{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#  L3 E - S5 2018-19 --- TDO --- séance 4 --- solutions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Autour des nombres complexes\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'/Users/ef_mac2/Desktop/cloud/enseigne/maths-sur-ordi/lgge_PYTHON/TDO_18-19/TDO-4'"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "%pwd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "os.chdir('/Users/ef_mac2/Desktop/cloud/enseigne/maths-sur-ordi/lgge_PYTHON/TDO_18-19/TDO-4')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from pylab import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from cmath import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "#  Exercice 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "La commande interactive ${\\rm \\texttt{input()}}$ permet de demander de rentrer une valeur au clavier.  Si  l'on écrit ${\\rm \\texttt{n=input()}}$, cette valeur sera affectée à la variable ${\\rm \\texttt{n}}$ et on peut \\^etre plus pr\\'ecis en indiquant ce qu'on attend \n",
    "${\\rm \\texttt{n=input('donnez-moi un nombre entier')}}$ ; par exemple :\n",
    "\n",
    "\n",
    "   \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "entrez un entier :16\n",
      "n = 16\n"
     ]
    }
   ],
   "source": [
    "n=input('entrez un entier :')\n",
    "print(\"n =\",n)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Ecrire un programme qui trace un polygone régulier à $n$ côtés ($n$ étant la valeur demandée par  l'utilisateur du programme) dans un repère orthonormé.\n",
    "\n",
    "Puis afficher le polygone et l'enregistrer dans un fichier pdf dont le titre indique le nombre de côtés du polygone."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "entrer le nb de cotes13\n",
      "le nombre de côtés est  13\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZQAAAEWCAYAAABBvWFzAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nBIUlFGOMMUHx/wEt3me0EeoLYgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11976a470>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "k=input('entrer le nb de cotes')\n",
    "print(\"le nombre de côtés est \",k)\n",
    "k=int(k)\n",
    "z=1+0.j\n",
    "x=[1]\n",
    "y=[0]\n",
    "for n in range(1,k+1):\n",
    "    z=z*complex(cos(2*pi/k),sin(2*pi/k))\n",
    "    x.append(z.real)\n",
    "    y.append(z.imag)\n",
    "\n",
    "plot(x, y, \"o-\")      \n",
    "xlabel(\"abscisse x\")\n",
    "ylabel(\"ordonnee y\")\n",
    "axis([-1.2, 1.2, -1.2, 1.2])\n",
    "axis(\"equal\")\n",
    "#legend([\"un pentagone\"])\n",
    "title(\"un polygone régulier avec %g côtés\"% (k))\n",
    "savefig(\"PolyRegulier_a_%g_cotes.pdf\"%(k))\n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Exercice 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "La fonction ${\\rm \\texttt{random}}$ permet de générer des valeurs aléatoires. Par exemple, ${\\rm \\texttt{x=random()}}$ génèrera un nombre au hasard compris entre 0 et 1 que l'on affecteraà la variable ${\\rm \\texttt{x}}$.\n",
    "\n",
    "\n",
    "\n",
    "Dans cet exercice, on  va chercher à caractériser l'ensemble ${\\rm \\texttt{E}}$ des points\n",
    "${\\rm \\texttt{M}}$ du plan d'affixe ${\\rm \\texttt{z}}$ tels que \n",
    "$$\\vert z+1\\vert +\\vert z-1\\vert \\leq 4$$\n",
    "On peut bien entendu étudier cette inégalité en coordonnées cartésiennes. Mais ici,  on va simplement prendre 2000 points au hasart (dans un rectangle  censé contenir l'ensemble ${\\rm \\texttt{E}}$) en marquant d'une croix chaque point ${\\rm \\texttt{M}}$ qui appartient  ${\\rm \\texttt{E}}$.\n",
    "\n",
    "1.a. Voici un script incomplet (à vous de compléter les points de suspension !) :\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEWCAYAAABxMXBSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x119983080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=[]\n",
    "y=[]\n",
    "for k in range(3000):\n",
    "    u=4*random()-2\n",
    "    v=4*random()-2\n",
    "    z=complex(u,v)\n",
    "    if abs(z+1)+abs(z-1)<=4:\n",
    "        x.append(u)\n",
    "        y.append(v)\n",
    "\n",
    "plot(x, y, \"+\")      \n",
    "xlabel(\"abscisse x\")\n",
    "ylabel(\"ordonnee y\")\n",
    "axis([-3, 3, -3, 3])\n",
    "axis(\"equal\")\n",
    "title(\"TDO5 - exercice 2\")\n",
    "savefig(\"exercice2.pdf\")\n",
    "grid()     ### permet d'afficher un quadrillage du plan\n",
    "show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.b. Quel est le rectangle qu'on a choisi (comme rectangle contenant ${\\rm \\texttt{E}}$ ) ? \n",
    "\n",
    "Pourquoi ?\n",
    "\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    " 2 . On considère la transformation du plan\n",
    "$$f : (x,y)\\mapsto \\left(\\frac{x}{2},\\frac{y}{\\sqrt{3}}\\right)$$\n",
    "Tracer sur la même figure les points correspondants à $E$ (comme dans la question 1.)\n",
    "et ceux correspondants à $f(E)$.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/ef_mac2/anaconda/lib/python3.6/site-packages/numpy/core/numeric.py:531: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEWCAYAAABxMXBSAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsvX+YVVd9L/xZKikWmkRiRJMgBynkrUKtTRDGoXdmnkhE\noaWxRoQQobES2xKZuVefGetz35npWyvUezNDk74NsepEkwBNK2/skBIIzxwqMGBirSa2hQnhJCTp\n9QeYRGgoiVnvH3t/9/nuddavvc+ZOcOc9Xme/Zxz9l57re/eZ+/1Xd/fQkqJgICAgIAAX7yu3gQE\nBAQEBFxYCIwjICAgICATAuMICAgICMiEwDgCAgICAjIhMI6AgICAgEwIjCMgICAgIBMC4wgImIAQ\nQvyjEGJtvekImJgIjCNgXEIIcYZtrwkhXma/bxJC9AghXhFC/Dzejgkh7hRCvE3p51IhxF8LIf6P\nEOI/hRCPCyF+X2lTFEKcY/0fHdurrT2klB+UUt5Tyz6FEJ8VQjwR3+8TQojP1rL/gAsHgXEEjEtI\nKafSBuAZAL/N9t0XN9shpfwVANMA3ADgrQC+S8xDCHERgEcAzATQBOASAJ8FsEkI8d+VITew/q8e\n/SusDkKIN9RjWAAfB/AmAEsBbBBCfKwOdATUGYFxBFzwkFK+IqX8IYCVAH4C4H/Eh24G8HYAN0op\nT8TtdgP4NIA/FUJcPBr0CCEWCSEOCSFeEEJ8XwjRGu+fJoR4Vgjx