Oraux_CentraleSupelec_PSI__Juin_2019.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "toc": "true"
   },
   "source": [
    "# Table of Contents\n",
    " <p><div class=\"lev1 toc-item\"><a href=\"#Oraux-CentraleSupélec-PSI---Juin-2019\" data-toc-modified-id=\"Oraux-CentraleSupélec-PSI---Juin-2019-1\"><span class=\"toc-item-num\">1&nbsp;&nbsp;</span>Oraux CentraleSupélec PSI - Juin 2019</a></div><div class=\"lev2 toc-item\"><a href=\"#Remarques-préliminaires\" data-toc-modified-id=\"Remarques-préliminaires-11\"><span class=\"toc-item-num\">1.1&nbsp;&nbsp;</span>Remarques préliminaires</a></div><div class=\"lev3 toc-item\"><a href=\"#Importez-les-modules-:\" data-toc-modified-id=\"Importez-les-modules-:-111\"><span class=\"toc-item-num\">1.1.1&nbsp;&nbsp;</span>Importez les modules :</a></div><div class=\"lev2 toc-item\"><a href=\"#Planche-160\" data-toc-modified-id=\"Planche-160-12\"><span class=\"toc-item-num\">1.2&nbsp;&nbsp;</span>Planche 160</a></div><div class=\"lev2 toc-item\"><a href=\"#Planche-162\" data-toc-modified-id=\"Planche-162-13\"><span class=\"toc-item-num\">1.3&nbsp;&nbsp;</span>Planche 162</a></div><div class=\"lev2 toc-item\"><a href=\"#Planche-166\" data-toc-modified-id=\"Planche-166-14\"><span class=\"toc-item-num\">1.4&nbsp;&nbsp;</span>Planche 166</a></div><div class=\"lev2 toc-item\"><a href=\"#Planche-168\" data-toc-modified-id=\"Planche-168-15\"><span class=\"toc-item-num\">1.5&nbsp;&nbsp;</span>Planche 168</a></div><div class=\"lev2 toc-item\"><a href=\"#Planche-170\" data-toc-modified-id=\"Planche-170-16\"><span class=\"toc-item-num\">1.6&nbsp;&nbsp;</span>Planche 170</a></div><div class=\"lev2 toc-item\"><a href=\"#Planche-172\" data-toc-modified-id=\"Planche-172-17\"><span class=\"toc-item-num\">1.7&nbsp;&nbsp;</span>Planche 172</a></div><div class=\"lev2 toc-item\"><a href=\"#Planche-177\" data-toc-modified-id=\"Planche-177-18\"><span class=\"toc-item-num\">1.8&nbsp;&nbsp;</span>Planche 177</a></div><div class=\"lev1 toc-item\"><a href=\"#À-voir-aussi\" data-toc-modified-id=\"À-voir-aussi-2\"><span class=\"toc-item-num\">2&nbsp;&nbsp;</span>À voir aussi</a></div><div class=\"lev2 toc-item\"><a href=\"#Les-oraux---(exercices-de-maths-avec-Python)\" data-toc-modified-id=\"Les-oraux---(exercices-de-maths-avec-Python)-21\"><span class=\"toc-item-num\">2.1&nbsp;&nbsp;</span><a href=\"http://perso.crans.org/besson/infoMP/oraux/solutions/\" target=\"_blank\">Les oraux</a>   <em>(exercices de maths avec Python)</em></a></div><div class=\"lev2 toc-item\"><a href=\"#Fiches-de-révisions-pour-les-oraux\" data-toc-modified-id=\"Fiches-de-révisions-pour-les-oraux-22\"><span class=\"toc-item-num\">2.2&nbsp;&nbsp;</span>Fiches de révisions <em>pour les oraux</em></a></div><div class=\"lev2 toc-item\"><a href=\"#D'autres-notebooks-?\" data-toc-modified-id=\"D'autres-notebooks-?-23\"><span class=\"toc-item-num\">2.3&nbsp;&nbsp;</span>D'autres notebooks ?</a></div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Oraux CentraleSupélec PSI - Juin 2019\n",
    "\n",
    "- Ce [notebook Jupyter](https://www.jupyter.org) est une proposition de correction, en [Python 3](https://www.python.org/), d'exercices d'annales de l'épreuve \"maths-info\" du [concours CentraleSupélec](http://www.concours-centrale-supelec.fr/), filière PSI.\n",
    "- Les exercices viennent de l'[Officiel de la Taupe](http://odlt.fr/), [2017](http://www.odlt.fr/Oraux_2017.pdf) (planches 162 à 177, pages 10 et 11).\n",
    "- Ce document a été écrit par [Lilian Besson](http://perso.crans.org/besson/), et est disponible en ligne [sur mon site](https://perso.crans.org/besson/publis/notebooks/Oraux_CentraleSupelec_PSI__Juin_2019.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Remarques préliminaires\n",
    "- Les exercices sans Python ne sont pas traités.\n",
    "- Les exercices avec Python utilisent Python 3, [numpy](http://numpy.org), [matplotlib](http://matplotlib.org), [scipy](http://scipy.org) et [sympy](http://sympy.org), et essaient d'être résolus le plus simplement et le plus rapidement possible. L'efficacité (algorithmique, en terme de mémoire et de temps de calcul), n'est *pas* une priorité. La concision et simplicité de la solution proposée est prioritaire."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib as mpl\n",
    "mpl.rcParams['figure.figsize'] = (10, 7)\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy import integrate\n",
    "import numpy.random as rd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "import seaborn as sns\n",
    "sns.set(context=\"notebook\", style=\"whitegrid\", palette=\"hls\", font=\"sans-serif\", font_scale=1.1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Importez les modules :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import integrate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy.random as rd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## Planche 160"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- $I_n := \\int_0^1 \\frac{1}{(1+t)^n \\sqrt{1-t}} \\mathrm{d}t$ et $I_n := \\int_0^1 \\frac{1/2}{(1+t)^n \\sqrt{1-t}} \\mathrm{d}t$ sont définies pour tout $n$ car leur intégrande est continue et bien définie sur $]0,1[$ et intégrable en $1$ parce qu'on sait (par intégrale de Riemann) que $\\frac{1}{\\sqrt{u}}$ est intégrable en $0^+$ (et changement de variable $u = 1-t$).\n",
    "- On les calcule très simplement :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def I(n):\n",
    "    def f(t):\n",
    "        return 1 / ((1+t)**n * np.sqrt(1-t))\n",
    "    i, err = integrate.quad(f, 0, 1)\n",
    "    return i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def J(n):\n",
    "    def f(t):\n",
    "        return 1 / ((1+t)**n * np.sqrt(1-t))\n",
    "    i, err = integrate.quad(f, 0, 0.5)\n",
    "    return i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc29ae167f0>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Valeurs de $I_n$')"
      ]
     },
     "execution_count": 4,
     "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": [
    "valeurs_n = np.arange(1, 50)\n",
    "valeurs_In = np.array([I(n) for n in valeurs_n])\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(valeurs_n, valeurs_In, 'ro')\n",
    "plt.title(\"Valeurs de $I_n$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- On conjecture que $I_n$ est décroissante. C'est évident puisque si on note $f_n(t)$ son intégrande, on observe que $f_{n+1}(t) \\leq f_n(t)$ pour tout $t$, et donc par monotonie de l'intégrale, $I_{n+1} \\leq I_n$.\n",
    "- On conjecture que $I_n \\to 0$. Cela se montre très facilement avec le théorème de convergence dominée."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc29adbbd30>]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Valeurs de $\\\\ln(I_n)$ en fonction de $\\\\ln(n)$')"
      ]
     },
     "execution_count": 5,
     "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": [
    "plt.figure()\n",
    "plt.plot(np.log(valeurs_n), np.log(valeurs_In), 'go')\n",
    "plt.title(r\"Valeurs de $\\ln(I_n)$ en fonction de $\\ln(n)$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Ce qu'on observe permet de conjecturer que $\\alpha=1$ est l'unique entier tel que $n^{\\alpha} I_n$ converge vers une limite non nulle."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 432x288 with 0 Axes>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc29a86a358>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fc29a8f7320>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7fc29ac1f400>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Valeurs de $n^{\\\\alpha} I_n$ et $n^{\\\\alpha} J_n$')"
      ]
     },
     "execution_count": 16,
     "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": [
    "valeurs_n = np.arange(1, 500)\n",
    "valeurs_In = np.array([I(n) for n in valeurs_n])\n",
    "valeurs_Jn = np.array([J(n) for n in valeurs_n])\n",
    "alpha = 0.9\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(valeurs_n, valeurs_n**alpha * valeurs_In, 'r+', label=r'$n^{\\alpha} I_n$')\n",
    "plt.plot(valeurs_n, valeurs_n**alpha * valeurs_Jn, 'b+', label=r'$n^{\\alpha} J_n$')\n",
    "plt.legend()\n",
    "plt.title(r\"Valeurs de $n^{\\alpha} I_n$ et $n^{\\alpha} J_n$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- On en déduit qu'il en est de même pour $J_n$, on a $n^{\\alpha} J_n \\to l$ la même limite que $n^{\\alpha} I_n$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Pour finir, on montre mathématiquement que $n^{\\alpha} (I_n - J_n)$ tend vers $0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 720x504 with 0 Axes>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d46487358>]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1d4656df98>"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Valeurs de $n^{\\\\alpha} (I_n - J_n)$')"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(valeurs_n, valeurs_n**alpha * (valeurs_In - valeurs_Jn), 'g+', label=r'$n^{\\alpha} (I_n - J_n)$')\n",
    "plt.legend()\n",
    "plt.title(r\"Valeurs de $n^{\\alpha} (I_n - J_n)$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Puis rapidement, on montre que $\\forall x \\geq 0, \\ln(1 + x) \\geq \\frac{x}{1+x}$. Ca peut se prouver de plein de façons différentes, mais par exemple on écrit $f(x) = (x+1) \\log(x+1) - x$ qui est de classe $\\mathcal{C}^1$, et on la dérive. $f'(x) = \\log(x+1) + 1 - 1 > 0$ donc $f$ est croissante, et $f(0) = 0$ donc $f(x) \\geq f(0) = 0$ pour tout $x \\geq 0$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d462721d0>]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d462fcfd0>]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1d46272710>"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Comparaison entre deux fonctions')"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.linspace(0, 100, 1000)\n",
    "plt.plot(X, np.log(1 + X), 'ro-', label=r'$\\log(1+x)$', markevery=50)\n",
    "plt.plot(X, X / (1 + X), 'b+-', label=r'$\\frac{x}{1+x}$', markevery=50)\n",
    "plt.legend()\n",
    "plt.title(\"Comparaison entre deux fonctions\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Planche 162"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On commence par définir la fonction, en utilisant `numpy.cos` et pas `math.cos` (les fonctions de `numpy` peuvent travailler sur des tableaux, c'est plus pratique)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return x * (1 - x) * (1 + np.cos(5 * np.pi * x))\n",
    "\n",
    "Xs = np.linspace(0, 1, 2000)\n",
    "Ys = f(Xs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pas besoin de lire le maximum sur un graphique :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sur [0, 1], avec 2000 points, le maximum de f(x) est M = 0.4812601808328304\n"
     ]
    }
   ],
   "source": [
    "M = max_de_f = max(Ys)\n",
    "print(\"Sur [0, 1], avec 2000 points, le maximum de f(x) est M =\", M)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Sur ces 2000 points, le maximum est atteint en x = 0.4062031015507754\n"
     ]
    }
   ],
   "source": [
    "i_maximisant_f = np.argmax(Ys)\n",
    "x_maximisant_f = Xs[i_maximisant_f]\n",
    "print(\"Sur ces 2000 points, le maximum est atteint en x =\", x_maximisant_f)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On affiche la fonction, comme demandé, avec un titre :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 720x504 with 0 Axes>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d45b94f60>]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x7f1d46061fd0>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x7f1d45b744e0>"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Fonction $f(x)$ sur $[0,1]$')"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(Xs, Ys)\n",
    "plt.vlines(x_maximisant_f, min(Ys), max(Ys), color=\"b\", linestyles=\"dotted\")\n",
    "plt.hlines(max(Ys), min(Xs), max(Xs), color=\"b\", linestyles=\"dotted\")\n",
    "plt.title(\"Fonction $f(x)$ sur $[0,1]$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour calculer l'intégrale, on utilise `scipy.integrate.quad` :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "def In(x, n):\n",
    "    def fn(x):\n",
    "        return f(x) ** n\n",
    "    return integrate.quad(fn, 0, 1)[0]\n",
    "\n",
    "def Sn(x):\n",
    "    return np.sum([In(Xs, n) * x**n for n in range(0, n+1)], axis=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On vérifie avant de se lancer dans l'affichage :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "In(x, 0 ) = 1.0\n",
      "In(x, 1 ) = 0.16666666666666663\n",
      "In(x, 2 ) = 0.049987680821294386\n",
      "In(x, 3 ) = 0.017874498250810132\n",
      "In(x, 4 ) = 0.0069477925896280456\n",
      "In(x, 5 ) = 0.0028398023087289567\n",
      "In(x, 6 ) = 0.0012011683591199485\n",
      "In(x, 7 ) = 0.00052074827894252\n",
