{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "a35eeb9f-df70-4ab1-a243-2d2025888eb0",
   "metadata": {},
   "source": [
    "# Exercice 1\n",
    "1) Combien y a t'il de dominos dans un jeu classique ?  \n",
    "Un jeu de dominos classique est composé de 28 pièces dont chaque moitié comporte un certain nombre de petits points allant de 0 à 6, sans doublons, ce qui donne 7 * 4 = 28 pièces.\n",
    "\n",
    "2) Pourquoi est-il possible que le jeu s'arrête sans avoir posé tous les dominos ?  \n",
    "Il est possible que le jeu s'arrete avant d'avoir posé tout les dominos car chaque moitié comporte un certain nombre de petits points allant de 0 à 6. Si les combinaisons de dominos disponibles dans la pioche ne sont pas compatibles avec les extrémités de la chaîne déjà construite, le jeu peut se terminer sans avoir posé tous les dominos. Cela dépend de la chance et de l'ordre dans lequel les dominos sont tirés.\n",
    "\n",
    "3) Pourquoi X et Y sont des variables aléatoires ?  \n",
    "X et Y sont des variables aléatoires car leur valeur dépend du hasard et des choix effectués tout au long du jeu. La variable aléatoire X représente le nombre de dominos posés dans la chaîne, et elle dépend du nombre de dominos tirés et de la possibilité de les placer à chaque étape. De même, la variable aléatoire Y représente le nombre de points restants dans la pioche, ce qui dépend également de la manière dont les dominos sont tirés et placés. En raison de la nature aléatoire du jeu, X et Y prennent des valeurs différentes à chaque partie, d'où leur caractère aléatoire. Pour comprendre leur comportement, il est nécessaire d'étudier leur distribution de probabilité."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f8b9e53-7277-4663-ad35-0db9e824d45f",
   "metadata": {},
   "source": [
    "# Exercice 2\n",
    "- Quelle structure de données pour représenter la pioche de dominos restants ?\n",
    "    - La structure nécéssaire est une file car on insere en queue mais on supprime en tete\n",
    "- Quelle structure de données pour représenter la chaîne de dominos déjà construite? (Sachant qu'il suffit de considérer l'information pertinente pour le déroulement du jeu.)\n",
    "    - Une liste car c'est une fassons simple de stocker les dominos mis en place sur le tapis\n",
    "- Comment savoir si le jeu est \u001c",
    "\n",
    "fini ?\n",
    "    - si on ne peut plus inserer en tete ou en queue les dominos de la pioche.\n",
    "- Est-il éventuellement utile d'écrire certaines sous-fonctions, afin de clarifier le code ?  \n",
    "    - Ca peut être plus simple à comprendre le code, notamment pour le comptage de Y."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "060f3b6e-ed57-4ecc-9338-f2491f54bd74",
   "metadata": {},
   "source": [
    "exemple de file en python :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "bee8d798-d9bb-464c-9b66-329678fa2fda",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "[2, 3]\n"
     ]
    }
   ],
   "source": [
    "queue = []                 # la file est vide\n",
    "\n",
    "queue.append(1)            # la file contient [1]\n",
    "queue.append(2)            # la file contient [1, 2]\n",
    "queue.append(3)            # la file contient [1, 2, 3]\n",
    "\n",
    "result = queue.pop(0)      # la file contient [2, 3]\n",
    "\n",
    "print(result)\n",
    "print(queue)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5fabca55-4ebf-4499-b652-86844be439e5",
   "metadata": {},
   "source": [
    "**Initialisation et affichage de la pioche**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "fe55883a-6887-43dd-9498-5333a51799e2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1, 1]\n",
      "[1, 2]\n",
      "[1, 3]\n",
      "[1, 4]\n",
      "[1, 5]\n",
      "[1, 6]\n",
      "[2, 2]\n",
      "[2, 3]\n",
      "[2, 4]\n",
      "[2, 5]\n",
      "[2, 6]\n",
      "[3, 3]\n",
      "[3, 4]\n",
      "[3, 5]\n",
      "[3, 6]\n",
      "[4, 4]\n",
      "[4, 5]\n",
      "[4, 6]\n",
      "[5, 5]\n",
      "[5, 6]\n",
      "[6, 6]\n"
     ]
    }
   ],
   "source": [
    "import random\n",
    "\n",
    "# initialisation de la pioche contenant 28 pièces\n",
    "pioche = [[i, j] for i in range(1,7) for j in range(i, 7)]\n",
    "\n",
    "# Exemple d'utilisation : affichez la file de dominos\n",
    "for domino in pioche:\n",
    "    print(domino)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "09689b16-24dc-4025-bad9-90d0fe385b6b",
   "metadata": {},
   "outputs": [],
   "source": [
    "def comptePoints(pioche):\n",
    "    return sum(sum(domino) for domino in pioche)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "id": "93e0c8d5-3a25-4277-9791-8e5d0fc67620",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X = 14, Y = 54\n"
     ]
    }
   ],
   "source": [
    "# Fonction pour simuler une partie du jeu de dominos\n",
    "def une_chaine_domino():\n",
    "    # Liste représentant les dominos sur le jeu\n",
    "    tapis = []\n",
    "\n",
    "    #initialisation d'une variable pour compter le nombre de pioche dans la pioche\n",
    "    cpt = 0\n",
    "\n",
    "    Y = 0\n",
    "    \n",
    "    # Liste représentant la pioche de dominos restants\n",
    "    pioche = [(i, j) for i in range(1, 7) for j in range(i, 7)]\n",
    "    random.shuffle(pioche)\n",
    "\n",
    "    # Tant que la pioche n'est pas vide et qu'on peut poser des dominos\n",
    "    while pioche:\n",
    "        domino = pioche.pop(0)  # Tirer un domino au hasard\n",
    "        #pioche.remove(domino)  # Retirer le domino de la pioche\n",
    "\n",
    "        if not tapis:  # Si c'est le premier domino, ajoutez-le directement\n",
    "            tapis.append(domino)\n",
    "        else:\n",
    "            # Vérifiez si le domino peut être placé à l'une des extrémités de la chaîne\n",
    "            if domino[0] == tapis[0][0] or domino[1] == tapis[0][0]:\n",
    "                tapis.insert(0, domino)  # Placez-le au début de la chaîne\n",
    "                cpt = 0;\n",
    "            elif domino[0] == tapis[-1][1] or domino[1] == tapis[-1][1]: # On regarde le second argument du premier couple du tapis\n",
    "                tapis.append(domino)  # Placez-le à la fin de la chaîne\n",
    "                cpt = 0;\n",
    "            else:\n",
    "                pioche.append(domino)\n",
    "                cpt = cpt + 1;\n",
    "                if(cpt > len(pioche)):\n",
    "                    break  # Si après un tour entier de la pioche est éfféctué sans pour voir placer un domino\n",
    "\n",
    "    # Valeur de X : nombre de dominos posés dans la chaîne\n",
    "    X = len(tapis)\n",
    "\n",
    "    # Valeur de Y : nombre de points restants dans la pioche\n",
    "    for i in pioche :\n",
    "        Y = Y + i[0] + i[1]\n",
    "\n",
    "    return X, Y\n",
    "\n",
    "# Utilisation de la fonction\n",
    "X, Y = une_chaine_domino()\n",
    "print(f\"X = {X}, Y = {Y}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0e26c4cc-b76f-40b6-9146-ee2ffb396909",
   "metadata": {},
   "source": [
    "# Exercice 3 (Analyse probabiliste).  \n",
    "Simulez un grand nombre de réalisations du jeu (au moins 10000).  \n",
    "Puis, à l'aide des méthodes déjà vues en cours et en TP :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "id": "c86fee95-c245-407b-b93b-4c53661b08a2",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Moyenne de X : 13.7448\n",
      "Moyenne de Y : 51.7941\n"
     ]
    }
   ],
   "source": [
    "# Nombre de réalisations du jeu\n",
    "nombre_de_realisations = 10000\n",
    "\n",
    "# Liste pour stocker les résultats des n réalisations\n",
    "resultats = []\n",
    "\n",
    "# Simulez le jeu un grand nombre de fois et stockez les résultats\n",
    "for _ in range(nombre_de_realisations):\n",
    "    X, Y = une_chaine_domino()\n",
    "    resultats.append((X, Y))\n",
    "\n",
    "# Vous pouvez maintenant analyser les résultats pour obtenir des statistiques\n",
    "# Par exemple, vous pouvez calculer la moyenne et l'écart-type pour X et Y.\n",
    "moyenne_X = sum(X for X, Y in resultats) / nombre_de_realisations\n",
    "moyenne_Y = sum(Y for X, Y in resultats) / nombre_de_realisations\n",
    "\n",
    "# Affichez les résultats statistiques\n",
    "print(f\"Moyenne de X : {moyenne_X}\")\n",
    "print(f\"Moyenne de Y : {moyenne_Y}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77af5a0a-2173-4e45-a519-4e877f728b18",
   "metadata": {},
   "source": [
    "1. Estimer et représenter la loi de probabilité de la variable X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "id": "ace07f8d-410d-4005-8188-d94264dc53a6",
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "# Extraire les valeurs de X à partir des résultats\n",
    "valeurs_X = [X for X, Y in resultats]\n",
    "\n",
    "# Estimation de la loi de probabilité de X\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.hist(valeurs_X, bins=range(min(valeurs_X), max(valeurs_X) + 1), density=True, alpha=0.7, edgecolor='black')\n",
    "plt.title('Estimation de la loi de probabilité de X')\n",
    "plt.xlabel('Valeurs de X')\n",
    "plt.ylabel('Probabilité')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b3857ed-b456-40ab-b7fa-575b7dd46b83",
   "metadata": {},
   "source": [
    "2. Calculer et tracer la fonction de répartition de X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "id": "62742df7-445f-48b9-8801-626a14137397",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "# Calcul de la fonction de répartition de X\n",
    "valeurs_X_triees = sorted(valeurs_X)\n",
    "fonction_de_repartition_X = np.arange(len(valeurs_X_triees)) / len(valeurs_X_triees)\n",
