{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "0c3a5122",
   "metadata": {},
   "source": [
    "## Introduction to signal processing: FFT\n",
    "\n",
    "Highly recommended to watch the youtube video by 3Blue1Brown to understand the concepts of Fourier Transform.\n",
    "\n",
    "[![IMAGE ALT TEXT HERE](https://img.youtube.com/vi/spUNpyF58BY/0.jpg)](https://www.youtube.com/watch?v=spUNpyF58BY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "03c4333d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bcaff8e1",
   "metadata": {},
   "source": [
    "## Toy Examples"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc1b664d",
   "metadata": {},
   "source": [
    "#### Ex 1: Create a sinosoidal signal with frequency 1 Hz and sample it at 10 Hz. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "b62bb047",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# simple sinus signal\n",
    "fs = 10 # sampling frequency\n",
    "t = np.arange(0, 10, 1/fs)\n",
    "s = np.sin(2*np.pi*t)\n",
    "plt.figure(figsize=(8, 2))\n",
    "plt.plot(t, s)\n",
    "plt.xlabel('Time [s]')\n",
    "plt.ylabel('Amplitude')\n",
    "plt.tight_layout()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2241446e",
   "metadata": {},
   "source": [
    "#### Ex2: Compute the FFT of the signal and plot the magnitude of the FFT.\n",
    "**Hint:**\n",
    "The output of the FFT is a complex number. The magnitude of the FFT is given by the absolute value of the complex number."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "898dde45",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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NFjx2yZxJO+XLM+vAMg3evQ6RZR1YtoH9KFQqAt60J8KmZhUAYejM/i5t0AO+QP0VnmoKhIPEdpUJPM+P6d8FAHr1I9jWqgYAHOk1jHmJn7t5WxHiI5PH5PxOnmA0rnFjUwozhV+brGP+Dba7XQu769WtfZxSkiwVWhMksJjj6rPY3xU8sNjcNCT+fdhmT2oGndg6VCasPdwPAPjz1Qvwm/8exqEePa58aQv+efMylGanARBuaO56aw/sTh7fnVuCa5ZWguM4nFRfgP/s7cHGY0MUWCSpAtebK23fTh6bm1XgeWBacSaKs1JRnJWKe86ahqfWNeJXHx7Ewqpc1PqUr6491IeH/nMIffoRAMCUokzcfkb9eFz+mLA5nOjWmP02SUeadfANHBKRdYiWw8lja4tK/PU3DYNBA4uDHhmLQCpy08Fxwo4LldGKgsyxvcFmB5oAsK1VNY6BBWUsSByxjEWdK7CwOXgYLHZkpY7dE21bq/vFokM99oHFsMUuLsaqLggcALAG7mMDw0EbuNc3Dnr9elPTEK5eWhWnqyXj4fUtbeB54JSpBbhoQTnmlGfjh69sQ/OgEVe8uAVv3LwMVXnpePDDg2hXmVCek4YnLpknBugns8CiaQj3nTt9nP82xJ8CJWUskg3rrzi5vlD8vdvPqMfm5iFsbVHjzjd34/2fngS5TIJ+/Qge+egQPjvYBwDISU+B1mTDy9+24LoTq6Ecw/e0eOJ5HlpTsAlL4WUdqvN9mqTHKesQrYPdOq8gaX3jIO49e5rfj7U7nDjaGzqwSE2Roiw7Dd1aM9pVxjEPLDo8DlK3tqjHvAePpkKRuBuxOWCyCtM2SrJTkZYihdnmgMZoHePAQi3+fDwCC3ZqkJ8hD/r3Ls1ORUGmHEPDgRu4eZ7H+gYhsJhfmYN9nVpsalZRYDGBDVvseGdHJwDgRycLDYNTCjPx7q0n4oevbEObyoQrXtyCq5dU4sO9PZBKODx7zQKvXqGTpwo7UfZ3aaEz2calj4gER9u3k8/GJuG19OSp7iyfVMLhmasW4rw/b8DBbj1+99lRTCnKwO8+OwrDiB1SCYcfn1qHO86ox4V/2YiWISNe39yGO86cOl5/jZCsdu9eB6+sg8oEg5+t0Z5SUwJMWEqyrEMsNjULQeb8imzs69JhX5cWaqPV7w6G5kEjLHYnMuTSoFUIgFAO1a01o23IhBOq84J+bLx53u/saFPD6eTHdE+LeyoUlUKROGHL8aQSDlmpMuRlyMU57sF6DeJpxObA3k6t+GvP1OBYaXM1blcHaNxmOI7DHI8+C3+BxbGBYfToRqCQSXDvWVNxw5od2NI8NC71myQ+3tvZCYPFjrqCDJw21X1yWpGbjnduPRHXvbodR/sMeParJgDAvWdNHfUGVZqdhimFGWgeNGJLiwrnzfHek0LGn9hjMUl3+SSbDpUJnWozZBIOy2q9ywdLslPxh8vn45a/7/TqfZpfkY0nLp2HWa5T6ru+MxX3vL0XL3/biutW1IzpgZmnQFkH1vfQqwuddSjOUvgNHCZS1iEWW1z9FZcsLIfF7sTRPgO+PTbod/8E66+YVZYV8ka9Oj8Dm5pUaBuHe492j8BCZ7ahod8wZlMkPQ+Wc6kUisQLi1Zz01PAcZwYWGjG8I11b6cWVrsTcpkEVrsTnRpzXKL2tYf6MK1YGXB8rCf2ghLqZAPwaOAO0GfBshXL6/Jx4pR8pKZIMDRsRWP/MO0wmICcTh6vbW4DANx40uitv0XKVLz14+W4fs0O7OvU4sS6fPz0dP/13CfXF6B50IiNTYMUWCQhVgahNlrH/OSQjPatK1uxqCoXGX5Gy549qxg3rKjBa5vbkC6X4r5zpuP6Fd6Tgi6cX4a/fHUMzYNGvLapDXd9J3FZC8+sQzvLOng0TEebdWATlibz7iSL3YEdbUJlw0n1BejVj+BonwHrGwIFFqwMKnTPApsEGe7IWY3Rim8aB3DhvLKYpzh1ugILdv+zrUU1ZoEFK4NKkXITanTzxLnSSUrjU1/HUopjORlqu6sM6jszirDucD+sdif6DSNiM2w0trao8ON/7ML8yhz85/aTQn58OBOhGNZnEWgy1DeNAwCA06YVQiGTYklNHr49NoRNTUMUWExAXzcMoE1lQlaqLOAEmpx0Od68ZRk2NA7h1GkFAUcgnjy1EK9vacemJpXfPz8esEOCiYi9DjqcPLRmm98Si2Qzkf9/h7KJ9Ve4ygj9+dX5M7G8Lh/zKrJRljP6PUMq4XDXd6bi7rf24pVvW3D9ipqAI6JD8cw6+AYO0WYdqvPdgURh5vGfdYjW7nYtRmxOFCoVqC/KxGnTCvHS+hZsODbo9xDgYDebCBX6Jp2974dbLfH7L47ize2d0JpsuDHELo1Q2LCa82aX4KN9Pdjepg65nyNe3I3b8gn1vKPAIsmx5XjjGViwxu0V9QU43KtHu0pID8caWADAoW5dWG+84kSoII3bDJva4K+B22ixY0erMGb29OlCycyKKQX49tgQNjerxPp8Etw7OzsxtSgz5K6QscDKLK5ZWuX31JRJl8tCZiGW1eVBKuHQOmREl8aEityJPylsaNiCHa1qbG9TY0ebGod79DhrZjFWX7c45q/tdPJoV5tQk58+Jm98cpkE2Wkp0JltUA1bEhJYdGvNyM+Qx+X0+al1jXj2y2OoK8zA0po8LKnJw9LaPFTkpk2oGwV/HE5eDMBPqg8cWMikkpDfdxfMK8NzXzXh2MAw1mxqxT1n+W/4BYRArdu31yHKrENVXgaq8tLESUueWYdOtQlfHOrD+XPLjtvAMJ42u/orVkzJB8dxWFydhwy5FEPDVhzu1YsTGwHhdeNwRBkLIbBoHTKGVbK8p0MLQCjNiiWw0Jls0JmFe7DLT6gQAotW9ZiVTU/Exm2AAoukx0qhclyNpOwJph6jJXlWuxO7XPseltXmYe2hPrHmNJaRnKxnw+7k0Tw4HDK12B5BKVRJlruB+3CvHos8bn63NKtgdThRmZcmjkA8qV74e2xrUcHucI75ApyJZle7Gve/tx9VeenYcP8Z43otR/v02NSkgoQDrj2xOuavl5WaggWVOdjVrsGmpiFctWRiNvQ3DQzjlW9bsL1VjRY/i6W+OjoQl+f6Sxta8OTnR/HYxXPww+Wx//8PR36mHDqzDUPDVkyN8zqd7a1qXL16Cy6cX4Y/X70w5q/35RFh/HHLoBEtg0a85RowUJKViiW1efjBsqoJO9r4YLcOOrMNSoUM82McwSmVcLj7rKm441978OrGVly8oBxa126HWLIOQuCQjqr8tIizDo99chhfHOqHIkWKa8fouT2RbXb1V5w0RQgy5TIJVtQXYN3hfnzTMOAVWHRqhABQLpVganFmyK9d5RoFbxixQ2uyBd1CbbU70TQwDADY3aGNKQhgjdsFmQosq8uDQiaUTTcPDqO+KPHVDe7leBRYkDjSGL2fWKx5cax6LA506zBicyIvQ46pRZniN3hHDLsseJ73agY/2qcPGliYrHb064UpMOEEFp4N3Ae7dV6BBRsze9q0QvHFZnZZNrJSZdCP2AM2fBM3dhrUoTZBa7IiZxxPU15zbdk+b05J3LILJ9UXYFe7Bt8em7iBxWOfHMY3rl4ijgOmFyuxpCYPS2rzcN+7+1y15iOoCjEMIZT/7O0GAKzZ1IofLKsak1O8gkwFWgaNCdll8fqWNjh54PODfUHHVYeL1Wc/cuEs9OpGsL1NjQNdOvTpR/Dxvh7saFVj6y++E49LH3NszOzyKfkRB6j+sg5ss7JhxI7T//hN0M9PS5H69Dn4zzrEgu1C2tuhpcAihGGLHftc7+kr6t2B8mnTCrHucD/WNw56Tfxi/RXTS5RICeO5kyaXojQ7Fb26EbSpjEEDi+bBYXFH1dCwBV0ac9Q7qtrVrAQ7HQqZFIuqcrGlRYVtreoxCSzYWG0KLEhcsVIodvMmZizGKLBgZVBLanLBcZw4lclzUkKk2lQmcdoVIGyzvCTI4SCrccxJTwl7BOg8Pw3cPM+L/RWnTysSf18q4bC8Lh9rD/djc7OKAosQ2JsCABzu1WPFlMBlEImkGrbg/T3Cje2P4ljzesrUAjz75TFsblZN2Abhg93Cv9FvLp6D780r8/q+efbLY2gaGEa72hhTYNHvas4EhNGRezuDb9mNl4IEbd/WmWxYd0jIMFjsTmxrVeO0aYUhPivI1zPboHfN9L9ySaW4WdpsdWB3hwY/fHUb+vQjGDRYUKicOKMkmY3HhMDiFD/9FTzPQ+MxYYllHdrVRnSqzWFlHdJSpJhbnu0OHqLIOkRLY7SiVycs72PTi0hg21tVsDt5MbBj2PfP7g4tdGab2Dvj3rgdfhN0dX66GFgEe5050qv3+vXuDk30gYXr3qPa9flLa/OEwKJFjR8sS3ywSRkLkhDuJ1aK13/HKrBgjdtslKCYsYghsNjbqfH6te8Lga9IGreZOX4auFuHhDc1uVSCE6d4lx+cVF/gCiyGjusNsPHg+UZ7uGf8Aos3t3fAandiXkU2TqiO3w3tgsocZMilUBtH1wZPBIMGC4aGLeA44NKF5aP6Tqrz0oXAQmXCKTEM4Nngs2Ty3V1dYxJYJGqXxUf7umF1OMVfb2gcjCmw6BTLKORiUAEIp68n1RegJj8DrUNGNPQZJlxgYbY6sMXVJ+dw8vjH1nZ0qIyuQMKMTrUJwyF6HfxlHSrz0vHTf+6G1eHELafUYtU547Oo0vM9KdSyVQKPXhvv99XKvHRxhPempiF8d24pAPfBx+wIXltr8jOwtUUtjp4PhB12MLvbNX6nUoWDfQ+zwGRZXR7wpXDgOhZ9FmojBRYkAdw9Fqx5W+H6fVvAz4kXu8OJnW2u/oo6YeZ/VZ5wc98RwzxpVkqzqCoHuzu0o14IfImN2xGcrvpr4GZlUEtqR49GZC+IO9s09CYShNnqEOtXASHbNB6sdif+sbUdgDBiNp4v8ClSCZbX5ePLowPY1DQ04QKLBtf3U3Veut9mdpaliHXRJft+WlqTh+1tany8rwcPXTAr4d87rBx0KM4Zi/d2dQEQsrM72jRY3ziIB2P4el0a4f9veYASvRklSrQOGXG0Tx90qtJ48cw6tKuMXgvhtra4F6Y++vHhgF+jJCvVO3jITxP7Hgoy/U+6efaaBbj1n7vxt01t+NHJteNSannYI7BwOHk09BkwvzJnzK9jomD9Ff4OmU6fXoTmwVZ80zCA784tBc/zUWYswpsMxYLCFVPysblZhd2u+41oiBkL12vmoqpcpEg59Ost6FCbEr5LjAILkhCjp0IJGQvVGGyePdyrx7DFDmWqDDNKhBcAdlOiMdmgH7FFtcyI9VdctaQSezq14gkrm1HvK5qMhdDArcDQsEVs4GY15/5OIacUZqJIqcCAwYLdHZpxO4VPdkf69F4lDKGyTYnyzs5O9OuFEpLz55bF/eufVF+AL48OYGPTEH5y2pS4f/1EOton/Juw71lfLK0fy6JLh5MXa+x/ft503PPWXnRrzfjiUF/Up4Phyne9TsTzNbCx34B9XTrIJBx+f/l8nPXUejQNDKNba0a5nxGp4ejSmAEAlbn+P39GSRY+O9gX8mAlkVivg2/gEG7WARD6d/yNZq3ITYsqyDxnVglmlmbhSK8ez/zvGB6+cNaYT9DyPTA52KOjwCIA1bBFfB/wrQQAhPfbVze2Yn3jIHiex4DBgqFhKyQcMDPAa5Q/4e6yYN9P319Whc3NKhzp1cNsdUS12ZwdvrDAIjVFivkVOdjZrsG2FvWYBRY0FYrElbt523sqlH7EDpvDGVbjU7RYGdTSmjxx7n+mQob8DDlURis6VKaIT3NHbA5xzNyKKQWozktHm8qEhj4DCur9BxYs9VkbxqhZhuM4zC3PwteuPotZpVniiNvTpxf5/fgVU/Lx4d4ebG5SUWARwCFXaVl9USaaBobRNDA85nP6/72rCw/95yAAIVuRiMdmdePbW9UTLoPF3lhnlPpvLnSf/EWfsdjfpYXWZIMyVYaFlTm47IQKPPvlMby3qyvhgUVBRvy3b7+7U5jWdOaMItQWZIiTwTY0DuKapdE18PuWUfhi/z4sEEwEnuehNlq9ex3En5vRozODD9HrUJKVKjZGsx/3vL0XAPDnqxfE/d9bIuFw3znTcNPrO/Ha5jakpkjxf+dNH9Pggt0os9c5VrpDRmMlcTNKlH4PB5fW5iE1RYJ+vQVH+wzo1QkB95TCzIhu9sPJWAwNWzBoEMpAz5heJB4WHujWYWltXiR/LWHAhetaPb+Hl9XlYWe7BltbVbhySWVEXzNSrGIlnzIWJJ58S6Fy0uXgOIDnhT8rUqYm7LFZupuVQTFV+elCYKGOPLA41KOD3cmjIFOOitw0zCjJQpvKhCO9+oCz0KPJWADCoryvGwZxoFuHmoIMWOxOlGanYmqR//F2K+oL8OHeHmxqHsJ9GJ/a3liN2BxQyCQJexNmb7DnzS7B67o2GCz2sMYFx8s/trbjwQ+FoOKqxZX4yamJySbUF2WiOEuBfr0Fu9o1Qef0++rRmvHwR4dw2aKKcdneHSpj4VkKFW2dMCuDOmVqAWRSCS5fJAQWG5uGYjrlD0eBMr4ZC5vDiQ/29AAArlgs3CicNq0Qu9o1WN8QQ2AhZiz8BxbstLaxfzim0b8WuwPdGvOowCGSrMOMEqXXJulgWQfP3pZIvi8i8Z2ZxfjV+TPx2CdH8OL6Zpisdjxy4ewxGaRgtTtxbEAIzq84oQJPfHY04Q3c0Z6oJ4NgZVCAcMp/Yl0+vm4YxPrGQdjsQh9TJGVQgHuHlcZkg85k8zvIxbcMdFFVLj4/1IfdHZqIA4sujQk8D6TLpSj0CJiW1ebjr183iweviSRmLCiwIPFiczhhcE0VyXMFFlIJh5y0FGhMNmiMtoQFFk4njx1troxFrXd6szovHXs6tFHVaLP+igWVwpSpGaVKfH4ocDnAiM2BHtd0jnBGzXpiQc/Bbh2UqcJT3XPMrK8VrjTu/i4dDCM2KKMo8xpPu9o1uGb1VlwwvxR/umJ+QoKLg6432Dnl2ZhRqsSONg2O9AYfFxwvL61vxhOfHQUA3LCiBg9dMCthNxocx+Gk+gK8v7sb3x4bCvsGiud5/Py9fdjUpMKONjVW1OdHVS4YLbvDicZ+oQdmZoCMhbCcDTBZHRgctkT1GrKh0bussCo/Hctq87CtVY0Pdnd5jZaMN3Z6F6+pUOsbBl2lmHJxaeZp0wrx1LpGbGoaijoz7M5Y+A+yKnLTkC6XwmR1oE1lDDi+MlDWoV0l/LxXPxIy61CaneoVOFTmpeHet/cBAE6uL8A/b14W9t+LbdueWZoVsHw1Hm4+pQ7pchl++eEB/H1LO0xWB3536dyE7xlqHhyGzcFDmSrDubNL8MRnR3G015CwCoGXN7Tgt58ewe8vn4crFyf2BDwRNrueD76N255Om1aIrxsG8U3DgDgZKtJDyXS5TMxAtKmMmJ+eM+pjWKaJHaosqs4RAot2zaiPDYXd31TleS//XFSdC6mEQ5fGnNBDFKeTF0vhqceCxA0bycpxQFaa++YkL0MOjcmW0MlQDf0G6Mw2ZMilmONzslAl1mhHEVi4+isWVuUAgHhDGqgcgH1zK1NlyA1z1Cwzr0J4jGMDw+KpHbtx8KciV6gRbleZsL1Vje/MjPP2LT94noeTh1hqFos/f3kMVocT7+/uxvK6/Li/SVntTjT2CwHgnPIszCzNEgOLROJ5Hk//7xie/fIYAOD2M6bgvnMSXxpxylQhsGA3UuF4e0enOCFFa7LhbxuDbxGOtzaVEVa7E+lyacCTcoVMirLsNGGPgMoUcWChM9nEPqlTPfqVrlhciW2tary3qwu3n1GfsH8f1mNhsNjjUqbGmrYvXlAu3jjOKc9GbrpwgLO3U4slNZGddvI8L/ZYBNqvIpFwmF6ixJ4OLfZ16iDhuFGBA/u10eoI+njpct8JS8GzDl8c6hN/vrFpCB0qU9ijh9n3g78xs/H2/WVVSJdL8bN39+G9XV0wWx14+qoFCS29ZK9nM0uyUJWXDqVCBoPFjqaB+Gdmd3do8LvPhcOSZ9Y14pKF5TEHL/F8TwmlW2tGm8oEqYQLmhE4fXoR8PFh7GzTiKfvsyLMWADC4aIYWPjpefEtA2U7rKJZlNcRoJQxUyHDnPJs7OvUYluLCpcuqoj47xEO/YgNDldDI/VYkLjRusqgstNSvF4k8jLkaB40JjSw2OaqmzyhJm/UCVGVK3PQoY68+XOvK2Ox0PWiEKocgC1NqsnPiPhGpThLITZwd2nMkEk4rAhx8rxiSgHaVR3Y1KQak8DiR6/tQPOgEWvvPTWmG6TDPXqv8Z+PfHQIS2ryxO3i8dDYb4DNwSM7LQXlOWnim2wiJ0PxPI/HPjmCVze2AgB+fu70MRsHzDbIHuzRQWO0hkxH9+lG8NtPjgAQbrq+PTaEV75txfUn1oxZKpv9W0wvUQbN5lTnp7uadk1YHOFN88amITh5YFpxJkqz3ad1351bgof/cxBtKhN2tmsivhkPV1aqDClSDjYHD5XRGtOJodpoxZdHhd0Vly923yBIJRxOmVqIj/b1YH3DYMR/F5XRCrPNAY4DynJSR2Ud2CZplsH92bv7gn49jhN6HXwDB9b7kJ/hf8KSPw4nj6fWNgKA+P/x7Z0d+Pm5M0J+Ls/z4v6KRJVB+bp4YTlSU6S46809+ORAL8w2B57/waKE9T2JgUWp8D00qywL21rVONiti2tgYRix4Z639oo3jz26Efx3fw8uWRjbjeqNr+1A25ARn98T23tKOFiQOa8iO2iGv6YgQzy0GzQIpXSzyyKftledn47tbeqAh5q+GYs55dlIkXJRLcrz3WHhaXltHvZ1arG9VZ2wwILd3ykVsjHtYYyHhFxtXV0dVCrVqN/XarWoq6tLxEMel8RRYz7Rqrgkz5S4wGJ7G9tfMfoNNdpdFgOGEXRrzeA49zjYitw0ZMilsNqdaB0aHaj4jnuLBGvgZhZV54YsS2Hp3M3N4Z9SR8tqd+KbxkF0qE1oi2FCDwCs3tAMQLi5W16XB5PVgXve2gObx1z+WB0Sy6CywHEcZomBhR58qFqMKD3y0SExqHjkwlljumOkKCsV04uV4Hl3HXEgPM/jVx8egMFix/zKHPzthiWYWZqFYYsdL7r+bcaCu78i+FbYWBZdrnctmTx1qnf2L10uE+fUs2boROA4TtxlEWufxX/2dsPm4DG3PHtUTwor89pwbNDfp45isTvQPDiMrxsG8LgrwOR54KLnNmHOw1/ghMf+h0ue34y739qLP61rxLuuTAmTLpdiRokSZ88qxk0n1+LXF83GmhuX4MufnYYjvz4PWx74Dt75yYn44xXzcdd3puLiheVYVJWLggiXxf13fw8a+g1Qpsrwm4vmAADe2dkV1mtFy5ARPboRyKUSLE1Q4OjPeXNK8PL1i5GaIsFXRwfwo9d2wB7H1zZPLDhnJ+qsZMdzMWg8PPLRYXSoTSjPScNPThPui15a3xLTa6nTyWND4yDaVCavseCJssX1unhSGMNOTvfIblbmpYklUZGocR2U+Xu/tDucOOZTBpqaIsUsVwCzuyOyciixFMrPvQfLzmxLYJ8F66+daP0VQIIyFm1tbXA4RqduLRYLuru7E/GQxyX31m3vb0A2x12ToIwFz/Mei/FGv3mwm5Ie7UhEdacsWzG1KFM83WDlALs7tDjSZ8DUYu8bIvYCEu3J+9yKHHwdZMysrxPrhMDiaJ8h6AjceOj3qI3WxrCXpEtjwsf7ewEAPz2tHgVKOc575lvs69Lh6XWNuP+80CeR4WCN23NcL9TTS5SQcMLp7IDBguKs+Pb79OtH8PoWYVfF7y+bl/AJHP6cVF+Ahn4DVm9oxrK6vIDPh4/29eB/RwaQIuXwh8vnIUUqwc/Onoab/74Tr29uw00n1yZ00AJz1HVTFKhxm4l2Hw3P82Lj9ml+ygqvWFyJd3d14ZP9vXjke7O9FsPFU36mHH36kZj7LN7dKdzcX37C6FPHU6YJN0v7u3QYGra4p+F5bJL27HsI1OvAyjM8sw7VroxDn34Eb2zrgEImwaFHz014eZ/d4cTT64RsxU9OrcOliyrwhy8aMGiw4KujAzh3dvBhA+sOC9mdE6pzx7zZ+LRphXj9xqX40Ws7sLlZhU3NqpgWGPrD87y4w4JlJ+a4DqcOdsevgfvjfT349+4uSDjgmasXYFqREv/c0o6jfQasbxz0O7kwHMNWuzgOvEdrTugOHp7nxYzFCj9jZn2dNr1QfD2fXRrdddUEmWjXOmSE1eFEhk8Z6KKqHOzr1Ea8KK9D5e6x8LW4Jg8cJzzmgH4ERXF+7wPcPWQTrb8CiHNg8dFHH4k//+KLL5Cd7X7yOBwOfPnll6ipqYnnQx7XAq1zFzMWCQosmgeHMTRshUImETMLnoqUCihkEljsTvRozWFPaxL7Kyq9t/POKM0SFuX16vG9+d47CdqinAjFzPV4YQ3WX8HkZyowo0SJo30GbGlW4UKf64mnbq1Z/HksgcWrG1vhcPI4qT5f/Pf63aVz8dM3duOF9c04dVohlteFfuEPhTVus22pqSlS1BYIW1UP9+rjHliwE6OK3LRxCSoA4JqllXh3Vyf2delw0XOb8OoNi0fdtKuGLeKSsDvOmIppruD4OzOLsKAyB3s7tXj+62Y88r3ZCb9escY4QRmLxv5h9OstSE2R+C0PWlKTK5Y8fHagD5f5uWGPB9ZnEcv27UM9Ohzu1UMulYivOxa7A10eE5aYxY/9Dxlyadi9Dp7DKNbcuARVeekozxnd66Az2/DGtg5Y7E7oR+xRneJG4t+7u9CmMiEvQ44bT6qFXCbB5SdU4KUNLXhre0fQwEJntuGl9UL27eKFiXtdDGZZXT5W1Bdg3eF+V1Ac38BiwGCB2ijsWGDfx+wg5XCvHg4nH3PvQpfGhF98cAAAcMcZ9eL30TVLq/DKxla8tL4l6sBCb3a/j/R4vL8kQvPgMAYMFihkEiyqzg358cvr8iGXSWC1O8VgLVLsdavNT3XDkT7/ZaCLqnKxZlNbRIvyeJ732GEx+t4jOy0Fs0qzcKhHj22t6oTcJwS6/5sI4hpYXHzxxeLPr7/+eq8/S0lJQU1NDf70pz/F8yGPa76jZhn2REtUYMHSe4uqcqGQjT6V4jgOVXnpODYwjHZV+NsnWcZigatxm5lZwua5j67VZzssItm67emE6lwoU2UoyUoNexnPSfUFONpnwObmoYQGFmyeNwDozNH9W2pNVry9Qyg78Ry9unJuKa5cXIF3dnbh3rf34vO7T/U7ni9cDicv1q96NvPPLM1C86ARR3r1OCPKN8NAul3Nr4kcXRrK1GIlPrjtJNz8+g60qUy47PnNeObqhTh7lrv/5pGPD0NttGJGiRI/Pd39b8BxHO47Zzp++Oo2/GtbB245tS6hfxed2SYGq6EzFq5yxggHMLAyqOV1+X7rtzmOw+WLKlylPp0JCywKMqPbZcHzvJh1uOX1nQAAq8OJW/+5Cx1qE/qCTFgyWoWeiVLfXod8d9M063V44P39eHN7J+76ztSg3xesX6lba0ZDnyHikZiRsNgdePbLJgDAbadPEbeyX7WkEi9taMH6xsGgU25eXN8MjcmGqUWZuCxBdeXhYNfXlYAbZ5atqCvMFJ/fws8l4vSuKYX+x5WHw+HksertfTCM2LGwKgd3fcc9Pe1HJ9fitc1t2NKiwv4urTh8JBI6j8Ci1zVNMVHYkIrFNblh9XKky4UpW//d34NTpkYXELLAQmW0jlrQe5T1V/j0wbCgJ5JFeYPDFphtDki4wO8/S2vzXIFFYg4g1caJOREKiHNg4XQKNY+1tbXYuXMn8vNjPyWdzLTi1m3vG0L2RNMkqMdiW4D9FZ6q812BRZgnng4nj/1dWgDuiVAMeyE46jNdyGJ3iAtqos1Y5GXI8eWq0yCXScIeTbpiSj5e3dgqvnAmSo/W/cIfbcbin1uFMYwzS7NGTWl5+MLZ2NGmQeuQEb/44ACe+/7CqEstWgaHMWIT0syeY39nlmbhv/t7E9LAzW6SywNsLh4r9UWZ+PD2k3DbG7uxuVmFH/9jJ+4/dwZuPa0O/zsygI/39UDCAb+/fN6oJruT6vOxvC4PW1vUePZ/x/Dk5fMSdp1shntZdmrIINLzDTqS0cobGoXSh2AlKJeeUIGn/teIrS1qdKpNYsOk08njYI8O3x4bQtPAMG4/ox71AXbKhFIQZPu2b9ahQ2VCu8e0JZOfrINnrTTLOlTlpaNHZxZLAP+36jRU5qX5PWzxFWrrtqcZJUp0a8042qdPaGDx5rYOdGvNKM5S4IfLq8XfryvMFJ+j7+zoxL1nj55i1qM142+uXqf/t3JGwke+BlPh+n/KDh7i6YhPGRQgNPLPLM3Cng4tDnbrYgosXvimCdvb1MiQS/HnqxZ6/X8sy0nD9+aX4f093XhpQwv++v1FEX99vdm9s6Q7wRmLjWIZVPhN/L+/bB7uP3d6RE3UnpSpKSjIlGNoePSCXnYwOdMnW1uWnSruJNrfpcWyMLL37MClNDstYOP0stp8rNnUJt4vxZvaKLy2TfrAAgBsNhtqamqgUqkosIhRoOUouXGe4+6J53lsaxVuqIO9ybEa7c4wA4tjAwYYrQ5kyKWY6jOvfbrrhaBHN+K1+KZTLWyFzZBLxRPKaERa/7isLh8pUmH047H+0X0f8eKZqtaaIw8sRmwOvLa5DYBQL+0bNGQoZHjmqgW47IXN+ORAL07bVRj1CFpWBjWrLMsrQGMNjokYOcveGCvGMWPB5KTL8fqPluKRjw7hjW0dePLzo2jo04tbZ285tc7vCSPHcfj5udNx2Qtb8N7uLtx6+pS4TuryJDZuhzG5RpmagrwMOdRGK9pV4S26NFntYu9VsMCiPCcNJ00pwMamIby6sRWzyrLw7bEhbDw2KPaNMU9ftSDk4/rybG59dWMrlKkpXr0OwbIOAMQFo8zd35mKusIMMZjI85iwZLU7sfDXa2G0OlzLJ8PrKwi1ddvTjFIlvjw6kNDpamarA899LZQx3Xnm1FEnzNcsrcLWFjXe3SlkWXzLff60thEWuxPLavNw5oz4ZiYjxU6QE3HjfNjVoD3L53toTlk29nRocahHH/Wm8T0dGjz9P2Fk9q8vmuO3KfjHp9Xh/T3d+OxAL9pVxogP1PQjY5Ox2N+lxf+OCP02kfS5pMmlUQcVTHV+BoaGrWhTGb0DiwAZC47jsKgqF58d7MPujvACi3CGxrD7o2MDw1ANW8TyzHhhGYuJNmoWSMBUqJSUFBw8eDDhTWiTARs36/vEYlOiEpGx6FCb0K+3QC6ViDOg/alyLX1qD7P5k5VBzavIGfWmlZWaIr5ZeO6z8Ny4PZbPp0yFTEzVfnawL8RHR68nxh6Lf+/uwtCwMG7z/Hmlfj9mfmUOVp0jnEA+8tEhDOije7Nhp7a+IwLZG7CQ0Qhefx4pdiJZlgSBBQCkSCX47SVz8euLZkMq4fDh3h706y2oLcjAvUF2VZxQnYczphfC4eTxzP8aE3Z94fZXMNUeG7jDsbVFBavDiYrctJDB0RWu0a2vbW7D/e/tx8f7eqAx2ZCpkGGRK2O5J8iUlhGba8LS0QG8vrkNv/nvYdzy950475kNmP3wF1i9oQUA4OSBp9Y14r1dXdjeqkavbkQ8jJhRokSmQoa0FCnyM+Qoz0nD1KJMzCrNEnsZfnJaHe49exouWlCOhVW5yPeZsCSXSXCi60R2vcc452AcTl686Q0rsHCVrTUE2OUTD69vacPQsAWVeWl+DxfOnV2CnPQU9OhGvMZWA8LN9vt7hCb3B747c9zf29nrQSJ6CDxHzXqKtYHb4eSx6p19cDh5XDi/DJcu8h+czCjJwunTC+HkgVe+bY34cXRj0GPhcPL45QcHhYlnC8oS2iDuj9gf5lHGqTPZxEW60/28/rn3WYQ3GcpzOV4geRlyTCsWsldsmXA8sfu7fMpYCK677jq8+uqr+N3vfpeILz9piBmLID0WkS59CWVnm/CNN68iO2jdZHWQ6Qz+7AnQX8HMLGXlAAbxRKHN9bUTdcIbzMo5Jfjq6AA+PdDrVQcbT54nSpH2WDicPF523VzddHJt0MlcPzl1Cj7Y3Y1jA8PY1a7Byrn+g5Bg2Buq75tIkVIhnnw39Bn8Li2KVrKUQvm67sQa1BZk4PY3dsNkdeDJy+aFrDH+2TnT8XXDID7a14PbTq/3++YXq0AndoFU56VjT4c27O9hzzKoUK85584uQUVuGnq0ZsyryMGpUwtwyrRCLKjMgcniwPxfr0WbyoR1h/thtNjd+x3CzDp4unJxxajlcHkZcnx+sA8/fWM3AMDsJ+hVyCS4eklVyK9/2vRC/O9IP9Y3DoY17rhfPwKbg4dMwqEkjGwpu4lt6DPA6eTjvk1eP2LDi66m67u/M81vaUdqihSXLqzA3za14s3tHTjDIyvxu8+PgueBC+aVYkEcv7+jxV4PBgwWWO3OuM34H7E5xJHnvhkLdqBysFsX1Xtul8aE1iEjFDIJHrt4TtDP/8mpU/BNwyDe2dmJe86aGtFJuGfzdr9+xO9uqFi9sa0dB7p1UKbK8MvzZ8b1a4ej1nXv4dnAzQ4ky3PS/I6UX1SdA0A4zAjn3y/YqFlPy2rz0dg/jO2tGpw3J/L31WBUASpWJoKEBBZWqxWvvPIK1q1bh8WLFyMjw/vG8KmnnkrEwx53QvVYWOxOmKwOsQkvHtgL64zS4Dc+7BuuU20K6xuVbeoN9MY0oyQL/zsy4FVSw144otlhEauzZxVDJuFwtM+AlsFh1MVQVxtILFOh1h7qQ5vKhOy0FFwVYmKS1DXS99jAcFTlA04nL5YI+E7z4DgOM0uV2NSkwpFefdwCC57nk6J5O5BTphZi/c/PgM5sE2erBzOnPBsr55Tgs4N9eGpdA166dnFcr8fp5MUeC98a40AiXXTJTuxPDaP0ITVFik/uOgUtg8PQmmzoUJvw+cE+rN7Q4lU+ecvfdwb8GhmusonqfO9N0lV56dCYrLjshS0ozlLg95fPD3q9M0qUWFiVi0KlQviRKfy3tiAjrPrl01zZy93tmrD6UdjfrywnLawJQjX5GZDLJDBahd6QcDdgh+tvG1uhNdkwpTADlywMXMZzzdJK/G1TK748OiCO0Pz22CA2NA4iRSqU9CWD/Aw5UlMkGLE50asLfyphKA19Bjh54esXKr1v5qcVK5Ei5aAfsUe8aA1w99OV54Te37C8Lg/zK7Kxr0uH17e0Y5WfnpdAPAMLJw/0Gyxxff0cMIzgD583ABCWlY7FCG1f1X52WQTKNDGzy9iiPCs61aG/x8SJUHnBn1ts6mRDf/yzjWydQF5GYifFJUJCAouDBw9i0SKh8aix0Tv1PxZp1Oeffx5/+MMf0Nvbi9mzZ+OZZ57BKaeckvDHjTd1gHFj6XKpOO5VbbTGNbAIJwUICA10HCdMSlEZrUH3PQxb7GgcEG56Fga48RS3OHtMhmIvHDVxeuOIRE66HCvqC7ChcRCfHeyL+2I2w4gNhhF3o10kgQXP83jRla247sTqsP792SlfVxQNjx1qEwwWOxQyCer9BFgzS7LEwCJetCabeMqcLKVQvnIz5BGdJq06exo+P9SHLw71o2nAgPqi+GUtujRmGK0OyKWSsDN8bKNsOBmLDpVw4iqTcOLMep7nhSZKj8Zoz83SfWGW3S2vyxsVOPj2OvhiZR6q4cBZW9YPct8503GWxxSvSFXlp6O2IAOtQ0ZsblaF3PUgNm7nhfe8lUklmFqUiUM9ehzp08c1sBixOfCqq6Rm1dnTgwY6U4uVOKE6F7vaNXh3Vxd+etoUPPHpUQDAD5dXx+0GPlYcx6EsJw0tg0Z0a+IXWHg2bvs+n+QyCaaXKHGwW49DPbqIA4s+vfCcKMkOfSPOcRx+ctoU3PbGbvxjSxtuPa0u7H0weo/3FADoDTLlKxq//eQIDBY75lVk4wfLqkN/QgKwCZFtHq9b7jJQ/9na1BQpZpdlY2+nFns6NSG/x9qD7LDwNNVVCtXYH/9lhOKC5IzE7dJKlIQEFl9//XUivmxY3n77bdxzzz14/vnncdJJJ+Gll17CypUrcfjwYVRVhU57JwuHkxfrJX3HzXIch7wMOXp1I9CYrDE3Q3kKN7BQyKQozUpFj24E7SpT0MBif6cWPC+c1gRqpGYZksY+gzgrPJat2/Fw/twSbGgcxKcHeuMeWPg21ukiaN7e3qrGvk4t5DIJrl9RE9bnVMTQ8Mgat2eUZvlNq7MG7sNxDCzYdRZkKsIaZTgRTC1WYlmtMH1nd4c2roHFEVcpwNTizLBLH/zVKvsasQmn6E98KmyStjt53Pv2PjGQ8Fdi5ClDLkVVfgaq8tK8gofNzSqs3tCC5XV5eOvHJ4Z1vZ7YklC7k4febB81BWvQYEHLkBEcB7/7NiJ12rRCtA4Zsb5xMGRg0alxNW7nhv+6NaNEmIl/tNcQ8utHomlgGAaLHbnpKVg5J/TXvWZpFXa1a/DWjg6UZKXicK8eSoUMd56ZmHLQaJWzwCKOfQTs9WtWmf+b09ml2TjYrcfBbn3EZS8sY1GaHd5N/rmzS8R9MO/u7Ar7dd73faRba0a8cqObmobwn7094DjgsYvnxLzPI1osizBosMBosSNDIRMPJINVWiyqysXeMBblGS12cT9OqACEDXYZNFigMVrjVrZksTswbBGCxLwJ2LydmLWo4+ipp57CTTfdhJtvvhkA8Mwzz+CLL77ACy+8gCeeeGKcry58erNNrDH23bwNCH0XvbqRiOe4hxLJNJPKvHT06EbQqTbhhCALcthivED9FYCQlVDIJDDbHOhQm1Cek4Yu1xt0OKUmiXD2rBL84oODONSjj2pCRzDsDZEt3dJG0Ij/8rdCtuKKEyrC3gxeHsOIxkOsDCrAG+5McVywIW49P11iGdTYp9oTaUZJFra2qMWypXgJd+O2J/am2a01Y0uzCv164ZDAMwPhL+vApsEAwoSlsuw0VPoEDtX5wpSl3PQUv8+H0uw0rN7Qgv1duqjqwBUyKZSpMhhG7BgctowKLFgz5fRiZUz7W5hTpxXgtc1tWN8wGPI53qkOv3GbYSUcR+PcwH00wNKwQM6fW4pHPz6ETrUZD/7nIADgp2dMSbqRl4mYDBWqnGZOeRbe3uk+aIlEn+sgqSzM1zOphMPNp9ThwQ8P4uVvW3Dt8uqw/v1YKRSbfOY50jwWFrsDD34oPB+uXV4d1Y6NeMlOT0Fuego0JhvaVSZML1GikZWBBukvW1Sdg79tQshFeexgIDstJWTZWqZChorcNHRpzGjsN4Q1cSocrIJBKuGgTJ14t+kJu+IdO3bg3XffRUdHB6xW75um999/PyGPabVasWvXLvy///f/vH7/nHPOwebNm/1+jsVigcXinoWu1yduMkckWBmUMlXmtzGXndhp4hhYDFvsYqASzptidX46trWqQ5ZSsMbtQGVQgLsPYH+XTmxCdfJAWooURcrxSQXmZchxYl0+NjYN4dMDfV7Lz2LV63rBn1GahV3tGhitjrAbEdkLY6jeCk/lOe6byEixxm3fiVDMlMJMpEg5GCzR1R/7k6yN27FiE5viHlj0Bb4pYlmHDrURHSoTOtRmV8mSu0b5mpe3BvzabFsuIOx4WTmnxJWFSEdZTmrYI1g9TS3KhFIhg8FiR0O/IeBzK5iCTAUMI3aohi2j9mGwMqhlcdoLsbwuH3KpBN1aM5oHjUH3b7Abk4oInrssIPS3JDQWbNJUuAFnmlyKixeU4x+u/Til2an40Um1cb2meBADizjtsuB5XgzOA92czi6PvoGbLUMNpxSKueKECjz8n4Po0pgxNGwJa2w6Gzdbm5+BliGj1xLWWKxe34KWISMKMhX42Tnj32tTnZ8BjUmLdpURaXIpzDYHFDJJ0LJpNhkq1KK8SCslphUr4x5YsFUCuenyuA9zGAsJCSzeeustXHfddTjnnHOwbt06nHPOOTh27Bj6+vpwySWXJOIhAQBDQ0NwOBwoLvaupy0uLkZfn/+xoU888QQeffTRhF1TtAKNmmXY78dz+zbLVuSmp/idrOCrWmz+DBxY8DwfsnGbmeEKLI70GcTyl+r89HEdb7hybgk2Ng3hs4O9cQ0sWI349BIldndowPNCGtu3adCXw8mLY+gieZNiN+g6sw3DFjsyw+zL4XnenbEo9/+GK5dJUF+kxJFePQ736uMSWLD/P8nYuB0LNg2qoT