{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# MDI 720 : Statistiques\n", "## Generalization\n", "### *Joseph Salmon*\n", "\n", "This notebook reproduces the pictures for the course \"Generalization_fr\"" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import seaborn as sns\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "from os import mkdir, path\n", "import statsmodels.formula.api as smf\n", "from matplotlib import rc\n", "from sklearn.linear_model import LinearRegression, SGDRegressor\n", "from sklearn.model_selection import GridSearchCV\n", "from sklearn.preprocessing import PolynomialFeatures\n", "from sklearn.pipeline import make_pipeline\n", "from scipy.interpolate import UnivariateSpline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "dirname = \"../prebuiltimages/\"\n", "if not path.exists(dirname):\n", " mkdir(dirname)\n", "\n", "\n", "np.random.seed(seed=44)\n", "\n", "###############################################################################\n", "# Plot initialization\n", "\n", "plt.close('all')\n", "dirname = \"../srcimages/\"\n", "imageformat = '.pdf'\n", "\n", "\n", "rc('font', **{'family': 'sans-serif', 'sans-serif': ['Computer Modern Roman']})\n", "params = {'axes.labelsize': 12,\n", " 'font.size': 16,\n", " 'legend.fontsize': 16,\n", " 'text.usetex': True,\n", " 'figure.figsize': (8, 6)}\n", "plt.rcParams.update(params)\n", "\n", "sns.set_context(\"poster\")\n", "sns.set_palette(\"colorblind\")\n", "sns.set_style(\"white\")\n", "sns.axes_style()\n", "\n", "\n", "###############################################################################\n", "# display function:\n", "\n", "saving = False\n", "\n", "\n", "def my_saving_display(fig, dirname, filename, imageformat):\n", " \"\"\"\"Saving with personal function.\"\"\"\n", " filename = filename.replace('.', 'pt') # remove \".\" to avoid floats issues\n", " if saving is True:\n", " dirname + filename + imageformat\n", " image_name = dirname + filename + imageformat\n", " fig.savefig(image_name)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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EDmn79u1ISkqCwWBw6tlOr1+/jueeew7t27fHq6++ipKSEtGRHBILCREROaSFCxdi8eLF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\nREQkHAsJERERCcdCQkRERML9f4vZ/un0+QgsAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "###############################################################################\n", "# Motivating example\n", "\n", "np.random.seed(seed=42)\n", "n_samples = 60\n", "sigma = 0.2 # noise level\n", "x = np.sort(3. * np.random.rand(n_samples))\n", "xx = np.linspace(-.2, 3.2, 200)\n", "\n", "def f(x):\n", " return np.sin(x ** 2) + 2. + x\n", "\n", "y = f(x)\n", "y += sigma * np.random.randn(n_samples)\n", "\n", "# Ploting Signal / Noise\n", "fig = plt.figure(figsize=(8, 6))\n", "plt.xlabel('$x$')\n", "plt.ylabel('$f(x)$')\n", "plt.ylim([1.5, 7])\n", "plt.xlim([-.5, 3.5])\n", "plt.plot(xx, f(xx), '--k', label=\"true signal\")\n", "plt.legend(loc='upper left')\n", "plt.tight_layout()\n", "plt.show()\n", "my_saving_display(fig, dirname, \"sin_signal\", imageformat)\n" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "plt.plot(x, y, 'o', label=\"noisy observations\")\n", "my_saving_display(fig, dirname, \"sin_signal_noisy\", imageformat)" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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zMzM6duxYw3behjSPF8hXX0d/hGmdmQxTSJJelQBF/PkK3IZhyDRNnTx5Us88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\n9+Shhx4qnzhxom77JN1zgr4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KTrquYdQiBiREROQ3aowmfFh5xiXnqjMDU7btZ0+JhzAgISIiv3H2cg1qTa3oHmmkzgws\n33XMZeej5nFSKxER+TzLiprCimqXn7uw4gxqjCbmKnEzBiREROTTmlpR40q1JjOO/noFfbt0YFDi\nRgxIiIjIZ7VmRY0jInK+QnAQ8FhkD7z8QF8mUHMDziEhIiKf5cyKGgmAYQo5JBLHXmesA7buP4PY\nlbvx2qcHHHsx2cQeEiIi8kmOrqgJkUowLqoHpv8nRfyuo7/iD2vKnOpdeeuLo4BEgjcfGeT4i6lJ\n7CEhIiKfpL9qdGhFzbHZo/HBpHuF4ZaRfbtgzbhoBDnYU2Kx5P9+5JJgF2JAQkREPkneLhghUvui\niRCpBF07trlpe1psOEqnjoBqSE+7z2VhBrDsy6MOvYaax4CEiIh8UmiwFGMje9h1bHJUj2ZXyAwP\n74yCSffi0uIkVGWMcqgNH1X9jBqjyaHXUNMYkBARkc+aOaqPzSGXIAkwY2Qfm+cKDZaib5cOCHbg\nyVhrMsNwzWj/C6hZDEiIiMhnDQ/v3OI8kCAJsHZ8tN3LdEODpfhzhH29LkD9UJCsLdeHuAIDEiIi\n8mlNzQMJkUrwxJCeKJ06AqnDw+06T43RhLOXajDt/91h97VH9rmVydJchGEdERH5PMs8kBqjCYZr\nRsjaBtsdKFjSzn9YeQa1JjNCpBKEhUpxqcb23BAnF+hQExiQEBGR3wgNlqJrR/t7LJpKO19rMqPW\nZN9E1a+O/cY6Ny7CIRsiIgpIrkg7z0mtrsOAhIiIApIzaecb46RW12FAQkREAcfRtPPNaSm/CTmG\nAQkREQUcR9PON8Xe/CZkHwYkREQUcBxJO98UR/ObkG0MSIiIKOA4knZe0altq/KbkH04E4eIiALS\nzFF9sHV/dYsTW4MkwOa/DsPQ22UO5zchx7CHhIiIApIjaefr85uEMhhxI/aQEBFRwEqLDUd0TxmW\n7zqGwoobmVrHRfXA9JF9OEfEgxiQEBFRQGtN2nlyHQYkREREcDztPLkW55AQERGR6BiQEBERkegY\nkBAREZHoGJAQERGR6BiQEBERkegYkBAREZHoGJAQERGR6BiQEBGRT6oxmnD2Ug1qjCaxm0IuwMRo\nRETkU8pOnMfyXcfxYeWNVO/JUT0ww42p3vfu3YuDBw9i3LhxCAkJccs1Ah17SIiIyGfklZ3EiHdK\nsXlfNWpN9WV6a01maPZWI27VbuSVnXTp9SoqKvDYY49h6NChePLJJ5GVleXS89MNDEiIiMgnlJ04\njynb9qPO3PT+OjMwZdt+fHPyQquv9eOPP2LChAm4++678fHHHwvbO3bs2OpzU9MYkBARkU9Yvut4\ns8GIRZ0ZWL7rmNPX0Ol0SE1NxcCBA/H+++/DbK6/YLdu3bB8+XLMnj3b6XNTyziHhIiIvF6N0YQP\nK8/YdWxhxRnUGE0OVew9e/YsFi9ejDVr1uD69evC9k6dOiEjIwPTpk1j74ibMSAhIiKvp79qFOaM\n2FJrMsNwzWhX5d4LFy4gNzcXK1aswJUrV4TtHTp0wIwZM5Ceno5OnTo53W6yHwMSIiLyevJ2wQiR\nSuwKSkKkEsjatvx4u3z5MlauXImcnBxcvHhR2B4aGoopU6bg9ddfR7du3VrdbrIfAxIiIvJ6ocFS\njI3sgc37qm0emxzVo9nhmmvXrmHdunVYvHgxzp49K2yXSqV45plnMGfOHCgUCpe1m+zHSa1EROQT\nZo7qgyBJy8cESYAZI/vctL22thbr169H//79MWPGDCEYkUgkeOqpp3Dw4EHk5eUxGBERAxIiIvIJ\nw8M7Y8246GaDkiAJsHZ8tFVytLq6OnzwwQcYPHgwUlNTodPphH2PPfYY9u3bh/feew/9+vVzd/PJ\nBg7ZEBGRz0iLDUd0TxmW7zqGwoobmVrHRfXA9AaZWs1mM/7nf/4HWVlZqKiosDrHQw89hIULF+K+\n++4T4xaoGQxIiIjIpwwP74yCSfeixmiC4ZoRsrbBVnNGdu7cidmzZ+Pbb7+1ep1SqcSiRYvwwAMP\neLjFZA/RhmyKi4uRn58PnU4Hg8Eg/JuIiAKbvUXzQoOl6NoxVAhGysrK8OCDDyI+Pt4qGBkyZAg+\n/fRT7N69m8GIFxOth0Sv1yM3Nxe5ubmQyWRYsGABJxMREQUwZ4vm7d27F3PmzMGnn35qtX3gwIHI\nzs7GuHHjEBTEKZPeTtQhm/Lycuj1egYiREQBLq/s5E11aixF87bsq8aacdFIiw23es2hQ4egVqux\nefNmq+3h4eGYN28eJk6ciOBgzkzwFaK+UzKZDDKZTMwmEBGRyOwtmhfdU4bh4Z1x8uRJzJ8/H//4\nxz9QV1cnHNe9e3dkZWXhueeeQ2hoqIdaT64iakCi0Wggl8uh1+thMBiQmpoqZnOIiEgE9hbNe+OT\nb9H78KdYt24damtrhX233HILXn31Vbz00kto3769m1tL7iJaQKJUKiGXy4UeErVaDY1GA5VKJVaT\niIjIw+wqmnf1EvBdIT5Z+T+A8Ubhu44dO2LWrFmYNWsW5HK5m1tK7iZaQNJ43ohSqURubi4DEiKi\nANJi0bzrvwP//gT47qP6f/9H27Zt8dJLL+HVV19Fly5dPNRScjdRAhKDwYCYmBiUl5cLPSQymYzL\nfomIAkyTRfNqa4D9RcC3W4Grhhvbg6RIS03FXPUc9OzZ0/ONJbcSrYfkueees5rQqtPpuNqGiCjA\nWBXNM9UClTuAbzTAlfM3DpIEAYMewCPPTse6WX8Sr7HkVqIEJDKZDJ06dbLaVlxcjPT0dDGaQ0RE\nIpo2IhxbCt6DWfs+oP/FeuddSkA5AUFdFMgaN0KcBpJHiNZDolKpkJ+fD5lMhlOnTkGlUiExMVGs\n5hARkYeZzWYUFhZCrVbDfOCA9c477gXiJgK39W2yaB75H9ECEplMxmW+REQByGw2o6SkBFlZWdiz\nZ4/Vvq4D7sH5e1Qw9RjUZNE88l9MYUdERB7z9ddfIzMzE19//bXV9mHDhmHRokV46KGHcN1U12TR\nPPJvDEiIiMjt9uzZg8zMTJSUlFhtj4iIwIIFC/DYY49BIpEAsBTNYyASaBiQEBGR2xw4cABz5sxB\nYWGh1fY+ffpg/vz5ePLJJyGVMvggBiREROQGx44dw7x58/DPf/4TZvONHCO333471Go1UlJSEBIS\nImILydswICEiIpf56aefsHDhQqxfvx5Go1HY3qVLF8yePRsvvPAC2rVrJ2ILyVsxICEiolb79ddf\n8eabb2L16tW4du2asF0mkyE9PR0zZsxAWFiYiC0kb8eAhIiInKbX67Fs2TIsW7YMly9fFra3b98e\n06ZNQ0ZGBm655RYRW0i+ggEJERE57Pfff8c777yDt956C+fP30jz3qZNGzz//POYPXs2unfvLmIL\nydcwICEiIrtdv34d+fn5WLhwIX7++Wdhe1BQECZPngy1Wo3w8HARW0i+igEJERHZZDQasWnTJsyf\nPx8nT5602qdSqTB//nwMGDBApNaRP2BAQkR2qTGaoL9qhLwds2cGkrq6OmzduhVqtRqHDh2y2vfH\nP/4RCxYswN133y1S68ifMCAhohaVnTiP5buO48PKM6g1mREilSA5qgdmsL6IXzObzdi+fTuysrKw\nd+9eq30PPvggFi1ahOHDh4vUOvJHDEiIqFl5ZScxZdt+1N3Ia4VakxmavdXYsq8aa8ZFIy2W8wX8\nzZdffonMzExotVqr7ffffz8WLVqE0aNHi9Qy8mdBYjeAiLxT2YnzNwUjDdWZgSnb9uObkxc82zBy\nm2+//RYPPfQQ/vCHP1gFI1FRUfjkk09QVlbGYITchgEJETVp+a7jzQYjFnVmYPmuY55pELlNRUUF\nHnvsMdx///3YsWOHsP2uu+7C+++/j7179+KPf/yjUPyOyB04ZENEN6kxmvBh5Rm7ji2sOIMao4kT\nXX3Qjz/+iLlz5+KDDz6wqjejUCgwd+5cPP300wgO5mOCPIP/pxHRTfRXjag12ege+Y9akxmGa0aW\ni/chOp0O2dnZ2LBhA0wmk7C9W7duyMzMRFpaGtq2bStiCykQMSAhopvI2wUjRCqxKygJkUoga8uv\nEl9w9uxZLF68GGvWrMH169eF7Z06dcIrr7yCadOmoUOHDiK2kAIZv0WI6CahwVKMjeyBzfuqbR6b\nHNWDwzVe7sKFC8jNzcWKFStw5coVYXuHDh0wY8YMpKeno1OnTiK2kIgBCRE1Y+aoPti6v7rFia1B\nEmDGyD6eaxQ55PLly1i5ciVycnJw8eJFYXtoaCimTJmC119/Hd26dROxhUQ3cJUNETVpeHhnrBkX\njaBmFlYESYC146OdTo5WYzTh7KUa1BhNtg8mh1y7dg0rVqxA3759kZmZKQQjUqkUaWlpOHLkCN5+\n+20GI+RV2ENCRM1Kiw1HdE8Zlu86hsKKG5lax0X1wHQnM7Uy86v71NbW4h//+Afmz5+P06dPC9sl\nEgmeeuopzJs3D/369ROxhUTNY0BCRC0aHt4ZBZPuRY3RBMM1I2Rtna9lw8yv7lFXV4eCggLMnTsX\nP/74o9W+xx57DAsWLEBkZKRIrSOyD4dsiMguocFSdO0Y6nQwwsyvrmc2m/Hxxx9jyJAhmDBhglUw\n8tBDD+Ff//oXPvzwQwYj5BMYkBCRRzDzq+uYzWbs2LEDw4cPx2OPPYaKigphn1KpxBdffIHPP/8c\n9913n4itrMe5QmQvh4dsLl++jKKiIhgMBmGiVKdOnSCTyRAbG4tevXq5vJFEZFuN0QT9VSPk7Zwf\nUnEXZn51Ha1Wi8zMTHz55ZdW24cOHYqFCxciKSnJK1K8c64QOcqugOTy5ctYu3YtTp8+DYVCAYVC\ngV69eiE2NhZAfdY/vV6PgoIC6HQ69O7dGy+//LJbG05E9Xzhi5+ZX1tv7969yMrKwmeffWa1feDA\ngcjOzsa4ceMQFOQdnd6cK0TOsBmQlJSU4PTp01CpVFAoFE0eM3jwYKufdTod1q9fj4iICCFoISLX\n85UvfmZ+dd6hQ4egVquxefNmq+3h4eGYN28eJk6c6FX1ZuydKxTdU+Y1ATN5hxbD6ZKSEgwePBjP\nPvtss8FIUxQKBZ577jn06tULn3/+easbSUQ386VJopbMr/Zg5td6J06cQEpKCgYPHmwVjHTv3h2r\nV6/G4cOHMXnyZK8KRgDOFSLntRiQJCQkOBSINKZQKDBmzBinX09EzfO1L/6Zo/o0m2TNgplfgTNn\nzuCll15C//79sXHjRtTV1QEAbrnlFixZsgRHjx7F3/72N7Rp00bklt7MmblCRBbeMeBIRA7xxS9+\nd2d+9XXnz5/Hq6++ir59+2L16tWora0FAISFhWHu3Lk4duwYMjIy0L59e5Fb2jxn5goRWTjc16dW\nq/HTTz/h3XffFbadPn2aq2uIPMhTk0RdvXLHHZlffd2lS5fw9ttvY+nSpTAYDML2tm3bYurUqXjl\nlVfQpUsXEVtoP84VotZw+P+GyMjIm5LsyOVybNmyBUlJSejYsaPLGkdETXP3F787V+64MvOrL7t6\n9Sr+/ve/480338Svv/4qbA8ODkZaWhoyMzPRs2dPEVvoOFaJptZwasjm4Ycftvo5LCwMf/nLX6DR\naFzSKCJqmTsnieaVncSId0qxeV+1EPBYVu7ErdqNvLKTTrW5sZYyv/pzMq3r169j7dq16NevH9LT\n04VgJCgoCE8//TQOHz6M1atX+1wwYsG5QuQsh3tIYmNjMXbsWERERCAuLs4qGZpMJnN5A4moaTNH\n9cHW/dUtTmx19Itf7CWbvpBTxVkmkwnvv/8+5s6di+PHj1vtGz9+PLKzszFo0CCRWuc6lrlCzf1/\nFOhzhah5DveQ5OfnIzU1Fb169UJRURHi4+MxaNAgjBkzBqdOnXJHG4moCe6YJCrmyp2WemaUK3cj\n94ujPtljYjabsW3bNkRHR+Ovf/2rVTCSlJSEPXv2YMuWLX4RjFikxYajdOoIqIb0RIi0/n/QEKkE\nTwzpidKpI5A6XPzcOOR9HO4hiYuLQ0JCgtW2qqoqFBUVQaVSuaxhRGSbKyeJipne3VbPjBlAxqcH\n8Pr2HzAu2jd6TMxmM0pKSpCVlYU9e/ZY7Rs5ciQWLVqEESNGiNQ69+NcIXKUU1OcL1++bDV5NSIi\nAhEREfgS2LkfAAAgAElEQVT888+52obIw1z1xS9mend7emYAwFjnfVlom/L1118jMzMTX3/9tdX2\ne++9F4sWLcKYMWO8ot6MJ9TPFWIgQrY5PGSTkJCAiooKlJWVWW1/6KGHUFpa6rKGEZFjWpokag/L\nyh17uHLJpiM9MxbelIW2oT179iApKQkjR460CkYiIiJQWFiI8vJyJCQkBEwwQuQIp1bZxMbG3lSj\nJj09nUM2RD5MrPTujvTMNORNWWgPHDiAcePGYdiwYSguLha29+nTB5s2bcK+ffswduxYBiJELWgx\nILl8+bLdJ0pISLipyJ6j5yAicYmxZNORnpnGxM5Ce+zYMfz1r39FZGQkCgsLhe2333471q1bh4MH\nD2LixImQSjlkQWRLiwFJU0MzjigrK0NFRYXTrycizxIjvbsjPTONiZV+/KeffsKUKVMwYMAAbNq0\nCWZzfQ9Ply5dsGzZMhw5cgRpaWkICQnxeNuIfFWLAUlsbCzkcjnWr1/vUGBSVlaGpUuXolOnTjcN\n7RCR67gjgZgYSzbt6ZlpiqfTj//6669IT09Hv379sHbtWhiN9cGQXC7HggULcOzYMcycORPt2rXz\nWJuI/IXNT/LgwYMxePBglJSUQK1Ww2AwQC6Xo3fv3kIiNIPBgFOnTkGv10MulyMuLg4vv/yy2xtP\nFKjcnUDM00s2LT0zz2/d79DrPJV+XK/XY+nSpXj77bethqHbt2+PadOmISMjA7fccovb20Hkz+z+\n0yIhIUHIP3LgwAHodDro9XoAQK9evRAbG9vkHBIicq28spM35eywJBBz9XJYTy7ZfDqmF14srIDR\nnvW/8Ez68StXruCdd97BW2+9hQsXbqzoadOmDZ5//nnMnj0b3bt3d2sbiAKFU32dll4TIvIssVO7\nu5P+qtHuYAQAch4d7LZ7rKmpQX5+PhYtWoSff/5Z2C6VSjF58mSo1Wr07t3bLdcmClQ2l/2WlZXh\nhx9+8ERbiMgGMVO7u5sjq22kQcCLI+5weRuMRiM2bNiAAQMGYOrUqVbBiEqlwoEDB7B+/XoGI0Ru\nYDMgKSoqwrp164SfuYyXSBzOpHb3JY6sthkf3dOlc0fq6uqwefNmRERE4JlnnsHJkzcqGv/xj3/E\n3r17UVBQgP79+7vsmkRkzWZA0rt3byxfvlz4uWFwQkSe40xqd1/j6TwoZrMZn332Ge69916oVCoc\nPnxY2DfqgQdQVlaGTz75BHfffbdLrkdEzbMZkEREROC+++7DuHHjsHTpUuh0Ovz0008ub4harXb5\nOYn8iVip3T3Jk3lQvvjiC8TFxeHRRx/F3r17he2SHgOA8QugjXkZy4+EeF16eiJ/ZfMbKzY2Ft9+\n+y3KyspQWloKrVaL0aNHQyKRYPDgwYiMjBT+UygUVkX37JWTk4PKykqnboAoUFiGNDbvq7Z5rKeW\nw7qDKysYN+Xbb79FZmYmduzYYb2j6x2AcgLMfe4DJBK3rVwioqbZ/SdUw/o16enp0Ol0OHDgACoq\nKrB7927k5eXh9OnTGDx4MB5++GGoVCq7ghOdTud864kCzMxRfbB1f3WLE1s9sRzW3dyRB2X//v2Y\nM2cOPvnkE6vtijv64nTEWJj7jwAkN3ca+/LKJSJf4nCfrqWAnkKhgEKhEHKTWBw4cABarRZZWVl4\n+OGHMWbMmBbPp9VqERcX16oU9USBwjKk0dzSX3ekdheTK/KgHDlyBHPnzkVBQYGQ4h2o/w6bO3cu\nioMioas82+I5LCuXCibd26q2EFHzHA5IFApFi/stOUrKyspw+vTpFo/VarVISkricA2RA9w9pOEv\ndDodsrOzsWHDBphMN1YcdevWDVlZWUhLSwOkwZgyu8iu81lWLvnqUBiRt3PLrLdLly4hJSUFqamp\nLR5nMBiE9PNEZD9Pp3b3Jb/88gsWL16MtWvX4vr168L2Tp064dVXX8XUqVPRoUMHAMDZSzUOr1zy\nVOZaokDjloAkLCwMBw8ebPGY4uJiJCYmuuPyRAHDk6ndvd2FCxeQk5ODFStW4Pfffxe2d+jQATNn\nzsTLL7+MTp06Wb3GsnLJnqDEV1cuuVuN0QT9VSPk7RgUU+uI8unS6XTsGSEil7h8+TJWrFiBnJwc\nob4WAISGhuJvf/sbXnvtNXTr1q3J1wbKyiVntRRsuLvAIwUeUQKSqqoq6HQ6VFVVAQAqKipgMBiQ\nn5+PxMREm/NUiHwN/4p0vWvXrmHt2rVYvHgxzp07J2wPDg7GM888gzlz5qBXr142zxMoK5ccYSvY\n8GSBRwocogQkjYdqNBoNTp8+bXPOCZEvaBh8/Pu0nn9FulhtbS02btyI7Oxsq4nzEokEEyZMwLx5\n89C3b1+7zxdoK5dssRVspD/QF7lfHvXLAo8kLtEHRDUaDYqLi6HT6ZCfnw+VSsXhHPJJjf+qlErq\nv5wbfm/zr0jn1dXVoaCgAGq1GkePHrXaN3bsWGRnZyMyMtKpc3PlUj17qkkv+eJo0zsbHcdl0uQo\n0QMSlUol5DYh8lVN/VXZ0jxJ/hVpP7PZjI8//hhz5sy5KUXAmDFjsHDhQsTExLT6Oly5ZF81aXtx\nmTQ5ymYtGyJqma2/Kptj+SvS19UYTTh7qcbl1YXNZjP+93//F/fffz/Gjh1rFYzExcXhyy+/RElJ\niUuCEQvLcFsgBiOOVJO2h68WeCTxiN5DQuTrWvNXpS//FenOVRZarRaZmZn48ssvrbYPHToUixYt\nQmJiIiQS+woN2oMrRhyrJm0PLpMmR7GHhKgVWvtXpa/+FZlXdhIj3inF5n3VwkPMMj8mbtVu5JWd\ndOq8e/fuxaOPPir0gFgMHDgQW7ZswXfffYekpCSXBiPuuhdf40g1aXsE4jJpah0GJESt4Iq/Ku3J\ngeFN7Jn4OGXbfnxz8oLd5zx48CBUKhWGDh2Kzz77TNh+xx13YOPGjaisrMT48eMRFOTaryx33Iuv\nsuRksYetsCXQlkmTazAgIWoFV/xVOe3DSp964NkzRGXv/JgTJ04gJSUFERER2Lx5s7C9e/fueOed\nd3Do0CE8/fTTkErd85e2K+/FH8wc1QdBNv53DpIArzzYr9njAm2ZNLkOAxKiVnDkr8rm+NIDz5Eh\nKsv8mKacOXMGL730Evr374+NGzeirq4OAHDLLbdgyZIlOHr0KF588UW0adPGZW1vzFX34k8sOVls\nBRtvPjIIpVNHQDWkpxCQh0gleGJIT5ROHYHU4VzOTo7jjCOiVpo5qg+27KtGawZufGVyqyNDVE0V\no/vtt9+wZMkSrFq1ClevXhW2h4WFYdasWZg1a5bH8hC19l78lb05WbhMmlyNAQlRK5nNrV+Z4CsP\nPGeL0RkMBixfvhxLly6FwWAQjmnbti2mTp2KV155BV26dHG6Xc6k5t/iwNydQFsx4kiwwQKP5CqB\n8wkjcpPlu463qncEAIKDgNBg161wcBdHi9HV1V7H0hV/xxtvvIHffvtN2BcSEoLU1FRkZmaiZ8+e\nTrfH2eW6ZSfOY9pHlc3ub+peAvGvfwYb5EkMSIhawVXJpIx1QBf15z6R+8KeYnSSulr0Pvkl+vX7\nE6qrbwQvQUFBmDRpEubOnYs777yzVe1oTYE3R3LHcMUIkWdwUitRK7gymZSv5L5oceJjnQmSA/+H\nWzfPQM6cdKtgZPz48aisrMTGjRtbHYy0Zrmuo0HkqrGRXh0gEvkLBiREreDqZFKAb+S+SIsNt15l\nYTZD+qMWss2zYC5ejl+rdcKxDz/8MPbs2YMtW7Zg0KBBLrl+a5brOhpE/uVu54eUiMh+DEiIWsEV\ny36b4gtLgYeHd8YHE+/BtlESRH8xD6ZP3oSh+riwf+TIkdi9ezc+++wz3HPPPS67bmuX6zoSRAba\nZFYiMTEgIWole5JJOcPbc1/s2rULI0eOxJ8efRT7934vbB82bBhKSkrw5ZdfIi4uzuXXdWa5bkOO\nBJGBOJnVXcUSiWxhQELUSraSSTnLW+vcfPfdd0hMTMSoUaOwe/duYXtERAQKCwvx7bffYsyYMS6t\nN9OQK3o47A0if7ty3auHzlyp7MR5qP57D8JmF+G2eZ8jbHYRnti0J2Dun8THgITIBRrOqQh20afK\n24YLqqqqMG7cOMTExKCkpETY3qdPH2zatAn79u3D2LFj3RaIWLiih8PeIHLHkV+9fpKxK7DAIHkD\nBiRELmJJJnUsc7RLzuctwwVHjx7FpEmTEBUVhcLCQmH77bffjnXr1uHgwYOYOHGi2+rNNMXemist\nLde1BJGj72o5IZsvTDJuDRYYJG/BgITIxbp1DG31yhtvyH3x008/4YUXXsDAgQPxz3/+U8hI26VL\nFyxbtgw//vgj0tLSEBIS4vG22VtzxdZy3eHhnXFre9v1cnxhkrGzWGCQvIX39AcT+QlHspk2Rexq\nqefOncObb76J1atXo6amRtgul8uRnp6O6dOnIywsTJS2NWRvzZWWOLJiZ9v+atQYh3hFr5WrOLNi\nyZ/un7wLAxIiN7ArmymA0Xd1wVfHfnPqYepqer0eS5cuxdtvv43Lly8L29u3b4/p06cjPT0dt9xy\ni8fb1ZLWFnhzZMWOsQ54YtO/8eqD/fwmURoLDJI3YUBC5AaWIYXmxuYtvSCpw8NFr5Z65coVrFq1\nCkuWLMGFCzfmCbRp0wYvvPACZs+ejdtuu83j7XKEszVXHCkWCAAfVf6MT6p+bjEtvS9xtlgikTtw\nDgmRm9yUzRT1X+pPDOmJ0qkjkDq8/oFW/zAN9XgwUlNTg1WrVqFv3754/fXXhWBEKpXi2WefxZEj\nR7BixQqvD0Zaw5nEdq2Z5OltOT6Yk4W8CcNdIjdq7ZCCOxiNRvz3f/835s+fj1OnTlnte/LJJzFv\n3jz0799fpNZ5nj3Da41ZJnkWTLrXruOdrUrsCfbcvzdMsib/xx4SIg8Qqxekobq6Omg0GkRERODZ\nZ5+1Ckb+9Kc/Yd++fXj//fcDKhgBnE9sZ28mXW/P8eGqFUtErcWAhMjPmc1mfPrpp7jnnnvwxBNP\n4PDhw8K+0aNHo6ysDB9//DGio6NFbKW40mLD8cUUJRyJSezJpOsrOT7sHV4kcicO2RD5sS+++AKz\nZ8/GN998Y7V9+PDhWLRoER588EGRWuZ9BnbrCAdGbeya5OlIjg97h3/cxRuHFymwMCAh8kP/+te/\nkJmZiZ07d1ptj46OxqJFi/DII4+4PcW7r3F0xc1jEd1bfGD7ao4PZ1csEbUWh2yI/Mj+/fvx5z//\nGcOHD7cKRvr374+CggJ8//33ePTRRxmMNMGRFScSALMe6NviMa2tSkwUaBiQEPmBI0eO4KmnnsKQ\nIUPwySefCNt79+6Nd999F1VVVVCpVAgK4ke+JfZWAbYnOZorqhITBRJ+OxH5sFOnTuG5557DoEGD\n8MEHHwj1Zm677TasXLkShw8fxjPPPIPgYD7s7GHPipvXHuyLNx4ZZPNczPFB5Bh+SxH5oF9++QWL\nFy/G2rVrcf36dWF7586d8corr2Dq1Kno0KGDiC30XU3VyAkOAsZG9sCsB/o6tPxVjBwfNUYT9FeN\nkLfjpFTyLQxIiHzI+fPnkZOTg5UrV+L3338Xtnfs2BEzZ87ErFmz0KlTJxFb6B9cteLE3hICrsjx\n4c3J14jswYCEyAdcunQJK1asQG5uLvR6vbA9NDQUL774Il577TV07dpVxBb6J1esOHFFVWJb8spO\n3hT0WJKvbdlX7Te1d8i/MSAh8mLXrl3DmjVr8MYbb+DcuXPC9uDgYDz33HPIysrC7bffLmILyR7u\nzPFhb/K16J4y9pSQV+OkViIvVFtbi7y8PPTr1w+zZs0SghGJRIJJkybh0KFDWLNmDYMRH2OrhIAz\nxfccSb5G5M3YQ0LkRUwmEwoKCjB37lwcPXrUal9ycjKys7MREREhUuvIXZyd/+GrydeImsIeEiIv\nYDab8eGHH+Luu+/GxIkTrYKRhIQElJeXY9u2bQxG/FBriu8x+Rr5EwYkRCIym834/PPPcd999yE5\nORlVVVXCvhEjRuCrr75CcXExhg0bJmIryV1aW3yPydfInzAgIRJJaWkp/vCHPyAhIQHfffedsP2e\ne+5BUVERdu3ahZEjR4rYQnK31s7/YPI18icMSIg87Pvvv8cjjzwi9IBYDBo0CFu3bsV3332HxMRE\n1pvxc87M/2iKPenuXZ18jcgdGJAQecjBgwfx+OOP45577sH27duF7XfeeSf+8Y9/oKKiAuPGjWMg\nEiBcNf/DVrp7VyZfI3InDigSudnx48cxf/58bNq0CXV1dcL2Hj16YM6cOXj22WfRpk0bEVtIYrDM\n/7AnKLE1/8MTydeI3I0BCZGbVFdXY9GiRcjPz0dtba2w/dZbb8Vrr72GF198Ee3atROxhSQmy/yP\nzfuqbR5rz/wPdyZfI/IEBiRENjharOy3337DW2+9hVWrVuHatWvC9rCwMLz88suYOXMmZDKZO5tM\nPsIdxfdcke6eSAwMSIia4WiyKoPBgLfffhtLly7FpUuXhO3t2rXD1KlT8corr+DWW2/15C2Ql/Nk\n8T0ib8eAhKgJjhQr+/3337F69Wq89dZb+O2334TjQ0JCkJaWhszMTPToYd/STAo8nP9BVI8BCfkk\nR4dRHGFvsqpBXdqi4n+3YeHChThz5sbyzaCgIEyaNAnz5s3DHXfc4dK2kX/i/A8iBiTkY5yt+eEI\nm8mq6kyo++FLJClfwJVfrSck/uUvf0F2djYGDhzokrZQYLE1/8OdgTiR2BiQkM9wZBjFWS0mqzLX\nAUe0gPZ94PxpXGmw65FHHsGCBQswdOjQVl2fqCmeCMSJxMaAhHyCvcMo0T1lrfqCbjJZldkMHN8D\naP8JnLVO4a0c8f+Q89abUCqVTl+TqCWeCMSJvAEDEvIJjtT8KJh0r9PXuSlZla4SKN0EVP9gfeBt\nd0E6chJ2vvc62obwY0Tu4alAnMgbiPZNajAYoNFoIJPJcOrUKQBARkaGWM0hL+ZMzQ9nx9eFZFUl\nX9UHIif3Wh9wazgQNwHoez/GD72dwQi5lacCcSJvINq36bp166wCkOTkZGg0GqhUKrGaRF7KmZof\nziaGqqysxM/vzQU+/8x6h7w7oJwADBgBBElZrIzczpOBOJE3EK24XklJCTQajfBzr169UFpaKlZz\nyItZhlHsYavmR3N+/PFHTJw4EdHR0djVMBjp2AWIfxGY/Hdg0CghGGGyKnI3VxXfI/IVovWQbNiw\nAQqFQvj59OnTSEpKEqs55MUcqfnx54ju/1kWCbv+Wjx9+jQWLFiAd999FybTjfLuXbt2xVMvzMBP\n4Q/g40PnmayKPM6VxfeIfIFo/wc3DEaqqqoAAKmpqWI1h7ycPTU/AOCjyp+xdf8Zm8siz549izfe\neANr1qxBTU2NsF0ulyMjIwPTp09Hx44dAYDJqkgUri6+R+TtRBuyAW5MbM3NzcWCBQvEbAp5iRqj\nCWcv1aDGaLLaPjy8M54cervN1xv/E7FYlkXGrdqNvLKTwv6LFy8iKysLffr0wfLly4VgpH379nj9\n9ddx/PhxZGZmCsEIYElWFcovfPK4maP6IMjGaCXnM5G/ELWPTyaTQaVSQaVSITk5Wfg3BR5L4qfC\nimoY64DgIGBcdE+hh6PsxHl88P1PDp/Xsizyrk5SfPPRJixZsgQXL14U9rdp0wZTpkzB66+/jttu\nu82Vt0TUaiy+R4FE1GW/DUuwq1QqqNVqBiQBKK/sJF7Yuh8Nv2+NdYBmbzU2763G2vHR2HnkV5vD\nNU0y1qJufzGS8iejxnBe2CyVSpGSkoI5c+agd+/erb4HIndh8T0KFKIEJFqtFikpKSgvL7cKSoCb\nAxXyb2Unzt8UjDRkBvD81v0IttVv3VidCajaCXxTAFz6FZZZIhKJBE888QTmz5+Pu+66qxUtJ/Ic\nFt+jQCBKQBIZGQmVSmUVeJSWliIhIYHBSIDJKjrUbDDSkNHe7hFzHXBod329mYvWkwETH34Ub72x\nCNHR0Y43lMgL2Cq+R+TLRAlILHNH8vPzAdRPNFQoFMzUGmBqjCZ8cfRX15zMbAaOlQPa94Bzx633\n9b4b0v83ER9tnMm/KomIvJRoc0giIiIQEREh1uXJC5y9dB1mZ+aFNHZqH1D6T+DMIevtPQYCcROB\n3tEwS4CnP9jL6qhERF6KmXRIPBLHopEgCawntlYfrA9EdPutD+xyBzBiEnDnMEBSP/ekzgxWRyUi\n8mIMSEg03TqG3hxkNCNIAswc2QfLvjoG87njQOl7wLFvrQ/qfDugfAroHwdImk6xw+qoRETeiQEJ\niSY0WIo/9OuCnUdszyPp37Ujln30Ncza94FDX1vvDOsKxD4JDP4DEGR7jgiroxIReR8GJCSqhUkD\n8X9Hdre80sZwFgc/XwlU/V/9KhqL9p2A+x8HohKA4BCHrsvqqERE3oUBCYmixmiC/qoRQ2+XYe34\nZjJRXrkAfLsFkv0lMJtqb2wP7QjEJANDHwVC2jp1fUt1VC6hJCLyDgxIyKMsKeI/rLyRcTI5qgfW\njY/GjiO/1meivGxA0L8/hOT7T2G6fu1G70lIO+CePwH3/hlo27Gly9jE6qhERN6F38jkMXllJ2/q\nCbEUwduyrxpvJ/bBwOP/xtt5y2DQ628cJA0BhjwMxIwH2std0hZWRyUi8i4MSMgjyk6cb7ZAGIzX\nUbevCNP/vgW4ahA2BwcHI+WZZ7EhKBbG9re4rC2sjkpE5H2aXhtJ5GLLdx2/ORgxGYH9xcB/PQ98\n9a4QjEgkEkyaNAkHDx5E3rq1SI6NtPs6IVIJhvWSN1uyndVRiYi8E3tIyO1qjCZ8WHnmxoY6E3Bw\nF1D2AaD/2epYyV2x2LNlLYbefaPezMxRfbB1f3WL+UokAD577n48eNetCA2W4puTF1gdlYjIhzAg\nIbfTXzWi1mSurzfz4zf19WZ+O2V90B33AHETYb6tH3r1HWC1a3h4Z6wZ18xKHNzo9Uga1M3qNayO\nSkTkOxiQkNvJ2kohPfU9TF9vAn750Xrn7YPr6830qh+WaWr1S43RhMciu2Ngtw74u/akQ70erI5K\nROQbGJCQW+3evRuZmZkw7dplvaNb3/pA5I57hHozgPXql+aWCO94PhaDbuvIXg8iIj/CgITc4vvv\nv0dWVha2b99uveMWBaCcANwVaxWIANarX2wtEWaBPCIi/8KAhFzqhx9+gFqtxtatW62233nnnXhg\n4lRsvHwnzJKbezUarn5pcYkwWCCPiMgfcdkvucTx48cxefJkREZGWgUjPXv2xJo1a3Dw4EH8V/ZM\naKePgmpIT4RI63tHQqQSPDGkJ0qnjkDq8PoejyaXCDdiKZBHRET+gT0k1CpnzpzBwoULkZ+fj9ra\nG/Vmbr31VsyePRtTpkxBu3bthO22Vr/ctES4BSyQR0TkPxiQkFN+++03vPXWW3jnnXdw9epVYbtM\nJkN6ejpmzJiBsLCwZl/f3OoXYYmwHVggj4jIfzAgIYcYDAYsW7YMy5Ytw6VLl4Tt7dq1w7Rp05CR\nkYFbb73V6fPL2wUjRCqxKyhhgTwiIv/Bb3Oyy++//47Vq1fjzTffxPnz54XtISEheP755zF79mz0\n6NGj1dcJDZZibGQPbN5XbfNYFsgjIvIfnNRKLbp+/TpWr16Nvn374pVXXhGCkaCgIKSkpODw4cNY\ntWqVS4IRi5mj+jRbi8aCBfKIiPwLAxJqktFoxMaNGzFgwAC89NJL+PnnGzVnHn/8cVRVVeG//uu/\ncMcdd7j82pZU8SyQR0QUODhkQ1bq6uqwbds2qNVqHDx40GrfI488ggULFmDo0KFub0dabDiie8pY\nII+IKEAwICEAgNlsRlFRETIzM7F3716rfQ888AAWLVqEe++7H/qrRo8ttWWBPCKiwMGAhPDVV18h\nMzMTpaWlVttjYmKwePFitO87FCu+PoEPPyqyqikzw0M9FSyQR0Tk/ziHJMDUGE04e6kGNUYTysvL\nMWbMGDzwwANWwUhkZCQ++ugj/Otf/8KxDnfh/63WYvO+amEprqWmTNyq3cgrO2n39YiIiJrDHpIA\nYVU595cTkGjfg/nHb6yO6devH+bPnw+VSgWpVNqqmjLNVer1VK8KERH5FgYkAUConHvhDKB9Hzi4\nC2bciDI6d+uBtxbOx+TJkxESEiJsd6SmTMGke2++Hiv1EhGRnRiQ+LmyE+fxwsb/g7lMA1T+L2Cu\nu7GzvRy47y+4eHciosY8aBWMOFtThpV6iYjIGZxD4sfOnj2Lp59/CeZ3nwcqSm4EI6EdgLiJwDN5\nwD1/glna5qbKuc7UlAFYqZeIiJzDHhI/dPHiReTm5mL58uW4cuXKjR0hbYGhfwSGjQXadrR6TePK\nuY7UlAGAF7dV4KURd7JSLxEROYUBiR+5cuUKVq5ciSVLluDixYs3dkiDgegk4L7xQIemh0kaV851\npKYMAGzZfwZb95+BfeELK/USEZE1BiR+Yu/evUhMTMQvv/wibJNKpaiLiIf5/seBsK42z/HitgrM\neqCvMLdj5qg+2Lq/2uYQjIW9wQjASr1ERGSNc0j8xKpVq4RgRCKR4KmnnsIPP/yAv7y8yK5gBKjv\n5WiYW8RWTZnWYKVeIiJqiAGJn3jmmWcQFRWF8ePHY9++fXjvvfdw11132VU5tyHLKphvTl4AUF9T\npnTqCIyPdl01X1bqJSKixhiQ+Im4uDjs378fW7ZsQVRUlLDdmV6Oxqtghod3xurkqBZecTNW6iUi\nIkcwIAkAzvRyWFbBWFhW3dgjRCrBF1NioRrSU3hNiFSCJ4b0ROnUEUgdzqRoRERkjbMKA4Sll2Pr\nfvuW5bZm1U1yVA+M7NsFI/t2YaVeIiKyC3tIAoijvRyNV8HYMx+l8fyQ+kq9oQxGiIioRQxIAoil\nl8MeTa2CsTUfhfNDiIjIWQxIAowzvRwNWeajcH4IERG5EueQBBhLL0dzBfDs6eUYHt4ZBZPu5fwQ\nIh+X+2wAAAugSURBVCJyGQYkASgtNhzRPWVYvusYCivOoNZkRohUgnFRPTB9ZB+7h1zq54cwECEi\notZjQBKg2MtBRETehAFJgKkxmqC/aoS8XX0Awl4OIiLyBgxIAkTZifNYvus4Pqy8MUSTHNUDMxwY\noiEiInIXrrIJAHllJzHinVJs3leNWlP9TNZakxmavdVWxfSIiIjEwoDEz5WdON/sihrg5mJ6RERE\nYmBA4ueW7zrebDBi0biYHhERkaeJOockPz8fAFBRUYGoqCikpqaK2Ry/U2M04cNK+2rXWIrpcaUN\nERGJQbSARK1WIzs7W/g5OTkZABiUuJD+qlGYM2JL42J6REREniTKkI3BYEBYWJjVNpVKhby8PDGa\n45fKTpzH37ZV2H18U8X0iIiIPEWUgESv12P9+vXQ6XRW2w0GgxjN8TuWVTXbKuwbrgGaLqZHRETk\nKaIEJAqFAoWFhVAoFMK20tJSKJVKMZrjV2ytqmlKS8X0iIiIPEG0PvqIiAjh3waDAWVlZSgsLBSr\nOX7DnlU1DdlTTI+IiMjdvGLSwPTp07Fx40arHhNynCOragDgL3f3wKxRfYVgpHFaeSIiIk8RPSDJ\nyclBamqqVY8JOceRVTUAsDo5Cl07hjKtPBERiU7UxGjFxcWIi4sT5o5UVVWJ2RyfJ28XjBCpxK5j\nLatqmFaeiIi8gWgBiVarhV6vR2RkJAwGA3Q6HbZv3y5Wc/xCaLAUYyN72HVsclQP/Pu0nmnliYjI\nK4gyZGMwGJCSkgKgPkGaRUJCghjN8SszR/XB1v3VLU5stayqefurY3anlS+YdK9rG0pERNSAKAGJ\nTCbDoUOHxLi03xse3hlrxkU32/NhWVUz9HYZ08oTEZHXEH1SK7leWmw4onvKsHzXMRRW3JioOi6q\nB6b/Z6Lq2Us1TCtPRERegwGJH2m4bHd4eGcUTLoXNUYTDNeMkLW1XsprmQBrT1DCtPJERORufMr4\nAVvLdpvq2bBMgN28r9rm+ZlWnoiI3E3UZb/Ueq1ZtjtzVB8E2VglzLTyRETkCQxIfJitujW2lu1a\nJsA2F5QwrTwREXkKAxIfZk/dGsuy3eakxYajdOoIqIb0FJKqhUgleGJIT5ROHYHU4eGubDIREVGT\nOIfERzlSt8bWsl1bE2CJiIjcjT0kPsqRujWWZbu2hAZL0bVjKIMRIiLyOAYkPsqZujVERETeigGJ\nj3K0bg17PYiIyJsxIPFhXLZLRET+ggGJD+OyXSIi8hecWODj7KlbQ0RE5O0YkPgBLtslIiJfx4DE\nj9Qv22UgQkREvodzSIiIiEh0DEiIiIhIdAxIiIiISHQMSIiIiEh0DEiIiIhIdAxIiIiISHQMSIiI\niEh0DEiIiIhIdD6dGM1kMgEAfv75Z5FbQkREFLgsz2HLc9kZPh2QnDt3DgAwYcIEkVtCRERE586d\nQ3h4uFOvlZjNZrOL2+Mx165dQ2VlJbp27QqplCnTiYiIxGAymXDu3DlERkaibdu2Tp3DpwMSIiIi\n8g+c1EpERESiY0BCREREomNAQkRERKJjQEJERESiY0BCREREomNAQkRERKJjQEJERESiY0BCRERE\nomNAQuRhxcXFyMnJsevY/Px8FBcXQ6PRQKPRuLll7mPvPRcXFyM/Px86nQ4Gg0H4NxH5P5+uZeOP\n8vPzoVAooNfrAQAqlcqlx3sjR+6huLgYOp0OiYmJkMvl0Gg0SExMhEKh8FRznabValFVVQWtVmtX\ne3NychAVFYXExETh5+LiYuFnX+DoPev1euTm5iI3NxcymQwLFizwife2sfz8fABARUUFoqKikJqa\navN4f/gcA/bdsy9/jgHAYDBAo9FAJpPh1KlTAICMjIwWX+Pr77Gj9+zUe2z2QXl5eeaioiJzQUGB\nuaCgoMVji4qKzHl5eeZTp06Z9Xq98G9vtGTJEnNRUVGzP7f2eG/k6D0UFBSY+/fvb+7fv7952LBh\nPne/ZnP9Pc6ZM8fmccOGDbP6ubS01Dx58mR3Ncut7L3ngoICs16v99rPqD0a3+fYsWPNeXl5zR7v\nD59jR+/Z1z/HS5Yssfp57NixLT6L/OE9dvSenXmPfW7IJicnBwqFAomJiVCpVDh16hSKi4ubPd7y\nF1d8fDxGjx4NhULhtVH45s2brf76jYuLa7Gb3tHjvZEz91BeXo4dO3agvLzcp3oLHFFVVXXTNrlc\nDq1WK0JrPEsmk3ntZ9QWg8GAsLAwq20qlQp5eXnNvsbXP8fO3DPg25/jkpISq/eoV69eKC0tbfZ4\nX3+PAcfvGXD8Pfa5IZvNmzdbdRPFxcUhPz+/xZstLy+HXq/36i85Rx9A/vDAcvYeZDIZZDKZu5rl\nFfR6PeRyudU2yz0bDAa/vn+NRgO5XA69Xg+DwWB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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Performing OLS\n", "X = x[:, np.newaxis]\n", "ols = LinearRegression(fit_intercept=True)\n", "y_pred = ols.fit(X, y).predict(X)\n", "\n", "# Plotting Signal / OLS\n", "fig = plt.figure(figsize=(8, 6))\n", "plt.plot(x, y, 'o', label=\"noisy observations\")\n", "plt.plot(X, y_pred, '-k', label=\"linear prediction\")\n", "plt.xlabel('$x$')\n", "plt.ylabel('$f(x)$')\n", "plt.ylim([1.5, 7])\n", "plt.xlim([-.5, 3.5])\n", "plt.legend(loc='upper left')\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "my_saving_display(fig, dirname, \"sin_signal_OLS\", imageformat)\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "OLS coef\n", "[ 2.27933767 0.99365503 0.00876502]\n" ] }, { "data": { "image/png": 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OIKC5udntMULxGo8YMWJA8OHr2ry9LgCcwz3V1dXYtGnTgLaVlJSgrKzM67+SkhLn81as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\nNTU19srKSntbW5vdYrE4/x+JXn75ZXtNTY3HnwP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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "OLS coef\n", "[ 1.10274056 5.6748322 -3.89572378 0.86254439]\n" ] }, { "data": { "image/png": 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DMzNJrCmJlsuwfGYSVt2nQLu5EwDw4IQMZI+eIGWo5CEu+yUiopAyN2U4tj4y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\nSMrKygAANTU1yMzMRGFhoZThhJ1ukxk7at3bu6b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EGo0GarUaAFBeXg69Xg+dTifVkIiIaJCF0jTPUxKrizg7AkBT8qOwx0eDR7Il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\nDjQ0NOhzTiKRSE4+u0t3ADLDgJVJDna7PeF9DodDn91vJja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hk59JWtSqVquZjBARRTlPNs176s3T+Kj1BgDAZrbg6rFzjhtlQOb9+UGKlAJJ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\n3bk2REREk6V5QNLY2IiGhoaEGRPKztismkz8bFcNSgrz0HH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HuDHkwcIM1o1EQ7EZksrKSmzZsgWbN2+G2WyG1WpFfX29UsMhIiIFON0evNpy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\nU0LJpfFyD8y/OIHM776GBd9/A5nffQ2P/PKEXM7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Signal / Polynomial Regression\n", "\n", "degrees = [2, 3, 4, 5, 6]\n", "colors = [2, 3, 4, 5, 7] # yellow was ugly!\n", "\n", "for i, degree in enumerate(degrees):\n", " X_poly = np.vander(x, degree + 1, increasing=True) # or with np.vander\n", " # Is equivalent to:\n", " # X_poly = np.column_stack([x ** i for i in range(degree + 1)])\n", " ols = LinearRegression(fit_intercept=False) # intercept already included!\n", " ols.fit(X_poly, y)\n", " y_pred = ols.predict(np.vander(xx, degree + 1, increasing=True))\n", " print(\"OLS coef\")\n", " print(ols.coef_) # not the small coef on dim 2\n", " # Signal / OLS\n", " fig = plt.figure(figsize=(8, 6))\n", " # plt.plot(xx, f(xx), 'k', label=\"true signal\")\n", " plt.plot(x, y, 'o', label=\"noisy observations\")\n", " plt.plot(xx, y_pred, '-',\n", " color=sns.color_palette(\"colorblind\", 8)[colors[i] - 2],\n", " label=r\"Polynomial prediction (deg={0})\".format(degree))\n", " plt.xlabel('$x$')\n", " plt.ylabel('$f(x)$')\n", " plt.ylim([1.5, 7])\n", " plt.xlim([-.5, 3.5])\n", " plt.legend(loc='upper left')\n", " plt.tight_layout()\n", " plt.show()\n", " my_saving_display(fig, dirname, \"sin_signal_poly\" + str(degree),\n", " imageformat)\n" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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DMzNJrCmJlsuwfGYSVt2nQLu5EwDw4IQMZI+eIGWo5CEu+yUiopAyN2U4tj4y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\nf8Z7T8ez0RSNAAAAAElFTkSuQmCC\n", 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WEgDIy8tTTt2UlJSIiENEROSj5+SX6G3y7Kvi534HUTHxghOFPyGFRK/XAwAyMzOVdUaj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\nFARYSMZIT9MRNL+zHU27H4dLOunzsYR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DkSYyAlp9DFzSOBx9PPSXlo7X6cbQ5Q70/9AK6Xo3IMsz3l4TrYUmWgu1NgJq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\nmdAaYgAA0o3uoJrcOnS5QwlRqgg18n9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XSU9PT0LxallZGcrKyvD8889ztQ1RGjl8oR97jnXjSlx1/5xcHZxLC1C10DTl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\ni0vyUD6b+9RkIrNBwF+sKcT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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "degrees = [3, 4, 5, 6]\n", "colors = [3, 4, 5, 7] # yellow was ugly!\n", "\n", "\n", "fig = plt.figure(figsize=(8, 6))\n", "plt.plot(x, y, 'o', label=\"noisy observations\")\n", "for i, degree in enumerate(degrees):\n", " X_poly = np.vander(x, degree + 1, increasing=True) # or with np.vander\n", " # Is equivalent to:\n", " # X_poly = np.column_stack([x ** i for i in range(degree + 1)])\n", "\n", " ols = LinearRegression(fit_intercept=False) # intercept already included!\n", " ols.fit(X_poly, y)\n", " y_pred = ols.predict(np.vander(xx, degree + 1, increasing=True))\n", " # Signal / OLS\n", " # plt.plot(xx, f(xx), 'k', label=\"true signal\")\n", " plt.plot(xx, y_pred, '-',\n", " color=sns.color_palette(\"colorblind\", 8)[colors[i] - 2],\n", " label=r\"Polynomial prediction (deg={0})\".format(degree))\n", " plt.xlabel('$x$')\n", " plt.ylabel('$f(x)$')\n", " plt.ylim([1.5, 7])\n", " plt.xlim([-.5, 3.5])\n", " plt.legend(loc='upper left')\n", " plt.tight_layout()\n", " plt.show()\n", "\n", "my_saving_display(fig, dirname, \"sin_signal_poly_all\", imageformat)\n" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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FUr3rfdRReCQlDnNTBNzQnRuwUtsxkBAREQCg1u5A7v4SrNheiM/2npY3t6sT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\nh84BAHp0jMCHD47iDrNERD6E35Ep4H2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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# defining a class for Polynonial Regression\n", "\n", "class PolynomialRegression(LinearRegression):\n", " \"\"\"PolynomialRegression Class, to perform for instance CV\"\"\"\n", " def __init__(self, degree=2):\n", " super(PolynomialRegression, self).