LAB02_Regression.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "45f80e9b",
   "metadata": {},
   "source": [
    "# 2CSSID-TP02. Régression et évaluation\n",
    "\n",
    "---\n",
    "\n",
    "Dans ce TP, nous allons traiter la régression binaire et logistique, ainsi que l'évaluation des deux types d'apprentissage automatiuque (classement et régression)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2245b050",
   "metadata": {},
   "source": [
    "- **Binome 01** : Ameur Nassim\n",
    "- **Binome 02** : Abdelmoumen Hatem Mohamed\n",
    "- **Groupe** : Il n'y a qu'un groupe => info inutile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "be907956",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "('1.26.1', '2.1.2', '3.8.0')"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import matplotlib\n",
    "import numpy             as np\n",
    "import pandas            as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "np.__version__, pd.__version__, matplotlib.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "741ccd6f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from typing          import Tuple, List, Type\n",
    "from collections.abc import Callable"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4e3e485",
   "metadata": {},
   "source": [
    "## I. Réalisation des algorithmes\n",
    "\n",
    "Dans cette partie, nous allons implémenter les fonctions de régression à partir de zéro (from scratch). \n",
    "Cela va nous permettre à comprendre COMMENT les algorithmes fonctionnent : leurs complexités (temporelles et spatiales) et leurs paramètres.\n",
    "Pour ce faire, nous allons utiliser la bibliothèque **numpy** qui est utile dans les calcules surtout matricielles.\n",
    "\n",
    "### I.1. Régression linéaire\n",
    "\n",
    "Premièrement, nous allons implémenter les fonctions nécessaire pour la régression linéaire.\n",
    "\n",
    "#### I.1.1. Fonction de prédiction\n",
    "\n",
    "$$Z = zf(X, theta) = \\theta_0 + \\sum\\limits_{j=1}^{N} \\theta_j X_j = \\sum\\limits_{j=0}^{N} \\theta_j X_j | X_0 = 1 $$\n",
    "\n",
    "- **X[M, N]** : une matrice de M échantillons et N caractéristiques. Afin d'introduire $\\theta_0$, cette matrice est augmentée par une colonne $X_0 = 1$. Supposons que cela est déjà fait. Donc, la caractéristique 0  est le biais.\n",
    "- **$\\theta$[N]** : un vecteur des paramètres (poids des caractéristiques).\n",
    "- **Z(X, $\\theta$)[M]** : un vecteur des préditions de chaque échantillon."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "535fe535",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1. , 1.7, 2.4])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# TODO: Combinaison linéaire\n",
    "def zf(X: np.ndarray, Theta: np.ndarray) -> np.ndarray:\n",
    "    return np.matmul(Theta, X.T)\n",
    "\n",
    "#=====================================================================\n",
    "# TEST UNITAIRE\n",
    "#=====================================================================\n",
    "# Resultat : \n",
    "# array([1. , 1.7, 2.4])\n",
    "#---------------------------------------------------------------------\n",
    "X_t = np.array([[1., 100.], \n",
    "                [1., 200.], \n",
    "                [1., 300.]])\n",
    "Theta_t = np.array([0.3, 0.007])\n",
    "zf(X_t, Theta_t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "42a9aaa1",
   "metadata": {},
   "source": [
    "#### I.1.2. Fonction du coût\n",
    "\n",
    "La fonction du coût calcule l'erreur d'estimation. \n",
    "Ici, nous allons utiliser l'erreur quadratique moyenne (MSE: mean square error). \n",
    "\n",
    "$$J = MSE(Y, H) = \\frac{1}{2M} \\sum\\limits_{i=1}^{M} (Y - H)^2$$\n",
    "\n",
    "- **Y[M]** : un vecteur des sorties réelles.\n",
    "- **H[M]** : un vecteur des prédictions où $H = Z(X, \\theta)$.\n",
    "- **MSE(Y, H)** : une valeur réelle représentant l'erreur de régression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0bb78d63",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.016666666666666673"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# TODO: Fonction du coût MSE\n",
    "def MSE(Y: np.ndarray, H: np.ndarray) -> float:\n",
    "    return 1/(2*Y.size) * np.sum((Y - H)**2)\n",
    "\n",
    "#=====================================================================\n",
    "# TEST UNITAIRE\n",
    "#=====================================================================\n",
    "# Resultat : \n",
    "# 0.016666666666666673\n",
    "#---------------------------------------------------------------------\n",
    "H_t = np.array([1., 1.7, 2.4])\n",
    "Y_t = np.array([1., 2.0, 2.5])\n",
    "MSE(Y_t, H_t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e543323b",
   "metadata": {},
   "source": [
    "Le gradient de cette fonction est calculé comme suit (Où $X^{(i)}$ est l'échantillon $i$ et $Y^{(i)}$ est la prédiction. $X_0^{(i)} = 1$) : \n",
    "\n",
    "$$\\frac{\\partial MSE}{\\partial \\theta_j} \n",
    "= \\frac{\\partial }{\\partial \\theta_j} \\frac{1}{2M} \\sum\\limits_{i=1}^{M} (Y^{(i)} - H^{(i)})^2 \n",
    "= \\frac{1}{2M} \\sum\\limits_{i=1}^{M} [\\frac{\\partial }{\\partial \\theta_j} (Y^{(i)} - H^{(i)})^2]\n",
    "= \\frac{1}{2M} \\sum\\limits_{i=1}^{M} [-2 (Y^{(i)} - H^{(i)}) \\frac{\\partial }{\\partial \\theta_j} H^{(i)}]\n",
    "$$\n",
    "\n",
    "$$\\frac{\\partial MSE}{\\partial \\theta_j}\n",
    "= \\frac{1}{M} \\sum\\limits_{i=1}^{M} [(H^{(i)} - Y^{(i)}) \\frac{\\partial }{\\partial \\theta_j} \\sum\\limits_{k=0}^{N} \\theta_k X_k^{(i)}]\n",
    "= \\frac{1}{M} \\sum\\limits_{i=1}^{M} [(H^{(i)} - Y^{(i)}) \\frac{\\partial }{\\partial \\theta_j} \\theta_j X_j^{(i)}]\n",
    "$$\n",
    "\n",
    "$$\\frac{\\partial MSE}{\\partial \\theta_j} = \\frac{1}{M} \\sum\\limits_{i=1}^{M} (H^{(i)} - Y^{(i)}) X_j^{(i)}$$\n",
    "\n",
    "- **X[M, N]** : une matrice de M échantillons et N caractéristiques. \n",
    "- **Y[M]** : un vecteur des sorties réelles.\n",
    "- **H[M]** : un vecteur des prédictions où $H = Z(X, \\theta)$.\n",
    "- **dMSE(X, Y, H)[N]** : les gradients de chaque caractéristique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "3f82adf2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ -0.13333333, -30.        ])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# TODO: Fonction des gradients MSE\n",
    "def dMSE(X: np.ndarray, Y: np.ndarray, H: np.ndarray) -> np.ndarray:\n",
    "    return (1/Y.size) * np.matmul(H - Y, X)\n",
    "\n",
    "#=====================================================================\n",
    "# TEST UNITAIRE\n",
    "#=====================================================================\n",
    "# Resultat : \n",
    "# array([ -0.13333333, -30.        ])\n",
    "#---------------------------------------------------------------------\n",
    "X_t = np.array([[1., 100.], \n",
    "                [1., 200.], \n",
    "                [1., 300.]])\n",
    "H_t = np.array([1., 1.7, 2.4])\n",
    "Y_t = np.array([1., 2.0, 2.5])\n",
    "dMSE(X_t, Y_t, H_t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68216bd2",
   "metadata": {},
   "source": [
    "### I.2. Régression logistique\n",
    "\n",
    "Ici, nous allons implémenter la régression logistique qui est basée sur la combinaison linéaire de la régression linaire.\n",
    "Il suffit d'appliquer la fonction logistique sur cette combinaison afin de la transformer à une probabilité.\n",
    "\n",
    "#### I.2.1. Fonction de prédiction\n",
    "\n",
    "La fonction logistique est calculée comme suit :\n",
    "\n",
    "$$\\sigma(Z) = \\frac{1}{1+e^{-Z}}$$\n",
    "\n",
    "- **Z[M]** : un vecteur des sommes pondérées $Z(X, \\theta)$.\n",
    "- **$\\sigma$(Z)[M]** : un vecteur des prédictions. \n",
    "- Normalement, cette fonction doit marcher avec un scalaire, un vecteur ou une matrice. Pour l'instant, nous nous intéressons par le cas d'un vecteur."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "cc7b9af1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.26894142, 0.73105858])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# TODO: Fonction logistique\n",
    "def sg(Z: np.ndarray) -> np.ndarray: \n",
    "    return 1/(1+np.exp(-Z))\n",
    "\n",
    "#=====================================================================\n",
    "# TEST UNITAIRE\n",
    "#=====================================================================\n",
    "# Resultat : \n",
    "# array([0.26894142, 0.73105858])\n",
    "#---------------------------------------------------------------------\n",
    "sg(np.array([-1, 1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "22dc6e90",
   "metadata": {},
   "source": [
    "La fonction de prédiction sera :\n",
    "\n",
    "$$H(X, \\theta) = \\sigma(Z(X, \\theta)) $$\n",
    "\n",
    "- **X[M, N]** : une matrice de M échantillons et N caractéristiques.\n",
    "- **$\\theta$[N]** : un vecteur des paramètres (poids des caractéristiques).\n",
    "- **Z(X, $\\theta$)[M]** : un vecteur des sommes pondérées de chaque échantillon.\n",
    "- **H(X, $\\theta$)[M]** : un vecteur des prédictions de chaque échantillon."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "85d16e75",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.73105858, 0.55724785, 0.14185106])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# TODO: Fonction de prédiction (régression logistique)\n",
    "def Hf_log(X: np.ndarray, Theta: np.ndarray) -> np.ndarray:\n",
    "    return sg(zf(X, Theta))\n",
    "\n",
    "#=====================================================================\n",
    "# TEST UNITAIRE\n",
    "#=====================================================================\n",
    "# Resultat : \n",
    "# array([0.73105858, 0.55724785, 0.14185106])\n",
    "#---------------------------------------------------------------------\n",
    "X_t = np.array([[1., -100.], \n",
    "                [1.,   10.], \n",
    "                [1.,  300.]])\n",
    "Theta_t = np.array([0.3, -0.007])\n",
    "Hf_log(X_t, Theta_t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e146af18",
   "metadata": {},
   "source": [
    "#### I.2.2. Fonction du coût\n",
    "\n",
    "Ici, nous allons utiliser l'entropie croisée binaire (BCE: Binary Cross Entropy Loss) comme fonction du coût.\n",
    "C'est la fontion utilisée dans le cas de classement binaire.\n",
    "\n",
    "$$BCE(Y^{(i)}, H^{(i)})\n",
    "= \\begin{cases}\n",
    "- \\log(H^{(i)}) & \\text{ si } Y^{(i)} = 1\\\\ \n",
    "- \\log(1 - H^{(i)})  & \\text{ si } Y^{(i)} = 0\n",
    "\\end{cases}\n",
    "$$\n",
    "Puisque $Y^{(i)} \\in \\{0, 1\\}$, donc : \n",
    "\n",
    "$$ BCE(Y^{(i)}, H^{(i)}) = - Y^{(i)} \\log(H^{(i)}) - (1- Y^{(i)}) \\log(1 - H^{(i)}) $$\n",
    "\n",
    "$$J = BCE(Y, H) = \\frac{-1}{M} \\sum\\limits_{i=1}^{M} [Y^{(i)} \\log(H^{(i)}) + (1- Y^{(i)}) \\log(1 - H^{(i)})]$$\n",
    "\n",
    "En pratique, on doit ajouter une petite valeur $\\epsilon$ à l'argument de la fonction $\\log$ afin d'éviter $\\log(0)$.\n",
    "\n",
    "- **Y[M]** : un vecteur des sorties réelles.\n",
    "- **H[M]** : un vecteur des prédictions.\n",
    "- **BCE(Y, H)** : une valeur réelle représentant l'erreur de classement."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "d315971c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.6181210324473608, 0.61812101133625)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# TODO: Fonction du coût BCE\n",
    "def BCE(Y: np.ndarray, H: np.ndarray, eps: float =1e-8) -> float: \n",
    "    return (-1/Y.size) * np.sum(Y * np.log(H + eps) + (1 - Y) * np.log(1 - H + eps)) \n",
    "\n",
    "#=====================================================================\n",
    "# TEST UNITAIRE\n",
    "#=====================================================================\n",
    "# Resultat (sans epsilon, avec) : \n",
    "# (0.6181210324473608, 0.61812101133625)\n",
    "#---------------------------------------------------------------------\n",
    "Y_t = np.array([1.00, 0.00, 0.0, 1.0])\n",
    "H_t = np.array([0.25, 0.25, 0.5, 0.9])\n",
    "BCE(Y_t, H_t, eps=0), BCE(Y_t, H_t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2e251194",
   "metadata": {},
   "source": [
    "Le gradient de cette fonction est calculé comme suit : \n",
    "\n",
    "$$\\frac{\\partial BCE}{\\partial \\theta_j} \n",
    "= \\frac{-1}{M} \\sum\\limits_{i=1}^{M} \\frac{\\partial}{\\partial \\theta_j} [Y^{(i)} \\log(H^{(i)}) + (1- Y^{(i)}) \\log(1 - H^{(i)})]\n",
    "$$\n",
    "\n",
    "$$\\frac{\\partial BCE}{\\partial \\theta_j} \n",
    "= \\frac{-1}{M} \\sum\\limits_{i=1}^{M} [ Y^{(i)} \\frac{\\partial}{\\partial \\theta_j} \\log(H^{(i)}) + (1- Y^{(i)}) \\frac{\\partial}{\\partial \\theta_j}\\log(1 - H^{(i)})]\n",
    "$$\n",
    "\n",
    "$$\\frac{\\partial BCE}{\\partial \\theta_j} \n",
    "= \\frac{-1}{M} \\sum\\limits_{i=1}^{M} [ Y^{(i)} \\frac{1}{H^{(i)}} \\frac{\\partial}{\\partial \\theta_j} H^{(i)} + (1- Y^{(i)}) \\frac{-1}{1-H^{(i)}} \\frac{\\partial}{\\partial \\theta_j} H^{(i)})]\n",
    "= \\frac{-1}{M} \\sum\\limits_{i=1}^{M} \\frac{Y^{(i)}-H^{(i)}}{H^{(i)}(1-H^{(i)})} \\frac{\\partial}{\\partial \\theta_j} H^{(i)}\n",
    "$$\n",
    "\n",
    "$$\\frac{\\partial H^{(i)}}{\\partial \\theta_j} \n",
    "= \\frac{\\partial \\sigma(Z^{(i)})}{\\partial Z^{(i)}} \\frac{\\partial Z^{(i)}}{\\partial \\theta_j} \n",
    "= [\\sigma(Z^{(i)}) (1-\\sigma(Z^{(i)}))]\\frac{\\partial}{\\partial \\theta_j} \\sum\\limits_{k=0}^{N} \\theta_k X_k^{(i)}  \n",
    "= H^{(i)} (1-H^{(i)})  X_j^{(i)}\n",
    "$$\n",
    "\n",
    "$$\\frac{\\partial BCE}{\\partial \\theta_j} \n",
    "= \\frac{-1}{M} \\sum\\limits_{i=1}^{M} \\frac{Y^{(i)}-H^{(i)}}{H^{(i)}(1-H^{(i)})} [H^{(i)} (1-H^{(i)}) X_j^{(i)}]\n",
    "$$\n",
    "\n",
    "$$\\frac{\\partial BCE}{\\partial \\theta_j} = \\frac{1}{M} \\sum\\limits_{i=1}^{M} (H^{(i)} - Y^{(i)}) X_j^{(i)}$$\n",
    "\n",
    "- \n",
    "Où $X^{(i)}$ est l'échantillon $i$ et $Y^{(i)}$ est la prédiction. $X_0^{(i)} = 1$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "49495c49",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.08333333, -0.25      ])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# La fonction de gradient BCE est la même que celle de MSE\n",
    "# Donc, je vais l'implémenter moi-même puisque c'est facile\n",
    "dBCE = dMSE\n",
    "\n",
    "#=====================================================================\n",
    "# TEST UNITAIRE\n",
    "#=====================================================================\n",
    "# Resultat : \n",
    "# array([-0.08333333, -0.25      ])\n",
    "#---------------------------------------------------------------------\n",
    "X_t = np.array([[1.,  5.], \n",
    "                [1., 10.], \n",
    "                [1.,  8.]])\n",
    "H_t = np.array([2.75, 5.25, 4.25])\n",
    "Y_t = np.array([3.00, 5.00, 4.50])\n",
    "dMSE(X_t, Y_t, H_t)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d589d278",
   "metadata": {},
   "source": [
    "### I.3. Descente du gradient \n",
    "\n",
    "**Rien à programmer ici**\n",
    "\n",
    "Dans cette fonction, nous allons itérer jusqu'à arriver au nombre max des itérations (pas d'autres conditions d'arrêt).\n",
    "\n",
    "- **X[M, N]** : une matrice de M échantillons et N caractéristiques.\n",
    "- **Y[M]** : un vecteur des sorties réelles.\n",
    "- **$\\theta$[N]** : un vecteur des paramètres (poids des caractéristiques).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "0e909e86",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([ 0.66487158, -0.1265281 ,  0.93802309]), 0.6851969300532375)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# La fonction de la descente du gradient\n",
