0.1-Monte-carlo-simulations.ipynb

{
 "cells": [
  {
   "attachments": {
    "image.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAAAv4AAAD8CAYAAAAPMqCbAAABdWlDQ1BrQ0dDb2xvclNwYWNlRGlzcGxheVAzAAAokXWQvUvDUBTFT6tS0DqIDh0cMolD1NIKdnFoKxRFMFQFq1OafgltfCQpUnETVyn4H1jBWXCwiFRwcXAQRAcR3Zw6KbhoeN6XVNoi3sfl/Ticc7lcwBtQGSv2AijplpFMxKS11Lrke4OHnlOqZrKooiwK/v276/PR9d5PiFlNu3YQ2U9cl84ul3aeAlN//V3Vn8maGv3f1EGNGRbgkYmVbYsJ3iUeMWgp4qrgvMvHgtMunzuelWSc+JZY0gpqhrhJLKc79HwHl4plrbWD2N6f1VeXxRzqUcxhEyYYilBRgQQF4X/8044/ji1yV2BQLo8CLMpESRETssTz0KFhEjJxCEHqkLhz634PrfvJbW3vFZhtcM4v2tpCAzidoZPV29p4BBgaAG7qTDVUR+qh9uZywPsJMJgChu8os2HmwiF3e38M6Hvh/GMM8B0CdpXzryPO7RqFn4Er/QcXKWq8UwZBywAAAGxlWElmTU0AKgAAAAgABAEaAAUAAAABAAAAPgEbAAUAAAABAAAARgEoAAMAAAABAAIAAIdpAAQAAAABAAAATgAAAAAAAACQAAAAAQAAAJAAAAABAAKgAgAEAAAAAQAAAv6gAwAEAAAAAQAAAPwAAAAAPsK92QAAAAlwSFlzAAAWJQAAFiUBSVIk8AAAQABJREFUeAHsXQd8FMf1fuoVCfWOhJCQ6Mh0DBhs3HtcYsdJXBO3xI5jO06P0+w4cZziFKc78T+9x7ETxw0wxcZgbDoIhEAgISEhJNQL/L9vdXvaK5LuTifpJN77/T7t7Ozszuynvd03b968EVFRBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGVAGlAFlQBlQBpQBZUAZUAaUAWVAGeiPgaD+DuqxIWUgCVdPA9KBVCAZiAYigHDbNgzbTqDDhnZsW4E64BhwFKgGaoDTgIoyoAwoA8qAMqAMKAPKgDLglgFV/N3S4pfMKFxlDnAWUARMALIAKvspAJV6f0kXLnQcYEegEqgASoF3gLeBRkBFGVAGlAFlQBlQBpQBZeAMZkAVf//888fjMucBy4DZwCQgAwgGfJKgkBAJjY6QrtYOOd1Fvd5n4UgARwfKgG3AWuBloApQUQaUAWVAGVAGlAFlQBk4QxhQxd+3f3QmTnsfsBKYBdCa77OSj3PtEpWSKBkLZkpsdpoEBfVcsrW2Xmp3lMrxXdDdT/vNo4cjA+wIrAb+CuwFVJQBZUAZUAaUAWVAGVAGxigDqvh79o8NRbErgcuBJUA+MCjuQsLDJXJcrIGo+DghYiakS3RhtgSFBEPpx+WDASj6p6nsnzotXY3NcuLdfdJSe1zaGhql9WSTtDc1SWdrG5ozaDmCK6wH/gP8EWgBVJQBZUAZUAaUAWVAGVAGxggDg1JexwgHfd1GJA5cD1wHLAdiAa8kNjlRkifmSWpBPra5kpw3QdIm5wOFEpuU6HCtk40Nsub1F6Hkn3LId96JiY2TpcsvltBQ9kV6pO3kSTm6e59U79svtQcOSm35IakpLUO6XBqOYt6v96MEnES8AeBIwG+BekBFGVAGlAFlQBlQBpQBZWAUM6CKv+M/j3xcDdwBLAc4QdcjGZ+VIVkzpkn+/DmSN/8syZtXIjHj6frvmby7eb0crjjgUeGCydOleCo9jAaW9tZWObj5XTmwcbOUv7VZKt7bLnXoGBijCAOfzhKMKrQR+BXwHMAIQyrKgDKgDCgDyoAyoAwoA6OMgTNe8b/gN9+Kaams+kpHQ/PNnU0tiZ3NLUHN1XVSu22PnDzU9/xXWvALzl4oU89fLlNXLpfYZEbn9F1e/s9fpb3dM5ed6OhYOfcCeh75Jm1wD9rz+lrZ8b/XpXTteowWlMrpU+5HGmLSUyR1drHEZKVKWEyUhEVHnwyNjvznuMy8+1+645OMJKSiDCgDyoAyoAwoA8qAMjAKGDijFf+Ewry7ci84+9twr4l2FwW/dnupHHljk/FvDI+JlsIli2T6RedJyZWXCi38/pR//4MeNZ7LZVfd5HnhAUo2nzgh7/3zP7L9v6/I7lVvSMvxE8YZaXOmSdq8GT3zDZyuERQc3FmxZtMTddv2fAWHOCqgogwoA8qAMqAMKAPKgDIQwAyciYo/ffUfAD5S8L7zc2LSuG6WewmJCJNQCZGZcxfJ7KsuldAwf4bed6xzJBV/a0voArTzlVWy+dWXpT2oG+FE+x6F6Ghskt1/fLHudFc3XYCeALiOgIoyoAwoA8qAMqAMKAPKQAAy0DtDNAAb5+cmxeF6jwK3A3FxE7PEndLPiDpRSQkSk5EskQnxKCoSkp0iIZbJtEbmGP3DaELhuSmSuHCacYcdJ5ulueqYtBw7Lqc6HdcTCI+LlaSpk5Jqt+79BArfDfwJ+BxQAagoA8qAMqAMKAPKgDKgDAQQA2eC4p8Avh8FbgXGAYbETWAo/l4JHxcDZT9FolOTJDg0pPcAUkcOlxv7s+csssfWdygwhnbK9u2SPTvfs98ReSHGF0yQ1toT6ATUSNsJLARsW04gLjdLoPizfATwIYCRkP4CfB4oB1SUAWVAGVAGlAFlQBlQBgKAgbGs+DMc56PAvYBLKE5OVIUWL9EpCVgsK10iYL3uT6j8U9ctGcPKf3nZXtm5/R23NMCnH52iRAOdLa3SdLhamqtrMdnXJfAROwCcgMAwqL8HHgTqABVlQBlQBpQBZUAZUAaUgRFkwNG0PYIN8XPVdDv5B3AhEO587bDICCm+4gJJPgvRamDlD41wKeJ8irF/shEW76aTkp6JRba4wJYfZe9uLqLruUwunul5YQ9KHirfJ9veY9TOgSUEcx2iksZLLCL9RIRHSs3mHdLVztD/DsJnazZwF8DewTrAfeggHFBRBpQBZUAZUAaUAWVAGRhaBsaa4n8e6Po3cAvgYsIPi4qUxTffKHf/9TeSNXuaVNdUoph3cvJkw5Ao/yOp+B8+VCbvbXnTOyJQmqMAM5cuk2u+8BljGePKnXuks81lMjBHAM4BbgNqgV4/IuyoKAPKgDKgDCgDyoAyoAwMDwNjRfGnH/9vgMeBVGfqqPCffesH5d6/PSdzr7tKImNjJHZcvFQdOSQdHS6WaufTXfap/DfB8p/hR8v/SCn+lUcOypbNG1zu0ZOM8IhIKTlrsYRHRUnximWy/N47JDg4RI5s3+WuA8DJ1VcDK4A1gK4GDBJUlAFlQBlQBpQBZUAZGC4GxoLifyfI+icwF3Dwv6E7TsnVl8nH//l7mX/D+yQ8OtrOK48lp2QIFd/u7m57vqeJJir/JxslPSPHL24/I6H4H62skHc2rcUt22bqenrzKBccEiLzF65AB4r6fI8w3GnR8iVyzp23SMuJk0YH4JQrt3ko/VGAIwGrAe8rx0kqyoAyoAwoA8qAMqAMKAPeMTCaFf8c3OqLwD2AywzT/IVz5c4//VpW3nenRMbZg/k4sBMeESEpaZmG5X+klf/hVvyrjx6RzRvfEMbt91Zo1Z+/cLkkpaS5PTUUvM645HyZf+M1Ult+SKpLy5zLcUEEuv/cAHC4oQpQUQaUAWVAGVAGlAFlQBkYQgZGq+JPf/F/AYXO3IxLS5EPPfMduf7Jr8n4zHTnwy77EXBXSQ0A5X84Ff9jNVWy6a3VUPq9n2sbDL/+uQvOQYdp4JWLo8ePl3nvf59MXrZY9m94W5qPu3j3cPW0mwF2BFYBKsqAMqAMKAPKgDKgDCgDQ8TAaFP8x4MHLhL1MEBXEbtwoumiD98g9z3/B5lQ4l3Emx7lPwuW/8G4/TQMyu1nuBT/utpq2fjmKjl1ynulPyiISv8ySUvPsvPuSSIpd4Kcc/dtcvpUt5Rv2iKnuhxcqxhSltb/y4BXgBOAijKgDCgDyoAyoAwoA8qAnxkYTYr/Mtw7fcLPcuYgvahQ7vnb/8kKKJeh4Z6F5nS+hl35rzwEn3/HFWqdy7rbp78/J/366vM/HIp//fFj8tb618WN3727W3LI45yIOfOX4v6yHfI93eH5RcuXGiMAh97dKvUVR5xP5YpqtwMVwFbng7qvDCgDyoAyoAwoA8qAMjA4BkaL4v8IbvNZoHcmKXZo5V9x9+1GeM6kCb4ppLiMXQzlH9bsqsEo/41Q/jO9n/A71Ir/ifo6KP2v+tSpodJ+1twliGI0wc6Vr4mYhPFy9s0fEC6gtn/dm87Wf/baGPmHfkScv+H9BAScpKIMKAPKgDKgDCgDyoAy4MpAoCv+nLT7N4Cr7zq0dXxWhtz951/LOXfdihCSwa535mMOlX+6svis/DfB8o+FvtKhJFNh9lSGUvFvOHEcSv9r0tXV6WlzLOUQGWnuYsnMzrXkDT5ZsGi+lFx1mZS+sV5OHmN4f7uQNEZouhTgmgxNgIoyoAwoA8qAMqAMKAPKwCAZcFCmB3ktf59egAuuBxZCg5bEKfmSsXCWpM2dLgWXnSsrP/cJmThrpoSHO7j6+6UNjE8/WOW/Eco/LeSeKv9DpfizE7Jh3avS2dnhEzez5yyW7JyJPp070Elh46Ila8V8ichJkcgUrAScnW7w1Xa8gafS9YcTf7my2CFARRlQBpQBZUAZUAaUAWVgEAwEquJPf35O9MwKjY6UgqtWStLUAolMjJfU2VMkflKOULE+VF4qUdGxEhefMAgK3J/ao/xn+2z5b4blv7HBc+V/KBR/zjvYsO4V6fRhkTKyMqtkoeRMyHdP0CBzq48eljfXviq1x45KRFK8xGZw3bXTEpebJeNyMqSh/LCc7urmwgs3AhXAe4CKMqAMKAPKgDKgDCgDyoCPDASi4k8r7x+BcbT0U+mPSk4QdgBSZxVLZEKvmz9j0B+tOixJyakSjQ6Av4Vx/tMwmbUKC111d3k/4bdH+a+H5Z8+//27I/lb8W9uPgnF+hVpb2/ziZYZs+fLhDwOuvhfeuYbYJIxovyYEhoZIdFpSdLR2CzBYaESk5kqx3cf4GFG/bkS4LO6ClBRBpQBZUAZUAaUAWVAGfCBgUBT/L+Ce/g2wLjucO+ZZFj6o5LHS8rMIgmNcB+xh+4suXmFPMXvQleiHrcfX5X/k9LQMLDy70/Fv6WlSTZA6W9ra/WJj+kz50rexMk+nevJSVwtuLWl2aUoVwOOTk/uiTp06jQ6AU3SVmdE96Tf/zkAG/V3lxM1QxlQBpQBZUAZUAaUAWVgQAb6N0MPeLpfC/wIV/sCYG/TeLj0jIPfd/L0yUKlsC/h5FW6tQyVxMbGyaIlKyUy0mWBYI+qrMEquZveesPBwu3RiT4Uam1tMVxo2rD1RaZOnyN5+UW+nOrROS3NTXK87lifZTknIqEgVxIKgcl5zuU+gIz/ABwFUFEGlAFlQBlQBpQBZUAZ8IKBQFGgfoM2f8ih3VAAc89ZKDET0hyy+9o5dqxKYsf1ugH1Vc7X/B7l/3xY0l/2yZJeU92j/M9dsBRRiPruxPjaPp5HCz/de2jx90WKp86W/IJiX071+Bz+nzyR2Kw0KbxkhRz633rpam+3nnIhdl4DLgB882OyXk3TyoAyoAwoA8qAMhAoDCSjIe8D5gD+9+F2vUsqGBuAXwO+RUFxvWZA59it6yPUSrpwMFyng9IfCt/6W37xA8maOdXjZtXWHPW4rK8FY2LHwfJ/vu+Wf0P5X4NY+r2+7b62xfm8Dvjyv4noPfTt90WKpsySgsnTfDnVq3O8+T8l5eXIfS/+SaIR+99JlmL/DWA4XgpOVeuuMqAMKAPKgDKgDAwBA0W45jcBuvYO1/c9AnUtB7iG0BkhI2nxp9L/AnCxlemwqCi584+/lOkXnifb3tsoJ07UWQ/3ma6rrZbTp08NOIm2zwt4eMBQ/pfC8v+Gr5b/Stm8cQ1WwV0mIf24L3nYHKNYB6L2UOlvwsrBvkhh0QwpLJruy6lencPJ2Pw/eSrx4xNl8lmL5MFX/infvfgaOVlTaz11LnbWA2cDvvV2rFfTtDKgDCgDyoAyoAyMJAO3o/KI7EUJMu0DmRKXHTnkband1SSvf3YP61kOMLDMmJeRtPj/Bew6KP0R42Ll4//+g6H0k/nklHSP/wFcnOpE/XGPyw+mYEwMLP9Q/iOjGG3Se6mproTPv38s/4zPz8W5GN7UFykonCZFU2b6cqrX5zRikjM7KZ5KcmqGUTRr+hT51OoXhYu2OckM7NPtZ+jfDk4V664yoAx4zEA4SkZ5XFoLKgPKwJnKQBZvfMFDecOi9LOuxCK7Hjd0vuKsKIBkpBT/34AD+nDZhe4cD/znrzJ5ySJ7XlKyZ/795gmMCT9cYij/nPDro/J/rIbK/+pBuf2ws/PW+teFk5t9kfyCKVI8bbYvp/p0jrf/n2TL/z8lP08eWfMfScqb4Fw3Lf8vA0YkKOeDuq8M+ImBElznCeA54LfA/wF3ACr9M3ANDv/cBpO3e/o/5Yw9SteGpwHyRHwLYKdJRRk4oxgIDh4+1XQ46wqUf+JIuPr8EDdv+PSPCw+WxbmxEh4dJSs/cY8ktBwUWQ3YhP2wkmMH3IZ+NMtYt7F1hyT66D5rlj3dXnSWdKe7KI32474kqPwvhs//ek749SGKzrGaKkP5n7uA7mzeCdcV2LhhFUY5HNxfPL4II/dMnX6Wx+U9KRjU1CBRm1/vs2js/t1S7KE7EjtUCW+95HAtPg+Pf/t++e+3vi8vbDok7V2nzeNLkKDb2EXAKTNTt8qABwyEoQwnt/DHQOWe/p5UvrYBVvk4dnjMFLoqLgOo1Kr0zcBVOGTEM7At20HeFgOM4qbiyAC/x4mWLK5ezrwzYsKh5b69SdItYA5QBbwDcGIoPwye+QijoIoycKYxMNyK/5dBsN3aU5wSKfcuTOnh/DUOArjKPNes/nM2/Mvt8ZaFF8qJOx51e2wwmdExsYbyz7j5ra3NXl+Kyv/bb67y+ry3MVpwvK7G6/N4Atc8YKx+f0v0uhck/s/UmdwLtSqvZOOLbovfUogFvoKz5bn1Fdbj52PnD8D11kxNKwNuGBiHPD6OVPZnAlaFHrtyHuCs+BtlrvlTCRaYC5Y/X72Z5UL4R6VfBgzT3TV/oW4mJm9U/lVcGXDnr+lbXGbXa4/VnM/hxqydJd5nA2DXM5ihogwoA70MDN94isgHUe3ne6vGV7OPBbmsZfyVjnxnlQS1ea+Ye1I/lX/G+Y+KivGkuEsZb11geAFfzuF5ObmTZPosr7tTPHVAoeI/XLL05htlXCqNOw5yHfa+7pCjO8pADwO0nl4GfAn4MXAnwB9CREJ+lEx9f4bkLEnAriF9DqNR6VdRBpSBgGHAWelnw+IDpnXaEGUgABkYrq8Ywy/+FLDXx5CdF33q/mGjJBiTSqPefnXI6jOU/6VQ/qN9U/6HrGGWC2fnTJSZsxcg8pH/DW5h5bskrLLMUtvQJmMwJ+QT//2bRCeOd67o08i41TlT9884BviuKQY+AHwboL/0jcDkkLDgoLSSOCn5aI5c8rMZsvLbU2XaDZnS0dSNw4bsNRO6VQaUgcBn4Lq/zxFCRRlQBgZmYDhcffLRjL8DvVEdoHje9KNvS+4MGOHW/d/ArfRTiShYpFuWXuGnq7leJjq6x/JvuP20NLsWGMGcrOw8mYXQmEOh9PO2htPab9KYNa1Y7v3bc/Ldi66VzrZ2M5sKHy267IWsNjN1e0YxwMXdrgE4WdKQ8NgQyZg3XjLnxkva7DgJi3b00jnVfUqO77H/ZveY5+lWGVAGlAFlQBkYSwzYLfBDdFNU9v8DJFmvf8mnPyGLPjj8rtgR+7ZKSM1ha1P8nqbyzwm/gWT5z8icILPnDJ3SL50YTdnIwDrDL5MWLZAPPvMd5w4N/bH/BuQMf4u0xhFmgFFQ6FYYG5MWLkVXpck5Xy+Sy5+dKfPvy5PsxQkuSj/b23CwVTpbDYs/J87QR1hFGVAGlAFlQBkYcwwMteL/OzA22cra3Ouvkise/Yw1a1jTw2GZptJP5Z+dgJGW9IwcKZl79pAubBb53loJbm4csVtdcOO1cunnH3aun76f/wKGY1TLuW7dHzkGOlF1JasPCQ+RwstSJXVqrASH9P+qq9tlt/arm8/I/e+0ZmVAGVAGlIEhZqD/r+HgKn8IpzOUm10mLpgjt/36Gfv+SCSiNmAAAivIDrVQ+eeE35FU/lPTs+SseUsQS28o/80j4+bj/P+77PMPyfwb6d3hILOx9zOHHN0Z6wzwx/0NoKKxolVe/9weaa7tGPCea3c3mWXUzcdkQrfKgDKgDCgDY46BodIIl4Aph+gqcWmp8Mf+vyFXQgf6D4Uer5bw3ZsGKuaX44byjxV+R0L5T0nNlLnzlw4538H1NRKx/S2/8DXYi9z886cla8ZU58vcjIzbnDN1f0wzwLCIXwUONld3yO4/Vw14s7W71eI/IEmuBUZ+SNO1TZqjDCgDyoAy0A8DQ6H4x6G+PwL0tTUkJCxM7vzjLyQ22cHV3zw87NvhcPcxbyoKC1EtovKPkJ/DJckp6TJ3wbKeVXOGuNLoN1+SoNOBsWZWSGio3IPOJVeBtghDGD0NOLicWY5rcmwyQFcvI95rTIr9VeT2Tjki0NozKkDt/4jbQmdmJkOU5QHzgEuADwMPAhxR+TnwE0BFGVAGlAFlYBQxMBSK/69x/wjX0ytXfvWzwkmYgSJDGdPf3T0ayj99/odB+U9KTpN5C8+RkBDHqCXu2uWPvKj17hfZ8se1fblG0oRsufVXP5QgR/emaFzrTwA7ASpjn4FU3CLDusZkzo+XyVen9XvHx3edNI/vQ2Lo/QDN2gJ7S8X+pwBHbj8B3ARcCJwFcNJ8b5Q27KgoA8qAMuAHBo7xGlt+dtAjF00/1Cf1ZfbRXnvCH9cN5Gv4e+Ij3Squst7wrMsvkgseuNeaNeJpM6b/UIb2dL5JU/l/Eyv8NjfbFQ3nYoPaT0xKgdK/HEq/v/+t7psVVrZDwqrK3R8cwdwZF58vF3zyXnnpSRr67TILqSeAT9lzNDEWGeAqXJ8FxqfNjJOFD+UPOLG3dneLyYP695tM2BT7+Lwo4YhJdEqERCNKUkwqkBwurzy8u7ekppQBZUAZ8A8Dz+Ey9+97sTYE8M8VPb/KWs+Lju6S/tQQaeX/npWO+Iw0w/pqzQuU9FDH9Hd3nz3K/0phnH9/K//jE5Jl/qIVEgp3l+GS4XSZ8vaervra52Xnq6ulYstW66m0XHJNiQ3WTE2PGQbG4U4YMiwlqRCT6x/JFyzW5XBznc3dUrG2TuLzY4RlKHW77R3xvQ6FdUcu+I7LnBllRRkYKwzwfcFRLBoLtgP6XQAJIyybUf+jAA3IfPkMx8hiO+p5G6BXwBkh/tQSfw/G4k3WuFDULb/4gUSO428r8MSM6d+dmj2sjYu0+fxveONlvyn/48cnyYLF50LpDxu+e+loG7HY/Z7cJJ+/j/7u5/LVuculo9lu0SVBvwWKAIZ9VBk7DETiVjiakxWfGyVLvjDJJV5/R3OnrPpcqRGzn2uIz7snT7IWjZf68laywCD++5lQUQacGOB3cg6QD9Bd8ADACBH6DgEJo1RoEaCRINfW/uXYck7Q87Z93YwcA1x88ykvq+d33Sp0TVTpgwFHc1gfhTzIvhVlllnLLbnjZply3jnWrIBLj5TFOjIyypjwGxM7+E5RXHyCofSHYQL1cErku29IcKs9BOJwVu1xXSn5efK+x77oXH4iMh53ztT9Uc0AH/4HgfxYuKMs/UKhhI9z/D10tp+SdV8r61H6RRrlFEw8PyiXzT8+KExDkJAOI6V/lIFeBvi+eBK4D7gMuBT4GPBtoABQGZ0MTEOzcyPjw2TaDXRWMORq/I22pXWjDIxZBvyh+DOKzzetDKUW5MsN333MmhWQaU9i+re3t0lTU6Pf228o/5jwGxNL+nyTuLjxsvDs8yQsvP+oJd5enW5IvO/+ZKQ6Tf21yd2x5XfdJsUrHPqkLMYPN4cRVUY/A5zF/nFgalRCmCx7tFCikhyV/lPdp+Stb5WJLVZ/Hcp+DqAvKdx+6rmhqH9/Dw/6t5eBFCQN1zHOdZh2U6bMAJiGJAGcQJ7OHZVRx4Dx/s9dkShT358hyVjkDxIBTB91d6INVga8ZMAfiv+PUKcRNo9108XiQz/9rjC0YqCLpzH931j1H6k8XO732+lR/ldKrA/Kf+y4eEPpDw/nu8p/Un30iPB++5OQuqMSsXNjf0UC6tgtv3haImJirG0iab+0ZmjaYwbGoySHUS8A/PH+8LhiNwWDkPdRYE54bIgshdIfk06Pn145deqUbHr6kFRtbmDmSYCjPceB/wLPALTyc/81QEUZsDJwLXaMyFArnyyWqddmSDHAdM7ZdAs3/I+vt54wxtP8vfHGJ9i2o/l2DR/fRNs8n+Rp9tF3jvCoKANjmoHBfrhpSr3RZCg4LFQW3H6TJE8pkK7O0eH+OJDlmop1d1e3vLNpnWx7d6N0d9MV2H9iKv/eXnERLP3hEY5KjrfXsJY/jdWM9+x6T95+cxX+d13SX4ciyojdf9p6esCmT53qlpBxUXLBZ+9HiE9+t+zC+LJ32/c04QkDHJ76PHAJcDNwB+BAKvaHUz6MypaERIbIki8WSvwE13lgW5+tlIOraeSXduCbQBV3bPIGth8B7gcqbXm6UQZMBuYwMfv2bIfIUMEhwTLrVkY0NYThTQf7HbVdKmA3HFK+Bvg+8AOAnWduvwNcBIzG++doDgwFvDWEAMuhLciQDDOhW2VgrDIwWLP80yAmODQqUjIWz5bk6ZMlaeEsWbcGizrB8p+RlStFU2ZKTIy9Nx1wPJox/U9HOliE7e3kfURERBiuLwfLS6W+vlbmYEVcf95TBHz+vRVfzumrjo6Odtmyab0cq+nRfXi/vO++JHr9C30dCpj8trZW2bt7mxyuKJNT7KwVpMjcB2+Tqre2StXG96S7zXDn/jIa/CxgzO4MmMYHZkOi0Sy6NmTEZUdJc027dHec4iQe9oR/CQx3T/A61HkBo/Ys+Wy+PUIP8uyy8y9VUvp8NffZxqeAMu5AaLWkuxd/eF8D7LO/kVYJLAb4IhruZ4sM0KoSxU5lTKqrgYXuZBxl6mjqpl8ZfxtNwFgUKsiPAIZCHJUQLuHxIcaCd7j3VOR/CJgPfBtoBkaLcORSohJ7FP/o3v9x8mi5AW2nMuArA4NR/G9DpTPDxkVLwZUrMZkuRhKLJ9oXTqIFme4xRysPSf6kKVJQNG14o854yIgnMf2pZJs+740N9fLG6/+RWSUL0bGZ4GEtgVusAfez+a010tLS+93qr1MRtm+rhFZXBOwNcUTmwP7dUrpnO0ZnuhzamTh1knS2tMq4nHQp/ccr0tXcyo/a14FPOhTUHWcG+HV8GMiNzYyUc75aKI0HW2XtY/up/J+LfCrWzwLDJRxxuCo4BBrHQ3mSOoMDEY5S9r9a2fFboyNLpfGHwHZbCTrzfgbIsu3T1KeKv42MANnQUnQlwFG5RKAR2AL8HTgGDIe0oZLW7rbuqOaaNhflv7Wug0o/20ELwlh9fuJxbxzhS04qipHJV6RJ09E2aavvkpi0CAmLCZHt+I2BiyKUYahkjgScAgJdOEJhOPWHj8NLBBLZOy/I8OEyMvWPMjBGGfB1iI5Wjq+Qk9zzFhlKf2RiPHrPRifagSr62O4r3SGvv/K8HD5UJuwQBJowpn9/EhHhaJHv6uqUzW+/Idu3bhK6koxWOVxxQNatfslB6ee9ON+v9f4Gco2ylh3u9NHKCln96r9l9853XZR+tiUsOkpiM9MkPC5WclcuNpt3JxKZ5o5uXRigcYAf9clRWLhp2ZcKJXJ8mKTOipNFn5lkxsk/H8c/6HLm0GScg8tyjoHM/VieZM93/U4ffhOd2Z8cNGt/Fom3bDs03dJ6aSr9zK7nH5WAYYBWZHbGLwao9FPYs+P/nfmTgOGSzazo3V8cllOdvfosJ4szzybvYNt70MwdG9uP4DaSk6fFyoRzEuWtp8pk23OVUvrvGtx/hWz79RGZfUc2JtMbVvOpKHvpKLltftCDwtFxqd3TInufrz7dXGOMALP57HSqKANjmgFfFf8vgJWs6PRkicnAexpuIeMn9W/9bofrxbvvbDDcgOqP1wYUqWZM/74aFRHpOtTLsuVle3A//5OW5l5reV/XCKR8dsa2v/e2vLt5vduOS1/3G9TeKlFvvxJIt2K05WTjCdmw7hXZtNFx5MJdQ+PyMoVzUWIzU4XPL4TD9N9zV1bzDN/du8HDrHCEvWPEHK7cakrGbCj/WCSLPs8QKmo3mMeGaDsf16UyIiV35Eju8iSXamq2NcrGp8pNVewvKGA+sGFIPwgYIT+xDVTh83imCt167gOSkotjZeW3i+Wav5bIhT+YJpnzaXwW+mOyE9r7EDJ36ITPT3PlxgZ55cHdsvOPVUL3sVce2i2HNxj9RboI/mnoqh/RK89A7SVhUSGSf0GybPl5BVwmjfacwN8/AHvaGjplyzMVMuNmu93kSuQblnSjZOD+MX5jHLGoWFMn7/3ycFD1OyeE9wrhH+ffoK96UuAyoC07oxnw5YFmj/h+skblydhmpGDYj53ogeVEfZ2h/FPp7Oyw97IHPnGIS/RnyY50svhbm9Jw4risWfWiHK2qsGYHbJq+7xvWvizlB/b22caIPiYNR25ZLcFtLX2eN9wHODeBHZjVr70odceqPao+GNGm4nJ7PlTjstLMc65GYpq5o1s7A7cgtZAfxGWfnyRxWa4d4Iw58bLoU3lQ/o1zLsff64yU//9QEfkYEMS42wWX9rx7rNXUlzXL+sfLpLvHOvs/HPu77Thb93HAHvLTlh+Im5+hUb8EngJoYGG7OZpyGXA2wOeUD7CzcoKsUS9TcAcTObK05AsFkoDVlYODg43nbtGn8iWhgHq/MQqwaJju9BjqeQyoaaholR1/qDTcxxp6FnyrRT5dWzx78aDgKBMq8TL5fWno8Bw1O9L/QRaH9VcAq4GdVP5rdzRJWkk8do05M+cxEeBiKCuheK9xJW8K3bZC0RGwifGgIc0PBOcAPQfQOHQWoKIMjHoGfPHx58eIQ68SHB4mQbD2xeVZR84944RuJqHHDgVMEGTG9D951UeN0QvnO+jLAm6WYwSjTfCTnzipWKZMKzE+VuaxQNrW1dbIO3BRMucr9NW2vnz8o9e92Ncpw55/ApOsX3/5X9LZ2eF13eywNh2pkZAIu+GQb3x+xK/w+mJj9wRa788LCQ+WxZg8a1O63N5tJtxtFnwy33AFgFXwKhTqAkyl2+05XmYWovwDQEjh5alG3G3n85uq2mTtV/ZLZ6vxId+A47+xlaEVGT/svkN+2soF0iYCjaHSQfQn7Th4W38FRtmxSWxv9qIEl1WXOaqUtzxR6vc1swjLUfEcDilHJQ8DVPryAcoBYDPA53wsSjZuago7/HSHaarkdAdjbsUfsb0Y4HPJ3xSfv9PlrxwPmvuxCVK9pQG7Rqfgn0wEsPD3JaGYuN3d2uOlxQ4AJ2u3sjvX26m+G+mJRk5PyHKONn0aqLTl6aaHAQ69fgVgpzBQ5Lcj3BD+aH4HvDrC7XBbvbeKfyyuwh+8IZ2NzTIuO11C0AHwRQLJP96M6d8xZZ7LrfSlCDsX5KRSujHNmbdEoqJNo4FzqZHZZ9t2bn/HozkWkW4s/iG1VRK+e9PINN5NrTXVldI5PsfNkYGzgmhFhMvPwZfXWQvzgzYF2GXNPEPTl+G+L6cVf9FD+ZI63ejn90tF9uIEOd2dJ29+t5zWwWtRmBr4v/o9ybOD9CGk4hWRd26yzLzF1cjQWtcpax4tFVofIVuBZwBzMtHNSC+hEtNXyE8cDzi58OlpmETZgYmTncZkytZ6brFvbLtMZcxQYAKu8b43KJin2kaPXK/S+7UyyrkWGLIcKvgbbRiySgLowsvYlpxlCXJodb3ZrH8jYfzAzAxs+fxtwZyHkraGLsPXHxN9U5DHjtl+IFClR/GPCJauDr6m0INrPiVh6AjYJApbjqoV8r3B3+J2jPaUv1LLAhcCvwJUehkgX4Gk9Pe2bORSHB5/P/DqyDWh75q9fYF+FpcyxvR4yZaqY4iQktH31UfZkb7cffpyfXF3e7REr3n9ReFCWIEg3V1dxhoEO7Zt9kjpZ5vddXSi3vyvBAXgxGxfOY5OTZLTLTRY2YVqxWP2vTM3cS5u/UZ698+9P08y5tl/7nZG6EpjnexoHshZmiTzP54Hzc3I4UvvEvOYj9s0nEcLW0z2wgSZc0+Oy2hax8lOeeOrpQgvaoz87ENZDslTUaNcB5xvjFp8xn3IT6NUAP6Jy440ohVxHkPR1Wky+7ZsWfhgvqz4WpFc/MNpAdhivzTpIK9yBD717p6vyvWGRZlFjHJMqAwJAwt41eSiWKnbY8xf449rbR81GflH1tVL1gK77hfoLjGG4h8SGYSwzj32AY4UhkDJtwmVtmKm0+fEGSuBF1xozAdj1mz+UXFg4LC5l7fCdd6VeexM2HJV74t/ZH8/B5b11/IP8Ebx54/hbsu5Mvvyi2Xy1JnWrBFLH0zNG3TdZkx/5wu5U4Sdy1j36X7ChbB27diCybM9Q4nW48OVbm4+KWuxpkLl4XKvqnSJ6gOFv69OkTcX9sf/yJv6+is7cVKRLLv9w85FaOkucM48g/YX4l5v4/2WfBSTZ6HIO8vh9fXyzw9vledv2yo12xudDxsTbufdk2vm34QELWS+SCJOMgwNaZhEvOCTnEfg+Lrqbj8l6x4rkwaEFoWwp/0tgEOsFHY6jJCfCx90H/LTKKV/AomBbWjMUbqWvPVUubSd6DEwd7Z0y5afHZTqrcbz1owy6wOp0WOsLRxhS45KCMPoktGZ5u29A5i/K+5b5V3sdNeVNktigX3aSWAoBdZWOqbDuUuDQFdHz/e5s60bFn/7+4UdA/IgCbaVfeMnRhnlkcUeAC3cKm4YKH+9zk3umZPF+T8bv1ce8Dcc6kULP4ay9i59SHi4XPnoZyQ+M106MEn3EBa3GkkpyyiQrNoKCR1EeM2+Yvq7KMIe3uj+0p1yvO6YnEXXnyj7S9HDswdXrProYdmCCdS+rKDsPKchvPQ9zMcY/AjG3pxiya0pH9yN+eHsTCwsN3X6HCmeMlte+d4zcrL6mHlV/h4+B9xqZpxB21m413uAoBkfwuTZC10nz1a902goZAxnyAHytV8vk2VfLMBK3bEONOWdl2xEANn8Y8Mwy94Vi7/iUKj/nXE4TEu/ET/ciByEhbqswjZs+FaZ1O42LJL82jwBGDvYrgDY6TBCfnIOgsqoYIDPyQ+AzyIka/ThjfXGAkvtiBvP/zeEIzk/Aqj8qwwNAyW8bBom7VdttnfsN1mqMn5Xln0m9wBTu7tPG+F9MSI4Efu0dgbq/6nH4h8OH38o/JTuDrTdUfFPZ/64DNo76X4WLLFYu4CTvCFpQDkTkBSAnPEBfRuwD0shfSaLu+dkKPn4rdPFh7t+Vs8O5a/q9gTqY9/LkOPXtDffXeoua2bJVZfI+KwMY4XXmbPny7yFy/26mq21Lk/S7eERUp6e70nRfsu4i+kfFhYGFwP7MGC/5zsfrD9+DAt+vSj0SR8O4ToJe3a9hxGH1T4p/YyiERZmGETszfWHtf9EzHipTjDepfbrDnciEguxlcw92+iI8T5D8X9dfudtzs24FhmOmqxzibG3X4Rb+gQQUnRVmhS/z9V9r3ZXk2x4Yr+pgL2Asmv50Vz71X1Ca5+zMAQgQ27ahB0pKuOeCK1pjwBZ8blRsuRzk6y+t8b5HEXb9PQhKCbGN5bK/jcA09S0AOnbWbCvkJ88phKwDBxAy74AvA1Vqru1toPPHP0xtgOPArQwqwwdA9N56aTiGDne4+ZDhfY9N9VRd1hqy+f/Ruqh8CQUGgauIOzynRKoYnzggqH+d9sGNbAQISz6bLYhPG4Md7ZghfKX7995euN3yyW6N5SxORQ6DeW+CdwM8B3HtKvFBJkqZwQD9iGyQL9bTxX/K3Ajk6w3c9GnqCf0Slp6lpxz3mVGVJtQhEwcCdmbM2XQ1Rox/d2sTOtsBfemIoad3LjhdSws9R787A3LlTene1yW9dDFiKvW+irOoxtBCN8Zuek1Xy9nP29vdjHS9herPX84ElTyC4umy4qVV0hWdp5DlefdfyciVxgfKzOfSv/95s4ZsM3DPT4EhOevxOTZm7Ndbrn+QLOs+/o+rtLLY6uA3wE/AdbTN3btl0vNaCvI6hWG3Jx9q135pzJuKgq9hRxT/OA+CEyMTetZLCx8XJhjCextfbZSDq429HxO0qClv9JWiErLvUDQtJvch/y0ldNNYDNwFM37LnAHwN8it48D7BSoDB0D/P1N5hydYLyrbYPn+5HXYqnSVPifRJ5pDNzJ4zU7mzD6R0O/IZPNRABueZ8SFgGLf2e30TwaMUIwAmATdAl6vBu62rvlxKHWoLrdJyUC7k824cQnFub9h5vRj5Dmt+M2QEUZCGgGPFX8+TG2S/6ieZI9Y6p930xQwZpUOFVWnH+l5OQ69BPMIkO6PZKcLU2R9hePz3VFr3/R5VxnhdilgAcZ+/ZulzfXvSqMpe9vaWiol7Wr/jvokQXnDg7nPQS3W9/73rf8FD4ipYbi7/25gz0jIzNHlq+8XIqmzJIQNx3SyNhYmXMN+7UO8lGHvbG7wyEYWtejc85OkJK77Uq6/Y4bjyBM5pf3S0dPvOu3cOAXtoPsBfwYeIvH1lD5RwfBWQqvSJWZHzY6E+z13Qksdi5j2+eH9D5gClcCXfYVrBDc+6G1n7IbCyiVPl/NfX6xnwLKuAPJAqgkIuRnmky91nXUgoVURhUDtKDVAm2jqtWjt7GFaHpo/IQoOXHQ/s53tiKZCn+a5TbZIevg3IxxGVFmNq8VqGIo/iFwHzzdo/f3uPrA598mtARFc5Df9Bxub+yWyHi+ogyJw1+69yRyMif9/zPmjsdaRsbxGchPNUrpH2UgQBmwP+n9tG8iji2xHl95/93WXZc0o+DMKlkoS5ZfJAmJKS7HhyrjdFCwXxRMxvSHad6hmZF9rN7rUMiDHcbSZ9Sf2hoatfwjXBNh3eqXpKWladAXdO7g+MPNpxIdsuYoGkOGT+LixsuiJStlzvxlEh3df90XPnyf4bJmad0EpK+07I/FJIerPwPEpZXEyfz7MXkWHXerNMPNYu1X7GEyt+HYjwDD7G8rx/QPgc1cAIchNW0TbW2HezaMSkMLPITK/z3AAu5YhPm0npUwljbnDcSkRloO9yTL/lcr235byR3+OFmvqZTwQ/wwEM0Y8DNvMerCrsoZzgCtQJMA9jwdH+4znJg+br+Y+akzxknNtpNmkZ1mwra1KvzmoS4k9ps7ti15t2vKTsdGepcWffj0Y1TD1hLD1SeCryFDGFgAcf3DpKORt4Y4poz60xvukx+UOcxnJCO6RNWXtUg63qM2mWUmsF0BsLPEEdJPASPr74oGqCgDnrwMPw6a7OUScrLlrKsv84i58eOT5OxlF0jJnMVC/+rhkNKsokFXY8b0t17IWSG2HvM23dHeJm+uf1X27t7qcYhNd3XQ15kr13IVZH+tiWC1+IfUHJbwPe+4q9qrvD1+cMHytMIwzPWYMWueLF1xsSQlu/tGuV4pfXKBFCxd5HyA1umxKvxCUelPTi6OlUWPTJJgp8mzjKiy5kv2MJl7UfY7QM9XsOfjxf37APr1fR/Y0gGrGM9pPNyKXUehBX7qdRnM5Nf1Y8Bc7tjkFmwXG7H2v1QocbA4Ogsme8rmnxw0s59F4i1zB9urgBRa3Nx1YCzlNOnIgIOPm+OhUb2XgNbz2aSy9RXgCYAdxYsAlb4ZMD6e4zG3puGQ8RumPXxf38UdjpRy72Rlq8RmGp12+sXkOpQInB1D8Q+Fq4+D2PV+4fMj4XGh0nHSNiSAfbsS1OPSM5llQkJ7XKIaMek3Ltv+3irgMcj5AN3U+OJjZ4EdAr53na0a7KBmA8ZIBLYqysCQMsCP9kByvbXAghuvse56lM7KmSjpGTmyr3SHMNLNUIa4PDEuUarHp0vaiaMeta2vQrR0Wxfz8jakZ1/Xtebv3b3NiPrDCafeCt2FNm98AwuGHfP21H7LW9csMGL391t64IPtoeF+mXQ9UE1BQUGSO3GyTC6eIeFQ/r2Vpbd/SErXrLeeRksNFWR7aAvrwVGcprL3CJDBYeqzP58PX1fLJw0HuIrlWsTGt63YSW37W0A7YAo/XKk2jMOWx78HfBKLaM1c/cVSOeerkyUuy/H7Nu0DmcZvf/dfq1khFTN2HvgBXWmuEJxUwG+go9Rsa5SNT5WbYw1/wdFXHEsY0TQuZLtDnO7FqdyZssv/8XiACkx/W/5QRiL6BaodMuE9U9lPZCQWumF0Yq2HpuoO/pY/BHA46JeAiiMD1IJtCis04B5TOK34HY7F+tyjcUBqMcE3GRODbe8OuvuU9XnGyB0wPhDBiOLDF5Fdte8d5Odvxli1uKPJtHU4NJbH03iyOWLgcLTH7TAeeTcyPx9rADDMYzs6EeAlGVnnAi8CrP4G4GJbmr2tZ4BNgLOwI9XpnKn7yoAvDPDB608uwsEsswBXPF1+123mrldb+lfTz5r+1vS7HkrZg7CRgxXnmP5WS/hgr209v/bYUVnz2gvWLI/SjBTkb6WfFds7OIzd72aug0eNsxQqyyyU7hBP+peWk7xMJqeky7IVl8r0mXN9UvpZ3dzrr5boRON9b9ZOrfUuc2eMbGlRehDIo1VuGazr4TH8nvQKY+OvfWwfhq4Ni99RHKG1tKW3hJEqt+xPRfqTtn0q8tvbsLosLf9NR11ds2d8MFsYOQhCRYPnXUFf2oUP5bldIbh+X7Osf7wMk/CMT+z/UP7vgLPscs44g/d/iXv/GcDO2GeBewAqIFQuFgJ8OfIf4H3vGCeNArkVbUzkSNYlP5kuK79VLBc/M0PO/my+GYf9PByfNQruY7ibmIcKI7hwHK32NtljJjzYGiMD9aUtktAbz5+d+kAU49kPYxQf9xqQYfHnCCJdGE2xKPkTkRcUkxwurccs/aLea9Eocg4QkYGwqK01nUbks/yViealltgSV2N7Kd5/weE98wOisM/R0AzbcW74vP4IeBb4HjAdcJYkZMwG0p0P6L4y4I6BgTSyO60ncVIvQ3gORuhvTb/r2mPVUv/f3w/mUn2eS2Vz8Y43/BrT35+uPs4Nb4frj7fiyzme1GHeZ/ieLRJaW+XJKf2W8UcnrK8K+CxNnTEHo0nZfRXxOJ/+7bOwIN2GXzs8kx/EBb7p8UUCuyB/67SyFxuTZ780SSLHOyr9XC3ViI2P6ByQ48A3gAbu9CWR8WECKz8ntD0APGXDw611HVNWfaFUVny90MVfn5GDTiHmd+nzNUaU3Lkfy5PMeQkuVRgTi7+23/CvxcENwG8AFuQ3uN924fiZKhG8cXbsIhNChQsxRSaE27bYT+rZf+njO8YiP7SyzuHoEdd+sD7ffL6mfaADEaEO875XAO8xoWJnYApT7DDV7mw2M3ebCcu2rxGikyhTBV/5jNDe6Dgjqfj/1tJmt8nQSLwSLdr86U67yT+WJ4THhkpzdbu7c43jUSnh5orhRplunM8JwzBScNhyGTPTZsbJu7+qMI53tXKtAGPtALpATQKuYMdjFiKfla86LmmIZFaxrp4v5RsBvkuXArcBhism3s8cLaCx5BHgGBACsOxFAHoxhryLv78A+P42hV0SdkZY5zoz04MtfyfXA3EelHUu0h//HLlYBfB9bvkPYM9VWPcnAD5L5j26lnLN6a9+szT/Mb8C9pgZfWzDkX8dwM6c65B0HyfZsgdqB5W/9QAVjxbbOUO+4QPRl1BROM968OybP2DdHVQ6OSVNpkNpGwrpCPN/TP+hsvgPxf0P5prmJObo9S8M5jLGufWxCVKTkDHo67i7AK38y1de5hel37z+invuMJPmltaViebOKN7yd34XUBIeh8mzj7oq43S/2/j9cjM2Pj/ijwP8uBQCmYBbYfQdXhNCK+p9AE1kTwJ7GYN9NZT/5hqLVQwHKLNvy5Fzv1ksFz49zVjttye39y86DtaJxVtx5BngbOD7wLeBSEClDwYu/uE0WfG1Iln4YD64xigLJljnLk/CxM04+CKPWeqM55Sx5K1Kv0kRra82yTETurUzUMwUV6o9vt/QP6gF77UfdU3wnULF1CpG+fbmLijNxjuBJu4Ua4FASodEwT+/i7fZI87rkRgWf4uPvxFSwCyMbUxyhMO7rQ3vrKhEqk2GZLATwEnBptTsPGld7PCjyA/NWZwglRsbjHDICZNizFEpKkb89tzMc4uvyZAJSxKMThl22bG/DaA7H69xMUYMgtjB4BwpCC3/XwP4rrwc+DLwLMB3Jkf/PBU+D/wg+qL0D1RHGAqcD1CRHkiuRYEiwBulf6Brmsf5HmAnqj8lhf9QlrkE8FbpxykDCl/G5wKfAdjBGBaxP6VuarsSeePMfMY6n/8B/g/8KPDLHiphTP+CytJBXd6M6d+dliNW3/dBXTTAT6bFP6i12S+x+/0x0bovuhKTUuUk3nj+lAmzZ0hqQb7U7CszL8sH9BbgS2bGKN3yHhbxw7DsC5g860bx2/LTCqlYW8/b4zg/3XsqgRuBywBqAvzI9H4lsUNh6D92JNbArx/D4vxgfQx4GuBIyaeh9Bes+eIeWf71IlibHd9rSVAy3EkHfLLfwMJgtg4DXQi+B/CDdidAhYND4l2AijJgZYCWRGOOijXTTFuUMKOcma9b4zdlKP7BYVCGe9zqDoIXdxZI/v6oVF4NpAFvAKbsQeKc2l1QcKfGGgot9jmSQANCwAmNElY57rQQYSjcbzpbehV3Z9s0R9Ta4dZoSuvxTmN0DfNJjKy4nCipL282D0v93hYpel+aVG8xBiuNYWp2tLb+6rBRpvy1WsldkShlL9Vy/yEgLKMkXhorWgwuU2fE9rz9TslMHKMBJIojCIxiVrGqXqbckCHVWG25emsje7jeKPko7iLsNMjU92fItBuM/rRLAV8zDq6qk43fK+fpy4HXmehHZvAYjUR9fS/6ObfPQ1wJnIuy4ZvHjtQ1wA/6KMzn3BglP/tz+ZIw0f03q49zB8zmqPY6zqer7shH4fcBfxjwJD8U4I+4L7nBeqBwySJjpVNrXiCn/R3T33SBCeR79kfb2MGJ3Py6BHdwBMp3Yez+nkW7fL/GSJw54+KVztVe4Zwxyvbfj/aeZ06eTXAzeXbbc4fNjw2/Yk8CBwB2/C8DKNGAi9JvHMEfvgx75gsYHbF5yOJHpx1gB6KMH8JV6BjQ938g4RyDdY+VmWFBj6D8t4BJwMcB6/tKFX8QouLAAJXVdk6k5GJSzrL/Bbv+udv52Bm+n4f7j+Kiec1V/NkasstMOG35frgLoNLvLMY5tdubJHWa3VA8zblQoO4zOIBVQkKCzLlFRrbpymOWCYXSbelMGu83utKZEp8fJY0HWs3dDs5TsqwOLJx83t3a6+nSeLhNYtMiTat/GO1aaWfFmR0oqdvTIsmTY82oSTR+yLQbM2TX749K7e4mowMRg9WFqahnzo+XPC7IiDVUfFTcjY7gpAv9P2CTMcf+bHjSoxjP+xzvJtIb830Vcj+9J8Q0L8GOVF+ynAcWPjjR70o/r8sAGPMfoM5viOEeZu4M5db6IbXWQ0vnudYMN4scWQ8HXNrfMf1DQkK86vgwjnwgyDgv2sEJ2IS/Yve3DHPsfn/wvfBD73e+DC0OGc6Zo2T/UrSz38mzu/9WJbv/Vs3b4VePlnUqRez9XO+gZiOjP2GHYgkmC9uGmxeiLJUD9h6/ARxklA9G+2GY0L6EVhhjjgE+YpA6gB0HKhgPAqEFl6Rio6IM9MkAH64XeHTD4/uE6z5wLQouLPf20+Xmas8s8x+WUbEzYCjndAPrJ36/WZi/x76kBgdqOSHW5v7HctMB6hPDLTehQm/g2j4n7aijoVPC4y1OEr3H+UwJXRsjMeHXlHHoSNms/9Tu32L+KUGvjzwAAEAASURBVJSkEYaSMg3zKRAFySYcLYEBpkYKL+tRtiddkmYaZHionmsN1O5tksJLUiQK9XChwqObT3COFY9XAF1lr9TK3n9WYySiC3M10Bn4zWHZ8QcO3notkTzD3SKKXl/J6QTLauw0KA0kBqFDEa0tNt24RdYf008jDEUueUpsP0UGdyipyF49R2qGRXofXcfqLsAu/fMMCY2IkDnXX2XujpqtP1aLtcb098bqf9a8JTJxEl3TRk5Y/8ySBR43IBJuPiHVFRJR+q7H5/RVcDhj9/fVBl/yc2bNEK5VYRGasT9k2R8tyRVo6AfY2L4mzxoLYj1nfBRozX8G2AIsBm4BZM6dudx4LByKXfqlAlP5PxsnfgSgu8DjQAXj+3ORr7ZG40OFrF7hHINNTx8y5xhQ82eHgVatTwERueckyazbs5BUUQb6ZeDvOPoWlc/NPz4oL35km7zyyd1S/hr7kUY4xB9ga/R0maFiMGBYPBMQhvN4qdHppqJKA4Avsp0ntR6Hv3uPEkzFKY95AS49I5p9aURoPN9bDopwb3eGL9EOrmBum9vgfKscuXyHmUfh5kNrPCUNlu9jWw23H/JN98iD7Cg0HmwzyjRXt5lrovB5fQD4C92Ntv7miCRPi5HaHU1Ss9X4fzXiGN+XjwL7OArB+Qq2kKqtyFsP/AR4GFBRBvq06V1p5SZ/4VyJiOI3eHTJCUwuPZqQPuhGmxZwc+KrJxdknP1pM+bK3AXnSFhYuCen+K1MEFYw5srJrL+7y3H4sr9KOIE5mqsWD1La/TS5epDN8Pn0aRee63zuBc4ZAb7P3t7tbGPJR3PcTp6teKPOuiDWr1CUH4cS4C4giEPE+RckI+mdJBXFyuLPF4htlctlOPs2gF+nx4AjXNmXoT7px2+Vrc9WmhZZ+ho8AdCV5zNALD+Ucz8+QZxXFsYxFWXAmQFTifoBDmwH6gEqTqsAPk+bAH9JEi50EfBBgJaxicBok0g0uIiaQDAM86d6Phf7kccOuy/yHk+qertRLC4dZ/lyoWE+x1DjQ0Itmn+vYm80pRVW9Cj49bsRau98xvCO6jnKib02LplRCpCXljpY+OOwQBrdqhor2swym3GMzymNL82VmxsM9x5O+oXwfchnmS/MfwD/o+W/YnU9Qi4bowUnkPdNgNsDwJeAe4FHgc8BfJ//EFgDVAIqykCfij8/2HaZesEKe3q0JfZmTxl0k82Y/t5Y/FtbjB+lEXVm2YpLJCExZdDt8OQC9NFfvHSl5OROMop3dTkqWP1dIwILX0X5I3Z/RsGQx+7v7z4Ge2z2FRc7X2IeMpw+A85FAmaf1ju++IOmwYex4GJX95iqdxp6JldRRRL5I/AqwB/K/UBI8TVpRhQYpH2SVEzsW9IbN/1cXORmgFaprwNV9MFe8+h+6WjueTb3vVCD0J7VOGS4Gz2FLT+CVNLGc0LbwofyDX9Y7KsoA54wcBqFNgAcafoY8EngZ0AV4C+5Ahf6DvAhgC+M64CvAR8HqEyPFpmBhobQd7yux9rPdhvKu483sBXnddIlJRlGAJt4PuxsnjG82x5tHmO7nNzsRo4zj3OUIi0+/JYuAjX0QywTglCmK58qlhXfmGy42jAPsgugAv9f7vBd19V2WsrhlgNhV+svTEB4jS8CrwE7gTW2/TJsKXyufw18FvgF8H2AbpAHAKuwE1AKlAM6FwokqDgyYHl27QcSkCq27yFRcuWl1t1RlS7LLJCuQUZ/Ce5ol6i3X8XiVp6/z1taaOTskajoGFm0ZKUUFE4zs4ZkGz8+UZYsv9ihk+GN4p9RWyF0bRqsDGXs/sG2zZPzp5yHUZooh/91HM5b6sm5I1xmMur/BBBSeGWaTL02w6U5tbuaZMMTZaal6d8o8C9gIsAPSBhXmeQiW4MV+guf/ZlJRlxrXOt8gFZRfiCp/FfTWrXmy/uFER62/LICWYb8BH/LgU8DqYx4sfjTGD2A9UxFGQggBqjovx9ms5AchFmceWs2/LJTTRe3hTjGjvdoERo1JGNeHNzsGs02v2sm3GxplWZn5yYbnIu0IWM7XVIYEcfm+pKFvMG/VJxr8t9+GC9Fpb2PQIPsMJ423JcSw41aqVJYLPpUtPfyAP3qGewgCmtnHNth8EnFfiuPQf4JbOto7Db98juxTz4PA6YcRYJKPd+TfB9aj2HXkIP4y87BWwD5VlEGvGLA3Rf1KlwBj3WPcMGutMJJ5u6o2/bE9B98+6PWvYCQnlEe379p8TdPoJtC8bTZsmDxuRIOq7y/JTMrF5b+8yUqynG+jDeKf86eTYNu1lDG7h904zy8ACc4TyiZ5VyaFr5Alglo3MNARN65yTL7FtfvLJXttQiTyaFiCD8cvwcygU8DUVRi6BrkL0mbHSeLPm231lNZuhGgNZ8ftZp6+KEaYd2M5hhWLw55PwJkxyMU3rIvTJKwaPurCNkqysCIMxCDFtC6L4uwRgLXSSi6Ik1m3451KbBKsE3RPQuHZ7JMgAsVXrbV8Mfn5FQIrdvOFmTmm3IXEk8CSwF3+gPLvck/DA+cvZB2RENYPlDF+CCH2SbdumkkrXj17MyYrjwMTdxab/DF4uSMnaXTlRvrjYhSW587YnYM+FE1rYBdSD8BcGTo+8ADwHpARRkYVgbc/XAvsLZgElbrHQrp7EC0heO1Q3Fpl2v6wwLNmP5xLTRYeiYtNlcf59IpqRlC158kLGDmLymaOks4mTgkpGfE0nrdrk4aFQaW8M52Sd67ZeCCA5Twx4TqAaowDh+rqRKiu5vvUv9L8QqX79Q5/q/Fb1dMx5U+A0RnL0qQOfe4Ku+MF7zmK/ZVcPlh/hWQYjsvlosbzb8vz+9+9BlnxcuiT+WZKsJlqG8RUAc8BmwH+BL4O/ACwFGHfPq/LkWEIEv0B2SrKAMBwcB0tCIidWasZGPxJaswNB9H2mwy10wE8HYW2haVkB+DBaRazWbSijyQ8CbNDoC7sm8js50hJpMRucYmfKEGai8+gm0MjQzqy6WQVnVa/SUyPlzm358nJXfnmuuMMJvvMGIVRwFWf26PHHydrzjDjeefTFjkNNK7APJcb8nXpDIwbAy4aoo9E/zsDSg+1z/6zin8IqjoH6tBzNljVXKi/rhMqC6TAntNQ5eoTM6WpsgYiW1rHlQl6ds3YKohdayBxerq41w6MjJKFi4+T/bt3S57dm3DYb4LvJdQWKZL5p4taemu1l3zap5a/POr9klIl92CYZ7u1daI3Z9V5NU5vhauP35MNq9/zVBUOX+CHark1HSJj0/EcK1bP02vqppx8fnywteftJ4zBTu8sG//LOuV/JtOxOWo9MfRwr7gASjviFFsFS6ExWg6DEcHeQ/4MTAO4HmJ/DgvehiW+SFyqcmc76Ag0TpGOQY8bqR6FIL7kZ4alRAmS7EgmDUetq2MbpSBQGDAeJjjJziOrJoNi5tgGI+5O97MC+DtMraNI32lL9aYzaRRwFNhB8CdtCOTiu2yxsp24ehdQ0VrPPbnA/iIBpwY/7QQLHDY3eHWkETF/zAwrQ1W/mKbC+UWRI2yyVHb9tfY8iNKaymt/H8C7IWQVlEGAoIBZ8WfP4B8a8umnGe8G6xZHqcbG09ILayytceOSl1tNayz6A6PgJgx/Uv20ZPAd0l6dzXWLLwe6l/QgBdpa20VhijsKxIJldPCohmSmJQmWzatFUYB8kaiY2Jl3oLlMi6O79O+xVPFf3IFjRCDkyMpOTLcsfvJMZ8tgtOhGEEpOSXd6ASkpGQIefJFcufOlvDoKOlosf9fOMTPYfHBPUS+NKbvc6i8fxpIZjSdRY+4Ku+Mm7/my6VGjGmU2wt8F4gAeF5aAhaZWfJZ+NFHOHYWcMy/0uPOw2vucXPhW5E3h24SVPot8ZXdFNUsZWBEGTCstI2HqAu6iiX/hOvRgMrhh6OEvupcgdbm5kPtf5+fWomPpSzjBNYp16TLlp9X8LIXAYGo+PN9KGFYkKvLtlKvMS2wV11pweEqlqnd2WM85HvVtrI4FX1T8adl5Tc2YKOiDAQmA86KP837xkQXNjc2OVGS83I9bnlra4uh5JvKfnu7+5ejxxf0Y0G6oAxW8Q87cUwy6w5LZXKOBy07LW3gYyDFMyk5VZade6n878W/eHDN3iJLzrlIwhGFZyDxxNVnfFO9pNeb766Brtj38UBYqbezs0OqKhEPHqBER8canYBkdAKS4V7lCWc8jx2z9OLJcugdGsjtci5SgaL4R6EtjwBZ8QgPtwTLifPDZRWuREml3xbP+SCOfQtgr/VhYEJcdmTPolsj60d/GdqygovaLPl8ocT7eYVGXFtFGfAnA3RPa6/e2hhxeD182C3uPnSnK8XiSTbZZCYCdMtvfXA6XPyqED7SJlTW/SW7caFDiIQzIRhaBjv1WFuhAHmFQKm/KvHTdQydJxjzds3FtUJjwxB1zG79p+K/AzhdvbUhqPlomxzuCbXJ6nmfvWYN5owN4ch2EL8hYTGO35XB3t4prGBsk96ulZnjujXa4Zo9+Bwu7mcT1tGXGPUzKEZCQbTfA02Qi/oyu3HRTkxfjfFXvjvF337tzGlT7Gl3CSqVtLQeg0Wfyn5TU6O7YgGRZ8b0H6yCWwTLuGeKP4L2ws9/IMWf5HiqjFqJ9PScri77y8t6ukO68DDfXYOTQI3dT5erQ+X7DPAOGfmIIwF0C6KLEFdk7ksmnDXLWfFf1FfZYc7HJ8rwh59If/hlbvzhO9tPydqv7ROGzoTQWvUEwDfdQ0Ahl3bnSruRcfZ+PrKHXeagxhtZ63y4KFlWMBz2hmiFyoCHDNDk+2fggxu+XSY5GxIkqTBWmo+1S/mrdcLFkyBbgK1MBKjwpXc+28Y5QZt/ZBhJqOC8wTw/yn9xrY9yocD8C1Nl918No/mVyHvSj3X47VLw8Be6+1DCoexyETib8H/OEZzN8Fie+9IDu6W7zX7sJbPQGNsewP3k/+OD7w7lbVV4cHFaJDP+fPWQ2tv299MOdvRnvP5ZdwPV/Zzl2yH4LAyPOCv+JdZqJ86jZ0Ov0K3iRH2tYdWnrz7Tp0/311nqPXe4U8FQ6BKh2NGifuTwQWk62SCM6T9YxX9iVZmsndEhnaHUvfqXViOkZ1r/hYb46ECuPkGnT4k/FP/9ltj9tLJnZE2Q43XHAu4ZaThxXIh9pTvgCx8iSUmpNtegDImLG+8wP6Dw7AWy9uccubXLNHtq5BL8Mt0HTGFkiWVfgfIOv3ir0IrAkJ2cXAepAx4HaNb7CDCDH7UlXyyUGMvy8sgfCTmHlYbHhVijf4xEO4a7zlhUaPxzhrtirc8vDPwHVwmDnfdaRK4JYfQai7yF9E8t+4GYnI9GJcbB974ZK8V291hg2Vnhu8Kfsh4Xez8smvGFl6cZ1nREFKOOkQeUA4EixuQnRjsLj+1RiSLjQqWj0W40O2lr6LPYJkLpz8eWmv9fgSHVjHH9kZIfouJbAI7SRAH+FPLN3uYvPbjor1HmFoCKFEer/Sn8v3Ik5w/9XPRpHLsGmA0kAo4fW2QMUviQcd4bezb/GOS1PD7dWfEvtJ6ZO2e2nITCXAsl/xgm5Bp++h5YkK3XGM40rbn07+ZET6s1dxLi5x88UCrlUHK7dqyRUEsAXm/bF3qqS/Ir98meCVMHPLWvyD4DnujHAgO5+mTVHh70pGc2d2/OFCOqUEHRNMmfxDT1U6weYh8VqpKTB/cZeYHy5xTmnJjRgWTHFmPkxXx+uJ20iN9HB5mAPb58Rqq3y7rvBEo4dL7siwUSkxqJ3V5h55whMquxNDyEQ3BU+s0PehwzuzpOCyOQBIA8hzbMYVzrMSacD5JiQbJTmh/SmwCVwTEwkr/Ff6Hp64B5AP/X7MhRCaSlNJCFnF3FBk66MFl2/ZUGVUPYmfFEnkEh3rcnbglU8F4Ebix7CVb/i1NMV6jrkfdNIFCkmQ1pg6KfnBFhtClyfJhYXEGMlykOsIf3BSAeaAXsviJIjzXhg/ENL27qt05l/fV+24brPuh0bXe7Q1U/nw1a/xwsgO4aYMsbqnb0U6X3h6yKfzBOz+YlghAtJq1kitQEN0nlq//2/qojcAaj23TPWeG2Zk6wnTipSLJy8qSm9C3J3MvOle9Cdx9PFP8ei7/v9fjjzM4BVu71x6Rexu4Pn7lIVkwrEUYsskpoWJikZWQbCJ4wEUuYfN96OKDSHViorfLIQQNsWGxsnGQunI3l57fJ6Z6J6dSWpwA7eXwE5GbUeXYYhqNpsY9z4w+/5ccVUrHOsEDyw/QEUGVp53eR/o3Fx9JyaESSx0ak1qGt9Oe4vOOPYGjrO9OuTkX7EiAfoBJ7EKC7xVpguIUdarqzjCaZj8ZmR9lG+7gaLYQcevpOuwtlrwb+DnjSAXgF5S7H6GNsPjoafHfBHWoW8vge3QUEghiRxlrBRTR4YVS0qJRwqdtjH5Q74dRIsyPglK27ysDoYIDKvinTkYgIGxctRe+/SDIWzcZaz5506s3TR3YbGho2YAPoFx9x6YcHLDdQgfT6Kolrdn4XuJ4VCBb/7n4U//CONsk7WubacC9zOpZeLrPnLHZR+r28TMAV55yV7OXzZfK1F0ooIvzYhIrHSMh1qPR8rmK7+DP58CumUdlRtv76sJT1LAPPr/m3gHLHEsbwtFOW7vqZAeNBic+Lksx58VJwSaqxsisjLq3EAk8qg2LgAzj7E8BkgEYrDiuyA3A38FFApX8GyBmt7VJ8VZrs/Ve1WfqfZsLDbRrKsQPgia9+G8o9z+uWPl8tk3vXOfggsqz6B4uMlLSg4tZuzM+YdEmKXPOXEplxUyYW6DI6RRyONCwpI9U4rVcZ8DcDVov/XIapnHjhUomIG4eZ3NH+risgrtc+ZY50J6RKSH3NoNozuWK3bCpe2O81nFfv7bfwEB3sz+I/CbH7B+P2xCYzVOrpc+kCNzYlLCZKIhPjJe+iJbLvby/zJmmtGm6hhfMqhpib/1CepM4wPHYc2rD7b1Wy5x/Gh5wfKlr2h2U2kkMjdMfOwAXfmWpPa8IvDNBSfSmjrsy8JUtyz0mCZTZIKhBZ592fVdCKzPki+4DX/FLb2LzIStxWOqN5cWqeLRzlYeRt9PF22QHwRP6HQhfC1z8x/4Jkc5XgPOQtBwLl/8WR0fzGg61CN5/GCg6YGsKX6ilbWjfKwJhgwNrjnhyfn40hLs5fwAyGaHo1jEGB9tSy6OJB39hkRsIZYGIzw5vWYwL0SAnr7u5nToY/3Hzap86TU+hIjVUxLf0xackSn5/D25w0zPdKheYm1jn3Y3mS7bgYltGUfS/VyLbnKpnG51x+BGwHLgPOBVSUgbHAwKW8iZm3ZUnBxan4PoUYa0/krUjC7yLXvD+jjLmjWwcG+GG/ljnFiKu/88/G+4K7fwb43hhKoS/8n1jBzj8elek3ZJh13YhEgrkzwtv9rL96W6PRDDNeP3bKjQz9owyMIQasin9u3IRM+62FREbY02Mt0brookHfUmxbkxHTv/8LnZZ1q1+S97a8KcO5pgHrYp2suy9JOFknaSfsQ719FRswv+XskfnWMiLPcEhoZLi9mrg84/eRZc8Y+gStnB9hNSV35Eju8iSXGg++USdbflph5v8SibcBukPwo3o70HsD2FFRBkYhA/xOYXU6kYnLk12an7kw3vAdx4F0IMalgGaQgduAqMz58Ygb3oKINRwYNPz6NzExDLIWdZTSfeYErOqZWD8AEg3cykQAyDtsAychV+CdWvqC/dv4bgC0TZugDPiVAavinxNqsfKHDpHiz2gvKamZMnX6WTJt5si4S3dl5El7wcxBE8lJvp5IxcH98vor/5ID+/dgkGDoRg15bdbBulhnf1J4eE9/hz06dip6nLSVLPOorL8LTSqcKmcvu1CKpszE6sepDmE4/VmXtQMc1uPnT+ViOGQ6KvkYEDTthkwpuNR1VKXq7QbZ9L1ycyD6Dyj7OnAnUAKYQmubijIw2hkI4lReeBa6CIM3BPXaAdyUcDnlTMugi08Jw/jmYoSk9IUa3j+t/M8x4aVw9NEKT09nfc8Cp1l/7rlJZmdtDvJWACMtHCXdx9j9bz5VbrpBUfunIUVFGRhTDIRa7ia9q6XNvhtisXTaM31KBMl4htnEgklcPTUxKVmCjfWwMZO42Ywy6NOFB3VS6+JLJGLf1kFdw5uY/gxruWPbJjmEkJbTZ87F+gKeukd61kSGWt2+dZOcbDwx4AlBCPnoD8W/dd558AkbmZEhagEJickGCotmCBcqIwe1CDvLNSa4boM/xGrx72pt5yVdTY7+qMjxGiT1PiCk8PJUmfr+DMej2KvZ3igbniwTW2RaTp4jbgGMqD+2hYSwq6IMjHoGaC2pwNT0CUferJecpY4jX9XvNZqLLR1HuZOj/m79ewN5uBwn0sqs23Nk5++qTEPBv5F1iPk+CjtYZwNveHF+Oco+D4/5K3b8vhJzNbJl848ZUEg+DJQCnG8wUsJn7JvAlUA2UAtw0rMaTkCCythiwKr4p52sOCqJxfnGHVoVHm9vmQs4UdHnCqlJKWk+rUzrbZ3elm+Zs1zifveUBHf5/rv2Jqa/2T4q5hvWviKZWbkyBaMeUVEc7fRdOI9g1/Z37CEoPblSdm2FxLQ3e1K03zJHihdIDOY5BGFS+EhLKEPQpmcZYFva2lqNGP1cUboWK0v76moVjOsGIbzb6e5T0nT4KC9NpZw+P3YnWWb6Wfi7NCbZhGMhGWep39cs6x8rEy44A3kVoLX/euB8Tn5k1J/VX+R3VEUZGDMM/A93csc7P6mQkMhQI2IS76wGSj/XrbAJy6j0MkC//oeAMIbSZHjKhp5Jq9D+jcWnekt6njIV/qtxCq1X3ij+rOVvwJzGw21ZdaXNkgfLf/lrdXRHfBD4AtAEjJTwo/i7kapc61UGhosBU6vgNubE/kOSNmeaRCbFY5U9z12Dw8LCYc1Pg7KfYSj70TGxw9V+r+vpgP/7IbjBlB/YK4vS8qTwyF6vr2E9wdOY/tZzmGa8+OqjR6SwaLrkFxQ7Hx5w/xRMvWX7dkvpnu3S3d01YHlrAX9M6mXs/lVHjuCheV7y8oske0K+hCFmf6AI1xPIQZsISiM6XOwEcDTgeF01ODN8XD1qbmhEhDRV1Uh9ablZPgeJoVT8+QH6BfCRHb+tDOLw82xYxyj4YMqar5Yyigl3NwDPApxocSUH0hY+6D7qD46rKAOjmYFVaPz0jubuhese24cVVvGwo0Pe0dBp3hOHb180d3QrceDgESAheVqsJCD87+YfGNZ1EvY0YCcOaW/kSRQezHC1Wf9Xy1+pDZtzd640HGoTGDNScd0HgCeADkBFGVAGhogBU/Hnjy6IUWoO/PcNmXzNBf1WR59KroxrWvW5Ym4gWH37a/SJE3VSXrZXKg+XC1c3pezNnjJoxd+M6d8YM76/6t0eo8K+e+e7A/rjuzt59asvSHOz96PaER2tkldd5u6SXuXtze7prLANdGHifVD5z8ufLOPGGRO3vLreUBeOixsvRH7BFPz/u6X+eK1tROCo8NnoT7h4V/l/18jpU/bgF/y9DLWsRgX0vbu39J/VIZ0nu2XKdWmy5tFSc2IeJ509AywDPgAYUX8y3UT94TEVZWCUM8Af3w+AUuBidIaTBb4/EPo20tL/b8DIwPZMlwQQQKU/Oz4nSgovS5WN8Fu3yW+wNXoAZoaX28Eo/WZVFUj8Grjj3V9UyPz78+TdXx6W1roOflTuA74LeGfNwgkqQ8LAHFz1OiATQG/bY/mtm5L8DXOCyR+Bt9wc7y9rKQ7eAHiqaLmr37z+MSS+DNSbGV5s2YaLAVN3HujUvtrBd9Uq4JcDXWAojpuNTzcv3tFwUg6//Kace+9H5AiU5Ha4TFDGQWlKToH7Dqz6SZhMGQIXiEAXKvhVsKwfgMJ/wk1YzSPJ2dIUGSuM0DMY8SSmf3/X90WB9+UctmFS5T4JsXV8+mtTf8dOoY9Yml3kUISdmIMYRSH4nLADkJaeHZAdQs4x4RwLY57FVJiXsGJv3bFqOQaXII4KtLT0PA9cFC4zO1d2Pv0HaTveaL3f4VD8WR9fjvwBPlD+Wm14xdrjpnvPbuR9D+BL+Q6gz6g/PKaiDIwRBqg4/NcGWhfodkLF394jR/pMl1wQ8BCQGAelfwbWPNj4nQPS3WkYu15C/msBQtDraEcu3BXPZ1SykrtyZPMPD3KuRgnyHwSo/BuTqrBVGTkG7kXVdG/1hwThIuw43gl4q/jfjHOiAH9ICi7i6z1dhHP9ofyyE3UuMKKKv0MvPhyuDYy6QzAOfFBwkH1CLhoa8EL/7oMHSuVQeWn/vt3wTafl+qx9mwZ1T4zpv6loAcZM+FwHtvjDzedISo60oMPUl9CnnoiKjpG8iZMlJ3dSQM7zMNvPFZ0zsiYYYB47Aqdg5Y+IjMS/NFhW4T6cJNlpfyh36cLwGPAwPpJsyAHg2wCtY3wpB037gPuoPzimogyMVQYaxuqN+Xhf/PicD3D0Lyy5OFaKr003lH66CkI2Av/HRADJc2hLWltD58x3f3FY5tybK1ueqRDuI/+LwFNA/8OxKKAypAwYCvL7/sD+GCaUfXq3NJTTFuW5MJpU9pIE4Xfq+Zv5OfNJ6TaU/st/NdOYEH50c4MZ2MKzhsBEkIdQwDCgmeWPmgkvt2Esf+43io3gGq21HV6dHh4fJgsfyDNG7nHiiCmMZs+FPSC7RMbH2dOjwbJvNvZ4XY3hzlNVeQheS6fN7H63tFwPVvHniME5SeNlU/spn9xv+m2gHw+mt52U1AaOtA1O9uRM8egCXLl4144tsmfXVsnKyZMCRHSyDy15dIWRKcSOgFViElxcl5Ksx4chTfeGR4A8YIdt+wC2IYVXpsnU61yj/uCYijKgDJwZDOTjNj8MFPJ2uTpu8pRY2fBNewAAKv0/BE7xeAAJeyS07H8aCtTkd39+2LD8czHCpsq2POQ/DtAi+iagMoIMhEQES/PRNq+VfjYZ83KM9RE4P22wsv4bZcYkda+vgyffovR7fbrzCZswOuWt0s9rcE7SO73r7jhfdtj2TcU/2lpjeFSkdXdUpHcglOXuAwe9bmsDJqkeTUiX9HpfO4A9Vebs3SSxt39RKg4dkL27t0obou0EilCRLZg8TWZufnnQTWpD+M6DaRO9ug596rmuQN2erT1fJq/OHvnCYVEuI4wuGcPQSvojErnAw0B43spk+6Rf7KsEEAN/vnrzoFoz0uebjR9sO8zr6NbvDPDbPQuglX8Grx6VECYzPpwl9ftbrJGOVuEQlWfD7I/tYOWmwV7A6Xy683wLeJA+/pyAPPujOVKxpl6qNjdwhPPjwArgLwANICojxEBUari1Zm+eA1qmnqzdMTiXalbOyFQ2uRtbB/9b80Af29/2ke9TdmNPdCye+yHA0w51EMr+Hzq1PG9ExVT8Hf6joQEUncVTdgy/7HEOAxeenip7YcEerOIf+c4qCf7gwzIBbi3ZsG7T1ah07/+z9x3wcRTX/2/vTr3YsiR3W83dkm3AuGCaQ42poSQEkpAQQvLLPwUCuKThVNsQWkIntEBIAqGG3mzANgYbN0kusq1mWe5Nvdzd/r9vpT3v7e3d7d7eSSd7Rp/R7byZeTPz3dndNzNv3pQTWxHqLcc66ryZla0GwSglpT3Eqp/2XOWQ0eRxqt3GHq++ktsJq1U6F0DQxccqyAsm8+FTh8/MolOgFyucQEAgcFwjwM88v3B5GXIAPIfHwI+DVybsElKcVPTVHOpfmEZlzyuz5YhSBP3n8fsOB+Lc8SzZEvgfY3b4VDbPOvbSQTT4pEwq/3c96/0XI449z+ytgd8Bz5Mg1vQskEG4yBFgoy4Rut0R5guVzYrQH4qP3TizQj+XY04NxW6NTORXJTg/3QZHHxT8TbQ1aJLKIaPotLJPyNV9GlLQhCEiHNALT1n9IbWccamyH6KgaBx020dhY/EWqty2mTo7e+4d5cDpyAUwscmn26pqK0kblpOz4VCIFpiLqhjB35sTy7kSFbU+baN7Q/Bn9aIF8JmD8EGcDj1BB8wZChd3CFiZCTOqfG/nV+tktx4qH/FrD4G7g2Xvl59CeWdmU2qOiyo/OEBbXt6rJt2Fi4fheT9QtJ1+5jRa/YQ/kPfDX4b506u2vrpXyhyeTFNw6FhDXTtURfbxAIBXO9kLJxAQCNhAQBX8/QQZA0HHRhHxn7UD6itVQ4psm/ZMWfGmIvirLeZDpUaPKab8/DG0Y/smqtqxxZL9eJWP2V/eiDoyf5RyNgDbsde6VNTNrjuUPoD2QS3qRHMJSX6PBzc/YCQQY0x40w0L/Tm8aW/mvCJyJAihP8aYC/YxQMCJftttYYbVOJpjUERfZTkRFW8MVnm2w5/S30Vpg5OJBWJnokSsbsACcdNe36QSz5y/Cv8ufF80h8kzolz/cvgfQid8CM/+ZxWm0MRrhpIr1UlHqlroaE0L7dvoU/lAUuEEAgIBKwgYCv59aUOvlcaGShsNm/5J2zeScy9Olh/kr4KRgMPQxk2YopzWy6f2xmL2n5fhps2crZjS1LfT0XiYkjHjb9fVj5tql0WfzO9MUB8TX/UDRgK+mNhc3AC2Q/jQolm/xkFp2GglnECgLyKQU5xBe9cpBnke64v1j3Gdgw6EsgpSqO1IJwTeBqp8Z786eFKrw0u578F/BB+Uh5q4D/xuQx3nw58Lf9nhytbMw5U7FeOt/UamUGZectAm8Mnl3Sea61cmguY5ASJ4QFUL/xz8pjDtPQXxP4L32/dpkEfFl/sbry6t604zDL83ww/tDgf7UfN3IsH/4F/SJOQPHE90TdDQ9Jdqfqazug2rgP0dXu3/c3D9DfiAjzdo7LT5OXwAnlecKjkAx9/4a+DPhvfTiEFY67R8eDTKz+Fr8Fyni+AvhO8PH8xp8zMWy+H5PrUFyxANuipBdGiZsQnPE82pNv3ttjt15VsBLNg8JFu3Wf7JuzER+rlAPrPg85UfUen6LwI2Fqd88T5JFk/31TeCbfev7x/uWdbnOj7CHrdH3xB+QHvSVXBhbJYvMS2hJ8sVZQVBgE9J7nbhPpBquhPtdzganKFv9JTvD6eUnJ4eN+trEbdhXgVRnKZ/KeHK9w5Q/RdHMdvdykI/C3KQhBUh44/4/Tk8C0+q0IPLPu9YCHkH/mfwj8CXQpTysCnJnR+zer+xK7luGCXAfKRwfgjwplJWkWKBPJy7FgmsvNO4z3Ie1X0fF1YEBf6gsXCsdbyXJZTQr03L1yzHToP/AQe63SX4DSb0q2m0vzkIfE9DuAnXF8CHEvo1yZXLdPy/Ap4xuAGeBw6hhH5E+znGYjY854+pU4Hp0Jbi7uhpuUZbei9dR8mmf8pnb1Pj5egz4Od2d0K9Zyvt2LZJuY51y9iEaQ3OLthZW6kcoMWWfFjHP2VF4GDEal3C2e63yq8vpfd0+D0eXPWefkD4Bl7XlzA73uuaW5JJe9cr+8seP97baqN9PIvGQqokrANZQ3HkWdkwP3gwWCYW5HhZmf35wRL1EP2fPVSOUTFK39JGjL50ILEX7hgCXhze9tLXlQl538DyWGzA1SCmXPnfkwz3kF39Ci8IdDmvB3yvUvgOUWn4Hc3XbPefTYCGc93vBf1Ao2tkh+xXv3SsvGC8YA2K3rixlKO1iVk9lq58Ce0IsymZVQ9f7sInn/N0uxn8e/79E4hXmcy4fZua6ONfbeWks+D5GaUz7xhNg6YoVeFgSNewq43e/Uk5p+GyHwyZ2GakemfatXy8nT0t12hL771r/Wm0kdTEdWgvucq/oMrtW+ij916DDfsNPSL0a+vK5jMrt29G+a9S/cdvUGKt0hm1SSxfm7Xdb5lxH8jQ0RYg+Ps9Lz3QBPU5tVtUvPFRXo52G9Ub+U+GycH0QWLmOgz2PIv2PnxrmHQiuksn/wMViCk/GEEjZmV1zWWqRPGrR4DfHyz80+Htx9Nih76Z9sIsGHc7BSs1EORXeSebMRyhSaN9jyvfGDNCf5Dymdy1xM7KMiZcSrbvPRzwfQsn9DN73nfU7XwXCCttMiv0c/6BE3jCX3G85KTwMiv0c67MYT4VNm09FIbR/mc8498HBf9+/bNtY9Nl038ITHvutsWr6eXHaNOkr9jiEY3MbqhsJS5/wzYrtt1fPajQNp++ysATaJHJ9ybtoTZNVcuJYOaUHwx16pBnIhQXAR9W22jszh6t+kzs5kcR1GcI8qoPapENPtyxVb1OlU3Q3xev/NK81eagXE6oiGfQWvbChUeAZ2TP5WSvfnN9+NQiBSOwEn7WB7dvEWiER+CL8ElEihMBAXVk4Tcj09nW1ufaPmZcCc0+71JiM5p2ziGIxsz2yLoKSnD3tGwYeMscmPkfvasiMMIihW33e2EiNFLH5kVHwrTp9FnnRMqiV/N1tvo9HlyXAEKMK7gP/FsiKGMX8qjCOmfnJdRIVitYMNZOqe1HOJL61CGfvj5NoFl1jIfWjjO3q2t52BqnI0iu7DQ1ka3rQTI5C2WC34mQxP7L50RA6VgbeeoykufqGIcT66oGzX0M/k34jhOr6ZZayzP9q+AZK+EEAr7ND/wh9bnWo13fZg82hLa0NJMTO41SUtOgtq6sfvjSxdtFWloGTSw5hcaNn0x1dVVUXVlBjQ38bTfv2KznLMWmf+QbnF1eNxXWb6etIyeYLzgGKUfsq6GUDvsyaqS2+1NT0ymvYDTOMyhS9ho4jrDKb/w7j8dDMjZLqwPI5sMBsmEkQqadhlcj8w/sMOjOW4bfG6LApwo8olEfHpj8MAr1YasmP4kCn1Asfo9IXstlwSxgt3eojCdoXCrabf/lc2KBx++VH8Nz/xJDzND3PkGD0/O4Zi+cQEAgYAIBVdXHT/D3QHBdu3o57a7fSbLc9f7hTaI5uYMpd+AQ5ZcHAvHq2BxpXv5oxR88sBeHaG2lvbvr0JbwKm5dNv0Lbc+Uj925udcFf66DXReJ7X7uJwVFY2ngoGFxP1hkfFgl6tDBvbR/3x46sH+Pb7CYlJSsmGBtawmYhOMZb+FOLAT45aFdrTixWm+9tQEPjXUWJ2SOE3ODnfVbLXCyjtlxmYMtGsbK8QZmzV6GkMV42gPrwTSz+x24rJ5yquDvO/IvOSeLhp0zg+p38SraMccmKZmm0tPSMyg3F4MADASycwZRQpye9st1Y9/a2kI1VRVUW72duC2hHKv72FWR4X0Cmc1HqCEtvDWntPRMam7Sai6Eql1XXGa/LGo4GnziOaW9hUZixt+u2zZ8nCkWfFjZ8JGFsCY0ltLRnnh2PJg9cvgQhPzdirB/+NAB3wBXW+/29jZl0Jg1dSwlb95CbQd9q0d+A2VtHnEtEBAICAQEAgKBPooAq0wlWtxzpRWo+DrJYn49VL5ZZYt8tCuMPDBMsJhf2w7Wd0/utlqkr1+4sFqPlJevWRcurVF8zAe1WsFflpxOqeDC00lyqar/RnXqojU3NUJYbaRqCNOsAtQ/K8e3GtA/KzusCaXgnGMTk5KSqhyiNXpsCe3GAIZXAY4eYQ2BQFefPZyaktMpvS0S9eNj/Mbs3EJrxrFlJmPHKxNjUB+eHX/r9X8bJwpCPePsr2IQs422bNpgeDZAEXT7Hd2rNUFYhCWz7f5tw8eETMdCfn7hGEXod7l49TU+HffV/RD0D+yDxyqQ28IGdjwXVHDRWbT1X2+St1NRAROCf3zeZlErgYBAQCAgEIgcgTeQ9SJ4s/brWVj+n6a4l3B9GbxPeNfEGV3ySupnuggWfHfCs7laM4558Kzcq5rEbCHrXHizQgmvUL6uyf84rq+CHwxvVsedVfTY4ARjwHW6An4ovCpn4zKk4yl/ns3VtiNkhkgj1Qox0M1Zo/PSEzOgxooqs+1yJ06cNeNYhebwof2Kr9iC02sh0ObksFrQYKgFDaH0jPiZAXZCiOOZafY801uNAUD9rlr/Gd8o2fQfUwfBf+x0dJvAfjNseD6NLz6ZkpNTTKkg6e8DD7byCsbQkGF5EP7XKysZ2jRj6+yr+dTljqAWDICM3KDBw5TZfVb9ikfXgdl6VtvZD38AKjytrdq9qdZqzM9CYloq5U4eR3vXsJo8sW66cAIBgYBAQCAgEDieEGChlX2kjjdas7fjeNVhvh0GyPtct4+UDW+GZm/HrbaTOZZ5VcGfy9ifNmygT8rzwHa5WcFfX0E++XfvnjrFc1wyZttzoffNakGs/8260/HgsgbkEPsJ2BDMs+c1Vduora1rlYZt+p+8fY2tavKKwdCDdVSfc2zgyio6xZOm0oDsgbZ4q5l578WkKdOV/QxlG1crg5mcI3spu+GgmiTi3wqoPGldQkKislE3HwOO1DRfV9Em6bVr3pB76OC+LmEfs/qh1KCsVNKLU3vZs8scOZQFf3U2wgobkVYgIBAQCAgEBAICAYFAryOgFfzrXUlJBWqN3BD8E6M0Ud8G/Xo+TZY9OxZ+eQBQBB31bLXAXvzlgQirABWNnkgb162iup1VFC2b/rzBlgV/FprHwtpQXsEoLACEV6WyCke//gPotDPOV+qe+c+7rWYPSK+33T8UKxSTT5pOTqe2ywRk6zGCjGUpVtXaz6o7mNVnoT8Wm3w87Tz50OVcKcrq5341LH4FAgIBgYBAQCAgEBAI9CUEtFJcfWfzMUMMnnbtPofoNolnY9m791aRb6QR3SIsc2Ozn+WlXypCpJqZN/naPcyrYHclVc8ZTqMxK58Y45UOVv8ZMWQ4DdqzQ21CxL+VQ/1t99fXVZPH3amsjrDZ1N52O7ZtotVyasyr4W479hx0tiirQazDJ5xAQCAgEBAICAQEAgKBPoeAduq5+mjVMdVlnvE/ERxb+CnbsJo+WfqWn9DPbWeb/m6HdmxkHRG26X9qx9GYC/1qzZI3riRnc4DdeTXa9O/W4f5qPpxx755dtOyDN2hz+TpLm2NNF2ohoReqPT3hPBrB/2i18nzU90S5ogyBgEBAICAQEAgIBAQC0UZAK/hXNNbWU+OuLsuenc1duu7RLjBe+LFJRz7ga+n7ryuWiYxs/Ks2/e3WOWVF6L0u0TwYLXVl6LLMtOVQxgDanzXIMCnjxrPtSz94nXbW7IhoY7Ih4zglqs9BR2MzHSzbxrXs0leL0/qKagkEBAICAYGAQEAgIBAIhoBW8P+SE9W8t5xa9h0kd5daQ7B8fZrOVl4++egt4s2wnZ2hVzZY3ceuS9oOS0d72TpVbB2fjJtUqreMZb3MbcPGhc3ENu43YD/E8o/fUaw5hc3QRxOweg/7qrc+Vk15buijTRHVFggIBAQCAgGBgEDgBEdAK/izQNPJ1ny2vfw+1XywklKTYq9DHS38+YCucK65uZFWf/4xrVr5ITU2mlOHUW36h+MdLj515VvhktiOT/n8PZK89lRgvNgnwBaNzDreYLvik/do3ZoVyiFpZvP1hXQpKWm0e+V62O9/i9oO+fqLPVNPfaHhoo4CAYGAQEAgIBAQCByXCGgV2PnwAJ6WLoT+Bh0s305ZHUl0+pw50H3fC8+HH+2hlhZ7h1rFCsWyDV/QviNNirUgNhvK5kOTYCOfnRubUrdtLaOqHVusW36BIFyB02vtmvZM+extarz8JkOb/tHCJDWMSpGZcupggagl2ezZG8c47sLm3z27d9KoMcVUOGo8rP84lchOHJR1EAdmcf9prNlOVx7LEndXfABZdu4gn+nZ9kMN9OLHuGfHHO/0VQz5HyOJK4GAQEAgIBAQCAgEBAJ9AwGt4M813g5fqFa9Zs06OumyOTR02EjFM72luan7BFQcjAQziuFUZVRePfHLNvjZFCd7dhmZ/WnAgFxFIGXVlEhdNGz6uw7tpcQta6hj/KmRViNkvoTqzZRQb1/9XG+7P2Shuki2pb918waqhYA/FAeLsYnNI4cP+vYBpLY163L0bpD3VmShf6gHzfXPGuBnanXTG+/rK1gHAp/IJ5xAQCAgEBAICAQEAgKBPoeAXvBndZ/z1VZUr16nXvp++eCmvLTRyoFRvCGWVT2UE1JhT51P742FLXVf4RYv2EQne7uObfrvHjCEhhyyZ8mRZ+RjJfhHY7a/LSGZqgf5xn0Rw9ba0qxsAI6YQQwzZmT0w0FyXSdKZ+cMIhdOmQ7mtq/4Qh9VrieIsEBAICAQEAgIBAQCAoG+goBe6vkYFb9drfyu8k3qpeEvz5j2z8pW/KgxE8njcWOWd7/vUKVonZ5qWHgPEytg3tKu4J+8dhlJmPWWdao0kaxGsBlSPrVXcZ3tlPJFwOy0ZYT2jJ5CUhJ44uTl48UlQ92LD4tTT43msFlXu3a9PqndI7z1/ERYICAQEAgIBAQCAgGBQI8hoBf8l6JklvoUeuO+A3Swto6yRw43VSE+1TWX9evh2XVAvWY/1IF4RYD3B7S2xpeqh6lGIVH//tk0cNoPybt5BTkgZEfqHBDWU1Z/SC1nXOpjwfrva7Ex1qpbiQ21006bTamp6ZS8YTk5mhussghI33LaRTR7yizaAjv9qrpUQKI4Jzgxg5+dDT397ln9jMx+Edd49+YKfd6P9AQRFggIBAQCAgGBgEBAINBXENAL/mwahxXFx6gN2Lr0Uzrt+m+qQUu/fFLtsOH5iueMTU0NygBA2SgMgTfeXRLqP27CFBo+shC63xIdLZ5JWeuW2ao22/RnwZ/VpHjDccWWUvCzrjbOWK74+F2aNnM2DYjCpl623X8oZxgVYkZ8yimnUV7hGCrfuEbR0bfV4BhnVledcnJ5wDkYq0855HBojVVFVoHa9aXU3uw3UOVnI0D3JzLuIpdAQCAgEBAICAQEAgKBnkdAL/hzDVjP3yf4b/5wWcSCv7456emZxD4fQiUfBOVe8Q7R6jf1yXo9LEkOKigaS2PGlpArIcFXn/2TzrAt+LNNf/fO7bS6plqxduNjHsEFqwitf/8VGlf2eQS5/bOw5SKtylEWBOhZZ16gzPzzCoA2zj9n74RYxWzq9LOI9fQTNPcoWrUpfes9PavNIFgfoem5iLBAQCAgEBAICAQEAgKBXkLASPBnZfGr1foYbHBUo2z9snCdnpFpi0csMg8cNJQmlJyiDFD0/A8MLaAhKRmU0dqoj7IUPvzvB+jg6FMt5QmWuLBmE0kYRNlxbLt/+7CxNABWkbSOZ9NHYLVjyNARkZtD1TKM4vXAQcMoZYg5FbRIit2ClS6ds66PpWMgggIBgYBAQCAgEBAICAR6EwEjnYhXUCGfJHm4bhcdqKrpzTr2SNlp6RlQmzlbUZ3hVQkj19aOw80sHG5lxINpRTXlmDuOzuTxmDqeiLbn6nJHKrb72RyqkWP79uMnnkRnnXMxDRo8zCjJcUVjy1Q1XwZs7H39uGqkaIxAQCAgEBAICAQEAiccAkaC/wGgsE2LxNpX39AGj6trNueoCLVfuZh4FjmUa29vpYph40IlMRWX3tZEQw/WmUobKtHAw3soq+lwqCSm4thiEbtw6jxpaRl06oyzafppXzFcETFVWB9IxPtaOppZpd/n+NQ63vgunEBAICAQEAgIBAQCAoE+i4CR4M+N+UTbos3vLdMGj5trVmOZfe6lVDR6gqkNoSwYN6T3V2z62wVh7E77M/Vjdm6xWw3qst1foPBpDzLjry+ErTad+ZWLFJUo7R4Ifbq+Gl7/+tv6qq8BwbcKpo8UYYGAQEAgIBAQCAgEBAJ9AYFggr+fWsP2zz4nd0dHX2iP6TqWTJlGk0+eSUkW7LqrgrE6Q266MIOEBbsrKcEdOaZOnJlQVF9hwNkaacfQUeR1OpVMfDYAb7o249hyTmHRODodG4CPN1f+7of6Jr2nJ4iwQEAgIBAQCAgEBAICgb6GQDDB/y005KjamM7WNvryv6+pwePid9Bg6xtDVVWYyiGjyO0w2hdtHhqX102F9dvNZ9ClzN9TSUk2Bg4qu4oRXWo+ari93do5Bek4CTclNU3N3ud/d5Vv0e9p4ZHQc32+YaIBAgGBgEBAICAQEAic8AgEE/xZ2PHTaV7z4vEj+GdAWLVygqvaS9rb2pTLzoREqhxSpJIj/rWj7jOmzr6az6GMbNrff5Bf/dVVDT9imACfjHu8uM+f+4++KdiJTTv1RBEWCAgEBAICAYGAQEAg0NcQCCb4czte0Dam4tOV5HG7taQ+e52Dg56sOr0ajH6m3Co/Tj/48G7KbD5iOWs6zIkO319rOZ8+Q4WBhSJ1VUOfNlT4eBL8N74ZoNXzv1BtF3ECAYGAQEAgIBAQCAgE+goCofRVXkIjmuEVPY72xiZa88IrNP3aq6PWNj69tjccn/Jq1ekF4vrsYdQYBZv+vEF3zbgZlqozqm4rSZZyBCZm2/3bYLtf7/rKjP++ffXkwr6ThMREfRMiDu8q20x7tvoZtOIO+nTEDA0ybl4wLjvFnZhHDu8QkhzoiPIQ3IpU3M/9HlnajT3Eu6lT2nOwsXTH1Meo04CFIB3nCFTdnN9fSsgsVPqITINxbPgQHHuSJnmlRpK8h2SSDrqlzg1Fi7ZwZ+2dl+hxfg+Oh+atuYkS+g+YmJfglQrQhwplSR5BstSGj0eVJHmrJY+7auSdW/HOEX3oeLjfog0CAbMIhBL8eecpq/tcrDJb8fTzURP89+2tpyMbVtPZKvMe+uVDqbKzB1ouLUAgZsEZM+Ynb2ODL5E7VtlZM3Y64cVsmkk01HzYdn9rcqBuvn6AY6ZSSUnJlJnZnxoarK9emOFvlObIoQO08YPXadyEyTQybxTgM4+fET+mLX34CX0Um17yGwnoE5gJV988foiU5LwKgv7XJVmeRS4et6mLbcfq7VQuQcdYZmB2yaHa+fSqR/a+UP15+Yezl9HxsdxmBrATME3lz4sHuVLoaxDqr0RfPhsQ4N2s9pFuQJSgQxn0J6CT1C4oOYSYT2Sv9+68JeXLu1OdcD/VcyfOdjikq7QNh65qZf7isru1tBPhunbu2KGyI/FneCFeIxEEfbx0qMt2A/oNXjC+1w2IMOpQM7+EN3VVI+4NWXY/lbdkE6s2WnZG9wDzep/lLSl7zjIzkSEkAkZYH8/93ai9om+F7CJhI0MJ/pz5MXif4L99+So6uncf9RtkXXBWa9Lc3EibStfS3j11NLLNz1a6miSmv/2zcigSE5RGAjHb9Lcr+LNN/7yje6mmvzn1o0GHdlP/CNSD9KAGs0wUMMDRZwwSzoaef08K/lyNTlghKl3/BdVUbaOJOG05O8d/v0KQqhqSefVp/atv6uOe1xOshPFRLcSX9j5Jki9SPsBKZt+XNwwraQA+0jc4JecNRTNKDtbOoD+t2lH616+/SJ4wGUV0H0KABTVyJP4F9/ob3EfM9o6uJqKPEF0uOZyX1yyYtNTrln9XcFfpx32o+VGpqiQ5JwG/H2uZOWT5IMInjOBfc+vECZLLcZvsoOsgxHcvg4bvTRhkJgGnsewlyXVrzYKS9ztl749HLS63ZHnC6B5g4IE+LQwjAIOoOiOsj+f+btRe0bfsdalwgj/rN++BV6RSr8dDnzz6NF3y27mWS3Vjf8D2ijKq3L6Z+GTU3nI5uZEJh0YCcZdN/6E05FC9reac1n6EarogDssnGif1am336wtsw1kFkbhc7Juo2rElkqy28zQcPUyfLf+AhgwdSROKT47IytC6V96gpgMsK/gcr3g94gtZuCi/emJiRpHzdmT5FQSSFM00mwUumqSSlI3QPTOKSq6vWuD5YcGiTZ9rYvvMJQZCp0BVJVlb4c52qXbUPWUn3OZpVsPIyS7+OfrGHfDpWkwiuYaIN9vpkmbXzi/5BCZ5f3UirwBEgl9fzbPyluEpw5Oz/g5lnW/ysmd4UT90SzFoOC9BcpRWzyu5LX9J6YOhU4tYgYA5BMS73xxOPZVKt5ZsWOx/tdTPn39RGzR1vauumpbiKMAPAABAAElEQVRBLWN7RXmvCv1c2Uj0+zmf0Yw/07eOsH+Sb9qGT03Z9He5O2G737bmCWlt93MbtM5ogKOND3Y9IHtQVNRtgvE3Q99dX0tLP/gfbd28wfJG9E8f/4e+CJ459RsJ6BMYhVmtJ2OUYzUE/j92Cf1GqSKkSdJkp+z8DB/lX0fIoXezSdKLEjmXa70rUfpu71aq50vf9tNRmbnZk5Y6yHFXNIR+vxZI0plYAViKFYDr/egicNwhsPXWMTnDk7I+Qh+6NpovXwj/yVCdeqB6QfFtxx1ookG9g4B49/cO7kFKNSP4/w15fVP0B6pqaMOb7wZh508+euQQrfz0PVq3ZgW1mTwV1p9DdENO6DRmDeDJU+sumEBcNXgUdTrDLZyELs8BlRUzNv3Zdn8ihH+7LpRFovb21ojYu1wuYJsTUd5oZvJ6PbRtaxkt/fB/xANOM+5AdQ1t+Xi5PunjekK48La5k4Y7khMwYJAmhUsLzaJq+OXw/8GpaU9C1ehN7NJcL5PcEDIvJvXwUf5DzfxJfw6ZTkTGJQK8uTsxLeUjzMzOCldB9IlK9I1PkO7f6CcYmcroWzJWR8KesucC/6dr5hX/NFwZIr7PIiAlJyb9GwL/jJAt6FJ5+gJ95tWu9wy9gfRlWCFoDpkPkTwwrZ5fcl24dCJeICAQ6FsImJFYK9CkVfCnqU374L6HafJFF6jBgF82fbll0waqrd4WENebBJ6VdjicEVUh2Iw/2/Svgk3/MbC0Y8exTf+tIyeEZBENNR8j2/3aQtWzCrQ0s9e8mnLo4H6zyWOarq21RRlwVldWUPGkqdSvP6tDG7t37vwryVBj07hduPZb6dLEGV5W3jo+D+NK3gxfYJigi7gLgv2z3g56puDuUkO9KFYTSiuQLoa29/WQ8ecgm+EzijX9BZj5T8Jy/K0hyhNRcYQAlruzMJu6DCtBxcGqxQNC6K8+6/ZK/yy8s9TwpVL13fxkx5D0q2GhZQH6iP8JfBrGGCLeWzNv4jqh9qMB5Ti5xGz8rehL5wRpjpsnEkiS//75jrK3g+0Lqr190hnY+PtL9McLg/CB8C/dV37LxLcn3lvOG8mFEwgIBI4DBAyFCoN23QuaT/Df/ulntKdiOw0eM8ovKXRLlY2WWzdvpM5OVpGOL8d66JG6YDP+zI83ytoV/FWb/g1p/Q2rmN7SQMMO1BnGWSEa2e7X5ndjRcEDIZhXR6w63j9RYSjOWuUUvfSHD+2nT5e9TSPyimABaAqxBSKta29thZnaV7Ukvn4SHhPw5twLV5MTG8b55K8gQr/shUB3V9MO728nvlge8sHojn8ZvF6uvW18Mblcz2FWb7JRTTDz/wsI/19C+Le1CdmIt6DFBIG/gqux0C8TrLnKd3U0ty4c/bftbGklqCt4uroNkc/CP1c9t/hrklO6E0JgUUAG6FRB+H8eA47JeYtLDwfEC0KfRGDNTUNh/lf6jWHlZWr1kHdOweKyZYbxGuLIuzZ+iuBXq2+fdLLklJ8zHERKlJOe7FiIdD/TZA24hHnQzbBIpX/7iz4XgJQgWEVA9C2riIVPb1bw59nPWviRzJItoLyz5D767hMPcFBxBw/spbKNa6ixB006qmWb/bVz0FSoTa89YdN/9K7Y2e7X48eDnNS0dD05bJgtJjmh8hOPB73trNlBu3fV0uixxVRQNA4rP11abksffJzaGhu1bWNTU3/REsJdTy8quQ2zZtON0uFZ2QPNjKsjmXUd+ZfNZVgBmJZW5FjskKRbjPijGX/DvoKl+fdt3m0UL2jxgUDV3JLLIVh9y7A2UMfwSnRJ/qLSzwzjgxPl/DvLXoaK2ReJDvoUq0D5gUmlEZj5vRn0OwLjBKUvIpCbPeBKCP6Z+rpjNbHDS94rChaXL9PHhQrn37VxLQaHF+PD/gUmGQJ0YSVZ+ubSs+kXs0OYFB65uOw9lBF09SlU+SJOIBAKAdG3QqETWVyX9GMu72PaZF/+9zXFtCfTtmxar1hViWehPzExiTJgaz4SxysZHaGs3eCLWzHc/iZfxT4/BlUBDjQ+6MuuC2a7X883mFqTPp0+zMJ0NtSp4tXxasbm8nXoq+8Tq6OxdamlD/5dX91XQAitZ6/JUTNvwkQEf6ch+S5ZXx92+C+MROhXmfAKQP7i0l+gC/BssYGTBkjJCX7PpkEiQepFBFjFBxqGjxhWAbrWHslzUQRCv4/d6Ds31kke77nob4aDP0mm/8ezxL4M4qJvIyBLVxo2QJaehND/jmFcGCJWhCqx0Hsl3jOdAUkx658/feI5AXRBEAgIBPokAlYE//vRQp9A1NnWTv/73RKqhAlHttYT745n+zHjFlE129tDrrwrPPkwLwOR3VJ5bNN/6MFAdZ7BsN3fr+WoJV5GibdCJcmMC6XWFC6/nVWVcLyjFX8Yh3+tXb2clj70dzpav0fLlhX9LW2ahQWVP6JfJWmZdF+7od9zWeGS8g0GcZZJeYs33ozVA0OTWujWF1fOKznTMlORoWcQkOmHmKE1HBF7Jfnr0TDPOvKush1ej3SFYYMwi5vTf8A3DeMEsc8hgK9YvlGlMfBbbkQ3S1POgJDk14zSY8+ReL8YASNoAoE+iIBZVR9uWhP8E/C3cIDd6hdeoazzToYRk65wPP+3I5CamQFn3fw9A+zb9OdNvvU5I/ygjMamXrbdXzO4wI9vsECkln2YX46NfRTB6hML+oH9e2jtv1gt38/xbNkmP0qIwI55E0dig+UlRv0fWv0PFCwpWxYiu9Uouand+6OMZAdm3pSDm/zy49Tfn4DwiR/RRoA3kDpz04d5JEeu1+HxYJy/oy9s8Ntw26C0NFfOEKckZ1OH82iDtG/n5L/sDWvBxAZUIbPy/g8MzP7PKBFmV/+D1Zy3jOIioRXcuXEVrD2tQ3kn6fNDcJsNGr+/I3blP56YnpriGI4W9UeXaPA66FBLNR0Kt28l4gINMlbdnN9fTkrLkxxycjQGTAZF+JH4vIWMtDEDk1zJgxyS1+H2ePZLB1v3du+z8Evbg4HhRmVhsn6FEd0STab38T67Sp8H6j6Kmq+e3lNhXrHK6tdvmENKyPY6Ow4dPthQN/WxelbLNO3YcEJ6kWO41ysN9MqdB71tnbXh9tOYZn4cJIyH57unYYyX57unv7dWBH++Jwvhb4TPgKeknP50pGYX9csfxsG4drYEf5OmSNmmv93DvAp2V9Lykg7qdCUqeLrcHaZMfYYD/+iUM4hggQg7d8MlhenVtrBpgiXIhDpVIjbQhlSNCpa5B+kt+w6RI9Vvo68Xxf/SShVcDgcLdE6DPPvd1LzQgG6LxIJ39fxJv8HxrgEH62DV4WtbbxkzbOy9FWyRKMDVzCv5AVak/PTRICA+jyX+L9XElXMnTnM6HTcgfLk6Q82Nc+IP40aCbfgq7PD5krzS8qZKz8OhBD6kvRmDH/8RrEx8GrGfQ/BCbFAO0MFzS96HzZweqhyWVuj4qixJV4DXHPDP8RWA7p5Fg6hm/kDeZLgFmw+fPHDowPNWBQYfvwguTi0owcDQQGiCig8Usm+LgGXILFgVegJ94YGARJJ0egAtBGEhrDl+b0HxHPSD78uyNBpJh6O/9PNlweZ/7hsZo7D5a0EJW3x5Bytc/61vP/LOaffWmbIJDBWomzD4GavyxAnXno7mtt9ohTEeOE0vLL4Sm3IwsJUnq7rtaCdvzAnQc1d5RfqLMxaSEtJTzkFf4mdgDvTehx5bKnaQy4lF8iEJSpuBy/te2fOqu6X9LdTZtxoeadmm80no1gaupcF5wIBsiSS7O96XEgwWMCUpLxQjthDkdciX69JUBjsEzMz7CBapTsd9/w7uA/PNVXk7KZEGZufgHmTvRD/4N/ZQPZO3ZJOh2kH1bWMLHK7E7+HdhxONqYDvJdutwBuNKM0low/uBb0a/fDppkrvU6HeaWr5/GtUf7x71mIg/09tOjPX/N5OSUq+Bc8PqtLlcLE/b0npYjUc7d+FMXy+o/3ut9q3QmHVU8+3Uf+I5fc2VJuN4qwK/vxyewpe2eGfmJFGTbv2UvqwQeRMsMoK85aSFU0jo+qbo6Wmpke0WVXlbmbGn9N2nHoueTevJEdH5IKzy+tWBH3VtCcPBBI9gWqXat3M/jou+CadnjWY1nzxCbU0N4XMZra9wZjwIKu+rjpYdFToQ4blKSf0trZYn8zFx4IaqndRQrqf2jNvTttotnLKTK4s3agXZDm/FxZ8ipZUHjXLy0q6L3ZsfHTGqJL5eHr8hWqY/UxKSmKh/Q9G/PC9uwIvngu1cTJ51yP8JV6GuYnpKf/EB/Y8bbz+WvlwklQAG39XpRc5r4dFmeuwuXSzPl1XWL4OVoemGscdo6Jep6Fepx2jdF25ZHoTV9v1dG2YN8xiW8ndeJEU+r6Y2gTd1yiDBaWZSDMzNzvnrtp5OXeNXLJxEWiQB2LrUL/vGZUACz7Pj76ztM4ozg6NPy5Q+fgL7iWGalonJ/IgKZxgs2Xu2IwUKekGCOEQtCWI9fye1vIxulZWoK7FBvRrhycNaK6Zl3UrhJZHjVJqaeD7a9wbTT+WMMBM/TfSrOV01XMnzsa+oadRge7Z5rAV0bK3fF01b+I1TsmxBC0+NrsdtPHYWyPRN5yS8xuO9NQjEHZ+V/nZxgdmh9gAa7lCQTNIfLCgTxBWk2VkSvwc8XssYpf/l61VOP35X8B8gJYJBvH/04b117KDTmYrY370rjMEHvSjdQdCvo9wHkqik/6Buz3bKO8xmjQCfG6HDPsLmDedn7+o7C9qHAt4iWnJS/Ac/AxtMb6LXfTByDMYCWZkFDl+XTu/+E/YTPqIyifYL7IGvk9lmYV+y4J/cnLSTch3K56fY8XJxLbQoy7498zzHd13v9W+dQxE/6uefL4N+0dMv7f+bQ0XikTyXgimiuTobe8gb6ebGjDrb9UNHjKCSiZPs5otovR21U/C6bw7MIUw+eSZVDxjNrWdEuZdZaIFrO6jurF1x65VmtXfzuFF1Jk/njL7ZdEZZ3+VBg4OvUJjR9WH65YLwT/WLiOjH519ziU0dvxky6ZHm3fvp86WVvKg/3Y7nu3/lRow8zutaMIkv9llXybsBG/rfM4XjPIF2+SGtGr4ccFKwDlWi6udWzw1KS1lbTihX88X36iTIJR9CeH/+/q4WId52R8zda86ndIreMEWWikPn9b+GLj8CSoxr++YV3hsBtsKE/Np+Ut+hlFyyS09a0S3S2OznU1HvbntTS39tL6jqbUgnNAPYSkzxZn0CeZj7oOwpAj9lusjURrUih6pmTfp55bzajJUz4eZUofj7WNCvyYyypd8Ai5WLZY5HU4WeI8J/SbL4T4Ff2/hzJINO24fP9pktoiTYd7CeMAoOe5mVbeIGXdnHLm49NqRizZeqPXBZu7tlqXPj+f63CSnvAF4ztbHBQ3DbK1y2Ni8krs5zfZfFI9ITE9dhYnFn7PQHzSfPkKShpPkeJhXovRRsQxj8735OtqoSDw93zaaYTlrPD3f8fK9jUTw52Xzhxn9JghQPHvatGsfBKk2UzeELevMmHUOTZ1+JiUl6yalTHGwnsiOmg+XFkoQTkvPpDPOupBGjOySP1pmXWS9grocqk3/zOajNOSg9UGVjh21zPyqj5QAdZ9Tp5+lCMw+ou4i3EBHlzwgaBfvAIZBCHzWAJvnPPvcS2nY8PwgqfzJXreHjlZ1fTd5tarb8eyyMsuoEsL9SrLDUHUCQvmHMTet6fUYDyxkaRrrLIaruxqPR3eg7JRex8fRUGdYTRf0V6IUCGcP8+FlQdNEOYJPvh04IPtDfM8vs8Ma4sDFCY705azXaodPqLyw+DQB9TRQy5B3wob68lB57cRNfKi8iVVPdD6khQJeDcCqz8uQQKbYKVvNy4OHSE8Orpk76SoIci8COwOdE7WE6PzyPp3khCTcC+ksuxwxeJ7gciYsZ7v4dnmFzi9vCBJf3N81qAyz1ucHiY9zslSMCr6Me+G32mC20pgx/3n1/AknJSQ6XrPVjyW6v3LexMlmy+0L6eLp+e5JvOLp+Y6n720kgj/ft9/C7+1oaKKjlTvZsH/Xb4g7ygJn8eRT6czZX6WeEgzV6tgtL9hptixs8gy61kxox5iTyJ1tf8abzXeOioLtfhl2BFtnXKhCofzyJAgLzNNP+wrxfdE7u6o+KalplJambAPRs45JOCUllU6aOotmnXl+yBN6ufDG2npllYr77uFt1UxigUhRXeOAaecIojPtpY9M84gwIeuz4pHbF5Adgnh2/0mnBNCDEBySg1VChhhGy3ItFGHeQdy7GMzUGKYBEV0pwZnoWhAsPiI6ZhMkcgSoSi09m1ypcsL/UOiMYHyRtR3+S/g3ofKyQ5mZCJYYh2ll9HM+g2jICTFwknOWEVfcu42gA9a4cVLGKOcz6AvBV4xkOgBMP0PdX4J/Fv6NUP2CW4b3zB2scmGllQ6nNweDhodxR5xW8kWSlmdAXQ7nMtRzbMj82I+B9i6H/wgY8MRXUIfnYaDkpI9YtzxoIrsRsveJYCxQfj5mrd/FrPXTfU14Rf+bi3sR8OEA7uvQ3pfxLL+NxwYCRxDHM/+Say0wOEmfAjw6ce824xcqS/LH8If0adQw6pHskhyPqOHj4Ddunu+wWOImGb37w+YzSBBvz3c8fW9dBniZIbUh0e/hH6z7eDUlZ2UqedqONFBy/65rlQkLmXkFo2nMuEnEtvR72rF6i91y9YIw26ufOGkq5eUbrOoirvW0OZTxvydtNZUt+chR2APRPnE6eftlG9Yld+AQDMTmKHr/R48cew/anfHnwniw1dzcaFhurIhZA3LpdKy+1NVWKmdL6O+bG6ZpGjHLz7/V7y4n2ePlqvCNquYLS06mqUbiInSjqyzxiTCxRHIlRKuB+uywPHIqaKv0dDNhvHMr8WH8iYeaV+r3KFTdXnIWxpCPBhGSvofl9T+NuqfM91GW3dIPvST7fcQdLvqXfqAB4fx9bGv5k7Z+ktPTkL94E3/s/RxUKf6A/DP9iN0B1H2lm7w3Hz5Uvn7qY8dskbMVGEdK+iWwSnIvJFGjB+GKmgXFP81bVPZXI762aBIZzvxilNEjfcRs3THD/hWkvSZIegz8vA9Urip7Z7aB/joEzFOQ78/oF4GzzMA7MTWJ6f8LwjuQDHUVEHMCIxRKGc5UQd928FLz7iBpTJMT01IfwL0oCJpB9j5Ebs/Dq2o2b2YVu+500vb5E4tc5PgmZph/C1rANxSfvH6UkPQs9gGdpckXtBirEXwuCHB/E5gHXV5G3PUuyXk99PXrMEB7C+E3ofq1rEc3IVttmD69LL/i9koLCu/cuFUbxWenSJLrFbx/DT7A2pR8LR/CjbutelXps/r+2715+AX9O0nJhWeXV0+17xI9574S7unnOxbv/kiwjvfnO5rfW6v4BLy0LDB4CGl/Cj3pcdtefp8GT59MDmzwHTpzCiYcuhYSWI+fdbAzMvtZYBvdpHZn+7k2WkGYT7Q95dQzQs4st2CGPR2CPz4qEbv0tuaI82ozhlM94tn50844H6curyY+3ZYdH2zV2dlhuBqg5R3qmnGvqeb9ST3r8IGjEXlFNGToSNqxfRNVV1YobeFaHNpSSYe3VlH9qvXU2ahYguPRzrxIaoiPxSCjfJ2KQG4UE3UaC48BM9/Qrw4YDJgpGQL/P1q9HT8Zd+dWw9Ea2/iGybEpziGZq8GPl+R9DlgkwgjVZSA8oBL5NFD1Wv3FBkieMPBzKPdTxX64HzUwwEv40IWdp3+okL8TPfaOz3eU3WkkZBXcV30E3J6t/Hnxe84UZeDC9fRzmGH6NXSjn4i62U9ZytHXVylYii/Bnxzy94wXPeTnn1xU+u2FANgPME2ArUJBjeASmElk1ZxLNVHdl87CQFpIil/f4pQQ9v/uaaVfF95f5tPNC8nBRGT1ghJYLKJvGyXFB/kwBqTfz19c9opBvNxtbeoP1fOKP4Twb7gvALxnTS+c9BPYC7jfgIdtkndP41WOIRmv49k7LyQzqPGhLjchzU1J6Sne2gWTNqFtWLmRV8md0sqCu0u3hMzfS5Fe2fsn4P8bFI9xi7/jFU8M6Kc5UjKxNynEwA2rle1Nrd/GYGe/P4euEA+gaueOnSo7Er9E3x2sTcPvtKysknFEpaVaep+87uHnO9rv/kgwj/fnO9rfW6sYdUnoVnMdS/9zXHp5g2/98i9p/YPP09HlZVC5uIAuuOhqRY+/N4V+rmZUBP/uU3tZmDzj7DkhhX4u0zNoBLHKT287T3o/amMznmEc68pPPmkGTZoyHdbTurpEMPWmMKx80dm5hnKxLz7WF66EBGXQef6cq7AH4BJKqGuk1Xc+QTXvr1SFfq4CzzQbCrqh6qeoL2ATo1GaDsmDmfjYO8ymG5bjJcNZ7ZAVglT3MA4Iuz6Y0K9mZtvlsAb7A3yLAwRBfIAj2yegMg/zi1X8BZixRzE6J3lvy1tctshI6NemZKERQurXIPR8qKV3X+f2dw78qQHdHkmC+VIDB7N9cTXjD6F/tr6a+DCV7/is9PqFIYR+NQ9vGva4ZRbSAp0D5jAjdVAv8njkr+H+/iCaQj9XB4LdbUbVgkC8x9PpPimI0O+XJX9J2UpIpVPg2TpWoHPQLWz9KzDCPoWfxV1thy/DffrIPDdlCbkYbf8B1A6ecCZKmzEQqIP/O++r4NUx87xilxIrTD8H/r9GCQFCv1oqD+ix6umbaFDpmt/9rR1t3wom9KvpRt65tR4vlcfVsPbXBfOx2nDfvY7T5zuGgMbz8x0P31u7gj+bDvPNisiQClY88g86umOnrdniaPUHNheanR3RBKivCl6vB6bv3TSxZCqdMu0MtCvBFxfqItxMe6i80Yprg3lRcpmrL5c5Mn+UMmjjVYBQG5rN1I/Vq/r1N5R7zGSPWhqWFb0t7fT27+6Cao9Hy5c/1vdoCWavk1Kc2UZpITQ0jl+05aBRXAxolUY88TE0rJtRWqZBEG7obGq5I1i8ns6HRIFWpqfzQoueFq0wVCtGgf+Ven7A+7OnFpWF+vgHZMHBPTei1U36CHJIPCsaVRfsXsie+BH8V94yPAX1HBLYcO8HetWIwDTHKP/4SxnUcBTb+seIfCXLSf4EcyH0yy04YGlSwZ2lr5rLYT7VjnklJRD2AgY7zAFmK39dePfmGrPc2IqS1y3fbJQeZeRNKyi+zCguGjQ+L2H/oQOXeMn7Z9ScVy8jccOQ6fvYl/CiMznzQM2CkvdYrS8SRtHIw4Mos890M3U+E6xMr1e+eezdFQeCxfvRPbIhH8gPeX7p+mAgXp/vWEIZz893vHxv7Qr+fP9+BH9EvZEsXD1z088UdRGV1lu/A3DIh9NlR5uJz7vyKKowBUVjLTWj7ZSzyZuYbClPtBNHMvhgYZ03LCclp9iuTjRWW2xXAgye/eHN1NbgN7EP9RC6IVLe7vYEHkG49fkhnDLfHnEQsnYZFiTDXKUV56VF4WbFAtlJmwJocuxm/BNkxxWYow14V7ll+uFCEzPS2roWLN5SjRl3ZPN3ENIKam6dOMGfai8EK31+nU7l5pbsH7Sk8rL7Oyg5fYThSorXsdwK72vmjk3DNHpEQr5hOV75jlhZx0qQ6GrDMkne+PSdZU8ZxwWndqmqyYYDFNi2vyp4TvsxfBgd7Nf/at/BgyMg7P4EA63tEXPFshpmSs9zuqRlbN6Uz1GImFekGT3euQtNPtM8ycKCVEBRMrU+vaT03wH0IIQdq8tqgBvGHMefi9vnO4ZQx/XzHSff24CPaQT3g0fVv9Lm271pK700b6GW1CvX0RA82epN/6xsy/WXk9OobepXLOeLVgbVdn8k/Hi2Ph1mSu26aOBvtw4rn/kXlb71vp7N30FYpyeaDTtTJFbzMRhRSq1medhNh6X6IDdIarfCu62j/Vkr6TktZhgDVhvw1YydbpfB+QT4TFcXLYlM/xaD+deN2iwnOC8yokdOkw1HzwkOd27kPKOb89lFW7Z7Whuy9P7zqo2+lVwzJSY7kr4NoTHRTNpwaXi2/6klZf8Nly7SeAzIZhnlxUrMbQtNCp36/J1u91zQAiYDMBg6XZ82FmFlALCk9MEnF5eOdXvlsyDI/oFXxAzrZKoCEjbzOz/CAOCVpbCmZSqLzUR4hxzJu7Ms4GUdkq1Mu/Xx4LNloYX7OLtr03qkKyb64uMqHI/Pd6wBiufnO16+t9F6oB/CzfwO/HT1pn704OM05fI5NHpWwP5DNUnMf3NyDVawY17qsQJaTruIUle+dYzQg1ctM+f0YGnGRQ3IzlX2DPBm4d5wh+vq6YVbf60vug6EX+iJVsJuuflggpQemEWWh7L+P2bQLQnfgYxMUGQqMNo4KsmyueVtLgJmCsfeW2G8chCiCg5Z8ujLhtAXjUmEgFJZ6IC6loHwJK8ISGySUHTX5m1QadiLOvsNVnAA2liTLMwlgwSrx4kzyl5nHn4iHniaK9xcqoUQkBZ2bYA2l8E/lQSb9SfBWtOvIGh+zXiDsH8GUyGv/KeFFgQ3Uzy7Eyn9SfOd0uRtgdD5gSZs6ZL7FIRkrIRJk/wzSiPYlnjRkvJaf3psQgv5fi4p/QTc2f9WOanVmXAW6nUGNsfPwOrOVND9jixHOISTLi+cMekJWrbx+hCJohQlf2mZkWS0R0vGfbDmZElqwqqf9Rk+a8X0eOqF8fh8xxCFuH6+4+h7Gy3Bn2/lN+E3wisSEav8PHn9j2lh6QpKSjGc+OI8MXMuqPj0zxoQM/5mGHeMmaLY9Hcd3GMmedTSGNnujxpzC4ycThexic2DB6JmjMNC6dixdd2N1Nbop23hBgP+gAVYl7HCmE1dYkMc8/J/fiChOlNS80HfaoVfRGkdVGicT7Kwx8CGWoBx4VGnFkwZz7PjgYIKdP5r50861UaBfkI/88EqwkAb/IyyHjYiwhIMC/59ym29Zcyw5ITkcbJDHg/hcQKEJAi4MuvKd608Qc8tKk4mT+XnZabVNKyWOfSkMYMwGAvcmC/L28BLtspPmx6ZK7pw0VJhfLTrdOkeEfz9Sybq3rD/BujsiQWjwhklk2Er+nScYH0ZBgNnAo+QG5Bxa7+DgXJ93qLSBXr+UQ3LFKUPpYXJj6g2oO8y67HnO8YQxffzHT/fW3/Bxd5NqUL22+EfVtkc3llHz970c7rx2cdUUo/9Zufg/R6bSUjzbVBs+l8Em/5PmM8ThZTtxTNgu793Bz1qM3IGDu4Vwf/NP91NlavWqNVQfx/BxUdqwM4vhMRD+CAGCIoOSWaBPPaCf5AZf0wymxb8MR293Q4GPZHXk+TKcRgUhNn6ZAgsYwyiIiZBaAu4nxEz44wSGaoPyJIc14I/n/KZWiSd5iQHq8ScjhN1ZgAbZe8IcNdAor3WkO1cSnJ9t+qFHS5B87oSkwxfjGij7WcWqjVbjQ1PGVt3ClrJGEYo2C4r5Zl19vfzSdgpsusy1Pta3NtzghWNuPk4ibk8b0nZc8HSCHrfQKBXn+8YQxTPz3c8fW+jKfjzLWXB6jL4CznAbs0Lr9Lo02fSWT/8Xhehh/73tpqP2syWGRfApv8Tfp9LNS5Wv00zvxor1pb5sp7/VtpgOZ+dDFuXLac3/3y3nsUWEG7REyMOdwkKgYKiJBVEzNNCRohchjP+ECotCDCyrZUPC9WNOKlT9uZQ6AnJiHnrM0L4C7yf+kRWwnzIlMFMeKxn/HG409WoJnuNk7xuqeO3RYu2VGiIfpflP56YntHPcRPOzrwV1faZ4YyBeO9XrjaAAfVObTja1xiYQ50jsEWgBMXFbB2gZldhwBpdwLqJXbNl2k3XbYXsSfB5snpu8fdhzvl+tCFwRYQLckg/x38h+DMWfdDFw/Mda9ji+/mOn++t0WSa3XvzLTDYr2Xy4u2/peove1b4i4eNpYwB2/RvGzVZC0dMr9sSkmlFO7ZfwgxpPLj+sBLENvV7yh3duw8qPj8gr5s1cXyOBdxvwPsRfbGRXMi03CgbTu7V6fgapbJH46PIMXtgOGvsdrdGrPtur1Yxyu0wEqViUxbUHqIq+EOA/sK4pvIoY3p0qBDar4WwebW/p2845cQzg5XAdtwh9NdAKL5bK/QHS6+lY5WpDQL7/7S0yK+lmAr+5JGPGNZNlmzro0JP3E+vUC0HKkBR2fSs8ovVb/6dZU+4vXQKdN4MP9aY9Z9aOXdSdPfBxKoxgq8fAvHzfPtVK/oB8XybwjQWgj+rGrDw7xOy3O3t9OjXr6eWo0dNVcpuoqSk5F49LVhb/3Yc/rU+e4SWFNPr7cNG094D++jLLz6NC5OqrG6VA7WrnnBske3hK75NTQe4C/q5uQjx/pOoOcysGwv+snQlH/UetYIMGLnSU66EcBZYhkwVo/6yY59Blj5LcndIrHsdxLE9/ih6icpRUOB0cJDSw5Fxj1YZp5EmVd82tsA4zj4Vj8EMIy44dq3MiF57+6QzcHovZnIlQzUYNQ8E2CN4xr4E//8A9z96ZLrW7fVM8e5uzMIBcJdiABCgW6fmNfuLwVdsBX+X8bkCXslgH4nZSnenwxg1v/vS/0c6Zu7aP8JaaMe8wn5YzXkVJ2B/ovW184t5UiMqrvDOjVs7Pe6rcY87jRg6yDvRiC5o8YtAPD3fMUepDz/fMcdGU4BLcx3Ny/fA7E/wd6hM2cLKI1d/l25592Ve+lTJMfnNGTgkJnytMm1va6XPVnxA7VlDaSo2uibgILBYu4rh45Ui9u7ZRWtXL6eTT8Ueru7TeGNddjD+vPqyZ3ddsOio0f/5/26j6jXr9PwgpNDf9ES7Ybm1cSWlZMBckW4jiYTDorOLL8AZV8pmOrvlGOWHVZ1vGYunxoMRIx59hTbqnrKdsJYCAd/fjJIsexfiRNffxXM7cLhTJTaB8+pnrr6eDmfSN0HDwUvRdZW3js/D+3VwAFdI7O3UwQMbP7djwTjsk5BfxWxukl9EdwDC/lIc8PWG7PW8m7dkU0B+ozw2aYdt5g+Z3SNLB2GsPsChjbb3i0BVbKwBa94ybLjXI6ASYQgud8owKVG6LCCZ7PgcNH7PRcV1W716Dc/cVQEMHZJPBSwgThAiQ0CKHaZx+HxHhpHJXH35+TbZxKgki8WMv1qxhbh4Vw3wb8XHK+jZH92iJcXkOh7UfBShf/kH1NTYQJ2uRKoaMiombdUyPZiZTQf6H9NW2LN7J61bswIrt5BPe9H1xH6LD+57mJY/8ay+lZtA+I6eGI0wHxmPWbG3jXlJNxvT7VMr502cDHWis404yV7peSN6X6dB+NwS2AYpP5AWl5QPDWsl0fUvXB39zQuuBKfhbD+EuO3dFl78qpNACZicMZzpb8GL43t5izZ+ZeSi0nt6SOiHsRkvbnfsnCS3+qmhqiVhpSEKKiyS4eAB81zRWYVLcOxW66v9haWlfG04GtcYwBg8c+gpUuAgNhrlncg80OEN+000MIm35zsabQrFo08/36EaFuW4WAr+XNWr4Wu0dV759PP0zl/+qiVF/bq3Bf82nulnob+pwde2rcPH+a5jdbFtWGAZu+trad2Xn+EbHtPvacgmpWdkUnIUTgIOVsj619+ml375e300g8+zYx36iGiFsZPiASNemD09p3p+8deM4uzSXJIDD49ulQFMcX8359250VjItFtob+eXA08KhmCS39vVMlO+V/Y8bpgOFommFZX8n2FchMSF2H6JrvELo+xQw3lZT6/6bn4yJO3AGWSoaXpl9+kjF5c+rc8TKizJUmao+HiIY1O8eFi2G9RlWPktEwcY0E2RugZx8gR9Yl5o6WhuLdPTIwljBekw76fQ58WzcOGG2wal6em2wijIKD/2rWD1TbioIiDLo6PKr5uZeL79UI3759uvtjEOxFrw581Oc+BZCPO5137zZ1r7cpT2gvm4dl2k4cTZlJRUHbXngkZCP5e+O3sYNaRkxKwiXsiC24YbT1rV11XThrW9K/zHajBWs3YjPfnd/yM+N0LjWD/1WnijD7wmmb3LgsXl7+LzaKiDjr0Nd7MVBXsl+Oeunl9yHabczvSndoUwrnvQiH5c0DCo0bcDUslMPhhJTzcbrp1f8jLOAVil9dCfPtdsfrPp8heXL0UfqTBKD4Ht92xO0SguEtr3FhT/BPmmGeWFefwAVRBvbsoIqIwFCIwQVv+Tv3jTOiM+wWhd7YiNABOszIjpMn0akBf6URlJzl8G0E0SpheW3IgBv8FmJml1lA/041VMnZPSs1y539YR7QUlKjJiIMneGiP6iUbDHq+AARDuv+VnuWr+uHxD1bwoACqebw2Ifef51lQ6dpexFvy55vyi+jq8b+ZVxkmuT93wE6ovC/iec3pbLlYCpplKqUJ/s2am35cPa6TbYjjrvzN3JLUmBR/w1O2soo3rP++1mf9Y7LvYX1lND1x2DXU0t/hgxgXPVPGs55taYoyuISPJdxnxhlBXkN7P8XK0NvpWzys+DdO5hrPHmJzb2yZ3/MOoHscDzSt51+vbgfd4ElY/ApZ59OmMwpVzJ07DAOprEHqn+3miLKP0NmkwwCQ/asQDbchKkxNeVmbmjBJYoG3/RfEICB68ryrAoY9uNhLkoQYwOCBxF6E0CD0oGe24BJii28e/w0Zew5UxCHM/rb292FDgDdUqtrKFtgfri4ZlheIXMs5LLxrHO+6pWjBhunGcNSpvIg6yEkRehxD8FTS9ZLBpLXDFJxzyDkr4Y7g0kcaL59sfuT7xfPtXOWahnhD8ufKs6/9zeN/yYWdrK70RaGud09pyudhI2huuS+h/nwyF/u4KseDvAyDKlawYEajmoy9iZ80OKt2wWk/ukXC0B2R8Iu89511OjfsO6OvP6jfse8TlLSn9O+7pUqPCIIidN3BAyTNLcVqmUbxZ2o55JSWQqd6AkJpilEfy0g+N9LeN0sYbDZsqw76DqleVf4ARa8CHFmLmt2tvG19stU0up/MmfR4Mnhq8expjsgzp2d34ULBZfwiMZzoGZ75gp4+suWloakKi9HeogBmuMMnk/Y2+vRzGZtREIzr62TBDehAibyjGM3CPcbQj7gYD8p7Gl1DX/fr64nlNJKdkOJDXp9WGE9NTfoW+OFBL6752t7W3GQ7WDdKaIsmejoCVGyUj3g0O2fW6XWtRrLLkktIeQB9I01cIq4r7WrZLllaC9DyOlzAW2HcatGWElVVIrDCegoeDV6Zj4uL9+Tbz7o8EmL78fEfS3kjyhP3oRsI0SJ5HQPf7OLhbA9QVg2Q1S5aIT+ztaacI/Z+y0N8YsuiGtH6Kyk/IRBFEsu3+mkEFpnLWVm+jsl4Q/lnHPzU9eqpOK5/5F7GlKJ17A+Gf6WixDspeueMGiFEBS79KwZL0zaIZJSsjtH8tVc8r+X8JDmkVzw4bNQQf42dHLil9zSgu/miBu8zx4TMSmPyqPnsZdM6JHvMjKgF8fhNcb9XMm3h6YJwxpXr+pBsR8319LAZPLxU8XR3tF5JSDPOVJQ/3ETQj0EFovKRo5qQVVbeWhB+967LzStDAAdkb0D/O10UpQfSP5VA3YkE3wHnavWUBxC7CeWZXqjDbnetKcP07WP8EO+PBRZCCe4Ks3GdZ5u9RoMNKEMxjPmhmFWYh9lTUzpv0SwwYDPdVgPl/x95bsSuwkMgp+X/ZWoXcLxtx4MGH5Ep8kycKjOLD0fhE1xlFJS/iXn7LKC0EtUcnvljuW7k3SnOi0PDSD5iI4BUvl+Q0pXLJK0t49z0Vy1Wy+Hq+A999Zt79kfSnvvx8R9LeSPL0pODP9bsN/tlIKmomDx8WlZDYs9+ZttYW+oyF/ubQQr9a/4oYqPuw7X6vw6kWEfa3uqqCypVT28MmjWqCAdlhZTzT5bUcOapPuxyEK/TEnggXLN5SDX2OnwTVo5KkU10OWlczf9JCMzNCC1mgmF98PmaE3nM4pAfQBkMdLsxS7/C2NfT0QMcGpNIefWaZHFeZGRQ1t3sfhMpKQH7Mco+QJOcy7H/4DeOm56+GWZCDXv8tSGAo8GHT4j/VtLH4zVtUvgL1/1sI3tMcidxHiu9gtZ0Q6ZQoCNxJ6B+L0T8+hfAwyjC9TK0e2cN6/4au8P6yvYYrKSSNy80ueS6U1SGOq1lQ/LPE9FScVivNMCygi5gbIq7XorBCca9R25UKSY4fOwdnfFFz68QJwSpYO3fs0O/Nn/Q+ehyrV7kC0snU3CF7DFdaAtJaJHhbO3+CAV3AC5DZQPYcj4mCjegbb1bOKzHcD6QvjvtS1dySy9OLnB+Cwdf08RwGXkc8Hu9DRnEnIs0jOzYYve8x+Lq4ZkHJEsY0GC6YqPiO7MTKiSRFNEALxldPj6/nO/J3v75dZsJ9+fk20z67aQJfWHY5hs//HSThZcSoC2k5AweHLz2KKRShH9Z7zAr9XHTVkCKaVfYJbPp3Rq0mqu1+KwyrdmxR7PuPn3iSlWy20kZT8NdVZA3C58FHD1RdAeGCMHv4DD62SRLPJOLrG5AeS/Eg3pFAjt/i8J1l+HC/jZdTHYTBXbAr3ozwQOQbho/JeAhz30D+YYFMjnFFvq1t7e3njIVZ0WPU+L7CjGENRJNZ2lryLKXLSVsglNei/Q1oVzvHu8n7f0WLy1eraSfeW34Is9s3Ato3VJrvVyIn9j/8/oYFJT+4gaTVXq+8TnLI68krH/FKzhFOSZ4ArH+Aso2XA2X5lbw7Sz/y8YvRxf5DZbdDoB6CGeKvGxUBejIwWJiYKN+Bsws+8Sr28+U6DI7qJa+3AVhlSU5pOLSjzgOWc5A224hPF413UsnXFS4p3xA8DWIk4mdnuD4N13HGqJKZ1fPpcagKrcZSxcEE2TEUOI5HueNR/mnIbDzg8Gd2LgSdSzCwQnb3Wh4k+0f3Togt5FTPnfgdnHHCwm7go8ZCWaLjSzzTn2CAvRqmctfAjC7eL9JJSD4NOJyJXP2C1R543Txqcfn2YPF26Pn3bd6NQddPoav1jGHdwRx1nOOSaA6E0DV4J32BfQ1VksdR7SFPrcOJWSJZHuyQaTASTsWJw1cAgP7B64T5baLrCu4qNxh4B891PMfwQWd4Z72KNgYMlPDszE1KS/1a9YLix8hLm6Fy04xpuXEwwDEJEw+nIM+0HsMmTp5vO+/+SLDqy893JO21mqc3BH+u41Xwb8NfwIFouWjrkYeqVyRCP/Njm/6VEP7H1m0Jxd50XMewIuoYOQZ2k6zLfzu2bVK+G+MmTDFdnp2EAwbk2MkeLG8ZIr4C3xYsQU/R8bJ5DEJOG+TQJyFQGS/B4IuMj+xs/Jut1Ktb5uj+4S+2meqWeVrlc8feX7HXTOJ4SQPhryZo8yRpJNdTQQe/TpkC9MLyl5S9iY/pnx3k+KVxmySeKR+BgRMmFYAjvrJdNwGfYuMMPJX5eV374esQDdkmtm7qY9T5wtWl104vmtQOHL4dtLQuEM7CYOYs3xqGdkVPaUzQFqEl7KRf5C8pfSVoGd0RXo/8rMMpXW6cThoBDf3fM4oKjijyWKnHrozzdlHRzn4kOV/n1LKcsAQ/80Ol78m4/DvLl0J4uxUVu9vX8TQVQK/BQIzOx+/5PgA08UEvZe9D+YvL/h40PgoReYvKnq2eW5yIbgEVuEDzvmoRqPtUtG0qHgXlYXB1PxHKe6b7Foa8k+hJwOD2/EWlb6k8xW8XAlgB+b3T6bjcqO8As9F4T93le36RRbkHRuBh4gE8AgYQRkmt0uLl+bb77rfabk7fl5/vSNprJU/QvmiFSQRp+SN7cVqiozSCvIZZYD6Rsgb0zKpyK6v3WJzp11Z6TzEmy6LkWmddRNNnnUPpGUEnn0KWtL2inCq2bAyZJlqRLldCtFipfCpwcTZ8o0ro7d+8JeX/gDbjBRAjt0W9LvwRluUn8XOmsowb9QJiy7CTPE+iAbYGaPmLyn6F+ccF0agpcKxsb2655LR761qjwc8Mj6+/SJ6nFm/8LsTgPwKLDjN5rKRBmw7DesWleUs23m8mX/6dZS+jVy0ykzZ0GvlVrAx8J3Sa+IvFWQX3Ysb7e6iZOxq1A5a/G7m47P9Fg1c4Hrh3T6C8a/ieh0sbSTz4NmLV6Eo+wC2S/Md7HqyArEcb/22nncD4NRxad7cdHqHyxsvzHY13f6h2Bovry893sDZFg95bgj/X3f3T6bm/jkYjmEdGZj9yOo0nWaNVBvPpEvrN6/Try+bNx4WXfZfcOUP0UZbDMtrbOv0CSkpKphkQ/tPSAiZJTfGs2FJK27byxHnfcckuxz7Udgb8wXirNR+kBYGyBALqHXYF3WNtkzfiA3EGXmTf52XMY/S+c8WqD8DDtt4zLCkt9nq9F0c6uIKw1Il6PCp5O86AjfX9PY3gQiIvhKnfuKmzBGW/G5XyIUGgXW94Ot0nYTb4DSs8MRD5NfIaW4sJwwiFNuJk8F/u+Kz0asnT+SHuSXOYLHEXzWp6nbLnNLRlZaSVQ96tEJIvylu8cWGkPCLJh3fBizggbCzU2p7ilZ5IeOjzgMkRvLvuk90dk7FyEXbVSJ//RAo/ubj0W4B9Pt4n1gbxyIQDIP/8+Y7SK6FGFpX7Fgz3eHi+o/XuD9bGUPS+/HyHapeduN4U/Mnl8EZtpjYte7AdHEzlVYX+luYmU+n1iVjonzbjbHImJFDLaXP00ZbD7cUzydtvgJKPrebMOP1cSk1Nt8yHM2zdvIFY9aevuDljMnkpPW4FYD60BwLq791e71gWjPBhWGsdW7mJBTKc/noVBKtTeIOodR5dOVB+TNWC8OUyxR8z9n/xerwT0K5HUKdN+D0KD91pfwe95JD8WO1n36GNE72y/FN8QyGwBVqN8OfIqiaKwP+4p7NzdN6i0h+NvHNrvT5NT4aLFm2pGLlo44Uer+dCtOEZ1PBQBOW3oF3Pkts9CULnJYV3b66xymMhBiLIew3OwJuJvC+bxLIaeynu6XS3jMpbXLaILS8xnrinvzC6n1wnqP0E3Gem23Ve8oTsK2b4834SCNGzZA9djXvxJtoRfmUKp6KhU31CXu+P9x8qLektdRgevMKy1w0d5B3jlb1/wv3baabN+jRo95d4Nm/cf/DAMLy7bum2IKRPZhi2eg9i/T4yrGQMiAuVZ6d0idftnY42hX3Hdz0b8quYuDiHVy95BdAtyfv0g7ZQ71OrWHfVsfef70jf/Vbba3Sbe/r5jnX/DtU/jNqvp4VU79MnjnH4H+Dvp/ead/4sGnnOTOqXPyxs0Wec/VXqB6s+sXKK0A/rPS0tNoT+mRD6ncbbKt549Z+Wqn7x5dcZpuf6ffbpB1iZiGzibULxKVQ4apwh72gQvV4Pvfsm3nb+J+0GsG7ec4D2rCmjzc++po9bDsJ58OE/zPqcvRzGRsFCbMjDQUfeAmh8DsaGJyz7SBixyqlQpN2P8B7MmO7xOuTd+F1T337knZ5UQ+lleGwVz2YlE9NSzga+Q2WHd6BEjv2YtRwhOaSd5PXsgCLHjl3eo1XxjOdSnPdQOG3SWZJTPhv9YggEMWy+pEGYDxyI/uHFQWA8MDgIve2DiFuPTYOfHDhYuob3DtgCT5eZrQo5E+QJDsmRB7WhPHwk9pJXKkD5+7wSrHN00GcFd5du0WXzBdksqZQgXYLNsGyyEGNf2oOB3OdP3Vn24UIISr6EcXzBZyPkZGef7fDKwMDB96BDdsgZwN2D673Apb5V8iwbv2hL3K04AmPH9+ZNGA9rV6ei/0zFM1GEd0x/CAtZ2D7CM0OH0Y5a9DF4by36Vq3s8ZZ3q67E8V2J/6pV3ZzfX0pOOxkbKthGP973tAUD3hHAfxfwr2uROj/q7T4jnm+ivvx8R+MpQN+MK3cfavMzeKVe/YpGUP75p1PqoGwaMBbfHYfxAkV6eiadfe4lMWtIa0uzotMfsdCf2z3TH0To54pHS/BnXmxliE2M8vkCkbjiSVMpv3BsJFlN5dmw9jPaWVsZNO3RqjpqqKmnves20Z5VG7Tp/ofAFfBR0cfVMhbXAgGBgEBAICAQEAgIBI53BIwl6d5r9c0o+qfwygzW0R07qal+H7XsPUh7126iYAd+TSg5JWY17gmhP9qVZ11/Vvth3f9IXNnGNVRTvS2SrKbyjBk/mRISEgPSQj+Z9m/cqgj9HU0ttB/3vNthsoR4s+Kl8ELo7wZF/AgEBAICAYGAQEAgIBCwgkDsd8NaqU1XWrbdzbaleQo/qaF6F6UNySUnDuZq2XeQElKT4VOUlLDBTJOmTKehw/KUcLT/2RX62byootMfYqZfrTNvsLXixoybFDJ5YmISDRw0jHbvqgmrVmPEaN+eXZSckhYT9akE7HFgbPbt3QXV5C45vqOxmfZv2EKdjS3UfrSRKt+A0nCLsmLBg0BeBfqDUT0FTSAgEBAICAQEAgIBgYBAwBwC8Sj4c823w78Jf7Hs8fQ7tKWS2huaFP0fFv4lj0xjT51GJ02dRbE6tIuF/pXL3yf+jcSxYHvqjLOC6vTreUZb8Gf+POOfM3CIIvyzbr1Vt3dPnbJZOLNfltWsYdMnp6TSiLxRqGMS1XyxjnauWEPNWN3hGf+6j78gT2s78zgKfyX8vzggnEBAICAQEAgIBAQCAgGBQOQIxJuOv74l/UF4Cf4r+ojcwnz6/j8epfxTT9JH2Q73tNDPFY6mjr8egCNHDtKq5R9idj2SPYASBlin0bDh+Xq2tsMHa3bS49f9gKpXrzXiVQ4ir/pUGUUKmkBAICAQEAgIBAQCAgGBgDUE4nXGX20FW275B3wSPJua8+1JaDl8hD579j/kbm+nsWefbnh4HtJbdopVHBzO1VMz/WoFYzHjr/JOTk4lNiVaD7UfGSY2rLo99XU4ICwTZyXwOCw67tMnnqWHr/oOHayuNWL4PIhfhT9oFCloAgGBgEBAICAQEAgIBAQC1hGId8FfbdGHuOBp4QvhuxT8ccFC7Pblq2jjG+9S0cxplDkwF9TIXXSE/uAmO0PVLJaCP5ebAtWaAQMGdgn/MCZs1e3ZvZMyIfhHekKwWt6R+j302LU30kd/fZQ8HQErEKzUzxu8F8BbH6GohYhfgYBAQCAgEBAICAQEAgKBAAT6iuDPFWczMzz7zyZ8CuB9rmHPPlrx1D+p5dBhGjv7DHJEcIIvH8r12Qq7M/0s9EcGaawFfwYrNTWNsgbkRCz8766vxWbfLGLzqZG4d+95gB7/5vdpz+YKo+ys2sP2+d8yihQ0gYBAQCAgEBAICAQEAgIBewhEJqXaK9NObj496xn4Rvgz4BPgFcez/1VffAn1nxdo8JgiGjiqUI0K+6sI/azeE+GhV10beSMX+rmCPSH4czmpaekQ3rOJhXgc4sIkS25P/U4lf1p6hul8NWs30gOXXkNfPP9fo1l+NuvzN/jL4feZZioSCgQEAgIBgYBAQCAgEBAIWELApzNvKVfvJ74HVeCZ//X6qhzeWUcPXHYt3T/natpTwcaBQrt4EPpD1zD6sQMHDaVTTj0jon0ROGqc1nz+Me3ftztsxY7u3UdPfOdHtPj0C6huI0/oBzhW8D8HntV7hGpPADyCIBAQCAgEBAICAYGAQCB6CPS1GX9tyw8g8Ch8C/wMeN4A7HMHqmrok8efoQPYPDr6jJmUmBJ4mFVrawut/PQ9asNvJC4XpjJPnWFvpl8tt6dm/NXylM26Gf2IdfetOl4p2L2rlgZkD1TUh/T53R0d9Nodi+jJ7/4f7Vy3EZsxAlYWOpDnQXi22hP8CF89YxEWCAgEBAICAYGAQEAgIBCIGIG+LPirjV6Ji6fhJ8CPhvc5Vv+p21BGnzz6NLUebaCC6aeQCweBsWPh9fMVH1FTU4MvvZULFvqnTmc7/dGBsKcFf25rRmY/YpUdVt+x6hg/PuRrRF6R76wCDw7j4k27j33zRtr03kfk6QzYvMvF8OFs/xsCgwAAB/tJREFUF8Gzypb1wwWQSTiBgEBAICAQEAgIBAQCAgHrCERHarVebrRzsO7/P+FL4afB+504xTPQO1Z+QcseeZKasQG4EAOAQ4f2U+WOzUhq3UVb6Oca9Ibgz+WypZ6U1HTau7uOg5acx+NRBj79+g2g9+97SLHJv+7VN6m9udmID6/QzIP/AbzQ5TdCSNAEAgIBgYBAQCAgEBAIxBCB40XwVyFiSZ43irJZyJPhfaY/cQ2b/x1UuWo1LX34SepMksiVlQELQNa2OcRC6Oe69Zbgz2X3w8m8Sckpygw+h806ZUVlbSn94xs30YbX36H2JkOBn+/FQ/Cs1rPCLG+RTiAgEBAICAQEAgIBgYBAILoIHG+CP6PDCuUsYD4MzzP/xfAueJ/zYAWAUhLI3dpG7rZ2ckH/35mY4IsPdhEroZ/L603Bn8vvD0s/CYlJtH9vPQdDOsasoXY3HdpcSYeraql+VcAea87PajyvwLNazwvwhno/oAsnEBAICAQEAgIBgYBAQCDQAwj4CcQ9UF5PFtGIwv4P/g/wf4S/Bt63AuBuaSPZ46Xm3fsVn9Q/k9KH5lJKThZJjsBVgFgK/ahXXLiCwrHkhfrO5vJ1AfVhnf62w0eB1QFqPXDYt2GXcdQ5Ns/5NjwfwmVoykeXXgQFAgIBgYBAQCAgEBAICAR6AIHjWfBX4eMp7BvgfwnPA4Br4VMaauspp3g0Lrtc+5EGYu9IcFFq7gBKG5xDiZnpSmTuwKHYyHtm1DbyqmXG42/R6AnEJju3bt6gVK+zpZWa9xyglr0HyNMeOGnfiJn/bscC/xvwjPPmbpr4EQgIBAQCAgGBgEBAICAQiBMETgTBX4V6Dy5uhOeZ6Nsba+q/C4E2lwV8rfN2uqmpfp/iWQUoGbrveTMHk8NgFUCb73i6dh3toIb1O6jV3UodTcFNnbKq1IGybbyx+j/wf4YXpjmPp44g2iIQEAgIBAQCAgGBwHGFwIkk+Ks3bj8u5sL/cv+6zbemXnj67yRJ8jsDQE14oKyCaj9YSSu8D1HagCwa95UzqGTOBTTp4vMptV8/NVmf/2WrR2XvfEgb3niHNn+wjI7s6prFHzS1mAafWmLYPofL6dlfvu0xT3vHbUgQfHRgmFsQBQICAYGAQEAgIBAQCAgEehoBqacLjLfyZj2xJMNTt/N+b3vn193NrWls+acNOuz7Syvo8NYqw+pKsN0/dPwYGnPmLJp4wVdo9FmzKCnFt33AME844vtvv0Tt7QH68obZUlLT6JzzLzeMM0Nke/s7YN2oHML+1mXLaSfOOlA2PBtkThs6kAaeNAH7HwaSMymBEjPS2/H7Uf9RI256+1vz6gyyCJJAQCAgEBAICAQEAgIBgUAcInDCC/7ae5Jz6aUZB9588+vk8XwX9Onw4U39IBEPBHIL82nklGIqnDEN5wRMpeG4diWYyg4OROvWrKBdddXKdbh/haPG04RitlYa3vGm3F1lm6nqiy8VU6a1azfQnoodQQV9A45e0HD8Lj2XMW7Y041bdh00SCNIAgGBgEBAICAQEAgIBAQCcY6AEPyD3yA2Bfot+CvhZ8AbqgOBbuh4MNB/6BAaWJRPg8aMppzCkbgupEGjiyh3VEHAoKCh4Qh9uvQt5URhQ4bdRJ7tP3P2HEpI6DqBmMm8GfdgdS3trdhO+7ZX4bqGdm/dTvt3VNKh2l3BTtANVQxv1GUbna/C8wm7YmYfIAgnEBAICAQEAgIBgYBAoC8jIAR/c3ePzft8HX4O/Ez4ofCRO0milMwMSs6A75eB/QKZlNq/H6UMH0gJeQOxkRi3BZuJJfzKXhxLgFl7nrn3trRTy6YaaoKFndajDdTW0EitjfCwRsSHadl0h5D/c/j34P8Jz3shhBMICAQEAgIBgYBAQCAgEDhOEBCCf2Q3cjyyXQE/G34SfC58VFwqrAwNmT6Z0obkEjYdKzw7GprowKbtdGBjBc4e4HOxouKOgksZ/Cfwr8Gz0C+cQEAgIBAQCAgEBAICAYHAcYqAEPyjc2NHgs158KfDsxmcAvgB8BE7Z2IiJaSnEG82xqbjiPl0Z2STm9XwLOivhP8QfhO8cAIBgYBAQCAgEBAICAQEAicIAkLwj92N/v/t3KEOwjAARVGDAYEhAQSS//8Q/gGDAzvF1N5LJrAkdTtNbmpmdlSXte1fgB4Q7ince7qlbhG6pmMabd/F/Tv1Ls7uyX+m7tN/pFcyCBAgQIAAAQIENiwwevG5Ycq/Xn2fp/shcEnntVPmQ+oh4p7cbbvUvT1z+q5z7/zszTqfn7rQn5JBgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgMB4gQWhIPHlJzLdxAAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #0086b3; width: 800px; height: 50px; padding: 10px; border: 3px solid #ccc;\">\n",
    "    <span style=\"color: #e6f9ff; font-weight: bold;\"><h1>Monte Carlo simulation</h1></span>\n",
    "</div>\n",
    "\n",
    "![image.png](attachment:image.png)\n",
    "\n",
    "Monte Carlo simulation is a powerful technique for modeling and analyzing complex systems by using random numbers. It's widely used in various fields such as finance, physics, engineering, and computer science. Following topics will be covered:\n",
    "\n",
    "- Introduction to Monte Carlo Simulation\n",
    "- Basic Principles\n",
    "- Steps in Monte Carlo Simulation\n",
    "- Statistics\n",
    "  - Probability Distributions\n",
    "  - Estimation and Sampling\n",
    "  - Confidence Intervals\n",
    "- Generating Random Numbers\n",
    "- Variance Reduction Techniques\n",
    "- Applications of Monte Carlo Simulation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Monte Carlo simulations and Machine learning algorithms\n",
    "\n",
    "- Monte Carlo simulations are a class of computational techniques that use random sampling to approximate and analyze complex systems or problems. \n",
    "- While Monte Carlo simulations themselves are not typically considered machine learning algorithms, they can be combined with machine learning techniques to enhance their capabilities. \n",
    "- It's important to note that the specific choice of machine learning algorithms in Monte Carlo simulations depends on the nature of the problem, the available data, and the objectives of the simulation. \n",
    "- Different algorithms may be more suitable for different scenarios, and their selection should be based on careful analysis and experimentation."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #ffbb99; width: 800px; height: 30px; padding: 10px; border: 3px solid #ccc;\">\n",
    "    <span style=\"color: #331100; font-weight: bold;\"><h2>Introduction to Monte Carlo Simulation</h2></span>\n",
    "</div>\n",
    "\n",
    "Monte Carlo simulation is named after the famous Monte Carlo Casino in Monaco, which is known for its games of chance. It is a computational technique that uses random sampling and statistical analysis to model and solve problems. By repeatedly sampling from probability distributions, Monte Carlo simulation allows us to estimate the behavior of complex systems or processes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #ffbb99; width: 800px; height: 30px; padding: 10px; border: 3px solid #ccc;\">\n",
    "    <span style=\"color: #331100; font-weight: bold;\"><h2>Basic Principles</h2></span>\n",
    "</div>\n",
    "\n",
    "The basic principle of Monte Carlo simulation involves performing a large number of experiments or simulations using random inputs to analyze the output. The results are then statistically analyzed to provide insights into the system's behavior or to estimate unknown quantities."
