 graphes-(24082019)_DILLMANN_V4.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Modélisation d'un réseau social"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Un réseau social est d'abord un ensemble de relations entre entités. Par exemple dans le cas des réseaux sociaux (linked-in, facebook, twitter, instagram, snapchat ...), les entités sont supposés être des êtres humains qui ont plus ou moins de relations avec d'autres êtres humains.\n",
    "\n",
    "## Quelques notions essentielles\n",
    "\n",
    "Pour modéliser ces relations on se sert d'objets mathématiques appelés les *graphes*. Quelques définitions sont essentielles pour pouvoir caractériser un graphe :\n",
    "> Un **nœud** sert à modéliser un individu, un lieu, ou tout autre une entité sociale.\n",
    "> Une **arête** représentée par un trait entre deux nœuds, sert à modéliser une relation non-orientée (qui ne se fait pas dans un seul sens) entre deux individus ou entités.\n",
    "> Un **arc** est une relation semblable à celle de l'arête sauf que dans ce cas il y a une orientation spécifique, par exemple A est un \"follower\" de B, mais la réciproque est fausse : B ne suit pas A. Dans la première partie nous allons voir des graphes non-orientés, ensuite nous nous intéresseront aux graphes orientés."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAADnCAYAAAC9roUQAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAC6pJREFUeJzt3V+MXFUdwPHv3d22/JPGUrFCCTEWNUYjAg1CIYUYownWP4kPok/4ZkwMSnge51VCkAdfNJHECMQ3MIaoUSgoGIIlxBjBiDEKSEvKn9pl2m539/pw7rDbZXbbzpzzm3/fT9Lspi333pmG77175px7q7qukSTFmBn2AUjSNDG6khTI6EpSIKMrSYGMriQFMrqSFMjoSlIgoytJgYyuJAUyupIUyOhKUiCjK0mBjK4kBTK6khTI6EpSIKMrSYGMriQFMrqSFMjoSlIgoytJgYyuJAUyupIUyOhKUiCjK0mBjK4kBTK6khTI6EpSIKMrSYGMriQFMrqSFMjoSlIgoytJgYyuJAUyupIUyOhKUiCjK0mBjK4kBTK6khTI6EpSIKMrSYGMriQFMrqSFMjoSlIgoytJgYyuJAUyupIUyOhKUiCjK0mBjK4kBTK6khTI6EpSIKMrSYGMriQFMrqSFMjoSlIgoytJgYyuJAUyupIUyOhKUiCjK0mBjK4kBTK6khTI6EpSIKMrSYGMriQFMrqSFMjoSlIgoytJgYyuJAUyupIUyOhKUiCjK0mBjK4kBTK6khTI6EpSIKMrSYGMriQFMrqSFMjoSlIgoytJgYyuJAUyupIUyOhKUiCjK0mBjK4kBTK6khRobtgHcDpVu9oKXAlsB84BNgMLwHHgMPBc3aqPDO8IJUUa9yZUdV0P+xjeUbWrGWAPcC2wF7ia9MZ2gKr5NQMsA3Xz6zzSG30AeBx4GniybtXL0ccvKa9JbMJIRLdqVxcBtwF3AOeTzlxb+tjUCdIZ723gbuCndat+I9dxSooxyU0YanSrdnU1cCfwJdKZ6ryMm++QzoAPAz+oW/WzGbctqYBpaMJQolu1qwuAe4Cvk85eswV3t0Q6290PfK9u1fMF9yWpD9PUhPDoVu3qZuBB4ELg3MBdHwOOALfWrXp/4H4lbWDamhAW3apdnQ/cSzqTRb6xa3WAB4Db61b99hCPQ5pq09qEkOhW7Wob6VPEDzHcN7frGPAicNOwB9WlaTTNTSge3apd7QCeBHaSPoEcFQvAy8CeulUfHPbBSNNi2ptQNLrN2ewZ4DJgU7Ed9e8k8BKw2yteqTybUHAZcDNe8zjpbDaKby6k49oJ7G+OV1IhNiEpee+FH5LGa0bpx4deNgO7SNNVJJVjEyg0vNBMAfkVeSc2l9YBbnE6mZSfTViRPbrNJOcXgfdn3XCMg8Aup5JJ+diEU5UYXriHNMl5HG3FYQYpN5uwStYr3Wbd9BOM148Qa3WAG71XgzQ4m/Buua9076S/OwGNki2k1yFpcDZhjWxXus2t2F4m3VR43B0HLnXurtQ/m9Bbzivdb5JuxTYJlkn38pTUP5vQQ5Yr3ebu7q8AOwbe2Om8Avyk+f7jwFeL7elVYOeo3G1eGifFm/As8MteOybd8nwncCNwada9ZmlCrivdPaSXWt6vV31f9o4JFwDXF92DNLnKNuHV5usO4JOrfu0i3UHhBeA+4L9Z95qlCbkeTHktEatM/kJaFf0e4CjwOmmldJkFhZtJr+uPRbYuTbayTehG9zpSbFd7G/gx6U65z5CeQZFHlibkutLdS+lPKBeA3zXf7yPdDK4GXiu2xy2k1yXp7JVrwjJwqPm+13KL84GPNN//L+ueszQhV3SvzrSd9f2B9AbuAj4MXNz8ftkhhmuKbl2aXOWacJj0E25Fei5wL8ebr+/NvveBmzBwdJtn0K/30vN4E/gT6Wg/3/xe9wxXNrrbq3Y1ritppKEo3oTu0MJF9B4gnSctOgb4RPa9D9yEHGO6V5JWbGzNsK3efgssksZvuv+UAdGdZXb5Fm65t91u/7vcXqTJso99lz/CI8tLLJXZQTe6F6/5/XnSrODfk4p0A3B59r13SM17ot8N5IjudtKFfhn/Ap4nLSJcPZrSfcMPkcZ2Cx3BUY6O8/JFKdw882X/n+lG92/A93v8+Q7gG8AVRfa+0aDGGckR3XMolbxlVqaIfYZT17V0o7tAGn7YVuQIqkUWc83wkKbCSU7OUaoJNSs/3V7BqXd06JCudA+SPgO6hBKT1ioGXGGXIyibKXUz9AOkK9kdwKfW/NkW0iD5m6Q3uUB0a+pqkcXZ/FuWJtcSS7M1hR4D9gZwovn+K7z7NjoLwM+A/5BmO+WbLtY1w4CzMnJEd4ESS/2OAY813x8nTXReq9N8PQh8LPsRUFHVc8wVGpiSJtMss0tVqfG+7tDCVnrft2wz6QLtZdLQZH7LrGS/LzmiexwKnNb2sxLVt5pf6zm0wZ8Npp5jbrHY1qUJtIlNi5RoAqxE95IN/k63amUW8NesTEjrS47oHib3G/waaSXJLPBt1h86eB74BcVmMCyxdPwxHvvRo61H+/6kUpo2VbvaC3yOEosjutH9wAZ/5x/N143C3L+a1Ly+5RiLfY7cNyj+Deks9Wk2Hqt9X/P1CGk4Ir/zSK9P0pnL34Su7gVWr+ieJD1r+K+kj7tuKHIEAzdh4CvdulUfqdrVYTY+95y5F4B/kl7ajaf5u9tIV8NLpH+MD2Y5gtUO160670JCacJlb0LXW6wMOR4gxRXStedR0jBjh3R9/UXSncbyG7gJuaZDHQC+MPBWFkkLIQBu5vQTM2ZIM+YOUSq6f86+RWk65GnCaquHEV9Y9X13Etd20u1oriLdFKuMgZuQK7qPA59l0DGcOeA7Z/nffGugPW7kBOl1STp7eZqw2kfpvRgiTpYm5Jpf+zRp6tgkWSC9LklnzyasI1d0nyTdxXKSzANPDfsgpDFlE9aRJbrN4yvuZmWYe9x1gLt9VI/UH5uwvpzLd+/LvL1hmqH3GjhJZ84mrLOhLOpW/TrwMJS6n1uYJeAhH78uDcYm9Jb7LHQXA65LHgEnSK9D0uBswhpZo1u36gPAA5RaH1beMeD+ulU/O+wDkSaBTXi3EuMt3yX34+DiHCEdv6R8bMIq2aNbt+p54GuM36eWHeDWulVP2jQXaahswqmKfLJYt+r9jNePFN0fIfYP+0CkSWQTVpScznE76Zmco74qZYF0nA4rSGXZBKCq60KP1QCqdrWNdGfcy4BNxXbUv5PAS8Bup4hJ5dmEwhOXm4PeQ3oRo3Z2WyAd1x6DK8WwCQGrRepWfRDYDfyd0RnPOUY6nt3N8UkKMu1NCFmi15w1rgPuZ/ifYHaAnwPXeYUrDcc0N6HomG7PHbarm4AHSc/zPDdw18dIc+5udZaCNDqmrQnhN6NoXtwVpDNLh/LrspdYOZPtMrjSaJm2JoRf6Z6y83Z1FXAn8GXSoyhzPsyuQzqpPATc5dJeafRNQxOGGt13DiJNI7kNuAO4ANhMf4/5OEH6BHKedC/P+xy3lcbPJDdhJKLbVbWrGeB60uPl9gLXkB431yE9fq4inamWSc8ArUlnwsOkuX9PkB6n8ZQ3IJfG3yQ2YaSi20vVri4EriS90eeQznYngOOkN/Y5H5MuTY9xb8LIR1eSJsmkPEpDksaC0ZWkQEZXkgIZXUkKZHQlKZDRlaRARleSAhldSQpkdCUpkNGVpEBGV5ICGV1JCmR0JSmQ0ZWkQEZXkgIZXUkKZHQlKZDRlaRARleSAhldSQpkdCUpkNGVpEBGV5ICGV1JCmR0JSmQ0ZWkQEZXkgIZXUkKZHQlKZDRlaRARleSAhldSQpkdCUpkNGVpEBGV5ICGV1JCmR0JSmQ0ZWkQEZXkgIZXUkKZHQlKZDRlaRARleSAhldSQpkdCUpkNGVpEBGV5ICGV1JCmR0JSmQ0ZWkQEZXkgIZXUkKZHQlKZDRlaRARleSAhldSQpkdCUpkNGVpEBGV5ICGV1JCmR0JSmQ0ZWkQEZXkgIZXUkKZHQlKZDRlaRARleSAhldSQpkdCUpkNGVpEBGV5ICGV1JCmR0JSmQ0ZWkQEZXkgIZXUkKZHQlKZDRlaRARleSAhldSQpkdCUpkNGVpEBGV5ICGV1JCmR0JSmQ0ZWkQP8Ht6ZWzTlytqoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Dans ce premier exemple on s'interesse \n",
    "# Exemple de graphe non orienté entre \"A\" et \"B\" \n",
    "\n",
    "# On va d'abord initialiser le graphe en question que l'on appelle \"G\"\n",
    "\n",
    "G = nx.from_numpy_matrix(np.matrix([[0,1],[1,0]]))\n",
    "\n",
    "# On va ensuite signaler la position des noeuds grâce à leurs coordonnées et leur adresse \n",
    "\n",
    "pos = {0: (0, 0),\n",
    "       1: (1, 0),}\n",
    "\n",
    "# On va enfin renomer les noeuds d'adresse \"0\" et \"1\" en utilisant \"A\" et \"B\"\n",
    "\n",
    "labels={}\n",
    "labels[0]=r'$A$'\n",
    "labels[1]=r'$B$'\n",
    "\n",
    "# Puis finalement on va afficher tout cela en couleurs \n",
    "\n",
    "nx.draw_networkx_nodes(G, pos, node_size=3000, nodelist=[0, 1], node_color='green')\n",
    "nx.draw_networkx_labels(G,pos,labels,font_size=22)\n",
    "nx.draw_networkx_edges(G, pos, alpha=0.5, width=6, edge_color='gray')\n",
    "\n",
    "plt.axis('off')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercices :\n",
    "- Quelles sont les lignes de code qu'il faut modifier pour remplacer le 'A' et le 'B' par 'Papa' et 'Maman' ? \n",
    "- Dans ce graphe on a une seulle arête et deux sommets, comment colorer les arêtes en rouge et les sommets en rouge ?\n",
    "- On veut faire un graphe vertical avec \"Parents\" en haut et \"Enfants\" en bas, comment s'y prendre ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dans cette cellule vous pouvez recopier le contenu de la cellule précédente et faire les modifications demandées\n",
    "#---------------------------------------------------------------------------------------------------------------#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dans cet exemple \"A\" et \"B\" sont en relation : cette relation va dans les deux sens, il y a une arête et deux nœuds. On appelle aussi ces nœuds des sommets. Finalement on peut introduire un tableau appellé **matrice d'adjacence** qui permet de relier très simplement \"A\" à \"B\".\n",
    "_____\n",
    "\n",
    "$$\\matrix{\n",
    " & A & B \\cr\n",
    "A & 0 & 1 \\cr\n",
    "B & 1 & 0 \\cr}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0xa21b24278>"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = np.matrix([[0,1],[1,0]])\n",
    "fig, ax = plt.subplots()\n",
    "ax.set_xticklabels([\" \",\"A\",\"B\"])\n",
    "ax.set_yticklabels([\" \",\"A\",\"B\"])\n",
    "plt.spy(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On voit, noir sur blanc, que le noir correspond à la présence d'une relation entre \"A\" et \"B\" et entre \"B\" et \"A\". Nous allons voire dans l'exemple suivant comment rélier entre eux six sommets en utilisant la même règle.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercices :\n",
    "- Quelles sont les lignes de code qu'il faut modifier pour que la case de la ligne 'B' et de la colonne 'B' soit en noir  ? \n",
    "- Comment modifier le code pour qu'il y ait une colonne et une ligne 'C' suplémentaires ?\n",
    "- Dans ce cas A est en relation avec B et B est en relation avec A (A et B ne sont pas en relation avec eux mêmes c'est pour cela que la diagonale est blanche). Modifiez le tableau pour que C soit en relation avec A et B et réciproquement. Quel est le point commun du nouveau tableau (\"A-B-C\") avec le tableau précédent."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dans cette cellule vous pouvez recopier le contenu de la cellule précédente et faire les modifications demandées\n",
    "#---------------------------------------------------------------------------------------------------------------#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Lien entre la matrice d'adjacence et les graphes\n",
    "Nous allons nous intéresser à la représentation d'un tableau de relations, sous forme de graphe. Nous commençons par une matrice (tableau de relations) de dimension 5 (on parle aussi de 5 *vecteurs*, mais cela fait partie du programme de mathématiques)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0xa21889908>"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = np.matrix([[0,0,0,0,1,0],[0,0,0,0,1,0],[0,0,0,0,1,0],[0,0,0,0,1,0],[1,1,1,1,0,1],[0,0,0,0,1,0]])\n",
    "plt.spy(A)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dans cet exemple tous les sommets sont connectés au point '4' mais ils ne sont pas reliés entre eux. On dit que '4' est la *star* du réseau. Cela se visualise de la façon suivante : "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "G = nx.from_numpy_matrix(A)\n",
    "nx.draw(G,with_labels=True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# En remplaçant les '0' par des '1' dans les vecteurs de la matrice B\n",
    "# modifiez le code pour que ce soit le vecteur '2' qui devienne la nouvelle \"star\" du réseau\n",
    "# On notera 'B' la matrice d'adjacence :\n",
    "\n",
    "\n",
    "B = np.matrix([[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0],[0,0,0,0,0,0]])\n",
    "G = nx.from_numpy_matrix(B)\n",
    "nx.draw(G,with_labels=True)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Représentation d'un réseau social sous forme d'un graphe\n",
    "\n",