    "def descente(X: np.ndarray, Y: np.ndarray, Theta: np.ndarray, # arguments obligatoires\n",
    "             it_max:   int = 100   , # nombre maximal des itérations\n",
    "             alpha:  float = 0.01  , # taux d'apprentissage\n",
    "             Hf:  Callable = Hf_log, # la fonction qui calule la sortie\n",
    "             Jf:  Callable = BCE   , # la fonction du coût\n",
    "             dJf: Callable = dBCE    # la fonction du gradient\n",
    "            ) -> Tuple[List[np.ndarray], List[float]]: \n",
    "     \n",
    "    couts  = []           # historique des coûts\n",
    "    Thetas = []           # historique des thetas\n",
    "    Theta  = Theta.copy() # une copie pour garder le contenu de Theta original\n",
    "    \n",
    "    # Ici, on boucle jusqu'à arriver aux maximum des itérations\n",
    "    for it in range(it_max):\n",
    "        H        = Hf (X, Theta)       # estimer la sortie\n",
    "        J        = Jf (Y, H    )       # calculer le coût\n",
    "        dJ       = dJf(X, Y, H )       # calculer les gradients\n",
    "        Theta    = Theta - alpha * dJ  # mettre à jour Theta\n",
    "        couts .append(J)               # stocker le coût courant\n",
    "        Thetas.append(Theta.copy())    # stocker les Thetas courants\n",
    "    \n",
    "    return Thetas, couts\n",
    "\n",
    "#=====================================================================\n",
    "# TEST UNITAIRE\n",
    "#=====================================================================\n",
    "# Resultat : \n",
    "# (array([ 0.66487158, -0.1265281 ,  0.93802309]), 0.6851969300532375)\n",
    "#---------------------------------------------------------------------\n",
    "\n",
    "X_t = np.array([\n",
    "    [1, 1, 0.2],\n",
    "    [1, 2, 0.1],\n",
    "    [1, 3, 0.4],\n",
    "    [1, 4, 0.3]\n",
    "])\n",
    "\n",
    "Theta_t = np.array([1., 1., 1.])\n",
    "\n",
    "Y_t = np.array([1, 0, 1, 0])\n",
    "\n",
    "Theta_P, J_P = descente(X_t, Y_t, Theta_t)\n",
    "\n",
    "Theta_P[-1], J_P[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4f01017b",
   "metadata": {},
   "source": [
    "### I.4. Regrouper les fonctions \n",
    "\n",
    "**Rien à programmer ici**\n",
    "\n",
    "Nous voulons créer une classe qui supporte la régression linéaire et la régression logistique.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "c118ece3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.86383643, 0.5273866 , 0.96123235])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# la fonction de normalisation\n",
    "# X: un vecteur de M échantillons et N caractéristiques\n",
    "# mean: un vecteur de N nombres qui représentent les moyennes des caractéristiques\n",
    "# std: un vecteur de N nombres qui représentent les écarts types des caractéristiques\n",
    "# si mean et std ne sont pas donnés, ils vont êtres calculés à partir de X\n",
    "def normaliser(X, mean=None, std=None): \n",
    "    if (mean is None) or (std is None): \n",
    "        mean = np.mean(X, axis=0) \n",
    "        std  = np.std (X, axis=0)\n",
    "    X_norm = np.where(std==0, X, (X - mean)/std)\n",
    "    return X_norm, mean, std\n",
    "\n",
    "def preparer(X, norm=True, const=True, mean=None, std=None): \n",
    "    X_pre = X.copy()\n",
    "    if norm: \n",
    "        X_pre, mean, std = normaliser(X_pre, mean=mean, std=std)\n",
    "    if const:\n",
    "        X_pre = np.append(np.ones((X_pre.shape[0], 1)), X_pre, axis=1)\n",
    "    return X_pre, mean, std\n",
    "\n",
    "def generer_zeros_1(nbr):\n",
    "    return np.zeros(nbr)\n",
    "\n",
    "def generer_uns_1(nbr):\n",
    "    return np.ones(nbr)\n",
    "\n",
    "def generer_aleatoire_1(nbr):\n",
    "    return np.random.rand(nbr)\n",
    "\n",
    "\n",
    "class Regression(object):\n",
    "    def __init__(self, alpha=.01, log=True, norm=True, const=True): \n",
    "        \n",
    "        self.norm  = norm\n",
    "        self.const = const\n",
    "        self.alpha = alpha\n",
    "        self.log   = log\n",
    "        \n",
    "        if log: # Régression logistique\n",
    "            self.Hf  = Hf_log \n",
    "            self.Jf  = BCE\n",
    "            self.dJf = dBCE\n",
    "        else: # Régression linéaire\n",
    "            self.Hf  = zf\n",
    "            self.Jf  = MSE\n",
    "            self.dJf = dMSE\n",
    "        \n",
    "    \n",
    "    def entrainer(self, X, Y, nbr_iter=100): \n",
    "        X_pre, self.mean, self.std = preparer(X, norm=self.norm, const=self.const)\n",
    "        Theta = generer_uns_1(X_pre.shape[1])# Supposons, les paramètres sont initialisés à 1\n",
    "        self.Thetas, self.couts = descente(X_pre, Y, Theta, \n",
    "                                           it_max = nbr_iter, \n",
    "                                           alpha  = self.alpha, # arguments de régularisation\n",
    "                                           Hf     = self.Hf, # fonction logistique\n",
    "                                           Jf     = self.Jf,\n",
    "                                           dJf    = self.dJf\n",
    "                                          )\n",
    "        \n",
    "    # La prédiction\n",
    "    # si classes=True elle rend un vecteur de 1 et 0\n",
    "    # sinon elle rend un vecteur de probabilités\n",
    "    def predire(self, X, classes=True, seuil=0.5):\n",
    "        X_pre, _, _ = preparer(X, \n",
    "                               norm  = self.norm, \n",
    "                               const = self.const, \n",
    "                               mean  = self.mean, \n",
    "                               std   = self.std\n",
    "                              )\n",
    "        H = self.Hf(X_pre, self.Thetas[-1])\n",
    "        if self.log and classes:\n",
    "            return (H >= seuil).astype(int)\n",
    "        return H\n",
    "\n",
    "#=====================================================================\n",
    "# TEST UNITAIRE\n",
    "#=====================================================================\n",
    "# Resultat : array([0.86383643, 0.5273866 , 0.96123235])\n",
    "#---------------------------------------------------------------------\n",
    "\n",
    "X_t = np.array([\n",
    "    [100, 20],\n",
    "    [200, 10],\n",
    "    [300, 40],\n",
    "    [400, 30]\n",
    "])\n",
    "\n",
    "Y_t = np.array([1, 0, 1, 0])\n",
    "\n",
    "# logistique\n",
    "reglog = Regression()\n",
    "reglog.entrainer(X_t, Y_t)\n",
    "\n",
    "reglog.Thetas[-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72549831",
   "metadata": {},
   "source": [
    "## II. Application et analyse\n",
    "\n",
    "Cette partie sert à appliquer les algorithmes, modifier les hyper-paramètres et analyser les résultats.\n",
    "Son but est de comprendre comment les hyper-paramètres peuvent affeter le fonctionnement d'un algorithme.\n",
    "\n",
    "### II.1. Régression linéaire\n",
    "\n",
    "Pour tester la régression linéaire, nous allons essayer d'estimer les prix des maisons en se basant sur leurs superficies.\n",
    "Pour ce faire, nous allons diviser notre dataset en deux : 80% pour l'entraînement et 20% pour le test (nous avons désactivé la dividion aléatoire afin d'avoir les mêmes résultats à chaque exécution)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "f3def278",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Superficie</th>\n",
       "      <th>Prix</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2104</td>\n",
       "      <td>399900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1600</td>\n",
       "      <td>329900</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2400</td>\n",
       "      <td>369000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1416</td>\n",
       "      <td>232000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3000</td>\n",
       "      <td>539900</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Superficie    Prix\n",
       "0        2104  399900\n",
       "1        1600  329900\n",
       "2        2400  369000\n",
       "3        1416  232000\n",
       "4        3000  539900"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "header = ['Superficie', 'Prix']\n",
    "houses = pd.read_csv('data/houses.csv', names=header)\n",
    "houses.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "6068aada",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(37, 10)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split  \n",
    "\n",
    "Xhouses = houses.iloc[:, :-1].values # Premières colonnes \n",
    "Yhouses = houses.iloc[:,  -1].values # Dernière colonne \n",
    "\n",
    "Xhouses_train, Xhouses_test, Yhouses_train, Yhouses_test = train_test_split(Xhouses, Yhouses, \n",
    "                                                                            test_size    = 0.2, \n",
    "                                                                            random_state = 0\n",
    "                                                                           )  \n",
    "\n",
    "len(Xhouses_train), len(Xhouses_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c71e2488",
   "metadata": {},
   "source": [
    "#### II.1.1. Taux d'apprentissage et convergence \n",
    "\n",
    "Ici, nous avons varié le taux d'apprentissage et affiché les courbes de la fonction objective en fonction de nombre d'itérations. \n",
    "Nous voulons tester l'effet du taux d'apprentissage sur la convergence de notre modèle de régression.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "7a34a29a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ITMAX  = 100\n",
    "alphas = [1., 0.1, 0.01, 0.001]\n",
    "\n",
    "# Création et entraînement des nouveaux modèles de régression linéaire\n",
    "for alpha in alphas:\n",
    "    # Création d'un nouveau modèle de régression linéaire\n",
    "    modele = Regression(alpha=alpha, log=False)\n",
    "    # Entraînement du modèle\n",
    "    modele.entrainer(Xhouses_train, Yhouses_train, nbr_iter=ITMAX)\n",
    "    # Visualisation de la convergence\n",
    "    plt.plot(modele.couts, label = 'alpha=' + str(alpha))\n",
    "    \n",
    "plt.xlabel('Nombre des itérations')\n",
    "plt.ylabel('Coût')\n",
    "plt.legend()\n",
    "#plt.autoscale()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "eb7143a3",
   "metadata": {},
   "source": [
    "**TODO: Analyser les résultats**\n",
    "\n",
    "- Que remarquez-vous ? (Il faut décrire les résultats).\n",
    "- Donner une hypothèse concernant le rapport entre le taux et la vitesse de convergence.\n",
    "- Essayer de justifier cette hypothèse par ce que vous avez vu en cours.\n",
    "- Pourquoi nous ne devons pas utiliser un taux égale à 1 avec seulement une itération en pratique ?\n",
    "- Pourquoi nous ne devons pas utiliser un taux égale à 1 avec plusieurs itérations en pratique (quel est le risque) ?\n",
    "\n",
    "**Réponse**\n",
    "\n",
    "- On remarque que le coût diminue pour chaque valeur de alpha:\n",
    "    - alpha = 1 : Dès les premières itérations, le coût diminue brutalement à une valeur très basse (proche de 0)\n",
    "    - alpha = 0.1 : La valeur du coût diminue assez rapidement pour les 20 première itérations, et se stabilise à la 20ème à une valeur proche de 0\n",
    "    - alpha = 0.01 : La valeur du coût diminue moins que les précédentes\n",
    "    - alpha = 0.001 : Pour ce taux d'apprentissage, la diminution du coût est la plus lente en comparant avec les autres\n",
    "- On suppose qu'en augmentant le taux d'apprentissage, la vitesse de convergence augmente. \n",
    "- On a : $w(i+1) = w(i) - a * (dJ/dw)(w(i))$, tel que les $w(i)$ sont les valeur theta, $dJ$ la dérivée du coût (gradient) et $a$ le taux d'apprentissage. Dans cette expression, on remarque bien qu'en augmentant le taux d'apprentissage, $w(i)$ arrivera plus rapidement à sa valeur minimale. D'un autre côté, si a est trop petit, les pas pris pourraient être minuscules, ralentissant ainsi la convergence du modèle.\n",
    "- Car la plupart du temps, on risque de ne pas arriver au point minimal dès la première itération.\n",
    "- On risque de sauter la valeur minimale, rester aux alentours et se bloquer sans arriver près de la valeur minimale."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "198937fb",
   "metadata": {},
   "source": [
    "#### II.1.2. Qualité de prediction \n",
    "\n",
    "Ici, nous voulons tester la qualité de prédiction de la régression linéaire : est-ce qu'elle estime les sorties d'une manière exacte ou au moins d'une manière rapprochée. \n",
    "Pour ce faire, nous avons entraîné notre modèle sur les données d'entraînement (en bleu). \n",
    "Ensuite, nous avons essayé d'estimer les résultats de test (en vert : les sorties réelles ; en magenta : les sorties estimées)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "8488257f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model  import LinearRegression\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.pipeline      import make_pipeline\n",
    "\n",
    "# Entraînement d'un modèle de régression linéaire \n",
    "regresseur1 = make_pipeline(StandardScaler(with_mean=False), LinearRegression())\n",
    "regresseur1.fit(Xhouses_train, Yhouses_train)\n",
    "\n",
    "Yhouses_pred = regresseur1.predict(Xhouses_test )\n",
    "Yhouses_line = regresseur1.predict(Xhouses_train)  \n",
    "\n",
    "# Visualiser la distribution des données d'entraînement et de test\n",
    "# Aussi, la ligne de prédiction et la prédiction du dataset de test\n",
    "plt.scatter(Xhouses_train, Yhouses_train, color='blue'  , label = 'entrainement'      )\n",
    "plt.scatter(Xhouses_test , Yhouses_test , color='green' , label = 'test'              )\n",
    "plt.plot   (Xhouses_train, Yhouses_line , color='red'   , label = 'line de prediction')\n",
    "plt.scatter(Xhouses_test , Yhouses_pred , color='violet', label = 'prediction'        )\n",
    "plt.xlabel('Superficie')\n",
    "plt.ylabel('Prix')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f564015a",
   "metadata": {},
   "source": [
    "**TODO: Analyser les résultats**\n",
    "\n",
    "- Est-ce que la régression linéaire peut prédire exactement les valeurs Y ?\n",
    "- Pourquoi ?\n",
    "\n",
    "**Réponse**\n",
    "\n",
    "- Non, car on peut remarquer que les données de tests ne corrèlent pas exactement avec les prédictions du modèle. Donc la régression linéaire ne prédie pas de manière exacte les valeurs de Y.\n",
    "- La régression linéaire est basée sur le fait de trouver une droite qui s'ajuste au mieux avec les données d'entrainement. Or, sur les données réelles, il n'y a pas de relation strictement linéaire entre les entrées et les sorties. La droite de prédiction ne fait qu'approcher les résulats réels et donc la prédiction n'est pas exacte."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0b0664ed",
   "metadata": {},
   "source": [
    "#### II.1.3. Qualité de prédiction avec plus de caractéristiques\n",
    "\n",
    "Nous voulons tester si l'utilisation de plusieurs caracétristiques peut améliorer la prédiction. \n",
    "Aussi, nous voulons tester la régression polynomiale (qui est une régression linéaire avec les interractions des aractéristiques). \n",