9+N5A8z2PjMWFi05FeA/78v2Mhsw7+sF6H6vwMr16Hhj4Drnl5Kwoy5fjnTcvi8kYnkXBYUJWDb48NYXeHNqrAIj9DjtYho9+sLVt4t7Q2Pm/06XIZFtfkYnOzCltaVEEDiy41CywiKIVyBYRtKiNMVnvYNfWhNLhqvyOZQnb10kr8Y2s7AKEvKBlLEcUMbJwyFl0aMwwWO+RSScAFeDNLsiDhgKFhKwYMFhRHsB+JZQ7KwiyFAoS+gOw04WRea7aFFViwUqgZpUq0DBnjMnK2Q2XCc18LG9t/df7MkKf4Y6G2IAN7O7Vo9Wjgnl6iDFqeVZaThpKsVPTpR4IuyusIs7+CmVasxFdHB+LaZ6ER+2vH//91NBISWDz++ON4+umncfvtt0OpVOLPf/4zamtr8ZOf/ASlpfEdyeWP741osNOFBx54AKtWrRJ/rdfrUVkZ3RKxeBKXowRIQXuOnI2XcPsrGHYDGWyqTLdWOG2RSbiQ867FU7tevTgJazwatz2dO7sED354EPu7dF5bhGPFNopX5Arj8XRmG3Rma8jAQmuyiiVykSzOyVTIkJOeAq3Jhm6NOewbjV7dCNRGK2QSDtOCLAqcVZqFI716HOnVx6VGPJknQsXCsyZXbbSGXWIiZB3cjdEs69CpNnkFKf/e3eX38zMVMqFEKS8dVfnuJunffnIYjf3DeOTCWbghwMn0hmOuaVBTC+N6erawUggs9rRrcO3yyBtBWdbWd/u2zmwTMzhLagOXaEZqWW0+NjersK1FFfB6rXanGMiF27wNCNmXgkwFhoYtaOwfjttYV5axCPa962t2WTZuP2MK9GY7Ll1UEZfriLd4l0Kxw5OpxZkBR3enyaWoL8pEY/8wDnbrIgos2HMiksMgQHiN15hsYVcmsM3bM0qy8OmBvphLoXiex8MfHYTF7sSKKfm4aEFZTF8vXsT+sCETRmxCNjWc/T2LqnPw6YHgi/IivQ9iuyzieVgUaNXARJGQwKK5uRnnn38+AEChUMBoNILjONx7770488wzE5YhKCgogFQqHZWdGBgYGJXFYBQKBRSK5Ou614gZC/8RK7shieeSvEj6K4DwpsqwMqiZpVkhT75miHXGBnESUHXB+DRuMwWZCiyrzceWFhU+P9iHW06ti8vX9TyRz0kXAotwJkOxf+/stJSguyv8Kc9Jg9ZkQ5fGFHZgwcqgphYrg/77sRIcNpY2VuyGIVknQkVLuMFPQ6fajKN9eqxwLV/jeR6Dwxb3dCWVO3BoVxvRr7eE+MqCE+vyhUxDvveEpUC9DpuaitDYP4z2IFnH9Q3hj5mNxEJXXxbrwYoUm+8/NOz9GrirXQ2eF0414zkOc1mdUFa1vVUd8LCqV2eGkwdSUyQojHAT78xSJb49ZsHRXn1cAgutySo+byLdm/Lzc2fE/PiJxF4XerUjcdn94TkRKpjZZdlo7B/GoR49vjMzvEljIzaHeKMYScYCgNgfpA1zuIeYsXD9e/dEUQpldzixq12DtYf7sfZwHzrVZqRIOfz6ouD7N8YSO3BsUxnF98Rwyv0WVua6AovAi/LYa2EkpVAA0Ngfvx5D9nxhhycTTUICi7y8PBgMQvRWXl6OgwcPYu7cudBqtTCZwlvGFA25XI4TTjgB69at8yq5WrduHS666KKEPW4ihCyFymCndeOXsWDfeAMGS8CaRVYGtTBI4zbDXhg61CYccjXIjXfGAgC+O7cEW1pU+ORAb9DAgm2eDqd0gE2FKs1OQ05aCtoR3shZ9u8dTTNleU4aDvXoIzrlOxiicZuZJY4Ljm9gcTz1WLCsAztF/OEr23DmjCJXAGEOOWEpUyETAwXPwGFz8xBeWt+CU6YW4B83LYvomtj3ekeAw4EBwwgO9+rBccApUwsi+tqhLKoUAovWIWNE2RumgL0GGr2DLrEMKg7ToDwtqMyBXCrBgMGCdpXJ71AJ1rhdkRt5CeeMEiW+PTYUtz4L9nUqctPCLn2cKEqyUyHhAKvDGXb/QTDhBxZZ+GBPd0QbuFnjdlqKFFlpkf07sPf/cIZ7WO1O8TWE/T20JltYpXUjNgc2NA5i7eF+fHmkHxqP9yKFTIJfXTAraPnfWPOcaMf6EkPt3gLci/J2tWsC9jR2ivdB4d171BdlQsIJ/68Hhy1xOcygjIUfp5xyCtatW4e5c+fiyiuvxN13342vvvoK69atw3e+851EPKRo1apVuPbaa7F48WKceOKJWL16NTo6OnDrrbcm9HHjTSyFCvDEYiPI4pmxiDSwyE5LESezdGpMo9LtDiePDa4lVeGcwOVlyFGcpUC/3oKd7cKJwniNmvV07uwSPPTRIezt1KI7wFzwTrUJV68WGmC/uu+0oA2tTicvNm+X5aQim715hHEq5Z5tHUVgEcVkqMM9/jdu+2JvZJ1qc1hLxIIxWe3i37MiZ/z//cPlL+vQrjaKv/bNOjh54H9HBsRfSzgh0PQXPFTnpSMnQNbh66PC1winFMCX+AYdIGPxrWvb9pyy7Ig2AIcjOz0FUwoz0DxoxJ4OTdgnwEyBq2xwyOD9Grhd7K+Ib2CRmiLFgsocbG9TY1uryn9gIY6ajTwgZgcr8doH0yDO9o//lvfxliKVoMQ17rxLa449sAgy/MATex08FEFmlmUNSnNSIw422URITRiHTqxxGxAyOpkKGYYtdvRoR0IGBT96bQc2N6vEX2enpeA7M4twzqwSnDqtIG49P/HCDhw9+8fCyVjMLc9BoVKBQYMFb+3owHUn1nj9ucPJi9Mow90nk5oiRXW+sOemsW84roFFfpJNYwtXQp4tzz33HEZGhH/wBx54ACkpKdi4cSMuvfRSPPjgg4l4SNFVV10FlUqFX//61+jt7cWcOXPw6aeforp6fJa5REsbZinUePZYcByH6vx0HOzWo101OrD4964uHBsYhjJVhjOmF4X1NWeUZKFfPyj2ESRDxqIoKxVLqvOwvU2Nzw/24aaTvWvRh4YtuO5v28VT9qaB4aDNqCqjFVaHExwHFGelIsfVDBfOqVSgpYnhYAFRVyQZi27hDXR2iIxFboZcbIw72meIaXcAO9HPVMgiPuFLNM9eB9/RrB1qd71vIOzNnvnNxXOEvoe8dJTlpIU1FczX0Qgn/3hiM+E71Ca/JSWsv+K0OJdBMQurctE8aMTuKAKLfNfiKM+Mhclqx4EuIRiOd2DBvqYQWKhx1ZLRe5E6o2jcZtiJa0OcSipYzXekZVATRXluGnp0I+jWmMWJP9HQj9jETNOsEBkLtuOiW2sOO8smjpqNsAwKAHLSWMYijMDCdTClVMgglXAoy0lFY/8wenXmoIGFxe4Qs3zXLq/Gd+eWYklNbsQjoMdSTnoKslJl4kLA4ixFWP8WcpkEd51Zjwf/cwjPftmEy0+o8AqaerRm2Bw85K7ANVxTizKFwKLfgJPjkNll7/Px2osx1hJWCsVIJBLcf//9uP/++xPxUH7ddtttuO2228bs8RJBTIWNUfO208mjK4r569V5GTjYrR81GWrYYscf1jYAAO46c2rY3yAzSpVY78pyKGSRfXMn0nfnlmB7mxqfHej1CiyGLXbcuGYHWofcDeyNIcZnsv6KYmUqUqQS8VQqnCV5alYKFUWKtCLCjMWgwYI+/Qg4LnSJACC86fbpR3CkVx9TYNHt0X8y1jW9PM9j0GDx3iLtETyE6nXwl3Wo8uh1yElPQdPAMM5+egMy5FL8YGlVTPXhPM+7t86GUQrgqywnFTIJJzYde/a0OJ08vnVNm4p3fwWzqCoX7+3qEnuxIuFu3na/Bu7t0MLu5FGanRrRuNdwLa3NA74GtrWo/f55Z4Rbtz3VF2VCKuGgNdnQr7dE3Ojri2UsImncnkjKc9KwA5qYG7jZmNmy7NRRy2h9ZaWmoCY/HW0qoVz3lKmhvy9Y2Ws0/57sYDGcQyd2k53lOqgqy0lDY/9wyMlQLYNGOJw8lKky/Pqi2UnTRxEMx3GoLcjAPtchQiSHKlctqcLL37aiQ23Cmk1tXstvxYOBvLSIFgBOL1Fi7eF+NMapgVsTQ2VCMkjYcaDD4cAHH3yAI0eOgOM4zJw5ExdddBFksuQ6gUxW7IQiYClUhrt8hm2qjkW/YQRWhxMyCYfSCF4AxclQKu/JUC9+04xBgwXV+em4bkX42SLPE6Pq/PSkmeF83pxSPPLxYexs16BPN4KS7FRY7A7c+o9dONCtQ16GHHPKs7GhcTDk2Llej9Q4AI+MRRg9FuwFJ4qmrkh3WbA+l7qCDGSEUaM9s1QYuxdrAzcLfMJdJhWpEZvDK8sQTdaBBQrVPk3S4WQdagoykCLlYLQ60K2Nbe9Hv94CrckGqYSLqgZaJpWgPDcN7SohA+MZWBzs0UFttCJTIQurRyoarOZ5X6c24texAtf3wJDHVKhtHmVQibhBOqE6F1IJh26tGV0a06jMRFcUW7cZhUyKKYUZaOwfxpE+fUyBBc/z4tKwaDJZEwF7rsY6UjXc/gpmdnk22lQmHOzWhxVYsOsri+LfMyc9/PcGdjDFAgu25TvUZCh2MzytWDkhggqmOt8dWIT7bwcIWYtVZ0/DPW/vxYvrm/GDZVViQNkeYdUG49nAHQ+xlDwng4Tc5R88eBAXXXQR+vr6MH26sEylsbERhYWF+OijjzB37txEPOxxJdRUKPaCw/YfxPoEZM2b5blpEaVAWY22Z8aiW2sWt0M/sHJmRAu0PN8E47npOlYl2ak4oToXu9o1+PxgL647sQY/e2cfNjYNIV0uxZoblmBflxYbGgdxLMSLS7fYXyG88EfSY8GeF9HUXrIei0GDBSM2R8gmc/f+ivB2DLAX91hrxLu17udiNIJlHdpVJgwYQmcdynK8N0n7Zh1ieQNOcc3KP9pnwNE+Q0yBBasNryvIiGpRHSC8iQplXUacOMU9gpH1R51Unx/xBLJwTS1SiuVhDX0GsdQkHKwUSj9iFxsxE9VfwWQoZJhTno19nVrsaFOPCiyi2brtaXpJFhr7h3G01xB2+ag/3VphL0OKlENdYfK8jsZTND1j/kQcWJRl4ZP9veLBSyh9YsYiilKoCHopWSlUlmtTc7nrYCZU4HXMdRDGxqZOFDUePRChemN8fW9+GV5c34yjfQa8sL4ZD6ycCcBjOV7UgcVwXMoYqXnbj5tvvhmzZ8/Gzp07kZsr1D5qNBrccMMN+PGPf4wtW7Yk4mGPK5oQNXYpUolYY6g2WmIPLKKM1MWRsx6BxZOfHYXF7sSy2jycOzuyuum6QuE01+bgvV44ksHKOSXY1a7Bpwf60DpkxH/39yJFyuGla0/A/MocmKzCRI6QGQufE6yIeixieMHJTU9BWoqwpbRXN4JaP82nntjkkzlhLi9jb8wN/YaYsmjshK08SON2oKxDu8qETk3orINSIfMqU4o06xCrGSVKHO0zoKFPj7NnRfY94omVccyI4MTOV3V+Or49NnpsNCtJTFQZFABIJRzmV2ZjU5MKuzs0EQUW2WkpkEo4OJy8WO/OxkjGa+O2P8tr87CvU4ttLWpcstC958FsdYjZk2gyFoDwvPh4n7tvJlqsDGpKYeC9DBNdvHZZRBpYsNfDcCdD9bAJgFFkYN1TocLPWGT7ZCxYKVYg7JR9atHEKpnzPHiMNCsnkXD4+bnTcdPrO/HapjbcuKIWJdmp7olQER5q1hZkQCbhhGZ53UhM+5d4nvdYkEeBhWjfvn1eQQUA5Obm4re//S2WLFmSiIc8rghPrOClUIAwx10ILMKbcR1MpDssGPbxXWozHE5hy/ZH+3rAccCDF8yKOHJPkbq3OCdTxgIAVs4txWOfHMH2NjW2t6nBccBTVy4Q0+HsxKdDbQo64o9NCWEZi0h6LMRxs1GUQnEch/LcNDQNDKNbYw4ZWLDa/XDfcGvyM5CaIsGIzYlDPTrMKcuOqpSNnUCmSDnsbFO7gweVO4iIJetQnZ+O7LTYsg6xml6SBaBH3IwcLXfjdvQ3BWxAgufhgH7Eht2uvodTwyj3iMWiqlxsalJhT4cWP4xgUZ5EwiEvQ45BgwVDwxZ0a82w2J3Iy5AH3J4cD0tr8/DShhYxO8KwMihlDEMH2MkrCxijdbw3bgOR9Yx1qk34/GAf5DIJMhQyZMilwn8VMo/XufD+X7HXw3a1KazMbx8rfY2lFMocTo+FdylUuKVinqVQE0mNa8dVtFm5M2cUYXF1Lna2a/DsV8fw+CVz0e5a9hvpAatcJkFtQQaODQyjsd8QU2BhsNhhcwjTayiw8DB9+nT09/dj9uzZXr8/MDCA+vr6AJ9FGP2IHQ6n8MTKCVAKBQgn0K2ITwN3tBmLspw0ofnT4USvzozf/PcwAODyRRVhl9D4uuWUWry5vSOmk9xEKM9Jw4LKHHE3xyMXzsaF892bSPMzFSjIlGNo2IqmgWHMq8jx+3XYiTw7UYqkjjaWUij2d2gaGBbLjQIZsTnQ5uqbCffmRCrhMKMkC3s7tfjec5sg4YTTs9x0OXLShf9+b0EZLlpQDkA44fU3YWl7m3DD9tgnR4I+XqCsQ3W+kHVI5pNaFgg0xHgyzW5AIy0F8ORvl8XmpiE4nDzqCjPitm0+EDbRZ0+QpVWBFGQqxMDiiOv/xZKa3IQGjYtr8sBxQMuQEQOGEXG8JBs1W5EX+Q4Lhp28Ng8Ow2J3RF3edrw3bgPuG2eDxQ79iA1ZQUZc/+KDA+IgAn/S5dKwD7IKMuXimPU2lTHoabnZ6hAPCUujKoVyj5sNVWLDtm5ni4GFqxRKZw74uSM2h3igMK1kYpVCzavIwVkzizCrNCuq13qO43D/eTNw5Utb8PaOTtxySp27FCqKaolpJUohsOiLrYyRNW6ny6Vh7cRKRgkJLB5//HHcddddeOSRR7B8+XIAwNatW/HrX/8aTz75JPR695tpVtbx2VgWC1YSE+qJFc/JUNEGFlIJh4rcNLSpTPjr183Y26lFulyKn587PepruXRRBS5dVBH6A8fBtcursb9Li3vOmobrV9SM+vOpRUoMDavQ2B8ssHBPPQKAbHGkYPB/R57nxebtaGsvw61LbhoYBs8Lz7GCCLIj319WhebBYRhG7HDywhui5wz2L48O4G+b2tCrNYfMOgDCqaRn4FDtEUiMd9YhFixYaxk0BlzUFIrF7kDzoJDxiKVBt9pjiy27AVnv2l+RqDGzntiOm5YhIzRGa0QjFgs8JkNtbxXm8C+tzQ/2KTHLTkvBzJIsHO7VY3urGhfMEw4XuthEqBimUZVmp4olrs0DxohKwzwdzzssmHS5DLnpKdCYbOjWmJFV6j+wcDh57HLtRTpzRhHsTh5Gi134YbXDbHXgisWVYZduchyHusJM7OvUomUweGDB9ixkyKVi70Mk2Os8W34XbJ+E2LztCrBY8/+IzQmNyX8fJnudz0lPiXhT/HhLkUrwyvWxVcAsrc3D6dML8U3DIB76z0EYXJO1oillnFakxCfoDVkKHcpE768AEhRYXHDBBQCAK6+8Unzj512LCS688ELx1xzHweEIvm12MgqnDApwBxbxWJLX4Wo6jDSwAIR6xDaVCW9u7wAA/PS0KTEvLEpWl51QgfPnlQYM+KYVZ2JLiypgA7fV7sSgqw6bnSixUymWqQr0Bme0OmC1C70D+VGUQgHh77Jwn3hmBr15N1sd6NR4lyktrclD0+DwqJp9Zp8r4wP4ZB3y0yGTcPjr183CNTx2XtQntsmuNDtVPPVsHhyOaKoJ0zxghN3JIytVFlWZBcO+5w0jdmhNNuSkp4iN24nsr2ByM+SoK8hAy5ARezo1OHNG+JlKlrkbMFiwsy3x/RXM0tq8UYFFtOWknjiOw4zSLGxvVeNonz6qwMLmcIoB5/FcCgUIByUssAj0PdQ0MAyT1YEMuRQvX7c45gmKADClIMMVWITXT1eSHflyPEA4XGQ9h1qTLWhg4S6FEj5GIZOiIFOBoWELerRmv4HFsQHX63zRxJoIFU8/P3c6vmkYFDNaRUoF0uSRv+9Md2V8Yp0MJS7Hi/I9PhkkJLD4+uuvE/FlJw2NuMMi+Pbi3DhlLExWu7vpMIo3Rc8JCmXZqbjl1LqYrifZBcsiTQ0xdq5fPwKeF3Z0sBd6lroGhMkegU5s2fMiNUUS9SbUcOuSPetu+/UjXj0Onk3T4fY6VOenY1OTcKK8vC4Pv/juTL9Zh+2tavz162ZU5aUft0EFINxATi9WYme7Bg19hqgCi0aPOvpYbgrS5FIUKRUYMFjQrjZBZZShW2uGXCbB8gSf/jMLq3KFwKJDG1lg4Tpl3dw8BIPFjkyFLKr/l5FaXpeH1za3ee2zECdCxbg/Y0aJEttb1WKfRKRaBo2wOXgoFbKYar0ngvKcNBzs1gdt4GYHGXMrsuMSVADAFNdo5+ZBY9CPY43TZVH+O3Ach5x0oY9IY7IG/Tp6n+ZtQJgMxQILf6XJ7HR96gSbCBVPs8uyceH8Mny8rwdAdGVQgLvs8NiAwe+y0XBRxiKA0047LRFfdtJwj5oNkbFIj09gwd4Qs9NSvF6UwuWZ5fi/lTMmbF1gPLATwkDpUPYGWOax/C1FKhFHbmqDBBbiDosYXnD8TVLxl3V4bXMbAODvW9rx9y3tQb+mMlUmlij5jmb17HX409oG/OWrJpTnpAcsExNHzR7nN0SA8FzZ2a6J+gYyng261fnpQmChMmLINSBgWW1eVCd30VhUnYN/7+4SpzqFi53qbW4WgtbFNblxu3kMhi2AbOg3iOVbYo9FlBOhGHF0ZV9sz4tpMQacE0E4u3n2dWkBAPMDvOZEo841+CJkxsLVuB3LotectBQMGiwhe/D0PqVQgNDXsa9LF7CBu3ES9OKE42dnT8NnB3phd/JRZxyr8zMglwnDSzo1pqiHz4gZiwnauA0kcEEeiV64EWu8eiyi7a9g2PKsxdW5+J5HM/NkNM01sq9ba8aw6wTVU2+ACSHZaSlCYGGyAvD/gqQ2CtmBSCdCOZ08BoeFvQ5skk2XxoyL/roJPVozBkNkHaQSDmU5qUH2OoR3PayWfm9n4JtH93K84z+wcDdwR3cDyW4KpsfhpqAqLwM72jToUJmw01WPnuhpUJ5YA/fejsgW5RW4dlmwYReJ2l/hKz9TgfqiTDQNDGNHmxrnzC6JSykU4A4Uo31esIEAk+FmkZWThhVYuF5/4qHONXWsZdAYtKnaPWo2+tezcEfOiuNmPQa+sNfRQCNnGwcosACEpaU/XF6N1za3YWGUzxOphEN9YSYO9+rR0GeIPrAIsWpgIqDAIgm5t24Hzx4kS2CxuCYPH99xMqYUZRz3J2ShZKeniGUlx/oNWFiV6/XnPVr/qfGc9BR0a81Bl+SJo2YzRjfZeWYd2n3KlTrVJljso/c6ePU6eGQdstPkYr/Mf+88GdNLlHGZsMQCi+ZBI3Rmm9/sGFseGO1yvIlkuqvpM+obyDiOiWTp/8aBYWxzNUGfNn3sAotpxUpkyKUwWh1o7A+/NKxA6f3mu7RmbAILQMjoNA0MY1urGsvq8qF3NX5WxPjcZf+ePbqRkNOO/JkMjdtMqNLOEZtDnJwWz8CiOj8dEk6YSDU4bBEng/liy/Fi6YFyT4YK/j7Pnn+ez5dggZfJaherFSbacrxEePCCWbhoQRnmRjnNEhD+Px7u1ePYwDDOmR364/3RTPCt2wAFFkkp1HI8Jl6BRTxO2uZWRP/NeLyZVqx0BRbDfgIL7+V4jLjLIsCplNPJi/PWNzQO4ql1jV7BQyRZB9brcMOKGly2qEIIJjyC2J1tary5vQNl2alRjwz2Jz9Tgcq8NHSqzdjfpRX3f3hib4AVkyBjwTIN3VpzxDeQwxa7OIUonoHF2kN9sNidKMlKxdSisbvZEBbl5WBzs7DPItzAIt8jyFbIJGP6OrS0Ng9vbOvA9la1uMMiP0OODEVsb6vZaSkozU5Fr24Ex/oNOKE6smCJvU4c743bQOhSqMO9etidPAoy5aNec2ORmiJFRW46