      "In(x, 8 ) = 0.00022991112607879838\n",
      "In(x, 9 ) = 0.00010290185158968158\n"
     ]
    }
   ],
   "source": [
    "for n in range(10):\n",
    "    print(\"In(x,\", n, \") =\", In(Xs, n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 720x504 with 0 Axes>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d458e57b8>]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d458e5b70>]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d458e5eb8>]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d458ee278>]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d458ee5f8>]"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1d45944860>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = 1/M + 0.1\n",
    "X2s = np.linspace(-a, a, 2000)\n",
    "\n",
    "plt.figure()\n",
    "for n in [10, 20, 30, 40, 50]:\n",
    "    plt.plot(X2s, Sn(X2s), \"-+\", label=\"n =\" + str(n), markevery=20)\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$S_n(x)$ semble diverger pour $x\\to2^-$ quand $n\\to\\infty$.\n",
    "Le rayon de convergence de la série $\\sum In x^n$ **semble** être $2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "def un(n):\n",
    "    return In(Xs, n + 1) / In(Xs, n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "un = 0.16666666666666663 pour n = 0\n",
      "un = 0.2999260849277664 pour n = 1\n",
      "un = 0.35757806637822104 pour n = 2\n",
      "un = 0.38869860804697826 pour n = 3\n",
      "un = 0.4087344681198935 pour n = 4\n",
      "un = 0.4229760485185215 pour n = 5\n",
      "un = 0.43353479550864377 pour n = 6\n",
      "un = 0.44150146121592054 pour n = 7\n",
      "un = 0.4475723004132197 pour n = 8\n",
      "un = 0.4522404636909894 pour n = 9\n"
     ]
    }
   ],
   "source": [
    "for n in range(10):\n",
    "    print(\"un =\", un(n), \"pour n =\", n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ici, `un` ne peut pas être utilisé comme une fonction \"numpy\" qui travaille sur un tableau, on stocke donc les valeurs \"plus manuellement\" :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "def affiche_termes_un(N):\n",
    "    valeurs_un = [0] * N\n",
    "    for n in range(N):\n",
    "        valeurs_un[n] = un(n)\n",
    "\n",
    "    plt.figure()\n",
    "    plt.plot(valeurs_un, 'o-')\n",
    "    plt.title(\"Suite $u_n$\")\n",
    "    plt.grid(True)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "affiche_termes_un(30)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La suite $u_n$ semble être croissante (on peut le prouver), toujours plus petite que $1$ (se prouve facilement aussi, $I_{n+1} < I_n$), et semble converger.\n",
    "Peut-être vers $1/2$, il faut aller regarder plus loin ?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "affiche_termes_un(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour conclure, on peut prouver que la suite est monotone et bornée, donc elle converge.\n",
    "Il est plus dur de calculer sa limite, et cela sort de l'exercice."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---\n",
    "## Planche 166"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "case_max = 12\n",
    "univers = list(range(case_max))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [],
   "source": [
    "def prochaine_case(case):\n",
    "    return (case + rd.randint(1, 6+1)) % case_max"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Yn(duree, depart=0):\n",
    "    case = depart\n",
    "    for coup in range(duree):\n",
    "        case = prochaine_case(case)\n",
    "    return case"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Avant de s'en servir pour simuler plein de trajectoirs, on peut vérifier :\n",
    "\n",
    "- en un coup, on avance pas plus de 6 cases :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4, 2, 5, 2, 4, 6, 3, 6, 6, 1]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[Yn(1) for _ in range(10)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- En 100 coups, on commence à ne plus voir de tendance :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9, 7, 9, 2, 4, 5, 3, 2, 5, 5]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[Yn(100) for _ in range(10)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pour l'histogramme, on triche un peu en utilisant `numpy.bincount`. Mais on peut le faire à la main très simplement !"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[4, 9, 3, 10, 0, 7, 1, 0, 8, 10]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([2, 1, 0, 1, 1, 0, 0, 1, 1, 1, 2, 0])"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "observations = [Yn(100) for _ in range(10)]\n",
    "print(observations)\n",
    "np.bincount(observations, minlength=case_max)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [],
   "source": [
    "def histogramme(duree, repetitions=5000):\n",
    "    cases = [Yn(duree) for _ in range(repetitions)]\n",
    "    frequences = np.bincount(cases, minlength=case_max)\n",
    "    # aussi a la main si besoin\n",
    "    frequences = [0] * case_max\n",
    "    for case in cases:\n",
    "        frequences[case] += 1\n",
    "    return frequences / np.sum(frequences)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.0902, 0.085 , 0.0832, 0.0838, 0.083 , 0.0822, 0.082 , 0.0894,\n",
       "       0.0808, 0.0728, 0.0792, 0.0884])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "histogramme(50)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "On va afficher des histogrammes :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "def voir_histogramme(valeurs_n):\n",
    "    for n in valeurs_n:\n",
    "        plt.figure()\n",
    "        plt.bar(np.arange(case_max), histogramme(n))\n",
    "        plt.title(\"Histogramme de cases visitées en \" + str(n) + \" coups\")\n",
    "        plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmgAAAGxCAYAAADWNkozAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzt3XtYVXW+x/EPiCiby1FnHO9po6g4TrnFO6JJGhMpFZjlMaaLlLdUzFIrPThaTlnHicspY8xTo1bWQHYZ0546NjGmmZcpnSQRxUS8jGHBBuX6O3/0tGcIFFSIH/h+Pc88z7D47cV3L5bxdq3txsMYYwQAAABreDb0AAAAAKiMQAMAALAMgQYAAGAZAg0AAMAyBBoAAIBlCDQAAADLEGi4Ytx00016++23G3qMJi0mJkZJSUkNPUaDq+25tnPnTjmdzlrvt7CwUBMmTNAbb7xxOeMBaAQINDR654uCBQsWaMGCBe6P//KXvygyMrLG/X366afq1atXnc6IK0ttz7UBAwZoz5497o+TkpIUExNT7drS0lI9+OCDuvvuu3XbbbfV2aw/hbS0NPXu3VtOp9P9vzvuuKPSmqNHj2ry5MlyOp0aNmyY/vCHP4i36cSVzKuhBwCuVCUlJfL29m7oMdBING/eXC+88EJDj3HJOnbsqP/7v/+r9nPl5eWaOnWq+vfvr8TERJ08eVKxsbEKCAjQ5MmTf+JJATtwBQ1XjLCwMKWlpUmS8vPzNWfOHA0ePFj9+/dXeHi4Nm3apNzcXN13332S5P6b/p/+9CdJUmZmpu69914NHjxYo0aN0lNPPaXi4mL3/r/++mvddddd6t+/v2688Ua98cYb6tWrl3JyciR9fxUhLCxML730kq677jqNGjVKkvTss89qzJgxcjqdGjVqlJ599llVVFS49xsTE6PHH39cM2fOlNPp1PXXX6+tW7dq+/btGjdunPr3769p06bJ5XJVeq7Jycm666671K9fP40dO1ZffvmlNm7cqBtuuEHBwcF65JFHVFpa6n7MyZMnNXfuXIWGhmro0KF68MEHlZeXd97jWVZWpuXLlyskJERDhgzRM888U+WKx8XuU5JSU1MVGRmp4OBgDR8+XH/4wx8kScXFxZo1a5aGDx8up9OpsWPHauPGje7HlZSUaPHixQoJCZHT6VRYWJjWrFnj/nxWVpamTJmiYcOGKTQ0VIsXL1ZRUZEkyRijhIQEjRgxQk6nUyNGjNCKFSuqnW/dunX6zW9+U2mby+WS0+nUtm3b3Me/pnNNqny19u2339YLL7zgvu3pdDr15ZdfSpI+//xzxcTEuM+9Z599VmVlZbU+zmvXrtXo0aPdV6f+/cryj5WXl2v16tW68cYbFRwcrKioKPfzkv51Hr/66qsaNWqUgoODFRcXV+n8u1g7d+7UkSNH9PDDD8vX11e//OUvFRsbq1deeeWCjzvfufLDPu+44w4NGDBAY8aMUUpKisrLyyVJOTk5lf5sSlWvnCclJenOO+/U8uXLNWTIEIWEhOjpp592H/eazjfgshmgkbvzzjtNYmJile3z58838+fPd388atQok5qaaowxZsWKFea+++4zBQUFpqKiwuTk5JjMzExjjDHbt283PXv2rLSvgoICExISYlasWGHOnTtnjh49aiIjI83SpUuNMcaUlpaa3/zmN2bhwoWmqKjInDhxwtx+++2mZ8+e5ujRo8YYY1JTU01QUJCJj483hYWFpqioyBhjzIYNG8zx48dNRUWF+fzzz82gQYPM+vXrKz2/QYMGmd27d5uysjLz3//932bYsGFm5syZ5syZMyYvL8+Eh4ebpKSkSs/1+uuvN5mZmaakpMTMnTvXhIWFmUcffdQUFhaanJwcM2jQIJOWlmaMMaa4uNiEh4eb5cuXm8LCQuNyucxDDz1k7r777vMe9+eff96EhYWZgwcPmuLiYpOYmGj69Onj/l5cyj5fffVVM3ToUPPJJ5+YsrIyk5+fbz777DNjjDFnz541aWlpJj8/35SWlpq0tDTTp08fc/DgQWOMMevXrzc333yz+eabb4wxxpw6dcrs27fPGGPMN998YwYPHmxefvllU1xcbL755htz9913m8cee8wYY8zf/vY3Exoaao4dO2aMMebMmTNm9+7d1c743XffmV//+tdm586d7m2vv/66uf76601FRYX7+F/KuZaYmGjuvPPOSl8vKyvL9OvXz2zcuNGUlpaanJwcExkZaZ577rlaHefDhw+ba665xnz11VfGGGNcLpfZsWPHeb8HiYmJ5pZbbjGHDh0y5eXl5v333zf9+vUzR44cMcZ8fx736dPHPPnkk+bs2bPmxIkT5vrrrzfJycnn3Wdqaqr51a9+ZUJCQkxISIiZMmWK2b9/v/vzL730komIiKj0mM8//9z07NnTFBQUVLvPC50rOTk55pprrjGvvPKKKSkpMfv37zcjR440q1evNsYYc/To0Up/Ns/3vfjhfC4uLjYHDx40YWFh5oUXXjDGXPh8A+oCV9DQJKSkpGjAgAGV/vfuu++ed33z5s317bff6tChQzLGqFOnTurRo8d513/00UeSpFmzZqlFixbq3Lmz4uLi9MYbb8gYo88//1xff/21FixYIB8fH7Vr107Tp0+vsh9PT0898sgjcjgc8vHxkSTdfPPNat++vTw8PHTNNddo3Lhx+uSTTyo9Ljw8XE6nU82aNVNkZKROnz6te+65R61atVLr1q01cuRI7du3r9JjbrvtNvXo0UPNmzfXuHHjlJOTo9mzZ8vhcKhTp04aOHCg+zEfffSRzp07p4ceekgOh0O+vr6aP3++PvnkE504caLaY5KWlqbJkyere/fu8vb21owZM9S6detKx+xi97lmzRrdf//9Gjp0qJo1ayZ/f38NGDBAktSyZUvdeuut8vf3l5eXl2699VZ1795dn376qft7WlRUpKysLJWWlqpt27b61a9+JUl666239Mtf/lK//e1v5e3trTZt2iguLk4bNmxQeXm5mjdvruLiYmVmZurcuXNq1arVeV+8HxAQoBtuuEF//vOf3dv+/Oc/Kzo6Wh4eHlXWX+y59mOvvPKKRo8erRtvvFFeXl7q1KmTpkyZ4r5CV9NxbtasmYwxOnjwoFwul3x9fTVw4MDzfr2XXnpJ8+bN09VXXy1PT0+NGTNGwcHBlf48eXl5ae7cuWrZsqXatWunMWPGaO/evefd58CBA/X222/rr3/9q95991339+LkyZOSvr8C6e/vX+kxAQEB7s9V50LnyrvvvqvAwEBNnDhRzZs3V+/evRUbG6v169fX4oj/S+vWrTVjxgx5e3ure/fumjx5slJTUyVd+HwD6gKvQUOTcP/992vmzJmVtl3oNs7kyZNVXl6uhQsX6sSJExo6dKgeeughdenSpdr1x48fV8eOHdWsWTP3tquuukrnzp1TXl6eTp48qdatW8vX19f9+U6dOlXZz89//nO1aNGi0rZXXnlF69evV25urowxKi4uVr9+/Sqtadu2rfv/t2zZstpthYWFNT7mF7/4RbWPyc7O1qlTp6r84Pb29lZubq7at29f5bmcOHFCnTt3dn/s6empjh07uj++lH0eO3ZMV199dZXt0ve3lJ555hlt2bJF33zzjTw9PVVUVOS+lRcZGam8vDwtX75chw4dUv/+/TVnzhz16dNH2dnZ+uKLL9w/wKXvb2t6eHjo9OnTGjRokB5++GH98Y9/1IMPPqg+ffpo+vTpGjp0aLWz3HbbbZo6daoWLlyo48ePa+/evUpMTKx27cWeaz+WnZ2tTz/9VFu2bHFvq6iocN9Oruk49+/fXytWrNCrr76q//qv/9LVV1+te+65RxEREVW+1unTp+VyuTRjxgx5ev7r7+9lZWWVzuef/exn8vL6148Ph8NR5fz7d//+XFu1aqV58+bpgw8+0EcffaTbb79dfn5+VUIsPz9fkuTn51ftPi90rhw/frzK8b3qqqt0/Pjx885YnY4dO1Y6Dp07d3b/5eJC5xtQFwg0XJF8fHw0e/ZszZ49W99++62WLFmiRx55RGvXrq30H+QfdOjQQbm5uaqoqHB//ujRo2rZsqXatGmjdu3a6cyZMyoqKpLD4ZAk5ebmVtnPj/e9e/duLVu2TP/7v/8rp9MpLy8vPf744/rqq6/q4VmfX9u2bdWlSxdt3ry51o9p3769jh075v64oqKi0nO+lH126tRJ2dnZGjlyZJXPrV69Wn/729+0atUqXXXVVfLw8FBkZKQ7VJo1a6bJkydr8uTJKiwsVGJiombMmKEtW7aobdu2GjRokFavXn3erz1+/HiNHz9eJSUlWrdunaZOnart27e7r3T+u0GDBqlt27bauHGjDh06pNDQULVr167a/V7oXPux6q7AtW3bVrfccouWLl1a7f5rc5xHjx6t0aNHq6ysTO+//77mzp2rvn376qqrrqq0LiAgQC1atNCqVavUv3//8+6vLnh4eLi/d71799aRI0dUUFDgvpL2j3/8Q507dz5voF3oXOnQoYP+8Y9/VNp29OhRdejQQZLcf5E6e/as+/OnTp2qsp8f/5k/duyY+y8WFzrfgLrALU5ckT788ENlZmaqrKxMPj4+atGihfs/wj//+c8lSYcOHXKvv+6662SMUWJiokpKSnTs2DElJCS4b2tde+216tKli5566imdPXtWp06d0vPPP1/jHAUFBWrWrJnatGmjZs2aaefOnXrnnXfq50lfwJgxY1RcXKykpCQVFBRIkr755ptKL8L/sVtuuUUvvviiDh06pJKSEj333HM6c+bMZe3zt7/9rVJSUrRjxw6Vl5eroKBAO3fulPT9sfL29lbr1q1VVlamV155RQcPHnQ/dtu2bdq7d69KSkrUokULORwO9/c0KipK+/bt06uvvqqzZ8/KGKPjx4/rgw8+kCR98cUX+uyzz3Tu3Dk1b97c/QO8uliXvo+L6OhorV+/Xm+99dYF3/biQufaj7Vt21bHjh1TSUmJe9vEiRP13nvvafPmzSopKVF5ebmOHDmijz/+uFbH+dChQ/rrX/+qwsJCeXl5yd/fX8aYamfw9vbWHXfcoeXLlysrK0vGGJ07d06fffaZDh8+fN7nWJMPPvhAJ0+elDFGBQUFWrFihfLy8jRixAhJ37/dyFVXXaWnn35aRUVFOnz4sFatWqWJEyeed58XOlduuukmHThwQOvXr1dpaakOHDigVatWub9PrVu3VufOnfX666+rrKxMX3/9dbXxfubMGT3//PMqKSnRoUOH9OKLLyoqKkrShc83oC5wBQ1XpJycHD311FP65z//KW9vb1177bV6/PHHJUlXX321YmJi9J//+Z8qKytTXFyc7rzzTq1evVq///3vNXz4cDkcDoWHh2vOnDmSvn9NzsqVK7Vo0SINGzZM7du3V0xMjHbt2lXllua/Cw0N1fjx4zVx4kQZYzR06FCNGzfuJ7+C5ufnp/Xr12vFihUaN26c8vPz9bOf/UzDhw+v9laYJN13333Kz8/XnXfeqYqKCkVHR1d63dal7PP222+Xp6enli5dqpycHPn6+mr8+PEaMGCA7r33XmVkZGjkyJHy9fVVdHR0pas8eXl5euKJJ3Ts2DF5eXmpV69eevbZZyV9f6vq1Vdf1YoVK/Q///M/Onv2rNq1a6ebbrpJo0ePVmFhoZ5++mkdPnxYnp6e6tatm5KTky/4vbvllluUkJCg1q1b67rrrjvvugudaz8WERGhTZs2afjw4aqoqNCaNWt0zTXX6MUXX1RCQoLi4+Pdtxt/iJeajnNpaamef/55ZWZmyhijjh07avny5ZVuT/+7+fPna+3atZo9e7aOHz+uFi1aqE+fPpo/f/55n2NN0tPTtXjxYhUUFMjPz099+/bVSy+95L4l3qxZM61cuVKLFy/WsGHD5OPjowkTJlzwLTYudK507txZq1at0jPPPKPly5erdevWmjBhgu6++27345966in97ne/08CBA9WrVy+NHz9eS5YsqfQ1nE6nCgsLNWLECHl6eurmm2/WvffeK+nC5xtQFzyM4Z0AgfqwZcsWzZo1S1988UW1t64A2CspKUk7duzgrTPQYLgeC9SR3bt3Kzs7W8YYHT58WM8++6zGjh1LnAEALhq3OIE68sObhebl5ek//uM/dN111+nhhx9u6LEAAI0QtzgBAAAswy1OAAAAyzSaW5wVFRUqLCxU8+bNeU0PAACwmjFGpaWl8vX1vaS3YGk0gVZYWKgDBw409BgAAAC11rNnzyq/yqw2Gk2gNW/eXNL3T9Tb27uBp6nZvn371Ldv34Yeo8nhuNYPjmv94LjWD45r/eC41q2SkhIdOHDA3S8Xq9EE2g+3Nb29vS/45pE2aSxzNjYc1/rBca0fHNf6wXGtHxzXunepL8viHwkAAABYhkADAACwDIEGAABgGQINAADAMgQaAACAZQg0AAAAyxBoAAAAliHQAAAALEOgAQAAWIZAAwAAsAyBBgAAYBkCDQAAwDIEGgAAgGUINAAAAMsQaAAAAJYh0Bq5ipKShh5Bkj1zAADQFHg19AC4PJ7e3jp49x0NPYZ6vPRaQ48AAECTwRU0AAAAyxBoAAAAliHQAAAALEOgAQAAWIZAAwAAsAyBBgAAYBkCDQAAwDIEGgAAgGUINAAAAMsQaAAAAJYh0AAAACxDoAEAfjIVJSWXvY/g4GAr5gDqE78sHQDwk/H09tbBu+9o6DHU46XXGnoE4IK4ggYAjZwtV4NsmeNKxJXJpocraADQyHFVCpwDTQ9X0AAAACxDoAEAAFiGQKsG9/IBAEBD4jVo1eBePgAAaEhcQQPwk7HlqrAtcwDA+XAFDcBPhqvTAFA7XEEDAACwDIEGAABgGQINAADAMgQaAACAZQg0AAAAyxBoAABUw5a3Y7FlDvy0eJsNoJGrKCmRp7f3Ze2jrn7zxeXOAdiEt4VBQyLQgEaOHyIA0PRwixM/GX7HKQAAtcMVNPxkuNIDAEDtcAUNAKrBFV8ADalWV9Dy8/O1aNEiffzxx/Lz89PUqVM1adKkateuXbtWL7zwglwul0aOHKnHH39cfn5+kqTc3Fz97ne/0549e9SsWTONHDlSixYtkq+vb909IwCoA1zxBdCQanUFbcmSJSovL1d6erpSUlKUlJSk7du3V1m3detWJScnKyUlRenp6SorK9PSpUvdn4+Pj1dAQIA+/vhjvffee8rJydFzzz1Xd88GAACgCagx0IqKirRp0ybFxcXJz89PQUFBio6OVmpqapW1aWlpioqKUlBQkPz8/DRnzhxt3LhRZ8+elSTl5ORo7NixatmypVq1aqUxY8YoMzOz7p8VAABAI1bjLc7s7GxJUo8ePdzbgoKCtHXr1iprMzMzNXLkSPfH3bt3lyQdOXJEvXv31l133aV33nlHAwcO1Llz57R582ZFRERc1MD79u27qPWXoi5eN1JXdu3adcHPM+ulqWnWxqQxHVdmvTTMWj+YtX7UNOuvg3rL29HwL20qKSrU3v0ZDT3GedUYaEVFRVVeI+bv76/CwsJq1/r7+1dZ63K5JH1/Ar3++usaMGCAysvLNWrUKE2cOPGiBu7bt69atGhxUY9pzGz6Q1cTZkVjOq7MWj+YtX40tVlteX1nfR7X4uLiy7qoVOMtTofDUSXGXC5XtS/sdzgc7hj797V+fn4qLy9XbGyswsLC9Pe//12ffvqpvLy89MQTT1zy8AAAAE1RjYHWrVs3SVJWVpZ72/79+xUYGFhlbWBgoDIy/nW5MCsrS8YYde3aVd99951OnDihSZMmydvbW61atVJ0dLTS09Pr4GkAAAA0HbW6ghYeHq6EhAS5XC5lZGQoNTVV0dHRVdZGRUUpLS1NGRkZcrlcSkhIUEREhHx8fNSmTRt16dJFr732mkpLS1VQUKA333xTvXr1qpcnBgAA0FjV6m024uPjJUmhoaGKjY3VAw88oCFDhig3N1dOp1O5ubmSpJCQEE2fPl2xsbEKDQ2Vh4eHFi1a5N5PcnKytm3bpmHDhmn06NEyxlT6PAAAAGr5RrUBAQFKTEyssr1jx47as2dPpW0xMTGKiYmpdj+9e/fWn/70p0sYEwAA4MrBr3oCAACwDIEGVMOW339oyxwAgJ9WrW5xAlcafg8jAKAhcQUNAADAMgQaAACAZQg0AAAAyxBoAAAAliHQAAAALEOgAQAAWIZAAwAAsAyBBgAAYBkCDQAAwDIEGgAAgGUINAAAAMsQaAAAAJYh0AAAACxDoAEAAFiGQAMAALAMgQYAAGAZAg0AAMAyBBoAAIBlCDQAAADLEGgAAACWIdAAAAAsQ6ABAABYhkADAACwDIEGAABgGQINAADAMgQaAACAZQg0AAAAyxBoAAAAliHQAAAALEOgAQAAWIZAAwAAsAyBBgAAYBkCDQAAwDIEGgAAgGUINAAAAMsQaAAAAJYh0AAAACxDoAEAAFiGQAMAALAMgQYAAGAZAg0AAMAyBBoAAIBlCDQAAADLEGgAAACWIdAAAAAsQ6ABAABYhkADAACwDIEGAABgGQINAADAMgQaAACAZQg0AAAAyxBoAAAAliHQAAAALEOgAQAAWIZAAwAAsAyBBgAAYBkCDQAAwDIEGgAAgGUINAAAAMsQaAAAAJYh0AAAACxDoAEAAFiGQAMAALAMgQYAAGAZAg0AAMAyBBoAAIBlCDQAAADLEGgAAACWqVWg5efna/bs2XI6nQoNDdW6devOu3bt2rUKDQ2V0+lUXFycXC5Xpc9v3rxZY8eOVb9+/TRq1Ci9//77l/cMAAAAmphaBdqSJUtUXl6u9PR0paSkKCkpSdu3b6+ybuvWrUpOTlZKSorS09NVVlampUuXuj+/bds2LVu2TIsXL9bu3buVmpqqoKCguns2AAAATUCNgVZUVKRNmzYpLi5Ofn5+CgoKUnR0tFJTU6usTUtLU1RUlIKCguTn56c5c+Zo48aNOnv2rCQpMTFRM2bM0IABA+Tp6ak2bdqoS5cudf+sAAAAGrEaAy07O1uS1KNHD/e2oKAgZWZmVlmbmZmp3r17uz/u3r27JOnIkSMqLy/X3r179e233yo8PFzDhw/XI488ooKCgst9DgAAAE2KV00LioqK5OvrW2mbv7+/CgsLq13r7+9fZa3L5dLp06dVWlqqjRs36uWXX5bD4dC8efO0bNky/f73v6/1wPv27av12ksVHBxc71+jtnbt2nXBzzPrpWHW+sGs9YNZ6wez1o+mNGtDqjHQHA5HlRhzuVxVou2HtT/+RwEul0t+fn7y8fGRJE2aNEnt27eXJE2bNk1Tpky5qIH79u2rFi1aXNRjGjObTuSaMGv9YNb6waz1g1nrB7PWj/qctbi4+LIuKtV4i7Nbt26SpKysLPe2/fv3KzAwsMrawMBAZWRkuD/OysqSMUZdu3ZVQECAOnToIA8Pj0seFgAA4EpQY6A5HA6Fh4crISFBLpdLGRkZSk1NVXR0dJW1UVFRSktLU0ZGhlwulxISEhQREeG+ejZ+/HitW7dO//znP+VyubRy5UqFhYXV/bMCAABoxGr1Nhvx8fGSpNDQUMXGxuqBBx7QkCFDlJubK6fTqdzcXElSSEiIpk+frtjYWIWGhsrDw0OLFi1y72fq1KkKDg7WTTfdpDFjxqhVq1Z69NFH6+FpAQAANF41vgZNkgICApSYmFhle8eOHbVnz55K22JiYhQTE1P9F/Py0sKFC7Vw4cJLGBUAAODKwK96AgAAsAyBBgAAYBkCDQAAwDIEGgAAgGUINAAAAMsQaAAAAJYh0AAAACxDoAEAAFiGQAMAALAMgQYAAGAZAg0AAMAyBBoAAIBlCDQAAADLEGgAAACWIdAAAAAsQ6ABAABYhkADAACwDIEGAABgGQINAADAMgQaAACAZQg0AAAAyxBoAAAAliHQAAAALEOgAQAAWIZAAwAAsAyBBgAAYBkCDQAAwDIEGgAAgGUINAAAAMsQaAAAAJYh0AAAACxDoAEAAFiGQAMAALAMgQYAAGAZAg0AAMAyBBoAAIBlCDQAAADLEGgAAACWIdAAAAAsQ6ABAABYhkADAACwDIEGAABgGQINAADAMgQaAACAZQg0AAAAyxBoAAAAliHQAAAALEOgAQAAWIZAAwAAsAyBBgAAYBkCDQAAwDIEGgAAgGUINAAAAMsQaAAAAJYh0AAAACxDoAEAAFiGQAMAALAMgQYAAGAZAg0AAMAyBBoAAIBlCDQAAADLEGgAAACWIdAAAAAsQ6ABAABYhkADAACwDIEGAABgGQINAADAMgQaAACAZQg0AAAAyxBoAAAAliHQAAAALFOrQMvPz9fs2bPldDoVGhqqdevWnXft2rVrFRoaKqfTqbi4OLlcripr8vLyNHjwYE2YMOHSJwcAAGiiahVoS5YsUXl5udLT05WSkqKkpCRt3769yrqtW7cqOTlZKSkpSk9PV1lZmZYuXVpl3dNPP60ePXpc/vQAAABNUI2BVlRUpE2bNikuLk5+fn4KCgpSdHS0UlNTq6xNS0tTVFSUgoKC5Ofnpzlz5mjjxo06e/ase82OHTuUnZ2tqKioun0mAAAATUSNgZadnS1Jla54BQUFKTMzs8razMxM9e7d2/1x9+7dJUlHjhyRJJWUlGjp0qWKj4+Xh4fHZQ0OAADQVHnVtKCoqEi+vr6Vtvn7+6uwsLDatf7+/lXW/vA6tJSUFA0dOlS9e/fWl19+eUkD79u375IedzGCg4Pr/WvU1q5duy74eWa9NMxaP5i1fjBr/WDW+tGUZm1INQaaw+GoEmMul6tKtP2w9sf/KMDlcsnPz09HjhzRm2++qbfeeuuyBu7bt69atGhxWftoTGw6kWvCrPWDWesHs9YPZq0fzFo/6nPW4uLiy7qoVGOgdevWTZKUlZXlvmW5f/9+BQYGVlkbGBiojIwMjRs3zv0YY4y6du2q9957T6dPn1Z4eLgk6dy5cyouLlZISIi2bNkib2/vS34SAAAATUmNr0FzOBwKDw9XQkKCXC6XMjIylJqaqujo6Cpro6KilJaWpoyMDLlcLiUkJCgiIkI+Pj6KiIjQBx98oA0bNmjDhg2aNWuWevbsqQ0bNhBnAAAA/6ZWb7P1CtRnAAAPaElEQVQRHx8vSQoNDVVsbKweeOABDRkyRLm5uXI6ncrNzZUkhYSEaPr06YqNjVVoaKg8PDy0aNEiSVLLli3Vtm1b9//8/f3l5eWltm3b1tNTAwAAaJxqvMUpSQEBAUpMTKyyvWPHjtqzZ0+lbTExMYqJialxn1FRUbzVBgAAQDX4VU8AAACWIdAAAAAsQ6ABAABYhkADAACwDIEGAABgGQINAADAMgQaAACAZQg0AAAAyxBoAAAAliHQAAAALEOgAQAAWIZAAwAAsAyBBgAAYBkCDQAAwDIEGgAAgGUINAAAAMsQaAAAAJYh0AAAACxDoAEAAFiGQAMAALAMgQYAAGAZAg0AAMAyBBoAAIBlCDQAAADLEGgAAACWIdAAAAAsQ6ABAABYhkADAACwDIEGAABgGQINAADAMgQaAACAZQg0AAAAyxBoAAAAliHQAAAALEOgAQAAWIZAAwAAsAyBBgAAYBkCDQAAwDIEGgAAgGUINAAAAMsQaAAAAJYh0AAAACxDoAEAAFiGQAMAALAMgQYAAGAZAg0AAMAyBBoAAIBlCDQAAADLEGgAAACWIdAAAAAsQ6ABAABYhkADAACwDIEGAABgGQINAADAMgQaAACAZQg0AAAAyxBoAAAAliHQAAAALEOgAQAAWIZAAwAAsAyBBgAAYBkCDQAAwDIEGgAAgGUINAAAAMsQaAAAAJYh0AAAACxDoAEAAFiGQAMAALAMgQYAAGAZAg0AAMAyBBoAAIBlahVo+fn5mj17tpxOp0JDQ7Vu3brzrl27dq1CQ0PldDoVFxcnl8slSSopKdGjjz6qUaNGyel0KjIyUh9++GHdPAsAAIAmpFaBtmTJEpWXlys9PV0pKSlKSkrS9u3bq6zbunWrkpOTlZKSovT0dJWVlWnp0qWSpLKyMnXo0EFr1qzRrl27NHfuXD300EM6fPhw3T4jAACARq7GQCsqKtKmTZsUFxcnPz8/BQUFKTo6WqmpqVXWpqWlKSoqSkFBQfLz89OcOXO0ceNGnT17Vg6HQzNnzlTnzp3l6empkSNHqlu3btq7d2+9PDEAAIDGqsZAy87OliT16NHDvS0oKEiZmZlV1mZmZqp3797uj7t37y5JOnLkSJW1eXl5ysrKUmBg4EUPDQAA0JR51bSgqKhIvr6+lbb5+/ursLCw2rX+/v5V1v7wOrQflJWV6eGHH1ZERISCgoIuauB9+/Zd1PpLERwcXO9fo7Z27dp1wc8z66Vh1vrBrPWDWesHs9aPpjRrQ6ox0BwOR5UYc7lcVaLth7U/jjGXyyU/Pz/3xxUVFZo3b56k71/bdrH69u2rFi1aXPTjGiubTuSaMGv9YNb6waz1g1nrB7PWj/qctbi4+LIuKtV4i7Nbt26SpKysLPe2/fv3V3trMjAwUBkZGe6Ps7KyZIxR165dJUnGGD322GM6deqUkpOT5e3tfcmDAwAANFU1BprD4VB4eLgSEhLkcrmUkZGh1NRURUdHV1kbFRWltLQ0ZWRkyOVyKSEhQREREfLx8ZEkxcfHKysrSytXrnRvAwAAQGW1epuN+Ph4SVJoaKhiY2P1wAMPaMiQIcrNzZXT6VRubq4kKSQkRNOnT1dsbKxCQ0Pl4eGhRYsWSZKOHTum9evXa//+/e73SXM6nVq5cmU9PTUAAIDGqcbXoElSQECAEhMTq2zv2LGj9uzZU2lbTEyMYmJiqqzt1KmTvvrqq0scEwAA4MrBr3oCAACwDIEGAABgGQINAADAMgQaAACAZQg0AAAAyxBoAAAAliHQAAAALEOgAQAAWIZAAwAAsAyBBgAAYBkCDQAAwDIEGgAAgGUINAAAAMsQaAAAAJYh0AAAACxDoAEAAFiGQAMAALAMgQYAAGAZAg0AAMAyBBoAAIBlCDQAAADLEGgAAACWIdAAAAAsQ6ABAABYhkADAACwDIEGAABgGQINAADAMgQaAACAZQg0AAAAyxBoAAAAliHQAAAALEOgAQAAWIZAAwAAsAyBBgAAYBkCDQAAwDIEGgAAgGUINAAAAMsQaAAAAJYh0AAAACxDoAEAAFiGQAMAALAMgQYAAGAZAg0AAMAyBBoAAIBlCDQAAADLEGgAAACWIdAAAAAsQ6ABAABYhkADAACwDIEGAABgGQINAADAMgQaAACAZQg0AAAAyxBoAAAAliHQAAAALEOgAQAAWIZAAwAAsAyBBgAAYBkCDQAAwDIEGgAAgGUINAAAAMsQaAAAAJYh0AAAACxDoAEAAFiGQAMAALAMgQYAAGAZAg0AAMAyBBoAAIBlCDQAAADLEGgAAACWIdAAAAAsQ6ABAABYplaBlp+fr9mzZ8vpdCo0NFTr1q0779q1a9cqNDRUTqdTcXFxcrlcl7QfAACAK1WtAm3JkiUqLy9Xenq6UlJSlJSUpO3bt1dZt3XrViUnJyslJUXp6ekqKyvT0qVLL3o/AAAAVzKvmhYUFRVp06ZN2rBhg/z8/BQUFKTo6GilpqZqyJAhldampaUpKipKQUFBkqQ5c+bolltu0eLFi2WMqfV+qmOMkSSVlJRcyvO8aBX+AT/J17mQ4uLiWq1j1ovDrPWDWesHs9YPZq0fTXHWS/VDr/zQLxfLw9TwyC+//FITJkzQvn373NveffddrVq1Shs2bKi0NjIyUrGxsYqMjHRv+/Wvf6033nhDFRUVtd5PdQoKCnTgwIFaPzEAAICG1rNnT/n7+1/042p1Bc3X17fSNn9/fxUWFla79sdD+Pv7u1+HVtv9VMfX11c9e/ZU8+bN5eHhUavHAAAANARjjEpLS6u0T23VGGgOh6NKRLlcrmq/oMPhqPSPAn5Y6+fnp4qKilrvpzqenp6XVKAAAAANoWXLlpf82Br/kUC3bt0kSVlZWe5t+/fvV2BgYJW1gYGBysjIcH+clZUlY4y6du16UfsBAAC4ktUYaA6HQ+Hh4UpISJDL5VJGRoZSU1MVHR1dZW1UVJTS0tKUkZEhl8ulhIQERUREyMfH56L2AwAAcCWr8R8JSN+/f9nChQuVnp4uX19fTZs2TZMmTVJubq5uuukm/eUvf1HHjh0lSWvWrNELL7ygwsJCjRgxQk888YT8/PwuuB8AAAD8S60CDQAAAD8dftUTAACAZQg0AAAAyxBoAAAAliHQAAAALEOg1bH8/HzNnj1bTqdToaGhWrduXUOP1OiVlJTo0Ucf1ahRo+R0OhUZGakPP/ywocdqUvLy8jR48GBNmDChoUdpMjZv3qyxY8eqX79+GjVqlN5///2GHqnRy83N1ZQpUzRo0CANHTpUCxYsqPVvo8G/rF27VlFRUerbt68WLFhQ6XMHDhzQhAkTdO2112rs2LHauXNnA03ZuJzvmB4+fFjTpk3TkCFDNHDgQN1zzz06ePBgrfZJoNWxJUuWqLy8XOnp6UpJSVFSUpK2b9/e0GM1amVlZerQoYPWrFmjXbt2ae7cuXrooYd0+PDhhh6tyXj66afVo0ePhh6jydi2bZuWLVumxYsXa/fu3UpNTVVQUFBDj9XoxcfHKyAgQB9//LHee+895eTk6LnnnmvosRqdX/ziF5o+fXqV9yEtLS3V1KlTNXr0aH322We6//77NX36dH333XcNNGnjcb5jWlBQoLCwML333nvatm2bgoODdf/999fqF6gTaHWoqKhImzZtUlxcnPz8/BQUFKTo6GilpqY29GiNmsPh0MyZM9W5c2d5enpq5MiR6tatm/bu3dvQozUJO3bsUHZ2tqKiohp6lCYjMTFRM2bM0IABA+Tp6ak2bdqoS5cuDT1Wo5eTk6OxY8eqZcuWatWqlcaMGaPMzMyGHqvRueGGGzR69Gi1atWq0vYdO3aouLhYsbGx8vb2VmRkpLp27crV31o43zG95pprdNttt6l169by8vLS3XffrWPHjunUqVM17pNAq0PZ2dmSVOlKRFBQEP8BqWN5eXnKysri14TVgZKSEi1dulTx8fHy8PBo6HGahPLycu3du1fffvutwsPDNXz4cD3yyCMqKCho6NEavbvuukvvvPOOioqKlJeXp82bN2vEiBENPVaTkZmZqZ49e8rT819pwM+wuvXZZ5+pVatWatu2bY1rCbQ6VFRUVOWXv/v7+/MaiTpUVlamhx9+WBEREdwyqgMpKSkaOnSoevfu3dCjNBmnT59WaWmpNm7cqJdfflkbN27UmTNntGzZsoYerdELDg7WoUOHNGDAAA0dOlQBAQGaOHFiQ4/VZBQWFsrf37/SNn6G1Z2TJ09q8eLFmjdvXqUIPh8CrQ45HI4qJ7LL5aoSbbg0FRUVmjdvnqTvX+uHy3PkyBG9+eabmjVrVkOP0qT4+PhIkiZNmqT27dsrICBA06ZN05YtWxp4ssatvLxcsbGxCgsL09///nd9+umn8vLy0hNPPNHQozUZvr6+crlclbYVFBTwM6wO5OXl6d5779X48eNr/TvICbQ61K1bN0lSVlaWe9v+/fu5FVcHjDF67LHHdOrUKSUnJ8vb27uhR2r0du3apdOnTys8PFwhISF64okn9OWXXyokJEQlJSUNPV6jFRAQoA4dOnDLuI599913OnHihCZNmiRvb2+1atVK0dHRSk9Pb+jRmozAwEAdOHBAFRUV7m0ZGRn8DLtM3333ne69916NGDFCM2fOrPXjCLQ65HA4FB4eroSEBLlcLmVkZCg1NbXWtYzzi4+PV1ZWllauXOm+QoHLExERoQ8++EAbNmzQhg0bNGvWLPXs2VMbNmwggC/T+PHjtW7dOv3zn/+Uy+XSypUrFRYW1tBjNWo//EOL1157TaWlpSooKNCbb76pXr16NfRojU5ZWZmKi4tVUVGh8vJyFRcXq7S0VIMGDZK3t7dWr16tkpISvfvuu8rOztaYMWMaemTrne+YulwuTZ48WU6nU/Pnz7+offLL0utYfn6+Fi5cqPT0dPn6+mratGmaNGlSQ4/VqB07dkxhYWHy9vaWl5eXe/uUKVM0derUBpysaUlLS9Nrr72m119/vaFHafTKysr05JNP6u2331azZs103XXX6bHHHpOfn19Dj9aoZWRkaNmyZdq/f788PT01aNAgLVy4UO3atWvo0RqVpKQkJScnV9p266236sknn9RXX32lhQsX6quvvlKXLl20ePFiDRw4sIEmbTzOd0wHDx6sBQsWyMfHp9JV9T/+8Y8aMGDABfdJoAEAAFiGW5wAAACWIdAAAAAsQ6ABAABYhkADAACwDIEGAABgGQINAADAMgQaAACAZQg0AAAAyxBoAAAAlvl/CMROi4xFo0MAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "voir_histogramme([1, 2, 3, 50, 100, 200])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On s'approche d'une distribution uniforme !"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On a tout simplement l'expression suivante :\n",
    "$$\\forall n \\geq 0, \\mathbb{P}(Y_{n+1} = k) = \\frac{1}{6} \\sum_{\\delta = 1}^{6} \\mathbb{P}(Y_n = k - \\delta \\mod 12).$$\n",
    "Avec $k - 1 \\mod 12 = 11$ si $k = 0$ par exemple. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On a donc la matrice suivante pour exprimer $U_n = (\\mathbb{P}(Y_n = k))_{0\\leq k \\leq 11}$ en fonction de $U_{n-1}$ :\n",
    "\n",
    "$$ P = \\frac{1}{6} \\begin{bmatrix}\n",
    "0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 \\\\\n",
    "1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1\\\\\n",
    "1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1\\\\\n",
    "1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 & 1\\\\\n",
    "1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1\\\\\n",
    "1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 1\\\\\n",
    "1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 & 0 \\\\\n",
    "0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 & 0 \\\\\n",
    "0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 & 0 \\\\\n",
    "0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 0 & 0 \\\\\n",
    "0 & 0 & 0 & 0 & 0 & 1 & 1 & 1 & 1 & 1 & 1 & 0 \\\\\n",
    "\\end{bmatrix}$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On va la définir rapidement en Python, et calculer ses valeurs propres notamment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "case_max = 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "P = np.zeros((case_max, case_max))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "for k in range(case_max):\n",
    "    for i in range(k - 6, k):\n",
    "        P[k, i] = 1/6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.        , 0.        , 0.        , 0.        , 0.        ,\n",
       "        0.        , 0.16666667, 0.16666667, 0.16666667, 0.16666667,\n",
       "        0.16666667, 0.16666667],\n",
       "       [0.16666667, 0.        , 0.        , 0.        , 0.        ,\n",
       "        0.        , 0.        , 0.16666667, 0.16666667, 0.16666667,\n",
       "        0.16666667, 0.16666667],\n",
       "       [0.16666667, 0.16666667, 0.        , 0.        , 0.        ,\n",
       "        0.        , 0.        , 0.        , 0.16666667, 0.16666667,\n",
       "        0.16666667, 0.16666667],\n",
       "       [0.16666667, 0.16666667, 0.16666667, 0.        , 0.        ,\n",
       "        0.        , 0.        , 0.        , 0.        , 0.16666667,\n",
       "        0.16666667, 0.16666667],\n",
       "       [0.16666667, 0.16666667, 0.16666667, 0.16666667, 0.        ,\n",
       "        0.        , 0.        , 0.        , 0.        , 0.        ,\n",
       "        0.16666667, 0.16666667],\n",
       "       [0.16666667, 0.16666667, 0.16666667, 0.16666667, 0.16666667,\n",
       "        0.        , 0.        , 0.        , 0.        , 0.        ,\n",
       "        0.        , 0.16666667],\n",
       "       [0.16666667, 0.16666667, 0.16666667, 0.16666667, 0.16666667,\n",
       "        0.16666667, 0.        , 0.        , 0.        , 0.        ,\n",
       "        0.        , 0.        ],\n",
       "       [0.        , 0.16666667, 0.16666667, 0.16666667, 0.16666667,\n",
       "        0.16666667, 0.16666667, 0.        , 0.        , 0.        ,\n",
