{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Théorème de Marcchenko Pastur "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.803231049452779\n"
     ]
    },
    {
     "data": {
      "image/png": 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1TOxn2+84kotyCuAqZ9hIiAghagldBM0mbO1BmDawEhNiVppnkbiSPHfDwE6yFCG+GJc/jp+IIQZsjRD8n5O4D0KlcPCCIyZCrOBAoCw/mmljzYkcgsMLGu8Cemj9k23nzvP0wg/nZYNk8X9+Lnw8x1hteG44F4o22/WX3zUEmU139qnD9jPtZxxJkTLu0yucYSMhIoSoJewEOzEp79omQtLiB2JiJmZWT7tLtXe2fiJiM7dgLCGxVF4EwgJ/145JFpMwJvqYsKAIsaLGxmbYu3J/zjgX7p/iBSLE9nQBNmgUMSdw9QC8ToH12BNbJllswF1rNiXHwOfGuBTu87YHN0z6/JsF0Na1jmmzkOxnyeP6CZ8CzKYL0yKVt57LVKwQRcq4n1HhDBsJESFE5ShixrZ3xTa7A5N1J2y8g53cOcHF7lJ5Z8t1eBdvJ95gRIjtOhtLAebdf1oWDLf5xoqHwuoNT7eJGuvK2Xnm9OTxiAt+lqwHKDLoyln9+FPJhA6BwdgMuEUQw0HBYfHLrEsF29B10zDr4xjT92l3k/A87boULtgGnw+b4gFr4WEArhcUFJw8H2uRSosj6bUVomgZ9zMqmmEjISKEGCiD8HXnNWP7u0yb3dEJCgdfRMz2Nuk0mfgJFKKEBbgwyfNx4jhrJ4kowNfonuA+sBzrI/BzbKwZC4P90eJgJ/e5O8xoEzGYoE84eFFrGdbBhD3zOdOSyR8TPI4REz5p4Ng3nHtMOOBjP26JlIaznOAYVoSwm64VIRQKPI+moGsv3T7xuUx8R/gcmunNze/IWkqAjWOJxZGUwQpxxhRdgWVEQkQIMVAG4esuYsbG/62LgNkdnS7w1qzOfVtzvk21zTo/VDglsAYwvgKP1soxkdradCFZrCUFFhKKEJwDPu8J10VzQqYlhxMxHykIIDasIMDzLX9tWgt222lmeOwvW6IWkCwgJHBesET4bWP7giCkYLBCBbxsz7mtYFaKEbqZCAu8+YZ9/Cy8CPFxLLaOSaz8/bAEwEUVzLCREBFCDJRB+brzmrExMdoU05gbJIbv3GrvUmlRybL+ABubcPBe89pSdgnu0gnTVPl52aBWWzMEy/G4av2TLbcEapTY17AuRQisFNynn/QBRAjFyMMb0iuVergN3xOP7Y+Bz+HQJfPbM2nGzxfn/tC6J1suGIoJCBFaQLgvikk7SdtAVcse82aFRfN3aFmSbGfhZF/O8lSk7HxZUsxHhbFGo0PrxSGyadOmMGfOnLBx48Ywe/bsYZ+OEKKH8CLKSaNfd5k2NfYP5x/f9poNTI3dPec9p7T3kiaw7ARit6FlBhP3YW7ypOiwJeCzypcTTvqxGBIKBMZ6cAL+TEohNy988uCtLn65F16+KzDO7f++bGHLiuOFAouP2X14K0dM4FnYOThNNHKc9HusZtFpLJUtVqTI/C2LiBBiKAzC151lxrYxHrRg+PiNPN1Z89ylxqw/ILYNJ2ErQmi9sFVWKUJiFgwLRQjPxbqhaKWgGwbr2e68nm5EyB7jf4fuvUvyPvmJ0i1iA0uJDWLF++R2iH/x4wRBrw13zIlaJ00R4j8j+9x3FoaosdYujpNhWyG25sywGcV6IxIiQohK+ro7CYQ8F/ZOF+widSCsi8jehftUWRT/8oXIrHCwj6BTrAYmZlYO/c5tD7elywIbG1Ik8JR4SwPdMcxWoWvo5pXrJlkkIEIQx3Lrg4+3YlCIDWJtmBgaBJxC1GCytdk6jO+g+4nvxYsQnK99Huss3M3322/OzplhM4r1RiREhBADp5NImOpdXZ4JpGjq5FTuUq31h6XT/fueiONYO6kQmZ/ss9wMHpZGZ7wIj/W71RvDE+MTctHAU4s/DwgK74axPWQeXLc5CajF67YxX8yyE0v/xR9TlrkdK69OZL80X7PuK1hTVqx8vO2zpcXGZi1lBSRz3MXqfJSFUaw3IiEihBgoeURCp7s6TBhpFpQ8nW/TJpCiAiivmPGpsrAE4HX8MViSdTk4cdo7fH+29vmM6QiizJ4Qvesj1gSvCJ1iRfiafT/tacgTGTukiBiy5//iBbPbxo+tkPqn8XoodAF5EYLjrxlfB7BYG8A++f3GrAllnNBHtd6IhIgQYqAUcYmk3dX510ieO7+si3E/zNqx88ZEygZuzboWzbgMK0LwGtaxxKwGWSIE2axp6QjW5VOUNBHi94n3w2qsFA+o92Frp0wVpjP7mCNg/2+FXqyzMcYcxp4/NwrFMk/ko15vREJECNFTOlkVQB6RkOeurlWIzHRijWUVwEJyxL4T5b8tiDkA6D/iLTOAFUnT+rtkuYmyuuTiXPdZ9sNJYgCTIkWID7TMazXgRJulM2zKcq+I7YvuEFseHtaINGKptlnr2kBTWp18hdSYG9C6t2ilsoXs7BgYNREyavVGJESEED2ll1aFrLs6Kxo4oTIw0x/TBi/612mN4IUawgJ3zrE79mYGxdpWsKR/PxRhTAWNxRhgebNHyvrWxG0nXyzZa+kPkv/7QmOd4OSadyLvpQhJOxdaHACFVZZbp4jbyDa2sxVgbVEyWjRiBezGxp9TxNJKZSm7NaEK9UYmtxvsIcuXLw+HHHJI2HnnncPuu+8e3vSmN4V77rmnn4cUQgwZXOhYaIqTRLfBcrG7On8svMZJhYGZ9piY5Jm5kXZO7PqKbSEUbH0OiBwKE/xhUsPEFXs/FCd8nWKEDdi4HJYBC2MnvEjjeT/97NbMzwm7wwRfRFa0n8HUiFk4dt5+4j63MZ7xgs85j6DC521jYLLg9+Lh920Ln+F7eOWF17WsQUk/n2nNkv4Ug7BS+RovftyNYgzWOe43WRuLyPXXXx9OO+20RIz89a9/DR/60IfCa17zmnDXXXeFHXfcsZ+HFkKMeLBcnrs6L1RYuZMuD1+YzJdit+fEgNGbzd0zwH68MKFwSKvdYMuC05rBnihproc0S0AeCwEMG0UzX7xoyWt1ieELlkE7pGW85IGfNz7TToG4Fhsciwwkpkif7eqVsPw9hSGAGLGuMogmuOvKbk2YSkffWgiRH/3oR23PL7vsssQycuutt4a/+7u/6+ehhRAjFCznJ3LvxrFFpuzdb5rvn5OJbz5nzylx54xflG0ZcG4bywyhC4il1DHZ4bjWHQUWzm0KIuDjO6ywwGTHDrJ8LSYIpiIS8jLV/Vux5rVDkYqstCKlTZq0lsSqytpAVJaBx/4QB0T3jB0vHB9NS1d7Vg2tVsOqG9ItvUhLr3SMCEq9gvnz482gtmzZkvzZErFCiNGkSLCcjyvhXR2wgoTbxzIZsE1a7xWY5NkAriVCGs0AVx7fWx5iE6cP8ISIYMdb2/k15qrwtT+4Tqx2hg8iZSO6v25r9OyOlq4T1BIpUpckDW4fKz2fR4S0hKB5f/68bLdi24jPgn3sMXf7pI+MFYf4jiBMbLwOvzNa0nxWDcdsma0JVWBgQmTbtm3hrLPOCkcccUTYf//9U2NKzjvvvEGdkhCiJMFysWJjWd1ymxaM9iwYiAob2MnJnC4R2wDOuki8z7zTpMygWOyLIgJixMZ9xCZev0+6KvD+vnTD/a3iYjwGsIIkNul2i3VNxOqUdCLLwkERUlTceJdYiGzPAmgQjvw8YtaisbGxtu8DYhhuFuDHFV02+KzZ8Tg2ZstqTagCA2t69973vjdcc8014Ve/+lVYuHBhbovIokWL1PROiBFiKs250prHdUoJpoWEEySbuH3zllXJc949c2KP+f/T+p4UoZt02KxtiqSy5oUCgRN4mmUhrRaJnfizBEk3DfLSxEunzzWP6PEWNo4ljC2467B/3xixrL1ZRoHSNb07/fTTw/e///3wy1/+MlWEgJkzZyZ/QojRJRYsRyHB4EG7jNuwdLaN4eA+8lRa9ZYO6yaxDeN8ESyIGFJ00veTbTfpsHT3HLpkfs8roMZouH4rWSLE9o1B5g4CR7kdXDt5qqt2wgohK5A6CRq7XlZXXZ9ZE8t0ogjxLkRZQSqQvgtjC0TIVVddFa677rqw99579/NwQogSYHtxECskeHfJZUxztXElAJODLYCWlRKMuh7MkkD2gy3zjVgBWEhikxXEEEQJ/mw8wVgkjTQGJ8ixyCSZBV63cSS+225ssu4lSdrq2FjH86RA2H+POYkIse+T/8dnjn11A0WI3TyWbUNY9j62XlpsDlO8Y9gxBEtImVNcq0xfLSJI3f36178evvvd7ya1RB555JFkOcw1s2Zl/8CFEOWj22Z0eTIPvJvEr5+VEszCZBAUPkjWTvB2v3DDMPARFhUbqAhRg/3FMjOysjzyZqBg8sUEm6dPDHh2XJz1EoifvJkyab1h8FnB/dVtldaWJSSyGfZ95+qNrXPE9wmRie/3yhWrwsMbJn83NkbIZsO0j4e10UZw1moXSxOXi2ZEhcgll1ySPB511FFtyy+99NJw8skn9/PQQoiSVU1NExJcRtLKuFOMxFKCvdCJ7deub2NB7MRjYzKsIMmim0wKujvyCIFOMRwxJnXrNXEe3ewPUIRY8UShgH3OeM60toDbqcAuvfbzsW6TL99wf+r7pQhhFhXddRQxLGzmXYi2Uq51IU6lz5AoiWsm9icRIkQ9q6bSTG6FBP7GPTPRMu5+UsiqtEogVnBO1rVi17eVNHGHzPbvVoTg/74Cai/pJELohuhGNEAUWChCIH6mmn1DEQLxYeNMeiFCWF0Wnz36+1h3C6vbHvCxH0+KIWFsiQXCgoXWkCEEiwePwcwbb/GwojQrc0v0FvWaEUIMrGpqmpCAzkirN+KLnPm7W65DQXHbgxtawa5wrdhMmpg1BxYPG0NgXQBcfxAFxTxwG8EqwAm5CGlio+h7yMpGiR3DWluKfGZcFwLhlgceb3vNplz799ASFWNjyXJ+1/jc3nrQomQdig5gLV8QJyAmNqZSEViUOH233+k/QojB8sIPX9MSFTblsZvaIn5ZWuovJx4WpwJ2uW3vjgsbJyb/ul2Oic93a+Xxj7jgZ4kQ6GWX2lhMSQwIp01PPTtwAUQwdxfxOuEzveHcY1pdg/OA7xE9aHyJeH5/seJozNg59cglyXfEcYjvCE3u+PkynsOnhOcZb0XHtpja/N1X14wQoprkdZHY9fOYuFlq3WcucDnuYpv1PiZ6hHiRAZAKa5vdeZHC5bA6cHICB+81r831hIyb5PjjIqQXjpq8MSWYgIclQkDR0Bd8pvjM8Jnm3mb9k4l44XdFAYRDYxmDhz0UIXYcJgGz4+4WG1Tq3YH8fiE20kRvp7ENN0/amMdyuoFEPuSaEUIUor12x4RVIivLIFZbxJZx5+TMUuu2oZxdjuBR4GuFWBHCYmX2XO3rTF1lxkysmJkt/W3pt/k4r7WkrMS64MagCwfWJlhQ4Erh8pcsmts2Drx1hS42fl++OB1cdPz+Y8IC+DilohWBpxK0LSYjISKEyI2/0Nosg1gzOgJBwrtIXrjtXSvvImON7WLHBNZdcqOZrCiOgO0RghLiXB+PVkwxaBYt4n3Aaq/olK1SBhGCINdnelhKPg3WDsHXYT9jLF+zoemqSfv86aqZ+J4mvm8AaxnHWZawoBiBELIxQXZdH8CalqWV5eYRnZEQEULkJmbZsGIk1oyu6F2k7f/Btux2cmidy3gXXEzdnL7tcVn6HZMdJjdb64KxB8iKsZM/Q+bsBBibELsRDZ2yVYYtQsAgRAhJC7mBCGEWk8fXMkGQqxcB4Nf3rm2NoTRhgHgSrsOmiFmxI/77UWBr75AQEULkLl5mAwCt6yXWH8bDzJa0u0geE/vEHSpFCEu9p7lZYsQyXhhMyddYY8K+1z132bEtSwXHfmj9k5P2j/c+fWxyu/syWzvKjs3QWbHy8Zb1iuLDixCmDzOwNCaQMVZ81hX3ie8D48wG18Jd9/Yv3jhJTKeJi7S6NqIYClYVQkShBcMH5fGCzpTIWG2QGJjsWZfDBwviztSXercWDIgSK0LSyoqzWJWNHbFpnTTZMziSNSZuXtk8PiYiW48Cx06rrppXhCTrjqAI6VT+3WO/jW5KvvMTsi43fE8Qj/i+fb+Z97xqn9a488dj/RlaOzD22FOI3z3Hmq0p04w9mWzRwz7e9oUbpxy0LeJIiAghplS8LO/F2AYgAm5D8zjvXu0x7lv+D62JCY8TWTPrUtNpbcAp1+dkRgHEFN63vGxhYoGxQbesFFp3imbsWPcYvrdYtkse8L2ywB0zcDAuvNhY8cD6towZL5opOPFdw2pBgQHh4ce1zfTBUbwIsbVIiPrU9A65ZoQQqXTyg+fNMvD7IuwF44uUtQUMjseC4BGTDyYNG1AaK/qFOcMGHAI8Yj+8g+ZdMe6W/9+vV7a5BrJiJXxti14HtVYFiMBbH3y8q0quZx3bHphM4Wnrw8TGjXf7sdgZu+vGgk05rgH3f+SF17XVROFxSEyQ5+mnJOKooJkQoiOxAk+dio/FYkWsULGwjDtcJMxi8TEhvlJnrH6Ihe4YBD7etWZTePqv29oEBrfrtveKaAef40sXz21ZHtAMr9WfpotsnFi/IHxniNmxFXOzMmL4HafFL3Fc83h4DSLEd/y1ImQqzR/rxCYVNBNC9Io010ssgybWHyYmULyZHcth7cAkhrtfuy7N5hAhqKgZ3B2xL6DF2AbGgKByJ7bFRGgPS/HSjQjBfh+44HU9KXBWFfA50lJ0pREhgCLExp3Q04Fle8zdvvUaP9MvucZ2eB3fGSxStlgdxxnHHfZLqxfjiWKuE45rDywhFi9CAERGVgBr3UVIUWQREUIULl7m3TOd7gBxB0lrB2NCaDK3lgsEs3KyOfHgZq8QnynD7bwlZJAuEkyKs2dtlxrIWnWysoBoueI63hqC17GlbZKXZo3w++S4sG43m8nF9HE7RmIulbRWAb6wHbD7kCWkP/O3YkSEED0tXhYDF29MEOwrwos7ffAQIzTpAyz7zE+b8SG2P8yfN21pWWewPVMtYSmxKb/9BpPiMMuvD5uYCKFY4OfCdSBCbCYMBcXcWdu1iQ6Mt7RvDtvQ+mVjMGypdVslF8f+zm0PJ+PGFtGzNWpi1jybbWXHJ4ueqaJqf5AQEaJm5L2rm0rxMo+dACAocFFnQzkbA8LaDnst/UFr4mr6+JvBpQCTGl1EtEjg7poiJKtjrOgfacKMgcYWfm8M/M1TGh4ixAeEWmEAbLwIBa8XDgiitfsiGJ88J1pAYmKkVxVVZV2ZQEJEiJqR967OXwTtJGCD/3DBtHedaRdUTAAINMQEYYMEAd0z377t4eRO1vPc2du3hMiOM6cnk56fvDjZwTpSZ2tF2bASxAccL56/wyT3li9cRvyYTerOmKCfWPq3z5wCaZM7Gyv6mBCKERuL0ouKqrKuTKAYESFqSFrabZ4Lqs+gKZI9YzMbMImgSy6tJL5qpg8i9ZkYWesCaxlhXxMxOLzowPdxWME4Hn6H9jvmeLKVd8889gW5qvv2O5NskL/DsqMYESFEJt3e1cUyaOy+kC3hg0zxOmI5cOcLs7e3YGDC8uKCkw7W3/TUs8mE9tnr/phYRjxpWS9Wd0iEDB5vlcJXkJVu7aF1ggGsFCMYV4wfsrEnear79oqs30ER1K+midJ3hagpnUqz20BAYO/W0DAMGQdMh2QVS/r7bWYCOtoilgSv4dFW3MTrWW4UmO5Z6fSZrY2oyV4MH5/GDAuXBTE+ljxVVxHHwVgPiFWIEGzHmBOIEFRwZfD0oEqt97qi6hk5WyRUGVlEhKgpne7qfCBgLIMGqY9cx2etsL6Hv/uNFSdLQwXHysHOM6eH/7NwbrglKas+2byEJfY79YJx99nbt2JB8rpmIIR5pHcduSR5hMUNy2gJ8ZM/BHI/q5v2o6LqRT2yrowyEiJC1BBbTwFBpCgm5jMB0Eodd7asI2JFCAtJMfCPAavWXJ6VCdFJhOC4i+bvkExaEiHDByKkk4A45Yi9k1oxsHoRjJNtjUayLC0I1cP1bO8ajkmIGV/WnesA3xEa9HJSzyrix9eLUKRFQpVRsKoQNcMXdfKPTKn07dd5x8bXs3rOWMsItgOxKpaeMZP1ojTc4bLzzOeEuTu01/oA/F5ihcqsyKTrpK1x3Fh21+KYpczWD7GCAxa7K1esCg9vaBbDY2sAwmwZFlYrWypsNy0SRgkFqwohct3VeVFi71pZh4FVUCkkrAiB+RzWFFsgipYR4huKZYHXORFxXblmhgMyjTY8+cwkwRFrDIjvyAsIuk5YbyaPRWT/Pea0WV7YsRlp37bqKcflRAG8tZMsCT4LpWz02royysgiIkTN4cWaLhWbiRAreY0JBf04rAjhXSsnnVgp8LymeVFOsoRk0e82tq+0svEUorSW8Fh0K9oS71VNhR1FiszfEiJC1ISsSo6+NDrcKQj883EenECsuTxtEuLEkjcwVdSHTlautDHD8RdzDwKKj0HWExFx5JoRQnSs5EhhAouHLY1ONwwyFCy8uLPzLUirCcGJZFJRKxUWqzx56oR0crWlCVcOnZgIIey+W9dU2FFEdUSEqAksYc2aBxQmTKelpYOWEV96GxYSXPwZwIrtbnng8cwmZUy7JL0UIb52hWiC7xWT8bBIEyGwghQhT60RC60h8O4Mop6I6B2yiAhRA3w8h+/TYbub+onEZy0gQwFxINgaF3sbU0IoVIqU8y6KDCtxBhnk6ANZsygacHzn6o3R5bTcxRrPgbqnwo4iEiJC1ABmH9gsGC8eYN2w69Ct8uC6zYkQYQVJVs20haU8WYGLaUGJYvTiOfKKkG6OyYq69tgUIYxLsqXRQS8LjYnBIdeMEDWwhvAizRRdKx4gOGyJaWQiYF0UqIIoWb3h6dbFHM+tyIiJkDQWzp0lETIi4HsiFAKD9PYwS8YLICtCMBYZDwJBnJYKyw7RorxIiAhRoyBVLyQA7jxtiWlUx+R2tJAAxpNkkTVZofCUneBEecHEbTx3CYwh6ic2jgQ1RQjEBGuB7DFvVktUMx4kSxBDjJStmJkYoBD55S9/GV7/+teHBQsWhLGxsXD11Vf383BC1BLfnM7C6pJ0q+DinSYFGIyK+I/mumtbF3wbT0IQK2LBnWqn+85+mfJF7/FzOywUMSFaNAg1Cza2s+5Bb93A+PzmeEYX0nh70XhOVFiIbN68ORx44IHhc5/7XD8PI0StocXDX4RbhcrGa4dQOMTEAi7oEB7sogtYmMy7csi0cXFCiUJLi6we1YLjIS2l9tkcpfstWaMDYw2uQfzhuHAPWpGB8WldM78695g2kYL1UE4+Branm1LUKFj1+OOPT/6EEP0jFpQXqypJ4QBgzn7ZnnNbYgOpuvhjTxA2K8tqXGfXs9VU5Y+vFqvWP5n5etGvO211WN0gMNKK7tnAVDa+s2AbVgH2HWzLXOpdlCxrZsuWLcmfrcwmhCgmRnix9k3paFZnLAiahOHPig2KC1zkj7zwuuixbJGytJgRSh5JktGnn2X57ViC1Y2p5cCOXYhbG1DtRQjxXXlV6n00KFWw6vLly5OSsPxbtGjRsE9JiNLGfngzMy6y9mJtL7pwuwBcjK1PncusuRziYu+lP5g0Ac1A69RxE7313ceAAJEIqRadvvMi68EVCNg7xgthWtUoIlADxwZUZ8WCWDfNCz98jUTICFAqIbJs2bKkLj3/Vq1qLzEtRJ1ERqfYj2/f9nDba/g/Uxnx+PYv3thaDteJr7HAizXM2V40NFzRKvCM6d/uJxBRfVj0LpY5g7AgChAbSwLxmjVOELeEBorY5x5zt0+WJcHR08YmdYb2IrqTGEkT5aJ8lMo1M3PmzORPiLr1fSExM3LMzMyLs3Wr2OUA4gMxH6wL4o/Dku+2iFnsPNMyXdRJt36gsJ3vQQRgwEA5/y/fcH+bEDl4r/mtcWUbJmLsnXjwotaYpKuF4/vTP22WarcipEihMopya0GRGCkvpRIiQtSFvAGmWbEfXN/WCOFFv5nmOFFinRd6X+rdXuQP+NiPJ2VGKPBU2O7KHGuxjsuxwGaOP67fzM5qFxYWLOM4Z3E9iJ9YobK08el/Ryr1XnMh8pe//CXce++9recrV64Md9xxR5g/f35YvHhxPw8txMgHmKZdnNPuDK0IwWu4SKNfh80igDsH2TGYGJql2+cnyxGYChECU7p1wQgBAeG7KLdStccQZJpvHwBWEJAmDLwlIy2DJrYtt88S82nbiQrHiNxyyy3hpS99afIHzjnnnOT/H/3oR/t5WCFGJg4kjy87ZmYm3J7YfeAizsmDgXvsqIuJAaXbkdIL9w0niu23m97jT0GUhawg0rTaL8z4TqshAhGSt2oMLHAcmxDA3pphRUS3RcpYvE+l3keLvgqRo446KjQajUl/l112WT8PK8TIFBrzIgMBpj4AlRdn1P2Aadvuk9sTK1R48bWv+QqptkMuJoq0CUeMPlnfbdoEjTp2kaK6beIGW+YRI3CxQPQ2Y5l2bSu7nmbJKCpGsE+8l9j62B9+cypqVj4UIyLEEOJAcEfIGA7vy0aQKdJtWeODYoJFw1hrwcaAWFieHdYOFBuzsEKq72qaVr5biKy+hkzlto9p2Fgmb7HIsmTw9V4GgotyMdaAiaKkoKAZ6okglXf27NnDPh0huoIXQFo9bCCprxDJyqYAYgViBNgLKP7vgwWxH9xxplVCZcbCVNu+i2rQSTSEgmMlrxiBRY9l2ftJWsCq6omUc/6WRUSIPhMLNuUdng0kZfVTiIqH1j2ZWEBue3DDpCBWihibDonnECK2UFm3k45ESPXplQsOYwVihDVGOlnVGKzqYd2ctBgp/F6KdNDNGwguyoGEiBB9JhZsyosq79TSUnO5nfV7sxsu3Cx4DQKEfWFiXXLtpCNrh5gqXthiPMFCl8e196Ub7k8evSCgOwUuxSv+9bCeuFPSss1E+ZAQEaKP2AJksT4YAAkLWRdLvMbaHzRvI/uFwoYX6hUrH492ybVIhIipAhHiBW1WcTta7ihgOP4hrr0VBFbACcG9dlJF4CKoqNnoICEiRJ/wVVDthdAHm9qLpb0Ac117t8kU3IP3mmeqqK5rEyG9igEQgkA00KVIl8yuO81I0sDTwDj87ceOa+vqzIrA/P83b1mVCBk73gnr3BRFRc1GCwkRIfqEzQSwF0Ist6ZsroPUXR/fYc3L/i6TF/ZYBUuJENFLYpVUIUayRAjAOMTYt9ZAjFm4EhnnhP1i//ydWBisXQQVNRs9JESE6BM2uM5eCBnfAezFEum2hCm6uFu0IgR3mE8/u621rGjKrSqniiwwHn2/GHDCwYvCZ376x2TcFsnAgsDwkz9dMv+9cn3ST4ZiZJ9lP+zoWsxDL1OBxWBQ+q4QAwTVTSEieDFntUff/wUm6dWPPzUpRTdNeMC1Q1dNmtiAiNm8ZWtPLvaiejD2yNOsedOsYWNFdAwrUugexLhFzxgfoG1dkl7cWDeNsl1GE6XvClFCfPAcrR68uMcCWgku1LY4GS7ys2dt15o4sD+IkLTYEMWMiE7ERAi4a82m1v/PPPYF4TPj6bQeLyZsSi8yu4Ad2xQYtnYOwO/BCg+5U6qPLCJCDADrt7YWEIoQK0Zw94j1036YeRuNCVEUa03DWGUgKcDYRBPFPIIWLhnMLP/3oIWt1FwKcO7bxk5RKNvaOCz0100dETFa87eEiBBTLKqUth2WQ3DAkmHTEP3Fl/iLcR5UF0T0CwqHTtY0/zqtIFZM0CUJwQ2riv0d2PUhwq2b0lYdFqNFkfm7r03vhKhak7qs7WBitvCCCtN2LA0RF2/cOcI3z+fBiBC81gmJENELbCE8CBCKECyni2WPudu3bcOMLS9SbKwTfjvWJWnjSyDsuR5EOkTH2eOPdntRfSRExMgCi0PahQrLi3bZhFCAYPDdbXnXxmP649gLKsUIy7VDTOBCzYwY6yPHNjB7P7ppS/R8sopETbXtu6gPeQTtoUvmt/4P0cAAUhu79LZDFrfWwWuwXoyliBm2G0BNHLok/3D+8W3ddCE6sI9YMCqORzemqD5yzYiRJa2R1VQaXMUi+m22it2nPw6D7my8h7075P7YzA7bWJN1WjZCrIaDEL2C48vHhFgoKpg9Y92Cfuz6cd+r32ev+9GI/iLXjKgFuCDZOyww1S6b3CegOZkR/5bYcXAXZy/K1uRMEYLHQ/du7g8FzKwIodXFg4lB1g2RBURBJyJtiJJxhfHFsedFCK0pzUrAk0UItkfMh4XWkKx6Ht1YO7p1nYryI4uIGHl4IeJkP9W6A7H0WVvXIO04fjsIjPuW/0NrOYNQvYWDMSJp6ZO+1XonlFVTT7oNXOa4gqUOLkRfq8aPV66fFqQK+lX7I610u2qNlA9ZREStwAXIWhx6IUJwYcO+8h6H5dl5B0n/+pEXXjdeK2Si8Ze9qGPygABB8bI0OLnknWQkQuoJx0fM8pEFg6YxDm2rAOKtJBQh7zpySZvoZpApglpjloteW0Hh1pQIqQYSImLkiXXZ7Cao1bcc5z4Bs2Jix8EjzdY0c3vRQXHAi7i/g+2kHSBklCEj8pDHxk0rHGuHYJzSIscg6jRXIcYtxvHnfn5v8pyuRcZI7bnLjol1ZaqBpmm/W4gOHLMXNx6iHEiIiJHGigcflV/Ut0yfNvD7tDEfWMbsGlx8mTXjL/TWbG3vMLk8Jixs5kGalQMTAY4vRLdYN6BtBzBmxnksNspb6CCq4X6kW4bNHBGMPdXA0bTfbfKbGy8CGLvxEKOHIuDEyJK3y2ZsWWxbXDj9chYl8+BCCysILroPrX8yER7Y5qb7103ysePi/paXLWzVFckiTx8YTAArHng856ckRHoMkS+eh/9TCvs4qRgQ1WxWx1gSiJJeWCliv1taXWLtEGQZGV0kRMTIUqTLpr2offa6e1ODWv0+cVfGCx/uEGPmZtxd4i8W6Aca4/vBhXOvpT/oSaCh6iuIbmjGLk0853+tIMEjJ3eOy7Rqv4yFAhQhqA3SK+zvlt1/bcXVmFgRo4eyZkSp6XXtANbtgG8ZLpapRurnuXPknWLRxnN5xUmRkvBCgCJjkSKc45zb+mwaZon1A1tvJ3YM1REpH8qaEZWhl7UDOgW1dhOpz0yaGL42Q9Hut3ktJBIhoihpY9H/miA6fL+XmAihZcS3OegFvkR8WgCrRMjoIiEialG0LE9Qa6fziKXu8iLpwTosU1205HZawKoQvQTjkGONjxS1SMFlewJaGzCWOZ6tCGFMCANWX3nhdT07x6n+bsVooBgRUXryxndMNai1G2sKt0cWC5rb8U4zy+LCctr0eXcTsCrEVLAWDRgV/ZhDCi6ENCwc/rcDdynX9i0PIEQQL4X/TzVeoxe/WzEaSIiIkQAXHIqQorUDigS1Zl0Q2SPGx4UwW8abrNNiRxD7gfX9xR9uJgWhin7CeCI7yvaY2+5msQ0cGajNcYnfAjNr8IhxHIub6sU4nurvVowOClYVtSzjXvS4NjAVF+ZtjUaSvou0XVyUcSGHCElL07Xlr7st3S7EVIiVZuf/bcCzTUO3GSqdmjyqwqmwKFhVVIph+ol/fe/alg/c+sGRqov/b3zq2VZGDB6ZpmujPGyRKFvREiKEfnhRb7ptapgWrB3bH8YZxqwdb7NnbZcIiYaJE4HLkCKEqbidmjziUSJEdIuEiCg1aX7ifosRlpc+Yt9dk4syj4OLL6tH4u+JcXcML/K8U7SFofB/upOsEAGxluuifmSJUdtZ18cxx9wTECGnHLF3VIzcYgrhYbxiPEJIMCOFwoLB1sxEiblJkiBWs40CSEW3yDUjalVHZCoumbTupMCnM+J5w5XSxkUfP7fVG57u+fmK6gHNMc3EDdGVh3FkxxUEBwRxo0BtGd/KoKirRV1wRS/n74EEq37uc58Ln/jEJ8IjjzwSDjzwwHDxxReHl7/85YM4tBhxskRG3gteN2LGRuczbTGrcJm3bPC5jSGxk4cQnWg4i8dBe85LCotdecuqtvXgXoFFhQKC2xK7nDAGxAoJumP4mJaZomwW0Wv6LkS+8Y1vhHPOOSd8/vOfD4ceemj49Kc/HY477rhwzz33hN13373fhxc1h71iaMWwF0jeAcZqfdh1GSSbZQGJgTvVxfN3mGRBybOtqDexAGaMoxvvWzfJ0gGBC8F74sGL2lJrAUTwoUvmt8YgRQnFRsyaQXFuq6na342yWcTIuWYgPg455JDw2c9+Nnm+bdu2sGjRovC+970vLF26NHNbuWZEt9AKYjNdrOjAXSUu4DYroFN5aU/sTjMLpeeKPOQt2W8FbSwry2OtHVwXvweMyWG4P0W12VSWrJlnnnkm3HrrreHYY4+dOOC0acnzG2+8cdL6W7ZsSU7e/gkxldLwvNhaczP+8ooQXznVZikUESGYNCRCRB44SjA+2SYgBlPGOb6zsmmwHiv9IvUc8U7gN/etTURGmitFpdPFyLtm1q5dG7Zu3Rqe+9znti3H87vvvnvS+suXLw/nnXdeP09JjAixuA5r5fB3af7OrVOMB6wZeUSIFTPfvGVVK0VXokL0G4qLNFceY48Q7+HdOXZ8MrWcWS2of4PxjOJ8GseiDJQqfXfZsmWJGYd/q1a1B2WJ+lk0bBMtLvuv8bgPCJOsBni4yNIKgqqsba81GuHtX5xslYtVU6U//IZzj0ku6kUu3jwjxYSIbkkbOxiFTCXHOEfKrrWgsC7IixfMHrearJ3UsFHWDlF5i8iuu+4apk+fHv785z+3Lcfz5z3veZPWnzlzZvInBC6SjOyHGPHWCyxHMF1W2iCECdMR6V6xcR24M7Q9MWhxgdC4eeVERgFoZhWsLVx8TPebwqbe9gJrIcEjYz5QI4TjnBWI+dptD24YaEViIUpjEZkxY0Y46KCDws9+9rPWMgSr4vlhhx3Wz0OLCgDxwQvpPst+2Ao6JbByZNUuYCVUG8uBDAJCawlN1rS4fPu2hxORQih2lH4ruhUO3YoQX8AMYx2WOXZwhsDxYttWILavFe3RJERl0neRunvSSSeFgw8+OKkdgvTdzZs3h1NOOaXfhxYjirVMwOpx8/3rW2KiaQmZH1asfLzjxZW1EQguyDRjMzUxqSw57mrxtRDwaHtudMpKEKKTayVPX6EZ0yEcxuuBNOLjmoGq9jHLqkgx0ouuuEKMnBB529veFh577LHw0Y9+NClo9pKXvCT86Ec/mhTAKgShZSJt8l/9+FOt0tK4uMZcN7Ri7DxeddL2xMA+V61/MlkPQsT7ySF0aBHBuuwVk2ciwR1seWsVi2GP6zyuPYoQC8UGRbJPxU3rDG17xthMMokRUSYGUln19NNPT/6EyIO3THjoF4f4YFEyL0YQzwFOPXJJ210hxAizCHz6ro03oU8dNNxkYLuTeiRCRBrdZqhQSMAVaS2DtjaOFxY22yvttTxiZFgtFkS9GIgQEaJfhZ7gYnlo/ZMtMYILNjJqmKLoL9rYB+5KmW1AUzUyaOw2ECH+ePh/lggRoihZLj+MP0zyFA6+bg3GOsZ/rMIphfhUq5+mWVF8LyYhpoKa3omRKM1OYNVgyWo2/7LigFYPCI095s1qExe8oHIdTgLMMABcllW7odkyHRPDQD4KUUMxYscohDbGuc+8YawTRAeu4ugU3Q/LhRrciZGurCpEt5w9XgHS1kMAuDjj4ouLsM1igYuFrcyDaTKXJUJwR0kRgkcIG0wIdN0QZigAag+JENEJCIc80GJngdjGOMRrHOcUIRjTtOg1A6rXtywXzACjmIeVMFZjB+uxDk8nIDZYEBDtDiRCRK+REBGlBBdKXGCZfmsv1LgQ0jfOC+SRF16XCAorWnABZ4ovsPvC9rC4YBtco20ZdxtQ6EWJXZ53ohH1pEjKLi0iHOd4nhbYCuufHZOMdeJvgWKEFkU2tyNpBQCzwPZWtEuEiF6iK6koHbxQ2mA81hTx4IJo3ShetFBg8O4S+4JFhdYPmrcB+89Y/GSA7IQZz5mWLMdEg/0KYUnrD4OxYq1rfuxQUKRtT5Ft3Ti07MUsFzY2iuKkW7cKey5RjFjLixBTRTEiotR1RGzEvu39QlEwbTwd12L7wngYVwJwkYb7h5aXPAGoPn03T10IIWIxRxg7SC9/7IktrZRdGCkQR5qnAy9EAQqXpXWL5uv83VBEdCNCFCMi+jl/63ZOlI5YUJ2P0qdvPHaRp1jxy33bdBY1s9k1nYDowAQyZ9Z2yb7wvJflu0V9wNjZf485Yc9ddmyNPSazeBESEyaxAmUxywVeh4uyG7dKTHT49HqJETFVJERE6YldDHlhBRAEMeuIvwO1VSixng0STKtZkjaBWCuIRIiIAcH6riOXJGMrZp2zVri0LC3SSNnWioE0ywViSmLiJA+wSsYsH0XTgIXIQq4ZUXo3DRrQoWrkr+9dm7hqaMngXaK1UFjXS4y019PcPEL0izzuF7+Or6TqK6160cCCf4w/kVtFDAq5ZkRlgPBoxnDs2uqma4PwGKPBImVpd5W8G6QIsbVDwF1rNinWQ/SETq46jL1nt27L5X5pjC9HTRyIaCsm8JtoNrZbG7VcsNeSD2gFcquIMiGLiMjFMEs9s+qpDyj1Qal4HT1ksgqRAVzQTzx4Uao7BvuxjfaEyEu3wcusb5NGTGR0+s297Qs3Jr9Z34eJlhJs/413qwu66A8qaCZ6TqxgUrc1CYrCZl6snEroe4clhCKlkwjBurCK0DwdS5W89cHHJUJqCKrlTpWnn023hGCs2fRdix1vfh089789iJJOwh+VVm3qrreU4HUhyoBcMyIXMZPuoPzN9ti4YHu3yg3nHtO6uHq8u8b+n2Xh/TrWrM40YlF9kEHrv+9O3ZS9G8aOS0+sg7Mt4Q44Fm1WF5/b314RC+UwfrNCFEFCRHQlCJi10o8LWtZFNnaxP+BjPw4vXjA7OknQYvKWly1s612Dm19bzj2tjohESL3IK0JmTB9Lan+kxYL4VHHrMoQIgXsQIHYDf9++7eFk2aF775KMUyzj+EcMCBvc8fzyNqMb1G9WiKmgGBFRGF8wqZ+VVduD89rFAp7fuXrjJJ+8XY93rMyWyfLhZzWyw4Ufr7PwlKg2vagN48crXYRZv5silo4ihcb6/ZsVwqMYEdE3BlHqGRdRXsTRQyYmQgCeI23XwjtNwsmEpm+KkFg4QJbGwAQgEVIfpiJCYA1Beq2NabIiJOt3UyQWK28zOpVnF2VHQkTkxt5x4a7KN9maKp8y+2LPDZiz6UYhbHYHfHAqBAdTFrlOjEaPghNFdcnTRwguGoDxdqbpe4SaNGyyCDHSGBfJnX43Vlzk6Q/TqRldv3+zQvQCxYiI0pR69n5viJF9lv2wLaOAx0dqonWz+NoMSQbN+icnHQO9PZ4Y36ZbA0eWC0dUh83PbO2YYgsrGQQGYjgQ28GYJNtNl/+HSLZVTdN+N0XiOtJKuvM1lWcXo4CEiBhIqecs3zfqhIAr/rVZ08DW97AXfkwEzBj43z9NFCCDtTqWrZCWyjtVJELqgR/TaSndi+fv0Cq2Z4XHwrmzkowYYLNg8vxu8vSHSYsR4fYqzy5GBQkRkYusmgV57qqyovzZvA6ChNUifbGxsfGJAIWYcEG3Aad7zM3u02HPQdVT6023Qag+g8Za45ol13dpjVsGRv9p49PJmGXQNaEAyPrdZFk68lo7pvqbFWJQSIiIodchsX1eWEHVwos+Td7IlLHkESHqkCtAVyIEMUXOeOBbCiDF1lv0IEKwrRUheQRAJ0tHsu9tjeR347Epv/2sdixEL1GwqhgYaVH+sILYTrg+OwYXfbyGwmV47MaqIREiuiXmwIA7EOORVVAZj4Qxbqv/YttYBgzcizHSLB0+yBQCg03vYoGnEPT9rHYsRC+REBEDJRblzwstBEjapROvwS2Du8u0MtlFMx6EyMNY5Dm8KxAAJxy8KFm2esPTyfOkh4sr1x7LgEkTCVlxHVhu4zqKZtgIUVZU0EwMFF4oKUbsBRM1Q7ybxWcqsB4D/PCPPbElaumQG0b0Gl8Iz7plmCZu45qwzLcQYCBrr0VC1m9KiGGhgmailGTVNMAfa4ZYGOzn26JveurZVLEhESJ6CYOcrZUtKy6Jlr5YLZx+iIROtUSEKDsSIjXGFhDzIIOFabWeLB93Gp1836yeas1zaTEjWCdPnEgzZXJyQJ8QxAvfWJE7ukM45hgDAu9K06W4Nly5YlXrNVu9FGKEBc2Yft5rVDlVjDoSIjWGKbXwa1uYUos/L0Y6+bjTxM2v712bmKh97QJcmOFmQaExCg5WTmUAa554j9jZIKWSmQxCxGik1IjBeIyBsQgrHYY/hjLcL/idPLyh6XqhBc9a+uhaxGOvRYIqp4oqoIi+GgMRQD82A0F9gzlcZFnDIE8gXFq9ECyHiRrVJy3YJ/vAwHqBTAC7HfcFEbNg7qy2QmacGJ5+dtukgmZYjjvVb97SvFMV9SKruWEMG1cEy8KpRy6ZVMsGcJ9nHTsRAwJ8qi3FCPFxJL2wjKhyqqgKEiI1B+IDIgQXVJZTt0F1RVuIp9ULsVUnvbCJCRA/qewxb1ZY/fhTkyaXtMkGy1koTdQLeE5i4wJiOK2aqBUhFLVZYoa/BxYvSxv/wP9meiUSVDlVVAVlzYiEtJ4u3bYQT4vkLxLhz7LwsGx4UcHsGQsnDp8146tiivpis13SXkdKbswa4rfn7yFxv7jiYUuW/SBx3cR+M7H1hagapciaOf/888Phhx8edthhhzB37tx+HUb0AOvHDi6orttAOBvJb8NJsJy9YXAcmLfRwI77ZZBs1nEwGcREyG8/dlzyms+akQipPnlLd0FEpMUcYTletyIEVjxboIwihGOY1j0rKrCMIiT2m/HrC1F3+uaaeeaZZ8IJJ5wQDjvssPCVr3ylX4cRU8THhLBuB3u6dCo1nbVfK2DsxZ0WYxwHx8QEcPNKBMc2Y1IAHmn2huvGmsljd7SzZ22XPC6av0Ouku+iWjQKxIbY1znGbLM6gmVoWodxauvZYJtfnXtM9PeQpzy7EGJAQuS8885LHi+77LJ+HUL0WITw4smYEV/3IG8gXNrFmNth+ZW3rGr51m3zMGv65uvoQ+N7e3iw7ov+7RrVEKk5sXHixYl9fuJ4ZdSYK+bG+9YlAsd3zoUQSYsHUfCoECMerLply5bkz/qYRP+AnzpW7REBrK+88Lq2ILxOgXCM57AXY6TswsqBi7gN6vvMT9tdQZZYZVWeH/blX7eTikRIdckKNPVgjFCM2IaJ/jmsZ4xXIvg9HLLX/EQ8s3geniNOyQZv2264sNjx3BQ8KsSIC5Hly5e3LClVhJN17K5oGAFsOBbOCULBnxNNz7GLZ+z8mbaLizIvxkxvbLZJnx8Wz98hucukCMljRse6mChsqqQlbfsiE5coN0VL9mN9pHpDaHDMsMQ6RAVSyLEcy1iADFgLHkUIHr9z28Pj209kdmFsFenrIkuIED0KVl26dGkYGxvL/Lv77rtDtyxbtiyJsOXfqlXVqgHByTrWjTOrSFi/xUjaRbJTUJ0tXsYqqYzxaAbsTQgBWkOsNMhb5wEThRUheZreSYSUD8R8xiqXdqKICMFvCOuj3gxEB4vjAcR7AAhvACsd4z+IFRcrL3hdq0S7bV6XdNgd/y0nRcw01oQYnEXk/e9/fzj55JMz11myZEnXJzNz5szkr6qk1dgYRLfMflhjfPGytBoKtGZQjODiTf97x2O4pnfsQMq7VE9aqm4s3VcMFnwvW/u0b1rXbDl2O945BlH/w9fK8UGl3k3JmCmKEdYQ4T4obIQQAxAiu+22W/InusdO1nmLhPWCtIqnVggVFTP2vSD4FHeYMF8TNuDCJGC5c/XG3KLAx5JwX2lBq2mpuhIh1QJjDY0PaVV7IpIJg7gOW1CPotbGHdmxHKtX48UIXTmxfQghShYj8tBDD4X169cnj1u3bg133HFHsnzfffcNO+20U6gzuHBRhAyqW2YvrDExMWNjQXDx54Wcabu8gIcCLhlvvZgxHRf/5pJYnEi/Yw5E+aB1jUGoHC/ewsFifLRecFziuR/z6EuUFhdlxQigVUUiRIgSC5GPfvSj4fLLL289f+lLX5o8/vznPw9HHXVUqDOxImGDFiPMXPEiJMtNY7fH3SOtH/Zuk2byU47YuxUUSGK1GrJSKwlECLMceiFEJELKT95quGmrYKxijMesFxQp/ndHi19s7FuLiLWqDOq3K0SV6ZsQQf0Q1RCZzLALHvECzYtplpsmFldixQitH15gQEh8xgXkMmMB+HV5cadJPWaxwF2vTcsU1RchEKVwuaSJDbxOywitaPwtwUpnu95a60VabY8096WNEcHYs1YV1QcRYur0rcS7yN8tc5Ctu1nO3VZQTTu3m1euy3VeTM/FhTkGBAYyaJp9Y5oixJbZZoouUoaxD4gQ5jH4JIupiJA82TZisMTKrUM/4LuCSM0yitByxpL/3FfTYtcUDjwGrReEvzvrhon9FhlfQhGC19E7Bo9s5KisGSEqVEek6gy7W6YXG77rrj83uF5g9YjFlfhYjtse3NDmi7egfgiW0YIC0XLo3ru0Zb7YeBLGhPiMmamCDr5AFpVyAMsXxIR3x2HSf8vLFiZC+K41m9pe89YybIsmdd+8ZVXb94r18NyWcI/FN+UJJo8V/bPrKWtGiKmh7rs1AC4Wxmt4sbH30h8kYgKT/n3L/2HStlZ42BbpnCxsHAiFQyzOw4oWm9LL8tnMWLDbWlETK1DWSzeNCqANFv95J/U61j8ZNjz1bOKOwXNY0fyYIBCzq8fddRxTGOexb9C6QfOmqduO0+89ap9SFSIUYhQoRfddUR7oEmGPDAILBC/cEBDoehsDF31AEcIupbhjtdB6wRLagI92gkCMCkUIshFwgUfGAp7bbbkOjhcTCWs29M6yIREyWGKfN8bU3FnbtQQoRAhExN88f/JFDNa6G8ZdeXvM3T4Ry1kipEjXWx9MniZCiuxTCJGOhEgNoO8bJmr6v+kGwYWcsR248Fs/Oq0hMI9bIBawDdanwJnxnGmTLBWsSmmx7haIEFuhFcGsEB24E6b4wf7T0n2R0QsT/M4pbd1ZqXYYFWtFsRgddmHGeKEVDOOKVUwnr7+2NYbedsji6D7Huggite5LxoIMKn5LiLoi10yNsG6W4LqKWjeIbe5l3R95YjZoRsckgs6mNp4EMRq2kR72jbtanpcVMJhgGLvi8XECqgtSPTgGbO0OOy4BxCo6M1NQx1K7OcbykFZXZ1DVj4WoEkXmbwWr1swcbsXELQ883oobAfTJ09fuL+42xTYG9k3rBapecsLgMbEdhQrvfo+88Lok2JDBhZg4OAF5EYLzQb8Q7MfGnEiEDAdYKp4z3tull3DcMX4JWBHA+CIGP2PMxEQIxxjGEq1vZQ4mF6KuyDVTIxBYapt80Q8OmlaRXZPXGLzKpnW4ONN9kyZCgBUONuD0zGMnLuyMAUHBM1pAcGxMZhQjsITYiQVZNADLkIEDNCUMH0zM/RCBsNJxHAIvDuDCo5sHwti6/2w68LuOXNISNXlcK1NpAJnVENKD5XhdCNFEQqQmsB5CUvfACAaIEVvEzNYYgejgclaV9MSiL8bcpIIJy9YYSdqvTxtLLCGWg/acl2zL84PpHcc/eLwQGs9DVBuMR98V14KxQxeeF8aMX2JsB8afrxdS107bQpQVuWZqgK+Y6tNtrbnb1xhhFdaYSwZ3pRATvq5Iw1W6ZPYB9s16DzZWJU1kwEKDZno4riqqVptYd2Ra0tLqf2C53w5j2rphhpVaO8xO20KMGgpWrQEs1Q54IWSxJly4nz93+1bRJ1zEuT5jRezFPlbTIbh1bBEpiguIEWQhAB+E6kWORMdoAc/ZeE/CnsCxBIsYG9HFJnDfUJHblWmi57lbMV6WcxOin6iOiIj6vhmMZ+NDaO2wvWBoVubcwkeW3fZlubHc3nVyf4wx4fGYNuyDUBHYaskSITJol49eiBCOKYoJjB9U3yUQJda9QlejbQXA7cqUbovfHUXIoDptCzFqSIhUlFiwHMVC03c+v1UnAdkHLFPtt7E1OpjVAjEyZu6GUWH11/eiG2/TH8/6Ini0sSHsAeJJqxMSo7TmO9Gxh0zWuhwDe8yd1erjAkFMiwLcdBy/KLzHdG8GVtssLwjhsoiRWKdtIUQ7ihGpKLFOoraOCC7s9jUsty4SW2MkZq2YqMjaPNYR++6arAsrSJr7xpOVCixGG1rO9t9jTrh55frMYFFmUmFsPTxeLZfBpvw/xykENseMrTljxzZr2Aw73XbYnbaFGBUkRCpKLFiO1Si9n5r/x+u8yDc76u7SsYgZJhCKGGBrOywab3YXC0QESMWdihBRf5j+wSJxaZ8xvl/2hSH+e549a7vw4LrNyfZp4hQWtzEjKih+mVZOlwwmcVZZ9WOGvZQIRPawJ/q0TttAYkSIdhSsWnGKBsv56qtZ8C42NsnweJyc/CRFM3paRUwxPBgvZK1qMez3DuGy284zU4WltXDEhCmPCfeLbTgH96Gf1OGageDl+LPxIUwXH3b/FwZ8q1GeqCubVFm1P4zixQXnygyZPMFy/q4tDQoITAJehMCKkiZCKFAkQoZPVml8jGMEFnvw3R66ZH5bDyAKEmZK3bl6Y+u1WKl/jgX7fwgIui98TIUdk7DaweLB0u6AcSJlESEg6xxkCRGiHQmRKcZdxOp0lEnMZF3Y084NNUU6wQJnMbcNl+Ffby05/Zh9MwNXi8aOICsZE5AETXFYzdaKEXz/v1u9Mbzyguta8Rr+u/Wftf1+b7xv3aQ0btSOIXa0NNqEadNt2CmmAs/p/rNCBueV9zcohCgXEiIDLlLUCzEz1WA53lX68/WmeG9CZwEzbI/JABf/NNcLt7eTFFMrcT5ZYqNI3AjCFyRC8hFzoUGE2OUQwoj7sLEfadvi+7x5fBwQ/o/WLvZ7sdtbAWuFKcZUp5gKWvd4rDyNGIUQ5UZCpCD24siLYpEiRd2ImW6sKJ2C5XhXafdpLSGx+A9mzEDEcPtGRgGyRqS4GdbF+bJ2CIMhOwVHiqmD7zHmjkFmS1rTuFYTw0ig6ar1TyYigFYNC79rjgsvQnw8B8Wtxzaco3XPit5kvIwXMqHQtdsJIcqP6ogMoUgR1mfwHgLzOllUuulbkdVJFMuRjWD3yQJRwE8gtsEYtsEf60QsHG+zvsfc7duO05xo5rfKsyN7gg3KcCxOilaE8LwtPHba5yLygc8e3xndMYCPWSIkrR4ILR34fnafPTO6jhenGHewgNjYIApoVFBN6wnDbJlmPZFdWi4/wN8ga4/gfFDTRggxOsgi0ue4i14EkeaxoniribWQIMuAF3tub/fBfjIQDrB2YDLAudHkjTRcuGSw/OaV68Jdaza1BApECNhzlx3D6g1PT8qAsGW4ca48VlqMgierymqW5QQde5/d2qh9ATSkx8LNYt1dL108ty3YMwaL1sWyoQ7ea16b2yWr7oyH4zIW/5H2G7Bjnd+5PXdaYyhwfDNFIUS5kRAZUpGiomKmk0soK/aEJu+0Y9C8TqGSuHuMyZ0XfRSOgrBgh1PbXAwWD95FswaJtbIABC3a7r4gTYRASDxjaofbfiZ53De7z272z6lqP5a8QIT4OAqIEHx3ey39Qea2sdPFeEDROms1g7WFY4HNEz3ebWJdLp1cj7Bw2LFuxxVbCcSKnwkhRgMJkSEUKepWzGRZUTpZTdJeA778dDzAdV1r4sIkZEUILSJYhxYOf2fM1u20ouy99AeZ1gorQgCeUujkiSEpkwgBUxEh3TYB5HZWhGCZ/S7J2FgIWTGfLNXP0v0UIPizAtbGhvD7sjVjYmLEjkV8txQlsd/JN1Y8lFje7Jhm8bPm+a2VEBFixJAQKUBW3AVf76eY6WRFyRNIa18DMTGECSPt3ADjPOykwRTamIWD4oSmfHTfzTMve7dNlgunquAzKCJCIAL2cFVuAawih+w9LxoQ2sk9BmB1gNvOZsmgPgjHDoNNreiwpdftcv87sWOM69Gy4scnK/hyO9tFWtkzQowmEiIDLlLUrZjJa0XpZDWJiRC+xskEE4AVOb6uiC3rDsuDnTTgfvETJyY5WwXTThhZbhZf9DdrsqTro9OdfdnxnwcF3OZntuYSuviMIURsZhM/c7hkJh1vbCwctGcz5iONCXHQ3B8nfVv7A/FF+P7Z/JAWMz+u0+rkWDGC/VO0pFlGmplf69pEiHcXCiFGA5V4HwHS0ntZ6tr7z3kxtwGo9gKOZBPMCzaolH56QEHS7KQ74fO3z727oFOwIibTObO2a9sm7U4cy/FXpCtvmaq09jIeJI+1wvb1sS4Tb6Hwn0+aFYHpsXYM2eBW7+qLjT8/VvPW22F5dx47rTUBg6CtCLEWFCHEcFGJ94qRZkXhXS/94t4Mzsmo+ddu6j7ywuvaJiYGu+J1+Px9zxneneKPk4Ct54DnnbIwYsW0AGMJKJCwPKkpUmBCZxZHXvHSz86/3YiQxOqxZWtLGNAy4utz8D3ydcbeWPC+bO0WisSs74f7pcDkoxUwaXEZvSr6512PbBXgLXuMRbFixXfglRgRYnRQHZERABaL2IWVNUEgNCAOrAjBcvjwiTV1Y11ONtYNw9omPvYEF3xc6D81/hr+j4mLJbo9rE+RVgPEOwgY0Lhg7qwpTehFLChlC2ZNgnDHK9VaVwYNFvgOuB6LwrEOi+1eS7GAZdYS0qym2ww4hYXDWkO8CMF6VoT4uAxbQydW+6NonRxgxQoa3SWxJOMZVjaQmp8NX/fxUmm1SIQQ5UUWkREn5luPBahissFrCBS1/nSmR3JfmLBYW8TGF2A9tFpnICEnfRSo8nEhsGZw/7C8+Dv2GcbdgMl0151mtDJuilLECjIKpE2hbDQH8HnyO7auDLjZfIwQloFmSnUzjgPfn3XJvHjB7MT1ggkcNThoxcBzVj+lBcZbLUBazEfeOjmxGBArony2Dc4lFsjK14UQo4WESAUoktbLu0wfTDiRMbPrpD4ydiKgFaVTTAheS8NnwiD1F/UuiggKiJln/rqtsAgZBeES69vjmwxC/F25YlW7K2Pa2CShQPHISX3FyseTfXjXixevaTU98qadF6mTY12PsWNQEDFA1Z9vNyn0QogaCJEHHngg/Md//Ee47rrrwiOPPBIWLFgQ/vEf/zF8+MMfDjNmzOjXYSsDg0dtiiyxqbN87JTWayua0sIRu5BbdwpFiI0v2MMERiKVk3CSZOwF9vXlG+6f1Co+RjdBpqcfvW/yGRU1wvtzyBMMOmiagaKTXVMUh9tNn4gLYTrsmg3NzxzEUl4Z08N9WKtKHotCkbTzonVyrEXFx0P59X1xs25S6IUQNREid999d9i2bVv4whe+EPbdd99w5513hlNPPTVs3rw5fPKTn+zXYSuD7a3BiToWkOrvaGMXfcSE2IqmseZgeLxy3MUSC0JlBctD994lmTjoEkjO1QQN/urcY1rn8JctzUmfbppOlTyL0KmU+ChbR7LEUcMUe6N1qlPBM/b74ToUmH6yz5rE86adT7XoX6cU+U4F/4QQo8dA03c/8YlPhEsuuSTcf//9udave/pumuhIEyE2BZeTgU23fcvLFk4SODEBE0wQqs3a8OtaVwEzXuw6uHulP79Xk76vsxFzY+TFZs7w/AdZ+bQXYoXHtl2OaSXj98sxwO+Ln1k/Ul276RQthKgepU3fxQnNn98MnouxZcuW5M++kToTC0S1Aan0nXM9m4Lb7EbarAfCycpOEBQjttCUtb54awcmOu/D534A3Te+hDcDD9nJdapixN+1T0VFU4RM5bxs4zffHyev28eWT7dkFXvjfhnnYdNXreWL+7XfrY/76aUY6UXRPyFEvRiYELn33nvDxRdfnOmWWb58eTjvvPMGdUojga+GShdIWjovoFCAG4WFqGKmcnt3iq66sSJmOB4mW0zarB9iRQgLplkri7Ws8P+t+hc5SnFj3f33mJM7dmSqAmcq2z797NbWOcyetV3yOVFAdBIhFCp4n7E06DzxDj7w2JY8x36bpdnjtUBi5dZl0RBClF6ILF26NFx44YWZ6/zv//5v2G+//VrPV69eHV772teGE044IYkTSWPZsmXhnHPOabOILFpU75bezD7gBG7rKnQSI2lVKe16PAbLd3szPmCNCVuLBFVdAau2Apb3xnoMjoUlZfF4cKsv754mJtjBdypCwlsnOtFt0CqPwYJteSu82v472I5Cs4iryaZW0/pkg5b9ucTSuiFULLaLc1oDOiBRIoQYmhB5//vfH04++eTMdZYsWdL6/5o1a8LRRx8dDj/88PDFL34xc7uZM2cmfyI7RgSTe1baJCYIW3Sqk0mcgYg2c8YGrdL9wJLwFC6whsQCEq1osoXDbNlwD2pZ3LVmU6GslqzqqEVECMAxepFBk0eEYHLn8fz7XZgSbxKz+lgXi01rbZ7H2vbKuWNxK4enSAM6HksIIQYqRHbbbbfkLw+whECEHHTQQeHSSy8N06apkGu3IiQWVJqWNonJLC2dN3Yna//PScfemds7/VseeLx1926bqNGkz/V4t24DOb3bx06wtMjsvP1zkpoiJEsYPPbERDxRN3iLQVER0o1LKPlcxquiwmoznljU2h8+q5ggSouxYSAyhSqgSKBbjt8FXGs2liQtWLVIAzq5coQQpc2agQg56qijwp577hkuv/zyMH369NZrz3ve82qTNdPthbpTHREGosIqYXvDpMUD+P9nFayyVgu7P7ucAoMxItx3FtweEyosILY7LAdh3nbuWYGcebcrmnHD9cdcddi8+/HN5LrNksGWG596tiXY9pi7fVIUDm4WxvkAjgdYsVjYjMfOkzGTpwHdVJvcCSGqSSmyZn7yk58kAar4W7hwYdtrJW7423Oszz3tQt1tPQXugxOGtZ4Am0ET65TqhQ8CVrmPiVbvE3Uq7OSJUuAUQ+zympXOauNDmhaWpnjBtnY0+P4naVgRUqTz7vPnbN9y5zTM9rc++HhHiwh76+Cz5ro2BiYLvh9+Dnzus4+yRIitZmu3W73h6fDYE8+0RAKX+++a5f3zuGnyNqCL1QiRCBFCFKFvQgRxJJ1iSepAPy/Usb4iNp2Xx2VGho3piAkmWih8+W8vKhiXYMUHJ+KYKPCuBpr5UaY8DUzSeWI20rrApgER4vdbJDDWd8Nlp9ss+HniuO951T5tZdf5fXiXlRVzL108t+VmiZVj//RP/9AmEj6VYqFgDRFfWbdtnXELnB2fzJZKC5S2Y5zjUSJECJEX9ZoZAP26UE+6a3UuHC9U4MLJAyZAxGqkTdCr1j8ZFs6diEuw691o/k9XhJ30Gc9wwMd+3LG2SJ6YDby3oiXirTXDiogsl0meeJA0d5EVFFjnwXWbW2XX2VXWvwcKQVpAxuvURcUkDonXKRK8NS1W+yUtvigWk5TVgC5trEmECCHyIiEyIHp9oc7Tz6ObxmMA+7EBoxYGVEJQsGiahdOw7c4am5Rp8eg0uVMAdHK/WNdHXscfXCqAYsSLEHtMf56LTM8dkhWzgvfKeis2cBeN6x7eMBHMa2vGcN94T9w1XVrAfudnHdvu4ukUw2HFCJ/7InmdGtB1O9aEEMIiITIgenmhTuvnAVEQm1xoXs/beMxOhtZasGDu9omQoBjBRMrgSNtUD5x+zL5J75ostwUsE7RKeGsEBYUVIRQbaVklRWqH0CIBslxAsEDQZeXdJo+OZ+148RMTQ9i/FSGAqdgEn6cdI1zHEisWZ108djmWxXrEWAsdv7eYha5TA7q0/jJ5mugJIcRQes0UpQpZM1kX6m7dM2mZODZ9F5O7P15ay/fYPtLcFJyEKQowUa9+/Kmueq1wH75uiX/dWyeKBKcWxdZOiVlrxsZF2+d+fm+rFshBe87LfT4+mJQxGYwRYbl2xmX4bfx5cn0Li83FXHE2U4tBzhA+fzj/+EKfk92fsmaEEKXMmhHtF2RM2GkBrKBIvYW09Xwxqizzeta5YtuH1j8ZtWbsYVwSWA/xIhQm7zpyyaT3xeUQT/6otG5YYWODNPGcoso3cEvrz9JNIzpffj5NhPD1tuaAz5lWSBTFLBA+DsN2Nk4bM0wD9iIE0AXkrW52LPTKQpe3K68QQqQhIdJnfOyFTb8FTIHtVKUyqx6JvQO2ExYntFgFVE+sDgkmZGAnZbopULuCje7spI/90yXDGBBkxzQyXBY8BuMurID404ank0cKOTthZ2XMWHGTBc/RC6BY4CldU8QXa+PnnoXtFWRFISdzfmcIPmXcB9fB69YFlpb90ilTi6/1wpWiJndCiKkiIdJn/IXaX/ApQjpdtLPqkVAccFKygbE+wDGPYPIBmrEYChTQsnfDnMx4XF9Iy1s8vMUCIgXPuYzrs+4FRBbEGAQQrDBMJc3CipDYe+AxEFviXUN4b17IeAsL1mVBN34GecB52waCaQGf/rvGNvw82F03TUCkZWpxWSz2Y5BxHarIKoQgqrk+QHDRZXEx3PkW8aHbbTnh2btc+xontCLgom+DGyEUCCZwTH5p2/D8bH8buAww0dBiQtcH01IpRoi1PWA9CgDWvXjlhdclx0M9DV9czZJYVcx+7XvwbH6m2TmXAa5+j0hhxmfh3znOD+8BVh/b9A+WIJ6zPydrYQK+joj9LhGv4b9rChdsc9/yfxjPWJpIp42JIP+dpAWvcl3GrAwCCmt/3q0YJeYrCyEqjywiI5TGm6ceiXUNxFxCneBdKDrpYqJtWQjMxI+JFROWvav1d/PJ3fv4pIdHnC/dEjYYMxZ4Gisvj3M58sLr2qwSsHL4FGCWnV+z8em2SdWXSMf+8Dqe2/dpQcVSuEL8azg/uKVsGitiV5rCpGkJ+vZtDyfPfXAvrRnM2sHnYEuzx6wUPpDVv47lMQERiwMpiytFFVmFEERCZMBMNUgwr5DxrxU1ux+x767h5pXrJ2XP8E4dJd65X9+d1YoMTJBwz9heJfZ1BMXmga4bwondV2zFfm8eLxsPEbBg7qywZkPT5UNRYK07aQGtsbL2dN3gNWuJYpyPFQqY8DmxUizZni2/OveYRFjhfCGcsgI+IQo7BYRmFTEra0qtKrIKIYBcMwOkk/m9WyFDWFzMv1bU7G4DV70LBKLD9q6xFTdjlTi/c9vDred8z7ZjLDNzbLl4TvrcDu/HngWe//Zjx7Wtj/3CEoHJnhklN5x7TPjGuw9LxIhNEWachT8mYZ0UC7ZfecHr2txK+Az4meP4sQwWWD5oieFx8d3QuoP92SBjD5bjPWS93kmEcL1uxlu/ibmPhBD1QhaRAZE2OYC8d6pZd7nAmvf9HXDeC7xNN75z9cZkmS01nvSeWf9k8jqEDSZ/YNNOvWWEooPWH9tXBXEY/2ePOZPScyk84LawHWA5kaNEvAXb4RxtMCePBwOIt4iwoZ/FHt/C7bA/71aiW8UHBNvPkdYcK4boruHn10tGKaVWFVmFEBIiA2Kqk0MeIdOLTIhmCe/54a41m1pZLvZOH4W8aC04+18n7sRtcSwey4oUBlVOuJWaVVApQpiey5RggkneN+EDPDdYPSgMfI+UCavNrsl+uA+8H/a68fjjA+uGAtjeZnZ40We/KwgbnyXEbxrHh9uq15QlDqQTo+A+EkL0HwmRATHVycEKGRskij+6B2xtCpvRUuQOmBMrJm66KKwlA24GLIe7o9NdLd+zrdY60VJ+IpC1OflPlKf3QbY4B7g4rEiw52aX4xytBSjWJdgXDMP5nHnsC5J1mdniU2QZD2JreuQpmc71Y0XPIE76YRGpi4VQCFENJERGUMj4miIs5e2LVvH1ovhJ3E6wvqR4nrta747hfuy54XULJnBrAUEZ+f8aryOCFF4IIVt0jNYHPPd1KBjsyffkRQjjYGyNE1habKwM32NWVVt+Rtgn3xuFXZq7p65pqqPkPhJC9BcJkRFkEKmP/hiYYDFlwvoAYJVhsTJO8lh29rgg8OeG9Wych40Z8W4cbOu792JawrJfL3118pzvFzEaFGKxCqLWOuKDNCmqrHiCQHjLyxZO+gyYsuyh6ElEkYlPgbvI75tZN7aeSl3v/kfFfSSE6D8SIiPKIFIf7V0+wL+cOFmsjG4P28PEpu760vEUGH4S9m4cihAbYBoLZoQLicuyxJgP7AVWDDEFF/Eg3v1Faw6tF1Z8xJoJMmZln2U/nGRtse/ffk5CCFFXJERqWhwtD7GS4rRY2Gqu1irihcCnIhN1W3qwmYRpZbHYIFXEidi6JSyv3kmMWRHCbXiuXA6riu39Yt1f1rJhi4vZR3tcrB8TIf79Y/mD6za3rEwelToXQtQBCZERpkjqY9HeHjb11sdLUIzY8IY0IUDLSVpQop2E6erxsRtMI0bNEbp1AGJFcN6xOhT2/V65oll63XcgppDC6z7FOeb+allGxs/BBtvabZP9GwFHMWUtLfwcWY+E+EycTs0QhRBi1JEQGVGKpj5mNc3zEx7dK7Z+Bt0XdjmMB+yAy2wYf+y8QYk+oPOQveclQgPLkOaKbJbNW7a2xAlLpPPYXozx/SYZRUYw+dTaZF/zJ/emsedoLS62OmqaqLPfCzojw+VDN5D9HlgO3i6je0ulzoUQdUFCZAD0utNoN6mPRQJcY111fT0O4ANKY23p8wYlMgWZlgIchyIH+Jof7OuSVjvEv18bk2ILl/ksoNg5xkRIzAIV+zzp8qEbyL4nWlJsEK1KnQsh6oaEyAAoYo3oZ+pj3gBXKx7sNnYStdVWAawkCPT07zOv0Dp0711anWxtwCqO+dzZM6M9YbJcPv65tbakpSJnub9snIzPhrGfe9b3guPyPZ1+zL6Tvod+xvsIIURZkRAZwXTbqaQ+Jtke4xkofsJLEw3WKgBoieDkTleN70PD95xHaKW9JxzTixCcP1w3sJqkvX9beMyee/LaePxGHhFi42L4aC0hscyfNKw1BdjYFr5XlToXQtQNCZEKpdvmgZ1wfTpslnXGWwVgCYHoYIyILbOO12xH2qLv0Z6HFRC+TwziR9Ia+XlxZSf4LDdS2nnYgNQ0S0je9+T3wfNSqXMhRF2REKlQum0nfGdcxk0wXiIr9ZUTMoSMn0RZZh3FxWwxsqmIEGCFg+0TQ9EDsqwaPjDVumc6FRPL6/7q9P46Wb4O3mvepKqrneJ9hBCiSkiI1KTTaNpdOVNRfcn1tG3spIk4B2CDQG97cEPXQouTP/eJmh/MnAEQOsCKEVtcLBZ/g/d15S2rWsGttotwlhjpVeVPL2i82PLl57n/vNYWIYQYdSRERrTTaJ5MHMB1Ynf4qANCN02s+VqaVQCwGJntlQKrw1SElq+fwbobrDWC5dyn7YAbCwb2vWp8YCpTkftd2dQLGv+ZxtKdiSwhQog6ICEyop1G82bicB07IcZiFGLN19ImUe73lgceb7lgvHunW6HlJ+rYORC/X3s8FlJjJVVfrMwWNhtk5VL1WBFCiHYkREa002iRTBwW9sKEzCBSYHujMFYElpG0ydIut7EuRVJp+zVRdxMMrIlfCCGGj4TICN8F55l87To23ZUxIbaKqg+azBvrAnFThpbuww4GFkIIUZyJClViJMFkG+u1EluHUHTQEgJRwqyUWKyIxVpd/nD+8eNumcn1POyxB+X6iAUDCyGEqLFF5A1veEO44447wqOPPhrmzZsXjj322HDhhReGBQsW9POwlcEHpNrnNlCTNT7SAkT9BM16HL6BWzepqGVJNe11MLAQQogKWESOPvrocOWVV4Z77rknfPvb3w733XdfeOtb39rPQ1YKBqTyzp7PaclgTY8k82O8/LhdP82CAdg8LquBW5FYl7TiYoMgJpCYNeM/D64PUTfq4D2kWX2q8h6FENWnrxaRs88+u/X/PffcMyxdujS86U1vCs8++2zYbrvt+nnoShCzNjA7he6VrMZv3DbL2pFlSRmVjI+YQGLWjE/P7ba/Tx16GAkhRKWDVdevXx++9rWvhcMPPzxVhGzZsiX5I5s2bQp1JxaQSvERc6v4ANFYMS1uv3DerFahr7xujF53Eu4FsePZz411SKbS36cOPYyEEKKSQuTcc88Nn/3sZ8OTTz4ZXvGKV4Tvf//7qesuX748nHfeef0+pZHDZ4OgMNcLP3xNaoBqmkiwIsRbUPKKkVG6Cy9Lf59+Uof3KISoNoVjROBeGRsby/y7++67W+t/4AMfCLfffnu49tprw/Tp08M73/nO0BiPT/AsW7YsbNy4sfW3atWqUBWm4s/3waaIESmaHUL3BbJivAXFLu8U58H1bexFme/C82QVjTp1eI9CiOpS2CLy/ve/P5x88smZ6yxZsqT1/1133TX5e+ELXxj+5m/+JixatCjcdNNN4bDDDpu03cyZM5O/KtKtJcFP8uyxwpLlebNDehnfMUp34cPs7zMo6vAehRDVpbAQ2W233ZK/bti2rdlN1caB1IVu/PlpTefoXrETziBTVRknErsLH1acSF1TeuvwHoUQ1aZvMSI333xzWLFiRXjlK1+Z1BBB6u5HPvKRsM8++0StIXWgqCXBZ4PY57ax3aArmFrrjncPlSVOpMw1T3pFHd6jEKL69E2I7LDDDuE73/lO+Pd///ewefPm8PznPz+89rWvDf/2b/9WWfdLr8uQe6uCfZ4nQHUQnH7Mvm0TX1lcNP3o71M26vAehRDVZ6yRFjlaApC+O2fOnCRwdfbs2aEK8C6WloSyTNx5iXX35XsBo/Z+hBBCDHf+VtO7AVIFf76/C7fWHVhHdBcuhBCiCBIiA6Iq/nzrHvLZGv51IYQQohMSIgOiav58WwgtlkZcpuwZIYQQ5UVCZECUtU9LN/gqrT6NmP1wypA9I4QQotxIiIjC+DTiWFM+Ba0KIYTIg7JmRKh7JpAQQojhzd+Fe80I4VGvEyGEEN0iISL60utECCGEyINiRESoe20