__init__()\n", " self.degree = degree\n", " self.fit_intercept = False\n", "\n", " def fit(self, X, y, deg=None):\n", " X = np.vander(X, N=self.degree + 1)\n", " super(PolynomialRegression, self).fit(X, y)\n", " return self\n", "\n", " def predict(self, X):\n", " X = np.vander(X, N=self.degree + 1)\n", " return super(PolynomialRegression, self).predict(X)\n", "\n", "model = PolynomialRegression(degree=3)\n", "\n", "\n", "# On the importance of cross-validation\n", "\n", "estimator = PolynomialRegression()\n", "degrees = np.arange(2, 12)\n", "cv_model = GridSearchCV(estimator, cv=5,\n", " param_grid={'degree': degrees},\n", " scoring='neg_mean_squared_error')\n", "# Note: in scoring above, neg means -MSE\n", "cv_model.fit(x, y)\n", "\n", "mse = [-cv_score for cv_score in cv_model.cv_results_['mean_test_score']]\n", "fig = plt.figure(figsize=(8, 6))\n", "plt.semilogy(degrees, mse, label=\"CV MSE curve\")\n", "plt.xlabel('Degree')\n", "plt.ylabel('CV MSE')\n", "plt.legend(loc='upper left')\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "\n", "my_saving_display(fig, dirname, \"CV_curve\", imageformat)\n", "\n", "best_idx = np.argmax(cv_model.cv_results_['mean_test_score'])\n", "best_deg = degrees[best_idx]\n", "best_mse = -cv_model.cv_results_['mean_test_score'][best_idx]\n", "plt.plot(best_deg, best_mse, \"*r\", markersize=40, label=\"Best degree (CV MSE)\")\n", "plt.legend(loc=\"upper left\")\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "my_saving_display(fig, dirname, \"CV_curve_and_best\", imageformat)\n", "\n", "\n", "# alternatively, onec can do it directly with sklearn:\n", "\n", "model = make_pipeline(PolynomialFeatures(degree=6), LinearRegression())\n", "y_pred = model.fit(x[:, np.newaxis], y).predict(xx[:, np.newaxis])\n" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "###############################################################################\n", "# SPLINE PART : Beware sicpy needs the points to be in ascending order!!!\n" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Z2Q2XTOCxJXOJOz2eDe//jexzRwBo1ej5bsIPeDTu67g1nYWuWifEejcZpT0K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t8ng8CgaDOdEePhAIpAUP27YVDAZdqshdAw/Z273/MIEEAJDXhgwkX/3qV9Xc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\narUsS16vl0ACAEARyGogAQAAGExOTdk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GAMUyJA0NDairq4PFYoHNZpOOExGnbIiIfOxOFy5122F3utDa3YmPr7QBAIqy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\nZDkjjLKJeKf3lLp9b8WtSY+JDBGeCy6QR0RkHAxIstz0eUj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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "MSE Polynomials = 2.1899671188674597)\n", "MSE Spline = 0.24984386133649528)\n" ] } ], "source": [ "# Follow guidelines from:\n", "# http://danielhnyk.cz/creating-your-own-estimator-scikit-learn/\n", "# for creating an sklearn compatible class\n", "\n", "class UnivariateSplineSmoother(LinearRegression):\n", " def __init__(self, s=4.):\n", " self.s = s\n", "\n", " def fit(self, x, y):\n", " self._spline = UnivariateSpline(x, y, s=self.s)\n", " return self\n", "\n", " def predict(self, x):\n", " return self._spline(x)\n", "\n", "# large curvature means s is small\n", "spline_smoother = UnivariateSplineSmoother(0.5).fit(x, y)\n", "y_pred = spline_smoother.predict(xx)\n", "\n", "# low curvature means s is large\n", "spline_smoother = UnivariateSplineSmoother(2.).fit(x, y)\n", "y_pred_bis = spline_smoother.predict(xx)\n", "\n", "# Plotting Splines\n", "fig = plt.figure(figsize=(8, 6))\n", "plt.plot(x, y, 'o', label=\"noisy observations\")\n", "plt.plot(xx, y_pred, '-', label=\"Spline: large curvature\")\n", "plt.plot(xx, y_pred_bis, '-', label=\"Spline: low curvature\")\n", "plt.xlabel('$x$')\n", "plt.ylabel('$f(x)$')\n", "plt.ylim([1.5, 7])\n", "plt.xlim([-.5, 3.5])\n", "plt.legend(loc='upper left')\n", "plt.tight_layout()\n", "plt.show()\n", "\n", "my_saving_display(fig, dirname, \"splines\", imageformat)\n", "\n", "\n", "estimator = UnivariateSplineSmoother()\n", "s_values = np.linspace(0.1, 10, num=20)\n", "cv_model_spl = GridSearchCV(estimator, cv=5,\n", " param_grid={'s': s_values},\n", " scoring='neg_mean_squared_error')\n", "# Note: in scoring above, neg means -MSE\n", "cv_model_spl.fit(x, y)\n", "\n", "mse_spl = [-cv_score for cv_score in cv_model_spl.cv_results_['mean_test_score']]\n", "fig = plt.figure(figsize=(8, 6))\n", "plt.semilogy(s_values, mse_spl, label=\"CV MSE curve\")\n", "plt.xlabel('s values')\n", "plt.ylabel('CV MSE Splines')\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()\n", "my_saving_display(fig, dirname, \"CV_curve_spline\", imageformat)\n", "\n", "\n", "best_idx_spline = np.argmax(cv_model_spl.cv_results_['mean_test_score'])\n", "best_s_spline = s_values[best_idx_spline]\n", "best_mse_spline = -cv_model_spl.cv_results_['mean_test_score'][best_idx_spline]\n", "plt.plot(best_s_spline, best_mse_spline, \"*r\", markersize=40,\n", " label=\"Best s value (CV MSE)\")\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()\n", "my_saving_display(fig, dirname, \"CV_curve_and_best_spline\", imageformat)\n", "\n", "# large curvature means s is large\n", "y_pred_bis = cv_model_spl.predict(xx)\n", "\n", "# Plotting Splines\n", "fig = plt.figure(figsize=(8, 6))\n", "plt.plot(x, y, 'o', label=\"noisy observations\")\n", "plt.plot(xx, y_pred, '-', label=\"Spline: CV choice\")\n", "plt.xlabel('$x$')\n", "plt.ylabel('$f(x)$')\n", "plt.ylim([1.5, 7])\n", "plt.xlim([-.5, 3.5])\n", "plt.legend(loc='upper left')\n", "plt.tight_layout()\n", "plt.show()\n", "my_saving_display(fig, dirname, \"best_spline_display\", imageformat)\n", "\n", "\n", "print(\"MSE Polynomials = {0})\".format(best_mse))\n", "print(\"MSE Spline = {0})\".format(best_mse_spline))\n", "\n", "\n", "###############################################################################\n", "# GAM PART :\n", "\n", "class GeneralizedAdditiveRegressor(LinearRegression):\n", " \"\"\"Fit Generalized Additive Model with backfitting\"\"\"\n", " def __init__(self, smoothers, max_iter=20):\n", " self.smoothers = smoothers\n", " self.max_iter = max_iter\n", "\n", " def fit(self, X, y):\n", " n_samples, n_features = X.shape\n", " self.y_mean_ = np.mean(y)\n", "\n", " residuals = y.copy()\n", " residuals -= self.y_mean_\n", " for i in range(self.max_iter):\n", " for j in range(n_features):\n", " if i > 0:\n", " residuals += self.smoothers[j].predict(X[:, j])\n", "\n", " self.smoothers[j].fit(X[:, j], residuals)\n", " residuals -= self.smoothers[j].predict(X[:, j])\n", " return self\n", "\n", " def predict(self, X):\n", " n_samples, n_features = X.shape\n", " y = np.ones(n_samples) * self.y_mean_\n", " for j in range(n_features):\n", " y += self.smoothers[j].predict(X[:, j])\n", " return y\n", "\n", "\n", "\n", "def f1(x):\n", " return np.cos(3 * x)\n", "\n", "def f2(x):\n", " return x ** 3\n", "\n", "def f3(x):\n", " return 3 * np.log(1 + np.abs(x))\n", "\n", "def f_true(X):\n", " return f1(X[:, 0]) + f2(X[:, 1]) + f3(X[:, 2])\n", "\n", "n_samples = 100\n", "\n", "x1 = np.sort(2. * np.random.rand(n_samples) - 1.)\n", "x2 = np.sort(2. * np.random.rand(n_samples) - 1.)\n", "x3 = np.sort(2. * np.random.rand(n_samples) - 1.)\n", "\n", "X = np.c_[x1, x2, x3]\n", "y = f_true(X)\n", "y += 0.1 * np.random.randn(n_samples)\n", "\n", "\n", "s1 = 10 * np.var(y)\n", "s2 = 10 * np.var(y)\n", "s3 = 10 * np.var(y)\n", "smoothers = [UnivariateSplineSmoother(s=s1), UnivariateSplineSmoother(s=s2),\n", " UnivariateSplineSmoother(s=s3)]\n", "gam = GeneralizedAdditiveRegressor(smoothers, max_iter=200)\n", "gam.fit(X, y)\n", "y_pred = gam.predict(X)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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VtYITEbme1/48iqR9uQAAX08Z1twXhza+ntf9c1kQUbOtP1yI+5L2W4+fGtkFr0zobvcF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\nunKHBjjS9NXRfWWz0U0O8Y1iqG2cqglqxgU9tXF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LGT58eJuOX79+fZPkZ9KkScTHx1s6LCGEEEKoYHNWGpV1k6lvCRiOnUaq9QFWpWzjpCGP\nC+UG1f530pDH6tRt7Y49JSWFv/3tbyQnJzN8+HAWL17c5P1nn30WgK1bt6LValm8eDGzZ88mOTmZ\nDRs2EB8fj16vB2DJkiVERESQnJzM2rVrKS4uvupnL1iwQLl2cnIyS5cuBWDNmjWsXLmS6OhokpOT\nlWToShYvXoyHh4dynF6v57nnnlPef+ONN3jxxRdJTk4GkIYM16Cspoqv60aItY4u3OQ3ROWIrkzV\nMavU1NRmr+l0OpKSklSIRgghhBCW9qW+4W/9rQFte1jaE6yImGoTI0QrIqa2+7xZs2ah1ZobY6xZ\ns4awsDCSkpKIjo4GGkZtoKFyaPXq1axevVq5Rn0lkV6vV44F84P1lu4Dk5KS0Ov1bNiwocnx7ZGU\nlITBYGgypeNvf/sbUVFRPPXUU83+ffWjRaJjEjKPU1pTBcC8wHCcbbBcDlROiIqKitDpdE1eq/8B\nNBgMyrYQQgghup5ao1F5Ouxs78BNfoObHZOWV4JDrcnaoakuNuS6dpWq2bL6xKZe4yRFr9cTHR3N\n2rVrm50XHx+vlNq1hV6vv+bStdTU1GbXqL/fTElJAWj2fv0cd9F+nzRZjHWkipFcnaoJkcFgaPZD\nVp8gFRUVSUIkhBBCdGE/52eQV1EKwPT+g3B3dG7yvtFoYs6bP1NyMQePK11AdAmXJyqN798CAgKU\nRONylydSrWnv8S1d4/J4DAYDYB7ZEpbTuFxO52S75XKgctvtKyU89QnS5SNHQgghhOhavsxo6C43\nN6D5SMCWtDzS8kvJK62yZljiGtWXnRkMBpYvX05AQECLpWv1La+XL1+uvJaYmEhqaqpyTv38HYPB\ncNV55PXXajzfJzExUSlp0+l0SsJ0pWkZADExMeh0uiaf+cQTTzBz5kx5EG9hjcvlbguw3XI5UDkh\n0ul0SlZer35ffii7t/SLpbyy6yyPfnaY5Z83f3L0c8YlvkrNpqyqRoXohBBCWMIXGQ3f77dcYf7Q\ne/syrRmOsBAPDw+eeOIJoqKiKC4uvmI5XGPvvPMOYO7+FhUVxbfffquMKG3YsIGUlBSioqJ45pln\nWp0TdLVr1Z8bFRXF6tWrm91j1tuwYQOFhYVERUUxffp0hg8fzpo1a9r6zxdttP5MQ3c5Wy6XA5VL\n5sLDw5slPkVFRe2eICe6hsLyauL2nGNtsp5jOSXK633cHFkzv+kwdfzBLF7Yno6zgx0zw3z41fUD\nmT7YG41GY+2whRBCdMCxwhyOF+UCMN4nkAHuzSs/3lw0kpiwvry3/RBnvrd2hKKjIiMjle5ul2vc\n8KCeVqttMeEICAi44jktXU+r1bJy5comjRgav3el7nJXukZL8Vx+7NKlS1v8t4qWlVZX8nVm1yiX\nAxVGiPR6PYmJicr+okWLmuzv2rVLFmbtZgwV1fzuq6P4r9zM774+1iQZArhYVk1BWdNyiZN55prz\nyhojX6bmcNPrexj5/Ha+OZpjtbiFEEJ03OfnGkaH5gdeeW6Gs4M994zx581Ftv30uC0qaqvVDkEI\nm/GV/qiyGOuCoEibLpeDThghql+UddOmTRQVFSl1pfVdRJKSkposvLpixQri4uJITExEr9cTGBgo\ni7J2EyaTiXf3ZvL7b46RU9y0rWhUgCdzhvVlSmgfwvr2wsvVscn7j0YH4e3uxDfHcsgrMSdLRy4U\nc8tbPzNraF/WzI9gkLe71f4tQggh2mfDuSPK9vygSBUjsY5dOWcZFDRQ7TCEsAnxjcrlYgfafjdF\niydE4eHhhIeHtzi8ePlqw4AMRXZTqdnFPBh/EGNdN1VHew0PjA3gyckhhPtevZ/QrGH9mDWsH1U1\nRj45lMXz209z4Ly5FjjheC7XPb+dV26P5L4x/lJGJ4QQNuZcSQH7LprnB0V4+jJE59Pk/ZpaIw72\n3WuB1q0X0niAaWqH0emuVt4mBEBRVTkJ548D0MfZjRv7D1I5otZ1r28jYVMi+mt57iZzzeitw/tx\n9HfTiFs0stVkqDEnBzvuGePP3icns+6u6/D1MLdsLa2q5YGPDnL4wpUnTAohhFDPF+caOnwtCG46\nOmQymRj34k4Wf3SAA5ndZ32XLVlpGE1GtcMQQnUbM1KprDU3xVoYPAJHO/tO+6xvj+VgqLj2Bly2\nXdAnurw/zhhMdHBvbgrzaf3gq7Cz03D/2ADmRfjy6GdH+GD/eX47JYSRftKeXQghbE2TcrnL5g9t\nOZnPgfMGDpw3cDSnhJ+fvMHa4XWKvIpS9uZnMs4nUO1QhFBV/JmDynZnlsvtOH2R295OJsSp/Jqv\nJSNEwmL+t/MMHx843+Q1B3u7a06GGtO6OPLe3aPYsHgsf589zGLXFUIIYRnZZQZ25pwBYGCv3ozs\n7dfk/f/uTFe2n5zcvebc/N/OXWqHIISqLlaU8t35kwD0c/Vgcr+QTvmccwVl3L5uLzVGE+kFZdd8\nPUmIhEX8d0c6y79IYfHHB/kx/WKnfpZGo2F+ZH+cHJr++CZnFHLWAr8UQgghOu6zc0cwYZ48ekfw\niCbzPI/nFPPtMXMrbj+tCwtH+F3xGl3V1uwTJByTbqii5/r07GFq6kpHFwWPxN7O8qlGaWUN89Ym\nk1+3oPP4IK9rvqYkROKavbgjnV9vNNeLV9YY2ZqWb/UYfjp3iRmv72bqK0mSFAkhhIoaL8a46LJy\nmee3N4wOPTYpuNmDrS7PtYTYj5M4mVfS+rFCdEMfnTmgbN8dMsri1zeZTPxi/SEOZpnnkAd5ufLK\ngiu39W+PbvZNJKztvb16ntzYMHn26RsH8dzN1l18y2