    "Pour ce faire, nous avons créé de nouvelles caractéristiques pour avoir une régression polynomiale : $X^5$ et $X^{10}$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "9ead22e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.preprocessing import PolynomialFeatures\n",
    "from sklearn.metrics       import mean_squared_error\n",
    "from sklearn.metrics       import mean_absolute_error\n",
    "\n",
    "degres = [5, 10]\n",
    "\n",
    "erreurs_labels = [1] + degres\n",
    "erreurs_mse    = [        mean_squared_error(Yhouses_test, Yhouses_pred) ]\n",
    "erreurs_rmse   = [np.sqrt(mean_squared_error(Yhouses_test, Yhouses_pred))]\n",
    "erreurs_mae    = [        mean_absolute_error(Yhouses_test, Yhouses_pred)]\n",
    "\n",
    "couleurs=['magenta', 'cyan']\n",
    "\n",
    "# Ordonner le dataset en se basant sur la superficie\n",
    "# Ensuite, récupérer la liste des indexes (positions ordonnées)\n",
    "idx = Xhouses_train[:,0].argsort()\n",
    "\n",
    "# Visualiser la distribution des données d'entraînement et de test\n",
    "plt.scatter(Xhouses_train, Yhouses_train, color='blue' , label='entrainement')\n",
    "plt.scatter(Xhouses_test , Yhouses_test , color='green', label='test'        )\n",
    "# Dessiner la ligne de décision\n",
    "plt.plot(Xhouses_train[idx], regresseur1.predict(Xhouses_train[idx]), color='red', label = 'ligne degré=1')\n",
    "\n",
    "# Entraîner des modèles polynomiaux et visualiser leur convergence\n",
    "for i in range(len(degres)):\n",
    "    regresseur = make_pipeline(\n",
    "        PolynomialFeatures(degree=degres[i], include_bias=False), \n",
    "        StandardScaler(with_mean=False),\n",
    "        LinearRegression()\n",
    "    )  \n",
    "    regresseur.fit(Xhouses_train, Yhouses_train)  \n",
    "    plt.plot(\n",
    "        Xhouses_train[idx], \n",
    "        regresseur.predict(Xhouses_train)[idx], \n",
    "        color = couleurs[i],  \n",
    "        label = 'ligne degré=' + str(degres[i])\n",
    "    )\n",
    "    Yhouses_pred = regresseur.predict(Xhouses_test)\n",
    "    mse = mean_squared_error(Yhouses_test, Yhouses_pred)\n",
    "    erreurs_rmse.append(np.sqrt(mse))\n",
    "    erreurs_mse.append(mse)\n",
    "    erreurs_mae.append(mean_absolute_error(Yhouses_test, Yhouses_pred))\n",
    "\n",
    "plt.xlabel('Superficie')\n",
    "plt.ylabel('Prix')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "110f715d",
   "metadata": {},
   "source": [
    "**TODO: Analyser les résultats**\n",
    "\n",
    "- Que remarquez-vous ?\n",
    "\n",
    "**Réponse**\n",
    "\n",
    "- En analysant ce graphe, on remarque que la droite linéaire (degré = 1) s'ajuste au milieu du nuage de points d'entrainement, elle est moins ajustée que les autres lignes (sous-apprentissage / underfitting). Pour la ligne de degré 5, elle s'ajuste mieux que la droite linéaire aux données d'entrainement et prédie mieux les données de tests que la droite linéaire. Pour la ligne de degré 10, elle s'ajuste plus étroitement aux données d'entrainement (sur-apprentissage / overfitting) mais elle ne donne pas nécessairement des meilleures prédictions pour les données de test."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "378df62a",
   "metadata": {},
   "source": [
    "#### II.1.4. Métriques d'évaluation de la régression\n",
    "\n",
    "Nous allons continuer avec l'expérimentation passée. \n",
    "En plus de notre but, nous voulons aussi comparer les différentes métriques d'évaluation.\n",
    "\n",
    "$$MSE(Y, H) = \\frac{1}{M} \\sum\\limits_{i=1}^{M} (Y - H)^2$$\n",
    "\n",
    "$$RMSE(Y, H) = \\sqrt{MSE(Y, H)}$$\n",
    "\n",
    "$$MAE(Y, H) = \\frac{1}{M} \\sum\\limits_{i=1}^{M} |Y - H|$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "4b0412f3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Degré</th>\n",
       "      <th>Erreur (MSE)</th>\n",
       "      <th>Erreur (RMSE)</th>\n",
       "      <th>Erreur (MAE)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>5.821821e+09</td>\n",
       "      <td>76300.858343</td>\n",
       "      <td>69100.263620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5</td>\n",
       "      <td>4.717470e+09</td>\n",
       "      <td>68683.844226</td>\n",
       "      <td>59658.565180</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>10</td>\n",
       "      <td>1.579423e+10</td>\n",
       "      <td>125675.109040</td>\n",
       "      <td>100288.435482</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Degré  Erreur (MSE)  Erreur (RMSE)   Erreur (MAE)\n",
       "0      1  5.821821e+09   76300.858343   69100.263620\n",
       "1      5  4.717470e+09   68683.844226   59658.565180\n",
       "2     10  1.579423e+10  125675.109040  100288.435482"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame({\n",
    "    'Degré'         : erreurs_labels,\n",
    "    'Erreur (MSE)'  : erreurs_mse   ,\n",
    "    'Erreur (RMSE)' : erreurs_rmse  ,\n",
    "    'Erreur (MAE)'  : erreurs_mae   ,\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "760dc3a3",
   "metadata": {},
   "source": [
    "**TODO: Analyser les résultats**\n",
    "\n",
    "- Est-ce que plus de caractéristiques peut améliorer l'estimation ? Pourquoi ?\n",
    "- Est-ce que plus de caractéristiques doit améliorer l'estimation ? Pourquoi ?\n",
    "- Une de ces trois métriques est robuste contre les valeurs aberrantes, laquelle ? pourquoi ?\n",
    "\n",
    "**Réponse**\n",
    "\n",
    "- Oui, ajouter des caractéristiques peut améliorer l'estimation, c'est ce qu'on a remarqué en comparant entre les erreurs de la ligne de degré 1 et degré 5. Cela s'explique par le fait qu'en augmentant le degré, on fournit plus d'informations au modèle et donc le modèle peut mieux approcher les relations non linéaires de plus en plus. Par conséquent, les prédictions pourraient être meilleures.\n",
    "- Non, l'ajout des caractéristiques n'est pas toujours garanti d'améliorer l'estimation. Cela peut augmenter la complexité dans le modèle conduisant à un sur-apprentissage (overfitting) et donc s'éloigner des valeurs réelles de test lors de la prédiction malgrès les bonnes performances sur les données d'entrainement (C'est ce qu'on a remarqué en comparant les erreurs des lignes de degrés 5 et 10).\n",
    "- Parmi les trois métriques, la MAE (Mean Absolute Error) est la plus robuste contre les valeurs abérrantes. La raison en est que la MAE calcule la moyenne des écarts absolus entre les prédictions et les valeurs réelles en attribuant la même importance à toutes les erreurs qu'elles soit grandes ou petites, ce qui la rend moins sensible aux grandes variations. En revanche, les autres métriques (MSE, RMSE) donnent plus de poids aux grandes erreurs car ils se basent sur le calcul des carrés des écarts."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f9e682e6",
   "metadata": {},
   "source": [
    "### II.2. Régression logistique binaire\n",
    "\n",
    "Pour tester la régression logistique, nous allons essayer d'estimer si un étudiant est admis en se basant sur deux notes.\n",
    "Bien sûr, il est admis si la moyenne des deux notes est supérieure ou égale à 10. \n",
    "Dans ce cas, la séparation entre admis et non admis est linèaire.\n",
    "Les données d'entraînement et de test ont été générées automatiquement en utilisant le script joint à ce TP."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "8bcfb731",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Note1</th>\n",
       "      <th>Note2</th>\n",
       "      <th>Admis</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>9.75</td>\n",
       "      <td>16.00</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.25</td>\n",
       "      <td>9.50</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.50</td>\n",
       "      <td>2.50</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>15.50</td>\n",
       "      <td>10.25</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.25</td>\n",
       "      <td>19.50</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Note1  Note2  Admis\n",
       "0   9.75  16.00      1\n",
       "1   2.25   9.50      0\n",
       "2   4.50   2.50      0\n",
       "3  15.50  10.25      1\n",
       "4   3.25  19.50      1"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "notes = pd.read_csv('data/notes.csv')\n",
    "\n",
    "# Extraction des caractéristiques \n",
    "X_notes = notes.iloc[:, :-1].values # Premières colonnes \n",
    "Y_notes = notes.iloc[:,  -1].values # Dernière colonne \n",
    "\n",
    "notes.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "44aea63f",
   "metadata": {},
   "source": [
    "#### II.2.1. Normalisation et convergence \n",
    "\n",
    "Nous voulons tester l'effet de la normalisation sur la vitesse de convergence du modèle.\n",
    "Pour ce faire, nous avons entraîné deux modèles : un sans normalisation et l'autre ave normalisation.\n",
    "\n",
    "**Remarque** : le coût du modèle \"avec normalisation\" n'est pas une ligne horizontale ; il suffit de désactiver l'affichage de l'autre courbe afin de le remarquer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "b545592b",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ALPHA = 0.01\n",
    "ITMAX = 200\n",
    "\n",
    "# Création des modèles\n",
    "reg_log_nonorm = Regression(norm=False, alpha=ALPHA, log=True) # sans normalisation\n",
    "reg_log_norm   = Regression(norm=True , alpha=ALPHA, log=True) # avec normalisation\n",
    "\n",
    "# Entraînement des modèles\n",
    "reg_log_nonorm.entrainer(X_notes, Y_notes)\n",
    "reg_log_norm  .entrainer(X_notes, Y_notes)\n",
    "\n",
    "# Visualisation de la convergence\n",
    "plt.plot(reg_log_nonorm.couts, label = 'sans normalisation')\n",
    "plt.plot(reg_log_norm.couts  , label = 'avec normalisation')\n",
    "plt.xlabel('Nombre des itérations')\n",
    "plt.ylabel('Coût')\n",
    "plt.legend()\n",
    "#plt.autoscale()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12a51ba8",
   "metadata": {},
   "source": [
    "**TODO: Analyser les résultats**\n",
    "\n",
    "- Que remarquez-vous ?\n",
    "- Donner une hypothèse (vitesse de convergence avec normalisation)\n",
    "- Essayer de justifier cette hypothèse par ce que vous avez vu en cours.\n",
    "\n",
    "**Réponse**\n",
    "\n",
    "- On remarque sur le graphe pour les cas :\n",
    "    - Sans normalisation: Initialement, le coût est assez grand, mais diminue rapidement sur les 30 premières itérations et se stabilise près de 1.\n",
    "    - Avec normalisation: Initialement, le coût est déjà réduit (proche de 0.395), et continue à diminuer linéairement au fur et à mesure des prochaines itérations.\n",
    "- On suppose le modèle avec normalisation converge plus rapidement (plus grande vitesse de convergence).\n",
    "- La normalisation des caractéristiques améliore la convergence car elle permet de mettre à l'échelle les caractéristiques de manière à ce qu'elles aient la même grandeur (même moyenne = 0 et écart-type = 1), donc la mise à jour des poids est plus cohérente et prévisible. En revanche, lorsque les caractéristiques ne sont pas normalisées, certaines d'entre elles peuvent avoir des plages de valeurs beaucoups plus larges que d'autres, et donc le gradient de la fonction de coût es plus grand pour certaines caractérisques que d'autres."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "28a7ac5e",
   "metadata": {},
   "source": [
    "#### II.2.2. Complexité du modèle et séparation\n",
    "\n",
    "Nous voulons améliorer la séparation entre les deux classes : \"admis\" et \"non admis\". \n",
    "Pour ce faire, nous avons essayer d'utiliser des caractéristiques complexes : $X^3$ et $X^5$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "a3f24fc0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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OJSsrr75o5YUXXmDBggXs37+fChUq8NBDD1k9twceeIDw8HCOHj3K+++/z4oVK3j55ZetzjF37lweeOABDhw4QMuWLRk1ahSPPvoo06dPZ//+/WiaxhNPPFHo886ePZvhw4fz66+/cvfddzN69Gj++ecfjEYjmzZtAiAuLo7k5GQiIyMtx91222388MMPXL16Nd/nXq5pwobJZNIAzWQyFfJATdNe1jStlqZpFPPmo2naLE3TUgtx/cOHNW3ECE3T6TStYUNNW7xY0zIyCvcchBBC2O/6dU3bsUPT1qxRX69fd3WLHGbNr2s0ItCIQPOYidZ7LNp9w9RXj5lYHlvz6xpXN9XtXblyRTt69Kh25cqVQh+7I36H5bXO77YjfofjG65pWo8ePbSFCxdqmqZp165d0+rUqaPt2HHjWt27d9cef/xxq2O6du2qtW/f3nJ/7NixWqNGjTSz2WzZ1qJFCy0oKMhy//r161q1atW0tWvXapqmafHx8Rqg/fLLL5qmadqgQYO0Bx980O52Dx48WHvooYests2dO1e76667rLYlJiZqgBYXF6dpmqb17t1b69Wrl9U+t956q/bss89a7gPa5s2brfaZNWuWVrFiRS0lJSXfdv31118aoB06dCjX57ljxw4N0L755hvLMdu2bdMAy89P3759tXnz5lmdd/Xq1Zq/v79VG1988UXL/b1792qAtnTpUsu2tWvXapUrV7bcL+x5s7KytOTzyRqgbfpsk5aVlWVpf2pqqs1zP3jwoAZoCQkJ+b5GrpLf72mRs0EhSY+ZI3kDz6NK6l8oxi0eeBB4FWiEGjaZasf1W7eGdevg8GHo2RMef1yth/buuyCfTgghhGNFRUFAAPTpA6NGqa8BAWp7GeDvdaOoR5YH7GwM69qqr1keue8nHC853b6ql/buVxhxcXH88MMPjBw5EoAKFSowYsQIli5datnn2LFjdO3a1eq47t2725yrdevWeHjc+MHx8/Ojbdu2lvt6vZ7atWuTkpKSa1smTJjAunXr6NChA9OmTWPPnj35tv3KlSs2iwQfPHiQHTt2UL16dcutZcuWAFZD+tq1a2d1nL+/f57tyqlRo0bUrVvXatvx48cZOXIkgYGBeHt7W4Y+njlzJt9z5WyD/78FdrLbcPDgQebMmWP1PB5++GGSk5O5fPlyrufw8/MDsHrN/fz8yMjIIC0trdDnTb2SyqGUQyRlJFHNqxqHTh3iUMoh0q+m5/mcqlSpAmB1LmGtbM80dJWKqGGOReUDvImqAPk68F8gElVk5GlUGf/83HILrFkDM2bASy/Bk0/CvHkwfboqGHLTHyohhBCFFBUFYWG2iy+fPau2b9wIoaV7SYKghkEYvA2cTTub6zA6HToM3gaCGkrxD2eyN/g6IyAvXbqU69evU79+fcs2TdOoVKkSb7/9Nj4+9r/ZqVixotV9nU6X67a8hvgNGDCA06dP88UXX/D111/Tt29fJk6cyH//+99c969Tpw6pqdafal+8eJFBgwbx6quv2uzvn6O6aGHalVO1atVstg0aNIhGjRrx4YcfUr9+fbKysmjTpk2BxUFytkGnUxM5s9tw8eJFZs+eTWguf2NyhtHczuGI817NusrJ1BtBNvv1yTRnci497+Iw//zzD4BNeBU3SI+ZO6sHLED1oD38778DUAVHzttxfKtW8PHHcPSo+iT3qaegSRN46y24aWKuEEIIO5nNEB5uG8rgxrZJk9R+pZjeQ09kiJofosO6wkf2/YUhC2X5BSfLDsg3fw+y6dBh9DY6PCBfv36dVatWsWDBAg4cOGC5HTx4kPr167N27VoAWrVqxb59+6yO/f777x3almx169Zl7NixfPTRRyxcuJAPPvggz307duzI0aNHrbZ16tSJI0eOEBAQQNOmTa1uuYWqvFSsWBGzHb/f58+fJy4ujhdffJG+ffvSqlUrm7BYFJ06dSIuLs7mOTRt2tSqV9JZ5/37yt95nqNCRdXnk7NgSLbDhw9jMBjynRtY3kkwKw38UL1mCcBjwEJUQJsO5P27cUOLFrB6NRw7Bn37qjcMgYEQGQlXrjinzUIIUVbFxkIeBQoAFc4SE9V+pVxoq1A2Dt9IA+8GVtsN3gY2Dt8oC5WXAFcF5K1bt5Kamsr48eNp06aN1W3YsGGW4Yzh4eEsW7aM5cuX8/vvvzNr1iyOHDni0LYAzJw5k08//ZQTJ05w5MgRtm7dSqtWrfLcv3///hw5csQqCE2cOJF//vmHkSNH8uOPP3Ly5En+97//8eCDD9oVtLIFBASwfft2/vjjj3yDVs2aNalduzYffPABJ06c4Ntvv2Xy5Ml2XycvM2fOZNWqVcyePZsjR45w7Ngx1q1bx4svvlgi572eZRu6svkb/NHpdGzcspG//vqLixcvWh6LjY3lrrvuKlYbyzoJZqWJL/AaKqBNBN5CBbTngL/sOL55c1i1Cn77De66C555RgW0hQsloAkhhL2S7ZzLY+9+bi60VSgJ4QnsGLuDNaFr2DF2B/Hh8WUylLlqAeeCuCIgL126lH79+uU6XHHYsGHs37+fX3/9lREjRjBjxgymTZtG586dOX36NBMmTHB4ezw9PZk+fTrt2rXj9ttvR6/X51t6vW3btnTq1IkNGzZYttWvX5/du3djNpu56667aNu2LZMmTaJGjRqF6mlasGABX3/9NUajkY4dO+a5n4eHB+vWreOnn36iTZs2PP3007z++ut2Xycv/fv3Z+vWrXz11VfceuutdOvWjTfffJNGjRq5/Ly+/r488swjzHpxFn5+fpaqjxkZGWzZsoWHH364WG0s63SalttYjPItLS0NHx8fTCYT3t7eBR/gKn+jhje+DWjA48AUVICzx4kTau7ZqlVQpw5MmwaPPQZVqzqpwUIIUQbExKjh4QXZsQOCg53dGuEgUceiCI8Ot1orzOBtIDIkstjBJyMjg/j4eKv1rYrCnGUm9kwsyenJ+Hv5E9QwSIaS5mPbtm1MnTqVw4cPF2uIn7gh/Wo6cefjCtyvRe0WeFXystxfvHgxmzdv5quvvnJm84olv9/TksoG8lNamtUB5qN60MKB94DGwFTgTzuOb9oUli2D33+He+6BZ5+Fxo3hv/+FS5ec1mwhhCjVgoLAYABdHisr63RgNKr9RKngygWcC0PvoSc4IJiRbUcSHBAsoawAAwcO5JFHHuHs2bOubkqZUd2zOp56z3z38dR7Ut2zutW2ihUr8tZbbzmzaWWCBLOyoDbwMiqgTQbeRwW0Z1Cl+wsSGAhLlqiA9p//qOqNjRvDa69BjrHBQgghAL1ezdEF23CWfX/hQrWfcHuuXsBZONekSZMwGo2ubkaZodOpYjP5MXobLRUfs/3f//0fLVq0cGbTygQJZmVJLWAuKqBNAZagAtrTgD1THRo3hg8/hOPHYehQePFFte2VVyA973UphBCO565zXcS/QkNVSfwG1nN+MBjKRKn88iT2TKxNT1lOGhqJaYnEnin9xVxKA03TSL+azvnL50m/mo7MuHE/NavUpEnNJjY9Z556T5rUbELNKjVd1LLST9YxK4tqAXNQgSwSVcXxPeAR1Npo9fM8UgkIgPffh+efV6Fs5kw1vPGZZ+CJJ8DLq4ATCCGKw5lzXYQDhYbC4MGq+mJyMvj7q+GL0lNWqrhyAWdhLfVKKolpiWSab6zx5an3xOhtlDf7bqZmlZrUqFyDi5kXyTRnWoYv3txTJgpHeszKsppABKoH7TlgFRAIPAnYM9y6USNYvFgVCRk+HCIiVGh7+WX4d5V4IYRjlZa5LuJfer0q8DFypPoqoazUceUCzuKG1CupnEw9aRXKADLNmZxMPUnqleKv/yUcS6fT4VXJi9pVa+NVyUtCmQNIMCsPagCzUAHtBeAjVEB7