{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Série de Fourier\n",
    "\n",
    "\n",
    "On considère une fonction $f(t)$ T périodique, continue par morceaux. \n",
    "$$f(t)=a_o+\\sum_{n=1}^{\\infty} a_n \\cos\\left(\\frac{2\\pi n}{T}t\\right) + b_n \\sin\\left(\\frac{2\\pi n}{T}t\\right)$$\n",
    "\n",
    "Le coefficient $a_o$ représente la valeur moyenne de $f(t)$ :\n",
    "$$a_o=\\frac{1}{T} \\int_0^{T} f(t) dt $$\n",
    "Les coefficients $a_n$ sont nuls pour $f(t)$ impaire :\n",
    "$$a_n=\\frac{2}{T} \\int_0^{T} f(t)\\cos\\left(\\frac{2\\pi n}{T}t\\right)  dt$$\n",
    "Les coefficients $b_n$ sont nuls pour $f(t)$ paire :\n",
    "$$b_n=\\frac{2}{T} \\int_0^{T} f(t)\\sin\\left(\\frac{2\\pi n}{T}t\\right)  dt$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10d087d68>]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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fPp+G9h7OmFY4eD7mSM6qKubr1xcnO21y/D5WLZrKqkVJfwrl+bmUjxLuxzIz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\nDRHvHQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10cceceb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "L=1\n",
    "N=10000\n",
    "nmax=50\n",
    "x=np.linspace(0,L,N)\n",
    "delta=0.2\n",
    "\n",
    "f_1=np.ones(N)\n",
    "for n in range(1,nmax) :\n",
    "    f_1=f_1+2*np.sin(n*np.pi*delta/L)*np.cos(n*np.pi*x/L)*L/(n*np.pi*delta)\n",
    "\n",
    "plt.plot(x,f_1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Si la fonction n'est définie que sur L/2, on peut choisir de compléter de façon paire ou impaire a priori."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10d1cb2b0>]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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MH//uK/z7r7zAnz60n562NIf7R/F8x9olLXzonmt557ZVbMy0cmJwnKcPD/Do\nK/08+ko/39h9clKtsHl5O++5bS23r19Cpj3NhbE8h/tHeen0MC+dHuJvnjhKzgtCPZWI8ZoV7bxl\ny3LWLm2hpzVNtuBzcnCcg2dHODYwxhMHzzGaC9pES1pTrOluZvOKdu7elCkH+niuwIXxPINjeS6M\n5zkxOMH+U8NkPZ+2dJzWdBDMKzqaymGa83yGJjxGsnnODk9wqM/DETx/6GlLc22mjXQiTiJu5Dyf\nC+N5hibynBvJkfP84NzUuNGWTtDRlGBFR5pUIk6qGLYjWY/RnMfwhIfn+/h+EIbxmJGIWfHv4LeF\ndDJR/oHsFRy5QvADIV/wMYxYLAj9UvjHiiGdjFk5zD3fJ+sFAR0vXm+l62OxcuhCMdT90g+R4HuY\nBV+XmBTqkwVhGnydw2HEghAvBvlsYVj6+hk/h7vsNcxszhCd/rXmqqP2HwmTv7QpGa/5dapRSXCf\nANZMen918WNTOOceAB4A2LFjR03/FT49Dz+pwmx5RzAKPjs0dUrg04cHuH1992Ujk/tuXMHaJS38\nxfcOcO9rluOA3/7SbpyDv3jv9st+e7nrugyf+ze38+HPP8f7P/00AKl4jH977yZ+7Z6NU643M95y\nwwp+fMtyvrv/LN9+8TRDE3nu3bKcH9+ynO1ruqbUs7o7GAX/9C2rcc7x8plhXjkzQndLiptWdU7b\nnpnMK/icGBynORmvqCXinCNfCAJPLRGJmkqC+xngOjNbTxDY7wF+rq5VRVSpfXFmKFv+2PHzY5wY\nHOeDd62/7Pp4zPjd+67nQ59/lo98eTej2QJPHx7gf/7szaxZ0jLt97h13RK+95E38egrfYznC7z+\n2h562tLTXgtBgN+7ZTn3blle8X2YGdev6OD6FR1zX1yUiMdYt7R17gsnfY9UQoEt0TRncDvnPDP7\nMPBtIA582jn3Yt0ri6B0Ihhtnpk04t519DwAt03qb0/2k1uv4aXT1/KX3z9AImb84du38K7tsy/M\naU7FecsNK65e4SIyryrqcTvnHgIeqnMtAixrT08Zce86ep7WVHzW0etH3rKZ99/ZSzIWm7MlISKN\nL1RL3gVWdDZx6sJ4+f1dR8+zfW33nH3c2dodIrK4RHfuXUj1Lm3lSP8ozjlGsx77Tw1xy9quhS5L\nREJEI+6Q2bisjdFcgTNDWQ71jeA7uGVd90KXJSIhouAOmY2ZYGbFwb4Rnjx0jpjB9rUKbhG5SK2S\nkNm0PFhRYoA9AAAES0lEQVQAs+fEBb7/8lluXddNZ7MeOIrIRQrukOlpS7NpeRuffeIoe08Mcc/1\nyxa6JBEJGQV3CN13wwpODI6TiBnvvkWHJYjIVOpxh9CvvHEjE57PjnXd5f1LRERKFNwh1JpO8Ptv\ne81ClyEiIaVWiYhIg1Fwi4g0GAW3iEiDUXCLiDQYBbeISINRcIuINBgFt4hIg1Fwi4g0GLuS041n\nfFGzPuBojV/eA/RfxXIage558Yva/YLuuVrrnHOZSi6sS3BfCTPb6ZzbsdB1zCfd8+IXtfsF3XM9\nqVUiItJgFNwiIg0mjMH9wEIXsAB0z4tf1O4XdM91E7oet4iIzC6MI24REZnFggS3md1nZi+b2QEz\n++g0nzcz+1/Fz79gZrcsRJ1XUwX3/L7ive4xs8fN7OaFqPNqmuueJ113m5l5Zvbu+ayvHiq5ZzN7\nk5k9b2Yvmtm/zHeNV1sF/293mtk/mNnu4j3/0kLUebWY2afN7KyZ7Z3h8/XPL+fcvP4B4sBBYAOQ\nAnYDWy655m3APwIGvBZ4ar7rXIB7vhPoLr791ijc86Trvgc8BLx7oeueh3/nLmAfsLb4/rKFrnse\n7vn3gT8rvp0BBoDUQtd+Bfd8N3ALsHeGz9c9vxZixH07cMA5d8g5lwO+CLzzkmveCfytCzwJdJnZ\nNfNd6FU05z075x53zp0vvvsk0OiHTVby7wzw68BXgbPzWVydVHLPPwd8zTl3DMA51+j3Xck9O6Dd\nzAxoIwhub37LvHqcc48Q3MNM6p5fCxHcq4BXJ71/vPixaq9pJNXezy8T/MRuZHPes5mtAt4F/NU8\n1lVPlfw7bwK6zewHZrbLzH5x3qqrj0ru+S+B1wAngT3Abzrn/Pkpb0HUPb905mTImNk9BMH9hoWu\nZR78OfC7zjk/GIxFQgK4FfgxoBl4wsyedM79aGHLqqufAJ4H3gxsBL5jZo8654YWtqzGtRDBfQJY\nM+n91cWPVXtNI6nofsxsK/Ag8Fbn3Ll5qq1eKrnnHcAXi6HdA7zNzDzn3P+bnxKvukru+Thwzjk3\nCoya2SPAzUCjBncl9/xLwH91QQP4gJkdBq4Hnp6fEudd3fNrIVolzwDXmdl6M0sB7wG+cck13wB+\nsfh09rXABefcqfku9Cqa857NbC3wNeAXFsnoa857ds6td871Oud6ga8Av9bAoQ2V/b/998AbzCxh\nZi3AHcD+ea7zaqrkno8R/IaBmS0HNgOH5rXK+VX3/Jr3EbdzzjOzDwPfJngi/Wnn3Itm9qvFz3+S\nYIbB24ADwBjBT+yGVeE9/0dgKfCJ4gjUcw28QU+F97yoVHLPzrn9ZvYw8ALgAw8656adVtYIKvx3\n/hPgM2a2h2Cmxe865xp210Az+wLwJqDHzI4DfwQkYf7ySysnRUQajFZOiog0GAW3iEiDUXCLiDQY\nBbeISINRcIuINBgFt4hIg1Fwi4g0GAW3iEiD+f+kr1IQsSC+3AAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d0f2ef0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f_2=np.zeros(N)\n",
    "for n in range(1,nmax) :\n",
    "    f_2=f_2+2*(1-np.cos(n*np.pi*delta/L))*np.sin(n*np.pi*x/L)*L/(n*np.pi*delta)\n",
    "\n",
    "plt.plot(x,f_2)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On peut reproduire la forme d'une corde pincée."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10d44b160>]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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lJ2vsLitgaPA3kVXgpHNEKMN6xNhdilJ+L9gRxG9uTOZ/pgxmw55yMuauodCp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\nYDT4lVIqwGjwK6VUgNHgV0qpAPP/ARw7D2NUQVroAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d24e898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "h=0.3\n",