Qy8diGIxgqajh3qZybX99Dfkll6ycKIYSw\nqKyyIqVcLsSjD6P7DFDeyzZU8O5ec+c5dyd7HokOUiXGzlbslMO8tckYKmRdItGznC8tYkd2Q7ns\n+E6YT/ev708RfzALADcnezY+GEVvN6drvq4kRKLDtpzM48H4hieBv5sWyt9nD7V6G2yNRsMXS6II\n7eMGQFp+KXPfTqa8utaqcQghRE/32dmGcrlFwSOb/D14addZqmrNpTQPjQ/EywI3MTZJm8+xnBLu\n+/AAxvp1J4ToAeLPHFR+/+8Muc7i94MJx3L4v4Tjyv47d15nseZakhCJDkm5YGDBO+bJbAAPjgvg\nn3OGqbYmkL+nK5uWTcCnl/kP7O5zl+SPkRBCWNn6s43L5UYq2yWVNbyy6ywA9nYanpzcOROt1eTr\nWrekhHsR2NXwZWoOf918Ut2ghLCijxt1l7troGXL5UwmEy9sT8dUd1v3f9MHccdIy81BlIRItFth\neTXz39lLcaW57/vMMB9eWzhC9QVSQ73d+foX43B1NP9Yf3b4Av/8/pSqMQkhRE+RWVrIj3XlcoM8\nvLmuUXe5t37K4FK5uYTsjhH9Ce7tpkqMnekmv7pycY0JtObmQi/sSCdPSrhFD3DKkE9yvh6AcM9+\nRPbub9HrazQavvzFOO4f68/sYX1ZGTPUoteXhEi0i9Fo4r4PD3AqvxSAcF8PPrl/LI42suL4uEAv\nPrxntLL/TOJxEo/nqhiREEL0DB+nNzwdXjSwabmch7ODsrD2immhVo/NGm4e0DB/NnxwFUN83Nmz\n/Hp8ejmrGJUQ1vFh+n5l+65OaKYA4Opozzt3XsdnD4zF3s6yD+Ft4y5WdBkaDUwK9kKjAZ2LA18s\nicLDxbbW950X2Z9nZgwGwGSCu9/fzznpPCeEEJ3qg0Y3RPeENr0henB8IGf+OJ2NS6IY7e9p7dCs\nYrxPIFpHFwDOVZ9n16+iGdbPQ+WohOh8JpOJD053Tne5y6c+aDQaXBztLXb9epIQiXbRaDQ8PX0w\niUvH89G9oxnk7a52SFf055lhzBraF4BL5dW8k6xXOSIhhOi+jhZmc7DA3PlpZG8/hnv6NjvGxdGe\nuRHNX+8uHO3smRNgXjC8pKaS5EtnVI5ICOvYdzGTk4Y8AKL7BjPQo49Frrv5RB4T1vxolYfakhCJ\nDrk5rC+zhvXr8PnVxloulBk4ZcjnWGEOJ4pyuVBmoKymyiLx2dtpeP+eUYT5uPPGHSOs3gpcCCF6\nksZPh+/ppHKZrmBeYLiy/fm5FGW7utbIbzam8i+Z1yq6oQ9ONxodttDv/9mCMu58fx/J+kLG/ndn\np6/tZVu1TsJmZRsq8NW6tPu8WqOR1MJsknLPsu/ieY4V5nDSkEdeRWmL53g7uzPQozcRXr5EeQcQ\n3TeYEV792920obebEykrpuJgI/ObhBCiOzKZTMr8AQ0aZf6A0WjiXz+cYnFUAP078PejK4oZMBQn\nO3uqjLVszEjl1Ym3YzTBza/vYdvpi9hpYKy/julDfNQOVQiLqDUale5yDhq7Zosxd0RFdS0L1+2l\noMzciGXUAC2hfTq3IkkSItGqTw5lsfjjg/xz9jAemxSMXSsT2YqrK/gq4yhfZx4jMfM4l6rK2/V5\n+ZWl5FeWkpyvZ21aMgD9XbXM8h/K3SGjmOobir1d25IcSYaEEKJzJeWe5WzJJQCm+Ibg726eI/RF\nSjb/9+1xVn53kn/OGcYT3bDV9uW0Ti7c5DeEbzKPkVtRQlLuWW7wDWFCkBfbTl/EaII739/Pvl/f\nQKBX9+u0J3qeH7JPkV1eDJgbi3i7XHvi8viGFPZlFgEQ5OXKR/eOsXgThctJQiSuKq+kksc2HKGs\nqpblX6QQ3NuVW8Ob14CbTCa2XkjjrZM/szEjlfLallfo9nZ2J8Ddk36uvfBwdMbRzp5ak4ni6gou\nVpZxtuQSOXW/XPUulBt4O+1n3k77mQFuOpaFjeeRodH4uPRq179nZ/pF9py7xIppg9p1nhBCiCt7\n7/Q+ZfueUHOXT6PRxF++M6/BU1FjJMjLVZXY1DA/KIJvMo8B8HlGCjf4hvDXmDCS9YVsTcsnv7SK\nhev2sfPxaJwdLD85XAhreu9Uo9//kNFXObJt3vopg7d+zgDA2cGOzx4YSx/3zl/EWRIicVW/+jyF\nvBLzvJ7Zw/pyy/Cm84bKa6p5O+1n1hz9UZlQ15i7gxPT+odyfd+BTOgbRISnL33a8PSguLqC/RfP\n81NeBluy0tiefZoqYy0A58uK+NOB7/jH4e95cPA4nhk5g/5u2lav+fuvj7Jq22kAJgZ5cX2IZSb9\nCSFET1VeU62Uy7jYO7AwaAQAG1OzOXzBAMBIPy23deNmCpebGxiOXdKnGE0mNpw7wvNRt+Jgb8fH\n945m9H92oC+sIFlfyJNfpPLqwhFqhytEh5VWV7Khbq5cLwdn5gVFXNP19ukLeWzDEWX/lQWRjAmw\nTldKSYhEi75KzSb+oLlrkM7FgTfuaFh8tbS6kpeO7eKF1B3kVjSd6KZzcmFh0AgWDRzJFN9QnO3b\n/2Pm4ejCFN9QpviG8rvIaZRUV/JlRirrTu1lc1YaJkxU1NbwyvEk1qYl8+vwyfxhxI30cmx5vQed\ni6OywvFD6w9x6Kkp8nROCCGuwcaMFIqqKgCYHxSJp7MrRqOJlXWjQwB/unmI6gt3W5OPSy8m9wth\nW/ZpzpVc4sDF84z29se7lzOfPjCWG15KoqrWyGu7zzEx2Iv7xwaoHbIQHbIxI5WSGvPCwwuCInBz\n6PhITkFZFQvf3UtljRGAh8YH8uD4QIvE2RYywUJcUWllDY9/3tAh54W54QzQuVJtrOW140kM+uyf\nPL3v2ybJ0KS+wXw45R6yY//Em9cv4uYBYR1Khq6kl6Mzd4eOZtPMZZy8/fc8NjQaV3tHAMprq/n7\n4a2Ef76KrzJSW7zG76aFMtpfB8CJvFJW/XDaIrEJIURPVT/PE2DxoLEAfHbkAgezzKNDI/prue0K\nZdbd3fxGT8o/z2j4Wzou0IsX5zV0ovvlp4c5UjeSJkRX07hc9r5BYzp8HaPRxH0fHuBsgXnO+Rh/\nHf+bf22jTe0lCZG4opWbT5JxyfyDOSW0D0vGBfDDhVOM2vgCj+zeoEygA5gfGMHPtyznxzmPc1fI\nKFwcHDs1tkFab16auIDTC//AL8MmYq8x/xhnlBYyd+ta7t7+AYWVzRs5ONjb8cbCEdTPy/vbljRO\n5bfc7U4IIUTLMksL2ZyVBoC/m47p/QdTazTxXOIJ5ZiVMWGtNuLpjuYHRirbn5093OS9hycGcd8Y\nfwDKq41YE8YQAAAgAElEQVTc/s5eDBUtz7sVwhZllxn4Lss8EuznpmWab8fnZlfVGtG5mO8dvVwd\n+fSBsZ2y+OrVSEIkmjlywcAL29MBcLTX8LdbQrhnx4fcmPgaqYU5ynG3BAzj8G2/ZcP0xUT5WG9Y\ns15/Ny2vRt/O4Xm/YXK/hu5FH6UfYOTG59mZnd7snDEBnjw2aSAAlTVGHvvsCCaTqdlxQgghru69\n0/swYf7+vH/QWOzt7Hh/XybHc82VA+MCPZkb3vH16rqygF6eRHmbS+GOFeVytDBbeU+j0fDq7ZFE\n+HoAYAJyiivVCFOIDvvozEGMdfdPd4eManP33ytxcbTng3tG8crtkbx39yiCe1u/A6MkRKIJk8nE\n8s9TqDGaABOzxpuY9+MrfJTesOjedb392D7rEb6a8Qsie/dXL9g6wz192TbrEd6atIheDuY5RBml\nhdyY+Br/O/pjs4TnrzFh9Neaj/vuZB4bU7KbXVMIIUTLTCYTb59sKJd7YNBYqmqM/Pm7htGhv8UM\n7VFzhy63MLihYcJnZ480ec/d2YFPHxjLvWMGsPfJGxjs076OqUKo7d1Te5Xt+0I7Xi5XT6PR8Eh0\nMHOGq/MQRRIi0cSp/FKS9YVgX41r6Am+NGznYmUZYG6W8PKE+ey99Ukm+4aqHGlTGo2GB4eM49C8\n3zDRJwiAGpOR5T99wZIf46msrVGO1bk68vytDTXcv/nyKBXVtVaPWQghuqpt2ac5VZwPmOePDtH5\nkJJt4FLdQopTQvswY4i3miGq7vaghrK5Ty8rmwMI69uL9+4ejc61c8vMhbC0wwVZHCwwN90a4dWf\nEb392n2NmlqjTY2MSkIkmhjs04u3HgzCddgByl0byuPmBUZwdP4KHh026ZqGRTtbiEcfts9+lCeH\n36C8tu7UXmZvfpOiRgvE3jnKj0nBXgCcKSjjPzual9cJIYS4sjdO7FG2Hw6bCMBof09O/990fjMl\nhH/M7tmjQwChWm9G9R4AwOFLFzhZ1HxpisvVGk2UVNa0epwQanq30dpDD9Q1U2mvZxNPMGL1Nr5P\ny7dUWNfEdu9shdXVGo386cAm7vrxHcoxJw86Jxc+mHw3G258AD83ncoRto2jnT3/GX8b795wl9Ll\n7vsLp5j87StcKDN389FoNLw4LwKNBob4uDN6QNf4twkhhNryKkrYcM5cAubl5NqkNKyPuxPPzw1n\nYnBvtcKzKU3K5s41HyVqLLe4kpg39nDX+/tlbquwWTXGWt5P3w+AvcZOWYy5PRKO5fDP70+RW1JF\nTNweMgubN8KyNkmIBAAXK0qJ2RzHyoOblUmyU31DOXLbU9wdOrpLPum7b9AYvrt5KZ5O5hXSD1+6\nwNSEVzlfWgSYGywkPDSeI09NZebQvmqGKoQQXca7p/YqC2XfP2gsrp3cWbQru9o8osaMRhM3vrab\nLWn5fH00R2lsJISt+e78SXLqOg3HDAijn6tHu87PLCznvg8b5qX/+eYw/D1dLRpjR0hCJDh48Tzh\nG15gS137VA0a/nTdTWyZ+TABvayzQnBnmewbyo+zH2NA3ejWSUMeUxJeQV9SCMDMoX1xcpBfAyGE\naAuTycQbJ35S9pcOGc/HB85zqaxKxahs1xCdD5Fe5uZD+y5mkl588YrH2dlp+Pusocr+098cY/fZ\nAqvEKER7rGvUTKG95XI1tUbuen8/F+vmGs4M8+HpGzvertuS5E6wh/v83BGiv3mJnErzqEkvexc2\n3byUP4+aadNzhdoj3MuXHbMfJdDdnNydLr7I9E2vkdtoLSUhhBCt23ohjZMG81yY6L7BVJS4cPcH\n+xn8j+95+6cMlaOzTXc0GiX65MyhFo+bG+HLb6aYl5CoMZq48/39FEiiKWzIpcoyNupTAfB0cuXW\ngOHtOv+5TSf48Yw50ffTuvDe3aNsZp2y7nHHK9rNZDLxr8Pfs+D7dZTX1i0IV96LB3vP46YBQ9QN\nrhOEePRh+6xHCe5lbqSQZsgn5rs3MVRVKMeczCth4bq9/HDKNib4CSGErXnp2C5l+9Gh0fz6y1RM\nJrhYVk1uie10jLIldwSPVLbjr5IQAfxj9jDGB5of3mVcKufBjw/KfCJhMz4+c1Dp2nvnwOtwaUe5\n7Kbjufxj6ykA7DTw0b2j8enl3ClxdoQkRD1QjbGWR3Z/xtP7vm14scgbn9xx/G3GdeoF1smCPXqz\nNeaX+NbVux4oOM/crW9TWVvDrjMFhP97G58dvsDT3xyTP0BCCHGZs8UFfKU/CkA/Vw/sDD7sTDc/\n7R3Y240nJ4dc7fQea6hnX0bUlc0dKDhP2lW6zTk52PHxfWPwrGvFvTE1hzU7z1glTiFaszatYe2x\nJYOj2nzeBUMF933UMG9oZUwYk0P7WDS2ayUJUQ9TVlPFgu/X8XqjlqnkBoJ+OM/NGIaHi4N6wVlB\niEcfNjVqtLA9O52Hkz5lXICO0D7mlZF/zijkq9Scq11GCCF6nFePJykr0y8JjeLpbxoWYV116zBc\nHO3VCs3mxQ5seNj4yRXWJGosuLcbb8c2jCqt+Poo+zMLOy02Idoi9VI2yfl6AIZ79iPKO6BN59Ua\nTdz7wQHySszlnzcN8eYPNw7utDg7ShKiHuRSZRk3bXpDecJnhwYywyB3IEFebiybEKRyhNYxorcf\nX814ECc78x/vdaf2svroNlbGNExofSbxOEajjBIJIQRAeU01b6b9DICDxo6ynH5kXDK3yp0S2ocF\nkf3VDM/mNZ5HFH/mYKvHz4/sz+OTggGorjVx53v7Ka6Q9YmEepqMDg2KanP3YQ0QM9QHBzsN/Tyc\nee/u0TYzb6gxSYh6iOwyA1MTXiUp9ywA7g5ODC4bD4W+APzp5iE9qtva9f0G8vb1scr+/+1LwNHz\nItf5aQE4cqGY+INZaoUnhBA25YP0/RRUlgFwk+8wXtuRDYC9nYaX5kd0yaUZrGmwzqfJIq3HC3Nb\nPWfVrcOVv0khfdyoqjV2aoxCtKTaWMt7p82Lsdpr7Li3HWsP2dlpWDFtED8+PomP7x1NPw/bmTfU\nWM+5A+7BMksLmZzwCocvXQCgt7MbK8MWcSLd/EMZ5uPOfWP81QxRFfeEjubZkTOU/cU/xvPItH7K\n/p82naBG/gAJIXo4o8nI8ynblf1L+r7Kzfny6wcS0V+rVmhdSuzAxs0VWh8lcnG0J/7+May+dTjf\nPjSePu5OnRmeEC36Vn+M3IoSAGb7D8XXrf2/8+ODvJg6yNvSoVlMpyVEcXFxJCYmEh8fT3x8/FWP\nTUxMJC4uDr1ej8FgULbFtTtbXMDkb18hzWDunObnpmXHrEf5cJdBOeYvM8NwsO+ZufGfR93MbYHh\nABiqK/jfua8ZF2RuupCWX8pHB86rGZ4QQqguIfM4x4vMIxqD3XzZc9y8KKuvhzN/ntn9upJ2lkWN\nEqKPzhxoU/OeIT69+O3UUJssMRI9x1t15bLQtmYKJpOJtLySzgzJ4jrlLnjVqlUEBAQQExNDbGws\nGRkZJCYmtnh8UVERq1evZsaMGUyfPp2AgAACAto2WUu07EzxRaYkvMKZEnMXoOBeXuyc/RgVJS7s\nyzSvOzS8Xy/uGOmnZpiqstPYse6GOxnkYX5qkVKYjS7krPL+37akySiREKJHW91odGiK53W4OJjn\nX74wNxytS9vb7vZ0Az36MMHHPFf3RFEehwo6VpZtqKimqkb+LgnruFBm4NvM4wD0denFLW1Ye+jN\nnzIIX7WN1T+c7jLzsTslIVq/fj0xMTHK/qRJk1odJUpOTmbLli0kJyc3OVd0zNniAqYmvEpGqbkz\nzSAPb7bPepQQjz6MCfDkyFNTWDTSjz/PDOvxT550Tq58Pv0B3Or66W/OS2FwaCkAJ/NK+VjmEgkh\neqj9+Zlsyz4NwMBevXn1pmmk/m4qz900hDtH9dyHaR11V0hDt7mP0g9c5cgr++ncJa57fgfPJBy3\nZFhCtGjdqb3UmswJ+AODxuJod/VuksdzinniixSqa02s+Ppol1nb0eIJUWpqarPXdDodSUlJVz1P\nq9XKqJCFZJRcYmpiQzI0WOvN9tmPEFi3KClARH8t8feP6dGjQ41FePVnzfh5yv75XofBsZy+vZxk\nTSIhRI/175RtyvaT4TfgYGdPSB93/hITJo0UOmBR8Ejs6v67fXzmIEZT20d6cosrmfZqEmcKyli1\n7TRbTra8npEQlmAymXjrZEO53IODx131+MqaWu56fz/l1eaf68VRAUwf4tOpMVqKxROioqIidDpd\nk9e0WvPkK4PBcKVTAIiPj1fmHMXFxVk6rB7jQpmB6Ymvc67kEmAeGfoh5hH83HStnCkeHDyORXUr\nipfVVjFolJ5Tf5jGfWMlURdC9Dwni/JYf+YQYG7G09rNkGidr5uWqb6hAGSUFrI791ybz+3r4cyz\nNzXM2br/owPklVRaPEYh6u3ISedUsXmEZ1LfYIZ69r3q8X/45jgHs8z3+oO93fnf/IhOj9FSLJ4Q\nGQwGioqKmrxWnyBd/nq96OhoZs2apcw50uv1rZbYiebyK0qZsel15Yd3YK/e/DDrlwxwN//3v1ha\nJaMdV6HRaHg9eiFBdSNpp8ou8GraLpWjEkIIdfzzyPeYMP/NiHAciqOmey/cbS13hYxStttbNve7\naYOYEtoHgAuGSh5af0j+rotO8+bJn5TtXwy5+gOR707k8p8d6QA42Gn48N7R9HLuOt8ZFk+I6keD\nGqtPhC4fOaoXEBDQ5Lzo6GgZJWqn4uoKYr6L42hhDgD+bjq2xjyMv7uncsyid/cx8vntfHzgPLVd\nZJKbtXk6u7LuhjuV/Wf3J3K0MFvFiIQQwvrOlRTw3inzuiPU2rPjZxcmrvlRmsxYwO1Bkco8jPgz\nh6g21rb5XHs7De/dNQovV/Oc1y9Tc4jbk9EpcYqeraCyjE/OHgbAw9FZqaC5kvySSh74qKGV/N9m\nDWVsgGeLx9siiydEOp2uWWlc/f6VkiWDwUBYWFiTc7RarbTdboeKmmpu27KWfRczAXMXkC0xDzPQ\no49yzJ5zl/j+VD5HLhTz9DfHMMoTpRZN8Q1l+bDrAagy1vLAzo/JKirjfzvPyJM4IUSPsOrINmrq\n57cU+IHRkfmR/XvsEg2W5OXsxhz/YQDkV5ay+fzJdp0f4OXK63eMUPaf3JjCidyu1eJY2L73T++j\nsrYGgHtDR+PueOUFVU0mEw+tP0R2sbl8c9qgPqyYGmq1OC3F4t9s4eHhzRKfoqIioqOjWzznoYce\nanKOXq+XBgttVGs0cvf2D/ihrguQzsmF72YuI0zXtM7z71vSlO3fTRuEo/xRu6q/j5mltOLem59J\n0GvrWP5FCt+ndY1uKUII0VGZpYXE1ZfKGO0g35/R/jqevnGQuoF1I/eENpTNvZ++v93n3zHSjyVR\n5vuk8moj93ywX1pxC4sxmUzEnWgol1s6ZEKLx775UwYbU83VSV6ujqy7c1SX7F7cKXfFixYtarLu\n0K5du4iNjVX29Xq98r5Wq8XTs+mwWmJiIk899VRnhNatmEwmHt/zOZ9npADgau/I1zN+wcjeTTvH\npWYX89VR8w+rr4czD46TZLM17o7OvH39ImW/xvsMOFbwrx9OqRiVEEJ0vv93aCtV9WVcBf1x0bjw\n/t2j5EGaBd3iPxytowsAX5xLobi6ot3XeHFeBKF93ADYl1nEX747YdEYRc+1J+8cKXXTBcZ6+zOq\nz4AWjx2gc6FvLycAXr9jBAFerlaJ0dI65dttxYoVStITFxdHYGBgk7WFkpKSmjRNiI2NJS4ujvj4\neFatWkVsbKysRdQG/+/QVl47sRsAe40d66fdx/X9BjY7blWjm/hfTw7BxfHqPeSF2Q2+ITw0ZLx5\nx84IfmlsPpnH/sxCdQMTQohOcqb4YsNEaqMd5AXy71uGM6yfh7qBdTMuDo4sDDaXvZXXVvPFueZL\nlrTGw8WB9+8Zjb2dBo0Gao1IWbewiLhGzRSWXWV0CGD2sH4ceWoq/5sf0aWXcum09g9Lly5t8b3Y\n2NgmI0Zarfaqx4vm3klL5tkDDaNwcZMWXnH1YP2lcj7Yfx4ArYsDD08MslqM3cG/x87hy4xUcitK\nwKMAtPn8+4fTfHzfGLVDE0IIi1t5cEvD3KGLA7g5dACPTQpWNabu6t7Q0bydZl7j5f3T+7hvUPv/\nrkwI8uKFucOJ8NVy42BvS4coeqDCynI+Tjc3SHB3cOLORosJt6SvhzOPX9/8gXxXIuPfXdDm8ydZ\nuusTZf+vo2JY0sL6EP/dmU5NXUe5X04MQlfXmUa0jZezG/8df1vDC76nWX9YT/rFUvWCEkKITnC8\nMJd3T+0179Ta41MRyrt3d835AF3BFN8QBtStEbjlQhpZZVdemqQ1y28IkWRIWMy7p/dSXlsNmJN2\nj7rSzsYKy6utHVank4SoizlScIHbf1inPMFbNmQCfxw5/YrHXiqr4o095kXfnOzteOKGEKvF2Z3c\nOfA6ptUtpIdTJSbvDJ7flq5uUEIIYWErkr/GWLfuEBf9+SB2PP08rtxZSlw7O40d99StSWQ0mfjw\ndPvWJLqaammPLjrAZDLx2vHdyv7DYRObHVNWVcP4F3dy7wf7u1ViJAlRF5JdZmDOlrcorja3Npw1\nYCgvT5yPRnPlp3ev7z5HSaV5Yuy9Ywbgp2ue5YvWaTQaXhw/D3tN3a+Lt563Dp7gYmmVuoEJIYSF\n7Mg+zdeZRwFwxplfD5/MTWE+KkfV/d0/aKyyve7U3mueA2QymXhzzzmG/usHcuraIAvRVjtz0jlW\nlAvAeJ/AKzZT+N3XxziZV8oH+89z34eWS+LVJglRF1FWU8XcrWvRl5on9F/X24/4affiYNdyg4Sx\nAZ7KitZPdcGe8LYksnd/Hh1a1zrezkRln1O8mnRW1ZiEEMISjCYjTyV/rez/Z8IcVs0ZcZUzhKWE\ne/kypo8/ACmF2RwsyLqm6/19axpLPzlM+sUyHv7kkDRZEO3y2ok9yvYvrzA6tPlEHi/vOguAs4Md\n/5g91FqhdTpJiLoAo8nI4p0fk5xvXqzWz03LVzMevGJdZ2Mzhviw7dFoTj49TToEWcBfRt2Ml5O5\nxSm6fP534BBGo/yxEUJ0be+fOqD8fRmq68vSsPHYy7whq7m/UTMFZQ5XBz04LpDebua5whtTc3h3\nb+Y1XU/0HLnlxXx69jAAnk6uLBo4ssn7heXVLIk/qOz/ffZQIvo3XXe0K5OEqAv4y8HNfFL3Q+rm\n4MiX0x/E392zlbMaDPbp1Vmh9Shezm78dfRMZd8/7DwtVCsKIUSX8MLOkzy043Nl/19j51y18kBY\n3l0ho3CoK8n+MP0A1fVrQHVAf60LryyIVPaXf5HCuYKya45RdH9vpf2s/Ow9MGgsbg5OTd5f/nkK\n54vM62VNDunNk91sXrokRDYuPv0gKw9uVvbfn3w3Y7z9VYyoZ1sWNoEhWnNd/f6CTD45e0jliIQQ\nomO+T8vnqT0JVNuZb3Km9RvMrVdYvkF0Lh+XXsz2HwZAbkUJiZnHr+l6saMGEHudeT0YQ0UND8ZL\nNYO4ulqjsUkzhUeGNi2X+/zIBd7bZx5t7OVszzt3dr/uk5IQ2bD9+Zks/vFjZf//jZ7F/KDIq5xh\n9vctaexMvyi1w53A0c6ef42do+w/vfdbqmprVIxICCHaLzW7mNs+2Iapt/kmxw47Xp3UcpMe0bke\naNRcYW1a8jVf7+UFkfTXmjsEfn8qX+a8iqv6JvMYGXVz1Gf4DSZM11d5L6+kkoc/PazsvzA3nIF9\n3KweY2eThMhG5ZQXc9vWtVTU3WzfHTKKP4y4sdXzTuSW8MeE40x+OYnb3r72L1XR3G2B4dzQz7wA\n2ZmSAuJO/NTKGUIIYTuyDRXMenMPJX2Og535wdlvwic3uQkS1nVLwDC8nd0B+Ep/lLyKkmu6Xh93\nJ+LuaJgD8rtvjnEqX9bPE1f28rFdyvZjQycp2yaTiUc/O0Jeibmr7qyhfXlofKDV47MGSYhsUFVt\nDbd/v47MukXaxnr78+akRW16cvfizob1cSYGe3VajD2ZRqPhH2NmK/vLd33LwawCFSMSQoi2MVRU\nM+etn9GbzkIv8xPh/q5anhs1Q93AejgnewfuDR0NQI3JyPun91/zNecM78eD4wIAKKuqZcnHB6mV\n0jlxmbSiPL7LOglAgLsntwQMU94rrqzhTN0cNE9XR+IWjei2o8iSENmg5T99wa7cswD4unrwxY1L\ncHVwbPW8grIq1tV1lHFxsGPZhKDODLNHm9RvIGEu5qckRodKHt22SeWIhBDi6iqqa7nt7WT2X8gD\n39PK669MXNBq11LR+ZYMjlK216YlW6Ts/YW54QR4mv+/PZhVxNGc4mu+puheXj6epGw/HDahSVMV\nrYsju5dfz19mhvHygggG6FzVCNEqJCGyMXEn9vB6XR94Rzt7Ppv2AAPcdW069809GZRVmTuE3D/W\nnz7uTq2cIa7FqzfMVbZ3lx3mbJFBxWiEEKJl1bVG7nxvH9tOX4T+p8DBXI59e1Ak84IiVI5OAIzo\n7aesSXTk0gX2Xzx/zdfUuTrydux13DTEm5SnphLZjdoki2tXXF2hzFlzsrNn6ZDxzY5xtLfjuZuH\ncPfo7t3QSxIiG7In9xyP72lof/rShPlE9wtu07k1tUZe2nVG2V/ezdoh2qJp/sGEONSNwtlX88j3\nieoGJIQQLXh511k2puaANg888wDQObnwvwnzVY5MNNZ4lOitNMvMT50xxIdNyyYQ1Lv7TYQX1+bd\nU/swVJu7TN458Dr6uvbcNSslIbIROeXF3P7DOqrqesAvGzKBZWET2nz+xtRs9IXmH+qbhngT7ttz\nf6it6T8T5kBdVcN3Fw9QWFGubkBCCHEFj00KZk6kJ/idVF57IWou/d1kxMCW3B0yCmd7B8C8JlFZ\nTZVFrttd532IjjOajLzUqJnCr4ZfD0BOcSWz437iaHbPKq+UhMgGVBtrid32Hlll5pKrCT5BrJkw\nr13XWLNTRofUMHdwCH2NAwAw2lfzxM7NrZwhhBDW52Cnoab/caVUbm5AeJPRCGEbvJzdWBg0AoCi\nqgo+PXu4lTPar7y6lt9/fVS6zvVwW7LSOF6UC5jvO8d6B9R1lTtMwvFcRr2wg8+PXFA5SuuRhMgG\nPL33G7Znm7vD9XXpxafT7leeELXFwfNF7Eg3dzkL7ePG7KHSOtWa/jiyoTvTR/qfLPZETwghOqqi\nuhb9pYYR6/+k7mBT1gkAfFzciZu0UEYNbNTSsIZ5HHEnLbusw7GcYkau3s6/fzjNL+IPyoKtPdia\noz8q28vrRoc+OXSBDUeyAXB3smdiUM/pViwJkco+OXOIF1J3AGCvsWP9tPva3ESh3rt1neUAfnX9\nwG63erCte3xMBO4V/QCo1lTyp5+3qRuQEKJHKyqvZvabP3HDy7vIuFTGntxz/H7vN8r7b05a1KPn\nCti6yf1CGKz1BuDHnDMcL8y12LX9tC6UV5tL83ekF8iCrT3UiaJcvsk8Bpjb7t8eFEleSSWPf35E\nOebFeeH4antO90lJiFR0vDCXB39cr+z/e+wcpviGtvs6/75lGJ89MJaYoT4sjgqwZIiiDezsNDw8\naLKy/+rJH6mqW1BXCCGsKauogskvJ/HDqYucu1TO7LW7iN32HjUmIwBPDr+BuYHhKkcprkaj0fBQ\no25fb1pwlEjn6kjcooYFW5/+9hjn6taZET3Hi0d3KtuPD5uEk70DT36RqizAOmdYX+4d0727yl1O\nEiKVlFZXcvsP6yipqQRgYfAIfh0+uZWzrszB3o4FI/qTsHQCOtfW1ysSlvfc9aOxL+0NQKmpjA/T\nD6gckRCipzmUVcSENTs5fME8H1Xnao9byAkySs0LsI7zDuBfY+eoGaJoowcGjcVBY75Fe+dUMpUW\nfMgWM7QvD4w13+yWVNby8KeHLbLmkegaCirLWHdqLwAu9g4sC5vA10dz+PCAuc271sWB1xZ23wVY\nWyIJkQpMJhMPJ33G0cIcAMJ0Prw1aVGP++HrTnSujvxlTMNcon8f+QFj3RNZIYTobBtTspn0v11K\nt9EATxfmTi8l+dJZALycXImfeh9O7ZifKtTTz9WD2+pG8i5WlvGZhZsrvHBbOP08nAHYdCKvSem9\n6N7iTuyhrKYagPtDx+JocuKXnzb8fK26ZTj+nt13AdaWSEKkgjdO7OGD9P0AuDk48tm0B9A6tb9O\ns1YmQ9qU/5sQRZS3uWTxWFEuX+uPqRyREKK7qzWa+FPiCeatTaa0bmHuUQO0/OpWF947ay61stfY\n8cm0+wn26K1mqKKdfjl0orL92ondFr12bzcnXlkQqez/emMqOcWVFv0MYXuqjbVNWm0/EX49v//m\nGOeLzA9Spg3qw9IJgWqFpypJiKxsf34my3/6Qtl/beJCwr18O3StW976idh397Ez/aIMd9sAjUbD\n7yOnKfv/PvKDitEIIbq7/JJK5rz5Eys3N6wttCDSlz/O68MfDn6lvPbfcXOZ7jdYjRDFNbix/yAG\neZibK+zMOUPqpWyLXn/BiP7cPqI/AJfKq1n+eYpFry9sz/ozh8gsKwJg5oAwasvdeH33OQBcHe2I\nu2Nkj61WkoTIioqqyrlj23tNFl+9b9CYDl3rWE4xicfzWH8oi/s+PIAMFtmGeYERSnegXblnSc7L\nUDkiIdRjMpmoMdZSY6yl1iglpJb2zbFcNp3IA0Cjgb/MDOO3s3y478cPqK0r2X04bAKPDZukZpii\ng+w0djzcaIH2N07ssfhnvDQ/As+6ucfrD2XxzdEci3+GsA0mk4nVKduU/aciphDh68GnD4yhn4cz\nK2cOJdTbXb0AVSbFxFZiMpn4xY/rSS++CMB1vf14cfxtHb7ey7vOKtuPRAdjL622bYK9nR1jXMJJ\nM2wHYOX+7/lq5mJ1gxKiE2WVFZGcpyelMJtjhblklF4is7SIS1XlGKorMDYavXaxd0Dr6IKPizu+\nrm2gq7UAACAASURBVFoC3HWEengzWOtNhJcvQ3Q+ONrZq/iv6VruH+vPN8dy2JqWz4f3jKafTzXT\nN71Oea15fsBtgeG8NGF+j33i2x0sHhzFH/cnUGWsZd3pvfx9zCzcHZ0tdn1frQurbx3O0k8O8avr\nBzI5pI/Fri1syw8XTnGwIAuAEV79md5/MBqNhttH+HHjIG88nHt2StCz//VW9NKxXXx2ztzf3cPR\nmU+m3Y+LQ8c6whVX1CgTIJ0d7PjFOGm1bUuGOIZAzS5wqOGbrFT0JYUE9PJUOywhLKK0upItWWl8\npT/KD9mnlYc8bVFRW0NFbQm5FSWkFjZ/Eu1kZ891vf0Y5xPIRJ8gbugXIr87jZwrKCOot5uyr9Fo\neOOOkRRX1FBgusSNia9TUGluoXx9v4F8NOVeHCTB7NK8Xdy5I3gkH6Tvp6iqgg/TD7C00aiRJTw4\nLoCoAE9G+Gktel1hW1anbFe2n4qY2uRBiZebkxoh2RRJiKxgb76e3yY31HO/ff0iBtWVVXXE+/sz\nKa40t+CMvc4P716We1okrt2jEwfxt0P9MXrrMWHiPyk7eWHCrWqHJUSHGU1GfrhwmrVpyWw4d0QZ\ngWiJu4MTPi7uaB1dcLZ3QAPUmkyU1FRiqKokr6JEWRensSpjLT/n6/k5X69M/B3Yqzcz/AZzk98Q\nbvIbgqdzz+t+ZKio5pmEE7y86wzfPjSemUP7Ku95ujpyqjSbmO/ilGRorLc/X01/ENcOPnQTtuWx\nYdFKI6aXjyfx0JDxFh3102g0kgx1c6mXskk4fxyAAW46/JEH6ZeThKiTFVWVE7vtfarr5g09PmwS\nC4NHtnJWy0wmU5NyuccmBV9jhMLS+nk4M9d3DF9UZ4LGxOsn9vDXMTdbtMxBCGuoqKnmvdP7eD51\nOyeK8pq976CxY6x3AJP6BjOytx/hnv0I8eiDzsnlqjdsRpORi5VlnC0u4HTxRY4X5XK44AIHC7I4\nU1LQ5NgzJQXEnfyJuJM/Ya+xY1LfYG4NGM68oIhrerDUFRiNJj48cJ7ff32MLIO5C9Qv1h8iZcVU\nZd7H5vMnmf/9O5TWmBdUHNPHn+9uXtYjE8fuaoJPEKN6D+BAwXkOFWSxK/cs1/cb2KmfmW2ooLeb\nE04OMtW8O2jc5GmM63BufPUn7h0zgP/MDZeH6nUkIepEJpOJpbs+UUpKRvcZwOqoaxsp2JleQGp2\nMQBjA3SMC/S65jiF5a24fjhffJEEnrmUGSv5IP0Ayyxc5iBEZ6kx1rI2LZk/H/yOrDJDk/e0ji4s\nCIrgtsAIZvgNplcHEn07jR0+Lr3wcelFlE/TFq/5FaX8lHeOH3POsj37ND/n65UGAbUmIzty0tmR\nk86KvV8T7tmP24NHcHtQJJFe/bvVXJkdpy+y4uuj/JxRqLzm7GDHwxODcHM0l8G9k5bMsqRPlQdu\nE3yC+OamX+Dl7HbFa4quSaPR8NiwaB7a9QkALx/b1WkJkdFo4q2fM1jx1VFWTAvljzOGdMrnCOvJ\nKLmkLBbv4eDM1p/ND1Pe33eeJVGB3DhYEiKQhKhTvX5iN5/ULabm4ehM/NT7cL7GRfFeSTqrbD8W\n3blPiETHTQz2YrDdYNLIBWDVoR0stXCZgxCdYWtWGo/v+ZzjRblNXp/gE8TjwyYxPygCN4fOqzf3\ndnFnTsBw5gQMB8BQVcG27NNsOn+CbzKPca7kknJsamEOqQc3s/LgZobq+rJo4EhiB45kuGfHljKw\nBXv1hTyTcFzpHldvZpgPLy2IZJC3OzXGWp78aSMvHt2pvD/bfyjrp94nI9Hd1F0ho1iR/DWXqsr5\n9OxhXigz0N/N8mVuqTnFPPzpYUwm+OvmNBaN9GOwTy+Lf46wnv+k7lBKlH1rBpJWbr4PeWCsPzcO\n7t6j7O0hCVEnOVSQxZM/f6nsx0Xfcc3lHdmGCj47fAGA3m6OxP5/9u47vMmye+D4N0n3ZnTRPSiU\nMsqGliFLCzJFAcWtqIhb8RVFX7e+4pafqy4URXAjQtm7jLKhQFtKoS3dBbpXmvz+eErayiqQNB3n\nc11cV57kSe6bQpOc5z73OT07XNPrCdNRqVQ8068nD+7dD7bFHCvJaZQ0ByGuVm55MU/tXMrC5D31\n7o/y6sTcHiOJNNP/XScrG8b7hjHeN4z5ej3xZ7P4KzWeP04eYnd+uuG8owU5vFoTHHVr48m0gHCm\nBYYT6Ng8qmaVVVUz8Zs4ViXWD4RCXO15f3wYY0LdUKlUpBaf4Y5Ni9iUfdxwzn0d+/FZxGSp0NeC\n2VlYcW/HfrwXvxGtXsfnCdt4pecNRh+nm6cTsyL8mb/1BBVaHTN/O8jqBwfIxbxm6nRFKdGJSoNm\nC5WGpCNKkZp2dpa8O66LOafW5EhyqAkUV1UwdcMPVFQrhQ8eCBnA1MDwa37dY3kleDgqV//u6euD\nraV8+DVl03t5Y1NYu3HxvYObzDgbIS5u5akEuv/5Xr1gqHc7b9ZFPcSK62eYLRj6N5VKRdc2nrzQ\nYyS7xj9Bys3P817fcQxw9at33sEzmbywZwVBv77FgGUf81H8ZjL/lfrX1NhaatBTW6K8g5MNX9zc\nnUOzr+PGLu4ALEnZR4+/3jcEQxqVmk/6TyQ68hYJhlqBh0MjUKEEJp8f3Wb4jmFsb4zpTAcnGwDW\nJuWxcHf6ZZ4hmqr5R7YY9hdaFXmAVvkO+f4E2Tv0b7JCZAKPbv/DsAG5q4sHH15Dv6G6BgW2I+WF\nESw7nE24l7NRXlOYjr21Bfd06s1neUlgoWVpWjyZJkpzEOJqaHXVPLdrOe/F15ZjdbK04c3eo3mo\n00A06qZ9zczfsS1PdR3KU12HcrL4NL+kHODnlH31Vo525KayIzeVJ3cu5TqPQKYF9mSyXzfa2Zin\nAaFer2ffqUJ+P5jJyzd0qtdD7oWRHTmSXcyzw4K5f4Cv4aJXWvFZZm3/nb/TDhvO7WDnxI9DbuM6\nz+BG/zsI8wh0bMd43y78lRpPTnkxPx/fy10d+xp9HCcbSz6Z1JXJC3YB8PTfh7mxizttpTRzs1Jc\nVcFHh7cYjkszlKyi4cHtuaO3t7mm1WRJQGRkC5N3890x5U3EVmPJ4mG3G7X0qYVGzcRunkZ7PWFa\nj0UE8cUPHujapaNDx9eJO5kbPtLc0xKC3PJipqz/gQ1ZyYb7hnsGs2DwNLztm1/vHz+HtjzT7Tqe\n6XYdSQW5/Jyyj5+O7zXshdKjZ31WMuuzknl42++M8AzmloAeTPANw9XG9HskDmcV8fvBTBbtPcXh\n7GIAIgPaElWnhPaQwHYcf2EElholEC2uquDdQxt499BGw1VegIm+Xfkq8hazBXXCfJ7oMpi/UuMB\n+OjwFu4M7mOSdLZJ3TwY18Wdvw9nk1tcyZx/jvDFLVdfIVc0vi8TthtK8VPgCpV2WGnUfHZzN0mB\nvAAJiIwoqSCXmbG/G44/GTCxWW/uFdeus7sjO+6YSt/l7wHwVdIO5nQf3uSvvIuW7fDZLMas/tpQ\noECjUvNW79E83XUoalXz/7/Z0dmVF8NHMbfHSPafzmDR8b0sPrHf8Pet1utYlZHIqoxEHoz9lSHu\ngUzwDWOCbxgBRtpzVFqpZUvKaVYczWH5kRwSc0vOO+frHan1AiKVSoWlRkVhZTlfJmzn3fiNZJcV\nGR53tbHng34TuC2wp3yhaaWGegTRvY0nB85ksvf0KTZnH2eIR5DRx1GpVHwyqStrj+VRWlnNl9tT\nuauPDxEBbY0+ljC+cm1VvUas5CrVPOeMCCZEimRckMkCoujoaHx8fCgoKABg6tSpRj2/qams1jJt\n40KKtRUATAsI596O/Yzy2lmF5egBz5qcXtG89HH3ZIRnR9ZmJnGy+AyrMxKJ8u5s7mmJVmprdgrj\n1nzDmcoyANpb2/PLsDtaZOqVSqUivJ0X4e28eLvPjezITeXnlH38euIAp0qVzxqdXs+GrGQ2ZCXz\n5M6lhDq7McY7lBu8OjHIPeCqVvjv+XkfP+5Jp6paf8HH+/m6ML2XF7f29Kp3f/yZLL5O2sk3STsp\nqCw33K9Wqbi/Y3/e7D1aVoVaOZVKxeNdBnPf1iUAfBC/2SQBEYBfWztevj6EZ5cdAeCh3w6w58kh\nWGia/0WTlm7BsV1klin7Jh0r3Sgqd6Bje3ueG97y3ueNxSQB0bx58+jWrRtRUVGG45iYGMPxtZ7f\nFM3ZvZw9+acAJc/384jJRruC9876ZD7ZksLErh78b2woge3kA7G5eaBTf9ZmJgHKMrYERMIcVqQf\n4aZ1Cyiv2Yzd1cWDf0bdh69Dy+9nplKpGODmxwA3P97vN45tOSf57eRBfjtxgNSS2l4/RwpyOFKQ\nw3vxG7HWWDDA1ZfB7oEMcg+gTztvdFoLknJLSMorIT6riDNlVURPqZ9KZKlR1QuGVCro79uGm7p5\nMKmbJ8HtlfdwvV7PoTOZF6yad854nzDe6jNasg2EwW2BPXlu9z/klpfwV2o8SQW5dHR2NclYTwwJ\n5Ptd6RzKKiI5v5S9pwrp69v8UmpbkypdNW8fXGc4Xjb+ZnYl6gnv4IyNFOO6KJMEREuWLGH27NmG\n48jISKKjoy8a4Fzp+U3NivQjvB+vVBCzUKlZNHQ6zlbG6RJeWqnlu7g0tDo9f8VnMf+mbkZ5XdG4\nJvp2xdXG3vABllFaQAc7KYwhGs/ytCNMWvcdlTVNPId6BPLn8HtwsTbOe1WzolfRu60vYU7ePNNp\nFHF5p9hxOonVWQnsyqsNSiqqtWzMOs7GrNoS11TYQrk9VNgrt6tsmD3KmwBnF0Oltwi/tqxMyGVY\nUDtGhrgS1ckVG2tILTlDfEEKP6dnsSc/nc3ZKeRVnJ9KZ6FSMy0wnGe7DqNbW9kzKuqzsbDkkdBI\n/rt3FXr0fHh4M/838CaTjGWpUfP5zd15d0MyH04Iw6+tNP1t6n44tpsTNenBwzyCGOIZyBB5G7ks\nowdE8fHx593n7OxMbGysUc5vajJLC7lr88+G4zd7j6bfvzqvX4vF+zI4U1YFwORunrg7SpnE5kin\nU1Ge6waOKejQE52wk//2HGXuaYlWYkV6/WBogm8YPw+9HRsjFny5nMLyKjIKysksqiCnqIK8kkrO\nlFVxpqyKgjItxZVaiiu0DAtuz9PX1U8Bivh4C6cKy9Hp9Oj0SprbhZLR/jMsiCeH1j63pEKL7+tr\n0OmhWqdHq9NRVa1Hqzv/2cvv78eb40aTXVbEylMJ/JRwiJWnEsGysv6J1mXKH/IMd3X6cx8ALla2\nOFhYYWdhhW0oxKJnVVIlDx4uo1RbddmfUVcXD+7u2Ifbg3rjbut42fNF6zWzcwRvHVhHebWWb5Pi\neLXnDSZLp4wMaEuk7B1qFrS6at44sNZw/FK4fM9oKKMHRAUFBTg717/y7eSklBkuLCw03L7a85sS\nnV7HnZsXkVuuXOG7vkMIT3cdatQxPos9abg9M8LfqK8