zw5cxg1ahTt27cnLS2NyZMnk52dzbp16077OEmSiI+Pr/2Ki4s7SzMWBKEuCnSfKwCpuijb2c5caZzu4MqlDfFrHFVVUCoXACCHX+33vIJJ0kajjf8vula7kCPvBGTUsuk4dqfgzH0U1Vnk9Ziq1kBWn5dYfcdGihv3ReOsqi540Y3wvBObGx+/FwtJovCGFNI33UP+nWkAxE9cT6e0iUT9udOz65Ik9LfHELqpPdobo8AF9rfzqey6FefScq+v6XiNr7ExZEMhLUa7f2Z2f2piVloMOTP1fo8tCOeLLVlbyMp1NwTPys1iS9aWOj+PujJnwX91Lrg6Xmmpe/NxdPTp+7tUVFTQtGlTkpKSuOaaa8jIOHVK1WazUVZWdsyXIAj1ixzgZYEAcnXmSnH6EVx5Wy1OVZBd7jLeir/BlW0LuIpBDkUK6erXWGeLpEtCmzgJbcsNSGGDQXWgFL2HY3cyrsL3fSrfXhXTlvR/LWbbwC9xGKMIP7yBi77rQavFj6CxnznAcUWFsGfilWyZdxuWllEYcspJuf4nWt/6C7r8Co/mIDfUYfquBSG/tERK1KHstlE1YCeW+/ahlvhX9k8fqdL903Ium1tEWEsnlhwNf18bxfI7zFgPiyyWUL+pqsovS3+pzcxLksQvS38565kgb+ZRV+YsBEadDq4UReGRRx6hT58+dOjQ4ZTHtWnThkmTJvH777/z7bffoigKvXv35sCBAyc9fsKECURERNR+JSUlBesSBEE4RzRa95uSK4BL+CRtzbJAXwosVH+o9fKhsvNIZTlF699eUrVqpXsqIT2RpPNrP45s7Iiu6Wy0TeciGTqCqxhX3iM4dndAKZ/h/YcQSSK342hW3rmdvJTbkFBJWv8+PSa3J3b3HyccfkIWCyjr14yN6+8i5/FeqBqJ2Onb6JQ6kQZfb/S4+bDuykjCNrZHd3csAI4vC6hI24rj9xLvruck4i5zMHh9IW0fq0SSVbJ/CGFWaix7pxo9nZ4gnHdqMkA1rwmqqp6TTJA386grcxYCo04HVw888ABbtmzh+++/P+1xvXr1YsSIEXTq1Im+ffvyyy+/0KBBAyZOnHjS48eNG0dpaWnt1/79nm1KFgTh/KENwrJAWetH5qomYeDlp1rZdWQ/j6IxeH/eo6gW99I3KaS7X+OcS3LYQLQt09EkTARNA7DvxJl9Fc7sIai2bV6P5zA1ZOvQb9lw/VwsEc0xlu8n9fdr6PDHDegrck/6mGOaD4fo2DehP5uWj6aiczy6Yiutxs6g3ZCpGDKLPZqDZNYQ8lFTTAtbI7cyoOY6sNy4h6qb96Dk+fcDrA2BTm9UMOCfIiI7OrAXyqwcFcFf10RSua9OfwQQBK8dnwGqcbYzQd7Mo67MWQicOvvK+uCDDzJjxgwWL15M48aNvXqsTqejc+fO7N69+6R/bzAYMJvNx3wJglC/BLqJMHBUQQt/MlfePVaqXhIIoMr+ZZtU20YAZGNnv8Y51yRJgyb6bvd+rJgnQdKjVszFsTvVvR/LVeL1mEXNBrJq5Bb2dXsaRdLQcNfP9JicQqONE+Ek/baOL3hR2TmeTf/cyd4J/XEZtUQu2kunzp/R6J2V4PSw+fAl4YSua4f+qXjQgPOXEirSMrB/XeD3B6zork4Griyi40sVyHqV3DkGZneOYdcnISe7PEE4Lx2fAapxtjNB3syjrsxZCJw6F1ypqsqDDz7Ir7/+yqJFi2jevLnXY7hcLjZv3kxCQkIQZigIwvngSEGLwO0x8SdzJcnVgZm3ywJr9lvJWp8aENdQVQXV6t6LKhk7+jxOXSJpItxFL1pmIIVfDTjd+7F2tcZV/KXXTYgVnYk9l77B2tvXURbfDZ2tlLYL7qXLD30xFZ6YFTs+wEIrc/DxXmxcfxel/ZqisThp9sxCUi/+CtPGfM+uyShjfDWR0BUpyJ1NUOzCOnYfVcN2oWR5VpXwVGQdtB9XyeC1hcT2seOskFn3bzMLL4+idJvGr7EF4VyrzQCdopmgxNnJBHkzj7oyZyGw6lxw9cADD/Dtt98ydepUwsPDycvLIy8vD4vlSEfEESNGMG7cuNo/v/zyy8ybN4/MzEzWr1/P7bffzr59+xg7duy5uARBEOqAQJdih6P2XHlblAJA9jFzpbpTb6rsZ7U3xwF3fyu0oE/2b6w6RjIko2vyO9qmc8GQAq7DuA6OxZnVE6V6n5k3KhqmsfaWFey87D2culAic5bR/es0mi9/Ecl5bIBzsr1Y1uRoMubexu6Jw3BGGglbn0dqr0k0Gb/Y8+bDnUyE/tMWw2uJYJRwLSinolMGtvfz/a5WaW7r4vKFxXR5rwxtqELBP3rmdosh4/VQlAAuoxWEs8npclJYVoh6io2tKipFZUU4A7mcwc951JU5C4GlPdcTON4nn3wCQL9+/Y75/ldffcWoUaMAyM7ORpaPxIXFxcXcdddd5OXlERUVRdeuXVm+fDnt2rU7W9MWBKGOqVkWGMhqgZI/1QJrgisvPxjX9GBSZf9erlX7Lvdv9C2RpDr30h8QcthAdC03ohR+iOvwi6iWNTizeiFHjkYT9waStoEXg2k40OXfHE6+ljYL7yc2cybNV7xEwx0/sH3A55Q2vvj0j5ckDt3ZieLBLWnxyDxift1O4zeXE/PLdvZ8OoyyS5qccQqSVsLwZDza4ZFY79+Ha2kFticP4PixiJCJzdB08L16pCRD6/stJA6zsfZhM7mzDWx+MYz9Pxvo/lkZ0V3Fhznh/KLT6njhzhcorzp1xU+zyYxOG9xiPt7Ooy7MWQisOvcO60nqc8mSJcf8+d133+Xdd98N0owEQTgf1S4LDOBnxJplgao/wZW3mavq4Erxd7+VPdM9nr6lX+PUdZKkQxP7GHLErbgOPYNSMgWlZBJK2S9oGr6KHH2PV8GlzdyETcP/pOHOn2i16GFCi7bT9YdLyEm9hz2XvIHTGFl77NHZK+PoKQA4EsLZ8cP1RP+2nRYPzyFkVxEdLv+GvLu7sO+1y3BFnLkCpKaVEdO81ji+LMD6zAGUNVVU9tiG/ql4DM/EIxl8X4QS2lTh0t9K2DfNyPrHwynZrGN+n2ha/7uKji9UoDX5PLQgnHUx5hhizDHnehpezaOuzFkInDq3LFAQBCEQgtJEuDpAUhx+7LnyMXOF7N+eGNWx1z2erqlf45wvJF082sTJaJv/g2TsBEoJrrwHcWZ2R6la5eVgEofa/ItVd27jYIcxACRumkiPye2I3fXrSR9y/H6souFtSd90L3ljOgEQ/9l6OnX6zLvmw2MbELaxPdqrIsChYn8tl8pu23Cu8Ky31qnHhma3Whm6qYCmN1tQFYkd74Yyu0sMeYtE8+HzTUZWBuMmjiMj69T9Ps9XM1fMZMwbY5i5Yua5noognJIIrgRBqJc0uuo+V4HMXOn8qBZYk7lSvCuyIKnuTWOq5GfBAWeOezzdhdXXTzb1RttiLZqEj0GORLWm48zqiTNnLKqzwKuxnMYotg/6gvX/WkxVVCsMlbmk/nEdHX6/Dn15zgnHHx9guSKNZH4yzN18ONnH5sOJekKmtyRkagukhlqU7Vaq+u3A+th+1Ar/NhgaG6j0+rqMS34tJqSxi8pMLUsGR7H63nDspaL58PlAVVWmL5lObmEu05dMr1eFEBRF4fdlv+NSXPy+7HcUL19LBeFsEcGVIAj1UjCXBZ7NPVc1dbJVyb+Xa9Vx0P0bXSO/xjkfuUu334eu1Q7kSHfAo5R8iWN3G5+qCpYk9WP1iE3s7fEfFFlLw92/0nNyOxpt/PSEsu0nVBSkuvnwurs48IRvzYclSUJ3QxRhm9qjGxEDKtg/OkRF560455Z6dS0nkzjMztANhSTfWwVA5iQTs1Jj2P+rf33WhOCrKesN1Lsy3jNXzMTucFdPtTvsInsl1FkiuBIEoV4KRnDlV5+r2syVt9UClZqTe3/Oo7kOuYfRxvs3znlM0jasXiq4DMmQCq6i6qqCF6NYNng1lqI1knnxa6y5fT2l8d3R2stou+C+6rLt24859mQVBZUQHdmv92fT8jup6BR3pPnwsGkYsko8u55oLSFfNMM0sxVSUz3qPjtVV+3GcmcWSqF/P/g6s8pFH5TTf2ER4clOrLka/rkpkmU3RWDJEx8d6qLjm9HWpya0iqLw5/I/j/nen8v/FNkroU4Sr5CCINRLNcGVMxh9rnzZc6Vxv9yqLi8/DNRmrvy7DtXpDq7QeFExr56STX3QtlyHJu4dkMNQLStwZl6EM+8xVNepq3adTGWDjqy7ZTk7L3v/SNn2b9JotuKVYxpA1zix+XACm5aPZu/r1c2HF2TRqfNnJLy/Cjz8WdEOMBOW3g79ww1BAsd3RVSmZuD4ocjvD9YNL3EweH0h7Z6pQNKoHPjVyOy0GDKnGL3u2SYE1/HNaOtTE9qjs1Y1RPZKqKtEcCUIQr0U1D5XvmSuqoMrrzNXtf1P/GkgrILLvb9I0sT6PE59IklaNLGPokvejmy+EXChFL6LY3cKSqmXe1VkDQe6PMyqUVspaD4U2WWnxfLn6fZNF8wHV5xw+PFZLLQyB5/oxcZ1d1F6aRM0VQ6aP7mAjpdOwbTlkGfXE6bB+FYSpr/aIKcYUQ87sdyRheW6PSg5JwZ53tAYIfXlSgYuLyKqswN7sczquyJYMjSSiizxMaIuOD5rVaM+ZK9OlrWqIbJXQl0kXhUFQaiXavpcBbJaoD97rmqWFHqajahV86HIn8yVUglq9ROhifZ9nHpI0iWiTfoRbZPZoGsBzhycB27EmX0Vqj3Lq7Fs5iZsunYGGUO/wx7SgLDCDLpO60OrRQ+jsZ+YETs+i2VtFU3GvNvZ8/EQnGYD4WsOktrjS5JeXIpk82yZn7ZHGKGrUzCMTwCdhHNmKRVpGdg/O+xb8+ujRHV2MuCfItImlKMxquQvNDC7cyw73jcF9CaG4L3js1Y16kP26mRZqxoieyXURSK4EgShXqrpuVhnClrULgv09QOuP8FVSfVvtCCH+j5OPSaHD0aXvAW5wXiQdKgVM3Hsbo/r8ARUxYvMjySRn3IrK+/cRm77UUioJKV/SI/J7YnJPPFD4An7sWSJ/LFd2LDxbgqvao3sUEh6fRlp3b4kfMUBz6ZgkDGMb0ToqhQ03UOhTMH6YDZVA3bi2mX1/FpOQtZCyuNVDF5XSMO+dlxVEulPhrOwbxSlGX7uCxR8Upu1OsVrhMT5m706XdaqhsheCXWNCK4EQaiXgtLnyo89V0eqBZ79DwGqq8T9G03ECcuGhCMkOQRtw5fRtdyEFHoZqBZch/6DM7MrStVyr8ZyhsSwbfBXpF8/D0tEc4zl+0n79UrazbwVXdXJl/odncmyJ5rZMf0Gdky7DntcKKbtBXToN4Xmj8xFLrd5NAdNhxBMS9tgeCcJTDKuvyuo7LIV23/zUH35GT5KeCsXl80rptsnZejMCoWr9cztHsPmF0NxeTY9IUCcLieFZYWonPzfVEWlqKwIZyDvNJ0lVrsVh+P0L+IOhwOr3b+bBoIQSJ63qRcEQTiP1PS5cgZyWWBNnysflldJWn8zV35Qqpekyeazf+7zkGRoi7bpQpTSb3HlPYZq24Izqw9y5Fg0cW8iaT1fWlncbACrRm6mxT8vkLT+XeK3TyNm71x29XuXvHZ3nLDc0zppJMbRU6onIlF4fQqllzWj6dMLiJuyiYSP1xL95072/N8QSgYnn/laNBKGBxuiGxaB5YF9uBaUY3suB8f0IkImNkPT2eTVc3PM2BK0HGMhYZCNdQ+HkzPDSMbrYez/1UiPz0uJ6X7+fZg/H+m0Ol648wXKq05djMVsMqOrSeefR0xGE8+OfJZDxafeexgfHY/J6PvPsSAEmgiuBEGol4KRuZI1fmSuagtanIPlK9XBlSSHn/1zn6ckSUITeQdy2FBc+U+jlHyJUvIFSvkfaOLfRY64xeMsoKILZXe/t8hvezNt540l/PBG2s0ZSfy2b9k+YCLWiObHHF+TwaoJspzRIez5/CoKbu5Ay/tnYcwqod3VP3D4lg5kvT0AZ+yZP1jKzQ2YZrbC8W0R1if2o2ywUNl7G/pH4zCMb4QU4vtCFlNjhYt/LmX/z1bWPRJO2TYt8y+JpvUDFjq+XIEu7Pxbjna+iTHHEGOOOdfTCIrkxGSSE898I0EQ6gqxLFAQhHopGNUCZX+qBcrVL7c+Lwv04wOqUlE9hzDfx7hASdoYtIlfoG32N5KhHbgO4cq5Dee+gai23V6NVR5/EWtvW8Oei1/HpTEQvW8+PSZ3IGntOyf9QT2+4EXp5c3ZsP4uDj7SA1WWaDBtC51TJxI7bYvHzYf1d8QQtqk92uujwAX2t/Kp7LoV51/elaA/cWxocoONoRsLaXa7BVSJnR+ZmN05htz5er/GFryTkZXBuInjyMjKOC+ODZZgzSGY11YXnrf67Gw9vyK4EgShXqrtc+UM3B4jf/Zc1S4LdPoYXPmxGV1Vqty/EcUsfCaHXoy2RTqahq+CZEStXIBjT0evC16oGh37eoxj9YhNFCf1Q+OsotXSx7loWi9CD2864fjjC14ooXr2/vcKNv89ksoODdEVVNF65O+0vfZH9PvLPLuWOB2maS0I+bklUiMdym4bVVfsxPLAPtRS/+5GGGJUek4qo++MYkxNXVTt07B0WBQrR5uxFYn9fsGmqirTl0wntzCX6UtO31KgLhwbLMGaQzCvrS48b/XZ2Xx+RXAlCEK9VLssMKDVAt0vmYpPfa58LGhRu/TMn8xVTXBV9/YlVGn2c8A0jS2RT7I29jZWNLiSlQ2uYW3M7WyJfJKssIkUGv7BKVWe66kiyXo0DZ5Fl7wFKfQKUK3VBS+6eF3wwhLdmvQbF7FtwOc4DBGY89bQ7duutFj2LLLz5Jvzj85kVXRLZNPK0WS/2BdFryF61m46dZpI/KdrPe6lprsqkrAN7dCNdfc+c3xeQEWnDBwzSry6lpNJGGhnSHohrR+sAkll77chzE6LYf/PBtF8OIhqSrIDZyzBXheODZZgzSGY11YXnrf67Gw+vyK4EgShXtIGoc/VuchcqZL7cZI/n0hVi3sMyej7GAGkonDA9AN/x/VjXuMmrG1wK7sj3uJA6FTyTTPJM/3BgbDv2B3xFhtj7uXv+IuZmRTB4viubIl8kkPG+bg4dyXpJH1LtE3noUn8BjSxqLYMnFkX4zx4/5HKjB4NJJGbOpZVo7ZyqNV1yIqTZqtep9vXaUQc+PukDzk6wFL1Gg7852I2rhlLWa/GaMvttHh4Lh36f03I9gLPphCpJeTjppjmt0ZONqDmOLBct4eqWzNRDvn3n0cXptLlnXKuWFqMua0Ta76Gf26JZNn1EVTliI8fgXZ8I+HTNRCuC8cGS7DmEMxrqwvPW312tp9f8eomCEK9VNNEOKDVAmv2XPnR5wqvs14ByFyp1YGIHOL7GAFSrt3OX/G9WdvgZgqNS0GVibR1o3nZg7QveovOBV/SqfAz2hf/j5ZljxBnGYLR2QhVclFqWM/uiLdYHjeQ2UmxrIm9idyQP1Dwog9VgLgLXtyOLnk7cuSdgIpS/AmO3Skopd4tObGHNWLL1T+z+eqfsYXGE1q8k64/XErrBfehsZWecPzxe7EsKbFsWTyCzHcH4grTY15+gLSLviBxwjIkh2fL/LR9wwld2w79Y3Egg3N6MZVpGdi/K/T7A0hsTweD1hTS/j8VyDqVnBlGZneKYc+kEJHFCqDjGwmfroFwXTg2WII1h2BeW1143uqzs/38iuBKEIR6KSjVAnU1mSvv901JNU2End7taanJXKH6UWVQqV5mJp3bwgKFhmUsTehJsWEVWiWMNiXPMzBnL/3yVpNW/CGtyh+naeVomlXcRauyJ+hY/C69Ds1icE4OAw9k07XgW5pUjMLgjMcpV5AT+iOrGl7DnMaJbIp6hFLdiXuWgs1d8GIS2maLQN8anHk4D9yIc/9wVMd+r8Y63Oo6Vo3axsGOYwFovPFTd/PhPSc2UT2m8TCALJH3QDfSN9xN8eCWyHYXTV9YSmrPSYSuO+jZtZhkjG80JnR5W+TUENRCF9Y791J19W6Uff5lCjUG6PhiJQNXFRJ9kQNHqcyae80sHhhF+S7RfNhfx9+Zr3GyO/R14dhgCdYcgnltdeF5q8/OxfMrgitBEOqlmj5Xgd1z5Ue1QK2PmauaZYF+ZK5UtTqzIxl8HsNfhw1LWN5wIE65lGhrHy4/uJ2U0pcwuZI8erzJlURS5W10KfyKwTk59M1dRcuyRzG44rBrCsg0v8/iRmksje/B/tDvzno2Sw69DF3LjcgNngdJh1r+B47d7XAVvo+qeh5QO42RbB/4Oev/tZiqyJYYK3JI++1q2v/5L3SV+Sccf3wWy94kgm2/38TOydfgiAkhdPMhUvtMpunTC5CrPLvToOkSSuiKFAwvNwKDhGtuGRWdtmL/v0N+92mL7ODiir+K6PTfcjQmlUNL9czpGsO2t00ooi2Wz46/M1/jZHfo68KxwRKsOQTz2urC81afnYvnVwRXgiDUS8HIXAVkz5WHy7Rq1Gau/KkpXxtcnZsmojb5EGsb3IxLthBXNZTeh+YR4kr0eTwJmSh7dzoWv8OgAwfomT+TRpXXI6k6ig2rWRd7O/MSm7HD/Bo22bO9R4EgyUa0DV9C2yIdKaQ3KBW48h7BmdUbxepdVq0kqR+rR2xmX7enUCQNcTt/oufkFOK3TD6hcuTxFQWRJApu7UD6pns4fFN7JEUl8d1VdOryGebFez27Fp2E4ZkEQte2Q9MnDCoVrI/up+qyHbi2Wry6luPJWmj7SBVD0guIu9yGyyqxcVw48/tEU7xRtN/0Vu2deU5ejVHiyB36unBssARrDsG8trrwvNVn5+r5FcGVIAj1UjD7XPlULfAcZq5QqyPMc7AsUEUlPeYubJp8wu3t6V4wHa0auKqFMlrirUPpXjCdwQcOkFLyCkZnAlZtLtuinmNeYhM2RT1MlSY7YOc845yM7dE2/xtNwicgm1Etq3Hu6YIzfxyq4nlgouhC2HPpm6y9bQ3lDTujsxbTbu6ddJo+EGNJ5kkfc3Qmy9kglF3fDGfbb//C1jgcY2YJHQZ9R8t7ZqApOXlFwuNp2hgxLWyN8cMmEC7jWllJZfdt2F7PRbX71xA7rLlCv1kldP+8FF2kQnG6jnm9otn0fCguz6YnAE6Xk8KyQtRTvEaoqBSVFeF0OevEscESrDkE89rqwvNWn52r51dSRThMWVkZERERFBRMxWyue6WKBUHw3tblEs/005OQrDBxa2DSV6ue3U36//bR8aEk+rzd2qvHln++gsIHfsF0dXsaTh9V+/1Jk6457eNMhVvpObk9dmMMyx7wLQvjzH0Ipegj5Njn0Ma94tMYvsozzmJl3DAkVUe/3HVEODoG/ZwKdnJCf2R3+DuUGtIBkFQtSZUjaF06jjBnctDnUEN15ODMfRi1/Bf3N/TJaBMmIof192ocyeUgad27NF/xAhqnFZfWRObFr7K/88Mgn7hnyTh6yjF/1pTZaPLcYhI+XQeAPT6UzPcHU3RtW4/noOy3Y30oG+csd5ENub2RkM+bobnI//5pljyZdQ+Hc+A3d0XL8FZOun9eRoPeAUw912OFZYWUV526EbTZZCbaHF1njg2WYM0hmNdWF563+szX59dSZuG+2PsoLS3FbDZ7dU6RfxcEoV46Uoo9cI1Lawta+FEt0Ps9K4HIXLnvyknS2X3JV1HZHvkiAC3LHj4rgRWAjJ6kyttpXHkbh40L2RnxGgXGJWSHTSI7dDJJlbfTtvR5Qp0tgz4XSZeIrsnPKGW/4cx9EOy7ce67HDlyFJq4t5G0nn1oUjU6srs/xeFW19J2/t1E7V9CqyWPEbd9GtsGfkFlg9RjjrdOGnlMgOUyG8j6YDAF/2pH8j0zCdlVRNubfqbw2rZkvj8IR3zYGecgJ+kJ+bUlzu+LsT6+HyXDSuXF29H/Ow7D8wlIob4XpgiJV+jzQykHfrOy7pFwyndpWXhZFK3us5D6SgW68Av+PvBpxZhjiDHHnDfHBkuw5hDMa6sLz1t9di6eX7EsUBCEeikYTYQlf0qx1y4L9K3PFV4URThxkOonQTq7VdmK9asoMaxBVg20KnvqrJ4b3OvpG1qv4OL8xVyS9w9xVUNBUtgf9jULGrUhPfouKjV7z8pcZPNwdMlbkaMfACSUksk4dqfgKpnq1Xp/S1Qr0m9cyPYBnx3TfLj5P+ORnMdW9DuhoiBQfnETNqy7iwNP90bVSMT8up3OqRNpOHnDCXu5TkaSJHS3RBO6qT3am6NBAfu7+VR02YpzYZnH13HysSHpWhtDNxTSfKQFVIldH5uYlRbDwVnnttKlUDdkZGUwbuI4MrIyzotxBd+c7/8eIrgSBKFeCo1Q6dhPoV1v//aFHE2uDpD8KsXuZUGLmiVfkl+bx2oizLObucoK/wSAxMqbMSgNz+q5jxdj602vwzPpm7uaOMsQVMnFvvAvWJDYmk1RD2OTDwV9DpLGjDbhI7TNl4EhBVyHcOXchjN7KKp9nxcDyRxMvYtVo7ZyOHk4suKk+cpX6f5NJyJy/jnh8OMDLNWoJfuVy9i4cgwVXeLRllhJvnsm7YZMxZBZ7NEU5Fgtpq+bE/J7MlKSDjXLTtWQXVju3ota7N8dDX2USo/Py+g3u5jQFk4sBzT8NTyKFSPMWA8HLhMtnF9UVWX6kunkFuYyfYl3veTOxbiCb+rDv4dfwZXT6SQjI4N//vmHv/7666RfgiAI50J8C3htnoMnvwtc6qp2WaAvcY62OmvkdeaqOrjyK3NVfc6zmLlySlUcNP0MQLOKu8/aec8kyt6NXodmcUnePzSwXI4qOcg0f8j8xJZsi3gRh+Rf9sUTsqk3uhYb0DR8BSQDasUcHHvae1223R7WiM1X/8Lmq35yNx8u2k6X7y+h9cIH0diOvY4TKgoCVWlxbFp2J3sn9Mdl1BK5aC+dOn9GwnurPP451Q2JIGxDe3T3NQDAMbmQirQMHL96FqSdTvzldoasL6TNI5VIssq+70OYnRbL3mlG0Xz4AlRTUhsIaAntYI0r+KY+/Hv4FFypqsr48eOJjY0lNTWVSy+9lMsuu+ykX4IgCPXFkVLsPmSuakqxO31bFuhXcEXNOc/eYoXDxvm45EpCnE2JtvU6a+f1VIytN30OLaBP/kIibRfhlCvYEfkS8xOTyQz7GIXgFlKQZD2aBs+ha7kRyXQxKJW+lW2XJA63voFVo7ZysMNoJFQab/g/d/PhzJknfcgxmSytzMHHe7Fx/V2U9muKxuKk+VML6HjJZEybPcvmSeEaQt5vgmlxG+TWBtQ8J5abMqn61x6UXP+eR60JOv+3giuWFRHRwYGtQGblyAj+Gh5JZbZYfHOhOL4RbKAawAZrXME39eXfw6c1Iq+88gqvvfYakZGRjBgxgsaNG6PVitoYgiDUbxrdudhzVZ1t8mtZ4NkPrg4Z5wMQX3XlKXuM1AUNrP3pm7eKg6Zf2Bb5LBW6nWyKeYBM8we0K36DBMs1QZ2/ZGiDttlSlOLPceU/VV22vSty7FNoGoxHko0ejeM0RrF90Jfkt72VtvPvJqQ0k7RfrySv7S3suuw9HKZjl2UeX/DCmhxNxtzbaPjVBpo9vZDwtbmk9viSnKd6c2BcH1TDmd/jtX3CCF3bDttrudjfzsP5WwkVS8ox/q8xuhExtR+YfBFzkZOBK4vY9r9Qtk4IJXe2gdmdYuj0RgUtx1pqOhYI9dTR2Qw4tgFsxxa+F8oJ1riCb+rLv4dPEdGkSZNo2rQpa9euJSZGVDgRBOHCEJgmwl5mvar3XMl+Za6q5+vHh1tvHQ5ZCEAD6+Vn7Zy+kpBJrLqBhKpr2Bv2OdsjX6BCt4PVDa8lxnopHYveI9LROXjnl2Q00fcgh1+FM/ch1PJfUApeRymbjrbR58ihl3o8VnHTy1k1cjMt/nmepPXvEr99GtF757HrsvfIT7ntmJ+B4wMsJIlDoztTPDiZFg/PIeaPnSS9voyYX7azZ+Iwyns1PvO1GGWMrySiuyEKyz37UNZXYb1rH47viwj5v6bILQxePTdH0+ihw7OVJF1nZc19ZgqW61n7oJl9Pxjp9nEZ5jYBbGon1BlHZzOOzmDUZDU6NO/gU+AerHEF39Snfw+fgqu8vDzuu+++Cz6wcjplnE5xu0wQtFoFrTZwhSPqqtomwucicwXuvVO+3KKvfaM6O29MdrmICt12AGJsl5yVcwaCjI4WFfeTVHk7uyLeZHf4OxQa/2JJQleaVI4ipeRVQlyNgnZ+Sdeoumz7rzhzHwD7Tpx7+yJH3YUm7k0kTZRH4yg6E7v7vUV+25toO28s4Yc30X72HcRv+44dAz7Fam5ae+zRSwRrAi1Ho3B2/HQDMT9vp/kjczFtL6BDvynk3XcR+17phxJ+5gBJk2YidFlb7O/lY3v5IK6F5VR0zsDwUiL6hxoiaXz/WYxIcdF/YTG7Pg5h0/hwDv+tZ07XGDqMr6DtY1XIOp+HFuqg47MZNfzNagRrXME39enfw6fgqnnz5pSVBX/Tb11VXm6gqCgcu93A2fqwIgh1m4pebyM6upzwcNuZDz9PSX4EV0cyV97dXT86uJIUF6rGnxs6Z+f1qli/GoBQRzIGJfasnDOQdKqZdiWv0az8HrZGjeNA6FSyw74ix/QjrUv/Q3LZY2jwbLmeL2TztehCL8OV/zRK8WcoxZ+jlP+JNuFjZPO1Ho9THt+Ntbetpcma/9J85cvE7J1D98nt2XPJG+R0uv/0gbokUXhDCqX9m9H06QXETdlEwsdriZ6xkz3/N5SSQWfuESZpJQxPxKMbHonl/mxcS8qxPXUAx09FhHzaDE3HEI+v5XiyBto8ZCHxKhvrHjKTO9fApvHhZP9kpPtnZUR3CWAPBuGcqc1mIKGepNefhG9ZjWCNK/imvv17+BRc3Xfffbz22mscOnSIhg3PbXnds6283EBeXixhYRE0aBCKVqs9myttBKHOUVV35dDS0kry8gxAQZ0LsFT1SPJGPWqFnOxlnFJbit2nzFV1kORtQQv5yMu0pLpQqfu35Uv16YC7Mt/5zORqwkUF39Gi7CG2RD1GkXEF26KeZV/Yl3Qo/h8JlmuDth9L0kSibTQRJeJ2nAfvAvsOnPuvQwq/Fm3CR0g6zzJoqkbHvp7PcrjV9bSdfxeROctos+gh4rdNZdugL6iKaVd77MmyWM7oEPZ8fhUFN7Wn5f2zMO4tpd1V33Poto7sfesKnDGmM85BTjZimtsKx6QCrM/koKyporLHVvRPJ2B4Jh7J4PsNg7BmCpf+UcLeb42kPxlOySYd8/tE0+aRKjo8X4HW9/hNqAOcLieFZYUn/cAN7kblRWVFOF1OdFrPXxuDNa7gm/r27yGpHpTgyM7OPubPqqryxBNPkJ6ezvPPP0+XLl0wm80nfWyTJk0CM9MgKisrIyIigoKCqZjNp3+j2LcvFr2+IYmJsedF9CwIZ4uqquTkFOBw5NOkSeG5ng6KAhl/S/z9o4asTRLFeRI2C+j0EB6t0qiVSo+rFDpdoRDp4T2i3T/ms+D2LSRcGsk1C7p6NR/r8izy+n2MNjmWxlufrv3+pEnXnPZxsqOSfh+EAbD0oXJc+jCvzgvg3H8LStn3aOLfRxPzsNeP99aa2JvJCf2BdsVv0Lrs6TM/4DygonIgdCoZkU9h1R4EoIHlClKLPiDcmRLccytWXIdfQSn4L+AE2Ywm7n/IUWORvFkmqiokbvyUln89jdZRgaLRs7fHc+zr/jSq5sQmvcfsxwLkSjtNXlxKwodrkBQVRwMTme8MpPBf7Tzez6cctGN9eD/OP0rcY7Y1YpzYFG0v73+uj2c9JLH+UTPZP7mzimHJTrp9XEZcv+BWfhSCq7CskPKq8lP+vdlkJtocXWfGFXxT1/49LGUW7ou9j9LS0lPGOKfiUXAly/JJAwlVVU8bYEiShNNZ91PzngZXTqdMVlYCiYmNCA8/8906QbjQlJVVcfDgQZo3zz2ne7Acdnj7Di0rfpMxhkKT9iqxjVUMJnA5ofSwRM5OicIDkNxV5ZkfHMSeea8+mb8eYt5Nm4nvHcHwJRd5NSfb6mxyL/4QbfNoGu8YV/v9MwVXktPGZe+7PywufbAElyHCq/PC2Q+uFiWkUqbfTM9DM4i3DAv6+c4mp1TBzog32G1+C0WyIalaWpQ/RNuSF9Cp3v/beEOxbsJ1cCyqZQ0Akqkv2kafIRlaezWOoWw/bRbeT2zmDAAqYjuwfeAXlCX0OOHY4wMsgLDVOSTfPRPT1sMAFA1NJvOjIdgbe/YBRFVVnD+XYH0kG/WQEyTQP9AQw8uNkML878WW86eBtQ+FYznoHqvlXVWkvV6BPuL8KucsCMK5409w5dGywBEjRogsDVQXr5BE2XlBOAWdTgtIuFzyOQ2upr2sYfVMmTFvuRh2vwvNKT6vrZkp8/5dWiY9peXxb5ynPK5GbRNhH6oF4uOeq5pqgQCS4u/NquB/uFRRqNDtBCDc0Tbo5zvbtGoY7UpepWnFaDZHPUae6Xf2mN/lQOhU2hf/l6TK25GCVPJeNqYiNV+BUvgBrkPPoVYtxbEnFU2DF5FjH0eSPFsuYzMnsWn4HzTc8QOtFz1EWMEWuk7rzf4u/yazzysoutDaY0+oKAhUdE9k4+oxJL75D43f+IfoWbsxp01k34T+5I/tAvLpPy9IkoTuhii0/cOxPnUAx9eF2D86hOPPEkI+aoJ2kH9BauJVNhpcamfjf8LY87mJPZ+bODjTQNf3y2l8Td1aslxfZWRl8O28b7l94O20b96+zh/rjWCNW99dSM+bR1HC5MmTgzyN84uIMwXh5Gr+b5zrfn9//aBh6L0urn7IddL51OzB6jZM4ZbxTr5+TovTDpoz7M+oqRaounwoaFFTiMLLxx5T0MKvcuxnh1WTV53R0RDibHrmB5ynQp0t6Hn4N/KNc9kc/W8qdDtYHzuSvWETSS36KGil2yVJgyb2UWTzcJwH70WtnIfr0DiU0mloEr9ADvFwn5skcajtzRQ3uYJWSx4hftt3NFn3Lg12/8b2AZ9R3PSK2kNPthdL1Ws4MP5SCq9LIfnemYSvyqHlg3OI/WErez4ZirX1masJS9FaQr5ohu6maCwP7EPda6fqqt3obovG8FYScozvNzL1ESrd/q+cJv9yl22v2K1l2Y2RJN1gpet7ZRgbiixWsKiqyvQl08ktzGX6kum0a9bulDfo68Kxwbo24YgL7Xnz6fZadnb2GasFlpeXn7BXSxAE4WyoLIXohCN/lqRjv2SZ2iyVPgRcDs969PrT58rnzJUkoVbvq5F8bSRc+yYW/A+UFs0+AIyuRGTfaiadV+Ksg7js4EbaFb+BRgmlyLicJQkXsSnqYexSSdDOK+mbo206B03iFNBEo9o24czsiTPvCVSlyuNxHKZYtg79lg3XzcIankRIaRadpw+g7ZzRaK3FJxx/dKAFYGnfgM1LRpD19gBcJh0Rf2fTqevnJP53OZKHP+vaAWbC1rdD/3BDkMDxXRGVaRk4fizCg50LpxXX18HgdYWkPFWJpFHZP93IrNRYsr4xnvObQPXV0SW1a0po1+VjvRGsceu7C+158ym4at68Oe+9995pj/nggw9o3ry5L8MLgiD4pU0PlUXfyBQePPUxdisU5sAfH2ho20tF40Ec4E+fq5pS7N5WC4QjFQN9XxZ49lKKFu0BAEKcSUE/V12hwUDrsqe54uAOEitvAkkh0/whCxJbsy908ikrYPlLkiQ0kSPQJW9HjrgVUFAK38axuwNKxXyvxipqPoRVozLY3+lBVCQaZXxFj69SaLBz+gk/N9ZJI48NsjQyuQ91Z8OGuyke0ALZ5qLpc4vp2OcrQtPzPLuWMA3Gt5IwLW2DnGJEPeTEcnsWluv3oOTYvbqW42lDIO3VCgb8U0RkqgN7kcyqMREsvTKSyn2iV2UgHd0IFo40gD1ZkFwXjg3WtQlHXIjPm0+vKp48IfX5SRMEoW67/SUnpQUS/75Iz+ePa/j7R5nNSyW2r5TYuEhi8bcyU/6j4ZEeeopyJW593oneg7ZFsq66FLvDh/1kvmauOLI0UFL9DK4I/j44q8Yd0Ya4EoN+rromxJVIt4Lv6Z0/nzBHW+yaw6TH3smyuH6U6TKCdl5J2wBt4+/QNpkBuiRwZOHcNxBnzp2oziKPx3Hpw9l1+Yesv/lvKqPbYqjKp+OfN9Lhj+vRV5x4p+L4LJatWSTbZtzMri+vwhEdQtiGfFJ7T6LJfxYhWzyr2KftGUbo6hQM4xNAJ+GcUUpFWgb2zw+jKv59roju4mTgiiLSXitHNqjkzTcwKy2WHR+GeJS5Fs6sJkNR8xnw6AawdfHYYF2bcMSF+LwF7ZbNgQMHCA8PD9bwwnlk8uSpaDRRTJ489VxPhf79r0SjiQrqOfbuzUajieLOO+/3a5y69Lydb5K7qLw2z0G7PgrzJ2l4Z5SW5wbqeLqvjueH6PjoPi1LpmpI6anw+nwH7fp49qGttqCFL5krXfU6RJc/mStfPwHWvNQH/6aXVePOVBhc8UE/V13V0HoF/Q9upH3xm2gUE4XGv1ic0InNUY/jlCqCdl45fBi6lluRox8CJJSSyTh2p+Aq/dGrG56liX1YfccGsnqOR5G1NNz9Kz0mt6PRps9PmcWqDbQkicN3pLJh490UXJ+C5FJp/NYK0rp+gflvz7YKSAYZw/hGhK5KQdM9FMoUrA9kUzVoJ8puq8fXcTKyDlKerGLw2kIaXGLHVSWR/riZRf2jKN3mf6XCC9nxGYoaJ8tU1IVjg3VtwhEX6vPm8YL4l19++Zg/L1my5KTHuVwu9u/fz/fff0/Pnj39mpxQ9+zdm03LlmkMHHg5s2dPPydzmDdvEUOGXM+AAf2ZM+fn0x57++13MW3adL755jNuvfXGszRDoS5o0k7lPz85sVXB3i0SRQcl7FYwhEBkvErzju7S7N6QA7Lnyp/gysd+PbW9kIKfubJpDgFgcF1YDeaPJ6OnVdlTJFbexOboR8g1/cYe8zscNP1Ix6IPSbBcE5QGxJImDG3CBygRN+M8OBZs23AduAkl/Du0CR8j6TzLKKpaA1l9XuZQ6xtImTcWc94a2s6/m7jt09g+4DMsUcknPOboyoKOuDB2TruOw3/soMXDcwjZXUSHy78h767O7Hu9P66IM6eKNR1CMC1tg/3jQ9jGH8S1tIKKLlsxjG+E/tG42j2QvjC3cdF/fjF7vghhw7gwClbomXtRDO2eqSTl6UpO0vZLOIOj99Uc7ehMRccWHevMscG6NuGIC/V58zi4evHFF2t/L0kSS5YsOWWABdCoUSPefPNNf+Ym1BPXXjuMnj0vIiEhLiDjXXFFP5o0aczChUvYv/8ASUknb1BUWlrKb7/NJDIyguuuuwqAyZM/oarKEpB5nEpiYgIZGauIiPCuL8LxAv28XUhU1V2gQtaAwQRtuqucLGujKO7iFp6SNH5UC9QeyVydqUfg8VSpOrjyuVpg9UWehbuEdrkAAIPSIOjnOh+YXE3pcfhX8o2z2Rj9AFW6LFY3vJa4qqGkFn9EqDM4e5NlU290LdJxFbyOUjABtfwPHJWL0cS9iRx1j8fNhysbpLL2lhUkpX9Ai2XPEbV/Md2/7khm71c40PWR2sC/xvGl24uvbsOGvk1pOm4R8V+kE/95OlGzdpP50RCKh7U64/kljYThoTh0V0ZieWAfrgXl2J7NwfFzMSGfNkXTyfeek5IMyXdbSBhiY91DZg7OMrDllTD2/2qg+2dlxFxU9/t01hW1GQqkk+4xlHBnKjo07wBwzo/16vXXi2urzxXwvHUhP28ef6xYvHgxixcvZtGiRaiqyqhRo2q/d/TXX3/9xZYtW8jOzqZbNw9LwgonWJC5hA6f9GRB5pJzPRW/RURE0LZtayIiAtNgU5ZlRo26DUVRmDJl2imPmzp1OhaLhVtvvRGj0X2XtEmTJNq29a7hprd0Oh1t27YmIcG/ZVGBft4uJG/doeXBNB271p7+BdubwAoC0+cK8Lqohf8FLWrOHfyNJXa5EACdcuZS3BeSOOsQ+uduoXXpOCRVR75pFosS2rPT/AYK/hVsOBVJNqBt+BLaFuuRQnqCUo4r936cey9Dte3wfCBZw/6uj7Jq5GaKmlyOxmml1V9P0nVqL8IObTzh8OMLXrgijGR+PJQt82/HkhyFIaeclGt/pPVtv6I7VOnZFJobMM1shfGLZhClQVlfRWWvbVifzUG1+peRDU1SuOTXEnp/W4IhVqF0i44FF0eT/mQYTs+md8FzupwUlhWesniLikpRWRFOl7NOHBusaxOOuJCfN0n1YcHjSy+9xGWXXcall14ajDmddWVlZURERFBQMBWz+dR3waxWLfv3x9OsWRJGY/DWDKiqSs8vL2dtbjoXJXRm5ZiFdSaqP9mywDvvvJ+vv57Grl3p/PbbDCZN+pY9e7K4+ebr+eqrj5k8eSpjxjzAl1/+H6NG3Vo71vr1G5kw4R3WrFlHfv5hzOZwmjVrwjXXDOU//3nitPPYty+bli070bx5U3buXH/S56dHj/6sXZvO2rVL6dw5FXDvuVq69B9criMlho+eX0xMFP/973ts2rSVmJgoMjM31V73M8+8yIIFi7HbHXTtmsZLL/2HxYv/5uWX32Thwj/p1+/iY56jESNu4auvPq49T825rdZDvP7620yZMpXc3HyaNk3i3/++l/vuG3vM/E/1vAFkZu7lzTffY8GCxRw8mEdEhJl27dowYsSttcfa7XY++2wyM2bMZdu27Rw6VEBEhJk+fXry3HNP1j4ngWS12tm7dz9JSXkYjefuBfOhzjqyt0q8NMtBp8sDl60p2VnF9x1WoI/QMvpwX68eq5RZyY4dD0CTsteRje6Gr5MmXXPGx/aemISx4gBrbl9LeVxXr+ftPHg3SvHnaBq+gqbBc14/3hsLE9pTrt9Kn/yFNLD2D+q5zlfl2u1sjLmPAuMSAMLt7Ugr+pRY2yVBO6equlCK/g9X/jhQq0AyoGkwHjn2KY+bD1cPRMKWr0he+jg6WwmKrCW721Ps7TkeRXviUr/jGxDLFgdJL/9No/dWIrlUHNEh7H1rAIdv6+BxE0klz4H1kWycv5S4x2xlwPhpU7SX+L/P23pYIv2JcPZNcze9C23upNvH5cRfHpwAuD4pLCukvKr8lH9vNpmJNkfXmWO9Eaxx67vz+XmzlFm4L/Y+SktLMZu9W4nkUxOSF154wZeHCR6al7mItbnpAKzNTWde5iIGtbz8HM/qzB5++ClWrVrL0KEDufLKQTRseOplQRs2bObiiweh0Wi4+uohNG2aRElJKdu27eDzz6ecMbhq2rQJl1/ejwULFrNkyTIuu+zYDyVbtmxl7dp0OndO9TiImD79N+bPX8ywYYO4777RlJW5XxBycg5y8cWDyM3NY9Cgy+ncOZUdO3YzaNB1J5zXE7feOpY1a9YxePAVaDQafvrpNx588Em0Wh133TXyjI9ftmwFV111E+XlFQwc2J+bbrqO4uISNmzYzIcfflobXBUVFfPoo+O45JJeDBkygKioSDIz9/Hnn7OZM2cBS5bMpFu3Ll7P/3zwYbqPe5PO4Ejmyoc75bqjNss7XGD0/ANtbebK5et11SwLDH7myiGXAKBTIoN+rvNVuLMtffIXsT/0W7ZEPU65fivL4i+lScVo2he/iUGJDfg5JUmDJuZh5PCrcObeh1oxF9eh51DKfkLT6EvkEA+Ddkkit+NoCpsPofWih2i462earXqdBjt/ZvvAzyltfOxr4vENiJUQHfsm9KfgxhSS755B6KZDtBr9B7E/bCHzo6HYmp45Uy/H6zB93xLH7yVYH85G2WWj6vKd6O5pgPG1RCSz74UpjA1Uek0po+ktVtY+YKYyS8uSIVE0H2Gh8//K0UfVzw34gRBjjiHG7FnGui4c641gjVvfXajPm0fB1V9//eXzCbzNbk2YMIFffvmF7du3ExISQu/evXnzzTdp06bNaR/3008/MX78ePbu3UurVq148803GTp0qM/zPldUVeX5xa+hkTS4VBcaScPzi19jYIv+dSZ7dSqbN2ewbt1SmjQ5c3+bb7/9AZvNxi+/fMc11xz771RY6Fnp4NGjb2fBgsV89dW3JwQ5X331Xe0xnpo7dyGzZ//MFVf0O+b748a9RG5uHq+++hzjxj1e+/1Jk77lrrse8nj8Gjk5B9m0aXntnZCHH76X1NTevPvu/50xuLLZbNx661gqKiqZMeNHBg++4pi/P3Agp/b3UVGR7N27mcTERscck5Gxjd69B/Lss68wb96vXs//QhaQPleA6uuyQD/3XAWr39LRHHIpADpFLGc9HQmJJpV3EG8ZRkbkM+wL/5zssEnkhfxOh+K3SaocEZyCF/rmaJvMRimdiivv36jWjTgzuyPHPIqm4ctIsmd7mOxhCWy5ejqxu36lzcL7CS3eQdcfLuVA2n3sueQNXIYT7/QevR+rsksCm1aMptHbK0l67W+i5mbSqdNE9r16GXn3dgXNmdfs6q6JRNs3DOszOTgmFeCYeBjnzBKMHzVFN9S/n79Gg+0MSS9k0/Nh7PokhKyvQ8idp6fr++UkXWvza+waGVkZfDvvW24feDvtm7ev88cKF4a68DNRF+bgD492HPTr14/LLrvMpy9vLV26lAceeICVK1cyf/58HA4HAwcOpLLy1Aufly9fzi233MKYMWNIT09n+PDhDB8+nC1bzr8a+jVZK1f1hyiX6qrNXtV1TzzxsEeB1dFCQk5cRhIT41mKePjwYcTERPPLL39SVlZW+32Hw8F33/2I0Wjklls8rxB49dVDTwisbDYb06f/TsOGDXjssQeP+bs777yNNm3OvCH7eK+99vwxKeY2bVrRp08PduzYRXn5qdPnAL//PoucnIPcdtu/TgisABo3PlIJzGAwnBBYAbRvn0K/fhfz99/LcTiCk+E5nzhs4PIwZpECUC3QfVJf91z5Wi2w+k5+kDNXKi5csvu1WquIVhye0CvRdC76jEvylmG2d8SuKWR97Cj+aXgF5Vov9kV5wd18+DZ0yVuRI26htvnwnlSUCu/eawpaXcuqUVs52NG9rLnxxk/oMbk9MZkzT3r80ZksVach55k+bFh7F2V9ktBUOmjx6Dw6XPY1IVsPe3YtkVpCPm2KaV5rpJYG1AMOLMN3U3V7Jsph/17fdGaVru+Vc/miYsJbO7Hmafjnpkj+viECS65/nWxUVWX6kunkFuYyfcn005akrgvHCheGuvAzURfm4C+PXh2ef/75E74GDhyIqqokJyczcuRInnrqKUaOHEmrVq1QVZWBAwfy/PPPez2hOXPmMGrUKNq3b09aWhqTJ08mOzubdevWnfIx77//PoMHD+bJJ58kJSWFV155hS5duvDRRx95ff5z6eis1dFqsld1/QfMmyVmN944HFmWuf76Oxgz5kGmTZtOTs6JTSp/+20mL730xjFfS5YsA9zBw223/QuLxcK0aUdKsv/55xwOHy5g+PBhREVFejyn7t1PnP+OHbuw2Wx07doJg8FwzN9JkkSvXt09Hr9G165pJ3yvJggqKSk97WPXrFkPwIABnt242LBhM7fdNpZmzTpgNDZEo4lCo4lixow52O12CgoKvZz9+eHwfijKPXNxPJcLZn2qYdXvMg4PtlTULAtExeuGppIk1d6NV53eBTmq7F5C6H+fq+AGV06pqvb3WlUEV96IsfWhX+462he/iawYKQhZxOJGqWyLeAEXgcmUHE/SNkTbeKq7+bC2Mdj34Nx3Oc6cMaiuEo/HcRqj2D7wc9JvXIglogXGigOk/Xol7Wbeiq7qxCDp+ObD1jYxbFl4B5kfDMIVpse8Moe07l/S+LW/keye/cxq+4UTtq4d+sfiQAbnj8VUpm3FMbXQ7/fOBn0cDF5bSLtnKpC0Kjl/GJmVFkPmZKPPBTiPLlF9poaqdeFY4cJQF34m6sIc/OVRcPXiiy/ywgsv1H7179+fxYsX89lnn7F9+3YmTZrEhAkTmDRpEtu2bePTTz9lyZIlXH65//uESkvdHzajo0+dzVixYgVXXHHsXfxBgwaxYsWKkx5vs9koKys75qsuOD5rVeN8yV7FxXne16ZHj4tYtOhPLrmkF9OmTef22++iSZP29Ox5OYsX/1173O+/z+Tll9885mvp0mW1f1+z7G/y5O9qv/fVV99W/90dXs2/YcMT51+z7+pU+8fi4rwvN32yjZFarTsz4TpDg9nSUvfP6skyUsdbvnwVvXsP4NdfZ5CW1pEHH7yb8eOf4vnnnyYtzV221marn5u0X77G3Si48vSxKhoNLPxa5ofXNZQVnHlcWXfkJdOv7FU9zVy55OoGuaqErJ65j5FwLBkdrcqe4vLcDOIsQ1AkOzsiX2Zxo04UGHxfnn/G84YPQ5ecgRzlbnyulEzCsTsFpexnrwKT4ib9WTVyM9ldH0eVZOK3T6PH5HbEbfvulM2Hj0xCIu/ei0jfeA/FQ1oi2100eekvUnt8SdiaHDwhmWSMbzQmdHlb5I4hqAVOLKP2YrlmN0q2f691GiOkvlzJoJVFRHVx4CiRWX13BIsHR1K+x7s9Xsc3Vj1dQ9W6cKxwYagLPxN1YQ6B4FNee/z48QwbNoyxY8eetOvy3XffzZAhQxg/frxfk1MUhUceeYQ+ffrQoUOHUx6Xl5dHXNyxvYDi4uLIy8s76fETJkwgIiKi9ispybulbMFQk7WST7HGXkaq89krb/eEXXJJb2bNmk5hYRYLF/7Jo48+wObNW7nqqpvIzNwLwFdffYzLVXzM1wsvPFM7RseO7enWrQurV68jI2Mbubl5zJ27kObNm9K/v3f7/U42f7PZfff90KGTL1HJz/ds6UqgREa6A7OTZfmO9/rrb2Oz2Zg371d+/30ab731Ki++OI4XXnjmhP8v9Y2uOslYU7nc5Tzy5XSAww7W6pXG7fqoFB6UKCs488+vfFTTUn/2XalnCKKP5/+eq5oPf8FtIuyqzlxp1dCg7Be6UIQ6W9Dz0Ey6Hf4RgyuOCt12lsX3ZX3MGOyyZ3tSvSVpzGgb/R/aZn+Dvg0483DuvwHn/utQHbkej6PoTOzu9xZrb11FRWxH9JYC2s+6ndRfr8RQtv+E44/PYtmTzGz77SZ2fj0cR6yJ0IzDdLxkCs2eWoBc6VmApOkSSuiKthhebAR6CeecMio6ZWD/5JDXGefjRaY6GbCsiLQJ5WhCVA4tNjCnawzb3zXhaaeEmjvzNe/nRzdUrYvHCheGuvAzURfmEAg+BVfr1q0jJSXltMekpKSwdu1anyZV44EHHmDLli18//33fo1zvHHjxlFaWlr7tX//iS/4Z5vdZWd/2QGUU2w4V1DZX5aD3VX/Mg0hISH063cxb731KuPGPYbFYmH+/MUeP/7OO93Zq0mTvuWbb77H5XIxatRtASkA0qZNKwwGA+vXb8RmO3ZpjqqqrFy5xu9zeKNbN3dFL0+en8zMvURHR3Hxxb2O+X5VVRXp6Sf2pqlPdAbIzpD57T0N37+qYepLGr59QcPXz2mY8qyGyeM0TB6n5fPHNGRtkigvhHIPPrPWLgvEt4qBUk3FQIeXywIlP6sF1i41DnLmSnI36JbVkKCe50IgIZFYdSOXH9xGs/J7AMgOm8TCRinsN00NWnESOfRidC03IMc+B2hRy3/DsbsdruIvvbq5Vx5/EWtuX8eePq+iaPTEZs2ix+R2JKb/H6jH/t+pyWLVBlqSRMHN7UnfdA+Hb+mApKg0em8Vnbp8TsSiLI/OL+llDP9JIHRtOzS9Q6FCwfrv/VT134Fru9Xj6zgZWQspj1cxeH0hDfvZcVVJbHg6nAWXRlOy+fR1wo6/M18735Pcoa8LxwoXhrrwM1EX5hAoPgVXer2e9PT00x6Tnp6OXu97L6gHH3yQGTNmsHjxYho3bnzaY+Pj48nPzz/me/n5+cTHn7yJq8FgwGw2H/N1rhm0BlaNWcSasUtO+bV67CIMWsOZBzsPrFixGqv1xDe4/PxDALVNfz1xyy3XYzKZ+O67H/nqq++QZZmRI28JyDwNBgPXX381+fmHeP/9T475u6+//p7t23cG5DyeuvrqITRu3IjvvvuRuXMXnvD3R2e0mjRJori4hIyMbbXfc7lcPPnkeA4f9mAN3HnMYILD2fDHhxqm/1fDHx9qmPWJhjmfa1jwlYYl32lYNl3mrx81FOdJmCJA70E84G/mitrMlXePDVjmKtjLAiX3/2mNCK4CRq9E0anoUy7JW0a4vR02zSHWNbiN5Q0HUan1LNDwliQb0ca9grblOiRjV1BKcB0ci3Pf5ai23R6Po2p07Ov5LKvv2EBJo95oHRW0WfQgXb6/FFPh9pM+5uhMljPWxK4p17Dtt39hSzJjzCqh/eCptLx7Bppii0dz0LQ1YlrUBuP7SRAm41peSWW3rdgm5KLa/cvkhrd0cdmcYrp9WoYuQqForY55PaPZ/GIorlPEb8ffma9xsjv0deFY4cJQF34m6sIcAsWnPlcDBw7kxx9/5I033uCxxx47Joiy2+28/fbbzJ07l5tuusnrsVVV5aGHHuLXX39lyZIlNG/e/IyP6dWrFwsXLuSRRx6p/d78+fPp1avXqR9UByVFNCYp4vSBZH3x3/++z5Ilf3PJJb1p3rwpRqOB9PRNLFy4lBYtmnHttcM8HstsNnP99VfzzTffc/hwAYMGXU5SUuCex9dff56FC5cybtxLLF36T22fq5kz5zJo0OXMnbsQWT47S6AMBgPff/8VQ4fewLBhNzJo0OWkpXWgrKycjRs3U1VlYd06996MBx+8i/nzF3HppUO48cbhGI1Gli5dRk5OLv36XVxbGKQ+cjmgTU+VBz9xEpuk4rSDRguSDLLs7lUqye6vGjoP7gVJsgQSoPq256q2HLu3mauA7bkKbmNnpTq4ktX6cROoLomx9eGy3HR2mf/HjohXORwyn0UJ7Wlb+iItyx5FxotGwB6SjalILVaiFL6P69B41MrFOPakomn4MnLMI0iSZx8hqmJSWH/z3yRu+ISWfz9D5MF/6P5NGlk9nye721OommPnfnTJdoDioa1Iv6QJTZ9bTMIn64ibvJGoObvJfH8wRde2PeP5JVlCf19DtMMisTywD9fcMmwvHMTxUzEhnzdF0zXUuyfmmLGh5WgLjQbbWPtQODl/Gsl4PYz9Pxvp/nkZsT2P/J+tvTOPdNLMo4T7Dn2H5u5tEOf62Lre/kUIDG9+LoP1M1EX5hBIPmWu/ve//5GQkMCzzz5L06ZNueqqqxgzZgxXXXUVTZs25bnnnqNRo0b897//9XrsBx54gG+//ZapU6cSHh5OXl4eeXl5WCxH7lKNGDGCcePG1f753//+N3PmzOHtt99m+/btvPjii6xdu5YHH3zwZKcQ6oB77x3NNdcMY/fuTKZMmcann35Fbm4+48Y9xooVC7zOJh7dz6pmmWCgJCU15p9/5nHDDcNZsWI177//KYcPH2bOnJ9JTm4BnLxIRbD06tWdtWuXcuedt7Nly1beeef/+PnnP9Dr9TzyyP21x1155WB+/HEKLVo047vvfmLatOm0adOalSsXel0y/3wja9zBVHiMiimc/2fvvMObKr84/rkZbbrSCV20hbJ32Xsv2SCiIspUARe4UMSfWxHcAxGUKUMRRWQje2/KKLOlBUoH3Tttknt/f4SUlg6StIUC9/M8eaDJe8/73pvk5p57zvkeXDzAyRUcXUDjZIps2WlMDpX5YbHt/EbCNkSubqYFFlQLHDduzR03MztXChudKyH/PlrFRq5EwZQ6q5SdqwpBgR1106fTPfYUXrquGBU5hLm/xU7fFqTYVUyKsiCoUHq9jrrWGQSnHiDlYIx/E8PlNog6K9KLBQXXm73IoTFhJNboi8KYR81979JyWUtc4oqWENxeiyW62BP53SOc3jGK7Dqe2MVlUe+Jv6j7+CrUcZkWLUERaIfjv7VwWFQdwUuFeCaHrA7n0b0djZRdtiiWg59Ix1VpdFiRisbbSPoFFVu7uHP8NRf0GaZzhsFoICk9qcSUTgmJ5PRkDEZDpRgr83BQGT4TlWEN5Ykg2ZjEGBcXx9tvv83KlSsLpXdpNBoef/xxPv/88xLT8kpdUAke6cKFCxkzZgxg6rtVvXp1Fi1alP/6n3/+ybvvvpvfRHjWrFkWNxFOT0/H1dWVxMTlaLUlN1DU6VRcu+ZD9eoBaDS2pzzKPDh07vwIBw4cISXlCs7Ozvd6OfccnS6PqKhrBATEodHcu5Pgd8+p0Ovg+W8MaL3K1/av7jsxZBl56kJ7tDWsS3+LrjcDw+VkfPa8hKZNUKHXFiwYXOJ2Tf7uj1fkBs72WUhcozFWr9mY8CnGG++icHsWlf8vVm9vKfGajRzw7odrbnO6xZXcPkOm7EhIXHNawhn318lTJoGkIDjjZeqnfoy6gmTwJUlCTF2IMe51EFMBFQqvqSir/A9BYYU6pCThfX45tbdPxk6XhCQouNriNSLbf4ioLvobXDCKBSDoDAR8uge/rw6iMIgY3DREfdGTG6OamMLSFiAm6NG9eg3DyhSTzZr2OMwJQtW17McuN1ngxJsuRP1mOj84BhppNTsd3z55JKUnkZFdcj9DraMWD61JHbkyjJV5OKgMn4nKsIaC5KTnMMlrEmlpaVbfQLfZuTKj1+u5cOECaWlpuLq6UqdOnTLVWt0LZOdK5k7Exsbh61v4ZsHSpX8wevREevXqzqZNf5Ww5cNFZXGurEWSLL4mY0GVXeSlGXjyTDvc6pR8viiO6IazMFxKwGf7JDQdgwvbLcW5avzPYKpE/Mv5XvOIafKcVXMCGBM+x3hjGgq3Maj8F1q9vaXEOvzLoaqDcc9tQ5e4gxU2j8wtchUJnPaYQrTTcgAcDNVomjwHn5wBFTanpI/DEPcSUvrN855dHVR+81E4dbTKjjo7gdo7JuNzfgUAOa7BnOv9K6mBRfv43e5gATiejKfWhHU4HzcpA6f2qEHE7L7kBrtbvAb9ulR0r1xFijZFhdXjvNB87o/gZlPVRCFi/7Pj6ItasqJMEevqI3No9mUG9p73T2G+jMzDSlmcq7K1GAfUajWNGjXKl0u/3xwrGRlLaNKkPb17D2Hy5Ld47bV36NFjIKNHT8TFxYUvvvjoXi9PphisuW1kTQr3rbRAG9QCzYIWBtuk2G0WpLhLfa5EwXSBqpDKv/5HpnjsxSq0TFxGu/hNOOqDyVFFc7DqQI54PYlOUXw7krIiqH1QB6xCFfA3qHwh7yKGqE4YYl5AMlreN1LvWIWz/ZdzcshadM7VcEi7TPM/u1Nvy3OodCmFxhZRFASym3pzau9YomZ0x6hR4bYtkpBm8/D99hBY2O5APcAN59CGqCeYehbqFySS2fQs+jWpFu9HSfj2yqPviUTqvJIFgkTUMgc2NPHi6p/2VjcfDosMY9rcaYRFht1x7PoD6xn/+XjWH1hv48rLvgYZ25CP8YNBmZ0rGZmHgQkTxnLjRgK//fY7s2f/woUL4YwY8RgHD26lceOG93p5MreRFAPbf1Nw6WhRryk3G1LiIOk63LgCcZEQfV6glGyEQpSt5spGQYubwgEKW6XY71LNlYQpWinYppUkUwa8dX3oHnuaWmlvgqTgutMfbPOrT5Tz/IqTbdcORV3rLAq38QCIKXPQhzdAzFhnlZ2kmgM4NCaM6KaTAPA7/SttFjXE69I/xY4vVI+lUhDzejtOHn+OtC5BKHMM1Ji6lcadF+N4+oZF8wtaJQ4/BOK4vQ6K2vZIsXpyhkeQ/WQEYpyt37mby3OC5l9m0mtPMq4NDOQmKNg/0o29w1zJjrbsEkySJFbtXEVsUiyrdq4qVZJaFEXW7F2DUTSyZu8aRLF8ettZswYZ25CP8YODRd/s7t2706NHD6Kjo/P/tuTRo0ePCl28jMzd4pNP/kdo6D6Sk6+Qm5tAdPQ5li79hXr16tzrpckUw9GNCua9qiI+6qYjJJoeANuWKHilhR0vNLFjcis7Xm9nx4tN1RxYbdmFjlmOXbRSTh1AUN0UtLBRit32yFUZt7cQSbjpXEmyc3UvUEmONEqdRde4I7jltkCvTCXU81n2eXcnQ3WhQuYUlG6o/H9FVX072NUEw3UMVwdiuDYCyWCZcwNgtNdysedPHHtiN1nudbHPiqXJv0NptHY4dllFI3C3C17oankQtnkk4XP6YdDa43IkhiZt5hPwwS6EXMtSlFUdXXA61gC7N31ACYa/U8lsGkbekqQyX+h6tjbQ+1ASDadnolBLXF+nYWOIJxHzHe4YxTJLVAN3lKRef2A9eXpTP8w8fV65Ra+sWYOMbcjH+MHBoquJnTt3snPnTrKzswv9bclDRkZG5m4TfV7Av7ZE9camqxZBuJX6V7+dhIefRFBDiX4TjLQbIiIIoMuyzLagKkPkqoxS7LaqBZrTAs2RpYriVuRKeYeRMhWJW15zOscdpGHylyhFRxI1O9nh14QL2s8QKVskpiQUTt1Q1zyFwvMNQIGY/rup+XDqUqsck7RqnTgyKpSoNu8gCkqqXlxFtePfFzv2dgcLhcCN8c04cfJ5Mrq6oHBMIeDH9TRt9SvOB6Mtml/QKNB86o/TgfoomjlCihHds1Fk97+EGJl7ZwOloLSHxu9n0edwEp5t8tCnKzgyScuO3u5kXCr+O3N7Y9XSGqqKosja/WsLPbd2/9oyR6+sWYOMbcjH+MHCIudKFEWMRiN16tTJ/9uSh9FYsXdJZWRkZIojO11ArQEn16LOlae/hGiANgNFnvnYyDMfG/CtJZGTYVnhlUJpGmdt3RSUveZKEG11ju5S5ArTfgmS7FzdaxSoqJ3xOt1jz1A1pw+ikMc59+ns9G1Ost2BCplTUDii8vkCVfAhBE1TMCZhvP4Mhqv9kPKuWGxHVGm43PFTjj59lBu1hxHV9t0Sx95ei+V07gq1PpyH041TiAEpSFVScNQdpXHvudR4dTOKzDyL1qAMccRpXz3sP/EHewHj1gwym50l9/t4qyPPt+Pa0EiPnSmEzMpA6SBxY5cdG5t7cu4LR27/it/eWLW0hqoFo1ZmyiN6Zc0aZGxDPsYPFnLNlYyMzAOHxlkiJ4N8h0mSbglcZKZCTqZAzs3WODkZmJoCW+h3KG7WTdnURPhmn6t710S4YqIWZiTB7DTKPy2VBSdDDdrd2EjzxCXYGT1JtzvDbp8OnHKfjEGwrD+UtSgcWqIKPoKy6icg2CFlbkIf0RBj0o9IkuU3FjKrhnBm0Kpi5dmLQxMZS+2pP+NyKoKLX0zk5KoPOffzZPI83RC8EvCdc4iQZvNw2xJhkT1BJWA/1Qen4w1QdnaGbJHcN6LJ7nIBY1jOnQ2UgkIJ9aZk0zc0EZ9euYi5Aienu/BfBw9SQk3f99ujGfnrKiaqUVzUykxZolfWrEHGNuRj/OBh0y/gtWvXynsdMjIyMuVGjSYS8VECJ3cUjUYdWqskORb8a5t+sBRKQIA8XZGhxZIvaGGwXdDC+siVSX3P5siVcHcELTBHrmTnqlIhIBCY9Qw9Yy4QmDkGBInL2u/Z5teQOIfyVZTLn1NQo6wyHXXNUwiOnUDMwhj3MobITki6s+U+n0KfRd1nFiKluHCq70aSe7Ukp6YfqV0aceWtIUhOeeQG2qO5kkaDAb9Ta9y/qJKyLbKtrK3BcUsdNLMDQavAeDiLrNbnyP04BimvbCl3zjVEuqxLpfWvadi5i6ScULOlnQcn33Xm1PmzhaIZZoqLahQXtTJTlujV7RGV0tYgYxvyMX7wsOkXMCgoiNq1a/Pcc8+xbNkyYmJiyntdMjIyMjbT4hGRRp1E5r6iYv6bSsL2CJzeJTDvVSWL31HS8hGRJt1MF0VKNTi53nSyLEBRhpqrfEELw12OXOWnBVZw5ArzhaYV2vYydw070ZPmSQtpH78ZB0MQOaqrHKw6gKNeT5GrsFx8whoE+7qoqu9E6fMjKJyRcvajv9wM442PkUTLUvQsocGmMSj12US1e4/UgC6mNMGbcuxGZwckhcCF5Y8S83IrJAGqLj1NSNN5eP551qK+DYJCwO65KjifbIhqgCvoJXI/jiWr9TkMh8oWARQECB6lo+/JJAKG6ZCMAudmOXGyd0M8ohoXvw23ohqlRa3M2BK9yo+olPB9LrgGGduQj/GDiU3O1ahRo9Dr9cyfP59Ro0YREBBA3bp1mThxIr///jvx8fHlvU4ZGRkZi5AkcPeG0Z8aadJd4t/vlbzbW817j6jZOFdJs14ioz4x4ulvGu/sBv0mGvOdrTtRpsiV8uYp18rIlZgfuarcaoHclPyWI1eVm6q63vSICaNW2hsgKYh2WsFWv/pccVpUIbLtgqBA6fki6lpnEZz7g5SHMeE9DJdbImYfLrP9KhdX4X5lK3ENniG+/kjTk5KIbvFYhDw9TmFRSEoFRncnor7qzeldo8mu74XdjSzqjlxNvWF/Ynfdsv5cCn87HP6qicNvNRCqqBDP6sjufAHdm9eQssr2/XLwEemwIo2OK1PR+Bixi/em9aJZ1F8/CWWuQ6GxEhLJ6ckYjAZ0eTr0+tJvnOj1enSWhudvYjAaSEpPKvEzUXANMrYhH+MHE5v0chctWgRAZGQkO3bsYPv27ezatYt58+Yxb948BEGgbt26dOvWjdmzZ5fnemVkZGRKxZy2HthQ4qMNeq6GCUSeFhAEU7pgQH1zwbBprL0jdH/GcmfnVs2VDYIW5rTAu1xzJeSnBVb0D/TNCwRJjlxVdlSSE41Sv8A/+wlOeI4n3e4UJ7zGct1pBU2Tf8bJUKPc5xTUAagC1yKm/44x9hWk3NMYItuh8JyCsupHCAonq20qc9MIOvw5OtcaXGvxmulJ0ZgfipZm96TKxmmkdA0hp6YfAJltq3Hy8HiqzdyP/8x9eKy7hHb3Va583p34cc1AUfrnVxAE1E94oOypJffNa+iXJpP33Q30a1JxmB2EqpfW6v0oSLUhuVTtmseh19Vc/82doCODqB3dhxqfROHeKzV/nNZRi1qlRq1SM330dG6klBx99PHwwVFjWe2aGbVKzftj3yejlCaA5jXI2IZ8jB9MytSMpEaNGtSoUYNx48YBEB4ezurVq/nyyy85f/48Fy5ckJ0rGRmZe0pgQ4nAhkXvChasHTY7WpZglmKXbIlc3UwLtDZydb+oBZopKcVFpvLhnteSrrFHCdd+zXm397nhsIXtvg2pl/YRNdOnoCjnhtCCIKB0HYHCqRfGuCmIacsQk75GTF+Nym8eCueeVtlzSgzDJf44Z/stRe/oVcixAgg6PANlop6r2pnoFnRDM24xAJK9imvvdSbp0XrUnLAelyMx1HxhI16/hxExpz+62h53nFvhqcJhQQ1yuvkhTA9HGaUju/8lcvv7kT25DpKr6YLYxTMXz0ALez3cxM5NotP8POJGpnDkBReyLttzYXxdgp7ModlXGWiqFD7/1PKvRS3/WlbNYQmeWk88tZ7lblfmFvIxfvAoc+5GdnY2mzdv5u2332bkyJFMnz6dhIQEnJyc6NWrV3msUeY+Z9Gi5SiV7ixatPxeL+WeMHbsCyiV7kRFXb0r8z3sx9sWLHWsoEDNlQ3OVb4Uu9WRK9NFWln7XFV85ErmfkSBmjrpb9E95hReuq4YFTmEub/Jbp92pKlPVsicgsoLVbWlqAI3gDoA9JEYrvTCcH08kjHFYjvu0bsx2LuSEtC1yGs+YYvxO/UL15tOIsO7OVC0N1Z2wyqc3j2ayC97YXRU47r7Kk1b/IL/F/stugmSdNWJt14cx1txH7OTLogI2K+PQdn7GP+0qcYHbQbwdqMhJF0tGpVbf2A94z8fX6rYhE/3PPoeT6Lea1kICokrvzuwoYkXUcs0JZaKhUWGMW3uNMIiw+64/sqAJcfBTEXtW0Ues8rwflSGNTxM2ORcbd++nf/973907NgRd3d3+vbty/fff4+zszPvv/8+e/fuJSUlhU2bNpX3emXuMVFRV1Eq3enb97F7toYtW7ajVLrzyCPD7jj26aefQ6l0Z/nyP+/CymQeBvJrrmzpdaO2reaq/CJXsnMlUzLOhjp0iN9Os8T5qI1upNofZadvC8Lc3sYolE16vCQULn1R1wxD4fESAGLqAvTh9RHTVlm0vU4biNKQjWPKpZsGlSj0WXhGrKX2jskk1hxIXIPRGO1db22zYDS6+c+Y/hAEBKOR7FZOXPmmBZntnVDqdQRN30GTDgtxDI0rdf6MJHv0OhV52PM3w/iOycThjZYMxrGQ8czHQZdFRpJ9oe1EUWTN3jUYRSNr9q4pVWxC5Qghn2fSc28ybo315CUpODjWld2D3ci6WvgyTpIkVu1cRWxSLKt2rqr0QgjWHIeK2reKPGaV4f2oDGt42LDJuerZsyefffYZkiQxbdo0duzYQWpqKtu2bWP69Om0b98elap8Uwlk7l+GDu1PWNghhg7tXy72evbsSmBgNbZt28m1a9EljktLS+Off9bj5ubKo48OLJe5beGzz94jLOwQ/v6+92wNMuWHuYlwmdQCrazXuiXFbmvk6ma+fgWrBZqpCFEEmbuDgEBQ1jh6xJ7FL2sYkmDkkutMtvs2JdF+V8XMqXRB5fsDqup7wK4eGOIxRA9Hf3UYkj621G2zPBuQ6+SH9/kVuMQdQaVLJejwTBpsGkOWV2Mi239Itme9whtJEggKdAtG4zEljwZ9f6Hu5B+o/v0KlA4xGBrHY/DR4XwijqbtFhA4fQeCzrIbE5EEM4upbKIPRhQ05RTv8Bn2/0QXuqgtKJ1uqVS6Z0sDvQ8m0/ijDBR2ErGb7NkY4smlOQ6Y24eZZb2B+0LG25rjUFH7VpHHrDK8H5VhDQ8bNqcFSpLE6dOnOXz4MEeOHCEsLEz2hsvI1asCx48rS3xcvXp/1jG4urpSr14dXF1d7zzYAhQKBWPGjEQURRYvXlHiuOXLV5GTk8NTTw1Ho9GUy9y24OvrQ716dVCr5YLUB4H8yJVNTYTNkStbBS3K1udKqvA+V/fnOUqmKBqjL60TV9Hmxho0Bj+y1JfY69OVEx7PkSekVsicCqeOqGuGoqjyP0CFlPE3+vAGGFPml3h9kVk1hMsdP8P73DKarB5Ip9keBB79inTvlpwavIbMqiGmgQW3v5kHHHToM2rteh1BNHBi6F6Ob/qCy++PIWFwOwTvBLI6KhGMEtW+2E9Ii19w2WtZarcBNRvozxe8SRRBOJKD04xzZD9yCTEit1jpdEul0hVqaPh2Nn2OJOHVPg9DpoJjk7Vs7+lO2nlFoWa0lb0JrTXH4fZGu+W1bxVlt6Jt309reBixyblKSkri77//ZuzYsURHR/PWW2/RsmVLPD09GTp0KD/88ANnzsiesTVcvSpQv76WVq1cSnzUr6+tlA6Wuabo8uUovv76Rxo1aouDgzdjx74AlFwDdPz4SYYPH0316o1wcPDG27sWbdp057PPvrzjnGPGPIUgCCxevLzEk8SiRcsAGDfumfznIiOv8Nxzr+TP6e9fj7FjX+DKlaI/mkqlO927D+D69RhGj56In19dVCoPdu7cC8ClSxGMG/ciNWs2xcHBGy+vGjRr1pFXX51WaE2l1Vzt3r2PoUNH4utbBwcHb4KCGjJs2DPs3Xug0LisrCw++GAGDRq0xtHRBy+vGgwY8Dj79h2847EqyL59Bxkw4HG8vGrg6OhDgwat+eCDGWRnF22meaf9vx+IjYDN8xUcXld+0uBCfp8rG5qHqm2MXAll7HMl3J0+V7fmk3+4HxR8cwbRI+Ys1TOeB+CKy69s92tAjMPqCplPUNijqvoRqppHETQtQEzFGPMshiu9kPIuF7tNfP0RHBp7jqh273Oh508ce3IPZwb9hcHB45ZTZS6svPm316V/CN77LjptEDFNJ5Ln6E36+imktW1AzNi+JAxsT2aHKlxa0Jc8X2ccLiXTuPtvBL+8EWV6rkX7EoM/3/AqqxmCZK/AuCODzOZhnJy8E4Ou8HfR2ka/rvWN9NieQovv0lE5iSTstWNTC0+E39uA4WZtZyVvQltc4+OSjsPtjXbLa98qym5F276f1vAwYtMVh7u7O0OGDOG7777j1KlTxMfH8/vvv/PUU09x8eJFpkyZQtOmTfHx8Snv9T6wJCYq0OlKd5x0OoHExMrbP+aVV6YyY8bXtGgRwuTJE2ncuEGJY0NDT9OxYx82bdpKhw5tefXVFxg2bBCOjg788sviO84VFBRIjx5duXw5qtiL/TNnznL06AmaNWtCs2ZNADh06CgtWnRmyZIVNG8ewiuvTKBjx3YsX/4nbdv25PLlqCJ2kpKS6dChN6dPh/HEE4/y3HOj0WpdiImJpW3bHixf/idNmzZmypRJPPXUcHx8fJgzZz5G450jBN9//zPduw9k69ad9OzZlddee5Fu3Tpz6tQZ/vrr3/xxOp2Onj0H8/HHs3BycmTy5IkMGtSPnTv30q3bAP788587zgXw55//0K3bAHbt2sfgwf2ZPHkijo4OfPzxLHr2HIxOV7QHSkn7f79w6aiC2ZPU/PuDhR2CLUBhFqWwIQhkFrQwNze1lPzIlc1qfzf3v8LVAs3nMNm5epBQS66EJM+lY9xunPS10aliOVz1UQ5VeRSdsvS0PVtRaJqiCj6I0vtLEByQsrahD2+EMfFLpGI+x7ku1bgeMomYphPJ9G6O0c4Zu6w4HJPP3xokGkEQsMuMpc6OVwCwz4gm6PDntF1Qh4brnkS3YDS5fl5cmziQpD6tSRgRwonQ54kfFwKAz9zjhITMxX3DJYv2Q0LBDrqTtrwdym4ukCNRc64rr84fjl9cYYU4axv9CgqoPSmHvqFJ+PTORdIrqLNjNO3mfYc2xqQcWFkjFaU1Pr79ONwefTFT1n2rKLsVbft+WsPDSrkURnl5edGpUycMBgM6nY7ExEQSEhJISEgoD/My9wmnT4dx7NguAgMD7jh26dI/yM3N5e+/lzF4cL9CryUlJVs037hxT7N16w4WLlxKt26dCr22cOGy/DFgaqD41FPjEUWJgwe35TtcAHv3HqB794FMmfI2//77eyE7Z86cY8yYkcyb9x1K5a0L9B9/nEdqahrffDODV16ZWGib5OSUO9Ycnjx5mtdfn46vrw979myievXA/NckSSI29lYR9RdffM/hw8d46qnhLFkyN/9E+fLLE2jfvhcTJ07hkUd64OJSstOTnp7OhAmTUalU7Nu3mSZNGgHw6afvMXLks6xcuZovv/yBd99906L9v19Q3nwbDOUYsLmVFmhD5OpmE2HJyrTA/CbCxsoduTI3D5aw4djIVHq8cjvRPfYkF1w/4ZJ2FrGOq0m030HD1C8JyhxX7hL8gqBC6fU6Cu0QDDHPI2Vtxxj/JmL6SpR+v6LQNCl1+3qbx+NxZQvHn9hDul/bfIn2WrvfxD4jmjT/DoR3+RJRYYdjykXqbRlPvc3juWiYjU6lQX9Ttt3o7kDEz/1JeLIhtSauR3M5lfpDVpLwRENixz5u0b6I1Rxx3FSbo+9uI+B7R4JivHlz3hNs7XCczZ2PYFAb86M2AztYVyPsFCTi8d0eNk8/Tv2NE9HG16TdL98S1W41l7ouzY9UNA5ubJXdiqS4qJWZ249DwZqhghSMwtiybxVlt6Jt309reFixOQySmJjIqlWreOGFF6hfvz7+/v48/fTTLFiwAKVSyYgRI5g7d255rlWmkvPGG69Y5FgVxMGhaC2Up+ed+4sADBnSH09PD/7+ey3p6en5z+v1epYtW4lGo2HEiOEArFu3maioq7zxxsuFHCuAjh3bMWhQPzZu/K+QHQA7OztmzvywRMeiuFouDw/3O6593rxFiKLIRx9NL+RYgemukp/fLfGLJUtWoFarmTHj/UJ3oJo1a8KoUSNITTUJd5TGmjUbSEtLZ+zYkfmOFZjq12bO/BCVSsXixUWl2++0/5Ud5c0yN5tF9opBKIsUuzkt0Fa1QJvV/u5WE2E5cvWgo5QcaJD6KV1jj+OW2xK9MpVQz2fZ692NTJVl0RxrEexqograitJvPihckXKOYIhogSF+OpJYNOIOoDDoUBhzEVUOJsfqJm7Ru/E+txydaw1OD/qLdN82ZHo340bd4STUfhS363tQ5mUChWXbnUPD0SRdIXZabeKfq4+kEKjyRxj9n5jJQP7lTp95SZSQJIlf3Fby2YvLOFkvAqWopM+eVkyd+yQ1rprO+dZGr8B0sbx699/ENdnJ3hefJ7bRTgRJSY39j9Fhzk94Xg6pVJGK0qJWZszHIT/6UoLjLmBbFKai7Fa07ftpDQ8zNkWumjRpQliYSStfkiSqVKnCY489Rrdu3ejWrRt169Yt10XK3B+0atXc4rHDhw/hu+/mMGzYMzz++FB69uxK587t8ff3KzTun3/Wc/Lk6ULPdenSka5dO2Jvb8/IkY/z/fc/s2LFX0yYMBaAtWs3kZCQyJNPDsPd3Q2AQ4eOAHDhwiU+/PDzIuuJj49HFEUuXoygZctm+c/XqBGEl1fR5n4DBjzCO+98xMsvv8n27bvp06cHXbp0IDi4ukX7f+TIcQB69+5W6rj09HQuX46ifv26VKvmX+T1rl078uuvizl58gzPPFOMgZuEhpqOYZcuHYu8FhgYQHBwdS5eDCcjI6NQBKyk/b9fqJDIVX7NlS1NhG/ez7K6z5VpRxSVPXIlyZGrhwVXfWM6xx0gwuU7zru9R5JmF9t9m1A/7SNqpr9aMc2H3cehcH4EQ+zLSBl/IyZ+hpj+Nyr/+Sgc2xcaL6o0hA7fiirHlAmhMOgQVZr8NMGITjPQO1ZFMOqRlGoQFBjs3VFnJ6DWJZkaEgPSt92pfuhTfM4uQWHUkeftjiolg5j3++D2ZwpOZ27wFW8wkLW8z4fEUvg3DABVDmptGro8HXq9njxtHvOf3ECTszUZvqELPokevLrgMXa3OsW6ngfQ5elw1DhafGwMRgNJ6UlISOQ5p3HysZnENNlOg3Uv45TiR6slM4g/v42cQUYcPe+9krP5OJSGXq9Hl6dDrVLn71txSEgkpydjMBpQqywXjSp4zMrTbkXbvp/W8DBj07fs+vXrDBkyJN+ZatiwYXmvS+Y+xNu7qsVj27Rpyfbta5kx42tWrFiVLz7RqlVzZsz4ID/Nb82a9SxZUlgR8L33TE4FmNL+vv/+ZxYtWpbvXC1cuPTma7e8jeTkVIA79rvKyios7ODtXaXYcdWrB7J//xY+/HAmGzf+x59/moq769WrwwcfTGP48CGlzpOWlo4gCPj6ll6XmJ6eUeo6zNubx93ZTvHvka+vNxcvhpOeXti5Kmne+wWV2vTDYqtPUhzmtECpLJErW6XYbYxcCflS7BVdc2VOhpDvhj4MKFBRO+N1/HIeJdTjeRIcthLmPpVop+U0S1yAm77ZnY1YiaD2Qx34F2L63xhiX4C88xgiO6LweAFl1RkIysLp0QaNKZNAVJmyDByTzmFUO5Hq1+GmQdP3WZMWhXNCKEa1E7lOpiiS842TVD/4EZ6X13O11ZvE138azcA/qbJ2H1XW7eXi7Odx2ZlMtU/20FW/iy2anmx8ojmHetZFUtyKGARUd6RabU/Akemjp3Mj5YbphUFw/QUQvzHivkZJ5yNN6BATgrqdHh6x/JioVWreH/s+GdmFfwcM71zh2kyR+N+88T7cg/9aGGnxfQbVBlkmyFFROGpuOw7F4OPhk+9gFrdvBdE6aq12EEo6ZmW1W9G276c1PMzY5FwlJiYWKZCTkbH2M9GpU3s6dWpPTk4Ohw4dY926TcyZM5+BA5/g1Kn9BAdXZ+HCn1i48KcSbTRu3JBWrZpz+PAxwsLO4eHhzubN26hRI4ju3TvnjzOLMKxZs4IBAyz/1Sptnxo1asCffy5Gr9dz7FgomzZt5Ycf5jJixDj8/Hzo0KFtidu6ubnm11bdHq0riHnd8fHF1y/GxcUXGndnO8X/mMXF3SjWzv3+PTenBZZvzZXJgbirkStlOdVccZdqroSKduJkKhNOhhq0v7GFq06LOOP+Oml2oezybUWt9Deol/Y+Ssmh3OdUaB9F7djVVIOVugAxeTZixr+ofOehcClwjr/tHJZZNQSFUYc2/hiJLv5IChUqXSpe4f/gdn0v4V2+xGivRZN+hcCjX1Ll0mrO9/6V2MbjAMje9y7Gx7/A54+dOF28xvVpfUgeWo+aE9ej3R/NkMWH6R4eS/jP/dHVLRr1r+Vfi1r+tQo/2R4M29LJmXQFZVQeOYPCMYzwIPvVumRIziUeAxfPXDwDswDw1Hriqb1tPh+oNR9ujE3myPNaMsJV7H3MjWpDdbT8PgON972LMBd7HEqg2H0rByrKbkXbvp/W8LBiU83V/X7BJVO5cHBwoGvXjnz55SdMm/YaOTk5/PffDou3HzvWJFqxYMFSfvvtd4xGI2PGjCz0OW3dugUABw8eKd/FA2q1mrZtW/HBB9P49tvPkSSJ9es3l7qNOYVyy5bS91Or1RIcXJ3w8Mtcvx5T5PVdu0xKiU2bNiryWkFCQhoXGl+Qa9eiiYiIJDi4eqmiGPcj5rRAsRyv9fObCBttaSJsVhq0UYq9rDVXFRy5EuTI1UOLqfnwWHrEnMMva3iB5sNNKq75sMoDlf98VEH/oVf5gP4ahqt9MUQ/jWRILHabjKrNyHX2x+/UXDwj1uKQGkH1Ax8SvO9dkqo/QnTTF0A04hO2GO9zy7ja8o18x8os457zz9MYtI7YJaSa/q7nxZnto7j8bW+MznZo910jpOUv+M/Yi2DhjRRVDy3OJxpgN6UqKEC/Ihld69P828aPD9oM4IM2A4s83m40hKSrTne0XbWjnj7Hkqj/ZhaCUiJ6tYYNTT2JXKJBLrmRkSl/Kq+u90OGl5eIRlP6WU6jkfDyejBqGQ4cOFys9Lc5smJN098RI4bh6OjIsmUrWbhwGQqFgtGjRxQaM3hwPwIDq/HNNz+xe/e+Ijb0en2R3lKlcexYaBHxC4AbNxIsWv+ECWNRKpW8996nRXpsSZJETMwteeNRo0ag1+t5552PChWfnjp1hsWLV+DqqmXIkP6lzjd4cD9cXbUsWrScsLBzheZ6++0PMBgMjB79VKk27kfMzpXRUH43hMqiFmhOC8TqtMCbzlUlr7kiv+ZKjlw9rGhEb1onrrzZfNifLHU4e326EuoxocKaDwtOPfjJw48dGhABMW2Zqflw2ooiBftZVZoQ1m85zolnaLBxFG3n18b/5BzS/DoQNuAPJJU9bjH78Dv1C+m+bYjoMsu0oSSaHoB9xjXs4lJIuXFT8EKSQCEQ90IrToQ+T8ojNVHkGgl6fxdN2i7A6bhlcvWCkxLNrACc9tTDEOyEC5mMYTHPMw83UoqM1+tUZCTZW2Rb5QBNP82k94Fk3EP05CUrOPSsKzv7uZEZKV8KysiUJ/e+slEGgMBAiXPn0kvtY+XlJRIY+GDcZpo16zt27txDp07tqVEjCI3GnhMnTrFt2y6Cg6szdGjpzkJBtFotw4YN4rfffichIZE+fXoQEFCt0Bh7e3tWrlxM//7D6dZtAN27d6ZRowYIgsCVK9fYu/cAnp4enD172KI5ly79g3nzFtGpU3tq1qyOVuvC2bMX2LjxPzw83BkzpnRHpXHjhnzzzWdMnvw2jRu3Z/DgfgQFBRAXd4M9e/bTr19vvvlmBgBvvvkKGzZsYenSPzh//iLdu3fmxo1EVq5cjcFgYO7cn+8YcdJqtcyd+x0jRz5Lu3a9ePzxoVSp4sm2bbs4diyU1q1b8MYbL1u07/cTt5yr8rNpVguUbIhcmdMCbVcLtNFpMddcYUSSpArLPriVFvhg3ASSsR3fnEF4xXQlzP1NolzmEeUyj1jHNTRN+gm/nEfLda6zeVuIMB4nwgmO2cHLuiDs865gjH4K0XkpKr+fEdS3lGzT/dtzYPwlvCJMinU5bjXJdq+DqDbV+HhGrMUu5wahj20BQBANSIISFKbPd82909G5ViejajN0C+qgGXerN2NeoCvn1jyB1/Iz1HjjP5xO36BJ+4XETGnDtfc6IzreucZF2cqJ9CVtOdjRjt5soRFh1OIz/mUQ++iAVIb74u4hBnrtS+b8N46EfeJM/DZ7NjX3pPFHmdR+IcesVi8jI1MGZOeqEhEYKBEY+HDc8Z04cRyurloOHz7G7t37kSSJwMBqTJv2GlOmvIBWq7XK3rhxT/Pbb6YeVeY0wdtp1ao5J07s4csvf2Djxv/Yt+8Q9vZ2+Pv7MXhwf558cpjF8z355DB0Oh379x/iyJFj5ObmUa2aHxMnjuONN162SJL+xRefp2HDBnz99Y9s2rSVzMwsqlb1onXrloUEMTQaDVu3rmHWrO9YuXI13347B0dHBzp3bs+0aa/RsWM7i9Y8fPgQfHyq8vnn37B69Vqys3OoXj2Qd999k6lTJ1sVLbxfyHeuKola4C1BCxv7XIm27kjBU72Rijr13+pz9XCcx2RKRy1pCUmeS7WskYR6Pk+m+gKHqw7DL2s4TZK/RyOWLuhjCZIk8W/G/xBQImHkmlrJTxovXpfGISZ+ipS5AX14Q5TeM1G4T0AQbn5GlXYk1Cl6zheMefieXUJcg1Fke9YHSTTd3JBEQMA/9CfcondyteWb6FyrA4Ul2zXjFoMgkDiyMWm9gqn+2haqrDyL/9cH8VhzgYg5/UjvWt2Cg6dgE30JJYQRrKAGUTzOnzTnOCsYQQKWC0jdjkINDaZmEzA0l8MTtSTssePE61qu/qGh9dx0XBvK318ZmbIgSLLIPenp6bi6upKYuByttmT5U51OxbVrPlSvHoBGY3cXVygjc3+g0+URFXWNgIA4NJqK7ql0Z66GCbzUzA6tl8TSmOIbVlrLiS+iODQ9grqjfOn2awOrts1YdJik5//EoW89vNeML/TaggWDS9zONXoPLf7oTLZ7bQ6Ou2j1miVjOvrzrgCo6+cgKCrGkb7u+BdHqjyGh64DneOL1vfJPLwY0XHB7WMuaWciCUZUoiuNk78mMGtsmZoPh+Vu5oeUoiJFL7tvooEUgCFmPFLOQQAEx46o/H5FsC+5XYxz/Amar+xCRMfPuN7sJVPKnySCQolL3FGarB5Ajlstzvf+5abzJRURzSgYyQJwX3+J4Jc2Yn/dpNwWNz6EKzN6YHQr+XsYdcKDD9qYmugKiHRiDwNZiz156FGxkb5spzvvHdpA9WbJlh2sYpBEiJjvQOjbzhgyFCjUEvXfyqLBW1koLcs4lJF5IMlJz2GS1yTS0tKsvuEvJ9rKyMg8sCgqIC1QUZYmwsoypgXa2g1ZKBCpslkUw4JpJHNOkZwWKFMYJRoapH5Kl9gjuOW2wKBI44TXePZX7UWWKsImmwWjVgURUPJvxv/Avj6qGntR+nwPCiek7L3oI5piTPgcqYT6Q72DJ5JCjVp302ERBFAoUWcn0mjd44hqJ661eNXkWJlfv42CkSyAlP61CT05gbjnTUJGPvNDadZ0Lu7/XrBsP1Gwmy7MYBrnqIcaA4NYyxt8ifJC0dpfaxAUUOu5HPqdTMKvXy6iXiDsE2c2t/Yk6Yic3CQjYwuycyUjI/PAUjF9rsxS7DY4EPmCFtY2ES6rFHvBOo+KE7UwX+TKUuwyJeGmb0bnuIM0TJmFQtSQ4LCN7b6NueTyldXppGfztnDFcKTIdhJGrhiOcDZvC4KgROn5MuqaYQjOfUDKxXhjGobLrRFzjhexadC4k1KtC1UurcYjagv26deoemElIat6oDDkENVmerHphLdzu4Nl1Npz+ce+nNn2DDm1PbCLzaT+Y6uoM+Jv1PGZFu1vMp7MYRK/8TRZOFKN62jHHkY3/TpSTtluaDhWE+m0OpX2S1Oxr2ok/ZyKrZ08OPGmM4asMpmWkXnokJ0rGRmZB5YKFbQoSxNhqyNXZWsiTME7+xUox26OXMk1VzKloUBF7fQ36R57Gi9dN4yKHMI83mCXT1tS1aEW2bgVtSr+MkZAwb8Z/8tXCxTsglAFbkTpvxiUHki6UAyXW2OIewtJzMnfzmjnQniXLxFEPQ02jKT1ksbU3zQahTGPsH7Lias/0ryAO65Rt2B0EScrvVMgoceeI/rN9khKAa+/zhHSZC5VlpyyyCYIHKE1n/EOJwhBMErkfRFHVouzGHaX3kz+jpYFCHw8l36hSQSNyEESBS5858SGEC/itsqlEDIylmKRc6VQKFAqlVY/VCo5pCwjI3PvUFQyQQubmwiXUYrdVMR/c+4KlGOXI1cy1uBsqEWH+G2EJP2CSnQl1f4ou3xbctbtXYzklrqtgTySxatIJaSgSoikiNcwcKvWUhAElG6jUNc6i0L7OGBETJqFPqIJYtbu/HE6t2AOjzlDROdZXO7wCWH9f+f4E3tIDeyGpLI3Gyt+YVLR9dzuYEkaFVc/7cap/ePIDPFGnaKj9rNrqT/gd+yjUgFTg2B1KXWrGWhZqhmFYU4DBD81Yngu2T0vkvPiFaS0sn3/7L0k2i1Op/O/KTgGGsm+omRnP3cOPaslN1nucyojcycs8n46d+4sNw6WkZG571DdzIYTRaG4unObyO9zZUsTYRsjV/lqgWWJOgkqkPKACqy5Qo5cyViHgED1zGfxyenPKfdXiHFaxUXXT4lx/IuQpHl45XYqdju1YM80zyNkigkl2nZRVEUtFFVlEFTeqAL+QMx4GkPMJMgLxxDVBYX78yi9ZyIo3QCIbTS28IYWnETqbx6PqLQjotNMDBq3/OeLKAoCWc18OL1vLH7fHCLg4924/3eZkGbzuPpRV3ihJZ+f+afUPlYunrl4BDogPdYQ3dvR6Ocnov8lEcOGNDQ/BKIe4Fbitpbg90gefUOTOPWuM5fmOBC5xIHYzXa0+DaDgGGlO78yMg8zFjlXO3furOBlyMjIyJQ/ygKlRgY9qMshs0WhLIMUu7nPla2RK5ul2MF0us+r2MiVnBYoYyMaoy+tE//kevZfnPJ4gUz1efb6dKZGxgs0SPkctVRML7+0AMgsue2F5Ax4lDynwmUg6lqdMca/iZjyC2LKPMSMdaj8fiZVP5DMTG5zqG45Vs7O4HGbbcek8/iELUZAwitiLRd6ziGxVlEVUN2C0fkOlqRWcn1qe5KG1KXmpA247rlKjdf/w2vlWcJ/7k9Osyol74B5Va5Ksqc1IKdFFk6fnUUZnUPOoxGk9vQm+/V6SB52uHjm4hloffGU2lmixbcZBD2h4/DzWtIvqNg3wg3/QTpafJeBo78sXiMjczty3p6MjMwDi7LAGU40AOXgXAllUAvMTwu822qBcDNyRcWqBd78SZHTAmVsxT97GFV03Qhzm8oVl/lEuvxEnMNamibPwSfnVnP55GR47z0wlPJxVqngo4+KOkEFEZSuqPzmIbqOxBDzHORdwnB1EJcuPcGqXd+RkeNtse1sz3qceGIn9bY8i2PKJZqsGUJ8nce52P179E6F7RR0sAB0dTwJ++9pvH89TtC07bgcuk7T1r9y/a0ORL/dAcmu5O6+SVedeLvREPQ6FWry6MtGurMd+63xGLZm8BfDOGkfwudha2xysAC82unpczSJsM+cOPeFE9f/1XBjlx0hszIIHqMrl6yAe0lYZBhLtyzl6d5P07BGw3u9HJn7HFnQQkZG5oGloHNlKKeATX5aoA1qgbeaCNsmaKEoS+TqpmJgSRLU5YE5LVCsQEVCmQcfO9GDZsm/0iF+K476YHJU1zhYdQBHvUaSqzClAWZmlu5Ygen1TMuE+FA4dUFd8yQKz6lIKGhW+w/eGdmAVnV/w3RXwjLbqdU6c/iZk1xpNRVRUOJ9cSVtFzXAJ2xJEcGK22uxUAjEP9+C0JMTSO5fG4VeJOCTPTRpMx/nI9dLXHtGkj16nelkp8eOfxnMV7xONP44kc0ofmN87q9knSlblElpD00+zKLPoWQ8WurRpyk4MsGVHY+4kRFesvNX2ZEkiVU7VxGbFMuqnauQ27/KlJUyRa4OHDjA1q1biYmJITe3aP6tIAjMnz+/LFPIyMjI2EzBtMDyUgw0S7HbVP50c1tEW9UCRVPBvGDDfbF8Ofa7oBYoR65kyoEquh50jz3Fedf3Cdd+Q7TTcm5oNtMo5RsknoYyNB8uDkHhgMpnJjdynkB3ZTzVqoTyTO9RtKy7jD92/ExyRnWL7IhqByI6zyS+7pPU3zIelxsnaLBpNN7nlnGh11x0rrfsmB2sglGsvGpazv89HM8/zxH86macwhJo3GkxsS+34uoHXRCd7hyCv0YgX/IGPdnKI2yiAeeQRijJm+GHemIVBIXtx86tsYGeu5O58J0jZz505sYOezY1t6PxB5nUeSU7X0jofuFM5BkiYyMBiIyN5EzkGRoHN77Hq5K5n7EpcmUwGBg+fDgdO3bk/fffZ968eSxatCj/sXjx4vz/y8jIyNwrFAXOcOWlGHhLLdCGyJXKHLmyreYKypIaeNNGBUauFOa0wAoUzZB5uFBJTjRK/ZIucQfQ5jUmT5nEca9RRDQcgMbrWoXMaVA258uVh1m7/zP0BnvqB21m2lON6NzkBwQrbhxkejfj6FOHiOg4A6PSHs8rW2i9uBHVjn8HYmE7RaJYgkDS4w04cXICN0Y2RhAl/L47TEjzX3DdFmnR/CJKttCHz3mbCIIRcozoplwju9sFjGdz7mygFBQqqP96No+cSMK7Ry5GnUDo2y5s7eRBysn7x7uSJIm/d/2dL9omCAJ/7/pbjl7JlAmbnKuvvvqKv/76i7Fjx3L06FEkSWLKlCkcOHCAmTNn4ubmxvDhw4mIsK3ruoyMjEx5IAgFGgmXW+SqPKTYbau5gjI4V4LZuapAx0cWtJCpINzzWtM19hj1Uz5FIdmR7rGBjnMbEDjoB1CU/+dNFNX8d2wan684Rfj1TtjbZfFYl1eYMqwTPh5hFtuRlGqutHmbw6NOkerfCZU+izo7ptDi9444JRa2Y+6LVdDRMng5Er5wEGfXPkluoBZNZCoN+y6n5nNrUSVb5iDdwJvveYWsN+uBswLjgSyyWp8j97NYpLyypQq61DTSdUMqrX5OR+0qknxMzZZ2Hpx63wnjfSAoaI5amZ0pSZLyo1cyMrZik3O1bNkyGjVqxK+//krz5s0BcHNzo02bNrz55pvs3r2bdevWsXnz5nJdrIyMjIy1mFMDy63mqgx9rmyNXJml2KEMioHCXYxcCXLkSqb8UaCmbvo7dIsJxSmtPSrHTBpMeoU2szrjFHCuQuZMSK3DD3/vZOXO2ejyXKjhe4CpTzanT6uPb7Y2sIwcjzocf2In53vOwWDngmvsQVr91ozq+z9EMBa1c3skK7VPTU6ceJ7YF1oiCeC9+BQhTefi+Zdl+y2hIPexAJxDG6Lqq4U8idwPYshqex7jUdtELswIAtQcl0O/k0lUG6xDMgicneHMphaeJOxX39nAPeL2qJUZOXolU1Zscq7Cw8Pp2rVr/t+CIKDX3/rBbtiwIQMHDmTOnDllXqCMjIxMWTCLWoiG8qnPMKsFSjb0ucqPXBnvQeQqv8S2ImuuzGmBcuRKpuJwMdSnzqk9hP34E4ZsZ9wb7qfD7BBqjvgYQWW5w2MpEgr2nn6Bz5ae5fTlgaiUefRv+x6e2S0Qsw9bbkhQENN0IofGnCUxeAAKUU/wgQ9otbQF2thDRYbf7mCJLvZEftuHMztGkV3XE7v4LOqO+JtOby2iCjcsWoIi0A6Hf2rhsLgGgpcK8UwOWR3Po3s7Gim7bFEsBz+Rjn+m0WFFKhpvIxkXVWzr5s6xV13QZ1Y+OcHbo1Zm5OiVTFmxybmys7PD0dEx/29nZ2du3Cj8xQ4KCuLSpUtlW53MA8GiRctRKt1ZtGj5vV6KzENIuUeubopS2CLFLpjFMKyt11IokW4W79uqGCiYBS3uglqgHLmSqWgEFFxbP4m9E8NIONIXhTqP2qPeo913rdDWOVIhc6ZmVeOX9WtYtGk5mTleqMUzGCLbYYh7HUm0PPqT61KNU0P+5Uz/FeQ5VME58QwtVrSn1s7XUOgL2ylSiwVktA/g5JFnuTatA6JKQcDO02ykL8NZSXHKhrcjCALqER44nWyA6kkPECHv63gym4dh2J5u8X6URMCwXPqdSqLGmByQBC7NdmRjiCcxG8uhF0Y5kR+1KkEURUCOXsnYjk3OVUBAANeu3SokrVevHrt37y70ITx48CAepTWXkLkviYq6ilLpTt++j93rpeSzb99BHn98DAEBDdBoquLpWZ0GDVozcuSzLF68oky2Zcfw/sccuSr3miubnKubcsUG6yM7Ze51dRdqrvL7XMmRK5kKxtnZ1GtKlxDIsffWc3LmMvLSPNEGn6Ld122p99xr2Dll4exsu+3iETh+aQQzfz+HXjMSEBGTvkYf3hgxc6vlkwgCN+o9yaExZ4mr/zSCJBJ47BvaLG6M+5XCdoqrxZI0Kq592JVTB8eR2tgfLRl8yrssZjQBXC0ynVpjwMWzcBGUoooaxyU1cFhdE6GaGulyHtmPXCJn4hWk1LKdJ+zcJdrMS6fL+hScqhvJvqpk92B3DozRkpt476NYBqOBpPQkpBKcUQmJ5PRkDOX1wyHzUGGTpEuXLl1Ys2YNkiQhCAJPPPEEb7zxBgMGDKBfv37s3buXvXv3Mm7cuPJer8x9yNCh/WnbtiW+vsU3YywLixYt59lnX0KlUtG3by9q1w5GEAQuXAhn48b/2LPnAKNHjyj3eWXuH8rduVLarhZoTgu0OnLFTedK1Je95qoCe1DlpwXKkSuZCsbDw9TE19RrSgCeQn+uF9HBr5JSdRnVH/2Gev3/xZjyC+R2K4Pt4nF29sLJYylixlMYYieCPhLDlV4o3Maj9PkCQelu0Vx6Ry/O9vuNuPpPUe+/iTikRdJsVS9iGo4lvOtXGDSF7dwu3Z7dxJuzh0bh+lEodb/ZSrvcg2y278upCY9w4cnOSErTOcfFM7fEBsLq/m6oOrmg+9919HMS0C9IxLAhFc13gaiHWrYfJeHbK4++JxI5/aEzF7935MpyB+L+s6f5VxkEPnHvmg+rVWreH/s+GdkZJY7ROmpRqypvzZhM5cUm52rcuHEYjUauX79OtWrVePnll9m5cyfr1q1j48aNALRu3ZrPP/+8XBf7sCBJRtLSDpCXF4ednQ+uru0QhPu3QZ+rqyuurq7lbjc7O5spU97GxcWZvXs307Bh/UKv6/V6du7cW+7zytxfmNMCK1Xkyijm35yyFFOvq5wy1FyZ0wIrzvFRyJGrh4bk5Ds5HyYnpSI5fBiuXCn4TBVgKXZ1RqId8jw6twj2+XQnMHMsjVK+JDPRo9zXrHDph9oxDOONaYjJsxFT5yNmrkPl8yMK16IZHpcvQ2JicZb6sr3RGfrET6Ph5dn4hS3EM3IDF3v8SEKdonZ0C0bf6o2lUpD2UXNOjq5BrUnrcd15hebfr6X2/qNEzB1AduOqd9wPQavE4btA1MPd0U24gngpl5wnLqMf6obmu0AUPrY7GSonaDYrk8DHdBx+3pW0syoOjHLlyh8aWv6QjmO1stV62Yqn1hNPrec9mVvmwcYm56p58+aFxCrUajX//vsvR48eJSIigqCgIFq3bo1CYX3W4e7du/niiy84duwYsbGxrF69miFDhpQ4fufOnXTrVvSuVGxsLD4+PlbPf69JTFxLePjb5OXF5D9nZ+dHrVqf4+U18B6urGTGjn2BJUtWcOnSCf75Zx0LFiwlIiKSJ58cxsKFP7Fo0XLGj3+R+fNnM2bMU/nbHT9+khkzvubIkWPExyeg1bpQvXoggwf345133rjjvGfOnCMjI4NBg/oVcazA9Lns1av4O5Zr1mzgxx/ncvz4SXJydNSqVYPRo59iypQXUCqVhfYLYPz4Fxk//sX87Y3GlPz/X7lylY8//oLNm7eRkJBI1apV6N27O++9N5XAwIBC88bGxjFz5rds3Pgf0dEx2Nvb4evrQ+fO7fn88w/yndCLF8OZP38J27bt4sqVa2RlZRMYWI2hQwcwffobONuS6/KQolJJgFABfa7KIGgBoDeCneWnYLNioO2RK9P2UkXWXOVHroxISCXWM8jc3yQnw3vvgaEUP12lMkV/KsrB2rQJ/vmnhBdP9EW5Now6Y6YRNGAOV50XEme/kSO/zSZ2z6Ml2jSvGazbP0Hpgsr3R0TtExhinoe88xiihyOkPYrKdzaC2nQtcvkyzJpV2l658DM/8tX4EXQ/8yxOyedpvHY4N2oNZX2nJ1ho/JAntN9T374nULgeSzNuMbk13QnbPBLDFxto9ukJXI7G0qTNfK6/2Y7odzoi2d/5fKPq6ILTsQbkfhpL3pdxGFankrkjA80X1VCP8rTqhtDteLY20PtwEudmOXF2hhMx6+3ZsNuTpp9lUuu5HJt6o8vIVEbK9aPcsmVLnnjiCdq2bWuTYwWQlZVF06ZNmT17tlXbXbhwgdjY2PxH1ap3vlNT2UhMXMvZs6MLOVYAeXmxnD07msTEtfdoZZbxyitTmTHja1q0CGHy5Ik0btygxLGhoafp2LEPmzZtpUOHtrz66gsMGzYIR0cHfvllcYnbFcTT0/SrHRkZhdFo+Z3yd975kEcfHcmFC+EMHTqQSZPG4+DgwNSp7zFixPj8cYMH92fQoH4ADBrUj/feeyv/YebixXDatOnBwoVLad68Ka+99iIhIY1ZuHAprVt35+LF8Pyx2dnZdOr0CD/+OI/g4Bq89NJzjB79FLVr12Tp0pUkJCTlj129ei0LFiylRo3qjBo1ggkTxuLh4c6sWd/Rp8+jhdQ5ZUqnvNMC89UCbYlcFXCurFUbLLeaq4pUCyxwv06OXj24ZGaW7niA6fXSokRlpXDEqijGbC3nfppN8ty9OOvrkaeOo+k7wwh591Hs3WOL3ca8Zlv3T+HUCXXNUBRe7wIqpIy/0YfXx5gyH0mSSohYFSVM6sCRZ04Q2fZdRIWKquGrGb50JB0vnOOf9GnFiiyYHS0J+LTKUfpOimRviIjCIBIwYx9NW/6Ky4Foi+YXNAo0H/vjdKA+iuaOkGpE99wVsvtfQowsW/MqpR00ejeLPoeT8GybhyFDwbGXtWzv7U7Gpfs3Q0dGpiA2Ra6USiUffPAB//vf/0oc8+mnn/L+++9juNMZ6jb69u1L3759rV5T1apVcXNzs3q7yoIkGQkPf5vilX5Md94jIqbh6dmv0qYInj4dxrFju4pEa4pj6dI/yM3N5e+/lzF4cL9CryUlJVs0X3BwdVq0COHYsVC6dx/AM8+MoG3bltSvXzc/+nQ7//23g5kzv6V37x6sWrUYJycnwKQc9OKLrzN37kL++utfhg0bxJAh/UlNTePffzcweHD/QlE3My+88BoJCYnMmfMNzz8/Jv/5OXN+5aWX3uTFF1/nv//WALBt2y4iI68wefIkvv76s0J2MjMzUatvpV08/fQTvPrqi9jZFVZX+vjjWXzwwQxWrlzNyJGPW3ScHnYqTC3QlsiVusDnUm8EB8tTbczOla1qgXejz5U5cgUgCXqQbPqJkZEpN/RX29Mt5gSHhY+J9ZuFT4fVeDbZwflfv+L6lrFQztFVQWGPyvtjRNfHMF4fj6Q7hjHmWcS0FdgJ84Bgi+yIKg2RHT4mofZjBG0ejveNS3x2CA5EHeVi78UEVB1TZBvdgtFc6voGkbGRoIVxQyL4cewIun52DscLSTTqupi4SS258nFXRBf7O65BGeKI09565H0XT+6HMRi3ZpDZ7Cz2H/hh93JVBKXtx861oZEeO1IIn+PAyXddSNhtx8bmnjScnkn917NRyKVOMvcxNoWXJEmySJ7ybkpYhoSE4OvrS69evdi3b1+pY3Nzc0lPTy/0uNeYaqxiShkhkZt7nbS0A3dtTdbyxhuvWORYFcTBQVPkOXNE6k4IgsDKlYvp0KENe/ceZMKEyTRt2gE3t0B69x7CokXLi0S0Zs/+BYC5c7/Jd6zMtmbMeB9BEPj9978smv/q1Wvs2LGHBg3q8dxzheVyJ0wYR716ddi+fTfXrhW+W1jcPjs7O2Nvf+vHzt/fr4hjBfDii88BJkdNxjLKu89VflpgWSNXBht7XYm2RoTuhlrgLedRjlzJVBaUaPC/8in7Xz5G2sUWqF1SafzqeFrN6IGDb0SFzKnQNEUVfBCl9xcgOCBlbaOeQyO6NfsKQbD8u5FRpQmj+rjyeXOBHCW0i4cnlo8n4MiXRc4FkiSxatXu/NQ9QRD4SnOQE6HPc2NUEwQJfH86SrOQebhttmy/BZWA/es+OB1rgLKLM2SL5E6NJqvzeYxnciw/IMWgUEKdl3LoeyIRn165iLkCp99z4b8OHqSckG/MyNy/VNinNyEhAQcHh4oyn4+vry8///wzLVu2JDc3l19//ZWuXbty6NAhmjdvXuw2M2bM4MMPP6zwtVlDXl5cuY67F7RqVfzxLo7hw4fw3XdzGDbsGR5/fCg9e3alc+f2+Pv7FRr3zz/rOXnydKHnunTpSNeuHQGoXj2Q3bs3ERp6mm3bdnL06An27z/Etm272LZtF0uX/s769X/mOy6HDh3FycmJhQuXFbsuBwcHLly4aNE+hIaa1tW5c/sieegKhYJOndpx/vxFQkNPExBQjc6d2+Pr68PMmd9y8uQZ+vfvQ5cuHahfv26R7SVJYuHCZSxZspwzZ86RlpaOKN66GI+Jqbyfg8pGuUeuCjQRlkQJQWGF06a8rebKCqSbt3Irc+RKUSBSJQp6S1ruyMjcNTKjmnDw1YMEDfmO2s/8D8+QHXT4qQnhSz7myppXkMTyvSQSBBVKrzdQaIdiiHkORdYOhnZ8g2a1VrJi+6/EJjW+o42zeVuIFI8SWR/+qwafHIJ28SK1d7+J98WVnOv9K1lVmuSPvWK41ePL3Aw3NC0C468DSXiyITVf2IAmKo0GA3/nxsjGRH3ZE4OnY0nT56OsrcFxSx30C5PQTb2GeCSbrDbnsJvqg/3bPgj2tleZONcQ6bIulahlGk687kJKqJot7T2oOyWbRu9loqr4S0kZmXLF4jPJkiVLCv0dGhpa5DkAo9HItWvXWLJkCY0aNSr7Cu9A3bp1qVu3bv7f7du3JyIigm+++Ybffvut2G2mTZvGa6+9lv93eno6AQHWRVzKGzs7y8Q3LB13L/D2trzOrU2blmzfvpYZM75mxYpVLFpkcnZatWrOjBkf0K1bJwDWrFmfLyph5r33yHeuzISENCYk5NYP1c6dexk1agI7duxhzpz5TJnyAgDJySkYDAY++mhmiWvLysq2aB/S000SriXtt6+vT6Fxrq6u7N+/hfffn8G6dZvYuPE/AAIC/HnrrSlMmvRs/raTJ7/F7Nm/EBDgz8CBffH19c53ED/6aCZ5eWXLe3+YyK+5Kre0wFvOlGiUUFrhXAmCYEoN1BuRbHSuyipocTf6XAFIyHLsMpUPSVQR9ffrxO8fSqPJz+IZsoN6z7+Ob9flnPl2PtC03OcU7GqiCtpGxIn5VOF1qvscZuoTzdl6/C02H/4fBrH4FD1Jkvg3438IKJEwcs0FRveA4REC044r0MYdodXSFlxp/TaRracXGps/t2BqhtuoRiPSegYTeuJ5Aj/cje/3h6m67DTuWyK4/E0fkobX50666IIgYDfOC1UfLbqXr2JYl0bep7EY/k5BMy8IVRvbhZYEAWo8rcOnZx7HX3Xh2l8azn/lxPV/7Wk1J52qneU6Y5n7B4udqzFjxhQKNa9Zs4Y1a9YUGWdOBXRwcOCDDz4on1VaSevWrdm7t2QJbnt7+0IpWJUBV9d22Nn5kZcXS/G3ewXs7f1wdW13t5dmMdaqCHXq1J5OndqTk5PDoUPHWLduE3PmzGfgwCc4dWo/wcHVWbjwJxYu/MnqtXTt2pEPP3yHZ599ie3bd+c7V1qtC4IgcONG2VNBtFoXAOLjbxT7elxcfKFxAIGBASxc+BOiKHLqVBj//bedH36Yx0svvYmbmxsjRjzGjRsJ/PTTrzRp0pB9+7bg6OhYyGZpjqFMUVTlHLkyC1qAqe5KaWVtgKBSIOmNVve6yhe0sNFLFFDdPLNUYM0VCpAUIIhyryuZSk1OXDBH3tmKf6+F1Hv2DVzrHKPd9y2JiZmGz9XpQPleIwiCQLLhWX75oy+PdXmZpjVX06fVpzQJXs2K7b8SFVf0t/32SJTJEPxZS2KXn5HFJ9tT8/J+ahz8BNcLS/BodZUrVQoPN0evjv/sS4tJcYhOdkTN6kni8PrUfH49TmEJ1H16NckrznD5h0fIq6a9474o/O1w+KsmhlUp6F69hnhOR3bnC9i9VBX7D/0QnG2vC3fwEemwIo3of3Uce8WFjEsqtvf0oOZz2YTMyEStlcPhMpUfi+O4CxcuZMGCBcyfb1K9GTx4MAsWLCjyWLJkCevWrSM6OppHHnmkItdeIqGhofj6+t6TuW1FEJTUqmXuC3a7k2L6u2bNGZVWzKIsODg40LVrR7788hOmTXuNnJwc/vtvR5ntOjs7FXmudesWJCUlc+mSZc6V8mYaV3FqhOZI2Z49+4vUF0qSxJ49BwqNK4hCoSAkpDFvvjmZZctMdWBr15p6xF2+HIUkSfTo0bWQY2Waq/LW3FVWylyqdLu9ApErWxQD80UtDNYtKF+KXbJxR+5C5ArkXlcy9xGSgutbxrNnwjni9j6KQmUgLvBjzjUPwa1B6bXbtpKW5c/8DX+zYMOfpGdXxdfzLFMe68Cwzi9jr77V0PZW1Kr4y7QERwUTO+ZxesBKch298Ui5yoot8L8j4Hjb/RMBBf9m/I+c+aPyn8ts5c+pQ+O5+l5nRLUCj/WXCGk6F+95x0C883lNEATUwz1wOtkQ9TOeIEHeDzfIbH4Ww5Y02w5OAaoNyqVvaBI1nzVlkkT84siGEE+ury9aiywjU9mw2LkaPXo0o0ePZsyYMYX+vf3x9NNP069fP9zdbevqnZmZSWhoKKGhoQBERkYSGhrK1atXAVNK36hRt04Q3377LWvWrCE8PJwzZ84wZcoUtm/fzosvvlic+UqNl9dAGjRYjJ1dYcfQ3t6PBg0WV9o+V7Zw4MBhdDpdkefNUSCNpqjow+1ERl5h9ux5ZGQU7bCenZ3NDz/8DEDHjm3zn3/55QkAPPvsS8WqEsbFxXPu3IX8vz08TJ/j6OjrRcYGBgbQrVsnwsLOs2DB0kKvzZu3iHPnLtC9e2cCAqoBEBZ2rtgoV3x8AnBrn4OCTCmqBw4cLlRnFR19nenTPyqyvUzpqNSmC4XyayJ867Rpi2KgWdTC5shVJa65gluKgaIgp/E8qDg7m/o8lYZKZRpXUQQFWTeutDXnpfgQ+ukqTn2+ErXem1zH87T5ohP1J72M0qHo7wvYtn9eXrf+HxrxGJ8tO8vBs2NQCBJdmv7ItKcaUS9wM15eYCCPZPEqEsWfJyREUqRoYuoMYt/oE/xbU4MCeOYirF8HnWJuGytew0Beod5Ykp2S6Hc7cfLws2S08UeVkUfNlzbRsNdSNBeTik5aDApPFQ7zq+O4rhZCkB1SVB7ZA8LJGReJlFy2k66dm0SrnzLotiUZ55oGcqKV7Bnqzv6RrugS5B56MpUXm6o3Fy5cWN7ryOfo0aOFmgKba6NGjx7NokWLiI2NzXe0APLy8nj99de5fv06jo6ONGnShK1btxbbWPh+wMtrIJ6e/W6qB8ZhZ+eDq2u7By5iNWvWd+zcuYdOndpTo0YQGo09J06cYtu2XQQHV2fo0P53tJGWls4rr7zF1Knv06FDWxo1qo+Dg4br12PZsGELSUnJtGgRwksvPZ+/zSOP9OTdd9/kk0++oE6d5vTp04OgoACSklKIiLjMnj0H+Pjj6dSvb6rja9euNQ4ODnz33RxSUlKpUsX06zh9uqnJ8ezZX9G5c18mTJjMunWbaNCgLmFh51m7diNVqngxe/ZX+XNv3bqTqVPfo0OHNtSuXQtPT3cuX77C2rUb0Wg0vPCCqebK19eHRx8dxN9//0vr1t3o3r0z8fEJrF+/me7duxAREVlu78PDgFmVv9z6XBW4JSVaqfgH3GokbLTVuSpjn6sKjlwJcuTqgcfDw9RAt7Q+Vs7OFddAGMCcGFNav6ugoFvj7rxmAWfn4TjH9eSM++tcdV5I0KAfqdV7DYHh83BNKZyJY8v+BQfD1KkU6HflCSwkPOcpAuyfx0MbxQuDH0Fh9wxK4zdM8zxCpphQoj0XRVXUgj04+pI38CKbo9bSfvun+KfHMH8HhNfrz5FOr5Hr4HZrLCbJds24W/0kcxpW4fTOUfj+dJTA/+3Edc9VQlr8wrX/dSbm1TZI6jtff6h6u+J8ogG578eQ9+MN9EuTMWxJR/NtIKphbmVqPuzdVc8jx5I487EzF7515OqfGuK229H8ywyCntLdqVRMRuauUyZpnNWrV7NixQrOnz9PdnY24eGmhqnnz5/n33//ZeTIkfj7+1tls2vXrqVKuC9atKjQ31OnTmXq1KlWr70yIwhK3Nw63nngfczEieNwddVy+PAxdu82pdUFBlZj2rTXmDLlBbTaO+d9169fhz//XMKWLds4fPgYy5atJCUlFa3WhYYN6zF06EAmThxXJAr24Yfv0KlTe374YS7bt+8mNTUNT08PatQI5P333+app4bnj/XwcGflykV89NFMfv11CTk5JulZs3NVt25tDh/ezkcfzWLz5m1s2LCFKlW8GDNmJO+9N5WgoMB8W717dycq6ip79uxn9eq1ZGZm4e/vy+OPD+XNN1+hQYN6+WMXLpxN9eqB/P33v/z44y8EBlbj1VdfZOrUyfz1V9FaR5mSKW+1QEEQUKgERINkW+Tq5oWKZGVaYJnVAjFtX9FCE+bIlVSBtV0PO8nJ99axAZP9ipjj8mVKbbbr5WVyUuCW41Se2InuNE9agDL8Ka7WmoDe+TIRjfricOVptKFfo8yrkr8O8/5b834EB99a/y16IRlPY7zxP8Tk7xHTfkPM3Iyr7/e4ax+3yDHxUAZAzRc4HjCKGvv+R8CJ76l1fj2BVw5zsfv33KjbrNB4cwQr38lSKoh9uTXJA+sQ/OJG3P+7TNC7O/BcdZaIuQPIanZnMS3BWYnmqwBUj7uje+4K4nkdOU9dRjXQFc0PgSj8bE/pUzlCyIxMAh/XcfhZLamn1Rwc60rUCg2tZqfjFGTDjS4ZmQpCkGxoRiWKIiNGjGDVqlWAqWYmJycnvy4lPj6eatWq8dFHHzFt2rTyXXEFkJ6ejqurK4mJy9FqS5Yk1elUXLvmQ/XqAWg0ct6vjMzt6HR5REVdIyAgDo2mcggafDFSxZ4/lTz3tYGBL5VPNOVX1x0YckSeutgebXXrdIKj63yGISoF370vY9/6lvO9YMHgUrcL+bMnHle3EdZvKfH1R1q9ZkPsFMTk71B4TUPl/dmdN7CRjdW8yVXeoFvMKVz1d5aalrGO5GSTYqqhlK+XSmWK0lS0g1XeXL4Ms2bdedzUqcU5KKVjzXFLTTWtQ2mfRe3R7xI0+DskScGBl4+REXlLTXDqVHBzK82uhHeHv7F3TWHwYJH60rj8msSSELMPYYwZh5R7FgDBZSAq3zkIautuVGtjD1Fv83ick8IASAgeyIWec8hzKWqnYBTLtGyJKr+dpvrUraiTc5CUAtdfa0f0ux0RLWx8LuWK5M6MI29mHOglcFWi+dwf9Vgv69pX3EZYZBjLNqyg19W3SfgpGDFXQOUs0uTjTGpPyimUWSAjUxZy0nOY5DWJtLQ0i274F8Smj+E333zDn3/+yYQJE0hJSeGNN94o9Lq3tzedOnVi/fr1tpiXkZGRKTfMghbllRYItxQDbRK0UNkaubpP0gLzI1eVw7l+0MjMLN1BANPrpUVSKiulRaxsGVcQa46b2b4x14nz877h4KsHOf/zd4UcK/M6SrLrUvMELT95hKZvPUWdZ6cQ5f0R//nXJNXuWKlrUDi2QRV8HGWVD0CwQ8pYiz68AcbkeUiS5dGZdN82HHnmOJfbfYCoUFPl8lraLmqA38m5cJsd3YLR+Q8ABIGEUU0IPfk8icPqIxglqn2xn6YtfkW752oxsxVFsFegec8Pp0P1UbRyhDQjuklXye5zETG8aL21JUiSxKqdq4hJi2Z3va/ocyQRrw55GDIVHH9Vy7Zu7qSff7BKKGTuT2xyrhYtWkSrVq346aef0Gq1xYasa9WqRWSkXBsiIyNzbzFLsZdXnyu4pRh4dwUtbqoF2roj+WqBFSxoYU4/lAUtZB4Q0i625uo6y0WynKqdp+lbI3Ctc5iTn6/gwOQj1Di3EkdDDU67TyFPkVLq9oLCHmXV91EFH0dwaA1iOsbYCRiiuiHlXrJ4HZLSjqj273PkmROk+bZBlZdOva0TabayGw4pxdspKHih93bm4opHObfqMXL9nHEIT6ZRj98IfmkjynTLei0qGzngtLse9l9UA0cFxl2ZZDY/S+5XcVbfnDoTeYbIWNN1ZWRsJFftTtJjWwotfkhH5SKSeMCOTS09CfvMCWOeVaZlZMoVm5yr8PBwOnXqVOoYT09PkpIsU5uRkZGRqSjMNVflGbkyKwaKNkWubp5277YUe346UgVLseerBcqRK5mHD6V9Fs3fN6X4Hv9oDfH7HyXrWn2cM9oTlDmWZPuDZCujLLKl0DREVWM/Sp9vQHBEyt6NPqIJxsRZSFZEoLO8GnLsyX1c7PYtRpUj7tG7ab2kCYGHZxYbCS/oYAGkDKpL6MkJxI0PAcBn3nFCms7Ffb1ljp6gFLCf7I3z8QYou7uATiJ32nWyOpzHeDLbIhuSJPH3rr8L9Vv9e9ffIEjUnpBD39AkfB/JRcwTOP2BM1vaepB8vEyyAjIyNmOTc+Xg4EBaWul9DK5cuYKbm5st5mVkZGTKDeXN39fyErQAUNxMC7RFLVAwpwXeZSl24W5JsSMLWsg8vDR+fQwK+2wiVvyPlDOdTU8qTDdEVOLNug3B8psygqBE6TkFda0zCE69QNJhjH8Lw+XWiDmhli9MoSS6+WQOjQkjOagXSoOOWnvepuWy1jjfKGrndgfL6Krh8pz+nNkykpya7thfz6D+0JXUfno16htZli0h2B7HjbXR/BIE7krEE9lktTuH7r3rSLrSz4fmqJVZJsDcHPlM5BkAnAJEOq9Jpe3iNOy9RNLOqPmvvQehbztjsMx/k5EpN2xyrpo1a8bmzZuL7VMEkJyczKZNm2jbtm2xr8vIyMjcLZSqm32uyvFaX8h3rmxpImyOXNmYFmhzzdXdaSKcX3MlyFLsMg8X3h1X4RmylZhtzxC746bojCCCqEQUckm1P4YgqVCK1ongAAh2NVAFbUbptxCU7ki6Exgut8QQPw1JzLHYjs61OqHDNnP2kUXoNe643DhBy6UtCd4zDYW+sJ1CdVg3Se9anZPHnuP6a22RFAJVVp4lpMlcqiw9DRboowmCgN1oL5xPNkQ1xA0MkPd5HFktz2LYV3yh4O1Rq4K2/t71d77DJQhQfYSOvicTCXwiB0kUOP+1ExubeRK/wzIhDhmZ8sAm5+qVV14hOjqaYcOGER0dXei1iIgIhg4dSlpaGq+88kq5LFJGRkbGVspbih3KWHNllmLX2yZoYbMU+12quVLcrLkS5ciVzEOEyjGN4OGfkx1fg6jVpv6cKIwgmS6z9HaxRDstwydnIC6G+jbNIQgCSvcxqGueRdA+BhgREz9HH9EUMWuvNYaIaziag2POEV9nOArJSPXDn9P6t6a4Ru8pMvx2B0t0VHPl8x6c2j+WrCZVUSfnUHvcv9Qf9Dv2V0rPajKj8FHjuLImDn8EI/iqES/mkt3tAjmvXEVKL3xuvD1qZeb26JUZTRWJ9r+l0/mfFBwDjGRFqtjRx4PDE7TkpcpNsWQqHpucq8GDB/PWW2+xceNGgoKC+OorU6PUqlWrUqdOHfbs2cO7775L9+7dy3WxlQXrxetlZB4OzN+NytTU0dxEWCzHNigKZVnUAm2NXJVRLfAu1VzdUguUI1cyDw/OQWFoax0n6q830Kd7mRwr8ZZyXXzADPIUKdTImFTmuQS1D+qAP1EFrAaVH+RdwhDVCUPMC0jGdIvt6J28CRu4klODVpPr5ItjyiVa/NGZOltfQJlb2E4RRUEgq7kvpw6M48pHXRHtlbhvvkxIs3n4zDkKomXnRvVQd5xPNkA91tO0pp8TyGwWhn6jyUnLj1pR/I+KQOHoVUH8+uXRNzSJWhNNeYGXFzqwoakn0WvsLVqbjIyt2NwRYMaMGWzevJkBAwbg6OiIUqlEFEUeeeQRNm7cyIcfflie66wUqFQiIGG4k56rjMxDil5vACSUysrT0LFi1AJvClqUSS3QtibCttZc3T21QHNaoBy5qgicnU39mEpDpTKNu9/w8irfcQWx5rhZsw6zXfdGuzFkuZJ8qmuRcQG9F5Po8ws1Mibhlte8yOvmGxFGcjEImeQqEiyaX6EdgrpWGAq3ZwEQU+agD2+AmLHOsh24SWLtIRwac5aYxiY71U7Ooc2iBnheLr6dTkEHS1Iruf52B04eeZb0DgEoM/MInryZRt2W4HDOMs18wU2Fw9zqOG6ujRBsh3RNT87gcLJHRaKP05GUnoRE8edaCYnk9GQMJSgWqV0kWn6fQY8dybjUMaCLVbJ3uBt7n3AlJ05uiiVTMZRJSqVXr1706tWrvNZS6VGpROzscklLy8LZ2cGirukyMg8LkiSRnp6Fvb3u5o2IysEttcDy+77mpwXaELkypwVaG7kSy+xc3XR6KrjmSlYLrFg8PEyNbkvrY+XsfP81EAZTY+CpU0vvY+XlZX0DYbDuuHl4WLeOjz6Cqw6BXHHK5vm3LuGS5gcoMSqyyHDbzpW6k6mSM5DAzNGoJdcitgSU5ChjCHObSqr9UZSiEw5Gf5ok/4ijMbDI+ELbKt1Q+f+C6PYUhpjnIC8Cw9WBKFxHoPT5FkFV1YKjAwaNG+d7/0Jcvaeo999zOKZG0HT1AOLqjeBSt2/ROxa2o1swulDz4Zx6XpzZ9gw+c48RNH0H2gPRNG31K9HvdOT6m+2Q1HfuP6XqpsX5eENyP7hO3vc3MPyejHFrOh98+jrpj4slpkRoHbWoVaXXVFXpoOeRo0mc+diZ8187Er1aw42ddjT7IoPqz+gqVbaFzP2PVc7VgQMHmD59OkeOHEEQBNq0acOnn35K69atK2p9lQ4Pjwzi4uy5fh20WifUapX8pZR5qJEkU8QqPT2LzMw0fHwqV/dSs1pguUauzIIWVir+mRZ0M3J115sI3+U+Vw9ozVVy8r13bMwOgCWEhkJMTMmv+/lBSIjp/5cvW+5QVNRYN7fSI0wFI3IV+V4EB1vuxHl4gELdgBuiH/oaK3DJdMRJX5sI7ddcc5mNm74x9VI/xMVQr9jtM1TnOFLlcTJV4Xjn9EMj+pBid4gdviG0TviLKrnd7rgGhVM31DVPYbzxPmLS14hpKxAzt6D0+Q6F61MW3wxODezG4VGnqLH/fQKPfY3P+RV4RG3hUrdvia8/spCDc7uDhUIgblJLkgfUIfjljXhsCCfwg114/nWOiLn9yWzpd8f5BUcFmlkBqB/3IOf5K4hnclBNSKRqP1c03weiCLSzaD+KQ6mBpp9mEvi4jsMTtKQcV3PoWVeiftfQ6scMnIPlVGaZ8sFi5+r06dP06NGjkELgtm3b2L9/P4cPH6Zhw4YVssDKhotLLpBISoqOmBgNlJAHLCPzcCFhb6/Dxyfz5nek8lCRgha21FzlC1rc7ZorsxT73aq5egAjV8nJ8N57UFpmuEplimRUhshRaCj8/POdx02cCFotzJp157FTp5r+rYixbm6WH1+w7r2o6PfOTR9Cg5TPCPV8nljHf8hV3EApOeCZ25GWiSuwE01GJaT8+iHz/y+6zkCnjKdF0lL8s4cBkKY+xQnPcUS6zLHIuQIQFI6ofL5AdH0C4/XxSLmnMF5/GjFtGSrfnxHsSo+CmRHVjkR0+YIbdZ+g3pbxuCScouHGZ/A+v5wLPX8mV3vLjjlFsKCTlReg5fzqx/FaEUaNN/7D6fQNGndcRMzk1lx7vwui452V+5QtnXA6WI+8WXHkfh6HYUMambvD0Hzmj/r5KggK26+93Jsa6LU3mfNfO3LmY2fit9qzsZkdTT7OpPaL2SjuHGSTkSkVi52rzz//HJ1Ox/Tp03n55ZcBmD17Nh9//DEzZ85kyZIlFbbIyoaLSy4uLrkYDAqMRoUscCHzUCMIoFSKlSoVsCAVUXNllmI32lBzhTk9xsaaK5vVArlLaoHSg6sWmJlZ+sU5mF7PzKwczlVpEavbx+XlWTa2tAhUWceqVJYfX/P/LRnr4XF33rtq2SPwzO1EnMNaQMA9rzXO+jqoJOd8R6qgMIOAQJr6NNecllIzYzJVc26VWbjqm+CR25GrzgvRKWOxN3ojWFgmr3BoiVDzKGLiLIwJHyFlbkQf0RCl90wU7hMRBMvsZPi05OjIowQemUWNgx/hFbkRt0UNiej0OddDJkEBO0WiWIJA4lONSO1Vgxqv/0eV38Pw/+YQnmsuED6nP+ndqt9xfsFOgf27fqiGuaObdAXj/ix0r1xDvzIFzZwglHU1Fu1HcShU0GBqNgFDcznyopYbO+048YYLV/7Q0HpuGm6N5CiWjO1Y7Fzt2bOHjh078vHHH+c/9+GHH7Jz50527dpVIYur7KhUlfeCUkZGxkR+n6tyDKSY0wJtilyZBS3uVeSqovtc5QtayBcnMg8fDsZq1MgsrAioU8ShV6QUK8FuUKQjoMBJXwu1ZGoyLJKHAjskIQ+16Iqd0dNix8qMIKhRVpmOQjsMQ8yzSNn7MMa+iJi2HJXfLwj2lsnBS0o1V9pOJ6H2MOpteRa3mH3U3f4S3udXcL73L2R73rJTUOjC7GgZqjhxackQEp9sSPBLG9FcTqVRn2XEj21K1MyeGN3u7CAp6zvguL0u+jkJ6N69jnFvJlktz2I/3Re7130Q1LZHsVxqG+m2OYWI+Q6cfNuZ5CNqtrTxpP5bWTR4KwulLCwoYwMWf1vj4+OLbQrcpk0b4uPjy3VRMjIyMuVFxaQF2q4WmC/FfpfVAoW7VXOVL8X+4EWuZGRs4YTneLb7NSbZ7kCR1+yMXqhEF3JUpp6hEiIK7Ei1O0aU86+46BtgELKRsO1GrmBfD1X13Sh9fgCFM1L2PvQRIRgTPkWy4lyQ7VmP40/u5kL3HzGonXGL2Ufr30IIOvgpQjFpAbf3xkrpV5vQ0AnETmwBgPfCkzRrOhePf85bth8KAbsXq+Ic2gBlHy3kSuS+F0NWu3MYj2dZvB/F2hag1rM59D2ZhP9AHaJeIOwTZza39iTxkNx8WMZ6LHau9Ho9zsVouzo5OaHXyz+iMjIylROzoIXN7aGKwdznSjTeh5GrCq65UiCrBcrImDGiQxTyUEpOeOS1K/K6i6Eu1TMncEk7i4vaz0m2P0icZgNHvZ5CwoBPzgDsJLf8yFWS/X6inH/lsvNs0tVnLVqDIChQer6EutZZBOd+IOVhvPEuhsutEHOOWr4zgoLrzV7k0JizJNboh8KYR81979JyWUtc4oraud3BMmrtifz+EU5vf4ac2h7YxWZS7/G/qPvEX6jjLBNCUgTZ4/hvLTQLqiN4KBFP5ZDV4Ty6d6KRcsqWSeToL9JxVRrtl6ViX9VI+jkVWzu7c+JNZwxl899kHjJkkX8ZGZkHGrNzZagIKXZb1AJtrLkqsxT7Xaq5yk8LlCNXMjIo0dDhxn/0vh6Z/5xeSMMg3Lpar5f6IQ1SPyVc+yWhHs9xtMoIMlWX8MztSHDGSwBkKaMI9ZjI/qo9CfWYwCXXWez0aUGEy/cWr0VQB6AKXIfSfykoPZB0JzFcboMh7k0kMdtiO7naAE4NXUdY39/I03jiknCKlsvbUGvnGyj0he3c7mABZHQMJPTYc0S/1R5JKeC5+jwhTedSZclJLCliFwQBu6c9cTrVENXj7mCEvC/jyWpxFsOuDIv3o3jbEDg8l36nkqj+TA5IAhe+c2JjMy9it9iuVCjzcGGVFPvSpUs5ePBgoefCw8MB6NevX5HxgiCwfn3xTehkZGRk7gYV00TY7FzdRbXAm/mNClt35K6lBd6UYpcjVzIy+ahF9/z/xztsIFGzi9rpU3EyBKPEnjrpb1Mn/W0uO88m0uUnslVRNE75BoBUu2NccP2UeIcN1Ep7k4CspxGFXK45/cYl7ee45jXFK7eLResQBAGl20gUzr0wxk5GTP8dMelLxIzVqPx+QeFkmTIhgkB8g6dJrt6H2jsm43N+BYHHvqJK+GrO9f6V1MBbdopTFJQ0Kq5+3I3EYfWpNWE9zifiqP3sOqqsCCNidl9yg92LTHk7iqpqHJcGo38iFd3LVxHDc8nudRH1s15oZlRDcLVd9s/eQ6Lt/HQCh+s4+pKWrCgluwa4U/2ZHJp9kYG9h6xkJlMyVjlX4eHh+c7U7WzatKnIc3KTXRkZmXtNfuSqAtQCbXKuzGmBVka9JMGcFljWJsIVrRZ4My1QjlzJyORTWCVQTazjP9iJHgRljsfJUBOAdPUZIl1mk6E+T0jyXNzyWpCtvEa4yzfEOvxDs6RfCcoal29HlTmRKJefSbU7brFzlb8GVVVUASsQM0ZiiJlkaj4c1R2F+/MovWciKN0ssqN3rMLZ/suJr/cUdbdOwiHtMs3/7M71xs8R0XkWBs0tO8UJXmSH+HBq31j8vjtEwIe7cdsWSUjzX7j6YRdiX2qV3xewNNQD3VB1dkE3PRr9vET0vyZi2JCG5vtA1IMs24+S8Hskj76hSZx+34mLPzoS9ZsDsZvtaPFNBgGP5cp9TmWKxWLnKjIy8s6DZGRkZCoZZkGLClELtKHmKl/QwmhjE2HJRhW+/JqrilXxy28i/ACqBTo731kuXKUq3Oj2XuJ3556t+eO0WsvGenlZPr+1Y609vtaMrUzvnX/2Y2SrIjnn9i5J9nuxN3pjUGRyQ7MZjdGXhqmzqJ75HCIGrjovJNppObXS38h3rMyy7krJEbXohk4Za/NaFC4DUNfqjDH+bcSUOYgp8xAz1qLynY1CO9RiO0k1B3CoWmdq7nmbaifn4H/6F7wur+NCj59IrD2kyPhC0u0qBTGvtyN5UF1qTlqP6+6r1HhzK15/niXi5/5kN6p6x/kFVyUOPwahftwD3cQriOG55DwWgf4xdzTfBKDwtl2YQu0s0fyrTAIfy+XwBC3p51XsH+mG/+86WnyfgaO/rBotUxhBkuQuTenp6bi6upKYuByt1vFeL0dGRqYcObxOwSePqqndUuSr/eUTTcmKzcWQZUTjpcbezbof7ZR3N5I2azsuL3XE8+vB+c8vWDC4lK3A9/QC6m8ZT2Jwf04NXWf1msXswxgi24A6CLs6UVZvbykn3V8mUvsjdVLfpUHax3fe4D4jOflWn6XicHauHD2uzISGlt7vys8PQkJM/798ufTeVF5eEBxcsWOtOb7WvheV7b1LtjtAuPZr8pSmg+OR246AzNG4GOoCkKDZznHP0WiM1egSZ1IaNKkGSggoSbE7zC6ftrRMXEG17CcKNSi2BTFrN4aY5yDvIgAK7XCUvj8gqLytsuMavYd6W57FKcVkJ77OcC52/wG9U8l28h0tUcJ7wQmC3t6OKj0XUa3g+tT2RL/dAcnesniAlCOS+3EMed/Em+4luSvRfBmA+mmPMmdUGXPh7OdOnJ3phGQQUGtFQmZmEjwuR45iPWDkpOcwyWsSaWlpaC29+3QTq9ICZWRkZO43lOry73Pl5FuG5if5kasHs8+VIr/P1YNZc+Xhce+dJ2uchMDA0tdbMFITHHzLybkTbm6mSE9527UGa98La8bfDUfMI68drRJX3hR/Udz67tx0kuI1m8hV3qB9/BYARAwIKPOVA8+6TcfRUB23vGYAZXKsABROnVHXPIkx4SPExFmI6X8iZm1F6f01CrfRFjsmadU6cWTUSaof+IjAI7PwvvgnHle3cqnL18Q1HE1xXkh+JEshEP9sc1L61iL45U14rLtEwKd78Vx9gfC5/cls43/H+QUHBZrPqqEe7kHOhCjE0Bx046PQr0zG4cdAFEG2n7+V9tD4/SwCHs3l8EQtyUfUHJmk5cpKe1r9lIFLzQcvYi9jPbJzJSMj80BjrrkqT0GLsiCozTVXd7fP1d0TtJDVAiuS5GR47707p7d99JHp/5aOtcZRsGYNlcGutdzNdQgICNxSoTM7ViJ5XHNeTEDmKFwM9W/2v1LdjFwJXHb+iUTNTmqnv4mjoXrZFlFwPQoNKu/PELXDMcaMR9KdwBgzFjFtBSq/uQh2ls0lqjRc7vQZN+oMp/6W8bjcOEGDzWPxOb+c873monOtUWSbgqmCef5azv81HM9V56jx6hYczybQuPMiYl9qxdUPuyI631m5T9nMEad99cn7Jp7cj2Mwbk4nM+Qs9h/5YfdCVQSl7c6oW2MDPXcnc/EHR06/78yNHfZsamZHo/cyqTslG4V8df1QI0uxy8jIPNCoKqDmqkzkS7FbF7kSy6gWmN9EuIKdHsXNmiu5z1XFkJlZ+kU/mF7PzLRubEWtoTLYtZZ7uQ5z9CldHYZRyMFV3zT/FQkjAgpS7I5ywe0j3HPbEJD5DArskCjfCg+FQzNUwYdRVv0cBA1S1hb04Q0xJn2HZEXdZ6Z3M46OPEx4p5kYVRo8rvxHm0WNqHbsWxCL2ikk3S4IJA1vQOjJ57nxdGMECfx+OEJI83m4/nfZovkFtYD9VB+cjjZA2dEZskRyX48mu/sFjGdzLN6P4lAood6UbB45noR391yMOoGT77iwtZMHKSdl7+phRnauZGRkHmjMdxDLs89VWbilFmhl5KqsaoHmRIW7FbkS5MiVjIyt2ImeCJKaPEUSYI5wKclVJHLE63GUohM1M17FxVA///XyRhBUKKu8hbrmKQTHLiBlY4ybgiGyI6LujMV2JIWKq62ncnjUKVKqdUZpyKbOzldp8XsHnBLDiozXLRhdyMkyeDoSvmAQZ9c9iS7IFU1UGg37r6DW+LWoki1zkJR1NThurYPmx0BwUWA8kEVW63PkfhKDlFc2QQqXmka6bkyl9a9pqN1Eko+p2dLOg1P/c8KoK5NpmfsU2bmSkZF5oDFHroq5SXpPMPe5wsY+V7bXXJnTAis2opSvFogcuZKRsRW16I5XbhdiHFdzQ7OFbOVVrjuuZJ93d4xCDnXTpuOfPeyurEWwr42q+naUvj+DwgUp5yCGy80x3HgfScyz2E6Oe21OPL6D8z1/xmCnxTX2EK1+a0aN/R8gGIvaub0BcWrvmoSeeJ6Yl1ohCVD1t1OENJmL56pzljUfVgjYPV8F59CGqPq5Qp5E7kexZLU5h+Fw1h23L9W2AMGjdPQ7mUS1oTokg8DZmc5saulJwj7blQpl7k9k50pGRuaBpqJrriRJQhJND9FoekhiKT/0tkauFGWMXAl3J3KV3+dKjlzJyNiMWnKhUcpXgJGjXiPZ7teEY56jEQW9SR0wayRAuacDloQgKFB6TEBd6yyCyyCQ9IgJH2G43AIx+5AVhhTENJ3AwTFnSag5CIWop8aBD2n1W3O0MQeLDDdHscyOluhsR9TXvTm9azTZ9bywu5FF3af+pu5jq1DHZFi0BEWAHQ6ra+LwWw0ELxVimI7szufRTb2GlFW2u3AOviId/0ij48pUND5GMi6q2NbNg2OTXdBnVI7sCZmKR3auZGRkHmgUNwNF5VlzJYkS13elsPvF8/zT+SjL6u5nccAeltXex1+tD/PfU2e4uCyWnBtF78YKtqoFmtMCy6HPVUV24BDyFc8qSahQRuY+xclQg+6xp2mY8gUNUj6lVeLvdIrbQ5XcrigxKd6VlA6oF9IqZE2CuhqqgH9QVvsDlFWQcs9giGyHIXYKkmh59CfPxZ/Tg//hTP/fyXOognNSGC1WtKf2jiko84ovZisYycpsW42TR8ZzbXpHRJUCz7UXadZkLlXnn7AsiiUIqJ/wwOlUQ9RPeYAIed/eILPFWQzb0i3ej5KoNiSXfieTCB5rSlu8NMeRjc08idl4ZyEOmfsf2bmSkZF5oMkXtCinQIoxT+S/EadZ2/s4l1bEAVC1pZagvl74dXbHwceOG8fS2fHsOTYMOUnmtduS7m+mBUq2pgXavCMFU1MqzvERJHMTYTlyJSNTHgRljSE480V8cwZjL3rdMVqVq0jgP//anHJ/BYNQ/qobgiCgdH0cda2zKFxHARJi8nfowxsjZm61xhA36j3BwbHniG0wCgGJgOPf0XpxY9yj/it2k4IOlmSv4tr7XTh1aDwZrfxQpedSa9IGGvZehiY82aIlKLxUOCyqgcO/tRAC1EiX88jue4mc56KQUsp2R87OXaL13HS6bkrBqYaB7KtKdg92Z/8zWnIT5SjWg4zsXMnIyDzQmNMCy6vm6uhHl4lan0j7L2szNqELQ/e0oveKxnT7tQE9FjVkwPpmPH2pA4+sakJGVA77p15CNN66GBJUZufKugWJZil2W2umhALOVQXWXSnkyJWMTLlT0KG6k3hFrOM/5CkTuKz9gW1+DYnXbK6QNQkqL1TVFqMK3AjqQNBHYrjSC8P1sUjGFIvtGBw8Odd3MaHDNqFzCcQhPYpmf/Wm/qaxqHKKOkm312JlN67K6d2jifyiJ0ZHNa67rtC0xS/4fXXA4tpW9SOuOIc2RP1CFRBAvziJzKZh6P+2fD9Kwqd7Hn2PJ1HvtSwEhcTVPxzY0NSLK79rLAmyydyHyM6VjIzMA41CZfr1MpRTIOXSH/E0nFiNJi8HolAKppqrgo+btVdB/b1o+V4w1zYnIRZUozKnBVopxW6uubJViv1WWiAVWnclyDVXFYqzc+nNe8H0urOzdWMrag2Vwa61VJZ1FMQaNcDqmc/RPn4Ljvoa5KiucsD7EY55jiJXkVgha1O4PIK65hkUHi8DAmLqIvTh9RHT/rQqBTm5eh8OjTnDtWYvIyHgG7aINosaUOXiqiKpfrcrCqJUEDu5DaHHnyO1e3WUOQaqT9tOk44LcTwZb9H8gosSh28DcdxRF0Ude6Q4AzlPXiZ7eARibNnOZyonCPk8k557k3FtqCc3QcGBUa7sHuJG1jX5UvxBQxbil5GReaAp77RAfboBJ1/7/L8F4baLHoH8yyCVRoFokBANBSNX97iJsGly22xYMo25z5XcRLhC8PAwNa8trceSs/Ot5rbWjK2oNdxru9ZSWdZRFqrqetE99jRn3aZz2eV7rjn/RrzDRpok/4B/9hPlLt0uKF1Q+X6P6PokhuvjIe88hujHEVwGo/Kdg6D2tciO0c6FS92/J77uk9Tf8ixOyedovHY4CbWGcKHHbPKc/QqNL9h4GCA32J2zG5+i6uKTVJ+6DefjcTRpt4CY19tybXonJM2dL3tV7Z1xOtqA3M9iyfsyDsOaVDJ3ZaCZWQ31GM+i53wr8GxpoPehZM594cTZGU7EbrRnY4gnTT/NpNbzOQiyn/VAIDtXMjIyDzTKcm4iXLW1KxeWxFLrSW+c/TXFjjHkGNEl6zn1/TV82rmiUBf4MbZVil1RRil2lAVXaNWWycmWX2gq8muuZCl2a7DmGFuDh0fFOAH3m937dR1lQSU50STlW6pljSDU8znS7U5ztMoIorNX0DR5Ng7GauU+p8KxPeqaoRgTP0VM/BwpYw36rF0ofb5A4TbeYsck3b89h585QfVDnxF0+DOqhP+D27UdRHT+gpjGz5q0z29SMIKlGbfYVMs1JoSUPjUJnrwZz38uUG3mfjxWXyBibn8yOgTccX5Bo0DzkT/qx9zJef4K4vFsdBOuoP8jGYefglAE29/RRkko7aDR9CwCHtVxeIKWpIN2HHtFy9WVGlrNSUdbV06pvt8RpIqUjbpPSE9Px9XVlcTE5Wi1jvd6OTIyMuVIehI8fTPStDonF6XyDhvcgYTj6WwYFIokQu0RPni38e6UWgAAg/VJREFU1uLgY4/STsCQLZIVk0vC8XQi/oxHEqHPn03w7eCWv332+rPcGLoQuxbV8DswOf/5BQsGlzqvY/IF2i6sh97ejT0v2VYHkBemBgyo60QjqP0t2iY5Gd57Dwyl+EoqlelOv4cHXHNczrEqI6mS04MON6wobn+IseYYg3Xvh4wMgEgeF11ncMH1EyTBgEp0oWHKF1TPfA6hgipERN1pjNfHIemOAiA4dUPl9wuCXU2r7DglnKb+lvFo444AkBLQjfO95pHjXqvY8QUjWQAeq88TPHkTdnEmNcPYiS24+kk3jFrLHCTJIJH3fTy5H8ZAjgSOCuw/8MPu5aoIyrJFAEUjhP/swKl3nTFkKVDYSzScnkn917NRyO2x7ik56TlM8ppEWloaWq3Wqm3lAKSMjMwDjbJAfN7moE8BqjTXMui/Fvh2cOP8whi2jz3L2t7H+afrMdb1O8HuF88T/ns83m3dGLSleSHHCsrQRDi/z1UZdiK/15XlNjIzS7+QB9Pr5qiLWdBClCNXFmPNMbb2/ZCRAVBgR7209+kWewL33LYYFBmc9JzIXu/uZKouVsycmsaogg+g9P4KBAekrB3owxtjTPwSyYpzUFaVxhwdcYBLXb/GqHLA/doOWi9pQsCRL4s9H94ueJE8tB4nTk4gfkxTAHx/PkZIyFzcNoZbNL+gErB/zQfn4w1RdnWBbJHcqdFkdTqP8UyOxftRHAol1Hkxh76hSfj0ykXMFTj9ngtb2nmQfEJOLrtfkZ0rGRmZBxpVgbt/5SVq4V7fiT5/NmFUdCcG72pBnz8a02NxQ/qsbMKg/5ozMsKkFujRqJiKd7MUu5U1V2JZa67gVt1VhQpa3EwLlGuuZGQqHVp9IzrH7aVR8jcoRUeSNLvY7teES9pZiFamC1uCIKhQer2GutYZBKfuIOVgjH8Tw+W2iLpTlhtSKLnW4lUOjT5DcmB3lIYcau9+kxbL2+GUUNTO7Q6W0d2BiHkDCNv0FLpgN+yjM2gw+A9qj16DKjHbsiXUtMdxc200PweBqxLxaDZZbc6h+yAGKde6m2W34xQk0mVdKm0XpmHnKZJ6Ss1/7T04+Y4zhrL5bzL3ANm5kpGReaBRFIxclUMquyRJiAYRSZJQOyrxbuVKjSFVqf2kDzUGV8G7jStqRyWSWHzGdb6gxb2MXFXARVT+FGYpdkGuG5CRqYwIKKmVMYXusWeomtMbUcglzP0tdvm0JtXueMXMaReMKmgrSr9fQeGGpDuGIaIFhvh3kUTdnQ3cROcWTOhjWznXez56eze08UdptbQFwXvfRWEobKeIoiCQ1r0Gocee4/qrbZAUAlVWnKFZk7l4/R5mcfNhu3FeOJ9sgGqgK+gl8j6LJavlOQwHyxYuFgSoPlJHv5OJBDymQzIKnPvSiU0tPLmxW84RvJ+QnSsZGZkHmoJpgeWhGLjtmTD+aHKQG0fTSx0nKErIxTdLsVvZ58osaKGQjBZdBBTPzahSBUauFGYpdjlyJSNTqXEy1KDdjU00S1yA2uhOmv0Jdvm05qzbOxix3OGxFEEQULqPR13rLILLUMCAmPgp+ohmiNn7rTFEbONxHBpzlhu1H0UhGqh+6FNa/dYM1+v7igy/3cESney4MrMnp/eMJqtRVdSJ2dQZ9Q/1hq7E7lrp53UzCj87HFbVxGFFMIK3CvGCjuwuF9C9ehUps2w3ljRVJTosT6PTX6k4+BvJDFexvacHR15wIS9Nbj58PyA7VzIyMg80CgUIgskZKQ/FwJTzWaRF5JCXZpuxskauoAzRKxtqrqyeIj9yJddcychUdgQEgrLG0iPmHP5ZTyAJRi66zmCHXwiJ9rsrZk61L+rAv1EF/AUqH5Nse2RHDLEvIRkzLLaT5+zLmUF/cXrQX+Q6+eCUfJ7mv3eizraXUOYVtmOOYhV0tDJb+XPq4Diuvt8ZUa3AY0M4ISFz8Z57DErIPCi0H4KAepg7zicbon7GEyTIm51AZshZDFvSLD8gJeA/MJe+oUnUfNaUthjxqyMbm3pyfa3tSoUydwfZuZKRkXngMcuxl0fN1fCjbZiY24OAnp62GVDdFLSwuonwrbSQMve6kmuuZGRkCqARvWmV+Dutb/yNvcGHTPUF9vp0IdRjEnrBsmiOtSi0j6KudRaF2xhAQkyejT6iIWLGRqvsJNR+lENjzhLTaBwCEtVCZ9NmUUM8Iou3U9DBkuyURE/vxMkjz5Le1h9VRh41X95Ew56/obmYZNH8gocKh/nVcdxQG6G6HdLVPLIHhJMzNhIxqWw3mexcJVr9lEH3rcm41DKQE6NkzzA39j3lii5evoSvrMjvjIyMzANPeTcSLgtmtUDJ6rTAcoxcVWDNlawWKCNz/+KXM5QeMeeonvE8AFEuP7PdryGxDmsrZD5B6Y7KfyGqoP9AXQP01zBc7Ych+mkkQ6LFdgwad873mc+Jx7aS4xqMJuMaIX/3o8GGp1FnF7Vze6pgToMqnNkxisvf9MbopMZ17zVCWvyC/8x9CBaKD6l6anE+3gC7l6uCAPplyWQ1CUP/ZzJl7XpUtbOePseSqPd6FoJS4toqDRuaehK1TGN7lrhMhSE7VzIyMg885rorg7588tWNetGiH8u8dAP6zNucDHPNldWRq4LOlW1eotJjCsqqnyCo79xE04yzs6lvUmmoVKZxAIJkTgusBJ7sfYI1x9ja90NGxlrsJDdCkufSIW47Tvqa5KiiOVR1EEe9niJXkVAhcyqce6KudRqF56uAgJi2DH14A4xpv1vlmKQE9eDQ6FNcbfEqkqDA59wy2iyqT9XzvxepVb3dwUKpIO7FVoSGTiCldzCKXCNB/9tJ4/YLcToRa9H8grMSzVcBOO6ph6KBBinBQM7ISHKGRSBG51m8H8WhcoCQGZn03p+Me4ievGQFB8e6smugG5mR8uV8ZUJuIozcRFhG5kFnpK8dGUkCP4bmEdigbKe88D/i2P3SBXota0RA7+JTAyVJQhAETn5zhbx0I01eCcDe3RQ+00ckcr3+TARne4KSP8nf5k5NhJEkun9t+gHdMzEOvZN3mfbDGpKTS++b5Ox8q2Ftqt0xdvq2xMFQjT7Xr92dBT4AWHOMrRkrI1MWDEI2510/IFz7FQgiaqMHjVO+JSDraQQqRlxBzD6EMeZZpNwzAAjOA1D5/WTVTSGA/7d339FRVdsDx7/33pnJpJPeKCHUhJLQmyBNAStPfXYBuz59Fp4+xWfvvmf/WbFh710UC02UXkJJ6KGnQHrPlHt/f4QEQgLMTGZIgvuzVtaS4dxzz0wkkz37nL2Dc5aT/Ms1BOWvByA/6Sw2j3+VmuD2jcYe2XgYwyDqg/Uk3vkb5sIqDE0h+7ah7Ll/JLq/a5X7jBqdmidzsf03F+wGhKhYn2yP+arIoxc8cpFuh43PBJDxWBB6jYIWYJD6WBldb6hC1Zo1tTioOU2EJbhCgishTnZTO1ooylV4YYWNzqnN+5E3/9pMirdUctoHvQnqYK1/3DAMaoocmIM0VLOCoiikP7OLjW/tY8Jnh3peOXYVsbfb4+BnIrHsiQZzHy/AGv2cBVW38+d1e5r8BaE1KDGvZX58Gn7OGCbtzfXq3FlZkH+MnUKRkZCU1HrmbQ1BkARtwhuKLCtYE3ENpZbanlIxlWeQWvgaAU73Ah5XGboNPf9JnPmP1p4RVYPRYv6HGnYtiuJ6lkZx2ui0/CkSlz6CqttxWILZPvIp9qVeD0fM0yjAAsx55XSe/iuRn2cCUNU1jO2vnUnpqE4ur8G5oYrqG3bhXF4BgDYyCOtrndC6WY9z5fGVbtFYcWMIBxZZAIgYamPwa6WEpkgrjOZqTnDV6to///777/zvf/9j1apV5OTk8PXXXzN58uRjXrNgwQKmT59ORkYGHTp04N5772XatGknZL1CiNavblug0wvvN+W7qwmM98McdPDs1MEsVVWeje/Gr2bIY13pfG4UAFH9g0l/1kFN8WFb5Oq2BTrdbzppqCbQ7c3rdeVj9dUC8e6be1YW/Pe/xx/373+7Fwj5at7CQrj/fnAc41tlMsHDD/suYHFnDdDy6xWtV5htEKNzVrIt5Gk2tXuQvIAfmWdNIbn4cZLKbkLx8ikTRbWgRd+PGnIBjuyrMaqW4sy5Ab3kQ0zxb6D49XBpHkOzsHPYfezvfj7JP19DaM4Sesz9BzGbPmbT6W9QGX5onsO3CdYFWvaYILZ8+DcOXNyLpH/+hP+2InqP/4Dca/qx64mxOEOPHyBpvf0JWNgD20v7qXkgG+eicioGZOJ3fzyW22JQTJ5nsUK6Oxn7axHbZvqz9j9BFCy18PPgCFJmVJB8ZwWaxeOpRTO0uk2aFRUVpKam8vLLL7s0fseOHZx55pmMGTOG9PR0brvtNq655hp+/vlnH69UCNFWqPVnrpo/l6NKR7OoqOaDb4gHE2G63aCm2N7gjJU5xIRuN3BUHQqk6gpa4HDt3NbhDjUSbr3nmdSD1QJ1L5+5OlZmyZNxvp63vPzYgQrU/v2xMkXN5c4aWsN6ReumYqZ76QzGZKcTXj0ch1rO+vBbWBQzijLTZp/cU7GmYOr8B1rs86AGYlQuwr49FeeBJzHcaClRGZHCqosXsWXMCzjMgbTbt4hB76XSadmTKE1UOjryPFbR2d1JX3s9udf0AyD2zTWkpc0k7Pstrj0PTcHv1hiC1qSgjQ+GaoOae/ZRMXwjzjWVLj+PJudWodsNVZyxtoD4M2rQbQobHgrilyHhFKxodTmUv4RWF1xNmjSJRx99lL/97W8ujX/ttdfo3LkzzzzzDMnJydx8881ccMEFPPfccz5eqRCirTCZaoMYbyR8AhP8KN9bTU1R7WR1e+dLd1ThqNQp232o+WbZjipMARqa9bAftebD/tvtXle1gUvbyFy13jUKITwX7EhmZN4i+ha8jEkPotD6J/PjU9kc+qhPmocrioYWcSvmLhkoQRPAqMG5fwaOrMHoVatdn0jV2Nv/FpZP3UBB4gQ0Zw1d/pjBwA8HE5TXeJ4jAyxnqJWsV85gw6+XU9U1DL99ZSSf/zndL/0Kc55rnzqonf0ImN0N65udIExDT6+iYvhGqu/bh1Ht/m6GwwW01xn5dTHD3ivBL0qnJMPMbyPDWXNXEI7mxW/CTa0uuHLXkiVLGD9+fIPHJkyYwJIlS456TU1NDaWlpQ2+hBAnL82Lmav2Y8PYv7yUXT/mY+gGjmon9kon2z7NQzUrbP98P7vn5FOZV8O6/9tDUHu/Bmez6poIAxgulvitH++lzJVhGBiGfvDLefCreW/sder7XEm1QCFOWgoqSeX/YGx2BjFVk9CVGja2u48FcYMosqz0zT0tnTB1/AktYRZoYRjVa3BkDcaRdzeGXuXyPNWhiaw97ycyJ76L3RpO8IF0Bn44mC6/341qbzhPU82HS0/txNpV17LvX8MwNIXILzaSljqTqPfXNapI2OTzUBQsUyIJWtcL03ntwAm2p3KpGJCJY5HrTZSbnhs6XVzNGevy6XRJFYausPm5QH7qF0Hub7JH8ERp88FVbm4uMTENq2bFxMRQWlpKVVXT/9ieeOIJQkND6786dPDNgUwhROtQ10TY6YVkSo8p8SSMC2PRLZv5cugK5l2ZyUc9FmMrdXDKCz3QrCo/nruW9zr+Qf7qMtL+1YmQRP9DE5gPK+XkZuZKb0bmyjB09IoFOLJvwLFjOPatSdg3x2HfkogjawDOvRfjLP4Qw7Hf7bkPV9/nSjJXQpz0ApwdGbp/NgMOfIjFGUGpZS0LY4ewPuxfOBTvp0sURUFrNxVz142oIRcCTvT8p7BvT0WvWOjOROT2msLSaZnkdb8Q1XDSacVTDH4/lXZ7jj+P7m9m1xNjWbf4Sir6RmMurKLb1d+TfPYn+O0sdmkJaoyZgE+64P9ZEkqcGX1rDZXjtlD1z90Ypc07s+oXYTDs3VJGfl2Ef3snFTtMLDgjjGXXhWAr8k2VR3FImw+uPDFjxgxKSkrqv/bskXLBQpzMDjURbv6biuanMubNFNL+1YnqQju5fxbTflw4gx/pQreLYxkzM5nBD3eh3x2dOHfBAJL+Ft3g+uZlrmqfiOpm5srQbTj2Xohj51j0kg9r5/AfjBo8CTXwVNCi0auW4dw3BcfuszHse92a/3B1mSsUHQPvZMOEEK2XgkKHyksZl51J+4pLQNHZHvIs8+NSOeC3wDf3NMVg6vAppg7fgCkebFtx7ByNI/sfGE7XdyPZA2PIOPtT1p37LTVB8QQUbaX/Z6Pp8esNaDUlDcY2lcWq6BfHuiVXseuR0eh+GmG/ZJHWbyaxL61wuWiReXIYQWtTMF8dWbum1w9QnpaBfXaxy8/jaBLOtHHG2gK6/aM20N0xy58fUyPY85Vfs+cWR9fmg6vY2Fjy8vIaPJaXl0dISAj+/v5NXuPn50dISEiDLyHEyauuoIXupQJ2/pEWhj7elcu3jWDK7pGMm9WrPjsV3juI/nclMuSxrkQPaOJni3bYj12npwUt3MsKOQ88iFH2PVrsc5h7FmNOWoKpw2eYEmZhav8B5sRfsHTfhanjtxi2LJy5/8IwPHux6poIg/crBgohWi8/PZqB+R8xNG82VkcCFeZt/Bk7htURV2NTi3xyTzXkXMxdM1HDrgdAL3oV+7YU9NLv3Jonv+s5LJ2Wyb6+tfMkrHudIbN6EbH9+ybHHx5gGWaNfXeNIH3ltZSc0gGtwk7S9F/oPfZ9/De6VglHaWfC/9VOBPzcDSXJgrHXTtXftlM5ZQf6geZtsTYHGwx4voxx8wsJ6eGgOlfjz4vb8cdFoVTltPkwoFVq86/qsGHDmDt3boPHfv31V4YNG9ZCKxJCtDbePHN1JEM3cNp1nLZDX8eqAqgoSn05dk8zV+6eudJLPkIN+wdaxK0oinbwzNXhX7Vnr9Tgs9CiHkQv/wkMm1v3qKMe1uHD2xUDhRCtX2z1GYzLzqBz2Y0A7A56m3lxvcjx/9Yn91O0UEzxr2FKnAeWruDYh2PPuTj2XOzWNmenXyibT3uN1RfOp7JdV6zl+0j95hx6/XAx5srG8xyZyaruEUHGb1ew/f8m4gi2ELJkL6mD3qT9Y4tQbK79rDeNCSFodS8s02NABccnhVT0ycD2YYHb1WWPFDXCzoQVBaTMKEcxGez92sqPfSPImmV15aiYcEOrC67Ky8tJT08nPT0dqC21np6ezu7du4HaLX1TpkypH3/DDTeQlZXFv//9bzZt2sQrr7zCZ599xu23394SyxdCtEJ12wK9XWSvNKuKbZ/msfqJnSy5aytL/r2VlY/sYPN7OeSvLcNe2fQb6uHl2N3haeYKvRTFHH/o/opyxJeKohxckxpQ27TTjTLHh2uYufLeCx4Z6d1xvp43KKi2L9SxmEy143zFnTW0hvWKk4fZCCW18BVG5i4iyN6dalMOy6InszzyAqpV7zYXr6MGjsHcZR1qxL8BFb30U+zbknEWv+9WYFLcYTTLp6xj16B/YygqMZs/Zeg7ycRmvn/UghX1mSxVIe/6AaSnX0/hGV1RbU46PvQ7fYe+TdCKfS7dXwlQsT7ZnsA/e6L28ccodFJ95U6qJm9D3+3Zh151NCv0faiC05cUEj7Qjr1EZfl1oSw4sx3lWdrxJxAuUYzmhsJetmDBAsaMGdPo8alTpzJr1iymTZvGzp07WbBgQYNrbr/9djIzM2nfvj333XefW02ES0tLCQ0NJT//I0JCArzwLIQQrcl9k8ysnasyfZad0Zc2/xxQyfZKlv1nO1lf70dRFTSrimpSUA5+XOWorM1gdTk/mkEPJNGuR2CD63dF3ItRVkNC5l2Yux76rf3tt8895n0Hvd+f4P1rSD/vRwo7T3J5vfZdk8C+G1OnX1DMCU2OMfRqcBbg2DUJTFGYOs5GUY/fIPNIOg6+61QbzZ6xJx+LHuH2HEeTlXXsflORke41+vX1vIWFx+4LFRTk+4a87qyhNaxXnHycShWbQh9iW8jTGIoTszOM3kXP0rFiKgq+Ka6gV63EmX0NRvVaAJSgSZjiXkWxdHJrnuC8VfT8+WqCD9TOU5A4kc2nvUZ1SNPz1DUfBsAwiPw0k87Tf8GcX4mhKuTcMpjdD4xCD3Stcp9hN7A9nUvNYzlgMyBIxfpoAuYbourbgHhKd8CWFwNY/2AQzmoFzd+gz4PldL+lElXiLKpKq7gx8kZKSkrcPj7U6oKrliDBlRAnt4fOMbFqjsatb9oZN6V5wVX53mp+u2ID+WvK6HtrRzqdFUlIZ38soSYUBWylTsp3VbNrTj5rntpJzLB2jHkjmaD2hwKV3bEPoBdWEr/2DizJh6qdHi+4GvDhEEJzl7N28ncUdDnb5TXrVatw7DoD0FFDL0MJGIZiigHFD/RKDEc2RtVK9JJPACemDt+gBp7i7ksDgIHBt51qo8yJe3Kx6jHHuUII8VdQbE5nTcRVlPitASCqajxphTMJdHT2yf0Mw46e/z+cBx4GowbUQLToJ1DDb0JRXN+4pTjtdFz5PxKXPIzmrMFhDiTrlCfY2+8maGKeBgEWYMqvpPO/fiXq4w0AVHdux/ZXzqBknOvP27mxiuobd+FcXAGANiII66ud0Hq6/wHYkcq2aqy4KYT9C2oDvvBBdga/Vkq7Pn/tiq/NCa5a3bZAIYTwNq1uF54XjgBt/zyPkq2VTPiiL4Mf6kLMoFD8Iy1oZhXVpGINNxPZL5gBMzpz2od9KEgvY+9vhQ0nqasYeIKqBar+AzAnzkcJGIle/CbOvZfj2DkWx44ROHadhjP7WvSSD1AChmNKXOBxYAW1lcOk15UQ4kjt7GmcmruMlKInUXUrB/x/Y15cH7YFP++T4jeKYkaLugdzl3SUgFNAr8CZewuOHSMxaja6PI+hmdk15B5WTFlLccIpmOwVdJ9/C/0/GUlAQeN5jqwo6IgMYOu755L57UXUdAjBuqOYXpM+ost1P6AVudafS0v2J2BeD6wvdIAgFeef5VQMzKTm8RwMe/NyJMHdnIz5uYhBr5ViDtEpXGHm5yHhrHsgEGdNs6b+y5LgSghx0vNmtcCyXdWEdPYnvFft4RNDb/zGph+sAhjeJwj/aAsV2Q3foerKsRsnqFoggGJNwdzxK8w99mPq/AemDl+itf8QU4evMCUuwNx9D+aOX6Nae7s995FUQ3pdCSEaUzHTvfQuxuasJ6J6