   ]
  },
  {
   "attachments": {
    "image-2.png": {
     "image/png": "iVBORw0KGgoAAAANSUhEUgAACUYAAAE0CAYAAADq/nt/AAAMPWlDQ1BJQ0MgUHJvZmlsZQAASImVVwdYU8kWnluSkEBogVCkhN4E6VVKCC10qYKNkAQIJcZAELEjiwquXVTAhq6KKHZA7IidRbH3xYKIsi7qYlfepIBlX/nefN/c+e8/Z/5z5tyZe+8AoHaCIxLlouoA5AkLxHGhgYyxKakMUg8gASLQAFZAh8PNFzFjYyMBLEPtj+XtDYBI26v2Uq1/9v/XosHj53MBQGIhTuflc/MgPgAAXsMViQsAIEp5s6kFIimGFWiJYYAQL5DiTDmukeJ0Od4js0mIY0HcBoCSCocjzgRA9TLkGYXcTKih2g+xo5AnEAKgxoDYLy9vMg/iNIitoY0IYqm+Z/p3Opk/aKYPa3I4mcNYPhdZUQoS5ItyOdP+z3T875KXKxnyYQmrSpY4LE46Z5i3WzmTI6RYBeI+YXp0DMSaEL8X8GT2EKOULElYotweNeDms2DOAB1iRx4nKAJiA4hDhLnRkQo+PUMQwoYYrhC0SFDAToBYF+IF/PzgeIXNRvHkOIUvtDFDzGIq+HMcscyv1NcDSU4iU6H/OovPVuhjqsVZCckQUyA2LxQkRUOsCrFDfk58hMJmdHEWK3rIRiyJk8ZvDnEcXxgaKNfHCjPEIXEK+/K8/KH5YhuzBOxoBd5XkJUQJs8P1sblyOKHc8Eu84XMxCEdfv7YyKG58PhBwfK5Y8/4wsR4hc57UUFgnHwsThHlxirscVN+bqiUN4XYNb8wXjEWTyqAC1Kuj2eICmIT5HHixdmc8Fh5PPhSEAlYIAgwgATWdDAZZANBR19TH7yT94QADhCDTMAH9gpmaESyrEcIr/GgGPwJER/kD48LlPXyQSHkvwyz8qs9yJD1FspG5ICnEOeBCJAL7yWyUcJhb0ngCWQE//DOgZUL482FVdr/7/kh9hvDhEykgpEMeWSoDVkSg4lBxDBiCNEG18f9cB88El4DYHXGPXGvoXl8syc8JXQSHhGuE7oItycJSsQ/RRkFuqB+iCIX6d/nAreEmm54IO4L1aEyTsf1gT3uCv0wcX/o2Q2yLEXc0qwwftL+YQbfPQ2FHdmRjJJ1yAFk659Hqtqqug2rSHP9fX7ksaYP55s13POzf9Z32efBNuJnS2wBth87i53EzmNHsCbAwI5jzVg7dlSKh1fXE9nqGvIWJ4snB+oI/uFv6MlKM5nvWO/Y6/hZ3lfAL5K+owFrsmiaWJCZVcBgwi8Cn8EWch1GMpwdnV0AkH5f5K+vN3TZdwOhX/jGzasDwPfQ4ODg4W9cOHy37k2D2//gN856AtxaPQCcO8KViAvlHC69EOBbQg3uND1gBMyANZyPM3AHPiAABINwEAMSQAqYCKPPgutcDKaCGWAuKAMVYClYBarABrAZbAe7wD7QBI6Ak+AMuAgug+vgLlw93eAF6AdvwScEQUgIFaEheogxYoHYIc6IJ+KHBCORSBySgqQhmYgQkSAzkHlIBbIcqUI2IXXIXuQQchI5j3Qit5GHSC/yGvmIYqgKqoUaopboKNQTZaIRaAI6Ac1Ep6DFaCm6GF2D1qI70Ub0JHoRvY52oS/QAQxgyhgdM8HsMU+MhcVgqVgGJsZmYeVYJVaLNWAt8DlfxbqwPuwDTsRpOAO3hys4DE/EufgUfBa+CK/Ct+ONeBt+FX+I9+NfCVSCAcGO4E1gE8YSMglTCWWESsJWwkHCabiXuglviUQinWhF9IB7MYWYTZxOXERcR9xNPEHsJD4mDpBIJD2SHcmXFEPikApIZaS1pJ2k46QrpG7SeyVlJWMlZ6UQpVQloVKJUqXSDqVjSleUepQ+kdXJFmRvcgyZR55GXkLeQm4hXyJ3kz9RNChWFF9KAiWbMpeyhtJAOU25R3mjrKxsquylPEZZoDxHeY3yHuVzyg+VP6hoqtiqsFTGq0hUFqtsUzmhclvlDZVKtaQGUFOpBdTF1DrqKeoD6ntVmqqDKluVpzpbtVq1UfWK6ks1spqFGlNtolqxWqXafrVLan3qZHVLdZY6R32WerX6IfWb6gMaNA0njRiNPI1FGjs0zms80yRpWmoGa/I0SzU3a57SfEzDaGY0Fo1Lm0fbQjtN69YiallpsbWytSq0dml1aPVra2q7aidpF2lXax/V7qJjdEs6m55LX0LfR79B/6hjqMPU4ess1GnQuaLzTneEboAuX7dcd7fudd2Pegy9YL0cvWV6TXr39XF9W/0x+lP11+uf1u8boTXCZwR3RPmIfSPuGKAGtgZxBtMNNhu0GwwYGhmGGooM1xqeMuwzohsFGGUbrTQ6ZtRrTDP2MxYYrzQ+bvycoc1gMnIZaxhtjH4TA5MwE4nJJpMOk0+mVqaJpiWmu03vm1HMPM0yzFaatZr1mxubR5nPMK83v2NBtvC0yLJYbXHW4p2llWWy5XzLJstnVrpWbKtiq3qre9ZUa3/rKda11tdsiDaeNjk262wu26K2brZZttW2l+xQO3c7gd06u86RhJFeI4Uja0fetFexZ9oX2tfbP3SgO0Q6lDg0ObwcZT4qddSyUWdHfXV0c8x13OJ410nTKdypxKnF6bWzrTPXudr5mgvVJcRltkuzyytXO1e+63rXW240tyi3+W6tbl/cPdzF7g3uvR7mHmkeNR43PbU8Yz0XeZ7zIngFes32OuL1wdvdu8B7n/dfPvY+OT47fJ6NthrNH71l9GNfU1+O7ybfLj+GX5rfRr8ufxN/jn+t/6MAswBewNaAHqYNM5u5k/ky0DFQHHgw8B3LmzWTdSIICwoNKg/qCNYMTgyuCn4QYhqSGVIf0h/qFjo99EQYISwibFnYTbYhm8uuY/eHe4TPDG+LUImIj6iKeBRpGymObIlCo8KjVkTdi7aIFkY3xYAYdsyKmPuxVrFTYg+PIY6JHVM95mmcU9yMuLPxtPhJ8Tvi3yYEJixJuJtonShJbE1SSxqfVJf0LjkoeXly19hRY2eOvZiinyJIaU4lpSalbk0dGBc8btW47vFu48vG35hgNaFowvmJ+hNzJx6dpDaJM2l/GiEtOW1H2mdODKeWM5DOTq9J7+eyuKu5L3gBvJW8Xr4vfzm/J8M3Y3nGs0zfzBWZvVn+WZVZfQKWoErwKjsse0P2u5yYnG05g7nJubvzlPLS8g4JNYU5wrbJRpOLJneK7ERloq4p3lNWTekXR4i35iP5E/KbC7Tgj3y7xFryi+RhoV9hdeH7qUlT9xdpFAmL2qfZTls4rac4pPi36fh07vTWGSYz5s54OJM5c9MsZFb6rNbZZrNLZ3fPCZ2zfS5lbs7c30scS5aX/D0veV5LqWHpnNLHv4T+Ul+mWiYuuznfZ/6GBfgCwYKOhS4L1y78Ws4rv1DhWFFZ8XkRd9GFX51+XfPr4OKMxR1L3JesX0pcKlx6Y5n/su3LNZYXL3+8ImpF40rGyvKVf6+atOp8pWvlhtWU1ZLVXWsi1zSvNV+7dO3nqqyq69WB1btrDGoW1rxbx1t3ZX3A+oYNhhsqNnzcKNh4a1PopsZay9rKzcTNhZufbknacvY3z9/qtupvrdj6ZZtwW9f2uO1tdR51dTsMdiypR+sl9b07x++8vCtoV3ODfcOm3fTdFXvAHsme53vT9t7YF7Gvdb/n/oYDFgdqDtIOljcijdMa+5uymrqaU5o7D4Ufam3xaTl42OHwtiMmR6qPah9dcoxyrPTY4PHi4wMnRCf6TmaefNw6qfXuqbGnrrWNaes4HXH63JmQM6fOMs8eP+d77sh57/OHLnheaLrofrGx3a394O9uvx/scO9ovORxqfmy1+WWztGdx674Xzl5NejqmWvsaxevR1/vvJF449bN8Te7bvFuPbude/vVncI7n+7OuUe4V35f/X7lA4MHtX/Y/LG7y73r6MOgh+2P4h/dfcx9/OJJ/pPP3aVPqU8re4x76p45PzvSG9J7+fm4590vRC8+9ZX9qfFnzUvrlwf+CvirvX9sf/cr8avB14ve6L3Z9rfr360DsQMP3ua9/fSu/L3e++0fPD+c/Zj8sefT1M+kz2u+2Hxp+Rrx9d5g3uCgiCPmyH4FMFjRjAwAXm8DgJoCAA3+Q1DGyc9/soLIz6wyBP4Tlp8RZcUdgAbYSH/jWScA2AOr5Rx4TgwAQPoLnxAAUBeX4Tp0VpOdK6WFCM8BG12l6Aq9aA74qcjPnN/F/XMLpKqy4T+0/wIHPnu6BXwUgwAAAIplWElmTU0AKgAAAAgABAEaAAUAAAABAAAAPgEbAAUAAAABAAAARgEoAAMAAAABAAIAAIdpAAQAAAABAAAATgAAAAAAAACQAAAAAQAAAJAAAAABAAOShgAHAAAAEgAAAHigAgAEAAAAAQAACUagAwAEAAAAAQAAATQAAAAAQVNDSUkAAABTY3JlZW5zaG90kh+edwAAAAlwSFlzAAAWJQAAFiUBSVIk8AAAAddpVFh0WE1MOmNvbS5hZG9iZS54bXAAAAAAADx4OnhtcG1ldGEgeG1sbnM6eD0iYWRvYmU6bnM6bWV0YS8iIHg6eG1wdGs9IlhNUCBDb3JlIDYuMC4wIj4KICAgPHJkZjpSREYgeG1sbnM6cmRmPSJodHRwOi8vd3d3LnczLm9yZy8xOTk5LzAyLzIyLXJkZi1zeW50YXgtbnMjIj4KICAgICAgPHJkZjpEZXNjcmlwdGlvbiByZGY6YWJvdXQ9IiIKICAgICAgICAgICAgeG1sbnM6ZXhpZj0iaHR0cDovL25zLmFkb2JlLmNvbS9leGlmLzEuMC8iPgogICAgICAgICA8ZXhpZjpQaXhlbFlEaW1lbnNpb24+MzA4PC9leGlmOlBpeGVsWURpbWVuc2lvbj4KICAgICAgICAgPGV4aWY6UGl4ZWxYRGltZW5zaW9uPjIzNzQ8L2V4aWY6UGl4ZWxYRGltZW5zaW9uPgogICAgICAgICA8ZXhpZjpVc2VyQ29tbWVudD5TY3JlZW5zaG90PC9leGlmOlVzZXJDb21tZW50PgogICAgICA8L3JkZjpEZXNjcmlwdGlvbj4KICAgPC9yZGY6UkRGPgo8L3g6eG1wbWV0YT4KpI6SzQAAABxpRE9UAAAAAgAAAAAAAACaAAAAKAAAAJoAAACaAADX4XmFTP4AAEAASURBVHgB7N0HeBTV3sfxfzohtNB7aKJSpBdBQbAXsKJgARv2rqjoVbBhwWu/KuqrYsfLtYIKKihVBUWKivTeCSWQRgjvnMVNdmbOZHaX7O6QfOd5fHfnzJkzs5+z7xwu++OcuAPGJmwIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAQBkSiCMYVYZ6k4+CAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACCCCAAAIIIIAAAggggAACPgGCUXwREEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAGCUXwHEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAAAEEEEAAAQQQQAABBBBAoMwJEIwqc13KB0IAAQQiJxAXFxe5xmkZAQQQiKLAgQMHong1LhUowFgSqMF7BBA43AUYT2LTg4wlsXHnqgggEBkBxpLIuLq1yljiJsRxBBA4XAQYRw6XnuI+EUAAAQRiKUAwKpb6XBsBBBA4zAT4S6PDrMO4XQQQcBTgL40caSJ+gLEk4sRcAAEEoijAeBJF7IBLMZYEYPAWAQQOewHGkth0IWNJbNy5KgIIlL4A40jpm9IiAggggEDZEyAYVfb6lE+EAAIIREyAvzSKGC0NI4BAlAX4S6MogwdcjrEkAIO3CCBw2AswnsSmCxlLYuPOVRFAIDICjCWRcXVrlbHETYjjCCBwuAgwjsSmpxhHYuPOVRFAIDIC5WEsIRgVme8OrSKAAAJlUoA/7JfJbuVDIVAuBcrDH/S92rGMJV7tGe4LAQTCEWA8CUft0M9hLDl0Q1pAAAHvCDCWxKYvGEti485VEUCg9AUYR0rfNJgWGUeCUaIOAggcLgLlYSwhGHW4fBu5TwQQQMADAvxh3wOdwC0ggECpCJSHP+iXClQEGmEsiQAqTSKAQMwEGE9iQ89YEht3rooAApERYCyJjKtbq4wlbkIcRwCBw0WAcSQ2PcU4Eht3rooAApERKA9jCcGoyHx3aBUBBBAokwK6P+wv6dmyTH5WPhQCCJQdgZYzl9g+THn4g77tQ3ukQDeWPPTn+R65O24DAQQQcBYY0ep/toOMJzaSqBToxpLdn/eKyrW5CAIIIHAoAlXOnmY7nbHERhKVAt1YcspbuVG5NhdBAAEEwhWYfEUF26mMIzaSqBToxpGoXJiLIIAAAhEQKA9jCcGoCHxxaBIBBBAoqwK6P+wTjCqrvc3nQqDsCBCM8lZf6sYSglHe6iPuBgEE9AIEo/QusSjVjSUEo2LRE1wTAQRCFSAYFapY5OrrxhKCUZHzpmUEECgdAYJRpeNYGq3oxpHSaJc2EEAAgVgIEIyKhTrXRAABBBDwrIDuD/sEozzbXdwYAgj8I0AwyltfBd1YQjDKW33E3SCAgF6AYJTeJRalurGEYFQseoJrIoBAqAIEo0IVi1x93VhCMCpy3rSMAAKlI0AwqnQcS6MV3TiSt3RgaTRNGwgggEBEBVKO+MjWPsEoGwkFCCCAAALlWUD3h32CUeX5G8FnR+DwECAY5a1+0o0lBKO81UfcDQII6AUIRuldYlGqG0sIRsWiJ7gmAgiEKkAwKlSxyNXXjSUEoyLnTcsIIFA6AgSjSsexNFrRjSMEo0pDljYQQCDSAgSjIi1M+wgggAACh72A7g/7BKMO+27lAyBQ5gUIRnmri3VjCcEob/URd4MAAnoBglF6l1iU6sYSglGx6AmuiQACoQoQjApVLHL1dWMJwajIedMyAgiUjgDBqNJxLI1WdOMIwajSkKUNBBCItADBqDCEdQ/9MJrhFAQQQMATAuVhmsBDhdY99wlGHaoq5yOAQKQFCEZFWji09nVjCcGo0AypjQACsREgGBUbd91VdWMJwSidFGUIIOA1AYJR3ukR3VhCMMo7/cOdIICAXoBglN4lFqW6cYRgVCx6gmsigECoAgSjQhUz6use+mE0wykIIICAJwQIRrl3g+65TzDK3Y0aCCAQWwGCUbH1t15dN5YQjLIqsY8AAl4UIBjlnV7RjSUEo7zTP9wJAgg4CxCMcraJ9hHdWEIwKtq9wPUQQCBUAYJRoYpFrr5uHCEYFTlvWkYAgdITIBgVhqXuoR9GM5yCAAIIeEKAYJR7N+ie+wSj3N2ogQACsRUgGBVbf+vVdWMJwSirEvsIIOBFAYJR3ukV3VhCMMo7/cOdIICAswDBKGebaB/RjSUEo6LdC1wPAQRCFSAYFapY5OrrxhGCUZHzpmUEECg9AYJRYVjqHvphNMMpCCCAgCcECEa5d4PuuU8wyt2NGgggEFsBglGx9bdeXTeWEIyyKrGPAAJeFCAY5Z1e0Y0lBKO80z/cCQIIOAsQjHK2ifYR3VhCMCravcD1EEAgVAGCUaGKRa6+bhwhGBU5b1pGAIHSEyAYFYal7qEfRjOcggACCHhCgGCUezfonvsEo9zdqIEAArEVIBgVW3/r1XVjCcEoqxL7CCDgRQGCUd7pFd1YQjDKO/3DnSCAgLMAwShnm2gf0Y0lBKOi3QtcDwEEQhUgGBWqWOTq68YRglGR86ZlBBAoPQGCUWFY6h76YTTDKQgggIAnBAhGuXeD7rlPMMrdjRoIIBBbAYJRsfW3Xl03lhCMsiqxjwACXhQgGOWdXtGNJQSjvNM/3AkCCDgLEIxyton2Ed1YQjAq2r3A9RBAIFQBglGhikWuvm4cIRgVOW9aRgCB0hMgGBWGpe6hH0YznIIAAgh4QoBglHs36J77BKPc3aiBAAKxFSAYFVt/69V1YwnBKKsS+wgg4EUBglHe6RXdWEIwyjv9w50ggICzAMEoZ5toH9GNJQSjot0LXA8BBEIVIBgVqljk6uvGEYJRkfOmZQQQKD0BglFhWOoe+mE0wykIIICAJwQIRrl3g+65TzDK3Y0aCCAQWwGCUbH1t15dN5YQjLIqsY8AAl4UIBjlnV7RjSUEo7zTP9wJAgg4CxCMcraJ9hHdWEIwKtq9wPUQQCBUAYJRoYpFrr5uHCEYFTlvWkYAgdITIBgVhqXuoR9GM5yCAAIIeEKAYJR7N+ie+wSj3N2ogQACsRUgGBVbf+vVdWMJwSirEvsIIOBFAYJR3ukV3VhCMMo7/cOdIICAswDBKGebaB/RjSUEo6LdC1wPAQRCFSAYFapY5OrrxhGCUZHzpmUEECg9AYJRYVjqHvphNMMpCCCAgCcECEa5d4PuuU8wyt2NGgggEFsBglGx9bdeXTeWEIyyKrGPAAJeFCAY5Z1e0Y0lBKO80z/cCQIIOAsQjHK2ifYR3VhCMCravcD1EEAgVAGCUaGKRa6+bhwhGBU5b1pGAIHSEyAYFYal7qEfRjOcggACCHhCgGCUezfonvsEo9zdqIEAArEVIBgVW3/r1XVjCcEoqxL7CCDgRQGCUd7pFd1YQjDKO/3DnSCAgLMAwShnm2gf0Y0lBKOi3QtcDwEEQhUgGBWqWOTq68YRglGR86ZlBBAoPQGCUWFY6h76YTTDKQgggIAnBAhGuXeD7rlPMMrdjRoIIBBbAYJRsfW3Xl03lhCMsiqxjwACXhQgGOWdXtGNJQSjvNM/3AkCCDgLEIxyton2Ed1YQjAq2r3A9RBAIFQBglGhikWuvm4cIRgVOW9aRgCB0hMgGBWGpe6hH0YznIIAAgh4QoBglHs36J77BKPc3aiBAAKxFSAYFVt/69V1YwnBKKsS+wgg4EUBglHe6RXdWEIwyjv9w50ggICzAMEoZ5toH9GNJQSjot0LXA8BBEIVIBgVqljk6uvGEYJRkfOmZQQQKD0BglFhWOoe+mE0wykIIICAJwQIRrl3g+65TzDK3Y0aCCAQWwGCUbH1t15dN5YQjLIqsY8AAl4UIBjlnV7RjSUEo7zTP9wJAgg4CxCMcraJ9hHdWEIwKtq9wPUQQCBUAYJRoYpFrr5uHCEYFTlvWkYAgdITIBgVhqXuoR9GM5yCAAIIeEKAYJR7N+ie+wSj3N2ogQACsRUgGBVbf+vVdWMJwSirEvsIIOBFAYJR3ukV3VhCMMo7/cOdIICAswDBKGebaB/RjSUEo6LdC1wPAQRCFSAYFapY5OrrxhGCUZHzpmUEECg9AYJRYVjqHvphNMMpCCCAgCcECEa5d4PuuU8wyt2NGgggEFsBglGx9bdeXTeWEIyyKrGPAAJeFCAY5Z1e0Y0lBKO80z/cCQIIOAsQjHK2ifYR3VhCMCravcD1EEAgVAGCUaGKRa6+bhwhGBU5b1pGAIHSEyAYFYal7qEfRjOcggACCHhCgGCUezfonvsEo9zdqIEAArEVIBgVW3/r1XVjCcEoqxL7CCDgRQGCUd7pFd1YQjDKO/3DnSCAgLMAwShnm2gf0Y0lBKOi3QtcDwEEQhUgGBWqWOTq68YRglGR86ZlBBAoPQGCUWFY6h76YTTDKQgggIAnBAhGuXeD7rlPMMrdjRoIIBBbAYJRsfW3Xl03lhCMsiqxjwACXhQgGOWdXtGNJQSjvNM/3AkCCDgLEIxyton2Ed1YQjAq2r3A9RBAIFQBglGhikWuvm4cIRgVOW9aRgCB0hMgGBWGpe6hH0YznIIAAgh4QoBglHs36J77BKPc3aiBAAKxFSAYFVt/69V1YwnBKKsS+wgg4EUBglHe6RXdWEIwyjv9w50ggICzAMEoZ5toH9GNJQSjot0LXA8BBEIVIBgVqljk6uvGEYJRkfOmZQQQKD0BglFhWOoe+mE0wykIIICAJwQIRrl3g+65TzDK3Y0aCCAQWwGCUbH1t15dN5YQjLIqsY8AAl4UIBjlnV7RjSUEo7zTP9wJAgg4CxCMcraJ9hHdWEIwKtq9wPUQQCBUAYJRoYpFrr5uHCEYFTlvWkYAgdITIBgVhqXuoR9GM5yCAAIIeEKAYJR7N+ie+wSj3N2ogQACsRUgGBVbf+vVdWMJwSirEvsIIOBFAYJR3ukV3VhCMMo7/cOdIICAswDBKGebaB/RjSUEo6LdC1wPAQRCFSAYFapY5OrrxhGCUZHzpmUEECg9AYJRYVjqHvphNMMpCCCAgCcECEa5d4PuuU8wyt2NGgggEFsBglGx9bdeXTeWEIyyKrGPAAJeFCAY5Z1e0Y0lBKO80z/cCQIIOAsQjHK2ifYR3VhCMCravcD1EEAgVAGCUaGKRa6+bhwhGBU5b1pGAIHSEyAYFYal7qEfRjOcggACCHhCgGCUezfonvsEo9zdqIEAArEVIBgVW3/r1XVjCcEoqxL7CCDgRQGCUd7pFd1YQjDKO/3DnSCAgLMAwShnm2gf0Y0lBKOi3QtcDwEEQhUgGBWqWOTq68YRglGR86ZlBBAoPQGCUWFY6h76YTTDKQgggIAnBAhGuXeD7rlPMMrdjRoIIBBbAYJRsfW3Xl03lhCMsiqxjwACXhQgGOWdXtGNJQSjvNM/3AkCCDgLEIxyton2Ed1YQjAq2r3A9RBAIFQBglGhikWuvm4cIRgVOW9aRgCB0hMgGBWGpe6hH0YznIIAAgh4QoBglHs36J77BKPc3aiBAAKxFSAYFVt/69V1YwnBKKsS+wgg4EUBglHe6RXdWEIwyjv9w50ggICzAMEoZ5toH9GNJQSjot0LXA8BBEIVIBgVqljk6uvGEYJRkfOmZQQQKD0BglFhWOoe+mE0wykIIICAJwQIRrl3g+65TzDK3c1aI6FKVZG4OGux7M/KEincbys/1IKEqtVsTezP2m1cq9BWXt4L4itVkbiEeBPDgf37pXCP0TfBbkbfxleqLHLggBzIy5UD+/YFeyb1IiRAMCpCsGE2qxtLCEaFiak5LWtrrmz6a6dkrt0rO9fvlR3Ga0F+oVRrUFGqN64k1RulSbrxX63mVSQ+wT4WaZqkCAEE/hEgGOWdr4JuLCEYZe6ftVty5dt5O2T91jzZmJkvm3fmS2J8nDStV0Ga1UuV5sZ/zYz3GXVSxShmQwCBKAkQjIoSdBCX0Y0lBKOCgKMKAgjEVIBgVEz5TRfXjSMEo0xE7CCAgEcFCEaF0TG6h34YzXAKAggg4AkBglHu3aB77hOMcnez1mj+7TyJT61oLZbVl54h+auW28oPtaDFd/MlrkIFUzO7J/5PNj9+n6mMHZGM9yZKcpMWJorcvxbK2qEXmMqsOwnVa0r6oCul0gmnSWLN2hKXlFRUpXDvHtnx/uuS+c6rRWW8ia4AwajoertdTTeWEIxyU3M/vnnJLpn55hJZ9NU62V/gHnxVAale1x0t7fo3JiDlzhtyjVFdv5D87ALTeV0HNZMz7m9vKrPuZBvBhZ/eWSpLp2+W3ZtzJHtHnsQnxktShQSpYoQXTr37GGneo7b1NPajJEAwKkrQQVxGN5YQjBLJ21cob03aKB//uEXmLgku2H9Eg1QZNqCxDOhdWxJISAXx7aMKAocmQDDq0PxK82zdWEIwqjSFaQsBBCIhQDAqEqrhtakbRwhGhWfJWQggEF0BglFheOse+mE0wykIIICAJwQIRrl3g+65TzDK3c1awwvBqD1Tv5GND9xqvbUysx+XnCIpLY+2fZ6CzRulYOtmW7m/IJxgVErzltLotf9KXIo5fOZvU73u+vRD2fLvkYFFvI+iAMGoKGIHcSndWEIwKgg4hyoqPPP5A7/KshnOzzaHU33FKiDV+/qjpf05GSVV41iIAo91+lzyc+zBqDMf6ODY0trft8s7V82wnRd4wjmPdZIO5zYJLOJ9FAUIRkUR2+VSurGkvAejvjdmh7rrtWWyfEOOi57+cNO6RkDqwkYy8IQ6ksiMgnqkMlqak1com4wgrnWrVz1FKiSbZ9O11mE/dAGCUaGbReoM3VhCMCpS2rSLAAKlJUAwqrQkD70d3ThCMOrQXWkBAQQiL0AwKgxj3UM/jGY4BQEEEPCEAMEo927QPfcJRrm7WWsQjLKKlP5+UsMMafLRZFvD2197tsSZm0INRsUlJkqj18dLyhH2EFbgxQlGBWpE/z3BqOibl3RF3VhCMKokMedjObvz5c3LfpQtS43lUQ9xO+WuttLzypaH2Aqn+wVCDUbty90vr5z7nWxfvcffhPaVYJSWJWqFBKOiRu16Id1YUl6DUcbqzXLPG8vl1QnrXd2CqdCve015995WLK8XDFYZqTP510y54OFFtk/z9ah20rO1sQw8W6kKEIwqVc5Dakw3lhCMOiRSTkYAgSgIEIyKAnKQl9CNIwSjgsSjGgIIxFSAYFQY/LqHfhjNcAoCCCDgCQGCUe7doHvuE4xyd7PWIBhlFSn9/WgFo6qceb7UGT7K9QMQjHIlimgFglER5Q25cd1YQjAqZEZRQZp3rp4ua37bHvrJmjPijOWTBr14rBzZp57mKEWhCoQajJrxxt/y7TP2H6Wt1yUYZRWJ7j7BqOh6l3Q13VhSHoNRBfsPyI0vLpEPp4Y3a6CT8TVn1JenrzUvL+1Ul/LDX4BgVHT7kGBUdL1LuppuLCEYVZIYxxBAwAsCBKO80AsH70E3jhCM8k7/cCcIIOAsQDDK2cbxiO6h71iZAwgggIDHBQhGuXeQ7rlPMMrdzVqDYJRVpPT3oxWMqvvAaKl8an/bByjMzZGc336W/FXLJKluA9n1+TjJ/nW2rR4F0REgGBUd52CvohtLCEYFq1dc77P7f5V5n64qLgh4F28sgdTs2NrSomcdqVSrguzfVyi7NmTL+kU7ZMmPm+RAoTG9iGZLSUuUq94/Qeq0ZHYIDU9IRaEGo96+Ypqs/Hmr7RppxjJGzXvUlsq1U2XHur3S9+ZWUqt5FVs9CqIjQDAqOs7BXEU3lpTHYNQdry6TN77e4EiWnBgnp3etIZ1bVpH6NZIlzxgPVm7Mlb/W7pVv5mSKClY5bQ8Nbiq3n9/I6TDlZUiAYFR0O5NgVHS9S7qabiwhGFWSGMcQQMALAgSjvNALB+9BN44QjPJO/3AnCCDgLEAwytnG8Yjuoe9YmQMIIICAxwUIRrl3kO65TzDK3c1ag2CUVaT098MNRqnzkho0Nt1Q4d4syV30u6nMv9Pw5Q8k9ZhO/l3f64H9+2XN4LMkf/UKUzk7sRMgGBU7e92VdWMJwSidlHNZ9s58ebr3RF/gyVqrdosqcsmrPaVa/YrWQ779TOPH8MlPLZC/vtf/kH5Er7pyqXE+26EJbDBCaKqfAreq9VIdQ03PnvS17DTCa4Gb6sMbPj9ZVGCNzRsCBKO80Q/qLnRjSXkLRqlg04WPOs80N7BPHXniqmZSvXKStuPWbMmVZ/+3VsZ+u0kbkIqLE/nsobbSp1269nwKy44Awajo9iXBqOh6l3Q13VhCMKokMY4hgIAXBAhGeaEXDt6DbhwhGOWd/uFOEEDAWYBglLON4xHdQ9+xMgcQQAABjwsQjHLvIN1zn2CUu5u1BsEoq0jp74cbjAr1TjLemSDJzY4wnaYCUasvOd1Uxk5sBQhGxdbfenXdWEIwyqpU8v7vn62WT++ba6tUsVqy3PLNqZJaJdl2LLBAzSA19qrpsnrutsBi33s129RdP54paqYitugJjOr6heTt2We6YLv+jeW8J7qYytiJrQDBqNj6B15dN5aUp2DUrr0F0vH6ObJ1l/m54Te6+ZyG8ujlzYwAmb/E+fXjH7fI0GcXywHN5FEqFPX5w22dT+ZImRAgGBXdbiQYFV3vkq6mG0sIRpUkxjEEEPCCAMEoL/TCwXvQjSMEo7zTP9wJAgg4CxCMcrZxPKJ76DtW5gACCCDgcQGCUe4dpHvuE4xyd7PWKPVglPrFQ/dLxj8XbvHdfImrUMF0G3umfiMbH7jVVBb0jsv1gm4nmIphXitqwaj3v5bkjGamT5L753xZe82FpjJ2YitAMCq2/tar68YSglFWpZL3f/jPXzL1P3/aKrU9o5Fc8HRXW7muYNemHHmm71e6Q3LJyz2k5Qn1tMcojIzAox0/k325+02Nd7ukuZxxf3tTGTuxFSAYFVv/wKvrxpLyFIx6xpjpaeQ7KwNJit4/YgSibj23YdF+MG/GTFgvw15frq3668td5IgGqdpjFJYNAYJR0e1HglHR9S7parqxhGBUSWIcQwABLwgQjPJCLxy8B904QjDKO/3DnSCAgLMAwShnG8cjuoe+Y2UOIIAAAh4XIBjl3kG65z7BKHc3a41DDUapGYrSevSRlCOO9v2XbCz/diA/Xwp2bJP8FUtl78wpsufHybJ/107fpQ8pGBUfL6ntOkvlvmdIhbYdJLFmbUmomi4H8vJk31Zj2Y0N64xrTZKsKV9L4Z4s60e17Vfsdrwk1a5rKs9Z+Jvkrzr4Q0xK8yOl6rkXG9fqKEn1Gkh8hVQpMK6Tv2617FuzSnZ//Ynk/rnAdL5/p2K344y2D/6Qn1C9ptQYepv/UNHrnmnfSvbsH4v21ZtdE8YXBcvUsnjWoFPBzkzZO/173zkqcFWxQ3HoQF1DXStw27dxnex459XAIslfs1KSGzc1lamdPdO+M/pph61cVxD4+QKPh9JG4Hnl6T3BKG/1tm4sIRgVWh99OXKezP3Yvlxnzytbyil3BT+zx/OnTZLMNXtsF+83sqN0vtD8zFq/MFP2bMsz1a3XqppUqZMqhfsP+Gaf+mPSOtn09y7J2pIjBUbIp6Ix61SlmhWkQdt0aXVyA6nfOvzlmHJ258tiY/m/JT9ukl0bsyVra64cKDzgu37VuhWlWY/a0ub0hq6zZZk+QMCO+gxr5233LTG42fgMe7bnSnZmniRXTJT0RmlSvVElSW+cZlyjkVSt6x4QWPv7dsneYV5Kr1qDilKnZVXfVbev2iPbVhaPm+Nu+8m2NGLL3nWNfigO36p7SaqQIHuN+wrcVIY4lCDbqjlbjdmpCgKb8L0/sg9hOBuKpYBglAUkhru6saS8BKP2Gc+rNlf/LBszzc8Y1R1ndqshH97XOuSeUf/Gos01v8haY3k96/bCjUfI5acE93zIzNonX/60XSbPzZR1xpix+Z/nYL0aydKwZoqc1LG6nNezllSumGC9jG1/9eZc+XPNXlN5gxopckyzSr6ynPxC+WT6Vpnw8zZRddW1ahszJzavn+r775RO1aVn64PPXFMjQewoh09mbpPpC3caznmyZec+SU6KlwbG58ioU0H6da8pp3WpIcmJxgPYZVu4cq9hYXZtk5EmjWof/IcrWdn75fWvN8jPf+2WhcbYkL/vgM9n1vOdJDU53ta6mi3skxlbZc7fWbJph3FvO/YZ95cvicaMj/UMn/rGPbYwDC7sXUeObqxfVlf19zTjs2XnHQzkzlu6R54Yt9p2rRGXNZVWGcVtVDWWdu3RqmTTncb4ovpkkvEdWLvV+A4Y39NC44Lq3tR3oE/7dDn/uFpSrVL5XSaWYJTtqxazAt1YQjAqZt3BhRFAIEgBglFBQkWhmm4cIRgVBXgugQAChyxAMCoMQt1DP4xmOAUBBBDwhADBKPdu0D33CUa5u1lrhBuMiktIkPQh10v1wddLXGLJf5FcuGe3bH/tOdn52YfSYvK8sGaMUoGfeg89K6kBQSDrZ/HvH8gzfox46kHJmvS5v0j7qvvsW54eaQSePpXad46QKmecpz2vqND4S/WsbyfItldGG4GpzUXF6k3zSXMlPq2yqSyYnWW9W8mB/Qd/FMh4b6IkN2lhOi33r4WydugFvrLadz0kVc8ZaDoezI5aXs8auFLnbXvpSdnx0ZuuTaj+bvrFLEmoYvkhonC/rDinl+zPtC+H5dpoOapAMMpbna0bSwhGhdZHk0cvlJlvLbGdVL9NulzzUR+Ji3f/oVad/N1zi+TvqRtt7XS/tIV0GtDUVP7UcRNsgZzzn+oi9VulyyfD54oKTrltzXvWkQtGdxW15F8omwqBff34Ain45wdcp3MTjR+Qjx96lPS+4eiglo/yt7Nl6W75+I6fZevy3f4ix9eExHhpd3ZjOe7qI6VGxsEf53WVH+v0ueTnmMNHXQc1kzMf6OCr/t51M2XptE26Ux3LajSp5Atb5eyyhyGGfthHGrar7niu/0CuEVoYffwEKTACBYFb1XoV5Y7vWQY20ET3nmCUTiU2ZbqxpLwEoz6duVWGPPWXFv6rx9rJcW0sf17U1rQXjjBmoHrWmInKug05ua68eFNLa7Ft/1Vj1ql/vbVC8gs0a/IF1FZhn3sHZsjt5zcKKLW/vfqZxaKW+QvcBvWpI2NuO1K++mW73PjiEtm+W7+UoP+c/sfW9C0p2KSuefZc/3Hrq7r3+95cLq9N3GA9ZNtPr5woLxkuKiRV0nbsLb/KH6vNAa9nrz9CrjqtnoyftkWGv7miKEAW2M7GcT0lzQjD+rc/jTae+niN77PnWp7h/jrW165HVZFhAxrLqZ3N48M2YwnGZoNnW6u77ndqWVmmjj44jukqvzlpo9z7xnJxu78UI2R2xwWN5N6LMkIar3XXPBzLCEZ5p9d0YwnBKO/0D3eCAAJ6AYJRepdYlOrGEYJRsegJrokAAqEKEIwKVcyor3voh9EMpyCAAAKeECAY5d4Nuuc+wSh3N2sNXThI1Vl96RlFMydZz0lu0lzqPjhaUlqG9i/Ad33xsVQ5tb/EpZh/DHBbSq9ip+5Sd8S/bbMhWe/Lup/57hgjkPVs0QxM1uO6z65CTpVPOss3+5W1vtN+/tpVsubys42Zq4r/9bWXg1GZb78s1S+/wfZx8pb8IWuudAmDGWelHdtb6o9+zXZ+9s8zZP2dV9nKKTALEIwye8R6TzeWEIwKrVfmfLRCJjw8T3uSWn7tpNvb+GY60lYIs1AXjOp93VEy+51lkp9tDgCVdIlq9SvKRc93D2r2KBUs+nLEPFkwYU1JTdqOqZmjznmss292JdtBS8Gv41fK16Pm25axs1Sz7cYbM3Oc+3gXOeYs/Q/7kQpGNetWW+aMs88WpsJsp9/Xznaf1oLfP1stn94311osva45Sk68LbQ/Y9gaKQcFBKO808m6saS8BKNufXmpvGUEUKxbO2MmpenPdrQWB72/0lhidexke2DzxI7pcnybao7tqBmPbnjxb/l8VmhB/Yv71pEXbmzpOOuSUzDqqEYVZeS7K0taSdx0r1WM2fZ+eamTMZNSiqncurPGmCVqsBE4+21p8Wx+1jrWfTVj34OXNpU7jZCP0+YUjEowJoNSfWn8uw/tFhiMmr98j/QfsUB2ZAU/3vobTTDC0q/eeqRcdEJtf5GUdjAq25gl8hbjs1iDbEUXdHijZo562bg33cxYDqeUiWKCUd7pRt1YQjDKO/3DnSCAgF6AYJTeJRalunGEYFQseoJrIoBAqAIEo0IVM+rrHvphNMMpCCCAgCcECEa5d4PuuU8wyt3NWkMXDlJ1nIJRaragxmO/MGYcam5tKuz9koJR1QYMllo3DxcxltELZ1PL1W1+eJgU5ubYTnf67LaKQRTs+OgtY8alJ4pqejkYpfo2450JWtPVg04VFfQqaatz/xNS5fRzbVU2PXSXMYPWl7ZyCswCBKPMHrHe040lBKNC65V18zPl9UFTHU9KM5aw63XtUb7l8BJTimebcDwhiAO6YFQQp2mrqJmdznuii7Q+raH2uCrcsW6vqFmVtq0I/gfqwMYatK0ug146VirXMgeD/XXUD9Gf3DMn5NCV/3z1mmDMeHHZa8dJ0261Aot97yMVjDr/qa7y2oVTbNdTSxbeOfUMUYGtkjanmapunniK1Gwa+qyLJV2rLB4jGOWdXtWNJeUlGNXh+jmyfIP9z9kq/KLCRtHclhn3ccHDi2TFRvv9BHMfxxrLsr1/byupWTXJVl0XjFLLr6ml5JzCRLZG/ik42VhW738PtnE6LD8s2CmDn/xT1DJw4WxqJiu15KCaCcm66YJRA3rVlv9N32IsMWetXbzvD0bNW5YlZ49YGPa9qRbVRJJj724lZ/c4OLtVaQaj1DKG5xvfgSXrsotvPoR3ahYqtfxj3fTQZpMM4RKeq0owyjtdohtLCEZ5p3+4EwQQ0AsQjNK7xKJUN44QjIpFT3BNBBAIVYBgVKhiRn3dQz+MZjgFAQQQ8IQAwSj3btA99wlGubtZaziFg5yCUekXXy01bxhmbaZ4v7BQ8pYtloLtWyWl2RGSWKd+8TGHd07BqKSGGZLx7kSJS7L/OKF+gdi3fo2oZeES0mv4ZnjS1jOuufurT2TzKCNcZdmcPntgtYJtWyRv6V++WadSWhwlibXrBh4ufm987lUXnij7Nh1c6qLxm59KUuODSz/FV0gtrhfw7kCB8UNKgXnJjRWndgp6Kb3ql13rW87Q36T2OsZ9Febn+av4XleefZzUe/g5qdjteFO52sl88yXZ/uaLtnJ/QVxSsjSbMMu2TGDh3j2yon9P06xZ/nN4NQsQjDJ7xHpPN5YQjAq9V9687EdZ/WvJs3MkGUvwNO5UU5r3qG38V0fqtKwa9pI1wQSjVCinVvMqUr1RmmwxlqXbvmqP4wermJ4it397muPMVu9dayw1N90+c4lqsJIx60fdow/OXrJh0Q7J3mlfWk7Vq92iitzw2UnapQUXTlwr44f9oqrZNjUDiLKq0aSyFBYUyuYluyRzrXkZJP9JKZWS5NqP+xp1K/mLfK9uwajP//WrLPp6XdE51mX31AHlmZhcHGyrbizdd/0nJ8p/+n8rW5btLjrX/2bI/x0vzY4tnhHEX+5/VUvwjT5+ouw3PlPg1vCY6jLUWIKRzV2AYJS7UbRq6MaS8hCMKinQsvC1rpJRRx8GjVS/nHH/fJmxaJe2eRV0aWvMYrXfSP+oWZicQkftm1eSac/YZ7rSBaOsF1KzQanzqxvL2i03wlkLV+qf1eq8cf9qLad3qWFtQtRsRypstjFTP5aoZfhaNU7z3f+85VmSk2d+hvobvOykuvKfm+1LDuqCUf5zSnr1B6P6DJsnvy7Rh4TVcn6dW1bxhYryjWf7ghV75K81+oBSn/bp8vlDbX2X3G3M9Njx+rmyx/jsalMGuq2CEWSOD1iet2OLSqKWawzcVCjq21/1y+nWNpbObds0zVd93rI9kmks56rbjm5cUWa/0NkX4NIdL2tlBKO806O6sYRglHf6hztBAAG9AMEovUssSnXjCMGoWPQE10QAgVAFCEaFKmbU1z30w2iGUxBAAAFPCBCMcu8G3XOfYJS7m7WGUzhIF4xKrFVHMj74RuJTK1qbMQI+BbL1mYcka8rXUrin+C/Lk41wUN1HXpCU5va/mPc34hSMqv/kq5LW0/7jaO7iRbL50btNS/2pUFCt2x+QKmee72+26PXA/v2yeuDJsm/j+qIy9cbps6tjhVm7jDDVfbJn+ndq17ep2bKqX3GjVB9iX4ZOVdhw7/Wyd4Z95gwV8Gry0eSDjQT8X7XMX+Y7rwaUmN9mvDdRkpu0MBXm/rVQ1g69wFTm38l4/2tjJq9m/l3fa+6f82XtNReaytROpb6n+8JR1gNqtig1a5TTlnZcX6n/xCu2w7sn/k82P36frZwCuwDBKLtJLEt0YwnBqNB7ZPXcbfL2FdOkcH8J001YmlUzSanZjVR4pln32pLe8OCPlZZq2l23YJRayu2kO9qYlq/LMpYl+vbfC2X+l2u0bfa9pbWo5fismwpEqWCUdVP33//hjnJU3/qmQwsmrJUJD/0mecYsItbtwme7SetTzTNT7d9XKC+eNVl2aMJO9YzA1VkjOogKC/k3NTPJn5PXyVeP/i57tpuDr6qO+gzqswRubsGowLrq/aMdP7Mt56eWRTzj/vbWqjLr7aUy6akFtvIO5zYxlhDsZCv3F/z2v1Xy+QO/+neLXs98oL10HVR6s1IWNVwG3xCM8k6n6saS8hCMWrRqr/S41f7/x2q5tK3jj5NEl1njSrMH1dJ5lxmzLFk3FYhSASE1S5N/U8/R96dskjvHLNMGi/77QBs5tXNxfXVeScEo9XnvvzhD7rigsSlM8/Wc7XLd839rl5y7+8LG8q9Lmvhvqej10fdXyVMf28epNk3S5LXbjxL16t/2GWPuEx+ulqfHr7HNWqXsf3+1izSubQ6nBROMalgzRdTsWR2M4JFqZ82WPBlxWRNRyxQ2HzLbdi31+R+/qpkMOaWebRm6341l9y5+/A9Zt9U8XqWmxMvaD3pqly6cbASb1Mxf1u3rUe2kZ+uq1uKifRWIUsEo61bLmAFMLZN4ZrcapkP/nbbFt3zgnhx7EGvs3UfLuT3tMzCaGigjOwSjvNORurGEYJR3+oc7QQABvQDBKL1LLEp14wjBqFj0BNdEAIFQBQhGhSpm1Nc99MNohlMQQAABTwgQjHLvBt1zn2CUu5u1hlM4SBeMqjN8lD54ZMxItPFft8jeWT9Ym/ftq9BS3Yee1YacVAVdMKpil57S4Nk3be3tmfadbHrglqJZlawVnGa02vXph7Ll3yNN1Z0+u1p2b82Q/r4ZqUwn/LPT4Lm3pGLnHrZD214ZLTvef8NW7sVglJr5qennMyShiv3HhTVXnSd5f/9h+xyqoO6Ip6Xyyf1sx9bddJnk/K6f7cRWuZwXEIzy1hdAN5YQjAqvj/6eulH+e+fPtkBNsK2pmZ3UcnbHDjlCVOiopK2kYFT/hzpKpwEHZ+yztqF+DJ88eoEvzGM9VqFyktz+3emiXv2bms3o5XO+sy2hV7Vuqlw7/kTH+9y2Msu3xJw1HFX3qGq+WZb87avXn95bJl+Pmh9Y5HvfuGNNuWJsL8fl6NQShm9dPk0K8sw/6NZrVU2uM+4tcItkMEqFs/59wkRbKE45Dpt+ljHLVHzgrRS9f+fq6bJ81paiffVGLQc4bNqZklq1/CxhZAIIcYdgVIhgEayuG0vKQzDqR2PJt34P2IORDWulyJ9vdHMV32EsFVcQQqBWNVjBeE5Urlg8e50qy80vlC43zRW1jFrg1tR4Vv/w7w6Sbix5p9v+WL1X+t41T3KM8wO3rkdVke+eNAdBSwpGfTC8tZzV3Ry68bc3ZuIGGfbaMv9u0es5xjJy79zTqmhfvVlrBHg73TjX93kCD5zYId2YYaqNNkSk6n1mhMLU0nvW7erT68sz15n/kYVbMGrwyXXl6WtaiJqdybp9NHWzXPPc39ZieWpoc7nurAa2cn/B1Pk75OwHF/p3i14nP9Feuh9dpWjf/yacYJQKianPZl1CT4W8fjRmAFPhKN22dH2O9L7zN7GGo45pWklmPNdRd0qZKyMY5Z0u1Y0lBKO80z/cCQII6AUIRuldYlGqG0cIRsWiJ7gmAgiEKkAwKlQxo77uoR9GM5yCAAIIeEKAYJR7N+ie+wSj3N2sNZzCQbZglLGWT7MvZ0lCNfO/nlbtbX3uUdk5/l1r06b9xBq1pMl/v5e4ZPuP3bpgVKNXP5IKbTqY2lCzOK265AzZn1nCck3x8dLotf9KhaPamM49sC9fVl3Q17fEn/+A02ff/vpzkjnWPiuS/7y0HidI/afG+HeLXp1mTfJiMErdtJphq9r5lxbdv//Njo/elG0vPenfLXqNS6lgLKM32zZjmJqJSy0jaPvn40Vn8iZQgGBUoEbs3+vGEoJR4ffL2nnb5fMHf5OtxtJ14W5qyb0ug5pJ35tbm2Z8CmzPKRh1RK+6cumrPQOrat+rQNGqX7bajp18Z1s57qriGQ6dZjW65JWe0rK3w9Kq/7TqNJNS4Llqhq3RvSZK9g7zTBpq2brrPzlJah9h/8E48KY/vW+u/P7Z6sAi3/KEd/14plSqWTxLSCSDUeriH940WxZP2WC6D7Uz8IVj5eiTzDNqqfK9mXnydG97mKrVyQ3koue7qypsQQgQjAoCKUpVdGNJeQhGfTJjq1w+2lhy2rKp2YYmPW5e4sxSxbfb2QgBWYMsunqBZWoGo1XvHStq2Tr/NmbCehn2+nL/btHrhEePkV5tDy51WlRoeaNmZ1KzNFk367lOwSg1s5SaYcppyy84II0unmmbmUot1/bzi51Np9344hJ597tNprI0Y0yc81JnUWGzkjY1W5aaNStwSzFCZAtf7+pb2s5fXlIw6r6LM+TeizL8VW2vQ59dLON+MAdak3z90cMWVgs8edOOfGl5+U+BRb73upm51IFwglHvfLtJbnppSdDXCKz40ufr5L43VwQW+d473Z+t4mFeQDDKOx2oG0sIRnmnf7gTBBDQCxCM0rvEolQ3jhCMikVPcE0EEAhVgGBUqGJGfd1DP4xmwjolISFBqla1z7gQSmP79u2TrKysUE45rOuq/qpWrZrsN5Y3ysvL8/0X+IHU8fT09MCiovc7d+6UwkLzv+grOsibqAtUqFBBKlasqL2u+k6r7zZb6AIEo9zNdM99glHubtYaTuEgazBKLYXXeOyX1tOlMHuvrDzneN+r7aCloNat90u1AYMtpZoZo+ITpMV382whqsyxL8v215+3nW8tSOvRxwguvWot9p2r2vBv2s9ujC/LT+koatYopy2pXkNfyMt6fI+xjODGB2+zFotXg1EpLVtL4zc/sd1vwZZNsvL8E2xBp0onnCr1Hn3BVj/zbaNf3nDvF9uJ5bSAYJS3Ol43lhCMOvQ+WjVnq8z5aIX89e0GUbMuhbOpJfYu/k8PbTjKKRh11Xu9Rc205LY5LY/X9sxGcsHorkWnf2GEvH4dv7JoX71Ry9oN/ci+zKupkrHjCz0dP0Gyd+abDjXvUVsGv3G8r0wtn/fcqd+Yjqud7pe1kNOHu4cKls3YLN88ucB2/vlPdRG1DJ9/i3QwSs0W9sGNs/yXK3pVywaq5QOt25xxK4zlBudZi2XQS8falia0VaKgSIBgVBFFzN/oxpLyHIzqYQSjvolQMEp19ur3e5hmgbrq34tFLYsWuKlAlAo3uW15xnKmTS6dLXtzzbPvqWXXPryveFlSp2DUxMeOkePbFD9vdddTyw2qZQcDNzWT0Z//Z34+djVmvVq8NjuwmtzYv4GxTF1zU5lu56812dLt5rm2Q8MHZsjwQcVhJ6dgVCNjyb3fXu4sKkzltKkZrbIsy84lG/Vb1E91OsVX7jRrllPwKJxg1M1GKGqsEY4K3Dq3rCxTRncILNK+V7OWtRjyk2Rmmf/uqk/7dPn8obbac8pSIcEo7/SmbiwhGOWd/uFOEEBAL0AwSu8Si1LdOEIwKhY9wTURQCBUAYJRoYoZ9XUP/TCaCeuUzp07y5w5c8I6N/Ck3Nxc2bx5s2zatElWr14tEyZMkC+//FJUEOhw31T/nHPOOXLzzTdLixYtpG7dupKUVDyVdXZ2tqxZs0YGDBggixYtkurVq8v27du1H/uJJ56Q4cOHa49RGH2B22+/XZ555hnthfv16+f7HmsPUliiAMGoEnl8B3XPfYJR7m7WGtpwkFHJGoyq1Pd0qffwc9bTZddnH8mWp0fYynUFKc2PNMJVX9gOWWeMcgoSbRh2jeyd/aPtfGtBfOUq0vyrX9QfDkyHrNfRffZ961bLqoGnmM6z7ajg1tSFEmcEowO3wy0Ype698dufS0qLowI/hu+9bmm8eo88L5X6nGarq7yUG1twAgSjgnOKVi3dWEIwqvT0c40fGdXMTMtnb5EVxn9qiblQthbH1ZHLXjvOdoouGFWzaWW5eaLL8zugpRfPnGy7nwZtq8s144pDT29c/IOs/d38v0nUUn+n3eP+Y7u61Ps3zJIlP2wMuKpIxWrJcs+sg0uSqmDTu9fMMB1XO1e+21syOrkHvGwnOhREOhilQmBqOT21rF7gpmb/UsvppaQVz+yijutm7KqYniJ3/XiGJCQ6/ygf2DbvRQhGeedboBtLykMw6gdjKb3+h7CUXjgzRqletwajet72qyxcaQ4eDRvQWB64tElQXxK1HKBaFjBwswaXnIJRavaq6gFLsAa24X9/8eN/yISfzGOJtX21FFzdATNEvQZuark9texeMFvGpbNkR1aBqerpXWoYy/AVB7ycglGv3nqkXNy3junccHcKjY+wenOO/Lk62xdY+3TmVu3EsqUZjDrpnt/ll8Xm2SqDDZWpz3nho4vkmzmZpo+s+lX1b1nfCEZ5p4d1YwnBKO/0D3eCAAJ6AYJRepdYlOrGEYJRsegJrokAAqEKEIwKVcyor3voh9FMWKeUVjBKd3E1286UKVPkqaee8r3q6ni9LCMjQyZOnCitWxf/ZYzTPffq1UumT59eYjBq/PjxvgCVUxuUR1eAYFRkvAlGubvqnvsEo9zdrDV04SBVxxqMqnrOIKl910jr6bJ51HDZ/dUntnJdQXxqRVHXs27WwFKl40+Seo//x1rtkPfzVy6V1ZedVdSO7rPvnTVVNtx9XVEdpzctvp8vamm5wO1wDEapGbzUTF7WbdcX42TLUw8WFcdXSDWW0ftJ4oxZAgO33IXzZO31AwOLeO8iQDDKBSjKh3VjCcGoyHVCljHbxMpftsiy6ZtlybRNkrPLPJuS7spq1qgj+9QzHdIFo9TSdmqZumC38cN+kYUT15qqp1ZNlntnHwwtqQOPd/tCVLjLuqVVL3lJI399tWScbrt7xlmi2vj5/eVMvIm5AABAAElEQVTy1WO/m6rExcfJv347RxKTSy8gFOlglPoAk0YvkFlvLTV9FrVz3hNdpF3/xkXle7blytMnfCUH1C/nAVu3S5rLGfe3DyjhrZsAwSg3oegd140l5SEYpcJIKpRk3RKM59jW8ceJWvaupK00glH7jWdJvYtmSm6+fXbCWlWL/zFeSfexdZf9Oa/qbxzXU9RSdmrTBaNqVEmSle+6B2eufPovGT99q68d//+xBqOcZnxS9Q/lczSrlyq/v9rFf1lxCkYtebu7acm9ohNKeKNmWlqwYo/8vS5b/jZmulqyPluWb8iRlZtytf1hbao0g1ENB82S3dnmUJi63qHYqfNXvHOs1Azye6TqH44bwSjv9JpuLCEY5Z3+4U4QQEAvQDBK7xKLUt04QjDqYE/syo6XA6L/3ybxcQekSqr9f0vEog8Pp2seMP5KZ1eO+R+N++8/KfGApCVj6vfg1V2AYJS7ka2G7qFvqxShgkgGowJv+cMPP5Q777xTNm40/6vjwDpee6/65bvvvpO+ffsGdWsEo4JiKtVKKtg0ePBgbZuDBg2SxYsXa4/5CwlG+SVK95VglLun7rlPMMrdzVpDFw5SdazBqOpDrpcaQ2+zni7rb7tCsufal8+xVfynoNnEnySharrpsDUY5XQt00lh7Oxbv0ZWXXRy0Zm6z77nh0my8V+3FNVxelNWglGqL5p+Nl3iAmZxVJ95/66dsvLsnnKg4OAPDJVPPEPqPvSsjWPL6BGy6/OPbOUUOAsQjHK2icUR3VhCMCo6PaFmGVKzMS3+foP88uEKKcgzL2Pkv4v6bdLl2o/N/1tCF4zqOqiZnPmA+5I5/na/f/4PmTbG/ufce3/qJ6lVkmW3MdvFv/t85a9eqq+3TT5N0hum+UJRKhwVuFnDWYHHwn0fjWDUlmW75T/9v7XdonXWL10YTJ107X/7Sv3W5j8f2BqjwCRAMMrEEdMd3VhSHoJRKlDUfPBsrf3C17pKRh1zoN5a8d3vNsnPlll+Auu8Zxy3ZCh9hwNnjFpmBHE6Xn/oM7gHXtf/ftnY7lLbmOVPbbpgVL3qyfL3W9391R1fgwlGfTJjq1w++i/HNsI9UCc9WZYaoSf/pgtGqfCXCoEFuy1dnyOq7z6culk273APODu1W1rBqPXGbIVHX/mz02UOqTyY7/EhXcADJxOM8kAn/HMLurGEYJR3+oc7QQABvQDBKL1LLEp14wjBKOM3jm3JcvKoxtoZTFU/JcYfkBkjV0mNyvq/k4pFXx4O19xhhM263t9Me6unt98jLwzZpD1GIQI6AYJROhWXMt1D3+WUUjscrWCUuuHdu3fL2WefLT/88EOp3X8kG1JL573wwgtBX4JgVNBUpVbx6aef9gXudA127NhR5s2zz+4SWJdgVKBG6b0nGOVuqXvuE4xyd7PW0IWDVB17MOoGIxh1q/V0WXfzZZIzz1i2LsityX+nSFK9Bqba1mBUrVvuk2oXDjHVKY2d/FXLjM91ZlFTus9e3oJRCqPeoy9IpRNOLXLxv1EzZ6kZtNRWb9RLUqlXcahMlR3Yly8r+vWUwj3mZSvUMTZnAYJRzjaxOKIbSwhGhdYT6l+JWTfLSqbWw7b9bSuyZPzdv8jGP3fajqkC/wxL/oO6YFSva46SE29zn6HW38bUl/6UH162/wh984RTpGazyrLhjx0yZsAUf/VSfb3rhzOlcu0K8tHNs+UvIxgWuFWpmyp3TjkjsOiQ30cjGKVu8rWLpsr6healiOKNGWPu+vFM3wxZqs7/XfqjrPltm3pbtNVuUUVu/MI8xhQd5I2jAMEoR5qoH9CNJeUhGKWgj7n2F1llzBBk3cbcdqQM6nNoS7MNeGSRTJprfqao6wQGo2b9uUtOGz7fevlS2V/7QQ+p+s9SoJEORo2ZsF6GvW4OypbGh2hkjDV/vN61qCldMOqYppVkxnMdi+qU9Gbiz9tl8JN/2pb8K+kcp2OlFYz6ffke6XXHb06XOaRyFXxTAbiyvBGM8k7v6sYSglHe6R/uBAEE9AIEo/QusSjVjSMEo0Se+aqGvPJtyf8I6+5+22RoX/3fR8WiLw+HaxKMOhx66fC5R4JRYfSV7qEfRjNhnRLNYJS6wezsbDnrrLNk6tSDP1aGddNROmnlypXSpEmToK9GMCpoqlKrSDCq1ChLtSGCUe6cuuc+wSh3N2sNXThI1bEGoyqf2l/qPjDaerqsv/Nqyf55uq1cW2D8Ut5iygJjdiLzXy5bg1EqFKXCUdbtgLG8bGHWLmtx0PvZc2fLpofvKqqv++zlMRiV1uMEqf/UmCIX/5usb7+UTQ/dJfEV04xl9GZLXHKK/5Dv1dpvpoPsOAoQjHKkickB3VhCMCr4rnhn6AxZPnOz7YSBz3eXo082h2BtlSwFOzdky4tnTJICzXJIV73XWxp3rFl0hi4Y1f6cDDl3VOeiOm5vvntukUx/7W9bteE/95cKlZMke0eePNlzgu24KqhUs+RZULQn/VOYmBIvN315iiQZM3R8OXKezP14ham6WkLvX/PONZaKNxUf0k60glFzxq2QCQ/Z/1HFmQ+0l66Dmvtm4Xqmr7GMniVMd/IdbeS4q488pM9YHk8mGOWdXteNJeUlGHXji0t8swdZe6N980oy7ZngwjbWc/37rYf+ImuNJVitW2Awat3WPGl1tX62IDVbUribmkVp7n86Fy0HGOlg1Fe/bJeBj/1hu121HKFasi/cTfWDCiD5N10w6qSO6fLJiLb+Ko6vKqR2yeN/SH6B5SEecEb9GinStG4F4z9jGe56FaRDi8qSnBQnZ96/IKDWwbelFYzavnufNL1stq19VXAo34GUpHiZY3wHUktxaVvtTca4kGBUjDsg4PK6sYRgVAAQbxFAwJMCBKO80y26caS8B6P2G6u59X64iWzelVhiRzWrvU8mDV9dYh0OmgUIRpk92Ds0AYJRYfjpHvphNBPWKdEORqmbVOGoE088UX766aew7jkaJ6lAlApGOW1qScBJkybJ77//LlWqVJEGDRrIsGHDJCsrS6pXry7bt2/Xnjp+/HgZMGCA9hiFoQsQjArdLBpnEIxyV9Y99wlGubtZa+jCQaqONRhVoU17afTqOOvpsuXfI2XXpx/aynUFibXqSNNPp9kOWQM2ad17Sf2nX7fVW3f9IMlZWHr/Glj32ctjMEriE4x++VESa9QymRfm5siKs46VSr1P1obiAmeUMp3ITokCBKNK5In6Qd1YQjAq+G744MZZ8vfUjbYTQp29yd/A6wOnyroF9tlBzn+qixxzVmN/NdEFozI615Qr3+ldVMftzSf3zJH5X64xVbMuY/dE9y8lZ7d5maC+t7SW3tcdZTov3J3Z7yyTb56wz3QybPpZUsn4cdltU8sR5mcfXPI0sG5SaoIkJMYXFUUrGJWbtU+e7j1R9uWap6BXoTYVbps9dql886T5x/G4+Di54/vTpUqd1KL75U1wAgSjgnOKRi3dWFJeglHjp22RK/+9WMv89ah20rN1Ve0xt8Kdewok49JZtiClOi8wGKWClnUvnCE5llDtqCubyU1nN3S7TNDHIx2MWrIuWzrfONd2P18+coz0PqaarTzcgkMJRqkAmgqiWbeWDSvK7ec1EhWw0gWRZv6xS06/zz7WlVYwSt1P40tmifrOBG7/uqSJ3H1h8Z8dAo/xvliAYFSxRazf6cYSglGx7hWujwACbgIEo9yEondcN46U92DUtL/S5KrX6gXVCR/dsl46Nc0Jqi6VRAhG8S0oTQGCUWFo6h76YTQT1iluwagjjzxSVq1aZWs7OTlZatSo4QsB1apVS4499lg55ZRTpFu3bpKQkGCrby1YvHixtGvXTvLzzX9Zb60Xq/2+ffvK999/r738okWLpGvXrpKTox9olM15552nPXft2rUyc+ZM7TEKQxcgGBW6WTTOIBjlrqx77hOMcnez1tCFg1QdazAqoVp136xB1vODDRKp86qdd4nUuuNBaxNiDUYlNWgsTcZ9a6u3+fH7ZPfE/9nKwy3QffZgP0+L7+dLXIp5xpA9U76WjQ/eZrudpIYZ0uSjybby7a89K5nvvGor9xdkvDdRkpu08O/6XnP/Wihrh15gKvPvZLz/tSRnmNf2zv1zvqy95kJ/FcfXmtffJemXDLUd3zTyDql8Sj9J69HHdGz/ju2y8pzj5cB+84/fpkrsaAUIRmlZYlaoG0sIRgXfHRMfmSe/fLjCdkKL4+rIZa8dZyt3K3jj4h9k7e/2fxxxycs9pOUJxX+ZpQtGpVZJljt/OMM3E5PbdVSg6LlTvpFdG7NNVeu3SZdrP+5bVKYLarXr31jOe6JLUZ1DebNsxmZ595oZtiYGvnCsHH1SfVu5teD3z1fLp8PtP6Qre9UH/i1awSh1vf8ZSyIumLDWf2nfq5r96vbvTpePbzd+VLcE35r3qC2D3zjeVJ+d4AQIRgXnFI1aurGkvASjco1AUmsjMLN11z4bdb/uNeX94a1s5cEU3PPGcnnly/XaqoHBKFVBF/a58tR68twNR2jPD6cw0sEoNQtTnQEzZH+heTamZ68/Qq46rXj8C+feA8/RWQUzY9TGzHw58gr7P8zscmQV+eqxY0TNruS0zVi0S864P7LBqL7DjBkYl2SZbmGgsZTja8aSjmwlCxCMKtknmkd1YwnBqGj2ANdCAIFwBAhGhaMWmXN040h5D0bd/HZd+WZ+paDAL+i2Wx4fuCWoulQiGMV3oHQFCEaF4al76IfRTFinuAWjmjVrVuLMSdaL1q5dWx588EG59tprJTGx5Cn+Ro4cKQ899JC1CU/sn3/++aJmd9Jt6vM98sgjukOURVmAYFSUwYO8HMEodyjdc59glLubtYYuHKTqWINRqqz55N98y6qp90VbYaGsGnSq7Fu/pqhI+yY+Xpp88I2okJB1swaj1AxGvuBRUpKpas6CX2XdDRebynQ7aum3eo++IMZ0GQGHD8i2/zwleUv+LCrTffaoBqNef04yx75SdD/WN9EMRqlAlQpWWbec+XOlQqt2xvKH5r7Y+fFY2frCKGt19oMQIBgVBFIUq+jGEoJRwXeAWgZOLQdn3dRycFe+21satK1uPeS4X5C337d0nW4GpOs/OVHqHlU8Y4YuGKUaPmVYW+l5RUvHa/gP/Dl5vYy7zf4Db5vTGsqAZ7r5q/lCRyp8FLipWaVu//Y0Salkfi4G1vG//+ndZbJuvnkGrBbH15H2Zx8cC3euz5ZnT7Y/e5t1ry1D3nQPC42/6xdZ+JU5hJSYkiD3zu5nCohFMxi14qctMvbK6X6CotcuA5vJnI/sIbrznuwi7foxo0cRVAhvCEaFgBXhqrqxpLwEoxTtE+NWy6gPzM9KVa5CkY9dEfrMTQtW7JHed86zhYRUm2qzBqMGP/mnfDZr28GD//xfNXPRgjFdJdVYvtRte+6TtaKuGbidaYS6zj+ueDbVSAej1LXbXzdHVmzMCbwN6dGqqnzzeDtTmdPOXWOWSaYxc1/gdn2/BqLCS/4t3GDU54bvZYazdfvqsXZyXJuSZwV7+Yv1cu//Lbee6lvi79TO9j8nTP41Uy54eJGtfknXuva5v+XDqZtN56RXTpRFr3WTyhUTTOW6HRXCm/P3btOhkztVl0FGuKqsbwSjvNPDurGEYJR3+oc7QQABvQDBKL1LLEp140h5DkZl7k2Q40Y0kX37jf9REsSWllwoMx9ZJeqVzV2AGaPcjagRvADBqOCtimrqHvpFByP8prSDUf7bPfroo2XChAmiglVOW15enrRo0ULWrVvnVCVm5UOGDJG3335be/3LL79cxo4dqz1GYXQFCEZF1zvYqxGMcpfSPfcJRrm7WWvowkGqji4YVf/JVyWtZx9rE7L7609l82P32soDC6qcdYHUufexwKKi97ZglHGk0ZhxUqF1+6I6/jfr77xasn+2/+DqP65eqw+5QWoMvTWwyPdehapUuMq/6T57JIJRyY2aSMaHk/yXLXrNfHeMbB/zTNG+9U00g1Hq2o1e+UgqtO1gvQ3t/porzzWFzLSVKNQKEIzSssSsUDeWEIwKvjuyd+TJ6F4TRc3AZN0q16og1/73RKlc2zy7nrWef3/CQ/Nkzjh7cEYFfe6ZeZYkVywOuzoFo9Tyc7dOOs1U19++/3X/vkJ587IfbTMXqeNnjeggXS4q/t9eP7+/3JgJ43f/qUWvJ9xwtPS5qeRZUHZvzpHnT/1GCizLO51wo3HujQfPPWDMDKL89mbmFbXtf3Pd+BOlXqviMJi/3P+auWaPvHLu95KfY146qGXvunLJKz391Xyv0QxGqc+kZuPaucE8G5fphv7ZSUlLFLVsYFIF9x+tdeeX9zKCUd75BujGkvIUjNq+e590vGGO7MgyP4/8PXSbsczaw0Oa+ndLfF27JVcGjvpDFq7c61jPGoxSwaYHx6601X9ocFO5/fxGtvLAgpWbcqTTDXOlwDKOqftV9+3fohGMUksSqqUJrdunI9vKiR3SrcWm/Yk/b5dBhpt1+8w4t2/AueEGox55b5WM/q/9H8L89koXaVG/5KVQ+z+wQH5YsNN6ayEHo/73YBtRYSXdNmbiBhn22jLboXsvypD7Lrb/w5zAiuu350n7a+dInvHng8Bt+MAMGT6o5HMD6x+u7wlGeafndGMJwSjv9A93ggACegGCUXqXWJTqxpHyHIx6+8eq8thnxf/QIZg+UTNGqZmj2NwFCEa5G1EjeAGCUcFbFdXUPfSLDkb4TaSCUeq2GzZsKFOmTJEjjjjC8VM88MAD8uijjzoeD+ZAenq61KtXT1JTU2XTpk2+//Yf4vI4Kvz01ltvaS8/ePBgeffdd7XHolmovjfqc9evX18yMzNl9erVcqifu6T7V9dTyyeqa6rZwDZs2CBbtmyRWIZgYhGMSjJmHlHfbWWhDDZu3BhRA7U0pZqJrW7dulJQUOALEu7YsaOkror5sVh+J2L+4YO8Ad1zn2BUkHgB1XThIHVYF4xKadlaGr/5ScDZxW93fTFOtjz9kBi/jhcX/vOuav8LpfZdxjFj1ijdpgtGVezUXRo8P9ZWfb+xhNvGEbdLzm8/246pgrQeJ0i9x16yzXCUt3yJrBnSz3SO7rNHIhiVVK+BNPnvFNO11U7OvF9k3c2X2cr9BdEORlXtN0Bq3+P+5wmdpf+eeXUXIBjlbhTNGrqxhGBUaD2gZl5SMzDptvRGadL7uqPkGGNGoIREhzFgW6788PJf2tmEVJtqNiE1q1Dg5hSMUnXqt06Xi//TQxvI2pe7Xz66ZbaoJeysmwpVqeXeVBDLv6lQ04tnThI1s1Pgpur0f6ijqGX1dFve3gJ5d+gM27KA8QlxvmtUqVP8I7IKg6lQmHVLq54ig//veKl7pH0mDvU53r58mjbc1W9kR+l8oTmAEM1glPocU1/609en1s9k3e9wboac81hnazH7QQoQjAoSKgrVdGNJeQpGKeJPZ26VIU/95ah9yYl15PErm0u1SsUh18DKKpikZhYa9dFqyTaecSVt1mCUqt/h+jmilnsL3CoaoctXbmkp5/bU/yCyy3hW9zNCO78vN88WpZaFW/xmN6lRJamouWgEo5ZtyJFuN801/lX7gaLrqjcNjPHpPWNJwk5HVDaV+3fUeWfcN1827TB//mb1UmWeEVxSM3f5t3CDUU7BIxU6UuEjp23EOyvl2f+t1R5+955WcnaPmrZjU3/fIWePWGgrf/DSJnLXAIdx1wg1qYDbGiNYF7hVMGawfMFYUlEtq6fb9uTsl3NGLpRfFpt/AEs0xutFr3eV+oZ9Wd8IRnmnh3VjCcEo7/QPd4IAAnoBglF6l1iU6saR8hyMOmt0I/l7Q2h/luvYNFfG3bIuFt132F2TYNRh12WevmGCUWF0j+6hH0YzYZ0SyWCUuqG2bdvKvHnzRIU7dNuKFSt8s0aFEqRQIRG11N1FF10k3bp1kwoVzP+SW4WD1q5dK5999pm88847vuvrrh1Ydtttt4kKvPg35XLhhRf6d02v48aNk19/LZ61Qx18//33fSEZ9V7dz80336ze2rZPPvlEli9fbitv1KiRDBw40FauClRAa9u2g1Orq7bV51ZLFXbs2FFSUooHx/z8fN+yh0uXLpWPP/5Y3nvvvUMO7DRt2lQGDBjgs1B9mZycbLpHdU3Vh+p6ylr32UwnHMJOrVq15PLLLze1cNZZZ0mvXr1MZf6d559/XtavN//QtWbNGlH9599uv/12eeYZ/Ywn/fr18816puqqUNKVV14paiYxNctZfEBAYu/evbJs2TJZsmSJvPzyy/LDDz/4mw/7tUOHDj7z8847T5o3b277/5/s7Gz5448/fN+7Dz74QLZu3Rr2tSJxYij//xyJ6x8Obeqe+wSjQu85XThItaILRqnyeqNekkq9TlZvbZsKK2V9N9E3K9OB3Gyp0K6zpHU9TiqferatbmCBLhiljtd//GVJO/7EwKoH3xvhqx3GUm45v/4kuYsXyYF9+aJmZap69kCpfNo5EqdZhnbL0yNl12cfmtrSffZIBKPikpKlxZQFB9cTMd2BiPrs2b8ZyzkZ425i7Xqy/c0XjXBZoa9WtINR8WmVpNnnMyXO8mcCyy37liTc8eH/WYvZD1KAYFSQUFGqphtLCEaFhp+zK1/GXDhFdqzd63hilbqpcuQJ9aRagzSparxXszbtWLdXtq/eI4u/3yAq6KPb1ExCV39wgmkZPVWvpGCUOq5mqTrhhlaS0amG1GxWRdTsSqvnbhO19N/6hfpw/Ml3tJHjrj5SnW7anJbdU5U6XdBU2p7ZyDezU4XKSaKWAVw8ZYNMG/O3bF1u/pFV1W91cgO56Pnu6m3RpmbbevX872Xzkl1FZf43qVWSpZcRLGvSpabPYJ8xO9TKn7fKN08u8Pn56/lfK1ZLlpsmnCIqVBW4RTsYpfpWzZZ1wPzbfuAt+d5f8XYvadJVH1iwVabAJkAwykYSswLdWFLeglEK/7rn/5YPptiDp/6OUYGjM7vVkM4tKxcFTpYYwdMla7Nl7tIsWbXJHGrxn2d9tQaj1HG1jJpaTk23DT2jvi8c1b55JamUmiBZ2fvli9nb5N/j14gKFVm3i06oLa/ffpSpOBrBKHXB4caSc/8xAmLWLTkxTu4xZjA6sX26tG6SJspy66598v73m+SFz9bJNuO9dVPLGN58TkNTcbjBqHnLsnzLG5oa+2fn8lPqydWn15NjmlXyleQYoeLvfsuUMROM8XChfaYofxs39G/gC8sFBrfUscXG96GrERCzbmpZxLsvzJDWGWm+2Z32GzMUnhew3KFaTlEtq6jbhpxcVwb0ri3qO1DFmIFyr/HnDjXL1tPGLFjqetat/7E15b17S54Z0nrO4bpPMMo7PacbSwhGead/uBMEENALEIzSu8SiVDeOlNdg1MK1KXLeM4203XBG+z2yZFOKLNtU/Ft2YMVJw1dLs9r2P1sH1uG9CMEovgWlKUAwKgxN3UM/jGbCOiXSwSh1Uy+88IJjUEgd7927t0ybNk29LXFTM0INHz5c7r77blMgqMSTjIOzZ8+WoUOH+oIkTnX37NkjaWlpToddy1Ug5sYbb/TVq169umzfvl17jgrl6AJQysApUKMCSYsWLZI+ffqICsGokE4w25w5c0QFvmbNmhVMdVMd9Rkef/xxn1so388vvvhCrr/++qKQmKnRQ9w55phjZP78+YfUytSpU6Vv375FbbgFoyZOnCh33nmnPPbYY7ZQWFEjljeffvqpDBs2LKyQmApdvfjii3LaaadZWnXeVbNIvfrqq3LvvfeKCml5YSMY5d4Luv+/Ihjl7matoQsHqTpOwajkZkdIxttfOM7+ZG0/mH2nYFRSwwzJeHeibfanYNoMrJOz8DdZf9sVciDP/GOL7rNHIhil7qXZFzMlobr9X0QH3qd6v6x3Kznwz4yN0Q5GqevX+deTUsUIlzluRiht5bm9pWC7t8KkjvfrwQMEo7zVKbqxhGBU6H2kQj1vDPrBtqxb6C0Vn6FmmLr45R7S4jj7LA9uwajiVoxManycqOXdStpUqOmO70+XlEr6vxhTS++t/vXgP7LQtaN+1FVL/amZopy2iukpctW7vY2gln3GDxV2evuKkv+3nPLYX3AwOKu7hroHtYTeEb3s/zsn2sEodX/q86jP5bRVq19Rbvv2dNNMJk51KdcLEIzSu8SiVDeWlMdglFqK7CpjOTgVOorkpgtGqSDmCXfNExXgcdrUc7KiMeOfCsU4bXXTk2XyE+2lSd0KpirRCkapWazaGcu6ZWY5/xijZjNKMoJSOXnOY4IKAH09qp2kWZYqDTcYpWaxajhwpqjQk9OWaszOVMEILzktqag7r7ox/vZsXVXeN2bE8m9qFqf6xrXctk5GwG7qaPMy4KcNny+z/rQHjf1tqe+AMlHXcNrUTGGTHm8nLRtWdKpSpsoJRnmnO3VjCcEo7/QPd4IAAnoBglF6l1iU6saR8hqMGjm+lrw/0z77tuqXV67aKEs2JsuzX9XQdtPVfXfIPf30v01rTziEwsw9CbJxZ6JUTC6URjX2SaJ+bpRDuIL51J3ZCbItK0Fy842VjSrvl1pVjH+oHV/y35eZWyjeKyvBqPyCONm2O0Ey9yYY/1uxUOpU2y9pRn9EclP/23WHcb0txnULD8RJnSoFUr3S/nL992MEo8L4xuke+mE0E9Yp0QhGNW7c2LfMm9MNPvjgg/LII484HfaVq1CMmgFKzWAUzpaXlycjRoyQJ598Unv6oQajxowZI9ddd52v7ZKCUePHj/fNwGS9Cbdg1Omnn+4LKjnNvGVtL3BfhcLeeOONwKIS359yyim+mYhq1nT/EVzX0M6dO+Wmm27ytaE7Hm5ZtINRF1xwgVx11VWi7EPd1Exaqk9/+umnoE9VZmppwMBZwII+2aioZu5SyzzOnOn+l3ChtBtOXYJR7mq65z7BKHc3aw1dOEjVcQpGqWMqOFN72EMSl2L+wUAdC2dzCkapttRsU+pa8RVSw2la8v7+Q9bdOkQK99h/JNF99kgFo2rder9UGzDY9TPEOhiV2qGrNHzxXcf7zP55uqy/82rH4xxwFyAY5W4UzRq6sYRgVHg98MekdfLx7T+Hd7LlLBVmumB0V2lzunmmC3+1UIJR/nOcXtUsS4NeOlYad3T+c7uaceqjW3+SzX87/9jq1L4qV8GrK8b2ss18FXjOjDf+lu+f/8NYkTa8v5Q6fuiRctLtbQKbLHofi2DU/C/WyCf3zim6B+ubXtceJSfe2tpazH4IAgSjQsCKcFXdWFIeg1GKWc3ic/NLS+U9YyajQ90eHtJUduwpsC3FpgtGqWupmX8ue+JP+XudfQagYO5FBWJUmOioRvZATLSCUeo+p8zbIVc/u1g7C1Qwn6OVMaPSV48dIyp0ZN3CDUapdt6evFFu+c9Sa5OHvH9ih3T5dGRbUzsXPLxIJv+aaSqz7uiCUSs25silxndg0arw/sFb1bREmWjYHdO0kvVyZXafYJR3ulY3lhCM0vfPj7c3lfxdm/UHSyo10pHxSRUkrW5Lqdaiu++/qkccK6k1Gpd01mF37EBhgWyc9aGsnzFWcrevlbydakw+YHz2VEmqVF0aHD9YmvUbfth9Lm7YmwIEo7zTL7pxpDwGo3L3xUnPEU1ld068rXOqViyU2Q+vlI07EuXExzJsx1VBTSOkMn3E6pACQ1nGtcb9pA9inXrMHl/oSbVdUBgnUxalyXszq8i8lami7tW/JRi326D6PmlSa5/0OTpbBvbcFdI9+Nvxv6qgz4TfKsuk+WmyNjPRCP8kGkt2F19P1TP+6s0XkFKhLDWTVv/OuyXdMApmCzYYtXJLknz/h/OfrS8xPmdqiEGkLcZn+eJX+z86VPfdqWmOdGhi/sfxgZ9n1dYkmTCvskxeUEk2GN+DXdn270nl1EKpV63A187Fxv21apAX2ERY79dlJslX84x/vDK/kiw2lngssPw7jaSEA8b3pMDohyw5t0uWNK7p/A9lwroBj59EMCqMDtI99MNoJqxTohGMUjc2d+5c6dSpk/Yev/zyS+nfv7/2mCrs3r27fPXVV5Kenu5YJ9gDatk0NQOQdfNyMGrUqFFy3333WW856P2srCzfkoarV692PUctUahmpbIumed6oqaCmjlKzWRUWlu0g1FqeTq1fF+42+LFi0UtiZeb6zyQ+dtWob2RI0f6d8N+zcnJ8QW5fvzxx7DbKI0TCUa5K+qe+wSj3N2sNXThIFWnpGCUOp7S4iip9+gLomZ1Cnbb9cXHklijlqT17GM6paRglKqorlH3waelQqtjTOe57ail/TY+cIvs36VfwkH32SMVjFKzRanZrxKqVivxtmMdjFL/NKHJuG8lqb5+uuFNI+80lkucUOJn4GDJAgSjSvaJ9lHdWEIwKvxeUMvV/fDKX7Ji9pawG6neuJIvMOMUilIN64JRHc7NkBoZlWXKi8GHi9S1Lh3T0zjP+S9p/B+kwJgl4/vnFsnssUtdl4jzn6Ne0xum+UJeDdtVDyz+f/bOA8ypogvDH9t77/Tee+9NQBSsqKgogoViAxQUpRcpiooKig3FjqAoUgTpSJPeOwvLsr33yj/n8ifk5s5N22QTdmeeR3PnzMyZud9k77CbN+dwr2NPpGLVRBYphIFYphYXFv2kyzP10fulJnBiUUR4xR5gFKVHfLfHOhRk8/+Y88r6AQiuZVx33v0I2y0FBBjlOO8E3llSWcEoza5Q1Kg3WVq460nm/xHZ18sZ85+ti6fuisD6AykYOveUxq30qgZGUSNFNJq6/DI+X39DNsZYpU6kJ1ZMaqxNB6ffvzzBKJo7Mb0QYz86bxQO0l9nx0Z+UvSlMAb98kpZwCjy98aXl/Dp2liea66NUv6NGVwVMYn5WL2bH0WQB0YdvZSNAW8eNRihigdG0SIoctnM76JZSsLrZp3XNcM98PVrjdC+oR/3XiqqUYBRjrOzvLNEgFH8/dkxriYKLAGj+O4Q2nIgGj7+LrzC66n0uHPMxflZ2D+rG3Li+Oll6U4iOgxBizHf3zk3JVbq0AoIMMpxtod3jlRGMIqAmde+V0Yep516tFMm5j526+9VQz6ojmPX3LkbSFGl7mpmOmhP0Evv2fzPSL58/gZ6NsnFmVg3vPJtJAjMMaVQOr+37k+SxprSX9PnwCVPfL09ADvOeCvgG00ftVc3l5voz0CulwekGk0naCoYRRDQ4Hf5nzPQOj54KgGD2ii/0K62RrJ/9k8gFq0L5nbpwaCyr15Q/i5IINRnWwJxQmXPuc7+byTQakTPdAxk8Ji5hXRa9FcIVu7zM+t3E3r/zXwkCWEM1KsMRYBRFuwy76FvgRuLhpQXGEVp2SjVF6/Ex8cjMjKS14QGDRrg0KFD8PGx3h+eZ86cqYBQHBmM4gpjpnHLli3o168fe3ipf4u7b9+++Pvvv2FJVCrecmguimD0/ffW+WWlvMEo3j2Za6MIUJRWz1AxlM7P0Di1NgLhaC8plaK9iqH3mb3W5Gjz8p77Aowyf5d4Kd4olduVB3ugJDXZoEMnH1+EjpsC3953G4weVRR3HSmfLULWlvUIe2MO/Ac/IvObuW41EuYZhlerODsjaPhY+D88zChclHtoL1KXL0HeUcM/w7x7txUYRTfs7OePoOdelSJuOXl5yzSQKqWluNi7mTaVXvUvVsGjsfzb0zl7tuHGpNHKscxS7ZPv4Nmqg6wtZ/dW3HhzjMxmrKIW3ao0JxuX7+uqSElozJ9olysgwCi5Hvau8c4SAUaVfVdijqZgx6dncWGX6RFD6nQKQ6en6qFBzwgp/Z2hVaiBUQ/MbYf4s+nYuOA4ov9LVk2hRwBRoz5RGDyjNSjFnTnl8r5EbJx/HJQ+0FAh2Kr7C43Q8r4aqsASb3xhbjE2vXsCx9ZeA10bKgSP9XutOSgtnaGyoMta5LIP2XWLoYhN7/Vahyz2IbZu6TmmMfq83ETXZPT61wn7cXLjdUU/gsSe/0kOSSs6CYNRBQQYZVSicuvAO0sqOxhF4lOqt2XrYrFqZxKOXzH+R2Q3lh7uga6hmDOiDiilHZXkjCLUeXqvdE3/ozRyV7/vAoKnDJXNLNrQW19fNho9qiFLlzbx0Rp4uHsonOkr0yrlpU/OY8Vm+ZkWGeSGc8s7qYy4bR753hms2iWHgqqFuOP0Vx1vd1K5+oIBXotWxeBGimHAjNLRTXqsBnq3NPxlSEo3ePiC/IOHu9oE4rfp8t85VJYjmTf8l4L5P18zmrbwgS6hoKhfBBxdY2cKpbm7nqy8Dx4YRRMRVDft28v4a38KS/eh/OY6AUxbFrZSXer24+mYzECuU1cNf6hVN8oTrw+pgcd6hUnvL1WHFbRBgFGOs7G8s0SAUfz9sTYYRbM4ubij5dgfENp6EH/SO8R6avloxO78xuBqBRhlUB7RaKYCAowyUzAbduedI5URjHpqaVXsu8DPPPH92BvoWP9WdNlvdvhj7ppQ7o70aZqLZc8p4RpuZ2Y0BkZRCru3V4YxgF/99w013y/1T8WrAw1HUtWM/YdFo3r5m0izgSjNeM1rMEvr9s2YWDSKkv8dSdNOr6aCUdT3/veq43Qs/29v5mpN/gi0IuCKV957MgH3t5P/vvPVtgAsWBtiFpjE8/36oBSM6pvGa+Ladp31wmvfRUhacTsYMfqxyFUzhiRhsJngmBG3DtkswCgLtoX30LfAjUVDyguMevHFF/HJJ5+orpHStqWkpMjaXV1dsWfPHtAa1UpMTAy2b9+OI0eOIDMzE61atULXrl2lSD1qYwja6Natm+Rb04dS4dWseZuKrVq1Kpo1a6Zplr2ePHkSsbHyb5mtW7cOH3/8sdTP2qn0ZJOzyqlTp7Bz507pnouKitCwYUM88cQToJSFhkrHjh1x4MABbhda8/Hjx0H3rVYoAtKuXbtw9OhRlDDwgPaF0sXVr19fbQhycnLQpEkTXLt2TbWPqQ0UvYkiUHl73/5Anu69Vq1aXBd79+6V3hO6jceOHcMbb7yhNZkDJe3evRv79+/HiRMn4OHhId3XM888Az8/9W/kkU4E9alFjWrZsqW0J4YidFE6Pto3mpfunfaxd+/eiIiI0N6H/sX58+dBIBmlkLRHEWCUcdV5z30BRhnXzRY9KM2dV4duUmQnigjl5O2Dksx0FCcnMjjpIArOn7LetE7O8GzaEu6NmsE5MBjOAUESqFMUew1F16+i8OplEIjl0MXJCa5hEXDy8UMVN3dp/SVZmQxES8LNYsMfgpfHfVVd9CW8OnZXTJX51yokzH9bYRcG8xQQYJR5etm6N+8sEWCU9VTPTMiToh+lXc9BGkttlM5eMxPzQOnr/CO94M+AHoJ6wur5gaI3mVoMgVEaHzmpBbi4OwFpMTnITslnkBRLzxrmIc1L8JV3EP+PKJrxxl7TY3NBkFQWu59s9oF1afFNFh3KS7oPgqJC2T2pRXAy5pvaKUJV9IEkJF7MRHZyPvIyCuEd7C5FxQphkZYo2pK5UJcp81qzz2dDtiDutDJq46BprdF+aB1rTlUpfQkwynG2nXeWCDBKvj9X4vOw+XAaYhkYE59aiIT/w5oU2SgswBXtGvjhLpZSzcfTMPAk92q8RvPuPJGBOHYmJKcXSan+CNQhGIaiRDWu4S2lkDDuyb49jl/Oxr6zmUhiuiWx+3BhEFldtn66j3r/v5fyXiEBVufZ2X6Jpa+jPY1iZ1R9dg42qOaJ+uxs93SXp6UguOng+SzsOZ0hgVKU6q9JDS/0aBEgjVVbfzFLMUuQVCaDhYvYtbeHMwJ9XNj7xo2C3RotBGVtP5bO3gOkXSH7oOimBGvR/pN+jdkaDEFxRie4wzsIMMpxNpB3lggwir8/tgCjaKYqTi5oN2kjAht240/s4Nasa8ewd7px6FaAUQ6+kXfY8gQY5TgbxjtHKhsYRYBSnzk1uQBMuH8xdk6P1v7bn9KxdZ9RCywTuKK4ON2U0ulRWj1TiiEw6vk+6Vi+3V9Ko2eKL/0+lGLv13ExaF7d8OeUm49745UVZYeiNPMHeBEcdQNNq/HnNQeM+m6nP2b9zofQKIUcpTekNIemlCtJbuj/Dv9zfG93SpUYrU3NR3s7h8FvNL+1yqTByaA9NVY2HPWRIpfppy80No7XPptFjhraxfCXM3nj7iSbAKMs2C3eQ98CNxYNKS8wilK0rVq1SnWNFBnqwoULsvbJkyeD0sjxCoEXS5YswaRJk0Dpw/TL888/j48++kgCWPTbqE4QEKX2K1b5EJeAl+XLl/OGSlGQvvvuO24bGW0FRhFkM2vWLMyZMwelLDKHbvH19cXSpUsxbNgwXbPsesSIEfjmm29kNk2F7pXumVcKCwulCFsLFy6UgCjdPk7sA3JKAzdlyhTQNa+sWbMGDz74IK+pzDaKyMRLjUiO27RpI8FjhiYxBYyiCEyjRo3CTz/9pHBFMBqlHiQYT60Q/ETvN/1CP/cE9FE7r6SmpoLSEa5cuVLRTPtNMN/jjz+uaNMYpk2bhtmzZ2uq5foqwCjjcvOe+wKMMq6b6CEUMKSAs38gav+xG1VcXBTdYsYMRf6JIwq7MJingACjzNPL1r15Z4kAo2ytetn9mwJGlX0W4aEsClA6wMV3/61w4co+0H59x73wYB+Ii1I2BQQYVTb9rDmad5YIMMqaCgtfQgGhgK0UEGCUrZQ13y/vLBFgFF9HW4FRNFtgg65oP3kLf2IHt0ZveB/nVyqjsTu5ejDYqzt8qzdHYWYCgpr0RVSXJxz8bsTy7hQFBBjlODvFO0cqGxi1eEMQPtkUxN2Ukb1YNNH7k2Vtw5ZGYf8FfgTuiSw60AsmRgcyBEbJJrSwUj+iEGteiwGluuMVikz0whcMiio14VsDPAcqNkrjtmNaNIuqquxgDhhFfbtOq82+5MBf35xHE/FY50zlJBwL7S/tM6883D4T859I1DatOeiLiT+Ea+vWuvhoeLzBtHp7znthxGdRXOjOkjVQYOP3hiVU6MhRAoyy4J3Be+hb4MaiIeUFRhE4QhF31EqHDh1kqb8oIs/Vq1cRFhbGHTJkyBCsXr2a26YxUsQcmpMgEl4hEOjbb7/lNUmQkKOBUffddx/Wrl3LXS8ZSbOLFy+qRn1asGABN51h9erVcfnyZfatPeUHyRTpqHv37jh48KDqvNQwcOBA/PXXX6pwVJcuXUARnKxdbA1GUYpF+hk5d+6c6tLr1q0LiqbF048GPfbYY1y46Z577gFFGuMVeu937twZcXFxvGatjdJTUppKXiFgMCoqCunpxglg3viy2AQYZVw93nNfgFHGdRM9hAKGFAh6ejSCXxiv6FJw6RyuDb9PYRcG8xUQYJT5mtlyBO8sEWCULRW3jm8BRllHR1t6oXSA/y4/r5ii9YO18MDctgq7MJivgACjzNfMViN4Z4kAo2yltvArFBAKWFMBAUZZU82y+eKdJQKM4muqBkZ1X3gGHsHV+YPYF8QLs1hqzrTriN+3Etd3fIWSghxu33aT/kZQ457cNkc2nv72JVzf/qViiR2n7oJ/nfYKuzAIBayhgACjrKGidXzwzpHKBEZRdKBes2siLo3/JazfJ8SgmV7UpV/2+mEKS3HHK7VDC7HprWu8JoXNHDCqenAxOrF0fk1YJCZvt5u4muyCTcd9cCH+VipxhfP/Gz5+Jh53t+SnJ3/w/eo4GeOuNlQCmwa0yEab2vmIYJGzXJxLkZzlgn0M4NnBoKrMPH7ADnL4wVMJGMRJ5WYOGEV+Xvk2AhRFiVcovSGlOTSlDFxQExfj+Xv8w4ux6FDvdhCYexbUMKhrh7p56Nowj6UMzEdOoRPT0AMnr7njFNOS6mqlR+NcfPUCf72kyyA2L0UkUyt1wwvRrk4+GlUtkCKY0d79d8kT0Un8+yI/3m6l2Dj5GiICTItipja3o9oFGGXBzvAe+ha4sWhIeYFRBI8QtKNWBgwYgE2bNmmbKUIPpU3jFYKZ1KIb6fefMGECFi1apG+W6pSCj1KS8Qr5dyQw6rfffgNF3TJWXnnlFSxevJjb7c8//8T999+vaCN9SCdeefvtt1Wjdun3p/2ifeOVzz//XLWN199Um63BKIqENXfuXKPLoUhcw4cP5/abMWMGZs6cqWjbtm0bevXqpbCTgUCzjRs3ctt0jfTsIOCM0uvxyujRo6XIUrw2W9oEGGVcXd5zX4BRxnUTPYQCGgUoBWJp/u1fFry79ELk7MWo4u6h6aJ9TXxvBjLW/KStiwvLFRBglOXa2WIk7ywRYJQtlLauTwFGWVdPa3u7sDMeP720FyXF8gi9NM8LK/ugarNAa09ZKf0JMMpxtp13lggwynH2R6xEKCAUUFdAgFHq2pR3C+8sEWAUfxfUwKgeiy7CI6gaf5CeNefGWeyb2QUlhbl6LUBI8/5oM+FPhd3RDcc/HYb4A/JsI26+Iej10XVHX7pY3x2sgACjHGfzeOdIZQKjdp+7FaWHtyNqkFN6rjO6TKulGsnop5evSwALz6euzVQw6sluGXiLRa3Sj/xEkZTeWxeMr7cF6LqVXb86MBUv9U+V2ahy9KoHHvlQ/ezrVD8P7w+LR6hfiWIsGZIynTHmqygcY0AQrzzdPQNTH0pSNJkLRu08441nP49U+CEDRUTaNSMaFKHKUDkf54Z7F/LT6EUFFWP7lGhtqu3cwipo+UZdrjtKx/3h0/G4pxUfNMspcMLL30Ri11lP7niKoLVv1mVu+r9JP4bh9//8uOMobeA4to/P9UnTpnTUdCxhfz776O9gfLY5UDXSVH8Gty0ZEa8ZUqFeBRhlwXbyHvoWuLFoSHmBUSEhIUhKUj6ANIumVGuUck1T/vnnH/Tt21dT1b5SerH69euDXk0pFMWH0pg1btxY0Z3gjdq1a0uRqfQbHQmMohR6dM9XrlzRX6ai3r59exw4cEBhJ8PRo0fRunVrRdu1a9dAUaP0y+nTp6U0b2rpBvX7BwcHS+kQAwOVHxZQ1KKIiAgUFBToDytT3ZZgVGxsLOrVqweKmmWsGAL5vv76azz77LMyF6GhoUhISGAHHTvF9Movv/yCoUOH6lnVq4Z+hvfs2WMwzZ+617K1CDDKuH68vRdglHHdRA+hgEaBGsvXwDWqGooT4uHk6weXUH5o2eLkRFwd2l8GUWl8iFfzFRBglPma2XIE7ywRYJQtFbeObwFGWUdHa3l5v896ePi5wSfEHdnJBUg4n8F1XbtjKJ5Z3oPbJozmKyDAKPM1s9UI3lkiwChbqS38CgWEAtZUQIBR1lSzbL54Z4kAo/iaWgOMIs8x2z7HmRWvKCZx8wtDr8WmRQlRDLaj4egnjyHx0B+yFXiF10O3+SdlNlERClhTAQFGWVPNsvninSOVCYwatyIC647wIxK9cncqXh7A/zx81JdR2HqKn05PPzWb2g6ZAkbNeDgJBEapFfZROyjy06nrfEBpcOtsvM9gHv2yYlcAZv8Wom+W6k1ZVKofGdzlxSJTGSqp2c7ozFLdUdQt/dKveQ6WjozTN8NcMIrAn56zaiEhgx9J6a0HkjGip+HMPR+yFHpLVFIlju2XivH33N5jisBFEaN4hXSh1ISGSjHjyGi9apGf5j2eiCEd5On/bqS6oO/cmtyUhu6uN/Ez2wv9qGX6a9hxmqVFZO9J3l5Q31/HXUermsY/b9f36+h1AUZZsEO8h74FbiwaYgiqIId16tQxCcgxNjkBJhcuXFDt1r9/f2zevFlqd3d3R1paGjw9lUSjqZGTdCeaNWsWpk6dqmvSXo8cOZIbGcqRwChK49aoUSPtmg1dEJSkBo0dO3YMrVq1kg03tC/z58/H5MmTZf2NVX7++WcpdRyvX7du3fDvv//ymiy22RKM+umnn/DEE6blLCeIj2A+XqHIY/Q+0y2PPvooCIDiFWr79ddfeU2qtvPnz0vwnH4HApQolWRODj+8sn5/a9UFGGVcSd5zX4BRxnUTPYQCGgUIjHKvr4SeNe2a1/jZE5H19533bUnN+h3tVYBRjrUjvLNEgFGOtUe81QgwiqeK/WwLuqxFbnqhwQU4OVfBmN/uQlh9P4P9RKPpCggwynStbN2Td5YIMMrWqgv/QgGhgDUUEGCUNVS0jg/eWSLAKL621gKj8tNisXNCXe4kfT9LgbO7N7dNYyzMTELCod+RcmIzS9EXi4L0OPYFXie4B1aVUvqFthyI8HYPMD/8D+o1fug1N+EicuLO6ZrgFVYX3lG3Ps8oLS5g6f++RtrZnci8epSlAcyGs5sXag96A+7+t77kdvmvBci4JP+yt3tABJoMXyLzG9SktzRWZtSp0H0lH9+I5JPsvlKuoiAjESX5WXDxDoQ7g8YItgppcTeCm90FFw9fnZH8y5ulJUg9sx2lRfIPcoOb9YOTy63UUdmxp6X7y4w+zLS4gCpOzghtda+09rzkq8i+Loe73AOj4FeztTRhQXo8YnctR/qFfchPjUFhZiJcWaQsz+AaCGF7ENnxMbj6BMkXx/7en3p2B278+700X35qLMBsnqG14BlWB77VW6Baz5FG3wNyp5WzJsAox9l33jlSWcAoivzUdXotFBYrgyjQDm1+6ypqhRZxN2stg6kmMKiKVwgo2jPrCrzdGdVjoBgDo1rWKGBAS4w2mpGaq80nvDH2a35UpcZVC/Hn60podxpLBfgTSwnIK7MfScLQLuowlu6YAfNq4nKiq65Juu7SIBffjlGmjTMXjCJni1hUrM/+CVTMQYbmTKPfxhuGlfqzNV7hrJHGb5p8FbXDbu/xxQQ3DJzPB6MCvEqkCFUeDFYyVBYzEOvr7fz1Trg3BcN7yEGuuWtC8c0Of67L1welYFTfNG6bvpHSO1KaR155gu3nTLavFa0IMMqCHeU99C1wY9GQ8gKjunfvjp07d6qukSIdHTx4UGo31PfNN9/EggULVP3wGigt2fr163lNILBm4sSJijZHAqPMhcEyMjLg56d88PDAKIpk9OWXXyrunwwPPfQQfv/9d26bmvHVV1/Fhx9+yG1+4YUX8MUXX3DbLDXaEowyNY0erd1QqkgeGLVkyRKMHTuWe9u1atXiRjHjdv6/kdJLPv3009wu9DN+6NAhbputjAKMMq4s77kvwCjjuokeQgGNAqaAUbmH9iL21Wc0Q8SrFRQQYJQVRLSiC95ZIsAoKwpsI1cCjLKRsBa6NQWM6jqyAfq/3tzCGcQwngICjOKpYh8b7ywRYJR99kLMKhQQCpingACjzNPLlr15Z4kAo/iKWwuMIu9bx4SimEE/+qXLnMPwqdpE33yrzgCaK+vfxcXfZuFmqeG0PwRX1X9kDmr0HcP39X/rkcUPI+noOlmf2ve8Lo1NOb0VZ759CbmJl2Xtlla6LzwrAUD64wlgit6wCJfWzEFpseEvPdBYF68ANB72ASI7P67vSlbPjb+A3ZOVvwf0/jgWzh4+OL/yLcRsWabQksCptq+txckvn5MAJl2nkZ2Govmob3CFwWAX2Xpvltz+MFy3H10TmNZ05GeI6DBEairOy8TRj4YwMEr9czbqSMBZ3QemoVqvZ6Vx4n98BQQYxdfFHlbeOVJZwKjvWdSkmSpRk4wBN5RyrdPU2sgrdOJu29zHEvFoJ3lkIP2OxsAoU1PypWQ5oxOL3MQrBPP8N/eKomnPeS/8up8PqU6+P8VoejpySPfecWotrgbWBKMIaiK4Sa388/Y11Azhnz9nYt1w33t80IkiKFEkJd1CEaraTK4L2l9eoWhgbz6QAtLVWqXbDH5ErAaRhfjj9Ri4OBkGsTTrSM1xRj8WeSozT/me9PcqxZ6ZVxTpGDVj79RXAUZZsHO8h74FbiwaUl5g1COPPIKVK1eqrpFSxV28eFFqpyg9P/zwg2pfU1O7aRxQOj21QsDUoMaIqAAAQABJREFUvffeq2h2JDDqnXfewdtvv61Yo5ohJSUFQUF63yRgnXlg1IwZMzB9+nQ1V7Cm1gRMjR8/XnUuSxpsCUYNGTIEq1evNmlZNWvWRHR0NLcvD4z6888/MXjwYG5/czUnJ4be4wRMfffdd9y5bGUUYJRxZXnPfQFGGddN9BAKaBQwBkZlrluNxPdm4GYR/xcSjR/xap4CAowyTy9b9+adJQKMsrXqZffPB6Nq4YG5bcvuXHgwWwFDYBRFirprfDMQGCWKdRUQYJR19SyLN95ZIsCosigqxgoFhALlpYAAo8pLaePz8M4SAUbxdbMWGEUg0JbRwYpIRjSrGhhVlJ2KE1+MlCIq8VfHt1bvMwqNnlzEIiHxP2NRA6MCG3bD0Y8fNQlU4s+stPLAqNzESzjJ7iv94n7lACOW8PYPo8nTHyujMv1/nBoY1fODaJz+ZiySjvG/jG8MjHJy80Dszm+MrO52c4tR37IoV/1waNFgZEYfut1g5KrZ818jqssTRnpV3mYBRjnO3vPOkcoCRt3/XnWcjuWnoDMlRdv478Lx12E+XNS6Vj5WviqHbvR33RAYRVGnjs6/ZDRalMZnqzfrIKeAD8QcnGsdQFYzF70WFFXBhxuD8OVWfmQka4JRNN/jH1fDwcsedKkorw5MxUv9UxV2Mrz3VzCWbeGvccYQlqawa4Zi3LBPqmL/JU+FXWMgyIiiPvVsnMtS3OXDic9QabobfDUEfY3pl4YJ96QYHK/f+Mq3EdhwlB9xkt6P9L6sSEWAURbsJu+hb4Ebi4aUFxj18ssv46OPPlJdI4E8lD6PiqGoQ6oOLGzYu3cvunTpohjtSGAUgUuUDtDUYg4YZShykanzmdqPohqRrtYstgSjCFz666+/TFquuWAUve86depkku+ydqKfJ0M/e2X1zxsvwCieKnIb77kvwCi5RqImFDCkQMSM9+HRtBWc/QPg5OUtAVAFl86j4Pwp5B7ci+ytGwwNF20WKiDAKAuFs9Ew3lkiwCgbiW1Ft4d/i2bf7JZ/q6t+9wgEVjec7sKKSxCudBRY/sxOpMXkII+l0yvMK4a7twsiGgcgqgn7Fnm/qqjZNkSnt7i0lgICjLKWkmX3wztLBBhVdl2FB6GAUMD2CggwyvYamzoD7ywRYBRfPWuBUVkxJ7B3WnvuJLxUetT/yIcPsnRthj8g5zpkxuCmfdFy7A9SpCX9PjwwKrzdgwwa2sAFt/THm1PXB6Mobd6xpU+y9Hw55riR9aXoSm0nrmdRtprK7FRRA6Mo0lTc3p8U/TUGQ2CUpo85rxS9i9ZpbuQtN59gdJ13nIFfweZMV2n6CjDKcbaad45UBjDq1HV3PLCoOncjCHTZPeMKQv3kfz/S77z1lBdGfRmlb9bWN755DXXD1b84bAiMMhaxSjvJ/y/uXVgD5+NupRnVbSOIxxpgVFFJFUQnueJCvBvOxbnjtwO+iE/nQ7s0v7XBqFX7/TD55zDdW9Ne12Gp8P5mKfF4pc+cWohJUa7TzYWlO2QRlEgf/bJwbQi+2Bqgb+bWKXJU+3r5aFkjHy2qF0iglK+n0id3MDNS6jtKgccrnz4bh7uamXfGLt8RgHfW8P+W9s7QRDzS0XAUM946HNkmwCgLdof30LfAjUVDyguMWrhwITdlHS36+vXrqF799sN/5syZmDZtmkX3Y+6g7du3o3fv3ophlQWM+umnnzB06FDF/dvC8Pnnn2PUqFFWdX2nglHnzp1Dgwbl883z0aNHY9myZVbV3ZgzAUYZUwiMslci3AKMMq6b6CEU4ClQhUWGvFnKwrmyb0yKYlsFBBhlW33N9c47SwQYZa6Kor9Q4LYCJUWlcHJxMvnbkLdHiitzFRBglLmK2a4/7ywRYJTt9BaehQJCAespIMAo62lZVk+8s0SAUXxVrQVGnfnuVcRsVf69180vDL0WX5NNfvNmKfbP6sYiDR2W2TUV98Ao+FZvwSI7FSDzymEU5ykjV1DfoEY90O6NTZph2lceGKVtNHDh7OZFfyCVenDBJtYm9dHxQdGwPENupTKiMZTmriDthk4P+aV3ZEN4hddD1rVjBqGwgPpd0OGtrfLBrKYGRik66hnMAaNofb7Vm6M4NwMZbI+Kc9P1vCmrTm6e8K3WDB7BNZCXFI3s6yel/VP2BOo9NAN1Br/Ja6r0NgFGOc5bgHeOVAYwilLoUSo9XulUPw/fjY3lNclsBAt1ZinsMnKVkZqo47O90/HmfcmyMboVQ2DUfW2zsGhYgm53g9eULo7SxukXc8EoSst3KcENF9h/lxLdcCXBFRTVKC7dFfQRgKnF2mAURcPqwrRWS3FHKeeaVC2QLe/4NQ88/EE1mU1TGdAiB5+MiNNUZa9pbD8f/bC6BILJGkyoEFTXgkFS3RvlogeLKEXp+gyVDzcEYckmZRYqzRhT0+hp+heXKj/71LSN7JWOyfervx81/e6kVwFGWbBbvIe+BW4sGlJeYNTx48fRvHlz7hp///13PPTQQ9q2KVOmYPbs2dq6LS82btyIgQMHKqaoLGDUihUr8NRTTynu3xYGilpE0YusWe5UMOrkyZNo2lT5LRRraqPxRe9litZVnkWAUcbV5j33BRhlXDfRQyggFLCvAgKMsq/++rPzzhIBRumrJOpCAaGAIyogwCjH2RXeWSLAKMfZH7ESoYBQQF0BAUapa1PeLbyzRIBR/F2wBhh1bfMSnP3xNe4EIc37o82EP2VtsbtX4NRXL8hsVPFkUE3T576UgCdNI0FU17d+jnM/v8EFbdpP3oLABl013aVXU8AoN98QBDbsAb/abeDi7oO8lGuo2f8VuAdESD6OfvIYEg/9IfNLwFC3+SdlNt3KhVVTcWXdu7om7TWBQDXuehFufqFaW17yVVxYPQ3x+37R2nQvmr+wHBQJSreYCkb51WqLgLod4F21sQQ4uXgFoHrv53Hyy+dw49/vdV1qr6lP0xFLEd7u9udihZmJOLbkcaSd/1fbT//Cv04HtHrpZxDQpikFGQk4uKA/cuLOaUza16iuT6LZc19p6+LitgICjLqthb2veOdIRQejCouroOv0WkjPdVaVP8SvWLVNtyE5UxmNSNMe7FuC3dOvwEVlGkNg1COdMvHOY4kaV0ZfywJGZec7SSkBV7MoUEev8tPVGV2AXgdrg1Hk/s0fw7D6Pz+9mW5Vn+uThjcGy9POzfszBF9v48Nvy567gT5Nc7m+yEjRsQiOIkiqLKUZiyL1yt2p6N2EH/lp+q+h+HGPf1mmMHnskA6ZmPe46e8pkx3bsaMAoywQn/fQt8CNRUPKA4yqW7cuLl68qLq+t956C/PmzdO2jx07FpTijVcoutSePXt4TRbZ1q9fz4VGKgsY9eGHH6rCSgcPHsTly5ct0pU36KuvvsKmTcpvlfD6mmq7U8GonTt3onv37tzbXLlyJdduqZFAwwsXLlg63KJxAowyLhvvuS/AKOO6iR5CAaGAfRUQYJR99defnXeWCDBKXyVRFwoIBRxRAQFGOc6u8M4SAUY5zv6IlQgFhALqCggwSl2b8m7hnSUCjOLvghoY1Wn6v/AIqsEdRLBSQdp1ZMeewbV/lqpGfqLBFNGJIjtpSnF+Fv59sxkInNEtPizaEEVIcvHkf7ibcfk/HHinD26WFOkOgyYSkq7RGBgV2vIeNHv+K7h6B+oOk12bC0YRsLRnalsGb8nTQ1Vxckbjpz5CtV7PyvxrKzdvStDX1U0faU2aC4K0us47ARcPX43JaMQoSnHXZPgnCqBK40ANjKpSxQkdpu6Ef+12mq7aV4Kb/n27FcDWql/cAyLR/d2zLMqtu34TS7N3CbvfUH4RO6BeJ3R4e7uivzAAAoxynHcB7xyp6GDUuiM+GLfiFhxq651YyqIS9WPRiXjFEcCoz/4JlCIW5RepRxrird2YzRZg1IFLnnjyk6rcqSMDirFjWrQmGKL0GO85uybi0lwV/YN9GLA2MxrGojFRasIFLK3ezjMsymIZS5va+fji+Rvw00uz9+q3EVh/1KeM3k0b/kSXDMx8JMm0zndILwFGWbBRvIe+BW4sGlIeYBQBMSNHjlRdX+fOnbFv3z5tO6V2oxRvvDJ+/HgQzGPrUlnAKEpZSKkLeeXee+8FgWOOXO5UMGrNmjW4//77udJGRkYiPj6e23anGAUYZXyneM99AUYZ1030EAoIBeyrgACj7Ku//uy8s0SAUfoqibpQQCjgiAoIMMpxdoV3lggwynH2R6xEKCAUUFdAgFHq2pR3C+8sEWAUfxfUwCh+b/OsgQ27o/2bm2WDLq+dj4u/zZDZJChnyg7412kvs+tXzq98C9Eb3tc3gyAuipCkKYbAqKrdh7OoSJ9pU+Zpxui/mgtGnf72RVzfroyCVOvucWjw2Hx994r6oUWDkHLyH4W90ZPvs0hTY7V2QxGjqji7otO03fCt0VLbX/9CDYwicKvJcH5gAPKxd3pHKf2fvr/6Q2aj9r0T9c3aOoFRBEjpFl56Rd32ynwtwCjH2X3eOVLRwagRn0Vh97mywy6m7CJFCvr8eX7KNnuDUZ9uDsT764NNuQ1Fn6igYjzSMROLWSo4XrEFGEXMar93auJqshJ2ojX8+HIs2tfJk5ZzJNoDjy7mp9F7unsGpj5kOiBEvpZtCcSe857IK7Q8glSHunlYPvoG3Fxuw7evfR+OPw/dhoJ5WlrL9kzPDLz9gOn3ba15belHgFEWqMt76FvgxqIhtgajOnToIEFPavd49uxZNG7cWLb2Tp06Ye/evTKbprJ06VK8+OKLmqrNXisLGPX0009zI2aRsOPGjcPixYttprE1HN+pYJShSF09evTArl27rCGP3XwIMMq49LxnogCjjOsmeggFhAL2VUCAUfbVX3923lkiwCh9lURdKCAUcEQFBBjlOLvCO0sEGOU4+yNWIhQQCqgrIMAodW3Ku4V3lggwir8LtgKjCNJpz6JFBdTvLJv4yIcPIemY/IvPYa0Ho9Urv8r68SrFeZnY9lIUbpbKUzlFdXmCRYD6WjtEDYyiyEvdFp4BpdEzVswFow7M7Yn0i/tlbqs4uUjRlDyC+B9C63ZOOb0Vh969R9ckXVfrORJNnlmqtRsCo2r0HYNGwz7Q9uVdqIFRvJSEuuPVNO0y5zB8qjbR7Sq7PrbkCSQc/E1mc2apC/t+liyzicotBQQY5TjvBN45UpHBqBupLug9pxZKb7MpNt0MZ8bR7GLp9EL9ShTz2BOM+np7AOb9YfyMqB1aiKYsHVyNkGL2XxFqBBehNnulVIOkYcMJ9RT3RQZbgFHkd+nmIHywng9j6UZEmvN7CL7dyU+jt+a1GDStVkDuzCqUgvHgZU/sOueJw1c8cfq6O8yNtPVQhywsePx2JMlZv4fiu538VHotaxSgapA8eqRZC9br/GjnTHRtoJ4+UK/7HVEVYJQF28R76FvgxqIhtgSjGjRogK1bt6JqVX5YOVrwpEmT8O6778rW7urqioyMDHh6esrsVDl37hyaNGmC0tJSRZuawc/PD/379+c2E4AVGxuraKssYFSdOnVw6ZL8WwQaMdatW4dBgwZpqia90l5TBDBeoTR6mZmZvCaLbYbAqLZt2+Lw4cMGfVMEsvffV37zhQYNHjwYf/31l8HxmsaaNWsiOjpaU5W9Ll++XBExbciQIfj1V/4voLNnzwZF8jKnNG3aVAEY0nj6OfntN/kvQ+b4tbSvAKOMK8d77gswyrhuoodQQChgXwUEGGVf/fVn550lAozSV0nUhQJCAUdUQIBRjrMrvLNEgFGOsz9iJUIBoYC6AgKMUtemvFt4Z4kAo/i7YAswytnNCy1f/AkhLQYoJt01qRHykqJl9gaPzEWte16T2dQq+2Z2Zan7DsmaCcwhQEdT1CCeug9MQd37p2i6GXw1F4za+mIEinPTZT4jOjyCFmO+k9kMVfZMacPSE56WdQmo30VKMagxqoFRpHn3d8/BzS9U05X7qgZG9f7kBkstyP9QnRyd+noUYnd9q/DZZ2miavpD6nzyy2dx498fZOMEGCWTQ1YRYJRMDrtWeOdIRQajPtkUpBrlyFYb8fqgFIzqm6Zwby8wKivPCV2m11aFenxZurdneqTjiS6ZEgClWPj/DfYAo+LSXdBrFh9sC/Iuwb+zouFU5Sa6z6iFxEwXxdIbRBZi3aRrCrslhuLSKjh3w+3/sJQX/rvoidxCwykJKVrU0fmX4ep8i8z7aGMQPv6bfyZ99cIN9GhcsUAmS3Q2NEaAUYbUUWnjPfRVulrdbCswiuCY1atXg9KCqZXc3FwQmJOQcJtM1PTdvn07evbsqanKXocPH44VK1bIbIYqs2bNwtSpU7ldKDrV/v3ybxdQx8oCRtG93rhxQ3Wf9NMcUn9D5eeff8Zjjz2m6FJcXCwBcomJiYq2shgMgVGmrN1eYFRERATi4vihK7OyslC7dm2kpKSYJI2TkxNOnTqFRo0aKfoTrEW+yrsIMMq44rznvgCjjOsmeggFhAL2VUCAUfbVX3923lkiwCh9lURdKCAUcEQFBBjlOLvCO0sEGOU4+yNWIhQQCqgrIMAodW3Ku4V3lggwir8L1gajwts/jAaPvgPPkJqKCUsKcrBlDIvEQXl/9IoxoEfTvTAzSXOpfXVycUPfZamgCE1U1MCoDm/vQEC9jtpxhi7MAaMKMhJAOuoX0qHWwAn6ZtU6DyJy9QlG749vf4leDYwKqNcJHd7erupb08ADowiIIjDKUDm1fAxidy6XdTEFcDr97UssxeCXZo+TDahEFQFGOc5m886RigpG0SO5z5yaICCJVyiqU7CPPFIfrx/PFsPSu+WopFmrHVaETZOvKobZC4xauc8Pb/8SplgPGbzdS/HruOuoH1HIbdc12gOMovlHLquKXWeVwV2o7cvnb8DT/Sae/IQfNGbS4GQ830cO99I4a5Sikir48V9/EOyUyeAztUL6tqqZLzWv/s8Pb/7I34tpDybhqR4Zam6EnSkgwCgL3ga8h74FbiwaYm0wql69eqCINwTHGLuv119/HYsWLeKue+zYsViyhJ9n+cqVK1LUqPz8Wz+0XAf/N4aHh+P8+fOgqFH65fjx42jZkp8DujKBUYbSum3btg19+/Zlvz8pf4HS17NVq1Y4dOgQCNTRL6tWrcIjjzyiby5z3RAYNXDgQGzcuNHgHPYCo2hRO3fuRPfu3bnr++CDDzBhgmm/yBl6r7711luYN28edw5bGk15v9hy/jvBN+/5KMCoO2HnxBqFApVbAQFGOdb+884SAUY51h6J1QgFhAJ8BQQYxdfFHlbeWSLAKHvshJhTKCAUMFcBAUaZq5jt+vPOEgFG8fVWA6MIMnL14qexkTyxv7cTUEPgjkdgFIIa90ZIy7vZNf9DVxpDkZ4o4pMtyl3L0uDkdusDYTUwigAjWq8pxRwwKvXMDhxcqIyO1fLFHxHe7iFTppP6XFozB5f+mKPo3+uj69r0f2pgVFTXYWj2nBxAUjhiBh4YRVBar8UxvO5aGw+McvUOZEAV/4vWmoFnVryCmG2fa6rSqylAlWxAJaoIMMpxNpt3jlRUMGrfBU88tVT92f3jy7FoXyfPos2h9G6U5k2t8HzbC4x6Z00Ilu/gp5mb8mAyhrNoUaaU6CRX9HtHCcvSWFul0iPf6474YNyKCLpUlPvbZcGHwV0/MEBJv1Baw53ToxHG0gCqlbXM96kYD0WzEwsENeHeFLg4Gf+8PjXbGfe+Wx3JnIhV5Hjy/ckY2euWxleT3XDX3BqK+cjQp2kulj1nGObVHxjPImodvapcP/Xr1jAXPh6mZwTT9+2IdQFGWbArvIe+BW4sGmIMjOrSpQsIRNIv7u7uCAoKQnBwMEJDQ0GRlwYMGICGDRvqd+XWjxw5gvbt26OkpITb7u3tjZiYGAQGBnLbCcB5+OGHcfWqknDVDAgJCQGBPc2aNdOYZK+jR4/GsmXLZDZNxRBs8vTTT+O779TDspIuatF+1AAhio5FUbJ4Zfr06aCoV6YWmpvWoF+OHTsGgpf0C0XtunDhAhdoor7r16/HsGHDkJamDLOo8UX7TlqrRQjr06eP1K7pb63XmTNnqqadoxR5r71mOCywPcGohx56SIqqpqbF4sWLQfAgRdtSK/Qz98cff4B+HvVLYWEhqlevDmtH6dKfh1cXYBRPFbmN99wXYJRcI1ETCggFHE8BAUY51p7wzhIBRjnWHonVCAWEAnwFBBjF18UeVt5ZIsAoe+yEmFMoIBQwVwEBRpmrmO36884SAUbx9VYDo3osugiPoGr8QRZak45twJEPH7RwtOFh/b7OZV+Kv/XlaB4Y5eIVgD5L4g070Wk1B4xK+G81ji19Umf0rcu2E9cjuEkfhV3NcHXTxzj300RFc9e5R+EddSszgxoYVe+hGagz+E3FWH2DAKP0FXGsugCjHGc/eOdIRQWjXvs+HH8e8uWKHxlYhB1Tr7LnK7fZqPFSghvuns8HXGjwQx2ysOBxeQYne4FRBBURXMQrutGMeO26thW7AjD7NxYdkVNsCUYVFleRUgFm5N46C3Wn93C9CWcGL+UUKNsIDFo+2jBoNGxJVexnKfF45aeXr6NdnXxek8L24YYgLGFpG3llWPd0TH8oWdvUeXotVYhq1fgYtKxRoO1r7OKVbyOw4ahyb12cgX9nXgGlG6xIRYBRFuwm76FvgRuLhhgDoyxyamRQenq6lCaPIjYZKoagFxqXmpqKiRMnSpF3Ll26pI1q5OXlhREjRkhtNWvySdHMzEwptVt2djZ3CZUJjCIBfvrpJwwdOpSrBRkJjps0aRL27duH69eva/sRgEXRvcaNGydBctoGnYszZ85IEb50TFa7fP755/H55/JvQWicl5aWYsGCBdL7Izk5WYK2yLZu3TpNF9gTjKLIWidPnkTjxo2169G/2L17txSBjUBAXdiO0uNRRCm6fx4URX5+/PFHPPmk8pdE/TlsURdglHFVec99AUYZ1030EAoIBeyrgACj7Ku//uy8s0SAUfoqibpQQCjgiAoIMMpxdoV3lggwynH2R6xEKCAUUFdAgFHq2pR3C+8sEWAUfxfKE4zKjj2FPVPachfi7h/OtZtidPUJQZc5h7RdeWCUd2RDdH3nmLaPsQtzwKjM6MMsElYXhUuK4ESRnEwt53+ZjOiNH8i7Mxrhrs9StdGw1MCopiM+Q9Uez8jHcmoCjOKI4kAmAUY5zmbwzpGKCEZRarOu02sjv4hPPr3QNw0TB6WUaWPuf686TscqAymQUy+3m9gz64qUqk4zib3AqNFfRWLLSW/NMmSvFKGIIhUZKwVMxydYurrj1/jRiWwJRtHaZqwOxQ+7lVGhDK37/acSMLhNlqEumMTS2v3O0tvxynN90vDGYNPeI9/t9Mes30N5bjD+nhSM7Xc7GAr1o/680ql+HlaMiTUJ2Dt13R0Pvl+dl8UX97TKxuLhpkPTvLU4ok2AURbsCu+hb4Ebi4aUNxhFUFS/fv1w8OBBo+t1c3PDnj170LYt/x/wug7ILwFRFGWKouTQWEOFIglRRCG1UtnAKIr8RaBaVFSUmiRaO0Ug8vf3R3x8vASXubjcyieu7aBzQSASRfZas2aNjtV6lxQxyVi6PN3ZKKoVRa/SFHuCUbSG1q1bS7CZsfcr9Y2Li4Ovry+ysrIQERFhMFVlRkYGunbtilOnTtHQci8CjDIuOe+5L8Ao47qJHkIBoYB9FRBglH3115+dd5YIMEpfJVEXCggFHFEBAUY5zq7wzhIBRjnO/oiVCAWEAuoKCDBKXZvybuGdJQKM4u9CeYJRpUX52DIqiH04KU9Z03TEpwzqGcFfoAXW8gajSgqysWUM+6D3pjyVUN0HpqDu/VNMvoNjSx5HwsHfZf09Q2uh+8KzWpsAo7RSVMgLAUY5zrbyzpGKCEZRarUZq/igCu3GXxOvoWFUYZk25qttAZj/Jz+CEjme82giHuucqZ3DXmCUobR/BDQtey4OFHlJrVA0plFfRGL/JX5kJRrXokY+Vo+/HehD4yuNRXnq8HYdTVX2OpDBOx+ZCO+cjLkFAckcGKh4s/R6e2dFw9NNfi7rD/liawAWruXvIaXi+/iZOPRrnqM/TFbPKXTCiE+jcCSaD42992QCKOWfplA6vf7v1ECpiuS9m+TgvWEJ8PNUX/vlRFc8yaJdqaXv+/6lWHSsa1maSM06HfFVgFEW7ArvoW+BG4uGlCcYlZCQgEGDBpkERWlupn79+ti/f79qSj1NP3Ne33nnHbz99tsGh1Q2MIrE6N27NzZs2KAagcigYJxGgmNGjhyJb775htNqHVNYWBiio9lB4ql++OnO5GhgFK3tpZdewscff6y7zDJdUxS0/v37Y+/evWXyU5bBAowyrh7vuS/AKOO6iR5CAaGAfRUQYJR99defnXeWCDBKXyVRFwoIBRxRAQFGOc6u8M4SAUY5zv6IlQgFhALqCggwSl2b8m7hnSUCjOLvQnmCUbSCXa83QF7KNdliag2cgAaPviOzlaVS3mAUrXXna/WQnyr/sNu/djt0nLbbpFspKcxlPuqjKFsedSOk+QC0mfCH1ocAo7RSVMgLAUY5zrbyzpGKCEY99EF1nLjGj+bUMKqAgVExZd6UhAwX9JhZSxVwaVUzH5SqTlPsBUZtO+2NFxjYpFYaMT0mDkpFp/q5cHO5TesQ1PTbfj98zyI10doNFQKQ9s2+IkXK0u1nLTCKfA5eWANn4wwHatHMPaRDJuY9nqipqr7Gpbmi5+ya+vyvtr+r80082S0TT3RJR+2wIq2dLrJYVLJ9Fzwxn4FV15L5+tD4HdOiEeonT2n3KkuBt56TAk8zQfXgYrxxX5KUVi8ioFhjBun54+4AfLsjQLrWNuhc1IsowoY3rupYKs6lAKMs2EveQ98CNxYNKQ8wiqIGLV26FFOmTAFFsjG3UKoxAnbU0uKZ42/x4sVS2jdjYyojGEWa9OzZU4ruFBAQYEwio+0E/CxZssRov7J2WLRokZRWzhQ/jghG0bopJd6nn34KZ2eWZLUMJT8/H/fccw/oPu1ZBBhlXH3ec1+AUcZ1Ez2EAkIB+yogwCj76q8/O+8sEWCUvkqiLhQQCjiiAgKMcpxd4Z0lAoxynP0RKxEKCAXUFRBglLo25d3CO0sEGMXfhfIGow4tGoSUk//IFkNRkbrNO4EqzvwPTHU7X/pjDnLizuuaENnxUYS2HqS12QOM4t0XLaj9m/8gsGE37drULmK2LsOZ715VNNcc8CoaDl2gtQswSitFhbwQYJTjbCvvHKloYNTZG24Y/G4NVdFfZyn0RrFUetYow5ZGYf8FL1VXG968hnrhtyJT2QuMSs12RseptVXXqGnwZnBTLQb/RCe5IsinFHFpzigu5aci1IzRffVlEY6aVivAA+2z8HD7W5GyrAlGfbPDH3PXqEcB012LORGTXv8hHH8c9NUdzr0muKlqYBE8WTQqitR0KcFNFYrTOHiQ6bDwCSWglZrjjEEM9ErKNP45dbBPCbLynRDC5k9Id0GJeiApUJSrJSPi0LeZ4ShXmvXdaa8CjLJgx3gPfQvcWDTElmBUZmYm1q1bh/feew+HDx+2aH2aQZGRkRJk8+CDD2pMZr1S2rcFCxaAwChToI3KCkaRqE2aNMGyZcvQrZvxXyJ4m3DhwgVMmzYNP//8M6/Z6jaKGrV27Vp06NDBqG9HBaNo4ZRikkAyipJmSaG0k5MmTcK///5ryXCrjjHlZ8yqE96BznjPfQFG3YEbKZYsFKhkCggwyrE2nHeWCDDKsfZIrEYoIBTgKyDAKL4u9rDyzhIBRtljJ8ScQgGhgLkKCDDKXMVs1593lggwiq93eYNRF3+bgctr5ysW0/jpj1C99wsKu64hK+YE9k5nf2/XS1nX+OmP2djntV3tAUYRsHVpzRztGjQXQU16o+1ra1HFyUVjUrwW52Ww++qEvKQriraWL/2M8LYPaO0CjNJKUSEvBBjlONvKO0cqGhhF8AxBNLxShXE+O6ZeRSQDXKxRfmURld76OUzV1che6Zh8f7LUbi8wiiZ/hUUo2mAgQpHqDVjQ0Kcppee7IY20JhhFgFfXGbVRLA++pFghwUvb2B7TXptSCoqq4KmlVVVT4Znig9enbe08fPF8HAgY4xWKNjVyWRSKSkxcKM+Jjo3udwGLkkUwVkUtAoyyYGd5D30L3Fg0hCCYkydPsh9Gy9/kRUVFSExMBKXKo/8otdlff/2Ff/75B4WFZcuHqn9TBOtMnTpVSvvm6mr8Ww3Xr1/HwoUL8cUXX4Ci6ZhaDIFRAwYMwKZNm1Rd+fr6Ijk5GW5uyvB5q1atwiOPPKIYawhQGz16tAQqKQapGE6fPg2KsqVfaM20dlMLQWgE2hBw5OTEkE4j5cyZM5gzZw5++eUXlJQYOQWM+DK3md6/w4cPx+TJk9GgQQPV4fSeJABJUyhS0+eff66pyl7pvv/77z+ZTa1CEbbi4ljOWw9lvtb58+dL61Ibq2un9/SoUaMwduxY7h7q9tVcb9++HbNnz8bWrVs1Jru/CjDK+BbwnrkCjDKum+hhHQWcfP3YH4nkz/XS7CzcLOdnt3XuRngpTwUEGFWeahufi3eWCDDKuG6ih1BAKGB/BQQYZf890KyAd5YIMEqjjngVCggFHFkBAUY5zu7wzhIBRvH3p7zBqKKcNOx+oymKclJlC3Lx9EfzUd8gtOVAmV1TKcxMwsEF/ZF944zGJL26ePii54dX4Ozuo7XbA4wqKcjG7jeboyA9TrsOzUVoy3vQcuwPcHLz1Ji0rwUZCTi8aDCyYo5rbZqLgPqd0eEteRYGAUZp1KmYrwKMcpx95Z0jFQmMIsik2/RaoIg8vNK+Th5+fDmW12SRLZOlU+s8rTYKi/mf+1O0n90zrsCFLceeYFReoROGflQVp2P56QUtunmVQbYCo2i6F5dHYNPx2+cibwlj+6dh/EB5+lZeP10bQVcPf1DNaMpA3TGGrjs3yMVnz8YpUgvqj6FoY2PYPVFavrKWGUOS8GRX8zOJlXXe8hwvwCgL1OY99C1wU6mG+Pn5oX///mjTpg3Cw8NBUYN8fHwQGxsLilh08eJF6fXo0aNWh7MqldDsZknbgQMHomnTptI11d3d3XHt2jVJY43ex44dA6VNtHcJDAxE9erVQYCap6cncnNzQdHLKGoYAWt3SqlTp46ke926dbW6E3B0+fJl7fv77NmzOH/+vMPdkgCjjG8J77kvwCjjuoke1lGg1q9b4RpZVeYsZ8823Jg0WmYTFaGAvgICjNJXxL513lkiwCj77klZZ185fj9Ob5b/MSyoujde2WD6lxvKugZrjY85moKvhu1QuHv8485o2DtSYS+L4cKuePwwZo/Mhau7M0b/1hfBNeV/nPr1tf049bdc48CqXnj177tl44vySzC33R8yG1V6v9gYPccov4Si6CgMBhUQYJRBecq1kXeWCDCqXLegUk/W+ZVDOHNNnlLh0V7h+Hxcw0qti7h50xQQYJRpOpVHL95ZIsAovvLlDUbRKq5t+RRnvx+vXBD7onHN/q+wCEn3w7dGSwY7eaM4Nx3xB1bjyrqFyEu+qhhTvc8oNH5qscxuDzCKFhC/7xccXzZcthZNxb9Oe1Tr+ayUVs8zrA6yWfSrtHO7cXXzxyxSVLSmm/a1ShUndJqxV9JBa2QXAozSVaPiXQswynH2lHeOVCQwauMxH7z8TYSq4LMeTcTjna0bUWfs8khsPu6tOueSEfHo3yLbrmAULS6OpWF78pNqiElRj/SndhMU7+XZ3ml4oksm7ppb02AKOVuCUdtOe+OFLwz/nWvzW1dRK9T8iGBXk90w749gbD3lrR/AUU0Whd2J6XRv6yzMG5oId9ebinae4UK8G6auDMWhK0rImNdf31abpT8cx0Cwe1pl6zdVuLoAoyzYUt5D3wI3YohQQCggFHAIBQQYZXwbeM99AUYZ1030sI4CPDAq7+gBXH/pKetMILxUWAUEGOVYW8s7SwQY5Vh7ZO5qfhm3D6c36UE7DIwapwftmOvXHv1jjqTgyye3K6Z+/JPOaNQnSmEvi+HCznh8P/pfhYsR3/ZArfahMjvBZ6f+vi6zBTAwavxm+bflCYya02aNrB9Ver/YBL0YHKVfKMNI2nX5h/vUx9PfFZ5+bvrdK31dgFGO8xbgnSUCjHKc/anoK+n48kEGRuXKbnNAuyD8OrWZzCYqQgGeAgKM4qliHxvvLBFgFH8v7AFG3Swtxp6p7ZBz4yx/UcxKYJCTmxcoEpNa8QypKUVUcg+U/1veXmAUrfO/+XdJwJPamiU7fXKulw5Qvz8P+KI+AozSV6pi1QUY5Tj7yTtHKhIY9c6aECzfEcAVnKI27Z11BQFe1s3C8zeDol5icJRaGdmbpdO7LxlJmc7oPrM2SjgxL8b0S8OEe0yPcjRyWVXsOqsEaeowSObvyUrYVrM2SkP3239++HRzoEnRkfy9SvEQS802rFsGaoTcgo1+3OOPGatCVR/3umBUdr4TOkypzU0XN6x7OqY/ZF6AjeLSKmg2sS5XQ7rH1rXysfJV+d+hNPdu6uulBDd8sSUAfxz2M5q2T+OT0vc90ikLD3XIRGRAscZs1itFwvpiawCOX/MwCJ5pnNaLKMLY/gyIapkN57IHnNK4dehXAUZZsD28h74FbsQQoYBQQCjgEAoIMMr4NvCe+wKMMq6b6GEdBQQYZR0dK6MXAUY51q7zzhIBRjnWHpm7GgFGmavYrf6OAEYV5hZzI0z1eaUpeo5uZNmNVeBRAoxynM3lnSUCjHKc/anoKxFgVEXfYdvenwCjbKuvOd55Z4kAo/gK2gOMopVkXT2Ko0seZ9GSrvAXZsTqHhDJoKit8AytrehpTzCKolod/+wpZFw6oFiXqYbwdg+i6chlcPH0UwwRYJRCkgplEGCU42wn7xypSGCU4yjt2CshwGjfBU9EJ7ohOtkFOQVOKGDp9ooYtEXp/+qGFaJt3Xw0jCzgQjcEeR245In/LnviIot45OF2E9UYHNS8ZgG61s9FhIVwkDHVLie6YsC8mqrdrBkRLCXLGefj3BGb5oLYVBfcSHdlUbec4coAO4Kf6L9w9l+tEKZV7XwGPqsuy6wGSuu37Yw309UVqdkuSGbroFSNpC/BaRQNq1ZoIRpFFVptTrMWaMfOAoyyQHzeQ98CN2KIUEAoIBRwCAUEGGV8G3jPfQFGGddN9LCOAgKMso6OldGLAKMca9d5Z4kAoxxrj8xdjQCjzFXsVn8BRlmmmz1HCTDKnurL5+adJQKMkmskarZTQIBRttO2MngWYJTj7DLvLBFgFH9/7AVG0WooGtTZ7ycgdvcK/uJUrD5RjdHyxZ/gHcWH/e0JRtGSb5aWsNR/7+LSH3Nxs8T0NEUunv5oNOwDRHV5QuXORcQoVWEqSIMAoxxnI3nniACjHGd/xEoMK7BkUxA+3BDE7USp6/bMvAI/T05ILu4IYbzTFBBglAU7xnvoW+BGDBEKCAWEAg6hgACjjG8D77kvwCjjuoke1lFAgFHW0bEyehFglGPtOu8sEWCUY+2RuasRYJS5it3qL8Aoy3Sz5ygBRtlTffncvLNEgFFyjUTNdgoIMMp22lYGzwKMcpxd5p0lAozi78+uiQ1BUY50SxUnF/T66Bpcvfkfqur2tcZ1wqE1uLDybeQmXjLozrd6C9S5702EtX1ASrWn1vnY0ieR8N9qWbN3ZEN0feeYzGaocurrUYjd9a2si3/tdug4bbfMZqhCUbHO/vga0i/sZamU1D+AdnJxQ0iLu9HoyffhEVTNkEvkpVwD7Zl+bqamIz5D1R7PGBxLjWdWvIyYbV/I+rn5haLX4hiZTb9yavkYxO5cLjO7egei9ydxMpt+5cLq6bjy1wKZme6xx6KLMpuo3FJAgFGO807gnSMCjHKc/RErMaxAfxYt6gqLGsUrD7OUf/OfSOQ1CVsFUUCAURZsJO+hb4EbMUQoIBQQCjiEAgKMMr4NvOe+AKOM6yZ6WEcBAUZZR8fK6EWAUY6167yzRIBRjrVH5q5GgFHmKnarf3FhKa4eTGbfFr8pc1C1RSA8/dxktpXj9+PU39dltoCqXhi/eaDMRpWYIykoyCmW2YNqeCOoho/MRhWRSk8hiUGDAKMMylOujbyzRIBR5boFlXoyAUZV6u0v880LMKrMElrNAe8sEWCU1eS1maOc+PNIO7sTBRnxKMxMkuAfz7Da8AqvJ/3nE8kiRFkrB4/N7kLpuDArGamntkhQU2FmIgg8o0JAkldEfQQ36Q1nd+W/55WehKWiKyDAKMfZYd45IsAox9kfsRJ1BdYd8cG4FRGqHVaNj0HLGgWq7aLhzldAgFEW7CHvoW+BGzFEKCAUEAo4hAICjDK+DbznvgCjjOsmelhHAQFGWUfHyuhFgFGOteu8s0SAUY61R+auRoBR5ipmfn9zwChzvAswyhy1AAFGmaeXLXvzzhIBRtlSceFbVwEBRumqIa7NVUCAUeYqZrv+vLNEgFG201t4FgoIBayjgACjrKOjNbzwzhEBRllDWeHDWgoUFFUBpcXTLTvPeOH17yOQluuka9ZeN61WgDWvGY4QqO0sLu5YBQQYZcHW8R76FrgRQ4QCQgGhgEMoIMAo49vAe+4LMMq4bmb3oG+23ZT/g9UkH5aOM8m5TidbzWPEr03AKCNz6ty1/S7vhDXaTx2TZhZglEkylVsn3lkiwKhyk98mEwkwyiayypwKMEomh90qAoyym/SKiXlniQCjFDIJg40UEGCUjYStJG4FGOU4G807SwQY5Tj7I1YiFBAK8BUQYBRfF3tYeeeIAKPssRNiTjUFxn4diT3nPVE7rAje7qW4keaKmJRbEQnVxnwyIg4DWuSoNQt7BVFAgFEWbCTvoW+BGzFEKCAUEAo4hAICjDK+DbznvgCjjOvmVqsePJu3lnUsuhGD3EP7JJuTlzcCho6AV5uOcK/fBE7ePrhZWIAbb4xB7n//ysZRxdk/EL79BsGrbWc4B4fCJSQUzoEhqOLshOLUFBQnxqM44Qayd/2D7O2bJF8KJzoGt5p14NmirY4FKE5KQM6+nZKN5vMb9DB8ut8F16jqcA4KQUlGOoquR7P/rkr3kblxDVBaKvNhrOJarabk071+Y3bfjUDruFlcjBJ2D4VXLyNnzza2/r9RnMJCo7NSVjDKvUETeHftDa/2XeESGgGXwGBU8fBAaXYmitNSURRzBTl7dyBn91bp/o2tv4q7B3x69YeTm7usa9Y/61Calyvto9+A+1mfAXCJrMbmDJeAt+KkeBRcPIusDWuke7xZUiIbT+v0v/8xeDRrA9ewcDj5+qMkLQVFsdfYfzHI2rJeGicbJCoGFRBglEF5yr2Rd5bcaWBUbloBYo6myrTz8HNFzbYhki0jLpelPYvFpT0JyEzIQ05KAdy8XOAT4oHAal5o2DsKDXpGSDaZE04lNSYHSRczZS2B1b0RVs9PspUUleLQqiuIPpCEuNPpUgo1mmvYZ10RUsdXNo4qlL6N+p7fEYeEC5nS2uh+XD2c4R3sDr8w9geTTmHS+gKreSvG8wzGwKiC7CKc3Hgd57bFIY3dT05qAUgv0iOUrbHxXVXZnOwsc+F/W403p8ZGHPG1Q8k4808sMuLzkJWUj+zkfBSyVHLS/YR7wo/9V69rOBr1jYKzq+E5KA3dl09u17jXvj7+SWc06hMl1anPsbXXEH82A7TXYDyzT7AHfMM8ULdLOJr0qypdawerXBTll0h7UVoih6Grtw6GV4DlqfSi/0tCQbY8lV5IbV8E17qVeiP+bDpbd560quKCEqycsF+xwhaDaqDZwGoye73u4bj0b6Ii9Z9PiDuqNg+S9VWr0HyX9iQqms3xoRhcjgYBRpWj2Eam4p0lAowyIhprvp5UgBPR2bKOVdnPcIvat54PJSy15w9bErDtaBqOXc5GOnuWerk7Y8WkxmhTX3mmFBbfxMb/UrD1SBriUguRkF6IxLRCFLPnWkSQGyKD3FE9zB33dwlBt6YBRjMbxbLz8jibV7eEs+ehZm6ab82/SfhjTzKi2fkaz+YM8XdF3ShP1I30RJ/WgejdMlB3uEnXqVlF+OdwGo5fycaJyzk4y84qF3YmhQe4ohE7c+9uH4R+bYLg6X7rDCkrGBXPNPr7YKqk2/XkAiQy3XLYmRDo44Iwdr/1WarUAe2C2L0EwIudz8YK6b3jeDoKi+W/j93F1uzqXAW0rxsOpOI3pt3VhHzEsjmd2NkVxfa+VR0fPN4nHG05+0t7umJzPPaczpDGpDGdwgPdUDuC/Vsh0gOP9ghDCzZeFPMUEGCUeXrZsjfvLBFglC0VF76FAkIBayggwChrqGgdH7xzRIBR1tFWeLGOAgRGbT5h2t/2aMZO9fPw3dhY60wuvDi0AgKMsmB7eA99C9yIIUIBoYBQwCEUEGCU8W3gPfcFGGVct4gZ78P3rntlHbO3bkDctHESGBT6+gy4MMBJvxAYlfPvVq2ZQKLQF9+AV+eeqOJimOzXDCrNYh/arv0VKcvehz6Ao+kTPmUB/O5+QFOVXgnIih0/En73PoywCdNAEJChQqBP0uK5yDtywFC3W21OTggY8hRCRk0w6rc0Pw+p3yxF+i/LUfPHv+EaWVXmP+/oAVx/6SmZTb/i5OOL0HFTFPeo309TJygt+bNFSP91hcHIXZ4t26Hakh80w7SvVx7uDbfqtRAx60M4+/lr7byL/BNH2PvgVS2IFfz8OAQNH8PrKrORzonvz0LhlQsyu6jwFRBgFF8Xe1l5Z8mdBkbt/Pwstnx4SiZhVLNAPPdjL+xcdhY7PzsLfdhF1plVPHxd8fCC9mjQK1K/SVbnQUedh9fH3W+0wJX9SVg78zBS9D7kJgejV/VFZJMAmS8Con5/6yDSbzCYx4TSfmgd9J/YHG6ehs8c3hoJ3hr399048ns0Nsw7zkCdIoMzBrH+Qz/qjPCGhp+bGiek7y62D0d+v4q066Z9k80r0B2tH6iJ3i83kUAwjS/dV0NgVETDAEk/Ao8MlSrs0+beLzZGj9GNDUIAF3bG4/vRSgB6xLc9UKu9/N8FpkaMIthqThsGK+uV3i82QS+2JiofD9qE5MtZej2MV59Z3gPfjNip6OjDgLrXtt8LJ/bhu7FyelMs6P2iXzo8Xgf3TpVD5Pp9HKEuwChH2IVba+CdJQKMMr4/L31yXgJddHsO6xuBpa80wH/nMvHKkgs4dVX5TF07uwV6trh9piRnFGHez1exalci0rLkIKaub93rOgxcGjO4Kkbdewsy1W3TXE/47CK+3HBDU5VeB3UKxo+Tm2LbsTSM+uAcCCoyVPq3DcI7I+ugAQORTSl/7k3G+E8vIIndk6ESwYCgOSPq4NGeYbAUjCpiZ9cCptuiVTESrGRoPmoLZhDxRy/Wx+BOt8Brtf7HLmWj+4TDiubo7ztLwNqw+adx6cYtIFbR6f+GB7uGYsnLDeDjeQvE+pYBUaQLQVdqhQLbkh4zn66NKHYWiGKaAgKMMk2n8ujFO0sEGFUeyos5hAJCgbIoIMCosqhn3bG8c0SAUdbVWHgrmwLmgFHsO/f48/VraBBp+Petsq1IjHYUBQQYZcFO8B76FrgRQ4QCQgGhgEMoIMAo49vAe+4LMMq4bmpgVBaDoyJnfQD2SSLXiS4Y5VajNqp+tIJFhwrj9jVmpMhL8TMmSBGZ9PuqgVEFF84g8Inn9Lur10tLEDP6ceSfPqbaxzUiCuFT3wVBReaU7J2b4dGoGVzC5ACBMTDKq20nhL89XzHOlLnzDu9H/Nw3pehbvP5qYFTSx/MYwDZJdV/1fVHUravD70PI2IkIeHiYfrNqXTPuZkG+ah/RcEsBAUY51juBd5ZUFDAqkEV4oEhRphb6QLHHqEbo/VITEEzDKzzoiMCo+t0j8OPYf6UIULxxumAURen5h4Fc+1ZcMDtTa1ANHzw0vx2qtwrmTSPZeGskMKpBjwjs/+GS6jj9BopaNXhmG7QcXEO/SVYvYRExVr12AKc3m661roM6LCLWE0u7cOEoNTCK9mjPNxeMAl668xD0RvAbQXC8cqeBUVMOP4CP7910K0qW3g09/WV3Fi3L+L9RVo7fx/0ZIajQ0HtMbzq7VQUYZTfpFRPzzhIBRilkUhjUwKjh/SNw//QTyGVwJa/oglEEEA2acgxnrpkG2er7e/G+qpj3bF19s1RXA6N6sShQkz6/CBb4yKRCkZ32Lm4LgrHUSjqLrPfasov4dacyip3aGLKPHlSVRWdKU9w/RXj6dWoz1aFnY3LxwgdncZRBTOaWx3uH490X6sKPRYTkFTUw6ue3m2LkorOq+6rvq2MjP2ya3wpL/ryOt76+rN+sWm/XwBf/LGwtRaFS7SQatAoIMEorhd0veGeJAKPsvi1iAUIBoYARBQQYZUSgcmzmnSMCjCrHDRBTGVXAVDDKzeUmZj+SiIc6mP8lOqOLEB0cUgEBRlmwLbyHvgVuxBChgFBAKOAQCggwyvg28J77AowyrhsPjCo4fwpudRoajPykAaMkKOrj77hRpYzPfrtH1t9/IH42A3b0Cg+M0uticpVS4F0b8QA/fR8jAKot/ZGlFWxjsj9jHQ2BUQGPDkfoy5NZiiM+bGDMN7WX5mQjdtwzyD9zQtFdDYxSdDTBQHCTsahcPDdpP3yB5E/f4zUJm44CAozSEcMBLnlnSUUAo8oibb1u4RKow0slx4OOKFXbhV3xoOhAakUDRlGavK+f3omkS/J0fGrjeHaKBHT3my3R8Un+B9m8NfL8mGrrMqI+Bkxswe1OUNSv4/fjzBZ5RBFuZwPGWh1CMeKbHooeamCUoqOJBoqE9fRX3VkKRWXo8jsNjJp69EEpStf2pWcUd9/6wZp4YK5h6LkwrxgLu/6leN9Sir9X1g9Q+HREgwCjHGdXeGeJAKOM7w8PjKI0cXtOZSIzVz3ykwaMopRvg6YcZ6nmLIOiNCuc8HB1zGBRhvQLD4zy9XJmYE+pSRGWdP11aeKP9e+0VIV1nlpwWkrJpzumLNeGwKjfWQq7UR+eQz5LZ2tpqRbqjnVzWkhp7PR9qIFRlEaPolSZU5rV8sbJaGXUMGM+Fj5fV4LGjPUT7YAAoxznXcA7SwQY5Tj7I1YiFBAK8BUQYBRfF3tYeeeIAKPssRNiTjUFTAGjwv2LsWRkHFrWKFBzI+wVUAEBRlmwqbyHvgVuxBChgFBAKOAQCtxpYFTuiU1wq9ESLv7h5aYf77kvwCjj8vPAKOOjAA0YFTH9Pfj2G8wdcrO4GPknDqM4MR43WcQmt5p1WGSl5ixaEYt9qlduFhXi0oB2CmjJFDCqNC8XFEGqJC0FrlHV4V7/VjoevSmkKqXUk9LQ6TX6DXxQit6kZ75dvXmTpYa7iKL4WLjVqivNc7uRf6UGRlHKvZrfrzcIGxVevYTi+BvSvTgHqaenKDh3CteeH8IoKfkHGaaAUaW5OaDxpdlZcGX3RCn2TClFcbFSmrwqrq5wr9cIzoH8SC2U9u/iXa0UazNljsrUpzKBUfY4G8x9L/HOkooKRlGKsYjGAVJUp9jjqQogRFe7QdNbo/1jdXRN0rWl0JEGjFo74zAOrryi8KsxUHq5qiwNYHZKPhLOZaimAHRxd8ZLf/YDRYLSL6aukeCgsPp+yE7OR9zpdNW5yP8Lv/RG1eZB+lPh+F/XsHrSfwo7GYiDpTG0Roo+lZmQh6sHk1V1f/mv/gip4yvzZSoY5caidkSyvXXzdgHtbS6DBdRKs4HV8Miijopme4FR347chevHUqX1FBeWcPeBID1nV/m/Jd7YOxhZTNPFd29URB6jqFgTdw2Ci5t8jO5Nn1gfg1WvK1Pu9nmlKXqObqTb1WGvKwsYdaeeJQKMMv6jw06KpWcAABeJSURBVAOjjI8CNGDU6yxq0+fr+GCqO3tmdGrsJ6VUo19FLsbm4eD5LC7QFOjrgivfdVFASzwwSn99lOqtVV0fhPq74Up8nsEITF9OaCSletP3sfVIGh6Yofzig6YfnScECNUI85AgsMtxeYrnnqav5lUNjEpjkanajPkPKZn8VH00V6PqXqgZ7gECnOJS1c8TShO4apoyKpUaGKVZG70SYNa2ni/82LlFYNv566bBbbUiPNCkhjcKGZh84koOElRSGYb6u+LSis66U4prFQUqExjl6OcJ7/cSAUapvHGFWSggFHAYBSobGOXIZwnvHBFglMP8qIiFMAU+2BCMrSe9kJ7rjPQcZ+QXVZH+dubvWYLqIcW4q1kOHuuUgWBf9S9eCiErpgICjLJgX3kPfQvciCFCAaGAUMAhFLjTwKjkH15D3tkd8Gn/MHx7jiwXQIr33BdglPG3rylgFEUmyjv6H/LPnkBpRjpcwqOQ+fcaFEZfQp21e+HsH6CYKHPdaiQvex8lqcmyNhob9c4ncG/YVGanSuyrzyD30F6Z3SAYxWCltF++Qcpn78nS8Hl36cUgpwX8dW34HQksBZ1ucfLxQ62fNvIBHzZH8pKFyNzwG0rYvWsKpc2jVIMezVprTIpXNTAqkt2/T49+iv5kSP1mKdJXfYeS9FsfCpONgKXQcVPh1bEbVRUlceE0ZPz5i8xuDIzK3rYRCQunojTr/1Fa2KcegU88i5AxE2V+dCsEryW9PwsZa3/VNSPkpTcROHSEzKapXHm4t2q6P02fyv5amcAoe5wN5r6/eGdJRQOjKP3c0MUslWdDf608xSxKxPntcfj9rYMo5ETl8Av3xKt/360AS0yBjghuqtUuBFEMcHJnH3hmxOWi47B6yE7Kx+dDtzFwVhktokabYAye0Qahdf20gfUKsotA8Mr6OcdAkZn0S8PekXhiSRd9M4ytkaIzDXm3A3xDPbRjaa5Dq6Kx6b0T3PVRWjZKz6ZfVk86wOCoGH0zKD3eoGmtQdGHdAtF1Vo/5ygO/xata5au753aCh0el0fBMgZGuXm64MF57dD4riht+kN2jDHQK00CtpKvZCnmoQ+9x/x+F8Ib3H4/UCd7gVG6C6T34tx2f+iapGtDsNLyZ3Yi+kCSYgy95xuzaGZq5eeX9yoifZE24zYPRECUl9owh7JXFjDqTj1LBBhl/MfFFDDKn50j3Zr5o019XwT6uCAmqQBP3RWBelGeaDHqAKLjlWmcn78nCpOH1kQIg2N0C0E+T7PITPvPKqMW7nqfpU5lgJNuMQRGUcbZ14bUwFtP1ISzTvrZbcfSWIq6c/9j70zguiq2OH4ECdDcERdkd0dLUbESBU1FTdG0MEytXKhccsN9Q9PU1Owlae5lvFwyM5VnqUVuaaKkz7XEBRVZFREUF9A3529zuffOzP//h5fyh/+cz6fPzJw7M/fe38Adb/fLOVxgB9PeYSQjtd3PfQQvDD8C8ddy1G5DHeedO8gbegc4Q0Vy79SSCQw0cMFZ2Hcy/12FHqOlCIzCdH0r/sPCZPj8m/qmBwzoVAMqq1KuIuyFaeyif79Op9aUG6b4QOcW2j+aMAVG9Q50hkXv1QGEyqgtI4DbuBXxQuDLkYCui4fVZcCy2d9cgnkbLtNpNOXVdS8J0/1pOlp5w5rAKEvfT3jvJRKMsvJfUHn7UoFioIC1gVGWvJfw9hEJRhWDXyIrvsR7BIyytXkEpfNfC6xYDeu+dQlGFWL9eQ/9Qkwjh0gFpAJSAYtQoFiCUad2P9bO1u6pAFK8574Eo0z/+JoCo+6ePg5JU0dy4RaHRk3A9QstkINnzN67C5ImDwfR/8kuXbUaeH6/l7m4G6sj4frqxRq/MTAqdWEEZH6/TtOfNiq8GgrOYyJoUynxfq6EhShtrDi9Hw6V3hys8RkaJMpV8uyJgGn+eIYRk5zHz4LynXrwDhOY7DBcHdZPc6yMnz+4fLJK4zM0yLlS509noCPasVTp0lBt4hwoFxRMXUqJwFZCaEfIu5Wp+IyBUQhFJU0dofRVV2otXSdMJ8gDsOjYWpFR4NikBW0qZeKItwjsdkhpywqrgNWBUU95b2AVN+7h7SUlCYxyb+YEoZEvgiOJZMGzayczIOq9A3D7BhuiuvPE5+GFfrU1w0xBR5iGr9fHflCmovZ8COusDI2BqySakd7qt6sJry3wM0RV0h/D9vkDKbB+xCEuwNV3WSuo07q6Zpixa/Tt6QFdI5oCL00gTnJyx1XYPCEW8h6wINaArwMA9aT2kKQDmt96OxOdCYGjwevbCu8Hx0d23QlpF7TQUqNOJJLTJ9pITsbAqHIkcki/Zf4a4I1eG5aYthDXNvFEhtptqDd4uSa8sVgbSaO4glHHt142rJn+Jn2CXCBk0Qt6t6GNINzH/tsN0dPUHUQpDdV9LKluVWBUMdxLJBhl+rfFFBjVyqcCrBnbAKpX0u4pOPM5EgGq2ZBY5iQhBCLCyEwiw4hJXv0OMpGj5gz0hqHBWpjSGBi1bGQ9CG1bjXuadTEphlR1+oPtmlaCLREkmq7KFm+5CpPXXFB5Hlcx7dyq8AbQ46X8fUfdKZfsQeEEclr9U5LardR5YNR/L2ZDwOg/mHvHcy0dUY+BjuhkeQRoHrU0Hr7cyZ4LIzgdXtwcHFQR+oyBUX3aVYMvyLl4hlGzMHoWz0TRtrBvr5knYddR9t8XewnshtG8pBlXwOrAKAveT3jvJRKMMv7zK49KBaQCRa+AVYJRFrqX8PYRCUYV/e+IvAKpgFTAtAISjDKtEdOD99BnOkmHVEAqIBUoJgoUazCKavyEASnec1+CUVR8cWkMjLoTewCujQ3TRGNSz1T57SFQZRAL2FwLHwy3D7HgkzKW5K+o/fNxKGWn/aiRsX41pEfOU7phRQRG3T17Eq5gCjn8us4xBIm8dsSCjaM2ysPD21mGlH3qIe5R0SQ9nvZjPx6/8dUSuL7iX+quTN2mTFnw2BQDtuUrMMd4YJTLwlXcyE8Z36yE9CXzmTk0DvKn225f/gD23uzHg7TPPoKbG79SuovAqEd378KlPp1IekP2QwYOrtirL1QdNVWZh1YwTeHFnoGAUaN4VqlvGDi9N4Y5lDpvihD2YjpbqcNqwSi63k94b6CnMbfk7SUlBYwqRSJNDNvWAZw8tenZ9Nqc/eUarBt2UO82RFQK3/OKxm8MOno+2I1EL2qhRHxSD7xwKBUwZZreMJ3dBzuCwIZ8lDVmcd9dgh+mHmW6uPk6wcCoAI1fdI1lK9vDqN2djQJLOFFM5Gn4dckZzZzYqBtQHd5c2krxJxKobHnIL0qbVjqMaQz+A+vSJrdEvVF3tXm3qgb9V2gjBRoDo4Jn+EKz1z3VUzD17Ov3YFH7HZB7L485NjyapO5T/WwUVzAKo3DNbxMNCDupDdMtjtvf1RC1TO3Hugim6jG7GTR91UPf3WLbVglG0dUoBnuJBKPoYolLY2DUKy2rQNSEhppoTOqZlm1PhLErzqtdhvqOj54HBKqMWe23DkGqLuXohN7uhuhP6nEiMArnx/OIDEEiPIc+XV0tJ3s4vUoLwHaccAwOnWEjWEX094TRvVxFpzD4c0j0x+fDDgNGkNIbD4wasOAMbNrHRtjDqFd4/6as/fhjcJgTbQtBJwSeqInAqPIk7esfX7QgaQe1kbzouKifk2HIZ3/RplLWqmoP/13mR/6SnP9vBdHPwpcEquvpX1WZR1b4ClgtGEXlsKD9hPdeIsEoulCylApIBSxVAasGo+iiWMhewttHJBhFF0mWUgGpgCUrIMGoQqwO76FfiGnkEKmAVEAqYBEKlAgwiir5hF4OeM99CUZR0cWlEIx6+BAS3gqG+xfPCQfbVnYC24qVmOMPLl8UwlTY+dmAjlBjtjYyFPoLAkYlzwiHrF3bcJjQ3NZsAfs6DTTHH+XlQXxAQ8WH9+C19YDSphXsd6lXIOSmp1KXsKzc/z2oEjaKOc4Dozw374HSztpoJo9yc+HS6+0gNy2FmUPvKBfUHapP/VjvNsBHCCFRE4FRCKwhuCaysq1fhppzljCHs3Zug+SZ4YyfOsq0bA0uC1fSplKmLfoQbn4XpbRlhVXA6sEoKskT2hvo9OaWvL2kpIBRDTu6QO9P+RFz1PogbxrZbSek6yIYYR8ESxAooiaCjjCl24ifguBZp/z0dHQMlgfXxsOPc4+rXYZ650kkKhVJs2fKMPUfAj7Z6Xc1XR1Iup+Jv2sj64mu8eWRPtAmTBxFhE6M0bPwXAjcqA3TC46J6aK4MO3bzcQ7SptWKrqUgWfIx1+R3c16YJgfS7UVBIzCaFGjSMo3Wzsb9RTc+raIODiy8SJzLIREp/IhUaqoFVcwCq9/6/Q4OPote4+YZrBJd/Zj/7/fPwB/7Ummt24o7RxsYew+Pkil6WhBDasGo+g6WPBeIsEoukjiUgRGYQSjI0uag2d1R+Hg9MwHDNyEneu5lhHCVHj86LksaBv+B1Y1VhAwav1kH+jiV0UzXt8ImngcDp7O1LgRDML0btTukH3Gtc9v8IBEf1IbRl86u7qlJqWd+ri6vnRbIoxfyQJiPDCqJUnZd+aydt/CFHUIa1Upz4eV1OfaejAd+s49rXYZ6sN71ILZ73gpfhEYhdGv1o7Pfy9TBvxdwTSE3aed0LvhnaAa8K8hdRg/dfxGdO5E9Nbbkg/qQt+Xte9h+j6yDWD1YBT9IbCA/YT3XiLBKLpAspQKSAUsVQEJRqlWpoj3Et4+IsEo1frIqlRAKmCxCkgwqhBLw3voF2IaOUQqIBWQCliEAiUKjKKK/sMvB7znvgSjqNjiUgRG3drxPaTMniAeWIAjNg6OYOfmBfZedaBsq7bwbGAQ8EKIFASMSujfFe5fEENbeHk1Zn32+Fyqa9WDUY5N/aDW4q9VPR5Xs/fsfJwOkDnCOkRwlR6MwuhS3jvjmAmydm+H5IgxjJ/nwEhYCFfhOdWWcyIOrr4fqrhEYFTGulWQ/jkLVtGBDo2bguvS9bSplBlRyyH9i4VKW1/BNHqYTk9vEozSK8K2JRil0+Qf3ht0s5ts8vaSkgJG9VvuD5jazhyLXX8Bts9kPxQP+iYQXJvkf/wVQUcIHCF4JDIenIPw0Nh9rwBCVeYYRnHCaE56w6hW5armA1mia9RDXvp51O2t0whos0kL2pAgfjD5aA+TEafU89A6QlCp5zLhctx1+O3Lc9zUhQUBo/wH1YMOoxvR6Y2WmLIPU/fprf3IRtA6rJ7iLs5g1JVj12Fln1+Ve6EV/PnH3wO15dy6T1IgRjPpEp/r6kbSQLIpYtVjLa0uwSjViljgXiLBKNX6CKoiMGpwl5qw8N3aglEFdyfduA9nEm7DrrgbsHJHEtzjpEstCBh1YrkfuFfL33d4V/Tup38CptRTmx6MOnY+G9qMZt8VMEUfpuozx7Jz8qDmG+wffejBKEy9Vz1kP9zP1UJYb3esAZ8NFUNH6msggbCgMYlQdSVVCyl3bFYZNk3L35NEYNTEN9xhYqi7ekpN/cTF29BqJBsdcsqbHjAuxE3TV90Q6SjBKLVK4roEo3TaFOF+wnsvkWCUbn1kUyogFbA4BSQYxVmSItpLePuIBKM46yNdUgGpgMUpIMGoQiwJ76FfiGnkEKmAVEAqYBEKlEgwiir7D70c8J77EoyiIotLERhlTkQm/ayl7OzA8bnm8IxXHXjG3Zukp/MCu1oeUNrJWd+V2y4IGBUf6GM0KhWeoPq0BVCuYzfNufRglCh6VfrS+ZDxbzYCkmYyVaP2bpIa0EH7QUQPRjk0aAyuKzapRj2upkfOJdGy1jB+kcNl0Woo06KV5nDerUy40MVP8YnAqNT50yHzBxZ8ogMdfJqA67INtKmUaZ/OgpubWICMdhDdmwSjqELiUoJRAm3+ob1BMLvQzdtLSgoYNeLHIKjs9qzw3tUHEk/cgOW9Y9QuQ73n3BaAKfKoiaCjd75qAx4txOlqVvfbAwlH0+k0hrJmo0rw7sZ2Gp+xBkb4wUg/ent7TRvwbJl/bt412pctDZNiu+uHCtuxGwgoNoMFxYZu7QDOtcsLx2Um50DymZuAMFL6hVuQfikbbiRkc0Eo/SQFAaOCZ5I0eq8ZT6Onnn+W7xYmApZvTw/oPquZ0q04g1F4E4sJ/KWPeoYpGhGcU0c9i9tM0jJOYT+8YxpDXIPiZBKM4qyWBe0lEozirI/OJQKj1k3yAUylV1A7e+UOnCYA1J9X78A58l/8tRw4n5QDWXe0EQB585oLRtmTSH2p3/rz/uZDM+2IJedgzU9JGp8ejIo5RiIkTT+h6YMNhMIQDjPXvPofBIygpTY9GIVa+L4fq+5iqH9KIjENIBGZzLU+c07B9kPXNd0REkNYjJoIjFo5uj6EBIjfE0+RtXvxA/b5/PnwutCvvTjyE66737Aj9PRKKcEoRQqjFQlGCeQpgv2E914iwSjB+ki3VEAqYDEKSDDKyFI85b2Et49IMMrI+shDUgGpgMUoIMGoQiwF76FfiGnkEKmAVEAqYBEKlGgwiir8f74c8J77Eoyi4opLERh1ZfBrcPcM+z/meTM94+ENFYJ7Q7mgYLCtUInXxSyf2WAUyfN0rnV9k3OaA0ZVCA4B53EfMnMVFAxzj4omIJj2L9n1YFT5Tj2g2pR5zLmSJg2D7L27GL/I4TxupkFv/fEL3V6CvIzHHyZEYFTKnElwK/o7/VClLQKjTAFV9vV8wG3VZmUeWpFgFFVCXEowSqyN4cj/uTeYmJ05zNtLSgIYhdGNph571axUayjKnYx7MK/VdkafwCENoO2w/LQ3POgIB4X/SqI2kfRuIsO58Rxq8wmqBSGLWqpdRutp52+RlH/ss/OVKU3Ar4+3MpZ3jc51ysPQHzoofUxVzh9IgbWD9zPdQiNfhPrttB+rMeXeqR+vAgI3lwn8hakJC2MFAaP6r2wN3i+JPy7rz/958C5Ijb+lcbs3d4IBawMUX3EHo/av+gt2LWT/HaP/+fg6bD/E709R7hsrmCZx9M+doZQN+cUpRibBKCOLZQF7iQSjjKzP34dEYNThyOZQn6TEM8fSCBC07pcU+Hp3sgGIMmcMr4+5YFRZknYzaYP2DxZ485kDRm3alwYDFpxhhpuTqk89KJCkBowjKQLVpgejon+/DqEfnVJ3MdS3RDSGdk3Nf5+buOo8fL41UTMPPjqTNvoDpuVDE4FRa8Y2gF7++SCzZhLSEIFRK0bVh96B4j3vLwLBNR8qwSi9nua2JRhlQqmnuJ/w3kskGGVifeRhqYBUoMgVkGCUGUvwlPYS3j4iwSgz1kd2kQpIBYpcAQlGFWIJeA/9Qkwjh0gFpAJSAYtQwCrAKKp0IV8OeM99CUZRUcWlCIw636kFPMzWfjTlzYKp6Fzmr2CiJfH6mvIVDRjVm4BRM5lLS/5wLGT9tJXxixyuy78Fh4bPaQ7rwaiKr/eHqiMma/pgI3HkO3DnyG+MX+RwGjYeKr0xgDmcEBoE969cMvglGMXIY7EOCUaZuTSF3BvMnF3pxttLSgIYZUc+3E6J66Hcp6kKwjwRPixE2TzEC7pFNFWG86AjTIU3+ag4GhPOPaPxZniEOXhU1ux1Twie4avyGK9mkdQ9CwKjmU5thzaEwKENFD/vGt18nWBgVD4EpHQWVC7FpsGat/YyR7tF+ELzkPxITZgi76sB++DaqQymr8hhW9oG8nIfMocLAkaFkUhbLiTilrm25NXdkPJnpqa7k2c5GB7dUfEVdzAqK+0ufNLuP/CQpItSm5tvFbL2gQYXwnnz20QzffwH1oUOYxqrhxWLugSjzFimItxLJBhlen14YBRCNikkIhNGZjJlGCmoy+TjTLQkY+Mc7W0g5x77DC4KMGrjnlQY9MlZ5nI3T28E7X0rM36Ro/u0ExBzXLsP6cGotbuSAfXWW8yCptCsTjm9W9ieuyEBPvomgTl+dnVLqFnF3uCXYBQjj0U7JBhl5vI8hf2E914iwSgz10d2kwpIBYpMAQlGFUD6J7yX8PYRCUYVYH1kV6mAVKDIFLBWMOp/AAAA//8/TOKVAABAAElEQVTsnQd8FEUbxh+SkEpII4QUWui9d6T3jo0iVRTxA6mCgCIIIoIg2FC6gEqTIkXpSO8SAkF6CyWkk9759j25y+3u7LWUu1xm/OHOvFP3mctOLve/9y3yQkgwMRUpUsTEnrwbV4ArwBWwPAVy8Dg0y81E/joJySEHcza3bVEUa/QaXFu/DTs3H71jsZ77N1tU1tuvsDcoNetruHboLpLhRXo6bretKbKxCk616sNv8WrYODqxqlW2rPjnSHv0EOmP6d8DpN27g5Sr/6Dc70dkfWI2rkbk9/NFdp9P5qN4lz4iG4RfD269UlVsY5RKfboQrp16impeZGbiduvqGptz45bw/3qVpqzOPPv8I8Tt3aEu6r2W334Mdt7i12ly0Dk8GjNY09elRTv4zf9RU1Znns2diri/tquLeq+sPUNWFm63r4MX6Wmq/k51GiLgh19lYz2bNx1xe7bK7GqDY426KL1sk7qouYZ/NRPP/9ioKUszDlVqoMyqbVIzIhbPQezWX2R2bshWoPLJm9mFl7mC9syX3YCCwRxng8JSFM2ss+Sza68ptrfEimPLr+PQkhDZ0qad7QVH16IyO8uQGJ2KBS13y6rajq6ONqOraeybxp/Btf2PNWXKeJR2wfh9XUQ2aWFJ572ICU0UmSu1KoVBP7UQ2XQVHl+NwfI3D8uavPplI9TpVUZjZ64xQFjjft1r1AwgZG6feIb1I09om1T5gT80R5W2vqp8akI61r1zAo+Co2Xt1AZ7Jzt4lnER/hVTXb3Kuar6rxtxHGE3nqubqa4VWvhgyIqWIlvopSisfOtvkY0KA75rhqrt/WR2JcP3PfYj4m68qLpcY28M/7mVxnbrWBh+GXVSU1Znhq9thXKNvNVF1XXzhLMI2fdIZHP3d8aEA11FtvSUTHxeX362Sl9X6k5pSRmY2/APdVFzbTe2BlqP0v97wK/vn8TNo2GafpShPxOMF9bl7ueMC5vvYdesf0T1VBi9syNKViwus1u6YWZ1+flujedJQT1L4v7I/vmy9NeSudY35vubWHdA/DPr4WqHB78017ukW4+T0e3jy3gW89/vwqwONFYFXyeUL+WkulYt44y2dT1Q9q1TsuZT+5XF9IFlRfaJP93Gyr+eiGwujrZ4ukn/2TVu6S2s2fdU1Le4sx0ebci+tzP/xqHT1CBRGyr8Nq0GejT1ktmVDI1GX8CNR0mi6s4NPbFlRvb7u2NXYtHjk2BRGyr8Oq06ejYtIbMrGVj35Whvg7DNLWHz8s+yl+8k4JWJ8mftmsnV8FpL8XmiPU/Ig0Q0G3tR26TKr5hQFf3alJTZ1Yabwr03FDSQpqVjK2NQ+1JSMy9LFCje+5jEAuHtt8l/npeNZUkGSz9PWO9LOq1JsSQJ+Vq4AlwBroBMgf3DHWU2az1H6EYt+SxhnSOpt/rL9ocbuAJcAa6ApSngUGmjbEnWfJaob7aIcJMmv/NiPfTVA/MrV4ArwBUoaArk4HFollvNlTcF6pUbCEixnvscjFKLqHxlQTYE19xuW0u508sa/yVr4Nww+4/56g6Zcc8Ru2kNEo7sRdrDe2qz5mrr5o7APWc1ZXXGHGBUUf8yKLfpgHoJmmvU6u8Qvfp7TVlXpkhRe1Q8LHywIIGypWBU0YCyKLdxv2womofmMzSVXr4ZjtXriJoTeHa/X0eNjYNRGiksPsPBKBO3yMCzwdjRWWeJtYBRo7a2h281d4MkeRISg2VvmAgdGQBGEXBD4I128q5QHGN2ZT/HtOtY+ZC9j7B5ovwseW+zAKHW9NB0YYFRNrZFMCOoL+hqSLq45R52zpR/qKsN0Jz6+Rb2LZB/yGznYIuGb5ZH3d5l4VPFjTnnj30P5giM6vJRbTQbWsmQW1G1IdiIoCPtVP/Vcuj9eQONyRrAqH8PPMbGcWc096TOdJxYEy3fqYKfhx/DvbMRarPq6lfDA+9taSeyFZQCB6NM2Kl8PEs4GKV/f3ICRg2Zfw07TkXKJvF2K4oP+gSoYJ8Kfk6y+pS0LJR8Qw6+mgOMCo9NQ8Wh8mfWvBEVMLqXv2ztSgYf4X6ShfvSTlIwKkwAyCoPy/lcvWdewZGgGO2pUKu8C04uyT5POBglksfiCxyMMnGL8uA8Yb0v4WCUifvDu3EFuAL5pgAHo3IgdS6fJaxzhINROdgf3pUrwBXINwU4GGWC1KyHvgnD8C5cAa4AV8AiFCjUYJR6B/S8OWA99zkYpRZP+WoyGGVjgwp7L8DG2UU0OEFRoe++rvIQJarQKth6eCFwl/yb2eYAo4rY2qLC4Sugq3ZKvnwBj0a/pW1SzBdr2wW+c76R1UvBKOHTcFQ8FAQCqbRT6p0beDi0l7ZJMW/n44dymw/K1pt46gieTBml6cfBKI0UFp/hYFQOt0jP2WDs6KyzxFrAqB6f1kOj/oEGSXJy9U3sX3hF1nbEr21Qpp6Xxs6CjgzxGLXvq2CcWnNLMw5ligiuJcb91VnlcUpUoVDYPv0CgnY8kNVOP98bDi52GjtrjVT57sa2CKjtqWmnK/P7h+dw5c9QWZNP/umDooK3EEqseQi8GrLyFZRvouwRg/ouFcCoZznwGFWzSwDe+LoJDaU3KXnaaj+uBlq9V1XT3xrAqMz0LCxs8yeSYlI190UZAtRoXxa12YOsTPF3sbpOr4OmgyqK2heUAgejcrBT+XCWcDBK//7kBIyq+vZZPIkS/6yXdLfH0a/rwd/LQXFyAogIJJImc4BRtAbffieRKHjX0069mpXAL1OzPd5q10nzx6/GovvHckhXCkZRv4ABpxAngWTb1HbHzjm1pcMyy88TM0C6S9dLXqDIG5Q6cTBKrUTBuHIwKof7lIvnCet9CQejcrg/vDtXgCuQ5wpwMCoXJM6ls4R1jnAwKhf2hw/BFeAK5LkCHIwyQWLWQ9+EYXgXrgBXgCtgEQpwMEprGxTeHLCe+xyM0tJNIWsqGOVQoQrKrN0pG9UQ70cuzdvAb8EyWV9zgFG0CPIYRZ6jpCl05BtIuSb/YEHajkLPUQg6aZKBUUKDsut2wz5Q7tXj8YS3kXT+pHQIWbnEmKnw6D9cZo/5bSUil36lsXMwSiOFxWc4GJVLW6RwNhg7OusssRYwikKbjdvbhemxSFsnAkW+EULdxT4Rh+GhNh8e7Q5Xb0dNcxYMZAgY9c/W+/hjhjw8TuOBFdD9E/nzVDPhy0x8eAoWd/wLBL5op+JCeKRJh7tpm5jAEjWgEHgUCk9fUs3VQZgrQzxXsRKOmHwsOxTtQgGyobbaqXpHf/T7pqm2SZan8HJfNtuFjFTxB+HGhNIjqOyD3Z3gVa6YbHypYdtH53F510OpGa9/1Ri1upfW2C0ajPqgOlq/n/2hu2bRjMzeLy/j9LrbshqCBM9vvCuy29rZYNLf3eDiqQxRiDpYWIGDUbmwIXl4lnAwSv/+mApGPYpMRfURcg+Cc4YFYlzfAJ0Tn70eh44fycPXmQuMaj7uIq7eF4eapZB0l35qpAoBqPNmhMr+c0Pw57koWTMWGNV+ShDO34iTtT2xpD5ql9d/nny9NRSz1sm9A08bUBbT+pfVjMvBKI0UBSLDwahc2qZcOE9Y70s4GJVL+8OH4QpwBfJMAQ5G5aK0OTxLWOcIB6NycX/4UFwBrkCeKcDBKBOkZT30TRiGd+EKcAW4AhahwMNphn1r0yIWm1+LkLw5YD33ORilfzNMBaNcO/dCqRnZII56pohv5iJ2yzp1kXn1mToXxXu8LqszFxiltJ7EU3/jydT3gSzxh+HaC3dpIYRsmv+jtkmTZ4FRJSd/Brfe8njuKVcu4dG4oXiRJv6mu2YwIUOh+Mqs3i7z0kVtnk4bjYTjBzXNORilkcLiM6aCUaGCVxOeGApIzgZGC50m1lliLWAU3Xivz+qjwRvldWpAXpjIG5M0lQh0VcE32nZTwajw23FY2ucgXmSJvfWQ9yUKT+cRIPZGqD0n5XfPviSDWshes6vgOWmR2HMSa43UlhKFTKPQabrSX19cxplf5GANQUQEE1FKjE7Fgpa7ZcM0HhCI7jPqyezahhtHnuK30XIvisaAUTRe7R6l8dqC/9ajPb52PupBAn7odUAGlJFnq/EHusJNAMvUyZLBqFferYIOE2qql6rzGiZ44qJQhYYkQ2E5Q8YyRxtTwSh+njB2Kw/OEg5GMXSWmEwFowgEIiBImpaPr4L+bX2kZlH5s/X3sOh3uUdAc4FRU1bcwU+7H4vWSIUhHUvh+zGVZXZtQ9CdBLSe9A9eiI9WVRMWGDV99V18/8cj7SFU+e5NvPDrtBogIEspRcWlo9nYi6CQfNL0x+xaaFsn+2zlYJRUIcsumwpG8bNEYV9zcJ6w3pdwMEpBZ27mCnAFLEaBnIBR/CxR2EYTzxLWOcLBKAWNuZkrwBWwKAU4GGXCdrAe+iYMw7tYuQKenp7MO0xPT0d8fDyzLjeNNkIoKnd3d+aQqampSEwUf1OQ2ZAbC4UCHIzSsc0v3xxUe+tTPEvIEDXkYJRIDmbBVDDKqX4TBHwrB6BSrgqAz/jheJGSzJzP4613UeL9D5l1z3dsRPjCmaI6n0/mo3iXPiIb/bX/1ivZ4X7EldmlUp8uhGunntkGIfciMxO3W4tDURT1DUDZDftQxC479JK6U8KRvQibPRkv0uV/9C/WpjNKzVwkhMYrqm4uurLAKFvPEii3cT8TbkoOvqgKh5eVIP/mtkPlGvBftAIUhlCakoPO49GYQSIzB6NEclh0gYNRebQ9ufiHI2sCo+zsbdBTgKPq9s725KC9AxQubvvUCzLvSNSmz9yGqNdX3I8FHRniMYrG2/npP7j4+z3KipJrSUcMXt4SPpXdRHYq0Ie9e+exQSW6t9G7OsGztBiqYq1RPTB5Bur/XTNReEB1HV0PLQnBseXXtU2a/PvbO6CUEJKNEnmu+qLRH8gQQjJpJwK83t/WHg7F2OfE039jsf7dEyqwSrsf5cs2LIG317UWmUMvRWHlW3+LbNqFJm9VQJepdZhewcJvxWHdO8cRHyH2akX96/Ypi75fNNQeCpYARpGec+puF62LChVb+qheI7IKBcNPrx/C02uxCrXZ5n5LmqJ6J/9sQwHLcTAqDzYsF88SDkbp3x9TwaiLt+LR9sNLsgm6NvLCho+VAZ/fj0fgvcXXkS4JqUkDjX+1NGYPFYPEE3+6jZV/PRHN4yIAvU83tRDZWIVxS29hzb6noqriznZ4tEHsuZBAozojz4FC/EnTmN4BmDs8EEUYwNI5wfPVa7OvgsLbsRILjIoR3jvXG3Ue0fHpsi4UDm/ZhKqwt5NP9igiFb1nBuPWY/n7vQ71PbBtZi3ReByMEslh8QUORuXRFplwnrA+2+BgVB7tDx+WK8AVyDUFOBiVa1LKBzLyLGGdIxyMksvKLVwBroDlKcDBKBP2hPXQN2EY3sWKFXByckJSkjxECN3ynj170KNHjzy/+9KlS+PhQ3koC5p47dq1GDZsWJ6vgU9QMBTgYJT+fUoVQtxsCIrGD6fDNYAUB6P062YqGGXj5IwK+4QwSALgKU2pd24i5rcVQmi4U8iMjYadAPM41W0Et74DhKuyN4vUOzfweOxQZCUlakCk/ACjaP1KnpyoLuXaZcTv/QMELmU+j4FjrfpwbtgMbuT1ysaWmjATC4yihh7930aJMR8x+6Q9uCvMtQMEO6U9fgjHqrUEzRrCrc8AJkyFrEw8HN4XpJ124mCUthqWnedgVB7vTy784ciawCi12o36BaoAEP/a/31JgICb2yfCBM9Id2RenKgPeRIat78LKNSYdmJBR4aCUUkxqfi2634kx8nBU0fXomg5ogrKNSoBv5oeKnDowYVIBO9+iJtHw7SXoMm3HlUV7cbW0JTVGdYa1XV0tS1qA+pbobkPfKu7C+tJx8OLkbj61yOE7JN70qA+lVqVwqCfxB+Erxz4N0KD5OGLKLxdh/E1VTCPvfAhOMFdkffi8Y8AhV3ccg+pCh9iO7vbY+xfneHkZk9TqpI+MIoaBTYtCfJUVbqecPYKYzwNicX98xE4sfImU2v6gJ2AMm/BI5h2sgQwitYzv/kuJMXKXyMUCo/ulYC42KdJaPhmIBMIozHO/XYHez6Xh8qiOnUinSk0Ir0eCmriYFQe7lwunCUcjNK/P6aCUWkZL+Df/yRSJeFVaUbyXDTx9dJoUcMNdoJ3vAwBgqLwcav2PsXvx8IhcVyoWeQrNd2xbVZNOGg9E/IDjKIFfLzmLr7bwT5/yJvTAMELVtNqxeHmYgeCwo5dicWSbY+QJIRmVUosMIrarhZgrfECtMVKzau7YXCHUmhZ0w0B3g64ci8RJ0Oeq9b2JEru5ZYgqrPfNUQFv2zvgzQuB6NY6lqujYNRebw3RpwnrM82OBiVx/vDh+cKcAVyrAAHo3Isof4BDDxLWOcIB6P0y8tbcAW4AuZXgINRJuwB66FvwjC8ixUrwMEoK95cK7w1DkYZvqlxwh+EB226i6AnyeBglH7dTAWjaOQya3fCoUIV/ZMY00IIW6fy6tT2vxA5+QVG2ZUshXKbDgjen7I/gDZm2ay2SmAUeaYi7ezLVmB1M8oWu/UXRCyeI+vDwSiZJBZr4GBU/mxNEYdi8H77RziU1h2alvUewhrBKLXqaq8TrLA76jZ07SqEbmw6qKK2SZVnQUeGglE0gCHACq1R3/rcfJ3xwZ5OoFB80sRao7SNulxEiBskDe+nrtO+jvilNcrUL6Ftwr4FwTj1M/vDZWpIYzsVL4q0pAyZZynRQFoFOwdb2DvZ4t2NbeFZphgMAaO0uqvm1Hc/1Tr4of+3zbS7qfKWAkb9+OohhF3X7+1pRlBfFSQluxHBkPw8DQtb79GpO4FWPT7VHfaQNbYl2TgYlfe7kZOzhINR+vfHVDCKRu74URDOCl6TlFJRAYoqLoBEsYKXpEwlGkrSmTw6uRezw9UV/32xI7/AqMjn6agleI1K1AE60VINOR/Vt6QERpEUbYTwexSGT1cyZK6Jr5XGrCHlZcNwMEomiUUbOBiVP9tjyHnCel/Cwaj82R8+C1eAK2C6AhyMMl07Y3vqO0tY5wgHo4xVmbe3JAXob4PPk+V/96M1FrV7ARd7udddS1o/X4vhCnAwynCtNC1ZD31NJc9wBQQFOBjFXwYFSQEORunfLe4xSr9GrBY5AaOc6jWG/+I1zBB0rLkMtb0Qwpnezmcwitbm0rIdSs1YABsXsdcMQ9ctbacERlE7+8BK8P1sMezLV5J2M7hMYf6ezZuu8rAl7cTBKKkillvmYFQe742B36RTr4L1HsJawCjyQMTyvKO+d6UrASPdPq7L9MbDgo6MAaOyBM8d+78Kxpn1t/XCT0rro9B5ry9qAn/BsxQrsdZIHqlSGKGDWP21bTbCB+sEiTUeIAdbE6NTseyNw3gueC/K7TT2z84gz1NKYBR59HoeJg9ppG8d5FVq4PfN4OzhIGtqKWDUiZU3cODrq7L1SQ26wChqu2XiWVzdy/bAQvXvbmiLgDrsMOtUXxASB6PycJdy4SzhYJT+/ckJGHXhZrxwVl1GCiMEnf6ZlVsQGPXw1//C3eUXGEWrOXwpBm8vus4Mc6e8WuUaJTCKetwWvlA0bMG/CL6nG45SHh3o16Ykvv1fZTg5yL3ucTBKl3KWV8fBqDzeEyPOE9b7EmsCo1JjwxD/MAhJEfeQHHFf+HcPWempcCpRFk4lA+H88p+LX1UB9rfL443hw3MFuAK5pQAHo3JLSR3jGHiWsM4RDkbp0JVXWbwC8ck2qD89kLnOjrUTsXS4OHQ5syE3FggFOBhlwjaxHvomDMO7WLECHIyy4s21wlvjYJSOTX35ZqDaW59qQuipW3OPUWollK85AaNoVLde/VByymzlCRg1CccOICPiGdxfG8SoFTyDmAmMosUUDSgL38+/hUPFqsy1sYx0P1nxcSje/TVRtS4wihqSdyqv9ybC482hzJCEosG0ClkJcQj/ejbi9+/SsoqzHIwS62HJJQ5G5dHuGPiHIunsrPcQ1gJGjdzcDpsnnEHsY8PAHfJw1OnDWmg+TBngZEFHxoBRav3vnY3A9ukXjIaKKHxa549qCV6VlD8sYa2x4ZvlVSHqjq8QhyFVr4d1pTB4bwgAVuXWpVjVKlvYjedY9dbfKq9Qio0kFaXreqH+a+XwxwwhPK1C0gdG0d7+8t5JUHhCQ1PNLgHoO68hyCsVK1kKGJWWnIEfeh5A7BPdr1t9YNTtE8+wfuQJ1q2iRHlXlccxZmUBMnIwKg82KxfPEg5G6d+fnIBRNPrmo+F45+vr+ifSavH6K94I9HXCgs0PtazZWXOBUbSCRxGpGDT/Gv4RwuUZmt5sXRKeAvz70+7Hoi66wChqmC6AyvM2PMDiraEGe9Sifl6CJ8Ql71dC7+ZiL4pUp04cjFIrUTCuHIzKo30y4TxhvS+xBjAq4dFV3P/razw9u0XwFp6uV3ACpAJ7ToNv8wEGAVJHx5dFWlyEaFy/loNR4+1lIlthL4SsGoknJ38RyWDvVhKtF98X2Sy9cHpWUyQ8DBYt06tmB9SfuFNk44X8U4CDUXmotZFnCesc4WBUHu4PHzrPFeBgVJ5LbDETcDDKhK1gPfRNGIZ3sWIFOBhlxZtrhbfGwSjGpkreDLCe+xyMYugmMflMnYviPV4XWTOePcG919qKbLoKjjXqwuvtMXBu8oquZki9EYKI7+YhOeg8bJxd4P/NWjhWqyXrow1GlZw0C259B4jaZEZH4m6vFiIbq1Dq04Vw7dRTVKUK09e6usgmLRRxcIT3mI/g2rm3ap3SenU5IzIc0au/x/Ndm+H17nh4DhmlrlJdE0/9jSdT3hPZWAWnuo3h/cFUOFSpwarW2F6kp4HGjPhmLjLCwzR2Vsahcg2UWb1NVkUepuL2bJXZ1Qbay9LLNqmLmmv4VzPx/I+NmrI0U7SUH8ptPiQDvJ7OGAfybMWTsgIcjFLWxqQaydlg7Biss8RawKhpZ3vBtqgNji+/LoSwu4vkuDRFeShsG0FRFGZNV9r20Xlc3iX+MNkUMIrmIA9OBxZdwZU9oUhNzNA1LXwqu6HjpJqo9IoypKQeYOuU8wjeLV5jy3eqoOPEmiAga++Xl0FAk67kX8sTPWfVg281d13NVHXkuenEiuv4Z+t9naHb3P2dhTXUQs2uAap+ez4PUoUWZE2gBqOeXovFT68Lz1qtRFDY1DM9QQDR4W9C9M7r5GaPZkMqotWoaqowTFpDibKkzc/Dj4lsVBi+thXKNfIW2bdNFV4HO8Uak1ajtrYXtctIzcQXjXYiM0Ps3lwpVKO6M93b8WU3cH4j+3VLIZ4+uaQcSo/GoZCC85rsZL622o+rgVbvVVVPV2CvHIzKxa3Lg7OEg1H69+fDZbex/M8nooblBY94l5c1Etl0FSgk3JcbH+DPc1G6mqFx1eL4Ynig6poseJnqO/MKTl2TnwXaYNT01Xfx/R+PROMGlHDAtVVNRDZWYdzSW1izT/wNZgrV92jDf96oWH3IlpqehVnr7mH9wWeIE0KxKiVax4xB5TCgrY8KcJonaKCdCFxa/5Hu90DU/pwQjnDqqju4KMBYusLYOtrboHtjL3z5TgX4eOgORX49NAmNx1zQXo4qv2ZyNbzWUnyeaDcKeZCIZmMvaptU+RUTqqo8VMkqXhqeRqeh2ttnII2Y+Nu0GujR1EupG7e/VICDUbn8UsjBecJ6X1KQwajUmCcIWTMKkVf2mySyCpDqNR1+LdhfsFMP+vfYAKTFR6qLqiuBUTVHrBDZCnvh6sp35GBUcW+0+SbULNK8yMpAcqT4/QQtxN61BOyciiuu6fSnjREfKgejGkzardiHV+StAhyMygN9TTxLWOcIB6PyYH/4kPmmQE7AqP3BxfD9fk/mWif3iMQrVXV/GY/ZkRvzTAEORpkgLeuhb8IwvIsVK8DBKCveXCu8tRe6/ippgfcb+eskJIcczJuVKbwZYD33ORiVN1ugNKp9uQpwqFBF8LpUDnY+vshKjEfa/TtIe3gX6Q/uIjNO8mGDjS0cK1eDU91GsC9XEVnJSULbe0gJvojUO4Z78VBaT07t5NHJuVFz2JcJhK1XCdi6uiFT8NaUKQBRyVcvISXksvBJqxDcOpeSnbcPnBs0U2ln6+6p0qNI0aLIjI5C2iPBtfyF0ypbLk3Hh7EQBUwFoyxk+UYtwxxng1ELFBqzzhJrAqMohBwlCmH38GIkHl+NQUJUClLi0lUelIr7OKlC0lGINXOlTOFD4AcXIvHs5nNQeDpaKwE1Ll6OKO7jiPJNSsLdzzlXl0detO6eCRe8aSUKwFg6MoUPyV08HVBc+EC+fGNvlAh0NXq+hMgUPL4Sg6gHCYgJTRBCEdqoxiHvRDSeq7ejbMzohwm4L9z7E6FfERvAo3QxlBbCu1GIN/LgZUhKT8n8b29DYpD8PA2p8Rko6mgLV2FvvYV5K7b0UQFyhoxliW3iniUjOTYN6cJroqjg7cpR8FZSTNDS1k4QTEeKD0/BorZ7ZMc2QVUTDnaFm2/uvqZ0LCXPqkwFo/JsQXk0cEE9SzgYlUcvCIVhKTxc8N0E3H2ajFDB85Kbix0qBzihSoCzcHVWlbW7ZgoUzdV7iSo46poA5Lg42aKSALC2qOGGqqXN/3xIy3iBY8ExIMjoWUwaYhIyQNCWr3BWNa1WHPUruuqEXbXv1ZA8zfH35VhBuxREPE9HUbsioFOopBCWl3RpXdudGTbPkLF5G8tWwFQwyrLvir06Sz9PWO9LCioYlZ4Yg/PzOiDhcQh7M4ywVn7zC5TrOlGxBwejFKURVVgaGJUc+QDHJ1cRrZEK1YZ8h9Jt35XZ1QYORqmVsJxrTsAoy7kLw1diyWcJ6xzhYJThe8tbWp4COQGjNp5yw4wt7C9lLBkShu71TA8rbnlKFfwVcTDKhD1kPfRNGIZ3sWIFOBhlxZtrhbfGwShhUxWAKPV2s577HIxSq8OvXAGugKUqwMGoHO6MnrPB2NFZZ4k1glHG6sLbcwUKugKn191WeQeT3kdgs5IYuuoVqblAljkYlYNty4ezhINROdgf3pUrwBXINwU4GJVDqXPxPGG9LymIYFRWWjIuLOyG2Funcyjuf92LCN8eqDt2C7zrdmeOx8EopiwyIwejZJJwQy4pwMGoXBAyl84S1jnCwahc2B8+hNkU4GCU2aTP94k5GGWC5KyHvgnD8C5WrAAHo6x4c63w1go1GGXgmwHWc5+DUVb4w8BviStgZQpwMMrEDTXwbDB2dNZZwsEoY1Xk7bkClqUAeR378dWDCL8VJ1tY/2+aolpHf5m9IBo4GGXCruXjWcLBKBP2h3fhCnAF8l0BDkaZKHkenCes9yUFEYwKWTUSj0+sYwpbRPAi7lm9HUrU6ggHt1LIykhHStQDPL//DyKD/hQ8fYrDL6sHsXN0ReOPj6BYQE21SXPlYJRGCp0ZDkbplIdX5kABDkblQLxcPktY5wgHo3KwP7yr2RXgYJTZtyDfFsDBKBOkZj30TRiGd7FiBTgYZcWba4W3VijBKCPfDLCe+xyMssIfBn5LXAErU4CDUUZuqJFng5GjF5pQesbqwttzBQqqAgRFHVh0Bad+viW7BdeSjph4qJsQ5tCwMIWyASzMwMEoIzbEDGcJB6OM2B/elCvAFTCbAhyMMlL6PDxPWH/jKmhgVHpCNI5OKCcAT2kyYYv5V0e9CTvg5FVGVkeGpPC7uLlpKsL/2cmsL1G7C+oL/aUp/kEQUuPCRWZHDz8mRCVqVMgK1gJGJTz5V4DpQkW7Z+/qheLlGohsvJB/CnAwygSt8+gsYZ0jHIwyYX94F4tRgINRFrMVeb4QDkaZIDHroW/CMFbRxcbGBiVLlkSpUqWEb1q8wLNnzxAREYHMzMx8uz/aj8DAQHh6eiIlJQVPnz5FZGSkwfM7ODio7qFEiRLIyspCeHi46h4yMjIMHkPa0FQwirQMCAhAWloawsLCEBUVpdJVOr4h5dKlS+Phw4fMpmvXrsWwYcOYdYYYSXMvLy/4+vrCzs5OpTntfX4CNkWLFoW/vz9o36Kjo/Ho0SOVboasX92GXjOkN93PvXv3EBcn/6a3uq01X/Nz33JDxxzF1zbxzQDruc/BqNzYTT4GV4ArkJcKcDDKQHVNPBsMHF3TjHWWcI9RGnl4hitg8Qo8vhKN9SNPwqtcMdg72SHyfjziwpKZ6+7yUW00G1qJWVcQjRyMMmDXzHiWcDDKgP3hTbgCXAGzK8DBKAO3IB/OE9b7koIGRj05+QsIwJGmosW80PLLqyjq4iGtEpUJqLoohOGLuXFCZKdCERs7tF5yH/auJWR13KBfAWsBo/TfKW+R3wpwMMoIxfP4LGGdIxyMMmJ/eFOLU4CDURa3JXm2IA5GmSAt66FvwjAW2eV///sfXFxcRGsjaGLVqlWIiYlR2QmG6d+/P15//XU0adIEtra2ovYERd29exfbt2/H1q1bce7cOVG9roKHhwfeeUf+poYAodWrV4u69unTB2PHjkX9+vXh5uamqTt79iyaNm2qKUsz7u7u6NatG3r06IEOHTrA29tb2kQF+BBos3fvXuzevRv79+9XQVeyhgoGQ8Eognu6d++ugpQ6duwIZ2dn0YgEZ4WEhGDbtm34/fffce3aNVG9rkJug1Fly5bFG2+8gTfffBN16tSBvb29aPr09HTVvtM6Cby6dUv+zWlRB61ClSpV0KtXLy1LdvaHH35AUlKSylCpUiWMGjVK9dojoInAPHWi1ynps379eqxbt04Fa6nr1FeCuHr27Kka45VXXgHtk3YiqO/OnTs4duwY5s+frwKutOutNV8owKgcvhlgPfc5GGWtPxH8vrgC1qMAB6P07GUOzwY9o8uqWWcJB6NkMnEDV8BiFXh0ORorBhzRu74Sga74344OsLXLfq+it5OFN+BglI4NsoCzhINROvaHV3EFuAIWowAHo/RsRT6eJ6z3JQUNjLrzx+e4s+NzmailmryJ2qPY4fWkjVOiH+HYpIpSs6pcb/w2eNfpxqzjRt0KcDBKtz681nQFOBhlgHb5dJawzhEORhmwP7yJxSrAwSiL3ZpcXxgHo0yQlPXQN2EYi+xC3pbI+5M0ffbZZ5g1axbeffddLFq0CK6urtImiuWDBw9i9OjRuHnzpmIbdQWBL0rtGjdujPPnz6NixYr48ccfVVCTup/2VQmMIghm/Pjx+Oijj0QglXZfpfzjx4/x6aef4ueff1Z5lVJqp7YbAkbVq1dPBfDUrCmPWa4eR3rduHEjJk6cyIR+pG1zC4wikGzu3LkqmEgbRJLOJy3/+eefqj6hoWKXs9J2VCbgavPmzawq+Pj4qDxnffnll5g0aRIzDI20Y3x8PEaMGIEtW7Zoqgi+ImjLUL1jY2NV9/3dd98hNTVVM441ZqwajMqlNwOs5z4Ho6zxp4HfE1fAuhTgYJTCfubS2aAwuqKZdZZwMEpRLl7BFbA4BQwBowiGGrS8BQKblrS49edkQRyMYqhnQWcJB6MY+8NNXAGugMUpwMEohS0xw3nCel9S0MCoa2vH4NHfK2Wilus6EZXf/EJmVzKc+KiGEFrvjqy6+tAfENBmhMj+/O55pElD6XkGwLVMHVG7jKRYxNw8KbLZOrjAs1oblS0zNQFPT29E5JX9SI56iNSYJ7BzLAZHYSyPKq3g12IQnLzLifpTIT70Ch4f/xnxDy8jJfoxstKS4CiEC3QqGQiXUpUQ0HoEHNx9Zf20Dax7cPGrCueSFbSbMfOG9s0JGJWVnoLwS7sRfe0wUmPDkPr8GdKehwlfYs9S3Zujhz8cS5RBqUavwb1Sc+Y6yai9VtqzkDXvy9qWbjsSJWp31tjJU5h2mfROEfZHO9m7esOtQmNtk2Ke1h4ZvBdRVw+o9jktToiykhIveDPzhH1xbziXqgxvIWyjV832sHUopjiOuuJFVoagy99C+Ejx5xReNTvAxs5B1Sw+NBiPjq5GgrD25MgHKpuzTwU4+1REMf8a8H9lqDCX2CmCevyCcOVglI5dyuezhHWOcDBKx/4YWfUkWvBQnWAHe7sseLtmwkv4Z2hKSLFBeJwtElNtUKKY0N8tA3Y2LwztbnS7jKwiiIq3RVSCLWyLvEAp9wy4OWcZPY65O1g6GJWWUQSRwr5GJ9rC2SELPu6ZcLEveDqbe59pfg5GmbALrIe+CcNYZBclMOrzzz9XAVMsb06G3AiFhvvggw+wfPlync11gVHNmjVTATLkzYcFb6kHZoFRBCHt2LEDZcqwY4ur++q7Xrx4Eb179waBUrqSPjCKIKCVK1eCPEYZmyjc21tvvaXyZKWrb26AUe3atcOGDRtUoQZ1zaVUR2sdN26cCihTakN2XWAU7dmKFSvQuXP2GxVdY2nXEQj3zTffoGvXrirwqlgx/W8ytPtTfunSpSqwT2q3prJVglG5/GaA9dznYJQ1/RTwe+EKWKcCHIyS7Gsunw2S0fUWWWcJB6P0ysYbcAUsRgF9YJSLpwP6fdMUZRtYX9gVDkZpvQwt8CzhYJTW/vAsV4ArYLEKcDBKsjVmPE9Y70sKGhh1c9M03N+7WCIqULxcAzT59LjwxVrDPHfe+v1TRATtkY1TpuNoATR6W2T/e2wA0uIjRTa/loNRc8QKke3hoR9x/ZcJIpuzAC61nHcF4Rf/wNVVI5GR/FxUr12gtQf2/hgVek0X4voVUUFB19ePQ+gR8TzafShva++Msp3HIbDHFNjYi6MkUH2GAOUc+Z+Pajwqq1Ol12ejfPcp6iLzSus9MtpX1rfyG3NRrtskUR9TwCiCoO78MQdh57aCwDJDkotvFZTtNFYGsFHfvz/wR1pClCHDaNoQnNT+p+z9Pf1pYwFGC9bUU4YgpAaTdots0gIBTHd3fYm7O78E5fUlCv9Yfci38BFgL10p4XEITn3SQNak9eL7sCnqgBDhdRV+aZesXtvg4F4KlV6bo4Lv6LVV0BIHoxg7ZqazhHWOcDBKvj8Es6w77i6rcBKAlv7NnsNW66g6ddMZKw6742qoA2KTsqM0lSmRjkMf/wc6ygYSDM+TbHDgajH8FVQMF+44ISlN/LNtIxS9i2egXfUk9GkUh/rlU1jDGGyLjLPDn5eL4c9LLrgfYa8CdYRgPqLkbP8CPm7pqOqfJtxnHJpVSjLokUP3suVsdnQo7UGr+qWiZZX/Igtp25XyW88XR4wAa0lTgGc6utRJkJphKBiVKbBIa46Kw/UG3XfEvmA2dNqrQTyqCTpoJwKbBjZX/j2A2t6PKIrdl1yxP7gYnsTYqfZZewzKuzplwVcA0eqVS8HAFs9R3V8Mzkrb8/J/CnAwyoRXAuuhb8IwFtlFCYwirz8E2uQ0jRkzBhQaTSnpAqModN/ixYv1rkMKRlGoOvK0ZAoUw1onQVEUhi8oKIhVrbLpAqMoLBwBUaZAUeoJCTQjmGjnzp1qk+yaUzCKALBNmzbBweG/bxzIJjDCQCEPyfOSUtIFRlEoQ9LblERaDxkyROWZSxqm0NDxCBpq2bIlTp06ZWiXAtfOqsCoPHozwHruczCqwL3U+YK5AoVOAQ5GvdzyPDobjH1Bsc6SggZGPQmJAcEh0tTgjfKwLar1Fx1pA17mCliBAuG34rDlw7NIiklDcmwaMjOy4FrSEX41POBb3R0NXi+P4j7yD6Gs4NbBwShhFy34LOFglDX8lPF74ApYvwIcjHq5xxZwnrDelxQ0MCr0yHL8u24s8wenTIf/gWAfQ7zwMAdQMOYUjCrbcQz+/WU8BLpIYQaxmSCnym/OxZUVIxB2ZpO4UkeJoK6qAxfJWhBwdHi0PFKIIWBUekI0jnzgJxszN8Co1NinOD+/E5LCbsnGN8RQvsdHAuzzmaipucCoxLCbuLr8bTy/d0G0HkMKvk37o9rgJbBzlkMU1F8JjGryyTEE/zRY4yHKkLkCe05DxVdnGtLUotpwMEprO8x8lrDOEQ5Gae3PyyyBPg0/DpRXCJZVI5+iVbVEhMXaYfY2bxy4wgZrlMAo8tS07qgbvt3ricQ0w/8eV0UAjD5/MwJ1yxoHSAU9cMTiPz1x9rYzCA4yJpX3TsPgls8xUPinDYNJxyAYqOMXZaVmVXmAAFjNfjOcWccydl9QBjef2suqvIpl4sycezK7oWBUanoR1Jyi38uibAItg4/gxevErPtaluwsgVA/HfLAlYfGfy5PgNTw1rHoWlcOfmXPwHMcjDLhNcB66JswjEV2UQKjcnOxBCpRmDVW0gVGEYhUt25dVjeRTRuMatCggQposbeXPwBFnYwshIeHq9ZCerGSLjCK1d4UW3p6Ouj+rly5wuyeEzCqVatWOHToEOzs7JhjG2sk8IZC261Zs4bZVRcYxeyQz8Zr166hTp06yMjQ/y2PfF5arkxnFWBUHr8ZYD33ORiVKy8/PghXgCuQhwoUejAqj88GY7eOdZYUNDDK2Hvm7bkC1qxARloW7OwN/wNkQdaiUINRBeAs4WBUQf7p4mvnChQeBQo9GGVB5wnrfUlBA6Oe3zmHs5+3UvwBolBlgQIwE9DmHcGbjqNiO2MqcgJG0TwUqs0QD0KaNQkefSj8WcKjqxqTIRnyONX4k6NwC2wkam6JYFRKzGNc+FKAohjhDEWL11Oo2PdTBJKHrZfJHGAUeQMLXj5MCHGYrF6G0VcHDz80nLJXCI1YWdZXCYyi8IkElxmT6LXYZMYxwcNafWO6mb0tB6OELbCQs4R1jnAwSv4joguMWv7uU5WHnwHfBSA0SvlzWBYY9Si6KEatKoUbT4yHZ2iVBCeNaBuDid2idIJK6js6eNUFE9aVQooABeUk9W4YjwUDn4G8WLFSYQejVh1xx/xdJQzlp1kSqmwf9ojCe+1jFOsLewUHo0x4BbAe+iYMY5FdjAGjgoOD8c8//4DCyz179gxly5bFgAEDUL++7l+oyPtUjRo1EB8fL9NAFxgla6xgOH36NJo3bw43NzfV+gID2USuujt5Avr999/x8OFDFQhUsWJFDBw4ENWrV1c3YV6PHDmCDh06ICtLjscaA0ZlZmaq1klaXrp0CbGxsSAdBg8ejMqV5b8Eay/m/PnzoBCDNIY0mQpGkW60t7rCDt68eRPHjx9XrZdgIQK0CKaqUqWKdBmacnJysmrf792T07iGglGk9fbt20F7HBYWBtpb8ibVuLFhsb1pMfT627NnD0JCQuDu7g4PDw/V66Vp06aatbIy9Hr4999/WVUF3lagwah8ejPAeu5zMKrAv/T5DXAFrF6BQgtG5dPZYOwLiHWWcDDKWBV5e64AV8AcChRKMKoAnSUcjDLHTwWfkyvAFTBWgUILRlngecJ6X1LQwCh6/Z2f1x4xN0/qfClSSDmPyi3gVaO96p9rQC1VeDqdnRQqcwpGaQ9LIc0o7B99+hn3MAipMU+0q5n5Ija2cPGtKvyrLIT0i0D8w2AhJF8cs23J+r1Q94PNojpLBKNCVr+Hx8fXitapLtDeuVdsCkcPf5Up8elNxAmemF68kH8WQ3BQ68XZnzmcntkESc9uq/plpiaqhxRdbezsUUT4+VQnWwcXtPnmoboIY0LpUajBE1NrIS1O2ZtJMb9qcPIur3e/vaq3Q4PJcqcCSmCUZsFChqA4Z+H1QUBdemI04u5fUgxNSNo2/vhv7e4Wny/UYJSFnSWsc4SDUfIfIV1g1IKB4fjpoAfuhmc/h+QjAFIw6vYzewxd6odwIaRdTpM+UInG//WkG+YIHq2M9RKltLa+Qji/LweEM+GowgpGZb0APt/hjfXH2GEElbTUZZ/SMxLvtovV1aTQ1nEwyoStZz30TRjGIrsYAkalpKSovP/89ttvzHsYNmwYVqxYodPb0Lx58zB9ejbFrx7IWDCKABn6d+HCBURERKjC7F2+fFkFGn311Vf48MMP1UPLrgRmUXi+/fv3y+rIMHLkSCxduhS2tvI4pOoOb7/9NtMLkqFgVHR0tCok3uHDh9VDiq4zZszA7NmzRTZp4d1338XKlSulZpUWBHux0tq1a0H7xErLli1T3TurjrxUzZkzB1988YUMxrKxscHHH3+MmTNnKmpGnsLIY5g0GQJGPXr0CG+99RaOHTsm6k5erWivx48XXBHrSbTXBO+R7tqJfqZ//PFHvPfee9pmUb5Xr17YtWuXyGYthQIJRl0/imJC7HXX1m/Dzs0nz7eC9dznYFSey84n4ApwBXKoQKEDo/L5bDB2e1hnCQejjFWRt+cKcAXMoUChAqMK4FnCwShz/FTwObkCXAFjFSh0YJQFnyes9yUFEYyKuXECFxZ0Frwwyb8wrPT6tHctAc9qbQVIqp3q6uRdTqmpzJ4bYBR56qn46qco1+1DFcRCk2Slp+Df9eMUASFq4+gZIIBOm/6DqcggpKyMVAR91w+RwXv/M2j9nyCc5nMvaVmgAmQsKpSeAIUdnVhe8HYUJlonFcp2Git4gJqKoi6eorqUqFAEfd9fAH4uiuxUaPHFZQEak39pOznyAY5PlturDfkOpdu+KxtHbTAGjLqxYTIe7P9O3VV0rdBnBsq0H4Wixbw09uSIe7i5eTqeXdiusWln6ozeAJ+GfbVNiqH01I3I+1Pt93+Bc8lAtQkUAjHk5/dB3qykycbOAe2Xx2heh9J6SywXSjDKQs8S1jnCwSj5T40uMKqafxr+fWwv7ySxaINRkQIM1eOr0ohKUP7MWtJdb1FXiDpaX6+FZfSOYWyD0Z2iMb6r+DNaGqOwglE7Lrhi8q+5/xnnt0PDeFg9xouTg1EMUfSZWA99fX0KSr0+MIrq+/Tpg3Pnzum8JYJftmzZAgKEWIkgpoCAAKSlpYmqDQWjkpKSMGrUKKxfv17UX10gr0fkGcjV1VVtEl0pFF7Xrl1VAJWoQlLo3bs3NmzYoHgf5EGIvF9JwRJDwCjq27NnT9y5c0cyq7hIsA4BWgQesRJ5mWJ56TLFY5Svry/u378PVuhB2qvWrVvjzJkzrGVobORFa+/evYpwVJs2bXD06FFNe8roA6MIYqtatSqePGF/e4bgqAcPHsDPz080rnaBPHI1atSI6eGL2tHP9YkTJ1Teo7T7qfMTJ07E4sWL1UWrukpfv5Z+c0lX9sO+TJ18AaLUWrCe+xyMUqvDr1wBroClKlCYwChznA3G7jvrLOFglLEq8vZcAa6AORQoLGBUQT1LOBhljp8KPidXgCtgrAKFCYyy9POE9b6kIIJR9BqMuLQbl38abHL4MoJIfIQvXpbtPA4ETelKuQFGVR/6gxDeb4RsGoKjjk2sgLSEKFkdeYpqMS9YAF4qyOoIjjo2qaLgqShCVEfhAzssixF5x7I0j1HxD4JwepY8gkOA8CXY6sOWiu5Hu0Bh445OFOAfAazSTtWHfq8Knahto3xeg1EJj6+pvEtJwyQSBFdj+I/wazlYuiRVmTxfXf9lAkIPL5PVO3qVVoFetvbOmjpdHqM8qrREgw//BHnBkibymHV8SlXZa4TatZx/TQRSSftaWrmwgVGWfJawzhEORsl/YnSBUfLWbEs573QcmP5A9ch7Z4Ufjv2b/VyQ9vByzUTzismoXjoVHsUycUMAmy7dd0TQA90hZZe+/RQda8m9600UwuftulRMOo2mXMUvFW2rJ6Fm6RQUEf4LeeyAKw8dcfWhA2KS2J9nU+dS7hk49ul94TNZzVCqTEEAo8hz1pTffBCTmO2x62msHW6HsT1/VfVNg7ebGOB2d87A14OfaW6+2/wyuBUmf36rGzSukIwWVZJR1S8FiWk2uBr6n8YhoQ6qsrqd9NqqWhJWjWR/pi5tW5jKHIwyYbdZD30ThrHILvrAqNdeew3btm0zaO3UlkLUKaV+/fph8+bNompDwCjyHNSlSxdVKDRRZ63CpEmTsHDhQi1LdpbCztWqVcvgsGgER+3YsSN7AEmuW7du+Ouvv0RWQ8CoevXqISgoSNRPqTB58mQsWLBAqRoNGzZUhTTUbmAKGEWevKZOnao9jCb/2WefYdasWZqyrsy3336LDz74gNnk559/xvDhw0V1+sAo8vy1aNEiUR9p4fPPP1d5rJLa1WXyNqXk5UzdhryYzZ07V10UXQlOGz16tMhmLYWCBkaZQ3fWc5+DUebYCT4nV4ArYIwChQmMMkYXc7VlnSUcjDLXbvB5uQJcAWMUKCxglDGamKst6yzhYJS5doPPyxXgChijQGECo4zRxRxtWWdJQQWjSL/Y22dwbc37SHjyr8lyEoBSut1IVOw7ExTCjZVyCkZR6Lwmnx5X9NATItzD42NrZFOT5yDyIKSUgn8agrCz4s9YqG2rr+9owtBR2dLAqHt/LsStLZ/Q0kSp6cyTIs9YokoqCEDU4dE+sjCCld74HOUFT1zSlNdg1NWVI/Dk5K/SaRHYc6rgHWyWzC41nP+yI2JuHJeaVXAYQWLqpARGUfi8pp+dgWvp2uqmsuvtbbNwd9eXMnu98dvgXaebzG6phsIGRlnqPtC6WOcIB6PkO2YsGFUjIBX1A1NQWwCNShbPxLPndqpQeg3KJ+P3c8UxbUNJ+SQvLRQW79NXI1DcSR5udF+wC6Zt9EF8MhtW8hVApb3THsDZXgyctp9bFg8j2cDP2C7RIM9PNhK4iZZD8NCc7d749YSb4no3jX2E+uVTRPUFAYwSLfhlYeMpN8zY4s2qwpIhYeheL4FZR8aktCKo85EcfKY6Aseof7e67P6JqTb44GdfHL/O/r3FzhY4M/su3Jzlrwkav7AmDkaZsPOsh74Jw1hkF11g1PXr11G9enWZdySlGyGdrl69qurDarNmzRpQKDrtZAgYZQjgcvDgQbRv3157aE1+48aNqnBqGoMBGQrPV7s2+5fL7777DmPHjhWNog+MIo9K5LHK0OTi4gIKi+fpKXYfq+5PIfcIDNJOpoBRt2/fRoUK8ofwzZs3VTCZ1MOX9nzaeXd3d9y6dQslSsi/aUPen0qVKgXy+qVOusAo8i5GnqAyMjLUzZnXwYMHY926dcy6qKgo1Zz6xmjevDlOnjzJHIOAQIL9rDFxMEr/rrKe+xyM0q8bb8EV4AqYVwEORplXf+nsrLOEg1FSlXiZK8AVsEQFOBhlObvCOks4GGU5+8NXwhXgCigrwMEoZW3yu4Z1lhRkMEqtH8EloYeX49nFHXiRma42G3X1qt4O9cZtZcJROQWjqgxYoAoRp7SgO3/MxZ0dc2TVNd9ZCb8Wg2R2tUEJMCIvUy6lKqubWRwYlRYXjrR4sacrWmwxv+oiT1eaG3iZib5+DBfmd5KaYS4wirxekfcr7URh6lotugX74soQg7p9xOU/cWnJq+qi5lqmw/9Q9a2vNWUlMMqrZkc0mLRL046VCTuzCcHLhsqqar33M3yb9pfZLdXAwSjL2RnWOcLBKPn+GApGFbV9gem9ozDolVj5IIKFHOR1nlcG9yLYXoVmvh6BQS2eM/uqjaFRRdHv2wBExAm0DCNN7hGFke0FT4MvU5YwZ40PKyAjS04+ORR9gaAv78LORgxSqfuqr0N+9MPpm87qoug6rPVzfNxHfAYURjCKPEWRxyhWIlBux6RQVpXGliE4o2o9uxzChTCLrDRvQDhebxzHqiq0Ng5GmbD1rIe+CcNYZBddYBRBTAQzGZOGDRum2OfatWuqMHTa4+kDoyhsXIMGDXTCWRQGLjY2VjH8Hcu7kvYaWPkhQ4Zg7dq1rCpcuXJFBk3pA6NY4eSYg2sZZ8+eDQKgWGn37t2qsHzadcaCUWXKlFGFo9MeQ53/+uuvQV64jEkEKRGsxErt2rXDkSNHNFW6wKhDhw6BwvPpSzQmtWUlCv3YpEkTVpXIVrFiRRXQJTK+LHAwiqVK4bGxnvscjCo8+8/vlCtQUBXgYJRl7RzrLOFglGXtEV8NV4ArwFaAea03pAAAQABJREFUg1FsXcxhZZ0lHIwyx07wObkCXAFjFeBglLGK5V171lliDWCUWjHyjETwTNS1w4gOOYzEsJvqKoOuSqBJTsGoBpN2w6um8t+4Q48sx7/rxF++pgU3nLIXntXaKK794cGluP7rRFm9pYNRsgXrMKTGPAGBQRFBfyL075VM8M0sYJRAKxwa5YXMtOwvgNNtEMhGQJtBSRjjxNSaSAq/I2pOkF6DyX9qbEpgVLkuE1C53zxNO1bm+d3zODvnFVkVB6NkknCDgQqwzhEORsnFMwSM8hC8+ax47zHqlEmVD/DScvCqC95f5cusNyZc2q5/XDFxvQ9znMCS6dgneI1SJ/L6VGtKBaRnysEo8mS0X2hLYf50pb+CimHqBvZ8PerHY26/cFH3wghG3X5mj65fssEod+dMHJ91H44CiKYrffOXJ1b/7cFsMrF7FIa2YgN3zA6FwMjBKBM2mfXQN2EYi+yiC4wiL0DPn+umTqU3VbRoUURGRqJ48eLSKhXcRPaEhGw3cPrAqB49emDPnj2ysbQNBD6dP39e26TJk71x48aasqEZuo/w8HCQBtJE3nZcXV2RmJgdg1UXGBUdHQ0vLy/pMHrLvr6+ePKEHQ/02bNnKo9I2oMYC0bp8rjUv39/bNq0SXt4vfn3338fFH6OlcaMGYMffvhBU6ULjKKwfOPGjdO0VcrUr19fFk5Q3Xbr1q14/fXX1UXFq7+/PyhUIytxMIqlSuGxsZ77HIwqPPvP75QrUFAV4GCUZe0c6yzhYJRl7RFfDVeAK8BWgINRbF3MYWWdJRyMMsdO8Dm5AlwBYxXgYJSxiuVde9ZZYk1glFS51NiniP73b0Re2Y/I4H1IT4yWNpGVyWuUd93uIntOwahXFlyHk3c50ZjahUcC8HNt7Rhtkyrf4ovLcPGtIrOrDRR+j8LwSVNBBKMI/kl4fA2JT24g8el1JD67jeRnd5CREi+9PVnZHGCUUpg+8vREHp8MTcE/DkLYud9FzR08/ND667samxIYVWP4T/BvNUzTjpWJDw3G6U/ln4lxMIqlFrcZogDrHOFglFw5Q8CoGa9GYoiCpyj1iJN+8cHOi67qouZqb/cCBwRAyc9Td7QdTQchM/A7f5y/yw69tnXCI9Qukx3e7vXFpXH5oYN2d02+aaVkfCGATaW9dMNRmg4GZAojGEUAWv1pFVQh9VgSvdYoDlP7RIEgKZ5yRwEORpmgI+uhb8IwFtlFCYwiIIoFBRlyExcvXgRBK6xEHnru3Mmm4fWBURRKLiYm250fa8zu3buDPCix0s8//4zhw4ezqvTayOtQo0aNmO0CAwNx7949TZ0uMIq8XinpoRlAIUP3ztoHgrMI3srMzH44GgtGTZ8+HXPnzlWYWYhDrieUnbSjnR3bdR+1I2Bq9OjRmi66wCgKU0jhCvUlXWCUoXAVvb4o7B4rcTCKpUrhsbGe+xyMKjz7z++UK1BQFeBglGXtHOss4WCUZe0RXw1XgCvAVoCDUWxdzGFlnSUcjDLHTvA5uQJcAWMV4GCUsYrlXXvWWWLNYJS2ki+yMhF7+wzC/9kphN1bhqz07A+AtdsVL9cATWee1DYhp2BUq0W34egZIBpTu6AERr2y4F8BqCqv3VSUf3x8LUJWvyeyUaGggFGpsWF4cnI9Hp9Yh6SwW7L7MNRgDjCKQLt/FveWLbHe+G3wrtNNZlcy3NryCSgkojS1WxoOO6f/HA4ogVE1310Nv+YDpV1FZQ5GieTghVxQgHWOcDBKLqw+MKq0V4bgeek+7NjR7TQDNp9ZnhkCr375FGway3b0oOksyfxy0g2f/e4tsf5XnCR4FxrVIfvz99nbvbH+mBuzLRkJzOrXPA6dayaifmAyKCRgTlJhBKNIr0Hf++PsHTasRvVuglcx8vrUuloSapZOgY3ciRc148lABTgYZaBQ2s1YD33t+oKcVwKjgoODUadOHZNubcuWLYreesh7k7Z3J11gFAErJUqU0LuGoUOHggAoVpo5cyYoJJ0piTwmvfnmm8yu0vvQBUbt2LEDffv2ZY6jz6gLMiNttKEeY8GoxYsXY/z48fqWkCv1GzZswMCB2b+w6wKjyPPUTz/9pHdeXWDUwoULMXnyZL1jEHSmBN5xMEqvfFbdgPXc52CUVW85vzmugFUowMEoy9pG1lnCwSjL2iO+Gq4AV4CtAAej2LqYw8o6SzgYZY6d4HNyBbgCxirAwShjFcu79qyzpMCBUcKXhGWJYvsYkRKf3sCVZcMQ9+ASs1ebb0JhXzz7w2MORvnJdKr8xlyU6zZJZL+68h0BdPpFZCMdSU9pin94GRcWdBG8eGV/EC9tIy3b2NkjKyNNaoY5wKgnp37D1RVvy9bSePphuFdqLrMrGe7t+Qq3fp8hq9b2MsbBKCF013BHmUbkMICn/FeAdY5wMEq+D/rAqPkDnuHVxro94umChYa1fo6P+0TIJ9ZhufbYAb0Xlma26N0wHgvfeqapIy9V5K3KkORkn4UGAqhVpyz9S0VtAeDxcs125GHIGLrudUCzOMx+Uxx6T9eY3ReUwc2n9rImXsUycWZOtpMTdYP4ZBvUnx6oLoquHWsnYunwpyKbdmHjKTfM2JL9+4J23ZIhYeheL0HbJMsv2FUCKw7Lo1XJGgoG8hzVqKKgseDZq3bpVBUo5eokuJ3iyWAFOBhlsFTZDVkP/ezagp1TAqP++usvdOtmOOWurcL69esxaNAgbZMm36lTJxw4cEBT1gVGnTlzBs2aNdO0VcoQ3EOQDyu98847WLVqFatKr23RokWYOFEer5s6du7cGfv379eMoQuMohByFErOlHTy5Ek0b87+pVrqfctYMGrt2rUYMmSIKcsyuo/UcxcHo4yWMFc78DcQ+uVkPfc5GKVfN96CK8AVMK8CHIwyr/7S2VlnCQejpCrxMleAK2CJCnAwynJ2hXWWcDDKcvaHr4QrwBVQVoCDUcra5HcN6ywpSGDUxUU9EHX1oEy2OmM2wqdBH5ldlyE56iFOTq0lgDapsmZSuIWDUX4yjXICRiU8uooL8zsjLYEdvYEmsy/mBSefCnAu+d+/YgE14F6xKY5OkHvQMgcYFXvrNM590VamS+3316NU4zdkdiXD9V8m4OGhH0XVRWyLosPyGBSx+S8qBwejOBgleoGYucA6RzgYJd8UfWDUgekPUM5bdyi6M7ecMHipv3zwlxY7G+PgwIwsZYi4RkAqdkzKhlgzBK5pxHI/nLrprDi/ropKpdLwStUktBI8HTWpkKTXM1ZhBaNikmzw5pLSoPs3NpH3KAp/qNa5rgCm8aRbAQ5G6daHWct66DMbFkCjEhh19OhRtGnTxqQ7+v7770Vh07QHadWqFY4fP64x6QKjfvnlFwwePFjTVilDHoYoVBsrjRs3DhRWzZREXovee0/ulpbGat26NY4dO6YZVhcYtWbNGrz9tvybBJrOOjJ//vknunbtymwREBCAx48fa+qMBaNWrlyJESNGaPrnZYa0pH1SJw5GqZUwz5WDUfp1Zz33ORilXzfegivAFTCvAhyMMq/+0tlZZwkHo6Qq8TJXgCtgiQpwMMpydoV1lnAwynL2h6+EK8AVUFaAg1HK2uR3DessKUhg1KVvX0fEpd0y2cr3+AiVXvtMZtdnODunFZ7fPSdrVmvkGvg2G6CxWy0YJWhG2ulKSeF3cOKjGrImOQGj/lncB5HBe2VjOriXQrkuE1Cyfi9mCMH0xGgcGSOHtMwBRqUnCGv5wPC1yG72peHSkr6IuPyXqNrFrypazA3S2DgYxcEozYvBAjKsc4SDUfKN0QVGEdB05au70Ac27blUDOPXlZIPngeWAM90HJnxQDQyeVLq920AboXJvS+JGuop+HukY3TnGPRtFK94z4UVjCLp6N4JjiJIKieppuBFamyXaLStnpiTYay6LwejTNhe1kPfhGEssosSGBUaGooyZcqYtObt27ejTx/2tzWkMI8uMGrZsmUYNWqU3jXogmyWLFmCCRMm6B2D1WDfvn0gD1esVLNmTYSEhGiqdIFROYHMLl++jNq1a2vmUWdSU1NBc2oDLsaCUQsWLFAMNxcUFISbN2+qp8vxlbxTEeSlTrr2jIfSU6uUd1ft103ezVKwR2Y99zkYVbD3lK+eK1AYFOBglGXtMuss4WCUZe0RXw1XgCvAVoCDUWxdzGFlnSUcjDLHTvA5uQJcAWMV4GCUsYrlXXvWWVKQwKh/149D6OFlMoG8anZEg0m7ZHZ9hnNzWyP29llZs3rjt8G7TnYEjQIPRiXH4fD/Ssrus0zH0ag6cJHMrm2I/veoEPKus7ZJlTcZjBLCnx35wF8IoRctGtPRwx9NZ50WQhjK16luaCyMlBz5AMcnV1F311yrDfkOpdu+qylLM6c/bYz40GCR2atmB+E1JobyWK8Lj8ot0GjaIVFfpUJGSjyOTayIjOTnoiYlG/RG3TGbNDYORnEwSvNisIAM6xzhYJR8Y3SBUWVLpOPgx2IIST4C8OtJN8z6nR2mjdU+J7bAkunYN02+pog4W3y9xwvbLxRHZg6jtpX2ysCq956gvHeabKmFGYwiMSj033whrN6xf03z0KUtaH0hrOGKd5+gOA+zpy2LKs/BKJkk+g2sh77+XgWjhRIYlZWVpQJv0tLkDyt9d3bhwgU0aNBA1owF8+QGGNWuXTscOsT+xXPHjh3o27evbC2GGAgMovWxkq+vL8LCwjRVusCohw8fomzZspq2xmSio6Ph4eEh63L9+nVUq1ZNZDcWjJo6dSrmzZsnGkNdIM1Iu7xKHIzKK2UNG5eDUfp1Yj33ORilXzfegivAFTCvAhyMMq/+0tlZZwkHo6Qq8TJXgCtgiQpwMMpydoV1lnAwynL2h6+EK8AVUFaAg1HK2uR3DessKUhg1KO/V+La2jEy2WzsHAQY5SDcAhvJ6pQMWekpAqATgMzUBFmTZp+dhWuZOho7C4DxazkYNUes0LShDIVEo9Bo0tRq0W04egZIzZqy0n29suBfpuckdcfHx9ciZLU8ykWLecFwKVVZ3Ux1PTTKS7hXsRcJCj9IYQh1pQf7v8WNDVNkTUwFoxLDbuLkNPmXv6sNWoLS7XV/MT7q2mFc/CobWFMvyniPUd8KYNRIdXfZ1VAw6vyXHRBz44Ssf5MZxw16LT7Y9w1ubJR77JJ6QONgFAejZC8yMxpY5wgHo+QboguMovByq0Y+kXeSWDafKY6PNynDopLmOSpW80/Dzg8fKo5B4NJPBzxwKMQFsUm2iu30VZBnqt/HP4KXqxCrTysVdjBKLcWl+45YdshDCGHohOQ00z1INa6QjDWjnsDezrhwi+p1WOuVg1Em7CzroW/CMBbZRQmMosU2btwY58+fN2rdJUqUAHmbcnR0lPVjwTy5AUaRZ6sHD+RUKy2AwCIChpKSkmTr0WWoWLEibty4ARsb+UMoLi5OBSsRPKZOusAoakcgVXh4uLq5QddatWohOFj8LQV1R/K+1L17d3VRdTUWjOrfvz82bNggGkNdmDJlCr766it1MdevHIzKdUmNGpCDUfrlYj33ORilXzfegivAFTCvAhyMMq/+0tlZZwkHo6Qq8TJXgCtgiQpwMMpydoV1lnAwynL2h6+EK8AVUFaAg1HK2uR3DessKUhgVHpCFP4eVxYvsjJk0lEYtqYzT8PB3VdWxzL8u+4DhB4Rg03UzqaoI9p+9wi2DsU03awBjDr1SX0kPL6muSfKEKzVcv412NjZi+zqwovMdFUYveQo+YflpoJRYWc3I/inIeopNNc6ozfAp6HuL7Vf/+1DPDzwvaaPOmMsGFW535dCyL7x6u6yq6Fg1K3fZ+DeHvnnJiVqdwF5HStSRP55knoy8phF86REP1KbNNf6E3aAxlAnDkZxMEr9WrCEK+sc4WCUfGd0gVGdayfi++FP5Z0klv3BxTB6DTuUnodzFppVNu6zbsnwoiJ5GRraKlZkYxWyBM4m+KEjTtxwxvk7jrgS6ggKuWdMopBvWyeEwqZIdq/cBKO6zS/DDP/nVSwTZ+bcy570ZY7WX396oMxOho7CXi3VsVcbT7lhxha2V68lQ8LQvZ4cvmZOJDGmZRTBhbtOOH7DCf/cc8K1Rw5ISdcSTNKeVXy1cTzmD3jGqiq0Ng5GmbD1rIe+CcNYZBddYNS2bdvw2muvGbXuadOm4YsvvmD2YcE8uQFG0WT37t1DuXLlmPOOGTMGP/zwA7NOybh06VJQSDdW2rNnD3r06CGq0gVGUcOFCxcqhq0TDaRVWLFiBd555x0tS3b2+++/xwcffJBtEHLGglEU1pAgNlY6cOCAYhhBVnuyEfzVokULZvXBgwcRG5t9wHIwiilTvhk5GKVfatZzn4NR+nWzlhY2Ts4oYi//A1Hm8+znWH7daxEHR9hIYOMXQjjVrJTkXF9CEUcn2Dg4yMbNjHsOIXarzM4NlqcAB6Msa09YZwkHoyxrj/hquAJcAbYCHIxi62IOK+ss4WCUOXaCz8kV4AoYqwAHo4xVLO/as86SggRGkTKXfxiAZxe2M0Vy8i6PwF7T4NdsAIrYFmW2SX3+DHf/mCtAUcuZ9b5C31oj14jqrAGMurTkVURc/lN0X1SoNvgblG4n9zr14kUWbm3+GPf3Lpb1IYOpYFT09WO4ML+TbMxSjV9H7VHrIdBEsjoyPDmxHiFrRglQnNjLCNVV6PMJKvT+hLKilBrzBEcnyj/sZu2xdkdDwSgKgXdiak2kxUVod1flyRtXrVFrBehM/re1lJjH+GdhDyQ8+VfWz7NaGzScsldk52AUB6NELwgzF1jnCAej5JuSG2DUudtOeOsHf/nggmVk+xhM7hHFrMtPI31McE/wJnVRgHdOCrDUKeFfTJJ+UGrPlIeo7JsdpUoXGPVm0zjM7We4s5GmM8ojKkHu1crTJRNnPy8YYJR0DzOyiuDGE/uXsJQApQmvjaQ09nmp7kveooK+vIuitvyzHLUmHIxSK2HElfXQN6K7RTfVBUYRPFGnTh1cuXLFoHuws7NTAUoE3LDS119/jUmTJomqcguMWrNmDYYNGyYaW124c+cOKleuDG0PT+o61pW8XlH4O4KdWGny5Mkq0Em7Th8YlZiYiPLlyyMiQv4Ls/Y46ryXl5cKWlJaAwv2MhaMornu37+vGOavdevWOHbsmHpJeq/r1q3D4MGDZe0yMzNBXr2ePHmiqeNglEYKs2Q4GKVfdtZzn4NR+nWzlhY+075A8e5yMPhWKyGEqZa3wPy4X8/B78HrvYmiqbLin+P+gC7IjI0W2XNaKPH+ZHi8JQdy7/ZsjswY87/pyun9FYb+HIyyrF1mnSXWCEZF3InDD70PisSnv2v3/7YZqrQVf3P7wNdXcXL1TVnbmVdeFdmstfBDrwOIuBsvur3KrUth4A/NRbbHV2Owov8RkY0K/RY3QbWO7D+QyRpbieHW8TD8+v4p0d0UdbDFqG3t4VU2+xv9oga8kGMFOBiVYwlzbQDWWcLBqFyTlw9kZgXafHgJQbfF52Lr2h74Y3YtM6+MT58bCnAwKjdUzJ0xWGdJQQOjyNPOmc9aIDlC/uGmWiVHD3941+0OpxJlVV6RsgTPR9Q+8dltRPyzC5lpbC8btvbOaPzxEVEYPRrTGsCom5un4/5fX6sl0lyL2NghsOdHAhw1CvbFvZGeEI340GDc3T0f0dfk70PUHU0Foyic3+H/lWQCTuQlqXy3SXCv1BxFbGxBHqtib59B6OHlCDv/u+IX9UrU6oR647bKYDiCqA6+W1w2F3lyKtt5nDBPM5VXJ4LlAtqMUN+aypMTaaCdvGp2QINJu7VNqvzjE+sQsmqkzE4G94pN4d/6bXhUbql6LSaEXkH0jeOg8IQpUaGyPrQXzeacRzE/4W+OWomDURyM0no5mD3LOkc4GCXfltwAox7HFEWb2WXlgwuWTrUT8MPwMGadOY3kUWrf5WKYt9MLT4X1K6U5b0Sgf3PhC9gv04NIe3SYW0ZdFF3b1UjCsneyP1MWVUoK5FWp1pQKEut/xYLkMYp5A1rG9Mwi+O2kG77d64k4HR67tghhC+uWTdHqWbizHIwyYf9ZD30ThrHILrrAKFrw/v370atXL6QK3in0pfnz54NCsLESQUk1atQAhdPTTrkFRrVr1w6HDh3SHlqUp7BwSmvTbuggeMqg8HJ9+7JduKanp6NChQoyT0v6wCiaY/Xq1SoPUPqgFALM1q9fDwp1x0oJCQkq0CgmJkZUbQoYtWDBAkVPVidPnkSrVq0MAspq1qyJoKAg2NraitZEhZ07d6J3794iOwejRHLke0HfazDfF2SBE7Ke+xyMssCNyqMlWToYRbf9YEBnpIXez1UFOBiVq3KaZTAORplFdsVJWWeJtYJR3/c8INOh77yGqNtb/Mec/QuvyMAo6mgOXRKiUpGWJA7HYWtXBG6+zrJ7yS3D9z32y8GoNr54a6kEjLoSjeX95B9I9FvSFNU7FVwwKjE6FamJYs1tBD/q7v7Kmt86FoZfRp2UbcHwta1QrhHbdbmsMTcYrQAHo4yWLM86sM4SDkblmdx84HxWoNXEfxB0RxxqonVtd+yaUzufV8KnywsFOBiVF6qaNibrLCloYBTdecKjq4LXh9YgyCa3EnmYIriGIBtpsgYwirwUnfioBrLSlT8gtbF3QlaaYV7JTQWjSNvTM5sg/uFlqcyaMoX2s3N0RXpijOC0PEtj15Wxc3YXwiiWQou5QaJmxyZWAN27rkRhE9v/FKlpYqjHKFUHwaEAvRaf3z2n6c/M0DeG9HhgJ1irSv/5su4cjOJglOxFYUYD6xzhYJR8Q3IDjKJRW84qh2fP7WQTeLlm4sgnD+Bkb9gzkgag8GyHQ1xkY5Ghun8qypRIV9WdveOEIwrthreOhY+b+G85rAEJUBr6o78QBs6RVQ1pmDdd4exobX98KIdJWQPfeWaPLl+yAStL8xi161IxhAihCKWJQgxO7B4FOxuBMtOTogXPWN2/Ko3IOPlrhLpO6x2Jt9vkf+QTPcs2WzUHo0yQnvXQN2EYi+yiD4yiRZ8+fRp9+vRBeDjbbZ2NjQ0otJtS6DkaQyksX26BUTTH+fPn0bBhQ8oyE4FJI0eOBHkwYiVXV1fs2LEDBFkpJfKKNHToUFm1IWAUdaLxBw0aBPIgxUqOQrikzZs3o2fPnqxqlU0pLJ8pYBR5ciKPWgRjsRKBcQMHDkRUlLKnEALFjh49Cn9/9oc0Xbp0wb59+0TDczBKJEe+FzgYpV9y1nOfg1H6dbOWFhyMEu8k9xgl1sOSSxyMsqzdYZ0l5gCA8loV8hhVEMGoTePP4Np+8R/LPUu7YNy+LnkmWWEHo3bO/AcXt9wT6etU3B5Tzyi/9+FglEiufCtwMCrfpNY7Eess4WCUXtl4gwKiAAejCshGmbhMDkaZKFwedGOdJQURjCJpnp3fistL38oVlciDEIU9K9X4DeZ41gBG0Y3d3CKExvtzEfMelYzkdSs58oGsOidgVIzgNenCV91UHqFkA+fA4ODhh9Zf3xWNcHPTNMVwgOqGOQKjhEGSwu8i+MfBiLt/UT2k0ddSTd5EjeFLQWuRJg5GcTBK+powZ5l1jnAwSr4juQVGjV9XCnsEgIaVpvSMxLvtDIdefhE8DH32O/tLZT+OeIoONf/7rHrONm+sO+7GmhIzX4/AoBbZnp6YjV4a9wcXw+g1pZhNGldIxq9jxH+Ha/hxIEg3aXJ3zsQ5IQSeQqRVUfN5O0tg9RF3kU1dyG8wasHAcPRtFKeeXnYdJIRJPCuExGOlDR88QsNAZZBZu8+Svzzxw35PbZMmP+iVWMx8NRv81VQU0gwHo0zYeNZD34RhLLKLIWAULZxCy82YMQMnTpzA3bvZv2g2aNBAZZd6BJLebKNGjXDhwgWpGbkJRvXo0QO7du2SzaFtIEBn9uzZOHUqOxwDeTnq3Lkz5s6di7p162o3F+XJaxbVS71eUSNDwShqS56VvvjiC5BHJu3wcm3btsWcOXPQokULasZMtAYKyUf7Jk2mgFE0xtq1azFkyBDpcJrygwcPVN62zpw5o3odqCs8PDwwatQoTJgwAd7e7IP19u3bqjCGUhCHg1FqFc1zle6HeVZh2bOynvscjLLsPcvN1XEwSqwmB6PEelhyiYNRlrU7rLOEg1GW4zGKg1H5//PCwaj819zUGTkYZapyud+PdZZwMCr3deYjmkcBDkaZR/f8mpWDUfmltP55WGdJQQWj6G5jbgifT+z8AlHXDuu/eYUWziUroOJrsxShKOpmLWBURlIsLn3zGmJuyr2wsuShkIT1xm8TQhc2l4WjywkYRXM9Oroa137+H2tatk34RNyv2QDYu/sqwl0sMCotPhKnPq4LuiqlnIJRNO6LrAzhtTgPd3fNV+WV5pLai7p4otqQb3S+/jgYxcEo6evGnGXWOcLBKPmO5BYYpQsuImDo4McP4OacJV+AxJKYaqPypBQWK3eMQR6g/v70gcZDEYFFBBix0itVk7H6PTHQxGpHtvN3nTDwO7YTja51E/DtUHEowD6LSiPkkQNzOGpLfXSl6ERbtJ1dDklpgsslRspvMGqGACQNEcAkpTTlt5LYfr44s/qddjH4qKeykxLtTuuPuWH2dvbn8hO6ReF/HcURp7T7FrY8B6NM2HHWQ9+EYSyyi6FglPbinz17pgJkfH19ERAQoF3FzB84cACdOsnd0VLj3ASjaDzyXDV69GjK6kx03xSSLiUlReXpyNOTTVZqD0LjLl26VNukyRsDRmk6CRkCzsgTF0FNPj4+2lXM/LJly1QwEqvSVDDK3d0dly9fVoXnY42rbYuIiEDx/7N3HuBRVF0Y/iA9IYEkBEhC7yBIk94RVERAxS4W7O23IygW7F2xoVJERKyogIqNohSlg3SEQICQRglppBL+eybMZmfmzrZks0Ny7vPgzL1z23xnnJNk3z0nIkIBs8j2ZpGmaAylT6R0gN9++639FMo5g1EGSSq1gcEo53LL3vsMRjnXrar0YDBKa0kGo7R6WLnGYJS1rCPzJQxGMRh1ZF+25kFtXY1S6TEYpTG9pSsMRlnHPDJfwmCUdezDOymfAgxGlU8/q49mMMo6FpL5krMZjFKVPbF3jQJIHd2qzVSgXpcdo9oPRpNh96Fup+EiCoUxQoX9mOWPtET+8ST7JjS54H60ufY1Tdvh5bOwfdbdmjZK0TfonYMICIvUtNtXkv6cgR2z77NvUs77v7YTITHNDO1qQ/qGBdj8/tVqVTnSvQwQUZMorZysUGq6g3+8j73fTcapwpOyLqA9N+hxBdpe9yYCakXhz//FozBH+wEtXWs8TPvZC90D3Yt9CWvQGn1f3mLfZDvP3LcOCfNfgDO7Rbbpp6SYi2jaDcX52dggok3RWH2RgVHUh4CwvfOfR/LKOSjOM0bv8A+JwJCpZRlS1jw/wJAaj6KJnXv3HP2Shnrm/vXY/cWjOJGwxmHqvJr+QYjpPAJtr39T2CrWMI99w8n0BCUNon0bnXe4/RPE9blO36ypZx/aAkoNqC8d7/wUsb2u0Tdbtv77OGO6Kf5cwzfmkvkRBqOMtqgoMOqUYJ6GvtgESccDjIuIlmb1ivDBuBS0alAovU6NuYU1cdvHcVi/z/j/EV2//6Lj+N+Fx+lUKct3huLWaXFq1XB8WMA2dzuBbWjfj3/lHvhz36xY/LYlzLAeNbSoX4iFIp1eoL88vdyxbD88IKJrmUVgojm8AUYt3BCORz6Xf54/uH0upt1uDGxCe6EyfWkdvPajHEDzEz+WvHdzCoZ1LI3iVTrC+F+y7bgP47ApUW7bN65Pw+jztH97NM5SfVoYjPLA1rKXvgfTWHKIJ2CUOzdCKeP69++PTZs2SYdVNBgVFBSEpUuXok+fPtL1PG2cM2eOw6hKnoJR7uwnNTUVFHkrKUn7C5k6h6dgFI3v168fCGCjVH4VVe68805MmzZNOh2DUVJZKq2Rf4FwLrXsvc9glHPdqkoPvzpRCGpzjuF2Tq5ZYWjzdkPUDXci+s6HDcscuPZCFB5KNLSXp6Hu3eMRef1thikYjDJIYtkGBqOsZRqZL6nuYFTu8QKk7DB+c6plP/kfFLxpUV9EjErfk4WstDzNbYVFBSG2vTbk9+GtxzHt6mWaflS5ekovtL9A/s07Q2cLNngCRhUXluDA+qPiG9jaP4TFnxsJSsPHxTsKMBjlHV09mVXmSxiM8kRJHmNFBRiMsqJVKm5PDEZVnJblnUnmS6oCGKXqUpCRLNKaJeDkkf3IO5Io/u1HwYkUASVFITi6EUKiGyO4bmPUim8PihRVncvpU0XIObxDpH/bhOykrTiVnyMgqGhFFwJ2zMAqb2iWm7xL2cPJtL3IP3ZI2UdYbBuU/msN/xBtSqfTJaeQfXCzEjEsJ3kn/IMjlL6RbfuDQCzTcvo08o4fUkCpkqIC+AWGwF8Aa0G166NGTX/TYZ5cKMxKx7HtSwRQdwiFWUdK5xdRrwIjYpQ9RrUbJNLmyQEAT9ar6mMYjLKOhWV+hMEoo30qCoyimeeKFHiTTVLg0fXQwNN4dMRR9GmTJ0CpQtQ8EzCp6FQNLNwYjmmLI7EvXQ5W+dc8jb+eOYB6EcU0lVKKS2qg3zNNcSzHT20yHEd1y8YN/TPRuYk23VtBUQ1sTgzBWyK928b95p8xf35PMnq20sK5by+KwtQ/zAOXEBz1yrXpmjUJiKLIVM9+XxdHsxy/x70BRq1JCMHY983/NndlryyRojAHMRGncEJEtMo86YdLupaCSikZARj4fBMI1yQtAX6ncX2/LFzX54QCwNl3ys6ridV7QvCKAKsOHpXblsb/9XSisrb92Op8zmCUB9aXvfQ9mMaSQ8zAqN27dysp366+WvvtA3duorCwEJTejoAbs1LRYBStQ5DS3Llzcdlll5kt61b7G2+8oaSScwSTOAKjXn75Zdxzzz2oXVv7w7w7mzhx4gQGDhyILVvk37SgucoDRtF4SuG3cOFCuBI9i/o7KpReb8qUKaZdGIwylaZSLjh6litlA2fBIrL3PoNRZ4HhquAWGYyqgkb14i0xGOVFcT2YWuZLqjsY5YGMXhviCzDK1ZthMMpVpbiftxRgMMpbyro/r8yXMBjlvo48wpoKMBhlTbtU1K4YjKooJcs/j8yXVCUwqvwK8QysACtgRQUYjLKOVWR+hMEoo30qEowicOYWEfFp5e5Q40K6lrDAEhScqolG0UVIzvAHgUqOilnKthnLIvHqwmhHQ5VrkSKNX1xUkUjnVwr+7E0LRGGx4zXbxxdggYj+pC9HsvxwvoiOlSeiIDkqESElyMmvichap0BglKvFG2AURfIaLOAmVwulLVw5OdHW/dG59bFgfbitbnZCYFV8ZBFCgkoUACxB6Kz7zqBh6GXds/DadWXREA0dqmEDg1EeGF320vdgGksOMQOjdu7ciS5duuCdd97B7bffjpo1Hb+U9DeXmJiIm266CcuXL9df0tS9AUbRArTfRx99FE888YTHQBJFZpowYQK++OILzZ5lFUdg1C233KJEeZo9ezYo/aC7hdLcjR07Ftu2bXM4tLxgFE3epk0bULo+grA8KQkJCXjmmWcUMM3ReAajHKnj/WsMRjnXWPbeZzDKuW4V3kN8q8oUn6/IxSpjHQ/XcBuM8nAdktMrEaPKsR+nJvbm3E4Xt2YHBqOsZReZL2Ewyjo2YjCq8m3hScSoyt8lr0gKMBhlnedA5ksYjLKOfXgn5VOAwajy6Wf10QxGWcdCMl/CYJR17MM7YQVYAbkCDEbJdfFFq8yPMBhltERFglE0O0VDuuzthkg94TgqknEn5i0UzejFq9JFOll5nwlf1sf3a51DO/LR8laCe+bcm6yAW7IezqJGyca42uYNMIqiaw0RYFSKi3bRg1EErt0wNd40FZ6r96bv161ZHqaLNH7hAiLjUqYAg1FlWrh8JnvpuzzY4h0dgVHt27dXdk/p21599VUFlnEGSB07dgwEAE2ePBnZ2c5zWDZs2BAEUfn5GQnP5557ToFsyiNhdHQ0Jk6ciGuvvRbx8eah7ezX+O+///DJJ5/g3XffRV6eNtWFfT/7c0rhR1GdZKnoCIyaNWsWwsPDlfu56667EBbmPGQqgVkEKZH2RUVF9stJz+vVq4fDhw/D39/oJF977TUF8pIOlDSOGjVK6d+rVy+XoDiKMPbiiy8qENmpU6ckM2qbhg8fjkWLFmkbz9Quv/xy/PDDD9Jr9o1du3bFhg0b7Jts5xTla/z48ba62QnZLT09HREREYYu33//PcaMGWNorwoNDEY5t6LsvV9dwKig1ucguE3p+99eqZxVy3Dq+FH7Jul5jcAgRFw4ynCtOOMYclcuNbRTQw3hA0J79ketwRchILYh/KJj4B9VFzXDaqEkOxPFR9LFvzTkbd+ErJ++Q3G6eZ5mZb7gENQaeAFqBmpT7GT98gNOF5eGiA3rNwQRwy8D3W9ArPAPFJL7j5+R+vx4BDZqipDO3Q17zfxpnlNQy692HYQPvQSh5/UpvY/ouvCLilHusVjoR/dRnJaMnBWLkfPn7zhdoA09q1/UGRhVs1aEWG8EwocMR0DjZvAX2p0uLEDx8WNincPI/ecv5Cz7DUXJxm9k6NcqLxjlXy9W2UdY38HwbxAP/7p03/5iL+K+01ORt2U9soUNChL+0y/ttB7UojXCh41E8DmdbbrWDAtHSU6WmDsNReKZKNi1DZkLv1bWcjphFe3AYJS1DCvzJWcLGJX2X6aSvix1VyZSdp1AZvJJhNQORK26wWjcJRptBseiYafSUNdHErLw/khjhNjLXj4PnUdrv0GVfSQfydsyDIai+RyVklOnsX/NEexachgZh08iR8yTcyxfpCaogYj6IajdIASRjWqh08jGqNfK+HMdzX3yRCEObTpmW2bFjN2aOl2g+xv1bFdbHzqp36Y26sSVfkOPUgEm/Xtccz00MhCNOpd9o277r0nY/WeKkjKQ+vsH+WHEk50VzVJJyxTt7xe16gYhvqM2bLgrEaNoH/8uPICUnZliztJQ5LT/8HrBaN67HtoPi1e00WxWUjlVXIKElWkGDpnmCAg2/o5mP8WpIjF2lXFsiz71lPsuyCkqTYMnvulIZc0XCUr/0lrpfwND/HHFGz3smxDTIhxRjWspbUX5p5C49ohw02cmOdOzkXgOQ+to/bxmkjMVSsF3SGj1n7DJYfHs5R4rANmlpl8NhEUHKTZv0q0uWg9sgPqtXYvwm3EoF+l7szTL1RbPSAPxrFChPW9ddEg8r8k4Qc/r0XxlneimtRDdpJayVuOudTXjrVZhMMo6FpH5Egaj5PZJOlKAeSvSsWlvDlIzCpEm/mWdLEZM7QDE07tW/D/fv2MdXNo3BoH+Jp8EyKdWWrfsz8H3K44gMS1fmZvWyMwtRlS4mF/MHRsdiN7ta+OK/iJdjpP3Z5F4p/31bwboaF+GdY2Cv3g/FYv2RWuPYf6q0vWSj5Wmx6D76NyyFq4f0gCdW5S+J+3HHxbvuM/+SMXqHVmg84zsIjSICkQz4SebNQjG1YPqo0NTx3+P+i/pJBJ0vqp5bAjaNCz1hZsTcpR9rd2dhZTjpRpE1vJHfeEP2zcOw8jeddGvQ234qfk87DeoOy8vGJV0tEDZy19bTiBFaJQufL2/sC3Zo7Hwh5f0isbFPaIRFODelz1pm9sP5Cr23ine+WkZRcozVSDSuzYQ90l2aBgThOHdo3B+lyjTD5Z0t1vtqgxGWcfkMl/CYJR17MM7YQVYAbkCDEbJdfFFq8yPMBhltERFg1G0AsE3t4rIUXtSnf/9w7gjbcvILjl444ZUW9o97dXSGqXiG/dRHNbsDZFddrutWb0ifHb3YTSoU5a2Tz8JRYIa8nxTZJx0/2d2mqtXqzz41TiNVf+V/r5iP3+0iDC1+vn99k3KOaWl6/pEc0M7NQw7NxdTxzn+/OnLfyLw9Df1pOP1jXowiq4fFykLxwjojaJPVUTp3fokPro1RUmxWBHzVaU5GIzywJqyl74H01hyiCtglLrxunXr4uKLL1YiSdWvXx8xMTEoKSlBcnKyAuSsX79egV0ohZ4VC0XAGjp0KAjGov0TjEWRnghoIjhm//79+PXXX7Fnzx6vbj8gIAC9e/fGkCFD0LhxY0RGRipRrQoKChQdCW5asWIFli5dqujr1c04mZxsThBThw4dQOAV6Ubw14EDB7B3715FKzpu3rzZ53t1cit82U4BBqPsxDA5lb33qwsY1fDDLxHSUfuhMMl0dOrryPhiholiZc1hfYcg7tUPyxrOnOUs+xUpTz2gaScgKvr2BxFx8eUCHnLxA0Lhd06uW4X0t59HUdIBzXxqJbRbb8S/86latR0TLuiKmiGhqD/pFYT26GdrV08I3EqeeDfqP/4SIkYYwcg9A9oJgEpO3AfEN0bdeycgrM8g1JAAquoa9keCegi2OvbRmzZgy/46nTsCowJbtkW9R58FwVgOi4C+jn74JjK+nOmwW3nAqMhrxiH6rkddunfSOfW5R1FyMtfhfugi2SnmvokIbN7KaV+lg7jXHDE/Pa9mz4drE52dvRiMspbdZL7E6mBUccEpLHl3O/6ZvRcElDgqTbvHYMRTnZUPA10Fo35/YytWfWKEI810IWhn2Xs7sOn7RAFCFTjaju1ak/PqYsAdbdGyX31bG52sFCDUH285jsCqGXCmMnJyF5x3VekfS/6cuhPL3t+h6da8Vz3c9El/HN2XjQVPb8DBjWXwldrx0hfPQ5fLmuD9S37HEdHPvrQeFIvrp/axb4IjMCquQyTmT1qvgGKaQboKfftv4D3tMOjudgpAprtsq26Ytx8Ln95oq6snDy0ebgPC1Db9cf03+/Dj5E36Zjyy7GIFytrwrZj7GePchgG6hqEPdkD/O9oorXuWp+Lzu1bpegDjZg8APYOOCsFL309cp0Bqjvqp1wjQG/18N4RFBalN0uO3j6zBtl+SNNe6Xt4Uo1/opsBQC57aoIB4mg66yjkXxmPYIx0R2dAxoKAbVmlVBqMqTWqnC8l8CYNRWtlWbDuBF+YewGoBilLKCWelrgClbhrWAI9d1USkJXD+x/cZvyRj5i8pCijjbG66TlAUwVGTb2yG6Aj5H7rXCajo/Mc2G6ZL/qov9qXmYewrO5CY6vgLFFcMqIf3722F0DMQFu1z/LQEnHLgv4lVunZIfUy+oZkCMhk2IBpGPbUFfwrQyL48eHkj3H9pQzz44R4s/Mf5l2XaNQ7F3MfPQcs4xx+oeApGEVD2zOz9+GBhklOb1w7zx5R7WmFMP8c+Q73fr5alYcoPSdghwChXCkFnd10SJ/7FMyClE4zBKJ0gPqzKfAmDUT40CC/NCrACLinAYJRLMlVKJ5kfYTDKKL03wChaJUtAPC/8UBfz10c4/dnXuCuIlHclGDfwBO4cmgH/ms5/YaL7eO1HWi/caYo82XpqW48WeXj3plREhzsPprErOQjj59YDHd0pwzvn4KWr0/HAZw2wfGflgVHF4pbu+SQWy3Y4/5uODIyiezxwNBAvL4jG0u1hHtmV5qDf70Z0ycbL16SLL4M4ty2NqW6FwSgPLC576XswjSWHuANGWfIGeFOsACvgtgIMRjmXTPbery5gVJ0rb0TMA5MMIuXv2IJDd1xpaNc3mEFFKU/ch5zlZRFFCIpq8OzbqDXoQv0ULtWLj6bj8P03ovDgfkN/MzAq8aqhiHv9YwQ2aWEYQw2eglEBDZug4Xtz4B+j/RBeuoikMWf5YqQ+8yBOS6IDmoFRmT9+i9ojndvDfjmC09JefsIUSPIEjKKIVfWfeBm1Bgy1X8rpOUWNSplwJ4pSk037EjBXb8ILSrQt004mFygyV9J9Y1F0+KBJj6rZzGCUtewq8yVmAJAVdk7RdAgiIcDH1eInIjBc+Ni5WPSi8cNdWcQod8CoAhGFg9LdUUQidwtFA7r8le7oOKKRbag3wSgCxGbdKCL0mcBbFQVGDb63Pf75bA/yRQQQV0ur/g0w5vXuCImQf7tw7ZcJ+Pl5o/1cAaPWzE2Q2t7XYBRBff98thdL3tkOgv3cKQRFjZzcFe2GxpkOMwOjIhuFKWuaDtRdIJvc++MwhMcE6674vspglO9toO5A5ksYjFLVAb75Kx33vLtb/MHe/T8CDxDRo759ugNCAs3hqMdnJgj45nDZgm6cERz04/Pnop4kup0ZGPXNkx1w0+s7kFcg/zKGfnmKzLToxU5467tDmPyZ8fcifX+1TpGtfn2pkxTkkYFR4y6MxdLNGTggomW5WsJD/fDxA22VqE1mYzwBoygS1s2v7cSaXdrIfWZrqO2PX9sEj1/TRK1Kjy9+kYhXv/bs94dbhEZv391Kqql0sWrQyGCUdYws8yUMRlnHPrwTVoAVkCvAYJRcF1+0yvwIg1FGS+QW1kSPSc2kMNH1fTMx+YojxkFutOw4HIT3fo3Cit2hoHRszgqlkRs36ARu6J+JsCDXfr+wn/NIlh9m/RWJL/+OAEV1cqVECghrdPdsXNkzE61j3QuiQrDRe79HY/qSOiKyruP7a1y3CHeen4GrRGpAKrdOi5OCUZTG78+nDxi2frKwBrpPai611XV9MvHsla7ZavnOMLy1KAo7hW3Mvp8SK/awXLIHdVMJaYHKPS/YGCEiB6utjo90X1f2ysblPbIQ6yAal+NZqsdVBqM8sLPspe/BNJYcwmCUJc3Cm2IFvKoAg1HO5ZW996sLGOUXGY1m81dIYZTEKwY7BFlEXho0//FvQwQjSoe3b1Q/Af6U/jCsQFHPvyNgmmHOjeGgB6X2O3DTKJwSafrsixkYlb99s5KKzb6v/bknYJQCRb3/uUgb51roVPv17M+zF/+E1MmP2Dcp52ZglKGjiw2FB/Yh6Z7rcCozwzDCXTCKomTFT5mlpD80TOZCA9kt+fF7kL/N+IE8QVEEXJWnUMrFQ3dd6zT1YnnWsNpYBqOsZRGZL7EqGHUyowDvXvw78jLd+6OFI8XLA0ZRpKjp1yxzOdKPbB8ER1GKtnMubKhc9hYYRSnRslJP4oRIN2hWKgqMMpvfWTtFJbpxZn9ECXBHX6oaGEUp9+bcvhL7Vqfrb9Wteq+xLTH8iU7SMTIwiiCn/OxCt7/lR1Gqrvugj3QdXzYyGOVL9bVry3wJg1GlGs1ZnIr73v/P7f/v7BUedG4pHCVLtTZhRgI+/NEzKEpdo7VIP/fXm10MqfXMwKhgAWnli3Rt7pSOzcKwdb9r0Y3s5yWI59aLjKlsZWCU/Th3zydd1xQTrm4sHeYuGLVqe6YSTetYluuAsP3CFDXqwwfagHTWl4kCgpvqIQSnznX7xXF4886WarXaHxmMss4jIPMlDEZZxz68E1aAFZArwGCUXBdftMr8CINRvrBE6Zp5AsD6Z08w/j0QjKPZ/jgm0rIRuBQTUYzGdYvRVEBDTeoWol18ofgSiHu/W8juiubeKSI5JR/3x+EM8U+kf0s5ESASa5xGg9rFIhLtKcSKY8PoIvRsmYcAP/e/tGK/LkFRu5MDse1QMLYfDsTBowFo0aAIRwWo1Vis0aNFPvq3zbXUFxIItCJdSCuyT6B/CWoFl6BurRKRer3YYfpC9d6PZfvhv5SgMxr7I1lonHLCT+gJBX4iAKq++NdU2LZbs3xL3b96D1Y8MhjlgVVkL30PprHkEAajLGkW3hQr4FUFGIxyLq/svV9dwChSJ+61j5WUcHqljr7/CjK+mqVvttVDuvZEw3c/s9XVk8yF3yD9tafUKsJ6DUDcG9Ntdf1J4f49KExMUCIb+UVGIaRzD9QMNX6YS+NSn38M2b8t0ExhBkZpOkkqnoBR9Z98FREXXSqZDUp6vPxtG1GclipSUp1CYONmCG53rohxavxD/OniYuy76DyU5Odp5nIVjDqVlYmCPTsE0OYv1uiIGkHm0Scopd7RD17TrEMVd8GouNenIaz3QMM81EBpAgv27MLpwgIEtTkHfnWi5P3E/SaOGawBtQica/rtUvjXa2AcI/KjFOzbg4L/tsNPRKsKatvBYaSu43M+xrGP3zLOU0VbGIyylmFlvsSqYBSl/tr4XaKpgAEiTU/DTlGo6V9TgZUIpHJWygNGbRSp8xY8uUG6BEX0adwlGsECREnbk4m03Zk4VST/Q09tkd7moSUXK38s2PRDIha98K9tzsK8Ytu5ekLp5wKC/dWqchw+qRMoTRoVWSo95YKT/3gLjAoM9UeDtnUQHO6PpC0ZcGSX9hfE4+opvQw79SYYtWtJMr6bsE44xNJlZZrTlcAQreaD/9cefW5upQxyN5XeP7P34NdXt5QuKPlvkEipFH9ulBJJKllESSt2ACDcPGsAmvWMMcwiA6P0nYLDAxDbvg5CRaSYo4k5ynOq76PWx37cFxTZy0qFwSjrWEPmSxiMggIPdbh9LdJPGIFefwHGdm5RC+2bhCEtoxCb9uZI+6lWnv1YO1zWV/v/+vr/sjFkvDFVqDqmQ9MwtIoPRYSIinQkswgrt2Ui66TRr1B/igJ1UXftz8JmYJQ6Px0jxDu+W6twUOSlnQdzseew9vcE+77255TajaJVFQjfSMCUTCPqHx8dhJ2f9LQfqpy7AkaRv1TXSTpSINbJMf2GNKV3WPP+eWgjIDF9cQeMImCs273rcShdHrWqcb1gnCNsTnbYlJCDk/nyr1tfKVIQznykrWYrlLawy93rpGkIKd1ijzYRaFo/GIkiYhY9T2a2pkk3TO0ung3HKQQ1i1fhCoNR1jGuzJcwGGUd+/BOWAFWQK4Ag1FyXXzRKvMjDEb5whK8JivACrirAINR7iom+ste+h5MY8khDEZZ0iy8KVbAqwowGOVcXtl7vzqBUeHnX6ykudMrRRGXDt15tb7ZVo958EnUueIGW109SbrvBuRtXqtWEfPQU6gzZqytrp5QWry0lyYaIgjV8PdH9O0PIfL629SutmPWou/FmMdtdTpxFYyi9ID5O/4FRVHyi6gjIk8dBUFcZukA9wxoJ4gfuw/fxScCzReuAkXZ0pesX37AsY/eRPExbdhV/3qxiH3hXQS3F4CUrhx+5FacXLNS0+oMjKL5U5+8H3lbN9rG1QgIQFjfIag/6RXUDDF+AHG6IB/7rzwfFHHLvrgDRoX27I/4N2fYD1fOCew6+v6ryJz/peZarf5DRQSol1AzvLamnSrHP/sIx6a9bWsngKzJF7/a6uoJpU9MmfQ/0HNoXyiFIaXcI+BOX4qSDiDxmgv0zVW2zmCUtUwr8yVWBKOSthzHjGuXSSNu1IkLVVLSNewcBT8BRamFovHMe3Qtco+bA1LlAaPMwJPB97XHgDvbigCF4lPWM4WgqB2/HwbBXUWSD0Fv/3KwAnWp/dUjpemjcfaFIio98NtF9k2ac1fAKILImnaPQXzHSNQSKdKyUvNAUYEaChjn/Ut+xxFdqsLWg2Jx/VRtxKDDW49j2tXLNGvbV2gNgq3OuTAeNegTZ1EEN4rUXSfw3fi1hjXoOn2Ifee88xHbrg5VbcWbYJRtkTMnC5/ZiA3f7tc0U6SliatHatrsK+6AUTlH85XIZwU5xkgiUY1riWf5PGEXAfideX4ozd7elWn44Yn10vSE9VpG4O4fhtr6q/syez7pOs19/gPnoO+tbRTN1TG7liZj/hMbkJdlhDgoReKge8XPGBYqDEZZxxgyX8JglIBP9mRj8KNGcImiJ82Z0B7NY7VgCqWAu3PKbvy9I9NgXIKiCI6yLy99cQCvfH3Avkk5J/Bm6v2t0aVluOZasYhW9/o3B5Ux9D62L/eOisfLt2pTeTsDo64/vz7euKOlJtIUpfSj1H5mJVT4hqn/a43LRVQk+0Ip9ijVnqykfdMPBP7YF2dg1IXnReHjB9uIbz4H2IZlih4eOD0AAEAASURBVPS3U0V0rZe/NGpGnWQaU7s7YNTr3x7E858n0jBNadsoFNMfaotOAoZTC9njjXnCHmI/+pQW5DbXC3ipZVzZMzL7j1T8T0Qf0xcC2j4SEabs75XsuzkhGze/vgv7hY/Xlyevb4rHrmqsb66WdQajrGN2mS9hMMo69uGdsAKsgFwBBqPkuviiVeZHGIzyhSV4TVaAFXBXAQaj3FVM9Je99D2YxpJDGIyypFl4U6yAVxVgMMq5vLL3fnUCoyjaEAE/NcPK/risqCb+Crx/zCCRmixVKmKz7/8UUX606RiK05Kx/4ohpZ/YnhnV9JvFCIhrpJmDIgwduHGk6dzUmaJRUVQq+1J0+CASrx5m3+QUjCrJO4n0VyYhe8kizTi14ioYRZGZGk2fpw6zHXNXLUPyxLs192y7KE78ouqi+QIBQNGn1Hbl+OwPcWz6FLsWwBEYVbB3F5IfvR0EDMlKsIimRJG5ZNGaTsybgyNTXtAMcxWMoohOjT/7EYFNtB/wEBR16LYxSrQvzcRnKgEN4tBo5vci1WKk5nJJbo7yXJXkZCvtod37Iv7tTzR9qJI5/yukv/GMoZ0aCJ5r+p14/qK1HwTRtYPjLhXRq3bSaZUvDEZZy8QyX2JFMIoAHAJx9CW6SS3cJCLmUNQlWckUHwZSyrIjCVmyyygPGEVp9AjYsi8UVeiJ9aP1r05bl38+24tfXymLCKVe6H1TK1w0wQijegOMqt+6thKVKbqpzn+e2UxFgFG16gbjhml9lUhR6j3aH0+K6Clz71pl0I/6yCCsqgRG/fD4emxeYPxQPq5DJMZ+1BcUbUxW0vdkYc4dK5GVZvyAm54deobsiyMwiiA30llWzJ7Rjhc3UtI+ysb4qo3BKF8pb1xX5ksYjAK+X3lEgCnGn++m3NMKt1wo/38wV8CzrW5ejZw8bSQhAoMS5/TRAEIDH9kkIgOV/myqWiWmdgD+ebcb6olIcGbl6he245d12jTfFL1q+VtdNUMcgVE3XxCLd+/VvnfUwSMmbcGKbSfUquYoi3yldjCDneh+CPayL2Z9qc89AvJ66ZYWpqkgCDB6cOoeQ+Ql+rVn5dvdQOCafXEVjEo5XqhEdNJHgRrQsQ7mPd1BmhqP1vl13XFc9cI2+yWV87HnN1AAN/UCAVcEXunL4lc7o0fbCH2zUt9xIBe97jdGtyQ9SVcuIurZ6OUGGfjvUQZJKqVB5ksYjKoU6XkRVoAVKIcCDEaVQ7wKHirzIwxGVbDIPB0rwAp4RQEGozyQVfbS92AaSw5hMMqSZuFNsQJeVYD/EOVcXtl7vzqBUaSQGRx05N2XcOKb2QYRCcJpNOM7Q3vG3Ok4+uEbtvaA2IYiTdoSW109yf7jR6Q++6halR7rP/EyIi6+XHONoh7tG9VX0+YoYtTpokIcvOVyULo+s2J27/qIUWbQUvKEu5G7aqnZ9AoQ1fKPzagRHKzpc+Lbz3DknRc1bWZrUKeke65D3hbjH+PtJwjrfz7iXp5q36Sckw77Lu4JgsTU4ioYFX7hKDR46nV1mO1o9mzYOoiT2iOvVKI72bfR+bHp7+D47NJ9mj1LhYcScfCmUUp6Pv14qodfOBohnbQfQpwuLMSxGe8qqf1kY6paG4NR1rKozJdYDYwiEOTNwUZIlKIQ3b/oAlCUHUcl4e90fHbbCmmX8oBRBKlQJB99uf0rEf1JRF6SlbzMQix+2/jhZ8t+DdBuaJxhSEWDUbSvmz8dIFLx+RnWUhsqAoy65Oku6H5Nc3VK6ZEieb099BdpBK17Fw4DRUJSS1UBo+hZfmvIIkPkM7LHw0uGIzRSDkWpOhzcdAwzr/9TrdqONG7CqktsdToxA6PaDonDte/31vS1r1CEqpd7LjSk72vQprYSmcq+r6/PGYzytQXK1pf5EgajgKWbMnDp5K1lQp05o2hJn45vZ2hXG2b+moIt+3LUqnKsFeIHivITElhTqR/PLkKzG/4xvE8cAUvqhJNm7cN785PUqnJs2iAYWz7uoWkzA6MiRWrUTR9210Qosh/4yW8pCnhk30bntMbmj0T6ce33LmzdaE+0N3354vFzcEmvaE2zGRjVRKSS2/xRd/iZLXJmlsemJ+Cjnw5r5qTKVQPrYcbDbTXtroJRj3y8F9MXJWvGkr1Wv9dNSemnuaCr3PbWLnzzl/aLJAEiuh/dSyORfo/Kuz8k4clPjfo8NbYpxl/ZWDdjWfWFuYlKKsWyFqBRTBAedTDGvm9VP2cwyjoWlvkSBqOsYx/eCSvACsgVYDBKrosvWmV+hMEoX1iC12QFWAF3FWAwyl3FRH/ZS9+DaSw5hMEoS5qFN8UKeFUBBqOcyyt771c3MCqkSw80fG+OQSxK2ZZ097WG9ug7H1aiG+kvHLjxEhTuK4OQagQEIqBRE303kdbtGE6d0EYHse/kF1EbjT9dKCJSNbBvVtLBuQNGZXw1S6R6e0Uzh77iKhhFkZ/86mijH9FcRSIl4OniYv20tnpYvyGIe+VDW109cQeMMrODOpftKL6e3eTzRSK6k/FDdH0kJVfBqJgHJqHOlTfalqATsp1iB/tUg5oeZypiP82+XQp/ET3KvlBKwP2j+ylNFP2pxe8bUSPQ+CF2cWoyjk5/G7nLF2ugLvu5qvM5g1HWsr7Ml1gNjPr3x4P4fsI6g3CtBjRQIuwYLkgaZgiY5JCASvSlPGDU0vd24K8PjZFAAkP90f+ONuhxbQsE26Xw0a/tSr2iwahbPx+Ixl3rOly6vGBUreggPLR4OPyDzOErdQM/P78Ja780fsg75rUeOPeSRmo30ScBPz+vTVFKF2kdSqXoqKyZm4BFLxrHPrLsYkTUN0Ya82YqPQLpCKjTF4LICCZzpcy4TjzLm43P8vjlI0CRutRiBka59AyM/MMQZS2yYRge/P0idXpLHBmMsoQZlE3IfAmDUcCJnGI0Gfu3AV4i0QZ3isTkG5sa0t25atUikYZtT1LZlwfUcQ2iAk2BJepTWHxaSQ1HkYTsiztg1JUD6mHmI23th2vOf99wHFc8Z4SA7xgRp6Te03S2q/y55QQIeNIXApUIWLIvZmDUm3e2xO0Xa3+Gtx+nnh9Kz0enu9aB0tnZl3aNQ7HmvfPsm1xOpScDqG4bHoe37mqpmU9WoXR3ne40/qzz0JhGePbGZsqQVdszMfwJY9RJinR1zaD6ePyaJgp8Jpuf28wVYDDKXJvKviLzJQxGVbYVeD1WgBVwVwEGo9xVzHv9ZX6EwSjv6c0zswKsQMUpwGCUB1rKXvoeTGPJIQxGWdIsvClWwKsKMBjlXF7Ze7+6gVGUq6jZPAGw1Nf98ZvS6V02wJC+rcncXwzwDaV6O3jzaOeCy3rU9ENAbDwCm7VEcLtzUWfM9ahZqyzChTrEnYhRJSdzkXjFYJzKylSHS4+uglHSwZLGGsEhCGzcHEHNWyG090CEDxluSKNHw9wBo9JenIisX36QrGZsqn3ptaj36GTDhZSn7kfOst9s7a6CUfFTZiH0vD62cXSS+/efSH7sTk2bWaXBM28gfNhIw+V9l/S2wXGNPv4awed0NvRRGwg8y9++GXmb1yF/5xbk79iiQHLq9ep6ZDDKWpaX+RKrgVF/vLkVK2f+ZxDu+g/7ovVALYhq6HSmYeP3iVjwpDF6XXnAqP/+SsXcu1eZLYmaItJDfMcoNOsZo0SQihfRmggacqdUJBglS1En20t5wag+41rhwvHnyqY2tB07kIN3h5e949UOQ/7XHgPvLoumUlXAqH9m78Gvrxo/9L9/0YUwS22oaqIet/+ahG8eXqNWbcebRUpJetbUYgZGPb5mlFNgb+49f+O/P1PUqZQjg1EaObiiU0DmSxiMKhWp693rsDfZmAJTlTBWgEyDO0eiV7sIdGsVgfZNQp1GO1LHunqk1G47D53Exj3ZeFdEZTqQlm8Y6g4Y9bSIUOQo2hCtM+jRTYY1nrupGR68vAx61XdYuysLQycYQVZXwSiKEpX8dV9bVC39/Pr6ja/uwPy/j2qaKcJT6jf9NClxZcDTwHPr4Mfny3xdieCrYq9aibzCEs180x9qi6sHaaEuTQe7Sptxq0Hp+OwLPRsLnu2oNJEd46/925AC0L5/y7gQDBFjKLVet1bhaB4borkX+758XqoAg1HWeRJkvoTBKOvYh3fCCrACcgUYjJLr4otWmR9hMMoXluA1WQFWwF0FGIxyVzHRX/bS92AaSw5hMMqSZuFNsQJeVYDBKOfyyt771Q6MEjKZRYE6MuUFnJhXFk2KohERGKUvR6e+jowvZuibDfVAAQwFt+mAwKYtBFzVAgGNmwkoqiFqBAQY+uob3AGj8jauQdL92khH+vmo7ikYRZGOQjqdJ2CuVuJeWiqgWEDDJvCvK/5gT183dlLcAaMoahdFjXKlBLfriEbT5xm6Hv3oTWR8Ps3W7ioY1WzBSvhHl31AbJugnCdJ941VQCeahtIhxr05A6Spq6XwQAJOrl6BnBWLbfO4Oraq9GMwylqWlPkSq4FRC5/eiA3z9huEo9RhzlKPqYMS1x7BrJuXq1XbsTxg1KniEsy5fSX2rzlim8/ZCaX9a9mvPlr1b6AcCZ5yVCoSjLp4Umf0vL6Fo+WUa+UFoy55RqTRu9oYAdBs4Ze6L0BBrjaCYefRTUC2UUtVAaNk0aiCwvzxxDrXAe3jh3LxzoW/qtLYjiOe6qxEKVMbZGAURZSiyFLOyjcPrcb237QpphiMcqZa9b4u8yUMRpU+Ewv/OQoCcAiccaWEitSaAzrWxvldopT0cfFuALVHMouUFHy7BQS1W0ST2ns4DwkpeQK2KZBGrbLfjztg1OzH2uGyvuY/Z29OyFGiLNnPT+fOIKEt+3PQ70Hj7w6uglEN6wZhx8ye+mVN6299dwiTPzP+fLHrk56Is9PdFTDKLOITLR5T2/nvi9SP7KcvZP+dYj9qeeXrA3jpiwNq1ekxOiJARCerg6FdozCiZzRqC5/DRasAg1FaPXxZk/kSBqN8aRFemxVgBVxRgMEoV1SqnD4yP8JgVOVoz6uwAqxA+RRgMMoD/WQvfQ+mseSQDh06oHHjxoa95eTkYPly4wccho7cwAqwAmedAgxGOTeZ7L1fHcEoApUoDZu+UJQegljUEnXDnQpEpdaVo0iptn/MIBQfSdM0q5WaoWGIGH4ZIkaMQVDr9mqz20d3wKjMhV8j/bWnna7hLhgVKECu2qOvQfiFo0RqvSin85t1cAeM2n/5QBSnp5pNpWn3qx2J5j+v1rRRJeuneUh7ZZKt3RUwqmZ4BFr8YkxFYZukHCeHH74VJ9eWpUGiZ6P+xBddgsr0y+b9ux7Hpr8jAKm1+ktVus5glLXMK/MlVgOjvrr/H+xcnKwRzl9EdHhq82WaNkeVE4dP4u1hRji2PGAUrZefXYSZIk1f+t4sR8tLr0U3qaVEReo4opESXUrWqSLBqBum9VNgLNk69m3lBaPGftxXAb/s53R0/uFli5G6WxslsVGXaNw2d5BtWFUBo2aO/QsHN2qjk9RvXRv3zB9qu1dnJwTkvdBlPkp06Z8IeiP4TS0yMKp2bCgeXjJc7WJ6ZDDKVBq+YKKAzJcwGFUm1nsiStOkWfvKGlw8C/SvgRuHxeKRKxvBDJCiVHC/rDuGOYtT8ceGDIfRhBwt6w4YNffx9hjZyzwtqxkY9en4dri8nzlQtS0xF30eMEZ3dBWM6t2+Nn57uZOj29Rc+37lEdz8+k5NG1UWvdgJ/TrUtrW7AkYtWnsM17y43Tamok4IZDr0hTYK7l3v7MYXS+W/vzpaN0Kk+r13dDzuHRUPOudSqgCDUdZ5EmS+hMEo69iHd8IKsAJyBRiMkuvii1aZH2EwyheW4DVZAVbAXQUYjHJXMdFf9tL3YBoewgqwAqyAJRRgMMq5GWTv/eoIRpFSjWd+j6A252hFE9DTvkv721KXNZrxHYLbdtD0cRSdqWatcMS/PUukyCtNXaAZaFYRKfxkUZfcAaOOfvAaMr6cabaCrd0dMIoiRFFko5oiXZ7LxeRe3AGjEoZ1QUneSdeWFNGqWq3YZeibu2IJkh+/x9buChhFEbCafvW7bUxFniTdd4MBZApq1Q7Rt96PsH5D3F9K6JzyzEPIWWoENtyf7OwYwWCUtewk8yVWA6O+uPdv7F6mTesVICJqPLnxUpfFJIDp5Z4LDf3LC0bRhEUitc26r/Zh5YzdyBVROdwtnUY2xmWvdJe5D1QkGPXAbxchqlGY0+2VF4y67YtBaNQ52uk6aoePrliClB0n1KpypH3SftVSVcCo9y75HUf3Zau3pRybdKuLW+YM1LQ5q8iibHW8uBGueKOHbSiDUTYp+KQSFJD5EgajtMKv252FF0Skn2WbM7QXXKjVqeWPxa92RuuGoZreRQKKGvvyDgWM0lxwUKEAsfRjvr5UBTDqou5R+OZJ7e97+vu0r1M0r7Gv7LBvUs71AJcrYNSnv6fg/g/2GOYqb0O9OoHYO7uXYZqfVh/Dy18lYuv+XMM1Zw1txHP0h3ie6LniAjAYZZ2nQOZLGIyyjn14J6wAKyBXgMEouS6+aJX5EQajfGEJXpMVYAXcVYDBKHcVE/1lL30PpuEhrAArwApYQgEGo5ybQfber65gVJ0rb0TMA2VRhVT10t98Fpk/fAH/erFo9v2farPtmPbyE8j6+TtbXT2pGRKK+CkCijqnLPKCek09ni4qQlHyIRQdPiD+ieOhROSKSEL1HnoKoT37q92UoztgVOrzjyH7twWa8bKKq2BUcIfOiH/rE1D0K7NSkpOFwkN0HweVf4WJCcj7d53Q7C/DEHfAqANjR6Awca9hDlmDX1RdNF+4ynApc/5XSH/jGVu7K2BUjcAgtFy8GahZ0zZOPSFbeFrovXTojqtQnKaNXKPOF9ioKUJ7DVDsTzAaPUeulNNFhUr6xPytm1zpftb3YTDKWiaU+RKrgVG/vPQvVn+ufZdQxKgnN10mhYlkCqfvycIHo/8wXKoIMEqdlACpff+kY++qNCT8nYZjiTnqJafHAXe0xfkP6gBfMaoiwahJG0YjMMT5h6DlBaOuntIL7S+Id3rPaoeply5G2n/aiFGNu9bFrZ+XwUJVBYz6/K5V2LNcG0kxUkBgD9pBYKouZkdKO0hglL7onyEGo/QKcd2bCsh8CYNRcsV3HMjFHxszsHRTBlbvykReQYm8o661Ub1gLHu9MwiUoUKRom56bSd+XG3+s21QQE00axAs/oWgeWwwWsSFYJhIqfbkp/uw4G/tuKoARnVqXgsr3u6qU868Om/FEdzyhjFi1K8i6lQfEX1KLa6AUWTPSydvVYfYjgSiqTazNbpx0q5RKBY+f650BAFuawVwt0Q8T4s3Hce/IoUhwXKuFIqu9aOYl6KSVffCYJR1ngCZL2Ewyjr24Z2wAqyAXAEGo+S6+KJV5kcYjPKFJXhNVoAVcFcBBqPcVUz0l730PZiGh7ACrAArYAkFGIxybgbZe7+6glF+kdFoNn8Favj5aYTL27QWSf+7AXWuuAExDz6puXa6sAD7RvVFSY42cgN1ovR59Se9oumvVEQUquxlvwrY6kvkb98MAlr0JV5EZiofGDVegFHGqCb6dVwFo2T7oblKsjOR8fWnyBH3U3jAmNqDIma1+HW9flm4A0YlP3YXcv9eZphD1kCRuRpNn2e4dHTq68j4Yoat3RUwijo3/XYpAmK1H8xn//EjUp991DaXV08ElEVpHoPbd0Jot14IPa8P6Dk1K1m/zkfaCxPMLlepdgajrGVOmS+xGhi1Zm6CSGsjYEddeWTZxYio71okPIo4RZGn9KUiwSj93HmZhTi8NUNJnZbwdzqSt2cY0p+pY/zEh9dPrBsNAr7sy9kIRl3waEf0vaW1/W04PKdIXhTRy750Ht0EZBu1mIJRfwxHnXjHEOqfU3di2fvGiCBmz8/CZzZiw7f71aWVY0hEICauHqlps68Q7ETQk76Mmz0ATbuXpY367bUt+PvTPZpufv4E+V1qmk5R01lU0kTawaki/aC+XP5qd1D0MbUwGKUqwcfKUEDmSxiMcq48wU07DuZi/X/Z+OvfE/hzSwYysotNB750S3PcN7qhcv3nNcdw7UvG1G1+NWvgyoH1MO6CBujWOkIKvtzw6o4qCUbJ0s6ZiikuvPNDEp4SkJi+7PqkJ+Kig2zNroBRB9Pz0eH2tbYx6sm8pzvggm5RatWrx/zCEvy7LwcUnWyZeJ5WbjvhELxb8FxHDO4U6dU9nQ2TMxhlHSvJfAmDUdaxD++EFWAF5AowGCXXxRetMj/CYJQvLMFrsgKsgLsKMBjlrmKiv+yl78E0PIQVYAVYAUsowGCUczPI3vvVFYwiteJe+xhhfQZphSsR0TtG90fss28jpGtPzTUCglKeekDTplbqjX8WtUdfo1ZtxyNvP48T331uq8tO4t/+BKHd+2ouuRcxqgLBKPEV5Ra/rEXNWhGa/VCEqIO3XYGipAOadvuKX0RtNF9k/OO+O2AUAU0ENrlSosbdq6Sj0/dNmfQ/5PxVlhbPVTAq/q2ZCO3RTzNd/q5tOHTbGE1bpVWELWr1H4q6/5sogK3SD7Ts1yZbJF5zgX1TlT1nMMpappX5EquBUWbQyZVv9kSH4cb/n2QK//TcJiXdnf6aN8Eo/VrZR/KxZMo2bJ5/QJrG6La5IgVdFy1AeTaCUe2HxePqd4xpf/R6UD1l5wl8NGaJ4dLge9tj0L3tbO3rvt6Hn541RtW74+vBiO/o+APnhU8L0GmeFnSiiX0BRtE+aD/6csO0fmjZr76+WVpfMX03Fr+9zXDtzm+GIK5D2QfcDEYZJOIGLyog8yUMRrkveIkI9vPtX+l4evY+pBw3fgFjdJ+6mDOhvTLxM5/tx9vfHTIsMvX+1hh7fgNDu30DpY+jNHL2pSpEjKL72TC1O1rFuwZNX/7sViwW0ZbsS7AAlNO+6aeJSOkKGEW2a3DVShCcZF9eubUF7hml/bKG/XVvntNePvzxMF775iByRVRLfXniuiaYeHUTfXO1qzMYZR2Ty3wJg1HWsQ/vhBVgBeQKMBgl18UXrTI/wmCULyzBa7ICrIC7CjAY5a5ior/spe/BNDyEFWAFWAFLKMBglHMzyN771RmMCj//YjQQAJS+HJs+RQA3/xNp1bTRpFIevxc5Kxbruyv1xrN/RFALbbQLSjOXePUwaX9bo4gS1Pyn1SCoyL74CowKbNoSTT7/2X4ryvnx2R+CdHFUQnv2Q/ybMw1d3AGjSvJOIvGKwTiVecIwj31DDX9/NP3uT/hHl0XVUK8fHHcpCvaUpbhwFYyKESkN64wZq05TehT5JpT59u7StktqkWPvMABueZvX4visD5Te9Sa8gFoDhmpGns7PU56R08XFmnb7il/tOmj23V+oERxs36ycJwzvLiJ5ZRnaq1oDg1HWsqjMl1gNjDq6PxvvjSgDJFUF4ztG4o6vh6hV0yNFbnpz8CJQqjt98RSMOpKQhW8eWqOfDkMf6oA2g2MN7fYNsqhBdP3Cx85Fn5tb2XeVptJzlnrNLEJSZaXSqyGildy7YChiWmihXM2NnanMn7Qem34wQrqXvyKiH40qi360a2kyvrzvH8MUrqTt+/iqpUjepv3gmyZyB4wKDg/A42tGGdZXG8zgPX3EqIObjmHm9X+qw2zH5r3q4aZP+tvqZienikrw9rBfkC0ik+jLpPUiVWJoWapEBqP0CnHdmwrIfAmDUcDd7+7Gxj3a6LRtGobiszNwk5lNDon/xzvdtU5Jl2ffh6IYUTQjKsOf+BertmvTkHZoGoa/3+lmP0R63vGOtTiQpn2PVBUw6prB9THtwTbS+7Zv3HM4D+fdu84AKrcW9ln/QVnEQhrjChhF/XrdvwGUKtG+dGsdLlIgdrFvMj2fMCMBR05ogbjbLo6zpfUbNmEzsk5qf88Y0bMunh7b1HROuvDHhuMY85wRqB0mIll9JyJaVffCYJR1ngCZL2Ewyjr24Z2wAqyAXAEGo+S6+KJV5kcYjPKFJXhNVoAVcFcBBqPcVUz0l730PZiGh7ACrAArYAkFGIxybgbZe786g1E1goLRfOEq1Ayr5VS8U1mZ2D+6r0iFp03dowwUcFOrP7cLkEqbzsiVaEMhXXqg4XtzDOv7Cowyg8WOvv8qMr76xLBP+wazqFnugFE0nytRo+pceSNiHphkv7xyTrrtHzNYk7LQVTAq/MLRaPDUa4Y5c1ctQ/KEuwzt9g3+deuh6TeLUSOwLIUGXc9e/BNSJz+idI15+GnUufx6+2HKedL9NyJvoxGWsO9Izwg9K/rCYJReEa5XhgIyX2I1MKpEpBqaImCQzNQ8gyQ3Tu+HFn0dR9qh6DoUZUdWPAWjKPrTGwN/NkzZ5bImuPRF7Qeq+k4HNhzFJzf8pW/GsEc6ot+tWihXFjGqVt1gjF8+wjBebfA1GEX76HBRQ1z5VumH9+q+9MeMQ7l4f+TvKNZF16jpVwMP/HqRJkWeWfq43je2xEUTO+mnttUT1x3BrJuW2+r2J+6AUZTq8Ol/L7Mfrjl3FYwqyClSIL2CXO0H2zTZLZ8NRJPz6mrm1VdWf74Xv7z0r74ZDdrUxt0/aGFdBqMMMnGDFxWQ+RIGo8T/12/sxLwVRzTKC3YU++b0RpQALh2VgY9swqa9WqiqXp1A7J3dSxkWd80q5ORpgd8hXSIxf3JHR9Ni16GT6HHfekOfqgJGUSrBdQJsahnnOGrUXe/sxhdL0ww63DY8Dm/d1VLT7ioYdc+7/+HzJamasVT58olzMKJntKHdvmHJpgxcNnmrfZNy/tWkc3Bxj9KxZDeyn31pWDcIO2Y69rfiuyGod+VKFAi41r4M7hyJBc86fl7s+1fVcwajrGNZmS9hMMo69uGdsAKsgFwBBqPkuviiVeZHGIzyhSV4TVaAFXBXAQaj3FVM9Je99D2YhoewAqwAK2AJBRiMcm4G2Xu/OoNRpFj9x19CxIgxTsXLXPAV0l9/xrRfs/krQHCMpoi0fAdvHaOJXmR/PahVO1AaPb86xpQ+JSdzkXBBV/vuCO3WG/HvfKppo0rq8xWXSi+k03lo+MFcwxr5O7bgsAB4SkSEI1mJvOYW1L1vguwSMn/8FumvPqm5FnXDnYi+82FNm30lY+50HP3oTRi+ki06UVSnmAfFfCLVnL7QmIzPp2maXQWjKEJYk9kLENhMG32FJiO46+gHr0IW2YnSDsZPmYXgtsZvTyfdcx3ytmxQ9hM+9BI0mCzuSVcK9+1B0n3Xg+A7WaGoWBTFq2a4NqqY7BmRja8KbRwxylpWlPkSq4FRpNj6b/bjx8nGFGQUIeead3ujRR/dO/uMzH9+sBPLPthhKrqnYBRNOOWCX5GRpI0MERDsB0qL5ghw+evDnVj6nnFPstSA8x5di62LtKmS6HX5yLIRCK9njDxH+7ICGEX76H5Nc1w8qbN4HRvf7xRxa/atK6SRj869pDHGvNadprAVAope6rHQVldPSG+CqGRaELw2965VSro+tb/90QyM+vn5TVj75T77rsr5fT8OM42C5SoYRRP9/ekeUNQwfQkMoWe5lynot2ZugoCiNstcqRJtiqJO2RcGo+zV4HNvKyDzJQxGAR//nIzx0/Ya5L9yQD1Mf7gtCJKSlaOZRTjn9jXIK9CCLPbRh7rcvQ4Jydqf5UOCamLTh91BkaVkJeloAUY9tQV7deOob2xUIHbPKoWu1LHrdmfh/Mc2q1Xbce7j7TGylznIuTkhR4myZBtw5uTT8e1web8YfbOtvi0xF30eKP1Z29YoTmYIra4aqH3H0X38uUUelTZe3P/XT56Dc5sbvzBDkND46XsxTdhGXwiqIv0IErMvroJRB0Wkr273rDcASPUjA5UUiL3aySMpJqbmKxHADh8rsF8WDWOCsHVaD9C+qNz/wR58+nuKpg9VnrmhGR65opGhXW1YuysLQ0W0KX25aVgDvHefFsjW96kOdQajrGNlmS9hMMo69uGdsAKsgFwBBqPkuviiVeZHGIzyhSV4TVaAFXBXAQaj3FVM9Je99D2YhoewAqwAK2AJBRiMcm4G2Xu/uoNRZhGb9Gom3Xs98v41flNa7Rf74nuoNfACtWo7ns7Px/HPP0bOX3+g6NB+UJQqSldHMFbEBaOk6dHUwRRJKF+sSX+Mh4CsKgOMqhEcgha/bUANP20aQdpT4f49yJg7A7lrV+LUieMK0EUgVZ3LrkNIV/NvHdO4pP8JqCo3xxbJyRkYReudFOtkL/65FCw6dQq0Vmiv/iDASFZKcrOx//JByjr2110Go8Sg0B4iHeBbM+2H287zt25C5sKvkb97G4qSDipp/MJ6D0Sda29FQGy8rZ96UpDwHw7eNFKtwr9eLJp9/6etbn9CaRdPzJuD3JVLUXxEfGtcUAyBjZsh5Lw+iLrxblA6PX3JXbEEyY/fo2+uknUGo6xlVpkvsSIYdaq4REmnR1GG9MXPvyb63d4GLXrXA6XXKxRpZg6sP4rtvx/G1p+1UJF+bHnAqO8nrsO/Cw/qp0RQmD9639QKXS5raot6RFGvkrdnYOO8RGyYt98whu7hocXDDYDPb69vwd+z9hj6x7avg57Xt0R4TDAIAIo7pw7qty4FLq0CRtGmm/WMQY9rW6BRl2iERQUpGiSuO4pVM3fjpC5dEPUn6Oue+cNQr5Xxw2NKh5iVpoUAaEztBiG45OkuaCbAIP8gP2QcysGhzccV+Cj3uPZDZuqvFjMwavm0XVgyZbvazXaMaR6OPuNaI6J+CHKO5aOeSBUY1yFSue4OGEXP8oeXLsaRfdm2udUTeg76jGuF5uJZbtQ5GsUFp0ARxnYtSREpBxPVbprjORfG46q3tTADdWAwSiMTV7ysgMyXMBgFbNmfg34PGqFeMgdFd7p/dEP061gHgf6l4EuyAGMoctBznyciLUObUo3GPDymESbf2IxOcceU3fhqmTHiUUztADx7UzMlypAalSrpSAE+X5qKGYtSkC559yoTiv/8+3F3NBPvVLWcrWAU7Z8gscevaYIBQl8CpI4I2IxSD377Vzp+WXdMvUXNkYC1mY+01bRRxVUwivo+O2c/3pxn/NkjQEDCj17VGMO6RoFSHgYH1gQBcF/9mYYp3ydJ7fKUSJE3/srGNK1SvhT2vlPYXVauG1Ifd4i0e51a1LKBVJQu8Oc1R/HyVwcMkB3N8Ym41yvEPVf3wmCUdZ4AmS9hMMo69uGdsAKsgFwBBqPkuviiVeZHGIzyhSV4TVaAFXBXAQaj3FVM9Je99D2YhoewAqwAK2AJBRiMcm4G2Xu/uoNR9Ilqs3lL4V8/zlTA4tRk7L9yiDR6kToo8rrbUPee8Wq14o4lJUh55iHkLPu1UsAo2njjT75HUOtzKu4eaCZxH1T2DGinHF0Bo5SObvzn+Gcf4di0tw0j3AGjaHDcax8jrM8gwzzuNJwuLMDhR25D3qa1mmFmAJ2mkwuV0wIUoyhTBGtVh8JglLWsLPMlVgSjSLXN8w/ghyfMoVbqQ2CNAqBSxYVSHjDq0OZj+PTm5YZUcPbLEqgTIj6kPik+4D6lS2Fj36/blc0w6lltZEG6vnqOSJ32sjF1mv1YOh85uQvOu6q50mwlMMp+nzVExIvTJUQHm5c2g2Nx3Qd9pB0oYtKiF40RL9TONL+fgAv0qfnU6/qjGRj1748H8f2EdfruhvrQBzug/x1tlHZ3wCgasO+fdCVilmFSuwZXnmWKmPW/ny9A7dhQu5GlpwxGGSThBi8qIPMlDEaJH5nFK2/001vwl0lkIzIJ/b9OAFOhgCazT2pT49mbLDzUD+veP88WDWrGL8l4+CNjNCp1DM1bW4C6BSJdaZ4uZanaR3+kyERR4f6Y/lBbBdw6m8Eo+3ujgEtO3I9ih7/f6YZzmoTZD1XO3QGjKL0hRfOSgW3qxKRzYEANKayk9iF46teXOyFCRMZUy4mcYlCKxf2S1MJqH9WGuSLa2Ml88+eJUg2uFc+TvySqozpXdTkyGGUdS8t8CYNR1rEP74QVYAXkCjAYJdfFF60yP8JglC8swWuyAqyAuwowGOWuYqK/7KXvwTQ8hBVgBVgBSyjAYJRzM8je+9UejBKyUUo3AnXMyvE5H+PYx2+ZXVbaa4aEouFHXyOoRcWnFkh56oFKBaMoMlP8lE9RIyDA4T27fVHAUc7AKIqwVSM42O2ps5csQtqLE0FAkr64C0YRJBf7wrsIbtdRP5VLdUq3l/LEvcj9+09Df4rI1fC9OR7PTROeLipC6tMPImfFYsP8VbWBwShrWVbmS6wKRhFUs+Sd7Vg5Y7db8BMpTmnKCvOKDeKXB4yiybb8dAjfPaaFJg2LOGnocFFDXC5Sx1G0IH3JTDmJdy76zSFURWOsBEZRRCVZZCf9venrDTtFKVAURZaSFQLL3rvkdxERyhg1TNZfbQutEyiNTmUGRlEkqynDfkFBrvF5UeekY3nAKBr/z+w9WPz2NpdBLhpjX0Ijg3DpC91AMJmsMBglU4XbvKWAzJcwGFWqdqZ4lwwV6eh2J530WH4Cp36Y3AFdWobb5iDYafgT/2LjHmP0OVsnD0/mPd0BF3SLwtkIRgUF1DSksnMmA0Xsel+klLtmcH1pV3fAKJpg+dYTuPXNXQ7hKOlCZxpbxYcIKKozKPqXvlAUqPMf2wSCpDwtrRuGYuFzHW2QnafzVJVxDEZZx5IyX8JglHXswzthBVgBuQIMRsl18UWrzI8wGOULS/CarAAr4K4CDEa5q5joL3vpezAND2EFWAFWwBIKMBjl3Ayy9z6DUeLD76Yt0OTzRaYCHhg7AoWJe02vqxconVqj6fOUFHNqm7NjUdIBZHw9C/UeegqoaUxfR+MrG4yiNSnVX/3HX6JTlwulditKPYw6V94oH+MEjCpOT8HRD99E/UmvoIZ/2Ted5ZOVtWZ8Pg1HCVwzCfniLhhFM1Mqwahb7isF5kzsUraDsjNKMZj+2tPIWf5HWaPuzC+qLuLfmOZRVC4Cx5In3YuTa1bqZq3aVQajrGVfmS+xKhilKrdraTJ+eHw98rOL1CaHRwKOxrzeHb+89K+Sds6+c3nBKJrr70/3KMAWpT1zt3S5rAlGPddNuAwRzsKk/P76Vqya9Z/J1dJmK4FRd3w9GHPv/huO0tjpb6b9BfG4/JXuoAhIjsr+NUeUFHGuzk3QEM1Nz4u+mIFR1G/FtN1YPGWbfoimXl4wiiZL35OF70R0qtRdJzRzO6u0HhSL0c93Q61oOURG4xmMcqYiX69IBWS+hMGoMoUPpOXjiue2eQRH1Y8MxIJnO6K9JJJRyvFCDH50EygFn6uFoJjHREq3+97/D/kmkaTOVjCqs0gj98gVjXHnOyJdq4NoSfZa1anlj7mPt0f/DsZU12o/d8EoGncsq0jR+Oc18rR96tz6Y7fW4Zg7sb1DaGnltkyMe2OnR+BVx2ZhmP/suVLoSr+X6lJnMMo6lpb5EgajrGMf3gkrwArIFWAwSq6LL1plfoTBKF9YgtdkBVgBdxVgMMpdxUR/2Uvfg2l4CCvACrACllCAwSjnZpC99xmMKtWt8UyRPq6NMX1cwZ6dODjuUufinunhVycKkdfeitqXXweKImVWSrIzcXz2hzjx3edKBKCom+5G9O0PSrurYFTwOZ3R6OOvDX1Snx+P7N8WGtr1DTEPPok6V9ygaSaQZ99IkYJIAhUFtz8XUePuQ1jvgZox+krBfztw5P1XkLdxjXLP8VNmgfZqKHZgFMFTMQ9M0nTJ37UNh24bg8AmzRFz/ySE9uhLP6xo+thXCKQ6NvM9ZP38nX2z4Txq3L2IvvV+TXtJfh72XdIbp8XRUQnu2EWB1pylFjx1/CgyvpiBE/O/cjqnul5oz36Iuv4OhHTtqTaZHgv370Hmj98KOy/AqcwTpv2q6gUGo6xlWZkvsToYRQoeP5iDH5/dhMS1R1BySp6ejV45TbrHYMSkzqjXKgLvi2hDR/ZpI2tc9VZPnCMiNtmXpe/twF8f7rRvQkhEICauHqlps68QqLP6s71Y+2WCU2ArqFYAzh3RCF3HNEVch0j7aUzPdy9LUeCrtP8ypX0oDR+l46Oy6pP/8PsbWzX9KGLWxDUjpVGpNB1F5aMxS5CyU/tu6jSqsQIu2fdN252JqZcttm9SwKaJ/4xUoiAtfXc7Nny732FEJNK15w0tMOie9o5chGYN0vqn5zZh5x+HZe5O6UvAUP872qLn2JZK2rrPbluhmYPS7o1fPgJm0amo877V6fjjzW1I2ZEhXWfYwx3Q77bSVHoEbH06brlmDaqMmz0ATcUz6KicEumz/pq6E+u/2e8UJotsGKak7+t2RamtHc07f9J6bPrhgKYLpdx7eMlwTZus8s1Dq7H9t8OaS7T2g79fpGnzdeWZ9safGfh3CN9YReZLGIzS2oJ+PCdI5u3vDymRmLRXjbVe7SJw07BYXN4vBiFBxoiC6ogMETnogwVJ+PCnww5T8UVHBGDiNU1w60WxSvq0qQsPY+LMBHUazVEFo7bsz0G/BzdqrlGFQKKRveoa2tWGzQk5IJhIXz4d3065H327Wj+Uno8Od6w1vHPV/aj96DjqqS34U5eikMCo5W91RdLRAjz96T4s/OeoSFEo/xmB5ujdvjbeu7cVCBZzVC6YuBmrd2ZpuozuUxdzJrTXtMkqn/6egte+PqjsSXZdbevZNgITrm6MoV2j1CaHxwIRRfHLZWl454ckJCQ7/h2I0utRBLCbLmigHDl9nlZaBqO0eviyJvMlDEb50iK8NivACriiAINRrqhUOX1kfoTBqMrRnldhBViB8inAYJQH+sle+h5Mw0NYAVaAFbCEAvyhhnMzyN77DEY5182THn616yC4fScENGyCgPjGIgKRSMmUlIiiA/tQKP4VpSUDAhSyL5TCLaTzeQpURBGLitNTkb9zK/I2r5OmiLMf681zApWCWrZV7oX2WJKbXXoPdC8H9xlBHRFhKahVW3Ev3RHUrBVK8k6i6FAi8rZsQMHeXS5v1a92JELP640Asb5feG3UDA3DKQGUFR9JAwFrpIteQ5cnd7Ojf70GYi994B/TAH6RUagRFIxiYUOK+FUo7q1w3x4BuBW6OWtp94C4RqXPSYM4kL7+0TE4lZMt7jNVPAMpQrsDbunm0SYsPojBKGsZSOZLzgYwSlWRIJm9K9OQmXoSOUfyFQiHoJg68WFo2a8+KK1bZRZK10dRgDKTT+KE+Eep8ErEh7LhYh+1G4QgQvxr1DnaaWQksz1TlCy6z4KTxQpIRJBVrbrBCApzPTKf2dzeaC8SETsObjyGw9uOIy+zEAXZxcq9kx4xzcPRom99+Aeaf+DvaE+kRcqOE0jenqGAcqeFGyZ967eujdYDxftdpFOqiEIp9bLT85TUeoK1A2keJp6xYJHaqiILpYpM2nJc3M8J5BzNxykRyaW48BRCRCpAsnGTbnVRr2VERS551s/FYJR1TCjzJQxGmdtnrwBZElPzcPBIAQgGOpJZBEqXF183CPHi/dK+SSiax7rnvyhl39pdWdiXkoeEFPEOEe+UlnEhCvTTWqRmaxgTbABQD4tIU/9sz8Sa3VkoFr6K+lDEoj4CGKL0clYujsAodd85eaewdHOGEqkrXaRJLSg8jXp1AhAndB7cqQ6aCZ9RWWXr/lwBV2WC9nFU2NtPRIpsLtYnO1PqvBbCVp4UYWbsOJCLQ+Jng4MiMhk9U1niWaBIY3Sf9Dx1EsBYA1HnIleAwSi5Lr5olfkSBqN8YQlekxVgBdxRgMEod9Tybl+ZH2Ewyrua8+ysACtQMQowGOWBjrKXvgfT8BBWgBVgBSyhAINRzs0ge+8zGOVcN+7BCrACvlWAwSjf6q9fXeZLziYwSn8/XGcFWIHqowCDUdaxtcyXMBhlHftUxZ24AkZVxfvme6p4BRiMqnhNPZ1R5ksYjPJUTR7HCrAClaUAg1GVpbTzdWR+hMEo57pxD1aAFfC9AgxGeWAD2Uvfg2l4CCvACrACllCAwSjnZpC99xmMcq4b92AFWAHfKsBglG/1168u8yUMRulV4jorwApYUQEGo6xjFZkvYTDKOvapijthMKoqWtU398RglG90l60q8yUMRsmU4jZWgBWwkgIMRlnHGjI/wmCUdezDO2EFWAFzBRiMMtfG9IrspW/amS+wAqwAK2BxBRiMcm4g2XufwSjnunEPVoAV8K0CDEb5Vn/96jJfwmCUXiWuswKsgBUVYDDKOlaR+RIGo6xjn6q4EwajqqJVfXNPDEb5RnfZqjJfwmCUTCluYwVYASspwGCUdawh8yMMRlnHPrwTVoAVMFeAwShzbUyvyF76pp35AivACrACFleAwSjnBpK99xmMcq4b92AFWAHfKsBglG/1168u8yUMRulV4jorwApYUQEGo6xjFZkvYTDKOvapijthMKoqWtU398RglG90l60q8yUMRsmU4jZWgBWwkgIMRlnHGjI/wmCUdezDO2EFWAFzBRiMMtfG9IrspW/amS+wAqwAK2BxBRiMcm4g2XufwSjnunEPVoAV8K0CDEb5Vn/96jJfwmCUXiWuswKsgBUVYDDKOlaR+RIGo6xjn6q4EwajqqJVfXNPDEb5RnfZqjJfwmCUTCluYwVYASspwGCUdawh8yMMRlnHPrwTVoAVMFeAwShzbUyvyF76pp35AivACrACFleAwSjnBpK99xmMcq4b92AFWAHfKsBglG/1168u8yUMRulV4jorwApYUQEGo6xjFZkvYTDKOvapijthMKoqWtU398RglG90l60q8yUMRsmU4jZWgBWwkgIMRlnHGjI/wmCUdezDO2EFWAFzBRiMMtfG9IrspW/amS+wAqwAK2BxBRiMcm4g2XufwSjnunEPVoAV8K0CDEb5Vn/96jJfwmCUXiWuswKsgBUVYDDKOlaR+RIGo6xjn6q4EwajqqJVfXNPDEb5RnfZqjJfwmCUTCluYwVYASspwGCUdawh8yMMRlnHPrwTVoAVMFeAwShzbUyvyF76pp35AivACrACFleAwSjnBpK99xmMcq4b92AFWAHfKsBglG/1168u8yUMRulV4jorwApYUQEGo6xjFZkvYTDKOvapijv5ec0xHD5WoLm181qFo6v4x4UVcEcBBqPcUcu7fWW+hMEo72rOs7MCrED5FWAwqvwaVtQMMj/CYFRFqcvzsAKsgDcVYDDKA3VlL30PpuEhrAArwApYQgEGo5ybQfbeZzDKuW7cgxVgBXyrAINRvtVfv7rMlzAYpVeJ66wAK2BFBRiMso5VZL6EwSjr2Id3wgqwAuYKMBhlrk1lX5H5EgajKtsKvB4rwAq4qwCDUe4q5r3+Mj/CYJT39OaZWQFWoOIUYDDKAy1lL30PpuEhrAArwApYQgEGo5ybQfbeZzDKuW7cgxVgBXyrAINRvtVfv7rMlzAYpVeJ66wAK2BFBRiMso5VZL6EwSjr2Id3wgqwAuYKMBhlrk1lX5H5EgajKtsKvB4rwAq4qwCDUe4q5r3+Mj/CYJT39OaZWQFWoOIUYDDKAy1lL30PpuEhrAArwApYQgEGo5ybQfbeZzDKuW7cgxVgBXyrAINRvtVfv7rMlzAYpVeJ66wAK2BFBRiMso5VZL6EwSjr2Id3wgqwAuYKMBhlrk1lX5H5EgajKtsKvB4rwAq4qwCDUe4q5r3+Mj/CYJT39OaZWQFWoOIUYDDKAy1lL30PpuEhrAArwApYQgEGo5ybQfbeZzDKuW7cgxVgBXyrAINRvtVfv7rMlzAYpVeJ66wAK2BFBRiMso5VZL6EwSjr2Id3wgqwAuYKMBhlrk1lX5H5EgajKtsKvB4rwAq4qwCDUe4q5r3+Mj/CYJT39OaZWQFWoOIUYDDKAy1lL30PpuEhrAArwApYQgEGo5ybQfbeZzDKuW7cgxVgBXyrAINRvtVfv7rMlzAYpVeJ66wAK2BFBRiMso5VZL6EwSjr2Id3wgqwAuYKMBhlrk1lX5H5EgajKtsKvB4rwAq4qwCDUe4q5r3+Mj/CYJT39OaZWQFWoOIUYDDKAy1lL30PpuEhrAArwApYQgEGo5ybQfbeZzDKuW7cgxVgBXyrAINRvtVfv7rMlzAYpVeJ66wAK2BFBRiMso5VZL6EwSjr2Id3wgqwAuYKMBhlrk1lX5H5EgajKtsKvB4rwAq4qwCDUe4q5r3+Mj/CYJT39OaZWQFWoOIUYDDKAy1lL30PpuEhrAArwApYQgEGo5ybQfbeZzDKuW7cgxVgBXyrAINRvtVfv7rMlzAYpVeJ66wAK2BFBRiMso5VZL6EwSjr2Id3wgqwAuYKMBhlrk1lX5H5EgajKtsKvB4rwAq4qwCDUe4q5r3+Mj/CYJT39OaZWQFWoOIUYDDKAy1lL30PpuEhrAArwApYQgEGo5ybQfbeZzDKuW7cgxVgBXyrAINRvtVfv7rMlzAYpVeJ66wAK2BFBRiMso5VZL6EwSjr2Id3wgqwAuYKMBhlrk1lX5H5EgajKtsKvB4rwAq4qwCDUe4q5r3+Mj/CYJT39OaZWQFWoOIUYDDKAy1lL30PpuEhrAArwApYQgEGo5ybQfbeZzDKuW7cgxVgBXyrAINRvtVfv7rMlzAYpVeJ66wAK2BFBRiMso5VZL6EwSjr2Id3wgqwAuYKMBhlrk1lX5H5EgajKtsKvB4rwAq4qwCDUe4q5r3+Mj/CYJT39OaZWQFWoOIUYDDKAy1lL30PpuEhrAArwApYQgEGo5ybQfbeZzDKuW7cgxVgBXyrAINRvtVfv7rMlzAYpVeJ66wAK2BFBRiMso5VZL6EwSjr2Id3wgqwAuYKMBhlrk1lX5H5EgajKtsKvB4rwAq4qwCDUe4q5r3+Mj/CYJT39OaZWQFWoOIUYDDKAy1lL30PpuEhrAArwApYQgEGo5ybQfbeZzDKuW7cgxVgBXyrAINRvtVfv7rMlzAYpVeJ66wAK2BFBRiMso5VZL6EwSjr2Id3wgqwAuYKMBhlrk1lX5H5EgajKtsKvB4rwAq4qwCDUe4q5r3+Mj/CYJT39OaZWQFWoOIUYDDKAy1lL30PpuEhrAArwApYQgEGo5ybQfbeZzDKuW7cgxVgBXyrAINRvtVfv7rMlzAYpVeJ66wAK2BFBRiMso5VZL6EwSjr2Id3wgqwAuYKMBhlrk1lX5H5EgajKtsKvB4rwAq4qwCDUe4q5r3+Mj/CYJT39OaZWQFWoOIUYDCq4rTkmVgBVoAVYAWqqAKyH/YZjKqixubbYgWqkAIMRlnLmDJfwmCUtWzEu2EFWAG5AgxGyXXxRavMlzAY5QtL8JqsACvgrgIMRrmrmPf6y3wJg1He05tnZgVYgYpRgMGoitGxImaR+REGoypCWZ6DFWAFvK0Ag1HeVpjnZwVYAVaAFTjrFZD9sM9g1FlvVr4BVqDKK8BglLVMLPMlDEZZy0a8G1aAFZArwGCUXBdftMp8CYNRvrAEr8kKsALuKsBglLuKea+/zJcwGOU9vXlmVoAVqBgFGIyqGB0rYhaZH2EwqiKU5TlYAVbA2wowGOVthXl+VoAVYAVYgbNeAdkP+wxGnfVm5RtgBaq8AgxGWcvEMl/CYJS1bMS7YQVYAbkCDEbJdfFFq8yXMBjlC0vwmqwAK+CuAgxGuauY9/rLfAmDUd7Tm2dmBViBilGAwaiK0bEiZpH5EQajKkJZnoMVYAW8rQCDUd5WmOdnBVgBVoAVOOsVkP2wz2DUWW9WvgFWoMorwGCUtUws8yUMRlnLRrwbVoAVkCvAYJRcF1+0ynwJg1G+sASvyQqwAu4qwGCUu4p5r7/MlzAY5T29eWZWgBWoGAUYjKoYHStiFpkfYTCqIpTlOVgBVsDbCjAY5W2FeX5WgBVgBViBs14B2Q/7DEad9WblG2AFqrzmtOMvAAAMRElEQVQCDEZZy8QyX8JglLVsxLthBVgBuQIMRsl18UWrzJcwGOULS/CarAAr4K4CDEa5q5j3+st8CYNR3tObZ2YFWIGKUYDBqIrRsSJmkfmRipiX52AFWAFWwBcKnD592hfLVuqaNcRNVv27rFRJeTFWgBVgBaquAvzDftW1Ld8ZK1DdFOAfgX1ncfYlvtOeV2YFWIGKV4D9ScVr6sqM7EtcUYn7sAKswNmiAPsS31iKfYlvdOdVWQFWoOIVYD9S8Zq6MiP7EVdU4j6sACtwtihQHXwJg1Fny9PI+2QFWAFWwAIK8A/7FjACb4EVYAUqRIHq8IN+hQjlhUnYl3hBVJ6SFWAFfKYA+xPfSM++xDe686qsACvgHQXYl3hHV2ezsi9xphBfZwVYgbNFAfYjvrEU+xHf6M6rsgKsgHcUqA6+hMEo7zw7PCsrwAqwAlVSAf5hv0qalW+KFaiWClSHH/Stalj2JVa1DO+LFWAFPFGA/YknqpV/DPuS8mvIM7ACrIB1FGBf4htbsC/xje68KivAClS8AuxHKl5TV2ZkP+KKStyHFWAFzhYFqoMvYTDqbHkaeZ+sACvAClhAAf5h3wJG4C2wAqxAhShQHX7QrxChvDAJ+xIviMpTsgKsgM8UYH/iG+nZl/hGd16VFWAFvKMA+xLv6OpsVvYlzhTi66wAK3C2KMB+xDeWYj/iG915VVaAFfCOAtXBlzAY5Z1nh2dlBVgBVqBKKsA/7FdJs/JNsQLVUoHq8IO+VQ3LvsSqluF9sQKsgCcKsD/xRLXyj2FfUn4NeQZWgBWwjgLsS3xjC/YlvtGdV2UFWIGKV4D9SMVryjOyAqwAK8AKVD0FGIyqejblO2IFWAFWgBVgBVgBVoAVYAVYAVaAFWAFWAFWgBVgBVgBVoAVYAVYAVaAFWAFWAFWgBVgBVgBVoAVYAWqvQIMRlX7R4AFYAVYAVaAFWAFWAFWgBVgBVgBVoAVYAVYAVaAFWAF/t+uHRQAAAAQEOvfWo+zCMYTAQIECBAgQIAAAQIECBAgQIBAT8AxqtepRAQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgTuBRyj7icAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgEBPwDGq16lEBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBO4FHKPuJwCAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAQE/AMarXqUQECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE7gUco+4nAIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIBAT8AxqtepRAQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgTuBRyj7icAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgEBPwDGq16lEBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBO4FHKPuJwCAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAQE/AMarXqUQECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE7gUco+4nAIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIBAT8AxqtepRAQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgTuBRyj7icAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgEBPwDGq16lEBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBO4FHKPuJwCAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAQE/AMarXqUQECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE7gUco+4nAIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIBAT8AxqtepRAQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgTuBRyj7icAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgEBPwDGq16lEBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBO4FHKPuJwCAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAQE/AMarXqUQECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE7gUco+4nAIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIBAT8AxqtepRAQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgTuBRyj7icAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgEBPwDGq16lEBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBO4FHKPuJwCAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAQE/AMarXqUQECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE7gUco+4nAIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIBAT8AxqtepRAQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgTuBRyj7icAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgEBPwDGq16lEBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBO4FHKPuJwCAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAQE/AMarXqUQECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE7gUco+4nAIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIBAT8AxqtepRAQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgTuBRyj7icAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgEBPwDGq16lEBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBO4FHKPuJwCAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAQE/AMarXqUQECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE7gUco+4nAIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIBAT8AxqtepRAQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgTuBRyj7icAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgEBPwDGq16lEBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBO4FHKPuJwCAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAQE/AMarXqUQECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE7gUco+4nAIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIBAT8AxqtepRAQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgTuBRyj7icAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgAABAgQIECBAgEBPwDGq16lEBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBO4FHKPuJwCAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAAAECBAgQIECAQE/AMarXqUQECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIE7gUGAAxM8a/Gt7oAAAAASUVORK5CYII="
    }
   },
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #ffbb99; width: 800px; height: 30px; padding: 10px; border: 3px solid #ccc;\">\n",
    "    <span style=\"color: #331100; font-weight: bold;\"><h2>Steps in Monte Carlo Simulation</h2></span>\n",
    "</div>\n",
    "\n",
    "![image-2.png](attachment:image-2.png)\n",
    "\n",
    "The general steps involved in performing a Monte Carlo simulation are as follows:\n",
    "\n",
    "- **Define the problem:** Clearly define the problem you want to solve or analyze using Monte Carlo simulation.\n",
    "- **Identify random variables:** Identify the uncertain or random variables that affect the problem.\n",
    "- **Specify probability distributions:** Assign probability distributions to the random variables based on available data or expert knowledge.\n",
    "- **Generate random samples:** Generate random samples from the specified probability distributions.\n",
    "- **Perform simulations:** Perform simulations by evaluating the system or process using the generated random samples.\n",
    "- **Analyze results:** Analyze the results of the simulations to draw conclusions or estimate unknown quantities."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #f0f0f0; padding: 10px; border: 1px solid #ccc;\">\n",
    "    <strong>Explore More Complex Applications:</strong>\n",
    "    <ul>\n",
    "        <li>Gradually move on to more complex simulations involving multiple variables and distributions.</li>\n",
    "        <li>Study how to model systems with uncertain parameters and propagate uncertainty through simulations.</li>\n",
    "    </ul>\n",
    "    <strong>Learn Variance Reduction Techniques:</strong>\n",
    "    <ul>\n",
    "        <li>Study techniques like importance sampling, stratified sampling, and control variates to reduce the variance and improve the efficiency of your simulations.</li>\n",
    "    </ul>\n",
    "    <strong>Dive into Advanced Topics:</strong>\n",
    "    <ul>\n",
    "        <li>Once you have a solid understanding of the basics, explore advanced topics such as Markov Chain Monte Carlo (MCMC) methods and their applications.</li>\n",
    "    </ul>   \n",
    "    <strong>Practice and Experiment:</strong>\n",
    "    <ul>\n",
    "        <li>Work on practical projects and exercises to reinforce your understanding.</li>\n",
    "        <li>Experiment with different scenarios and distributions to gain hands-on experience.</li>\n",
    "    </ul>\n",
    "    <strong>Utilize Resources:</strong>\n",
    "    <ul>\n",
    "        <li>Make use of online tutorials, textbooks, and courses specifically focused on Monte Carlo simulation.</li>\n",
    "        <li>Refer to resources like books, online forums, and research papers for in-depth understanding and application.</li>\n",
    "    </ul>   \n",
    "    <strong>Join Communities:</strong>\n",
    "    <ul>\n",
    "        <li>Engage with communities of practitioners and researchers in fields related to Monte Carlo simulation.</li>\n",
    "        <li>Participate in discussions, ask questions, and share your knowledge and findings.</li>\n",
    "    </ul>\n",
    "</div>\n",
    "\n",
    "Remember, learning Monte Carlo simulation is a gradual process, so be patient and persistent. It's an incredibly versatile tool that can provide valuable insights into complex systems. Best of luck on your learning journey!"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #ffbb99; width: 800px; height: 30px; padding: 10px; border: 3px solid #ccc;\">\n",
    "    <span style=\"color: #331100; font-weight: bold;\"><h2>Statistics</h2></span>\n",
    "</div>"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #99ccff; width: 800px; height: 30px; padding: 10px; border: 3px solid #ccc;\">\n",
    "    <span style=\"color: #331100; font-weight: bold;\"><h3>1. Understand the Basics statistics</h3></span>\n",
    "</div>\n",
    "\n",
    "1. **Probability:**\n",
    "    \n",
    "    Probability is a measure of the likelihood of an event occurring. It quantifies the uncertainty associated with different outcomes in a given situation. Probability values range from 0 (impossible event) to 1 (certain event). In statistics, probabilities are often expressed as percentages or decimal values between 0 and 1. The probability of an event A is denoted as $P(A)$.\n",
    "\n",
    "    Example Formula: $\\boxed{P(A) = \\frac{\\text{Number of favorable outcomes}}{\\text{Total number of possible outcomes}}}$\n",
    "\n",
    "2. **Random Variables:**\n",
    "    \n",
    "    A random variable is a variable whose value is determined by the outcome of a random phenomenon or an uncertain event. It assigns a numerical value to each possible outcome of the event. Random variables can be classified as discrete or continuous, depending on whether their possible values form a countable set (e.g., integers) or an uncountable set (e.g., real numbers).\n",
    "\n",
    "    Example: Let X be a random variable representing the number obtained by rolling a fair six-sided die. X can take on values {1, 2, 3, 4, 5, 6}.\n",
    "\n",
    "3. **Mean:**\n",
    "\n",
    "    The mean, also known as the average, is a measure of central tendency. It represents the sum of all values divided by the total number of values. In probability and statistics, the mean of a random variable is often denoted by the symbol μ. It provides an estimate of the \"typical\" value or central value around which the data tend to cluster.\n",
    "\n",
    "    - **For a discrete random variable $X$:** $\\boxed{E(X) = \\sum (x*P(X=x))}$, where $x$ represents each value of $X$, and $P(X=x)$ is the probability of $X$ taking that value.\n",
    "    - **For a continuous random variable $X$:** $\\boxed{E(X) = \\int (x * f(x))~ dx}$, where $f(x)$ is the probability density function (PDF) of $X$.\n",
    "\n",
    "4. **Variance:**\n",
    "\n",
    "    Variance measures the spread or variability of a set of values around the mean. It quantifies how the values deviate from the average. A higher variance indicates a greater dispersion, while a lower variance indicates more closely clustered values. In probability and statistics, the variance of a random variable is often denoted by the symbol σ^2.\n",
    "\n",
    "    - **For a discrete random variable X:** $\\boxed{\\text{Var}(X) = \\sum ((x - \\mu)^2 * P(X=x))}$, where $x$ represents each value of $X$, $\\mu$ is the mean of $X$, and $P(X=x)$ is the probability of $X$ taking that value.\n",
    "    - **For a continuous random variable X:**  $\\boxed{\\text{Var}(X) = \\int((x - \\mu)^2 * f(x))~ dx}$, where $\\mu$ is the mean of $X$, and $f(x)$ is the probability density function (PDF) of $X$.\n",
    "\n",
    "Reference: For a more detailed explanation of each, please following github Repository: https://github.com/arunsinp/Statistics-fundamental"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #99ccff; width: 800px; height: 30px; padding: 10px; border: 3px solid #ccc;\">\n",
    "    <span style=\"color: #331100; font-weight: bold;\"><h3>2. Learn Probability Distributions</h3></span>\n",
    "</div>\n",
    "\n",
    "Here are some commonly used probability distributions in Monte Carlo simulations along with their probability density functions (PDF) or probability mass functions (PMF) and formulas:"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2.1. Uniform Distribution:\n",
    "\n",
    "- **PDF:** $\\boxed{f(x) = \\frac{1}{b - a}}$ for $a \\leq x \\leq b$\n",
    "- **Formula:** Generate random numbers uniformly distributed between a and b. \n",
    "- Used when all values within a given range are equally likely.\n",
    "    - **Parameters:** minimum value (a) and maximum value (b).\n",
    "    - **Example function:** `numpy.random.uniform(a, b, size)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define the parameters of the uniform distribution\n",
    "a = 0  # Minimum value\n",
    "b = 10  # Maximum value\n",
    "\n",
    "# Generate x values within the range [a, b]\n",
    "x = np.linspace(a, b, 1000)\n",
    "\n",
    "# Calculate the PDF values for each x\n",
    "pdf_values = np.full_like(x, 1 / (b - a))\n",
    "\n",
    "# Plot the PDF\n",
    "plt.plot(x, pdf_values)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Probability Density')\n",
    "plt.title('Uniform Distribution PDF')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2.2. Normal (Gaussian) Distribution:\n",
    "\n",
    "- **PDF:** $\\boxed{f(x) = \\frac{1}{\\sigma \\sqrt{2\\pi}} ~\\text{exp}\\left(-\\frac{(x-\\mu)^2}{2\\sigma^2}\\right)}$\n",
    "- **Formula:** Generate random numbers according to the normal distribution with mean $\\mu$ and standard deviation $\\sigma$.\n",
    "- Used to model continuous variables with a bell-shaped curve.\n",
    "  - **Parameters:** mean ($\\mu$) and standard deviation ($\\sigma$).\n",
    "  - **Example function:** `numpy.random.normal(mu, sigma, size)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define the parameters of the normal distribution\n",
    "mu = 0  # Mean\n",
    "sigma = 1  # Standard deviation\n",
    "\n",
    "# Generate x values within a certain range\n",
    "x = np.linspace(mu - 3 * sigma, mu + 3 * sigma, 1000)\n",
    "\n",
    "# Calculate the PDF values for each x\n",
    "pdf_values = np.exp(-(x - mu)**2 / (2 * sigma**2)) / (sigma * np.sqrt(2 * np.pi))\n",
    "\n",
    "# Plot the PDF\n",
    "plt.plot(x, pdf_values)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Probability Density')\n",
    "plt.title('Normal Distribution PDF')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2.3. Exponential Distribution\n",
    "\n",
    "- **PDF:** $\\boxed{f(x) = \\lambda * \\text{exp}(-\\lambda x)}$\n",
    "- **Formula:** Generate random numbers according to the exponential distribution with rate $\\lambda$.\n",
    "- Used for modeling the time between events in a Poisson process.\n",
    "    - **Parameter:** rate ($\\lambda$).\n",
    "    - **Example function:** `numpy.random.exponential(scale, size)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define the parameter of the exponential distribution\n",
    "lambda_val = 0.5  # Rate parameter\n",
    "\n",
    "# Generate x values within a certain range\n",
    "x = np.linspace(0, 10, 1000)\n",
    "\n",
    "# Calculate the PDF values for each x\n",
    "pdf_values = lambda_val * np.exp(-lambda_val * x)\n",
    "\n",
    "# Plot the PDF\n",
    "plt.plot(x, pdf_values)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Probability Density')\n",
    "plt.title('Exponential Distribution PDF')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2.4. Poisson Distribution:\n",
    "\n",
    "- **PMF:** $\\boxed{P(x; \\lambda) = \\frac{e^{-\\lambda} * \\lambda^x}{x!}}$\n",
    "- **Formula:** Generate random numbers according to the Poisson distribution with average rate $\\lambda$.\n",
    "- Used for modeling the number of events occurring in a fixed interval of time or space.\n",
    "    - **Parameter:** average rate ($\\lambda$).\n",
    "    - **Example function:** `numpy.random.poisson(lam, size)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.special import factorial\n",
    "\n",
    "# Define the parameter of the Poisson distribution\n",
    "lambda_val = 5  # Average rate\n",
    "\n",
    "# Generate x values within a certain range\n",
    "x = np.arange(0, 21)\n",
    "\n",
    "# Calculate the PMF values for each x\n",
    "pmf_values = np.exp(-lambda_val) * (lambda_val ** x) / factorial(x)\n",
    "\n",
    "# Plot the PMF\n",
    "plt.stem(x, pmf_values)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Probability Mass')\n",
    "plt.title('Poisson Distribution PMF')\n",
    "plt.grid(True)\n",
    "plt.show()\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2.5. Binomial Distribution:\n",
    "\n",
    "- **PMF:** $\\boxed{P(x; n, p) = ^nC_x ~p^x ~ (1 - p)^{n - x}}$\n",
    "- **Formula:** Generate random numbers according to the binomial distribution with parameters $n$ (number of trials) and $p$ (probability of success).\n",
    "- Used for modeling the number of successes in a fixed number of Bernoulli trials.\n",
    "  - **Parameters:** number of trials ($n$) and probability of success ($p$).\n",
    "  - **Example function:** `numpy.random.binomial(n, p, size)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import binom\n",
    "\n",
    "# Define the parameters of the binomial distribution\n",
    "n = 10  # Number of trials\n",
    "p = 0.5  # Probability of success\n",
    "\n",
    "# Generate x values within a certain range\n",
    "x = np.arange(0, n + 1)\n",
    "\n",
    "# Calculate the PMF values for each x\n",
    "pmf_values = binom.pmf(x, n, p)\n",
    "\n",
    "# Plot the PMF\n",
    "plt.stem(x, pmf_values)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Probability Mass')\n",
    "plt.title('Binomial Distribution PMF')\n",
    "plt.grid(True)\n",
    "plt.show()\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2.6. Geometric Distribution:\n",
    "\n",
    "- **PMF:** $\\boxed{P(x; p) = (1 - p)^{x - 1} * p}$\n",
    "- **Formula:** Generate random numbers according to the geometric distribution with probability of success $p$.\n",
    "- Used for modeling the number of trials required to achieve the first success in a sequence of independent Bernoulli trials.\n",
    "    - **Parameter:** probability of success ($p$).\n",
    "    - **Example function:**  `numpy.random.geometric(p, size)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjcAAAHHCAYAAABDUnkqAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/P9b71AAAACXBIWXMAAA9hAAAPYQGoP6dpAABCgklEQVR4nO3deVyU5f7/8feAwAACYsiikeBSRrikJpqaVm5ZFpZLq0blOV+To0aeflopUZrpMbPFND2ZlVl2tDpZHZeD2mpSmqappYZLpaCpoCKLcP/+8DAxATqDAzPcvJ6PB4+Hc8019/2551Lm7XVf9z0WwzAMAQAAmISXuwsAAABwJcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAKesW7dOFotF69atc8v+Fy5cKIvFor1791b7vu69917FxMTYHu/du1cWi0UzZsyo9n1L0hNPPCGLxVIj+wLMhHADVCAzM1PJycm69NJLFRAQoICAAMXFxWnUqFH6/vvv3V2eyyxevFizZs1y2/5Lg1Lpj5+fnyIiItSzZ089/fTTOnz4sEv2k5eXpyeeeMJtgexcPLW2suPi5eWlxo0bq0+fPuXqjImJkcViUa9evSrczvz5823b+fbbb23tpcGtop+5c+dW56GhDqjn7gIAT/PRRx9p6NChqlevnu666y61bdtWXl5e2rlzp9577z3NmTNHmZmZatq0qbtLvWCLFy/Wtm3bNHbsWIdfc8011+j06dPy9fV1WR2jR4/WVVddpeLiYh0+fFhfffWVUlNTNXPmTL377ru67rrrbH3vuece3X777fLz83N4+3l5eUpLS5Mk9ezZ0+HXzZ8/XyUlJQ73r4pz1fb4449r/Pjx1br/c+ndu7eGDRsmwzCUmZmpl19+Wdddd50+/vhj3XDDDbZ+VqtVa9eu1aFDhxQZGWm3jbfeektWq1X5+fkV7mPOnDmqX7++XVtCQoLrDwZ1CuEGKGPPnj26/fbb1bRpU6WnpysqKsru+WnTpunll1+Wl1fdm/TMz8+Xr6+vvLy8ZLVaXbrt7t27a9CgQXZtW7ZsUZ8+fXTbbbdp+/bttrHw9vaWt7e3S/f/Z6dOnVJgYKB8fHyqdT/nU69ePdWr575f05deeqnuvvtu2+OBAweqTZs2mjVrll246dq1q7755hstWbJEY8aMsbX/8ssv+vzzzzVw4EAtW7aswn0MGjRIYWFh1XcQqJPq3m9o4BymT5+uU6dO6bXXXisXbKSzHzajR49WdHS0XfvOnTs1aNAgNWzYUFarVR07dtSHH35Y7vU///yzBg8erIYNGyogIECdO3fWxx9/bNen9FTNu+++q7S0NDVp0kRBQUEaNGiQcnJyVFBQoLFjxyo8PFz169dXUlKSCgoKyu1r0aJF6tChg/z9/dWwYUPdfvvtOnDggO35nj176uOPP9a+fftspwNK15eU1vDOO+/o8ccfV5MmTRQQEKDc3NxK19xs2LBB/fv3V2hoqAIDA9WmTRs9//zzjr715bRt21azZs3S8ePH9dJLL9naK1pz8+2336pv374KCwuTv7+/YmNjdd9990k6u06mUaNGkqS0tDTbsT7xxBOSzq6rqV+/vvbs2aP+/fsrKChId911l+25smtuynruuefUtGlT+fv7q0ePHtq2bZvd8z179qxwlqjsNs9XW0Vrbs6cOaOnnnpKzZs3l5+fn2JiYvToo4+W+zsQExOjm266SV988YU6deokq9WqZs2a6Y033qj4DXdA69atFRYWpszMTLt2q9WqW2+9VYsXL7Zrf/vttxUaGqq+fftWeZ9AVTBzA5Tx0UcfqUWLFk5Ni//www/q2rWrmjRpovHjxyswMFDvvvuuEhMTtWzZMg0cOFCSlJWVpauvvlp5eXkaPXq0LrroIr3++uu6+eabtXTpUlu/UlOnTpW/v7/Gjx+v3bt368UXX5SPj4+8vLx07NgxPfHEE/r666+1cOFCxcbGatKkSbbXTpkyRRMnTtSQIUP0wAMP6PDhw3rxxRd1zTXX6LvvvlODBg302GOPKScnR7/88ouee+45SSp3euCpp56Sr6+vxo0bp4KCgkpPRa1evVo33XSToqKiNGbMGEVGRmrHjh366KOP7P4n76xBgwbp/vvv16pVqzRlypQK+2RnZ6tPnz5q1KiRxo8frwYNGmjv3r167733JEmNGjXSnDlzNHLkSA0cOFC33nqrJKlNmza2bZw5c0Z9+/ZVt27dNGPGDAUEBJyzrjfeeEMnTpzQqFGjlJ+fr+eff17XXXedtm7dqoiICIePz5Ha/uyBBx7Q66+/rkGDBunhhx/Whg0bNHXqVO3YsUPvv/++Xd/du3fb3sPhw4drwYIFuvfee9WhQwddccUVDtdZ6tixYzp27JhatGhR7rk777xTffr00Z49e9S8eXNJZ097Dho06JwzYEePHrV77O3trdDQUKdrA+wYAAzDMIycnBxDkpGYmFjuuWPHjhmHDx+2/eTl5dmeu/76643WrVsb+fn5traSkhLj6quvNlq2bGlrGzt2rCHJ+Pzzz21tJ06cMGJjY42YmBijuLjYMAzDWLt2rSHJiI+PNwoLC21977jjDsNisRg33HCDXW1dunQxmjZtanu8d+9ew9vb25gyZYpdv61btxr16tWza7/xxhvtXluqtIZmzZrZHWvZ59auXWsYhmGcOXPGiI2NNZo2bWocO3bMrm9JSUm5bVe0rX/961+V9mnbtq0RGhpqe/zaa68ZkozMzEzDMAzj/fffNyQZ33zzTaXbOHz4sCHJSE1NLffc8OHDDUnG+PHjK3yu7PuTmZlpSDL8/f2NX375xda+YcMGQ5Lx0EMP2dp69Ohh9OjR47zbPFdtqampRtlf05s3bzYkGQ888IBdv3HjxhmSjDVr1tjamjZtakgyPvvsM1tbdna24efnZzz88MPl9vVnkoz777/fOHz4sJGdnW1s2LDBuP766w1JxrPPPmu3nxtvvNE4c+aMERkZaTz11FOGYRjG9u3bDUnGp59+ahuzsmNUemx//qno7yPgLE5LAf+Tm5srqfzshXT2FEOjRo1sP7Nnz5Z09n+da9as0ZAhQ3TixAkdOXJER44c0e+//66+fftq165d+vXXXyVJn3zyiTp16qRu3brZtlu/fn395S9/0d69e7V9+3a7fQ4bNszuf7wJCQkyDMN2uqVs+4EDB3TmzBlJ0nvvvaeSkhINGTLEVs+RI0cUGRmpli1bau3atQ6/J8OHD5e/v/85+3z33XfKzMzU2LFj1aBBA7vnXHEZc/369XXixIlKny/d50cffaSioqIq72fkyJEO901MTFSTJk1sjzt16qSEhAR98sknVd6/I0q3n5KSYtf+8MMPS1K5U5xxcXHq3r277XGjRo102WWX6eeff3Zof6+++qoaNWqk8PBwJSQk6Msvv1RKSkqFC9C9vb01ZMgQvf3225LOLiSOjo62239Fli1bptWrV9t+3nrrLYdqA86F01LA/wQFBUmSTp48We65V155RSdOnFBWVpbdAsvdu3fLMAxNnDhREydOrHC72dnZatKkifbt21fh6a7LL79ckrRv3z7Fx8fb2i+55BK7fiEhIZJUbr1PSEiISkpKlJOTo4suuki7du2SYRhq2bJlhfU4s0g2Njb2vH327NkjSXa1u9LJkydtY1ORHj166LbbblNaWpqee+459ezZU4mJibrzzjsdvqKqXr16uvjiix2uqaL39tJLL9W7777r8DaqYt++ffLy8ip3WigyMlINGjTQvn377Nr//HdIkkJDQ3Xs2DGH9nfLLbcoOTlZFotFQUFBuuKKKxQYGFhp/zvvvFMvvPCCtmzZosWLF+v2228/b8C95pprWFAMlyPcAP8TEhKiqKiocgtDpT8uTf3zjeNKLxMeN25cpYsmK1qf4IjKrgiqrN0wDFtNFotF//nPfyrsW9HMVGXON2tT3YqKivTTTz+dMzhZLBYtXbpUX3/9tZYvX66VK1fqvvvu07PPPquvv/7aoeP18/Nz+RVwFovFNiZlFRcXu2Tbjjjf35Xzufjiiyu9f01FEhIS1Lx5c40dO1aZmZm68847HX4t4EqEG6CMG2+8Uf/85z+VkZGhTp06nbd/s2bNJJ2dDTnfh0DTpk31448/lmvfuXOn7XlXaN68uQzDUGxsrC699NJz9nXFaaPSxaPbtm1z6oPQEUuXLtXp06cdutqmc+fO6ty5s6ZMmaLFixfrrrvu0jvvvKMHHnjA5Xf53bVrV7m2n376ye7KqtDQ0ApP//x5dsWZ2po2baqSkhLt2rXLNuMnnV2sfvz4cY+499Idd9yhyZMn6/LLL1e7du3cXQ7qKNbcAGU88sgjCggI0H333aesrKxyz//5f7zh4eHq2bOnXnnlFR08eLBc/7J32O3fv78yMjK0fv16W9upU6c0b948xcTEKC4uziXHcOutt8rb21tpaWnl6jUMQ7///rvtcWBgoHJyci5of+3bt1dsbKztsu0/76+qtmzZorFjxyo0NFSjRo2qtN+xY8fK7af0Q7X08ujSq5/+XF9VffDBB7a1VJKUkZGhDRs22N37pXnz5tq5c6fd34EtW7boyy+/tNuWM7X1799fksrdVXrmzJmSzoZzd3vggQeUmpqqZ5991t2loA5j5gYoo2XLllq8eLHuuOMOXXbZZbY7FBv/u0Pr4sWL5eXlZbc+Y/bs2erWrZtat26tESNGqFmzZsrKytL69ev1yy+/aMuWLZKk8ePH6+2339YNN9yg0aNHq2HDhnr99deVmZmpZcuWuey0SPPmzTV58mRNmDBBe/fuVWJiooKCgpSZman3339ff/nLXzRu3DhJUocOHbRkyRKlpKToqquuUv369TVgwACn9ufl5aU5c+ZowIABateunZKSkhQVFaWdO3fqhx9+0MqVK8+7jc8//1z5+fkqLi7W77//ri+//FIffvihQkJC9P7775e7621Zr7/+ul5++WUNHDhQzZs314kTJzR//nwFBwfbwoC/v7/i4uK0ZMkSXXrppWrYsKHi4+OrvE6oRYsW6tatm0aOHKmCggLNmjVLF110kR555BFbn/vuu08zZ85U3759df/99ys7O1tz587VFVdcYVu87mxtbdu21fDhwzVv3jwdP35cPXr0UEZGhl5//XUlJibq2muvrdLxuFLTpk1t9+kB3MYt12gBHm737t3GyJEjjRYtWhhWq9Xw9/c3WrVqZfzf//2fsXnz5nL99+zZYwwbNsyIjIw0fHx8jCZNmhg33XSTsXTp0nL9Bg0aZDRo0MCwWq1Gp06djI8++siuT2WXR1d0Oa1h/HFJ7eHDh+3aly1bZnTr1s0IDAw0AgMDjVatWhmjRo0yfvzxR1ufkydPGnfeeafRoEEDu8twz3WJ9p8vBS/1xRdfGL179zaCgoKMwMBAo02bNsaLL75Y8Rv8p22V/vj4+BiNGjUyrrnmGmPKlClGdnZ2udf8+VLwTZs2GXfccYdxySWXGH5+fkZ4eLhx0003Gd9++63d67766iujQ4cOhq+vr92l18OHDzcCAwMrrK+yS8H/8Y9/GM8++6wRHR1t+Pn5Gd27dze2bNlS7vWLFi0ymjVrZvj6+hrt2rUzVq5cWW6b56rtz5eCG4ZhFBUVGWlpaUZsbKzh4+NjREdHGxMmTLC7FYFh/HGJ9p9Vdon6n0kyRo0add5+le2nrHNdCv7nv7eAK1gM4wLmjQEAADwMa24AAICpEG4AAICpEG4AAICpEG4AAICpEG4AAICpEG4AAICp1Lmb+JWUlOi3335TUFCQy2/JDgAAqodhGDpx4oQaN2583pue1rlw89tvv5X7VmUAAFA7HDhwwO4u8RWpc+EmKChI0tk3Jzg42M3VeKaioiKtWrVKffr0kY+Pj7vLqfMYD8/CeHgexsSzVNd45ObmKjo62vY5fi51LtyUnooKDg4m3FSiqKhIAQEBCg4O5heFB2A8PAvj4XkYE89S3ePhyJISFhQDAABTIdwAAABTIdwAAABTIdwAAABTIdwAAABTIdwAAABTIdwAAABTIdwAAABTIdwAAABTqXN3KK4uxSWGMjKPKvtEvsKDrOoU21DeXnwxJwAANc0jZm5mz56tmJgYWa1WJSQkKCMjo9K+CxculMVisfuxWq01WG15K7YdVLdpa3TH/K815p3NumP+1+o2bY1WbDvo1roAAKiL3B5ulixZopSUFKWmpmrTpk1q27at+vbtq+zs7EpfExwcrIMHD9p+9u3bV4MV21ux7aBGLtqkgzn5du2HcvI1ctEmAg4AADXM7eFm5syZGjFihJKSkhQXF6e5c+cqICBACxYsqPQ1FotFkZGRtp+IiIgarPgPxSWG0pZvl1HBc6Vtacu3q7ikoh4AAKA6uHXNTWFhoTZu3KgJEybY2ry8vNSrVy+tX7++0tedPHlSTZs2VUlJidq3b6+nn35aV1xxRYV9CwoKVFBQYHucm5sr6ey3lhYVFV1Q/Rsyj5absSnLkHQwJ1/rd2crIbbhBe2rJpW+Lxf6/sA1GA/Pwnh4HsbEs1TXeDizPbeGmyNHjqi4uLjczEtERIR27txZ4Wsuu+wyLViwQG3atFFOTo5mzJihq6++Wj/88IMuvvjicv2nTp2qtLS0cu2rVq1SQEDABdW/8YhFkvd5+636fIN+31H7Zm9Wr17t7hJQBuPhWRgPz8OYeBZXj0deXp7DfWvd1VJdunRRly5dbI+vvvpqXX755XrllVf01FNPles/YcIEpaSk2B7n5uYqOjpaffr0UXBw8AXVclHmUb2x69vz9uvTPaHWzdysXr1avXv3lo+Pj7vLqfMYD8/CeHgexsSzVNd4lJ55cYRbw01YWJi8vb2VlZVl156VlaXIyEiHtuHj46Mrr7xSu3fvrvB5Pz8/+fn5Vfi6C33Tu7QIV1SIVYdy8itcd2ORFBliVZcW4bXysnBXvEdwHcbDszAenocx8SyuHg9ntuXWBcW+vr7q0KGD0tPTbW0lJSVKT0+3m505l+LiYm3dulVRUVHVVWalvL0sSh0QJ+lskCmr9HHqgLhaGWwAAKit3H61VEpKiubPn6/XX39dO3bs0MiRI3Xq1CklJSVJkoYNG2a34PjJJ5/UqlWr9PPPP2vTpk26++67tW/fPj3wwANuqb9ffJTm3N1e4cH2s0ORIVbNubu9+sXXfOgCAKAuc/uam6FDh+rw4cOaNGmSDh06pHbt2mnFihW2Rcb79++Xl9cfGezYsWMaMWKEDh06pNDQUHXo0EFfffWV4uLi3HUI6hcfpa4twtT6iVWSpIVJV6l7y0bM2AAA4AZuDzeSlJycrOTk5AqfW7dund3j5557Ts8991wNVOWcskGGr14AAMB93H5aCgAAwJUINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQINwAAwFQ8ItzMnj1bMTExslqtSkhIUEZGhkOve+edd2SxWJSYmFi9BQIAgFrD7eFmyZIlSklJUWpqqjZt2qS2bduqb9++ys7OPufr9u7dq3Hjxql79+41VCkAAKgN3B5uZs6cqREjRigpKUlxcXGaO3euAgICtGDBgkpfU1xcrLvuuktpaWlq1qxZDVYLAAA8XT137rywsFAbN27UhAkTbG1eXl7q1auX1q9fX+nrnnzySYWHh+v+++/X559/fs59FBQUqKCgwPY4NzdXklRUVKSioqILPII/FBWdKfPnIhVZDJdtu6aVvi+ufH9QdYyHZ2E8PA9j4lmqazyc2Z5bw82RI0dUXFysiIgIu/aIiAjt3Lmzwtd88cUXevXVV7V582aH9jF16lSlpaWVa1+1apUCAgKcrrkyBcVS6du5cuUq+Xm7bNNus3r1aneXgDIYD8/CeHgexsSzuHo88vLyHO7r1nDjrBMnTuiee+7R/PnzFRYW5tBrJkyYoJSUFNvj3NxcRUdHq0+fPgoODnZZbXmFZ/RIxhpJUt++fRTgW6veWjtFRUVavXq1evfuLR8fH3eXU+cxHp6F8fA8jIlnqa7xKD3z4gi3fgKHhYXJ29tbWVlZdu1ZWVmKjIws13/Pnj3au3evBgwYYGsrKSmRJNWrV08//vijmjdvbvcaPz8/+fn5lduWj4+PS990H8Pyp23X3nBTytXvES4M4+FZGA/Pw5h4Fpd/zjqxLbcuKPb19VWHDh2Unp5uayspKVF6erq6dOlSrn+rVq20detWbd682fZz880369prr9XmzZsVHR1dk+UDAAAP5PbphZSUFA0fPlwdO3ZUp06dNGvWLJ06dUpJSUmSpGHDhqlJkyaaOnWqrFar4uPj7V7foEEDSSrXDgAA6ia3h5uhQ4fq8OHDmjRpkg4dOqR27dppxYoVtkXG+/fvl5eX269YBwAAtYTbw40kJScnKzk5ucLn1q1bd87XLly40PUFAQCAWospEQAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCqEGwAAYCpOh5vTp08rLy/P9njfvn2aNWuWVq1a5dLCAAAAqsLpcHPLLbfojTfekCQdP35cCQkJevbZZ3XLLbdozpw5Li8QAADAGU6Hm02bNql79+6SpKVLlyoiIkL79u3TG2+8oRdeeMHlBQIAADjD6XCTl5enoKAgSdKqVat06623ysvLS507d9a+fftcXiAAAIAznA43LVq00AcffKADBw5o5cqV6tOnjyQpOztbwcHBLi8QAADAGU6Hm0mTJmncuHGKiYlRQkKCunTpIunsLM6VV17p8gIBAACcUc/ZFwwaNEjdunXTwYMH1bZtW1v79ddfr4EDB7q0OAAAAGc5HW4kKTIyUpGRkZKk3NxcrVmzRpdddplatWrl0uIAAACc5fRpqSFDhuill16SdPaeNx07dtSQIUPUpk0bLVu2zOUFAgAAOMPpcPPZZ5/ZLgV///33ZRiGjh8/rhdeeEGTJ092eYEAAADOcDrc5OTkqGHDhpKkFStW6LbbblNAQIBuvPFG7dq1y+UFAgAAOMPpcBMdHa3169fr1KlTWrFihe1S8GPHjslqtbq8QAAAAGc4vaB47Nixuuuuu1S/fn01bdpUPXv2lHT2dFXr1q1dXR8AAIBTnA43Dz74oBISErR//3717t1bXl5nJ3+aNWvGmhsAAOB2VboUvEOHDurQoYNd24033uiSggAAAC5ElcLNL7/8og8//FD79+9XYWGh3XMzZ850SWEAAABV4XS4SU9P180336xmzZpp586dio+P1969e2UYhtq3b18dNQIAADjM6aulJkyYoHHjxmnr1q2yWq1atmyZDhw4oB49emjw4MFVKmL27NmKiYmR1WpVQkKCMjIyKu373nvvqWPHjmrQoIECAwPVrl07vfnmm1XaLwAAMB+nw82OHTs0bNgwSVK9evV0+vRp1a9fX08++aSmTZvmdAFLlixRSkqKUlNTtWnTJrVt21Z9+/ZVdnZ2hf0bNmyoxx57TOvXr9f333+vpKQkJSUlaeXKlU7vGwAAmI/T4SYwMNC2ziYqKkp79uyxPXfkyBGnC5g5c6ZGjBihpKQkxcXFae7cuQoICNCCBQsq7N+zZ08NHDhQl19+uZo3b64xY8aoTZs2+uKLL5zeNwAAMB+n19x07txZX3zxhS6//HL1799fDz/8sLZu3ar33ntPnTt3dmpbhYWF2rhxoyZMmGBr8/LyUq9evbR+/frzvt4wDK1Zs0Y//vhjpbNGBQUFKigosD3Ozc2VJBUVFamoqMipes+lqOhMmT8XqchiuGzbNa30fXHl+4OqYzw8C+PheRgTz1Jd4+HM9pwONzNnztTJkyclSWlpaTp58qSWLFmili1bOn2l1JEjR1RcXKyIiAi79oiICO3cubPS1+Xk5KhJkyYqKCiQt7e3Xn75ZfXu3bvCvlOnTlVaWlq59lWrVikgIMCpes+loFgqfTtXrlwlP2+XbdptVq9e7e4SUAbj4VkYD8/DmHgWV49HXl6ew32dDjfNmjWz/TkwMFBz5851dhMXLCgoSJs3b9bJkyeVnp6ulJQUNWvWzHa35LImTJiglJQU2+Pc3FxFR0erT58+Cg4OdllNeYVn9EjGGklS3759FOBbpavsPUJRUZFWr16t3r17y8fHx93l1HmMh2dhPDwPY+JZqms8Ss+8OMKtn8BhYWHy9vZWVlaWXXtWVpYiIyMrfZ2Xl5datGghSWrXrp127NihqVOnVhhu/Pz85OfnV67dx8fHpW+6j2H507Zrb7gp5er3CBeG8fAsjIfnYUw8i8s/Z53YlsOfwGVnbM7l559/dnjnvr6+6tChg9LT05WYmChJKikpUXp6upKTkx3eTklJid26GgAAUHc5HG727t2rpk2b6s4771R4eLjLCkhJSdHw4cPVsWNHderUSbNmzdKpU6eUlJQkSRo2bJiaNGmiqVOnSjq7hqZjx45q3ry5CgoK9Mknn+jNN9/UnDlzXFYTAACovRwON0uWLNGCBQs0c+ZM3XDDDbrvvvvUv39/2xdnVtXQoUN1+PBhTZo0SYcOHVK7du20YsUK2yLj/fv32+3j1KlTevDBB/XLL7/I399frVq10qJFizR06NALqgMAAJiDw+Fm8ODBGjx4sH799VctXLhQDz30kP7617/qnnvu0f3336+WLVtWuYjk5ORKT0OtW7fO7vHkyZP59nEAAFApp6ddmjRposcee0y7du3S4sWLtWHDBrVq1UrHjh2rjvoAAACcUqVLevLz87V06VItWLBAGzZs0ODBg116zxgAAICqcircbNiwQa+++qreffddNWvWTPfdd5+WLVum0NDQ6qoPAADAKQ6HmyuuuELZ2dm688479emnn6pt27bVWRcAAECVOBxuduzYocDAQL3xxht68803K+139OhRlxQGAABQFQ6Hm9dee6066wAAAHAJh8PN8OHDq7MOAAAAl7iwO/ABAAB4GMINAAAwFcINAAAwFcINAAAwFafDzdq1a6ujDgAAAJdwOtz069dPzZs31+TJk3XgwIHqqAkAAKDKnA43v/76q5KTk7V06VI1a9ZMffv21bvvvqvCwsLqqA8AAMApToebsLAwPfTQQ9q8ebM2bNigSy+9VA8++KAaN26s0aNHa8uWLdVRJwAAgEMuaEFx+/btNWHCBCUnJ+vkyZNasGCBOnTooO7du+uHH35wVY0AAAAOq1K4KSoq0tKlS9W/f381bdpUK1eu1EsvvaSsrCzt3r1bTZs21eDBg11dKwAAwHk5/PULpf72t7/p7bfflmEYuueeezR9+nTFx8fbng8MDNSMGTPUuHFjlxYKAADgCKfDzfbt2/Xiiy/q1ltvlZ+fX4V9wsLCuGQcAAC4hdOnpVJTUzV48OBywebMmTP67LPPJEn16tVTjx49XFMhAACAE5wON9dee62OHj1arj0nJ0fXXnutS4oCAACoKqfDjWEYslgs5dp///13BQYGuqQoAACAqnJ4zc2tt94qSbJYLLr33nvtTksVFxfr+++/19VXX+36ClGjiksMbcg8qo1HLLoo86i6tAiXt1f5MAsAgKdyONyEhIRIOjtzExQUJH9/f9tzvr6+6ty5s0aMGOH6ClFjVmw7qLTl23UwJ1+St97Y9a2iQqxKHRCnfvFR7i4PAACHOBxuXnvtNUlSTEyMxo0bxykok1mx7aBGLtok40/th3LyNXLRJs25uz0BBwBQK1TpaimCjbkUlxhKW769XLCRZGtLW75dxSUV9QAAwLM4NHPTvn17paenKzQ0VFdeeWWFC4pLbdq0yWXFoWZkZB7936moihmSDubkKyPzqLo0v6jmCgMAoAocCje33HKLbQFxYmJiddYDN8g+UXmwqUo/AADcyaFwk5qaWuGfYQ7hQVaX9gMAwJ0u6FvBYQ6dYhsqKsSqyk42WiRFhVjVKbZhTZYFAECVODRzExoaes51NmVVdPdieDZvL4tSB8Rp5KJNskh2C4tLRz11QBz3uwEA1AoOhZtZs2ZVcxlwt37xUZpzd3ulfviDsnILbO2R3OcGAFDLOBRuhg8fXt11wAP0i49S1xZhav3EKknSP++5UtdeHsWMDQCgVnEo3OTm5io4ONj253Mp7YfaqWyQuSomlGADAKh1HF5zc/DgQYWHh6tBgwYVrr8p/ULN4uJilxcJAADgKIfCzZo1a9Sw4dkrZdauXVutBQEAAFwIh8JNjx49KvwzAACAp3H4izPLOnbsmF599VXt2LFDkhQXF6ekpCTb7A4AAIC7OH0Tv88++0wxMTF64YUXdOzYMR07dkwvvPCCYmNj9dlnn1VHjQAAAA5zeuZm1KhRGjp0qObMmSNvb29JUnFxsR588EGNGjVKW7dudXmRAAAAjnJ65mb37t16+OGHbcFGkry9vZWSkqLdu3e7tDgAAABnOR1u2rdvb1trU9aOHTvUtm1blxQFAABQVQ6dlvr+++9tfx49erTGjBmj3bt3q3PnzpKkr7/+WrNnz9YzzzxTPVUCAAA4yKFw065dO1ksFhnGH1+p+Mgjj5Trd+edd2ro0KGuqw4AAMBJDoWbzMzM6q4DAADAJRwKN02bNq3uOgAAAFyiSjfxk6Tt27dr//79KiwstGu/+eabL7goAACAqnI63Pz8888aOHCgtm7darcOp/TLNPniTAAA4E5OXwo+ZswYxcbGKjs7WwEBAfrhhx/02WefqWPHjlq3bl01lAgAAOA4p2du1q9frzVr1igsLExeXl7y8vJSt27dNHXqVI0ePVrfffddddQJAADgEKdnboqLixUUFCRJCgsL02+//Sbp7KLjH3/80bXVAQAAOMnpmZv4+Hht2bJFsbGxSkhI0PTp0+Xr66t58+apWbNm1VEjAACAw5wON48//rhOnTolSXryySd10003qXv37rrooou0ZMkSlxcIAADgDKfDTd++fW1/btGihXbu3KmjR48qNDTUdsUUAACAu1T5PjeSdODAAUlSdHS0S4oBAAC4UE4vKD5z5owmTpyokJAQxcTEKCYmRiEhIXr88cdVVFRUHTUCAAA4zOlw87e//U3z5s3T9OnT9d133+m7777T9OnT9eqrr2r06NFVKmL27NmKiYmR1WpVQkKCMjIyKu07f/58de/eXaGhoQoNDVWvXr3O2R8AANQtToebxYsXa+HChfrrX/+qNm3aqE2bNvrrX/+qV199VYsXL3a6gCVLliglJUWpqanatGmT2rZtq759+yo7O7vC/uvWrdMdd9yhtWvXav369YqOjlafPn3066+/Or1vAABgPk6HGz8/P8XExJRrj42Nla+vr9MFzJw5UyNGjFBSUpLi4uI0d+5cBQQEaMGCBRX2f+utt/Tggw+qXbt2atWqlf75z3+qpKRE6enpTu8bAACYj9PhJjk5WU899ZQKCgpsbQUFBZoyZYqSk5Od2lZhYaE2btyoXr16/VGQl5d69eql9evXO7SNvLw8FRUVqWHDhk7tGwAAmJNDV0vdeuutdo//+9//6uKLL1bbtm0lSVu2bFFhYaGuv/56p3Z+5MgRFRcXKyIiwq49IiJCO3fudGgb/+///T81btzYLiCVVVBQYBfEcnNzJUlFRUUuXQBdVHSmzJ+LVGQxXLbtmmR/HGdYJO4BSseAsfAMjIfnYUw8S3WNhzPbcyjchISE2D2+7bbb7B6761LwZ555Ru+8847WrVsnq9VaYZ+pU6cqLS2tXPuqVasUEBDgsloKiqXSt3PlylXy83bZpmtU2eNYs2ZNrT0OM1q9erW7S0AZjIfnYUw8i6vHIy8vz+G+FsMw3DbFUFhYqICAAC1dulSJiYm29uHDh+v48eP697//XelrZ8yYocmTJ+u///2vOnbsWGm/imZuoqOjdeTIEQUHB7vkOCQpr/CM2j61RpK0ZeJ1CvC9oFsIuU3Z4/h2/DUKCaw4NKLmFBUVafXq1erdu7d8fHzcXU6dx3h4HsbEs1TXeOTm5iosLEw5OTnn/fyu8ifw4cOHbV+Uedlll6lRo0ZOb8PX11cdOnRQenq6LdyULg4+1/qd6dOna8qUKVq5cuU5g410dgG0n59fuXYfHx+Xvuk+xh93Zz677doZbuyPox6/KDyIq//O4sIwHp6HMfEsLv+cdWJbTi8oPnXqlO677z5FRUXpmmuu0TXXXKPGjRvr/vvvd2rKqFRKSormz5+v119/XTt27NDIkSN16tQpJSUlSZKGDRumCRMm2PpPmzZNEydO1IIFCxQTE6NDhw7p0KFDOnnypNP7BgAA5uN0uElJSdGnn36q5cuX6/jx47bTR59++qkefvhhpwsYOnSoZsyYoUmTJqldu3bavHmzVqxYYVtkvH//fh08eNDWf86cOSosLNSgQYMUFRVl+5kxY4bT+wYAAObj9LmTZcuWaenSperZs6etrX///vL399eQIUM0Z84cp4tITk6u9DTUunXr7B7v3bvX6e0DAIC6w+mZm7y8vHKXbktSeHh4lU5LAQAAuJLT4aZLly5KTU1Vfn6+re306dNKS0tTly5dXFocAACAs5w+LTVr1iz169ev3E38rFarVq5c6fICAQAAnOF0uGndurV27dqlt956y3YX4TvuuEN33XWX/P39XV4gAACAM5wKN0VFRWrVqpU++ugjjRgxorpqAgAAqDKn1tz4+PjYrbUBAADwNE4vKB41apSmTZumM2fOnL8zAABADXN6zc0333yj9PR0rVq1Sq1bt1ZgYKDd8++9957LigMAAHCW0+GmQYMG5b4VHAAAwFM4HW5ee+216qgDAADAJRxec1NSUqJp06apa9euuuqqqzR+/HidPn26OmsDAABwmsPhZsqUKXr00UdVv359NWnSRM8//7xGjRpVnbUBAAA4zeFw88Ybb+jll1/WypUr9cEHH2j58uV66623VFJSUp31AQAAOMXhcLN//37179/f9rhXr16yWCz67bffqqUwAACAqnA43Jw5c0ZWq9WuzcfHR0VFRS4vCgAAoKocvlrKMAzde++98vPzs7Xl5+fr//7v/+zudcN9bgAAgDs5HG6GDx9eru3uu+92aTEAAAAXyuFww/1tAABAbeD0d0sBAAB4MsINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwFcINAAAwlXruLgCoDsUlhjIyjyr7RL7Cg6zqFNtQ3l4Wd5cFAKgBhBuYzoptB5W2fLsO5uTb2qJCrEodEKd+8VFurAwAUBM4LQVTWbHtoEYu2mQXbCTpUE6+Ri7apBXbDrqpMgBATSHcwDSKSwylLd8uo4LnStvSlm9XcUlFPQAAZkG4gWlkZB4tN2NTliHpYE6+MjKP1lxRAIAaR7iBaWSfqDzYVKUfAKB2ItzANMKDrC7tBwConQg3MI1OsQ0VFWJVZRd8W3T2qqlOsQ1rsiwAQA0j3MA0vL0sSh0QJ0nlAk7p49QBcdzvBgBMjnADU+kXH6U5d7dXeLCfXXtkiFVz7m7PfW4AoA7gJn4wnX7xUeraIkytn1glSVqYdJW6t2zEjA0A1BHM3MCUygYZvnoBAOoWwg0AADAVwg0AADAVwg0AADAVwg0AADAVwg0AADAVt4eb2bNnKyYmRlarVQkJCcrIyKi07w8//KDbbrtNMTExslgsmjVrVs0VCgAAagW3hpslS5YoJSVFqamp2rRpk9q2bau+ffsqOzu7wv55eXlq1qyZnnnmGUVGRtZwtQAAoDZwa7iZOXOmRowYoaSkJMXFxWnu3LkKCAjQggULKux/1VVX6R//+Iduv/12+fn5VdgHAADUbW4LN4WFhdq4caN69er1RzFeXurVq5fWr1/vrrIAAEAt57avXzhy5IiKi4sVERFh1x4REaGdO3e6bD8FBQUqKCiwPc7NzZUkFRUVqaioyGX7KSo6U+bPRSqyGC7bdk2yP44zLn2PapJZxkOSbQxq61iYDePheRgTz1Jd4+HM9kz/3VJTp05VWlpaufZVq1YpICDAZfspKJZK386VK1fJz9tlm65RZY9jzZo1pjiO2jweZa1evdrdJaAMxsPzMCaexdXjkZeX53Bft4WbsLAweXt7Kysry649KyvLpYuFJ0yYoJSUFNvj3NxcRUdHq0+fPgoODnbZfvIKz+iRjDWSpL59+yjAt3bmxrLHcd111ykk0OrmiqrGLOMhnf3fyurVq9W7d2/5+Pi4u5w6j/HwPIyJZ6mu8Sg98+IIt/3G9/X1VYcOHZSenq7ExERJUklJidLT05WcnOyy/fj5+VW4+NjHx8elb7qP8ccXM57ddu38MLU/jnq19heFWcajLFf/ncWFYTw8D2PiWVz+OevEttz6Gz8lJUXDhw9Xx44d1alTJ82aNUunTp1SUlKSJGnYsGFq0qSJpk6dKunsIuTt27fb/vzrr79q8+bNql+/vlq0aOG24wAAAJ7DreFm6NChOnz4sCZNmqRDhw6pXbt2WrFihW2R8f79++Xl9ccFXb/99puuvPJK2+MZM2ZoxowZ6tGjh9atW1fT5QMAAA/k9rn65OTkSk9D/TmwxMTEyDBq71UvAACg+rn96xcAAABciXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADAABMhXADeLDiEkMbMo9q4xGLNmQeVXGJ4e6SAMDj1XN3AQAqtmLbQaUt366DOfmSvPXGrm8VFWJV6oA49YuPcnd5AOCxmLkBPNCKbQc1ctGm/wWbPxzKydfIRZu0YttBN1UGAJ6PcAN4mOISQ2nLt6uiE1ClbWnLt3OKCgAqQbgBPExG5tFyMzZlGZIO5uQrI/NozRUFALUI4QbwMNknKg82VekHAHUN4QbwMOFBVpf2A4C6hnADeJhOsQ0VFWKVpZLnLZKiQqzqFNuwJssCgFqDcAN4GG8vi1IHxElSuYBT+jh1QJy8vSqLPwBQtxFuAA/ULz5Kc+5ur/BgP7v2yBCr5tzdnvvcAMA5cBM/wEP1i49S1xZhav3EKknSP++5UtdeHsWMDQCcBzM3gAcrG2Suigkl2ACAAwg3AADAVAg3AADAVAg3AADAVAg3AADAVAg3AADAVAg3AADAVAg3AADAVAg3AADAVAg3AADAVPj6BQDVrrjEUEbmUWWfyFd40NlvNOduywCqC+EGQLVase2g0pZv18GcfFtbVIhVqQPi+AJQANWC01IAqs2KbQc1ctEmu2AjSYdy8jVy0Sat2HbQTZUBMDPCDYBqUVxiKG35dhkVPFfalrZ8u4pLKuoBAFVHuAFQLTIyj5absSnLkHQwJ18ZmUdrrigAdQLhBkC1yD5RebCpSj8AcBThBkC1CA+yurQfADiKcAOgWnSKbaioEKsqu+DborNXTXWKbViTZQGoAwg3AKqFt5dFqQPiJKlcwCl9nDogjvvdAHA5wg2AatMvPkpz7m6v8GA/u/bIEKvm3N2e+9wAqBbcxA9AteoXH6WuLcLU+olVkqSFSVepe8tGtXLGprjE0IbMo9p4xKKLMo+qS4vwWnkcgNkRbgBUu7IBoLZ+9YL9nZa99caub7nTMuChOC0FAOfBnZaB2oVwAwDnwJ2WgdqHcAMA58CdloHah3ADAOfAnZaB2ocFxQBwDma803JxiaGMzKPKPpGv8CBrrV3kDVSGcAMA51B6p+VDOfkVrrux6Ox9e2rLnZbtr/o6i6u+YDaclgKAczDTnZbNeNVX2XsPbcg8ysJuSCLcAMB5meFOy2a86mvFtoPqNm2N7l7wrd7Y5a27F3yrbtPW1MqQBtci3ACAA/rFR+m/KT1sj/95z5X64v9dVyuCjWS+q77MNgtVXGJo/Z7f9e/Nv2r9nt9rVcgsy1Nm0lhzAwAOKnvq6aqY0FpxKqqUma76Ot8slEVnZ6F6x0XWijEyyzooT7qLt0fM3MyePVsxMTGyWq1KSEhQRkbGOfv/61//UqtWrWS1WtW6dWt98sknNVQpANROZrrqy0yzUGaZgfK043B7uFmyZIlSUlKUmpqqTZs2qW3bturbt6+ys7Mr7P/VV1/pjjvu0P3336/vvvtOiYmJSkxM1LZt22q4cgCoPUqv+qpsHsOis7MFteGqL7PMQpllHZQnHofbT0vNnDlTI0aMUFJSkiRp7ty5+vjjj7VgwQKNHz++XP/nn39e/fr109///ndJ0lNPPaXVq1frpZde0ty5c2u09rIMw5DfmQJJUklenkrOuP2trZKSwjN/HMfp0yqxePY/qsrYHQfj4XaMh/tZJD3RO1Zj3tksSXYfRKWB54nel8uSf1olNVybs8J9/vh9e75+JXl5NVBR1WRkHtXR33Pkd44+R38vUMaOX5XgwaGzsuMo8PaVLBa7mbQuzS+qkZoshmG47V9nYWGhAgICtHTpUiUmJtrahw8fruPHj+vf//53uddccsklSklJ0dixY21tqamp+uCDD7Rly5Zy/QsKClRQ8Mc/gtzcXEVHR+vIkSMKDg522bGczDmhQ926umx7AADUZok3TVFBvT8iz8zBrTWgTdXX3uTm5iosLEw5OTnn/fx263+fjhw5ouLiYkVERNi1R0REaOfOnRW+5tChQxX2P3ToUIX9p06dqrS0tHLtq1atUkBAQBUrL89SWKiWLtsaAADm8vMPm/XJL99V+fV5TszC1c65YSdMmDBBKSkptselMzd9+vRx6cyNYRgy+vRx2fbcqejMGa1Zs0bXXXedfOqZ/q+Ix2M8PAvj4Tn+uyNb01b+pKwTf8zORwb76ZE+l6rX5eFurMwxxSWG+r3wpbJPFFR69+uIYD/9529dPfqqr8qOo8DbV1LpXbz9lDz0mgs6jtzcXIf7uvVfZlhYmLy9vZWVlWXXnpWVpcjIyApfExkZ6VR/Pz8/+fmVP6Pp4+MjHx+fKlZeCV9f127PTbyKimT4+sovONj17xGcxnh4FsbDc9zYOUT9OrXQ+t3ZWvX5BvXpnqAuLcI9Ogj82aO3tdfIRZskVbwOasKt7RUQ2qCmy3La+Y4jdcAVsvpd2GekM//e3Hq1lK+vrzp06KD09HRbW0lJidLT09WlS5cKX9OlSxe7/pK0evXqSvsDAMzL28uihNiG6hBmKKEWfgFo6d2vI0PsL8GvTXe/ljzvONw+p5qSkqLhw4erY8eO6tSpk2bNmqVTp07Zrp4aNmyYmjRpoqlTp0qSxowZox49eujZZ5/VjTfeqHfeeUfffvut5s2b587DAACgSvrFR6l3XGSt/6b20uPwhJk0t4eboUOH6vDhw5o0aZIOHTqkdu3aacWKFbZFw/v375eX1x8TTFdffbUWL16sxx9/XI8++qhatmypDz74QPHx8e46BAAALoi3l6XGLpOuTqUzab/vcO9MmtvDjSQlJycrOTm5wufWrVtXrm3w4MEaPHhwNVcFAABqI7ffoRgAAMCVCDcAAMBUCDcAAMBUCDcAAMBUCDcAAMBUCDcAAMBUCDcAAMBUCDcAAMBUCDcAAMBUPOIOxTXJMM5+X6kzX51e1xQVFSkvL0+5ubl867EHYDw8C+PheRgTz1Jd41H6uV36OX4udS7cnDhxQpIUHR3t5koAAICzTpw4oZCQkHP2sRiORCATKSkp0W+//aagoCBZLLXrG1drSm5urqKjo3XgwAEFBwe7u5w6j/HwLIyH52FMPEt1jYdhGDpx4oQaN25s94XaFalzMzdeXl66+OKL3V1GrRAcHMwvCg/CeHgWxsPzMCaepTrG43wzNqVYUAwAAEyFcAMAAEyFcINy/Pz8lJqaKj8/P3eXAjEenobx8DyMiWfxhPGocwuKAQCAuTFzAwAATIVwAwAATIVwAwAATIVwAwAATIVwA5upU6fqqquuUlBQkMLDw5WYmKgff/zR3WVB0jPPPCOLxaKxY8e6u5Q67ddff9Xdd9+tiy66SP7+/mrdurW+/fZbd5dVJxUXF2vixImKjY2Vv7+/mjdvrqeeesqh7x3Chfvss880YMAANW7cWBaLRR988IHd84ZhaNKkSYqKipK/v7969eqlXbt21Vh9hBvYfPrppxo1apS+/vprrV69WkVFRerTp49OnTrl7tLqtG+++UavvPKK2rRp4+5S6rRjx46pa9eu8vHx0X/+8x9t375dzz77rEJDQ91dWp00bdo0zZkzRy+99JJ27NihadOmafr06XrxxRfdXVqdcOrUKbVt21azZ8+u8Pnp06frhRde0Ny5c7VhwwYFBgaqb9++ys/Pr5H6uBQclTp8+LDCw8P16aef6pprrnF3OXXSyZMn1b59e7388suaPHmy2rVrp1mzZrm7rDpp/Pjx+vLLL/X555+7uxRIuummmxQREaFXX33V1nbbbbfJ399fixYtcmNldY/FYtH777+vxMRESWdnbRo3bqyHH35Y48aNkyTl5OQoIiJCCxcu1O23317tNTFzg0rl5ORIkho2bOjmSuquUaNG6cYbb1SvXr3cXUqd9+GHH6pjx44aPHiwwsPDdeWVV2r+/PnuLqvOuvrqq5Wenq6ffvpJkrRlyxZ98cUXuuGGG9xcGTIzM3Xo0CG731shISFKSEjQ+vXra6SGOvfFmXBMSUmJxo4dq65duyo+Pt7d5dRJ77zzjjZt2qRvvvnG3aVA0s8//6w5c+YoJSVFjz76qL755huNHj1avr6+Gj58uLvLq3PGjx+v3NxctWrVSt7e3iouLtaUKVN01113ubu0Ou/QoUOSpIiICLv2iIgI23PVjXCDCo0aNUrbtm3TF1984e5S6qQDBw5ozJgxWr16taxWq7vLgc4G/o4dO+rpp5+WJF155ZXatm2b5s6dS7hxg3fffVdvvfWWFi9erCuuuEKbN2/W2LFj1bhxY8YDnJZCecnJyfroo4+0du1aXXzxxe4up07auHGjsrOz1b59e9WrV0/16tXTp59+qhdeeEH16tVTcXGxu0usc6KiohQXF2fXdvnll2v//v1uqqhu+/vf/67x48fr9ttvV+vWrXXPPffooYce0tSpU91dWp0XGRkpScrKyrJrz8rKsj1X3Qg3sDEMQ8nJyXr//fe1Zs0axcbGurukOuv666/X1q1btXnzZttPx44dddddd2nz5s3y9vZ2d4l1TteuXcvdGuGnn35S06ZN3VRR3ZaXlycvL/uPMG9vb5WUlLipIpSKjY1VZGSk0tPTbW25ubnasGGDunTpUiM1cFoKNqNGjdLixYv173//W0FBQbZzoyEhIfL393dzdXVLUFBQubVOgYGBuuiii1gD5SYPPfSQrr76aj399NMaMmSIMjIyNG/ePM2bN8/dpdVJAwYM0JQpU3TJJZfoiiuu0HfffaeZM2fqvvvuc3dpdcLJkye1e/du2+PMzExt3rxZDRs21CWXXKKxY8dq8uTJatmypWJjYzVx4kQ1btzYdkVVtTOA/5FU4c9rr73m7tJgGEaPHj2MMWPGuLuMOm358uVGfHy84efnZ7Rq1cqYN2+eu0uqs3Jzc40xY8YYl1xyiWG1Wo1mzZoZjz32mFFQUODu0uqEtWvXVvh5MXz4cMMwDKOkpMSYOHGiERERYfj5+RnXX3+98eOPP9ZYfdznBgAAmAprbgAAgKkQbgAAgKkQbgAAgKkQbgAAgKkQbgAAgKkQbgAAgKkQbgAAgKkQbgAAgKkQbgAAgKkQbgAAgKkQbgDUeocPH1ZkZKSefvppW9tXX30lX19fu28mBlA38N1SAEzhk08+UWJior766itddtllateunW655RbNnDnT3aUBqGGEGwCmMWrUKP33v/9Vx44dtXXrVn3zzTfy8/Nzd1kAahjhBoBpnD59WvHx8Tpw4IA2btyo1q1bu7skAG7AmhsAprFnzx799ttvKikp0d69e91dDgA3YeYGgCkUFhaqU6dOateunS677DLNmjVLW7duVXh4uLtLA1DDCDcATOHvf/+7li5dqi1btqh+/frq0aOHQkJC9NFHH7m7NAA1jNNSAGq9devWadasWXrzzTcVHBwsLy8vvfnmm/r88881Z84cd5cHoIYxcwMAAEyFmRsAAGAqhBsAAGAqhBsAAGAqhBsAAGAqhBsAAGAqhBsAAGAqhBsAAGAqhBsAAGAqhBsAAGAqhBsAAGAqhBsAAGAqhBsAAGAq/x87ZcO4Plw1SgAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import geom\n",
    "\n",
    "# Define the parameter of the geometric distribution\n",
    "p = 0.5  # Probability of success\n",
    "\n",
    "# Generate x values within a certain range\n",
    "x = np.arange(1, 11)\n",
    "\n",
    "# Calculate the PMF values for each x\n",
    "pmf_values = geom.pmf(x, p)\n",
    "\n",
    "# Plot the PMF\n",
    "plt.stem(x, pmf_values)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Probability Mass')\n",
    "plt.title('Geometric Distribution PMF')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2.7. Gamma Distribution:\n",
    "\n",
    "- **PDF:** $\\boxed{f(x; k, \\theta) = \\frac{x^{k - 1}}{\\theta^k  \\Gamma(k)}~ \\text{exp}\\left(-\\frac{x}{\\theta}\\right)}$\n",
    "- **Formula:** Generate random numbers according to the gamma distribution with shape parameter $k$ and scale parameter $\\beta$.\n",
    "- Used for modeling continuous variables with skewed distributions.\n",
    "    - **Parameters:** shape ($k$) and scale ($\\theta$).\n",
    "    - **Example function:** `numpy.random.gamma(shape, scale, size)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import gamma\n",
    "\n",
    "# Define the parameters of the gamma distribution\n",
    "k = 2  # Shape parameter\n",
    "theta = 1  # Scale parameter\n",
    "\n",
    "# Generate x values within a certain range\n",
    "x = np.linspace(0, 10, 1000)\n",
    "\n",
    "# Calculate the PDF values for each x\n",
    "pdf_values = gamma.pdf(x, k, scale=theta)\n",
    "\n",
    "# Plot the PDF\n",
    "plt.plot(x, pdf_values)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Probability Density')\n",
    "plt.title('Gamma Distribution PDF')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2.8. Beta Distribution:\n",
    "\n",
    "- **PDF:** $\\boxed{f(x; \\alpha, \\beta) = \\frac{x^{\\alpha - 1} (1 - x)^{\\beta - 1}}{B(\\alpha, \\beta)}}$, where beta function $B(\\alpha, \\beta) =\\frac{\\Gamma(\\alpha)\\Gamma(\\beta)}{\\Gamma(\\alpha+\\beta)}$ is normalization constant (here $\\Gamma(n) = (n-1)!$).\n",
    "- **Formula:** Generate random numbers according to the beta distribution with shape parameters $\\alpha$ and $\\beta$.\n",
    "- Used for modeling continuous variables constrained between 0 and 1.\n",
    "  - **Parameters:** shape parameters ($\\alpha$ and $\\beta$).\n",
    "  - **Example function:** `numpy.random.beta(alpha, beta, size)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import beta\n",
    "\n",
    "# Define the parameters of the beta distribution\n",
    "alpha = 2  # Shape parameter\n",
    "beta_val = 2  # Shape parameter\n",
    "\n",
    "# Generate x values within a certain range\n",
    "x = np.linspace(0, 1, 1000)\n",
    "\n",
    "# Calculate the PDF values for each x\n",
    "pdf_values = beta.pdf(x, alpha, beta_val)\n",
    "\n",
    "# Plot the PDF\n",
    "plt.plot(x, pdf_values)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Probability Density')\n",
    "plt.title('Beta Distribution PDF')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2.9. Lognormal Distribution:\n",
    "\n",
    "- **PDF:** $\\boxed{f(x; \\mu, \\sigma)=\\frac{1}{x\\sigma\\sqrt{2\\pi}} \\text{exp}\\left(-\\frac{(\\text{ln}(x) - \\mu)^2}{2\\sigma^2}\\right)}$\n",
    "- **Formula:** Generate random numbers according to the lognormal distribution with parameters $\\mu$ (mean of the underlying normal distribution) and $\\sigma$ (standard deviation of the underlying normal distribution).\n",
    "- Used for modeling variables whose logarithm follows a normal distribution.\n",
    "    - **Parameters:** mean of the underlying normal distribution (μ) and standard deviation of the underlying normal distribution (σ).\n",
    "    - **Example function:** `numpy.random.lognormal(mean, sigma, size)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAjcAAAHHCAYAAABDUnkqAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/P9b71AAAACXBIWXMAAA9hAAAPYQGoP6dpAABjqElEQVR4nO3deVxUZfs/8M+ZlX2TVUDAfReXMHfLhbSn0sps1aj89jNJizZt87FF03zMFss0LStN08qe0sckcsk0N0RNRUVRFGVRlmGdGWbO7w+YAQR1RmfmMMPn/Xr5kjlz5pyLW/Rc3vd137cgiqIIIiIiIhchkzoAIiIiIltickNEREQuhckNERERuRQmN0RERORSmNwQERGRS2FyQ0RERC6FyQ0RERG5FCY3RERE5FKY3BAREZFLYXJDRHZx5swZCIKAr776yubX/uqrryAIAs6cOWPza1/p8ccfR3R0tPm16fuaP3++3e8NAP/+978hCIJD7kXkKpjcENVhemju27dP6lCaja1bt0IQBPMvtVqNkJAQDB06FLNnz0Z+fr5N7lNeXo5///vf2Lp1q02uZ0tNNba6fy4ymQwtW7bEyJEjG8QZHR1d7zw/Pz9069YN//d//4fdu3df99p1f4WGhjrgOyNXp5A6ACIiAJg6dSpuueUWGAwG5OfnY+fOnZg5cyYWLFiA77//Hrfffrv53MceewwPPvgg1Gq1xdcvLy/HrFmzAABDhw61+HNLly6F0Wi0+Pwbca3YXn/9dUyfPt2u97+WESNGYMKECRBFEZmZmfj0009x++23Y8OGDRg1apT5vNjYWLzwwgsAgJKSEhw7dgxr167F0qVL8fzzz2PBggVXvXZd7u7u9v2GqFlgckPUTFRWVkKlUkEma5odtoMGDcL9999f79jBgwcxcuRI3HfffTh69CjCwsIAAHK5HHK53K7xlJWVwdPTE0ql0q73uR6FQgGFQrp/qtu3b49HH33U/Hrs2LHo3r07Fi5cWC+5CQ8Pr3ceAMydOxcPP/wwPvjgA7Rr1w6TJ0++5rWJbKVp/itH1MQdOHAAo0aNgo+PD7y8vDBs2DD8/fffDc47dOgQhgwZAnd3d0REROCdd97Bl19+2aBeJDo6Gv/617+wY8cOxMXFwc3NDa1bt8bXX3/d4JqnT5/GuHHjEBAQAA8PD9x6663YsGFDvXNMQz2rV6/G66+/jvDwcHh4eECj0eDxxx+Hl5cXsrKy8K9//QteXl4IDw/HokWLAACHDx/G7bffDk9PT0RFRWHVqlX1rl1QUIAXX3wR3bp1g5eXF3x8fDBq1CgcPHjQBi1bX48ePbBw4UIUFRXhk08+MR9vrOZm3759iI+PR2BgINzd3RETE4MnnngCQHWdTFBQEABg1qxZ5iGQf//73wBgbpNTp05h9OjR8Pb2xiOPPGJ+r27NTV0ffPABoqKi4O7ujiFDhuCff/6p9/7QoUMb7SWqe83rxdZYzU1VVRXefvtttGnTBmq1GtHR0Xj11Veh1WrrnWfNz5WlunXrhsDAQGRmZl73XHd3d3zzzTcICAjAu+++C1EUb/i+RNZgzw2RlY4cOYJBgwbBx8cHL7/8MpRKJT7//HMMHToU27ZtQ9++fQEA2dnZuO222yAIAmbMmAFPT0988cUXVx1KycjIwP33348nn3wSEydOxPLly/H444+jd+/e6NKlCwAgNzcX/fv3R3l5OaZOnYoWLVpgxYoVuPvuu7Fu3TqMHTu23jXffvttqFQqvPjii9BqtVCpVAAAg8GAUaNGYfDgwZg3bx5WrlyJxMREeHp64rXXXsMjjzyCe++9F4sXL8aECRPQr18/xMTEAKhOrtavX49x48YhJiYGubm5+PzzzzFkyBAcPXoULVu2tGl7m9pk8+bNePfddxs9Jy8vDyNHjkRQUBCmT58OPz8/nDlzBj/++CMAICgoCJ999hkmT56MsWPH4t577wUAdO/e3XyNqqoqxMfHY+DAgZg/fz48PDyuGdfXX3+NkpISTJkyBZWVlfjwww9x++234/DhwwgJCbH4+7Mktis99dRTWLFiBe6//3688MIL2L17N+bMmYNjx47hp59+qneuJT9X1igsLERhYSHatm1r0fleXl4YO3Ysli1bhqNHj9a7Z2VlJS5dulTvfG9vb6uGG4kaJRKR2ZdffikCEPfu3XvVc8aMGSOqVCrx1KlT5mMXLlwQvb29xcGDB5uPPfvss6IgCOKBAwfMxy5fviwGBASIAMTMzEzz8aioKBGAuH37dvOxvLw8Ua1Wiy+88IL52HPPPScCEP/880/zsZKSEjEmJkaMjo4WDQaDKIqiuGXLFhGA2Lp1a7G8vLxe/BMnThQBiLNnzzYfKywsFN3d3UVBEMTVq1ebj6enp4sAxJkzZ5qPVVZWmu9jkpmZKarVavGtt96qdwyA+OWXX16tKevFunbt2que06NHD9Hf39/82vTnZGrDn3766bp/bvn5+Q2+FxNTm0yfPr3R96Kiohp8X+7u7uL58+fNx3fv3i0CEJ9//nnzsSFDhohDhgy57jWvFdvMmTPFuv9Up6WliQDEp556qt55L774oghA/OOPP8zHLP25uhoA4pNPPinm5+eLeXl54u7du8Vhw4aJAMT//Oc/9e5z5513XvU6H3zwgQhA/Pnnn+tdu7Ff1/t5IbIEh6WIrGAwGLB582aMGTMGrVu3Nh8PCwvDww8/jB07dkCj0QAANm3ahH79+iE2NtZ8XkBAgHm440qdO3fGoEGDzK+DgoLQoUMHnD592nxs48aNiIuLw8CBA83HvLy88H//9384c+YMjh49Wu+aEydOvGqB5lNPPWX+2s/PDx06dICnpyceeOAB8/EOHTrAz8+vXgxqtdpct2MwGHD58mV4eXmhQ4cOSE1NbfReN8vLywslJSVXfd/Pzw8A8Ouvv0Kv19/wfa6sCbmWMWPGIDw83Pw6Li4Offv2xcaNG2/4/pYwXT8pKanecVMx75VDlJb8XF3LsmXLEBQUhODgYPTt2xd//fUXkpKS8Nxzz1kcs5eXFwA0+DO85557kJycXO9XfHy8xdcluhoOSxFZIT8/H+Xl5ejQoUOD9zp16gSj0Yhz586hS5cuOHv2LPr169fgvKt157dq1arBMX9/fxQWFppfnz171jzsdeW9Te937drVfNw0lHQlNzc3c52Hia+vLyIiIhrUd/j6+taLwWg04sMPP8Snn36KzMxMGAwG83stWrRo9H43q7S0FN7e3ld9f8iQIbjvvvswa9YsfPDBBxg6dCjGjBmDhx9+2OIhDoVCgYiICItjateuXYNj7du3x/fff2/xNW7E2bNnIZPJGvwchYaGws/PD2fPnq133JKfq2u55557kJiYCEEQ4O3tjS5dusDT09OqmEtLSwGgwZ9hREQEhg8fbtW1iCzBnhuiJuJqs3/EmyjCvFqvzdXuZUkMs2fPRlJSEgYPHoxvv/0Wv/32G5KTk9GlSxe7TJnW6/U4ceLENWs8BEHAunXrsGvXLiQmJiI7OxtPPPEEevfubX6wXk/dHilbudrie3UTQltf+0o3+3NlSkCGDRuGuLg4qxMbAOZCa0vrdIhuFpMbIisEBQXBw8MDx48fb/Beeno6ZDIZIiMjAQBRUVHIyMhocF5jxywVFRV11Xub3re3devW4bbbbsOyZcvw4IMPYuTIkRg+fDiKiorsdr+KigqLhituvfVWvPvuu9i3bx9WrlyJI0eOYPXq1QAsTwYsdfLkyQbHTpw4UW9mlb+/f6PtcmXvijWxRUVFwWg0Nrh/bm4uioqKHPIzYI3S0lL89NNPiIyMNPcwEtkbkxsiK8jlcowcORI///xzvWnIubm5WLVqFQYOHAgfHx8AQHx8PHbt2oW0tDTzeQUFBVi5cuUN33/06NHYs2cPdu3aZT5WVlaGJUuWIDo6Gp07d77ha1tKLpc3+F//2rVrkZ2dbfN7HTx4EM899xz8/f0xZcqUq55XWFjYICZTrZNperRp9pOtkrD169fX+5737NmD3bt311v7pU2bNkhPT6+3yvLBgwfx119/1buWNbGNHj0aALBw4cJ6x02L5N15551WfR/2VFFRgcceewwFBQV47bXXuI0EOQxrbogasXz5cmzatKnB8WnTpuGdd95BcnIyBg4ciGeeeQYKhQKff/45tFot5s2bZz735ZdfxrfffosRI0bg2WefNU8Fb9WqFQoKCm7oH/rp06fju+++w6hRozB16lQEBARgxYoVyMzMxA8//OCQBfr+9a9/4a233kJCQgL69++Pw4cPY+XKlfUKrG/En3/+icrKSnOR8l9//YX//ve/8PX1xU8//XTNZflXrFiBTz/9FGPHjkWbNm1QUlKCpUuXwsfHx5wMuLu7o3PnzlizZg3at2+PgIAAdO3atV6NkjXatm2LgQMHYvLkydBqtVi4cCFatGiBl19+2XzOE088gQULFiA+Ph5PPvkk8vLysHjxYnTp0sVceG5tbD169MDEiROxZMkSFBUVYciQIdizZw9WrFiBMWPG4Lbbbruh7+dmZWdn49tvvwVQ3Vtz9OhRrF27Fjk5OXjhhRfw9NNPSxIXNU9Mboga8dlnnzV6/PHHH0eXLl3w559/YsaMGZgzZw6MRiP69u2Lb7/9tl6xb2RkJLZs2YKpU6di9uzZCAoKwpQpU+Dp6YmpU6fCzc3N6rhCQkKwc+dOvPLKK/j4449RWVmJ7t2745dffnHY/9hfffVVlJWVYdWqVVizZg169eqFDRs23PQWAR999BEAQKlUws/PD506dcKsWbMwadKkBsXPVzI94FevXo3c3Fz4+voiLi4OK1eurFdU/cUXX+DZZ5/F888/D51Oh5kzZ95wcjNhwgTIZDIsXLgQeXl5iIuLwyeffGJeRRmoLvT++uuv8eabbyIpKQmdO3fGN998g1WrVjXYn8ma2L744gu0bt0aX331lTnxmzFjBmbOnHlD34stpKWl4bHHHjMXHkdGRuKuu+7CU089hbi4OMniouZJEG+mWpGIrPbcc8/h888/R2lpqd23ECAiao5Yc0NkRxUVFfVeX758Gd988w0GDhzIxIaIyE44LEVkR/369cPQoUPRqVMn5ObmYtmyZdBoNHjjjTekDo2IyGUxuSGyo9GjR2PdunVYsmQJBEFAr169sGzZMgwePFjq0IiIXBZrboiIiMilsOaGiIiIXAqTGyIiInIpza7mxmg04sKFC/D29uZqmURERE5CFEWUlJSgZcuW112wtNklNxcuXDDv/UNERETO5dy5c4iIiLjmOc0uufH29gZQ3TimPYBsRa/XY/PmzRg5ciSUSqVNr0212M6OwXZ2DLaz47CtHcNe7azRaBAZGWl+jl9Ls0tuTENRPj4+dkluPDw84OPjw784dsR2dgy2s2OwnR2Hbe0Y9m5nS0pKWFBMRERELoXJDREREbkUJjdERETkUpjcEBERkUthckNEREQuhckNERERuRQmN0RERORSmNwQERGRS2FyQ0RERC6FyQ0RERG5FCY3RERE5FKY3BAREZFLYXLThBiNIgrKdBBFUepQiIiInFaz2xW8qTpXUI4nvtqLk3mliIsJwOeP9oa/p0rqsIiIiJwOe26aAFEUkfR9Gk7mlQIA9mQW4KV1ByWOioiIyDkxuWkC/j5dgL1nCqFWyLB0Qh8o5QJ+P5aH3acvSx0aERGR02Fy0wT8kHoeAHBvr3CM6ByCcX0iAQAf/5EhZVhEREROicmNxERRxNbj+QCAu7q3BABMHtIGggDsyLiEcwXlUoZHRETkdJjcSOz0pTJcKtVCpZChV5Q/ACAywAP927QAAPyYmi1leERERE6HyY3Edp8uAAD0jPSDm1JuPn5vzwgAwMbDFyWJi4iIyFkxuZHY3jPVyU3f1i3qHR/WKRgyATieW4LsogopQiMiInJKTG4kduyiBgAQG+lb77ifhwq9WlUPU/2RnufwuIiIiJwVkxsJVRmMOJ1fBgBoF+zd4P3bOgYDALYwuSEiIrIYkxsJnblcDp3BCA+VHOF+7g3eH9apOrn5K+MSKvUGR4dHRETklJjcSOhEbgkAoF2wF2QyocH7HUK8EeythrbKiANZRQ6OjoiIyDkxuZGQObkJaTgkBQCCIJgLjfdkFjgsLiIiImfG5EZCZy5V19u0CfK66jlxMQEAgN2Z3IqBiIjIEkxuJGSa4h3h37DexuTWmuQmNasQuiqjQ+IiIiJyZkxuJHS+8PrJTdtgLwR4qlCpN+JwdpGDIiMiInJeTG4koqsyIldTCQAIv0ZyIwgC4qKre2/2ZBY6JDYiIiJnxuRGIjnFlTCKgFohQ5CX+prn9mzlBwA4eK7I/oERERE5OSY3EjlfVL3bd7ifOwSh4TTwumIj/QAAaUxuiIiIrovJjURM9TbXGpIy6RbhC7lMQI6mEjnFlfYOjYiIyKkxuZHIhZqZUo2tTHwlD5UC7WvWwkk7x7obIiKia2FyI5H8Ei0AINjHzaLzTRtrHuDQFBER0TUxuZGIKbkJ8r52MbGJue6G2zAQERFdE5MbieSX1iQ315kpZRIb6Q8AOJxdDINRtFtcREREzo7JjUSs7blpG+wFT5Uc5TqDeU8qIiIiaojJjQREUaytubEwuZHLBHQNr667+Se72G6xEREROTvJk5tFixYhOjoabm5u6Nu3L/bs2XPN84uKijBlyhSEhYVBrVajffv22Lhxo4OitY0SbRW0NftEBVo4LAXAnNwcuaCxS1xERESuQCHlzdesWYOkpCQsXrwYffv2xcKFCxEfH4/jx48jODi4wfk6nQ4jRoxAcHAw1q1bh/DwcJw9exZ+fn6OD/4mmHptvNUKuKvkFn+uS0sfAMCRC+y5ISIiuhpJk5sFCxZg0qRJSEhIAAAsXrwYGzZswPLlyzF9+vQG5y9fvhwFBQXYuXMnlEolACA6OtqRIduEtfU2Jqaem6MXNDAaRchk117ZmIiIqDmSLLnR6XTYv38/ZsyYYT4mk8kwfPhw7Nq1q9HP/Pe//0W/fv0wZcoU/PzzzwgKCsLDDz+MV155BXJ54z0gWq0WWq3W/FqjqR7S0ev10Ov1NvyOYL7e9a6bU7P1QgsvlVUxRPqq4KaUoUxnQEZuMWICPW88WCdmaTvTzWE7Owbb2XHY1o5hr3a25nqSJTeXLl2CwWBASEhIveMhISFIT09v9DOnT5/GH3/8gUceeQQbN25ERkYGnnnmGej1esycObPRz8yZMwezZs1qcHzz5s3w8PC4+W+kEcnJydd8/8+LAgA5dJrLVtcLhajlOKsXsHLjdvQKbN5Twq/XzmQbbGfHYDs7DtvaMWzdzuXl5RafK+mwlLWMRiOCg4OxZMkSyOVy9O7dG9nZ2Xj//fevmtzMmDEDSUlJ5tcajQaRkZEYOXIkfHx8bBqfXq9HcnIyRowYYR42a8ypP04BZ06hY+tWGD26s1X32G04irN7zkMZ0gaj49vfbMhOydJ2ppvDdnYMtrPjsK0dw17tbBp5sYRkyU1gYCDkcjlyc3PrHc/NzUVoaGijnwkLC4NSqaw3BNWpUyfk5ORAp9NBpVI1+IxarYZa3bC2RalU2u2H+3rX1mgNAIAWXmqrY+ge4Y9Ve84jPae02f/ltOefIdViOzsG29lx2NaOYet2tuZakk0FV6lU6N27N1JSUszHjEYjUlJS0K9fv0Y/M2DAAGRkZMBoNJqPnThxAmFhYY0mNk1VYbkOAODvYX3MXVrWrHVzoRii2LyHpYiIiBoj6To3SUlJWLp0KVasWIFjx45h8uTJKCsrM8+emjBhQr2C48mTJ6OgoADTpk3DiRMnsGHDBsyePRtTpkyR6lu4IYXl1UVRfh7WZ7TtQ72gkAkoKtcju2ZncSIiIqolac3N+PHjkZ+fjzfffBM5OTmIjY3Fpk2bzEXGWVlZkMlq86/IyEj89ttveP7559G9e3eEh4dj2rRpeOWVV6T6Fm5I8U303KgVcrQP8cbRixocuaBBhL99iqKJiIicleQFxYmJiUhMTGz0va1btzY41q9fP/z99992jsq+bqbnBqhezO/oRQ2OZBcjvkvj9UlERETNleTbLzRHppobvxvouQGAzjUrFR/L4QaaREREV2Jy42BVBiNKKqsAAP432HPTMbQ6uUnP4R5TREREV2Jy42DFFbUrLPq631hy0ynMGwBwrqACJZVcaZOIiKguJjcOZqq38XFTQCG/seb381AhzNcNAJDOoSkiIqJ6mNw4WJFpppTnza3L0ymsZmjqIoemiIiI6mJy42BFNT03NzokZdIxtHpo6uhF9twQERHVxeTGwUq0pmGpm0tuzD03LComIiKqh8mNg5lmSnm73dwSQ6bk5nhOCYxGbsNARERkwuTGwWyV3ES38IBaIUO5zoCsAsu3gSciInJ1TG4cTFMzFdz7JoelFHIZOtTU3RxjUTEREZEZkxsH09T03NxszQ1QW1TMlYqJiIhqMblxMNOiezc7LAXU1t2w54aIiKgWkxsHs1XNDcBtGIiIiBrD5MbBantubn5YitswEBERNcTkxsFKzDU3N99zU3cbhuOsuyEiIgLA5Mbhaoelbr7nBmDdDRER0ZWY3DiYLQuKgdqhKW7DQEREVI3JjQNVGYwo0xkA2C65YVExERFRfUxuHKhUW2X+2tbDUtyGgYiIqBqTGwcy1duoFTKoFLZpem7DQEREVB+TGwfS2HAauAm3YSAiIqqPyY0Dldu43sakI5MbIiIiMyY3DmSqufFQyW16XfN0cK51Q0RExOTGkcq11T03nirb9txwrRsiIqJaTG4cqExX3XPjqbZxz03NdPDzhRXmuh4iIqLmismNA5WbhqXUtu258fVQoiW3YSAiIgLA5MahTAv4edq45gbg0BQREZEJkxsHKjMXFNu25wYAOoaZZkyx54aIiJo3JjcOZJoK7mXjYSmAPTdEREQmTG4cyDwV3MYFxUD9bRgM3IaBiIiaMSY3DlRumi1lh2Gp6BaecFPKUKE34OzlMptfn4iIyFkwuXGgMtM6N3YYlpLLBHQIqa67SeeMKSIiasaY3DhQbc+N7YelANbdEBERAUxuHKq0pufG1uvcmHCPKSIiIiY3DmXqufGyQ0ExULfnhsNSRETUfDG5cSBTzY091rkBgI41yU12UQWKK7gNAxERNU9MbhzItIifPWZLAYCvuxLhfu4AgHQOTRERUTPF5MZBDEYRFXpTzY19hqUAoFMY626IiKh5Y3LjIKbEBrDPCsUmprobTgcnIqLmismNg5h2BBcEQK2wX7NzOjgRETV3TSK5WbRoEaKjo+Hm5oa+fftiz549Vz33q6++giAI9X65ubk5MNobYx6SUsohCILd7mOaDn48l9swEBFR8yR5crNmzRokJSVh5syZSE1NRY8ePRAfH4+8vLyrfsbHxwcXL140/zp79qwDI74xpk0z3e1UTGwS1cIT7ko5KvVGnOE2DERE1AxJntwsWLAAkyZNQkJCAjp37ozFixfDw8MDy5cvv+pnBEFAaGio+VdISIgDI74xpp4bd5V9m1wuE9CBi/kREVEzZt9uhOvQ6XTYv38/ZsyYYT4mk8kwfPhw7Nq166qfKy0tRVRUFIxGI3r16oXZs2ejS5cujZ6r1Wqh1WrNrzWa6ge+Xq+HXm/btWBM12vsuqUV1TG4KWQ2v++VOoR4Iu1cEY6cL0J8pyC73ksK12pnsh22s2OwnR2Hbe0Y9mpna64naXJz6dIlGAyGBj0vISEhSE9Pb/QzHTp0wPLly9G9e3cUFxdj/vz56N+/P44cOYKIiIgG58+ZMwezZs1qcHzz5s3w8PCwzTdyheTk5AbH/ikUAMihLSvFxo0b7XJfE8Pl6nttP3wKHfUn7XovKTXWzmR7bGfHYDs7DtvaMWzdzuXl5RafK2lycyP69euHfv36mV/3798fnTp1wueff4633367wfkzZsxAUlKS+bVGo0FkZCRGjhwJHx8fm8am1+uRnJyMESNGQKlU1n/zcA6QfgihQQEYPfoWm973SsFnC7Hui70oMHpg9OjBdr2XFK7ZzmQzbGfHYDs7DtvaMezVzqaRF0tImtwEBgZCLpcjNze33vHc3FyEhoZadA2lUomePXsiIyOj0ffVajXUanWjn7PXD3dj19Yaq3/3VCvs/peqS4Q/AOBicSXK9CL8PFR2vZ9U7PlnSLXYzo7BdnYctrVj2LqdrbmWpAXFKpUKvXv3RkpKivmY0WhESkpKvd6ZazEYDDh8+DDCwsLsFaZNVJoLiu23OrGJj5sSEf7V2zBwE00iImpuJJ8tlZSUhKVLl2LFihU4duwYJk+ejLKyMiQkJAAAJkyYUK/g+K233sLmzZtx+vRppKam4tFHH8XZs2fx1FNPSfUtWKSiZiq4m9L+yQ1Qd6VizpgiIqLmRfKam/HjxyM/Px9vvvkmcnJyEBsbi02bNpmLjLOysiCT1eZghYWFmDRpEnJycuDv74/evXtj586d6Ny5s1TfgkXMU8EdldyEeiP5aC6ngxMRUbMjeXIDAImJiUhMTGz0va1bt9Z7/cEHH+CDDz5wQFS25fDkxrwNA4eliIioeZF8WKq5MA1LeTig5gaoTW5O5JagymB0yD2JiIiaAiY3DmKuuXFQctMqwAMeKjm0VdyGgYiImhcmNw7i6GEpWZ1tGI5yaIqIiJoRJjcOUung5AYAOtcMTR29wKJiIiJqPpjcOEiFA9e5MenS0hcAcORCscPuSUREJDUmNw5SrnN8z03X8OqemyMXNBBF0WH3JSIikhKTGwcxFRQ7suemfYg35DIBBWU6XCyudNh9iYiIpMTkxkGkqLlxU8rRLtgLAPBPNoemiIioeWBy4yCmmhtHbb9g0jXcVHfDomIiImoemNw4iBTDUgDQpaWp7oY9N0RE1DwwuXEQU8+No1YoNmHPDRERNTdMbhzAYBShN1TPVlIrHJvcdArzgSAAF4srcblU69B7ExERSYHJjQNoqwzmr92Ujm1yL7UCMS08AbD3hoiImgcmNw6g1dduXOnonhsA6FxTd/MP626IiKgZYHLjAJU1PTdKuQC5THD4/c11N9nsuSEiItfH5MYBTD03UvTaAJwxRUREzQuTGwfQVpmSG2ma27TH1JnL5dBU6iWJgYiIyFGsftp++eWXKC8vt0csLqtSogX8TAI8VQj3cwcAHGNRMRERuTirk5vp06cjNDQUTz75JHbu3GmPmFyO1D03QN2iYiY3RETk2qx+2mZnZ2PFihW4dOkShg4dio4dO2Lu3LnIycmxR3wuwTQVXCVhctO1pamomHU3RETk2qx+2ioUCowdOxY///wzzp07h0mTJmHlypVo1aoV7r77bvz8888wGo3Xv1AzYi4olmhYCqhbVMyeGyIicm031ZUQEhKCgQMHol+/fpDJZDh8+DAmTpyINm3aYOvWrTYK0fmZpoK7SdlzUzMd/GReiXmfKyIiIld0Q0/b3NxczJ8/H126dMHQoUOh0Wjw66+/IjMzE9nZ2XjggQcwceJEW8fqtJpCz02IjxqBXmoYReDoRQ5NERGR67I6ubnrrrsQGRmJr776CpMmTUJ2dja+++47DB8+HADg6emJF154AefOnbN5sM6qKRQUC4KAHhHVvTcHzzG5ISIi16Ww9gPBwcHYtm0b+vXrd9VzgoKCkJmZeVOBuRJTQbFUU8FNukf4ISU9D4fOF0kaBxERkT1Z3ZUwZMgQ9OrVq8FxnU6Hr7/+GkB1L0FUVNTNR+ciKvXS99wAQPfI6p6bQ+fZc0NERK7L6qdtQkICiosbPhxLSkqQkJBgk6BcjannRurkpkeEHwDg9KUyFFdwpWIiInJNVj9tRVGEIDTc/PH8+fPw9fW1SVCuprbmRtphqQBPFSL8q1cq/ofr3RARkYuyuOamZ8+eEAQBgiBg2LBhUChqP2owGJCZmYk77rjDLkE6O9NsKTel9Ft59Yjww/nCChw8X4QBbQOlDoeIiMjmLE5uxowZAwBIS0tDfHw8vLy8zO+pVCpER0fjvvvus3mArqDSPCwlbc8NAHSP8MWGwxdxiDOmiIjIRVmc3MycORMAEB0djfHjx8PNzc1uQbma2nVupO+56V5Td8MZU0RE5KqsftpOnDiRiY2VmkpBMQB0i/CFIAAXiiuRX6KVOhwiIiKbs6jnJiAgACdOnEBgYCD8/f0bLSg2KSgosFlwrqLSXHMj/bCUl1qBNkFeyMgrxaHzRRjWKUTqkIiIiGzKouTmgw8+gLe3t/nrayU31FBT6rkBqutuMvJKcfB8MZMbIiJyORYlN3X3iXr88cftFYvLaipTwU16RPjhx9Rs1t0QEZFLsrorITU1FYcPHza//vnnnzFmzBi8+uqr0Ol0Ng3OVTSFvaXq6m7eY6oIoihKHA0REZFtWf20ffrpp3HixAkAwOnTpzF+/Hh4eHhg7dq1ePnll20eoCvQ6pvG3lImncJ8oJAJKCzX43xhhdThEBER2ZTVyc2JEycQGxsLAFi7di2GDBmCVatW4auvvsIPP/xg6/hcgrnnpglMBQeqk6yOYdU1VAc5NEVERC7mhrZfMBqrH9a///47Ro8eDQCIjIzEpUuXbBudizD13DSVYSmg7no3XMyPiIhci9VP2z59+uCdd97BN998g23btuHOO+8EAGRmZiIkhDNvGmPquWkqw1IAEFuT3KRlFUkaBxERka1ZndwsXLgQqampSExMxGuvvYa2bdsCANatW4f+/fvfUBCLFi1CdHQ03Nzc0LdvX+zZs8eiz61evRqCIJi3hmiqKptgz02vKD8AwKHsIugNRmmDISIisiGLt18w6d69e73ZUibvv/8+5HLreybWrFmDpKQkLF68GH379sXChQsRHx+P48ePIzg4+KqfO3PmDF588UUMGjTI6ns6WlObCg4ArQO94OOmgKayCscuaszDVERERM7uhrsSdDodzp8/j6ysLGRlZSEvLw8XL160+joLFizApEmTkJCQgM6dO2Px4sXw8PDA8uXLr/oZg8GARx55BLNmzULr1q1v9FtwiCqDEVXG6unWTannRiYT0LOVPwAg9WyhxNEQERHZzg3Nlho0aBDc3d0RFRWFmJgYxMTEIDo6GjExMVZdS6fTYf/+/Rg+fHhtQDIZhg8fjl27dl31c2+99RaCg4Px5JNPWhu+w+nqDPk0pZobAOhlSm5Yd0NERC7E6mGphIQEKBQK/PrrrwgLC7uprRguXboEg8HQoBA5JCQE6enpjX5mx44dWLZsGdLS0iy6h1arhVZbu0GkRqMBAOj1euj1+hsL/CpM16t73ZLy2oUNBdEAvb7p1Ld0D6+eDp56tsDmbWFPjbUz2R7b2THYzo7DtnYMe7WzNdezOrlJS0vD/v370bFjR2s/etNKSkrw2GOPYenSpQgMDLToM3PmzMGsWbMaHN+8eTM8PDxsHSIAIDk52fx1kRYAFJALIn7b9D+73O9GVVYBAuQ4X1SJ1es3wkcldUTWqdvOZD9sZ8dgOzsO29oxbN3O5eXlFp9rdXLTuXNnm61nExgYCLlcjtzc3HrHc3NzERoa2uD8U6dO4cyZM7jrrrvMx0xr7igUChw/fhxt2rSp95kZM2YgKSnJ/Fqj0SAyMhIjR46Ej4+PTb4PE71ej+TkZIwYMQJKpRIAcPZyOZC6A24qBUaPjrfp/Wxh2dmdOJFXioD2vTGys3NM5W+sncn22M6OwXZ2HLa1Y9irnU0jL5awOrmZO3cuXn75ZcyePRvdunVrELg1CYNKpULv3r2RkpJins5tNBqRkpKCxMTEBud37NixwUyt119/HSUlJfjwww8RGRnZ4DNqtRpqtbrBcaVSabcf7rrXNtSUNbkr5U3yL1PvaH+cyCvFoewS3NkjQupwrGLPP0OqxXZ2DLaz47CtHcPW7WzNtaxObkzFv8OGDat3XBRFCIIAg8Fg1fWSkpIwceJE9OnTB3FxcVi4cCHKysqQkJAAAJgwYQLCw8MxZ84cuLm5oWvXrvU+7+fnBwANjjcVtWvcNK1iYpOerfzx3Z5zSM3ijCkiInINVic3W7ZssWkA48ePR35+Pt58803k5OQgNjYWmzZtMhcZZ2VlQSZrOlOordXUdgS/kmnG1KHzxdBVGaFqonESERFZyurkZsiQITYPIjExsdFhKADYunXrNT/71Vdf2TweW9JW1fTcNLFp4CatAz3h665EcYUexy5q0CPST+qQiIiIbsoN/Tf9zz//xKOPPor+/fsjOzsbAPDNN99gx44dNg3OFVTqm3bPTfVifn4AwKEpIiJyCVY/cX/44QfEx8fD3d0dqamp5jVkiouLMXv2bJsH6OzMPTdNNLkBuJgfERG5FqufuO+88w4WL16MpUuX1qtcHjBgAFJTU20anCvQ1dTcNOValt5R1cnN/jMFEkdCRER086x+4h4/fhyDBw9ucNzX1xdFRUW2iMmlmHbcbso9N7GRfpDLBFworsT5QssXSSIiImqKrH7ihoaGIiMjo8HxHTt2NPlNLKWgM1RvmqmUN93kxlOtQNdwXwDAXvbeEBGRk7P6iTtp0iRMmzYNu3fvhiAIuHDhAlauXIkXX3wRkydPtkeMTs00LNWUkxsAiIuuHprak8miYiIicm5WTwWfPn06jEYjhg0bhvLycgwePBhqtRovvvginn32WXvE6NRMw1JNPbm5JToAS//MZM8NERE5PauTG0EQ8Nprr+Gll15CRkYGSktL0blzZ3h5edkjPqenNxcU3/ju6Y5wS3QAACAjrxSXS7Vo4dVwywoiIiJncEPdCaIoQqPRICQkBHFxcUxsrsHUc6Nq4j03/p4qtA+p/nPce4ZDU0RE5LyseuLm5ORgwoQJ8Pf3R0hICIKDg+Hv748nnniiwc7eVM0ZCopNTL03HJoiIiJnZvGwlEajQf/+/VFaWoqEhAR07NgRoiji6NGj+O6777Bjxw6kpqayF+cK5pqbJjwV3CQuJgArd2cxuSEiIqdmcXLz4YcfQi6X48iRIwgKCqr33uuvv44BAwbgo48+wquvvmrzIJ2Zs8yWAmp7bo5c0KBUWwUvtdUlWURERJKz+Im7YcMGvPrqqw0SGwAIDg7GjBkz8Msvv9g0OFdQW3PTtAuKAaClnzsi/N1hMIpIPcu6GyIick4WJzcnTpxA//79r/p+//79cfz4cZsE5Up0TjIV3CSOdTdEROTkLH7iajQa+Pn5XfV9Pz8/aDQaW8TkUvQ1BcVNeW+pum6JqU5u9mQyuSEiIudk8RNXFEXIZFc/XRAEiKJok6Bcid6Jam6A6qJiADhwrgiVeoPE0RAREVnP4opRURTRvn17CELjtSNMbBrnLOvcmLQO9ESwtxp5JVocyCpCvzYtpA6JiIjIKhYnN19++aU943BZ5pqbJr5CsYkgCOjfpgXWp13ArlOXmNwQEZHTsTi5mThxoj3jcFnONBXcpH+bQKxPu4Cdpy4jSepgiIiIrOQ8T1wn5SwbZ9Zl6q1JO1eEMm2VxNEQERFZx3meuE7K2WZLAUBkgAciA9xRZRSxh1PCiYjIyTjPE9dJOVtBsUn/1oEAgF2nLkscCRERkXWc64nrhJxtET+T/m2rh6Z2nrokcSRERETWsfqJu2XLFnvE4bJqC4qdY7aUSb/W1cnNkQsaFJXrJI6GiIjIclYnN3fccQfatGmDd955B+fOnbNHTC7FGQuKASDYxw1tg70gisDfp1l3Q0REzsPqJ252djYSExOxbt06tG7dGvHx8fj++++h0/F/941xxoJik/41s6Z2cWiKiIiciNVP3MDAQDz//PNIS0vD7t270b59ezzzzDNo2bIlpk6dioMHD9ojTqdl2n7B2QqKgdrkZieLiomIyInc1BO3V69emDFjBhITE1FaWorly5ejd+/eGDRoEI4cOWKrGJ1a7QrFzpfc9I1pAUEATuaVIk9TKXU4REREFrmhJ65er8e6deswevRoREVF4bfffsMnn3yC3NxcZGRkICoqCuPGjbN1rE6ptubGuQqKAcDfU4Vu4b4AgO0nOTRFRETOwerk5tlnn0VYWBiefvpptG/fHgcOHMCuXbvw1FNPwdPTE9HR0Zg/fz7S09PtEa9TqTIYYazZT9QZh6UAYHC7IADA9hP5EkdCRERkGYv3ljI5evQoPv74Y9x7771Qq9WNnhMYGMgp46gtJgacb7aUyeD2QfhkSwb+PJkPg1GEXOZ8PVBERNS8WP3EnTlzJsaNG9cgsamqqsL27dsBAAqFAkOGDLFNhE7MVG8DOG9y07OVH7zVChSW6/FPdrHU4RAREV2X1U/c2267DQUFDdc9KS4uxm233WaToFyFvl5y45w9Hkq5zLxaMYemiIjIGVid3IiiCEFo+KC+fPkyPD09bRKUq6i7r1RjbeYshrQPBgBsY3JDREROwOKam3vvvRcAIAgCHn/88XrDUgaDAYcOHUL//v1tH6ET01dV19w4a6+NyeD21ZtoHjhXhOIKPXzdlRJHREREdHUWJze+vtVTgkVRhLe3N9zd3c3vqVQq3HrrrZg0aZLtI3RiOoMBgHOucVNXhL8HWgd54nR+GXZmXMKobmFSh0RERHRVFic3X375JQAgOjoaL774IoegLKAz99w4d3IDAEPaB+F0fhm2n8xnckNERE3aDc2WYmJjmbo1N85ucHvTejeXIIridc4mIiKSjkU9N7169UJKSgr8/f3Rs2fPaxbHpqam2iw4Z2dObpx8WAoAbo1pAZVChuyiCpzKL0XbYG+pQyIiImqURcnNPffcYy4gHjNmjD3jcSk6J9564UruKjn6xgTgz5OX8Ed6HpMbIiJqsixKbmbOnNno17ayaNEivP/++8jJyUGPHj3w8ccfIy4urtFzf/zxR8yePRsZGRnQ6/Vo164dXnjhBTz22GM2j+tmmVYodoWaGwAY3ikEf568hN+P5uH/BreROhwiIqJGSf7UXbNmDZKSkjBz5kykpqaiR48eiI+PR15eXqPnBwQE4LXXXsOuXbtw6NAhJCQkICEhAb/99puDI78+XZWp50byZraJYZ2q17vZd7YAhWU6iaMhIiJqnEVPXX9/fwQEBFj0y1oLFizApEmTkJCQgM6dO2Px4sXw8PDA8uXLGz1/6NChGDt2LDp16oQ2bdpg2rRp6N69O3bs2GH1ve3NlQqKgeop4R1DvWEUga0nGk8+iYiIpGbRsNTChQvtcnOdTof9+/djxowZ5mMymQzDhw/Hrl27rvt5URTxxx9/4Pjx45g7d65dYrwZpuRGqXD+mhuT4Z1CkJ5Tgt+P5mFszwipwyEiImrAouRm4sSJdrn5pUuXYDAYEBISUu94SEgI0tPTr/q54uJihIeHQ6vVQi6X49NPP8WIESMaPVer1UKr1ZpfazQaAIBer4der7fBd1HLdD3T7xXa6t8VMsHm95LKkHYB+GRLdc9NWYVWkplgV7Yz2Qfb2THYzo7DtnYMe7WzNdezKLnRaDTw8fExf30tpvPsydvbG2lpaSgtLUVKSgqSkpLQunVrDB06tMG5c+bMwaxZsxoc37x5Mzw8POwSX3JyMgDgQK4AQI6C/Dxs3LjRLvdyNKMIeCvlKNEasOj739DBT7o1b0ztTPbFdnYMtrPjsK0dw9btXF5ebvG5FiU3/v7+uHjxIoKDg+Hn59foOjemDTUNNVsOWCIwMBByuRy5ubn1jufm5iI0NPSqn5PJZGjbti0AIDY2FseOHcOcOXMaTW5mzJiBpKQk82uNRoPIyEiMHDnS5omYXq9HcnIyRowYAaVSict/ZwGn0xEZHobRo3vY9F5S2qk/grX7s1HiG4PRozs6/P5XtjPZB9vZMdjOjsO2dgx7tfP1Olfqsii5+eOPP8zFwlu2bLmxqBqhUqnQu3dvpKSkmNfPMRqNSElJQWJiosXXMRqN9Yae6lKr1fU2+TRRKpV2++E2XdsgVieBaqXCpf4ijegcirX7s7HleD7euqerZDue2/PPkGqxnR2D7ew4bGvHsHU7W3Mti5KbIUOGNPq1LSQlJWHixIno06cP4uLisHDhQpSVlSEhIQEAMGHCBISHh2POnDkAqoeZ+vTpgzZt2kCr1WLjxo345ptv8Nlnn9k0LltwpUX86hrYLhAqhQznCytwIrcUHUK5oB8RETUdFm+cWVdhYSGWLVuGY8eOAQA6d+6MhISEG5oKPn78eOTn5+PNN99ETk4OYmNjsWnTJnORcVZWFmSy2qLVsrIyPPPMMzh//jzc3d3RsWNHfPvttxg/fvyNfCt2ZZ4t5SJTwU08VAoMbBuIP9LzsPlIDpMbIiJqUqx+6m7fvh3R0dH46KOPUFhYiMLCQnz00UeIiYnB9u3bbyiIxMREnD17FlqtFrt370bfvn3N723duhVfffWV+fU777yDkydPoqKiAgUFBdi5c2eTTGwA19pb6krxXaqTz//9kyNxJERERPVZ/dSdMmUKxo8fj8zMTPz444/48ccfcfr0aTz44IOYMmWKPWJ0WqbtF1xlEb+6RnQOhVwm4OhFDc5eLpM6HCIiIjOrn7oZGRl44YUXIJfLzcfkcjmSkpKQkZFh0+Ccnattv1BXgKcKt7auHoZk7w0RETUlVj91e/XqZa61qevYsWPo0cN1pjvbgs5Fa25MRnUNA8DkhoiImhaLCooPHTpk/nrq1KmYNm0aMjIycOuttwIA/v77byxatAjvvfeefaJ0Uvoq19t+oa6RXULwxs//4OC5ImQXVSDcz13qkIiIiCxLbmJjYyEIAkSxdjXal19+ucF5Dz/8cJMt7pWCq22ceaVgbzfcEh2APZkF2PRPDp4cGCN1SERERJYlN5mZmfaOwyWZC4pdcLaUyaiuodiTWYD/Hb7I5IaIiJoEi5KbqKgoe8fhkly95gYA7ugailm/HMW+s4XI1VQixMdN6pCIiKiZu6FF/ADg6NGjyMrKgk6nq3f87rvvvumgXIWrLuJXV5ivO3q18kNqVhE2/ZODif2jpQ6JiIiaOauTm9OnT2Ps2LE4fPhwvToc0/5C1myc6epqp4K7ZkGxyehuYUjNKsKvhy4wuSEiIslZ3aUwbdo0xMTEIC8vDx4eHjhy5Ai2b9+OPn36YOvWrXYI0Xm5ekGxyb+6t4QgAHvPFOJ8oeVb0hMREdmD1U/dXbt24a233kJgYCBkMhlkMhkGDhyIOXPmYOrUqfaI0WnpagqKXXlYCgBCfd1wa0wLAMB/D16QOBoiImrurH7qGgwGeHtXb5QYGBiICxeqH2ZRUVE4fvy4baNzcqZ1blx5tpTJPbEtAQA/H2ByQ0RE0rL6qdu1a1ccPHgQANC3b1/MmzcPf/31F9566y20bt3a5gE6s+ZQUGwyqlsYVHIZjueWID1HI3U4RETUjFn91H399ddhNFY/tN966y1kZmZi0KBB2LhxIz766CObB+jMancFd+2CYgDwdVfito5BAID17L0hIiIJWT1bKj4+3vx127ZtkZ6ejoKCAvj7+5tnTFE1V944szH3xIbjtyO5+OXgBbwc3wEyGX8eiIjI8W7qqXvu3DmcO3cOAQEBTGwa0VwKik1u7xgMb7UC2UUV2He2UOpwiIiombL6qVtVVYU33ngDvr6+iI6ORnR0NHx9ffH6669Dr9fbI0an1ZxqbgDATSnHHV1DAQDr07IljoaIiJorq5+6zz77LJYsWYJ58+bhwIEDOHDgAObNm4dly5ZxKvgVTMmNuhnMljIZ0zMcAPDrwQuo1HNBRyIicjyra25WrVqF1atXY9SoUeZj3bt3R2RkJB566CF89tlnNg3QmTW3nhsA6Ne6BcL93JFdVIHfjuTgnthwqUMiIqJmxuqnrlqtRnR0dIPjMTExUKlUtojJJYiiaN4V3NW3X6hLJhMwrk8EAGDtvvMSR0NERM2R1clNYmIi3n77bWi1WvMxrVaLd999F4mJiTYNzpmZdgQHAGUzGpYCgPt7R0AQgL9OXcK5Am7HQEREjmXRsNS9995b7/Xvv/+OiIgI9OjRAwBw8OBB6HQ6DBs2zPYROilTrw3g+ntLXSnC3wP927TAXxmX8UPqeTw3vL3UIRERUTNiUXLj6+tb7/V9991X73VkZKTtInIRpq0XgOZVc2PyQJ9I/JVxGWv3ncfU29txzRsiInIYi5KbL7/80t5xuBxTMbFcJkDeDB/s8V1C4e1WvebNrtOXMaBtoNQhERFRM3HDXQr5+fnYsWMHduzYgfz8fFvG5BJ05plSzS+xAarXvDFtpvn9vnMSR0NERM2J1clNWVkZnnjiCYSFhWHw4MEYPHgwWrZsiSeffBLl5SweNdE3s9WJG/NAn+rhyv/9k4OCMp3E0RARUXNh9ZM3KSkJ27Ztwy+//IKioiIUFRXh559/xrZt2/DCCy/YI0anZNpXqrkVE9fVLdwX3cJ9oasyYi17b4iIyEGsfvL+8MMPWLZsGUaNGgUfHx/4+Phg9OjRWLp0KdatW2ePGJ1Sc1zA70qCIOCxW6MAAN/uPgujUbzOJ4iIiG6e1U/e8vJyhISENDgeHBzMYak6zDU3iuZZc2NyV4+W8HFT4FxBBbadZG0WERHZn9XJTb9+/TBz5kxUVlaaj1VUVGDWrFno16+fTYNzZnoOSwEA3FVyjKupvfl211mJoyEioubA6r2lFi5ciDvuuKPBIn5ubm747bffbB6gs2JBca1Hb43Csh2Z+ON4Hs4VlCMywEPqkIiIyIVZ/eTt1q0bTp48iTlz5iA2NhaxsbF47733cPLkSXTp0sUeMTolU82NqpltvdCYmEBPDGoXCFEEVu7OkjocIiJycVb13Oj1enTs2BG//vorJk2aZK+YXIK2igXFdT12axT+PHkJ3+87h+eGt4ObUi51SERE5KKsevIqlcp6tTZ0dfpmvojflW7vGIxwP3cUlOmw/kC21OEQEZELs7pbYcqUKZg7dy6qqqrsEY/L4FTw+hRyGRIGRAMAvtiRyWnhRERkN1YXFO/duxcpKSnYvHkzunXrBk9Pz3rv//jjjzYLzpmZkhs1a27MHrglEgt/P4mMvFJsO5mP2zoESx0SERG5IKuTGz8/vwa7glNDOs6WasDHTYkHb4nEFzsy8cWfp5ncEBGRXVid3HCHcMvoWVDcqISBMfhy5xn8lXEZRy4Uo0tLX6lDIiIiF2Pxk9doNGLu3LkYMGAAbrnlFkyfPh0VFRX2jM2p6Vhz06hwP3eM7hYGAFj2Z6bE0RARkSuy+Mn77rvv4tVXX4WXlxfCw8Px4YcfYsqUKfaMzamZVyhu5tsvNOapgTEAgP8evICcYs6+IyIi27I4ufn666/x6aef4rfffsP69evxyy+/YOXKlTAajTcdxKJFixAdHQ03Nzf07dsXe/bsueq5S5cuxaBBg+Dv7w9/f38MHz78mudLhbOlrq5HpB/iYgJQZRSxZPtpqcMhIiIXY/GTNysrC6NHjza/Hj58OARBwIULF24qgDVr1iApKQkzZ85EamoqevTogfj4eOTl5TV6/tatW/HQQw9hy5Yt2LVrFyIjIzFy5EhkZzettVNMBcXNfW+pq0m8rS0AYNWes7hcqpU4GiIiciUWP3mrqqrg5uZW75hSqYRer7+pABYsWIBJkyYhISEBnTt3xuLFi+Hh4YHly5c3ev7KlSvxzDPPIDY2Fh07dsQXX3wBo9GIlJSUm4rD1sw9N5wK3qhB7QLRI8IXlXojlu1g7Q0REdmOxbOlRFHE448/DrVabT5WWVmJ//f//l+9tW6sWedGp9Nh//79mDFjhvmYTCbD8OHDsWvXLouuUV5eDr1ej4CAAIvv6wgclro2QRCQeHs7TPp6H77edRZPD24DXw+l1GEREZELsDi5mThxYoNjjz766E3d/NKlSzAYDAgJCal3PCQkBOnp6RZd45VXXkHLli0xfPjwRt/XarXQamuHPTQaDYDqfbJuttfpSqbr6fV6VOqqV3CWQ7T5fVzF4Db+6BjihfTcUizbcQrP3tbGos/VbWeyH7azY7CdHYdt7Rj2amdrrmdxctMU17d57733sHr1amzdurXBkJnJnDlzMGvWrAbHN2/eDA8PD7vElZycjMwsGQAZTp08jo3lliVqzdGtPgLSc+X4YlsGwkuPw82K/TSTk5PtFxiZsZ0dg+3sOGxrx7B1O5eXl1t8rtWL+NlSYGAg5HI5cnNz6x3Pzc1FaGjoNT87f/58vPfee/j999/RvXv3q543Y8YMJCUlmV9rNBpzEbKPj8/NfQNX0Ov1SE5OxogRI7C59BiQn4NuXTtjdL8om97HlcQbRWz/+C+cvlSOHO+OeGZo6+t+pm47K5UcyrIXtrNjsJ0dh23tGPZqZ9PIiyUkTW5UKhV69+6NlJQUjBkzBgDMxcGJiYlX/dy8efPw7rvv4rfffkOfPn2ueQ+1Wl2vTshEqVTa7YdbqVSipuQG7ir73ccVKAFMG94e01an4Yu/zuDxAa0trr2x558h1WI7Owbb2XHY1o5h63a25lqSV7smJSVh6dKlWLFiBY4dO4bJkyejrKwMCQkJAIAJEybUKzieO3cu3njjDSxfvhzR0dHIyclBTk4OSktLpfoWGmUqKOZU8Ou7q3tLdAz1RkllFZb8eUrqcIiIyMlJ/uQdP3485s+fjzfffBOxsbFIS0vDpk2bzEXGWVlZuHjxovn8zz77DDqdDvfffz/CwsLMv+bPny/Vt9Ao8/YLXKH4umQyAS+M7AAAWL7jDPJLuO4NERHdOEmHpUwSExOvOgy1devWeq/PnDlj/4BsQMeNM60yvFMwYiP9kHauCIu2ZODfd3eROiQiInJSfPLaCde5sY4gCHg5vrr3ZtXuLJwvtLwqnoiIqC4+ee1Ez+0XrNa/bSAGtG0BncGIBZtPSB0OERE5KT557cRcUMztF6zyyh0dAQA/HsjGofNF0gZDREROiU9eO9FxWOqGdI/ww709wwEA7/x6DKIoShwRERE5Gz557aS25oazpaz10h0d4KaUYc+ZAmz6J0fqcIiIyMkwubETzpa6cWG+7vi/wdX7TM35Xzq0VQaJIyIiImfCJ6+dmAuKWXNzQ54e3BrB3mpkFZTjq7/OSB0OERE5ET557UTPnpub4qlW4KWaqeEfpZxETnGlxBEREZGz4JPXTnScLXXT7usVgV6t/FCmM+DtDUelDoeIiJwEn7x2woLimyeTCXh7TFfIBGDDoYvYfiJf6pCIiMgJMLmxA4NRhLFmBjMX8bs5XVr6YmL/aADAzP8eYXExERFdF5+8dmCaKQWw5sYWnh/RHkHeamReKsPn205LHQ4RETVxfPLagWlICmByYws+bkq8fmcnAMAnWzJwKr9M4oiIiKgp45PXDuonN6y5sYW7e7TE0A5B0FUZMf2nf8zDfkRERFdicmMHujqbZgoCkxtbEAQBs8d2g5dagbRzxdh2ke1KRESNY3JjB5wpZR8t/dzx6ujq4akN52Q4e7lc4oiIiKgpYnJjB6bViZVc48bmHoqLRP/WAdAbBcxYfwRGjk8REdEV+PS1A+4rZT+CIOCdMZ2hkonYe6YQX+08I3VIRETUxPDpawemYSmucWMfkf4euDuquo3f25SOYxc1EkdERERNCZ++dsCaG/sbGCJiaPtA6KqMmPrdAVTqubgfERFVY3JjB9wR3P4EAXhvbBcEeqlxMq8UszcekzokIiJqIvj0tYPanhs2rz218FLjPw/0AAB8vessUo7lShwRERE1BXz62oGOyY3DDGkfhCcHxgAAXlp3CBeLKySOiIiIpManrx2YZkuxoNgxXr6jA7q09EFBmQ7PrEytt7cXERE1P3z62kHtOjcsKHYEtUKOzx7pDR83BQ5kFeGdDUelDomIiCTE5MYOWHPjeK1aeGDhg7EAqutv1h/IljYgIiKSDJ++dqCvs7cUOc7tHUMw9fa2AIDpPx5Ceg7XvyEiao749LUDc88Np4I73LTh7TGoXSAq9UZM+nofLpdqpQ6JiIgcjE9fO+AKxdKRywR89GBPRLXwwLmCCjz9zX5oq7jAHxFRc8Knrx3U7i3FgmIp+HuqsGziLfB2U2Df2ULM+OEwRJEbbBIRNRdMbuzAPFuKPTeSaRvshc8e6Q25TMCPB7Lx6dZTUodEREQOwqevHXC2VNMwsF0gZt3dBQDw/m/H8XMaZ1ARETUHfPragWmFYjULiiX36K1R5hWMX/j+ILYez5M4IiIisjc+fe2Aw1JNy2ujO+HuHi1RZRQx+dtUpGYVSh0SERHZEZ++dsBhqaZFJhMwf1wPDG4fhAq9AU98tRcnc0ukDouIiOyET187MG+cye0XmgyVQobFj/ZCbKQfisr1eHTZbpy5VCZ1WEREZAdMbuxAX8UVipsiD5UCXz5+C9oFeyFXo8VDS//G2ctMcIiIXA2fvnbAYammy99ThVWTbkXbYC9cLK7EQ0v+RtblcqnDIiIiG+LT1w7MKxRztlSTFOStxqpJfdE6yBMXiivx0NK/ca6ACQ4Rkavg09cOOFuq6Qv2dsN3k25FTKAnsosqMG7xLhYZExG5CD597aB2WIoFxU1ZiI8bVv/frWgX7IUcTSUe+HwXDp4rkjosIiK6SZInN4sWLUJ0dDTc3NzQt29f7Nmz56rnHjlyBPfddx+io6MhCAIWLlzouECtoOPGmU4jxMcN3z/dDz0ifFFYrsfDS//GrlOXpQ6LiIhugqRP3zVr1iApKQkzZ85EamoqevTogfj4eOTlNb6KbHl5OVq3bo333nsPoaGhDo7WcjoWFDsVf08VVk66Ff3btECZzoCJX+7Bpn9ypA6LiIhukKRP3wULFmDSpElISEhA586dsXjxYnh4eGD58uWNnn/LLbfg/fffx4MPPgi1Wu3gaC1nmgquZEGx0/BSK7D88VswsnMIdFVGTF65H0u2n+Ju4kRETkgh1Y11Oh3279+PGTNmmI/JZDIMHz4cu3btstl9tFottFqt+bVGowEA6PV66PV6m93HdE0A0BkMAAA5jDa/B9W2s63bVg7gwwe64Z2NKqzccw6zN6bjVF4pZv6rY7PshbNXO1N9bGfHYVs7hr3a2ZrrSZbcXLp0CQaDASEhIfWOh4SEID093Wb3mTNnDmbNmtXg+ObNm+Hh4WGz+9RVXFIGQMC+PX/j8jG73IIAJCcn2+W6t8iA8mgB68/IsGbfeRw4mYWE9kZ4SPa3RVr2ameqj+3sOGxrx7B1O5eXW75kh8v/cz1jxgwkJSWZX2s0GkRGRmLkyJHw8fGx6b30ej2Sk5OhVLsBlVoMHjgA3cJ9bXoPqm3nESNGQKlU2uUedwKIT89D0trDOFEMLDnthUUPxaJdiJdd7tcUOaKdie3sSGxrx7BXO5tGXiwhWXITGBgIuVyO3Nzcesdzc3NtWiysVqsbrc9RKpV2++E2rXPjrlbxL5Ad2fPPEADu6BaOiAAvPP3NfmReLsd9n+/GvPu7464eLe12z6bI3u1M1djOjsO2dgxbt7M115KskEClUqF3795ISUkxHzMajUhJSUG/fv2kCssmuP2C6+ga7otfnh2IgW0DUaE34NnvDuDtX4+a/4yJiKjpkfTpm5SUhKVLl2LFihU4duwYJk+ejLKyMiQkJAAAJkyYUK/gWKfTIS0tDWlpadDpdMjOzkZaWhoyMjKk+hYaZeq54To3riHAU4UVT8Rh8tA2AIBlOzLx0JK/cb6QWzYQETVFktbcjB8/Hvn5+XjzzTeRk5OD2NhYbNq0yVxknJWVBZmsNkG4cOECevbsaX49f/58zJ8/H0OGDMHWrVsdHf5V6aq4t5SrkcsEvHJHR/SI8MOLaw9i39lCjPrwT8we263ZDVMRETV1khcUJyYmIjExsdH3rkxYoqOjm/y6I0YRqDLW9NwwuXE5d3QNRZeWPpi6+gAOZBXh2e8OYNuJfMy6uws81ZL/dSIiIjSB7RdcTVWdUgw1kxuXFBnggbVP98PU29tCJgDr9p/HnR/9ib1nCqQOjYiIwOTG5qrqdCyx58Z1KeQyJI3sgO8m3YqWvm44c7kcD3y+C//+7xGUaaukDo+IqFnj09fGTD03ggAoZNwV3NX1bd0C/3tuMMb3iYQoAl/tPIM7PtyOnRmXpA6NiKjZYnJjY/qa5EatkEEQmNw0B77uSsy9vzu+eTIO4X7uOFdQgYe/2I2X1x3E5VLt9S9AREQ2xeTGxkzDUpwG3vwMaheE354fjAn9ogAA3+87j9v/sw3f/H0WBmPTLoQnInIlfALbmGlYSqWQSxsIScJLrcBb93TFD5P7o3OYD4or9Hhj/T+4Z9EOHMgqlDo8IqJmgcmNjVXVGZai5qt3lD9+eXYg3rqnC7zdFPgnW4Oxn+7EtNUHcK6Ai/8REdkTn8A2ZhqWYnJDcpmACf2i8ccLQ3F/7wgAwM9pFzDsP9vwzq9HUVSukzhCIiLXxCewjemN1UXEnAZOJkHeaswf1wO/PjsQA9q2gM5gxBc7MjF43hYs3nYKFTqD1CESEbkUPoFtjD03dDVdw33x7ZN9seKJOHQM9Yamsgrv/S8dg+b9gaXbT6Ncx/VxiIhsgU9gG6stKGbTUkOCIGBI+yBsmDoI79/fHZEB7rhUqsO7G49h8LwtTHKIiGyAT2Abqy0o5mwpujq5TMC4PpH444WhmHdf/SRn0Nwt+PD3kygoY00OEdGNYHJjY+Z1bthzQxZQymV44JaaJOf+7mgV4IHLZTp88PsJ9H8vBa+vP4zMS2VSh0lE5FS4jbGNmYeluIgfWUEpl+GBPpG4t2c4Nv6TgyXbT+GfbA2+/TsLK3dnYWTnEDzePwa3tg7gytdERNfB5MbGzNsvKJnckPUUchnu7tESd3UPw9+nC7D0z9P4Iz0Pvx3JxW9HctEmyBOP9I3Cfb0i4OuhlDpcIqImicmNjXH7BbIFQRDQr00L9GvTAidzS/DlzjNYfyAbp/LL8NavRzHvt3Tc1b0lHrk1Cj0ifNmbQ0RUB5MbG+NsKbK1diHemD22G2aM6oj1aRew8u+zSM8pwdr957F2/3m0D/HCvb0iMLZnOEJ83KQOl4hIckxubKyqZhE/zpYiW/N2U+KxW6PwaN9WSM0qxLd/Z2HD4Ys4kVuK9/6Xjnmb0jGgbSDu6xWBkV1C4KHiX28iap74r5+NcbYU2ZsgCOgdFYDeUQH4991dsPHwRfyYeh57zxTiz5OX8OfJS/BQyTGsUwju7BaKIe2D4a5isk1EzQeTGxvTc1iKHMjXXYmH4lrhobhWOHu5DD8dyMaPqdnIKijHLwcv4JeDF+ChkuO2jsG4s1sYbuvARIeIXB+TGxvjruAklagWnnhueHtMG9YOaeeKsPHwRWw8nIPsogpsOHQRGw5dhLtSjkHtAnF7x2Dc1jGYNTpE5JKY3NgY95YiqQmCgJ6t/NGzlT9eHd0Jh84XY+Phi9hw+CLOF1Zg89FcbD6aCwDoFu6L2zoGY1jHYHQL94VMxllXROT8mNzYGGdLUVMiCAJ6RPqhR6Qfpo/qiCMXNPgjPQ8p6Xk4eK4Ih7OLcTi7GB+lnESglxoD2rbAgDaBGNAuEMGe/OeBiJwT//WyMfbcUFMlCAK6hvuia7gvpg5rh/wSLbYez8Mf6XnYfiIfl0q1+DntAn5OuwAAiArwQLhSBuGfHAxqHwJ/T5XE3wERkWWY3NgYe27IWQR5qzGuTyTG9YmErsqIfWcLsDPjMv46dQmHzhfjbEE5zkKGnWsOQRCADiHe6B3lj1uiA9An2h/hfu5cPJCImiQmNzZmWudGJeeMFHIeKoUM/dsEon+bQLyIDtBU6rHzRB5W/ZGKi0ZvnMwrQ3pOCdJzSrBydxYAINTHDX2iq5Od3lH+6BDqDSVX5iaiJoDJjY1xWIpcgY+bEsM6BUObacTo0QNQVGnE/rMF2HemEHvPFuJIdjFyNJX49dBF/HroIoDqn/nOLX3QPdwX3SP80D3CF62DvCBnkTIRORiTGxvjsBS5oiBvNe7oGoY7uoYBACp0BqSdK8K+MwXYe7YQB7IKUVJZhQNZRTiQVQTgLADAUyVHl3Bf9IjwRacwH3QM9UHbYC/+/SAiu2JyY2N6rnNDzYC7Sm7e2BMAjEYRZwvKceh8EQ6dL8ah80X4J1uDMp0BezILsCezwPxZhUxA22AvdAz1RscwH3QM9UanMB8Ee6tZw0NENsHkxsa4/QI1RzKZgJhAT8QEeuKe2HAAgMEoIiOvFAfPF+Gf7OLqmp2LGmgqq8z1O6iZmQUA/h5KtA32Qpugml/BnmgT5IUIfw8ObRGRVZjc2JjWUP27l5pNS82bXCagQ6g3OoR644E+kQAAURRxsbgSxy5qkJ5TYv79dH4pCsv12HumEHvPFNa7jkouQ0ygJ1oHVSc7rYM8EdXCE60CPBDopWJvDxE1wCewjelqkhvu30PUkCAIaOnnjpZ+7hjWKcR8vFJvQEZeKU5fKsOpvFKcyi/FqfwynM4vhbbKiOO5JTieW9Lgeh4qOVoFeCAywAOtAjwQ1aL26wh/d6gV/HtI1BwxubGhKoMRerH6f5GeKjYtkaXclHLzAoN1GY0isosqzMnOqfxSnM4vxbmCClworkC5zlA7xHUFQaierh7m64YwP3eE+7lXf+1b87WfG1p4sueHyBXxCWxDFXqD+WsPNf/HSHSzZDIBkTU9M0M71H9PW2VAdmEFsgrKca6gHGcvlyOroPZXuc6Ai8WVuFhcCWQVNXp9lUKGMF83tPStTnZCfdwQ7K1GkLcbgn3UNV+r4cH/rBA5Ff6NtaGymjEphUyAiouZEdmVWiFH6yAvtA7yavCeKIq4XKbD+cIKXCyqQHZRRU2iU4ELRZW4UFSB/FItdFVGnL1cnRhdi5dagWBvNQK9axOeYG8387EADxUCvFRo4amCm5L/sSGSGpMbGyqvqSb2UMnZ1U0kIUEQEOilRqCXGrGRfo2eo6syIldT3bNzoah6mCtPo0VeSSXyS7TIK9EiT6NFhd6AUm0VSrVVOH2p7Lr3dlfKEeCpMv9q4amCf53XdY/5uivhwX+FiWyOf61sqFxXm9wQUdOmUsjMQ15XI4oiynQG5GkqkVeirU16ahKg/BItLpXqUFCmRUGZDnqDiAq9Adk1vUUWxyKTY86RbfDzUMHHTQkfdyV86/1SwNej+msft9rj3m5KuCll/M8U0RWY3NhQma4KADg+T+QiBEGAl1oBr6sMf9UliiJKtVUoKNOZf10u06GwzmvzsXIdCkp1KNFW/5uhMwrI0WiRo9FaHaNcJsBTJYe3mxJeagU81XJ4uSnhrVbUvFbAy00B78a+Vivg7aaAu0oOD5Uc7kr2OpNr4FPYhkw9N54sJiZqdgRBgLdbdW9KVAtPiz5jMIooKKnAfzclo2ffASjTiyiu0KO4Qg9NRVWdr/W1X1fWHjOK1dfQVFZBU1llk+/DXVmT6JgSHpUCHlcc81BVJ0QNzlUqat6Xw00ph5tSBrVCDrVCBrWy5ncFe5rI/pjc2FBRuR4A4O3GZiWi65PLBPh5KBHoBnQL94VSqbT4s0ajaK4HKqmsQllNXVDdrxt7r1SrR5nWUO91pWnfGFTP+qzQG4DrlxfdMLVCBreaZOd6v6uvclylkEElr/5dKZdBKRcaOVb/PIgGVFQBWr0BcrkCMq587bKaxFN40aJFeP/995GTk4MePXrg448/Rlxc3FXPX7t2Ld544w2cOXMG7dq1w9y5czF69GgHRty4XE0lACDEx03iSIjI1clkAjxrhpdCfG7uWqZEqVxnQIXOgHJ9Ve3XOgPKdVXmryv0hjpfV9W8bzpWZT5Hqzeisqr2d1GsvZ+2yghtlfHqAdmVAtP3plR/JRPqJEZyqGoSpMYSI4VcgEImg0ImQCGv/pxcJkBZc9z8tVwGpUyAXCarOa/6a+UVn1fIa76uiUEhF2quYTpe//Om8+Sy6vPkggCZDFDIZJDJALlQfZy9YtUkT27WrFmDpKQkLF68GH379sXChQsRHx+P48ePIzg4uMH5O3fuxEMPPYQ5c+bgX//6F1atWoUxY8YgNTUVXbt2leA7qJVbUj1eHuqtljQOIiJr1E2U7EEURegNYm2yozdAW1X7u7bmuLbKgEqLfjdCV2WA3iBCb6h+rTcYoav3uwjdFceqjGK9uKqMIqqMBlToAcA2w3pSkwm4IgGq/lohEyCrSYDqvm/6+prv1fu86foyyAWY3zNdQyETAIjQXBQgZZeD5MnNggULMGnSJCQkJAAAFi9ejA0bNmD58uWYPn16g/M//PBD3HHHHXjppZcAAG+//TaSk5PxySefYPHixQ6N/Uqm2RHBPkxuiIhMBEGASlHdKwIJO7a1Wh1+2fg/3D58JCCTmxOfxpIjnaEmQaoyQmeoTqQMRrF6JXqDiCpjdbJUZag+Vp0oVSdbBmN1Mldl+rrO5ww1n6t3ntFYfZ1651UfN32tr7mH4YoE7UpGETAaqq8rpWgvadd6kzS50el02L9/P2bMmGE+JpPJMHz4cOzatavRz+zatQtJSUn1jsXHx2P9+vWNnq/VaqHV1s5A0Gg0AAC9Xg+9Xn+T30GtfWcLsf3EZQBAuI/Kptem+kxtyza2L7azY7CdHcdgqIJSBrjJRSiVAqCSA3CuCSCiKJoLyY1idbJjMIowiCKMNQmW6X2DKMJguPI9seazQJXRCKMR9d83fc58XTT4bN371d4D5tc6fRWKLmTa/GfamutJmtxcunQJBoMBISEh9Y6HhIQgPT290c/k5OQ0en5OTk6j58+ZMwezZs1qcHzz5s3w8Lj6+hbWOl8GeCjkiPISUXY6FRszbXZpuork5GSpQ2gW2M6OwXZ2HLa1ZWQ1vwDA6vGIUNu3c3n5tVcSr0vyYSl7mzFjRr2eHo1Gg8jISIwcORI+PjdZhXeFkfklSPv7T8SPHGHVrAeyjl6vR3JyMkaMYDvbE9vZMdjOjsO2dgx7tbNp5MUSkiY3gYGBkMvlyM3NrXc8NzcXoaGhjX4mNDTUqvPVajXU6oY5p1KptPkPd3SQN47K7XNtaojt7BhsZ8dgOzsO29oxbN3O1lxL0ooflUqF3r17IyUlxXzMaDQiJSUF/fr1a/Qz/fr1q3c+UN31dbXziYiIqHmRfFgqKSkJEydORJ8+fRAXF4eFCxeirKzMPHtqwoQJCA8Px5w5cwAA06ZNw5AhQ/Cf//wHd955J1avXo19+/ZhyZIlUn4bRERE1ERIntyMHz8e+fn5ePPNN5GTk4PY2Fhs2rTJXDSclZUFmay2g6l///5YtWoVXn/9dbz66qto164d1q9fL/kaN0RERNQ0SJ7cAEBiYiISExMbfW/r1q0Njo0bNw7jxo2zc1RERETkjKRdZYeIiIjIxpjcEBERkUthckNEREQuhckNERERuRQmN0RERORSmNwQERGRS2FyQ0RERC6FyQ0RERG5FCY3RERE5FKaxArFjiSKIgDrtk63lF6vR3l5OTQaDXectSO2s2OwnR2D7ew4bGvHsFc7m57bpuf4tTS75KakpAQAEBkZKXEkREREZK2SkhL4+vpe8xxBtCQFciFGoxEXLlyAt7c3BEGw6bU1Gg0iIyNx7tw5+Pj42PTaVIvt7BhsZ8dgOzsO29ox7NXOoiiipKQELVu2rLehdmOaXc+NTCZDRESEXe/h4+PDvzgOwHZ2DLazY7CdHYdt7Rj2aOfr9diYsKCYiIiIXAqTGyIiInIpTG5sSK1WY+bMmVCr1VKH4tLYzo7BdnYMtrPjsK0doym0c7MrKCYiIiLXxp4bIiIicilMboiIiMilMLkhIiIil8LkhoiIiFwKkxsbWbRoEaKjo+Hm5oa+fftiz549UofkcubMmYNbbrkF3t7eCA4OxpgxY3D8+HGpw3Jp7733HgRBwHPPPSd1KC4pOzsbjz76KFq0aAF3d3d069YN+/btkzosl2IwGPDGG28gJiYG7u7uaNOmDd5++22L9ieiq9u+fTvuuusutGzZEoIgYP369fXeF0URb775JsLCwuDu7o7hw4fj5MmTDouPyY0NrFmzBklJSZg5cyZSU1PRo0cPxMfHIy8vT+rQXMq2bdswZcoU/P3330hOToZer8fIkSNRVlYmdWguae/evfj888/RvXt3qUNxSYWFhRgwYACUSiX+97//4ejRo/jPf/4Df39/qUNzKXPnzsVnn32GTz75BMeOHcPcuXMxb948fPzxx1KH5tTKysrQo0cPLFq0qNH3582bh48++giLFy/G7t274enpifj4eFRWVjomQJFuWlxcnDhlyhTza4PBILZs2VKcM2eOhFG5vry8PBGAuG3bNqlDcTklJSViu3btxOTkZHHIkCHitGnTpA7J5bzyyiviwIEDpQ7D5d15553iE088Ue/YvffeKz7yyCMSReR6AIg//fST+bXRaBRDQ0PF999/33ysqKhIVKvV4nfffeeQmNhzc5N0Oh3279+P4cOHm4/JZDIMHz4cu3btkjAy11dcXAwACAgIkDgS1zNlyhTceeed9X6uybb++9//ok+fPhg3bhyCg4PRs2dPLF26VOqwXE7//v2RkpKCEydOAAAOHjyIHTt2YNSoURJH5royMzORk5NT798PX19f9O3b12HPxWa3caatXbp0CQaDASEhIfWOh4SEID09XaKoXJ/RaMRzzz2HAQMGoGvXrlKH41JWr16N1NRU7N27V+pQXNrp06fx2WefISkpCa+++ir27t2LqVOnQqVSYeLEiVKH5zKmT58OjUaDjh07Qi6Xw2Aw4N1338UjjzwidWguKycnBwAafS6a3rM3JjfklKZMmYJ//vkHO3bskDoUl3Lu3DlMmzYNycnJcHNzkzocl2Y0GtGnTx/Mnj0bANCzZ0/8888/WLx4MZMbG/r++++xcuVKrFq1Cl26dEFaWhqee+45tGzZku3swjgsdZMCAwMhl8uRm5tb73hubi5CQ0Mlisq1JSYm4tdff8WWLVsQEREhdTguZf/+/cjLy0OvXr2gUCigUCiwbds2fPTRR1AoFDAYDFKH6DLCwsLQuXPnesc6deqErKwsiSJyTS+99BKmT5+OBx98EN26dcNjjz2G559/HnPmzJE6NJdlevZJ+VxkcnOTVCoVevfujZSUFPMxo9GIlJQU9OvXT8LIXI8oikhMTMRPP/2EP/74AzExMVKH5HKGDRuGw4cPIy0tzfyrT58+eOSRR5CWlga5XC51iC5jwIABDZYyOHHiBKKioiSKyDWVl5dDJqv/qJPL5TAajRJF5PpiYmIQGhpa77mo0Wiwe/duhz0XOSxlA0lJSZg4cSL69OmDuLg4LFy4EGVlZUhISJA6NJcyZcoUrFq1Cj///DO8vb3NY7e+vr5wd3eXODrX4O3t3aCGydPTEy1atGBtk409//zz6N+/P2bPno0HHngAe/bswZIlS7BkyRKpQ3Mpd911F9599120atUKXbp0wYEDB7BgwQI88cQTUofm1EpLS5GRkWF+nZmZibS0NAQEBKBVq1Z47rnn8M4776Bdu3aIiYnBG2+8gZYtW2LMmDGOCdAhc7KagY8//lhs1aqVqFKpxLi4OPHvv/+WOiSXA6DRX19++aXUobk0TgW3n19++UXs2rWrqFarxY4dO4pLliyROiSXo9FoxGnTpomtWrUS3dzcxNatW4uvvfaaqNVqpQ7NqW3ZsqXRf48nTpwoimL1dPA33nhDDAkJEdVqtThs2DDx+PHjDotPEEUu00hERESugzU3RERE5FKY3BAREZFLYXJDRERELoXJDREREbkUJjdERETkUpjcEBERkUthckNEREQuhckNERERuRQmN0RERORSmNwQERGRS2FyQ0ROLz8/H6GhoZg9e7b52M6dO6FSqertTExEzQP3liIil7Bx40aMGTMGO3fuRIcOHRAbG4t77rkHCxYskDo0InIwJjdE5DKmTJmC33//HX369MHhw4exd+9eqNVqqcMiIgdjckNELqOiogJdu3bFuXPnsH//fnTr1k3qkIhIAqy5ISKXcerUKVy4cAFGoxFnzpyROhwikgh7bojIJeh0OsTFxSE2NhYdOnTAwoULcfjwYQQHB0sdGhE5GJMbInIJL730EtatW4eDBw/Cy8sLQ4YMga+vL3799VepQyMiB+OwFBE5va1bt2LhwoX45ptv4OPjA5lMhm+++QZ//vknPvvsM6nDIyIHY88NERERuRT23BAREZFLYXJDRERELoXJDREREbkUJjdERETkUpjcEBERkUthckNEREQuhckNERERuRQmN0RERORSmNwQERGRS2FyQ0RERC6FyQ0RERG5FCY3RERE5FL+PzpxEo/7vndCAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import lognorm\n",
    "\n",
    "# Define the parameters of the lognormal distribution\n",
    "mu = 0  # Mean of the underlying normal distribution\n",
    "sigma = 1  # Standard deviation of the underlying normal distribution\n",
    "\n",
    "# Generate x values within a certain range\n",
    "x = np.linspace(0, 10, 1000)\n",
    "\n",
    "# Calculate the PDF values for each x\n",
    "pdf_values = lognorm.pdf(x, sigma, scale=np.exp(mu))\n",
    "\n",
    "# Plot the PDF\n",
    "plt.plot(x, pdf_values)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Probability Density')\n",
    "plt.title('Lognormal Distribution PDF')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2.10. Triangular Distribution:\n",
    "    \n",
    "- **PDF:**\n",
    "    $$\n",
    "    f(x; a, b, c) = \n",
    "    \\begin{cases} \n",
    "        \\frac{2}{b - a} \\cdot \\frac{x - a}{c - a} & \\text{for } a \\leq x \\leq c \\\\\n",
    "        \\frac{2}{b - a} \\cdot \\frac{b - x}{b - c} & \\text{for } c \\leq x \\leq b \n",
    "    \\end{cases}\n",
    "    $$\n",
    "- **Formula:** Generate random numbers according to the triangular distribution with minimum value a, maximum value b, and mode c.\n",
    "- Used when data is limited to a known minimum and maximum value.\n",
    "    - **Parameters:** minimum value ($a$), maximum value ($b$), and mode ($c$).\n",