OtQmNA8YAwYW7PU+HoFFsD1HPM+7S6E8dqgEy1g0DQhlXPkZcrFXaTKTSrhR79eRmhZjthFw389RYEHiKuweizhNhYo1Y0G8TS3OxMamIb8N3D1a/6U+Oa6Rs9ta1chQyEY1SftmHZ798tior+2ZdajKy/AqVyrNSRWzDlev3oKtLWrMr8z2eyPmWaMdbwsqc9GpNmNvR4DAwnWDNhkyFtnpKSjJSkWffgSNfQYsjuC0nU0dK1Iq4pIyZ2l79hw7bVrhmGcfF1XlYnOzsIH7+8uqwvocz8kpC6tyxrThf5mrsf1Qj07coVERp9fQacVK9OpG0NA3HFFg4RlwToaMBXudGDRY/C6rY1nZ+RU5cX8+1xVmoENtQsvQME6c4n/IARs3G0tpJ7sP0AQ5QDRZHbC7ygE9M8HBluRR43b8sVLoWCZDUfM2SQiNa5N2sOV4gDujYbI6wtoAGggFFvHFTqJ9m3KdTh57XG90m5tV6NGNiMEDm7P+5vYOsQwpmGuWVnkFDr5Zh2CE5lJ1wPKBeNbu+1pQmYOP9/WISwY98TwvnjxOhuZtQDhV7tOPoKE/ssCiMc6blat9vvfHYsysr0XVOQAQUQO3Z8Yi0fsrfJVkp6I6Px3tKhP+s7cbQOxlUMz0EiXWNw5GfIPCPr44SxF279NElpuegrQUKcw2B3p1I6gt8K5rFwOLOJZBMXUFmfimYRAtASZDma0Osay5JKaMBTtADJyxYKNmZRIOaR73ASxL068fgd3hhMyjpHWibtxOZp77iXz/f4eL/TtTxgLAwoULwz4R2L17d7we9rjEMhChnlhKhUycca02Bh9FF4jTyYulUBRYxM5ktYN3/fzbY0N45KNDrs3SRnRqzOIeio9co+38mVue7bdJ+sH/HMT6xkE8fsncsE90/fE3GcpTPGv3fbkbuLWjmh41JhtGbML/n1jeiCeSGa4byEhT5+y0MV7/RjnpKeJeDQkHnFxfEJevG4kFlUIZQsugEVqTNawb4zS5VJyoNhb7K3wtrclDu8qEjU3CDPxoFmv5w/5dI31eTIaN2544TijxbB40okdrHhVY7O/SAQDmJaBEbkpR8MlQbFBHpkIWcZ+MJ3cpVOCMhc5j1Kzna2pBpkK8R+g3WLwObCiwiL/ynDSky6UwWR1oU5lQH0U5qco1+p8CCwAXX3xxvL7UpBduKRTHcchNl2PAYIk6sBgctsBid0Iq4VCaMzlu5mLhdPIYMFjEEiVhv4PR9XOzuA+EYWNbfS2sysGMkiwxaPj8UB8+3teDSxaW4+mrFvj9HHYqFesLDisf6PKTseB5Xrw5SUSN9uyyLKRIOaiMVnRpzF59PSyDUqhUTJqRxez/8dGIAwv3AsN44DgO1fnpONitx4LKnLCzX/GUlyHHrNIsZKbKoDKGF1gAwE9Pn4IjvfoxmwjlaVldPt7d1QXX/ldU5sUpYxFiH04gk6lxmynPTUfzoHFUBlZntqFlSMgmxHPULFNXEHyXBetriPWQJFds3g6SsTC7Grd9BmJIJBxKslPRqTajV2v2CiyOxflwggj/v6cWZWJflw6N/YaIAwubwyk24VNgAeDhhx+O15ea1Hied2/eDuOJlZfhDiyiwcqgyjxq8Cc7Ni1jdOBg8so6BJKdliKeIC2tycPFC8tRlZcOi92Bm17fiey0FHxw20len2O02PHxvh7XuFn/4rWRsyJIxmJo2AqNyQYJh6hOW0JJTZFiZmkW9nfpsKdT6x1YTKIdFoznaNFgYyt9JeJkur4wEwe79Th9elHcvmakPrnr5Ihr4W8/oz5BVxOab5YkXhmL+qJMcJywu2Zo2IKCMJtrj7pGzbKJY5MBe73o8nk9O+DKVlTnpydkdOeUQiFj0aUxwWJ3jOrviUfjNuBZChX4vcHduD36QKAsWxiY0a01Y7Hr9wwjNvH1nyZCxde0YiX2denQ0GfAd+eWRvS57N+Y4xDVTrFkQT0WScZkdYg3rqHGzQKxN3B3qCZfGZRn1qFdZfRqkvaXdfAllXAoz0nzKlcSF8TlCr0O1/1tOzY0DuLiheVi2dI3DQMA/L/RsBPiYONm49XUxTIWPVrzqJtZdkJak5+RsKzBgsocIbDo0HjtPWEZlMnQuM1MKcyEVMJBZ7ahX28J63RTY7SKG8+nxjGw+Nk50zG1WIkfnVQbt68ZqYk2rroiNw1l2anivoJYd1gwaXIpqvPS0aYyoaHPgIL60IGFZ7ZxMmUsAo2cZfsrAi3jjFWhUgGlQgaDxY52lWlUkB+PUbNA6ImBgLsUKit19C2dv8lQx1wToQqVk6MXZyx5buCOFOuvzU2Xj8miz0RJSGDhcDjw9NNP45133kFHRwesVu+bXrVanYiHPS6wAEEuk3g1YQWSG2TkrNPJY1eHBnPLswPeJB6vjdtGi91rm7TXhKUwsw5if0O+d69DaXZqyKas6cWZ2ODTfMl2WPg7kc9JC/7mYbU7YXClSGPdyFmanQaOA0ZsTqiMVq/T0KNjUKO9sCoHf9/SPqqBO9j/n+NVaooUNflCKUdDvyGswII9pypy00YtYIxFZV76uJ7+T0Qcx2FpbR4+3NsDjnPvDYiHacVKMbA4KYyel8FhS0KzjcmK/T/3nXy0V5wIlZgRxBzHoa4wA/u6dGgZHB71mikux8uO7fVMXJBntgXMarIyWb8ZCz//f47FuZSSuIUaOet08tjXpcWssqxRWS734eHEzVYACQosHn30UbzyyitYtWoVHnzwQfzyl79EW1sbPvzwQzz00EOJeMjjBotY89LlYZ3e5aX7DyycTh73vbcP7+/uxg+XV+Gxi+f6/fx4bYsda04nj37DiN/AIdKsg2/gwLIOsZjq59RC3Lrt5+Yjx+PNwx8WcErikCKVyyQoUirQr7egW2P2CizYRKhEjJplWJPuoR49rHYn5DIhSJuMpVAAMKMkSwgs+vQ4LYxpTOJEKKqNTgpLa/Px4d4eFCtT4zrudkaJEmsP94fdZ8FuZBKZbUxGgXZZ7HdlLBYkYCIUU1co1NP767Po07HR4rEFm+z13uHkYbDY/TaCezZv+2KBDTu4AeI//IG4sWCtTTW6RM7mcOLet/fiv/t7sagqB/+8eRnS5e7b8ONhhwWQoMDijTfewMsvv4zzzz8fjz76KK655hpMmTIF8+bNw9atW3HXXXcl4mGPC+wGMtSoWcbfkjye5/HbT4/g/d3CCMQPdnfjgZUz/S5uSuaMRaCsQ7vahK4wsw7V+aOnK4WbdYjFNLH50j0xpDvADgt2rQCgNVnhdPKQ+KRBPcugfP8sGuU5aUJgoTV7jWJsGIOb1pr8dOSkp0BrsuFIr158/Mk2apaZXqLEJwd6w27gTuSeERK58+aU4I1t7Th7VnFcv6548hlhYDEZFuN5YqWTvTqz+NrZpxtBv94CqYTD7LLELU2sc02havYzGcrdvB3b61lqilQcqas1+l+kKTZv+/mzcj+7LGgiVOKUZKWKE/ZaBo3isk+r3Yk739yNLw71AwB2d2jx03/uxsvXLRYP19RhTgRNdgkJLPr6+jB3rnBCnpmZCZ1OaKK64IIL8OCDDybiIY8b4Y6aZfz1WDz/TTNe3dgKQKi51I/Y8emBXlyxuHLU549nYBEo69Du+vnQcPC+EZmEQ3lumt/RrPHIOsSCbS0eNFigMVqRmyFHb7BSKNe1Onlg2Dr6VCreJxnluenY3aH1qkt2OnkxRT69JHEpco7jML8iB+sbB7G3U+sOLCZhjwXg3cAdjsY+4SaGMhbJIS9Djk/uOiXuX1ecDBVmY/9k2rjtqVipgFQijFQdMAh9SqwMalqxEmnyxGVvprhe5/3tsmCBRTw2fuemp8Csc0BjsqIqf/R7ddCMhStjwjLmgOdEKCqFijeO4zC9WImd7Ro09hswszQLIzYHbn9jN748OgC5VIK7z5qKv3x1DOsbB3Hfu/vwzFULIJFw4hJECiz8qKioQG9vL6qqqlBfX4+1a9di0aJF2LFjBxQKWh0fjCbCBl32BFS5bsLf3N6BP3zRAAD41fkzYbE78YcvGvDurq5RgYXZ6hCbQBMVWPhmHTx/dKnNsDqCZx1y0lP8Bg5jkXWIRYZChvKcNHRrzWjsN2BZXT56WCmUnxOs1BQpFDIJLHYndKbRp1KqeAcWfiZDdWvNMFodkEsl4ibmRFlQ6Q4srocwiYtNQ5tsgQVrtD02MBxyqRLP8wndM0KSR01BBlKkHIxWB7q1Ztdiy8AmY+M2AMikEpRkpaJba0a31oSS7FSxDCpR/RVMXaE7Y+EZ/JmsdvFmPx47ebLT5ejRjQQslXX3WARu3taYbDBZ7bA5eHEjeH3R5HqujJWpHoGF2erAj/+xE98eG4JCJsHL1y3GqdMKMassC7e8vhMf7etBbnoKHvnebCqFCuaSSy7Bl19+iWXLluHuu+/GNddcg1dffRUdHR249957E/GQxw12cxVpKZTGZMVnB3rxyw8OAABuO30Kbj6lDn26EfxpbQO2t6rROmT0WiDUpRGyFcpUWdR1+55Zh3bfJulYsw556RN65Nq04kwhsBgYxpKaPDFjEajmNic9Bf16C7QmGyp9RvJr4jRqlvG3y4Klx+sKMxI+enhBVQ4Ad4MlS9MrY1wmNRFV5qaLpQ7tahOmFAY+RRw0WKAz2yCVcOJNDTk+pUglmFKYiaN9BjT2G4IGFg4nL/ZzTaZRsww7xOnWjuCEavdEqERs3PZUk58BjgMMI3YMDVtRqBQOTlk/g1IhgzIOr2esmTfQOHJx3Kyfx8pKTRGnV/VoR8SvUZKVOqHfX5PZdFcmaF+nDj96bQe2tKiQliLFqzcsxoopwiCGM6YX4U9Xzsfdb+3F61vakZehiNvkx/GWkMDid7/7nfjzyy+/HBUVFdi8eTPq6+vxve99LxEPedyItBSKPQHbVSbc/dZeOHngmqWV+Pm50wEIpyWnTivENw2DeG9XJ35+7gzxcz3LoIKl2Y0Wu1ewEGvWodojcEjmrEOsppUo8XXDII71G6AyWmF1OMFxQHFWgMAiTS4EFn42rKri/ILDdlmw4BLw6K8YgxPPBa4RkK1DwpblyThqlpFIOEwrzhRnnwcLLBrEccDpk6pBd7KaVqzE0T4DGvqGceaMwD0cHWoTRmxOpKZIkrJfLtHKc9OANqGc0unksb9TKL9OxGI8T6kpUpTnpKFLY0bL4LAYWPTFaTkew173NQH2VQUrhQKEcihD/zB6dWZ0ql37KyZZZmsssWzyxqYhAML29TU3LsGSGu8Tw4sWlENjtOKRjw/j6f81QukaF0wZizAsX74cy5cvH4uHmvDcGYvwnljsBNviamReOacEj1081ytQuOKESnzTMIh/7+rGqrOni/ORWWBRkZuGHq3Zb/AQadbBN+Mw0bMOsZhW5N6ey07ki5WBFxGKuyz8jJxVG4WStVhHzTLsBt6zFCoRS9cCyc2QoyZfmNO/t1M7aRu3meklwlKloyGWKo3lvxEZf9NLlMC+0Bu4G1yL8aYWKSf0/PtouUs7TWhVGWGw2JGaIhmTHoIphZlCYDFkxLK6fABwl73G6fUs1J4jNorc37hZQCiHauwfRo+rNBcApk2ikcRjzTNoU6bK8PcfLcXCqly/H3vDSbVQm2x49stj4r8jBRYB/OMf/8CLL76I1tZWbNmyBdXV1XjmmWdQW1uLiy66KFEPO+FpxYxFeDfjniVTK6bk45mrF4x6YzlrVhHkUgn69CN48D8HUVeQgQ61CX/f0g4A+OJQvzipINjjVAcoVzqesw6xEBfluE6KAP+jZhm2y8Lfm4c4hjjOPRaGETv0I0JPx1jXaC+ozBEDCzbhazJmLAB3+Qq7QQyEprlMLuzfOdTEsMnauM2UeyzJ2+cqr5xTlj0m70t1hRlY3ziI5gH3ZKi+ODZuA56lUP4Di5AZC4+Rs6xkjl5DEqcgU4EFlTno0pjx2o1LMKc8eK/PvWdNhcZoxT+2CvdkFFj48cILL+Chhx7CPffcg9/+9rdwOBwAgJycHDzzzDMUWATBauzCzVgoZFLcfHItujRm/OycadjTofWesKQSfs7Klf61rcPv15FJOFTkpvkNHCZz1iEW9UWZ4DihjOlAt5Ca9zdqlnFvWPVXCiVkLHLj9IKToZCJI1+7NWakFUnFySZj9YazoDIHH+7twd5OrRhUTdaMxTxXk+nmZhVGbI6AZU4Nrmkuk/UGcrJhQX5ziMb+r48OAEh8s3Kyco9UHcH+LlcZVIL7K5g6V+liy5B7MhQ7SIp7KZSf9wa7w4lhCxs36/+WrtxjSV6Da6rcVJoIlVD//ukK2J3OsHbbcByHR743G3KZBO0qE2aVTuw+qYQEFn/5y1/w8ssv4+KLL/bqt1i8eDHuu+++RDzkcYOdSPirpR+22MWAodMVNLCfd2nM+PxQX1iPcXJ9AeZVZOP5b5oBAI9fMhdXLq6grEOcpcmlqMxNR4fahG8aBgEEP8FiwaTOT8aCBZz5GfGbqlaekyYGFilSDlaHExly6Zjd3C9wpYb3dWrFvoJggdfx7ISqXJRlp6JHN4Ivjwzg/Hmjy6E8xwHTaePkUJ6ThnS5FCarA20qk9+N2k0DBuzr0kEm4bAySBnd8azMY8rdHlfGYt4YBVlTXEMUWjx2WbhHzcapFCotcMaClc8AgUuhWMbicK9eXB47lV5DEkoq4SCVhN8HJ5VwePCCWQm8orGTkMCitbUVCxcuHPX7CoUCRuPoec/Ejd1Abjw2iP8d7vfqdVAFaNxiAmUdqlxL4q5ZvRWHevQ4a2YRrl9Rg79tasWIzYkVU/IpqEiQacVKdKhNONQjlLgEu3EO9uahjnMpFCDctBzq0aNbaxZ7dKYWK+OygC8cM0uVkEsl0Jhs2O/K6EzWUiiJhMMli8rx16+b8f7uLr+BRbfWDJNrHHCNn1n25PgjkXCYWqzEvk4tGvsNfgOLf7sWoZ4+vRAFmZNznDs7DBm22HHQ9VqSyI3bntihSKfGLG5aZhMA452x8DcVio2aTZdLA/bvsfcd9j5UnpOGTD8LcwmJh4Q8s2pra7F3715UV1d7/f5nn32GWbOOj4gsEax2J8w2oWzsj2sb/X5Mrr+9DvnCf0uygvc6XHFCBQ71HMY7O7vw3XmlGLE5IeEm7ynxWJhWnIn/HXH3r/jbYcHkBGjQczr5iKeFhcOzgZsFrWO5dE0hk2JWWZZXj0XFJH4uXrKwAn/9uhnfNA5iaNgy6iaR9cBMKcqkg4BJZHpxJvZ1atHgp7Hf4eTxgSuwuGxRxXhcXlJIk0uRnyGHymiFw8mLkwjHQpFSgQy5FEarAx0qE6YWK8VSqECjxSMV6L0BCL51m/G9DlqMRxIpIYHFz3/+c9x+++0YGRkBz/PYvn073nzzTTzxxBN45ZVXEvGQxwW5TILLFlVgV7vaPZo137vXIZYZ/xctKMfjnx7F4V49Pj8olE2VZqeJ6+RJ/PmWrAQrM8pJc5VC+WQs9CM2OJw8ACA3zKb+cLC5+N0as/j1x3oE4YLKHHGXhVwqmbQnroDQkzO/Mgf7OrX4aG8PfnRyrdefi+OA6aZgUmGvIf4mQ21uHkKffgTZaSk4c2bRWF9aUinPTRMPSOZV5ITcVB4vHMehrjATB7p1aB40oiwnDXpXeVJJnEqhcoKMmw3VuC1ch29gQWVQJHESEljceOONsNvtuP/++2EymfD9738f5eXl+POf/4yrr746EQ953PjTlfMT9rVzM+Q4e1YxPjnQi+e+agKQuI3bRODbIBd0KpR4KuX95sHK45QKWViNYOFiQU6X1gyD681pLDMWALCwKgevbRZ+XpqTOmZlWMnq0oXl2Nepxft7ukYFFmJ/BTVuTyqsUb/BT2Dx711dAIDvzS+L62vDRFSWnSY2bi8Y4yb2KYUZONCtQ8vQMOqLhJ4LZaosbuVGbCqUfsQ+qok/2NZtRiGToiBTQf0VZEwk7Kj6lltuQXt7OwYGBtDX14fOzk7cdNNN6O7uTtRDkjBcsVhIlw8YhBcYCiwSa0phJti9slwmCbqHIlCPhbiNM84j6CpcpVBtQ0a0qVwToUrG9jR8YaV7tvdknQjl6cL5ZZBJOBzs1o86oRYnQtFNwaTC/r3bhowYcZXKAkI/ARvYcemi8nG5tmTi2Z81VhOhGHEy1KAx7o3bgHc2Qu/RrA2El7EA3JOhACqFIomV8BqYgoICFBUVoa+vD3feeSfq6+sT/ZAkiFOmFqLEY/NzFTWBJlRqihQ1+cIJVnlOWtD0vGcdLc/z4u+z9H68Z1uzG3md2QYnL5yKFY5xKVJlXpr496LAQvg3PmOGUNLy/m73IYzd4RTn5FMZw+RSqFQgJz0FTh5o8tiV8OmBXozYnKgrzBizRuVk5vn6MS/BG7d91bkmQzUPDse9cRsAZFKJuJXZd+Ss3hVYhCqTZv19HAe/QwAIiZe4BhZarRY/+MEPUFhYiLKyMjz77LNwOp146KGHUFdXh61bt+Jvf/tbPB9S1NbWhptuugm1tbVIS0vDlClT8PDDD8NqDT5JabKRSjhcdoL7dKuSMhYJx8qhSkO80bA6WqvdiRGbU/x9jThqNr6BRU56CtLl7vKJ6SXKMatLZjiOE2+KJutEKF+XuU6fP9zTLfa+tKlMYz4OmCQHjuP89lmwMqjLFlWM+fdtMmIZ2LLsVBQqx/aApK7AnbHoiXPjNhNoMpS7FCp4YMGGtFTmpiNdThOhSOLENbD4xS9+gQ0bNuD6669HXl4e7r33XlxwwQXYuHEjPvvsM+zYsQPXXHNNPB9SdPToUTidTrz00ks4dOgQnn76abz44ov4xS9+kZDHm8guP6FS/Hkl3cwl3AzXVuXK3OBBXIZcCpmrbsqzz0KVoFIojuO8blLHq8Tmp6dPwdmzinHpwsk71cbTGTOKkJ2Wgj79CLY0qwC4byjrx3AcMEkeM3z6LDrVJmxrVYPjgEsWUhkUIGTjz59XivvPmzHmj11bkAGOE7K/bKRrSVZ831tzAmzfZqVQoQKLyjzhemi5Jkm0uIatn3zyCdasWYOzzjoLt912G+rr6zFt2jQ888wz8XwYv8477zycd9554q/r6urQ0NCAF154AX/84x8T/vgTSW1BBn5yWh3ah0yYG2LVPIndD5ZXYdhix/eXVQX9OI7jkJOegqFhK7Qmm5i6VicoYwEIWYJjrMRmnN5wltTkYUlN3rg8djJSyKS4YF4p3tjWgfd3d+HkqQXiqFmaCDU5iRkL1/OAlcmtmJJP48Jd0uRS/PX7i8btscuy09CtNWOr6zAg2KCOaIiToXynBpqDb91mLllYjm6NGZedQAc4JLHiGlj09PSIeyrq6uqQmpqKm2++OZ4PERGdToe8vOA3LBaLBRaLRfy1Xq9P9GUlhQdWzhzvS5g0ipSpYW/UzE5zBxaMJkE9FgCSImNBRrt0UQXe2NaBzw/14TcWu5ixoP6KyYmdMjf2D4Pneby/x10GRZJDXWEGurVmGCzCjX6o0tdI5YjDPbxLocJt3s5Jl+NXx8lmZ5Lc4loK5XQ6kZLifnJLpVJkZGTE8yHC1tzcjL/85S+49dZbg37cE088gezsbPFHZWVl0I8nJJHYqZRuDEqhAO++BhpBmDwWVeWgJj8dJqsDXxzqc++woDKGSWlakfDv3q0145vGQbSrTMiQS3HenJJxvjLCsA3cTLBlqNHIDVAKFW6PBSFjJa4ZC57nccMNN0ChEBqnRkZGcOutt44KLt5///2wv+YjjzyCRx99NOjH7NixA4sXLxZ/3dPTg/POOw9XXHFFyIzJAw88gFWrVom/1uv1FFyQcZPjZ+RsQkuhXBmL0uzUkCdeZOxwHIdLF1XgqXWNeHN7B9qGhHHAlFWanLLTU1CSlYo+/Qie/OwoAGDl3FJqwk0iUwq973PinrEQS6Giy1gQMlbi+qp0/fXXe/36hz/8Ycxf84477gi5VK+mpkb8eU9PD8444wyceOKJWL16dcivr1AoxECIkPGW7TFyllEnsBRqxZQCTCnMwEULqAE02VyysBxPrWvEjjYNAKF5c6yn3ZDkMa1EiT79CI66+ixod0VyqfPIWGSlypARp+V4TI6f9wbAs8eCAguSHOL6zF+zZk08vxwAYQ9GQUFBWB/b3d2NM844AyeccALWrFkDiSThazoIiaucNDZScGwCi0KlAl/+7PS4f10Su8q8dCytycP2NjUAob+CxopOXtOLM7GhcRCAkGlcXps/zldEPNV5ZCwS0VAfetwsZa9Icjhu7rx7enpw+umno7KyEn/84x8xODiIvr4+9PX1jfelERI2dirFeizMVgfMrm27iQgsSHLzPJWmMqjJzbNx/9JF5TR2OMmUZKWKe4HiuRyPYe8NGqP70GnE5oDVLuw8olIokiyOm8Bi7dq1aGpqwldffYWKigqUlpaKPwiZKHxnlatdp1NyqQSZcU6tk+T33XmlkMuEl+nxGgdMkgPbhwMIU8NIcuE4TsxaxLtxG/Ac7OEOLNjWbQkHZFC/DUkSx01gccMNN4Dneb8/CJkosn2at9XDbCJUCpXBTEJZqSm4+eRaFCoVOGN64XhfDhlHs8qycOmictx2+hTUFozPtEUS3FTX9K6KBCyeZVOhPJu3PZfjUQaLJAsKcQlJIuxUijXoqYzCjpW8DGranazuP2/GuGwTJslFKuHw1JULxvsySBC3nT4F2WkpuGJx/DNK7L3BZHXAYndAIZO6+yuocZskEQosCEkibNysznUqxU6nEjFqlhBCSPxMLVbike/NTsjXVipkkHCAkwd0JhuKsqTiRCjqryDJ5LgphSLkeOA7UlA1nLjleIQQQiYGiYTz2GUhvD+4S6HojJgkDwosCEkibNwsS3cncjkeIYSQiYNltFkmm0qhSDKiwIKQJKJMlYH1aOvMNvENhEbNEkLI5OY7NVBnoq3bJPlQYEFIEpFIOPFNQmeyiaVQFFgQQsjk5rskz70cjwILkjwosCAkybB0t9ZsS+jWbUIIIRNHtk8PHuuxoIwFSSYUWBCSZLLFUymbuCCPAgtCCJnccsXmbVfGwjUVKiuVmrdJ8qDAgpAkI2YsTFZq3iaEEALAvSRPaxQyFVQKRZIRBRaEJBnWoKcyWsUmPRo3Swghk5uYzTYLB06em7cJSRYUWBCSZFjGol1lBABwnDsFTgghZHJiGQu2x4LGzZJkRIEFIUmGnUo1DwqBRU5aCqQSbjwviRBCyDhje47YVCgaN0uSEQUWhCQZlrFocQUWVAZFCCHEc4+F08nDYHE1b9PmbZJEKLAgJMmwN4+hYQsAatwmhBDiPmTSmmwwWOzgeeH3qRSKJBMKLAhJMiywYGjULCGEEJbNtjqc6NePAAAUMglSU6TjeVmEeKHAgpAkk53mHUhQYEEIISRdLoVcKty2tatMAGgiFEk+FFgQkmQoY0EIIcQXx3Hi+wObGkiN2yTZUGBBSJLJSfMNLBTjdCWEEEKSCQssOtSujAVt3SZJhgILQpKM7wlUXgadSBFCCAFyXOPIWSkUZSxIsqHAgpAkI5NKoFS4T6EoY0EIIQRwL8ljpVDUY0GSDQUWhCShbI8+Cxo3SwghBHAvyevSmAFQxoIkHwosCElCng3ctCCPEEIIAOS4SmPtTmGJBe2wIMmGAgtCklCOx8hZylgQQggBvN8bANq6TZIPBRaEJCFWCpUul9LyI0IIIQDcPRYMlUKRZEOBBSFJiI2czU2nbAUhhBBBjs97ApVCkWRDgQUhSYj1WORnUmBBCCFE4LtAlTIWJNlQYEFIEmJ1tLR1mxBCCOObxaZxsyTZUGBBSBJaUZ+PgkwFzplVMt6XQgghJEn49lhQKRRJNjROgJAkNLssGzt++R1wHDfel0IIISRJZFMpFElylLEgJElRUEEIIcSTQiZFutw9KTAzlc6HSXKhwIIQQgghZIJgfRbKVBmkEjqAIsmFAgtCCCGEkAmClT9RfwVJRhRYEEIIIYRMELkZQkBB/RUkGVFgQQghhBAyQbBx5Flp1F9Bkg8FFoQQQgghEwRbkkelUCQZHZeBhcViwYIFC8BxHPbu3Tvel0MIIYQQEheseZtKoUgyOi4Di/vvvx9lZWXjfRmEEEIIIXF1/rxSnFCdi0sWlY/3pRAyynEXWHz22WdYu3Yt/vjHP473pRBCCCGExNXM0iz8+6crsGJKwXhfCiGjHFedP/39/bjlllvw4YcfIj09fbwvhxBCCCGEkEnjuAkseJ7HDTfcgFtvvRWLFy9GW1tbWJ9nsVhgsVjEX+v1+gRdISGEEEIIIcevpC+FeuSRR8BxXNAfO3fuxF/+8hfo9Xo88MADEX39J554AtnZ2eKPysrKBP1NCCGEEEIIOX5xPM/z430RwQwNDWFoaCjox9TU1ODqq6/Gxx9/DI5zr7d3OByQSqX4wQ9+gNdff93v5/rLWFRWVkKn0yErKys+fwlCCCGEEEImIL1ej+zs7LDujZM+sAhXR0eHVxlTT08Pzj33XLz33ntYtmwZKioqwvo6Op0OOTk56OzspMCCEEIIIYRMauzQXavVIjs7O+jHHjc9FlVVVV6/zszMBABMmTIl7KACAAwGAwBQSRQhhBBCCCEuBoNh8gQW8VJWVobOzk4olUqvsioydlhkTFkjQs8FwtBzgQD0PCBu9FwYOzzPw2AwhLUj7rgNLGpqahBNlZdEIokow0ESJysri14sCAB6LhA3ei4QgJ4HxI2eC2MjVKaCSfqpUIQQQgghhJDkR4EFIYQQQgghJGYUWJCko1Ao8PDDD0OhUIz3pZBxRs8FwtBzgQD0PCBu9FxITsfNuFlCCCGEEELI+KGMBSGEEEIIISRmFFgQQgghhBBCYkaBBSGEEEIIISRmFFgQQgghhBBCYkaBBSGEEEIIISRmFFgQQgghhBBCYkaBBSGEEEIIISRmFFgQQgghhBBCYkaBBSGEEEIIISRmFFgQQgghhBBCYkaBBSGEEEIIISRmFFgQQgghhBBCYkaBBSGEEEIIISRmsvG+gGTjdDrR09MDpVIJjuPG+3IIIYQQQggZNzzPw2AwoKysDBJJ8JwEBRY+enp6UFlZOd6XQQghhBBCSNLo7OxERUVF0I+hwMKHUqkEIPzPy8rKGuerIYQQQgghZPzo9XpUVlaK98jBTJjA4pFHHsGjjz7q9XvFxcXo6+sDIKRpHn30UaxevRoajQbLli3DX//6V8yePTuix2HlT1lZWRRYEEIIIYQQAoTVIjChmrdnz56N3t5e8ceBAwfEP/v973+Pp556Cs899xx27NiBkpISnH322TAYDON4xYQQQgghhEwOEyqwkMlkKCkpEX8UFhYCELIVzzzzDH75y1/i0ksvxZw5c/D666/DZDLhX//61zhfNSGEEEIIIce/CRVYHDt2DGVlZaitrcXVV1+NlpYWAEBrayv6+vpwzjnniB+rUChw2mmnYfPmzeN1uYQQEjO10YqtLSrwPD/el0IIIYQENWECi2XLluHvf/87vvjiC7z88svo6+vDihUroFKpxD6L4uJir8/x7MEIxGKxQK/Xe/0ghJBkcf97+3H16q3Y2a4Z70shhBBCgpowgcXKlStx2WWXYe7cuTjrrLPwySefAABef/118WN8m0p4ng/ZaPLEE08gOztb/EGjZgkhyaR5cFj478DwOF8JIYQQEtyECSx8ZWRkYO7cuTh27BhKSkoAYFR2YmBgYFQWw9cDDzwAnU4n/ujs7EzYNRNCSKQGDRav/xJCCCHJasIGFhaLBUeOHEFpaSlqa2tRUlKCdevWiX9utVqxfv16rFixIujXUSgU4mhZGjFLCEkmZqsDwxY7AGBomAILQgghyW3C7LG47777cOGFF6KqqgoDAwN47LHHoNfrcf3114PjONxzzz14/PHHMXXqVEydOhWPP/440tPT8f3vf3+8L50QQqLiGUwMUmBBCCEkyU2YwKKrqwvXXHMNhoaGUFhYiOXLl2Pr1q2orq4GANx///0wm8247bbbxAV5a9euDWtLICGEJCPPYGLIYB3HKyGEEEJC43iaYehFr9cjOzsbOp2OyqIIIePqi0N9+Mk/dgEAagsy8PV9p4/vBRFCCJl0Irk3nrA9FoQQcrwb8spYUCkUIYSQ5EaBBSGEJCnPSVAGix0jNsc4Xg0hhBASHAUWhBCSpHwnQdHIWUIIIcmMAgtCCElSvg3bNHKWEEJIMqPAghBCkpTviFnKWBBCCElmFFgQQkiSYhmKnPQU169p5CwhhJDkRYEFIYQkKZahmFmS5fVrQgghJBlRYEEIIUnIaLHDZBWmQM0sFQIL6rEghBCSzCiwIISQJMSCiLQUKarz0wFQxoIQQkhyo8CCEEKSEAssCpUKFCoVXr9HCCGEJCMKLAghJAmx7ERBphwFmUJg4TslihBCCEkmFFgQQkgSGnRNgPLKWFApFCGEkCRGgQUhhCQhd8ZCgYJMOQDAaHXAZLWP52URQgghAVFgQQghSYj1UxRkKpCpkCE1RXi59t3GTQghhCQLCiwIISQJsYxFoVIBjuM8+ixGxvOyCCGEkIAiDiykUikGBgZG/b5KpYJUKo3LRRFCyGTnmbEAIPZZDFLGghBCSJKKOLDged7v71ssFsjl8pgviBBCiHfGAgBNhiKEEJL0ZOF+4LPPPgsA4DgOr7zyCjIzM8U/czgc2LBhA2bMmBH/KySEkEmG53n3HotM78CCJkMRQghJVmEHFk8//TQA4Q3vxRdf9Cp7ksvlqKmpwYsvvhj/KySEkEnGaHVgxOYEABQohUwwLckjhBCS7MIOLFpbWwEAZ5xxBj744APk5OQk6poIIWRSY2VQGXIp0uXCy3Sha+TsIGUsCCGEJKmIeixsNhva29vR09OTqOshhJBJTyyDcmUpPH9OGQtCCCHJKqLAIiUlBRaLBRzHJep6CCFk0vNcjsdQ8zYhhJBkF/FUqDvvvBNPPvkk7Hba/koIIYkQNGNhsAaczkcIIYSMp7B7LJht27bhyy+/xNq1azF37lxkZGR4/fn7778ft4sjhJDJKFjGwmxzwGh1IFMR8cs3IYQQklARvzPl5OTgsssuS8S1EEIIwejleACQoZAhXS6FyerAkMFCgQUhhJCkE/E705o1axJxHSE98cQTeP/993H06FGkpaVhxYoVePLJJzF9+nTxY2644Qa8/vrrXp+3bNkybN26dawvlxBCoua7HI8pyFSgQ23C4LAFNQUZ/j6VEEIIGTcR91iMl/Xr1+P222/H1q1bsW7dOtjtdpxzzjkwGo1eH3feeeeht7dX/PHpp5+O0xUTQkh0BoetAIAC14hZxt1nQQ3chBBCkk9UufT33nsP77zzDjo6OmC1Wr3+bPfu3XG5MF+ff/6516/XrFmDoqIi7Nq1C6eeeqr4+wqFAiUlJQm5BkIIGQtDATMWrl0WNBmKEEJIEoo4Y/Hss8/ixhtvRFFREfbs2YOlS5ciPz8fLS0tWLlyZSKu0S+dTgcAyMvL8/r9b775BkVFRZg2bRpuueUWDAwMBP06FosFer3e6wchhIwXnufFwMGzxwKgjAUhhJDkFnFg8fzzz2P16tV47rnnIJfLcf/992PdunW46667xJv9RON5HqtWrcLJJ5+MOXPmiL+/cuVKvPHGG/jqq6/wpz/9CTt27MCZZ54JiyXwm/ATTzyB7Oxs8UdlZeVY/BUIIcQv/YgdVrsTgP8eC4AyFoQQQpJTxIFFR0cHVqxYAQBIS0uDwWAAAFx77bV4880343t1Adxxxx3Yv3//qMe76qqrcP7552POnDm48MIL8dlnn6GxsRGffPJJwK/1wAMPQKfTiT86OzsTffmEEBIQmwilVMiQmiL1+jMWaAwarKM+jxBCCBlvEQcWJSUlUKlUAIDq6mpx4lJra+uYLG2688478dFHH+Hrr79GRUVF0I8tLS1FdXU1jh07FvBjFAoFsrKyvH4QQsh4CdRfAbgzFkOUsSCEEJKEIg4szjzzTHz88ccAgJtuugn33nsvzj77bFx11VW45JJL4n6BDM/zuOOOO/D+++/jq6++Qm1tbcjPUalU6OzsRGlpacKuixBC4ilQfwXgmbGgwIIQQkjyiXgq1OrVq+F0CvW/t956K/Ly8rBx40ZceOGFuPXWW+N+gcztt9+Of/3rX/jPf/4DpVKJvr4+AEB2djbS0tIwPDyMRx55BJdddhlKS0vR1taGX/ziFygoKEhowEMIIfEULGNR6JGx4HkeHMeN6bURQgghwUQcWEgkEkgk7kTHlVdeiSuvvDKuF+XPCy+8AAA4/fTTvX5/zZo1uOGGGyCVSnHgwAH8/e9/h1arRWlpKc444wy8/fbbUCqVCb8+QgiJB3fGQj7qz1gWw2J3wmCxIys1ZUyvjRBCCAkmqj0WGo0Gr776Ko4cOQKO4zBz5kzceOONo0a/xlOo/o20tDR88cUXCXt8QggZC0MGthxvdMYiTS5FpkKGYYsdQwYLBRaEEEKSSsQ9FuvXr0dtbS2effZZaDQaqNVqPPvss6itrcX69esTcY2EEDJpsIyFv1IowGNJHvVZEEIISTIRZyxuv/12XHnllXjhhRcglQqjEB0OB2677TbcfvvtOHjwYNwvkhBCJouhIM3bgBBwtKlMGBqmkbOEEEKSS8QZi+bmZvzsZz8TgwoAkEqlWLVqFZqbm+N6cYQQMtkMBmneBjyW5BlGxuyaCCGEkHBEHFgsWrQIR44cGfX7R44cwYIFC+JxTYQQMinxPO/OWAQILFjAQRkLQgghySbiUqi77roLd999N5qamrB8+XIAwNatW/HXv/4Vv/vd77B//37xY+fNmxe/KyWEkOOczmyDzSEMqvA3FUr4fdplQQghJDlFHFhcc801AID777/f759xHCfOV3c4HLFfISGETBIsW5GVKoNCJvX7Me6MBQUWhBBCkkvEgUVra2siroMQQia9gRD9FYBHxoICC0IIIUkm4sCiuro6EddBCCGTHuubCDQRCvDIWFApFCGEkCQTcfM2IYSQxAg1EQpw914MDVtDLg4lhBBCxhIFFoQQkiRC7bDw/DOrwwm92T4m10UIIYSEgwILQghJEkNhZCxSU6RQpgpVrNRnQQghJJlQYEEIIUmCBQqFQTIWgDvwoJGzhBBCkknEgcUNN9yADRs2JOJaCCFkUnMvx/O/w4Jh5VA0cpYQQkgyiTiwMBgMOOecczB16lQ8/vjj6O7uTsR1EULIpCM2b2emBv04ylgQQghJRhEHFv/+97/R3d2NO+64A++++y5qamqwcuVKvPfee7DZbIm4RkIIOe45nTxUbNxsiIxFIWUsCCGEJKGoeizy8/Nx9913Y8+ePdi+fTvq6+tx7bXXoqysDPfeey+OHTsW7+skhJDjmtZsg90pjI/NzwjeY8FGzlLGghBCSDKJqXm7t7cXa9euxdq1ayGVSvHd734Xhw4dwqxZs/D000/H6xoJIeS4x7IPOekpkMuCvzSLS/IoY0EIISSJRBxY2Gw2/Pvf/8YFF1yA6upqvPvuu7j33nvR29uL119/HWvXrsU//vEP/PrXv07E9RJCyHHJ3V8RPFsBuJu3adwsIYSQZCKL9BNKS0vhdDpxzTXXYPv27ViwYMGojzn33HORk5MTh8sjhJDJIZzleIyYsTBYE3pNhBBCSCQiDiyeeuopXHnllUhNDTy1JDc3F62trTFdGCGETCaDYSzHYzzHzTqdPCQSLqHXRgghhIQjolIou92OH/3oR2hqakrU9RBCyKQ0GEHGIt/VvG138tCZaRofIYSQ5BBRYCGTyVBdXQ2Hw5Go6yGEkEmJZSxCjZoFAIVMiuy0FOHzqM+CEEJIkoi4eftXv/oVHnjgAajV6kRcDyGETEpDrh0W4TRvA559FhRYEEIISQ4R91g8++yzaGpqQllZGaqrq5GRkeH157t3747bxRFCyGQxJGYswgssCjLlaBqgjAUhhJDkEXFgcfHFFyfgMuLr+eefxx/+8Af09vZi9uzZeOaZZ3DKKaeM92URQkhALEAIP2MhDNCgJXmEEEKSRcSBxcMPP5yI64ibt99+G/fccw+ef/55nHTSSXjppZewcuVKHD58GFVVVeN9eYQQMorDyUNtdJVCRZCxANwlVIQQQsh4i2nzdjJ66qmncNNNN+Hmm2/GzJkz8cwzz6CyshIvvPDCeF8aIYT4pTFZ4XDy4DggLyN08zbgDkAoY0EIISRZRJyxcDgcePrpp/HOO++go6MDVqv3adl4NnVbrVbs2rUL/+///T+v3z/nnHOwefPmcbqqyFjsDhzrHx7vyyCEjKHmQeF7nucBjTG8DATPC//d26nBwW5doi5tXORnyiHl3Ls5jFYHjBb7OF7R2EqXS5GpiOztWWu2wWp3JuiKCCHjKTVFivqizPG+jLBEHFg8+uijeOWVV7Bq1So8+OCD+OUvf4m2tjZ8+OGHeOihhxJxjWEbGhqCw+FAcXGx1+8XFxejr6/P7+dYLBZYLO4TP71en9BrDMbucGL6rz4ft8cnhIy/pY9/GdHHNw8accFfNiboagghhCQDhUyChsdWjvdlhBRxKdQbb7yBl19+Gffddx9kMhmuueYavPLKK3jooYewdevWRFxjxDjOewstz/Ojfo954oknkJ2dLf6orKwci0v0S0rbcwmZ9KQSLqwfx7vJ9HcNhJ4LhBDmuM1Y9PX1Ye7cuQCAzMxM6HRCCv6CCy7Agw8+GN+ri1BBQQGkUumo7MTAwMCoLAbzwAMPYNWqVeKv9Xr9uAUXHMeh7Xfnj8tjE0IIGX9Pfn4UL3zTjBtW1OCR780O63OuXr0FW1vU+PPVC3DRgvIEXyEhhAQWccaioqICvb29AID6+nqsXbsWALBjxw4oFOFNM0kUuVyOE044AevWrfP6/XXr1mHFihV+P0ehUCArK8vrByGEEDIe2LjhSPaTiMsVw5woRgghiRJxxuKSSy7Bl19+iWXLluHuu+/GNddcg1dffRUdHR249957E3GNEVm1ahWuvfZaLF68GCeeeCJWr16Njo4O3HrrreN9aYQQQkhQBVFsVB+KcAcKIYQkSsSBxe9+9zvx55dffjkqKiqwefNm1NfX43vf+15cLy4aV111FVQqFX7961+jt7cXc+bMwaefforq6urxvjRCCCEkqEgzFla7E1qTTfhcylgQQsZZxIGFr+XLl2P58uXxuJa4ue2223DbbbeN92UQQgghESlUuhYfhpmxUBmFj0uRcshOS0nYdRFCSDiiCiwaGxvxzTffYGBgAE6n99zs8R45SwghhExUhZmpAAD9iB0jNgdSU6RBP54tSCzIVAScfkgIIWMl4sDi5Zdfxk9/+lMUFBSgpKTE64WM4zgKLAghhJAoZaXJIJdKYHU4oTJaUZ6TFvTjWX9FAfVXEEKSQMSBxWOPPYbf/va3+L//+79EXA8hhBAyaXEch4JMOXp0Ixg0WEIGFixjQf0VhJBkEPG4WY1GgyuuuCIR10IIIYRMepFMhmKjZgsy5Qm9JkIICUfEgcUVV1wh7q4ghBBCSHxFMhmKMhaEkGQScSlUfX09HnzwQWzduhVz585FSor3FIq77rorbhdHCCGETDasXyKcjMUg9VgQQpJIxIHF6tWrkZmZifXr12P9+vVef8ZxHAUWhBBCSAwKXCNnI8lYUGBBCEkGEQcWra2tibgOQgghhMBdCjUURmAhbt2mUihCSBKIuMeCEEIIIYnDmrcHwymFoowFISSJhJWxWLVqFX7zm98gIyMDq1atCvqxTz31VFwujBBCCJmM3BkLa9CPG7E5YBixC59DGQtCSBIIK7DYs2cPbDab+PNAaOsnIYQQEptwMxasDEoulSArNeLKZkIIibuwXom+/vprvz8nhBBCSHyx7MOwxQ6z1YE0udTvx7GMRqFSQQd7hJCkQD0WhBBCSBJRKmSQy4S352AN3O7+ClqORwhJDhHnTi+55BK/JyMcxyE1NRX19fX4/ve/j