UIYQQw6NWQoTN2tIazCndtJ61UYQQQgyPWrlm2KzNuw44oeL1qgiuNPcIluP1ftdGwfJRq40ihBBi8NTKIhK7W4/d1Y86tjuufU++T8xUqVJtFCGEEMOhVkLEixH2SamSCKmT4BJCCDH61LaOyAs/fE0r0+MP5x8fqojqewghhBgGqiOSM910+thYarppL2MphoXqewghhCg7tRMi1kVx5rETLgwrRqoSvKr6HkIIIcpOrWJE0uIksIzxFHw+6m4M1fcQQggxCtRKiMTSTW1g56d/+oeAjNOqiRCg+h5CCCHKSK2ESFq6KSZlZtBUIZYiq74HXxdCCCHKQK2ESJFYilEWI1Ot76EKtEIIIQZF7YJVs9wYSOPFY6z6ap2oSwVaIYQQw6fWFhHFUsRRQTQhhBCDotZCRLEU9a5AK4QQYvjUtrKqyEcdKtAKIYToLaqsKnqCCqIJIYToN7V2zYh0VBBNCCHEIJAQEZNQEK8QQohBISEiJqEgXiGEEINCwapdoqJfQgghRBwFqw4AFf0SQgghps5AhMiWLVvCS17ykjA2NhbuuOOOUAVgCfFVWFX0SwghhChhjMgHP/jBsGDBgvA///M/oUqo6JcQQghRcovINddcE6699trwyU9+MlQRiA7W2ahC514hhBCiMkLkz3/+czj11FPDV7/61bDDDjuEKqKiX0IIIUQJXTNIxjn55JPDe97znnDwwQeHBx54IFcsCf5s1G2ZUdEvIYQQYsAWkaVLlyZBp1l/d999d7j44ovDE088EZYtW5Z738uXL0/Sffi3aNGiMGpFv3wAqxBCCCF6WEfkscceC+vWrctcZ8mSJeHEE08M3/ve9xJhQrZu3RqmT58e3vGOd4TLL788l0UEYkR1RIQQQohq1hHpW0Gzhx56qM21smbNmnDccceFb33rW+HQQw8NCxcuHOmCZkIIIYSY+vzdtxiRxYsXtz3faaedksd99tknlwgRQgghRPVRZVUhhBBCVL/p3V577ZVk0gghhBBCEFlEasinMrJ6sByvCyGEEINAQqSGqGGfEEKI2rlmRDl75PC5GvYJIYQYBhIiNUUN+4QQQpQBuWZqjBr2CSGEGDYSIjVGDfuEEEIMG7lmalr6XQ37hBBClAEJkT5lpPgJ3U78ZW3YByRGhBBCDBIJkRpmpMAqEzsXPsfrQgghxCDoW9O7XjDKTe8oPhh/URYRIoQQQpRp/lawap9QRooQQgjRGQmRPqGMFCGEEKIzihHpA8pIEUIIIfIhIdJjlJEihBBC5EdCpMcoI0UIIYTIj7JmhBBCCNFTlDUjhBBCiJFAQkQIIYQQQ0NCRAghhBBDQ0JECCGEEENDQkQIIYQQQ0NCRAghhBBDQ0JECCGEEENDQkQIIYQQQ0NCRAghhBBDQ0JECCGEEEOj1L1mWH0epWKFEEIIMRpw3s7TRabUQuSJJ55IHhctWjTsUxFCCCFEF/M4es6MbNO7bdu2hTVr1oSdd945jI2NZSoviJVVq1ZVvjme3mt1qdP71XutLnV6v3qv6UBaQIQsWLAgTJs2bXQtIjj5hQsX5l4fH07VBwPRe60udXq/eq/VpU7vV+81TidLCFGwqhBCCCGGhoSIEEIIIYZGJYTIzJkzw7//+78nj1VH77W61On96r1Wlzq9X73X3lDqYFUhhBBCVJtKWESEEEIIMZpIiAghhBBiaEiICCGEEGJoSIgIIYQQYmhUVohs2bIlvOQlL0kqst5xxx2hirzhDW8IixcvDttvv314/vOfH/7pn/4pqURbRR544IHwL//yL2HvvfcOs2bNCvvss08Swf3MM8+EKnL++eeHww8/POywww5h7ty5oWp87nOfC3vttVcydg899NDw3//936GK/PKXvwyvf/3rk+qSuBZdffXVoYosX748HHLIIUkV7N133z286U1vCvfcc0+oKpdcckk44IADWsW9DjvssHDNNdeEOnDBBRckY/mss87q2T4rK0Q++MEPJj/+KnP00UeHK6+8MvnBf/vb3w733XdfeOtb3xqqyN13352U/P/CF74Qfv/734dPfepT4fOf/3z40Ic+FKoIBNYJJ5wQ3vve94aq8Y1vfCOcc845iZC87bbbwoEHHhiOO+648Oijj4aqsXnz5uT9QXhVmeuvvz6cdtpp4aabbgo/+clPwrPPPhte85rXJO+/iqDiNybkW2+9Ndxyyy3hmGOOCW984xuTa1OVWbFiRXINhgjrKY0K8sMf/rCx3377NX7/+98jNblx++23N+rAd7/73cbY2FjjmWeeadSB//zP/2zsvffejSpz6aWXNubMmdOoEi9/+csbp512Wuv51q1bGwsWLGgsX768UWVwLbrqqqsadeDRRx9N3u/111/fqAvz5s1rfPnLX25UlSeeeKLxghe8oPGTn/yk8apXvapx5pln9mzflbOI/PnPfw6nnnpq+OpXv5qYtevC+vXrw9e+9rXEnL/ddtuFOrBx48Ywf/78YZ+GKGjpwV3kscce29ZTCs9vvPHGoZ6b6O1vE9Th97l169ZwxRVXJNYfuGiqymmnnRZe97rXtf12e0WlhAhuOk4++eTwnve8Jxx88MGhDpx77rlhxx13DLvsskt46KGHwne/+91QB+69995w8cUXh3e/+93DPhVRgLVr1yYX7uc+97lty/H8kUceGdp5id4BFyriB4444oiw//77h6ryu9/9Luy0005JpVHMOVdddVV48YtfHKrIFVdckbhREQvUD0ZCiCxdujQJjsn6QwwBJia0HV62bFkYVfK+V/KBD3wg3H777eHaa68N06dPD+985zsTQVbV9wtWr14dXvva1yYxFLB+Vfm9CjGKd8533nlnMnlVmRe96EVJIsTNN9+cxHKddNJJ4a677gpVY9WqVeHMM89MLO4ILu8HI1Hi/bHHHgvr1q3LXGfJkiXhxBNPDN/73veSCzrB3Rcm6He84x3h8ssvD1V5rzNmzJi0/OGHHw6LFi0Kv/nNb0bGRFj0/SIr6KijjgqveMUrwmWXXZaY9UeFbr5bvEfcXW7YsCFUxTUDl+m3vvWtJLOC4CKO91hlix6uS7hrtu+7apx++unJd4hsIWS41Qm4LJDNh2DOKnH11VeHN7/5zck8audVjGdcf5Ghal/rhueEEWC33XZL/jpx0UUXhY9//OOt55i0EI2PKH2kCFbpvaaZRAEGxqhQ5P3CEoJMoYMOOihceumlIyVCpvrdVgWILHx/P/vZz1oTMsYtnmMSE6MJ7mff9773JULrF7/4Re1ECMfxKF178/LqV786cUNZTjnllLDffvsloQFTFSEjI0TygpoaFvjvAFQq0q2qBMyBSKV65StfGebNm5ek7n7kIx9J3uuoWEOKABECS8iee+4ZPvnJTybWBfK85z0vVA3E+yAAGY+4+2AtnH333bc1rkcVpO7CAoI4rpe//OXh05/+dBLoh4tb1fjLX/6SxDORlStXJt8lgjj99WrU3TFf//rXE2sIaokw3mfOnDlJ3Z+qAff/8ccfn3yHCAfAe4cA+/GPfxyqxs477zwp1odxiT2LAWpUmJUrV1Y2ffe3v/1t4+ijj27Mnz+/MXPmzMZee+3VeM973tN4+OGHG1VNY8V3GfurIieddFL0vf785z9vVIGLL764sXjx4saMGTOSdN6bbrqpUUXwfcW+R3y/VSLtt4nfbRX553/+58aee+6ZjN/ddtut8epXv7px7bXXNurCq3qcvjsSMSJCCCGEqCaj5WQXQgghRKWQEBFCCCHE0JAQEUIIIcTQkBARQgghxNCQEBFCCCHE0JAQEUIIIcTQkBARQgghxNCQEBFCCCHE0JAQEUIIIcTQkBARQgghxNCQEBFCCCHE0JAQEUIIIUQYFv8/Qxjb/BNF/jkAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import numpy.random as npr \n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "N=10000\n",
    "rho=0.8\n",
    "\n",
    "X=npr.normal(0,1,N) # X= G_1\n",
    "Y=rho*X + np.sqrt(1-rho**2)*npr.normal(0,1,N) # Y= rho*G_1 +  sqrt(1-rho^2)*G_2,   G_1 indep. G_2\n",
    "\n",
    "# XY= rho*G_1*G_1 + sqrt(1-rho^2)*G_1*G_2\n",
    "# EXY= rho*E(G_1^2)=rho\n",
    "# cov(X,Y)=rho \n",
    "\n",
    "# Deuxième méthode Cholesky :\n",
    "# Gamma=[1,rho],[rho,1]\n",
    "# A=np.linalg.cholesky(Gamma) matrice triangulaire inférieure\n",
    "# G=np.normal(0,1,(2,N)) # G=(G_1,G_2)\n",
    "# Z=np.dot(A,G)# Z=(X,Y)\n",
    "\n",
    "# Corr(X,Y)=Cov(X,Y)/(sqrt(Var(X))*sqrt(Var(Y)) )\n",
    "\n",
    "plt.plot(X,Y,'x')\n",
    "\n",
    "# Méthodes empirique Monte Carlo pour le calcul de la covariance\n",
    "cov_XY=np.mean(X*Y)-np.mean(X)*np.mean(Y)\n",
    "print(cov_XY)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Soit $X$ une matrice aléatoire de taille  $M\\times N$ dont les entrées sont des variables i.i.d gaussiennes de moyennes 0 et variances $\\sigma^2<+\\infty$. Soit $H=\\frac{1}{N}XX^{\\top}$ et $M,N\\to+\\infty$ de sorte que le rapport $M/N\\to q\\in(0,+\\infty)$. Alors la densit\\'e des valeurs propres de la matrice de corrélation de $X$ est :\n",
    "\n",
    "\n",
    "\\begin{equation}\n",
    "\\rho(x)=\\frac{1}{2\\pi\\sigma^2}\\frac{\\sqrt{(\\lambda_+-x)(x-\\lambda_-)}}{xq}\\times 1_{x\\in[\\lambda_-,\\lambda_+]}\n",
    "\\end{equation}\n",
    "avec \n",
    "\\begin{equation}\n",
    "\\lambda_+=\\sigma^2(1+\\sqrt{q})^2, \\quad\\mbox{ and }\\quad \\lambda_-=\\sigma^2(1-\\sqrt{q})^2.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quelques fonctions utiles pour python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 0 0]\n",
      " [0 2 0]\n",
      " [0 0 3]]\n",
      "[1. 2. 3.]\n",
      "[[1. 0. 0.]\n",
      " [0. 1. 0.]\n",
      " [0. 0. 1.]]\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "A=np.diag((1, 2, 3))\n",
    "print(A)\n",
    "w, v = np.linalg.eig(A) # eigenvalues and eigenvectors\n",
    "print(w) \n",
    "print(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 4, 1, 2])"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def myfunc(a, b):\n",
    "    \"Return a-b if a>b, otherwise return a+b\"\n",
    "    if a > b:\n",
    "         return a - b\n",
    "    else:\n",
    "        return a + b\n",
    "    \n",
    "#a=myfunc([1,2], 3)\n",
    "#print(a)\n",
    "\n",
    "f=np.vectorize(myfunc)    \n",
    "f([1, 2, 3, 4], 2)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "#try:\n",
    "    # Bloc à essayer\n",
    "#except:\n",
    "    # Bloc qui sera exécuté en cas d'erreur\n",