tGo+NpYYBjqGsJgWATw9v58XwES1iA7to\n2mKzT3DTugWGYGiib1cWX3c7VhrjJwicKa3kUFYRFVodI0Pqp/AM/2wbu9MLLvsaLrbnB2mnCstJ\nPVN22eeWVFbXO1ap4HTp5QMRgOKa57rbOnJncB96O3Ri5br1YFUOdgWo7YuwsC+myrIIverCe4PO\nVpZxtvLy8zzHwcKaSHd/RngGM9G3q8nSnkTL42rjwF3BffgiYTtl1VV8dnSbVDAV/HR8L8eL8gHo\n09avRe4NNRWjfyIWFhYaCiOccy7gKSgoOC/AudLzm5J3D21kTYayL8TNxoEFg6cZ9Qvu7rSzxKUp\nue1hHo4MDpQrNM3Z7IhurF69FewLyKksYHN2CkNNtBlWCFA26Y9d87Vhz9B4nzCjBUMlFVp2pp1l\n24kzxKWdZc+pAkPQ0tPLiT1P1b845NfGtkEBUVlV9Xn3tbW1pLhCi0attKVUq1SoVBiaVJ7jaF3/\n76VRq/BrY4tapUKjVmFR88faQo2VRo2tpQZbSzV2Vho8/7X6HtDWlhUzBuDhaI2nkw2u9lao1Sqq\ndNUkFeZy6EwWyUX5HC86TUZpAVllReRXlFJSVWkoka1SKUGPs5UN7a3t8XVog5+9C13beNK9rSdh\nLu5YSENVcZWeDBvCFwnbAfjkyBae7jrUqG0+LqasqprPYk8wK9Ifawv5/9tUaHXVvL5/jeF4z14X\nPm1/gocj/c03qWbE6AHRhQKYcwHPv1eCrub8pmJnbiov7F5hOF4weBoeRm64WXd16KGBflJmtZkb\n0bE97sv9yOYAAO/vj5WASJhMZmkhUauiDdXkhrgHXnMwdDCzkCX7Mlh3LI+dqWcvmHoGkJRXgl6v\nr/eeNTy4PZYaNZ5O1rg5WONqb0VbOyva2FniZG2Bo40FDlYW5wU1AHufvrqVd2sLDSfmXt1Vczsr\ni3olsc+xVGvo4uIhRQ6E2XVydmOCb5ihUeuCY3E81DnCpGNuSs7n7p/3kXK6lAqtjjkjOpp0PNFw\nPx3fS1JhTSpvqRO6Imd6ejXdRYWmxugBkbOzM4WFhfXuO3d8oeDnSs9vCgory7lt449o9ToAngob\nYvSqYWfLqvhpr7K5185KI12FWwC1WsXj4f14PjkeNNUsz4inqKocR0sppy6Mq1xbxaR135FeU1q6\nextP/hpxzzXvGVqblMfra5Iu+JiNhZruHZzo7ulEmIcjWp0eS01tQDRrUACzBgVc0/hCiPqe6zbc\n0Kh13qGN3B/S36SrjraWGk6cUZp9vrY6kdt6ekmhhSagSlfNK/tW196R7c+9/XwZ6C+ZRQ1l9A0M\nYWFhF9wnFBFx4asWV3p+UzBr++8k1+Ro9mrnxVu9xxh9jO93pVFWpQRc03t54XyBvHrR/DzYPxBN\nkXLVWYuW7xP3mnlGoqXR6/XMiP2FHbmpAHjaOrF81P0Nrian0+lZm5jL3Yv2kpJfWu+xMaG1KyYB\nbe24u68PX9zcnf1PD6XozdHseHww0VN68MSQQCylV4kQJjfAzY8h7oEAHC/K57cTB006Xl9fFx4Y\n4AdAWZWOp/8+bNLxRMN8f2yXYe8QJc4461x5+8ZQ806qmTHJJ9aUKVOIiYkxHG/durVeo9W0tLR6\nj1/u/KZkYfJuFibvAcDewopFQ42/OVmv19dLl3tYiim0GG3trLjeravh+P0DW804G9ESfXJki+E9\nykZjwZ8j7sbL/vLpxzlFFby1Nongt9Yx8ovtLNiVblilPqdje3u+vzWclBdGcPyFEXw7LZwHBvrR\nvYOTNGsUwkye6z7McPvtg+vQ6y+cymosb47pTDs75SLtbwcyWZOYa9LxxKVVVmt5bV/t3iFy/Hkj\nqjOuDlKV+EqY5BNs9uzZhqAnOjoaX1/fej2FYmNjWbx4cYPPbyqSC/OYGfu74fiTARMJMUFVoKpq\nPbf39sLHxYYBfm0I92q6e6nElXspsq/SvwQ4Xp5FUoF8mAjj2JF7kmfilhmOv46cctk2APFZRdy3\neB++r6/h+eVHSTlduyr056GseueqVCru6OODv6TICNFkRHl1pnsbpdHMvtMZxJw6atLx2tpZ8eaY\n2tWHR/84RKVWZ9IxxcV9lbiDkyVK3yGKXQh39uUhuZB+xUzSmBVgxowZF31s6tSp560AXer8pqBK\nV81tG3+kWFsBwNSAcO4O7muSsaws1LwwMoTnhnckq6jcJGMI8+nv1wZPnR+ZKB9a7+yNJfq6CWae\nlWjuTleUMmX9D1TVlNd+LHQQtwX1uuj5u9LO8saapPOCHoBhwe24r58vE7tK4QAhmjqVSsWc7sO5\ndeOPALy2bw1RXp1NWojpvv6+fLn9JLvTCziaU8zHm1N4ZpgUCWpsJVUV9fcO5fgz/95uaNRShOtK\nSY5DA/1370p25qUB4OfQhs8HTjZ51TeNWoWXcyvsIt/CqVQqng4faDhen3fY5CkOomXT6/Xcv2UJ\nqSVKmf5+7X2Y13fsRc//dOsJ+n64uV4w5GCt4bHBASQ8N4x1MyOY3tsb+wtUfBNCND23+PcgxEnJ\nWNmWe5L1mcdMOp5GrWL+Td0Mx6+uTiSrUC7gNrb5R7aSU16sHBS25Y7QMGmie5UkIGqAdRlJvH1g\nPQAalZqfhkxv8AZlIS7k6YgwBrsrFbeSi/LZlnPyMs8Q4uK+OxbHH6mHAHCxsmXxdXdccm/juC7u\nWFsob/9uDlb878ZQ0l8cxUcTuxLi6tAocxZCGI9Greb57sMNx3X70ZjKAL823N3XB4CiCi1zlps2\nVU/Ud7aijP8dXG84tj0TxP/GSiGFqyUB0WXklZdw+6ZF6FGu4P83fBQR7v4mGUtbrePttUmkn214\np3PRfN0R1Ntw+4fk3WaciWjOUoryeWz7X4bjzwdOxt+x9gqhtlrHidP1q8X5tLFl7siOfDAhjBNz\nR/Ls8GCpZClEM3dbUC/8HdoAsD4rma3ZKSYf860xnXG0tkClAltLNbqL9CYTxvfOofWGPnM3+/Vg\nxR0j8HSSNh5XSwKiS9Dr9dy3ZQmZZUpfpCHugTzffYTJxlt2OJs5y4/i/8Za3liTaLJxRNNwi38P\nrGuu4i9O2UdFtdbMMxLNjU6v467NPxv2Nk4P7MXUwHDD43GpZ+n74Wau/2I75VXV9Z47d1QITwwJ\nxNZSOs0L0RJYqjU81612lejlfatMPqaHkw1fTenB7ieG8Onk7qhl70qjOFVSwIfxmwGwUKl5q89o\nhga1N/OsmjcJiC7h06OxLE1TGp61sbJl4ZDb0KhN9yP7NPYEANU6Pd08mmZTWmE8Lta23OitLG+f\nqSzj9e3bzTwj0dx8kbCdzTVXgX3sXZg/YBIAFdpq5vxzhAEfb2ZfRiFJeSW8tda0ewqEEOZ3d8e+\n+Nq7ALAmI4nNWcdNPuaU8A709JZquI3ppb0rKauuAuCBTgMIdpJg6FpJQHQRB09n8nTc34bjryKn\n4OPgYrLxEnOLWZ2YB4CPi029Boii5QrWBBhuf31U0uZEw6WXnOU/u/4xHEdH3oKLtS0HMgrp/cFm\n3l53jHPZK6HuDozoKB+YQrR01hoLXugx0nD8370rzTgbYQqHz2bxbVIcoPTDfCl8lJln1DJIQHQB\nZdoqbt240JDC9GCnAdzk3+0yz7o2n9dpxPrgQD9pcthKzB3YH5VOSZvL5BTx2WfNPCPRHOj1emZu\n+42iKiVV7o6g3lzfIYRPNqfQ76PNxGcVAUolqJdGhbDvqaEMCWpnzikLIRrJ3cF96u0l2mDiinN1\nVev0fL0jlXnrZUXaVB6N/duwr12X442dSop8GYN8676Ap+OWEn82G4AuLu6832+8SccrrdTybZxS\n0ttSo+K+fpdupChaDkcra3rYByoHah1zNm8x74REs/Bn6iGWpR0BwNXGnld7jObmBbt47M9DVNQ0\nSOzi7sDOxwfxSlQnrCzkrV6I1sJKY8HcOqtEc/fENEprB221jkHzt3L/kv3MXZHA8fwSk4/Z2qzN\nSGJddoJyUGXJfcERONpIewRjkE/Jf/nj5EE+O7oNUJaeFw2djp2FlUnH/HlvBmfLlFzQyd088ZAq\nIa3K7F61PYlisg6dt/ldiLpKtZU8saO2qtzr4Tdyw2d7+P1gbU+hmRF+7HpyCL28TZfmK4Rouu4M\n7kOQo7IqvDXnBCvSTV8S20KjZqCfsjJVWa3j2WVHTD5ma1Kt0/Hglj8Mxw4Fwbx2fZgZZ9SySEBU\nR3rJWe7f+ovh+N0+Y+netoNJx9Tr9YZiCgAPR/qbdDzR9EwJ7oI11gBU2ebzzW7Tb4IVzdfbB9YZ\nGrAO9QhkRue+DAlUvvg4Wlvw6129+XRyd6keJ0QrZqnW8GrPGwzHz+9ZgU6vM/m4L10fQjs7pYT/\nbwcy2ZicZ/IxW4tvk+JILslRDsrteSdyGC7SLsFoJCCqUa3TMX3jT5yuUPp1jPPpwqzQSJOPuzP1\nLLvTCwDo6uHIIOkw3OpYqDWM9qy5yqPW8+6eHeadkGiykgvzeOfQBkBpEj1/wCRUKhWfTOrK9F5e\nxD0xmMndTXsRRwjRPEwLDKd7G08A9p/OYEnKfpOP6WJryatRnQ3HT/4VT7X0JrpmRVXlPLOztoiO\nf0VXZvT3N9+EWiAJiGq8eWAtm7KVK/Oetk58M2gqKpXp6+l/Vmd1aFakf6OMKZqep8MHGG6naE+y\nO02KK4jz/WfXP4ZiL4+GRtK15suOjaWGhdN70cnNwZzTE0I0IWqVmjd6jzYcv7hnJZWN0O/ugQG+\ndHFX3ov2nirk+11pJh+zpfvv7tUUaGsabBe15cvR10nxLSOTnyawNTvF0MBMhYqFQ26lvY19o4w9\nb1wX3hrTmW6ejtze27tRxhRNT4S7Py4WNf/nHM7w3pYE805INDlbs1P47eRBAFTVltztN8jMMxJC\nNHU3eocS6eYPwLGiPL5MMH2/OwuNmvfH1+5teWHFUUoqpPH41UoqyOWjI0oTVnQqrrPvx6hOruad\nVAvU6gOi0xWl3LrxR3Q1FVjmdB/O8A4dG218VwdrnhvRkf1PD8XBWiqFtFZqlZppgT2UAxXsOJuE\nTtIMRA29Xs+TO5bWHmf7MW3BAaqqTb8nQAjRfKlUKt7pM9Zw/Mq+1RRUlpl83Bs6uzG6s9JPMbOw\ngnkbkk0+Zkv10NY/0KG816tOe/P5uAGXeYa4Gq06INLr9dy/ZQlpNRuUB7j68XLP680yF0mVE9OD\nexpuBweWolbL/wmhWJC0h7j8mrSTClusCr14a0xnLCVlQghxGRHu/tzkp/RSzKso4X8H1zfKuPPG\ndeHcx9i8DcmcKjB9INbSLEs7zLrsRABUWitmBA6S1GgTadWfpp8nbOOP1EMAOFvZsGjodCzVUplJ\nmEeEmx8d7JwAWJt5jPxy6eEg4HRpBTM3164OWecFEzNjIBO7eZpxVkKI5uSt3mOwUClf+T6I30Rq\n8RmTjxnm4cgDA/wAGBHcHm21ZD1ciTJtFY9t/9Nw/OGAcbw1upsZZ9SytdqA6MDpDJ7cWfslzDAt\nFAAAIABJREFU46vIW/B3bLwKb7ct3MPcFUdJPytXTIRCrVJzs193AKr1Ov6sCdZF61VcoaX/979S\nrlaCY02ZM+tvH8ew4PZmnpkQojkJcXblwU5KqlV5tZbndi9vlHFfuaETax4cwNL7+uHX1q5Rxmwp\n3jqwlpTi0wBEuvnzSNf+tLUzbV/M1qxVBkQlVRVM3bDQUK3pgZAB3Ozfo9HGP5JdxKK9p3hjTRLX\nfRrbKB2kRfNwS0Dt/8NfThyQTt+tWFlVNTd+vY1jqsOG+/5v0HgG+ktpfiHElXu55w24WNkCsOj4\nXmKzT5h8TDdHa0aESAGAK5VUkGtIbdSo1Hw68CbUqlb5lb3RtMqf7qM7/uRogdLcqquLBx/2n9Co\n48/fcsJw+4EBfrJ/SBhEuPnhaaukza1KTyTo7VUk5BSbeVaisWmrdUz7YTebzsSDVQUA/doG8GD3\nxrtwI4RoWdrb2PNyeO0+6cd3/tkozVrFldHr9czc9juVumoAHgwZSPe20l/O1FpdQPRj8h6+TYoD\nwFZjyeJht2Nr0XidfgvKqlhQU5PfxkLNff19G21s0fSpVWom+inlSvUqPTjm839bT5h3UqLR6QEb\nS8A11XDfxxFjL3q+EEI0xMOhEXR2Vqq/7cpL5/tjuxttbL1ezz+Hs5n6/W5p1noJC5P3sDYzSTmo\nsiIxXlKkG0OrCogSC3J5MPZXw/HHAybSxcWjUeewYFcaJZVK1H9bLy/a2Us+qKhvkm+dTZNOeXwX\nl0ZheZX5JiQanaVGzeDelWBZCcBYn1D6u/qZeVZCiObOUq3h/X7jDMfP7lrGmYrSRhn70T8OMfbr\nnSzZn8EPu9IbZczmJq+8hCd2/lV7R0ZH5g4PNd+EWpFWExCVa6uYsuEHSrTKF4xbA3tyX8d+jToH\nnU7PJ3XS5R6JDGjU8UXzcJ1nkCHPG8fTFFVWsCBOPjxak8pqLe8c2mA4frHHKPNNRgjRooz2DmW8\nj5KJkFtewot7Yhpl3AlhtRegX4w5SllVdaOM25w8tXMpp88FqIXtGOsTxtAgWSFqDK0mIHo67m/2\nn84AINixPV9ETG70vTsrjuZwLE/ZJD84sC09vZ0bdXzRPFiqNYz36aIcqHXgcIZPtqRIo9YWblNy\nvqHq5MLkPYb+aKM6hNDPVVJrhRDG81H/CdholGbwnyVsY0+e6S+6jerkyqgQ5ct9ekE5n2xOMfmY\nzcmK9CP8kFyTwlitQZXZkf/dKKtDjaVVBERLUvbx6dFYAKzUGpYMuwNHS5tGn8fHdX75Hxskq0Pi\n4ib51U+bS8orISYhx3wTEiaVkFPM+G920v+jLexKO8NbB9YZHpvbY4QZZyaEaIn8HdvyQveRAOj0\nemZu+41qnekLLPzvxi6G22+uTeJ0aaXJx2wOCirLmLG1dksH2QHc27MjXTwczTepVqbFB0THCvO4\nf+svhuMP+o2nZzuvRp/HkewiViXmAuDjYsPEro27d0k0L9d7hWB3rtiHYz6g46NNcjWtJTpTWsn4\nb3ZSUK4lo7CcR9eu51hRHgCD3QMY4hFk5hkKIVqiZ7oOpaOTsmKzMy/NcOHYlHp6OzO9l/IdrKBc\ny1trj5l8zOZgdtwyTpUWKAfFztgUefNKVIh5J9XKtOiAqFxbxS3rv6eoSilbe7N/d2Z2jjDLXPak\nF2Bjofy4Z0UGYKFp0T96cY3sLKyI8uqsHFhowb6AVYm5HMkuMu/EhFHpdHqm/7iXxFwllbaTmz3l\nLicNj8/pPtxcUxNCtHA2FpZ8PnCy4fj53StIKz5r8nFfH90Zq5rvQJ9sSSHtTOtuUL/yVALRiTuU\nA50aMjrx5JAgvJxtzTuxVqZFfyt/Yudf7KvZNxTo2I6vIm8xW8+f6b29SXtxJG+O6cz9UmpbNMAE\n37DaA8d8oH7apWj+Xl2dyIqjSiqki60lL05wY9+ZU4DSI80QFAshhAkM79CRu4P7AFCsrWDW9t9N\n3izev60dMyOUqpkVWh0vr0ow6XhN2emKUu7ZvLj2juwA2miceHZYsPkm1Uq12IDox+Q9fJGwHVD2\nDf1y3R04W5k32m7vYM2cER2l1LZokDHeoahrAniVUz7hXo5cF9TOzLMSxrLiSDavrk4EQKWCRbf3\n4uf0HYbHn+46VJo2CyFM7t2+42hvbQ/A32mH+Tlln8nHfGFkRxytlaIO38WlcTirdWY/zNr2O5ll\nhQB4W3hgedaH50d0xMW28fpjCkWLDIiOnM2u12/oo/4T6NXe24wzEuLKtbexJ9LNHwC9VTk/3N2J\nqT0bf/+bML60M2VM/3Ev5y7E/ndUCH4eepalHQHA09aJWwN7mnGGQojWop2NPR8PmGg4fmT7H2SV\nFpp0TFcHa565Ttkf2dvbhXJt6yvB/VPyHkPw6WRpw9ZJ95H43HBmDfI378RaqRYXEJVqK5m8boGh\n39C0gHAe7DTQbPNJziuRWvviqp3rFQGwNO2wGWcijEVbreO2H/dwpkxptju6sxsvjgrhw/jNhnMe\n6zII65qSuEIIYWrTAsKZ6NsVUNK4Zm4zfercU0MD+f3uPux4fBC9vF1MOlZTk1KUz8xtvxuOP+4/\nAV+HNvi3tcPWUmPGmbVeLS4gmrN7BUcKlJz8zs5uRJtx35Ber+fWhXvwfW0NL8UcpaIVXgER16bu\nPqKlafFmnIkwlu/i0tiSchoAL2cbvr81nIKqMhYeV/pP2FlY8mCnAeacohCilVGpVHw28CbaWtsB\n8GfqIX48vsekYzpYWzCpm2erSw2u0lVz28afKKwqB+AW/+7cWbOPS5hPiwuIlqYqXxrtLaz4bfid\nOFham20uW1JOE5d2lrySSn47kGmoqiJEQ3V0dqWzsxsAO3JTySotZH9GAXNXHDX51TthGvf08+XV\nqE5YadT8NL0X7R2s+SZpJ6VaZcXojqDetKn5UiKEEI3Fw86JT/rXps7N2vYHJ4tPm3FGLdPLe1ex\nPVepJmqtt6UnfamsNn0PKHFpLfYb+pcRN9PFxby9ft7dkGy4/fTQoFZ3FUQYx3if2kZ2ty1dTfh7\nm3hjTRIbkvPNOCtxtTRqFS+OCuH4C8MZEtSOap2O/ztS2//jkdBIM85OCNGa3RrYk6kB4QAUVpVz\n56afG6VhK0Bc6lke//NQi77YtyL9CG8eWAuAChUVKZ14ftkxpn6/28wzEy0yIHokNJLbgnqZdQ4J\nOcX8fTgbAHdHa6b3ls3w4uqMrRMQFVjmGG7XDbhF83Oux8Ty9COk1FyFvc4jiK5tPM05LSFEK3Yu\ndc7bzhmATdnH+d/B9SYfd/bfh+n30WY+3pzC0vhsk49nDmnFZ7lj0yLDsXNhMJQqP+eHI/3NNCtx\nTosLiHq18+K9vuPMPQ0+2HTcUEHq0UH+WFvIJjlxdQa6+dGmpmR8Qmkank5K2fblR3JabanS5mbl\n0RwOZl64atP8I1sNtx8NHdRYUxJCiAtqY23HgsHTDMcv7V3JlmzT9sDr51tbVOHFmKPodC1rlaiy\nWsvUDT+QX1EKQBc7X86mKhe/hgS2ZVSIqzmnJzBBQBQdHU1MTAyLFy9m8eLFlzw3JiaG6Oho0tLS\nKCwsNNy+Fv83cBJWZq7OlFtcwYI45e9hZ6XhoYH+Zp2PaN4s1Bpu8OoEQIm2kjF9avtYvbdRVoma\nupyiCm7/aS99PtjMexuS633QJxfmsSpD6UXkY+/CeN8uF3sZIYRoNMM7dOS5bsMBqNbruHXDQvLL\nS0w23uRunoR3cALgYGYRi/dlmGwsc3h8x19sq9k31MHOifzEIEDZRvHG6M6ypaIJMGpANG/ePHx8\nfIiKimLq1KmkpqYSExNz0fMLCgp49913GTlyJCNGjMDHxwcfH59rmoOHrdM1Pd8YPtmSQrlWybm9\np6+PNGIV16xu2pylyxkcrJUVx4W7T5FRUG6uaYkGeOSPg+SVVFJZrWNDcj51P/eiE2sbsc4I6Y+F\nWlaShRBNw6u9biCiphdeemkBd25ehE5vmv1EarWK10d3Nhz/d2UC2hZSaOCrxB18nrANAEu1hsku\nI8g+q/zdojq7MihQGq43BUYNiJYsWUJUVJThODIy8rKrRHFxcaxZs4a4uLh6z22uiiu0zN9yAgC1\nSqmzL8S1ivLqhLrmm/TqzATu7+cLQGW1jg83HTfn1MQl/Lo/g1/2ZwLgYmvJFzd3N1wJrKzW8m1S\nHAAalZp7O/Yz2zyFEOLfLNUaFg2dbkjZXp5+lNf2rTHZeGNC3Rjo1waApLwSftidbrKxGkts9glm\n1ek39G6f8fwcW2w4fj2q84WeJszAaAFRfPz5PVKcnZ2JjY29wNm1nJycrnlVqCmJ3n7S0HBxSo8O\nBLazN/OMREvQzsaeAa5+ACQX5TOxtxOWGuWL9efbTnK25v+caDpOl1Yy6/eDhuMPJ4TRwdnGcPxX\najw55coH41ifULzsnRt9jkIIcSm+Dm1YOOQ2VDXpXS/vW8UyEzUJV6nqrxK9ujqRSm3zXSVKKcpn\n4rpvqdQpPShnhPSnNMuN3OJKACZ29aC3T+tqSNuUGS0gKigowNm5/ge6k5OSvlZYeOHNxACLFy82\n7DmKjo421nTMZkyoO/f188VKo+bZYcHmno5oQW70DjXc3lVwnOm9vAEoqtDyWewJM81KXMx/lh0h\np+aDb3RnN+7s413v8S8SthtuSyNWIURTNcYnlJd7jjIc377pJ46ezbnEM67esOB2DA1SUshOnC7j\n27hUk4xjaoWV5Yxb8w25NfuuBrsH8Eb4WObVqQ77yg2dzDU9cQFGC4gKCwspKCiod9+5AOnf958T\nERHB6NGjDXuO0tLSLpti19R1cnPgq6k9yPjvKHp6yxVfYTw3+tQGRDGnEnh2WJDh+I+DWS26d0Nz\ns/l4Pl/tUD7I7aw0fDq5W71Ns8eL8lmbmQSAr70L13eQD0YhRNM1t8dIxtZ8BhVUljN2zdcmKbKg\nUql4Lar2/fD11UlUaKuNPo4pVVZruWndAuLPKuXDAx3b8fvwu6muVnF9iCsqlZJB1L2D+fe8i1qX\nDYgKCwsv+eecc6tBdZ0LhP69cnSOj49PvedFRES0iFUiQAopCKPr3sYTz5qiIZuyjuPT1orHBgfw\n1ZQebHkkUqrUNBGVWh0P/HLAcPzqDZ3wb2tX75zvavYOAdwX0g+NusV1QBBCtCBqlZqFQ26ji4s7\noKRuT16/gMpqrdHHGhzYjlEh7QGw1Kg5nl9q9DFMRafXcfeWxYYLXs5WNiwbeS/tbezxcLJh0R29\nOfD0UN66UfYONTWXrE8dExNz2T1Ajo6OzJ49G2dn5/NS484dXyhYKiwspG/fvsTFxRked3Jyuuay\n20K0VCqViijvTnybFEelrpoNWcl8NLGruacl/uX9jckczVH2BvX0cuLxwQH1HtfpdSw4tgtQOpXf\nFdyn0ecohBBXytnKlr9H3kv/vz8mr6KEjVnHuXfLEr4fMg21yrgXdd4cE8rU8ELu7OONpaZ5XDDS\n6/U8E7eMRcf3AmCl1vDXiHsIrQkiz+nqKStDTdElA6KoqKgGV34LCws7L/ApKCggIiLios+5//77\n6z0nLS2tWRZY0Ov13LxgF2NC3bmjtzdWFs3jl1c0P6O9Ohsqk8WkH61Xjls0Db5tbHF1sCKvpJLP\nb+6Oxb8+zNdnJpNachaA4Z7B+Dm0Ncc0hRDiiinpX3cxcuUXVOqq+fH4HjrYOfFO37FGHaePjwt9\nmlnBgVf3reaD+E2AcrHrx6G3MdQj6DLPEk2FUb+5T5kypV7foa1btzJ16lTDcVpamuFxJycnXFzq\n/2ePiYnhmWeeMeaUGsWyw9n8fjCL+5fsZ/KCXeaejmjBRnboaCi/HXMq4bzH08+WUd3COnw3N7f1\n8ibxueH8NL0X/XzbnPf4t3XS5e7p2LcxpyaEENdssEcgPwy51VB5bt6hDbx7cIN5J2Vm7x3awMv7\nVhmOPxkwkZv9ewDw5baTLN57ql5TbtH0GDUgmj17tiHoiY6OxtfXt94KU2xsbL2iCVOnTiU6OprF\nixczb948pk6d2ux6Een1el5fk2Q4vutflaSEMKY21nb1ym8nFeQCkJJfyowl+wl8cy0/7z1lzikK\nlJ5D03p6nXd/QWUZv51U9hc5WdowyU9SHoUQzc+UgHA+6j/BcDx71zI+PbLVZOOl5JeyNjHXZK9/\nLd4/tJFn4pYZjt/qPYZZoZEAnCmtZPayw0xbuIdeH2xq1mXEW7pLpsxdjRkzZlz0salTp9ZbMXJy\ncrrk+c1BzNEcdqYq6S+d3Ry4qZunmWckWrrRXp2JzTkBKKtEHZ1dScwtNlQ1e211ItN6eqFRS5GF\npuaXEwcor9mEPDWgB3YWUnxFCNE8PdplENllRbxxYC0As7b/gbXGgvtC+httDG21jpm/HeS7uDTc\nHKxJfn44NpYao73+tXrn4Hr+s+sfw/Hz3UfwXPfhhuMPN6VQWK685/fo4CRbKpow+Ze5Bnq9nv+u\nTDQcvzQqBLV8CRUmFuVdW5J0RfpRAK7v5Ep/XyUFNSG3hMX7ZJWoMX257SQzfz1AbnHFJc9bmLzb\ncFuKKQghmrvXekXxVNgQw/H9W3/h86OXLsZ1JSw0ajIKy9Hq9GQUlvP1jqbRl0iv1/PinpjzgqHX\ne9VmOZ0tq+KjzccBUKtg7siOjT5P0XASEF2D5UdyiEtTVodC3R2YEt7BzDMSrUGvdl642tgDsCEr\nmYpqLSqVipfrNHl7dVWi7CVqJGfLqnh++RE+33aSjm+tI6uw/ILnpRWfZWOW8uEY4NCWCDf/Rpyl\nEEIYn0ql4t2+45jVubaA1sxtv/P+oY1GG+OlUSGG22+vO2b2vkTVOh0zt/3G6/vXGO57KXwUr/eK\nqtf+4pMtKRTUrA7d1suLjq4OjT5X0XASEF0lvV7Py6tqN7W/NCpEUpREo1Cr1IzsoHxAlFVXGdLn\nbujkygA/ZRN/Qm4Ji2QvUaN4bXUi+aVVAIwMccXDyeaC5y1K2Wu4PT2ol/SNEkK0CCqVik8GTOKJ\nLoMN9z0d9zf/iVuGTn/te2b6+7Xhhk6uAKQXlPPtTvO1ZymuquCmdQv4ImG74b53+tzIKz1vqPee\nXlhexQcblQtgKhXMHRly3muJpkUCoqu0ND6bXWlK49ku7g7c0kNWh0Tjub5D7ZvrqlNK2qZKpeLl\n62vvf3llAlXVsoHTlE6cLmX+lhMAWGnUvDM29KLnLkzeY7g9PbCXqacmhBCNRqVS8X6/8TzffYTh\nvncObeD2TYuoMELz1rqrRG+tO2aW4gTpJWcZvPz/WJoWD4BGpeabQVOY3W3YeefO33KCM2XKhbJp\n4V50cpPVoaZOAqKrUK3TM3fFUcPxyzd0ktUh0ahG1Q2IMmpXKq/v5Eqkv7JKlJxfatYraa3B3BVH\nqawJOh8d5E9gO/sLnnfgdAYHz2QCSspjZxe3RpujEEI0BpVKxRu9R/NBv/GGktyLju/luhWfkVFa\ncE2vHRHQlpEd2wOQeqaMhbvTr3m+V2JjVjJ9/v6IfaczAHCwsGbpiHu4p2O/884tqdDy/sZk4Nzq\nkOwdag4kILoKheVVBLdXvvj08nZmslSWE43My96ZLjXdr/fmZ5BbXgwoH0hvjqldpXhlVSJlVebN\nt26p9qSf5cc9Slqii60lz1/iQ+/HOqtDtwf1NvnchBDCXJ4IG8KSYbdjrVEKGW/PPUmfpR8Rm33i\nml537qja99g31yahbYQMCJ1ex7sHNzAi5guyy4oA8LF3YeuNsxjjc+GMgM+3nTSkUU/u5kkXD0eT\nz1NcOwmIrkIbOyv+uKcv2x8bxKc3dZPKcsIszq0S6dGzNqO2F9aQoHZEdVbyrTMKy/ly20mzzK+l\n+8+yI4bbz48Ipq3dhUto6/V6Fp/YD4BapWJaQHijzE8IIczlZv8ebBw9kw52TgBklhUyZMWnvH1g\n3VXvKxoa1J7BgW0BJQNi8b4Mo833QjJLCxm96itm71pGdc2ch3oEsnPsY3Rve/FtEjtSzxhu1w3i\nRNMmAdE16O/Xhv5+53eiF6Ix1N1HtLpOQATwelRnXGwteWN0Z+7r79vYU2vx1iXlsSYpDwDfNrY8\nOijgoufuzEvlZLHyATnUPRDPmi8IQgjRkvV39WPXuCcYWNNMvFqvY87u5YyM+YKUovyres266Wef\nxp4wxjTPo9fr+Sl5D93+fJdVGbWtVZ4OG8qaGx7E4zLv4Uvu7MPGhyN4+foQenRwNskchfEZvTGr\nEKJxDPUIxFKtoUpXzapTCej1ekOVm94+LqS/OBJ7a/kVNza9Xs8LdfcQXh9yyUaBS1L2G25PCehh\n0rkJIURT4mnnxIbRM5m7J4Z5hzYAsD4rmW5/vsdbvcfwcOcINOqGX5sfFeLKjaFuRAa05eEIf6PP\nN6Uon0e2/8Hy9Nr3eDcbB74ZNIUbfbo0+HWGBLVjSFA7o89PmI6sEF2B+VtS+ONgJnq99HcR5mdv\naU1kTS+b9NICEgpy6z8uwZBJVFXrGdGxPfZWGjq52nNHb++LnqvT6wwBkVqlYrJ/98aaphBCNAlW\nGgve6TuWmOtn4GmrrK6UaCt5bMef9P77QzZlJTf4tVQqFcvu78+cER1xtrU02hyLqsp5fvdyQv+Y\nVy8YGufThQMTn76iYEg0TxIQNVDamTJm/32Ym77bxYjPt0nTS9EkjOxQmz6wNjPpEmcqDUTFtbOy\nUPP66M4cf34EP93eCwvNxd9Gt+WcJL2mutJwz2BcbaT0qhCidbrBqxOHJ83mno59DfftP53B0BWf\nMXb11+zOa9zKcaD0FXrn4HoCf3mLtw6sM5QId7NxYPF1t/PXiHtwt718UYRqnZ6ddfYOieZHAqIG\nmrP8COU1de+7ejhJmW3RJIzwrBMQZVw4ICoq1zJ3xVG8Xl3NjpPyhm0sbo7W9PJ2ueQ5ddPlpkox\nBSFEK+dibcs3g6ayLuohurp4GO7/J/0Iff7+kNGroolJP3pFhReKK668z1Fa8Vnm7FqO3y9v8J9d\n/5BXUQKAhUrN410Gc/SmZ5kSEN7gBtq/H8yk/0dbuO7TWLbL52yzJDk1DbA15bShvK6TjQUvStUQ\n0UT0ae+Nk6UNhVXlrM9KplqnOy8f+9u4VN5YowRLj/15iG2PDpLKiI1Ap9fx68kDgPIhO8m3q5ln\nJIQQTcMwz2D2TniSLxK28/r+NWTVlLSOOZVAzKkEghzbcXtQL24L7EWIs+sFXyOnqIKPNh9n/tYT\n/HNfPwYFXnrPTkFlGcvSjvBD8m5WZySi+9f2h5v9u/Naz6gr7hOn1+t5s+YzdmNyPvkllVf0fNE0\nSEB0GdU6PY/9echw/MoNnXB1sDbjjISoZaHWMNQjkL/TDnO2soy9p0/Rp71PvXMeGujP/209QWJu\nCTtTz/L9rnTu7udzkVcUF/PP4WwOZRUxK9Ifhwbsz9qek0pGaSGgpMu1s7lw01YhhGiNLNQaZoVG\ncm/HfnyesI33Dm3kVE2KcXJRPq/sW80r+1bT0ak9UV6diXTzp7+rL34ObVCpVPwVn8Wba48B8Pa6\nYyz7V0B0pqKU3fnpbMs5ybrMY2zJTkH7r5UnjUrNZL9uvNBjxCVLaV/KyoRc9mUo7/XdPZ0YEyqN\nt5sjCYgu45udqexJV35BQ90dmBXpb94JCfEvIzw78nfaYUBJm/t3QGRloebDCWGM+WonAM8tP8Kk\nbh5G3ZDa0ul0euYsP8LBzCLmrT/GjscHE9T+0gHO7ycPGm5LMQUhhLgwWwtLngwbwiOhkfx24gCf\nHo1lc3aK4fGkwjySCrfwyZEtANhZWBLk2B5PW0dsAgopr1DxT0ECE1YmotdUkVteQnJRHrnlJRcd\ns4OdE3cF92Fmpwh8HC6d+nw5b687Zrj93PDgBqfZiaZFAqJLyCuuYM4/tc0XP5rQFctLbKAWwhxG\ndAg23F6beYz/dB9+3jmjQ90Z28WdZYezyS6q4KWVCXw0UVK4GurPQ1kczFRSOnzb2BLYzu6S5+v1\nekNApELFRN8wk89RCCGaM0u1hmmBPZkW2JMTRadZlLKXv1MPsz03FT216W2l2ioOnsnk4JlMsEf5\nAyzNyLrk6/vauzDauzO3+PfgOo+gKyr3fTHbTpxmY7LSUymwnR239PC85tcU5iEB0SU88/dh8kuV\nylw3dfNgVKcL57EKYU5hLh642zqSXVbEluwUKqq1WGvO/9X+YEIYqxNzqdDqmL8lhTt6e9PH59qu\njLUGer2eN9bWFqz47/WdLnsFcP/pDFKKTwMw2D0AtwZUKRJCCKHwd2zLnO4jmNN9BHnlJWzJTmFn\nXiq78tI5VpjHyZIz5+0BqsvVxp4QJ1e6uLgz0M2Pga7+dHJ2NfrqTd3VoWeHBV2y6qho2iQguoj1\nx/JYsEspAelgrZGr6aLJUqlUDPcMZtHxvZRVV7Et5wTXeQafd15we3teGNmRl2IS0OnhwV8PsOOx\nQfIGfhmrEnINabPdPB0Z18X9ss+pmy53k183k81NCCFauvY29kz068pEv9rvYZXVWk5XlHK6spT3\nNiXxzY40QMUd4f58NrEX9pam3+sdn1XE0vhsANwdrbmrj+zNbc7km9BFeDnbMCxY2aD3xujOeLvY\nmnlGQlzciDoB0PpLNLl7dlgQnd2UXjh70gv4eEvKRc8VijfrrA7NGd6xQRX66gZEk/zkYooQQhiT\nlcYCDzsnurh48PbwfthWO0O5A7/sOk1pRePM4d0NtZ+1TwwOwMZS0zgDC5OQgOgiQlwdWPvQQH6/\nuw+zIgPMPR0hLmlY3YAo89hFz7O20PDFzbUb/KO3p6Ktbni/h9Zmy/F8Nh1XUt+CGpgfnliQS/xZ\n5aph3/Y++Dq0MekchRCiNXN1sObefr4AlGt1zN9ywuRjnioo48c9ShaRo7UFMyP8TT6mMC0JiC5B\npVIxqZunNGEVTV6AQ1t87ZX9QDtyUynVXrwPwpCgdjw40I8ZA3zZ8bikzF1K3fzw/wyW2R1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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xx = np.linspace(-1, 1, 100)\n", "fig, axes = plt.subplots(nrows=1, ncols=3, figsize=(12, 5),\n", " sharex=True, sharey=True)\n", "\n", "for j, (smoother, ax, f) in enumerate(zip(smoothers, axes.flat, [f1, f2, f3])):\n", " f_j = smoother.predict(xx)\n", " ax.plot(xx, f(xx) - np.mean(f(xx)), \"--\", label=\"true\")\n", " ax.set_title(\"$x_{0}$\".format(j + 1))\n", "plt.ylim([-1.5, 1.5])\n", "plt.xlim([-1., 1])\n", "plt.tight_layout()\n", "plt.legend(loc=\"upper left\")\n", "plt.show()\n", "my_saving_display(fig, dirname, \"GAM-true\", imageformat)\n", "\n", "\n", "fig, axes = plt.subplots(nrows=1, ncols=3, figsize=(12, 5),\n", " sharex=True, sharey=True)\n", "for j, (smoother, ax, f) in enumerate(zip(smoothers, axes.flat, [f1, f2, f3])):\n", " f_j = smoother.predict(xx)\n", " ax.plot(xx, f(xx) - np.mean(f(xx)), \"--\", label=\"true\")\n", " ax.plot(xx, f_j - np.mean(f_j), label=\"prediction\")\n", " plt.ylim([-1.5, 1.5])\n", " plt.xlim([-1., 1])\n", " ax.set_title(\"$x_{0}$\".format(j + 1))\n", "plt.tight_layout()\n", "plt.legend(loc=\"upper left\")\n", "plt.show()\n", "my_saving_display(fig, dirname, \"GAM-true-predict\", imageformat)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": true }, "outputs": [], "source": [ "###############################################################################\n", "# Robustness PART :\n" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": true }, "outputs": [], "source": [ "np.random.seed(seed=42)\n", "n_samples = 60\n", "sigma = 0.2 # noise level\n", "x = np.sort(3. * np.random.rand(n_samples))\n", "xx = np.linspace(-.2, 3.2, 200)\n", "\n", "\n", "y = 3 * x\n", "espilon = 5 * np.random.randn(n_samples)\n", "espilon[1] = 70\n", "espilon[2] = 50\n", "espilon[3] = 45\n", "espilon[5] = 48\n", "\n", "y += espilon\n", "\n", "# Performing OLS\n", "X = x[:, np.newaxis]\n", "ols = LinearRegression(fit_intercept=True)\n", "y_pred = ols.fit(X, y).predict(X)\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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jj2J0dBRWqxVWqxW1tbVoaGgAAHi9Xvh8Phw7dgxerxcbN27Egw8+WNCGExER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\nUaKlGkrR4u/esgkkvb296OzslC43NjbC6XQWJJA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "d = {'temp': x, 'dens': y}\n", "df = pd.DataFrame(data=d)\n", "mod = smf.quantreg('dens ~ temp', df)\n", "res = mod.fit(q=.5)\n", "\n", "# Plotting Signal / OLS\n", "fig = plt.figure(figsize=(8, 6))\n", "plt.plot(X, 3 * X, '--k', label=\"true\")\n", "plt.plot(X, y, 'o', label=\"noisy observations\")\n", "plt.plot(X, y_pred, '-', label=\"linear prediction\")\n", "plt.xlabel('$x$')\n", "plt.ylabel('$f(x)$')\n", "plt.xlim([0, 3])\n", "plt.legend(loc='upper right')\n", "plt.tight_layout()\n", "my_saving_display(fig, dirname, \"robust_ols\", imageformat)\n", "\n", "plt.plot(x, res.predict({'temp': x}), linestyle='-',\n", " label='LAD statsmodel', zorder=2)\n", "plt.xlim([0, 3])\n", "plt.legend(loc='upper right')\n", "plt.tight_layout()\n", "plt.show()\n", "my_saving_display(fig, dirname, \"robust_lad\", imageformat)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [ "\n" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.0" } }, "nbformat": 4, "nbformat_minor": 2 }