+nTp8flAgkhhJDJhOM4FGYq0K01Y3DYgsq8dL8fRxOhCCHJJuKMRXZ2Nr766ivs3r1bDDD27NmDr776Cna7HW+//Tbmz5+PTZs2xf1iCSGEkMmA9VkEW5I3RBOhCCFJJuKMRUlJCb7//e/jueeeg0QixCVOpxN33303lEol3nrrLdx66634v//7P2zcuDHuF0wIIYQc79hkqGBL8gYpY0EISTIRZyxeffVV3HPPPWJQAQASiQR33nknVq9eDY7jcMcdd+DgwYNxvVBCCCFksih0bd8eMgQeOctKoShjQQhJFhEHFna7HUePHh31+0ePHoXD4QAApKam0oQKQgghJErujMVIwI9hzduUsSCEJIuIS6GuvfZa3HTTTfjFL36BJUuWgOM4bN++HY8//jiuu+46AMD69esxe/bsuF8sIYQQMhm4eyyCZSyEP6OMBSEkWUQcWDz99NMoLi7G73//e/T39wMAiouLce+99+L//u//AADnnHMOzjvvvPheKSGEEDJJFITTY0HjZgkhSSbiwEIqleKXv/wlfvnLX0Kv1wMAsrKyvD6mqqoqPldHCCGETEKsvCnQHguz1YFhi93rYwkhZLxFHFh48g0oCCGEEBI7MWMRYNwsCzgUMgkyFTG9lRNCSNxE9Wr03nvv4Z133kFHRwesVu/6z927d8flwgghhJDJimUhTFYHjBY7MnyCB89RszQshRCSLCKeCvXss8/ixhtvRFFREfbs2YOlS5ciPz8fLS0tWLlyZSKukRBCCJlUMuRSpKYIb9H+yqEGaTkeISQJRRxYPP/881i9ejWee+45yOVy3H///Vi3bh3uuusu6HS6RFwjIYQQMqlwHBe0z2KIluMRQpJQxIFFR0cHVqxYAQBIS0uDwWAAIIyhffPNN+N7dS5tbW246aabUFtbi7S0NEyZMgUPP/zwqDIsjuNG/XjxxRcTck2EEEJIIgXrs6CMBSEkGUXcY1FSUgKVSoXq6mpUV1dj69atmD9/PlpbW8HzfCKuEUePHoXT6cRLL72E+vp6HDx4ELfccguMRiP++Mc/en3smjVrvEbdZmdnJ+SaCCGEkERyL8kbvcuCMhaEkGQUcWBx5pln4uOPP8aiRYtw00034d5778V7772HnTt34tJLL03ENeK8887zChbq6urQ0NCAF154YVRgkZOTg5KSkoRcByGEEDJW2JK8YBmLQtphQQhJIhEHFqtXr4bT6QQA3HrrrcjLy8PGjRtx4YUX4tZbb437BQai0+n+f3v3Hh9lfeb//z2Tw+RIhAQDLAkHoaIi5dQirgpUBS3riVXxsGjk0OUHKEgtyuIBqJqCqKxSUFYFXItQt2pXaxVUEqyHFRF+oFQpgkIJiIAlMQkzycz9/SPcd2ZynBAy9z0zr+fjkYeZe+7MXMDHzH3d1+f6fNShQ4d6x6dNm6aJEyeqR48emjBhgn7xi1/I7W7xjC8AAGxlViwa7rGoqWJQsQDgJC1OLNxud8iF+vXXX6/rr7/+lAbVnK+++kpPPvmkHn300ZDjv/71r3XxxRcrNTVV77zzjn75y1/q8OHDuvfeext9La/XK6+39pe2uekfAAB2CqdiQY8FACc5qX0sjh8/rm3btunQoUNW9cJ05ZVXhv06c+fO1bx585o8Z9OmTRo8eLD1uKSkRJdddpmuu+46TZw4MeTc4ASif//+kqT58+c3mVgUFhY2GwMAAJHWdMWCHgsAztPixOLNN9/ULbfcosOHD9d7zuVyye/3h/1a06ZN0w033NDkOd27d7e+Lykp0YgRIzR06FAtX7682dc/77zzVFpaqm+//Va5ubkNnjN79mzNnDnTelxaWqq8vLzw/gAAALSRjpk1/RN1E4tyb7UqfDWftVQsADhJixOLadOm6brrrtP999/f6MV6uHJycpSTkxPWufv379eIESM0aNAgrVixIqy+iS1btiglJUWnnXZao+d4PB55PPxiBgA4S8eMFEk1054Mw7B22DYTjbTkhHo7cgOAnVr8G+nQoUOaOXNmq5OKligpKdHw4cOVn5+vRYsW6bvvvrOeM1eAeu2113Tw4EENHTpUqamp2rBhg+bMmaNf/OIXJA4AgKiTc6JicbwqoHKfXxknkggzsaBaAcBpWpxYXHvttSoqKtIZZ5zRFvE0aN26ddq1a5d27dqlrl27hjxn7p2RlJSkpUuXaubMmQoEAurZs6fmz5+vqVOnRixOAABOlbTkRKUlJ6jC59d3ZV4rsaht3GapWQDO0uLEYsmSJbruuuv03nvv6dxzz1VSUlLI83fccccpC85UUFCggoKCJs+pu9cFAADRrmOmR98cqdDhH7zqkZMuqXbDPBq3AThNixOL1atX66233lJqaqqKioqsOZ9STfN2WyQWAADEo5yMmsQieMlZlpoF4FQtTizuvfdezZ8/X/fccw8bzwEA0IYaWnKWpWYBOFWLMwOfz6exY8eSVAAA0MbMBm4qFgCiQYuzg1tvvVVr165ti1gAAEAQc8lZKhYAokGLp0L5/X4tXLhQb731lvr161evefuxxx47ZcEBABDPqFgAiCYtTiy2b9+uAQMGSJI+++yzkOeCG7kBAEDrmD0W5kpQhmFYFYvTqVgAcJgWJxYbNmxoizgAAEAdOSeSh8MnqhQ/eKt1vCpQ8xwVCwAOQwc2AAAOVVux8J6oVtRULjI8iUpNTrAzNACoJ+yKxZgxY8I67+WXXz7pYAAAQC2zQdtXHVDp8Wp23QbgaGEnFllZWW0ZBwAAqCMlKUGZnkSVeat1+AcvK0IBcLSwE4sVK1a0ZRwAAKABOZkelXlrqhWsCAXAyeixAADAwcxpT8EVCxILAE5EYgEAgIN1DFoZiqlQAJyMxAIAAAfLCVoZiqlQAJyMxAIAAAczl5w9XOazNsqjYgHAiUgsAABwMHOTvO9+8Fob5bHcLAAnIrEAAMDBrE3yyrz6jh4LAA5GYgEAgIOZFYs9h8vlqw7UHKPHAoADkVgAAOBgZnXiB2+1JCkzJVEpSQl2hgQADSKxAADAwbLTQ/spOlKtAOBQJBYAADhYSlKC2qUkWo9z6K8A4FAkFgAAOFxwMkHFAoBTkVgAAOBwwckEK0IBcCoSCwAAHC64YsEeFgCcisQCAACHC65YsNQsAKeKmsSie/fucrlcIV/33HNPyDl79+7VFVdcofT0dOXk5OiOO+6Qz+ezKWIAAE6N4OlPTIUC4FSJzZ/iHPPnz9ekSZOsxxkZGdb3fr9fo0ePVseOHfWXv/xFR44c0a233irDMPTkk0/aES4AAKdE8PQnKhYAnCqqEovMzEx16tSpwefWrVunHTt2aN++ferSpYsk6dFHH1VBQYEeeughtWvXLpKhAgBwylCxABANomYqlCQtWLBA2dnZ6t+/vx566KGQaU4ffvih+vbtayUVkjRq1Ch5vV5t3ry50df0er0qLS0N+QIAwEmCqxTZNG8DcKioqVhMnz5dAwcOVPv27fXxxx9r9uzZ2rNnj5555hlJ0sGDB5WbmxvyM+3bt1dycrIOHjzY6OsWFhZq3rx5bRo7AACt0T0nXWnJCepyWqo8iQl2hwMADbK1YjF37tx6Ddl1vz755BNJ0p133qlhw4apX79+mjhxop566ik9++yzOnLkiPV6Lper3nsYhtHgcdPs2bN17Ngx62vfvn2n/g8KAEArtEtJ0ru/HK4//H/n2x0KADTK1orFtGnTdMMNNzR5Tvfu3Rs8ft5550mSdu3apezsbHXq1En/93//F3LO999/r6qqqnqVjGAej0ceD/NVAQDO1ikrxe4QAKBJtiYWOTk5ysnJOamf3bJliySpc+fOkqShQ4fqoYce0oEDB6xj69atk8fj0aBBg05NwAAAAAAaFBU9Fh9++KE++ugjjRgxQllZWdq0aZPuvPNOXXnllcrPz5ckjRw5UmeffbbGjRunRx55REePHtVdd92lSZMmsSIUAAAA0MaiIrHweDxau3at5s2bJ6/Xq27dumnSpEmaNWuWdU5CQoL+9Kc/acqUKfrnf/5npaam6qabbtKiRYtsjBwAAACIDy7DMAy7g3CSY8eO6bTTTtO+ffuodAAAACCulZaWKi8vT//4xz+UlZXV5LlRUbGIpLKyMklSXl6ezZEAAAAAzlBWVtZsYkHFoo5AIKCSkhJlZmY2uUwt2o6ZGVM1AmMBJsYCJMYBajEWIscwDJWVlalLly5yu5veqYKKRR1ut1tdu3a1OwxIateuHb8sIImxgFqMBUiMA9RiLERGc5UKk60b5AEAAACIDSQWAAAAAFqNxAKO4/F49MADD7AjOhgLsDAWIDEOUIux4Ew0bwMAAABoNSoWAAAAAFqNxAIAAABAq5FYAAAAAGg1EgsAAAAArUZiAQAAAKDVSCwAAAAAtBqJBQAAAIBWI7EAAAAA0GokFgAAAABajcQCAAAAQKuRWAAAAABoNRILAAAAAK1GYgEAAACg1RLtDsBpAoGASkpKlJmZKZfLZXc4AAAAgG0Mw1BZWZm6dOkit7vpmgSJRR0lJSXKy8uzOwwAAADAMfbt26euXbs2eQ6JRR2ZmZmSav7y2rVrZ3M0AAAAgH1KS0uVl5dnXSM3hcSiDnP6U7t27UgsAAAAACmsFgGatwEAAAC0GokFAAAAgFYjsQAAAADQaiQWAOBgy4q+0kULN+jgseN2hwIbVfkDuvq372vm77faHQoANIrEAgAc7M+fHdDeoxX65JujdocCG+09WqGt+/6h1/7/ErtDAYBGkVgAgIOVe6slSRU+v82RwE4V3pp//yq/IV91wOZoAKBhJBYA4GBmQlFxIsFAfCr31f77V5JkAnAoEgsAcDCzYlHOxWRcqwhKLIKTDABwEhILAHCwyqqahIK71PEteCoc0+IAOBWJBQA4lK86oCq/IYm71PHO7LGQQqsXAOAkJBYA4FDBF5DBF5aIP8GJZTljAYBDkVgAgEOFTH+p4mIyngWPhcoqKhYAnInEAgAcKrRiwcVkPKugYgEgCpBYAIBDBV9A0mMR38rpsQAQBUgsAMChgpMJVgKKb1QsAEQDEgsAcKhKlhjFCaE9FowFAM5EYgEADhW8KR49FvEtOLEoZywAcCgSCwBwqOBkgp2341twMkH1CoBTkVgAgEOFVCxo2I1rVCwARAMSCwBwqMqgZKLKb8hXHbAxGtgpZOlheiwAOBSJBQA4VN3pT5VMgYlbFfTbAIgCJBYA4FB1LyDZyyJ+ldNvAyAKkFgAgEPVbdKlaTd+BS8xS78NAKcisQAAh6qfWHBBGY981QFV+Q3rMQkmAKcisQAAh6o79Ykdl+NT3YSygnEAwKFILADAoepeQFKxiE91eyrotQHgVCQWAOBQFVV17lQzBSYuVdZJJCp9fhmG0cjZAGAfEgsAcCizYpGZkljzmDvVcam8zjioDhjy+dnTBIDzRG1iUVhYKJfLpRkzZljHDMPQ3Llz1aVLF6Wmpmr48OH6/PPP7QsSAFrBnPLSMcNT85i59XHJHAc5J8aBRJ8FAGeKysRi06ZNWr58ufr16xdyfOHChXrssce0ZMkSbdq0SZ06ddKll16qsrIymyIFgJNnXjzmZNZcUFKxiE/mOGiXkihPYs3HNn0WAJwo6hKLH374QTfffLP+67/+S+3bt7eOG4ahxYsXa86cORozZoz69u2rVatWqaKiQqtXr7YxYgBoOcMwVHFi74KOVmLBXep4ZI6DtOREpXtqpkOxCzsAJ4q6xGLq1KkaPXq0LrnkkpDje/bs0cGDBzVy5EjrmMfj0bBhw/TBBx9EOkwAaBVvdUD+QE2DrjkVisQiPpk7sKclJyg1KUESu28DcKZEuwNoiTVr1ujTTz/Vpk2b6j138OBBSVJubm7I8dzcXH3zzTeNvqbX65XX67Uel5aWnqJoAeDkBScR2enJkqRyL9Nf4pGZRKR5EpXuqUksKhgLABwoaioW+/bt0/Tp0/XCCy8oJSWl0fNcLlfIY8Mw6h0LVlhYqKysLOsrLy/vlMUMACfL7KdISXLXrgpVxV3qeGQuN5uenKC05JqxQMUCgBNFTWKxefNmHTp0SIMGDVJiYqISExNVXFysJ554QomJiValwqxcmA4dOlSvihFs9uzZOnbsmPW1b9++Nv1zAEA4zIpFWnKi0k7Mq+cudXwq9wX3WJyoWNC8DcCBomYq1MUXX6zt27eHHLvtttvUp08f3X333erZs6c6deqk9evXa8CAAZIkn8+n4uJiLViwoNHX9Xg88ng8jT4PAHYoD5pXn5bMvPp4FtpjYe5pwlgA4DxRk1hkZmaqb9++IcfS09OVnZ1tHZ8xY4Yefvhh9e7dW71799bDDz+stLQ03XTTTXaEDAAnzbxwTE9OVHoyG+TFs9oeiwSrYkG/DQAniprEIhyzZs1SZWWlpkyZou+//15DhgzRunXrlJmZaXdoANAiFUEXk2bFgrvU8akyKMlMS6ZiAcC5ojqxKCoqCnnscrk0d+5czZ0715Z4AOBUMasTaUENu+y2HJ/MzfBSk0kyAThb1DRvA0A8KfcGN2+bPRZMf4lHZkJZMy2O5m0AzkViAQAOVBG0xGh60PQXwzDsDAs2MBPKNE+CtUJYOdUrAA4U8cTi+PHjkX5LAIg6FUGbopkVC3/AkM8fsDMs2KDSR8UCQHSISGIRCAT061//Wv/0T/+kjIwM7d69W5J033336dlnn41ECAAQVay71EkJSktKsI7TZxF/yoP6bVJp3gbgYBFJLB588EGtXLlSCxcuVHJysnX83HPP1TPPPBOJEAAgqpgJRJonUYkJbiUn1vy6ps8i/lhjITmBigUAR4tIYvH8889r+fLluvnmm5WQUHvnrV+/fvriiy8iEQIARJXafSwSQv5byZ3quGIYhiqqTowFTyI9FgAcLSKJxf79+9WrV696xwOBgKqqqiIRAgBEleDlZmv+e+KCksQirnirA/IHahr2gysWlVWMAwDOE5HE4pxzztF7771X7/hLL72kAQMGRCIEAIgq1m7LJxIKa/8CdlyOK8G9FGnJiUpNZudtAM4VkQ3yHnjgAY0bN0779+9XIBDQyy+/rC+//FLPP/+8Xn/99UiEAABRxUwg0k+sCGVNgaFiEVfMBMKT6FaC2xWy9DAAOE1EKhZXXHGF1q5dqzfeeEMul0v333+//vrXv+q1117TpZdeGokQACCqVNSpWNC0G58qg/orJIVslsieJgCcJiIVC0kaNWqURo0aFam3A4Co1liPBXeq44tZsUizmvhrxoFh1PRfpAQtRQwAdmPnbQBwoMZ6LJhbH19qK1c1//6pQYkEYwGA07RZxaJ9+/ZyuVxhnXv06NG2CgMAolLdHgvzv1Qs4kttxaLm49rtdik1KUGVVX5V+PzKtjM4AKijzRKLxYsXW98fOXJEDz74oEaNGqWhQ4dKkj788EO99dZbuu+++9oqBACISsF7F9RWLJgKFY9qeyxqKxXpnprEgs0SAThNmyUWt956q/X9v/7rv2r+/PmaNm2adeyOO+7QkiVL9Pbbb+vOO+9sqzAAIOocrwrI7Mut7bGgeTsemRvhpSbVflynJlO9AuBMEemxeOutt3TZZZfVOz5q1Ci9/fbbkQgBAKJG8J1oc069tUEeOy7HFTORDKlYmNUrxgIAh4lIYpGdna1XXnml3vFXX31V2dnMEAWAYJVBDbtud02vmnlhWVlFxSKe1F12uOb72iVnAcBJIrLc7Lx58zRhwgQVFRVZPRYfffSR3nzzTT3zzDORCAEAokZ5naVma76nYhGPzLGQnhzcY2H225BYAHCWiCQWBQUFOuuss/TEE0/o5ZdflmEYOvvss/X+++9ryJAhkQgBAKKGmTw0dJeai8n4UuENXW5Wqp0eR48FAKeJ2AZ5Q4YM0e9+97tIvR0ARK26m+MFf0/FIr5Y1StP7ce1VbFgLABwmIgkFnv37m3y+fz8/EiEAQBRwbwTnd7AxaS5/Cjig9lvk95Qkkn1CoDDRCSx6N69e5Ob5fn9fFACgKnpigUXk/Gk7g7sUlCSyVQoAA4TkcRiy5YtIY+rqqq0ZcsWPfbYY3rooYciEQIARI3yBubVs0FefKrw1k8yzR4LKhYAnCYiicWPf/zjescGDx6sLl266JFHHtGYMWMiEQYARAVr74Lgu9RB018Mw2iyCozYYVUsQqbFnWjepscCgMNEZB+LxvzoRz/Spk2b7AwBABzHrEqkBlcsTlxYGobkrQ7YEhcir7KB5WatpYepWABwmIhULEpLS0MeG4ahAwcOaO7cuerdu3ckQgCAqNFQ87Y5/UWq6bNICXqM2NVwjwXLzQJwpogkFqeddlq9sr1hGMrLy9OaNWsiEQIARI3yBubVJ7hdSkly63hVQBU+v7LtCg4R1XCPBf02AJwpIonFhg0bQh673W517NhRvXr1UmJixLbSAICoULvEaOjvx/TkRB2v8nFBGScMw1BFldljEbzzNiuEAXCmiFzVu1wunX/++fWSiOrqam3cuFEXXXRRJMIAgKhgzp0P7rGQai4uj5Qztz5eHK8KyDBqvk8P2YWdigUAZ4pI8/aIESN09OjResePHTumESNGRCIEAIgatT0WdRKLJHZcjifBCWRwj405LYrEAoDTRCSxaGxpxCNHjig9PT0SIQBA1KjtsQit8prTYahYxAczgUxNSpDbXfsZmm5VLBgHAJylTadCmftTuFwuFRQUyOPxWM/5/X5t27ZN559/fluGAABRp6KJHguJHZfjRUXViaVm61auglaFCgSMkKQDAOzUpolFVlaWpJqKRWZmplJTU63nkpOTdd5552nSpEltGQIARJ2G9rGQaqfAULGID7U7sDecYEpSZZU/ZFliALBTm/42WrFihSSpe/fuuuuuu5j2BABhsHbernunOpkdl+OJOQ7S6iSYKUluuVw1myVW+EgsADhHRH4bPfDAA5F4GwCICead6rpToczdt6lYxIfaikVoYuFyuZSWlKByn/9E8uFp4KcBIPLaLLEYOHCg3nnnHbVv314DBgxosHnb9Omnn7ZVGAAQVQIBQ5VVDU+FSj/xmB6L+FBp9VjU/6hO8ySq3Oe3kg8AcII2Syyuuuoqq1n76quvbqu3AYCYYiYVUgMVi2QqFvGksYqFVJNkfidWhgLgLG2WWARPf2IqFACEx0waXK6aufTB6LGIL7U9FvU/qlPZJA+AA0W048vn8+nQoUMKBAIhx/Pz8yMZBgA4VmXQUrN1p5CaPRZcTMYH89+5sYpFzTlULAA4R0QSi507d2rChAn64IMPQo6bG+f5/XxIAoBUO/2lbn+FVHsxyVSo+FC7A3vDPRaS6LEA4CgRSSxuu+02JSYm6vXXX1fnzp2bbOQGgHhmLTXbQGKRxvSXuFK7A3sTFYsqxgIA54hIYrF161Zt3rxZffr0icTbAUDUKvc1vClazbETFQsvFYt40NRUqFSr34axAMA53M2f0npnn322Dh8+HIm3AoCoVtnI5njBxyq5Sx0XmmreTrdWCGMsAHCOiCQWCxYs0KxZs1RUVKQjR46otLQ05AsAUKO2x6KhigXz6uNJbY9FA9PiPFQsADhPRKZCXXLJJZKkiy++OOQ4zdsAEKrpHgtWAoon5pS31KQGkswTx+ixAOAkEUksNmzYEIm3AYCo13SPRW3zdiBgyO1mIYxY1lTFIp2KBQAHikhiMWzYsFa/RmFhoV5++WV98cUXSk1N1fnnn68FCxbozDPPtM4xDEPz5s3T8uXL9f3332vIkCH67W9/q3POOafV7w8AkdDk3gVBF5jHq/0NJh+IHRVhJJn0WABwkoh8Km3btq3B4y6XSykpKcrPz5fH42nyNYqLizV16lT95Cc/UXV1tebMmaORI0dqx44dSk9PlyQtXLhQjz32mFauXKkf/ehHevDBB3XppZfqyy+/VGZm5in/cwHAqWbegU5r4C51SmKCXC7JMGr6LEgsYltFGI38TIsD4CQR+VTq379/k3