    "f_3=np.zeros(N)\n",
    "\n",
    "for n in range(1,nmax) :\n",
    "    f_3=f_3+2*h*np.sin(n*np.pi*delta/L)*L**2*np.sin(n*np.pi*x/L)/(n**2*np.pi**2*delta*(L-delta))\n",
    "\n",
    "plt.plot(x,f_3)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kSu/eJP32G8nLV1Tqd5fJ/iMHhhfsoH88iRl5jGpVk+ibfmz8chaK/DyGfPU9\ndd1aPHqAIh8OfAam9tB8UtHmnJwcQkJCcHJyKnOZzSdiZA3DtxTObdg8EhR5lXPeV4BeFSO6TpnO\n0K/no6Ovz+4F3/HvD3O4Ex9bVKZt27ZYWFjg5eVFTk4OtqZ6rBrTjGUjm5KWnc/Apaf5ZNt1UrPy\ni47JvnKFiJGjiH73PdS0daj1zwaqffABUgnJ/koiqatT44fvqdKrF0kLFpCycmWlf3eZTA4ML9i6\nMxHYmOhikxnOtu++QN+oKsO//ZnqdeuVfMC5ZZB6G7r9UGyuQWBgICqVCicnp0cOCb8bzpzTcxi9\nfzSfHP8E70hvVOLxTR0AWLpA/2UQcxG8ZhY2Y71BrBzqM/KHhbiPnkhs0E3WzHqPU1s2UJCfh7q6\nOn369CEzM5MTJ04AhR3a3ZwtOTyzA5Pa27H9cjSev/iwY7svUe+8S8Sw4eRHRFB9zlfY7d6Fbnkm\nIT6kKDj06EHiz7+Q8tdflf21ZW84ObvqCxQUn8G5sFQ+ss9h74KFmNe0Y8Bnc9CrUkpmz4wE8P0J\n7LuCffF1m/38/DA2NsbKqvjE8fNx55l6bCoATqZOnI07y76wfdhXteedRu/Q0bYjatJjng8a9IH2\nH8Pxn8CyMTSf+NTf+VWkpq6Oa8++OLRqi+/6VZzdvpGAk954jp2MXZNmNG7cmHPnztGsWTOqVq0K\ngIG2BrN71GdgXQMufTqXev+cJklLB+2xk3CYOgm1B5YrfRqShgY1fvoRgMT5PyPy8zF7550nOkf6\noUOkrlpNXlgYGmZmVOnRHZO330bdoPLnZsheLXJgeIHWnQ2nVn4s+Ue9sLR3oP8nc9DW0yv9gGNf\ngyIXun1fbHNWVhahoaG0adOmWMdlfFY8M31nUkO/Bn92/hMLfQsUKgUHww+y7NoyZvrMpFaVWoyo\nP4KOth0x1ytjnQX3zyD+Ohz4FKo1gFptKvr1XzkGJqb0nP4RDT27cPSvpez4YS51m7Wi2aDh+Pv7\nc+TIEQYPHgwU9iOk7/VC+v57mqSnk9JrMP/TbUJUmiajjoQ9NnNrUkQYVw7uJSkiDG09fWydG9HQ\nswu6hlWKyvwXHCRNDZIW/o4oKMBs2rTHToRT5eaS8MMP3Nm0mQTHOkQ3qE1mThY6+/7Fev8eWs37\nEYNGjSrnR5O9kuThqi9IZp6CTl9tZ2DUFsyrWzD065/Q0S/jSS3hJixtDa3eg67ziu26ePEie/fu\nZfLkyVgf8ilxAAAgAElEQVRaWhZtn+kzk+iQUOY7zKOGfS00q99/SlWqlByOOMxffn8RmBoIQK0q\ntXA2c8bZzBk3Czfsq9oXf5vIvQsrOhb2OUz2LeyDeEMpFQVc3LODs/9uRpIkTFt7EhyfyPjx46mu\nrU38l1+R6eODjosLlt98g45DPe7mFBRlbjXR1+Z/PR3p19iq2I1cCMH5nVs5tXk9GtraWNatR05G\nOkkRYWjq6NJywBBce/ZDXeP+M51QKon78kvubv8X0wnjMf/ww1KDQ15ICDEzZpIbHEyARyvCUxMx\ntbbFonYdEoICSEmMR69AgeewMTgMHvrMf0fZ8yUv7fmSW3c6lGvL5mGjlsHY+X9Qxfwxk6P+GVqY\nBfX9q6BXPAX26tWryczMZOrUqUU3BL/EG5xatZueae2Lyum5WVC1b10kzfs3eyEEIWkh+Eb7ci3p\nGv7J/iTlJAFQRasK7jbu9KjdgxaWLdBQ04DkYFjhCSZ2MO5AYRK+N9jdxAS81ywn5NIFcuo1oqqO\nLp127YbcXMxnfIDJqFFID6Um8Yu5y/92+nEtKo0WtU34pp8z9SwMEULgu34Vl/buwLFNBzqOewed\ne806yVERnNy0ltsXz1GtVh26TJ6Ghd39tcCFSkX8N9+QtnEThp07Y/n9d8WahIQQpG3ZSsL33yPp\n6RHS1Z3Am9doO3Q0zfsOQlJTQwhB6AkfDi/6hSw1qO/UmI6zZpf9Fit7pciB4SUmhGDKxz9TL9KX\nntM/xrFN+7IPiDgNq7tDx6+g3cxiu9LS0vjtt9/w8PCgQ4cORdt3LPuLZuH10G5dDeMW1mRfTiTD\nNxqdBqaYjqiPpF56c0NsZiyXEi5xNu4sxyKPkVmQiYmOCZ1rdqZ77e40uZOA2qbhhYsC9f/ztcyp\n9KQC9+3Ga/dOMqrbYhMVSr/pMzFtVHrHskol2Hwxih/2B5KVp2Bc29q0ybjMxX830rhrLzzHTi7x\nqT/43GmOrlpKdvpdmvUeQKtBw9HQKhyEIIQg9e81JP78MxomJpiMH4eeqysFcXHcWb+B7PPn0WvV\nktBWrlw+eoAW/YfQduioR66Rm5DAwfcmEqKmxMCwCt3e/4SaLk/eSS57+ciB4SV2xi8cn29nYFjb\nganfP2bBOiHgry5wNwqmXQat4k9vJ0+e5MiRI0yfPr1oMZ24m2EUrI0kzC6ZDpMGFpXNPB1L2u7b\nGLS1wriXXbnqmqfM42T0SfaF7cM32pc8ZR4WehZ0VK9Kh1vHadb+czRbT3uyH+A1oszIIHnpMlLX\nrUOprYVXjx7kKfIxirlN60HDaNq9T7Fmn4elZuXz4/5ArnkfoXPyMYxcWjHus8/KHHKcm5mJz7qV\n+PscoaqlFV2mTMfa8f5otJxr10j44Udyrlwp2qZuZob5e+8SpC1xavN6GnftiefYKaUvBpWWxpXx\n47iozCJLWxOXjt1oN3xM0RuM7NUkB4aX2NxPv0Yv7CLDf1yEVa3H5DQK2AubR0Dv38H17WK7hBAs\nXboULS0tJkyYULTtxvyDKNLzqDajCdamxSdN3dkVQtaZOExH1kfX2eyJ6p1VkIVPlA8Hwg5wJu4M\neco89FUqWldrirvjYNpZtaOqTtUnOuerSgjB3V27SPxpPso7dzAa0J9qH3xAcHIymzdvxloT7l6/\niJltLbpMmoalvUOp54r0u862774gxcCajVW70tahOnP7OFHbrOyRS+HXr3B4+SLSk5No3KUn7Ya/\njZbO/aa9/PBw8kLDUDc2RsfZiWvehzi2ahn123nQ/d0ZxWfTl0CZnk7YxAlcT44j3NwYHQND2g0f\ng7N7p8ceK3s5yYHhJRUTHc+GWZNQ1GnG7HlflF1YqSjMhwTwzhlQL/7kGRERwerVq+nduzeurq4A\n5ATfIeUvP/Y5nmfSmA8fOaVQqEhcdg1Fcg4W05uiYaLzVN8jR5HD2UhvfI/N5rhaAUnqaqhJajQy\nb0QH6w6427hjZ2T3WqaKzgsNJX7OXLLPn0e3USMsvvwC3XvzR4QQrFq1irS0NHq2boHv2hVk3kml\nabfetBk6qtiNGwrX7v73h7kYmprx1pwf2XIjhV8O3SJfoWKKex3eda9TZubW/NwcTm5cy5WDe6li\nZk7nCe9Rq7HrI+WuHNzLsVXLqOPWkj4zP0OtnCnZlZmZRE2cRMKtAIJbu5KQGI9lXQc8x02heh37\nJ/jVZC8DOTC8pBb9sIDcK950/GIBTZ0f8x/WpTWFayMM2QD1ez2ye+vWrdy+fZuZM2eida+dOfSP\n06THpxA1StDboU+Jp1Wk5pKw8DKa1fQwn+KCpF6Bp7/UUFQrOhJgaIJPs+H4xp8jIDUAAGsDa9xt\n3Olg0wFXC1c01co3u/dlpcrNLUyLvWIlarq6VPvwQ4wHD3rk6TkyMpJVq1bh6elJCzc3Tmxcw7XD\n+zA0NcN91HjsXFugLCjg2uF9nN66ASNzCwZ/MQ8Dk8JlWBPTc5m3L4BdV2OxMdFlbh8nPB0tyqxb\nTOBNDv75O3dio7Ft2BjXnn2pYV+fzDspXNi1jZsnvKnj1oLeMz5FXePJ/g7KzCyipkwm+/IVMt8e\nzqXbAWSn38WlY1faDh1dbAit7OUmB4aXUHZ6BosmjybNzJ7vF/1UduH8bFjkWjgkdPyhRzp409LS\n+P3332nevDndunUDIC/8LknLrrPSYgcfvjcXQ63S1yjOvp5E6j+BGLS3xrhHOVd6K034KVjbF2q3\ng+Fbic9N5nj0cXyjfTkXd448ZR6Gmoa0tWqLu407ba3bUkXr1bqZZJ46RfzcrymIjKRKn95YfPwx\nGmalN8Vt3LiRsLAw3n//ffT19YkJCuDQn7+TGhN1/28pBHauzek65f0SJzWevp3Ml7v8CUnMpHMD\nC77q3QDrqqWPEFLk53P1kBfnd20jJ/1u0XY1dQ2a9RlI68HDy/2m8DBVTg4xMz8k09sbw3HjCK5m\nxJWDe9HW06ft0NE07NgFNbWKr0khe7bkwPAS2rZ2IxFeG7AaM5uh3VuXXfjkr3BkDozZV+Jkst27\nd3Pt2jWmT5+OkVHhTSVplR9JodH81f4gv3T59bH1ubMjmKxz8ZiOdULXweSx5ct0eR3snlqYv6nH\n/KLN2QXZnIs7h0+0Dz5RPqTmpqIhaeBq4Vr0NmFjaFPGiV8sRVISCT/8SLqXF1o1a1J9zlfot2r1\n2OOSkpJYsmQJzZs3p3v37gAoFQoiblwhLvgWaupq1GzYmBr16pd5nnyFir9OhvH70WAEgmme9kxs\nZ4eWRulveYr8fKL8r5MaG42Wnh61G7kWvY1UhFAoiP/6G9K2bMGob180J43n2Pq/iL7pV7jc7KRp\nVKtVvkENshdDDgwvGSEEP0wcT7pC4qsVy8te8Ss7FRY2hpqtYPjmR3anpKSwePFi3NzcitZdyI/J\nJHHRFf4230WT/h70tOv5+DoVKElcfBVlRj4W7zdFvYr2Y48p06HP4fQi6PFziWkzVELFjeQb+EQV\nBomQtBAA6hrXxcPGA3cbd5zNnB+fouM5EAUF3Nm4kaRFfyDy8jCdPAnTCRNQ0y7/b7R7926uXr3K\n1KlTi0aMPa2YtBy+2XOTA/7x1DHX55u+zrSu+2SDByqDEIKUZctIWvg7+q1bU2PhQoKvX8JnzQpy\nMtJp2r0Prd8a8Uhfiuzl8FzXY5AkqZskSUGSJIVIkvRpCfsdJUk6I0lSniRJsx7aFy5J0g1Jkq5K\nkvRq3e2fgP+Va2hlJGLUuN3jl4E8uQDy0gvnLTxECMHevXvR1NSkXbt2RdszjkWSr6HgkNlZ3G3c\ny1UnSVMdk+H1EfkqUjcFIVQVfEjoNBfqdYP9n8DtY4/s/q9z+v2m77Oj7w729d/Hx80+xkTHhFV+\nqxixbwSeWzyZc3oO3pHe5ChySrjIs5d58hSh/fqT8N336Lq4YLd7F+bvvfdEQQHA3d0dNTU1jh17\n9Ld4UlbGuiwb5crqsc1QqATDV55j+sYrJKbnVvjcT0KSJMzeeQfLefPIOneOyLdHU9e+PmMXLKOh\nZxcuee3k75nvcuvcKV7Fh05ZoQq/MUiSpA7cAjoD0RSu4zxMCHHzgTLVgJpAP+COEOLnB/aFA25C\niOTyXvNVfGP49Yu55AZfZdDPK7G3LuO1Pi2qsG+h4SDot+SR3RcuXMDLy4tevXrh5lYY+Avis0hY\neJmd1XwIbXKHBe4LnqhuWRcTuLPtFobuNhh1q/VExz4iLwP+6grp0TDRu2gt6se5m3eXkzEn8Yny\n4WTMSTILMtFW16aVZauiJicz3Wf7hJwfHUPCd9+ReewYmra2WHz6KQYe7hUaWXX06FFOnDjBxIkT\nH0lw+LRyC5Qs873NEp/baKmrMaNzPd5uVRONigwieAqZx48T/cEMNIyNsVm5Am07O2KCAji6cjFJ\nkeHYNmyM55jJmFq/vE2Fb5rn+cbQHAgRQoQKIfKBTUDfBwsIIRKFEBeAgkq43isnKz2DguDLpFs1\nLDsoAPjcS5Dn/tkjuyIiIti/fz9169aladOmRdvTj0Wi0oR/qnjRpVaXJ66fnms19JtVJ8MniqzL\nCU98fDHahjBsI6hpwMahhfmVysFI24iedj2Z32E+x4ccZ0WXFQyqN4hbd24x58wcPLZ4MMJrBCuu\nryD4TnClPo2KggKSV6wgtFcvss6exfzDmdjt3YOhp0eFh9u2adMGPT09jhw5Uml11tFU54NO9Tg8\noz2uNavyzd6b9Fp0kovhqZVy/vIyaN+emmvWoMrLI2LYcHJu3ChKU+45bgoJocGs/Xhq4Sp4OdnP\ntW6yiqmMwGAFRD3wOfretvISwBFJki5JkjSptEKSJE2SJOmiJEkXk5KSnrKqL8aef/egLpQ07/aY\ndv/4G3D1n8L2eePiT1lpaWls3ryZqlWrMnDgwKKZsQXxWeTcSMavViT52graWz0mvUYJJEnCuG8d\ntO2MuLM9mLzw8t3MS1W1ZuHSoKmhsH0iqJRPdLimuiYtLVvyafNPOTDwANv7bGdak2kIBL9f+Z0B\nuwfQ/d/u/Hj+R87FnaNA9fTPG9mXrxA2YCBJvyxAv20b6uzdg9nEiahpaT3+4HLQ0dGhffv2hIWF\nERISUinn/E9NU33+Hlu4MFB6TgGDlp3ho63XSMl8fgsq6TZ0ptbGf1AzNCTy7TFknT2Hmro6Tbr2\nYtyvfxatgrdqxhQCTnjLzUuviMpoShoEdBNCTLj3eRTQQggxtYSyc4DMh5qSrIQQMfeamw4D04QQ\nx8u65qvWlPTthAnkKFTM+WslmqW97gsBa/sUBofpV0D3/gzivLy8oklTEydOxOzeMEkhBMl/+ZEf\nncE79eZhZ2nPbx6/PXU9VdkFJC65hiq7APNJLsWysZZ6TK4Cka9CzUATSe2hp+sLK8HrQ2g7AzrN\neep6PSgpOwnfaF98onw4G3f2/lBY67a4W5d/KKwyLY3EXxaQtnUrGpaWVP/icww9PSuljg9TKBQs\nXrwYTU1NpkyZUnkr7D0gO1/B70dDWHkiFH1tDT7u5sCwZraoPfw3eUYKEhKJmjCe/IhIrH5dgGHH\njkX74kKCOPrXMhJCg7FydKLThHcxs3nMjH/ZM/E8m5JigAcfb63vbSsXIUTMvf9NBHZQ2DT12rh+\nzR/djHhMmrQrPSgA3DoIYccLm5AeCAoqlYqdO3eSmJjI4MGDi4ICQM61JPJC0khvpU5YQSRdaj55\nM9KD1PQ0MRvjBBpqJK24Tn5cVonlhBDkBt8hcdk1YuecIe67c8T/eJ7MM7HFO7CbTQDXsYVDb29s\nq1Dd/mOuZ86geoP4o+MfHB9ynIUeC+lUsxPn4s7xyYlP6LCpAxMOTmD9zfVEZ0SXWPe7u3dzu0dP\n0v79F5Nx46izd88zCwoAGhoaeHp6kpiYyPXr15/JNfS0NPi0uyP7329HfUtD/rfDj/5LT3MjuoJv\nf+WkaVEN27Vr0XZ0JHr6+6Tt3Fm0z7KuAyPm/ULnSVNJiY5k3Sfvc2rzOhT5+WWcUfYiVcYbgwaF\nnc8dKQwIF4DhQgj/EsrO4YE3BkmS9AE1IUTGvX8fBr4WQhwo65qv0hvD/Dnfowo8y5BfVlLLqpSF\ncJQFsKQVIODds6B+f2aqt7c3vr6+dO3alVYPjJ8vSMwmcfFVNC30+Nv1IJtvbcF3iC8GWhVPclaQ\nnEPy8uuocpUY962DXpNqSGoSQgjygtNIPxpJfkQ66lW00G9eHTU9TbJvJJMfdhddZ1NMhjjeT+2t\nyC+c/BZ7GcbuB6umZV/8KZVnKKx9qjaJ3/9A9tmz6DZqRPW5c9BxdHwm9XmkfioVK1euJDMzk2nT\npqFZzjWen4YQgl1XY/nWK4DUrDxGtqzJh49ZGKiyqLKyiJo6lewzZ7GY/Rkmo0cX25+dfheftSsJ\nOOFNVcsadJrwHrbO8qJAz8tznccgSVIP4DdAHVglhJgnSdIUACHEMkmSqgMXgSqACsgEGgBmFL4l\nQOFqcv8IIeY9fP6HvSqBISs7h4UTRpJnYc/cX8vIonpuOez/CIZtAofuRZv9/PzYtm0bjRs3pm/f\nvkUdofkxmST/7Q8qgdnURvQ40pv6pvVZ5Lmo0uquuJtH6sZA8sPTUTfRQbOaHgWJ2ShTc1E30sLQ\n3Qb9ZtWR7k20EkKQeTKGu15h6LqYYTLU8X7TUmYSrPAo7GuY5AOGZad3qAxR6VFFk+oCwy8y8HgB\nXa4IFLpa5I0fSMMJH6KnVbHlNZ9UWFgYa9aseSRF+rNyN6eAXw/fYu2ZcEz0tfhfz/qPLAz0LKjy\n8oidNYuMw0cwnTgR85kzHrlm+PUrHF25hLSEOOq386D9iLEYVK3gJEvZY8kT3F4C6//ZScKulTiO\n+Yie3Uu5EeSkwe9NoLozjN5dlC4hNjaWVatWYWlpydtvv42UoyI3KJXcgFRyAlNR09fEfJwzl4Uf\nEw5N4Md2P9LDrkel1l+oBDnXk8i+moTybh7qxtroOpmh19i8KCA8LON4NHf3hWHobo1RtwdSbcRd\nh1VdwcIZxuwFjQpOpitP/RUK7mzZQuLChagyMghob8tStzskaGajo65Dyxot8bDxoL11+2c+FPY/\n27Ztw9/fnzFjxlCz5vNpZy9tYaBnSSiVhbOkN2/GqF8/LL/5Gumht6SC/DzO/buZi3v+RV1Tk1aD\nhtOkW+8y05TLKkYODC+Bz6dMQzsrmdmr16OuUcqktkOfw+k/YPJxsHQBICMjg+XLlyMJGO7UCyk0\nh4KoDADUq2ih62yGYUdb1PU1mX1iNt5R3ni/5Y2OxtNlSq1MQgjSdoYUptoY3QDdBg8Mz/XfAVvH\nQJOR0OePZ7rAT84NP+K/+orcmzfRa9ECi9mz0XGoR4GygIsJF4uanGKzYgFwMXPB3cYddxt36hrX\nfWZP1bm5uSxfvpzc3FzGjBlDtWqPWbmvkjy8MND4trWZ3tEefe1ndxMWQpC8ZAnJi/5Av0N7rH/9\nFbUSVoO7ExeD99/LCbt6CVNrWzzHTsHW2eWZ1etNJgeGF+yiXwg+33yATvPuTP3wvZILpYbC4haF\nK6H1XYwqu4DMoGQ2HNpGSk4avfNcMcUQLWtDdBxN0KlvgqalftFNK6sgC48thekvvmr16CzpF0UU\n3EvtnZKLxfQmxVN7H5sHx3+Cbj9CyymVfm1lZhZJCxdyZ8MG1E1NqD57NobdupV4oxdCcOvOraIg\n4ZfiB4CVgVVRv0RTi6aVnhU2OTmZv//+G6VSSY8ePXBycnomI5VKkpKZx48HAtlyMRpLIx2+7NWA\nbs7Vn2nz0p3NW4ifOxedhs7YLFuGRtVH1+wQQhB6+Tzefy/nbmIC9Vq1w33UeAxNn3/aj9eZHBhe\nsK+//hV9/6MMmf8n1ralTOvYMhpx6yg5nbzJ8s8jN+QOvho3CVGPp4dlG5xcXdBxqIq6Yclj6rfe\n2srXZ75mXfd1NK72ci29qEjJIWHRFTTMdKk2udH9zmiVCraMgqD9MHI71PGotGtmHDlC/DffokhM\npOqwYZjP+AB1w/I3mSRmJ+Ib7YtvlG+FhsKWR0pKCtu2bSMuLg59fX1q1KiBmZkZpqammJiYYGlp\nia7us8s3dCkilf/t8CMwPoMO9cyZ28eJWo9ZGKgiMo4cIebDWWjWqIHNihVoWZf830RBfh4X9/zL\n+R1bQU2i1cBhuPbsJzcvVRI5MLxAdzKzWTRpDBpmVsz+vZQsp1EXKFgxhlSdnylIN0DdWBv/agmc\njLyEh7sHHdzL7pxUCRX9d/VHW12bzb02v5QL4uT4p5Cy7ib6zapTdeADa0/kZRQuV5oe80RpM0pT\nEBtL/LfzyDx2DG0HByy/notuo4qNdMkuyOZs3Fl8onzwjfZ9JCusu4071obWFbqGUqkkMDCQoKAg\n4uPjSU1NRaFQAKCpqYmHhwetWrV6Zn9bhVLF2jMRLDh8i3ylinc61OGdxywMVBHZly4R9c67qGlr\nY7NyBToOpa9qdzcxAZ+1