AshnKR6Lhg3h3XdVQBs5EubMUQFt7lwwmZzUaCHKH5nrIkTJc9UCzuIGTVPDRfOTmJYowxpFmSfBrDzxAWagAtoMYA3QBFVmP/+/h4rRCG+/DSdPwujRqucsIEAFtQsXnNRoIcoPmesiRMlz1QLO4obs4XD5yTRncjFTCpKJsk2CWXnkA7yICmizgPWogDYBOGPH8QYDvPUWnDoFDzyg1kILCFBDHSWgCVFkMtdFCNdwxQLO4oaCQllh9xOitJJgVp55A8+jAtoc4BOgKfAocNqO4+vXVyWjT52CcePg1VfVvLRZsyBVxoILUVgy10UI1wltFUpCeAI7xu5gTegadozdQXx4vISyElDQuliF3S8iIoIOHToUo0WQkJCATqfjwIEDRT7H+fPn8fX1JSEhoVhtcSZHPM/S4L777mPBggWubkaBJJgJ8EIVB0lAlduPApqhqjgm2HF8/fpqzZ5Tp2D8eHj9ddWDNmMG/POPc9osRBkkc12EcC1ZwNnauHHj0Ol0vPLKK1bbt2zZ4tBCDwUtWvzr/l/pauzKfaH3OeyaBTEajSQnJ9OmTZsin+Pll19m8ODBBAQEOK5hqKIbW7Zscci5HPE83UlMTAw6nY4LN43gevHFF3n55ZcxuXltBAlm4obqqHL68agFq7egAtr/AafsON7fH954A+Lj4eGHYcECFdBeeAHOn3dWq4UoM2SuixAiN6YMU57zT5PSkjBlOO/NZuXKlXn11VdJdeJImIIWLf5s3Wc8POFhdu3axblz55zWjpz0ej316tWjQoWirSx1+fJlli5dyvjx4x3cMvtkZto37LO4z7O0aNOmDU2aNOGjjz5ydVPyJcFM2KoOTEUFtFeAz4HmwHjsC2h+fmrds4QEeOwx1ZsWEKDWRfv7byc1WoiyQea6CCFyMmWYCPk4hN4repNosq7UlWhKpPeK3oR8HOK0cNavXz/q1avH/Pnz891v06ZNtG7dmkqVKhEQEGAzbCwgIIB58+bx0EMP4eXlRcOGDfnggw8sj+e1aPH1jOts/3w7Tz/5NAMHDmTFihU2137llVfw8/PDy8uL8ePHk5GRYfX4uHHjGDJkCPPmzcPPz48aNWowZ84crl+/ztSpU6lVqxYGg4Hly5dbjrl5iF9qaiqjR4+mbt26VKlShWbNmlntf7MvvviCSpUq0a1bN6vthw8fZsCAAVSvXh0/Pz/GjBnD3zneGwUHB/PUU08xbdo0atWqRb169YiIiLB6HQGGDh2KTqez3M8evrlkyRIaN25M5cqVAYiOjqZXr17UqFGD2rVrc88993Dy5Mk8n2d2j9P27dvp0qULVatWpUePHsTFxVk9j08//ZROnTpRuXJlAgMDmT17NtevX7c8rtPpeP/997nnnnuoWrUqrVq1Yu/evZw4cYLg4GCqVatGjx49rNpi73mXLFnC0KFDqVq1Ks2aNeOzzz6zPJc+ffoAULNmTXQ6HePGjbMcO2jQINatW5fn98wtaMKGyWTSAM1kMrm6Ke7hkqZpCzRN89M0Ta9p2jhN044X4viUFE2bNk3TqlVTt2efVdvcyHXzdW1H/A5tza9rtB3xO7Tr5uuubpIo5+RnUoiy48qVK9rRo0e1K1euFPrYRFOiFhgZqBGBFhgZqJ25cEbTNE07c+GM1fZEU6Kjm62NHTtWGzx4sBYVFaVVrlxZS0xU19i8ebOW8y3k/v37NQ8PD23OnDlaXFyctnz5cq1KlSra8uXLLfs0atRIq1WrlvbOO+9ox48f1+bPn695eHhov/32m9U1s7KytLSMNO3vS39raRlp2pIlS7QuXbpomqZpn3/+udakSRMtKyvLsv/69eu1SpUqaUuWLNF+++037YUXXtC8vLy09u3bWz0PLy8vbeLEidpvv/2mLV26VAO0/v37ay+//LL2+++/a3PnztUqVqxoeY7x8fEaoP3yyy+apmnaxIkTtQ4dOmg//vijFh8fr3399dfaZ599ludr99RTT2khISFW21JTU7W6detq06dP144dO6b9/PPP2p133qn16dPHsk/v3r01b29vLSIiQvv999+1lStXajqdTvvqq680TdO0lJQUDdCWL1+uJScnayn/vp+aNWuWVq1aNS0kJET7+eeftYMHD2qapmkbN27UNm3apB0/flz75ZdftEGDBmlt27bVzGZzrs9zx44dGqB17dpVi4mJ0Y4cOaIFBQVpPXr0sLRx165dmre3t7ZixQrt5MmT2ldffaUFBARoERERln0ArUGDBtr69eu1uLg4bciQIVpAQIB2xx13aNHR0drRo0e1bt26Wb1G9p7XYDBoa9as0Y4fP6499dRTWvXq1bXz589r169f1zZt2qQBWlxcnJacnKxduHDBcuyXX36peXp6ahkZGbl+z/L7PS2pbCDBLBcSzPJwSdO0NzVNq6epgDZW07TfC3H8X39p2nPPaVr16iqgTZvmFgFt09FNmuENg0YElpvhDYO26egmVzdNCCFEGVCcYKZptiFs95nduYY1R8sOZpqmad26ddMeeughTdNsg9moUaO0O++80+rYqVOnarfccovlfqNGjbT777/fcj8rK0vz9fXVFi9enG8bevTooS1cuFDTNE27du2aVqdOHW3Hjh2Wx7t37649/vjjVsd07drVJpg1atTIEkY0TdNatGihBQUFWe5fv35dq1atmrZ27VpN02wDy6BBg7QHH3ww37bmNHjwYMvrlW3u3LnaXXfdZbUtMTHREiQ0TQWzXr16We1z6623as8++6zlPqBt3rzZap9Zs2ZpFStWtAS1vPz1118aoB06dCjX55kdzL755hvLMdu2bdMAy89v3759tXnz5lmdd/Xq1Zq/v79VG1988UXL/b1792qAtnTpUsu2tWvXapUrV7bcL8p5L168qAHal19+adX+1NRUm+d+8OBBDdASEhJyfW3cIZjJUEZhv6rAJNRwxjeAr4CWwAPA73YcX6cOzJ+vhjiGh6tFqwMCYOpUSElxUqPzF3UsirANYTZj98+mnSVsQxhRx6Jc0i4hhBAim9HHSMzYGAJrBnIq9RQ9l/XkVOopAmsGEjM2BqNP3vOzHOXVV19l5cqVHDt2zOaxY8eO0bNnT6ttPXv25Pjx45jNZsu2du3aWf6t0+moV68eKfn8/x8XF8cPP/zAyJEjAahQoQIjRoxg6dKlVtfu2rWr1XHdu3e3OVfr1q3x8LjxttfPz4+2bdta7uv1emrXrp1neyZMmMC6devo0KED06ZNY8+ePXm2G+DKlSuW4YTZDh48yI4dO6hevbrl1rJlSwCrIX05XycAf3//fF+nbI0aNaJu3bpW244fP87IkSMJDAzE29vbMvTxzJn810fK2QZ/f1UJOLsNBw8eZM6cOVbP4+GHHyY5OZnLly/neg4/Pz8Aq9fcz8+PjIwM0tLSinzeatWq4e3tbdfrU6VKFQCrc7kbCWai8KoAT6EC2kJgO9AKGAPE5X2YRe3aanHqhAR4+ml4/31o3BimTIE//3RWq22Ys8yER4ejodk8lr1tUvQkzFlmm8eFEEKIkmT0MbJ66GqrbauHri6RUAZw++23079/f6ZPn17kc1SsWNHqvk6nIysrK8/9ly5dyvXr16lfvz4VKlSgQoUKLF68mE2bNhW6ul5u1y5MewYMGMDp06d5+umnOXfuHH379mXKlCl5Xq9OnTo2BVMuXrzIoEGDOHDggNXt+PHj3H777fm2Nb/XKVu1atVstg0aNIh//vmHDz/8kH379rFv3z6g4OIgOduQXYEzuw0XL15k9uzZVs/h0KFDHD9+3CqM5nYOR583+zz2vD7//Fsp/Obw6k4kmImiqww8CZwEFgExwC3AaMD2AzVbtWvDSy+pgPbMM/DhhyqgTZ4Mf/zhrFZbxJ6JzbPKFahwlpiWSOyZWKe3RQghhMhPoimRMZvHWG0bs3mMTUEQZ3rllVf4/PPP2bt3r9X2Vq1asXv3bqttu3fvpnnz5uj1Rasie/36dVatWsWCBQus3qgfPHiQ+vXrs3btWsu1s8NGtu+//75I1yxI3bp1GTt2LB999BELFy60Kl5ys44dO3L06FGrbZ06deLIkSMEBATQtGlTq1tuoSovFStWtOqJzMv58+eJi4vjxRdfpG/fvrRq1coh1TU7depEXFyczXNo2rSpVa+kK87r6amKx+T2+hw+fBiDwUCdOnWK3EZnk2Amiq8yMBE4AbwNxAKtgZHA0XyOy1arFsyZowLatGmwbJkKaJMmQXKys1pNcrp957Z3PyHKA3OWmZiEGNYeWktMQoz0KAtRAhJNiQSvDLYMX9z90G7LsMbglcElFs7atm3L6NGjWbRokdX2Z555hu3btzN37lx+//13Vq5cydtvv51vj1JBtm7dSmpqKuPHj6dNmzZWt2HDhlmGM4aHh7Ns2TKWL1/O77//zqxZszhy5EixnmduZs6cyaeffsqJEyc4cuQIW7dupVWrVnnu379/f44cOWIVhCZOnMg///zDyJEj+fHHHzl58iT/+9//ePDBB+0KWtkCAgLYvn07f/zxR75Bq2bNmtSuXZsPPviAEydO8O233zJ58mS7r5OXmTNnsmrVKmbPns2RI0c4duwY69at48UXX3T5eRs1aoROp2Pr1q389ddfXLx40fJYbGwsd911V7Ha6GwuDWa7du1i0KBB1K9fP9fF8nQ6Xa63119/Pc9zRkRE2OyfPX5XOFklYAJwHFgM7AHaACOAw3YcX7MmRESogPbcc7BypQpoTz0FZ886vLn+Xv4O3U+Isi7qWBQBkQH0WdmHUVGj6LOyDwGRATIXUwgnSkpLsgplMWNj6GHsYTXnLHhlcL4jQBxpzpw5NsPGOnXqxIYNG1i3bh1t2rRh5syZzJkzx6pUeWEtXbqUfv364ePjY/PYsGHD2L9/P7/++isjRoxgxowZTJs2jc6dO3P69GkmTJhQ5OvmxdPTk+nTp9OuXTtuv/129Hp9vqXX27Zta3ldstWvX5/du3djNpu56667aNu2LZMmTaJGjRqF6mlasGABX3/9NUajkY4dO+a5n4eHB+vWreOnn36iTZs2PP300/m+h7ZX//792bp1K1999RW33nor3bp1480336RRo0YuP2+DBg2YPXs2zz33HH5+fjzxxBMAZGRksGXLFh5++OFitdHZdJqm2U6wKSFffvklu3fvpnPnzoSGhrJ582aGDBliefyPm4azffnll4wfP54TJ04QGBiY6zkjIiLYuHEj33zzjWVbhQoVCtVtmZaWho+PDyaTCW9v78I9KXFDJrACmAecBsKAmUDbfI7JyWSCRYvUotVXrsD//Z8KbAaDQ5pnzjITEBnA2bSzuc4z06HD4G0gPjxeFvQV5V52oZybf1eyF76WNdaEyFtGRgbx8fFW60vZK3sds5RLKTaFPrJ70nyr+RI9OhqfyrYhRrjOtm3bmDp1KocPHy7WED9RfIsXL2bz5s189dVXee6T3+9pSWUDly7zPWDAAAYMGJDn4/Xq1bO6/+mnn9KnT588Q1m2ChUq2BwrXMATeAQYB6wCXgbaAaGogNa+gON9fGDGDNVj9tZbKqB9+CGMHw/Tp4OxeBOe9R56IkMiCdsQhg6d1RvO7DebC0MWSigT5V5BhXJ06JgUPYnBLQbL74sQDuZT2Yfo0dGkZ6Zj8Lb+YNLoY2TnuJ14eXpJKHNDAwcO5Pjx45w9exZjMd+ziOKpWLEib731lqubUaBSE9///PNPtm3bxvjx4wvc9/jx49SvX5/AwEBGjx5dYEnQq1evkpaWZnUTDuQJ/B+qpP4S4BegAyqgHbDjeB8fePFFNcRx1ixYvx6aNIEJE6CA721BQluFsnH4Rhp4N7DabvA2SA+AEP+SQjlCuJZPZR+bUJbN4G2QUObGJk2aJKHMDfzf//0fLVq0cHUzClRqgtnKlSvx8vIiNDT/N8pdu3ZlxYoVREdHs3jxYuLj4wkKCiI9PT3PY+bPn4+Pj4/lJr9ATlIRGI8qqb8M+BXoCAwBfrbjeG9veP55FdBmz4ZPPoGmTeGxx+D06SI3K7RVKAnhCewYu4M1oWvYMXYH8eHxEsqERXkveCGFcoQQQgjnKzXBbNmyZYwePbrAsdkDBgzg3nvvpV27dvTv358vvviCCxcuWE2+vNn06dMxmUyWW2JiyZWeLZcqAg8Cv6HmoB0BOgP/AX6y43gvLzWUMSEB5s6FTZugWTN45BG1rQj0HnqCA4IZ2XYkwQHBMhxLWEjBCymUI4QQQpQEl84xs1dsbCxxcXGsX7++0MfWqFGD5s2bc+LEiTz3qVSpEpUqVSpOE0VRVADGotY9Wwu8BHQB/ODfKV4FqA48C/qpUPkyLL0EH5qheSy83wiCGzqr5aKcyKvgxdm0s4RtCCs3w12DGgZh8DYUWCgnqGGQC1onhBBClA2lIpgtXbqUzp070759QdUibF28eJGTJ08yZsyYgncWrlEBGAOMAjahhjoWigdQHTI94bsDsLMl9KkJzWLhAwloomik4MUNUihHCCGEcD6XBrOLFy9a9WTFx8dz4MABatWqRcOG6s10Wloan3zyCQsWLMj1HH379mXo0KGWdQqmTJnCoEGDaNSoEefOnWPWrFno9XpGjhxZ5HYmpSVJxaOSoAeGF+cEnsBt8PdlGL8btraCPrWgaSy81xD6Fm99DVG+5Cx44ZEFQafB/yIkV4fYRpDlcaPgRXBAsN3nNWeZiT0TS3J6Mv5e/gQ1DCoVgSa7UE54dLhVIRCDt4GFIQvLRc+hEEII4UwuDWb79++nT58+lvvZq5GPHTuWFStWALBu3To0TcszWJ08eZK///7bcj8pKYmRI0dy/vx56tatS69evfj++++pW7dukdooa4SUQnWqwqe94fwV+L/d8FlL6FcbAr+D9wxwZ4CrWyhKgexCFkOPQmQ0GHMUa030hvAQ2HxL4QpeRB2LyjXYRIZElopgE9oqlMEtBpfKYCmEEEK4O5cuMO2usheRO3LmCIM2D+JU6ikCawayc9zOPMvVCjf2zxV4+AfY0gKy6kLgXni3AfRv7OqWCTcWkxDDomf7sPHfukE5KyVl/fs1bDg89eoOu3rMZIFmIcqv4iwwLYQoGe6wwHSpqcroCgPXDrSEspixMRLKSqtaVWBTbzhfA8K+g4QmENIQGu+GL065unXCTQU16MHb/1M9QTf/ocy+/9ZXeoIa9CjwXAXNVwOYFD2p3JXhF0KUTREREXTo0KFY50hISECn03HgwIEin+P8+fP4+vqSUMSKzcXx3HPP8eSTT5b4dUXpJsEsHwmpCZZQZvSRtc1KvRqV4ZPecL4mjPgOzgTCwAAI2A1bT7q6dcLN6Hfvob7JnOcfSQ+gwQUz+t17CjyXLNAshHAIsxliYmDtWvXVXDIf5uzduxe9Xs/AgQNL5HoARqOR5ORk2rRpU+RzvPzyywwePJiAgAAAYmJi0Ol0XLhwwTGNJO8AOWXKFFauXMmpU/IBsLCfBLP8XKvCB/0/plYFI5cuUWK3K1dc/cTLuBqVYV1vSK0F930HSY1hUGNotAc+y3tZBVHOJNs5d8yO/WSBZiFEsUVFQUAA9OkDo0aprwEBaruTLV26lCeffJJdu3Zx7tw5p18PQK/XU69ePSpUKFo5hMuXL7N06VLGjx/v4JbZp06dOvTv35/Fixe75PqidJJglp8Ff9CvZTeqV6dEb1Wrwt13w759rn4ByjjvSrD2dvinNoz8Ds42gsGB0HAPbD7u6tYJV/O3c7FkO/aTBZqFEMUSFQVhYZB0U8/72bNquxPD2cWLF1m/fj0TJkxg4MCBluJsOb3yyiv4+fnh5eXF+PHjycjIsHp83LhxDBkyhHnz5uHn50eNGjWYM2cO169fZ+rUqdSqVQuDwcDy5cstx9zcE5Wamsro0aOpW7cuVapUoVmzZlb73+yLL76gUqVKdOvWzXK+7IJzNWvWRKfTMW7cOACysrKYP38+jRs3pkqVKrRv356NGzdazpXftRs3VvPVO3bsiE6nIzg42HLcoEGDWLdunX0vtBCUknXMXKXOyGn8nXkB3+p+zLx9BrWr1imR66amwltvQbdu0L8/zJoF3buXyKXLJ+9KsOZ2+CATHvsO1gVCqAEa7IXI2jCsuatbKFwhKAgMBvXGJ7caSTqdejyo4EWVgxoGUbtKbc5fOZ/nPrWr1JYFmoUQtsxmCA/P/e+Qpqm/RZMmweDBoHd8hdQNGzbQsmVLWrRowf3338+kSZOYPn06Op3O8nhERATvvPMOvXr1YvXq1SxatIjAwECr83z77bcYDAZ27drF7t27GT9+PHv27OH2229n3759rF+/nkcffZQ777wTg8F2Tv+MGTM4evQoX375JXXq1OHEiRNcyWeIUWxsLJ07d7bcNxqNbNq0iWHDhhEXF4e3tzdVqlQBYP78+Xz00Ue89957NGvWjF27dnH//fdTt25devfune+1f/jhB2677Ta++eYbWrdujaenp+Wat912G0lJSSQkJFiGUwqRHwlm+dj56lOWqoxvXNzKzrCSq8r4yCOwcSPMmQM9esBdd6mA1qPgOgOiqKp7wke3w3uZMDEW1gRAmBHq74WFteDeFq5uoShJej1ERqpPo3U66zdF/74hYeFCp7wREkIIi9hY256ynDQNEhPVfjl6axxl6dKl3H///QCEhIRgMpnYuXOnpWdo4cKFjB8/3jJk8KWXXuKbb76x6TWrVasWixYtwsPDgxYtWvDaa69x+fJlnn/+eQCmT5/OK6+8wnfffcd9991n044zZ87QsWNHunTpAlBg0Dl9+jT169e33Nfr9dSqVQsAX19fatSoAcDVq1eZN28e33zzDd3//RQ8MDCQ7777jvfff5/evXvne+3s5Zhq165NvXr1rNqQff3Tp09LMBN2kaGM+TD4GIgZG0NgzUB8q/ni5elVYtfW62HECDh0CDZsUB/a9+wJd94J331XYs0on6p7wsogMNWDsbGQ0gCGt4D638P6OFe3TpSk0FD1CUmDBtbbDQa1PdS+8vaxZ2Lz7S0DOH/lvBT/EELYcuB818KKi4vjhx9+sKwlW6FCBUaMGMHSpUst+xw7doyuXbtaHdc9l2E+rVu3xsPjxttOPz8/2rZta7mv1+upXbs2KSkpubZlwoQJrFu3jg4dOjBt2jT27Mm/8NKVK1fsWprgxIkTXL58mTvvvJPq1atbbqtWreLkyZNFuna27B65y5cv27W/EBLMCmD0MbJz3E6XLS7t4QH33gu//gqffAJ//qlGTvXtC7t2lXhzypeqFWFFEJj84cFY+Msf7msEIWPhl19c3TpRUkJDISEBduyANWvU1/h4u0MZSPEPIUQxOHC+a2EtXbqU69evU79+fSpUqECFChVYvHgxmzZtwmQyFepcFStWtLqv0+ly3ZaVlUVuBgwYwOnTp3n66ac5d+4cffv2ZcqUKXler06dOqSmphbYrosXLwKwbds2Dhw4YLkdPXrUMs+ssNfO9s8//wA3etWEKIgEMzsYvA0uCWU5eXioEVUHDsCmTXD+PPTuDXfcATt3urRpZV/VirAsCL5pAFSGo39Ap05qPP9PP7m6daIk6PVqiNDIkeprIYcvSvEPIUSRZc93zR5CfTOdDoxGu+a7Fsb169dZtWoVCxYssAosBw8epH79+qxduxaAVq1ase+mamXff/+9Q9uSrW7duowdO5aPPvqIhQsX8sEHH+S5b8eOHTl69KjVtuz5X+YcywzccsstVKpUiTNnztC0aVOrm9F4Y6mkvK6d2zmzHT58mIoVK9K6deuiP2lRrkgwK2U8PNQH9T//DJs3q0IhwcHqtmNH7nODhYNU/HdK5rZtsHIlHDsGXbrAoEGwf79r2ybcWlDDIAzeBnTk/sZKhw6jt1GKfwghbGXPdwXbcObE+a5bt24lNTWV8ePH06ZNG6vbsGHDLMMZw8PDWbZsGcuXL+f3339n1qxZHDlyxKFtAZg5cyaffvopJ06c4MiRI2zdupVWrVrluX///v05cuSIVa9Zo0aN0Ol0bN26lb/++ouLFy/i5eXFlClTePrpp1m5ciUnT57k559/5q233mLlypUFXtvX15cqVaoQHR3Nn3/+adWTGBsbS1BQkGVIoxAFkeIfpZSHBwwZojptPvsMZs9WvWdBQfDss7ZTYoQD/P7v1+MVoN0DsGYU/O9/8MEHcOv/Qa8geOxRaF30xTBdrWVLsGNIvigkvYeeyJBIwjaEoUOHxo1PULLD2sKQheg9pJCIECIX2fNdw8OtC4EYDCqUFWJotb2WLl1Kv3798PGxHTE0bNgwXnvtNX799VdGjBjByZMnmTZtGhkZGQwbNowJEybwv//9z6Ht8fT0ZPr06SQkJFClShWCgoLyLUXftm1bOnXqxIYNG3j00UcBaNCgAbNnz+a5557jwQcf5IEHHmDFihXMnTuXunXrMn/+fE6dOkWNGjXo1KmTpTBJfteuUKECixYtYs6cOcycOZOgoCBiYmIAWLduHREREQ59HUTZptM06WO5WVpaGj4+PphMJry9vV3dHLtoGmzdqgKajK4TRVWvngr2jz4K8gGf40UdiyI8OpyktBtvrIzeRhaGLCS0lePfWAkh3ENGRgbx8fE0btzYroIUeTKbVfXF5GQ1pywoSCrD5mPbtm1MnTqVw4cPWxUeKQlffvklzzzzDL/++muRF8kWJSu/39OSygbyk1JG6HRqRN0998Dhw3D1qqtbVAYdBP4P2AA0zuVxsxm++QaWLIGEeOjWHR5+GNq1K9l2FlFGBixdClOmwKuvwrRpKqBVrerqlpUdoa1CGdxiMLFnYklOT8bfy5+ghkHSUyaEsE/2fFdhl4EDB3L8+HHOnj1rNV+sJFy6dInly5dLKBOFIj1muSiNPWaiBOwBegJHgbyHtauAtnEjzJ0LR46UukXoTp6EefPUNLo6dWDqVHjsMahWzdUtE0KI0slhPWZCCKdxhx4zKf4hhKNlL0L3669qEbpz50rVInRNmqies+PHVS/sc89BYCD8979w6ZKrWyeEEEIIUTZJMBPCXnUBHTAC2AjkvtTKDdmL0B08qHrQStkidI0bw4cfqoA2eDBMn662vfYa/LvsixBCCCGEcBAJZkLYqxkQC9QD7gXao+ab2RPQhg2zXYSuTx/4t3KTOwsIUIUnT5xQhb9efFEFtFdegfR0V7dOCCGEEKJskGAmRGH0BL5CzTdrgOo9awusA2zXlrR28yJ0Fy6ocFZKFqFr1Ajee08FtHvvhZkzVUCbNw/S0lzdOiHsZ84yE5MQw9pDa4lJiMGcVdAvrxBCCOF8UvwjF1L8Q9jte2A2EA20BGagwpo9RfY07cYidL/8ooY5RkSosHbzIqJuKDFR9ZotWQLVq6vldW65pejnq1oV+vUDT0/HtVGIm+W2ZIHB20BkSKQsWSCcRop/COH+3KH4hwSzXEgwE4X2AyqgfQG0QAW0+7A/oOVchK5XL7h3AVy5FSbqoLoT2+0ASUmqvP6HHxZ/mYZGjeD552HcOAlowvGijkURtiHMaoFvuLHI98bhGyWcCaeQYCaE+3OHYCZDGYVwhNuAbaiA1gy4H7gFWA1cL+DY7EXofvxRBbSMDAgPhec06J8C19z7sxODAd56S43MLM7twAHo1k2V5m/WDN5/HzIzS/zpiDLKnGUmPDrcJpQBlm2ToifJsEYhhBAuI8FMCEe6Ffgc2I8a2vgAas2zldgX0AYOhL0/wOYlUPkM7DkGvXtC9P/cfg5a5crg41P0W/v2sG6dWiC9Rw+YMAGaNoXFi2XBdFF8sWdirYYv3kxDIzEtkdgzsSXYKiGEM0RERNChQ4dinSMhIQGdTseBAweKfI7z58/j6+tLQkJCsdpSFM899xxPPvlkiV9XFI8EMyGcoTPwKfAT0BoYhwpqq+w4toIOhoRAp0ZQvTtcrQEDQqBbd/jiS7cPaMV1yy2wdq1amzsoCJ54QgW0Vfa8dkLkITk92aH7lSVSDKUUMJnUuPHcJCWpxwtJ0zTSr6Zz/vJ50q+mk9vMlnHjxqHT6XjllVestm/ZsgVdCc6F3rt3L3q9noEDB5bYNY1GI8nJybRp06bI53j55ZcZPHgwAQEBAMTExKDT6bhw4YJjGkneAXLKlCmsXLmSU6dOOexawvkkmAnhTJ2ALcAvQDvgSzuOyS6/31kHWZ7w6TbVY6bXw8C7oeMQCD0FD2pQhqshtmoFH38MR4+q3rQHH5T100TR+Xv5O3S/siLqWBQBkQH0WdmHUVGj6LOyDwGRAUQdi3J100Q2kwlCQtQyK4mJ1o8lJqrtISGFCmepV1I5lHKIuPNxxF+IJ+58HIdSDpF6JdVm38qVK/Pqq6+Smmr7WElZunQpTz75JLt27eLcuXMlck29Xk+9evWoUKFCkY6/fPkyS5cuZfz48Q5umX3q1KlD//79Wbx4sUuuL4pGgpkQJaEDEIWac1aQ7N/KysAV4IgO+t8FG7+Dp4/AsSWwOQA+/hve3lvme9BatFDFQLKywCwf5IsiCmoYhMHbYCn0cTMdOozeRoIaBpVwy1wnuxjKzUM8z6adJWxDmIQzd5GeDikpcOqUWl4lO5wlJqr7p06px+1cWDL1SionU0+SabaexJtpzuRk6kmbcNavXz/q1avH/Pnz8z3vpk2baN26NZUqVSIgIIAFCxZYPR4QEMC8efN46KGH8PLyomHDhnzwwQcFtvfixYusX7+eCRMmMHDgQFasWGGzzyuvvIKfnx9eXl6MHz+ejIwMq8fHjRvHkCFDmDdvHn5+ftSoUYM5c+Zw/fp1pk6dSq1atTAYDCxfvtxyzM09UampqYwePZq6detSpUoVmjVrZrX/zb744gsqVapEt27dLOfr06cPADVr1kSn0zFu3DgAsrKymD9/Po0bN6ZKlSq0b9+ejRs3Ws6V37UbN24MQMeOHdHpdAQHB1uOGzRoEOvWrSvwNRbuQ4KZECXJng/esnvMuv/7NRVYD9ylg4W3QIM68MRxuPV+eKEHdOmiyu5nB7SyndOEKBK9h57IkEgAm3CWfX9hyEL0HvaUUi39pBhKKWIwQEwMBAbeCGd79twIZYGB6nGDocBTaZqaS5mfxLREq2GNer2eefPm8dZbb5GUx3DKn376ieHDh3Pfffdx6NAhIiIimDFjhk2IWrBgAV26dOGXX37h8ccfZ8KECcTFxeXbng0bNtCyZUtatGjB/fffz7Jly6zat2HDBiIiIpg3bx779+/H39+fd9991+Y83377LefOnWPXrl288cYbzJo1i3vuuYeaNWuyb98+HnvsMR599NE8n+OMGTM4evQoX375JceOHWPx4sXUqVMnz3bHxsbSuXNny32j0cimTZsAiIuLIzk5mchI9Tdp/vz5rFq1ivfee48jR47w9NNPc//997Nz584Cr/3DDz8A8M0335CcnExU1I0PVG677TaSkpJcMsdNFI0Es0IyZZjynECelJaEKaPw47yFsJL9/00WUAl4DFXl8R9gKvCrDt5qAd9Fw7ffQrXqMHgwdO4MW7aoE1wBkil40WshypHQVqFsHL6RBt4NrLYbvA3lrlS+FEMpZYxG63DWs6d1KDMa7TrNxcyLNj1lN8s0Z3Ix03rc+NChQ+nQoQOzZs3K9Zg33niDvn37MmPGDJo3b864ceN44okneP311632u/vuu3n88cdp2rQpzz77LHXq1GHHjh35tmfp0qXcf//9AISEhGAymSyBBWDhwoWMHz+e8ePH06JFC1566SVuyWVRzVq1arFo0SJatGjBQw89RIsWLbh8+TLPP/88zZo1Y/r06Xh6evLdd9/l2o4zZ87QsWNHunTpQkBAAP369WPQoEF5tvv06dPUr1/fcl+v11OrVi0AfH19qVevHj4+Ply9epV58+axbNky+vfvT2BgIOPGjeP+++/n/fffL/DadevWtTy/ajWroVXWLHMGs69/+vTpfF9j4T4kmBWCKcNEyMch9F7Rm0ST9SdOiaZEeq/oTcjHIRLORPFcBj5DrYt2FTWP7DFgK/Aqal2z66gqjn36wK6dsGOHKm049EloOB+6pcDtGjwJ/Omi5yGEGwptFUpCeAI7xu5gTegadozdQXx4fLkKZSDFUEoloxFW3zQefvVqu0MZUGAoy2+/V199lZUrV3Ls2DGbx44dO0bPnj2ttvXs2ZPjx49jzjEGvV27dpZ/63Q66tWrR0pKSp7tiIuL44cffmDkyJEAVKhQgREjRrB06VKra3ft2tXquO7du3Oz1q1b4+Fx422vn58fbdu2tdzX6/XUrl07z/ZMmDCBdevW0aFDB6ZNm8aePXvybDfAlStX7Fqz7sSJE1y+fJk777yT6tWrW26rVq3i5MmTdl/7+D/HbeYMZqCGdF6+fLnAdgj3ULQZjeVUemY6KZdSOJV6iuCVwcSMjcHoYyTRlEjwymBOpZ6y7OdT2celbRWlVCzwMvAVEAjogDuAt27aL/s3NwsVvNKCwRAMlc2QpIOkDKh6AN7rAN00eMBD9cSVXBEtIdyW3kNPcECwq5vhUlIMpRRKTIQxY6y3jRlTqB4zT71nkfe7/fbb6d+/P9OnT7fMjSqsihUrWt3X6XRkZWXlsbfqLbt+/bpVz5OmaVSqVIm3334bHx/732vldu3CtGfAgAGcPn2aL774gq+//pq+ffsyceJE/vvf/+a6f506dewqmHLx36pW27Zto0ED6978SpUqFXjt7M6Aa+ZrVsdmmjP5Jf4X4EavmnB/0mNWCAZvAzFjYwisGWgJZ3sS91hCWWDNQGLGxmDwLnictxBWfkL1bvUGvgVGAJuA5sBJ4I88jjuDWjttyL/HjdfDZx7w2UFo856ad/bUl7BxI2h5/+cnhChfpBhKKZOz0EdgIOzebT3n7OZqjXmo7lm9wHDmqfekumf1XB975ZVX+Pzzz9m7d6/V9latWrF7926rbbt376Z58+bo9UWbt3n9+nVWrVrFggULOHDggOV28OBB6tevz9q1ay3X3rdvn9Wx33//fZGuWZC6desyduxYPvroIxYuXJhv8ZKOHTty9OhRq22enuq1z9mLeMstt1CpUiXOnDlD06ZNrW7GHIE7t2trmsZfV/8CyDVQnvztJBUqVsh1aKdwT9JjVkhGHyMxY2MsYaznMtV1nx3KjD72DykQgiPAZuBtIAUYBEwBst8LZa+HVpnce7wCgKOocvy9cz7QHQZ1h9tS4dfb4N620GY2zJgBYWHgUTo/k/nrLzViUwhRPNnFUMI2hKFDZ1UEpDwWQ3FrSUm2hT6y55xlbw8Ohp07CywAotOpwH0y9WSe+xi9jXmuUda2bVtGjx7NokWLrLY/88wz3HrrrcydO5cRI0awd+9e3n777VyLcNhr69atpKamMn78eJuesWHDhrF06VIee+wxwsPDGTduHF26dKFnz558/PHHHDlyhMDAwCJfOzczZ86kc+fOtG7dmqtXr7J161ZatWqV5/7ZvYupqanUrFkTgEaNGqHT6di6dSt33303VapUwcvLiylTpvD000+TlZVFr169MJlM7N69G29vb8aOHZvntS9mXqR6zepUqlyJvTv24uvvS6VKlajurYL1gR8O0OG2Dpj1MuG8tCid785czOhjZPVQ63Heq4eullAmCi8amAnUA95DhbCcH1BXBy6hAlwu/0+aLplIIulGKMu68TUpLYnLT1aCzLoQuR3q14cRI6BtW1i3rlTVnu/QQQWytm0hPBxKaBkbIco0KYbiPvJd7NnLC3x9bQt95CwI4uur9rNDzSo1aVKziU3PmafekyY1m1CzSs18j58zZ45N70ynTp3YsGED69ato02bNsycOZM5c+YUecgjqGGM/fr1y3W44rBhw9i/fz+//vorI0aMYMaMGUybNo3OnTtz+vRpJkyYUOTr5sXT05Pp06fTrl07br/9dvR6fb6l6Nu2bWt5XbI1aNCA2bNn89xzz+Hn58cTTzwBwNy5c5kxYwbz58+nVatWhISEsG3bNksp/LyunWnOpEKFCkyZO4Woj6K4u9PdPPPQM5brffXpVwwdPdTuuYXC9XRabku9l3NpaWn4+PhgMpnw9va2efzmOWUgPWaiGJKAmkC1f+9noXrH9MAy4P+AbcAA68Oyi9GkXEqx+dlLNCXSZ3kfmmvN2TZ7G7oHdLAI+P57mD0boqPVCs6T5kLbIdBcD7Wd/USL58IFWLQI3nwTrlyBhx+G556Dm4bkCyEKyZxlJvZMLMnpyfh7+RPUMEh6yhwsIyOD+Ph4GjdubFMQIvVKKolpiVZvnj31nhi9jTdCksmk1inLrUcsKUmFskIOJ9A0zVKlMXv4Yl49ZaJotm3bxtSpUzl8+LBV4RFHSb+aTtz53Jcb2P3tbiLnRLLmmzW09muNVyX7gnt5lt/vaUHZwFGkx6yQcoaywJqB7H5ot9Wcs5urNQpRIANQNcd9D1QoA8j+fzaXUSc3F6PJ/tnL/hk9aTpJnD6OywMuw1rUPLVu3eDLL1VAa9gMHt0NvdKhwwWYmAWnbK/jLmrUgJkzISEBXnwRPv5YfVA8caLd0yuEELnILoYysu1IggOCJZSVILsXe/bxyXuYosFQpDHeOp0Or0pe1K5aG69KXhLKnGDgwIE88sgjnD171innz2/OYMblDGa+MZOqlarmOWdQuB8JZoWQlJZkU+ijh7GHTUGQ/NaGESJXef1/2Orfx878ez9H/7a9xWiqraim5q2l5zhv164Q/Sl89gAEbIekaPggBZqbYXIWnHf8U3QUHx8VzBISVFBbtw6aNoXHH5eAJoQoPYqy2LMofSZNmmRVxMORsucM5qbvPX1p06lNvnMGhfuRYFYIXp5e+FbztRm2mF0QJLBmIL7VfPHylO5i4SAegBewM/eHc/7sZRejyRnKjF5GtUj1s0CzXE4wqAOcHAYxzeHWt8H8ISzMgFFHIfO6s56VQ3h7wwsvqIAWEQEbNkCTJjBhApw5U9DRQgjhWkVd7FmInIo7Z1C4F5ljlov8xpGaMkykZ6bnWhI/KS0JL08vWcNMONY54BvgP0CN3HfZk7jHUiEUYPdDu+lh7KHu5Ld+2c2P7ToA9/8DicHg/zDMC4L774cK7l/ANT0d3n0X/vtfNR3jwQfh+eehUSNXt0wIUd7lNnfl/OXzxF+IL/DYxjUaU7uqm08CFi4ncwaLr9zPMdu1axeDBg2ifv366HQ6tmzZYvX4uHHj0Ol0VreQkJACz/vOO+8QEBBA5cqV6dq1Kz/88IPD2uxT2SfPdcoM3gYJZcLx6gMPkGcoSzQlMmaz9aKjYzaPuTHfMb+/y5eAnMUZb+8A794BOh1UG6TSTYsWsHw5XLuWx0ncg5cXPPssxMfDSy/B5s1qiOMjj6heNSGEcLWcn4UXZ7FnIW4mcwaLzx36qlwazC5dukT79u1555138twnJCSE5ORkyy17QcG8rF+/nsmTJzNr1ix+/vln2rdvT//+/UlJSXF084VwuWIVozkPLABmA/uB7JGLXwLoYOoQOHAA2neEhx5SAW3pUrcPaNWrw7RpKqDNnw+ffgrNmsG8ea5umRCivMpeZDkz88bQxeIu9iyEcKzLly8DULFiRZe1wW2GMup0OjZv3syQIUMs28aNG8eFCxdsetLy07VrV2699VbefvttQK2EbjQaefLJJ3nuuefsOkdJdVcKURxJaUn0XtHbek6Zj9EmrO0ctzP3Xt40YCxq7bSmQAMgA9gHBAK7UL11AL/+CnPnwsaNEBCgxgiOHQue7v9J7uXLqqk//ig9Z0II19A0jTNnznDt2jXq169vKZ1uyjDlWwDE6G2UkThCOJmmaVy+fJmUlBRq1KiBv7+/zT4llQ3cfuJITEwMvr6+1KxZkzvuuIOXXnqJ2rVzH2udmZnJTz/9xPTp0y3bPDw86NevH3v37s3zGlevXuXq1auW+2lpaY57AkI4SXYxGiDXYjTBK4PzL0bjDWwGYoFnUEHsDmAyMIYboQygXTv45BM4fFgFtEcfhZdfVgFt3Di3DmhVq0LLliqYCSGEK+h0Ovz9/YmPj+f06dPWj13T8c+VfzBn3RhXrvfQU6tKLf659A//8E9JN1eIcqlGjRrUq1fPpW1w62AWEhJCaGgojRs35uTJkzz//PMMGDCAvXv3WoYF5PT3339jNpvx8/Oz2u7n58dvv/2W53Xmz5/P7NmzHd5+IZzJp7IP0aOjcy1GY/QxsnPcTksxGlOGifSr6Rh8DGpOmR711QOS2ifhs9gHr//zgnHA6Hwu2qYNrF+v6tTPnQuPPaYC2vTpaj5apUpOe77OIAvrCiFKiqenJ82aNbMazpjNnGXmp+SfSLmUgm81Xzr7d5a/RUKUoIoVK+aaLUqaWwez++67z/Lvtm3b0q5dO5o0aUJMTAx9+/Z12HWmT5/O5MmTLffT0tKctuaEEI7kU9knz2Eu2WHNlGEi5OMQmvzShPkvz7f0rOGh1sjJ7lnb5b+LinMqwgCgVgEXbt1aLSA2c6aqtPH442oS13PPwfjxpSKgRR2LIjw63GrdQYO3gciQSEJbhbqwZUKIssrDw8Om2lu225vcXsKtEUK4m1K1jllgYCB16tThxIkTuT5ep04d9Ho9f/75p9X2P//8M9+uyUqVKuHt7W11E6KsSM9Mh3Mw7ZNp/HDXD5w7eg5QoazP8j6cSj3FpfOXyKyZCX8ChVky55ZbYM0aOHoUgoLgySfVYmJvvw0ZGU55Po4QdSyKsA1hNovBn007S9iGMKKORbmoZUIIIYQor0pVMEtKSuL8+fO5TsoDNUygc+fObN++3bItKyuL7du3071795JqphBuxeBt4JMHPuG79t9xx693cHTEUX774DeGvjOUk6aTBNYMZHuT7VTbUw1acKM6Y2G0bAkff6wCWp8+EB6uAtpbb7ldQDNnmQmPDkfDtu5R9rZJ0ZOs5nsIIYQQQjibS4PZxYsXOXDgAAcOHAAgPj6eAwcOcObMGS5evMjUqVP5/vvvSUhIYPv27QwePJimTZvSv39/yzn69u1rqcAIMHnyZD788ENWrlzJsWPHmDBhApcuXeLBBx8s6acnhNswNDIwaPUg3uv/Hh1PdsT/KX9mrZzFyu0rOXDoAHVH14U/gGGoioxF1aIFrF4Nx45Bv34waRIEBkJkJFy54pgnU0yxZ2Jtespy0tBITEsk9kxsCbZKCCGEEOWdS4PZ/v376dixIx07dgRUqOrYsSMzZ85Er9fz66+/8p///IfmzZszfvx4OnfuTGxsLJVyzF85efIkf//9t+X+iBEj+O9//8vMmTPp0KEDBw4cIDo62qYgiBDljdHPSO+3etM4vDHvdXmPVn+1YtTBUXh95KUqML4JPPbvzrktovE88Bzwlx0Xa94cVq6E336Du+6CZ55RAe3NN1X9+hKm08E//8C338K5tGS7jklOt28/IYQQLmA2Q0wMrF2rvppllIMo/dxmHTN3IuuYibIo5/pmAJWvVaZ/Rn8Wj1qMv68/5LLUmZU5wOuo0PY4MAXwtfPiJ06o6o2rV0OdOmoF6MceU7XsS8CJEzBiBPz8M7TtcoFDrcIgcDvo8j5mx9gdBAcEl0j7hBBCFEJUlBoyn5Rj9IPBoEZnhErxJuF4JZUNStUcMyFE0dy86PTuh3ZT37c+n3p9Sq/vepHolfcCpxYzgQRgEvAe0BiYiioYUpCmTWH5coiLg4ED4dlnoXFj+O9/4dKloj4tuzVtCvv3w+efQyV8YPU3sOw7ONnPpndQhw6jt5GghkFOb5cQQohCioqCsDDrUAZw9qzaHiXFm0TpJcFMiDIuKS3JKpTFjI2hh7EHMWNjCKwZyKnUUwSvDM533pVFbeAlVECbDHyACmjPoOaoFaRJE1i6FH7/Hf7zH7X+WePG8NprcLEw5SALT6eDe+6BH37Q8fzi3ZBVAVZ/DUt3w4m7QFOhDGBhyEJZQ0gIIdyN2ax6ynIb7JW9bdIkGdYoSi0JZkKUcV6eXvhW87WEsux1zIw+Rks4863mi5enl/0nrQXMRQW0qcASVNGQpwF7pmY1bgwffgjHj8PQofDii2rbq6+WSEB7+bGebPzqLHUeHgPo4KP/wZK91D47mk/u3SjrmAkhhDuKjbXtKctJ0yAxUe3n5sxZZmISYlh7aC0xCTFSCVgAMscsVzLHTJQ1pgwT6ZnplkWnc0pKS8LL0yvPhartcgFY+O/tKvAo8CyQ+8oWts6cgfnzVW+at7cqFvLEE+BViLBYBOYsM7tOx/LVVxqff9CJIz/7cNttMGsWDBigQpwQQgg3sXYtjBpV8H5r1sDIkc5vTxFFHYsiPDrcaqSKwdtAZEikfDDopmSOmRDCYXwq++QaykD9Z1CsUAZQA4hA9aBNB1aihjg+BZy14/iGDWHxYjh5UlXpiIiAgACYNw/S0orXtnzoPfT0aRzM/Ef7cGi/D199BRUrqmlwXbvCtm25j5gRQgjhAnmsY1vk/Vwg6lgUYRvCbKYPnE07S9iGMKKOyRy58kyCmRDCcWpwo0jIi8BHQBPgSewLaEYjvPOOCmgjR8Ls2SqgvfSSUwMaqN6xO+9UI2C++QYqVVJz0m67TRUNkYAmhBAuFhSkqi/mNZxBp1P/jwS5Z/Emc5aZ8OhwtFzWpMneNil6kgxrLMckmAkhHM8HFcwSgBnAGqAZcMbO4w0GePttOHUK7r9fBbP27eHaNee0NwedDvr2hV27YPt2VdH/P/+BF15w+qWFEELkR69XJfHBNpxl31+4UO3nhmLPxOZbaEtDIzEtkdgz7j9HTjiHBDMhHMSUYcrzD25SWhKmDFMJt8gNeAMvADuBK6igVhgNGsCiRWruWUJCiS5OrdPBHXfAzp1qjewjR0rs0kIIYUsWVFZCQ2HjRvX/Q04Gg9ruxuuYJafbUx3L/v1E2VPB1Q0QoiwwZZgI+TiElEspVpUP4cYaYr7VfIkeHV38+VylUaXiHl/cExSPp6dLLy+EKO9kQWVroaEweLAae56crOaUBQW5bU9ZNn8v++a+2bufKHukx0wIB0jPTCflUoplTbBEk1qwOefCzimXUkjPTHdpO4UQQpQysqBy7vR6CA5W85GDg90+lAEENQzC4G2wrJl5Mx06jN5Gghq65xw54XwSzIRwAIO3wWbB5j2Je2wWds6rMqIQQghhQxZULlP0HnoiQ9QcuZvDWfb9hSEL0Xu4f8gUziHBTAgHyblg86nUU/Rc1tMqlOUc3iiEEEIUqAwtqCyU0FahbBy+kQbe1nPkDN4GNg7fKOuYlXMyx0zkzmSC9HQ1hv1mSUlq4V+fcjhXqgBGHyOrh66m57Kelm2rh66WUCaEEKLwku0sAmHvfsIthLYKZXCLwcSeiSU5PRl/L3+CGgZJT5mQYCZyYTJBSAikpKjKT8YcoSIxUY3l9vWF6GgJZzdJNCUyZvMYq21jNo+RHjMhhBCFVwYWVBa503voCQ4IdnUzhJuRoYzCVnq6CmWnTqkQlqgKWVhC2alT6vF0KWSRU85CH4E1A9n90G6rOWfZBUHKpWqADpgF7C7C8V5e6uvjj0NcnOPaJYQQ7qyUL6gshCgcCWbClsGgesoCA2+Esz17boSywED1eG7DHMuppLQkm0IfPYw9bAqC5LewZJlWH4gC/gZ6AXcC3xXi+DvvVOuZxcTALbeoRad/+80JDRVCCDdSyhdUFkIUjgQzkTuj0Tqc9expHcqMMiwvJy9PL3yr+doU+shZEMS3mi9enl4ubqkLDQEOAhuBP4EgoC+wy45jPTzgySfh5EnrgDZqFBw75rQmCyGEy5XiBZWFEIWj07TcarCWb2lpafj4+GAymfD29nZ1c1xrzx4VyrLt3g09eriuPW7MlGEiPTM915L4SWlJeHl6lYnFpR3yPLOALcAcVFgLRg1zDLazEVevwrJlMH++KkYzfDjMnKnCmhMMGqSy4aefOuX0QghRMLO51C2oLERZUVLZQHrMRN4SE2GMdSELxoy5MedMWPGp7JPnOmUGb0OZCWUhH4fQe0VvmzlziaZEeq/oTcjHIZgyTPmfyAMIBX4GNgMmoA8qmO0ACvq4qFIlmDABjh+HxYth715o0wZGjIDDh4v03IQQwq2VwgWVhRCFI8FM5C5noY/AQNVTlnPOmYSzcik9M52USyk2BU1yFj5JuZRCeqadhWE8UEMcfwI+BdKBO4DewLfYF9AefVQFtPffh337oG1b1YN26FARnqEQQgghhGtIMBO2kpJsC3306GFbECS/RS9FmWTwNtgUNNmTuMem8ElePYd50gH/AfYDnwOXUfPPbge+oeCA5ukJDz8Mv/8OH34IP/4I7dpBWBj8+mshn6UQQgghRMmTYCZseXmpdcpuLvSRsyCIr++NEuaiXMlZ0ORU6il6LutpFcqKtV6bDrgH+BHYClxFVXDsBXyNfQHt//5PBbSlS+Hnn6F9ezU5/uDBordLCCGEEMLJJJg5g8mUd29SUpJ63J35+KjFo3futK2+aDSq7bK4dLlm9DGyeuhqq22rh6523CLaOmAgsA/4ArgO3AX0BP5HwQGtYkV46CG15tmyZarXrEMHGDoUfvnFMW0UQgghhHAgCWaOZjJBSAj07m07DysxUW0PCSkd4SyvdcoMBgll5VyiKZExm60Lw4zZPMbxi2jrgAHA98CXqEAWAnTPcT8/FSvCgw+qNc9WrFCFQTp1gsGD4aefHNtWIYQQQohikGDmaOnpkJJiWyQjZzGNlBS1nxClUM5CH4E1A9n90G6rOWcOD2egAloIsAfVY6YH7ga6AtsoOKBVqABjx6o1z1atUl+7dFF18Pfvd3x7hRBCCCEKSYKZoxkMtkUy9uyxLaaRV2+UEG4sKS3JptBHD2MPm4IgSWlOKgyjQw1p/A4158wTNSftNlTREHsC2pgxcPQorF6t5qLdeisMHAg//OCcNgshhBBC2EGCmTPkLJJx6pRaoDlnKLt53pYoE0wZpjwDSVJaUsFre5UCXp5e+FbztSn0kbMgiG81X7w8nVwYRgf0A2JRVRuroKo6dgE+w76Adv/9KqB9/LH6/ezaFe6+W5XcdyJzlpmYhBjWHlpLTEIM5iyzU68nhBBCiNJBp2laQW9hyh2Hre69Z48KZdl271Zl50WZk73wcsqlFJvKhNlD/3yr+RI9OrrULzRtyjCRnpmea0n8pLQkvDy9Sv45akAMMBvYCXQEZgKDUSGuIGYzfPIJzJmjhjn27w+zZkH37oAa8ejhAZ9+WrxmRh2LIjw63CrAG7wNRIZEEtoqtHgnF0IIIYRTOCwbFEB6zJwlMVENmcppzBhZmLmMcvjCy27Mp7JPnuuUGbwNrgmeOqAPKpztAHyAoaiAthnIKuB4vR7uu08tSr1unaqe2qOHCmh79jikiVHHogjbEGbTq3o27SxhG8KIOhblkOsIIYQQonSSYOYMOQt9BAaqnrKcc84knJU5Tlt4WRReMCqc7QRqA6GogLYJ+wLaiBGqvP6GDXDunOr1/n4v/HO+yE0yZ5kJjw5Hy2WMZfa2SdGTZFijEEIIUY5JMHO0pCTbQh89etgWBMlrnTNRajl14WVReLcD21Hz0HyBMKA98AkFBzQPD7j3XrUo9caNcDUTvvsO+vaFXbsK3ZTYM7H5FkTR0EhMSyT2TGyhzy2EEEKIskGCmaN5eYGvr22hj5wFQXx91X6izHH6wsui8HqhKjjuBuoDw4F2wAbsC2jDhsHtt8Ott8H582otwjvuUAut2yk5Pdmh+wkhhHBf9hR5kkJQIjcSzBzNxweio9WbtpurLxqNant0tCzQXEaV2MLLovB6oNZA2wMYgBFAW2AdUND/hzod+PvDzz/D5s2Qmqp6voODYccOKKCGkr+Xv11NtHc/IYQQ7inqWBQBkQH0WdmHUVGj6LOyDwGRAVbziO3ZR5RPEsycwccn73XKDAYJZWWUSxZeFoXXHYgG9gKNgJFAG2ANBQc0Dw8YMkQFtE8/VQvF33GH6kX79ts8A1pQwyAM3gZ0eZSI1KHD6G0kqGFQEZ+UEEIIV7OnyJMUghL5kWAmhAO4fOFlUXjdgC+AfUATYDTQGvgY+3rQ/vMf2L8fPv8cLl9W889uvx2++cYmoOk99ESGRKpDbwpn2fcXhixE76Ev/vMSQghR4uwp8hT+ZTjhX0ohKJE3CWZCOIDbLLwsCu82YCvwA9AMuB+4BVgNXC/gWJ0O7rkHfvwRtm6Fq1fhzjuhVy/46iurgBbaKpSNwzfSwLuB1SkM3gY2Dt8o65gJIUQpZk+Rp6T0JJLSpRCUyFsFVzdAiLLAp7IP0aOjc1142ehjZOe4na5ZeFnkKtdFsm8FPoc/d/5Jrf/WouIDFWEO8CLk8uGmNZ0OBg6Eu+9Wc0gjItQaaN26qYWq+/cHnY7QVqEMbjGY2DOxJKcn4+/lT1DDIOkpE2WGOcssP9+iXHJk8SYpBFV+ubTHbNeuXQwaNIj69euj0+nYsmWL5bFr167x7LPP0rZtW6pVq0b9+vV54IEHOHfuXL7njIiIQKfTWd1atmzp5GcihJsuvCxsmDJMhHwcQu8VvW3m/SWaEulxsAe3D7md9D3pamjjONS6aPYsY6bTwYAB8P338OWXatuAAdC9u7qvaeg99AQHBDOy7UiCA4LlTasoM6SggSjPHFm8SQpBlV8uDWaXLl2iffv2vPPOOzaPXb58mZ9//pkZM2bw888/ExUVRVxcHP/5z38KPG/r1q1JTk623L777jtnNF8IUQqlZ6aTcinFpihLzuItKZdSMLU2wRbgF0AHnCzERXQ6CAmBPXvgf/9TRUPuvhu6doVt2wqs4ihEaSMFDUR5Z0+RJ4OXAYOXFIISeXNpMBswYAAvvfQSQ4cOtXnMx8eHr7/+muHDh9OiRQu6devG22+/zU8//cSZM2fyPW+FChWoV6+e5VanTh1nPQUhRClj8DbYFGXZk7jHpniLpfezA1CtiBfT6eCuu2D3bjXnzNNTzUm77TZVNEQCmigD7Cl6IAUNRFlnT5GnyAGRRA6QQlAib6Wq+IfJZEKn01GjRo189zt+/Dj169cnMDCQ0aNHFxjkrl69SlpamtVNCFF25SzKcir1FD2X9bQKZQ5fEFynU0VBYmNV1cYqVVRVxy5d4LPPJKCJUs2eogdS0ECUB/YUeZJCUCI/pab4R0ZGBs8++ywjR47E29s7z/26du3KihUraNGiBcnJycyePZugoCAOHz6Ml1fuFfHmz5/P7NmzndV0IYQbMvoYWT10NT2X9bRsWz10teNDWTaTSa171revWvssJkYVCRk8GNq0geeeg1GjVIgTohSxt1CBFDQQ5YE9RZ6kEJTIi07T3OOjWp1Ox+bNmxkyZIjNY9euXWPYsGEkJSURExOTbzC72YULF2jUqBFvvPEG48ePz3Wfq1evcvXqVcv9tLQ0jEYjJpOpUNcSQpQeOeeUZcurx2yQn5om9mlR31eaTGrOWUqKCmTGHOffsAHGjoWMDBXQ5sxRYc2jVA1oEOVYTEIMfVb2KXC/HWN3EBwQ7PwGCSGEg6WlpeHj4+P0bOD2//Nfu3aN4cOHc/r0ab7++utCvxg1atSgefPmnDhxIs99KlWqhLe3t9VNCFF25QxlgTUD2f3Qbqs5ZzdXayy29HQVyk6dguBgSPz3/ImJMH26CmX+/uDjA6Gh0LEjbNoEWVmObYcQTmBP0QMpaCCEEAVz62CWHcqOHz/ON998Q+3atQt9josXL3Ly5En8/aX0qBACktKSbAp99DD2sCkIkt+cmUIzGFRPWWDgjXC2Z4/6euqU2r5vH3z3HezaBXXrQlgYdOgAGzdKQBNuzZ6iB1LQQAghCubSYHbx4kUOHDjAgQMHAIiPj+fAgQOcOXOGa9euERYWxv79+/n4448xm8388ccf/PHHH2RmZlrO0bdvX95++23L/SlTprBz504SEhLYs2cPQ4cORa/XM3LkyJJ+ekIIN+Tl6YVvNV+bYYs5C4L4VvPFy/OmOalXsG8ts7wYjdbhrGfPG6Es5/DGoCBVIOS776BePbj3XmjfXg15lIAm3JQUNBBCiOJz6RyzmJgY+vSxHZc+duxYIiIiaNy4ca7H7dixg+DgYAACAgIYN24cERERANx3333s2rWL8+fPU7duXXr16sXLL79MkyZN7G5XSY0jFUK4hinDRHpmeq4LgielJeHl6WW1IPigzuBxED6tAjwBPAMUdRWOPXtUKMu2ezf06JH3/nv3wuzZaj20W26BGTNUWNNL74NwP+YssxQ0EEKUOSWVDdym+Ic7kWAmhMhp0CDwuA6ftgeyO+izA1rdQpwoMfHG8MVsN/eY5eX771VhkC+/hFatVEAbPlwCmhBCCOFkUvxDCCHciSfwCpAAPAW8AzQGpgEpdhyfM5QFBqqespxzzhILKDjSrRt88YWai9a4sSqt36YNfPwxmGXhXiGEEKK0k2AmhBCFUQeYhwpok4D3UAFtCvBnHsckJVmHspgYNXzx5oIgSXYUHLntNti2DX74AZo2hfvvV0McV6+G69eL++yEEEII4SISzIQQoihqAy+hAtpk4ENUQHsG+OOmfb28wNfXdthizoIgvr5qP3vdeit8/jns3w8tWsADD6iAtnKlBDQhhBCiFJJgJoQQxVELmIsKaFOBJaiA9jSQvSC1jw9ER8POnbZzyYxGtT06Wu1XWJ07w2efwU8/qWA2bhy0bAkrVkhAE0IIIUoRCWZCCOEINYHZqID2LLAcCATCgXOo0GWwrQIJqO1FCWU5deoEW7bAL79Au3bw4IOqJ23ZMrh2rXjnFkIIIYTTSTATQghHqglEoALadGAVKqA9CZwtget36ABRUXDggPr3+PEqoC1ZIgFNCCGEcGMSzIQQwhlqADNRAe0F4GNUQHsCsKPGR7G1bw+bNsHBg6o37eGHoVkz+PBDyMwsgQYIIYQQojAkmIliMWWYSErL/V1mUloSpgxTCbdICDfjA8xABbSZwFqgCfA4UECFfIdo1w42boRff1UVHR99VAW099+XgCaEEEK4EQlmoshMGSZCPg6h94reJJqs32EmmhLpvaI3IR+HSDgTAsAb1XOWgBrquAEV0CYAZ0rg+m3bwoYNcOgQdO8OEyaocvuLF8PVqyXQACGEEELkR4KZKLL0zHRSLqVwKvUUwSuDLeEs0ZRI8MpgTqWeIuVSCumZ6S5tpxBuxQs19yweVc1xI9AUeBQ4XQLXb90a1q2Dw4ehVy+YOFEFtHfflYAmhBBCuJAEM1FkBm8DMWNjCKwZaAlnexL3WEJZYM1AYsbGYPDOoxKdEOWZF6p6YzzwMrAZFdAeQfWqOdstt8CaNXD0KPTuDU8+CU2awNtvQ0ZGCTRACCGEEDlJMBPFYvQxWoWznst6WoUyo4+x4JMIUZ5VR61/Fg/MBz4FmgH/B5wqgeu3bAkffaQC2h13QHi4CmhvvSUBTQghhChBEsxEsRl9jKweutpq2+qhqyWUCVEY1YApqID2KrAVaA6Mp2QCWosWsGoVHDsG/frBpEkQGAiRkXDlCphMkJRHOcmkJPW4EKWd2QwxMbB2rfpqNru6RUKIckSCmSi2RFMiYzaPsdo2ZvMYm4IgQgg7VAUmo8LY68AXqID2IHCiBK7fvDmsXAlxcdC/PzzzDDRurMrvBwVB4k2/14mJaihkSIiEM1G6RUVBQAD06QOjRqmvAQFquxBClAAJZqJYchb6CKwZyO6HdlvNOZNwJkQRVQWeRgW0BcD/gJbAWOB4CVy/aVNYvlwFtOBgOH0aEhLUotVxcWqfxET12KlTkJIC6VLoR5RSUVEQFmbbK3z2rNou4UwIUQIkmIkiS0pLsin00cPYw6YgSF7rnAkh7FAFCAdOAm8C36AC2hggrgSu36SJquIYGwteXvDPP6qy48SJcPvtKpQFBqphXwYp9CNKIbNZza3UNNvHsrdNmiTDGoUQTifBTBSZl6cXvtV8bQp95CwI4lvNFy9PLxe3VIgyoArwJCqgRQI7gFuA0cBvJXD9Xr3gyBEwGtUb1HffVT1otWrBtm1quxClUWxs3vMnQYWzxES1nxBCOFEFVzdAlF4+lX2IHh1Nema6TUl8o4+RneN24uXphU9lHxe1UIgyqDLwBKpq4zJUJcdbgBHAjH//7SxGo+o969nzxra0NBXapkxRvWhe8kGMKGWSkwu9nznLTOyZWJLTk/H38ieoYRB6D72TGiiE42Rez+Td/e9y8p+TNKnVhMe7PI5nBU9XN0v8S4KZKBafyj55Bi9Zv0wIJ6oMPI6q2rgcmAe0AYajAlprJ1wzMRHGWBf6wd9fFf+YORP++1+YPBmeeAK8vZ3QACGcwN+/UPtFHYsiPDrcapi+wdtAZEgkoa1CndFCIRxi2tfTeGPvG5i1G8Nyp3w1hcndJ/Pana+5sGUimwxlFEKI0qwS8BiqIMhiYC/QFhXQDjvwOjkLfQQGwu7d6mtiIuzZo4Z5jRgBs2erKo4vv6x604Rwd0FBan6kTpf74zqd6i0OCiLqWBRhG8Js5k6fTTtL2IYwoo5JkRDhnqZ9PY3X97xuFcoAzJqZ1/e8zrSvp7moZSInCWZCCFEWVAIeRQW094EfUAHtXuBQMc+dlGQdymJioEcP9TUwUG0fNQqmT4eTJ2HkSJgzR5UanztXyugL96bXq/X6wDacZd9fuBCzDsKjw9GwLRKSvW1S9CTMWVIkRLiXzOuZvLH3jXz3eWPvG2RezyyhFom8FCqYHTx4kJdeeol3332Xv//+2+qxtLQ0HnroIYc2TgghRCF5Ag8DvwMfAvuBrsDf+R1UAC8v8PW9EcqyC30YjTfCma+v2s9ggLffVgFt9GjVcxYQoILahQvFaIQQThQaChs3QoMG1tsNBrU9NJTYM7H5VhnW0EhMSyT2jBQJEe7l3f3v2vSU3cysmXl3/7sl1CKRF7uD2VdffcVtt93GunXrePXVV2nZsiU7duywPH7lyhVWrlzplEYKIUqGKcOU5xuPpLQkTBnS81FqeHKjQMgV4EIxzuXjA9HRsHOnbfVFo1Ftj45W+2UzGOCtt1Rv2gMPwPz5KqBFREhAE+4pNFRVGt2xA9asUV/j49V2IDndviIh9u4nREk5+c9Jh+4nnMfuYBYREcGUKVM4fPgwCQkJTJs2jf/85z9ER0c7s31CiBJiyjAR8nEIvVf0tlkYPNGUSO8VvQn5OETCWWmTx7SZQvPxyXudMoPBOpTlVL++GiZ26hQ8+CC8+qoKaLNmQWqqgxonhIPo9WrY7siR6qv+RqVFfy/7ioTYu58QJaVJrSYO3U84j93B7MiRI5ahijqdjmnTpvH+++8TFhbG1q1bndZAIUTJSM9MJ+VSimVh8OxwlmhKtCwknnIphfTMdJe2U5RS/v7w5puqB2L8eHj9dRXQZsxQi1YL4eaCGgZh8Dagy+PTDh06jN5GghoGlXDLhMjf410eR6/LfzkHvU7P410eL6EWibzYHcwqVarEhZuGn4waNYolS5YwYsQINm/e7Oi2CSFKkMHbYFkYPDuc7UncYwll2QuJyzIIoljq1YMFC1RAe+QReOMNFdBeeAHOn3d164TIk95DT2SIKhJyczjLvr8wZKGsZybcjmcFTyZ3n5zvPpO7T5b1zNyA3cGsQ4cOVnPKst13330sWbKEp556yqENE0KUPKOP0Sqc9VzW0yqUGX2MBZ9ECHv4+ales/h4mDABFi5UAe355+Hv4lQqEcJ5QluFsnH4Rhp4WxcJMXgb2Dh8o6xjJtzWa3e+xtQeU216zvQ6PVN7TJV1zNyETtM027qvudi8eTO7du3izTffzPXxNWvW8OGHH+Ya3kqbtLQ0fHx8MJlMeMsiqaIc2pO4h57Lelru735oNz2MPVzYItcaNAg8PODTT13dkiKIAfqgyug3dW1T8vXXX6on7e231f0nnoBnnoG6dV3bLiFyYc4yE3smluT0ZPy9/AlqGCQ9ZaJUyLyeybv73+XkPydpUqsJj3d5XHrK7FBS2cDuYFaeSDAT5VnOOWXZynuPmQSzEvT33zcCmqbBxIkwZYoENCGEEC5TUtlAFpgWQljkDGWBNQPZ/dBuqzlnN1drFKWAH6oyYxgQBWS5tjkFqlNHldZPSIDwcHj3XTXEcepUSElxdeuEEEIIp5FgJoQA1DplNxf66GHsYVMQJL8FVoUbagXsBOoAw4COwEbcP6DVrq0Wpz59GiZPhvffVwHtmWfgjz9c3TohhBDC4SSY2UEW1hWlnT0LR3t5euFbzddm2GLOgiC+1XzJ0rJK/yLUJhMk5REwk5LU42VJEPANEAv4AvcC7YENuH9Aq1UL5s5VPWhTpsCSJdC4MTz9NCTLQr7CNcxZZmISYlh7aC0xCTGYs8yublKpIK+bEPmTOWa5yDmO1KSZCF4ZjG81X6JHR+NTOY9FVIVwU9kLR6dcSrGZJ5Y9dDH75xvUema5lcRPSksiS8tixMYRdp3LbX9XTCYICVHD4mJiwJhj3lxiolpU1tcXoqMtiyaX6jlmudkDzAa+Am4BZqKGOpaG2gWpqWrB6oUL4epVVXL/2WfVQtZClICoY1GER4dbfUBl8DYQGRIpVRnzIa+bKM3cfo5ZZmYmcXFxXL9+3ZHtcStJpiRZWFeUeoVZONqnsk+e65QZvA146DxK/yLU6ekqlJ06pUJY4r/z5rJD2alT6vF0N34OxdUD+B8qoBmB+4C2wFrA3T/ArlkTIiJUD9r06bBqFQQGwlNPwdmzrm6dKOOijkURtiHMZtTA2bSzhG0II+pYlIta5t7kdRPCPoUOZpcvX2b8+PFUrVqV1q1bc+bMGQCefPJJXnnlFYc30JUGrh0oC+uKUs+RC0eXiUWoDQbVUxYYeCOc7dlzI5QFBqrHDW78HBylOxANfA8EAKOANsAa3D+g1agBM2eqgPbCC/DRR9CkiSqzn9cwVSGKwZxlJjw6HA3bgUbZ2yZFT5LheTeR100I+xU6mE2fPp2DBw8SExND5cqVLdv79evH+vXrHdo4V0tITSj3ZcJF2eDIhaPLxCLURqN1OOvZ0zqUGUvBc3CkrsAXwD6gCTAaaA18BLj7oAgfH5gxQwW0GTNg7VoV0CZOvNEbKoQDxJ6Jzbf4kYZGYloisWdiS7BV7k9eNyHsV+hgtmXLFt5++2169eqFTqezbG/dujUnT550aOPcweqhq0vHG00hCmD0MbJ66GqrbUX9+XbkuVzGaITV1s+B1avLXyjL6TZgK/Aj0BwYg5qDtgr3D2je3qrnLCFBDXVcvx6aNoUJE+DfkR1CFEdyun3FZuzdL6eyXBTDma9baVaWv+ei6AodzP766y98fX1ttl+6dMkqqJUVYzaPkbWbRJmQaEpkzOYxVtuK+vPtyHO5TGIijLF+DowZI70sAF2Az4D9qHL7Y//9uhL3D2heXmruWXw8zJkDGzeqgPbYY6r0vhBF5O/l79D9skUdiyIgMoA+K/swKmoUfVb2ISAyoMzMu3LW61aalfXvuSi6QgezLl26sG3bNsv97DC2ZMkSunfvXqhz7dq1i0GDBlG/fn10Oh1btmyxelzTNGbOnIm/vz9VqlShX79+HD9+vMDzvvPOOwQEBFC5cmW6du3KDz/8UKh2ZQuoGSAL64oywZELR5eJRahzFvoIDITdu63nnEk4UzoDnwI/o+aejQNaAsuBa65rll28vFS1xvh4eOkl2LQJmjVTVRwTElzdOlEKBTUMwuBtQEfuH0Lr0GH0NhLUMMjuc5aHohjOeN1Ks/LwPRdFV+hgNm/ePJ5//nkmTJjA9evXiYyM5K677mL58uW8/PLLhTrXpUuXaN++Pe+8806uj7/22mssWrSI9957j3379lGtWjX69+9PRkZGnudcv349kydPZtasWfz888+0b9+e/v37k5KSUqi2AWwbuU0W1hWlniMXji4Ti1AnJdkW+ujRw7YgiBSQuKEjsBn4BbX+2UOogLYU9w9o1avDtGkqjM2bp9Y8aNYM/u//1PdaCDvpPfREhkQC2ISM7PsLQxai97Bv3YnyUhTD0a9baVZevuei6AodzHr16sWBAwe4fv06bdu25auvvsLX15e9e/fSuXPnQp1rwIABvPTSSwwdOtTmMU3TWLhwIS+++CKDBw+mXbt2rFq1inPnztn0rOX0xhtv8PDDD/Pggw9yyy238N5771G1alWWLVuW5zFXr14lLS3N6gZg8DFYLazr5elVqOcnhDuwd+Foe36+HXkul/HyUuuU3VzoI2dBEF9ftZ+w1gHYBBxEhbX/Q81FWwJkuq5ZdqlWTS1QfeoUvPIKfP45NG8ODz0EZXB+tHCO0FahbBy+kQbeDay2G7wNbBy+sVDrcZWnohiOfN1Ks/L0PRdF4zYLTOt0OjZv3syQIUMAOHXqFE2aNOGXX36hQ4cOlv169+5Nhw4diIyMtDlHZmYmVatWZePGjZbzAIwdO5YLFy7waR6rw0ZERDB79myb7dmLyCWlJeHl6eW+C+aKojOZ1HpVuZVGT0pSb859Sv/33ZRhynfh6ML8fDvyXC5TyO97mVtg2lEOAXOBjUBD4HnUcEdPF7bJXpcvw/vvw2uvwV9/qfmFL7yg5qMJUQBzlpnYM7Ekpyfj7+VPUMOgQvf4rD20llFRowrcb03oGka2HVnUproVR7xupVl5/J6XFW67wLRer891WOD58+fR6x33y/XHH38A4OfnZ7Xdz8/P8tjN/v77b8xmc6GOAbUEgMlkstwSb5pfYvA2uP8bTVF4JhOEhEDv3rZzihIT1faQELVfKVfQwtGF+fl25Llcxscn73XKDIYyEcZLRFtgAyqgdQMeA5oB7wFXXdgue1StCk8/rXrQFiyA//0PWraEsWPBjrnMonzTe+gJDghmZNuRBAcEFylclMeiGI543Uqz8vg9F4VT6GCWVwfb1atX8fQsDR+T2qpUqRLe3t5WN1EOpKdDSoptwYechSFSUtR+Qoi8tQbWAYeBHsDjqID2Lu4f0KpUgfBwNZzxjTfg669VQBszBuLiXN06UYZJUYzyR77noiB2B7NFixaxaNEidDodS5YssdxftGgRb775JhMnTqRly5YOa1i9evUA+PPPP622//nnn5bHblanTh30en2hjhHlmMFgW/Bhzx7bwhB59awIIazdAqwFjgBBwBOoBavfAfKu2eQeqlSBp55Sv/uRkbBjB9xyC4weDb/95urWiTJIimKUP/I9FwWxO5i9+eabvPnmm2iaxnvvvWe5/+abb/Lee+9x+fJl3nvvPYc1rHHjxtSrV4/t27dbtqWlpbFv3748y/J7enrSuXNnq2OysrLYvn17oUv5i3IiZ8GHU6egZ0/rUFaeFxsWoqhaAR8DR4Fg4ClUQHsL9w9olSvDE0/AiROwaBHs3KkC2qhRcOyYq1snyhgpilH+yPdc5KfQxT/69OlDVFQUNWvWLPbFL168yIkTJwDo2LEjb7zxBn369KFWrVo0bNiQV199lVdeeYWVK1fSuHFjZsyYwa+//srRo0epXLkyAH379mXo0KE88cQTgCqXP3bsWN5//31uu+02Fi5cyIYNG/jtt99s5p7lpaQm+JUXpaJYxJ49KpRl271blVAXAin+UWxxwMuosOYHPAs8AlRxZaPsdPUqLFsG8+erwjDDh8OMGdC6tatbVqLKe9EGZ5PXt/yR73npUlLZoFhVGbMPzV5kurBiYmLo06ePzfaxY8eyYsUKNE1j1qxZfPDBB1y4cIFevXrx7rvv0rx5c8u+AQEBjBs3joiICMu2t99+m9dff50//viDDh06sGjRIrp27Wp3uySYOY4pw0TIxyGkXEqxKq8ONxYq9q3mS/ToaNeFs5xzyrJJj5nIQYKZgxxHBbSPgLqogPYopSegrVih1kJLTIR771UBrU0bV7fM6aKORREeHW5V5tvgbSAyJFI+3RdClAtuHcxWrVrF66+/zvF/K1c1b96cqVOnMmbMGIc30BUkmDlOUloSvVf0tlqQ2OhjtISy7O07x+3Ms9KfU+UMZYGBsHq1mvQvwxlFDhLMHOwEKqCtBuoA01AVHau6slF2ysy8EdBOn4awMJg5E9q2dXXLnCLqWBRhG8JsFsTNng8jQ6+EEOWB25bLf+ONN5gwYQJ33303GzZsYMOGDYSEhPDYY4/x5ptvOqONohQzeN9YpPtU6imCVwazJ3GPVSiLGRvjmlCWlGRb6KNHD9uCIEl5LwYphCiCpsBy1BDHgahg1hhYAFxyYbvs4ekJjzwCv/8OH34I+/dDu3YqoP36q6tb51DmLDPh0eE2oQywbJsUPQlzlrmkmyaEEGVSoXvMGjduzOzZs3nggQestq9cuZKIiAji4+Md2kBXkB4zx8vZQ5YtZw+aS2SvY5aSYtszlt2T5usL0dGyrlU5Jz1mThYPzANWADWBqaiS+9Vc2CZ7Xbumetpfegni42HoUNWD1qGDq1tWbDEJMfRZaTvd4GY7xu4gOCDY+Q0SQggXcdses+TkZHrkUhShR48eJCcnO6RRouwx+hhZPXS11bbVQ1e7LpSBClvR0arq2s3DFY1GtV1CmRDO1xj4EDUHbQjw/L/bXgMuuq5ZdqlYER56SK15tmyZ6jXr2FEFtF9+cXXriiU53b7/0+3dTwghRP4KHcyaNm3Khg0bbLavX7+eZs2aOaRRouxJNCUyZrP1HMQxm8eQaEp0UYv+5eOT9zplBoOEMiFKUgDwAWoOWijwIiqgvQK4+zrvFSvCgw+qNc9WrIDDh6FTJxg8GH76ydWtKxJ/L3+H7ieEECJ/hQ5ms2fPZubMmYSEhDB37lzmzp1LSEgIs2fPZs6cOc5ooyjlbi70sfuh3VZzzlwezoQQ7qUR8B4qoN0LzEKFtnlAmuuaZZcKFWDsWLXm2apV6muXLmo87P79rm5doQQ1DMLgbbBZCDebDh1GbyNBDYNKuGVCCFE2FTqYDRs2jH379lGnTh22bNnCli1bqFOnDj/88ANDhw51RhtFKZaUlmRT6KOHsYdNQZCcZZiFEAKAhsC7qIB2HzAb1YP2MqUjoI0Zo4LZRx/B8eNw661wzz3w44+ubp1d9B56IkMiAWzCWfb9hSELZe0lIYRwkGKtY1ZWSfEPxykV65gJUQAp/uEmkoBXUfPRqgJPA08BpeFPh9kM69fD3LlquOOAATBrFhRijU1XyW0dM6O3kYUhC6VUvhCiXHDrdczKOglmjmXKMJGemZ5rSfyktCS8PL0klAm3JsHMzZxFFQZ5H7U49SQgHKjhuibZzWyGTz6BOXNUb1r//iqgde/u6pbly5xlJvZMLMnpyfh7+RPUMEh6yoQQ5YbbBTMPDw90utzHmVtOptNx/fp1hzTMlSSYCSFykmDmppJRPWjvA5W4EdBqurBN9jKbYeNGFdCOHoU771QBrWdPV7dMCCHETdwumH2azzuSvXv3smjRIrKyssjIyHBY41xFgpkQIicJZm4uGXgdVTCkIiqcTQJqubBN9srKgk2bYPZsOHIE+vVTAa1XL1e3TAghxL/cLpjlJi4ujueee47PP/+c0aNHM2fOHBo1auTI9rmEBDMhRE4SzEqJP1ABbTFQATX/7GmgtisbZaesLIiKUj1ohw7BHXeogHb77a5umRBClHtuu8A0wLlz53j44Ydp27Yt169f58CBA6xcubJMhDIhhBClVD1gARAPPAq8iSqz/zzwt+uaZRcPDwgLgwMHVA/a+fPQuzf06QMxMa5unRD5M5vVz+nateqr2ezqFglRKhUqmJlMJp599lmaNm3KkSNH2L59O59//jlt2rRxVvuEEEKIwvFD9ZzFAxOASFSZ/emUjoAWGgo//wybN8OFCyqcBQfDjh0g9bqEu4mKgoAA9XM6apT6GhCgtgshCsXuYPbaa68RGBjI1q1bWbt2LXv27CEoSBaVFEII4aZ8UdUbE4CJwFuoHrRngb9c1ir7eHjAkCEqoG3ZAmlpanhj796wfbsENOEeoqJUT2/STWuRnj2rtks4E6JQClWVsUqVKvTr1w+9Pu8SuVFl4JdQ5pgJIXKSOWZlxN/AG6iAlgU8DkxFBTh3p2mwdasqEvLTT6p6Y0QE9O0LBVRMFsIpzGbVM3ZzKMum04HBAPHxkM/7RiFKg5LKBhXs3fGBBx4osFy+EEII4bbqAPOAZ1Dzzxb9eytO9cZqqPlsj//7b2fR6dQnBPfcA198oQLanXdCjx6qSMidd0pAEyUrNjbvUAbqw4TERLVfcHCJNUuI0szuYLZixQonNkMIIYQoIbWBl4DJwEeAqRjnOoUqLvI6MAUV0KoXt4H50Olg4EC4+26IjlYBrX9/6NZN9aDddVfpCGhms3rDnpwM/v4QFCS9Kg5SYouBJyc7dj8hhP3BTAghhChTaqFK6hdXBDAfeBEV0J5BzWnzcsC586LTwYABEBIC//ufCmghIdC1q+pBCwlx34AWFQXh4da9LQYDREaqwieiyKKORREeHU5S2o3X1uBtIDIkktBWDn5t/f0du58Qomjl8oUQQgjxr0aoxa1PAPcCM1FVIOcD6U6+tk6nQtiePSqg6fWqN61bNzXk0d2KhEixCKeJOhZF2IYwq1AGcDbtLGEbwog65uDXNihIBeq8PgDQ6cBoVPsJIewiwUwIIfKgaaog3i+/gKenq1sj3F5D4F3gJDAC1ZMWALwMpDn52jqdGsb43Xfw9ddQsaIa8njbbapoiDsENLNZ9ZTl1pbsbZMmyRpYRWDOMhMeHY6G7WubvW1S9CTMWQ58bfV61csJtuEs+/7ChTJEVYhCkGAmhBA3ycpSH9x37AhDh0Lz5mqkmBB2MQLvoALaKGAuKqDNpXjz2eyh00G/fmr+1jffQJUqqmjIrbfCZ5+5NqAVpliEKJTYM7E2PWU5aWgkpiUSe8bBr21oKGzcCA0aWG83GNR2GZoqRKFIMBNCOIfJlPebsKQk9bibycpS7yU6doRhw6BOHdi1C779Fm65xdWtE6WOAVWa/yRwP6rnLACYDVxw8rV1OlVKf+dO9QNcvToMHgydO6tuYFcENCkW4TTJ6fa9ZvbuVyihoZCQoBZAX7NGfY2Pl1AmRBFIMBNCOJ7JpOa99O6tPgHPKTFRbQ8JcZtwlpUFn3wC7dvDvfeCr++NDgeZHiGKrQGqLP8pYCzwCiqgzQJSnXxtnQ769IGYGPWG2cdHdQN37Ki6hbOynNyAHKRYhNP4e9n3mtm7X6Hp9aok/siR6qsMXxSiSCSYCSEcLz0dUlLg1Cn1n3R2OEtMVPdPnVKPpzu7MkL+zGZYvx7atYPhw6F+fdi9W03R6dXLpU0TZVF9YCEqoD0IvIYKaDOBf0rg+sHBKpzt3Am1a6tu4Q4dYNOmkgloUizCaYIaBmHwNqAj99dWhw6jt5GghvLaCuHOJJgJIRzPYFCf0AcG3ghne/bcCGWBgepxg8ElzTObYe1aaNsW7rtPNSO7qF2PHi5pkihP/FELXMcD/wf8FxXQXgTOl8D1b78dtm9X43R9fVU1xPbtVbexMwOaFItwGr2HnsgQ9dreHM6y7y8MWeic9cyEEA4jwUwI4RxGo3U469nTOpQZjSXeJLNZTYFo0wZGjYKAANi7V63T2717iTdHlHf1gAWogPYI8AYqoD0P/F0C1w8KUuN1v/tODR8cPlx1H69f77zKiFIswmlCW4WycfhGGnhbv7YGbwMbh290/DpmQgiH02maO9TQdS9paWn4+PhgMpnw9vZ2dXOEKN327FGhLNvu3SXeLZXdQ/bSSxAXp5Z5mjVLVRIXwm2koHrP3kF9bPoEarHqOiV0/T17VPnRr76CVq1g5kw16dIZPVhms5rImZysQmFQkPSUOYg5y0zsmViS05Px9/InqGGQ9JSJMsNVP98llQ0kmOVCgpkQDpJzTlk2F/SYLV4Mjz8O99yj3mveemuJXVqIwvsL1ZP29r/3JwJTgLoldP3vv1cBLToaWraEGTNgxAgJTkIIl4o6FkV4dLjV0hAGbwORIZFO7xEuqWwgQxmFEM6RM5QFBqqespxzzm6u1uhE585Bw4bw+ecSykQpUBdVuTEBeAq1aHUAMA3Vq+Zs3brBl1+qgBYYCKNHQ+vW8PHHsvizEMIloo5FEbYhzGa9vrNpZwnbEEbUsSgXtcyxJJgJIRwvKcm20EePHrYFQfJbbNbB8ioEJ4TbqgPMQwW0ScB7QGNU79mfJXD9rl1h2zbYtw+aNoX771cL+q1eDdevl0ADhBBCDV8Mjw5Hw3aQX/a2SdGTMGeV/g+OJJgJIRzPy0tVe7t52GLOgiC+vmo/IUT+aqMWp04AJgMfoALaZGA/cKAYt0t2XP+222DrVvjxR2jRAh54QM1BW7lSApoQwuliz8Ta9JTlpKGRmJZI7Jn/b+/O46Kq9z+Ov8YFSQPUFMFAUXPLXMrK1GtYeVOvt1xazAw1rduipq1muaRW2p6VmbdSTEvLUrt1vZZZkAptLje1fuaCCgrS5oCYaHB+f3wv6MiAoMycWd7Px2MeOmfOOfOBwzlnPvP9fj/fNV6MyjOq2R2AiASgiAgzPiU3t2RJ/NhYM49SWJhZT0TKpy4wDZOQvfi/xwtnuM96mAIjI4FTfU9y8cXwr3/Bhg0wdSoMGwbTpsGECaY1rZo+UohI5cvMzazU9XyZrqIi4hkREaUnXjbNXyYSEOoAUzAJ2vYz2M8x4C3MBNfPYhK0UZw6QbvoIli+HDZtMgnarbeaBO3RRyEhAapXP4OgRERcRYdFV+p6vkxdGUVERPxRBHDxGTw6A7OBncBA4DFMkZEngJxyvH+HDrB0qUnQOnSAESNMV8c334RjxyrlRxQR6daoGzHhMSUmTy/iwEFseCzdGnXzcmSVT4mZiIhIMIvFzJ22ExgETMUkaI8DznJs3749fPAB/Pe/0LEj3HYbtGgBr78OR496LGwRCQ5Vq1RlZq+ZACWSs6LnL/Z6MSDm61NiJiIiIhCDmTttF3ALJjGLwyRq5UnQ2rWDJUtg82ZTMOSOO0yCNmeOEjQROSMDWg/g/Rvf59zwc12Wx4TH8P6N73t8HjNv0QTTbmiCaZHAMnGiqfC9e7fdkYj4kf3A08AcoAamZP9YoHY5t9+61Yw9e+89M650/HgYPhxq1PBEtCISBAoKC1izdw2ZuZlEh0XTrVE3r7SUaYLp/4mLi8PhcJR4jBw50u36iYmJJdYNDQ31ctQiIiJ+riGm8uMu4FbgKUwL2mTg93Js36YNLF4MW7bAX/4CI0ea+dBmzYIjRzwVtYgEsKpVqtI9rjuD2g6ie1z3gOi+eCKfr8r47bffUlBwfMK4LVu28Ne//pUbbrih1G3Cw8PZtm1b8XOHZpYVERE5PdGYsvzjMC1oz2ASttFAh/Ls4HwY8A5c+rQZizY6GSZ9D/36wVVXQUjI6cVVB7gCP/iKWUSkfHw+Matfv77L8xkzZtCsWTPi4+NL3cbhcBAVFVXu98jPzyc/P7/4eU5OecpRiYiIBJEo4HlMgvYMJlk7XJEdxABjzOM3YO7/HmeiDabc//UoQRMRv+dXl7GjR4+ycOFChg8fXmYr2KFDh2jcuDGxsbH07duXrVu3lrnf6dOnExERUfyIjY2t7NBFREQCQwPMvGe/AQfP4PHdDrjpTnDUgQYtYfpsyPyj/NuvxeR6A4G2wGLgeAcb8UEFhQUk7U5i0eZFJO1OoqBQB8yf6XhWPr8q/vHee+9x8803s3fvXho2bOh2ndTUVLZv3067du1wOp08++yzfPnll2zdupWYUia1dddiFhsbq+IfIgFCxT9EfNj27fDEE7BwIdSvDw89ZCo61qxZvu2/wlSO/A/QGpgI3AgE1tATv7f0x6WMWTmGjJyM4mUx4THM7DUzYCrqBZNgO57eKv7hV4lZz549CQkJ4aOPPir3NseOHaN169YMGjSIadOmlWsbVWUUCSxKzET8wM6dJkF76y2oVw8efBDuvBNq1Srf9t8AU4AVQCtgAnATStB8wNIfl3L9e9dj4fqRs2gOqkAqdx4MgvF4qirjSfbs2cNnn33GbbfdVqHtqlevzoUXXsiOHTs8FJmIiIicsWbNYO5c+Okn+Pvf4eGHoWlTePZZyMs79faXAv/GJGjnYeZiOx9YAPzpwbilTAWFBYxZOabEh3igeNnYlWPVDc5P6Hh6lt8kZvPmzSMyMpI+ffpUaLuCggI2b95MdHS0hyITERGRStO0Kbzxhuni2Levmf+sSRN4+mk4dOjU218CfAR8h2k5G4JJ0N5CCZoN1uxd49Ld7WQWFuk56azZu8aLUcnp0vH0LL9IzAoLC5k3bx5Dhw6lWjXXQpJDhgxh/Pjxxc+nTp3Kp59+yq5du9iwYQO33HILe/bsqXBLm4iIiNgoLg7++U/YsQMGDIAJE0yCNmMG5OaeevuOwIfAekxiNhQzBi0RJWhelJmbWanrib10PD3L58vlA3z22Wfs3buX4cOHl3ht7969VKlyPL/8/fffuf3228nKyqJOnTp07NiRlJQUzj//fG+GLCIiIpWhcWN47TV45BGYPh0mTTLdG++/H0aNgrCwsre/CFgObMIUCbkVmAYkADU8GrnnVAeuA5rYHcipRYeVr8dSedcTe+l4epZfFf/wFhX/EAksKv4hEkDS002r2RtvwNlnw333wejRUN779X8xiVmyJ4P0sDzgGKYV8BGgqb3hlKWgsIC4mXHsy9nndlySAwcx4TGkjUmjahVVavF1wXo8VfxDRERE5GSxsTBrlqniOGgQTJ1quj1OmwZO56m3bw+8D/zsx49fgKeAj4EWwHBgZwV+h15UtUpVZvaaCRyv2lek6PmLvV4MqA/xgUzH07OUmImIiIj/iYmBV16BXbvglltMqf24OJgyBQ4etDs6z6oJ3AfsAp7BzOHWEhgG+GAR6gGtB/D+je9zbvi5LstjwmMCsrR6oNPx9Bx1ZXRDXRlFAou6MooEgf374amnTMGQGjVg7FjzqF3b5sC84A/gn5hWtAMWXHUAen0HF50N3bpBVd9ovSgoLGDN3jVk5mYSHRZNt0bd1LLix4LpeGqCaRspMRMJLErMRIJIZqYprf/aaxASAmPGwL33Qp06dkfmeYuWw93r4eCdQBTwDjR4A14dYypbishp0RgzERERkYqKjoYXXoC0NBgxwlRwjIsz39D89pvd0XnO0qUweAAcfBxoBowBroADn8N1f8BLn9ocoIicihIzERERCTxRUfD88yZBu/12eO45k6A9+ij8+qvd0VWuggLTMljcCSofmAWcB4wGLocxPWBQIfxoW5QicgrqyuiGujKKBBZ1ZRQRDhwwrWevvgpVqpg50O6/H+rVszuyM5eUBFdcUcYKIcBwiHwBfg6FPkCkd0KTAOIAemLm0Auyph1v5QZ+McG0iIiIyBlp0ACeeQYefNC0nr38snkUJWj169sd4enLzDzFCkeB1+CZ7vDHQHgHCLBGQ/GCPOBNoA0wEbgeCMxaH7ZRYiYiIiLBIzLSVG8sStBeecU87r4bHnjAvO5voqPLt16jBtAduMOTwUhASwWmADcBrYFJwA0oQaskQdYQKSIiIoLpwjh9uhmDNmYMzJ4NTZqYhC072+7oKqZbNzOvm8Ph/nWHw0zM3a2bd+OSwNMZWIlJ0OKAQcAFmFbYAvvCChRKzERERCR41atnJqfeswfuuw/mzDFFQu6/H7Ky7I6ufKpWhZkzzf9PTs6Knr/4os/MZyYB4DJgBfA1pgjoYEwXx4XAnzbG5eeUmImIiIjUrQvTppkE7cEH4Y03TAvavfeWYwyXDxgwAN5/H84913V5TIxZrnnMxBMuBT4GvgWaAwnA+cAClKCdBiVmIiIiIkXq1IEpU0wZ13HjYN48aNoUxo71/QRtwAAT9xdfwDvvmH/T0pSUieddDHwEfIcZezbkf//ORwlaBSgxExERETlZnTrw2GMm0Rk/HubPNy1o99wD+/bZHV3pqlaF7t1h0CDzr7ovijd1BD4ENmDGng0DWgHzgGP2heUvNI+ZG5rHTCSwaB4zETljTie89BK88AIcPgy33QYPP2y6CoqIe5uAqcAyoBHQ2NZoTlvOnzlEpGoeMxERERH7RUSYb3nGjDHznz3/PLz++vEELTbW7ghFfE8HYCnwX2AOcMjWaE7fUUwlSg9Ti5kbajGTQOM84iT3aC4x4SW/2c3IySAsJIyI0AgbIvMOtZiJSKXLyTHznz33HOTmwogRpstjo0Z2RyYilcxbuYHGmIkEOOcRJ73e7kV8YjzpznSX19Kd6cQnxtPr7V44jzhtilBExA+Fh8Mjj5hvfKZOhSVL4Lzz4I47TGVHEZEKUmImEuByj+aSnZfNrt930X1+9+LkLN2ZTvf53dn1+y6y87LJPZpra5wiIn4pLMx0Zdy9Gx5/HJYuNQna7bebiogiIuWkxEwkwMWEx5A0NImmdZoWJ2cp6SnFSVnTOk1JGprktpujiIiU09lnw0MPmWTsySfhww+hRQszBm3XLrujExE/oMRMJAjERsS6JGdd53Z1ScpiIzRoXUSkUpx9tpmgOi0NZsyAjz4yCdrw4bBzp93RiYgPU2ImEgScR5w4HA4W9F/gsnxB/wU4HA6NLxMRqWy1asH995sE7ZlnYMUKaNkSbr0VduywOzoR8UEqly8S4IqKf+zP3V/itUEfDAKgYVhDVg5eGdCVGUVEbFGzJtx7rykK8s9/wlNPmTKxgwfDhAnQvLndEYqIj1CLmUiAyz2ay/7c/ex17mWvcy+NIhqxbvg6GkU0Kl62P3e/in+IiHhSzZowdqwZb/b887BqFbRqBUOGwE8/2R2diPgAJWYiIiIi3nLWWXDPPSZBmzkTPv8cWreGW26B//s/u6MTERspMRMJcGEhYTQMa0ijiEbFrWRd53Ytbj1rFNGIhmENCQsJsztUEZHgERoKo0aZ8WYvvwzJyXD++aaL448/ntm+v/oKnn4aDh2qnFhFxCuUmIkEuIjQCFYOXsm64etYdN0il9cWXbeIdcPXaXyZiIhdQkPh7rtNgjZrFqxZA23awKBB8MMPp7fPmBgzt1pCAvz5Z+XGKyIeo8RMJAhEhEZgWRYJyxJclicsS8CyLCVlIiJ2q1ED7roLtm+H2bMhJQUuuAAGDoQtW8q/n4ICqFfPlOj/7TeoVg0sy3Nxi0ilUWImEgTSnekuE0qvG77OZcLpdGe63SGKiAiYBO2OO0yCNmcOfP01tG0LN9wA+0tW1y2halXTCnfOObB5Mxw4AA6HSc6UoIn4NCVmIgEuIyfDJSlLGppEl9guLhNOd5/fnYycDLtDFRGRIiEhcPvtpmLj66+b+dDOPvvU2xUWmn87doT8fNOVsSghczhgzx4zv9rw4ZCT47n4RaTClJiJBLiwkDAia0UWJ2WxEbEAxEbEFidnkbUiVfxDRMQXhYTAbbfBd99BePip16/yv492oaHwxx+mG6TDAVlZJsHr0gVeeAFWroT16z0bu4hUiCaYFglwRcU/co/mEhMe4/JabEQsycOSCQsJ0zgzEZFAUFhokrPOnc3z33+HxYvh8cdNMZG4OHjpJRg2rHwtcCLiNUrMRIJARGhEqYnXycmaiIj4saJui4WFZrzanXdCXh5ERsKDD8LEiUrIRHyUEjMRERGRQHH4MHzxBUyZYsaY5efDyJFw661w0UVmnYICUyRERHyKxpiJSMALC4N9+8yXxdnZdkcjIuIha9aY6o39+pkEDeCqq8wE1kVJGSgpE/FRSsxEJOCNHAnjxpnK03FxpiBZVpbdUYmIVJL162H0aIiPh88/N3OfffABtGxpJq7WBU/ELygxE5GAV6uWGfe+ezc88AC88QY0bQr33afPKyLix7ZuNRe3Pn1g1iy45hpYvRoWLYL27eHii+Hnn02FRs1hJuLzfDoxe+yxx3A4HC6PVq1albnNkiVLaNWqFaGhobRt25YVK1Z4KVoR8XV168LUqSZBe+ghmDsXmjSBsWMhM9Pu6EREKmjlSpg0CaKi4LXX4MMPoVu346/XqmW6NG7dakrmi4hP8+nEDKBNmzZkZmYWP9auXVvquikpKQwaNIgRI0awceNG+vXrR79+/diyZYsXIxYRX1enDjz2mEnQHn4Y5s83Cdo995ixaCIifuH++2HvXli3Dv7xD7OssNAU9wC45BLzryaSFvELPp+YVatWjaioqOJHvXr1Sl135syZ9OrViwcffJDWrVszbdo0LrroIl555ZUy3yM/P5+cnByXh4gEvtq1YfJkk6BNmAALF0KzZmaohhI0EfELMTFQs+bx51WqHC/uUbu2+XfnTvfbHjsGCQnw5ZceDVFEysfnE7Pt27fTsGFDmjZtyuDBg9m7d2+p66amptKjRw+XZT179iQ1NbXM95g+fToRERHFj9jY2EqJXUT8Q0SEScx27zZT/LzzjhmDNnIkpKfbHZ2IyCmU1k2xdWvzWtFnp5PHme3bB5s3m6IhV1wBycmejVNEyuTTiVmnTp1ITExk5cqVzJ49m7S0NLp160Zubq7b9bOysmjQoIHLsgYNGpB1itH948ePx+l0Fj/S9UlMJCiFh8Ojj0JammlJW7wYzjsP7r5bCZqI+KEqVcx8IaUlXHFxsGEDLFsGBw9C9+7mkZTktRBF5DifTsx69+7NDTfcQLt27ejZsycrVqzg4MGDvPfee5X6PjVq1CA8PNzlISLBKzwcHnnEtKBNmQLvvWe6ON511/EvnkVEfF6rVvDDD6b5/+BB9y1rVaqYec82bDDFQ3JyTOtZUel9VXMU8RqfTsxOVrt2bVq0aMGOHTvcvh4VFcWBAwdclh04cICoqChvhCciASYszBQH2b3bVKR+/33TgnbHHWaZiIjPa9gQhgw5Pt6sNA4HXHutmRPtX/+CvDwzOfXll8NnnylBE/ECv0rMDh06xM6dO4mOjnb7eufOnVm9erXLslWrVtG5c2dvhCciAerss015/bQ0eOIJ0+uneXO4/XazTEQkYDgcZj60b7+Fjz+GI0fgr3+Fv/wFPv1UCZqIBzksy3fPsAceeIBrrrmGxo0bs3//fiZPnsymTZv44YcfqF+/PkOGDOHcc89l+vTpgCmXHx8fz4wZM+jTpw+LFy/mySefZMOGDVxwwQXlft+cnBwiIiJwOp3q1igiJeTlmSmDnn4afvvNfBndq5d90wSFhJjPTWedZc/7i0gAsyz4z39Mv+5vvoHLLjPzjVx9tS0Xve++U48F8b7Dh3MYOtTzuYFPJ2Y33XQTX375Jb/++iv169fnL3/5C0888QTNmjUDoHv37sTFxZGYmFi8zZIlS5gwYQK7d++mefPmPP300/ztb3+r0PsqMROR8jh8+HiCdlIvaq+LioJx40w3SyVo4uuWL4dNm0zX4FtusTsaKRfLgk8+MQnaV19Bp06mSpKXvpX68kvz1p9/7vG3EnEjBwjyxMwuSsxEpCL+/NO0otklM9Mkh2+9BfXqmW6Xd97pOrWRSGV4+WUzEXtCgvl7O9nvv8MFF5h/N22CFi1KrvPuu3DzzWYe5KJ9jhpV+nvu3m0mgC/N5MmmAUe8xLJg1SrzS09NNZNYT54Mf/ubRxK05GSTkH3xBbRvD5MmwZVX2tdDQYJTTk4OjRopMbOFEjMR8Ue7dsGTT8L8+VC37vEErVYtuyOTQGFZ5kNxUpJp9erb1/X1m2+GRYtg5kyTwJ1sxQpTALB2bXj1VXjgAVPpNDHRdAl2pygxa9/ebHuyogrv4mWWZYqCTJkC69bBxRebBK1Pn0rJmpKSTO6XnAwdOphdX3utKSIp4m3eyg2UmLmhxExE/FlamknQEhOhTh148EEzF5sSNKkMu3dD27amRXbrVtNKC6Zq6Q03mErrq1eX/GyenAy9e5v1V62Cli0hI8MMVfrpJ1iyBPr3d/9+TZrA0KHmb1p8jGWZ/oVTpsCaNXDRRSaLuuaaCidolmVaxqZMMV0XL7zQJGensSuRSuWt3EDfO4jPcB5xkpGT4fa1jJwMnEecXo5IxD81aQKvvw7bt5sPuo8+auaRfeopOHTI7ujE38XFwXPPQXa2mdsPzBjLu+4yU0zMm1fyQ/R335kP17GxsHatScoAYmLMB/AOHWDQIJOwiZ9xOExZ/eRkk6CFhZmm1I4dTbNqOb7/L2p8u/xys6u8PFOxf/1600qmpEyChRIz8QnOI056vd2L+MR40p3pLq+lO9OJT4yn19u9lJyJVEBcHMyZYxK066+HiRPNshkzIDfX7ujEn/3jH9Czp2klW7TIPP/lF3jxRWjc2HXdrVtNfYjzzjMNKo0aub5er55pJenc2XyRkJLi/j3374dZs0xr8Jtvws6dHvnR5HQ5HKa5NCnJPGrXNgf0wgvNHCNFgwpPUDRc7S9/MZVl8/NNhf5vv1UrmQQndWV0Q10ZvS8jJ4P4xHh2/b6LpnWakjQ0idiIWNKd6XSf3714efKwZGLCY+wOV8Qv7d1rkrI33zRzs91/vym6oMucnI59+0yhjz/+MB+o//53+Oijyn+f0op/OBwweLCpjKpuuj7qxFKK7dqZyh39+2M5qvDpp+al1FS49FLTZdHOaUdEyqIxZjZSYmaPk5OwBf0XkLAsoUSyJiJnJj3ddGt8/XXzgXbECFMsRATMOLAOHcq37sSJ8PjjUL067NkD0dGVH092Nrzyiin80ayZaXjZsMF00f36axgwAD74oPTtt2zxTMIoFbB7txl4uHMHVoNo/hU+mK+3n8Nll5nhaD17KiET36bEzEZKzOxzYnJWREmZiGfs22cStPfeg4ICu6MRX/HCC+WbWyw727SY/fyzef7Pf8Ltt3s2thMdPmzqTGzbZsYiXXSR+/WWLDHFb8QH/HkM8vJofex7JjReyF+f6oHjhutValF8nhIzGykxs1dKegpd53Ytfr5u+Dq6xHaxMSIRcR5xkns0121X4oycDMJCwogIjbAhMrHLgAFm6NCMGfDss6Y745YtJceQedITT8CECfDSSzB6tPfeN9B5/HxPTTX9GD/5BM4/3zS93nADVK16BlGLeI6qMkpQSnemk7AswWVZwrKEEgVBRMR7VJxHTrZggUnK/v53GDfOdDXMzTXdYr2pqFS/nRO8BxqvnO+dO8PKlSZBa9TIlOS84AJ45x0130tQU2ImPuPkMWbrhq+jaZ2m7Pp9F93nd1dyJmKT3KO5ZOdllzgXTzxns/OyyT2qUo/BYN8+M3l03bqm+yLAwIGm8udnn5lKoN7