    "    \n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Matrices de Wishart "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "    \n",
    "# Definition of the Marchenko-Pastur density\n",
    "def marchenko_pastur_pdf(x,Q,sigma=1):\n",
    "     \n",
    "    #Q number of lines/number of columns converges to Y\n",
    "    b = (sigma*(1 + np.sqrt(Q)))**2  # Largest eigenvalue\n",
    "    a = (sigma*(1 - np.sqrt(Q)))**2  # Smallest eigenvalue\n",
    "    return (np.sqrt((b-x)*(x-a)) * ((x>=a) & (x<=b))) / (2*np.pi*sigma*sigma*x*Q)\n",
    "\n",
    "    \n",
    "def compare_eigenvalue_distribution(correlation_matrix, Q, sigma=1,  show_top = True):\n",
    "    \n",
    "    e,ev= np.linalg.eig(correlation_matrix) #compute eigenvalues of the correlation matrix\n",
    "               \n",
    "\n",
    "    x_min = .0001 if (sigma*(1 - np.sqrt(Q)))**2 < .0001 else (sigma*(1 - np.sqrt(Q)))**2\n",
    "    x_max = (sigma*(1 + np.sqrt(Q)))**2\n",
    "    \n",
    "    \n",
    "    \n",
    "\n",
    "    bins = 50\n",
    "    #plot histogram\n",
    "    plt.hist(e, bins=bins, range=(x_min, x_max), density=True, alpha=0.5, color='b')\n",
    "    #density=True  efféctifs normalisés pour récupérer une approximation de la densité\n",
    "   \n",
    "    # Plot the theoretical density\n",
    "    f = np.vectorize(lambda x: marchenko_pastur_pdf(x, Q, sigma))\n",
    "    # f = ? \n",
    "        \n",
    "        \n",
    "    x = np.linspace(x_min,x_max,5000)\n",
    "    plt.plot(x,f(x), linewidth=4, color = 'r')\n",
    "\n",
    "#fin de la fonction\n",
    "    \n",
    "# Create the correlation matrix and find the eigenvalues\n",
    "N= 500  #rows\n",
    "T= 1000 # columns \n",
    "X= np.random.normal(0,1,size=(N,T))# Wishart Matrix dont les entrées son N(0,1) unidimensionnelles\n",
    "\n",
    "H = np.corrcoef(X) # H=XX^T/N il faut diviser par les variance pour avoir la coreelation\n",
    "\n",
    "#print(cor)\n",
    "#Correlation matrix\n",
    "# \n",
    "Q= N/T\n",
    "compare_eigenvalue_distribution(H, Q, sigma=1, show_top=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['BANSWRAS.NS']: ValueError(\"time data 'yahoo' does not match format '%Y-%m-%d'\")\n",
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['NSN.DE']: ValueError(\"time data 'yahoo' does not match format '%Y-%m-%d'\")\n",
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['ETEC.OB']: YFTzMissingError('possibly delisted; no timezone found')\n",
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['ALRN']: YFTzMissingError('possibly delisted; no timezone found')\n",
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['CE2.DE']: YFTzMissingError('possibly delisted; no timezone found')\n",
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['TTM.V']: ValueError(\"time data 'yahoo' does not match format '%Y-%m-%d'\")\n",
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['SUL.AX']: ValueError(\"time data 'yahoo' does not match format '%Y-%m-%d'\")\n",
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['BFK']: ValueError(\"time data 'yahoo' does not match format '%Y-%m-%d'\")\n",
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['GDF-H.V']: ValueError(\"time data 'yahoo' does not match format '%Y-%m-%d'\")\n",
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['S10.SI']: ValueError(\"time data 'yahoo' does not match format '%Y-%m-%d'\")\n",
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['RHL.AX']: YFTzMissingError('possibly delisted; no timezone found')\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['BANSWRAS.NS' 'NSN.DE' 'ETEC.OB' 'ALRN' 'CE2.DE' 'TTM.V' 'SUL.AX' 'BFK'\n",
      " 'GDF-H.V' 'S10.SI' 'RHL.AX' 'H' 'SUNPHADV.BO' 'SWS' 'AFFW.OB' 'K90.DE'\n",
      " 'KB2.DE' 'GOE.PA' 'TCN.AX' 'BUSE']\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['H']: ValueError(\"time data 'yahoo' does not match format '%Y-%m-%d'\")\n",
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['SUNPHADV.BO']: ValueError(\"time data 'yahoo' does not match format '%Y-%m-%d'\")\n",
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['SWS']: ValueError(\"time data 'yahoo' does not match format '%Y-%m-%d'\")\n",
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['AFFW.OB']: YFTzMissingError('possibly delisted; no timezone found')\n",
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['K90.DE']: ValueError(\"time data 'yahoo' does not match format '%Y-%m-%d'\")\n",
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['KB2.DE']: ValueError(\"time data 'yahoo' does not match format '%Y-%m-%d'\")\n",
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['GOE.PA']: YFTzMissingError('possibly delisted; no timezone found')\n",
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['TCN.AX']: YFTzMissingError('possibly delisted; no timezone found')\n",
      "C:\\Users\\lione\\AppData\\Local\\Temp\\ipykernel_26712\\440845266.py:17: FutureWarning: YF.download() has changed argument auto_adjust default to True\n",
      "  prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
      "[*********************100%***********************]  1 of 1 completed\n",
      "\n",
      "1 Failed download:\n",
      "['BUSE']: ValueError(\"time data 'yahoo' does not match format '%Y-%m-%d'\")\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(0, 20)"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import datetime as dt\n",
    "from pandas_datareader import DataReader\n",
    "import yfinance as yf\n",
    "    \n",
    "np.random.seed(777) #Jackpot\n",
    "size = 20\n",
    "    \n",
    "start, end = dt.datetime(2012, 1, 1), dt.datetime(2013, 12, 31)\n",
    "tickers = pd.read_csv('yahoo_tickers_2010.csv', header=None)[0]\n",
    "tickers = np.random.choice(tickers.values, size=size, replace=False) # Choose a random set of headers\n",
    "print(tickers)\n",
    "prices = pd.DataFrame()\n",
    "for ticker in tickers:\n",
    "    try:\n",
    "        prices[ticker] = yf.download(ticker,'yahoo', start.strftime('%Y-%m-%d'), end.strftime('%Y-%m-%d')).loc[:,'Close']\n",
    "    except Exception as e:\n",
    "        pass               #ignor exceptions\n",
    "    \n",
    "   \n",
    "returns = prices.pct_change() \n",
    "#Computes the percentage change from the immediately previous row by default. \n",
    "#This is useful in comparing the percentage of change in a time series of elements.\n",
    "#example :\n",
    "#s = pd.Series([100, 150, 180])\n",
    "#print(s)\n",
    "#print(s.pct_change())\n",
    "returns = returns.iloc[1:, :]# Remove first row of NA's generated by pct_changes()\n",