    "Nous allons passer à une partie plus pratique de l'activité dans laquelle on s'intéroge sur un exemple réel de réseau d'influence qui à eu des repercussions très importantes sur l'histoire Française du XVIème sciecle avec la personne de Catherine de Médicis. Comment une femme issu de la bourgeoisie financière de Toscanne peut elle arriver au niveau de gouvernement suprème d'un état, et œuvrer pour l'arbitrage délicat entre les partis antagonistes qui déchiraient le pays ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [],
   "source": [
    "## En utilisant l'exemple précédent faire la liste des enfants issus de Catherine de Médicis, \n",
    "## en dessinant comme arête la relation mère-fils"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Les rêgles de fonctionnement des familles de Florence\n",
    "\n",
    "La découverte du nouveau monde à ouvert des perspectives commerciales exigeant des investissements financiers très importants. Or dans la pratique financière établie au Moyen-Age l'importance d'une lettre de change (ce qui est un chèque aujourd'hui) est cruciale pour l'économie. À la fin du XIV sciècle une famille de Florence, la maison de Médicis est un exemple de réussite par la mise en place de banques. Pendant plusieures générations ils vont mettre en place un réseau de gens de confiance pour assurer la tenue des postes de change filiales d'une maison mere. Le choix des familles en relation faisant ainsi l’objet d’un soin particulier. Une banque recrutait ses membres au sein du clan familial ou parmi ses alliés, c'est à dire des familles associées par des marriages. Les Médicis furent extraordinairement efficaces pour créer un réseau de familles florentines. Dans l'exercice suivant nous allons étudier ce type de réseau.   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [],
   "source": [
    "# D'abord on importe le graphe des familles florentines du module NetworkX\n",
    "# Le travail des chercheurs Ronald L. Breiger et Philippa E. Pattison sert \n",
    "# de point de départ pour cette activté\n",
    "\n",
    "G = nx.florentine_families_graph()\n",
    "G.edges(data=True)\n",
    "adjacency_matrix = nx.adjacency_matrix(G)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercice : \n",
    "- En utilisant la commande \"plt.spy\" indiquez quelle est l'index de la famille la plus populaire ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gFApx//59VlNDYWEhvL29FTcoX19f2NvbK/Gdqh9l1/gaZpntFc3a2lrY2NgoJZpc3KTv3buHf/zjH3jw4IHGry2noXehXAwFAoHCu1D+u9ajR49Wz1VTU4OTJ0+Cpmk8fPgQgYGBCAkJgYdHx/a36rs3pq5AhE+PUcZbrr6+XjE+7M6dO5g9ezYoisKYMWNUmoGUlpYiNjaWJYZ8Pp91g/Ly8tKK/VdcNLfI1zKVEU0zM7N2l2RtbW1haWmp9M/4ww8/BJ/PxxdffKHif4mO0ZR3oa2tLeuBa8SIES02tzx69Aj79+/H/v37YWtri9DQUAQGBrZrjVGfvTF1ESJ8BkBDb7nmxkclJycrxocNGTIEFEVh7ty5Sk3qVwaGYfD48WPWNJDk5GQMGDCAJYbDhg3TyDSQhuhSVyfDMKiurlaq+aeurg7W1tZKNf8MGTIEp06d6nBGpG6a8i5MS0uDi4sLSwyb8i6UyWS4fv06aJrGhQsX8MYbb4CiKEyePLnF30l99cbUZYjwGTBlZWU4fPgwaJpGcXExgoODERISgoED1T+nsy3U19cjOTmZdZPKzc3FiBEjWGLYt29fta6H6ZLwdQSxWIzy8vJ2i2ZZWRlkMhns7e3RrVu3dolmR7JMVdGUd2FpaSmrFO/n58cyO66oqMCxY8dA0zRycnKwZMkSUBQFZ2dn1rn1zRtTXyDCZ2BIpVJERUWBpmlERUVh2rRpoCgKkyZN0olmk4qKCkWJVH6jMjIyYt2gvL290bVrV5Vd01CET1k2bNiAmpoavP/+++0WTaFQqMgy25NpqnstsynvQnNz80bdyubm5nj48CHCw8Nx4MABODo6gqIoLFiwAE8qZY06rBmJGKVReyDMToJMWA0T696wGb8UnQeytxBpkzemPkKEz0DIzMwETdOIiIiAg4MDKIrCwoUL1TIuSpMwDINnz56x1goTExPRr18/lhi6uro2uZm+LRDha5mhQ4eCpmn4+fm1+2vlWWZ71zHLy8vB5/OVav5RJstsybtQ/jvm6emJnJwcRERE4Nq1axgY8hXKOjug4W+OrF4IQXQkLFxfh3HXHqh7FIeS375Bn9DdMLH+n8u8Nnhj6jNE+PQYgUCA48ePg6ZpPHr0CEuWLEFISAiGDRvGdWhqRSwW48GDB6ybVHZ2Ntzd3Vkl0v79+7fpBkiEr3nS0tIwefJkPH36VKMzMOVrmco0/wiFQqU7Zhs+PDXlXZifn48RI0ZgsJsXrnYZDxmv9SpK3q8r0XX0Ipi7jGa9z4U3pqFAhE/PkMlkuHXrFmiaxm+//YZJkyaBoii8+eabSmc8+oBAIEBcXBxrHUcikbAaGnx9fWFjY9Poa4nwNc+XX36J4uJi7Ny5k+tQ2kx9fb1SHbPyLLMlcezUqRPKyspwt6wLHpsPAYxb/puT1pQjd08o+oT+ANNufVmfadIb09AgwqcnPH36FPv370d4eDgsLCxAURQWL16Mnj17ch2a1iIfmCwXw/j4ePTu3Zu1juPu7g4+n0+Erxk8PT2xc+dOjBs3jutQ1A7DMKiqqmqTUKbbjkRN96Etn08qQdHxTTCx6Y1ub65s8hh1emMaMkT4dJja2lrF+LCkpCQsXLgQFEVhxIgRnHfK6SJSqRQPHz5kiWFWVhZqa2uxatUqhRg6OTmRf18Ajx8/xqhRo5CXl6cTjVGapDVvTIaRoeS3byAT1aJnwEbwjJveDvGaS0/8GuyjrjANFs1uiCJ0GIZhEB0drRgf5ufnh2XLlmHGjBmNxocR2oexsTFcXV3h6uqKt99+G8CLCR4WFhbo27cvzpw5g08//RQ1NTWK0qhcDLt3785x9JonMjISs2bNIqLXBFb85m+tDMOg9OIPkNZUoOe8z5sVvRfnMdzlCXVChE9HyM/Px4EDB0DTNKRSKSiKQkpKitaO+dIXzM3NAbyYTCInPz9fkRF+9913iI2NRffu3VmNM56ennr/IBIZGYnNmzdzHYZW4mJnBTOTgkYWYQBQdvlHiEtz0GvhlzAybb5xhW9iBJfe3E8u0kdIqVOLqa+vx7lz50DTNO7evYuAgABQFIVXX32VlNo0SGvNLTKZrM3ehfri/p2bmwt3d3cUFBQYdNNUczTnjSmpLMLzvaGAsSl4Rv/LlG3ffA8WwyayjiVdneqDCJ8WkpSUBJqmceTIEQwbNgwURSEgIECRfRA0izJdnS97F0ZHR6O8vLzRwORevXq1fjItZNeuXYiPj0d4eDjXoWgt6vTGJHQMInxaQmlpKQ4dOgSaplFWVoaQkBAEBwdjwIABXIdm8KhqO0NRUVGjaSBdu3ZlrRVqg3dhW5gwYQI++OADvPXWW1yHorWo2xuToDxE+DhEIpHg8uXLoGkaV69exfTp0xEaGoqJEyfqTUlMH1DXPr6mvAsfPHiAwYMHs6bOuLi4aFUDSVFREZydnZGfn6/365gdhczq1E6I8HFARkYGaJrGgQMH0LdvX8VsP10fH6avaHIDe1u8C/38/NCnTx+NxNMUP//8M27cuIEjR45wFoMuQdwZtA8ifBpCIBAoprk/efJEMc19yJAhXIdGaAWuJ7e05F0oL5F6e3trzEJqypQpePvttzFv3jyNXE8fUMYbk6A+iPCpEZlMhps3b4KmaZw7dw6vvfaaYnyYpj3lCMrDtfC9jNy7sGGJtKF3oVwM1eFdWF5ejv79++P58+caE1p9oi3emAT1Q4RPDWRnZyM8PBz79+9H165dFePDDHGTsz6gbcLXFHLvwoZi+Pz5c4wYMYLVPNNR78L9+/fjzJkzOH36tAqjJxA0i0EKX0m1CCfjc5FeIIBAKIEV3wQudlaY56X8U1dtbS0iIyNB0zRSUlKwaNEiUBQFT09PFUdP0DS6IHxNUV5ejri4uEbehQ23U7TXu3DGjBmYP38+goKC1Bg5gaBeDEr47udU4MebWbiVWQwArM2l8jr7BOceWDHeCe59W6+zMwyDv/76CzRNIzIyEqNGjQJFUXjrrbdgZkbKFvqCrgrfyzAMg6dPn7K2U8i9CxuKYXPehVVVVbC3t8ezZ89IIxZBpzEY4VNlZ1VeXh4iIiIQHh4OhmEQGhqKJUuWcNppR1Af+iJ8TSEWi5GamsraaJ+dnQ0PD49G3oXHjx/H/v37cfHiRa7DJhA6hEEInyr20ohEIsX4sL/++gtz585FSEgIRo0aRcaH6Tn6LHxN0Zx3oYmJCXx9fbF8+fJmvQsJBF1A74WvpekJNQ9voeLuEUgFxTA2t0G36WvB7ztc8XlnU2NsHm+DO2cP4ciRI3B1dUVoaCjmzJmjE9M1CKrB0ITvZRiGQVZWFjw8PBAaGoqUlBTEx8ejT58+rL2Fbm5upMRP0An0vqf+x5tZEEoai17dk0SU3wxHj5kfo1OfwZBWlzU+RiTGh/QVhDjZIiYmBo6OjpoImUDQKng8Hh48eAA/Pz/s2rULQGPvwl9++QVZWVlwdXVlieHAgQNJRYSgdeh1xtfchHQAKDjwL5i7TYal++QWz0EmpBMMPeMDgCVLlmDkyJF47733mj2muroaCQkJrI32xLuQoI3otfDtu/UIO65mNhI+RibFs+0BsB67GNX3o8BI69Fl0EhYTwxt5I/FNzHC+28MxjvjBmoydIIWYejCV19fDzs7O6Smpra7gauhd2F0dDTi4uIM0ruQoF3odakzvUDQZLYnrakAZBLUZtxFr6CvwDMyRnHkl6j88xhsxi9lHSuUyBCfVQCBRw9YWlqSsg3B4Lh27RqGDBmiVNdy7969MXPmTMycORNAY+/CiIgIpKenK7wL5YKoT96FBO1Dr4VPIJQ0+T7v/7I6S6+3YGJh++K1z6wmhQ8ALt+4jSNr3oRQKISNjQ1sbGxga2sLW1vbNr8mZp0EXeXUqVMICAhQybmMjIwwdOhQDB06FCEhIQBeDH9ITExEdHQ0Ll68iE2bNrG8C+ViqKvehQTtQ6+Fz4rf9LdnzLeAsWXb1xnm+E/FjgOfor6+HhUVFSgrK0NZWRnKy8tZrx89eoTY2NhG75eXl4PP57dLKOWvLSwsSJZJ4AyJRIKzZ89iw4YNartGly5dMHr0aIwePVrxnty7MDo6Grt3727kXejn54cRI0aQ7mqCUui18LnYWcHMpKDJcqeF6+uoij+PzgO8AGMTVMWdRRcnn0bH8U2M4NLbEgDQqVMn9OzZEz179mxXHAzDoKqqqpEgyl+XlZUhKyurSTGVZ5ntFU2SZRJUwZ07d9CvXz/0799fo9ft2bMn/P394e/vD4DtXRgdHY1jx44pvAsbrhdqm3chQTvR6+aWlro6GakEZVd/Rs3DW+CZmMLcZSxsJlLgmXRiHcd1V2d9fb0ia2wu02zqdUVFhSLLbK9okiyTjSE3t6xcuRJ9+vTB+vXruQ6lEU15FxYVFcHLy4slhmSiEuFl9Fr4AGDZgThcSStscUxZc/B4wJShvbAvyFv1gakZeZbZVqFs+FokEim1jqmvWaahCp9MJkPfvn1x/fp1ODs7cx1OmygtLUVMTAxrHmnnzp1Z2yk06V1I0E70XvhamtzSGp1NjXFs2UiDM4aUZ5ntFc3y8nJ06dJFKdHU5izTUIXvzz//xLJly5Camsp1KErTnHfhwIEDWeuFQ4cOJR6ZBoTeCx/wYlbnpjPJkPLaXvt/eVYnoXUaZpntFU2RSKRU84+1tbXas0xDFb4PPvgAFhYW+M9//sN1KCqlLd6Ffn5+cHBw0NqHMULHMAjhu379OoK/+H8wH7MEIqmsw+4MBNXTMMtsj2jKs0xlRNPc3LxNNzZDFD6GYeDo6IjffvsNbm5uXIejdtriXejj4wMrKyuuQyWoAL0XPoFAADc3N+zduxf2rqOw52YWbmQUg4cXm9PlyP34Jjr3wIoJTgZX3tRVZDJZix2zLb2ur69vU8fskiVL8Ndff7GO1feyWEJCAhYsWIDMzEyDzHpa8y6UC2Jz3oUE7Ubvhe+f//wnAOCXX35RvFdaLcLJhFyk51dBIBTDim8Kl96WmDtCeQd2gu4hEona1DF7+PBh+Pn5sTpm1Z1lcs2GDRsglUqxbds2rkPRGlrzLpSLYf/+/XXiZ2zI6LXw/f7771i+fDmSk5NJiYKgNC+XOuVZpjIds2KxWOl9mZrKMhmGwZAhQ3DgwAH4+DTe20r4H815FzZcK/Tx8SHehVqG3gpfeXk5XF1dERERgUmTJnEdDkGHUeUanzzLbG9ZtmGW2V7RbG+W+eDBA0ydOhVPnz4lmUs7YRgGz58/Z60VNuVd6O7ujk6dOrV+QoJa0FvhW7JkCWxsbPDDDz9wHQpBx9GG5haZTAaBQKCUaDbMMtsilIcPH4ZIJMKPP/6o92uZmuBl78Lo6GiFd2HD5hniXag59FL4Tp06hY8//hhJSUkwNzfnOhyCjqMNwtcRhEJhu6b/JCUlwczMDLW1tTA3N1dqX6aurGVyRUvehXIxJN6F6kPvhK+4uBhubm6IjIzEq6++ynU4BD1A14WvPWRlZWHMmDF4/vw5eDweBAKBUmuZEolE6X2ZhppltuRdKBdDrr0LS6pFOBmfi/QCAQRCCaz4JnCxs8I8L91qDNQr4WMYBnPnzsXAgQPx9ddfcx0OQU8wJOH76quvkJ2djb1793boPPIss72iWVFRAQsLC6VEs0uXLnqVZb7sXRgdHY2MjAwMHTqUtV44aNAgtXsX3s+pwI83s3ArsxgAWPOP5VvBJjj3wIrxTnDvq/1bwfRK+A4fPowtW7YgPj6eODoTVIYhCZ+fnx+2bNmC119/nZPry9cylZn+I88y2yuaupRlNvQulAtiRUUFfHx8WGLYXgeZljh4LxtbLqZDKJHqzfAPvRG+vLw8eHh44Pfff4eXlxfX4RD0CEMRvpycHHh6eiI/P18nN2U3zDLbI5qVlZUwNzdXSjS1Icts6F0oH9DdtWtXVuOMst6FL0QvDXXixg43zaEL4x71QvgYhoG/vz+8vb31bq4ggXsMRfh27tyJ+/fvIywsjOtQNIpMJkNlZaVSoimVSpvdd8lVlvmyd2FMTAzLu1AuiK15FzY14F8Qfw41KddQX5wN8yHj0d3//Sa/VtsH/OuF8IWFhWH37t24d+8e2RtDUDmGInzjxo2GXvEFAAAgAElEQVTDRx99pDB/JbROXV2dUn6ZAoFAo1lma96FcjFs6F3YlKVbbcafAI+HuicJYMT1zQqftlu66bzwPX36FN7e3rh+/TpcXV25DoeghxiC8BUUFGDIkCEoKCiAmZnudOfpKvIsU5mOWZlMptQWk5ezzJa8C119XsWhKhc0V+Esv30AUkFJs8IHcG/i3RK6saLbDDKZDKGhofjggw+I6BEIHeDMmTOYOnUqET0NYWRkpDBvbi/yLLM5cXz48GGT71dWVsLS0rJJcfTw8MCECRMglUpRVFSEK1lVENuIARPl13p5AE4m5OKdcQOVPoe60Gnh27t3L2pqavCvf/2L61AIBJ0mMjIS7777LtdhENpA586d0blzZ1ZZsi00zDKbEs3CwkKUlZWhpKQEpd1f7ZDoAS/cb9Lzqzp0DnWhs8KXlZWFTZs24e7duzrTikwgaCPykteZM2e4DoWgIhpuC1Fm+EDPeSNVIg4CoVgFZ1E9OqkYUqkUISEh2LhxI5ydnbkOh0DQac6dO4fXX3+djPfTQkQikVLiVVlZ2eJQ8549e8LFxUXxvqmpKZ49e4aMjAwkJSUhQVynkvit+Nq5LUYnhW/Hjh0wMTHBqlWruA6FQNB5IiMjsWjRIq7D0Fs6MmC8vr6+xcYVZ2fnZrdLNLcXUywWIyUlBdHR0Th37hxiYmLw7NkzeHp6ws/PD+PGjUPtUwkyJfXgmbC75BmZFJD/x8jASOoBI2PwjBpvi+CbGMGlt6Va/k07is51dT58+BDjx49HTEwMHB0duQ6HYADoc1enQCCAg4MDcnNziWdlKzS0lGrvGDaujIsZhkF2djZr0sv9+/fRv39/1gZ3BwcHnDhxAjRN4/nz55i/9B84bzwSYin7977iziFU3j3Ceq/r6EWwHru40bW1uatTp4RPLBbj1Vdfxdtvv4133nmH63AIBoI+C9+RI0dw8OBBXLhwgetQNALDMEqvfcmzL2UGb2tqEk55eXmjLQqmpqYskfP29oalpSWkUimuXbsGmqbx+++/Y/LkyaAoCm+88QZMTEya3MfXVrR9H59OlTq3bdsGW1tbLFu2jOtQCAS9IDIyEgEBAVyH0W7k2Vd7xUuefTUnUt27d8fgwYObFDILCwvOx5M1RCQS4f79+6wh1gUFBfDy8oKvry9CQ0Oxb98+ODg4sL7u0aNH+Prrr7F//350794doaGh2L17N7p168Y67r0JTrjzdwlrcktb4ZsYY8UEpw59f+pEZzK+pKQkTJ48GQkJCY1+kASCOtHXjK+2tha9e/fG48ePG930NIE8+1Jm7UskEim1idvGxkYn55AyDIOsrCxWJpeSkoJBgwaxPPyGDh3a5Biy6upqnDx5EjRNIy0tDYGBgaAoCu7u7i1eV19ndepExicSibB06VJs376diB6BoCIuXboEHx+fDotefX29UuJVXl6Ozp07NytS3bp1w6BBg5oUMm3LvlRNSUlJo8HT5ubmivFic+fOhZeXV4uduAzD4I8//gBN0zh9+jTGjBmDtWvXYvr06W0e7SgXL+LOwAEbNmzAgwcPcPr0ab3+ZSdoJ/qa8S1evBhjxozB8uXLwTAMqqqqlLIDaph9tScL09XsS9UIhcJGVkMlJSXw8fFhubH37t27TefLyclBREQEwsPDYWpqCoqisGTJEtjZ2SkdY3JuBfbczMKNjGLw8GJzuhxGUo9OnTrhtSG9sGKCk9YOpm6I1gtfdHQ0Zs6cifv376NXr15ch0MwQHRJ+BpmXy0JVnFxMa5du4ZXXnlFUW6UZ1/tLSHqe/alSmQyGTIzM1kil5aWBhcXF1YDirOzc7vMZYVCIc6cOQOaphEbG4v58+eDoij4+vqq9GdTWi3CyYRcpOdXQSAUw4pviszYG3CzqMXWzzeo7DrqRquFr66uDp6envjiiy8wb948rsMhGCiaFr6G2Vd7S4jy7Ks1wXr06BFOnz6NY8eOKToPibOJ6iksLGQ1n8TGxsLW1pYlcp6enujcuXO7z80wDOLi4kDTNI4dO4YRI0aAoijMnj1bqfMpy507d/Dee+8hOTlZY9fsKFotfOvWrUNeXh6OHj3KdSgEA0ZZ4ZNnX8p0HvL5fKWaNywtLdv0hP+Pf/wDw4cPx/vvNz9dn9A+amtrkZCQwLL+qaysZDmj+/j4dNgdvbCwEAcPHgRN06irq0NISAiCg4PRr18/FX0n7UMqlcLe3h537tzBoEGDOImhvWit8N2+fRsLFy5ESkoKJx1nBALw4qnayMgI2dnZ7V7/EgqFsLa2VqrzUJ3Zl0QiQe/evREXF4dXXnlFbdfRZ6RSKdLT01kly8zMTAwbNozlbzdo0CCVlBrFYjEuXryIsLAw3Lp1C7NmzQJFURg7dmy7SqLqYvny5ejfvz8+/vhjrkNpE1opfNXV1XBzc8POnTvx1ltvcR0OQQ8Qi8VKTd0oLy+HRCJB3759273+1dbsS9Ncu3YNn3zyCWJjY7kORWfIy8tjiVxcXBx69erFEjkPDw+V2zqlpqaCpmkcPHgQgwcPBkVRmDdvHiwttWsU2NWrV7F+/XrExMRwHUqb0ErhW758OYRCIWia5joUghbBMAyqq6uVWvtqLvtqS+ehmZmZzjS3tIUVK1agX79++OSTT7gORSuprq5GXFwca21OKBSy1uVUsQ2kOcrLy3HkyBHQNI38/HwEBwcjJCREq8uIYrEYvXv3RkJCAmcl1/agdcIXFRWFf/7zn0hOTkbXrl25DoegBuTZlzJ7v8zMzNqceakq+9Klrs7WkMlksLe3x+3bt7X6RqopJBIJHjx4wBK5x48fw93dnbU25+joqNbsXSqV4urVq6BpGpcuXcKUKVMU48Oa2pCujYSGhsLNzQ1r167lOpRW0bjwlVSLcDI+F+kFAgiEEljxTeBiZ4V5Xg4wltTBzc0Nv/76K9544w1NhkVoJ/LsSxnxqq2tbVPnYVOvueg81Cfh++OPP7BixQqd6sBTFQzDICcnh7UxXD4JqqHIubq6auz37O+//0Z4eDgiIiLQq1cvUBSFRYsWwdbWViPXVyUXLlzAtm3bcOfOHa5DaRWNCd/9nAr8eDMLtzKLAQCiBhsg+SZGYABYVudgsOQJDu/aqomQCHiRfVVUVCi1cbk92VfD0qGlpaVWLMi3FX0SvnXr1qFr167YtGkT16GoncrKSsTFxbHW5mQyGWtdzsfHB9bWmt1wXVVVpXBCyMzMxOLFi0FRFFxdXTUah6oRiUTo1asX0tPTO7RZXhNoRPhezHtrfeQNZDLwO5ngs+naPedN22AYBjU1NUqJV21tbbOdh9qYfXGBvggfwzBwdHTE+fPnMXz4cK7DUSkNPebkItfQY06e0fXr14+ThiOGYXD79m3QNI0zZ85g/PjxoCgK06ZN06u/o8DAQIwbNw7vvvsu16G0iNqFT1+HnKoDiUSidOdhp06dms2wWus81KXsiwv0Rfji4uIQGBiIjIwMrew2bStt9ZgbPnw4TEy4HUf87Nkz7N+/H+Hh4ejcuTMoikJQUJDeTqGKjIzEvn37cOXKFa5DaRG1Ct/9nAos/OUey9bi2bdzWccwknpYek6D7WT2E0JnU2McWzZSJ+a+NaRh9tXe9a+Wsq/W9n2puo2a8D/0Rfg+/fRTAMDWrbq1lNCUx5yJiYmiZOnn5wcvLy+tMdKtq6vD6dOnQdM0EhISsGDBAlAUBW9vb51+4GgLNTU16NOnD2eOH21FrcLXmpGhrF6I3F1B6Dnvc/D7sUsvXBsZyrMvZZo3TE1N2y1eJPvSXvRB+BiGgbOzMw4fPgxvb+00BwVerBMlJyezpp/k5eXBy8uLtTanbS4tDMMgNjYWYWFhOH78OHx8fEBRFGbNmgU+n891eBolICAA/v7+oCiK61CaRW11gJJqEW5lFre4plebcRfGXbrCrO+wRp8xDHAjoxil1SKlrevl2Zcy4lVTU6PIvpoSqf79+8PT07PZfV8EgjaRmpqK+vp6eHl5cR2KAoZh8OjRI5bIpaSkwMnJCX5+fpgwYQI++uijZj3mtIGCggLF+DCRSISQkBAkJSXpxF42dREQEIDDhw8bpvCdjM9t9ZjqlGswHz6p2fSfB+BkQi7+8eoris7D9oqYPPtqLtt65ZVXmnyfZF8EfSIyMhJz5szhtNTWksecr69vmzzmtIH6+npcuHABNE3jzp07mDVrFvbu3YuxY8fqfSmzLfj7++Pdd9+FQCDQmvLzy6it1Ln2WCLOJOU1+7mksgjP972NPu/8DFPr5ltfRRm3Ufzbt7C2tlZq3xfJvggdRR9Kna6urti3bx9Gjx6tkeu15DHX0DG8rR5z2kBycjJomsahQ4fg4uKiGB9mYWHBdWhah7+/PwIDAxEYGMh1KE2itoxPIJS0+Hl16nWYOQxtUfQA4I1pMxF+civJvggEJcnMzERpaSlGjRqllvPLPeYaTj+Re8z5+vpi8uTJ2LhxY7s95rSBsrIyHD58GDRNo6ioCMHBwfjzzz/h5OTEdWhaTUBAAE6dOmV4wmfFb/nUNanX0XXk3BaPAYBull107o+FQNAmTp06hdmzZ6vs76g5jzl5Jrd48WKlPea0AalUiqioKNA0jaioKEydOhVbt27Fa6+9prVrjdrGjBkzsHbtWtTW1qJLly5ch9MItQmfi50VzEwKWBNa5Ahz0yCtLkUXlzEtnoNvYgSX3to1hZxA0DUiIyOxbds2pb62NY+5NWvWwNfXt8Mec9pAZmYmaJpGREQE7O3tQVEUfvrpJ9jY2HAdms7RrVs3+Pj44NKlS5gzZw7X4TRCbcI318sBO65mNvlZTeo1dBn8KozMWn4SYADMHaFdbcsEgi7x9OlTZGdnY/z48a0e25rH3FtvvYUvv/xSZR5z2oBAIMDx48dB0zQePXqEoKAgXL58We8m23BBQECAoqlK2+B0H1+LMDKM6muOI+9NUnlcBEJ70OXmlh07diA1NRW//vpro89a8piTZ3Tq8JjjGplMphgfdvbsWUycOBEURWHq1KkwNTXlOjy9oaCgAEOGDEFBQYHW/Q5pfHJLWzHhyVB95gvMe80PmzdvJuUGAmfosvCNGTMG69evx7hx4zj1mNMGnj59qhgfZmFhAYqisHjxYr0o02orY8eOxSeffILp06dzHQoLrZ7VOXWQJT777DOcPn0aX3zxBUJDQ8niMkHj6JrwyT3moqKi8Nlnn8HJyQnZ2dksjzlfX18MGDBAb0qWzVFbW6sYH5aYmIiFCxeCoih4eXnp/feuDXz//fdITk5GWFgY16Gw0Cp3Bh4P4JsYY8M0F9aA6oSEBKxatQr19fXYvXs3/Pz81B0ygaBAm4WPYRjk5uaymk/kHnNWVlZgGAZ79uyBm5ubXrkAtATDMIiOjgZN0zhx4gR8fX1BURRmzpxpcOPDuObZs2cYMWIE8vPztaqMrDE/vuTcCuy5mYUbGcXgARA24cc30bkHVkxwanIwNcMwOHjwID7++GNMmTIF27Zt09sJ5wTtQpuETyAQIDY2tk0ec6+//jree+89zJ49m+uwNUJ+fj4OHDiA8PBwiMViUBSFpUuXat1cT0PD19dXsR1EW9C4A3tptQgnE3KRnl8FgVAMK74pXHpbYu4IhzbN5BQIBNi8eTP279+PDRs24L333tOqJwmC/sGV8Mk95hquy7XVY660tBQDBgxAfn6+Vu6jUhX19fU4d+4caJrG3bt3MWfOHFAUhdGjR5NSppawbds2PHv2DHv27OE6FAUaFz5VkZaWhtWrVyM/Px8//PADJk0i3Z8E9aAJ4ZN7zDUUuaY85oYNG9amB72wsDBcvHgRJ0+eVGvcXJGUlASapnH48GEMGzYMFEUhICCAjA/TQv7++2+MGzcOz58/15phJDorfMCLm8Xp06exbt06+Pr6Yvv27QY9FZ2gHtQhfOXl5YqSpTo85qZPn46goCAsWrRIpXFzSWlpKQ4fPoywsDCUlZUhODgYwcHBGDhwINehEVrBzc0Ne/bswZgxLQ8t0RQ6LXxyamtr8dVXX2H37t1Yt24dPvjgA7KITVAZHRW++vp63L9/X2Mec5WVlejbty9yc3O1djp+W5FIJIrxYVeuXMH06dNBURQmTZqkNdkDoXX+85//oKKiAjt27OA6FAB6Inxynjx5gnXr1iElJQXff/89/P39uQ6JoAe0R/gaeszJy5YNPebkIqdOj7lDhw7h6NGjOHfunFrOrwkyMjJA0zQOHDgABwcHhIaGYsGCBbC2btz4RtB+UlNTMX36dGRnZ2vF2qteCZ+cy5cvY/Xq1XBycsL333+PQYMGcR0SQYdpSfjkHnMNfeYaeszJS5aa9JibM2cOZsyYgZCQEI1dUxUIBAIcO3YMNE3jyZMnCAoKAkVRGDp0KNehEToIwzBwcXHBwYMH4ePjw3U4+il8wIvy0s6dO/HVV19h2bJlWL9+PVn4JiiFXPjkHnMNG1C0zWOupqYGffr0wZMnT2Bra8tZHG1FJpPh5s2boGka586dw6RJk0BRFN58803Sra1nrF+/HgzDYOvWrVyHor/CJycvLw8fffQRbt26hW+++QYLFizQilSboN009JgLDg6Gt7c3Hj58qPCYk5cttc1jLjIyEj/99BOioqK4DqVFsrOzER4ejv3798PKykoxPqxHjx5ch0ZQE/Hx8Vi0aBEyMjI4vwfrvfDJ+eOPP7By5UpYW1tj165dcHV15TokghbR0GMuJiYGsbGxsLGxga+vL44dO4a7d+/qhMdcYGAgxo8fj3feeYfrUBpRW1uLyMhI0DSN5ORkLFq0CBRFwdPTk/MbIUH9MAwDR0dHnDt3jvP7r8EIH/DCduWnn37C559/joULF2Lz5s1ksdwAaegxJxe7hh5zvr6+LI85bZrc0hIikQh2dnZIS0uDnZ0d1+EAeHGzu3fvHsLCwhAZGYmRI0eCoijMmDFD6yb2E9TPunXrYGppC8dJi5BeIIBAKIEV3wQudlaY59W2ISaqwKCET05JSQk+++wznDlzBlu2bAFFUVpVriKojtY85uRi15LHnK4I3/nz5/H111/j9u3bXIeCvLw8HDhwADRNg2EYUBSFJUuWwN7enuvQCBxxP6cCX5yKQdzzWpiZmbFMyuVjKyc498CK8U5w76vehMQghU9OfHw8Vq1aBYlEgt27d8PX15frkAgd5GWPufj4ePTs2bNDHnO6InwURcHDwwNr1qzh5PoikUgxPuyvv/5CQEAAKIrCqFGjSCnTwOmoUYGqMWjhA140MRw8eBCffPIJpk6diq1btxJ/Lh2hurqa5TEXExODuro6lXvM6YLwicVi9O7dG4mJiejbt69Gr52YmAiapnHkyBG4urqCoijMmTNHo1s4CNpLR6zp1CV+Bi98ciorK7F582ZERERg48aNWLFiBUxMTLgOi/B/SCQSPHz4kDX95NGjRxrxmNMF4bty5Qo+++wzREdHa+R6JSUlOHToEGiaRkVFBYKDgxESEgJHR0eNXJ+gGzRnRi6tq0LpxZ0QZifCqLMVbMYHw3zYBNYxnU2NcWzZyCbdejoKEb6XePjwIVavXo3CwkLs2rULEyZM4Dokg6Mlj7mGIqcpjzldEL53330XAwYMwEcffaS2a0gkEly6dAk0TePatWvw9/cHRVGYOHEiWSMnNMmyA3G4klbYqLxZfPZrgGHQbdpq1Bc+RtHJ/8Au6Bt06vGK4hgeD5gytBf2BXmrPC4ifE3AMAxOnTqFdevWYdSoUdi+fTvx9FIj7fGY4wJtFz6pVAp7e3v88ccfcHJyUvn509LSFOPD+vfvD4qisGDBAnTt2lXl1yLoDyXVIoz+6jqriQUAZPVC5Hy/EH3e/hGmti+anUrOfQtjy26wmRDCOtbMxAh/fjxJ5d2epJbXBDweDwEBAZg6dSq2bdsGDw8PfPDBB1i3bh1pwe4grXnMBQYGYufOnU16zBGa5s8//0SvXr1UKnqVlZU4evQoaJrGs2fPsGTJEly/fh1DhgxR2TUI+s3J+Nwm35eUPQfPyEghegBg2tMRomcpjY7lATiZkIt3xqnWgYMIXwt06dIFmzdvRkhICN5//30MHz4c33//PaZPn851aDpBSx5zvr6+GDlyJNasWdNmjzlC00RGRiIgIKDD55HJZLhx4wZomsb58+fx+uuvY+PGjZgyZQpZ7ya0m/QCQaNsDwBk4jrwzNjmyEZmXSCrr2t0rFAiQ3p+lcpjI7/NbWDAgAE4e/YsLl26hNWrV2Pfvn3YsWOHWspKukxrHnNffPEFvL29dd4qR5uQl+V///13pc/x5MkTxfgwGxsbUBSF77//Ht27d1dhpARDQyCUNPm+kWlnMCK2yDGiWhh1anoqkkAoVnlsRPjawZtvvqmwPBo5ciTeeecdrF+/3iDbtlvzmKMoCvv27SNro2omNjYWXbp0abeDQU1NjWJ8WGpqKgIDA3HmzBl4eHioKVKCoWHFb1peTGztwcikEJc9V5Q764uewLRBYwv7PKqvBhHhaydmZmb4+OOPERQUhI8++ghDhgzBN998g/nz5+vtmlRrHnPjx4/HRx99pFaPOULTyMucbfndYxgGf/75J2iaRmRkJEaPHo2VK1fC39+frF0TVI6LnRXMTAoalTuNOvHRxXkUKu4cQrepq1Ff9Bi1WdGwC/qm0Tn4JkZw6W2p8thIV2cHuX37NlatWgVbW1vs2rULw4cP5zqkDqONHnNcoq1dnQzDYNCgQTh+/DhGjBjR7HHPnz9HREQEwsPDwePxFOPD+vTpo8FoCYZGc12dQNv28QHq6+okwqcCJBKJYvj14sWL8fnnn+vM8GuhUIikpCRWybK4uFirPOa4RluFLzk5GTNnzsTjx48bZXwikQhnz54FTdOIjo7G3LlzERoaCj8/P72tTBC0j+b28bUFso9PRyguLsaGDRtw7tw5bNmyBSEhIVq1sVcmk+Hvv/9midzLHnO+vr5wcXHRqri5RluFb9OmTaipqcH27dsBvMgAExISQNM0jh49Cnd3d8X4sC5durRyNgJB9TQ3uaUtkMktOkZcXBxWrlwJhmGwe/du+Pj4cBJHUVERS+RiY2NhbW3N2hg+YsQIrfeY4xptFb7hw4fj559/xqBBg3Do0CGEhYWhqqoKISEhCA4ORv/+/bkOkUAgszoNCZlMhoiICHz66aeYPn06tm7dqlZ36fZ6zBHajjYKX2pqKsaPH49x48bhxo0bmDFjBiiKwvjx40m2TtA6iDuDgVFZWYnPP/8cBw8exL///W8sX768w5uB5R5zDTeGN+Ux5+TkRG6CKkCbhO/hw4egaRr79u2DhYUFvvjiC8yfP5/sjSRoPcm5FdhzMws3MorBw4vN6XLkfnwTnXtgxQQntZQ3G0KET0M8ePAAq1atQklJCXbt2oXx48e3+Wvz8vJYIif3mJMLnJ+fH9zd3cHn89X4HRguXAtfRUWFYnxYbm4uli5dit9++w27d+/GxIkTOYuLQFCG0moRTibkIj2/CgKhGFZ8U7j0tsTcEcSBXS9hGAYnT57EBx98gNGjR+Obb75ptMG7uroa8fHxrLW5uro6lsipwmOO0Ha4ED6pVIrr16+DpmlcvHgRkydPBkVReOONN5CTkwM/Pz/k5eWRUWIEghIQ4eOAmpoabN26FXv37kVQUBCcnZ2RmJiI6OhoPHr0CG5ubqwGFHV4zBHajiaF79GjR4rxYd27d0doaCgWLVrEetD59ttvkZ6ejl9++UUjMREI+gZ5XNQQDT3m5GVLoVCIX3/9FUZGRggKCkJYWJjGPOYI2kN1dTVOnjwJmqaRlpaGwMBAnDt3Du7u7k0ef+rUKWzcuFHDURII+gPJ+NSE3GOu4dqc3GNOXraUe8xdvHgRa9aswZAhQ7Bjxw4MHKhaCw5Cx1BHxscwDO7evYuwsDCcPn0aY8aMAUVR8Pf3b/HBJy8vD8OHD0dBQQF5QCIQlIQInwp42WMuJiYGT58+haenJ2ttriWPOZFIhB07duCbb77BihUr8Omnn5JNx1qCKoUvNzcX+/fvR3h4OExNTRXjw+zs7Nr09T/++CPu3buHAwcOqCQeAsEQIcLXTl72mIuJiUFSUpLCY04ucsp6zOXm5uLDDz/En3/+ie3bt2Pu3LlkfY9jOip8QqEQZ8+eRVhYGGJjYzF//nxQFAVfX992/2wnTZqE1atXY9asWUrHQyAYOkT4WqGhx5xc7Bp6zPn6+qrFY+7mzZtYtWoVevbsiR9++AHDhg1T6fkJbUcZ4WMYBvHx8aBpGseOHYOnpycoisLs2bOVnpRTXFwMJycnFBQUkGk7BEIH0HhzS0m1CCfjc5FeIIBAKIEV3wQudlaY56W5PRzN0dBjTi5yDT3mQkJCsHfvXo14zE2YMAGJiYnYu3cvJkyYgKCgIHz++efo2rWr2q9NUJ6ioiIcPHgQNE2jtrYWISEhSEhIQL9+/Tp87rNnz2LKlClE9AiEDqKxjO9+TgV+vJmFW5nFAMCyqpDv2p/g3AMrxjvBva/6nQ1a85iTly21wWOuqKgI69evx4ULF7B161YsXbqUTGTRIK1lfGKxGBcvXgRN07h58yZmzZoFiqIwduxYlf6cpk6dipCQECxYsEBl5yQQDBGNCJ82zGnTB4+5mJgYrFy5EsbGxti1axe8vVVv10FoTHPCl5qaCpqmcejQIQwaNAgURWHevHmwtFS9cWZFRQX69euH58+fq+X8BIIhoXbh42Iytz57zMlkMoSHh2P9+vWYMWMG/vvf/6J79+5ch6XXNBS+8vJyHDlyBDRNIz8/H8HBwQgJCcGgQYPUGsPBgwdx4sQJnD17Vq3XIRAMAbUKX3NeTJKKQpRG7UH983TAxBTmzqNh8/oy8Iz+V1JsqxeToXrMVVRUYNOmTThy5Ag2bdqEd955h4yvUhM8Hg+XLl0CTdO4dOkSpkyZohgfpqky+KeFUEgAACAASURBVOzZszF79mwsXbpUI9cjEPQZtQpfc+67hcc3wbiLNbq9+R5kwhoUHvsMFu5TYOU943+BNeO+Szzm2KSkpGD16tUoKyvD7t27MXbsWK5D0huysrJA0zT++9//wsvLCxRFYdGiRbC1tdVoHNXV1bC3t0d2djZsbGw0em0CQR9RW4pQUi3CrcziJtf0JJWFsPLyB8+kE4wtOqGzoxfEJc9YxzAMcD29GBev3UZaUmyTHnOrV682eI85V1dXXL9+HcePH0dgYCDGjRuHr7/+Gvb29lyHppNUV1fjxIkToGkaGRkZWLx4MYAX5sJc8fvvv2PkyJFE9AgEFaG22t/J+NxmP7PynoGah7chEwshqSpB3eM4dHYc0eg4obAOH+6NRHZ2Nvz9/REVFYXS0lJcvnwZmzdvhr+/v0GLnhwej4cFCxYgPT0d/fv3h7u7O77++mvU19dzHZpOwDAMbt++DYqi0LdvX5w5cwbr1q1DTk4OvvvuO67DQ2RkJAICArgOg0DQG9RW6lx7LBFnkvKa/ExckoOSc9tRX/QEYGQwH/4auk1f2+QUi9ke9tixwEMdIeotWVlZWLt2Lf7++2/s3LkTb775JtchaSU5OTmK8WF8Ph8URSEoKAi9evViHcelH59QKISdnR0yMzPJQx6BoCLUlvEJhJIm32cYGQqP/xtdnF9Fvw8i4bDmMGTCalTcpJs5j1hdIeotTk5OOH/+PL799lusXLkSs2bNwuPHj7kOSyuoq6vDkSNHMHnyZHh4eCAvLw9HjhxBSkoKPvjgg0aixzVRUVHw8PAgokcgqBC1CZ8Vv+nlQ1ldFaSCYliO8AfPxBTGna1g4fY66h41vYbCN2r7NggCG39/f6SmpsLX1xc+Pj7497//jdraWq7D0jgMwyAmJgbLly+Hg4MDwsPDERoaiufPn2PPnj3w8fHR2nmopMxJIKgetQmfi50VzEwan964S1eYdO2FqsSLYGRSyITVqE65BtOejo2O5UnFOPHL9xg8eDCCgoKwa9cuREdHQyQSqStsvYPP52P9+vVISkpCRkYGhg4disjISM5Kd5qksLAQ27dvh6urKwIDA2Fvb4/ExERcvnwZCxcuBJ/P5zrEFhGLxTh//jxmz57NdSgEgl6htjW+kmoRRn91nTWaTE594WOUXf0Z4qIngJEx+P1cYTt5OYzNX9qzJxVjiVUGJr7qg+zsbMUWhszMTAwfPpzlhuDk5KS1T+3axI0bN7Bq1SrY2dnhhx9+wNChQ7kOSaXU19fjwoULoGkad+7cYY0PU/b3g6s1vqioKPz73//GvXv3NH5tAkGf4WQfX1vg8QBvO1PYpJ7EyZMnMXLkSFAUhRkzZkAikSAhIYE1fkwgEMDX15e1ab1Hjx6q/6b0ALFYjD179uDLL7/E0qVLsWnTJpW7S2ialJQUxfgwZ2dnxfgwCwuLDp+bK+F755134OTkhA8//FDj1yYQ9BlOJre0hYaTW2pra3Hq1CnQNI379+9j0aJFoCgKnp6eiqf4goIC1izO2NhY2NrasmZxenp6GszG9rZQWFiITz/9FJcuXcK2bdsQFBSkU9NtysrKFOPDCgsLFePDnJycVHodLoRPKpWiT58++OuvvzBgwACNXptA0Hd0blZndna2ogXdysoKFEVh8eLFjbI7mUyGzMxMlvtCWloaXFxcWGLo7OysUzd7dRAdHY2VK1fC1NQUu3fvxogRjfdUagtSqRRXrlwBTdO4fPkypk6dCoqi8Nprr6ltfBgXwnfr1i2sXbsWiYmJGr0ugWAI6Kw7g0wmw61bt0DTNH777TdMmjQJFEVh6tSpzc6srKurUwyvlothaWkpvL29WSPP7OzsOvDd6iYymQxhYWH47LPPMGvWLGzZsgXdunXjOiwFmZmZCA8PR0REBPr06QOKorBw4UKNTDPhQvhWr16Nnj174rPPPtPodQkEQ0BjfnzJuRXYczMLNzKKwQMgbMKPb6JzD6yY4NTqYOqXEQgEOH78OMLCwvDkyRMEBQWBoqg2NW4UFxezHNZjYmJgYWHBapwZMWKEVtsVqZLy8nJs2rQJR48exX/+8x8sW7aMMz/CqqoqHD9+HDRNIysrC0FBQQgJCcHw4cM1GoemhU8mk6Ffv364cuUKhgwZorHrEgiGgsaET05ptQgnE3KRnl8FgVAMK74pXHpbYu4I1Tiwp6enKzKDvn37KjIDa+u2iSnDMMjKylJkhNHR0UhNTcWgQYNYYjhkyBDODWrVSXJyMlatWgWBQIBdu3ZhzJgxGrmuTCbD7du3FZn8hAkTFJm8qampRmJ4GU0L37179xAaGoqHDx9q7JoEgiGhceHTFBKJBFFRUaBpGleuXMG0adMQGhqKSZMmtXtNTyQS4f79+ywxLCgogJeXF2u9UN8GQzMMg6NHj+LDDz/ExIkT8fXXX6vNw/Dp06eKtVsLCwvF2q02TCzRtPB99NFHMDMzwxdffKGxaxIIhoTeCl9DSktLcfjwYdA0jdLSUgQHByM4OBgDBw5U+pxlZWWIjY1liWGnTp1Ya4Xe3t564ZZdXV2NLVu24JdffsHHH3+MNWvWoFOnTh0+b11dHU6fPo2wsDAkJSVhwYIFoCgKXl5eWrUnU5PCxzAMnJyccPLkSXh6emrkmgSCoWEQwteQ+/fvg6ZpHD58GEOHDgVFUZg7d26H1/AYhlFsspevFyYlJcHR0ZElhsOHD9dZw9i///4ba9aswePHj/HDDz9g8uTJ7T4HwzCIjo5GeHg4Tpw4AR8fH1AUhZkzZ2rtJBVNCl9SUhLmzJmDR48eaZX4Ewj6hMEJn5z6+nqcP38eNE3jjz/+wJw5c0BRFEaPHq2yG45YLEZKSgpLDHNycuDp6cnaaN+vXz+duckxDIPz589j7dq1cHNzw3fffQdHx8bj5l6moKAABw4cAE3TEIvFoCgKS5cuhYODgwai7hiaFL6NGzdCKBTim2++0cj1CARDxGCFryH5+fk4ePAgaJqGRCJBSEiI2m7KlZWViIuLU4hhdHQ0ALDWCn18fNC1a1eVX1uVCIVCfPvtt9ixYwdWrlyJjz/+uNFwAE08XGgCTQrf0KFDERYWhpEjR2rkegSCIUKErwHyKf40TeP48ePw9fVVexmOYRjk5OSw9hYmJibCwcGBJYZubm6cdTW2xLNnz/Cvf/0LsbGx+O677zBr1iwkJyc3KicHBASoZHwYF2hK+NLS0vDGG2/g2bNnBj9UgUBQJ0T4mkHeeEHTNBITEzXaeCGRSPDgwQOWGD5+/Bju7u6s9UJHR0etyZxOnz6NFStWoKamBhYWFnj77bc73ECkLWhK+L788ksUFRXhhx9+UPu1CARDhghfG3j69CkiIiJA0zTMzc0VTt2abLWvqqpCfHw8SwxFIhFrb6GPjw9sbW01FtPLW0amTp0KGxsbHD9+HBRFYePGjTo//BrQnPB5enri+++/x/jx49V+LQJBGUqqRTgZn4v0AgEEQgms+CZwsbPCPC/V7MPWFET42kHDzdVnz55VbK6eNm0aJ2XI58+fs7ZTxMfHw87OjiWG7u7uMDNT7S9kRkYGaJrGgQMH4ODggNDQUCxYsEAxJKCwsBCffPIJoqKi8NVXX2Hx4sVak5kqgyaE7/Hjxxg1ahTy8vL0ejACQTe5n1OBH29m4VZmMQCw7Obkk7cmOPfAivFOcO/bvslbXECET0leHqe1ePFiUBSl8XFaDZFKpUhLS2OJ4d9//60S70KBQIBjx46Bpuk2j4W7d+8eVq5cCT6fj127dunsvjRNCN/27duRmZmJn3/+Wa3XIRDaizpmLXMNET4VwOUA5dao+f/t3XdcU9f/x/FXUFRo3QsVHNStOKriRtyKo/7qtlWJ2tZaQMFZ92iVulCxLf22Nc660KK2VOvGqkURUFFQoS4UBARlr+T+/vBLvqQiskICOc/Ho4+HTW5uThx5c8895/NJStLoXejr60tCQoLGdoo39S7MKgS+bds2jh07pi4EPmjQoDxf4SqVSnXx65EjR7Jq1Sq9Kn6dF8URfF27dmX58uUMHDhQq+8jCPlR1N119IUIviKki5Y5BZHVuzDrfmH23oWdO3fGwsKCgIAA9uzZk2vrp/yIjY1l6dKlHDx4kBUrVvDJJ5/o1e9JbrQdfOHh4bRt25aIiIgiqYgjCEUhq5/qs7+9SLp5mvToB7zTohc1hjq/duyLv37h5V+/UGvcV5g0bKfRT1UfieDTkuJqkloUVCoV169fx8PDg99//53IyEhkMhmNGzfG1taWLl26YG1tXSS9C69fv46joyOJiYls3bqVbt26FdGn0B5tB5+7uzt+fn7s2LFDa+8hCPn16S4/TgY/IynkEshkpNz3R8pIfy34MuIiiD78FaqUBKoPdcGkYTtkMhjYsjYeH3fU0ehzJzYLaUm1atX44osv8PPzw9vbm+TkZLp3746NjQ0KhYLExERdDxFJkrh8+TLTp0+nb9++PH78GDc3N5KSkoiPj2fbtm00a9aM48ePM3ToUKpVq0b//v1ZtGgRR48eJTIyMt/v2bZtW86fP8+cOXMYM2YMkyZNIiIiQgufruQ4dOgQI0eO1PUwBEEtJjGN83ejkSQwbdYN06ZdMTLJeYV27EkPqtrag9H/SjFKEpy9E83zxLRiGnH+iOArBlZWVmzcuJHHjx/j4uKCl5eXumWSj49PsTc5ffr0Kd988w0tW7bE3t4eS0tLbt68ibe3N6NHj6Z8+fKYmJjQtWtXZs2axd69ewkLC+PevXs4OztTtmxZvvvuO1q2bEmDBg0YM2YM69ev58KFCyQlJb31/WUyGRMmTCA4OJi6detiZWXFhg0byMjIKIZPr1+ioqIIDAwsUN1TQdAWz2vheTouKeQvZEZlMXmv02vPyQBP/7ydp7iJ4CtG5cqVY8SIERw5coTg4GBat27NjBkzaNKkCV999RWPHz/W2nunpaXh6enJkCFDaNWqFaGhofz888+EhISwYMGCPLVUqlmzJnZ2dqxYsYLjx4/z/PlzTp06xfDhw9UVXGrVqkW7du347LPP+PnnnwkKCkKpVOZ4vooVK+Lq6srFixc5deoUbdq04eTJk0X90fWal5cXgwYN0tsC3YJhComM19iykBNVegovzu+gar9Pcnw+NVNFSESCNoZXaCWzTUApYGZmxuzZs3FxccHPz49t27bRrl07OnTogFwuZ8SIEa/VviyIgIAAFAoFe/fuxcrKCnt7ew4cOFAkHeVlMhlNmjShSZMmfPzxx8D/ehf6+vpy7tw5vvnmm7f2LmzWrBne3t4cO3aMzz77jPbt27Nx40YaNGhQ6DHqu8OHDzN16lRdD0MQNMSnZr71mBcX9vBOqz4YVzHL5Tz6OYsjFrfokZSUFLy8vFAoFFy7do0xY8Ygl8vp1KlTvvbdxcTEsGfPHhQKBS9evFAvrMlLFwVtyOpdmL3qTPny5TX2Fnbo0IGKFSuSkpLC+vXr2bRpEzNnzmTu3LlF8gNAYWhrcUtcXBwNGjTg6dOnJbaOqVA6zdofgFfgU43H4nx2oYyPUS9uebrNEWXCc/jvgjdVcjxG5U2p1GUUlbuMAuD/2tXDbWy74h18Hojg01OPHj1i586dbN++nQoVKqjLpNWuXTvH4zMzMzlx4gQKhYJTp04xdOhQ5HI5vXv31ruCx5Ikcf/+fY0tFdevX6dRo0bqMLSwsODHH38kMDAQNzc3hg8frrPqL9oKvp07d3L48GG8vLyK/NyCUBge58NwO3WXtEwVkkoJKiUv/voFZcJzqg92BKMyqNKSINttjIgdzlTtOw0Tyw4YlTOhQlkjnPs35TMb/avXK4JPz0mSxIULF1AoFHh5eWFjY4NcLmfIkCEYGxsTEhKiLh/WoEED5HI5Y8eO1fu2Rv+WkZHBjRs3NDbah4eH06hRI548eYKFhQVubm7Y2toWewBqK/g++OADRo0axcSJE4v83IJQGE+ex2Oz/jxKjHhxYQ8vL+7VeL5y9/FU6fmRxmPh302hup0TJg1fXeGVL2vEpfl99LKGpwi+EiQxMZGDBw/y448/EhQUxDvvvENmZiZTpkzB3t6eFi1a6HqIRerly5dcvXqVy5cvs3//fm7fvo2pqSm9evWie/fuWFtbF0vvQm0EX0JCAvXq1ePRo0fqGqeCoA+yGk2/M3AW8ZUaUZC/+fq+j08sbikhVCoVvr6+nD59mtu3b9OtWzeqVKnCxYsXOX36NPXr16d27drF2p1B2ypXrky/fv3o168fS5YsISIiAgcHB86dOwfA8ePH8ff3x8LCQqNdk772LszO29ub7t27i9AT9Ma9e/eYNWsWoaGhbN26lTqtujDux79Jych5VXZuKpQtwwxb/SvWkUW/bv4Ir7l//z7Lli3D0tKSOXPmYG1tTWhoKMePH2ffvn08ePCA1atX89dff2FpacnYsWM5fvz4G7cQlGR16tTh0KFDHDt2TL15/vz58+zbt49u3brh5+eHvb09VatWpXv37jg7O7Nv3z7++eefYt8r+TZi07qgL5KSkli4cCFdu3alV69e3Lx5k0GDBtHWogqL7JpjYpy/mHhVq7O53pYrAzHVqZeSkpI4dOgQCoWCoKAgJkyYgFwup1273FdHxcXFsW/fPhQKBU+fPmXSpEnY29vTtGnTYhp58VEqlfz0008sXbqUUaNGsWrVKvXVbvbehVmLZ9LT09UFufPbu7CopzpTUlIwMzMjNDS0UPVPBaEwJEniwIEDzJ07l549e7J27doc9/OK7gyC1kiSxKVLl1AoFBw6dIju3bsjl8sZOnRogfrpBQUFoVAo2L17N02aNEEulzNmzBgqVqyohdHrTmxsLEuWLMHT05NVq1YxderUHItfP3nyRGM7RVbvwux7C9/Uu7Cog+/IkSNs3ryZM2fOFNk5BSE/bt68iZOTE7GxsWzdupWePXvmevyN8Bd8dy6Us3eikfFqc3qWrH58vZvVZIZtY72+0ssigk/Hnj59qu7uLpPJkMvlTJw4kbp16xbJ+TMyMvD29kahUHDu3Dk++OAD5HI5NjY2erfNoTACAwNxcHAgNTUVd3d3unbtmuvxWb0Ls4dhVu/C7GHYuHFjjIyMijT4Jk2ahLW1NQ4ODkV2TkHIixcvXrBs2TL27t3LsmXL+OyzzyhbNu9LPZ4npuHpH05IRALxqRlUqmBM8zoVGfV+yerAjiQUu9TUVOnAgQPS4MGDpapVq0qffPKJdPnyZUmlUmn1fZ89eyZt2LBBat26tWRpaSmtXLlSevjwoVbfszipVCpp9+7dUt26daXJkydLERER+Xp9YmKi5OPjI61bt04aPXq0VL9+falq1aoSIC1dulT67bffpKioqEKNMS0tTapataoUHh5eqPMIQn4olUrp559/lmrXri19+umnUnR0tK6HpFMi+IqJSqWSrl27Jjk4OEg1atSQ+vTpI+3atUtKSkrSyViuXr0qzZgxQ6pevbrUr18/ac+ePVJycnKxj0Ub4uPjpblz50rVq1eXNm7cKKWnpxf4XBERERIgLVy4UOrXr59UuXJlydLSUho3bpzk5uYmXbx4MV+/b3/88YfUtWvXAo9HEPLL19dXsra2lrp06SL5+fnpejh6QUx1all0dLS6fFh8fDz29vZMnjyZhg0b6npoAKSmpnLkyBEUCgVXr15l9OjRyOVyrK2tdVYppaiEhIQwc+ZMwsPD2bJlC3379i3QebLf41OpVNy5c0ej6kxwcDAtWrTQKMHWtGnTHKeSP/nkE5o3b87s2bML9dkE4W2ioqJYuHAh3t7erFmzhokTJ5aq2xuFIYJPCzIzM/njjz9QKBScOXOG4cOHI5fL6dWrl17/xQsPD1ffbzQ2NlbfbzQze3MRWn0nSRJHjhzB2dmZjh07smHDBurXr5+vc7xtcUtKSgoBAQEaYfj8+XM6deqkEYbVq1enbt26+Pr66qxuqlD6ZWZm8t1337Fq1SomTpzIsmXLSlwlJ20zyOCLSUzD81o4IZHxxKdmUqlCWZqbVWJ0h8LdoL19+7Z6JaWlpaV6JWWlSjk3cNRXkiRx8eJFFAoFhw8fpkePHuoVpuXKldP18AokJSWFtWvXsmXLFpydnZkzZ06eWwEVZFVndHQ0V65c0QhDY2Nj0tPTWbx4MdbW1nTo0AFTU9OCfBxByNH58+dxdHSkVq1abNmyhZYtW+p6SHrJoILv+uMXfHsulPN3owE0+k1lLcm1bVaTGb0a09Yib0tyX7x4od47Fx4ert4716xZM218hGKXmJio3lN4+/Zt9Z7Ctm3b6npoBfLgwQNcXFy4fv06bm5uDBs27K1TukWxnUGSJCZOnEh6ejpmZmb4+voSFBREkyZNNKrOtGjRIsftGIKQm/DwcObMmcPly5fZsGEDI0eOLPG3KrTJYIKvKDdhqlQqzpw5w7Zt2/D29mbAgAHI5XL69++fr6XBJU1YWBg7duxg+/bt1KhRA7lczoQJE6hevbquh5ZvJ0+exMnJiUaNGrFp06ZcN/kXRfCpVCosLCw4ffo0zZs3BzR7F2ZdGUZGRtKxY0f1FKm1tXWemgQLhiktLY2NGzeyYcMGZsyYwYIFC8QsQh4YRPC9Cr1gUjJy7yic3auyOy00wi/ri3/Hjh1Ur16dKVOmMH78+BL5xV8YSqWSM2fOoFAo8Pb2pn///sjlcgYMGFCigj89PZ0tW7bg6urKtGnTWLx4cY598Yoi+C5fvsy0adO4detWrsdl712YFYjly5fX2FuY1btQMGze3t7MnDmTli1b4ubmhqWlpa6HVGKU+uC7/vhFjoVWM2Ie8/zP70l/FkoZk8pU7S3HtFk3jWNMjMuwfWJbQi79WWqm+orav6d6J06ciFwuL1FTvREREcyfP5+zZ8+ydu1axo0bpzFNVBTBN2fOHExNTVm5cmW+Xif9t3dh9qvC69evY2lpqRGGrVq1KlE/dAgFFxYWxqxZs7hz5w6bN29m8ODBuh5SiVPqg+/TXX6cDH6mMb0pqZQ8/fFzKrYfTMWOw0l9FET0oZXUkW/BuFq97AeSfv8aHZKvlfjFHcXh1q1bbN++nV27dvHee++VuMU9Fy9exMHBgUqVKuHu7k6bNm2AwgefJElYWlri5eVVJD8wpaenc/PmTY0wDA8Pp3379hphaGFhIe7zlCJJSUmsWbMGDw8P5s6dy6xZswpUzlAo5cEXk5hG92/OaCxiAUiPfkDkzjlYuBxUfzE827eE8nWbUsVGsylouTIyLi/oW7LK8ehYRkYGx48fL3HbOeDVNO6PP/7I0qVLGTt2LCtXrqRatWqFCj5/f3/GjBnDvXv3tBZEWb0Ls4ehTCbTuFdYHL0LhaInSRKenp7Mnj2bHj16sG7dOnHft5BK9dyI57XwnJ/I8TtMIj364WuPGslkePqH85nNe0U6ttLM2NiYYcOGMWzYMPUG/lmzZunlBv5/K1OmDNOnT2f06NEsXrxY3dxXqVQWeLVlVgsibV59Ze9dCK++LB89eqQOwZUrVxIQEICFhYVGGJaE3oWG7NatWzg6OhITE8OuXbvo1auXrodUKuj3j9+FFBIZ/9rVHoBxdXPKmFYm3vcQkjKTlPv+pD4KQspMe+3Y1EwVIREJxTHcUqlmzZrMmjWLwMBADh06RExMDB07dqRv377s3r2b5ORkXQ8xR9WrV+f777/H29sbgC5duuDr65vv80iSpJPeezKZjAYNGjB69GjWr1+Pj48PcXFx/PLLL7n2Lrx//77e9S40RC9fvsTZ2ZnevXvz4Ycf4u/vL0KvCJXqqc4pO65yJiQqx+fSo+4Te/IHMqIfUq5OY8qYVoYyxtSwm/nasX2b1+LnyZ20PVyDkZaWxtGjR1EoFPz999+MGjUKuVxOly5d9PKelEwmY+fOncyfP5+BAwfi6upK7dq18/TaW7duMWjQIB49eqSXny0hIQE/Pz/1laGvry8ZGRkavQutra2pWrWqrodqEFQqFTt27GDhwoUMHTqU1atXi56NWlCqg2/W/gC8Ap/m6djIXXN4p3VfKrZ/fYXU/7Wrh9vY3JvACgXz5MkTdZm0MmXKYG9vX6RtmYpC1uKW+Ph4Vq5cyY4dO1i0aBFffPHFW6cJV61aRUxMDJs3by6m0RZeYXoXCgXn5+enblXl7u5Op07ih21tKdXB53E+DLdTd3Oc7kyPuo9xtXpIkooEf28S/H+n3iceyMpqfpFVKGuEc/+m4h6flkn/asTbrVs35HI5w4YN0/kX7L9XdQYHB+Pk5ERERARbtmyhT58+b3xtu3bt2LJlCzY2NsUxVK14W+/CrEBs3LixXl7V6rvo6GgWLlzIb7/9xurVq5k8ebLeLwIr6Up18L1pVSdA3JltJF4/gaRSUt6iFdX6f4Zx1devMsqXNeLS/D5iVWcxSkpKUpdJCwoKUu+dbNdON1fdOW1nkCSJX3/9FRcXF6ytrVm/fv1rxa/DwsLo3r07T548KXVlyJKSkvD399cIw8TERDp16qQRhjVq1ND1UPVWZmYmHh4erFixgo8//phly5ZRpYr+dy8vDUp18EHO+/jySlKpeK98IscXjxT793Tkn3/+UZdJq1atmrpMWnF+oea2jy85OZlvvvmGrVu34uLiwuzZs9XFr9euXcs///yDh4dHsY1VlyIjIzXuFV69epUaNWpodKho3759nouDl2Y+Pj44ODhQo0YNtmzZQuvWrXU9JINS6oPvTZVb8qJ8GRl1bu/nWfAVtmzZQv/+/bUwQiEvVCoVZ8+eRaFQ8Ntvv9GvXz/kcjkDBw7UesWSvGxgv3//Pi4uLty8eZNNmzYxdOhQOnfuzFdffWWwf2/+3bvQ19eXkJAQWrRooXG/8E29C0ujJ0+eMHfuXP766y/Wr1/P6NGjxfSwDpT64IPC1er8qHMDjh07xqxZs2jfvj0bNmzQ2z1ohuLly5fs378fhULBTw7MtwAAF+pJREFUw4cP1WXSsoo/F7X8VG45ceIETk5OmJub4+/vT1RUlNgnl82/exf6+voSGxurniLNCsO8rpotKdLS0nBzc2PdunV8/vnnfPnll7zzzju6HpbBMojgg8J3Z0hNTWXdunVs2rQJJycn5s2bh4mJifYHLuQqODhYXSatQYMGyOVyxo4dW6QVSvJbsiw9PZ3Ro0dz4sQJXFxcWLhwYY7Fr4VXsnoXZt0vvHLlCpUqVdLYTlGSexf+8ccfzJw5k2bNmuHm5kbjxo11PSSDZzDBB3Aj/AXfnQvl7J1oZLzanJ4lqx9f72Y1mWHbmDbmOd9kfvjwIXPmzMHPzw83Nzc++OADMVWhBzIzMzlx4gQKhYJTp04xdOhQ5HI5vXv3LvQ0WkFqddrY2DB16lROnjzJ+fPnWbduHWPHjhV/V/JAkiTu3bunEYZBQUE0bdpU435h8+bN9XrRUFhYGM7OzgQHB7Np0yaGDBmi6yEJ/2VQwZfleWIanv7hhEQkEJ+aQaUKxjSvU5FR7+e9A/vp06dxdHTEwsKCLVu2lKhuBKVdTEwMv/zyCwqFgri4OCZPnoy9vT2NGjUq0PnyG3zPnj2jWbNmREZGUqFCBS5cuICjoyNVqlTB3d0dKyurAo3DkKWlpREYGKgRhs+ePaNDhw4aYagP+z+Tk5NZs2YN33//PbNnz8bFxUXnW3KEf5GEAktPT5c2btwoVa9eXZo7d64UHx+v6yEJ/+Lv7y85OjpKNWrUkGxtbaUdO3ZIiYmJ+TpHfv+ZeHh4SOPGjdN4LCMjQ/r222+lmjVrSo6OjlJcXFy+zim87vnz59Iff/whrVixQrKzs5OqV68u1atXT/rwww8lV1dX6ezZs1JCQkKxjUelUkkHDx6U6tevL40dO1Z69OhRsb23kD8GecVX1CIjI1mwYAEnT55k7dq1TJgwQUxp6Zm0tDSOHTuGQqHg0qVLjBw5ErlcTrdu3d76Z5XfK74BAwbw6aefMmrUqNeei4mJYdGiRRw5coSvv/4auVxuMCsatU16S+/CrPuF2uhdePv2bRwdHYmKisLd3R1bW9scj4tJTMPzWjghkfHEp2ZSqUJZmptVYnSHvM82CYUngq8IXb58GQcHB0xNTXF3d9fZhmshd0+fPmXXrl0oFAokSUIulzNp0qQ3TpPlJ/hiY2Np1KgRT58+zXXV3rVr13BwcECpVLJ161asra0L9FmE3L2td2FWGBa0d+HLly9ZsWIFu3btYsmSJcyYMSPHUL3++AXfngvl/N1oAI2iGlnrC2yb1WRGr8a0tRCb2LVNBF8RUyqV/PzzzyxZsoRRo0axatUqqlWrputhCTmQJIm///4bhUKBp6cnXbp0QS6XM3z4cI17MvkJvu3bt3P06FEOHz781mNVKhW7du3iyy+/ZPDgwaxZs4ZatWoV+PMIefPixQv8/PzU2yl8fX0xMjLSuFfYsWPHXFcGZ/3ZLViwgCFDhrB69eo3/tkVdkW5UPRE8GlJbGwsS5YswdPTk5UrVzJt2jS9XoFm6JKTkzl8+DAKhYLr168zfvx45HI57du3x8jIKM/BN2zYMMaNG8dHH32U5/fO61WDoB3Sv3oX+vr6EhAQQP369TXC0MrKCmNj43xdrRdmD7EIP+0RwadlgYGBODo6kpyczNatW+natauuhyS8xYMHD9Rl0ipVqsSNGzeIiop6a3uY+Ph4zM3Nefz4cYH2Ed6+fRsnJyeePXuW630iQfsyMzMJCgrSCMP79+9TsWJFEhIS+Pjjj5k3bx6WlpZvnCLNqhr17G8vkm6eJj36Ae+06EWNoc4ApMc84vlvG8mMiwCgnFljqvb/jHI16mNiXIb9n3Z547YqoXBE8BUDSZL45ZdfmDdvHv3798fV1RUzMzNdD0t4C5VKxfnz5+nTpw+VK1emT58+yOVyBg8enOMV2d69e9m9eze///57gd9TkiQOHz6Mi4sLXbt2Zf369ZibmxfmYwiFlJmZyQ8//MDy5cuxsbHBysqKGzduaPQuzLpXmL13YVad4KSQSyCTkXLfHykjXR18qtREVKlJlKlcCyQVCf6/k3j9T+pO3YpMBgNb1sbj4466/OilllhOVgxkMhkfffQRISEh1KpVi9atW7Nx40YyMjJ0PTQhF0ZGRvTu3RuAR48eYWdnx5o1a7CwsGDu3Lncvn1b4/jDhw/z4YcfFuo9ZTIZI0eOJDg4mKZNm9KuXTvWrFlDWlpaoc4rFMyFCxfo2LEjBw8e5MyZMxw6dIjly5dz+PBhnjx5QkBAAFOmTCExMRFXV1caNGhA06ZNGTt5GqdvRyBJYNqsG6ZNu2JkUknj3EYV3qVsldrqK0aZzEh99SdJcPZONM8TxZ+7NogrPh24c+cOTk5OPH78GHd3d/r27avrIQm5+PfilpCQELZv387OnTuxsLBQL4hp0aIFYWFhRdo54p9//sHZ2Znbt2+L6h/F6OnTp8ydOxcfHx/Wr1/PmDFj8rTqM6t3odvxm5yNMUUl+9/MQJzPLpTxMeorviyP3MYipaeAJFG550dU6T4OEL1AtUlc8elAs2bNOH78OKtXr2batGmMGjWKhw8f6npYQh41b94cV1dXHj16xLJlyzh9+jRNmjTBxMSEwMBAVKq8L2R4G0tLS44cOYK7uzvOzs4MGzaM0NDQIju/oCk9PZ21a9fSpk0bGjRoQHBwcL5KzZUpU4bWrVtT0aK5Rujlpr7zfiycD1BtwHTK1f5fyKVmqgiJSCjQ5xByJ4JPR2QyGSNGjOD27du0adOG999/n1WrVpGamqrroQl5VLZsWezs7Dh48CB2dnbY2Ngwb948GjVqxNKlSwkLCyuy9xo0aBA3b96kR48edOnShUWLFpGUlFRk5xdeddawsrLi/PnzXL58mdWrVxe4uHh8ama+jjcqV4F32w/m+W8bUSa9yHYecTtEG0Tw6ZiJiQlLly7l2rVrBAYG0rJlS44ePZrvosiC7qSlpXHq1Ck2b96Mv78/R48eJT4+nq5du2Jra8uOHTuKJKTKly/P/PnzuX79Og8ePKBFixYcOHBA/F0ppPv37zNixAi++OILNmzYwO+//06TJk0Kdc5KFQqwHUWSkDLTUCY8z3Ye0dJKG0Tw6YmGDRty6NAhfvjhB+bPn4+dnR13797V9bCEPDh9+jStWrWiTp06ALRt25ZNmzYRHh6Ok5MTnp6emJubM3XqVP76669CB1W9evXYs2cPu3fv5uuvv6Zv374EBQUVxUcxKMnJySxbtoyOHTvSqVMngoKCGDp0aJGcu7lZJcqXffX1KqmUSJnpoFKCpELKTEdSKUm5H0B6ZBiSSokqLZm40z9hVOFdjGtYAK/u8TWvU7FIxiNoEotb9FB6ejru7u6sWbOGadOmsXjxYtHPTYfeVrll6tSptG7dGmdn5zceExERwe7du1EoFGRmZmJvb8+kSZMKvVUha6n9ihUrmDBhAsuXL6dKFbH3KzeSJPHrr7/i4uJC586dWb9+PRYWFkX6HjGJaXT/5gxpmSpeXNjDy4t7NZ6v3H08xjUb8MJnN8qEGGRly1GuThOq2tpTrtarLiLlyxpxaX4fUcNTC0Tw6bGIiAjmz5/PmTNnWLt2LePHjxfFr3Ugt+DLzMzEzMwMPz8/GjZs+NZzSZLElStXUCgUHDhwAGtra+RyOR988AEVKlQo8Bijo6NZtGgRx44dY/Xq1UyePFkUv85BcHAwTk5ORERE4O7urt6uog1Z+/gK8g0r9vFpl/iXocfq1KnDzp072b9/P+vWrcPW1pYbN27oelhCNj4+PjRs2DBPoQevQrRz5854eHgQHh7OpEmT+OmnnzA3N+eLL77Az8+vQFOhNWvW5D//+Q/Hjh3jhx9+oFu3bly9ejXf5ymt4uPjmTNnDjY2NgwdOpSAgACthh7AF7aNqVC2YGUKK5Qtwwxb0aldW0TwlQDdu3fHz8+P8ePH079/fxwdHYmLi8vz62MS0/A4H8as/QFM2XGVWfsD8DgfJjbHFoFDhw4xcuTIAr3W1NSUCRMmcPLkSa5du4aZmRljxoyhTZs2bNy4kaioqHyfs2PHjly6dInp06czfPhwPvnkE6Kjows0vtJApVKxc+dOmjdvTmxsLEFBQcycORNjY+0vGmlrUYVFds0xMc7f1+yrWp3NRbkyLRJTnSXM8+fPWbx4Mb/++iurVq1iypQpbyx+LVqhFI03TXWqVCrMzc05d+4cTZs2LZL3UqlU+Pj4oFAoOHLkCLa2tsjlcuzs7PL9Zf3y5UuWL1/O7t27WbZsGdOnTzeo4tf+/v44OjqSnp7O1q1b6dy5s07GIboz6B8RfCVUQEAADg4Ob/xHLf6xFZ03Bd/FixeZPn06N2/e1Mr7JiQkcODAARQKBaGhoXz00UfI5XJat26dr/PcunULR0dHYmJi2Lp1KzY2NloZr754/vw5ixYtwsvLi6+++oopU6bo/H7njfAXfHculLN3opHxanN6lqwfQns3q8kM28biSq8YiOArwSRJYvfu3SxYsIABAwbg6upK7dq1RSuUIvam4HNxcaFSpUosX75c62O4e/euukxa3bp1kcvljBs3Tl0Q+W0kScLT05PZs2fTo0cP1q1bR7169bQ86uKlVCr5z3/+w7Jlyxg3bhwrVqzI8+9PcXmemIanfzghEQnEp2ZQqYIxzetUZNT7ogN7cRLBVwrEx8ezatUqtm/fztR5K/FKaEjU30dybIUCkPIgkNg/PVDGR1OublNqDHGmbOVaohXKG+QUfJIk0ahRI44dO4aVlVWxjUWpVHLy5EkUCgUnTpxg8ODByOVy+vbtm6d+j0lJSaxZswYPDw/mzJmDs7OzRtPdkurixYs4ODhQqVIl3N3dadOmja6HJOgxEXylSHBwMKM2/0lSZUuS7/2dYysUZfJLnvzwCdUHO2Ha2JoXPrtJDb9FnUkbxBLqN8gp+Pz8/JgwYQJ37tzR2RaT2NhY9u7di0Kh4NmzZ0yePBl7e3saN377asCwsDCcnZ0JCQlh8+bNDB48uBhGXPQiIiKYN28eZ8+eZd26dYwbN05s+RHeSqzqLEVqWliSWbMpGBm9sRVK8t3LlKtRn3ea90BWthyVe0wgI+o+Gc8fi1Yo+XDo0CE+/PBDnX7JVqtWTb0Fwtvbm+TkZLp3746NjQ0KhYLExMQ3vva9997j6NGjbNq0CScnJ4YPH16ktUW1LT09nfXr12NlZYW5uTkhISFin6uQZyL4ShHPa+FvPSYj+iHG/60MAa+K45atYkZ69CMAZICn/9vPY8gkSSrUNgZtsLKyYuPGjTx+/BgXFxe8vLzULZN8fHzeuDfQzs6OoKAgunXrRufOnVmyZAnJycnFPPr8+fPPP2nTpg1nzpzh0qVLrFmzRlQ2EvJFBF8pEhIZr7FlISeqjFSMyr+j8ZhR+Xde9QNDtELJi1u3bpGWlkbHjvo3JVyuXDlGjBjBkSNHCA4OpnXr1syYMYMmTZrw1Vdf8fjx49deU758eRYsWEBgYCChoaG0aNECT09PvSt+/eDBAz788EM+//xz1q1bx++//15k20gEwyKCrxTJSysUI+MKqNI0f6JXpScjK2eS7TyiFUpu9GGaMy/MzMyYPXs2N2/eZO/evTx58oR27doxYMAA9u7dS0pKisbx5ubm7N27lx07drBixQr69ev3Wpd5XUhJSWHFihV06NCB999/n1u3bjFs2DC9//0X9JcIvlIkL61QjGs2ICPqvvr/VempZMZFUq5m/WznEa1QcqNv05xvI5PJ6NSpE99//z3h4eHI5XIUCgXm5uZ8/vnnXLlyRePqztbWloCAAEaMGEGvXr1wcXHh5cuXxT7urGLSLVu2JCgoiICAABYvXlyomqaCACL4SpW8tEIxbdqV9JiHJIVcRMpM5+XFvRjXaohxddEKJS/u3btHdHQ03bp10/VQCsTExITx48fz559/EhAQQL169ZgwYQJWVlZs2LCBZ8+eAa+a7Do6OnLr1i3i4+Np0aIFO3bsyHN3+cKWyQsJCWHQoEEsXryYn376iYMHD1K/fv23v1AQ8kBsZyhF8tIKpUrPj7Lt44uiXJ3/7uOrUhsQrVBykn07g6urK48ePeK7777T8aiKjiRJXLhwAYVCgZeXFzY2NsjlcoYMGaIuk3blyhUcHBwoU6YMW7dupUOHDjmeq7Bl8hISEli5ciXbt29n4cKFODg4FEtdTcGwiOArZUQrlKKXPfg6deqEq6srffv21fGotCMxMZGDBw+iUCi4c+eOukyalZUVKpWK7du3s2jRIoYPH87XX39NjRo11K8tTJk8SZLYs2cP8+fPZ8CAAaxZswYzMzMtf1rBUImpzlJGtELRnocPH3L//v1SXevy3XffVW+BuHjxIqamptjZ2dGxY0e+//57RowYQXBwMBUqVKBly5Z8++23ZGZmZiuTl3voAUgSpGQo+do7mN1/PyAwMJCePXuyadMmPD09USgUIvQErRJXfKWQqNVZtLKu+DZt2sSNGzfYtm2brodUrJRKJadPn0ahUPDHH38wcOBA5HI5ZmZmODs7E60yJb3HDGKuHsuxTF7akxBeXNhNemQoyIyoUN+Kqv0/o+y71SgjZZJ0dDUrZ01l6tSpeSq7JgiFJYKvlBLdGYpOVvD17NmTBQsWMGTIEF0PSWfi4uLYt28fCoWCp0+fMnHiRK6Ub0doiikpbyiTlxLmhyojFZNG74OR0av7y4mx1B67EiQVfZrWYNuUrjr+ZIIhEcFXiolWKAUXk5iG57VwQiLj+eXgr/zf0MF4bf+WwMPfU6eaWPUKEBQUxPeK3fxm1BlZ2XLqx+N8dqGMj9EojJ5dWmQoz375kvouBwGxoEoofiL4DIBohZJ3ua1KlKkyKVeunGjem43H+TDcTt3V+H16W/DFXz1CUrAPdSZtAF79EObcvymf2bxXLGMWBMNpx2zAqr9bXnyp5MHbpoclo7KkZar48/YzfO7GiOlh8lYmL7v0qPu8vLiXmiMXqx8TZfKE4iaCTxDI34Kg7KsSgVIdfikpKcTGxhIbG0tcXNxrv76Y9h4Y187TuTLinhJ1YBlV+31KBQvNLvKiTJ5QnETwCQbv+uMXzFmxlrjAk6+tSJSUGcQcXUdaRCjK+Chqj19NhQavmpymZKj42juENuZV9PoeqVKp5OXLl28Mr9x+Da/aH2X9V7VqVY1f16zwDtF5aOaQ+TKKZ3sXU7n7ON5t3ee150WZPKE4ieATDN6350JRmValcrex6hWJ2ZU3b0XFjh8Q4+X62mtTM5V8dy60WDb9v+3qK/uvsz+WkJBAxYoV3xhe9erVw8rK6rXHq1WrhomJSa5j8jgfRth/7/FJKuWrEnnZyuRhVAZlUhzP9i6kYochVGxv99o5RJk8obiJ4BMMWkxiGufvRmPa9FXtzbTIUJQZMernZWWMqdTpg1f/Y/R6vYfszXvzslCoKK6+cgqoatWq0bp16xwfr1y5stb2x43qYI7bqbsAvLy4T6NMXtKts1TuPh5kMjJfRPLyr728/Ot/z9ef7QmABIx631wr4xOEnIjgEwxaXpr3vo1KpWLFzhO0N3n+1vDKuvp6U3jVrVtXHWD/PsbExETvWvHUeLc8vZrW5GTwM6r0/IgqPT/K8bgqPSbk+LhM9mpLjVhdLBQnEXyCQcvvqsScZKjA50YY8anX1SHVqlWrHMOrSpUqpa46yRe2jblwL4aUDGW+XyvK5Am6IIJPMGh5ad6bFx269uDnyTnvWyvt2lpUYZFd8wKWyWuu1wuDhNJJBJ9g0PLSvDdv5zHsVYlZWzpEmTyhJBDBJxi0V817I0lNz8hxRaLMqAxSZgavlmCApMp89VwZY/X9NrEq8ZWPuzSkjXkVUSZP0HuiZJlg0LKa9z47u+uNjXvDv5uCMj5K47l6038WzXtzIcrkCfpMBJ9g8ETzXkEwLKIRrWDwRPNeQTAsIvgEg5e1KtHEOH//HMSqREEomcTiFkFArEoUBEMi7vEJQjaiea8glH4i+AQhB2JVoiCUXiL4BEEQBIMiFrcIgiAIBkUEnyAIgmBQRPAJgiAIBkUEnyAIgmBQRPAJgiAIBkUEnyAIgmBQRPAJgiAIBkUEnyAIgmBQRPAJgiAIBkUEnyAIgmBQRPAJgiAIBkUEnyAIgmBQRPAJgiAIBuX/AbXIwsW86fzpAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# On va déclarer un nouveau Graphe qui partant de la même matrice d'adjacence dispose les familles au sommet d'un\n",
    "# polygone proche d'une ellipse\n",
    "G2 = nx.from_scipy_sparse_matrix(adjacency_matrix)\n",
    "nx.draw_circular(G2,with_labels=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On remarque tout d'abord que la famille qui rayonne le plus est la famille d'index '1', c'est la seule qui puisse mettre en relation '2' et '10'... Elle a donc un rôle privilégié."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Dans ce graphe il y a 15 noeuds et 20 arêtes\n"
     ]
    }
   ],
   "source": [
    "print('Dans ce graphe il y a', len(G.nodes()), 'noeuds et', len(G.edges()), 'arêtes')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Affichage\n",
    "# On choisit de représenter les relations\n",
    "# La famille Medici aparaît bien au centre du graphe\n",
    "\n",
    "pos=nx.fruchterman_reingold_layout(G)\n",
    "nx.draw_networkx(G, pos=pos)\n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# on peut dénombrer les relations qui sont représentées ici\n",
    "# en utilisant l'attribut \"size\" du graphe\n",
    "G.size()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On va maintenant signaler plus clairement les relations de la famille de Medici elle même."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Acciaiuoli', 'Medici', 'Castellani', 'Peruzzi', 'Strozzi', 'Barbadori', 'Ridolfi', 'Tornabuoni', 'Albizzi', 'Salviati', 'Pazzi', 'Bischeri', 'Guadagni', 'Ginori', 'Lamberteschi']\n"
     ]
    }
   ],
   "source": [
    "# Les Noeud correspondent bien à chacune des familles avec l'orthographe italiènne\n",
    "print(G.nodes())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# On va chercher tous les noeux\n",
    "nx.draw_networkx_nodes(G,pos,\n",
    "                       node_color='k',\n",
    "                       node_size=5,\n",
    "                       alpha=0.8)\n",
    "\n",
    "# Puis on s'interesse en particulier à ceux qui sont liés aux Médicis                       \n",
    "nx.draw_networkx_nodes(G,pos,\n",
    "                       nodelist=['Acciaiuoli','Medici', 'Barbadori', 'Ridolfi', 'Tornabuoni', 'Albizzi','Salviati'],\n",
    "                       node_color='r',\n",
    "                       node_size=500,\n",
    "                       alpha=0.8)\n",
    "# On affiche les arêtes\n",
    "nx.draw_networkx_edges(G,pos,width=1.0,alpha=0.5)\n",
    "\n",
    "# On souligne celles qui sont directement en contact avec les  Médicis\n",
    "\n",
    "nx.draw_networkx_edges(G,pos,\n",
    "                       edgelist=[('Medici','Salviati'),('Medici','Barbadori'),('Medici','Ridolfi'),('Medici','Acciaiuoli'),('Medici','Tornabuoni'),('Medici','Albizzi') ],\n",
    "                       width=8,alpha=0.5,edge_color='r')\n",
    "\n",
    "# On va clairement identifier le noeud qui correspond aux Médicis\n",
    "\n",
    "H = G.subgraph('Medici')\n",
    "labels = nx.draw_networkx_labels(H,pos,font_size=10)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les [Médicis](https://fr.wikipedia.org/wiki/Maison_de_M%C3%A9dicis) sont au centre d'un réseau de 15 familles, dont les relations sont modélisées par des arêtes. Par leur position ils contrôlent un grand nombre de relations, on peut ainsi mesurer leur popularité. On comprends le rôle essentiel de cette famille dans la politique économique et culturelle du XIV et du XV sciecle à Florence et partout en Europe ! Imaginons cependant que les Medici aient une famille \"rivale\", on prendra celle qui a le réseau le plus éloigné, pour l'exemple il s'agit des [Strozzi](https://fr.wikipedia.org/wiki/Famille_Strozzi) la deuxième famille plus influente selon le calcul .  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Medici', 6), ('Strozzi', 4), ('Guadagni', 4)]"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "noeuds_et_aretes = sorted(dict(G.degree()).items(), key = lambda x: x[1], reverse = True)\n",
    "## On veut savoir quelles sont les trois familles les plus puissantes\n",