Kwi5cBZz21p0njwNy7qll5eVjxwYXqA/V28j88DfNJ0wC4/O7o8WEIK8\nxVNIjh6EpG+Ace86RGqnsmnzJpydnRk4cOBjbwYnok/w7tF3+a7td/Su0/vZfJFKcPdgOBneURgP\nqItBc8v7O+6Ew3IP0DeDCUdA59H1CB5H5OeTum49SYsXgxCYT52KyehRj3RyVpRSpSw2FPb23dtA\n5WeFValUpKenk5KSwvnz5wkKCqJp06b07t37mQb+hPRcvvUKYM+1WGqa6jGnjxMeDs+m7yMvOJjI\niZNQZWVhs3QJem5l36OCL5zh2KplZN5JpUnXXrQdOgot3dLXpJCVTQ4ML4gQgs8nTEFXkcX/Vq8t\ncW3cgjMHSdwlUDfUwGxqO1Lz7rJy5UrMzMwYO3bsY8e4CyEYsW8EidmJ7B+wH031Zz8+/WkJlSB5\ntR95oXepNqURWjYPNO2Enyyc42DnUZhevJwLvQghyPTxIfGHH8mPiMDA3R2Lzz8vtXmiskWmRxYG\niWgfLidcRimUmOqYFr1JtLBsga5GxZqBhBAcPXqUkydP4u7ujru7e+VUvgynQpL5YpcfoUlZdHOq\nzpe9G1DDuPKbswpiY4kcP4GC2Fisfv0VQ8+ymxPzsrM5uWktVw95YVDVBPfRE6jXsu1L+Zb8spMD\nwwty+MQlrv/xFVU9BjFuyphH9ou8fBK+2Y1KpUO1We4o9TVZvnw5eXl5TJo0iSpVHt+GfTD8ILN8\nZ/F166/pb9//GXyLyqXMKiDxjysIpcBiauPi6z5cXAV7Z0DradDl28eeK+/2bRK+/4GskyfRql0b\ni88+xaD9k+eHqix38+5yIuYEvlG+RVlhK2sorBCCnTt3cu3aNcaOHftchrfmKZSsPBHGomPBqEkS\n0zvaM65N7TIXBnoaitRUoiZNJjcgAMt532Lcr99jj4m9FciRv5aQFB6KjZMLnmMny6k1npAcGF6Q\nr2Z9gV70DaYsW4OR8aPNI2mrvMi8VQWzjunodO7Jv//+y40bNxg9ejS1az9+ic2M/Az67+qPoZYh\n23pvQ/0VWU4xPy6LpKVX0aimR7XJLkgPtmN7zYILK6DfMmg8rMTjlenpJC9eTOr6Dajp6WE+9T2q\nDh9e6c1GFfHgUFjvKG/isuKAig2FzcvLY9myZQghePfdd4vW9n7WolKzmbvnJkcCErCvZsA3/Zxp\naVfxVeAepMzMInpa4Szpap98gunYMY89RqVScv3IQU5tWkteTjZNu/em1aDhaOs938mKryo5MLwA\nETGJbPpwIpJ9Mz7+5vNH9iuS0oj/5Qp6htcwmf0+t4KD+eeff+jQoQMeHuUbnfPlqS/ZdXsX67qv\nw8X81RrrneOfQsr6m+g2MsdkiMP9G6SyANb1h6hzhUuZ2jQrOkaoVNzdsYPEBb+iTE3F+K23MH9/\nOhoVXBHtWStrKGyXml3oWqsrDUwblCtIREREsHr16if6/0llOXIzgTl7/Im+k0P/JlZ81sORaoaV\nN19GlZ9P7KyPyDh0qNRZ0iXJTr/LqU3ruH7sIHpVjGg/YiwN2nmU2HQru08ODC/Agp+XIi540fnz\n+bg0fHQt39TFO8iOMqL6SE1U9VqwZMkSNDQ0mDJlChrlGI63KXAT887NY0LDCbzf9P1n8RWeuXTv\nSNIPRlClay2qeDyQezE7FVZ4QkF24UglIyvywsKI+9/n5Fy+jG6TJlh8/j90nZxeXOUr4L+hsMci\nj3E29iwKoaC6fnUamTeioVlDnM2cqW9SHz3NkjtWt2/fzs2bN5k6dSpVS5gH8Czl5CtZ7B3Cn8dv\no6OpzqwuDoxsWRP1SsrcKpRK4ud+XbiW9MABWM6di1TO4anxt4M5tmoZcSFBWNZzpNP4d+V1p8sg\nB4bnLC+/gB/HjUYYmvLV0j8e2V8QFUfC4iAMTG9g/NE0Tp06xeHDhxkzZgy1atV67PmPRx9n2rFp\ntLNqx0KPha9ME9LDhBCkbgoi53oSpiMboOv0QPNEYgCs7IyoakeqxgiS/liKpK2NxSefYDSg/2vT\n2Xg37y7HIo9xMuYkN5JvFDU5SUjYGdnRsWZHhjkOK9Y3kZ6ezqJFi7C3t+ett956IfW+nZTJV7v8\nORmSjLNVFb7p60wT28oJUkIIkhctInnJUgw8PLBa8Atq5ZzHIVQq/I8f4/iG1eRlZeL2f/bOOzyK\nsuvD92xJNr1X0imB0CH0GnovIr0KiKIoINhBsb2iiCICigh89A7Se+g9QICEmoQ00nuyKdvm+2Mj\nBGkhPZL7unKRnafM2c0yZ+Y85zm/PgNp+fpw5AalX3alslHlGMqYzVv3ErXldzyGvMugQT2faE/+\nZRO58dY4TnJE6+LNggULcHJyYvTo0S+c+07KHcbsH4O7uTv/1+P/nnlXWVkQ1VoSll5Hk5CN3eRG\nGDg9ig/nHV1F7Bdfk5NsgGknPxy/nIPcoWzKRpQXSTlJ3Ey+SXBSMFcSrnAh9gLGcmM+9P2QQbUG\nPUoc5/EAACAASURBVOz3T6XdkpQJfVlEUWTP9Vi+2XOTxKw8hjVz4+Me3lgal8zaR8r69cR/8y1G\njRvjumQxUkvLQo/NyczgxJoVBJ84gqWjE13fnFJVufVflKUeQxVA8NGDZMtN6dev6xNt6nuh5MQ7\nYuochtSrPgEBAWRnZxcqBTExO5F3j76LqYEpv3X6rdI7BQBBLsV2jA+CQkbyqmC0WSq0GRnE/ziP\n+9Pmo8o1w7llKi5DPf/zTgHA1siW9i7tmdxoMsu6LWP3wN3Us63HnHNz+Dng54eqZ61atcLY2Jij\nR4+Wm62CINC3oTNHZ3RgfBtPNgdE0Wn+CTYHRKHTFf8m03rECKr98gu5N24QMXo06ri4Qo81MjOn\nxzvTGDz7OxBhyzefc2DJLyjTUott16tGlWMoAW7cDMU8JQyzhu2Qy5+MjWZsP49ADmaDu6PT6bh4\n8SLu7u64uj5fJF2lVTHt+DQyVBks7rwYB5PSL1ddVkjNDbEd44M2S0X8LycI7dGblJUrMe/bF6/9\nh7Do2wfh2Ldwe295m1rmuJu7s7TLUoZ6D2Vl8Er+uvEXoJcJbdeuHWFhYYSGhparjWYKObP7+LDn\nvbZ42Zrw0dbrDF56jluxGcWe27xHd1yX/Yk6Jpbw4SPIe8n36lavIWN+WkTzAYO5dfoEK6a9xeW9\nO9Hm7yqv4sVUOYYSYN/W7egQGDDsyT0FqmuB5KS6YeYZi8TJg9DQUNLS0vB9wY5PURT57sJ3XE+8\nzndtv6O2ddkIypQl6ge3UN/fiU6pQNF0LB5bt+D8v++Q2dtDv9/AuQlsnwTxT2g+/eeRSqR83uJz\nenn2YuHVhZyM1qvdNmvWDAsLC44cOYJOpytnK6GOkzmb32rFvNcbcD9JSZ/fTvPNnptk5hZdhxvA\npGVL3NesRlSriRgxkpzAwJcaLzcwpN3wsYz9aRHO3nU4vnoZaz5+n8iga8Wy61WhRByDIAg9BEG4\nIwhCiCAInzylvbYgCOcEQcgTBGHmy4yt6Cizc9HcvkCOUx08XJ2faM/YfQOJkInpkD4ABAQEYGJi\nQp06T2YtFWTTnU1sv7edSQ0m0dX9yfBUZUabnk7s7NlEjh2LNuEahp4aJCbeaFILxJPlRjBsHRiY\nwoZhoEwuP4PLCUEQ+LrN19S0qsnsM7NJzklGJpPh5+dHbGwsN2/eLG8TAZBIBAb7uuI/owNDm7my\n4sx9Os8/we5rMRRnDVPh44PH+nVILCyIeGM8WadOv/Qc1s4uvPbJHPp/OBuNKo8t33zO7l/mkpGU\nUGS7XgWK7RgEQZACi4Ge6FXZhguC4POvbinA+8BPRRhbodm6bR8KbS6+PZ4Uyck7c4zcLA/Mamcg\nsbIjKyuLu3fv0qhRo+empwbEBfDDxR/o4NKBdxs9o2R3Icm7f5/4H34kdvZsMg4cRCzHu0xRFMk4\ncJDQ3n1I274Dm4kT8Nq1E9s3O6Koa0P63jBy7xaIB5s7w7D1kBkPm8fo9zu8YhhKDfmh3Q9kqbKY\ne1GvAtigQQPs7e3x9/dHq9WWs4WPsDQ24H8D67PjnTbYmxvy3oarjF5+kdDErCLPaeDmhse6tRh4\neBA1eTLpe14+tCgIAjV8WzB2/hJaDx5J2OWLrJw+mfPbN6HVvHrfqcJQEk8MzYEQURTDRFFUARuB\n/gU7iKKYIIriJeDff4UXjq3ohJ46jNLQkh5d2z12XNRqSD8UhUSSjsngfgDcvHkTURRp0ODZG9Ni\ns2KZcWIGLmYufN/u+2IVZsv0P8b9/gNIXbuWzEOHeTBtGpETJqBJLfvFOHV8PNFT3uPBtGnI7e3x\n3LIZ+5kzkRgZIUgErId4I3cwIXn9LdQJ2Y8GujTVh5UiTsP+j8rc7opATauaTKg/gQPhB7gYexGJ\nRELnzp1JSUnhypUr5W3eEzRytWTnu235un9drkWn0WPBSX46eIccVdGcmMzODvfVqzBu3JiYmTNJ\nWb2mSPPIDQxp9fpwxv38O56NmnJm0xrWfDyV2Ht3ijTff5mScAzVgKgCr6Pzj5X22HLn/OVgLNKj\nsPHtgET6+L6CnL27UOV5Yt5MeKhaFRQUhJ2dHQ4OT19EztXkMvXYVFRaFQs7LcTMoOjyi3khITyY\nPh1Db29q+B+l5tkzOH71FTlXrhI5ZgyaxMQiz/0yiDodqRs2ENarN8ozZ7D/8EM8Nm9C4fP4g6HE\nUIrNWB8EmUSfqaQscA/RcCi0maqvq3TprzKxu6Ixvt54qplW47sL36HWqalVqxZubm4cP36cvLy8\n8jbvCaQSgTGtPPCf0ZG+DZxZdCyErr+c4MjN+KLNZ2aG61/LMO3Smfj//Y+EX38tcpjKwt6BfjM+\nY8BHX5CXrWT97JkcX70MdW5ukeb7L1JpFp8FQZgkCEKAIAgBiWV0UXsRR3b8jVaQMGjI44vOojKT\n9PMgN4jDpJ9+T0N6ejqRkZHUq1fvqXOJoshX577idspt5rabi6fFi+smPQtRpyPmk0+RmJjgumQx\nMjs7BKkUq6FDcF26FNWDGCLfnIQ2q+iP+IVBee4c4YOHEPfV1xg1bIDX7l3YTBj/zF2tMisFNqN9\n0KTlkbLuFqKmQNir85dQsxvs/xjunypVuysiCpmCj5p9RFh6GDvu7UAQBLp27YpSqeTcuXPlbd4z\nsTMz5Oehjdg4qSVGcikTVwcwcVUAUSnZLx78LySGhrgsWIDl4NdJ/v0P4r6cg1iMUFr1ps0ZN/93\nGnbpweW9O1n14bvcPX+6WOsi/xVKwjE8AArmXbrkHyvRsaIo/imKoq8oir52dnZFMrQkSUnPRBJ6\nGZVLfRwdH6+emblpJ1qdHRY9XBCk+o/4n4XCus8o6bA8aDl7wvYwpfEUOrg+X6TnRWQeOEBuUBAO\nn3yM7F+flUnLFrgsXKh/onj/fUSVqljnehq5t28TOfFNIt8YjyY1Bed5P+K6fDkGL0jPBTB0N8fq\n9VrkhaWTtiv00X9SiRQG/QXWXvr1htTwEre7ouPn6kcju0b8ce0PcjQ5uLq6UqdOHc6ePUtWKTv5\n4tLSy4Z9U9vxac/anAlJousvJ1h8LIQ8zctd2AWZDMevv8bmrbdI27yZB9OmoyvGE5OhsTFdJr7L\nkC+/R2ZgyO5f5rLusw+IuPFyWVD/NUrCMVwCagqC4CkIggEwDNhVBmPLla1b9mCoU9Gm7+MiOdrY\naDLv2qOwCEfRutXD40FBQTg5OWFr+2QJ5iMRR/j1yq/09OzJm/XfLJZdolZLwq+/YujtjXmfPk/t\nY9q2DU7ffIPy7DliZs0qsQVpdUwMMR9/wv2Br5Fz4wb2H31E9f37sXhJoRmTxvaY+bmivBhH1umY\nRw0KCxi+EUQtbBiuV4J7hRAEgWlNp5GYk8iG2xsA6Ny5M2q1mpMnT5azdS9GLpXwVofqHJ3RAT9v\ne+YdvEPPX09xJiTppeYRBAH76dNw+OwzMg8fJurNSWgzi/ddcPWpz5h5v9F98jSy09PY+u0sdvzw\nFSkx0cWat7JSbMcgiqIGmAIcBG4Bm0VRDBYE4W1BEN4GEATBURCEaOADYJYgCNGCIJg/a2xxbSpt\nRFEk+uxRsoxt6dCu+WNtGRuOICLDYnCLh8dSUlJ48ODBU58WgpOD+fTUpzSwa8A3bb4pdj2grOPH\nUUdEYjt58nMrTVoOHIDdtGlk7NpN/Pdzi/X4rMvOJuHXXwnt0ZOM/fuxmTCeGocOYjP+DSSGRatX\nY97VHaO6NqTvCyPnTsqjBpvq8PpKSLwNO97Wa0i/QjR1aEq7au3468ZfpOelY2trS5MmTQgICCA5\nuXKk9DpbGvH7qKasfKMZWp3IyL8u8N6Gq8RnvFyM33rMaJznzSP7yhUixowt9rqZRCKlXscujF+w\nlPYj3yD6VjCrZr7L8TXLUasq3jpOaVIiawyiKO4TRbGWKIrVRVH8Lv/YH6Io/pH/e5woii6iKJqL\nomiZ/3vGs8ZWdI6fuYKFMo5qLTshKXDxVV0PRJngialLNPIatR4eDw7W+7p/O4Z4ZTzvH30fK4UV\nv/r9iqG0+EW/UtauRebkhFmXzi/sa/PWJKzHjSN1zRoSFy4s0vmyr1whtE8fkn//A7Nu3ah+YD/2\nM2citXh5qc6CCBIBq6HeyB1NSFl/+/FMpRqdodt3cHsPnJhbrPNURqY2mUqmKpNVwasA6NixI1Kp\nFH9//3K27OXw87bn4LT2TO1ck4PBcXSef4IVp++j0Rbe2Vv07YPr70tQhYcTPmIkqsjIYtslMzCg\nWb9BTPj1T+p27MLlPTtY+/FU4kLuFnvuykKlWXyuSJzcvRu1IGPQ0EeZtaIokv73TSSCEvPhjxfR\nCw4OxsXF5bFyydnqbN7zf48sdRa/dfqtyCpfBckLCSH73Hmshg0rVNliQRCw//ijh4t5iYsWF/rJ\nQdTpSPpzGRGjxyBIZbivW0u1n+Yhd35yk19RkRjkZyrJJSStCkaXXSBTqeVkaDQKTvwAwTtK7JyV\nAW9rb3p49GDtrbUk5yRjZmZGq1atCA4O5sGDwi7vVQwUcinTu9bi0LT2NHG34us9N+m76AyXIwqf\nUm3arh3u/7cSXWYm4SNGkltCG/+MLSzpNuk9Xp/1Laq8XNbPnsmZzeteidIaVY7hJYlLTMUwIhDR\nqxFWBRTacv2Pk5ftinm9DCQ2jxZ8k5OTiYuLe+xpQSfqmHVmFrdTbvNj+x/xtvYuEdtS1q1DMDDA\ncsjgQo8RBAHHOXOwGDiQpEWLiJvzFeILvvialBSi3nqbxJ9/xqxbVzy3b8O4adPimv9UZJb6TCVt\nWh7J628j/nM3KQjQ52dwaQ47JkPsq1Xq4J1G75CnzXtYR6l169YYGxtz+PDhSplV42Frwqo3mvH7\nyCakKlUM+v0sH2+9ToqycMkRRg0b4r5+HYJcTsToMSgvXCwx29zrN2LsvEXUadOB89s2sP7zGSRF\nhpfY/BWRKsfwkmzZvBO5qKHLwEcataJKQ9qxdGSyGExef1y79p8wkk+BvP2l15dyOOIwM3xnFDsD\n6R+0mZmk79yFee/eyF5SyEWQSnH633fYTJpE2qZNRIwbhzom5ql9lecvcL//ALIvXMBxzpdU+/ln\npGZF329RGAzdzbEaWJO8kDTS9oQ9apAZwtC1YGwNG0ZA1qtT5sDTwpN+1fux+c5m4pRxKBQK2rdv\nT3h4OCEhIeVtXpEQBIGe9Z04OqMDb7X3YtuVaDrNP87Gi5GFqtxq6OWFx4b1yJwciZo4kYxDh0rM\nNoWJKT2nzKDfjM/ITEli7afTOL1xDbnKip0NVlSqHMNLoNHqSLx4DKWZI82aNXp4PGvHQbQaGyzb\nGiIYPi57GBwcjKurKxb5MfejkUdZEriEftX7McZnTInZlr5zF2J2NlYjRhRpvCAI2H8wHecf5pJ3\n6zahffqS8NNP5N68iSYxEeX580RPn07kuHFITEzw2LxJH7IqI/EcE18HTNtXQ3kulqzzsY8azBz0\nZTOyk2HTaNCUfPptRWVyw8no0LH0+lIAfH19sbKyqjAF9oqKiaGMT3vVYe/77ahlb8Yn228w6I+z\nBD1If+FYuaMjHmvXoqhblwfTppO6aXOJ2lazeWvG/bSYmi3acGHHJv56bwLntm74zzmIKsfwEuw/\neg6L3GS82j0qaqfLUJIRKMPQ6A6Kbv0e65+UlER8fPzDMFJIagifnfqMejb1+KLVFyV2URVFkdSN\nG1DUr49R/advoCssFv3747nzb8z8/EhevoL7rw3iXrv2RI57A+WJk9i+MxnP7dtQ1C77aq8WPTxR\neFuRtiuUvLC0Rw3OjWDAYog6D3s/gEoYSikKzqbODK41mB33dhCZEYlMJqNTp07Ex8dXyFIZL4u3\noxmb3mrJz0MaEpWSTb9Fp5mzK5iMF1RulVpa4rZyBSbt2hL35ZckLllSouE1YwtLer//IaN/WIhL\nnXqc3bKOZe+O5/TG1WRnvNh5VQaqHMNLcHH/XlQSAwYMerQ/IGPTQUTREMteXvCv9NB/wkh16tQh\nPS+d94+9j7HcmAV+C0okA+kfcgICUIWEYjVsWInMZ+DiQrX5P1HjxHGcf/oJh1mzcFmyhJqnTmL3\n/vsPS3yUNYJEwHp4bWQ2CpLX3UKTUiC9sd4gaDcTrq6BC0vLxb7yYFKDScglcpZcWwJAvXr18PDw\n4PDhw6SnV/6LlCAIvNbEhaMfdGRkC3dWnQun8/wT7Ax88NyLvcTICNdFi7Do34+khb8R/823JV5A\n0t7DiwEfzmb0DwvxaNiEC39vYdmU8Vw9sLtSrvMUpMoxFJJ7EXGYxQRh4N0MU1O9FKUmNpGsUEuM\nLW8ib9bpsf6iKBIYGIiHhwcmZiZ8eOJDYpWx/NLxlxIX3EndsBGJuTnmvZ6UFC0Ocnt7LPr0xnrU\nSMw6+SExMXnxoFJGopBhM8YHUSuSvPomurwCO2f9Pgfv3nDwUwitXKmbRcXWyJbhdYazL2wf91Lv\nIQgC/fr1Q6vVsnv37kodUiqIhbGcbwbUY+e7bXC2UDB1YyAjll0gJOHZG9sEuRyn77/H+o03SF2/\nnpiZM0tlp7+9hxd9p3/CuJ8W41qnHv4rl+K/cmmldg5VjqGQ7Ni0DSk6eg19/eGx9I0nENBi8VrL\nJ/pHRESQmppKo0aNWHB5AedizzG75Wwa2Td6om9xUMfGknHoEJYDBxZaPL2yI7czxmZEHdTxSlK3\n3EH8Z2FSIoHXloJdbdgyDpIq5yLsyzK+7nhM5CYsDlwMgLW1Nd27dyckJKRcZUBLgwYulmx/pw3f\nDqhHcEw6PX89xQ8HbpOtenomnSCR4PDxR9jPnEHGvv1EvT0ZnVJZKrbZuLgx8OMvadp7AIEH93Bm\n09pSOU9ZUOUYCkFOnorc66dR2nhSp05NAFR3wsiJd8DU6S7SWk2eGBMYGIiBgQHhinBW3VzFMO9h\nvFbztRK3LXnlSgCsx5bcQnZlQFHLCouenuQEJZPpX2BTk6EZDN8AEple4Ce38odTXoSlwpIxPmM4\nGnmU4CR9+NLX15emTZty5swZDh48iOY/lHsvlQiMaumO/8yO9G9Ujd+Ph9L155McCo575l26zcSJ\nOH33HcoLF4gY9waalJSn9isugkRCh9ETqOfXjQs7NhF6ueTSZsuSKsdQCLb/fRgTdSYNuj4S40nf\nHoCEDMyGPhm+ycnJITg4GOcaznxz6Rt8HXz5qHnJawloUlJI27IViz59SnRjWWXBtF01jJvYk3Ek\nkpygAvV2rDxgyGpIvQ9bx4Ou4ojZlBajfUZjaWjJb1d/A/Sx+d69e9OsWTPOnTvHokWLOHjwIAEB\nAdy9e5fY2NgKWa77ZbA1NeSnwQ3Z/FYrTA1lTFpz+bmVWy0HvYbLbwvJu3uXiJGjUJfSZkBBEOg8\n/m3sPapz4PcFlXJBusoxFILbx/aTIzelTx99NlLelevkpTth5vUAiaPXE/0DAgJQq9Vsy92GrZEt\n8zvORy6Rl7hdiQsXIqpU2EyaVOJzVwYEQcBqYE0MXM1I2XwHdVyBEIFHW+g1D0KOwOEvys/IMsLU\nwJQJ9SZwJuYM52PPAyCRSOjduzcjR47EysqKCxcusGfPHtavX8/SpUv58ccf2blzJ8pSCq2UFc09\nrdnzfls+71WH82HJdPn5BL8dvffUyq1mnTrhtvwvNElJhI8YSd69e6Vik8zAgJ7vTkeVreTU+v8r\nlXOUJlWO4QVcvHoLy9RwLJt2QCaX6Utf7L2JREjF5F86DAAajYYLFy+QZZZFgjSBRZ0XYa2wLnG7\ncoKCSdu8BasRIzD0Krp2Q2VHkEuwGV0HwVBG0qpgtFkFFhd9x0OzN+HcIghcX35GlhHDag/D1cyV\nb89/S5720dNAzZo1GTt2LLNmzWLatGlMmDCBIUOG0KRJE65du8bSpUupKBonRUUulfBmey+OzOhA\nlzoOzD98lx4LTnHq3pPvy9jXF/e1axB1WsJHjSb7ytVSscnWzYOmfQYSdOwwMXdvlco5Sosqx/AC\nDm3bjhYJg4YNAiDvzFlUymqY+6QjsXxSFyLgcgBZmVkEGgcyr8M8alrVLHGbtFlZxMyYgczODrsp\nxdOE/i8gNTfEdowP2kwVyf8W+OnxPXi2h91TIapyxnsLi0KmYHbL2URkRLD02pMpuxKJBEtLS1xd\nXfHx8aF3795MnDgRrVbL6tWrySxm6eqKgJOFEYtHNmH1+OaIosjo5Rd5d/0V4tIfr9yq8PbGY8MG\npJYWRI4fT+bx46ViT6vXhmFsYcmpDasqVZZSlWN4DilpGUhDL6Nyq4+Tkz2iTkf64UikkmRMBj35\ntJCbm8vBowdJUCQwqt0o2ru0L3GbtFlKot+ejCo6Gud5Pxa7iul/BQNXM6xfr4XqfsbjAj9SOQxe\nBebVYONISP9v19dv5dyKftX7sSJoBZfjL7+wv7OzM6NHjyY3N5fNmzf/Z9Jb29ey48C09nzQtRZH\nbsbTef5x/joVhrpA5VYDFxc81q/H0MuL6HenkPb33yVuh1yhoOVrQ4m+GUTE9dJ5MikNqhzDc9iy\naScGOhXt+unrH+Ue2oc6zwXzJiKCsekT/VfuXImoErFraMfYumNL3J7sK1cJHzyY7CtXcP7xB0ya\nN3/xoFcI40b2mHXUC/wozxUom2FsrRf4UefAxhGgenlZycrEJ80/oZppNT488SEJ2S+uH+Xo6Eif\nPn2Iiori/PnzZWBh2aCQS3m/c00OT+9Ac09rvt17i76/neZS+KOMJJmNDW6rV2HcvBmxn3xK8vIV\nJW5Hgy49MLdz4PTG1ZXmqaHKMTwDnU5H7LmjZJo40L6tL6Iql4zTmchkSRj3f1IZ7dj1Y8TdiiPD\nIYNZ3WaVaA2h3Dt3iJr8DhEjRqBTKnFbuRKL3r1LbP7/Eubd3FHUsSZtTyi5IQVKN9vX1kuDxl6H\nne/+p8tmmBmY8XPHn8lSZzHx0ESScl6skNagQQO8vb3x9/cnNbXwJa8rA242xqwY14ylo5uSkaNm\n8B/nmLnlGslZ+nUYqakprkuXYtazBwnz5hH/47wS3SUtlclp+dpQ4sNCiLhWOUqVlIhjEAShhyAI\ndwRBCBEE4ZOntAuCICzMb78uCEKTAm3hgiDcEAQhUBCEgJKwpyQ4cuw8ZjlJuLXtgiAIZO/Yilrj\ngnk7SwT54xlGEUkRHNx9kDx5Hh+P/Bi5tGQykPLC7hM9bbq+mmlAAHYffED1gwcwaVH1pPAsBImA\n9TBvZHbGJK+7jTop51Gjdw/o8iUEb4eTP5WfkWWAt7U3SzovIU4Zx9A9Q7kQe+G5/f9JbxUEgcOH\nD5eRlWWHIAh0r+vIkRkdmNyxOn9ffUCn+SdYdyECnU5EYmBAtZ9+wmrECFJWrCD2088Q1c+vyfQy\n+LT3w9Tahgs7t5TYnKVJsR2DIAhSYDHQE/ABhguC4POvbj2Bmvk/k4Df/9XuJ4piI1EUfYtrT0lx\nbt8eVBIDBr3eF116EhmBpsiN4jDq2vGxftmqbJb83xLkGjkDXhuAg3nxy12IKhVJv//O/f79UZ48\nic3kt6lx5DC2k958ZXY3FweJoQzbsXURBEheFYwut8DmrjbToP4QOPYt3NpdfkaWAb6OvqzqsQpD\nqSETD01k3IFxrL+1nhuJN8hWPxlOMzc3p02bNty8eZOIiIhysLj0MTaQ8XGP2uyf2o46TmZ8viOI\ngb+f5UZ0OoJUisPsWdi+/x7pO3cSPeU9dDk5L560EEhlcnz7DCT6ZlClyFAqiSeG5kCIKIphoiiq\ngI1A/3/16Q+sFvWcBywFQXAqgXOXClExCRhFB0HNZliYm5K1YSda0QbLPrUQJI9CRDqdjrmr5mKU\nZYRPOx9a1nmyNMbLknvzJvcHDyHx14WYde1C9UMHsZ86tWqR+SWRWSuwGVUHTXIuKRtuPyqbIQjQ\nbyE4N4Htb0FcUPkaWsrUsanD9n7bmek7k+ScZL6/+D0j9o2g5fqW9N3Rl49OfMTam2t5kKXf7NW6\ndWvMzMw4ePBgpYmHF4WaDmZseLMlvw5rxIPUHPovPs0XO4PIyNVg9847OM6ZQ9bJk0SOn4C2hIoR\n1u/cHYWpGRf+rvhPDSXhGKoBUQVeR+cfK2wfETgiCMJlQRAqxE6t7Rt3IEVH90ED0EbcJTPcDSPr\nKAybNnys35LdS5A8kGBSy4ThnYYX65yiRkPikiXcHzIUbUoKLksWU+3nn5HZFl/y81XF0MsSy/7V\nyb2TSvrB8EcNciO9hoPCHDYMB+WLY/CVGYVMwdi6Y9k9cDf7X9vPAr8FvN3wbTwtPAlMDOSHSz/Q\nY1sPhuwawrprG6nfuBExMTEE3Qj6zzgHUSeiytWQl6NBlatBo9ZvfuvfqBpHZ3RgTCsP1p6PoPP8\n4+y4Go3l0CFU++UXcoKCCBs1juzImGd+Fhq1lpRYJeHXk7h3KZ7Y0HR0T9GtNlAY0bhHX8IuXySx\ngivAvVgYuPRpK4riA0EQ7IHDgiDcFkXx5L875TuNSQBubm6lZoxGoyXt6kl0lm40aViHlHl/IeKF\nxbC2j/Xbc3EPCVcT0Npo+WDYB8U6Z861a8R98y25QUGY9+6N4+xZSC0tizVnFXpMWzihjlWSdSIa\nuaMJJo3t9Q3mTjBsHazoCZvHwOi/QWZQvsaWAS5mLriYudDZrfPDY/eTwzm88wpZ/jKyc025i4jU\n1pi/N+/j1NJEDBVy5IZSAHRaHTqdqP/RiohaERGQSgUkMgkSqYBEIiDqRHSi/oIs6kTEf34XRSQS\nAYk0v69UeNQu6ucVdY/GIRH0c0sFpDIJCDxq/3f//LmlcglSmQSJTIJWpUWVp0Wdp9XfghZEAJlM\ngtRAgodcyiyJJckJedz58w6/Su5iKBiga7NA3/d/txGE2xgayzEwlqEwliGRSshKzSUrLe+JuY3M\n5Pj28qR+h2qPRRka9+xLwO7tBOzaRs8pM0rhL1wylIRjeAC4Fnjtkn+sUH1EUfzn3wRBEHagPleK\nGAAAIABJREFUD0094RhEUfwT+BPA19e31G5j9h44gakqHadeg1FdPkd2ck1MPWKRuT0qqx0UEcS5\nA+fQKDR88sYnSCXSIp1LHRNDws+/kLFnD1I7W6ot+AXzHj1K6q1UkY9lXy80CdmkbruL3NYIA9d8\nKdJqTaH/Ytg+EfZ/CH0W6ENNrxDK9DzOL45HHWNJrXo2mHjCrcxgUqMyMVdKuWPvj42RK44G1bA3\ntsNcYaV3ABIh/wKv/7x0WhGtVodOoyP/eg4SAYkgIEgEBIk+MUCAh05Fp9Vf2AUhv00QkPzze/6P\nKIroNCI6rQ6tVu8sBMmT/fTnybdDo8v/EZEZSDAwlCFXSJErpEgkwsPza9U6NGodWpUWTf7vLkBk\neg6Xo9PI1emoX92S5hY6snfuQCMxxLBzT7RG5uRla9CqtVTztsLc1ggLO/2PgUJGapySGycecGrT\nXaJupdBtYl3kBvprhJGpGfU7dSPw0F7aDBuNua19uf3tn0dJOIZLQE1BEDzRX+yHAf/Wl9wFTBEE\nYSPQAkgXRTFWEAQTQCKKYmb+792Ar0vApiJz5dA+DKRGDOzfg/R5G5EI9pgPf1QoLyUzhbXr1yIR\nJIwdNRYr05fTVwbQqVQkL1tG8p/LALCZ/Da2EydWCL2D/yKCVIL1yDokLA4kafVNHN5rhNQ8Xyip\nwWBICIbTv4BDPWj+ZvkaW4aocjTs/OUqmal59HmvIe51bQDwoyE6nY5FSxchZKRyqfoewrPCAXAw\ncqCVcytaO7empVNLrBQv//2vDAzMyuOHA7dZGBCNU66Cb6a8Tq25n6JdsReXRb9h0rr1M8daO5vg\n1diOG8ejObX5Hvv/uEHvyQ2QyvWR+6Z9BhB4aC+X9+7Eb2zF/L4Ve41BFEUNMAU4CNwCNouiGCwI\nwtuCILyd320fEAaEAMuAd/KPOwCnBUG4BlwE9oqieKC4NhWVu2HRmMbfwdCnJcLZo+TlVMesoQpJ\n/sKvRqth/or5GOQZ0KZXG3xc/p189WKU5y9wv19/kn5bhFnnTlTfvw/7qVOrnEIpIzWRYzvGBzFP\nS9Lqm4jqAgXWOn0BtXrC/o8h7Hi52ViWiKKI/5rbpCXk0OedBg+dwj9IJBJ6d+uNmCPyebXPOTDo\nAF+2+pIGdg04GnmUj05+RMfNHXnjwBusv7W+UBvpKhM2pob8+HpDtk1uhYWRnIlHE1jQ/0NERyci\n33qbjP37nzteEAQa+LnSaXRtom6mcHLT3Ydt5rb21G7dnhtHD5KTVTHLkAiVcXHJ19dXDAgo+S0P\nP81diHD1EL3n/IzVusvoRGMcv+iJYKiPPc9dM5fc0Fzsmtrxbt+Xq1GkSUkh4YcfSN+5C7mrK45f\nfolp2zYl/h6qeD45wckkr7mJcSM7rIZ6P9qImJsBy7tBZiy86Q821cvX0FLm7sU4Dq+4SauB1WnS\n3f2Z/VatWkV8fDxTp07F0FD/lKXVaQlODubUg1MciThCSJpeEKmRXSO6uneli3sXnE3/O2XgNVod\nq85F8Mvhu8hzslgcvB6rsFs4zPoc65EjXzj+3N+hXDkQgd/o2vi00X8uiZHhrP5wCq2HjKTVoOIl\nrrwMgiBcLsy2gKqdz/nk5qnJuXGWLNvquN4MRK1xwaKN8UOn8H+H/4/c0FxwhXf6vPOC2R4h6nSk\nbtlCaM9epO/bj83bb+G1e1eVUygnjOraYN7NnezARLJOFqibpDDXC/wIgj5TKTej/IwsZVQ5Gs5s\nDcHe3YxGXZ+fyNG5c2eys7MfK5UhlUhpYNeAdxu9y47+O9jZfydTGk0hV5vLvIB5dN/WnUG7BvHL\n5V+4FHcJta7kNoqVBzKphAltPTk6owNtG3sxzmc011zrE//NtyQu/O2FmVst+nnhUtuKU5vukp6o\n3z9i5+aBZ2Nfru7fjVpV8XQxqhxDPjt2HcZYk0XjDn5kXJYjN4zFqLs+c8P/uj+hZ0LJMc/hk9Gf\nFLrcRd69e0SMHkPc7C8wrFkDrx3bsZ82DYlCUZpvpYoXYObnilEDW9IPhJNzK/lRg7WnXuAnOQS2\nTfzPCvxc3Huf7EwV7Yd7I5E8/7vs4uJC7dq1OXv2LNnZT68x5WXpxVsN32JL3y3sHbiXD5p+gIWh\nBauDVzP+4Hjab2zP9GPT2XZ3W6HKc1RUHMwV/Da8MSvfastfXSdx0K05SUuWEPbZbETts78rEolA\n57F1kEglHF11C13+nprm/V4nJzOD4GNHyuotFJoqx5DPLf8D5MhN6ZCVjlZni0V3NwSphLsxdzmy\n8whqAzXT35iOwuDFF3VtZibxP/xI2MDXUIWE4PTdt7ivXo1hjRpl8E6qeBGCIGD1ei3kzqakbLyD\nOr6AUI1ne+j5A9w7CEe/Kj8jS4mUWCXX/aPxaeOMg4d5ocb4+fmRl5fH6dOnX9jXzdyNN+q9wYru\nKzg17BQLOi6gu0d3biTdYM65OXTa3Imx+8eyKngV0ZmVs9Jtmxq27J3eEfkns9jq3QnVjm2cHjWJ\nvOxn75I2tVLQbmhNYkPSue6v39JVrU5dnGp6E7BnO7rnOJbyoMoxANduhmCREoa9TzOUd+0wNItG\n0bolaco0lq9ZjiAKDBk2BEcrx+fOI2q1+rBR9x6k/N//YTGgP17792E5aBCCpOqjrkhIDKTYjPFB\nMJCQtOomWmWBcEfzN/UiP2d+hWubys/IUuDM1hDkhlJa9n9SefBZODg40LBhQy5cuEBaWlqhx5ka\nmNLZvTNzWs/h8OuH2dp3K5MbTUapVvJTwE/03N6TwbsH88e1P7iTcqdSbaYzlEl5t1NNxq2cx7HO\nI7C9epaDfYZxISjymWO8Wzji0cCWC7vCyEjOQRAEmvUbRHpCPHfPv9jpliVVVytg39a/0SHQ19AM\nHSZYDGyMVqdl3sp5KHIUNOvWjCZeTZ47R861a4QPHkLc7C8w8PDAY8sWnL/9Fpl1yau3FRaNWkvU\nrRRi7qU+dSfmq47MwhCb0T5oM/JIWXcLseBn1PNH8GgHu96D6ApT27FYRAYnExmcjG8vD4zMXm4z\nn5+fHwDHjh0r0rkFQcDb2pvJDSeztd9W9r22j5m+M1FIFSwJXMLru1+ny9YuzDk7B/9I/6fWcqqI\nuFob887i2SRP/RzP2BASJozn8xXHScx8ct1AEATaD6sFgsCpjXcRRZEavi2xcnbh0q7tFcoxvvKO\nIUuZi/b2BRSOtdEmemFs/wADn9rM3zQfeZIc24a2DGg54JnjtRkZxH71FeHDhqNJTsb5p59wX7cW\no3p1y/BdPEn8/QzWfXGeXb8GsmP+VTZ9d4nUuMqt7VsaGLqZYzWwJnlh6aTtCXvU8I/Aj5mjXuAn\nI6b8jCwBdFodp7eGYG5nRIOOLi893tLSkpYtW3Lt2jXi4uKKbY+rmStj645lTa81+A/x5+vWX9PQ\nriEHwg8w9dhU2m5sy6RDk1h3ax1xyuKfr7RpO3kUzouX4JGTROfFsxj21VbWnAtHq3v8Ym9mraB5\nH0/CbyQTFpiIIJHQrO9rJISHEnEjsHyMfwqvvGPYsm0fRtocellUBySYD+nAhuMbyL6Tjegs8m7/\np6eliqJI+p69hPbqTdqmzViNHoXX3r1Y9OldoloMRSElVsnu3wKRSAV6Ta5P1/E+5GSq2PHzVdIT\nS6Za5H8Jk6YOmLavhvJcLFkXCgj8mNjoBX5UWXqBH3Xl/eyuHo4kNVZJm0E1Hm60elnatm2LQqEo\n8bLctka2DKw5kJ87/sypoadY3m05I+uMJC47jrkX59J1a1eG7RnGn9f/JDQttELdWRfEplMHaqxZ\nhZNUw1z/haxcdYgBi89wLerx8FvDTi7YuJhyatM9VLka6rTzw8TKmks7t5aT5U/yyjuGsFOHMTFx\nxVBVG1OPBAKUUQSfCCbHNIePx36M5ClrA6rISKImvknMzJnIHR3x2LIZx88+Q2pa/pvURFHk+Nrb\nCBKB/tMa49nQjlrNHRnwQRN0Gh0HlwWhVVeFlf6NRQ9PFN5WpO0MJS+swH9kBx947U+ICYSdUyql\nwE9KjJJLe8Kp3tgOr0ZP6pQXFiMjI9q3b09oaCihoaElaOEj5FI5zZ2aM8N3BrsG7GLXgF1MazIN\nqUTKb1d/Y8DOAfT9uy/zA+ZXyFRYo4YN8dqwDktzYxZe+BPLe0EMWHKGWX/fID1bb6tEKqHjSG+U\n6Xlc2BWGTC6nSc9+RAZdIz4spJzfgZ5X2jGcuRSMZUYUHe2aIQi5ZPVozM6tO9FKtUweMxljQ+PH\n+uvydRLC+vYjJzAQh88/x2PTRozqlm/YqCAhAQnEhqbTakB1zG0faTdYO5nQaUwdEiMzubT3fjla\nWDERJALWw2sjs1GQvPYWmpQC4vG1e0OnWRC0FU7/XH5GFoG8bDX7l97AwEhKu2G1ij1f8+bNsbS0\n5PDhw2WiD+1p4cmE+hNY12sdRwcfZXbL2VQzrca6W+sYf3A8HTZ2YOaJmewK3UVKbsqLJywDDKtX\nx2PDeoycHPjsxB98ZpHE+guRdJp/nK2XoxFFEUdPC+q1r8aNY9EkRGTQsGtPDIyMubhrW3mbD7zi\njuHojh3YGblhKtRE4ZPJou0rkWlk9BzYEw97j8f6Zp06zf3+A0j8dSGmHTvitW8v1qNHIUiLVkCv\nNFCrtJzdHoKtqym1Wz8pd+HVyA7vlo5cPRRJckxWOVhYsZEoZNiMrYuog+TVwejyCqQQtpsB9QbB\n0W/g9r7yM/IlUKbnsevXQDISc+gxqT4mFobFnlMmk9GpUyfi4uK4fv16CVhZeOyN7RniPYSlXZc+\nTIXt6tGVy/GX+fz053Tc1JHR+0azMmglERnlKzQkd3LCfd1aFN7etF0zj90103C3MWbmlmsMXXqe\nO3GZtBxQHSNzA46tvY3c0IiGXXty7/wZ0uJiX3yCUuaVLYmRkJzO8injGFhtCBaGJvzlGYg2WodH\nGw/GdR33sJ8qMpL4uT+Q5e+P3N0Nx88+w7RDh2K+g9Lh0t77XNx9n4EzGuNc8+nFzXKyVKz/8gJW\njsYMnNHksZLAVejJvZdK0oogFHVssBlV59FnpMqGlT31G+AmHNaHmcoAZXoeMffSyErJQ6vR6SuG\nKmTIDaX6EtP5ZaZl+f+qcjRE303lxvFoNCod3d+sh2eDktP10Ol0LF++nNTUVKZMmYKxsfGLB5Ui\nOlHHrZRbnIw6ybGoY9xK0SukVbeoTie3TnRy64SPjQ8Soezvg3VKJdHvvY/y7FnsZszAv1F3vt9/\ni4xcDePbeDDA1orjK2/RelANavqa8teU8dTz60qXiS9XcqewFLYkxivrGBYvWYVdwA1a2/fnlNtF\n7iRkIveS8/mYzwHQ5eSQtHQpKctXIMjl2L4zGasxY5AYVMya/Vmpuaz78jzu9WzpManec/veOhuD\n/+rbdB5bh9qtKqyQXrmSefoB6XvCMOvkikU3j0cNGTHwZ0eQKWDScTAuvXTkvGw1p7eGcOd83CMF\nusIigHtdG9q8XgMrx5Jf+4qLi+PPP/+kfv36DBw4sMTnLw4xWTEcizqGf6Q/l+MvoxW12BnZ0d6l\nPe1d2tPSqSXG8rJzZjqVipiPPyZz/wGsx49HPvk95h2+y4aLUTiaKZgkNUMdk83wL1pwftsybp46\nxpuLVmBiWfKVa6scw3PQanX8b/x4htoNJMU4lX2SMFSWKr6Z8g1ymZyskyeJ+/ob1NHRmPfti/3M\nmcgdKmbd9H84vCKY0CuJjJjT4rG1hach6kS2/3SZ9MQcRn7VEkNjeRlZWXkQRZHUbffIDojHekRt\njBsUWLSNDoCVvcC1OYzeoU9tLWGyUnP5++erZCTnUr9jNbxbOGJpb4xULkGj0qLK1aLO1T7UHtCo\n8zUI1PonClsXM4zNS/cm5ujRo5w6dYohQ4bg41M2T08vS1puGicfnORE1AnOxpwlS52FgcSAZk7N\naF+tPX6ufjiZlv7NkajVEv/d/0hdvx7zvn1x/u5brsYpmbUjiKgHmbyZpcCxugWdh9nzfzPewbfP\nQDqMGl/idlQ5huew99BpdFuOUsOmFRuMT6GSqZn+7nSscwXiv/+ezAMHMPDywnHOl5g0b16ClpcO\ncWHpbPvxMk17utOyf+GqgiZGZrLl+0vU6+Ci33RTxROIGh2Jy26gjsnC7u2GGFQzfdR4bSPseAt8\nJ0Cfkl2QVuVo2DI3gOz0PPpMaYhTjYqp5qfRaFi5ciWJiYlMnDgRe/uKffOk1qq5knCFE9EnOBV9\nivCMcADqWNfBz82PTq6dqGVVq9TSzUVRJHnpnyQuWIBJ69ZUW7gQ0ciItecjOPR3CG0ypaibWVEz\n5xh3z55gzI+/YeNSsmqVVY7hOcyb+hH9DDux0ziAdEkOg4YPxOP8bRIXLEDUaLCd/DbW48dX2LBR\nQXQ6kS3fXyInU82IOS0wUBRee+nkxrsEnYhm8KfNsHMzK0UrKy/aTBUJiwIBEfspjZEW3DF8aDac\nXQi950OziSVyPlEUObw8mJDLCfSf1phq3hVbCCc9PZ1ly5YhiiKjRo3CyanyhCbD08M5FnWMY1HH\nCEwIRESkmmk1/Fz98HP1o7FDY+SSkn8aTNu2ndgvvkDh7Y3rn0uR2doSn5bD2u8uos3ScNw5h26h\na3B092DIl/9DUkSFyKdR5RieQWhEDBFzNxFuKydCmkjT+tWov/4QucHBmLRpg+OXX2BQiprSJc31\nY1Gc2nSPbhPrUtPX4aXG5mWrWffleSzsjHhtZtOqhehnoHqQReIf15A7mWD3ZgOEfzaI6bSwYRiE\n+us1oz3bFftcoVcTOLA0iBb9PPHt5Vns+cqCpKQkVq9ejVKppFWrVjRp0gQrK6ty3+j5MiTlJHEi\n6gT+Uf6cjzmPSqfCVG5Ka+fWdHDtQNtqbbFWlNx6UtaJE0RPm47Mxga35X9h4O5OUnQWm7+/RJyh\nyKW8q3RJOoZPr0H0HPtGiZ23