y9dfm37g4771noPPq+X7ZZfCf/5gD2bSpqebSpg0sXAh//nnm+xfxM0rMxCdk5GS4JGVJQ5PoEtuFpKFJLslZafOciYjnxITHlDgXU9JTSpyzqpgaHEaMgIMHTSvZicU+Xn0V6tc3E5rv2VN577dxo/upsJYuhfnzzSTqvXtX3vsFO1vO90svhX//G775Bpo3h4QE08VxwQIlaBJUNMbMDY0x876irhPZedklCn0UfUsXWSuSlYNXahyLiE1UnEfmzIE77zStY0uWlHz9gw/Ma1deaVrPKqPSXvfuZs6yzp3NhNQFBaYq49q1UKOGKV5z7bVn/j7iytbz/bvvYOpUU07zvPPMQMLBg6FaNc++r0gpVPzDRkrM7KHiAuIt/v63Zmf8Ks4TvNLSzFRUNWuaSaOLxned7OabzaTTs2ZVTjXEN94wCd/WrWYS68JCOPdck/zdfz+0anXm7yHu2X6+b9hgErQPPzRzJUyYYEqGKkETL1NiZiMlZiKBy99bZ+2MXy1mIsHDp873jRtNgrZ8uRmL9uijprtj9erejUOClqoyioh4gL8XsrArfhXnEQkePne+X3ihKQO6caOZ/XzECGjZ0jSnHjvm3VhEPEiJmYgEFX8vZGFH/CrOIxI8fPp879DB9Gv973+hY0czo3nz5vD663D0qPfjEalkSsxEJOjERsS6fMjoOrery4cQX++W5+34w0LCiKwVWWL/J8YRWSuSsJCwSn1fkbI4jzhLTQ4ycjI0r95p8ovzvV07U33m++9NRcc77jAJ2pw5StDEr2mMmRsaYyYSHGwf2H6GvBm/vxdMkcDi72NFfZ3fne9bt8K0aaZEZ0wMPPII3HqrKdspUgk0xkxExIPSnekkLEtwWZawLMFvxkp5O/6I0IhSu0fGhMf41oc0CXj+PlbU1/nd+d6mDSxeDFu2wF/+YsqBnneemVwvP9/u6ETKTYmZiAQdnxvYXkH+Hr/ImfL3saLiIeefD++8Az/8APHxMHq0KbM/axYcOWJ3dCKnpK6Mbqgro0jgysjJID4xvsSYrJOTneRhyT75oc7f4xepTD5V0l18z7Zt8MQT8PbbEBUFDz9sCoaEhtodmfgZdWUUEfGAyh7Y7u0CBH4xMF/ES2IjYlnQf4HLsgX9Fygp8xKfL8DSsiW89Rb8+CP06AFjx5p50GbOhD/+sDc2ETfUYuaGWsxEAltlDWy3qwCB3w3MF/EQtZjZxy8LsOzYAY8/DgsXQv368NBDpqJjzZp2RyY+Ti1mIiIeUlkD2+0qQOB3A/NFPEBjLe3llwVYzjsPEhNNF8feveHBB00L2nPPQV6e3dGJKDETETldKkAgYg+fngQ5SPj19a9ZM5g7F376Cf7+dzP2rGlTeOYZJWhiK3VldENdGUWkItSdSsS7/LIbXYAKiOtfWhpMnw7z5kGdOvDAA6bk/tln2x2Z+Ahv5QZKzNxQYiYiFeXvk1WL+BuNtfQdAXP92737eIIWEQH33w8jR0KYiikFO40xExHxE/4+WbWIP9JYS98QUNe/uDiYMwe2b4frr4dJk6BJE5Os5frQWDkJWErMRETOgAoQiEiwCtjrX+PGMHs27NwJAwfCY4+ZpO2JJyAnx+7oJIApMRMROU0qQCAiwSoorn+xsTBrlknQBg2CqVNNgvb44+C0eY42CUhKzERETpMmexaRYBVU17+YGHjlFdi1C265xSRmcXEmUTt40O7oJICo+IcbKv4hUjoNuHel34eIBKugvf7t3w9PP23Go9WoAWPHmkft2jYH5mUFBbBmDWRmQnQ0dOsGVavaHZVHqCqjjZSYibinEtUiIiL/k5lpErTXXjMJ2pgxJkGrU8fuyDxv6VLz82ac0FU1JgZmzoQBA+yLy0NUlVFEfE7u0Vyy87JLDOw+cQB4dl42uUdVvUpERAJcdDS88IKZB23ECDNBdVwcTJwIv/1md3Ses3SpqVqZcdL4wX37zPKlS+2JKwCoxcwNtZiJlO7kKlwL+i8gYVmCywBwv5lUVEREpLIcOADPPguvvmq69I0eDffdB+ecY3dklaegwCSfJydlRRwO03KWlhZQ3RrVldFGSsxEynZiclZESZmIiAiQnW0StFmzoEqV4wlavXp2R3bmkpLgiitOvd4XX0D37p6OxmvUlVFETsl5xFlqKeKMnAycRzxTzjc2IpYF/Re4LFvQf4GSMhERkchIM/Zs924YORJeesm0Mj38MPz8s93RnZnMzMpdT1z4dGI2ffp0LrnkEsLCwoiMjKRfv35s27atzG0SExNxOBwuj9DQUC9FLOI9RYU44hPjS0zime5MJz4xnl5v9/JIcpbuTCdhWYLLsoRlCf47maiIiEhlq18fZswwCdro0aYFLS4OHnrItKr5o+joyl1PXPh0YpacnMzIkSP56quvWLVqFceOHePqq68mLy+vzO3Cw8PJzMwsfuzZs8dLEYt4j12FOE4eY7Zu+DqXyUSVnImIiJygXj2YPt0kaGPHwuzZ0KQJPPCAGZfmT7p1M2PIHA73rzscZmLubt28G1eA8KsxZj///DORkZEkJydz+eWXu10nMTGRsWPHcvAMJvzTGDPxF94uxJGRk0F8YnyJ/Z8cR/KwZLfz2oiIiAS9X3811Rxfegn+/BPuugsefBCiouyOrHyKqjICnJhGFCVr778fcCXzNcbMDafTdMmqW7dumesdOnSIxo0bExsbS9++fdm6dWuZ6+fn55OTk+PyEPEHsRGxJA1NKm6x6jq3q0erI4aFhBFZK7LE/k+MI7JWJGEhYZX6viIi4r/sGg/ts845Bx5/3LSgPfAAvPGGaUG7917/GJs1YIBJvs4913V5TExAJmXe5DctZoWFhVx77bUcPHiQtWvXlrpeamoq27dvp127djidTp599lm+/PJLtm7dSkyM+2/wH3vsMaZMmVJiuVrMxF+kpKfQdW7X4ufrhq+jS2wXj7yX84iT3KO5blvEMnIyCAsJ0+TSIiICHB8PnZ2XXeILw6LeFpG1Ilk5eGXw3jt+/91MzPzii5CfD//4B4wbBw0b2h1Z2QoKYM0ak0xGR5vuiwFUIv9EKpd/krvuuov//Oc/rF27ttQEy51jx47RunVrBg0axLRp09yuk5+fT35+fvHznJwcYmNjlZiJX1DpehER8VXqAl8BBw+a7o0vvAB//HE8QTu5ZUq8Tl0ZTzBq1Cg+/vhjvvjiiwolZQDVq1fnwgsvZMeOHaWuU6NGDcLDw10eIv5AhThERMSXxYTHuHS57z6/OynpKS73rqShSUrKAGrXhkmTTBfHRx+FhQuhWTMYNar0CZ0loPh0YmZZFqNGjWLZsmV8/vnnNGnSpML7KCgoYPPmzUSrbKcEmIycjBI3ti6xXUrcAEvr1y8iIuIN3h4P7fciImDiRJOgTZwIixaZBG3kSEjXF66BzKcTs5EjR7Jw4ULeeecdwsLCyMrKIisriz/++KN4nSFDhjB+/Pji51OnTuXTTz9l165dbNiwgVtuuYU9e/Zw22232fEjiHiMCnEEJg2Sl2CncyAwxUbEsqD/ApdlC/ovUFJWlvBw03KWlgaTJ8PixXDeeXD33bB3r93RiQf49BgzRylzJMybN49hw4YB0L17d+Li4khMTATg3nvvZenSpWRlZVGnTh06duzI448/zoUXXlju91W5fPEXKsQRWDRIXoKdzoHApfHQlSA3F159FZ55BnJyYPhwGD8eGje2O7KAp+IfNlJiJiJ20CB5CXY6BwKTt+fcDHiHDh1P0JxOGDYMHnkE4uLsjixgqfiHiEiQ0SB5CXY6BwKPxkN7wNlnw0MPmTFoTz4JH34IzZvDbbeZbo/it9Ri5oZazETETuryI8FO50DgUPdUL8jLg9deg6efht9+gyFDzNi0pk3tjixgqCujjZSYiYjdvDlpuIgv0jkQODQe2ksOH4Y5c+Cpp+CXXyAhwSRo551nd2R+T10ZRUSCVLoznYRlCS7LEpYlaF46CRo6BwJLRGhEqd1PY8JjlJRVlpo14d57YdcuePZZWLkSWrWCoUNh+3a7o5NyUGImIuJDNGm4BDudAyJnqGZNGDvWJGjPPw+rVpkELSEBfvrJ7uikDErMRER8hAbJS7DTOSBSic46C+65xyRoL74In38OrVvDLbfA//2f3dGJG0rMRER8hCYNl2Cnc0DEA0JDYfRo2LkTXnoJkpLg/PPh5pvhxx/tjk5OoOIfbqj4h4jYRYPkj9PvIvCU55gCOu4inpSfD3PnwvTpkJEBAwfCxIkmWRO3VPxDRCQIaZC8UVRiOz4xvsSYonRnOvGJ8fR6uxfOI06bIpSKKu8xBXQOiHhSjRpw112mIMjs2ZCSAhdcYBK0LVvsji6oKTETERGfk3s0l+y87BIFH04sDJGdl03u0Vxb45Ty0zEV8TE1asAdd5gEbc4c+OYbaNsWbrgBNm+2O7qgpMRMRER8Tkx4TImCDynpKSUKQ5TWsiK+R8dUxEeFhMDtt5uKjW+8Ad99B+3awfXXw/ff2x1dUNEYMzc0xkxExDec2JpS5OTCEOJfdExFfNyxY7BgATzxhKno2L8/TJoEHTrYHZltNMZMijmPOEstDZyRk6ExFiISsGIjYlnQf4HLsgX9F5zWB3hdS31DZR5TEfGA6tVh+HBTUn/ePNNqduGFJkHbuLHi+ysoMJUgFy0y/xYUVHbEAUOJmY/TAHgRCWbpznQSliW4LEtYllDhSYZ1LfUdlXVMRcTDqleHYcNMgpaYaAqDXHQR9O0L69eXbx9Ll0JcHFxxhSnPf8UV5vnSpZ6L248pMfNxGiwtIsHqxOtc0zpNWTd8ncv4pIp8kNe11DdU5jEVES+pVg2GDjVznr31lvn34ovhmmvMeLTSLF1qxqllnNRTYd8+s1zJWQlKzHycBkuLSDDKyMkocZ3rEtulxPWwtK6JJ9O11H6VfUxFxMuqVYOEBPjhBzMGbft2uOQS6NPHVHQ8UUEBjBkD7kpZFC0bO1bdGk+ixMwPxEbEuty4us7t6nJjU798EQk0YSFhRNaKLHGdO/F6GFkrsnhC4vLQtdRenjimImKDatXglltg61Z4+21TIKRTJ+jdG776yqyzZk3JlrITWRakp5v1pJiqMrrhq1UZU9JT6Dq3a/HzdcPX0SW2i40RiYh4jvOIk9yjuW5bsTJyMggLCTutyYZ1LbWPp46piNiooACWLIGpU003x549oXNneOyxU2/7zjswaJDHQzxTqsooLjRYWkSCTURoRKldC2PCY07rA7yupfbyxDEVEZtVrQo33WQmpV682LSElScpA4iO9mho/kaJmR/QYGkRkTOna6mIiAdVrQoDBx5P0KpVK31dhwNiY6FbN+/F5weUmPk4DZYWETlzupaKiHhJlSomQVu0yP3rDof598UXTTInxZSY+TgNlhYROXO6lopIIHIecZb6hVJGToZH5mYs93tefz188AGce67rSiEhpqvjgAGVHpu/U/EPN3yt+IcGS4uInDldS0UkkDiPOOn1di+y87JLVJYt6rodWSuSlYNXVtq17bTes6DAVF/ctw/S0kyytmkTxMfD5MnQvfvxVjQfpeIfUkyDpUVEzpyupSISSHKP5pKdl11inOyJ42mz87LJPZpr73tWrWqSr8GDYcIE2LABli+HnBy48kqToH3+ufs5z4KMEjMRERERET8TEx5TYpxsSnpKifG0pX0hZdt7OhzQty+sXw//+hccPgxXXQWXXw6ffRbUCZq6Mrrha10ZRURERETcObG1qsjJ42l9+j0tC1asgClT4NtvoUsXMwatRw+f6eKorowiIiI+yo4B9yIi7sRGxLKg/wKXZQv6L/BYUlbp7+lwQJ8+8PXXJkErKICrr4auXeGTT4KqBU2JmYiISAUUDX6PT4wvMfdZujOd+MR4er3dS8mZiHhFujOdhGUJLssSliV4dG5Gj7ynwwG9e0NqKqxcaRKyXr2gc2f4z3+CIkFTYiYiIlIBdgy4FxFx58TrTtM6TVk3fJ3L+C9PJGcef0+HA3r2hJQU02JWtSr87W9w2WWmRS2AEzQlZiIiIhVgx4B7EZGTZeRklLjudIntUuL6VFq3a59/T4fDdGlcuxZWrYLq1U2Xx0svhY8/DsgETYmZiIhIBZ04MfWu33fRdW5Xlw8qnhzbISICEBYSRmStyBLXnROvT5G1IgkLCfPr98ThMIVA1qwxVRvPOguuuQYuucRUdQygBE1VGd3wx6qMmjhVRMT7UtJT6Dq3a/HzdcPX0SW2i40RVa5y31ucTsjNhRg3rYQZGRAWBhG6B4lUNjs+/9n+mdOyICnJVHFMToYLL4RJk0wJfg9VcVRVRik3DUQXEfE+Owbce1O57y0H9poB+vHxkH7Sz56ebpb36mWSNxGpVBGhEaV2m44Jj/FIgmTHe7pwOOCKK0xy9sUX5kuf/v1NgrZ0KRQWevb9PUiJWQDQQHQREe+yY8C9t5X33nL4twOQnQ27dkH37seTs/R083zXLvN6ru5BIlLJunc3yVlSEpxzDlx3nUnQPvjALxM0JWYBQAPRRUS8x44B93Yo770luvUl5kNR06bHk7OUlONJWdOm5nV33RxFRCpDfDysXg1ffgn168P110P79rBkiV8laBpj5oY/jjEDe2Z+FxEJNkVd/LLzsktcX4uuw5G1Ilk5eGVAjO0t973lxBay4hX/l5TF6h4kIl60bp0Zg7ZqFbRpY8agXX89VDm9Nilv5QZKzNzw18QMAn8guoiIL7B98LuXlfvekpICXY+vx7p10EX3IBGxSWqqSdA++QTOPx8mToQbbjBzo1WAin+cYNasWcTFxREaGkqnTp345ptvylx/yZIltGrVitDQUNq2bcuKFSu8FKm9An0guoiIr7B98LsXlfvekp4OCa7rkZBQsiCIiIi3dO4MK1eaBK1xYxg0CNq2hXfegYICu6MrwecTs3fffZf77ruPyZMns2HDBtq3b0/Pnj3Jzs52u35KSgqDBg1ixIgRbNy4kX79+tGvXz+2bNni5ci9KxgGoouIiHeV+95yYjfGpk1NS9mJY86UnImInS67DFasgK+/hiZNYPBg08Xx7bd9KkHz+a6MnTp14pJLLuGVV14BoLCwkNjYWEaPHs3DDz9cYv2BAweSl5fHxx9/XLzssssuo0OHDrz22mvlek9/68qYkZNBfGJ8iclNT76hJg9LVgEQEREpl/LeW9b+dTHRf7/JtdBHbGzJZC05WQVARMQ3fPstTJ0KH38MLVrAhAmmNa1aNbereys3cP/uPuLo0aOsX7+e8ePHFy+rUqUKPXr0IDU11e02qamp3HfffS7LevbsyfLly0t9n/z8fPLz84ufO/8310pOTs4ZRO891hGLulXqUnhWIR/1/4gIR4T5A3JE8FH/j+izqA91q9TFOmKRg3/8TCIiYq/y3lv+rF6TnLp1TeWzjz4ycwrl5Jh/P/oI+vSBunXNpLB+cl8VkQDXsqVpLduwAZ56CoYMgYYN4ZJL3K5elBN4uj3LpxOzX375hYKCAho0aOCyvEGDBvzf//2f222ysrLcrp+VlVXq+0yfPp0pU6aUWB7rh1Wk2oxr43b5bnbTaHQjL0cjIiKBoMx7CxecsKL79di9GxrpHiQiPqxHj1Ou8uuvvxIR4bkxxD6dmHnL+PHjXVrZDh48SOPGjdm7d69Hf/lSupycHGJjY0lPT/eL7qSBSMfAfjoG9tMxsJd+//bTMbCfjoH9nE4njRo1om7duh59H59OzOrVq0fVqlU5cOCAy/IDBw4QFRXldpuoqKgKrQ9Qo0YNatSoUWJ5RESETgCbhYeH6xjYTMfAfjoG9tMxsJd+//bTMbCfjoH9qpzmPGjl3r9H936GQkJC6NixI6tXry5eVlhYyOrVq+ncubPbbTp37uyyPsCqVatKXV9ERERERMRuPt1iBnDfffcxdOhQLr74Yi699FJefPFF8vLyuPXWWwEYMmQI5557LtOnTwdgzJgxxMfH89xzz9GnTx8WL17Md999xz//+U87fwwREREREZFS+XxiNnDgQH7++WcmTZpEVlYWHTp0YOXKlcUFPvbu3evSrNilSxfeeecdJkyYwCOPPELz5s1Zvnw5F1xwQWlvUUKNGjWYPHmy2+6N4h06BvbTMbCfjoH9dAzspd+//XQM7KdjYD9vHQOfn8dMREREREQk0Pn0GDMREREREZFgoMRMRERERETEZkrMREREREREbKbETERERERExGZBm5jNmjWLuLg4QkND6dSpE998802Z6y9ZsoRWrVoRGhpK27ZtWbFihZciDTzTp0/nkksuISwsjMjISPr168e2bdvK3CYxMRGHw+HyCA0N9VLEgeexxx4r8fts1apVmdvoHKhccXFxJY6Bw+Fg5MiRbtfXOXDmvvzyS6655hoaNmyIw+Fg+fLlLq9blsWkSZOIjo7mrLPOokePHmzfvv2U+63o/SSYlXUMjh07xrhx42jbti21atWiYcOGDBkyhP3795e5z9O5ngWrU50Dw4YNK/G77NWr1yn3q3Og/E51DNzdFxwOB88880yp+9Q5UDHl+Rx65MgRRo4cyTnnnMPZZ5/Nddddx4EDB8rc7+neQ04UlInZu+++y3333cfkyZPZsGED7du3p2fPnmRnZ7tdPyUlhUGDBjFixAg2btxIv3796NevH1u2bPFy5IEhOTmZkSNH8tVXX7Fq1SqOHTvG1VdfTV5eXpnbhYeHk5mZWfzYs2ePlyIOTG3atHH5fa5du7bUdXUOVL5vv/3W5fe/atUqAG644YZSt9E5cGby8vJo3749s2bNcvv6008/zUsvvcRrr73G119/Ta1atejZsydHjhwpdZ8VvZ8Eu7KOweHDh9mwYQMTJ05kw4YNLF26lG3btnHttdeecr8VuZ4Fs1OdAwC9evVy+V0uWrSozH3qHKiYUx2DE3/3mZmZzJ07F4fDwXXXXVfmfnUOlF95Pofee++9fPTRRyxZsoTk5GT279/PgAEDytzv6dxDSrCC0KWXXmqNHDmy+HlBQYHVsGFDa/r06W7Xv/HGG60+ffq4LOvUqZN1xx13eDTOYJGdnW0BVnJycqnrzJs3z4qIiPBeUAFu8uTJVvv27cu9vs4BzxszZozVrFkzq7Cw0O3rOgcqF2AtW7as+HlhYaEVFRVlPfPMM8XLDh48aNWoUcNatGhRqfup6P1Ejjv5GLjzzTffWIC1Z8+eUtep6PVMDHe//6FDh1p9+/at0H50Dpy+8pwDffv2ta688soy19E5cGZO/hx68OBBq3r16taSJUuK1/nxxx8twEpNTXW7j9O9h5ws6FrMjh49yvr16+nRo0fxsipVqtCjRw9SU1PdbpOamuqyPkDPnj1LXV8qxul0AlC3bt0y1zt06BCNGzcmNjaWvn37snXrVm+EF7C2b99Ow4YNadq0KYMHD2bv3r2lrqtzwLOOHj3KwoULGT58OA6Ho9T1dA54TlpaGllZWS5/5xEREXTq1KnUv/PTuZ9IxTidThwOB7Vr1y5zvYpcz6RsSUlJREZG0rJlS+666y5+/fXXUtfVOeBZBw4c4N///jcjRow45bo6B07fyZ9D169fz7Fjx1z+rlu1akWjRo1K/bs+nXuIO0GXmP3yyy8UFBTQoEEDl+UNGjQgKyvL7TZZWVkVWl/Kr7CwkLFjx9K1a1cuuOCCUtdr2bIlc+fO5cMPP2ThwoUUFhbSpUsXMjIyvBht4OjUqROJiYmsXLmS2bNnk5aWRrdu3cjNzXW7vs4Bz1q+fDkHDx5k2LBhpa6jc8Cziv6WK/J3fjr3Eym/I0eOMG7cOAYNGkR4eHip61X0eial69WrF2+99RarV6/mqaeeIjk5md69e1NQUOB2fZ0DnjV//nzCwsJO2YVO58Dpc/c5NCsri5CQkBJfCJ0qVyhap7zbuFOtArGLVLqRI0eyZcuWU/aF7ty5M507dy5+3qVLF1q3bs2cOXOYNm2ap8MMOL179y7+f7t27ejUqRONGzfmvffeK9c3c1K53nzzTXr37k3Dhg1LXUfngASTY8eOceONN2JZFrNnzy5zXV3PKs9NN91U/P+2bdvSrl07mjVrRlJSEldddZWNkQWnuXPnMnjw4FMWetI5cPrK+znUW4KuxaxevXpUrVq1RGWVAwcOEBUV5XabqKioCq0v5TNq1Cg+/vhjvvjiC2JiYiq0bfXq1bnwwgvZsWOHh6ILLrVr16ZFixal/j51DnjOnj17+Oyzz7jtttsqtJ3OgcpV9Ldckb/z07mfyKkVJWV79uxh1apVZbaWuXOq65mUX9OmTalXr16pv0udA56zZs0atm3bVuF7A+gcKK/SPodGRUVx9OhRDh486LL+qXKFonXKu407QZeYhYSE0LFjR1avXl28rLCwkNWrV7t8G32izp07u6wPsGrVqlLXl7JZlsWoUaNYtmwZn3/+OU2aNKnwPgoKCti8eTPR0dEeiDD4HDp0iJ07d5b6+9Q54Dnz5s0jMjKSPn36VGg7nQOVq0mTJkRFRbn8nefk5PD111+X+nd+OvcTKVtRUrZ9+3Y+++wzzjnnnArv41TXMym/jIwMfv3111J/lzoHPOfNN9+kY8eOtG/fvsLb6hwo26k+h3bs2JHq1au7/F1v27aNvXv3lvp3fTr3kNKCCzqLFy+2atSoYSUmJlo//PCD9Y9//MOqXbu2lZWVZVmWZSUkJFgPP/xw8frr1q2zqlWrZj377LPWjz/+aE2ePNmqXr26tXnzZrt+BL921113WREREVZSUpKVmZlZ/Dh8+HDxOicfgylTpliffPKJtXPnTmv9+vXWTTfdZIWGhlpbt26140fwe/fff7+VlJRkpaWlWevWrbN69Ohh1atXz8rOzrYsS+eAtxQUFFiNGjWyxo0bV+I1nQOVLzc319q4caO1ceNGC7Cef/55a+PGjcUV/2bMmGHVrl3b+vDDD63vv//e6tu3r9WkSRPrjz/+KN7HlVdeab388svFz091PxFXZR2Do0ePWtdee60VExNjbdq0yeX+kJ+fX7yPk4/Bqa5nclxZv//c3FzrgQcesFJTU620tDTrs88+sy666CKrefPm1pEjR4r3oXPgzJzqOmRZluV0Oq2aNWtas2fPdrsPnQNnpjyfQ++8806rUaNG1ueff2599913VufOna3OnTu77Kdly5bW0qVLi5+X5x5yKkGZmFmWZb388stWo0aNrJCQEOvSSy+1vvrqq+LX4uPjraFDh7qs/95771ktWrSwQkJCrDZt2lj//ve/vRxx4ADcPubNm1e8zsnHYOzYscXHq0GDBtbf/vY3a8OGDd4PPkAMHDjQio6OtkJCQqxzzz3XGjhwoLVjx47i13UOeMcnn3xiAda2bdtKvKZzoPJ98cUXbq89Rb/nwsJCa+LEiVaDBg2sGjVqWFdddVWJY9O4cWNr8uTJLsvKup+Iq7KOQVpaWqn3hy+++KJ4Hycfg1Ndz+S4sn7/hw8ftq6++mqrfv36VvXq1a3GjRtbt99+e4kES+fAmTnVdciyLGvOnDnWWWedZR08eNDtPnQOnJnyfA79448/rLvvvtuqU6eOVbNmTat///5WZmZmif2cuE157iGn4vjfjkVERERERMQmQTfGTERERERExNcoMRMREREREbGZEjMRERERERGbKTETERERERGxmRIzERERERERmykxExERERERsZkSMxEREREREZspMRMREREREbGZEjMRERERERGbKTETERG/N2zYMBwOBzNmzHBZvnz5chwOR4X2FRcXx4svvnjGMWVmZnLzzTfTokULqlSpwtixY894nyIiEriUmImISEAIDQ3lqaee4vfff7c7FADy8/OpX78+EyZMoH379naHIyIiPk6JmYiIBIQePXoQFRXF9OnTy1zvgw8+oE2bNtSoUYO4uDiee+654te6d+/Onj17uPfee3E4HC6tbWvXrqVbt26cddZZxMbGcs8995CXl1fq+8TFxTFz5kyGDBlCRETEmf+AIiIS0JSYiYhIQKhatSpPPvkkL7/8MhkZGW7XWb9+PTfeeCM33XQTmzdv5rHHHmPixIkkJiYCsHTpUmJiYpg6dSqZmZlkZmYCsHPnTnr16sV1113H999/z7vvvsvatWsZNWqUt348EREJcErMREQkYPTv358OHTowefJkt68///zzXHXVVUycOJEWLVowbNgwRo0axTPPPANA3bp1qVq1KmFhYURFRREVFQXA9OnTGTx4MGPHjqV58+Z06dKFl156ibfeeosjR4547ecTEZHApcRMREQCylNPPcX8+fP58ccfS7z2448/0rVrV5dlXbt2Zfv27RQUFJS6z//+978kJiZy9tlnFz969uxJYWEhaWlplf4ziIhI8KlmdwAiIiKV6fLLL6dnz56MHz+eYcOGVco+Dx06xB133ME999xT4rVGjRpVynuIiEhwU2ImIiIBZ8aMGXTo0IGWLVu6LG/dujXr1q1zWbZu3TpatGhB1apVAQgJCSnRenbRRRfxww8/cN5553k2cBERCVrqyigiIgGnbdu2DB48mJdeesll+f3338/q1auZNm0aP/30E/Pnz+eVV17hgQceKF4nLi6OL7/8kn379vHLL78AMG7cOFJSUhg1ahSbNm1i+/btfPjhh6cs/rFp0yY2bdrEoUOH+Pnnn9m0aRM//PBD5f/AIiLi9xyWZVl2ByEiInImhg0bxsGDB1m+fHnxst27d9OyZUuOHj3Kibe6Dz74gEmTJrF9+3aio6MZPXq0S2L21Vdfcccdd7Bt2zby8/OLt/3222959NFHSU1NxbIsmjVrxsCBA3nkkUdKjcvd5NaNGzdm9+7dZ/5Di4hIQFFiJiIiIiIiYjN1ZRQREREREbGZEjMRERERERGbKTETERERERGxmRIzERERERERmykxExERERERsZkSMxEREREREZspMRMREREREbGZEjMRERERERGbKTETERERERGxmRIzERERERERmykxExERERERsdn/A08ucVUyrYK5AAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "# ce block du code est pour filtrer les avertissements concernant la convergence du modèle\n",
    "# en général, lorsque e nombre des itérations n'est pas suffisant pour atteindre l'erreur minimale\n",
    "import warnings\n",
    "from sklearn.exceptions import ConvergenceWarning\n",
    "warnings.filterwarnings('ignore', category=ConvergenceWarning)\n",
    "\n",
    "degres = [3, 5]\n",
    "couleurs=['red', 'magenta', 'blue']\n",
    "\n",
    "# Une fonction pour dessiner le plan de séparation binaire étant donnée un modèle\n",
    "# modele : c'est un modèle enttraîné pour la prédiction binaire\n",
    "# ax: un objet de type matplotlib.axes.Axes; les axes sur lesquels on va dessiner\n",
    "# xrange: une liste des points sur l'axe X\n",
    "# yrange: une liste des points sur l'axe Y\n",
    "# couleur: la couleur du dessin (de la ligne de séparation)\n",
    "# label: l'étiquêtte du dessin (la ligne de séparation)\n",
    "def dessiner2D(modele, ax, xrange, yrange, couleur='red', label=''):\n",
    "    # Créer une matrice de (xrange X yrange): notre plan de dessin\n",
    "    XX   = [[[xr, yr] for xr in xrange] for yr in yrange]\n",
    "    # Représenter le sous forme d'une matrice de (xrange X yrange)/2 échantillons et 2 caractéristiques\n",
    "    XX   = np.array(XX).reshape(-1, 2)\n",
    "    # Prédire les probabilités (estimation) et retransformer vers notre plan (xrange X yrange)\n",
    "    grid = modele.predict(XX).reshape(len(xrange), len(yrange))\n",
    "    # Dessiner des lignes qui passent par les valeurs 0.5\n",
    "    cs   = ax.contour(xrange, yrange, grid, colors=[couleur], linewidths=(1), linestyles=('-'),levels=[0.5])\n",
    "    # Affecter l'étiquêtte à la ligne de séparation (qui es un contour dans notre cas)\n",
    "    # plt.clabel(cs, inline=1, fontsize=10)\n",
    "    # cs.collections[0].set_label(label)\n",
    "    fmt = {cs.levels[0]: label}\n",
    "    ax.clabel(cs, cs.levels, inline=True, fmt=fmt, fontsize=14)\n",
    "    \n",
    "\n",
    "\n",
    "X_notes_train = X_notes[:80, :]\n",
    "X_notes_test  = X_notes[80:, :]\n",
    "Y_notes_train = Y_notes[:80   ]\n",
    "Y_notes_test  = Y_notes[80:   ]\n",
    "\n",
    "# Trouver les indexes ordonnées \n",
    "idx2 = X_notes_train[:,0].argsort()\n",
    "\n",
    "# Sélectionner le cas \"admis\" dans l'entraînement et le test\n",
    "oui_train = Y_notes_train == 1\n",
    "oui_test  = Y_notes_test  == 1\n",
    "\n",
    "# Dessiner les cas \"admis\" et \"Non admis\" de l'entraînement et du test\n",
    "fig, ax = plt.subplots(figsize=(10, 5))\n",
    "ax.scatter(X_notes_train[oui_train, 0], \n",
