{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# MATH60629\n", "# Semaine \\#3 - Apprentissage supervisé - Exercices\n", "\n", "Ce tutoriel explore des modèles d'apprentissage automatique pour la classification. C'est à dire quand la variable cible est une variable catégorielle." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import pandas as pd\n", "import numpy as np \n", "import matplotlib.pyplot as plt\n", "import sklearn as sk\n", "%matplotlib inline\n", "from sklearn.datasets import make_classification\n", "\n", "# Code to obtain utils.py\n", "#!rm -rf 80-629\n", "#!git clone https://github.com/lcharlin/80-629/\n", "#import sys\n", "#sys.path += ['80-629/week3-Supervised/']\n", "\n", "from utils import generate_data, plot_predictions, plot_svc_decision_function" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Commençons par générer trois jeux de données\n", "\n", "Nous utiliserons 3 jeux de données pour la classification binaire. Chaque donnée est en deux dimensions. \n", "\n", "Chaque jeu contient un ensemble d'entraînement et un de test. De plus, chaque jeu de données a été généré par une processus génératif distinct. Cette diversité, nous permettra d'explorer les proprietés des modèles de classification.\n", "\n", "Pour l'instant, vous pouvez comparer les jeux de données visuellement. " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "datasets_train, datasets_test = generate_data()\n", "\n", "for i, (ds_train, ds_test) in enumerate(zip(datasets_train, datasets_test)):\n", " ds_train = datasets_train[i]\n", " ds_test = datasets_test[i]\n", "\n", " X = ds_train[0]\n", " Y = ds_train[1]\n", " \n", " X_test = ds_test[0]\n", " Y_test = ds_test[1]\n", "\n", " plot_predictions(i+1, X, Y, X_test, Y_test, pred_train=Y, pred_test=Y_test )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Classification avec un modèle linéaire" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.1. Classification binaire à partir d'un modèle de régression linéaire" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La semaine dernière, les exercices ont porté sur les modèles de régression linéaire appris en minimisant l'erreur quadratique moyenne. Dans ce cas, nous pouvions estimer les paramètres de manière analytique (par exemple la diapo 31 de la deuxième semaine).\n", "\n", "Dans un contexte de classification, et comme discuté dans les capsules, nous pouvons ajouter une règle de décision en plus du (ou après le) modèle de régression qui permettra de classifier les valeurs prédites (*réelle*) dans une classe ou une autre (*binaire*).\n", "\n", "Nous exprimons la règle de décision sous la forme $sign(y(x))$, où $y(x) = W^\\top x$ est notre modèle. \n", "\n", "Nous définissons: \n", "\n", "$$ sign(a) = \\left\\{\\begin{array}{} \n", "+1, &\\text{si } a > 0\\\\\n", "-1, &\\text{sinon}\n", "\\end{array}\\right. $$\n", "\n", "Donc, cette règle de décision définie implicitement une frontière de décision. Du côté $a>0$ les points appartiennent à une classe ($+1$) et de l'autre côté ($a\\leq 0$) à la seconde classe ($-1$).\n", "\n", "Implémentons un classificateur en utilisant ce modèle avec une règle de décision." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Modèle linéaire pour classification binaire\n", "def OLS(X, y):\n", " # Note: on transforme simplement les cibles de {0,1} à {-1,+1}\n", " Y = (ds_train[1]*2)-1\n", " Y = Y.reshape(100,1)\n", "\n", " # On calcule les paramètres du modèle\n", " # (c'est le même calcul que celui de la semaine dernière pour w_ols)\n", " A = np.linalg.inv(np.dot(X.T, X))\n", " B = np.dot(X.T, Y)\n", " \n", " return np.dot(A, B)\n", "\n", "# pour obtenir la frontière de décision visuellement\n", "def calculate_decision_boundary(W):\n", " x_1 = np.linspace(-10,10) # <- pour x1;\n", " \n", " # Le but est donc de calculer x2 à partir de x1 et des poids.\n", " x_2 = (-W[0] - W[1]*x_1) / W[2]\n", " return x_1, x_2" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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3A4jsoGjxaXJuygw1tjSgIJg37FxBMA+NLQ02tYiIJlS9j4GNCYypzSVjDGCNFdAMPZ9OH9rRfhjralpxfeB+rKtpRUf74Uyb7mkfWDoTH1g60+5mEE2Ke4bFiUykJqbJjXVhdaKh894zqYTEkToicisjmz/WAFZjS8OwNUPA6EAn1T7U7EILXq5gx5kH5AXuuRMkMpESNjJD7vpfoCG02DMXUSKiVBnrPMea2pxqoJNKH2pmoQVWsCNyPnfdCRKZRB1YM+SeaXJERH6VytRmswaLzCy04JcKdswIkZtxzRD5khKOQgigMJfBEFFWdK0arKxGlCZ1gsyQmVJZf5QqVrAjcj4GQ+RLiqYjmJeDQEDY3RQiIppANovemFmsxszAioiswWCIfEkN6wi6qHgCkWsZGaEL++NfzBBRBrJZ9KYhtBi377wO5dVlEAIory7D7Tuvy2haG6uAEjkf7wYnwg3zPEnRoq6qJEdE5GeD1eSy02+btf5oslVAich6vBskX1LDuqv2GCJyLWMgiQNLNAlGBVA3Fr1hFVAiZ2MwNBbjwn1h//BjXsg9QdGiKHZZWW0iIr9SNZ1Fb4jIErwbJF9SwzqmFufb3Qwi/+BAEk2CEo6y6A0RWYLB0Fg4tcPT+jUdc6YG7W4GEVmJ/bdnqGE9K2W1ich/WE2OfEkNR7lmiIjIJfq1KIMhIrIEe5aJcETRkxSNo4xEnsU1n56jaix6Q0TWYGaIfEdKCTUcdWVVIiIiP1LCOoveEJEl2LOQt6QwAhyOxqDHZNb2qyCiLOOaT3P0tQM9zYB+AsitAspbgLKQLU1Rw1FMY9EbIrIAM0PkO6qW2K+CUy6IiJLrawe6mwC9C4CMf+9uip+3gaJNnBnavKoNm1e1ZalFROQVHBonb0hjjUC/sZM51wwReRszQpnraQakOvycVOPnbcgOcWozEVmFd4PkO6qxkzmnyRERJaefSO+8xfo1fcypzUY26Mj+rmHH2/Y1ZqdxHsbfJfkB7wbJG9JYI6CE45khjjISEY0htyoxRS7J+Sxj0RsishKDIfKdgTVDNk2T40gbkYOx6EJceUt8jdDQqXIiGD+fZZoeQ3ScojdGX8q+1TxmZtv4dyGnYzBE3pLCDYyRGeKeFUREYzDWBTmgmtzg1Gb22URkPgZD5DtKooBCttcMcV47kYNxo9bRykK2ldIeSkmx6A37UvOYkW3jNY/cgqW1yXeUxChjkPPPiYgcz8gMlbACqCexJDrZjT0L+Y5qU2aI89qJHIwbtTrWwHYInCaXdZO5TvGaR27BYIh8RwlHIQRQlMcLKxGR06kDFUB5y+IlnEZHTsGehXxH1XQE83IQCAhbPn8yHX1H+2G0NXeg90QfZlSVobGlAQ2hxSa2jsjnrMgIMds0KUqiAigzQ+7E4IacjsEQ+Y4Sjk64ENeJOtoPY0fTs9DUCACgp6sPO5qeBQAGRETkWQOZIW6U7SmcRkdOwQIK5DuKpruyRGtbc8dAIGTQ1AjamjtsahERjatrVfzrwv74l3FMaWHRGyKyEodZKDscNE1EDetjbt7nZL0n+tI6T0TkBUbRG1aT8yZmhMhu7FnIdxQtimIXjjDOqCpDT9fowGdGVZkNrSGiCbFCnSkUTYcQQGGu+/rtbOOUM6L0cZocWcuB00TUsO74qkTJ9l1obGlAQTBv2LmCYB4aWxqy2TQi53NAP0PmUcJRW4veEJG3pXxHKITIAdAJ4B0p5WesaxKRtZRwFHOmOjsYSsYoksBqcpQK9tkOYkdGyEPZKDWsu67oTbYrf7JMNVHm0uld/gbAKwCmWNQW8iIHThNRNd2xJVonuqA1hBYz+KFU+a/PNvqZC/uHHzug36HMKVrUVUVv/Fj5k8EXuVlKwZAQYg6A6wC0ANhoaYuILNavOX+aXDp4EaKR2Gf7mAcDQjdMbR5qvMqfVgVDLFNNlLlUe5cHAXwTQKmFbSEvc8iFWEoJNRy1LTM00YWKFzQyiT/7bAdmomny4pkh9wRDfqr8yel55AUT9i5CiM8AOC2lPCCEWDXO85oANAFAVVWVaQ0kMlM4GoMek64aZRwLL0KUDPtsn/NgQKiEdUwrzre7GSmzs/In+3+i9KVyR/hxAGuFEJ8GUAhgihDix1LKrwx9kpRyJ4CdAFBfXy9Nb6lbOP0C5PT2WUzV4pv3ZXv+ebqBCy9oNAnss33av3mVoum4bGrQ7makrLGlYdiaIcC7lT85m4G8YMJgSEr5vwD8LwBIjDLePfKiSuQWSji+eZ/bKhMlw4sQJcM+mwB4KiC0c2pzJlj5k8hd3H9H6BROX7Tq9PZliRo2MkPZ/afPwIWIKDOKC4ve+K3yJ69p5GZp9S5Syn0A9lnSEqIs6NeMzJB7RhknwosQjYV9NrmdUfSm2EN9ttXcOujm1naT+7lrqMXJnL5o1enty5LBNUP2/NNnJ09ElDqj6E3QRdXkiMhd2LuQrwysGXLR/HMiIr9SMix609F+2HdrdtxaYdSt7SbvYDBkNqdnXJzePoupiWCoxGXzz52IFyzKiM+z065mw99O0dIvetPRfnhYNbeerj7saHoWADwfEBFR+nhHSL5ijDJ6ac0QEVmIwZutMil609bcMaysNQBoagRtzR2eDobcWqjHre0m72AwRL5ijDKauWbIb9MxOKWBMsKKlu5l499ucDuE1Aewek+M3vB0vPNeYfTFRJQeBkPkK0pilLEob/SFNZObek7HIPIoBm+OYBS9SWdq84yqMvR0jQ58ZlSVmdYuJ3PrwJRb203ux2CIfEXVdATzcxAIiFGPnT3Vj1N/PovrA/ennOHx43QMTmmgjLCipXvZ+LfLpOhNY0vDsEEqACgI5qGxpcH09jkBs/VEk8NgiHxFCUdHlWjdvKoNZ0/14+1X3xs4l2qGx6/TMYg8j8GbI2Qytdnos/00fZmIMsdgiHxFDesoSTL3/NSfz446l0qGx8/TMTjqSBlhUOFeNvztjKnN6Ra9aQgt9k3ww2w90eQE7G4A+UhfO/BmDfBqIP69rz3rTVC00ZmhbfsaoScuuCNNlOFpbGlAQTBv2DkvT8cg8p3qfQzgbKRaUPSGiGgo9i6UHX3tQHcTINX4sd4VPwaAslDWmqFoOoqTjDBmmuHhdAwiIuuMV/SGhmNGiCgzDIYoO3qaBwMhg1Tj57MYDKlhHZcE80edn8yCWz9Nx3AaTgshS3CdkGOomo7iMYreEBGZgdPkrNa1avDC6mf6ifTOW0QJR5NmhhpCi3H7zutQXl0GIYDy6jLcvvM6BjlERDZSwlEE0yirTUSULvYwlB25VfGpccnOZ1F8lDH5P3tmeNyDpWTJEtxbyHGURGaIiMgqDIaswovqcOUtw9cMAYAIxs9nUTwzxH/2RERuoIb1UUVviIjMxB7GTdwcUBnrgnqa41PjcqvigVAW1wsBxoWVo4xux1KyZAnuLeQ4ipZ8ajMRkVkYDFmFF9XRykJZD36G0vQoIlHJzBARkUuoYR1Ti0cXvSEiMgvvCt2AU+4yM+L3pGqJzfsSmaGO9sMsie1yzAiRJdi3OoYSjmLOVN6qEJF12MNYjRdVx1DCg5v3dbQfHlZKu6erDzuangUABkRERA6hapza7AacskxuxtLabmDsgF60Mv7FHdHHZ5Qzv7A//pU4VhOb9xUX5KKtuWPYnkIAoKkRtDV3ZL25RESO09cOvFkDvBqIf+9rt+Xz+y/0ovjCj7P/+UTkG8wMkW8oWjwzFCzIQe+JvqTPGes8EZFv9LUPr/6pd8WPgeys+0x8voypUCOFCOaczu7nU8q4zQF5ATNDTjLRBq3MCKVmjEzaQGYoPxczqsqSvnSs80REvtHTPHwbBCB+3NOc+ntMJrOU+PxwLBe6zEVx3oX0P5+IKEXMDJFv9BuZofwcNLY0DFszBAAFwTw0tjTY1TwiImfQT6R3fqTJZpYSn6NGigAgHgyl8/mUNdzmgLyAwZATsFqcNUb8/lSjgEJBLhYliiSwmhwR0Qi5VfEAJtn5VIyXWUolGEp8vqIXAgCCuRfT+3xyPAZP5CQMhsg3FM2YJhevTNQQWszgh4hopPKW4ZkdABDB+PlUBusmm1lKfP6wzJDx+eRIDGrIzRgMOQE3aM2KoZkhIiIag5G96WmOBzC5VfFApCwEnP3HiV8/2cxS4vP734t/VrBgCjBzJ4snOFwq2R4WXCAn4l0h+YaRGSrK454VBl6IiCipstDw4KNrVTwQSmU693iZpTQ+Xy2/BsBLKK75MVA2Lb32ExGliMGQkzAjZCklsXlfICDsbgoRkXeNl1lKg7FRdjY3XeUAUfrSyfaw4AI5EYMh8g0lHEUwn//kAU5VIMoKL019Tnc698jMUgaMqc0lnNpMRBZiD0PO0Nc+6VHEiahhHcUFnCJHROQGxtTmYBb6bQ4QZS6TbA9/r+QkDIbIfu9uAPoeASDjxxbtdq5ozAwZOFWByEJe3i4hiz/DQNEb9ttEZCH2MGSvvvbhgZBhrD0pJnFToYZ1lDAzRETkCv1ZLHrDAaLJ4++M3IrBENmrpxmjAiGDybuNK+EoLinKM/U93Y4XLyILcLsEU6gsekNEWcBgiOw1XsAzdE8KE6adKJqO2ZcUptM6dLQfRltzB3q6+pBXkIM7H72eG7USEWWBHUVvOEBE5D8MhsheY23OB2H6buPxUcbU/8l3tB/GjqZnoakRAEBEi2JH07MAwICIiCaWzYyQB7NQnNpMRNkQsLsB5HPlLfHN+IYRQNn64euFqvfFv4pWxr+M4zQo4SiK09ivoq25YyAQMmhqBK23/FtanztUR/thrKtpxfWB+7GuphUd7Yczfi8iIi9j0Rsiygb2MmQvkzbnS4Ua1hFMY7+K3hN9Sc9HEot60zUy09TT1cdMExFNjocr13E7BCLKBmaGyH5lIeBDx4EFsfj38QKhDDJCABDWY4hEZVqb982oKkt6vrw6+fmJjJVpamvuyOj9iIi8TElzajMRUSYYDJEvGPtVBNOYJtfY0oCC4PDqcwXBPDS2NIx67uZVbQMlWccyVqZprPNERBMyYQqxUynhKDNDRGQ5BkPkC/1a+pv3NYQW4/ad16G8ugxCxDNCt++8LuMpbWNlmsY6T0TkZ6qmc8NVIrIcexm389D8cCup4fg6n2Cao4wNocXjBj9GNujI/q5hx8nKsza2NAxbMwSMnWkiIkqLB68B8cwQb1OIyFoTZoaEEIVCiN8JIQ4JIY4KIf42Gw0jMpOSQmbI6kpvZmeaiJJhn02W6lo1OAhnMTWspzW1mYgoE6kMuWgAVksp+4UQeQD+UwjxH1LK/7K4bTQeOysIuTAbNZAZGuPCmmmlNyMDNF5GaKiJMk1EJmCfTa6n6VFEojJpZijV/pbcy86/8YEDBy7Nzc39IYBF4HISr4gBOKLr+l9feeWVp0c+OGEwJKWUAPoTh3mJL2lqE4ksNpAZGmPKxXiV3hi8kJuwzyZLZHkATtXGH8ByOgZs7pWbm/vDmTNn1pWXl58JBALsOz0gFouJnp6ehd3d3T8EsHbk4ylNxhVC5AA4AOBDAL4vpXzJ3GZS2owLkB0ZIRfuZ2FkhsYKhiZb6Y0XPGfy6w0J+2xyOyU8empzOms0yZ0c8jdexEDIWwKBgCwvL+/r7u5elOzxlIIhKWUUwFIhxCUAnhZCLJJSHhn6HCFEE4AmAKiqqppks4nMNVhNLvko44yqMvR0jQ58WOmN3Ih9NpkuywNwEw1gOZVDbuZpcgIMhLwn8TdNOu0xrV5GSnlWCLEPwLUAjox4bCeAnQBQX1/Pf0TZks2sjB3ZqMnoawd6mgH9BNST6wB8AcExLqys9OYtvCGJY59NbmVMbR5aATTdNZrkPvwbj23jxo2zSkpKovfdd98ps9/7N7/5TfCWW26puXjxYmD16tV9u3bteisQ8M9yqVSqyZUnRhchhCgCcDWAV61uGNGk9LUD3U2A3gVAQtEuAgCK1H9J+nRWeiOvYJ9NE5pMRbgsbeo6kBly2T5D2/Y1Ytu+RixaWY1FK6sHjomcbMOGDdUPP/xw1/Hjx48cO3ascPfu3VPsblM2pdLLVAL4p8Qc9ACAn0gp/93aZpGjOT0jBMQzQlIdOFT1QhTlXkTOe/OXzMgAACAASURBVM3A1FDSl7DSm3f4fHSRfTZN3pDMOnKrgPIWoCx532kFY2pzsgIKPvv/2Zfc9je+a9mj8wHge7+75TUz3m/Hjh3TW1tbK4QQqKuru/DMM8/8eejjDzzwwIzHHnusPBKJiJqaGm337t1/Li0tje3atWvq1q1bZwUCAVlaWhrt7Ox8rbOzs3DdunVzI5GIiMVieOqpp/60ePFizXivrq6uvP7+/sDVV1+tAEAoFHrvmWeemfqlL33pnBk/ixukUk3ujwA+nIW2EJlHPzHsUIkUoTj3wqjzVvDpDTg5BPtsGlOqRXCMzLoxoKR3xY+BrAVEanj8CqBOx/6fMtXZ2Vm4ffv2yhdffPHVyspK/dSpU6NGBEKh0JlNmzb1AsCdd945q7W1dUZzc/Ppbdu2Ve7du/f1uXPnRnp7e3MA4KGHHirfsGHDqdtuu+39ixcvCl3Xh71XV1dXXmVl5cAagerq6vC7776bZ/GP6Sju7GXIfk5fN5RblZgiF6fqhSjOuxA/T77BGxKiDIzIrAOIH/c0Zy0YUjRjmpw7S2uTPxgZoTd+f7Jk6PFkMkTPPffclOuvv/5MZWWlDgAVFRXRkc85cOBA0ZYtW2afP38+R1GUnJUrV/YBQH19fX8oFKq54YYbzoRCoTMAcNVVVynbt2+vfPvtt/NvuummM0OzQgAQ341hOCFEps13Jf+sjiJ/KW8BRHDgsD9ShGBeOH7eIptXtWHzqjYc2d+FI/u7Bo5TeQ0RkeWM9T5FK+NfY63/GSuDnoXMuiFZZoj9JfmBlBJCiHGL2jQ1Nc3dsWPHiddff/3le+6556SmaQEAeOKJJ058+9vfPvnWW2/lL1269PLu7u6c9evXv/+zn/3szaKiotiaNWtq9+zZUzr0vWpqaiJDM0FdXV35M2fOjIz8TC9jMETpMRbeXtgf/5rMQlwrlYWAmTuB3GoAAmp0KoqDc7I6552IyJXGyqBnMbNuZIaK8pgZIuf63u9uee17v7vltXkfmdU/7yOz+o3jybzntddee27Pnj3Turu7cwAg2TQ5VVUDVVVVEU3TxJNPPjnNOH/06NGC1atXKw8++ODJqVOn6seOHct/+eWX8+vq6rR777339Kc+9amzBw8eLBr6XtXV1ZHi4uLYr371q+JYLIb29vbpn/3sZ89O5mdwG06TI+8qCw0EP8qvXkBZkbVTYNNZtM/Sz0Rkm4mmN5e3DF8zBMQz7RZm1kdSwzqC+TkIBAT7yzTwd+N+9fX1Fzdt2vTuihUrFgQCAblo0SL1qaeeOj70OZs3bz65bNmyutmzZ4fr6urU/v7+HAC466675hw/frxASik+8YlPnFu+fPmF5ubmmT/96U+n5+bmyvLy8sjWrVtPjvzMhx9+uOuWW26Ze/HiRdHQ0HDuxhtvTG3HeY9gMETpcdteQwmqpmNWWaHdzSAicj4jg25rNbkogi4rq03+ZVYVOcMdd9zx3h133PHe0HPf/e53B4KYe+65p+eee+7pGfm6vXv3/mnkua1bt3Zv3bq1e7zP+8u//Ev1jTfeODqZNrsZexqruSxo8Co1HM1aVaJURuR8Xvo5bfw9EWXZkMy6HdSwjuLEhqvsLyfG7BlR5hgM0WipBHAuC+76NZ1ViTyAF3hKmxUDUn4b5LLh51WYGSKiLGFPY5VU93OgrFDDOoIO3K+CN/XjGznaGSwrsLM5RJQlalhHScHwASz2l2Nj9owoc867OyT7eDSAC+sxRKKSmSEPUPvi2yPwgk8TsqI/82gfOSYbf14lHMUlFhe9ISICGAxZx6WFBrzI2K+CUy7cxwh2vnTJdwAMBkNE5G2qpmP2JSx6ky4OEBGlj3eHNMijAZwSTuxkXuDuzJCfsyEfWDpz2LEffweUJiv6M4/2kWOy8edVNJ0DWESUFdx01Wpj7fBNWaNqo3cyJ3fZtq/RkgCIO9qTaZy6AbVLKeEopzYTDbFx48ZZW7ZsqbDivX/zm98Ea2trF1ZVVS26+eabL4vFYqOe853vfKd8x44d0634fLNs3rx55sTPGo13hzSax4K3fiMYcukoI0umDvLjz0yTZEV/5rE+ckLj/bwWZY3ipbXd2WcTuc2GDRuqH3744a7Vq1crq1atmrd79+4pX/rSl84Nfc43v/nNUfsamUnXdeTmDv4/H4lEkJeX3rrB1tbWym3bto27p1IyzAxR+lw2AqompskFOcpICUZG6Mj+LhzZ38UMEWXO6A8v7I9/uax/TFtfO/BmDfBqIP49esr0jxgoesNgiNzgzCPT8MasxXg1cCXemLUYZx6ZNtm33LFjx/Ta2tqF8+fPX/i5z31u7sjHH3jggRmLFi2qmz9//sJrrrnmg+fPnw8AwK5du6bOmzfv8vnz5y+sr6+fDwCdnZ2FixcvrluwYMHC2trahYcPHx5WlrWrqyuvv78/cPXVVyuBQAChUOi9Z555ZurIzxyamVq2bNn82267bfbixYvrampqFv3iF78oAeIBTVNT05za2tqFtbW1C1taWi4FgJ/97GeldXV1C2traxfeeOONNRcuXBAAMHv27MV333135ZVXXjl/165dU5ctWzb/9ttvn/2Rj3xk/re//e2KkydP5l5zzTUfXLRoUd2iRYvq9u7dWwwAfX19gS9+8Ys1xuf86Ec/umTDhg2zNU0LLFiwYOHatWtH/c7Gw56GPE9x+TQ5lkwlIkfoawe6mwCpxo/1rsQDr5qaIRosesMBLHK4M49Mw+m7qiEvxpML0XfzcfquagDA1PXvZ/KWnZ2dhdu3b6988cUXX62srNRPnTo16n+EUCh0ZtOmTb0AcOedd85qbW2d0dzcfHrbtm2Ve/fufX3u3LmR3t7eHAB46KGHyjds2HDqtttue//ixYtC1/Vh79XV1ZVXWVkZMY6rq6vD77777oQpGV3XxeHDh1/5l3/5l7L77rtv1rXXXvv6Aw88UN7V1VVw9OjRl/Py8nDq1KkcVVXFrbfeOnfv3r2vXXHFFdrnP//5mr//+78v37Jly2kAKCwsjB04cOA1APjhD3946dmzZ3N+//vfvwYA119//dyNGzeeuuaaa/rfeOON/GuuuWbesWPHjm7evLlyypQp0ddff/1lAOjp6cm5+eabz/7oRz+69NVXX3053d+5O+8O/cgJC3bdUla2rx3oaQb0E0BuFdSz3wFQzAsrDWCASabxU1GFnubBQMhCA0VvXDq1mXyk977ZA4GQQV4MoPe+2ZkGQ88999yU66+//kxlZaUOABUVFdGRzzlw4EDRli1bZp8/fz5HUZSclStX9gFAfX19fygUqrnhhhvOhEKhMwBw1VVXKdu3b698++2382+66aYzixcvHlaWVUo5qg1CiAnbeeONN54BgI997GPKN77xjXwAeP7556esX7++x5jeVlFREX3xxReL5syZo11xxRUaANx8883vff/7378UwGkAaGxsPDP0fb/85S8P/N5eeOGFKW+88UaRcdzf359z5syZwK9//espTz755DHjfHl5+ajfUTrY05C3JBm5VHrbATShxKWZIQNv2InIVvqJsR8zMQg0svlBl1cAJR+IduendT4FUkoIIUZHKEM0NTXN3b1795tXXXXVhdbW1un79+8vBYAnnnjixPPPP1+8Z8+esqVLl15+8ODBo+vXr39/xYoVytNPP122Zs2a2ocffvj42rVrzxvvVVNTExmaCerq6sqfOXNmJNnnDlVYWCgBIDc3F9FoVIzV9mTB1lClpaWxsY6llOjs7HylpKRk1HumErClimuGnM5J89GNynhFK+NfVlTKm+zPl2TkUo3EL6hBlwdDZD6rqtSRD7m9cmgqfW9u1RgPFIxxPjOKg4vedLQfxrqaVlwfuB/ralrR0X7Y7iaRnXJmhtM6n4Jrr7323J49e6Z1d3fnAECyaXKqqgaqqqoimqaJJ598cmCN0tGjRwtWr16tPPjggyenTp2qHzt2LP/ll1/Or6ur0+69997Tn/rUp84ePHiwaOh7VVdXR4qLi2O/+tWvimOxGNrb26d/9rOfPZtJ26+++upzjzzySHkkEo+lTp06lbN06dKL77zzTv6RI0cKAKCtrW36ihUrzo/7Rgmf+MQnzv3d3/3dpcbxb3/72yIAWLVq1bnvfve7A+d7enpyACA3N1dqmpZ2lMRgiDLnxIXCSUYu+yPx/++L8jjKSESUsfIWQASHnxNBoPJRUz9GHdgbzlnBUEf7YexoehY9XX2QEujp6sOOpmcZEPnZjC3vQBQOr0MtCmOYseWdTN+yvr7+4qZNm95dsWLFgvnz5y/csGHDZSOfs3nz5pPLli2rW7FiRe28efMuGufvuuuuObW1tQvnzZt3+fLly88vX778wuOPPz6ttrb28gULFix84403Cm+99db3Rr7fww8/3LV+/fqa6urqRTU1NdqNN97Yl0nb77rrrp45c+aEFyxYcPn8+fMXPvroo9OCwaB85JFHjt94440frK2tXRgIBHD33XenVJlu586db/3hD38orq2tXfjBD37w8h07dpQDwNatW989e/ZsjlEs4uc//3kpAIRCoZ66urq0CyiIidJXmaivr5ednZ2mv6+vOXE+upltGrkeqWhlZu/9Zs2QRb1xLb//n/jxa9fhlW9/YTItJJ8QQhyQUtbb3Y5sYp/tY+n2vSPWZKK8BSgLmdqkvUe70fT4Afz7HZ/Aotllpr73ZKyraUVP1+h7xPLqMjx2/E4bWkSA+X32oUOHji9ZsqQ35ReceWQaeu+bjWh3PnJmhjFjyzuZrhciax06dGjGkiVLakaed9awC7mDkwsplLcMXzMEQNFLUZyfXq16p+FCfyJyhLKQ6cHPSHZlhibqZ3tPJB8sH+s8+cTU9e8z+HE3BkNu4YRAw0pmVWQyLtJDq8nlrkSwsGSSDSTyCScNbpD1HFgNTwkba4acNbV5RlVZ0szQjCrnZK+IKH0Mhih9Drx4DjNi5FL5bSeKCy4kfarTMy5G+47s7xp27NT2ElGWObUfnoTBanLZuUVJtZ9tbGnAjqZnoamDhbYKgnlobGnISjuJyBoMhshZLLigq2HdcSOMRI7j5OmvZD0H/Z0VLT5NLuiwojcNocUAgLbmDvSe6MOMqjI0tjQMnCcid2IwRJmbzMUzizda/VoUZUXD1wxlK+My2ffl5qBElJSHg1c1rCOYn4NAwLx9RMaTTj/bEFrM4IfIYxgMkeepmo5ZZYV2N8PXGMy5gNOnv5JvKOEogg7cY4iIvIm9DWWXDaOZapILq9UZF7MzTwwiiFLgp0DOw8GrqukoLsj+FDn2s+RkGzdunFVSUhK97777Tpn93nfcccfsn/70p9PPnTuXo6rqf5v9/k7HYIg8Twnbc2ElFoBwJQ/dVJM7MTNElF2f+9znzt59992n6+rqFtndFjuwt6HssmE0U9WiY+5XYdVNOdf6EGWRh9fPTCjdn9EFvxtFc27RG/bplNTxZfMBADW/e82Mt9uxY8f01tbWCiEE6urqLjzzzDN/Hvr4Aw88MOOxxx4rj0QioqamRtu9e/efS0tLY7t27Zq6devWWYFAQJaWlkY7Oztf6+zsLFy3bt3cSCQiYrEYnnrqqT8tXrxYG/p+n/zkJxUz2u1WDIas5IKLjteF9RjC0ZhjL6xex6CQiNKlhEcXvSHyi87OzsLt27dXvvjii69WVlbqp06dGnUDEwqFzmzatKkXAO68885Zra2tM5qbm09v27atcu/eva/PnTs30tvbmwMADz30UPmGDRtO3Xbbbe9fvHhR6Lqe7R/J8RgMkT2yFCCqic377JpywZt/oizw8PoZ07goe6ZqOmZf4qyiN5zyS0kZGaGLvy8ZdjyJDNFzzz035frrrz9TWVmpA0BFRUV05HMOHDhQtGXLltnnz5/PURQlZ+XKlX0AUF9f3x8KhWpuuOGGM6FQ6AwAXHXVVcr27dsr33777fybbrrpzMisEAEBuxvgSV2r4l8X9se/jGPKOiUc70O4Zshe2/Y18qaBiFKSrOgNkV9IKSGEkOM9p6mpae6OHTtOvP766y/fc889JzVNCwDAE088ceLb3/72ybfeeit/6dKll3d3d+esX7/+/Z/97GdvFhUVxdasWVO7Z8+e0uz8JO7B3oY8TdXszQwRURY5MMuRFiuzNS7KnikO3CibU34pKSMDZOKaoWuvvfbcF7/4xQ9961vfOjVz5szoqVOnckZmh1RVDVRVVUU0TRNPPvnktMrKyggAHD16tGD16tXK6tWrleeee+6SY8eO5b///vvRuro67fLLLz997NixgoMHDxatXbv2/GTb6SXMDFmhel/8K1AW/zKOKeuYGSIiykBfO/BmDfBqIP69rz1rH61qUQTHKHpD5HX19fUXN23a9O6KFSsWzJ8/f+GGDRsuG/mczZs3n1y2bFndihUraufNm3fROH/XXXfNqa2tXThv3rzLly9ffn758uUXHn/88Wm1tbWXL1iwYOEbb7xReOutt7438v3Wr18/p6Ki4oqLFy8GKioqrti4ceMsq39OJxFSjpuJy0h9fb3s7Ow0/X1d5/VL4t9rz9rbDh/77Zu9+B8/fAn/0rQcH/3AdLubQy4ghDggpay3ux3ZxD7bZiPX8xStjH+3axCtrx3obgKkOnhOBIGZO4Gy0Niv6WkG9BNAbhVQ3jL2c8cR1mOovfc/cPenanH76nkpvYbZGu9J529qdp996NCh40uWLOk16/3IOQ4dOjRjyZIlNSPPc+jFCsaFLdY3/DgbFzYXTIHIpv7ENLmxSmsTEdEIPc3DAyEgftzTnDzAGRk86V3xYyDtgMgoesM+m4iyhb0NeZqamCYXdNj8cyKiAWat5zFrMEw/kd75dIOncQxMbU5hnScrvHkP/6ZkBwZDVrBjoaqLyqZmk8JRRiKi9ORWxbM7yc4nk27wNI6Bojdc50lEWcI7RPI0VWNmiIhcYrIZIbMGw8pbkq8ZKm9J/vx0g6dxpJMZYoU37+HflOzAYMhK2czKuKhsajYpNm+6SkTkOsbUtlQLIqQbPI1jcDsE7w1g8QafyJnsvUNM9cadN/g0UoqVi9RwFEV5OcgJCBsaSUSUBRMNhmVyDS0Lpb7eJ93gaRyZFL3JJLhgYOJs/LtQNk24z5AQ4jIhRIcQ4hUhxFEhxN9ko2GUIT/saWRULtK7AMjBykVJ9sHo13TuMUS+wj6bbFEWAj50HFgQi3/PIBACBoveeGmd5+ZVbdi8qg1H9nfhyP6ugWOidGzcuHHWli1bKqx47zvuuGP2zJkzrwgGgx8e6znt7e1l3/rWt2Za8flmue+++y49f/582nuoptLb6AA2SSn/IIQoBXBACPFLKeXLabfSkOr8ZhYFoGTSqFykarorpsh1tB9GW3MHek/0YUZVGRpbGtAQWmx3s8idzO+zyR08cA0dKHpj0TQ5VisjGu1zn/vc2bvvvvt0XV3dorGeEwqF+gD0WdWGSCSCvLy8MY9T8Q//8A8VX/va194vLS2NpfO6Ce8SpZTvAng38d/nhRCvAJgNgBdWskcalYuUcNTxc8872g9jR9Oz0NQIAKCnqw87mp4FAFcFRLypcAb22eRmA0VvPJQZYlEAb/v5I53T/vm+38w+092fP3VmSfjLW1a88+n19e9P5j137NgxvbW1tUIIgbq6ugvPPPPMn4c+/sADD8x47LHHyiORiKipqdF2797959LS0tiuXbumbt26dVYgEJClpaXRzs7O1zo7OwvXrVs3NxKJiFgshqeeeupPixcv1oa+3yc/+Ulloja1trZO7+zsLG5raztxww031JSWlkYPHTpU3NPTk3f//fe/vW7dujMAcO+991b85Cc/mS6EwCc/+cm+hx9++J3f/va3Rbfddlv1hQsXAtXV1doTTzxxvLy8PLps2bL5y5Yt63/ppZdKPv3pT589cuRI0dSpU/XDhw8Hr7jiCvWBBx44ecstt1S98sorRdFoVDQ3N5/8yle+clbXdWzYsGHOvn37pgDAV7/61V4pJU6fPp23cuXK2qlTp+ovvfTS66n+vtPqbYQQNQA+DOCldF43SqqL/bNdFMAFo2aEtCoXqWHd8dMt2po7BgIhg6ZG0Nbc4apgiJzHtD6b3MmFhXWMzFBRnjWDWAxMyEw/f6Rz2j/e9cvqyEU9AABn3u3P/8e7flkNAJkGRJ2dnYXbt2+vfPHFF1+trKzUT506Nep/hlAodGbTpk29AHDnnXfOam1tndHc3Hx627ZtlXv37n197ty5kd7e3hwAeOihh8o3bNhw6rbbbnv/4sWLQtf1zH/gIU6dOpXX2dn56sGDBws///nPf2jdunVnfvKTn0x59tlnpx44cODV0tLSmNH2m2++ee73vve9E9ddd13/17/+9Vn33HPPrF27dr0FAGfPns35/e9//xoA3HDDDTV/+tOfCl944YXXc3Nzcfvtt89uaGg499Of/vR4b29vTn19fd3atWvP/eAHP5je1dVVcPTo0Zfz8vJw6tSpnIqKiugPfvCDiv37979eWVmZ1g+Z8l2iEKIEwFMAvi6lPJfk8SYATQBQVZV+OU2ilKVRuUjRoigtdHYw1HsiedZ5rPNOw2knzsQ+m9zIy0Vv2Cd6zz/f95vZRiBkiFzUA/98329mZxoMPffcc1Ouv/76M8YNfUVFRXTkcw4cOFC0ZcuW2efPn89RFCVn5cqVfQBQX1/fHwqFam644YYzoVDoDABcddVVyvbt2yvffvvt/JtuuunMyKxQptauXXs2JycHV1555cX33nsvDwB++ctfTvnKV77Sa0xTq6ioiL733ns558+fz7nuuuv6AeBrX/vaezfeeOMHjPf58pe/POz39IUvfOFMbm78vm3fvn1TnnvuuUtaW1tnAoCmaeLNN9/Mf/7556esX7++x5hGl+x3lI6U7hKFEHmIX1TbpZT/muw5UsqdAHYCQH19vUzp01MdpcpWRshF86p9LY3KRWpYR2VZYZYbmJ4ZVWXo6Rod+MyoKrOhNeQFlvXZ5E4uupZlq+iNkwITDiC515nu/vx0zqdCSgkhxLh9clNT09zdu3e/edVVV11obW2dvn///lIAeOKJJ048//zzxXv27ClbunTp5QcPHjy6fv3691esWKE8/fTTZWvWrKl9+OGHj69du/Z8pu0zFBYWDrRRSjm07Wm9z8j1PSUlJQPHUkrs3r37zSVLlgwL4FL5HaUjlWpyAsCjAF6RUn7XrA8mmpQUKxcpWtTxBRQaWxpQEBy+SLAgmIfGlgabWpSebfsasW1fIxatrMaildUDx2QP9tnkZqrm/KnNRIapM0vC6ZxPxbXXXntuz54907q7u3MAINk0OVVVA1VVVRFN08STTz45zTh/9OjRgtWrVysPPvjgyalTp+rHjh3Lf/nll/Pr6uq0e++99/SnPvWpswcPHizKtG2ptP3xxx+fYVR0O3XqVM706dOjU6ZMif7iF78oAYBHH310+lVXXdWfyvs1NDSce+CBBypisXh89MILLxQBwNVXX33ukUceKY9E4ksMjN9RcXFxtK+vL+1qcqm84OMA/i8Aq4UQBxNfn073gxzNKEddtDL+5Yfy1D6hhJ1fWrshtBi377wO5dVlEAIory7D7Tuv43ohypT3+2zyrHjRG+uCISeVtWbJbff78pYV7+QV5g7LbOQV5sa+vGXFO5m+Z319/cVNmza9u2LFigXz589fuGHDhstGPmfz5s0nly1bVrdixYraefPmXTTO33XXXXNqa2sXzps37/Lly5efX758+YXHH398Wm1t7eULFixY+MYbbxTeeuut7418v/Xr18+pqKi44uLFi4GKioorNm7cOCuTtn/xi188t2bNmrNLly6tW7BgwcL7779/JgA89thjf77nnnvm1NbWLvzjH/9YtG3btpOpvN+2bdtO6rouFixYsHDevHmX33vvvbMTP2fPnDlzwgsWLLh8/vz5Cx999NFpQLyQwpo1a+Z99KMfrU2n3cJIbZmpvr5ednZ2mv6+luP0OM+pbf4P/M9PzMXmNQvsbgq5hBDigJSy3u52ZJNr++yJuLVPd2u7TRD64X9Bi8Sw+7aPDZwzc+sBJ01JG7nectHKagDOaJubmN1nHzp06PiSJUt6U32+FdXkyBqHDh2asWTJkpqR55mLHsqHFx4vC+sxhKMxy/arICIicylaFFOKBqcNm7X1gBMLvbCynTd8en39+wx+3I3BEHnWhbD39qsgohS4tSiOW9ttopFFb7j1ABFZjXeJ5Fn9if0qShy+ZoiIXMSHAUo2jSx6Y9bWA07OwjipLUR+xGCIzOHAGwRViwdDTq8mR0Qmc+FmowDc224TKWF92AAWtx4gG8RisZgIBALccsBDYrGYABBL9hjvEsmzlMQ0OadXkyMiF+AUtqxQteiwqc2NLQ3D1gwBk9t6wO9ZGCdmxhzoSE9Pz8Ly8vI+BkTeEIvFRE9PTxmAI8keZzBEk+PgGwSvZYZ4ESNKkwP6oYy4td2TlKzojbEuyKxqcn537GC33U1wPF3X/7q7u/uH3d3di5DaFjTkfDEAR3Rd/+tkD3rjLpG8L4MgayAz5JFgiIhsxClslhsoejOiz24ILWbwM0nGYJrapw