TB2DIAg9gF8BKfCXKIpz/9Uu5Lf3ArKBcaIoXinM2KdRHMew5qsf\nMVHZcV0eQY2cRJruPo7UxhrHTz/FrGfPSvVlTn6QxZa5AVSraUmf9xoWyfbb52I5uuoWncbUpk7r\n/464SkmTfSORlHW3MW5ij9XgAuGG3HT4qysoE+DNY/rS3UVEo9Kyfs4FDIykDPmsGRJp5ckmVyqV\n7N+/n6CgIADMzMxwdHTEwcHh4b82NjZP3TBa0chWZ3M+9jwno09yIvoESTlJCAg0sGuAn6sfndw6\n4WlRfKedc/06UW+9DTIpbsuXo6hVi+BTDzi+7g7UMeda0Ca8M24hbzeYt98ejYGs+J9dmTkGQRCk\nwF2gKxCNXgN6uCiKNwv06QW8h94xtAB+FUWxRWHGPo2iOobcPBX7P1/KNdNk3KOiaXHuHNbDhmE3\nfRpSs8oVSkmLz+bvX64i6kSGzmpe5IVGUSeyY/4VUuOzGflVSxQmVQvRzyLjSAQZRyKx6OWJWfsC\n9YaSQ2FZJzBzgomHwbBo36WLe+5zac99Bkyv+CGkZ5GSkkJISAhRUVHEx8eTlJT0cCOckZERDRs2\npEmTJhV+PeIfnpUK62nhSSdXfSpsPdt6RU6FzQsJIXL8BMS8PFz/WoaiXj2Or7vDzdMx1OzgwLmz\nyzFNuEukfUNef+st2tUrXjSjLB1DK2COKIrd819/CiCK4vcF+iwFjouiuCH/9R2gI+DxorFPo6iO\nYf0n3xNqqMY8V6BuggTrnj0wcHBAp9PHdhH1MXtRFBF1IqKoF/SSSCVIZcLDOzjxYZ/8/gVeS6QC\nUrk+pxxAlaNFlat5mEGi0+pAImBoJMPQWIahkQyJTJ9/rs7VkKtUk5utQZ2jQZWnRSaXoDA1wMhM\njrG5AXIDKfHhGQSdeIBUJqH/9MbYupg+722/kKToTDZ/d4m67arRYYR3seb6LyPqRFI23CYnKAmb\nsXUxql0gtBB2HNa8BrW6w9B18JJ3xhnJOayfcwHPBrZ0f/P56caVCY1GQ2JiInFxcYSEhHDr1i10\nOh0uLi40adKEunXrPpQMrQzEZsXqU2Gj/LkcdxmNqMHWyJZ21drRwaUDLZ1bYiJ/ufRgVVQUkePe\nQJuWhusfv6No6suxNbe4fS4Op+qmpChPknbrOKLUCEsXX3ya16LN60VLES5Lx/A60EMUxYn5r0cD\nLURRnFKgzx5griiKp/NfHwU+Ru8Ynju2wByTgEkAbm5uTSMiXn5n47KP55FmqMEooRECZfhlFNBv\nRpJJkEoFdKI+vq/TPP2zl8klGBjJkCukaNU6cjLVaDWPyg8IAng2sqPt4JqYWZeMGtypTXe5fjya\nwZ/4Yu9eOAGXVxGdSkvi79fQpORi/24j5PYF8uEvLIX9H0HbD6DLly8174E/bxBxI5kRX7Ussb9p\nRUSpVBIYGMjVq1dJSkpCJpPh5uaGl5cX7u7uODs7I61A1QSeR3peOiejT3Iy+iRnHpwhU52JTCKj\nmUMzOrh2wM/Vr9Da1+r4eCLfGI86JgaX3xZi0rYtN0/HcHHPfbLTVeg0iUgtw0kwzaFGrgGj5n5W\nJJv/c46hIEV9YshLSyUw4BxN2ndHp9Ghzb8wC4K+Vo4g6GumP/xdIiCKIjqtiE4j6i/O+X0kEgEE\nvWyfIBEQJPrjOp2IVq3PJxdFUX+BN5A+sbAriiIatQ5Vjkb/JKERkRtKUZjIn6h+KYoi6jwtOZkq\nVDlaLOyMMDAqfPZRoT6bbDXr5lzAzMqQQR81rVTx7bJGk5ZHwqKrSAyl2L/bCMk/+0BEEXZPhSur\n4LW/oMHgQs334E4qf/9yleZ9PWnWu3IsOBcXURSJiooiODiY+/fvk5CQAIBcLsfV1RV3d3e8vb1x\ndHy+OFZFQa1TE5gQ+NBRhKWHIdfKaSxvTF2LujTzaEaL2i0weE6moyY5mciJb5J39y7Wo0ZhOfh1\ndHIFUX8f447/MS43csNDa8aYr6cXea2mKpRUxUtzLyCeQ38F49vLgxb9Cq/w9SqSF55O4rIbGHpZ\nYDuuHoI03/FrVLBmADy4DG/sg2pNnzuPTiey+btL5OWoGTmnJTKDynG3XNJkZWURGRlJeHg4ERER\nxMfHA4/U4+rWrYuFhUU5W1k4dDode47s4er5q4/tWNcJOmR2Mnx8fOjWvBvmxk8+mWszMkiY9xNp\nW7c+rOSbZ2DA/r59kUtNGdOuEfZdexTZtrJ0DDL0C8idgQfoF5BHiKIYXKBPb2AKjxafF4qi2Lww\nY59GlWMoPY6uvsXtc7H0n9oIl9rlpz5XGVBejCN1+z1M21bDsk8BR6pMgj/9QKfWZyqZPzu3/9rR\nKE5vuUf3N+tRo2nlWJAtC5RKJcHBwVy7do0HDx4A4ObmRr169ahRo0aFTYfV6XRs27aN4OBgfHx8\naNmyJWq5muO3j3P73m0k8RKMtEZo0aKx1uBe053eLXrjau362DzqmBiU5y+QkZ3G0sggDPPM6YM7\njb8cUyyZ4LJOV+0FLECfcrpCFMXvBEF4G0AUxT/y01UXAT3Qp6u+IYpiwLPGvuh8VY6h9FDnafUb\n5rLUDPqoKZb25VsgraKTtiuUrLMxWA2uhUnTAvtI4oJgeTewrw3j9oL8yTIlKbFKNv/vEq61rej1\nToMKeaGrCCQnJxMUFERQUBCJiYkAmJub4+HhgZeXF9WrV8esgmQV7t+/nwsXLtClSxfatm37RHu2\nOhv/6/5cvXGVnAc5GKgN0Apa8izy8KrhRc/mPXG3dwcgICyATds2Yaw0xk9Vj5Y9HFG0L95emaoN\nblUUmbT4bLbNu4yBQsrAGU0xtao8WSNljajVkbQiiLzwDOzeaoChW4HwwK3dsGkU1B+iF/spcOHP\nVarZ9uNlcpVqhs1uXiIlsV8FkpKSuH//PuHh4dy/f5/sbL02tKOjI7Vq1aJ27do4OTmVi5O9desW\nmzZtokWLFvTs2fOF/XU6HQF3AjgRcIKUqBQMVfrvgEqhQocOw1xDdIKWzipv6hrJsP18WLHfV5Vj\nqKJYxN1PZ9eCQAyMZPR4qx6OnpUjvlseaJVqEhYHIqq12E9pjKzgRf7EPDj2LXT5CtpOA/SOd//S\nG6QlZNN/WmOcK2gtpIqOTqcjPj6ekJAQQkJCiIyMRBRFLCwsqF27NrVr18bNza1MspzS09P5/fff\nsbKyYsKECchkL5ccIooiASEB+F/2JzkhGQEBOwc7BoSaosjwxn6sEwZ1ahfbzirHUEWxSYrOZO/i\n62Sl5VGjqT0e9W0xMpWTl60hNU5Janw2mcm5KNPyEEWQygTkhv/f3p1HV13fCR9/f+6efSOEEAiJ\nIQtLARWXh7pgUWTRMk7VulQda6VOpz2d7Rl96jNPe85szEx7ZrPqqGOxM7VoxVHcwLECztS6CyIh\nCwECIYGEJGTPXX73+/zxu4YEIyTkJjf35vM6Jyf3t937/Z7k/D73910+XxeeJCcenwuPz4k7Mior\nHAoTDFiEAp/9trCCZmDeh9N1ak0Bh0swlolkDjUDGURN2CAOez6Jwyk4nYLDaW+Hw5HRY1aYcORa\nsOeViENOjR4TweHAnrsSNgPXmXD41Ii0yKi0z64BBp1nX3NqJJtdBl8wzHlHOwm4ndROT8EKGyzL\n2GVs3o2z+zDOoksJuKdzuLINl8fJqvULmT1P+3Gipaenh5qaGqqqqqirqyMUCpGUlDTwJFFSUnLG\nUUHnyhjDL37xC+rr67nvvvvIycmJyvt2b3qWk7vySS8/TvrdN0blPTUwqKgI9IX44NVDVL7diL8n\ndOqAQHqOj/RpSaRkenE4BMsKE+y3J/QF+iyCfotAX4ig37Jv+h4Hbq8Tl8eJy2MHgrB16sZvDUod\nLU4ZCBb2j32Ttm/+5nOBQByfBQpHJFjYN/fBAcCET93YHQ75XNAwZvDkRUM4DBh7ouNn7zlwbmQC\n5OD3zQqFWRiyaHU52J/qweF0YFkGKxgifKIeK2SQzHyKFs/k/GsLtfloHAUCAfbv308RVPp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      "text/plain": [
       "<matplotlib.figure.Figure at 0x10d1d8390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "f_4=np.zeros(N)\n",
    "\n",
    "for t in range(8):\n",
    "    for n in range(1,nmax) :\n",
    "        f_4=f_4+2*h*np.sin(n*np.pi*delta/L)*L**2*np.sin(n*np.pi*x/L)*np.cos(10*t*n)/(n**2*np.pi**2*delta*(L-delta))\n",
    "    plt.plot(x,f_4)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Raw Cell Format",
  "colab": {
   "name": "python4tp.ipynb",
   "provenance": [],
   "toc_visible": true
  },
  "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"
  },
  "toc": {
   "base_numbering": "0",
   "nav_menu": {
    "height": "369px",
    "width": "618.333px"
   },
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table des Matières",
   "title_sidebar": "Sommaire",
   "toc_cell": true,
   "toc_position": {
    "height": "calc(100% - 180px)",
    "left": "10px",
    "top": "150px",
    "width": "165px"
   },
   "toc_section_display": true,
   "toc_window_display": true
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