FE61gg3ht7Mwdhil5g0+uafi1xNT4kK0uFdADcKoWox9exrO/Y9g6K6fYaoM78HqixayedzLOMxBtMtezOD300hc8giKs/E8hwdYAMWTurIm/TpybhyAoUDMrLX0S32d8K83ufY8VAXLjdEErUnBNDEEbAY1D2ZTMWwjzpUVLj+PJudWoMtVVUxaW0DCOdUYDoXMJ4L4eXAE+UvMzZr7r0iCKyHESe9Qn6vmzxUQ60dVvp3S7bV9Q5ra965qtY/lLi7GVuogMP6IniL1BS1OTLXA2oqADgzDQFEDUAOGoIb8DS30EtSQyagBQ1HUAAzDO32pFCRzJYQ4uiBHV07Jm09aweuY9FCK/VYwP64/m0IfRqd5RRuaoigqWviNmLtmogSdBYYN54H7cWQNQq9a4cZEKvvS/sGyaRnkdz4D1WkjafH9DPpgIMG5jec5sqKgHuzHjhcmsmH+FCq7R2DJraDnRV/S48IvMOeUubQEtZMf/t92xX9WIkqEhr6uiopTNlF9916Myub9DA9I0Dnl8xJGfFyMX7ST0o0mfhsdxqrbg7GXS/NhV0lwJYQ46Wl1wZWj+W8OHSdEYLKqLLxhEzu+O0B1gR1bqYOaEgfVhXaq9tso3lrJhlf2sPjOrbTrGUjC2IZVAOqqBRonqFqgc+8l2LelYBznlwh3ziEcc56DmStvVgsUQpxcFFQSy69jXHYmsZVnYyh2NrV7gPlx/Si0LPPNPc0dMHX8Dq39x6BFYtSsw5E1FEfuHRh6pcvz1IR0ZN3ffiDjjI+w+UcSlL+egR8NpeuCf6Ham57n8ExW2fAOrF15DXvuHoFuUon4ZjP9UmcSPSv9qBUJGzwPRcF8aQSB63phuigMdLA9m0fFwEwcC1wL0o4+N3Q4v4Yz1hXQeWoVGApbXw5gTv8Icn5xrRDHX50EV0KIk563+lwZhkFkv2BOebEHmr/Kz39fx/uJf/DZgGV8O3ol345ZxeeDl/NZ6lL+uH0LUf2DGfFMN4I7WhuUAlY0T89cHQyu3EzBGTUbwbYN9FK3rvNUXa8r6XMlhDgef2c8Qw58y8ADH+PnjKbMksnvscNYH3Y7DuUY5Ss9pCgKWujFtc2HQy8FdPSCZ7Bv64NePs+dichLvoRl0zLJ7XkpiqHTcdWzDHm3D2G7m56nQfNhq4k9D49m3dKrKO8fi6m4mq7XzSZl0kf4ZbnWdFmNMhPwfhL+X3dBSTCjb6uh8vQtVN2wC6Okefvg/cINhrxRyqmziwjo5KRip8bCs8JYemUINYWSxToWCa6EECe9uuDK2cxEiqLUvqHEjwzj/CWDOOunfvT5ZwdiBocQmOBHcKKV9mPDGHBfZ877cxBnfJtGeEpQ7XY85bA3I7NnTYT1um2BbvagMnddi6WXjho03q3rPCUFLYQQ7lBQaF95MeOyM+lQfgUoBttDnmdufG/2W3/1zT1NUZjaf4ip42wwtQd7Fo5d43DsuwbDWezyPPaAKDLP/JC1f5tNdVB7/Euy6Pf5OHr+fA2m6sbzHHkWq7JvDOv+uJKdT4zFaTXRbt5O0vrNJO75ZeB0bXeD+cx2BK3thfn6qNo1vZ1PeWoG9m9dfx5HE3eajUlrCuh+SwUoBjs/9OfHvhHs/txPmg8fhQRXQoiTXl1w5c0mwqpJpf3YcIY+3pXTPuzDmT/044xv0xj7di8GzOhM9MCQ+mxVg8AKUEwndlvgiaYgBS2EEO6z6BEMKHiPYXk/4e/oRJVpF4tjTmdVxDRsaoFP7qkGn4G5awZq2D8A0Ivfwr4tBb30K7fmKUg6g2XTMtibWjtP/Ia3GDIrmaitjec5sqIgJpXsfw1j7eprKTm1E1qVg87//o0+I2cRsH6/S/dXQjT8/68jAfO6o3b1w8i2U/X37VRevB09t3kfdJmDDPo/Xc7434sISXZQs19j8WXtWHReOyr3SShxJHlFhBAnvbozV94oxX40tUUjDn1B46CqnrluW6C7wZVnpdjduoduw6jZhqF7XoNXlcyVEKIZYqonMi57A51LbwZDYU/Qu/wWn8y+gM99cj9FC8EU/zKmxN/B0h0cOTj2nI999/kY9lyX53H6hbBl/MusumgRFWE98KvIpc9359P7u/OxVDSe58gsVnXXcDJ+uYxtr52BI9SP4JU59B3yFh0eXIhS49qHVaZTgglclYLlzljQwPFVMeWpGdjezae5rW0jh9iZsLyA3veVo5oNsmf78VNqBNve8MdL9ZBOChJcCSFOeiZz7RuKN6oFHo2iKA2+jjm2rhS7u9UCD0aJ7p65cuseNRnYs/pjVK/yeI664EoyV0IIT5mMIFKL/o9RuX8SbOuFTTvAiqgLWRZ1HlVatk/uqQaOxNxlLWrkPYAJo+wr7NtTcBa941ZgUtL+FFZMSWfnkHvQVRPRW79iyKwU4ja806hgxZEVBVEU9l/VjzVrr6fg7O6oDp0Oj/9B6qC3CFq616X7K/4q1scSCFycjJrmD0VOqq/dReWZW9F3Nq95leYHve+rYMLyAsIH2bGXqqy8KYR5p4dRtk1r1twnCwmuhBAnPbWu8nlr+V3/4LZAtzNXSt22QDcLWjhL3chEGWA4ar88VLctUDJXQojmCrcNY3TOKnoU349imMgJ+Jq58cnsDHoTA+8f+lFUK6aYxzB1WYli7Q/OIpzZV+HYdTqGLcvleXSTlaxTHmPlZSsoje6PubqI5J+vIu2L07CW7GjymsMzWfb4YDZ/cQGbPz4PW0wgAZvy6XPqu3S+/WfUctfK1Wv9AghcnIzfYwlgVXD+VkZ5v0xqXsxzu8/ikUJ7ORn/eyH9ni5DCzA48LuFOQMi2Ph0AD7cXNEmSHAlhDjpaV5sIuwNSl1BC0/PXBnuPRHH7jOxb++Ls+B5DNtODL2mUU+rQ39WAQUMz98d6wtaSOZKCOEFGn4klzzE6JxVtKsZhEMtJT3iWv6MGUe5aZtP7qlaUzElLUOL+S8oVoyK37Bv64Mz/zkMN34Gl0enseqyZWwb9V+cJivhu+cyZFZvOqx6rsk3pQZbBRWFgvOTSV97Pfuv6ItiQNzLK0nrN5N2v2x36f6KScHvzlgCV6agjQyCCp2aO/ZSeepmnBlVLj+Ppqga9Lilkklr8okZW4OzSmHtPcH8eko4RWtNzZq7LZPgSghx0jvURNi75WMPP1/ljro+V+6WYtc9bCKsBp8DehnO3Duwb03CsXMMeuErGLYsDL3yYDXDg28Hilbb6KQZwZV6sImwlGIXQnhTqL0vp+YuoXfhM2i6P/nW+cyP68vW4Gd8sg1ZUUxokXdi7rIOJeBUMCpx5k3HsWMEenWGy/MYqondg+5k+ZT1FHUYjeaopNuC6Qz4eDiB+RsajT/yLJYj3J9tb51NxuxLqE4MxbqrhJSzPqHrVd9hKnCtP5fW3UrAr92xvtwRQlScyyuoGLyRmkeyMWqad2AqqLPO6J+KGfxmCZYwnaI1Zn4ZFs7ae4NwNC9+a5MkuBJCnPRUL5ViP9zXp67kdb957Poh3/2LD/a5Mlwss1vH02qBWuSdWHpkY+r8O2r4PzAc+3Dm3op9a3ccuyahF83EqNmCoVcDBmACmpO5kibCQgjfUNDoWjadsTkbiKoah1OtIiP8Dn6PHUqxOd039/TrhilxHlrc66CGYFQtw5HVD8f+B9wq/lMV1pU1f5/LptNex2EJITR3OYPe70/nPx9AcTScp1FFQaDktCTS11xH9j8HYSgQ/cF60lJnEvF5pmvNh1UFy7VRBKX3wnRGKNgNah7JoWLwRhzLmtdTTFEgaUo1k9YW0H5yNYZDYeN/A/l5QAT7/zA3a+62RoIrIcRJz+SDaoF1NSt0uweZK5Nnfa7qqwV6WNBCDRiOKe4lLN13YUqci9puGoZ9F86cG7FvS8Gx52/oJZ+DUUlzSj9J5koI4WuBjiSG7/+VtII3MOmhFPutYmHcQDLb3YuT5hVtaIqiqGjh12HumoESfDYYdvQDD+PI6o9eudSNiVSy+17H0mmZHOhyDqpup/PShxn0QX9CshvPc2SApQda2PnM6az/fRqVyZFY9lfQ47Kv6Xn+51j2udYoXm1vwf/rLvh/0Bkl2oS+sZrKUZupvmMPRkXz9s/7x+qc8lkJp3xWjH+8k7JtJuaNDWflP4Oxl/41mg9LcCWEOOlp9dsCvTenaq59k9AdHhwKrtsW6O6ZK82zbYFNUQNHY0p4E3O3LEwdf0QNvQSjZhN64XO1xSwUz98epImwEOJEUFBILL+G8dkbia+4AENxsiX0MebHp1Hg94dv7mluj6nDt5jafwZaNEZNJo4dw3Hk3IrhdD37YwtOYP2537DhrE+xBUQTVJDJgI+H023erWi2hvM0qigIlA9JYO3yq9lz70h0s0r4D1tJS51JzBurQXchi6UomC8MJ3BtL8yXhYMBthf3U94vE8dvrgVpx9J+cg2T0gtIurJ2X+C21wP4MS2C7B8tzZ67tZPgSghx0qsraOHN4Kou+6S7WfHv8Gvdzlx5WC3wqPMdPGulBk/E1P59zF03Y0r4CCXoTNAiPJ5XrW8iLMGVEML3rM44Bud/zqADX+DnjKHcvIlFMaNYG3YzdqXM6/dTFAU19O+Yu2aihl4BGOiFL2Lf3hu9/Bd3JmJ/jwtZOi2TnJQpKBh0WPMig9/tTfjOn5u85PAAy/Azsef+UaxbdjVlg+MxldbQ5aaf6HX6B1i3Frq0BDXChP87nQn4vitKRwvGThuVZ2yl6uqdGIXN29ptaWcw+PVSxvxSSFAXB1V7NX6fHMbiy0OpPnDyZrEkuBJCnPQ008E+V16sFliXuXKzcF8tTzNXHlYLPJq6fly1hTmcoJhRQ87B3Ol71IDhns9bn7mSM1dCiBMnofJ8xmVvpFPZ1aAY7Ah5mXnxvcm1/uiT+ymmCEzt38PU6WcwdwL7Lhy7JuDYNw3D4VpwA+Dwj2DjpHdJP/9nqkI64V+6i7QvJ5I8ZxqmqoJG44/cKljZO5r1C6ey4+nTcAaYCf19N6kD3iD+6SUuv8+YJoQStCYF8z+iQAH7+wWUp2Zg/6rI5edxNDGj7UxcVUCP2ytQVIPdn1n5KTWSXZ9YXTkq1uZIcCWEOOn5ZFugVrct0IPM1cHgytMzV540ET5WZcPaxsfacZsfu+pQE2HJXAkhTiyLHka/wjcZnvcrAfbOVJl2szTmTFZFTMGmNg5UvEENOh1zlw2o4bcACnrxu9i3p6CXfO5WRdnCxNNZPnUDe/rdgoFCXMa7DJ2VQvTmz5psPtyAppJzy2DS11xH8fjOaNUOEu+ZR98R7xCQnuvS/ZVgDf/nOxKwoAdqTytGnoOqi7Oo/Pt29GzXemsdjSkA+j1Vzml/FtKuj52afJUlU0L5/dx2VOw6ucKRk+vZCCFEE+q3BXozc2Vqxpmrg9sC3c1c6fWZK/cyQoZtO/qBhzEqfmv8d85yDPue2rLsNZsxajaiV63BcBa7dY/DHWoiLJkrIUTLiK4ez9ic9XQpnQ6Gyp6g9/ktvid7Aj7yTfNhLQhT3AuYOv8JfsngyMOx90IceyZj2Pe5PI/TEsTWsS+w6pI/KY9IwVK5n94/XESfbydjKWs4T1MVBWs6tyNz9iVse+MsHO2sBK3JJXXY23S8dz5KtWs/k03Dgghcnozl7lgwgePbYspTM7G9k+9R+5HDhQ9wcNqSQnrfX45qMciZ48dP/SLY+pp/c+ootSoSXAkhTnqm+jNX3tvjXV/Q4kRWC9Q8qxaol83BWfgiGNW18xh6fRNMvWgm9i2dsG/tin1bMvZtvXBkDUAv/sCtexxOkcyVEKIVMBmB9Cl6hlG5iwmx9cam5bMq6jKWRZ1LleZ6wOMONWAY5qQ1qFH3g2LGKPsO+7YUnIVvuBWYlMYPY8Xlq9kx9H501UTU9u8YOiuF+HVvNKrm2iiLpSjsn5rKmnXXk39eTxSnQfv/LiZtwBsE/7HbpfsrVhXrwwkELk1GHRgAJU6qr99F5YSt6NuqXX4eTdEs0PveCiasKCByuA1HucqqW0KYOzaM0k1as+ZuDSS4EkKc9HzR50ppRuZK8fTMleJp5morijkJxdKzbgXU/fhXg89A8R+IEnwWWvzbaFEPghrk1vxHUiVzJYRoRcJtQxids4rk4kdQDDO5Ad8zNz6ZrKBXMPB+ukRR/TBFP4QpaTWK/2DQS3HmXIdj5xiMmq0uz2OY/Ngx4iFWXLGGktjBmGyl9Pz1Ovp9Pg7/oobzNFVR0B4bxJZPzmfTZ+djiwvCf2shfca+T9I/f0Irda1cvdY3gMBFPfF7qj34KzgXlFHeP5OaZ3MxPNm5cZjQZCfj5hXR//lSTEE6+YstzBkYQcaTAXipblOLkOBKCHHSq9sW6M0+V/XbAj3IXNVtCzQc7p65OhhcuXvmSq8A1Q/U4PqH6s9XaVGgV6FaB6GFTUMNuw5M8aB7XmGrvomwlGIXQrQSKhZ6lNzLmJw1hNUMxaGWsS7iJv6IGU25aYtv7mntjanzYrSYZ0AJwKhciH17X5z5T2O48SFZRWRvVl2ymK2jn8VpCiBszwIGv9eXjiv+12RT+SMzWYWTe7Jm7fXkXZUGQOzrq0lLe52wH10L9BRNwe/2GIJW90IbEwzVBjV376PilE0411W6/DyanFuF7v+oYlJ6AXETa9BtCuvvD+bnIeEUrjI1a+6WIsGVEOKkV9dEuIn3II+p5roAyZNtgQcLWrhdLfBgQQs3M1dooeAsAb226lODwhXO/RjOYgwOzmlU1f2Fe/c4TH0TYSRzJYRoXULsvRiV+wd9C/8PTQ+kwLqIefF92RLyhE+2MiuKhhY5HXPXDSiB48Goxpl3J46soejVa12fSNXYM+B2lk3bQGHH8WiOarr+/m8GfDSUoP2N5zkywHK2s7L9tTPZ8PNlVCe1w29vGcmTP6PblG8wHahwbQld/AiY0w3r650gVENfXUnF0I1UP5iNUdO8DGBgR51R3xYz5O0SLBE6JRvM/DoinLX3BOGoOv71rYkEV0KIk15dtUCvZq7qz1x58IZyMDDDwzNX7mauFP+BGPad6KXf1c5jOOs/NXUWfwTO/ah+vQ+O1gADQ/f83UyaCAshWjMFjaSymxmbvYGoqtPQlRoyw+5hYewQii2rfXNPS2dMnX5Bi38L1HYY1atwbB+II+8/GLrrZ5iqQzuTfsEvbDz9Lex+7QjJW8XADweS9Md/UB0N52lqq2DpmETSV1/HvulDMVSFqE8y6Nf3dSI/2tCoImGTz0NRsFwZSdC6XpjObQcOsD2eQ8XAjTgWu95Euem5ofPl1ZyxLp+OF1Zj6Aobnw5kTv8I8uabmzX3iSTBlRDipFff58qbmavmnLmq3xZ4Ys5cqUFnoQafi3P/DOx7LkAv+QC9+H3su89Bz38MNfQylKDxBxdnQTHFoChWt+5xuPpqgZK5EkK0YoHORIbv/5n++e9idoZR4reGhbGDyWh3F07F++kSRVHQwq7C3HUjSvB5gAM9/3Hs21PRK/5wZyJy+lzFsmmZ7O92HqruIHHZ4wx6L43QvcefRw8ws+vJcaz/YxoVfaIxF1TRfdq3JE/+FMueUpeWoMaZCfi8C/4fJ6HEmNA3V1M5ZjNVt+3GKGteaV5rlMHwD0o45Yti/BOclG83MX9COMtvDMZW3PqbD0twJYQ46fmkz1UzqgVycFsgbma9dA+rBSpaEFrMU6jtpmGUzcaZfS3OnBswKhaghl2DFv04ihZWO1gLQ4u6DyXkXLfucbj6PleSuRJCtHIKCh0rpjAueyMJFRdhKE62hv6X+XFp5Pv97pt7mmMxd/wSU4cvwRQHti04do7CkXMzhtO14AbAFhTHhnO+ZP05X1ITGEtg0WYGfDqS7r/dhFbTcJ6msljlA+NZt/Qqdj10KrpFI+yn7fRLfZ3Y11aC7tp7m/n8MILW9cI8LQIMsL9ygPK0DOxzSlx+HkfT/pwazlhbQNfras91Zb0VwI+pEez91q/Zc/uSBFdCiJNe3Zkrr1YLPNhE2HDxDajBtXXntZweZq48ODymmBMwJbyNuUcOpsSFmBIXYO6+G1P8TBRz7KFxqh9q0Gmo1r5u36N+jrptgZK5EkK0EVY9hkH5nzBk/3dYHfGUm7fwR+yprAm/DrvS/EChKWrIeZi7ZqK2uxow0Atfxr6tF3rZbLfmOdDtPJZNyyS799UAtF/7CkNm9SIi68cmxx8eYBlmjX0zTmHtimsoHdYerdxG0i0/03vc+1g3u9Z0WQkz4T8zkYAfu6F0tmDssVN1zjaqpu1Az2/e+4A5xGDgS2WM/a2Q4K4OqnM0/vh7O/68JJSq3NYZxrTOVQkhhBfVNxF2eLHPVbOqBdZlrjysFtiMGrWK1g41YBhqwDAUrV2zG0I2pa4Uu2SuhBBtTVzV2YzNziCx7DoAdgW/wdz4XuT6/+CT+ylaO0wJb2Lq9CuYk8CxF8fus3DsvRzDke/yPA5rGJsmvMmaC36jKjQJa/leUr8+k5QfL8dc2XieIzNZVcmRbJg/haznT8cZaCbkzz2kDXyDhCf+QHHxvco0PoSg1SlYbosGFewfFVLRNwP7p4XNfq+JHmVnwqoCkv9dgaIZ7PnSyo99I9jxntWVo2InlARXQoiTnk9KsR/MPnlS0KI+c+XmtfUFLbxY9rBB5UBvzVmfuZLgSgjR9liMdqQVvs4puQsJtHel2rSPpdFnsyLyImrU/T65pxo0HnPX9agRdwAqesmH2Lf1xFn8kVuBSVGncSybup7dA/6FoajEbvyQIe/0JGbjR0ctWFGfyVIVcv8xiPT06yma2AW1xkmnBxbSd9jbBK7Ocen+SqCG9b8dCPi9J2ovK0a+g6ordlB13nb0vTaXn0dTTP6Q+mg5py0uJKyfHXuxyrJrQll4djvKd7aekKb1rEQIIXykPnPVSvpc1Re0cDdzpTQ/c3UiSOZKCHEyiKwZxZictXQtuRPF0NgX+Blz41PYHfg+Bt5PlyhqAKbY/2HqvATFrw84C3DuuwzH7rMx7Htcnkc3B7Bt9NOsvGQJ5ZF9sFQX0OvHy+j79Vn4lTY9z+FbBWs6hbLx24vY8s452CP8CVy3n77D36HT3XNRK137uW4aHEjgsmT87o8Ds4JjdgnlqRnYZh7waDv94cL7OTjtz0L6PlqG6meQ+4sfP6VFsvnFAPTm1dLwCgmuhBAnvbrgyps/dOsLWnjSod58cFugu2eufJC58oVDpdhb9zqFEOJ4TEYAvYv/y6m5ywmx9cWmFbA6cgpLoidRqe32yT3VgMGYuqxCi34EFAtG+Wzs21JwFr6KYbj+vlEWN5gVl68ia8Qj6JqFyB0/MuTdXiSkvwLHm0dRyL+sD+lrr+fAhSkoukHCs0tJHfgGIQt3uXR/xaLid288gcuT0YYEQplO9c27qTx9C84trpefb4pqgpR/VzJxZQFRo2w4KxXW3BHM3DFhlGRozZq7uSS4EkKc9HzR50ppVubqYBNhNzNX+sEmwmorz1zVlWL3RUNOIYRoCe1s/Rmds5KUosdRDT/2+//MvPheZAW/hNGMputHoyhmtKh7MSetQfEfDno5zpx/4Ng5GqNmk8vzGJqZnUPvZfkV6RTHD8dkK6PH3Jvo/+loAgo3NxjbVEVBe3QgWz/4Gxu/vpCahGD8txXR+7QPSLpxNlqxawGS1sufgAU98Hu2AwSoOH8vp2JAJjX/zcXw5NzyYUJ6OBn7SxEDXynFFKxTsNTCz4MjWP9wIM7m7UL0mARXQrRxhuGkpGQ9Bw78TknJegyjFeTEW5m6PlfeTPjUbQs0nJ4UtDj4o9fdzJXqebXAE0k16vpcyf+LQoiTh4qZ7qUzGJO9lvDqETjUctaF/5PfY0+h1Jzpk3sq1hRMnRehxb4IaiBG5SLs21NxHngcw3D9A6zKiGRWX7yILWNexGEOpN2+RQx6L5VOyx5vsjH94QEWQNGZ3UhPv47c6/oDEPtWOmlprxP23eZG1zb5PDQFv5ujCUpPQTstBGoMau7dR8WIjTjXVLr8PJqcW4Wu11RxxtoC4s+sQbcrZDwaxC9DwslfduKbD0twJUQbVlCwhJUrr2PDhvvYsuVZNmy4j5Urr6OgYElLL61VMfkgc9WcPleHzlx5WordsydiGA7sO0ZizxrqVi8VdynUbQuUzJUQ4uQT7OjByLzfSS14BZMeQpHfUhbE9WNzyGPoeD9doigqWsQ/MXfJQAmaBIYN5/7/4MgajF612o2JVPb2/yfLp2VQkDgRzVlDlz/+w8APBxGcu7LR8CMzWc5QK1kvTWLDb5dT1TUcv+xyki/4gu6XfIU5r9ylJaiJfgT80BXrW4kQpqGnV1ExfCPV9+zFqHK/QNThAtrrjPyqmOEfFOMXqVOSYea3UWGsviMIR0WzpnaLBFdCtFEFBUvYtOkpbLaGfShstgI2bXpKAqzD+KaJsOfVAuvPXLlb0KLZZ65UjMo/MKqWgVHj4Rwu3EWaCAshTnIKKp3Lb2RcdgYxlWeiKzY2ht3LgrgBFFlW+Oaelk6YOs5GS3gPtHCM6nQcWYNw5P4bQ69yeZ7qkE6sPe9HMia9j90aTvCBtQz8aAhdFv4b1d50FunwTFbpqE6sXXUNe+8cjqEpRH65kbS+rxP13rqjViRs8DwUBcsVEQSt64XpgjBwgu3pPCoGZuL4vczl59H03NDxwhrOWJdP4uVVYChseTGQn/pHkPubpVlzu0qCKyHaIMNwkpX15jHHZGW9JVsED6ovaKEr6M37YKxefbVAD7YF1meuHB5mrgzPgitFUan/se/hHC7dh7ptga17+6IQQjSXv7M9Qw98z4D8D7A4Iym1bGBh7FDWh/0Lh+L9dImiKGjtrqhtPhxyEaCjF/wP+/ZU9IqF7kxEXsrlLL1yI3k9LkYxdDqt/B+D30ul3Z4FTV5yeICl+5vZ/dgY1i2+ivK0GMxF1XS75nuSz/oEv53FLi1BjTET8FES/l90QYkzo2+toXL8Fqpu2oVR2rzfX/wiDYa+Xcqo74oI6OCkYoeJBWeEseyaEGxF3m9BcjgJroRog0pLMxtlrI5ks+VTWuqbPeBtjXbYlmunl37fb1Yp9uZmrpqTglMOvhhu7NV3l2SuhBB/JQoKHSouY1x2Ju0rLgVFZ3vIs8yL68MBv/m+uacpBlOHTzB1+BZM8WDbimPnaBzZ12M4S1yexx4QTcZZH7N28ndUByUQULyN/p+Nocev16PVNJ7nyLNYFf1iWf/nlex6dAy6n0bYr1mk9ZtJ3P8td/lcsfmcdgStTcF8TWTtmt7IpzwtA/sPxS4/j6OJn2hjUnoB3W6qBMVgx3v+/JgawZ4v/XzWfFiCKyHaIJutyKvjTnZ1mSvwXlGLumqBRjNKsbubuaqrFuhp5qr24roXw4eZK2kiLIT4C/LToxiY/yFD9/+Av6MjleYd/Bk7ltURV2NTC31yTzXknNosVtj1AOhFM7FvS0Ev/dateQq6nM2yaRnsTb0BgIR1Mxk6K4XIbY3nObKioGHW2Pfv4aSvupaSkR3RKux0/tev9Bn9Hv4ZB1y6v9LOhP8rnQj4tTtKFz+MvXaqzttO5WVZ6Aea915iDjYY8FwZ4xcUEdLDQXWuxp+XtOOPC0KpyvF+KCTBlRBtkMUS5tVxJ7vDgytvFbVoTuZKiwjAelp3/IZ1cuu6+mqBzTo8dvDF8GHmSpEmwkKIv7DYqjMZm72BzmU3ArA76G3mxqeQ7f+1T+6naKGY4l/DlLgALF3BkY1jz2Qcey7CcOx3eR6nXyhbxr/K6gsXUBnWDb/ybPp+O5le31+EuSKv0fgjs1jV3SPI+PVytr80EUewheBl+0gd/CbtH/kdxebaTg3TqcEErUrBMj0GVHB8XkRF3wxsHxRgNDPVFDnMzoQVBfS6pxzFZLDveys/9o1g+1v+Xs1iSXAlRBsUEpKCxRJxzDEWSyQhISknaEWtm0+2BdYVtPAgc2XpG0/s7GuJfOUCt66rC65Uw+nSoeEmHdwWaPjwzJWUYhdC/NWZjWBSC19hZO4igm3J1Gh5LI8+j+WRf6day/HJPdXAUzF3WYcaeTegoZd+hn1bMs7id90KTIo7nMryK9aya9Bd6IpGzJbPGDorhdiMdxu99zTqjaUq5F03gPS111N4RldUu07HRxaROvgtgpbvc+n+SoCK9cn2BC7uidrXH6PASfVVO6k8Zxv67uZVY9Ss0OfBCiYsKyR8gB17icqKG0OYPyGM8izvNB+W4EqINkhRNJKSrjnmmKSkq1GUlu1S3lpoGihK7RuCtyoGHirF7qUKGS4w1ENRoscVA0/AmSspxS6EELUiak5hdM5qupfcg2JoZAd+wdy4FHYFvoOB9w/9KKo/ppgnMCUtR7GmgrMQ575pOHZNxLDtdHke3ezP9lFPsvKy5ZRFpWGuLiRlzjRSv5yItaTpeQ7PZNnah7Dp6wvZ/P5k7FEBBGQeoM+od0m881fUCtcCJK1/IIFLkvF7OB78FJw/l1KeloHtlf0YevNeu3Z9HIxfVEjaf8vQ/A32L7DwU78INj0b0OzjAxJcCdFGRUQMo2fPuxplsCyWSHr2vIuIiGEttLLWqW5roNcLWnhy5spDdZkraE5wVTeH77JKiiHVAoUQoo6GlZTixzg1ZyXtagZg14pZE3kVi6NPp8KU5ZN7qv79MSWtQIt+AhQ/jIpfsG/vjbPgRbcqCZfH9GflZcvZfsoTODU/Inb9wuB3e9N+9QugN56nwVZBRaHgol6sWXc9+y/tjaIbxL+wnLT+bxD6m2vPWzEr+N0dR+CKFLThgVCuU33bHirHbMa50fXy801RTdDztkomriogerQNZ5VC+t3B/DYynJIMzz+cluBKiDYsImIYAwfOpHfvR+jefTq9ez/CwIGvS2DVBM3LjYSVZpy58lTDzJWnT8T3Z65UpFqgEEIcqZ09jVG5S+lV9F9U3coB/9+YF9ebbcHP+WQbtaKY0aLuxtxlHUrASNArcObeimPHSIxq16sJG5qZXUPuZvmUdRS1H4XJXkH3+bcx4JNTCChoPM+RZ7EcEQFsm3Uumd9dRE3HEKw7iul1xsd0ufZ7tCLXAiStp5WAeT2wvtgBglScSyqoGLSRmsdzMGzN20ES3NXJmJ+LGDyzBHM7ncJVZn4bG+7xfBJcCdHGKYpGaGgfoqJGERra55hbAQ3DSUnJeg4c+J2SkvV/qT5Y9b2uHN7pb1G3LdCjaoEe8k7mqm5boC/PXNVtC5TMlRBCHE7FRLfSOxmbs47I6jE41So2hE9nYewwSszrfHJPxa87psQFaHGvghqMUbUEe1Y/nPsfxtBdP8NUFd6dNRfOZ9P4V3FYggnNWcrg9/uRuORhFGfDeY6sKAhQPLEra9ZcR84/BmIoEPPuOvr1fZ3wrza59jxUBcsN0QSl98I0MQRsBjUPZlMxdBPOVc3rKaYokDStmjPSC0g4u7pZmztabXD18ssvk5iYiNVqZciQISxfvvyoY2fNmoWiKA2+rFbrCVytEK1fQcESVq68jg0b7mPLlmfZsOE+Vq68joKCJS29tBPC25mrFtkWeFjg7GnmSqnfFngCqgVKKXYhhGhSkKMbI/J+I63gdUx6CMV+K1gQN4CNoQ+i07yiDU1RFBUt/AbMXTNQgs4Cw4bzwAM4sgaiV61wYyKV7NQbWDY1g/yks1CdNpIWP8CgDwYQnNP4d/UjAyw92I8dz09gw/wpVPaIwJJXQc+Lv6TH37/AnFPm0hLUjhb8v+2K/7udUSJN6BuqqBixieq79mJUNi+L5R+vc8oXJQx52/VeYY3W16wV+Minn37K9OnTeeCBB1i9ejWpqalMmDCB/fuPXk4yJCSEnJyc+q9du3adwBUL0boVFCxh06anGjUettkK2LTpqb9EgFV/5sprBS08rxZ4OMMwMHQdQ9dr96/rTtCP8uagKOh15dhbc0ELQwpaCCHE8SioJJZfx7jsjcRVTsZQHGxu9xDz4/pR4LfYN/c0d8DU8Tu09h+DFoVRsx5H1lAcudMxdNezPzUhHVg3+Ts2nPkxNv8ogvI3MPDjYXRdMB3V3nCeRhUFgbLhHVi74hr2zBiBblKJ+HYz/fq+TvQ76S5Vw1UUBfMl4QSuTcF0URjoYHsuj/L+GTjml7r8PJqeG9qf43mA2yqDq2effZZrr72WK6+8kpSUFF577TUCAgJ4++23j3qNoijExsbWf8XExJzAFQvRehmGk6ysN485JivrrZN+i6CpLnPl7YIWHlQLNHSdqoXbyb/pS3JHvcTeHk+yp8PDDP/PGAY9Npneb95GzLJvMZcWNL724LkrtTWfuTIkcyWEEK7yd8Yz+MBXDDzwCRZnFGWWTBbFnMK6sFtxKOVev5+iKGihF9c2Hw69FNDRC57Dvq0PevlcdyZif8+LWTYtk9zky1EMnY6rnmPIu30I29X0PA2aD1tN7HloNOuWXkX5gDhMJTV0vX42KRM/wm97kUtLUKPMBLyfhP+3XVHamzGybFRO2ErVdTsxilpma3qrC65sNhurVq1i/Pjx9Y+pqsr48eNZsuTon66Xl5fTqVMnOnTowLnnnktGRsZRx9bU1FBaWtrgS4iTVWlpZqOM1ZFstnxKS10/3NoW1R1XaqK4kYfzebYt0LA5OHDJB+Sd/joVH68BwG9gBwImJVPcfTC20CiCd64n+d27SX35OvwKG/ZDMZqduaoLrnxYLfBgAGcoJ3fALoQQ3qKg0L7yIsZnb6Jj+TRQDLJCXmRufG/yrD/75p6mSEztP8TU8UcwdwD7Dhy7xuPYdzWG07XgBsAeEEnmGe+Tft6PVAd3xL9kB/2+GE/POVdhqm48z5FbBSv7xrBu0TR2PjkOp7+JdvN3ktZ/JvHPLQWHax9gmieFEpTeC/P1UbVrmlVAeVom9m+LXX4e3tLqgqv8/HycTmejzFNMTAy5ublNXtOjRw/efvttvv32Wz744AN0XWf48OHs3bu3yfFPPPEEoaGh9V8dOnTw+vMQorWw2Vz7AenquLbKZPJunytPqwUWP/wrlbMzCX/6bDoeeJi4Rf8k+uMriHzzIjKvfJq1t7zNksfns/6GV7AW7KXrF082iAgPBVcePpG6bYG+PHNVty1QMldCCOEWix5O/4J3GJY3B39HJ6pMu1gSM5FVEdOwqcf+oNRTavAkzF0yUMNvAkAvfhv7thT00q/cmqew8ySWTdvA3rSbMFCIz3iHIbNSiNryZaOxRwZYmFSypw8lffV1FI9JRKtykHjXXPqOnEXAujyX7q+EaPj/X0cC5vdA7e6HkWOn6u/bqbx4O3ruiXs/anXBlSeGDRvGlClTSEtL49RTT+Wrr74iKiqK119/vcnxM2bMoKSkpP5rz549J3jFQpw4FkuYV8e1VXUFLbzW58rDaoHln64h5IbhhPxzJIqm1p65OviFYdSet9KdFPQdw46zbiEi43fUw6pw1G0LbO6ZK8OX1QLrS7FLtUAhhPBETPUExmVvIKn0VjAU9gS9y2/xyewN+MQ3zYe1YExxL2Hq/AdYeoAjF8ee87HvPg/DnnP8CQ5yWoLZMu4lVl+8iIrwnvhV5NLn+wvo/e15WMobztNURcGaLmFkzrmUba+fiSPUj6BVOfQd+jYdHliAUuPae4ppRBCBK1Ow/DsWNHB8VUx53wxs7+bXvtf6WKsLriIjI9E0jby8hlFqXl4esbGxLs1hNpvp168f27Zta/Lv/fz8CAkJafAlxMkqJCSlUaPhI1kskYSEpJygFbWMuoIWXq8W6GbmyiitRos79DPn8CqnKAqoKqi1VQF1sx+K7mgQSDU7c3UCzlzVNxFW7D75JUAIIf4KTEYQfYueZ1TunwTbUrBpB1gZdQnLo86jSsv2yT3VgBGYu6SjRv4HMGGUfY19WwrOonfcCkxKEkaw4oo17Bh6L7pqInrb1wyZlULc+rcbFaxoFGQpCvuvTGPN2uspOLcHqkOnwxN/kjrwTYIXu5YQUawq1kcTCFySjNo/AIqdVF+7i8oztqJn1bj8PDzR6oIri8XCgAEDmDv30EE4XdeZO3cuw4a51hjV6XSyfv164uLifLVMIdoMRdFISrrmmGOSkq4+Zn+sk0FdQQun3Vt9rjyrFug3uCPl763Ese/oZV5VWzWWolw6zHuXkqR+GNqh5sG6lzJXJ6KJMOCTxphCCPFXEm4bxpicNfQsfhDFMJET8A1z45PZEfQ6Bs0rPd4URbViinkUU5dVKNaBoBfjzL4Kx67TMGzbXZ5HN1nZMeIRVly+itKYgZhrikn+5WrSvhiPf3HjeY4MsuzxwWz+/AI2fXI+tphAAjYX0HvMe3S+7WfUMtcCJC0tgMA/euL3eAJYFZxzyyjvn0nNi3kYTt98+NfqgiuA6dOn88Ybb/Duu++yceNGbrzxRioqKrjyyisBmDJlCjNmzKgf//DDD/PLL7+QlZXF6tWrufzyy9m1axfXXHPsXyiF+KuIiBhGz553NcpgWSyR9Ox5FxERrn1w0ZapPspcGU7DrU/z2j00EWdBBdmDnqPgX99S/mk6VQu3U71kJ2Eb/yR26dd0+fp/DH78b1hK9rPj7FvQzX7119dlrjyuFqicuMwVSDl2IYTwBhULPUseYHTOKtrVDMKhlrI24gb+jBlHuanpnVrNvqe1L6akJWgxT4FixaiYi31bH5z5z7pVYbgiqi+rLl3C1lH/w2nyJ3z3PAa/24cOK59tssrUkVsFC8/ryZp115M3tS+KAXGvrKRfv5m0m+Pa81ZMCn53xBK0OgXt1CCo1Km5Yy8Vozbh3FDl8vNwlen4Q068iy66iAMHDnD//feTm5tLWloac+bMqS9ysXv3blT1UFxYVFTEtddeS25uLmFhYQwYMIDFixeTknJyb3MSwh0REcMIDx98sHpgERZLGCEhKSd9xqpOXebK04TPkerOXNXOaaCZXcuI+fVvT+wvN1D8wBzK315O2auL4eCnZ2mAbrLgtPhT0nUgWefeTkV8twbXe+vMFfjuPJRy2FuLZK6EEMJ7Qu19OTV3CduD/4+N7f5DvnUB8+L6kFzyEF1Kp6N6+Vd7RTGhRf4bNeR8HNnXYlTMx5n3L/TST9Di30K19nFpHkM1sWfQHeR3+xs9f7mWsD3z6bbwX8Rs/oSNp79JRVTfBuOr356K9ap36//sDPNn+xtnk39RL7r840esO0tIOedT9l/am51Pn4YjMuC4a1C7Wgn4uTv2t/OpnrEPfUUlFUM2YrkrFr+7YlH8vJNzUowTcbKrlSstLSU0NJT8/I8ICTn+N0eIOobh9Emw4nRWs2PHu1RX52C1xtG581Q0zdrsNfhqvb6e2xv+c7qZ9QtU7njfzqiLmr+Nwlbm4O2IhQBcXTwac4D7z1WvtGHfkIsjuwSj2sG8xSOwhURR3r4HusW/yWsGv9uHoPwNrLngV4o6jW9yzLE49lxS+6YY+zxaxK1uX+8KHTvfdbIAcMaeQiz6yV0sRQghWkKFKYv08Os44F97lKZdzQD6FbxFqD3VJ/czDAO96E2ceXeCXgKKGTVyBlrkPSiq3/EnODQRcevfouvvd2CuKUFXTewaPIOdQ/6DYWo8z+FBFoBaYaPjAwuJ+7/lKAbYowLIevZ0Ci5MqT277AI920b1zbtx/FC7RV9NtmJ9vROmoUEAVJVWcWPkjZSUlLhdm6FVZq6EaAsKCpaQlfVmgx5SFksESUnXNGub3caNj1NYuLz+zyUl6eTl/UR4+GCSk+/xeA2+Wq+v5/aWuoIWXqsWaDr0A9ydfduGYYBTB01FDbDgN7gjdW8l+ZWnHRqo67XFLY68/uC2PsXTPlX12wJPVOZKKgYKIYQvBDqSGL7/V3YHzmJD2HSK/VaxIG4AXUvvpGfxA2g0/aGspxRFQQu/FjX4TBw5N2GUfYN+4GH00s8xxb+JGjDc1YnI6XsNBUln0GPuTURt+4bOSx8hessXbDz9TUoTGs5zZBZLD7Sw8+nTyL8whS7XzyYw4wA9rviGwo83kPXSJGztjx8MqfEW/L/sguPzIqqn70HfWE3lqZux3ByN30Pxbr0ujeZu1tVC/EUVFCxh06anGjXntdkK2LTpKQoKjt7w+liODKwOV1i4nI0bH/doDb5ar6/n9iatrs+VL7YFulEx8MDlH7Kv79PYVh6n4lETgRVQX9xC8bRh14k4c4WCYhyseChnroQQwmcUFDpVXMm4nEziKy7AUJxsDX2S+fH9KPD7wzf3NMdj6vAVpvafgxYNNRtx7DgFR86tGM5yl+exBcWz/pyvWH/259QExBBYuJEBn5xCt3m3oNkazlNX7OLw81jlgxNYt+xqdt8/Ct2sEv7jNtJSXydm5irQj/++rCgK5gvDCVrXC/MVEWCA7f/2U94vE8f8UtdfkCNIcCWEmwzDSVbWm8cck5X1lluHPaF2K+DRAqs6hYXLcTqr3VqDr9YLvnstfMHbpdgV7fDgyvVthvZN+3FsL0AvrfbovoeqBTazibAPgys4lL2SRsJCCOF7Vmccg/M/Z/D+r/FzxFJu3sSi2JGkh9+IXfE8UDgaRVFQQy/A3HUjartpgIFe+CL27b3Qy+a4MxEHul/AsmmZ5PSahoJBhzX/x5BZvQjf0fQ8hwdYhkVj770jWbv8GsqGJGAqs9Hl5jn0Ou0DrFtca7qshJvwfyuRgB+6onSyYOyyUfn3LNefwxEkuBLCTbXnio79D9Zmy6e0NNOteXfsePf4gw6Oc2cNvlov+O618IX6bYHeCq4UxaNeVwmrppNY81/8x3X36L7NrhZ4goKeuoqBkrkSQogTJ75qMuNyMulUVlsxe2fwa8yL702e9Sef3E8xhWNKeAdTp5/BnAj23Th2T8KxdyqGw7XgBsDhH87Gie+w5vxfqApJxFq2m7SvJpH80xRMVY3nOTKTVdUrivULppD17Ok4A8yELtpN2oA3SPjfYnC49gGo6fRQgtakYLk52uV1N0WCKyHcZLMVeXVcnepq1zqgV1fnuLUGX63XnWs8mdvb6qsFOr3T5woObQ10t9dVHcOpYzjdK67htWqBPs4mqkbtfaRaoBBCnFgWPYx+hW8wInceAfYkqkx7WBJzBisjL6VGzffJPdWg0zF33YAacTugoJe8h31bMs6ST91qV1KUeBrLpm1gd//bMFCIy3yfoe8kE73p00bNh+vUZ7I0ldybB5G+5jqKx3dGrXHS6T/z6Tv8bQLX5Lp0fyVIw/psBwJ+6urymo8kwZUQbrJYXKt85uq4Olara02vrdY4t9bgq/W6c40nc3tbXR9eb20LhNreGeBe5qqOI7eUkv/Np/jhX7BvPeDydXWZq9a/LfBgcCWZKyGEaBFRNWMYm7OOLqXTwVDZG/gxc+OT2RPwEQbeLxauqIGYYp/F1Hkxil8vcB7AufdiHHsmY9j3uTyPbg5k25jnWHXJYsojemGpOkDv2RfT55tzsZQ1Pc/hWwVrOrcjc/YlbH3zbOxhVoLS8+g7/G063jMPtcq19yTToCCX13skCa6EcFNISEqjZrxHslgiCQlxr89a585Tjz/o4Dh31uCr9YLvXgtfqNsW6K0+V9CwkbC79P3llL25lJIn55Ez5hWKn5yLpTjvuNcdCq6aWS3Qx1X81LptgVItUAghWozJCKRP0TOcmruUEFsfbFo+q6IuY2n0mVRqxyms5CE1YCimpNWoUQ+AYsYo+w77thSchTPdymKVxg9lxRWr2THsAXTVTFTW9wydlUL82tfBOM6uD0XhwJS+pK+7nvzzk1GcBu2fXkLqgDcJWbS7mc/w2CS4EsJNiqKRlHTNMcckJV3tdo8nTbMSHj74mGPCwwejaVa31uCr9YLvXgtf8EXmqn5boAeZKywm9JJqIt++iLDHz6D0pT/o/+wVxCz/HlNF8VEvM5pb0ALJXAkhxF9NmG0Qo3NWklz8CKphIc//J+bF9yIr6BUMmt/78UiKasEU/SCmpNUo/kNAL8WZcz2OnWMwara4PI+hWdgx/EFWXLGakrghmGyl9PztBvp9Nhb/wobzNFVR0B4TxJaPz2PjFxdgiwvCf1shvce9T9LNP6GV1njt+R5OgishPBARMYyePe9qlLWxWCLp2fMuj3s7JSffc9QA68g+V+6swVfr9fXc3lR35spbpdgBVHPtj1DDgzNXiqqgaCqGzUnwlEG03zyDA/1Oo8dH99Nn5i2EZf6JWlPZ6Dq9mWeulPptgb7NKNUVtJA+V0II0TqoWOhRci9jstMJrx6GQy1jXcRNLIoZSZlpk2/uae2NqfOfaLHPgRKAUbkQ+/a+OA88ieHG+1BFZG9WXfwnW0Y/h9MUQNjehQx+ry+dlj3Z5Pvh4QEWQNE5PViz9npyr04DIHbmatJSXyfsB9cDPVdJE2EhPBQRMYzw8MEHK+YVYbGEERKS0uwsTXLyPTid1ezY8S7V1TlYrXF07jwVTWvcDNCdNfhqvb6e21vq+1z54MyV08VKRA2YNVAVOFhfQw20sP1vd7LrtGvo+vXTJL93N/mp49k38iIq4rvX971q/pkr3/e5AlCRaoFCCNEaBTuSGZm3iB1Br5EZdjeF1sXMj0+jZ/EDdC29A7Vuh4OXKIqGFnEbavC5OHJuxCj/Gef+Geiln6PFv4Xqn+baRKrG3gG3kd/1XHr8egMRu36hyx8ziNryOZsmvEV5dMN5Dg+wrFe9i7OdlaxXzyT/ol50ufFH/LcXkXze5+T/PYWs50/HERXolecrmSshmsEwnJSX76C0dBPl5TuO2c/J6axm27bX2bDhQbZtex2n8+h9jlTVTFTUcGJixhIVNRxVPfoPOkXRCA3tQ1TUKEJD+7RYQNNa1nE0rWVboOHUMXQdo9IGCuhFVejlNThyS/ErzMZUU8m28/7N9r/dSfTqOQx+7FxCdq0/dP3B/xc8LsV+goIrxZBtgUII0VopaCSV38TY7AyiqyaiKzVkht3DgrhBFFtW++aels6YOv6EljALtDCM6tU4sgbiyLsHQ3e992N1aGfWnj+HzImzsFvDCNm/moEfDCRp0QxUe1XT1xwWaJWOTmTtqmvZN30ohqoQ+Xkm/fq+TuSH649akdAdkrkSwkM7d85i377v4LC9yjt3ziIh4RwSE6c1GLtx4+MNGgSXlKSTl/dTo61+AAUFS8jKerNB/yiLJYKkpGuatcXOV/O2FfUFLbxYGVyrK2jhxrbA/X97h6qfN9f/ueju2RTdPRuA4TzaYKzDP6T2PlWHOtU3uxR7/SeSPi5ogZRiF0KI1i7A2ZFh+39kT+AHbAi7nVLLWhbGDqZL6XR6ljyIyQjw6v0URUFrNxU1cAKO3H9ilH6Bnv8EeumXmOLfRA0c6epE5PaaSmHiBLrNu4WYLZ+TuPxJorZ+xabT36SkfeN5qt+eivWq2p6ieoCZXU+OI//CFLpe+wOB6/fT/crviPo0g+0vTaKqncXj5yjBlRAeqA2svmnib/T6x+sCrCMDq8MVFi5n48bH6wOsgoIlbNr0VKNxNlsBmzY95fEZJl/N25bUBVcOu/f6XCmm2uS/O5mrgL/1wZQUAbpO+Qer8RvaEevILqDrrFrbG0PRMFQVFAVD0dBslVRFd6q/vq1sC5QmwkII0TYoKHSsuIKYqgmsC7+FfYGfsi30f+QEfEW/greIrDnV+/c0x2Lu8Dl66dc4cv4Bti04do5CDbsRLeZJFC3EpXlsgbFknP0ZeVu/ocfcfxBYtIUBn45ib+qNbB/5JE6/Y89T0T+OdUuvIv6ZpXR4bBFhc7bTL20mmfcO9/i5SXAlhJt03XYwY3V0+/Z9R8eOl2IY+lEDqzqFhctxOqtRVTNZWW8ec2xW1luEhw92a8udYTh9Mm9bU1/QwpvbAk3uNxEOvrK2YIkju4Sq37YScEYKITefAsCut8897vWHgqvmNRF25yCxJw41EZaCFkII0Rb46dEMyv+E9hWXsTb8RirM2/kjdjSdyq6lV/FTWHTv96xUQ/6GOXAMztw70YvfRC96Fb3se0zxr6AGn+3yPPndJlPcYTRdfv83CevfoP3aV4nc/j2bx79KQZez6scdeQ4LwDBr7Lt7BIWTe9DlhtmELN5L57vnev6cPL5SiL+onJw5cNyypTo5OXPYseNdl+bcsePdg8UgCo45zmbLp7Q007WFHuSredsatT5z5cU5689cuV/QQosIJPKNC/E/67AeYIYBun7wywm6E+WI8oZ6c0uxn7AmwpK5EkKItiiu6mzGZWeQWHYdALuC32BeXC9y/I/9wbKnFK0dpoQ3MHWaC+YkcOzFsfscHHsuwXAccHkeh7Udm0+fyeq/z6OyXRes5XtJ/eZsUmZfirmy8TxHVhSs6hnJhnlTyHphAs5Az7cFSnAlhJuqq3NdHlddnePi2BxstiKXxro6zt3x7s7b1vjizJXiwZkroLaJokXDOqIz5sTwwyZUaqsCqiqoGqgahtZwg0HzM1cnpolwXXAlmSshhGh7zEYoaYWvc0ru7wTZe1BtymFZ9LmsiLyIatW134PcpQaNxdx1PWrEnYCKXvpJbfPh4g/caj5c3HEMy6esY9fAOzEUldhNHzPknWRiMj9oVLCiUW8sVSH3xoGs/eNKz5+Hx1cK8Rdltca6PM5qjXNxbBwWi2vpdlfHuTve3XnbGp9sCzyYuXK6cebKvj2fkkd/pXru1kZ/p1VX4FeYg/XAbgJyswjI2UbQ7kxMlaX1Y5pdLfAENRGu2xYomSshhGi7ImtGMiY7nW4ld4Ghsi/wM+bGp7A78D0Mml9Z70iKGoAp9r+Ykpah+PUBZz7OfVfg2H0Whn2Py/Po5gC2n/pfVl66jLKovliqC+j10xX0/fpM/Ep3N3lNg+bDHVw789UUCa6EcFNc3ESO/09HJS5uIp07Tz3OuFqdO08lJCSlUSPeI1kskYSEpBxzzJF8NW9bU9/nqoWbCFf9uoXSl//EqKoNOgxdx3DWbiuM/+Mzhv9nNMPuP40hD01iyMNnMuiJvxG77Jv665tbLVCaCAshhHCHhpVexU8yOncFoTX9sGtFrI6cypLoiVRoO31yT9V/IKYuq9CiHwPFglH+Y20Wq+BlDMP1rfhlsQNZedlKtp/yGE7Nj8gdPzFkVi8S1rwMTcxz5FZBj9be7BmE+ItRVQsJCeccc0xCwjmoqgVNsxIePviYY8PDB6NpVhRFIynpmmOOTUq62u2iE76at63xSZ8rk/t9rhzb8jF1DsfcI7r2AUWpbSYMFPQeRVnH3hT0Hs3GK55gx1n/xOnXsAxum6kWiPS5EkKIk0k7W39OzV1GStETqIYf+/1/YV58b7YH/59P2m4oihkt6h7MXdJR/IeDXo4z92YcO0/FqNnk8jyGZmbXkHtYcUU6xfEjMNnL6THvZvp/MoqAgsbzNDfAkuBKCA8kJk4jIWEyjf8JqSQkTG7Q5yo5+Z6jBlhH9rmKiBhGz553Nco0WSyRzSqX7qt525L6M1fezFzVVwt0/VM0vcKGYtFQQvzqH1OU2nlsQeGoDhulnXqTO/w89o28mJrQaLTqivqx9ZkrT/c31mWu8PW2wIMFLSRzJYQQJw0VM91L72Zs9joiqkfhVCtYH34Lv8eeQql5g0/uqfglY+q8CC32JVCDMCr/wL49FeeBRzHc+KCwMqInqy/+nc1jX8JhDqJd9p8Mfj+VTksfa/SeWv3+pR6vV0qxC+GhxMRpdOx4KTk5c6iuzsVqjSUubiKq2rjCTHLyPTid1ezY8S7V1TlYrXF07jwVTbM2GhsRMYzw8MEHq/wVYbGEERKS0uzMkq/mbSvq+1w5vNfnypPMlRpqRS+pRi+sgtiQ+sAKwFJeiKmyBEWvDdY0WxUoCsphVTj0g5krz89cnajM1cFtgZK5EkKIk06Qozun5M1nR9BrZIbdTZHfUubH9adHyX10L7kLFc+r7TVFUVS0iJtQg8/GkXMDRvlPOPffh17yOVrC26j+A1ycSGVfv5vI73I2PX67kcgdP9Llz3uJ3vIZmya8TVmMi/Mcg2SuRJtlGE5KStZz4MDvlJSsxzC8k5Ku62O1fftM9u37Dl23HWOsg5KSDZSUZFBSsgH9GGkRu72S/PzFlJRkkJ+/GLu98qhjbbYyNm9+ka1bX2Hz5hex2cqOMW85a9fezfLl17B27d3Y7eWuPVEv89X3w1vqgitvnrmqrxbodD248uvfHsfuYip/yDh4rY7hqH2tYpZ/j6W0gIr4brV/p2pgGKj2mvrr67YF4unrqzTzeldvU1fQQjJXQghxUlJQSSr/B+OyNxJbeQ6GYmdTu/tZEDeAQssy39zT0hFTx9loCR+AFoFRsw5H1mAcuXdi6Ef/vepINSEdWfe3H8g44wNs1giCD6xj4IeD6bLwTtRj/H7mCslciTapoGAJWVlvNujfZLFEkJR0TbO2uO3cOetgg2C9wWMJCec02OoHsHbtHZSXb6v/c1XVLpYtu5SgoK6kpj7dYOySJRc2CNKczhJWrboKVbUwbNhnDcYuXXopTuehf9h2ezUrV05D0wIYOvSjBmNXrbqhQWl4uz2f5csvx2qNZcCA1xqM9dVr5uu5vaU+uGrhaoH+ZyQTcE4viu+bg23VXgLOTMEwDCq/3UDiTxvJHfo3CpNHALX7xG0hkejmQ1sIm10tsL6JsI+3BUrmSggh/hL8nQkMOfANewM+Zn34rZRaNvB77HC6lN1KcvEjmIxAr95PURS0dpehBp2GM+dW9NJP0AueRi/7GlP8G6iBY1ydiLzkyyjsdBrd5t9G7KaP6bTyaaK2fc3qUc97vD7JXIk2p6BgCZs2PdWoMa7NVsCmTU9RULDEo3lrA6tvaNwgWGffvm/YuXNW/SNHBlaHKy/fxtq1d9T/+cjAqsHMuo0lSy6s//ORgdXhnM5Kli49tAf4yMDqcNXVuaxadUP9n331mvl6bm/yRZ8r1YM+V2qQH2GPn0HQlIFU/bSR/H98QcFNX1K9cDvZI/7O9snTcQSGAmAPCGXnpH9wIHV8/fVtps9VfbXA1pXBFEII4X0KCh0qL2Vc9kY6lF8Bis72kOeYF9eH/dbffHNPUzSmDh9j6vgDmNqDbTuOnWNx7LsWw1ns8jz2gGgyz/yItZO/pzqoPQHF20n7+myP1yXBlWhTDMNJVtabxxyTlfWW21vS6rYCHkvdFkGHo/KogVWd8vJtOByVVFcXHnNbYd29q6sLqakpPmpgVcfprKSmphi7vfy4zYyrq3Ox28t99pqB774fvuCTaoEHS7G7c+YKwBQfSuQbF9J+9/3E/nYDsb/dQIes/7D58kexhUbXjzPMFopSRlDRvuehx+pLsbfyPldInyshhPir8dMjGVDwHsPyfsTf0YFK8w4Wx5zGmvBrsKlFPrmnGnwm5q4ZqGG1HyrrxW9i39YLvfRbt+Yp6HIWy6ZlsDf1huMPPtZ6mnW1ECdYbTGGgmOOsdnyKS3NdGvenJw5NM5YHUknJ2cOW7Y879KcW7Y8T3r67S6NTU+/nbVr73Rp7Nq1d5KZ+ahLYzMzH/XZawa++374gi+3Bep216sFHk5r5491aCLWoYmoof6NOsc3pT5z1dxqgb4uaGHItkAhhPiriqmexNjsDDqX3gzAruC3mBufzL6AL3xyP0ULwRT/KqbEhWDpBo5sHHsmY9/zdwz7sT+MPpzTL4Qt418l/fwfPV6LBFeiTbHZXPvUw9VxdY6XBTp8XHV1notj846biarjdFbicBy9aMXhHI4yamryXRpbU5Pvs9fMnWs8mdvbNHNt4NLSfa6OSTl+JcPmn7k6sX2udB+XfBdCCNE6mY1gUov+j5G5iwiy96RGy2NF1N9ZHnkB1VqOT+6pBo7C3GUtauTdgIZR+gX27Sk4i9/FcOEDzDol8SM8X4PHVwrRAiyWMK+Oq2O1xro8zmqNcXFsDJoWcPyBgKYFYDIFuzTWZArGzy/SpbF+fpE+e83cucaTub3NJ2eu6jJXbpy5ai69mdUClfo+V749c6XWZ65afkuoEEKIlhNRcwpjstPpUXwfimEiO/BLfotPZmfQmxh4//1TUf0xxTyBKWklirUfOItw7puGY9fpGLadXr/fkSS4Em1KSEhKo0a4R7JYIgkJSXFr3ri4iRz/n4NKXNxEune/zaU5u3e/jbS051wam5b2HKmp/3NpbGrq/0hJudelsSkp9/rsNQPffT98wXQwpvDmtkBFO/HBVX3myuMncmIzV4ZkroQQ4i9Pw4/kkoc5NWcF7WoG4FBLSI+4lj+jx1NhyvLJPVX/NExJy9CinwDFilHxG/btvXEWvOjTs+ASXIk2RVE0kpKuOeaYpKSr3W6Mq6oWEhLOOeaYhIRzUFULJlMAQUFdjzk2KKgrJlMAVmt4k02Fj7y31RqOn1+742a6NC0AP792mM1Bx822Wa2xmM1BPnvNwHffD1+oS/g4nd5vIuxOn6vmqj9zZTSzWqDP+1zVZa6kz5UQQoha7expjMpdSu/CZ9B0f/L95zEvrjdbQ572SXVZRTGjRd2Nucs6lIBTQa/AmXsrjh0j0KszvH4/kOBKtEEREcPo2fOuRhkTiyWSnj3v8rivUmLiNBISJtP4n4VKQsLkBn2uUlOfPmqAdWSfq2HDPjtqgHVkn6uhQz86aoB1ZJ+rAQNeO2qAdWSfK1+9Zr6e25t8U9Cirlqg+wUtqpftonDGbMrfW+nWdcbBsoetvaCFasiZKyGEEI2pmOhaNp0xOeuIrB6NU60iI+xOFsYOo8S8zif3VPy6YUqchxb3KqghGFXLcGT1w7n/IYzjVHV2lzQRFm1SRMQwwsMHH6xWV4TFEkZISEqzMySJidPo2PFScnLmUF2di9UaS1zcxCaDo9TUp3E4Ktmy5Xmqq/OwWmPo3v02TKbGwdGwYZ9RXV1IevrtOJ2VaFoAaWnPYbWGNxo7dOhH1NQUs3btnTgcZZhMwaSm/g8/v3aNxg4Y8Bp2ezmZmY9SU5OPn18kKSn3YjYHNRrrq9fM13N7i6kuuPJiIqU5Z67s67IpfWYBAef0ImjKQJevqy/F7nHm6tCZK8MwUFwoouHRbZDMlRBCiKMLcnRlRN48dgW9xYawf1Hst4IFcQPoVnoXPYrvQ8PPq/dTFBUt/AbU4LNxZN+AUf4DzgMPopd+jhb/FmrAEK/cR4Ir0WYpikZoaB+XxhqG0+Vf/F3ZIljHZAogJeUel8ZaLEF06HB+fdBmsTQOgOqYzQEkJJxdP9ZsPvp2QbM5iNTUJ11agzuvmbt8Obc31GWuWk21QFPt/3+Gw72sV7NLsTf4se/EV28DddsCJXMlhBDiaBQUEsuvIaZqEuvCbyYn4Bu2hD5Gjv/XpBW+QUTNcO/f05yAqeN36KWf4cz5J0ZNBo4dw1EjbkWLfgRFDWzW/BJciZNeQcESsrLebNCPyWKJICnpmhO2ZW3nzlkHmxTrDR5LSDinwXZDd8cK19U1EdZ9kbnyILhSTLVbCg2Hmw2vm12K3Xzovw37oTNYXlbXRFgyV0IIIY7H35nAkANfsy/gC9aF30SZJZNFMafQuewfpBQ/gdlwraKyqxRFQQu9CDVwPM7c29FL3kcveA699CtM8TNBG+rx3HLmSpzUCgqWsGnTU40a3dpsBWza9BQFBUt8vobaYOkbGjcp1tm37xt27pzl0VjhHs3kgz5XzThzhflg5tTNa+szV83tcwU+PXclZ66EEEK4K6HyAsZlZ9KxfBooBjtCXmZefG/yrD/75H6KKQJT+/cwdfwRzJ3AvgvHrgk4cv7h8ZwSXImTlmE4ycp685hjsrLe8mk5Tl23HcxCHd2+fd+h6za3xgr3+aLPlVJXLdCDM1eHMleHgqurrvr2uNcZSl21QA+fiHLktkDfOHTmSvpcCSGEcJ1Fj6B/wTsMz/uVAEciVabdLImZyMqIK7CpBcefwANq8CTMXTaghv8TUNBLPvR8Lu8tS4jWpfaM1bH/Edps+ZSWZvpsDTk5c2ichTqSTk7OHLfGCvdpPuhz1awzV/WZq4bBx/ECrGZXC+TEZK7qS7FL5koIIYQHoqvHMzZ7PUmlt4KhsjfoA+bGp7A34BPfNB/WgjDFvYip8yKwdPd4HgmuxEnLZivy6jhPVFfnujzOnbHCfXVNhHVdQfdgF19T6s9c6d7JXLmiudUCa6sD1vW68t15KKkWKIQQorlMRhB9i55nVO5igm0p1Gj7WRl1CcuizqVK2+eTe6oBIzAn/uH59V5cixCtisUS5tVxnjheo9/Dx7kzVrhPPSxh461y7KrWnGqBB3/82t3bNtf8aoEc1kjYl2euDlYLVCRzJYQQonnCbUMYnbOansUPohhmcgO+Z258CjuCXsc47q4f9ymq52XgJbgSJ62QkJRGjW2PZLFEEhKS4rM1xMVN5Pj/zFTi4ia6NVa4Tzs8uPLS7/vNqhZ4cFug4Wlw5WlBCzghwZVSVy1QtgUKIYTwAg0/epY8wJicNYTVDMahlrI24gb+iBlNuWlLSy+vngRX4qSlKBpJSdccc0xS0tU+bXTrSs+shIRzUFWLW2OF+0yHVSD3VlGLZhW0qDtz5XTv2rpS7Epzasof1kjYV+qqBRo+LJohhBDiryfE3otRuYvpU/gCmh5IgXUR8+JS2RryX3Qfvq+5SoIrcVKLiBhGz553NcpgWSyR9Ox51wnpc5WYOI2EhMk0/uemkpAwuUHvKnfGCvccvi3QW+XYm1WK3cM+V3WZK9VwguHpgd6D56F8mrmSbYFCCCF8Q0GjS9ktjM3eQFTVaehqNRlhd7EwdjDF5jUtujZpIixOehERwwgPH3ywemARFksYISEpPs1YHSkxcRodO15KTs4cqqtzsVpjiYub2GQWyp2xwnWaBopiYBhKG98WeCgFp+iO+uqBbt784GQ+LGhhSEELIYQQvhXoTGT4/p/ZHTiLDWH/osRvDQvjBtG19E56ltyPZvif8DVJcCX+EhRFIzS0T4uuwZVtf56MFa7TTLVZK69lrppTil2rK2jhWRNhqD135VlwdQIKWtRlruTMlRBCCB9SUOhUcSUxVZNYF34L2YGfszX0SbIDvqRfwVtE1ow8oetptdsCX375ZRITE7FarQwZMoTly5cfc/znn39Oz549sVqt9OnThx9//PEErVQI0VaoXm4kXJ+5ak4TYadnpdihGeeuTsCZK6XuzJVkroQQQpwAVj2WwfmfMWT/N1gd8VSYt/JH7CjSw2/ErpScsHW0yuDq008/Zfr06TzwwAOsXr2a1NRUJkyYwP79+5scv3jxYi655BKuvvpq1qxZw+TJk5k8eTIbNmw4wSsXQrRmpvpGwopX5juUufLgzNVRmggfj94guGpmI+ETceZKMldCCCFOoLiqcxmbnUHH8qsA2Bn8GnPje5HrP/uE3L9VBlfPPvss1157LVdeeSUpKSm89tprBAQE8Pbbbzc5/oUXXmDixInceeedJCcn88gjj9C/f39eeumlE7xyIURrVleO3Vt9ruqyT7qbFf8Ov9bdJsIoh35se5q5UhTfNxFW5cyVEEKIFmIx2tG/4C1G5M4j0N6NatM+lkafxcrIy3yexWp1Z65sNhurVq1ixowZ9Y+pqsr48eNZsmRJk9csWbKE6dOnN3hswoQJfPPNN02Or6mpoaampv7PJSW1L3JZWWUzVy+EaM26n2KjukKhxmmntLT589nNNsJODSQgxkxpqXs/P5zo2E9NRA2wNLq2qurYi9vdfhygUGmrwqG6/0Qc2iAMcyya3Yx6nHt5ymk3E1owGj9n9HGfjxBCCOELQVUDGFryO1tDHiMr5GXy7auwVdpxcOz3perq2r83PKjK2+qCq/z8fJxOJzExMQ0ej4mJYdOmTU1ek5ub2+T43NzcJsc/8cQTPPTQQ40e79z52D2RhBAnh2f6+2DSz5pxbaSHWxXmd27GTQHmNvN617zXrBdHCCGE8JbNfEOUy6MLCgoIDQ116w6tLrg6EWbMmNEg01VcXEynTp3YvXu32y+gaFmlpaV06NCBPXv2EBIS0tLLEW6Q713bJN+3tku+d22XfO/aLvnetU0lJSV07NiR8PBwt69tdcFVZGQkmqaRl5fX4PG8vDxiY2ObvCY2Ntat8X5+fvj5+TV6PDQ0VP7Hb6NCQkLke9dGyfeubZLvW9sl37u2S753bZd879omVXW/PEWrK2hhsVgYMGAAc+ce2q6i6zpz585l2LBhTV4zbNiwBuMBfv3116OOF0IIIYQQQghva3WZK4Dp06czdepUBg4cyODBg3n++eepqKjgyiuvBGDKlCkkJCTwxBNPAHDrrbdy6qmn8swzz3DmmWfyySefsHLlSmbOnNmST0MIIYQQQgjxF9Iqg6uLLrqIAwcOcP/995Obm0taWhpz5sypL1qxe/fuBmm64cOH89FHH3Hvvfdyzz330K1bN7755ht69+7t0v38/Px44IEHmtwqKFo3+d61XfK9a5vk+9Z2yfeu7ZLvXdsl37u2qTnfN8XwpMagEEIIIYQQQogGWt2ZKyGEEEIIIYRoiyS4EkIIIYQQQggvkOBKCCGEEEIIIbxAgishhBBCCCGE8AIJroCXX36ZxMRErFYrQ4YMYfny5S29JHEcv//+O2effTbx8fEoisI333zT0ksSLnjiiScYNGgQwcHBREdHM3nyZDZv3tzSyxIuePXVV+nbt299I8xhw4bx008/tfSyhJuefPJJFEXhtttua+mlCBc8+OCDKIrS4Ktnz54tvSzhgn379nH55ZcTERGBv78/ffr0YeXKlS29LHEciYmJjf7NKYrCTTfd5PIcf/ng6tNPP2X69Ok88MADrF69mtTUVCZMmMD+/ftbemniGCoqKkhNTeXll19u6aUINyxcuJCbbrqJpUuX8uuvv2K32zn99NOpqKho6aWJ42jfvj1PPvkkq1atYuXKlYwdO5Zzzz2XjIyMll6acNGKFSt4/fXX6du3b0svRbihV69e5OTk1H/98ccfLb0kcRxFRUWMGDECs9nMTz/9RGZmJs888wxhYWEtvTRxHCtWrGjw7+3XX38F4O9//7vLc/zlS7EPGTKEQYMG8dJLLwGg6zodOnTgn//8J3fffXcLr064QlEUvv76ayZPntzSSxFuOnDgANHR0SxcuJBRo0a19HKEm8LDw/nf//7H1Vdf3dJLEcdRXl5O//79eeWVV3j00UdJS0vj+eefb+llieN48MEH+eabb0hPT2/ppQg33H333fz5558sWrSopZcimum2227jhx9+YOvWrSiK4tI1f+nMlc1mY9WqVYwfP77+MVVVGT9+PEuWLGnBlQnx11BSUgLU/pIu2g6n08knn3xCRUUFw4YNa+nlCBfcdNNNnHnmmQ3e70TbsHXrVuLj40lKSuKyyy5j9+7dLb0kcRzfffcdAwcO5O9//zvR0dH069ePN954o6WXJdxks9n44IMPuOqqq1wOrOAvHlzl5+fjdDqJiYlp8HhMTAy5ubkttCoh/hp0Xee2225jxIgR9O7du6WXI1ywfv16goKC8PPz44YbbuDrr78mJSWlpZcljuOTTz5h9erVPPHEEy29FOGmIUOGMGvWLObMmcOrr77Kjh07GDlyJGVlZS29NHEMWVlZvPrqq3Tr1o2ff/6ZG2+8kVtuuYV33323pZcm3PDNN99QXFzMtGnT3LrO5JvlCCHEsd10001s2LBBzg+0IT169CA9PZ2SkhK++OILpk6dysKFCyXAasX27NnDrbfeyq+//orVam3p5Qg3TZo0qf6/+/bty5AhQ+jUqROfffaZbMdtxXRdZ+DAgTz++OMA9OvXjw0bNvDaa68xderUFl6dcNVbb73FpEmTiI+Pd+u6v3TmKjIyEk3TyMvLa/B4Xl4esbGxLbQqIU5+N998Mz/88APz58+nffv2Lb0c4SKLxULXrl0ZMGAATzzxBKmpqbzwwgstvSxxDKtWrWL//v30798fk8mEyWRi4cKFvPjii5hMJpxOZ0svUbihXbt2dO/enW3btrX0UsQxxMXFNfrQKTk5WbZ0tiG7du3it99+45prrnH72r90cGWxWBgwYABz586tf0zXdebOnSvnCITwAcMwuPnmm/n666+ZN28enTt3bukliWbQdZ2ampqWXoY4hnHjxrF+/XrS09PrvwYOHMhll11Geno6mqa19BKFG8rLy9m+fTtxcXEtvRRxDCNGjGjUZmTLli106tSphVYk3PXOO+8QHR3NmWee6fa1f/ltgdOnT2fq1KkMHDiQwYMH8/zzz1NRUcGVV17Z0ksTx1BeXt7gk7sdO3aQnp5OeHg4HTt2bMGViWO56aab+Oijj/j2228JDg6uP9sYGhqKv79/C69OHMuMGTOYNGkSHTt2pKysjI8++ogFCxbw888/t/TSxDEEBwc3OtMYGBhIRESEnHVsA+644w7OPvtsOnXqRHZ2Ng888ACapnHJJZe09NLEMdx+++0MHz6cxx9/nAsvvJDly5czc+ZMZs6c2dJLEy7QdZ133nmHqVOnYjK5Hyr95YOriy66iAMHDnD//feTm5tLWloac+bMaVTkQrQuK1euZMyYMfV/nj59OgBTp05l1qxZLbQqcTyvvvoqAKNHj27w+DvvvOP2gVFxYu3fv58pU6aQk5NDaGgoffv25eeff+a0005r6aUJcdLau3cvl1xyCQUFBURFRXHKKaewdOlSoqKiWnpp4hgGDRrE119/zYwZM3j44Yfp3Lkzzz//PJdddllLL0244LfffmP37t1cddVVHl3/l+9zJYQQQgghhBDe8Jc+cyWEEEIIIYQQ3iLBlRBCCCGEEEJ4gQRXQgghhBBCCOEFElwJIYQQQgghhBdIcCWEEEIIIYQQXiDBlRBCCCGEEEJ4gQRXQgghhBBCCOEFElwJIYQQQgghhBdIcCWEEOKkNHr0aBRFcXm8oiiMHj3adws6AWbNmoWiKMyaNaullyKEEH9JElwJIYRw2c6dO1EUpcGXxWKhQ4cOXHrppaxbt87juSUwcM3JEAQKIcTJytTSCxBCCNH2dOnShcsvvxyA8vJyli5dyscff8xXX33F3LlzGTFiRAuvUAghhDjxJLgSQgjhtq5du/Lggw82eOzee+/lscce4z//+Q8LFixokXUJIYQQLUm2BQohhPCKf/7znwCsWLGiwePffvst48aNIywsDKvVSu/evXn66adxOp31Y6ZNm8aVV14JwJVXXtlg22GdVatWcfPNN9O7d29CQ0Px9/enT58+PPnkk9jtdp89L5vNxrPPPkv//v0JDAwkODiYkSNH8t133zUaO23aNBRFYceOHbz44ov07NkTPz8/OnXqxEMPPYSu642uqays5N///jcdOnSof33eeOMNFixYgKIo9UFs3Z8BFi5c2OA1amor5S+//MLw4cMJCAggIiKCqVOnUlBQ4NXXRgghREOSuRJCCOFVhwdEM2bM4MknnyQhIYHzzjuP0NBQFi1axJ133smyZcv4/PPPAZg8eTLFxcV8++23nHvuuaSlpTWa94033uD7779n1KhRnHHGGVRWVrJgwQJmzJjBihUr+PLLL73+XGpqapg4cSILFiwgLS2Nq6++GrvdzuzZszn33HP5v//7P26++eZG1915550sXLiQs846iwkTJvDNN9/w4IMPYrPZeOyxx+rHOZ1OzjrrLObPn0+fPn249NJLKSws5F//+lejc1WJiYk88MADPPTQQ3Tq1Ilp06bV/92Rr9d3333H7NmzOfvssxk+fDi///477733Htu3b+ePP/7w5kskhBDicIYQQgjhoh07dhiAMWHChEZ/d//99xuAMWbMGMMwDOOXX36pH1teXl4/Ttd144YbbjAA44svvqh//J133jEA45133mny3rt27TIcDkeDx3RdN6666ioDMP74448Gf3fqqaca7rzNAcapp57a4LF77rnHAIz77rvP0HW9/vHS0lJj4MCBhsViMfbt21f/+NSpUw3A6Ny5s5GdnV3/+IEDB4x27doZwcHBRk1NTf3jb775pgEYkyZNavDcMjIyDKvVagDGAw88cNx11ql7DU0mU4PXw+FwGKNHjzYAY8mSJS6/JkIIIdwj2wKFEEK4bdu2bTz44IM8+OCD3HnnnYwaNYqHH34Yq9Van5l56aWXAJg5cyaBgYH11yqKwpNPPomiKHz88ccu37Njx45omtbgMUVRuOmmmwD47bffmvu0GtB1nVdffZUuXbrw0EMPNcjIBQcHc//992Oz2fjqq68aXXvfffcRFxdX/+fIyEjOPfdcysrK2Lx5c/3jH3zwAQCPPfZYg+eWkpLClClTPF77pZde2qCoiKZpTJ06FWi8bVMIIYT3yLZAIYQQbtu+fTsPPfQQAGazmZiYGC699FLuvvtu+vTpA8DSpUsJDAzk7bffbnIOf39/Nm3a5PI9bTYbL730Ep988gmbNm2ivLwcwzDq/z47O7sZz6ixzZs3U1RURHx8fP1zPdyBAwcAmnwOAwYMaPRY+/btASguLq5/bO3atQQGBtKvX79G40eMGMHMmTM9Wrur9xdCCOFdElwJIYRw24QJE5gzZ84xxxQWFuJwOJoMTOpUVFS4fM8LLriA77//nu7du3PRRRcRHR2N2WymuLiYF154gZqaGpfnckVhYSEAGRkZZGRkHHVcU88hJCSk0WMmU+1b7uGFPEpLS+nQoUOT88bExLi1Xk/uL4QQwrskuBJCCOETISEhKIpCfn5+s+dasWIF33//PRMmTGD27NkNttAtXbqUF154odn3OFJdgHL++efzxRdfeH3+unvUZcCOlJeX55N7CiGE8B05cyWEEMInhgwZQkFBAVu3bnVpfF3A1FRmZfv27QCceeaZjc5dLVq0qJkrbVpycjIhISGsXLnSZ6XeU1NTqaioID09vdHfLV68uMlrVFWV7JMQQrRSElwJIYTwiVtuuQWAq666qsn+Srm5uWzcuLH+z+Hh4QDs2bOn0dhOnToBNCojnpGRwRNPPOG1NR/OZDJx4403smvXLu64444mA6wNGzawf/9+j+9x2WWXAbUNmA/vgbVp0ybefffdJq8JDw9n7969Ht9TCCGE78i2QCGEED4xceJE7rvvPh555BG6du3KxIkT6dSpEwUFBWzbto1Fixbx6KOPkpycDMCwYcPw9/fn+eefp6ioiKioKKA28Bg8eDCDBw/ms88+Iycnh6FDh7J7926+++47zjzzTJ9t23vooYdYvXo1L774IrNnz2bUqFFER0ezb98+1q9fz9q1a1myZAnR0dEezX/llVfy/vvvM3v2bPr168ekSZMoLCzkk08+4bTTTuP7779HVRt+Djp27Fg+++wzJk+eTL9+/dA0jXPOOYe+fft64ykLIYRoBgmuhBBC+MzDDz/MqFGjePHFF5k7dy7FxcVERETQuXNnHnzwwfrMDdRmZL744gsefPBB3njjDaqqqoDa4ErTNH744Qfuvvtu5syZw4oVK+jWrRtPP/00kyZN8llw5efnx08//cRbb73Fe++9x5dffklNTQ0xMTGkpKRwww031FdH9ISmafz444888MADfPzxxzz//PN06dKFZ555hvDwcL7//vtGxSnqzpfNmzeP77//Hl3Xad++vQRXQgjRCijG4XVshRBCCNEq3HvvvTz22GP8+OOPTJo0qaWXI4QQwgUSXAkhhBAtKCcnp0HDYYDMzEyGDh2KpmlkZ2fj7+/fQqsTQgjhDtkWKIQQQrSgG2+8kZ07dzJ48GDCwsLYvn0733//PXa7nbfeeksCKyGEaEMkcyWEEEK0oA8//JDXXnuNjRs3UlJSQlBQEIMGDeJf//oXEyZMaOnlCSGEcIMEV0IIIYQQQgjhBdLnSgghhBBCCCG8QIIrIYQQQgghhPACCa6EEEIIIYQQwgskuBJCCCGEEEIIL5DgSgghhBBCCCG8QIIrIYQQQgghhPACCa6EEEIIIYQQwgskuBJCCCGEEEIIL/h/VpDYJyLriBoAAAAASUVORK5CYII=", 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" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10, 5))\n", + "plt.plot(X[y==2, 0], X[y==2, 1], \"g^\", label=\"Iris-Virginica\")\n", + "plt.plot(X[y==1, 0], X[y==1, 1], \"bs\", label=\"Iris-Versicolor\")\n", + "plt.plot(X[y==0, 0], X[y==0, 1], \"yo\", label=\"Iris-Setosa\")\n", + "\n", + "from matplotlib.colors import ListedColormap\n", + "custom_cmap = ListedColormap(['#fafab0','#9898ff','#a0faa0'])\n", + "\n", + "plt.contourf(x0, x1, zz, cmap=custom_cmap)\n", + "contour = plt.contour(x0, x1, zz1, cmap=plt.cm.brg)\n", + "plt.clabel(contour, inline=1, fontsize=12)\n", + "plt.xlabel(\"Petal length\", fontsize=14)\n", + "plt.ylabel(\"Petal width\", fontsize=14)\n", + "plt.legend(loc=\"center left\", fontsize=14)\n", + "plt.axis([0, 7, 0, 3.5]);" + ] + } + ], + "metadata": { + "celltoolbar": "Tags", + "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": "3.13.1" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/week3/lectures/Lecture09_SVM.ipynb b/week3/lectures/Lecture09_SVM.ipynb new file mode 100644 index 0000000..6181a2d --- /dev/null +++ b/week3/lectures/Lecture09_SVM.ipynb @@ -0,0 +1,2287 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# Lecture 9: Support vector machines (SVMs)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "skip" + } + }, + "source": [ + "![](https://www.tensorflow.org/images/colab_logo_32px.png)\n", + "[Run in colab](https://colab.research.google.com/drive/1t9EbYLj41BV5KnTU-zFIVM-K87yatl5e)" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:07.514586Z", + "iopub.status.busy": "2024-01-10T00:20:07.514123Z", + "iopub.status.idle": "2024-01-10T00:20:07.521951Z", + "shell.execute_reply": "2024-01-10T00:20:07.521418Z" + }, + "slideshow": { + "slide_type": "skip" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Last executed: 2024-01-10 00:20:07\n" + ] + } + ], + "source": [ + "import datetime\n", + "now = datetime.datetime.now()\n", + "print(\"Last executed: \" + now.strftime(\"%Y-%m-%d %H:%M:%S\"))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Large margin classification" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Logistic regression with Hinge loss\n", + "\n", + "Recall cost function for logistic regression, with $\\ell_2$ regularisation, is given by\n", + "\n", + "\\begin{align*}\n", + "C(\\theta) = -\\frac{1}{m} \\sum_{i=1}^m \n", + "\\left [ \n", + "y^{(i)} \\log(\\hat{p}^{(i)})\n", + "+\n", + "(1 - y^{(i)}) \\log(1 - \\hat{p}^{(i)})\n", + "\\right]\n", + "+\n", + "\\frac{\\lambda}{2m}\n", + "\\sum_{j=1}^n \\theta_j^2,\n", + "\\end{align*}\n", + "\n", + "where \n", + "$\\hat{p} = h_\\theta(x) = \\sigma(\\theta^{\\rm T} x) \\quad \\text{and} \\quad \\sigma(t) = \\frac{1}{1+\\exp{(-t)}}.$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Recall, the bias $\\theta_0$ is not regularised, i.e. sum over $j$ starts at 1." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Plot sigmoid" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:07.563118Z", + "iopub.status.busy": "2024-01-10T00:20:07.562607Z", + "iopub.status.idle": "2024-01-10T00:20:07.972568Z", + "shell.execute_reply": "2024-01-10T00:20:07.971878Z" + } + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "%matplotlib inline\n", + "import matplotlib\n", + "import matplotlib.pyplot as plt" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:07.976305Z", + "iopub.status.busy": "2024-01-10T00:20:07.975558Z", + "iopub.status.idle": "2024-01-10T00:20:08.219979Z", + "shell.execute_reply": "2024-01-10T00:20:08.219258Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "t = np.linspace(-4, 4, 100)\n", + "sig = 1 / (1 + np.exp(-t))\n", + "plt.figure(figsize=(8, 4))\n", + "plt.plot([-4, 4], [0, 0], \"k-\")\n", + "plt.plot([-4, 4], [0.5, 0.5], \"k:\")\n", + "plt.plot([-4, 4], [1, 1], \"k:\")\n", + "plt.plot([0, 0], [-1.1, 1.1], \"k-\")\n", + "plt.plot(t, sig, \"b-\", linewidth=2, label=r\"$\\sigma(t) = \\frac{1}{1 + e^{-t}}$\")\n", + "plt.xlabel(\"t\")\n", + "plt.legend(loc=\"upper left\", fontsize=20)\n", + "plt.axis([-4, 4, -0.1, 1.1]);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Hinge loss\n", + "\n", + "Logistic regression cost function for reference: \n", + "\n", + "\\begin{align*}\n", + "C(\\theta) = -\\frac{1}{m} \\sum_{i=1}^m \n", + "\\left [ \n", + "y^{(i)} \\log(\\hat{p}^{(i)})\n", + "+\n", + "(1 - y^{(i)}) \\log(1 - \\hat{p}^{(i)})\n", + "\\right]\n", + "+\n", + "\\frac{\\lambda}{2m}\n", + "\\sum_{j=1}^n \\theta_j^2.\n", + "\\end{align*}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "#### Positive training instances\n", + "\n", + "For $y^{(i)}=1$, replace cost $-\\log(\\sigma(\\theta^{\\rm T} x))$ with *hinge loss* $\\max(1 - \\theta^{\\rm T} x, 0)$.\n", + "\n", + "For training, we want not just $\\theta^{\\rm T} x \\geq 0$ but $\\theta^{\\rm T} x \\geq 1$. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + }, + "tags": [ + "inclass_exercise" + ] + }, + "source": [ + "#### Exercise: \n", + "\n", + "Plot cost $-\\log(\\sigma(\\theta^{\\rm T} x))$ and hinge loss $\\max(1 - \\theta^{\\rm T} x, 0)$ ." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "-" + } + }, + "source": [ + "Logistic regression cost function for reference: \n", + "\\begin{align*}\n", + "C(\\theta) = -\\frac{1}{m} \\sum_{i=1}^m \n", + "\\left [ \n", + "y^{(i)} \\log(\\hat{p}^{(i)})\n", + "+\n", + "(1 - y^{(i)}) \\log(1 - \\hat{p}^{(i)})\n", + "\\right]\n", + "+\n", + "\\frac{\\lambda}{2m}\n", + "\\sum_{j=1}^n \\theta_j^2.\n", + "\\end{align*}" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:08.223354Z", + "iopub.status.busy": "2024-01-10T00:20:08.222895Z", + "iopub.status.idle": "2024-01-10T00:20:08.226877Z", + "shell.execute_reply": "2024-01-10T00:20:08.226303Z" + }, + "tags": [ + "inclass_exercise", + "solution" + ] + }, + "outputs": [], + "source": [ + "t = np.linspace(-4, 4, 100)\n", + "sig = 1 / (1 + np.exp(-t))\n", + "cost_one = -np.log(sig)\n", + "cost_one_hinge = np.maximum(1 - t, np.zeros(t.size))" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:08.229821Z", + "iopub.status.busy": "2024-01-10T00:20:08.229175Z", + "iopub.status.idle": "2024-01-10T00:20:08.462823Z", + "shell.execute_reply": "2024-01-10T00:20:08.462159Z" + }, + "slideshow": { + "slide_type": "fragment" + }, + "tags": [ + "inclass_exercise", + "solution" + ] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(8, 4))\n", + "plt.plot([0, 0], [0, 5], \"k-\")\n", + "plt.plot(t, cost_one, \"b-\", linewidth=2, label=r\"$-\\log{(\\sigma(\\theta^{\\rm T} x))}$\")\n", + "plt.xlabel(r\"$\\theta^{\\rm T} x$\", fontsize=20)\n", + "plt.axis([-4, 4, 0, 5]);\n", + "plt.title('Cost for $y=1$', fontsize=20)\n", + "plt.plot(t, cost_one_hinge, \"r-\", linewidth=2, label=r\"$\\max(1-\\theta^{\\rm T} x, 0)$\")\n", + "plt.legend(loc=\"upper right\", fontsize=20);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Negative training instances\n", + "\n", + "For $y^{(i)}=0$, replace $-\\log(1-\\sigma(\\theta^{\\rm T} x))$ with *hinge loss* $\\max(1 + \\theta^{\\rm T} x, 0)$.\n", + "\n", + "For training, we want not just $\\theta^{\\rm T} x < 0$ but $\\theta^{\\rm T} x \\leq -1$. " + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + }, + "tags": [ + "inclass_exercise" + ] + }, + "source": [ + "#### Exercise: \n", + "\n", + "Plot cost $-\\log(1-\\sigma(\\theta^{\\rm T} x))$ and hinge loss $\\max(1 + \\theta^{\\rm T} x, 0)$." + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:08.466146Z", + "iopub.status.busy": "2024-01-10T00:20:08.465732Z", + "iopub.status.idle": "2024-01-10T00:20:08.470442Z", + "shell.execute_reply": "2024-01-10T00:20:08.469824Z" + }, + "tags": [ + "inclass_exercise", + "solution" + ] + }, + "outputs": [], + "source": [ + "cost_zero = -np.log(1-sig)\n", + "cost_zero_hinge = np.maximum(1 + t, np.zeros(t.size))" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:08.473267Z", + "iopub.status.busy": "2024-01-10T00:20:08.472901Z", + "iopub.status.idle": "2024-01-10T00:20:08.747961Z", + "shell.execute_reply": "2024-01-10T00:20:08.747253Z" + }, + "tags": [ + "inclass_exercise", + "solution" + ] + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10, 5))\n", + "plt.plot([0, 0], [0, 5], \"k-\")\n", + "plt.plot(t, cost_zero, \"b-\", linewidth=2, label=r\"$-\\log{(1-\\sigma(\\theta^{\\rm T} x))}$\")\n", + "plt.xlabel(r\"$\\theta^{\\rm T} x$\", fontsize=20)\n", + "plt.axis([-4, 4, 0, 5]);\n", + "plt.title('Cost for $y=0$', fontsize=20);\n", + "plt.plot(t, cost_zero_hinge, \"r-\", linewidth=2, label=r\"$max(1+\\theta^{\\rm T} x, 0)$\")\n", + "plt.legend(loc=\"upper left\", fontsize=20);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Replace costs with hinge loss functions\n", + "\n", + "Recall logistic regression with $\\ell_2$ regularisation cost function is given by\n", + "\n", + "\\begin{align*}\n", + "C(\\theta) = -\\frac{1}{m} \\sum_{i=1}^m \n", + "\\left [ \n", + "y^{(i)} \\log(\\hat{p}^{(i)})\n", + "+\n", + "(1 - y^{(i)}) \\log(1 - \\hat{p}^{(i)})\n", + "\\right]\n", + "+\n", + "\\frac{\\lambda}{2m}\n", + "\\sum_{j=1}^n \\theta_j^2.\n", + "\\end{align*}\n", + "\n", + "Replace costs for $y^{(i)}=1$ and $y^{(i)}=0$ with hinge losses given above:\n", + "\\begin{align*}\n", + "\\min_\\theta\n", + "\\sum_{i=1}^m \n", + "\\left [ \n", + "y^{(i)} \n", + "\\max(1 - \\theta^{\\rm T} x^{(i)}, 0)\n", + "+\n", + "(1 - y^{(i)}) \n", + "\\max(1 + \\theta^{\\rm T} x^{(i)}, 0)\n", + "\\right]\n", + "+\n", + "\\frac{\\lambda}{2}\n", + "\\sum_{j=1}^n \\theta_j^2.\n", + "\\end{align*}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Introduce $k^{(i)}=1$ for positive instances ($y^{(i)}=1$) and $k^{(i)}=-1$ for negative instances ($y^{(i)}=0$):\n", + "\n", + "\\begin{align*}\n", + "\\Rightarrow\n", + "\\min_\\theta\n", + "C\n", + "\\sum_{i=1}^m \n", + "\\max(1 - k^{(i)} \\theta^{\\rm T} x^{(i)}, 0)\n", + "+\n", + "\\frac{1}{2}\n", + "\\sum_{j=1}^n \\theta_j^2\n", + "\\end{align*}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "The convention is to weight the fidelity term by C rather than regularisation term by $\\lambda$ (thus $C$ plays the role of $1/\\lambda$).\n", + "- Large $C$ $\\rightarrow$ little regularisation \n", + "- Small $C$ $\\rightarrow$ greater regularisation" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Constrained objective problem\n", + "\n", + "So far we considered the *unconstrained* objective problem by adapting the logistic regression cost function:\n", + "\\begin{align*}\n", + "\\min_\\theta\n", + "C\n", + "\\sum_{i=1}^m \n", + "\\max(1 - k^{(i)} \\theta^{\\rm T} x^{(i)}, 0)\n", + "+\n", + "\\frac{1}{2}\n", + "\\sum_{j=1}^n \\theta_j^2\n", + "\\end{align*}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "We can also consider the *constrained* objective problem:\n", + "\\begin{align*}\n", + "\\min_\\theta\n", + "\\frac{1}{2}\n", + "\\sum_{j=1}^n \\theta_j^2\n", + "\\quad\n", + "\\text{subject to}\n", + "\\quad\n", + "k^{(i)} \\theta^{\\rm T} x^{(i)} \\geq 1 \\ \\text{for}\\ i=1,2,\\ldots,m\n", + "\\end{align*}\n", + "\n", + "(Follows intuitively by considering large $C$.)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Intuition for large margin classification\n", + "\n", + "Decision boundary defined by $\\theta^{\\rm T} x + b = 0$ (where here $\\theta$ does *not* include bias and $b=\\theta_0$; in notation above $\\theta$ did include bias, i.e. $\\theta_0$ term).\n", + "\n", + "Consequently, $\\theta$ is orthogonal to decision boundary." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Recall constrained objective:\n", + "\n", + "\\begin{align*}\n", + "\\min_\\theta\n", + "\\frac{1}{2}\n", + "\\sum_{j=1}^n \\theta_j^2\n", + "\\quad\n", + "\\text{subject to}\n", + "\\quad\n", + "k^{(i)} \\theta^{\\rm T} x^{(i)} \\geq 1 \\ \\text{for}\\ i=1,2,\\ldots,m\n", + "\\end{align*}" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Projection\n", + "\n", + "Note that the term $k^{(i)} \\theta^{\\rm T} x^{(i)}$ is related to the projection of $x^{(i)}$ onto $\\theta$:\n", + "\n", + "$$k^{(i)} \\theta^{\\rm T} x^{(i)} = p^{(i)} \\| \\theta \\|,$$\n", + "\n", + "where $ p^{(i)}$ is the projection of $x^{(i)}$ onto $\\theta$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Attempting to minimise $\\| \\theta \\|$, hence requires $p^{(i)}$ to be large $\\Rightarrow$ large margin classification." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Graphical illustration\n", + "\n", + "\n", + "\n", + "(Note difference notation used: $w=\\theta$ without bias.)\n", + "\n", + "[Image source](http://www.saedsayad.com/support_vector_machine.htm)\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Training SVMs" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:08.751989Z", + "iopub.status.busy": "2024-01-10T00:20:08.751391Z", + "iopub.status.idle": "2024-01-10T00:20:08.757625Z", + "shell.execute_reply": "2024-01-10T00:20:08.757013Z" + } + }, + "outputs": [], + "source": [ + "# Common imports\n", + "import os\n", + "import numpy as np\n", + "np.random.seed(42) # To make this notebook's output stable across runs\n", + "\n", + "# To plot pretty figures\n", + "%matplotlib inline\n", + "import matplotlib\n", + "import matplotlib.pyplot as plt\n", + "plt.rcParams['axes.labelsize'] = 14\n", + "plt.rcParams['xtick.labelsize'] = 12\n", + "plt.rcParams['ytick.labelsize'] = 12" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Load data and train" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:08.760717Z", + "iopub.status.busy": "2024-01-10T00:20:08.760092Z", + "iopub.status.idle": "2024-01-10T00:20:09.136447Z", + "shell.execute_reply": "2024-01-10T00:20:09.135746Z" + } + }, + "outputs": [], + "source": [ + "from sklearn.svm import SVC\n", + "from sklearn import datasets\n", + "\n", + "iris = datasets.load_iris()\n", + "X = iris[\"data\"][:, (2, 3)] # petal length, petal width\n", + "y = iris[\"target\"]\n", + "\n", + "setosa_or_versicolor = (y == 0) | (y == 1)\n", + "X = X[setosa_or_versicolor]\n", + "y = y[setosa_or_versicolor]\n", + "\n", + "# SVM Classifier model\n", + "svm_clf = SVC(kernel=\"linear\", C=np.finfo(float).max)\n", + "svm_clf.fit(X, y);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Plot decision boundaries" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:09.140117Z", + "iopub.status.busy": "2024-01-10T00:20:09.139447Z", + "iopub.status.idle": "2024-01-10T00:20:09.143979Z", + "shell.execute_reply": "2024-01-10T00:20:09.143319Z" + } + }, + "outputs": [], + "source": [ + "# Bad models\n", + "x0 = np.linspace(0, 5.5, 200)\n", + "#pred_1 = 5*x0 - 20\n", + "pred_2 = x0 - 1.8\n", + "pred_3 = 0.1 * x0 + 0.5" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:09.147122Z", + "iopub.status.busy": "2024-01-10T00:20:09.146671Z", + "iopub.status.idle": "2024-01-10T00:20:09.152212Z", + "shell.execute_reply": "2024-01-10T00:20:09.151513Z" + } + }, + "outputs": [], + "source": [ + "def plot_svc_decision_boundary(svm_clf, xmin, xmax):\n", + " w = svm_clf.coef_[0]\n", + " b = svm_clf.intercept_[0]\n", + "\n", + " # At the decision boundary, w0*x0 + w1*x1 + b = 0\n", + " # => x1 = -w0/w1 * x0 - b/w1\n", + " x0 = np.linspace(xmin, xmax, 200)\n", + " decision_boundary = -w[0]/w[1] * x0 - b/w[1]\n", + "\n", + " # On the margin, w0*x0 + w1*x1 + b = +/- 1\n", + " margin = 1/w[1]\n", + " gutter_up = decision_boundary + margin\n", + " gutter_down = decision_boundary - margin\n", + "\n", + " svs = svm_clf.support_vectors_\n", + " plt.scatter(svs[:, 0], svs[:, 1], s=200, facecolors='#FFAAAA')\n", + " plt.plot(x0, decision_boundary, \"k-\", linewidth=2)\n", + " plt.plot(x0, gutter_up, \"k--\", linewidth=2)\n", + " plt.plot(x0, gutter_down, \"k--\", linewidth=2)" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:09.155462Z", + "iopub.status.busy": "2024-01-10T00:20:09.155013Z", + "iopub.status.idle": "2024-01-10T00:20:09.547975Z", + "shell.execute_reply": "2024-01-10T00:20:09.547289Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(16,4))\n", + "\n", + "plt.subplot(121)\n", + "#plt.plot(x0, pred_1, \"g--\", linewidth=2)\n", + "plt.plot(x0, pred_2, \"m-\", linewidth=2)\n", + "plt.plot(x0, pred_3, \"r-\", linewidth=2)\n", + "plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\", label=\"Iris-Versicolor\")\n", + "plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\", label=\"Iris-Setosa\")\n", + "plt.xlabel(\"Petal length\", fontsize=14)\n", + "plt.ylabel(\"Petal width\", fontsize=14)\n", + "plt.legend(loc=\"upper left\", fontsize=14)\n", + "plt.axis([0, 5.5, 0, 2])\n", + "\n", + "plt.subplot(122)\n", + "plot_svc_decision_boundary(svm_clf, 0, 5.5)\n", + "plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"bs\")\n", + "plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"yo\")\n", + "plt.xlabel(\"Petal length\", fontsize=14)\n", + "plt.axis([0, 5.5, 0, 2]);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Adding training instances outside the margin will not alter the decision boundary. \n", + "\n", + "Boundary is defined by *support vectors* that are located on the edge of the margin." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + }, + "tags": [ + "inclass_exercise" + ] + }, + "source": [ + "#### Exercise: what value would you guess for the weights $\\theta$ (excluding the bias)?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + }, + "tags": [ + "solution", + "inclass_exercise" + ] + }, + "source": [ + "From plot appears $w \\sim [1, 1]^{\\rm T}$ (or slightly more accurately $w \\sim [1.1, 0.9]^{\\rm T}$).\n", + "\n", + "Let's check:" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:09.551525Z", + "iopub.status.busy": "2024-01-10T00:20:09.551157Z", + "iopub.status.idle": "2024-01-10T00:20:09.555816Z", + "shell.execute_reply": "2024-01-10T00:20:09.555293Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1.29411744, 0.82352928])" + ] + }, + "execution_count": 13, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "svm_clf.coef_[0]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Feature scaling\n", + "\n", + "SVMs are sensitive to feature scales, hence feature scaling is important if features not already of similar scale." + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:09.558797Z", + "iopub.status.busy": "2024-01-10T00:20:09.558365Z", + "iopub.status.idle": "2024-01-10T00:20:09.771970Z", + "shell.execute_reply": "2024-01-10T00:20:09.771227Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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cCE9PTyQnJ8PDwwMAEBQUhOnTp+PAgQOIjIy05o9BRFb25ZfAyy8DOTl/bmvdGli9Ghg71np1EZHtsMmpMbVaDQBo0aKFaLufnx8cHBzg5OQEtVqNpKQkTJ482RCCAGDKlClwc3PD9u3bm7RmIrItX34JjB8vDkEAkJtbsf3LL61TFxHZFpsMQoMHDwYATJs2Denp6cjOzsYXX3yBjz76CLGxsWjWrBlOnz4NnU6H3r17i/o6OTkhJCQEp06dskLlRGQL9PqKkSBBMN5XuW327Ip2RCRtNhmEhg8fjjfffBNJSUkIDQ1FYGAgJk6ciFmzZuHdd98FAOTl5QGoGCWqzs/PD1evXq31HBqNBmq1WvQiovvDkSPGI0FVCQKQnV3RjoikzSbXCAEVa33Cw8Mxbtw4eHt749tvv8Xy5cvRsmVLzJw5EyUlJQAApVJp1NfZ2dmwvybx8fF44403GqV2IrKu//2edM/aEdH9yyaD0LZt2xATE4OMjAy0bt0aADB27FiUl5dj/vz5eOqpp+Di4gKgYmSnutLSUsP+mixYsABxcXGG92q1GgEBAffwpyAiazExUNygdkR0/7LJqbEPP/wQoaGhhhBUafTo0bh79y5OnTplmBLLM/ErXV5eHvz9/Ws9h1KphIeHh+hFRPeHgQMrrg6TyUzvl8mAgICKdkQkbTYZhK5duwa9iVWMZWVlAACdTofg4GAoFAqkpaWJ2mi1WqSnpyMkJKQpSiUiGySXV1wiDxiHocr3773H+wkRkY0GoY4dO+LUqVPIyMgQbf/888/h4OCAHj16QKVSISIiAps3b0ZhYaGhzaZNm1BUVISoqKimLpuIbMjYsUBiItCqlXh769YV23kfISICAJkgmLrA1Lp++OEHPPLII/D29sbMmTPh7e2NPXv2YO/evXjhhRfwf//3fwCAkydPIiwsDF27dkVMTAxycnKQkJCA8PBw7N+/v07nVKvVUKlUKCgo4DQZ0X2Ed5Ymur819PvbJoMQABw/fhxLlizBqVOncPPmTbRt2xbPPvssXn31VSgUf67xTklJwfz583Hy5Em4u7sjOjoa8fHxcHd3r9P5GISIiIjsz30bhJoagxAREZH9aej3t02uESIiIiJqCgxCREREJFkMQkRERCRZDEJEREQkWQxCREREJFkMQkRERCRZDEJEREQkWQxCREREJFkMQkRERCRZDEJEREQkWQxCREREJFkMQkRERCRZDEJEREQkWQxCREREJFkMQkRERCRZDEJEREQkWQxCREREJFkMQkRERCRZDEJEREQkWQxCREREJFkMQkRERCRZDEJEREQkWQxCREREJFkMQkRERCRZDEJEREQkWQxCREREJFkMQkRERCRZNhuEpk6dCplMVuMrNzfX0Pbo0aMYMGAAXF1d0bJlS8TGxqKoqMiK1RMREZE9UFi7gJr89a9/RUREhGibIAiYMWMGgoKC0KpVKwBAeno6hg4dii5dumDVqlXIycnBypUrkZmZib1791qjdCIiIrITNhuE+vfvj/79+4u2paSk4O7du3j66acN2xYuXAhPT08kJyfDw8MDABAUFITp06fjwIEDiIyMbNK6iYiIyH7Y7NSYKVu3boVMJsOkSZMAAGq1GklJSZg8ebIhBAHAlClT4Obmhu3bt1urVCIiIrIDdhOEysrKsH37doSFhSEoKAgAcPr0aeh0OvTu3VvU1snJCSEhITh16pQVKiUiIiJ7YTdBaP/+/bh586ZoWiwvLw8A4OfnZ9Tez88PV69erfF4Go0GarVa9CIiIiJpsZsgtHXrVjg6OiI6OtqwraSkBACgVCqN2js7Oxv2mxIfHw+VSmV4BQQE3PuiiYiIyKbZRRAqKirC7t278eijj8Lb29uw3cXFBUDF6E51paWlhv2mLFiwAAUFBYZXdnb2vS+ciIiIbJrNXjVW1VdffWV0tRjw55RY5RRZVXl5efD396/xmEql0uRIEhEREUmHXYwIbdmyBW5ubhg9erRoe3BwMBQKBdLS0kTbtVot0tPTERIS0oRVEhERkb2x+SB048YNHDx4EE8++SRcXV1F+1QqFSIiIrB582YUFhYatm/atAlFRUWIiopq6nKJiIjIjtj81NgXX3wBnU5nNC1WadmyZQgLC8OgQYMQExODnJwcJCQkIDIyEsOHD2/iaomIiMieyARBEKxdRG369++Pixcv4urVq5DL5SbbpKSkYP78+Th58iTc3d0RHR2N+Ph4uLu7W3wetVoNlUqFgoIC0c0ZiYiIyHY19Pvb5oNQU2EQIiIisj8N/f62+TVCRERERI2FQYiIiIgki0GIiIiIJItBiIiIiCSLQYiIiIgki0GIiIiIJItBiIiIiCSLQYiIiIgki0GIiIiIJItBiIiIiCSLQYiIiIgki0GIiIiIJItBiIiIiCSLQYiIiIgki0GIiIiIJItBiIiIiCSLQYiIiIgki0GIiIiIJItBiIiIiCSLQYiIiIgki0GIiIiIJItBiIiIiCSLQYiIiMgaBMHaFRAAhbULsDU//PADHnjgATg6OhpeTk5OovdeXl5wcnKydqlERGRPbt8GsrKAGzcAtboiCMlkgIcH4OsLBAUBnp7WrlJyZILASAoAarUaKpXKorbff/89hgwZYni/Z88ejB07tsbgVPlydXVFamqq6Fhr1qzB/v37a+xT+erWrRsmTZok6vvFF1/g7t27tfZzdHREu3bt0KJFC0M/nU6H69evm2wrk8ka8CkSEZGRoiLgxAkgP78i+Jj62q3c7uMD9OkDuLk1fZ12qvL7u6CgAB4eHnXuzxGhenB0dBS912q1KCsrQ1lZWa39XFxcjLadPHkSu3btMnvOMWPGGAWh+fPn4/Lly2b7fvjhh3jxxRcN7y9evIhOnTqZbKtQKETBKC0tDUFBQYb9n3/+OVauXGk2fLVu3Rpvv/226NibNm3C77//Xms/JycndOrUCaGhoaK+x44dg1wuNxsYXVxcIJfLzX4mRERN4sqVihBUGX5qGnuo3H7zJrB/f0UYCgxsmholjkGomtmzZ8PBwcEQbEy9fH19RX3c3d0RGhqKsrIyUSiq+tJqtXB2djY6n7nwVKl6+GpI39r66XQ66HQ6lJSUAAAcHMTLyPLy8nDy5Emz5+zcubNRENq6dSv27dtntm9sbKxREAoLC4Mlg5fffvstRowYYXifnJwsGq2rbcTu0KFDohBVWW9N7Su3t2/fHlFRUaI6vvvuOxQXF5sNjP7+/vD29jb0Ky8vR1FRkWG/XC7nKB2RvbpyBfjpp7r1EYSKV2U/hqFGxyBUzRtvvFHnobVhw4Zh2LBh9Trfu+++izfffLPW4FVWVgYfHx+jvitXroRara6xT2UoCw4OFvVr1qwZnnzyyRpDW9WXqfCmUCig0+lq/blMBTetVmvRZ1K9r16vtygEmepbUlKC27dvW9S3eug7fvw4Nm3aZLZfZGSkURCaN28ezp07Z7bvypUrMXfuXMP73NxcBFb7h6+mAHbgwAF07NjR0G7Pnj145513zI6a+fr64p///KfoHF999RUyMzPNBregoCB0795d1PfMmTNwcHCoNWwqFAoGOpKWwsKKkaCGOHEC8PLiNFkjs+kgdPLkSSxZsgQpKSkoLS1Fu3btEBMTg9jYWEObo0eP4tVXX8XJkyfh4eGB6OhoLF++HG528gdHpVJZvDapuqeeeqpe/YKCgvDll1/Wq29cXBzi4uIgCAJ0Ol2NAcrU9NSKFStw48YNk2Gt6qtnz56ifoIgYM6cObWGvZoCo7OzMzp06FDr+QRBMLk+ytIRN1ML5+/laF1N067Vw2FOTg6OHDli9pyBgYFGQeizzz6zaIp2+vTpWLt2rWhbv379UFxcbLZvYmIixo0bZ3iflpaGcePGmQ1fjo6O2LFjh2hq+euvv8a+fftqHeFzdHREQEAAxowZI6rjyJEjolG3mgKcl5eX6JciQRAgCIJRYCYyKS2txmkwfTlw5Jwv8m47w8+zFAO73IDc1B8rQagIQ1XWpNK9Z7NB6MCBAxg1ahRCQ0OxaNEiuLm54cKFC8jJyTG0SU9Px9ChQ9GlSxesWrUKOTk5WLlyJTIzM7F3714rVn//k8lkhi8MS1UPOJZSKBRYtWpVvfoOGTIEGRkZtbbR6/UmR6uWLFmC2NhYsyNuzZs3N+r7j3/8Azdv3jQ74lZ9tE6pVGLYsGFmw2JZWRmUSqWorzWmWevSV6EQ/3NTVFSEK1euWNS3ekhNTU3FRx99ZLbfwIEDjYLQ7NmzLZreffPNN/Haa68Z3t+8eRO+vr5Go1+mXtu3b0e3bt0MfQ8fPowVK1aYnaJVqVR4/fXXRXUkJSWZXVtXOc1afe3flStXRH9Xq7447dqIbt+uWBhtwpc/tcLLG0OQc9PVsK21912snpqOsf1yxY0FoeI4t2/zarJGZJNBSK1WY8qUKRg5ciQSExNr/A1s4cKF8PT0RHJysuE3t6CgIEyfPh0HDhxAZGRkU5ZNdkoul5tcyO7r62u0HsxSU6dOrVe/Vq1a4cCBA/Xq+9JLLyEmJsZs+DI1WvePf/wDU6dONRv6evXqZdR36tSp0Gg0dZ7elcvlaNmypVE7U9OudVnnVlu/hvSt7FdeXg6NRgONRlNj3+rnuHLlikW/nPn6+hoFoY0bN2Lr1q1m+06ePNloKrdXr17Ir+ELuWpAWr9+PSZMmGDYd/bsWYwfP97sNKujoyPWrl0rGjn7/vvvsX//frP9WrRoIVrPB1TMAtS2tq6ynmbNmpn8O2szsrJMXh325U+tMD6hP6qPE+XedMH4hP5InJtqHIZksorjMQg1GpsMQlu3bsW1a9ewbNkyODg4oLi4GC4uLqJApFarkZSUhDlz5oj+Ek6ZMgVz5szB9u3bGYRIUhwcHKBUKo1Giizxl7/8pd7nXbNmTb36DRw4EHl5eUbbTU27Vg9vcXFxmDRpUq3r3LRarcnRupkzZyIvL8/sNGvXrl1F/eRyOfr37282LJaVlRlNl9riaJ0gCNBqtdBqtUbTrIWFhRatcQNgNDL3448/4p133jHbr3fv3kZBKDY2Fj/++KPZvgsXLsSyZcsM7+/evQsfH59apzorXx9//DFCQkIMfX/66SckJCSYDV+urq6YP3++qI6jR4/iwoULxv1++QWOGg0c5XI4yuXw8fBAoE9zvLwx5H8hSAbgJiruaewIAY4AFJi9MQRP9MkVT5NVjgpRo7HJIHTw4EF4eHggNzcXY8aMQUZGBpo1a4ZnnnkG7777LpydnXH69GnodDr07t1b1NfJyQkhISE4depUreeo/hudWq1ulJ+FiOrGkmlXf39/+Pv71+v4MTEx9erXvHlzHD16tF59p0yZgieffLJeo3UzZ87EyJEjzfY1NVo3duxYFBYWmp1m9fLyEvUTBAFubm6G/eXl5TX+bLYyWldSUmK42rU2d+/eFb2/fPkyduzYYbafm5ubURD65JNPsH79erN9x/bti1mPvS2aDgNCAWSL2mXfdIDL03IoHSsClKNCgVVTpuDp8HBDm0uXLmHChAlmA5+joyPefvtt0VWpx44dQ1JSktnROk9PT0RERIhqy8jIqHG0rur5nZyc7G4dnU0GoczMTOh0OjzxxBOYNm0a4uPjkZycjPfffx937tzB559/bvhN0s/Pz6i/n5+f2UWj8fHxeOONNxqlfiKiqpycnERfSHURHh6O8CpfhHXxySef1KvfX/7yFxQWFhrel5eX1xjAXF1dRX2nTZuGoUOH1mtt3ZQpUxAeHm52xK36WihBENC9e3eza+t0Op11gptCgbzb1a/ANdW3HGX6cpTp/9yn1en+vKReJkNhYSFOWHg12tKlS0XvU1JSjKZeTenWrRt+/fVX0baXXnoJBw8eNNt3zpw5ojWdgiCgRYsWZgOUo6Mj3nrrLdHgxn//+1+89957ZgNfQ+8LbZNBqKioCHfv3sWMGTPwr3/9C0DFbzZarRZr1qzB0qVLDcnf1DSAs7Oz2d8MFixYgLi4OMN7tVqNgICAe/hTEBHdH+oy7dqmTRu0adOmXud56aWX6tXvgQcewH//+1+z7Ux9YT755JO4fPmy2VEzUwvLn332WfTt29e4/X//izKdDmV6Pcr0evRs2xZ+nqXVeg9FxfRYmejVvsVtOClKDX1Vrq4V64T+d35zty6pylZG627cuGFR34KCAtH7y5cvY8OGDXU+Z13ZZBCqXARX/fLwSZMmYc2aNUhNTTX8FmJqwWJpaanZhXT1XUtBRET2yVSYcXV1Nbp3l6UeeeQRPPLII8Y7DhwAqn2p68tvoLX3XeTedIEAGYDN4togoLV3CX5b/a3xpfRVbrHSs2dPlJeXQ6/Xm50u9ay2wDo6Oho9evQw28/U6OWYMWPQpUsXs4Gxffv24p9br0fbtm1rHOGrOu3akOBmaVtTbDII+fv748yZM6LnYwEwDKXevn3b8GGbWmyZl5dX7/UDREREDeLr++dDVf9H7gCsnpqO8Qn9IYPwvzBUQfa/JdTvTU03DkEyWcXzx0SbZFAoFFAoFHW6eq59+/ZGQcVSs2fPrlc/FxcXXLx4scb9Vaddq9/Ad9iwYThz5ozZqdK7d+9iypQp9aoPsNEg1KtXLyQlJSE3N1c0F3z16lUAFZeYBgcHQ6FQIC0tDdHR0YY2Wq0W6enpom1ERERNJigI+P13o81j++UicW6qifsIleA9U/cRAirCVJXnPd5vapt2dXd3N7p605SGXuxkk0u7K0NM9dX469atg0KhwODBg6FSqRAREYHNmzeLFvVt2rQJRUVFRo88ICIiahKenhWjOCam4sb2y0XWv7/F4cXJ2Bp7DIcXJ+PSv781HYIqR4N4D6FGZZMjQqGhoXj++efxySefQKfTYdCgQUhOTsaOHTuwYMECw7TXsmXLEBYWhkGDBiEmJgY5OTlISEhAZGQkhg8fbuWfgoiIJKtPn4qnyJtYoC13AAZ3s2ABsUxWcRxqVDKhodedNZKysjIsX74cGzZswNWrV9GmTRu89NJLRvOUKSkpmD9/Pk6ePAl3d3dER0cjPj4e7u7udTqfWq2GSqVCQUFBnR+6SkREZKQ+T5+vql8/Pn3eAg39/rbZINTUGISIiOieu3Kl4sGplfcCMqfyUvk+fRiCLNTQ72+bnBojIiK6LwQGAl5eFWEoP9/kM8gA/Lnd27siBLm5NX2tEsUgRERE1Jjc3IAhQyqeIp+VVRGICgoMd4uGSlWxKDooiAujrYBBiIiIqCl4eoqDTmUQIquyycvniYiI7nsMQTaBQYiIiIgki1Nj1Xz00Udwd3c3+YTb2p6aa66tXC43+ZwbIiIish5ePv8/lZffNaa6BCdL29YnlDX02Ax0RERkK3j5vB2pfECcvZPL5XYZ4Kq/5HK5tT9KIiKyMgahatatWwdHR0eTT7ut7em397K9Tqez9sdQK71eD71ej9LSUmuX0iAymcwuA1z19px2JSKqPwahaqKioqx+Z2lBEOoUsOoayhorwJlqa8sEQYBWq4VWq7V2KQ1mTwGutrYMdETU1BiEbJBMJoOTkxOcnJysXUqDCIIAvV5vlwGu+qu8vNzaH2et7CF4WsLUtKs9jthx2pXIfjAIUaORyWRQKBRQKBRwcXGxdjkNUl5ebpcBrvqL065No/KXGXsLcNXbctqVpIBBiMgCDg4OUCqVUCqV1i6lQeoy7dqYAe5eBD5bJggCNBoNNBqNtUtpMHsJcObaM9BRTRiEiCREKtOu9jRix2nXplF92tVeR+w47XrvMQgRkd25X6dd7SnAVW+v1+ut/VHW6n6ZdnVwcLDLAFe9rS1NuzIIERFZkdSmXW0twJnabsvKy8slMe1al5DVUAxCRETUYPf7tKutr5kz9eK0q2UYhIiIiP7nfpx2tecp17KyskafdmUQIiIiug9JZdr19u3b6Nu3b72PzyBERERENsvctKtarW7Q8R0a1JuIiIjIjjEIUeMQBGtXQEREZBanxujeuH0byMoCbtwA1OqKICSTAR4egK8vEBQEeHpau0oiIiIRBiFqmKIi4MQJID+/IvhUHQkSBKCgoCIY/f474OMD9OkDuLlZr14iIqIqODVG9XflCrB/P3DzZsX7mqbDKrffvFnR/sqVpqmPiIjIDI4IUf1cuQL89FPd+ghCxauyX2Dgva+LiIioDjgiRHVXWFgxHdYQJ05UTKsRERFZkU0GoeTkZMhkMpOvY8eOidoePXoUAwYMgKurK1q2bInY2FgU8Qu2caWlGU2DleY7oPCiosZXaX61P2qC0PAwRURE1EA2PTUWGxuLPn36iLY9+OCDhv9OT0/H0KFD0aVLF6xatQo5OTlYuXIlMjMzsXfv3qYuVxpu365YGF1Fab4Djr/shfKymp8k7OAooO/qW3D2+d+zbwSh4ji3b/NqMiIishqbDkIDBw7E+PHja9y/cOFCeHp6Ijk5GR4eHgCAoKAgTJ8+HQcOHEBkZGSdz/nSSy+hWbNmtT7pdsKECQissr4lNzcXKSkpZp+a6+TkhM6dO4vOV1JSAkEQ4OjoCIVCAZms5jBhE7KyjK4OK1M71BqCAKC8TIYytcOfQQioOE5WFoMQERFZTb2CUHFxMdq1a4fr16+jbdu2+O233+Do6GjUrqSkBEOHDkVqaiqUSiUOHDiA8PDwOp2rsLAQLi4uUCjEparVaiQlJWHOnDmGEAQAU6ZMwZw5c7B9+/Z6BaHNmzebbdO3b19REEpLS8PEiRPN9nNycoJGoxFtmzt3Lj766CPDe4VCYTJQPfroo1i7dq2o71NPPYVr167VGtocHR0xceJE0ed++/ZtrF271mRQq75t0KBBcHV1NfS9eeECrmVnw1Eur3gpFNAUOaEQCiiggBxyKKCAgyWzrpWjQkRERFZSryDUrFkzLFy4ELNnz8alS5fw6aef4oUXXhC1KS8vx9NPP43U1FQ4ODhg8+bNdQ5Bzz33HIqKiiCXyzFw4ECsWLECvXv3BgCcPn0aOp3O8L6Sk5MTQkJCcOrUqVqPrdFoRKGkLs8qqR76ysrK6tXPVF+dTgedToeSkhLR9nwTgeHo0aO4YsGl6D169BB99teuXcPf//53i2q+ePEi2rZta3i/5bvv8PKGDWb7BSAAn+Ez0bYXd7yPo9lnDAHKEKZatBCFsSeeeAIxMTGivrNmzTI8b6a20Ddy5EhRSM3Pz8fx48fNhkVHR0e0bt1aNCJXXl5uWJtGRET3p3pPjc2YMQOrVq3ClStXsGzZMjz77LOiL/rZs2dj165dAIBVq1bVOsVVnZOTE8aNG4cRI0bAx8cHZ8+excqVKzFw4EAcPXoUoaGhyMvLAwD4+fkZ9ffz88ORI0dqPUd8fDzeeOMNo+3Hjh2DUqms9Um3nTp1EvXp0aMHVq1ahbKyMmi1WpN9tFqtySDUuXNnDBkyxGT7qu+9vb2N+tY3gFnaz6ivIKBMp7Oon6kRoTz1bVy6ft248YULorcdO3YUvRcEAR988IFF5927d68oCJ08eRIjR460qK9erxeFnldeeQWrVq2qdarT0dERAwYMwJo1a0THevHFF5Gbm2t21O3xxx/HwIEDDf2Kiorw6aef1hrYKo/Rs2dPNGvWzNC3sLAQt27dMlmvXUy7EhFZQb2DkFKpxOuvv44XXngBWVlZ2LBhg+G3+ISEBLz//vsAgHnz5uHll1+u07HDwsIQFhZmeD969GiMHz8ePXr0wIIFC7Bv3z7DiIlSqTTq7+zsbDSiUt2CBQsQFxdneK9WqxEQEIAuXbqIptos0bFjR6Mvb0vNnTsXc+fOrVffy5cv1xrYKsNUYLX79QQGBuLLL7+sMbRVfalUqj87ymToFhCA5wYPRpleX/HS6VBSWI6b5xyg+9//6aFHC7QwqtfD2QW+Hh6GfmV6PbQmglX14KazMHyZ6mtp6HNwcICDgzi8VfbVarXQarU19q3++QLA4cOH8dtvv5k9b8uWLUVB6ObNm5g5c6ZFNZ85cwZdu3Y1vN+2bZvRSFpVldOuQUFBOHv2rGjfnDlzcOjQIbOjZsOGDcP06dNFfRctWgS9Xm/RNGvVz6qgoAC//PKLRaN1DzzwAIMcETWKBi2Wnjp1Kt555x1kZGRg+fLleO6557Br1y688sorACrWsLzzzjv3pNAHH3wQTzzxBL788kvo9Xq4uLgAgNGaGwAoLS017K+JUqk0GaLsSeWXRF2pVCo8+eST9Trn8EGDMDwkRLSt8KICP//d/ILnz55+Be7txKFGUKmgf+QRUfiq/r+LXC7Hzz//bDa0lZWViYIBAHTo0AFvvPGG2cBoSmBgIPr06WM2aFYdlanU5KN1FvStadoVAC5duoTTp0+bPaeXl5dREEpISDD7iwcA7Ny5UxSE/vvf/2LQoEFm+wEVI2VVP+c333wTK1assGjUrOoaPKDil6DLly/X2s/R0RFDhgzBgAEDDP00Gg22bdtmNvA5OjqiU6dOorV1paWlKC4uFrWRy+UMd0Q2oEFBSC6XY+nSpZg4cSIuX76Mv/3tb9i0aRMEQcCQIUOwcePGe/oXPSAgAFqtFsXFxYYpscopsqry8vLg7+9/z85LVfj6/vlQ1YaSySDz9YVCoYBCoagxvDo4OKBnz571OkXHjh3x+uuv16vvvHnzMG/evHr1PXnyJDQaTa3TnWVlZWjfvr2oX/PmzfHZZ5+Z7VdWVgYvLy9R33bt2iEqKspsWGzVqpVRvY6OjnBxcUFZWVmtI3CWrHOztG9DQl9xcTEKCwvN9jP1Z2rfvn1IT08323fZsmWiIKRWqzF16lSz/QDgxIkTovWLiYmJeOaZZ0RtZDKZUYBq3rw5fv31V1G7JUuW4MCBA2ZHzR5++GFMmzZN1DchIQEajcZsYOzduzcCAgIM/e7evYtz586ZXZPHaVe6HzT48vno6Gi89dZbSE9Px7p16wAA3bt3x65du+Dk5FRjv82bN+PIkSP4+eefcfr0aWi1WmzYsKHWf2guXrwIZ2dnuLm5ITg4GAqFAmlpaYiOjja00Wq1SE9PF22jeygoqOIBqlU4epTDwVEwex8hR49y8UZBqDjefUg0pVgHHh4eRl+Ylho+fDiGDx9er747duww/LcgCNDpdBaPfn3//fcWTbN2795d1C8gIACvvPKKRSN91a8a9fX1RZcuXcwGRlsJbqb6CoJgNO1afXoWAH777TekpqaaPaderzcKQsuXL8etW7fM9t28eTOefvppw/uzZ88a3cOtJjdu3ICPj4/h/erVq/H222+bDVBdunTBv//9b9Gx3n77bVy4cMHsiFu/fv1Eyyf0ej2++uors2vyHB0rLoqoGpD1ej10Oh0cHR1Nfv50/2twEJLJZJg+fTpeeuklABVrHvbu3Wv2i+C1117D5cuX4ePjAz8/P1y+fNmw78aNG/D19RW1/+WXX/D111/jscceg4ODA1QqFSIiIrB582YsWrQI7u7uAIBNmzahqKgIUVFRDf3RyBRPz4qnyN+8aRgVcvYpR9/Vt1CmrvkfEUePcuN7CHl78x5CNqjqSIUlqq5xqosOHTrUe+rckrV1giCgvLzcaHtSUhJKSkrMXqBQ/Z5fHh4e+PDDD82O1Gm1WqN/v1q1aoXHHnvMbOCr3g+o+KK2hK2Evjt37pgcqa+uuLjYaNvu3bstCn2vvfaaKAiVlJRYfEHODz/8IPoz+9VXXxn6yuXyGkfOPDw8jK5GXrVqFfbt22c29IWGhuK5554T9V23bh3u3r1rtm+3bt1Eo7gajQZZWVm1hj25XG7RZ0EVGhyEMjMzsXjxYsP74uJii9berFu3Dh06dECbNm3w1ltvYcGCBYZ9EyZMgIuLC8LCwtC8eXOcPXsWa9euhaurK9566y1Du2XLliEsLAyDBg1CTEwMcnJykJCQgMjIyHr/ZkwW6NOn4inyVabHnH2qBR1zZLKK4xA1EplMZvILwdSVppZwc3PDiy++WK++kZGR9bqvGQBs374d5eXlZkOUqYs8EhMTUVpaaja89ejRQ9SvefPmePHFFy0aras+8u/u7o6AgACTbatOu9pKcKvaV6/XQ6/Xo7S01Kifqc/3119/RVJSktlzjh8/3igILVmyBLm5uWb7/t///Z/o9jQXLlxAt27dau1T+cvM77//Lpry/OSTT/DWW2+ZDV9t27bF6tWrRcf86KOPkJmZaXZtXY8ePdCvXz9RX0umdh0dHeHt7V3rTFJjaVAQun79OoYPH478/Hx4e3vj5s2bKCwsRHx8PBISEmrtGxERUeO+MWPGYMuWLVi1ahXUajV8fX0xduxYLF68WPSIjZ49e+LgwYOYP38+5syZA3d3d0ybNg3x8fEN+bHIHDe3ihBT16fPV9WnT8VxiMgsBweHel3gUd/w1b59e3z44Yf16hsXFye6IrcqQRAMoUgwsc7wiy++QGFhodnwVT0IODs745133rFobV3z5s1FfX18fBAeHl7r9K5WqzUZhOob3BrS15J+ldOu1aeU8/PzkZmZabZ/cHCw0badO3fi0KFDZvvGxcWJgpBer8ejjz5qth8A7N+/X/Rndu/evRg9erTZqdKGhqd6B6Hi4mKMHDkSFy9ehJubG5KSkrB06VJ89dVX+PDDDxEXF2dyUaYlYmNjERsba1HbAQMG4Mcff6zXeagBKq/+OXGiYmTIksXTMtmfI0EmLjknovtb5U1Ra/riateuXb2O6+LiYrhaua4iIiJq/cW8NuvWrcO///1vs8HN08QSgLVr16K4uLjG4FX53w899JCon0qlwjPPPGPRaJ2zs7Oor5OTEzw9PUVtTE0fm/rfxxqjdVqtttarXStZJQjpdDpERUUhLS0NCoUCiYmJCA0NxZIlS7B7926UlpZi6dKlRjeZo/tMYCDg5VURhvLzjZ5BZlC53dubI0FEdN9oyG1YnnjiiXr1CwoKwmeffWa+oQmzZ8/G7NmzRdtMTbua8vHHH+P27dt1nmZ1cHDAokWLLApu1UfrPDw80LNnz1rPVzk9W9u93syRCabGJ8144YUXsH79egDA+vXr8fzzzxv2jRs3Dl9++SUUCgXOnz9vdHmwKZVrhMxdNdaY1Go1VCoVCgoK6nxDRULFU+SzsioCUUFBRfCRyQCVqmJxdVAQF0YTEdE919Dv7zqPCC1ZssQQghYvXiwKQZX7d+3aBZ1Oh9dffx1btmypc1Fkhzw9xUGnMggRERHZsDrdNGH9+vWG53M9//zzWLJkiVGb7t27Gy5F3LZtm0V3q6X7EEMQERHZAYuD0HfffYcZM2YAAB599NFa1/8sXrwYDg4OKC8vx2uvvdbwKomIiIgagcVTYyNGjLB49Xe3bt0svgkYERERkbXwfuJEREQkWQ2+s3R9rVu3DikpKQBgWEe0bt06JCcnA6i4P1DVu2kSERER3WtWC0IpKSn49NNPRdt+/PFH0c0RGYSIiIioMdXrPkL3I95HiIiIyP409Puba4SIiIhIshiEiIiISLIYhIiIiEiyGISIiIhIshiEiIiISLIYhIiIiEiyGISIiIhIshiEiIiISLIYhIiIiEiyGISIiIhIshiEiIiISLIYhIiIiEiyGISIiIhIshiEiIiISLIYhIiIiEiyGISIiIhIshiEiIiISLLsJggtW7YMMpkMwcHBRvuOHj2KAQMGwNXVFS1btkRsbCyKioqsUCURERHZE4W1C7BETk4Oli9fjmbNmhntS09Px9ChQ9GlSxesWrUKOTk5WLlyJTIzM7F3714rVEtERET2wi6C0Lx58/CXv/wFer0e+fn5on0LFy6Ep6cnkpOT4eHhAQAICgrC9OnTceDAAURGRlqjZCIiIrIDNj819sMPPyAxMRHvvfee0T61Wo2kpCRMnjzZEIIAYMqUKXBzc8P27dubsFIiIiKyNzY9IqTX6zFr1iy88MIL6N69u9H+06dPQ6fToXfv3qLtTk5OCAkJwalTp2o8tkajgUajMbxXq9X3rnAiIiKyCzY9IvTxxx/j8uXLePPNN03uz8vLAwD4+fkZ7fPz88PVq1drPHZ8fDxUKpXhFRAQcG+KJiIiIrths0Ho5s2beP3117Fo0SL4+vqabFNSUgIAUCqVRvucnZ0N+01ZsGABCgoKDK/s7Ox7UzgRERHZDZudGnvttdfg5eWFWbNm1djGxcUFAERTXJVKS0sN+01RKpUmAxQRERFJh00GoczMTKxduxbvvfeeaHqrtLQUZWVlyMrKgoeHh2FKrHKKrKq8vDz4+/s3Wc1ERERkf2xyaiw3Nxfl5eWIjY1F27ZtDa+ffvoJGRkZaNu2LZYuXYrg4GAoFAqkpaWJ+mu1WqSnpyMkJMQ6PwARERHZBZscEQoODsauXbuMtr/22msoLCzE6tWr0b59e6hUKkRERGDz5s1YtGgR3N3dAQCbNm1CUVERoqKimrp0IiIisiMyQRAEaxdhqcGDByM/Px+//vqrYdvJkycRFhaGrl27IiYmBjk5OUhISEB4eDj2799v8bHVajVUKhUKCgpE9yQiIiIi29XQ72+bnBqri549e+LgwYNwcXHBnDlzsHbtWkybNg2JiYnWLo2IiIhsnF2NCDUmjggRERHZH8mPCBERERHVF4MQERERSRaDEBEREUkWgxARERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQERERSRaDEBEREUmWTQahM2fOICoqCu3atYOrqyt8fHwQHh6Ob775xqjtuXPnMHz4cLi5ucHLywvPPPMMbty4YYWqiYiIyN4orF2AKZcvX0ZhYSGeffZZ+Pv74+7du9i5cydGjx6NNWvWICYmBgCQk5OD8PBwqFQqLF++HEVFRVi5ciVOnz6N48ePw8nJyco/CREREdkymSAIgrWLsIRer0evXr1QWlqK8+fPAwD+9re/YePGjTh//jwCAwMBAAcPHsSwYcNEgckSarUaKpUKBQUF8PDwaJSfgYiIiO6thn5/2+TUmClyuRwBAQG4c+eOYdvOnTvx+OOPG0IQAERERKBjx47Yvn27FaokIiIie2KTU2OViouLUVJSgoKCAnz99dfYu3cvJkyYAADIzc3F9evX0bt3b6N+ffv2xXfffdfU5RIREZGdsekgNHfuXKxZswYA4ODggLFjx+KDDz4AAOTl5QEA/Pz8jPr5+fnh1q1b0Gg0UCqVJo+t0Wig0WgM79Vq9b0un4iIiGycTU+NzZ49G0lJSfj000/x2GOPQa/XQ6vVAgBKSkoAwGTQcXZ2FrUxJT4+HiqVyvAKCAhohJ+AiIiIbJlNB6HOnTsjIiICU6ZMwZ49e1BUVIRRo0ZBEAS4uLgAgGhUp1JpaSkAGNqYsmDBAhQUFBhe2dnZjfNDEBERkc2y6SBU3fjx43HixAlkZGQYpsQqp8iqysvLg5eXV43TYkDFSJKHh4foRURERNJiV0GocqqroKAArVq1gq+vL9LS0ozaHT9+HCEhIU1cHREREdkbmwxC169fN9pWVlaGzz77DC4uLujatSsAYNy4cdizZ49oWuvQoUPIyMhAVFRUk9VLRERE9skmb6j45JNPQq1WIzw8HK1atcIff/yBLVu24Pz580hISEBcXBwAIDs7G6GhoXjggQfw8ssvo6ioCCtWrEDr1q1x4sSJWqfGquMNFYmIiOxPQ7+/bTIIbdu2DevXr8fp06dx8+ZNuLu7o1evXpg1axZGjx4tanvmzBnExcUhJSUFTk5OGDlyJBISEtCiRYs6nZNBiIiIyP7cl0HIGhiEiIiI7I9kHrFBREREdK8xCBEREZFkMQgRERGRZDEIERERkWQxCBEREZFkMQgRERGRZDEIERERkWQxCBEREZFkMQgRERGRZDEIERERkWQxCBEREZFkMQgRERGRZDEIERERkWQxCBEREZFkMQgRERGRZDEIERERkWQxCBEREZFkMQgRERGRZDEIERERkWQxCBEREZFkMQgRERGRZDEIERERkWQxCBEREZFkMQgRERGRZDEIERERkWQxCBEREZFkMQgRERGRZNlkEDpx4gRmzpyJbt26oVmzZggMDER0dDQyMjKM2p47dw7Dhw+Hm5sbvLy88Mwzz+DGjRtWqJqIiIjsjcLaBZjy9ttv48cff0RUVBR69OiBP/74Ax988AF69uyJY8eOITg4GACQk5OD8PBwqFQqLF++HEVFRVi5ciVOnz6N48ePw8nJyco/CRERUYXSK6Uoyy+rcb+jjyOcA52bsCICbDQIxcXFYevWraIgM2HCBHTv3h1vvfUWNm/eDABYvnw5iouL8fPPPyMwMBAA0LdvXwwbNgwbN25ETEyMVeonIiKqqvRKKY53Oo7y0vIa2zg4O6Dvb30ZhpqYTU6NhYWFGY3mdOjQAd26dcO5c+cM23bu3InHH3/cEIIAICIiAh07dsT27dubrF4iIqLalOWX1RqCAKC8tLzWESNqHDYZhEwRBAHXrl2Dj48PACA3NxfXr19H7969jdr27dsXp06dauoSiYiIyM7YTRDasmULcnNzMWHCBABAXl4eAMDPz8+orZ+fH27dugWNRlPj8TQaDdRqtehFRERE0mIXQej8+fN46aWX0L9/fzz77LMAgJKSEgCAUqk0au/s7CxqY0p8fDxUKpXhFRAQ0AiVExERkS2z+SD0xx9/YOTIkVCpVEhMTIRcLgcAuLi4AIDJUZ/S0lJRG1MWLFiAgoICwys7O7sRqiciIiJbZpNXjVUqKCjAY489hjt37uDIkSPw9/c37KucEqucIqsqLy8PXl5eJkeLKimVylr3ExER0f3PZoNQaWkpRo0ahYyMDBw8eBBdu3YV7W/VqhV8fX2RlpZm1Pf48eMICQlpokqJiIjIXtnk1Jher8eECROQmpqKHTt2oH///ibbjRs3Dnv27BFNax06dAgZGRmIiopqqnKJiIhq5ejjCAfn2r9yHZwd4Ojj2EQVUSWZIAiCtYuobvbs2Vi9ejVGjRqF6Ohoo/2TJ08GAGRnZyM0NBQPPPAAXn75ZRQVFWHFihVo3bo1Tpw4UaepL7VaDZVKhYKCAnh4eNyzn4WIiAjgnaUbS0O/v20yCA0ePBj/+c9/atxfteQzZ84gLi4OKSkpcHJywsiRI5GQkIAWLVrU6ZwMQkRERPbnvgxC1sAgREREZH8a+v1tk2uEiIiIiJoCgxARERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQERERSZbNBqGioiIsXrwYw4cPh5eXF2QyGTZu3Giy7blz5zB8+HC4ubnBy8sLzzzzDG7cuNG0BRMREZHdUVi7gJrk5+dj6dKlCAwMxEMPPYTk5GST7XJychAeHg6VSoXly5ejqKgIK1euxOnTp3H8+HE4OTk1beFERERkN2w2CPn5+SEvLw8tW7ZEWloa+vTpY7Ld8uXLUVxcjJ9//hmBgYEAgL59+2LYsGHYuHEjYmJimrJsIiIisiM2OzWmVCrRsmVLs+127tyJxx9/3BCCACAiIgIdO3bE9u3bG7NEIiIisnM2G4QskZubi+vXr6N3795G+/r27YtTp05ZoSoiIiKyFzY7NWaJvLw8ABXTaNX5+fnh1q1b0Gg0UCqVRvs1Gg00Go3hvVqtbrxCiYiIyCbZ9YhQSUkJAJgMOs7OzqI21cXHx0OlUhleAQEBjVcoERER2SS7DkIuLi4AIBrZqVRaWipqU92CBQtQUFBgeGVnZzdeoURERGST7HpqrHJKrHKKrKq8vDx4eXmZHC0CKkaRatpHRERE0mDXI0KtWrWCr68v0tLSjPYdP34cISEhTV8UERER2Q27DkIAMG7cOOzZs0c0tXXo0CFkZGQgKirKipURERGRrbPpqbEPPvgAd+7cwdWrVwEA33zzDXJycgAAs2bNgkqlwsKFC7Fjxw4MGTIEL7/8MoqKirBixQp0794dzz33nDXLJyIiIhsnEwRBsHYRNQkKCsLly5dN7rt06RKCgoIAAGfOnEFcXBxSUlLg5OSEkSNHIiEhAS1atLD4XGq1GiqVCgUFBfDw8LgX5RMREVEja+j3t00HoabEIERERGR/Gvr9bfdrhIiIiIjqi0GIiIiIJItBiIiIiCSLQYiIiIgki0GIiIiIJItBiIiIiCSLQYiIiIgki0GIiIiIJItBiIiIiCSLQYiIiIgki0GIiIiIJItBiIiIiCSLQYiIiIgki0GIiIiIJItBiIiIiCSLQYiIiIgki0GIiIiIJItBiIiIiCSLQYiIiIgki0GIiIiIJItBiIiIiCSLQYiIiIgki0GIiIiIJItBiIiIiCSLQYiIiIgki0GIiIiIJItBiIiIiCTrvghCGo0G8+fPh7+/P1xcXNCvXz8kJSVZuywiIiKycfdFEJo6dSpWrVqFp59+GqtXr4ZcLseIESOQkpJi7dKIiIjIhskEQRCsXURDHD9+HP369cOKFSswb948AEBpaSmCg4PRvHlzHD161KLjqNVqqFQqFBQUwMPDozFLJiIionukod/fdj8ilJiYCLlcjpiYGMM2Z2dnTJs2DampqcjOzrZidURERGTL7D4InTp1Ch07djRKgX379gUApKenW6EqIiIisgcKaxfQUHl5efDz8zPaXrnt6tWrJvtpNBpoNBrD+4KCAgAVQ2xERERkHyq/t+u70sfug1BJSQmUSqXRdmdnZ8N+U+Lj4/HGG28YbQ8ICLi3BRIREVGju3nzJlQqVZ372X0QcnFxEY3sVCotLTXsN2XBggWIi4szvL9z5w7atGmDK1eu1OuDpD+p1WoEBAQgOzubC88bgJ/jvcPP8t7hZ3lv8HO8dwoKChAYGAgvL6969bf7IOTn54fc3Fyj7Xl5eQAAf39/k/2USqXJkSSVSsU/lPeIh4cHP8t7gJ/jvcPP8t7hZ3lv8HO8dxwc6rfs2e4XS4eEhCAjI8Nobc9PP/1k2E9ERERkit0HofHjx0Ov12Pt2rWGbRqNBhs2bEC/fv245oeIiIhqZPdTY/369UNUVBQWLFiA69ev48EHH8Snn36KrKwsrF+/3uLjKJVKLF682OR0GdUNP8t7g5/jvcPP8t7hZ3lv8HO8dxr6Wdr9naWBioXRixYtwubNm3H79m306NEDb775Jh599FFrl0ZEREQ27L4IQkRERET1YfdrhIiIiIjqi0GIiIiIJItBiIiIiCRL8kFIo9Fg/vz58Pf3h4uLC/r164ekpCRrl2V3ioqKsHjxYgwfPhxeXl6QyWTYuHGjtcuyOydOnMDMmTPRrVs3NGvWDIGBgYiOjkZGRoa1S7M7Z86cQVRUFNq1awdXV1f4+PggPDwc33zzjbVLs3vLli2DTCZDcHCwtUuxK8nJyZDJZCZfx44ds3Z5dunkyZMYPXo0vLy84OrqiuDgYPzrX/+q0zHs/vL5hpo6dSoSExMxe/ZsdOjQARs3bsSIESNw+PBhDBgwwNrl2Y38/HwsXboUgYGBeOihh5CcnGztkuzS22+/jR9//BFRUVHo0aMH/vjjD3zwwQfo2bMnjh07xi+eOrh8+TIKCwvx7LPPwt/fH3fv3sXOnTsxevRorFmzBjExMdYu0S7l5ORg+fLlaNasmbVLsVuxsbHo06ePaNuDDz5opWrs14EDBzBq1CiEhoZi0aJFcHNzw4ULF5CTk1On40j6qrHjx4+jX79+WLFiBebNmweg4lL84OBgNG/eHEePHrVyhfZDo9Hg9u3baNmyJdLS0tCnTx9s2LABU6dOtXZpduXo0aPo3bs3nJycDNsyMzPRvXt3jB8/Hps3b7ZidfZPr9ejV69eKC0txfnz561djl2aOHEibty4Ab1ej/z8fPz666/WLsluJCcnY8iQIdixYwfGjx9v7XLsmlqtRseOHREWFobExMR6P14DkPjUWGJiIuRyueg3Q2dnZ0ybNg2pqanIzs62YnX2RalUomXLltYuw+6FhYWJQhAAdOjQAd26dcO5c+esVNX9Qy6XIyAgAHfu3LF2KXbphx9+QGJiIt577z1rl2L3CgsLodPprF2G3dq6dSuuXbuGZcuWwcHBAcXFxSgvL6/XsSQdhE6dOoWOHTsaPfCub9++AID09HQrVEUkJggCrl27Bh8fH2uXYpeKi4uRn5+PCxcu4N1338XevXsxdOhQa5dld/R6PWbNmoUXXngB3bt3t3Y5du25556Dh4cHnJ2dMWTIEKSlpVm7JLtz8OBBeHh4IDc3F506dYKbmxs8PDzw4osvorS0tE7HkvQaoby8PPj5+Rltr9x29erVpi6JyMiWLVuQm5uLpUuXWrsUuzR37lysWbMGQMXTqceOHYsPPvjAylXZn48//hiXL1/GwYMHrV2K3XJycsK4ceMwYsQI+Pj44OzZs1i5ciUGDhyIo0ePIjQ01Nol2o3MzEzodDo88cQTmDZtGuLj45GcnIz3338fd+7cweeff27xsSQdhEpKSkw+m8TZ2dmwn8iazp8/j5deegn9+/fHs88+a+1y7NLs2bMxfvx4XL16Fdu3b4der4dWq7V2WXbl5s2beP3117Fo0SL4+vpauxy7FRYWhrCwMMP70aNHY/z48ejRowcWLFiAffv2WbE6+1JUVIS7d+9ixowZhqvExo4dC61WizVr1mDp0qXo0KGDRceS9NSYi4sLNBqN0fbKYTUXF5emLonI4I8//sDIkSOhUqkM69mo7jp37oyIiAhMmTIFe/bsQVFREUaNGgUJXydSZ6+99hq8vLwwa9Ysa5dy33nwwQfxxBNP4PDhw9Dr9dYux25Ufj8/9dRTou2TJk0CAKSmplp8LEkHIT8/P+Tl5Rltr9zm7+/f1CURAQAKCgrw2GOP4c6dO9i3bx//LN5D48ePx4kTJ3hvJgtlZmZi7dq1iI2NxdWrV5GVlYWsrCyUlpairKwMWVlZuHXrlrXLtGsBAQHQarUoLi62dil2o/LfxBYtWoi2N2/eHABw+/Zti48l6SAUEhKCjIwMqNVq0faffvrJsJ+oqZWWlmLUqFHIyMjAnj170LVrV2uXdF+pnPIuKCiwciX2ITc3F+Xl5YiNjUXbtm0Nr59++gkZGRlo27Yt16810MWLF+Hs7Aw3Nzdrl2I3evXqBaDiz2dVlWt76zKFK+kgNH78eOj1eqxdu9awTaPRYMOGDejXrx8CAgKsWB1JkV6vx4QJE5CamoodO3agf//+1i7Jbl2/ft1oW1lZGT777DO4uLgwYFooODgYu3btMnp169YNgYGB2LVrF6ZNm2btMu3CjRs3jLb98ssv+PrrrxEZGdmge+FITXR0NABg/fr1ou3r1q2DQqHA4MGDLT6WpBdL9+vXD1FRUViwYAGuX7+OBx98EJ9++imysrKMPlwy74MPPsCdO3cMifybb74x3OFz1qxZUKlU1izPLsydOxdff/01Ro0ahVu3bhndQHHy5MlWqsz+/PWvf4VarUZ4eDhatWqFP/74A1u2bMH58+eRkJDA374t5OPjgzFjxhhtr7yXkKl9ZNqECRPg4uKCsLAwNG/eHGfPnsXatWvh6uqKt956y9rl2ZXQ0FA8//zz+OSTT6DT6TBo0CAkJydjx44dWLBgQd2WEwgSV1JSIsybN09o2bKloFQqhT59+gj79u2zdll2qU2bNgIAk69Lly5Zuzy7MGjQoBo/Q/51rZvPP/9ciIiIEFq0aCEoFArB09NTiIiIEHbv3m3t0u4LgwYNErp162btMuzK6tWrhb59+wpeXl6CQqEQ/Pz8hMmTJwuZmZnWLs0uabVaYcmSJUKbNm0ER0dH4cEHHxTefffdOh9H0o/YICIiImnjhCQRERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQERERSRaDEBEREUkWgxARERFJFoMQEdml4uJitGjRAjKZDO3atUNZWZnJdiUlJQgLC4NMJoOzszN++OGHJq6UiGwZgxAR2aVmzZph4cKFAIBLly7h008/NWpTXl6Op59+GqmpqXBwcMDmzZsRHh7e1KUSkQ2TCYIgWLsIIqL60Gg06NixI65cuYKgoCBkZGTA0dHRsD82Nhbvv/8+AOC9997Dyy+/bK1SichGcUSIiOyWUqnE66+/DgDIysrChg0bDPsSEhIMIWjevHkMQURkEkeEiMiu6fV6dO3aFRkZGWjTpg0yMzOxa9cuTJw4EYIg4KmnnsKWLVsgk8msXSoR2SAGISKye1988QUmTpwIAHjhhRewadMmaDQaDBkyBPv27YOTk5OVKyQiW8WpMSKye9HR0QgJCQEArFu3DhqNBt27d8euXbvMhqATJ05gxIgReOCBB9CsWTP85S9/wfbt25ugaiKyBQxCRGT3ZDIZpk+fbnjfsmVL7N27FyqVqtZ+hw8fxsMPP4yUlBRER0djxowZ+OOPPzBhwgQkJCQ0dtlEZAM4NUZEdi8zMxNhYWHIz88HALi7u+PixYvw8fGpsY9Op0Pnzp2Rk5ODY8eOGUaUCgoK0LdvX2RlZRnWHRHR/YsjQkRk165fv47hw4cjPz8f3t7eAIDCwkLEx8fX2u/777/HhQsXMGnSJEMIAgCVSoWFCxdCq9WavDcREd1fGISIyG4VFxdj5MiRuHjxItzc3JCUlIQxY8YAAD788EPk5ubW2Dc5ORkAEBkZabTv0UcfBQD85z//uec1E5FtYRAiIruk0+kQFRWFtLQ0KBQKJCYmIjQ0FEuWLIFMJkNpaSmWLl1aY//MzEwAQIcOHYz2tWzZEm5uboY2RHT/YhAiIrs0Y8YM7N27FwCwZs0awyjOQw89hCeffBIA8Mknn+DChQsm+xcUFABAjQuqPTw8DG2I6P7FIEREdmfJkiVYv349AGDx4sV4/vnnjfbLZDLodDrDnaeJiExhECIiu7J+/Xq88cYbAIDnn38eS5YsMWrTvXt3jB8/HgCwbds2nD592qhN5UhQTaM+arXa7OX3RGT/GISIyG589913mDFjBoCKBc1r1qypse3ixYvh4OCA8vJyvPbaa0b7K9cGmVoH9Mcff6CoqMjk+iEiur8wCBGR3RgxYgTKysogCAL27dsHhUJRY9tu3bpBr9dDEATs3r3baP+gQYMAAAcOHDDat3//flEbIrp/8YaKRCRJOp0OnTp1Qm5ubo03VPztt98QFBRk1TqJqHExCBGRZB0+fBiPPvoonJ2dMXHiRLi7u2Pnzp24fPkyVq5ciblz51q7RCJqZAxCRCRpx48fx+LFi3H06FGUlZWhe/fuiIuLw4QJE6xdGhE1AQYhIiIikiwuliYiIiLJYhAiIiIiyWIQIiIiIsliECIiIiLJYhAiIiIiyWIQIiIiIsliECIiIiLJYhAiIiIiyWIQIiIiIsliECIiIiLJYhAiIiIiyWIQIiIiIsn6f8fVGgJ18bj9AAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "Xs = np.array([[1, 50], [5, 20], [3, 80], [5, 60]]).astype(np.float64)\n", + "ys = np.array([0, 0, 1, 1])\n", + "svm_clf = SVC(kernel=\"linear\", C=100)\n", + "svm_clf.fit(Xs, ys)\n", + "\n", + "#plt.figure(figsize=(16,4))\n", + "#plt.subplot(121)\n", + "plt.plot(Xs[:, 0][ys==1], Xs[:, 1][ys==1], \"bo\")\n", + "plt.plot(Xs[:, 0][ys==0], Xs[:, 1][ys==0], \"ms\")\n", + "plot_svc_decision_boundary(svm_clf, 0, 6)\n", + "plt.xlabel(\"$x_0$\", fontsize=20)\n", + "plt.ylabel(\"$x_1$ \", fontsize=20, rotation=0)\n", + "plt.title(\"Unscaled\", fontsize=16)\n", + "plt.axis([0, 6, 0, 90]);" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:09.775249Z", + "iopub.status.busy": "2024-01-10T00:20:09.774779Z", + "iopub.status.idle": "2024-01-10T00:20:09.988009Z", + "shell.execute_reply": "2024-01-10T00:20:09.987234Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.preprocessing import StandardScaler\n", + "scaler = StandardScaler()\n", + "X_scaled = scaler.fit_transform(Xs)\n", + "svm_clf.fit(X_scaled, ys)\n", + "\n", + "#plt.subplot(122)\n", + "plt.plot(X_scaled[:, 0][ys==1], X_scaled[:, 1][ys==1], \"bo\")\n", + "plt.plot(X_scaled[:, 0][ys==0], X_scaled[:, 1][ys==0], \"ms\")\n", + "plot_svc_decision_boundary(svm_clf, -2, 2)\n", + "plt.xlabel(\"$x_0$\", fontsize=20)\n", + "plt.title(\"Scaled\", fontsize=16)\n", + "plt.axis([-2, 2, -2, 2]);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Hard margin classification\n", + "\n", + "Hard margin classification corresponds to strictly imposing all training instances correctly classfied." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Problems with hard margin classification\n", + "- Can fail if data not linearly separable.\n", + "- Sensitive to outliers." + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:09.991474Z", + "iopub.status.busy": "2024-01-10T00:20:09.990918Z", + "iopub.status.idle": "2024-01-10T00:20:09.999255Z", + "shell.execute_reply": "2024-01-10T00:20:09.998651Z" + } + }, + "outputs": [], + "source": [ + "X_outliers = np.array([[3.4, 1.3], [3.2, 0.8]])\n", + "y_outliers = np.array([0, 0])\n", + "Xo1 = np.concatenate([X, X_outliers[:1]], axis=0)\n", + "yo1 = np.concatenate([y, y_outliers[:1]], axis=0)\n", + "Xo2 = np.concatenate([X, X_outliers[1:]], axis=0)\n", + "yo2 = np.concatenate([y, y_outliers[1:]], axis=0)\n", + "\n", + "svm_clf2 = SVC(kernel=\"linear\", C=10**9)\n", + "svm_clf2.fit(Xo2, yo2);" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:10.002384Z", + "iopub.status.busy": "2024-01-10T00:20:10.001828Z", + "iopub.status.idle": "2024-01-10T00:20:10.200031Z", + "shell.execute_reply": "2024-01-10T00:20:10.199283Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# plt.figure(figsize=(16,5))\n", + "# plt.subplot(121)\n", + "plt.plot(Xo1[:, 0][yo1==1], Xo1[:, 1][yo1==1], \"bs\")\n", + "plt.plot(Xo1[:, 0][yo1==0], Xo1[:, 1][yo1==0], \"yo\")\n", + "plt.text(0.3, 1.0, \"Impossible!\", fontsize=24, color=\"red\")\n", + "plt.xlabel(\"Petal length\", fontsize=14)\n", + "plt.ylabel(\"Petal width\", fontsize=14)\n", + "plt.annotate(\"Outlier\",\n", + " xy=(X_outliers[0][0], X_outliers[0][1]),\n", + " xytext=(2.5, 1.7),\n", + " ha=\"center\",\n", + " arrowprops=dict(facecolor='black', shrink=0.1),\n", + " fontsize=16,\n", + " )\n", + "plt.axis([0, 5.5, 0, 2]);" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:10.203351Z", + "iopub.status.busy": "2024-01-10T00:20:10.202872Z", + "iopub.status.idle": "2024-01-10T00:20:10.408005Z", + "shell.execute_reply": "2024-01-10T00:20:10.407286Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# plt.subplot(122)\n", + "plt.plot(Xo2[:, 0][yo2==1], Xo2[:, 1][yo2==1], \"bs\")\n", + "plt.plot(Xo2[:, 0][yo2==0], Xo2[:, 1][yo2==0], \"yo\")\n", + "plot_svc_decision_boundary(svm_clf2, 0, 5.5)\n", + "plt.xlabel(\"Petal length\", fontsize=14)\n", + "plt.annotate(\"Outlier\",\n", + " xy=(X_outliers[1][0], X_outliers[1][1]),\n", + " xytext=(3.2, 0.08),\n", + " ha=\"center\",\n", + " arrowprops=dict(facecolor='black', shrink=0.1),\n", + " fontsize=16,\n", + " )\n", + "plt.axis([0, 5.5, 0, 2]);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Soft margin classification\n", + "\n", + "\n", + "Allow some margin violations by varying hyperparameter $C$.\n", + "\n", + "\n", + "Recall, large $C$ corresponds to small regularisation and thus few margin violations. Small $C$ corresponds to greater regularisation and thus more margin violations." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Load data" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:10.411326Z", + "iopub.status.busy": "2024-01-10T00:20:10.410852Z", + "iopub.status.idle": "2024-01-10T00:20:10.418578Z", + "shell.execute_reply": "2024-01-10T00:20:10.417946Z" + } + }, + "outputs": [], + "source": [ + "import numpy as np\n", + "from sklearn import datasets\n", + "from sklearn.pipeline import Pipeline\n", + "from sklearn.preprocessing import StandardScaler\n", + "from sklearn.svm import LinearSVC\n", + "\n", + "iris = datasets.load_iris()\n", + "X = iris[\"data\"][:, (2, 3)] # petal length, petal width\n", + "y = (iris[\"target\"] == 2).astype(np.float64) # Iris-Virginica" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Train SVMs" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:10.421567Z", + "iopub.status.busy": "2024-01-10T00:20:10.421137Z", + "iopub.status.idle": "2024-01-10T00:20:10.424523Z", + "shell.execute_reply": "2024-01-10T00:20:10.423871Z" + } + }, + "outputs": [], + "source": [ + "# disable convergence warning from early stopping\n", + "from warnings import simplefilter\n", + "from sklearn.exceptions import ConvergenceWarning\n", + "simplefilter(\"ignore\", category=ConvergenceWarning)" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:10.427696Z", + "iopub.status.busy": "2024-01-10T00:20:10.427158Z", + "iopub.status.idle": "2024-01-10T00:20:10.441192Z", + "shell.execute_reply": "2024-01-10T00:20:10.440527Z" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/sklearn/svm/_classes.py:32: FutureWarning: The default value of `dual` will change from `True` to `'auto'` in 1.5. Set the value of `dual` explicitly to suppress the warning.\n", + " warnings.warn(\n", + "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/sklearn/svm/_classes.py:32: FutureWarning: The default value of `dual` will change from `True` to `'auto'` in 1.5. Set the value of `dual` explicitly to suppress the warning.\n", + " warnings.warn(\n" + ] + } + ], + "source": [ + "scaler = StandardScaler()\n", + "svm_clf1 = LinearSVC(C=1, loss=\"hinge\", random_state=42)\n", + "svm_clf2 = LinearSVC(C=100, loss=\"hinge\", random_state=42)\n", + "\n", + "scaled_svm_clf1 = Pipeline((\n", + " (\"scaler\", scaler),\n", + " (\"linear_svc\", svm_clf1),\n", + " ))\n", + "scaled_svm_clf2 = Pipeline((\n", + " (\"scaler\", scaler),\n", + " (\"linear_svc\", svm_clf2),\n", + " ))\n", + "\n", + "scaled_svm_clf1.fit(X, y);\n", + "scaled_svm_clf2.fit(X, y);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Compute support vectors" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:10.444584Z", + "iopub.status.busy": "2024-01-10T00:20:10.444121Z", + "iopub.status.idle": "2024-01-10T00:20:10.451499Z", + "shell.execute_reply": "2024-01-10T00:20:10.450894Z" + } + }, + "outputs": [], + "source": [ + "# Convert to unscaled parameters\n", + "b1 = svm_clf1.decision_function([-scaler.mean_ / scaler.scale_])\n", + "b2 = svm_clf2.decision_function([-scaler.mean_ / scaler.scale_])\n", + "w1 = svm_clf1.coef_[0] / scaler.scale_\n", + "w2 = svm_clf2.coef_[0] / scaler.scale_\n", + "svm_clf1.intercept_ = np.array([b1])\n", + "svm_clf2.intercept_ = np.array([b2])\n", + "svm_clf1.coef_ = np.array([w1])\n", + "svm_clf2.coef_ = np.array([w2])\n", + "\n", + "# Find support vectors (LinearSVC does not do this automatically)\n", + "t = y * 2 - 1 # t = +/-1\n", + "support_vectors_idx1 = (t * (X.dot(w1) + b1) < 1).ravel()\n", + "support_vectors_idx2 = (t * (X.dot(w2) + b2) < 1).ravel()\n", + "svm_clf1.support_vectors_ = X[support_vectors_idx1]\n", + "svm_clf2.support_vectors_ = X[support_vectors_idx2]" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Plot" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:10.454748Z", + "iopub.status.busy": "2024-01-10T00:20:10.454166Z", + "iopub.status.idle": "2024-01-10T00:20:10.900018Z", + "shell.execute_reply": "2024-01-10T00:20:10.899257Z" + }, + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(16,4))\n", + "plt.subplot(121)\n", + "plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"g^\", label=\"Iris-Virginica\")\n", + "plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"bs\", label=\"Iris-Versicolor\")\n", + "plot_svc_decision_boundary(svm_clf1, 4, 6)\n", + "plt.xlabel(\"Petal length\", fontsize=14)\n", + "plt.ylabel(\"Petal width\", fontsize=14)\n", + "plt.legend(loc=\"upper left\", fontsize=14)\n", + "plt.title(\"$C = {}$\".format(svm_clf1.C), fontsize=16)\n", + "plt.axis([4, 6, 0.8, 2.8])\n", + "\n", + "plt.subplot(122)\n", + "plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"g^\")\n", + "plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"bs\")\n", + "plot_svc_decision_boundary(svm_clf2, 4, 6)\n", + "plt.xlabel(\"Petal length\", fontsize=14)\n", + "plt.title(\"$C = {}$\".format(svm_clf2.C), fontsize=16)\n", + "plt.axis([4, 6, 0.8, 2.8]);" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercises:** *You can now complete Exercise 1 in the exercises associated with this lecture.*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Non-linear classification with polynomial features" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "So far we have considered linear classification only.\n", + "\n", + "Most data-sets are not linearly separable." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### 1D example \n", + "\n", + "Consider 1D feature space with $x_1$, which is clearly not linearly separable.\n", + "\n", + "However, if augment feature space with $x_2=(x_1)^2$ we see that the resulting 2D feature space is linearly separable." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:10.903323Z", + "iopub.status.busy": "2024-01-10T00:20:10.902893Z", + "iopub.status.idle": "2024-01-10T00:20:10.908148Z", + "shell.execute_reply": "2024-01-10T00:20:10.907548Z" + } + }, + "outputs": [], + "source": [ + "X1D = np.linspace(-4, 4, 9).reshape(-1, 1)\n", + "X2D = np.c_[X1D, X1D**2]\n", + "y = np.array([0, 0, 1, 1, 1, 1, 1, 0, 0])" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:10.911084Z", + "iopub.status.busy": "2024-01-10T00:20:10.910698Z", + "iopub.status.idle": "2024-01-10T00:20:11.175999Z", + "shell.execute_reply": "2024-01-10T00:20:11.175328Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(16, 4))\n", + "plt.subplot(121)\n", + "plt.grid(True, which='both')\n", + "plt.axhline(y=0, color='k')\n", + "plt.plot(X1D[:, 0][y==0], np.zeros(4), \"bs\", markersize=10)\n", + "plt.plot(X1D[:, 0][y==1], np.zeros(5), \"g^\", markersize=10)\n", + "plt.gca().get_yaxis().set_ticks([])\n", + "plt.xlabel(r\"$x_1$\", fontsize=20)\n", + "plt.axis([-4.5, 4.5, -0.2, 0.2])\n", + "\n", + "plt.subplot(122)\n", + "plt.grid(True, which='both')\n", + "plt.axhline(y=0, color='k')\n", + "plt.axvline(x=0, color='k')\n", + "plt.plot(X2D[:, 0][y==0], X2D[:, 1][y==0], \"bs\", markersize=10)\n", + "plt.plot(X2D[:, 0][y==1], X2D[:, 1][y==1], \"g^\", markersize=10)\n", + "plt.xlabel(r\"$x_1$\", fontsize=20)\n", + "plt.ylabel(r\"$x_2$\", fontsize=20, rotation=0)\n", + "plt.gca().get_yaxis().set_ticks([0, 4, 8, 12, 16])\n", + "plt.plot([-4.5, 4.5], [6.5, 6.5], \"r--\", linewidth=3)\n", + "plt.axis([-4.5, 4.5, -1, 17])\n", + "\n", + "plt.subplots_adjust(right=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### 2D example" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:11.179245Z", + "iopub.status.busy": "2024-01-10T00:20:11.178843Z", + "iopub.status.idle": "2024-01-10T00:20:11.327960Z", + "shell.execute_reply": "2024-01-10T00:20:11.327250Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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QuN7jTG5VaImqVPjvkSWnpNEBj2FkCQAQCwQ3wMbCCRSIXirvNWUYhmZXzFa6I131Rr3SHemaXTFbY3uNtfSoW6IwsgQASBSCG2Bj/kCxZk1D5UjET6ruNdV0tE2S6o36iEfdUn3EEgCAWCC4ATZXVCR97WtmtwLJqOVom1+ko26pPGIJAECsENyAJMCIBuKh5WibX3tG3ZJtxNJf6n7bNrNbAsDK7FSRF9ZHcAOSACMaiDX/aFua0uSTr9XtaUpL2bVu4ZS6BwC7VeSF9RHcgCSRbCMaMNep+lNyH3UHDG2S5JNPe2v36lT9KbkyXAlunbnCKUiS7NraXNvjYRYAYMeKvLA2ghsAoBVXhkuVN1fq4ImDQY/5SoevpFxoQ/iba7/1luQK8efBLAAkMyryIh4IbgCAgApzC1WYW2h2M2wv2UaWwt0CweWShg5NTJsAq4lFRV6gpTSzGwAAQDJ64QVp0yY23wZSTdPRtqb8o26GYZjUMtgdwQ0AgDj42tcaRpwIbUBq8Y+2Nd1GRWo+6ga0B8ENAAAAiIGmFXkD8VfkZdQN7UFwAwAAAGIgkoq8QKQoTgIAQATY8B5AMFTkRTwR3AAAiECgDe9Pn/Zq7dp3NHLkN5WR4aTUPZDCqMiLeCG4AQAQoZYb3nu9UnX1UQ0ZIjmd5rUrERhxBABzENwAAEDYAo04tsSIIwDEHsENAABEpOWIIwAg/qgqCQAAAAAWR3ADAAAAAIsjuAEAAACAxRHcAAAAAMDiCG4AAAAAYHEENwAAAACwOIIbAAAAAFgc+7gBAJBC3G42zwYAOyK4AQCQItxuqV8/qa4u+DGZmdL27YQ3ALAapkoCAJAiampChzap4fZQI3IAAHPYNrh5PB794he/UPfu3ZWVlaURI0Zo5cqVbZ43Z84cORyOVpfMzMwEtBoAzFFeVa4BTw5QeVW52U0BAADtYNupklOnTlVZWZnuvPNO9enTR6WlpbrssstUUVGhkSNHtnn+U089pTPPPLPx5/T09Hg2FwBMYxiGZr45U9tqtmnmmzM15pwxcjgczY4pryrX7a/frscufUwX97zYpJYCAIBgbBncNmzYoJdfflkLFizQtGnTJEnXXXedBg4cqHvuuUfvvvtum/cxceJE5efnx7upAGC6FbtWqHJ/pSSpcn+lVuxaoXG9xzXeHk6wAwAA5rLlVMmysjKlp6frlltuabwuMzNTN954o9atW6e9e/e2eR+GYai2tlaGYcSzqSnJ7ZY2bw5+cbvNbiGQOgzD0OyK2Up3NMwqSHeka3bF7GbvfYGCHQAAsBZbBrctW7aob9++ysnJaXb98OHDJUlbt25t8z569uyp3NxcdezYUVOmTNHnn38ej6amHH/Fsm98I/ilXz/CG5Ao/lBWb9RLkuqN+mbhLJxgBwAAzGfLqZLV1dUqKChodb3/uv379wc996yzztJtt92mCy64QC6XS2vWrNGTTz6pDRs2aOPGja3CYFMej0cej6fx59raWkmS1+uV1+tt78NJKgcOSHV1zpDH1NVJBw54FaALI+Z/3nn+zUMfmC9YHxiGoVlvzVK6I70xuEkN4WzWW7NUXFSslbtXNo62Sf8Odst3LNfYnmMT8wCSgF1eB6dPS1Lo9+iG47yy+ENpxS59kMzoA3Px/Jsv3s+9LYPbyZMn5XK5Wl3vrwx58uTJoOfecccdzX7+3ve+p+HDh+vaa6/VwoULde+99wY9d/78+Zo7d26r6ysqKpSdnR1u85Parl25kka3edzate+ouvpozH5vqIqiBw9mqbb2jKC35+ScUpcuwf9mEJ5wqroivlr2wZbaLdpUvanVcfVGvTZVb9KvXv6VXjrwktKUJp98jbenKU13vnanFvRdwFq3CFn9dXDwYJaczjHyeoMX5HI66/X++xWqrrbn+6LV+yAV0Afm4vk3z4kTJ+J6/w7DhvNhBg4cqK5du+rNN99sdv1HH32kc889V7/73e/0ox/9KKL7LCgo0Lnnnqvy8uClsgONuBUWFqq6ulp5eXmRPYgktWWLNGJE29/mrl/v1ZAh0f8+r9erlStX6pJLLpHT2fr3ut3SwIEZqqsL/uEzM9PQhx+eZrPZdmqrDxB/gfrAMAxdWHqhtlRvaRbK/NKUpl6de2nn4Z1B7/evV/+VUbcw2el14HZLhw4Fvz0vz56bb9upD5IVfWAunn/zHTp0SAUFBTp69GjIWXztZcsRt4KCAu3bt6/V9dXV1ZKk7t27R3yfhYWFOnz4cMhjXC5XwJE+p9PJC+RfMsL8i8rIcCqWT1mwPjh6NJzNZh06ejS27UlFvA5iL9IS/U37wHPao89qPwsY2iTJJ5/2HNkjhxwy1Pr7uzSlae7bc3VZ38sYdYuAHV4HvXo1XJKVHfog2dEH5uL5N0+8n3dbBrfBgweroqJCtbW1zdLs+vXrG2+PhGEY2rNnj4bEYggIAGIg2hL9rgyXKm+u1METBwPefur0KV3+P5er5mRNwNt98mlv7V6dqj8lV0brL6wAAEBi2TK4TZw4Ub/5zW/0zDPPNO7j5vF4tHjxYo0YMUKFhYWSJLfbrRMnTqh///6N5x48eFBdunRpdn9PPfWUDh48qPHjxyfuQSApuN1STeDPvZIkj0cKMEjbKD/fnlOSEH9t7b0WjsLcQhXmFga9ffOPNgcNdpL0lQ5fIbQBAGARtgxuI0aM0KRJkzRjxgx98cUX6t27t5YsWaI9e/bo2WefbTzuuuuu0+rVq5uVte7Ro4euuuoqDRo0SJmZmVq7dq1efvllDR48OOJ1cUht/q0P2pqKGUpmprR9O+ENzTUt0V9v1DeW6B/ba2xMpy22FewAAIB12DK4SdLzzz+v2bNna+nSpfrnP/+pr3/96/rrX/+qUaNGhTzv2muv1bvvvqs//elPqqurU48ePXTPPfdo1qxZVIaMgfz8hjASKsxkZjYcZ3c1NdGFNqnh/JoaghuaazraJjXfey3SUTcAAJAcbBvcMjMztWDBAi1YsCDoMatWrWp13e9///s4tgpFRQ0jSKGmDzI9EAiu5WibX7xG3QAAgD3YNrjBuoqKCGZAe7UcbfNj1A0AgNSWZnYDgHjyT90MJVmmbsL+/KNtaUHemtOUptkVs2XD7TcBAECUGHFDUmPqJuzkVP0puY+6Q+69Rol+AABSE8ENSY+pm7CLtvZekyjRDwBAqiK4AYCFUKIfAAAEwho3oJ3CWT/XFtbXAQAAIByMuAHtFM76OY9HcoWY1cb6OgBIXm43a6wBxE67gtvx48fVs2dPffHFFzrnnHO0fft2OZ3OVsedPHlSY8aM0bp16+RyubRixYo2N8gG7IT1cwCAQNxuqV8/qa4u+DGZmQ1fAPLvCIBwtGuqZIcOHTRz5kxJ0u7du7VkyZJWx/h8Pl177bVat26d0tLS9MILLxDaAABASqipCR3apIbbQ43IAUic8qpyDXhygMqrys1uSlDtXuN26623quhfXxH96le/ktfrbXb7nXfeqVdffVWS9Mgjj2jixIlRNBOpyO2WNm8OfnG7zW4hAABAYtkhYNiNYRia+eZMbavZpplvzrTsfqntXuPmcrl0//3366abbtKePXu0ePFi3XLLLZKkhx9+WI8//rgkadq0abrjjjti01qkjHCnmHz4YeLaBACwJrdbOnBA2rUrV1u2SBktPt2wlgzJomXAGHPOGDkcDrObZXsrdq1Q5f5KSVLl/kqt2LVC43qPM7lVrUVVnGTq1Kn69a9/rR07dujBBx/U9ddfr1dffVXTp0+XJF1zzTX69a9/HZOGIrWEO8Xk0KHEtAcA0JoVim/8+4s+p6TRAY9hLRmShV0Chp0YhqHZFbOV7khXvVGvdEe6ZlfM1theYy0XiqMKbunp6Zo3b56uvvpqffrpp/rJT36ipUuXyjAMFRcXq7S01HIPGAAARM8qxTciWUtGcIOd2Slg2EnTMCxJ9Ua9ZUNx1Pu4TZ48WYMHD5YkLVq0SB6PR4MGDdKrr76qM844I+A5+/bt029/+1uNHTtWRUVFOuOMM9StWzd973vf0/r166NtEgAACCJW64cpvgEklj9g1Bv1kpoHjHhIhbV0TcNwU/5QbLW1blEHN4fDoZtvvrnx527duun1119Xbm5u0HMef/xx3XXXXaqqqtLYsWP185//XCNHjtRrr72mCy+8UH/4wx+ibRYAAGjBP0r2jW8Ev/TrR/EnwGoSHTDsUqwjWi3DsF+8Q3F7RR3cdu7cqZKSksafjx8/LleoHYclDR8+XKtWrdInn3yiRYsWaf78+SorK1NFRYXS09P14x//WB6PJ9qmAQCAJhglS5z8/IapoqFkZjYcB7Ql0QEj0Fq6ZOMPw2lB4lCa0iw36hZVcPviiy80fvx41dTUKC8vT5J07NgxzZ8/P+R5V155pS666KJW1//Xf/2XiouL9c9//lMffPBBNE0DAAAwTVFRw/q+TZuCXyiYgnAkOmC0HN2z6rTBaJ2qPyX3Ubd88gW83Sef9tbu1an6UwluWXDtLk5y/PhxTZgwQVVVVTrzzDO1cuVKzZs3T3/+85+1cOFC3X333fqP//iPiO/X6XQ2NKxlLV8AAAAbKSoimCF6iQ4YdirWEQ1XhkuVN1fq4ImDQY/5SoevyJUReiZhIrUrHZ0+fVqTJk3Sxo0blZGRobKyMg0ZMkRz5szRa6+9prq6Os2bN09PP/10RPfrdrtVXl6ugoICDRo0qD1NQ5LwTzFpq1pZXp5UXZ24dgEAACRSIgNGy8qVfslawbIwt1CFuYVmNyNs7Zoqeeutt+r111+XJD399NMaN64hfZ933nn67ne/K0l67rnntGvXrrDv0+v16gc/+IE8Ho8eeughpaent30SkhZTTAAA4WAtGVJBYW6hhhYM1dCCoTp88rCmvDJFh08ebrzuqzlfjcnvsVuxjlQT8YjbnDlz9Oyzz0qSSkpKdMMNN7S6/dVXX9Xp06d1//3368UXX2zzPn0+n6ZOnaq3335bN998s37wgx9E2iwkoXCmmHi9iWkLAKC5cGdGxDsw+b/oO3DAq7Vr39HIkd9URoazVVv5og/JoGW1xzHnjInZCFjTtXSBpmX619Il26ibnUQU3J599lnNnTtXknTDDTdozpw5rY4ZNGiQJk6cqGXLlunll1/WvffeG3Lao8/n0w033KCXXnpJU6ZM0e9+97vIHgEAAEg4f2AKVYEyUYGpqEgqKJCqq49qyBDJ6Wz7HMCOAlV7jNW6s0jW0llp3VcqCTu4LV++XLfeeqskady4cSHXr5WUlOhPf/qTfD6f7rvvPr322msBj/P5fLr++uv1/PPP65prrlFpaanS0qLeoQAAAAQQ61Eyim8AidNy/Vms153ZsVhHqgk7uF122WXyhjkv7dxzz1V9fX3IY5qGtquuukpLly5lXRsAhKm8qly3v367Hrv0MV1U2Hp7FSAQK42SAYhMIqo92q1YR6oxpea+f3rk888/r0mTJumFF14gtAFAmFqucVj7w7VmNwk2wigZYD/hVHtE8jMluM2bN09LlizRmWeeqb59++qBBx5odcwVV1yhwYMHJ75xAGBxLdc4rNy90uQWAQDiqeVom1/TUbf/1+P/mdAyJJIpwW3Pnj2SpC+//FK/+tWvAh5z9tlnE9wAoIVAaxxKVpfovq/cZ3bTAABxEG61x+IfFpvQOiSSKcGttLRUpaWlZvxqmMDtZj0FECuB1jhsqt6krVlbNUETTGwZACAeIqn2iORmSnBD6nC7pX792q5gxmbaQNtCrXF4sfpFzTRmmtg6AEA8UO0RfgQ3xFVNTejQJjXcXlNDcAPaEmqNwycnP9HK3Ss1oR+jbgCQbMKp9hhu9XfYF5umAYANNF3jEIhDDpWsLpFhGAluGQAASARG3ADABtpa42DI0Ge1n+lU/SmmywAxxDptAFZBcAMAGwi1xuH06dNau3atvjv2u4Q2IIZYpw3ASghuAGATwdY4eL1eVWdX66s5XzWhVUDyYp02ACthjRsAAAAAWBzBDQAAAAAsjuCGuMrPb5j/H0pmZsNxAAAAAAJjjRviqqioYdE2FbkAAACA9iO4Ie6KighmAAAAQDSYKgkAAAAAFkdwAwAACIB12gCshKmSgAW43awDBACrYZ02ACshuAEmc7ulfv1Cb/Kamdnw4YEPBwDMlmpfNLFOG4BVENwAk9XUhA5tUsPtNTV8eABgLr5oAgDzsMYNAACEJZIvmgAAsUVwAwALKa8q14AnB6i8qtzspgAAAAthqiQsIdXWTACBGIahmW/O1LaabZr55kyNOWeMHA6H2c0CAAAWQHCD6VgzATRYsWuFKvdXSpIq91dqxa4VGtd7nMmtAgAAVsBUSZiONRNAw2jb7IrZSnekS5LSHemaXTFbhmGY3DIAAGAFBDcAsAD/aFu9US9JqjfqG0fdAAAACG6AyfLzG6aChpKZ2XAcklPL0TY/Rt0AAIAfa9wAkxUVNazfozhL6mq6tq2ppqNurHWDFfi/aGprTTJfNAHWUV5Vrttfv12PXfqYLu55sdnNQRQIboAFFBURzFKVf7QtTWnyydfq9jSlaXbFbI3tNZYKkzAdXzQB9kK14uRCcEPSYosB2MGp+lNyH3UHDG2S5JNPe2v36lT9KbkyXAluHdAaXzQh1hgRih+qFScXgluSS9XwwhYDsAtXhkuVN1fq4ImDQY/5SoevENoAJCVGhOKn6frpeqO+cd00Mzjsi+CWxOwSXuKxZiKSLQYIbjBbYW6hCnMLzW4GACQcI0Lx03L9NOum7Y/glsTsEl5YMwEAQOphRCh+Wj63fjzH9kZwgyWwZgIAgNTCiFD8UK04ObGPGwAAABKK/Svjp2m14kD81Yp5ju2H4AYAAICE8o8INZ3GJzUfEUL7RFKtGPbCVEkAAACLSIVq0OxfGV9UK05eBDcAAAALsEs16Gixf2X8BatW3HTPvK/mfNWEliEaBDckpXhsMQAgcdiQF6nILtWgo8WIkDnYM8/+bBvcPB6P7r//fi1dulT//Oc/9fWvf10PPPCALrnkkjbP3bdvn+666y6tWLFCPp9PxcXFevTRR9WzZ88EtDxxUjm8sMUAYF98uACSH/tXJh575tmfbYPb1KlTVVZWpjvvvFN9+vRRaWmpLrvsMlVUVGjkyJFBz/vyyy9VXFyso0ePaubMmXI6nXr00Ud10UUXaevWrcrLy0vgo4ivVA8vbDEA2JMVP1wwAgjAztgzLznYMrht2LBBL7/8shYsWKBp06ZJkq677joNHDhQ99xzj959992g5y5cuFA7d+7Uhg0bNGzYMEnSpZdeqoEDB+rhhx/Wgw8+mJDHkCiEFwB2YsUPF4wAArA79sxLDrbcDqCsrEzp6em65ZZbGq/LzMzUjTfeqHXr1mnv3r0hzx02bFhjaJOk/v37a8yYMfrjH/8Y13YDAEJrWSLcCqXBA40AAoBdsGde8rBlcNuyZYv69u2rnJycZtcPHz5ckrR169aA5/l8Pr3//vs6//zzW902fPhw7dq1S8eOHYt5ewEAbbPih4uWbeKDDgC7Yc+85GHLqZLV1dUqKChodb3/uv379wc87/Dhw/J4PG2e269fv4DnezweeTyexp9ra2slSV6vV16vN7IHgZjwP+88/+ahD8yXLH2woqr5VB4//4eL5TuWa2zPsaa2KVhbkqUP7CwZ+uD0aUlyhnGcV1Z8mMnQB3YW6Pk3DEOz3poVcs+8WW/NUnFRMVPAYyDef/u2DG4nT56Uy9W6RGxmZmbj7cHOk9SucyVp/vz5mjt3bqvrKyoqlJ2d3XbDETcrV640uwkpjz4wn537wDAMTd8xXQ45ZKj1aJZDDt352p1a0HdBwj5c+NvU8gNPmtKCtsXOfZAs7NwHBw9myekcI683PegxTme93n+/QtXVwT+vmM3OfZAMmj7/Xp9Xuw7uCrln3q6Du/S/f/tfOdPa/tIAoZ04cSKu92/L4JaVldVs5Muv7l9177OysoKeJ6ld50rSjBkzdPfddzf+XFtbq8LCQhUXFydVNUo78Xq9WrlypS655BI5nbzhmIE+MF8y9IHntEe1n9QGDG2SZMjQsbRjunjcxQnb22lF1Qp98t4nra73yadPTn4i59ecjaNuydAHdpcsfVBc7NOhQ4E/ZEtSXp5UVFScwBaFL1n6wK6CPf9DRw1VzYngJca7ZHdhM+4YOXToUFzv35bBraCgQPv27Wt1fXV1tSSpe/fuAc/r3LmzXC5X43GRnCs1jNQFGq1zOp28QZmMPjAffWA+O/eB0+nUxps3trkh75lZZyakPYZhaO7bc0NOL5r79lxd1veyZqNudu6DZGH3PujVq+FiZ3bvA7tr+fz3zOupnnnJtVexVcX7796WwW3w4MGqqKhQbW1tswIl69evb7w9kLS0NA0aNEgbN25sddv69evVs2dPdezYMS5tBgCEZqUNeU/Vn5L7qDvk9KK9tXt1qv5UwkYAAQCpzZZVJSdOnKj6+no988wzjdd5PB4tXrxYI0aMUGFhwz/8brdbH3/8catzKysrm4W37du366233tKkSZMS8wAAIMbeO/aevv7011VeVW52U5KCK8OlypsrtemWTUEvlTdXEtoAk5RXlWvAkwNs955n13bDGmw54jZixAhNmjRJM2bM0BdffKHevXtryZIl2rNnj5599tnG46677jqtXr26Wdnmn/zkJ/r973+vCRMmaNq0aXI6nXrkkUfUtWtX/fznPzfj4QBAVAzD0NL9S/XJyU/YIDqGrDQCCODfDMPQzDdnalvNNlu959m13bAOW464SdLzzz+vO++8U0uXLtXtt98ur9erv/71rxo1alTI8zp27KhVq1Zp1KhReuCBBzR79mydd955Wr16tbp06ZKg1gNA7KzcvVKfnGwoosGePACSnX9fMsle73l2bTesw7bBLTMzUwsWLFB1dbXq6uq0YcMGjRs3rtkxq1atCrhJ6le/+lUtW7ZMR48e1bFjx/SXv/xFvXv3TlTTASBmDMNQyeoSpf3r7dzsDaKZBgQgngzD0OyK2Up3NGyZYPZ7Xrjs2m5Yi22DGwCg4RvcTdWbGoto+DeINuOb3JbTgPhAAiDW/KNW9Ua9JHPf8yJh13bDWghuAGBTLb/B9TPrm1ymAQGIJ6u954XLru2G9RDcAMCmWn6D62fGN7lMAwIQb1Z6z4uEXdsN6yG4AYAN+YNSWpC38TSlJTQ4MQ0IQCy1XC9rtfe8cNm13bAmghsA2FAkG0THG9OAAMRSoPWy4bznfXL4k4S850XCSu/VsD9b7uMGAKnOv0H0wRMHdfr0aa1du1YjR45URsa/39a/0uErCdkguunatqaajrqN6z0uwJnmK68q1+2v367HLn1MF/e82OzmAFDg9bLjeo9rfM9ryjAMXffn6/TRwY9UlFukM9LPMKPJQTV9rw4mUe/VsD+CGwDYlH+DaK/Xq+rsag3pNkROpzOhbWg6DSjQN8r+aUBje4213EazbIabGG63VFMT/Pb8fKmoKHHtgbU1HcGvN+obR+7H9hrb+J7X1N8/+bs+OviRJOm9z9+z5BdFgdoNtAfBDQDQbpFMA7LaN8rBvtVH7LjdUr9+Ul1d8GMyM6Xt2wlvaNByBD/UyH2okMeXMEhGBDcAQLvZdRoQH/gSo6YmdGiTGm6vqSG4ofXr0i/Y6zOSkAckA4IbACAqdpwGxAc+wHoiWS8bacgDkgFVJQEAKYUqmID1RFo2n73RkIoIbgCAlMIHPsB6Ilkvy95oSFVMlQQAG6BsfWzYuQomkMwiWS/rOe2xbVEkIBoENwCwOMrWx46dq2ACyS7c9bLBQt76z9ZrwbsLNP3C6bq83+W8hi2MLyPbh+AGW/LvC3T6tLRrV662bJGa7DvMvkBIKnYqW2/1f4ztWgUTQHMtQ55hGLr1r7dq95HdWrx1sW49/1YTW4dQ+DKy/QhusJ3m+wI5JY1udQz7AiFZ2KlsvV3+MbZjFUy7ys9veD9uax+3/PzEtQnJyU5fcKU6+qr9KE4C24lkXyDA7loW0rByAY1A/xgjtRUVNXyJtmlT8AtfsiFaLSvFWrFCbHlVuQY8OUDlVeVmN8VUdugrKyO4AYBF2alsPf8YI5iiImno0OAXQhuiZfUvuFrORkjl90Wr95XVEdwAwKLsVLaef4wBmMEOX3AxG6GBHfrK6ghuAGBBdtqniH+MAZjF6l9wMRvh36zeV3ZAcAMAC4qkbL3Z+McYsJ5UWFNlhy+4mI3QwA59ZQdUlQQAC4qkbL3X601gy5pjQ2vAeuxS4TVaVt+XsWVVYD8rVweOF6v3lV0Q3ADAouxQtp5/jAHrSZVy61bfl7FpPzTVdNQtGfslEKv3lV0Q3GA77AsEWAf/GAPWYqe9H2PBql9wMRuhNav2lZ0Q3GA7/n2Bamqk06e9Wrv2HY0c+U1lZDgbj8nPp8Q0kCj8Y5w6yqvKdfvrt+uxSx/TxT0vNrs5CKDlKE8qju5YAbMREA8EN9hSUVHDxeuVqquPasgQyels+zwAQPukyropO2NNlXUwGwHxQHADAABtSpV1U3bGmiprYTYCYo3tAAAAQEjsRWV9lFsHkh/BDQAAhMReVNZnp70fAbQPUyUBAEBQrJuyB9ZUAcmP4AYAAIJi3ZR9sKYKSG5MlQQAJER5VbkGPDlA5VXlZjcFYWLdFABYB8ENABB3LUvJ80HfHlg3BQDWwVRJAEDcUUrenlg3BQDWQXADAMRVy+IWFLWwF9ZNAYA1MFUSABBXlJIHACB6BDcAQNy03LjZjw2cAQCIDMENABA3LUfb/Bh1A6yBaq+AfRDcAABxQSl5wNqo9grYC8ENABAXlJIHrC1QtVcA1kVVSQBAXFBKHrAuqr0C9kNwAwDEDaXkAWtqOtomNV93yh6LgDUxVRIAACCFUO0VsCeCGwAAQATsXomRaq+APRHcAAAAwmT3SoxUewXsi+AGAECKs/sIUiLZvRIj1V4B+6I4CQAAKazlCNKYc8ZQVTCIZKjESLVXwL4IbgAApLBAI0jxrCpYXlWu21+/XY9d+pgu7nlx3H5PPCRLJUaqvQL2xFRJAACSRKRTHltWF4x3VUE7rw+jEiMAsxHcAABIAu0JRS2rC8a7qqCd14dRiRGA2QhuAAAkgUhDUaJHkBI9uhdLVGJMHArlAMER3AAAtsIHu9baE4oSPYKU6NG9WKISY2LYeSotkAgUJwEAxEQiik5QATGwSItmNB1BChRG/CNIsaqW2LIao59dqjJSiTExEl0oB7AbRtwAAFFL1Dfldl4jFS/tmfKY6BGkZFgfVphbqKEFQ4NevprzVbObaGt2nkoLJAojbgCAqCXim/Jk2EMrHlqOtvmFGnVL5AhSokf3ko2dt0+IRLJstQDEEyNuAICoJOqbcjuvkYqXaIpmJGoEifVh7Zcqa77YagEIDyNuAICoJOKbcruvkYqXSEKRWeuvWB/Wfqmy5qs9o8ZAKiK4AQDaLVGBig92gdklFBXmFqowt9DUNthNvKcGW2UKJlNpgfAR3AAA7RbvQFVeVa6fLf+ZfPLxwS4IQlFyiudItpWqs9ph1BiwCoIbAKBd4v1Nuf/D5ceHPlZGWgYf7JAy4j2SbaUpmHYZNQasgOAGAGiXeH9T3vTD5WnfaT1+6eO6sPDCgMfywQ7JJJ4j2VaszsqoMRAeghsAoF3i+U15oA+Xz7/3vH467KcpOR0SqSPeI9mU3Qfsi+AGAGi3eH1TzodLpKp4jmRTnRWwN9vu43bkyBHdcsst6tKlizp06KDi4mJt3rw5rHOnTp0qh8PR6tK/f/84txoA0Bb2dEIq849kb7plU9BL5c2VUU0/bhraJOvviVheVa4BTw5QeVW52U0BTGXLETefz6cJEybovffe0/Tp05Wfn6+FCxdq9OjR2rRpk/r06dPmfbhcLi1atKjZdbm5ufFqMgAgTJT+R6qLx0i2XcvuW6kCZlNW2U4BqcWWwa2srEzvvvuuli1bpokTJ0qSJk+erL59+6qkpEQvvfRSm/eRkZGhKVOmxLupAIAI2PXDJWB1di27b6UKmH5WDZNIfrYNbl27dtWVV17ZeF2XLl00efJkvfDCC/J4PHK52n7Tqa+v1/Hjx5WTkxPP5gIAwmTXD5eA1dmx7L4VK2BK1gyTSA22DG5btmzR0KFDlZbWfIne8OHD9cwzz2jHjh0aNGhQyPs4ceKEcnJydOLECZ111lm65ppr9NBDD+nMM8+MZ9MBACHY8cMlYBd2K7tvxSJFVg2TSA22DG7V1dUaNWpUq+sLCgokSfv37w8Z3AoKCnTPPfdo6NCh8vl8euONN7Rw4UK99957WrVqlTIyAj8tHo9HHo+n8efa2lpJktfrldfrjeYhoZ38zzvPv3noA/MlWx90y+6mbtndQh5jtceabH1gR/SB+WLZB4ZhaNZbswJWwJz11iwVFxWbEpRWVAUOk8t3LNfYnmMT3p6meA2YL97PvcMwuTyXz+fTqVOnwjrW5XLJ4XAoPT1dP/rRj7Rw4cJmt7/11lsaM2aMXn31VV1xxRURtePBBx/UrFmz9D//8z+6+uqrAx4zZ84czZ07t9X1L730krKzsyP6fQAAAAhsS+0Wza1q/ZnLr6RniYbkDElgixrC5PQd01V1sqrZdO40palnVk8t6LuAUbcUd+LECX3/+9/X0aNH47IUy/QRt7ffflvFxcVhHbtt2zb1799fWVlZzUa+/Orq6iRJWVlZEbfjrrvu0uzZs1VeXh40uM2YMUN3331348+1tbUqLCxUcXGx8vLyIv6diJ7X69XKlSt1ySWXyOl0mt2clEQfmI8+MB99YL729MGbu9/UXSvu0qNjH9WYc8bEuYXJL1avA8Mw9MvSX4YsUvTXk3/VzKtmJjQorahaoU/e+6TV9T759MnJT+T8mtPUUTfeh8x36NChuN6/6cGtf//+Wrx4cVjH+qdCFhQUqLq6utXt/uu6d+8ecTuysrKUl5enw4cPBz3G5XIFLHridDp5gZiMPjAffWA++sB8VumDVC5V7nQ6tXrv6jYfv2EYun/1/fr40Me6f/X9GtdnHKMlMRLt68Bz2qPPaj8LWaRo37F9MtIMnZFxRrt/TyQMw9Dct+eGDJNz356ry/peZvrfkVXeh1JRvJ9304Nbt27dNHXq1IjOGTx4sNasWSOfz9esQMn69euVnZ2tvn37RtyOY8eOqaamRl26dIn4XAAArCLVS5WH+/ipDGhdVixSRMVbWIHpwa09Jk6cqLKyMr3yyiuN+7jV1NRo2bJluvzyy5uNiu3atUuS1KtXL0kN0ym9Xq86duzY7D5/+ctfyjAMjR8/PkGPAgCA2Ev1QLJy98o2Hz+VAa3PahUwrRgmkXpsG9z+8z//U9dff70++ugj5efna+HChaqvr29VPGTMmIY563v27JEkHThwQEOGDNE111yj/v37S5L+/ve/a/ny5Ro/fry+853vJPSxAAAQK6keSAzDUMnqkjYfvxXLzMP6rBYmkXrS2j7EetLT07V8+XJdddVVeuyxxzR9+nTl5+frrbfeUr9+/UKe26lTJ33rW9/SypUrNWPGDN1zzz369NNP9eCDD+p///d/W+0NBwCAXfgDib98etNAkgq2HtuqTdWbQj7+puG2KX/IM7nYNgAEZduUctZZZ2nRokWqqanR8ePHtWrVKp1//vmtjtuzZ0/jaJvUENyWLl2qnTt36vjx46qrq9OHH36oGTNmsJATAJJEeVW5Bjw5QOVV5WY3JWFSPZAYhqEXq19s8/G3DLd+qRZyAdiPbYMbAACBtCxOkeyBxS/VA8nK3Sv1yclPQj5+f7hNC/LxJ01pKRFyAdgTwQ0AkFQCFedIdqkeSPxr2xwKvI7P//g9pz1hVwYEAKuxZXESAAACSdXiHKleqvxU/Sntrd0rQ4GDqf/xOxwOKgMCsC2CGwAgaaRqtcBUL1XuynBp3fXr9OcVf9bIkSOVkdH6443/8VMZEIBdEdwAAEmh5WibX6qMuqV6ICnMKVSv7F4a0m0IxcYAJCXWuAEAkkKqF+doSypW2gSAZEJwAwDYXqoX52hLqlbaBIBkQnADANheJMU5UlEqVtoEgGTDGjcAgO2lenGOUFK10iYAJBuCGwAgKaR6cY5gUrXSJgAkG6ZKAgCQpJqOtjXlH3VjrRsA2AfBDQCAJEWlzeRDdVAgdRHcAABIQlTaTD5UBwVSG8ENAIAkRKXN5EN1UCC1UZwEAIAkRKXN5EJ1UAAENwAAkhSVNpMH1UEBMFUSAADAwqgOCkAiuAEAAFga1UEBSAQ3AAAAy6I6KAA/ghsAAIBFUR0UgB/FSQAAACyK6qAA/AhuAAAAFkZ1UAASUyUBAAAAwPIIbgAAAABgcQQ3AAAAALA4ghsAAAAAWBzBDQAAAAAsjuAGAAAAABZHcAMAAAAAiyO4AQAAAIDFEdwAAAAAwOIIbgAAAABgcQQ3AAAAALA4ghsAAAAAWBzBDQAAAAAsjuAGAAAAABZHcAMAAAAAiyO4AQAAAIDFEdwAAAAAwOIIbgAAAABgcQQ3AAAAALA4ghsAAAAAWBzBDQAAAAAsjuAGAAAAABZHcAMAAAAAiyO4AQAAAIDFEdwAAAAAwOIIbgAAAABgcQQ3AAAAALA4ghsAAAAAWBzBDQAAAAAsjuAGAAAAABZHcAMAAAAAiyO4AQAAAIDFEdwAAAAAwOIIbgAAAABgcQQ3AAAAALA4ghsAAAAAWBzBDQAAAAAsjuAGAAAAABZHcAMAAAAAiyO4AQAAAIDFEdwAAAAAwOJsGdyqq6t17733qri4WB07dpTD4dCqVasiuo99+/Zp8uTJ6tSpk3JycvSd73xHVVVV8WkwAAAAAETBlsFt+/bteuihh7Rv3z4NGjQo4vO//PJLFRcXa/Xq1Zo5c6bmzp2rLVu26KKLLtKhQ4fi0GIAAAAAaL8MsxvQHt/4xjd06NAhde7cWWVlZZo0aVJE5y9cuFA7d+7Uhg0bNGzYMEnSpZdeqoEDB+rhhx/Wgw8+GI9mAwAAAEC72HLErWPHjurcuXO7zy8rK9OwYcMaQ5sk9e/fX2PGjNEf//jHWDQRAAAAAGLGlsEtGj6fT++//77OP//8VrcNHz5cu3bt0rFjx0xoGQAAAAAEZsupktE4fPiwPB6PCgoKWt3mv27//v3q169fq9s9Ho88Hk/jz0ePHm28T5jD6/XqxIkTOnTokJxOp9nNSUn0gfnoA/PRB+ajD8xHH5iL5998/kxgGEZc7t/04Obz+XTq1KmwjnW5XHI4HFH9vpMnTzbeV0uZmZnNjmlp/vz5mjt3bqvr+/btG1WbAAAAACSHQ4cOKTc3N+b3a3pwe/vtt1VcXBzWsdu2bVP//v2j+n1ZWVmS1GzkzK+urq7ZMS3NmDFDd999d+PPR44cUY8ePeR2u+PSOWhbbW2tCgsLtXfvXuXk5JjdnJREH5iPPjAffWA++sB89IG5eP7Nd/ToURUVFUVViyMU04Nb//79tXjx4rCODTS9MVKdO3eWy+VSdXV1q9v813Xv3j3guS6XK+BIXW5uLi8Qk+Xk5NAHJqMPzEcfmI8+MB99YD76wFw8/+ZLS4tPGRHTg1u3bt00derUhP2+tLQ0DRo0SBs3bmx12/r169WzZ0917NgxYe0BAAAAgLYkfVVJt9utjz/+uNl1EydOVGVlZbPwtn37dr311lsR7wkHAAAAAPFm+ohbez3wwAOSpH/84x+SpKVLl2rt2rWSpPvuu6/xuOuuu06rV69uVt3lJz/5iX7/+99rwoQJmjZtmpxOpx555BF17dpVP//5z8Nug8vlUklJScDpk0gM+sB89IH56APz0Qfmow/MRx+Yi+fffPHuA4cRr3qVcRaqumTThzR69OhWwU2SPvvsM911111asWKFfD6fRo8erUcffVS9e/eOW5sBAAAAoD1sG9wAAAAAIFUk/Ro3AAAAALA7ghsAAAAAWBzBDQAAAAAsjuAWgerqat17770qLi5Wx44d5XA4tGrVqrDPnzNnjhwOR6tLZmZm/BqdZKLtA0nat2+fJk+erE6dOiknJ0ff+c53VFVVFZ8GJ6kjR47olltuUZcuXdShQwcVFxdr8+bNYZ07derUgK+D/v37x7nV9uPxePSLX/xC3bt3V1ZWlkaMGKGVK1eGdS5/57HR3j7g/T42vvzyS5WUlGj8+PHq3LmzHA6HSktLwz4/mvcqNIimD0pLSwO+DhwOhw4cOBDfhieJyspK3XbbbTr33HPVoUMHFRUVafLkydqxY0dY5/MaiF40fRDr14BttwMww/bt2/XQQw+pT58+GjRokNatW9eu+3nqqad05plnNv6cnp4eqyYmvWj74Msvv1RxcbGOHj2qmTNnyul06tFHH9VFF12krVu3Ki8vL04tTx4+n08TJkzQe++9p+nTpys/P18LFy7U6NGjtWnTJvXp06fN+3C5XFq0aFGz63Jzc+PVZNuaOnWqysrKdOedd6pPnz4qLS3VZZddpoqKCo0cOTLoefydx057+8CP9/vo1NTUaN68eSoqKtJ5550X0Rd1sXivQnR94Ddv3jydc845za7r1KlTbBqY5B566CG98847mjRpkr7+9a/rwIEDeuKJJzR06FD93//9nwYOHBj0XF4DsRFNH/jF7DVgIGy1tbXGoUOHDMMwjGXLlhmSjIqKirDPLykpMSQZBw8ejFMLk1+0ffDQQw8ZkowNGzY0Xrdt2zYjPT3dmDFjRqybm5T+8Ic/GJKMZcuWNV73xRdfGJ06dTKuueaaNs//4Q9/aHTo0CGeTUwK69evNyQZCxYsaLzu5MmTRq9evYwLLrgg5Ln8ncdGNH3A+31s1NXVGdXV1YZhGEZlZaUhyVi8eHFY50b7XoUG0fTB4sWLDUlGZWVlHFuY3N555x3D4/E0u27Hjh2Gy+Uyrr322pDn8hqIjWj6INavAaZKRqBjx47q3Llz1PdjGIZqa2tb7S2HtkXbB2VlZRo2bJiGDRvWeF3//v01ZswY/fGPf4xFE5NeWVmZunbtqiuvvLLxui5dumjy5Ml67bXX5PF4wrqf+vp61dbWxquZtldWVqb09HTdcsstjddlZmbqxhtv1Lp167R3796Q5/J3Hr1o+sCP9/vouFwudevWrV3nxuq9KtVF0wdNHTt2TPX19TFoUWq58MILdcYZZzS7rk+fPjr33HO1bdu2kOfyGoiNaPqgqVi8BghuJujZs6dyc3PVsWNHTZkyRZ9//rnZTUoJPp9P77//vs4///xWtw0fPly7du3SsWPHTGiZvWzZskVDhw5VWlrzt4/hw4frxIkTYc35PnHihHJycpSbm6vOnTvrpz/9qb788st4NdmWtmzZor59+yonJ6fZ9cOHD5ckbd26NeB5/J3HTnv7oCne780Ti/cqxEZxcbFycnKUnZ2tb3/729q5c6fZTbI1wzD0+eefKz8/P+RxvAbiJ9w+8IvVa4A1bgl01lln6bbbbtMFF1wgl8ulNWvW6Mknn9SGDRu0cePGVh8OEFuHDx+Wx+NRQUFBq9v81+3fv1/9+vVLdNNspbq6WqNGjWp1fdPncNCgQUHPLygo0D333KOhQ4fK5/PpjTfe0MKFC/Xee+9p1apVysjgbUlqeJ7b+lsNhL/z2GlvH0i831tBtO9ViF52dramTp3a+KF106ZNeuSRR3ThhRdq8+bNKiwsNLuJtvTiiy9q3759mjdvXsjjeA3ET7h9EOvXQMp+QvL5fDp16lRYx7pcLjkcjqh/5x133NHs5+9973saPny4rr32Wi1cuFD33ntv1L/DThLdBydPnmy8r5b8ld78x6SK9vTByZMno3oO58+f3+znq6++Wn379tWsWbNUVlamq6++OszWJ7f2Ps/8ncdONH/rvN+bL9r3KkRv8uTJmjx5cuPPV1xxhcaNG6dRo0bpV7/6lX73u9+Z2Dp7+vjjj/XTn/5UF1xwgX74wx+GPJbXQHxE0gexfg2k7FTJt99+W1lZWWFdtm/fHrd2fP/731e3bt1UXl4et99hVYnug6ysLEkKOKe7rq6u2TGpoj19kJWVFfPn8K677lJaWlpKvg6Cae/zzN957MT6bz2V3+/NEI/3KkRv5MiRGjFiBK+Ddjhw4IAmTJig3NzcxjW4ofAaiL1I+yCQaF4DKTvi1r9/fy1evDisYwNNlYmlwsJCHT58OK6/w4oS3QedO3eWy+VSdXV1q9v813Xv3j3q32Mn7emDgoKCmD+HWVlZysvLS8nXQTAFBQXat29fq+vbep75O4+d9vZBKKn6fm+GeLxXITYKCwvj+qV4Mjp69KguvfRSHTlyRGvWrAnr75fXQGy1pw+Cae9rIGWDW7du3TR16lSzmyHDMLRnzx4NGTLE7KYkXKL7IC0tTYMGDdLGjRtb3bZ+/Xr17NlTHTt2TFh7rKA9fTB48GCtWbNGPp+v2YLn9evXKzs7W3379o24HceOHVNNTY26dOkS8bnJavDgwaqoqFBtbW2z9VDr169vvD0Q/s5jp719EEwqv9+bIR7vVYiNqqoq3u8jUFdXp8svv1w7duxQeXm5BgwYENZ5vAZip719EEx7XwMpO1Uy3txutz7++ONm1x08eLDVcU899ZQOHjyo8ePHJ6ppKSNQH0ycOFGVlZXNPtRu375db731liZNmpToJtrSxIkT9fnnn+uVV15pvK6mpkbLli3T5Zdf3mw+/a5du7Rr167Gn+vq6gJWNPzlL38pwzB4HTQxceJE1dfX65lnnmm8zuPxaPHixRoxYkTjgmb+zuMnmj7g/T6xqqur9fHHH8vr9TZeF8l7FaIXqA8CvQ6WL1+uTZs28ToIU319va666iqtW7dOy5Yt0wUXXBDwOF4D8RNNH8T6NeAw2FwmIg888IAk6R//+Idefvll3XDDDY07od93332Nx40ePVqrV69utndPdna2rrrqKg0aNEiZmZlau3atXn75ZZ133nl65513lJ2dndgHY1PR9MGxY8c0ZMgQHTt2TNOmTZPT6dQjjzyi+vp6bd26lW8Aw1BfX6+RI0fqww8/1PTp05Wfn6+FCxfK7XarsrKyWbXCs88+W5K0Z8+exv8OGTJE11xzjfr37y9J+vvf/67ly5dr/Pjx+tvf/taqbHEqmzx5sl599VXddddd6t27t5YsWaINGzbozTffbKwUxt95fLW3D3i/j50nnnhCR44c0f79+/XUU0/pyiuvbBy1/NnPfqbc3FxNnTpVS5Ys0e7duxvfdyJ5r0Jo7e2DPn36aMiQITr//POVm5urzZs367nnnlNBQYEqKyvVtWtXEx+VPdx555367//+b11++eXNilz4TZkyRZJ4DcRRNH0Q89dATLbxTiGSgl6auuiii1pdd9NNNxkDBgwwOnbsaDidTqN3797GL37xC6O2tjaRD8H2oukDwzCMvXv3GhMnTjRycnKMM8880/jWt75l7Ny5M1HNTwqHDx82brzxRiMvL8/Izs42LrroIqOysrLVcT169DB69OjR+PM///lPY8qUKUbv3r2N7Oxsw+VyGeeee67x4IMPGqdOnUrgI7CHkydPGtOmTTO6detmuFwuY9iwYcYbb7zR7Bj+zuOrvX3A+33s9OjRI+h7/u7duw3DMIwf/vCHzX72C/e9CqG1tw9mzZplDB482MjNzTWcTqdRVFRk/PjHPzYOHDhgzgOxIf/7S1ufe3gNxE80fRDr1wAjbgAAAABgccxJAgAAAACLI7gBAAAAgMUR3AAAAADA4ghuAAAAAGBxBDcAAAAAsDiCGwAAAABYHMENAAAAACyO4AYAAAAAFkdwAwAAAACLI7gBAAAAgMUR3AAAAADA4ghuAAAAAGBxBDcAAAAAsDiCGwAAARw/flxdu3aVw+FQz5495fV6Ax538uRJXXjhhXI4HMrMzNTbb7+d4JYCAFIBwQ0AgAA6dOigmTNnSpJ2796tJUuWtDrG5/Pp2muv1bp165SWlqYXXnhBo0aNSnRTAQApwGEYhmF2IwAAsCKPx6O+ffvK7Xbr7LPP1o4dO+R0Ohtvv/322/X4449Lkn7729/qjjvuMKupAIAkx4gbAABBuFwu3X///ZKkPXv2aPHixY23Pfzww42hbdq0aYQ2AEBcMeIGAEAI9fX1GjBggHbs2KEePXpo586devXVV3X11VfLMAxdc801evHFF+VwOMxuKgAgiRHcAABowx/+8AddffXVkqSbbrpJS5culcfjUXFxsd544w2dccYZJrcQAJDsCG4AALTBMAwNHTpUW7dubbxu0KBBWrNmjXJzc4Oe98ILL2jNmjXatGmTPvjgA506dUqLFy/W1KlT499oAEBSYY0bAABtcDgcuvnmmxt/7tatm15//fWQoU2S7rvvPj3zzDP69NNPVVBQEO9mAgCSGMENAIA27Ny5UyUlJY0/Hz9+XC6Xq83zFi1apD179ujgwYO69dZb49lEAECSI7gBABDCF198ofHjx6umpkZ5eXmSpGPHjmn+/PltnnvxxRerR48e8W4iACAFENwAAAji+PHjmjBhgqqqqnTmmWdq5cqVuuKKKyRJCxcu1L59+8xtIAAgZRDcAAAI4PTp05o0aZI2btyojIwMlZWVaciQIZozZ44cDofq6uo0b948s5sJAEgRBDcAAAK49dZb9frrr0uSnn76aY0bN06SdN555+m73/2uJOm5557Trl27TGsjACB1ENwAAGhhzpw5evbZZyVJJSUluuGGG1rd7nA4dPr0ad1///1mNBEAkGIIbgAANPHss89q7ty5kqQbbrhBc+bMaXXMoEGDNHHiREnSyy+/rA8++CCRTQQApCCCGwAA/7J8+fLGsv3jxo3T008/HfTYkpISpaWlyefz6b777ktUEwEAKSrD7AYAAGAVl112mbxeb1jHnnvuuaqvr49ziwAAaMCIGwAAAABYnMMwDMPsRgAAkIwWLVqktWvXSpI++OADbd68Wd/85jfVu3dvSdLIkSN10003mdlEAIBNMFUSAIA4Wbt2rZYsWdLsunfeeUfvvPNO488ENwBAOBhxAwAAAACLY40bAAAAAFgcwQ0AAAAALI7gBgAAAAAWR3ADAAAAAIsjuAEAAACAxRHcAAAAAMDiCG4AAAAAYHEENwAAAACwOIIbAAAAAFgcwQ0AAAAALI7gBgAAAAAWR3ADAAAAAIv7/zfg5bG10vSWAAAAAElFTkSuQmCC", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "from sklearn.datasets import make_moons\n", + "X, y = make_moons(n_samples=100, noise=0.15, random_state=42)\n", + "\n", + "def plot_dataset(X, y, axes):\n", + " plt.plot(X[:, 0][y==0], X[:, 1][y==0], \"bs\")\n", + " plt.plot(X[:, 0][y==1], X[:, 1][y==1], \"g^\")\n", + " plt.axis(axes)\n", + " plt.grid(True, which='both')\n", + " plt.xlabel(r\"$x_1$\", fontsize=20)\n", + " plt.ylabel(r\"$x_2$\", fontsize=20, rotation=0)\n", + "\n", + "plt.figure(figsize=(10, 5))\n", + "plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:11.331500Z", + "iopub.status.busy": "2024-01-10T00:20:11.330810Z", + "iopub.status.idle": "2024-01-10T00:20:11.339010Z", + "shell.execute_reply": "2024-01-10T00:20:11.338465Z" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/sklearn/svm/_classes.py:32: FutureWarning: The default value of `dual` will change from `True` to `'auto'` in 1.5. Set the value of `dual` explicitly to suppress the warning.\n", + " warnings.warn(\n" + ] + } + ], + "source": [ + "from sklearn.datasets import make_moons\n", + "from sklearn.pipeline import Pipeline\n", + "from sklearn.preprocessing import PolynomialFeatures\n", + "\n", + "polynomial_svm_clf = Pipeline((\n", + " (\"poly_features\", PolynomialFeatures(degree=3)),\n", + " (\"scaler\", StandardScaler()),\n", + " (\"svm_clf\", LinearSVC(C=10, loss=\"hinge\", random_state=42))\n", + " ))\n", + "\n", + "polynomial_svm_clf.fit(X, y);" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:11.342040Z", + "iopub.status.busy": "2024-01-10T00:20:11.341364Z", + "iopub.status.idle": "2024-01-10T00:20:11.553315Z", + "shell.execute_reply": "2024-01-10T00:20:11.552726Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_predictions(clf, axes):\n", + " x0s = np.linspace(axes[0], axes[1], 100)\n", + " x1s = np.linspace(axes[2], axes[3], 100)\n", + " x0, x1 = np.meshgrid(x0s, x1s)\n", + " X = np.c_[x0.ravel(), x1.ravel()]\n", + " y_pred = clf.predict(X).reshape(x0.shape)\n", + " y_decision = clf.decision_function(X).reshape(x0.shape)\n", + " plt.contourf(x0, x1, y_pred, cmap=plt.cm.brg, alpha=0.2)\n", + " plt.contourf(x0, x1, y_decision, cmap=plt.cm.brg, alpha=0.1)\n", + "\n", + "plt.figure(figsize=(10,5))\n", + "plot_predictions(polynomial_svm_clf, [-1.5, 2.5, -1, 1.5])\n", + "plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Adding polynomial features leads to a combinatorial increase in the dimensionality of the feature space and thus is computationally costly." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "There are much better ways to perform non-linear classification with SVMs, where computational tricks can be exploited..." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Non-linear classification with kernels" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Similarity features and landmarks\n", + "\n", + "Compute new features based on proximity to landmarks.\n", + "\n", + "Consider landmarks $l^{(1)}$, $l^{(2)}$, $\\ldots$\n", + "\n", + "Then for each training instance $x$, compute features $f_j = \\text{sim}(x, l^{(j)})$, where $\\text{sim(.,.)}$ defines a *similarity* function.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Similarity functions\n", + "\n", + "The Gaussian radial basis function (RBF) is a common *similarity function*:\n", + "\n", + "$$\n", + "\\phi_\\gamma(x,l) = exp( - \\gamma \\| x-l \\|^2),\n", + "$$\n", + "\n", + "where $\\gamma$ controls the width of the kernel.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### 1D example (from above)\n", + "\n", + "Consider landmarks at $x_1=-2$ and $x_1=1$." + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:11.556833Z", + "iopub.status.busy": "2024-01-10T00:20:11.556239Z", + "iopub.status.idle": "2024-01-10T00:20:11.561660Z", + "shell.execute_reply": "2024-01-10T00:20:11.561119Z" + } + }, + "outputs": [], + "source": [ + "def gaussian_rbf(x, landmark, gamma):\n", + " return np.exp(-gamma * np.linalg.norm(x - landmark, axis=1)**2)\n", + "\n", + "gamma = 0.3\n", + "\n", + "x1s = np.linspace(-4.5, 4.5, 200).reshape(-1, 1)\n", + "x2s = gaussian_rbf(x1s, -2, gamma)\n", + "x3s = gaussian_rbf(x1s, 1, gamma)\n", + "\n", + "XK = np.c_[gaussian_rbf(X1D, -2, gamma), gaussian_rbf(X1D, 1, gamma)]\n", + "yk = np.array([0, 0, 1, 1, 1, 1, 1, 0, 0])" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:11.564642Z", + "iopub.status.busy": "2024-01-10T00:20:11.563993Z", + "iopub.status.idle": "2024-01-10T00:20:11.979858Z", + "shell.execute_reply": "2024-01-10T00:20:11.979177Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(16, 4))\n", + "plt.subplot(121)\n", + "plt.grid(True, which='both')\n", + "plt.axhline(y=0, color='k')\n", + "plt.scatter(x=[-2, 1], y=[0, 0], s=150, alpha=0.5, c=\"red\")\n", + "plt.plot(X1D[:, 0][yk==0], np.zeros(4), \"bs\", markersize=10)\n", + "plt.plot(X1D[:, 0][yk==1], np.zeros(5), \"g^\", markersize=10)\n", + "plt.plot(x1s, x2s, \"g--\")\n", + "plt.plot(x1s, x3s, \"b:\")\n", + "plt.gca().get_yaxis().set_ticks([0, 0.25, 0.5, 0.75, 1])\n", + "plt.xlabel(r\"$x_1$\", fontsize=20)\n", + "plt.ylabel(r\"Similarity\", fontsize=14)\n", + "plt.annotate(r'$\\mathbf{x}$',\n", + " xy=(X1D[3, 0], 0),\n", + " xytext=(-0.5, 0.20),\n", + " ha=\"center\",\n", + " arrowprops=dict(facecolor='black', shrink=0.1),\n", + " fontsize=18,\n", + " )\n", + "plt.text(-2, 0.9, \"$x_2$\", ha=\"center\", fontsize=20)\n", + "plt.text(1, 0.9, \"$x_3$\", ha=\"center\", fontsize=20)\n", + "plt.axis([-4.5, 4.5, -0.1, 1.1])\n", + "\n", + "plt.subplot(122)\n", + "plt.grid(True, which='both')\n", + "plt.axhline(y=0, color='k')\n", + "plt.axvline(x=0, color='k')\n", + "plt.plot(XK[:, 0][yk==0], XK[:, 1][yk==0], \"bs\", markersize=10)\n", + "plt.plot(XK[:, 0][yk==1], XK[:, 1][yk==1], \"g^\", markersize=10)\n", + "plt.xlabel(r\"$x_2$\", fontsize=20)\n", + "plt.ylabel(r\"$x_3$ \", fontsize=20, rotation=0)\n", + "plt.annotate(r'$\\phi\\left(\\mathbf{x}\\right)$',\n", + " xy=(XK[3, 0], XK[3, 1]),\n", + " xytext=(0.65, 0.50),\n", + " ha=\"center\",\n", + " arrowprops=dict(facecolor='black', shrink=0.1),\n", + " fontsize=18,\n", + " )\n", + "plt.plot([-0.1, 1.1], [0.57, -0.1], \"r--\", linewidth=3)\n", + "plt.axis([-0.1, 1.1, -0.1, 1.1])\n", + " \n", + "plt.subplots_adjust(right=1)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "Training data *are* linearly separable in new feature space." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + }, + "tags": [ + "inclass_exercise" + ] + }, + "source": [ + "### Exercise: What are new feature values corresponding to the instance at $x_1=-1$ ($\\gamma=0.3$)?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + }, + "tags": [ + "solution", + "inclass_exercise" + ] + }, + "source": [ + "$x_2 = \\exp(-0.3 \\times (1)^2) = 0.74$\n", + "\n", + "$x_3 = \\exp(-0.3 \\times (2)^2) = 0.30$\n", + "\n", + "Let's check:" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:11.983440Z", + "iopub.status.busy": "2024-01-10T00:20:11.982863Z", + "iopub.status.idle": "2024-01-10T00:20:11.987586Z", + "shell.execute_reply": "2024-01-10T00:20:11.987051Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Phi(-1.0, -2) = [0.74081822]\n", + "Phi(-1.0, 1) = [0.30119421]\n" + ] + } + ], + "source": [ + "x1_example = X1D[3, 0]\n", + "for landmark in (-2, 1):\n", + " k = gaussian_rbf(np.array([[x1_example]]), np.array([[landmark]]), gamma)\n", + " print(\"Phi({}, {}) = {}\".format(x1_example, landmark, k))" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### How set landmarks?" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Common approach is to set a landmark at the location of each instance in the training data-set." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Kernel trick" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For SVMs it is not necessary to actually compute new features for each kernel.\n", + "\n", + "Instead, can be done implicitly, providing *considerable* computational saving." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "SVM are well suited for small to medium sized data-sets, with complex structure." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "The kernel trick is based on Mercer's theorem." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "#### Mercer's theorem\n", + "\n", + "For (feature) mapping function $\\phi(x)$, the inner product of two transformed vectors can be computed implicitly by the evaluation of the kernel function $K$ by\n", + "$\n", + "K(x,z) = \\langle \\phi(x), \\phi(z) \\rangle .\n", + "$\n", + "\n", + "There is therefore no need to explicitly compute $\\phi(x)$.\n", + "\n", + "Moreoever, it is not necessary to even know the explicit form of the (feature) mapping function $\\phi(x)$.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "(We will not cover the kernel trick and Mercer's theorem in any further detail.)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Common kernels\n", + "\n", + "Some common similarity function, or *kernel*, include the following.\n", + "\n", + "1. Gaussian radial basis function (RBF):\n", + "$\n", + "K_\\gamma(x,l) = exp( - \\gamma \\| x-l \\|^2),\n", + "$\n", + "where $\\gamma$ controls the width of the kernel.\n", + "\n", + "2. Polynomial kernel:\n", + "$\n", + "K_{c, d}(x,l) = (x^{\\rm T}l + c)^d,\n", + "$\n", + "for constant offset $c$ and degree $d$.\n", + "\n", + "3. Linear kernel, i.e. linear SVM:\n", + "$\n", + "K(x,l) = x^{\\rm T}l.\n", + "$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### 2D example (from above)" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:11.991176Z", + "iopub.status.busy": "2024-01-10T00:20:11.990615Z", + "iopub.status.idle": "2024-01-10T00:20:12.002315Z", + "shell.execute_reply": "2024-01-10T00:20:12.001682Z" + } + }, + "outputs": [], + "source": [ + "from sklearn.svm import SVC\n", + "\n", + "gamma1, gamma2 = 0.1, 5\n", + "C1, C2 = 0.001, 1000\n", + "hyperparams = (gamma1, C1), (gamma1, C2), (gamma2, C1), (gamma2, C2)\n", + "\n", + "svm_clfs = []\n", + "for gamma, C in hyperparams:\n", + " rbf_kernel_svm_clf = Pipeline((\n", + " (\"scaler\", StandardScaler()),\n", + " (\"svm_clf\", SVC(kernel=\"rbf\", gamma=gamma, C=C))\n", + " ))\n", + " rbf_kernel_svm_clf.fit(X, y)\n", + " svm_clfs.append(rbf_kernel_svm_clf)" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:12.005352Z", + "iopub.status.busy": "2024-01-10T00:20:12.004809Z", + "iopub.status.idle": "2024-01-10T00:20:13.099222Z", + "shell.execute_reply": "2024-01-10T00:20:13.098533Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(16, 8))\n", + "\n", + "for i, svm_clf in enumerate(svm_clfs):\n", + " plt.subplot(221 + i)\n", + " plot_predictions(svm_clf, [-1.5, 2.5, -1, 1.5])\n", + " plot_dataset(X, y, [-1.5, 2.5, -1, 1.5])\n", + " gamma, C = hyperparams[i]\n", + " plt.title(r\"$\\gamma = {}, C = {}$\".format(gamma, C), fontsize=16)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "**Exercises:** *You can now complete Exercise 2 in the exercises associated with this lecture.*" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Regression" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "fragment" + } + }, + "source": [ + "Can also use SVMs to perform regression, in addition to classification.\n", + "\n", + "General idea is to reverse the objective: rather than fitting the largest possible margin between two classes, SVM regression fits as many instances as possible within the margin. \n", + "\n", + "The width of the margin is controlled by the hyperparameter $\\epsilon$." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Linear regression" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:13.103087Z", + "iopub.status.busy": "2024-01-10T00:20:13.102462Z", + "iopub.status.idle": "2024-01-10T00:20:13.107290Z", + "shell.execute_reply": "2024-01-10T00:20:13.106674Z" + } + }, + "outputs": [], + "source": [ + "np.random.seed(42)\n", + "m = 50\n", + "X = 2 * np.random.rand(m, 1)\n", + "y = (4 + 3 * X + np.random.randn(m, 1)).ravel()" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:13.110249Z", + "iopub.status.busy": "2024-01-10T00:20:13.109685Z", + "iopub.status.idle": "2024-01-10T00:20:13.118040Z", + "shell.execute_reply": "2024-01-10T00:20:13.117503Z" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/sklearn/svm/_classes.py:32: FutureWarning: The default value of `dual` will change from `True` to `'auto'` in 1.5. Set the value of `dual` explicitly to suppress the warning.\n", + " warnings.warn(\n", + "/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/sklearn/svm/_classes.py:32: FutureWarning: The default value of `dual` will change from `True` to `'auto'` in 1.5. Set the value of `dual` explicitly to suppress the warning.\n", + " warnings.warn(\n" + ] + } + ], + "source": [ + "from sklearn.svm import LinearSVR\n", + "\n", + "svm_reg1 = LinearSVR(epsilon=1.5, random_state=42)\n", + "svm_reg2 = LinearSVR(epsilon=0.5, random_state=42)\n", + "svm_reg1.fit(X, y)\n", + "svm_reg2.fit(X, y)\n", + "\n", + "def find_support_vectors(svm_reg, X, y):\n", + " y_pred = svm_reg.predict(X)\n", + " off_margin = (np.abs(y - y_pred) >= svm_reg.epsilon)\n", + " return np.argwhere(off_margin)\n", + "\n", + "svm_reg1.support_ = find_support_vectors(svm_reg1, X, y)\n", + "svm_reg2.support_ = find_support_vectors(svm_reg2, X, y)\n", + "\n", + "eps_x1 = 1\n", + "eps_y_pred = svm_reg1.predict([[eps_x1]])" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:13.120834Z", + "iopub.status.busy": "2024-01-10T00:20:13.120604Z", + "iopub.status.idle": "2024-01-10T00:20:13.125151Z", + "shell.execute_reply": "2024-01-10T00:20:13.124515Z" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([6.52640746])" + ] + }, + "execution_count": 36, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "eps_y_pred" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:13.128852Z", + "iopub.status.busy": "2024-01-10T00:20:13.128404Z", + "iopub.status.idle": "2024-01-10T00:20:13.611003Z", + "shell.execute_reply": "2024-01-10T00:20:13.610305Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def plot_svm_regression(svm_reg, X, y, axes):\n", + " x1s = np.linspace(axes[0], axes[1], 100).reshape(100, 1)\n", + " y_pred = svm_reg.predict(x1s)\n", + " plt.plot(x1s, y_pred, \"k-\", linewidth=2, label=r\"$\\hat{y}$\")\n", + " plt.plot(x1s, y_pred + svm_reg.epsilon, \"k--\")\n", + " plt.plot(x1s, y_pred - svm_reg.epsilon, \"k--\")\n", + " plt.scatter(X[svm_reg.support_], y[svm_reg.support_], s=180, facecolors='#FFAAAA')\n", + " plt.plot(X, y, \"bo\")\n", + " plt.xlabel(r\"$x_1$\", fontsize=18)\n", + " plt.legend(loc=\"upper left\", fontsize=18)\n", + " plt.axis(axes)\n", + "\n", + "plt.figure(figsize=(16, 5))\n", + "plt.subplot(121)\n", + "plot_svm_regression(svm_reg1, X, y, [0, 2, 3, 11])\n", + "plt.title(r\"$\\epsilon = {}$\".format(svm_reg1.epsilon), fontsize=18)\n", + "plt.ylabel(r\"$y$\", fontsize=18, rotation=0)\n", + "#plt.plot([eps_x1, eps_x1], [eps_y_pred, eps_y_pred - svm_reg1.epsilon], \"k-\", linewidth=2)\n", + "plt.annotate(\n", + " '', xy=(eps_x1, eps_y_pred), xycoords='data',\n", + " xytext=(eps_x1, eps_y_pred - svm_reg1.epsilon),\n", + " textcoords='data', arrowprops={'arrowstyle': '<->', 'linewidth': 1.5}\n", + " )\n", + "plt.text(0.91, 5.6, r\"$\\epsilon$\", fontsize=20)\n", + "plt.subplot(122)\n", + "plot_svm_regression(svm_reg2, X, y, [0, 2, 3, 11])\n", + "plt.title(r\"$\\epsilon = {}$\".format(svm_reg2.epsilon), fontsize=18);" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "subslide" + } + }, + "source": [ + "### Non-linear regression" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:13.614588Z", + "iopub.status.busy": "2024-01-10T00:20:13.614131Z", + "iopub.status.idle": "2024-01-10T00:20:13.619620Z", + "shell.execute_reply": "2024-01-10T00:20:13.618994Z" + } + }, + "outputs": [], + "source": [ + "np.random.seed(42)\n", + "m = 100\n", + "X = 2 * np.random.rand(m, 1) - 1\n", + "y = (0.2 + 0.1 * X + 0.5 * X**2 + np.random.randn(m, 1)/10).ravel()" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:13.622590Z", + "iopub.status.busy": "2024-01-10T00:20:13.622133Z", + "iopub.status.idle": "2024-01-10T00:20:13.634075Z", + "shell.execute_reply": "2024-01-10T00:20:13.633427Z" + } + }, + "outputs": [], + "source": [ + "from sklearn.svm import SVR\n", + "\n", + "svm_poly_reg1 = SVR(kernel=\"poly\", degree=2, C=100, epsilon=0.1)\n", + "svm_poly_reg2 = SVR(kernel=\"poly\", degree=2, C=0.01, epsilon=0.1)\n", + "svm_poly_reg1.fit(X, y);\n", + "svm_poly_reg2.fit(X, y);" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": { + "execution": { + "iopub.execute_input": "2024-01-10T00:20:13.637220Z", + "iopub.status.busy": "2024-01-10T00:20:13.636764Z", + "iopub.status.idle": "2024-01-10T00:20:14.087863Z", + "shell.execute_reply": "2024-01-10T00:20:14.087257Z" + } + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(16, 5))\n", + "plt.subplot(121)\n", + "plot_svm_regression(svm_poly_reg1, X, y, [-1, 1, 0, 1])\n", + "plt.title(r\"$degree={}, C={}, \\epsilon = {}$\".format(svm_poly_reg1.degree, svm_poly_reg1.C, svm_poly_reg1.epsilon), fontsize=18)\n", + "plt.ylabel(r\"$y$\", fontsize=18, rotation=0)\n", + "plt.subplot(122)\n", + "plot_svm_regression(svm_poly_reg2 , X, y, [-1, 1, 0, 1])\n", + "plt.title(r\"$degree={}, C={}, \\epsilon = {}$\".format(svm_poly_reg2.degree, svm_poly_reg2.C, svm_poly_reg2.epsilon), fontsize=18);" + ] + } + ], + "metadata": { + "celltoolbar": "Slideshow", + "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": "3.13.1" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}