    "\n",
    "# Traçage de la fonction de répartition de X\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(valeurs_X_triees, fonction_de_repartition_X, marker='o', linestyle='--', color='b')\n",
    "plt.title('Fonction de répartition de X')\n",
    "plt.xlabel('Valeurs de X')\n",
    "plt.ylabel('Probabilité cumulée')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a2ad312-ce07-4e6c-bbc8-32dffc8e1625",
   "metadata": {},
   "source": [
    "3. Estimer l'espérance de X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "id": "b9e399bf-d2c0-4112-9de4-531b2cbc08cb",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Espérance de X : 13.7448\n"
     ]
    }
   ],
   "source": [
    "# Estimation de l'espérance de X\n",
    "esperance_X = np.mean(valeurs_X)\n",
    "print(f\"Espérance de X : {esperance_X}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "960e3b9c-624d-426a-8940-e194d816eaa1",
   "metadata": {},
   "source": [
    "4. Estimer la variance de X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "id": "ca825519-d205-4f18-ad8d-490da5ba5058",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance de X : 7.432672959999999\n"
     ]
    }
   ],
   "source": [
    "# Estimation de la variance de X\n",
    "variance_X = np.var(valeurs_X)\n",
    "print(f\"Variance de X : {variance_X}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7963e4a2-7435-4598-8c49-6050fcb4167b",
   "metadata": {},
   "source": [
    "5. Mêmes questions pour la variable Y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "id": "2449c9ab-2193-4bbc-9526-12df626063e8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Extraire les valeurs de Y à partir des résultats\n",
    "valeurs_Y = [Y for X, Y in resultats]\n",
    "\n",
    "# Estimation de la loi de probabilité de Y\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.hist(valeurs_Y, bins=range(min(valeurs_Y), max(valeurs_Y) + 1), density=True, alpha=0.7, edgecolor='black')\n",
    "plt.title('Estimation de la loi de probabilité de Y')\n",
    "plt.xlabel('Valeurs de Y')\n",
    "plt.ylabel('Probabilité')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "id": "d14357e5-0d2f-4861-8593-49194aff2426",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calcul de la fonction de répartition de Y\n",
    "valeurs_Y_triees = sorted(valeurs_Y)\n",
    "fonction_de_repartition_Y = np.arange(len(valeurs_Y_triees)) / len(valeurs_Y_triees)\n",
    "\n",
    "# Traçage de la fonction de répartition de Y\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(valeurs_Y_triees, fonction_de_repartition_Y, marker='o', linestyle='--', color='b')\n",
    "plt.title('Fonction de répartition de Y')\n",
    "plt.xlabel('Valeurs de Y')\n",
    "plt.ylabel('Probabilité cumulée')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "378db2ce-e8a3-4b88-9075-30a127e72421",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Espérance de Y : 51.7941\n"
     ]
    }
   ],
   "source": [
    "# Estimation de l'espérance de Y\n",
    "esperance_Y = np.mean(valeurs_Y)\n",
    "print(f\"Espérance de Y : {esperance_Y}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "61e30edb-0da8-4bc7-b05c-fa60bd63734f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance de Y : 466.43230518999997\n"
     ]
    }
   ],
   "source": [
    "# Estimation de la variance de Y\n",
    "variance_Y = np.var(valeurs_Y)\n",
    "print(f\"Variance de Y : {variance_Y}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f1dfb9e6-76fe-4aa2-abad-823d30e9e70f",
   "metadata": {},
   "source": [
    "6. Estimer la probabilité de succès au jeu"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "6d9906a0-0abb-4da7-b072-0d3dd9e1ffee",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nombre de jeux finis : 0\n",
      "Nombre de jeux non finis : 10000\n"
     ]
    }
   ],
   "source": [
    "# Définition du nombre de dominos dans un jeu classique\n",
    "nombre_de_dominos = 28\n",
    "\n",
    "# Compter le nombre de jeux finis (X égal au nombre total de dominos)\n",
    "jeux_finis = sum(1 for X, Y in resultats if X == nombre_de_dominos)\n",
    "\n",
    "# Compter le nombre de jeux non finis (X différent de 28)\n",
    "jeux_non_finis = nombre_de_realisations - jeux_finis\n",
    "\n",
    "print(f\"Nombre de jeux finis : {jeux_finis}\")\n",
    "print(f\"Nombre de jeux non finis : {jeux_non_finis}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "b8ab8855-2232-41d3-8886-f87f815234b1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probabilité de succès au jeu : 0.0\n"
     ]
    }
   ],
   "source": [
    "# Estimer la probabilité de succès\n",
    "probabilite_de_succes = (jeux_finis / nombre_de_realisations) * 100\n",
    "print(f\"Probabilité de succès au jeu : {probabilite_de_succes}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b00417a8-24aa-4a24-a490-7a2eb13056bc",
   "metadata": {},
   "source": [
    "7. Estimer le nombre médian de points restants dans la pioche"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "49adddee-61a7-4cd5-ba93-c1648e4c22d4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Nombre médian de points restants dans la pioche : 51.0\n"
     ]
    }
   ],
   "source": [
    "# Calcul de la médiane des points restants dans la pioche (Y)\n",
    "median_points_restants = np.median(valeurs_Y)\n",
    "print(f\"Nombre médian de points restants dans la pioche : {median_points_restants}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8bf0079e-641d-499e-82fa-7a5f39194498",
   "metadata": {},
   "source": [
    "# Exercice 4 (Covariance et corrélation) :"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b52ef252-f23b-4087-8158-052dc6de28dc",
   "metadata": {},
   "source": [
    "1) Effectuer 200 réalisations du jeu et représenter les valeurs correspondantes de X et Y sous la forme d'un nuage de points (avec un point (x,y) pour chaque réalisation de X et Y observée). Interprétez le résultat."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "c66c8f57-b527-4d67-b184-2b16e764d744",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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FClBbt27N9DnnJPbp06enO7eykprcKqXUgw8+qNq3b6+UUsput6syZcqoSZMmZZjcunpe5uRamlFym9Fr0blzZ1W5cuU0y1w991yNOyOpn2fdu3dP8zqMHTtWAWmS29wcJ1V0dLQqW7as83rhasOCO0i3BDerXLkyjz/+OIsWLeLChQu53t+Nd9larVauXbtG1apVCQwMZM+ePc51a9eupXnz5tSvX9+5LDg4mH79+qXZ3/r164mKiuLRRx/l6tWrzh+j0UizZs3YtGlTlvH8/PPP3HXXXTRt2tS5rGTJknl+nFRPP/00ZrPZ+fjZZ5/FZDLx888/A7BhwwZSUlIYMWJEmj5CTz31FP7+/vz000/ZHuPhhx8mKCjI+Tj1a+J//vkn220DAwOJj49P87WrK37++WdMJlOaTvtGo5HnnnsuTbnIyEh+/fVX+vTpQ2xsrLMer127RufOnTl+/HiWd9rfyN/f39mXsFOnTi5to5Tim2++oUePHiil0ryWnTt3Jjo6Os15eCvefPNNQkJCMBgMzJgxw+XtbnxvXL9+nejoaFq3bp0mnurVq1O/fn2+/PJL5zK73c7KlSvp0aOHcx9ff/01AQEBdOzYMc1zbNSoEb6+vs7zdf369cTGxjJmzJh0ffdcHWKoQ4cOlCxZkvDwcB588EF8fHxYvXo15cqVA3L2mrv6vk9VqVIlOnfunGbZ119/TevWrQkKCkrz3Dt06IDdbmfLli2Aa+d6YGAghw8f5vjx4y7VBeB8L48cOTLN8lGjRgGkew/XrFnT+R4F/fpzxx13uPR+zY1Bgwal6Yt783Vi3759zq/Yr1275qzH+Ph42rdvz5YtW5xfF7t6Xc+Mh4cHgwYNSrPs66+/5s4776RGjRppXsd77rkHIMtrbk5iz42+ffuyefNmLl68yK+//srFixcz7ZLg6nnp6rU0Mze+FtHR0Vy9epW2bdvyzz//EB0dnaasK+eeq3FnJPXz7LnnnktzPRkxYsQt109W/P39mTlzJpGRkTz88MPprg2FicndAQj9jszly5fz9ttvu9T3MiuJiYlMnTqVpUuXcu7cOZRSznU3vvFOnz5N8+bN021/8x3WqR86qRe8m/n7+2cZz+nTp2nWrFm65XfccUeeHidVtWrV0jz29fUlNDTU2cfr9OnTGR7fYrFQuXJl5/qslC9fPs3j1EQ3o76WNxs6dChfffUVXbt2JSwsjE6dOtGnTx+6dOmS5XanT58mNDQUX1/fNMtvfh4nTpxAKcX48eMZP358hvu6fPkyYWFh2cY6fPhwDAYDFSpUYNSoUXTo0CHNHw4ZuXLlClFRUSxatIhFixZlevzc8Pf354477uDq1auULl3a5e1+/PFHpkyZwr59+9L0Kbw5yXz44YcZO3Ys586dIywsjM2bN3P58mUefvhhZ5njx48THR1NqVKlMjxW6nNM7Rebm6H95s6dS/Xq1YmOjuajjz5iy5YtaW50zMlr7ur7PlWlSpXSLTt+/DgHDhzIdJix1Ofuyrk+efJk7r//fqpXr07t2rXp0qULjz/+eJZ9+E6fPo3BYEgXc5kyZQgMDEz3Hr75/Qr6e9aV92tuZHedSL3mDRgwINN9REdHExQU5PJ1PTNhYWHpbno7fvw4R44cyfZ1zEhOYs+Nbt264efnx5dffsm+ffto0qQJVatWzbDPrqvnpavX0sxs3bqVCRMmsH379nQ35kVHRxMQEOB87Mq552rcGUk912/+3CtZsmS6us/NcW6Ueq/ErY7FXFAkuS0EKleuzGOPPcaiRYsYM2ZMuvWZtfDY7fZ0y5577jmWLl3KiBEjaN68OQEBAWiaxiOPPHJLf0mnbrN8+XLKlCmTbr3JlDenUEEdJy8YjcYMl9/4gZOZUqVKsW/fPtatW8eaNWtYs2YNS5cupX///nz88ce5ji21Hl966aVM/6p2ZYiob7/9ltWrVzNz5kyqVatG9+7dmT59uvNGlOyO/9hjj2X6weeOmw9+//137rvvPtq0acO8efMIDQ3FbDazdOnSdDd2Pfzww7z66qt8/fXXjBgxgq+++oqAgIA0SZnD4aBUqVJ89tlnGR4vL8eXbdq0qfODpGfPnrRq1Yq+ffty7NgxfH198+w1z0hG4606HA46duzI6NGjM9ymevXqgGvneps2bTh58iTff/89v/zyC0uWLGHGjBksWLCAwYMHZxmbqy3fuXm/5kZ2x0193aZPn56mJf1GqQlYbq/rmb2OderU4f33389wm/Dw8Ez3l5PYc8PDw4MHHniAjz/+mH/++SfLscNdPS9z4+TJk7Rv354aNWrw/vvvEx4ejsVi4eeff2bGjBnpXgtXzr2CiLsgj1NYFJ6M4TY3btw4Pv30U6ZNm5ZuXepfYDffzZlRK+PKlSsZMGAA7733nnNZUlJSum0rVKiQ4Z27Ny+rUqUKoH9QdejQwaXncvNxMvrK8ebxY3N7nFTHjx9Pc7d7XFwcFy5coFu3bs54Uo9/47A7KSkpnDp1KlfHvlFWH7wWi4UePXrQo0cPHA4HQ4cOZeHChYwfPz7TJKRChQps3LiRuLi4NB8aN9dj6nMym823/FxiY2N5/vnnadiwIcOHD8doNNK7d2+mTJnCo48+mmFrXqqSJUvi5+eH3W7P9vgFOfPPN998g6enJ+vWrUvT6rl06dJ0ZStVqkTTpk358ssvGT58ON9++y09e/ZMs12VKlXYsGEDLVu2zHLA/dTz+tChQ3ky7qzRaGTq1KncfffdzJkzhzFjxuToNXf1fZ+VKlWqEBcX59L55cq5HhwczKBBgxg0aBBxcXG0adOGiRMnZprcVqhQAYfDwfHjx7nzzjudyy9dukRUVJTzPV7YpZ4b/v7+2dalq9f1nB5///79tG/fPsfvxZzEntv3ed++ffnoo48wGAw88sgjWcbkynnp6rU0Iz/88APJycmsXr06Tausq93mchN3RlLP9ePHj6f5PLty5Uq6byZyc5yiSPrcFhJVqlThscceY+HChVy8eDHNOn9/f0qUKJGuT8y8efPS7cdoNKZrkZg9e3a6Vt7OnTuzffv2NAPoR0ZGpmuJ6ty5M/7+/rz11ltYrdZ0x7ty5UqWz6tbt278+eef/PXXX2m2yevjpFq0aFGa7efPn4/NZqNr166A3n/RYrEwa9asNPX04YcfEh0dne34ia7y8fEB0v9Bcu3atTSPDQaDsyUzq+F3unXrhs1mSzPkjN1uZ/bs2WnKlSpVinbt2rFw4cIM+3C7Uo/jxo3jwoULLFy40Nny8MEHH2A0GrOdrSk1Ef7mm284dOhQlsfPrI7yg9FoRNO0NO+DiIgIVq1alWH5hx9+mD///JOPPvqIq1evpumSANCnTx/sdjtvvPFGum1tNpvzOXXq1Ak/Pz+mTp2abtKFW205bNeuHU2bNmXmzJkkJSXl6DV39X2flT59+rB9+3bWrVuXbl1UVBQ2mw1w7Vy/uYyvry9Vq1bN9r0AMHPmzDTLU1sg8+o9nN8aNWpElSpVePfdd4mLi0u3/sbXzdXrek706dOHc+fOsXjx4nTrEhMTiY+Pz5PYc/s+v/vuu3njjTeYM2dOht/qpXL1vHT1WpqR1Ovhzd1CMvoj2VWuxp2R1K5is2fPThPTze+N3B6nKJKW20LktddeY/ny5Rw7doxatWqlWTd48GDefvttBg8eTOPGjdmyZUu6GaQA7r33XpYvX05AQAA1a9Zk+/btbNiwgZCQkDTlRo8ezaeffkrHjh157rnn8PHxYcmSJZQvX57IyEjnX9v+/v7Mnz+fxx9/nIYNG/LII49QsmRJzpw5w08//UTLli2ZM2dOps9p9OjRLF++nC5duvDCCy/g4+PDokWLqFChAgcOHHCWy+1xUqWkpNC+fXv69OnDsWPHmDdvHq1ateK+++4D9JbFV199lUmTJtGlSxfuu+8+Z7kmTZrw2GOPZXsMVzRq1AiA559/ns6dO2M0GnnkkUcYPHgwkZGR3HPPPZQrV47Tp08ze/Zs6tevn6YV6mY9evSgZcuWjBkzhoiICGrWrMm3336bYX+7uXPn0qpVK+rUqcNTTz1F5cqVuXTpEtu3b+fff/9l//79mR5n9+7dzJ07l2HDhqXpUxUWFsbkyZMZOXIk33zzDb179850H2+//TabNm2iWbNmPPXUU9SsWZPIyEj27NnDhg0biIyMBPQ/6AIDA1mwYAF+fn74+PjQrFmzLFuGb1X37t15//336dKlC3379uXy5cvMnTuXqlWrpjkPU/Xp04eXXnqJl156ieDg4HStHW3btmXIkCFMnTqVffv20alTJ8xmM8ePH+frr7/mgw8+4MEHH8Tf358ZM2YwePBgmjRpQt++fQkKCmL//v0kJCTccleUl19+mYceeohly5bxzDPPuPyau/q+z+7Yq1ev5t5772XgwIE0atSI+Ph4Dh48yMqVK4mIiKBEiRIunes1a9akXbt2NGrUiODgYHbt2sXKlSuz/COqXr16DBgwgEWLFhEVFUXbtm3566+/+Pjjj+nZs2eG4xTnxq5du5xje96oXbt2tGrV6pb3azAYWLJkCV27dqVWrVoMGjSIsLAwzp07x6ZNm/D393fO0OXqdT0nHn/8cb766iueeeYZNm3aRMuWLbHb7Rw9epSvvvrKOb5xbmNPvRa+9tprPPLII5jNZnr06OFMel2pp3HjxmVbztXzMifX0pt16tTJ+W3EkCFDiIuLY/HixZQqVeqWbwh3Ne6MlCxZkpdeeompU6dy77330q1bN/bu3cuaNWvSbZOb4xRJBT9Ag8hs/Eql/n/8xhuHAlNKH37kySefVAEBAcrPz0/16dNHXb58Od1QYNevX1eDBg1SJUqUUL6+vqpz587q6NGjqkKFCmmGBVFKqb1796rWrVsrDw8PVa5cOTV16lQ1a9YsBaiLFy+mKbtp0ybVuXNnFRAQoDw9PVWVKlXUwIED1a5du7J9vgcOHFBt27ZVnp6eKiwsTL3xxhvqww8/zHB4mFs9Tmqd/vbbb+rpp59WQUFBytfXV/Xr109du3YtXfk5c+aoGjVqKLPZrEqXLq2effZZdf369TRlMhsK7MbhZ1Ld/DrYbDb13HPPqZIlSypN05zDyaxcuVJ16tRJlSpVSlksFlW+fHk1ZMiQdOOqZuTatWvq8ccfV/7+/iogIEA9/vjjau/evRkOp3Xy5EnVv39/VaZMGWU2m1VYWJi699571cqVKzPdv81mUw0bNlRly5ZV0dHRGa6vX7++KleunIqNjc0y1kuXLqlhw4ap8PBwZTabVZkyZVT79u3VokWL0pT7/vvvVc2aNZXJZMrRsGA3D5fnig8//FBVq1ZNeXh4qBo1aqilS5dmONRPqpYtW2Y45NSNFi1apBo1aqS8vLyUn5+fqlOnjho9erQ6f/58mnKrV69WLVq0UF5eXsrf3181bdpUff7551nGm9V1wm63qypVqqgqVao4h9py9TV39X1foUKFTIfpio2NVa+++qqqWrWqslgsqkSJEqpFixbq3XffdQ7F58q5PmXKFNW0aVMVGBiovLy8VI0aNdSbb76ZZji/jF4jq9WqJk2apCpVqqTMZrMKDw9Xr776apqh0LJ6DjcP35UZINOfN954I8N9pQ7HdeOYyEplPqTj3r171QMPPKBCQkKUh4eHqlChgurTp4/auHGjs4yr1/XMhgLL7L2SkpKipk2bpmrVqqU8PDxUUFCQatSokZo0aVKG14CbuRK7UvowVGFhYcpgMGQ7LNiNQ4FlJrNrsSvnpVKuX0szOvdWr16t6tatqzw9PVXFihXVtGnT1EcffZThUHqunnuuxp0Ru92uJk2apEJDQ5WXl5dq166dOnToUIaf+bk5TqqsPgcLE02pfO5VL4qUESNGsHDhQuLi4jLtDF8YLVu2jEGDBrFz585CfxenEIVNUX3fCyFERqTP7W3s5nnir127xvLly2nVqpV8wAlRTMn7XghR3Emf29tY8+bNadeuHXfeeSeXLl3iww8/JCYmJtOxMoUQRZ+874UQxZ0kt7exbt26sXLlShYtWoSmaTRs2JAPP/yQNm3auDs0IUQ+kfe9EKK4kz63QgghhBCi2JA+t0IIIYQQotiQ5FYIIYQQQhQbktwKIYQQQohiQ24oAxwOB+fPn8fPz69A57sXQgghhBCuUUoRGxtL2bJlMRgyb5+V5BY4f/484eHh7g5DCCGEEEJk4+zZs5QrVy7T9ZLcAn5+foBeWf7+/vl+PKvVyi+//OKcj17kjNRf7kkd5o7UX+5JHeaO1F/uSR3mjjvqLyYmhvDwcGfelhlJbsHZFcHf37/Akltvb2/8/f3lDXULpP5yT+owd6T+ck/qMHek/nJP6jB33Fl/2XUhlRvKhBBCCCFEsSHJrRBCCCGEKDYkuRVCCCGEEMWG9LkVQgghihClFDabDZPJRFJSEna73d0hFUlWq1XqMBfyo/6MRiMmkynXw7JKciuEEEIUESkpKVy4cIH4+HjKlCnD2bNnZXz2W6SUkjrMhfyqP29vb0JDQ7FYLLe8D0luhRBCiCLA4XBw6tQpjEYjZcuWJSUlBV9f3ywHsxeZczgcxMXFSR3eoryuP6UUKSkpXLlyhVOnTlGtWrVb3q8kt0IIIUQRkJKSgsPhIDw8HE9PT2JiYvD09JTE7BY5HA5SUlKkDm9RftSfl5cXZrOZ06dPO/d9K+TVFEIIIYoQScREcZYX57e8Q4QQQgghRLEhya0QQgghCp0PPviA7du3uzuM28K+ffuYPn06NpvN3aHkCUluhRBCCFGovPfee3z77bc0bNjQ3aFkKSIiAk3T2Ldvn1vjqFixIjNnzrylbSMjI+nduzd33nknJpPrt2JFREQQFBTk9ueeEUluhRBCCJGvBg4ciKZpaJqG2WymUqVKjB49mqSkpHRlt27dyvLly/n+++/x8PBwQ7SuCw8P58KFC9SuXTtfjzNx4kTq16+f6fqdO3fy9NNP53i/Sin69+/PK6+8wr333pujbcPDwzl69Gi+P/dbIaMlCCGEECLfdenShaVLl2K1Wtm9ezcDBgxA0zSmTZuWplzLli3zrDXQbrejaVq+3YRnNBopU6ZMvuw7J0qWLHlL22maxo8//nhL2xqNRkqXLp1pa69SCrvdnqPW4Lzi1pbbLVu20KNHD8qWLYumaaxatcq5zmq18sorr1CnTh18fHwoW7Ys/fv35/z582n2ERkZSb9+/fD39ycwMJAnn3ySuLi4An4mrjtxKZJWUzcA0GrqBk5cinRzREIIIUT+8/DwoEyZMoSHh9OzZ086dOjA+vXrnesdDgdTp06lUqVKeHl5Ua9ePVauXJlmH6tXr6ZatWp4enpy99138/HHH6NpGlFRUQAsW7aMwMBAVq9eTc2aNfHw8ODMmTMkJyfz0ksvERYWho+PD82aNWPz5s3O/Z4+fZoePXoQFBSEj48PtWrV4ueffwbg+vXr9OvXj5IlS+Ll5UW1atVYunQpkHG3hN9++42mTZvi4eFBaGgoY8aMSdOXtV27djz//POMHj2a4OBgypQpw8SJE3NVtzd3S9A0jSVLltCrVy+8vb2pVq0aq1evTrPNoUOH6Nq1K76+vpQuXZrHH3+cq1evOtevXbuWVq1aERgYSEhICPfeey8nT550rr+5W8LmzZvRNI01a9bQqFEjPDw8+OOPP1x6XfOaW5Pb+Ph46tWrx9y5c9OtS0hIYM+ePYwfP549e/bw7bffcuzYMe6777405fr168fhw4dZv349P/74I1u2bLmlpvmCUP21n+gwYztRyfo0dVHJdjrM2E71135yc2RCCCGKJKUgPt49P0rdctiHDh1i27ZtaWahmjp1Kp988gkLFizg8OHDvPjiizz22GP89ttvAJw6dYoHH3yQnj17sn//foYMGcJrr72Wbt8JCQlMmzaNJUuWcPjwYUqVKsXw4cPZvn07X3zxBQcOHOChhx6iW7duzmRt2LBhJCcns2XLFg4ePMi0adPw9fUFYPz48fzvf/9jzZo1HDlyhPnz51OiRIkMn9e5c+fo1q0bTZo0Yf/+/cyfP58PP/yQKVOmpCn38ccf4+Pjw44dO3jnnXeYPHlymkQ/L0yaNIk+ffpw4MABunXrRr9+/YiM1BvUoqKiuOeee2jQoAG7du1i7dq1XLp0iT59+ji3j4+PZ+TIkezatYuNGzdiMBjo1asXDocjy+OOGTOGt99+myNHjlC3bt1sX9d8oQoJQH333XdZlvnrr78UoE6fPq2UUup///ufAtTOnTudZdasWaM0TVPnzp1z+djR0dEKUNHR0bcUuyuqjf1RVXhF/6k+9ge1atUqVX3sD85l1cb+mG/HLm5SUlLUqlWrVEpKirtDKbKkDnNH6i/3pA5zLjExUf3vf/9TiYmJym63q+vXryt7TIxSeppZ8D9xcS7HPmDAAGU0GpWPj4/y8PBQgDIYDGrlypVKKaWSkpKUt7e32rZtW5rtnnzySfXoo48qpZR65ZVXVO3atdOsf+211xSgrl+/rpRSaunSpQpQ+/btc5Y5ffq0MhqN6fKC9u3bqxdffFHZ7XZVp04dNXHixAxj79Gjhxo0aFCG606dOqUAtXfvXqWUUmPHjlV33HGHcjgczjJz585Vvr6+ym63K6WUatu2rWrVqlWa/TRp0kS98sorGR5DKaUmTJig6tWrl+n6ChUqqBkzZjgfA2rcuHHOx3FxcQpQa9asUUop9cYbb6hOnTql2cfZs2cVoI4dO5bhMa5cuaIAdfDgQaWUUidPnlSA2r17t1JKqU2bNilArVq1yrmNK6/rzW48z2/mar5WpPrcRkdHo2kagYGBAGzfvp3AwEAaN27sLNOhQwcMBgM7duygV69eboo0rROXIkmxZ10mxa6Xq1o6uGCCEkIIIQrQ3Xffzfz584mPj2fGjBmYTCZ69+4NwIkTJ0hISKBjx45ptklJSaFBgwYAHDt2jCZNmqRZ37Rp03THsVgs1K1b1/n44MGD2O12qlevnqZccnIy/v7+ADz//PM8++yz/PLLL3To0IHevXs79/Hss8/Su3dv9uzZQ6dOnejZsyctWrTI8DkeOXKE5s2bo2mac1nLli2Ji4vj33//pXz58gBp4gMIDQ3l8uXLmdTcrbnxGD4+Pvj7+zuPsX//fjZt2uRsnb7RyZMnqV69OsePH+f1119nx44dXL161dlie+bMmSxvIrsxJ3Pldc0PRSa5TUpK4pVXXuHRRx91nowXL16kVKlSacqZTCaCg4O5ePFipvtKTk4mOTnZ+TgmJgbQ+/lardY8j73fwh14GP//6xsPg0rz/43l/ni1Q54fv7hJfY3y47W6XUgd5o7UX+5JHeac1WpFKYXD4UD91yVAeXnh+O8zrMB5ekI2X1GnUkrh7e1N5cqVAViyZAkNGjRg8eLFPPnkk87P4R9++IGwsLA023p4eDifc+rzT5X6u8PhcP54eXk5y4L+GW80Gtm5cydGozFNTKn/P/HEE3Ts2JGffvqJ9evXM3XqVN59912GDx9O586dOXXqFD///DMbNmygffv2DB06lOnTp6c7visxgp6r3Pz1vt1uz/Qr/9RYs+oScPNxjUZjmseapmGz2XA4HMTGxnLvvffy9ttvp9tPaGgoDoeDHj16UL58eRYuXEjZsmVxOBzUrVuXpKSktOfgf8dNPZaXl5fzd1de15ul7ttqtaZ5vcD160WRSG6tVit9+vRBKcX8+fNzvb+pU6cyadKkdMt/+eUXvL29c73/m42tl/HyNxrf/KLanR3YRfbyun/S7UjqMHek/nJP6tB1JpOJMmXKEBcXR0pKCgCx7ryBOjbW5aJWqxWbzeZMdgBeeOEFxo0bx7333ku5cuXw8PDg2LFjGbboxcTEULFiRdavX59mH1u3bv0vlFgMBgNJSUkopdKUqVatGna7nVOnTmXY4hr73/MICAigb9++9O3bl0mTJrFw4UL69+8P6IlYr1696NWrF40bN2bChAmMHz/eeQN7fHw8MTExVK5cmR9++MH5TTPAxo0b8fPzw9/fn5iYGGw2GykpKWlitNlsWK3WNMtulJycjN1uz3S9w+EgKSkpzfrExMQ0j5VSzjK1atXihx9+IDg4ON1oBna7nYiICI4dO8b777/vbC1PnVAjdb/x8fGA3sc5JiaGhISENK8F4NLrerOUlBQSExPZsmVLukklUo+RnUKf3KYmtqdPn+bXX391ttoClClTJl0zvs1mIzIyMsuhOV599VVGjhzpfBwTE0N4eDidOnVKs/+80mrqBudNZKC32L7R2MH4XQaSHf//1UWgh1Fabl1gtVpZv349HTt2xGw2uzucIknqMHek/nJP6jDnkpKSOHv2LL6+vnh4eBAbG4ufn1+ar8ALK7PZjMlkSvMZ279/fyZOnMinn37KqFGjGDVqFOPGjcPDw4NWrVoRHR3Ntm3b8PPzY8CAATz33HPMmzePt956iyeeeIJ9+/bxxRdfAODv74+/vz+enp5ompbmOA0bNqRv374MGzaM6dOn06BBA65cucLGjRupWrUqDz74ICNHjqRLly5Ur16d69evs337dmrVqoW/vz8TJkygYcOG1KpVi+TkZDZu3Midd96Jv7+/82v91K/9R4wYwYIFCxg3bhzDhg3j2LFjTJs2jRdffNHZpdJkMmGxWNLEaDKZMJvNmeYgHh4epKSk8M8//6RZ7ufnR5UqVTAYDHh6eqbZ3svLK81jTdOcZV588UWWL1/OM888w8svv0xwcDAnTpzgyy+/ZPHixfj6+hISEsKKFSuoWrUqZ86cYcKECWn26+PjA4C3tzf+/v7OxsHURD71dcnudb1ZUlISXl5etGnTBk9PzzTrMkvub1aok9vUxPb48eNs2rSJkJCQNOubN29OVFQUu3fvplGjRgD8+uuvOBwOmjVrlul+PTw8MhwY2mw258tF9rMhzegwI/0UgskOjWS7lqacXORdl1+v1+1E6jB3pP5yT+rQdTeO2Zqa0ObnGK55KXUChxtjtVgsDB8+nOnTpzN06FCmTJlCqVKlmDZtGkOGDCEwMJCGDRsyduxYDAYDVapUYeXKlYwaNYpZs2bRvHlzXnvtNZ599lm8vLwwGAzO/d9cJ8uWLWPKlCm8/PLLnDt3jhIlStCsWTPatWuHpmk4HA6ee+45/v33X/z9/enSpQszZszAYDDg4eHBa6+9RkREBF5eXrRu3Zovvvgi3fEMBgPh4eH8/PPPvPzyyzRo0IDg4GCefPJJxo8fnyamm+sio/q5uf7+/vtvZ66Tqn379mzYsCHDfd4Y383LypUrx9atW3nllVfo0qULycnJVKhQgS5dumAymdA0jS+++ILnn3+eunXrcscddzBr1izatWvn3MfN5+DNdZEqu9f1Zqn7zuja4Oq1QlOpnSbcIC4ujhMnTgDQoEED3n//fe6++26Cg4MJDQ3lwQcfZM+ePfz444+ULl3auV1wcLBz+JCuXbty6dIlFixYgNVqZdCgQTRu3JgVK1a4HEdMTAwBAQFER0fnS8st6MOApd5U5mFUvNPUzui/jM7k1mKEv9/sni/HLm6sVis///wz3bp1kw/FWyR1mDtSf7kndZhzSUlJnDp1ikqVKmGxWIiJicHf379IJLf55c0332TBggWcPXs2x9s6HA6pw1zIr/q78TzPqOXWlXzNra/mrl27aNCggbMfxsiRI2nQoAGvv/46586dY/Xq1fz777/Ur1+f0NBQ58+2bduc+/jss8+oUaMG7du3p1u3brRq1YpFixa56yll6u83u2MxZrxOElshhBAie/PmzWPnzp38888/LF++nOnTp2f41ba4vbm1W0K7du3IquHYlUbl4ODgHLXSutPfb3bnxKVI+i3cAdgJ9DDy2ZBmMvyXEEII4YLjx48zZcoUIiMjKV++PKNGjeLVV191d1iikCnUfW6Lo6qlg/nj1Q78/PPP/PFqB/k6TgghhHDRjBkzmDFjhrvDEIWcdDIRQgghhBDFhiS3QgghRBHixvvAhch3eXF+S3IrhBBCFAGp3dhcHcheiKIo9fzOTbdN6XMrhBBCFAFGo5HAwEAuX77snO40KSlJhrG6RQ6Hg5SUFKnDW5TX9aeUIiEhgcuXLxMYGJhu6t2ckORWCCGEKCJSZ9+8cuUKiYmJeHl5FYkZygojpZTUYS7kV/0FBgZmOcusKyS5FUIIIYoITdMIDQ0lKCiIjRs30qZNGxl15xZZrVa2bNkidXiL8qP+zGZzrlpsU0lyK4QQQhQxRqMRm82Gp6enJGa3SOowdwpz/UknEyGEEEIIUWxIciuEEEIIIYoNSW6FEEIIIUSxIcmtEEIIIYQoNiS5LWhKYRgxgpDDh90diRBCCCFEsSOjJRS0zz7DOG8eLTUNR0wMvPEGFLK7DIUQQgghiippuS1o99+PY8AANKUwTpsGLVrA8ePujkoIIYQQoliQ5Lag+flhX7yYv0aPRgUFwa5dUL8+LFkCSrk7OiGEEEKIIk2SWze50KIFtt274e67ISEBnnoKHngArl51d2hCCCGEEEWWJLfuVK4cbNgA77yj97tdtQrq1oX1690dmRBCCCFEkSTJrbsZDPDyy/Dnn1CjBly4AJ06wahRkJzs7uiEEEIIIYoUSW4Li4YNYfduePZZ/fH770PTpiBDhgkhhBBCuEyS28LE2xvmzYPVq6FkSThwABo3htmz5WYzIYQQQggXSHJbGPXooSe2XbpAUhI8/zzcey9cuuTuyIQQQgghCjVJbgurMmXg559h1izw8NB/r1MHfvrJ3ZEJIYQQQhRaktwWZpoGzz2nj4Vbty5cuaK34A4bpg8fJoQQQggh0pDktiioXRt27IAXX9Qfz5un98Xdt8+tYQkhhBBCFDaS3BYVnp76CArr1kFoKBw5oo+m8O674HC4OzohhBBCiEJBktuiplMn/Waznj3BatXHyO3UCc6dc3dkQgghhBBuJ8ltUVSiBHz7LSxapA8ftnGj3if3m2/cHZkQQgghhFtJcltUaRo89RTs2QONGkFkJDz4IDz5JMTFuTs6IYQQQgi3kOS2qLvjDti2DV59VU94P/oIGjSAv/5yd2RCCCGEEAVOktviwGKBt96CTZsgPBxOnIAWLeDNN8Fud3d0QgghhBAFRpLb4qRtW9i/Hx5+WE9qx42Du++G06fdHZkQQgghRIGQ5La4CQqCzz+HTz4BPz/4/Xf9ZrMVK9wdmRBCCCFEvpPktjjSNHj8cb0Vt0ULiImBfv3gsccgOtrd0QkhhBBC5BtJbouzSpXgt99g0iQwGuGzz6BePfjjD3dHJoQQQgiRLyS5Le5MJnj9dT2hrVxZ73/bti2MH69PAiGEEEIIUYxIcnu7uOsu2LcPBg7Up+udMgVatdJHVhBCCCGEKCYkub2d+PnB0qXw5ZcQGKiPhVu/vj42rlLujk4IIYQQItckub0d9ekDBw5Au3YQH6/PavbQQ/osZ0IIIYQQRZgkt7er8HDYsAHeflvvl/vNN/qQYb/+6u7IhBBCCCFumSS3tzOjEV55Bf78U5/G99w56NABRo+G5GR3RyeEEEIIkWOS3Apo1Ah274YhQ/S+t9On6zegHTni7siEEEIIIXJEkluh8/GBBQtg1SooUUIfWaFhQ5g3T242E0IIIUSRIcmtSOv++/WbzTp1gqQkGDYMevSAy5fdHZkQQgghRLYkuRXphYbCmjUwcyZ4eMBPP0GdOvoyIYQQQohCTJJbkTGDAV54AXbuhNq19Zbbbt3g+echMdHd0QkhhBBCZEiSW5G1OnX0BPeFF/THs2dDkyawf7974xJCCCGEyIAktyJ7np56F4W1a6FMGTh8GJo2hRkz9Kl8hRBCCCEKCUluhes6d9ZvNrvvPkhJgZEj9WXnz7s7MiGEEEIIQJJbkVMlS+rDhS1YAF5e+ixnderAd9+5OzIhhBBCCEluxS3QNH3Chz179LFwIyPhgQfgqacgLs7d0QkhhBDiNibJrbh1NWrA9u36FL6aBkuW6Mnuzp3ujkwIIYQQtylJbkXuWCzw9tvw669QrhwcPw4tWsDUqWC3uzs6IYQQQtxmJLkVeaNdO/1ms4ceApsNxo6Fu++G06fdHZkQQgghbiOS3Iq8ExQEX34Jy5aBry/8/jvUqwdffOHuyIQQQghxm5DkVuQtTYMBA2DfPrjrLoiOhkcfhf79ISbG3dEJIYQQopiT5FbkjypV9JbbCRP0qXyXL9dbcbdudXdkQgghhCjGJLkV+cdkgokTYcsWqFgRIiKgTRs94bXZ3BycEEIIIYojSW5F/mvZEvbv17smOBwweTK0bg0nT7o7MiGEEEIUM5LcioLh7w8ffwyffw4BAfDnn1C/vn7zmVLujk4IIYQQxYRbk9stW7bQo0cPypYti6ZprFq1Ks16pRSvv/46oaGheHl50aFDB44fP56mTGRkJP369cPf35/AwECefPJJ4mSWrMLrkUf0IcPatNFnMxs0CB5+GK5fd3dkQgghhCgG3JrcxsfHU69ePebOnZvh+nfeeYdZs2axYMECduzYgY+PD507dyYpKclZpl+/fhw+fJj169fz448/smXLFp5++umCegriVpQvr0/68NZber/cr7+GunVh0yZ3RyaEEEKIIs6tyW3Xrl2ZMmUKvXr1SrdOKcXMmTMZN24c999/P3Xr1uWTTz7h/PnzzhbeI0eOsHbtWpYsWUKzZs1o1aoVs2fP5osvvuD8+fMF/GxEjhiN8Oqr+vS91arBv/9C+/b6VL4pKe6OTgghhBBFVKHtc3vq1CkuXrxIhw4dnMsCAgJo1qwZ27dvB2D79u0EBgbSuHFjZ5kOHTpgMBjYsWNHgccsbkHjxrB3Lzz1lN739p13oHlzOHrU3ZEJIYQQoggyuTuAzFy8eBGA0qVLp1leunRp57qLFy9SqlSpNOtNJhPBwcHOMhlJTk4mOTnZ+Tjmv8kFrFYrVqs1T+LPSuoxCuJYRYLFAnPnonXqhPGZZ9D27EE1bIhj+nQcTz2lTwxxA6m/3JM6zB2pv9yTOswdqb/ckzrMHXfUn6vHKrTJbX6aOnUqkyZNSrf8l19+wdvbu8DiWL9+fYEdq0gwm/GcPp0GH3xAqf37MQ4fzuWPP2bf8OGkBASkKy71l3tSh7kj9Zd7Uoe5I/WXe1KHuVOQ9ZeQkOBSuUKb3JYpUwaAS5cuERoa6lx+6dIl6tev7yxz+fLlNNvZbDYiIyOd22fk1VdfZeTIkc7HMTExhIeH06lTJ/z9/fPwWWTMarWyfv16OnbsiNlszvfjFTl9+2KfMwfD2LGE7txJmdGjsS9ZgurcGZD6ywtSh7kj9Zd7Uoe5I/WXe1KHueOO+kv9pj07hTa5rVSpEmXKlGHjxo3OZDYmJoYdO3bw7LPPAtC8eXOioqLYvXs3jRo1AuDXX3/F4XDQrFmzTPft4eGBh4dHuuVms7lAT/CCPl6RMmoUdOwIffuiHT6MqUcPeP55mDYN/qszqb/ckzrMHam/3JM6zB2pv9yTOsydgqw/V4/j1hvK4uLi2LdvH/v27QP0m8j27dvHmTNn0DSNESNGMGXKFFavXs3Bgwfp378/ZcuWpWfPngDceeeddOnShaeeeoq//vqLrVu3Mnz4cB555BHKli3rvicm8kbdurBzJzz3nP541ixo0gQOHnRvXEIIIYQotNya3O7atYsGDRrQoEEDAEaOHEmDBg14/fXXARg9ejTPPfccTz/9NE2aNCEuLo61a9fi6enp3Mdnn31GjRo1aN++Pd26daNVq1YsWrTILc9H5AMvLz2p/flnKF0aDh3C1Lw5lVev1qfyFUIIIYS4gVu7JbRr1w6VxdSrmqYxefJkJk+enGmZ4OBgVqxYkR/hicKka1d9ZrMnn0T78UfqfPQRjrNn9Sl9b+iTLYQQQojbW6Ed51aIdEqVgtWrsc+ejd1iwbB+PdSpA99/7+7IhBBCCFFISHIrihZNwzFkCJvfew9Vrx5cuwY9e8Izz0B8vLujE0IIIYSbSXIriqS48HBsf/wBL7+sL1i4EBo1gt273RuYEEIIIdxKkltRdHl46NP1btgAYWFw7BjcdZc+XJjd7u7ohBBCCOEGktyKoq99e/1ms969wWaDMWOgQwc4e9bdkQkhhBCigElyK4qH4GD4+mv46CPw8YHNm/Vxcr/6yt2RCSGEEKIASXIrig9Ng0GDYN8+aNoUoqLg4Ydh4ECIjXVzcEIIIYQoCJLciuKnalX44w8YPx4MBn0s3Pr1Yft2d0cmhBBCiHwmya0onsxmmDwZfvsNKlSAf/6B1q1h0iS9X64QQgghiiVJbkXx1qoV7N8P/frpIyhMnAht2ujJrhBCCCGKHUluRfEXEACffgqffQb+/nr3hPr14ZNPIIvpn4UQQghR9EhyK24fffvqrbitWuk3mA0YAI8+CtevuzsyIYQQQuQRSW7F7aViRX2YsClTwGiEL7+EevX0ZUIIIYQo8iS5FbcfoxFeew22bdNHVjh7Fu65B159FVJS3B2dEEIIIXJBkltx+2raFPbuhSef1Pvevv02tGihT+MrhBBCiCJJkltxe/P1hSVLYOVKCAqC3buhYUNYtEhuNhNCCCGKIEluhQDo3RsOHoT27SEhAYYMgV694OpVd0cmhBBCiByQ5FaIVGFh8Msv8O67YLHA999DnTr6MiGEEEIUCZLcCnEjgwFGjYIdO+DOO+HiRejcGV58EZKS3B2dEEIIIbIhya0QGalfH3btgmHD9MczZ+o3oB065M6ohBBCCJENSW6FyIy3N8yZAz/+CKVK6X1yGzeG2bPlZjMhhBCikJLkVojsdO8OBw5At26QnAzPP6//fvGiuyMTQgghxE0kuRXCFaVL6y24c+aApyesXQt16+rLhBBCCFFoSHIrhKs0Te+Du3u3PmXvlSvQowcMHaoPHyaEEEIIt5PkVoicqllTH01h1Cj98fz50KiRPtuZyDWbzcFfp66x5tAF/jp1DZvN4e6QhBBCFCEmdwcgRJHk4aGPh9u5MwwYAEePQrNm8OabetJrkL8bb8XGI5dYtjWCiGvxWO0OzEYDFUN8GNiyIu3vLO3u8IQQQhQB8gksRG507KiPotCrF1itMHo0dOgA//7r7siKnI1HLjF1zVH+vhyLn6eJsCAv/DxN/H05lqlrjrLxyCV3hyiEEKIIkORWiNwKCYFvvoHFi/XhwzZt0m82W7nS3ZEVGTabg2VbI4hNslI+yAs/TzMmgwE/TzPlg7yITbLy8bYI6aIghBAiW5LcCpEXNA0GD9b73TZuDNevw0MPwRNPQGysu6Mr9PacvU7EtXhCfCwYburSYTAYCPGxcOpqPHvOXndThEIIIYoKSW6FyEvVq8O2bTB2rJ7wLl0KDRroN6CJTF2LT8Fqd+BlMWa43stixGp3cC0+pYAjE0IIUdRIcitEXjOb9RvLNm2C8HA4eRJatoQ33gCbzd3RFUohPhbMRgOJKfYM1yem2DEb9RZcIYQQIiuS3AqRX9q21Wc2e+QRsNvh9dehXTuIiHB3ZIVOw/AgKob4cC0+BYcjbb9ah0Nvsa1UwoeG4UFuilAIIURRIcmtEPkpMBBWrIDly8HPD7Zu1SeA+Owzd0dWqJhMBga2rIifp5kz1xOJTbJicziITbJy5noi/p5mBrSoiMkklywhhBBZk08KIfKbpsFjj8H+/dCiBcTE6I/79oWoKHdHV2i0v7M0r3atQfVSfsQm2Th3PZHYJBt3lPZjTNcaMs6tEEIIl8gkDkIUlEqV4LffYOpUmDQJPv9cb8n99FNo3drd0RUK7e8sTdtqJdlz9jrX4lMI8bHQMDxIWmyFEEK4TD4xhChIJhOMHw9//AFVqsCZM3o/3Nde0yeBEJhMBppWCqFr7VCaVgqRxFYIIUSOyKeGEO5w1136mLiDBoHDAW+9pY+ocPy4uyMTQgghijRJboVwFz8/+Ogj+OorCAqCnTuhfn1YsgSUcnd0QgghRJEkya0Q7vbQQ/qQYXffDQkJ8NRT8MADcPWquyMTQgghihxJboUoDMqVgw0b4J139EkgVq2CunVh/Xp3RyaEEEIUKZLcClFYGAzw8svw559QowZcuACdOsGoUZCc7O7ohBBCiCJBklshCpuGDWH3bnj2Wf3x++9Ds2Zw+LB74xJCCCGKAEluhSiMvL1h3jxYvRpKlNAngGjcGObMKfY3m9lsDv46dY01hy7w16lr2GyO7DcSQggh/iOTOAhRmPXoAQcPwsCBsG4dPPccrFmjj7JQuvjN2LXxyCWWbY0g4lo8VrsDs9FAxRAfBrasKDOUCSGEcIm03ApR2JUpAz//DB98AB4e+u916sBPP7k7sjy18cglpq45yt+XY/HzNBEW5IWfp4m/L8cydc1RNh655O4QhRBCFAGS3ApRFBgM8PzzsGuXntheuQL33gvDh0NiorujyzWbzcGyrRHEJlkpH+SFn6cZk8GAn6eZ8kFexCZZ+XhbhHRREEIIkS1JboUoSmrXhr/+ghEj9Mdz50KjRrBvnzujyrU9Z68TcS2eEB8LBkPay5LBYCDEx8Kpq/HsOXvdTREKIYQoKiS5FaKo8fSEGTP0PrhlysCRI/poCu+9p0/lWwRdi0/BanfgZTFmuN7LYsRqd3AtPqWAIxNCCFHUSHIrRFHVqZN+s9n990NKCrz0kr7s3Dl3R5ZjIT4WzEYDiSn2DNcnptgxG/UWXCGEECIrktwKUZSVKAHffQeLFunDh23cqM9s9u237o4sRxqGB1ExxIdr8Sk4bmp9djj0FttKJXxoGB7kpgiFEEIUFZLcClHUaRo89RTs2aP3v42MhN69YfBgiItzd3QuMZkMDGxZET9PM2euJxKbZMXmcBCbZOXM9UT8Pc0MaFERk0kuWUIIIbImnxRCFBd33AHbtsGYMXrC++GH0KCBfgNaEdD+ztK82rUG1Uv5EZtk49z1RGKTbNxR2o8xXWvIOLdCCCFcIpM4CFGcWCwwdSp06QKPPw4nTkCLFjBpkp70GjO+YauwaH9nadpWK8mes9e5Fp9CiI+FhuFB0mIrhBDCZfKJIURx1LatPmXvww+D3Q7jxkG7dnD6tLsjy5bJZKBppRC61g6laaUQSWyFEELkiHxqCFFcBQXB55/DJ5+Anx/88Yd+s9mKFe6OTAghhMg3ktwKUZxpmt49Yd8+aN4cYmKgXz+MAwZgio93d3RCCCFEnpPkVojbQeXKsGULTJwIBgOGzz/n7hEj0LZudXdkQgghRJ6S5FaI24XJBBMmwB9/oCpVwvvKFYzt28P48WC1ujs6IYQQIk9IcivE7aZ5c2w7d3Lm7rvRHA6YMgVatdJHVhBCCCGKOEluhbgd+fuz94UXsH36KQQG6mPh1q8PS5eCUu6OTgghhLhlhTq5tdvtjB8/nkqVKuHl5UWVKlV44403UDd8+CqleP311wkNDcXLy4sOHTpw/PhxN0YtRNGh+vSBAwf0ocPi4+GJJ+Chh/RZzoQQQogiqFAnt9OmTWP+/PnMmTOHI0eOMG3aNN555x1mz57tLPPOO+8wa9YsFixYwI4dO/Dx8aFz584kJSW5MXIhipDwcNi4UZ/8wWSCb77Rhwz79Vd3RyaEEELkWKFObrdt28b9999P9+7dqVixIg8++CCdOnXir/+mE1VKMXPmTMaNG8f9999P3bp1+eSTTzh//jyrVq1yb/BCFCVGoz6D2Z9/QvXqcO4ctG8PL78Mycnujk4IIYRwWaFOblu0aMHGjRv5+++/Adi/fz9//PEHXbt2BeDUqVNcvHiRDh06OLcJCAigWbNmbN++3S0xC1GkNWoEe/bA00/rj999F+66C44ccW9cQgghhItM7g4gK2PGjCEmJoYaNWpgNBqx2+28+eab9OvXD4CLFy8CULp06TTblS5d2rkuI8nJySTf0BoVExMDgNVqxVoAQyKlHqMgjlUcSf3lXpZ1aLHAnDlonTphHDIEbd8+VMOGON55B8eQIfrEELc5OQdzT+owd6T+ck/qMHfcUX+uHktTqvDeGv3FF1/w8ssvM336dGrVqsW+ffsYMWIE77//PgMGDGDbtm20bNmS8+fPExoa6tyuT58+aJrGl19+meF+J06cyKRJk9ItX7FiBd7e3vn2fIQoajwiI2k4axal9u0D4GLjxuwdPpyUwEC3xiWEEOL2k5CQQN++fYmOjsbf3z/TcoU6uQ0PD2fMmDEMGzbMuWzKlCl8+umnHD16lH/++YcqVaqwd+9e6tev7yzTtm1b6tevzwcffJDhfjNquQ0PD+fq1atZVlZesVqtrF+/no4dO2I2m/P9eMWN1F/u5agOHQ4Mc+ZgGDsWLSUFVaoU9iVLUF26FEywhZCcg7kndZg7Un+5J3WYO+6ov5iYGEqUKJFtcluouyUkJCRgMKTtFmw0GnE4HABUqlSJMmXKsHHjRmdyGxMTw44dO3j22Wcz3a+HhwceHh7plpvN5gI9wQv6eMWN1F/uuVyHo0ZBx47Qrx/aoUOY7rsPhg+Hd94BL6/8D7SQknMw96QOc0fqL/ekDnOnIOvP1eMU6hvKevTowZtvvslPP/1EREQE3333He+//z69evUCQNM0RowYwZQpU1i9ejUHDx6kf//+lC1blp49e7o3eCGKm7p1YedOeP55/fGcOdC4Mezf7964hBBCiBsU6pbb2bNnM378eIYOHcrly5cpW7YsQ4YM4fXXX3eWGT16NPHx8Tz99NNERUXRqlUr1q5di6enpxsjF6KY8vSEDz6Arl1h4ED43/+gaVN4+2144QUwFOq/l4UQQtwGCvUnkZ+fHzNnzuT06dMkJiZy8uRJpkyZgsVicZbRNI3Jkydz8eJFkpKS2LBhA9WrV3dj1ELcBrp0gYMHoUcPSEmBkSOhc2c4f97dkQkhhLjNFerkVghRiJUsCd9/DwsW6P1uN2yAOnXgu+/cHZkQQojbmCS3Qohbp2kwZIg+8UODBhAZCQ88oE8CER/v7uiEEELchiS5FULkXo0a+tS9o0frCe/ixdCwIeza5e7IhBBC3GYkuRVC5A2LBaZNg40bISwM/v4bmjeHqVPBbnd3dEIIIW4TktwKIfLW3XfDgQPw4INgs8HYsXDPPXDmjLsjE0IIcRuQ5FYIkfeCg+Grr2DpUvD1hS1b9HFyM5kSWwghhMgrktwKIfKHpulj4e7bB82aQXQ0PPIIDBgAMTGZbmazOfjr1DXWHLrAX6euYbM5CixkIYQQRV+hnsRBCFEMVKkCv/8OU6boP598oj/+9FNo0SJN0Y1HLrFsawQR1+Kx2h2YjQYqhvgwsGVF2t9Z2k1PQAghRFEiLbdCiPxnNsOkSXr3hIoV4dQpaN0aJk7U++WiJ7ZT1xzl78ux+HmaCAvyws/TxN+XY5m65igbj1xy61MQQghRNEhyK4QoOC1bwv798Pjj4HDoCW+bNtj+PsGyrRHEJlkpH+SFn6cZk8GAn6eZ8kFexCZZ+XhbhHRREEIIkS1JboUQBcvfX++a8PnnEBAA27ejNaxPjV++JcTbjMGQ9rJkMBgI8bFw6mo8e85ed1PQQgghigpJboUQ7vHII/qQYW3aYIyP57Wv32Hc8kn4xKe/2czLYsRqd3AtPsUNgQohhChKJLkVQrhP+fLw66+cfWkcNoORFns28c6U/tQ6tjtNscQUO2aj3oIrhBBCZEWSWyGEexmNhE6dxORXl3AmJIwS1y8zbubzPPrdPIw2Kw6H3mJbqYQPDcOD3B2tEEKIQk6SWyGE25lMBtr268rQUYtZ1bgbBqXoue5TJr39FNrfx/D3NDOgRUVMJrlkCSGEyJqMcyuEKBT0cWwbsqzk6/xVoxmvfPMu1f79m+XzhnLq1TeoUaONu0MUQghRBEgziBCi0Gh/Z2mWDmxCz8nD2P3jb0S3bItHSjI1Jo2Gnj3hyhV3hyiEEKKQk+RWCFGomEwGmlYK4Z57GhCw5Vd4/32wWGD1aqhbF9atc3eIQgghCjFJboUQhZfBAC++CH/9BTVrwsWL0KULjBgBSUnujk4IIUQhJMmtEKLwq1cPdu2C4cP1xx98AE2awMGD7o1LCCFEoeNycrtv3758DEMIIbLh5QWzZ8NPP0GpUnDokJ7gfvCBPpWvEEIIQQ6S22bNmvHWW2/hkA8RIYQ7deumt9h27w7JyXoXhW7d4MIFd0cmhBCiEHA5uf3uu++YN28eLVq04Pjx4/kZkxBCZK1UKfjhB5g7Fzw99ZvM6taF7793d2RCCCHczOXktlu3bhw+fJgaNWrQoEEDZs+enZ9xCSFE1jQNhg6F3buhfn24elUfLuyZZyA+3t3RCSGEcJMc3VAWEBDAsmXLWLZsGS+++CIBAQEEBwen+RFCiNzY9s9ZKo75yfmz7Z+zWW9Qsyb8+Se89JL+eOFCaNRIT3qFEELcdnI8Q9nOnTsZP3481apV46WXXsJkkknOhBB5o+KYn9It67voAHCAiLe7Z76hhwdMn64PEzZgABw7BnfdBVOm6Emv0Zh/QQshhChUXM5MbTYbEyZM4N1332XYsGG89dZbeHp65mdsQojbSEaJ7c3rs0xwAdq3hwMH4Omn4ZtvYMwYWLsWPvkEwsPzMFohhBCFlcvdEho2bMjnn3/OunXreP/99yWxFULkmWy7HuSkXHAwfP01fPgh+PjA5s36zWZffZW7IIUQQhQJLie3TZs2Zf/+/bRr1y4fwxFC3I70rgd5Vw5NgyeegH37oGlTiIqChx+GgQMhNvZWwxRCCFEEuJzcLlmyBD8/v/yMRQgh8lbVqvDHHzBunD6V78cf6yMrbN/u7siEEELkE5l+VwhRvJnN8MYb8NtvUKEC/PMPtG4NkyeDzebu6IQQQuQxSW6FEG634um6eVouQ61awf790K8f2O0wYQK0basnu0IIIYoNSW6FEG7XorJrIxm4Wi5TAQHw6af6j78/bNumd1NYvhyUyt2+hRBCFAq5Sm6TkpLyKg4hxG0uu2G+sh0GLCf69dNbcVu10m8w698f+vbVbzwTQghRpOU4uXU4HLzxxhuEhYXh6+vLP/99pTd+/Hg+/PDDPA9QCHH7iHi7e7quByuerpu3iW2qihX1YcKmTNEnefjiC33IsN9+y/tjCSGEKDA5Tm6nTJnCsmXLeOedd7BYLM7ltWvXZsmSJXkanBDi9tOicjgRb3d3/uS6K0JWjEZ47TW9e0KVKnD2LNx9N4wdCykp+Xfc25zDoTh3PRGAc9cTcTikS4gQIu/kOLn95JNPWLRoEf369cN4w5SW9erV4+jRo3kanBBCFIimTfUxcZ98Uu97O3UqtGypT+Mr8tSJy7HM33ySuZtOADB30wnmbz7Jicsy/rAQIm/kOLk9d+4cVatWTbfc4XBgtVrzJCghhChwvr6wZAmsXAlBQbBrFzRsCIsXy81meeTE5ViWbo3g0PloArzMAAR4mTl0PpqlWyMkwRVC5IkcJ7c1a9bk999/T7d85cqVNGjQIE+CEkIIt+ndGw4ehPbtISEBnn4aHngArl4FwGZzsPt0JAC7T0diszncGW2R4XAo1h26RGR8CtVK+eLraQLA19NEtVK+RMan8MvhS9JFQQiRa6acbvD6668zYMAAzp07h8Ph4Ntvv+XYsWN88skn/Pjjj/kRoxBCFKywMPjlF5gxA159FVatgh072Dt5Bu9TkfPX43i+Orz23SHKBvkysGVF2t9Z2t1RF2rnohI5eSWO0ABPNE2DG3JYTdMIDfDkxOU4zkUlEh7s7b5AhRBFXo5bbu+//35++OEHNmzYgI+PD6+//jpHjhzhhx9+oGPHjvkRoxBCFDyDAUaNgr/+gjvvhAsXaPDUI3RdNp0ggx0AXw8Tf1+OZeqao2w8csnNARdu8Sk2kmx2vC0Zt6l4WYwk2+zEp8iscUKI3Mlxyy1A69atWb9+fV7HIoQQhU/9+tj+/ItNPQfRcdNK+m79hpan93Fy9Av4epagvNnEmeuJfLwtgrbVSmIyydw4GfGxmPA0GUlIseHnaU63PjHFjofJiE8mya8QQrhKrsJCCJGNPdeSmdz5WSY89TbRvoFU+PckbUeNos26r0ApQnwsnLoaz56z190daqEVFuhFlZK+XIhOQt10g55SigvRSVQt5UtYoJebIhRCFBcu/YkcFBSk95FyQWRkZK4CEkKIwuZafApWu4M/7mjKb0/P443v36P1yd0M+XYWtfZvY2a/MUR6BHAtXsbGzYzBoNG5dmnORydy/HIcYf76OOlxSTbOxaQQ7GOhU63SGAyufdYIIURmXEpuZ86c6fz92rVrTJkyhc6dO9O8eXMAtm/fzrp16xg/fny+BCmEEO4U4mPBZndw9roV5RnAc30n8cnF77njo2W0OrmLO999kik9RxLyqIwYk5WqpfwY1LIi6w5dIuJKDHhCdKKVOmEBdKpVmqql/NwdohCiGHApuR0wYIDz9969ezN58mSGDx/uXPb8888zZ84cNmzYwIsvvpj3UQohhBvVDQ3Aager3YGnERzAqe7dmWCoz9TvplPjcgQzVkzA5nseZrwP3nK3f2aqlvKjcjtfzlyNZf/2swy7uyrlS/hJi60QIs/kuM/tunXr6NKlS7rlXbp0YcOGDXkSlBBCFCYHLkRjNmloChJtkGzX+4z+L6Q89z0+gw8b3w+AadFCaNQI9u51Z7iFnsGgERak960NC/KSxFYIkadynNyGhITw/fffp1v+/fffExISkidBCSFEYXItPoVkq52MphdIMZmZ0v4pnu73FkklS8PRo9CsGbz7LjhkggchhChoOR5zZdKkSQwePJjNmzfTrFkzAHbs2MHatWtZvHhxngcohBDu5u9hIiFFT25NGqSO9mUygN0BNgUbw+uy/4fNNJs2Fr77Dl5+GdasgY8/hnLl3Bm+EELcVnLccjtw4EC2bt2Kv78/3377Ld9++y3+/v788ccfDBw4MB9CFEII97oan4xz9CoNUmeIdSj9MYBScNHDF775BhYv1vvd/vor1K0LK1e6I2whhLgt3dJo2c2aNeOzzz7L61iEEKJQuhKbgsGg9zKwOcD4X0LrUPpj0Cc0uxKbApoGgwdDmzbQrx/s2gUPPQSDBsEHH4CfjAgghBD5SSZxEEKIbJQJ8Mh5uerVYds2GDtWT3iXLoUGDeDPP/MpSiGEECDJrRBCZKtN5RLYs7k3zO7Qy6VhNsObb8LmzRAeDidPQqtW8MYbYLPlW7xCCHE7k+RWCCGy8d2BcxmOlHAj9V+5DLVpAwcOwCOPgN0Or78O7drBqVN5HKkQQghJboUQIhvnriehkfkF04B+X9m560mZ7yQwEFasgOXL9X63W7dCvXrw6ad5Hq8QQtzOcp3cxsTEsGrVKo4cOZIX8QghRKETFuSJQp+ZLCMO9JbbsCDPrHekafDYY7B/P7RoAbGx8Pjj+o1nUVF5GrMQQtyucpzc9unThzlz5gCQmJhI48aN6dOnD3Xr1uWbb77J8wCFEMLdetUNI7s5tLT/yrmkUiX47TeYPBmMRr1Ft149+P333IYKgMOhOBuZwNGLMZyNTMDhyK5ThRBCFB85Tm63bNlC69atAfjuu+9QShEVFcWsWbOYMmVKngcohBDutuWfqxizuVoaDXo5l5lMMH48/PEHVKkCZ87o/XBfew2s1luO9cTlWOZvPsmM9X8za+NxZqz/m/mbT3Licuwt71MIIYqSHCe30dHRBAcHA7B27Vp69+6Nt7c33bt35/jx43keoBBCuNvF6BsmcciEUnq5HLvrLti7FwYO1AfSfestaNkSbuF6euJyLEu3RnDofDSB3mYql/Al0NvMofPRLN0aIQmuEOK2kOPkNjw8nO3btxMfH8/atWvp1KkTANevX8fTM5v+ZkIIUQSFeJmxZ5Pc2pVe7pb4+enj4H71FQQFwc6d+pi4H35Itln1fxwOxbpDl4iMT6FaKV/8PM0YDRp+nmaqlfIlMj6FXw5fki4KQohiL8fJ7YgRI+jXrx/lypWjbNmytGvXDtC7K9SpUyev4+PcuXM89thjhISE4OXlRZ06ddi1a5dzvVKK119/ndDQULy8vOjQoYO0IAsh8lRkomstsq6Wy9RDD+lDht19N8TH6zOd9e4N165lu+m5qEROXokjNEBvZIhJtHI1LpmYRL2LQ2iAJycux3EuKjF3MQohRCGX4+R26NCh/Pnnn3z00Uf88ccfGAz6LipXrpznfW6vX79Oy5YtMZvNrFmzhv/973+89957BAUFOcu88847zJo1iwULFrBjxw58fHzo3LkzSUlZDMkjhBA5cCkmJU/LZalcOVi/HqZN0yeB+O47qFsXNmzIcrP4FBtJNjtJVju7Iq6z/Z9r7Dh1je3/XGNXxHWSrHaSbXbiU2TyCCFE8WbKSWGr1UqNGjX48ccf6dWrV5p13bt3z9PAAKZNm0Z4eDhLly51LqtUqZLzd6UUM2fOZNy4cdx///0AfPLJJ5QuXZpVq1bxyCOP5HlMQojbT7ZDfOWwXLaMRhg9Gjp0gL594dgx6NgRRo3SZzzzSD8dsI/FRIrNwZ4z17HZFb6eJsxGE1a7g8uxSVyLTyY82BsfS44u+0IIUeTkqOXWbDYXaIvo6tWrady4MQ899BClSpWiQYMGLF682Ln+1KlTXLx4kQ4dOjiXBQQE0KxZM7Zv315gcQohirc8HwrMVQ0bwp498Mwz+uP33oNmzeB//0tXNNTfk2Srg+sJVgK9TMQl2bgYk0Rcko1ALxNRiVZSbA5C/eXeCCFE8ZbjP+GHDRvGtGnTWLJkCSZT/rYA/PPPP8yfP5+RI0cyduxYdu7cyfPPP4/FYmHAgAFcvHgRgNKlS6fZrnTp0s51GUlOTiY5+f/7xsXExAB6y7Q1F0PwuCr1GAVxrOJI6i/3pA5z5rcTl/A2K2z/zeLgYVBp/gcwGfRyXWqF5u3BzWaYNQutY0eMQ4ag7d+PatQIx7RpOJ55Rp8YAjh3PREfM1g0B0cuRGO74caxCwaNYG8z3ib4NzKOsCCvvI3xFsg5mDtSf7kndZg77qg/V4+lKeXirbj/6dWrFxs3bsTX15c6derg4+OTZv23336bk91lyWKx0LhxY7Zt2+Zc9vzzz7Nz5062b9/Otm3baNmyJefPnyc09P8/UPr06YOmaXz55ZcZ7nfixIlMmjQp3fIVK1bg7e2dZ/ELIURe8rh+nQazZlF6714ALjZuzL7hw0kODHRvYEIIUQASEhLo27cv0dHR+Pv7Z1oux02vgYGB9O7dO1fBuSo0NJSaNWumWXbnnXc6Z0IrU6YMAJcuXUqT3F66dIn69etnut9XX32VkSNHOh/HxMQQHh5Op06dsqysvGK1Wlm/fj0dO3bEbL7FoYNuY1J/uSd1mDNrD1/g9e8O4WE24mEyYLfZeLlOCtMPWjCaTCTbHCRb7UzuVTvvW25v9uij2OfNw/Dqq5TZtYvOL7+MffFi/mnahocX/kmSzY6nQUMzaCilN+wqhyLJofAyGfliyF1UKuGbvzG6QM7B3JH6yz2pw9xxR/2lftOenRwntzfe3JXfWrZsybFjx9Is+/vvv6lQoQKg31xWpkwZNm7c6ExmY2Ji2LFjB88++2ym+/Xw8MAjgxsyzGZzgZ7gBX284kbqL/ekDl3TuWYY7/5ykosxiQR7G/C0mIEUzBYzSTbF9SQ7oQFedK4ZhtlszP+AXnxRv9msXz+0gwcx9eyJ+eEBpITfh83sgdVoxG5XzuTWaDBgc9iJTXFw7HIC1UODsj9GAZFzMHek/nJP6jB3CrL+XD1OjocCK0gvvvgif/75J2+99RYnTpxgxYoVLFq0iGHDhgGgaRojRoxgypQprF69moMHD9K/f3/Kli1Lz5493Ru8EKLYsFiMDG5dCQ+TkcgEK4kpdgASU+xEJljxNBl5slUlLJYCSGxT1akDf/0FI0YAUOnLj/l+6QjuvPQP8cl2Eq0OkmwOEq0O4pP1eDVN41JMLsfiFUKIQi7HLbeVKlVC0zK/b/iff/7JVUA3atKkCd999x2vvvoqkydPplKlSsycOZN+/fo5y4wePZr4+HiefvppoqKiaNWqFWvXrpXZ0oQQeerx5hUBWPL7KWLi9YkQkq16i+2TrSo51xcoT0+YMQO6dCHpsf5UvXqWrz8eyfQ2/fmwSU/QDChAAVYHWIxQJiD9t1ZCCFGc5Di5HfFfK0Eqq9XK3r17Wbt2LS+//HJexeV07733cu+992a6XtM0Jk+ezOTJk/P82EIIcaPHm1fk4UbhrPvfORyn9zK5V2061wwr2BbbjHTujGPXXjZ06k2Hv/9k3KaPaPfPbl7q/iKX/EpgAOzo18t7qpZyb6xCCJHPcpzcvvDCCxkunzt3bpppcYUQojiyWIx0qRXKz6f30qVWaMH0sXXBIYcHLz06ga5//sT4XxfT6vR+1nz0HGO6PMe6O1oA4GU2cOhSDE0rhbg5WiGEyD951ue2a9euzlEMhBBCFKxr8Skk2Rx8Xr8L9w74gANlqhKUFMvCVW/x9ppZeKckkmS1cy0+D6YIFkKIQizPktuVK1cSHBycV7sTQgiRA14WjSSbPmz5PyHl6P3YdObd9SAONB458As/LXue6meP4WXJbq41IYQo2nLcLaFBgwZpbihTSnHx4kWuXLnCvHnz8jQ4IYQQrtkbEZXmsdVo5p22A9lSqSHv//g+la5f4JtPX2aH4QwseReMhaM7hRBC5LUcJ7c3D7FlMBgoWbIk7dq1o0aNGnkVlxBCiBw4F5WU4fI/y9elyxNzeGvdXO49+jutls2Ek7th+XL4b8xwIYQoTnKc3E6YMCE/4hBCCJEL5YIzH/4wxtOX4feNZlPlxkzdtBDL779DvXowfz48+mgBRimEEPnvlvrcnjx5knHjxvHoo49y+fJlANasWcPhw4fzNDghhBCuGdisYtYFNI1v6rQnaftOuOsuiI6Gvn3h8cf13wuQzeZg9+lIAHafjsRmcxTo8YUQxVuOk9vffvuNOnXqsGPHDr799lvi4uIA2L9/v7TqCiGEm/xx6hrGbO4VM2qwRQuA33+HiRPBYIBPP4X69WHr1oIIk41HLjFo2U5e++4QAK99d4hBy3ay8cilAjm+EKL4y3FyO2bMGKZMmcL69euxWCzO5ffccw9//vlnngYnhBDCNRejkzEatEwv6gbAaNC4GJ0MJhNMmAB//AGVKkFEBLRpA6+/DlZrvsW48cglpq45yt+XY/H10HvF+XqY+PtyLFPXHJUEVwiRJ3Kc3B48eJBevXqlW16qVCmuXr2aJ0EJIYTImVL+HiilMBrAx2LAYtQwGcBi1PCxGDAa9NFtSvnfMP1u8+awbx/07w8OB7zxBrRuDSdO5Hl8NpuDZVsjiE2yUj7IC1/P/5JbTxPlg7yITbLy8bYI6aIghMi1HCe3gYGBXLhwId3yvXv3EhYWlidBCSGEyJnaof6YTQbsChwOB0YDmAwaRoP+2K7AYjJQO9Q/7Yb+/vDxx/DFFxAYCDt26N0Uli4FpfIsvj1nrxNxLZ4QH/0bv8i4lDT/h/hYOHU1nj1nr+fZMYUQt6ccJ7ePPPIIr7zyChcvXkTTNBwOB1u3buWll16if//++RGjEEKIbKQ4FJVK+GAAEm2QaFUk2RSJVkWiTb/YVyzhS4ojk4T14Ydh/35o2xbi4+GJJ6BPH4iMzJP4rsWnYLU7iEuyceDfaE5diwfg1LV4DvwbTWySFavdITOoCSFyLcfJ7VtvvUWNGjUIDw8nLi6OmjVr0qZNG1q0aMG4cePyI0YhhBDZ8LGY8Pc0YzYZuPm+Mg0wmwz4e5rwsWQxAmT58rBxI0ydqvfLXbkS6taFX3/NdXwhPhaSbA7+jUokxa4w/BekQYMUu+JcVBJJNoezZVcIIW5VjpNbi8XC4sWLOXnyJD/++COffvopR48eZfny5RhlxhshhHCL0r4enI9KwqEUJX1MmA36Bd5sgJI+JhxKcSE6idK+HlnvyGiEMWPgzz+henU4dw46dICXX4bk5FuOr3ZpfxKT7TiUntDemNwaNHAoSEyxU7u0f9Y7EkKIbNzSOLcA5cuXp1u3bvTp04dq1arlZUxCCCFyaN+5KJJtdmx2xeV4G1YHOACrAy7H27DZFUlWO/vORbm2w0aNYM8eePppve/tu+/q4+MeOXJL8f164jIKhQbYlR4X/8VnV3rrslKKX09cvqX9CyFEKpdmKBs5cqTLO3z//fdvORghhBC35lp8Ctfik7Fn0qXWruBafHLO+rT6+MDChdC1KwwerI+s0LAhvP8+PPMMaNkMrHuDi9F6q6/JADcPiKD9t/zGckIIcatcSm737t3r0s60HFzohBBC5B1Pg4bVnnUZq10vl2M9e0KzZjBwIPzyCwwdCj//DB9+CKVKubSL1KHKALwtBsyaAux4mQyYjBopNkf6ocqEEOIWuJTcbtq0Kb/jEEIIkQs/Hjzncrm7a5bJ+QFCQ2HNGpg1C155BX78Ub/ZbOlSvWU3G6lDlSX91x/B8F9jiEHTQOkty17mDIYqE0KIHLrlPrdCCCEKj3NRrnU3cLVchgwGGDECdu6EWrXg0iXo1g2efx4SE7PcNHWoMqOmkZDiIPG/ZuZEq52EFAdGTct6qDIhhHCRSy23N9u1axdfffUVZ86cISUl7YXy22+/zZPAhBBCuK5csCeccrFcbtWtqye4r7wCs2frP7/+CitW6Osy4GMxERrgxZXYZCLjU0hNYRVgNECQt4nQAM+shyoTQggX5Ljl9osvvqBFixYcOXKE7777DqvVyuHDh/n1118JCAjIjxiFEEJkY1yXO/O0XLa8vPQuCj//DKVLw+HD0KQJzJihT+V7k1B/T5KtDjRNo16YP5VCfACoFOJDvTB/NIOBFJuDUP88SL6FELe1W5rEYcaMGfzwww9YLBY++OADjh49Sp8+fShfvnx+xCiEECIbsVYHJX2zngChpK+FWGv6xDNXunaFAwegRw9ISYGRI6FLFzh/Pk2xCzFJeJgNBHqZiUqyYzHqHz8Wo4GoJDuB3hYsJgMXYpLyNj4hxG0nx8ntyZMn6d69O6BP6BAfH4+mabz44ossWrQozwMUQgiRvfgUG00qBRPqn3GCG+pvoWmlYOJTbHl/8FKl4PvvYf58vUV3/Xq9e8KqVWnis5gMVC3lR4rNwflovY/u+ehEUmwOqpT0wcNkyJ/4hBC3lRwnt0FBQcTGxgIQFhbGoUOHAIiKiiIhISFvoxNCCOESH4uJFJsDfy8LlYK9CPIy4WsxEORlolKwF/5eFpJtjvzr06pp+ti3u3dDgwZw7Rr06gVDhkB8vDO+E5djsRg1QgO9AAgN9MJi1Dh5OS5/4xNC3DZynNy2adOG9evXA/DQQw/xwgsv8NRTT/Hoo4/Svn37PA9QCCFE9lL7tEYlWinh50H1Mv7UCgukehl/Svh5EJVoLZg+rXfeqU/dO3q0nvAuWgQNGxL69yFnfME+FjyM+lBgHkaNYB9LwcUnhCj2XE5uU1to58yZwyOPPALAa6+9xsiRI7l06RK9e/fmww8/zJ8ohRBCZCm1T2uQt5nrCVaSbXYcSpFss3M9wUqgl7ng+rRaLDBtGmzYAGFh8PffGFu3pOe6T/Axwsmr8Zy9rndLOHs9kZNX4/EyG6XPrRAiT7j8/U/dunVp0qQJgwcPdia3BoOBMWPG5FtwQgghXJPap7Vh+SAiriYQmZBCfLINo8FAKX9PKoZ4E51oLdg+rffco99sNmQI2sqV9F45j6p7/uDV+18mMrjk/5dTYDTos5RJn1shRG653HL722+/UatWLUaNGkVoaCgDBgzg999/z8/YhBBCuMjHYsLTZMTTbKRxxSCaVw6haaUQmlcOoXGFIDzNRjxMxoLv0xocDF99xbXZC0jw8KLePwf4esGzPPzPdgDCg7yoWsoXm93BtbhkvM3Ggo1PCFHsuJzctm7dmo8++ogLFy4we/ZsIiIiaNu2LdWrV2fatGlcvHgxP+MUQgiRhbBAL6qU9OVCtP61vr+XmRK+Hvh7mQG4EJ1E1VK+hP13I1eB0jTiHn2M5176kMPhd+KTGMeLSyfR4IMPSLh6HbvdDmgoNArD/GQOh+JsZAJHL8ZwNjIBh8yaJkSRkuMbynx8fBg0aBC//fYbf//9Nw899BBz586lfPny3HffffkRoxBCiGwYDBqda5cm2MfC8ctxxCZZsTkcxCZZOX45jmAfC51qlcZg0NwSX6LVjrVSZQYOepcPWjyCXTNQftMmFswcgtq+g5gkKyV8Lc5ped3lxOVY5m8+yYz1fzNr43FmrP+b+ZtPcuJyrFvjEkK4LsfJ7Y2qVq3K2LFjGTduHH5+fvz00095FZcQQogcqlrKj0EtK1K7bABRCVYirsYTlWClTlgAg1pWpGopP7fF5mMxcSYygSvJihmtH+Oxx6YSX6oU4VGX+HrFKwz4ZRnnrsS6dSiwE5djWbo1gkPnown0NlO5hC+B3mYOnY9m6dYISXCFKCJu+SqyZcsWPvroI7755hsMBgN9+vThySefzMvYhBBC5FDVUn5UbufLuahE4lNs+FhMhAV6ua3FNlWQh4mzkf8/Fvqe8JpsnjED29TF3H9oMyO2fk6bU3sI7v4dBOfRFME54HAo1h26RGR8ChUCPfkzIpLoRBsBXibuqhjM6agkfjl8icolfN1el0KIrOUouT1//jzLli1j2bJlnDhxghYtWjBr1iz69OmDj49PfsUohBAiBwwGjfBgb3eHkcaS7f9gv6nrqs3Hh9H3jWJjpSZM+WUeDc8fI6VZY5g/D/r318fJLSDnohI5eSWOoxdiWHvoYpq+v/v/jaFCiDdeZiPnohILXd0KIdJyuVtC165dqVChArNnz6ZXr14cOXKEP/74g0GDBkliK4QQIkv/RmY+fu3qmm3pOmg2O8rVwpKYAAMHwsMPw/XrBRZffIqN7SevcupaQrqb2hQQcS2B7SevylBlQhQBLie3ZrOZlStX8u+//zJt2jTuuOOO/IxLCCFEMRIW5OH8XeP/P3wM/z0+F1CKRx99iz8GvQAmE3z9NdStC5s3F0yAdsWFmOQsi1yISSZd87MQotBxObldvXo1999/P0ajjEEohBAiZ+6tFZb9B47BSOkpk2HbNqhWDf79V58IYswYSEnJ1/i+3H06T8sJIdwnV6MlCCGEEK6wG6BckD7GrgIc/y13/PcYoFywF3YD0KQJ7NkDgweDUvpUvs2bw9Gj+Rbfv9ezbrXNaTkhhPtIciuEECLf+VhMVC/jR4BnxvcxB3iaqF7a7/+HAvP1hcWL4dtv9VnO9uyBhg1h4UI94c1j5YI987ScEMJ9JLkVQgiR70L9PUm2OvC0GGkQ5kfQf0lukKeJBmF+eFqMpNgchPrflDz26gUHD0KHDpCYCM88Az17wpUreRrfqHvuwHjD4AypfYFv/JA0ano5IUThJsmtEEKIfHchJgkPswGU4uCFOK4n6aMOXE+ycfBCHCiFxWTgQkwGoyqULQvr1sF774HFAqtX6zebrVuXZ/H5+ljoWifU+Ti1u4TjhjJd64Ti62PJs2MKIfKHJLdCCCHyXXyKjQvRiUQmWLE7VJrREuwORWSClQvRiZkPtWUwwMiR8NdfULMmXLwIXbrAiBGQlPkwYzkxp29D7q0bmqYFF/QW23vrhjKnb8M8OY4QIn+5b55DIYQQtw2zUePU1QTsDoWXScPTpAF2vMwGNA2S7IqIqwmYb84sb1avHuzaBaNHw5w58MEHsHEjrFgBderkOs45fRsSF5/Ce78e49/IJMoFezLqnjukxVaIIkRaboUQQuS7/52PIcVmx6jpE49Z/xsv1mpXaJreOppis/O/8zHZ78zLC2bPhp9+glKl4NAhfYSFDz4AhyP77bNhMRtpVCGYZpVDaFQhGItZhsAUoiiRllshhBD57lJMMgZNw2ZXxDsUHkY9uU1xKJLtekuLyahxKZuJFNLo1k2/2eyJJ/REd8QIWLMGli6F0NBsN8/I8u0RLPn9FFdik7ArhVHTmO73N4NbV+Lx5hVvaZ9CiIIlLbdCCCHyXZkADxxKkVm7qgNwKEWZAI9MSmSiVCn44QeYOxc8PfWbzOrWhe+/z3GMy7dHMH3dMS7GJOJhNhLkbcbDbORiTCLT1x1j+faIHO9TCFHwJLkVQgiR79pULoE9mx4DdodeLsc0DYYOhd279T65V6/qw4U98wzEx7u0i5QUO0t+P0WyzU6wtxmL0YBDgcVoINjbTLLNzod/nCIlxZ7z+IQQBUqSWyGEEPnuuwPn8rRchmrWhB07YNQo/fHChdCokZ70ZuOXoxe5EpuEp8lAXLKDmCQrMYk2YpKsxCU78DQZuByTxC9HL956fEKIAiHJrRBCiHx37rprw3W5Wi5THh7w7ruwYYM+Pu6xY3DXXfoUvvbMW10vRidjcyiSbQ6sdgcGTcNk1DBoGla7g2SbA5tDcTFapt8VorCT5FYIIUS+KxvoiUKf9ctswDmWrFHTH2s3lMsT7dvDgQPwwANgs8GYMfosZ2fPZli8tL/eJ9juUP8ltf/NUKbpN7rZHQqlFKX9c9gnWAhR4CS5FUIIke9aViuB2aChAKXAqOnprFHTUEqfDcxk0GhZ7Rb63GYmJARWroQPPwQfH9i8Wb/Z7Ouv0xWtWdYfi8mIXYHNaifFbifZpv9vs9qxK7CYjNQs65938Qkh8oUkt0IIIfKd3QEVQrwwaGBTYHPoQ4HZHAqb0ltIK4R4ZXvTWY5pmj5U2N690LQpREVBnz4waBDExjqLWe2KSiW80YAkByTbIMWu/5/k0FtxK5bwdo7PK4QovCS5FUIIke98LCbqlguiTpg/HkbNOSSYA/AwadQJ86duuSB8LPk0/Hq1avDHHzBunD6V77JlUL8+/PmnMz6T4Yb+ETfTwGQw5F98Qog8I8mtEEKIfBcW6EWVkr6UDfTmyZYVaFUlBIBWVUJ4skUFygZ6U7WUL2GBXvkXhNkMb7yhd0+oUAH++QdatYJJkyhpMRBxNQGHAm+zhqfJgMWo/+9t1nAoOH0tgZLeMg2vEIWdJLdCCCHyncGg0bl2aYJ9LJyKTKJSCV8AKpXw5VRkEsE+FjrVKo3BkFnTaR5q3Rr274d+/fQRFCZOJKF1a0pe+RezARxK781gMmhomv7YbIAkq50Nf1/K//iEELkiya0QQogCUbWUH4NaVqR22QCiE60ARCdaqRMWwKCWFalayq/gggkIgE8/1X/8/Qnet4tVS4bT53+bcPw3JFiSVR8CzKHA22JEIUOBCVEUSOchIYQQBaZqKT8qt/PlzNVY9m8/y7C7q1K+hF/BtNhmpF8/aNmSaw88TMjev5iy6j2a/72TyV2HEevl5xzdISHFjkEz5Hx6YCFEgZOWWyGEEAXKYNAIC9L71oYFebkvsU1VsSI+v29h9t0DsGkGuv9vC6sWD6fxmYMYNA2jprA6wNNspEP10u6NVQiRLUluhRBC3PauJNvZ8MBgHn58OhGBoYTGXGHZJ2MYvv5DrEkpmDSNCiHeXElIcXeoQohsSHIrhBDithefYiPAy8z5O+rS48lZfFmnIwYUz/65km8+fZkGiZcI8DITn2Jzd6hCiGxIciuEEOK25202cjUuGQ+TgTsql2FR/7GMf2wCMV5+1Ll4go/nDqXx+pV4m+RjU4jCrki9S99++200TWPEiBHOZUlJSQwbNoyQkBB8fX3p3bs3ly7JUC1CCCFcp887pqHQUEqRZLXxc/UW9H9+IQeqN8TLmsTzX75LiQGPwtWrbo01KcnGih0RAKzYEUFSkrQmC3GjIpPc7ty5k4ULF1K3bt00y1988UV++OEHvv76a3777TfOnz/PAw884KYohRBCFEWJVjslfC3EJFnZfTaGc9HJXIu3sg9/7u85kfc7DcZmNOH9849Qty6sX++WON/75RjN3v6VaWuPATBtrf74vV+OuSUeIQqjIpHcxsXF0a9fPxYvXkxQUJBzeXR0NB9++CHvv/8+99xzD40aNWLp0qVs27aNP/+bUlEIIYTIjo/FxJnIBK4nWNOtU5qBWQ168szwuVir3QEXLkCnTjByJCQlFViM7/1yjAW/nSQm2YpJ00eYMGkaMclWFvx2UhJcIf5TJJLbYcOG0b17dzp06JBm+e7du7FarWmW16hRg/Lly7N9+/aCDlMIIUQRFeRh4mxkgvOxAdBI+yG5ySuM5K1/wtCh+oIZM6BZMzh8ON/jS0qy8cm209gcCm+ThuW/vr8WkwFvk4bNoVi+/bR0URCCIjCJwxdffMGePXvYuXNnunUXL17EYrEQGBiYZnnp0qW5ePFipvtMTk4mOfn/Z5mJiYkBwGq1YrWm/6s9r6UeoyCOVRxJ/eWe1GHuSP3lXmGrww+3HcdkUJjQk1qN//5Ren9clVpu3zmGzpyJ1rEjxqefRjtwANW4MY6pU3EMHarP25sPvtwVgdWWgp9Jw2LSsBj0iCwGBSYNI4oUawpf7jpF32YV8yWG4qawnYNFjTvqz9VjaUoplX0x9zh79iyNGzdm/fr1zr627dq1o379+sycOZMVK1YwaNCgNIkqQNOmTbn77ruZNm1ahvudOHEikyZNSrd8xYoVeHt75/0TEUIIUex4REXRYNYsSu/ZA8Clhg3Z+/zzJN/U4CKEyBsJCQn07duX6Oho/P39My1XqJPbVatW0atXL4xGo3OZ3W5H0zQMBgPr1q2jQ4cOXL9+PU3rbYUKFRgxYgQvvvhihvvNqOU2PDycq1evZllZecVqtbJ+/Xo6duyI2WzO9+MVN1J/uSd1mDtSf7lX2Opw3ua/mbf5FAbA+N+MaQqFprfhYncoHMDQdpUY2q76/2+oFIb58zG88gpacjKqZEnsixahunfP0/hW7Ihg2tpjmDS9S4LFoHilrpVpB8ykODRSbA5sSvFKlzuk5dZFhe0cLGrcUX8xMTGUKFEi2+S2UHdLaN++PQcPHkyzbNCgQdSoUYNXXnmF8PBwzGYzGzdupHfv3gAcO3aMM2fO0Lx580z36+HhgYdH+vnBzWZzgZ7gBX284kbqL/ekDnNH6i/3CksdPtWyOvM2nyHR7sBoB4MBZ2rrcIAdDQ+TgadaVk8f7wsvQPv20K8f2oEDmHr1gmefhXffhTz6NvDhxpV4f8MpYpKteKN3RQBIcWgk2hQJNgjwtPBw40qYzYX6o73QKSznYFFVkPXn6nEK9Q1lfn5+1K5dO82Pj48PISEh1K5dm4CAAJ588klGjhzJpk2b2L17N4MGDaJ58+bcdddd7g5fCCFEEeHtbebBxuXQADtgdYDNof9vR/+wfLBROby9M/lwrV0bduyA1G8M58+HRo1g7948ic/T00T/FhUwGTQSbIoUmwOAFJuDBJvCbNB4vHkFPD0lsRWiUCe3rpgxYwb33nsvvXv3pk2bNpQpU4Zvv/3W3WEJIYQoYga1rEiVkj7cfEuYAahc0odBLStmvQNPT3j/fVi3DkJD4ehRfTSFd9/Vm39zaVSnO3imbRX8PczY/utRaFOKAE8zQ9pWYVSnO3J9DCGKgyL3J97mzZvTPPb09GTu3LnMnTvXPQEJIYQo8hwOxbpDl6hW2o8Od5Tkz4hIohNtBHiZuKtiMKejkvjl8CUql/DFYMhmRIROneDAAXjqKVi1Cl5+GdasgY8/hnLlchXnqE53MKxNFb7cdQqu/Y9XutzBw40rSYutEDco8i23QgghRG6di0rk5JU4vMwGDpyPJcmmMBo1kmyKA+dj8TIbOHE5jnNRia7tsEQJ+PZbWLxY73f766/6zGYrV+Y6Vk9Pk/Omsb7NKkpiK8RNJLkVQghx24tPsXE1Lpljl2K5HJuEp9lAkLcFT7OBy7FJHLsUy9W4ZOJTcjBJgqbB4MF6v9tGjeD6dXjoIXjySYiLy78nI8RtTpJbIYQQtz1vs1FPXpNsBPtY8DAZMWgaHiYjwT4W4pJsXItLxttszH5nN6teHbZtg1df1RPejz6C+vX1G9CEEHlOklshhBC3Pf32LA2Fhs1m5+TlWP53PpqTl2Ox2ezOdbc8MLzFAm+9BZs2QXg4nDwJLVvClClgt+fV0xBCIMmtEEIIQaLVTglfC9fiktnzbwxX463EJtu5Gm9lz78xXItLpoSvhURrLhPRtm31m80eeURPasePh3btICIiL56GEAJJboUQQgh8LCaOXIghLiXj5DUuxc6RCzH4WPLg5q3AQFixAj75BPz84I8/oF49+Oyz3O9bCCHJrRBCCOFnNnAlLiXLMlfiUvAz59HHpqbB44/D/v3QogXExMBjj0HfvhAdneWmDofi3HV91IZz1xNxOG65s0S+cTgUZyMTOHoxhrORCYUyRlF8yfghQgghbntT1h5xudy7DzXIuwNXqgS//ab3x508GT7/HLZuhU8/hdat0xU/cTmWdYcuEXElhlaeMHfTCSqW9Kdz7dJULeWXd3HlQmqMJ6/EkWSz42kyUqWkb6GKURRv0nIrhBDitvdvZFKelssRkwlef13vnlC5Mpw5o/fDHTcOrFZnsROXY1m6NYJD56MJ8NKnAQ7wMnPofDRLt0Zw4nJs3seWQzfGGOhtpnIJXwK9C1eMoviT5FYIIcRtr1yQR56WuyV33QX79sHAgfp0vW++Ca1awfHjzhnUIuNTqFbKF9//Jm7w9TRRrZQvkfEp/HL4klu//r85Rj9PM0aDhp+nudDEKG4PktwKIYS47T3RonKelrtlfn6wdCl89ZV+49lff0GDBkTNWcDJy7GEBngCEJtoS/N/aIBnzmZQyweps7ylxhiTaOVqXDIxidZCE6O4PUifWyGEELc9g8lACR8zV+OtmZYp4WPGYCqgNqGHHtJbcvv3h82bCX5hKI83uZsfh01iZ7KZuMRk6laEvyIi8fXyoGIJb5Jt9pzNoJbH4lNsJNnsJFkNHL0QS2RCCjaHA5PBQLC3pVDEKG4P0nIrhBDitudjMdGmeinC/mt1vFnZAE/aVC+VN0OBuSo8HDZsgGnTUGYzDXZu4tnnH6Dcnq14/jdqg6fZwJXYJPacvk6yzVGw8d3Ex2IixeZgz5nrGU5hvLsQxChuD5LcCiGEuO2FBXpRpaQvdcMDGdKyAneW8SUswJM7y/gypGUF6oUHUrWUL2GBXgUbmNEIo0dj/2Mb58tUoETMVaYvfImBq+ZhsFqxmAwEeZuJSrSSYnMQ6p9xcl4QQv09SbY6uJ5gJdDLTLLNQVRCCsk2B4FehSNGcXuQ5FYIIcRtz2DQ6Fy7NME+Fs5EJ9O8Sgl6NgyjeZUSnIlOJtjHQqdapTEYNLfEd6FqTaZMWs6PLe4DoPv6L2jz8suUOnvSmUxaTAYuxOTDaA6uxhiThIfZgNmgcfhCDCcuxXLqSjwnLsVy+EIMZoPm9hjF7UGSWyGEEAKoWsqPQS0rUrtsAFEJViKuxhOVYKVOWACDWlZ06xit8Sk28PFm26g3eHfoO0T7BBAQEcHb056i3+4faVQ+EA+Twe19bqMSUohOtGKzKzRNw2jU0DQNm10RnWglKsEqfW5FvpOOL0IIIcR/qpbyo3I7X85FJRKfYsPHYiIs0MttLbapfCwmPE1GPM1GDPffx4dNGtNv1ihK793LoM/f4/jxv1g+eIJb+7N6Gg2cvpaAzaEo4WvGoUABGmDQICrRxpnIeDyN0q4m8pecYUIIIcQNDAaN8GBvapTxJzzY2+2JLfx/n+AL0UkopYgPKsGf48ezdvAr2MwWqu36nTGvPkzYtk1ui/FibBIpNgcmg95aazIaMBsNmIwG/bFBI9nq4GKsdEsQ+UuSWyGEEKKQS+0TbDRorDt8iW0nr4LBwAd3dmboCws4F14V7+vXMPS4F4YPh4SEAo/xeoIVs1HDw2wk0erA5lAopbA5FIlWBx5mI2ajxvWEzIdbEyIvSHIrhBBCFCU3NSRHlK3M9MmfEPX00P9r777Do6ryP46/p2bSGyQhQEKVDtIFFFAQ2LUhuGKjybru/kAFXCyLKOoKVtRVhEVXsMG6uGIHRAREukREFGlSlJJQ08uU+/vjQtZQAxMyk+Hzep48yS1z7zfHkflwOPccc8fkydCunbnaWSVKjHQS7rQT67IT6bTh8RoUuX14vAaRR/eHO+0kRjortS658CjcioiIBLljS9t6fQa9mybTuX41ADrXr0bvpskU253MvGkUvs/mQkoKbNwIHTvCpEnmUr6VoE3teOokRpJX4iUlJoza8eHUjA+ndnw4KTFO8kq81K0WSZva8ZVSj1y4FG5FRESC3G+XtrVarUSHmw+ORYfbsVqt/1vatmNXWL8err0WSkrg3nuhVy/Yvfu812i3WxnSpQ7RLgc7DuSzN7uQzJwi9mYXsuNAPjEuB4M718FeWau8yQVL7zAREZEgd2xp24hTzIYQ7rT9b2nb6tXhgw9g6lQID4eFC6FlS3j//fNeZ48myTROieZwoYfM3BKyckvIzC3hcKGHRinR9GiSfN5rEFG4FRERCXLHpgIrOMUcsYUlXsLstv9NBWaxwJ13QkYGtGkDhw5B//7wxz9CXt55q/O5zzcx/4d9+AxwWMFpNb/7DJj/wz6e+3zTebu3yDEKtyIiIkHut1OBeb1e9h4pBGDvkUJzO7vo5MsDN24MK1bA/febgfdf/zLD7po1FV5jUZGHN5fvxOMzCHdYcNpt2O1WnHYb4Q4LHp/BWyt2UlSkRRzk/FK4FRERCXLHpgIrKPEwa82vfLExE4AvNmYya82vFJR4Tr08sNMJTz4JX34JtWrBli3QuTNMmABeb4XV+G7GLvKK3Tgs4PFBscdLsdtHsceLxwcOC+QWuXk3Y1eF3VPkZBRuRUREqoCdBwvYfqCAYo8Xm8UMsTaLhWKPl+0HCth58Axz23bvbj5sduON4PHA2LFw+eWwc2eF1Lf7cBE+wwy2Xp+BBQtWqwULFrw+A4/PHJ6w+7AWcZDzS+FWREQkyHk8PmYs20Gxx0uTlGjSEyMASE+MoElKNMUeL28s34HHc4Zpv+Lj4d//hjfegKgoWLoUWrWCWbP8rrFGnAswl9y1Wi1YLOaUvBaLuW0cd57I+aJwKyIiEuQyfjnMjoP5JEY6sVgsFHvMqFjsMbBYLCRGOtl+IJ+MXw6f+WIWCwwaZC7ycMklkJ0Nt9wCAweaP5+jyxpUw241w63hM/AZBt6j3w2fgQHYreZ5IueTwq2IiEiQO5hfgtvro8Tj5ad9uWw/YM54sP1AHj/ty6XY48Xt9XEwv6T8F61f3+y5HT8erFZ4+224+GJYtuycavQYZk+y5ejPHh94j373GGYvbnpiJB7jTFcS8Y/CrYiISJBLjHTi8RnsOlRAYYkX29EHx2xWC4UlXn45VIDHZ5z90rZ2OzzyiBly69aFHTuga1d4+GFwu8/qUpFOO9WjXThOPhUvDjtUjw7733RlIueJwq2IiEiQa1kjFrfHwO0Dhw2sRx8os1osOGzg9oHHa9CyRuy53aBzZ3OYwqBB5nK9jz8Ol10G27aV+xLJUWHsOVKEBQvVI2xEOW2E261EOW1Uj7BhwcLe7CKSo8LOrUaRclK4FRERCXLr92bjsIHdaqHIY1DoNqfwKnR7KfIY2C0W7FbzvHMWE2M+aPbvf0NsLKxaZQ5TmDEDjDOPJVi3+wjFHnMxiVy3gdtnYGB+z3UbhNltFLm9rNt95NxrFCkHhVsREZEgZ46lteCyW7EcN5WtxQIuhxWwnN2Y21MZMMCcMqxbN3M1s6FDzenDDh06Y40erw+b1WLOkoCBYZjfLZhDKDxnOy5Y5Bwo3IqIiAS5+AgHJV5zmq+kKCfxEc6j+50kRZk/l3h9xEc4KuaGaWmwcCFMnGiOy33vPWjZEhYtOm2Nbq+Bx+sjLtxBbLiT2Ajze1y4A4/Xh9trVFyNIqegcCsiIhLkUmJchNmteH0GYCHMYX58hx3tsfX4DFwOKykxFTiHrM0GDzxgLt970UWwezf06AH33QclJ/a+pkS7cNqteHwGYE4D5vH6jtZs4PEZhDmspEQHfp5bn89g92FzCePdhwvx+TSFQyhRuBUREQlyRR4f6YkRhDls5BR5KD66WEOxx0dOkQeXw0ZaQgRFZ1rE4Vy0awcZGfCnP5ljb595xpwfd+PGsjV6faVTgWXmlnAov4TDBR4O5ZeQmVuCFUhLiKTIex5qPAtbs3KZsngbkxdtBWDyoq1MWbyNrVm5Aa1LKo7CrYiISJCLdNpJS4ikbXociZFO3EdDrNvjIzHKSdv0ONISIs/fNFuRkfDPf8KcOZCYCN9+C23bwtSppQ+bRTrtOGxWjg0KPtYXWvrdAg6bJaBTgW3NymX6sh1s2JNNbLg5PCI23MGGPdlMX7ZDATdEKNyKiIgEuZpx4dSvHoXDZuPaVjW4onESAFc0TuLaljVw2Gw0SIqiZlz4+S2kb1/zYbMrr4TCQvjLX+C66yArq3QqMK/PR1KUk7gIB9EuO3ERDpKinHh9