    "noeuds_et_aretes[:3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*On va faire la même étude avec une autre famille influente : les Strozzi, pour visualiser leur influence il faut superposer les deux graphes, en rouge les relations des Médicis et en jaune celle des Strozzi*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0xa21d20b00>"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# On va chercher tous les noeux\n",
    "nx.draw_networkx_nodes(G,pos,\n",
    "                       node_color='k',\n",
    "                       node_size=5,\n",
    "                       alpha=0.8)\n",
    "\n",
    "# Puis on s'interesse en particulier à ceux qui sont liés aux Médicis                       \n",
    "nx.draw_networkx_nodes(G,pos,\n",
    "                       nodelist=['Acciaiuoli','Medici', 'Barbadori', 'Ridolfi', 'Tornabuoni', 'Albizzi','Salviati'],\n",
    "                       node_color='r',\n",
    "                       node_size=500,\n",
    "                       alpha=0.8)\n",
    "\n",
    "# Et enfin on s'interesse à ceux qui sont liés aux Strozzi                       \n",
    "nx.draw_networkx_nodes(G,pos,\n",
    "                       nodelist=['Strozzi','Ridolfi', 'Bischeri', 'Castellani','Peruzzi'],\n",
    "                       node_color='y',\n",
    "                       node_size=500,\n",
    "                       alpha=0.5)\n",
    "\n",
    "H = G.subgraph(['Medici','Strozzi'])\n",
    "labels = nx.draw_networkx_labels(H,pos,font_size=10)\n",
    "\n",
    "nx.draw_networkx_edges(G,pos,width=1.0,alpha=0.5)\n",
    "# L'instruction suivante vous permet de sauver la figure avec les\n",
    "# relations entre Strozzi et Médicis\n",
    "#plt.savefig(\"Medici_et_Strozzi.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercice\n",
    "- Quel est le nombre de de sommets d'un centre du graphe au plus éloigné des autres sommets ?\n",
    "- On veut faire la même étude avec une autre famille influente : les *Guadagni*, pouvez vous superposer les deux graphes comme nous l'avont fait pour les *Strozzi* ?\n",
    " "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Dans cette cellule on cherche à reproduire l'analyse précédente\n",
    "# on s'interesse à ceux qui sont liés aux Guadagni   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Acciaiuoli': 0.07142857142857142,\n",
       " 'Medici': 0.42857142857142855,\n",
       " 'Castellani': 0.21428571428571427,\n",
       " 'Peruzzi': 0.21428571428571427,\n",
       " 'Strozzi': 0.2857142857142857,\n",
       " 'Barbadori': 0.14285714285714285,\n",
       " 'Ridolfi': 0.21428571428571427,\n",
       " 'Tornabuoni': 0.21428571428571427,\n",
       " 'Albizzi': 0.21428571428571427,\n",
       " 'Salviati': 0.14285714285714285,\n",
       " 'Pazzi': 0.07142857142857142,\n",
       " 'Bischeri': 0.21428571428571427,\n",
       " 'Guadagni': 0.2857142857142857,\n",
       " 'Ginori': 0.07142857142857142,\n",
       " 'Lamberteschi': 0.07142857142857142}"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# On peut calculer le degré de centralité \n",
    "# Cette mesure nous permet d'obtenir l'activité du nœud étudié\n",
    "\n",
    "degree_centrality = nx.degree_centrality(G)\n",
    "\n",
    "# Pour afficher le contennu de cette variable on l'appelle tout simplement :\n",
    "degree_centrality"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Les *Strozzi* apparaissent vraiment comme plus \"excentrés\" que les *Médicis*. Ce problème qui les contraindra à l'exil peut être anticipé en utilisant la théorie des graphes. On peut maintenant se posser la question autrement : \" qui peux jouer le rôle d'intermédiaire entre les *Médicis et les *Strozzi* ? \""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[('Medici', 0.56),\n",
       " ('Ridolfi', 0.5),\n",
       " ('Tornabuoni', 0.4827586206896552),\n",
       " ('Albizzi', 0.4827586206896552),\n",
       " ('Guadagni', 0.4666666666666667),\n",
       " ('Strozzi', 0.4375),\n",
       " ('Barbadori', 0.4375),\n",
       " ('Bischeri', 0.4),\n",
       " ('Castellani', 0.3888888888888889),\n",
       " ('Salviati', 0.3888888888888889),\n",
       " ('Acciaiuoli', 0.3684210526315789),\n",
       " ('Peruzzi', 0.3684210526315789),\n",
       " ('Ginori', 0.3333333333333333),\n",
       " ('Lamberteschi', 0.32558139534883723),\n",
       " ('Pazzi', 0.2857142857142857)]"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#La centralité de proximité\n",
    "#Un nœud plus central a une distance plus faible à tous les autres nœuds.\n",
    "import operator  # Cette instruction sert a importer la fonction \"sorted\"\n",
    "\n",
    "closeness_centrality = nx.closeness_centrality(G)\n",
    "sorted_closeness_centrality = sorted(closeness_centrality.items(), key=operator.itemgetter(1), reverse=True)\n",
    "\n",
    "# Pour afficher les differentes familles on fait simplement appel à la variable :\n",
    "sorted_closeness_centrality"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On remarque que la famille *Ridolfi* arrive en deuxième position. Est ce possible d'imaginer qu'elle puisse servir d'intermédiaire entre les deux familles rivales ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-1.0361195445560858,\n",
       " 0.9666984453804162,\n",
       " -1.0824537916926678,\n",
       " 1.1232543082417157)"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# On va montrer que les Ridolfi sont les seuls intermédiaires directs entre les Médicis et les Strozzi.\n",
    "nx.draw_networkx_nodes(G,pos,\n",
    "                       node_color='r',\n",
    "                       node_size=100,\n",
    "                       alpha=0.8)\n",
    "\n",
    "\n",
    "H = G.subgraph(['Medici','Strozzi','Ridolfi'])\n",
    "labels = nx.draw_networkx_labels(H,pos,font_size=12)\n",
    "\n",
    "nx.draw_networkx_edges(G,pos,width=0.5,alpha=0.5)\n",
    "plt.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Nous présentons maintenant les résultats sous forme d'un rapport technique. Il est intéressant de retrouvers des définitions comme :\n",
    " \n",
    "- > **Centre** : Sommet le plus proche de tous les autres dans un graphe\n",
    "- > **Diamètre** : Plus grande distance entre deux sommets quelconques du graphe\n",
    "- > **Distance** (entre deux sommets) : Nombre minimum d'arêtes entre deux sommets\n",
    "- > **Graphe** : Représentation schématique d'un réseau\n",
    "- > **Rayon** : Distance d'un centre du graphe au plus éloigné des autres sommets     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sommet arête {Sommet à atteindre:longueur, }\n",
      "\n",
      "Acciaiuoli {'Acciaiuoli': 0, 'Medici': 1, 'Barbadori': 2, 'Ridolfi': 2, 'Tornabuoni': 2, 'Albizzi': 2, 'Salviati': 2, 'Castellani': 3, 'Strozzi': 3, 'Guadagni': 3, 'Ginori': 3, 'Pazzi': 3, 'Peruzzi': 4, 'Bischeri': 4, 'Lamberteschi': 4} \n",
      "\n",
      "Medici {'Medici': 0, 'Acciaiuoli': 1, 'Barbadori': 1, 'Ridolfi': 1, 'Tornabuoni': 1, 'Albizzi': 1, 'Salviati': 1, 'Castellani': 2, 'Strozzi': 2, 'Guadagni': 2, 'Ginori': 2, 'Pazzi': 2, 'Peruzzi': 3, 'Bischeri': 3, 'Lamberteschi': 3} \n",
      "\n",
      "Castellani {'Castellani': 0, 'Peruzzi': 1, 'Strozzi': 1, 'Barbadori': 1, 'Bischeri': 2, 'Ridolfi': 2, 'Medici': 2, 'Guadagni': 3, 'Tornabuoni': 3, 'Acciaiuoli': 3, 'Albizzi': 3, 'Salviati': 3, 'Lamberteschi': 4, 'Ginori': 4, 'Pazzi': 4} \n",
      "\n",
      "Peruzzi {'Peruzzi': 0, 'Castellani': 1, 'Strozzi': 1, 'Bischeri': 1, 'Barbadori': 2, 'Ridolfi': 2, 'Guadagni': 2, 'Medici': 3, 'Tornabuoni': 3, 'Albizzi': 3, 'Lamberteschi': 3, 'Acciaiuoli': 4, 'Salviati': 4, 'Ginori': 4, 'Pazzi': 5} \n",
      "\n",
      "Strozzi {'Strozzi': 0, 'Castellani': 1, 'Peruzzi': 1, 'Ridolfi': 1, 'Bischeri': 1, 'Barbadori': 2, 'Medici': 2, 'Tornabuoni': 2, 'Guadagni': 2, 'Acciaiuoli': 3, 'Albizzi': 3, 'Salviati': 3, 'Lamberteschi': 3, 'Ginori': 4, 'Pazzi': 4} \n",
      "\n",
      "Barbadori {'Barbadori': 0, 'Castellani': 1, 'Medici': 1, 'Peruzzi': 2, 'Strozzi': 2, 'Acciaiuoli': 2, 'Ridolfi': 2, 'Tornabuoni': 2, 'Albizzi': 2, 'Salviati': 2, 'Bischeri': 3, 'Guadagni': 3, 'Ginori': 3, 'Pazzi': 3, 'Lamberteschi': 4} \n",
      "\n",
      "Ridolfi {'Ridolfi': 0, 'Medici': 1, 'Strozzi': 1, 'Tornabuoni': 1, 'Acciaiuoli': 2, 'Barbadori': 2, 'Albizzi': 2, 'Salviati': 2, 'Castellani': 2, 'Peruzzi': 2, 'Bischeri': 2, 'Guadagni': 2, 'Ginori': 3, 'Pazzi': 3, 'Lamberteschi': 3} \n",
      "\n",
      "Tornabuoni {'Tornabuoni': 0, 'Medici': 1, 'Ridolfi': 1, 'Guadagni': 1, 'Acciaiuoli': 2, 'Barbadori': 2, 'Albizzi': 2, 'Salviati': 2, 'Strozzi': 2, 'Bischeri': 2, 'Lamberteschi': 2, 'Castellani': 3, 'Ginori': 3, 'Pazzi': 3, 'Peruzzi': 3} \n",
      "\n",
      "Albizzi {'Albizzi': 0, 'Medici': 1, 'Ginori': 1, 'Guadagni': 1, 'Acciaiuoli': 2, 'Barbadori': 2, 'Ridolfi': 2, 'Tornabuoni': 2, 'Salviati': 2, 'Bischeri': 2, 'Lamberteschi': 2, 'Castellani': 3, 'Strozzi': 3, 'Pazzi': 3, 'Peruzzi': 3} \n",
      "\n",
      "Salviati {'Salviati': 0, 'Medici': 1, 'Pazzi': 1, 'Acciaiuoli': 2, 'Barbadori': 2, 'Ridolfi': 2, 'Tornabuoni': 2, 'Albizzi': 2, 'Castellani': 3, 'Strozzi': 3, 'Guadagni': 3, 'Ginori': 3, 'Peruzzi': 4, 'Bischeri': 4, 'Lamberteschi': 4} \n",
      "\n",
      "Pazzi {'Pazzi': 0, 'Salviati': 1, 'Medici': 2, 'Acciaiuoli': 3, 'Barbadori': 3, 'Ridolfi': 3, 'Tornabuoni': 3, 'Albizzi': 3, 'Castellani': 4, 'Strozzi': 4, 'Guadagni': 4, 'Ginori': 4, 'Peruzzi': 5, 'Bischeri': 5, 'Lamberteschi': 5} \n",
      "\n",
      "Bischeri {'Bischeri': 0, 'Peruzzi': 1, 'Strozzi': 1, 'Guadagni': 1, 'Castellani': 2, 'Ridolfi': 2, 'Tornabuoni': 2, 'Albizzi': 2, 'Lamberteschi': 2, 'Barbadori': 3, 'Medici': 3, 'Ginori': 3, 'Acciaiuoli': 4, 'Salviati': 4, 'Pazzi': 5} \n",
      "\n",
      "Guadagni {'Guadagni': 0, 'Tornabuoni': 1, 'Albizzi': 1, 'Bischeri': 1, 'Lamberteschi': 1, 'Medici': 2, 'Ridolfi': 2, 'Ginori': 2, 'Peruzzi': 2, 'Strozzi': 2, 'Acciaiuoli': 3, 'Barbadori': 3, 'Salviati': 3, 'Castellani': 3, 'Pazzi': 4} \n",
      "\n",
      "Ginori {'Ginori': 0, 'Albizzi': 1, 'Medici': 2, 'Guadagni': 2, 'Acciaiuoli': 3, 'Barbadori': 3, 'Ridolfi': 3, 'Tornabuoni': 3, 'Salviati': 3, 'Bischeri': 3, 'Lamberteschi': 3, 'Castellani': 4, 'Strozzi': 4, 'Pazzi': 4, 'Peruzzi': 4} \n",
      "\n",
      "Lamberteschi {'Lamberteschi': 0, 'Guadagni': 1, 'Tornabuoni': 2, 'Albizzi': 2, 'Bischeri': 2, 'Medici': 3, 'Ridolfi': 3, 'Ginori': 3, 'Peruzzi': 3, 'Strozzi': 3, 'Acciaiuoli': 4, 'Barbadori': 4, 'Salviati': 4, 'Castellani': 4, 'Pazzi': 5} \n",
      "\n",
      "\n",
      "Nombre de relations en moyenne pour parvennir à toutes les familles 2.32\n",
      "\n",
      "---------------------------------------- \n",
      "\n",
      "RAYON : 3 \n",
      "\n",
      "DIAMETRE : 5 \n",
      "\n",