       "        0.        , 0.        ],\n",
       "       [0.        , 0.        , 0.16666667, 0.16666667, 0.16666667,\n",
       "        0.16666667, 0.16666667, 0.16666667, 0.        , 0.        ,\n",
       "        0.        , 0.        ],\n",
       "       [0.        , 0.        , 0.        , 0.16666667, 0.16666667,\n",
       "        0.16666667, 0.16666667, 0.16666667, 0.16666667, 0.        ,\n",
       "        0.        , 0.        ],\n",
       "       [0.        , 0.        , 0.        , 0.        , 0.16666667,\n",
       "        0.16666667, 0.16666667, 0.16666667, 0.16666667, 0.16666667,\n",
       "        0.        , 0.        ],\n",
       "       [0.        , 0.        , 0.        , 0.        , 0.        ,\n",
       "        0.16666667, 0.16666667, 0.16666667, 0.16666667, 0.16666667,\n",
       "        0.16666667, 0.        ]])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy.linalg as LA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "spectre, vecteur_propres = LA.eig(P)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On a besoin d'éliminer les erreurs d'arrondis, mais on voit que $1$ est valeur propre, associée au vecteur $[1,\\dots,1,\\dots,1]$ avec un $1$ seulement à la 8ème composante."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1.        +0.j        , -0.16666667+0.62200847j,\n",
       "       -0.16666667-0.62200847j, -0.16666667+0.16666667j,\n",
       "       -0.16666667-0.16666667j, -0.16666667+0.0446582j ,\n",
       "       -0.16666667-0.0446582j ,  0.        +0.j        ,\n",
       "        0.        +0.j        , -0.        +0.j        ,\n",
       "        0.        +0.j        ,  0.        -0.j        ])"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.round(spectre,10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.+0.j,  0.+0.j,  0.-0.j, -0.+0.j, -0.-0.j, -0.+0.j, -0.-0.j,\n",
       "        0.+0.j,  0.+0.j,  0.+0.j, -0.+0.j, -0.-0.j])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.round(vecteur_propres[0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$P$ n'est pas diagonalisable, **à prouver** au tableau si l'examinateur le demande."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## Planche 168"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Soit $f(x) = \\frac{1}{2 - \\exp(x)}$, et $a(n) = \\frac{f^{(n)}(0)}{n!}$.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [],
   "source": [
    "def f(x):\n",
    "    return 1 / (2 - np.exp(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Soit $g(x) = 2 - \\exp(x)$, telle que $g(x) f(x) = 1$. En dérivant $n > 0$ fois cette identité et en utilisant la formule de Leibniz, on trouve :\n",
    "$$ (g(x)f(x))^{(n)} = 0 = \\sum_{k=0}^n {n \\choose k} g^{(k)}(x) f^{(n-k)}(x).$$\n",
    "Donc en $x=0$, on utilise que $g^{(k)}(x) = - \\exp(x)$, qui donne que $g^{(k)}(0) = 1$ si $k=0$ ou $-1$ sinon, pour trouver que $\\sum_{k=1}^n {n \\choose k} f^{(k)}(0) = f^{(n)}(0)$. En écrivant ${n \\choose k} = \\frac{k! (n-k)!}{n!}$ et avec la formule définissant $a(n)$, cela donne directement la somme recherchée : $$ a(n) = \\sum_{k=1}^n \\frac{a(n-k)}{k!}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Pour calculer $a(n)$ avec Python, on utilise cette formule comme une formule récursive, et on triche un peu en utilisant `math.factorial` pour calculer $k!$.Il nous faut aussi $a(0) = f(0) = 1$ :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import factorial\n",
    "\n",
    "def a_0an(nMax):\n",
    "    valeurs_a = np.zeros(nMax+1)\n",
    "    valeurs_a[0] = 1.0\n",
    "    for n in range(1, nMax+1):\n",
    "        valeurs_a[n] = sum(valeurs_a[n-k] / factorial(k) for k in range(1, n+1))\n",
    "    return valeurs_a"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour n = 0 on a a(n) = 1.0\n",
      "Pour n = 1 on a a(n) = 1.0\n",
      "Pour n = 2 on a a(n) = 1.5\n",
      "Pour n = 3 on a a(n) = 2.1666666666666665\n",
      "Pour n = 4 on a a(n) = 3.1249999999999996\n",
      "Pour n = 5 on a a(n) = 4.508333333333334\n",
      "Pour n = 6 on a a(n) = 6.504166666666667\n",
      "Pour n = 7 on a a(n) = 9.383531746031748\n",
      "Pour n = 8 on a a(n) = 13.537574404761907\n",
      "Pour n = 9 on a a(n) = 19.530591380070547\n",
      "Pour n = 10 on a a(n) = 28.176687334656087\n"
     ]
    }
   ],
   "source": [
    "nMax = 10\n",
    "valeurs_n = np.arange(0, nMax + 1)\n",
    "valeurs_a = a_0an(nMax)\n",
    "\n",
    "for n in valeurs_n:\n",
    "    print(\"Pour n =\", n, \"on a a(n) =\", valeurs_a[n])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 720x504 with 0 Axes>"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d45585588>]"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d460c6a90>]"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d4556e5f8>]"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '$a(n)$ et deux autres suites')"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1d4556eda0>"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "plt.plot(valeurs_n, valeurs_a, 'ro-', label=r'$a(n)$', markersize=12)\n",
    "plt.plot(valeurs_n, 1 / np.log(2)**valeurs_n, 'g+-', label=r'$1/\\log(2)^n$')\n",
    "plt.plot(valeurs_n, 1 / (2 * np.log(2)**valeurs_n), 'bd-', label=r'$1/(2\\log(2)^n)$')\n",
    "plt.title(\"$a(n)$ et deux autres suites\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- On observe que $a(n)$ est comprise entre $\\frac{1}{2(\\log(2))^n}$ et $\\frac{1}{\\log(2)^n}$, donc le rayon de convergence de $S(x) = \\sum a(n) x^n$ est $\\log(2)$.\n",
    "- On va calculer les sommes partielles $S_n(x)$ de la série $S(x)$ :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Sn(x, n):\n",
    "    valeurs_a = a_0an(n)\n",
    "    return sum(valeurs_a[k] * x**k for k in range(0, n + 1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut vérifie que notre fonction marche :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour n = 0 S_n(x) = 1.0\n",
      "Pour n = 1 S_n(x) = 1.5\n",
      "Pour n = 2 S_n(x) = 1.875\n",
      "Pour n = 3 S_n(x) = 2.1458333333333335\n",
      "Pour n = 4 S_n(x) = 2.3411458333333335\n",
      "Pour n = 5 S_n(x) = 2.4820312500000004\n",
      "Pour n = 6 S_n(x) = 2.583658854166667\n"
     ]
    }
   ],
   "source": [
    "x = 0.5\n",
    "for n in range(0, 6 + 1):\n",
    "    print(\"Pour n =\", n, \"S_n(x) =\", Sn(x, n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [],
   "source": [
    "valeurs_x = np.linspace(0, 0.5, 1000)\n",
    "valeurs_f = f(valeurs_x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<span style=\"color:red;\">Je pense que l'énoncé comporte une typo sur l'intervale ! Vu le rayon de convergence, on ne voit rien si on affiche sur $[0,10]$ !</span>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 720x504 with 0 Axes>"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d455ca748>]"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d4536def0>]"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d455cae48>]"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d455caeb8>]"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d455b8550>]"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d455b8828>]"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d453bf898>]"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d4536d860>]"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, '$f(x)$ et $S_n(x)$ pour $n = 0$ à $n = 6$')"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1d455b8fd0>"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure()\n",
    "for n in range(0, 6 + 1):\n",
    "    valeurs_Sn = []\n",
    "    for x in valeurs_x:\n",
    "        valeurs_Sn.append(Sn(x, n))\n",
    "    plt.plot(valeurs_x, valeurs_Sn, 'o:', label='$S_' + str(n) + '(x)$', markevery=50)\n",
    "plt.plot(valeurs_x, valeurs_f, '+-', label='$f(x)$', markevery=50)\n",
    "plt.title(\"$f(x)$ et $S_n(x)$ pour $n = 0$ à $n = 6$\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Planche 170"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [],
   "source": [
    "def u(n):\n",
    "    return np.arctan(n+1) - np.arctan(n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 720x504 with 0 Axes>"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d457a2a90>]"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Entier $n$')"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Valeur $u_n$')"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Premières valeurs de $u_n$')"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "valeurs_n = np.arange(50)\n",
    "valeurs_u = u(valeurs_n)\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(valeurs_n, valeurs_u, \"o-\")\n",
    "plt.xlabel(\"Entier $n$\")\n",
    "plt.ylabel(\"Valeur $u_n$\")\n",
    "plt.title(\"Premières valeurs de $u_n$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut vérifier le prognostic quant à la somme de la série $\\sum u_n$ :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5707963267948966"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pi/2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.550798992821746"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(valeurs_u)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.01273069820194558"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "somme_serie = pi/2\n",
    "somme_partielle = sum(valeurs_u)\n",
    "erreur_relative = abs(somme_partielle - somme_serie) / somme_serie\n",
    "erreur_relative"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Avec seulement $50$ termes, on a moins de $1.5\\%$ d'erreur relative, c'est déjà pas mal !"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$(u_n)_n$ semble être décroisante, et tendre vers $0$. On peut prouver ça mathématiquement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On sait aussi que $\\forall x\\neq0, \\arctan(x) + \\arctan(1/x) = \\frac{\\pi}{2}$, et que $\\arctan(x) \\sim x$, donc on obtient que $u_n \\sim \\frac{1}{n} - \\frac{1}{n+1} = \\frac{1}{n(n+1)}$.\n",
    "On peut le vérifier :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 720x504 with 0 Axes>"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d453292b0>]"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Entier $n$')"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Valeurs de $u_n / \\\\frac{1}{n(n+1)}$')"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "valeurs_n = np.arange(10, 1000)\n",
    "valeurs_u = u(valeurs_n)\n",
    "valeurs_equivalents = 1 / (valeurs_n * (valeurs_n + 1))\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(valeurs_n, valeurs_u / valeurs_equivalents, \"-\")\n",
    "plt.xlabel(\"Entier $n$\")\n",
    "plt.title(r\"Valeurs de $u_n / \\frac{1}{n(n+1)}$\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Pour $e = (e_n)_{n\\in\\mathbb{N}}$ une suite de nombres égaux à $0$ ou $1$ (*i.e.*, $\\forall n, e_n \\in \\{0,1\\}$, $S_n(e) = \\sum{i=0}^n e_i u_i$ est bornée entre $0$ et $\\sum_{i=0}^n u_i$. Et $u_n \\sim \\frac{1}{n(n+1)}$ qui est le terme général d'une série convergente (par critère de Cauchy, par exemple, avec $\\alpha=2$). Donc la série $\\sum u_n$ converge et donc par encadrement, $S_n(e)$ converge pour $n\\to\\infty$, *i.e.*, $S(e)$ converge. Ces justifications donnent aussi que $$0 \\leq S(e) \\leq \\sum_{n\\geq0} u_n = \\lim_{n\\to\\infty} \\arctan(n) - \\arctan(0) = \\frac{\\pi}{2}.$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Pour $e = (0, 1, 0, 1, \\ldots)$, $S(e)$ peut être calculée avec Python. Pour trouver une valeur approchée à $\\delta = 10^{-5}$ près, il faut borner le **reste** de la série, $R_n(e) = \\sum_{i \\geq n + 1} e_i u_i$. Ici, $R_{2n+1}(e) \\leq u_{2n+2}$ or $u_i \\leq \\frac{1}{i(i+1)}$, donc $R_{2n+1}(e) \\leq \\frac{1}{(2n+1)(2n+2)}$. $\\frac{1}{(2n+1)(2n+2)} \\leq \\delta$ dès que $2n+1 \\geq \\sqrt{\\delta}$, *i.e.*, $n \\geq \\frac{\\sqrt{\\delta}+1}{2}$. Calculons ça :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import ceil, sqrt, pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Se(e, delta=1e-5, borne_sur_n_0=10000):\n",
    "    borne_sur_n_1 = int(ceil(1 + sqrt(delta)/2.0))\n",
    "    borne_sur_n = max(borne_sur_n_0, borne_sur_n_1)\n",
    "    somme_partielle = 0\n",
    "    for n in range(0, borne_sur_n + 1):\n",
    "        somme_partielle += e(n) * u(n)\n",
    "    return somme_partielle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [],
   "source": [
    "def e010101(n):\n",
    "    return 1 if n % 2 == 0 else 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour delta = 1e-05 on a Se010101(delta) ~= 1.06408\n"
     ]
    }
   ],
   "source": [
    "delta = 1e-5\n",
    "Se010101 = Se(e010101, delta)\n",