tXJCUlaezYsXr66aeVkpLS4DlvvvlmyOMVK1bo9NNP1+bNm3XRRRfJMAwtXrxYc+bM0ZgxYyRJq1atUm5urlavXq1///d/P3V/IABoI+VBO2/X5Xa7lJqUoAqf/8QFZdM3ZBDdzCb9tAZ6LFKTzMSCigUA54jIqlCvvPKKevfureXLl2vr1q3asmWLli9frjPPPFOrV6/Ws88+q3fffVf33ntv2K957NgxSVKHDh0kSXv27NHBgwc1cuRI6xyPx6Nhw4bV2/EbAJyq0tf4pmg1x9kkLx4EAoa1rHBD1StzN+4KVggD4CARqVg89NBD+s///E+NGjXKOtavXz917dpV9913nz7++GOlp6frl7/8pRYtWtTs6xmGoZkzZ+qCCy5Q3759JUkHDx6UJOXm5oacm5ubq2+++abR1/J6vfJ6vdZjlr8FYKemmrelmikwh39gCkysC96rpKHqlbVZIuMAgINEpGKxfft2devWrd7xbt26afv27ZJqpksdOHAgrNebNm2atm3bphdffLHec3WnXJlL2jamsLBQWVlZ1ldeXl5YMQBAW2hqXr3EXhbxwkwYXC4pJan+R7VVsaByBcBBIpJY9OnTR7/5zW/k8/msY1VVVfrNb36jPn36SJL2799fr9rQkNtvv13/+7//qw0bNqhr167W8U6dOkmqrVyYDh061OTrzp49W8eOHbO+9u3b16I/GwCcSta8+kYqFuxlER8qrP6KhAZvjtX2WDAOADhHRKZC/fa3v9WVV16prl27ql+/fnK5XNq2bZv8fr9ef/11SdLu3bs1ZcqURl/DMAzdfvvteuWVV1RUVKQePXqEPN+jRw916tRJ69ev14ABAyRJPp9PxcXFWrBgQaOv6/F4ml2RCgAipdJq3m6sYkHTbjywlpr1NDYlrub48aqA/AFDCexpAsABIpJYnH/++fr666/1wgsvaOfOnTIMQ9dee61uuukmaxnYcePGNfkaU6dO1erVq/XHP/5RmZmZVmUiKytLqampcrlcmjFjhh5++GH17t1bvXv31sMPP6y0tDTddNNNbf5nBIBTwZwCk9pIYpHO/gVxoakd2KXQ5v4KX7UyU5IiEhcANCVii6BnZGRo8uTJJ/3zy5YtkyQNHz485PiKFStUUFAgSZo1a5YqKys1ZcoUa4O8devWsYcFgKhRu9tyI1Oh2HE5LjTXxO9JdCvB7ZI/YKjS5yexAOAIEd1daceOHdq7d29Ir4UkXXnllc3+rGEYzZ7jcrk0d+5czZ0792RDBABblXubW27WXA2IikUsq2hmHLhcLqUlJajMW81YAOAYEUksdu/erWuuuUbbt2+Xy+WykgSzIc3v55ciAPgDhrzVAUlNLDd74nglTbsxrbkei5rnTiQWVK8AOEREVoWaPn26evTooW+//VZpaWn6/PPPtXHjRg0ePFhFRUWRCAEAHC94hZ/mNsjjLnVsa67HouY5lpwF4CwRqVh8+OGHevfdd9WxY0e53W653W5dcMEFKiws1B133KEtW7ZEIgwAcDTzAjHB7ZInseH7PtaqUNyljmlm4thYE3/wcyw5C8ApIlKx8Pv9ysjIkCTl5OSopKREUs0GeV9++WUkQgAAx7OmvyQ3vHeBFNS8zV3qmGY18TcyJS74OcYCAKeISMWib9++2rZtm3r27KkhQ4Zo4cKFSk5O1vLly9WzZ89IhAAAjtdc47bExWS8sJq3G9mBPfg5eiwAOEVEEot7771X5eXlkqQHH3xQ//Iv/6ILL7xQ2dnZWrNmTSRCAADHC+cude2qUFxMxrJyKhYAolBEEotRo0ZZ3/fs2VM7duzQ0aNH1b59+0bL/QAQb8xkocm71ObFpJeLyVhm9k00Vb1KZRd2AA7TponF+PHjwzrvueeea8swACAqVJo9FklNLzEqSRVVVCxiWUUzG+RJtStG0bwNwCnaNLFYuXKlunXrpgEDBoS1wR0AxLPyMObVp1OxiAvWcrNN9licWHqYsQDAIdo0sZg8ebLWrFmj3bt3a/z48fq3f/s3dejQoS3fEgCiFj0WMJnJAhULANGkTZebXbp0qQ4cOKC7775br732mvLy8nT99dfrrbfeooIBAHWUhzGv3nzueFVA/gC/R2NVeD0WNG8DcJY238fC4/Hoxhtv1Pr167Vjxw6dc845mjJlirp166Yffvihrd8eAKJGZdA+Fo1J99Tewa6s4oIyVlWEMxaoWABwmIhskGdyuVxyuVwyDEOBQCCSbw0AjmdNf/E0Pv3Fk+iW+8Rieuy+HbusaXFNjAV6LAA4TZsnFl6vVy+++KIuvfRSnXnmmdq+fbuWLFmivXv3WrtxAwCCGnabuEvtcrmsHoxypsDErPA2S6RiAcBZ2rR5e8qUKVqzZo3y8/N12223ac2aNcrOzm7LtwSAqFUexhKjUs3+BWXeanZcjlH+gCFvdU1Vv6mxwD4WAJymTROLp556Svn5+erRo4eKi4tVXFzc4Hkvv/xyW4YBAFGhMoyGXenE9JgyLz0WMSq4AtF0xYLmbQDO0qaJxS233MLO2gAQpnB6LKSgJWepWMQkM1FIcLvkSWx8xrK5xwVLDwNwijbfIA8AEJ5weiyk2sSCO9WxyeqvSEpo8uYcy80CcJqIrgoFAGiceYGY2mxiwQVlLLOWmm1i122pNgH1VQdU5WelRQD2I7EAAIcIZ+dtqXYKDKsBxaZwx0FwYzdJJgAnILEAAIcw58qnN3On2rygZP+C2GTtwN7MOEhOdCspoWaqFEkmACcgsQAAh6jwhrfcbBr7F8Q0axwkNd8GmZpEvw0A5yCxAAAHqPIH5PObexfQYxHPKsKsWEi1O3NXUL0C4AAkFgDgAMFJQnMVC3Zcjm3h9lhIQUsPMxYAOACJBQA4gJkkJCW4lNzE3gVS7T4X9FjEpvIwN0qUgioWJBYAHIDEAgAcoDzM/oqac6hYxLLaXpvmEwt6LAA4CYkFADhApS/8i0k2yItttftYNJ9k0mMBwElILADAAVo0/cVcbpbEIiaFuwO7RI8FAGchsQAAB7AuJsO4S22uFlTh5WIyFpX7wp8Wl84KYQAchMQCABzAvDA058w3heVmY1tlC6pXqfTbAHAQEgsAcABzjnw4FQuWm41tViN/WD0WCSE/AwB2IrEAAAdoSY+FtdwsFYuY1LIeC5abBeAcJBYA4AAt2hTtxHQpX3VA1Sd260bsMBPGVFYIAxBlSCwAwAHMO85hXUx6as+pqOKCMtZUtiDJpHkbgJOQWACAA5RbPRbNJxbJCW4lul2S2L8gFpVbK4SFn2SWs0IYAAcgsQAAB6iweiyav0vtcrnYvyCGVbRgF3YqFgCchMQCAByg3Jr+0vxdaimoaZeKRUyp8gfkO9E3w3KzAKINiQUAOEBlCzZFk4I2yeOCMqYEVx6oWACINiQWAOAA5hz5tDDm1UtcUMYqM1FMSnApObH5j2h6LAA4CYkFADhAS5ablUSPRYwqb0F/hUSCCcBZSCwAwAFastysxP4Fsap2Slx448AcL9UBQ75q9jQBYC8SCwBwgBZXLDxm8zYVi1jSkh3Y655Hvw0Au5FYAIADtLzHwpwKRcUillRYe1iEl2AmJbitXgzGAgC7kVgAgAO0vMfCnFvPXepYUttjEV6CKdUmmVSvANiNxAIAbOarDqg6YEiixyLetXTZ4eBzGQsA7EZiAQA2C646hHunOt3DBnmxqKU9FsHnskIYALvFZGKxdOlS9ejRQykpKRo0aJDee+89u0MCgEaZc+OTE91KSgjv1zIXk7GppVPipOBGfpJMAPaKucRi7dq1mjFjhubMmaMtW7bowgsv1OWXX669e/faHRoANMicG38yd6mZ/hJbzCb+cKfESVJaEkkmAGeIucTiscce04QJEzRx4kSdddZZWrx4sfLy8rRs2TK7QwOABp3UXWqat2OSNRbCXB0s+NxKkkwANgv/UywK+Hw+bd68Wffcc0/I8ZEjR+qDDz6wKaqW2fT1Ud2+eovdYQCIoIOlxyVJ+/9RqWfe2x3Wz7z7xSFJ0ke7j+q8h99ps9jscONP80MurLf9/Zg+3nPUxogixxwLL368T+3TksP6mbf/WjMW7nl5uxa//bc2iw2APXrnZujR636s09ul2B1Ks2IqsTh8+LD8fr9yc3NDjufm5urgwYMN/ozX65XX67Uel5aWtmmMTQkEDN363MdMbQDi2IN/+muLf8a8GI0Vj7+90+4QbHe03MdYACCp5v/rx9/eqcIx/ewOpVkxlViYXC5XyGPDMOodMxUWFmrevHmRCKtZbrdL944+W//xyna7QwFgg7wOqRrcrUNY5wYMQ3/cWtLGEdnjZ31OV1ZqkvV4w5eH9I+KKhsjiry6fwdN+fpIubbs/UfbBgTAVjcP6WZ3CGFxGYZh2B3EqeLz+ZSWlqaXXnpJ11xzjXV8+vTp2rp1q4qLi+v9TEMVi7y8PB07dkzt2rWLSNwAAACAE5WWliorKyusa+OYat5OTk7WoEGDtH79+pDj69ev1/nnn9/gz3g8HrVr1y7kCwAAAEDLxNxUqJkzZ2rcuHEaPHiwhg4dquXLl2vv3r2aPHmy3aEBAAAAMSvmEouxY8fqyJEjmj9/vg4cOKC+ffvqjTfeULdu0TE3DQAAAIhGMdVjcSq0ZB4ZAAAAEMtacm0ccxWL1jLzLDuXnQUAAACcwLwmDqcWQWJRR1lZmSQpLy/P5kgAAAAAZygrK1NWVlaT5zAVqo5AIKCSkhJlZmY2uvcF2pa55O++ffuYjhbnGAswMRYgMQ5Qi7EQOYZhqKysTF26dJHb3fSCslQs6nC73eratavdYUBi+V9YGAswMRYgMQ5Qi7EQGc1VKkwxtY8FAAAAAHuQWAAAAABoNRILOI7H49EDDzwgj8djdyiwGWMBJsYCJMYBajEWnInmbQAAAACtRsUCAAAAQKuRWAAAAABoNRILAAAAAK1GYoGo4fV61b9/f7lcLm3dutXucBBBX3/9tSZMmKAePXooNTVVZ5xxhh544AH5fD67Q0MELF26VD169FBKSooGDRqk9957z+6QEGGFhYX6yU9+oszMTJ1++um6+uqr9eWXX9odFmxWWFgol8ulGTNm2B0KTiCxQNSYNWuWunTpYncYsMEXX3yhQCCgp59+Wp9//rkef/xxPfXUU/qP//gPu0NDG1u7dq1mzJihOXPmaMuWLbrwwgt1+eWXa+/evXaHhggqLi7W1KlT9dFHH2n9+vWqrq7WyJEjVV5ebndosMmmTZu0fPly9evXz+5QEIRVoRAV/vznP2vmzJn6wx/+oHPOOUdbtmxR//797Q4LNnrkkUe0bNky7d692+5Q0IaGDBmigQMHatmyZdaxs846S1dffbUKCwttjAx2+u6773T66aeruLhYF110kd3hIMJ++OEHDRw4UEuXLtWDDz6o/v37a/HixXaHBVGxQBT49ttvNWnSJP33f/+30tLS7A4HDnHs2DF16NDB7jDQhnw+nzZv3qyRI0eGHB85cqQ++OADm6KCExw7dkyS+B0Qp6ZOnarRo0frkksusTsU1JFodwBAUwzDUEFBgSZPnqzBgwfr66+/tjskOMBXX32lJ598Uo8++qjdoaANHT58WH6/X7m5uSHHc3NzdfDgQZuigt0Mw9DMmTN1wQUXqG/fvnaHgwhbs2aNPv30U23atMnuUNAAKhawxdy5c+VyuZr8+uSTT/Tkk0+qtLRUs2fPtjtktIFwx0GwkpISXXbZZbruuus0ceJEmyJHJLlcrpDHhmHUO4b4MW3aNG3btk0vvvii3aEgwvbt26fp06frhRdeUEpKit3hoAH0WMAWhw8f1uHDh5s8p3v37rrhhhv02muvhVxE+P1+JSQk6Oabb9aqVavaOlS0oXDHgfkBUlJSohEjRmjIkCFauXKl3G7ujcQyn8+ntLQ0vfTSS7rmmmus49OnT9fWrVtVXFxsY3Sww+23365XX31VGzduVI8ePewOBxH26quv6pprrlFCQoJ1zO/3y+Vyye12y+v1hjyHyCOxgKPt3btXpaWl1uOSkhKNGjVK//M//6MhQ4aoa9euNkaHSNq/f79GjBihQYMG6YUXXuDDI04MGTJEgwYN0tKlS61jZ599tq666iqat+OIYRi6/fbb9corr6ioqEi9e/e2OyTYoKysTN98803Isdtuu019+vTR3XffzdQ4B6DHAo6Wn58f8jgjI0OSdMYZZ5BUxJGSkhINHz5c+fn5WrRokb777jvruU6dOtkYGdrazJkzNW7cOA0ePFhDhw7V8uXLtXfvXk2ePNnu0BBBU6dO1erVq/XHP/5RmZmZVo9NVlaWUlNTbY4OkZKZmVkveUhPT1d2djZJhUOQWABwvHXr1mnXrl3atWtXvYSSomtsGzt2rI4cOaL58+frwIED6tu3r9544w1169bN7tAQQeZyw8OHDw85vmLFChUUFEQ+IAANYioUAAAAgFaj8xEAAABAq5FYAAAAAGg1EgsAAAAArUZiAQAAAKDVSCwAAAAAtBqJBQAAAIBWI7EAAAAA0GokFgAAAABajcQCAAAAQKuRWAAAQhQUFMjlctX72rVrl92hAQAcLNHuAAAAznPZZZdpxYoVIcc6duwY8tjn8yk5OTmSYQEAHIyKBQCgHo/Ho06dOoV8XXzxxZo2bZpmzpypnJwcXXrppZKkHTt26Oc//7kyMjKUm5urcePG6fDhw9ZrlZeX65ZbblFGRoY6d+6sRx99VMOHD9eMGTOsc1wul1599dWQGE477TStXLnSerx//36NHTtW7du3V3Z2tq666ip9/fXX1vMFBQW6+uqrtWjRInXu3FnZ2dmaOnWqqqqqrHO8Xq9mzZqlvLw8eTwe9e7dW88++6wMw1CvXr20aNGikBg+++wzud1uffXVV63/SwWAGEdiAQAI26pVq5SYmKj3339fTz/9tA4cOKBhw4apf//++uSTT/Tmm2/q22+/1fXXX2/9zK9+9Stt2LBBr7zyitatW6eioiJt3ry5Re9bUVGhESNGKCMjQxs3btRf/vIXZWRk6LLLLpPP57PO27Bhg7766itt2LBBq1at0sqVK0OSk1tuuUVr1qzRE088ob/+9a966qmnlJGRIZfLpfHjx9er0jz33HO68MILdcYZZ5zcXxgAxBGmQgEA6nn99deVkZFhPb788sslSb169dLChQut4/fff78GDhyohx9+2Dr23HPPKS8vTzt37lSXLl307LPP6vnnn7cqHKtWrVLXrl1bFM+aNWvkdrv1zDPPyOVySZJWrFih0047TUVFRRo5cqQkqX379lqyZIkSEhLUp08fjR49Wu+8844mTZqknTt36ve//73Wr1+vSy65RJLUs2dP6z1uu+023X///fr444/105/+VFVVVXrhhRf0yCOPtChWAIhXJBYAgHpGjBihZcuWWY/T09N14403avDgwSHnbd68WRs2bAhJQkxfffWVKisr5fP5NHToUOt4hw4ddOaZZ7Yons2bN2vXrl3KzMwMOX78+PGQaUrnnHOOEhISrMedO3fW9u3bJUlbt25VQkKChg0b1uB7dO7cWaNHj9Zzzz2nn/70p3r99dd1/PhxXXfddS2KFQDiFYkFAKCe9PR09erVq8HjwQKBgK644gotWLCg3rmdO3fW3/72t7Dez+VyyTCMkGPBvRGBQECDBg3S7373u3o/G9xUnpSUVO91A4GAJCk1NbXZOCZOnKhx48bp8ccf14oVKzR27FilpaWF9WcAgHhHYgEAOGkDBw7UH/7wB3Xv3l2JifU/Unr16qWkpCR99NFHys/PlyR9//332rlzZ0jloGPHjjpw4ID1+G9/+5sqKipC3mft2rU6/fTT1a5du5OK9dxzz1UgEFBxcbE1Faqun//850pPT9eyZcv05z//WRs3bjyp9wKAeETzNgDgpE2dOlVHjx7VjTfeqI8//li7d+/WunXrNH78ePn9fmVkZGjChAn61a9+pXfeeUefffaZCgoK5HaHfvz87Gc/05IlS/Tpp5/qk08+0eTJk0OqDzfffLNycnJ01VVX6b333tOePXtUXFys6dOn6+9//3tYsXbv3l233nqrxo8fr1dffVV79uxRUVGRfv/731vnJCQkqKCgQLNnz1avXr1CpnABAJpGYgEAOGldunTR+++/L7/fr1GjRqlv376aPn26srKyrOThkUce0UUXXaQrr7xSl1xyiS644AINGjQo5HUeffRR5eXl6aKLLtJNN92ku+66K2QKUlpamjZu3Kj8/HyNGTNGZ511lsaPH6/KysoWVTCWLVuma6+9VlOmTFGfPn00adIklZeXh5wzYcIE+Xw+jR8/vhV/MwAQf1xG3UmtAAC0seHDh6t///5avHix3aHU8/7772v48OH6+9//rtzcXLvDAYCoQY8FAACq2Txv3759uu+++3T99deTVABACzEVCgAASS+++KLOPPNMHTt2LGSvDgBAeJgKBQAAAKDVqFgAAAAAaDUSCwAAAACtRmIBAAAAoNVILAAAAAC0GokFAAAAgFYjsQAAAADQaiQWAAAAAFqNxAIAAABAq5FYAAAAAGi1/wflPcloK+3t6QAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 800x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the frequency spectrum\n",
    "s_fft = np.fft.fft(s)\n",
    "s_fft_re = np.real(s_fft)\n",
    "s_fft_im = np.imag(s_fft)\n",
    "\n",
    "N = len(s)\n",
    "freq = np.fft.fftfreq(N, 1/fs)\n",
    "\n",
    "fig, axes = plt.subplots(3, 1, figsize=(8, 6), sharex=True)\n",
    "axes[0].plot(freq, s_fft_re)\n",
    "axes[0].set_ylabel('Real part')\n",
    "axes[1].plot(freq, s_fft_im)\n",
    "axes[1].set_ylabel('Imaginary part')\n",
    "axes[2].plot(freq, np.abs(s_fft))\n",
    "axes[2].set_xlabel('Frequency')\n",
    "axes[2].set_ylabel('Magnitude')\n",
    "\n",
    "plt.tight_layout()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b12fb34e",
   "metadata": {},
   "source": [
    "#### Ex 3: How does the frequency spectrum look like if the signal does not center around 0? Why?\n",
    "\n",
    "**Hint:**\n",
    "\n",
    "$$s(f) = \\int_{-\\infty}^{\\infty} s(t) e^{-2\\pi ift} dt$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "dea28e7c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# simple sinus signal\n",
    "fs = 10 # sampling frequency\n",
    "t = np.arange(0, 10, 1/fs)\n",
    "s = np.sin(2*np.pi*t) + 1\n",
    "f, axes = plt.subplots(2, 1, figsize=(8, 4))\n",
    "axes[0].plot(t, s)\n",
    "axes[0].set_xlabel('Time [s]')\n",