      "decré d'eccentricité: {'Acciaiuoli': 4, 'Medici': 3, 'Castellani': 4, 'Peruzzi': 5, 'Strozzi': 4, 'Barbadori': 4, 'Ridolfi': 3, 'Tornabuoni': 3, 'Albizzi': 3, 'Salviati': 4, 'Pazzi': 5, 'Bischeri': 5, 'Guadagni': 4, 'Ginori': 4, 'Lamberteschi': 5}  \n",
      "\n",
      "nœuds au centre: ['Medici', 'Ridolfi', 'Tornabuoni', 'Albizzi'] \n",
      "\n",
      "nœuds en peripherie: ['Peruzzi', 'Pazzi', 'Bischeri', 'Lamberteschi'] \n",
      "\n",
      "densité du réseau : 0.19047619047619047\n"
     ]
    }
   ],
   "source": [
    "# Nous souhaitons avoir un rapport concernant le graphe \n",
    "\n",
    "\n",
    "G = nx.florentine_families_graph()\n",
    "\n",
    "pathlengths=[]\n",
    "\n",
    "print(\"Sommet arête {Sommet à atteindre:longueur, }\\n\")\n",
    "for v in G.nodes():\n",
    "    spl=nx.single_source_shortest_path_length(G,v)\n",
    "    print('%s %s \\n'% (v,spl))\n",
    "    for p in spl.values():\n",
    "        pathlengths.append(p)\n",
    "\n",
    "print('')\n",
    "print(\"Nombre de relations en moyenne pour parvennir à toutes les familles %s\" % (sum(pathlengths)/len(pathlengths)))\n",
    "\n",
    "\n",
    "\n",
    "print('')\n",
    "\n",
    "print(\"---------------------------------------- \\n\")\n",
    "print(\"RAYON : %d \\n\" % nx.radius(G))\n",
    "print(\"DIAMETRE : %d \\n\" % nx.diameter(G))\n",
    "print(\"decré d'eccentricité: %s  \\n\" % nx.eccentricity(G))\n",
    "print(\"nœuds au centre: %s \\n\" % nx.center(G))\n",
    "print(\"nœuds en peripherie: %s \\n\" % nx.periphery(G))\n",
    "print(\"densité du réseau : %s\" % nx.density(G))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercice\n",
    "\n",
    "- Quelle est le nombre d'arêtes d'un sommet au centre du graphe au **plus éloigné** des autres sommets ?\n",
    "- Quelle est le **nombre maximal** d'arêtes entre deux sommets quelconques du graphe ?\n",
    "- Quelles sont les trois familles qui sont à **trois** intermédiaires des Médicis ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gQrWc5PB9ziQj4zz22aeAtm1hxAgLJwwfDn362O+ua9fiRSbbctRRqWRmfgPMFpE8rCnoedTyC11ZxDR7IbjFnAmMV9VHgm17YCIjg2jceCR//nkoo0Zl0LAhXBMIPHXoAJMm2VV30CCYORMKCjbTrNlacnMnYRVF/YFDVfXX4LjL8ZnSmCMiHTDN2k3A06r6f1E6zz5Ad3XpxWoTVJa9SFl5uiWjwCRELsT+522Ar4C3NEr5zzWBmHq6qmVWJcGGDVnAVxQW9qKk0Ee3bmZ0Dz5YyckpIDf3blW9P4gfHQ2cIiK7A1uwuJ9X3MWAIOXrBOAIbMb8FlXdHOXTHoL9wJ3q8x5WSNENS/uqKFnA9aq6Hng4cKoOBkaIyBbgJVVdGvHRJjkJVxwhFuyfjcX/SqpGygX+D+vuWqIXG9TD9wZ6YDXky4DJqvpbVAZdSwnieBcAewLvAlNLykCI0rlHA6PVE+4jgkBjrEiiLRWbqMwCTlXLDNn+eCKNsIyJfbCS69dicCFOChLO6AKIxQHvA87AYnWpWAghDVNBGqaWsVCx44m0BY4HdscmWT4FvtAErINPBoI7iwuxWOGzqvpjHMZwc5D25EQIscyQpykSstnW+CpbtuRRp84qUlMHaGguprzjinTGCjMAXlHVRZEZcXKSkEY3RHD1PRarwlkPvB9MplT9mFYTH/KC6wA/YV7wymoOt0YT3Dr2BE4BfgaeUdVq/S+qMZY04AZVvTke56/piAnfDMHE3Jtgob7NwEfMmPE4PXu214KC/1T6uCL1gYFAB+BbLPxQ6ybAE9roxgIR2QvzgnejyAuekYhecKAGtR9WAipYTPwbjXwvsaJzmoLWGUBn4DPgbVWN68y0iHQDWqvqG/EcR21AQhWeYdkIInIT8LCqri39leUc1zQ2TsfuXt9Q1TnVHmySUOuNbjiBF9wHS+Kvg9X9vxdPL1jsFu904O+Yh7AFK68E80DqAd8BDwATItVePMi1vAi723hZVRNGvk9EBmPG32P0cSD4blyiqrdH4Fh1scyjbthd54R43UHFCje6ZSAie2OydS2wpPupmBecH5Pzm4f5GGZcG5Wze2bwdxjwhFo6T+XPafG3szD5zPGq+ntVjhNNROQWVb0p3uOozYjIv4GxkUzJDH5vZ2HKgm9jfetqnIFyo1tBAi+4L6aOlgZ8j3nBEc9DFVNYexH4Cza5URmygFnYzPLGCp1PJBWbPOkDzMdibVsqed6Y4ZNo8ScofhmsqrdG4dhpwEnYb+0XTHWunNK45MGNbhUJkvOPw1LbQl7wzOp6wYHB/QSLoZYlb1kWW7DQSPeyDK+I7IBlIeyBeRbTE92zCFKRrlDVO+M9ltqOiNwIPK6qf0TxHHsA52BhrveBTxP9O1oebnQjQDAr2xe7MtfB+m29p6qrynpdiccyUZdTqbrBDbEFK4k9ZttQQ5BCdwG2/VlV/ama54oZItIHSFPVj+I9ltqOiDTFLoC3xOBcqVgmU29M/OiFRAx9VQQ3uhEmSK0KecHNMS94CvBleV5wUI75MsW7ZVSHLGCIwrPBuHpjt23LsZSvTRE6T8wQkWsw78rF6RMAEbkBeDKWBlBEdsO8312wu8IPk6lIxo1ulAm84COAQ7Eij5AXXOxLKjZZ9hsWrogcqpvYZZd/smZNOywE8m68U76qg0+iJRYi0gRrQjA6DudOwX5bR2F5/M9XJqMlSIc7DOuw0QPLBNoEvAo8pOacRBzXJogyqpoNvAO8E3ib+wJnBm2Lsgm8YFSPofKTZuWzZUtdXnutmfbu/c+IH9up9ajqOhHZLCK7RUvcqIxzF2JlyB+LyM7AOYH2ymeYc1HqnaVY6frbmEhPBkVaL02AvwFXinXBuECrLqBfInHV061tqPFdoCc7HFPxPwHI55VXHgEasXy5qaqBSepddVXJB+vRo2InrVcvnd69+4H1jRORHct7SaISXKiSMo5Xw3kU6+4RN1R1tao+gIlnrQduEZEbRWTPbfcV05eYjXW5aMD2djAd83pPBKZK5USAysWNbhwJSiD3BT7j6693Lm//YnzxRWX27iTWN+6EJI+FHowriyUcwXcqO2jvHhdEpCDQD14IXA3cAjwCHC8i/xWR00UkPQjjfYBlQ6SWfkTAPOCOmHNU3vlbiMirFRmrG904Eqh0Hc4xxwzj9ddLnjz75Rc47jhrWTQ6LGzWMJA+HTECunSxZffd4aKLYOzYom177gl9+qQBe9aAvnFdsDxiJ/GIt7ebo6pdVLUDpkQ4WFXXq+rDWEPOFcAI/va3Jyko2JVwg1tQ5hRHBnBh0Jm6VFR1papu15++JNzoxpd+wHu8//56dtyxkLkltI/76it4/nmYNw9eecVaYIdz88323KefQtOmFo4YPNi2zZoFLVvC3/++GWgaizcUScS6daVL0dxD3UQu2qjNBKW7m0SkZbzHgqVK7g0gIucBX2KVnTtz112tSEmpT8OG5rAceijMmAFt2sCaoLhu9mxrigtwwgnQqVNdmjdfIiIbRORCEXlcROYFy2oRGSnWHLdC6mludOPL2VjlmXLmmXlMmLD9HkcfbcY0IwNOO836xG2LKpx7LgwbBgceWLR96FA48kjo3z+fIr2GhEagi8CDYhqsm7FJjFxR3ciPPw4SGCEm0ekkHo8Bl8VzACJSBxOwWigi+2OavoeraheggBdf7IGIkJVlcydffgk9e5Z+wHffhQULUnjhhWWYtzxRVS8Jjncq1ndufGXG6NkLcSJILD8S6EBKCuy+e11E4Iortt2x7McAo0aZR3vRRUXbxo+HFSvgoYfAJgIqXagRS8RS6h7DPJS6bBtvE2lE27aNgBuAG8TickMUXJIzQVDVjYE3uIeq/hykZO1GkTzkOuD/otQoNLwn3HTgCewCcCAwK+gNl8GyZWmA9X8bMKCk42zPmjVw6aXdsHZgG2Bro4RXgKtUdUWgMV0h3OjGj4FYgcLlAAK/0KdPS379tfheH35oveEyMmDiRHjyyeLPT5pk+0ydWrRtzhy4+26YPh1SUsCkHxNSkSsIHdwFDKZiVXghYe3jge8ELld4IVrjcyrNY7RqdZPYxfAaLKyVh1U/1gE2C4wBHtXIOgI5gfe5lSBF82lVvWHrtsLCDcAO1KtnhjdEnTpQGNwMbg5rcFFQAGedBUOHLtGhQ8PDB2OB16tSGelGN36cDdwR9ngqp512LrffXtyV7dkTzj8ffvgBzjkHDjqo+FHuuQdWroRDDrHHp5xik2/r1sERR9i2tm036uuvawk+clwREw56ExPaqWzZc1qwjBPYXa3FuxNHBNJRvYu8vL9SWJhHSkpocji8A0V9LK3rerH89YsrKsxUBT4G3haR77A0sfq8/favnHhiO7YNrbZpY87K8cfDa68Vbb/+emjfPo+hQx8KbRKRK4FGqnoHVcAr0hIEsUaLnxD5AolNwJkKkyN83Goj8AwwgOqXPWdjHu9z1R+VUxXEpEc/BDpR8QvoZuBXoLda38Oqn18kU1UbBnnovbGwQh2gFRa62gLkMXTow9x//wM0bNiAzMyiA0yfDn/9KzRvbpNrs2fb3aMI7L9/Id99t4jCQgVGYNrVedj3DszrfQ+YFGRPlD1WN7qJQRD/WggcYA8jxm/AHppgE2lR0JnIBNppgoZRajLBHcsnWB51ZQsJ8rHGsQeqOQiVO7cp5fUKzl0Ha+c1DZhTUkVa8DubhV0c0ipwiizgPoWIlZ670U0gBLoCn1N9hbEQ2cCJapoLCUNQ4fMbkU1jywM+1KKmik6MELgZ+CdVv4BuAV5XE7Ep+1yh3HbzXtMxQz0dmK2quRUc7y5YRVpzSu44HiIbC1H0j+TknxvdBCP4Av+D6ocZsoFn1BoMJhRi8exHKb8bRmXZDOyrJnztxAAxo/UHVuFVHTYDrRSKdaIIBKN6YC206mGe52eYal+Vc7bFLvjPU1BwJCKQkhLu9WZhMd+HgesinW3hRjfBCG5/nsBa9VTN8BYUbCY19QPgtGik5wTpbh8HD3fFzrE6eHxIeR6HmJdxYFn7bMe//w3NmsHf/17WXluA/1b1VlBE+gN7q6pPypWAiAzHvNECLFx1OSefPIQJE06jQYPqXkBzgJsRuR9T/jqcojLcJcDNqhpR4RkAOeigscyevQFTK6uP6Ta8ADxXlXBHRfDshQRDQQX+isW5bsCu7hWP8arm8M47S7jqqsH6889RkXAMusB2ARCRUUCmqt5dkdfK4sVptGvXqVi6TuSoi+kYV8noenfh0hGR7pgWczdV3RKUk6czZ87Z5OSk06AE/6CggEr8nzPIzLyJOnXSyM+fAdwXKPRFDRFpB3yl8GS5O0cQr0hLQNRqzG7BrvjzsFBBWQLohdgt0beIHMmpp/bll1+GB72mYoqIXCsii4Llb8G2vYPHYznkkIX8/PMWdtzR0nE6d4bu3eGPoOPLm2/a7HHXrnDMMUXbAb7+2tLg9tmnKF/5o4+gX7+ifS69tIukpJwXnPfooFRzoYiME5H0YPuvIjJKRL4WkQUism+w/RIxT8vZnt2ANaFb+qAh5UBWr07niCOK0hO3La/9+GP7X3bsCBdfDFu2WGZASBukY0fLEFi5Eg4/PAO7w7sbKyluHfyfronSezoTeClKxy4VN7oJjMICtdbUPbCQw1JswmhzsORhvdCewarbDlDr05aJKSMNj+V4ReQQ4Fws/a07cIWIdAqePgB4gqysf9CyZQEbNkCfPjB/vhndkBHt3RtmzjQDe9pploccYuFCmDwZPv/cfti/l6DymJKSQuPG6UEs8ElggKp2xG4dw0tUf1fVrsDjWAzdKZsPgFYislREHhaRPqg+SosWMGWKLUCx8tqDDoJBg+Cll+x/l58Pjzxi2+fNs+W44+Caa6BFC5g/P4u8vNOAccBrqroiWm8maDSbGij9xRQ3ukmAwnyFwQr7YXHeVlgzyYYKeytcpHabtDVAr6o/AF+JSLkzwhGkF/ZjyQ5aAU0EQoXtP6rqLELfuYwMS0QH04tYvtzWf/7ZPNyOHeHee2Hx4qKj9+sH9erBLruYcZ41q+RRpKWlAPsD36vqj8HWZ7D8zRCvB3/nYELWThkEF/IDsQvXauAl6tY9d7sdw8trv/vOVO723dceX3ghTJtWtO/LL8PcuXDH1hoD4eSTOwOXABdH6a2EGIiV8cYcN7pJhkKewhqF1WoSdqXvq/ousJuIdI3R8MqKPYc8CtPzTQ/L1ElNNS8I4MorTbhn4UJ4+OHiJZkl6VCEl28CbN4s/PnnlnLGAjbpBjYp5HMbFUBVC1R1qqqOBK4iN7c/207Eh5fXljVJv3gxjBwJL75YtP/KlelMnnw7cGZg5KNJR1VdGOVzlIgb3ZrPfcCFMdLRnQb0F5GMIJ/yVCyHMpwFlJXPuWGD6QKrwtNPF39u4kSLCa5ZYxVEBx0ErVvbDzg3F9avhw8/LCAvT7EZ732CzscA5wGfRuZt1j5EZD8R2UdEGorI0cBVwK6kpuaycWPJ1rVdO7uD+eEHe/zssxZS2rDB9AyeeQZ2DrT78/KgX798VP+lqkuj/F46ABWSYYwGbnRrOEEfqZHAyED2Lprn+gprIT8LmAk8sq03EdTZly50MmoU9O9vP87mzYs/d/DBFpLo3t0E3Zs3t9vXfv0sHHH++bDHHiuDsWRjWSCvi8hCzLMdF7E3W0sQkR1E5ARgGFZ19iNW9voncDx77vkYxx+vWyfSwqlXD556Ck4/3f4/KSmm9TxxoingXXpp0YTa9Ok5zJ2bRmHh6DCt2mh1ojidOIUWwPN0aw2BtugAVb017mOxCb7hRK7yztiyJY8hQ8bx1FP/UdVfy39B9RBrtXQsFsvugr2ffEx39VPMy58SJSnDqBB09+2JTeDWwS6SnwOzSsq/DvLKf6H6GsdZwC5apGcQFUSkAfAvVR0VzfOUOQY3urUHEekHpKlq3K7ysLUMcwXF1aciwQ80atSdzMxzMSMwHZhcVlfYqiCWCzwS6BxsKunikY8l/OcA9wJjIt1VNhIEXXR7Y+8lBSsOmA7MrejnFuSVP0DVqyizsc/nhnL3rCYichGW4fNNtM9V6hjc6NYuROR6TA0pbjEtiGi5c4hiOhOBlmqCO3UoAAAf0UlEQVQvTHd3I/C8qv5cnRMEpaPjMO+2MjoD2ViHgTPUwi5xQ0R2w6Q022Ne6hosFj9fVavkkQfe7qNYtVrl/p+5ufnUqTOFlJTjY3FHICJ3qup10T5PmWNwo1u7EJFUbHJtpKquj9s4TOFpEaZzWt1Ycw5Wtlliq5jglvlcLM3uM+Cdynq/Yul607EGhVVtyZ0DDFMzUDFBRFphRrZdsGkVFvpYHMT7I3Me6/TxP2zCsqKGN5uNG79ijz0WsGHDP6pq9CtKkMWzv6rGVfTejW4tRER2AkYDf4/kD6/S47B849mYB1nVuuAcbOLuGC1KAyv5fOb99sCUyDKBF1R1eQXG2TY4x45Uf/I5GxiqVpQRUYL3tydmZPfG8rZ/wTzZbzXKP/bA4z0fu4tpihnfklL3NmHFPXcC92EVgYOAG6P5fRSRW4Bb493c1I1uLSWoFDteVe+M6zjM8H4CtKDy0oBZmHD22Wo/4oqf1y485wCtgRlYyCWvhPGlYWlu+xK5bJ8coLtWs518YGT3wYxsG8zILsM82R+jbWRLHZcZ2p5Y6/M+FHm+OVgxyp3A++HhBBHpjBUsjIjGuEWkEeZk3BLpY1d6LG50ay8icgawRVXfjOs4TB5wBAUF/0IV6tQpS+MUzEstBC7Raqb+BIbrMOBkzAt9QVV/ChvbSOBfRLajhwI/AO3VSrkrM9YDMEMWSqdaCkyriMceLwIjTHjFZIn7WRn5McBtkTa8InIpMFVVv4/kcas0Fje6tRsRuQl4RVW/jftYDjjgfyxcuJrU1MuxDrI5FL89rY8ZmXuAFyOdXhS0ejkHu0X/kmnTptOr13Iin2UB5qVfXZbClYikYB0OemOC24XAN8CnqlojO2SISC+s626FVOsqeEwB7lTVayN1zOrgRreWExRM3AcMV9VoNQisyDjaAb1V9TEAMaPbBdgJuw39P0wAKOppV8GP9GAef/x2zj+/N+np0VJr+06LJrhC/4suWNZFU8zILsQ82RLUfWomQcVbO1V9MELHOxhoE+9Uya2oqi+1fAGaYYY3JY5juA3IiPdnEYylAJjHfvvlctJJyvr19sRvvykDBpT8oj59lFmzyj5w69bK6tW2/sADyn77FdK06WfAU1hc+2agP9As3p9BvBcs3HNJBL9b6fF+T6HFy4Ad1LRRnwXKbMsQLURkd2CdRqEzQBXJQbUn334LTZrA//5nW1u0gFdfjcwZHn4YJk7M49FHZwPDVPVIVR2hqm8E/49ajaq+DWwQkfOqcxwRaQxkawX7p8UCN7oOAKo6F/hdRI6Lw+n/iukFJxJdgRy6d4ffgvDp8uWmFQuQk2OiLZ06wZln2uMQEyaY1kCHDnBdCXn4gwfDTz/B6aenM336YUA/EXkoyu8n6VALB4iIDKzGYc7B2u8kDG50na2o6vNAdxHZK1bnDFK3VFX/jNU5K8hu5Odb54NTTtn+2Ucegfr1YcECGD4c5syx7StXmqH95BMT6Z41ywRewhk7lq3i3/ffH3MR7WRCVZ8FdhKRkyr72lDesqoui/zIqo4bXWdbbgWGBcIgseBiYtyjqgJk0LTpXTRrtgPr1sHRR2+/x7RpcF5w59upky1gRrZvX5MsrFMHzj23uHD39kSlWVxNQlXHAW1F5KhKvrQ78EUUhlQt3Og6xVArELgVGB14ClEjaJnSRBMv/SmHtWuvZPnyDeTmFsV0t6Wkj0crnQ2UaB5+QqKqY4BuItKz3J2LOAmYFKUhVRk3us52qOoq4FVMqDqanI9N4CUiC9hxx3TGjIG77zaR7XB694bnn7f1RYsszADWkPHTT01ovaDA4rt9+pR8BpvcSThPLIH5L3BEkAIGgEAjgSEC3wj8KbBJ4DfZuPEhDj88VSOsMBcJ3Og6JaKqM4FMEflLNI4fCO/sowlQlFEKvwL5dO1qHYtffLH4s0OGQGamhRXuugsOOcS277Yb/Oc/1h23c2fo1g1OPbXkM5gGwJxovomahFr+163AKdKgQWex9d8xY9wOaAw0BFpQv/7lTJs2VGCymGZGwuDFEU6ZiMhtwGMa4c6sQQnyz4FxTyiCsMfJTJs2gh499ic1NVrOySZMuLtSuhG1HRk9OpVjj13EIYe0JiWlPCH8XGAlcIhaQ82440bXKRMRqYuJcF9T0TxaMenDegRC3mqVVeHHFOAeVU2Y1udByW0f4ChMD+FtcnMLSEv7nMoL8VSEXOB/6u3fK43A7aheTcUne3OBb4FuidDFw8MLTpmo3QLfDowqbWJNoJPACIFPBNZhmgirsUmizUG87XGBc8S6LBwFfBSr91AWItJBREZgVUt1MZ3hUao6R9PS5gFzsYtHpMkH7o/CcRMeEdlVRF4UkR9FZImIvCsm71j+ay1UMIwHHmhAdgWkN/r2hdmz04E9adBgZVUbtIrIYBG5oCqv3Y54l8T5khwLpgdw+dbHqqmonoPqfFSzUM2twIE2orqJSZPmsnlzmzi+l92xRot3YqLbDUvdV7U1qpkRHkQmqlfG+