    "    - **Example function:** `numpy.random.triangular(left, mode, right, size)`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "def triangular_pdf(x, a, b, c):\n",
    "    if a <= x <= c:\n",
    "        return (2 / (b - a)) * (x - a) / (c - a)\n",
    "    elif c <= x <= b:\n",
    "        return (2 / (b - a)) * (b - x) / (b - c)\n",
    "    else:\n",
    "        return 0\n",
    "\n",
    "# Define the parameters of the triangular distribution\n",
    "a = 0\n",
    "b = 10\n",
    "c = 5\n",
    "\n",
    "# Generate x values within the range [a, b]\n",
    "x = np.linspace(a, b, 1000)\n",
    "\n",
    "# Calculate the PDF values for each x\n",
    "pdf_values = [triangular_pdf(val, a, b, c) for val in x]\n",
    "\n",
    "# Plot the PDF\n",
    "plt.plot(x, pdf_values)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Probability Density')\n",
    "plt.title('Triangular Distribution PDF')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# Define the parameters of the triangular distribution\n",
    "a = 0  # Minimum value\n",
    "b = 10  # Maximum value\n",
    "c = 5  # Mode value\n",
    "\n",
    "# Generate x values within the range [a, b]\n",
    "x = np.linspace(a, b, 1000)\n",
    "\n",
    "# Calculate the PDF values for each x\n",
    "pdf_values = np.piecewise(x, [x < c, x >= c], [lambda x: 2 * (x - a) / ((b - a) * (c - a)), lambda x: 2 * (b - x) / ((b - a) * (b - c))])\n",
    "\n",
    "# Plot the PDF\n",
    "plt.plot(x, pdf_values)\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Probability Density')\n",
    "plt.title('Triangular DistributionPDF')\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #ffbb99; width: 800px; height: 30px; padding: 10px; border: 3px solid #ccc;\">\n",
    "    <span style=\"color: #331100; font-weight: bold;\"><h2>Generating Random Numbers</h2></span>\n",
    "</div>"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #99ccff; width: 800px; height: 30px; padding: 10px; border: 3px solid #ccc;\">\n",
    "    <span style=\"color: #331100; font-weight: bold;\"><h3>Random Number Generation</h3></span>\n",
    "</div>\n",
    "\n",
    "Random Number Generator refers to a process or algorithm that generates a sequence of numbers that appear random. These numbers are typically used in various fields and applications where randomness is required, such as simulations, cryptography, statistical analysis, and gaming. \n",
    "\n",
    "- Each random number generation method has its own characteristics, advantages, and use cases. \n",
    "- The choice of method depends on the specific requirements of the application, such as the need for reproducibility, security, or true randomness. \n",
    "\n",
    "#### Applications of random number generation and simulations:\n",
    "\n",
    "- Monte Carlo Simulations\n",
    "- Computational Biology\n",
    "- Gaming and Animation\n",
    "- Cryptography\n",
    "- Optimization and Search Algorithms\n",
    "- Neural Networks and Machine Learning\n",
    " \n",
    "#### Categories of randaom number generators\n",
    " \n",
    "It can be classified into different types based on their underlying mechanisms and properties. The main categories of RNGs are:\n",
    "\n",
    "1. **Pseudorandom Number Generators (PRNGs):** PRNGs use deterministic algorithms to produce a sequence of numbers that mimic the properties of true random numbers. PRNGs start with an initial seed value and generate subsequent numbers using mathematical operations. While the generated numbers are not truly random, they exhibit statistical properties that make them suitable for many practical applications. Examples of PRNG algorithms include the \n",
    "   \n",
    "   - linear congruential generator (LCG), \n",
    "   - Mersenne Twister, and \n",
    "   - XORshift.\n",
    "\n",
    "2. **True Random Number Generators (TRNGs):** TRNGs generate numbers from physical processes that are inherently random, such as atmospheric noise, radioactive decay, or electronic noise. TRNGs produce true random numbers that are not predictable or reproducible. They rely on unpredictable natural phenomena to generate randomness.\n",
    "\n",
    "3. **Cryptographically Secure Pseudorandom Number Generators (CSPRNGs):** CSPRNGs are PRNGs designed to provide secure random numbers for cryptographic applications. They meet specific criteria to resist cryptographic attacks and ensure the generated numbers are suitable for sensitive applications. Cryptographic algorithms such as AES-CTR (Advanced Encryption Standard in counter mode) or HMAC-DRBG (Hash-based Message Authentication Code - Deterministic Random Bit Generator) are commonly used to construct CSPRNGs.\n",
    "\n",
    "4. **Quantum Random Number Generators (QRNGs):** QRNGs leverage quantum mechanical phenomena, such as the randomness of quantum measurements, to generate truly random numbers. Quantum processes, such as measuring the spin of a single photon or the quantum noise of a semiconductor, are used to produce random numbers that are inherently unpredictable. QRNGs are considered the gold standard for randomness due to their basis in quantum mechanics.\n",
    "\n",
    "\n",
    "> **Note:**\n",
    "> - PRNGs are widely used for most applications due to their efficiency and suitability for many scenarios, while TRNGs and QRNGs are preferred when true randomness is \n",
    "> essential. \n",
    "> - The choice between PRNGs and TRNGs depends on the specific requirements of the application. \n",
    "> - PRNGs are widely used due to their efficiency and ability to generate long sequences of seemingly random numbers. \n",
    "> - TRNGs, on the other hand, provide true randomness but may have limitations in terms of speed, resource requirements, or availability.\n",
    "> - CSPRNGs bridge the gap by providing high-quality random numbers suitable for cryptographic applications using deterministic algorithms with strong cryptographic\n",
    "> properties."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #99ccff; width: 800px; height: 30px; padding: 10px; border: 3px solid #ccc;\">\n",
    "    <span style=\"color: #331100; font-weight: bold;\"><h3>Examples</h3></span>\n",
    "</div>"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example-1** Simulating rolling a fair six-sided die and calculating the average value after a large number of rolls.\n",
    "\n",
    "- Check the file: https://github.com/arunsinp/MonteCarlo-simulation/tree/main/Other-example"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example-2:** Random walk problem\n",
    "\n",
    "- Check the file: https://github.com/arunsinp/MonteCarlo-simulation/tree/main/Other-example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #ffbb99; width: 800px; height: 30px; padding: 10px; border: 3px solid #ccc;\">\n",
    "    <span style=\"color: #331100; font-weight: bold;\"><h2>Variance Reduction Techniques</h2></span>\n",
    "</div>\n",
    "\n",
    "- Variance reduction techniques are methods used in Monte Carlo simulation to improve the efficiency and accuracy of estimates by reducing the variance of the results. By reducing the variance, these techniques can lead to faster convergence, lower computational costs, and more precise estimations. \n",
    "- The error in a direct Monte Carlo simulation goes as $\\sigma/\\sqrt{n}$. So there are two ways we can reduce the error. \n",
    "  - Run the simulation for a longer time, i.e., increase $n$ or \n",
    "  - find a different formulation of the Monte Carlo that has a smaller $\\sigma$. \n",
    "- Methods that do the latter are know as variance reduction. \n",
    "\n",
    "Some common variance reduction techniques along with the mathematics involved:\n",
    "\n",
    "  ##### 1. Antithetic Variates:\n",
    "  The antithetic variates technique exploits negative correlation between pairs of random variables. Instead of generating independent random samples, this technique generates pairs of samples with opposite values. By taking the average of each pair, the variance of the estimator can be reduced.\n",
    "\n",
    "   - **Mathematics:** Mathematically, suppose we have a random variable $X$ and its antithetic variable $Y$, where $X$ and $Y$ are negatively correlated. The estimator for a function $f(X)$ can be calculated as:\n",
    "   \n",
    "       $\\boxed{\\text{Estimator} = \\frac{f(X) + f(Y)}{2}}$\n",
    "\n",
    "   - By using the antithetic variates technique, the variance of the estimator can be reduced because the negative correlation cancels out some of the random fluctuations.\n",
    "\n",
    "<div class=\"alert alert-info\">\n",
    "\n",
    "- If X and Y are independent, then var(X + Y) = var(X) + var(Y). If they are not independent, the covariance enters. \n",
    "- Letting $\\mu_X$, $\\mu_Y$ denote the means of $X$ and $Y$, we have\n",
    "\n",
    "\\begin{align*}\n",
    "\\text{var}(X + Y) &= E(X + Y)^2 - (\\mu_X + \\mu_Y)^2 \\\\\n",
    "&= E[X^2] - \\mu_X^2 + E[Y^2] - \\mu_Y^2 + 2(E[XY] - \\mu_X \\mu_Y) \\\\\n",
    "&= \\text{var}(X) + \\text{var}(Y) + 2 \\text{cov}(X, Y)\n",
    "\\end{align*}\n",
    "\n",
    "- The covariance is $\\text{cov}(X, Y) = E[(X - E[X])(Y - E[Y])]$, where E[X] and E[Y] represent the expected values (means) of X and Y, respectively. \n",
    "    - When $\\text{cov}(X, Y)>0$ indicates that when $X$ is above (below) its mean, $Y$ tends to be above (below) its mean as well. In other words, $X$ and $Y$ have a positive linear relationship.\n",
    "    - When $\\text{cov}(X, Y)<0$ indicates that when $X$ is above (below) its mean, $Y$ tends to be below (above) its mean. $X$ and $Y$ have a negative linear relationship.\n",
    "    - When $\\text{cov}(X, Y)=0$ indicates that $X$ and $Y$ are uncorrelated. It means that there is no linear relationship between the two variables.\n",
    "- **Definition of Antithetic:** Random variables $X$, $Y$ on the same probability space are antithetic if they have the same distribution and their covariance is negative. \n",
    "  - Let's consider two random variables, X and Y, defined on the same probability space\n",
    "  \n",
    "    $P(X = x) = P(Y = x)$ for all possible values of $x$ and \n",
    "\n",
    "    $\\text{cov}(X, Y) < 0$.\n",
    "\n",
    "  - **Derivation:**\n",
    "  \n",
    "    \\begin{align*}\n",
    "    \\text{cov}(X, Y) &= E[(X - E[X])(Y - E[Y])] \\\\\n",
    "    &= E[XY - XE[Y] - YE[X] + E[X]E[Y]] \\\\\n",
    "    &= E[XY] - E[X]E[Y] - E[Y]E[X] + E[X]E[Y] \\\\\n",
    "    &= E[XY] - 2E[X]E[Y] + E[X]E[Y] \\\\\n",
    "    &= E[XY] - E[X]E[Y]\n",
    "    \\end{align*}\n",
    "\n",
    "    - Since we assume $X$ and $Y$ have the same distribution, we can rewrite the expectation terms as follows: $E[X] = E[Y] = \\mu$.\n",
    "    - Therefore, the covariance expression becomes: $\\text{cov}(X, Y) = E[XY] - \\mu^2$.\n",
    "    - Now, let's consider the condition for antithetic random variables: $\\text{cov}(X, Y) < 0$.\n",
    "    - Substituting the covariance expression, we have: $E[XY] - \\mu^2 < 0$\n",
    "    - This inequality implies that the expected value of the product of $X$ and $Y$ i.e. $(E[XY])$ is smaller than the square of their mean $\\mu^2$, indicating a negative covariance.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####  2. Control Variates: \n",
    "\n",
    "The control variates technique involves using an auxiliary random variable that is known or easily computable. This auxiliary variable should be correlated with the primary variable of interest. By introducing this control variate, the variance of the estimator can be reduced.\n",
    "\n",
    "- **Mathematics:** Mathematically, suppose we have a primary random variable $X$ and a control variable $Y$. We assume that there exists a linear relationship between the primary and control variables, such that:\n",
    "\n",
    "    $\\boxed{X = X' + a * (Y - E[Y])}$\n",
    "\n",
    "    Here, $X'$ is a known quantity, a is a coefficient, $Y$ is the control variate, and $E[Y]$ is the expected value of $Y$. The estimator for a function $f(X)$ with control variates can be calculated as:\n",
    "    \n",
    "    $\\boxed{\\text{Estimator} = f(X) - a * (Y - E[Y])}$\n",
    "\n",
    "- By choosing an appropriate value of the coefficient a, the variance of the estimator can be reduced. \n",
    "- The control variate effectively reduces the variability in the estimation by leveraging the correlation between the primary and control variables."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####  3. Importance Sampling: \n",
    "\n",
    "Importance sampling is used when the probability distribution of the random variable of interest is difficult to sample directly. Instead, it samples from an alternative distribution that is easier to generate. The samples are then weighted to account for the difference between the desired distribution and the alternative distribution.\n",
    "\n",
    "- **Mathematics:** Mathematically, suppose we have a random variable $X$ with probability density function (PDF) $f(x)$ and a known alternative distribution with PDF $g(x)$. The estimator for a function $f(X)$ using importance sampling can be calculated as:\n",
    "\n",
    "    $\\boxed{\\text{Estimator} = \\frac{1}{n} \\times \\sum \\frac{f(X_i)}{g(Xi)}}$\n",
    "\n",
    "- Here, $X_i$ represents the generated samples from the alternative distribution. \n",
    "- The weight factor $f(X_i) / g(X_i)$ accounts for the difference between the desired distribution and the alternative distribution. \n",
    "- By appropriately selecting the alternative distribution, the variance of the estimator can be reduced, resulting in more efficient estimations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####  4. Stratified Sampling: \n",
    "\n",
    "Stratified sampling divides the probability distribution into several sub-intervals or strata and generates random samples from each stratum. This technique ensures that samples are taken from different regions of the distribution, reducing the variance of the estimates.\n",
    "\n",
    "- **Mathematics:** Mathematically, let's consider a random variable $X$ with probability density function (PDF) $f(x)$ and cumulative distribution function (CDF) $F(x)$. The stratified sampling technique involves dividing the range of $X$ into $k$ strata (sub-intervals) with boundaries $a = x_0 < x_1 < x_2 < ... < x_k = b$. Within each stratum $i$, a random sample $X_i$ is generated according to the PDF $f(x_i)$.\n",
    "\n",
    "- The estimator for a function f(X) using stratified sampling can be calculated as:\n",
    "\n",
    "    $\\boxed{\\text{Estimator} = \\frac{1}{k} * \\sum \\frac{1}{n_i} * \\sum f(X_{ij})}$\n",
    "\n",
    "- Here, $n_i$ represents the number of samples generated in stratum $i$, and $X_{ij}$ represents the $j^{\\rm th}$ sample in stratum $i$. \n",
    "- The estimator averages the function values over all strata, giving more weight to the strata with fewer samples."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####  5. Importance Sampling: \n",
    "\n",
    "Importance sampling is used when sampling directly from the desired distribution is difficult. Instead, samples are generated from an alternative distribution that is easier to sample. The samples are then weighted to account for the difference between the desired distribution and the alternative distribution.\n",
    "\n",
    "- **Mathematics:** Mathematically, suppose we have a random variable $X$ with PDF $f(x)$ and an alternative distribution with PDF $g(x)$.\n",
    "- The estimator for a function f(X) using importance sampling can be calculated as:\n",
    "\n",
    "    $\\boxed{\\text{Estimator} = \\frac{1}{n} * \\sum (f(X_i) * w(X_i))}$\n",
    "\n",
    "- Here, $X_i$ represents the generated samples from the alternative distribution, and $w(X_i)$ represents the importance weights defined as $w(X_i) = f(X_i) / g(X_i)$. \n",
    "- The weight factor accounts for the difference between the desired and alternative distributions. \n",
    "- By appropriately selecting the alternative distribution, the variance of the estimator can be reduced, resulting in more efficient estimations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #ffbb99; width: 800px; height: 30px; padding: 10px; border: 3px solid #ccc;\">\n",
    "    <span style=\"color: #331100; font-weight: bold;\"><h2>Applications of Monte Carlo Simulation</h2></span>\n",
    "</div>\n",
    "\n",
    "Monte Carlo simulation has a wide range of applications across various fields. Here are some common areas where Monte Carlo simulation is used:\n",
    "\n",
    "1. **Finance and Risk Analysis:** Monte Carlo simulation is extensively used in finance and risk analysis to model and analyze complex financial systems. It helps estimate the value of financial derivatives, assess investment portfolios, simulate stock price movements, and evaluate risk exposure. By generating multiple scenarios based on random variables, Monte Carlo simulation provides insights into the potential outcomes of financial decisions.\n",
    "\n",
    "2. **Engineering and Reliability Analysis:** Monte Carlo simulation is applied in engineering to analyze the reliability and performance of systems. It can simulate the behavior of complex engineering structures, evaluate the impact of uncertainties on performance, and optimize system design. It finds applications in fields such as structural engineering, mechanical engineering, aerospace engineering, and reliability engineering.\n",
    "\n",
    "3. **Physics and Particle Simulations:** Monte Carlo simulation is widely used in physics to model and study the behavior of particles and physical systems. It is used to simulate particle interactions, analyze the behavior of quantum systems, and study the statistical properties of physical phenomena. Monte Carlo methods are also applied in fields such as computational physics, astrophysics, and nuclear engineering.\n",
    "\n",
    "4. **Optimization and Decision-Making:** Monte Carlo simulation is used in optimization problems where the goal is to find the best solution among many possibilities. It helps evaluate the performance of different strategies, simulate decision outcomes, and identify optimal solutions. It finds applications in fields such as operations research, project management, and supply chain optimization.\n",
    "\n",
    "5. **Queueing Theory and System Performance Analysis:** Monte Carlo simulation is employed in queueing theory to analyze the performance of systems with queues, such as call centers, transportation systems, and manufacturing processes. It helps estimate system metrics like waiting times, queue lengths, and resource utilization. Monte Carlo simulation allows for experimentation and optimization of system parameters to improve overall performance.\n",
    "\n",
    "6. **Environmental Modeling:** Monte Carlo simulation is used in environmental modeling to assess and predict the behavior of natural systems. It aids in simulating weather patterns, predicting climate change impacts, evaluating pollutant dispersion, and assessing the risks associated with natural disasters. By incorporating random variables and uncertainties, Monte Carlo simulation provides valuable insights into environmental processes.\n",
    "\n",
    "7. **Healthcare and Medical Applications:** Monte Carlo simulation is applied in healthcare and medical research for various purposes. It can be used to model and simulate disease progression, evaluate treatment effectiveness, estimate healthcare costs, and assess the impact of different interventions. It helps researchers and practitioners make informed decisions based on probabilistic outcomes.\n",
    "\n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #ffffcc; border: 1px solid #ddd; padding: 10px;\">\n",
    "<div style=\"background-color: #99ccff; width: 800px; height: 30px; padding: 10px; border: 3px solid #ccc;\">\n",
    "    <span style=\"color: #331100; font-weight: bold;\"><h3>Pseudorandom Number Generators (PRNGs):</h3></span>\n",
    "</div>\n",
    "\n",
    "Pseudorandom Number Generators (PRNGs) are algorithms that generate sequences of numbers that appear to be random but are actually determined by a starting value called a seed. Unlike 'true random number generators', which generate numbers based on unpredictable physical processes, PRNGs use deterministic algorithms to produce sequences that exhibit statistical randomness.\n",
    "\n",
    "#### How a typical PRNG works?\n",
    "\n",
    "- **Seed Initialization:** The PRNG is initialized with a seed value, which can be a number, a combination of numbers, or even a system time value. The seed determines the starting point for generating the sequence of numbers.\n",
    "\n",
    "- **Number Generation:** The PRNG uses a `mathematical algorithm` to generate a sequence of numbers based on the seed. Each generated number is typically used as the seed for generating the next number in the sequence.\n",
    "\n",
    "- **Repeatable Sequence:** PRNGs generate a sequence of numbers that is deterministic and repeatable. If you start with the same seed value, you will get the exact same sequence of numbers every time. This property is useful in situations where you want to reproduce results or debug code.\n",
    "\n",
    "- **Periodicity:** PRNGs have a finite period, which is the number of unique values the generator can produce before the sequence repeats. The period depends on the algorithm and the size of the seed. A good PRNG should have a long period to avoid predictable repetitions in the generated sequence.\n",
    "\n",
    "#### Common PRNG algorithms\n",
    "\n",
    "- linear congruential generators (LCGs), \n",
    "- Mersenne Twister, \n",
    "- XORshift, and \n",
    "- multiply-with-carry. \n",
    "\n",
    "> **NOTE:**\n",
    "> - Each algorithm uses different mathematical operations and has varying properties in terms of period length, statistical randomness,\n",
    "> and speed.\n",
    "> - It's important to note that PRNGs, by their nature, are not truly random. If an attacker can determine or predict the seed used in a\n",
    "> PRNG, they can reproduce the entire sequence of generated numbers. This makes PRNGs unsuitable for cryptographic purposes, where true\n",
    "> randomness is essential.\n",
    ">\n",
    "> - To mitigate this issue, cryptographic PRNGs (CPRNGs) are designed to provide a higher level of security. CPRNGs combine a PRNG \n",
    "> algorithm with additional entropy sources, such as hardware events or user-generated data, to enhance the randomness of the generated\n",
    "> numbers.\n",
    "\n",
    "When using PRNGs, it's crucial to select an appropriate algorithm and seed carefully, depending on the application. Additionally, it's recommended to periodically reseed PRNGs with fresh entropy to maintain randomness and security.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #ffffcc; border: 1px solid #ddd; padding: 10px;\">\n",
    "\n",
    "#### 1. **Linear congruential generators (LCGs)** \n",
    "\n",
    "- Linear congruential generators (LCGs) are a type of PRNG algorithm that generate a sequence of numbers using a linear equation. \n",
    "- LCGs are a specific type of random number generator that can be described by a linear recurrence equation.\n",
    "\n",
    "> - **Note on Linear recurrence equation:** \n",
    "> A linear recurrence equation is a type of mathematical equation that describes a sequence of values based on previous terms in a\n",
    "> linear fashion. It is a recursive formula that expresses each term as a linear combination of one or more preceding terms.\n",
    ">\n",
    "> - The general form of a linear recurrence equation of order $k$ is:\n",
    ">    \n",
    ">    $\\boxed{x_n = c_1 * x_{n-1} + c_2 * x_{n-2} + ... + c_k * x_{n-k}}$\n",
    ">\n",
    ">    - In this equation, $x_n$ represents the nth term in the sequence, $x_{n-1}, x_{n-2}, ..., x_{n-k}$ represent the preceding terms,\n",
    "> and $c_1, c_2, ..., c_k$ are constants.\n",
    ">    - The equation states that each term $x_n$ is obtained by multiplying each preceding term $x_{n-1}, x_{n-2}, ..., x_{n-k}$ by their\n",
    "> respective constants $c_1, c_2, ..., c_k$ and summing them together.\n",
    ">    - A linear recurrence equation can be initialized by specifying the initial terms x_0, x_1, ..., x_{k-1} to define the starting\n",
    "> conditions of the sequence. Once the initial terms are provided, the recurrence equation can generate subsequent terms by applying the\n",
    "> formula repeatedly.\n",
    ">\n",
    "> - Linear recurrence equations are commonly used in various fields, including mathematics, computer science, physics, and engineering.\n",
    "> They are particularly useful for modeling processes that exhibit a linear relationship between current and past states, such as\n",
    "> population growth, Fibonacci sequence, and certain recursive algorithms.\n",
    ">\n",
    "> Note that the linear recurrence equation used in the context of pseudo-random number generators, such as the Linear Congruential \n",
    "> Generator (LCG), is a specific type of recurrence equation tailored for generating pseudo-random numbers and may have additional\n",
    "> components, such as modular arithmetic and additive constants, to ensure desired properties of randomness and periodicity.\n",
    "\n",
    "\n",
    "- The equation has the form:\n",
    "\n",
    "    $\\boxed{X_{n+1} = (a \\times X_n + c) \\% m}$\n",
    "\n",
    "    where \n",
    "    - $X_n$ = is the current number in the sequence, \n",
    "    - $X_{n+1}$ = is the next number in the sequence\n",
    "    - $a$ = is the multiplier, \n",
    "    - $c$ is the increment, and \n",
    "    - $m$ is the modulus (Example: Modulus of 7 divided by 3: $7 \\% 3 = 1$. When 7 is divided by 3, the remainder is 1.)\n",
    "\n",
    "- LCGs are simple and computationally efficient but have some limitations. \n",
    "- The quality of the generated sequence depends on the choice of parameters. \n",
    "- Poorly chosen parameters can result in shorter periods and patterns in the sequence. \n",
    "- However, carefully selected parameters can produce sequences with acceptable statistical properties.\n",
    "\n",
    "- To generate random numbers using an LCG, you start with an initial seed value, $X_0$. \n",
    "- Applying the formula, you calculate $X_1$, then use $X_1$ to calculate $X_2$, and so on. \n",
    "- The modulus operation ($\\%$) ensures that the generated number falls within a specified range, typically between $0$ and $m-1$.\n",
    "\n",
    "> **Some basic rules and recommendations for choosing a, c and m:**\n",
    "> 1. **Modulus ($m$):** \n",
    ">   - The modulus $m$ should be a large prime number or a power of $2$ to ensure a long period and good statistical properties.\n",
    ">   - Choosing a modulus that is too small may result in a short period and a higher likelihood of the generated sequence repeating.\n",
    ">   - A common choice for m is $2^{31}$ or $2^{32}$ for 32-bit generators.\n",
    "> \n",
    "> 2. **Multiplier ($a$):**\n",
    ">   - The multiplier $a$ should have certain properties to produce a good random sequence.\n",
    ">   - It should be a positive integer that is relatively prime to the modulus $m$ (i.e., the greatest common divisor of a and m should be $1$).\n",
    ">   - Multiplying a seed value by a relatively prime multiplier helps to maximize the period and improve the randomness properties.\n",
    ">   - Some suggested choices for the multiplier include prime numbers, numbers with many primitive roots modulo $m$, or values that are congruent to $3$ or $5$ modulo $8$.\n",
    "> \n",
    "> 3. **Increment ($c$):**\n",
    "> \n",
    ">   - The increment $c$ is an additive constant used in the LCG formula.\n",
    ">   - It is recommended to choose a value that is relatively prime to the modulus m to ensure a full period.\n",
    ">   - In some cases, setting $c$ to an odd number can help achieve a full period.\n",
    ">   - However, note that setting $c$ to $0$ or a multiple of $m$ will result in a generator with a period of $1$.\n",
    "> \n",
    "> 4. **Seed:**\n",
    ">\n",
    ">   - The seed is the initial value used to start the LCG sequence.\n",
    ">   - It can be any non-negative integer.\n",
    ">   - Using a different seed value will produce a different sequence of pseudo-random numbers.\n",
    ">   - For reproducibility, it's common to initialize the seed with a fixed value or use a system-provided source of randomness.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets first understand the intiation and class:\n",
    "- Class refers to a blueprint or a template for creating objects in object-oriented programming (OOP). \n",
    "- The class has an `__init__` method, which is a special method called a constructor and is used to initialize the object's attributes when an instance of the class is created.\n",
    "- In Python, `self` is a conventionally used parameter name in methods within a class. \n",
    "- It represents the instance of the class itself. When a method is called on an object, `self` is automatically passed as the first argument to the method, allowing the method to access and manipulate the object's attributes and perform operations specific to that instance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example of how, class is intitiated"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Arun\n",
      "35\n",
      "Hello, my name is Arun and I am 35 years old.\n"
     ]
    }
   ],
   "source": [
    "# Example-1\n",
    "class Person:\n",
    "    def __init__(self, name, age):\n",
    "        self.name = name\n",
    "        self.age = age\n",
    "\n",
    "    def introduce(self):\n",
    "        print(f\"Hello, my name is {self.name} and I am {self.age} years old.\")\n",
    "\n",
    "# Creating an instance of the Person class\n",
    "person1 = Person(\"Arun\", 35)\n",
    "person2 = Person('Nidhi', 31)\n",
    "\n",
    "# Accessing the object's attributes\n",
    "print(person1.name)  # Output: Arun\n",
    "print(person1.age)   # Output: 35\n",
    "\n",
    "# Calling the object's method\n",
    "person1.introduce()  # Output: Hello, my name is Arun and I am 35 years old."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Hello, my name is Arun and I am 35 years old.\n",
      "Hello, my name is Nidhi and I am 31 years old.\n"
     ]
    }
   ],
   "source": [
    "person1.introduce()\n",
    "person2.introduce()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A init called\n",
      "B init called\n"
     ]
    }
   ],
   "source": [
    "# Example- 2\n",
    "# Python program to demonstrate init with inheritance\n",
    "\n",
    "class A(object):\n",
    "    def __init__(self, something):\n",
    "        print(\"A init called\")\n",
    "        self.something = something\n",
    "\n",
    "class B(A):\n",
    "    def __init__(self, something):\n",
    "        # Calling init of parent class\n",
    "        A.__init__(self, something)\n",
    "        print(\"B init called\")\n",
    "        self.something = something\n",
    " \n",
    "obj = B(\"Something\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Name: John, Age: 25\n",
      "Name: Jane, Age: 30\n",
      "Employee ID: E123\n"
     ]
    }
   ],
   "source": [
    "# Example-3\n",
    "\n",
    "class Person:\n",
    "    def __init__(self, name, age):\n",
    "        self.name = name\n",
    "        self.age = age\n",
    "\n",
    "    def display(self):\n",
    "        print(f\"Name: {self.name}, Age: {self.age}\")\n",
    "\n",
    "\n",
    "class Employee(Person):\n",
    "    def __init__(self, name, age, employee_id):\n",
    "        super().__init__(name, age)\n",
    "        self.employee_id = employee_id\n",
    "\n",
    "    def display_employee(self):\n",
    "        print(f\"Employee ID: {self.employee_id}\")\n",
    "\n",
    "\n",
    "person = Person(\"John\", 25)\n",
    "person.display()\n",
    "\n",
    "employee = Employee(\"Jane\", 30, \"E123\")\n",
    "employee.display()\n",
    "employee.display_employee()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- **PRNG class**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "class PRNG:\n",
    "    def __init__(self, seed):\n",
    "        self.seed = seed\n",
    "        self.multiplier = 1103515245\n",
    "        self.increment = 12345\n",
    "        self.modulus = 2**31\n",
    "\n",
    "    def generate(self):\n",
    "        self.seed = (self.multiplier * self.seed + self.increment) % self.modulus\n",
    "        return self.seed"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1103527590\n",
      "377401575\n",
      "662824084\n",
      "1147902781\n",
      "2035015474\n",
      "368800899\n",
      "1508029952\n",
      "486256185\n",
      "1062517886\n",
      "267834847\n"
     ]
    }
   ],
   "source": [
    "# Example usage\n",
    "prng = PRNG(seed=1)\n",
    "for _ in range(10):\n",
    "    random_number = prng.generate()\n",
    "    print(random_number)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- **Example: Print ten pseudorandom numbers using the LCG algorithm:** In this example, the LCG is initialized with a seed value of $1$, multiplier $a=1103515245$, increment $c=12345$, and modulus $m=2^{31}$. The `generate()` method calculates the next number in the sequence based on the LCG formula and updates the seed for subsequent iterations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Example-4 on LCG\n",
    "class LCG:\n",
    "    def __init__(self, seed, a, c, m):\n",
    "        self.seed = seed\n",
    "        self.a = a\n",
    "        self.c = c\n",
    "        self.m = m\n",
    "\n",
    "    def generate(self):\n",
    "        self.seed = (self.a * self.seed + self.c) % self.m\n",
    "        return self.seed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- The `generate()` method calculates the next number in the sequence based on the LCG formula and updates the seed for subsequent iterations. \n",
    "- It generates and prints ten pseudo-random numbers using the LCG algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1103527590\n",
      "377401575\n",
      "662824084\n",
      "1147902781\n",
      "2035015474\n",
      "368800899\n",
      "1508029952\n",
      "486256185\n",
      "1062517886\n",
      "267834847\n"
     ]
    }
   ],
   "source": [
    "# Example usage\n",
    "lcg = LCG(seed=1, a=1103515245, c=12345, m=2**31)\n",
    "for _ in range(10):\n",
    "    random_number = lcg.generate()\n",
    "    print(random_number)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "2.5234517478384078\n",
      "0.8812504541128874\n",
      "5.772811982315034\n",
      "2.22554265987128\n",
      "3.7566019711084664\n",
      "0.2566390484571457\n",
      "4.472812858875841\n",
      "1.184600037522614\n",
      "8.738137057516724\n",
      "9.946342753246427\n"
     ]
    }
   ],
   "source": [
    "# Example-5\n",
    "class LCG:\n",
    "    def __init__(self, seed, a, c, m):\n",
    "        self.seed = seed\n",
    "        self.a = a\n",
    "        self.c = c\n",
    "        self.m = m\n",
    "\n",
    "    def generate(self):\n",
    "        self.seed = (self.a * self.seed + self.c) % self.m\n",
    "        return self.seed / self.m\n",
    "\n",
    "# Example usage\n",
    "lcg = LCG(seed=42, a=1664525, c=1013904223, m=2**32)\n",
    "for _ in range(10):\n",
    "    random_number = lcg.generate()\n",
    "    scaled_number = random_number * 10  # Scale the range to 0-10\n",
    "    print(scaled_number)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "class LCG:\n",
    "    def __init__(self, seed, a, c, m):\n",
    "        self.seed = seed\n",
    "        self.a = a\n",
    "        self.c = c\n",
    "        self.m = m\n",
    "\n",
    "    def generate(self):\n",
    "        self.seed = (self.a * self.seed + self.c) % self.m\n",
    "        return self.seed\n",
    "\n",
    "\n",
    "def generate_random_numbers(lcg, n):\n",
    "    random_numbers = []\n",
    "    for _ in range(n):\n",
    "        random_number = lcg.generate()\n",
    "        random_numbers.append(random_number)\n",
    "    return random_numbers\n",
    "\n",
    "\n",
    "# Example usage\n",
    "lcg = LCG(seed=1, a=48271, c=0, m=2**31 - 1)\n",
    "random_numbers = generate_random_numbers(lcg, n=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plotting x_n with respect to x_{n-1}\n",
    "x_n = random_numbers[1:]\n",
    "x_n_minus_1 = random_numbers[:-1]\n",
    "\n",
    "plt.scatter(x_n_minus_1, x_n, s=1, color='black')  # Decrease the point size by adjusting 's'\n",
    "plt.xlabel('$x_{n-1}$')\n",
    "plt.ylabel('$x_n$')\n",
    "plt.title('$x_n$ vs $x_{n-1}$')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Example:** example of an LCG implementation with chosen parameters, and I'll present the generated pseudo-random numbers in a table format."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n          (a * X_n + c)        X_{n+1}         % m          \n",
      "1          48271                48271           48271        \n",
      "2          2330089441           182605794       182605794    \n",
      "3          8814564282174        1291394886      1291394886   \n",
      "4          62336922542106       1914720637      1914720637   \n",
      "5          92425479868627       2078669041      2078669041   \n",
      "6          100339433278111      407355683       407355683    \n",
      "7          19663466174093       1105902161      1105902161   \n",
      "8          53383003213631       854716505       854716505    \n",
      "9          41258020412855       564586691       564586691    \n",
      "10         27253164161261       1596680831      1596680831   \n"
     ]
    }
   ],
   "source": [
    "class LCG:\n",
    "    def __init__(self, seed, a, c, m):\n",
    "        self.seed = seed\n",
    "        self.a = a\n",
    "        self.c = c\n",
    "        self.m = m\n",
    "\n",
    "    def generate(self):\n",
    "        new_seed = (self.a * self.seed + self.c) % self.m\n",
    "        return new_seed\n",
    "\n",
    "def generate_table(lcg1, n):\n",
    "    header = ['n', '(a * X_n + c)', 'X_{n+1}', '% m']\n",
    "    table = [header]\n",
    "\n",
    "    for i in range(n):\n",
    "        random_number = lcg1.generate()\n",
    "        row = [i+1, lcg1.a * lcg1.seed + lcg1.c, random_number, random_number % lcg1.m]\n",
    "        table.append(row)\n",
    "        lcg1.seed = random_number\n",
    "\n",
    "    return table\n",
    "\n",
    "\n",
    "# Example usage\n",
    "lcg1 = LCG(seed=1, a=48271, c=0, m=2**31 - 1)\n",
    "random_table = generate_table(lcg1, n=10)\n",
    "\n",
    "# Printing the table\n",
    "for row in random_table:\n",
    "    print('{:<10} {:<20} {:<15} {:<13}'.format(*row))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- `<10` specifies that the value should be left-aligned within a field of width 10 characters.\n",
    "- `<20` specifies that the value should be left-aligned within a field of width 20 characters.\n",
    "- `<15` specifies that the value should be left-aligned within a field of width 15 characters.\n",
    "- `<13` specifies that the value should be left-aligned within a field of width 13 characters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #ffffcc; border: 1px solid #ddd; padding: 10px;\">\n",
    "\n",
    "#### 2. **Mersenne Twister**\n",
    "\n",
    "- The Mersenne Twister is a widely used PRNG algorithm known for its long period and good statistical properties. \n",
    "- It was developed by Makoto Matsumoto and Takuji Nishimura in 1997. \n",
    "- The Mersenne Twister generates numbers based on a large Mersenne prime number as its period.\n",
    "- The algorithm utilizes a state vector of 624 32-bit integers and generates numbers using a non-linear recurrence equation. \n",
    "- It has a period of $2^{19937-1}$, which means it can produce a vast number of unique values before repeating. \n",
    "- The Mersenne Twister is known for its fast generation speed and good statistical quality, making it popular in various applications.\n",
    "- **Mathematics of Mersenne Twister:**\n",
    "    - Mersenne Twister is based on a linear recurrence equation with a state size of 19937 bits, which is a Mersenne prime number $(2^{19937} - 1)$.\n",
    "    - The recurrence equation calculates the next state by combining the current state with a carefully selected matrix multiplication operation.\n",
    "    - The algorithm employs a tempering mechanism to enhance the randomness of the generated numbers. It applies a series of bitwise operations, including XOR, shifts, and masks, to transform the state and produce the final random number.\n",
    "- **Conditions for using Mersenne Twister:**\n",
    "    - Mersenne Twister is commonly used in various applications that require high-quality pseudo-random numbers, including simulations, scientific research, gaming, cryptography (non-cryptographic applications), and general-purpose random number generation. \n",
    "    - It provides a good balance between performance and randomness, making it a popular choice.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #ffffcc; border: 1px solid #ddd; padding: 10px;\">\n",
    "\n",
    "#### 3. XORshift\n",
    "\n",
    "- XORshift is a family of PRNG algorithms that use bitwise exclusive OR (XOR) and bitwise shift operations to generate random numbers. \n",
    "- XORshift algorithms are known for their simplicity, high speed, and good statistical properties.\n",
    "- XORshift algorithms work by applying a series of XOR and shift operations on the current seed value to produce the next number in the sequence. \n",
    "- Different XORshift algorithms have different shift constants and bit patterns to ensure a good distribution of generated numbers.\n",
    "\n",
    "    XORshift algorithms typically have shorter periods compared to more complex algorithms like the Mersenne Twister. However, they are well-suited for applications that require fast random number generation with good statistical properties.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<div style=\"background-color: #ffffcc; border: 1px solid #ddd; padding: 10px;\">\n",
    "\n",
    "#### 4. Multiply-with-carry\n",
    "\n",
    "- Multiply-with-carry (MWC) is another type of PRNG algorithm that combines multiplication and carry operations to generate random numbers. \n",
    "- It was introduced by George Marsaglia in 1991.\n",
    "- In MWC algorithms, a sequence of numbers is generated by multiplying a seed value with a multiplier, adding a carry value, and taking the remainder modulo a modulus value. \n",
    "- The carry value is then updated based on the multiplication result.\n",
    "\n",
    "\n",
    "MWC algorithms can produce long periods and exhibit good statistical properties when properly implemented. They are relatively simple and efficient, making them suitable for various applications where high-speed random number generation is required.\n",
    "\n",
    "It's worth noting that while the algorithms mentioned above are widely used and well-known, there are many other PRNG algorithms available, each with its own characteristics, advantages, and limitations. The choice of algorithm depends on the specific requirements of the application, such as period length, statistical properties, speed, and security considerations.\n",
    "\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reference\n",
    "\n",
    "- https://www.sciencedirect.com/topics/mathematics/variance-reduction-technique\n",
    "- https://www.value-at-risk.net/linear-congruential-generators/\n",
    "- https://beckassets.blob.core.windows.net/product/readingsample/713991/9780387004518_excerpt_002.pdf\n",
    "- https://www.math.arizona.edu/~tgk/mc/book_chap5.pdf"
   ]
  }
 ],
 "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": "3.11.3"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}