    "axes[0].set_ylabel('Amplitude')\n",
    "\n",
    "# plot the frequency spectrum\n",
    "s_fft = np.fft.fft(s)\n",
    "s_fft = np.abs(s_fft)\n",
    "\n",
    "N = len(s)\n",
    "freq = np.fft.fftfreq(N, 1/fs)\n",
    "axes[1].plot(freq[:N//2], s_fft[:N//2])\n",
    "# axes[1].set_xlim(0, 5)\n",
    "axes[1].set_xlabel('Frequency [Hz]')\n",
    "axes[1].set_ylabel('Amplitude')\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "aba64e2d",
   "metadata": {},
   "source": [
    "### Ex 4: Can the real part of the FFT output be negative? Why? Modify the signal above to test your hypothesis.\n",
    "\n",
    "**Hints**:\n",
    "$$e^{i \\theta} = \\cos(\\theta) + i \\sin(\\theta)$$\n",
    "$$sin(2 \\pi f t) = (e^{2\\pi ift} - e^{-2\\pi ift}) / (2i)$$\n",
    "$$cos(2 \\pi f t) = (e^{2\\pi ift} + e^{-2\\pi ift}) / 2 $$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3002e800",
   "metadata": {},
   "source": [
    "Phase shift in time domain corresponds to multiplication by a complex exponential in the frequency domain\n",
    "$$s(f) \\xrightarrow{\\text{time shift by } \\theta} s(f)e^{-i2\\pi f\\theta}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "1cea14e6",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\mzhao\\.conda\\envs\\eff_env\\lib\\site-packages\\matplotlib\\cbook\\__init__.py:1335: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.asarray(x, float)\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# simple sinus signal\n",
    "fs = 10 # sampling frequency\n",
    "t = np.arange(0, 10, 1/fs)\n",
    "s = np.sin(2*np.pi*t - np.pi/4)\n",
    "f, axes = plt.subplots(2, 1, figsize=(8, 4))\n",
    "axes[0].plot(t, s)\n",
    "axes[0].set_xlabel('Time [s]')\n",
    "axes[0].set_ylabel('Amplitude')\n",
    "\n",
    "# plot the frequency spectrum\n",
    "s_fft = np.fft.fft(s)\n",
    "\n",
    "freq = np.fft.fftfreq(N, 1/fs)\n",
    "axes[1].plot(freq, s_fft)\n",
    "axes[1].set_xlabel('Frequency [Hz]')\n",
    "axes[1].set_ylabel('Amplitude')\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0c8774b",
   "metadata": {},
   "source": [
    "### Ex 5: Can you modify the signal so that its frequency spectrum only has non-zero values for positive frequencies?\n",
    "\n",
    "\n",
    "**Hint:**\n",
    "\n",
    "$$s(f) = \\int_{-\\infty}^{\\infty} s(t) e^{-2\\pi ift} dt$$\n",
    "\n",
    "$$\\int_{-\\infty}^{\\infty} e^{-ift} \\, dt = 2\\pi \\delta(f)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b97352f1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# simple sinus signal\n",
    "fs = 10 # sampling frequency\n",
    "t = np.arange(0, 10, 1/fs)\n",
    "s = np.cos(2*np.pi*t) + 1j*np.sin(2*np.pi*t) # or np.exp(1j*2*np.pi*t)\n",
    "f, axes = plt.subplots(2, 1, figsize=(8, 4))\n",
    "axes[0].plot(t, s)\n",
    "axes[0].set_xlabel('Time [s]')\n",
    "axes[0].set_ylabel('Amplitude')\n",
    "\n",
    "# plot the frequency spectrum\n",
    "s_fft = np.fft.fft(s)\n",
    "\n",
    "freq = np.fft.fftfreq(N, 1/fs)\n",
    "axes[1].plot(freq, s_fft)\n",
    "axes[1].set_xlabel('Frequency [Hz]')\n",
    "axes[1].set_ylabel('Amplitude')\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "38533a22",
   "metadata": {},
   "source": [
    "## Real world acoustic signal from a railway track \n",
    "- extracted from the dataset for the first graded assignment\n",
    "- sampled at 20 kHz\n",
    "- an acoustic signal "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "97aadde7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(419093,)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "signal_file_path = 'acoustic_signal.npy' # Fs=20000Hz\n",
    "x = np.load(signal_file_path)\n",
    "Fs = 20000\n",
    "x.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf85408c",
   "metadata": {},
   "source": [
    "#### Ex 5: extract accoustic data sample from the mortar class under speed 80, plot the signal and its FFT."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "id": "74f54f0d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.fft.fft(x)\n",
    "Xfreq = np.fft.fftfreq(len(x), 1/Fs)\n",
    "fig, axes = plt.subplots(2, 1, figsize=(8, 4))\n",
    "axes[0].plot(x)\n",
    "axes[0].set_xlabel('Time [s]')\n",
    "axes[1].plot(Xfreq[:len(X)//2], np.abs(X)[:len(X)//2])\n",
    "axes[1].set_xlabel('Frequency [Hz]')\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5aba8e1d",
   "metadata": {},
   "source": [
    "#### Ex 6: To reduce noise, apply the provided `smooth` function and compare results with and without the smoothing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b4cf1e11",
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.signal\n",
    "\n",
    "def smooth(x, window_len=30, window='hanning'):\n",
    "    if x.ndim != 1:\n",
    "        x = x[:,0]\n",
    "    if x.size < window_len:\n",
    "        raise ValueError\n",
    "    if window_len<3:\n",
    "        return x\n",
    "    if not window in ['flat', 'hanning', 'hamming', 'bartlett', 'blackman']:\n",
    "        raise ValueError\n",
    "    s=x\n",
    "    #print(len(s))\n",
    "    if window == 'flat': # moving average\n",
    "        w=np.ones(window_len,'d')\n",
    "    else:\n",
    "        w=eval('np.'+window+'(window_len)')\n",
    "\n",
    "    #y=np.convolve(w/w.sum(),s,mode='valid')\n",
    "    y = scipy.signal.convolve(s,w/w.sum(),mode='same')\n",
    "    return y "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "id": "c6a94ce7",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\mzhao\\.conda\\envs\\eff_env\\lib\\site-packages\\matplotlib\\cbook\\__init__.py:1335: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return np.asarray(x, float)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Frequency [Hz]')"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, axes = plt.subplots(2, 1, figsize=(8, 4))\n",
    "X = np.fft.fft(x)\n",
    "Xfreq=np.fft.fftfreq(len(x), 1/Fs)\n",
    "axes[0].plot(Xfreq[:N//2], X[:N//2])\n",
    "axes[0].set_ylim(-100, 2000)\n",
    "axes[1].set_xlabel('Frequency [Hz]')\n",
    "\n",
    "\n",
    "X_smooth=smooth(X,500)\n",
    "Xfreq_smooth=np.fft.fftfreq(len(X_smooth), 1/Fs)\n",
    "axes[1].plot(Xfreq_smooth[:len(X)//2], X_smooth[:len(X)//2])\n",
    "axes[1].set_ylim(-100, 750)\n",
    "axes[1].set_xlabel('Frequency [Hz]')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6d027ff3",
   "metadata": {},
   "source": [
    "#### Ex. 7: We provide the code to plot 2 figures, one giving frequencies content of a signal from 0 to 10Khz and another from 0 to 1Khz. Why it is interresting to make zoom to the frequencies 0 to 1Khz?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "b7adfc88",
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Frequency (Hz)')"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Fs=20000\n",
    "\n",
    "X = np.abs(np.fft.fft(x))\n",
    "X = smooth(X,500)\n",
    "Xfreq=np.fft.fftfreq(len(X))\n",
    "\n",
    "fig, axes = plt.subplots(2, 1, figsize=(8, 4))\n",
    "axes[0].plot(Xfreq[:len(Xfreq)//2]*Fs,X[:len(Xfreq)//2])\n",
    "axes[0].set_xticks(np.linspace(0,0.5*Fs,11),np.linspace(0,10000,11,dtype=int))\n",
    "axes[0].set_xlabel(\"Frequency (Hz)\")\n",
    "\n",
    "axes[1].plot(Xfreq[:len(Xfreq)//2]*Fs,X[:len(Xfreq)//2])\n",
    "axes[1].set_xticks(np.linspace(0,0.5*Fs,101),np.linspace(0,10000,101,dtype=int))\n",
    "axes[1].set_xlim([0,1000])\n",
    "axes[1].set_xlabel(\"Frequency (Hz)\")"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "adbfbe16",
   "metadata": {},
   "source": [
    "#### Ex 8: Subsample the signal x by N  Please explain why the spectrum amplitudes are decreasing when N increases, What can you do to counteract this effect?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "id": "199d5888",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(83819,)"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# subsample the signal x by N\n",
    "N = 5\n",
    "x = np.load(signal_file_path)\n",
    "x_subsampled = scipy.signal.decimate(x, N)\n",
    "x_subsampled.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "id": "9f3f4bd6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the spectrum of the subsampled signal on top of the spectrum of the signal with max sampling frequency \n",
    "\n",
    "X = np.abs(np.fft.fft(x))\n",
    "X = smooth(X, 500)\n",
    "Xfreq = np.fft.fftfreq(len(X), 1/(Fs))\n",
    "fig, axes = plt.subplots(2, 1, figsize=(8, 6))\n",
    "\n",
    "\n",
    "axes[0].plot(Xfreq[:len(Xfreq)//2], X[:len(Xfreq)//2], label=\"Original signal\")\n",
    "axes[0].set_xlabel(\"Frequency (Hz)\")\n",
    "axes[1].plot(Xfreq[:len(Xfreq)//2], X[:len(Xfreq)//2], label=\"Original signal\")\n",
    "axes[1].set_xlim([0,1000])\n",
    "axes[1].set_xlabel(\"Frequency (Hz)\")\n",
    "axes[0].legend()\n",
    "\n",
    "\n",
    "# Subsampled signal\n",
    "X_sub = np.abs(np.fft.fft(x_subsampled))\n",
    "X_sub = smooth(X_sub, 500)\n",
    "Xfreq_sub = np.fft.fftfreq(len(X_sub), 1/(Fs/N))\n",
    "axes[0].plot(Xfreq_sub[:len(Xfreq_sub)//2], N*X_sub[:len(Xfreq_sub)//2], label='Subsampled signal') # Modifications necessary here \n",
    "plt.xlabel(\"Frequency (Hz)\")\n",
    "axes[1].plot(Xfreq_sub[:len(Xfreq_sub)//2], N*X_sub[:len(Xfreq_sub)//2], label='Subsampled signal') # Modifications necessary here \n",
    "axes[1].set_xlim([0, 1000])\n",
    "axes[1].set_xlabel(\"Frequency (Hz)\")\n",
    "axes[1].legend()\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62d91c61",
   "metadata": {},
   "source": [
    "#### Ex 9: What happen when N = 12 why it does not happen before when N=5?\n",
    "\n",
    "\n",
    "**Hint:**\n",
    "Take into consideration the new max frequency after subsampling considering the Shannon Nyquist theorem."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "203b40ac",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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