RkCnAvP5DOZvyORQfgkNk6KIcpkhO8plp2FSFIfyS/j8h0wNUQgBCrciIiJBzmq10Lt5MgmRTrYdKCDaZfY6RrscbDtQQEKkk17NkrFaLWe4UgVITYV582DSJHA64eOPoWVLtr/z3tGpwKwcKfJQUOKl2OOloMTLkSIPYTZrQKcC232kkG3786gR68Jy3JQTFouFGrEutmblsftIYUDqk4qjcCsiIlIFNEiKZmiXOjRPjSW70Fw9LLvQTYuasQztUocGSdGVV4zVCqNGwerV0KwZZGbS6PabGPnRy4R7iuHocrsWzGnBMMyXeLxGwKYCyy/xUOTxEnGKYRHhThvFHi/5JZ5KrkwqmsKtiIhIFdEgKZq/dK/P8MsbADD88gb8uVv9yg22v9WqFaxZA3ffDcBNqz7k7Wn30D7nF2LDHcSE24kNd5AQ6cDrA7fXR0KApgKLdNpx2W0UnCK8FpaYC1BoeeCqT+FWRESkCrFaLdSMN8fW1owPr5yhCKcTHg4vvsi+f7/Pwah4Gu7fyb9eGcEtK97HaQG7zYJhgMcHYQ4bSRU5XdlZODZueW92EcZxK64ZhjkeuFLGLct5p3ArIiIifjvSrQdjxr3JkkaX4PS6uefTKTw3/QGiD+0/Ol2ZlbSE8NJpzCrbb8ctb8nKI6/I7MHNK/KwJSuvcscty3mlcCsiIiJ+i3TaiUuvxVsPvMCzfUdSaA+j49YMZr18J9ftXH3+pysrh6AatyznjcKtiIiI+K10ujK7He78E/94eha70hsRX5jDhDcfYfAbT9I42hrwf/YPunHLUuEUbkVERMRvx09XVtzgIma//B+W9bsdn8XCZYvmMOTu/lgz1ga61OAbtywVSuFWREREKsRv/9n/SIGbn7Pd/PfGu/j4mTfw1EjFuW0rdOoETz4JXm+gy5UQpfkuREREpMI0SIqmXvcodh8pJL/EQ6TTTs24VliHXgV33gnvvQcPPmguBPHmm5CWFuiSJcSo51ZEREQqlM9nsDe7kO0H8tmbXWguaZuQAP/5D7z+OkRGwpIl0LIlvPtuoMuVEKOeWxEREakwCzdmMmPZDnYczMft9eGwWamTGMmQLnXo0SQZhg6Fyy6D226DVavgppvgs8/gpZcgJibQ5UsIUM+tiIiIVIiFGzOZOPcnNmflEu2yUzM+nGiXnc1ZuUyc+xMLN2aaJzZoAEuXwrhx5rq8b74JF18MK1YEtH4JDQq3IiIi4jePx8eMZTvILXKTFh9OtMuB3Wol2uUgLT6c3CI3byzfgefYIg4OBzz2mDk8IT0dtm+HSy+F8ePBc/IlckXKQ+FWRERE/Jbxy2F2HMwnMdKJ1Vo2XlitVhIjnWw/kE/GL4fLvvDSS+G77+DWW8Hng0cfha5d4eefK7F6CSUKtyIiIuK3g/kluL0+wp22kx4Pd9pwe30czC858WBsLLz9NrzzjjnudsUKaNUK3ngDDOM8Vy6hRuFWRERE/JYY6cRhs1JYcvL5awtLvDhsZg/uKd1yC6xfbz5wlpcHQ4aYD5wdPnzq14gcR+FWRERE/Namdjx1EiM5mF+Cz+ej2O2loMRDsduLz2f22NatFkmb2vGnv1B6OixaBE88AXa7OX1Yy5aweHGF1VpQ4OaVxZsBeGXxZgoK3BV2bQk8hVsRERHxm91uZUiXOoTZbWzcl8v2A/n8cqiA7Qfy2bgvF5fdxuDOdbDbyxE9bDb4299g+XJo2BB+/RWuuMJc/KHkJMMazsLYOd/T+okveGXxdgBeWbyd1k98wdg53/t1XQkeCrciIiJSIdITI6hbLYIwuw2vYeD2+vAaBmF2G3WqRZCeGHF2F2zfHjIy4I9/NMfePvmkuXzvpk3nVN/YOd8za/Uuir2+0gBkBYq9Pmat3qWAGyIUbkVERMRvPp/B/A2ZRDjt3Ny+Fn2apdCtURJ9mqVwc/taRDjtfP5Dprla2dmIioJXX4X33zdXOcvIgDZtYNq0s3rYrKDAzXvf/IrPALsF7FYLYH63W8BnwHtrf9UQhRAQ1OF24sSJtG/fnujoaJKSkujbty+bjvvbWlFREcOHDycxMZGoqCj69+9PZmZmgCoWERG5MO0+Usi2/XnUiHVhs9moGR9Bw6RoasZHYLPZqBHrYmtWHruPFJ7bDa6/Hr7/Hnr2hIICuPNOc9/+/eV6+bTl20p7bC1WC8disXF02woUe3xMW77t3OqToBHU4XbJkiUMHz6clStXsmDBAtxuN7169SI/P7/0nFGjRvHxxx8ze/ZslixZwp49e+jXr18AqxYREbnw5Jd4KPJ4iXDaT3o83Gmj2OMlv8SPBRpSU2H+fHjuOXA64cMPzYfN5s8/40t/PVRU+rPXZ+A52oPs8Rl4f9Ob/NvzpGo6+TswSMybN6/M9owZM0hKSmLt2rV07dqV7Oxs/vWvfzFz5kyuuOIKAKZPn06TJk1YuXIll1xySSDKFhERueBEOu247DYKSjxEuxwnHC8s8RJmtxF5ivBbblYrjB4NPXqYU4f9+CP06QP33GOOyXW5TvqyWgnmfh9gMcBydL8Fc3SDcdx5UnUFdc/t8bKzswFISEgAYO3atbjdbnr27Fl6TuPGjUlLS2OF1qcWERGpNDXjwqlfPYq92UUYx42FNQyDvdlFNEiKomZceMXcsFUr+OYbGDHC3H7xRfMBtO9P/lDYHzvVw3Y00R4/UvfYts1inidVW1D33P6Wz+dj5MiRdOnShebNmwOwb98+nE4ncXFxZc5NTk5m3759p7xWcXExxcXFpds5OTkAuN1u3O7zP5D82D0q416hSO3nP7Whf9R+/lMb+idY269n40T2Zefzc1YOKTEuwp1WCkt87Mspolqkkx6NEvF6PXhPvs7D2bPbYdIkLFdeie2OO7Bs2IDRvj2+CRPwDR9u9vIedSC/iPrVwtl5qAAAh9Uo/e47ek56QgQH8osIc1qOv5McJxDvwfLey2Ic/9erIPWXv/yFuXPn8vXXX1OrVi0AZs6cydChQ8sEVYAOHTpw+eWX89RTT530WuPHj+fRRx89Yf/MmTOJiDjLaUpEREQk4JxHjtD65ZdJ+eYbADJbt+bbu+6i+Oi/9krVV1BQwC233EJ2djYxMTGnPK9KhNsRI0bw4Ycf8tVXX1G3bt3S/V9++SU9evTg8OHDZXpv09PTGTlyJKNGjTrp9U7Wc1u7dm0OHDhw2saqKG63mwULFnDllVficJw4LklOT+3nP7Whf9R+/lMb+ifY28/nM4ch5Jd4iHTaqRHrwmqthN5Qw8D6z39ive8+LEVFGNWq4f3nPzGuuYZfDxUw8t11FJZ4iA+3czi/mOGNCpm8KZz4yDAOFZq1Pj/gYmolqKPrTALxHszJyaFatWpnDLdBPSzBMAzuuusu5syZw+LFi8sEW4C2bdvicDhYuHAh/fv3B2DTpk3s2rWLTp06nfK6YWFhhIWFnbDf4XBU6h8SlX2/UKP285/a0D9qP/+pDf0TzO1XJ8kZmBvfdZf5sNmtt2JZtw57//7w5z9j+9tjuA0rxT4rPqud2EgLUEhspAuf1UaJz4fDsGK124O2TYNRZb4Hy3ufoH6gbPjw4bz99tvMnDmT6Oho9u3bx759+ygsNOfIi42NZdiwYYwePZpFixaxdu1ahg4dSqdOnTRTgoiIyIWqaVNYuRL++ldze+pUki/vQtuDP+OwWdh2IJ9dh8wssetQIdsO5OOwW6gW5aTQXVEDgiVQgjrcTpkyhezsbLp3706NGjVKv959993Sc55//nmuvvpq+vfvT9euXUlJSeH9998PYNUiIiIScGFh8MwzsGABpKYStm0Lj0z4I3/4chYWrw/L0VESFgtggMdr4LRb/Z+qTAIuqP8Llmc4sMvlYvLkyUyePLkSKhIREZEqpWdPWL8e3x13YJ8zhzs/m0bnrd8weeCDgIPa8eEYFiu/HCmixOOjRozmua3qgrrnVkRERMRviYnsfvUtZgwdS6HTRYvNGTw7YSipy5aBBY4UeoiLcOK0W9mboxXKqjqFWxEREQl5+W4vq3tczyvPzWZrnSZEFebR/plnuPONiaQ5vbRJiyPMbvVveWAJCgq3IiIiEvKOLQ+cn16XTyb/h6V/uAPDaqXn6nlMmjiUBts2VMzywBJwCrciIiIS8n67PLDP7mDtH0fx9eOPk5NUg7i9vzDkgUHcNG86NaM0DVhVp3ArIiIiIc9qtdC7eTIJkU62ZOWRV+ThULNm/PP52azp1Bubz0uHGf/Aenl32L490OWKHxRuRURE5ILQICmaoV3q0Dw1luxCNwBZtnDWPPEy+ya/CjExsHw5tGoFb78Nwb+Iq5yEBpaIiIjIBaNBUjT1ukex60Au3634heGXNyCtWjTWyxvA73rAwIGwbJn5/bPP4JVXIC6uUmv0+Qx2HyksXb64Zlx45SxfHCIUbkVEROSCYrVaqBkfzndAzfjfBMe6dWHxYnjySRg/HmbNMoPuW29B166VUtvWrFzmb8hk2/48ijxeXHYb9atH0bt5Mg2SoiulhqpOwxJEREREjrHb4aGHzFBbvz7s2gXdu8PYseB2n9dbb83KZfqyHWzYk01chIN61aKIi3CwYU8205ftYGtW7nm9f6hQuBURERE5XseO8O23MHSoOfZ2wgTo3Bm2bDkvt/P5DOZvyORQfgkNk6KIdjmwWS1Euxw0TIriUH4Jn/+Qic+nccBnonArIiIicjLR0fD66zB7NsTHwzffwMUXw2uvVfjDZruPFLJtfx41Ys3lf3MK3RzIKybn6INvNWJdbM3KY/eRwgq9byhSuBURERE5nRtugPXr4fLLoaAA7rgD+vWDAwcq7Bb5JR6KPF6K3D7W7DjMip8Psurng6z4+SBrdhym0O2l2OPVCmrloHArIiIicia1asEXX8DTT4PDAR98AC1bwoIFFXL5SKedEo+PtTsPsT+3CJfDRnykE5fDxv7cIjJ2HqbY49MKauWgcCsiIiJSHlYrjBkDq1ZB48awdy/06gX33gvFxX5dukaMi2K3jyOFbuIjHITZrVgtFsLsVuIjHBwpdFPi8VEjxlVBv0zoUrgVERERORutW8PatfB//2duT5oEHTrADz+c8yX35hQR5jCD7OECN8UeLz7DoNjj5XCBm7hwB067lb05RRX0S4QuhVsRERGRsxURAZMnw8cfQ/Xq5pjcdu3gpZfO6WGz/BIPTruVNmnxJEW7KHL7OFJQQpHbR1KMi7bp8YTZrRpzWw4KtyIiIiLn6uqrzWD7u99BURHcfTdcdRVkZp7VZSKddlx2Gy6HjXZ14ulUL5EOdRPpVC+RdunxuBw2wuw2jbktB4VbEREREX+kpMCnn5q9tmFhMHcutGgBn3xS7kvUjAunfvUo9mabww5iwh1UiwojJtwBwN7sIhokRVEzLvy8/AqhROFWRERExF8WC4wYYc6F27Il7N8P11xjjsstKDjjy61WC72bJ5MQ6WRLVh65RW48Ph+5RW62ZOWREOmkV7Pk/y0VLKekcCsiIiJSUZo3N2dTGDXK3J4yBdq2NVc7O4MGSdEM7VKH5qmxHClws+NAPkcK3LSoGcvQLnVokBR9nosPDRq4ISIiIlKRXC5zBoU+fWDIEPjpJ3M53wkTYPRoc0qxU2iQFE297lHsPlJIfomHSKedmnHh6rE9C+q5FRERETkfevUyHza77jpwu805cq+8En799bQvs1ot1E6IoHFKDLUTIhRsz5LCrYiIiMj5Uq0azJkD06aZ04d9+aU5Jve//w10ZSFL4VZERETkfLJY4I47zHG3bdvC4cNwww0wbBjk5QW6upCjcCsiIiJSGS66CJYvhwcfNAPv66+bq52tXh3oykKKwq2IiIhIZXE6zQfLFi2C2rVh61bo3BmeeAK83kBXFxIUbkVEREQqW7du8N13MGCAGWofegi6d4edOwNdWZWncCsiIiISCPHxMGsWvPkmREfD11+bD5vNnBnoyqo0hVsRERGRQLFYYOBAsxe3c2fIyYFbb4XbboPs7EBXVyUp3IqIiIgEWt26sGQJjB8PNhu88w60amX25spZUbgVERERCQZ2OzzyCCxdCvXqmeNvu3WDcePMRSCkXBRuRURERIJJp06wbp25dK/PB3//O1x6KWzZEujKAPB4fKzdeQiAtTsP4fH4AlxRWQq3IiIiIsEmOhqmT4d334W4OHMu3NatzblxDSNgZS3cmMnQGWsYO2cDAGPnbGDojDUs3JgZsJqOp3ArIiIiEqxuvBHWrzenCcvPN1c1+8Mf4ODBSi9l4cZMJs79ic1ZuUSF2QGICrOzOSuXiXN/CpqAq3ArIiIiEsxq14YvvoCnnjLH5f73v+aUYQsXVloJHo+PGct2kFvkJi0+nCjX0XDrspMWH05ukZs3lu8IiiEKCrciIiIiwc5mg/vug5UroVEj2LMHevaEMWOguPi83z7jl8PsOJhPYqQTq7VsfLRarSRGOtl+IJ+MXw6f91rOROFWREREpKpo2xbWroU77zS3n30WLrkEfvzxvN72YH4Jbq+PcKftpMfDnTbcXh8H80vOax3loXArIiIiUpVERsLUqfDBB1CtmjmzQtu28Mor5+1hs8RIJw6blcIS70mPF5Z4cdjMHtxAU7gVERERqYquu8582KxXLygqguHD4ZprILPiH+xqUzueOomRHMwvwecrO67W5zN7bOtWi6RN7fgKv/fZUrgVERERqapq1IC5c+GFFyAsDD791HzY7LPPKvQ2druVIV3qEO1ysOtwIXlFHgDyijzsOlxIjMvB4M51sNsDHy0DX4GIiIiInDurFe65B9asgebNISsLrroKRoyAwsIKu02PJsk8+LvGXJQUTV7x0XBb7KFRcjQP/K4xPZokV9i9/KFwKyIiIhIKWrQwA+4995jbkydDu3bw3XcVdoseTZKZPqQ9T1zfHIAnrm/O64PbB02wBYVbERERkdDhcplDFObOheRkcxaFDh1g0iRzKd8KYLdbaZueAEDb9ISgGIrwW8FVjYiIiIj4r08f+P578wGzkhK4917o3ducHzfEKdyKiIiIhKLq1eHDD81pw8LDzVXOWrSAOXMCXdl5pXArIiIiEqosFnPBh4wMaN0aDh2Cfv3gjjsgLy/Q1Z0XCrciIiIioa5xY3Pp3vvuMwPva69BmzbmA2ghRuFWRERE5ELgdMJTT8HChVCzJmzZAp07w8SJ4D35ymNVkcKtiIiIyIXk8svNlc3+8AfweOBvf4MrroCdOwNdWYVQuBURERG50CQkwLvvwowZEBUFX30FrVrBrFmBrsxvCrciIiIiFyKLBQYPhnXroGNHyM6GW26BgQPNn6sohVsRERGRC1n9+rB0KTz8sLmU79tvw8UXw7Jlga7snCjcioiIiFzoHA549FFzeEKdOrBjB3TtagZetzvQ1Z0VhVsRERERMXXpAt99B4MGmcv1Pv44XHYZbN0a6MrKTeFWRERERP4nJgbeeMN8uCw2FlatMocpTJ8OhhHo6s5I4VZERERETnTTTeaUYV27Qn4+3H47DBhgrnIWxBRuRUREROTk0tLgyy/NhR7sdpg9G1q2xLJ4caArOyWFWxERERE5NZsNHngAVqyAhg1h925svXvT9I03oKQk0NWdQOFWRERERM6sXTv49lu44w4shkHDOXOwDRoU6KpOoHArIiIiIuUTGQnTpuGZPZuiuDh8o0cHuqIThEy4nTx5MnXq1MHlctGxY0dWr14d6JJEREREQpJx3XUs+Oc/MTp0CHQpJwiJcPvuu+8yevRoHnnkETIyMmjVqhW9e/cmKysr0KWJiIiIhCRfWFigSzipkAi3kyZN4o477mDo0KE0bdqUqVOnEhERweuvvx7o0kRERESkElX5cFtSUsLatWvp2bNn6T6r1UrPnj1ZsWJFACsTERERkcpmD3QB/jpw4ABer5fk5OQy+5OTk/npp59O+pri4mKKi4tLt3NycgBwu924K2H95GP3qIx7hSK1n//Uhv5R+/lPbegftZ//1Ib+CUT7lfdeFsOoAuuoncaePXuoWbMmy5cvp1OnTqX777vvPpYsWcKqVatOeM348eN59NFHT9g/c+ZMIiIizmu9IiIiInL2CgoKuOWWW8jOziYmJuaU51X5nttq1aphs9nIzMwssz8zM5OUlJSTvubBBx9k9G+mrsjJyaF27dr06tXrtI1VUdxuNwsWLODKK6/E4XCc9/uFGrWf/9SG/lH7+U9t6B+1n//Uhv4JRPsd+5f2M6ny4dbpdNK2bVsWLlxI3759AfD5fCxcuJARI0ac9DVhYWGEneQJP4fDUalv8Mq+X6hR+/lPbegftZ//1Ib+Ufv5T23on8psv/Lep8qHW4DRo0czePBg2rVrR4cOHXjhhRfIz89n6NChgS5NRERERCpRSITbAQMGsH//fh5++GH27dvHxRdfzLx58054yExEREREQltIhFuAESNGnHIYgoiIiIhcGKr8PLciIiIiIsco3IqIiIhIyFC4FREREZGQoXArIiIiIiFD4VZEREREQobCrYiIiIiEDIVbEREREQkZCrciIiIiEjJCZhEHfxiGAUBOTk6l3M/tdlNQUEBOTo7Wsz4Haj//qQ39o/bzn9rQP2o//6kN/ROI9juW047ltlNRuAVyc3MBqF27doArEREREZHTyc3NJTY29pTHLcaZ4u8FwOfzsWfPHqKjo7FYLOf9fjk5OdSuXZtffvmFmJiY836/UKP285/a0D9qP/+pDf2j9vOf2tA/gWg/wzDIzc0lNTUVq/XUI2vVcwtYrVZq1apV6feNiYnR/1B+UPv5T23oH7Wf/9SG/lH7+U9t6J/Kbr/T9dgeowfKRERERCRkKNyKiIiISMhQuA2AsLAwHnnkEcLCwgJdSpWk9vOf2tA/aj//qQ39o/bzn9rQP8HcfnqgTERERERChnpuRURERCRkKNyKiIiISMhQuBURERGRkKFwKyIiIiIhQ+G2Eu3evZvbbruNxMREwsPDadGiBd98802gy6oyvF4v48aNo27duoSHh1O/fn0ef/zxM64xfSH76quvuOaaa0hNTcVisfDBBx+UOW4YBg8//DA1atQgPDycnj17smXLlsAUG4RO135ut5v777+fFi1aEBkZSWpqKoMGDWLPnj2BKzgInek9+Ft//vOfsVgsvPDCC5VWX7ArT/tt3LiRa6+9ltjYWCIjI2nfvj27du2q/GKD1JnaMC8vjxEjRlCrVi3Cw8Np2rQpU6dODUyxQWjixIm0b9+e6OhokpKS6Nu3L5s2bSpzTlFREcOHDycxMZGoqCj69+9PZmZmgCpWuK00hw8fpkuXLjgcDubOncuPP/7Ic889R3x8fKBLqzKeeuoppkyZwssvv8zGjRt56qmnePrpp3nppZcCXVrQys/Pp1WrVkyePPmkx59++mn+8Y9/MHXqVFatWkVkZCS9e/emqKiokisNTqdrv4KCAjIyMhg3bhwZGRm8//77bNq0iWuvvTYAlQavM70Hj5kzZw4rV64kNTW1kiqrGs7Uftu2bePSSy+lcePGLF68mPXr1zNu3DhcLlclVxq8ztSGo0ePZt68ebz99tts3LiRkSNHMmLECD766KNKrjQ4LVmyhOHDh7Ny5UoWLFiA2+2mV69e5Ofnl54zatQoPv74Y2bPns2SJUvYs2cP/fr1C1zRhlSK+++/37j00ksDXUaVdtVVVxm33357mX39+vUzbr311gBVVLUAxpw5c0q