    "print(\"Pour delta =\", delta, \"on a Se010101(delta) ~=\", round(Se010101, 5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Pour inverser la fonction, et trouver la suite $e$ telle que $S(e) = x$ pour un $x$ donné, il faut réfléchir un peu plus."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [],
   "source": [
    "def inverse_Se(x, n):\n",
    "    assert 0 < x < pi/2.0, \"Erreur : x doit être entre 0 et pi/2 strictement.\"\n",
    "    print(\"Je vous laisse chercher.\")\n",
    "    raise NotImplementedError"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ca suffit pour la partie Python."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## Planche 172"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "from random import random\n",
    "\n",
    "def pile(proba):\n",
    "    \"\"\" True si pile, False si face (false, face, facile à retenir).\"\"\"\n",
    "    return random() < proba"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- D'abord, on écrit une fonction pour **simuler** l'événement aléatoire :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "def En(n, p):\n",
    "    lance = pile(p)\n",
    "    for i in range(n - 1):\n",
    "        nouveau_lance = pile(p)\n",
    "        if lance and nouveau_lance:\n",
    "            return False\n",
    "        nouveau_lance = lance\n",
    "    return True"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([30, 70])"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lances = [ En(2, 0.5) for _ in range(100) ]\n",
    "np.bincount(lances)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pn(n, p, nbSimulations=100000):\n",
    "    return np.mean([ En(n, p) for _ in range(nbSimulations) ])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Par exemple, pour seulement $2$ lancés, on a $1 - p_n = p^2$ car $\\overline{E_n}$ est l'événement d'obtenir $2$ piles qui est de probabilité $p^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.75054"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pn(2, 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Avec $4$ lancés, on a $p_n$ bien plus petit."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.56445"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pn(4, 0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- On vérifie que $p_n(n, p)$ est décroissante en $p$, à $n$ fixé :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.97283"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pn(4, 0.1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10047"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pn(4, 0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- On vérifie que $p_n(n, p)$ est décroissante en $n$, à $p$ fixé :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.86535"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pn(6, 0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.80335"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pn(20, 0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.80053"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pn(100, 0.2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Notons que la suite semble converger ? Ou alors elle décroit de moins en moins rapidement."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Par récurrence et en considérant les possibles valeurs des deux derniers lancés numérotés $n+2$ et $n+1$, on peut montrer que\n",
    "  $$\\forall n, p_{n+2} = (1-p) p_{n+1} + p(1-p) p_n$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Si $p_n$ converge, on trouve sa limite $l$ comme point fixe de l'équation précédente. $l = (1-p) l + p(1-p) l$ ssi $1 = 1-p + p(1-p)$ ou $l=0$, donc si $p\\neq0$, $l=0$. Ainsi l'événement \"on obtient deux piles d'affilé sur un nombre infini de lancers\" est bien presque sûr."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Je vous laisse terminer pour calculer $T$ et les dernières questions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## Planche 177\n",
    "\n",
    "- Le domaine de définition de $f(x) = \\sum_{n \\geq 1} \\frac{x^n}{n^2}$ est $[-1, 1]$ car $\\sum \\frac{x^n}{n^k}$ converge si $\\sum x^n$ converge (par $k$ dérivations successives), qui converge ssi $|x| < 1$. Et en $-1$ et $1$, on utilise $\\sum \\frac{1}{n^2} = \\frac{\\pi^2}{6}$.\n",
    "\n",
    "- Pour calculer $f(x)$ à $10^{-5}$ près, il faut calculer sa somme partielle $S_n(x) := \\sum_{i=1}^n \\frac{x^i}{i^2}$ en bornant son reste $S_n(x) := \\sum_{i \\geq n+1} \\frac{x^i}{i^2}$ par (au moins) $10^{-5}$. Une inégalité montre rapidement que $R_n(x) \\leq |x|^{n+1}\\sum_{i\\geq n+1} \\frac{1}{i^2} $, et donc $R_n(x) \\leq \\delta$ dès que $|x|^{n+1} \\leq \\frac{\\pi^2}{6} \\delta$, puisque $\\sum_{i\\geq n+1} \\frac{1}{i^2} \\leq \\sum_{i=0}^{+\\infty} \\frac{1}{i^2} = \\frac{\\pi^2}{6}$. En inversant pour trouver $n$, cela donne que le reste est contrôlé par $\\delta$ dès que $n \\leq \\log_{|x|}\\left( \\frac{6}{\\pi^2} \\delta \\right) - 1$ (si $x\\neq 0$, et par $n \\geq 0$ sinon)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import floor, log, pi"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [],
   "source": [
    "delta = 1e-5\n",
    "\n",
    "def f(x):\n",
    "    if x == 0: return 0\n",
    "    borne_sur_n = int(floor(log((6/pi**2 * delta), abs(x)) - 1))\n",
    "    somme_partielle = 0\n",
    "    for n in range(1, borne_sur_n + 1):\n",
    "        somme_partielle += x**n / n**2\n",
    "    return somme_partielle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pour x = -0.75 \tf(x) = -0.64276\n",
      "Pour x = -0.5 \tf(x) = -0.44841\n",
      "Pour x = 0.25 \tf(x) = 0.26765\n",
      "Pour x = 0 \tf(x) = 0\n",
      "Pour x = 0.25 \tf(x) = 0.26765\n",
      "Pour x = 0.5 \tf(x) = 0.58224\n",
      "Pour x = 0.75 \tf(x) = 0.97847\n"
     ]
    }
   ],
   "source": [
    "for x in [-0.75, -0.5, 0.25, 0, 0.25, 0.5, 0.75]:\n",
    "    print(\"Pour x =\", x, \"\\tf(x) =\", round(f(x), 5))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- L'intégrale $g(t) = \\int_0^x \\frac{\\ln(1 - t)}{t} \\mathrm{d}t$ est bien défine sur $D = [-1, 1]$ puisque son intégrande existe, est continue et bien intégrable sur tout interval de la forme $]a, 0[$ ou $]0, b[$ pour $-1 < a < 0$ ou $0 < b < 1$. Le seul point qui peut déranger l'intégrabilité est en $0$, mais $\\ln(1-t) \\sim t$ quand $t\\to0$ donc l'intégrande est $\\sim 1$ en $0^-$ et $0^+$ et donc est bien intégrable. De plus, comme \"intégrale de la borne supérieure\" d'une fonction continue, $g$ est dérivable sur l'intérieur de son domaine, *i.e.*, sur $]-1, 1[$.\n",
    "\n",
    "- Pour la calculer numériquement, on utilise **évidemment** le module `scipy.integrate` et sa fonction `integrale, erreur = quad(f, a, b)`, qui donne une approximation de la valeur d'une intégrale en dimension 1 et une *borne* sur son erreur :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import integrate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [],
   "source": [
    "def g(x):\n",
    "    def h(t):\n",
    "        return log(1 - t) / t\n",
    "    integrale, erreur = integrate.quad(h, 0, x)\n",
    "    return integrale"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- On visualise les deux fonctions $f$ et $g$ sur le domaine $D$ :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 720x504 with 0 Axes>"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d442255f8>]"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f1d442c9e80>]"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f1d44225780>"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Représentation de $f(x)$ et $g(x)$')"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAmkAAAGzCAYAAAB0PIAGAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvnQurowAAIABJREFUeJzs3Xd4FHXiP/D3bN9s300jdEOViITeSwhFFCkBRVEPQTkPy8lX72zYPf15d6LonYVDRYETxYBBUaRDCF1ABWkB6enZvskmm53fH8E9YigBNplN8n49zz3P7WRm9p0Fkrfzmfl8BFEURRARERFRRJFJHYCIiIiIqmNJIyIiIopALGlEREREEYgljYiIiCgCsaQRERERRSCWNCIiIqIIxJJGREREFIFY0oiIiIgiEEsaEVXzzTffYMKECbDb7VJHuWL33Xcf3n///Tp9z/bt22P79u3XfJ433ngD/fv3R3JyMvbs2YNt27Zh3LhxCAaDNTr+wQcfxNKlS685R7jU9/xEkhOJKGLcddddYqdOncQuXbqIycnJ4qhRo8TPP/+8TjNs3rxZnDJliuh2u+vsPe+66y7x7bffrrPjwq1du3bitm3brukc69atEwcNGiQWFxeHtt1yyy3iunXranyOw4cPi3379hVLS0uvOkc4P1Mp8hM1JLySRhRh/vjHP2LPnj3YtWsXHnzwQTz33HPYuXNnrb1feXl5ldf9+vXDxx9/DL1eX2vvSdWtX78egwYNgsViAQBkZWXB5XJh0KBBNT5H27Zt0bx5c3z99de1FbPG6nt+okjAkkYUoWQyGUaNGgWTyYSffvoptN3v92P27NlITU1Fjx49MHnyZPzyyy+hr99999145ZVXMGPGDCQnJ2P48OFYvnx5ta8/8sgj6N69O2bPnl2j8y5cuBCpqalITk5G37598eSTT15Rptdeew2PPfYYunbtikGDBuHzzz8HADz33HPYtWsXPvjgAyQnJ6Nfv36h4xYtWoSbb74ZycnJGDBgAF588UWUlJRc8ri7774b77zzTugcDocDTz31FPr3748+ffrg4YcfRm5ubo2yXUhRUREeeughdO/eHUOHDsU333xTbZ/LfR6/l5KSgi+++ALLli1DcnIyli9fjlWrVqFv376Qyf73Y3rJkiXo27cvvF4vACAvLw/Dhg3D3LlzQ/v069cPa9asueh7XSrbpf4sLmTVqlUYMWIEunTpgqlTp2Lu3LkYO3Zs6Gu1kZ+oUZH6Uh4R/c/5Q03l5eXi8uXLxXbt2olr164N7fPEE0+IU6dOFXNzc8Xy8nJx4cKFYu/evUWn0xk6R+fOncX169eL5eXl4vr168VOnTqJe/fuDX29S5cu4qZNm8SKigrR5/Nd9ry//vqr2LlzZ/HQoUOiKIqix+MRd+zYcUWZunfvLm7btk2sqKgQV6xYIXbs2FE8efJkte/7fN9//714/PhxMRgMitnZ2eKwYcPE2bNnX/Dzuti2++67T5w6dapYVFQkut1u8fHHHxfHjh0rBgKBGmX7vXvvvVe8//77RYfDITocDvGBBx6oNtx5uc/j9wKBgHjjjTeG/oxEURQnTJggfvjhh1X2q6ioEMeOHSu+9dZbYmFhoThy5Mhq3//KlSvFvn37XvB9apKtpsOdX331ldi3b19x27ZtYiAQEFesWCF26tRJfOqpp2o1P1FjwitpRBFm7ty56N69Ozp37oy//vWv+L//+z+kpKQAAOx2O5YtW4bnn38ecXFxUCgUmDx5MsxmM9avXx86x5AhQzB48GAoFAoMHjwYqampSE9PD309NTUVAwYMgEwmg1arvex55XI5RFFEdnY2PB4PdDodevTocUWZRo4ciV69eoWuEBoMhkteXQKA4cOHo2XLlhAEAYmJibjzzjuxZcuWGn+W+fn52LRpE5566ilYrVbo9Xo899xzOHjwIH7++ecrzpaXl4esrCw88cQTMJlMMJlMePzxx6vsU9PP43zZ2dkIBALo0KFDaJvL5YLBYKiyn0wmw1NPPYX58+fjD3/4A4YOHYqHH364yj56vR5Op/OC73M12S7E7/fjtddewzPPPINevXpBLpdj1KhRiIqKQqdOnWotP1Fjo5A6ABFVNX36dDz88MPweDx47bXXsGXLFkybNg0KhQInT54EAIwfP77KMeXl5cjLywu9btasWZWvN2vWDIcOHbro1y933ubNm2P27Nn47LPP8Nxzz6F169a49957MWrUqBpnio2NrfJ1nU4XGva6mJUrV+Kjjz7CiRMnEAgEEAgEYLPZLnnM+X4b1mzevHlom8FggNVqxdmzZ9GlS5cryvbb+c7//K70s7yQffv2oW3btlCr1aFtJpMJbre72r4tW7aEQqGAUqmsVhABwOPxwGQyXfB9ribbhezcuROBQAAjR44MbSsrK4PH48H1119fa/mJGhuWNKIIpdfr8fzzz+Omm27CokWL8Ic//AHR0dEAgBUrViAuLu6ix545c6ba6/j4+NDr8+8TAlCj86ampiI1NRWBQACrVq3CY489hqSkpBpnuhRBEKpty83NxcyZM/Hmm28iJSUFKpUK8+fPx6effnrJ48732/d8+vRpJCYmAqgsAXa7HQkJCVec80LnO336dJV9rubz+Pnnn5GUlFRlW6dOnXDkyJEq24qKijBlyhSMGTMGS5Yswa5du9C9e/cq+xw5cqTaua4k2+U+UwAoLi6GwWCo8vdo9erVEEUxdDWwNvITNTYc7iSKYCqVCg8++CDee+89eDweNG3aFKmpqXjxxRdDRczj8WDjxo3Iz88PHbd+/Xps3LgRFRUV2LhxI1avXl3t6sn5LnfeY8eOYePGjfB6vVAoFDAYDBBFETKZrMaZLiUmJgbHjx+vss3r9SIYDMJisUClUuHgwYNYtGjRZY87X2xsLAYMGIDXXnsNxcXF8Hq9ePnll9GmTRvccMMNNcp2vri4OPTp0wf/+Mc/4HQ64XQ6Qw9e/OZqPo99+/ZVKybDhw/H1q1bQ3OMORwOTJkyBUOHDsWsWbNwzz334NVXX4UoilWO27x5M1JTUy/4PjXJdrnPFADatWuH3Nzc0N+xLVu24NVXX0Xr1q2h1WprLT9RY8OSRhThxowZA5PJhHnz5gGonPC0Y8eOmDp1KpKTkzFy5EgsWbKkyi+7CRMm4PPPP0f37t3xyiuv4JVXXkFycvIl3+dS5y0vL8d7772HgQMHomvXrnj99dfx97//PTTUV5NMl3Lvvffi8OHD6N69OwYOHAgASExMxKOPPoqZM2eia9eu+Pvf/44xY8Zc9rjf+8c//oHo6GjceuutGDp0KLxeL95//33I5fIaZbvQ+WQyGVJSUjBu3DjcdNNN1fa5ks+jvLwchw4dqlbS+vTpA6PRiI0bN8LtdmPq1Kno1atXaIhw+vTpOHv2bJV7DbOzs3Hy5EmMHj36ovkvl60mn2mHDh0wc+ZMPPHEE+jTpw++/fZbDBgwIDR8XJv5iRoTQazpT1Eiqhfuvvtu9OzZs9oN2VT/bNu2Da+//jrS09OrDVFfyEMPPYQhQ4YgLS2tDtL9T2lpKUaMGIEXXngBQ4YMCW2vL/mJIhVLGlEDw5JGte2nn36CVqtFmzZtkJOTg5dffhl+vx/z5s2rURkjoprhgwNERHRFsrOz8cYbb8Dj8SA6OhrDhg3DQw89xIJGFGa8kkZEREQUgfifPUREREQRqF4OdwaDQXi9XiiVyhrN6UNEREQkld+ektfpdFd0W0C9LGlerxeHDx+WOgYRERFRjbVr167acmmXUi9LmlKpBFD5zapUKonTEBEREV1cWVkZDh8+HOovNVUvS9pvQ5wqlarKWndEREREkepKb9HigwNEREREEYgljYiIiCgCsaQRERERRaB6eU/apZSXl+P06dMoLS2VOork5HI5zGYzoqOjORM4ERFRPdPgStrp06dhMBjQqlWrRj2H2m9zsuTl5eH06dNo0aKF1JGIiIjoCjS4yyulpaWw2WyNuqABlU+QqFQqNG3aFF6vV+o4REREdIUaXEkDrvwR14aMw5xERET1E3+DExEREUUgljQiIiKiCMSSRkRERBSBWNIk4nQ6cd9996Fnz554+OGH8dZbb2Hu3LmXPU4URYwfPx5Hjhypg5REREQklQY3BUd98eGHHyImJgbbt2+Hw+HA6NGjsWrVqsseJwgCpk6dirfffhvvvPNOHSQlIiIiKfBK2gUULVtS6++RlZWFESNGQBAEZGRkoH///oiKiqrRsampqdi+fTvy8/NrOSURERFJhSXtAuwZ6bV27rKyMnTr1g379u3DzJkzkZKSgg0bNqBnz56hfd58801MmzYt9Prdd99FWloafD4fAECj0aBTp07IzMystZxEREQNXbC0FIVLPkPA5ZQ6ygU1+OFOV9YmuDatv+LjTr/2Yo33NQ4cAmO/gTXaV6VS4csvv8TEiROxa9cuAECfPn3QunXr0D7Tpk1Damoq9u7di+PHj2PZsmVYvHhxlSttiYmJOHDgQI0zEhERUVWOVd/CsSIDxr4DAKNJ6jjVNPiSVlPlhQWoKCoMvS49VFmA5LZoKKNjwvpeBw4cQPv27UOvXS4XdDpd6LXRaMS0adMwa9YsOJ1OLFiwADabrco5dDodcnJywpqLiIiosajwuOH47mvouvaAqmkzqeNcUIMvacZ+A2t8les32VMmoc38xbWUCDh48CA6duwYem00Gqst3dSxY0fMnj0bL730Elq1alXtHF6vF0ajsdYyEhERNWTFS5cg6PfDmnab1FEuivekSeDgwYPo0KFD6HX79u1x/Pjx0Ovs7Gw8/fTTmDBhAtLTL3x/3NGjR6sUPSIiIqoZ/6kTcK5fDdOQYVA3bS51nItiSbsAy5i0Wj3/gQMHqpS0QYMGYceOHQCAvLw8TJ8+HbNmzcLzzz+PgoICrFmzpsrxfr8f+/fvR//+/Ws1JxERUUMjiiIK//spZFE6WMdNlDrOJbGkXYCtFv/QiouLUVxcjHbt2oW2jRkzBpmZmXC73Zg+fTruuecejBw5EiqVCtOnT8ecOXMQDAZD+69duxY9e/ZEXFxcreUkIiJqiLy7dqDkwH7Yxt8GuV4vdZxLCmtJW7hwIcaPH4+kpCQ8+eSTF91v+/bt6NChA5KTk0P/W7Kk9ucmiwRWqxX79++HSqWqsm3ChAn47LPPkJGRgSlTpoS+dscdd+Drr7+GTFb5RyWKIubNm4dHHnmkrqMTERHVa8ESHwo/+wSqZi1gHDxU6jiXFdYHB2JjYzFjxgxkZmbC7/dfcl+bzYasrKxwvn299uijj9ZoP0EQsHTp0lpOQ0RE1PAUfbkYAbsdzWbMhCCXSx3nssJa0oYPHw4A+Pnnn5GXlxfOUxMRERFdtZIjh+Bctxqm1JHQtGkrdZwakWwKDofDgX79+kGtViMlJQUzZ86sMlcYERERUTiI5eXI/+gDKKw22NJulzpOjUny4MB1112HjIwMZGZm4pNPPsGBAwfwt7/9TYooRERE1MAVpX+O8pyziPnDfZBpNFLHqTFJSlpMTAzatGkDmUyG5s2b4y9/+QtWrVolRRQiIiJqwHwH9sPx/QoYB6dC17mL1HGuSERMwSEIAkRRlDoGERERNSAVXi/y//MulLFxiL7jLqnjXLGwlrRAIAC/349gMIiKigr4/X6Ul5dX22/btm04c+YMRFFETk4O/vnPf2LYsGHhjEJERESNXMHCjxFw2BH3x4cgU9efYc7fhLWkvffee+jcuTPmzp2L5cuXo3Pnznj22WcBAMnJydi1axeAyhn3J02ahC5dumDSpElo3749Zs2aFc4oRERE1Ii5t2TCs3UzrLeOh+a6NlLHuSqCWA/HGf1+P/bt24ekpCSo1eoqXztw4ADXtPwdfiZERNSYlJ09g1MvPA11q9Zo+sSzks+JdqnecikRcU8aERERUTgE/aXI/febkKnViP/TI5IXtGvBkhaB3nrrLcydO/ey+4miiPHjx+PIkSN1kIqIiCiyiaKIgk8/QtnZM4j740NQWKxSR7omLGkRxm6348svv8Rdd13+KRRBEDB16lS8/fbbdZCMiIgosrkzN8CdtQmWW8cjKqmz1HGuGUvaBeQVSbfYe0ZGBvr374+oqKga7Z+amort27cjPz+/lpMRERFFrtJjR1Hw6UfQXp8E65g0qeOEBUvaBRTY02v1/MFgEO+//z569eqFfv36YenSpejevTuOHz+ODRs2oGfPnlX2f/PNNzFt2rTQ63fffRdpaWnw+XzQaDTo1KkTMjMzazUzERFRpAo47Mh5+5+Qm0yV96HJGka9kWztzrpid22C3bX+io87dvrFGu9rMQ6BxTiwxvu/++67yMzMxNKlS2EymfCnP/0JFRUVaNGiBQ4dOoTWrVtX2X/atGlITU3F3r17cfz4cSxbtgyLFy8OXW1LTEzEgQMHavz+REREDYVYXo7cf81G0OdDs1kvQW4wSh0pbBp8SaupsvICBCoKQ699pZWlRyGPhkoZE7b3cTgc+Oijj7BkyRI0bdoUAJCSkoLS0lLIZDK4XK5qC80bjUZMmzYNs2bNgtPpxIIFC2Cz2UJf1+l0yMnJCVtGIiKi+kAURRQs+Ail2UcQ/+BMqFu0lDpSWDX4kmYxDryiq1wAsC97EpLaLK6VPNu2bUObNm2QmJgY2uZwONC+fXsAlYXM6/VWO65jx46YPXs2XnrpJbRq1arK17xeL4zGhvNfDkRERDXhXPM9XJvWw3LreOh79JI6Ttg1jEHbesRut8NgMIRei6KI9evXh0pa+/btcfz48SrHZGdn4+mnn8aECROQnl79frmjR49ysloiImpUvD/uQeF/P4EuuRusYydIHadWsKRdQIyl9p4KadOmDfbu3Ytjx47B4/Hg9ddfx+HDh0MlbdCgQdixY0do/7y8PEyfPh2zZs3C888/j4KCAqxZsyb0db/fj/3796N///61lpmIiCiSlB7/FbnvvgV1i1aI++PDDeZBgd9rmN/VNYqzTay1c/fo0QPjx4/HhAkTMHbsWFx33XVQKBShK2FjxoxBZmYmfD4fPB4Ppk+fjnvuuQcjR46ESqXC9OnTMWfOHASDQQDA2rVr0bNnT8TFxdVaZiIiokhRXlSInLf+DrnegCYz/wqZpv4tnF5TLGkSeOaZZ7B7926sWbMGKpUKXbp0CQ2BWq1WTJgwAQsXLoRer0dGRgamTJkSOvaOO+7A119/DZlMBlEUMW/ePDzyyCMSfSdERER1p8LnQ86br0P0+9Hk/56AwmyROlKtavAPDkSavXv3Ijo6GgkJCdixYwf+8Y9/4J///GeVfR599NEanUsQBCxdurQ2YhIREUUUMRBA7r9moyznLBIeewrqps2ljlTrWNLq2C+//II5c+agrKwMLVu2xAsvvIA+ffpIHYuIiChiicEg8j58HyW/7EPs/TMQdX2S1JHqBEtaHbvzzjtx5513Sh2DiIioXihatgRBjweerZthnTAJxn5XNq1WfcaSRkRERBHLnlE59ZR55C2w3DxG4jR1iw8OEBERUURyrPoWAGAcOAS22ydDEASJE9UtXkkjIiKiiFK0bEnoChoAuDatr1xZYEwabONqb5qsSNMgS5ooio2ubV+MKIpSRyAiIroi6hatAJkM2g7Xo+SXfWgzv3aWaox0DW64Uy6Xo7y8XOoYEaOkpARKpVLqGERERDXi3fND5WoCra5Dk0celzqOpBpcSTObzcjLywvNyN9YiaIIn8+HM2fOIDY2Vuo4REREl+X9cQ9y/v0m1C1aIuGxpyDTaGAZU3tLNUa6BjfcGR0djdOnT+PQoUNSR5GcUqlEXFwcjEaj1FGIiIguyfvzj8h9ZzbUTZsj4fGnIdfpAKBR3YP2ew2upMlkMrRo0ULqGERERFRDvn0/IXfOP6FMaIqEvzwDuU4vdaSI0OCGO4mIiKj+8P2yDzlz/gFlkyZo+tdnINezoP2mwV1JIyIiovrBt//nyoIWF4+mf5kFud4gdaSIwpJGREREdc675wfk/PtNqJokVA5x8v7paljSiIiIqE65d2xF3gf/grpFKyQ89hSHOC+CJY2IiIjqjCtzA/I/+gCatu2RMPOvkGmjpI4UsVjSiIiIqE44165CwYKPoO10A5o88hhkao3UkSIaSxoRERHVOvt3X6Po80XQJXdD3J/+DJlKJXWkiMeSRkRERLVGFEUUpy+G/ZsM6Hv2Qdz0ByEoWD9qgp8SERER1QqxogL58/8Dd+YGGAenIuaeqRBknKK1pljSiIiIKOyCfj9y350D34+7YR07AZYxaRAEQepY9QpLGhEREYVVhceNnLf+jtKj2Yi5ZxpMKcOkjlQvsaQRERFR2JQXFeLsG68hkJ+P+AdnQt+9p9SR6i2WNCIiIgoL/5lTyHnjNQRLSpDw+FPQdrhe6kj1GksaERERXTPfL/uQ+85sCCoVmj71AtQtWkodqd5jSSMiIqJr4srcgPz5/4EqrgmazPwrlDGxUkdqEPgcLBEREV2xomVLIAaDKPpyMfI/fB/aDtej6ayXWNDCiFfSiIiI6IrZM9JRnnMWnh1bYRyUgpi7p3KS2jDjp0lERERXpMLlAgB4dmyF7bbJMN90C+dAqwUsaURERFQjRcuWwJ6RXnXbF4sQ9JfCNm6iRKkaLpY0IiIiqhFNm3aQRekgKBSocDnRZv5iqSM1aHxwgIiIiC5JFEXYv/sGObP/HxQ2G5o9+7LUkRoFXkkjIiKiiwqWlaFg/n/g3pIJXfeeiLtvBmQaDSxj0qSO1uCF9UrawoULMX78eCQlJeHJJ5+85L7fffcdhg4dii5dumDq1KnIy8sLZxQiIiK6RgF7Mc689iLcWzJhHTcR8TMehUyjAQDeg1YHwlrSYmNjMWPGDKSlXbpdHz16FE8//TRefvllbNu2Da1bt8Zjjz0WzihERER0DUqzj+DUi8+gLOcM4h9+DNYxaRBkvEuqLoV1uHP48OEAgJ9//vmSV8aWL1+OgQMHom/fvgCARx99FH369MHJkyfRokWLcEYiIiKiK+TavBH58/8DhcWKZo8/DXWz5lJHapQkuSft8OHD6Ny5c+i1wWBA06ZNcfjwYZY0IiIiiYiBAAo/Xwjn6pXQduyE+AcfhVxvkDpWoyVJSfP5fDAYqv6hG41GeL1eKeIQERE1egF7MXL//RZKsw/DNOwmRN8+mSsISEySTz8qKgoej6fKNrfbDZ1OJ0UcIiKiRs13YD/y3nsbQX8p4h54BIbefaWORJCopLVr1w4HDx4MvfZ4PDh9+jTatWsnRRwiIqJGSRRFOL77BkVffgZlbDyaPvEsVE2bSR2LzglrSQsEAqioqEAwGERFRQX8fj9kMhmUSmWV/W699VZMnDgRW7duRXJyMt566y106dKF96MRERHVkWCJD3nz3of3hx3Qde+FuGl/hEwbJXUsOk9Yn6V977330LlzZ8ydOxfLly9H586d8eyzzwIAkpOTsWvXLgBAYmIi/va3v2HWrFno1asXjh07hjfeeCOcUYiIiOgi/KdP4dQLT8O7Zxdsk+5G/IOPsqBFIEEURVHqEFfK7/dj3759SEpKglqtljoOERFRveHeshn58/8DmVaL+Bl/hrZ9R6kjNXhX21v42AYREVEjEPT7UbhoPlyb1kPTrgPiZ/wZCrNF6lh0CSxpREREDZz/zCnk/XsOynLOwDJ6HKxjJ0CQy6WORZfBkkZERNRAiaIId+YGFCz8GDKNFgmPPYWopM6XP5AiAksaERFRA1O0bAksI29B/ifz4NmWBe31SYib/hAUZrPU0egKsKQRERE1MPaMdHi2ZaE8Pw/W8bfDcssYLo5eD7GkERERNRCiKMK59nsAQLCsDE2ffI5Pb9ZjLGlEREQNQMHiBXCuXBF6XWEvxpnXXoRlTBps4yZKmIyuFksaERFRPefduxuerEwICiVskyajcOF8tJm/WOpYdI04QE1ERFRPBf1+FHz6EXLe+jvkZjOavfgqzKkjpY5FYcIraURERPWQ/8Rx5H7wDsrPnoF5xM2wTZgE4dxa2ZYxaRKno3BgSbuEvKIliLNxHJ+IiCKHGAzC8f0KFH25GHKDEQmPP11t7jPeg9YwsKRdQoE9nSWNiIgiRqC4CHn/eRclB/ZD160HYu+dDrneIHUsqiUsaRcRqHABAEr9J6BWtYAgCBInIiKixkoURXi2ZqFg0ccQywOIvXc6DAOH8HdTA8eS9jt5RUtQYE8Pvc4+9QQAQKO+DnHW26DTXg+ZTCVVPCIiamQCLicKPvkQ3h92QJ3YFnH3z4AqvonUsagOsKT9TpxtYmiIc1/2JCTETIfbtxse3884kfP/IBPU0Ed1hkHXFYaoZCgUXGKDiIhqh2fXDhR8Mg8VJT7YbrsT5pG3cOWARoQl7TKsphRYTSkIBsvgLdkPt/cHuHy74fLuBABo1Ykw6LrBoOsGDYdFiYgoDCq8HhQsnA/P1s1Qt2yNhPufhbpZc6ljUR1jSbuEGMv/HmGWyVQw6JJh0CWjiSiitOwE3N4f4PbuRn7xF8gv/gJKhQ2GqK4w6LpCp+3EYVEiIrpi3p/2IP+juahwu2AdOwGWW8ZCUPDXdWPEP/VLuNiTnYIgQKtuBa26FWKtaSgPOOD27Ybbuxt29yYUu1ZDJqihi+pcWeyiukLJYVEiIrqEYIkPhZ8thGvTOqiaNkOTR/8CTavrpI5FEmJJCwOlwgyrMQVW4/nDorvh8v0Ad7Vh0a7QqFpWGRblfGxERI2b75d9yP/wfQSKi2AeNRrWsRMhU3E0prFjSQuzqsOiU88Ni+6G2/vDRYdFOR8bEVHjVOHzoWhx5dUzZVw8mj79ArRt20sdiyIES1otqjosOh7lAQc8vj1wnTcsKghqAIDdtR6GqK5QKEwSpyYiorrg3fMD8j+ZhwqnA+abRsM6dgJkarXUsSiCsKTVIaXCDItxCCzGIcgtXIxCx1cQRT8A4Ez+BwAAhdwGm3kkjLpuUKsSpIxLRES1oHDxQgTsxfBs3wJVsxZo8ufHoWmdKHUsikAsaRKJj56E+OhJACrnY0ts/hpcnl1we39AXtEi5BUtglqZAIOuO4y67tBq2kAQODcOEVF9JYoiPNv/wWHxAAAgAElEQVSy4Fj5DSCXwzpuIiw3j+GTm3RR/JsRIbTq1tCqWyPONhFl5QWV87F5d6HQsQKFjuVQyE2h+dj02hs4vQcRUT0SKC5C/icfwvfjbgBA85f+H9RNOe8ZXRpLWgQ4fz42AFApY2Azj4TNPBIVFR64fXvh8u6C070Fdtc6CIIahqjOMOi6w6DrCoWci+sSEUUiMRiEa9M6FCycDwQCoe2nnvkLAMAyJg22cXxwjC6MJS0CXOrJTrlcD7OhP8yG/giK5fD6zq164P3h3KoHAqI0HWDUdYdB3w1qZXzdBScioosqO3sGBZ9+iJKDv0DbsRNi770fyth4ZE+ZhDbzF0sdj+oBlrR6RCYoYdB1gUHXpXJ6D/8xuLy74PLuQm7RAuQWLYBa1ayysOm6Q6u+LnQfG+diIyKqG8GyMthXZMC+IgMylRoxU+6HcVAKlw2kK8aSVk8JggCtJhFaTSLibLejrDyvsrB5dqHAnoEC+1dQyC0w6LrBqOvGudiIiOqA75d9KPhkHsrzcqHv0x/Rk+6CwlR1xRnLmLSLHE1UlSCKoih1iCvl9/uxb98+JCUlQc05ZaoJVLjh9u6B27sLHt+PCJ6b5sOo7w2jrgcMumTIZVESpyQiajgqXC4Ufr4Q7qxNUMbGIeaeaYhK6ix1LIoQV9tbeCWtAVLIDbAYB567urYjtN3l2QaXZxsAAfqoG2HU9YRR140T6BIRXSVRFOHO3IDCzxchWFoCy+hxsIwexyWdKCxY0hqwONvE0BDnvuxJ6JT4X/hKD8Pl3QmXZyfO+ubibMG5Bw/0PWDU9YBKGSNxaiKi+qHs7BnkfzIPpYcOQNOuA2L/cB9UTZtJHYsaEJa0RkQQZNBpO0Cn7YB4210oLTsBl2cnXN4dyC38FLmFn0Kjbl15hU3fA2plU97oSkT0O8GyMti/Xgb7t8sh02gRO/WPMPQfBEHGCccpvFjSGonfz8V2/rqicbaJ8JflnrvCtgP5xZ8jv/hzqJQJMOp6wKjvee5JURY2ImrcvHt+QMF/P0GgIB+GfgMRfftdkBuNUseiBoolrZG43JOdalU8YlSjEWMZjfJA8bknRXei0PE1Ch0ZUCis5+5h6wGdtgMEQV5HyYmIpFeen4uCRZ/A9+MeqBKaIeGJZxHVsZPUsaiBY0mjapQKK2ym4bCZhiNQ4YHbuxsu7w7YXWtR7FwJucxQObWHvkeVJao4FxsRNTS/zXnmWLEcUMhhu/0umIeN5HqbVCf4t4wuSSHXw2IcCItxIILBUrh9P8Hl2QGXdwcc7g2QCRrodV1g1PXkXGxE1GCIogjf3h9QsOgTBAoLoO/dD9G3T4bCYpU6GjUiLGlUYzKZBiZ9T5j0PREUA/D69sPl3Qm3d+e5qT2AE2f/DqO+F4y6bpDL9RInJiKquaJlS2AbNxFlebkoXPQJfD/tgaophzZJOixpdFVkggIG3Y3wlR5GoMIZ2u727YbbtxtnIEAf1RlGXS8Y9d2hkPPGWiKKbPaMdEAUYf92OQSFEtF33A3T0BEc2iTJ8G8eXZPqc7F9hhL/Mbg82+D0bD83F9s86LTXw6TvBaOuBxQK82XOSkRUd0RRhHf3TgCAffnSyuWcbp8MhdkicTJq7FjSKKwEQUCUJhFRmkTE2e48Nxfbdjg923C24EOcLfgIUZoOlYVN3xNKBe/vICLp5H8yD671a6ps82zdDGVsHGzjeI8tSYsljcLmUnOxxVpvg7/sNJyebXB5tyOncD5yCucjStP+3D1sPaFSRkuUnIgamwqXC0XLvoBrw1rIdHrYxt+GggUfoc38xVJHIwphSaOwudSTnYIgQKNuDo26OeJsE1FadgYuz3a4PNtDqx1o1W1g1PeCSd8TKmVcHSYnosZCDATgXLsKxV99iaC/FKbUEbCOmQC5Xo+CBR9JHY+oCpY0koRG1RQa63jEWsfDX5YDl3cHnJ7tyCtahLyiRdCoW8Ok6wWjvhfUqiZVjuV8bER0Nbw/7UHhfxegPPcstEmdEXPHPVXW2rSMSbvE0UR1TxBFUZQ6xJXy+/3Yt28fkpKSoFarpY5DYVRWnn/uHrbtKPFnAwA0qhaVQ6L63tCommJf9iQkteGQBBHVTNnZMyhcvAC+n/ZCGReP6DvuRtSNXbnUHdWZq+0tYb2S5nK58Oyzz2LTpk3Q6/V44IEHMHny5Gr7LV26FM888ww0Gk1o27///W/07ds3nHGoHlIpYxFtGY1oy2iUlRfC5d0Bl2c78ou/RH7xEqhVzQEA/rKzUKsSJE5LRJGswutBcUY6nGtXQaZSwTbpbphTOaUG1R9h/Zv60ksvoaKiApmZmTh16hTuvfdeJCYmonfv3tX2veGGG/DFF1+E8+2pgVEpoxFtHoVo8yjkFHyKIue38JedAgAcOfl/AACdphMS4u6HWhkvZVQiiiBiIADnhrUozvgSQY8HxoFDYE27HQqjSepoRFckbCXN5/Nh5cqV+Oqrr6DX69GxY0ekpaUhPT39giWN6Eo0ibkHTWLuAVA5H1t89D1wurfCW7ofR048Co36Opj0fWDS94JKGStxWiKSQuV8Z7tQtOS/KM/NgbbD9Yi+426oW7aWOhrRVQlbSTt+/DgAoE2bNqFtHTt2RFZW1gX3P3ToEHr16gWz2YzRo0fjgQcegIKXoKmGfrvCVlZecG7i3K2hhw606jYwGfrAqOvFaT2IGonSY0dRuHgBSg8fhLJJApr8+S+I6sL7zqh+C+uVNJ1OV2WbwWCA1+uttm+PHj3wzTffoGnTpjhy5AhmzpwJQRDw4IMPhisONWDnz8emUsacdw9bHpznCltu4QLkFi5AlKY9TPreMOp7ceJcogaovCAfRemL4dm2BXKDETH3TINxUAoEuVzqaETXLGwlLSoqqloh83g81YobADRv3jz0/9u3b48HH3wQH3zwAUsa1cjFpt9QKeMQYxmDGMsY+MvOwunZDqdnK3IKP0FO4aeVKx0Y+sCk68mlqYjquQqvF/ZvvoJj9XcQBAGW0eNgGTUaMm2U1NGIwiZsJa1Vq1YAgKNHjyIxMREAcODAAbRt2/ayx/JyNIWbWpWAWOs4xFrHnZs4dyuc7q3IKfgIOQUfn1tLtA+M+p5c/J2oHihatgS2cRMrHwpYvxrFX6Uj6PPC0HcAbGm3Q2G1SR2RKOzCeiVtxIgRmDNnDl599VWcPn0a6enpePPNN6vtu3HjRnTq1AnR0dE4evQo3n33XYwYMSJcUYiqqJw4dwJiLGnnlqbaAqdnK84WzMPZgo+g1yadu4etB+RyPQBOmEsUaewZ6VA3b1n5UEBeLrTXJyH69rugbtlK6mhEtSask9m6XC7MmjULmZmZ0Ol0+NOf/oTJkyfj7NmzuPnmm7FixQokJCTg9ddfR0ZGBnw+H2w2G2699VbMmDEDSqWyRu/DyWzpWomiiNKyE3Ceu8JWHsiHAAX0ui4w6/viVN7bnDCXKEKUHDqAM6+9CABQJTSDbdJkRN3QhaMwVG9cbW/higPU6ImiiBL/MTjdWXB6tiJQYQcAmPT9YTb0hT6qMwSBTx4T1bX8+fPg2rCm2nbLmDTYxvFKN9UfEbHiAFF9JAgCojSJcHt3hwoaADg9m+H0bIYAJczGgTAb+iFK0wGCIJMwLVHDV16Qj6KlX8CzLQuyKB0st4xB0Rf/RZv5vLpNjQtLGtE5cbaJofvQ9mVPwvWJC+Hx/QinOwsO92bYXWuhkFthMvSBWd8PGnVrDrcQhVHA5YR9+TI416+GIJPBfNNoWG6+FXKdHkVf/FfqeER1jiWN6CJkggJGXTcYdd0QDJbC5d0NpycLxY6VKHKsgEoZD5O+H8yGvlCrmkodl6jeCpb4YF+5Ao6V30AsL69cxmlMGhSW/81taBmTdokzEDVMLGlEF3D+hLkAIJNpYDb0hdnQF4EKD1yeHXB6slBgX4oCezo0qlYwGfrBpO/DVQ6IakgsL6+cTuPrZQi63dB17wVb2u1QNUmoti/vQaPGiCWN6AIuNf2GQq6H1ZQCqykF5QH7uSdEs0LLUkVp2p8rbL05BxvRBYjBINxbN6N42RIECgug7dgJtol3QnNdotTRiCIKSxrRNVAqLKF1RP3luXC6t8LpyTo3ae586KM6w2zoD6OuO2QyjdRxiSQlBoPw/rADRcuWoPzsGahbtkbslPsRldRZ6mhEEYkljShM1Mp4xFrHIcYyFv6yk3C4t8DpycLpvH9BJqhh1PeEydAfem0SBKFyXUFOmkuNgSiK8O3djaKlX6Ds1AkoE5oifsaj0HXvCUHGp6WJLoYljSjMBEGARt0S8eqWiLPdDl/pITjcmXB6tsHhzoRCboZJ3xdmwwAU2NNZ0qjBEkURJft/QtHSL+A/dhTK2DjETX8Q+t79WM6IaoAljagWCYIMOm1H6LQd0SR6Cty+vXC4M1Hs/B5Fzm8BAAXFX8Fk6AeVMkbitEThU3LoAIrSP0fp4YNQ2KIRe+90GPoNhKDgrx2imuK/FqI6IpOpYNL3RKn/BNzenaHtecWLkVe8GAp5NGKt42DS9wqtIUpU35QePYKipV+gZP/PkJstiL7rXpgGpUCo4bJ/RPQ/LGlEdez3k+a2a/k2HO4sONyZOFvwH+QUfAyDrivMhv7Q65IhE/jLjSJX0bIlsI2bCP+JX1G0dAl8P+6GzGCAbdLdMKUMg0ylkjoiUb3FkkYkMZUyNvTAQan/VzjcmXB4tsDl3QGZTAeTvjfMhv6I0rTnklQUcewZ6Sg7cxreXdshi9LBmnY7zKkjIdNqpY5GVO+xpBFJ6PxJcwVBgFZzHbSa6xAffRc8vp/hcG8OLUmlVMTAbOgPs6E/VzggyflPn4J9eToAwLfvR1jGpME8fBTkOp3EyYgaDpY0Igld7MlOQZDDoOsCg64LKoKlcHt3wuHejAL7VyiwL4NWnQizYSBMhr5QyA11nJoaM/+pk8h9dw7Kc86EtomlpbBnVBY2rgxAFD4saUQRTi7TwGwYALNhAMoDjnMLvm9ETuHHyC38FAZdN5iNg2CIuhGCwH/SVDv8J0+gOCMd3h92QNBoYRk9DuYRo/DrQ/ejzfzFUscjapD4E52oHlEqzIi23Ixoy80o8R+Hw7URDk8WXN4dkMuNMOv7wWwcBK26VegYTphL18J/4lcUZyyFd/dOyLRaWG4dXzmsqecTyES1jSWNqJ7SqltBG9MK8dGT4fb9CIdrI4qdq1Hk/A4aVQuYDYNgNvTjhLl0VUqP/wp7xpfw7vkBMm3UuXvOboJcV7WcWcakXeQMRHStWNKI6jlBUMCo6wajrhsCFW443VvgcG9CbtEC5BYtAgA4PdtgiOoKmYzTIdCllf56FMVfpVdOpRGlg3XcRJhSR170gQDeg0ZUe1jSiBoQhdwAm3kEAhUulPiPAggCAE7lvgUA0KhaIyF2KrTqNhAEQcKkFGlKj2WjOCMdvh/3QKbTwTr+tspyFhUldTSiRosljagB+v2EuS0TnoLDtQku704cO/0sVMoEWAwDYTYOgFJhkzgtSUUURZQeOoDir5ehZP/PkOn05+Y5GwGZluWMSGosaUSNgCHqRhiibkRF0Fe50Ltr07nlqD6HTpsEi3EQjLqeHA5tJERRhO+nvbB/vQyl2YchN5pgu+1OmIYM4yS0RBGEJY2ogTt/wly5LApWYwqsxhT4y3PhcGXC4d6E03n/gkwWBbO+HyzGwdCor+NwaAMkBoPw7tqB4m++QtnJ41DYohFz91QYBgzm8k1EEYgljaiBu9iTnWplPOJsExFrTYO35ADsrvWwuzeg2LW68ulQ42CYDf2hkBvrODGFy2/raoqBANxbN8O+YjnKc89CGd8EsdMegKFPfwgK/hogilT810nUyAmCDPqoTtBHdUJFxb1werbA7tqA3MJPkVe4CAZdd1iMg6GPupFrh9Yz9ox0KIwm2L9djkBRIVQtWiF+xqPQde8JQcY/S6JIx5JGRCFyuQ5W0zBYTcNQ6j8Ju2sDHO5MuLzboZBbYTEOhNkwGGpVvNRR6RKCJSVwrl8NAChY8BE0bdoh5p5piOrchcPYRPUISxoRXZBG3QJNYu5BXPSdcHt/gN21AQX2DBTYv0KUpiMsxiEw6XtCJtNwVYMIUeFxI+ed2Sg9dKDK9tLswyg9lg3djckSJSOiq8GSRkSXJBMUMOl7waTvhfJAMRyuTbC7N+BM/rvIKfgYJkMf2F3rEGudwKs0EikvKoRj5Qq4Nq2D6PdD17UHLLeMxemXnuG6mkT1GEsaEdWYUmFFjHUsoi1j4Cs9eG44NAsAkH3ycViMg2E2DIBCYZY4aePgP3USjm+Xw719CyAIMPTuB/NNo6Fu1lzqaEQUBixpRHTFBEGAx7cPDvfG0DZ/+RnkFi1CbtF/YdT1gMU0FHrtDXzYIMx+m4DW/u1y+H7aC0GthmnYSJiHj4LSFl1lX66rSVS/saQR0VX5/aoGSW0Wo7TsDOyudedWN9gBpSIGFuMQWIyDoVRYJU5cv4nBILw/7IT9u+XwHzsKudEEa9rtMKUMq7bo+W+4riZR/caSRkRho1E1RZPouxFnmwSXZyfsrrXIL/4C+cVfwqBLhsWYAkNUMq+uXYFgWRncWzbB8d03KM/LhTIuHjF/uA+GfgM5AS1RA8eSRkTX7PxVDQBAJihhNvSF2dAX/rLcyqtr7o1we3+AQmGFxTAEFuMQqJTRFzkjVXi9cK5fDeeq71DhckLd+jrEP/godN04xxlRY8GSRkTX7FLTb6hV8YiPvhNxttvg8u6G3bUWBfalKLAvhT7qRliNKTDoukIQ+OMIAALFRXCs+hbODWshlpYiKulGmG++FdoO1/PpWaJGhj8ViahOCIICJn1PmPQ9UVaeD7trA+yu9TiZOxsKuRlm4yBYjSlQKeOkjioJ/4lf4Vi5Au4dWwFRhL5XX1huGg11i5ZSRyMiibCkEVGdUyljEWe7DbHWNLh9e2F3rkOhfTkK7RnQaW+ovLqm7wFZA766VrRsCaxj0uD7aQ8c33+LkgP7IWg0MA0dDvOwm6CMiZU6IhFJrOH+BCSiiCcIchh13WDUdUN5oCh0de1U3hzICwywGAfDYhoKtbJyGaqGsrJB0O+HPSMdnu1bUZ57FgqrFbbbJ8M4aCjkUVFSxyOiCMGSRkQRQamwIdaahhjLOHh8P8PuWoNCxwoUOr4+d+/aMBTY0+t1SQs4HHCu/R7O9WsAADKNBnEPPAx9914QFPxxTERV8acCEUUUQZDBoLsRBt2NKA8Uw+5aj2LnWpzM/ScAIL84HRbjkHo175r/1Ek4Vn0L9+aNgCj+b/vxY8h7/x2UjTnLOc2IqBqWNCKKWEqFFaIYRKCiOLQtv3gJ8ouXQKVMQELMvdBpO0XkvGuiKMK37yc4vl+Bkn0/QVCpYBoyDKbhN0EV3wTZUyZxXU0iuiSWNCKKaL9f2aBty7dgd66F3bUBx8/+DSplPKzGVJiNg6CQGyROWzn5rGdbFhzfr0DZmdOQm8yVKwMMSYVcL30+Iqo/WNKIqF5RK+MRHz0ZsdaJcHl3oNi5GrlFC5FX/DlM+j6wmoZBq25T53OKBRwOONevhmv9GlS4nFA1b4HY+2fA0LMPBKWy2v5cV5OILocljYjqjfNXNpDJVDAb+sNs6I9S/0kUu9bA4cqEw70JGlUrWE2pMBn6Qy7T1Gqm0uPH4Fz1HdzbtwAVFYjqnAzzyFHQdky6ZFHkPWhEdDmCKJ53F2s94ff7sW/fPiQlJUGtVksdh4giREWwBE53Foqda1BadhwyQQuzcQCsxmHQqJuH7X3EQACe3TvhXPUdSrMPQ9BoYOw/GKbUEVDFNwnb+xBRw3C1vYVX0oiowZDLtLCaUmExDkWJPxvFztXnng5dBZ22E6ymETDqukEQ5Fd1/gqPG64N6+Bc9z0CxcVQxsYh+s57YOg/mPObEVHYhbWkuVwuPPvss9i0aRP0ej0eeOABTJ48+YL7Lly4EB988AE8Hg8GDRqEV155BXq9PpxxiKiREgQBUZq2iNK0RXz0XeeK2mqcyp0NpcIGq3EYLKYUKOTGGp3Pf+oknKtXwr01E2J5ObTXJyHm7mmIujGZi50TUa0Ja0l76aWXUFFRgczMTJw6dQr33nsvEhMT0bt37yr7ZWVl4V//+hc+/vhjNG/eHE8++SRefvllvP766+GMQ0QEhdyIGMsYRJtHw+3djSLn98grXoz84i9hMvSF1TQCUZrE0P7Hs15Eq37PQwwG4d27G87V31Uu2aRSwdBvIEzDRkLdNHxDp0REFxO2kubz+bBy5Up89dVX0Ov16NixI9LS0pCenl6tpC1duhTjx49Hx44dAQAzZ87E2LFj8cILL0Cr1YYrEhFRiCDIYNR3h1HfHaVlZ1Ds/B4O1yY43JugVbeBzTwCRn1veOIOwPH9CjjWfI9AQT4UVhtsE++oXLKJV/uJqA6FraQdP34cANCmTZvQto4dOyIrK6vavkeOHMGgQYNCrxMTK/8r9sSJE+jQoUO4IhERXZBG1RQJMVMRZ5sEh2sTipyrcDrv3xBOzQVUQME3C6Bt0h7Rt90JXdceEORXdw8bEdG1COuVNJ1OV2WbwWCA1+u94L4Gg6Havh6PJ1xxiIguSyaqoT5igZhtB3oAoqocAOD/M+DHIZTaS5Ao6yVxSiJqrMJW0qKioqoVMo/HU624/bbv7wuZx+PhgwNEVCcCTgdcG9fBuX4NKuzFUNuiEWscC+PAITiQNx3R5tGwu9ah1HIS2af+CptpBMyG/pDV8pxrRETnC1tJa9WqFQDg6NGjoeHLAwcOoG3bttX2bdu2LQ4ePIjRo0eHjhFFES1btgxXHCKiKkRRRGn2YTjXroJn5zagogLapM4w3zMVUTd2/d9Tmnk4t6LBBDg9W1Dk+B5nC+Yht+gzWI0psJpGQKWMlvabIaJGIaxX0kaMGIE5c+bg1VdfxenTp5Geno4333yz2r7jx4/H448/jtGjR6NZs2aYM2cORo0axYcGiCjsgn4/PNuy4Fy3Cv4TxyHTamFKGQZTynComiRU21+f1xFoA8hkaliMQ2A2DIav9BCKnCtR6PgGhY4VMOp7Ito0ClpN2zpffoqIGo+wrjjgcrkwa9YsZGZmQqfT4U9/+hMmT56Ms2fP4uabb8aKFSuQkFD5Q3HBggX44IMP4PV6MXDgQPztb3+r8XAnVxwgosspyz0L5/o1cG/eiKDXC1Wz5jClDIeh7wDINFc3bFlWXoBi5yoUu9YiGPRBq06EzTwKJn0vCALnBieiC7va3sJloYiowRADAXj37IJz3WqUHNgPyOXQd+0B09Dh0LTvGLarXhXBUjjcm1Dk+A5l5TlQyC2wmUbAYhoKhdxw+RMQUaPCZaGIqNEqLyqEa+M6uDatR4XDDoUtGtbxt8M4cAgUZnPY308u08BmGg6rMRUe348odHxbOUGuPR1mw0DYTCPDulYoETVOLGlEVG8ULVsC27iJAAAxGIRv309wrV8N797dAICoG7rANOU+RHWum+WaBEEGgy4ZBl0ySv2nUORcCYd7E+yutdBpb0C0eRT0UTdCELh0FBFdOZY0Iqo37BnpMA8dAVfmejg3rEWgIB9yowmWm2+FcdBQKGNiJcumUTdH09j7EWe7HXbnOhQ5v8eJnNehUjaBzXwTLIaBVabwyCtagjjbRMnyElHkY0kjoogniiJKDx8EAPz6fzOAQACa9h1hS5sEffeeEBSR86NMITcixjoW0ZZb4PRsR5HjW+QUfIS8os9hNabCZh4BpcKKAns6SxoRXVLk/GQjIvqdYIkPOe++jZKf9/5vYyAAANB2uB6G3n0lSnZ5gqCA2dAPJn1flJQeQaHzWxQ6lqPI8Q1Mhn5SxyOieoAljYgiiiiK8B8/BteGtXBvy4Lo90Pd6jqYhqQi/+O5aDN/sdQRr4ggCIjStkMLbTucLZiP4nP3rQHAvuxJAIAYSxqvqhFRNSxpRBQRKnw+eLZuhnPjOpSdPA5BpYK+V1+YhgyD5rrKVUzyP54rccprkxAzBQkxUxCo8ODgr/dBITcjUOGA27sLalU8TPo+nG+NiEL404CIJCOKIkqPHoFrw1p4dmyFWFYGVYtWiLl7KvS9+0H+u7V/LWPSJEoaXgp55cTd7Vq9A6c7C4WOb3A679/ILfwMNvNNsBqHQi6PkjglEUmNJY2I6lyFxwP3lk1wbVyHsjOnIWg0MPTpD+PgoVC3uu6ik87+Nv1GQxBjSYNMUMJiHAyzYRA8vr0odHyDvKJFKCheCospBTbTTVwnlKgRY0kjojohiiJKDx2Ac+M6eHduhxgoh7p1ImKm3A9Dr76QNbK1e8+/B00QhNB8ayX+X1FoX4Eix3cocnwHk743os2jodW0ljAtEUmBJY2IalWFywVX1ka4Nq5Hee5ZyLRaGAcOgXFQCtQtW0kdL+Jo1a3RPP4hxJVPQpHzO9id6+D0bIFO2wnR5luhj+rMRd2JGgmWNCIKOzEYRMmB/XBtXAvPDzuBigpo2rSDZdoD0PfsDZn66hY4b0xUymg0ib4bsZY0FLvWosjxLU7kvAaNuhVizLfCqO/NlQyIGjiWNCK6Zr8t1xRw2OHavBGujesQKMiHTKeDKWU4jINToG7KtSyvhlwehRjLaNjMI+F0b0aB/WucynsbquLPEW0eDbNhIGQyldQxiagWsKQR0TURAwHYM9LhP3Ecvp/2AMFg5WoA42+DrltPyFQsEOFQ+ZDBEJgNg+D27kKBPQNnC+Yhv3gJbOZRsBqH8YlQogaGJY2IrkrZmdNwZW6Ae0smAMD/61GYR94C44DBUDVJkDhdwyUIMhj1PWHQ9YC35BcU2jOQV/QZCuxfwWocDtv/b+/O46MqD/WBP2dmMklmyyyZTMiCGBBIDdkICbsWgyiyBkFQsVqo18qtQpVCbV1ui1Z/9bpg1WpLaxW1FQOES6lo3YkhJDjTP1oAACAASURBVCAosoSdkD2TSTJbJsuc3x+RKYEASZjkzCTP9/Phj5kzc/KcDDPz5Czvq78ZIQo9AM4PShTsWNKIqMu8bhfshQVo/PIzeI4d6bCsraEe9du2QAgJ6VdDZQQqQRCgUV0LjepauJtOoKY+r33aqYZtMGivg8kwg/ODEgU5ljQiuqSzQ2c0fvkZHEU72wecjYmD6bY7oZ0wCQpdBI7evTDopmvqT8LDrsbg6OXwNFegtn4rbI2foa7xYwCA23MS4aFDpA1IRD3CkkZEnWqts6Ix/wvYv/wMLdVVEMLCoR0/CbpJ1yM0YRiHgQhAocpBUMj1ENHqu+9Y6WoAgF57HeIsP5UqGhH1AEsaEfmILS1w7t2Nxi8/g+vbfYAoInzkD2CYPQ+ajCzIQkM7fV5/ma6pP7CY5vsOce4/uhAW0yLU1m9Dvf1zNLdUI8qYA3V4Eks2URBgSSMieEpPo/HLT2H/age8DjsURiMMM+ZAN+k6hERFX/b5PActcJkNs2GKuBm2xk9QY9uCk+VPIjx0GMzGudCq0lnWiAIYSxrRANXmsMO+Mx/2/C/gOXEckMuhSR8D7aTroUpKhiDjQKnBzmxo38Mpkylh0t8EQ8QNqG/8HDW2PJyu+D3ClENgNs6FTj2GA+MSBSCWNKJ+7uxAs0D7mGbOb/bCnv85nHv3AG1tUA4egsg7fgTt2AmQa3USpyV/Ov/KTpkQAmNENgy661Fvz0eNbTNKK59HqDIOZsMcRGjGQRDkEqUlovOxpBH1c7a8XKjTMmDP/xz2nfnw2u2Q6yKgz74J2omTERp/ldQRqY8JggIG3XXQayeh0bET1bZNOFP1B1TXvQ+zYTYitJMgE/j1QCQ1vguJ+qnWehvsBTsAAGee+CWgUECTlgHthMlQjUqBIOcek4FOEGSI0I6HTjMWduduVNs2oaz6NVTX5SLSMAsG7fWccopIQixpRP2It7kZzq+LYc39B1qrqzoubG1FSEws1Knp0oSjgNU+i8EYaNUZcLj2otq2ERU1f0FN3SZEGmbAqMuGTNb5lb1E1HtY0oiCnCiKaDp2BPYdn8NRWACv2/X91ZmzoR0/GacfeYgDzVKXCIIArToNGlUqnO4DqLFtRGXtW6i1/R8iDbO+L2vcs0bUV1jSiIJUi7UW9vwvYc//HC1VlRCUSmhGZ0I78TqEJ17LqzOpx86dcsrpPojquvdRWfsmam1bLihrnB+UqPewpBEFEW9TExy7d8G+43O4Dx0ARBFhIxJhmDGnfbDZ8PALnsOBZulKqMMTcXXso3C6D5xT1v4PZsNsGHRTOD8oUS9iSSMKcGJbG1zffQt7wQ44dxdBbPZAYY6CcfY8aCdMRog56pLP50Cz5A/q8B/g6tjH4HB9h+q691FR+wZqbFsAAF6xBTIhROKERP0PSxpRABJFEZ6Tx2H/agcchV+hrbEBMrUa2vGToB03AWHDR3KkeJJE+yHQA3A1HURrWx0A4MCxxQCASMNcRJtukzIeUb/CkkYkoXMHmgWAlppq2At2wP7VDrRUlgMKBdSp6dCOmwR1ciqEEO6tIOmdnR9UFEV8d2wRVGEj4Go6jAb7F1AqjNDrfshx1oj8gO8iIgnZ8nKhn3oTHLt2wl6wA01HDgMAwkYkQn/TLdCMyYJcrZE4JVHnzu7NvTr2CTjd+1FdtwHlNetQY8uD2TAXBt11EFjWiHqM7x4iCXibm+Ha9zUA4MSD9wFtbQiJiYXx1oXQjp2AkEizxAmJusZsmPf91aCjoA5PgsP9Daqt76O85k+ord+CKON8RGjGc25Qoh5gSSPqI6LXi6aSQ6h55000nz75nwVtbQAAzZixMM6YI004oh4698pOQRCgVaVAE54Mh+trVFn/gTNVf0CNLQ8W423QqkfzXEqibmBJI+plnrLS9gsACnagtc4KITQU2gmToR03EeXPPsWBZqnfaR8UNx0aVSoaHYWoqnsPpyufRXjoUFhMt0EdPopljagLWNKIekGLtRaOXQWwF+S37zWTyaBKSoFpwe1Qp42GLDRM6ohEva59btBx0GkyUW//EtV17+Nk+VNQh/8AFuNtUIWPkDoiUUBjSSPykzZ7IxxFhbAXfoWmwwcBAKFXD0XkHXdDkzUOCl3EBc/hQLM0EAiCHAbd9YjQToCt4WPU2DbheNnj0KrSEGW6DeGhQ6SOSBSQWNKIroDX7Ybz62LYd+bD9d23/7kAYO58aMZOgNISfcnnc6BZGkhkQghM+ptg0F0Pa8N21Nq24Fjpaug0Y2ExLkCoMkbqiEQBhSWNqJvElhY4v9kLx858OPftgdjcDIUpEvpp06EdOxHK+ME834boEmSyMJgNs2HUZaO2fius9dvQ6CiEXnsdooy3QhkSKXVEooDAkkbUifMHmRXb2uA++B3shV/BWbwLXrcLcq0OuknXQzN2AsKGXsMJzYm6SS5Xw2K6DaaIm1Bjy0Ndw4docOTDFHETzIbZkMs5RiANbCxpRJ2w5eXCOOdWNB07AsfOr+DYVYC2xgYIYeHQjB4DzdgJUP0gCYJcLnVUoqCnUERgkPkumPQ3o7ruPdTWb4Wt8ROYDXNgjJgGmUyJKusGTuROAw5LGtF5PKWnAQCnfvEgWmuqIShCoEpNgzZrAlQpaZAplRInJOqflCFmxFmWwaSfgSrrO6i0vg1rwweIMi5AjS2XJY0GHJY0IgAt1VWo+uvraDr4ne++1ppqAEDEjTcjcsHtUkUjGnDCQ6/CkJhfwuHajyrrOyirfhUAYHd+DY0qled80oDBkkYDVou1Fo6iQjh2fQXP8WMAgLBrRkCTNR616//KQWaJJOZ0H4Tbc9x3+1TFMwAAvfaHiLP8l1SxiPoMSxoNKK22OjiKC+EoLEDT0RIAQOhVV8M0fxE0WeN9c2bWrv+rlDGJCO1TTp09xLn/6EIMirwb1baNqLd/Cq/ohsV4G0KVgyROSdR7/FbSmpubsWbNGmzbtg0KhQKLFi3Cgw8+2OljCwsL8aMf/Qjh4eG++x555BHMn8/zDcj/Whvqv99jVoCmI4cBUYQyfjCM826DZsxYKKMv/JDnILNEgcekvwl63WTU2v4Ja/1WNDqKYIzIRpRxHhRyndTxiPzObyXt5ZdfxuHDh/Hhhx/C5XLhnnvuQVxcHObN6/zLzmQyIT8/318/nqiDtsZGOHbvgmNXAdyHDrQXs9g4GOfc2l7MYmIv+XwOMksUWMyG9u8SuUwFi2k+jBFTUVP3PuoaPkS9/UtEGXJg1E+DTAiROCmR//itpG3cuBFr1qyB0WiE0WjEPffcg9zc3IuWNCJ/a3M4/lPMDn4HeL0IiY6BYVYONJljERobL3VEIuqh86/sDFHoERO1FMaIaai0vo1K63pYGz5EdOQd0KkzeXEB9Qt+KWkNDQ2orq7GyJEjffclJibi+eefv+hz6uvrMWHCBISGhmLKlClYsWIF1Gq1P+JQP3fuQLNtTiece4rgKNr5n2mZoiwwTJ8FTdY4KOM4+j9RfxYWGo8hMathd+5DpfUtlFY+D1XYCERH3gVV2FCp4xFdEb+UNJfLBQDQaP4zOrROp4PT6ez08QkJCcjLy0NCQgLKysqwevVqPPnkk3jqqaf8EYf6OVteLpSWaNgLC+Davw9oa4Mi0gz9tFugyRyH0KuGsJgRDTBadQo0qiTYGj9FVd0GHD/zK0RoJsJiWshppihodamkLVmyBDt27Oh0WWxsLDZt2gQAcDgcvr1hdrv9onvGzGYzzOb2q+ji4+OxcuVKLF26lCWNLsrrdsO5bw8cu3YCAKpefxkKown6qTe1F7Orh7KYEQ1wgiCHMSIbEdrxqLHltc8J6ixEpH4GIg2zIJeFX34lRAGkSyVt3bp1l31MVFQUDh06BIvFAgA4ePAgrrnmmi6FEAQBoih26bE0cLS5XHDt3Q1HUSGc+/YAXm+H5a11VgihYQhLGCZRQiIKRHKZCtGmRTDqslFl/TtqbJtga/wEUcbbYNBdD0HgPLsUHPx24UBOTg5effVVjBo1Cm63G2+88QbuvffeTh+7c+dOxMfHIyYmBpWVlXj22WcxdepUf0WhINbmcMD5dTEcxYXt55i1tkJuMCLihmnQZGQi7JoROPbj2znQLBFdljLEjPjon8HUdBMqat9Eec3rqGv4AIPMd0Md/gOp4xFdlt9K2rJly2Cz2TB16lTfOGnnXtmZlpaGP/3pT8jIyMDBgwexcuVKNDY2Qq/XY+rUqVi+fLm/olCQabM3wrGnGM6iQrgO7m8/x8wUCX32NGgyxiI0YSgEGf/yJaKeUYVdg4TY36DRUYBK6zs4UfYbRGjGwWK6g+erUUATxCA8zujxeLB//34kJSUhNDRU6jjUA60N9XDuLoKjuLB9HDOvFyFRFqgzsqAZk4XQIQkXPcfs3Ks7iYi6w+v1oMa2BbX1WwAIMBvmIFI/AzKZElXWDZzEnXpFT3sLp4WiPtM+JdMuOIoL0VRyCBBFhEQPguGW2dBkZEE5+KounfzPgkZEPSWThcJimg+D7jpU1q5Hdd17sDV+hkGRd6LGlsuSRgGFJY38prM9XC3WWjiLC+EoKvTNlamMjWsfYHbMWChj43hVJhH1OWVIFAYP+jkcrv2oqH0DpyufAwA0NZ9BmDJO4nRE7VjSyG9sebkwzZ2Pluqq9knMiwvhOX4MAKAcPATGnNugyci87JRMRER9xek+CE/zGd/to6cfBgBE6mchOvJ2qWIRAWBJIz9pLi8DAJQ+vhqeUycBAKFXJ8A0fxHUGVlQWqIlTEdE1DmLab7vEOf+owth0GXD1vgxbPbPoAyJ5pAdJCmWNOoRURThOXUCtW//DU1HDvvuP1vQIqbeBPMdd0sTjoioh2KjlsIYcQMqat5Aec3rsDV+jBjzEoSHJUgdjQYgljTqMtHrRVPJITh274JzTzFarbWATIbwxGuhHj0Gtevf4PhlRBS0zIb2YaPCQ6/G1bFPoMGRj8rat3DszK9gjJgKi/E2yOWcY5r6DksaXZLY0gLXd9+2T2L+dTG8djsERQjCk5JhnHMr1GmjIddoAQC169+QNiwR0RU498pOQRCg106EVpWGqroNqGvYjgZHIQZF3okIzURe8ER9giWNLuB1u+H8di+cxbvg/GYvxCY3hLBwqFPToEnPhCo5FbKwsAueZ5g9r5O1EREFL7lcjRjz3TBor0N5zZ9xpupl1DV8ghjzjxEWGi91POrnWNIIQPuo/86vd8Oxuwju776F2NoCuVYHbdY4qEePgSoxCUJIyCXXwfHLiKi/Cg+7Gglxv4Wt8VNUWd/B0dLViNRPh9k4D3LZhX+0EvkDS9oAcdExzPYUwbm7CO7DBwFRhMIUCd2UbGhGt8+TyemYiIjaCYIMxogboNOMQWXtO6it/z/UO/IxKPJu6NRjeAiU/I4lbYA4O4ZZc3kZHHuK4Ny9C54TxwEAypg4GGbMgXp0JkKvGsIPGiKiS1DIdYiz3Aej7ocor1mH0srnoFGlIsb8YyhDoqSOR/0IS1o/J3q98JxoH1D21CMPoeX78cxCE4a2j2E2egyU0TFSRiQiCkqq8BEYGv87WBu2o9r6Ho6cfhgW43yY9NMhCHKp41E/wJLWD3mbm+E++B2sG99D86kTvvvPFrSIG6fDfPtdUsUjIuo3BEGOSP106NSZqKj5Kyqtb6PekY9Y808QHjZU6ngU5FjS+ok2hwPOfXvg/LoYrv3fQGxqghAWBnVGFjTpGah6/WWOYUZE1EuUIZEYPOhhNDp3oaLmDRw782uYIm5GlGkBLyygHmNJC2ItNdVw7imG8+tiuEsOAV4v5HoDtGMnQp0+usMVmVWvvyxxWiKi/k0QBERosqAJT0KV9V1YG7ah0bkLMeYl0KrTpI5HQYglLYiIogjPyePtxWzvbjSXngYAKGPjYJg+C+r0DIQOSej0ikyOYUZE1DfkcjViopYiQjsR5dV/wqmKZxChGY9BkXdBodCjyrqhw8C5RBfDkhbgxNZWuA99B8eeYji/3o02Wx0gCAgbPhKmhYuhSR+NkKjLT17OMcyIiPqWOnwkhg5+GrW2Laip2wS7ax+iTXegxpbLkkZdwpIWAM4fw6zN6YTr271w7imG69u98LrdEJShUI1KhjrtNqhT0iDX6iRMTEREXSETQhBlnIcIzTiUVf8J5TWvAwCaW6o5XAddFktaALDl5UI3+Ydwft2+t8x96ADQ1ga5LgKaMeOgTh+N8B+MgkyplDoqERH1QL09H66mg77bJaceAACYDTmwmBZIFYsCHEuaRESvF55TJ+DcuwcAcOqh/wYAhAyKgX7aLVCnZyAsYRhH/Cci6gcspvm+Q5z7jy6ERpUCh2sfnO4D8DRXIFQ5SOKEFIhY0vqQ1+OB+8C3cH69B/bCryB6mi54jCZzHM8fIyLq564atBr19s9RUfsmjpb+AhbjQpj0N0MQ+Ic5/QdLWi9rrbPCuXcPnHv3wH1wP8SWFsjCw6FOToUqNR3q5FSc+Nm9HMOMiGiAMBvmQRAEGHTXQ6NKRnn1OlRa30KDYydiLfchTBkrdUQKECxpfiZ6vfCcPAHn3t1w7t2D5tMnAQAKcxR012dDnZaO8OGJEBT81RMRDUTnXtkZojBi8KCH0eDIbx8Et3Q1ooy3IlI/g1NLEUuaP3g9TXB9tx+uvbvh3Pc12hrq24fJuGY4TAtuhzp1NEIGxVx04nKOYUZENHAJggC9diLU4UmoqPkLqqzvotFRiFjLMu5VG+BY0nqoxVoL177vD2Me+A5ia/thTNWoFKhTR0OVnAq5RtuldfEcNCIiClHoER+9Ao2OnSiv+QuOla6GxbQIpoibeK7aAMWSdgnnjl/WfhjzOJxft+8tO3sYMyTKAt2UbKhTeRiTiIiujCAIiNCOgyo8EeXVr6Oy9k3YncWIjfoplCFmqeNRH2OjuARbXi5CBw9p32PW4TDmiC4dxiQiIuqJEIUegwethM3+KSpr3sTR07/AIPOPoNdex++cAYQl7SKajh4BAFS+9L89PoxJRETUU4IgwKibAk14Es5UvYKy6j+i0VmMWPNPoFBESB2P+gBL2nmsmzbAlpfb4T6v242QQbHQjp8kUSoiIhqolCFRuDr2MVjrt6HK+nccaVqJWPNPoNOMkToa9TJBFEVR6hDd5fF4sH//fiQlJSE0NLTXfs7Ruxdy/DIiIgoYTZ5SnKl+GU2ek9BrJ2OQ+W7IZSqpY9Fl9LS38HIRIiKiIBEWGo+EuDUwG+ai3v4ljp5eDVfTEaljUS9hSbsEjl9GRESBRiYoYDHdhqtjnwDgxfEzj6O6bhNE0St1NPIzlrRL4PhlREQUqNThIzAs/hlEaMaiuu4fOFH2WzS31AIAqqwbJE5H/sCSRkREFKTkcjXiLD9DbNT9aPKcwNHSVWhw7ESNLffyT6aAx5JGREQUxNona5+MofFPIzQkGqWVLwAAvN4miZPRleIQHERERP1Avf1LuD3HfLcPHL8bAGA2zOswqTsFD5Y0IiKifsBimu8rY/uPLoRCbkRbWyMUci1EUeRMBUGIhzuJiIj6oWGDn4FGNQoVtW+gtPJ5tLW5pI5E3cSSRkRE1M+YDfOgkGsxeNBKWEx3oNFZjKOlq+FuOi51NOoGljQiIqJ+5uxhT0GQwWyYiYTYxyGiFcfPPAZr/QcIwsmGBiSWNCIion5O9f2Yajz8GVxY0oiIiAYAHv4MPixpREREA8QFhz/LHkdd4ydSx6KLYEkjIiIaYNoPfz4NVdhIlFe/jrLq1+H1Nksdi87jl5K2bds2LFy4ECkpKVi8ePFlH79r1y7MmDEDKSkpWLBgAY4cOeKPGERERNRFCrkOQ2J+iUjDbNgaP8GJsid8c39SYPBLSdPr9bjrrrvwk5/85LKPtdlsuP/++3HvvfeiqKgI2dnZuP/++9Ha2uqPKERERNRFgiBDtGkRBkc/BE9zBY6V/hIO17dSx6Lv+aWkjR8/HtOnT4fFYrnsYz/66CMMGTIEs2bNglKpxNKlS+F2u1FUVOSPKERERNRNOs0YDI1/EgpFBE6WP4UaWx6H6QgAfX5OWklJCUaOHPmfADIZRowYgZKSkr6OQkRERN8LVcYgIW4NdJosVFnfbR+mw+uWOtaA1uclzeVyQavVdrhPq9XC6XT2dRQiIiI6h1wWhnjLg4g2LUajsxjHzzyK5pYqqWMNWJedYH3JkiXYsWNHp8tiY2PxySfdu3RXpVLB4XB0uM9ut0OtVndrPUREROR/giAg0nALwkKvQmnlCzhW+ivER6+ARnWt1NEGnMuWtHXr1vn1Bw4fPhwbNmzw3RZFEYcPH8bSpUv9+nOIiIio5zSqJCTEr8HpimdxsvxJDDLfDVPEjVLHGlD8crizra0NHo8Hra2t8Hq98Hg8aG7ufLyVqVOn4sSJE9i6dSuam5uxbt06hIeHY8yYMf6IQkRERH4SGhKNhLjfQKtKRUXNX1Be/Wd4RY7G0Ff8UtLy8vKQnJyMJ554AsXFxUhOTsaSJUt8y2+55RZs2bIFAGAwGPDyyy/j1VdfRUZGBrZv345XXnkFCsVld+oRERFRH5PLVBg86GFE6mehrvHfOFn2JFrbGlFl3XD5J9MVEcQgvMbW4/Fg//79SEpKQmhoqNRxiIiIBoR6+w6UVb8GhVyPltYaJA37u9SRgkJPewunhSIiIqIu0Wsn4urYJyB+f8jT7toncaL+jccYiYiIqEuqrBtQY8v13T5V/jsAgNkwDxbTfKli9Vvck0ZERERdYjHNR9Kwv/sOc2pUKQAAUWyBKHqljNYvsaQRERFRj1w16Bcw6LJRW78FpVVr4fV2PrID9QwPdxIREVG3mQ3zIAhyxJiXIDTEgkrr2zjRasVVg1ZCIddJHa9f4J40IiIi6raz56C1z1AwE/HRK9DkOYljpb+Gp7lC4nT9A0saERERXbEITRaujn0MXq8bx8seh7vphNSRgh5LGhEREfmFKuwaJMT9D2SCEifK/gcO17dSRwpqLGlERETkN6HKGCTE/QYhIWacKn8GDfYCqSMFLZY0IiIi8qsQhREJsY8jPGwoSqvWwlq/XepIQYkljYiIiPxOLtdgSMyvoFWno6L2r6iy/gNBOBOlpFjSiIiIqFfIZEoMjv459NrrUWPbhPKadRz0ths4ThoRERH1GkGQIzbqv6CQR6C2Pg+i6EFs1H0QBLnU0QIeSxoRERH1KkEQEB25CDJZGKrr/gGvtxlx0T+DTGANuRT+doiIiKhPRBnnQiZTorL2LZRWtCA+ejlkMqXUsQIWz0kjIiKiPhOpvwUx5iWwu/bgVMXv4fU2SR0pYLGkERERUZ8yRkxFbNRP4XTvx8nyp9HmdUkdKSCxpBEREVGfM+iuQ7zlAbiajuBk2VNoa2NROx9LGhEREUkiQjsOg6NXwO05gZMVv0Ob1y11pIDCkkZERESS0WkyEB/9ANxNx3Cq/Gm08Rw1H5Y0IiIiklSEJgvxlv+Gq6kEpyv+H7xej9SRAgJLGhEREUkuQjsecZZlcLoPfn/VZ7PUkSTHkkZEREQBQa+d+P1Vn9/hdOX/wuttRpV1g9SxJMOSRkRERAHDoJuM2Kh74XDtQ2nVWtTYcqWOJBnOOEBEREQBxaD7IbxeDypq3wAAiKIIQRCkDSUBljQiIiIKKFXWDR32oH13bBEAwGyYB4tpvlSx+hxLGhEREQUUi2k+LKb5EEXRV9AspkUwG2ZLnKxv8Zw0IiIiCkhnD3FGaMajyvou6ho+ljhR3+KeNCIiIgpYZsM8mI1z0eZ1orzmz1DItdBpMqWO1Se4J42IiIgClsU0HzJBgcHRP0d46DCUVr0EV9MRqWP1CZY0IiIiCngyWSiuilkJhdyAUxW/R3NLtdSReh1LGhEREQUFhVyHITGrAbGtfZ7PNofUkXoVSxoREREFjVBlDAYPegjNLVU4XfkcvGKr1JF6DUsaERERBRV1+A8Qa/kpnO4DKK9+DaIoSh2pV/DqTiIiIgo6eu1ENLdUobpuA0KVg2E2zJQ6kt9xTxoREREFJbMhBzrNWFRZ34HduU/qOH7HkkZERERBSRAExEXdhzBlPEqr1sLTXCl1JL9iSSMiIqKgJZOFYfCghyFAwOnKZ9HmdUsdyW9Y0oiIiCioKUOiEB/9IDzNZSiregWi6JU6kl+wpBEREVHQ06hGITryTjQ6i2Ct3yZ1HL9gSSMiIqJ+wRQxHTp1Jiqt7/aLqaNY0oiIiKhfEAQBsVH/hRCFCaWVL6I1yGckYEkjIiKifkMuVyM++kG0ttpQVv1qUA90y5JGRERE/YoqbCgskXfA7twNa0Pwnp/GkkZERET9jiniZmjVGaiqfRdNnlKp4/SIX0ratm3bsHDhQqSkpGDx4sWXfOyZM2cwYsQIpKWl+f6tXbvWHzGIiIiIAJw9P+1eyORqnKn6Q1BOxO6XuTv1ej3uuusuHD9+HIWFhV16zs6dOxEaGuqPH09ERER0AYVch9ion+B0xbOortuAaNMiqSN1i1/2pI0fPx7Tp0+HxWLxx+qIiIiI/EKnzoBeez1qbVvgch+WOk63SHZOWnZ2NiZPnoxVq1bBarVKFYOIiIj6uUHmuxCiiMSZ6lfh9TZLHafL+rykGQwGvP/++/j000+xceNGuN1u/PznP+/rGERERDRAyGUqxEbdi+aWStTYNkkdp8sue07akiVLsGPHjk6XxcbG4pNPPunWD1Sr1Rg1ahQAIDIyEo8++igmTpyIhoYGREREdGtdRERERF2hUY2CXjsJNbYtiNCMR1hovNSRLuuyJW3dunW9GkAQBAAI6sHmiIiIKPBFRy6G3bkXZTWvIyH2fyAIgT0SmV/StbW1wePxoLW1FV6vFx6PB83NnR/z3bdvH44fPw6v1wubzYY1a9YgMzMTer3eH1GIiIiIOqWQ6xAduRjupiOwNX4mdZzL8ktJy8vLQ3JyMp544gkUAu7PTgAADVtJREFUFxcjOTkZS5Ys8S2/5ZZbsGXLFgBAaWkpli5divT0dMycORNKpRLPPfecP2IQERERXZJeOwmqsBGoqvsH2rwuqeNckiAG4XFGj8eD/fv3IykpiWOtERERUbe4m47h2JlfIVI/E9GRd/T6z+tpbwnsg7FEREREfhYeNhR67XWw1v8LnpZKqeNcFEsaERERDTgW022AIEO19X2po1wUSxoRERENOCEKI0wRN6PBkQ9Pc4XUcTrll7k7iYiIiIKN2TALbV47ZLLAPL+dJY2IiIgGJLlcjdioe6WOcVE83ElEREQUgFjSiIiIiAIQSxoRERFRAGJJIyIiIgpALGlEREREAYgljYiIiCgAsaQRERERBSCWNCIiIqIAxJJGREREFIBY0oiIiIgCEEsaERERUQBiSSMiIiIKQCxpRERERAGIJY2IiIgoACmkDtAToigCAJqbmyVOQkRERHRpZ/vK2f7SVUFZ0lpaWgAAJSUlEichIiIi6pqWlhaEhYV1+fGC2N1aFwC8Xi+cTidCQkIgCILUcYiIiIguShRFtLS0QK1WQybr+plmQVnSiIiIiPo7XjhAREREFIBY0oiIiIgCEEsaERERUQBiSSMiIiIKQCxpRERERAGIJY2IiIgoALGkEREREQUgljQiIiKiADQgS9q2bduwcOFCpKSkYPHixZd9/K5duzBjxgykpKRgwYIFOHLkSIflzz//PLKyspCRkYHHH3/cN21VoGpubsZjjz2GjIwMjB07Fi+++OJFH/vHP/4RaWlpvn/JyckYOXIk6urqAACrV69GUlJSh8cE+pyq3dn+wsJCjBw5ssP2bdiwoUfrChTdyfzZZ59h0aJFyMjIwIQJE/DLX/4SjY2NvuUvvfQSrr322g6/nxMnTvTFZnRZY2MjHnzwQaSlpWHSpEl4++23L/rY9evXY9KkSUhLS8Py5cvhcDh6tJ5A0tXcmzZtQk5ODtLT0zFp0iT87ne/6/BeDsb3OtD17d+4cSMSExM7bN9XX33V7fUEoq5mf+yxxzps/9nX+6zFixdj1KhRvuXZ2dl9tQk9tn79euTk5CApKQmrV6++5GP/9a9/4YYbbkBqaip+/OMfo6qqyrdMss96cQDKz88X//nPf4ovvfSSeOedd17ysXV1deLo0aPFvLw80ePxiK+99pqYnZ0ttrS0iKIoiu+9956YnZ0tlpaWilarVVywYIH44osv9sVm9Nhzzz0nLliwQLRarWJpaamYnZ0tvv/++1167tq1a8XFixf7bq9atUr8/e9/31tRe0V3tn/nzp3i+PHj/bKuQNGdzFu2bBE///xz0eVyiQ0NDeK9994rrlq1yrd87dq14vLly/sqeo889NBD4rJly0S73S4eOHBAzMrKEgsKCi543I4dO8SsrCzxwIEDot1uF5ctWyb+4he/6PZ6Ak1Xc7/99ttiUVGR6PF4xKqqKjEnJ0dcu3atb3kwvtdFsevbn5ubK86fP/+K1xOIepp91apV4urVq32377zzTvGdd97pzah+t337dvGjjz4SH3vssQ6fXec7evSomJqaKubn54tut1v8zW9+I95xxx2+5VJ91g/IPWnjx4/H9OnTYbFYLvvYjz76CEOGDMGsWbOgVCqxdOlSuN1uFBUVAQByc3Nx9913Iy4uDkajEffffz9yc3N7exOuyMaNG3H//ffDaDQiLi4O99xzT5cyi6KIzZs3Y+7cuX2Qsvf0dPt7e119pTuZZ86cicmTJyM8PBw6nQ4LFizAnj17+jhxz7lcLnzwwQdYvnw5NBoNEhMTMW/evE63d+PGjcjJyUFiYiI0Gg1WrFiBbdu2we12d2s9gaQ7uW+//XZkZGRAqVQiKioKs2fPDqrXujP+et2C9fUHep7d5XJh+/btQf95f+ONNyI7Oxt6vf6Sj9uyZQsmT56M8ePHIywsDMuXL8fevXtx+vRpANJ91g/IktYdJSUlGDlypO+2TCbDiBEjUFJSAgA4cuRIh+WJiYmorKyE3W7v86xd0dDQgOrq6gsyn38ItzPFxcWoq6vDjTfe2OH+9957D5mZmZg7dy62bdvm98z+1JPtr6+vx4QJEzBlyhSsWbMGTqezx+uS2pVmLi4uxrBhwzrc98UXXyAzMxO33HIL1q9f79e8V+rkyZMA0CHzxbb3/Pfy0KFDAQCnTp3q1noCyZXk7uy1Dqb3OtD97T98+DCysrIwbdo0/OEPf0Bra2uP1hNIepr9ww8/hNFoxJgxYzrc/8ILLyArKwsLFy5EQUGB3/NK5fzveq1Wi9jYWJSUlEj6Wa/o9Z8Q5FwuFyIiIjrcp9VqfV/ULpcLWq3Wt0yn0wEAnE5nh/sDhcvlAgBoNBrffTqdzrc9l7Jp0yZMmzYNarXad9/ixYuxatUqaLVa5OfnY/ny5TCbzRe8sQNFd7c/ISEBeXl5SEhIQFlZGVavXo0nn3wSTz311BX9LqVyJZkLCgqwYcMGvPvuu777br75ZixYsACRkZHYt28fHnjgAWg0GsyZM8f/4XvA5XJ1+P8KdHz/nv/Y89+zWq3Wd15aV9cTSLqz/efavHkzdu/ejc2bN/vuC7b3OtC97R8zZgy2bt2K2NhYHDlyBCtWrIAgCFi2bFmPf4+BoKfZN23ahDlz5kAQBN99Dz/8MIYOHQqlUol//vOf+OlPf4rNmzdjyJAhvRG9T3X2/j/72SjlZ32/25O2ZMkSjBgxotN/U6ZM6fb6VCpVh5OHAcBut/v+05+//OwetPPfFH3lctuvUqkA4ILMl8vrdrvxwQcfXPDle+2118JgMEChUOC6667DzJkzsX37dv9vWBf5e/vNZjOGDRsGmUyG+Ph4rFy5Eh9++CEA9Ph32Zt66/Xft28fVqxYgRdeeAHXXHON7/5hw4bBYrFALpcjPT0dd911l6Sv//lUKtUFH6QOh6PT7e3sve5wOKDRaLq1nkDSk9wff/wxnnnmGfz5z3+G2Wz23R9o7/Wu6M72x8fHIz4+3ne0ZNmyZb7tC9bXH+hZ9vLycuzateuCz/uUlBRoNBoolUrMnTsXo0ePxmeffdYbsfvcpb7rpfys73d70tatW+fX9Q0fPrzD1XyiKOLw4cNYunQpAOCaa67BoUOHkJ6eDgA4ePAgoqOjJduL1pXtj4qKwqFDh3zn5B08eLDDF29nPvroI+j1emRlZV3ycef+1SWF3tr+swRBgCiKAICIiIgrWldv6I3tP3DgAO677z6sWbMGEydO9FvWvnD2L/xjx475Dl9ebHvPvpdnzpzpe44oirjqqqt8r3lX1hNIurP9QPuh60ceeQSvvfYaEhMTL7luqd/rXdHd7T/Xudt3JeuRWk+y5+XlIT09HfHx8ZdcdzD8H+iq4cOH49ChQ77bDocDZ86cwfDhwyX9rO93e9K6oq2tDR6PB62trfB6vfB4PBe9lHzq1Kk4ceIEtm7diubmZqxbtw7h4eG+Xfw5OTn429/+hrKyMtTV1eGVV17BvHnz+nJzui0nJwevvvoq6urqUFZWhjfeeOOymTdv3ozZs2df8Kb84IMP4HQ64fV6sWPHDmzZsgU33HBDb8a/Yt3Z/p07d6KsrAyiKKKiogLPPvsspk6d2qN1BYruZC4pKcHSpUvx61//utPL7f/973+joaEBoijim2++wVtvvdXh9yM1lUqFadOm4cUXX4TD4cChQ4eQm5vb6fbm5ORg48aNOHToEBwOB1588UVMnz4d4eHh3VpPIOlO7oKCAqxcuRIvvfQSUlNTL1gejO/17mz/559/jtraWgDtheaVV17x/V8O1tcf6Fn2zi4Qa2xsxJdffun77tyyZQuKi4sxadKk3t6EK9La2gqPxwOv1+v77u9smKxZs2bhiy++QEFBAZqamvDCCy8gNTUVgwcPBiDhZ32vXz8agHJzc8Xhw4d3+HfuUBzTp08X8/LyfLd37twpTp8+XRw1apR46623iiUlJb5lXq9XfO6558TMzEwxPT1dfPTRR8Xm5uY+3Z7u8ng84qOPPiqmp6eLmZmZ4vPPP99heWpqqlhUVOS7XVlZKSYmJoonT568YF2LFi0S09PTxbS0NHHmzJni1q1bez3/lerO9v/lL38RJ06cKCYnJ4uTJ08Wf/vb34p2u73L6wpE3dn+1atXiyNGjBBTU1M7/DtrxYoVYmZmppiamipOmzZN/Nvf/tan29IVDQ0N4s9+9jMxNTVVnDBhgrh+/XpRFEWxrKxMTE1NFcvKynyPffPNN8UJEyaIqamp4gMPPNDhtb7YegJdV7f/zjvvFBMTEzu8ztOnT/etJxjf66LY9e1/+umnxXHjxokpKSnilClTxBdeeKHDZ3mwvv6i2L33wJ49e8SUlJQO//dFURStVquYk5MjpqamiqNHjxbnz58v7tixo0+3oyfWrl17wff92aE4zv+u27ZtmzhlyhQxOTlZvOeee8TKykrfMqk+6wVR/H4/PhEREREFjAF5uJOIiIgo0LGkEREREQUgljQiIiKiAMSSRkRERBSAWNKIiIiIAhBLGhEREVEAYkkjIiIiCkAsaUREREQBiCWNiIiIKAD9f14iYoYHEtPdAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "domaine = np.linspace(-0.99, 0.99, 1000)\n",
    "\n",
    "valeurs_f = [f(x) for x in domaine]\n",
    "valeurs_g = [g(x) for x in domaine]\n",
    "\n",
    "plt.figure()\n",
    "plt.plot(domaine, valeurs_f, \"+-\", label=\"$f(x)$\", markevery=50)\n",
    "plt.plot(domaine, valeurs_g, \"+-\", label=\"$g(x)$\", markevery=50)\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.title(\"Représentation de $f(x)$ et $g(x)$\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- On conjecture que $g(x) = - f(x)$.\n",
    "\n",
    "La suite des questions est à faire au brouillon et sans Python :\n",
    "\n",
    "- On trouve que $f'(x) = \\sum_{n\\geq 1} \\frac{n x^{n-1}}{n^2} = \\frac{1}{x} \\sum_{n\\geq 1} \\frac{x^n}{n}$ si $x\\neq0$. Or on sait que $\\log(1 + x) = \\sum_{n\\geq 1} \\frac{x^n}{n}$ et donc cela montre bien que $g(x) = \\int_0^x - f'(t) \\mathrm{d}t = f(0) - f(x) = f(x)$ comme observé.\n",
    "\n",
    "- On trouve que $g(1) = - f(1) = - \\frac{\\pi^2}{6}$.\n",
    "\n",
    "- Par ailleurs, un changement de variable $u=1-x$ donne $g(1-x) = \\int_x^1 \\frac{\\ln(u)}{1-u} \\mathrm{d} u$, et une intégration par partie avec $a(u) = \\ln(u)$ et $b'(u) = \\frac{1}{1-u}$ donne $g(1-x) = [\\ln(u)\\ln(1-u)]_x^1 + \\int_x^1 \\frac{\\ln(1-u)}{u} \\mathrm{d}u$ et donc on reconnaît que $$g(1-x) = \\ln(x)\\ln(1-x) + g(1) - g(x).$$\n",
    "\n",
    "- Je vous laisse la fin comme exercice !"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "# À voir aussi\n",
    "\n",
    "## [Les oraux](http://perso.crans.org/besson/infoMP/oraux/solutions/)   *(exercices de maths avec Python)*\n",
    "\n",
    "Se préparer aux oraux de [\"maths avec Python\" (maths 2)](http://www.concours-centrale-supelec.fr/CentraleSupelec/MultiY/C2015/#oMat2) du concours Centrale Supélec peut être utile.\n",
    "\n",
    "Après les écrits et la fin de l'année, pour ceux qui seront admissibles à Centrale-Supélec, ils vous restera <b>les oraux</b> (le concours Centrale-Supélec a un <a title=\"Quelques exemples d'exercices sur le site du concours Centrale-Supélec\" href=\"http://www.concours-centrale-supelec.fr/CentraleSupelec/MultiY/C2015/#oMat2\">oral d'informatique</a>, et un peu d'algorithmique et de Python peuvent en théorie être demandés à chaque oral de maths et de SI).\n",
    "\n",
    "Je vous invite à lire [cette page avec attention](http://www.concours-centrale-supelec.fr/CentraleSupelec/MultiY/C2015/#oMat2), et à jeter un œil aux documents mis à disposition :\n",
    "\n",
    "## Fiches de révisions *pour les oraux*\n",
    "\n",
    "1. [Calcul matriciel](http://www.concours-centrale-supelec.fr/CentraleSupelec/MultiY/C2015/Python-matrices.pdf), avec [numpy](https://docs.scipy.org/doc/numpy/) et [numpy.linalg](http://docs.scipy.org/doc/numpy/reference/routines.linalg.html),\n",
    "2. [Réalisation de tracés](http://www.concours-centrale-supelec.fr/CentraleSupelec/MultiY/C2015/Python-plot.pdf), avec [matplotlib](http://matplotlib.org/users/beginner.html),\n",
    "3. [Analyse numérique](http://www.concours-centrale-supelec.fr/CentraleSupelec/MultiY/C2015/Python-AN.pdf), avec [numpy](https://docs.scipy.org/doc/numpy/) et [scipy](http://docs.scipy.org/doc/scipy/reference/tutorial/index.html). Voir par exemple [scipy.integrate](http://docs.scipy.org/doc/scipy/reference/tutorial/integrate.html) avec les fonctions [scipy.integrate.quad](http://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.quad.html) (intégrale numérique) et [scipy.integrate.odeint](http://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.odeint.html) (résolution numérique d'une équation différentielle),\n",
    "4. [Polynômes](http://www.concours-centrale-supelec.fr/CentraleSupelec/MultiY/C2015/Python-polynomes.pdf) : avec [numpy.polynomials](https://docs.scipy.org/doc/numpy/reference/routines.polynomials.package.html), [ce tutoriel peut aider](https://docs.scipy.org/doc/numpy/reference/routines.polynomials.classes.html),\n",
    "5. [Probabilités](http://www.concours-centrale-supelec.fr/CentraleSupelec/MultiY/C2015/Python-random.pdf), avec [numpy](https://docs.scipy.org/doc/numpy/) et [random](https://docs.python.org/3/library/random.html).\n",
    "\n",
    "Pour réviser : voir [ce tutoriel Matplotlib (en anglais)](http://www.labri.fr/perso/nrougier/teaching/matplotlib/), [ce tutoriel Numpy (en anglais)](http://www.labri.fr/perso/nrougier/teaching/numpy/numpy.html).\n",
    "Ainsi que tous les [TP](http://perso.crans.org/besson/infoMP/TPs/solutions/), [TD](http://perso.crans.org/besson/infoMP/TDs/solutions/) et [DS](http://perso.crans.org/besson/infoMP/DSs/solutions/) en Python que j'ai donné et corrigé au Lycée Lakanal (Sceaux, 92) en 2015-2016 !"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "----\n",
    "## D'autres notebooks ?\n",
    "\n",
    "> Ce document est distribué [sous licence libre (MIT)](https://lbesson.mit-license.org/), comme [les autres notebooks](https://GitHub.com/Naereen/notebooks/) que j'ai écrit depuis 2015."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.7"
  },
  "notify_time": "5",
  "toc": {
   "colors": {
    "hover_highlight": "#DAA520",
    "running_highlight": "#FF0000",
    "selected_highlight": "#FFD700"
   },
   "moveMenuLeft": true,
   "nav_menu": {
    "height": "511px",
    "width": "251px"
   },
   "navigate_menu": true,
   "number_sections": true,
   "sideBar": false,
   "threshold": 4,
   "toc_cell": true,
   "toc_position": {
    "height": "295.217px",
    "left": "928px",
    "right": "12.25px",
    "top": "72.95px",
    "width": "179.75px"
   },
   "toc_section_display": "block",
   "toc_window_display": true
  },
  "varInspector": {
   "cols": {
    "lenName": 16,
    "lenType": 16,
    "lenVar": 40
   },
   "kernels_config": {
    "python": {
     "delete_cmd_postfix": "",
     "delete_cmd_prefix": "del ",
     "library": "var_list.py",
     "varRefreshCmd": "print(var_dic_list())"
    },
    "r": {
     "delete_cmd_postfix": ") ",
     "delete_cmd_prefix": "rm(",
     "library": "var_list.r",
     "varRefreshCmd": "cat(var_dic_list()) "
    }
   },
   "types_to_exclude": [
    "module",
    "function",
    "builtin_function_or_method",
    "instance",
    "_Feature"
   ],
   "window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}