    "           X_notes_train[oui_train, 1], \n",
    "           color='green', marker='o', label='Admis (entrainement)')\n",
    "ax.scatter(X_notes_train[~oui_train, 0], \n",
    "           X_notes_train[~oui_train, 1], \n",
    "           color='green', marker='x', label='Non Admis (entrainement)')\n",
    "ax.scatter(X_notes_test[oui_test, 0], \n",
    "           X_notes_test[oui_test, 1], \n",
    "           color='red', marker='o', label='Admis (test)')\n",
    "ax.scatter(X_notes_test[~oui_test, 0], \n",
    "           X_notes_test[~oui_test, 1], \n",
    "           color='red', marker='x', label='Non Admis (test)')\n",
    "\n",
    "# Créer l'espace des notes : entre 0 et 20 avec une résolution de 50\n",
    "xrange = np.linspace(0, 20, 50) # Note 1\n",
    "yrange = np.linspace(0, 20, 50) # Note 2\n",
    "\n",
    "# Dessiner la ligne de séparation dans une régression linéaire\n",
    "reglog1 = LogisticRegression(penalty=None)\n",
    "reglog1.fit(X_notes_train, Y_notes_train)\n",
    "dessiner2D(reglog1, ax, xrange, yrange, label='X')\n",
    "\n",
    "modeles = [reglog1]\n",
    "\n",
    "# Dessiner la ligne de séparation dans une régression polynomiale\n",
    "# Le modèle dans ce cas est un pipeline qui commence par créer des caractéristiques polynomiales\n",
    "# ensuite passe le résultat vers un modèle de régression logistique\n",
    "for i in range(len(degres)):\n",
    "    modele = make_pipeline(PolynomialFeatures(degree=degres[i], include_bias=False),\n",
    "                           LogisticRegression(penalty=None))\n",
    "    modele.fit(X_notes_train, Y_notes_train)\n",
    "    dessiner2D(modele, ax, xrange, yrange, couleur=couleurs[i+1], label='X^' + str(degres[i]))\n",
    "    modeles.append(modele)\n",
    "\n",
    "plt.xlabel('Note 1')\n",
    "plt.ylabel('Note 2')\n",
    "plt.legend(loc='upper right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dc6b28ab",
   "metadata": {},
   "source": [
    "**TODO: Analyser les résultats**\n",
    "\n",
    "- Que remarquez-vous (les nouveaux modèles ont-ils été capables d'améliorer le modèle initial: l'adjustement/fitting et la généralisation) ? \n",
    "- Donner une hypothèse (Quelle est la raison d'amélioration/détérioration ?) \n",
    "- Essayer de justifier cette hypothèse par ce que vous avez vu en cours.\n",
    "\n",
    "**Réponse**\n",
    "\n",
    "- On remarque sur le graphe que les trois modèles tentent de séparer les élèves admis des non admis. Sur ce graphe, on peut facilement voir que le modèle de régression linéaire sépare le mieux entre les deux classes de manière générale mais il est le moins ajusté au données d'entrainement. En revanche, le modèle polynomial de degré 3, se trompe sur quelques points et est plus ajustée aux données d'entrainement que la droite linéaire, et enfin le modèle de degré 5 est surajusté (overfitted) aux données d'entrainement et se trompe le plus sur la prédiction faite sur les données de test.\n",
    "- On suppose que la raison de détérioration est l'overfitting (surajustement) du modèle aux données d'entrainement. Celà pourrait être du à la capacité des caractéristiques polynomiales à capturer des relations plus complexes dans les données.\n",
    "- Lorsqu'on augmente le degré du polynôme pour modéliser les données, on introduit davantage de paramètres et de caractéristiques dans le modèle. Or les nouvelles caractéristiques ajoutées dépendent plus ou moins des caratéristiques d'origine (relation entre X et X²). Et donc le modèle trouve plus de relations entre les caratérisques d'origine (X) et les sorties (Y) et donc s'ajustura mieux aux données d'entrainement. Cet surajustement du modèle le plus souvent éloigne les prédictions du modèle des valeurs réelles de test."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cec7b167",
   "metadata": {},
   "source": [
    "#### II.2.3. Métriques d'évaluation du classement\n",
    "\n",
    "Nous allons continuer la comparaison entre les trois modèles de classement.\n",
    "Cette fois-ci, nous allons utiliser des métriques d'évaluation, parce que la méthode visuelle n'est pas toujours évidente surtout lorsqu'il y a plusieurs caractéristiques.\n",
    "Nous allons utiliser les métriques suivants :\n",
    "- Courbe ROC\n",
    "- Exactitude (Accuracy)\n",
    "$$Acc = \\frac{TP + TN}{TP + FP + FN + TN}$$\n",
    "- Précision, Rappel et F1-score\n",
    "$$P = \\frac{TP}{TP + FP}; R = \\frac{TP}{TP + FN}; F1 = \\frac{1}{\\frac{1}{2}\\frac{1}{P} + \\frac{1}{2}\\frac{1}{R}} = \\frac{2 P R}{P + R}$$\n",
    "- Corrélation de matthews\n",
    "$$CCM = \\frac{TP \\times TN - FP \\times FN}{\\sqrt{(TP + FP) (TP + FN) (TN + FP) (TN + FN)}}$$\n",
    "\n",
    "En plus, nous allons comparer ces trois modèles avec d'autres :\n",
    "- Un modèle alèatoire\n",
    "- Un modèle qui retourne toujours des 1 (classe positive)\n",
    "- Un modèle qui retourne toujours des 0 (classe négative)\n",
    "- Un modèle qui retourne l'inverse des sorties réelles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "03b93a7d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([0, 0, 0, 0, 1]),\n",
       " array([1., 1., 1., 1., 1.]),\n",
       " array([0., 0., 0., 0., 0.]))"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "\n",
    "class Aleatoire:\n",
    "    def predict(self, X):\n",
    "        return np.random.choice([0,1], size=len(X))\n",
    "    \n",
    "class Pos:\n",
    "    def predict(self, X):\n",
    "        return np.ones(len(X))\n",
    "\n",
    "class Neg:\n",
    "    def predict(self, X):\n",
    "        return np.zeros(len(X))\n",
    "\n",
    "class Inverse:\n",
    "    def predict(self, X):\n",
    "        return 1 - Y_notes_test\n",
    "\n",
    "modeles2 = modeles.copy()\n",
    "modeles2.append(Aleatoire())\n",
    "modeles2.append(Pos      ())\n",
    "modeles2.append(Neg      ())\n",
    "modeles2.append(Inverse  ())\n",
    "\n",
    "X_t = [0, 2, 3, 5, 6]\n",
    "\n",
    "modeles2[-4].predict(X_t), \\\n",
    "modeles2[-3].predict(X_t), \\\n",
    "modeles2[-2].predict(X_t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "4e7b0c59",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.metrics import roc_curve, auc\n",
    "from sklearn.metrics import accuracy_score\n",
    "from sklearn.metrics import precision_score\n",
    "from sklearn.metrics import recall_score\n",
    "from sklearn.metrics import f1_score\n",
    "from sklearn.metrics import matthews_corrcoef\n",
    "\n",
    "degres2 = ['X']\n",
    "for degre in degres:\n",
    "    degres2.append('X^' + str(degre))\n",
    "\n",
    "degres2 =  degres2  + ['aleatoire', 'uns', 'zeros', 'inverse']\n",
    "couleurs= ['red', 'magenta', 'blue', 'orange', 'cyan', 'green', 'purple']\n",
    "\n",
    "ACCs    = []\n",
    "Ps      = []\n",
    "Rs      = []\n",
    "F1s     = []\n",
    "MCCs    = []\n",
    "\n",
    "for degre, modele, couleur in zip(degres2, modeles2, couleurs):\n",
    "    y_score     = modele.predict(X_notes_test)\n",
    "    fpr, tpr, _ = roc_curve(Y_notes_test, y_score)\n",
    "    roc_auc     = auc(fpr, tpr)\n",
    "    plt.plot(fpr, tpr, color=couleur, label='ROC de \"{0}\" (surface = {1:0.2f})'.format(degre, roc_auc))\n",
    "    \n",
    "    ACCs.append(accuracy_score   (Y_notes_test, y_score                 ))\n",
    "    Ps  .append(precision_score  (Y_notes_test, y_score, zero_division=0))\n",
    "    Rs  .append(recall_score     (Y_notes_test, y_score                 ))\n",
    "    F1s .append(f1_score         (Y_notes_test, y_score                 ))\n",
    "    MCCs.append(matthews_corrcoef(Y_notes_test, y_score                 ))\n",
    "\n",
    "plt.plot([0, 1], [0, 1], 'k--')\n",
    "plt.xlim([-0.05, 1.05])\n",
    "plt.ylim([-0.05, 1.05])\n",
    "plt.xlabel('Taux de faux positifs')\n",
    "plt.ylabel('Taux de vrais positifs')\n",
    "plt.title('Courbes ROC')\n",
    "plt.legend(loc='lower right')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f777e096",
   "metadata": {},
   "source": [
    "**TODO: Analyser les résultats**\n",
    "\n",
    "- Quelle est le meilleure modèle selon ROC ? Expliquer.\n",
    "- Quelle est le plus mauvais modèle selon ROC ? Expliquer.\n",
    "\n",
    "**Réponse**\n",
    "\n",
    "- Le meilleur modèle selon ROC est le modèle linéaire \"X\". Ce modèle présente une courbe ROC parfaite (surface = 1.0), ce qui signifie que le taux de vrais positifs est à son maximum (1.0), et donc le modèle est capable de bien classifier les individus à la classe 1 (respectivement il est aussi capable de bien classer les individus à la classe 0). Donc le modèle est capable de parfaitement distinguer les deux classes.\n",
    "- Le plus mauvais modèle selon ROC est le modèle \"inverse\". Ce modèle présente une courbe ROC de surface = 0.0, ce qui signifie que le taux de faux positifs est à son maximum (1.0), et donc le modèle donne toujours des prédictions fausses pour les individus qui réellement appartiennent à la classe 1 (respectivement il donne aussi toujours des prédictions fausses pour les individus qui réellement appartiennent à la classe 0). Donc le modèle n'attribue aucun individu à sa bonne classe."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "c8ea79e6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Degré</th>\n",
       "      <th>Exactitude</th>\n",
       "      <th>Précision</th>\n",
       "      <th>Rappel</th>\n",
       "      <th>F1 score</th>\n",
       "      <th>matthews</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>X</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>X^3</td>\n",
       "      <td>0.75</td>\n",
       "      <td>0.818182</td>\n",
       "      <td>0.750000</td>\n",
       "      <td>0.782609</td>\n",
       "      <td>0.492366</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>X^5</td>\n",
       "      <td>0.80</td>\n",
       "      <td>0.833333</td>\n",
       "      <td>0.833333</td>\n",
       "      <td>0.833333</td>\n",
       "      <td>0.583333</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>aleatoire</td>\n",
       "      <td>0.65</td>\n",
       "      <td>0.666667</td>\n",
       "      <td>0.833333</td>\n",
       "      <td>0.740741</td>\n",
       "      <td>0.235702</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>uns</td>\n",
       "      <td>0.60</td>\n",
       "      <td>0.600000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.750000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>zeros</td>\n",
       "      <td>0.40</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>inverse</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>-1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       Degré  Exactitude  Précision    Rappel  F1 score  matthews\n",
       "0          X        1.00   1.000000  1.000000  1.000000  1.000000\n",
       "1        X^3        0.75   0.818182  0.750000  0.782609  0.492366\n",
       "2        X^5        0.80   0.833333  0.833333  0.833333  0.583333\n",
       "3  aleatoire        0.65   0.666667  0.833333  0.740741  0.235702\n",
       "4        uns        0.60   0.600000  1.000000  0.750000  0.000000\n",
       "5      zeros        0.40   0.000000  0.000000  0.000000  0.000000\n",
       "6    inverse        0.00   0.000000  0.000000  0.000000 -1.000000"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame({\n",
    "    'Degré'         : degres2,\n",
    "    'Exactitude'    : ACCs   ,\n",
    "    'Précision'     : Ps     ,\n",
    "    'Rappel'        : Rs     ,\n",
    "    'F1 score'      : F1s    ,\n",
    "    'matthews'      : MCCs   ,\n",
    "})"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f01b1f47",
   "metadata": {},
   "source": [
    "**TODO: Analyser les résultats**\n",
    "\n",
    "- Quelle est le modèle qui illustre l'inefficacité de l'exactitude dans le classement binaire ? Expliquer.\n",
    "- Quelle est la métrique qui nous indique qu'un modèle a la capacité de faire de bonnes prédictions en inversant les classes ? Expliquer.\n",
    "- \"X^3\" vs. \"uns\" : quelle est le modèle parmi les deux qui détecte plus de cas admis ? Quelle est la métrique qui assure cela ?\n",
    "- \"X^3\" vs. \"uns\" : quelle est le modèle parmi les deux qui assure que les admis détectés sont vraiment admis ? Quelle est la métrique qui assure cela ?\n",
    "- F1 score : pourquoi nous utilisons la moyenne harmonique entre la précision et le rappel et pas la moyenne arithmétique ? \n",
    "\n",
    "**Réponse**\n",
    "\n",
    "- Le modèle qui illustre l'inefficacité de l'exactitude dans le classement binaire est le modèle \"uns\", il obtient une exactitude de \"0.6\" ce qui semble plus ou moins élevé pour un tel modèle. Le modèle \"uns\" prédit toujours correctement la classe positive, mais dans le cas où sur les données de test, le nombre d'individus appartenant réellement à la classe positive est plus grand que ceux appartenant à la classe négative, l'exactitude sera assez grande malgrès que le modèle ne fait que prédire la classe positive et est incapable de distinguer les individus de la classe négative. Ce qui rend l'exactitude inefficace dans ce cas.\n",
    "- La métrique qui indique la capacité d'un modèle à faire de bonnes prédictions en inversant les classes est le coefficient de corrélation de Matthews (MCC). Dans ce cas, le modèle \"inverse\" obtient un MCC de -1.0. Si le modèle fait de bonnes prédictions en inversant les classes, on a donc: TP = TF = 0 (le modèle ne fait aucune prédiction correcte). En replaçant cela dans la formule du MCC, on obtient (ce qui fait que l'MCC sera toujours égal à -1 dans ce cas):\n",
    "$$CCM = \\frac{- FP \\times FN}{\\sqrt{(FP) (FN) (FP) (FN)}} = \\frac{- FP \\times FN}{\\sqrt{FP ^ 2 \\times FN ^ 2}} = \\frac{- FP \\times FN}{FP \\times FN} = -1$$\n",
    "- Le modèle \"uns\" détecte plus de cas admis avec un rappel de 1.0, car il prédit toujours la classe positive, identifiant tous les vrais positifs. En revanche, \"X^3\" a un rappel de 0.75, détectant 75% des vrais positifs. La métrique qui assure cela est le rappel (un rappel élevé signifie que le modèle réussit à capturer un pourcentage élevé de cas positifs parmi tous les cas positifs réels).\n",
    "- Le modèle qui assure que les cas admis détectés sont vraiment admis est le modèle \"X^3\". Bien que le modèle \"uns\" détecte tous les cas positifs, il a une précision de 0.6, ce qui signifie que sur l'ensemble des cas qu'il prédit comme positifs, seuls 60% sont réellement positifs. En revanche, \"X^3\" a une précision de 0.818, ce qui indique que parmi les cas prédits positifs, 81.8% sont réellement positifs. La métrique qui assure cela est la précision (une précision élevée indique que le modèle a plus de vrais positifs parmi les prédictions positives).\n",
    "- Si on utilise la moyenne arithmétique, et une des métriques (rappel, précision) est élevée et l'autre est basse, la moyenne arithmétique pourrait sembler acceptable, masquant la mauvaise performance pour la métrique la plus petite. En revanche, en utilisant la moyenne harmonique entre la précision et le rappel, on accorde plus de poids aux résultats les plus faibles. Ainsi, si un modèle a une excellente précision mais un rappel très bas (ou vice versa), la moyenne harmonique sera plus basse en conséquence, reflétant la mauvaise performance sur l'une des métriques. Et donc c'est plus interessant d'utiliser la moyenne harmonique plutôt que l'arithmétique pour le F1 score."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "b50c8f20",
   "metadata": {},
   "outputs": [],
   "source": []
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