3fT6fkZKSYjzzzDOl+44cOWKEhYUZs2bNCkCFwe349juZ1atXG4Cxc+fOyimqijlVG/76669GzZo1jQ0bNhjp6enG888/X+m1VQUna78BAwYYt912W2AKqoJO1obNmjUzHnvssTL72rRpY4wdO7YSK6s6srKyDMBYsmSJYRjm54bD4TBmz55des7GjRsNwFixYkVAalTPbSX56KOPaNeuHX/4wx9ISkqidevWvPrqq4Euq0rp3LkzCxcuZPPmzQB89913fP311/zud78LcGVV0/bt29m3bx89e/Ys3RcbG0vHjh1ZsWJFACururKzs7FYLMTFxQW6lCrD5/MxcOBAxowZQ7NmzQJdTpXi8/n49NNPueiii+jduzdJSUl07NjxtEM/5ESdO3fmo48+Yvfu3RiGwaJFi9i8eTO9evUKdGlBKTs7G4CEhAQA1q5di9vtLvNZ0rhxY9LS0gL2WaJwW0l+/vlnpkyZQsOGDZk/fz5/+ctfuPvuu3njjTcCXVqV8cADD3DTTTfRuHFjHA4HrVu3ZuTIkdx6662BLq1K2rdvHwDJycll9icnJ5cek/IrKiri/vvv5+abbyYmJibQ5VQZTz31FHa7nbvvvjvQpVQ5WVlZ5OXl8eSTT9KnTx8+//xzrr/+evr168eSJUsCXV6V8dJLL9G0aVNq1aqF0+mkT58+TJ48ma5duwa6tKDj8/kYOXIkXbp0oXnz5oD5WeJ0Ok/4S30gP0vsAbnrBcjn89GuXTsmTJgAQOvWrdmwYQNTp05l8ODBAa6uavjPf/7DO++8w8yZM2nWrBnr1q1j5MiRpKamqg0loNxuNzfeeCOGYTBlypRAl1NlrF27lhdffJGMjAwsFkugy6lyfD4fANdddx2jRo0C4OKLL2b58uVMnTqVbt26BbK8KuOll15i5cqVfPTRR6Snp/PVV18xfPhwUlNTy/RGCgwfPpwNGzbw9ddfB7qU01LPbSWpUaMGTZs2LbOvSZMmeqL1LIwZM6a097ZFixYMHDiQUaNGMXHixECXViWlpKQAnPBEa2ZmZukxObNjwXbnzp0sWLBAvbZnYenSpWRlZZGWlobdbsdut7Nz507uvfde6tSpE+jygl61atWw2+36bPFDYWEhf/vb35g0aRLXXHMNLVu2ZMSIEQwYMIBnn3020OUFlREjRvDJJ5+waNEiatWqVbo/JSWFkpISjhw5Uub8QH6WKNxWki5dupwwdcbmzZtJT08PUEVVT0FBAVZr2beszWYr7b2Qs1O3bl1SUlJYuHBh6b6cnBxWrVpFp06dAlhZ1XEs2G7ZsoUvvviCxMTEQJdUpQwcOJD169ezbt260q/U1FTGjBnD/PnzA11e0HM6nbRv316fLX5wu9243W59tpyGYRiMGDGCOXPm8OWXX1K3bt0yx9u2bYvD4SjzWbJp0yZ27doVsM8SDUuoJKNGjaJz585MmDCBG2+8kdWrVzNt2jSmTZsW6NKqjGuuuYYnnniCtLQ0mjVrxrfffsukSZO4/fbbA11a0MrLy2Pr1q2l29u3b2fdunUkJCSQlpbGyJEj+fvf/07Dhg2pW7cu48aNIzU1lb59+wau6CByuvarUaMGN9xwAxkZGXzyySd4vd7S8WUJCQk4nc5AlR1UzvQePP4vBA6Hg5SUFBo1alTZpQalM7XfmDFjGDBgAF27duXyyy9n3rx5fPzxxyxevDhwRQeZM7Vht27dGDNmDOHh4aSnp7NkyRLefPNNJk2aFMCqg8fw4cOZOXMmH374IdHR0aV/zsXGxhIeHk5sbCzDhg1j9OjRJCQkEBMTw1133UWnTp245JJLAlN0QOZouEB9/PHHRvPmzY2wsDCjcePGxrRp0wJdUpWSk5Nj3HPPPUZaWprhcrmMevXqGWPHjjWKi4sDXVrQWrRokQGc8DV48GDDMMzpwMaNG2ckJycbYWFhRo8ePYxNmzYFtuggcrr22759+0mPAcaiRYsCXXrQONN78HiaCqys8rTfv/71L6NBgwaGy+UyWrVqZXzwwQeBKzgInakN9+7dawwZMsRITU01XC6X0ahRI+O5554zfD5fYAsPEqf6c2769Oml5xQWFhr/93//Z8THxxsRERHG9ddfb+zduzdgNVsMQ8s7iYiIiEho0JhbEREREQkZCrciIiIiEjIUbkVEREQkZCjcioiIiEjIULgVERERkZChcCsiIiIiIUPhVkRERERChsKtiEgl6969OyNHjgx0GeUyY8YM4uLiAl2GiEi5KdyKiJTTNddcQ58+fU56bOnSpVgsFtavX1/JVQW/AQMG0KFDB7xeb+k+t9tN27ZtufXWWwNYmYiEIoVbEZFyGjZsGAsWLODXX3894dj06dNp164dLVu2DEBlJyopKQl0CaVeeeUVdu3axZNPPlm67/HHH2fv3r28/PLLAaxMREKRwq2ISDldffXVVK9enRkzZpTZn5eXx+zZsxk2bBgHDx7k5ptvpmbNmkRERNCiRQtmzZp12usWFxfz17/+lZo1axIZGUnHjh1ZvHhx6fHx48dz8cUXl3nNCy+8QJ06dUq3hwwZQt++fXniiSdITU2lUaNGgBksGzZsiMvlIjk5mRtuuOG0tcyYMYO0tDQiIiK4/vrrOXjw4AnnfPjhh7Rp0waXy0W9evV49NFH8Xg8p7xmYmIi06ZN47HHHmP9+vV88803TJw4kddee434+PjT1iMicrbsgS5ARKSqsNvtDBo0iBkzZjB27FgsFgsAs2fPxuv1cvPNN5OXl0fbtm25//77iYmJ4dNPP2XgwIHUr1+fDh06nPS6I0aM4Mcff+Tf//43qampzJkzhz59+vD999/TsGHDcte3cOFCYmJiWLBgAQDffPMNd999N2+99RadO3fm0KFDLF269JSvX7VqFcOGDWPixIn07duXefPm8cgjj5Q5Z+nSpQwaNIh//OMfXHbZZWzbto0//elPACec+1vXXnstN910E4MGDcLtdjN48GB+//vfl/t3ExEpN0NERMpt48aNBmAsWrSodN9ll11m3Hbbbad8zVVXXWXce++9pdvdunUz7rnnHsMwDGPnzp2GzWYzdu/eXeY1PXr0MB588EHDMAzjkUceMVq1alXm+PPPP2+kp6eXbg8ePNhITk42iouLS/f997//NWJiYoycnJxy/W4333yz8fvf/77MvgEDBhixsbFl6powYUKZc9566y2jRo0aZ7z+oUOHjPDwcCM5OdnIzs4uV00iImdLwxJERM5C48aN6dy5M6+//joAW7duZenSpQwbNgwAr9fL448/TosWLUhISCAqKor58+eza9euk17v+++/x+v1ctFFFxEVFVX6tWTJErZt23ZWtbVo0QKn01m6feWVV5Kenk69evUYOHAg77zzDgUFBad8/caNG+nYsWOZfZ06dSqz/d133/HYY4+VqfWOO+5g7969p702wKxZs7BYLBw4cICffvrprH43EZHy0rAEEZGzNGzYMO666y4mT57M9OnTqV+/Pt26dQPgmWee4cUXX+SFF16gRYsWREZGMnLkyFM+4JWXl4fNZmPt2rXYbLYyx6KiogCwWq0YhlHmmNvtPuFakZGRZbajo6PJyMhg8eLFfP755zz88MOMHz+eNWvWnPP0Xnl5eTz66KP069fvhGMul+uUr/v555+57777mDJlCosWLWLIkCF8++23hIWFnVMdIiKnop5bEZGzdOONN2K1Wpk5cyZvvvkmt99+e+n422XLlnHddddx22230apVK+rVq8fmzZtPea3WrVvj9XrJysqiQYMGZb5SUlIAqF69Ovv27SsTcNetW1euWu12Oz179uTpp59m/fr17Nixgy+//PKk5zZp0oRVq1aV2bdy5coy223atGHTpk0n1NqgQQOs1pN/pPh8PoYMGUKPHj0YNGgQL7zwArm5uTz88MPl+h1ERM6Gem5FRM5SVFQUAwYM4MEHHyQnJ4chQ4aUHmvYsCHvvfcey5cvJz4+nkmTJpGZmUnTpk1Peq2LLrqIW2+9lUGDBvHcc8/RunVr9u/fz8KFC2nZsiVXXXUV3bt3Z//+/Tz99NPccMMNzJs3j7lz5xITE3PaOj/55BN+/vlnunbtSnx8PJ999hk+n690JoXj3X333XTp0oVnn32W6667jvnz5zNv3rwy5zz88MNcffXVpKWlccMNN2C1Wvnuu+/YsGEDf//730963RdffJEffviBH374AYDY2Fhee+01rr76avr373/KB+1ERM6Fem5FRM7BsGHDOHz4ML179yY1NbV0/0MPPUSbNm3o3bs33bt3JyUlhb59+572WtOnT2fQoEHce++9NGrUiL59+7JmzRrS0tIAs0f1lVdeYfLkybRq1YrVq1fz17/+9Yw1xsXF8f7773PFFVfQpEkTpk6dyqxZs2jWrNlJz7/kkkt49dVXefHFF2nVqhWff/45Dz30UJlzevfuzSeffMLnn39O+/btueSSS3j++edJT08/6TU3b97M2LFjeemll0p7oo9dZ+jQoQwZMoTi4uIz/i4iIuVlMY4fyCUiIiIiUkWp51ZEREREQobCrYiIiIiEDIVbEREREQkZCrciIiIiEjIUbkVEREQkZCjcioiIiEjIULgVERERkZChcCsiIiIiIUPhVkRERERChsKtiIiIiIQMhVsRERERCRkKtyIiIiISMv4fXsTAiqkJgUkAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "# ... (votre code pour obtenir X_valeurs et Y_valeurs)\n",
    "# Effectuer 200 réalisations du jeu\n",
    "nombre_de_realisations = 200\n",
    "resultats = [une_chaine_domino() for _ in range(nombre_de_realisations)]\n",
    "\n",
    "# Extraire les valeurs de X et Y dans des listes distinctes\n",
    "X_valeurs = [X for X, Y in resultats]\n",
    "Y_valeurs = [Y for X, Y in resultats]\n",
    "\n",
    "# Ajuster une régression linéaire aux points\n",
    "coefficients = np.polyfit(X_valeurs, Y_valeurs, 1)\n",
    "slope, intercept = coefficients\n",
    "\n",
    "# Créer un nuage de points\n",
    "plt.figure(figsize=(8, 6))\n",
    "plt.scatter(X_valeurs, Y_valeurs, alpha=0.5)\n",
    "\n",
    "# Tracer la droite de régression linéaire\n",
    "x_range = np.linspace(min(X_valeurs), max(X_valeurs), 100)\n",
    "y_fit = slope * x_range + intercept\n",
    "plt.plot(x_range, y_fit, color='red', label=f'Régression Linéaire')\n",
    "\n",
    "plt.title('Nuage de points de X et Y avec Régression Linéaire et Médiane de Y')\n",
    "plt.xlabel('Valeurs de X')\n",
    "plt.ylabel('Valeurs de Y')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7519b9b8-2845-4e62-aa12-9e430bfea27e",
   "metadata": {},
   "source": [
    "On peut voir ci-dessus sur le graphique, que la covariance est négative. Les valeurs X et Y ne sont donc pas indépendantes."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e625af4f-7df2-4f31-8f55-d7b9e2b96d78",
   "metadata": {},
   "source": [
    "2) On définit le nombre Z = X × Y comme le produit entre X et Y . Expliquer pourquoi Z est une variable aléatoire."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "78884a6a-548d-4f24-af2c-e0c2220d4e53",
   "metadata": {},
   "source": [
    "Z est une variable aléatoire car c'est un produit de variables àléatoires."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ebc19dda-96ab-4a8a-a9b9-159e59277b6f",
   "metadata": {},
   "source": [
    "3. Estimer l'espérance de X, Y et Z. Véri\u001c",
    "\n",
    "er et justifier si X et Y sont indépendants.\n",
    "4. Estimer la covariance des variables X et Y , puis leur coefficient de corrélation. Commenter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "id": "fa92c9dc-cd8f-45b4-8b33-8e98c333c419",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "esperance de X :  13.715\n",
      "esperance de Y :  51.925\n",
      "esperance de Z :  663.19\n",
      "covariance de X et Y :  -49.207412060301515\n",
      "X et Y indépendants ? :  False\n",
      "Moyenne de X : 13.715\n",
      "Moyenne de Y : 51.925\n",
      "Écart-type de X : 2.5305681180319963\n",
      "Écart-type de Y : 19.82421183805298\n",
      "Coefficient de corrélation entre X et Y : -0.9808815438670045\n"
     ]
    }
   ],
   "source": [
    "esperance_X = np.mean(X_valeurs)\n",
    "esperance_Y = np.mean(Y_valeurs)\n",
    "\n",
    "# Calculer la moyenne de X et Y\n",
    "moyenne_X = np.mean([X for X, Y in resultats])\n",
    "moyenne_Y = np.mean([Y for X, Y in resultats])\n",
    "\n",
    "# Calcul de Z = X * Y pour chaque réalisation\n",
    "Z_valeurs = [X * Y for X, Y in resultats]\n",
    "esperance_Z = np.mean(Z_valeurs)\n",
    "\n",
    "# Calcul de la covariance entre X et Y\n",
    "covariance_XY = np.cov(X_valeurs, Y_valeurs)[0, 1]\n",
    "\n",
    "# Vérification d'indépendance\n",
    "independants = abs(covariance_XY) < 1e-10\n",
    "\n",
    "# Calculer l'écart-type de X et Y\n",
    "ecart_type_X = np.std([X for X, Y in resultats])\n",
    "ecart_type_Y = np.std([Y for X, Y in resultats])\n",
    "\n",
    "# Calculer le coefficient de corrélation entre X et Y\n",
    "coeff_correlation = covariance_XY / (ecart_type_X * ecart_type_Y)\n",
    "\n",
    "# Afficher les résultats statistiques\n",
    "print(\"esperance de X : \", esperance_X)\n",
    "print(\"esperance de Y : \", esperance_Y)\n",
    "print(\"esperance de Z : \", esperance_Z)\n",
    "print(\"covariance de X et Y : \", covariance_XY)\n",
    "print(\"X et Y indépendants ? : \", independants)\n",
    "print(\"Moyenne de X :\", moyenne_X)\n",
    "print(\"Moyenne de Y :\", moyenne_Y)\n",
    "print(\"Écart-type de X :\", ecart_type_X)\n",
    "print(\"Écart-type de Y :\", ecart_type_Y)\n",
    "print(\"Coefficient de corrélation entre X et Y :\", coeff_correlation)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "00f62cdd-479d-41c4-a744-e45f8695bc33",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "e5eb343c-8c24-4aad-99a2-ac4845b6e3ba",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c610f536-e7e0-4506-ac84-7fea99c07ea3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "404779e1-3ddd-4531-a20b-23f6d4f7af28",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "c1318715-6282-4311-8f8f-027e84d482a3",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.11.5"
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 },
 "nbformat": 4,
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}