38ap89eMCnNwWHbugC9KvR61aGoZhUrqS5rCS/P3nXXzSRAiXVUu8M6NQdVnS4iB4hIL1RXAy9jalwNK3GYRgAcd1xHUlMXC/wbeGDb8EM0CPRUTwP2x8RzXlTV/yvvdQorBK4AHiEyYYYc4KvgeLWRI4A8VR0b2qCq84LW7h9jAkdpwL9V9c0gX/xloCWQylNPNWPjxvqsXGmTlc2aWZHJBx/AyJGwZQvstZd1IW64zVczPT2dO+5oDqwRkYmYlnM94AENCS2JZGL93k7C/lenqurvIjIKyNRIqJ/F2+r7kjwLIDzyyEcUFOSgWhCBg2aiOgfVFlEabxrWJeIOzMAfUOVjqQ7DPPrqDCob1Rmo1o/3/zKO36GrgftK2F4H2CFYb4bpDQswABi3db/16+1/EO7prl6t9OqlZGba4zvuUEaPtvVwT3ePPQqZNOmo4BxNgr8ZWNuopsFjBU4O1u8KjD/AKGxeo9qfgXu6ToUQEFTvRrU7IpHSl22A6cXOEeih1vWgWmyVZTRPJQX4gAi0gVG4TyyN7AnMO6qs3GM2MAG4yrMVSkSA20WkN3bnszumIbwQuFtE7gQmobp9Bd/MmbBkCRx+uD3OzYXu3Us+S3p6SCD/ahHpH6y3wjpwrMUm3UIFFXOAEsoRq4cbXaeijAYGIxLpmfw6wM7AF2Kzy+Xe8peEiLQFTsd0eL8CblfViBo3hVfEmlM+hv0YhbKbVComVr4WuFhNvrG2sxhry7Mt52LfgwNVNU9ElgP1VHWpiBwInAD8h5tuKuCWbTruqFqp9oQJ5Z999ep1ItIXm8ztrqrZIjKVIqH6PA1cWyzTIeI20rMXnHIR+AvwT6KTOgWmP9AMeCnU2qVC4xJpGswq34EZwXGqep2qvhZpgxtCYZXCKVgy/gPYbXAelnO7AWv3notlb7yJ6cLu6QZ3K58AdYP2OcBWkfHWwB+BwT0ieIyItMCkGZ8DHmfy5M0UFBTSqBFs2mQHOOww+Pxz+OEHe5ydDUuXbn/mwsJCLrvsB6yIYn1gcNth7Zpihnu6TpmITX69QPQMbog6QDfgEmBcqeOx0MZJWAhhLfCqhvU0ixUKK4DrgOuCvOS9sXBJHvCz2ticbVBVDW7r7xeR67FQy3IsZjpGRGYD87C8WjCD+ICIpANbaNnyRlJT7+OyyzI4/nirAJwyBcaPh7PPtok0gFtvhX2LZaFlsWlTLllZAO8Bg0VkAfAdENMCHS+OcMpE4H/ARdiEQyzIwjzDrdVDQeFCb8ybzcNibnPUv7w1kqAi8CTgICzX+3VV/W7r8xbiOZTKxdU3AXtoAggMudF1SkVgB2AVsTO4YGk6t6pNqrTH0rzqA9OADzUBBUyc6iMiaVictRewBbuwzi3pwio2wTYPC0lV5G49Gzg5UUI8bnSdUhG4EisgiJW2rpGdncWOOz5MXt4i4A1V3RTT8zsxIbiDORxruw5WpTi9IpkmYnm7U4BdKT1XPAebDOun8HH1RxwZ3Og6pSIW76pQeWZEKSzMJCUloX4oTmQIUvo6Y5ORGcDnwAdahR5mAulAP+B6bGIzdIxULEx1L/BEosXXPXvBKZFAI6EtInD++UVP5OdbV4STKtk9xWrgbf2EE+DPMkJrY8dm8K9/DansmJ3ERUT2FpHrgP9gBvIeVb1BVSdVxeACKOQqvKw2AdseyxQ5DegJtFC4K9EMLnj2glM6nYBsGjTYgUWLrPFiRgZ8+CHsvnv1jvzuu2U/f8UVqVhaj5PEBOlepwO7Yal141R1XTTOFRTWJFQvtNJwT9cpjU6ELsrHHw/vvGNbJ0yw1JwQWVlw8cVw8MHQtSu8+aZtL6tbbps21lkB4JlnbJ/OnYs86lGj4PbbY5o76UQGEdlJRC4JcqcHYil916vq49EyuMmGe7pOaexAKCXnrLPg5pstpLBggRnZ6dNtr9tugyOPhCeftJDBIYfAUUfBo48WdctdsMA6KGzL4sX2+s8/N+GSdWG/ydTUypbZOnEiEKU5GWtbvw5L8Xo8vqNKXNzoOqVRdBfUqRMsX25e7gknFN/rgw/grbesjxjA5s3w88/WAffqq4teH+qWG84nn8DAgWZwAZo0CX82qk0xneoRFCscg2Uf5ABvAS957nT5uNF1SiMHE9o2j/OUU+Caa2DqVFgbNjehCq+9Bvvtt/0RymsmrFr6PoWFcVf4d4oTpHj1wopUFBMTGl5dMaHahsd0ndL4jqIUHAspjBgBHTsW3+vYY+HBB4taj3/9tf0trVtuOH/5C7z8cpERDw8vrF+fJyI3hy1Xi8iJItJOIqdyllQINBa4WmChwO9B99uVAp8LnC6VVz4r/5zGgSIyEmsEWR8Yrao3qWqFcmqd4rin65TGXMIr0Vq2hKFDt9/rppvg73+38IGqTZJNmmTdci+6yLZ36VLULTec9u1h+HBrUZ6aahNx48ebyPOff85T1RGwNbezKbAXlh40IOjdFrqV3YzNXP8I/FjTJmzExOJHYZkAhRQvVmmMZQd0BB4LyrbvVCt7rfo5RfbD0q8aYxKH/1XVCvTHccrDiyOcUhFrb71LHE69CbhErWNAuYjJTe4JtMUM806hpzAj9SuBQQZ+U9WkCV0I9AAmY4Z2ey3Z7dmMvd++Cr9V6lwiLTHD3hxYik2IxV2roKbhRtcpFbGKniuxyp9YkgPsqiaTWC1EJBUTxN4rWFpSPKy2DjPGPwE/aQU7HscCMSW1qVRe4S0f+APoUl7bcRFpiqV27YkZ61dVdVXlR+tUFDe6TqkI7Inqkgh2iqgI+cAzCn+NxclEpAlFBnlPisSswYRXllPkJa+N1ey82B3Gd1j326qQCyzBhOGLjVlEGgKnYrnYa4DX4iGPWVvxmK5TOiJtWbx4De3atSAlJVaTrnnEsDV5EP9dB8za9rlgwq4NZpAPBZqGtaEvBFZSZJB/jbAC2mCKXwAqSzqm8dsXmBLEwI8DumO6BBNV9fnqDtKpPO7pOtshIj2w2N4Utmz5lvT0ecRG3jEHeE7hshicq1oE6VMtKPKSW2Ex19APagMWsngNa1GjmOLVVar6RZnHNmfod6z1kHW1zcys/CBVlVWrZtGiRVdM8+A9YGZFvHUR+UJVe1T+pE55uNF1tiIi3YDzgC+BV0LpQGKtekYTfYnHVcA+ClWwMImFiOyIGePPsMyD+sHjnsDjFA9brA43hGLKWc+g2ghV2GGHqhldgIKCPNLS8rSwsEL/OxFJTaaJxmTEwwsOgVj4RcAC4NoSbpPvx2KAB1O9W96yyAYG1gSDCxDM+s8RkQJVvRNARE7HtF//C+wPjMdS4dJFZAoWw21MixaXc+qp9ZgxAyZOtAP+85/WlmanneDFF03pbdw4eOwx6367997w7LNWer1sGZxzjinCHX00pKamBucXrK348ZjnfauqvhQ0ahyJNQXtAhwgIpmqWppOrVMdItXP3pfkW7CY353Y7Xx6mfuqNkB1Dqo5URhMNqonx/vziNJnXEBRz68NWLdbMIdnh2C9GabCJUAbRJQZM8IPojz3nK2PHq1ceaWtr1lTtM/w4cqYMbZ+8snK00/b+pgxeaSlbQnOMwD4EAuDNAd+xnJ8+xJqk1Q07sx4f3Y1dYn7AHyJwz8d9gBuA/4GZFT4dWZ4P0Y1M0KDyUV1E6rHxPszieJnnRm23h2L7wpWPfYQdncxjyBNDmjDbrttLnaQlBQlL8/Wf/xR6dzZ1qdOVXr2VDp0UNq0US6/3LY3aaLk5tr6n3/mhxnd+4CLw8bzLCYm3heYUtq4fYns4uGFWoSI7AoMwfJf/6OqlbqVV8gS62N1GXAP1gW3qt+hLGA2cG5lk/iTFVWdISLNgJ2BE4K/B6q1HV9OKHSTnp6LfbYlE0qgGDTIwg+dO1sl39Sp2+9jqWOhzJOyxDCyKvVmnCrj2gu1ABFpKiL/xuK296nqPZU1uCHUin0fxZT638AqoCpaHlqIxWyXYSlRR9QWgwsgIu2wW/u1WHntH4HBPQJovXXHnJxszPM1Cgvh1Vdt/YUXoGdPW9+0yVqQ5+UV6VwAHH64xX0Bnn02hYKCkD7CNOBMEUkVkZ2xDstfRf6dOmXhnm4NRkQaY8YtHRirqmVWJ1UGhRXAGWITQZdgWQ/7Arls3pxGvXpbinalPpYLOx14APh824T9GkyGiMwL1gW4UFULROR54G0RmU1RzNdYt2494Z0zGjQw7eEDD4TGjeGll2z7LbfAoYdC69YmRLQpkFt44AGbSHvgATjhhGwKC0MVhW9gIY752Od/raquCi4GTozwlLEaSCAqfTlWzTRWVVfG5Lzmxe3HtdfexF13vYEVOqwH5il4DX8lEHgdyxipzt1oFnCtwsORGZUTCdzo1iCCCqq/Ykn741R1eZzGMVpVR8bj3DUFgcOwbsiV1V0IJwtr0FhtDQsncnh4oQYgImnAhcA+wBOqujTOQ/IreTVRmCmWHz2UqhWl5ABnuMFNPNzoJjGBgtbZWEL705oAfalEpA6Wm+pUn39jMfPzqZzHmwMMViin7bITD9zoJiFB3f9pmNbqBFV9Ls5DCqcJNmnmVBMFFUvxWwrcgmV/lFUltgnLJjlXrQjCSUA8pptEBGWcJ2A9ql5X1WlxHtJ2iMgBQEdVfSneY6lJiIUYzgaux4oowku162IqaXcBk9XvNBIaN7pJgogciVUPvQt8qAn6jxORXlhJ8cfxHktNRCztbF/M8DbASotXqAmQO0mAhxcSHBHpjsksTgWGJaqxDaMZVvzgRIEgv/m7YHGSEDe6CYqIdMUKDr4CrtHk6brajBIEwR3HMdzoJhhBTPQiYBFwnUa2G0EsaIqVuTqOUwJudBMEEdkLuBS7NR+uqrlxHlJVqacJ1NzRcRINN7pxRkRaYSW7fwCj3WA5Ts3GjW6c2EZm8U5V3RTnITmOEwPc6MYYEWmKGdsC4H5VXR/nITmOE0Pc6FYAMZX/U4H+wC6Yfuwi4HGtYHqUiOyAySzWJcIyi47jJA9udMtATId2OHA1JlvYKOzp44B/iHXOvUatC8L2xzCZxUux8thHVbXWiHY7jrM9bnRLISi7/AATkylJbCQkDN0H+FTgLIW3t75epC4ms9gSk1ms8QUDLnbjOOXjRrcEAjHuN4FuVKzleH3gRYFjEPkKuAAr1XxSVWtT5ZCL3ThOOdS6HmkiMlxEFovIAhGZJyKHlrDbScChDBpUb2tvqtI44QT480+A+vz556uI/AeYparXhQyuiNy4zRi+iMibSTyaAmviPQjHSWRqlacb6BicBHRT1S1BZ9b0Ena9lrIl9Ip4N0yytFGjxhQWvqzWVjucG4HbQw9UtUflRp7YiE0O7sMdd/RgxYpcgVRXunKckqltnu5uwBpV3QKgqmtUdaWIjBCRWSKySHbeeQKFhV2LvWryZDjjjKLHU6fCySfbeps2sCZw7gYMyGDvvd8LPOnLAETkDoLmhEEzQkSkSp14Ew2B1gJ3A6uBLxg27D4efPB/wCqBG8VajDuOE0ZtM7ofAK1EZKmIPCwifYLtD6nqwaragSZNduXNN4uLyxx9NMycCVlZ9vill+DMM7c/+pNPwg8/rAUOAq4Wkaaqej2Qo6pdVPXc6L212CImor4E+BuW1dGI9PT6pKbWx0Rv/g18L9Z91nGcgFpldFU1EzgQuAzzzl4SkUHAESLypYgs5NdfO7N4cfGwS506cNxx8PbbkJ8P77wDp566/QnGjIH27VsDM4FWWM+yGoeYkPqz2ARiSeEZgAysjfgHAp1jNTbHSXRqldEFUNUCVZ0adKu9CjgXa1E9UFU70qXLe2zevP0LzzwTXn4ZPvkEDj4YGjUq/vzUqfDRR/Dll8tVtTPwNRXLfIgLItJfRFRE2lXqdZDOr79OYODAsnt2rVwJAweCpd69UIXxLQ9i7jV54tGphdQqoysi+4lIuPfZhSIx6DUi0pCvvupKSkrqdi/u2xfmzoVx40oOLWzYADvuqDRs+GFgyA4LezYv6NibSJwNfAacVcnXnUbLllJuVkeLFgT7CNBG7A6jStS0iUendlOrjC6WkfC0iCwRkQXAAcAoYBywEJhIfv5MVq/+icLC4h0aUlPhpJNsUu2kk7Y/8nHHQV6ekpFxFNZEcGbYs48BC0ITafFGRBoCh2PFG2eFbb9WRBaKyPxgAhAR2VtEPgq2zWXx4htYvrwRHTrYi5Yvh169oFs3W774omh7aJ+nnqpHv37PhZ1nkoj0DdbPDs65SETuLGW8NWLi0XEAUFVfwhbgIM455xXy83Mq+eICVGfEe/wVfI/nAU8E619gRSDHB+v1g+1Ngr9fAv2D9XpkZq5h2TKlfXs7WFaWkpNj60uXKgceaOvh+zz1lHL++b+HnX8S0BdoAfyMZTnUAT4B+gX7LAeaBeuZ8f7MfPElUkutytMtCxFpicV4v+G3384iNfUhrLKs7NiloVj76/OjOMRIcjZwf7D+YvA4BXhKVbMBVHWdiDQCdlfVN4JtmwVSWB2m1ZOXB1ddBfPm2d3A0qUln9E6GW/LwcBUDcR/gjuB3sDE6r9Fx0lMar3RDQRprsSMzq1qGQ6IGeC6wBnYZFBp5AKZwFEKP0R5uNUmkJY8EuggIoqVPCvwWvC32O4lHGI1sNPWR/fdB82bw/z5UFgI9UqYO6xTB7JC+XZA0QRjScd3nBpNbYvpbkVEUkTkfGAE8KKq3hEyuABBRdVfgQuBuUAOsCV4uhDzbDOxzIeOatkKycBA4BlVba2qbVS1FSZPuQ64WETqA4hIE1XdCPwqIv2CbXX5448nKCws6m6xYQPsthukpMCzz0JBCYVorVplM3VqTvCZtwIOCZ75EugjIs1EJBXzuD+N2jt3nASgVhpdEekJ3AcsVdNI+Lmk/RRU4TW1mfeDsXLe2zBDfTmwi8IwhZWxGnsEOBt4Y5ttr2Hx1beA2SIyD7gmeO58rNBjAfAFl1zyASJF35srroCnn4bDDrPQQoMSbgp69cpk3bp52GTl3dhFDFX9P+AGYAowH5irqm9G7J06TgIiqtveUdZcRGRP4ApM+/ZlrU1vPoKIXXxupOywS4gc4Hw1w+44tZ5aYXSDrg1/wwzAI+rNH6uFWCz2HszbL2uiMQf4h8LYmAzMcZKAGm10gzjhIKAt8KCqrorviGoWAv2Am4D9sTh3HSAfm5z7AhilMD1+I3ScxKPGGl0ROQqTcRyvqvPiPZ6ajEB7oAcWbtgIfKywIr6jcpzEpMYZXRHZDxO0mQa85XFbx3ESiRpjdEWkCdZAcg3wmKrmxnlIjuM425H0xRGBkMylQHMsbuvtYhzHSViS1uiKlZWeBByBddv9Js5DchzHKZekDC+ISCfgYmCyqr4f7/E4juNUlKQyuiLSHIvbrsDam+fHeUiO4ziVIimMrojUA4ZgergPquqfcR6S4zhOlUjomG4Qtz0dE0h5RFV/jPOQHMdxqkXCeroicjAmtv26qrrylOM4NYKEM7phYuJLgOdUtbCclziO4yQNCWN0AzHxq4KH/wvXtnUcx6kpxD2mK6bNeh5Wv/+Qqv4S5yE5juNEjah5umLKU5cCewI/AeMUvi22j0gvrJPBC6r6ZVQG4jiOk0BUyeiKSAHWBaAO8A1wYaihYaC1ej9mcOsAaUAeJvn3GDAMExMfAswCXgmJ0ojIzcA0Vf2omu/LcRwnIamq0c1U1YbB+vPAHFW9F7Y2dLyDkroKqGYzbtzHXH75FGCsi4k7jlPbiERMdzrQCUBSUibSqdOJ5OXVYehQuOwyeOstGDHC9szJqU9OzonUrXsLW7bMCLpypwIdVFVEZDwwSVVfjcC4HMdxEo5qNaYUkTrA8VioAZ577hbmzdvC7NkwZgysXQunnALz5tnSuTNcc00+mzevU9UuqtoFeA9rVug4jlPjqarRzQg6xs4GfgaeAGD48Avp1CmDww6DX36B778vesVdd0FGBlx9dR4W90VEzgC6AddX/S04juMkD1UNL+QEXupWRKQv0I3MzHU0aNCMvn1h82Z78uOP4ZVXYNo0sGaFy0SkPTAa6K2qBVUch+M4TlJRrfDCNjQG1tOgwZ0sWZLNzJm2dcUKuOIKePllyMjIAv6DSEPgReACVV0dwTE4juMkNJEsjngPGIzIBRx++B8ccsgeqML48SmsXQv9+hWyYcMWVqw4ClgLtAbGBZNpbOs5O47j1ESiWRxxIDAYa3/+IzBWYW5UTuY4jpMkJIz2guM4Tm0gkjFdx3Ecpxzc6DqO48QQN7qO4zgxxI2u4zhODHGj6ziOE0Pc6DqO48QQN7qO4zgxxI2u4zhODHGj6ziOE0Pc6DqO48QQN7qO4zgxxI2u4zhODHGj6ziOE0P+H1nJkJg+rbP2AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# L'objet de ce code est de détérminer la taille des Nœuds en fonction de leur degré de centralité\n",
    "\n",
    "G = nx.florentine_families_graph()\n",
    "\n",
    "\n",
    "j=0\n",
    "Proximite=[]\n",
    "for i in closeness_centrality:\n",
    "        Close=closeness_centrality[i]\n",
    "        Proximite.append(Close)\n",
    "\n",
    "node_sizes = [3 +  pow(10 *i,4) for i in Proximite]\n",
    "\n",
    "M = G.number_of_edges()\n",
    "edge_colors = range(2, M + 2)\n",
    "edge_alphas = [(5 + i) / (M + 4) for i in range(M)]\n",
    "\n",
    "nodes = nx.draw_networkx_nodes(G, pos, node_size=node_sizes, node_color='cyan')\n",
    "edges = nx.draw_networkx_edges(G, pos, node_size=node_sizes, width=0.5)\n",
    "labels = nx.draw_networkx_labels(G,pos,font_size=10)\n",
    "\n",
    "\n",
    "ax = plt.gca()\n",
    "ax.set_axis_off()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Exercice : \n",
    "- En une phrase décrivez la relation entre la taille du nœud et sa position dans le graphe"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Autres exemples d'application des graphes\n",
    "\n",
    "Les Exemple du parcours :\n",
    "Si l'on prends l'exemple le graphe des distances séparant deux gares connectées directement (et non les autres gares à un horizon plus lointain) sont connues.\n",
    "\n",
    "L'algorithme de recherche du trajet optimal calcule, le minimum de distance entre la gare d'arrivée et chaque gare intermédiaire. La meilleure solution est déterminée au fur et à mesure, ainsi que le chemin associé. C’est bien là tout l’intérêt de l’algorithme : donner la distance minimale et le chemin entre une gare d’arrivée et une autre gare (la gare de départ)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Conclusion\n",
    "\n",
    "On voit comment la famille Médicis a compris le \"résautage\" pour changer le monde. Dans notre étude nous avons prouvé que quelque soit la représentation choisie (il y en à une infinité) un graphe permet de visualiser des relations entre individus. C'est donc un outil de choix pour la gestion des réseaux sociaux."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.1"
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 },
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}