075uDaaFdeeeVpAGvtbgdlD+8SaXx97UBPM6CfAHKrgPIWoCw0+LiDbxDURAGFoMunyTmxJCwRkdmMojec2my+kRkhZoiIBjEYorH1tQPdTYBU48d6V/wYGB4QWSndaXhDHu/XjGpy/GeeLgZcRGNw0ICP1xhTm4vZZ5vuA0tnAhgcVDOOiYjBEI2np3kwEDJINX5+ZDBk1Q2CdjDjl6qaMeXC3aOMTi4JS0RkFk5tto5x3fjSJd8ZdkxEDIZoPPqJ9M5boWDp8OOJMkJDMkjK6Y8B+LhnCihkA6fkEZFdBoveuHsAy8mYESIajXeJNLbcqvjUuGTnrTYyuAmkv6eEGslDwAWGtQAADvVJREFUYV4AOQFhXrtsxICEiLxscDsE3ppYhdcRotHY49DYyluGrxkCABGMn8+2kRmikZIUclD+cBjF+c5dJOrErAun5BGRXQaK3jAzRERZxGCIxmasCxqvmpxVTKhSp4ajrq8kR0TkF/0soEBENmCPQ+MrC2WvcpwZhgRN/ZruyIW4bliX46S2EJE/GEVvGAwRUTaxxyFnm0SVOjWsj7qoOjHwICIiQElMkyvKY0afiLKHwRB5lqJFUVrovH/iXJdDRDSaGo6iKC/HM0Vv/IjXNXIj590pknkmsd7GC9SwjplTCgG4Y2oaEZHv9LUPrEtVTn8TxXkft7tFROQzDIbIsxTN2QUUGIhNjEErkYf1tQ+rWKqGIwjmnI6fd9NaVeKAI7kagyEvSrIBKQDfZYjU8GABhfGmprHTJiKyQU/zsK0b+iNFCOZeAHruZzBERFnDYIg8S9GirErkYOMFoRxlJPIB/cSwQ1UvQkmeOuo8OR/XwpKb8U7Ri0zYo8ftwnoM4WgMxSM270uWEeINNxGRRYasCRq1V11uFaB3DTxViRRiSr4SP59lHe2H0dbcgd4TfZhRVYbGlgY0hBZnvR1ElH0MhsiTLoTj+1UEmRlynFSCUI4yEnnAsTog/DqAWPxY74qvEQLiAVF5y/A1Q3oRKovPxs9nUUf7YexoehaaGgEA9HT1YUfTswDAgChN7KvJjXin6GU+zAgZjP0qRmaGhuINNxGRhcJ/xkAgZJBqPFM0dENvo5qcXoLglL8Ayj6f1Wa2NXcMBEIGTY2grbmDwRCRDzAYIk9SE8FQppkhTpmwTjpBKANUIhcypmhDS/740DVBQ4IiNbYXxSWzLG1aMr0n+tI6T0TeYm8w5OM1LWQtRYtPkytJobT2yBtuTpkgIrLQGGuCFC2KYH72b0tmVJWhp2t04DOjqizrbSGi7AvY3QAiKyhaIjOUwYV1vCkTZJ5t+xqZ+SGyW1878GYN8Gog/r2vffLvWb0v/pW/AKNuM0Qw6Zogo+hNKgNYZmtsaUBBMG/YuYJgHhpbGrLeFiLKPnsyQ9wHhyymJAooFGcQDHHKBBH5wohNT0cVOJisnAogH0DsQmJqXD6QV5X0vQeK3tiQGTIy/pwaTeRPXDNEnjS4Zij9UUZOmSAiXxix6SmA4QUOJmvkAOfAWqLRBore2JAZAuIBEYMfIn+yJxjiPjhkMWPNUCaZocaWhmFrhoDUp0ywMh0RucZYm5uavelpCrNBBgawbMgMjcR+nMhf/LFmqGvVuCNS5D2TyQw1hBbj9p3Xoby6DEIA5dVluH3ndRw1JCJvGWtzUxs2PR0YwLIpM0RE/mXvEAwzQmSRfs3YZyizf+LpTplIZSNRIiJHGbHpKYAxCxyMq699YK8g5FbFXz90ml0Ks0GUSfbZZmA/TuRP9uejrcRCDb6lhqMozAsgJyDsbgoRkTON2PQ0aSAzEZOKMAwUvclwbzgiokyx1yFPUjQ9qyOM6WwkSkTkGEM2Pc1IOkUYxhmIHFwzZN80OfbjRP7k7WCIhRp8Sw1HM1ovNBZeHIlswv7b2UwqwjC4ZsjbtyVE5DzsdczGC7cjZDszZEglWGJgRURZZeV1KbcqPjUu2fk0OCEzZGDfTOQv/giGGJj4jhqOmnJR5YJaIptwzac7mFSEwcgMOaG0NhH5C3sds/DC7Sj9mo7SQmf982ZgRURZlY3rkhlFGBDfdJVFb4jIDs66WyQyiRrWMXNK4aTfhwtqiWzCNZ/uMdkiDIhPbS7heiEisgF7HrPwwu0oimZuAQUzMLAioqxy0XUpPrWZtyRElH0T9jxCiF0APgPgtJRykfVNItdx4IVWDZtbQIGBC7mJp/ptB/UrZB1F00et8+TAERFlQyp3iz8CsANAm7VN8QheuB1BMbm0tpl4Yacs+BHYb5PBBdclNRxlWW0issWEPY+U8tdCiBrrm0KOkWqmx6FFIyLRGMJ6zJLS2pmMVHJ0k7KN/Ta5jRIeXDPEYjNElE0BuxtALtO1ajDocSjVR5v3bV7VNnCjQETkCBlcJ1hAgYjsYlrPI4RoAtAEAFVV6W22Rg6RbqbHoYtzlcTmfcUmbt6XyUglRzfJydhnk5Mo2mABBRabIaJsMi0YklLuBLATAOrr66VZ70sO4dApcckM7GTu4VHG8QKtjvbDaGvuQO+JPsyoKkNjSwMaQottays5E/tsMl0614m+9mF7E6naQyguuDQLjSQiGs67d4uUvkwzPQ4LiIydzM3MDGUyUmnH6GZH+2HsaHoWmhoBAPR09WFH07MAwICIiJyhrx3obgKkGj/Wu6CEdQTlawAGix8yI0RE2ZBKae1/BrAKwAwhxNsA/h8p5aNWN4wcxqFT4pIxpsl5ec+KsQKtdTWtA4GQQVMjaGvuYDDkI+y3HcgFfeekpXqd6GkeDIQARGI5CEfzURz5NwA3WNhAIqLRUqkm9+VsNIQcxOUX68ECCuaX1s5kpDKbo5u9J/rSOk/exH6bHE0/MexQjRQCAIKBbjtaQ0Q+592hc7KGCwKlgQIKHl4zZBgZaM2oKkNP1+jAZ0ZVWbaaRERDuWi9pWkm+tlyqwC9a+BQ0YsAACWFRRY2iogoOZbWJs8ZXDPk/WBopMaWBhQE84adKwjmobGlwaYWERGNUN4CiODA4UBmaNrn7WoREfmY/+4WyfMGq8mZP03O6Yx1QawmR+QQLlpvmTVlofj3RDU5Rc4FABRPXWljo4jIrxgMkbf0tUN59z8BfAbBE/OBivsHL7w+0RBazOCHiJytLDTQNyt/6gXwkqeL3hCRc7HnIe9IlGtVw3+FghwNubE/x8u3Ar4LiIjIYZgRGpPq46nNRGQ/rhki70iUa1UihSjOvRg/J9X4+RE62g9jXU0rrg/cj3U1rehoP5zlxhIRETBkOwQfTm0mIvtxGIa8I1GuVYkUoTjvwqjzBm5MSkTkHEbRmxIfVAAlIudhZoi8I7cKQLxM67BgKHHe0NbcMebGpERElF0DRW/ymRkiouxjMETekSjXqkYKETSmyYlg/PwQ3JiUiMg5jMwQCygQkR3Y85B3GJWJou+jJK8PyK2OB0IjiidwY1IiIudQwzoK8wLICQi7m0JEPsTMEHlLWQiqWILg1GuBDx1PWkWOG5MSETmHEtZZSY6IbMPehzxnogsrNyYlInIOVYuykhwR2YbBEHmOoukonqAqETcmJSJyhn6NmSEisg+nyZHnKGGOMhIRuYUajk44gEVEZBUGQ+QpkWgMYT3GUUYiIpdQwjrLahORbRgMkaeoYaNEKy+sRERuoGpRDmARkW0YDJGnGJv3ccoFEZE7KGGdU5tdZPOqNmxe1WZ3M4hMw2CIPGVw8z5eWImI3EANMzNERPZh70OeomjxzFAJM0NERK7Qn0IFULKfkQ06sr9r2PG2fY22tYnIDMwMkacoiWlyQY4yEhE53mDRG2bzicgevGMkT1ET0+SKOf+ciMjxBoreMDPkeEYGiBkh8hpmhshTmBkiInKPgaI3zAwRkU14x0ieYowyMjNEROR8A0VvmBlyDWaEyGuYGSJPMQooMDNEROR8zAwRkd2ElNL8NxWiB0CX6W9srhkAeu1uRIrc0la3tBNgW63glnYC47e1WkpZns3G2I19tunYVvO5pZ2Ae9rqlnYC7LPJQpYEQ24ghOiUUtbb3Y5UuKWtbmknwLZawS3tBNzVVopz09+MbTWfW9oJuKetbmkn4K62kvtwmhwREREREfkSgyEiIiIiIvIlPwdDO+1uQBrc0la3tBNgW63glnYC7morxbnpb8a2ms8t7QTc01a3tBNwV1vJZXy7ZoiIiIiIiPzNz5khIiIiIiLyMV8HQ0KIG4UQR4UQMSGE46qUCCGuFUK8JoR4Uwix2e72jEUIsUsIcVoIccTutkxECHGZEKJDCPFK4m//N3a3KRkhRKEQ4ndCiEOJdv6t3W0ajxAiRwjx30KIf7e7LeMRQhwXQhwWQhwUQnTa3R5Kj9P7bID9ttnYZ1uH/TZRnK+DIQBHAHwBwK/tbshIQogcAN8HsAbAQgBfFkIstLdVY/oRgGvtbkSKdACbpJR1AJYD+L8d+nvVAKyWUi4BsBTAtUKI5Ta3aTx/A+AVuxuRogYp5VKWaXUlx/bZAPtti7DPtg77bSL4PBiSUr4ipXzN7naMYRmAN6WUx6SUYQBPAviszW1KSkr5awDv292OVEgp35VS/iHx3+cRvxDMtrdVo8m4/sRhXuLLkQv8hBBzAFwH4Id2t4W8zeF9NsB+23Tss63BfptokK+DIYebDeCtIcdvw4EXADcTQtQA+DCAl+xtSXKJKQwHAZwG8EsppSPbCeBBAN8EELO7ISmQAPYKIQ4IIZrsbgx5DvttC7HPNhX7baKEXLsbYDUhxP8HYGaSh5qllD/LdnvSIJKcc+wok9sIIUoAPAXg61LKc3a3JxkpZRTAUiHEJQCeFkIsklI6an6/EOIzAE5LKQ8IIVbZ3Z4UfFxKeVIIcSmAXwohXk2MkJNDuLjPBthvW4Z9tnnYbxMN5/lgSEp5td1tyNDbAC4bcjwHwEmb2uIpQog8xC+q7VLKf7W7PRORUp4VQuxDfH6/0y6sHwewVgjxaQCFAKYIIX4spfyKze1KSkp5MvH9tBDiacSnNfGi6iAu7rMB9tuWYJ/9/7dz/6oYxXEcx9+fRUlGSRkY5Bpkk+w2i8nqBtyEOzAro1KkWJRiQYkLcBnqa3geRf6UenTO0+/9ms74HU6fcz6/8zu/kTO3pQ/cJtdft8BSksUkE8AWcNzxTGMvSYAD4Kmq9rue5ydJZoariySZBNaB526n+qqq9qpqvqoWGNyjF319oCaZSjL9fg1s0M8XFY0vc3vEzOzRM7elz5ouQ0k2k7wAK8BJkrOuZ3pXVa/ALnDG4IfRo6p67Haq7yU5BK6B5SQvSXa6nukXq8A2sDY8pvNuuDrWN3PAZZIHBi9Y51XV6+NPx8AscJXkHrgBTqrqtOOZ9Ad9zmwwt/+Jmd02c1v/LlVuZ5YkSZLUnqa/DEmSJElql2VIkiRJUpMsQ5IkSZKaZBmSJEmS1CTLkCRJkqQmWYYkSZIkNckyJEmSJKlJliFJkiRJTXoD/owoa+ibEasAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for i, (ds_train, ds_test) in enumerate(zip(datasets_train, datasets_test)):\n", " ds_train = datasets_train[i]\n", " ds_test = datasets_test[i]\n", "\n", " X = ds_train[0]\n", " \n", " # On ajoute une colonne de 1 aux données\n", " # Ça nous permet d'apprendre le biais (w0 dans: w_1x + w0)\n", " X_b = np.array([np.ones(len(X)), X[:,0], X[:,1]]).T\n", " ####\n", " \n", " Y = ds_train[1]\n", " X_test = ds_test[0]\n", "\n", " # Comme plus haut on ajoute une colonne de 1 aux données de test\n", " X_test_b = np.array([np.ones(len(X_test)), X_test[:,0], X_test[:,1]]).T\n", " ###\n", "\n", " Y_test = ds_test[1]\n", "\n", " # 1) On (estime) entraîne les paramètres\n", " # k est le nombre de classes et dim est la dimensionalité des données \n", " W = OLS(X_b, Y) # dim x k\n", "\n", " # 2) Une fois les paramètres obtenus, on peut obtenir les prédictions \n", " # a) for test data\n", " y_x = np.dot(W.T, X_test_b.T) # valeur réelle\n", " pred_test = 1*(y_x>0)[0] # valeur binaire\n", "\n", " # b) Idem pour l'ensemble d'entraînement\n", " y_x = np.dot(W.T, X_b.T)\n", " pred_train = 1*(y_x>0)[0]\n", "\n", " \n", " # 3) On calcule aussi la frontière de décision \n", " # pour pouvoir la visualiser\n", " line_x, line_y = calculate_decision_boundary(W)\n", " \n", " \n", " # 4) Rendu visuel\n", " plot_predictions(i+1 ,X,Y, X_test, Y_test, pred_train, pred_test, line_x, line_y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Question 1 (Classification linéaire):** pour lequel des jeux de données le modèle atteint-il la meilleure performance? Expliquez en vos mots." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.2. Machine à support de vecteurs (*Support Vector Machine (SVM)*)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour entraîner et évaluer un SVM, un modèle introduit brièvement dans les capsules, nous utiliserons la libraire sklearn." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour commencer, nous allons générer des données linéairement séparables." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(-0.5, 2.2)" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# let's load a linearly separable dataset\n", "X_l,Y_l = make_classification(n_features=2, n_redundant=0, n_informative=2,\n", " random_state=1, n_clusters_per_class=1)\n", "fig = plt.figure(figsize = (10,5))\n", "xfit = np.linspace(-2, 2)\n", "plt.scatter(X_l[:, 0], X_l[:, 1], c=Y_l)\n", "\n", "for m, b, d in [(1.5, 1, 0.2), (10, 1, 2), (-1.5, 1.2, 0.2)]:\n", " yfit = m * xfit + b\n", " plt.plot(xfit, yfit, '-k')\n", " #plt.fill_between(xfit, yfit - d, yfit + d, edgecolor='none',\n", " # color='#AAAAAA', alpha=0.4)\n", "plt.xlim(-2,2)\n", "plt.ylim(-0.5,2.2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dans la figure ci-haut, nous remarquons qu'il y a plusieurs frontières de décision qui peuvent parfaitement séparer les deux classes (jaune et mauve). Il y en a en fait une infinité. \n", "\n", "Un SVM choisit la frontière de décision qui maximise la marge. C'est-à-dire la distance entre la frontière de décision et les points de chaque classe les plus proches. \n", "\n", "Pour pouvoir visualiser ce concept, nous allons maintenant entraîner un modèle SVM." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "SVC(C=10000000000.0, break_ties=False, cache_size=200, class_weight=None,\n", " coef0=0.0, decision_function_shape='ovr', degree=3, gamma='scale',\n", " kernel='linear', max_iter=-1, probability=False, random_state=None,\n", " shrinking=True, tol=0.001, verbose=False)" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# on commence par ajouter le classificateur SVM\n", "from sklearn.svm import SVC \n", "model = SVC(kernel='linear', C=1E10)\n", "\n", "# Avec la fonction fit(), on entraîne le modèle (on apprend ses paramètres)\n", "model.fit(X_l, Y_l)" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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Jv32YsvXlTofXqmiSpZRKveCx4OoAeAmFDQG/AAHwH4B4d3c6uqyjBV/TIxQK6e8Y+OA/nxKuqr8AwO11M/vNrxyIqPXSJEsplXIiAaT4BUxwLJFYLv5gJ8i7FGl/n9OhZSUt+Go/y7KIRqPakwW43C5ooFaY26Npxdb0t6GUsoW42hMLXA055xHsdB+uvAsR8TodVlbSIpn203lvWxzx64PxBeon9FbcYr+RezsQUeulE9+VUrbx+XzccMMNToeR9XSukP0CgYC25Rq7D+3LyVcdxwt/fxWMweVyYYzh2qcuJ7cgx+nwWhVNspRSthERPB59mbGbJln207Zc13m3jOGosw9m5mtz8Ad9DD9pKO1KtIbYtrTFKKVss2HDBmbOnMmQIUMoLi52OpysFQ6HdUK2zdatW8fs2bMZOnQoRUVFTofTKnTt05mTLj/W6TDqmfXGlzwz4UVW/7iO/gfsyjk3n06P3bo6EovOyVJK2aY2yaqqqnI6lKyme+rZr7YtV1dXOx2K2o43H/sft5z6NxZMX8y6lev5+MUZXDrkGpYvWulIPJpkKaVso5OF00OHC+2nbbn1i8fi/OsPkwlXRTYfM5YhVBnm8RufdSQmTbKUUrbRN6b00CTLftqWW7/1qzYQDcfqHTfGsGD6Ygci0iRLKWUjfWNKD02y7KdtufXLL8rDWFbScx26OjOPTpMspZRtYrEYLpdL35hsZFkWkUhEJ77bLBaL4Xa78Xq11ltrFcwLctgZB+EL1q3h5c/xc8b1JzsSk64uVErZ5qCDDmL48OFaJNNG2sOSHgcffDAjRozQttzKXXb/+ViWxfvPforb7cLldvGbCWMZduIQR+LRJEspZSt9U7KXJlnpo2259fP5vVz96Hh++4/z2LS2jA7di/H6nOt91CRLKWWbzz77jHA4zCGHHOJ0KFlLk6z0mD59OtFolIMPPtjpUFQj5BbktIrq8zonSyllm6VLl7J06VKnw8hqmmSlx7fffst3333ndBgqw+wwyRKRR0VkjYh83cD5Q0Rkk4h8VfN101bnjhGRxSKyVESuSWXgSqnWT1e92a82ydKJ7/YKhUL6O1ZN1pierMeBY3bwmI+NMXvVfN0CICJu4H5gJNAfGCsi/VsSrFIqs+h2L/YLhUKA9mTZTT8wqObYYZJljPkI2NCMaw8BlhpjlhljIsCzwAnNuI5SKkPpdi/20+HC9NAkSzVHquZkHSAic0XkDREZUHOsK7Biq8esrDmmlGojfD4fOTnOTz7NZppkpYe2ZdUcqVhdOAfY2RhTISKjgKlAXyDZWlfT0EVE5ELgQoAePXqkICyllNMuu+wyp0PIeuFwGBHRIpk2u/zyy50OIe2+nbOML96eS05BDiNO3Z/2Hdo5HVLGaXGSZYwp2+r/XxeRB0SkhETPVfetHtoNWLWd60wCJgEMHjy4wWRMKaXUFrXDWFrDSaWKMYa/n/8gH/xnOrFwFI/Pw6Q/TubPL/yB/Y7Z2+nwMkqLhwtFZCep+esWkSE111wPzAb6ikgvEfEBY4BpLb2fUiozVFRU8Mwzz/DDDz84HUpW01Vv9isrK+OZZ55h+fLlToeSFrNen8OHz00nXBUmHrcIV0cIV0W49fS7iYQiToeXURpTwmEK8BnQT0RWisg4EblYRC6uecgpwNciMheYCIwxCTHgUuAtYBHwnDFmgT0/hlJqe0xkNtbGS7DWnYRV/g+M1Zy1LE1TWVnJkiVLqKqqsv1ebZlOyLZfbVuurq52OpS0ePuJDwhVhusdFxHmfqBv402xw+FCY8zYHZy/D7ivgXOvA683LzSlVCpYVc9B2W1AYqk/sSWY6ueh5FXEZd/O9DohOz00ybKftuUtjE7maRKt+K5UFjMmDOV3sDnBAiAC1iZM5aO23lvfmNJDkyz7tbW2fMRZBxPIrf+zGssw6BAtd9kUmmQplc1i35J8oW8Ewh/Yeuu29sbkFE2y7NfW2vL+x+3LiFMOwJ/jx+V24Qv68Of4uP7ZK/EH28bvIFV0g2ilspmrEEy0gXMl9t7a5aKoqEgnZdtMC77az+VyUVhY2Gbasohw9WPjOX78MXz+1lfkFuRw8OkHUthRSzg0lSZZSmUxcXfFeAdCdC4Q2+pMEMn9ja337t+/P/3769CC3bQny34DBw5k4MCBToeRdv0G70K/wbs4HUZG0+FCpbKcFN4P3oFAACQv8d/8yxH/CKdDUy0Uj8eJxWJtpodFqUyjPVlKZTlxFSHFz2Fiy8FaB55+iCvP9vtOnz6dH3/8kTFjxth+r7aqrc0Vcsqnn37KTz/9xGmnndbgY6KRKE/d+gKvTXqXcGWYfY7ck4v/fg6de3dKY6SqtdEkS6k2Qjw7Aztv9zHGRAEXIu4W32/NmjX8/PPPLb6OapgmWemxevXqHbblW0+7mznvzCNcnSjWOePVz5n/8SIe++Ze2pUUpCNM1QrpcKFSChP7Dmv9GZjVe2BW74m18XcYq7RF19S5QvYLhRKlOfT3bK8dteWVS1bxxVYJFoBlGcJVYV596O10hKhaKe3JUqqNM1YpZv3pYMpJ7OFuQfg9zIZlUPxqs/fE0+1e7Ffbk6W/Z3vtqC1/P/9HPF43kW0KwkdCUb6ZtbTF949Gorz75Ee8/+ynBPMCHHfRkbqHYIbQJEupNs5UvQQmQiLBqhWF+EqIfg6+/Zp13XA4TG5ubkpiVMnpcGF6hMNh2rVruHxB176dicesese9Pg+99+jRonvHY3GuPuxmvpv7w+atbua8O48TLxvJuNvPbNG1lf10uFCpNDCx5ZiqFzChdzGmlW2wGv+WuhXhaxgDse+3+1RjIpjQ25iqZzGxup/Yi4qK6NixYwoDVdvSJCs9iouL6dChQ4Pne++5M3336YXXX7ffwuP3MPqSo1t0709emlknwQIIVYZ56R+vsXbl+hZdW9lPe7KUspExBlN2M1S/CLhAXIAPiiYj3n5Oh5fgGUhii9Ekm996Go7RRJdgNpwFRMDEE8cCI5F2dyDi4pRTTrElXLWFJlnpceqpp+7wMRNeu45/XvoIHz43nXjMos/evbjyXxfRoVtxi+4947Uvkm7W7Pa4mfvBAo74tZZiac00yXKIscpBvIjoXIqsFn4Lql8Gal4kDUAlZuNF0OH9Zs93SiUJnoCpvB+sCBCvOeoD7+7g3TPpc4wxmNJLwGyseyL8JoSGQfB4W2NWCTrxvfXIyQ/ypycu4w///i3xWBxfwJeS67brUIDb46o3HCkuIb9Qh+NbOx0uTDMT/Rpr3WjMmqGY1ftibbwEY23c8RNVRjJVz5K0h8iUQmxR2uNJRlx5SPFL4D8aJAhSADljkcJHNyeBJjwDa/2pWKv3wVp3Aqb6mUTNrW2ZakzVFOLxOA888ABffvllmn+atiUcDuNyufB49POyXaLRKA888ABz585t1OPdHnfKEiyAkeMOx+Ot/+/r8XnY96hBKbuPsof+ZaaRia9ODK+Yyi0Hwx9iNpwLxVNbRa+GSjGTZK4TAC4w9YcAnCLunZDCfyQ9Z8KfYjZewuZ5W7FFUHYHyTeeBkyEcDjMmjVriERa2fyzLBMOhwkEAvraYSOn2/LOu3fjqkcu5p4L/4XL7cYYi5z8HCa8dm3S5Eu1LvovlEam6j9JNuuNQXx5Ym85316OxKVsFDgOoouo35slNVvdtH6m/C7qT4yPkDzJCkBwtM4VShOtRWa/1tCWDxt7EMNOHMKC6UsI5PrZbUgfXC4diMoE+q+UTrGlJN6ctiWJ5fIq60jOaeDtB5JTc8QLBJB2/4eI18nQGi/2XQMnDBAAaoZGJAe8/ZCcsa3ijakt0CTLfq2lLfuDfvY5fA/677+rJlgZRHuy0sm3D4Q/oF6vgImDdzcnIlI2E/FB0TOJ4p7hj8FVggRPRjzdnQ6t8dwdIf5T/ePSDoqnQegliK9B/AeC/3BEPK3mjSnbaZJlP11coFpCk6w0kuDJmMpJYEXZsoorAP4DEU8fJ0NTTWSMBUQR2fELr4gHAkcjgZbVy3FM7mVQdjN1hzyDkHsxLk9nyBtf7yler5fevXuTn5+ftjDbolAotN0imarlfD4fvXv3Ji/P/k3VVfbRJCuNxJUPxS9jyv8O4fdBApBzOpJ7odOhqUYyJoYpvxeqnwQTwri7IPk3IoFDnQ7NNq6ck7BMJVRMBFMN4oPcC5Hc3zT4nC5dunD22WenMcq2SXuy7NetWzdty6rZNMlKM3F3Qtr/1ekwVDOZ8tuh6gU2D/nGV2JKL4eiRxHfYEdjs5Mr9yxMzhlgykDyE71zynGaZCnVuunsOaUayVgVUPU89VfahTAV9zsRUsoZqxQT/RpjldY7J+JGXIWNSrBmzpzJvffeSywWsyNMVUOTLPt99tln3HvvvVhW/b0JldqRHb5aisijwHHAGmNMvTXnInIm8KeabyuAS4wxc2vO/QCUk5iAFDPGZO9HfZX9rLUg7rr7KNeKLUt7OKlkTLxm+5+XQbxgopjgr5CCPyPibvL1Kioq2LRpE25305+rGicWixGPxzXJsllFRQXl5eW6ok81S2P6/B8H7gMmN3D+e+BgY8xGERkJTAKGbnX+UGNMktLQSmUYd+fEpsn1CHgHpD2cVDKVD0D1VCC8pUhq9VSMqwTJ/12Tr1fbw6JFMu1Tu4IzENCtuewUCoWyPpGNx+K8/sh7vPXY+xhjOPrcQxl1QfJK86ppdvgbNMZ8JCI9t3N++lbfzgC6tTwspVofkQAm73yoeIS6K+38SN6lToWVGpWTSTYMStVkaGaSpW/+9tLSAumR7W3ZGMONJ9zFvA8XEq5KJO7LF67g06mzuPOtG/SDUguluv9zHPDGVt8b4G0R+UJE2sQSOhP5Eqv091gbzsOqfAbT4LYqKhNJ7qWQ/ydwdQEC4N0HKXoS8fZ3OrSWMeVNO74DbeHTv9O0Fll6ZPu8twWffsP8j7YkWADhqggLZyxh7gcLHIwsO6SsL1BEDiWRZA3f6vAwY8wqEekIvCMi3xhjPmrg+RcCFwL06NEjVWGllVX5FJT/FQgDBiJzMNVToPh5RLLzk5CxNiaW9bs6t4lPPCKC5J4BuWc4HUpqeXaHWJIXVM/uzbpct27d6NChQwuDUtujSVZ6dOvWjXg8vuMHZqj5H39DJLTtdm8Qqgwx/+NF7HVoZmz/1VqlJMkSkT2BR4CRxpj1tceNMatq/rtGRF4GhgBJkyxjzCQS87kYPHhwsokvrZqxKqD8LhIJVq1qiC3HVL2I5J7pVGi2MNYGTOnvITILcIOrHbS7A/EP3+FzVesjBTclNionDFgkOrl9SMFNzbreQQcdlLrgVFKaZKXHwQcf7HQItirs1A5fwEuosu6G9YGgn8JO7R2KKnu0eLhQRHoALwFnGWOWbHU8V0Tya/8fOAr4uqX3a7WiXyVWZdUTgtBbaQ/HbmbDOIjMBKJACKzVmI3jMQ3uc6daM/HtjRQ/D4GR4N4FAscgxc8jvn2cDk01QCe+q1Q46JT9cbnrpwLiFg45/UAHIsouO0yyRGQK8BnQT0RWisg4EblYRC6uechNQDHwgIh8JSKf1xzvBHwiInOBWcBrxpg3bfgZWgfJJ9EDUO8EuArTHY2tTHQhxJcB29ZAimAqn3IiJJUC4t0VV/t7cHV4A1f7fyDefs2+1j333MM777yTwujUtnTie3rcfffdvPfee06HYZvcghz++s5NdOheTCDXTyDPT0nXIu5860by2uc6HV7Ga8zqwrE7OH8+cH6S48uAQc0PLcN49wRXEcSrqVtIKYDk/tqpqOwR/wVIVv8oDvHl6Y5GtUIVFRVtYo6ek3S40H7GGMrLy9Pelr//+keevOV5lnz+HV377MSZN5zCniNSs7jGGMOP3/xEdXk1u+zVE6/PS7/9+vD0Dw/yw4IVYAw9B/ZARChdu4n5Hy0it10Ogw4ZgNujde+aSotgpIiIQOGjmA3ngSkFBEwU8q9AfPs5HV5qefuDiSQ54Qff0CTHVVtSWyTT5/M5HUpWC4fDeDweLfhqo2g0ijEmrW156Zffc+WIGwlXRzCWYfUPa1kwfTHXPnU5w04c0qJrr/ruF248/k5WL1+H2+1CXMJVD1/MiFMOQEToNXDLorNn73qZJ2yfchcAACAASURBVG9+PlErS8Af9HHX2zfSa4+dW/ojYoxh3kcLWTh9CYU7tWfEKfuTkx9s8XVbI02yUkg8PaHD/yA6F8wm8O6NuAqcDivlxL0TJngSVL/ClnpRHnAVIDljnAxNtQI6Vyg9sr20QGvgRFt++E9P1puEHq6KcP/lj3LgCfs1u1fNsiyuPvxm1q5cj7G2jLb89dz72Ll/N3bu3x2AWDTGxy/N5KlbXyASim5eeVhVVs21IyfwzI8PNVj9Ph6PU7qmjPzCXHyB5IlpNBLl+mPvYNHMb4lUR/AHfTx01eP87f2/0GevXs362Voz3ScgxUQE8e2F+A/OygSrlhT8BfKvB09fcO0EwdOQ4qmIq53ToSmH6TBWemiSZT8n2vI3s5YmPb7xl1IqN1U1+7rzP15E+caKOgkWQDQc49WH3gbgv5Pe4ZSO47jz1xMJV9Ufragqr2bh9MVJr//WE+9z2k4XcPYu4/lV8Xn887JHiEXr71366oNvs/CzxYQqQlhxi+qKEJWbqrj11L9jku6okdm0J0s1i4gLyT0Nck9zOhTVyng8Hvbdd1+tk2WzUCikvYU283q97LvvvpSUlKTtnoUd21FVVl3vuNvrJpDb/GSvdE1Z0l4wK26x7qcNfPbq5zx01RN1ipJuS0SoKq9fYHvWG1/yz/GP1EnM3nr0fayYxeUP1q1D/uaj/0uawK3/eSM/Lf2Fbn07N+XHavW0J0splVIFBQWMHj2aLl26OB1KVtOeLPu1a9eO0aNH07lz+t74x157EoGcuv+u/qCPYy84okV7CQ4Y1o9YpH7PUiDXz9BR+/D0bS9uN8ECiEXjDBhWf9XxU7c8Xy9xCldHePuJD6murJuUbduTtoU0sDdsZtMkS2UtY6ox8VUYU/+FRdnHsqys7PZvbTTJsp8Tbfmocw9hzLW/IpDrJ5gfwBvwctiZB3HBX89q0XVLuhRx/Phj6vSG+YI+OvXsyGFnDGftyvUNPldcgj/o47f/OJfcgpx651f/uC7p81wuYdPass3fR8JRKjZVJn1sYad2dM2yXizQ4UKVhYyJYspug+qXAAHxYfKvxpVzutOhtQnz589n6tSp/O53v6OwMLtqxLUmmmTZb+7cuUybNo0rrriCdu3SM99URDjz+pM55arjWPPjOop2ak9uu5bXqzLGcMFdv2bAgf145b43qSyr4pDTDmT0JUfhD/rZfWhfpr8yu15S6fa6OfrcQxh98dH02Tv5xPR+++3CjFc/r9cR5fa6KelatPn796d8woafS5Ne45DTD8zKsi+aZKmMYky8ZvVmGHx7J90T0pRNgOqX2bzFkQlB2QSMqxgJHJHegNugcDic9mXvbZEmWfZzsi37g3669+va4uusWPwTE8c/wrwPF+LxeTj8zIO4eeof65VMOO+2MXzx7jzCleHNiZY/x88l95zDsRccud17nHfrGL58bz7hqvDmRMuf4+e828bUGeL8+MUZWPFkRbvh3ac+Ytzt2bX9HOhwocogJroAs3YEZuM4TOl4zJr9sarrbiJgTDVUvwhsOzkzhKm4P22xtmW6utB+xhhNstIg06vqb1pXxu8OvJ657y/AiltEqiO8++RHXDdyQr3H7ty/O/fNuJ1hJw6hqHMhuw3pw/VTrthhggXQa4+d+ccnt7HfMXvTriSf3oN25k9PXMoJ40fWeVxuu/pDjbUqS5u/crI1054slRGMiSQ2MDab6p7Y9EeMd3fEU1Mgz9oENNDlbP1sZ4iqRigUwuPx4PHoy4tdotEolmXp6kKbhcNhfD5fg3WhWrs3HnmPSChaZwgwGo7y3dwfWPLFd+y67y51Hr9z/+78+cU/NOteuwzqyYTXrtvuY371u1H875lPkp4bcGDzt/FqzTKz5SjbGKscY1U4HUZ94Q+pv1ciQAxT/eKWb10lIMk+dQp42s4uT06qfWNS9qntLdTfs70yvS0v/fJ7ItX1yyWICCu+WZX2eHYb0peR5x9W77gv6GXcndk3VAiaZKkaJvY91vpTMGuGYtYMwVp/Bia2wumwtrA2UXdPyFoxsLasihHxQP7VwNbzDQQkgORfaXOQCqB3794MHarbK9lJq+qnxy677MKQIS3bysZJffftjS9YP0m0LEOP3Vs+36s5rpp0Cbe+eg299tyZwk7tGH7SEO6fdVdWVnsHHS5UgLGqMOvH1Oy5WJPIROdgNoyBDu8j0go+yfmGgonXPy45iP/QOodcOadhXCWJOVjWKvAOQvKuQLy7pSnYtq1//9RsZKsapvPe0mPAgAFOh9AiI8cdzn/++grRcHRzfSqv38uu+/am7z69HYtr/2P3Zf9j93Xs/umkPVkKQm8kVuvV6SmywFRB6F2noqpDPN0h5wzq9lAFwTMQtkmyACRwGK6SF3F1/AxX4UOaYKVRdXU1sZjWJrOTJlnpkeltuaA4n3/OuJ19jxyE25OoGH/Mbw5jwuvbnzvVmmxaV8b0V2Yz76OFWFbylYmtmfZkKUx8BZBkZYcJQ/yn9MZiwhD+AKyN4BuKeLZ0IUv+NeA/AFP1HzDVSGA0BI9HxJ3WGNX2PfHEE7Rv354xY3SzcLtk+qq3TPHYY49RUlLCaae1fPuwsvXlvP7IeyyevZTee+7MsRceQdFO9teR69qnM3e8cb3t97HDlDtf5qlbnsfj82CMIbddDne9fRM9dnNmqLM5NMlSiLc/RnLBbFOJV3zgTd/Qj4kuxGw4B4jVDA0aTPBXSMHNiY23RcB/COI/JG0xNZcx1ZjKx6H6FRAPBE9Fcs5AxOt0aLYLhUL65m8znZOVHqlqyz8vW82lQ68hVBUhUh1h1utzeOHuV/nHJ7fRa2CPFESafb56/2uevu1FIqEokVAUgFBFiOtGTuDJZfdnTOFSHS5U4D8M3F2ArRMAH7h7ge+AtIRgjIXZeFGiRIOpJFHnKgyhaRB+Oy0xpIoxccz6X0PFAxBfBrElUP53zMbftontZrR+k/10uDA9UtWWH7zycSo2Vm5e6RcJRakqq+beiye1+NrZatoDb9XbS9GYRI/g4tlLHYqq6TTJUoh4kKJnE3OeXMXg6gC5ZyNFTyGSpiYSWwAmSekIU4WpejY9MaRK+AOIf8fmivMAhCAyC6LzHAoqPbRIZnpokmU/YwyRSCQlv+Mv3p2HlWRj5IUzlhCPJVnQYxNjDD8sWMHCzxYTCdUv7dCalG9MXkpIXEJVWXWao2k+HS5UAIgrHym4HgocGrs3ERosImq2vzN8a2MinycWDdQTh+iX4Mveel2xWAzLsvTN32bhcBiv15uxRTIzQSQSwRiTkiFZn9+btF6V2+NGXOkZ9vr5+9XccNwdrFm+DpfHhTGG3z1wAUecOSIt92+qESfvz6IZ39brzYrHLHbfv69DUTWd/oWq1sG7B8mTrCAEjk93NC3j3glI8sIsXnB1THs46XbEEUfQs2dPp8PIatpbaK+lX37PbaffzWcPz2PKTdNaPDx19G8OxReoOx/T6/dw6JhhaUmUjTH86chbWbl4FaGqMFVl1VSXh/jHRf9i6Zff235/gFBVmI2rSxs9ZeKocw+he78uBHIT7dzlEvw5Pn77j3MJ5gV38OzWQ5Ms1SqI+JB2fyORnNS8GEkOeAcgOSc5GVqTSfB4qLfiUQAfBA53IqS08Xq9DB8+nG7dujkdSlYLh8M66d0mC6Yv5oqDbmDmq19i/ezmm/8t5feH/pk5781v9jXPu3UMexy0O/4cH8H8IIFcP3336c34ib9JYeQNWzRjCaVrN9UbsoyGorxy/5sNPCs1qitD3HnWRE4qPpcze/6WM3pczIz/frHD5/mDfu799DbGTxzH/sfty1HnHcrfP7iFUecfYWu8qabDhaoeYywIvYKpmgImBIFjkdyzEbH304MEDoUOb2CqXgJrHeIfkVhNmGklGqILE4sGYotI1B7zgLsHUjgRSbrlT/aIRqNUVFSQn5+vexfaSFdw2ufBKx8jXBXBMhZxYniMl3BVhAeueJRH5t/TrGv6g37ufOtGvp+/nB8WrKTbrp3TWgy0dG1Z0tV4lmXY8PNGW+99+9h/MOfdeUTDiXpj637awG1j7uHuD2+ut3fitnwBH8ecdyjHnFe/FmKmaFRPlog8KiJrROTrBs6LiEwUkaUiMk9E9tnq3Dki8m3N1zmpClzZx5Rdhyn7C0S/gtg3UHEfZv0YjLF/oqS4u+LKvwxXu5uRwOEZl2BZlU9hNl4Csa+BOIktfXxI4STE08fp8Gy3YsUK7r33Xn76Kb311doaHS60z9KvfgAgRBU/8i1hEpOsly9Y2eJimL322JlDxwxLe7X1/gfsSixSv6iqP8fPUBsrr69duZ4v3p23uQRDrUh1hP/cNdW2+7YmjR0ufBw4ZjvnRwJ9a74uBB4EEJEi4M/AUGAI8GcRsb/6mmo2E1sG1a+B2Xr1RhhiyyGUWaUU0slE52OtGw3lt5AoP1ErDqYaU/mAU6Glla56Sw9NsuxTUJQHgEVi1Z+r5m0yt11Oxi40aN+hHaf98cTN85sAfEEfHXuUcNS5h9h237Ur1uHz168NaIzhp6W/2Hbf1qRRLcYY8xGwYTsPOQGYbBJmAO1FpDNwNPCOMWaDMWYj8A7bT9aU0yJfkLxZVGEin6bkFib+Myb0Hia6KCXXc5qJr8JsOAtiixt4RBzCM9Iak1M0yUoPTbLsc+rvj8ef48ci0Wvlwo0/x89JVxzrcGQtc85fTuOGZ69k8NGD6DekD+f85TTum3kHgRz72lH33boSDUfrHXd73QwY1ja2OkvVpImuwIqtvl9Zc6yh46q1cpWAuOpuYwiAD1ydW3RpYyxM2Y1QPS2x0s7EMZ4+SNEjiCtzOzhN1dNg6r+Q1OHO/lWFoNu9pItOfLfPyVcdx8Y1m3j83ifx4sHv8jNy3GGcecPJTofWYkOP3Tflw4PGGN6Z/CHP3jWV0jWbGHBgP8bdcSY9B3QnvzCPE383ilfue3NzKQZxCYEcP6dfnWGrxpspVUlWsrX3ZjvH619A5EISQ4306KHbDDjGPxwkWFPnaet/KheSc0qLLm2qpkD1f4HwltpXsUWY0j8iRQ+36NqOii4BtpdkBZHci9IVjaO0J8t+WvDVXi6Xiwv/ehY9DunAW6+/za0TbiWvXa7TYTXayiWrKN9YyS6DdsYX8KXsumt+XMuzd01l/keL6LxLJ8