2/HvqUKIJ4UQH49//5IQ4n8J\nIZ4RQvxICHGXEOKN8bHW+NxOIcT/AfC1eP8KIcS/CCFeEkIcF0IsjfcXhRB/wGj6pBDi32Jp4V+F\nEL8Z779CCPH3QoifxFLEp03XJaX8CynlP0spX5VSHgXwIIDm0biHAeMbgXEETBhIKX+BaDL7rXjX\nEgD/KKU8qzT9ewCTEUkhhC8KIX4qhDhIE30eCCGuBLALwJ8hkoQ+A+DvhRCXSylPA7gFwJeFEG8B\n0AfgX6SUX49P3wRgLoDfAPCrAK4E8H+z7t8a9zkTwHohxHsBfB2RFHUpgP8GoKSh6UYAPYikhYsB\n/A6AU0KI1wH4BwDfj8e6DkC7EOIDHtcpEN3nH/rcl4CJhcA4AiYankc0uQLAmwH8h9pASvkqgJ/G\nxwGgE8A7EE2edwP4ByHE7JzjrwHwkJTyISnla1LKvQAeA/CheOw9AB4AsC/edyuQTMTrAXRIKU9L\nKX8O4M8BcFXQawC6pZT/JaV8GcAnAHxVSrk3Hus5KeW/a2j6AwB/IaV8VEZ4Ukr5NIAFAC6XUv6p\nlPK8lPIpAF9WxjShB9H88bVMdydgQiAwjoCJhisBnI6//xTA29QGsX3gzfFxSCmPSCl/Hk/I9wA4\niHii15z7Q2ZE/y1Nk5kAbozVVC8IIV4AsFih424A8wAMSClPxfsuB/DLiGw0dN7ueD/hJ1LKc+z3\nDADHzbfC2W4mgCsUWv8EwHRbZ0KIDYikl2VSyv/yGD9ggqEeBraAgFFBrHr5bUQGccSffy6EmKKo\nq34PwH8BOGzoSiIyBFcekPJdDjJOAviGlPKTBhpfj4hxfB3AHwkhvialfBIRE3sZwLuklM9Z6FLH\n8pGMTO1OAjghpZzj0QcAQAhxC4AuAP9NSvms73kBEwtB4gi44CGEeIMQ4tcAbENkB7g9PvQNAM8C\neEAIURBCTIr1938JoEdK+WLsrvsBIcTkuJ+bENkKduck514Avx33+fq431YhxFXx8T9BxABuAfAl\nAF8XQrxeSvkaIjVRX2z/gBDiSoe94SsAfl8IcZ0Q4nVx+/9L0+5vAHxGCHGNiPCrQoiZAL4D4Oex\nwf2NMb3zhBALdIPF9+bPASyJ1VoBDYrAOAIuZKwUQpwB8CKAbwE4BeAaKeXzABCrUd6PaGV9BMBL\niJjK56WUX4r7mITIkP0TRKv+2wD8rpTyWB6CpJQnAaxAxCB+Eo/9WQCvE0JcA+C/A/h4bMjfjIiJ\ndMWndwJ4EsBhIcRLiCQmo2uwlPI7AH4fkZH9RQD7Eamf1HYPAPgCgPsB/BzA/wdgWkzDckTG+BPx\n9f8NIrdlHf4MwGUAHmXqurs8bkvABIMIhZwCAgICArIgSBwBAQEBAZkQGEdAQEBAQCYExhEQEBAQ\nkAmBcQQEBAQEZMKEjON485vfLAuFQr3JqCnOnj2LKVOm1JuMUUUjXCPQGNfZCNcITKzr/O53v/tT\nKeXl7pYTlHEUCgU89thj9SajpigWi2htba03GaOKRrhGoDGusxGuEZhY1ymEeNq3bVBVBQQEBARk\nQmAcAQEBAQGZEBhHQEBAQEAmBMYREBAQEJAJgXEEBAQEBGRCYBwBAWOEvr3mvIm2YwEB4w2BcQQE\njAH69h7Dln0jxuO2Yz59BwSMJQLjCAjwRDUTtMoYajnZV8N0AgLyYEIGAAYE1BokMXQsmZvrPEKh\na1f8LdqnO7bxujnOcfr2HstMS0BArRAYR0CAB/Ks6k3qqRWzJ+HB46+gY8ncZPIvdO1CadOyTPTk\nZToBAdUiMI6AAAtMEoPPBK0yBsKDx1+p6CsvSpuWZWY6AQHVIjCOgAADTBKD76peVSfRecViEet2\nn3VO9ur5Ono4Q/LtJyCgWgTjeMCERC2Mzx1L5qK0aVlqgi9tWuY9CW/ZN5LQ4WI2umMqk+hYMtco\nnfTtPWa85mA8D6g1AuMImJDgk6VpQs3KXPKolEyTNu/LRQc/TsxMRceSuaPKIILLbwBHYBwBFySy\nTGSmCTXLRGuTGDgtfXuPodC1K6VCKnTt0koPOjrU8+lcdQwVqspK10+ha1duBhCklgCOYOMIuCCh\nc401u75WD5uaidNCn7qJ1sfWoPO0KnTt8laPcYM7SSbBeB5QawTGEdAQoAl14axpOHLidMV+Uh3V\nwohsYh7kQnv1m16H771i99YiyYBLDHScziOmwr+rDKIaFdPKrcPGexWM7Y2NwDgCLhj4uMbqVtmm\nFbe6P8vK3kXLln0jySSvTuqFrl142BHDwSUYOu4rUXHJhujIA840AgI46so4hBBfBbAcwI+llPM0\nx1sBPAjgRLzrm1LKPx07CgPGE1wBc3kiu32gUzH5BO9Va7B2ueICaSM7fVfvg9pPlnvko+4K7r6N\nh3pLHAMA7gTwdUubb0spl48NOQETBboJVdfGR4rhEzGpfnQTpakv9VMdxyUREC1qMKFJSrGNRddi\nmuzz2ImofWAejYO6Mg4p5T8JIQr1pCFg/GDnyHm0tkbfXatYmmxtEz/BNEGqBm0fI7JukuT2EZ1h\nW+0zq7GaMy2dQwAxApN0w8eiNibpTKciK3TtcjK30ZL2AsYnhJSyvgREjGPQoqr6JoBnATwH4DNS\nyh8a+lkPYD0ATJ8+/Zrt27ePEsX1wZkzZzB16tR6kzEq2DlyHjfMuQjrdp/FwNIpAJD6nud8vl8H\nXf98386R80lqEB14OwAV41Bf9Gnqb8XsSUYaTTRTX7x/03Ws2302yY3lO7ZKOx+X2ruuZyI/rxwT\n6Trb2tq+K6W81qfteGccFwN4TUp5RgjxIQBbpJROS9+1114rH3vssZrTWk8Ui0W00nJ8gkG3Os+y\nKjet7m19mDyQXC6+Jpj60vWZxz3WRofq5UQSgjq+bwoVOt/V1tbfeyY9P2GfV46J9F4KIbwZx7gO\nAJRSviSlPBN/fwjAJCHEm+tMVkANoXM7zRu05lKnuILibGk/1NQjPE5CB1UNlhdEs6sIFL8OPunr\njOS6FCrqvaHz6Z7SObbroXsUVFYTH/U2jlshhHgrgB9JKaUQ4r2IGN2pOpMVUAP4ruR9z6cJ7/BT\np6yxB3nSmOsYUpa05qrUcfWb3Os1Ooc21SBus6HYvLlMzNV0b3ziSeh7Fu+q4Il1YaPe7rjbALQC\neLMQ4lkA3QAmAYCU8i4AHwHwh0KIVwG8DOBjst66tYCawGVIdk3sPkwgb8S0ypSISZAHlMqcCKbA\nONVwfPRnrzlp4EZsDlIj6RiAbwp4k8eVr7Fcd3901+m6vsA4LlzU26tqleP4nYjcdQMaACtmT6q6\nD9+VrE2tZVt9+3guZaHTh17u2eTKsKvSrfbvw3DVe+MbTxLyWTUOxrWqKmBigyY1mqi4h0+WaGfe\nlq9kXcxBR4sNWfJQmdJ1cDpVO4RpJa/aYHwli7zlbk0wxZNwWmnfitmToNqMqymKFTDOIKWccNs1\n11wjJxqGhobqTUIu3L7nqHHfzM7B1P5P3/1w1eOpfVZ7no5+aj+zc9B63NQ3nWsa9/Y9R5M2fNON\nZaObj2Nq46LdBpUmfk2u5zXv/zTecKG+lzoAeEx6zrHj2qsq4MKHbnVuUmmocQG+3lTVphC3tTOt\nhPMkRSQ6CTp6beqwavJo6e6HGg2fB1loCpg4CKqqgDGFzUtHha+aJa+3VLX1xH37WzhrWnLOln0j\nFQF5Oq8oW5lYTh+PoLdFkNuuSWeIN90LkwqOrpF+r9t9Fthdtsuo/2U1ddYD6o/AOAJqDpd+n4PS\nnKs6ct+JpRq3TpOra5bzdf0Bdgb276d/kfrNJ98dtzYlfZEnF/doMtFAE7Mpp5W64s9jNAeijLnc\n8436V69nYOkUa2BcVkkt6zkBo4vAOAJqDnVyMeVqKnTtSiZK2k/eOTpG4uPqmoXhmFxdaz1BqWPp\n3HF1Xkm1oMWUMdcWh0I0m8Z2HePfa2EMD0kUxx8C4wjIjFoFb+km+bxqJ36+bzs+Tq0ZhppkUScF\nqCt2W3nZvHEbrkhvOs+Wot4U16KOS9JjROvzVf+XJoTgwfojMI6AzKimbCtfkap9+MZxjIZbZ9aI\n56yTl4nmKy+d7BWQ5xucp0LXt+k375fT6mJ8XJ1G7YvF57V9+8Jm46ExAuqHwDgCagLT6pJedp/J\nXs3UmjU9Ri3gYgjENF3qE1sxJaoKSGPZ0oe4oI7jClJcuXUYO25tyvwf0VjqMdqvPe+V8r3Magw3\nMSt17ID6IDCOAC9kXeWbVtE8aaBrks6zsq8WWdNmAP6rX2IYo6Gzt9UEoe+AvRysiyFzry36/0zp\nV1bMnlTV9ZmyCqvfuUNBwNghMI4AL2RZ5XNmojN4037q1wbTRK5GnfvC5LbqUq3ZVtuA3oXWxFxX\nzJ5k9DzzYZQ22n0n64WzpmXKWcX7p4SGNsmmWCym9mWNYNdlALAxxICxRQgADKgJbLaLjiVzU2nJ\nXSnJfZB31c7PU1OlE3jAnCmtutonTfi8XWnTsoRp8riVB4+/knie6VKcu2AaRz2XJtyVW4eTsenz\nyInTWDhrWqoP3/FpLJUGPiahFoF/fNESMD4QJI6AzMgSrOdKSc5Xuu+JbeP1yGlk8jAiWlUPJ3W1\nbWJkOkmt2lWyTiox3X/dWKb76HvfubeVel9I8nrPpHJ/Pq7VNsmO1FE0Xl5pKaB2CIwjwAu6Gt0+\n7XWrYJPKi3vi6NxVTSk7XBOGa0LUrZJt6cxpLC6N2OhbOGsaFr3jstQ+9XuW6/FN5MiPk12i0LXL\nKJlkBdGhqpK27BvBwNIpiVrLx/BP7WzqKBpPjf0xXVfA6CEwjgAv6Lx3aD9BNYLbXEg51JWrLTjN\nFntgsg/4GH0JOsbA6dJNkq5xSDWkgxoZnmUCdK3odTYISg3CwRcEebzVdPRSyhFOV5AMJg4C4wjI\nBdsKkY67oItqNunEfSabWqQQVydRNW7BFVthgytVhw0+rrIuhwUAVXsg2eJRnnvhnPYck8RhuyaT\nOkqXkiYwprFHYBwBWrgkCtM5WWwTlfEHZwH4ZYbVrZx9YIrANk00rgJF6jXQb3XiA9yeW64J0CRt\n8X5N3k4kmdjsG6rkpYNNquLfB5ZOiaQOC9S+bK7d9D+YpMVax/ME2BEYR4AWXKKgyciWRyprTW9T\n0SIT1MmUVD/VMCs+tmuFalrxqio2+k0rez6pJ55HX96Tyo7rc99cNJriONSxTbAFLFYDouvKSyc7\n26qSp3pvTQgp28cewR03wAmTCyt34cw60VB73tfA0impCY7bNEzuojaaCFkmFlPNCl3/Puo4tW9y\nxwXSbr9ZodYgIZdfn75qNdGSVMWZKn0naYPoMqmxCKqEw+8tHTNJQdz2FDA2CBJHQALfoDjTuT6q\nDh+Y1EN53XSz5tbKwgSz3DOa4N4z6Xms233WWe/bRaNLSrFNtFySVPv3tRHovJtsgYE62K7RlFxR\nR1+waYwtRFQxsE6DC/FVAMsB/FhKOU9zXADYAuBDAP4TwDop5T+7+r322mvlY489Vmty64pisWit\nb1Br2CZAnZrGV8dsKzT0nknPJ9eoprbQTXT8XDpu0pGbaOPj8LamsSgDrI4GXT8VhvCeHhRbWyPG\nMflRoKdHS5dKvwkm3b+rP1Oq+7yodK0uGm0cpjQhpuvUXaPtWQDGjpGM9Xs5mhBCfFdKea1P23pL\nHAMA7gTwdcPxDwKYE28LAfx1/BkwBjBNkkD+F1PnrUTgcRxcFeTrLlppbDcHkxFUew3/7iqipPUk\n6+kxM4OeHqC3F4VSCRtv+hPg+uV2xqH05aLHhloFVZqyA5ukG5v7tE97GkdlErbnKMR0jD7qyjik\nlP8khChYmqwA8PW4kPphIcSlQoi3SSn/Y0wIbGDwVZ7JfXQ0Irxr1afN+0eFLSgxC770xDeBXV9F\n4dyC1FiJB1hvb7T/nnvQMTBg7qinB8PHT6Hp3juTvgCzgdjnvriYrk8BJ6KBJnKXMT2rutKWkSDY\nMMYX6qqqAoCYcQwaVFWDADZJKQ/Ev/cB6JRSVuihhBDrAawHgOnTp1+zffv20SR7zHHmzBlMnTp1\nTMdct/ssBpZOwc6R83jw+CsYWDolObZz5DxumHNRSh3Bj+tA/ahYMXsSbphzUcU10vg22rKOReOZ\n6FCv0zYW3QNCa1sbAKDQOZhq99c/3I4PDt5rpBUASmvXorRuXaofXV8AcPWbXofPLXyjtT8bqrmv\ndNzVTv0vv3jk5Uw028ax/bcq6Nni56rp+6tBPd7L0UJbW5u3qmrCMA6OYOPID5tu35TqgeBaqbts\nFOo1qivjamwcOph05zp7SvuB+9C/+KaydMLVSLEKqgLd3dGn7hhvQ33Rpmnf37wq+lx8U+qa88Am\nVfgE6qnQ0ZLnec0zji6WxCQ1UkbiWsZ7NKqNA1LKum4ACgCeMBzbCmAV+30UwNtcfV5zzTVyomFo\naGhMxvnoXYfkzM7Biu32PUeTNrfvOapto7YzgdqqUK9R18Z2zDQ+b6ueZxyjuzv52te8SkogtU8C\n0Vjd3dExZetrXlXRnm8zOwfLfWiO8+3Qmg1Je9s9kS0t5mMWmP5P27200iHtz6vtGaFjvuPQcZ9r\nMD131WCs3suxAIDHpOe8Pd7jOL4F4OMiwiIAL8pg3xhVqOm+edwCxQ7oVoVZ0nJz1Dp4y+ZpowPX\n7afAVv3tB7dV7EuNJSX69hxN9hc6ByPJoLcXECLaMtCrQ/uB+8r96+I/enqA/fu9+lJR61gYF2zX\nzI/ZxqRjFEui9kkxQPy5JVQTPxMQoa6MQwixDcAwgKuFEM8KIT4hhPiUEOJTcZOHADwF4EkAXwbw\nR3UiNQD6uhoqTC+jGrAGQPvCq+1MLzmf8HX9muqDqKlKTAkNAUSTsTrpM0ZQ2rw8Yg49PeUxYvWU\nSx1S2ry8/GlhLADQdO+dCfMqbV4ebZMfTTNpnTrMw9UX8LvndH9cwXi1AqkRN143R/tMET07bm1K\n0UL3ne7Nyq3DRtVr8LzKj3p7Va1yHJcA/niMyGlY2FxXeRv1RdNF7Nqy4vp4OfmmLeEuujSuSgcd\n57TbSqdW2BdstglEkkVp83IUzi3Axr3H0NHSAhSLKO3vBTZbT0V/8yq0H9yWfGbB8JoNaCKm0Nqa\nljSICbW0RPs9mAe/ly6vMvW++8L2jC16x2XWQEeXe61O2iCodjkgW3LJAD3qHccRMA6QJ1eSLXU6\n4Hbr1MVNrJg9CXnsjKpPP5CeHEx0Dt98G46cOIVFzzwOrN4Uub52DkZG2OuvjiwMqjQgZTJZp6QG\nlVF0d1sZT4pZ6MaxoOneO4Fv3GFWT5HB3aNPHifhG12fxzBvWzjsuLVJm1+L/3aV8NXtMwWN2hIq\nBvhhvNs4AsYZVDsHqTVUVceWfSPWFOk6nbrqJlmLOACCThVDKqBFJ59I0dFx8P7oJNPEu38/0N1d\ndpUlM7YG3PYBlN1rV951COjuTrykEg8sgvpbhRAYPn6qYtyT8xeUbSt0DUIYJQ/bat2Upwuorc1D\np27U0bll30iq3K0PdPYb2s/HD8iGwDgaDK6XRM2VpGMIavJByo5LcL3YrpUe0VhtzijTZEQ0q0h0\n+82rUxM3ucKmJvOennIfOgN4LG0kTIjGjqWUHZ96H9DbWzZ6F4va821ouvdOnPz196b2zXj8Ued5\nxER06dxtDJ+gFtrKCjU5omo/0U30tI+rGnk7dZ9OerJdT0A2BMbRYHC9JGo0MJ9kTS+lqWIfZUZd\nuXXYOJ4pWtgXnMnopBj1d/uB+wAhIlUUAxmdv/1QHN3NIrZTXlVsJd9x/dWRLcEicSQMoKUl+qR2\n3d2AlJHEYfOIits/e/Hl2jG0jEJtJ2Va4ujttXoiHX7qVMWCAYD1fwT0k7NuH5XRdcHHG86nLVCZ\nWiZ4VlWHYOMIcELn+URpIHxePJtBulo9s8l+oUog/YtXR5N0rBpSDdKFzkGUNi3DjJ4edFx/NTp0\ng9GELER6MvaxT6hG7N5eFM4tiBiZzTge933VSz/xt4Oo7QoFoFRK7dIFzdF9VGuJ0PEjJ05bc3rp\n/gvdvqwOEKZqgNTG117Br9lWWybYPtwIjKMBUI2RkxgDX9FRX1klA9tYSQXA3eYqeKoKy7TC1RWV\naj+4DbK7B1v2jWi9mL70xDcBLAN6etDXvDo6N56AyXuqAr29/gyEJA/WRtunDTHjGr75tshAzo3g\nREdvb9mjivD003q3YgDtzasA6FV3KlRPuNHwTtI9IztubUqeH1tyS1/jPrWtRX6yRkXdU46MBkLK\nETN8XxJbeg+epiNr/QUbs6JrtGWj5TS4aCP0L14dMQuDp9OLb7kCl/z4+WRiTtqrUNOD0ISNmDGS\nJxZQnqhjj6nhNRuiyd4DJ+cvsNsqZs6MmAHrv2JcFbydSjf9H62t6Pv83d7/Z9b6G7r/3pRtV4Ur\nnYjv+ep33e8saNSUI8HGEaAF2QwItCJVval0ldqyGC1rRVuqb55DSghj5Dfhkh89l/pd4ekkZeQN\nxXNJKV5LordH7wkVt/NlGoBit5Ay3a+UEdMgm4nqPWUCHVO8q1L/x/790b2d/Kj2v1SDJ+n/555O\n1J5Xc7RFolsDMBWQNKmDz/k+gaUBfgiqqgkK0wrMRyWhW0XyYD+1YBEvnqMykjweK7YqeDSmSluq\nTWw/2HjdamDP6sQQXugcjIonqQyET74g9U1kIC9lIZwnPoyDAVP9m8AlIVUq0tkrgEpjuqqeMoH6\nttUN6e3Fls4FFbt1SS59YAoe9VGTqhUACVkXILbU+cGrKjsC45igsEVwu6Dqf9WXjn/SWARdHEBW\ncNWFSgugN3JW6N8nPxoVSmIw2hRIfRNP2jy9BxCprrD4prjvBVh416FoEhUC/c2rEgmlv2sXSpvL\nXlRJdUHAHiHOGQWf0HUMh1RUBGI0qvHdBFU1bYg8P/DXv48H/u5AsttnwaFrwwNFVQbisr25Ajur\ntd3VupZMQ8E3G+KFtIXsuOmsoj4Za336od9qxtFagV+jKfutKRtqksE2w5bKOBtluIlAbZSxpZRS\ndneXv7N++ppXVdIQ00ltknHUjdDdnbou63mGrLzG/ZprSl2vJcuv7vn56F2HjP/j7XuOav9LW0Zl\n03Pkm7nXN4su9ZnlXBsaNTtukDgmEFxeJHlALreqykCXpyoLnXno4aovNb9S+4H7gZ65kUfU9VeX\n80iZPKIQZZwdXrMhkk580dsbqa9YihGjJCNE4tZr9aASAg8suwU3Dn4FHT096NhclkCM56nqNm64\n94WrpoiUaO/pAQyeTiZs2TeCFbMnYd1u/3K8OpdvW+2VahAkiuoRjOMTCKYguGr7tKXdzsM8TDrl\nnSPntQbMlVuHtWlOKtDbW06ToWEGSQR4jPaD2yKjNXeV5eohIUDJs668dHIyptpPtSh0DuKz8z4c\nBdjRRE4qJVPqETKOE7jB3pauhK6xtbXSyK9rG2f/dUE1Mt8w5yJthD4Fharnqe18UoXoxlWPZcm0\nHOCPwDgmMPJ4kdjSoutQy9XbDXMuSqUzAaIJY8etTdZ6Edue251ENfcvXh2dGDODZMXe0gLZ3RN9\nV/X8OpCyJs4we/Bz70/68s5myz2iLJM5pUk/cuJ0wqiSiVznCSYlTNkg+x85lop6N4LOtzEZOubB\nOIgh0PO2bvdZo22CMxRVgrRB9eoiqcT0jNsWPAFVwlendSFtwcZhr3rne55uf157iUlXzXXlQ0ND\nFfpwF32H1mzIZttoaUnsDl62gLhKH7ejqHaHChsE2Qvi80dlU8eQ0s/O47KBuM7V/K/q/zKzczD1\nvPI23hUYNW1sz0MWG0eWYy40qo0jSBwBmWBK7+Fznm71p0tHoqaX4KtIVa2w6sql0RfpkCJo+mtt\nrchTpQVTW3VcfzVKm5cnksbCWdNSqjBenQ9A2uUVwOEZ85KsuKTmSjLrxt8LnYM4PGOek6zkPI0U\n0L/4JndW3Z6e8r3gYL8LnYNpVVicV0sd07TiV0G5r5L+NdmUVWlYp2YConxZpmMhJmPsECLHLxD4\nRKjaonh5pLcrNQNh4axp2oldTQOii9a2QY3i9Yn3qOhfZ8zVjUXGcf6cs3NtxvMEUkY0b16OZy++\nPMobpYLHUThqcaiwueoSo0hcgw1tuVtw+4H77Oo0HnnuC8M8oYvoLnTtwsDSKcnzaora5u7VJocJ\nl5Gc+svyXKtqMl2/vmjUyPHAOC4QZH1AbbUNbJO8Ld2HLuVDnrxFK7cOWxMfqhOL2j+fELbf35XU\n09CBgv76mldHKc4zTOi1hOrltfKuQzhy4jTaD9yH/sU3mSf72Fvq2UveYmZYcaBhEnPDJKrDM+bp\n74+JeZhvyub6AAAgAElEQVQCCclrK2NaEl2cjY5x2AIK+bNH7fkxn8nep/88aFTGEVRVExiqaqiW\n3iOkLiC4jO98P9WJNqUoUftW++dqr8Nvn59qp3o8UV1w0dsTFT7yhYzTjFxyibstqXLi8bkaKkUH\nIkM+AOz4j4ejNO9veD6lBkvQ0pJM1n17j2HxH36tTFNMH4CKSZ5PoP3Nq6Lqhqoaqrs7yparWzSa\nggjJA4vSkij/mVqca8XsSQAqU9SQd5op260Ouuy49Cyo0mpQV40NgsRxgSDrysa1qgf0Yrlu9eWb\nyM628jNJKq6+rBKNb7Q0LCtvjzKrRlVSDpVPig5iNo6kinxVzZMpJllyyf5gkKaG12yA2F/EopNP\nJBKPTT2mTbJI8wRPqAi9xGlTVXGYngHTc2RSi9oSGNJ5gNlzK29cEdC4EkddAwCFEEsBbAHwegB/\nI6XcpBxvBfAggBPxrm9KKf90TIkc5zA99GpeoWpgS0GdR1XFocshVOjaZX2Rk2suFtMZXw3g+n+A\nueiaDMRxn2TXaH//XOBAeYzELvL001EJ2XMLyjmweB8a6JjXlZe+Udv2gcdO4sb4eyp1eEsLIASS\nf5iPxe4Fla3dsm8EWL0U2+/vSpotnHVZ6pr4+TNMMR3K98Mz5gGro1eWB/htvG4Odo6UrAGABNuE\nD6Sfb54LzRbsqsJlgwvuudlRN8YhhHg9gL8CsATAswAeFUJ8S0r5r0rTb0spMxYuaBy4ksXZ6n6r\nBm6CK2+PLfGgT78q/boodJ2qivoWvT3A9Wy1bJg4CbSyrlhhG2pU0PcSfe/t1UdqU3Bc1y5tvQ0O\n7Qo/bntjdzcwKKMEhrEE07fnKLbsG8FzqTxZ8f31lLRSzKanBzj5RMI0m+69E9Bl7CXPKQ8D/6J3\nXGa0TxSLz2PLJ6+vkBL48+ijOlWfb55QU81hRuD3KmCU4Ou3W+sNQBOAh9nvzwH4nNKmFcBg1r4b\nKY5Dl7dH18Yn3w+15VDb6PL8ZPHFN51nivOo6JvlikriMaSUsqXFHYcwc6Z+P51LdHZ3J3mjssY6\nJPdHiQUxjsuh9JPKpaVCFz+i65tiL+L7luearJvmv5Wy/Lzq8ovpwJ8rUy4003OuxpDcvueod46r\natGocRx1s3EIIT4CYKmU8g/i3zcDWCil3MDatAL4JiKJ5DkAn5FS/tDQ33oA6wFg+vTp12zfvn10\nL2CMcebMGUydOhVAlJrjweOvVLRZMXsSbphzkbUNAAwsnWIcZ93us6nj6m9de1efvJ8vHnkZR3/2\nmpb2JW87j6lTpyZ9cnrpesgziZC1il5p7VoU7rkHAFAcGgIAtLa1Jb8nf/w2nPv6Hcm+akD9FwYG\nUFq3Dut2n62gtzg0hMLAQEKTDoXOweS/3TlyHrPuGXBGr5fWrkVp3Tq0trWhODSE1rY2o12D3xPC\nxrsfxpb1HwAQSUu/+6sXaWksrV2LW39tJT63MK1uo+d13e6zCe1ZnhUTdOfuHDmfPPfqGL5j5gV/\nLy90tLW1eds4fCSDy3y5UJYNwEcQ2TXo980A7lTaXAxgavz9QwBGfPpuNInDN2rWtuIjZM0cSqs7\nF9QIYx0tn777Ybd0xFbgiXQQ709W+Y4VMo+6phV4X/Oqimy5uVbnhFhq4dc/PGNedat7g1Tl6peu\nxxhZ7pDW1GzA2i2+VttqX/efuqTerBkQbGPXWtqQMkgcRgghRgD8C4CvAfhH6TrBE0KIJgA9UsoP\nxL8/FzOyL1rOKQG4Vkr5U1vfjeBVlSV7KNdB+3iQ2AICbVlRfWDzgNn45T0pvTgQG08NOn1yvfXO\nHcWR0SPKtFqvKAnLX4+4ZGwS3Q5/CYkH/vXtOZouSxv3ba3xYYMarMgrG8b7CucWoLR5OV666Jdx\n8fn/rOyDbCBSav9TXgZYB10AXzUliG3nj2aNjUb1qvKRDAQiA/Y2AE8C+HMAc305k6XfNwB4CsAs\nABcB+D6Adylt3oqyy/B7ATxDv21bkDjS8F1p6ewZeXNe6fpx2S/UsVIrXSkTSYHo9K7BwfMz6a6v\nhjr/vuZV8m+X3VKmWx3ftZqPJZWUPYLO57mi6Fyf3FM2iYKD0cSlL9s4JKmp/ym3cWj/U81/rtuX\np/aL7pkdDWlDysaVOLJO9m2IbA0vANgPoCnL+Zr+PgTgGIDjAD4f7/sUgE/F3zcA+GHMVA4DeJ9P\nv43AOEbD+OcyYFeTDE7Xh2kSIRVGhaFZmewqmIsn4zi0ZkN6oosnSFvCRCODqSZpoIX5zOy0FKfq\n7jYyA34NNWWKnHl5MhBVFeVruDY9Z3kYh6vPatGojMNHVXUZgDWIbBA/AvAVAN8C8BsAHpBSzvIS\nbcYQE11VNVpFbsjlFXDXYc47lm9MybbndqdVQASWYiNx9Tz8Jb176syZ6L/qfWg/cD8Ov30+Ft3y\ne+Vgv/i5p1iN/uZVUTEoV31w03X55LwygdRmUkZquWIxCgo8cH9FcCC56XKUNi+PVGazL0tUTEA5\nctyWksVZq1zKcgAdqct47IyUqfgbAClVFYdOTWoK2DO5gduC+HxyWlUD3fhBVWWWCo4B+J8ArtIc\n6/TlUGO5NYLEQfBRVelAK7EshsxaShw2tQUfz7Tq5itc+q1bHacM6QSX+saxpVbyUkrZ3R2pp1wr\ndp+yrqp0ZekvdX/YPexrXiVPXny517WkJNQ8EojUp033XYmPhiSgPrO1ksp1tDaqxOGTq+pqKeX/\nI6V8VsN0NutOCBhbVFOFT5d3SPd7tEGrWlq1En3a4ktSov3A/Sm62g/cX+6reXUU1UwZcLt2RanP\neYW/eJV9cr6m6JEyloqUZBFXybtx11ftF6gLIlShpkrXjI2WFvTtOZoUayJphOd/6l98UzkhYtyH\nLn8WEEsRrkJN3d3J+YXOwUgKaY4KZqmp1YmWnSPn7X3GGM0gPV0q/9E0lDcSQq6qCwQmkThvnh3V\n08rmkQIgie7OM5bLY4b6Ja+qQteucgoPHaTMlladopsnP+rMSwWUPaX6m1dBdvek63d0dyd1zRNa\nAG3qDgjhl2LdpS5SQTU3NP0ac3IZ4PLM8u6PPLHiZ6pYLOJ7r1xR4flU60mb92lTV1H0elaVlUsF\nFlRVE2hrJFVVFrhEd1UdZavclmVMDpNHlZRRHAe1kVI61TspY7aUVtWKtwdWFjUNUxHx48/MX5Dd\naM5VZ9QffaqGaVPfOdVvPnEgqpdVoq5T/lsCr+aoO+7zzPiolHwN6XmM5KaYJvU6JwoQKgAG6OCq\nwaxbDWZJna7Dln0jFRXbCGo/FOmeqC9sK/Xu7lR8hFWK6O5OqbyslfakhwTe2xtJCXGyQXXsGY8/\nWlb/UH+ufnUSB/UROwMk94M+eZU+KaNaGXuOJskNAbgrAkKfeJGjtHl5KkEih606Y17QCp+enWrh\nqk3uoiOgEj5eVXMB/DWA6VLKeUKIXwfwO1LKPxsLAvOgkVRVeeHKRprXc0tVR7gCvHTZcRPEXjvG\nIkYq8lS2s0CtvgegzABoUldUX7mD8kzgAXqKRxgAQIhInfTM4/6qMSkrM/2CBTN69NHfvCrKGmwo\nJ+uCTwp+U+Zln2fJpBbLoqryUeeumD0JWz55vVd/4x219qrajyj47nts3xO+Ik09tqCqcsOUVE6F\nTbVkam9Tial9qW2zqJSoLalNKGCOez2l4glyqHFojEQtRoiPu/rta14lh2fMq05VZlJBcVUe0RT/\nB1yNlznViZrGhW0+Kp/b9xw1qqpM57m8+3wSHPrA1d7HEyuoqvxUVb8spfyOsu9Vfz4WMB7BV2Oq\nSsBXtWTrW+fNoqZY5ytKatv+foM0w1Quhc7BlDqGVsxksC5NLhchIlVcSgoyeBjp0H5wG9DSgiMn\nTqVVQ3St3HCuO//9c7Ho5BP+UohmjESNJctqL/Ks6n8k/k9I6hECpc3LI3pjZDGWAyhX+9PAxwsr\nj4pH592n9lkLtZVLnWZS5wak4cM4fiqEmA1AAklW2/8YVaoCxhz8ZVdfHioLagu+4oxAp0OmPgmq\nfSUL2g/ch44lc5PiTClXUQDo6YmKN1EZWUWdxAPkVKhMpdA5iL7P3x1N/Pv3a20aHBV9svxPLnvD\n8JoNkT2DGARgtI10fGG9vuTszJkA9Pm7iLaE6ZIcoY7FZAz1egqdg4krsNZWwJgKTdJZywwD8H5W\n+Bg+8Kldo+uLvx+hzge8VFXvAPAIgP9ElG7kAICCr0hTj60RVVVZg5p8PKykrF4VkKU2wkPL12jV\nI4fWbIgaKKoZl/qHBwnevueol6eT2o5nzSXV10fvOpT6nVf9lXtT1VN8H/XPjmmDJDU0kdrNmsk3\nrvOh+5/5OKb/uBaqIp/nzoWP3nVITz/rS5cuRUWjqqq8J2MAUwD8im/7em4TmXG4dL2m47r9ppf0\no3cdyh1x63qBbf2kXkKaqHTX4TExV0S6W/T2o7LRWHySjxnfp+9+OJnQU4ynGhfeDAyrwpW2pUU+\nM39BtJ/fJ2lmzglzMtxfW6YDX2SJ8q52gcPtL/xdcr0Hjco4nKoqIcR0IcRXAPydlPLnQoh3CiE+\nMUoCUIADLv2x6bhuv0l9RKnTVRuFD3zaeaunuGonVje5bApAOoo8lTLc5rIbLY7c9g+LuqnQOZic\n3794daTm4d5JcanZjoP3ayPWC+cWRGqkmBZOlxauoMHYXlKm6SZ9u/37IxdiIG2/EEJvm5EycW/u\n23tMe39b29q0tpCsah5Tzir6dKlIXdCp0eiTgl7VdyREnvvZOAYAPAzgivj3MQDto0VQgD90Lw7t\nr3V/VBvcBTVSWIX3xEFuqISenvJ6FwBkpf49gRBo+sTvRWN5RJcD/skXbf2VNi9HafNyPHvx5Wg/\nuK3MwBiz6dt7DIV77ilP1IhsDyfnL9BOSlq6bMyEI2YsZNNRP9HTk/qPKtKymEAMvKcneiZMxnKq\nyc7gY2MgmJ4VU7ocl91s5dbhiufb9EzzfquNZZqI8GEcb5ZS/i2A1wBASvkqgF+MKlUBKfTtPYZ1\nu89WrKwAvTRAwU66F4Ueep3nlLrCqja3j0nK8XrpeJxEDPW8ZDXMpYCYuXxs9SZ0HIwnbg/mUTGp\n+kKVQKQsx5zQBMxW41xiaj9wH4BIEpjx+KPoX7wawzffpjXkp+CTwbe7O7oXijca0UixGil66H6S\nZxfLUZXqizHw0ublWnqKQ0NRGwNTcRmgAbdkanu+dVj0jsucHlPqb6KB3rFqnDomFFy6LABFAJcB\n+Of49yIA+311YfXYJrKNw5ViwXbclMpBd44tHqNae4dp/9DQkJTd3ZUZW2OQXj0xlht0+VnjFnjd\nD5sBOWucCd9stT54n2pKD5/xrAZ6m91EsUuk7GTKNSf/OZDYQ2zjunT/JgO0CXlreOjGpO+m/nxS\njRAa1cbhwzh+E8BBAC/Gn8cA/LrvAPXYGpFx+BTBMb0AunN03lU+L2fWACqOoaGh1AQmpZQpI65r\nItQZb22TdtxXMl4WZpDRkJ0ySHv0nam9bps503yMYMt5pd4bAhnkbecD8sTatdbnhD+LWRcmuufY\n9gzr2pADCO03Vb900RUYh61RVOb1XQDmAZjk23m9tonMOFwJ4Gz7TYzD9yWtxnPFx1OLGIdtle0l\nTfCxTZM2obu7zGTI3feSS/JN1j6bpydUqs5GFu8p3TXye0JMjx3j3lbWqoO8b5+NjyOzSw1ZPQFV\n2KRm2/ug60fKtAsv0daojMM3yeF7Abw7lj5WCSE+XgMtWUAOkG7VZNRTda9ky6D2On2wj75243Vz\nMgdbcRw5cdqsX449plrb2gDog9cIXlHQcfQ0enqMXlCJjefcArQf3JZ8R28v8OKLACqD+YbXbIim\nRE88sOyWpI/EVuDyhFID+ISIzpk5M2Vj6NtztDLwMb4u1RgPlP938vRKvKGQ9kIzRu739/tXRyTb\niMYwbrPJqTDZyBbOmlbxHJEnoK69GszK+6ZxV24ddl7WkROnrbQ1FFycBcA3ABwC8P8CuCPe/tKX\nM9Vjm4gSB6UcJ/iu/nUqIn5ullWdbmVok1bUsU0bgSQO3Wo5+a6syHV69kNrNsjb9xy12weUVXfF\nGLb8UMrKXrVHpOJINBJE6jp96ZLSnVbdsJ28+PL0/5ZVashRV70izkOB7v/3DRa0SQqu2CRT/+ox\nl4RM7YPEYca1AJqllH8kpbwt3j5dC6YlhFgqhDgqhHhSCFGRt1lE+Mv4+A+EEL9Zi3EvRDx4/JVc\nfut54j6yuDm6+tflvOJ9ptoODOg70RRfohV5adOyCqmi6d470XHw/mglLaU+NoM8nViOp9QYsWRQ\nkaaDoEthEsdJLJx1GToO3p/yiOISBElWHIXOwShNyiPH9HTFlQYT2oGKOI1EGlK8n6566SdAT4/R\nA4quTeve3NubpHU3pqOfObNCEutffJP2+VTjJgCkJN8sz7jOXdf07B45cTpTDAlJyAtnTUvtV9Oz\nr9t9tjFdc12cBcADAN7my4l8NwCvB3AcUUqTiwB8H8A7lTYfAvCPAAQib64jPn1PRIlDXZnZJA6d\nlMG9RXw9WdTzXRKDL/26PkzSwRNzfiPXipev1nVSSYUEYZIwXJJHHppsq3Sf8UxjK/uT/wflNCA2\n764KicRAS6qeucv+otg51GfCx75me/58bHpqXwSbVKE7N0gc5c2nHscQgN8A8B0A/8UYzu9Uw7CE\nEE0AeqSUH4h/fy7u94uszVYARSnltvj3UQCtUkprksWJUo/DVduAr9i5rcIUzEYxGVlqbehsIK7+\ndVBrG2hrcFCtCfpsbUX/q1e4M8ta6kecnL8gFWyXBVR2FkKgb8/RVMwD1bF4YNkt+Oy8D6O0eXlF\nmVVnbQ5Ot5TRvdi8PD2W6dr4fp8aHHmh9J2pNC2V2fV4JgBzLRfdeUBlzIWujQ6657TQtasigzNh\n4axp2HFrU2pcoq1RS8f6MI4W3X4pZYYiydp+PwJgqZTyD+LfNwNYKKXcwNoMAtgkpTwQ/94HoFNK\nWcEVhBDrAawHgOnTp1+zffv2asgbd1i3+ywGlk5Jvq+YPQk3zLmo4vjOkfN48PgrqbYE9Ry137y0\n+Jy/c+R8xdg7R85j1j0D2sm1tHYtCvfcY+2zODSUjN/a1mY8p7R2LUrr1qG1rS1VuKg4NAQAieqo\nODSEl//3V/DBwXud16PSoVM/ZcHGux/GtTvuwc377q84Vlq7FgCc90MHfk823v0wbphzEQoDA6m+\n6J4UOgfRfuA+tB/chpE58zFn5HFjv+emT8fkH/3IePwP7/wHrHzXVOvzoT4TalvdM0PtAFifO7WN\n6zlVj+vaf/HIyzj6s9cwsHRKcvzMmTOYOnWqsd8LCW1tbbVjHKOFWjMOjokicXDYVvlANi8Pa9U9\nDxglhoygVV7HkrnlfEceoFVvUqFv07JyTiqgrMdnz/bwzbeh6d47U5Njzar1uVb8VUgEw2s2YNWV\nS50R7cNrNqDpG3ekr910T1ta3N5dFvQ3r4rsR1xCdLX1gOtZcknKWSR0FSu3Dqc8s3yq/228bg7e\nM+n5hpQ4fJIcflgIMSKEeFEI8ZIQ4udCiJeqJxPPAZjBfl8V78vapiGwYvYkY3GkvEyDfmdFtedr\n+6JJX1fISAGpSihlB7nSkpEyZeTt6UmYBoBUDYuKFBt5USM1kc443XTvnV5pUFZduTTtfmxjxMVi\nOSUJyob5lBMBWSk07sztB7dVphKh9jEo4aPJSE7I6vBhc9rQFYNS3XBN4K62anubG3Ewjhs2AE8C\n+DVfo4nvhiio8CkAs1A2jr9LabMMaeP4d3z6nojGcW6E07kV2ox8WYyKowG1TK2JniTa2GFEJmN6\nYlTX9NvXvEprcOcG4xR9cKcb4UZ2bkj+6F2HjAbrJF057KlB1P5zb+Q+G6OCZiD9/8MSWT9zZtTG\n1zDP/jNXpgMdfB01fNv6Bvj5tuHtGt047jPBH/TtLOuGyGvqGCLvqs/H+z4F4FPxdwHgr+LjjwO4\n1qffic44bMWRVKZg8hQZC/ikQeFIrtHBOGhLosilLE9clK7D4/wELDYjNXkT4u+cwfCUJqnxbKk+\nHFtf86pyJLtH+0NrNlTEkOj+fx8mw/N/pQpBqRHjHOy4qZCTLU5DRRbG4erLJ1NBnqJRwavKn3Fs\nAbADwCoAH6bNd4B6bI3AODh0boK8bd5qfnngCjjkSO3P4N764kW/nJospZSpT9vE+8z8BekJkc4F\nypMfD/KLj6sTo7Z/U6oSw4qdMz4+yfpWK3QxoZRUhrTEU5HMD2mJpIKBmhiHen3KdWdx/c4TjOqD\nWkocKq2BcZgaAF/TbF/1HaAe20RnHDpVFUFdUb3vi49YX7xaq6yIFt8VH0dK4sgzcWY5R0qzdEBJ\n/giWyZm+0/XxsrLJZOyiS2pic/j18Oht3peUzrgPzgQ4vanxOKPMKzExumZ2Dmon1GoXLnnP92E0\nvn2HJIfR9gYPG8jvZ7ecBIwlVEMewcdovmXfSEXxpWprDeg8wHS+89pxyOiax+Cc5Rxb3qViURut\nroJ7ZJUmP6odf/v9XYAm7oE8w/qbV6E/vl/tB+5DIc6fUALS90LKcmEkGqenR+sd1d+8Cv3nFqAE\n6KPXEdUF6QCAzezE+HqtsRomDzG2r7R5edRvHMfBn0N6Nqqp86KCjNO6ImIdS+YmTiS28XydPFz9\nNAxcnAWRJ9NOAD+Ot78HcJUvZ6rHNhEljk/f/bC3yG5Kha5bVdmkF1+YpIustpVk9cb16nkzw3pu\nau0J+kx0/tQn+65KFdqVd3d3Ntrz1BuvUp2lSiHJvXeN69Hvz9797or/N686yPSb92uy7bnGzip5\nG+1yEwCoca6qrwH4FqLSsVcA+Id4X8AY4oY5F1ldEXkdZjXbqJovKosLpLpP14by+uhWbVv2jVTk\n+zH1k4CXNKUVtaXWNz8vK3g0OK8C2HTvnRX1t2lFvuNT70toSlxoyb2Vn2OQBpL2QHmqpfOk9CN8\n/3537Aj/NCAVxyIEDn/177Xtnr348oh2XfwHc+0l/Et/v/E/9nVfzVoRUCdhu55zOoc+a+Ey3Ajw\nYRyXSym/JqV8Nd4GAFw+ynQFZASvwwyYg50oxfrG6+YkE7ou1TS9GOrLaFN/qWNTvztubap4yUz9\nrNw6jMNvnw/R25M+wNNrcNDE29Lir6pSS83GnxXJAmkyV8uw0veenvLEqyZNjGl5YNktqaFT7QGg\nUKhMamgD0dbdbWcKakJEDQqdg+kJX0oseubx9L2I8ewl083Bkpra4q1tbUldckKeYFUTdKWPAXNS\nTcCv7KutBnmWfiY6nDYOAKeEEGsA0FOzCsCp0SMpwAWTPlaVMjh4fh2yY/A29GKo0bumF0llKtTX\nwlnTEiah1jw4/NQpY90Ewo7/eBg4+YRex84D9dTo5ziDKwD35Msn07jt8M23JQ+4OomfnL8AM3Tn\nHD+FJqCs96dJOI6ofmD5J3Djrq/aaXn6aUBK9C9e7RfFzuwew2s2QHs3OUOxMI5vP9QLTC7n8bJF\nXnvlp2ppif4HIZJ0MKWe8rPkM9GanivVJtKxZC46lszFyq3DFcF7HPy5do1Bn6qdL9g1KuGTq2om\nohocTQAkotocn5ZSPjP65OXDREw5okumZnvRiUEcfupUokoipqBL6MZfMFOyNxU8+Zsq4XDmRGOa\nQJPCxi/vwYPHX0nyJqUipqVMRYAn6h220f3QJRz0RksLCos+G43N3w3OjHxSiEiJw2+f701DpvQn\nl1wCvPii+xqlTKcgaW31SzVSRUqS4TUbktQuHFdeOhnPvXCuor3JSJ78l450NroFEt+vS6ypnm96\n3m0SEtHdqEkOnaoqKeXTUsrfkVJeLqV8i5Tyd8cz02gkmGoPAOUXj1Zj9CI1b9oHoPJlINUUvRC6\nfnU1DjhM9hD15aYXMpUeorUVW9Z/IGVnSBCrhRKmAZTrUzAvo44lcyPvJjhWyLbFkjoJtLZWSjAs\no23FZ2z3KHTtwsdWb9LXAtGg/eA2c70LFXGFQuM1kmTG6RYiuTYTTcn+YjH67pGKhc4h2w1P7VLa\nvBylyY+itGmZlmnY4Fq46Op60H4gXbESsEs7qorVls5n43VzGl5NBVgYhxDijriIknYbSyIDsmHh\nrGnGkpm2F9hX96wyCN3KjMR7nWFcazcpleyDmlKL6wziLkN6nNNJLQVb6ByMyscimggPv32+duU9\nvGZDuR8fOl10xTQseubxdDsfhwAdNDTTtZ2cv8CY+4r2VzgmmGju7k6erySRYXwtG+9+uKJ8bFY7\ngUkla5K06bkHyqosHXiZWBqj2pxrjQabjYN0Pc0A3okoehwAbgTwr6NJVEB28Adfp/N11So3qQTU\nF2rhrGmplZht1QcgsWmoqoOKGs+lUkpVlYJmMk7sDnSMr66ltE/g8bEmAGBSTGnz8qhe9rkF5eyv\nGiSSD4unODl/AX6raxdKQGUSRd11EFPghmXFsE7tCucWoLT9jyN7iA2ckSqZazdeNweitwe/9aFu\nbH+hyyqRJTEeiLyprnrpJ5WNiFayLSl2oVn3DGDhzbcZ7W6pzMgxVIZAz5nJvsH79M3Q3Lf3mNUm\nQs+7OgapfgNiuPx1ARwG8Ab2exKAw77+vvXYJmIch8tf3JZaRJeipJo0DjyViC1nFu9XV1XNSAOU\n/E8EHvNAdPCo5yxxDZa2SSqQnMd5jEQSJ5I15oKuR0rv3FV8XOd18/up++3Y1AwA/H/juarUZ9L3\nOfON+fDtzxXbZBvPFg8S4jjMeBOAi9nvqfG+gHEEWp3pfM1VkZ3bGOi3S22g82UnqPYPdT/1q0ov\n6nkDS6dEbWfONF+oqr7hEkeWyPFisTwNEqTE8JoNToO2r8G7/eC2cpyIQhulMe/bc1Srmurbewzo\n7S3f7zj1eQW6u9P10KX0rn+RupcuTzQFHQfLY6hqIaq9DkTPpbpSz2IfcK3yfSPQXbFNtjGDGqsS\nPpRG0WAAACAASURBVIxjE4DvCSEGhBD3APhnAH8+umQF2GB7mUwBghyUhoH/dkFnMOcvrc4QzoOk\n1BgR9Xvq2kqlMn1M/TK8ZgP6mlenJlQAZaMyMQH6tNkI9u+PJktup2htjepaSJnfvkCIaUgMzoqh\nuf3gNpQ2L0fHF9ZrYy6I4ZQmPxq13bQsYQicgRTOLaiMeWE0qHEkuRktvy6Lbcm0cLDZK3TwjfnQ\nlTpW+3UxH/V5zBNI2HCwiSOI0prPAPBWACvi7a2+4ky9tomuquJZVKtVO+VJcqgmVdSN/9G7DhnP\nod/etDP1VPLbpYbhdSlYm4qsr7rjpnHifSk1miEFhy4jrbZN3I9THRVnmh2eMS9VaySrGstHZeZU\nddH9NUBVS9oy3LpUUlnTlPiqUXXtfcZUn89GVVW5GwCP+3Y2XrZGYBwmu4WUfsygmqy4unNt+apc\nEwZ9HxoaqnixpZTZJkY+uXEmYpnk1UmTaEgVOGJ9JnmsdMzMMDGfvPjy7NeRYeOMKmFWdG9Vphr/\n5u0y3Wd2b5MU8Mpz8em7H9Y+Oz650apJpW6yWfD9fFHD9/uMqT6fgXGYGgD3AFjg2+F42CYi43Al\nOdROuAqy1EbICj6+joGp4+kS0vHNuOrVpRfPuhEDydjHoTUbKmt1EOL9NOk5DeiGsVPFqdRP+g6L\nVNDdnSRhTDERKAWawKShGMnx+P6o0hL9Tgz+Uqb68JlQbZKALuGgz3PqctDgCxXTc+g7prroCYzD\n1AD4dwCvIqrC9wNElfh+4DtAPbaJyDhUiUP3AlQU51GO+4rj1D4LdIyDMxDXy6h7+a0qEykrJ2Da\nV4tNlVo4dPvU/Zo++UR8+56jKa8rOpaanDWqtqx08zGTyZn9Jgkr9R+5mJPh//CZUF2SctbnVIWO\nQeg8Dm3PdxYpyCRZXYjIwjh8clV9oHYWlYC82DlyHut2VyZ0A9KeJYWuXVpjty7uwlYbwSc/jy4Q\nq9C1qyLoj3zxTWkfaN97Jj2PdbvPAohqU1hTcOhiHnh6DfrNvwPp+Iks4HUw1P5UQ7EhBQWPT0m8\nrQ6m70dp0zJgcnd0Tw6icgw+rqkuBjOAl9TxNyu/Y/Qj8oQqxLEoQNo7qv3gtuheCpGkFUkhHqv/\nwCr0L74JK2ZP0t6GrAkGuVE9b60YNQMufwd0/amGfBpXjesAolRAjQivlCMALgXw2/F2abwvYAzx\n76d/od3Po2V1MKVmAKrP8mmKDD9y4rTWbdcnMp1e2v7FN5XXswT1twlqtlnuasonVugzxELKlCeX\nFXFSv9R4asS14l5cHBoqjxnTkkziSiqVvr3Hyvm4OHp6Ijdc6od/+twjQnc3+hffhO33dyVpQgil\nzcvRfnBbmYHH18jzhfGMwoXOQbQfuN8rGE99Ln2y3Po+P317j1U8lzqXcdNzr1tEBaThZBxCiI0A\n7gPwlni7Vwhx22gTFpDG5xa+MZ3bCdELQCnLde6CK7cOO1dxHHnqDlACRU6TrjaHrd4BYefI+RS9\n/YtXV+Zb8og3ODxjXkUOJRNKm5db+2yafVn0paenksF0d0fSBZustfEWSsR3a1ub/TqkTCKykziI\n2AWZ+k4mVUsNkkLnYCovlZqjitKQtB+4Dx9bvcl8r8iVmKdyd7grP3j8Fetxcu+2xUjo3L114FkI\nOpbMTXK0mVy/q3WrDXEd8LJx/ADAFPZ7Cqq0cQCYBmAvgJH4802GdiVENpV/QQb9WyPYOGzV0Ez7\nVb2vDSY9r6mdyQUzi4eMzuV4Zuegt0E8ZZCWsmwzcEWJx21TNgpTnW+TvYX6qEFVvrHahmfMS9lW\nMrv2gjkMyPzOFzrPJvU5sj0/Og8q1U6i2jZ8bHw+z22jGsd9bBwCANeT/CLeVw26AOyTUm4SQnTF\nvzsNbduklD+tcrwJBZd6yoSsQX8qyO5hq8XB2/LxeFp3E1Q7TlIfoXk1OsByOlE9cCX9dyqiO17R\nk+qlQi8vI339opNPVEo1CvqaV2NL54Kkv/7mSI9fkVPLs5hUf/Mqay4sL5Ddg9t1hEjvlxJ9e49B\n9Pak7EU6+tsP3BfT5JnaPVrYVdQD8bWhcagrePU5NdWO4TDZ21T4Pvcmm0ZABN/SsUeEED1CiB5E\nuau+UuW4KxC5+SL+/N0q+2so2IohmcRo39QMrn4Aczp3lS5SG+igUw9QeVydmqu/eVWiskmQoWZE\nhTG3tTWxX6jqnJPzF6Sv4/qrI/3/4S8BKEd9JyAVWqy2cqnHAKTUTonax5XGXDJVGVUc5DTQfk77\nkrmQ3T2pfe0H7se253YDKDPW9oPbsjEyumamKrOl+ecwpSChVOhcPWXKLrBy63DqGD1nfPGiPkdc\nNRXUTdXBWcgJAIQQvwlgcfzz21LK71U1qBAvSCkvjb8LAD+j30q7EwBeRCTlbJVS3m3pcz2A9QAw\nffr0a7Zv314NieMOZ86cwdSpU0d1jJ0j53HDnIsq9un01StmT8INcy7Cut1nMbB0irWt6zwCv0Y6\nrrZrbWtDcWgoshMAeOHd78al3/8+gGgl/Rt/th6tbW3YePfD2LJ+7BwC/3H5Ghz92S9SK/nDM+Zh\n2//83wkdpbVrUVq3LrmmwsAACvfcY+vWCn7t/HqLQ0MoDAwAQFX960D3vjg0VPG82P5//h/q/ns6\nX33+qL0O6rPEP33H9IGJLmBs3suxQltbm3chp9x2CtcG4BEAT2i2FQBeUNr+zNDHlfHnWwB8H8B/\n8xl7ots4Rgsuva+v3SOPXlrK9DWmdNEZ7AY+evoULcwekkSEu8ZR27S0VPSly0JL98EYHEh2lVrZ\nSYguTm+Gvl94yxXmazf8h/z/N/3XNjucab8tgE/3rLlS3tQKjWrj8FFV5YKU8v1Synma7UEAPxJC\nvA0A4s8fG/p4Lv78MYCdAN47WvQ2GmqVoM0Wl6F6WwHuZHH0PZVRlzyaPBIPth/chpPzF1jVRYkL\nshIb0XTvnX7qGrWM7P795poarG1p83K0H7gPi04+kfZ4Iqmf3G4NsQGJR5VPVUEp9ao8upc0JhW0\n4ojv8yU/fr7yfLItWWBLaOnr0aRTU+lUVuQSrj5ri95xWaptUE3VGL4cppYbgC8B6Iq/dwH4C02b\nKQB+hX0/BGCpT/9B4nBD9YbSrdhUaSJLNDmXGEzeWDoPFefKUF3xG1bQFBHNV8rJbw71fOqbr/z5\nuTXadBIPv8Y8Hk4mySC5Tooq5xISNIkY+b1GOjWJrzTJI6ptEkdW6dS23yaZjBaCxDG22ARgiRBi\nBMD7498QQlwhhHgobjMdwAEhxPcBfAfALinl7rpQe4EhizRhMmgeOXG6qsAn8r6yGeV9+qdrSXz1\nudRh8mJqaYlsDZuWpdprV52awDr67GtendQP90a8Gk+kAoOU1HH91RVV83icShIAySFlRWxGRRuC\nLgCSrk2RRCq8w5R4GTpe6NqFw0+d0g53+KlTKQnhweOveMVImJ4/3+A8oNKjKvHGa+S056MNXw5z\nIW2NLnG4dM+m1Z3J992n3yx0cFpcdBlXkI5Mt0l8hkdb7abEJuhsLTz2gVbllGMqtYqfOTNZsfO4\nCSllWjrw3HwqEKboUeErrcT3Ibl2z/93Zueg1l5l+u3qT602qHtWssYM1QqNKnH4xHEETBC4fNMX\nzpqmTf0A2HXEPnmtCKbV4cbr5iS5qjhdRqmE7ABqDqkYsqW1/KO1NdpYfANaW83uvGwV37FkLlAo\noKSp951Kz7FpGYaf2xBVYkTkztvfvCpyc43P7dt7DO0H7ktdeyne3wE/HJ4xz16BUMoob9SmZcBm\ntkK3Xa8KbsPp6QG6dlkj1F1Qnw3Ts2J6xlz1xgn0rGy8bo62Vrma6ypv7qsABInjQoFPzXEf7xLe\n1qevPDpo31WfSgPZOFxpsumaUvUybJKDspLmacGtXkbMzqEdK+6P2wWSrLYWml6ePl1/TLE9JND9\n5p9KmyQ9uiIlpNKqs3Pof3hm/gItXX+77JaK/86Vidnnea0WOs8tW5kBXwk6CxpV4qj7JD8aWyMy\nDoL6wuheDnUiN6W6rqVR00Qrx9DQkDctKegmat2x+HeiRrJN8KZ+LduhNRuSydmmTko5AegmfxNT\nybKfG8NtLr4zZ9oZsOd/p0L3X+rOr1VBMZUe3eIoC+PwpatRGUdQVTUouIiuUzW53BezpmRYuXU4\nSchoVlXlS4WiVVfp9lEaEvpNx5XUJcbzHWi6984oBUfP3EhVdq9epdTa1hbRMLnbv3PuokuqJB3d\nhFgt19e8Gh29vSh0DqKEyGjPAxQXPf0Emkp3ALMv01+vLX28BVEwoFuFmUXNyaGqmeh5NT1frt+q\nWisvXY2CwDgmAFx5enReQartQu2Df+cxFVn0wpz5HDlxOunLxHCKxXLcgOmaTF5aw2s2lDPZRp1V\ntKEcTUBknyh0Dpb7U+M3bEzDVAuDnUvJV6w2iWIxmvyzxI5wL61i0czg4km+4+D9AMr2GG6XWfTM\n4ymPq5PffAgzHn8UQNk+w++Rjemr/4kugtzm/ZR1klYndvqus4HwGCL+vIUcVPkRGMcEgG0y1r0c\nNAFv2TdSUeSG9uteKEo2lyVRXB7omIYLTd+4o/yjp0e7Em8/uA3tB+6P0rUDKE1+FFgSXyetqH0k\njQzFe2yG7OEZ89H0jTui/2jyo9ZxKfivXVdMSgdqZ7sWxR14Bh9v8U1oP7gtxRR8pEwXc9ExIHoO\ns+ZT08G24Mh6rm+SxkZEYBwNCnUSUBkJz3hrS6pow8qtw4mkwfu88tLJONh1XUV1t/dM0tMG6DOi\nauGa+IVAO32nok5cDeM4/9mLL8fiRZ9F+6tXpPJSaaviEZRMtsWhIbS2tqYzyzrGbT+4LerngLQz\nDJKGpCx7kPFPT5Q2LwdaWpKJ3mfiNDF8k8SiHs/av25ip091nC37RiqKO6nMJGTE9Ue9AgADRgk+\nKyuuniJ0LJmbZCcF0oGApgJPrhQSO25tSr18G6+bg9KmZXjuhXPJmISaVFlrbc1eElZKf919dzeu\nevHHKG1aFqUgZzj88duMqUCGj59Kzifo7qlPVl3n5K+mOuHBf93dKVdjWwqXk/MXpIpJqTA9Q7pi\nY/x/zlKJLy+IDnVMWgCpaW0CcsDXin4hbY3sVSWlv0usyYXR5pXl46WlO+5KB6EGjRE+etchrUux\nE6o7rstDioL0fDbPRIQpb6UYh9ZsiK6TJSCsKr2ISoeJLu5lZfKeir+bnhMdbEGAtn6q9apSnyld\nPx+965DxWXMheFUFr6qGQ1aRW115qYGAeYIATWoJXS1ywrrdZ4HdaQM4V3Xlgo+uX/UYUosjEfhq\nHXGBqeuvNnabUl3FRZaavnEHSuvWJTaYvr3HsCW2J3iBGeb79hzFln0jaKdAQwCFcwuwcc/RssE/\npvnkr783Mnyb7gPz1MpqCNdhxexJXsWbTClEbOeqqUT4s8RVa0dOnM6d3DBII3YExtFgcLkrAuXJ\n2mQo17lCqkzCZAjl5/A+Cl27MLB0ClpbW3NdVwVaWoDW1mRyL3QORlXu1AlaYQYpqCosi2uqsX+O\n3l6c/OZDKMSeSwCboDbbL4f3kdCA2MDPxixtXh71RWqo2OA/4wffKVcI1DGP7u5INcUM/yZvJB+m\nQvUrbG1NsLnC2hwnuH1DtXmY7G3B8J0PXoWcLjRce+218rHHHqs3GTVFsVjMNanaVm86DyxAzwho\nP3lWlTYty8QUCKYSssQ4vvfKFQDMNg/Xi669Xg+j8APLbsGNg1+Jzv/C+minKUbCNvlmtbFkhZSR\nLadYLLsnf2E9Cos+W05GGNtarIxMobWPpJQY/D+ySa2mY7rn1dfgnKVdFvhcT1bkfS/HI4QQ3oWc\ngnF8giPPaso3Y2nWzKYE3WqT9tFqUWdkVfvW1fHQMpzYKFxR/4K+S4nPzvtw+XxaeRuMx4mxW4WF\naRyeMc94zKfOCOGlX5oC7N+fvt79+1MeQ3SvKGYlsWTE30/OX1CWmLq7ge5uq3NCHnXPzpHzqd+u\nTLVqKVhbrRaVNhsTcB0PyIfAOBoYFNDHf5smCZNnlfoyqy+6K3KXkIfBqbEAxskpniS//VBlcSUI\nARQKqeSDieusgREktgvuJbXnKPr2HE2YE3lI0ac1MaGKlpb0ZM9w8fn/jMju7Unt3/Gp96WvSYhy\nsJ+SJn3GD76T0N/XvDq5P6b/2AbT86IGAFKchg59e4/hyInTFYsQXTS3SuOWfSMpl23VY4sf97me\nAD8ExtEg0E2qHUvmVkSI04tK7bkR0yZdcImhb++xTD77NBlQrWjOlEzMzCZtqEyN+v+tD3Xj8Ix5\nyeT+letujr4//XQUJd21C+0H7kPh3AJ7lT2a1Jmdg+4d3Z9ktQ8kq3ojYgZ1cn6UVTeJCEeZ8ajn\ntx/chtLm5ZW1NGL0N69C356jKXpVd9++5tWpiZUHgQLp/5j+UxVZGH7Wuiy6/abn0CTFqpIrwVWB\nMMCOYBxvEGTNvUMvbZ4ocTKo+0YJ06RbLBYr0qqr8DHu65hTot+m75uBTzzydXwCSAzTpU3LALHc\n7eFE5VO5DYQZzpNSrN3dUaS3K2gvBqX7SIo5PXIsieDWST+UQkVlHuRtVVLTjy++Cf2KUZj+K673\n102mPs+Db54oVwoTrnbzNa7r8lapGA0bR6MiSBwNCF+1E39hVZWWrT/qkxuqdatYHzpVqMFduklC\nVVtpV7QzZ1aocFJeUzYJobs7MlAb0PSNO6LJT/XKctTqVtH+fnaPpEzTJCUWzrpMK3GQGouCCrme\nn1bnqgoHSEtueewaJmlAJ6WaJNKFs6bhyInTXlKQ7jkkOvi5/PyA2iBIHBMYttWabvVlsknQRKO6\nOBJsaR5oPFUtZgJ/wX1iQ2iSU8dy9d/35T3ldhkSHBY6B1HqUVarvb2RV9L1V0fMorUVO/bvBz6F\ndP+xhFJauxaFe+4xjsH7LdF3TmPMQJq+cQf6Pn5bEkuSSCCblqE/+V/1OcfUOB81B5lpcq+VG6tP\nWhlbKhzd+Dap2kciCfBHYBwTGHkDAU0MoBo6AL8X1jYZ6fJrqSoybqOxqTi0kwwF/BncaskzqtC1\nC9vv70oZvJNAQFIzUVLCg9sq8kX1Na/GFpVxSBn9R5uXl9vFNoqO668uG8opEaMGZFcxGYBd998U\n9Eku2IB/zrAVsydlGttW/S/LM5wln1VAfgTG0YDwyWCqm3xsqz014M+UXbda2kz9meihPqwTjqKW\n6mteDexZXY6+7u5G/yPHovxU1JeiIqI6F/SZSoB4821RQsOYqWxZ/4FKGoRAu2K8Fr09FTmx1GSM\nvORsafPyKNlinHFXhc4pAdAzGp8JWpUG+W8KADSNzWGSXvJktPXJ8hxQA/jmJqnlBuBGAD8E8BqA\nay3tlgI4CuBJAF2+/Td6riodTLl3dJXT6NOVX8oEU1tX/h+6Rp47y3RelhxHvB9nDq+4QmCyH0i1\nzZpXanjGPDmzczDKWyVl0l8qP1Sct0pb0pa+2xC3M5Xa9anEZ8pPxp8HW8U9XTXHWsJWqtb0jNai\nNKwLjZqrql7G8ScAfBjAP5kaCCFeD+CvAHwQwDsBrBJCvHNsyJt48BXPybBsKrjjA9NK0Vfl5aMq\ny6Ju8HUpBlDhYovu7nL7yY/qPa5aWoyZbRedfKIc0R3fxyRmhNs+hEiru2JVWaFrFwrnFljjZfh1\n8uuj3yb3Z5NxXLUz0b0YDRWPK8CP05F1/GDLGD3URVUlpfw3ABB2F8X3AnhSSvlU3HY7gBUA/nXU\nCWwg6F4uneFy4axpuVxza01bHpiizTnMhuAF2EjncPsCf3aLRSAuDlWBOK9VE5CUi+0/tyDymKJA\nQx7op7wTidfU5G5gSU+yPzWRxqo2X2OxzlbEz/fNE2Vzt31P2sSh7YscJnQ5pmzn2GjhbYItY/RQ\n11xVQogigM9IKSsSSwkhPgJgqZTyD+LfNwNYKKXcYOhrPYD1ADB9+vRrtm/fPmp01wNnzpzB1KlT\nR6XvqD50ZanPFbMnpfYPLJ1S0765HtzUznVeVlCQoa0fasOvd+fI+VT71rY2lNauBQCU1q1LHW9t\na4uKNcWfuv6pb7UN/206X+1Dhy8eeRlHf/aa8z8zXavrP1PHV3+7nldqT580ZlY6dGOPJUbzvRxr\ntLW1eeeqGjXGIYR4BMBbNYc+L6V8MG5TRI0YB0dIcpgfZEhWs4kSqHpfnjrRLiM1XaPqIlxLI6eP\nd5CXB5HFu4mkiOGbb0uXtI2x8ct7sOWT11f007f3WFQjnEs17P30icbPWmXPdX9N/5kuQWa6frz5\nefUpDWxKlKlm6eVJN+uBRk1yOGqqKinl+6vs4jmkyyBfFe8LGAPsuLVJ623z3Avnkhe/lqqAqM+o\nHgeg9/TJw6zKffvHI3ipyAxMY+XWYeyIVUerrlxajsNgSEk6rJ8t+0bQsYn1myH5IUH1ijPVBafx\nCFnjM9R7lMcDip9L+3Up/E100jMYbBljj/EcOf4ogDlCiFlCiIsAfAzAt+pM04SH+hKqGWqB/Lpj\n2wvesWQuBpZOqYhw5ufVpLysQo/LBpAVR06cjtx5awGFOanGfdX4bYvg59BlIDZF9OtKxBIttt9Z\noDIGXTla/iyodAZbxtijLoxDCHGDEOJZAE0AdgkhHo73XyGEeAgApJSvAtgA4GEA/wbgb6WUP6wH\nvY0GnccN/+5KVQKUJxp1EjC109FAEwpPj+EL2+QDVNbCttGSFbqMrDajvE/6F9M4HC7GkgemoNC8\nfakLEZ7FwEYvpyPv/QqoHerCOKSUO6WUV0kpf0lKOV1K+YF4//NSyg+xdg9JKedKKWdLKb9QD1ob\nDbqVKJBOU+JTf4NP+jaYVBc2nXuhaxdWbh2uOKbLT8Wzuqp5j2znZIFaS4JDvUe6lXutapqoUL3J\nTBOuK/twLWCShkz06qAyfv4ZpI6xRYgcD/DCWL2YpNNWGYoaCaybpHV2FzWrqy1NiW2fDTtubTLq\n73niPWpTjQeQb2Q9zzBL42dJ3aFj/HnzVJFtypYuxsYIbTaqgPogMI4AI1Qbg2kfwTSp+abTXjF7\nErZ80jzBmCZmnfeN6bsurbuuXRZDPJ8YuVGae/1QzIINtkJHPDZBlwpdhc4jLiuyMhsTdIw4i43E\n9v+bnrGA0UVgHAFG6AKpbMFV/BjPuqpOOKYJqVgsGvsEolW0iRn4ghvabefpGAygZyh8YqS04Crt\nnO51uyPvMbVv04SnJm/k/eWZMLnBW702n9oXrjxVQBSDYfJSzZuy3eQtVk933EbFePaqCrhA4Kx9\n4XGeDuoEs+PWJq39RWcj4Mf5d5qATO14e52twWUH2XFrU1KS12T3yAPqz3Z/fQ3tphW8r73FJyXM\ng8dfMdLCmSDZqkwVBlUE19vxgSBxBFQNnSqCdOy2F91VMMiW+gKoXHW7YCr8Y8sEvHDWNOy4tani\nuCqx2NJ3c+kLiKK0XUFjPllfqV8+GfuosVzgHnGuaos2uCru6a7PN+UIR2AmY4/AOAKqgm7yVe0E\nNntBHn20TiXGaeHgk4pJr66q1oDKCGXTBOqapHX3Z93us9j4it2GYrMv6Fb8WewxLobHVXQ6O5DP\nb9O+PFDzWtUyhiQgHwLjCMgFW9oItaKcb4ElV2I8Dt1kcfipU1oGlkeqUdvojPp8DFf/xJyi63we\nra3ZJjtXxmJfA7+vwVvH8E0ShMvuoGbAtd1DEyMLGF8INo6AXFAnJB5gp+q11fNUPXoeTxjSjXOm\nUI0nEfcWU11ZCS41ignVRjmr9bb5Pt2kytv50quzj1CKfT5eHqjXr9KnftfFvfDSsSHgr/4IjCMg\nM0y1ybfsG8HCWdOMSfHohdelwMgyNgCt5xJQaRz3ZUpcMlj0jsuM7dTrcwX4ceSdfHWuvB1L5mqD\nMjlcXmNqfzqHAZ0XHffKUqUF+o/V0rFZYXIGqEU0fED1CKqqgEzIkn3VptqgiS8rVH2+y4CbJxmj\n7RxiWDwxn++5tZrsdHXTVcnAt+6ILsaG77cZ/W0ussXi80b6Oa2HnzqVopuOm9RUPkb0gNFHYBwB\nmWAymJq8qkxQI8STCcpiNCb1lDqpkeeTy1BeS4zFxGWb5NVcYDzS2xaL4WL6WRwP8sKUCZfbkeg5\n44wpBPeNHwTGEVAVTFIDtzfQROdyL41qG+gTIeapMVHBlCwTjyv4TXeMmKNvGpCs0BmyTfeRoKZk\n0U3OtuO8DYdL0qM+814z9W9Lux6YxvhBYBwBuZHHfsALBxW6diWqCtf5upgIdWw1CZ5tctTBFneg\n80Si/nVSWC0imbk7s0qnyZtLZ3sy/U8uVaHLG83HO4vgqomi0h6kjPGNYBwPyA31hXZFLvPJg9qQ\nZJJVFaJThVXjvpk3M2610GX5JXD1E5faVObgYgDcO4qf4zMh+0Siu0AMUPWmctVZ0anQAsYHgsQR\nUDO4VqFcPaUzqtoMqgSabHTR3IA5rsF3onRFs5vyZfEcVXy/a1xfF2Kd5GGCj7SVJX4FsEsVPoxL\nN55JkrTRHTA+EBhHwKhDp5fX2QSuftPrjInxCL42CoLqLWQ7xyfSmVKom7yJqB818lyle+XWYa3b\nryvDsO7aOOoRLJdVGqhGRRYwPhBUVQGjAu4WaprQr7x0MoByLMTnFr4x93imuAauvjIVUVInKlIH\nmVb4pvTuJrWOqgb74pGXceTE6YqgtpVbh43xFKaEjdSvzhmAvo+V+o2Ps3PkvPF+6NKG8ADMoJYa\n/wiMI2BUwHXTukjhjiVz8dwL52o6pi5YzHZcpTVLFT51ciYVl60PGl9lkMS8TOo3HdQcXKVNy4wu\n0H/33ZMV+2zMJC+j4ff3hjkXeWXaJQRbxoWFoKoKGFOok7kr3qPaMXy9jFzqEVduLld7m8rJFA/D\n4zV0NhsVPJZF5/3FYXNvNbn7Bk+nAEJgHAFjBooU5hPZkROnUejahYWzpuEPr87ep2mCPvzUJwQF\nqgAAClFJREFUqWQF7xN9TN9NRY5MhmKb7YG7H5vAgxfVyVxdhfu4vdbKPkAu0zZbDmC+/ytmT0rs\nVcFmMfFQF8YhhLgRQA+AXwPwXinlY4Z2JQA/B/ALAK9KKa8dKxoDag91lapOhLoKgL59qpHOPMaC\nT2yuiZfbRHxW1bpJUZ381RoZxWIxqgKIMuMkVBNEx8e+8tLJWu8vDldUuUmyUcfTMTb+XwbpZOKh\nXhLHEwA+DGCrR9s2KeVPR5megHEGUtH4utByQ7EuJQrv19VnlsqEeZnLlZdOxkeumQFgdPIxHey6\nLvmuMlRbDRFbdb9qmVrAxEFdjONSyn+TUh6tx9gB4wc2+4bqsgu4J/SFs6ZpA+QAv0y5akZWU8Cb\nzSVYB1UNBgDPvXBO613kkxLdNZ7rmAlkZFfp4XTZ7l9QSTUOhJSyfoMLUQTwGYuq6gSAFxGpqrZK\nKe+29LUewHoAmD59+jXbt2+vPcF1xJkzZzB16tR6kzGq4NdIqpyBpVOS4+t2n01+7xw5jwePv6Lt\nZ2DplKStrh8X8pyj0kfYOXIeN8y5KLXvzJkz2HBAJG3X7T6LFbMn4cHjr6T2DSydYrxOtb2Nli8e\neRlHf/aatg+VNqKZxuT3Mgsa4XkFJtZ1trW1fdfXHDBqjEMI8QiAt2oOfV5K+WDcpgg747hSSvmc\nEOItAPYCuE1K+U+usa+99lr52GPaLi9YRAkAW+tNxqhi45f3GJkBT4aowidwj/rIG0DoA536R80w\n6wrQ41H1uqSGvJ3pfphose0n1OI+AI3xvAIT6zqFEPVnHF6DOxiH0rYHwBkp5f9ytQ2M48IEv0Zu\nuHVNZDodPo/uzpq+gry8yCvLZhdxTbS68ck4rqPZ1ZftfgDutOlZ7keee0dohOcVmFjXmYVxjFt3\nXCHEFACvk1L+PP5+PYA/rTNZAWMMn3xJLs+mPOA5pFzFmUypz11p3X0M9T7jqcdNx4gGH4TSrAE2\n1MU4LoS4QQjxLIAmALuEEA/H+68QQjwUN5sO4IAQ4vsAvgNgl5Rydz3oDRh7bLxujvckV63BVpc5\nthro0oaokziXHGg8XdoUbpCuhfHZl1G5kj0GNDbqInFIKXcC2KnZ/zyAD8XfnwLw7jEmLWCcIEv9\niGoLKZFEYUt6qPapkxayZInl8SVqWhJXWg6f8caSyQQ0HsatqiogQEUWdZEvuLShC9Yz9amriOfD\n7CLmdBbYba7prTtPN4ZtYs8z6Y9WJcOAiYfAOAIaEnlSqttgkxR437qSubbstr7SSC1QDQMOaCwE\nxhEwoZDFLsLzMHHQPlrhm1LEqyk7bONQe15bnauqqpmw8xjZAwKqQWAcARMKPhNo1tgIbpfgthBq\n7/KeMsGXIbnUR6MhiQTDeIANgXEENBzUFb46CZugq2QIuIPxCOpkrDIkoieri+1oIEgwATYExhHQ\n8HAZpXk7U5pxn5KttZyMgyE7oJ4IjCOgoWGSAlTo1FtcWqmVasfXxTYYsgPqicA4Ahoavqtzm3or\nSz/V0BMkiYDxglBzPCAgB8bTJB4M2QFjjcA4AgIyYrxN1OOJiQU0BgLjCAjIiDBRBzQ6AuMICAgI\nCMiEwDgCAgICAjIhMI6AgICAgEwIjCMgICAgIBMC4wgICAgIyIS61hwfLQghfgLg6XrTUWO8GcBP\n603EKKMRrhFojOtshGsEJtZ1zpRSXu7TcEIyjokIIcRjvoXkL1Q0wjUCjXGdjXCNQONcp4qgqgoI\nCAgIyITAOAICAgICMiEwjgsHd9ebgDFAI1wj0BjX2QjXCDTOdaYQbBwBAQEBAZkQJI6AgICAgEwI\njCMgICAgIBMC47hAIIT4khDi34UQPxBC7BRCXFpvmkYDQogbhRA/FEK8JoSYUG6OQoilQoijQogn\nhRBd9aZnNCCE+KoQ4sdCiCfqTctoQQgxQwgxJIT41/hZ3VhvmsYagXFcONgLYJ6U8tcBHAPwuTrT\nM1p4AsCHAfxTvQmpJYQQrwfwVwA+COCdAFYJId