    "                            #iloc gets rows (or columns) at particular positions in the index \n",
    "                            #(so it only takes integers).\n",
    "returns.dropna(axis = 1, thresh=len(returns.index)/2, inplace=True) # Drop stocks with over half the data missing\n",
    "returns.dropna(axis = 0, thresh=len(returns.columns), inplace=True) # Drop days without data for all stocks\n",
    "\n",
    "\n",
    "tickers = returns.columns # Remove tickers that were dropped\n",
    "\n",
    "returns.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['BANSWRAS.NS', 'NSN.DE', 'ETEC.OB', 'ALRN', 'CE2.DE', 'TTM.V', 'SUL.AX',\n",
      "       'BFK', 'GDF-H.V', 'S10.SI', 'RHL.AX', 'H', 'SUNPHADV.BO', 'SWS',\n",
      "       'AFFW.OB', 'K90.DE', 'KB2.DE', 'GOE.PA', 'TCN.AX', 'BUSE'],\n",
      "      dtype='object')\n"
     ]
    }
   ],
   "source": [
    "print(returns.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
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       "        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]),\n",
       " array([0.  , 0.01, 0.02, 0.03, 0.04, 0.05, 0.06, 0.07, 0.08, 0.09, 0.1 ,\n",
       "        0.11, 0.12, 0.13, 0.14, 0.15, 0.16, 0.17, 0.18, 0.19, 0.2 , 0.21,\n",
       "        0.22, 0.23, 0.24, 0.25, 0.26, 0.27, 0.28, 0.29, 0.3 , 0.31, 0.32,\n",
       "        0.33, 0.34, 0.35, 0.36, 0.37, 0.38, 0.39, 0.4 , 0.41, 0.42, 0.43,\n",
       "        0.44, 0.45, 0.46, 0.47, 0.48, 0.49, 0.5 , 0.51, 0.52, 0.53, 0.54,\n",
       "        0.55, 0.56, 0.57, 0.58, 0.59, 0.6 , 0.61, 0.62, 0.63, 0.64, 0.65,\n",
       "        0.66, 0.67, 0.68, 0.69, 0.7 , 0.71, 0.72, 0.73, 0.74, 0.75, 0.76,\n",
       "        0.77, 0.78, 0.79, 0.8 , 0.81, 0.82, 0.83, 0.84, 0.85, 0.86, 0.87,\n",
       "        0.88, 0.89, 0.9 , 0.91, 0.92, 0.93, 0.94, 0.95, 0.96, 0.97, 0.98,\n",
       "        0.99, 1.  ]),\n",
       " <BarContainer object of 100 artists>)"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "\n",
    "import numpy as np\n",
    "    \n",
    "log_returns = returns.apply(lambda x : np.log(x+1)) # compute the log returns pct=(R_2-R_1)/R_1;  log(pct+1)=log(R_2/R_1)\n",
    "\n",
    "# Faites un histogramme des log_returns \n",
    "\n",
    "#print(returns.columns)\n",
    "plt.hist(log_returns.values.flatten(), bins=100)\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "#print(log_returns)\n",
    "\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 0\n"
     ]
    },
    {
     "ename": "ZeroDivisionError",
     "evalue": "division by zero",
     "output_type": "error",
     "traceback": [
      "\u001b[31m---------------------------------------------------------------------------\u001b[39m",
      "\u001b[31mZeroDivisionError\u001b[39m                         Traceback (most recent call last)",
      "\u001b[36mCell\u001b[39m\u001b[36m \u001b[39m\u001b[32mIn[56]\u001b[39m\u001b[32m, line 5\u001b[39m\n\u001b[32m      3\u001b[39m T, N = returns.shape\n\u001b[32m      4\u001b[39m \u001b[38;5;28mprint\u001b[39m(T,N)\n\u001b[32m----> \u001b[39m\u001b[32m5\u001b[39m Q=\u001b[43mN\u001b[49m\u001b[43m/\u001b[49m\u001b[43mT\u001b[49m\n\u001b[32m      7\u001b[39m correlation_matrix = log_returns.interpolate().corr() \u001b[38;5;66;03m#If Nan do interpolation\u001b[39;00m\n\u001b[32m     11\u001b[39m compare_eigenvalue_distribution(correlation_matrix, Q)\n",
      "\u001b[31mZeroDivisionError\u001b[39m: division by zero"
     ]
    }
   ],
   "source": [
    "#Compléter en appliquant le theoreme de Marchenko Pastur\n",
    "\n",
    "T, N = returns.shape\n",
    "print(T,N)\n",
    "Q=N/T\n",
    "    \n",
    "correlation_matrix = log_returns.interpolate().corr() #If Nan do interpolation\n",
    "\n",
    "\n",
    "\n",
    "compare_eigenvalue_distribution(correlation_matrix, Q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7fae6e0f9ad0>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae6e137b10>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae6e120e90>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae6e10bb50>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae74880ed0>],\n",
       "       [<matplotlib.axes._subplots.AxesSubplot object at 0x7fae748b6b90>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae748f53d0>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae76d59bd0>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae76d65750>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae76da8110>],\n",
       "       [<matplotlib.axes._subplots.AxesSubplot object at 0x7fae76f45f90>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae75cf9d50>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae766e5e50>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae6e106390>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae76540210>],\n",
       "       [<matplotlib.axes._subplots.AxesSubplot object at 0x7fae6e0e5c10>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae748028d0>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae7483cc50>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae74a93910>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae74acec90>],\n",
       "       [<matplotlib.axes._subplots.AxesSubplot object at 0x7fae74b06950>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae74b43cd0>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae75f57990>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae75f95d10>,\n",
       "        <matplotlib.axes._subplots.AxesSubplot object at 0x7fae75fcc9d0>]],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x1440 with 25 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "indices= ['BANSWRAS.NS','BDCO','BFK', 'BRK-A', 'CDNS', 'BUSE','CE2.DE', 'DSG.TO', 'FINPIPE.NS','GCG-A.TO' ,'H', 'JHX','KFS','ML.PA','LRE.L','NAII', 'OISL.NS', 'NOK','PFIZER.NS',  'S10.SI','STCINDIA.NS', 'SUL.AX', 'VNP.TO', 'WCH.DE'] \n",
    "\n",
    "new_log_returns= log_returns[indices]\n",
    "\n",
    "new_log_returns.hist(bins=30,alpha=0.5,figsize=(15,20))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "491 24\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "T, N = new_log_returns.shape\n",
    "print(T,N)\n",
    "Q=N/T\n",
    "    \n",
    "new_correlation_matrix = new_log_returns.interpolate().corr() #If Nan do interpolation\n",
    "\n",
    "\n",
    "\n",
    "compare_eigenvalue_distribution(new_correlation_matrix, Q)\n",
    "\n",
    "# 24 indice c'est trop petit par rapport 491 "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.13.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}