b86UT6H9CPZya8yLN3TSVUmfjbn/naF8z9YAEPfH4X3Xbtwvl3nEm3vp15/m/T2LS+nEGHDOA3E86gY48OKYutNUtVkrUS6L7V992AVTXHD9nm+AfJLmCMmQRMAhg8eHD27z3SSol4oejpxOTt+KpEr5YEkHZ/R9xdWnbxqieAbSv1xiAyHWOVI678ll3fKb69IDKDuhXeawUg//eJlZNtQJ8+fQgGg7jdmbVgIZPUFsnUJMteewzag+IOxRmTYK1ZsY6bjr+LlUtW4fa6MZbh0vvGcdTZh7T42qu++4XfDv4Toaow8Wic5QtXMOfdeVz5r4uYcufUOgVDjYFwdYSnbnuRayZfhogwctzhjBy34/I1a1as4+E/PsmsN77CH/Qy6vzDOeOGU5LO68oUqUqypgGXisizJCa5bzLG/CwibwG3bzXZ/Sjg2hTdU9lEPL2g5A2I/5DocfL0Tc0qv203oN7MVdNzlplJluSMxVQ+UTNkWLv6yA/efZCiSVlftmFrXbt2pWtXnRFgJ+0tTI9MasvGGK49ZgIrl6zCilubP8tO/O3D7Lx7N/rt17KVzY/f9CzV5dWb62wZA+GqCPdf/hhud/05vFbcYtGMJU26R0VpJeP3u4ay9eVYcYuqMnj+7v/y7Zc/MOG/mZs2NLaEwxTgM6CfiKwUkXEicrGIXFzzkNeBZcBS4GHgtwDGmA3ArcDsmq9bao6pVk5EEE8vxLtb6soo+A8haV7vKsbgxtp0M9aag7HWjsKqfDZRrysDiKsIKX4R/EeA5CbmteVekJhr1oYSLID169ezYYP+idtJk6z0yKS2vPTL71nz49pEgrWVSCjKy/98o8XXn/v+gqR7L4arwkSSTGwH6NJnpybd481H/5dI5Lb6GSLVEea+/zU/LFixnWe2bo3qyTLGjN3BeQOMb+Dco8CjTQ9NZRvJ+x0m/D5Y5SSG1jyJCfAFN8L6X4G1Hqip5VJ+Byb2NdLuNgcjrsvEV0H4k0Qi5T8UceVsPiee7kjhfQ5G1zq8+eabVFVVccEFFzgdStaqTbJ04ru9Xn/9dSKRCOPGjXM6lB0qXVuGK8kQvbEM635a3+Lrt+tYwIZfSutf38CBJ+zHjP9+UWdvRn+OjzOva9pOHQs/W0I4yf6OLo+LZfOW03NA9yTPav0ys+iHykji7oSUvA5548E3HIJjkeKpEPsBrE1sTrAAqIbql7E23YpVfg8m+k2L7m1MBBP5EhNd2Oi9s7ZmlU/ErD0aUzYBU3YDZu0wTGR2i2LKRlqJ3H66gjM9Mqkt99tvF2KR+j1K/qCP/VOwmvD0q0+sV+rB6/cy7MT9+NPkyzji1yPwBbx4/V6KOhfypycuY+Dw3Zt0j54Du+NNVlPLMnTZpVOL4neS7nuh0kpc7ZG8i4GLNx8zkRnULeBZKwrVTwGCqXwMk3chrrxLm3xPE3oPs+mPJFZLWiDtoXAS4t21cc+PzIbKf7N5YntNjmY2XgQdZyCSuhU8mS4cDpOXl+d0GFlNhwvTIxwO0759e6fDaJSConzOuP5knr3z5c2r/HyBRMIz6oKW7/V32BnDWfXdL/znrqm4vW5ikRj7HDmIqx65BJ/fy5X/uojx955HZVk17Urym1W09dgLj+TFu/9bp66Wx+eh+25dWzynzEmaZCnneXpAxEPdnqxapuYrBBX/wgRGIZ7Gb0lhYj9iSq+kThJnqjAbzoaOHydWU+7oGtUvkDwJBCLTa+aaKdAimemgSVZ6ZFpbPvP6k+mzdy+mTnyd0nVlDP/VEE68dCQ5+S3fc1ZEOOumUzn5yuNYsXgVxV0KKelSVOcxvoCvRSUjijsX8vcPbubvFzzI9/OWIyIccPxgrvzXRUn3XcwUmmQpx0nOWZiq50meZG0tDqH3IK8JSVZ1Q9cNJ+ZXNaa0ggnTQHk3SMN+jpkk096YMpEmWemRiW156Kh9GDpqnx0/sJly8oP0G7z9TZ1bos/evXjw879SXRnC43Xj9WVu6YZammRtxcRXQWQ2uNqD78BG9XKolhNPTyh8ELPpWrBKSRT2tKif2LhAmthkrbUkT7IssBq3+7wERmFCHwBVdU+YKPgOaFo8WW706NEUFmZu9f5MUDsny+fTYWo7nXDCCRQVFe34gTZbu3I9z941lbnvf02HHiWM+eOJDDpkAMYYFs38ll+Wrab3oJ4ZOzE8mWBu9izq0CSLRI0RU34XVD0N4iZRqD4ARZMRb1+nw2sTxD8MOnwI1iqMVQrrx1C/uKdA4Oh6zzXWJgi9nlid6N0PfEM2dy+LbwQm9GZNHa46TwLffo0Lzn8E+A9MDA2aKhJ/Nh4o+HOLC6ia+E8Qehcw4D8C8XRr0fWcNmDAAKdDyHq1PSyZullxpnCqLVeUVvL+lE9YvXwtnXt34pFrnqa6IkQ8Fmf5wpXM/2gRF/z117zxyHv89O3PiEuwYhZ7HTaQP7/4h6zo/ckmmmQBhP8HVVNIbPdSe7ASs/EC6PB+Ro8Hb48xcYjOSwyH+fZ2vKaTiIC7K+LuilVwA5TdxpadmQwU3Fiv6ryJzMFsHJdImggltgTy7guFDyV6IgNHQtVjEF3M5nlVEoTgKYgn8cnPWBsg+k3i3p6dk8Tlgvb3QeQzTOgdcOUjwV81aW5YMlbl01B+55afr/zvmPw/4Mo9p0XXdUo0GmXFihV06tSJ3NzMqJKdiTJxGCvTRCIRVq5cmfa2vGzecq46+CZi0TjhqjBuj5t4LF7nMeGqMA9e+TgYQzy2pabUl+/N5+nbXuTcW8akLV61Y5pkUbOnXr3tXgBTCrEF4B2Y9pjsZqILMBsvrOmZEcBgCu7EFazfU+QEV87pGP+hiQQYwH8Yss0my8ZYmNLL6laSN1UQ+RxT9RKSe3rNNkFPYaqeg9B/QXKQnDHgP6qmB/P2RIItfjARjHcvpPBBxFV3hZyIC/zDEj1uLWBMHCKzMbGlNQnWNnO6yv+G8R+KeDJv/87S0lImT57MKaecwsCB2fc301pokmW/jRs3MnnyZE477TT69++ftvvecea9VG7a0uu+bYK1+Xi0/vFIKMrTE17E5Xbx6xtPaVFPpzGGuR8s4JtZSynpWsTwk4bWK+GgGkeTLKg/lLSZC0yS5CvDGRPGbDgHTFndE5uuxnh3bzVv8OLuCDnb+VQW+6aBrXqqIfQC5J6euI74kdyzIPesOo+yKv8D1c8BkS0T2KNfYjZdixT+MzU/xFZMbDlmw1lgymu24Ek2ad6C0FuQl3nFPHVCdnpokmU/J9ry+p838tPSX1p2EQPP/d80LMvi3Jub16MVCUW45pgJfPvFMqLhCL6AjwevfIy7P7yFnftnz7yvdNFBfYDAKCDZRDsD3j3THY3tTPk99RMsAGI15QoaeF5kFlbpVVgbL8JUv4IxybdTSPpcqwoT/6lJz9nhNeOra1b+JdOIId6qR5Mk0REI/w9jVbQ0vDqMMYm6WtbqmsSwoVWJtSUrUs9YVVgVD2CtHYm17kSsyv8ketZSRJOs9NAky35OtGWX20Vj/va9fi85BQ2XZQhXhXnpnteIRXe0Wju5l/7xGktmLyVUGSIes6iuCFG+oYLbxtzT5GutWbGOx296lglj7+HVh96murKBUjhZTJMsQHJOBe+uQO02KR4gAAW3Oz5PKdVMZA5UTW7gbAys5Ht1WRUPYDZckBhyC7+P2XQTZsNvMGb7f8jGRLA23YBZMxSzbhRmzf5Ylc+28KcAE18HpX8AkiUJQSR4aiMukizRhEQPZkObWTdT/DuI/8yOX0TdiXlkKWZMBLPhdKh4MBFLbCGU347Z9IeU3aN21Ztu92KvTKpEnqmcaMuFHdvRa2APxFX3A6K4BJdbyCkI4gt42euwgdw67RqC26l/FYvGqSpr3ijMm4+9X297G2Ng1dJfWLuy8Vv0LJi+mHH9r+C5v77CB/+ZzqSrJ3PBwKvYtK6h193spEkWNcNJRVMS++QFjoecs5GSqbiCI50OLeVM5SQarkcVRJIU1jTxNYk35zrz1qohNh/C723/fmW3QPU0EosKqhNDZeV3YELbf96OmKqnqL/6sIZ3EAR/teOL+IaT9E/AVQSujvWPt4RVWbNytSE1iX3epYinV2rvDRB6G2IrqPs7q4bQe5jotym5hfZkpUc4HNZE1mZOteXrplxBu5ICgnlb/n2NZfAGvPiCPu75+FZuf+069hzRn8e+uZcOPUqSXieY5ye3fU7Sczu0nW3HjGU1eK7uJQx3nf1PQpVhopHE+02oMsz6nzfy1C0Nj5ZkI02yaoh4keBxuNr/DVfBNS1eOdZqxVc2fM7TC/xJinNGZpJ0+p6pSqy2a4CxqqD6FepXS6/GVDzQmGgbFv2K5ENuQcg5F2lEPS3JvwKkAKitN+QCAki7W1O/otS7O8mHMH3gG4Hk/S6R2OddlNr71jCRmdSr81UrOicl9+jTpw9jx47VlYU20+FC+/Xt25exY8eSk9PMRKWZuvbpzNPLH2T3/XetGT5MCFdGKFtXzuM3bBkFKO5cyHVPX44/WLdemj/Hz3m3jcWdZMPoxjjirMQ+hNvaqVdHOvbo0KhrrF+1gfWr6o+KxCIxPnl5ZrPiylSaZLU13iEkX+/ggcLHkGS9LZIHSZMOV6Jwa0NMKQ3OjbJaOMHTsyuQrB6MQbyNm7gv7q5IyWuQex5494LACUjxc4h/RMtiS3Yv8UHBBBJz/2p/x0Hw9ETaT0TyLrY3sXfvxJZkcuvA3CnrtSsoKKBfv354PLqexi6WZRGJRDTJslm7du3o169fsxOVlvD5vSyevRQrXrfXyIpbfPHePKJbbQQ9cNhu3PHmDey+f1+CeQG69+vCH/59CcdddFSz73/qH46n9547b+5NC+T6yWufy3XPXNH4nyHgw7KS94j529gqRX01bGMk7wJMaBqYChJV1UnUjcq9AJe7gUrd/mFsSQy25tv+3CdXRxAfmG17siQxpNcCknMWpvq5mlV6W+LBOwjxNH4zUXF3QPJ/36JYGn0vT3dMzliILQKCSOBICI5Oy7w/CZ6cGCqu87onIDngH56Se/z8889UVlbSp0/mbuba2kUiid5bTbLstWrVKqqrq9llF/u2kNke09CQXZLDexy0OxOn356ye/uDfu6dPoHP35rLoplL6NC1mINPP5Dcgsb36hUU59P/gF1Z8Ok3dWp5+XN8jL449XNOWzPtyWpjxN0ZKX45MffM1RE8/ZGCCUju+IafIz6k6DGQIpDcRM8Wfii4CfH2287zPJB/NXVXbgpIEMlr/KeipNf2dEcKnwBPPxIJoA8Co5DCh1p0XTsYY2GV/hGzfixUPQnRuRCdAe7uaVtYIe6dkMKHaxLfIBAAT1+k6OmUbR81e/ZsXnnllZRcSyWn897SY+bMmUybNs2x+x908v54vHU/2LpcwqBDBqSlorvL5WLIyL055y+nM+qCI5qUYNW67pkr6Ny7E8H8AMG8AL6gj6HH7suJl42yIeLWS3uy2iDxdEfa/7Vpz/EOhI6fQOSLRF0x3371CnYm48o5HePqgKl8ILG6zrsXkndFSrYrEt8gpORVjKkGvI2ah+WI8DuJiee1c9NqVmSa0vHQ8bO07ZEpviHQ4SOILwP8myvep4rOFbKfJlnp4XRbvvCvZzH/40VsXF1KdXmIYF6AQF6Aqx6+2LGYmqq4cyGPLrqX+R8vYs2P69h18C702K2r02GlXSt9V1KtkYgH/EOb/rzAYUjgsGbfN9F1HmswGRFpeClza2CqXiT5ywDi8wAAIABJREFUpPM4RL8E35C0xSLigiYMpzZFKBTSVW820zIZ6eH0Cs6C4nz+veAepr8ym2XzltO1b2dGnLI//uCOEz9jDN/N/YE1P66j7z696dCtOA0RJyci7DkifRXzWyNNslSrZYyFqXwYKh8GU45xd4W8a3EFM21Mv6El0bLd5dKZxulP/22B9mSlRzgcdnyVrMfrYcQpBzDilAMa/ZxN68q45ujbWLlkFS63i0goSt99enPMeYdy0Cn7k1+449EHlVo6J0u1Wqbin1DxQE3RUJMoP7Hp95jwp06H1iQSPDExwbz+GfDtnfZ47KJJlv00yUqPdLbljatLeW3SO7z64FusWbGuRde689cT+f7rHwlVhqkqqyYWibFoxhL+edkjjO1+MZ+/PTclMa9csor5Hy+isqyhLelULe3JUq2SMZHEtjf1Nu4OYSrubfFGzWkVGAmhNyHyUc1KSx+IC2l/b6K0Q5Y4+eSTHVny3pZokpUep556alpKkbz3zMfcfcFDiAjGGB76/ROMu+MMTrr8uCZfq2xDOXM/WJB08+hYJE4sEueWU//G87880qhhx2RK127ixtF38v38H3F73cQicc7+y6mc/scTm3W9tkCTrFbExH/CVDwM0S/A3RPJuxDx7uF0WM6wNjY8lBZbnt5YWkjEBe0nJjafDn+KuNpB4FjE7dxcCTvstNNOToeQ9WqTLJ2TZa90tOWNq0u5+4KHiGyzhc2/r5vC4KP3bvIk8VBFCHFvf3BKRPjqf18z9Nh9mxwvwM0n/41vv/w+kcjVfP596tYX6Dmge7Ovme0aNVwoIseIyGIRWSoi1yQ5f4+IfFXztURESrc6F9/qnHNrYls5E/ses240VD8HscUQfhuz/kxM6H2nQ3OGq6jhbWg8LV+ZmG4igvj2wZV/GZJ7dtYlWMYY5syZw5o1a5wOJauFQiFEBK83PStS2yLLspgzZw5r16619T6fTp2dtMZzPBrnw+emN/l6HbqX0K44f4eP27puVVOs+XEtSz7/rl5PWagyzAt3v9qsa7YFO0yyJFEC/H5gJNAfGCsidZYLGGOuNMbsZYzZC/gn8NJWp6trzxljjk9h7FnFlP89URph876CBghhyv7ScGG6LCbihdzfAtuuHAwg+Vc6EZLajnA4zLRp0/juu++cDiWr1c4VSvm2T2qzUCjEtGnTWLZsma33icfiSTvrjWUlHfLbERHh9/++BH+OH5crefuIxyz2Pnxgk68NULa+Ao8v+eDXxtWbmnXNtqAxPVlDgKXGmGXGmAjwLHDCdh4/FpiSiuDalMgsNldg35q1Hqz6e0C1BZJ7PuRfC67OgDdROLXwYcSn3dKtjc4VSg9dXGC/dLXlA0bvm3RKhNfvZfhJTS+VA7DvkYN48Iu7OO7ioyjq3B53TUFTr8+DL+jj6sfGE/z/9u48TIryWvz49/Q2OwjDKgiiIqJRg4AhejFxx0QxiQZQb1wuXqPo9SYuMYbEqDHqLyYRjcaoBM2qJuZGiaJAIIK5rugVFQyKRGUgbAMMMDNdvZ3fH92Dw0yP9Mx0dXXXnM/z+DBdVV19KF+6zrz1vuet7lrJm2GHDs06UTocCTHhdPtO7kguY7KGAGtbva4DsrYAERkOjAAWt9pcLiLLSHfR3K6qT3QxVn8L7APJ7R3s65kL7ooIUjUNqqZ5HYrZC0uyCsOSLPcVqi0PGNafi245h4e+9yjJeBJNpQiXhznz8kkcNGZEl8+736gh/Nc9F3PFz6az8sV3eeWZ16msqeD4c/6NAfv16/J5I2VhZtx1ET+7Yjax5hiqEC4L0au2hrOvPqPL5/W7XJKsbP2OHT2/mgY8rqqt+zqHqep6ETkAWCwib6lqu2cKInIJcAnAsGG5LfDrK1UXw44fsudsujIoPw0RG+TqR5raiu64HZwFgED5JKTmOuSTFt0uUpZkFYYlWe4rZFs++6ozGH/aGJb84QWS8SQTz5rQrQSrNRHhsGNGcdgxHS991lmnXng8Q0YO5k93PsXmtfWMm/RpvnLlF+iVw1iwniqXJKsOaL3+xlBgfQfHTgP2WARPVddn/lwjIs8BY4B2SZaqPgA8ADBu3LgeNwhJKr6KJj6Epl+DhNMLH5dNRHrf5HVoxgWqcbR+CiTXs3scXvNcNPZ/0O9ppKNB/0XKKpEXRjQa9bxIpt8Vui0PHz2U878/pSCflQ+fOvYQPnXsIV6HUTJySbJeBUaKyAhgHelE6ty2B4nIKKAP8GKrbX2AJlV1RKQfcCzQuUXzeggRQXpdi1Z/HRL/hOBAJGhT4n3LWZQeb7d7ogNAHFIbwVkK5cd7FVmXDB8+nBkzZtCnTx+vQ/E1x3Ho27ev12H42ogRI0qqLTds2UE8lqB2cB+bEFGE9ppkqWpCRK4A5gNBYI6qrhCRm4FlqtpSluEc4FHdcyrcaOB+EUmRHmR/u6quzO9fwV8k0AsiR3odRlFRTYFuB6kp2GLKbtP4KtDGLDui6RIelFaSFYlEGDBggNdh+J49LnRfqbTlTWu3cNt5d/GPV1YjAWHA0Fqu+82VjP5MaZS42bYxPQa5z8DSGx7RGTkVI1XVecC8NttuaPP6xizvewHoodU0TT6kmh6DlvIWEkIrL0Kq/ytd4LOESWgEKpWZsh2td5RDKD9jMgpp7dq1rF+/nvHjxxMIlPb/m2JmSZb7Wtry0UcfXbQ9Q8lkkqs+dwOb19aTSqZnpa9bvYHrTr6Zh9+9m76DircX7sN36rjt3Lv46B91AAw7ZCjfeeQbnS6+Wirs29AULW2eBztuTfdiEUsnJI1z0MZ7vQ6t+8pPBalmz3+CQZDeUHaCV1F12Xvvvcezzz5btDclP0gmk8TjcUuyXLZq1Srmz5/vdRif6I3Fb7OjfufuBKtFMpHk2TmdL2D9v0+8wozx1zFl3//kprN+zIfv1OUr1D00N0a56rjvsebND4g7CeJOgjVvfsA3J36PaJPjymd6zZIss5uqk57xViTFT3XXz2i/dmFzOtHSzhfrKyYiZUjtHyHyb6Sfwgeh7Dik9rGSfCRqRTLdZ0vqFIbjOJSXlxd1W9700RZSyfbf07FonPXvb+jUuZ649xlu+/e7ee+1NWzbsJ3/feIV/usz1/PRP9blK9zdnn/8JWJOYo/yYKoQd+I8/6eX8v55xcCSLIOqQ6rhu+jGseimiejm49DoIq/DgtS/sm9XB7Rt8lV6JDiYQN/ZyMC3kYFvE+hzPxIc6HVYXWKPsdxnZTIKoxTa8qjxB2UtZFpeVc7hE0fnfJ54LM5DMx/BadWLpKpEmxx+9f3H8hJra5s+2kK0Mdpue7TJYdNHW/L+ecXAkiyDNlwPzU8CMVpmuOn2b6bLCXgpdHD27YHeIP6Zxi4SLLmSDW2Vwo2p1FmSVRil0JYPOGI4R518BGWVkd3bwpEQfQftw+enHpPzedI9Yu1XGtGU8s5L7+Yl1tZGjT+Qiqr2PbHllWXpxNGHLMnq4TS1FaILgLbPw6Porvu8CGk3qfkW0PYfZDlUf6uou/J7olK4MZU6S7IKo1Ta8g1/vJrzb5zKvgcNov/QWs6YcSr3vHIbZRW5x77PgN4dLhg9YFjXq8N3ZOwpRzJs9BAi5R8PiYiUhxl+6FCOOsmfc+Ryml1ofCy5ASQCGsuy78PCx9OKRMZB34fQnT+GxLsQHIJUX4mUn+RpXKa9KVOmkEgk9n6g6TJLsgpj6tSpJJPFP+YzFA4x5ZrJTLlmcpfPUdWrks9PPYYlf3yRWPPH94CyygjnzTwrH2HuIRAIcMfiG3nsR0/y118vAYGTz/8cU7/1Jd/OSrYkq6cLDgfNdnMMQPjTBQ+nLYmMRWptvfFiZ4Ox3ddSidySLHdVVHRtAeVS9Y37v04wFGTx759HAkKkPMIld3yN8ZPGuPJ5FVXlXHjTVC68aaor5y82lmT1cBKoQqumQ+McPp7JJyAVSPVlXoa2B001oc1PQOwFCO6LVJ6LhPbf85jkBoi9DNILyo5FJJL9ZCbvnn/+eQYPHsxBB/lzXEUxsNmFhbF06VKGDBnCgQce6HUo3bZreyPPzlnMyhffZdihQzn9kpPoN6R2j2MiZWGunn0ZM2ZdyM6tu6jdty/BkLdjRJt3NfObmx9n0e+eB+DE8ybytRvOpqK69BJgS7IMUn0lGhwCjQ9AaitExiLV17RLYryiqQa0/ixIbiadCIbQpkehz71I2UQAUjtnQeMvQUKk1zQPQd+HkfChuX+O8zy641ZI/hMCtVB1GVJ5Xk7jv1QdQAu2mLemdoCzBEilSz8EvC0+uHTpUsaPH29JlovscWFhLFmyhM9+9rMln2RtWVfPjHHX0bSzGacpRvipEP8z6ynuWHQjo8a1/7tVVFcURRKTTCb55nE38NE764g7cQCe+Nkz/N+it7j31dtL7rFiaUVrXCEiBCrPJtB/AYGBy9KlBMLFszSDNs5Ojx3b3dOWAKJow3WoplDnf6HxIcBJL1Wju0C3o9suzrmeljovo9suh+T7QApSm2HnHWjjg5/8vuQGUlunoxvHoBvHkKo/N73Qt4tSzc+im/4N3XED2vB9dNNxpJr+x9XP/CRWJLMwHMchEAgQCtnvxm5JJBIkk0lftOUHv/07GrbsxGlKj7WKOwmad0b5yfSfexzZJ1s2fznrV2/YnWBBuo7Wuvf+xbL5yz2MrGssyTLFL7qAdHmJNrQJkv9Emx6jfdFS0rW04q/n9BG666dA2/otzdD4C1Tj2d6Cahytn5Z+hEkCSEL8dbR+CprKsi5hHmhyCzRcm45VG4EmwIEd30eT+S8emItYLP3/xg83pmJmBV/d56fewlfmvZ61PMNH76yjscGd76d8eO+1NUQb21d/jzY6vPf6Gg8i6h5Lskzxk8rs2zWZ3pdtoeX0G9MLLuci0cE/Xo1Danv2fc4S0AagdW9ZKl0sNfp0bp/bWc4C0o9D20pB9Bl3PnMv/HRjKmbRaNSuscv81JY7KuUgASEUKd7e0IH796e8qn3s5VVlDBze34OIuseSLFP0pPJrIG3HCgQhNAoJDkYqvghkGUugSQiPze1DOlqUWUIQ6GCV+ORH2Utf0OTeI0N1gGx1bZJoypsq+DYguzBalnsx7vFTW/7i10+irGLPyT+hcJCjTxvTqVpahTbxrAlEKiJI4ONfJiUglFVEmHjWZzyMrGssyTLFr+LLUH4mEElXepdKCA5F+vwsvb/8DAh/qlWPVxAoh143IYEOesHakOpv0r7waQVUXdLxWoKhQyDbPqlCwrkvbdEpZZ8ne09WBCk/0Z3P3IsBAwYwc+ZMDj64gwr9Ji8cxyESsRmzbho0aBAzZ870xQSOadd9KV0VviJCRU0F5dXlDD9sP66eXTyzxrMpryxj1t9v4ZDxBxEKBwmFgxwy/iDu/PstRZ0cdkSKZTHg1saNG6fLli3zOgxTZDS5DmLLITgAwmP3GJuimgBnERr9KwT6IJVTkFDnvig1+jd0522Q/ACkL1RfilRe0OEYGNUUWv8VSKzm4zFjYQgOQvo941oJidTOO6HxYdJV+hUoh8qzCfT6niufZ4rD/fffT01NDeeee67XofjW+8s/4N4r57DyxXepqC7n9EtP4YKbphAKF+/jtb358J061iz/kMEHDGDU+IPyMqavcUcTjQ1N9BvS19XZfju37QKgpk+1a5+RLyLymqqOa7fdkixj9qSqOX8RaWoXumsWNM8FUlA+Cam52vWSChpbjjY/CaSQitPbJZ2FVFdXx9tvv81xxx1HZWVuPYem8+6++26GDBnCWWflvxK3gX/9cyPnH34ZWxo304f+BCVIWUWEz545npm//0bh41mzkYW/WULj9kY+c/o4xpzwKc8nPTTtbOaOi+7l5adfQwIBqntX8t+/uIRjJo/3NK5i0FGSVbrpuTEu6cwXmQSqkV7fhV7fdTGiLJ8bORKJHFnQz+zIhg0beOmllzj22GO9DsXXbOC7u/5051PsdHbSQD19SK/b5zTHeOGJV9hcV0//obV7OUP+LH7keX5y8S9IJZIk4knmzV7M2FOO4IY/Xu1pnaibz/4xby5dSdxJrxKytTnGrefexU+X3MTBY0u7rphbbEyWMaZbbLmXwrCB7+5677U1JBLpci3S6tYYLguzdtX6gsXRtLOZn/7nL4g1x0jE0zOXo41RXluwnBeefLVgcbS14YNNvPX8O7sTrBax5hh/+PFcj6IqfpZkGWO6paVIZjjcwQQB021+KpJZrA789P4QTCdYAfn41hh34gwdOahgcSx/bkXWZW2ijQ6LH/l7weJoa/PaesJl7R9+qSrrV2/wIKLSYEmWMaZbrEim+/xUv6lYnX3VGQQiQqDVbTFSEeEzXzyKAcMKV58pFO543cBwxLtfZPb/1H7E2vRiAYQiIY44Lvfly3oaS7KMMd2STCbtMZbLLMly374HDuKCm6cyePhARITyqnLOuPQUvv3b/y5oHEcen32Ae3lVGZP+4/iCxtJaTZ9qvvLfX9yjUGggGKCiqpyzrzrds7iKnQ18N8Z0yxlnnEExzlL2Ez8VySxml19zKTOu/jrQuQkw+RQpC3PTE9/ie2fcDkAymQJVJs84lTEnHO5JTC2m33ou+43alz/+5C/srN/JmJOO4MKbp9JvSOEmBZSanJIsEZkE3EW6yuNsVb29zf4LgTuAlsXT7lHV2Zl9FwAtU69uUdVf5SFuY0wRsUeF7rKerMIphrZ85OcO49F1D/Di3GU07Whi7ClHsu+BhRsX1hER4dQLj+fUC73rUSs1e02yRCQI3AucDNQBr4rIXFVd2ebQx1T1ijbv7Qt8HxhHumria5n3bstL9MYYzy1atIiamhqOPvpor0PxLZvBWRgLFy5kn332Yfx47+s+VdZUcOJ5E70Ow3RTLmOyjgZWq+oaVY0BjwJn5nj+U4GFqro1k1gtBCZ1LVRjTDFasWIFa9eu9ToMX7OerMJYsWIFdXV1XodhfCSXJGsI0PobtC6zra2zRORNEXlcRPbr5HuNMSWqZXahcY8lWYVhbdnkWy5JVrYH1G1Huf4F2F9VjwD+CrSMu8rlvekDRS4RkWUismzz5s05hGWMO1TjpHbeSWrjWFIbDiFVPwWNv+11WEVJk5uJNr1PJLTL61B8zZIs96mqJVkm73JJsuqA/Vq9HgrsUf5WVetV1cm8fBAYm+t7W53jAVUdp6rj+vcvXE0SY9rShu9A40OgO4EUxN9At/47mvjA69CKhmqSVMN3iP/r8yR2Pkmk+XpS2y7n468Bk0+O4xAKhQiFbEK4W+LxOKlUymZwmrzKJcl6FRgpIiNEJAJMA/aooS8ig1u9nAy8k/l5PnCKiPQRkT7AKZltxhQlTW6C6LNAtM0OB22c7UlMxUgbH4Tmp4jHHaqrElRWJMFZiu64zevQfMnWLXRfPB6nurqaiooKr0MxPrLXX4tUNSEiV5BOjoLAHFVdISI3A8tUdS5wpYhMBhLAVuDCzHu3isgPSCdqADer6lYX/h6dpqpFMVXXFJnkhyBhaNcjk4R42wm1PVjTr4EoFRUBrr6sT2ajA81/QnvdgIjVOc4ne4zlvqqqKq655hqvw8hKVXll3us8df9CmhujnHDORE4+/zhPK8Cb3OTU96yq84B5bbbd0Orn64HrO3jvHGBON2LMK42vQHfcBPHlqFRAxRSk5hrSnXSmxwsOB41l2wHh0QUPp2ilOhqDFc/8ZwlBPlmS1bM9eN1v+ct984k2pn/5W/Xyahb86jl+8rcbs65zaIpHj/p1UxNr0a3nQfwNQEGboOlRdPtVXodmioQEB0D5qUCbcRkSQaou9iSmohRJD7vcsCnBI3/eyeYtmTXNQgciYslAvlmS5b7169fzyCOPUF9f73Uoe9j44WaevOeZ3QkWQLTJ4f03PuCFJ1/9hHeaYtCzkqzGh7P0UkTBWYIm12V7i+mBpPftUHk+SDUgEDoc6fsbJDTC69CKhtR8B6SKhh0B3n0/RjwRACqQXjd7HZovWZLlvoaGBlatWkU8Hvc6lD28uWQlwVD7W3W0McpLT73mQUSmM3pUkkViJelhY21IBGzmmMkQCRPodQ2Bga8jA/9BoN+fkPARXodVVCQ8Eqn9C1FOhcBAyvc5A+n3JyQydu9vNp0WjUZt1pvLWqrqF9t1rulbnXWMYzAUZJ8BvTyIyHRGz5oPHD4M4m+SHjPSijpgvRQmC5sc0TEJDSUeuQCp7E9F/2uRUJXXIfmW9WS5r1hrkY095QhCZSHYuef2UDjIadNP9CYok7Me1ZMllReme632UA5lJyDBfb0IyZiSVqw3Jj+xIpmFUaxtORwJ86OFN1C7b18qasqp7FVBRXU51z50OUMPtvtWsetRPVkSGgp9f4/uuAXir4NUQsU5SM2VXodmTEkKh8PU1tZakUwXJRIJUqlU0d38/SYcDtO/f38CgeLrezjwyP35/Uf3serV94k1xxg9YSSRcpsRXwp63DejhEcjtb/zOgxjfGHChAlMmDDB6zB8rVh7WPzmmGOO4ZhjjvE6jA4FAgFGf2ak12GYTiq+lN0YY8xuxTog2xizd5ZkGWO6bMGCBTz99NNeh+Fr1pNVGM8++yzz5s3b+4HGdEKPe1xojMmfdevW2QxMl1mSVRjr1q0jHC7tZWp21O9kwwebGHzAQGr6VHsdjsGSLGNMNziOQ+/evb0Ow9csySoMx3Gori5cYhKPxdn4wWZ69auhV9+abp0rmUhy14wHWfTbpYQiIRKxBJOmn8CMWRcRDNqyO16yJMsY02VWWsB9lmQVRiHb8rzZf+WBa39DMpkiGU8y4YyxXPvQ5VRUdW3c3a9v/AOLf/88sWicWDRdB3L+Q8/Rd1Afzpt5Vj5DN51kY7KMMV0WjUbt5u+yloHvdp3dVai2/Or8N/j5Nx6msaGJ6K4ocSfOy0+9xo8uuKfL53zinmdwmvZcMs5pcvjzXTZe0muWZBljumzAgAHU1tZ6HYavWU+W+1S1YG350dv/jNPk7LEtFo3z8tOv07BlR6fPl0qlaNrRnHXfru2NXYrR5I89LjTGdNlFF13kdQi+5zgO4XDYxta4SESYPn16QT5rS1191u2hSJDtmxro3a9z6xEGAgEOOHI4a5Z/2G7fyLEHdilGkz/Wk2WMMUXMxr35y+HHHUogmOXWqzD4wEFdOucVd0+nrDKCBNIzfQMBoayyjBmz7Jcgr1mSZYzpkm3btvHzn/+c999/3+tQfM2SLPfV19dz3333sWbNGtc/67zvnkVFdfkeiVZ5VRnTbzuXSFnXSkgcPnE0d79wK8edPYFho4fwuanHcs/Lt1mF+CJgjwuNMV3S3NzMpk2bSCQSXofia5Zkua+5uZmNGzeSTCZd/6zBIwZy32s/4rc/eJzlS1bQb9++TPv2l5lw+thunfeAI4bz3UevylOUJl8syTLGdEnLgGxb7sVdjuPYNXZZodvy4AMGcu1Dlxfks4y37HGhMaZLrLRAYViZDPdZWzZusSTLGNMlVlqgMOxxofusLRu3WJJljOmSyspKRowYYY+yXGZJlvuqqqqsLRtX5DQmS0QmAXcBQWC2qt7eZv9VwMVAAtgM/IeqfpjZlwTeyhz6kapOzlPsxhgPHXzwwRx88MFeh+FrqmpJVgGMGjWKUaNGeR2G8aG9JlkiEgTuBU4G6oBXRWSuqq5sddj/AeNUtUlELgN+BEzN7GtW1U/nOW5jjPG9eDyOqloPizElKpfHhUcDq1V1jarGgEeBM1sfoKp/U9WmzMuXgKH5DdMYU2wWLFjA7NmzvQ7D12xAdmHMnz+fOXPmeB2G8aFckqwhwNpWr+sy2zoyHXim1etyEVkmIi+JyJe6EKMxpgjt2LGD5ubsa6aZ/LAB2YXR0NBgbdm4IpcxWZJlm2Y9UOTfgXHA51ptHqaq60XkAGCxiLylqu1KRIvIJcAlAMOGDcshLGOMl2yskPssySoMa8vGLbn0ZNUB+7V6PRRY3/YgETkJmAlMVtXdS4yr6vrMn2uA54Ax2T5EVR9Q1XGqOq5///45/wWMMd6wG5P7LMkqDGvLxi25JFmvAiNFZISIRIBpwNzWB4jIGOB+0gnWplbb+4hIWebnfsCxQOsB88aYEmU3JvdZVf3CsKr6xi17fVyoqgkRuQKYT7qEwxxVXSEiNwPLVHUucAdQDfxRRODjUg2jgftFJEU6obu9zaxEY0yJGjFiBL179/Y6DF9rGfgeiUQ8jsTfRowYQW1trddhGB/KqU6Wqs4D5rXZdkOrn0/q4H0vAId3J0BjTHGaNGmS1yH4nvVkFcYXvvAFr0MwPmUV340xpki1JFnWk2VMabIkyxjTabFYjFtvvZVXXnnF61B8zXEcIpEIgYB9VbslGo1y6623smzZMq9DMT5k/3KNMZ3mOA6xWMxu/i6zyQXus7Zs3GStyhjTaS0Dsm2skLui0ahdY5dZWzZusiTLGNNpVr+pMKwny33Wlo2bLMkyxnSa3ZgKw5Is91lbNm6yJMsY02nV1dUcddRR9OrVy+tQfM2SLPfV1NRYWzauyalOljHGtDZw4EAmT57sdRi+Z0mW+wYNGmRt2bjGerKMMZ2WSqVQzbpOvMmjaDRqSZbLrC0bN1mS5TOqDhqdjzY9giZWex2O8amlS5fygx/8gFQq5XUovpVKpYjFYpZkuey5557jlltusUTLuMIeF/qIxlehW78GxEGT6W0VpyG9bkPE8mmTP47jEAqFrLaQi2KxGGClBdzmOA7hcJjMurvG5JV9Q/qEqqLbLgXdDtoIRNP/RZ+F6NNeh2d8xsYKuc9mvRWGtWXjJkuy/CLxLui29tu1GW16pPDxGF+zG5P7LMkqDGvLxk2WZPlGDOigu1udgkZi/M9xHHuM5bKWSuSWALjL2rJxk43J8ovQaCCcZUc5VJxZ6GiMz40ePZpkMul1GL7W0pNlCYC7Dj30UBv0blxjSZaq9JXzAAAHUklEQVRPiIRgnzvRbTOAJBADqYTQKKRymtfhGZ8ZO3as1yH4nj0uLIxx48Z5HYLxMUuyfETKjoX+89Hm/4HkpvTrsuPTCZgxedTU1ERZWRnBYNDrUHzLkqzCsLZs3GRjsnxGgoMIVM8g0PtGpPxkS7CMK+666y4WLlzodRi+ZklWYdx5550sWrTI6zCMT1mSZYzpFFW1IpkFEI1GEREikYjXofhWMpkkHo9bWzausSTLGNMpsVgMVbUB2S5rKS1gRTLdY5MLjNssyTLGdIqVFigMq9/kPnska9xmSZYxplPsxlQYlmS5z9qycVtOSZaITBKRVSKyWkS+nWV/mYg8ltn/sojs32rf9Zntq0Tk1PyFbozxQmVlJSeeeCIDBw70OhRfsyTLfVVVVZx44okMGDDA61CMT+116pmIBIF7gZOBOuBVEZmrqitbHTYd2KaqB4nINOD/AVNF5FBgGnAYsC/wVxE5WFWtiqExJaq6upqJEyd6HYbvOY5DRUWF12H4Wk1NjbVl46pcerKOBlar6hpVjQGPAm1LiJ8J/Crz8+PAiZIerXkm8KiqOqr6T2B15nzGmBIVjUbZvn07qVTK61B8zZZ7cZ+1ZeO2XJKsIcDaVq/rMtuyHqOqCaABqM3xvcaYErJy5UpmzZrFrl27vA7F16LRqD0udNlbb73FrFmzaGpq8joU41O5JFnZ5g+3Xeipo2NyeW/6BCKXiMgyEVm2efPmHMIyxnghEokwaNAgSwBc1q9fP/r27et1GL5WVlZmbdm4Kpdy4HXAfq1eDwXWd3BMnaRLjPcGtub4XgBU9QHgAQAR2SwiH35CTP2ALTnEbtqza9c1dt3auOyyy3I91K5d19h167pOXbtOtOWewNpd1wzPtjGXJOtVYKSIjADWkR7Ifm6bY+YCFwAvAmcDi1VVRWQu8HsR+Snpge8jgVf29oGq2v+T9ovIMlW1VT27wK5d19h16zq7dl1j163r7Np1nV27/NprkqWqCRG5ApgPBIE5qrpCRG4GlqnqXOCXwG9EZDXpHqxpmfeuEJE/ACuBBHC5zSw0xhhjTE+Q0+rBqjoPmNdm2w2tfo4CX+3gvT8EftiNGI0xxhhjSk6pVnx/wOsASphdu66x69Z1du26xq5b19m16zq7dnkkqlkn+xljjDHGmG4o1Z4sY4wxxpiiVhJJlojcISL/EJE3ReTPIrJPB8d94hqLPZGIfFVEVohISkQ6nDEiIh+IyFsi8oaILCtkjMWoE9fN2lwbItJXRBaKyHuZP/t0cFwy097eyMxE7pG6szZsT5fDtbswUxKopZ1d7EWcxUZE5ojIJhF5u4P9IiJ3Z67rmyJyVKFj9IuSSLKAhcCnVPUI4F3g+rYHtFpj8TTgUOCczNqJPd3bwFeApTkce7yqftqm7wI5XDdrcx36NrBIVUcCizKvs2nOtLdPq+rkwoVXPHJsQ7vXhgXuJL02bI/XiX9/j7VqZ7MLGmTxehiY9An7TyNdcmkkcAlwXwFi8qWSSLJUdUFmuR6Al0gXNW0rlzUWexxVfUdVV3kdR6nJ8bpZm8uu9VqmvwK+5GEsxa47a8P2dPbvr4tUdSnpcksdORP4taa9BOwjIoMLE52/lESS1cZ/AM9k2W7rJHaPAgtE5DURucTrYEqEtbnsBqrqvwAyfw7o4LjyzFJaL4lIT03EurM2bE+X67+/szKPvB4Xkf2y7Dft2XdbnuRUJ6sQROSvwKAsu2aq6pOZY2aSLmr6u2ynyLKtR0ydzOXa5eBYVV0vIgOAhSLyj8xvO76Vh+tmba69mZ04zbBMmzsAWCwib6nq+/mJsGR0Z23Yni6X6/IX4BFVdUTkUtI9gie4HlnpszaXJ0WTZKnqSZ+0X0QuAE4HTtTsdSdyXifRb/Z27XI8x/rMn5tE5M+ku+J9nWTl4bpZm8tCRDaKyGBV/VfmEcOmDs7R0ubWiMhzwBigpyVZ3Vkbtqfb67VT1fpWLx/ExrPlqsd+t+VbSTwuFJFJwHXAZFVt6uCw3WssikiE9NI+PXbGUmeISJWI1LT8DJxCeuC3+WTW5rJrWcuUzJ/tegVFpI+IlGV+7gccS3r5rZ4mlzbU+nruXhu2gDEWq71euzbjiCYD7xQwvlI2Fzg/M8twAtDQMgTAdE5JJFnAPUAN6cdYb4jILwBEZF8RmQe7xyq0rLH4DvAHVV3hVcDFQkS+LCJ1wGeBp0Vkfmb77msHDAT+LiLLSS/g/bSqPutNxMUhl+tmba5DtwMni8h7wMmZ14jIOBFpmd01GliWaXN/A25X1R6XZHXUhkTkZhFpmXH5S6BW0mvDXkXHszV7lByv3ZWSLsWyHLgSuNCbaIuLiDwCvAiMEpE6EZkuIpdmHqlCehm9NcBq0j2AMzwKteRZxXdjjDHGGBeUSk+WMcYYY0xJsSTLGGOMMcYFlmQZY4wxxrjAkixjjDHGGBdYkmWMMcYY4wJLsowxxhhjXGBJljHGGGOMCyzJMsYYY4xxwf8HVpRTFEvQ+XwAAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize = (10,5))\n", "ax = fig.add_subplot(111)\n", "im =ax.scatter(X_l[:, 0], X_l[:, 1], c = Y_l)\n", "ax = plot_svc_decision_function(model,ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dans la figure ci-haut, on voit que le SVM a choisit la frontière de décision (ligne pleine) qui maximise la marge (la distance entre la ligne pleine et chacune des lignes en pointillé). \n", "\n", "De plus, les points qui touchent aux lignes en pointilée sont appelés vecteurs de support (support vectors)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Maintenant que nous avons revu la base des SVM, on peut utiliser un SVM pour classifier le jeu de données #3 (celui sur lequel notre modèle linéaire initial fonctionnait le mieux et qui est le mieux « adapté » aux modèles linéaires)." ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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8E41CiJxXvWC7utt2LBYjGo0SDAZZs2aNxek6J61NSHwGySVg7w2e41HKk/X7LPp0Ke889SHxWIKjJ49m9GmHdPpRj+Zyupz8/qXfsGnNFtZ9+wO9Bvak9357WR2rXZAiSQiRs7p27cqoUaPw+Xy1CqZBgwaRl5cnO9zamDar0OELIP096BgoT6Zth/ESypG9/nnP3PoSL9//XxLROFrD7OnzGHHcgfzhlWulUGqBnvt0p+c+3a2O0a7Id5MQImfl5eUxceJEevToUevctiFDhnD88cdLgdTGdNVjkFoFOgKYmT91KbrsuqzdY+u6Yl760+vEI/GaHVmxqjhff7CIr99flLX7CAFSJAkhcpxpmlRVVVFUVFTTBgAgkUhI5+22Fn0DSNS5aEJyMdosz8ot5r33TYM7rmKVMWa9Picr9xCimhRJQoicNm3aNJ5++mnsdjuFhYWEw2ESiQR33303c+bIL82OxpfvRdnqjxDaHXbyCnwWJBIdmRRJQoicVlRURElJCaZp1uxqc7lc5OXlSRuAtuY5BXDVuWgD5xCULZCVWxx68ogGrzucdo7/ydFZuYcQ1aRIEkLkNMMwSKfTlJWV1fRKqu6bJG0A2pbK+yU49gW1fURH+UAVogruy9o9vH4Pd02/CX+BD1/Aiy+Q2bL+y0cvpe/+cm6fyC7Z3SaEyGk7L9g2DIN4PE5VVRWGYbBy5UqL03UuypYHxmsQ/wRS34K9F3gmoJQ3q/c5YOxgXtr8JAs+XEwiluDgY4bhL/Bn9R5CgBRJQogcV7dXEmQKpmAwSGVlJfF4HLfbbWXETkUpO3jGA+Nb9T4ut5NDTzy4Ve8hhBRJQoiclpeXx3HHHUefPn1qiqFQKMTAgQNxuequjxFCiMaTIkkIkdOUUhx55JFAph2AzWYjHA5z8MEH06NHD4vTCSFymSzc7qB06gd0ag26utuaEB1YJBLhhx9+wGazUVRUVLNge9u2bbLDTQjRbFIkdTA69T3mtonobSeht52OLh6HTnxldSwhWtUXX3zBU089RTqdrtnhBjB16lQ+/vhji9MJIXKVFEkdiNZJdPh8SK0EYkAUzM3oksvQ6a1WxxOi1RiGgWmalJaWYhhGrTYAMpIkhGguKZI6kvgnoKNAnSk2nUJHX7MkkhBtoe6utkQiQWVlZU1zSSGEaA4pkjoScyvodAMPJCC9sc3jCNFWdm4DULclQCQSIRqNWhlPCJGjpEjqSJy76hniQ7kOa9MoQrQln8+Hx+OpGUmCHc0lqz8WQoimkhYAHYhy7o92j8tMu1H9ztkNjr7gOd7KaEK0KqUUZ5xxBkVFRRQUFGC32wmFQgwaNIhzzjmnpnASQoimkCKpg1GFD6IjL0H0edAJ8E5E+S5BKafV0YRoVYMGDar5uPrcNr/fz+DBgy1MJYTIZVIkdTBK2VH+88B/ntVRhGhTZWVlrF27lqFDh9ba1bZ+/XqSyST77ruvxQmFELlGiiQhRE7T6W0Qm853S5bw+tsl9LzqjxiGwerVq9Fa89FHHxGPx6VIEkI0mRRJQoicpeOfo0svB21ieCohFmXbd2UUFf2GVCpFeXk5wWCQxYsXo7VGKWV1ZCFEDpHdbUKInKR1El161fbeYHGChXYgSbh4PkbefGBHS4BYLCZtAIQQTSZFkhAiNyUXATv6gvl8NrweRagkQpFnJkCtlgDSVFII0VRSJAkhcpSdut3liwrthEtMAgEPDoejVnPJztwrSWvNinmr+XL6PMKbS6yOI0TOkDVJQojc5BwGygO6qubS6Sf4cXt82HxnEwyuIxwOU1RUxJQpU+jSpYuFYa0T2lTCjRPuZPOaLdgdNhKxFKdeMYGf33eRrNESYg9kJEkIkZOUsqMK/wrKD/gAJ1275BHoMgE8J9Wc22a329lrr71wuVxWR7bEHWc/wPplPxCrilNVFiUZT/LW39/jo+c/szqaEO2eFElCiJylXAejun6KCvwelX8N5Y4n+HzxGZSXV2AYBiUlJZimyerVq5kzZ47Vcdvctg0hVn79HemUWet6rCrOqw+/bVEqIXKHFElCiJymbHko3ySU/1Kq4n14//332bRpE8FgkHQ6TVlZGcuXL+eDDz5Aa73nF+xAqsqj2B32hh8rrWrwuhBiBymShBAdRvUi7Z0XbFd/HI/HqarqXIVB7/164vTUP5LI6XIw+rRDLUgkRG6RIkkI0WF4PB78fj+hUKhm6//ObQA62w43u93Ob/5xOW6fC5s98+Pe7XVR1KOQc64/rVXuqc0KzKpnMctuwqyaijYrWuU+QrQF2d0mhOhQqs9ty8vLw+VyEQqFGDBgAJAZVerbt6/FCdvW6NMO4ZEv/8jrj8xgy9piRh5/ICdddiz+An/W76VT69Ghs4Fopsmn8qIrHwNjGsrRJ+v3E6K1SZEkhOhQDMNgzZo1KKVqCqbCwkJsNhulpaVWx7PEPsP6cvXff97q99Hlt4MuBbYvFN/eDV2X34YKPtnq9xci26RIEkLU0NqE5ELQleA8GGXLszpSk51wwgk4nZl1OIZhsGnTJmw2G9deey1er9fidB1cYhY1BVINc/t1IXKPFElCCAB0ahU6fCnockCBTqHzb8Dmv8DqaE3i8XhqPg4GgyxdupR0Oo3P57MwVWdhB1INXJdfNSI3ycJtIQRam+jwJWBuznSw1pVADCruRScWWh2vSSKRCG+//TZr167FMAxM06S0tJTVq1fzxhtvdLo2AG3KOxGo27TTBd6TrUgjRItJkSSEgOS87YVR3QIigY4+b0WiZrPb7cyZM4d169bV2tUWCoWYP38+lZWVFifMHWXbyrnrvL9wkvc8TnSfyx/O+BPbNu56h6DKvwkcA0H5AE/mT8cAVP7v2i60EFkkY6BCCDC3T7HVfwDSubVt3u12k5eXRzgcZsSIEUBmV1vXrl1rPs7Pz7cyYk5Ip9JcNeZmNn+/lXQyDcCX0+exYt5qnlnxCC5P/WNelC0fjFczRXdqNTj6g3OknBEnclajR5KUUnal1Hyl1PTWDCSEsIBrBOhE/evKi/JMaPs8LVR9bpvP58PtdhMOh2uaS3a2XknNNWfGfMKbS2oKJAAzbVJVGuHTV2bv8vOUUijXKJTvnMyfdQokrTWbvtvCxtWbZepTtHtNGUm6ClgKBFopixDCIspWhM67GiofBmJkpt28YN8XvKdYnK7pgsEgK1asQClVUzAFAgHsdjuhUMjqeDlh/bINJKLJetejlTG+/3Z9s17zu2/WcsfkByheHwIFxl5BbnnxGgYcvE9L4wrRKho1kqSU6g2cDEijCyE6KFvepZleNp6TwDUG8m9CGS+gVP1plfauS5cu2O12kslkTa8km81Gt27dSCbr/+LviNYv38Atp93L6UU/4YJ9/o9XH3oL06y7PX/X+g7ujctb/0gTb56HfkOa3hgyWhnlN+P/wA8rNhGPJohHEmxctZlrj7mVqvJIk19PiLbQ2JGkB4HrAZnI74S0TkDsXXRyKcrRH7wnopT0m9E6io5Mg9i7YCtC+S9EuXL7PCzlOgTlOsTqGC02evRoxowZA2Sm3pYsWUI6nWbKlCmdYn3M1nXF/PKw3xKtiKG1pqoswlO/e56Nqzfzy4cvbdRrHHLicIyeRWyObSW1fcrN7rDhL/Qz9szDmpzpk2lf1pq6q5ZOpfn4pS846bJjm/yaQrS2PY4kKaUmAlu11vP28LwpSqmvlFJfFRcXZy2gsJZOh9DbJqDLb4bIP9Dlt6OLj0WnN1gdzVJax9ChyVBxHyRnQ/wddPhnmFX/tDqagFqFUDAYRGtNSUlJpyiQAF5+4E0S0UStNT/xSJwZT35A2bbyRr2G3W7nwc/u5Kizj8DpduJwOTjilEN45Mu7G1y0vSehjSXEo/XXvcUicUK72TEnhJUaM5I0BjhVKXUS4AECSqnntNYX7vwkrfUTwBMAo0aNktV4HYSu+COkt7CjQVwEzBi67BZU8Ckro1lKR16F1Doy63eqRaHiQbT3bJRNlu5ZSWvNiy++yIABA+jRoweQ2dVWVVXFRx99xKRJkwgEOu5/o28/X14z+rMzp9vJuqUbOGBs4772gi4BfvvcVfz2uZZnGjp6EC6vi1hlrNZ1j9/D0NGDWn4DIVrBHkeStNa/1Vr31lr3A84FPqxbIIkOLP4+9TvompD4Aq0b6qzbScTfB6L1rysnJL9u8ziiNqUUGzduZP369bV6JZmmyffff8+2bdssTti6+g7pjc1Wf9QsGU/SvV9XCxLBgeOGMGhUf9zeHaNQbq+LAcP7MfyYYZZkEmJPpJmk2IPdTU90jqmLBtmCNPz1a1CFbZ1GNGDnNgBer5dQKFSrYOrIJl97Ks46U2Iuj5ORxx9Etz5dLMmklOLuGb/j4jvOZe8hvek7uBcX3XYO9757Czab/CoS7VOTmklqrWcCM1sliWifPCdB9HVg5x1BDnCPQym7Vaksp3wXomPvUnu6TWUKJOdBVsUSO6k+t63643A4TCAQwOFwdPg2APscsDe3v3EDD/3iCbasK8ZmtzH+vCP55SONW7TdWlxuJ2ddcwpnXZN7bSVE5yQdt8Vuqfwb0MmFkP4h02xQucEWRAXusDqapZRrODr/Rqi4B5QDMMFmoIr+2WkWB7d3hmEQiUSIRqMYhsHatWtRStUUTB3diGMP4F8rHiZSHsHldeF01d/OL7KnqjyC0+Vo1qJ20X5JkSR2S9kCYPwXErMgtQLs+4D7KJSSbx2b/3y091RILgRbPjgOkAKpHenevTt9+vQhFosRDAZZtGgRqVSKfv36kU7XX9TcESml8Bf4rY7RoS35fDl//tnjbFi5GWVTHHnGofz6b1Pk//cOQn7TiT1SygbusZl/RC3KlgfuMVbHEA3o378//fv3BzKjSlprwuEwJ510ksXJ9kyn1qOjL0F6A8o1GrwTUcpjdSxRx6bvtnDjhDuIVcVrrs16fQ7bNoT5yyede7S9o5DVckKIDi8bC7a//XIFN0y4g3N6TeG6Y29j8WdLsxWvFh2fhd42Ear+CbHp6PI70NtOQ5sVrXI/0XyvPfw2yUTtXb7JeIqVX3/H90uad3SLaF+kSBJCdFjPP/88b775Zs3htqFQiC1btvDwww/z3XffNfp1Fs5cwvXH3sbX731DeFMJS7/8hhfvvI6lnz2H1tk75kRrE112HZn2EtW/fKOQ3oiu6rx9ydqrtUt/aLCLuN3hYPOarRYkEtkmRZIQosNKJpNs3rwZj8eDz+cjHA7X/NmUXkmPX/Ovmm7RR55UyovfLOH6h1fRt+dd6K1j0Iks9cZKrwFd1cADcYjNyM49RNYMHT0Il6f+gvhkPMk+B/S1IJHINimShBAdVnWvJK11zcd5eXm4XK4mTb19v3gdAD36xrnukXV4/Sb+gInXnwZdii65DG1m4ZBW5QW9i0No5bzEdufU/5uA2++u1bjT7XMx9szD6b63NU07RXZJkSSEaFBVWRUz/vkBL/7pDZbPXWV1nGYJBoPEYjGi0WjN1v/qNgBN6ZVU0CVzjMexZ5Vgtzd06pKG+Ictzqvse4GjP/V/NHtRvgta/Poiuwq7FvDXufcy9qwjyCv007W3wYW3nM31/7rC6mgiS2R3mxCinsWzlnHTSXehTU0ynsLhcnD4xBHc9J9f51R35J3XIhmGwcKFC0kmkwSDQbZs2dLo1znnhtN56nfPEyhMYW/op6ZOg67MSmZV+Cg6/GPQpdtfOwXeE8E7KSuvL7KrR79u3PzC1VbHEK1EiiQhRC3pdJpbJ91HtGJHN/F0Ks3st75m5guzOOb83GkF0a1bN4YOHYrD4agpmMLhMAMGDMDn86G1blRvqzN+dRKVpVUs+HwqE84rweuvOyWmwXVEVjIrR2/o+gEkZoO5FZzDUY69s/LaQjSXaZp89b+FLJ+zCqNXkHGTj8Af8Fkdq9VJkSRaTOs0JL6E9BZwHYRy9Lc6kmiB5XNXk4zV37EVq4oz46kPc6pIKiws5Oyzz651LRQKMWLECEaMGNHo11FKcdEfJpOInko6PAXNQlT1AcfKC95zs1rIZHqTZafoEqKl4tE41x5zG2uXrCdaGcPjd/OP65/lgZm3se+BHbuAlyJJtIhOb0CHLtw+NaBBmzmWotgAACAASURBVGjPcaiC+zr12W45TTe05mb7Q+auH2vPUqlUTa+k6rVIWmtM08Rub/z3qcvrQe/1NMRmoKNvgnKhfJPBdWSr5BaiPXj5/v/y3cLvSWx/85RpnhnnrvP+wj+XPGhtuFaWO4sLRLukS34F5qbMtmUdAWIQ+wAdecHqaKKZBh0yAIer/vsnj9/NhEvGW5CoZaZNm8Y///lP3G43eXl5hMNhotEod999N3Pnzm3y6yllR3knYgv+HVvRIyj3WDmORnRo7z/7SU2BtLPNa7aydX3jW2nkIimSRLPp9BZILQfqrs+IQvT5NsyxCbPiAcySyzErn0CbpW12747I7rBzy0vX4PG7cXldoDIF0vBjhnHMebk3YuL3+wmHw7XaAHg8Hmw2W6c46FaIFtvNm4CO/gZBpttE8+k4u6yzdbRtIiQXbd8JlAISEP8s05m4y6uZ7dSiWYaPH8az3z3GzBc/pzxUwfDxwzhg7OCc/IEYDAaJx+NUVVURDAZZuXIlSikMw5AiSYhGmHDx0Tx35ysktjdUhUzdtFf/HnTtbViYrPVJkSSaz94HbEWZ6bZaXOBpm0NEddlN26f5qsVBJ9EV96EK/9ImGTqqwq4FnP7LE62O0WxaRyHxNUV5m9HaJBwOYxgG8+fPJx6PEwwG2bBhw64/P70VHXkOEgvAORDl+wnKIV2URedz5tUTmfvOAlbOX0MimsDtdeF0O7j5xY7f+kCKJNFsSikovB9dclmmTwwJUD6wdUf5p7T6/bVZBamGmhyaEP+41e8v2i8z+jaU/xawE7QnoaqEbZuHEgweAGTaAASDQZYsWUI6na63eFun1qJDZ4KOAQlIfoWOToOiZ1Cu4W3/BQlhIZfHxQMzb2PhzCUsm70So1eQsWcejsfntjpaq5MiSbSIch0CXf6HjrwE6R9Q7sPBczJKtcFfHuUkM91X/4BJVMfv3yEaplNroexGINPnqTCgOXykpovzTlzB6UBmh9uAAQOw2WwNF0kV92xvDlm93i4FOoUuvwXV5c22+2KEaCeUUgwfP4zh44dZHaVNSZEkWkzZe6Dyf9X291UutPtYiH8A7LzzwgO+c9s8j2gfdPQVIFXz7zabYsJ4PygHKd9iIDOSNGzYMPr23cX0WeIL6m9IAFKr0DqKknPUhOgUpEgS7YpOLkZH3wI0ynMiynXQbp+vCu5EhzdCeiVgyyzgdo9F+X/eJnlFO2SWsnORBJBMaioqExj5VQQCgZpeSZFIBNM0ycvLq/0ayldnrVs1O1D/1HchRMckLQBEu2FWPIQOnQ+RpyHyNDr8Y8zy+3b7OcoWwNZlGir4H1TBH1Fd3sBW9BhKyS+yzkq5xwO1p1s/+DTC357ZhnYeUWtX2yOPPMLMmTPrv4jvAsBT56ILvCejlLy3FKKzkCJJtAs69R1UPUlmHYkJ6MzHkWfRyRV7/HzlHIrynIBy7NvKSUW75z4KXMOBHVNiRtBHUg2jMlpAMBisGUkKBoMNtgFQ/p+D5zjADSoP8IBrJCr/923zNQgh2gV5SyTah/hHNLgGhGRmzZFzv7ZOJHKUUnYoehJib6Gj/wXlxeg7BlzLatoARCIRotEohmGwdu3aBl7DgSr8Mzq9AVIrwd5XCnAhOiEpkkQ7Ub1TrS47KFdbhxE5TikHeE9DeU8DoIsqRanlhEKhmjPcqtsALFq0iFQqhcNR/8ehsvcCe682zS6ywzRNVs1fQzplst/IfbE75CxJ0XRSJIn2wTMBKhpaf6TAc0KbxxEdSyAQwOFwEA6Ha3a0hUIhDMNAa004HKZbt24WpxTZsmLean5/2p+IlEdQSmF32rn5hasZcdyBVkcTOUbWJIl2Qdm7Q+BOMmtAfNv7HLkhcGvm3bwQLWCz2Zg4cSJDhgyhqKgIpVRNwXTqqafW390mclYsEuf6424ntDFMtDJGpCJKRbiS35/+J0KbSqyOJ3KMjCSJdsPmOw3tGQuxmYAG99Eoe8c+F6gj0lpTvH4bbp+bgi4Bq+PUGD58R6fsgoICQqEQBQUFjBgxwsJUIts+f30OZrr++kYzbfLBvz9h8rWnWZBK5CopkkS7omxB8E2yOoZoItM02bxmK6sXfs/jV/+Lsm0VaNNk6Oj9uek/V1HUvdDqiFRVVbFx40YGDBhQa1fb1q1bSaVS7LWXHIjcEZRtqyCVrN+FPxlPUrKlzIJEIpfJdJsQokXmvjOfc3v/nJ8d8BtuP+sBiteHSEQTJOMpFn26lOuPux2ttdUxWbZsGf/+978pLy/HMAxCoRBaa958803effddq+OJLDno6KHY7KredU+ehxHHHmBBIpHLpEgSQjTbumUbuO2s+ynZXEoilqj3eDqVZvPaYpbNaegg4tp0ahVm+d2Ypdeio2+hdXKPn9MU1bvaqne4xWKxmjYADfVKErlp3wP35shJh+Px7zg/0u1zs/8hAxj5o9138BeiLpluE0I02xuPvUMqkdrtc2w2RfH6bQw+bOAun2NGp0PZTWTO4EujY+9DZCoEn0VlqQXEzlv/DSOz1q26YFqwYAHJZBKnMzud2rXWkFyQOSLFNRxlK8rK64rGuf5fVzDzhOG8/eQHpBIpjr9oHBMuGY/NJuMCommkSBJCNNvm77aQTjXUBHSHVCLFfqP67/JxraNQfjOZbuvVIpBaBtHXwTc5K1mr2wCEQiH69esH7OiVVP1x9+7dW3wfnVqHLrkYzDBgw0zH+fy9USz6OvOLesDwfVp8D7F7NpuNY84fyzHnj7U6ishxUlYLIZpt+DHDcHt3PdLj9rk5+twx9Oi3mx5EiQU0+KNIR9HR6S0PuZ1SqmbBdnUbgOpeSUDNUSUtobVGl1wG6Y2ZA3J1JTZbkpFHzmb9Ny/z6zE38/qjM1p8HyFE25AiSQjRbCdddiz5Rj4O145BabvDhsfvpu/g3ky578f85snLd/8iykfmrL4G2PzZCwuccsopHH/88djtdgoLCwmHw3Tp0oUf//jH7LNPFkZ4UsvA3ELdI3a8fpNTLi4mHk3wj+ufpWxbecvv1QhaJzArHsHcOg5z62jMstvRZmmb3FuIjkCm24QQzeYv8PP4vHt5/o+v8fnrc/EFvJxx1clMuPholKq/w6hBzgMyh8jqqtrXlRflOy+refv06VPzcfUON6fTSf/+u54ObBJdCTR8/EWgKLN2y+508PX7ixh/7pjs3HNXUbRGl/wMEl8D8czF6IvoxCfQ5S2Ucu/284UQUiQJIVqosGsBl//5Yi7/88XN+nylbFD0JDr8E2p+meskeC9CuY/KWk6AiooKVqxYwf77708wGGT9+vVorVm/fj3l5eUMGzasZTdwDgNdv0dPLKL49K1MryilqLXzqtUkv9k+lRnf+SKY2yD2DnilqaIQeyJFkhDCcso5CLp9ConPwSwD16Eoe4+s3yccDvPmm29SWFiIYRjE43GqqqqYP38+K1eubHGRpJQXHbgFym9H6zhKaWIRxeb1Lt5+Lrj9OYqRx+/+DLGq8gjP3vYyH73wGUopjr9oHOf/7ky8fk/jw6SWUHfaDwAdQSe+rjn8Vwixa1IkCSHaBaWc4B7Xqveo2ysJdrQEmD9/PvF4HLe7ZaM8Nt9ZaOcgiDzH5tXf8urjUWb+txt2pwOfE+5880Zcnl0vdk+n0vz6yJvZsHITyXhmiu7VB99i/geLePiLuxu/jd2+FygH6HidBzxg79e8L06ITkaKJNEp6NgMdOXfwNwKzpGo/KtRjiytQxE5Iy8vD5fLRSgUYsCAAUD9gqlnz557fB1tlkD0TXR6E8p1CLjHodSOtUjKeQCq4F72GgEX3FnK4KMX4fG7GTXhINze3RdhX06fx5bvi2sKJIBELMm6pRtY8OHixp9k7xoLqhB0DNhpClA5UL7TG/caQnRye3xLopTyKKXmKKUWKqWWKKVua4tgQmSLWfUUuvRGSC0FMwTx99Chs9CpNVZHE21s5zYAhYWF2Gy2es0l90QnFqKLj0FX3AeRf6LLrkGHz0XrWIPPL+peyLEXjGXM6YfusUACWDHvO6KV9V8rEUuy8uvGf88qZUcZz4NzJODM/OMYhAr+W5pbCtFIjRm3jQPHaK0PAoYDJyilDm/dWEJkh9ZxqHwYiO58NdODp/JRq2K1iNYas+olzOITMLcegVn6G3TqB6tj5YzqXW02m42ioqJ6I0m7o7VGl161fSde9SLzCCSXo6ueyUq+nvt0a3Bht8vrpEe/rk16LWXvgc14DtXtS1S3T7F1eRPlHJyVnEJ0BnucbtOZkykrt//r9rcju2pqIkQ7k14PNLQV3YTE/LZOkxW64o8QfRH09sIv9hY6vn1bt303TRsFABMmTKg5fmTnNgBXXnklBQUFu//k9PdgljTwQAyib0Dez1ucb9zkI/jHDc8SjyRqDga22RQen4cjTjukWa+pbPktziVEZ9SoFYBKKbtSagGwFXhPaz27dWMJkSW2rpnt5A1x9G7bLFmgzTBE/rOjQALAzOxYivzLqlg5JRAI4PV6AWqm3rTWGIaBw7Gn9412dvkeUTXcH6mpvHle/vLpnQwcuS8OlwOH087+hw/koVl34nJn52w5IdpCIp7kmVtf5NxeU5jU5RLuv/SvhDc39Caj/WrUwm2tdRoYrpQqBF5TSg3TWi/e+TlKqSnAFIC+fftmPagQzaFsBWjPCRD7H7X7xXhQ/l9YFav5kitBuUEn6j4A8bkgAwYNSsSTJGMJfAEf0WiU2bNns//++2MYBslkkoqKCsLhMKtWreK4447b9QvZ+2R2jaXXULtY8oA3O2fMAfTdvxePzbmHipJKlFLkFWa387gQbeEPp9/LN58sJRHN/Lx6/9lPmPfuQp5a+iDePK/F6RqnSceSaK1LgZnACQ089oTWepTWelTXrk2bNxeiNamCu8A7EXADHlBFELgD5R5tdbSms/dsoEACsIGjX1unafeiVTH+dMmjnF74E87sdikXD/oVCz5axMcff8zatWtrrUXasGEDn332GbFYwwuwIbPwWxU9CqoAlB9wAV5wH47ynZv1/PlFeVIgiZy0asEaFn26rKZAgkx7i8rSKt5/7lMLkzVNY3a3dd0+goRSygscByxr7WBCZItSbmwFf0R1m43q+i6q2+fYfLnZSE85+oJrJJlfzjtzo/w/tSJSu3bnOX/m4xc/JxlPkk6m2bhqM3dNfphIabTerrbG7nBTjgGobp+gAnei8n+DCk5FFf490+dJCAHA6gXf09DJRLGqON9+sbztAzVTY6bbegLPqEwTEBvwktY6e0dzC9FGlM0H+KyO0WKq8FF02U0Q/wCwga0IVXCH7FqqY8vaYhZ8uJhErPaatFQixeo56zhgZIhAIIDdbiccDtec6xYOh+nVq9duX1spD3hPbrXsDUnEEnwy7UvWL9tAv2F9GXPGobJGSbRbPfbp1uD5jS6Pk7777/7vV3vSmN1t3wAHt0EWIUQjKFsequhhtFmFTi7OLOJ2SIFU1+Y1W3G6nfWKJDNtEtmWJBwOY7PZCAaDNW0AlFKN6pXU1op/CHHl4b8lUh4lWhnDm+fhyd8+x6Nf/pGi7oVWxxOingOPGkLXvl3YsGIT6dSOZqYOl4MTfnqMhcmapklrkoQQ7YM2S9Ell0DJz6DsGnTxMZhlt6J1A2d1dVJ9h/QmEa+/s9HhtDPooIFEIhFM06zZ4eZwOAgEAlRWVjbwatZ66PInKNlSVtNkMloZI7ShhMev/lezXk9rzdcfLOIvP/8bj1z5JMvnrspiWiEy6/fu//BWRv7oQBxOO3annX0P2psHProtpwp7OZZEiBykS6+H5BIguWOTVfQ1tGN/lD/7C4hzUVG3AiZcPJ73pn5MPJLZ2aiUwu1zc8N919Bj78x0gGEYrF69Gq01V155ZSPaALQt0zSZ+84CzHTtAjidSjPrjblNfj2tNff/9K98Mu0LYlVxlE3xv6c/4rwbz+CCm8/KVmwhKOpWwF3TbyIWiZNOpvAX5N4mBBlJEiLHaLMcErOAuqMkUYhkp+tzR3Hlo5fy07vOo9veXfEFfBxx6igenf1HevbrXrNeIhgMkkqlKC8vb3cFEmzfUdfQCtjtjzXV4s+W1RRIANrUxCMJ/nP3q2xZW9yirEI0xONz52SBBDKSJETu0RF2+f5Gl7dplPbOZrMx6aqTmXRV7UXW6XSa6dOnM2DAgFq72srKyvjyyy+ZOHEiPl/7WOSvlOKIU0bxxZtf1V7b4bRz1FlNPyHq8//OrRlZq3ufOTPmc8ovftSivEJ0JDKSJFpMm2F0Yg46vdHqKJ2DrTvYGprTt4P76LZOk5PsdjvLli1jzZo1tXolxWIxvv3223a3ePtXf72Mbn274M33YnfY8eZ76Nm/B7/480+a/FoenwubvX53cGVXeHx7PoBXdCzpdJpErKHeawJkJEm0gNYmuvx2iE6r6QKt3UegCh8i01JL7I7WGpILIL0JnAegHH0a9XlKKSj4I7rkCiABpAE3KD8q78rWjNyhVC/YDgQCOJ1OQqEQ/fr1A6jVEqA9KOpeyNPLHmL2W1+zfvlG+g3tzagThmNvoNjZk2POH8tL979Za1QKQJtwxKmjshVZtHOxSJy/XvU0H/z7E1LJNHsP6c1Vj0/B2KsIbepdbuHvbKRIEs2mI89C9DUgsaMLdPwLdPltqIJ7LM3W3ul0MbrkJ5DeCCjQKbT3ZFTgbpTa8wCvch8JXV7JnDyfWgvuQ1G+81G2YOuH7yAMw2Dt2rUopSgqKiIcDlNUVNRu2wDYHXZGN/OA2531GdSLKx66hMd+9RR2hz3z7WdqbnnpN9LduxO5/ewHWPjRjj5iaxat4+qxt+BwObDZFMZeRdz84jUMHLGvxUmtJUWSaL6qp4FonYtxiE5HB25HqbpdoUU1XXoNpNaQGQXaLjoD7TgQ5T+/Ua+hHANQBXe0TsBOwDAMvvnmG5LJJIZhUFxcjN1up7CwkHA4bHW8VnXSZcdx5BmHMfedBThcDg49cXjOnKUlWm7Td1tqFUjVtNYkt7fN2Lh6C9cecyv//v7xTl08y5ok0Xy6YhcPmKDrLwwVGdoMQ3I+tQokILM77VkrInVKXbt2xTAMIpEIwWCQkpISTNNkr732atY0Vq4JGPkce8FYxp19hBRInczG1ZtxNqJbezpl8tELs9ogUfslI0mi+VyHQvxDap+GTuaUdJVnSaScoKPsendapE2jdGZDhgxhyJAhQGZUKZ1OU1ZWxtlnn21xstyitWb+h4uZ+eIsHE47x190NIMPG2h1LLEbew/pXW8UqSHxSJxtGzr2qOqeSJEkmk3lX49OzNn+Sz9F5he/GxW4Qxb87Y5tr8zuNHNznQcc4DnOkkid3c473IqKiixOkzu01jxw2eN8/NLnNY0p333mYyZfdyoX/WGy1fHELnTpZTDunNF8Ou0L4pFd72zz5nkYOnpQGybL2PTdFv5xw7PMe28R3jwPp10xgcnXnZZZQ9fGZLpNNJty7IPqMh1854PjQPCchjJeRrmPsDpau6aUQhX8CZQXqB7y9oKtKyrvCiujdTrTpk3jgw8+qNUracuWLfzjH/9gw4YNFqdr/5Z8vrymQILqxpRxXrz3dTat2WJxOrE71z55OeffNImiHoW4fW4CRn6tKTiX10W/YX0YNeGgNs1VsqWUKw69kVmvzSFSHiG0Mcy/73qFP138aJvmqCYjSaJFlL0nKnCz1TFyjnIfDsab6Mh/IL0OXIejvJNQtsZNU2qdgOSiTKHlGCwjd81UVlZGZWUlxxxzDC6Xi3A4zIABA9iwYQNbt26lV6/cOa3cCl/8dy6xBhpTohRzZyzg1P+b0PahRKPYHXbOv+lMzr/pTACSiSRvPPoO7zz1Iaap+dFF4zjjqpOw2dp2LOWNv/6PeCSOae5YxhGPJPj0ldn89K5iuu/dtU3zSJEkhEWUoy8qcGOTP8+Mvgvl1Z9ngiqCoidQTlkH0lTV57YppQgGg4RCIQoLC7HZbB1+h1s2uH1u7A476WTtTQg2m8Llld2tucTpcnLWNadw1jWnWJrj28+XN7heyuVx8v3idW1eJMl0m8hpOrUes/RqzC2HYhYfi1k1Fa3NPX9ijtKp76HsWtCV2/+JgLkBXXIRWu95IWZnEKmIsmr+GkqLy/b43GAwSEVFBYlEoqa5pM1mo6ioqF32Smpvjr1gbIPrRLTWjDm95T2dROfTb2gf7M7631OpZIoe+3Zv8zxSJImcpdPF6NAkiM0AXQrp9VDxALr8VqujtRodfZnMIvm6D8S2H3rbeWmtefrm5zm7+2X8ZvwfOL/v5dx9wUMk4rsuHqvXIoXDYQzDoKSkhHQ6jWEYMpLUCL0G9OSXj/wUl8eJN9+DN9+Dx+fmlhevIb9IdriKpjvjVyfhdNWe5HK6HQw6ZAB7D+7d5nlkuk3kLB2Zun1n3c4jR1GIvorOuxJlb9th2TaRLqbBIgkNZklbp2mQTn6DrngYUsvA0R+VdyXK1frHXbz95Pu8+tBbJGIJErHMtVmvz8Yf8HLV41Ma/JyuXbuy7777orXGMAxM06S0tJR+/fqxeXPd3YeiISf+9FjGnH4oX/1vIXaHXRpTihbpuW937n33Fv485e/8sHwjNpti7JmH7/LvcGtTWus9P6uJRo0apb/66qusv64QOzND50FyXv0HVB6q8BGUe0zbh2plOjodXXYzULefkh0cQ8E5COW72LL1SToxFx2+FIjtdNWDKnoU5T6qVe/9k4FXsnF1/cLG5XHyeukzOF27b563bt06nnrqKS644AIGDpT1XUJYLVIRxel27PHvbjYopeZpreu9m5PpNpG7HPsCDfTN0Cmwd9BdSZ4J4BwAeOo8oCH1TWYULXQmOv6ZFenQ5XdTu0ACiKHL72z1e5dtK2/wupnWNVvUd6V6JAmotRapNd5ECiEax5fvbZMCaXekSBI5S/kvYUefoWoucA1HOfpZkKj1KeVEBf8N+deDcwTYupH5a1w95ZgGYuiy31nzCz61ouHr6e/RuqFpwuwZOmYQDXVCCPYs3O3ZU6+++ipTp07F5/PhdrsJh8NUVlbywAMPMH/+/FZMnPs2rNrEI798kmuO/j1P/vY5Qpvax5SvENkiRZLIWcoxAFX0d7D3IVMsucBzHKrwr1ZHa1VKubH5L8RmvECmOGpgN58ZBtOCZn62XXSrVvk0OOqXRZfdcyEevwebPfNjTSlw+1xc+ehlu+0jZbfb2bp1K0opDMMgFArh8/mIRCKyw203lny+nF8cfB1vPfE+iz5ZyqsPvsVlQ6/mh5WbrI4mRNZIkSRymnIfgeryPqrbp6juc7EVPtjohowdgsrfxQOmNefn+acAdRftesD/01ZveLnPsL78dd6fOO7Co+izfy8OP2UU931wK4dPHLnbzzMMg6qqKuLxeE0bgNKtZXz78Sr+9ItHuP3sB1g6e2WrZs9Ff5nyN2JVcdKpTI+kZDxFVVmEJ66banEyIbJHdreJnKeUAhW0OoY1fD+BinuB6E4XneAeZ0mxqHw/RusyqHoSUKBN8F2A8l/eJvfvPbAn1z3dtKNddl6LZBgGc76Yy6UHXM2a0pXEUjE++/5L5sz4muueuoJxk0e3RuwWKw9XENoQpse+3fH6665Xy75oVYwfVmysd11rzYIPF7f6/YVoK1IkCZHDlO9cdGolRF8G5cosWncORRXc0yr308lv0dFXQVeh3D/KFGNqx4C0UgqVdyXa/zNIbwV7V5Rq39vBdz7c1jAMFs5cQrLUgS1lJ0kC09TEIwkevuIfHDnpMEsO2dyVRDzJX372Nz5++QscLgdm2uTcG0/ngt+d2aojd06XA5vdRjpVf6rXF2jf/72FaAopkoTIYUrZUAV/QOf9X6Yvkb0nyjGgVe5lVk2FivuBBGCiYzPANRoKH61VKGVyecDRt1VyZFswGGT48OEEAgFsNhubVm8hL2XgxY/e/j+FIhFLsvn7rfQa0NPqyDUe//XTfPLKlyTjSZLbm2a+cM/rdO1tMOHi8a12X4fTwdHnjmHmC5/X3Bcya8BOveKEVrtvZ1BZWsXiz5bhC3gZOmYQdnv7Kco7IymShOgAlL0rtGLzTJ0OQcV9wE5b6XUEEp9D/GPwtN4v5NbmdDo5/fTTAYhGo7j9LpJlcQpVF3zsWPOVTqV3u0uurSXiSd59Zma9c67ikTgv3vt6qxZJAFc+cinhjSUs/mwZDpeDZDzJ2LOO4JzrTmvV+3Zk//3rO/z92mdxuOxorfHmebnnnd+xzwF7Wx2t05IiSQixZ4kvyPy4qNNvSEfQsXdQOVwkQWYtTTQaxefzMWLcgcx/bSnEM9c1Ji63m4OPPYCCLgGro9aIVkR32eahZOuez61rKW+el3v+dws/rNzEptWb6TesL117G61+345q+dxVPHH9s7U6xkcrYtzwozt4/oe/y4iSRWR3m2gRrTXajKB1es9PFrlLuaHBJS42UL62TpN1M2bM4NFHHwVg1PgRDD9hKE63g42e1VS4Sxg6ehC/fe4qi1PWFjDyCRj1dzcqBUOOGNRmOXoP7MkhJxwsBVILTX/ivXqjggDxSIJvPv7WgkQCpEgSLaDjn6C3HYfeOhK95WDM8rvlJPqOyj2WhqskF8p3ZlunybrCwkIikQjRaBTDMBh81ABe3vwkk/7vFC6+9xzu//DWdjXVBplF8r985FLcXlfNNZvdhsfv4bJ7LrAwmWiOilAF2mxgZFBBVVndY4hEW5EiSTSLTixEl/wS0uup7vJM5AV0+e+tjiZagVKeTONOlQfKD/gAN+T/GuUcZnW8Fqu7w62srAyXz8UBhw7FtLdup/CWOPKMw7jnfzcz6oTh7DWgB0efO4bH5t7DPsNyY9G82GHMGYfh8bvrXU8lUhx41BALEgmQNUmimXTlX6m3PoUYRKej829A2QqtiCVakXIdAt0+h/gnoKPgGoOyd7E6VlbsYzwTSgAAIABJREFU3CupumAqKSkhGAyyYsUKTNPEZmuf7ymHHTmYP779O6tjiBY6+pzRvPn4u6xZtJZYVRz1/+3deXxU9dX48c+ZfSYLJAMislpEVHalijsIKO5Vn9altda1rVq11se6tD+tXbS1j1pbrI/V1vbRUq2WUlQWqyjijsoiohZc2IKEmeyZ/X5/f0wSEmZCEpLMnQnn/Xr5ariTufdwG5KT7z3fcwQ8fi8X/eRrWR+rqtzQJEntmdQnQLalYTekKkCTpD5JxAe+E+0Oo8eVlZUhIoTDYQ488EBgZ3PJVCpFTU0NZWXtjFxRqge4PW7+56XbWTr3VV7+++uUlBVx2ndOZNzRB9kd2l5NkyS1Z1zjIPV55nETb5qlplThcLlczJo1iyFDhrR59DZmzBhmzZqFx+Pp4AxKdZ/b4+bEi6Zx4kXT7A5FNdEkSe0ZZzs7WVwH7V2z01SfcdRRO0eOFBUVEQqFGDBgAAMG9I1HikqprsvPh+wq/0WeyX48tb7d3i35ypgEVsOjWJWnYFWeiFX3W4ylu0n2NrFYjC1btmCMaRl0C1BTU0MoFLI5OqWUHTRJUnvG1LVzPAJkznPKZ6b6Kqi7B1LrIfUZNDyECV+AMfm7q0n1vPfee48//OEPNDY2EgwGWxKjuXPnsmjRIpujU0rZQZMktWfcE7Ifdx2ISOF0hjWJ1RB/E4i2OhpLJ0uxF2yKStmhdS1SeXk5dXV1xOPxNgmTUmrvokmS2iNSemtTp+XmhMgB+JDS22yMag/EV0K2buGmERNfkft4lG1atwFo/rg5YaquriaV0q7ySu1t9uokyRgLk9qBMbv2+1EdEfc4JPgP8J8JrjHgOxUJPoV4ptgdWtc4B6XbFmTwgXNIzsNR2TXUNLB90w4sq/ce5fbv3x+Hw9GSGMHO5pKWZVFT0/vz0JRS+aXgdreZ5AZMw+PpTs+eqUjga4ij6422rMb5UHcnmIb0eQNfQ0puQrL+wFTZiOtLSL+77A6je7zTQXzpifat+z6JE/GfYVtYKq2hpoFffWsOby96D4fDQVH/ANc9+G2OPL3nk3Gn00n//v3bJEmhUIgRI0a0fNx8XCm1d+hwJUlEhonIUhFZJyJrRcS2KY8m9gpmx1kQmQvxl6H+N5gdp2KscJfPQ+2PwYRJd42OQePfMbU/7ZW4Vf4S8SDlfwXXgYCX9ArSUKTsUcShPxDtdttZd/P2wvdIxJLEInHCFdX8/Px7Wf/ep71yvdmzZ3PkkUfi9XopLi4mHA4zaNAgzjnnHAYPHtwr11RK5a/OPG5LAj8wxhwMTAWuEpGcD5IxxsLU3ES6wLa5NiAKVghT/2DXzlU/h7aFuk3niszDWA3dD1YVFHHtj2PAAmTgEmTAM8iAFxDPRLvD2utt3bCNdW/+h0S87S7DRDTBU/cs6JVrHnjggQwZkn7M2lyw7fV6GT9+PMXFfbv/lzEJrPo5WNuPxvpiMlbVVZjkRrvDKnh1VfUsfOQFnr73GT5bu8nucFQXdZgkGWMqjDHvNn1cB6wDcl+skdoMVn2WFxIQfb7r58rKAVZVVyPLOWPVYZKfYUzc7lD6FHEORlzDEck27V7lWuWmEG5PZkWAZRm2rN/WK9dsaGjggw8+IBaLtemVtG3bNjZs2NAr18wXpua/of5/wapMlyHEXsCEzsakdtgdWsF694U1XDD8Ozxw3Z945ObHufrwm7j/6ocLrpfc3qxLhdsiMhKYDLzZG8Hs/uIBdq4g7aKrNUnuCUCWH4TiBOc+XY0sZ4yJYVXfgNl+JCb0Fcz2qVgNj9sdllK9Yv/xw0nEEhnH3V4XE6f1zmJ2RUUFTz75JNu2bSMYDFJfX08sFmP58uU880w7DVT7AJPcDNEXaLvCboGJYhr/aldYBS0eS3DHOb8m2hAj2hAjEU8/Mn7+zy+xYvFKu8NTndTpJElEioGngeuMMbVZXr9CRFaIyIrKysqejDF9fucAcE8io9Zc/BD4ZtfOVXxtuli3TaLkh+LrEMnfGU2m5kcQXQzE04XGph7qfoWJaj8f1feUBks48+rZ+Iq8LcccTgf+Yh9nX3tqr1xz111tsLMlQJ9uA5D8uJ1dnnFIvJfzcPqCVS+txWQZAh5tiLH40aU2RKT2RKeSJElv+XoaeNwY849sn2OMecgYM8UYM2XgwIE9GePOOPrfB64vpVeVpBjwgO8riP+crp3HPQYpnwueY0H6g2sM0u9OHEVdS7ZyyVj1EF1IutC8tQimoWs1WUoVist/eSFX338pI8cNI7hfGTO/cRy/f+dXlO9b1ivXa24D0HonW/NuN2MMVVX5/zh+j7iGQ9YO825wjc55OH2BlWq/XUUqWVhTCfZmHbYAkHSBxiPAOmPMPb0f0m5icQ6A4AJIvg+pL8A9DnHuu2fnch+ClD/cwxH2IquKnY0bd5HqnfoMpewmIpx08XROunh6Tq7ncDgoKyvLaAMwatSolo/74sBbcR2AcU+AxEqgVa2juJHAhbbFVcgmThuLZWWuJPmKfMy68HgbIlJ7ojMrSUcDFwIniMjKpv9O6eW42iUiiHs84pu5xwlSQXLuC5Itp3WA+7Cch6NUX9W8q83tdlNaWprRXLKvkrIHwTcb8ADO9Ap72Z8R1zC7QytIvoCXm/7yPbx+D26vCwR8RV6mnn4YU0/X79mFQnqjyn7KlClmxQod6dDTrMYnoPYXQKTpiAPEjwSfRlxfsjM0pfqMyspKnE4n5eXlPProoySTSS677DI2btzIwIED8fv9dofYq4xJgEkgjoDdofQJO7aEWDr3VeprGvjy7MmMPWqM7qDNQyLyjjEmo0ttwXXc3ps5AudinPti6n8PqQrwHIYUfw9x7W93aEr1Ga1rKoPBIOvWrQNg+PDhdoWUUyLudoq41Z4YMCTIV2/Q7v2FSpOkAiPe4xGvPs9Wqrc0NjayevVqRo8eTXl5OY2NjUQiEUKhEJs3b2bq1Kl2h6iUypG9esCtUn2ZMRYm/i4m9irGRDp+gwIgHo+zaNEiPvvss5Y2AOFwmPXr17N48WKSyWy7wJRSfZGuJCnVB5nEh5iqy9O9tBAghSn5KY6ALvt3pLS0FJfLRTgcZtiwdNFyc68kYwzhcJh99snfprNKqZ6jSZJSfYwxCUz4IjC79PSp/RHGcwjiOsCewApEcxuA5l5JIkI4HGb06HS/IE2SMsVjCZY//QYfv7OBoQcOYfr5R1NUqoXfqvBpkqRUXxN/lTa9blokMI1PIqW35Dqi3TImBokPwVGaN5sQmue2uVwu+vXrRygUaqlFCoVCNkeXX2pDdVx9xM1Uba8hWh/FV+TlTz/6K/ct/xnDxuR+zKdSPUlrkpTKU8lEkvdeXMNbC98jUt+FmiIrY2pQkxRY+fUD3mqch9k+FVN1MWbHmVg7zsCkKuwOi2AwSFVVFcaYloTJ5/MRCAT6btftPfTwzY9TuWkH0fr03LdoQ4y6cAO/vuQBmyNTqvt0JUmpPPTB6x/x4zPuIplIzwpLJS2uf/g7nHDeMR2/2XN49hETEkC8M3o40j1nEquh9jbaDFVNfowJXwIDnutSLxljYunJ9VLWIz1ojjvuOKZPn46IEAwGWbNmDcYYrrzySgIBfYzU2vKn32z5Om1mjOGjtzcQaYjiL/LZFFnnReojLJ/3FjWVtUycNpbRh2rfOZWmSZJSeSbaGOOWU35BQ01jm+P3XPp7xkwZxZADBu/2/eLcF1N0CTQ+Cs272sQProPAN6uXou48Y4XTk+Ub/0bbqfMAFlgVkPwA3GM7ca5GTO3tEH0OMOAYCP3uQLzHdStGn2/nD/by8nKi0SiRSITi4uJunbcvcrjafyDhcOR/08SPVmzgh7PuwEpZJOJJnC4nR5x6KLfOvQ6HQx+27O30K0CpPPPms+9iWZkDMFPJFEsefalT53CUfB/pPwe8s8BzFFLyI6T8L+lGgTYyyY2YypOg/n/B2t7OZzk7/VjQ1Hy/afBzHEiAtRVTdTUm8UG34kwkEixZsoT169e3tAFo7pO0YMEC4vFsNV97p5kXHofb2/bryuF0MGn6WLx+r01RdY5lWdx+1q9oqGkkUh8lGU8Sa4zx1nPv8sJjr9gdnsoDmiQplWcaahoxqcxxQclEitpwfafPI95jcJTNwVH+KBL4KiKengxzj5i6O8HUAbHdfFIc3BM6PleqAmKvZTlXHNPQveHVLpeLt99+mw0bNrQZdFtTU8M777yjdUmtXPSTcxk1aST+Yh9urwt/iY+BQ4Pc8Ker7A6tQ5+s+jxjxRbSdVULH3nBhohUvtHHbUrlmckzxmVdSfIV+zjy9IzRQoUl/hqQ+XdrIX4o+jbi6N/xuVJbQTxgdk2SLEh+2p0oEZGWgu2ysjIcDgfhcJiDDz4YSCdMgwYN6tY17LJja5gFDyzmP+9+wgGT9+eMq2YzYL/yPT6fv8jH/a/9nNXLPmDDys/Yb9S+fHn2JJwuZw9G3TtSKSvdRizba8lU9hfUXkWTJKXyzOD9B/GVa07hX3MWEW1IJwC+Ii/jjz2YKSdNtDm67vKzc0BzawLuI5HibyHeaZ07lWtUlgQJwA3uQ/c8xCbl5eUtw2779+/f0jcJCrcNwOcfbOKao24lEUuSiCVYufR95s9ZxH3Lf8b+4/Z8Np2IMPH4sUw8vuM6snxywOSReHweInVta+N8AS+zvjnNnqBUXtHHbUrlocvv+gY/mXcjx597FFNPP4zr//BdfvqvHxZ+IWngXGDX3U5u8J2BI/ho5xMkSK82Bb5OOvFq5gDxIcWXdjvU5jYAlmW1rCp5vV6Ki4sJh8PdPr8dfvu9R4jURUjEEgAkYkkaayP87upHbI7MHk6nkx8/cT2+Ii8eX7quyl/s4+CjDmT2JdNtjk7lA11JUipPHTpzAofO7Lg2p5BI8VWY5HqILUtPmjcpcI9DSm/bs/OV3IRxjoDGP4JVA54jkJIbEOd+Hb63NlzH8n+8RbQhypdnT8pofFheXo7X66WhoYFgMMjGjRsxxjBw4MCCLdx+/5V1mMxyN9YsX4cxpkfaJxSaidPG8pcNc1g6dzlVX9QwafpYJs8YX/i/kKgeISbbv5humjJlilmxYkWPn1epXDImDiaJOLQvTk8zyc8g+RE4RyLuMTm//tuL3uMn//U/iKR7UIlDOPOq2Vzxqwt3xtgqaXjzzTdZuHAhN9xwA0VFRQWbTJzR78KMR0uQfpy7oO4xGyJSKj+IyDvGmIyiT02VldqFsaqxqr6H+WISZvthWDvO6vaWctWWuEYivpNsSZCijTHu+Oo9xBpjRBtiJGIJ4pE4C36/mFUvrd0ZY6tEqHUbgEJNkABOuviElsdKzdw+NyddrI+W9ibxaJyGmga7wygImiQp1YoxJj0cNvYikARSkFyLCX8dk6q0OzzVA959fjUOZ2aiE2uM8fxfXmpzbP78+bz22mstBdvhcJht27bx2GOPsX17e32e8tdld17AxGlj8fo9BEr9eP0eJh5/CJf/8ht2h6ZyoK6qnju++mvO7H8R5+xzKZeNv551b/7H7rDymtYkKdVaYiWkPgcSbY+bBCbyBFJ8tS1hqZ6TSlmQpcrAGEgm27YnqKiooLa2luEDRxJrjBEKhdhvv/1Yv349kyZNYp999slR1D3D6/fyi+duZeOHW9j04RaGHTSE4QfpENq9xc2zf86GVZ+RjKfHFn2+dhM3zrqDR96/h32GD7Q5uvykSZJSraU2kr1xShyS63MdjeoFh84cn7UHjq/Iy4wL2s7Gq9lSz0O//T+eSC7ik9hHrF7wMQ8vSg9uLdQdbgDDNTkqWOFtVTz563/x7vOrGThsAF/9welMmj6uw/f9591P+PyDTS0JUrNkPMm/HljMZXfpamI2+rhNqdZcB6V3XGXwgXtSzsNRPa+oNMD1j3wXj9+Dy+MCSffFOfacqUw5aef/x1vWVzDv14uoqakm2hDDmXTy6cefcevJv6CkpKRgeyWpwhWqqOKKCTcw/3eL+HTNRt567l1+dPqdneoOXvHJFzicmT/yk/Ekn6/b3Bvh9gm6kqRUK+Ieg/EcDvE32TnuwgGOYsR/jp2hqR50wnnHMPbIMSz923IaayNMPX0KBx8xuk1R9oIHl+BIOjEYEsRx4SFiNVC5KUSsarAmSSrn/nbnPBpqGkgmdv4iF2uM8+AP/syMbxyHx9v+bMZRk0a2eV8zj9/DuKMP6pV4+wJNkpTahZQ9gKmfA5En0x2dvdOQkhsRR4ndoakeNGjEQM774Vntvr7tk+04k268+DFYuPFgYZGSJD5HEcXFxRnvMSYKeBDRRXrV81YsWZU10THGsPmjrXxpwoh23zvkgMEcceqhvPnsu8Qj6T5fDqeDQLGPky+b0WsxFzpNkpTahYgHKfk+lHzf7lCUjSadMI4VS1bha0x39E41PYaNxBu54JJz2XfkzqJtE3sFU/sTSG0G8WL8FyAl1yPS/m/2SnVV+b792fzx1ozjqUSKfgNLO3z/LY9fy5N3z2fB75cQbYxx+MmTufTOr1Narr8AtqfgkiRjVWFq74TY4vQB70lI6U2IY88HNCql1K5O+tY0nvqfBYQrqkjEk7jx4HK7mDR7bNsEKb4KU3UV0NSk0USg8XGMqUP6/cye4FWf9LX/PoOPVmwg1rhzZqHL42LcsQcTHFzW4ftdbhcX3HIOF9yipQOdVVBrwsYkMaFzIfpM+huRiUD0GUzoXIxJdHwCpZTqJH+xnwdW/JKRJw8iPrCO0RNGccTJhzL7u9Oora3lgQceYO3atelHs+w6aDcKkfkYq9aO0FUfdcSph3Hxz87DG/ASKPXj8bkZd/RB/OhvuurdWwprJSm2FKxK0k3+miXTx2JLwXeiXZEppfqg0mAJJ3z9GMZM259rr72WOXPmUFVVRSAQoLKyksrKSg7e5xOyNl4SN6QqwNHxYxClOuuc607jlMtn8vnaTZTv21/7G/WyglpJIvkfMI2Zx00k/ZpSSvWwYDBIdXU1qVSK8vJywuEwLpeL0tLS9A4311iyfis1SXAOzXm8qu/zF/k46PDRmiDlQGElSa79QbIMG5UAOPfPfTxKqT4vGAxijKGqqopgMEg4HMYY0/Jxugu7t+2bxA+BixBHUY/E0FgX4Y1n3mHFklUk4lpaoFSuFNbjNu8MkFIwUaB5G6QTpAR8M+2MrFNM4n2IvQJSBL6TEaf+FqBUvmue2xYKhSgvLyeZTFJbW0swGGTNmjXgOgAJPoapvQsSa8BRBkWXIYGe6WD8wl9f4d4rHsTpcgLgcDj46b9+yLhjDu6R8yul2ldQSZKIB4JPYmpvg9jL6YPe45DSn6Rfy1PGGEztrRB5lnSBpxvqfg3970N8J9gdnlJqN4LBIGPGjMHr9eLxpL/PhEIhRowYQTQaJZVK4XKPR4KP9/i1t6yv4N7LHyTW1Nem2S2n3skTWx/CX+Tr8WsqpXYqqCQJQJyDkLIHMSY9iLIgmrbFlzUlSJGmA+mdMKbmevC+jojfttCUUrvn9/s5//zzAaipqQHSc9umTJnCuHEdz8zqjiV/finrnDmANxa8w/Tzju7V6yu1tyuADCM7EUdhJEiAifyTnQlSaw6IvZ7rcJRSe8CyLEpLS3G5XC0jSYwxpFLZk5ie0FDdkLXDspWyaKzNsolFKdWjCiPLKHjZpsp35jWlVD5YuHAh999/PyLSssPNsizuvvtuXn755XbfF4vEWPDgEm497Rf8+tIH+GjFhi5d94jTpuAr8mYcN5bFobMmdPnvoZTqmoJ73FaIxP8VTPQFMleTLPBOtSOkLjGpbZj636WLzh3lSNGl4Du1zTBQpfqyQCBAdXU1iUSCYDBIZWUlDocDr9dLOBzO+p5oY4zvTb2Zik+2E2uMIQ7hpSde5erfXsrsiztXi3jYrAlMnjGe915YQ7Qh/ZjeV+TlK1efzOD9B3XqHJZlMffOefzjvmeoq2rgSxNGcNVvLmH8sVr4rVRHNEnKBc+x4D8DIvNJN8JM33bpd2/e1yOZVCVmx5lgaoEUWBXpIvTkBqTkWrvDUyonmne4NbcB+Pjjj7Esi2Aw2PLobVfP/eHfVHzyBbHGdNG1sQyxxjhzrvkj0849Gl8gc4VoVw6Hg9uevoFX573F0rnLcfs8nHLZDCZN73wt1IPX/5nnHn6hZZTFhpWfcfPJP+feZXcw+tAvdfo8Su2NNEnKARFB+v0UE7gAYsvAUZxuAVAA8+ZM45/A1LOz5QLp5p0ND2OKLka0m7DaCwSDQWBnG4BUKkVNTQ3BYJBNmzZhjMlYWX3l6TdaEqTWHE4HH729nonHj+3UtZ1OJ8f915Ec919HdjnuhtpGnn3oeeLRtr2V4pE4j//sKW7/x41dPqdSexNNknJI3AeDu8CWuGNvAFma14kbkh+DZ0rOQ1Iq11r3Sho2bFjLx+Xl5cRiMRoaGiguLm7znpLy4ozzQLrouqg0S1PcXrB94w6cbhfskiQZY/h0zcacxKBUIdPCbbV7ziFkLS43CXB0riZCqULn8/k46qijGDx4cEvCFA6HGT58OMccc0zW95x51eyMomsRIbhfGaMmjeztkAHYZ/gAUolkxnERYf/xw3MSg1KFTJMktVtSdBkZIxfwgGcy4hpmR0hqN4zVgFV7F9b2o7C+mIpVc4dOou8hJ554IqNGjaK4uBiPx0MoFGLw4MHMnDkzYxUJ4LBZEznvprNwe90ESv34S3zsM3wAP3/2lpxteigqDXDqFbPw7lL/5PF7+MaPv5qTGJQqZB0+bhORPwKnAduNMb3bOU3lHfFMxPT7JdTevnMcjOdopP/ddofWZxgTB5Po9pwvYyxM+MKmYc/pIl0iT2Dir8GABYi4ux/sXsyyLGpqaigrK2tpAwAQi8VIJBJZE6Wv33oOp317Fh+8/jGlwRIOnjoah6P3fjfNVhv1nXsuov8+/Xj63gVtdrcdMFnnXSrVETHG7P4TRI4D6oG/dDZJmjJlilmxYkUPhKfyhTEpSG0BRwniKLM7nD7BWDWYmh9B7EXAAtdopN/PEff43b8vtQNMIziHtmmoamKvYqqvSr/WmgSQfr9EfCf1wt9i77Fs2TJefPFFbrnlFubPn09FRQXXXHMNv/3tbxk0aBBf+9rXdvv+9Ss/ZfGfltJYG+Hosw5n6mmH9UjCFIvEeOi//4/Fj75EPBpn7JFjuOaBy9h//Ihun1upvYWIvGOMySiy7XAlyRizTERG9kZQqnCIOMGlNQw9xRiDCV8CyQ9pKYxPfpheCRqwCHHum/me1HZM9bXpIao4wVEC/X6JeJtGUyTXgcncTYVpxCTWapLUTc073MLhMOXl5axbt45UKrXbNgDN5s9ZyB9ufIxELIFlGZY99ToTjh/LHfNvxOl0diuu28++m9Uvf9Cyg+39Vz/kumN+zCMf3MuAIcFunbunJOIJXnriNV7951uUBks47duzOPCwUXaHpVSHtCZJKTsk10JyPRk7B00S0zg349PTSdVFkFgJxIEIWNsxVd/FJD9Lf5JzKEi23jsBxKkJbne13uEWDAaxLIvq6uqWR2/trcrXhup46L//j1gkjmWlPyfaEGP1sg94Y8E73Ypp00dbWLNsXcYW/0Qswfw5i7p17p6SiCf4wbTbuP/KP/DqvLdY/McXuf74/8czDz1vd2hKdajHkiQRuUJEVojIisrKyp46rVJ9U3IjZJ09GG9KnnaRWAVWBW36VaVPhGn8a/pD7wkgRbT9Zy3pxMl3co+EvTdrvaut9cfBYJBEIkFdXV3W97334vu43JmL9tH6KC//vXuzGzd9uBWnO3MlKhFPsv69T7t17p7ywuPL+XTNxpaO4VZTU83ff/9RGrLMnzOp7VjV38faNgHri0Oxam7DWPW5DlspoAeTJGPMQ8aYKcaYKQMHDuyp0yrVN7nHgMk2GNUH7kmZh60vyP7PNQmpTQCIeJDgk+CeQvpJugvcE5Hg37pdFK7A6/VSUlLSspIEO3slAe2OJ/EFPFmPi0MIlHSv4/7wg4dkHYDr9roZfVh+dNNe9vfXWhKk1lxuJ+8v/7DNMWMimNA5EF0ERNONbCNPYcIXtrtSp1Rv0maSStlAXKMw3qMh9ioQbTrqSBdZB7IUALvHZa83wg+enfP/xLkfEnwMYzUABnFkb2io9sysWbMoLS0lEAi0zG0bP348p5xySkuytKvJMycgjswt/x6fm9mXTO9WPEMP3I9J08ex8sU1LY/cRNLnPvOq/Fg9LC4rRgR2zXGMMRSV7pIkRp4Dq462K6YJSH0K8bfAe0Rvh6tUGx2uJInIXOB1YIyIbBaRS3s/LKX6Pun/Gyi6HBwDQYrBdwoyYB7i6Jf5uc4h4P8K0PqHihscZYj/nMzPdxRpgtQLJkyYwMiRI9NNIZsKtouKijj88MMpLc0+osfjdfPzZ2+hqF+AQIkff7EPj8/NN28/l4MOH93tmG576gec9p0TCZT4cbqcTJw+jt+8+jOCg/NjF+pp356Fx59ZKxco8XPIUWPaHDOJtUDmIzhMKt3hX6kc67AFwJ7QFgBK9TxjLEzkKWh8DKx68J2IFF9REDMA+4poNEpFRQVDhw5l/vz5bNmyhWuvvZZwOEwkEmHIkCHtvjcejbNi8SqiDVEmzxhP2aD+OYzcXk/86p/85fYncXlcYMAb8PDLJT/OaFNgNcyFuruASNsTSADp/zvEm727uVLdtcctAJRS+UHEkX4Ul+1xnMqJTz/9lCeeeIIrrriCYDDI2rVrSSaTLF68mKqqKq688sp23+vxeTjqzC/nMNr8ce6NX2H2JSewetk6ivoFmDjtkKytD8R/Oqb+PjAxwGo66kqPQPIcldOYlQJtAaCU6iOMMax78z+88cw71OzonVEsu+5wM8ZQXV1NMBjcbRsABf0GlHLs2Udw6Izx7faGEkcxEvw7eI4g/ePJBd4ZSHBum8apSuWKriQppQrets/Ti362AAAHm0lEQVS288MTf0rVtmrEISTjSc676Swu/H89O5+sda+kUaNGtXwcDAZJJpPU1tbSr19mTZnqPHENR8r/jDFJwKHJkbKVfvUppQqaMYYfn34X2z75gkh9lMbaCPFogifvns+bz3a9WaMxBhN7A6vmdqzaOzGJD1pec7vdlJaWtvRHgrZ9kzrqvK06T8SlCZKynX4FKqUK2sZ1m6n4dHtLN+tm0YYY//zdwi6dyxiDqb0ZU/1tiMyFxj9jQudhNTzS8jnNu9r8fj9+vz+jb5JSqu/Qx21KqYLWUNOI05X9973acBc7NSfehuhCMM27qwwQhbr7ML5TEee+zJgxo6WmprkWqaSkhPPPP5/99ttvz/8iSqm8oytJSqmCdsDk/TFWZsG0x+/h2LOnZnlH+0xkCZhollccEFsGwNChQxk8eDCQrlEKhUKICGPGjKGkpKTL8Sul8pcmSUqpgubxebjmgcvwBjw4mjpbewMe9hk+gDOuPKlrJ3P4yP5tUVqGB0ciEVatWkVNTQ3BYJCamhoSiQTbtm1j9erV3fvLKKXyij5uU0oVvJnfOJ4Rhwxj/pxFhLZWMfW0QznxW9PxF/m6dB7xnYFp+AuZg4RNeoAwUF9fz7x58zj77LNbCrarqqp4//33ef311xk3bhwOh/7+qVRfoEmSUqpPGH3ol7jhkfabOXaGuA/ElNwAdXeDOAEBk0LK7kcc6UdpZWVliAihUIgxY9JjNZoH3aZSKWpqaigry4+RIEqp7tEkSSmlWnEUfRPjOxlir4B4wDutzRw8l8tFv3792mz9D4fDDB06FEgnTJokKdU3aJKklFK7EOdACJzd7uvNu9p8Ph9FRUWEQiEmTJgApBMmpVTfoA/OlVKqi5p3tRljKC8vJxwOU1xcjMfj0SRJqT5EV5KUUqqLjj32WI499lggvaq0YcMGRITLL7+c0tJSm6NTSvUUXUlSSqkuKi0tpbS0FBGhvLycuro64vE4AwcOxOv12h2eUqqHaJKklFJdFI/HeeWVV9i4cWObGW5bt27l3//+N6nUri0ElFKFSJMkpZTqIqfTydKlS1m/fn2bJGn79u0sX76c6upqmyNUSvUETZKUUqqLnE4n/fv3b+mPBLT5WIu3leobNElSSqk90LyrzePxUFJSQigUallVCoVCNkenlOoJmiQppdQeGDJkCMXF6SaTI0aMwOfzEQgEGDx4ME6n0+bolFI9QYzJnJ7d7ZOKVAKftzo0ANjR4xfqm/RedY7ep87Te9V5eq86R+9T5+m96hy779MIY8zAXQ/2SpKUcRGRFcaYKb1+oT5A71Xn6H3qPL1Xnaf3qnP0PnWe3qvOydf7pI/blFJKKaWy0CRJKaWUUiqLXCVJD+XoOn2B3qvO0fvUeXqvOk/vVefofeo8vVedk5f3KSc1SUoppZRShUYftymllFJKZZGzJElE7haRD0VktYjME5H+ubp2IRGRr4rIWhGxRCTvKv3zgYjMFpGPRGS9iNxkdzz5SkT+KCLbReR9u2PJZyIyTESWisi6pn9719odU74SEZ+IvCUiq5ru1U/sjimfiYhTRN4TkWfsjiWfichnIrJGRFaKyAq742ktlytJzwPjjDETgI+Bm3N47ULyPnA2sMzuQPKRiDiBOcDJwCHA+SJyiL1R5a1Hgdl2B1EAksAPjDEHA1OBq/Rrql0x4ARjzERgEjBbRKbaHFM+uxZYZ3cQBWK6MWZSvrUByFmSZIxZYoxJNv3xDWBorq5dSIwx64wxH9kdRx47HFhvjPnEGBMH/gacaXNMeckYswzQIWIdMMZUGGPebfq4jvQPtSH2RpWfTFp90x/dTf9pYWsWIjIUOBV42O5Y1J6zqybpEmChTddWhW0IsKnVnzejP9BUDxGRkcBk4E17I8lfTY+QVgLbgeeNMXqvsrsPuBGw7A6kABhgiYi8IyJX2B1Ma66ePJmI/BvYN8tLtxpj5jd9zq2kl7cf78lrF5LO3CfVLslyTH+TVd0mIsXA08B1xphau+PJV8aYFDCpqa50noiMM8Zo3VsrInIasN0Y846ITLM7ngJwtDFmq4jsAzwvIh82rYTbrkeTJGPMzN29LiIXAacBM8xe3Hugo/ukdmszMKzVn4cCW22KRfURIuImnSA9boz5h93xFAJjTLWIvES67k2TpLaOBs4QkVMAH1AqIo8ZY75hc1x5yRiztel/t4vIPNJlFXmRJOVyd9ts4IfAGcaYxlxdV/U5bwOjRWR/EfEA5wH/sjkmVcBERIBHgHXGmHvsjieficjA5p3JIuIHZgIf2htV/jHG3GyMGWqMGUn6e9SLmiBlJyJFIlLS/DFwInmUdOeyJul3QAnppbSVIvJgDq9dMETkLBHZDBwJPCsii+2OKZ80Ff9fDSwmXWD7pDFmrb1R5ScRmQu8DowRkc0icqndMeWpo4ELgROavjetbFoBUJkGA0tFZDXpX1ieN8bo9nbVHYOA5SKyCngLeNYYs8jmmFpox22llFJKqSy047ZSSimlVBaaJCmllFJKZaFJklJKKaVUFpokKaWUUkploUmSUkoppVQWmiQppZRSSmWhSZJSSimlVBaaJCmllFJKZfH/AUTgW1h0BarjAAAAAElFTkSuQmCC\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X, Y = datasets_train[2]\n", "X_test, Y_test = datasets_test[2]\n", "\n", "# On commence par définir le SVM \n", "model = SVC(kernel='linear', C=10e6)\n", "\n", "# Puis on entraîne ses paramètres avec la fonction fit()\n", "model.fit(X, Y)\n", "\n", "fig = plt.figure(figsize = (10,5))\n", "ax = fig.add_subplot(111)\n", "\n", "plt.scatter(X[:, 0], X[:, 1], c=Y)\n", "plot_svc_decision_function(model,ax)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "À la prochaine nous obtenons la performance du SVM sur l'ensemble d'entraînement et de test. \n", "\n", "(Pour mieux comprendre, vous pouvez voir la documention (en anglais) du classificateur SVM [ici](https://scikit-learn.org/stable/modules/generated/sklearn.svm.SVC.html). Nous y reviendrons à la semaine #4.)" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Accuracy train: 79.0 %\n", "Accuracy test: 79.0 %\n" ] } ], "source": [ "acc_train = (sum(model.predict(X)==Y)/len(Y))*100 #QUESTION - complétez ces deux lignes\n", "acc_test = (sum(model.predict(X_test)==Y_test)/len(Y_test)) *100 \n", "\n", "print(\"Accuracy train: \", acc_train, \"%\")\n", "print(\"Accuracy test: \", acc_test, \"%\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On note que notre jeu de données n'est pas séparable linéairement, c'est-à-dire que les deux classes se chevauchent et il n'existe pas une frontière de décision linéaire qui permet de parfaitement les séparer. \n", "\n", "Bien que les SVM aient une assise théorique, ici nous essaierons plutôt de raffiner notre intuition sur ce modèle. \n", "\n", "Le SVM tente de maximiser la marge tout en minimisant l'erreur d'entraînement. Dans le cas de jeux de données non séparables linéairement, ces deux objectifs peuvent être contradictoires.\n", "\n", "Pour calibrer les deux objectifs, les SVM utilisent un hyperparamètre (dans sklearn il est dénoté par la lettre 'C').\n", "\n", "Tel que vu la semaine dernière, en apprentissage automatique, il est important de trouver les bonnes valeurs à un hyper paramètre. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Question 2 (SVM): (Sauter si manque de temps)** en vous référant à la documentation des SVM [ici (en anglais)](https://scikit-learn.org/stable/modules/svm.html#svc) trouvez l'hyperparamètre qui contrôle la régularisation et changer le pour obtenir une marge plus « soft ». Vous pouvez ensuite mesurer la performance de votre modèle. Y'a-t-il des gains?" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Accuracy train: 79.0 %\n", "Accuracy test: 79.0 %\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "X, Y = datasets_train[2]\n", "X_test, Y_test = datasets_test[2]\n", "\n", "# nous créons un modèle de classification SVM \n", "model = SVC(kernel='linear', C=10e6)\n", "\n", "# nous apprenons ses paramètres.\n", "model.fit(X, Y)\n", "\n", "fig = plt.figure(figsize = (10,5))\n", "ax = fig.add_subplot(111)\n", "\n", "plt.scatter(X[:, 0], X[:, 1], c=Y)\n", "plot_svc_decision_function(model,ax)\n", "\n", "acc_train = (sum(model.predict(X)==Y)/len(Y))*100\n", "acc_test = (sum(model.predict(X_test)==Y_test)/len(Y_test)) *100 \n", "\n", "print(\"Accuracy train: \", acc_train, \"%\")\n", "print(\"Accuracy test: \", acc_test, \"%\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Maintenant, entraînons un modèle SVM sur nos trois jeux de données \n", "\n", "(*Note: on vous suggère de complétez la question précédente avant de lancer la prochaine cellule qui pourrait sinon prendre beaucoup de temps à se terminer.*)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for i, (ds_train, ds_test) in enumerate(zip(datasets_train, datasets_test)):\n", " ds_train = datasets_train[i]\n", " ds_test = datasets_test[i]\n", "\n", " X = ds_train[0]\n", " Y = ds_train[1]\n", " \n", " \n", " X_test = ds_test[0]\n", " Y_test = ds_test[1]\n", " # 1) on entraîne les paramètres\n", " model.fit(X, Y)\n", "\n", " # 2) On obtient les prédictions\n", " # a) pour l'ensemble de test\n", " pred_test = model.predict(X_test)\n", "\n", " # b) pour l'ensemble d'entraînement\n", " y_x = np.dot(W.T, X_b.T)\n", " pred_train = model.predict(X)\n", " \n", " # 3) visualisons les résultats\n", " plot_predictions(i,X,Y, X_test, Y_test, pred_train, pred_test, plot_svm=model)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Modèles probabilistes" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1. Modèle Bayesian Naïf (Naive Bayes)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour l'instant, nous avons exploré des modèles linéaires pour la classification (pour rappel, un modèle est linéaire si ça frontière de décision est linéaire)\n", "\n", "Maintenant, nous explorerons un modèle de classification Naive Bayes. Le modèle a été introduit dans les capsules et nous verrons qu'il peut apprendre une frontière de décision non linéaire.\n", "\n", "De plus, le modèle Naive Bayes est un modèle probabiliste. Entre autres, il assignera donc une probabilité à ses prédictions (par exemple le modèle pourrait prédire qu'un point fait partie de la classe +1 à 70%) plutôt que seulement en prédire la classe." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Dans nos trois jeux de données synthétiques, la variable cible a deux valeurs possibles$y \\in \\{0,1 \\}$ (ou de manière équivalente -1 et +1). \n", "\n", "La variable cible est donc une variable binaire que l'on peut modéliser avec une distribution de *Bernoulli*\n", "$$P(y=k ;\\pi) = \\pi^k(1-\\pi)^{1-k}.$$\n", "\n", "Les variables indépendantes $x \\in \\mathbb{R}^2$ sont des variables continues. Comme discuté dans les capsules, nous pouvons donc les modéliser avec une distribution gaussienne \n", "$$P(x; \\mu, \\sigma) = \\mathcal{N}(x_j | \\mu_{jk}, \\sigma^2_{jk}).$$\n", "\n", "En modélisant les variables cibles et indépendantes avec ces distributions le problème sera donc d'évaluer les paramètres de ces distributions:\n", "- la probabilité d'un succès $p_k$ pour la Bernoulli et \n", "- le vecteur des moyennes $\\mu$ et les variances $\\sigma^2$ pour la Gaussienne.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La procédure pour apprendre le classificateur Naive Bayes est décrite ci-dessous. \n", " \n", " 1. Calculer estimateur du maximum de vraisemblance (*MLE*) pour les paramètres de la distribution : \n", " $\\theta \\in \\{$ $ \\sigma^2_{jk}, \\mu_{jk}, \\pi $ \\} en utilisant l'ensemble d'entraînement.\n", " 2. Utilisez les paramètres estimés avec la formule de Bayes pour obtenir des prédictions : \n", " \n", " $posterior \\propto joint \\space distribution = class\\space conditional * class\\space prior$\n", " \n", " $P(y = k|x) \\propto$ P(y = k, x) = P(x | y = k) P(y) ." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nous allons maintenant implémenter un modèle NB pour nos trois jeux de données synthétiques.\n", "\n", "\n", "Commençons par préparer nos données." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "# on utilise le jeu de données qui contient \n", "# les deux cercles concentriques\n", "X, Y = datasets_train[1] \n", "X_test, Y_test = datasets_test[1] # idem pour le test\n", "\n", "# le code suivant \n", "# on veut obtenir une structure qui nous indique quelles sont les données\n", "# qui appartiennent à chacune des classes\n", "\n", "#class indices\n", "i_c0 = (Y == 0)\n", "i_c1 = (Y == 1)\n", "\n", "X_0 = X[i_c0] #data of class 0\n", "X_1 = X[i_c1] #data of class 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1.1 Entraîner le modèle (vous pouvez sauter jusqu'à 2.2 s'il manque de temps)\n", "\n", "Rappel: Pour entraîner le modèle Naive Bayes, il nous faut trouver 1) les prieurs (*class prior*), 2) les probabilités conditionnelles par classe (*class conditional*), 3) combiner les deux termes pour obtenir le postérieur sur y. \n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Les prieurs\n", "\n", "On débute en calculant les prieurs (prior probability) pour chacune des classes. L'estimateur de maximum de vraisemblance (maximum likelihood estimate ou MLE en anglais) d'une variable aléatoire avec une distribution Bernoulli est simplement sa moyenne échantillonnale:\n", "\\begin{align}\n", " \\hat{\\pi} = \\frac{\\sum_{i=0}^n y_i}{n}, \n", "\\end{align}\n", "avec $n$ le nombre d'observations dans notre ensemble d'entraînement." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Question 3 (NB):** À partir de l'équation ci-haut, écrivez le code pour estimer $\\hat{\\pi}_1$ pour la classe 1 (variable `prior_k1` dans le code) et $\\hat{\\pi}_0$ pour la classe 0 (variable `prior_k0`). \n", "\n", "Attention, pour $\\hat{\\pi}_0$ il ne faut utiliser que les données de la classe 0 (et idem pour la classe 1)." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "def calculate_prios(X_0, X_1, Y):\n", " # À faire: calculez la prieur pour la classe 1\n", " prior_k1 = sum(Y) / len(Y) #QUESTION\n", " \n", " # À faire: calculez la prieur pour la classe 0 \n", " prior_k0 = 1 - prior_k1 #QUESTION \n", "\n", " #let's store the priors in a dictionary\n", " prior_dict = {\"class 0\":prior_k0 , \"class 1\":prior_k1 }\n", " \n", " return prior_dict" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1 1 0 1 1 0 0 1 1 1 1 0 1 1 1 0 0 0 1 0 0 1 1 1 0 0 1 0 0 0 1 1 1 1 1 0 0\n", " 1 0 0 1 1 1 0 1 0 0 1 0 1 0 1 0 0 1 0 0 1 0 1 0 1 1 0 0 1 0 1 0 1 1 0 1 1\n", " 0 1 0 1 1 0 0 0 0 0 0 1 0 0 1 1 0 0 1 1 0 1 0 1 0 0]\n" ] } ], "source": [ "print(Y)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{'class 0': 0.5, 'class 1': 0.5}\n" ] } ], "source": [ "prior_dict = calculate_prios(X_0, X_1, Y)\n", "print(prior_dict)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Maintenant que nous avons les prieurs, il faut trouver les paramètres de la Gaussienne des probabilités conditionnelles de classe. \n", "\n", "(*Remarque:* même si la Gaussienne n'est qu'un terme d'un modèle complet (NB), on optimise en général le log de la vraisemblance ce qui a pour effet de séparer les termes de l'objectif et donc pour optimiser les termes de la Gausienne nous pouvons utiliser les estimateurs de maximum de vraisemblance (MLE). \n", "\n", "Comme expliqué [ici (en anglais)](https://www.statlect.com/fundamentals-of-statistics/normal-distribution-maximum-likelihood), la MLE de la **moyenne** d'une Gaussienne est simplement la moyenne échantillonnale:\n", "\n", "$\\hat{\\mu} = \\frac{1}{n} \\sum_{i=0}^{n} x^{(i)}$. Pour notre algorithme, il faudra calculer cette quantité pour chaque classe ($k$) et pour chaque caractéristique ($j$):\n", "\\begin{align}\n", " \\hat{\\mu}_{jk} = \\frac{\\sum_{i=0}^{n} \\mathbb{1}(y^{(i)}=k) x_{j}^{(i)}}{ \\sum_{i=0}^{n} \\mathbb{1}(y^{(i)}=k)} \n", "\\end{align}\n", "(*Notez, $\\mathbb{1}(y^{(i)}=k)$ vaut 1 quand $y^{(i)}=k$ et 0 sinon.*)\n", "\n", "\n", "De plus, la MLE de la *variance* d'une Gaussienne est simplement la variance échantillonnale: \n", "\n", "$$\\hat{\\sigma}^2 = \\frac{1}{n} \\sum_{j=0}^{n} (x^{(j)} - \\mu)^2$$\n", "\n", "(*Comme pour la moyenne, il faut calculer la variance par classe et par caractéristique de x.