5ZX6pGBQMAltabiFHGqwD+h5TynQAWAfjjCfpf\nGhEYxwUCKeUeKeWr8c//v737DZGqisM4/n3MymrDtIzwT6gg2gvRJCQRMkpIKgpJUKIgisLITAvq\nhSEFviiMBMmoF9UbLYsUDTW1wjArQyxTY9EihMxASKM2IcueXtyztAzmNrW719XnAwMz55579pkL\nM7+5d2bP2Q4MrTNPd7Hdantf3Tm6wUTgG9vf2j4OrARurzlTl7O9FThSd47uZPsH25+X+78ArcCQ\nelP1rBSO3ule4N26Q0RThgDfdXh8kLPszeZMJGk4cDXwWb1JelbfugPE3yS9D1xxkk0LbK8tfRZQ\nnSqv6MlsXenfPM+I052kFmAVMM/2z3Xn6UkpHKcR21NPtV3SPcCtwI3uxf+A09nzPEN9Dwzr8Hho\naYteSNK5VEVjhe3VdefpablU1UtImgY8Dtxm+1jdeaJpO4BRkkZIOg+YBbxTc6b4DyQJeAVotf18\n3XnqkMLRe7wAXAy8J2mXpJfqDtQdJE2XdBCYBKyXtKnuTF2h/LBhDrCJ6svUt2x/VW+qrifpDeBT\nYLSkg5LuqztTN5gM3A3cUF6LuyTdXHeonpQpRyIioik544iIiKakcERERFNSOCIioikpHBER0ZQU\njoiIaEoKR0QnJLV1wRgbztQZjePsk5/jRnRCUpvtlrpzRJwucsYRUUhaI2lnWWPhgYZtS0r7B5IG\nlba5ZU2G3ZJWlrYWSa9J2lPa7yjtByRdJukiSeslfSlpr6SZZfszHcZ6rrQNkrRK0o5ym3ySzPMl\nvVrujy1jXti9RyrOdjnjiCgkDbR9RNIFVFOETLH9oyQDd9leIWkhcLntOZIOASNs/ybpEts/SXoW\nON/2vDLmANtHJR0ArgGmANNs31+296eaM+4TYIxtdxjrdeBF29skXQlssn1VQ+Y+wIfAEmAB8Ijt\nj7v7WMXZLYUjopD0FDC9PBwO3GR7u6QTVMXgD0kjgdW2x0vaCLQBa4A1ttsk7QRm2f66YewDVIVj\nILAZeBNYZ/sjSX2BneW2rrQfl3QYONRhmEHAaNttDWOPBHYDL9t+rKuOR8Q/yaWqCEDS9cBUYJLt\nccAXQL9/6N7+aesWqlX9JgA7SgE4Jdv7S/89wCJJC8s8VhOBt6lmP95YuvcBrrU9vtyGNBaNYhRV\nARvc+TON+P9SOCIq/YGjto9JGkO1JGi7PsCMcv9OYFu5RDTM9hbgibJ/C9USvw+17yhpQMc/Imkw\ncMz2cmAxMKGs69Df9gZgPjCudN8MPNxh3/GNoculrqXAdcClkmY09onoalmPI6KyEZgtqRXYR7U8\nb7tfgYmSngQOAzOBc4Dl5Y1bwNLyvcQiYJmkvcAJ4Gmg43oNY4HFkv4EfgcepJr1eK2kfmWsR0vf\nuWWs3VSv1a3A7IbcS4BltveXmWi3SNpq+3AXHJOIk8p3HBER0ZRcqoqIiKakcERERFNSOCIioikp\nHBER0ZQUjoiIaEoKR0RENCWFIyIimvIXNJOBjEd4RM4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10bf9e160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x=[]\n",
    "y=[]\n",
    "for k in range(2000):\n",
    "    u=4*random()-2\n",
    "    v=4*random()-2\n",
    "    z=complex(u,v)\n",
    "    if abs(z+1)+abs(z-1)<=4:\n",
    "        x.append(u)\n",
    "        y.append(v)\n",
    "plot(x, y, \"+\")      \n",
    "xlabel(\"abscisse x\")\n",
    "ylabel(\"ordonnee y\")\n",
    "axis([-3, 3, -3, 3])\n",
    "title(\"TDO5 - exercice 2\")\n",
    "savefig(\"exercice2.pdf\")\n",
    "grid()     ### permet d'afficher un quadrillage du plan\n",
    "#show()\n",
    "axis(\"equal\")\n",
    "s=[u/2 for u in x]\n",
    "t=[v/sqrt(3) for v in y]\n",
    "plot(s, t, \"+\", color=\"red\")   \n",
    "show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Exercice 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "Pour tout nombre complexe ${\\rm \\texttt{c}}$, on définit $l'ensemble$ $de$ $Julia$ $J_c$ à partir de l'étude des suites récurrentes:\n",
    "$$\\left\\{\\begin{array}{l}\n",
    "z_O \\in \\mathbf C\\\\\n",
    "z_{n+1}=z_n^2+c\n",
    "\\end{array}\n",
    "\\right.\n",
    "$$\n",
    "Suivant la valeur $z_0$ de d\\'epart, la suite sera bornée ou ne sera pas bornée. Les valeurs $z_0$ pour lesquelles la suite est bornée sont les éléments de $J_c$.\n",
    "\n",
    "\n",
    "Voici un programme pour tracer l'ensemble de Julia :"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZIAAAEICAYAAAB1f3LfAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\npZRyRQOJUkopVzSQKKWUcuX/ARdOcbdWQFX3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110af1278>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "c=-0.8+0.2j\n",
    "\n",
    "a,N,Nb_iterations=1.5,1000,50\n",
    "x=linspace(-a,a,N)\n",
    "y=linspace(-a,a,N)\n",
    "U=[]\n",
    "V=[]\n",
    "for Re in x:\n",
    "    for Im in y:\n",
    "        z0=complex(Re,Im)\n",
    "        z=z0\n",
    "        p=0\n",
    "        while abs(z)<2 and p<Nb_iterations:\n",
    "            p=p+1\n",
    "            z=z**2+c\n",
    "            if p==Nb_iterations:\n",
    "                U.append(z0.real)\n",
    "                V.append(z0.imag)\n",
    "plot(U,V, \".\")      \n",
    "\n",
    "axis([-2, 2, -2, 2])\n",
    "title(\"ensemble de Julia pour Nb_iterations=%g et depart %g + %g i\"% (Nb_iterations,c.real,c.imag))\n",
    "savefig(\"ex3_ensemble-de-%g.pdf\"% (Nb_iterations))\n",
    "grid() \n",
    "show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " 1. Executer ce programme en faisant varier la variables ${\\rm \\texttt{Nb\\_iterations}}$ parmi les valeurs 10, 20, 30, 40, 50... \n",
    "\n",
    " 2. Comprendre ligne à ligne ce programme.\n",
    "\n",
    " 3. Quels sont les nombres complexes que l'on retient comme étant dans dans l'ensemble de Julia ?\n",
    " \n",
    " 4. Sur le même principe, on prend $z_0=0$ et l'ensemble de Mandelbrot est obtenu en ne retenant que les valeurs de la constante $c$ pour lesquelles la suite obtenue est bornée. Dessiner l'ensemble de Mandelbrot."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Ensemble de Mandelbrot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYAAAAEICAYAAABWJCMKAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAFBKKZf6/x21EGnbubXTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1199d10b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a,N,Nb_iterations=1.5,1000,100\n",
    "x=linspace(-a,a,N)\n",
    "y=linspace(-a,a,N)\n",
    "U=[]\n",
    "V=[]\n",
    "for Re in x:\n",
    "    for Im in y:\n",
    "        c=complex(Re,Im)\n",
    "        z=0\n",
    "        p=0\n",
    "        while abs(z)<2 and p<Nb_iterations:\n",
    "            p=p+1\n",
    "            z=z**2+c\n",
    "            if p==Nb_iterations:\n",
    "                U.append(c.real)\n",
    "                V.append(c.imag)\n",
    "        \n",
    "plot(U,V, \".\")      \n",
    "\n",
    "axis([-1.6, 0.7, -1.2, 1.2],'equal')\n",
    "title(\"ensemble de Mandelbrot pour Nb_iterations=%g\"% (Nb_iterations))\n",
    "savefig(\"ex3_Mandelbrot-avec-%g-iterations.pdf\"% (Nb_iterations))\n",
    "grid() \n",
    "show()\n",
    "\n"
   ]
  }
 ],
 "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