*)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Question 4 (NB)**: completez l'implémentation des estimés MLE:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "def calculate_MLE(X_0,X_1):\n", "\n", " # Calculez les statistiques pour chaque classe et caractéristique\n", " class_summaries = dict()\n", "\n", " feat_0_class_0 = np.mean(X_0[:,0]), np.std(X_0[:,0])\n", " feat_1_class_0 = np.mean(X_0[:,1]), np.std(X_0[:,1])\n", "\n", " # les ajouter au dictionnaire\n", " class_summaries['class 0'] = [feat_0_class_0, feat_1_class_0]\n", "\n", " feat_0_class_1 = np.mean(X_1[:,0]), np.std(X_1[:,0]) #QUESTION <- à compléter (classe 1 caractéristique 0)\n", " feat_1_class_1 = np.mean(X_1[:,1]), np.std(X_1[:,1]) #QUESTION <- à compléter (classe 1 caractéristique 1)\n", " \n", " # les ajouter au dictionnaire \n", " class_summaries['class 1'] = [feat_0_class_1, feat_1_class_1]\n", " return class_summaries" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "class 0\n", "[(-0.007192166649648344, 0.704420431973722), (-0.008230521965483994, 0.6846599657190768)]\n", "class 1\n", "[(-0.003679746221999508, 0.36171707161392364), (-0.011058582492496059, 0.3425693756367293)]\n" ] } ], "source": [ "class_summaries = calculate_MLE(X_0, X_1)\n", "\n", "# on visualise les résultats\n", "for c, class_summary in class_summaries.items():\n", " print(c)\n", " print(class_summary)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour résumer :\n", "\n", "- Notre dictionnaire `class_summaries` (voir ci-haut) contient une liste avec les moyennes et variances échantillonnales pour chaque classe et chaque caractéristique.\n", "\n", "- Notre dictionnaire `prior_dict` contient les prieurs pour chaque classe.\n", "\n", "Voilà, nous avons terminé d'entraîner le classificateur Naive Bayes!\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1.2 Tester notre modèle" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Puisque nous posé comme hypothèse que les caractéristiques ($x$) viennent d'une distribution gaussienne, nous devons implémenter la fonction de densité (PDF) de la gaussienne. Cette fonction retournera la `fréquence relative` d'une donnée étant donnée les paramètres de la gaussienne ($\\mu, \\sigma^2$): \n", "$$ \\mathcal{N}(x,\\mu,\\sigma) = \\frac{1}{ \\sigma \\sqrt{2 \\pi}} e^{\\left(-\\frac{{\\left(\\mu - x\\right)}^{2}}{2 \\, \\sigma^{2}}\\right)} $$" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "def Gaussian_PDF(x, mean, stdev):\n", " exponent = np.exp(-((x-mean)**2 / (2 * stdev**2 )))\n", " return (1 / (np.sqrt(2 * np.pi) * stdev)) * exponent" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nous pouvons obtenir les prédictions de notre modèle.\n", "\n", "*Rappel:* il suffit d'utiliser la formule de Bayes." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "test point: [ 0.7078584 -0.721475 ]\n", "value of feature 1: 0.7078584041289085, value of feature 2: -0.721474995667992\n" ] } ], "source": [ "# une donnée (de test)\n", "test_point = X_test[2]\n", "print('test point: ', test_point)\n", "print(f'value of feature 1: {test_point[0]}, value of feature 2: {test_point[1]}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Fonction pour calculer la probabilité postérieure d'une donnée de test." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "def calculate_probability(x_test, class_summaries, prior_dict):\n", " # nous allons conserver les probabilités prédites \n", " # dans ce dictionnaire\n", " resulting_probabilities = dict() \n", " \n", " \n", " for c, class_stats in class_summaries.items():\n", "\n", " prior_c = prior_dict[c]\n", " # put P(y) in the dictionary containing the result\n", " resulting_probabilities[c] = prior_c \n", "\n", " for i, feature_stat in enumerate(class_stats):\n", " mean, stdev = feature_stat\n", " resulting_probabilities[c] *= Gaussian_PDF(x_test[i], mean, stdev) \n", " return resulting_probabilities\n", " \n", " " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.7078584 -0.721475 ]\n", "{'class 0': 0.05728953380422133, 'class 1': 0.010803175622848884}\n" ] } ], "source": [ "print(test_point)\n", "probs = calculate_probability(test_point, class_summaries, prior_dict)\n", "print(probs)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`probs` est un dictionnaire qui contient des quantités proportionnelles à la probabilité postérieure de chaque classe pour chaque donnée. \n", "\n", "Notre fonction de décision sera simplement de prédire la classe avec la probabilité la plus élevée.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Question 6 (NB)**: pourquoi dit-on que le modèle NB est naïf? Référrez-vous au code de la fonction `calculate_probability` qui implémentante l'hypothèse naïve." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Réponse**: la ligne 14 dans la fonction `calculate_probability` (*resulting_probabilities[c] *= Gaussian_PDF(x_test[i], mean, stdev)*), \n", "implémente l'hypothèse que les caractéristiques sont indépendantes étant donnée la classe. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**(Bonus) Question 6 (NB)**: Pourquoi les supposées probabilités du modèle NB ne sont pas normalisées?\n", "\n", "Indice: voir la formule pour calculer les postérieurs au début de la section." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Réponse**: Nous utilisons des postérieurs non-normalisées pour calculer les postérieurs." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2 Utilisation du modèle NB\n", "\n", "Nous pouvons maintenant utiliser notre modèle NB sur nos trois jeux de données:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "def train_NB(X,Y):\n", " #class indices\n", " i_c0 = (Y == 0)\n", " i_c1 = (Y == 1)\n", "\n", " X_0 = X[i_c0] # données pour classe 0\n", " X_1 = X[i_c1] # données pour classe 1\n", " \n", " prior_dict = calculate_prios(X_0, X_1, Y)\n", " \n", " # Calcul des statistiques pour \n", " # chaque classe et chaque caractéristique \n", " class_summaries = calculate_MLE(X_0,X_1)\n", " \n", " return prior_dict, class_summaries\n", "\n", "\n", "def test_NB(X, class_summaries, prior_dict):\n", " result = []\n", " for x_test in X:\n", " probs = calculate_probability(x_test, class_summaries, prior_dict)\n", " result.append(list(probs.values()))\n", " return np.array(result)\n", " \n", " " ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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VQ9WdipHKFEAMQhFXkXopqHO2b9qrjWXbVXO4TsPyBmn+ypmaWToxkVIC8CiSKqA7kl3pkigCQOdiGVbuUds37dW6BS+rsb5JklRdWad1C16WpFAkVqG6/QEQSVXahD6IxFMx+rEy9VNZAQCf6KrOiSO2byzbfjGhatVY36SNZdtDkVQBYUNSBXRHshI9hjYCQOx8GBtrDtd1a33QhPL2B4QaSRXSK56K0Q+VKUkSgFRLVlwhPnWtox6qOGL7sLxBqq68PIEalnfFr3wD4EMkVYiNlyphL5Ql0WP7cWgjkGG0eMNP5q+ceck9VZLUu19PzV85M4OlSj/+XxEWJFUIrnQmLCRJAFIlWT3h9Kh3XwKxvfW+KWb/A8KBpAoRnVUY6a6EY/ni4GRdWHjhQsILZQA8jlnEAsZLMTjFZpZOJIkCQoKkCsGTqdbYEF0oAEijZPWE06MeP14rAFdAUhV2V0pA0lUJx5IIJVoWhr6kDT0JSKZAzCJGvCEGAwg0kioET2fJV+tysnGhACAdkhVTiE3dQ0wHEAOSqrCLtfcn1ZVJd3qhGPriWdz7glSK9XPkqc8djS6fIAYDCDCSKgRXuipsLhQAIHhIiAF0Q2CTKk+1VPqBVyqJdE5/jqQLxL0v8C1P9pTS6HI5XgMAARTYpApIqlQOSwQAeA8JMYBuCFxS5cmWynTzWgXgtfIg5UL1/wbP8HRPKfEvuKjjACiASRWQVIypB9LKkwkRwo14DyAGgUuqPN1SmWpeSwC8Vh4AoRCquI/MoY4D0EbgkiogqRhTD6QFQ7cBAH4W2KQqlBWx1xIAr5UHABA+qaqDqOMAtBHYpKojtHwiblSWQEqFeug2AMD3QpVUhYbXEgCvlQfdxoUuAF+pnCE17pZ6T079PU/UcZ5EvYV0C0VSxVh9APAH4nIbDCsDAN8IRVIFID40SADwlfYz8klS1qBIj1UIklNiNPUWMicUSRVj9eFJtEID6CgOMFU3APhOKJIqAPGhQQKAr4R0Rj56Zz5BvYVMCVVSxT8WPIFWaABdxYGQJgYA4GehSqoAxIcGCQC+ErJElN6Zy/EaIN1IqoB0oxUaQCxxgNgQeiRJgH+QVAFeRdIFpNX2TXu1sWy7ag7XaVjeIM1fOVMzSycm7wD8TyPFSL6AzCGpAjKFCyvAM7Zv2qt1C15WY32TJKm6sk7rFrwsSclNrNojDqADfph4wotlAjKJpMqraNEMLyayANJuY9n2iwlVq8b6Jm0s2554UsX/tP/xngG4ApIqAEDo1Ryu69Z6IJW8PPGEH3rRgEwgqfIaWjTBRBZA2g3LG6TqyssTqGF5gxLfOf/T/kWdDCBGJFUAgNCbv3LmJfdUSVLvfj01f+XMDJYKYefF3h8v96IBmURS5TW0aKIV7z2QNq33TaV09j/+p/2HOhlAjEiqAHgOLaDIhJmlE1M70x8QIMRn4FIkVV5FaxgAAN5AnQzgCkiqgFgx/CPlmFUKAAD4UVamCwAgAZUzPkn2AAAAkBH0VAFXwpS6acOsUgA8g1gPoBtIqsKKysLfSPQAAAA8g6QKuBKm1E07eqgAZAyNVgDiQFIVA18PRWpfGVBZBAOJHgBkBnEXQAeSMlGFmc02s3fN7ICZLevg+d5m9pPo8781s4JkHBdIq/wdVKIIDOI20InWWN93euRB7AcQg4R7qswsW9L3JH1e0hFJb5rZVufcW202u19SrXPuj8zsLknflvQXiR471Xw9vfOVeqRoaQsG3j/EIchxG0gZRnoA6EIyeqqmSDrgnDvonPtY0mZJt7Xb5jZJP4z+vkXSTWZmSTg2gABYNmPjxUYLpAVxG7gSeqgAdEMy7qkaJemDNstHJH2us22cc81mVidpqKSaJBw/ZXw9vfOVeqSoKFKDlkv4Q2DjNpAyjPQA0IVkJFUdtVy6OLaRmS2QtECS8vLyEi8ZAE/z9RBbfyNuhwUJQPrUbZKqy6Tmw1KPPGn4SmlQaaZLBSBNkpFUHZH0qTbLoyUd7WSbI2bWQ9IgSSfb78g595SkpySppKTksso7U3x9gUdFmh6MtYe/BD5uAynTUVyv2yQdXyC5+shyc2VkWSKxAkIiGUnVm5LGmtkYSR9KukvSX7bbZqukeyS9IelOSa8556h8gVgEOEHz9RBbfyNuBx0NPelVXfZJQtXK1UfWk1QBoZBwUhUda/+QpG2SsiVtcM7tN7MVkiqcc1slPSPpR2Z2QJGWzrsSPS4SQOWafIy1h48Qt4Ekaz7cvfUAAicpX/7rnHtF0ivt1i1v83uDpHnJOBYQGiFqaaaHKv2I2wFHQ0/6VM6Q1EtS4+XP9eA+QyAskpJUwSdCdJGeMbyWgOcx3BRJ12uM1HT40iGA1i8yWQWAUCCp8jOSomALYEszF7NAksQaFwIQNzyrfUNlr3HSx3+Q9DGz/wEhRFLVDb6/IAzgRToAxIop/JF0jbs/+T07R+qbQ90KSdKuXbuu6dGjx9OSJkjKynR5kLAWSfuam5u/dv3115/oaAOSKj9iGF+4xPu+euhzwcUskCTEf+/I3xF5/Rt3S70n8x60QYyXevTo8fSIESOKhw8fXpuVlcXMqT7X0tJi1dXV448fP/60pLkdbUNSFQPfXhB2VtkS+AGEEFP4I2naJ7eNuyPrqF/xiQkkVMGRlZXlhg8fXnf8+PEJnW1DUuVHDONDVzzYks3FLIBA6z050yXwBN82QqdGFglVsETfz06HcpJUxcB3F4QevKgGAK/wfAyH99G4CZ9asmTJyP79+19YsWJFVbL3/etf/7rf/fffX9DQ0JA1a9asug0bNnyQlRWe28lIqvyMII6OeLiy52IWSJCH/78B3zVCI6kWLVqUv379+spZs2admzFjxtgtW7YM/MpXvnI60+VKl/Ckj0mwesd8fwSI/B2RR9/pkUfrshSpiFsrYwAAEL+29SuQoMVTnilaPOWZomTtb926dUMLCwvHFxUVjb/99tvHtH9+7dq1wyZMmFBcVFQ0/pZbbvnMmTNnsiRpw4YNg8eOHXttUVHR+JKSkiJJqqio6DNx4sTicePGjS8sLBy/d+/e3m33VVlZ2fPs2bNZN99887msrCyVlpZ+9NJLLw1O1rn4AT1VQCplsjWZih4ILv6//SdEvYu+aIAOuIqKij5r1qzJfeONN97Jzc1trqqqym6/TWlpae3SpUtrJOnhhx8eWV5ePqysrOzE6tWrc1999dX3xowZ01RTU5MtSU888cTwRYsWVT344IMnGxoarLm5+ZJ9VVZW9szNzW1qXc7Pz//42LFjPVN8mp5CUhVkbQM391kB8AiGBgHAJ1p7p95/82j/tsv/9J/3vxvvPrdt2zbw1ltvrc3NzW2WpJycnAvtt9m1a1ff5cuXjzpz5kz2uXPnsqdPn14nSSUlJWdLS0sL7rjjjtrS0tJaSZo6deq5NWvW5B45cqTXXXfdVTtx4sTGtvty7vI5Ocws3uL7EsP/gFRoHWZ5fmfkwbBLAAgn6gNkgHNOZtbl7IMLFiwYs27dusPvvffeW48++ujRxsbGLEl67rnnDn/rW986+sEHH/SaPHnytcePH89euHDhyZ/97GcH+vbt2zJnzpzCrVu3Dmi7r4KCgqa2PVOVlZW9RowY0dT+mEFGT1VYdHVzM71WANIgHdMt0wsGwG9ae6SS0UPVavbs2afvvPPOP3rssceqRowYcaGqqiq7fW9VfX19Vl5eXlNjY6Nt3rx5SOvwvf379/eeNWvWuVmzZp3btm3b1QcPHux18uTJC8XFxY3XXnvtiYMHD/bevXt337lz555p3Vd+fn7TVVdd1fLLX/7yqpkzZ57btGnT0L/6q786keh5+AlJVVCRKGUWM3QBSDbiiT9RHyADSkpKGpYuXXps2rRp47KystyECRPqX3jhhUNtt1m2bNnRKVOmFI8aNerj4uLi+rNnz2ZL0uLFi0cfOnSot3PObrzxxtM33HDD+bKyshHPP//80B49erjhw4c3rVq16mj7Y65fv77y/vvvH9PQ0GAzZ848PW/evLo0na4nWEdjIL2gpKTEVVRUZLoY/hVL8G5/n1Xf6Vf+G3QPlWhomdku51xJpsuRTrHG7VT2ULX2gk2Ynp/0Y2Qc8cTfeP88Ldkxe8+ePYcmTZpUk6z9wRv27NkzbNKkSQUdPUdPVdAwIYW38LoDSBRxPRh4v4BAI6kKM4YkAMiAVPQe8aWjSeSlOsFLZQGALpBUBQ2JEgAEQ/s4TlxPHK8hgBQhqQKVi1dQ2QMJo4cqAV4aZuilsgBADEiqgqq7U6ZTYQGAN5BQJB+vKYAUI6kCMo3KHiHGPVAe4qVhhpksixfOH4DvkFQFWSwX61zQA4C3pDKhCGuM91LCCGTQkiVLRvbv3//CihUrqpK971//+tf97r///oKGhoasWbNm1W3YsOGDrKysS7b5h3/4h+H9+vVreeihhz5K9vGTZdmyZSNWr159vLt/R1IFZFpXlT0XAAio9t8rRY+Vh3gp3mSih4pGRiAuixYtyl+/fn3lrFmzzs2YMWPsli1bBn7lK1853Xabv/3bv61OZRmam5vVo8cn6U1TU5N69uzZrX2Ul5fnxpNUZV15E/hW/o7Io+/0yKN1ubvbAADSL5nxuHJG5HF+Z+TRuhw21HEJWzZj48VGECRR7ZND9P7IiXon63q9P3Kiap8ckugu161bN7SwsHB8UVHR+Ntvv31M++fXrl07bMKECcVFRUXjb7nlls+cOXMmS5I2bNgweOzYsdcWFRWNLykpKZKkioqKPhMnTiweN27c+MLCwvF79+7t3XZflZWVPc+ePZt18803n8vKylJpaelHL7300uD2x1yyZMnI5cuX50jSlClTih588MFREydOLC4oKJjw85//vL8USYwWLFgwurCwcHxhYeH4lStXXiNJP/vZzwYUFxePLywsHD9v3ryC8+fPmySNGjVq4iOPPJJ7/fXXF23YsGHwlClTih566KFRf/Inf1L0rW99K+fo0aM9brnlls9MmDCheMKECcWvvvrqVZJUV1eXdeeddxa0HufZZ5+9etGiRaMaGxuzxo0bN37u3LmXvWZdoacK8AqGZSJE+F4peA5DBJEptU8O0YnF+XINkc6OC8d66cTifEnS4IUn49llRUVFnzVr1uS+8cYb7+Tm5jZXVVVlt9+mtLS0dunSpTWS9PDDD48sLy8fVlZWdmL16tW5r7766ntjxoxpqqmpyZakJ554YviiRYuqHnzwwZMNDQ3W3Nx8yb4qKyt75ubmNrUu5+fnf3zs2LErdhE1Nzfb3r173/7JT34yaMWKFSNnz5793tq1a4dXVlb23r9//1s9e/ZUVVVVdn19vT3wwANjXn311Xevu+66xi9/+csF//iP/zh8+fLlJySpT58+Lbt27XpXkp5++ulrTp06lf3mm2++K0m33nrrmCVLllTdcsstZ99///1et9xyy9iDBw/uX7ZsWe7AgQMvvPfee29JUnV1dfa999576tlnn73mnXfeeau7rzlJVRjEUjFQeQBAcJEwIEEM2U2hmhWjLiZUrVxDlmpWjIo3qdq2bdvAW2+9tTY3N7dZknJyci6032bXrl19ly9fPurMmTPZ586dy54+fXqdJJWUlJwtLS0tuOOOO2pLS0trJWnq1Knn1qxZk3vkyJFed911V+3EiRMbLymuc5eVwcyuWM558+bVStKf/umfnvubv/mbXpL02muvDVy4cGF167C9nJycC2+88Ubf0aNHN1533XWNknTvvfd+9L3vfe8aSSckaf78+bVt93v33XdffN1ef/31ge+//37f1uWzZ89m19bWZv3qV78auHnz5oOt64cPH37Za9QdJFWAFwXgAogKF7Hg8wHP8WG8hc9dON6rW+tj4JyTmV2e6bSxYMGCMVu2bDkwderU8+Xl5UN37tw5QJKee+65w6+99tpVW7duHTR58uRrd+/evX/hwoUnp02bdu7FF18cNGfOnML169cfmjt37pnWfRUUFDS17ZmqrKzsNWLEiKaOjttWnz59nCT16NFDFy5csM7K3lHS1taAAQNaOlt2zqmiouLt/v37X7bPWBK/WHFPVRRjhBGXsN6XAMCfuKcIcVq9Y75W75ivCdPzNQvRgpoAABr9SURBVGF6/sVlJEH2iI+7tT4Gs2fPPr1169Yhx48fz5akjob/1dfXZ+Xl5TU1Njba5s2bL97DtX///t6zZs06993vfvfo4MGDmw8ePNjrrbfe6lVcXNz4+OOPn/jCF75wavfu3X3b7is/P7/pqquuavnlL395VUtLizZt2jT0tttuOxVP2W+++ebTTz755PCmpkhOVlVVlT158uSGDz/8sNe+fft6S9LGjRuHTps27UyXO4q68cYbT3/729++pnX5N7/5TV9JmjFjxunvfOc7F9dXV1dnS1KPHj1cY2Njt7MtkirAy9J4AZSshoXW/ezbWal9OytpsAAyhUaf+PHaIZ2GLf9Q1ueSnhZZnxYNW/5hvLssKSlpWLp06bFp06aNKyoqGr9o0aJPtd9m2bJlR6dMmVI8bdq0wrFjxza0rl+8ePHowsLC8WPHjr32hhtuOHPDDTec/9GPfjSksLDw2nHjxo1///33+zzwwAOXTYm+fv36yoULFxbk5+dPKCgoaJw3b15dPGVfvHhx9ejRoz8eN27ctUVFReOfeeaZIf369XNPPvnkoXnz5n2msLBwfFZWlh555JGYZhJ86qmnPviv//qvqwoLC8d/5jOfuXbdunXDJWnVqlXHTp06ld06Kccrr7wyQJJKS0uri4uLuz1RhV2pOy1TSkpKXEVFRcqP036M8ITpkfsCaX1Bl9pPJNF3euSnj1uAkzVcj/+pCDPb5ZwryXQ50ildcRsx8vHw4YzjtQudZMfsPXv2HJo0aVJNzH9Q++QQ1awYpQvHeyl7xMcatvzDeO+nQurs2bNn2KRJkwo6eo57qoCQS/bNx8zqBmQYs4fGj9cOmTJ44UmSKH8LfVLFBWCApbIyDMBEEgCANKGuAAIv9EkVEHapaliggQKIU6IX4DT6xC9Nr932TXu1sWy7ag7XaVjeIM1fOVMzSyem5FgA0oOkKooLwABJ5/ANLlYAAJ3poD7a/lKO1j32WTXWR2Y2q66s07oFL0sSiRXgYyRVACTRsABkXLIbhNr/HT1XsUvya7T93yZq43c/r5pjg2RZTi0XLv36nsb6Jm0s205SBfgYSVUHuL/K5xj6AiAOxH4kXf4Obd+0V+v+1wtqPB/5miB3oeOvv6k5HNfs0wA8gqQqrEg44sPrBiBVUtUgxIx2GbWxbPvFhKorw/IGpaE0CLslS5aM7N+//4UVK1ZUJXvf3/jGN0Y9//zzQ0+fPp1dX1//38nev9eRVLWR7KmlkWFcMACIAbEfqRRLD1Tvfj01f+XMNJQGSJ3bb7/91COPPHKiuLh4QqbLkgkkVWFDi2V8eN0ApEr7eJLsuMKQ6IwaljdI1ZWXJ1ZZ2SbX4lIy+x8NAz51aEqRJKngP99Nxu7WrVs3tLy8PMfMVFxcfP6ll176Q9vn165dO+wHP/jB8KamJisoKGjcsmXLHwYMGNCyYcOGwatWrRqZlZXlBgwYcKGiouLdioqKPvfdd9+YpqYma2lp0QsvvPD7iRMnNrbd30033XQuGeX2K5KqNvjOKg+h8geQJsR+pNL8lTO1bsHLF2f7kyI9Uw899SUmpkDKVFRU9FmzZk3uG2+88U5ubm5zVVXVZWNQS0tLa5cuXVojSQ8//PDI8vLyYWVlZSdWr16d++qrr743ZsyYppqammxJeuKJJ4YvWrSo6sEHHzzZ0NBgzc3N6T4lzyOpCpt0tlgGKTGipRdAsqW7B5y4lRGtiVM6vpeKoaw+1dpD1fBm/0uWE+ix2rZt28Bbb721Njc3t1mScnJyLrTfZteuXX2XL18+6syZM9nnzp3Lnj59ep0klZSUnC0tLS244447aktLS2slaerUqefWrFmTe+TIkV533XVXbfteKpBUdYjgk2ZtLyQYZgcgQ4j9PuDTOmFm6UR6pZBWzjmZmetqmwULFozZsmXLgalTp54vLy8funPnzgGS9Nxzzx1+7bXXrtq6deugyZMnX7t79+79CxcuPDlt2rRzL7744qA5c+YUrl+//tDcuXPPpOds/IGkKqzS0UPl5cSou2Xy4jkA8LdEesCJSegAQ1l9qrVHKon3VM2ePfv0nXfe+UePPfZY1YgRIy5UVVVlt++tqq+vz8rLy2tqbGy0zZs3D8nNzW2SpP379/eeNWvWuVmzZp3btm3b1QcPHux18uTJC8XFxY3XXnvtiYMHD/bevXt3X5KqS5FUIXO6Sr64YAAAtPJDYx3gISUlJQ1Lly49Nm3atHFZWVluwoQJ9S+88MKhttssW7bs6JQpU4pHjRr1cXFxcf3Zs2ezJWnx4sWjDx061Ns5ZzfeeOPpG2644XxZWdmI559/fmiPHj3c8OHDm1atWnW0/TEXLlw4+sUXXxzS0NCQlZOTc11paWnNd77zncu2Cypzrsuewa7/2GyIpJ9IKpB0SNJXnHO1HWx3QdLe6OJh59zcK+27pKTEVVRUxF02eMCVKr32lWTf6Z9sn6oKs6tjJmN7IMrMdjnnSjJdjvaI2z4X1pgU1vNG2iQ7Zu/Zs+fQpEmTapK1P3jDnj17hk2aNKmgo+cS7alaJumXzrnVZrYsuvxoB9udd85NTvBYCJquhr5QUQKpQtyG/zBZEACPSzSpuk3SjOjvP5S0Qx1XzggjL1Z63a2YqcgRPMRtPyMmdU/dJqm6TGo+LPXIk4avlAaVZrpUAAIo0aQqxzl3TJKcc8fM7JpOtutjZhWSmiWtds691NFGZrZA0gJJysvLS7Bo8I1MXxRwcYJwIW7Dv7oTp+s2SccXSK4+stxcGVmWSKwAJN0Vkyoz+3dJIzp4qqwbx8lzzh01s09Les3M9jrnft9+I+fcU5KekiJj87uxf6B7uptAkXDBR4jbIUBMurLqsk8SqlauPrKepApAkl0xqXLO3dzZc2ZWZWa50dbOXEknOtnH0ejPg2a2Q9JnJV1WOQNpxWxSCCjiNqDIkL/urAeABGQl+PdbJd0T/f0eST9rv4GZDTaz3tHfh0n6M0lvJXjcuC2bsfHi9zcg4CpnfJIoAWjlu7gNxKVHJ8NRO1sPAAlINKlaLenzZva+pM9Hl2VmJWb2dHSbYkkVZrZH0nZFxuZTOSPz8ndEHn2nRx6tyyFEY0OoELfb4LMfYMNXStbv0nXWL7IeCKklS5aMXL58eU4q9v2Nb3xj1IgRI67r16/fZzvbZtOmTYMee+yxjoane8aKFSuuOXPmTLdzpIQmqnDOfSTppg7WV0j6WvT330iamMhxkqG10ty3s/KSZb5tPIAY1gd0yk9xG0hI631TzP4HpMXtt99+6pFHHjlRXFw8obNtSktL6yTVpaoMTU1N6tmzZ6fLsfiXf/mXnK9//esnBwwY0NKdv0t09j/A/0KcbNHYgLDisx8Sg0pJouALrzxZMeTHK349qvb42V6DR/T/+O7l0z784sKSk4nsc926dUPLy8tzzEzFxcXnX3rppT+0fX7t2rXDfvCDHwxvamqygoKCxi1btvxhwIABLRs2bBi8atWqkVlZWW7AgAEXKioq3q2oqOhz3333jWlqarKWlha98MILv584cWJj2/3ddNNN565UpvLy8qEVFRVXbdy48fAdd9xRMGDAgAt79uy5qrq6uuc3v/nNI/fdd1+tJD3++OM5P/3pT4eamW666aa69evXf/ib3/ym74MPPph//vz5rPz8/Mbnnnvu0PDhwy9MmTKlaMqUKWd/+9vf9v/iF794at++fX0HDx7cvHfv3n7XXXdd/dq1a4/ef//9eW+//XbfCxcuWFlZ2dGvfvWrp5qbm7Vo0aLRO3bsGChJ99xzT41zTidOnOg5ffr0wsGDBzf/9re/fS/W1zs0SVVrRUnFGQJ8j8tFfN4BdIoYCXjCK09WDPnXxb/Ib2pozpKk2mNne/3r4l/kS1K8iVVFRUWfNWvW5L7xxhvv5ObmNldVVWW336a0tLR26dKlNZL08MMPjywvLx9WVlZ2YvXq1bmvvvrqe2PGjGmqqanJlqQnnnhi+KJFi6oefPDBkw0NDdbc3Bz/CbdRVVXVs6Ki4p3du3f3+fKXv/xH9913X+1Pf/rTgS+//PLgXbt2vTNgwICW1rLfe++9Y/7pn/7p8Je+9KWzf/3Xfz3y0UcfHblhw4YPJOnUqVPZb7755ruSdMcddxT8/ve/7/P666+/16NHDz300EOjZs6cefr5558/VFNTk11SUlI8d+7c09///veHVlZW9t6/f/9bPXv2VFVVVXZOTs6F73//+zk7d+58Lzc3t1snGZqkCsDlSRaNDQgrPvsAvOLHK349qjWhatXU0Jz14xW/HhVvUrVt27aBt956a21rYpCTk3Oh/Ta7du3qu3z58lFnzpzJPnfuXPb06dPrJKmkpORsaWlpwR133FFbWlpaK0lTp049t2bNmtwjR470uuuuu2rb91LFa+7cuaeys7N1/fXXN3z00Uc9JekXv/jFwK9+9as1rcPvcnJyLnz00UfZZ86cyf7Sl750VpK+/vWvfzRv3rxPt+7n7rvvvuR1+vM///PaHj0iac6OHTsGbtu27ery8vIRktTY2GgHDhzo9dprrw1cuHBhdevwwI5eo+4IXVJFxRkiIW597WxoEwBw3yngLbXHz/bqzvpYOOdkZl1+d+CCBQvGbNmy5cDUqVPPl5eXD925c+cASXruuecOv/baa1dt3bp10OTJk6/dvXv3/oULF56cNm3auRdffHHQnDlzCtevX39o7ty5Z+ItX6s+ffpcLKNzrm3Zu7Wf9vc/9e/f/+Kyc05btmw5MGnSpEsSwVheo+5IdPY/RDGDFLzs4O7jOrj7uPbtrNS+nZWXfV5X75hPgwNCic8+gEwbPKL/x91ZH4vZs2ef3rp165Djx49nS1JHw//q6+uz8vLymhobG23z5s1DWtfv37+/96xZs85997vfPTp48ODmgwcP9nrrrbd6FRcXNz7++OMnvvCFL5zavXt333jLFkvZf/SjHw1rnYGvqqoqe+jQoRcGDhx44ec//3l/SXrmmWeGTp069Wws+5s5c+bptWvX5rS0RPKs119/va8k3XzzzaeffPLJ4U1NTWo9jiRdddVVF+rq6rqdI5FUAQHUeqE4YXq+JkzP16cnj9CnJ3t6BlMA6cLXSQCecvfyaR/27NPjkp6Wnn16tNy9fNqH8e6zpKSkYenSpcemTZs2rqioaPyiRYs+1X6bZcuWHZ0yZUrxtGnTCseOHdvQun7x4sWjCwsLx48dO/baG2644cwNN9xw/kc/+tGQwsLCa8eNGzf+/fff7/PAAw981H5/CxcuHJ2Tk3NdQ0NDVk5OznVLliwZGU/Z77zzztNz5sw5NXny5OJx48aN/+Y3vzlCkn7wgx/84dFHHx1dWFg4/ne/+13f1atXH41lf6tXrz7a3Nxs48aNGz927NhrH3/88VHR86wePXr0x+PGjbu2qKho/DPPPDNEikxYMWfOnLGf+9znCrtTbmvtavOakpISV1FRkeliXFH7YVYTpudLYpghvKH9/SLJuH+Ee1BiY2a7nHMlmS5HOvklbiOKYX/ARcmO2Xv27Dk0adKkmli3T8Xsf0i+PXv2DJs0aVJBR8+F7p4qIExIfAB0imQqqWhwQiK+uLDkJEmUv5FUJYgZpLxt+6a92li2XTWH6zQsb5Dmr5ypmaXh/U7TZPRQ8b0+AAAAlyKpQmBt37RX6xa8rMb6yA2I1ZV1WrfgZUkKdWIFAEierhqcaHwCwoOkKkkImN6zsWz7xYSqVWN9kzaWbSepigO9sgAAxKylpaXFsrKyvDl5AbqtpaXFJLV09jxJFQKr5nBdt9YDANBdHTU4tX5tBcOlQ21fdXX1+OHDh9eRWPlfS0uLVVdXD5K0r7NtSKoQWMPyBqm68vIEaljeoAyUJji4KADSiwtywH+am5u/dvz48aePHz8+QXyFURC0SNrX3Nz8tc42IKm6Aioz/5q/cuYl91RJUu9+PTV/5cwMlgoAwinoEwe1vU5guDSuv/76E5LmZrocSB+SKgRWa2Ud5EocQHAFacZNJg4CEHQkVZ0IUmUWZjNLJ1JhA0CGhXXioGRdM3ANAngfSRUAAB4UpCFkTBwEIOhIqjoRpMoMAAApc3UaEwfFh1EzgH8wGwkAAB62esd8319Ez185U7379bxkXdAmDtq+aa/uKyjXrVnf1H0F5dq+aW+miwQgjeipugK/V2QAAGS6xyPoEwelaiIORs0A/kFSBQAAUi7IEweFdSIOAJ8gqQIAIODo8UjMlV63VE/EwfsFeB/3VAXYshkbL1YEAAAgNTqbcIOJOIDwoKcqYGiFBAB0hrqhe2K9F23+ypmX3FMlBW8iDgBdI6kKoIO7j2vZjI1MwQoAQBoEfSIOAFdGUhUQ7VvTDu4+nsnioAskuQDgD925Fy3IE3EAuDKSqoD69OQROrj7uD49eQQX7wAQYjTkAEDqkVQFREetaUxS4S2Z/p4YAEB8iNMAroSkKsCSWQmQAPgL7xcAGnIAIH1IqgKGytK7+J4YAACAYCKpQpdo6fQX3i8ArWjIAYD0IakC0owLGwAAgGAhqUKXaOn0F94vwB/S+T9KHACA1MvKdAEAAAAAwM/oqUJMYm3ppIfEG3j9AW/ivkcACCZ6quBLy2Zs5Hu4AAAA4An0VCEp/Nz66qeyAvC3MN73GMRzDeI5AUgMSRV8xc/JGwAAAIKJpApJ4cfWVxI0AJkShjgTxBgbxHMCkBwkVfAVPyZvAAAACDaSKiSVn5IcEjQASJ0gxtggnhOA5CCpgi9RkQEAAMArSKoQeslI0Gi1BICOBTEuBvGcACQmoe+pMrN5ZrbfzFrMrKSL7Wab2btmdsDMliVyTABA/IjbAAAkX6I9Vfsk/bmkf+lsAzPLlvQ9SZ+XdETSm2a21Tn3VoLHBjKOmaDgQ8RtxIyYBgCxSSipcs69LUlm1tVmUyQdcM4djG67WdJtkqicPY7KFAge4jYAAMmXjnuqRkn6oM3yEUmfS8NxgZRjJigEFHE75FLRC0+cBBBkV0yqzOzfJY3o4Kky59zPYjhGR82hrpNjLZC0QJLy8vJi2DVSgSFtgL8RtwEASK8rJlXOuZsTPMYRSZ9qszxa0tFOjvWUpKckqaSkpMMKHPAiEk54CXEbiUpmLzwNdQDCIB3D/96UNNbMxkj6UNJdkv4yDcdFnBjSBoQecRsAgG5IKKkysy9LekLScEkvm9lu59wtZjZS0tPOuS8655rN7CFJ2yRlS9rgnNufcMkBAN1G3EZ3JKNRjYY6AGGQ6Ox/L0p6sYP1RyV9sc3yK5JeSeRYiF+8FRkVHxA8xG0AAJIvHcP/AABAyNFQByDISKoCjJuDAQAAgNTLynQBAADwo2UzNl5srAIAhBs9VQHGzcEAAABA6pFUAQDQDQytBgC0R1IVAlT0AAAAQOqQVAEA0A0MrQYAtMdEFQAAAACQAHqqAACIAz1UAIBW9FQBAAAAQAJIqgAAAAAgASRVAAAAAJAAkioAAAAASABJFQAAAAAkgKQKAAD42rIZGy9+bxgAZAJJFQAAAAAkgO+pAgAAvtTaO7VvZ+Uly3yHGIB0o6cKAAAAABJATxUAAPCl1h4peqgAZBo9VQAAAACQAHqqAACAr9FDBSDT6KkCAAAAgASQVAEAAABAAkiqAAAAACABJFUAAAAAkACSKgAAAABIAEkVAAAAACSApAoAAAAAEmDOuUyXoUNmVi2pMoWHGCapJoX7z7Sgn58U/HMM+vlJwT7HfOfc8EwXIp1SHLeD/FmRgn9+EucYBEE+v9DFbCSXZ5OqVDOzCudcSabLkSpBPz8p+OcY9POTwnGOSI6gf1aCfn4S5xgEQT8/IBEM/wMAAACABJBUAQAAAEACwpxUPZXpAqRY0M9PCv45Bv38pHCcI5Ij6J+VoJ+fxDkGQdDPD4hbaO+pAgAAAIBkCHNPFQAAAAAkLDRJlZnNM7P9ZtZiZp3OXGNms83sXTM7YGbL0lnGRJjZEDP7hZm9H/05uJPtLpjZ7uhja7rLGY8rvSdm1tvMfhJ9/rdmVpD+UsYvhvO718yq27xvX8tEOeNlZhvM7ISZ7evkeTOz8uj5/87M/jjdZYT3ELMvbkfM9hhiNjEb6EhokipJ+yT9uaRfdbaBmWVL+p6kOZLGS7rbzManp3gJWybpl865sZJ+GV3uyHnn3OToY276ihefGN+T+yXVOuf+SNI/Sfp2eksZv2585n7S5n17Oq2FTNyzkmZ38fwcSWOjjwWSvp+GMsH7iNkRxGwPIWZLImYDHQpNUuWce9s59+4VNpsi6YBz7qBz7mNJmyXdlvrSJcVtkn4Y/f2Hkm7PYFmSKZb3pO25b5F0k5lZGsuYCD9/5mLinPuVpJNdbHKbpI0u4j8kXW1muekpHbyKmO1bxGyfI2YD8QlNUhWjUZI+aLN8JLrOD3Kcc8ckKfrzmk6262NmFWb2H2bmh0o8lvfk4jbOuWZJdZKGpqV0iYv1M3dHdJjFFjP7VHqKljZ+/r9DZvn5s0PMFjHbp/z8fwekTI9MFyCZzOzfJY3o4Kky59zPYtlFB+s8Mz1iV+fXjd3kOeeOmtmnJb1mZnudc79PTglTIpb3xNPv2xXEUvZ/k/Rj51yjmS1UpIV3VspLlj5+fv+QAGJ2TIjZ3kLM9vf7B6RMoJIq59zNCe7iiKS2LUqjJR1NcJ9J09X5mVmVmeU6545Fu+FPdLKPo9GfB81sh6TPSvJyBR3Le9K6zREz6yFpkLoeuuAlVzw/59xHbRb/VT66/yBGnv6/Q+oQs4nZxGxf8vT/HZApDP+71JuSxprZGDPrJekuSb6YbUmRct4T/f0eSZe18prZYDPrHf19mKQ/k/RW2koYn1jek7bnfqek15x/voDtiufXbqz6XElvp7F86bBV0vzojFI3SKprHRYFXAEx23uI2cRsIJycc6F4SPqyIq0rjZKqJG2Lrh8p6ZU2231R0nuKtASWZbrc3Ti/oYrMIPV+9OeQ6PoSSU9Hf/9TSXsl7Yn+vD/T5Y7x3C57TyStkDQ3+nsfSc9LOiDpPyV9OtNlTvL5rZK0P/q+bZc0LtNl7ub5/VjSMUlN0f/B+yUtlLQw+rwpMpvW76Ofy5JMl5lH5h/EbGK2Vx/EbGI2Dx4dPcw5vzQOAQAAAID3MPwPAAAAABJAUgUAAAAACSCpAgAAAIAEkFQBAAAAQAJIqgAAAAAgASRVAAAAAJAAkioAAAAASABJFQAAAAAk4P8HkVxsSljC26gAAAAASUVORK5CYII=\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "for i, (ds_train, ds_test) in enumerate(zip(datasets_train, datasets_test)):\n", " ds_train = datasets_train[i]\n", " ds_test = datasets_test[i]\n", "\n", " X = ds_train[0]\n", " Y = ds_train[1] \n", " \n", " X_test = ds_test[0]\n", " Y_test = ds_test[1]\n", " # 1) entraîner le modèle\n", " prior_dict, class_summaries = train_NB(X,Y)\n", " \n", " # 2) Prédire\n", " # a) pour les données test\n", " posterior = test_NB(X_test, class_summaries, prior_dict)\n", " pred_test = np.argmax(posterior,1)\n", "\n", " # b) pour les données d'entraînement\n", " posterior = test_NB(X, class_summaries, prior_dict)\n", " pred_train = np.argmax(posterior,1)\n", " \n", " #4) Pour la visualsation\n", " i_c0 = (Y == 0)\n", " i_c1 = (Y == 1)\n", " \n", " # TRAIN: obtenir les vrais et faux positifs.\n", " i_c0_t = (pred_train[i_c0]==0); i_c0_f = (pred_train[i_c0]==1)\n", " i_c1_t = (pred_train[i_c1]==1); i_c1_f = (pred_train[i_c1]==0)\n", " \n", " plot_predictions(i,X,Y, X_test, Y_test, pred_train, pred_test)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Question 7 (NB):** Pour quel(s) jeu(x) de données le classificateur NB a-t-il le mieux performé? Comment en venez-vous à cette conclusion? \n", "\n", "Pourquoi semble-t-il moins bien modéliser les données du premier jeu de données?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Réponse possible**: Il a le mieux fonctionné pour les jeux de données 2 et 3. Pour ces jeux de données, les probabilités conditionnelles des classes en fonction des caractéristiques peuvent en effet être modélisées avec une distribution gaussienne. \n", "\n", "Par contre, pour le premier jeu de données (les deux lunes) ce n'est pas le cas." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "En pratique, vous ne voudrez sans doute pas réimplémenter le modèle NB pour chaque type de variable cible ou caractéristique. La libraire `sklearn` a une implémentation du modèle NB. Essayons là. " ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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Lli2xevVqvPXWW6hWrRref/99pUNkmU1mj2UvlcUvv/yCBQsW4Msvv0T9+vXx73//G5MmTUKjRo0QEBCgdHikcWpoWbsCoLnRcjMAycVs+waATcYrpJTJ+q+JAPYh/9gI4+1WSik9pJQe9vb2FY2ZiKhS5ebm4tNPP0XHjh0xbNgwpKenY/369Th79izeeecdVKtWTekQDVhmWwif3jGPkhUiKuzAgQMYMGAAnnvuORw4cAALFixAUlIS/vOf/6BRo0ZKh0dmQg0ta4cBtBZCtADwJ3QX95EFNxJCtAHQEMBBo3UNAaRLKbOEEHYA/g/AoiqJmhRlKbWe5v75CMjJycGmTZvg5+eHs2fPws3NDRs3bsSIESNgbW2tdHhFYZlNFoNlLxVl//79mD9/Pvbs2QM7OzsEBARgwoQJqFu3rtKhkRlSPFmTUuYIISYC2AXdNNDRUsoEIcR8APFSyjj9pm8C2CylNO5u4wZghRAiD7pWwkDjGcnoL7zpJ1KX7OxsbNiwAf7+/rhw4QI6duyIzz77DEOHDoWVlRo6PRSNZbb5s5Ru5kRlIaXE999/jwULFuDHH39EkyZNEBoairFjx6J27dpKh0dmTPFkDQCklF8D+LrAunkFlv9TxH4HAHQwaXCkauZ688CbJfOVlZWF6OhoBAYG4tKlS+jSpQt27NiBgQMHqjpJM8Yym4i0YG/sScT47sWNS2mwc6qP0X6e8PQqWxEkpcTXX3+NBQsW4Oeff4ajoyPCw8Px7rvvombNmiaKnOgvqkjWyHR400+kDhkZGVi1ahWCgoKQnJyMbt264eOPP8aAAQMgRFFzdhApw1K6mZN52xt7EhHeXyErPRsAkJqUhgjvrwCgVAlbXl4evvjiCyxcuBBHjx6Fi4sLoqKiMGbMGFSvXt2ksRMZY7JGpIDH3QTxZsl83L9/H1FRUQgJCcG1a9fwwgsvYP369ejbty+TNCIiE4nx3fsoUTPISs9GjO/eEpO13NxcbN26FX5+fjh58iSeeuopREdHY9SoUbC1tTV12ESFMFkzc7zpJ1JGWloaIiIiEBYWhps3b+LFF1/EZ599hhdeeEHp0IhKhdcL0rIbl9LKtN4w2ZO/vz/OnDmDtm3bYsOGDXjjjTdgY8PbZVIO//qIqlBZu6XyZkl7bt26hfDwcCxduhR37tzB3/72N/zrX/9Ct27dlA6NiMhi2DnVR2pS4cTMzql+vuWHDx9iw4YNCAgIyDfZ02uvvabWGXnJwjBZsxC86ScyrevXryMsLAzLly/HvXv3MHjwYHz44Yfo0qWL0qGRibHnApH6jPbzzDdmDQCq17LFaD9PAEBmZiaio6MRFBSk2cmeyDIwWSOqQpXZLZU3iOqQkpKC4OBgREVFITMzEyNGjICvry86dOCkh0RESjGMSys4G+RzQ1ohLCwMwcHBSElJQffu3REVFYX+/ftzHDGpEpM1IqJyuHTpEhYtWoTVq1cjJycHI0eOxNy5c9G2bVulQ6Mqwtl2idTN06vDo6Tt3r17iIyMxOsuoUhNTUWvXr3wySefwNPTk0kaqRqTNSIFVEaLGm8QlXHhwgUEBgZi/fr1AIC3334bPj4+aNWqlcKRERFRQbdv38ayZcuwZMkS3L59G/369cOHH36IHj16KB0aUakwWSMiKoXffvsNAQEB2LhxI2xsbPDee+9h9uzZcHJyUjo0Ughn26WqwL+v8klNTcWSJUsQERGBu3fvYuDAgfjwww/RtWtXpUMjKhMma0QawxvEqnXixAn4+flh69atqFmzJiZPnozp06ejadOmSodGGsf/YaLKl5KSgpCQEERFRSEjIwPDhg3D3Llz0blzZ6VDIyoXJmtEREX45Zdf4Ofnh7i4ONStWxdz5szBlClTYG9vr3RopDJMtsgURjRYBABIT8sCwOT+cYzHEWdnZz8aR+zm5qZ0aEQVwmTNAlW0wOcFQx348zeNH3/8EQsXLsTu3bvRqFEjzJ8/HxMnTkTDhg2VDo3MBMedElWe8+fPPxpHLITIP444qTeQBMB5n8JREpUfkzUisnhSSnz//fdYuHAhfvjhBzzxxBMICgrC+++/j7p16yodHhFZEEPybmhRq1W/OgAm8wWdPn0a/v7+2LRpE2xtbTFu3DjMnDmT44jJ7DBZsyAVrc1lbTCZGyklvvzySyxcuBC//PILHB0dsXTpUrz77ruoVauW0uGRmeK4U6LyO378OBYuXIjPP/8ctWrVwrRp0zBt2jQ4ODj8tVFSb93XjP35l9nCRhrEZI2ILE5ubi62bdsGf39/nDhxAi1atEBUVBTGjBmD6tWrKx0eEVmwxyXzlprkHzx4EH5+fvjqq69Qr149zJ07F1OmTIGdnZ3SoRGZFJM1C1LR2lzWBpPWZWdnY9OmTfD398fZs2fRpk0brF+/Hm+++SZsbW2VDo8sTFl7NbDMJUsjpcS+ffuwcOFC7NmzB40bN8bChQsxYcIENGjQoPgdDS1obFEjM8BkjYjMXlZWFtatW4egoCD88ccf6NixIz777DO89tprsLa2Vjo8IqJCimtRs4ShCFJKfPPNN/Dz88OBAwfQpEkThIaGwtvbG3Xq1Kn4CZjEkYYwWbNAFS3YzfHCYInM+UJvkJ6ejlWrVmHRokVITk5G165dsWTJEgwcOBBCCKXDIyqRJd2cEwFAXl4eduzYgYULF+LYsWNwcnJCREQE3nnnHdSoUaPsB2QyRmaAyRqRxvCG7fHu3r2L5cuXIywsDKmpqejVqxfWr1+Pvn37Mkkj0pC9sScR47sXNy6lwc6pPkb7ecLTq4PSYSnCnIci5OTkYPPmzQgICMDp06fx1FNPYc2aNRg1ahSqVatWeSfixCOkQUzWiCyMOdfW37x5E0uXLsWyZctw584d9O/fH76+vujRo4fSoRGVmTnfnJfG3tiTiPD+Clnp2QCA1KQ0RHh/BQAWm7CZm6ysLMTExCAwMBCJiYlwd3fHxo0bMWLECHZRJ9JjskakEeacZFXU1atXERoaio8//hgPHjzAkCFD4Ovriy5duigdGhGVU4zv3keJmkFWejZifPdadLJmDmV+eno6Vq9ejeDgYFy5cgXPPvssFi9ejIEDB8LKysp0J+bEI6RBTNaILIw51dYnJSVh0aJFWLNmDbKzs/HGG29g7ty5aN++vdKhEVUaLf+PVsSNS2llWk/qd/fuXURGRmLx4sVITU1Fz549sXr1arz88svsok5UDCZrRBphTklWRZ09exZBQUHYsGEDhBB4++23MXv2bDz11FNKh0ZElcTOqT5SkwonZnZO9RWIhiqiYBf1fv36wdfXFz179lQmILaokYYwWSOyUFpM9k6cOAF/f39s2bIFNWrUwPjx4zFjxgw0b95c6dCIqJKN9vPMN2YNAKrXssVoP08Fo6paWq+cS0lJQWhoKKKiovDgwQMMHjwYvr6+8PDwUDo0Is0wYcfg0hNC9BdCnBVCnBdC+BTx/hghRKoQ4rj+9a7Re28LIc7pX29XbeREVS9w3+hKvXD79I55dEOgVocOHcKgQYPQuXNnfPPNN5g9ezYuXryIpUuXMlFTCMttMjVPrw6YuPIV2DvXhxCAvXN9TFz5ikWPV9OKixcvYsKECWjRogXCwsIwePBgnDp1Ctu3b2eiRlRGiresCSGsASwH8BKAKwAOCyHipJSnC2z6qZRyYoF9GwH4NwAPABLAEf2+t6sgdCIyISkl9uzZA39/f+zZsweNGjXCRx99hA8++AANGzZUOjyLxnJbR+utHsVR0+fy9OpgkcmZVieUOnPmDAICAhAbGwsrKyuMGTMGs2fPRqtWrZQOjUizFE/WAHQFcF5KmQgAQojNAF4FUPCiX5R+AL6TUt7S7/sdgP4ANpkoViKzodabASklvvzyS/j7++PQoUNo0qQJQkJCMHbsWNSpU0fR2OgRlttE9MixY8fg7++Pbdu2oUaNGpg4cSJmzJiBZs2aKR0akeapIVlzBHDZaPkKgOeK2G6oEOIFAL8DmCqlvFzMvo6mClSN1HKDTVRRubm52LJlCwICAvDrr7/C2dkZkZGR+Mc//oEaNWooHR7lZ9HltlorOkqjpFi1/LnMjVYmlPrpp5/g5+eHb775BvXq1YOPjw+mTJmCJ554QunQiMyGGpK1ouZqlQWWdwLYJKXMEkKMA7AeQJ9S7qs7iRDeALwBwMnJqfzRkurtjT2JGN+9uHEpDXZO9THaz9Miu9E8jlpuBh4+fIhPPvkEgYGBOHfuHNzc3LB+/Xq8+eabsLW1VSQmeiyTl9sss4nUSUqJ77//Hn5+fti/fz/s7Ozg5+eH8ePHo0GDBkqHR2R21JCsXQFgPENAMwDJxhtIKW8aLa4CEGS0b+8C++4r6iRSypUAVgKAh4dHkQmdlhRVA5p4/Cpadm6i2hq4qrA39mS+2cNSk9IQ4f0VAJhlwqZ0olURBR+K+swzz2Dr1q0YMmSIaR+KSpXB5OV2actsJf4H1FLRURalaTXT4udSC1P9zNT0O8jLy0NcXBz8/f1x+PBhNG3aFGFhYXjvvfdQu3ZtpcMjMltquCM6DKC1EKKFEKIagDcAxBlvIIRwMFocBOA3/fe7ALwshGgohGgI4GX9OrJQMb57803zDABZ6dmI8d2rUETqV9mzSz5OWloaAgMD4eLigsmTJ6NFixb45ptvEB8fj6FDhzJR0waW20SVwHg2XrXOzJuTk4NPPvkEHTt2xJAhQ3Dz5k2sXLkSiYmJmDJlChM1IhNTvGVNSpkjhJgI3cXaGkC0lDJBCDEfQLyUMg7AJCHEIAA5AG4BGKPf95YQYgF0Nw4AMN8waN3cGdeAJh6/CgBIT8vCqf1JFl0reuNS4QeolrReq7Q4tiQ1NRVLly5FREQE0tLS0L9/f8ydO1e5h6JSuamh3FbD/4Ca/98KKkurmZY+l9LU8HdoKpmZmVi/fj2CgoLwxx9/wN3dHbGxsRgxYgRsbBS/fSSyGKr4b5NSfg3g6wLr5hl9PwfAnGL2jQYQbdIASTPsnOojNalwYmbnVF+BaAgALl++jNDQUKxcuRKZmZkYOnQo5syZg2eeeUbp0KgCWG4TlV/BJG9Eg0VIT8vK955SCd/9+/exYsUKhIaGIiUlBV27dsWSJUvw97//nT0fiBSgimSNys+4MFe6gFeD0X6e+casAUD1WrYY7eepYFSVTwtjS86dO4egoCDExMQgLy8Po0aNwuzZs+Hm5qZ0aFUjqbfuq/M+JaMwW1r4H1Aj/pwqlzn9Hd66dQvLli1DeHg4bt26BU9PT2zYsAF9+vSBEEXNC0REVYHJGmlaUTM/Tlz5CmeDVNCvv/4Kf39/bNmyBba2tvD29saMGTPg4uKidGhERKpQVJKnVMKXkpKCxYsXIyoqCvfv38egQYMwZ84cdOvWrUrjIKKiMVkzI1qu0SuP4mZ+nLjyFay9OEnh6KqGmn7nBw4cgL+/P7766ivUqVMHM2bMwNSpU9GkSROlQ6tahha1jP35l9nCZhJq+h8oDXNogaHCtPj7TExMRHBwMNauXYvs7Gy88cYb8PHxQYcOrNwkUhMma6RZJc38yJa0qiGlxO7duxEQEID9+/ejcePGWLBgASZMmICGDRsqHR4RkaoV9egEU0tISEBAQAA2b94Ma2trjBkzBrNmzUKrVq2q5PxEVDZM1khTjLs9ymKevGRuMz+qUV5eHrZv3w5/f38cPXoUjo6OfN6OgaEFjS1qZMScZw0kbfj5558REBCAL774ArVr18aUKVMwbdo0NG3aVOnQiKgETNZIMwp2eywOZ340nezsbMTGxiIwMBBnz57FU089hVWrVuGtt95C9erVlQ7PdJh4EZEGSSnx3//+FwEBAdizZw8aNmyIefPmYdKkSWjcuLHS4RFRKTBZI80oqttjQeY486MapKenY82aNQgODsbly5fRqVMnfPrppxg6dCisra2VDk+dmNiREXOaNZDULy8vD3FxcfD398fhw4fh4OCAkJAQeHt7o27dukqHR0RlwGSNNKOk7o1CoMiZH4uaLZLj2Urvzp07iIyMxJIlS5CamooePXogKioKAwYMsIypnDlZCBFpSHZ2NjZv3ozAwECcPn0aLVu2xIoVKzB69GjUqFFD6c6j/SoAACAASURBVPCIqByYrJFmFPfAa3vn+kXO/ljcbJEALC5hK2tt/rVr1xAWFoaPP/4Yd+/eRf/+/TF37lz07NnTlGESmT22qJEpZGRkIDo6GsHBwUhKSoK7uztiY2MxYsQI2NjwVo9Iy/goeg3w6R3z6Gbbko3280T1Wrb51pXU7bGk2SKpaBcvXsSECRPg7OyM4OBgDBgwAMeOHcM333xjmYma8z7dq2Yv3cuwTESkAmlpaQgICICLiwsmTpwIR0dH7Ny5E7/++itGjhzJRI3IDPC/mDTD0BpW2m6NxXWbtKTZIks7A11CQgICAwOxadMmWFlZ4e2338asWbPQunXrqg2YiIge6/r161iyZAmWL1+Ou3fvol+/fo96P1hEF3UiC8JkTcU41XNhnl4dSt2Fsbhuk5wt8i8///wz/P39ERcXh9q1a2Py5MmYNm0aHB0dlQ5NXdiaRkQqcPHiRYSEhGDNmjXIysrCsGHD4OPjg2eeeUbp0IjIRJiskdka7edZaKp/S5gt0jipL2oGOsODrAMDA7F37140bNgQ//73v/HBBx9wKmeyWKwMIzVLSEhAUFAQNm7cCCsrK4wePRqzZs2Cq6ur0qERkYkxWVMxTvVcMWXtNmnu8mQetm7disDAQBw5cgRNmzZFaGgovL29UadOHaXDIyKiAg4dOoSAgADExcWhVq1amDRpEqZNm4ZmzZopHRoRVREma2TWytJtUuuK6zY7f/cbcB2dg6CgIAQP/x2tW7fG6tWrMWrUKPN+kDVRKbC7ubKKerwKYNmVbFJKfPfddwgICMC+ffvQqFEj9n4gsmBM1jSANw1UHg9zM3EiZR9atpyLP//8E08//TQ+++wzvPbaa3yQdVXhc9mIilXU41WW/nMnpJTIzc57tM5SHrmSm5uLzz//HIGBgTh69Ch7PxARACZrRGbDkNRP/r9IHPnzO6w//QNu3bqF3r17Izo6Gi+99BJnCSMqgN3NlVPU41VyHuYW2s7wyBVzTdaysrLwySefYNGiRfj993L0fkiLBVJ9gZxLgI0TYO8H1PcyfeBEVCWYrBGZiStXriA0NBQfH4pEdt5DvPrqq/Dx8UG3bt2UDs3yGFrUMvbnX2YLG9EjZXmMijk+cuX+/ftYuXIlQkNDkZycjGeeeabsvR/SYoGr3oBM1y3nJOmWASZsRGaCyZoGsQaYjJ05cwaLFi3CJ598gry8PHiN8sKsWbPQvn17pUOzHEzGNI/ladUr7vEqxW1rLm7cuIFly5Zh2bJluH37Njw9PbF27dry9X5I9f0rUTOQ6br1TNaIzIKV0gFQyXx6xzxKzujx9saexD9cwjHQagH+4RKOvbEnlQ7JZH755Re89tpraNeuHTZv3oyxY8fiwoULWL9+fdkStbRY4LwLcMZK9zUt1lQhWw7nfbpXzV66l2GZiB4Z7eeJ6rVs862zsimcrJjLI1eSkpIwefJkODk5Yf78+ejVqxcOHTqEPXv24OWXXy5fN/WcS2VbT0Saw5Y1DeGsZSUrarC6uQ1Ml1Li+++/R2BgIPbs2YMGDRrA19cXkyZNgr29fdkPyC40FVOwu+PvDYDqnZmYEZVCwcer1GlUE+l3swDIvzYSQN+3O2q6DE9ISMCiRYuwceNGAMCoUaMwa9YsuLm5VfzgNk66cruo9ZaMvR3IjLBlTaUMLWqn9ifh1P4k+PSOQeLxq0qHpWpFDVY3DEzXutzcXGzZsgUeHh54+eWXcebMGQQHB+PSpUtYsGBB+RI1oOQuNPSXpN5/XfzLgi1qREUy9IJY/NYOAMC0DYNRo061R7NAPiKBw1+fVyDCijt06BAGDx4Md3d3bN26FRMmTEBiYiLWrl1bOYkaoJtMRNTKv07U0q0nIrPAljUNadm5CQL3jWaLWjGKG4Cu5YHpWVlZ2LBhAxYtWoRz586hdevWWLVqFd56663KeUYau9A8XlJvIOu4rsWsIOd9uvet6gN5abqXYR8maURFKq4XRMHKNgMtleFSSuzatQuBgYHYv38/GjVqhHnz5uGDDz6AnZ1d5Z/Q0AOCs0HqcHInMkNM1hRUUtLF6aTLrrjB6locmH737l2sWLECYWFhSElJQZcuXUzzjDR2oSmZIVHLS9Nd/HnhJ6qw4npBWFkL5OXKQttroQzPycnBli1bEBQUhBMnTqBZs2ZYvHgx3nvvPdM/I62+l+UmZ0QWgMmaBjFxK9poP89CtbNaG5h+7do1hIeHY/ny5UhLS0Pfvn0RExODvn37VuwZacU9h8feL/+YNYBdaAyMEzWDolrYDIkbEzmiUimupSwvV6J6LVtNleEZGRlYt24dQkJCkJiYiLZt22Lt2rUYOXIkqlWrpnR4loflMZkhVSRrQoj+AJYCsAawWkoZWOD9aQDeBZADIBXAP6WUSfr3cgEYpvy7JKUcVGWBl1NZJgphYlZ6BQer2znVx2g/T00MTE9MTERISAiio6Px8OFDvPbaa5g9ezaeffbZih+8NJOIsAtN0ap3/qs7jVV9Th6iZ2llNlWu4npB2DvrymwtlOF37txBZGQkli5diuvXr+O5555DaGgoBg0aBCsrTgdARJVH8WRNCGENYDmAlwBcAXBYCBEnpTxttNkxAB5SynQhxPsAFgF4Xf9ehpSyiMEkloHdJPPz9Oqgygt7cY4fP46goCB89tlnsLGxwejRozFz5ky4urpW3kke9xwedqEpmnENraFFraREzUKSOJbZVFEl9YJQexmenJyMsLAwrFixAvfu3UP//v3h4+ODF154oWK9H6hyWUh5TJZB8WQNQFcA56WUiQAghNgM4FUAjy78Ukrj6fwOARhVpRFWMo5Hs2xSSuzfvx+BgYHYtWsX6tati+nTp2PKlClo2rRp5Z+Qk4hUHFvUjFlcmU2VS4u9IH7//XcEBwcjJiYGOTk5GDFiBGbPno3OnVnvQESmpYZkzRHAZaPlKwCeK2H7dwB8Y7RcQwgRD113m0Ap5Y6idhJCeAPwBgAnJ+1PnsBnrmlPXl4evvjiCwQFBeHnn3/GE088AX9/f7z//vto0KCB6U7MSUQqhklaQRZfZrO8rTi1t6AZ/PLLLwgKCsL27dtRvXp1vPvuu5g+fTpatmypdGhEZCHUkKwV1W+g8HRQAIQQowB4AOhltNpJSpkshGgJYI8Q4qSU8kKhA0q5EsBKAPDw8Cjy+FXB+CLPC71lyMrKwieffILg4GCcPXsWLVu2RGRkJMaMGYOaNWuaPgBOIkKVy6LKbLI8Ukrs3r0bQUFB2Lt3Lxo0aIA5c+Zg0qRJePLJJ5UOj4gszGOTNSHE9wCmSylPmCiGKwCaGy03A5BcRBwvAvAF0EtKmWVYL6VM1n9NFELsA/A0gEIXfnPDrpTqZ5h+f8mSJUhOTsbTTz+NzZs3Y+jQobCxqcJ6Ek4iYlFYZpsOezSYN8P0+4sWLcLx48fh6OiIkJAQeHt7o27dukqHR0QWqjR3jLMAhAkhkgDMlVKmVHIMhwG0FkK0APAngDcAjDTeQAjxNIAVAPpLKa8brW8IIF1KmSWEsAPwf9ANZFcdXuQtx7Vr17B06VJERkY+mn5/3bp1ePHFF5UbgM5JRCwJy2yiMkhPT8fatWsRGhqKP/74A23btkV0dDS8vLzMe/r94h7poiWcop8swGOTNSnlUQB9hBBDAXwrhPgcwCIpZUZlBCClzBFCTASwC7ppoKOllAlCiPkA4qWUcQCCAdQBsEV/s2uY7tkNwAohRB4AK+jGP5wu8kRmismeepw/fx4hISFYt24dHj58iKFDh2L27Nnw8PBQOjSyICyzTYc9GszLrVu3EBkZifDwcKSmpqJbt24ICwvDwIEDzX/6/dI80sXcMLEjjRJSPn4ogNBdbdsD6AFgIYBMAHOklBtMG55peHh4yPj4eEXOzYu8+YmPj0dQUBC2bdsGW1tbvP3225g5cyZat26tdGhkhoQQR6SUJdYAsMw2LZbj2nb58mUsXrwYq1atwoMHDzBgwAD4+PigZ8+eljP9/nmXYiaecgaeuljV0ZSdIfEyPAezpn5YbEmJmELJWmnKbKKSlGbM2v8AtASQAN0UzGMAnAEwWQjRU0rpbdIIiVRISonvvvsOQUFB2LNnD+rXr4/Zs2dj0qRJcHBwUDo8smAss02PSVrl2Rt7ssqm8E9ISEBwcDBiY2MhpcSbb76JmTNnomPHjiY5n6pZ0iNdCiZ2bGEjjSnNmLVxABJk4Sa4D4QQv5kgJrPGi7y2FRyA7uDggODgYHh7e6NevXpKh0cEsMwmjdgbezLfw7FTk9IQ4f0VAFRawialxE8//YSgoCB8+eWXqFWrFsaPH49p06bB2dm5Us6hSVp/pIsh0aqqxIsJHimoNGPWTpXw9iuVGAuRahUcgN6mTRusWbMGXl5eqF69utLhET3CMrt02JVReTG+ex8lagZZ6dmI8d1b4WQtLy8PO3fuRFBQEA4ePIjGjRvjo48+woQJE9C4ceMKHdssWNIjXao6sSOqZBWaP1xKmVhZgRCZWnm629y8eRPLly/HsmXLcOPGDXTr1g2LFy/GoEGDzH8AOpkdltmkJjcupZVpfWlkZWUhNjYWwcHBOHPmDJydnbFs2TL885//RK1atcp9XLNT0Ue6qGUmyapqUVNZF8ojR448YWNjsxqAO3STNZG25QE4lZOT826XLl2uF3xTDQ/FJjK5sna3SUpKQlhYGFatWoX09HT8/e9/x6xZs9CjRw/LGYBOZIb4GBX1sHOqj9SkwomZnVP9Mh/r7t27WLlyJcLCwpCcnIzOnTtj48aNGD58eNU+11JLyvtIF63OJGlGLWo2NjarmzRp4mZvb3/bysrq8TMFkqrl5eWJ1NTUdlevXl0NYFDB95mNk0UoqbuNsV9//RWjRo1Cq1atsHz5cgwbNgwnT57Ezp07tT9TWFqsbgawM1a6r2mxSkdERBZstJ8nqteyzbeuei1bjPbzLPUxUlJS4OPjg+bNm2PmzJlo27Ytdu3ahaNHj+LNN99komYKqb75u08CuuVUX2XiMSXnfbpXzV66l2FZee729vZ3maiZBysrK2lvb58GXUtpISzFyCKU1N1GSol9+/Zh0aJF+Pbbb1GnTh1MnjwZU6ZMQfPmzas4UhPRak0oUSXjs9LUw9CroTyzQZ45cwYhISHYsGEDcnJyMHz4cMycORNdunQxddjqU9VdEi1pJsmiqKMrpBUTNfOi/30W2YjGZI0sQlHdbSTy8KDxRXTt2hXx8fF48skn4e/vj3HjxqFhw4YKRWoiJdWEMlkjIoV4enUo02QiBw8eRFBQEL744gvUqFED77zzDqZPn45WrVqZMEoVU6IiTuszSZaHOlrTVG/atGlN69Spkzt//vxrlX3sH3/8sdY777zjkpmZadWnT5+06Ojoy5Yyd4BlfEoz5dM75lHtMJXMuLtNLrKRhMPYL8Kx78Y63LlzBytWrMDFixcxZ84c80vUANaEEhUQuG80W9U0wjCzY8+ePfH888/jhx9+wL/+9S9cunQJkZGRlpuoAcp0SbT3080cacxcZ5I0ltRb98rYr3sZlqlKjB8/3jkyMjLp4sWLpxITE2ts3brVYp6XxGSNLIKnVwe8Ffp/SK5/CHuwGKewE81bNsW2bdtw5swZeHt7o0aNGkqHaTrF1Xiac00oEWlaVlYW1q5dC3d3dwwaNAiXLl3C0qVLcenSJcyfPx/29vZKh6g8JSri6nsBTVYCNs4AhO5rk5XspaFyU7uuaTO165o2lXW8iIiIxq6uru3atGnTbvDgwS0Kvh8aGmrn7u7u1qZNm3b9+vVrde/ePSsAiI6Obti6dev2bdq0aefh4dEGAOLj42t06NDBrW3btu1cXV3bnTx5Mt8zkZKSkmzv379v9eKLLz6wsrKCl5fXzR07dphhzXrR2A1SgzibWfGKmp6/xf/VRVhYGFavXo309HS88sormDVrlvYnDCkLS3qmDhFpWlpaGlauXIklS5YgOTkZnTp14syOxVGqS2J5Z5LUMj6v7ZH4+PgaISEhDgcPHjzj4OCQc+3aNeuC23h5ed2ePn36DQCYNGlS0/DwcDtfX9/rgYGBDrt37/69RYsW2Tdu3LAGgGXLltmPHz/+2vvvv38rMzNT5OTk5DtWUlKSrYODw6NZ4pydnR+mpKTkn53IjLHUI7NRcHr+80lnMPrtaCTLU7CyEhg5ciRmzpwJd/ciJ9sxbxV9pg4RkYn9+eefWLp0KaKionDv3j307dsXa9euxUsvvWQ5FWtlxYo4egxDa9q5w8l1jJfDfnnnbHmPuWvXrnoDBw687eDgkAMATz75ZG7BbY4cOVJz3rx5jvfu3bN+8OCBda9evdIAwMPD476Xl5fL0KFDb3t5ed0GgO7duz8ICQlxuHLlSrU33njjdocOHbKMjyVl4blULKlMYLKmQZzNrGgxvnuRmf4QN3ABifgJN3ABNrnV4VbvBXybEINmzZopHaKyLLEmlIhULyEhASEhIYiNjUVubi5GjBiBGTNmWObMjmXFiriqZ8EtagZSSgghSpyN0tvbu8XWrVvPd+/ePSM8PLzx/v376wLAxo0bL+3Zs6d2XFxc/c6dO7c/fvx4wrhx42717Nnzwfbt2+sPGDDANTIy8uKgQYPuGY7l4uKSbdySlpSUVK1JkybZRZ3XHDFZI7OQk5ODE0k/4gL+h7u4iuqog7Z4CU7wQLV7NZmoERGpiJQSP/74I4KDg/Hll1+iZs2a8Pb2xvTp09GiRaHhL1QSVsQpRwNdIg0taJXRombQv3//u8OGDXtq7ty515o0aZJ77do164Kta+np6VZOTk7ZWVlZYvPmzY0M3RgTEhKq9+nT50GfPn0e7Nq1q0FiYmK1W7du5bq5uWW1b9/+emJiYvXjx4/XNE7WnJ2ds2vXrp333//+t7anp+eD2NjYxhMmTLhe0c+hFUzWNIwtasD9+/exZs0ahIWFIQlJqA07dMRgNEVHWOv/vO2c6iscJRERAUBubi527NiB4OBg/Pzzz7Czs8NHH32E8ePHw87OTunwiPLTQDKmBA8Pj8zp06en9OzZs62VlZV0d3dP37Zt20XjbXx8fJK7du3q5ujo+NDNzS39/v371gAwderUZhcvXqwupRQ9evS4261btwxfX98mW7ZsaWxjYyPt7e2zAwICkgueMzIyMumdd95pkZmZKTw9Pe8OHz686AfomiFRVD9Qc+fh4SHj4+OVDoMq4Nq1a1i2bBkiIyNx+/Zt9OjRA/27jsCRj+/hYcZflTvVa9li4spXyvQcHyI1E0IckVJ6KB1HVWKZrX0ZGRlYt24dFi9ejPPnz6Nly5aYPn06xowZg1q1aj3+AERKKC5ZM6zP2K/7WrNX0dvBNGX2iRMnLnbq1OlGZR6TlHfixAm7Tp06uRRcz5Y10pSzZ88iNDQUMTExePjwIYYMGYKZM2eiW7duAIC9zxSeDZKJGhGRMm7cuIHIyEhEREQgNTUVXbt2xZYtWzBkyBBYWxeaQK5s2OpBplIwGePfGimIyRppwoEDB7Bo0SLExcWhWrVqGDNmDKZNmwZXV9d823l6dWByVlppsRyUTkQmkZiYiMWLFyM6OhoZGRmW+cgUMl+cxp+qEJM1Uq3c3Fzs3LkTwcHBOHDgABo2bAhfX19MnDgRTz75pNLhaVtabP7pnnOSdMsAEzYiKrfDhw8jODgY27Ztg7W1NUaNGoUZM2agXbt2lXcStnqQqTEZIxVhskaqk5GRgZiYGISGhuLcuXNwcXFBeHg4/vnPf6J27dpKh2ceUn3zP5cH0C2n+jJZI6IyycvLw9dff43g4GD88MMPqFevHmbMmIFJkybB0dFR6fCITIdJHFUBJmukGjdv3kRkZCSWLVuG1NRUdOnSBZs3b8bQoUNhY8M/1UqVc6ls64mICsjKysLGjRsREhKC06dPo1mzZggNDcW7776LevXqme7EWmr1KG13c3ZLVyc1/22RxeAdsIpZykOvExMTERYWhujoaKSnp2PAgAGYOXMmevfuzbENpmLjpOv6WNT6suANBlGJzLEcv3PnDqKiohAeHo6UlBR07NgRGzZswOuvvw5bW9vHH8BSlLa7ObulE1EJrJQOgCzX4cOHMWLECLRu3RorVqzAiBEjcPLkSXz99dfw9PRkomZK9n6AKDBdtqilW19ahhuMnCQA8q8bjLTYSg2ViNQhKSkJ06ZNQ/PmzTFnzhy0b98eu3btwvHjxzFq1KiqT9Sc96m75aOk7ubl2Y5I5aZNm9Z03rx5JplU4Mcff6zl6urazsnJyX3MmDHN8/LyCm2zaNEi+4iIiMamOH9l8fHxaVLWfdiypkKGmthT+5PyLZtDzSzHNqiEoba2Iq1iHPdGVIihvDYwh3L82LFjCAkJwaeffgoAeP311zFjxgw8/fTTCkemcqXtbs5u6USPNX78eOfIyMikPn36POjdu3frrVu31hsxYsRd421mzZqVasoYcnJy8g3Lyc7OLnMlVXh4uENgYODVsuyjipY1IUR/IcRZIcR5IYRPEe9XF0J8qn//ZyGEi9F7c/Trzwoh+lVl3FR6mZmZWLNmDdzd3TFw4ED88ccfWLx4MS5fvoygoCAmakqo7wU8dRFom6f7WtYES4s3GEm9/xrnQhXCctu8SSmxa9cuvPjii3jmmWcQFxeHyZMnIzExEbGxsUzUSqO4buUF15d2O6Lyuh3VCOeadsAZqy4417QDbkc1qughIyIiGru6urZr06ZNu8GDB7co+H5oaKidu7u7W5s2bdr169ev1b1796wAIDo6umHr1q3bt2nTpp2Hh0cbAIiPj6/RoUMHt7Zt27ZzdXVtd/LkyerGx0pKSrK9f/++1YsvvvjAysoKXl5eN3fs2NGw4DmNW/a6du3a5v3333fs0KGDm4uLi/u3335bB9AlXN7e3s1cXV3bubq6tvPz83sCAL744ou6bm5u7VxdXdsNHz7cJSMjQwCAo6NjhxkzZjh06dKlTXR0dMOuXbu2mThxouOzzz7bZuHChU8mJyfb9OvXr5W7u7ubu7u72+7du2sDQFpamtWwYcNcDOdZt25dg/HjxztmZWVZtW3btt2gQYMK/cyKo3jLmhDCGsByAC8BuALgsBAiTkp52mizdwDcllI+JYR4A0AQgNeFEO0AvAGgPYCmAL4XQrhKKXOr9lNULkPNq5ZrYg1u3bqFjz/+GMuWLcO1a9fQuXNnxMbGYvjw4RzboHWVNe6NNIfldmEFe0S493LO91Ur5fjDhw+xadMmhISE4NSpU2jatCmCgoLg7e2NBg0aKB2ettj75R+LBhTd3by021HRtDDRjJJuRzXC9anOkJm6BprclGq4PlVXMDUcd6s8h4yPj68REhLicPDgwTMODg45165dK/SEey8vr9vTp0+/AQCTJk1qGh4ebufr63s9MDDQYffu3b+3aNEi+8aNG9YAsGzZMvvx48dfe//9929lZmaKnJycfMdKSkqydXBwyDYsOzs7P0xJSXnsTWROTo44efLkb59++mn9+fPnN+3fv//voaGh9klJSdUTEhJO29ra4tq1a9bp6eli7NixLXbv3n22Y8eOWUOGDHEJDg62nzdv3nUAqFGjRt6RI0fOAsDq1aufuHPnjvXhw4fPAsDAgQNbTJs27Vq/fv3unzt3rlq/fv1aJyYmJvj4+DjUq1cv9/fffz8NAKmpqdZjxoy5s27duifOnDlzuvioC1NDy1pXAOellIlSyocANgN4tcA2rwJYr/9+K4C+Qjeg6VUAm6WUWVLKPwCc1x+PFJaYmIhJkyahefPm+PDDD/H000/j+++/x9GjRzFy5EgmauagMsa9VRVDi1rGft2LLWwVxXLbzNy5cwdBQUFo0aIFxowZAyEE1q9fjz/++AOzZs1iolYe9b2AJisBG2cAQve1ycrCvRhKux1RedyY7/goUTOQmVa4Mb/cXZp27dpVb+DAgbcdHBxyAODJJ58sVNl25MiRml26dGnj6urabtu2bY0TEhJqAICHh8d9Ly8vl9DQUDtDUta9e/cHoaGhDr6+vk3OnTtXrU6dOjJfuFIWPHyp5jUYPnz4bQB4/vnnH1y5cqUaAOzZs6feuHHjUg33oU8++WTuiRMnajRr1iyrY8eOWQAwZsyYm//73//qGo4zevTo28bHffPNNx8luT/99FO9yZMnO7Vt27bdwIEDn7p//7717du3rX744Yd6U6dOvW7Yzt7evtwVkoq3rAFwBHDZaPkKgOeK20ZKmSOESAPQWL/+UIF9zaY/nVZqYo398ssvCAkJefRA1DfffBMzZsxAhw4dlA6taKyRK7/KGPdGWsVyuwCt9ohISkrC0qVLsWrVKty/fx99+/ZFdHQ0Xn75ZU7yVBnqe5WuTCztdvQXPhy9dHKvVivT+lKQUkIIUTiDMuLt7d1i69at57t3754RHh7eeP/+/XUBYOPGjZf27NlTOy4urn7nzp3bHz9+PGHcuHG3evbs+WD79u31BwwY4BoZGXlx0KBB9wzHcnFxyTZuSUtKSqrWpEmT7KLOa6xGjRoSAGxsbJCbmyuKi72oZNBY3bp184pbllIiPj7+t6ISzMoqQ9XQslbUJyn4Uytum9LsqzuAEN5CiHghRHxqqknHH1qcvLw87Ny5E7169cJzzz2H3bt3Y+bMmfjjjz+wfv169SZqVHEVHfdWVQyzxtXspXupfRY59TN5uc0y27SOHj0KLy8vtGrVCsuWLcPgwYNx7NgxfP/99+jXrx8TNSJzYd3kYZnWl0L//v3vxsXFNbp69ao1ABTVDTI9Pd3KyckpOysrS2zevPnRGLmEhITqffr0ebBkyZLkhg0b5iQmJlY7ffp0NTc3t6wPP/zw+ssvv3zn+PHjNY2P5ezsnF27du28//73v7Xz8vIQGxvb+NVXX71TnthffPHFu1FRUfbZ2bpc79q1a9adO3fO/PPPU4jlQgAAIABJREFUP6udOnWqOgDExMQ07tmz570SD6TXo0ePu0FBQU8Ylg8cOFATAHr37n138eLFj9anpqZaA4CNjY3MysoqUwGrhmTtCoDmRsvNACQXt40QwgZAfQC3SrkvAEBKuVJK6SGl9LC3t6+k0C1bZmYmVq1ahXbt2mHQoEG4ePEiQkNDcenSJQQGBqp70hB2i6PH4d9ESUxebmu1zA7cN1q1rWqG2Xj79OmDLl26YOfOnZg8eTIuXLiADRs2oHPnzkqHSFR6rIQrHbt5f0LUyD/PvaiRB7t5f5b3kB4eHpnTp09P6dmzZ9s2bdq0Gz9+fPOC2/j4+CR37drVrWfPnq6tW7fONKyfOnVqM1dX13atW7du361bt3vdunXL2LBhQyNXV9f2bdu2bXfu3LkaY8eOvVnweJGRkUnjxo1zcXZ2dndxcckaPnx4Wnlinzp1amqzZs0etm3btn2bNm3arVmzplGtWrVkVFTUxeHDh7dydXVtZ2VlhRkzZpSqlnDlypWXjx49WtvV1bVdq1at2kdERNgDQEBAQMqdO3esDZOpfP3113UBwMvLK9XNza1ME4yIxzX9mZr+Iv47gL4A/gRwGMBIKWWC0TYTAHSQUo7TD1R/TUo5QgjRHsBG6MY7NAXwXwCtHzdQ3cPDQ8bHx5vmA1mAGzduIDIyEhEREUhNTcUzzzyDmTNnYtiwYfmmNFW1gt0navbSfWVBTwYq7VIjhDgipfRQOIYqLbdZZldMVlYWYmNjERoaitOnT8PR0RFTpkzBe++9h/r16ysdHlHFqLSsNjBFmX3ixImLnTp1ulHqHW5HNcKN+Y7IvVoN1k0ewm7en+WdXIRM58SJE3adOnVyKbhe8Ttr/ViGiQB2AbAGEC2lTBBCzAcQL6WMA7AGwAYhxHnoambf0O+bIIT4DMBpADkAJmh9RjE1O3fuHMLCwrBu3TpkZGTgb3/7G2bOnIlevXppr8uMoVBXeSFPCuA4iMdiua0NN2/eRFRU1KPZeDt16oQNGzbg9ddf5yRPZD5YNj9ew3G3mJxpl+LJGgBIKb8G8HWBdfOMvs8EMLyYff0AqHD6OfMgpcSBAwcQGhqKHTt2wNbWFqNGjcL06dPRrl07pcMjUgYTOJbbKnbhwgUsWbIE0dHRSE9PR79+/TBz5kz06dNHexVrREQWThXJGqlPbm4utm/fjpCQEPz8889o1KgR5s6di4kTJ6JJkyZKh1d5LPhmm4rBVlfSqIMHDyI0NBSff/45bGxsMHLkSEyfPp2TPBERaRiTNcrn/v37WLt2LZYsWYLExES0atUKERERGDNmDGrXrq10eETKYhdJUpnc3Fx88cUXCA0NxYEDB9CgQQP4+Phg4sSJaNq0qdLhlR3/p4iI8mGyRgCA5ORkLFu2DFFRUbhz5w66d++O4OBgvPrqq7C2LjQjK5H5480iqdiDBw8eVaxduHABLVq0QHh4OP7xj3+gTp06SodHRESVhMmahpjiYau//vorQkNDsWnTJuTm5mLIkCGYPn06unfvXmnnUBXW2lJFsIskKSwlJQURERGIiorCrVu30K1bNwQGBmLIkCHarlhjqzURUZGYrFkgKSV2796N0NBQfPfdd6hVqxbGjh2LKVOmoFWrVkqHVzV4I0BEGnLy5EksXrwYsbGxyMnJweDBgzFjxgw8//zzSoemLqUp21n+E5nEtGnTmtapUyd3/vz51yr72B988IHjli1bGt+9e9c6PT39WGUfX82YrGmAoUXt1P6kfMtlbWHLysrCxo0bsXjxYpw6dQoODg7w9/fH2LFj/7+9u49uokz7B/69Wl5apeWlQKlgKSwg5V3JVljtA4Jv+FJYiyycuiKibOEIEsADj3D87UFX6nNoaQMiIlARBReKQn+/dRdQARUFCT5FrCAiFGShhUKhhdLatPfvj0zZGpuSNi8zSb6fc3IyyUwmVybtdee6554ZtGvX7sYr8GeOvbYhvLYQuYE/8sgHlFLYsWMH0tPTsX37doSHh2PKlCmYOXMmevTooXd4nsW91kTUgDFjxlyaM2fOufj4+H56x+JrLNaCQO21dpYtW4bCwkL0798fb7/9NsaPH4+WLVvqHZ5nNLaBr7nctNcREXlZZWUlNmzYgIyMDBw6dAidOnXCK6+8gtTUVERFRekdnjG5MoySQy0pmBUk3AYAiPv6B0+sbtmyZVEWiyVaRBAfH39ty5YtJ+rOT09Pb5+dnd2hqqpK4uLiKnNyck5ERETUrFmzpu2iRYtuCQkJUREREdVWq/UHq9UaNmnSpG5VVVVSU1ODzZs3/9S/f//KuusbOXLkVU/E7Y9YrPmB2j1ojd2j5ngR6wceeADvvPMO7r333uC71k5tY3y0jf2+tlhrDDbsRORFFy5cwJtvvomlS5eisLAQ/fr1Q3Z2NiZMmBA4HWs3wvxKZHhWqzVs8eLFMV999dWRmJgYW1FR0W8OmE1JSSmZPXt2MQDMmDHjFovF0n7+/Pnn0tLSYrZv3360W7duVcXFxaEAsHTp0g7Tpk0rmjp16sWKigqx2Wy+/kiGxmItwCil8MUXXyA9PR25ubnXL2JtNpvRr18A7jlubE9py0G/fswfBkSks2PHjiEzMxPZ2dkoLy/H/fffj7Vr1+K+++4Lvo61pnJlGKWzZdgRR4Gsdo9axf5Wv3rsxh62bdu2RT766KMlMTExNgCIjo6udlzmwIED4S+99FLnsrKy0KtXr4YOGzbsMgCYTKYrKSkpccnJySUpKSklADB06NCrixcvjjl9+nSL8ePHlzjuVQt2LNb8SEN71Gw2GzZv3oz09HTs378fUVFRWLBgAaZNmxZYF7F2l2Pj7AoOnSEiD1NKYc+ePcjIyMCWLVvQvHlzpKSkYNasWYHZseaIeZTIbymlICKqoWWmTJnSLScn59jQoUOvWSyWqN27d0cAwPr16099+umnN+fm5rYeNGhQ37y8vPzU1NSLiYmJVz/88MPWo0aN6rV8+fKCpKSkMt98GuNjsebnLl++jFWrVsFiseDUqVPo2bMnli9fjokTJ+Kmm27SOzzva2rPKH8gEJEOHDvW2rVrhxdffBHPPfccO9Y8wZXc7thusCOOAlntHjQPHrP24IMPlo4dO7bHiy++WNSpU6fqoqKiUMe9a+Xl5SGxsbFVlZWV8v7777eLiYmpAoD8/PyWI0aMuDpixIir27Zta3P8+PEWFy9erI6Pj6/s27fvuePHj7fMy8sLZ7H2HyzW/NTJkyeRlZWFVatWoaysDMOGDcPSpUvxyCOPICQkRO/wAguHyhCRm4K+Y60WC6TAx+804JlMporZs2efTUxM7B0SEqL69etXvnnz5oK6y8ybN+9MQkJCfOfOnX+Jj48vv3LlSigAmM3mLgUFBS2VUnL33XeXDhky5Nr8+fM7bdq0KapZs2aqQ4cOVYsWLTrj+J6pqaldPvzww3YVFRUh0dHRA1JSUoozMjJ+s1wgEqUa3IsZkEwmk7JarXqH0ST79u1DRkYGcnJyEBISgnHjxsFsNsNkMukdWuBjA0QGICIHlFJB9Q/vzzm7oKAAFovlesfa8OHDYTabg7djzbFYCx9mv9czrzK3e5bjYQZBvl29kbMPHjxYMHDgwGJPrpP0d/DgwfYDBw6Mc3yee9b8QHV1NbZs2YKMjAx8+eWXaN26NebMmYPnnnsOt956q97hBY8gb3CIyHV79+5FRkYGNm/ejJCQEPzpT3+C2WzG4MGD9Q5NXxypELgaez1T/g0QuYTFmoGVlZVhzZo1yMrKwokTJ9CtWzdkZmbi6aefRkREhN7hEfkv/kggL7DZbNc71r766it2rPkL5gHv4PVMiTyCxZoBnTp1CkuXLsVbb72Fy5cv46677sLixYsxevRohIb+5lIW5CtscAIfv2NqgrKyMqxevRpZWVkoKChA9+7dYbFYMGnSJLRq1Urv8IyJ/2OBx9XrmfK4RaJGYbFmIFarFRkZGdi4cSMAIDk5GbNmzcKdd96pc2REAYI/EsiDajvWVq5cidLSUtx1111IT09nx5onGel/1EixGBmvZ0rkUSzWdFZdXY3c3FxkZGTgiy++QGRkJGbOnInp06eja9eueodHAH/gBwN+x9QIX3/99fUTPQHA448/DrPZjISEBJ0jIzKAG13PlMctEjUKizWdlJWVITs7G1lZWTh+/Dji4uKwZMkSPP3004iMjNQ7PHIFGxrjudF34uxHQmMukk5ByfFET5GRkTCbzZg+fTpiY2P1Di/wGKkDxUix+BNuHyKPYLHmY47How0dOhSvvfYaxowZg2bN+HUYEn/gBz729JITpaWlWLNmDSwWy/UTPWVlZWHSpEk80RORO5hnA86sWbNuadWqVfXChQuLPL3u6dOnd960aVNUaWlpaHl5+f/Wt8x7773XOj8/P/zVV18t9PT7e8rChQs7ms3m4oiIiBpXX8PqwEe+/vprLFmyBJs2bQIAjB07Fmazmcej+SP2shpPY78Tfld0AydPnrzesVZaWoq7774b6enpSEpK4vFovmCkDhQjxUIUpMaMGXNpzpw55+Lj4/s5WyYlJeUyACdntnFfVVUVmjdv7vSxK958883oZ5999iKLNYOoPY3zkiVLrg+b4fFofox71AIff4QFvbrXRxMRjBs3DmazGb///e/1Do08iYUXBZGPVljbbVj4eeeSwist2nZq9cuElxL//VCq6aI761y2bFmUxWKJFhHEx8df27Jly4m689PT09tnZ2d3qKqqkri4uMqcnJwTERERNWvWrGm7aNGiW0JCQlRERES11Wr9wWq1hk2aNKlbVVWV1NTUYPPmzT/179+/su76Ro4cefVGMVksliir1XrzO++8cyo5OTkuIiKi+uDBgzefP3+++csvv3x60qRJJQCwYMGC6I0bN0aJCEaOHHl5+fLl//7yyy/Dp06d2vXatWshXbt2rVy/fn1Bhw4dqhMSEm5LSEi4sm/fvlYPPfTQpe+++y68bdu2tkOHDt00YMCA8vT09DOTJ0+OPXz4cHh1dbXMnz//zBNPPHHJZrNh2rRpXXbt2hUJABMnTixWSuHcuXPNhw0b1qtt27a2ffv2HXVlW7NY84LS0lKsXr0aFosFBQUFHDYTaFi0GQ97vskNNpsNH3zwAZYsWYK9e/eiTZs2vD6aURjpf9lIsRC56KMV1nZvmXd0raqwhQBAydkrLd4y7+gKAE0t2KxWa9jixYtjvvrqqyMxMTG2oqKi3ww3SElJKZk9e3YxAMyYMeMWi8XSfv78+efS0tJitm/ffrRbt25VxcXFoQCwdOnSDtOmTSuaOnXqxYqKCrHZbE3/wHUUFRU1t1qtR/Ly8sL++Mc/9pg0aVLJxo0bI//xj3+0PXDgwJGIiIia2tifeuqpbkuWLDn18MMPX5k5c+Ytc+fOvWXNmjU/A8ClS5dC9+/f/wMAJCcnx/30009he/bsOdqsWTM899xzne+5557STZs2FRQXF4eaTKb4pKSk0jfeeCPq5MmTLfPz879v3rw5ioqKQqOjo6vfeOON6N27dx+NiYlx+UOyWPOgEydOwGKxYPXq1SgrK7s+bIancSYiMp5Lly5h1apVWLp0KU6dOoXf/e53vD5aoHMcMn20jf1U8yzEKEBtWPh559pCrVZVhS1kw8LPOze1WNu2bVvko48+WlJbcERHR1c7LnPgwIHwl156qXNZWVno1atXQ4cNG3YZAEwm05WUlJS45OTkkpSUlBIAGDp06NXFixfHnD59usX48eNLHPeqNVVSUtKl0NBQDB48uOLChQvNAWDHjh2RTzzxxPVjxqKjo6svXLgQWlZWFvrwww9fAYBnn332wuOPP969dj0TJkz41XZ67LHHSmrPM7Fr167Ibdu2tbFYLJ0AoLKyUo4dO9bi008/jUxNTT1fO0yyvm3kqpAbL+I9ItJORHaIyI/afdt6lhkkIl+JSL6IfCsif6oz720ROSEiedptkOPrvU0phS+++ALJycno0aMHli1bhqSkJOzfvx+ff/45HnvsMRZqge7abvvt5HDubdNb11380eVlgZC3jx07hhkzZqBLly544YUX0L17d2zduhU//PADpk+fzkKNiAJGSeGVFo153hVKKYiIamiZKVOmdFu2bNmpo0ePfj937twzlZWVIQCwfv36U6+88sqZn3/+ucWgQYP6FhYWhqampl7cunXrsfDw8JpRo0b1ys3N9cgwtLCwsOsxKqXqxt6o9TgeX9aqVavrj5VSyMnJOXbkyJHvjxw58v3Zs2cP3XHHHRWubCNX6VqsAZgH4BOlVE8An2iPHZUDeFIp1RfAgwAyRaRNnfkvKKUGabc874dsV1VVhfXr1yMhIQGJiYnYuXMn5s6di4KCArz77rswmUy+CoWIyJf8Mm8rpbBr1y6MHj0avXr1wooVK5CcnIxvvvkGO3fu5IlDgkVtZ05Ia/t9jXYuAna0UYBq26nVL4153hUPPvhgaW5ubrvCwsJQAKhvGGR5eXlIbGxsVWVlpbz//vvtap/Pz89vOWLEiKuZmZln2rZtazt+/HiL77//vkV8fHzlggULzt1///2X8vLywpsamyuxr1u3rn1ZWVlIbexRUVHVkZGR1f/6179aAcDq1aujhg4desWV9d1zzz2l6enp0TU19vptz5494QBw7733lq5YsaJDVVUVat8HAG6++ebqy5cvN6r+0rtYGw1grTa9FsAYxwWUUkeVUj9q02cAnAPQwWcROrh48SLS0tLQrVs3pKSkoLS0FMuXL8fPP/+MV199FZ07d9YrNPK12r044cPsN+7VoeDgV3n7l19+wbp16zB48GDcc8892LNnD+bPn4+TJ09i7dq1uP322/UIi4jIJya8lPjv5mHNfrVnqHlYs5oJLyX+u6nrNJlMFbNnzz6bmJjY+7bbbuszbdq03xzcO2/evDMJCQnxiYmJvXr27FlR+7zZbO7Sq1evPj179uw7ZMiQsiFDhlxbt25du169evXt3bt3nx9//DHsL3/5ywXH9aWmpnaJjo4eUFFRERIdHT1g1qxZtzQl9rFjx5aOGjXq0qBBg+J79+7d5+WXX+4EANnZ2Sfmzp3bpVevXn2+/fbb8LS0tDOurC8tLe2MzWaT3r179+nZs2ffBQsWdNY+5/kuXbr80rt377633XZbn9WrV7cD7CcaGTVqVM8777yzl6sxS+1uQT2IyCWlVJs6j0uUUr8ZUlNnfgLsPw76KqVqRORtAEMBVELr4VVK3XCcq8lkUlartVGxHjlyBFlZWVi7di2uXbuGkSNHwmw2Y9SoUQgJ0bvmJV059siyYCMvEpEDSinddt3rkbebkrOLi4uxYsUKvP766ygsLER8fDxmzpyJP//5zwgP91qnLfkTnpCIfMAbOfvgwYMFAwcOLHZ1eW+cDZI87+DBg+0HDhwY5/i8108wIiIfA+hUz6z5jVxPDIB1ACYqpWp7CP4bQCGAFgBWApgLYKGT108BMAUAYmNjXXpPpRQ+/vhjZGZm4qOPPkLLli2RkpKC559/HgMGDGhM+BTIeHZI/8AfZi4zQt5uSs4GgPz8fGRmZuLdd99FRUUFHnjgAbz99tu4//77G32cAhFRIHgo1XSRxZn/8nqxppS619k8ESkSkRil1FmtUT/nZLlIAP8AsEAptbfOus9qk5Uikg1gTgNxrIT9hwFMJlODuxOvXbuG9957D5mZmcjPz0fHjh3x17/+FVOnTkXHjh0beikFI14kmwKMEfJ2Y3J2TU0Ntm3bhiVLlmDHjh0ICwvDk08+ieeffx59+vRp6KUUzJijicgP6H3q/lwAEwGkafdbHRcQkRYAPgTwjlJqk8O82h8MAvtxE9+5E8zZs2fxxhtvYMWKFTh//jwGDBiA7OxsjB8/HmFhYe6smoj0wmLa0wyTt8vLy7Fu3TpkZWXh8OHDiImJwd/+9jdMmTIF7du3b+pqiYiIDEPvYi0NwEYRmQzgFIDHAUBETABSlVLPABgH4L8ARInIU9rrntLOIPaeiHQAIADyAKQ2JYhvvvkGWVlZ2LBhA2w2Gx555BGYzWYMHz6cw2boxnhB5uDC71n3vH369Gm8/vrrWLlyJS5evIjBgwdj3bp1GDduHFq0aPLZqImI/EVNTU2NhISE6HfiCfKompoaAVBT3zxdizWl1AUAI+t53grgGW36XQDvOnn9iKa+d3V1NXJzc5GZmYnPPvsMrVq1wtSpUzF9+nT06NGjqaslIqNhMe1Reubtffv2ITMzEzk5OaipqcFjjz2GmTNn4g9/+AM71igwME+Ra747f/58nw4dOlxmweb/ampq5Pz5863hZKSJ3nvWdFFUVIQePXqgoKAAXbt2RXp6OiZPnozWrVvrHRr5MzaunmW0Hy0cTqmbkpISDB06FHv37kVkZCRmzJiB6dOnIy4uTu/QiIh8zmazPVNYWLiqsLCwH/S/DBe5rwbAdzab7Zn6ZgZlsXb69GkkJiYiPT0dSUlJaNYsKDcDUXBhUeW3CgoKICKwWCx46qmnEBERoXdIRJ7FziBqhMGDB58DkKR3HOQbQVml9OnTB5999pneYRDZsVH+NaP+aOFwSt307t0b3377LUJDQ/UOhYiIyKeCsljjBVGJiPxHeHg4CzUKbOwMIiIngrJYIzKEG+1BCoZGu77PaPTPb7R4iIiIKGCxWCMiIiIyAnYGEZEDFmtEenG2B8mox2x5kiufMZA+LxERBZ5AbJ/JcHi6TyLyrJPD/9OAEREREVGTcc8akd4ce+SMfsyWJwTDZyQiosAUDCNgyDBYrBGRZ7DxIiIiIvIoFmtEenClkAmGIicYPiMRkT9ih5tzHB1CPsRijYg8g40XERERkUexWCPyJQ4VJCIiIzN6O2WkeIwQAwU8FmtE5FlsvIgoUBmpUCCioMBijciXOFSQiMgYvJGHnV03059yvVFjN/oePyIvYbFGRP6NDTYReRsLBSLSCYs1Ij2wgSci0oc3Ci/HdR5tY7+vuey59/A1o8Vq1D1+RF7GYo2I/BN7uonIV4KpUAiGz0jkR1isERERUfDwRuHlbJ0sfDyP25KCDIs1IvJP/DFERL4WyHnG2VDOXpd0CYeI7FisERERUfDxRuHluE5/K+4q87y3bnasETVJiN4BEJEbTg63937WNoLBqOsuNv5E5N9ODtc/j3fdBbQcBCAUCGltPzlKzWVjxEYUxLhnjcgb2INIRET+wnEIZM0V762b7SNRo7BYI/JHJ4fbh6vUnhb62m77HraWg/RrANkAExE1jlELmfC77W2Mnm0KEQHQuVgTkXYA/g4gDkABgHFKqZJ6lqsGcEh7eEoplaQ93w3A+wDaAfgGwJ+VUr94P3IiJ4za8BJ5CPM2UQCq74RNnhr6yJNBEblF72PW5gH4RCnVE8An2uP6XFNKDdJuSXWefw3AEu31JQAmezdcIoPoust+hq7wYfZjC8KH2R/r0QjWHs9wbbf9xuMbAh3zNpE76ubI2mNuw4fZb0Y6BtdIsRAFMb2LtdEA1mrTawGMcfWFIiIARgDIacrribzCyA2vv2LxZzTM20SBypttFttDoibR+5i1aKXUWQBQSp0VkY5OlgsTESsAG4A0pdQWAFEALimlbNoypwF09nrERJ7k7rAQdxs+TwxL4RCXYMO8TdQUDQ2TZ94kIie8XqyJyMcAOtUza34jVhOrlDojIt0BfCoihwCU1rOcaiCOKQCmAEBsbGwj3pqoCdjwuo/H/+nGCHmbOZvIy5hTifyC14s1pdS9zuaJSJGIxGi9szEAzjlZxxnt/riI7AJwO4DNANqISDOtl7YLgDMNxLESwEoAMJlMTos6Ip/QuxDxxvuzwQ8YRsjbzNkUcDgKgYiaQO9j1nIBTNSmJwLY6riAiLQVkZbadHsAdwH4XimlAOwEMLah1xORCyrz7Dcj4fF/RsW8TeTPeFIoIr+i9zFraQA2ishkAKcAPA4AImICkKqUegZAPIA3RaQG9uIyTSn1vfb6uQDeF5FXAPwvgNW+/gBETaJ3D6vj+xO5jnmbyB3sdCKiRhB7R2dwMZlMymq16h0Gkf7DYY62sd/XXlw7fJj9nj8mDEtEDiilTHrH4UvM2UReoHf7EySCMWeTZ+m9Z40ouOndSLYcZL+vPXaNiIiIiAyDxRpRMPP1cEz25BIRGYOn8jDzOpFX6X2CESLyFzwInYiIiMinuGeNKNjU1wvqqz1qvGYaEfkT5irnmNeJfILFGhE1jA0yERERkS5YrBEFCz2LLr0vVUBE1BjspLox5nUin2CxRkQNY4NMREREpAsWa0TBwghFFws9IvIHRsiX/oLbhsirWKwRkWvYIBMRERH5FIs1omDDoouIyDXMl0SkM15njYi8g9dlIyIiInILizUiIiIiIiID4jBIIvIsnvKaiIiIyCO4Z42IiIiIiMiAuGeNiDyLp7wmIiIi8gjuWSMiIiIiIjIg7lkjIu/gHjUiIiIit3DPGhERERE5x0uxEOmGxRoRERGRP2IRRRTwOAySiIiIKFC5c7InXoqFSHcs1oiIiIj8CYsooqDBYo2IiIgo0HiioOOlWIh0x2KNiIiIyJ+wiCIKGizWiIiIiAKNJws6FoNEutH1bJAi0k5EdojIj9p923qWuUdE8urcKkRkjDbvbRE5UWfeIN9/CiKi4MG8TWQgXXexkCIKcHqfun8egE+UUj0BfKI9/hWl1E6l1CCl1CAAIwCUA9heZ5EXaucrpfJ8EjURUfBi3ibyJyzoiPya3sXaaABrtem1AMbcYPmxAP6plCr3alREROQM8zYREZGP6F2sRSulzgKAdt/xBsuPB7DB4bm/ici3IrJERFp6I0giIrqOeZuIiMhHvH6CERH5GECnembNb+R6YgD0B7CtztP/DaAQQAsAKwHMBbDQyeunAJgCALGxsY15ayKioGKEvM2cTURE5INiTSl1r7N5IlIkIjERBC4OAAAHy0lEQVRKqbNao36ugVWNA/ChUqqqzrrPapOVIpINYE4DcayE/YcBTCaTasxnICIKJkbI28zZRERE+g+DzAUwUZueCGBrA8tOgMNQGu2HAkREYD9u4jsvxEhERP/BvE1EROQjehdraQDuE5EfAdynPYaImERkVe1CIhIH4FYAux1e/56IHAJwCEB7AK/4IGYiomDGvE1EROQjul4UWyl1AcDIep63AnimzuMCAJ3rWW6EN+MjIqJfY94mIiLyHb33rBEREREREVE9WKwREREREREZkCgVfCfZEpEyAD/oHUcD2gMo1juIBjC+pjNybADjc5cv4uuqlOrg5fcwFBE5D+AqjPvd8+/SPYyv6YwcG8D4gCDM2eRZwVqsWZVSJr3jcIbxucfI8Rk5NoDxucvo8fkzI29bI8cGMD53GTk+I8cGMD4iT+AwSCIiIiIiIgNisUZERERERGRAwVqsrdQ7gBtgfO4xcnxGjg1gfO4yenz+zMjb1sixAYzPXUaOz8ixAYyPyG1BecwaERERERGR0QXrnjUiIiIiIiJDC4piTUQeF5F8EakREadn/RGRAhE5JCJ5ImI1YHwPisgPInJMROb5ML52IrJDRH7U7ts6Wa5a23Z5IpLr5Zga3BYi0lJE/q7N3ycicd6MpwnxPSUi5+tsr2d8GNsaETknIt85mS8iYtFi/1ZE7vBVbC7GN1xELtfZdi/5OL5bRWSniBzW/m+fr2cZXbehv2POdjs+w+Vs7f0Mm7eNnLO19zds3mbOJvIypVTA3wDEA7gNwC4ApgaWKwDQ3ojxAQgF8BOA7gBaADgIoI+P4vsfAPO06XkAXnOy3BUfxXPDbQFgGoAV2vR4AH/34ffpSnxPAVjm67817b3/C8AdAL5zMv8hAP8EIACGANhnsPiGA/h/emw77f1jANyhTUcAOFrP96vrNvT3G3O22/EZKme7uj30yttGz9na+xs2bzNn88abd29BsWdNKXVYKWXYi2C7GF8CgGNKqeNKqV8AvA9gtPejA7T3WatNrwUwxkfv64wr26JuzDkARoqIGCg+3SilPgNwsYFFRgN4R9ntBdBGRGJ8E51L8elKKXVWKfWNNl0G4DCAzg6L6boN/R1zttuMlrMBY+dtQ+dswNh5mzmbyLuColhrBAVgu4gcEJEpegfjoDOAn+s8Po3fJhtviVZKnQXsSQ9ARyfLhYmIVUT2iog3fxy4si2uL6OUsgG4DCDKizHV+94aZ99VsjbcIkdEbvVNaC7R82/NVUNF5KCI/FNE+uoVhDZM63YA+xxm+cM2DATM2fUzWs4GjJ23/T1nA8bPOczZRE3UTO8APEVEPgbQqZ5Z85VSW11czV1KqTMi0hHADhE5ovUYGSG++noXPXYqz4bia8RqYrXt1x3ApyJySCn1k2ci/BVXtoVXt9cNuPLe/xfABqVUpYikwt6bPMLrkblGz23nim8AdFVKXRGRhwBsAdDT10GISCsAmwHMVEqVOs6u5yVG2oa6Y852j5/lbMDYedvfczZg7JzDnE3khoAp1pRS93pgHWe0+3Mi8iHsQyM80vB7IL7TAOr25HUBcMbNdV7XUHwiUiQiMUqps9qwgHNO1lG7/Y6LyC7Ye6+80fC7si1qlzktIs0AtIbvhmncMD6l1IU6D98C8JoP4nKVV//W3FW3kVVKfSQiy0WkvVKq2FcxiEhz2Bv995RSH9SziKG3oREwZ7vHz3I2YOy87e85GzBwzmHOJnIPh0FqRORmEYmonQZwP4B6z2ykk/0AeopINxFpAfvB114/e5cmF8BEbXoigN/0KotIWxFpqU23B3AXgO+9FI8r26JuzGMBfKqU8lUv2Q3jcxgLnwT7GHqjyAXwpHZ2rCEALtcOqTICEelUexyLiCTAnscuNPwqj76/AFgN4LBSKsPJYobehoGAObtBRsvZgLHztr/nbMDAOYc5m8hN7p6hxB9uAP4Ie69JJYAiANu0528B8JE23R32M0AdBJAP+1AXw8SnPX4I9rMY/eTj+KIAfALgR+2+nfa8CcAqbfoPAA5p2+8QgMlejuk32wLAQgBJ2nQYgE0AjgH4GkB3H//N3Si+Rdrf2UEAOwH09mFsGwCcBVCl/d1NBpAKIFWbLwBe12I/hAbOxqdTfM/V2XZ7AfzBx/HdDfvwmG8B5Gm3h4y0Df39xpztdnyGy9nOtodR8raRc7b2/obN28zZvPHm3ZsoxSG5RERERERERsNhkERERERERAbEYo2IiIiIiMiAWKwREREREREZEIs1IiIiIiIiA2KxRkREREREZEAs1oiIiIiIiAyIxRoREREREZEBsVgj8hAR2Ski92nTr4iIRe+YiIiofszZROQPmukdAFEA+T8AFopIRwC3A0jSOR4iInKOOZuIDE+UUnrHQBQwRGQ3gFYAhiulyvSOh4iInGPOJiKj4zBIIg8Rkf4AYgBUstEnIjI25mwi8gcs1og8QERiALwHYDSAqyLygM4hERGRE8zZROQvWKwRuUlEbgLwAYDZSqnDAF4G8FddgyIionoxZxORP+Exa0RERERERAbEPWtEREREREQGxGKNiIiIiIjIgFisERERERERGRCLNSIiIiIiIgNisUZERERERGRALNaIiIiIiIgMiMUaERERERGRAbFYIyIiIiIiMqD/D6OZhUAjlDevAAAAAElFTkSuQmCC\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from sklearn.naive_bayes import GaussianNB\n", "\n", "for i, (ds_train, ds_test) in enumerate(zip(datasets_train, datasets_test)):\n", " ds_train = datasets_train[i]\n", " ds_test = datasets_test[i]\n", "\n", " X = ds_train[0]\n", " Y = ds_train[1]\n", " \n", " \n", " X_test = ds_test[0]\n", " Y_test = ds_test[1]\n", " # 1) Instancions le modèle \n", " # avec les probabilités conditionnelles gaussiennes\n", " model = GaussianNB()\n", " # on apprend les paramètres du modèle sur les données d'entraînement \n", " model.fit(X, Y)\n", "\n", " # 2) On peut utiliser le modèle pour obtenir des prédictions sur\n", " # a) sur les données de test\n", " pred_test = model.predict(X_test)\n", "\n", " # b) sur les données d'entraînement \n", " y_x = np.dot(W.T, X_b.T)\n", " pred_train = model.predict(X)\n", "\n", " \n", " # 4) on visualise les prédictions ainsi que la frontière de décision.\n", " plot_predictions(i,X,Y, X_test, Y_test, pred_train, pred_test, plot_nb=model )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.3. Les modèles NB pour la classification de texte" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Après cet aperçu des modèles NB, nous explorons leur application pour la classification de documents.\n", "\n", "Cet exemple vient du livre [Python Data Science Handbook](https://www.oreilly.com/library/view/python-data-science/9781491912126/).\n", "\n", "Comme nous l'avons abordé dans les capsules, en classification de texte, les caractéristiques de chaque document sont le nombre d'occurrences de chaque mot.\n", "\n", "Nous commençons pas télécharger un jeu de données contenant en ensemble de documents. (Ce jeu de données `20newsgroup` est standard en apprentissage automatique). Chaque document est associé à une classe qui correspond au thème du document. \n", "\n", "Les 20 cibles/thèmes possibles sont ci-bas:" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "['alt.atheism',\n", " 'comp.graphics',\n", " 'comp.os.ms-windows.misc',\n", " 'comp.sys.ibm.pc.hardware',\n", " 'comp.sys.mac.hardware',\n", " 'comp.windows.x',\n", " 'misc.forsale',\n", " 'rec.autos',\n", " 'rec.motorcycles',\n", " 'rec.sport.baseball',\n", " 'rec.sport.hockey',\n", " 'sci.crypt',\n", " 'sci.electronics',\n", " 'sci.med',\n", " 'sci.space',\n", " 'soc.religion.christian',\n", " 'talk.politics.guns',\n", " 'talk.politics.mideast',\n", " 'talk.politics.misc',\n", " 'talk.religion.misc']" ] }, "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from sklearn.datasets import fetch_20newsgroups\n", "\n", "data = fetch_20newsgroups()\n", "data.target_names" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour simplifier les choses, nous allons garder que les documents associés à quatre de ces catégories." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "categories = ['talk.religion.misc', 'soc.religion.christian',\n", " 'sci.space', 'comp.graphics']\n", "train = fetch_20newsgroups(subset='train', categories=categories)\n", "test = fetch_20newsgroups(subset='test', categories=categories)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Voici un exemple d'un document (chaque document est un courriel qui a été envoyé sur une liste de diffusion associée à un thème): " ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From: dmcgee@uluhe.soest.hawaii.edu (Don McGee)\n", "Subject: Federal Hearing\n", "Originator: dmcgee@uluhe\n", "Organization: School of Ocean and Earth Science and Technology\n", "Distribution: usa\n", "Lines: 10\n", "\n", "\n", "Fact or rumor....? Madalyn Murray O'Hare an atheist who eliminated the\n", "use of the bible reading and prayer in public schools 15 years ago is now\n", "going to appear before the FCC with a petition to stop the reading of the\n", "Gospel on the airways of America. And she is also campaigning to remove\n", "Christmas programs, songs, etc from the public schools. If it is true\n", "then mail to Federal Communications Commission 1919 H Street Washington DC\n", "20054 expressing your opposition to her request. Reference Petition number\n", "\n", "2493.\n", "\n" ] } ], "source": [ "print(train.data[5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nous pouvons convertir, chaque document en vecteur de chiffres en utilisant l'encodage [TF-IDF](https://en.wikipedia.org/wiki/Tf%E2%80%93idf). \n", "\n", "Ensuite nous créons un `pipeline` pour utiliser un modèle de classification **Naive Bayes multinomial**." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "from sklearn.feature_extraction.text import TfidfVectorizer\n", "from sklearn.naive_bayes import MultinomialNB\n", "from sklearn.pipeline import make_pipeline\n", "\n", "model = make_pipeline(TfidfVectorizer(), MultinomialNB())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On peut entraîner le modèle sur les données d'entraînement et prédire les cibles des données de test: " ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "model.fit(train.data, train.target)\n", "labels = model.predict(test.data)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On évalue ensuite la performance du modèle. \n", "\n", "Pour commencer, nous utiliserons une [matrice de confusion](https://fr.wikipedia.org/wiki/Matrice_de_confusion) :" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import seaborn as sns\n", "from sklearn.metrics import confusion_matrix\n", "mat = confusion_matrix(test.target, labels)\n", "sns.heatmap(mat.T, square=True, annot=True, fmt='d', cbar=False,\n", " xticklabels=train.target_names, yticklabels=train.target_names)\n", "plt.xlabel('cible')\n", "plt.ylabel('cible prédite');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nous observons que le classificateur arrive à bien départager les documents traîtant de l'informatique (`comp.graphics`) de ceux traîtants de l'expsace (`sci.space`). Mais le classificateur a plus de difficulté quand il s'agit des documents des deux autres catégories (`soc.religion.christian` et `talk.religion.misc`) qui semblent en effet plus similaires." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Nous pouvons de plus classifier n'importe quel nouveau document aussi court soit-il, en utilisant la fonction ``predict()``.\n", "\n", "Pour simplifier davantage les choses, voici une courte fonction qui retourne la prédiction la plus probable d'un document donnée en entrée:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "def predict_category(s, train=train, model=model):\n", " pred = model.predict([s])\n", " probas = model.predict_proba([s])\n", "\n", " for i, name in enumerate(train.target_names):\n", " print('%s -- %.2f'% (name, probas[0][i]))\n", "\n", " print('\\n')\n", " print('prediction:', train.target_names[pred[0]])" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "comp.graphics -- 0.20\n", "sci.space -- 0.42\n", "soc.religion.christian -- 0.25\n", "talk.religion.misc -- 0.13\n", "\n", "\n", "prediction: sci.space\n" ] } ], "source": [ "predict_category('sending a payload to the ISS')" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "comp.graphics -- 0.25\n", "sci.space -- 0.15\n", "soc.religion.christian -- 0.40\n", "talk.religion.misc -- 0.21\n", "\n", "\n", "prediction: soc.religion.christian\n" ] } ], "source": [ "predict_category('discussing islam vs atheism')" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "comp.graphics -- 0.58\n", "sci.space -- 0.16\n", "soc.religion.christian -- 0.15\n", "talk.religion.misc -- 0.11\n", "\n", "\n", "prediction: comp.graphics\n" ] } ], "source": [ "predict_category('determining the screen resolution')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "N'oubliez pas qu'il ne s'agit que d'un modèle probabiliste relativement simple qui utilise les fréquences de chaque mot dans un document. Néanmoins, les résultats sont intéressants. \n", "\n", "Conclusion, même un algorithme relativement simple (et naïf!), entraîné sur pas mal de données, peut obtenir des résultats impressionnants." ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 4 }