{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "[Table of Contents](./table_of_contents.ipynb)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# The Unscented Kalman Filter" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "%matplotlib inline" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", " \n", " " ], "text/plain": [ "" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#format the book\n", "import book_format\n", "book_format.set_style()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the last chapter we discussed the difficulties that nonlinear systems pose. This nonlinearity can appear in two places. It can be in our measurements, such as a radar that is measuring the slant range to an object. Slant range requires you to take a square root to compute the x,y coordinates:\n", "\n", "$$x=\\sqrt{\\text{slant}^2 - \\text{altitude}^2}$$\n", "\n", "The nonlinearity can also occur in the process model - we may be tracking a ball traveling through the air, where the effects of air drag lead to nonlinear behavior. The standard Kalman filter performs poorly or not at all with these sorts of problems.\n", "\n", "In the last chapter I showed you a plot like this. I have altered the equation somewhat to emphasize the effects of nonlinearity." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from kf_book.book_plots import set_figsize, figsize\n", "import matplotlib.pyplot as plt\n", "from kf_book.nonlinear_plots import plot_nonlinear_func\n", "from numpy.random import normal\n", "import numpy as np\n", "\n", "# create 500,000 samples with mean 0, std 1\n", "gaussian = (0., 1.)\n", "data = normal(loc=gaussian[0], scale=gaussian[1], size=500000)\n", "\n", "def f(x):\n", " return (np.cos(4*(x/2 + 0.7))) - 1.3*x\n", "\n", "plot_nonlinear_func(data, f)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I generated this by taking 500,000 samples from the input, passing it through the nonlinear transform, and building a histogram of the result. We call these points *sigma points*. From the output histogram we can compute a mean and standard deviation which would give us an updated, albeit approximated Gaussian.\n", "\n", "Let me show you a scatter plot of the data before and after being passed through `f(x)`." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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PZv15JGWoWdA0IC4Hx5hIBMdYx3Jgvvfasd/IuFh/7pcf+4t/+yRJGTrO1jY32tcb5a3o6608n6txs/NMv9+/6WO8F+f8p5566qbn/Lf7Wd5s/+/WGvNWv2Nf/Nsnr/rur8/xlx/r2WX4uxlIR+C+IlgeXOzCQBR2puB4HSIipKOwLw0tJ5grJTHox3LgVBNKseA3T5fhRB0mUpBVwfVhpQ8RCQ7kgrnueB0udeC2DOS0oE3HDub50Th85WtPMtOBmAqqEMxbZ1vB+Q5EYdVYW4u8YB5dn4NdH1pmcK4Dm9avzfNyUg36LfeCtWl9HXA9WDGCa+vY0LYgpb42h18+f3fM17671v198sknN9YNzwVRgnzktXab52HLCc5xVwpM/9rrdkYNjl/tBdd9KAtrerC3hffC3uutvIYbnfNvWhjYs2cPr776Ks1mk7/6q7/iZ3/2Z/nOd76z8b0gCFva+75/xd8u5/I2V2v/Rtpczq//+q/zr/7Vv9r43G63GRsb48Mf/jCpVOq653ij2LbNk08+yaOPPoqiKG9Jnz8IvBXa4+lKm//19ad56H0Psb2YukKzcXSmQafa4+COPKNZjaMzDebnGvgIFJIqBydy1LomUtckp6n4QKvSpdzSGcvEuHN3EYCpcoflZo8Vo8V4KY0siMzV+yQH4qys9uiaDoVigiM7Crw43aBt2FgCHFtZRSym+aHdAyyfrxKVBUpRmVfnm8xX+ySjMsOZDIs9gxXbophUqRomza5BKqZSjKao9S1WLZOYIqLLHlpEpKOI9D0TQfQQbQfRFVhVNRY6LlFVYV80Tr47y8SuvbQNn6jv01loo0s+rifStiz2D6YYHE5xdLZJNCLhaQJWSsWkhxS12FlMkctEePZindHRPPftLvC3x5ap9ywqXQsTj0I8Qrogc3gsjSwKtHQX03YxZ+tMFuIMpDSSUQkBGExFkSWRS5UeaU1mebbB8moXVRKxXI879pSQRAkBn0OjaZ69UKU912QhKvPJByaIqfLrasUg0GbZrselSo/JYqCFG0xFWGmbnFpscu7EK+w4cDuCIKAKAgOJCLsGE5xf6W7R0q2z0NCZKnfYU0oymtXe0Dh9K/t6K89nM290nlnXjN8M78U5/5FHHiGfz1/3HC/n7XqWN9v/u73GvJn7sFnDrgg+X/jykyhj+zm4o8hoVtsyH+wpJQE2jrU+L/zh//s8PWx6JnxjGaIRAVkQ8ByFpbpHtW+jm2D50FLS/NwDE4xkY1yq9klFZabKbS41qtR9hR27BvHNVVSzTSQbp+NBIaZwXybCfN0gXozTVURKGR+z0efOvYMsNvpcKHfYPhRjLCIwc+4MY3ffQfN8A0ORGMvG6Dgufb/HPRMZal2LixfrjAzk0VQZ1ffZPZCgkIjwtdNlllZ7aMU4Bw+UqHVN1J6N57moS12GUgoeIlOrHXzZZ38pwX2TBebqOttyGi3dJhGR+P58izFFpG97HJzMs70QZ6Ghc2qpjee59Cs9Fus69x0YoZSO8uJMnYMTORRJZKrcYbIQ5dhzTzN44DDFpMaL0w3mG33GsjEO7siz2Ogzt9Bi+1iapO2zp5TkxEKDlZOrjJfSDKRi5OMKt49lWGmbfOdchaVan6QmkUlrlMtdTjYaLDV19uzfzj+4b/tbPi7f7ffireDtuIYbnfNvWhhQVZWdO3cCcPjwYV566SX+y3/5L/ybf/NvgECDMzQ0tNF+dXV1Q6NTKpWwLItGo7FFU7S6usoDDzyw0WZlZeWK41YqlS39vPDCC1u+bzQa2LZ9hfZoM5FIhEgkcsXfFUV5ywfP29Hnu0m50+dCVUeWZcZyV97DzdiuR7llkE+o1LoWpXQURRIZzSUYjsFoLoGiKJQ7faZWe1R6NsVEhOm6zmLLxPHh2EKbo7MN2pbDw7sKjGTjrLR0zq12MS2H752vMpiKMpqN4ToQkSUcD0ZyMWRZ5o7xLJIk80O7C/yfowtMV3u0DJuRbJy4KnN+xWB8wCSlKTQMh1RUJh6RGExFGUpr5OIRWrqF7vokogoT2Ri3jafZO5xmpqrjey4jmRiXqh3OLHepdHT6rstAMopue1iug+37REXoOS6+D6IkYhk+jutSb+tYLgzKImdWu1gNaK8sEJEk9gwmaRgWc7UeuumCAKbtcnS6Tlt3KaZVHt0/yOGJApl4lIbusGsgzlJDp9K1eG6mzoVqj2cv1BAFnyOTA+waiOP5PotNg2rHoqU7SCLcPpZhsW0wMZBAN12OLbWZqfQopTR+9M5hcskoe0pJCkmNclun3Tf57rk6qx2b75xbRlNFOqZLQ/cBgdMrPb56YoX37R646nhZH0cIIpWuSb1nsaMQJx1TWemY9CwPWZbJJaN4vs9gFAZSGjXdRfB96rrLV0+ssNw2kWSZO7dlKbeM18ZYXkKW5Y3P62Nx/fPNcHlfb4S3oo/rcbPzzBuZk8I5P+DtfpY32//bscbcyPvyeud5vT6mFtp890Kdet/hkT0FEEAWJRRZptZ3uVDV2VmMc2A0SykdpW85uMsdcskotb7DhaqObrzm9tBxodP3AZ/lXuAOlo8EmmqA56ZbmO40R8bz2L6HLIvEFJmYLNDULY7OtGjrNvlElJZu0bU9XN9ncjBFRHUxHJ+G4TCYVBjNxCmlo4Fbpi8giyLnKjpTdbhPVviR20bIaApN3ebMcoeYJtPSXXxRZCSrcWSyQFSVqXZNbt8WvAt3jmU5OJJhLBNDlkSaps5AWmNPKUkp22GyGOe7UyvkExFyMZl8Kk7TcNkzlAZgsW3jCz6qLDOYibLYMFBkGUVRGMwInF7u4CCSiqpsL0oMrR0HRFY6JqWUxp6hNINJhS934NXTFT56cIhdpRSIIpOFGNWezfcXWpxZbKMpEo/sLzGaT5CMqTR1lw8fLDFX16n1LFY6Nl3DodoxkSWR6dUeT5+rUEpHsV2Hatvh/Gr/bd0bvRf2Xm/lNdxoP296RvN9H9M02b59O6VSaYt5w7IsvvOd72xM+nfffTeKomxps7y8zMmTJzfa3H///bRaLV588cWNNi+88AKtVmtLm5MnT7K8vLzR5oknniASiXD33Xe/2UsKuQqldJS9pSSldPR125ZbBmfLHU4utjhb7lBuGQAokrjhyjNf75NPqKSjMufKXbqmjed6lNIRal2Tl2YCQSCnRZjIJ9EUmdmazmrLZLrS5/xKl2rHJCpLNHSbV+eavDBdZ6HRZ7mls9zUmWv0+erxZWbqfTRVZjCtsbMY5yMHSozkowjApWqPxUYfAYHhTIyO6VJu6xwaSfHQrjx3j2XYlo8zVIjR6DvgCxwcTvHI3hJt0yMb17hrW4Z8IoIqSQxnNUrpKMOpGOmIQimlMZlN8ON3jHD3WA5VFLBdH0QBVZGodwxemW5xognlhoHlueSTUR7YUaCQVJGEwNRqOw66ZePhMZ6N47nw/EwdgPt35DFsjxdnasQjEosNne/P1Vlt97AcB8txeHWuzlS5zcVKh+l6nwuVHhdXdQzH58hkgZWWTdtwuWMkzaGRNIWkyoWVLvWexUrboNoNFo5ULIKqSkRkiX3DSX5od4FdA0kkER7YXeCByRxJTWW5pTOajTJT7XC+3MZ2PWzXw3E9dhbjANR6Frm4iiyJzNT6zNYMcnGVUjrKVLnDmXKPFSMQWG4fzfDIvkGKyQjpeISDwykOjqQ3xtrmMTaWi21sQi7//ma4vK83wlvRxw8at+qc/3Y/yx+EsXIj78vrnef1+jg4kubgcApfEFhpm+Qj8ODOAqO52MYaM5qLbfQ/Ve5wutxhqtzZ+L6jX/v8ZSCrSayvUkkJzpXb/OXRWb52cplvnC5T7Rkoqoxp+/RMB3wfTRURRYl0ROGRvYPctz3HRw8O8tDOPANJmZFsjHRM5my5Ta1vc9+OLPdtzxORJKIixBWRfDKCLIkUEhHu2Z4lIUtMrbQZTKr8s4d3snckQ1SV6Voeta5FrWthOLBrIMWuUorBdJRMVCarKcTUQNFxvtxhrm6gKRLv312ilI7SMhxkSWQ0F2NnMU4xEeHuiSxDKY0jk3kG01Hm631WWgYIAl3dJpeMsLOYYCAdxXE9YorAS9N1vnZ6eeOZJiOBRbiU0rhne54f2lVEEkUafZvJfIJcQmW2alDrmMxUujx1pky9b9Ho22Q1hUxUxnE9/ub4Ei/MNohIAh3T4eJql/OrPXTTwQV817/B0RjyTnJTloF/9+/+HR/72McYGxuj0+nwxS9+kW9/+9s8/vjjCILAr/zKr/Bbv/Vb7Nq1i127dvFbv/VbxGIxfuZnfgaAdDrNL/zCL/Crv/qr5PN5crkcv/Zrv8ahQ4f40Ic+BMC+ffv46Ec/yi/90i/x3//7fwfgn/7Tf8qP/MiPsGfPHgA+/OEPs3//fj75yU/yu7/7u9TrdX7t136NX/qlX3rL3H1CtrK+ANwIpXQU3XYot3TG89oWAcL14Nh8k5bpcWA4TSmtMVPrM13psdK1ODScohAPNHkP7ywwUQgWh74VaO9/+PYhBODCSoedxQSyJGJ7HnN1neFshFMLTV6YqSO4Pq8sNpksJhAQ+OHbh3FdDwSBSt+klI5gez5d06HZtblU6SIioNseJxY7IPgICBwYSXJ4PMuFlQ5/9coiuukynItxx1iaO7alKTf7rLYhHlE5t9LhpdkG+B7xiEI2ptDo2zQNm+W2ged7RKIqMR9uH86jyvDSdAWbYMOfi4tERQEXl1rbYSQTZyitcWqhiWX7IIpkIxKO6/PKUgtDd4ioEk+frxFVJGbqBrvzMXwPzq00iUdkxjIJzq20mVrtkYvJZOIRhlJRHt5TJKpIJCISTd3mtrEUXcMhGZU5ttBGkwWqPYt9pSQrLZ2/enmRfErlJ+4Y5eO3D7OnlAyEhI5JMR0lFZVYbpoc3p7npeka9b5JMa5ydKbJYDrKJ+4IppoLld6GUClL4sbYOLI2PkbXNgEHR9K4jsOCfn5t7AVj4s5tWYY2aR2VdLAhySdU5uv9LdrIdeFjPK/hrAkj76VN+TtBOOffGmy25u4tJa/6Pl3vd5vbrb/TV1McxVSZDx8cCo4Vk5DErYkPLl9jDo6kN/6/vgZ13a19SgQbGUWEiAorHZd1MaSUFnFFBVn0sV1YbRkcX2jxgb0D/NhdSaodk/Jpg2RUYVcxsLLKosCXjy+xoxDnYrVHpWOhWz47ignOr3ZZaOjcNZ5mutZHdxwaFnz1VIWILKFFRFRJYjQTpd61kUSJQyNZBtNRXplrsKeUZGcxjuN6DKajG//uWw4nF1tcrPaYqfXxBTi71OLCahcEgclcsJGXJZFiIkI+oW4IWzN1nYQqMlPTOTKZo9a1OFvuBIJCMoIPeK5Lo+9werHFTE2nsmaFTUsijuux0NDJq7Bnd4Ezy+2NY7UMh1xMoZBIsLeUpNwxKbcMnr9U46WZGggCCVVCkiTKLYMfvXOYI5M5OobDvTuyRFWJyXycwUyEL31/nrgChdTrKxRD3nluShhYWVnhk5/8JMvLy6TTaW677TYef/xxHn30UQD+9b/+1+i6zqc+9SkajQb33XcfTzzxBMlkcqOP3//930eWZf7hP/yH6LrOBz/4Qf7sz/4MSZI22nzhC1/gl3/5lzcyUHziE5/g85///Mb3kiTxla98hU996lM8+OCDaJrGz/zMz/B7v/d7b+pm3Aq8GbeJ1/v95u+afZsXphs8vFve0q5pQaRnU0xrWzaChuWQiSsU4xGqPZNcXGWikGR7MciuM1XuMLXapZiMMJqL8yN3pJmudvnG6RX2DiVwPVDEYEK0HZ96XyeiSgwmVOo9j75pYzkCmgrPnm+x2OojAA9OFnhgZ4FGz6RreGwvxAA/8POs9Pg/RxfYVUxiOS6GE7iq1PomL882uX0sw9dOrdAzHW4bSTGYiqLbNudXOqiKxJ6BJGN5jb97dZm2aWNaLtmYQiGusn0wzky1RyEbQ5JN2jUHWZCYq+ukl9pUOibj+TiSCH3LIyL73D6aZTATodt36PVdElGZ2UaPTt/m3okch7elqXdNyu0+iiiwo5jitrEcr8xXKSVUohGRjm5xcrlFLKJQSKgcm7eo9WzuGc/QNl0M02a62iMTk5Flke15DcfzkQQwLZf5lk5CDZ5ps2/zzMUajZ5F23DpGg5nlls8e6FGNq5y75FxiskohURky8ZgfeysL/x9y6HSNTcWfAg2DYcnciyfDHyUR/NSsPlf+53tehvWJYCVlsGFSg94bUNRXvtbWpNp6YE27XoC7Zt9N96LhHP+Dwabx+bbwbo2f28pyVguxny9z9lyUCvieu/M+u82t1PWhPzN79Ll79ZYLnbNDDyb28VUmXu3b43tkIHNv3TX/rM8MA1wNn03U/c4slOjZ3vcPZbj/EoL0/NZbZvctS3H6GiMqdUunudz27YMtuOhWy4nFtu0ejbFdJTBpMJAQuXuiSypqMxtYylaPYcz5Q57BlNYFbh3e5ZK1yYVkelZLrsGkhtz30QxwdHpGn93Ypm7x9IMZWIb2n1ZEjm11OLEQoOG7jCZjzGai7Pc0nnxUoOIKnH7aBpFkZgqd2jpDuN5jcePLzLf0Hn0QIm9pSRd3aLea+K4HqO5GI7rAYEQVetaGJbDC9N1bM/j7okMwiblfLmtc3a5zVwdnMUWT5ypAj4fu20Ex/VYbulcrPY4MJwmqtu8PNNkLB9hsphgpWUwV+tTykRZaulMLbfZM5RiNKfx9FSNY4ttfuLuEbqGgyzJDCQF7tuRu8FRGfJOclPCwJ/8yZ9c93tBEPj0pz/Npz/96Wu2iUaj/MEf/AF/8Ad/cM02uVyOP//zP7/usbZt28bf/d3fXbdNyJVsnrwvn7Bv9veXLxKbv9tTSlJpG+wpJV/TOsUkMirsH04xmk9s/AZgoWWS1mReXWhhuR5ZTd6izd1TSrJQ67LY6FPrW0CWasdksaEzlIpyZDKPYTlIosCewTjHFlwGBmLcv7vI+XKXQjLCSsuimIzSzXsYps2rSy1iaoOPZIY4uxykAAWfV+db1HsmzZ7JTK2P5/v84/vG0G2XO8eznCsH5+H7HjPVLjlN5YHJAglNZabWIRlVicoCK22Lr58os9wy2DeUJCKJnFlusaeUYSAR4eWZOr4rMDmQ5KV6DywbxwPTdehZLo1+EEyniAJ7SwnumMiSjEg8frKMAJiez3g6RjPqbCxw51bbmLZLPqUxXkiw2tYRRQlBgE7fJhNXScoyumVzqWKTiMg8srfAUFLjW1OraIrCw7vyuD4stHROLHawPRfD9khEZZ6/UKPWs1hu9dldTDJZ0NiW1dhejNPq2zQMC912GY5IIApUOgYZLfBZvHwjvz7uTi62+M65CsCWGAAIslJ891yF7QM6Y9n4huVgfaytb/R3FuNXuLGt/3tz7MobHdu3KuGc/4PBlnk7+db7Q1+uzb+edv96v1vn8nfpeu+W7XqUO4Fgf2yuwcVqjwd3FDYUQVvatQwUYLOnUBQwCCwEKlsFBROo9iwymkqtZ7F3OMN0rUfbsHlhus4PHxriI/tKPD9d4+mpCi3T4afuGeGj+wc5MJLi1GKbF2e6nFnuoSgi8YiKZTs0dJuDw0l2FeOcPwPJiMS+oQy5hMpUucN4McG+TckNMpqCZbs8c7HG/hGHQyMZ8gmVxXqfvmExXdNRZIFSOo8siRwYSeO6Ho7nUUppRFV5o++Vls5T5yo0ezZ3jWeZKCR47uIq1a6B4bgba+rUSmdDybLS8tiW1zi/2qXRs3j0wBCKJPLKXINLlT5T5S6X6rDHE9g1mGDXQBJlTVhpGQ75NfdNw3IYykb4oV0DNHWbJ0+tUOtZ3JbUqPQsTiy0SceD8bnSNXA9F91yKbcNYqqEYTvM1nTu33ndYRXyLvCG6wyE/GBxo1rNzZP3G9n8XG+RuLxvVZFp6w5t3QnMlgUNSYTBVIRyy0C3HV6eaXJ4PMPeUpKUJmPaDpWOQaPv8MJMnYZuc+e2LG3dYbltsdzQuXcyi+N6HBhJU+0YNPqB3TiqyuTiKsPZCGOFBIv1PreNZNhVTFFt9TnW7PO+XXnGsnEGUipVw6aYinKu3OLpCxXOLLdIRGV8z6fet0hEZPJxlbgis9wy8XyR2VqfQkJlrtbn7HIHURCIKhIXKl0OjGaYrvZZbPQBn4uVHqVkYNI13CAWYbVrs0fwySVVcokIdE0GYxGyEdBSEVKewK58kuVWncVGj2w8QjqukokH/rIZTeHUcoeFRo+OYTNYTDJRTDJd76GIMJFL4Pkeo2mNs+UWEVVCcHyafRPT9skmotQMi5wewXRdOqZNV08wPB7jttE0+FBKa5xb7TKa8nE9n9Wuh+t7RGSBbbkYjuPx9IUKz1+sM5LVsBzYMZCga3kkVJn7duS5cyzDdKXH//n+EiPpKP/04R0bi/v6uHNcD1kSmSzGqbQNJotxjk7XNjYDg0mFpgVK36Y932KxYfDQmkBxtY3+5eN+s/UhlpOvEEJuZmyHhLybbBmbnvs6ra/P1daKy91Ab9Qt9Frtbka4WGmbXKjqpDWZi5U+Ld3Cucq7um4J1tQgjeY6EqAQpHc2vSvP8cEdRfIJBR8REZ/BRBRP8BHF9XPVuH0szZ/NNFhs9vnmaZUjO4v0LI/ZWp9UREJEIBtXkUWR5y80cT2P5Ggaw3YwXTi30mM0l6StO7R0h1rXQkmLLNT72J5HtWcSj8rUOhaFuMqd27Is1Ps8eWYF03FRZJHD41lkSdyw0EwUkzx9vkK5bfPQrsJG34NJhfFsnG05KKU0Ti62eOZCnb7hcHS6zlA2xo5CHMt2ODbf49hcDVmUiEclzi61MRyPgWSU0VycWs9i12CCgbjE6tIcuWSEB3cPMLr2TPMJlagssljvM1mMI0sijx0aZjAdxa922TucoJCMcNtolo5hM7XSRQDGszEM0yObiKBbLudXujR6JvWuRd9yrzkOQ949QmHgPcKNbuw3T96bJ+jLzdDXekmvt0hcq+918rHALWB98pfEQLN++1iKXWum6YWGEVgGYoHPfa1nbZzLI3uLnF/pMFGI88zFKjsKcXYOJnnqbIWuadMxHLblNTqGy7nlFq8stkmvBWM9carM0bkmsYjEY7eNUus47BlMMp7TMCyPRESi0TOodQXyqWAD//CuAVRF5KXpBhfKXfaX4uwfTaOI4trE2sWqtGkbFk9frFLrmjhesIjNVruIokg8IqHbLt2GzUgmytjOGMWkxqtzLXKaTKdrUelbpFQopJPYno8iKzy4I8/plRaqJNIxTFY6BrrjcHsxywf2Fvn6cQfBCzROza7JnsEE+ZjKdy5Wman2uLDaA9FnOBVjLB2jbTustg2GU1FqPYuZWpd0PIIi+lys9CkmW8zWdaodg/GcSUJT+O5Mk47lgO8hiAKLbQPPF9mW13juoo4vuNw5niEiC0RlgUxew3U87hnPcfu2LLbrUe0agLhlcS+tBbEtt3TahkMuriJJIi9crFHtWXTXsoWstE10F+4eTa+5HrzmWnb5Rn+d6y0wr/eOXGtsv96iFS5qIXBz4+Bmx8zmsWm/SWHgrbCAvd7534xwMZiKIMsyKU3GdT0Kidc2xZvPsdoxWW4Z1K2tvzcJXIMcDy4PTR2OgeNCVFFJREVOLXSIKCIisLuYoNzWaRkOnuvzwM4ii80upXScdFSm3DI4udwiE5MYzyVYbRmk4xEWmjqKBN+9WOWFaYnVLhR0m+WWzoGRNAlVxLAcFup9nr9Uo9o1cXyPyWwMTRLYlgnSsTquh+P53DGWZiIfxMbZrkela264P47nY2TjKl3dotozGc9rVDsmDnBoKMVEMcGI6/EP7h5hsdFnqWkyUQwytTX6DpdWe3Qsh4QqUUprxCMyCQ1szwviQwYDd75MVCKpQqVjcGg0u/FMV1oGXz2+yLmVHqsdnXhUZUchju15fPmVJVqGzft2Fqh0TFqGw+1jaWodi7bhcP+OHLbn89J0gx0DMdqGxUrbpK0HDzC0xP5gEQoD7wJvx+bhWhv76/W/eYLe7CMKvO5LerOLwWYf0VxcIdE2WWwYdE2HWtfc8P8+PJ7llfk6F6s9PnJgkFFF3vB/1BSZvuVT7ZnM1fq4ns+ugQRpTeHodJ3ljsnBoRRJTaHRtRlIqpiOy3fPV7FsG1n0sOxgErx3MsupBYGZRp90VOUf3bMNw/Wodk1OLDRo6w4RWeSRfSXOLnc4vtyiadrEojI+AtW2wUuzVVZbJtmEgggcNV1KySh3jGZwPY+ebrNQ62HZHhMDcQaSMW4bSzNXM3hxuoJhe9iOh+d5KB786B0lGobHsfkmD+0ewBMELpabdEyHlbbO8fk2mizTNR3mm308H56/VKVluAw3IxwcyZJUZMbSMRw8cvFIkHrV8zkYTfOdnkXHdtg3nGK+ZnD7WIodxQSny12iihi4DlV7HF9scXhbhr7lkYpKtHSffYMJIoqIKisc2Z5jz1AKfHB8j795ZZmTiy3uGAviDiRBoJQOFrz37RrAF6DSMWkbr/n0r5uf17NnuK5HrW+zeyBBKa0FC6NtMxqHsazGxZpOQ7cZeZ1xFyzAdY5M5q5wM3g9zf+1xvTrLVrhohYCNzcO3siY2exu+WZ4Mxaw9XNwXO+KGJ2b7WehoeNu0uTXuxZdy2NUla9IMABwx7ZASPi7F+dobPrd+pu6LghECAQEgFIhzngxzkAqwnPnKnQdl6gjcHKxzYVyh0xS5d7tebSIwu1jafYMxTk238LxPO7fmefYfIPpao9X5lqcXOzw6L4BDo6kKaUiSALM1Pp0VmE8r9Ho2zx9rkJDt7lY6QXJM1IqPh4XVnos1vvMNwwMz2e63sN1fRKqRESWGVyzpjuuR71ncXKxRTERoW04NHoWF2tdqi2Ljx0qUUxEeHhXYSM9aa1rcf+OIt87v8JTZ6uMZKKYrk8qKvEzR7bR7FkbKU8LiQhN3aZpBNYLgOcv1Tk4FGMiAfdOZDfuefCMejgOxNUgMPqFCzUMy2X/cIrhrEbWkji/2qVn2VQ6Jo7jcqnRJ6nKvG9XkXJb58JKh2JMQRIDK05UCcbv3ydL7K2g8AmFgXeBt2PzcK2N/Ztx/7naS7p5MZha6bBQ721s3uDaFoXN1Hs2MzUd3XLZM5igEI9sZD9o6DZLTZPZWp9m3yaZUzlb7iCvZT2o90xKaYWRjEZGkzkwkkYAzix3KSZkGn0Hw3FoGS7v35snHVcwz9UYiGkIwxK1rs1Co4+myPQsHwmBXcU4tu9xcrFDMRGl1rXpmTaX6n3GKz32Dadp9R3SkcBns61bnFnpUusYpGMytutS6Rp4wPZ8gscODpJLKkyv9IhGZCQBVro6Z8ttREFAEqBrunR1i1wyguuJeAZYro8qC8w0dDLzDSKSiBqR2Tuc4kO7B0AUObXU5uXZGtWeyXBKI6IoWI6PJAvM1jtoskIsItIyfGZrfRp9m7gqc3hblqFUF9v1mCwkSGkq9+8scHqpxXy9x1RZ5fxKj+WmjigEglciKnFkZ57nL9SwPMhFooxko5xf7fLArgId3WGm1gm0aE2Dcsbk0FqGKMf1ePLMCqmowu5Scovfqe16QcB4VCYdUzg6G7iK5ZMRqh2TwfXx4wWpaEeyGg3DpdIxeerMCtJVMo+sZ+PQFJF6z9wQIK/1jmwey+vj9Vrv5estWn+fFrWQt4+bGQdvZMysj8+dhesUJLuBTcvNZIa7nHVhe7Nr54vTNQ6OpK8oAHg9yi2DU0ttZjpBgoDZhrkl7ud652hf9mpvNhREAUkCc814MpqKsm8oxfG5OieW29w+kg4UIMsdqrpJw3Z5YIfI7sEEZ5faVHomTcPmO1NVDMcjE4/w0aEkyYhMuW3wI7cPc26ls5ZAIsXBkRRPt87zwX2DTK32We2YlFIRjs83aRsW8zWddFyh2bcYy0U5PJ5DAL5yYhkQODKZ5VIlSGZR61t4rk9SUzhX7pLdrpCLq6x2TA4NpWikLQzH4WLV4cBwcL83r/WO56NbDpbjMd/QiUclDoxmmCgm0W2HheUugxltzcIajL2FeuDS2tRtTA+iymsJP8otg/OrXWRZ4P+5awQRkZZpIwmBYDaWi3NhtcX/faXM7qEEO4uxQMHXt8hFFMptnbSmkIkpzLd1Zis9dDuwPsCbG4fvNLeCwicUBt4F3u7Nwxvp/2qafLj2hmlnMU4urnKu3GWm1uehtQnkRl6YwVSEI5M5lluBiTaqyuwsyiy3dBp9m7u3Zbh3e4471jQfaU0mn1BZaXnk4iqjmThROfAvrXetjfSkI9k0iw2DQlJlRylGPhlh/3CaVs8OJvOOybenKszWeuwsJrl3MovgB9kUnp6qstqxGM1EicgioqCwLauR1RQuuh513SCfUOhaLjONPrppkk2oJCIKC3Wddk8nE1Ox3CBrQ8fwqPQsioLIobE0r8y3cFyPmVqHqCqD5zGYiZKKKoxnE/SXW/iI+J5HIabQ0x0W2jq1tsnuwRSpuMorcy3yMYXRbJy+6TKWixNTJe7cJnN2qcWx+QaO5zOQ0hhNR0lHZVRFotIxeW6mSioq0zEdJMEnpojM1/v8r6MLWK7PWDaKhIfvewxnE1iOhygKeK7PgZE0I9kIsiAyVW7z7KU6j59c5s7xHJoisS2vBQuZ51JIRBjNxVio90lEZFJRmcliHNf1yGoKtutxbK7BC9M1JFHkjrE04CNLgWn7mYs1ZEncyCBiOUEq2v2jwVhY7QSZpi5PfbgehLxnILFRu+D1uHyCv9Z783qL1t+nRS3k7eNmxsEbGTMbcTLXsQy8M5sWfyMz14vTtY3g/8uz/qxzrfSjC3GFrgMCbAgBtuvxylzjqsLF+jtuXuUY6xhAUYXeWoTx1EqLes/ittE0Cw2duydzLDcNRtIx8jGF+WaPC5UOqgzfPFvhwZ05bhtO8/Jsk3PlFqeXOtw2NspoNs5cw6BtOMhiEDsmiwLbD8XJR2CpoWPaDjuKcZ45t8r3F1psy0Tomh4ZTaZtOExXdXYUkyQ1maF04J46UUhQ7djEIxIvTgfZgsayGoosIa+lWH7+UpULKx1kSaJvmezelPp1PRVsKR3lwqqApshEZJGUpuB6HmeX2qiKRCoqb3wWJWEtZiDGaC7GQ5JIKiJwPhZY7dfn1XxCxXM9DNtjKK2xazDJYrPPx24bIqbKKGmR6WqH7QMxNFmkY3q0DAtZkrBdn9mazngeUloQH5eLKZxaanFoW/Y6T/AHk1tB4RMKA+8Cb/fm4c30/3ra0s0vxWguRjER2fi8zuu9MMpawRSAQjJQ89iex/nVLklVpDSQYKKYwHY9vnZikfm6TjIqE5UljkzmGV1zM5mp9TeCUO+eCDb2Y9k4uYRKs2txdLpOtW3QtlyWWiaDSZW4KjNb6eF6cGA4yGF9qdLHdjySiohpu0zm42QT0UDgqPZo9y0WGjqG5XBgKE0uFkEAJF8kG1coJTUc18fGp9ozeGmmwaP7B9lZjDO12iVeFklGJQRfZKmpU26beB7sGUrguAJnVjpsE8G0bU4tdXA9j47poMgwmNJIRRWW6jqNnklEgJbpMFmMs9oxODiSIaZKJFQZ2/GIR0RymkIqolDp2eTjCkbEo2WYNHULw/b5f5+fIaKoHN6WYSAZJSIKrLRMput9VFliXymBIIrsLMa4Z3uW7882cFw4vtSgZ7vYtsNCw2SyEOdDh7dhWA6rHYue6fO108vcsy2IGdg7lKLWs7hU6XGx2uP7c03u2pZZCxK0AQHH8zaeaVKTObXQQJOEjSJlpxpwfqp6RbXhy8flej7yPaUgiO+NaGfDTX3IDzLXS8m5ztu9aVnfPK73v7kOwLW4VvrR28cynIkHlr9YNFhHXplr8J1zFVzXYzQX31iHbNcjqUpMFjSibM0YdDnNTamGDMPBdT26dlDk8LtnV7lrPMfOUpJqu8/JxTYnltp8cM8AXd2i0bX44duHafUtfAR830cAFho9Xp1rsncowd3jeT7QMdlVSjKYilAz4H+9vEijb/OBvUVEUWY0HeWhPUUurHTZO5Tk3h05Gl2LRt+lbbjcM5GjY7hM5BLsLcnM13t0LY+0FlRfz8ZkFho9ZqpdvnZimelanw/tK7CnlNtIF7qulFtXfIxm4hwcS1FMR7htrWCZ6XisdPpM5BNsy2s0+w71jomAQLllMLZW4M22bfLRwGo/tdpjuaVTTERQZJmhjEYhHuHlmQaG4zNd6aFbHgv1HucrXSZyMfLxCNDhA3sHMGyfiUIM3Q4UQNsLcYazUZ4959LV65iGc9Xn9oPMrbA2hMJACHBtX9DX2zBd7pd9vQDMdY2W7XqcXGhTX6tA29Id4qpI13Bo9T36TpBFyHU9vnuuRt9wSEcVhrIx9gwmWagHQsCRyUATdaHSI6GKXKz22JbTWKj3OLHcZqHeRxBEJosxZEHkwHAaQYSZqs4OOQjyAhjORnnhUoVKz8L3fAYzUbK+zyuzdfYNp9hWjFNKRZmtdKl3LW4by/Lo/iEODqdo6DaVlsF8XSeXUHjxUgV8j3RUodo1aesOM80ePgJdx8HDJ6WJ9A2PaERg92CCqXKbkyuwcLxMpWeiCDCcj4MvMZiWaeo2U+U2jg/T1TaWI7CjGEOVJbqGzUA6ynBOY+dgCmmt6qOsW3xg/wC3j2URBIHHTy7z9RMLJKMKUVkiIonsHEqhyCJaRKbc1BnOxDg8kaWYjPDCpQZj2Rjfn23w1FSVTEzGF0DXXXaVUsiVHruGUiy3dHaXkrxvV4H5Rp9zyx2en6lRSmsbm/d8QsV1PS5Wems1BzRGsipPn68zVzfYORAECF+q9JiuGvTtKglNpdzs4XgwnlLYU0peNUB9s4VgXTOZ1tQrxt7NBsOHhPx95M2O6ZuNBbtaHYDL+7iexS0fZctxDq6l1LQ9j2MLDZZb0Y155NWFFo2+RTEFnfaV5y4R1BvYLCgIIpxabhFXRRRFxLRAEQUEfLIxleFMlI5hM1lM0rfaXKr0efJUmVcXW8gCjGQ0mj2HuCahKRKtnsNK26BneUTlYD2rGWDLLj4+Hd1meyHGkR1ZFFEkocpMV/tM5mMcGs3iC0E9nMF0dEu6Y8NyeGBHHsdzkQWR+Vqfr51cZrKQQFMkdhTi7C6laBsOx+YaFBKRjUruxxYavHTJIZtQuWMsQ8/y6BgOiiLR7FscX+jw0nSLn75vFHwPx4dcTNmwxCzU+9iOg+sFlgHLdjizbJCdzPNDu4sb99IXBA4OpygkIjx/qU6lEySA6BkuWkSm0TeZrfuM5hLYHvQsj2IiSDhxcqHBl1+Zp6r7PHlmhZ86sv11x2LIO0soDIQAbHH/2Zyv/UYWl9dbQNb9TO/eFlQKXWmb1HrWRvBoMRFhMB2lkIxQbukIfqDFmchqPLwrj+cHRYfctYqyL0zXqXUNxrIa+4bSG1Ucvz/X4FjPwvd9UhGVjx1McWgkSzah8sLFGsO5GNWeydPn6kwWYpRbJpbrsNoKAplHUzHu25FFEgSevVTj1HLgQ3pkssgPHxrifx+dY67a45kLFXqWw+GJHLWVLl8+tkgxHuWlWYPZSpeoKlLpGLR1m0REwvV9BhJRHFRGEhpd0+bCaodLKz12ZFMMpDXOz0G73kEARFVhWzLK3ZM5FuoGs/Ue9b4JtkvHcikkYoxm4kzXeyy3+kxXu/QsB8/3kX0w7MC0a1geqajMt86sgu/j+CJ3j+XIJhQuVfocm23Q0h2O7MihCAKiJDCWjfHidJ1m3+LuiSw93WEsp3FoNEVnLbVdMiIhCCLfn63T7rs8srdAz/JYbVvotse6jnBz8aHbt2W3aPoAFhsm47nXqgMfHAlS9QFr8SE2sggDqRj1rkV9LeBtvdZAKR1U9VztGBubhsvH3/UCikNCQrYS+PK3WG7pV32frsflCqV1q20pHb3mGuJ6MFPtIcsyo7kYMVVmNBfn5FJrYx1YVyiM52PcsS3D//fpc1f0IwNpFVQFbBuqa4EE1TYcn2siyQK7CnGyhQiKInGu3KFnOwxlNLJ2lEbf4sBoiogkcsdomoWmQUyVycUUpla7PLAjxwf3FVlpm3z37AqiKLLc0unoBmebMJL0cRyf52fq7DJsOoZN23QZz2m0dIunpnrEoxK7igk+dOA1N5uFep/ymrtsz7R44uQqQ+koqx2dpu5QSkc4OJoJ4vKyMU4utjhX7nCx2mP3YJKDI2lOL7V46lwF0/L42KESd2zLbQgbqR15klGZ2bqOLIo0dIfFVp/teW0tXgCev1TD9VwsK7AMtA2XlmFR6Zrcsz2PIon0LYdyS6eQiDCyZpl3XI9yS2e2rtPVHRYbBtWuxXA6RlKV6Bk2R2frfH+uTrlpkNAkwOEf3DN6k6My5J0gFAZCgK3m5ZuNlr+xQmaBuRVeSyW3vmjsLSWJqTKaImM6MJKJ0K708AWIRVVSURkBaK5VbZwsxoOc0+cqvDBT50cODXP39jyPHRrGcFwqHYNSWmN7IYEiiTx3ocILlxrEIjK1jkEmLrOzmEBWJL52fInltkEhGWXPYCKIMdBthtIxdDNIcaqpAsVkhCM7BlGVKku1PlPLbV68VOXkQpu24TKShq5pIosejutzfrXNQtPAd10+uG+IeyazPHlyFVv2sQSPsWychbbOscUmHcPG9uD+8TyG63N+pc25Wh8bH8P22TkQZ89Qiv/94gy647OjGKOYjnB2tcPxxTaNnoksQjIW+HiW0jGGklFenmtwqdrhxGKHvcU4H9k/yEO7Cnz5lSV022P3oLbmpuVzYqnNQzvz+ECzb7Pc7PPKdJ2O5XL/ZI6dxRRnVzqM5uIkVYn5lo6MhCjabM/Hg4Jr1S6m5eLaHpoaxCQ0+iZ/88oC+waTfPjQ8MYCNJiO8uDOAguNHs9crPIgQZGh7YXkRsD4/uEU/WxQpG5zQPLDewY2ChnVetaWTcPVNx2XJxwMCQm5GqV0lOWW/jrv09W5XKHkuN7rxi80LXj2Yo2e7fGxg0NsLya2WP3WteflVqCNH8spLPeu7EcBujZ4l6UdvXcyxeHJPK/MNnlptoEsikwUYxi2Ry4W4d7tWVq6xcyqwWAqQjqm8vJcgyOTecYLQVzcCxdrTBbifGWpzdFLdSw8HtqZp2U4zFV1VnUYdD32DCfRDYd0ROb7sw0yCZX7JnIcHhd5YbrGUkNntqZTTEa5f2eRhXqfvz2xiGN7jOVirLYNZElgKB1lJBfjngk4MplntqHT7NtsLwQxBI7r4boelY7JycUWD+0uYjgOJxc7tI0gcrrWtTbu3/v2DKBerLF/OEiL3erbnFjsMNfQyWoqt4+lkQU4WQ7W5gd3FrhY6fCtM6tk4yr7hgK3pIuVHq/MNzeeE8BEMcFovR8khIjLSKLIUErj6QtVvju1Qt/2iCkSB4czqJLIdLVHq/f3z03oViAUBkKA17cAXE/7/3qFzNb9TPMxidMbx4pgb9Ic2Wta/53FoBT7scUWq22DHYMJWobD3sEkozlxS6zCt84u8+J0k+cv1Wn0Lbbn45yvdGjpLo7nU+0EwVbllkE8IvLU6TK645GKKXQsF8Fy0R2fQ8NpElGJb09VeGW2SSGhMprTeOy2Ab5+ssJsTcdy4KGdeXYPxvncE6fpmg6zlR4RSeDQcJJURKHdd/AR8XywXR/ddFjtmLw832S22ufkcpt7JjIMpWOMZQQO+mmWGjrfO1dB9GHXQIJ4LMJstYvjupwpt0moMjuKCaZXg7oF6ZhC1/G4UOmwayDBB/cWeHW2jeP71Ps6rb5DPCKhKiKVnslYNspAQsH0PSIRmaPTDc6utPnA3kF++r5xlpo6X/7+Apbr0urbxCIKY9kolypdeqZDUlPZNZDEsBxs22GymOX4QoNyUyefiFCIR0loKqO5WLCJ0IOq0P3vXOSuiRzlRp/nLlQ5s9wmoki0TZd63+SebTlKaY3Zmr4WPxCQT6iktSDVniL4HJeDBerVhTaJSBCMfLnbwfUqDF/u43yzY/tWSCkX8u7xZsbXeuXet3JsKpJ4RRXwG+VyhdLm+f1aZFQoFmPM1s0ttUguryGyXpvEcT2KIlQuyyhkAP5VZP7ljoHjC8QiMu2qhSjA3tIQhbhKJq7Qt3yisozlwpHJAi/N1PnWuQrZ+RY/cfco5VaQ0vjJU2WePL1CSzcpJjR2DCTZnk/yYlfH9qFtOQyvFaucKrfRIjK3j2VeqybseSymIiy1TAzHYbrSDTKeeQJt0+HF6Rpd02EiF2dyMM54PsH2QrDh7ljuhnAG0DYcUlGZmAovXKqRiSl87NAIw+kG6ZjCQqPHpUqPZESiY7pYrsNMzSAXVzm8Pb+R7e3McpvT5Q6ljMadoylOEljtR/MJTiw0uVDpcr7cYTij8cpsncF0BMt1ObHQJJdQqXeD4nDVrslS26DVCywJhuVwvtxipWMwmo3xsYPDfGD/IH/69CXOrbSxnKtUhgt51wmFgfcYb9fm5fW0/86a7+FgOrrFzQhuLPCt3DK4sJab2fE8igmZpbbJnqEUB4df629dszxRTPABhjBdkASfLx9bRPQEarrJ9kKSxYaO6XpMLbc4W+7Q6tsYnsftwxnu3p6l0beJqQJ7S3F2F5OUOwaeDzXDpNI1aVkO5ZZJ07AQ/Dh3jWfQFJlX5ur0LY9ERGa+2WW5beF7HuOFJNm4ylAyqH68czBNudnlu+er9AyTnm4jSj4P7RkgHVF4aqqC6Xostvp4Aih+kG50tt7A9mA0rVHXHQaTEZYafTqWzR1jWXwPzlc7OK7P/pLCYErD8JoUEyoIPlHZJR+PcnAkzUguynMXapiuxx3bsuRiKv/32CKrbYuIJKJIIo8fX+LVhSalZATL9Vlp9blzW5bljsXegQR3TuRQRJGvnlhiqWXQ7NvU+zYdwyWr+ewbTpJLqLwy16DRt3l03yDfm6rQ0m1M22FbMc6eUhpJgNGsxnxDZ6XtcXS2wUcPBFooYKPgzsnFIPtHrWtRSq6VtW+bNPo2GU3eCFjfPK5ga+GxzdyIm9v1MrDcCinlQt493sz4Wi/e+EZ+ez3eaNzBzRQaW68zAHD3eI7RnL1WhPDqtQsUSUSWRE4ttYJdy2UWAB9ICND3gzoD6zHEqgSW7WI6NrbjElUUVts6uu2xZyhFq29zbsXinvEcO0sphnMxVjo6pxbb/O3xJRKKjOl5/D93DFHtWrhekKTgyGSRWtdCUxXuGYAP3b2N3aUk/59vX0SUBLbn4+wtpbhQ6SHXejxxssyOgQQ7i3G+P9vku+er3DuRYyQbYVcpwffOrtI3XTqWw/em6qTvCOa5csvYCBheV5q5rkejH8TUlVsGZ5faKKJI1/KQJJfZmsFi00BTJHQ7yH7kuj7xiES5ZWy4ED2wq4AkCkwW4yw0dGoGTJU7yLLMw3sHkESBh3YXefpchb87sczewUSQQepSA/DpWUFNhLSmstzq8t2pKt+ZWiUVVblY6TCSjvOP7hvjrvE8U+UOcVVCEAQcz79uJfiQd4dQGHiP8XZtXq6n/V+oB8FOm104Xo/1FHL1nrWl/5lqh2+cqvDQnhzDaZ/dpSQd3dni3wgCd3uBRuKjB4eYrXV55mIN3bSxXJ9MTGLHQIzBdJRiLMLJcoeObTOWibF3JEkiInN6qcl8XcewPY7NttAdh7FsnIlcnINjgavQbLXPbSNp0nGVUwstyh2TVFRmLJfA8V1enWsjiz6qLCHgM5jQWG4bfPBgknsmcszUFM6WO5xf6ZDURMYzCVpdi4gkYdge51c7+AiokoBpw3cvVLBtBw+RvUNp0ppMpWtydLZBrWvyC+/bwUQ+xvfOV3j+Yo0LtT626zJT7VKM5dg1kKTaMWnqNh3TZTAZIxPrMtvo4ro+p5c6dA2b4WyUO7dleOrMCkstg6gskoqoXKx0aek2iahMIa5iuD61jkkhEeEDewY4sdRivq5z22iKhCpybKHNqcU2iYhCpWPiui6yIpPQFAwvSANrOPDI3iIdw8VwfGRJIqcFFYfltaxS6xqvdbef/Frq0IVGH9cLLAOVns2ZpTaPnypzeDzL4bWgxbdC8L1eBpZbIaVcyLvHmxlf6+6WP6hj81qKqfW5f7UVbEBX2iYI4pZaJFf7/boL0+YSIgKvOQEKIqSkwNow0w3+Nle1uJjrcr7SxUfgwHAaUZA4NlsnJgvct6NA1wzmvKPTNQqJCB/aV2K60sfxPLq2g+36nF3usnsohSwIPLJvEGXNZ37vUBKnAEcmczw1VUV3XHxXIJeI4gtg2Q6rfYuL1S47BmLsG0pzfKHFfLVPuamjyjLv311AiyikNJfbRzOMZoPsaNPVLt84vcKH9g+yezC1oSxxfB8ZNjbzputxYqHJ3uEUo9nAan6fm8X2PFbaelC7JRWlpdscX2yjKQK67bOjEMcX4G9fWcD1fFb6kDMdUppMTJXZP5xmtWUwlI5QjClcqHQZykQZykbYNZAkqsp0TZtzK20GklFUWaBnudQ6Laodiwd2FhjNxPnO2RWOL7ZZrHfwgbZuhQqWH0BCYeA9xlu5ebnaZLwezLU5L/RySyeqiKSi8kYZ9ddj88Zvc5EZw3IYTKtEZQnP83j2fIXZuk42pnLf9hzj+RiFZISVls7jp1a4eyxNNqGycyCJY/mk4xK66XNsoc37oipDozGKMZWFWp9G3+Lx4yvEIyKrHYt6zyS6loMZATzPIKEp1Domo3mNM8sd7hrLMNPocXSmhuV4PLJ7gI8eKuF48PiJZW4fTrHUDKwJewaS1HSLnuFyYqFBpWeRT0TRLY9MXKHcNvnCCzNkNBXD9Wj1Le4az7F7IMWF6TkcPwiaTWkKs/UeIHKp0mKlY9LVbf7u2CJ3b8uy0jQYTEWxHJeJfJLltkU2Hvi7Xqp06VsuzZ7JQCrKzoE4FyptzlU6iIKI68O+wRRd2+VsucNIViOrqSQ1GaepI0nQ6No8sncg0Jqtdvn+XJNHDwyiiAJz9T73bs/y8J5BOpbLcCbCnlIS1/V4aaaL5bnUuhaDa+MvoYhEYlHq3TaTxThzdR0fGEhGNgSB9YDFgyNpdhTjVDsmC40+l1Y6NK3XXBcc1+PobJ2LlT6juSCTxluxqFxPgxlmHAp5O3kz42vd3fIHlWsppl6b+xWWhUAbvWcozcHh9BbB4fLfr7uSpjSoB3/eEg3UcSEtQXVTalHdBtNxeGjnAB3d5ZNHxmgaDjO1Ls9cqqLIInP1Lt845XByuc14LsahkTSKKJGPqbxvT55G16Kpewi+jyhL1NbcY565WGUkpVIzgsJpviCwYyBOTLWYKGqU2zpPnl5hsqBxaDTNgzuKTBQT/NQ923h1rsGx+RaKKrC3lOLgSIb5ZlC7YP+aJWCh0eN8ucveoQSKKFJu6dT7NrIgIEoiuuXx4YNDPHFymRNLbUoZjd2DgYvlycUWmZhCuWXhegLbixrVjkW1a4AvoEgChUSOes/ifLmPg8tKG/T5BmOFBENpjecv1an3Aou55fropkuja3HbaIbhXIy27tA1HF6dbxNXJQ4MZRjLazx7cRUHkbgq8dUTS5iOh+O41Ps2rueTjatXeA+EvPuEwsB7jLdi83KtNKPrk/PeUnJLteOW4TCYjIIgcHKxdUNZKNZ9QC9nopjgsUPDG76IZxqBT/mBkSTlts7Fag8BKMQjRBWRk4sdRvIa27IaHcvljtE0c3UDz/VwffjqsSUaPZtCPMJ4Ic72QrD59UUBx/Vo9mwyCYXZapdLKzqC7zNX10lGFR47WGL/SJpvn13h3HKQ//+ZS1WycZXD27LcMZZlIKmSSUZ4aqqCLArEVInnp6vkYlHu2Z7h0HAKCRjLx2j2VrnUMqi0DLSIRDYeJROReXm+ScsET/CIKhID6Sjbiwm+cmKRi+UOmiKQiKq0dJNvnF3F8Txiisxyy8BDYN9QEgQBTZGCojOqjKbKXFhpY9ku7b5DV3fZXoiwHFUoZaI4ns9UuYMk+nQNl4FkBFEUGEpGqfZtuqbL/pE0p5aaGLbDQqPHxVqPqCJSiAcZJXYU4jR0Z6PwW1rrYjsi6UEFWRCYqwVZmhYbPZZagXDy4YNDVwiYC/UeZ5bbGykFv3ZimR2FOA/uzNORg4V2NJ/gnu15htLaxvhZ5/ICZG8lYcxAyNvNe2WM3WhK0c3F05ZPBm436xnCNvezrnRar3LcMx2eOlNBv8xFaAs+WO6Wj7QNF0UQMF2X/9/ROX70zhGSEYVq12VqMfCbn4v00B2PhCrRtxyO7MxRSkW4azzP8fkGc40G24tRJvLJjcq9rb5Npa2z1IIdDZ18TCGuplhsVonKMo7n0TMd6l2HjxwqsbMUZNOzPY+mbjFeCCwAO0spFEmkodt851yFZs+ibbpEJYHxokar5/BMswo+7C4lt7gNKZLII/sGKaYC11Db9XjqzAonl9q8b1eBI5N57LViY2fKHQ4Op9g7nELwQZZE7tuRx/U8RtMRnrPmOLS/tFEzYiKvccdoimrXJK7KtPoWC3UDR2jSNhwkSWRHIc7HDpY4udDgzHKbqCpiODCWibHQMIhrQfIP3/MZymi0TZt88trZpULePUJhIOQKNmeF2FmMY1hBwNPV4gE2B3GeXGzdcBaKdR/Q9cwx65qfzanW9gwm8QFVFonKMpcqvaDab9/hkb1FhpIRGn2HrCbT7LsYpk0pqbFzIE0+oXJ0psbZ5TbjeY1dpRTjhTiKKHKh0mNnMU65pXOu3AkCnTIaVgHeN5nn1YUmDd3mwGiaetdieyHOHaMpTi50WOnp3DaaJpdU6doOp863ed/OHLtKSeJRmWIyiiKCFhFZaPSpdmwWmjpzjT6LDZ1oRCKbiqAKIjvyCZ65VOHcioEAjER9BjMauu1T75mYtosigRZREHywHR/TtZjIJYgrEuW2zlKzS9+y0S0P205hOC6TxQQvTVdZbBnk4gq+79M2LTqGSqNvMlftAT5D6Qj3jmdZ7Vq0dIcT801+/OEJJEnm4EiaY3MNji92KKZUBKCt23iej+P7nFxs0eg7dM0gM8RoLsa+4RQLjT4zlS4JTWFfMUYppaE7LjOVHg/tLm5YkvIJFWUtbqGU1vj+XIOLlT7b8lF8Hy6t6hwYtuk4r/mxjuViV6QHLaWjHJ2ucbHa48EdhS3fX22TdbMbrzBmIOTt5p0aYzc79m+2/UYK6YkgvupaKUU3x5BJYhBLtLn/y5VO61WOdxbiDKZVatcoQawAggCbzzStQVaVOVvtcHaxhWF7eD6UshrFhILtB8fPRxVM38fF51tTqxQSQfX6vlWh2rPoWx5zNQNZEFmo98hoCvuHkhiOQ2UWpqs9YhGFO0bTHNmeY7IY59xKhw/uG2C5FbhaKlKQYe2vv7/Isfkmjx0c5PBa6k57rUL7QzvyJFSJLx9fJqqK7C4mcHywbZf7duSZKCRYWXOrXCemvlaQ0VlTgg2lIhwYSZPWAkWJKIncPprmod1F6l1rY41NR2XapkvX8hiKwf078iiKzHy9T9fyGM2p7CylmCgmUST42vFlhrIaS02DQlxhJBdjVylFVBZ4daGNKgsU4lGG0xEWmgaTSRV8+P58E98Hy/LpXFeaC3m3CIWBkCu4PD5g3U//oV2FqwZ2rf/talkoNi8o1zrOuuYnGZV56uwqcVVm33Bqw9VkKK0xmI4ylNYYz2nM1nVOLbZ4aqrKrsEE+0ppzq92kSUBWQqKiR2b62E6HhdWu4xko2S7NnuHggVqPUfyxUqfhmHT7ts0exYP7i4y3zRwfYHldp+XLlR5eaGJ4PsMZWLobmAWdT2fZs8hF1VwUxppTUWsG5xa6lBIqNg+vHCpimX7TA7EuXcyS73r4no+QymNTEylZ7msdvvgQ1YDzSWYmPsWoiwxW+sRVRSy8QjxiIzheMiCgCdK9E2PnYNpRromlusxWw38YaMKRCSVY/MNzpXbeD7sKsRJDan0HIe5RhfP81lsG5S7Jpos0bddPn7nCH/2vUs0bYfZms7kQBLb9TAch0xMZlc+juP6dE2HVs/mwkoHVZHRVAFNVdBtB9v1KCYilJt9Kh2Lvu2xr5RElkT2FRPcNhqUoH9xusZTZ1eptA0+fHBooxr1Y4eGgSDl6FBKo9o12T+U2NAcXsukXG4ZaxWNr1xg1jcVm/Od3+zGK4wZCHm7eafG2PXG/tU2/m9MSAmyuPWsNx7YfPn9uLy6+O8+cf6qv3MB0wkyC238zQVVk5hMJ8hFZF6aaxARBPqGg+v7ZOIq//DwGAg++EFF9O+dryIgkIrI+ILA7oEE90xkubDS5eh8g5lKD0USkcQgbsP2YPdAgtF8oIiQJJEnTpZZbpvsHogjyVBu60yspU29ezzDciNwi1y/5wv1PkdnmxyZzAVZkxyXlb7FB/cMcGKhxXLbpNW3OTbX4LlLVTqGwwf2DHBkZ1AUbL3eSi6mUkyoKLK4UZvFcT0ODKXIJVSePleh0jMRfIFCQiWjKbT6FtOui7tpCr08M9S6UFbt22vuRwaSKLDQ6FPrmCzUeyiiiCBIPLp/gGhEwjxX40KlC77AaDZGVJaYbwRCU8gPHqEwELKFq5l61yv9Xr7JXw/qXTfxXs1FaUsWoqSC6627fUhbJpnvnKuwZyBBKqowWYxz57bsloJRAJWuyW1rxaueOLmM4TgkVBlZElEUib2ZwIXkL16cZa7e565tafYOJRlMqERkn5T22nDPJVTGc1Eiss/JxTa1ns3L0zWWWiZ7Swl8F759ocLF1Q5JTWF3KYmmyDR6NlPlDqbtstjRiSoyF1e6dAyLkZTGbeNpuobL6cU6sUhgKbhrW45vnl4hH48wUYxR7dr0TZu+6ZJPRhkvJDhzsUzP8uj2LRKaSkQUyWkKluOy0tIDN6CMwv7hJJlYFNd1UWQJBWhJAo4P5ZbJjoEIWSnCRw8Ng+dzsd5lVyHJpUqXhuVSjGs8um+Q4wttFps9vnqqzEw9qPS7PR+j1bc3NuuNvo0kCLwy12IgEyGpKsiIDKYjvDTdoGPYvDrfYraus7+UQpJE9g2lKSSjuK7HpWqf4wttHjsU5KW2XY+kKjGQUHD9QJO4vknfrNHfVUoxoFt858wylhMsuNdLa/vgzvzGONw8PtdT1TqutzGO1ttcK0jxcq7ldvdece0IeXu4mfHxdlcNXudqQse1XEI3t7tRN7yNFNLXSfV7o9exbik+X25T7Zrcvi1LTJVJaypZoHGV33uAfpnnac2ClaZBXlPZOZhEURR8QaRjOOTjETIRhcF0lGPzbcAP1jpB4OsnyrR1h+3JCLdvy1LrWkiSyGg6SlwWma70ma71GM1o7EjC3RNZFEVhod4nHZUxnQiZmIIWkWiVg9iriBJo8NOaSi4ZYaGhM7XaY0chTiERwfVei7+brfaJRqSgsn0yGqRxTkR49lKNCys9LMfl6FwDee15rHZNWj0LAYH9QylGc4FS7Gunl/Fdn3u35ym3dE4stdlXSlBMRmmt1e25c1uWhCrwwnzwDBCvblFNqhKTBY2EJjOS0ZjMx3h1rs7XT60wlIiybzjOzkKSiCrRNlxGs1GmpjqossCuYoJTyy1M26fc6N/UuAh5ZwiFgZAtXC2F6GZ/zs3tnrlQpW3YfGj/4IZZ+Ho1CPBcmtZWtw+4UvOztZ8gROzkYovvnKvgrsUZ+MCh4TQ7BpMAG9WMbc+jozt0DZuVpkkpHeXpi1VSmspoLkEmpvCN0yvsGkzwwqUaUVni0EgaDzg510K3XPLxCPW+QyaqEItIDCc1MprKrsE4Z8otmn2TWRFsy2PPQJRy06Ku2+RjKrIoUev2kSUZRZTIxFWOztT52sky4BOTJUYKWpBS1PMwPJ9sVKZpw6gi0EZgtWOuuVrFsR2XREQipsoUE1Ee2TfAUtMgKkkkNZn5io4nipRSUep9C8936Zoe927PMl3rsVAziEgiB0ayCEAmrrK9mODQaIavHlvkzEqHV+abZKIK7987QERRGBXYMCdrqsALFxukIwp3jWVZbBpMLXc5s9JFEwVcz+V8uc1oNkZcCZ7ZPdvz2K5HpWtQ7QTxBuvBwq8utFBkZWNcXD7WUprMVLnDbLXL/311ibwNdzV0ZhuBb8DVLFPrAXODl2k11wvabR5Hl2+83qiLRug+FHI93snxcaPHup6y5vLK85vbz9f7N3wtjuuxco0142auY726+LMXK8yuRQTfvi3LycUWvkRgBgAyAjTXooizclCBeGVTALEIbMtqnFxqUUhGKcQU2pZNMiIji7DYMriw0uXASJKZSg9NFTkx3+Rsuc2Zcot7J/OMZeNrdVQinGjrrHZsRvMalZ6FbrmsFU2n3DKYWumQisrsHkxwvtxhtqojeAJZTabWs1io9ykmIjy6f4Cu5fDMpRrlts6P3jbCjmKci5U+hmVh43PbQJKH9w5srIkt3aLeMdk7lERTBUZzCb55ZpXhbJTBZJRMPAK+z2A6SkyVma50wRNoGBYvzTR4dN8AH9g7wJ5SknrXopAMCpdVOiZTnT6L3UBRV+u1r3C7XJ+7l1s6K80GHzo4CAKcXmzTNWxWRVDbIn2zTduwGMlEuWMsy3zTICLBxWqPxabBaDrGAzsKNzUuQt4ZQmEgZAuvV0Bsc7vJYpxLld51zcIb/qFreaWT8mtuH33L4eRii4Mjae5dSxWZ1l7LRjSYjrJjIBFsehs97tueDbQjF2vM1vrsKiUZyWrIkshMrc9MTWc8r7FnKEl0TVv+6kKTpabB+3cnODiS5uWZGmeWWsxWOsw2dIazGrmEiuDDWDHG4cks2/Nxljsmvb6J7wtUeibfvVDlge05PrRvkMWazly9Dwgka30m8nGmVtvUDZtaT8dyPAbiKqbnoYoC9Y6FIvlYjsdUrYPuuQwmolTaOjNVnW5fJ65AIqpgOj6q5ZJOyOh2ULTM8j2GMxIe4HhQ65j0bY8DQ0laukM8JnFoNMNio8/3zlcodwyeOlehaVhIEkQlmUxM5sfuHuP0UouXZ5skIgJLbYtq28C2PRLDKYrJCFFZ3vBvddwgPeh9O7JEFIWJQoKRXIyZWpcPRmUmshpfOVnmUr3H92fq7B1O0ZttEFWDaaVjelQ61oZW7OBIesPKNJqL0bccrKUWmipupJl1XY/T5Q7bczGGMlHsSpA+cG8peU0N5bqgCGyMo8u1oNcqPHaz2s+rvScQWgpuZa727N8u15/1eXRz7oU3c6zL3UFer831CFxK64DPQzdg7bBdj5oR/F9Rrlx7aj2L8WwcURAoJCIb77m+KUC4tTmdkAiTpRSRZo+5RtAop0LXctAUCdtyONXqE1UUtLxMLhFFFgFB4IVLFU4udlnp9GnrDhlNxhcAX0C3HY5O18hoCsmIxKsdg10DeX7myBhLjT7fvRCkvD6yc4BcXKXWs2j0LE6XOxTiMilNYV8pTUJTcVyPqdUOqy2d2XqfattE8gUACokI359rcs94GkkUODyeI6YGaT7LLYMXpyu8utDkjtE0o7kMhmmz0jYopVQe2l1kqtzZqEp857Yso7kYH799mIVGj9majiyJFBMypxdbtAyHXFylZTjUuwanl7tYJszUepxe7oLgs9zSN4S6dQ+BJ08t8Uy9R3a6RlRV0BSZPQMptGiQvCKhSpxZalPv2wymYuSTKvW2RUQQ2TmQYCIfZyhUnvxAEgoDIVvYrD263iKgSCL3bM8zlotfYRa+lv/pqaU2Mx24Y20lu3wTt+56ZHsegg/VrknLcJitdnnidJkP7ytxeCLPrm6gJd49GGzwV1oGh8ezyJJILqFyarHBYscgo6lEIxIjGY3bxzPBpJbSiEdkFls9LMfjzrEMpuVyfrXHvZNZDo1mqXZ0js81ycZkivEIg8kIbcvh/GqPpBZk69mWi9PqmfQtD1WSuGcijywIZDWV/3V0ERWw8Jha7rDc0YnKIrsH0jT6JicXmvzw7SM8dmCY//ncJSwHZAFmazqSAAdHs4xmE5RbfTKxCKm4zEhao6e7/OXzM8iigCrJPLw7x/PTFrP1HudXe+woxohKMjFVIhYViSkaEVnE8l0uVfpcqvSQRZHZWp+xrMZkPs6lSgvdcohKIo7r8+xclZ7hsLuY4OhCE8Py+ODeIgeGUozmYhydrvGdqSrbMlHKbZMfvm2Ir50s47lQiKvsH0oHQkRCJaPJ7B5MktEkzpW7FBORLXUFTi+2ePZSjdW2zkA6RjEZpCktpqLsKSW5fTTFt789x0hWIxaNMF3pbrj7bHYrWrcsrWfT2OxqsM7rpQ69Ge3n5e/J+vgOLQW3Jld79m9XStpyy2CqHKTcXefNpyd9/WQPm9tcS/ANNoy5jX+/Hittk4UeHJtvcniyeNW1Z/PaMrK2bvyPpy5u9LFZFjBtODHXJpOQNv7melDtOxQ0Bd126Zku2zJx3r93gJ3FBNmEype+P8fx+Ra1rsXooUEikozn+bi+y/acxrfPljlT7rFrMMEdYxkKSZWpcpeBtMa55Q5TdfjmqRU0VWH/SJqpcodtucBldVtW49him4Zub2QTOr3UYmq5i+f73D+ZIxpRNuLYAEzXR1FkvnuhRmJNOfb8pTqFpMKeUpIP7Rskk4jS7Bo8P12naTqstA00SeDccgvTDlKDrsfH3T2RZ6LwWjrUetfijm1psppCMRFhIqsxV9e5aMLxhTaqIjGRi9MynI1kIOsW2Fw8ykQ2Rt/wiEYgHZeYb/Y5mE3ygf1DDKaiTA7GafQs7p3M4V/ysR2fix2dl2bqPCtJ5BMR/tF9E687PkLeWUJhIAS4coK/EU3ntSrAbs4dv55mtJSOshBXWDXghek60Yi6ZRO3/rvnL9Vo9C183yetRdhRjDFb6VLuWJxZbnN4e55iIoIA7B9Jc3KxxWrHYCAZpFY7udiirjtYjsfugTg926PSNllqBK432YTKzmKC3YMxFuoWhWSUly7W0aISxWSUC5UeJ+brTFc7zAIf3D/ErsE4J5fa+D5sy2nEVZmlRp99pRSi6NPoWXQMi77j8/JslU7fJJ+MMByLge+z1NDxXI+xHBTTEeabBn3DoWu47BlKY1oOdAwaosShsTyTxQTnVjrM1wIf3hwKjb5Fx3BZburYrofnwXemoniez0A8guP6LDVNUnGZVCzN3dvStAybl2YccrEoyYjE9GqHu8czjKYj7BrQUBQZSRA4OlcjFVE5vtjifLnDaseg1rVY7uj4rs/USpdCIoJuOyw2+iiiwNRKF8sNUvEdHM3Q6plM5uMbAlyuq6IqMjsHVWodC9e3N57x+sYpoynYrstK2ySfiHBwJE1MlTcEQ1kSyUe5bPxtXv4D1n8D3PSmfp3rCb438i6Egca3Lm/02b8Ra1IpHcVxkvQvvn7bt4trCb6KJF6R7et6DKYiJGSo9+wrMtBtrmuzfn8USeTe7XkGEjDbvbK/vg+40G29ZjooJkEVBPYNpSmmVF6ebiJIPudXO+QTEapdk5MLXao9Kyg6mQ383k3X4bmLDWbqK6iiiKZKDKei3D6Wpdmzg014z0IQBGQBVjomT54u07Uczq90Mewghqpp2KSiUlA8crpGKa3x0O4irufT0G3uHc/SsVySmsyz56skohKllIYsipxb6bLc0imuxRNEZIl/dO/4hrbecT2G0hrNnsm3Ti9zodKn3Anm0s2W/fWsTLbrsaMVBz+wtr4wU2dHIc7+kTS3jSRpLsHd2zKM5OOYpsN0rbclzu7kYotzq11GMxrpmMq+oSRdy+aZ83VausvZpRaCD6PZOEtNk2cuVGj1HcayUU4tNGj0XERcGt1rpIMKeVcJhYEQ4MrMK+sBZZszsdzMgrXc0q9IM1pIRNiZhPu25zb6W9/4zdf7pDSZ8XyMAyMpmv0gd73ggyLLfOLQIA/tHADg6GwDEJAkkVrPQvCh1rM4uRgIIJIvcPd4jvfvGaShBwG/MUVgphpsdF+cbVBKqGTjES6U28zWezyyN+h7PK+xqzjCcxerNHomUUVkPB/n744tMZTRKCQjrHZMvj/f4KDnsX8wxZMzqwgiyIJA33IYTGn86F0jZDWVpZZJw7QwbY/9I2lycYXRTIy9Q4EGqZCI0OwLrNRAlwXKTZ1nLlZxbA9fANdz8TyfaFTmzrEcuu3Q1U1qPRvLcBEEgdvGMhwYTvLM+ToTBY1vT1WYbehUuybZuMpAMsLXTy7z8lyT4wtNvj/f5txKF1/wSUUVhjMx0gmVhCIRkUQkWaQYV0GAckun1jV5Zb4ZFKhZ6XLfjhyJiEI6JpJLRhF8j67l8Y2zq3QMh4PDSe7fkaetO8zXe0ytdjk0nNoS4FtKR1lwPUYzcVq6RdvwqHWtDaFyod7nmYtV9E2pQUZzMY6s/dt2vauOx/X6FY7r0bccal1ri3bxRgTba70b8PoWhpBbjzf67N+INUmRREazGsffQk+0m0nBuzkw/80IvrbrsdI2GYvD/uHUVfvanEBis5CRTirQtW/oOJYLfdtFiwiosojlexwaTLKnlOLMcpttuSg/cscQjZ7JvqE0Dd2mbTjsKaXpGB6KBJIgYNg+hgNt3eFDB0oUkxEymsJEPkJjaYZEMkqtYzNb6bHcMtg3lFhLomCAD57ncnGlg6yIfPzQCB86UOLYXIPljs5spc8z51bp2YGleqIYuGNWOgbnV7skozK6bfHStE4p/Voa1tFcjHu35/jmmRVOLLdRRZHbR5I8dvvwFXUe1l1y94+kKaU1ZmodZqpBIHKlY9DoO5QigYBW65i8NFun2rYpJqOU1mq7TBbjjGaiJDWVkazGnduyzFS63D2Ro2tYfPGlOQ6P5zmyI0+rb1F1ffqWQ8yQmSyksGyPVk/n4FjqDY+bkLePUBgIAV7TajmutyWgbP0z3JymtZiIUFzTUMB6CsgeigwThfiWBWa97PrBkRR9y6PRCzI3aIpMx7BYaev86J3D7BvOYLseh9cKkq0HHOcTKitrGTHKzT6G47EtpTFeTDDselxY6XCx2ucbZyp89OAgou8z3+gzV++jRSVWOjrnV9ocnWnw43ePAJBPRiilouwbSXF0ps5MtU/Xcomdq5KJyfRNl7PLrSDjjiyQjao8dqjEVLlDo2dxcbXLYCqKJArcPpZDEURUGS5W+sQiEt85X6Gr21iOS0N3KGgwmE3StS0M0yEeFYlFZKptD/CJSwqZqIIqSbR1F0EUadg2GU3B8Xyev1jnXKXLYrNPuWsRUyUWG32ycYWeKeO4Hvm4wkQhztG5BkNplbbh0tItCokopu1wstala9hokkg2EaGU0RjNxhjNRimlo5xdanNy0aVvOIzm4ty3PYcsicw3ejR1B8t2uVTpcXpZ4OCYgabI7C4lafQsHtpd3Hjm61oqgI8eKuE6Hk3dJp9Qt2Q3wSdQYW2i0jWp96yN2hSXs7l+RaVr0tId0ppMS3duegyvE2r9Q94OflDG1dWEkutVD14PzH8zsTHrbqPzPfjhVOQ6fQWWwM3CyVLtxgQBgEQswt3jWbJahGNzLcpNnQcm8+DD9GqX2WqX9+8dIBvXaPQtXp5tsi0X5f4dQ0QVmXPlDiBwaDQKPjS7BjOVDrbvc26mQ0wWUER4/74imiKT0RQOjLgUEhHOrXbJaDK5uMqlik7PMkhIAsutIL7uYqXHTLVH27QQPYH9Iyke2l2k3DLQbYdL1T4dy0ZTBF642EQU4P4dJtsLrxVlKyYiPLQrT7VtMlPXMW2Pei+Y0zfH633j1DIvzDT4yIFBFFHk6EyDVt9iZzHOpWof23FY1OErx5cRZJHRVDTInBSR+LvjS/iCzx2jGXxBQBJ8Do6kUSSRiWKC+7bn+D9H52kbLnFVpJiI8OH9JRzfp9zqU+2Y9GMqtufwleNdXp5t8kO7h97w2Al5ewiFgRBga6DvZkvA5s+vx+aN3NRKh1xc3ZLKUTfjzJ9+LWBs/Tdnl9osNnQOjqTIxVVWOya5uEopHQ20+W2TWtfEdj1mKl3OLLfwEXDWUqvlE4Ff5bMXq8RViT2lBB3T5YWLVWaqXeYbBpblYNoO355apWnY6GZgmp2rdekZHgvNPtLa6+B6Hj3DpZhSefp8jUJcppiKIEk+5ZbBzmKBjxwo0ejbiGJgTVBEmY7hsNIxqHdMzq920R2PUjrCgzsLjOQ0Xp6rUe/YDKWjLDT6dHULURRxXY+6AY8eSrHQMFjtWkiez2A6hiTK5BIqd41nuGssjem6xGWJbFJlodmn3DapdGyGkhFE36eUjmG6HgOpCBcqXXTTZUcxRVSVSEYjpKIyD+0qcngiy7dOr9I1HWTJZKps0uhbqKJAKRNDtxy0SJSJfIypchfD9tkznCKqSKTjUUazGiO5GCcXW3QMl10DCRKqBIKPJEobQeUJVaRtuKy0jS2ZotY3FTuLcWq6ycVqj1Ja29jI7yzGeXBngVdW1sZVp4/jetR6Fvm1sXG1sVdKR6/wN978/81BwjfqphFq/UPeDt6OcXUjY/pGKgVfS1C5XnrSm7UeL8QVuk4QO7A9Grmin/VUpZcns4hKr9P5JsYLCX5o9wDfm6rQNRx84Gy5zXS1T9uyafdsVlsGt23LcmqhxUylh+d5fPvsCrsGk9w1nqHWMXFcj1cXW8zX+iw1DVLRIMObgE/PDnQWjb5FvW8zlNEYSEc5t9IJqqABkwWNO7elmK72aPRthtIak8U4ru8znM7St1we3BUEAdd7FqlosBb5Lvge7B5KkI5KZDWF6WqXl2eaTOQ1Zmo64HN4PEfXrDC10qXaMdk9+No9KLcCzX98LbHDudUuM5U+Hj7z9T75ZATPgaN9sGs9htIxVkWLVEzh5ZkGpu3Rs4P71DIs8OHYXINCIoIsiaRjCsPZGOPFOCBwernNbaMZFqpdvnqiTDoqE1Elan0T3XJo98KiYz+IhMJAyBYuX6Cut2BdXlBsPSPMnsHkRlaFzQFIiiSyor82+fcth6fOrOD4Pg/syHN4Ir+xUdxYqFIaOwfjlFIa5ZbBE6fLLDdMdgxovLrQoLFmLi6lNeYafaodiwd35lhq6pxYamJaLgOJCANpjYu1Hi3TIqXKPLCjgGV7TK20MWMuD+wsktUUdg8mee5CjTvHs+wbCvLzH1toIQoCMUVhshBnsanTsxzSmoTh+ERkha5l843TDSp9G9H36Ok2XRt8t883T5fZP5Kl3DEQPJ9ERCETUUhGZA4MZTi90GS606FtONw2msZ2XC7WewwlNDRJptY3+daZFY7NNoNJ1bAYSEXomQ6G6dCVBM4ZNm3dYnsxxvZ8gguVDnsH04zkIiy1Dcaycc6U2yw3Bd6/dwDwiKkyuwaSDKc16lmbbt8mHVcpJFR8BFZaBpGcxkytRy4us9SQOLw9z3SliyYJHJtrUO/bFJOBFej5S3WiSlCTYbIY54WLNeJJDdcLBD5VCVbxsVxsw51nuaVzfjWwSECwgU9rclBwbi0V7cJaatGdxTgHh9NX3XRcrsm8PJYllpOviCe4mvYzzAoU8oPGzYzJG3E9urzN/5+9Pw2S5Dzve9Ff7pm1r93V+zL7hp0ASICkKK6SKFm2jmVf+TKsEz7yB8tyOCx9sR2OsG+EwhFe7vlgn/BxOBzysWVbPtc6tkRRpEhK3AAQAGcIzL73vlR17UtW7pn3Q3YXegYzgxkQIEGq/xHAdFVnZ9by5vu+z/P8n///XnP8/eb9d/KSeRS60+MzOa4mY2rK3ee5u19gP/0veHvbEAA64O/+B/Hmxg8F6v2YsnpoPEkhpbE4lmCn73I4kaSmuay3babyzq5PSpLu0OflW002OzanpzJ84/oOrYGL4/sokkTPsrFckbGMgR+EpAR4ZamJ7UUcHUvStwNsz6c99MnoYiwMIYpoqoyqyOR0Gdv1CcKQDx8qIkTw8lKDP3xjg2I6Ntfc66M7u9rG9iNOTWRpD33OrXWQRHhzvc3xyuyoYRugnDUYy+icmsrGsqLEVKJKVucjh2KfgVJS23WzD9lomVhuyHha57mFHKs3rzE7k2e+nKQ79GgObGp9j4QiIkQCPTvgyakcjYHDa8stIiFCEgVmsgaltEqz73Ch2uWU61NIKnzj6g7nVtsUUzIIEkkNyhmNx+cLHOCDh4Ng4ADvGvsnbz8IuVEdcKicYLqQGKnG7M8gjWc0JhNvTf6XNrtc3OpxZjLDZ07HZcPlRpzZKKbUURnyF56YHlGBfvrYGB0rpsd0LlcRBZFSSmM8q3N6IsuyaiIiklAl2gMwVJnZYhqBkGJCo+94yIbEVF7naDlNLinTHvpstizMVMDLt+qcXemwWDbQZZGl+oCNtsmp8QzzYykWxlK8vtziZn0AERyfyPDsfJ5az2arbXFYj3sRvKCG0HWQBBjYPt2hgypAKArUukMUSaBregxsF1WVUMVYPalv+ax1Y3nSK9UuPdvDcQJapo+m9pkrJhk4ARlDZjKbJDcucbnaQyAgqcnM5JNsdWKr+aNjaY5UMvz/Xt9gtdlnu23hh7BYTrBUN+k7Ps8vFkhoKrNRFC+yUciRsTQN0+HmTtyQq8kikiASRHG15eJ2j3xSJaerzBR08kYs/5pQBRbLWVKaws1qnyvVPvmkyqFykhs1k6PjMW1sb3MD7L7OFJWsQdqQ+e/fWyObUHfdjE02zLekRX+QBt57cZ3v9Td3N7/vPXcQHBzg/cCDNvoPMgS7Hx6GevRu5XR/kGveC8pdAgF3S4veLULhhSF/cqnK8D6JZZ9Ylc2P3nrcHjrcrA7IGgo5XaUz9IhCqHYsxtIaxytpbtQGdGwP3/epdh1qA4e5vMGRsSQ7XZu1xpD20Ikz4BmDlqkynU8ykzfY6bsoEUzlEpTSGgvFJN++1cT2FbqWy9Oz5ZHU8nhWp7nrCPzHF7fY6tp8ZLHI0fE0222bnuVR2qXXKpLIE7N5giDEi0Im0gaSLFLrWvzhG1sst4a8udbh//2RBSDurzg1kYkN1NbanF1tk0+ofPzYGDOFBLIkcmGzR1KXODqW5tRkhmJKo2/tUjiFiNk0fPxYmVrf4Uu3a0wX4sqwH4Lq+hyfSDORNVht2YgiTGR0rldNGrKLJonMFlMIgBfC2bU2lazGfCHJx46XSKoSqw2L3rCOJj9CaecAPzQcBAMHeNfYP3lvtIZIInc0ON0r27R/8j89lSUIQkqpuER8abPLa0tNdvoO8m5z8R422kNeX47VD57ZbTp+brFIKa0xX0qx0RpiuiFzRYOu5ZNQBaYKCZ6czTJfTJM2ZLIJGcsNqPVdohC+ebNBUpMoJVXaggChgKbI7HRsUrrMVrdBGAhM55L0nCDmuDaHvHi0jCFKOH6AJomkVAkrqaBJEkPfZz4hIYoSSUNmvpQi3G1i6wxcNFmkuqsIlEtqXNru0rd8Gk6cBVospeP+g1MVgjDijy5uUXc9oihe6CzXY+iEdE2X8piOJIlosoguKzw1n8MLIWkoTGcNxrIGa/UhE1mdmzs9lnb6KLLElY0OO6bH0PVpDVI8MVsgo8v811dXcf2I1ZbF505V6Fk+m22bo+MpKvkEsgBbHRtVFBlLqrgBrLdsqt0aM3mda9UB3aHHWNZgLm9wspLm1FSWzfaQrc6Qp+ayIz7suZUOz8zlOL5rGjddSPDVS9u8stziubkc212Las8mDGEso5FNGg8ci+9EubgX1/lef3N38ztwIBl6gPcND8qqP8gQ7H54FKnQd6u89W6u+ajnKaZUgiA2xdpzKq91LZZ2TETh3n/vA0UddB86u20Fa/U+lhMylU9iuT6doUff8mlbHroscWGtxUrLwvMCnCDA9UOCIKLWd/ju7SZjaZ3jE2lOTk5h+wEX13p4oUA5pWGHEZIIBR1ePFLCCSJeu93E2DVf7FkekcDIfX2jFVMdvTDk5GSaiYxGJAh4YcjRSpJ8UqWU1Pjype2RkedGx6Y9dKl1XZ6ez9M2PQ6Np5jMGeSSGm+stSmntBEtF+BKtcda06SSVkcUWoCsoZDWJbq2z+FSkpbpUkzrtAYu1Y7J9q4xcESsmjdfTPDJkxV2uvbIBVqRRF44HB9nuz6bXQchikgZCrIAT8zlOL/eQ0TgE8fHeHKuQCml4UcRX728Tb3v0OofqAl9EHEQDPwE4EdFbdg/ee/ndz7o9QRhTPuYLsacy0rW4NWlFo2BQ8f2eWI6iySJHKukuVntcXW7iyiJZHWZteYQ2w3Y6dvkkypDN5ZWW6kPuLTZIYgCCkmD69U2sgiWF9AxPcYXdWpdm7WWRdt0mS7otC2PruUxndOJdnmdzx8ucXmjQ9/zkQFNlQkTUFYU1ls2KVWi1nc4t9pipTkkpUhU+y71oUtKkVhtmXSHLs2+zWQ6wdhkjrGczrn1NsN+gOX55NNJGn2HgRMyVTB4eibP99fbBCpkkiqVlIodQb3vUkwqWE5AGAnkUyKCALYboisSqihyo9ZnMhfz92s9l8WxNEfKGd5Ya7JSF7i62aE5dGMnZVVCkUV8P0BXVD5yOM2N7diMpjP0uFntc269iwKcms5xdbvHR46UKCRVcoaCrsbUnXMrTTZ7Q0wnYK6UQAD6TkDKkDlRSRFEAsFun4mqyPQsn+bAYafncKvWJ2W4JFURiJD3NfvGeth5bu30eXwmR23gIQsgirH04DsFA3djv6FdPM4eLnupSCJPzubfVtX6UTd5HuAnEw8alw9jCPZ+XXsPe5tY4F25Cr9bNAcuoiRS3N3gXqv2mS8Y/MKTk7x8bWvkQHw3RCBtiHS8WKBAEyGTUHl8OnaZr3UsfvrEGNdqPRo9lzfWuqiKRFKT2K7bpA0ZQYjY7FoIgsBkVscJInZ6Ns8vljgyluaxWoZUQuHyZo+UptBtwJtrHb632qLadfjYsSJr9SEdy+VWbcCR8cxINrtluoRRhCgIfOJ4mWbf4dvXayw3LV44FCe/blYHHJ9IsVBM88xcHj+K5as32iavL7V5djHHx4+P89KNOvW+QzmljWi55ZRG3pBpDz02evZIoW26kOCFwyVs16djxZHS/s93p+8ShnGFv28HpHWR1ZbFVseib/t07ViZbWa36r/RGrLdt+g7HglVZ2B5REJMJXpsJkPHdPHCuBr70q0G2x2TpXrcJ+f44R3f2QE184OBg2DgJwA/KsOju2/ivWuvt4ZvK/FCvEF7owHd6zv81PH9mtQRpZTGdOEtCscba21eXW6w03b48OEilYzBbCGB7Xn82dU6s0WDhWKCN9darLSHNLsuzy7mkUSRqZxBShc5v9Hlixe3MV2fgeNxu9Zns2uR1Eocr2TQZIlcUuFWrc9Sw+L4RIZj42kWSyk+c3IcK4g4u9rCdkOyhsqJiRRfv7LDcsNkaWfAeFZjppDmQ7MFLle7pAwJ3xep92w0WSJA5exqC9ePmMzpZDSVo6UkURSy07VJ6irnN7qstSxyYqzxfLNhoisyZ9eGWI5Px3LRZRFdFRk6AUEUcaiQZOgH7HQtHp/O8sxigT++UANitZ3DY2muVQf0TZfbdZPxTFx6niulWKkPaJgWv/jkBPPFFAPbZzKrcXO7y2RWI6OpEIVc2OwiiQInJ7N3NINP55MUDI2u5VLrueQTKuNpHcuNyCdV2qYLQrzJP1xOYrs+fhgyVzbIJhUWiknGszozheTbNttnl5vsDFxWm0OemC2Q1gRuXYJCUnnksXm3od2jZC/vPvagInCA9wsPGpfvd+P6w5z/UV2F3ysUUyrFpDpSrdkTiri63b0vTQigboFghQjEGW5RFPjU0RKSLHFpu8etnQERESEiRCGFlMbj03nKKRXHjzgxkWajY7PdsZjKJ3jhcJnvrbS4sNnham3A5x+b4MRUji9f2CKhisyNJfivV+HGpS1yCY2PHy0xV0ryjcsNKhkNcV8P3POLxVjxrmux2rKo9iy+cqlGtWshAY2BRy6psjCWoGv6XPf7nJqMewc22jayCAld4shYrKK3t5m/m5brByFrLZvZvDGqDOx9hufWOrSHLk/MZDlUTqKIsZnYWEdFFOPjymmNm7U+t3cGfPnCFofG02R0hbPLDTqDFG3b4/urbXqWR9pQGE9rSJJEVpNAgEbf4dxqlwsbPWo9iyCMaPRtmn17N6Hl3/GdHRg2fjBwEAz8BOD9kKh7mGj9fjfx/XwGrmz1uN0DrWONrgHw9HweWXxL1eK7t+ucW+1wYiLNdFZnsZRkqpDg46rMwHLpOwFpTWa1Y9Hsujw1n+P5+SKllMaVag+BiI8fG0dAYKtt8/LNJvWBiyCEsXuvLOL6IRM5nTdWO2x2LNK6gu372J7PZEEnZagc233dpuNxabuHLAgslpMQhWy0hzR6Fi8cHuOx6SxjGRUBWJUEBm5A13R4qTlEU+Aji2N87kyFL1/aZqNr0R36VHIJJlI6160urYFHNwT3+g7NgceR8RRZTSZCYkI0MFQJywsxbRsRgVJaozF0iESB2WKCmWyCjx4p0Oo5fOt6g0+eKPPhxQLfuLaDrggsllJIgogqCNT6NhvtAb97dp2prIHjhWx1Lb54fhtRjDhRyVGSVHw/wNlr2NvNDlY7QxaKSZ6cyVJKaUiyiCLGrs/fulbj3GqfjCFTSqojf4rXVlq0Bi5TWYPLm32m80kSqnyHSd3e+MgZCkEQ0bZ8ZEmkb/sMg7cqA3c3rD9ofN5taHeAAxzg0fGorsL3w/28DJr2nepye2gOXLrWW9noPVpTw/RIGzAY3vs6IYwCAYC2FfEnV+sMXB/LdvEjUCZzTObjCnbPiU0PV1omCVUmnVSZFeCx6QxzpRQLpRSThQTNgcv1nT7fvLZDKanyyu0GYxkDoljtJ6MrFBIaHzlSpjFwqBQ0Pn18nJShjt7zeFbn0maXE1NZZElkaWfASmOAJgmcnC5wZFcoQ5kTqQ9cXM/Hdn3GsjpZQyatSiyUXPTdSueeYzHcGdhNFRIcGUuBEItA7GE8q7NYTnJ21eXmzoDlukk2oTIxMDg5meGCBhudIePZBB8/WqJjOnRMj67pEgYhf3h+m/GMxlQ+wcAOyBgqzy4UODWV5cJam8bAoef4EIk8uxBXVy9sdkkq4q6anYTpBCyMJ982xn7Q8XWAHxwHwcBPAN5NBumdNvsPE63ffRPvP+e9qBYnJzM8WYLPPh43C2+0hlyv9QmCEGk3c+EHId++3qDed5gvGGx0bTY7Dp9X5V3upc7zlseNmskTU0n0eXnEZYw5mQE3qibz5S5npnLkkgqOF7FU77PaHNK3YyOsN1Y7PD6Tpef62F7IdE7hVs3kVm1ApRDbuG+0h3xvuYkmC/g+nFvvIAoCY2mdQkJjrenz5mqLpKYgRCGlhMrtHSgmFCzfRxIiCqkEc2Npzq11uFYb4AUBh8opJnIGoiAiiyKFpIAzgLlCAk1xEEToOjG95omZAglVRhIirisCIiJJTWGzO+RQIUVv6PHS7QY3aj1cPyQMIr52YRtZlri+08e0AxQBUkmZY5UkfgTrnSFhEDC0PVaaQ05NpTEUCUGKUHYbmUUBBrvlZASB1caA2w0TXZGYLSX4+TNTo3LxhbU2S414dU5pEhc2erQsj48fGWMub9AauAh7Y2qrx0IpNRpj+8dfJEBKk5kvxQoYnueNGs69IBypVe3h8laXjVYsSbonYbuf0rC/5+QABzjAo+NersIPQx26m6Z3r/Wk1nPYMOH8eodnFst3nOd+cqfzpQTN+wQCEAcD+5ExJE5OZhnYLuc32mQ1GccP6Dg+aVVhsZjkuUN5Lm10WW9ZfONKFTeMOFROkU3EQhc9y+fIRIZcQqFr+2x3bVRZZDKrsdEcEkVwbDyNoSvcqg2QJJEPzRXQVRlDFfnqpW1ePBrLhn7rRp1qZ8hGx6bWtVBEkYVSiheOlJjIGlyv9cnoMuWUyo2dAV++ss18PoGqyJRT6VF1YaM1xPYDvnFth0+dHOfo+FtGXnsUq6QqcnGjQ8ty0SSJ5xeLTGQNPnda49pWj4tbPQBURaLWk9i2YPnyDrPFJHOFBLIk4RPgR3C4nOLzj1dIGwoz+STyLrVWlkRaA5c3NjrcqPaZLyT4uSemmCsmWa0PiAjpWSEnptL8669fZ7MX8MU3tviZ09N3jLGDisCPHgfBwJ9TvNNm/2Gi9btv4vvJO+4hococzYGuyLy61OKZuRxZXd5VmkmSMWS+dW2HclplKqczV0xwcbNHKER3ZEEiQBJhvpQelUf3mlLThkzbsrm13eP7q21m8wYJXeXJ2QJBKBBEISfGUlyp9pnMJ5iXBPxKyMCOCMNYhzqnKSgS/F8vr7DSNEkZKjM5je3OkErG4MnZLCcnM7x0c4e0rtHoW7x6u8V8OYkkgAvIgkQ5p/L5xyeZLSa5UR1wfCxN3/GpDxws18QJQyRBZK6YphG2kCWR2XyCjbZF27Sx/Yiu5aLIIuc2WrRMj2JKIQgD6j0HRfF4bTXiRCVNrRvzQzVJZKNjsVhKslBIMpkzECSRnY7DJ4+NcXIyy5cvbtO1PGp9h47lcriS4Zn5Ile2Opzf7FNKqczmDSJEbD+g2bfRFJkgigjCuMHO392c39jVxRZFgSdnsjT6Ll3LJdmXKOyWqDc6NsfG0wzdAD+KRk1vdyukdIYeA9dntW7y/GJ4R8N5tWu/zWNgu2txozpgpTnkxd2NxMNQGh7FcfUAB/ig4UEZ9Xsd+16P6z3+Owj3vc/upundaz0Zz2ik5Ljyt7+CDG9fW/YCkK7p8kgq9WGEIkZMZg16VoChibhBRH8YSynLskSj7+IEIMsilaTGbF5HEASubvcop7TdREOOzJESF9barDVNZEVivpTg61d26PqgyrtCFEOfo+NJKlmDW3WTlUaXr19tYPs+nzo5Qb1nM5HVWGlZvHi0xCdPjlNOaqOerGrX4nZ9yHMLefwg5Fs3htRkh8msOFIj2pvjkqrEZtvi8kZnZNz4+Gx+RLFyPJ8r1T4nKikem47Pd3a1w/OLBT51qkIlF3sdLNXNeH0V4KmZHBM5gxO7FdVaz8FyA1KGyrMLZa5V++iyhCyJDByPr1zYYrFgYNk+iihS77ss7QyQRIE3N3qcmsyx2rTwvZCULhEC5YT6oG/sAD8iHAQDf07xTpv9R43WH8WmPs4pRLtmZgYrzSGllMZLN+pc2uoxndMpZw1sPyKXVCGKj4U9AxWPjC6NMiS36iZJVSQIQy6v91nvWFhuSH3g8PxikTNTGfJ5g0+fGqdtuuQSCo1hQBRFXNka8NyhAkHocricY6Nt07U9/j9/eJnlpslcIcHPnBzjdt0kFAQSuozlhrQtl4QqEwohYykdPwrIqBIpJYEsi9iej+2GvHq7gS5JuGHAofEMYRSy03VYbQ9otG2OVTK4TsANG4ZbXbKGQsf0qOQTlBIak1mDNzc6VDsWtgt+EFDL2YQCRER4fshkxqA9cLG8gEpGY7tj4vgeoRBxpJxivWnSswMapkPbdLmx0yejqth+gCZLpFSJ5w+ViQDTjZjJ65TSGpvtuOn30lYXTRJZKMWmMmlVYqNt0nMCNAkmsirHJrKxqY8ASVWi2rO5stnlmYUiL+5WfIppnWbfpi7HTW+Hy8lYXSMIR1J6t2p91js259faVDIarh83nI/nEm/zGDhWSbPdGXJk/C2llf2UhvtthB7FcfUAB/igodZz2Bq+5dfyILybcf1OAcQe/33v53thj563WE7y+nKT01PZe6rLzafjivH9TMz23oMfhLy61MT1o9g/4B7XTItghXf+rueEvLTUIq3JHCknqWQTSFKE40Sc3WhxopLB0OIG4ulcjlPTWRRR5OVbDQa2v8vxt8kYMt+8VmO5YeJHUUyPTGsUEwqeDIfGUkxkDf7sep1sQolpkkKE7YQkFYl8UqU1cOnZAYbmIQkC84UURyqZO1Sdot3/y5LIdCHJbHFIEIQ4fsg3rtZ48Wh5NMcZqsitnT43dwZc2OrSHnhsdYdMZhPs9B08P2CxlODoWHpUxd27QkKVeXahyNXtLn96pcZnT5aYTcHpqQznNwdMF3w+cWKcN9falNKxdHetazNXNNjuWrSGLhutAa8tNbm4JWPaPoeKSU7PZAkiuLbVIwhDsoZCGJrUTR/bCVDhbQ3EB/hg4CAY+HOKd9rsP6qT5X7pRuCeTq/FRKwvPJU30LW3Mrx7m8VIEDg9mebIWBpEgXrf5tMnx9FlifGsznpriKGKNPs2fhSNshx7m0o/DNnqWBwZS5NVJHYGNrIADdPl8ptbPLOQ59p2n0o6zkyYts+t+oCFUgLHD3h9pcXt+gC/FtEZxvKfLdvl+xsdlnZMpjIGT8/mcfyQ5Z0BqiLhegG3ql3cIGLg+RiKQmfoktFkQlngRnVAKanz+EyWruWRNFSs5oCl+oDtjk05rcWNzEpsGuMT0ew7VNI6pydzrLeHyLLAT52YICULbLYdnDAkZ6icmcpQTuvcqA24stXD8gJOlNIsjGeZyRmU0xo3qgOubHcpJFT8MOL2jklz4FIoy+RlFQkPP4hG0qx79vQbXZvn54vkDIXXl9uYXkA2UkjrIjd2BlR7Lo9NZ9juOdT6DgPbR5Qk8kbs61DtDckZSvy973pEFBIKEVBOa6OKzuWtLtWuNaL6/C8fmuXSZpe8oXC92mfdhHS1jyzLbxuv16t9buyYTOTeoirsyfg9SJ/9URxX3wscVB1+MvBB+R7v9mt5EN7NuH4YM767qUN3Y2+z+fpy844Kwd2QRJjOG/cN1oGRvOpeAKLx9mBAAnQtDghaJuwx5T0PFvMJkoaKJIi0bBddkvjeUpO27ZJQ4iy3LAgUUxqKGK9Fc0WDUjpPfeDQs01cz+frV3fQ5ZgP33cCtpoWuZTCTR9cL+5zKiRjL4PVpsVyY0DXdHl8JsvJiSyvL7VwAx+Bt8o5Q9dnpdFHl2Iln67tc7SSHtEej09k2Ok7bHcGXNjoY/s+P3NmilrX5pWbdZabQwoJhcmsQRTC5Y0+AztEIOJGdUBSlwlC0NXY6EyT4gbevQTMzWqf67U+x8cTFHeHSMt0sLyY5tUauruJuFjaO6NJSJKEEEHPCiGCFxeL7PQdaj0nNjQLfLpWwOGxJCuNIbcbJlEQ8sljFfyoymcfrzxw7BzgR4ODYOAA98SDMkr32mztN7I5u9zkdsPkhUMlFsqxB8CrSy2ens2M/n67a1FMqSTUeJPn7Tac2q7P2dUOSVXg0naf6azOX3hqmvNrbW43TDKaxEbHZiylMF3WRqXTW3UTXQZdlfjFJyZJKRKDIOCxuRx9y+N8x+FGtcvFjT7ORIoXFktAyFpryHbX4vWVDkdKCR6fzpI2FL59Y4fe0KHesbmtDXD9kENjSY6UU3z9ao3Nrs2JSho3CNkaOExmDD5xrMyfXq2z1bYIszpPTuew/ZBSWuVKrU+955DVZW7W+7henFXXRYHjlQz17SopQyEQYBqB1tDh69drHC4l0SSJ2ZwBokgpa/DyrQaqJLDdc1EkmdXWANP18COoDR2Sssix8RRIEhtdiyiKUFSRZt8hCiNkSeBW3aSU1GkOXV6+2WC+mOL4eJr1tklQNxnY3q4KUIr/9aMLfPtajfObPeaKCY5X0kiixImJLCcmslzd7tIY+Axsj48sFkdVnLjMvUNGk1AVmUOl5Eg2dk9zO6GKfG+lTVrvU0wqHBlLU941kZNF6CfjCsC9NjP3ahLe31twbDw90me/n/LVHvZcTt+Pzd5B1eEnAx+E79ELQmo9h5zKQ43Rd5P0uZ8Z3/3cgR+Ed9PI/6BgfaM1xLvH3yRk8EPwA5AlRtKj5RSoqkQpqYAkcHoyy8s36vhCSCWtM1NIUd3V8k8bEtZYim9er5PUJHqWD4JAOa1hSBq6LGJoEqcncyw1TN7c6GLbAW0HvrvUZracJqPLHK3E5lxPTGe4Wu3StyNevlXnjZUezy7mmM4lqXbjTfalzS5fu1ynlFF4RhJHCj8Qf3enp7KcX2tjWiq2E7Desrm02eX2jsl628QLAjRZpZDSkEToOQGL5QQnJrNkE3VmCglsL67a/9n1Ojd2elyrmfwvz8TiDxNplVOTKaZzOuvr8TX3Apr20KPVdxAQcDyf9eaQ8YzOiQmdUkpDlQVcP+RD8/Gc/1++t8rry20qOR1FjtebWt9hu21S7dp0bRcRiVr3kYheB/gh4ZFWvH/6T/8pH/rQh0in04yNjfGLv/iLXL9+/Y5jfvVXfxVBEO747/nnn7/jGMdx+I3f+A1KpRLJZJJf+IVfYGNj445j2u02X/jCF8hms2SzWb7whS/Q6XTuOGZtbY2f//mfJ5lMUiqV+Dt/5+/gugcD7b1AJavf1+hmozXkpZsN/CC8wxl2Zld14XZ9SPdt+m8Re14x319r819fW+PsSnP0272/jzeSEUfGYiWh9Y7N169s8+WLW7x0vYYgiZyeTKPIMhsdh1rXxnZ9UqpIKRlLaE7nk+RSOtOFBJe3erQGLnMlg7yhMZHVmMsbZBMKXzy/zZVqj1v1AbMFgzMzWTRVptqzQRBAENAUiVMTWSZzBtWuzf/z5iamFzCWUlgcT7NYTGLIEjO5BBttm8bQYSqf4ONHysyVUxQMBT+M2GwPcZyQnhPrOc8WEpQyBmYQU31kERRJYjJlkFIUEAQCP6CU1EioMrfbJmdXmnRNl5SqIIgCG+0h3aGDE0bMlZJ8eKFIrWvx3eUWryy1OVJO8sSuvfzhUorL6z2u1+ImL02RGc9o+FHIVs/CC+PS7XJjSFKNv6mlxpCN9pDO0OPZxSJHxlM8u1Dgrz43z8eOlvGDkO1eXIl58WiRz5ys7Ja3Y6m7+sChZTq0hwFZXWa9Y/LqUpPz621evtXga1drCBCb5UQR311q8X99d5WXbzdoDlym87G3wEbbZLkxGKlP7WEv+5hQ38pp7PUW7Emhzuw2OO5tZvaMxPbgBSHrreGIk/zSzcaoOfJhsf8c98KD7qUPMg7m+zvxoO/xncbAD4q982+0hlyv9um4b//du7n2ve6Lvbn47obevfd+v3vpXrjXPfogeEHIcmPAesscZa/3XstGa8iXL23fs2fA8cH1oOOCGcRZzgQwOZZhOpegkDIwZAnL8fF8mM0lKKVVdEngybkcIgKbLZvLGx3cICSjyQzdgFu1HrMFg47tkdIVsoZC2/J47lCRJ6az/NzjFRYycGQsxeWNDq8sNbmy1Y2llSsZzkzl6ToOthOg6QJHxtJMFRJM53Q22iazBYMnZtKUUyo3dwY0+w636iYbrSHL9QHn19pc3+mz1XX42ccq/OxjE5yeyvL0fI6sJtOzPTZ7Npbro8gKmiwynU9iuSGaIrPdsenZcdXiMyfH+fiRElM5g1rX4suXtvnK9R02Wg5/crVO046r9i8eKXNqKksQxM3DhYRCKalhaBIpPabAvrbSQlckDo2l0FWZ+XKKxyaz2F7ERE5nJmew1Biy3DARJJHO0GG17TFwHGTxoDr6QcQjVQa+9a1v8eu//ut86EMfwvd9/uE//Id85jOf4cqVKySTb8lFfe5zn+N3fud3Ro9V9c6Gkb/7d/8uX/ziF/m93/s9isUiv/mbv8nnP/95zp07hyTFVJJf+ZVfYWNjg6985SsA/M2/+Tf5whe+wBe/+EUAgiDg537u5yiXy7z00ks0m03++l//60RRxL/6V//q3X0aBxjhXg1cd6oDxbzGu4/xg5BnF/Moojgqde4ZkhUTEm/6cGO7hxeEBGHIcn0wOkbZ3UjumZfNlVNc2uwycGK9/ObA5vxqh7/2/NzomgPH43dfXaGU1Hj+UJHnF4sUUioX1tsUDIWXbzVIagqPTWWx/QjXjxh6EZ2hx2I5jSwIVPIGExk9dh3uOBwfT/PsYpE3V9qstodoskAQRlQ7FqoksWPagMhKc42MIeP6IQ3LoV9zsZyQ2VKCgRthdmz6rs8rtxus1gfMFpPMKEmSqoSiSKT9kLSqIAALKfgrL86z3LawgpDtjhm7FpseHz5UQBIF/vjiNsttk6fnC8zkdL59q8lE1qDWd9BkCUNV0DQJVYqYLySoZA3+55ubLNXMEf9VV2RUQaSU0pnMJVhqmvTtWLmomIq5ntmEsjsGBL59rcaO6fHRw0WeXyxxbLdZeaUx4CuXqwzdgCPjKZ5fLI2agvcqA13b55m5QiyF2ne4sN5juW4ykzMYz2rcrg+wvYAXDpdG8qSNgcdkTme9ZZLRUqybcO5ijayh8lefnX1HesL+CtX+7OX96BJ3UxLeEiW8Ew+iiLxTxvjHVS3jYL6/Ew/6Hh+lavBu6Eb73YiPVdIMb7+7a9+NhzUee5h76b3ARmvI75/dYOD4Ixf6vUB9o22S0mRUeFtAkNWg47x19wbAkFjI4QsvzHN1s4sVhNS7FroqcqKc5/XlNvW+y9MLeV48UqJuulzdHpA2ZGw/4I31Dlc2e+z0LGaKafq2x3hGob1r0tizAxaKBk8UISBitWMRBBG2H/DSzcaI2z+wYmfjvUBC79q8sdlhaWfIR48UqPZcbM9n6AeUMxqeFzBwVL5xY4cwgNmCThhGSKLIeCauhCuiiK4qHBvLcnIixemp3EjqeXq30u56Pg3T40QlPaqgf/LkBNerfdKqREZXODKWZLUxJCICc2+Ma6y3hvTskIHjERGrBimiQK3nst62aPRcTk2kR0FNIaVSTGscqsRGlOdWWjRMl59/fBLXD1nd6QCQ0SVePFp6z8fNAX5wPFIwsDdR7+F3fud3GBsb49y5c3zsYx8bPa9pGpXKvXlh3W6Xf//v/z3/6T/9Jz71qU8B8Lu/+7vMzMzw9a9/nc9+9rNcvXqVr3zlK7z66qs899xzAPy7f/fv+PCHP8z169c5duwYX/3qV7ly5Qrr6+tMTk4C8C//5b/kV3/1V/nt3/5tMpnMPa9/gDvxsAvT/gVn/4Z9P0Z0oPkc8r5egUpWj6lAnse6CUPF59n5PNO5JC/fatCzPX7m9AQL5dQdC66yuxgMXR8/jLhV7XNkPMP47nUvbXZZ2ulzdbvPVM5jIpdkOp/kpRt1XrndxPdDREQmszofO1riv5/dIKlKeH7My5QlkUrOIAwCVlsWpuNzfbtHEGV5Lm8wmU9SyWps9x1u1AYkNIkwdOkNPcYyGqWUTkZXqEypbDZtVjsm0wWD5+YLuD6stwZstS0GlkvPBa07RJJEnpotghDwpu2y07epdi0CE65U+2RTOklFJKErJNwIiLD9kLbpoAgiKzsmph3y156bQUCgMXB4/lCBnh3Ss1yemikwk08xV0pi+wGGIiGK0BnYeAgcMjRURebpCYNn5gqUMyrrbZsIaA5im3hZENB2ZfK2exalhMLAiT8j2/O5tNmjPrAZOgGPzaQ5VsmO3C/nigYrjT6lpMbx8XgROrfc5HsrLSayOpM5jbbl0RzYtEyXq9t9jk/kyBoqnzo1wfm1Nhstk3PrHartPJMGLMzn6LlvbdLvHrP3ogDtb8rbyyy+k2qWF4QcGkuNxtf9xv/d5/lJ1ck+mO8fHo8yBt7N5n2/rvx4JqaEvJtr342HNR57mHsJ3nk9eXtS6e2YzBvkDYVjlTTrrSGW5/O1yzV0VaScVFnIwfXOW8fLgK4JeM5bc8TeT6WEzMs369yum9R6sZsuQBCFFNMqT0xnmc4lY4GFgYOmiRiqwJ9drbPVGbDZtkhoIkMnpDV0SakSj08XKKU0VprDURP06cUimx2LNze7tHoO1YHDSkNBlmITzMVyAlkUaQ1jktOZiQxEkE+qWG5EJauy1t6VNg0gDCMIY9O0E5Usry41+O5SE4gwNJXD5SQfO1oeVWj3+uf2eqYubXapmy4brSF5Q6bY1liqmyMZ73IqzcePjcW9dpFAThPZbsWf2dCN5bcfm8lwuyZweatLKanyieNjCILAyzfq1HFZb1msty1qXZudvs1Wx2Emb8RUpq0uPcvj+3mDFw+X+Lkn5tj5zi0KGYPlukkl++OXHPlJxw/UM9DtdgEoFAp3PP/Nb36TsbExcrkcH//4x/nt3/5txsbGADh37hye5/GZz3xmdPzk5CSnT5/mlVde4bOf/Szf/e53yWazo4UB4PnnnyebzfLKK69w7Ngxvvvd73L69OnRwgDw2c9+FsdxOHfuHJ/4xCd+kLf25wYPuzDtX3AezK+OaPQdTNcia8i0TJeVeh9ZEjk5kWImCdMnyjw+FzeDJTc7NMxwpCpzr3MmVJkj5Qw3qya1vkNz4LLdtfjWjToTGZWZfILPPVbh9EQOPwip9R0qaRU/itBkg+lCij+5XOXr12qkVJnJQYJTk30en81zabNLWpXoWD71rkXXdlltDHhmPockwlg2we2ayVhSRZYEpnNJ2o7HsbEUhyopdrouxbTKd2416Q1dJrOJ3YU74tJGE5GIlBLzWHVFom06SELIUwtFbmwPsCKPgi5zpQH/99kNZEkkpcWmMmMJlY7r8dr31hFEmC0nSbsK9Z7Fn17doT5wUMR4YV4oGFytBtzcMelaHmvNIY7vc3oyQxiCKgls9ixmi0kem4q5/isti1NTOQZ2g+vVPofHkjw1l+P2zgBDklksJeg5Hm074NxKi3xSI8hpDJ0ABZHPnRrD0GVKKY0ZJba8P7vc5Pe/v8XiWILPnZrg65e3ObvSYqkRVzSeWyjyxloHQ5H4+JEipYxOMaUydH2+cbVG3XRoD1yiCG7WTcQh/M0T4/SciGJKZX2312B/Y/C9xvDe5mm/WtG9sH8s+0E4Mjrab4p29/i/1zl+HDP/j4qD+f7+eJQx8G4273sOsteqfYhi+pwXhFT7w1Gy5b3CD1IJeKf15I7eg7RCEMZqYdNFaVQZ/unj4xRTKpc2u+z0bcIgIqXJ5BIyPTtge3DnOQNgo3fvit6Vahc7FAjDkFI6pjotN0wGls9sOcmTs0XGszov3dzhdmNA1lA4Mz1GreeR1yVCQSClygxDH02T8MOI9bZJNqHw9HwewpAgjL+f6XySK9sDtnsOthdydqVDc2Dz2TOTPH+oDMAba22apsvx8TSHx7NkDBlD7pIzFMZSOq8HYLk+h8spSmkNL4xomA6RIJLQJBRZxHJc0kYWyw2pZPU7VIL2PuN630GMAAHOrXQopTWCICSIoLxLoVQkkaEbS10fG0uwcyX++/Nrbb5yscbjs2k22w5LjQH1nsP/9jGNw2NpxrIGkggTWY2h6zGWSmNoMks7LY5NpHh6VicIAr58aZs31zusNIeMJRUWymmiUEBXDmhCH0S862AgiiL+3t/7e7z44oucPn169PzP/MzP8Jf/8l9mbm6O5eVl/tE/+kf89E//NOfOnUPTNKrVKqqqks/n7zjf+Pg41WoVgGq1OlpM9mNsbOyOY8bHx+/4fT6fR1XV0TF3w3EcHMcZPe71YtMNz/PwvHu1JT069s7zXp3v/UYxIXG4ZFBMSG+99t0mtT21ir2fK2kFwgAvDNhoW1yv9vH99IjbXUhIjKcVTNtjOq9TTmtU2wMubwypDxy22hkkEU5WktQ6Mce1Z3mIQmzjuNEccHmrx0ZS4eRkhpbpMZ7RUKR4AhxYLgPLQRGKHBtLEPh52pYPRGw2TD52qMha0+b6dhfXD9noWMwVY0nKgSoRRCGphEQxpaJLEV96c52VpsXjM1lm8hpDx0BXRBRZIqdJNKSI/352je3OkLGUxmbHJZuQWSwmuVUfIBDx3GKer16qxc22hQRZTeL6dp/lhsnNnQGyCKXxNLPZJPW+Q7Vn0TU9/CBkPKPx/bUhakYgCiFnSKR0hZ2+w1YnRETAtD2GrkNCVZjPGPzcyXFu1mK3zFxCJSEL3NoZkFAljlcyPDWXpdWz6DshXhBr+l+t9jg0liQMI25sd+mZDvmEhC6KrDb6fPtWA00UIAoRooib1T6hADNZg4V8nNWaziWIhNhF+latS8/xcX0PO4BKRuO5hQLjaYWcLjFfMDhTyVDrmHz3VgMnDDlUTvHEdIZTEynyhkRj4FBMaiw1hpxfbeIFEefXOxyvJHnu5Bgb7SEv3WowsKDWHbJQzrDRjvnSh8rJO8ZsRhNIKZDRhPhe3h2/XhCyVDchCkdj9F7YG8t3n/du7B//P2q823nm3c5LP47zPfxw5vx3g3czlvbm6oIRb6Y2WgOWGvYdc/B7gXvN7cWExEZzMJqP74e778X7vYe9e6zjwuXNDsDoWpW0wkZ7SL1r4XgBXdvjcDnF4zNZdnoO5RT0Om+d8+4wYL/06HbL5cy0hCTIWK5PGCi0TYecrnF6Mo3luJxbGuAHEWlNppTQ6PZdMqrEU7PjHBpPUe+7DF2flCphBSHfud6g1rV5Zi5Pc+CwboK63iKhK4ylZA6Xs0iSyJcvbLPesegMLIa2w5WtHkfGU5STCmlN4GatT1KTOLvSJKMrfGg+z1MzGfwootqzuLjRo2e7pHWVJ2ezzBcMvnOrztANaPYtMgkNRYRnFwrMF3QKCYmh7WA7LmlVJEiqTOV1BrZHVpPoDT3KSYVjYwk2mgPSusQrtxpEgoAu+tzuQte0yOkSpbRMRpcZ6D5jSZmNlkmzN+S5+Rw5XeJ23eOPL1ZpmQ4LpRR5x8PxfGzbZXsYEIYBqgjHSglqfZcLGx36ToAiwfXtLqcn3/tK3o/b3uteeD/ew8Oe610HA3/7b/9tLly4wEsvvXTH83/lr/yV0c+nT5/mmWeeYW5uji996Uv8pb/0l+57viiKEARh9Hj/zz/IMfvxT//pP+Wf/JN/8rbnv/rVr5JIvLeZva997Wvv6fneCUEYN0/lVHjAXP1QaNqwNYTJ3Y9k7+fivsTQ3vWGt+GCGD9e6cOtLvR8eKoIOQ02TFBFUDy42IWpBPz7//GnDHyY2D2/EcGbnet0PGgNoeHCS3qsGZ2SYT4NVRO+tQZeCMu3b/PJqfh9Xm3Dxg40qlsMN67hBnBzB8YNGBchaDa5/uY6mgALMhwWBgjtOl/+syVe3gHThevXASHupi/qMPTh/7hxE8uD6gB8AXp2n/oAXu/22ErF731tFb5/CZpW3G/c7sO1FZhIwpEMZF3oDmEQWNR6bTaHYEiwtjHgP2+s0bLipjc3iL0XtrebLGQhssETYeACIUwoMKZ5vHFjheoGnM5D1YK8CnUbxBBqHvS2QRQgrUBRgzdacKMFOw7s7HRjupAbL5SvXN3gZCF+z0stmErCilNl6ENZgiiCK7fhpgjDEmwb8ft8oxnL+CVkqG80kEQY9uDLq/DHQCUJagivbYEmQTSEpAAdD9adZZYvxGOlZsffUceGHTv+jvUAAgdubMKOBcMuVAy49NpLXCJ+ru9BPwX7+xH3xuvV3TG697igxOfuZOHCA3xu9o/lHzflz0edZ4bDR2uO3sOP43wP95/zv/GNb7znc/4PG5dee+mOOfi9QhDG99DKpfh+KGrx/XGvdeBu3H0vvtN1ggg2r7zB9vX4Onv339496Yaw3IdgE9q7vevtzv3PKQL7R0M+hOraOqEALRu2VBgE4CrwzZc3sIN4vp9LwWEVenV4dTley67oUDKg7cZr2IYTz2lzSVBrsNGNz+mGcOXN81zvgRPAsVw8n5omlD1Yv17nX7wBmybMpuCxYnz+qx0Y06HtxM+/vAG3evGa5EfQtuPrJlUIa/G83uvFn81yB0wPWi5867W4Z+KSAS0HVvvxGqFI8WdoBbCjQ9uK3/sbCWh5sfLSqgkFFS6rcKULwf/8BoeyYNhwux7P9RMClHwYLrf42vYFdizY6sbrzwRgbsB36vE6I/a2CIFbbahZkA4GuD4sdeM+j6QA1y5c5IvbF9+z/crd+GHvvd4PvJfv4WHn/HcVDPzGb/wGf/iHf8i3v/1tpqenH3jsxMQEc3Nz3Lx5E4BKpYLrurTb7TuyRTs7O3zkIx8ZHVOr1d52rnq9PsoOVSoVXnvttTt+32638TzvbRmkPfz9v//3+Xt/7++NHvd6PWZmZvjMZz7znnFOPc/ja1/7Gp/+9KdR3ske8r243l1Z0MVyEkUS3zGD8zDnvLsy8KDzbbQtpI0uM75PMaXx9FweRRKp9RwKSYWdnoPve7z08iscOvUEYxmdx2dyI873+fUOhulx3JBYbVo8PZujPnC5uTOgPJYiF0bclDepd2yMnE7p5CSyIHJ7pcljWZ+TU2memM5hez6tc5scKiY5OZmmlNKQRZGNzpDy1R0OzeRJajKaImBdqTNwPcopjUvbffIJhYXpHFttk52dAWNFjRNpjWxCpZDUWG0O6A59kqoIAgy9kIQqkbYDjo+nkISI/3l+CzWlMkwaPDGrYS+3EKOIjuOjpiN+6elpNFniT6/uIAoWx7IJ5ksG519ZAV9GTyf41JNj7HRdWpYb9wQsFDEdH6855LmjJSYLCZYv77DZt2l5Hh87WuSJdIJqb8jNusnzR8tEkUDn3DrzMwKZoc+RcgpdkmgOLG7uDMgmFMK0Qc/xKJcjXjg+zkcW83xnqcUnjpSoDzxeX2phyCDLEtmcwYcraZ43HUopDSL4ypUdECI+dazM2ZUWV6oDWgmF42Mprt9ukU+ojI8r3Nrp0bUCnPEihibz1EwOQ43VjDbbFq8tt3huocB86a2m1KHrc26lwbU3vs/xZz6CLCu8vtLCCCKmx1OjsXP3eN0bT7Wew0bb5JXbbeaOFHlmvnCfkfvw98IHySPg3c4ze5nxR8GP63wP95/zP/GJT1Asvl33/keBRx1je9/95z77/q0xG22Ll283IIInD5cYz2gP9Rof5r3sHWM7Dr//9Vf42IefYejGEsLTeYOh63Nlq8fHxlO0zbiBdb8Xwf/34ldp3UUVyikgi/EGt7vPhGArhL4ZS4vOT6f4yOEi17b7tE2XyekckgADO+Cp+TzPLxYYuj7/4aVlzFofL4hIjWdICBGfO17mpVtNunbAY7NZPnWygheE/N/fW+XGm9f53IdPkzF9blV7HFss8cxcHnnXP+e15RapIGQxCimmDI5PpDkRhJzpDNnputT6Dp8+WUZXZJ73fGpdm/rAY+D4HB5LIksCPStgoZTgcctjoZTgRs0krYosNS1EQaCS1SilNP7o4jZKw+T4E1MYishO32UsrVJKafy3s+us10yeOV7hZ2YLpHWJb11v0LU9JjIKmy+9yWd/6nlOTBVG1aG9vo1bV6rMn6zwzHyezbbFi2GILIpM5Q022xbiuU3W2iZ/7bkZqj2Hwmqb7620OD5XxNBFNs6tY7ugyJCbW+D0Y5Ms1c3Rd/5ezLM/7L3X+4H34z087Jz/SMFAFEX8xm/8Bv/jf/wPvvnNb7KwsPCOf9NsNllfX2diYgKAp59+GkVR+NrXvsYv//IvA7C9vc2lS5f4Z//snwHw4Q9/mG63y+uvv86zzz4LwGuvvUa32x0tIB/+8If57d/+bba3t0fn/upXv4qmaTz99NP3fC2apqFpbzdqURTlPR8878c574Vqf8ithsXhcpJTu5bjt+rmrknTO5vS3AuKwh3OltOKssshVe7YgO1JME4XEkwXU9RNj6bpcqSSJaFrVLs208UU1a7NStuJy8MaPDaTZzwXy5BWsgq1jsPths2hcoLHZ/PMl10qWR29NeTiVp/Vts1zCwWenClwSeiBFNEZBrQti0bfo5LTmSulWe04WI7HeFpHkgTqA5/lhkXSUGj3HXIJjQiBxfE00/kEkSDwyq0WnzheYiyrM5VPoikiIQIpXWU8p/O95TZeFEuuPblQ5I/e3KRphdT7FrIkM5s3eG6hwFhO5/J6lzASSCoyjaGNH4VM5RJ0bYeG5ZJSZLwAeo7P0A/jUrYsIEkSGQlcATq2y80dkxCBnuPTs3xWmkNu7PQxnQBBFFgsO3SHPqutIRHw2nIb12uRTcj0bZ9UQkOTBU5P5zg2nsL1YTKnsdowmSkmeWI+3gRd2+pzo9pDEOFKtUdCEdlsW2z0XK5v92nbHo0wZKtrc3w8zadOTXBiOt5UD12fxbpJ03RZbtpkUwalpIvpBLh+xEIpxanJNH3bJ6HKqJLAE9NZXllugygiyzKIErIs88KRsRGHdQ+9vsdW1+NKBzLrfV44MsYLh8fY7lp0bJ/mMBiN77vH697j8VwCTVU5PZVFUd5dEXTv/vpB7qf3E486zzzKsT/u8z38cOf8d4t3O8bez/cwXZR4QYjvx717853cjuPXxDu7Iu++3/l8bJ72+EyBnhONehSub/R4aalNa+ijKjLHK2kS+84p3aMQ1LkPE0IDUoZILq1SySYYyyZ4banFMAjRFBFFUmhZJusdm9T2IHb7jWLVnq2uQy4pk9I0tvs+hyo5OqYDosyl3WO3Ox6qCB87OsYXL26z1nU46XpMFVPUujYI8NxiiUiAwA/pWB6CILLasdhu23xvtUNExHTNIGNoZHWZ6/VY8Wg8qzNdSDGW1ble7YMostJyQBBZ69h0hx6fOTmOrsojAYQnZnPMFRJMZA1W2hYT+QSnp7LUujY/+9gkU2sdPnq8QikVl21OTHn8wRtbPDmd4ekSHK7kUBSF6aKEF8F2zyGXVJnMJcglVb5xvYEfRghE9JyAZ0URRZb50GIB+0bA9ze66KpCLqGR0BVWOkMqaY2UrlJICdheRNP0UGSZU9P50Xf+Xs6zH6R7+93ivXwPD3ueR1ohf/3Xf53/8l/+C3/wB39AOp0ecTWz2SyGYTAYDPjH//gf80u/9EtMTEywsrLCP/gH/4BSqcRf/It/cXTs3/gbf4Pf/M3fpFgsUigU+K3f+i3OnDkzUps4ceIEn/vc5/i1X/s1/u2//bdALDX3+c9/nmPHjgHwmc98hpMnT/KFL3yBf/7P/zmtVovf+q3f4td+7dd+5MoSP0zc3di7Z971qMoSjyqdWO3avLrUBARe3G2eOz2V5dJmdyTruN+kBhg5EPtByPm1Nl37rRROEAXU+84d15guJPj0qXEafYepQoK/kJ0mpW0TRiBJInlDYSJn8NhMhryh0OjbtIc+jh8hihKrjQGbXYuUKiNLEmld4lbDZCpvYCixM+PtnT6W43JoLEPTdJEFuLjR4dRkhqHto4jxyrPRcWj0u2x0hqiiQN/yEEWfsGBwrdrnjY0OkiCQM2LjrLW2RVKVOTGV5upWD9+PaA9d+o5PLqHymZPj/Om1KtWOjSIKjCWhOJZjo22x1bP45PEKluvzrZt1AiEkqYnkEiq1ns3tusnHjpRI6QUyqsirqw26Qw9NTSKLAhdW2xyfyvKzZyZZLCd55WadZt/lwmYPRRHJ6yozxQSHK0nOrjXp931eu91grTFAU1WOlOMgT5clFstpEopEGMK3rtU4MZElEqDZd0AQkAUBP4romg6WF7Hdt8kkVU5UMkzlE3x/tcuJyTQz+dglOmvEKkWqIpHVZVaaFk/P5+4ILPeaFp9bKGAuw3MLhTukZ++lRnK3Ssnez/dyPX0U/KQqBT0MDub7Hw4+iGPsbpfhR1EJeqfM7v71oKjHAhHZ5Fsblj2DsmOVND3Lf9vnoskicG9PBQlISNDfbcUQJXhypogkCqR1hQurbUzHp5jUyRkap6azeH6GcytttrsWs3kDQxaYGMvQtTuUkjqGKoEgUMnqfOrkOOfX2lzd7jFb0Dk1lSFsQs8OyBs6BV3l0Fia5sDl2zd32Grb/OJTU/Qtnxu1PpIgUMkaZHWZS6YPUYjjR6y3bI6MSbTCkNuNPodKSdqCyNnVDofGknQtf1dNKoors8CN2oBqz2I8a4zmz2rXxQkCrlV7lFIaxyrp2El4z3ulmKJlutyo9knpMq/djisDAzcgp8YsgGklTvp1hh4v327ywqEiv/DENOstk/MbXQxZwAsjnDBkrmBg+zCwPJbqJssNk4mczocPl9lsWwx9n6ShcmQsjaaKVHsOzx0uvS3580G8B/684ZGCgX/zb/4NAD/1Uz91x/O/8zu/w6/+6q8iSRIXL17kP/7H/0in02FiYoJPfOIT/Lf/9t9Ip9Oj4//3//1/R5ZlfvmXfxnLsvjkJz/Jf/gP/2GkOQ3wn//zf+bv/J2/M1Kh+IVf+AX+9b/+16PfS5LEl770Jf7W3/pbvPDCCxiGwa/8yq/wL/7Fv3jkD+HHGXerWLxbZZNHlU6sZPWRPfx+lZc9NZa7g5Q9adGOC68tt0CQOFpJUUyp1Lo2eUPhSrVPJWfw5GyeatemmIqdEHv2XunUoecGtIcuczkDXVcYOHFA8eZGD8vzEIBPnyhzabOHocmAQBjAsakUh0tJbjVMlup9Xl9uMpbR6Foem+0hU/kEqizy+29s4gYhuiIiCLG+8ocWi6w1+gxsj47pktVF8kmNXELhUClBY+Bh2REfPVbgmfk8S3ULQ5FpDx0yRhFJEGgOHYZ2yGrD5Lo/4Mx0Bs+PMF0PKTKYTMKZuSKC0GKnb6NJAhfrserF9243UVWFzx4r0LE9zq22EIGn5vJAyNmNNpWsxPGxNK8ut1htmyiyyJGxFBc3unzxwhaJXW+DJ6ez1Psei8UEdk7jUDmN4/oMPA9ZETg5nuLzT8Ql3NeXW6w2h2SSKkVDoT30+eqVGl4QMLADjlVSRIjIAkSCSChEPDOX42glg+1DZ+gBER3To212EIDZokHPDigkVdKqRN1scXkDTDdEEsVRYKlIIvOlJJUUzJeSo4XjfuP7br+AR5VuvN9m5s+LUtC9cDDf/3DwqGPMC0KadvzvDysB+igqQe/0XvavB/fCnlEZQNZ4e7NPz7m/uVpCjHnxe0hpcXAhCiICEZe2TEREFseSvLnWZSyr0TFdrlV7HCdNGIRc2OwxX0hwqJRgtTVElaW4Mj0b09xsz+fKVocgzPD8fJ7Vq3GCS9dkfvGpKZ5fLKNIInlD5Xp1wM1qH0WROFRKUkppscpZGFJIKcwWx8glVfqWR8N0+f5Ki7WWTUZVmJlLMl9O0hzYcTCjSswXE0wV4v9apstSfcjFzR75hMrzi0Wemcvz0s1YWjsS4FqtSzFpoMniKLi6udPl917bIJuQkAWJkxNpHpvO8Xtn4Y8ubPHZM5OMZ3Q2W0OemMlSTmlUsrHq23Z3yMW1HpEQUUxpZA2FXisW6nhsJkd34JA2VL57o4EoCRRVFVGIsMOIW5t9vDBiYHlvCxj/PM+zHxQ8Mk3oQTAMgz/5kz95x/Pous6/+lf/6oFmMYVCgd/93d994HlmZ2f5oz/6o3e83gHeGQ8rnbh/07SXOdrTdJ8vGGQNmWJKfdvN3bVcvnV1G02I1Q9kWR5leW/VTU5MZKnkEhyrpDm73OR2w+RQKUnH9ikm4wWhabrkDYXe0GOj49CzBtR6Fks1k2cPFXn9doObOwM6QxfTC5nK6jw1l+Plmw1WG7G51q2dPrWugySJnJzK8NxCkWvbPYpJje/catDoWUzlE8zkEtT7FklN4eXrO3H5U4oXuqyh0hk6DJyQna7LdMHgE8eznJnO8p3rOwRhRM+y2ezYvHqjjiCK5BMaZyYNdEni/HaXastiLGNgBwFTBYOVDrH6kCQhijLnN7qstYfosoAlRDi2x2bPIiSikNGRlNgvQZVEUpqC4wVc2h7QMj3KaZ963+Wb1+uMpVQGto/peCwUU5i2T9aQsf2Qa1s9DCVWIcolZVbqFvPlNF4Ap6ayXN/u4QYhqijy4pExbD/glVt1LDvg0naHrCGRT+ocGUvjV2PZScuD6VwSXZXJGDJt02XoBlzd7gICT8zkOD6ZQRFjPq2EQM8OOTKeZCJrvG387ZceBO65Yd8zuztcTr4tYH1Y/CDGTT+pOJjvP5io9Ry2hvG/D0PdeS/wTpnbh5Xy3Y97BTUPU2Fo3qcfMi2BH96pLpRPKaw3h4xnND68WCSIQq4LA0zbp5RVsP2AN9e6BIAXxfPNz54ZJ5/QuLzVw3JddFWilNLYaA2pdi2+v96h2Xdxiz7VnkPPhWrPIatJVLJxb4MiiXzqVIVKzmCxnORmtU/OUGgMHG43TIIgiv1cFBnbCRg4IXlD4fHZAk/MRhwqJ7EDWKkP+LPrDXKGzNALqGT2vgcDBIGMLjGV1dBUiUJK5cpml0gQGE9rXK32edMJODoecng8Q8/ymSkkWG700VWJJ2fzzOQTVDLxa+750Ok6NPoON6t9vnqlxvFKiiCESIiTOxlD3XVgzjNfTNG1PC5t9XD9JBlNYrXpM10ySBsJLmx0MAWBjY5NZ+iSS8nsdB388P1x6T7AD4YfyGfgAD85eNjI/H6a7sCoMlDr2iOq0t6E/tKNOl++tEPJgWf3nW//InNEEllvDbldN2lZDrOhwfHx9MjJWJbEUSXBD0K8MOS12022eg7rzSGKrBAJYPtRrGQjCOSTGrYTstm1EEWBxXKax6azqLJIKakhCHC4kqJne0gRPL1QRBckNnoWA9fndsPEDUI816OQ1/mZUxMIksBXL9dIyQKOH7LUGJJQZfww5I8ubuN5AX4UMXA9rtR6nK5kSKoKYxmdtdaQpCxiBgE5TWaga1za6rLZBsnt8tHDJY6UkzhB7Jbshj4928d0fdZaAwxVYTKjoysi377VYCpjcHI8w1rH5MxkjtsZjZ9/fJJa32Xo+MwVE8wUEtT6FlttGz+AU1MZXltq8fpyI5Zb1RUOlZM4OUioIrd2ujR6Ljd2BnxoPseTs0WmCwm+emmbl2+3cVyXth1Q7znMFZNs9y1W2xayICKKjJypl+sDGqZLq28ThiCKEf6udGnMO4WPHS0zsH0en82TUN8+HTVtePl2gxeEfTrru+Nlb9NQ7dpcr/XjMvg7mCLdDwdl6gP8uGA8E3Pt9wQefhh4mHuqPnBome7bnOnh3pv8ewU11a7N5a0u212LJ2fz9wwITs2pnFu924M4pgapgALs1RxqPY/XVlrkEgoty+eFwwUkQWC9ZTOZU0ev+3gliUjEle0e88UElQmdC5tdSkmFE5MZbD/gD86uockSCUUgl1QZuCHLDZO+B0v1AZvdOIP/yx+aZaGUojlwR9TZ2w2T7tAla2gcKieJgNbQQ4gian2XWs/m2ScmSRnqiP9/fq1NJwrJJWUKhsLaWlx9/96KyKdOKgS7ZpmiCOWUgab0uV03Gbgej8/lmCsmEYS4qua4HiuNPoYqYvsBZ6ZS/PTxcZbrJq+ttHh2Lsd8CsZPjVNOaRytpGkOHBKaQhCE1LoW37nVRBFgYSzBdD5Bz/bRZBhLKdTNuNfN8UKOVjJsNC28MGIyo5HIG7y52SEhi6h56Z6mjgf40eMgGDjAI+FBm6bxrD5SULg7YHjxaJmh4/LGG1t851YdQ9VGlJD9C0clq/PC4RLVrkVr6FHtWiPnTXl3YZB3ueMxlSTFpc0ui+UkVze7JFWBja5NFEZYbkCr7zD0feZTSXIJncPjsRNkz/ZZaZhc2OgwdGOvgr4TcLScZMexOTKWYraQ4KzVRJEE8pU0QydkZ+jyxHSW+XKShUKSSIi4vtnl4mZnV8c6xI9CIsD3A3bsgEuEDJwQP/TxfQhFaA89KpUExwyZq9tdJg1IlFMocpwBGrg+JyczLDUGTBcT9EyPSlZjo+1geyYDL8ByAlb8AUEYUe3EC3EYwZcu1XB9n52+iyjA//qRBV5fafKdm3Um8jpPzuQ4PpHGdFx6Q5+QiKu1PgICt272cbyQyVyc6QtDMFSRL1/YZCKt8dxCjo2GxWRBZzyr0zBdLmz0SOoSnzhWZrqQHAVvAAPbI2WoiKLAbDGFKglEgkB36LDVc5BEAVWR7zD66louL92o89xCLtYJ3E31FVPqqPK0PygtplSCIKTed9hoDd8WiD4M7rfZeRQu9AEO8G7wqGNMkUSKOj+y8Xiv17tndEUUmwPejXslkQpJhYQU/7uHSlZnu2vRNF2qXZuZQmI0H7x4tEzWUFneensgsIcAyMjQ3m1HKxgx3fD0ZAbLC3n5Zoufe6yCJHZJGQqmFVDKqNT7HmkD0prEescmrffZ6Vk0+i5eAFl9yHbHIowiSkmNlCHz9FyOKIy4FIHrB/QsD9eLTTcNRebyVpcgCPGjiIQiMD6eQpcljlTS3Kj2OTqeYjyj861rO8iSgK7Kd/TkrTQt6n2LQlJlMm0QzMSeLvW+R7VnsdqyAHhiJkc5rVPv2zw+k+VmrcelrR45XaWYVEkbCi/f7GKtdVmum7yx3iUMIzSpihdF1LoOT01nUOX4u7nVsJAlkY8eHRutwxFQTslc2+4znUtwcjLLUt3kRnWAIssUdAkhEkAIKCc0ygmNIAwppA1mchrVjsVqe0jaUBhPHwQDH0QcBAM/YXi/Ny/32jTtTfTHK+mYC7qviXm/6lAprbEygCdUhQ8tFu5LSZouJPCDkK3ukJduxS6UaU1mcSzNoVKSlaY1sl7f45eut4YsNU3WmxYfOVJkZtck6+uXthl4IUVDwVBFBGCpPuRQOcFURmM8o+PummJd3uyy1jLp2wEJTaGQUtFlCUOTeGquwO36gHJCo9l3yRkKS40Blze7CILAWFrn6ESKN9Y7CKKAH4TkkxqCIFBJ6TjpiKQoE6kRrh8yltJJ6hKFhM6VrR4TSTgxX8QPQ67XHDqmhxhZdG2ftKZwppKllNGQxTaTuQSSJNLs2zRMl2p3SAis7cTcVE0WCImw3QDHj9BVmXrP4UZtQNeKc2ZTOYPNrkPHdDhRiRswDVkkCCNUWeTIWJpXbjf40qVtbtcHfH89bgSezugMg5DpfAJVkekNTTRZZL6Q4OmF4h3Z/elCgp89M8lGy+Rm3UQSIp47VGKpbvL8YoErW10Grk/PsskY+dHYfWO1yVeu7BAEPkUtljbco5TtVZ6AES2o2rURJXFEJ3sv6T4H9KEDvN/4cRtj96sOb3c1mqZ7Xwfvu2lELdNjGEDL9MgmY8MxRRJHPWN768NLN+p86VKVIAx5cq5I9wEeSgFvBQIAY8U0Lx4u89h0hq9fqdF3PNZbFuWsQRiERILAY5NZLm72EAQ4PZ3FcgIWiklWWxa6IpHSZFKGwuFyGj+MsLyAnKEwnUtS7Zo4AfR2xTBOTKbIGwrFlEohGSctuqaLF0Vcq5rMFhPsDGxeutniLz41iaHIKIrEkXRcGela7kjS8+n5HNWuhhBB1wl44XCZtCrxtes1djo2bhCyWEzwzHyR82ttvn65zuOzadZbNj3bw5AFvrvU51ApwVTeoJBUeOFImflykp2uTc8OSesipvbWdzWe0ZBlGdv1Obva4Zm5XLzWmC7HKllu7pgsNYdc2eoyk0+SW1RQxFj56OxKk29fb/CnN3YYTyf4qeMVAM4uN1huDVlvmsgSrDQGPDbz7qSeD/D+4SAY+AnDgxaWhw0UHjWguLtasD9gWG8NR6pDlYxMXoczU5k7VGHupV70ylKDq5td3DCia3qkVHnUgLWySxr1gpDlxoBq16KU0shocVZdlyXmyynOLjcZuCHHxlMcnkgzX0yx0hxwu95jPKvihyGVjEGj7/DTx8YYS2v8x1eWSWoyRUOhZwU0TAfFkdhomsiCwI16n/bQ5VQlTSWtsaSIBFGEKgl89WKNldaQE+NpjlTSrDUGmG5AQpFJCxFBBNWuw4mJHLNFg/rA4fxaB0MRCV1Yaw64sTNgKpfgzEyWMIwQhYjNrsP3N3rkdZmVlkkhoaKqMl3bZyZvkNEUhq7L5aFLPq2S0RVu75jIkkDfcTm70sD2QyoZDVWW2G7blFIq2x0T2wkQRBg6AaokslBKoMoyCVXCCQJ6ls9k1sANI46Pp+nbAeMZneOVDB3L40Y1xPR9VlsW59fanJzKcr3aZ7Gc5Ea1TymtUUxrfOdWk4iI1243kSSRiayBrsj8P9/fQgBmCikmsrEy00IxyYdms8zkDJZX39IY309Hu1U3OV5J3/H83r/vRk3rYcf2AQ7wXuPHbYzd6/XeaxO/H4r0Fs1vj0Z0P7rTqME4CFlvDXl6Pnb6XSgm478n3vTfD/uKifSHLpbncXmrx9ANmS0YrDZM8imFkxMZHD8iZyToOwFDx+W7t5rMlZJMRxFhGPLsXJ6GGUAUIYgCT89lmcgmaPRtqj2LlumzkIGFcpLNtsNqw+I1vUXH8iilNGzPpzFwiMKQSkbnUCmJ5ftEQBCG2K5PTpfJJhReXWqRVAWu75gATGQNhm5IUhXJahJ5460KytVaH9sLKCU1mgOXUkqjlFHw/Yiu5ZExFGZLKS5vDPAjeGwqO6JdffiQyqu362z1OyyUM7h+TNXaGb7Vf1XtWbiBT33g8MRsfkTN/ZnTFS5s9Gj2XXq2z1haHzVWd8zYG+HQWAJZCLlV76HJEqttC1GI8PyIvgPfvdXgF56cfdRhd4D3GQfBwE8YHrSwPGwGau+4PXoO8DYpsP24X4Px3kZtT3WokJBYLsFcKXnP1zJ0/RHlJwzizfOx8TRHKikm0ga6KlNIqRwaS1FIqbyx1ua1pSa3agPKGZXnFgo8v5Dn1FSWjdaQ15ZbmI7H8bEUlhtys9rnWrXHrdoAAZgrpmL3QxGub/domw4ZXSGbUMmndOaKOqbrs9o0ubbTp5zUmS0YVDsWV6txufSFIyVu1kyaAxdZipjJGCyWUpRTGle3+rRMl47osdNzSGoSXctFkwVs1+eVpSae7/PMXJ5qA755YRvTDenbPoEAVzZ7GHJcdejbDoauMrA9rlU7PHeoTEKVmc0nOXIyzWu3Gqw0h3z+zBQLYykurXdZaQxo9h3eWO+S1WV+4YkpNFlk4ITosszHj47T7Ds8PV/kf3x/nVZPQtFEDpXTJHWZQ6UU9b5DKaPx3OESQgReGNIdesyVU0SNAabjc2wsRX3gxb0epsuVap9rW11u1k0msjpnpjKkNJm8IRMJAlldxg9CjlXS/IUnKrQHLovlJH3L53A5Nh7TVZXL1QGu+/ZxNnTjRWqPjnB3tep+Y3E/HjbgPVC5OMD7jfd6jL0X1eEHneN+r/ed3sd+mt/e8Q+iO+2tEVlDZiKfJGWoHE/pHCqLXKnfuwlVJO4bsHcfn9+yCNji6dkCH1oosN2x+G9vrpPTVdZbMQ1psZxkLK3ye1e20TWFJ2byfH+lxdev1+mYLkcnsshinB3XZZmUpsRNx2HIoZLBIC5q8JEjRUwnIAoirlZ72F7ImakMlhtgKBLjGY3HdzfOhizHPW8rLYggqcZa+0fKaUoJmcVykoQqEwQhSw2bruUib/X49IlxnpzK8Y1rdcYzKkfGU6O1/kNzBV5dapFNKDw7X8DxfURBJGco+EHI0I19a/wgZLVpQwSSKHKonORGtcetHlzZ6nG7YcWKfQWD7j4lv52+TSGh8uRsjls7JsIwRECg2rWxPJ+bOwMWigZCBF+5WsNyA45X0jx/uEhCEVCUHW5X+zw+98Ew+zvAnTgIBn7C8KAJ+WEzUPszsHd7CbzTQnP3Jn+/XrXneSOLetuNm49s1x+VjS9tdvnGtR2ubWlkkyrTeYNyRielqeiqzK26SaprsdK0sD2ftabN6ckM0zmD5abJa0tt5ktJetZunVgA0/Xp2gHZRMCtloWhiDw+m+Pp2TyaIpFLqpRSDsutIedWWqiyyOnJLKEAxyoZJFEgCiLqA4cgiBvMdgZO7OngRzw/XyChSCgZDS+MCMOI19ba/FxmnGfmc1xa7yGKMXfe8X0EAaodi9l8khcOFyGMeGw2x9frm4xJKgPHZ6ZkMJHSuS628SIJlxAngKKhUkxrKIrMfCGFEAm8utxks21ys2niBRFvrneIgLMrLRqmu/sZh9iOwlJ9yP/r2VkaA4cbNZNyWqXWd7hR7WJIMk4Q0B34HC5FvL7S4tpWD8cP+d5yG12Rubrd4/RUhqEbN7dVu3GTtSKKnKik6Ns+T8/nKWfioCl9q4Ehi9S6NtmEzJmpPLoal6BfXWrx/GKB+WKaarfFzWqfgRtyvJKOA0jA930uvt2YlubAHUnY3k1HeNBYfNjfHeAAP854L8b2+3F/POx9u4eRH0FKHclVK5LI1fsEAhC7D9j7Hk8ZMJnTOT6RYqGcZCyp0ByMcaSSxA8hbaicW21jOi47A5fHcwZD10MSBGZzBrqqMJU3sH2fibRK13bJ2QpPz+diekxa4Y+/CasXq3z+sQkmsjpBBEEQsO7YlJIanz41zuWNDrWezfm1Ns8sFKlkDb59s05aEymndZbqQ2wn5PWVJtsdm6yhcHomT3vos1hM4Ec6Fzd3e6TSGqIo8MRsjg8tFEf+QhFQSKocHU/x+Gye15bqFNIy9Z7Nq0stPtodkjF0DpfjtWe7G9NQj48nKSUV3HU4OZkhEkRu7UTkkiqVrMFG22SpMSSliSzVfSbz6mgPUE7HsqPfW26y1hqiSJBSFbKGQlqXCSMBWRRwQvDcEC+Ejbb57gfRAd43HAQDf47wsBmo/WXa53ef22/mtH+RuFclYO/4+wUOtZ7D2dU2jYHDRaHHz56JA4bTU1nqPRs3iOhbLgvlNJIQS4qWUxqHy0nW2ybBSJosQlMkPnumxLnlJq8utRg4Dn3bZb6U4rn5An4QYnkBQzfgu7ebPDmb54mZLGdmclzd6pLWJY6WC1ze6nJ2tUXLdLhZ72PIMteqPfpOgBfCeEanMXDp2x6+H7JYiBV/Lmz16Nk+R8dTGKrIubUWMhHLOyb1gcvrq03GUiqWH7DTsXlsJkshmaBr+zhRRBiE/M83NtnpwV/92DQpXWOj47DRNvF9gYVygo8dGeNWY8DhUopUQsPxfF5earC806cxcBm4HqfHsnheQH1g8+3rO6zWBzhByERWQ1dFytm3SvGllMb31loQhrRNh/G0xtMLOWw3QFclnpnL86VLVdKqQikT9xFc2WpzZWtA4PvoqsSWJGG5Ib2hS60fK0kMvYDpQnLUw2G6Ia8ut7DcgI8fK+EHIRstk2xC4U4BwNhIp7LbfA6wUE7heR5XxN0sZX94zzH2IDzouHdLzThoKD7Au8EPc9y8F7Sj94O69E7nvPsz2r9e7QUPe5ve/RCINzIKcLfqqG4o/NIzs7x8o873VlqkdYVCWkMWJW43TPK6x9KOySdPlZnMJtBkid9/YxNJjHh6Jk85Y9C3PL5xrc7OwOK7Sy2eXSzy+ccmgdi00g1gJq/T6Dn0ZJ+xjMbxSgZ7t19LlkRMN6Lac1Blk+lCXP0c2D6SoFDJxKWF8ZTC2ZUWA9tjqTmknNHpWi6VbB5ZEql2Y6Wmas+iOXBHhpjrreEoM59PyJycynJ+rc0bqx2GbhBXBZyAfDI2/9qf7BOIhT88z6O/24vxoYUiAnC7PkQRRa5t97m40eEzZyaododM5VVmCwkOlZMjilDeUDgynuTmTp8gDPn5xyYAgTc3O+x0bPpDn4AIzwfTekDTxwF+ZDgIBg5wX9ztQglvn9DvVQnYm8CX64NRBnihnBrpSheSCs8vFtlomSNFBIjNZj5zeoI31trsyCIZPdaWL6fj5rPGwKFvBxytpDk9lUVXujRNl1rXxvZDrmx10FSJxsDjY0fLTGQMnprLcWGjx1pjgOV79Ic2DdPglZt1zq50MFSJybxORlP4+JEyZ5fauF5Ie2CxVNeQBSilVaYLBltth5VGxHpryFZvyJMzeT56tEy1Y3N4PM0Xz29ybatPQhNpDlyems1zeiLLcwt5WqbPN25U+fknZwiCkO+vtBEDGEQR222T2hC2uy5/9/lDrDZNvnJxi67l8txikXRSQWtD3/ZYLCd45VaD791u0BmGKCIMLY+bzT62FxJEEX3fYeCGJFRIaDJj2SRHx1IgvqXGJCFgevH3OJZW2e47XNrsc6Sc4Mx0jlxSJQKmsjqWF2F7EQICb2x00TWZhXyC9tBhoz2klFT56LExdEUcuYcWUyoZXaaY0nD8gHJa58+u16l1bT53psKLR8ojmdjnF4ujHpI9TnExpXJ+tYXrxz4D59Z6o3H0boLa9dbwjo3Y+2HOd4AD3A8/zHHzbsb2gzbiP6zXtdEa3rFewFvU0dNTWRKqTLVrv+3vZEASIKmBbd/pTTxTNjAtj6vbPVqmzYlKHiIoGAozGY0QmCkYZHSFz56aZOj6dIY216omgQBHx1OcnMqSTyqsNk1uVk1OT2bwg5CvXK6y2jBZ78PRssCVaqzfP3DjjffevAbw7GKeuaJOJWOMEmUnJ9J0hi5eGLLasriw0abed5gsJHh2oUAlY7BqWCPe/t6cud42mSsb+GHI2eUmXdsno8t0bZfu0KO82eV2fYjpBlSyBk/MZNBlmSOVNEt1c1RpObvaBgSmC0k2mn2udmKa0IePjI8SRlO+ShAFVPsOq40+AcLu+ymg7K4nG60hX7+2w1rTpDVw2fFt/uLT0+QTGhe3utyomWiKRCWtMXQCHp8/aB7+IOIgGDjAI+HuCf2dM0hv5XH2dKW3OhYdK1ZkkMviHbrDe41oG60hb661OLvW4anZLNWui66KVNI6i+XkqLcA4gzHa0st+m7ATD5BSlM4v95lM2UzndcZOgGCIJLTFFK6ykpjgD6e5mPHSkQR3N7pcW27zydOlJnI6lhuwFbXIQxCbreGJGSZpCYSRCHlpM5UzqDesfh+FMtl7vRstns2Wx0LTRZIyELsaTCWYiyb4Eglw9Vqn/liGtsOuFHvc73Wx3J9/ChElQV0EW43+6w2Y3O0laaF6YR850Ydy48z+PPFFGem0yiSRDGtMLAdnBDqfZuu7TGdT4AYsdVwKKYUMoaC5UXs9GxSqsR0MTmSZf3Y0TJ/crFKIalR7bo8MZvDtj38MGKzNeTMZJZvXq3zxnqXv/DkFFM5gyubHfwgdk1eadhkDI1jlQzjOYObOwM+dXJ8pPQDoCgSHz1copI1GM/qTGQMGgNn5Cmw3hresxG4mFL5xtUa59c76CY8sW8cPUqGde/YvYZj+ME3Yj9uzZ4H+GDggz5u3qni+17DC0I22hbB2xg/d+b996ij9Z7NZ05P3PPz2zMMs3ennr1NjQ94fsR3bzdQZRFdkRnPKGx2HVZaQwxFQhIFDpWS9O1gpHp3ciqH6UUMnYBSSiNrqHz06DiVao+uFcTzLLEJVzGp4ugQhXF180QlzZXtHt+4tsNf/tAsG63hqCF3rWUxnY/d1JcbA756uYYfhTQHDllDoZjSMGSZE5UUAjCW1WM+/86AIAjjTXt7yFrTZiZvcGmzT1KTGE/rnJrK7mbzTXKGwqFygsem05hOMJpvX19ujj7LT5wYj3vVuha263NkPMXRDCRViZvVHtWeBRGstWzyhsZ8KcHiWJqbOwMubvTRZZmBG47kviOgkk3gBxHXa33Or3X4K8/NMZMzsOyAlWafi1s9VElCkyUO8MHDQTBwgEfG3QvF/TZY04UEL+7b5I1nNMZ1uLbd4+x6j6QqsVBKU8kad2jD7ylP9OyApCqTT6pYbkRal0AQ+OPzW2x0bSY2VBRF5rn5Ar/01BQnJ1IcGUujqzKRAIooYrs+KU1Gk6FrJ3D9AEESuLjR59lFiY2OTdv02e6YXNpQAYEwiAjDgO7QIwoiIiXkytaAxsCiO/QRo5j7aLo+ry416FsBfcejPXAwZAHLjRjLyRTTOl1ngB+G5AwZ2/f53loLCYF8SsVq+eQMjY8fKfL6+Zss14a8vtTg2fkiT0+neXXVw/UjDpeSXPY8mpbNt244TOcTPDlTQlM69C0PWYiwPPBcn57jI8oS04Ukzy0USRkK1Y5NMa1yZirHeFZnozXk7HKTazt9spqMKkvUezYN06c5iJvFTlYy7Axsrm73UASB09MZVppDpvNJfvrYOGPpHn4YoinZ2PymbXF5o4PphkiiyDNzOYpJlWOVND3LR5FEjlQyHNkdP+utIcWUyuFyctTctscLrnZtIkHg9GQKx4GpvIEsx1PVxm4AAXdu7O+nfX6t2udwOTm6zsO6o94PBw3FB3g3+CCOm/33zDtVfB/2PA97b1W7NterfZr2Ww7jd68XwIg6GgnCyHdgv1oQ3FkJ2Hu8t900bY/z/Q6fOVnhyHgaXZP4g+9vQRhSMHS8CFKGClGE5fn86dUd/ChkoZjA3N3s7r0/b59zrhfGFJvHplNUV2EYRJzM6RRSKj3bZ7tn8a3rVVK6RncY+7+IAgwcjy+d30RVRCLAkETOb/aYzScoJhWmswbn1tqcW++wXDd5ZqHAwPZ5Y73DRsdhrmggiXG13HRCho7LzZ0BRyppTk5laZkukQBd26fet2lZHv5uIDFbMFDFOBlX69roqsxqy+LiVo9PHS9TNODCVhzwZA2FJ2dy1Ps2S80h04UEh0tpUorMG+vdWFq1oI6+q59/bBLL81lpmZycSvMzj01wfq3NasuiPnRY2enTGQRkE9EBTegDioNg4ACPjIdZKPYm0D2DqL2FQhJBEiWem8+PNu7A27JSfhDyoYU8R4dxmfbImE8xpXJps4vrhySHLn4kMBzGPMojlQwpQ+XyVpeE6iGL4kgSLZuQ0SSRsYyHaYdM5wyOTqTJ6wo3aibL9QF10+U7N+rMF1M0TZvu0EMSBU7P5Hj+UImztxpstgf0bRfXDxjPJThVSbPcsTlSSDKv6Hz96pCB5RMikNIVNpsmjhvxRxe2mcjqSIJAGEWMZXRUUaCc0FkcS/DZE2X+9OxNeq7Ha0sNIkHgWs2k1veYSOtM5xN8f71Dq9Unm9R48vFJ5opJEprMK0t1JvM61ZbFRtvC8uHx2Qy6JnGtPuDxyQybXQtJjHmdq02T3z+3jiQInKqkmS6m0CTQNYm+EwApzq91WGsP0USBsbTK5WqHumnzqRPjfPzo+C4HNqQ9dHl8xgBkVttDVlsWj81kMOQ98zCf69VYUWm7a3F6Kktz4GJ5PudWOjy/WBjJDdYHDt3dxu94gclRTEh8ZTWuKCGI3KqbHC4nR03G+3EvisH+Dc5+CtLDqA0d4AA/bnjU8Xz3PP5oFd+3rvnGWpuW6Y7O8zCoZHV8P836Fbhe7SPL8ug17Kf17VFH90uW3t0zAKDzVuNwyFsBQr1rE0kqO12L/+3jhwHYbFq4YUhGj+cpSRRAEGjuOiiHYYg+nkESA9KGzKu36ry50eX4RHp0vc7Qw/ICrm71aTuwqImEgsArS00s1yMKodp2+eTJHJX5An4U0TZdrm53+fLFGj93psJfenoahYg/ulwjoQlc2OyjSWB7EXlD4uJmh6HrcXIiSy6hsNYacrSSZqaQpJhS0RWZl282WGmYXN7ocJGIsyttho6HpsR02VrPpjf0WG1bhEHIzm4T9zev1fj5J6eYKxq8se7iByE5FU7PF/Cj+P2VU9qosfmp3d4AhLhJec8gbc9HyA9CbtX6XK0O+MTxMbwAbtQGtE2HvK5wZqZA1hggK9Koon+ADxYOgoEDPDL20zmW6wOAETdyb9LeLws32uSlFXIqnJnOMl1MjRas/SZle+e4XusTBCGSJNKzfCpZnZX6AMfzySUUepbOYslgupBkPKuzXB/gByFZXebsapudvoMAVLIGKU3i29ebzBYTLJYNCmmdhVIa2/VZaw5o2Q6GLHFmMocoRtxuuFiOz1jO4MhYGsfxuVLrs9N1WCglcIKI2WISTZKI/JDxXIJiQubiZhc3CkkpCsWkxnpzSNdyubbTZ2lHQhAkTk5kcL2A2y0TP4yYKyX4P7+zwkofVD3CiSJ8P+Dp2RwD2+PTp8Z5fDrL2aUm3YEFosB4VievK6zU+wwtn6EaIAgwcCGMoG/5OH6EKLr0CwnqfZu1+gBVlpgvJlhuDMgZKp89U8GQJBCgNfQ4VE7i+iFbHYfu0KVje0xlDCaLCYq6xguHyuhqLA24WE6yVAc/DHlztYMbBBRTOo2+Q7XX51MnxkbZ+D134G9crREJxLKxu1m2/WNpT8sadoNCz6PjxpuFYxPZURBw/43OnduE/dnYe21u3gtPjgMc4L3EDzLuHrUv4UEb/oetZFS7Nk3TpZhU3zFwuPv803mDogbH7gruH9SH5r2dVwTAWArqA9jrQDOIf5YFkUiEc2sd/s9v3OQjh0pkEyqrjQHbbYv20GehnOTImEIpqZFNKGy1LF5faRL4ApIocqPe58pmF1EIcT24tNnho8fGaJvxOrFtwOMzBURJwLR90uM5NCVip+fhhyHz5RTVrs1qc4jrh+iKiKJI+EFIKqGwUEyiiFBLuBwdSzFXTJJSJP79y6u8udWjPQw4NZnmWnWALIp84sQ4zYHL6aksKU3itdtNaj2HpXqfUBBY7ViIEWR0mZ97fAJDlmgMHKo9h/mCznrT4uWlJsWUSimtU0ioo0TdQilJte+x2XGYkESOjKeQRAFFFPjqlRopXY77z3hrrL661KJl2qQ0lcVSgtXGAFmIRj1/Wz2bUxNpckmZzbaN6T7IJeIAPyocBAMHeGjsX6hmCok7DMVe3F249ibxPU3pPZpIJatDGCCJsYkUcEcgcXdWartrsdN3KCRViimVs8tN/vTaDpYb8MxcjoHjUcnGWeDl+oAvXtxEiAQ+eWKM05MZGn0b2/e5sNGhPfCYLRk8O5fn6YXiiI6y0RryxFwBaV1gs28TESHLErIoUsoZhCEs103miimemy8ysF0ESUQC1tsm9a6DKAk0eha2r5DWVQ6PJzk9keHlWw3e3OoS+j6qLHBsPMvA80loIovlDN2hx61mnzfX2vQcjzCEExM5nprOs9Gy+EatxvUdkwg4v95B1SRSSZUzEzluVnv8/sYGm504459KyfRbPocqOrosU0qq1E2PoRuw2RlSTqhcNx1kERRZwvND/CDi4noX0/EBgVNTaSw3NsI5M5Vl6Ia8vtREVxVeOFrkyHiam7UBoiRwaiJLOaXhhyE7XZur1ZgLaigyPctnvW3RmfNIF9RRNl+SRKpdm1rHjBfgYnK08d8LHgFu1c1RYLjRtkjL8Wbh7mDz7o3S3RSDBzVE7s9m7bkY342DRuED/Cjwg4y7eym53S3LuR8Pu+F/UICy/5qPErzs9QzAW6aCd5+zmFLf1vh/rwZigNb/n73/jLEkzc97wV/4iONtnpO2MivLd7Wp9m48p2c0JIdc3nspXWJnxb1ailhSJAiSECDwCwWIJERZgAIEXa1A6orilbTS1Q6dhmPY49pOV7vyJit95vH+hDf7ITKzs7Kr7fQMe4b5AIPqORknIs45b7zv+zfP81igyLCrKr0bFOi6zPHpPFc2+lyu9ZFlkaHpUR85lFMaHz9ZppRSGXkhkRDr/RdTKjM5HUOVuGsqzZWtAeWUTr3n0Bq73GyNCIk4U81S65vMp6CUUrnnSIHjFZMb9SGGJnGzXufC5oD5UlxRSKgitxomvh/x3I0mkiTx4JEcGT3O4quSRHPsslhOo2kysyWD7shBkgQWikkkUSQSBC5u9ulbPqeqadK6ykTW4Np2H0EQeeJokVxC5ksX6zSHLvfMhZyezMbtTmHIpU0fJ4i4eyrD8Yk0K12LE9U003mDy3f4TeO1OYnt+tzSTNKaiB+GXKvHY9QPQqoZlVJKRpcltgcW//X8FuWUwv3zBaZzsVfPVtfmemtIQpLI7jNPO8SHB4fBwCHeNQ4uVPsNxfZvqHY32kuNMeWU9oYyhOfRsGC5NUaR5Td5GOxiP4kYYKNr8tJqF0ORuHs6w9Fikq2+c/vNhQKRENEzPVa7Jpe3BlTSGhlD4mbD5NhEgqQm8WevbsSuuCmVSlbndDXNRFrlT1/bwvcjTk4m0GUJTRKx/JB7ZrKkNJkVOcL2Q7Z7FouVNKVEikzCwnIDXC/AdoSY6yBKfONGhxduddDkWHlBjAQ2eyamG9IfeyiSyMfPVGh/x2XgeCRlkZwGjy/mKaZ1Xt/ss9YaMRoHbPXGNEcOvh+gyRKGInFle0Sjb5E0FIxQptm3kSWBIJQJw4ja0KOYkikn00iigBO46IqErkj8f7+zxlbfIqFKVDI6377RwPEjHj1WoJAQaY1sjhRTrLTH/M+PzJJSpT27+xdvdXn4aA6Al1a7dE0XXZZ4eKFAzlBQFYWCIfPYYpG7prM0+jYpVaSwYzIUBCFLjSE36yNaQxcnjG5rE9vfArTbU9zbZzr2TiTH/WPo7Y6Ns1k7Y+946Y6bmA874fMQP5z4bsbdQef3g5XZ91v9ersA5e0Circ7/52e74PvudN1q1kdDTgw+zMKYsOxgzg7mePMdI5W32K+kKKa1rnZGBGGEWd2VOkmsjqXN/tc2ujx+sYATRGxg4BCQqN/tcHN9pgT5SSiKCIIIrbvs96xWWtb3GwM8TuQ75jMT8RJnhdXupybyfL5c1NAyEZ3TN/28bwAQ5V4cD7Hw0eLrHcsuqaHJIqcmkxzfCLJK+s9LtcGiBFYTkBj4JLSVVKGylPTub0kRjml7Y2R7b6GH2Y4NhFv/AHOTGXJJWTO7hhwPrPUQpXA0CTOTBX41JlJOiOXxXJyTxVoP/wg5Op2n1vNER8/VaGYUslv97nZGLHatXh0vrinqNQZO0iiyHwpyVROY6FoUEzp5A2ZW22XjK6S0mTay02ilE7/kDPwocRhMHCId42DC9VB6dH9JVw/COmMndtcjDe6Fq+2QFlq87GTlb1AYjcDlDFkrtWGezJyu/3kSVUkn4hbUx5aKLLRMSkk1T0lg5lCgs/eXaU1dDhaTvLCUpuB5ZHRFe6ZzXKzEfezn19Z5npzyERK52ZzyLFyhlfWu2z0LCKg7/pM5xNM5xO8vNrj/iN5ZBGWWmMqGY2FUorawObJxTILpSRWEPIXF7a43hqhSiIpXWWhlMD3IzKGxJnJLGemcqx3xmz1TEaOjx8KXN4aMnICDE2k3bGp2x7DAF7dHPDQvEZClmKCmgQJQ8Z1wfN98qkEn727wqXtAZMZAwFY6Y5YbsS98FP5BFIk4vg+q00Tyw2pZhJokkQxofHcUota30QQInKGRt90sLwQTZa4VR9heSFXtocktDYbHZO7pnP87OMLeEHI6+tdZAnmS3GWSJfjjXRrZPP6+oD5ooamiJSSGroqUx/YfOVynWxCQZJE+pbPdE5jvpikmtGwvIjFUtz7utkxSamxqlRiJzjY7SleuQjPLLV4QohVkPwdPokXhCy3RnzpYo37ZrM8tli+Y3Zx99/9nIKZQuKOQex+fBgJn4f44ccHNe7uZNh1EHfi2bzdud5tgLK7oR85Hk9fbfAjZyqcqGRu+7sfhBwtJzGXbn9vrW9zaau/xzE6yA9SJPGOnAF4M5EYoD60sVe7rHUcHL/P3dNZJtIazYHN5sAmWu0xXzT4zlqHzsAloylEUYiEwEbH5H+6f4piSmM2ZzByA3JJla7pUk7rPHO9SWfskALun8tRzerYrk9SlRm7IXOazFJjHItWEOHvOLjrmo4Xwo/cVWWzY+4prCmSSDGt8RcXagwdn5m8QdZQePBInpmddilZErlWH1JIxsms3XahXELh6taAa40hd01m+eTpym1BWN908YIIRRKoZhNs9Syevtrg9GSGWt/hvpkU2yY8t9Smmk/w3FKLb1xtMLB9OiOHj5+q0rV8tgY2GU2hlNKQd34LIRLQZBHb9SgnMvy/PrJIJMBmd8x4a0A2oaLGeTFsNyClHW47P4w4/FUO8a7xTgvV/ok8byi3bdi9IGRzR0puJhcbYO1OZvW+zc3mGNfzubyTCTo7nWW9M+ZI0WAmH5cq9y8KD8zn8YOQG7UBkQDtoUPHdLl5ccjYDXhkvsCjx0o0hzaTWYOB6WGoIglVZOy4nF/tc6NmEgoR7aGDIglMZRPkdYWe7dEcOqw0R4iSSNd00CWBe6ZzeH4Hy/XpmB6dkcNEyiAIBRbLCc7O5CkmFW61LB44UmCumGbgeNSHDqudmIhVSEMxqRGFEZ4fUU5peEmZsmTx/3h0jo4Z8LWxzfFqDlUWuWc6y2ubfba7Y+aKEs/e7JBQZbwgIIhgPp9kKp/AcwNOTWVoDT0aPZNLW31aIwdNEjlaSuJ7AZsjB12R0VQJxw+51TTJGirdsc1rGz3um81xeiqN7QQsNUaMLJ+V1pD/8p0O37rRYiZvsNQYsd63aPVdpnfMc15caXN1u8+pyQyKJFJI6lSyCq2RQzmt7PALxrRHDtcbI05X0zywkEERY3fi/XrXd3Qmjd4Yf7sBoiyJ1PsWF9f7eH6Arsic21lQD45VLwjZ7lt7PIU7+Wcc4hA/TLiTYded8c6Sve+1nWhXyndkOdyojbh7OnNbMFDbme+PlWJlnP3YbRHd9Y+RDx4A5DWoHywNvAWWWyP+xadPkXllA0NWCMKISkqj3rexLA85H/fwD8Y+uiIxtG06lkvBV5EkkZWOiSZLvLY9QJMkNFXG8SGlKfzkAzO0RzY3brQRhPh7mi+n+F8fngOgkFIJghA/DOnbAVlN4thEEj+MuLI9IAhCqlmDkRvuBWw360NqA5tT1RQ/fm6GW80xJ6vpvSp5JatTSKq0xy4XN/t0xi6FZHydy7Uhd09l9gKHXSJ2JavziVMTXNzsEYZwozEio0ls920mMzpBGHJ1e8DrbVi/XOOzZyfxvAAvDEmqItFOzeXERIrOyEUQ2PM++PF7pvCDkCvbA55batMcevxPD85Q71l8/WqTKIq/b9uNv9+B6XCtNuTckeK7+wEP8X3DYTBwiPeEt1o0drM9CVXkem3EIwv5vezr7nvWOiaSCJoicbM53lOQ2W0PyRgy5YzOyWqap6/UeWW9x1ze4Cfun9m7zm7JMyELbAzi/lFZEEmqMgIRaUPl9JREOR0HDsstk2pa28lKV/jG9RYbPZOkLJFMKBwtJmiMXJ6+0sD1RwysdX76oRnmizr1gc2RUkzmOr/aw1AkJrMJFFmm1jd5frnNYjFFPhkrOwwsl+bQYq09JqmKVNIyT1+LybWzhSSm6zOwXGoDi/WuydD2mc4b6LJCWgcvEPj2tSZXN4c8sJDnaDHJZs/Gdn3ySQ2iiOeWO6Q1iXJKx/UCro1sKimNhK5QSus0hy7FjMrZqSwr3SHNscP20CFtyJytZDh3JM8zS21mcjpXa0M8PyQWyRN4aL6AHwlMZbW9ftELmwMu1wbYfiwP+tp6j2MTaWay8e/02noXQuhYLglF5CPHJ9BVmZX2kM2OtUdwkySRxVKSs1MZIkGgZ3p7v/2jR4t44RsZf9P1+eLLGyQ1CUmEJ46VqGT1PTnSU9V0TF5vwenpNHMFg/bY3ZMePIha36Zv+5zYxz04xCH+umM/z+aD4Mjsl/I9VU0zsjS2+jalpHZb7/9e1SLxht78/nXl3Fx+L6i4tNVnpRkH/7t6+ab75msLQF6BoQf7m1AyqoAfwhPHK7SHNhc2BqiyiCQKXKoNqY9ioy5dFumObUJCjuQT3DWTx3I8tnoOzaHD2ekMI9tFFiKOlZNkDJlvX28iSgI9F1ojZ+8zFFIq12pDvDBk5Ma8pBlgu2/RMV3CIE5AfaU14iPHSxwrv9Ea2TV9sgmVJ49PYLnhniLbUmMMRDx6tEg5pZFLKAgRjB2fF261efJYkbunMjx54o0K6e5auViKkzYXNoeIQoTrRfwvD04zXUhytJzk2RtNan2bKR3OzOYpJTVuyTInK1keXciT0BXShsx2Hz51ZoKl+pAbjRGTO/4xFzf7PH68hB8GLLctXl3rcGlzwI3GkHLS4EsXtzD9CNOOeWyuf2cS+CH+anEYDBziPeFOi4YXxE6IS60xRwpxtkfeyeJe2urTHDmcnc7y+GIRdx3umcnRMQNs18f2/B0d5Dib8fBCkfWOSSQIJBWRq1sjcok6hqbi72R4O6ZDzQux3ZCHFwsYkggC9O2AYkJhtTXm3z+7wv1zOdwdEy0/AFEUSOkyRHGvemfsokkiKVWimo3lPoMwYr1j0bcCvr3UZKNroigix8opHl8s0TM9ZEng6vaAa9sjTMdjZPnkkhqGKpM1ZKZzOps9m6evtrjZGFLJaHz01AQAf/76NqbjUUxrTGYS/I17qgxNh+dfqXO9PiQgQldFeqbNt7oWrh+SSynMFVJM5w2SCY9PnCrTHrr8t/OrtEYu7aFFUo9Jb/WBzVJjzGxBo5qfoG+5DGyfYkIjk1KpDywcL0AUwPZ86sOYSFfNGPTsePFbaY0YuQHTeYP5YpLJjMZa18ZQBF5Z6xMJUMkYdEYuD84X+Z8fdHh9s4+mxL2tszvtPKen06Q1mSCCclJlvpzaU9Y42L7wylqXxjD2OKj1TJ5d7vDIXIaiFhMMN3o2zyy1mCsYzOaT1Ps2YzfkiWPlPcnSOxEO4bsjOR4qCh3i+4G/irH2Tmpb74SD93zwOfMCnZQRz9sH1YGqWZ2VxoCGGbsMX2sMbpMn3eX5NEcOzy+1aA09pB0umfUWfUJDD2QRCN8ICLSExuVa7JXyydMTZBMKc4UENxpD1toWOUNBFEUa4xHNgUM5o/E3H5pDV2Vs12eza9LNanTGLs/c6lIfujx1V5Va3+K1jT6lhMyD5XhNW26N+OrlOpWMys2GyUIpbuW85vu0xi7XagOm8wYTGQPT9XhhpYMqSxyrZOMWoZTK0XKCo6UE0zvfE0DGkAmCkJQuc2GjRwTIokAkwEZnxOvrfcoplQiRzsgla6h730nfdLneiFgoJXjqzATbfYtXVvtsdG1+5K4qFzf7tMYujaGNLIEkC1ytDaikVdK6yFQhwWbP4dkbTV5a6XPvXJrNrgNihB+E/I8Lmzx9tcm9MxmeOD7Bdt9hpWVSG1iUkzqaHNEc2uiqRFJXsLxDJaEPKw6DgUPchndalN5KonGpOaZveVTnC8yX3ujz3C35tkcu86UkRR06Yw8EkVc3+nRNl82uvadbDPHkJ0QRHztZ5rlbHY5PpEkZKkPb5fxql7PTWWRRYKVlYjsBrhRSSKicqBjU+xYvrrbZ6FrMZhPcM5ehP/QI5Ih6z+b1jQGbvTFWPiSjKYwcn4wRT8JeIHB8IslCMcHFjS6W67PcHuL4EbIgcPdMjsvbQ5K6xGpzTBQFrDRGtMwIQ7ao5jSOTWSYzIo0hhYzOZ3FiRROEPH8UoepnMaxcoqNzpj5XILJYhIBgbWexYUOFFojUqrERFrD8+HBIwUMVWEyFxvXFJIqPzY7hSIIfPtqg+bARZbBdAJc32WzYyGLAg8dybDUGuMH0LV8prMG98zmeH6pRVKVGdkeIyekmDAopDQenC9geyG36mMGts9mL/73vtksjy6W46zckZCbzSFLLZPjEylAxA/i8vZn757i3FzhtnExX07xxLEyjaHDRFrj3I5O9UpzRGvkUEypt5Ed22OXMAi5XhtxZjLJ4wsFnjpT5oVvXtkbZ33T5bVxPF4ePVrk7FT2DbWgrLind+7vk6o9qCT0TmP9nQiMhzjE9wJvNdbea5DwfoOKd2oFeitTv9220N0WvYNCELub+v3S0bvvfWG5w80BXN4a0HPCN8mT7gpJ5A2F7UHcerrcGuEfuDcdyOrQtyGhgCrBtgk5BR6YLdHoWax2LepDi9NTOWwvxPUFnjhWYjKr8QfPrHD/bJbzq30+eaoCwIWNLl3LY2THm1dDUfjEiRLVnM4Lt9o8eCSL6/k4voC00yLUGjps922OV5JMpBQubw7Y7NqYvk/fdPGDCEkokVBk2mOHkeUhCW9w5vwgZKPrEIQhmtrn3Fx+T7Wvb/vcqA/Z6NlMZlQiQUSIQrpjH9sL4lakHYOx3d+qktV56kyVC5tdllsmHz1e5p7ZPLYbwo4qUXvskjcUBpaCooIQRZxfGeBGPp4PaUPFcnwUWaSUiV3tN7sO56ZzyJLIesem1rcYuR7ZhMo9M1nWuyZXtgeIQkAllWSmFBAGsYmnIkncga98iA8BDoOBHyJ8ENml97MBqmZ1njhWAuLSs+n6fPniNk+eKO+VfHelRXsuXNoaxJvQI/k9M5ZiSt2TfLyw0eVKbUQ+WeLz983sLRDP32xwYb3HXdNpHlucAJq8uNwlrYm0Ry4CsNqO7dMn0w4ZXWahlMJ0I0aOw3eWe+iySCGp8chCkZ7lMZc3qGR0zq/5bPZMTldTfP1Gi7ETMJNLMJHRGdkB1Wz8XRiqSL1rIggCR0spprIJrrcGpBUZQ5OZKyR4bbPHeseka7r8Px9bYCJn8I3LdZ692WZku3ihQH3k8BN5Az+KuFUf0jHh69ebVHIJTMdj7EaossATiwUubff46pUGGV3GUCWu18a0bJdjE2keOVbklZUuxydSrLdNrrfGzGQ1tofx51ckkWJS48J6l9c3elTSGpPZJMWUgq5KzOZ0zk7nuNEYcmFrSDEpEYaQUhX8MP49rtWHuJ7Pq+s9fD+KKxRanH26WhtyqpreKxdX9m3AT1bTNAc2R8vJnRK4w//nG0sYOwSymR0eyO7va7s+L612sf2IyXwSy3ujnxngqTPVPWfpO/la7Oqd797XO43hO21m9o//O0k1HlYJDvFB4O2y6vvxXgwev5cB7Fsp++wme+7UondQino/qlmdRxYKWKtwZipDx7xzxnjXuVxX5T0xiYNqQh7gA6IEQwd2u4gcH17b7iNEcfUhikJUSWLu1ASSCNmEwu997SbPr3TY6lkU0job7TEv3mrTHDt85FiJo6UkxZSGochUsnosGFEb0Oxb3OpYNEcSugXnV7qU0jqfO1slZyhc2RqR0BUenDdI6hIbXZtCQuF4JcXYi/jM6SqVtM7pqQwvLLVY7ZocyRsxn07gtu9093t2/JBiSuNoKclfXmuS0mROVFPoqoQuy2DE89JulXUirVNOaZgujOy4VjKwfMpZg2JS5ex0lnrfZqU9ZKUNkgAfOzlBLqWz0Ta50RrTGto8v9yhmND49JkKpZRGaxhXtje6YxZKOtvdJLYbsdIyaQ49jleTlFIaYRBR71s8PJfjGzdaDG0XVZZIG3eu4B7irxaHwcAPEd7tQvBOff9vpb2+e42DG6iDhMxvX2/yZxdrAPzovdN7i1QxIZFTYzOUW02TyayBLomstk1eW+viByGvbPbQZYnJjMZdO6pCtb6N5flc2R7F6gU79yEA620TTYaZYpKcobBYTrDRHXK9MWK957AwkeRjJye40ehzcWNETo8no4wuUx84dE0PVZb45OkJWiObZt+hPrAY+3Gf/9mpDDkjJhWP3YAgCFjrWay2TVQ5VsC5f77ApY0eVhCR0iR0SWQqq6MqEl+/3uBoKYUqSwgi5JIqfdPF8QKSmkx/7GDoMhMJKBdil+JqzmDkBFh2wPn1Lr2hF8uk6gqyJNEc2sxmE/zoR6Z4Za3LVt9mumCgKBI5Q6aU1BEliZHjEUVxmXa1O8ZyfNRignNzWR5ZKPLV6w1eWukxckPmSwanqklsJ2Bg+2QMhWdudMgaKtvdMZsdm62+ycdPVpjJJVlqjXE8n9SOLvfFzT5PX23QHNg8dXZybxxc3BoQhCEDJ2CjPWJjYPP4fIFSSnuT+6kXhHsqFLokktYl2nasQrXadThVTd82rnflE+HNFauDmcg74U6bmYOtDgelGt/p2TrEId4N3s5Yaz/eTfvOWwWwHyTudN7dzP1+d+C3uq87SZLOl5JMJCChygyc6DaH8P1rFMDIcrEcl3NzZTQRnH1t5zKxrKgbcFvVwIpgo9Hn4YUKJ6fSRESstW2WGiMemM9zdWuAF4VkNJGpbIIjJYMICTcI8f2IIIzojD26Y5fTk1luNoY8t9RClSQquQT5pMajR7P8ydNbvLjSpZIzeGKxxHbfIqVLJEIBQRSZzhksltN7ikEbHZPtvkXCUPjqlQalpIYkCgxMj3La4NGjcZXVD0L6lsvlzX5cMU6pnJnO0hm5fPJ0bHp213SWy5t9rtfHLJQNmiMn5uKNXVwvpNazeGA+hy5Lt/GlMobMxc0+uUSc6Ye4zUqRRBZKadbaNqWkSimtoUsSSV2mmjWYKSTQVZn1zpgvXaxT71t0LJeJtIauSjQHFsWEzGTO4NvXG9SHO2FbBI2+gx/BjfqAhKrccVwc4q8Oh8HAhxzvJSP5bheCt5qkd1UeTlXTb3mtd8oGATx5onzbv3vEsh31iMmszuaOT0A1q7PcGvK1Kw10TUQSBBRFIJuMSVi5hMKLyx2SishkXmemoFNNG1ytDZkvGHzq9AStscupahpdlWm3x2Q0ldNTGVKqyqlqZmexhW9nWszmkwxsl6m8zqXtIe2RvTNhxVnol9e6DG0PXZWQRIHrjTHNgc3FrT6zBYMjhSRzuQSfOFHm9fUBqiLzzRtNWmMHTRSwfI+u6WHoMgVd5cJWj5uNMTN5g6QqM19Mstm3SGlxpunF5S5rLZMjaUglDUIBho5POSUjKiKVtEYYQjmbxQsFNjojLtcGVLM6Lyy3+dNXN1huW+iqwJlKji88eoT60GOtM+KFpSEJTUUUBD51aoLRfBEEAV1VQRToj1ycKKA9tOnZLkIEvbFHJqlQ0GXqQ5uXVzostUyWGkPGXsBKe8Q9szmyuszl2oDtXkz0O15No8sCphvw0nIbACcImcxoLBSTfPNmG0GQOFFO8aP3TDFfTqGr8ps2Fz3T4+krLSpZHVmELTMO/g5KDB4MXA9upna9LuAN1aqDz9CdNjPfzabsEId4t3i34+ndKPm8VQD7bvB2iaGD3J47nfftrvd25mFv9xng9jUK4C+vNan3baq5BPtNiDXi+SGI4n8PIoygktPIGCrXtwfIosBqx6KaNRAlkXMzeY4UUkiSwGIlTTmt4wUe2z2brZ5DORVxaavPc0sdjpR0akOXjx4rcdd0lo7psdIyudGHlOeT1uIEzAvLHVKagCTIbPUsNjsWuZRCMR1XGCBW40lIEj96d5WZXAJJFgn8kNrAZqM7ppI1WG1buFt9vnmjSaNvcWY6x3bPxPQj5goGm12HyaxBNWuw0jYRgFtNk4wukktqLDeHjN2Qas7g2NwbikQzhQSvrHVjadFqmkcWCqy2Bvxf12C1PeZIOcORgg6CTimpcWwixcj2SRvy3u9dTKk0hzbb/QSdkUV75NHsx2tpNhG3w+qKxFJjyJFCCsvrEEYwcqE7dN40n79fHAwaD/H+cRgMfMjxXsq+73YheKuF6ODrd1oo3ikbBHGm557Z/G2a8RCrR7g+1AYWD8y/oZ0sAPWBzanJJFPZBJIkIQnQHDrUejFhONBUprIGCAJdy4sVGgoJ5sspNjomlhf39290xqx2TD5zV5XJTOx0fL0+4JnrDTZ7O+pDksTzSx2aQ5tSQmO6qLLUNMkmFI4UE3xnuU3fdLn7TJZrtREvr7bo2wGTWS1Wj7B8lltjeraHoYmYnkcUhjiCwGbbZOz6FEWDe2fzbPZNkqpMJaMxdAMyukIppTOb12kPHK5u9WmPHDo2KN6ASk7jrmoWyw0QorglRpYEhnbAWnvMkWKCk9U0C8Ukr651sZyArC4SBCEXa33migYnJjM8c7POVs/m7lmNtC7zE/fN4AVgeT61gc2fvb7JtUas/CGIImEYkdUVghAiIjo7ChsPzOWZyOikdYXr233WOzZfvlTjaClFQpFYaY3RVZHl1pi+5dO3+vRMl7EbkNUlsgmN5bbJJ09PIAsCsiTu/e53Gqtnp7MEQUg2oeB7PpoIExmNbNK47bh3Clz3G4stTiTf0njp3T4zdzrusHXoEAfxbsfEB+lj8d2c6+0SQ+9kWvZu7+vdVNXuFMxbns96Z8xd01meOlOhtSNEsV8tyCNO4ySBnAE9K64O7HKMWyZc3BxwdXtI14xbK8MwYuh6ZDWJxaNFZEmk1re41TLpjV0UWWamYJA1ZJ46W8UNAs6vdplwFT5yrMBPPjBD1lB5Za3Lc9cbbI7gHKAqMsvNMattk/ligocX0iyUEnzrRgvPD7m6NUBVJE5W0siCQG3oIIkwX0wxX4qFFS5fa1Dvu3z27gqnqmkMVeSFpRb1kY3aGDIwXewgRIgi2lbMj5ovp7jPD/jG1TqmF3LPzAQ36zHX7WQ1ydnp7M582CEIQ05U03stnEEEXctDFCUGHmz3HYZun9WOhSSKzOSTaLLI+eaIZ280uXsm5n5VsjpnJrNMpB1sP8mfv14jDCN+7J4Kth8xX0pwairDp09XWO+N2RqYJDQYuCBEH1xF4LaqWPrQ2fi7wWEw8CHH9yIj+VaLx3txcX07QuauzvTufe/nDKyP4dZSl0+cjnu71zsmWUNBU0RuNccYqsLpqhH3Jo4c2qbHuekcfhiCAJIo0jU9BNgjigJ8/VqT6/URBUMhlZAREXhlswfE0qO6LPHoQp77ZnLcbI1Zbpmcnkxj+SF5Q0OVQo6WElze6nN9x4BrLj+g7wQQwURa5VQ1x/FqkoHpcqs5ZqNnMp3TSSoyJyayHK8kaQ4cLqwPWCgnGDoeQzuWUjM0mYQi0RzZuEHEa+sdpB1r9kJSpTa26Q1sFAm8SoSuKXhhwOvrPao5jTAKWO2YrLRHPDBfZGC6rHVNJgsJTlVTXNgeIEUCbSv+bjKqRiGlktFkLtWG/NnrWyR1lYwmsdqxWO/YFBMaHzk5Qa3n4Ho+UQTTWR3H82iPHIppnZbpoSgShaTEL37yGLYfst41+drVBvfP5cgnFBKSQNpQyRouAzs22Bk5PklNYrU1ojFyKac1HjtWfsexmVBlHlwo8spal8ubfVpOTDg/GAy803NRzb7hjr2/MvBB4pBgfIiD+EEbE++UGHo707Lv9hpvh90q4TNLbQRiftGDC6mYA6XB9k73yV6RIARFFlDEiCh8o10oAJqjuI1yOpfgWCVDx3R4calLQpUYuR4nSikQYbk5oqUrnDuSIwwClppjrmwPKSZ1EorC65t9jk6k6YxdLDfkZDXNVF4jq8G5+Txnp7JkDJlSWqOUjk0qNzom610L14sVhU7v8KtGlst3lttc3h4w9AIeXShxdjrLJ09OcKMx5Gg5yVrHIpdQmC9nsIOQc3M5btTG1PoOS40xxXS8htb6Npe3enz1apOJlMpCMcFq12KzZ+0lS+L5sLBX1e+MXE5UyM4cswABAABJREFU0lzZ7tMcOhwt6NxbgGDHA2G2oGPIcfX6J+6f2eMq7CZY5osGr6z3SGoSC6UkU1mdy7Uhr64PcPyI+sBlKqex0jZJqiJCCK4XV290/YPbdt42tsJDpaLvBofBwIccf5VOqG9Xun0rPff9OtMHCW3VtMJsEmaOF/eyFbuksJyhst2zECIopTRWOtZO9j+JH4T8yYVNbjVMPn9fFaKIy7UB9b7DVF5nsZTkRDlJwZBJazLbQ5uO5eH5IUlVYrGcZL6YQpZEbjbHyKLAds/m4aNxYLDasbj/SJ6u6REJAvOlJG3TwVAVVEXirukCEykFPwipD1xEAfwoznDUBjaSIDGV1fnM2SnWmiNMz8fz4MJmD8fzUSUZywnQFIHtlsNya4hPxGzB4MG5SWbyCb7SHyCJIoW0xsMLRbojh9c3eiy3Ta41RlSzKkfyBvWRjesEvN7os942GZgethew1jIpZVTqfZuUJvP5+6d47EQBx4345vUmaU1hqT0iIcvcNZVGIqSQ0jhTzVDrNggiIc7yayLbPZuB6TOdE/nKpTobfZOx7aNJEn/zkXnqfRvT8RnbHn4AZhDh+wGlpEolJZBJq4y8kFJSRRJE+q4fa/1bLgPLf8esaa1v0xw6ZHSJhRQUksptbQbv1Nqw+/p+HsvbGy+9Pxy2Dh3iIH7QxsS7SQzd6dl5L1WxgwaAd6oq3+l8u1VCL4z9BiBed4ID0qIGcb9714ve5EKsAemEgiErPDRf4vhEgvrA5lbbxPMDlhsjXl3tEkaQMSTuni7QH7v07QBdFbm+3WelY3F0wiBqgOsEvLrWwXJD8gmFcsbgZA6mM/pe4PTQQpyE2FX0OTWZ4crWkJHjUs0atEcuT99s0jI97pvJcLKa2VPcSxkqhqby4q02L630+fRdZZ48UeR4JUHWiKvKC4MkQRSiSSLrvTGuD/mkymIpzuIP7JAHjuRZLCURJZHl1oie6XF2OstMIUGtH3vXfOVKHV0RqaR1pvIGRSNOztWHLkdLiT0ztNlCgh+9d3pPFarWtxg5Hm4QMqlpDO2As7NZ3CDEC+Du6SSSCK+t9rhcG1DO6KgIsbw33Nkq+n3itrF1GAx8VzgMBg7xltjNKOxO0tWsjh+8YQ4F3DaBH+xd3f3vvX/DAFWGB+cLIIp7Pd+VbKx6cHm7jyTFRjQpVdzzH/CCkJmsQRjEmYWu6ZM3ZGRBJGfIrLZtOqbN2A7wCTHtgBMTKY4Wk7y02iOMBI6UUtxsDFhqDpnKJChkFEppjdW2zaWNLqWUwo2ayQPzWX7jx+5is2vyrWtNXl7v0R7FOsmLxTS6JnDfkSKnJzO8ut5DlwUkUcAPI/7i4jbfWe6w3TNpj2O335QmM5lNgABrLQvf8xk5EVkDVFXGieDhhTztNehreY5WMzT6Nt9aarHRGZPRFVKGzPbAQRFAU2QEMc6gT+U0qukE0zmd7thlZLtc3ezx7esJdE2hb7qkdYUfv2+ShWKSWy0TQYDtns3lxhhrrc/V7SGiKCJLYPs+i+UMzb4FQuw7ebSSZqag7/hFeLy00majZzNXSvCR42XOHQmwPZ8vXaiz3BkzX0qQ0VQyCZnFiRQrLRNDFTm/0kMSwdhRIXo7ZRQ/CCkkFDphiCrFlYGbLWvvfe/U2rD/9e9lK89fZaB+iA8nfpDHxHt5Vt5vBeSt2jrudL6EKjNTSHJxq08xqe5xDxIKb0gGARbxRuZOe8yUCvP5NI8s5Dk3X0ARRW61TLojl5m8wXTWwA8jVppD/EhDUwReW4+deueKBpEgktZlTk/FnK2tnarqyPW42QhJqRICcH6tx/m1HqIo8tETE3hhyFcv1/mRMxXOzeXJJRRaQ4dCSqXRt5lMa4QBfOxE5TbvldXmCMtxmczq6OqQrKHQMz1utcZsdW2ShsTA9Lm2PcBQJM5MZzk+keKe+SKGLJMzFHRVvk1tbb0z5ls3WnviDsWUyp+91tjhIWQQJZHO2COnQq6UZOSFpDSZ5mDEhS2fleaQBxaKJFQZXZXZ6Dk0hxaKKHJ2Okdr5PD8SpvawKY+cCilZQxFRZQkzk7mmMyr1Psuc2WDMBT45Jl3rhAf4vuPw2DgBxy7cpzAXi/2B4k7TdLP3+rwKLFiyzspYux/zfQ82nZ8z+2hF1vSl5OxB0E5xXQhwcXNPl4Y8vJaj2wintgADE3hkQUDLwwJooBSOsnZGQMhYk+B5tX1AScnc9S6JsW0zvFy7LyYS6hsdMf8H8+uMrQ9TlQyHCklmMkmeMZtsdm3eHmty0I5xdnpHNOFBM/caFAb2RwpGswUdXpDj83+iOuNIctNk6fOVJgvJvj6tQa+HyJJIoWEynp3THvs4LkBGUNmupDmaDHF5e0+QRTRMR08QBIFxEigmtZJayLLI6imZZKqyFbfIq3JJDWR2YKBjIjtBWiKyHQmwcnJNPWRTcJTKaR13DDiaDHNUmvA2Au4sDVAFOBmY8hMzuDXPnuanumSMmSO5A0QROZzCTb6JlsDi4QsEQlwqzmmP3YRZRHPjyikNTRZ4MH5MgMrQJIE2sPY7+DhhQKnpnMokshyc8TJSYtj1QTzpRRbPYfjEylaY4enrzV5eCHHRE4lZcgsFN+sVHVQGnF3XBSTCltX48rAKVl+U9b1Tq0N+4PVg1KhP6ibtEMc4vuB9yJjuusE/l4rIG/V1vFWfLViSt3zE9m9v8b4zec96D2wi/sX8kDEcsfEUCUeP14mn1CYKRrcaoyAWFJTFAWCIKTWseg5PhGQMuS4971a4p7ZPCDQHblMZDRStsiLy10MTSQrQxAGXKuPkUWJxxdLtEYOm12LSxu9uG22PiRC4NvXm3RNDxB4/FiJ+Z3qpR+EvLDU4kuXtgGBhaKBHwRc2OhTG9gktTjZdmwirpQrkkDWkFgsp9nqO3zjWp2RHXCikubBamZvH7BL9u2OXZwg5MsXt0kbMt++0cF0Pe6dzXOqkqaSVpBEmM0b1Icu6x2Lb95s094JYAa2vxdIzBcN7ppKMXYCpnfGydgKCIMI2/PZ6th8+myOhxbytIcOIzfg1fVNFEnGiSLG3hulnTsR1Q/5V381OAwGfsCxnyj55PcgK3XnjVf0pr+9U1bJC0JeWulyqQsvrXR58GiJU9X0njulv+M22RjabHYC3DBgKhf/vZLVOTuVxQ9CLm8PcH2f7yx3mC8lSGoqd01lqWQMbLeLIgqoskIuIdO1PHqWz9XaiAcWctw3l8dQBI5X08wX4rahU1NZlhpDBo5HUhGZyOp89dI231pq0xk63DedY76c5Mr2iM1bY3qWz1Ij4mlZYjqn0bM8+pZL3oj780tJnVxSwXNC7CigNXAZmF0sL0SV4iyTIAScmy2w1rO50Riy0hxyswetsIMb+AztkObQIggiNkUL0w0IopBKSqc5djhFhkcXCnTNmGTcGjvMFQ10RcTQJI6UUnRHDmudEV4E/+2ldSZ21HUqaZXpvIYkZsglFK40hpiuR0KUeWC+QHfooigCHc2lPbLpjnzSusx8KUlCFRjYAScqKR5cKOIFIa+sdTlaTnJ6Mk0ppTFdSOy5Af/5a5uMbI9SWmNxIi6FA2x0TLwwRBHFPX+CXffR3Q39LupWXBlYmMjsvfZ2ZF4gbgXbqVS9k1TuIQn4ED8M+CDG8buZz3c35Ptlft93y9C+YOCt+Gq719mvHjaXh6vdt/8sEvHmxg8jllsj1joj1tom7ZFDIa3THjr0LI/TlTSfPFHm5bUuKy2Ttb7JkXyCVEKjNXSRxJjoK4siiijQt31WWyZTeYOHF/JkdIn6jS26pk8ppTKRSeCFIX4Ycv+RLAM74IuvbDGwPKpZjalcAs8PeGChgCFLe4m8Z5ZaXFjrMXICjk2k6Fg+r28M6Fguph1yZirD/UeynJvL4wUhQ9una/lIksBm10KTRUzPZ2D7exKg+zfZT54o88WXN7jctbhrMsNn76lyaT12k5d35MEBpvMGshy7L6d1GS8KGVpx++yuxPcr6z3OTmcw3ZCLm33yhsJsIcFEWiWtK4zd+LcyFJmbzQ5fu7JN3/JIayL1gcNW13rT7/zdENUP8cHgMBj4Acd+ouT3ok/14CQ9U0jw5D5313erw17r2yy3x3QcuNEYoWvK3sTWHDmxm+2OC+1K20KSBXRZ2tvYzRYS9C2X9tCmPfK5tNnHCyIqaY/pjMbN5oiR48f9npaLgE5z5HCrMaQ5dtEVgYwh8ejRMqsdkwubXdK6ytBySCUUmgOXruXzxZc3GDo+nhcQhAHXWyMQ4MnjeVojk42eyUwhyVRW4/xaj/bA5q6pLFldZr1v4gQhSUVhLp9g6AWoRGwM7NjszDC44QUkhbh1qJgy0CSRm80B4wAMxycII+6aSnF5O8LzA/7WQ3PcbIw5v95h5Pm0TJeX1zrcNZ0jbwgsN0e4XoiUUDG9AEOLHYzHTsDxiSwjy+FybUB35FA3Xbpjl7/1yBy9sUPSUDhRTuL4EW4YklYkVlomD1fzZBMqMxmdq40RM/mdcrkqcX6tR0S8AXj6Sp2LWwOagwwDO2Clbe45Sa93TMZuyEI5xXwhtVcKt12fL1+uE0YRpZTGfDHBUtNksZzYG1O7FafpjEJCiisD74S34qu8k1TuYeXgED8M+CDG8buZz++UHPpePEMHq3z7n+Wx9+bjFdhTGVIBXYJBAFsdk1AQMW0XTZLwQwE/CNAVmYfn8xydSHGlNiSVVCnYAVt9k3zK4GjZYFWWqGRVbjVMrtdHPDyf55Mny8wUDNY7Jj1TICCi40CnbTGR1pkvJXlhqc1m3+ae6SwPLWSp93W6pksQCVza6DF2A/wwYOyGSKLIZ++qslhKYrsBEHL/XJ7vrHQopRRKhsqxIynuPVLgSDG5tyFfasdV3M7IpjW0uf9InolshstbQza6cenkZnOMJsdqSmenMxTSO/LJikQYRPiALMRmjzfrNrURrLbG9OyAvu1z105F5mZtwIWtPjcbffwQbtRGLJSTNPs2jh9QTmmcqKS4Xh8zX07w2saAp682mS2MsPyQjfaYsePjJ1UsJ6BvvWEZ90ES1Q/x3eEwGPgBx0Gi5PfjeruZmv2kzrcjzu1mdR6ez2OtwYmJ1J5PAUDf8imnNE5V0qx3x2R3nGTvms7uEU5N1+f/emmNq7Uhc8UExyfSFBIySw2Ljf4WaU3h/iNZ8kkV24+oZgy6Y5eO6eG4Pi8utwkikSCIsNyQG80RfhBxYjLNA3MFJtIqLy13uWH5SAKM3IDNrk1i7KKIIglNZq1jIiKQS2oUEiqW62E6PiERTculNrCQRYHHj5ZIyiJ/fqnOfTNZJnMJDEniruk09y/keG4ptnvM6zKbfZtGzyICRm5Ez/a5fyGWu7u8NaAxtPnfPnqUh9YLnF/r8spaG0WUUCWRp6/UWG5bZHSJ2UKS++ZynF/tcm2rz9ANdmQ/BYQIEppMRRSRJLhVH9Ice4RhyNjxIRKoFnTmyklEEe6bzrHWt3h9o4/thWz3HQxNiSf9aprm0OHpK3WCCM5OZXjyRJnOyL1t8a5mdR5fLLLRNakNLCZ2y/9hSBBG3D2dYb6UwnZ9+pZLKRVL1q13TIoplWPlJBudIQMXXl/vM1MM3qQKtD/zlTFkskasfnFQ0vbtFph3I6d7iEP8VeHdjscPmrj8Vue7U1WumFLJGjLFlPqW932nz+EF4V7bqKK8ueVVlsQdrlIsKXqqmqaYUqmP3ny/R8sK3bFHwwRVAkMDPCjkNG5sDQlDQIRSSiFpyGz3bOZLea5sjQiIuG86y33TWUCgktWpDyw2+jaTWZ0wFDhaTqKrMqoicX1rwAsrHRbKST5+ooS8AeJcidWOxfnlNqYXoskCL692cfyAtKFy93Seb99oUB/biJFI3wqxPZ9MIv7OSimNibRK1/R5frmLIokkVZmNvg2iyCOLZdojd09wQ0LEcgOu1oY0hza5hMLRcgpRgFfX+1QzBqeqaZZbQ7b7NgvlJJ2hzVNnq1huiO36FJIqpZTGS6s9mkOT611wrjZI6gpiFHEkb7ARhPzltQavr/dJqDIfPVHiWCXJ2PK4Xhvz8FFlj59wvTEkZ2g8sVjkG9ea3GqbPL6QZ7aYYqtvEhCRTSosTKTvOJ6+FyIPh3j3OPz2/5rj/XIO3q2D5u6x1+pDsppIUY0XGFm+3XCqmFJ5ba3LcsuklFRRFJmB5e8FHl+9tM35tR4JTeL0VIZ63+VYOcHYaTNb0HluqYMqRciSxIlqmulCgu2BxXwxSUqTmC0mqPUteqYfS6kVU9w3m0VTJQZ2wM36gI2BTTGh8sB8AVkSKOoq0wWDu6ezmF4AkUA5p2M7Pj3L59H5Ipe3h2y0RvgIRFGE7UaYjs8ra0OW22OyusRk1iAMI8ZeSDmpcaKaod6zyRdVErLI8UqWzWbc0hOFEYORi+2GjGyfF1a6FJM6miIytDz6lo8q2Ezndbpjj9mczkzeoG+6FNIqA8fnte0+RBH1gUkpo7FYSCNLIieLCeoDh3rfYatvce5Ijus1j6MTSWbyBu2hjxVEfOVaC02OLXxOVJIYmshMPs7UpVWJWhDgR6BJIp84XSGhymQNleXmaI9PsrBjKnZhu8+thkljaOP6AqW0Qtd0aI5sHlkssbkz9iBuH3r+VodHjxaQJZHO2GfoxZWkjb57m18AwKWtPkEQ8zWyusxK26Kc0vaC4/dD5jysFBziw4T30sf/QQaw7+XZqfdtlhrj25693fvelX/eLze9e976wGHLjP9d0LU9LXyIeFKKnc2DIKQ5dPZUbZabo/3c4T2YTkh7ZypxAjBNMGSwnRBVkZjJJSilNJYascjBwkSCUlrDciNyCZlK1uC19cHe3PPyah8i8IMIVYax42O7Plld5quXenxnpUtj6PDQkTyqDOWcxuXGkPrA4kQpTTmj8V/PbwIRnzk7yXJnzOtbPXRB5nP3TTKdN2iNHMrpuIJ9ozGkO/Y4UjB4+GiBG7Uh14UhjhNgqLGoxu56mTFkgiDk9FSKet/h2vaQU5NpTlTTtHban3Zx72weXZHZ7Jg8d6sDwEdOTLDRf8P4S5ZEbCeFXLvG6ekMXdPj5ZUBptfgc3dP8dSZKqenMiiiwOmpLDdqQ0auRymrkEvGwUwhpdIbu9wyx2gSyKLAsVKCXELl7HSeseux0RqRTmho8mGS5cOIw2Dgrzn2T8C7pOB3knCEd+8uabqxcUxCFWkMXS51waiPuGs6d5tK0Str3T250IePTJEy1NsywF3Tp5zRuWcqywNHinRGLl+/WudybcCV7T6rXZPO2OVIMc25uTwbHTO2VE8p1EceD2QMPnN2iosbXb74yhbTxQSqKmF7AVu9EaWUTiVlMfZ8trojumZMai6mNSJBZLaocd98ATEMWe1ZROGIqVwCTRGpD0KKKY0jxSzX60NMN+Bz90xjuSGKKvPccofZfIKMEZdnZ/I6QRCx1R3TGLr0LIfpJLha/HlfWe3hBiH3zeTomB7fvtli4HjcP5vj8cUi653Yy+HUdJYH53Jcr415cbVNPqkwm0kgSgKzBYNCckDO0DBtj+uNIboqo8gSN2oD1jux4lE6oZJQRM5MZmMidmfM+fUehiwydkRaI5etay1OTtg7qhMOYQhZXWIiG/MDEgUZLwjZ7lsE4Rv9/oYq4joh01kdQ5O5Xuvj+jFHoD5wmC+lyRtxC5AXhtQGFs2xtccT8YOQEJgtGqQ0lZPV9F6lCGC7b9EYOhSSKnlDYaVt3jb23s0m6eBm6wdNGvIQP9x4N+Pxgw5g319wcbve5+797nLC9rfv7aKS0ZhKxP8Ce+TUUkqjusNxao1d8vuqDn4QogP2gasPzYBdBsLuVnjsg+v53DtX5IHZPP/jYg1RiOWbZ7LxHJzWRGRJomd6BGHIRnccz+UFnam8yrM3Oiy3Rjh+xMOLeX7kVIX75rJkkwoPHslzZirDxZdg2DI5OZHCsgOySY2pvMG9s1mmsgbZhMLXrjS4WTc5XU0zX0zStTxMd6f33/TwvIDuOG6fuW+uwOPHS1yrDWKp6SP524wa1zsmGz0bEHjiWJkTO9KkFzb6vL7R55HFAs2Rw/agT3/s8OhiiceOFVnrjEkbKn4QklJFhraL7frIkshU3sAOYeyEHJtI0x47zBdTe5XW49WYs7XeMVlpmwQhHC0mWWvbzOZN1rtjbjbHZDSJK9tDWoOYN1Yb2EykNKppg1v1EV4Q3uYgfYgPDw6Dgb/m2DUj2cWe7NvOBn2X2PlWKkH7e0v3y5DuLiIXN/s8s9TmicUi+YTC0IPMjunI7vv8IOR6bUTekNEkCV2NJ/+Xltt7pNTHF4vkEjJBCN++3uToRAo/Al0SWO+blBManzlb4ROnK0C8UXR9n4yusliJHRc3OiavrnXZHtgkdZEXl1rcaA6ZySc5OZGiY7pc2x6x1bWw/IjTlRSVjMrJaoq+5SILAksdi+bAwnRc5ktpfurBWf78lS0UTUCVRRZLaURBYKM9JpNQUISIckpFVQSWOxYbXYcfv3+Sa40Ra32LRs9CFCKKOuQm0qz1LG61xyQNGVkSSRsKt5oDRm5IY+BwZjpDz/KxvAhFEDlZzVDJ6miKQKPvMpFRscIQTZE5Xs4wkdX4yqUazaGDKgn8xP0zLDWG/OcX1sklZBbKKR48UuCFlQ7TWZ2e6SGJAo4fkUkoTKY1Bo6LoclIQoScVLlSG+JHCosVCdv1uVEbsD2wuFkfUUqpFFJxleDrV2vcaI54YrFISpUxvYCx7ZFVVe6dznB2Oku9b5M1FG7WR3RND4mYM9AeuYxcHzcEXRYZueFeILA7xg46YeuqfBv58WA28k6bnMPN/yE+zDgo73ynzfl7HcPvtNl/rxK9+3lk++9795nbn2Daf65iQqKos/d6/MyHzKjy3msj20MSxL2kgyyJpBWwD/AGwmCHMHzgszQGDj9+LoPrB0SE6KKAoYhc3BrSHjssltM8upjiZDVNa2jz0loXWRDJJ1QyukwlqyEJEX3HZyKhcm17wJXtEdN5g1PVLJ2xF/seRKDLMscmUghRxImJNBfW+zRGLu2RwyNHC5RTMo8vluP5bacV9mQ1zWpzxIXNAWMnNoy0PJ/LW306Y4+kLiMd/N5SKo8eLTJ0PF5d6zBfSJDTZVbaIy5u9almVKaLKTbaY86v9djqO5ybzXGskqGQUGIuXXNMa2Sz3bcpJVVyhkzPgWJSYeQErLddXH/EsX3CDTM7yZIHj+Sp9S38KGRgx3y/Rt/GdgMeWyggCAKO36XRH2N5PpoqIQgRSVViZHs0+gdDuUN8GHAYDPw1wVtN5vs5B/sn7l3jJ6Lotl7Qg9i/EB1cREzXx/Z8HlnIc99cns32CFmCyaxOJRuXR4up2ChLEuF0NcvQDfYUZv7HhRqVrM7n75ve6deUafYtrg8cgjDC9QNkWWAw9jl6JMMjR8skVJnr9QHPL7Xomg6KJGOoeeoDm69eriMKcGYyzYnJNC+vrWK5AZoo4EYRC6UMx8sZTlRS/NmFbS5vDVhqmtxsmFRzOooo4vkBtuNjeT6266HJEgPXw7ciRrpPMaVj+yGaH5LTFfqOSwikNQVdkdjqW9yoDTg3k+PyRg/b9TE0mbYJvulQSqjMl1JUsiqKpGB5Hpe2I8a2y1p7xMjzmMkn0WWBW80R377exA5CUrrM0XKKxsBhfbuPJgpcqY2YHOqcrGTRJIHjk2lm8glm8glSmgwR3DOX5/xqm5dXO3zL8cnoCmcmMzx6tEhr5MSEYSGikhYY2CGdsYcoiowdn62OxdevNoiArKHSs122ejZpQ+XK9gBFFHlischP3D+zN+a2uzZnj0R88nR1R0c8wYlqmsbQ4Wg5gbyjMKRIIo8dLWKtQimpoWsqGUPmyxe38cOIyZzBubn8bUHqQfLjwWzknTY57+S6/X6fq0P89cP3aiy805h8r+1w73S+90oSfrvrH/zbrgJZZ+xytGjQMGGlNWZ+IvOmanMlq/O5u6duu5dKVidlCDR35CkzEowDGESgC/H/BGC4k33uW7DetkloMqWkStNy+PrVOqokMpnX+cSpMosTaV5aafPKeh9NlkinRCpZja2uQyWtIQkig/qQ7ZFDwdB48EiOUkrDD0Ku1Qb0XChr8aZdk0W2Bg5fuVSj3nNZqOj4Yay6M3Z9NE3eW/vOTmdpj1wu1wdc2OyTNSSOlNK0Rw71ocNiOcHiRJqu6fHKWpdcQuHF5Q5zBYPZfJKV5og/fm2bQlqllNC490iWe2ayPLJQJJfSeWg+z3ypSUaXGXsRxYRCBDRHDhldRpN1lhpjlq0xaU3CEODe2RyIEv5OhdcPQl5Y7jCwPf7G2UlmCgm6lsdqx8IJAhRBYOh4XNzsk00o3D2djcUiBhYrjTFpAxwnwIsiIgHCCMYHI7lDfChwGAz8kOLgwvROC8DB46tZne2+tueMqGTFtwwmds93kEh2cbPPC8tdPnYi3qRPZDQqOkxktL0+01xCQRHFPUWk1a7Fxc0+R8tJ7pvLkE/EZjO718wsFrm82SelSuSTCoulJBld4+x0nCEHWG2Pefpag0pWYyabYKtn0TNdlhpDFktJ5sspkqrM337sCBc3BuiaRG/s8ehiHk0WKSU1PuL4/PFrLklZ5GazT3ts88CRPM2xTtaQCSOBSs7g9dUunbHHdE5Hk2TmsgatsUt77JCUJTJGAiECIgE3CBhaPs/cbOMGEZvdMa2xj+H46CGIpk9kCEQinJ7KMZtPcmm7T723Sm/sYXshdhBxspImb2gIwoDltslya0zfcvm7H11EkwW2BzZZXSavK/yNuyu8cKvNRt/mj1/eopLSkSSRsRtyspLmWm3IK6s9VlojREmglFTww4ie5VFMa4wcn6QmcXoyu9f7u9Ie8dVLDS5u96n1bebySe6dybLUGHGtPuSFpRaKInH3fIYH5otsdkxao7gEvtQaM5PT9/SpFUnca+va7lv0bX+vP3ihlEQS4Px6jyeOTXCtNuTC1oCpjIYsiby03N6T0ds/Ju9kfnfw9bfCe82yHnIMDrGL79VY+H6Rg3dxp839+72Hg5y0Wt/ey4oLwM0BGMsddE1ltpDY4wXscocOimO0Ry59842WpME+01lJgJmCRnPk3NZH5Pohlu/Q33FMd4IA0/Fpmi5PHnfZ6Jr8+WtbDJyAo8UEK02LYlJFEiFtyNh+QCGpMpPVuW+2gBeGfO1Kg7NhSEaXadqgd03uny+wUDDItcdUMxrbA5djE2k2uw5bPZPe2Kfej826djkWM4UEjx8t0hv73D0dyz2nNJl632YqZzBfSlHrW1yvjahkVS5t9Kn3LTa7NvfNZPnxe6ps9iyu18c8upjnC48t7P1GGx2T01NZhIi9ufuF5S4ZXURRZI5PpNBkidmcwdDx2bqwTn3gMFNMsVBK75G3K1mNm/UBL620sP08V7YHZDSJBAJXa2O2+iZX6kNyhgKiwGTW4MnjZRpDh6mMjq6J5EQZKlmWO2NOT79BID7EhweHwcAPKd5rL/SdCMG7mzR/Z0K/Vh+y3bc4N5d/U+bLC8I9vfjdku7JaprmwOZkNX74O2MPM4gJY61x3KPZGjqM3ZAjRYPW0CGhint69I4vUBu4e5vDvaAjrfFfvrNGSpP50bunYt3osUt9p/x4fbtPCFSTOnPFFLWBTXtkcXlrSEqTOVJKMbQDgiCkkFIJo5CpvM562+Ti9oD20OJIMUValfn4yQm+dbNFfWChKxK+D6Iocnwiw2w+wRom0xmDe2azrDQtBnaAJAp0hi5dWSCrK2z3HRYnFKZyKZKyTMfyaHZtJFFEBtK6RFXyUVIKIJDRZJZbJrmEyvPXm4gCZA2JpCLslFkdaj2XB49kuXs2xx8+u8rAdhCIMzt/+voWL6128aOI/DUF348NuMopmbbpcm17wHwpwcjx+Ma1Ou2hw/Fyhu7YwfRiFaKr9T5zhdjefr6QYLqQIKHG3IAr2wMQYTaX4FOnKlR22osmsgZDOzaTm8wZzOST1Ps2//mldZojm5+8b4p7Z7JEgrA3RoA9OdG+7ZPT5dscrhHA9QMubPR4/HgJmOBkNQ5irteGrLStN/lrvJXi1bvJoL7XLOthm9EhdvG9GgsftKvxuznfweTQ+72Hg6Tg27wMPI9jGXhkoUBxp7UQ2PEZid50rl1VOustHMbGITSGTty2s4O8BildZLaYojf2SBkS3ZGD7/uEQUh76CIACCL3z6aYKye5uj3kVDXD0A24uNnjylafCIGJrI6uyjQ7Y242RnRMh48ulihrUEioyKLIxe0hIOBHAgulJDO5JPPFNNW0yjPLbfwwvO3zKZLIsYkMDy946LLAS2s9Ojsb8HxC2eNOfWetQ9+0GLk+9xeyPDhfZKaQIGWoDK80mMj6SKKIoYr86asbOG5AbeQgiSKllMajR4txkETE8Yk0QzdAlkRURcZD4N7ZLC+9CJe2BnviHtt9i/bYxXY8lppj2qaHJsuMbB9JEHhkoYAsirx0q8vY8RhaHt+63mCulCKrq9w/X8A2fVZ7Jmcms7HEtenxwq0Onzg19Z7H0iG+t3hPtczf+Z3f4aGHHiKdTjMxMcFP/uRPcu3atduOiaKI3/zN32RqagrDMPj4xz/OpUuXbjvGcRx+6Zd+iVKpRDKZ5POf/zwbGxu3HdPtdvnCF75ANpslm83yhS98gV6vd9sxa2tr/PiP/zjJZJJSqcQv//Iv47p30hr464dqVr+tRWJ3Mn+r8vXB43ffI0viXt91IanSHDq8stZ9Y7PGG6Xf5g6Zc/ccA8tH3VEFgpgoVtGhPrDomh6L5STllMaxcpJ63+JLF+oIwNmpLGenszx6tMCjR4t7ZWNvZ5N4dWtAvRdnepojh5PVNMWkiuX5/I+L24y8kLunsvzNh+f4yPESHzle5BMnJ7hrOsuTJ0o8slikPbTZ7jtcqw/p2T6lZOzmG/ohV7eHfOtGjVxCo5rXmcrp9E2P76y0CYnIpzSOV5LomohARCqhcHIyw8dOFrlvJoPtBHgEnJhIMldI4AYBi+UEZ6fTjP2AybxOLq2R0WUm8yr3zxYJI7iwOeRGY8xra126psOzNxu8utGlnNV54liZoR2w1jK5vNWnPrTZHDg8v9RBUyXm82nOTGbY6Fq4YYShizw4l0dTZPxIQBRgrWPyb79+kxeX26x3bG7Wh7xwq8P11ohqVmemkMT1wPRio7a/uLjFrdaIgRPQHr1hGLbds/D9kJSuYO4sKn3bp5xSOTubZSKr8chCLBVqeT5hGJFPqMzkknzidIWJtIahijx7s8n1+iBuJ3PjQKCU0rjZHO/JzhY1KCVVLteG3GqOeXihSNZQOTeX54ljJR49WnjHALf2PexRfafn6gcZh/P9e8MP01j4oJ6dXU7ao0eLt3nT7AYYEwmYL8Uu9M/favP8rQ6yJPLk8fKeZOX+e7rZHJN5G9uRjgPBvmpB24EvX27Q7Nt84fF5HpgtxNfNJJgvJmmOHbKGwkMLOQxF4uJ6n/tmcxyrZjg3lyelSWz2bHRF5MREimJKpZzS+NjxIroi8fTVBn0X7pvLkjcUZvI6981lKe9swOfLKRbKKRYrGTKGwjM3Oth+wHwxsZf0qGR1FidSHCunSKoSkSAiCwKRAK+tddnojumOXLa6sV9NKa1R2WnLLaZUPnqixMdPlFlr2/z3l9f4g2dX+S8vr9O3Pe6bye5V3fu2z4lqGl2V6YxjKWzXi9X1Lm8NGHjgegG2G6/X5+Zid+JsMvYE+uixIscnUnz6rgpP7Lgn3z2TZ3EyzX1TORAiXt/sM7Q8brXGTKZUXEKcIMJ0XDIJhbQhcWoq+12NqUN8b/CeKgPf+MY3+MVf/EUeeughfN/nN37jN3jqqae4fPkyyWQSgN/93d/ln//zf84f/MEfcOLECf7RP/pHfPrTn+batWuk03GG+Fd+5Vf4kz/5E/7Tf/pPFItFfu3Xfo0f+7Ef4/z580hSLKP1Mz/zM2xsbPClL30JgL/7d/8uX/jCF/iTP/kTAIIg4Ed/9Ecpl8t8+9vfpt1u87f/9t8miiJ+7/d+7wP7gn5QcZvT47voZX2rzM/+TM5MIcEra909j4Dd43dLv+W0dlvVYP97TdfntfUeYQgDK6CcNSjvbPxOVdNUMwaVrEo1Y+ydd7dEvL9sLEsioiTyidMlgjDiRmOEH4Zsdh1m8hoZXeHu6QzVjIEfhFzZ7uNFMBi73D2T5Vg5w43akCu1IcWEwkRGjyXTJrPoqsxUSmGjb+JHIRNpla2uQ9/ycIOI5sihmjE4WU5yfXvI01eaVNIaYRjSHbhsDW1eWGqx1TPJGAquF5FQIKUpFJIaq+0R51e75HWFTEJhs2shiCJuFMvhVdIKSU0mEnZcev0AJ4yYTemkdYWJrIEbjHDCgHJSxfNCXthuc+9Mjntm8rTGDq4fMpnS6ZgOZ6ZzNAcOrZFFFMUSgK4fcaQcy61WshqzBYOJtMb/+ugcnbHLszebjN0Qzw/Z6puogoChCIwsl+VmnNVabptsDx1eXu0gigJbPZOPnaogRPD8xTaSICJJAs8stUgqIjMFg1LyDXfiztjl0kaXVzcGLJRiz4iu6SGJItWssacnvtGN2ws+dnKCat7k7PQbi8i78dc4zNp/dzic7//64oN6dt6tD85+88z9bX/7167de5FV3pAM2oEG7FpZOfuCARGYSKp4fsTQcllqj1htW6gyeEFEQlN4MWqz0bW51hiQUhUeXSztqekFYZzBP1XNUM0abHRNzq/2ePBIHkkS+eOXN2h34S8u1pFkEQGBrCGTTWrokrjXurory9zoOdysD9keOGR0BV2NK6FLjTH3zmb4+MkJbD9gvW0jRBFLTZPO2EYSRGQZfC9grWOT1Pr0LZ9j5WTM88sYrLYtMprG4kQSVRa5eyrLAwvFvYquvK8y0xw5XK/FVYzFsk5OjzkDqz0TM4j2zCNlScTx4bHFIn4Yxi2biyUqWZ2XltvkDIWPHi/zo/dM8n88s8x2z2ajY7LRtZnK6VRSBkcKSVbbI2w3ZCJtkNUPG1I+jHhPv8ruRL2L3//932diYoLz58/z0Y9+lCiK+Jf/8l/yG7/xG/zUT/0UAP/+3/97KpUKf/RHf8TP//zP0+/3+Xf/7t/xH/7Df+BHfuRHAPjDP/xDZmdn+epXv8pnPvMZrly5wpe+9CWef/55HnnkEQD+7b/9tzz22GNcu3aNkydP8uUvf5nLly+zvr7O1FRccvpn/+yf8bM/+7P81m/9FplMhh90fFCEtPfby3qn6x9UcIE792gffO8ra12evtbCNuETlRQL+1QK/CBkupDg8/fNvM3iE+2UV+FEJUW9b/Hicoex45NURIIwNhqbL8UbyYubfZ5fbtHoOhRTCs2Bx6PH8lSyOivtIWEUkU3EXINq1iBtyHzrWgPT9jkxkaE5dBhaHnMlgQeP5EmpKvmUzGprzMvrPVRRwPJ8EFS6lsuVrQEbfZPNzogwhMVSClWReGm1SxCEXN4YkFBlymkN1w+YzOrIYgEn8CkZCjcD8EOB1tBlaAe8utYlCKCQVhjYHreaI05MZ3h4oUCtFy97aUMiRGCxnEKWBf741S26lhdv3t2AtdaInhvQNl0WSykWymmcwKeY1Hhmqclmz6Q+dEgbCpYbktZVdEWhOTSZLSYJIhAFgavbQ1bbNo2BxQNHcvzNh2Z4Za3LyAl44VabCLh3rkA5pSEhktIE+mOfztgh0DUqaR1xRyHIUEWubfcRBAFJBMcNcIKQo+Ukk/v6/9c7Jpe2BqwM4w3FwwvFvZFguj4XN/ucnc7uGYzdCe9GieUQb43D+f6vH/bP2x80B+Ygf2A/DgpZ7Lb3HVy7ZgsJzDsUK5x9/70/TnABQRLoOS7XmyPKCYWzM1nmiwYhImlV5LXNAYoocLyc4dxclqPlJH/8ygZpQ2G9YyEJAkEY8Z9eXOPBhTy7LT5nJrMYj4j88dcbLHfG6IqM6wUkVYVq1qM9io29immN/3Z+g1Ja5cnjJebyBsstE5GQkeUSCVAbmvSvW2iSTC6hgBCSSxqcmjJizhlQ61vcaIzJGXELbmfkst23aA4dwjAkoQgginz8xAQpQ2a9Y/HaWpcz01kubfYppbW97/rcXJ5yStv7nq5t94liaxmmcvpt5pEQuxR/6VKNaOez7xf4+Nzdkwwtn79xdpIbjSF+JLA4keTy1oAXlzucrqaxvJDFYgJDV6mmjfc4ct4dDprYHeK94bsK0fr9PgCFQixNuby8TK1W46mnnto7RtM0Pvaxj/Hss8/y8z//85w/fx7P8247ZmpqirNnz/Lss8/ymc98hueee45sNru3MAA8+uijZLNZnn32WU6ePMlzzz3H2bNn9xYGgM985jM4jsP58+f5xCc+8d18tA8FPihC2vvN8hy8/tspEh28v4PvPVlNc2m9zXKNvRLxLp5ZarFYSvLgQvGOG7Zd6To/CLlWH+J6PjcbI2p9m6QuM3ACKmltj5T69JU6jh8yuaMnvVBI8q1bbXLJWLlorW2T1hVOTaa4dy7PZsfkPzyzzDO32kiigC4JiAi8stkliEBTYtOtlKbwrRtNBpaLIgixnbsYb3JTqkUppeNMpEkqMnPFNBEB7bFNGITURnFr1JF8kpHjc7ySQRSGXK05DD2PvA75UpqtoUkYhfg+6ArcNZkjrSlIosiDswVGjsvN+pj6yOFHz1Y5WY3Lz8/dbLMxsBjZHmldQpIEmqbLw/MF0qrM6WqGc/N5Khmd//3rN6kPXEIi+qbD0NKwPB/fDrFcj8+erTB0fARB4EZ9QDgEQ/G4Uhuy1Yv5FF94/Ch/+uoGVw2FalrjZDVNQpX57N1VLm30aI4dZnNGXBLeISRnDJkvvrzB5e0hJyspCkmNnuWjSSIP7Wz292cBN5IKI/8NU6JdXNzs843rTYDbgoR3M4bfCoeqQO+Mw/n+w4MghI2uxUxR+r4qF323537+VhsQYv5A+s47tv33cHDt8oIQTQKC299zJ1lRgKk0/OS9k1geDGyftuOTMRQ0ORZFKCVV+naA7Xocm0jx2LES//nFNV5a7XKykuH0VAoBgZfXOjRHLuWUyqfOVPGDkJdWezwwl+FsEcx8muSOotBEWmM2p/PFi9ustkestMesd8YoIvz0Q3M0dpT6Rp5HEAmcnkqzXB/hhiE5Q+VENYMswNAOmM3vJNfCkFJKo2u6RILAtdqQckqjb/vU+ibfutHi3pk8RycSrHYdTk2m2exaAHTGLs8vd5hIazx4JE81a1DJ6rdVCohCVnQwDJWR5XOtPkTeWddnCwlu1AZEwLnZHDOFBIWUysaOwIfl+Xz5Uo2R4/MT901jeSF5Q+HV1R4dy2V7YCEJIlPZBKYb7AUdHzQOmtgd4r3hfQcDURTxq7/6qzz55JOcPXsWgFqtBkClUrnt2Eqlwurq6t4xqqqSz+ffdMzu+2u1GhMTE2+65sTExG3HHLxOPp9HVdW9Yw7CcRwc540cwmAwAMDzPDzvg5G72j3PB3G+YkLiWMmgmJC+6/NV0wqEAV4YvPPBb3H9ja7FtdoQ308zk3/76H7/e/tji29ca2DIIlEEveGYyztmJ47ns9wa4rg+1YxGJaNRHzhUMtrtSjBpJd6w9UQutOJSpCFLnCqnmMhqWG5IvWey3jH59o0GR0tJVEUiCENWoojTlSTLzRGlhMJsXqc1tLFdn2ev1/iLS01s36OaUskaCitdk7HlMrJ9eqaN6YVcrw85Wkwyn08gFBKsdEakVQXH92n0TXoji9lCigfnC8wVkmz1bSaSBqWETntsM5dLoMoOK60hIyckq0tsDyw2O2OEMECN4CMnC5RSUyy3Lb5+tU7KkDEUia2ByUNHcqy3Rjx9vYnjeGiqzFpnzHROpzmwCYKQxxeKXNnuM3B8ZMGnM3QI/ICkKnCtPmAyq3FhrctW3+SuagpVEBiZPglZ4uJ67Kq5PbCppFU+dnKCyxs9umOHRmBzeiLNyYkUjh/SHlpc3exg2h6qJOL4AX/26iaT2dgsqDWyeXW1x9FSimJSZa1jxnp/UYihSJyaSPC/PDDF0AlojRzumcnheR6vrfdojz2sSgpFEjleNriShIIh3jb+jxZ1amWDo0X9HZ+Ld/sMvZex/WHA+51n3u888oM438P3Z87/fsPzPHouXNrsAXyg4/WDXHMOIqMJzORUSinttvMfvM7+eyAM4rnf89hoO3g7RoQH4QNpAYYHeMcLpTQL5RTfutEhZ0isd2Jln0ub0B67/K0HZyklJP7sVou1joXtevTHHvdOpXnqbIWpnMFac4Wu6TK5sz7UemNSmkRzZOI4GhM6lOYz9MyQXEJhMqtjez5j0+dLF2ukNYnm0MHzff7P55ZZnEhxtJQgZyicrKa4Xh+iSCLTOY1Pn67Qs31W2iZpVcT3fV5Y7tAaOYwcn6msQSmlsN01cVyX+bzGja0ePdMloQikNYXr203EKKSckkmrAvdOpzBtDy+MuLzV58p2DyGKyCQ0prI6987mKBjxWpuQ4wp8OaXs/UZxomSMIUNrYGHaTiwG4gSYbtyCutk1MZ2Am7U+hqqQ1yUeO5pnq2fRtx38EK5t93BCWG0NOV5OfqBjC+J1Yirx5vXiBwkf5P7x4DnfCe87GPh7f+/v8frrr/Ptb3/7TX8ThNtDvyiK3vTaQRw85k7Hv59j9uN3fud3+If/8B++6fUvf/nLJBIfbBbkK1/5ygd6vu83ghB6LuRU2N2T775mLsHrd0hGBWFM2CKCov7G+5b6cKkLaSXu5/y3f/4iggApBUo6DGzQ2/BS8xLrYxi4kFQguaMhPZ+Kz9VzISHCShcaQxAFcDtwIhvLyjnLsG3CdhO0DrgCRAFsW6CKkFbBXQfPh5dqcO0a2AE0zPj8ugyrAXghmA4EAmxvmmQMEAKwgxZOAJoA7Ta4KmyPYnk7FVizuiTtLn4OtkzYlCEXxN+H1B1yjwoVA9ZDyNtDbnbAd8AZeJwowa2rl7gewGud+DtpiGA5YEUgDVo0LOiMY61mWXd47doyz3owl4zdNpNKXMDWPGiOQBgP+YsXWvQcqKbgW61btOyd70OAoR9PAIOww1+sr9J1YDoJvRsN/ul5qJkQOaBEsLnVi3kHFvTqW3gRjFxIyLAtwLMeGCo8UoahC5ttaNXB6IIar+m8tgJDB6wQvvy1mxR3klJfvwptG9ZG8Xe1psPqGI6mQJHha1/9GpIIrg/r43hcNF1o3WDvHO80dt/teH+rsf1hxXudZ0zTfOeD7oAfxPke3nrOf/rppz/wOf/7iZwKjeuv4K58/8br+3mu9qNtx/PiVAKu62+sF//xi1+5bb240/XadixDeiQJnbfgjI/fLEDEi8tdHk28iBJAO4DLW/GaMJMGa6vLi9+6henDogCCC9J2jZQDUwa89NwSQQjdMZQ9uDcFl17f5JIASRlaDjzfjEUOLr/yEn0LIjGeFxtWvI60bGiEYPvQE2Fzq0HJgLsLkEvDX1yFtWH8OY0UvDq6RRDB9T609XjtszwwTdgYgZyGRAou9WDkxWvowIWUD95Wn6eXYLsPVitea66G8MorYPpg+TCbgIYTf58JGapJuLJD6VgawKsvXqJsQFCAxuU3freVAazsrLnLl2E2CRsDCIGVIP6OkjKYt7boRtC7Bpd7YPWhPozXBDuK16cvh23c5fc+ft4Nijp8/S+/9r05+fcRH+T+8d3O+e8rGPilX/ol/viP/5hvfvObzMzM7L1erVaBOIszOTm593qj0djL6lSrVVzXpdvt3pYtajQaPP7443vH1Ov1N1232Wzedp4XXnjhtr93u108z3tTBmkX/+Af/AN+9Vd/de//DwYDZmdneeqppz6wnlPP8/jKV77Cpz/9aZQf4Ma13Uzpyeq7y5R6Qchr6z2G9RGSJHBusbT3vr7l8o1rLVQ54usvvMZnnjjHTD6FLIlUMhqdsUchqXB5a4A6dPGDkLWeSdP0cP2QmXsmySUUvny5Tjqrs1gJKJkek1mdUlplOmcwX0qiSCI36kNa5zfpjB3Gts9PPjTFjdqQrumzUDL4qQdmOb/a4+L5daazBvfNZvjq1Tam71EyVJpjl87YQQtCSoaKD8zmDHRN5uGFIhvdMTe3B6TDIVNZDbs5IuH6RGFEIIgMdYProcyPnCszU0jTMz36po2hyvQtj9O6zBE/ZK1jk/YHTCdcjuQNwlGdG0GZvuWxao6RBIGCrjCZl+mOPSrTWayuDQmPXErl1ESGq/UBWD7ZaoZux6TvBEwVDD52JB+7Ph8rstmzeG2jj5hQkMppHi4kyKVUhDBCEgVkSeLydp9vXG+QSsn8355YwFBErry2xfSExM+cKFHN6Hh+yGubA65uDqhmNcZuiOn7fORYmVJK5tr2mGJK4eEdEuDXLjfYHlhoksBP3j/D0A64tDUgqUogRFTTOkd2fjPT9Xl5rUt66CBJIoEf4fRtjk4meOGlV3jyI0+yUM7w3FKbVy/XuO9UhadKyTdVj97v2P1BxPudZ3Yz4+8FP6jzPbz1nP+JT3yCYvHtW8w+rNj97f/Wj39/15jv9rnygvC2qu/NWo9/9cVnefCe05w7VX3TOXevd7ScZKNrMd7oc2omi3zx5dtagkTiTWlKADe6zWKAjAxrWpX/7YkFhpbLtb9cIqPL3DWVpW8HpKdSFGWZ+w2Z9tgjqYnMEvPYnJ7Do/N5ZEmMC5tAsT6ikFQ4M5WhPnAYWRb/9Wsvkp1awEkIzOQNNNOhXhtx10SSEJH1rokMnJpM8sytuP3oJx+cQZZEzOtNWtsD9DDiSCVuU5rKG1zeGtAZe5yZylDJaJxf7XCrafL4YjGuqF9vstw2SSgi9xST3DWdoT12+PPXayzkIyYzBnMFnfWeE3vOJGS6pk8+IXMSkb5pk0voVLMaZ6YyrDYHLH35eRYWF1BVhXvPTrJQSuIFIZtdi+xGH3G9TzYh8YXH5xnaAaNrDS5vDdAkgVwaTk+mefzUBJWMxp++tkXLaXGyrJIduKz3hqw2LGwf8lMzfO5zZ97z+HnH8fVDsPf6XnyGdzvnv6dgIIoifumXfon//t//O1//+tdZWFi47e8LCwtUq1W+8pWvcO7cOQBc1+Ub3/gG//gf/2MAHnjgARRF4Stf+Qo//dM/DcD29jYXL17kd3/3dwF47LHH6Pf7vPjiizz88MMAvPDCC/T7/b0F5LHHHuO3fuu32N7e3luIvvzlL6NpGg888MAd71/TNDTtzb1kiqJ84IPne3HO7ydmitKe3vD+Dddb9VbXhiY9J+R4NbNHBIW4/9PyAuojF10SqOowk0+hyLG1fELXSOha7EppBUzmE6RVibW+xclqmulcgnuPFHl1rcty2yZC5JGFAhFwq2lyvTFmo+fw0mqPp85WuVYfYXsB610TSZRYbpr4kUA6IVPMJOmYAYIIEQLbQ4fHDJWPnCix0jY5O5NhZHrUBi6bnRFRKKBoEndPZRk4HgPLIwgjZFnh/tk8qijSGLpkDY1qJsGxSoLrtSGvrfUopnVmSmnapo3nC7y22eFGY0RGV/jYyRILxSQ36gMsx+fl9T4nE9ALfLpjmzCMyKVlzh0pktJkvnKlxjdvdogiUGWRqaxCFIHlhsxkE0wVU2wNbPqWS2vkstm3mS2nyBga12omkijSM2O5t+bIJa0p5JIKjywUuXcuz0p75zvSVWYLSaYLCbwIbD9AkiSOlDO0Ry5u2KdtuZhBwOfumeJYOb1nJFQfBWSTKgk9Xuh//P5Z/s/nV3h2ucNkvsdTZydpjj2u14YMbI/awCOV0JktaFzbGPDVKy0MReKemQxD30eSBWRZpqJDJZugNvQop3WmcglmC8k9AvqdxuNbjd0fRrzXeea9HPuDPt/D93fO/37j+/0Z3stzdafnUlG4rZdblhUSChybyFDJJagN3Tc9xwgi232L9Z6NIovMFpLkNKjtYwzvtg0FERTTApv7eoUkBVojj9bY49p2n0vbQ45PJBFEiaQG988XWe9Y5AwFL4JvXmtRG9hoCkiixENHiyiyzDNLLaazGhlDoZQ2SOgahhPx5xe2ea0Bs6rFiWqW49U0Ob3AYmXM48fLXNnsY18NSRkyAyckigSmcgbTxRT1vs3jx8rcP1/gpeUOkSDw6uYQXVOp5pJUc1BIqTx9rYkfRZyezjG/M+999KTI0e6Y82s9NoY2FdOgnDL43D1TFNMaPdOjY3o8ejRFaYco3Bo5tE2PibTGp+6qcq023HNBfmVjRNuGOUNDUWVaY4+FCYn20GOl63BmKsvA9vBDuLI9opo1SOoy9bFDEARMpA2qGY0LmwNaY42vX2/SGXuUEhqREBEhklBBluH0bP57Om4Pn+03n+vd4D0FA7/4i7/IH/3RH/HFL36RdDq916uZzWYxDANBEPiVX/kVfvu3f5vjx49z/Phxfvu3f5tEIsHP/MzP7B37d/7O3+HXfu3XKBaLFAoFfv3Xf5277757T23i9OnTfPazn+Xnfu7n+Df/5t8AsdTcj/3Yj3Hy5EkAnnrqKc6cOcMXvvAF/sk/+Sd0Oh1+/dd/nZ/7uZ87VJb4HuKtCGbFlEoxqd6m8LLeMblaG5JURTK6wpGCRrAFL6/36Fs+haTOkzsT/35p0o2OiSpK+KHAfDkmpt41neWTQ4fZgoHlhZyopgmCENtXeHmlw4XaiPbIoT3yqfVsbC8grYvcao8ZmB6zhQS+77PRHbPWsZlIa4xsn0vrPawgIm/IeD6cO1JkvTvmRmPA9sDmp85N87l7p3j6Sp3nbrbJpRWKaZWEJtMYOJQTOtmkStpQODWV4+LWgJQhI4YR/79XNtnu2whhhChBFIVYvs+N+pC1jonlhgwsl6EDXaBYVXB8B0XR0WWREJjOGUzlDFabA9IJDT8MuVLr0XM8CgmNh46WKaYkGr1krPMQRaz3bIoJjaPlJEPbp5DSqA9NRrbHetekkFAJo4i/uLjNSmtMNa/z0w/MUsnEzsCKJKKIIt+81WRo+yzVhzx4pEAUhvQsj62+jeUEzBQSbHRMLM/HtF3qA5tcQsFQ4g3DT9w/QzGl8eSJ8m0KFrYf0B27e07VZ6ezbHbGLLdN0obM6cksrZFDY2Az9GJC2GrX4Vg5+SbFqYNkw++VEspfRxzO94fYj/ciV/1uiMjTeYPTOXhgPk975N7x+ObIoWt6nJhI7RFf70RA1YFiVqA3jtjPL05pAposkjUULmwNGVqxjr4ohtzYHvEfn1tBUWQgIqGKqIrIyUqSC5s9PN+lPXIopuDCRpfrWxKyLJAxFB6Yy1NMx0ppWQ1yCZWEJuAHIZsDh3NHYj8USRKZLydJaxKtkc+Tx2VmigYvLLXY7Ns8sVgip8pMZA38IODMZCyfvCu5veu6fvdU5jbZ7oVyiplCAlkUefZWiz95dZOpbIJHF4scr2T2foP9ikzzBQNJEjk7nWWja/LCrTZj26OS1UkoscSvIktU0jp9299Tfto1BA0FgVvNEQPHw1BkjlWSpBWFphMwsD2+s9KlPnQpJCRWOybzBYMT1RRGV6Y+tOMKiyTRH394vEEO8QbeUzDwr//1vwbg4x//+G2v//7v/z4/+7M/C8Df//t/H8uy+IVf+AW63S6PPPIIX/7yl/c0pwH+xb/4F8iyzE//9E9jWRaf+tSn+IM/+IM9zWmA//gf/yO//Mu/vKdC8fnPf55/9a/+1d7fJUniz/7sz/iFX/gFnnjiCQzD4Gd+5mf4p//0n76nL+AHHd8rFZS32mRVdxwR/SDEdH3aozib0x659C3/NmfZ3U1bMRVnnDOawNVX4IG5HLIUVwaKqVjh51QlvScrWcnq3D+XI5tQ9iTOBpaPoSmsd0xeWunTGtoMnIC1tokkicxkDT5+okzPCdjsjulbLn0roDm0WZxIIssyF7YHpNsm86UEHz9V5uvXmvzltQZhJLA4keLkZJZKVufVtQ7bfQsRkVxS5fxyG1GEe2czlNIaQyekPbTpmS5ty8WLQlIJmVuNAc2BQz6psT2yWWmZiELERNZA8MF2Qgamh+sFNAcOxyczfP6e41zY6EF3m3XTw/MFZvMGWwObb1yrs9w2mc8bdO24Lares+iNPSYzOo8dLVLJ6HhAx3IRBZGcISOIAjNFg9W2SQTMFQ0MVeD69hBFCpjJJXD9gJWexY3GkIl0gk+cKrHZt3ltrUsxrfHCcgc3CCknVW7UTNZ6FlEQ8cTRAtVsgo+dmthTB2mNHPqmRyYps9Edc3V7xCdOTZDSFJ46G2dxd91FdysJq22Ti5t9zs3lSagyZ6dzXK2NWGvbsWNn1sD2PLbNuGS/a4i3q/+9Kz24f4y9tNxmqTXmicXSm7TND8oa/rBXDD4IHM73P3w4uF683/Vjo2Py/K0OD8zn9oL/2wQf3kLB7uD1ivquBLBy2/G3GVkmFKo71eZa30aXeDMEaA8jxgfYxX0rYmB7LDVG/L8/ehTHC/m/PzKHG0V880abjY7J0YkUiijQtz1EIU7AiIJIQhUpJTW6poftgCN7jEc+USdirWMyV0iQNxQWs6CoEpc2R7SGPp86PRGroXVMbjXj9QZg7IZk9ATfutZGlUXyyTgZUkypEEXIkoSuxt/l7tpouz6PLxaYzBiYrr/XpjWwfKpZnQcXijSHDqsNk+2+zeXagM7Y5ROnK3tB1e53OrRdXlrpkNZlbtSG3GyMaI1sPD9koZRgMQsfOV7aq1psdMesdizmCgZrbZu8IXOimsb1fMZuwGDs8eBCAUMR6Ixd2kOX+aJBJa1zrT5i5ISstC1KaZmMppCcyKJLEj9y5s1iAXcaG4f4/uI9twm9EwRB4Dd/8zf5zd/8zbc8Rtd1fu/3fu9tzWIKhQJ/+Id/+LbXmpub40//9E/f8Z5+mPG9koLbP5kfvIYsiVytDWmOHPqWv6f/f6ycfNPk7wch9b4dZ5HbI+oW6Iq81+ax3jH3siC7E0B75NK3fTpjF2nfpHCsnKQ7lnhuqcNM3mDsBNQGFkfyBmfvzaPLEnZgsT1weXQhz836iO2ujaYoZA2JlYbL1c6AztDh3iM5TlXTrDUtnNBnuTlkq2OxkTW53hyRVmWOFJPU2hb/43Idywu4bzbHp3IGuYRIvR8xVzTIJWRcL2KtOeZsdZJT1SxPHMvzl1eb3KwNSeky907n2Oxa2EGAGogcLycRRZFCUmW5OeJYJcU3tkFLC6RzCRYrGdwoYmi6hGGAJslMpxOcm8myaiiMnYCu6fDMrQ6m4/L/Z++/nmS57jxP8OPaPbTMjNR582oFeUGCAEiQVUWW6qqamu6Z3t7enZm1tTHbx/1H9n1tH3bMxrbNemy6bbq6u8iqohYgAfACuFqnVhEZOsK13AfPTOS9uJAESBSZ35fMjAz3EH78nPMT3+9XlETGTsDJeg4/TmiPPMIwpm+H3NkdMXY82mOfBCgZKmEcI4oilxpFzk3lMN2IgRVwfXvAzsDm9P5GupbV+daZGqtdi4Ed8E93muT0Mo2izo2NPrVcKlXXHDqsdGyWapm0TanvcG9niBvCi4slumOPq+t9yplUpeio1f2Bed2BjN3SvsrEo7aVSryK6WahmlN5b6N/WNZ+UnqwNXRZblsMnfeVE44uLk/KGh5XDj4ex/P97x+enMs/bP34ZBuzhM7Yw/KdDxz/SV7/QFrU9kPu7424NFM8fK2jRpYH5pQHUpgD5/FzKkCYpHyBg78PZoFKViKnydxvjZFEgT8+3+BXq12WJgrMlww6ls9kTufbFyd4Z73PLx91ebRncXGqQDGr8nDP5JXTNf7lS9Pc3R7x1mqXvu0TJwJfW9JpFDS0XXj2yiy3dkZsDbzDtpytvsXe2MHxfSaKBmcaec428pQzCuMgwvEC8obMre0hCAL1vPbY+nlgcLZYNVjuWPzkfpOb22Muz+aZq+QP190T1Qyvna1Szqj0bZ9fPOoQxTF//szMoYx3o6hzdbXD7e0hthuwNJnnj8/V8cOEq+t9almVfCb93sMYBk7Agz2TnaGDJCT0HJ9nZuts9hxaY3Bt51DS+8xknu/darLRt6lkNCo5jW9fmMAPYmw/wfFjVEnECgN6UcKNrSGL9Q9W875IWdtjfDyOreA+Z/y2jC8OJutqTuVUPXuYQf+8IuqjJeEnszxHs7FdMyX8PrmhhwNd6R6Q8No+WXg6A5MF7fAzhFHMQtV47P0fbBb3xh4ZVeTm1gBREnh2towbJqlN++aQKycqOEHEZs9BkyVUReZkLcvrZ+rkVYkV0eHrZ6tIokDXCug4Hu2xmwYxXsTrZ2r86cUJrm70uLY95G5rRLWgcX9nxNgLsZomPcfHCQO8IGLsBjzcMxES2Og5LLdHnJnI44cRK22Ld1a7PDNXIaOr5FWZlxarTJUzyKKAoclMZDQSAfxYQBLg3dUebpjwwmwRNwQhTtAFgYvTeUQEKoZGVpOYKGlMl3VMP0KVZearWSbzGt2xx0rbJAxjEAUuT5U4X8+yLJv85eUGN7dHJElC1/KJkpiFSg5VFhAEAUUWQBTI6io3t7vc3xsxsn3GTojthnzjXJ0T1TS7qyoejp9+x4Yq8NMHHdqWy5mJAt++OIkkiXxlqUJn7NJ3Ar56oszpiTzXtoZ0xh4PWyZDJ+C5ueLh5uJJ87rZSobXz04cVopO1bNUMhIPi2k7wVFvgefny4fj772NPj3L5+xknldP1Q7PdTD+jgYNBw6nR7OPx5moY/y+4JOM5w+by59M4nzcxuzA++VgDXja8bd3huwOnQ91pWdf5vrOzohfrPSB931DnnxfB5ny5tAlfiL7b0hgRymReDqXGoTt7guoRFFMlCT0rYC+HbHaHvGT+21yRpuFapacKrE5sBm6EV9dqrI3djHdKE1QyAK3dkZAQj2vM1XO8OdZlTiBYkbGdEMetSzCEE5N5NFVlXClC8DV1S5vr/ZYaZvkVIXpUuZw3tJUmV+v97m3m36/GU0lr0uHa+BBsiOrikBCyVDoWT49O6Rv+YycmMp+VeHNlR5t08FyI+YqMFPWiJKYe80x9Xz30LunOXQZuTEJCas9m4ValkY5Tb4YqsSL8wX+39fg+q0meUNlvpKlbMjs9gU2ew5hDEMnQJTSZNapiSxhnLDTT8kbf36pwUxZY+hElA2Z1Y7F7tAhiGCjZ6IoElVDxRm51PLq4bV7msN0o6j/Xs/NX9bPdhwMfM74bRlfHEzW5xr5w0y9/FvKeB4NFDKVD1qdH7RkhFHMi4slFFE8nPwPysLwfql5sWpg+jFuGPGwOeL0RJ5LM0VaQ5drGz3eXuvztaUKjaJONadye6fPr9d7tMYOhiIxcAKubQz55vk6i/UcpyUxbUsRYiw3oZhRUQSB+XKWMIiZKRvU8hrrPYexH9C2PGYLOl89WWOlNWbghZyrZsllVEjguWeL7I59TuyXe3+92sN2Qyw/xA1jMrKEosBq3+K1s3XeWe1xbWfE6YksWVVi7EYQJ6x2LSRRpGDIFHSVmYJBiMD/9auz/PJXe4xzOX76qMvPHuyxNfR5dqbAzsCltTlgvpLBdEPGnp9mnkQRL0mw/QA/AF0T6ds+USfhTmvE//LGGrIsktNTU6KsKrPZt3D8mJyuMFsx6I5HGDKUswozeYPpgo4XxOyNPa6tD3hxIV1I7uwMSQSBibzOiYk8/o7J0kSVubLBetfiuzeavHa6guMnOH7E5bMTzFYy5AyVgiHTGXsIQobZcvYjJ78wirm+0WfohlycTrknJTW9l8420sDkIHs4V8mw2bPpWj7VrPrU1p9qTqVoyFRz6mMOpwc4zkQd4/cJn2Q8P2kQ+TTDSHj83vm48xy0hR7F06p/Tx534HlzYbqAJMtcmil+qAPywf1+e2fI+InXGu8HAjKk2pfh+xWtnp3wP56u85XFKroq88x0jpEbMVfRmC1nWGnbLO9ZDCyfW9tDlvcsLC9k5IX8qxdneHZWpmP69B2TWlblufkyyx2L3b7Fe5tDqlmVaSGtbuwOHS7OFLi22eP2dmrStVjNkddFMpp4uNHvWj45VSSKY8Iw4eRslttbA95e69EZu/zJxSnONfJUcypTRYPdoQOCwNdOVnnlZJXJosFsOcN620STE85N5dkdeCzVs9RzGlNFg+bA5UErJfoeBFLfOFNjuqzyy+UePdNjpWPT36++v73aIwaemS0gSxJnpwp0TRdDFclrErIskQDnJtOKxFtrPbJKGqzIkpjyF/bn37Hr84M7e7hhiOkGCMCrS1WaPYtfLI/55cM2r5xKFcCe5jAN7/MNDx7/fcKXdd05DgY+ZzyZ/f6i8LSMzqd1GP6k+CSl5KOPN4cubzzqMHID/vzS1Ps28081PEuo5TQaksgP7+zyD3f3OFnL8v94/RSyJNJ3QpIETk+km8Gu6bNQy/GPt1pYfsBfXp5mpCk82DPpjj22ejaVnMpaZ0yzb7Nn+jSKGiVDQ5UEgjjh5s6QhWqOUkbl3GSOMIxxvJiR6dOzAyZzGl87V+fR7ph7LZNTjSwTCZhuxGzVwPIjWqaLLIjkVInljoUmS+wNPf63tzcpZlUkIcH1Ijb6Fq+crOP6GW5sDajmVc7WC4RxxLPzVabLOr2Rw4MRZBSfsRfQGjuISOwOXaIkoWSoVDMKuwOHnh1CIvD66TrVjMJWx4Q45GQ9x5WlKpYb0By5PGyPySgKYRSxvGcxmVdYqKYLTD6rYjs+A8tn5EUEYYCmSpybyiEicnt3yE/u7TFXyXBlsUrfDpnMa+Q0hdx+T+tCNcPIDdnqWsRxgqHJKGLCi4vlw435wQKuKBLnSgaVnMrbq93HWn3C/UAyjGLeXOkRxSk5/CB47LrwswdtzjQKH3CofvIeOOARPNZu9gSP5Sg+qzP3MY7xZcTnOZ4/7t55Ek9mO59W/fswZNRUtvmAJ7A3dtkd6o9VFA4+1+7Q+cDxCaCJkMTQGsXIIockYieAza6NKksIJFycKvLfXZll4IbMlnSGdsil5/MYmoyhZrm1MyD2UnPE2VKWxXqOrZ7Natfk+uYQQ0u5BHuWjywKnJ3IIe2kleof3O0wU1b52YMOqiLyL56ZYqqY4a3VLn/33i5jJ0w3+pN5NBlalo8bJnTHHus9Bz9OWG7bXN5vq20OU5HUvh0QRRFThRyL9dSQcbNn86P7e7SGPn92eZJvnE7bbio5lZO1HBlFIo5jnCBko+VQ2Rf32OpbiCKIksSl6Syvnalzvzlmyw0QgVpe44f32mz2bIpZFTuIkESRubzMRtelUTRojRzWOha1rIokJax1xgRxzErbIquI3G+O0FWRgR2y1jGp5g2miwa/XG4z8uBea/zYNT368+Me/33Al/WzHQcDnzOOkqI+Kz5JGenJjM4XGWE+jTRczanc2h6yO3CQRYFvnZ88VBFKN4sG7236h6XP5tBNHSWPfEaAl5eqhxOfKEpM5jTqee3wPOcbeVRJRJbEw5aQjCpxabZEnCQoosREUUESYaVjszl0WCxn+OH9PfaGLqWsytgOaY3SDPJcyWB9kDB2PQQgr5WQRYF7zQGqJJA1FCYKGj+7t0c5p/HCfJHm0OHdjSHVrEZBl1PCmSQiSgJZTUJE4F8+P8uNzSFrfRPLD6nlNbYHFhEikwWdZ+fKvLBYpW+5vLHcJkZgqpLB8UP+j/c2ebgLC+GYUxN5KlmVoR2xsjdmaSLPUs2gPfIJopiMIjJ2Q3aGHku1HC+dqHN7t89CJYfp+Jh+zCtLNd5dH1DPKfhBzMgNWKrnGVoBpQxcXx9QMBRePllh7ER4MSxUdRRR4sGeiSIIBElCHB9k2BJKWZVaLlXlUESRCzNF7jfHOH7EiwsihixydXtIo2QcLuqXZoqPqUw92eoTRjFbfYuVtsVSPXtYRToIJoI4AgGGbsBy22a2kv3QrObRTNIBR6CaUw+Jx0/Dh2VFj3GMf474PMfz0zYsH7UuPS1h9GnfzwFPQEj4QEXh4HzPz5eZ1WHLffxYVU67jpwIhBgMAcwEall42BnzT3dbGIrE107XeGG2zOlGnjce7PHThx1mSjpdK+D1M3VmChkaeYNvnq2nPgB+SNv0iOKEu9sjBOCZuQK9kU9el7GDiK4JhuvjRiG6YlDOajw3V+TPL6c9+2EcM3JDlts25/o23bHHZs/lm6fqzFbSFt9aTmO+YmD76bq41bN5Y7nDQsWgklF40PL4Lze2KRsK/+2VeRpFne9caLA7cqjnNII45u3VHgVNQpKkfed6j4EdUMmqdPcrH7d3Riw3x8wXdc5Mpm29eVWia7rECSSJgOVE7IYuJydyzFUM3l7pkzcUHN/n9taA9Z5DTpORRXhzZcCtnTF/89w0m90x1zdHtE2XF+bL5LVUReilhTIrHQvHC8nJcH6y9Ng1fdoY+U3H8pe1FQe+vOvOcTDwJcRvUkb6Im4CZX8zfpQ0XDRk2mOPtY6J5cfUC/phv6ciiTQKBpIweuzznKq9byrTHLqP8QwaRZ1vnZvgtTM1hCRtGdnq2Tw7Xz6cMA9aQi7NFJkrZ9nqWax0HM5MpkHD39/aZWSFnDiV5bWlKr9e6+MEIZIsMjI9oihhoqDxbLZE1/ZZ71r83fVtVvZMLD+imFH4i2en+cebu+yNPIoGTBUzfPfWDlt9m1JGwfJjXpgvU9IU9kyPO80Rxf3ysaHKbL3r4AchYpSQ0WUsL+TW9oiOGfDSYpkf39vD8UMkUWCzY9EyfTKaiEZKrD5dzzJ0QyayGrsjh+a+alEtq3NussDSRIYf3m3jeAE/e2ThBSGiINJzPOSByO7ApZKR2RrY5LUCuirzzbMNemOXdSfNCqUkNhkhEbC8iKIhM1nOcHtzQF6VyBc0roQVAFw/5GQ9y93miIdNk0pexQ1igjjm2bky7ZGbeiqUsuiyTF6V+MHtXe42TaL9gG+5Y1HPaZxt5GkObPKqtD9OHa5u9DG9EEmUWKzlPzDeqxpcvtg41Df/MDyN8H6u8f75vsyLwzGO8bvAR90TT9uwfNS69HlkO5/koj3tXIokPmY4doCBn8qLioCyHwgAFLIaiiiQNyROlLLMlzJ8/26LnaHN0A3J6zJuELI39hjZPqWcyvNzRRoFgzeWOziez1rP5fnZIudn8syUNHpjH1EUeGauSNlQefsaNO+18SLIqgr//Uuz1LPaoXDG107WERJ4e63Hj+7sYvkxiiIyW6nvq9f1+cpShdly5vBzb/VshrbPeiLw1RNl2mOP61t9frXSo5rT+Ovn5zjdSOf3A37B0PbxQ5nJvMh3LjV4Z63PxX2p74PkyC8e7LHZc/iHW01iRCbyGssdk62uTRRCI6/ywmIZkoRvnpvkxmaq6NQde2QUkeWuhYBAI6uy3rNZqmU5N5VDFkVu7Iy42xyQxLBYzRKT8KhtcrqRZ63jUC/oTBYyfON09XPlNz4NX9ZWnC8zjoOBLwGenJQ/68R6kJHt7ev4fhHqQgcT9UFlIIzzyELay30UspSq5RzlEhytDDz5GY/2dG/2bH76YI+hHfAXl9M2o6O8hCCKaZsepayKuT0ip8u0TY9nZovs9F1yhsqVEzV+/KDNg+aYi0AYJogq+FGMoaq8OF9GV2S6tkspp/JiNcsLJ8oMbB8niJnMa/z189MsVLO0Rg5CInChUeClE2Xu745Y7lj4QcjNzSFnG3l+eKfFnukzW9YZWCFTJYPdrR66JGL7AQNb4r31LrIE3zpTp2OHrPVs2mOPoi4xlYMwSfCjmDgW2HNdkihmOqcjKSIIsDPyUjK0ExIlDkTQtRwUUaSS05krZbD8iAetAV0r5NWTdRZrGQxN5lf3fSRJYKNrsjiRZaPrEiYxRUMhZyj8+E6TrYGLIkBGl8kqMlfX+zxsW7xyqoIfhIzcgJIhs9O3+fdvb9AauKiqhLDP6GsUDd5c6eGHEZemC9RyqUTp0AkIo5j7zTEjN+La1oiBE3B1vU8cJ1xsFLg0W3rqeJdEUnfpj2HjfxThHT64OBwHB8f4fcfn4QVwFB+1Ln0e2c6P4yEcQP6Q2/WgWGAdEcGyHR+ELFP5LMgSQRjhehF3miOIYbak843T9ZRwWzS4sTVEl0V+8bDNwAnw9yviuiqTU0XWug5+EKHJAq+eqjO2fQQBJvI6iiyiKhK6InNtKyUevxjHDOyAUjYlP6+0TbKaxP/wyglmKxmurnb5h5st/vzyJCdq73OaZisZvnOhQcdMCbqKIvHKUo27rdFhyyy8fy0KRvp9uWHETt9jtW2hKjI902ckhYfr9v/55QUGls/e2CeKIxJB4Lm5ErMFnRvjDQxV5lwjz3Lbpmf6NAoGkwWNnYGH40dkdYmlWpafP2xzfXPIX1xq8FfPzRFEMZ2xS16RsfZbiwqGjCaJjOyAv3l+mrdWVK5tjfjFWo9Ekj7QBvZ54pPsoY7XgMdxHAx8CfDkpPxZJ9aDMms1q37u/WhPm6ifny8z9SE304HaxMH/5ioZgiB46vmeRKOoc7KWZqNvbg1SUxRVPtzE/fhui1s7I8438vvynBb390xePVk9lK4E+G9emOH7t1tcbBRYH9i8eqKKqkpsdB2enSvz4mKVO7tDvnt9lwszJX5xv8dXTpbpWx6mF/Krh20MWeJvX5xDFgUSQaRjejzcMxk5ProMThCy2bXQVJn5skGCRC1nsNUz2ejayKLA0kQO4phfrXRxg4RCRsL2YyQSZstZzkzkePvOiM7YI2+kXITtvo3pRThxRENTCYIQWZU4N1MgZ8hsdhzWeyYjN6Kclbg0XcSPEuYrGdY6Y4qGQGtosWe6zJcNtkcOEzkFL4gREyH1IshnWKznGFgelZzOztChObBRVZmFWo7ATdAkkbdX+6y0R5CIXJwtIokCb671uLs74sXFCi3T4z+8s8XfPD/NxZk8v3y0h6JoTBR1Xj1VI4hj2uPUPGipnmWqmKpHlTMqBV1GUSQMRX7qhBzFsNV3mK1KH+qEDfBkv/LHZS4PyOsvL1U+QCw+xjH+OePg3jhQeYOnb/Y/bdLpk6xLH7bB+qQbr0/yPDt4/G+d9wOBJ9EaJ+QGHqfqORZqWZ6fLzF2QzZ7Npt9m+2Bi+WG2EGMvdpDliX+y7UdVvoOr50ss5jPs963ubYxoDV2CMKYrukRI/DGozbPTBe5XIZiSeNh28ZQRcqGwouLJYQE7u6MuNscc6JmYLphKvgQxdhelAo7aBJBFKEr4mOJvEZRp+8EDN2QWk6jmlV55WSVr56sfUBtp5pT+cHtXTqWT9lQcIKA29tDXj1TB+Bec3wYyLy8VOHffHWB/3Bti+lKhrKu8Ox8GeKIwUqq3CbLMmvdVI5psZ7j33xlgbWOybubAxYrGb55bpKMJiGKAn9yfvJwzv2r5+Z4fr7Kja0+d5smZydy1As66z2Hha7NiwsVHrYsGnntqW1gnyc+yVg9rh48juNg4EuAz4tQcvQ8X3Sk+1HmNcBjvx8QOz/pebd6NrWcRi2rcqc5pp7XmK1kD1tAEkHg0nSB187UGTkhBUOmUTIOqxPvbfQ528hzopLj66ciOmZAwVAYeyHnyhnmylnyhsyP7jZ5e7XHet/itJVFUeH6eo+H7TFuEDF0A1a6Fn92aZqhGzF0HAqahOWH+GHCdy5NEcci22Ob7tilM3LwooT5ShYnChGBjALT5QyOFxCEIYogYNoRmqZQ1hRqRY3WyEVMoJhRUcWU5LxYzTNb0rH8gEd7JntDl5wukddlTtazNDWP+WoWWRTJ6goC8OajNrsDmyBOMGSZgRdRMiRIBMI4JhHga6eqfOt0jbYV8MrpOittC0UWKWZk1tomOzEUNQVVENm1bYoZmXwss9K2gIS7O3lePFHmxESWM/VUyWp3YDN0ArpmmpH60d0u766PKBkaXzlRZbNnM3Stx8yDAHRVfqwl4EljMEjL/7d3RrSt4DCT9GQFDPjUKiopHtfRP84UHePLjKdxr56Gw7bMeva3zpn5sA3Wh0mNPokPC9KPSml7R4IBlSfv4scRAEvVDGVDI6+J3Nga0jY9ijmVs40Cfdfn2kaf7tijXtR5aTKPHUSISYwfxCTATEHDzyjkVYkb2wP8IGSymCWJBe63TNwYOh2b202TgqHghTFFTaZv+1hBjCpCEMTkdYW/fjZ1UH/9XGq8ZXoRoihwbWPARDHlBxy0yLbHHux7ffQsn/vN8eF396A14gd3WvzJhUm6Y48f3GtjKCIXpoqYTsC1rSHlnMIL81UWqgbNoUO0X8E9UP351cMuipS6Jp+eyLAxTlWRjsrGbvVsgjhGllI5astPDUBfPTVBTlXQVZmhk763SzNFZisZXD9EAL6yVKWUlXm0N8aLYt5a6aTO83mN843i75xA+2Ul8v6ucBwMfAnweU3Kv01iypMa7h+2OTv6ezUjHXowID49mHCCkH+81SQREr5+ssbADshq0qHyTBjFVDNpNkORREZOiCKJTBUNlH2S8Y/v7XF7q4/px2Q1iVpOI6eL/Ph+m1vNEf/6yjz/8dcb/Lu31xGShFxGZWj5mEFMUVeYLWWYzKls9dOy7s/vt9gbe+yOHCQEJnIqoihyopol8+wU/+uv1uhYDn6UEm0vTuVZ69nI4gDLh1ubfVw/JqOpvDhfRVMlJvMqQzdipTWkY3tUDKhMFtgcpU6/z56sMHJcfrXWRxUELD8gilLnyDu7Q+bKGb59YZJGKUNn7PLeeo8bm33sMOJkJcvzc2Umyion63ketiyiKGHohPQzAf9wdw83iDjdSC3ut3o2m32Ll05UeX6hyNnJAiVd4T/f3OX8VJ7TtRzrPRvLDSlnFAZWiOVGJKLAjx+00WWJr5+u0SgY9OyQ71ycYGkieygVGEYx5ybT0vajtoUbRqzsmbx2pn64KQiimFvbQx40x0iimFaV8golFapZhfbYOyQl39oe0h57HzDpedqkfnQTcRB0KPtSeAeVq6eN6eNM0TG+bHga9+pp+KRJoacFv79pQPxR6jAHUqNbPTuVu9wPaoIopjk+mjD64Pb+4LMXDRlV5NBp2H/ieQagq9Df/8dEBs5PlSjnVN5d6xOTMJFTKWVVGqUMlzJFdFnGkOH8dIlGQec/vrtNGMPVzQE9KyCnKzxsmWQNiZ7tgyhysp5FVSSqWZm5LJx8pkFG7ZDRFOIo5r3NAbtDF0MRMb2QgRtwfirHXz0/i+PHh2Ibz82X6Vs+fpQQRRFhLHG/NeZkLYvlBdzeGQIJeyMXL4wodRQGdkDX8ri2MeD0ZA5NFlmqZbk4XSCryciNLK2xT8FQeNS2KBoyfTsgjmMMVeTtlQEZRWJkBuw6Pm+t9/inW7u81YKZd7f5n75+6nBNv7s7ZKfvMl0yeGm+Qi2nHRqJLrctrq73yakie2YaodVzGj+4t0ciJJRaKnd3TRRRZL1tstY3ubs7xHImvxTz65eVyPu7wnEwcIxPjYMN3oHj8Ie1Jz35+1bXPPRgkOXoA06Yt3eG+EFEFCeIgsDDvTHvbQ6ZKhtossjVtQ47A5dqTme2kjrVHpRAH7TGlDMKX1mqUslIrLZtijmVWSMtt2aVlMMQBQnvrvX49UYfRRR4caFKNauz3Dex7JDFUwaIWQQExp6JH8bc2BnS6ju4YURn7PLH5xoIgsAvH7XZHXqIgsBMJUs5o+JHMaYfoYkijUoGgQSBhDhOeQh/+/wUpbzB7a0Bq50eQz+ERMRLwAojypqCJAtEScTIS5UgyrrMyJEIACsMWG+n2fPJokFOU3D9kDdXukhCQkmXMbIy22OHjuvRGvmstMbYUUijoPP62To/vd9mrWfzsDnm/FSRII55Z33AVEFjppzjmbkyPdPnOxcaDNyQUk7n//mds3TGHhdnivzdu1v8crVHFCfkNJm8JnFmMs9MJYOuyjSKU4cbiaMO09WcStv0uLcz5Pv3UlWhC9PFQ6+JPdMjCCNePFU+lBaVxFSH/BePerTHHre2h4fOpEczjE+b1I9WECpZlaETHj73k7QSHeMYXyY8jXv1NHzSTc7Tgt+Dxw4kfz9tUPBR6jAHUqNhFD8W1LRGHo86zqGj7oHC3FEcfHZDFRk8YTp2FJoCLyyWubXZp+WApkg8ao/JDWUQYCqvY/sxy20LVRI5Uc3wyskqz86XyagyHdOlnld4QS3xqDXG8iLqBZWMIlJUJM5NFQmiiEpeRxLSuWn3FnhhQjmvsTN0OFnPcHm2QKOoM7QjEEJMN0aUJN5a7pIIsDvUDyWWv3V+kusbfa6u99kZuphuyMDyuLs74trWkL2RiyyLvDBbopVReHO1T1mXyWgynbFLa+QzX9ZZrGZZ6znocno9Z4vpfBxGMc2Bzc7I459updywqYKWzu+WT9v0eKNnIQJtM+DqapdqXuPu7oggiGgUdZbqGWo5jY7pMXRDzk7mWapn+dWKy2rbZa6qs1TPcmOrz1rHJKfJRHFMQVdw/YD7eybvru7Rd+DN5S5/++LCJx5Tx/jt4DgYOMYH8GHZ1AM8TQkIHs9EHbjDXpopHgYMeV1CE8F0fXSVw2Di4NitnsWDocczcwUUQWRn4BDHCaYTcm/gcH1zwGzV4KUTVQqGzI3NPrpEWjnYd3OURBEngKEbpu0stSz/7q11KobGbEln5EW8u95DEUX+7PIUl2ZK3NkZc2mqSN8MONMosDvweNQcIUkCX52v4kcxURzj+iG9sce1zQEL1RzrXYvO2OPSdAE3ipEFieWejSiKnJ0sYPkhmwMbxwsJ44TW2Od/u7pNNZ9+NzPFLBcbZTQZfnZ9gDV0udAosN63ebQ3QpdlXpgts2d5DN2I0A+xCVAVkbym8LMHLVRZ5uHuiIetMZWsyutnG5yoZ3h7tcfVtR6yKDBR1JktGoQxmE7Idy42GLs+r5yusdo2ub01YK1t0ew73Nwe8ag1RpBETtayLFYzPGyPGDsBf3JhiqKh8jcvzFLNaXz1ZJWVtsWD5pir6wMSAbpjD9Px0VWZ2UqGRlFPeRU9C9MLWN6zuDSVQ5UlXjtTZ2/o0rYcGkUFIUlomT5jN6322EHAng03NoeESYJMqoTUM/1PPE6PKlB9mELJAY4zRcf4MuNp3KvfBE8Lfg9+P9iww6erkn1U++jBWrHVszlVzzKZT0UBKlmFopWKDKz1HE7Vs0+9r+cqGd5e7X5oW5AKxAlc2+jjuaALkDdUepaPgMB8NcMfnZ3g3c0hURzhhQn/n5+tslBN1eomSwY/vdfkB3f3qOTUQynpkq4ycAY0xx5/+8I0l6dLPNgbgyDQswIGPkhjnySOSSK4tTOiUciwUM3gBGMKmsHLSzmub/b5wb1dTtfyCAjc2h4ydEJO1bMkgCILXFtPfRaqWZ1vX5zgmbkiGVXhrbUuXSdgNog4O5HlK0tVnpl3MD2ft1cGiILA5VkoGqmiWyWroqsysiTyqG1xeiKPJIq8uFjmnbU+XhSz2jY5P1Xkmfky9axK1dlGlUV+vdbn+fkiphuS02TOTOZIgJ8/bLPVt7k4U2CyqDNbydAeu/yoY1PwIr57fYe26TGwAmQhNbp0AxMJgYHpMrZTT7ilev5DruAxfpc4Dgb+wGH7Ibe2h1zalyCDx0uyR7OpB3iaEtBRCcetns27G13e3RgSRTGzlSz3mmM0MWFtDD+812aymOHlpephj/hkUSchVY9RRJH3tgYEQcIfn6/zyuk6P73fwg8LfOVEmZdOVHlvo8/3b+8xWdR5fr7EuakChipgaCKvna4yW9Y4M5Fna+iw0XfoWwGimKOcUSg0ihSM1B/gV486bA1dnp8pIkkCuizwqDlGQOC52RLPzJf4yd0Wphfxb19a4Hu3mvhxiBMEWG7AWsfE9HwymsZUUcVQRQxB4NRElqHrs9q3QEgIo4Qo9tkzHda6Y1ojn7lyhv/Ty/OEfsDdhytU6znyukx76DCURb55dpLLcyV+/KDNlcUMmiQyVdC43zZpjx1+dK9NLatR0mTmqllemC8zU07bc0ZOiCQICMD5mSJD2+Pt1QFvr3d5YaHKqydrPGyOeXu1ixfGnJ/KMlvOsN23aY48Bo6PkAiMnJC/e2+bvbGHIor8+TMzjJyQb52fpDV0yWkSC1WDyaJBZ+zxDzeb6KrEiVqO1/bHxcAOeGO5y9mJHJCQM1S+M1M6NNWRENju+3z1RDkt3e9zP7b6Dte7QGuEJstU8zojJ3yqzO0nGafHOMYxPhqHAccTrvKfFE9WG57299FEEkDPChg6IWVDoWikmez7rTFRFCM9Ufm7NFPkQk3gTuf9kEAHJAGKWbBc6B6wiRMwdIU/uzSFKguoikLOUPnaqSrNocOdnQHNkQNJjCYLCFtDmn0bgYSilrbj7I5cnDDmXCPPes9BESV0VUZVZKpZlUpWwY/BD0N6VpC69E4V8IOI+YrBW8sd7mwPiYn5xcMO7232sdyIS3MlyoZCfb/tZqVt47ghfpJwaarIK6drZDSZK4tVbD/k9taQkRVwfXuIJknU8xZX9o3aFCH1MtgcWGx2HeYrBo2izmbf4tm5MgtVg3s7I0RJwPFjzkzm+cXDPR60LNb6Ns/PlEiApRzMLJZZ77vUshovzJdSt3vglytd9sYOq20TgBfm0+rNhakieUPhYXPEe1sDMpLEt85PEEQJP7rb4icP2pQyKl4cE5JKv4rHdKwvJY6DgT9wHDWCOvAJ+Di954/KoDaHLm+udGmNXLJq2q9/YFq21hmhy/DsbJHFeuqY+OZKFxA4OZHq659p5CkbCsRDFBkuz5bTHktN5ZWTaalyq2dztpEnutygltPIGzL3d4cEvsg/3mrRyGuUsho/ut9mMq+SkSREIcEKIyZkg/PTBcIo5rvXm3hRRDWj8rBj0h77rLVHrHRsMprEuUaBX6/22Rk52G7Io5bJxekSHdNBEkTyZZndkUsURHR8G1mMGbkRA8vnmYUyp+s5+qbPvd0+miqhyyLljMZ8OYsmm8RCwq3NAaWMwrQBtVIGXRHJGgojy2d75OKt9jCEVJ40UmTu74346lKVH90LaY89KlmVV09VmakZBGFMe+Tw8wced5sm8xWdgR1xd3fIVs9GkUQmCwaNgsZP7rUw/ZDrG32mShncIKY5HDD2AuIEdEXECXwqhsF81SCjSpyoZo+0c4Ws9W2ERKCW01is5XluPoMbRnTHHpdmU8Ox1bZJXpV47WSVC/tBykHVaG/sUsmofOdC49DS/vSRzL4AGAoUdRUnZJ+A/P5YPCpz+3Hj9OPs7Y/Jw8f454QPU9n6NPgojsxnrZI9GYB/5M99R/rJgoYsy7h+yPKexZWFEpWsyt7+/Hb0vs6oMtlMBrAOH3MBErDN1Hn4KPKqhKHJVDIKQZyw2U+P+8WjLjlF4MpCidfP1HHDmObAZbUTUdlX71EVkbEdYrohL1+ocn66gChJKW/twNG3a3KjAzV1iBXGZHWZ7a5F1w4Z2gHNkcfYCwnDhEpGpZpTmczpyKL4fhVk5NC2HM7NFDg5keP1c5Pcb4756YM2uiLTHrlc3xpQNGQuzxbYHfksty0axbTNSpZE1nsOfTutqg6dAMuLUq6ClRp/vrXa41wjj1PL8uN7bQxV4uWTFSpZlfc2BrRGDlUH/nqxzOJERBjFmEOP2f02o6Hj43oJ1bxGwVAJn2jBFEWRlb0xQRTTKGnkNJkwgYqh8tJile2+xU7PxPJSd+tjfPlwHAz8geMgC3vUJ+CgnPtZNkeNos7LS1WCOH7MTVaWRGwvZiYDX12qktE1gijmZSCIY4QkJR9NFnVaQ5c/u9zY189Xub095GQ9iyKKvLnSA5L9vtK0zeh7N7b5hzt7zJQ0HD+mOXI4N5FH12XOTuZRZYmO5XN6IkujYKQeCDmVMI4J45goSvj7mzsMbY84I3N5usjluTx3dywMVeI7F6d4NzOgnFXJ6TKSKHBzd8CFiRx/en6Snz9qM5PT0tYWz8aLYvwwpjnySOIYy42o5XWmyxn8IOLO7pCe6REnAte3B+z0XUYmRGOX2XIGRRSIk4SdvknZKLPneDzcHWO5PpGQOhAXDZX5Uo6posbe0OW7N3YZuyETBZ1SVsbzE/KyyNcvTNIdu2z1HKaLGaoZhUetEe9tjsjIIiM/4qwuo6oyOz2bztglAQxNxvQiVjo2fTNgpmow9iNO5lQqWZW7Oy5RnDBb1ChmVdY6YwpGGWf/mNlyhrEb8qA5BgHOTObJqDJFQ2WzZ7M7dFhrm0T1HLW8Rtv0mDyiRFXNqQCcKcDlmQLXtsc09knicMTltCh+onH6cVWCY/LwMf45YeDD/eYYWZY/83j9IipnT1s7Psw1PNgPBtLHtP2sc4J8hF9QzakfUKnbaFsfeF1IacdPGpI1BxZhFHFt06ZneQyskL9+vsFUXuVnjzoIiYAkCqiSREyq/CYlAromEcQwP2NwfWvIT+62+b+8soATxLhhxNW1HqVMquIWJ2AGETlDQRUlwgR0WeAbZ2qEcUzb8lnv2TRKOn9WnuJ8o8BSPcs7a31ML+DqRp/mwKFiaHxjXyHvbCOPG4RYns90QeP1MzVESeK5uQpXjsxzP3u4x2bX4ZXTFb6yVCGMYjqmRymjstwa83DPYuwEJAIkgsijlnnY+nNQWUiAKMrTubO+f/2Uw1aug+/9ykKFh3smJ2qpGh9wqHY0XzH40d1dwiQmSRJWOiZRIvL1UxVeP13nfnPM0Iv44/MzbPZt/pvnpn7TYXaMLwDHwcAfODKqfFgROIpPszl6Mqv6NN32RlHHmcyxo77/2MFzN3s2t3eGVLLpPx+1rUM5tPfWuzxs23zr3ATPz5d5ef/YMIp5Y7nDyVqW2bLBQiXDt87VGbsB37+1hxck6Do8apucaxQ4J4soosjYC/jPVzd4ebFCVlfoWwF7IwdDkqhkFKp5g2fnyghJgiyLlA2ZxarBP91sstIZc3IyTzWr4AYRt1pjLDdga+ASxmmr08mJAnlV4fZWn7YVkDEkFFWimFFYrGS5tzvcL5WKhHGIBOgyNP20n/LWdp/W0CWKErKayoXpAlrTZKdvkVNlEhRUUWR35DB0fAISwjhiYHkkCbhhyMgFVRC51RxRzqucqOVSnoUms9ZxyGckzk3mWJrMcW1zwPMnysyVszSHNre2hvzsYRtVFnjlzATVvMqd7THzFYOhG9IaupQNhaV6hqUkw3rP4Z3V1EV4tW1hqDK6LKArIrd3TBaqBrIoPqYGlKpCRbQGPidqCZ2xx88fdmiPXC5MFw8VMHpjF0mEhVqWXEY/XJiOjrdPOk4/LtN53FJ0jH9OKKkpf+Y3Ga9fFEfmo+7JJyWoj+Jp3jRHK3qQCka0nQ++pgLEQPTE42MnIKMp9KwxlYxCRpHpjH3qRQNVEolJWGnbFHSFr5+tc297SEaXqedVNFmkoClcnE64u2PxqDXG0BR2+zYbPZvr66kb8GwGlILBUj3Dpdky93aGvL3W5/t3mqiKwolqyuHa7jtIogAI+GHCrZ0RuwObsR0ymU+P3x06jPYJugPL50f32sxXMkwXNYaujxOEnKoUDiuiZUPlfmCiyzJnJgustk22+yPmylmem6+wOXAoZlVemamy3XXwwphyRqZkKIctul4IC+UMq2HaNnxjq8c7G31enC8zWdTpmj7PzZeZq2Sp5lS2ezbNkUNel7D8mHfW+mwNPAq6xuuna8yWDX7+sMtCNUt77JPTlZRXF0b87JHND++3OTdT+Q1G2DG+CBwHA8d4Kj7N5uhpk/+HcREeDNPy9pmptBcxiFJirh+EtMcJ9ZzGuUaezZ7FP9xsUsjKTBU0lupZtno2YZTq5a/sjfnVozamGzKZV5kq6+iySGMiz/BkwJWFChv7mtW3miOenS4iSiIPdkdc2xyw3Xc42yiQ1QRubI2J4phiRufydJHFWob7zTGGLJIIAv/LL9a5vTukYMgkSYIoiNQzGl3bo5hRqLkqqpKWP4u6ylrfwnQDZipZTlayjKyAIEi4udmnYwc0Cjr1rM7OyOXO3hgxjokSaI1cJFmkkk8n+fONPHlDZbVnUzI0gkihnFEIRdjp2zh+xLOzZSYKBh3To5HTOD1VYKfvMlUyWG+b3G2lbsnPzZWYr2c4OZlHEmGj6zCwQ05UsphOxM/2Wqx1bQaWh+fHRDpMFjUUUeTF+RLnZ4qstC3CKObq+gBIuLJQBiEt849dH0mSGVoelh9zbWOAIkvMlrNMFnV+fLd1qAY0dELqeZ2JskMUw5lGnr7lEyWwO0xL55NFndZAwV5+P3N4MF4OytMH6iNHM1ifBU9uUA58MY7bhY7xu8Y/x/a1o2vHk+//qN/ApanHk0Yfp/AVRDFFQ+ZEHpbHjz2NA0q1RppUcfYpBaIksN3dr3jGGkVD5t31AUkSo0oSl2cKlLMKphena8P2iOmSxvmZaWTR59bOmGpGplZQyBkyOVXGy+tcEAW2Bi7vbAywPSj7ARs9h9lylsValh/dbbM3CkiEgHOTORpFgygSyBsyl2cK1DIaWz2Lja5N3lA5NZGjUTB41LEo6TK7Q4eOFVDNq2RVkb+7scPADmibId+5mMpEn2vkeeV0jYHtc6aRJ4hido/4CUwWda4sVKjlNTpjj5Y5RBIFvFDi+/dayKLIt89Pcq6RZ2y73B3AD+7ssTFwuLszJgFGbogkiZydTD1ltvo2/+GdLSw/5C8vT3FpOo8iwWbPomhU+PalKX5+fw/LD/nejV3uNEdM53WQwA9CTMfD9Z8M2Y7xZcBxMHCMp+LTZI2eFjg8yUVoDl1WuxZ2mGb1N3s21Zx6qC0PAmcamcO2ompOJYpi2qaHpqSmV8t7ZqoMIcBa26Jt+jheSF8SaQ4cfjz26dlpJuLZuQrfvjiFANxtjbm62kOSRTqWw7NzJWRRpGd7KKLGfCXDbEVHk0RkWcZ0QvZGLq2xS06TeeVklbs7fSbyGllZJqfLOGHAyAmo5bL82aVpbjUHdMYefdvDjyIMVeJCI0/X9BEEgZmCRi6jc0FMECWRnKZwyvZwvJC7e2PEBE7WckwWdTb7Drd3hryzMeDe7gg7iHlmqoAXgRvEXJwu0B64ZPQYAYE7uyMsNyRTz/PiQoWiYTK0AvK6wq3mEEMWiZOY1Y7NN07X+db5SaYKNje3+3SsgO6+u+SNjR66IjFbzfDSQoXW0OWtlT7zlQyrHYusodAcCJxrZHnUGnNts4cdxEhiqnM9VTTIGzLfvb5D3lCZKRtMFnVubQ9BEKjntbTPtm+z3bcwJJG313o0ijrfuTTFext9upbPXEX80I3PUYUg4ANkxM+Co8EsfLyB2SfFP8eN3DE+Gr/ta/phWfbPo03oi8JHcXWO+g20Rt6nOm/X9Bk6IYMjdsMSj1cDPEA6Ijd0ZqKArsmokogsCfQtn4WazosLFW5tjajmdS7PFGmbHlt9h7whUTI0+nZAOatytpFlreMgigI7A4/TEwrnp/J4nsH91pipvMKvWmB7EYkQ8Ou1Po2iiiiI1HIKXpxg+QmvnKxRf1YjEaAz9nhna8BK28b0U0PMvhMQxCkXoWwoPNgzKRkSi7UqthejSR10WWCubHC2kT802/y7d7fY6Du8tdzlwnSRoRtysp628bSGLpYfM6fIPDefQZZElupZHjbHzIQq230vdYfvWViejxXA0A14caHMiwtl3DDi3bUBIqmwh+1F9EyPel7lUj7Pc/tyrG+vdtnsu3QsH/V+i+U9iyRJWB9YrHVtdvo2CQJ5VSCjytTy2qcfVMf4wnEcDBzjY/FxC+DTAocnuQiNos7Xlqr4m+n/f/Gww2LVoGcHFHSZc9MFZsuZxyTlJksG6z2XqaLCpZkiZUNhq28BAi8tlLi5PeSPzk3w43ttajmd5tDB9EKemy1ytpFnu2eT35dae2+jT3to44TwFxcM6gWFzV7IVt/lzGQWP4LZckrs2h25ZBUZXZFZ7VsMNjwGbowycpiv5tjsWoBIXpM5WS/w7QsTIMCmYuPGIRlVwQoiOpaP5YWQJOQMjTCOOFnPUc3pjF0fVRa4vT2gO/ZwwnQiPj9TJKsr7A1dHrVHLJs+tZKOpitkgPVe2h6UCLBYzXK/NcKLImo5nUvTRepZjbbhcnt7iOP6FHUZEBg4AVVD415zzNJEju2uxT/daWHIMmen8pR1hcmiSjmjc7Kaozn2aA7cNMsWBLy3ZeG4EdPlDF3T5ZcrPYI45rWlKkuNlPw9VxEZOyGiKFHNpUoZ612Lt1a6XJopUt9Xpri3M+QHd/eQJSjnNGr7fIuDPuGD9p/7zTED/3FToicDzwPFk99kk/ZREou/CY55CL9/+G1f0w+r0H4ebUKfFz7q3nua8twhH+CIX8KHneNJc0uAnArd/VLA03LMR20ImkOX9tBhHERkg4jtYarZH0YwUTQgSVL+WBTj+SFlI89G30WTRSw/ZiKvs9l3OV/JU8lrrLRtBODdjQGtocs3z9YoqDA/maeUVdgaugRBTK2k8MJCmd2hx+lGnlMTacLiwI09o4gYqsSJCQNVUjDdkK7psdX3uLJQop7XeND0aY5MeqbH2I2w/Ihb2wPOTOa5cqLK1dUu93ZM6gWFRBBwgpA4iilmUrOxU/Usp+qpbKoiiXzlRJXVtsla1+HKQolTE0U2exbfu9WkmpGZz8KJaoapgsFMJcMPbje5sT2gbXq0xg6zpQxjL2KurLNYy3Jto89z82UuzRTZ7lm8tzXg5uYQQRJYrOVQRDhRzXGiluGt5R4jz8PuOJSyx8HAlxHHwcCXGL/LzOJn6cs+emzX9D9gO69IIlWN/ccSajkNSRLpWj6GItM1/UMTsbWuw2RRYej41HJlAB60xrQtD1kQKegSqiLz67U+17aGvHqqwnNzJd5c6fHqqTo90+c/vLOVLjpZlamCgS4LmG7Eru2yM3ZZKGd4/VyFqbzB9++1eGfd58WFEkkS0zMD5qsZ3lvvISswW9H5q2dmkUUYOxHVrEbXDjgzmWO9a7M9cPHjBNuP+cqJMj3bp5HX2IpcgtilYEhs9QN+/rBDTleYKhpMlzRymspL8xXGbZNnZ4t89+YukghZReGZ+TIPmyMuNEpcnClydblHKaPSHrjYfsxae0THDBBImChlubs9QhZF5qsGfpCw2XfIGRoXp3Ns9Bx2xw7rA4e5is6vHvX49UqXxWqGFxfLTJUz5A2ZjCrTdwPURABJoJgVCQIYmAFOFHFWk2iUDXK6TBwlrHUsxn5ERhZ4abHM2ImRxFQJ6I3lDqbj8WjPYrKg0hx6zJQ1Vjo2siRQUBW+earOYj33gbFezakUDZmx/Lgp0ZNGSB+lFvRJ758ng9nPa5P3RfIQgig+dPNWlM/99Md4Cp40W/xt4MMqtJIIs2XjC1kXPu2682lViQ79Brom+51+H3qOg3mgmlMPz9V/CmfgKI76EAwcj2+eqXOmUWC6oPGfb+6SIFAyFCQp5TL99F6L9Z5DQkKUJLhezFcWpskZKqbjY7ohmzj7AgcJQRzzrXN1umOPcN8Y8dJMgVJG435rm4emRSWvsjv0uNscI4kCC9X3vRMuTRdZ7Yy5uT3mwnSJuXKWII5pDh38KKRtpuaOYRRTzqqEQcSJapbVrokbJNxtjvY/W0AkxLx+tk69kGGzZ3FrZ0QUJ1yeLTFZ1Lm+0We5Y/EqtSNcvpSkPVfJUM2puGFIs++yBmz0HLZHPuXWmDBJeGa6wHLHQldlihmNag4SRP7+RhPTC+lbPt+5lPr13NgZEkfw+qkabdPjH2+3mC7o7A5dgjhhq+9i+xFbPfNjx9RnwfGc+JvhOBj4EuOTbsK/iKDhyYxMuL8QBvtZhqfhgCeQ12WubQx5ealyOAEdzfTOlA10LZWMW4RDLsBkUedUPctad0zbcqjm0+EZxDH/cGObnzzo8NrpKlNFg6trAyDB8UJGto+IwGI1S8f0kSWR3aFDOauQJBFz1Qwv5Su8+ajL2AswJJENy+bm7oiYhCuLVc5PFXhzuceDPZOKoVIrqLT7DrtDF1mCiZyBKsOdXYu8JpHXZL59cZLFSpafP+qgKCITWZXdsYi6r04hCiJJHJEk7CsRqez2LXaHLstu2j+ZURUuTeWJhA1kVcIPI0w3oCcFzFUMKlmd9YHNtfUeXcdnoWzQCSLaYxvTDhEEmKtmeW62iCrLTBbTrMv/7euL3N8do0gCGUPm7u46Q89HFtOWqpIuoSkCbhTz69UuYZyqOY3ckHpe41Q9y4VGkY7lsdKxefVMFduPmCsb/Ncbu+RVGV0RuLreZ7DSIaeruGHCv/3aIicncuRViRtbI0wvIqNIlLMqnXFAFMeIosArS1XcMGG2kj3MmB0d6+tdix/e26PivC89+FFGSE/beH+eWdzPco99kSZmrZF36OZ9Qj/OtP028DSN/M+CL3v72Ke9bz5L0Ht0PfiwcwRRzDurXa5tDSllFM5MpnLUczWJ23ufrO98Z7TvazJfYatn8/UzNW5sjVjr25hO6gswdAJ6ls/ZiSySJOAEyb6Tus6ve6mi3MgJcIOIgi4xdiPmyjKaGtHr+2QlUj1+QaRgyEQxPD9XopbVCOKIjhlwfaOP6ad+BQebcF2RuTRTxPZD/t2v1pgqZ6hlNYZuyJ3tIetdh6migawpJMIIEKkVZGpZjeW2zXJ7RN/0edQ2KWd1Ls4U6Vs+iSAAaavugz0T0w0OW3Mn99X+wijm7vaAjunRHfm8sdJh2INTisRUyaDvhJhOwEQhg64pzJcNTk/m6ds+eU3G2BcCiRJ4b6NPTpOQECnmZGbLWVb3TB41h4xtD0OXCUMI/AAhTpgqZR+7Rp/X/XA8J/5mOA4GvsT4pJPsF1G6ftJV+MDoSZbED828HvAEDsylnjxfGOY/QAgFHju3LIls930kBHQ5dVIc2AHrPQfTDeibPvWcRiWr4gQ+17ZGJAiMvHRxODmRI4hjHu6ZjB2fh22L1Y7DX1xuUMwojFwfQxMpZVTu7g5pDizu7Jj8ty9MM1/JEEQhuwOHjZ6J6Ucs1LKcqGRRFJGyobNUg97Y5a3VHposMls0KBkS9axOa2QxW9IZBxG6LLHZM7nXGjPyQrY6FrEosNW3edA2kQSRB3sJU0UdkYRWB4Kgw0snqtRzKvdbFq4f0TaHhDHsjlxcN+YrV8r8/95YZ2CGiAKcbeT4xpkJTkwWuLZfun57tcfF6Rznp0uM3BDPi3lhoYIqwd3dMff3TOarWf7k3DTrXZPrG33++GKDl5dqvLfRR0xAliRyhsqpRoHF2vutW2udMV0zQJdFdE2hntN59VSdMEoYuRFvLXdRFZl6TuPbFye5vTVk7IUsVnKca6Ra4tt9j2peRZflQznRgwxgwZDZ7Nnc3OpzfXvIUgLXNwc8u5AqXrVN71B29Cg+jnz4tPH6aXCU+Phkxet3gcmCxnQm/XmM3w5+00rPwfgLo5hH+/KYv6v2sU/T2vNx+CxBb6Oo43hZNu+k7yWjKIdmZwfGVgBXN/rc3Rnz3FyRE7Vc6mSf0QD7qefNidCoqKx0fGIgI8Lby52UpzR0mS5pjL2A/3Jtm7YZcHm6wHRRw/NDfvqwzYsLVU5O5Li5NWBge7y92kMRYWQH/Px+h2I2VQfa6luM3IhyRgEB7rdMzjYKPD9XIozS6sE7mwMWKgaO7xDEaUWpmlMP+XJT+1LJ372+w08fdnj9dI3/+fVTdE0f1w9Z69qHIgkLVYMoTliqZWgUDRIBpssqbzzqstlz2RlsMV82OD9VRFdlnCDkrZUuF2cKnKjWgZQLda6Ruv9+/26Lru3RHfsUDZkkSogT2Bk6XJor0bd97CBCFuCZ2SJemLDRtbm1M0IVoWMH/PH5OqYTcnd3xFItw1wlQ14XaY4cfrnao2MFZDWJpYkie2ObICF1bR4/zhX5vPYvx3Pib4bjYOBLjE86yX5RetEf5+Z6cBMftG8s1bO0Ry5fPVnF8ePHnqtIIrNlgxtP2UM9WQp+9VS68avkVHRlzNlGnnpOI6eL3NgaYwYR5yYLqIrGO6tDZsoG5/cnuQetMVklJQdbbkxBU1AkkVP1HJIocnN7wGrHJK/JXJmvktMk3CghZ8g0igY3d4b84mEbJwyZKhr8yYVJohiubXR5d+QxUzV4bqFCQoIkivx/31jFUFIHyPWOw0bPZraUoZ7XuNcyaQ1dEOCnjzqYXkiSJCRxzAsLVXpOQEaRWe6M2erBaDRkYAf8m68s8NycxJ2dEa4XU86plHWFO4Mx/+m9XVpjm6wmUDQUKjmdrhWwea+FH8JEVqU99vi7ayO2+x5XFsskAlQyMrOVDLoqk8QxGVWhJXhMhjqrPQtFFJkpG/zgbgvTDzgxkT1ciAqGzL9/a40ogcVqhm+erbFQy/LmozYPo5hGTmO6agAijbyGrqav1Ry66JrMTCXDTCVD1/SZqWQ44wQ8aJpIos9sJUumIh+SA+9sD1nrOtTyKs/MFHF2uvzsYRdJlpkqGgydkK7pk6l8/NT15Bj+TRado8TH5tD9nXMAFEmkqvM7D0r+kPCbVnoOxt+pepZzv+N+/y/CcOzTQJFSkYCW83gm98C0EgReXqrw4kIZSRSoZbVDFbHl5tMDAQBVhqwqUdeg5YEowX+9vcvFqRJZQ8J0fAI/Jq/JLJQzPDNf4s7OmO2Bw8gLGFge93dDfrk64JmpPNsDD1mEoRMSkdDZcxlaAcWszemJHOWMStOGWcfj1vaAvh3QGnkYqoQiCdTmSuyNXd5ZH1DPp2IKe2MXIeHQXfk7lxq0Rg5nptI1rJpTubZh8eJiGRL4yb0Wjh9SL2hU8xprPYdzjTxfPz3JiWqerZ7FTx+0+cnDLrsjn7+4PMX93RGP9sw0iNpvw5T32y/fWeviRzEvL1bQZYkwiVnbs7hr7TJ0ArYHDstdi0fNMQVd5cJMidMT2f2qR8zdXRNdFRGAta4DYkLRKCKQ0HdCxq7NfNFgtaRxaaZMOSNxvxXw1ZN1corCn11uPHbNPq/9y/Gc+JvhOBj4PcBvY/J+Gg5u3oP2jaKR2rQ7fvyBLM/s/t8HPX2I72emDjaCXdNnrpI53Ej29h8fOSGL9RyL3Rz3dkwUUaBj+Xxlocz/8OoCJHBhpsjt7SG7A5e9ocMLi2VyqkzOkqnkVXRV5vxUgfVeme/d2AZD4YXFEiICt3aG3Ngc8sxciaHlM1HSmCkV+eaZCbb6Lntjm7dWeympuaBRzes8P1emNbJ52BqhKxKXZkpkFIHNvk0YgRUEDGyPUkHhlcUamiLzw3tNMqqEF8YsTWQRui5hGBLFYMhwdiF1W/7HO6kM5+WZArmMQmfk8kAWkUWBW5s9tgcejZLG+akSoiQwdAMyssTZmSx/cmGSW1t9tnpjVrtj/tWVWdY6Fu9tjeg6ARNZjUAUuLE1xA5Cnp0tMbB9EhL+/Zsb5DUZEqhkVe63xjSHDvd2h/zofoeiLtMaeizWs4QxeBGEUcJ7W0Pu71l8danCehhTyarM7iuHHLSXXd/oM3RDLk4XuTRTJIriQ3fqo2PJdHxaoy6KaPCvXpjhurvCwukql2aKh5N8wUgVLI7K1n5YpvPo47/JovMkwfkYx/i0eLLa+mV5L0fxWapnn/SYIIoPte1nK5mnZnIPTCsPnpPOIwb3dkaEcYImi1QzAm03eeprRDFc33mfVJDR4NsXGgRBTCGjcGNzSJwk5HWFmUqOoqGCkCaeLkznqeQMWmMbJYFXTlUQBImsJjG0A3YGDn9/e5dxd8ySmKdvh0SRiRPC3aZF3/WZKeqoiszF6TxZTUGWRHYGHutdm4fNcSqL3RqT0xXOTuX350fIaCq/eNAljtK59+cPO5yayBDFCW+t9ljrWsyVMsyU3w8kbT/kzs6Qr56s0iimvjwHrsQjN6aSU+iMfYaOf+j8fmt7yMM9E8eLmClnMJS0/XKmaNBagXGYMLR8Rk5AJaPx/EKRi/vO8RlV5vJsmZEbMV3WGVgBOV1isZbll4/a3NoZ8+qpGllVxi4bXJmv8fUzNa4ud7H81A5u6IWsdCxmK+/Lyv6u9i/HeBzHwcAxHsMnUXU4dH/dv4mPZh26pv+YW+RhlofUDXLLSn0GBq75oVrxW/v+AM/OFQ5bR66udvnVco+RE9IzAywvRl6qsljLc685Tl0O3RBZgJbpocsSBV1hd+CiOAFuGHFre0wtp1LL68wWM5SyKj+72yWIY2Qx4hcP26y0TYq6wsXZMht9mx/e63BuMoOmCChiTBBFVA0VQxW4te2SiOz3YIKuK1RyBmfqOWw/QlckyobKV0/WSIS0h1MUQFUlJvMGi9Uci7Us/3hzlx9vwgvzJQxN5tbmgJvbNpAwWdDpjT22uybztTwvzFeJki5nJvOcnsxxf29M1/TIKjKFrMr/fnWTvhciCAJ9O+CH9/aQhYS8KpORBMIEMopERpGYrRpcXe+yO/Rojlx6ls9CNcs3z03SyBusdCxu74xY79hcnMoxX8lgBzF5TeJsI0/ZUHhxsUxZVxg4ASVDYbVr0R4nbPVs5P3xc3W9jx/F1LIqBUPm+kafB610LC3uc0oOSIW/7lkM3YDVRzYTeQ1DhSuLFRRFPhx7b692+fG9Pdojl+9cmjrUL39apvPJx3+TRed40TrGb4Iv0/j5sPfyWapnH3fM0faoAwf51ySRRl75QCb3aaaV3bHH2yt9Tk4YTBQz7A6eHggADI9YEGcF+O+vLJHTJL73oMNfXm7wV89NU86qECcMnIDTjTz3d0dsiwKiIPL8fIF31iKGxRAEiSv7stinJguEK21yikQoS+lcUtVZbpqUNHj5ZIV31gcokowui2Q1BcuPKcUx0yWNizN5Xlyo8tN7LZa7NrW8ymRBx/bHnJ3M850Lk6nUs3nAFZP45aMOth8TJxGzRf1wY17cb9j/xYM2f3+rCcBfPjvDYj3HWtvkUXuMocLZiTxvr/UY2B5T5SyVrErX8qllNVRJYmAHXO+OgISXT5RZzII0WyCKE3KajJKRuDxT5n5zTM9KyR2VnJq2RpFwf8/k8nQBXZa4uTuiNfRQRAFFkZgu6uQ1hebA4VdrXXojj1/bHQxdwfKPHYi/jDgOBn7P8VmUIZ7WG/1RWdWjC8vR9o2jWZ4winmwZ2LsK810Lf/QXGW0nzFWJBHbD7m5NcDxAx61TFRF4vpmnx/daTF0Av7oQp1GIZV7a5seZxoqfhCyNF9kqmhweTpPQsJC1eDkZIGdocWNrTFTpSEgUMtrFHWNKAZFFHhhoYCuKxiywFbf4epal62OxcAJ+JcvzKIKCY4fM1XKMHYChraP5YcUDZVSRqWa1ZktZ7izO6aR1Xh+roSAyLWtHpoiAQJ/9942f/bMNKIAPdMlr6vc3hlyarKAG8Q8O1/m9v3U3r3ftgiChNJ+xupCo0gYxtza7LPSGnOqnuPUZAFVlFjpmKy0TQZWgKEIeGGMIEFGlpirZBn7Id+/3UQSBGo5FVmGUgJBINJ3A+pFBT9MmCrrTGY0frbcxvTC1G9BEunbIRDTtX36DkwWDSbzGv39dp4LM0X6TsDJRoHW0OW7N3fJ6TLnp9KxcHtnSEGXubJQpjl0WO+5XN/sc21jyNDzkUSJ2Ur2cOw0hy5DN+SZ6RKbA5t6TqX/lDF6aaZIe+SSCMJhy86Hjc9jZ+FjHOOT47PcLx93zNH2qJeXKu8/N/5kJOBaTmOqrPHyUo2xHzGMP/4YAQgS+OVqh78pzLA0keXsZJ5STj/MkHdtn/bDNn4YY9o+7/QdZFFgoZ7jgixycabIVs/mZw/2iOOYRBBYrOex3YCsrrDethl7AUEMp+s5zk+VcMOI5sDGC0MWqlk6Y4+VjsPrlRwZVaaUVVmqZSloMggClax66PJ7bqrID+61uLkx4L2NIUEYk9NlGoUswb4j/Z3tIY2iQSWnIkhwoqqn7USkSbT//Z0tVjtjMorChakccZIQxunrXJop0hq6uH54GAgJ+9/vZEHDjsEce+wOPc5M5Hj1TB1ZFA99XRpFnaurXX650uX52SKvn67x7HyZIIo5O1kgCocsVDPU8gauH9IxPQaezFwxA0nEesdH8yL2hu5HXrtj/G5wHAz8nuPTEh8/rDf6aBXggAB1UAX4sHMqknjY8hNGMZIgUNJhoqDRsQLCOGbkRlQyCq4fsto2aQ4d7jTHTBc0EASiKMYNEx62TXRZYqGa46UT1UODql8+bHN1bUjekDlRy7PZc+g7IW+u9ilndWpZgzge0TcDvnFugubQZr6aIauJdMYpSWp76CEKAqcbWU5PFGmObWpZndvbqa28ofR56USNpqEytEK6tsc7Gz2iGNzIR1dl5so695omfSuklpcx3ZCMIpNRJbq2z93tIWenirz5KKBvewRtkASBvuWRUUUS4I2VLgIClazCVMlgYHnc3h4wcHx0TcL1I7YGNl6YIOgJJV2jntEY2x4gUdIV8oZKEifMljNYXkC8fz4/hNX2iNMTU4y9kCCKyWkKz82XmSnq+9rTVbZ7Nl4Y44YRfhgSRXCukePBrkXZUFisZXnjrXX2Ri73dofsmangdz2nkdNk8ppI2VCYLOq0TY+u5TNVNJAkkSiJ9glrCs/PF5ksGo8pVB1sJg7GVjUjcTdOK0mzVelwnGVUmW+dn+TW9vCQTPxhmc4vUzb2GMf4suOz3C8fd8wBJ2yyqB+29QEETwkGnpa8Wqzn+OvnZg/nh5oInQ8JCA5MyBLABzbaJu9u9nn5RI2BG7A+cBAS8MKYzZ6Focmsdi0kWUKPEvwIZAGqeZ37zTFlQ2F74GDaES8tlRAS2A5i9oYOYzeikZfJ5lOFPEVReG+jz82dEZ1RwL94TuW5+TKyJHK2kefqapeHeyZ5TUSUREoZmbKh8M5ql5WORUFPWzTf2xrSHHtMZFXKhsb5qQLnpgu0hg6/Wu5gBzHnp3L8+F6HkePzoDWmmkvX7UZB53Q9iyDActcio8qcm8rx/HwaMLRNjwfNMZIoIkkiph/TkES2+w5+BF8/WeHq5uBQkQjg3GSeSk7lvY0+WU1CV0S2Bi4vLlbJqKngw8gO6VkB76z3mC5l6Jg+O0OXIIoo5zXGQchy2yf0oT0+Dga+jDgOBn7P8WmJjx/XG32Q5SkaMkMnrcl+1DkPgpGCLvOVExVutaBnBax1baIYzjRy1HMab650iZKE+YrBKycr1LMaAydg4IYoIpyeKHBxKsdz+wHNwXs0HZ/NfmrB/ouHHZ6bLfCdCxOEUcJW3yIRoJ5TWelY1HYGrHVsHrXHCEJCQdf42lKFnCZhujFRDH4YUcsalHMq02UdWUrwgoQgCHlxoUKjkMHQBDa7Dj3TxdAU3tno8a2zEyiyyPWNIZfnipyZ9DFkkXrR4M1He5hOSEYX+falBkKS0Bl53GwOmS4YTBV1Rh4kSsRkUWfo+OiyzNANCcIQQ1VolAwcP6KgKphiRDmj8cxskWbfxo9AUwTOTOXxgpi3N3qM7YCcLnNmokA9p9M2XfZMn92Bw2wlQ8/yuLbV52+fn2OqYOCGCZvdMXdaI1qWj0DC2A251zJ5ZjZP3pA5OZFLZfjGAX6YYDkhl+cLh/3856cLPGiOubo+QJZE6jmNek7DCULeWe/TKGiM3IgzkzmunKgetoO9DJyo5x7bVChFka2uSddNnVaDBAZ2cPhaB0S8W9t8KdR9jnGMY3wQQRRza3tIz/Lpmj5KUXxsbYn2g/3JkkDX9D+gtPS04MD7iMrAk+FFMSPRs33utEbYYUwcRYQx9CyP9Z7NszMF/u1X5um7qezxRtclb8i0xz4PW2O+cabGmYkcSQLnGgWWu2ki7EQ1y4P2mKEdkIjpurnVs7m5PUAVBb5+tkrZUA7NvjZ7Nstti72hh66IgM/byy4J4AQxggjz5RxXFip863Sdq+s9MpqK7fmcnsgxW86w3rG4vtknoym8cqrC5ek8v14ZEMXxYVX11GQWWRQpZRTW+/ahrCi8796+UDWQRfHQyTiMYt5a7bE8gnrHoW+HdEybuYpBZxzw8lKF+80xP763x5mJLJemCoy9iHCfExhGMX/9/DQzJZ090+PuvTaXp/NkNYmRk9AoquQVibXWkJGXemQc48uH42Dg9xyfhfh4dFN2dDIGDk13KjmV+80x1Zz6AWLYwaR9YNJT1GUGbshUQUMSU8LYUZIYkHIKhg49OyCKIjZ6Di/MlwBww5BTEzmem6/QNX3IcViVCHIqL/kReVWiOUyz9IuGyi8etoli0GToux6en6ApMs2hy97IoWiofHUxz6WZEg/2TCDg+nqfnZGDSEIQRzw3X+KlhRprXZN31vuU8zr/+so8QRzzH369QRjFFHSJsiHTtwNGTsDNnQF5LW0PGtgBy+0xbdNjpWdRzWr8qxfmqOVU/v32Jn0noJrViBGoZyBXy7PeHbM9dJnIq5ysFzBUie7IY6NnMXR9DFVBk0RcNWa5OWaioDNZNFAlCSeMsd2IRl5jZKfuxwPL43utMa+drPDt85PMVXMMLA9JgIEZMrACrixW+YoA232TakZmqWKw2rYwdJlTExk0SWa93+P2zojnZktcniuiySLrPYepYnr9rq52yWoSC1WDyX0S24Em+2AYsDf2mCpomF6QanIDu8M0iHsSQRTz3kafvaEDQuq0ujvyeGO5C8BU0aBr+QgJh0HugTneUb7Kk78rkvil13g/xjG+CHyacf9JyPif5HF4fwN60GbymH9NXmHgp8F+2woYOuEHlJaeVtlWDtL/nwCGqrBQy3GhUaCa17i+McQMAiI/oW/5PNqz+dYFma/NlPbXMJE3HnYIooiBHRLHMV0roFZQkSWBUkYlUQWu74yYLmlsdh1cF4aOz82tAZtdm74VMF0yWOs56Kq8Lydq8cJCiWfmiiy3TFpjmzceDclrMov1HAVNYq6q89x8Oc3mz5S4utrlzTWbH9zb41nL4x9v79K1Ai7PlHh5qc5U3qBrhzTyxqFYw1vLHb5/r8W3z02yVM2y0Xa5uT1ippKlOXTIqiKNQvreRk54GHB99USF3YcwdAPaI4++FTC0fKI4YXfosFTPou+30m73bf708jSyJB5yQF5eqvLyUpWfPdhDLKcOxq4fMVsxuLYxwA8lzkyXWG6bLNTyn+ziHeO3iuNg4A8Av0mrxNHJG97f4I2ckKET0hqmvft3d4eMnJArC2WunKgekjoPbNFnK+Jj9vNPOsmeqOeYrWTSCXBlDGLCo5ZJ3/HpWwFLtQxBHHP1YYeZssZGz+FkLUtjX26yntN47XT9cBE56FO/szNkec9CkUSur6feAJdmSjwzU+LSvstjFEVs9lz6VsCJSpZH7TFbPYd3VrpcnC0yV83wn69t4ocxj1pjurZHVlcoGCqaKvHL5R6mF+G7EV4Q03I84hBW9sbYQchMwWCimqM99rD9iH+42SKIYk4UM3zlRJWe6ZEA1YyMKhcwvYCcpvDyySrdkce93SGynGZ7pvI6L5+qcn1jyNtrPQxN5exElr99cYa1Tqp69OrJCc428iy3HDQZWqZPlAj8zXMzPGiNcTWZxUqWel6jNXJ5Z7VL3/ZZ6zlkDZWAhLfWOsyXMlQLOhtdh62uxZ3tIS8v1fjbF+YwVJFfPmxTNhSub/T53s0mhpoqSyzW0sVcllITnjCO+aNzEySkLV/y/tgYuiFnGnkmi/pjqlPvbyAUfC0NHt0g5uxElqV6lrETcrKeRUjeH0dPjtOn/T63f+7P25PjGMf4suPTjPtPSsb/JOc+2vp34MB7rpGnmlPZ6tvkZViqZ4liiPaNJ4+2Ej2tsj1dk+m1Qj4JJFnkQiOPqkiYTkgxI1MXVcauTyVfZbvncntrQHfsMXRD/CBi5AZUMyoXTxcQBYmC4eIHEd+/u4dAwmIthxtF6FLaStP14Kf3O7y3MWK+qlHMKBiahCzCamfMoz34wd0WX10sU8/rPOpYvLhQpJ7XyRsKphPw69UBnX2SriIINIoGxYyC5UTkDAE3jEhiONMo8JfPTJNRZXRVZr6SoWN56PvJuActk62BzdX1Pv/3107QKBrUchrtscf37+wxVdSZKhiHUt4HgdxEQaOkwdeWKpyoZbm5PeLsZJ7VrsW93RG3d/o0Rx6KADsjj4HlEZYMZkvaoYLRj+7vsdV3mMipvLXcpeMELJR01ro2qihBkhBECds96xNdu2P8dnEcDBzjMTyZ5X8aOezo72EU07V8yobK0AlYbtvMVrKHmYo0EEirBbbr0XXTsvB63zv0JzgICtK+cYN6XiOvS4iSeHjekRszsNNSbnfs07M8SNJJ81wjf7g5PT2RZ6Geozl0+OnDNrWcxjdPT7IzdNgYOogJfOP0BMWcyn98b4ucLlPLGlyczqMroEoShiwx8gKsIMJQJDbaJiRQ1BUedkxGdkA9r9PI6aiayDtrPd7bHBAGMWcaeb6+VGe1a7PRNYnchFAQWKhl8MOYG5s9Nocu1YzKVs/m9s6QKwslfuHCzmqPnumgyTJBlPCoOeZec0TfCnhpsUQUi2Q1GdePeO10lWpOYXfk8pMHewRxzH93ZY6BncXQZJ6vVjHUEUEQ80cXGyxWsqm6jyDwqDni3p5JzwmYrhiYGyFxDPNlA00W2B44tEceiiSQiCKLVYOZcuZQB/tg8z1yI378oM1rp6q8uFhiqZ4jpymPjY/rm31+cLvNlcUiiiJzsp76F7h+SEmXOdvIc2t7yJ3dISM34PmZUnpNJ/NUMhJ334X1rsWP7ncpZhRW2hZDJzxsUztwg/24cfrk/48Jxcf4Q8KnGfefloz/ScQlDhzGDxx4N3s295tjxmH6nLfXewztgEbRONTFP6g2HFS2qzmV1baJIEjAJwsGNtom612HybxGKasxmde5utHj1taIK/Mlrpwo83DP5Mb2iFdOVTE0kXpOwQsTZsvpnGn5ITt9jySJCZOEke1TyqlYfsKLC0WyXTgzkaU59vjaUo3VrsWtnRGWG+KFCS/MldBVkeW2zemJPK+drFIyFIz9VtDLM2VkUeLRnsk/3mjiRhFnJgs8P19isZZluqxzd2dA1/L4yokKiQCrbZPJos6ZRp67uyNubI341rk6Xz9bpZJXcP2EROBwo75Uz7JUzfDiiQqyJB5KeQNc3+rTHlhsjqA99pktpwmdMIpZ6djsDFMOXV6X+fMLk+yMPObLBt+7s0scJXz1hMjpRp5KVqFn+3THHkgChiQytiM0VcJ2Q4a2hywKVLPHpmBfRhwHA8d4DEflQF/bn8iPZnue/P2orGhr6BLEaWvQVs8+rCIctGdc3xywZaVKDwtVg5tbA0RJAMqH552tZHj1VI0wikkEEBI4P1VAlkQmizoCcHNniCrBTEk7zCT9/fVt/o/3djg9medPLkxydbPPasekkdf4n795ku2+zXev77LcGfPuRh9IsP2IC1N5MiqECfzyUY+EBE2SWKhmaY4clltjfnJ/j6ETMFVKKOsqBU3m9GSerb5LRpD42qkaUZiw0bN5bq7IxakCAyd1ynXcAF2GqXyGvVHAextd/AjOVXPsKR6aKDKyfWYy0FVk2sMENw7Y7kW0xx6ljMy5yQK1fJaB5eNHMQ9bFsttGz+K2eiYhHHMw7bFd2+1KOgKi/U0G5/XZK63RjwzV2KxnmOrZ1PJKMyUs+wOXXRF5PnZEs2By9AL0RWFhaqMJojsDVxIYLqY4fREniQRsd2QG1sDtnrpRZwua8S9hOU9k6EXYroh56aKQNo2tNyxmCio6KrIiWqWUk4/lBfsWS6VbLp5eLBnEoYRUZzw3uaA+sDj5aUKd3ZGbIyhvDsip8mcrGW5NFNMycVPyNg+Wf36sN+PcYw/NHza1rhPS8b/JJXnpwXjB470kwWNk7Usy/tcgYM2wQPp6aPVvzdXemx3H3ewFQEFePzRFHEMcRRTymqUMul258pChbWWRcf0OdMQaI89epZPOSNzda3Phakiz8+nMp57QxdFEjC9gIwigSBgByGXy0XmyllOT2R4KMJU2eClE1V0VWbkRkiIvHqyhqZIXJwp0ijqPGiZdCwPWRR5Z3MACZxp5Fms55ipZIjiHbwoppqRuXKiQtfy0CSB7iht9elYPo/aJlEiUMulrbZlQ8FQBHp2RNf08EKYKRpsDh26psd6b0DP9sgrEntmgBvEnJrQaQ4dXD9kophKV2/2PKwIHu6ZXNsZ8tJ8hVpOQxQFJvI6J2oZnpkps1jPcQl4c7lN3/IhEVhuW/Qsn7dWB7RHDoYq8acXJwFY2bNRQ/C8CE1XOJnVOTd13Cb0ZcRxMPAHig9bII7KgT4t0/PkcU96DQCHrUFP9n72rABj/6W6Y487zTGXpwuHFu0FQ+b29hDbD7m9PWQin6oO/emlxqH2dKNo8MN7e6zsjVnes5FFgZdP1XntTJ0ojlmsZTEUmfONAo92TcIY7mwPccIIQRS4PFNkZ+giJAJnG3nGbsTba33kBCAhr0mEMXTMVPHAckPKORVZFtjoWqx1bEo5lZdPVDFUkbu7Y6aKOn96aZLltsXNzQH/65vrVHMaOwOXzUGA6Vs0CiNqWQU3SDfdlbzG14sGhiKwsmeiyPC1k3WGTkjftHHDmGpepKCr1LIq0yUNRYTZahZDEZnIq/y//vE+2wOHy9NFvnGuwcjx8aOI1tDhrdU+z80VCZII0wt4tDfmezd3yKgiL85XaJs295omP7u/h+lHXJousDSRZ3lvRD6j8txciebYQ5HAjRLcMHVYVmWRm1tDTD/glaUapydy3N0d87A1Jo5T/e8gjnl3fYAownzF4EQtS85QD8fJi3HMdt9CFkRKhsLQ8YljuDJfplE0DsdRz0qViiRR4vx05rBn+EC+9pO4ED+J4zahY/yh4csw5p8MGI460iuSyJUT1cOK8lGeAbzf5peuTRWKGvSC98+dAEUd9p4iUhNGUMmnhoNeEPL9222eny/wzfOT5HWR4r5yW0aT2Ona9GyPcuZ9tbIHzTFrHYs7zSHtgct0JcPpRh5FlBi6IXd2xtztQ+l+h4yhktMkCrrMi4tlFqrZ1C1dlXl2vkx77PL2ag9JFHlxvsRsJcvk/uc1vYDbO2PCOMYNZbZ6Nj++12Hs+8yXslyeKZBVFGp5lUZBPay8X13v0zF9VFGkltXoW2NWOjaSlH4v0yWd5fYYSxSp5RTyqkRr6LLWdVjr2pycyFHJ65QMibEPRkam3wv49VqfP7/U4K+emWa1O+bG5oiJnHOYVHpvY0hWkSllFJ6dKyILAn96aZKVvREn63k0ReS99QGrXYvWyCZOBMaOR88OeNgc8cJi7Qscbcf4LDgOBv6AcHQj/2ELxNNMX47iaccdzeScncwfBgEHFYEDKdIL0wV27sFy2+LkRJ4/OjdxmOm91xwzclz+8dYeOSPt79zSlXRjPvY4UUvf+2RR5/XTNQZ2Klv53uaQxXr6epdnU57AztBjYPkMXR8nDPnh3T38MGJ74HBmIkfJUBm7ASVD5ZnZDN+90WTg+uR1haqh0XU8wiRh7AY8M1ugZfnMFDM0RzaSIOJHMVsjl9mCwVbXZr1rM3ZCMqrE3b0xnh9xdjLPUi2DIsGZepFqTkUUUkLbRMFA02TmyxnmywaOHzMeQz2v8trpCVw/wI9iTkzk+fvr2/yi12bP9KgXDBZqEIQxP7vfIRaglFVZqOToWT4rXRNNkrDsgL2Rw9DR8YOEu7tjHD/m3fU+YyegOfBom2mr1dDykGWJRl5n6AxYbpvEccKVhTIXZiBBJK+K/PH5OrosUctpvL3Wx48COpZPOatwejKLJAkUNIk317oMLB8SeG6uxIXpIroiU9kP+Ko5ldbA4Y1HPWZKBggwVzIYexGzlezh2AuimCAM2czCuak8JyYKAGz27N+I/Hs0M3lMJj7G7xM+KsFz9OeXCdGhdHDucD052OgCTO5zjw4+04l6DvGJWzXh/UBAIQ0MOvt/NwoC5yZzXJopcnWtS62gcK5RQFdTj5u+HfDSQpn7zRFvrvXIKjLztSxbfZsHTZOFqsGzc0VyusTNnQGvLtUoZVTcKGZjd8jXTpQY+3Bja8Dr5xs8apnc2B4ysH0kUWClbbHVswjitOVmaAVYQchMUePFE9XDtc/xAiwvpJpVKRoKpyfyGJrMu6t9KnmVs408RUMnq4ps9l28CGbLWc42cmzcMnlmvoQsiYzcCEUWWaxkGLsRURRT0BUsL8IJEq5tjbiyUGK2pB2KM9RzGq7n85+vQd0OWapmsP33jd06Y4/bOwMSIWG2kmWrbxERoyoib630KBqppHV76DJ0U8nW3aFHlCQYqoAmy5ybzvPddzcZuPCfrm/zr19e+mIH1jE+NY6DgT8gPKbk8BkXiKcddzSTc1RN6OhrzpZ1Hu4OyIjpBDRbzXF6/3lKMf15rxkRx2mP5UwpgxvGOH5waP7yxnKHmaJOGCc8N1dCEkSenS/RKOps9Wy+d2uXrCpzfrqA6QS4Ycxax0KT0171sRPyzmaPZ6ZL2H7EW6s9rm/16Vrppn+hkuXXqwP+4lKD/3Jjl/WuTTmjMlsxUIEwSajoCrmsipQI3G2NGDhpKfvdzYCirhPHqUvxw70RmqJwsl5gupZhb+yx2zeJYshoEmISszt0Gbs+qgTrJlibA5pjj7yuMPYCTDfE8lKVorEfsmRI3N0Z8sZKl3pO40QlR0TCva7FC7rC15ZqvLPW41ZrhCqKnG4UmMgbaQk8K3FmIseDPZNyTuPSTJGdUY7dnstc1eDrp+okosCdrSHrXYueHXBxOs+9ponpBjxq2/zLK7PMljMMnAA3DLm5M2KlbXN6Msc3TtcJo5jNvoMoiEgijLyIt5a7JAK0Ry6SJFLUZX76oMPO0CarSKy0BSRR5NxUgcmi/oHN/uooHUeKJB72HcOHyw5+HI5mKJ883zGO8c8ZH5Xg+V2N74+7Rw/UhGRZfszTBkhlh5cqjyWngihO+4I+7PV4PxAAGDpgBRHXN/p0xn5qLjm0kUWJjZ7NmYkctZzG1fUBkiAgSgK3t0ds9WzMIOKrJ1KfAFEQeXauzLmpIkM3ZH17wLWtIZN5FUMGO4gZOwEIAmEYcX1rgB0ETOR0WkOXkZuWMvKGzPbA4efLPWYrWWo5jZwq8vx8DUlMHeKnijr1os4/3WniRTGTeY2pgsFcOYvrh2z2XaZL6fp7faPPz5e79JwgVcjb5wRUciq/eNAmTBJO1nKcbuSRBQFZEgmjmPe2BwiJQC2vs7Jn0hrZrJrgjxyunKjghgluGPF3Vzfx/ZCZcoYr+14FK20by40Qk4ShE+x746h4YUwUpxXkruXz+tkabhjxRtBhtTlmcSqLvWnx55dnf5MhdYwvCMfBwB8Qjm7kP+sC8TTZ0WpO5dJ08fD8Rzd0B4+9t97jv95skbfhbwvaByzo5yoZXD/kmfki89VUJej7t1sUM8qhFvJax+L6Rp++4yMmAov1HC+fTMuNu0OHnCZzopahntOYLmq8tdpFQWCypPM3z88wctZ40Bmx1reYKWbJaxLLHQvTDTnbKNAepxKetZzC5dkyuiJSyWpYfoiRUQmCBE+LUYOIrudRyaj8i+dmubU5YLNvMnQ9ZosGe3HCZMGgllVpmS4TWZXmwMFyQ2bLGfK6zHbfpWN59O2AOAHLBqtv0xw6FAyFge2TUWRKWY1qXsf1Au7sjDFdH4SE2ZLBc/MVhrbPuUbCZCEDSYwup6033zo3wUzR4O+v77LWtXhzpYPpBciihC6l6h7LbZvdkU0lr5GIAtfW+3hRgqSIVDQJRZHwgpAoEtgdpaobAL/e6BFH8OJ8CUkSGbohU8VU2edPLkzSGrogJMiCSN8J6Y4cEkHkfCNPyVDQNZGlWpbFeo7JgsZU0WCyqB96B+wOU9KgACCkHBN437zowGjsk7Y//HPMmB7jGJ8Wn3U8f5EVso+6R4MoJkpScuvT33Py2HMPzCv5BA7EB3DDhP/07iZnp4vkVJFfrfb42YMOSxM5NFnmpcUyzZEDYsK3ztbZGXgEYcQ7G32KhnJ4nqKhoMgC2/3/P3v/HSNJmt/5wZ/wEZmRPrMqy3VVte+e7ulxO24dd7mW3N0TSR313kn7knqF0wsI0EHQHV5AAgRIfxACZF4B7wkQBOGgw93p1VGvzonkcbm75Brujtse296VN5mVPjMiw0e8f0RVTXVN95idGXJ2t77AYLoyw2b84nmen/t+x5yZygN5tkcupqEQJ1DLKTwxX+TN9QGTRYOVe226Y49HZ0s8s1ihmtNoj9KM7IkJk2JWxQ1D/uRKB0lMiTP2SpMuzBT4wY0mV7eGzJUMTk3kWOk6nK3n0FWZclZlYPv8tN/msdkiye5v2xsHyJLIhZkCVzcHhEnCwPYQJQlJFNAVeT9wRiyQCAl3GiOuN0acqRkcM8HQZNq2R3OQ9ro1hy66JPKtC3WePVEjiGJKGYWeI6OIAhdm8nzmdJW8kY7JixWDrrPDVFGlklN5ba3PlfUBHdunoAnU8lpKDXuETxyOnIFfIRxWEf6wg//eQL/HEAHvjLbunTNvyHRGY5Zvb9MceizqGkEUs9KyaAwdqjkd4mQ/vSmL3q6irUTekFlpjwiTmFpe54n5IgPHh0TkykYfN4y4s2NRMmTqeYNbzRHbPRtRSAefxVqOF+608KOY4+UsWVUmSmImclkymshiLYckiqy0x/Qdn1s7I8pZjWeOV7i5PUKXZU7VTCbzBnEc0Rh4rHdsdkYuv3lhmt96cpYf3dxhoz+mbfu4UYLthzSHDo2hT8VQyekKhYzGbDFDVldZ7YyI4hhDkZAEkFSoZFR6jo+QxJTNNBo0Xciw0rFYtT0mJIFjU0XGQYgIvHh3B0WWeGaxjCQkNCyftu1jeSGTBZ227bFjuWiSgKnK7Ixcpgsad3fGWEHMWsdmx/JJNnp4fsibm0Oemi9gqApWEPOTWzvsjDwKmXTCu7OTCsz0bJ+CoTJbzt6nMH2rOSKKYppDl+bQ4288Po2myvRsn4HnE8YxbdtDlUUMWWLk+Hzx3AQFIy0h2tMOaI08Xl/rcWYiw8ndXrMgiulY/j6d7V7T+sG+lPey0z2bPPw+HOEIvwz4ee354+wpOOygHHQ8mkOPpsN+79nB7ycL+j5V9OEy1HHw0NO9A6YuUspqSAgsVFMldTkjoEsiiihwbaPPxjBNJeyRUTSHPl07YGqXiQdgsZbhj97YZKUz5umFEoKU9nOpksQogK4V8tpqj6EbU8kqLJRNEOCxucJ+sEMRRao5DUUUccOIf355Az+OKBgqVzb6BHGeru1zdXPAMycqdCyPQlZDV2XO1tX93/BELcvLy10QEpxqlm8/f5wgivn+tW2ubvRp9MdIkoQsCCSIbPUcmgMH24/ZHjhcmCnwzUvT+6xubhhh6gpFFXRdZqlpI4oC1ZzBI9MmQyfaJwUBUBSJJ+eK3N2xGEgSyy0bSXLo2j7qrgMxkERsv48up316d1pDfM+ja3mIB5y8I3xy8IFXgj/+8Y/55je/yfT0NIIg8K/+1b+67/vf//3fRxCE+/579tln79vG8zz+4//4P6ZarZLNZvnWt77FxsbGfdv0ej2+/e1vUygUKBQKfPvb36bf79+3zdraGt/85jfJZrNUq1X+7t/9u/i+/0Fv6VcOe4N/Y/DusuB7TkOwW795+O96QX/HYuxw9HYPGVXmM6cmmMum7BEAG90xf3h5nX/84gr/x+U1/uUbW7RsH5KER2YKnJvOoyoytxojVjsuBV3hZC1DPa9jqCqaLHB1a8hLd9MozErHAUhTllHC2It45kSZvu1xt21zYztlZIiAIEz48d02d5oOcQy2H3NiIsvF2RI5TcFyQ25tj0AARRZ5ZLrAZ05VqWR1/DhNVXdtj5dWOvxsuYuQgB/GPFIv8dRcmam8ge2FqLJAa+zx9PEKj84W8aKIkeux1XdYaVtkVZmKqaEIMFXU0CWRsR9TNjQUReBGY8jOYMypyTzztRyPHyvw9PEyN3dGXG8M2eg5LHXH3OvYiCRp050A3ZFPGCeICFRMlTNTeaYKGapZlXEQMV/K8PufnudEJYMdRmwPXZIk4dFjJb55aYanjpU4OZnnTD1HRpbQZZHG0OXq9pCsJrNYyVA2U3rUMIopmypRFONFMV0rvb+O5XFhpsDxWobZgs5Sa8xSe8x8Kb2Ojb7LT263CKKYiqlSyao8c6ICSSp0c30rrRG617L3z3OylgXSpsLmrv0etsvDqBd0Tu5Smj5smyM8GEfj/S8vDvZzvR+n+oMcM9h91w5nHA7OPZN5jelMOh/s7bexG0zqWP6+Y/L6Wi8VKNzVIShowv75DgeZDy9ooijmRDVDvaARxDBTyTBV1rmyNWC9N+aV5R5RmFDUFJbb6fhUNRV+/7OL/I3HZgD48e0dbm8PKZs6VVOlPw5o9tNM9FxR56kqPL1YZLGSBRIUUaJe1skbMlVT51ZzxA9uNLnVHNEZeby01OXKRo/WyOPidJ6TtSzXGyPaI49yVqU18rjTGPHciSqPzhSY3WX02/sNE9I57njFZOCGbHTHXN0c0LJ97jQt2lZALafxhXOTnJ1KA3X1vEE5q9LZVYJerJnoqszV7RH3dmx+eGsHO2I3m+0jiwLNgY8bQM8OeGNzwE/vttno2RR1mXrBoJLTmcqnGY6N7pidgYMXJnRHfkozvmNjBzEnJvOcqxcY+TDw4Qe3Wh/azo7w0eMDZwZs2+bSpUv8+//+v8/v/M7vPHCbr33ta/yv/+v/uv+3qt6/MPxP/pP/hD/6oz/in/2zf0alUuHv/b2/xze+8Q1effVVJCl9vf/23/7bbGxs8J3vfAeA//A//A/59re/zR/90R8BEEURv/mbv0mtVuMnP/kJnU6H3/u93yNJEv7BP/gHH/S2fqXwftPJewP3Hr3bYan4B0Wi9qK3HcvfZ3s5qCgridyXjchqErPFLOfqJo6fUMzIiJLI0Anv45eumRobPZtXV/tc3RxRzCp8+ewkS20bP0qIkpiRn8pSPn6sxGbX5oYg8tZGn9WOy3Re4/SEScfy+bUzNVRZoj1KJ6onFioMnZCKqfLEMZf1ns2rqz0EBObLGUZeyPbI4cbWkFeWuxyvZvnsyRprXYeltoXvRzRGDiM3RFZAk2V8K2S+ahKFqYLl1fUeoiji+DGhHBMnKXWqCDh+yM0eLF9r4vkRhiYjSvD6cp8wCnGDhIlShjfWu8iSwELZoJRREISE8/U8URix0hlTMBTOTxcIooR7OzamIZLXFMLdxXY9b5DVJUQ3Yqak8y9e2+BW00JTRE5OZJkoGMhCOtE+uVBBU2RubA0JojGKIpMkCZBgyCLL7TGl9R6bPY8oTpWY25ZPFEfECFTzKgnQHLisdhx6Y5/H5gqQwGrX5dHZHCM3xItiLi+nysIDN+UOFyUROYpTNqHdJreUOaPPs8fLzJYz+/Z4szHa1xzYs8vDUCQRWRK52RghH2UDPhCOxvtfXjwos/tRHXMPhzMO9809cURFT9/Pje6Yl5a6PDVffAcLXcf2kQUBURLpWD7x277AO4SID7v6rTH88ZvblE2NhapJ0VSw7JChF7FQFElEkUpWpZLT2RmMGTgBPUdm5IbMz2R5daXD9e0hcRxzfqrAs4sl3lgfkiQJ82WDIIoZBZB1I3Q17U273bQZOT5vbo7IqCLTxQxhAgQhnaHLvbbFU8fLnK6bXJhOG39L2XSOmyjorLYtfnizyel6jgvTKVXzZEGnY6X9aQM35OxUfp98Y0/rp5pVkafynJo095nXPrVYYW6XpWmB+5XZ95gDL80VaPTH3Hh9lcVKllo+ZUy6sTVAEhL8KGa2oFPJaby62keU4Ovnp6iZKittm7WuSxxF3NtxUGSBuaqBKgj0xiGnajmaozHLbYusJuCFCadq+Y/C1I7wEeMDOwNf//rX+frXv/6u22iaRr1ef+B3g8GAf/gP/yH/5J/8E770pS8B8E//6T9lbm6O73//+3z1q1/lxo0bfOc73+Gll17imWeeAeB/+V/+F5577jlu3brFmTNn+O53v8v169dZX19nenoagP/+v//v+f3f/33+4A/+gHz+yOAehvebTt4bNPYWXYfpQh+2TxjF+1HYPSXiPUVZR95jj5CYLWf4tx5Lm4n2Brs9/vg9xcq9c6VlIRqWF5LVZJ6aL3OynudkPc/l5Q6rHRtJTBukFClVGd4auMxXs6y2Xdpjn82egyDAztBDlARsL+LJxSzd3QG1OYiZLWeYLOi4YczdxhBVElAF+NO3trnXsllpWVh+xMWpPIOxT9fysN0AUUhIAEkU+NGdHXRZ5OmFClEsoPZsxm6MpCSYmsxS1+Kbj86w3U+ZsQ0FqjqoOZW8piIj0LHT+tJ6TiKMEwZjj51hgOMH/OTemNuNEYVsSnl6pzWi0XfQVZnJgsZMOcNG1+Z6M61/NVWFOIbJos5kTmWj5/IP/3KJ11Z7OEHC4/NFJkydxnDAm5sDmkOf+XLK9PPEfJFj5V07iBNeWOpwd8fC8kIuzeV59niZ7YHDnaZNY+hiKDK6KnFqIstax2UqbzBfMeiOfYoZleWWTZREWF5ErWAQRzH3WmMgSSe/AzoCGx2LrZtp5LA5SgXntgfOfqRs7Ie0LI8zu4rYB+3ycFTyYQ7wwe2Aj612+hcVR+P9Jwf7PVoHlNw/TL3/+w0KfZBzHGbrOpwlPjj3jIOAjsuBbF2y76wfzFpcmC7cpyvSs9+9zEQhbSQGyMkwkU+Vfs9OmUzlDW42bM5PBXzm7AQlXWWubPC/v7zKYBxQzulUsxod2+fNtR6vrw2YyOuUDYVKTkdTZH7z0hTNgcOrq33eWO9xtwPt7IBPHa9QNTV+ttZl0tQpaA4DL0K1fUZOQJAk3NwaIiLy7EmBhUqWRICVroOpilxe7TNT0nhlucP1xhBDFlFliXstm1JGIRGgoMsUdZnjtSxXNwccr2W5sTXCVEQePTFJ17o/U3awNHivzOfgM90j/JAF+Bc9MNZ6XJgtM3JCNnrpHBRFCV4IupwuF4d2uPuMDcpZmxO1LEVDYRzsMFnQaVk+QZjwzIl0PNfaaTBmcSLP54pZ/t3n59/1+R3hrwcfS8/AD3/4QyYmJigWi3z+85/nD/7gD5iYmADg1VdfJQgCvvKVr+xvPz09zYULF3jhhRf46le/yosvvkihUNifGACeffZZCoUCL7zwAmfOnOHFF1/kwoUL+xMDwFe/+lU8z+PVV1/lC1/4wjuuy/M8PO9taZLhMC1DCIKAIPgAhYjvgr3jfFTH++tGPaekg3ViMJlT0skgjgjiwzGZA0hibjVGBGGIIomUswonKgZhGPCWCz+63eT5EzGL1WxKcZbuRD2nAAmVjMSbqx06dkA4nccNQr5/Y4ezUzmOFXUWaxkem82n1xHFhFFIVhOoZlTKGYmx60ES88UzVRpDl+MTBhlJ5ng1Q3fgcrcx4ty0iS4JXFvv0nMCNroph37JUJivGHz3eour2wMyskzekMhoMhNZmdZQoKJL9McBuipyopLFiSOiKCGM4cZGj5EdIGRlNFGg6/mcr+cIk4SdvkPfdllr29wwh/za2UlaI4eW5XGhDJ97ZoE3NkZcXu0y9n1KGRFDV+g5Lp6bLoa7lsO1jRFdK0BTRHwvRIwTcpqMFyUMxiGnJkyyYsJKa4QbRARhzE/u7FDPG1QNmTvbA5Z2RmRUgbKp8OSxIjc2h6x2x5ydyOB6Hi8t2fSdgGcWSvTGIUM34OxUDiFOMCSJQkmhYiiQxDwyZaYaCr5Jxw6oFzRI4JWVHhtdO+UB1yRubA54fb3HU/NlTk9kuNO0ODWZp2sHCMBMyUAR3rYDkoimAxtdi9myyYmqQdfy2OhYzJYMmn2H7silm1WYLRn32eVGz+FWY0QY5tLvdm35sO0e3A54xz6fVPy848zHMS59Usd7+KsZ8/+qsGerx6u79fdBQNN6p51/EDzonXjYed/vOfaOufd+NvvKA/fb6Fpsjd9+v59dLDGZUwiCYP+cZ+p750z2j5u8R6Xfwaf6m49O8flHJmkOXTa6Y85Nmnz+dJmzdYOhE1HJKvzpW1v86HYbWRT4t58wkSWwbI96VsJURYoZlc+drnFlc8CLd1s8cazIZF6HJCEKIkYBWF7AanvEZneM50U03IiJnMrjswVsN2CjPWayoPA7j02hqWlW9/XNAYYiYioiWUUgikJcX0aTRKZMjTiKmckraIpEzw6BmNuNNAN9daNH0/LJygINyyerSCRJQr2gs9SyCcIQ1w+5u2Pz/Mkyy+0xt5oWAnB60qRiaiy1bBwviyKJeJ6HoYCpiqy0Rry12ubSXJF6XqaSVZHFNBM7k9cYaRJBGEIi8vRCkcm8xs7Q44tnqmkN01SelbaNmCRc3+7juBGVjMJW3+FYMctw7FPJKA9+eB8Cvwxrr4/jHt7vsT5yZ+DrX/86f/Nv/k3m5+dZXl7mv/gv/gu++MUv8uqrr6JpGo1GA1VVKZVK9+03OTlJo9EAoNFo7E8mBzExMXHfNpOTk/d9XyqVUFV1f5vD+K//6/+a/+q/+q/e8fl3v/tdMpmPtnTge9/73kd6vF8ERHFKFZeTYRTC+nVoOjC9+9NujUEToX39OsEG3DDu36cfpH+PfLAjyCvgL8O9Ibzega17UNbBaML3bqbH7LiwYadKk9si9O6lx7g7hKoGTgxBlNLNCUDbg44DQi891lqQ7rvjwqadHk8FJAH8CMZAM4b5PJwuwN0QNrd2yGmQU9LPrg7BFOCeDcsWaAqYCvzJz4ZIYrqvE6TXVJRBD6Hb2OJ1ZwtNgJ/sQBJD/ydv0vega8M4AD8Gb+QzBrZ2QnzgtRsOTpTWykZWyCs3bfoBFBUo6bC92mdlCRrj9J51AQpZuNeCTRnuLEF7nP4mVQNyos/K3bu0nHSfF502Ww6cyUNGhX6wys0BbFrQW4YtF0oqTGThj/9imQ0LLpRAV9LffdsBU4a5LOyM4KURZGSYyYImw7AHrWCN/2sptYcbGajsBiavH7KljgeTOlx9+SfcEN+2FW8Z3jrw9/he+veDbPFB3z1sO3h/+3yS8EHHmfF4/N4bfQB8ksd7ePiY/4Mf/OAjH/M/buzbqgqSmD7792vnH8l5P+A53mu/KE7nhr33+/B3HTedQypaer976IXv/xreuLtOp7HOhg1BAp3VOzxZS4+/YsGVOB33/RHkDbh5rcfNQbrvMxPpPLARQv9eej0vNeC1a1BWYTILagQFFfJWgz/5cYM7/XROKOzOPUv2MggQWLDZBluFhRz4IVh9eLGZjsWqCE4EPR28MWRDWOpBYbzGggnrdjoW3unCnSGYEsQCTOmpANtaALeXljmbT+eGH0Vwrw/DEH56Ob0eYzehtHobpjLpve3N0ZMGnCuCsHGVl3bgzgBu3EjnlOlM+nu92UnH8JkM/HRrdz+d1BkK03F/HKXH6rtwzUnHfiuEjQ7sjOFHQ4vaeI3Fwvt/hh8Uvwxrr4/yHt7vmP+ROwP/zr/z7+z/+8KFCzz11FPMz8/zJ3/yJ/z2b//2Q/dLkgRBeLsY8OC/P8w2B/Gf/Wf/Gf/pf/qf7v89HA6Zm5vjK1/5ykeWZg6CgO9973t8+ctfRlE+eu/3rwNBFNMcekweogQ9/Pl+5Gq3yTOKYqRdpUlII0BvvvgT/saXP8Ns2bxvn4wqsb3ZJ4pgIqtwesLk1KTJnabF0yWd4tUm/XHARF7nqdO1/WPuXUM5q9C1AybzGps9B/Veh6migZDEdKyAvutT0FVMQ8H1Az57qsrIjXCCkObQJyHB9QL+8ctr7AxcwjhBM0SSBLwoIcllOPfoDNOOz+vrfcZ+iKTKhOUMxwsJGU1C7zpc2eqR0RVEXSGMHU5N5jhZzzOd17i2NWDgBYQRlAyFoqlTz6u87m1wd6NPqGYYBxF5U0YIY3JCmm6PEgFJSmj2fBIiQjcijhISXWFxusDQiyjqMlNFA0kQsYOASpCkVKKyREGT6K72mMhrFAwNMwioZDSeP1Fmu++yPfQw/RB96DFdMtja6KPW8jx2vIIiQnVnzLhrc2qxQrxjoUsCUkbB7buISsDU2SqKLFMwJOa8gFeW+5y8VKfuRVSaNqcmTJ5cSBeDe/YSRDHXt4acn86jSOI7nmFz6HFts8/O7df52lff+S4dtL2Dx/1VKe/5eceZvcj4R4VP8ngPDx/zv/CFL1CpVB5+Y59gfBLnmIfNEe/2/XvdxzuzA+lxCq98n+67JKYPYsUGyTRx1JDpvE5hpkRpsYgsiIzbNghwXJaYbllEccz56SJnPZ9iRiGrKyyWDX5wq8WXz08yciPmNwe8tNJlveswUStwdiLDzZ9e5dipUwzcBM32+dqFCfwgoZxVqJoa91o2nysb3NgeMXACzp0o0xr5NNd6ZDQJWYDOOMK2PR67MMk3SllyurSbOU3nQNXyEJKE2o5Na3OIIgtIksCJmQITfsRWz2HgBESVDAgC1sjjZEmmbMr83z41RxALlLMKO0OPMI5JkrSEaGJ3rA3DgJuXX+BrX/0yXwgTXrjb5oljRZbaDjUz7f/SVnpMlXRkQaSgS1h+TNVUWW6PyekyNTMlr5DFVGz0peUOeU2mkFWpLfX481vbdC2fpL7Ab3zh9M9taw/DJ/G9+KD4OO7h/Y75Hzu16NTUFPPz89y5cweAer2O7/v0er37okU7Ozs8//zz+9s0m813HKvVau1Hh+r1Oi+//PJ93/d6PYIgeEcEaQ+apqFp2js+VxTlIzeej+OYHwQfJXd0YzTm1o5Nyw72G5P2Pr/bdkBIawInixkQRLYHDkttG0kQ+MypGhk9/c0XayI3ZFis5fd/m9mKhCzLuH7IWs9lvmIwW0opKy8vd/jTqy0uHcvhRqAoMqfqeWYr5r668WbHYb0/ZqMv8ORCJb02waOUVVnvO9xujBi5IROmiiRK9NyQL52fZLnjcrs5Io5j7rbGTBcNHp3N8+RClb7lUc2lAliGIpCQOgSjIOL8bJFyTuON5R53OhZDL6RgKPz26VkuHCvixTE5XcYQRUqZtFb2ezealLMqmihxp5U2n/32E3OM/JBbDZ8TtRyi3Uct6LyxNsTzI05N58krCrohM7BTdoeFmkrP8bBcizCCRBD43JlJXrjbojv2WV8aM1c2mSprBEGErIicnDC51RziBRF5TeW5ExVWOhbLHYc/u77DxZkiBUPBlkSqCMzXTFb6DuMo5srGgHrRYKaoM1dJ9RFoJix1xgw3AxYrJidqJp86XuXN9QFDL2FnELDUcXhjfUS9lOHcdIF6wQBRomP5+89uvTvGCmDoJUDE3bZDwQ7o2j4tO+DCTBo68lce/C7t2Z68W8e69++58jvf719mfNBx5uMekz5J4z381Y75f9X4JN3DwffxQe/gu33/sPvYmxsOqtlf3Ri+o2n4IHIihDE4u39bETw5X6JiqixUMlxeH/CjW20KpspTx0rMlrKMXJ9/c2Wb1Z7N9e0Rnz41QcmUubw25K2NITcbFkMv5sRkjqlShi9nVO7sjChnVBYrGU7kQBJlwtjn0yfLPH28dl8PkyzLbPRs1vup/sqdnTEt26O32/9WMHUK2YTaYpknFytkVJkgipmtCIy8mK4TMRiHFLMaT8yXOV7LYcgCt1s2p6byrHdcjpUz1Ex9t7fCI4wT+mOfcZAQJBKLEybr3TErPY+CIXNvxwYSnj1eoe9GbPcd7g1hY+CzOJHn65fmeH2tx1rfZXPg8dR8icWaya3GkHttm4wuU8lo/NqZGrWCgaGI/OBOm3NTeVa7NrIA93ZSco9vPTbNs6cqvLLSomsFyIL0sdrtJ+m9+HnxUd7D+z3Ox+4MdDod1tfXmZqaAuDJJ59EURS+973v8bu/+7sAbG9vc/XqVf6b/+a/AeC5555jMBjwyiuv8PTTTwPw8ssvMxgM9ieQ5557jj/4gz9ge3t7/9jf/e530TSNJ5988uO+rU88Piru6GC3Gbigy3Rsn8bA3W9IOkz1eLaeQ94VoTpRTYXDDvJLb/QcDjM7Hmxw0tW02aw5SOs7i4ZCNa+QxAIFQ2F2t5F17IfsDFyubPR4a3PI3Z0RpYxKz/ap5XTutWyiJEFMoJLVGDkBO7bPbMnA1GRubg3pOQGbfYdaLqWdfGqxTGPgsNG1yWoKc2WDnZHLbMnASxIkUWAypzFyo7SRSpKwXB+BVJnY8UNeW+2jSRKDccD1/hgSmCoZnJnM89R8kZyh8IcvB2z1x3RHHqW8xsZojO2nAi+fWqxRzGi0bY+8pmDqCtYuFVySxCxWc1QljWeP17C8kKETcqsx5JWVHo4XpBkJ2aZhuTh+QCIIqKJInMDJiRxPnSiz0XfYGXkkJIRxQmPgMFPOMPRDBGC163BhtghJwnJ7jBPG1Is6rhejKAJOEJPVZLwgwvUj7CDitdUePSekZMh8+ZFJJFHgKxfqOLu81reaI1qWt8/4Uy/ouH6IqYoYqsjtxmjXCcxwdXOwT383WzJ4nbcbzvfsul7QH9j8+KBGyA/rFH+cgky/jDga7z84Pik29nE2Iz/o+yCK9xuID65XDl7Hwblrj4hi8C7egBfDwSqiUxWB2bKJ7YeM/Zg4SrDciEIW6nkjna+cgERM0BSJ505U+MLZGkKS0ncu1rJ892oD01CJo5jLaz2G4wDLDbiyPmS7n0UATkxm8RMYuTHXNwcUMgobXZtLu6q9r6726dkeUwWNtu2TUSRsJ6CjSEzkdSRZRlPld1CwnqxlqeU0EmAip1EzNW41R+R1ma/V83heyL2dEaEn8akFE1kSaY4CChmZrb7Hem/MciddB0zuUoHnDZkoiqmaqVOW6rsk7LjwykoXRZZpWR6tkbc/jwO8vtHnTtPi0myeExMm612Xu00LVZFwvIBbjRFRGHGzOWJn5NIeecwWM6y1bQZOgKYqTOQTnlq8v2TwCJ8MfGBnwLIs7t69u//38vIyb7zxBuVymXK5zH/5X/6X/M7v/A5TU1OsrKzwn//n/znVapXf+q3fAqBQKPAf/Af/AX/v7/09KpUK5XKZv//3/z4XL17cZ5s4d+4cX/va1/g7f+fv8D//z/8zkFLNfeMb3+DMmTMAfOUrX+H8+fN8+9vf5r/9b/9but0uf//v/33+zt/5O78SzBJ7+LjVVRsDl7stm5O1LLPlt1lZ9j7fYxeSDzC27J334PU0Bi63GiP6/u41j8b3RXz27qExcPnp3TZDN+DL5yZ59niVxsBFlQV2+h4vLW/z2cGYxsDjZnOIH0SUMiqzRYO2HdAbh5QyChlN4urmkMfniyxUDTZ6LscnTWRRZLnlMFcxWKxmCOOErZ5Hb+zzwlIHx494fK6ILIqs9xz8JEYVBJ44VmY6p/GTex1my1kyqkDPDsjrEjIiP7jVYrllU8/rIIIggKZJFHSV33xsGl2WWGrZPH96gqvrfUqmjueF2GGIE8Q4IZyqZ8loMpfXusRxjCGLjGQRy/OpmDpeHHFr2+LTJ2s8V6vwf766SRjECEkECRQyErIk0B/76GKaObjTsnB25eSHY5/BOKBt+ZyZyFHIKiy1LAa2z3MnqlzfHOJHMUVdZiKns9l3mSnqnJ0usNl18MMQChrnJnO8dK/DyA+YzCvIisi1ewNOT+R4c33ARMHA8WNaVqqwXMtp97EEvb7W4+pGn+bQY2swZqnt8JkTFRQxbeCumVrKRhIE3BvA6HaLz515mx50j+r2oI09zOH9IE7xu/Giv5/9fxlxNN5//Hg/NnaY9eqv6zoehvdiqHuQ4GVz6LE1Zl+EEg7QUB9QIt97F/eY6t4NCZCXob/rEZSyGU5NZvnhrTZelHoRoghnp/Jc3ewzdEMenS1wcarEhWn42oVpdFXm2taAclalYur8rWcX2OiOWe/Z0LYREDAUhVxJIaPKvDaAi1bA1y7UaY887rVs1rtjnF2q6z3uI0WScALwk4AgEGiN0sb2UxenGfnRfrAtb8i8vtrlVD3H5O7zLmYUhAScIMQPQnpxyrz0s+UutxvWO+b7vCHT6Dt0bIkX7nTZ6nl8/swEc+VMmpX1Y+q7v+uJWpYo0NjKwdMLZcIo5nbD4kQtw1OLaSndRnfMxZk8SQKn63meWqggiR1eW+3zxHyRmbzJK8s9diwPEoEJU8MJImISvndjh57lMXB9JElgvefw3KHn9klxiH+V8YGdgcuXL9/H3LBXj/l7v/d7/E//0//ElStX+Mf/+B/T7/eZmpriC1/4An/4h39ILpfb3+d/+B/+B2RZ5nd/93dxHIdf//Vf5x/9o3+0zzkN8L/9b/8bf/fv/t19Fopvfetb/I//4/+4/70kSfzJn/wJ/9F/9B/x6U9/GsMw+Nt/+2/z3/13/90H/xV+gbHHz/zs8TKLNXP/8z06xQ/7gh0cZB7mbByeCB40KdQLOmGYY3wvHfzvtp39bQ/ew2RBJ6uKtO100L8wU6A1dGmPQ1ZbFmMvIm8o1HI6E6bKSsehPfKo5Q0WqhlWWzZhnHC3OeT65oB6XiOMBeYrBsvtMUEYYrkJfhgwkTeI45i25SALMXGcMFfJcmLSpKgp/Pq5KpIg8Rc3m9zYHvLC3Q49N6BiahyvmpgZlUfqec5O5VFlmSROODWZ462NAZ+arzEOfJwgZnVnyHrf41PHKynVp6FwZbPLwAkQBTGto1VhacdmredSzihs9V3sIKKiq3hlkwvTqYrjyPH4wc0mspAunDtjB0OV0ZSEUlbfzWDIlPMaOVmhbbk0BmO2+i6yNGIiq5LXFK5uD/jNi9NIksjdrk0ho/DpE2X+5WsbvLXhksQxA8fHC2OeWqhwtp7jR7db6USe0+k6ASQJJydyXN0c4QYxkpA6IOVsWh7VsX3KmXRxv2cj+0rDwMgLyRsKZyZE3DDkx3d2sL2Ir19II79vrvdpOKC5wT5dram+U+/iIN4vpeiDtn3QYuijcqp/UXE03n/8eD82dtA2U7atd+LDLqjez3V82HMcvI9yViEjQU6X9h2Evej/QSXyPYfg/ZwvAOwDqQFrnFJtGrJITpWo53RevNfmxdstnDBGFkXyukwInJ8095XNNVnku1cb5HSZkxM5Nro2l1e6TBcMLkyryKKQlhiNXX78WiqMOFvJcrqeoz3y+NK5GlsDl6KhsNJzeHK+uO/IJILAayt9ajmdmVIGXZU5Wc/v/67fvbrNd643kUQBXZZ4aanLQsVgpTOmN/bRFRFZEHjmeBlTk5gqaJyczO0/H4Cu5aMoEidrJj0nYLqksd61U3HHXWHQMIq517aJopgkSZB2W28awzTw0xg43G0M6TsBAzfkzGQOXZa51xpTL4zpjDyW2zaPzuUZ+RHHJ7LEUcL5aYW1joOhKVSyGkPbozkc44cBiS+iKe9cdj5sHXOEvzp8YGfg137t13bFhx6MP/uzP3vPY+i6zj/4B//gXcViyuUy//Sf/tN3Pc6xY8f44z/+4/c83y8/Hvw8PmxUFB4e8Xm/WgUHjz2Z15DElDd+rxZ0D1Ecs9GzaQwcek6A5YY0hg6JAL1xyFzZYK6sI4sitazGGxtDnpovM1P2uNUYpcq7JNzbGXNiIsHyYkBAAAaOz0zJ5HbDZqM3xvNDKqaOLAoM3Ii+HbDZdZgs6RwrGfz0TpeMKqHIIiQBXhixPRwjArNFjS+em+D2zohLcyVyskwEvLzUZhxG/OWdFqIoEMURmwOXpZ0R612bOBEpZhS6lk/ZUJCA3jhAFBPCJKblwI3GCE2RuDRbYuz1WO3YnJ7IUTQ0PnumynTZwA8T7jWGNIceX784xcgJqeZ1cqqCoUlkVZnpcgZNEpgvZ4miiFfX+rSGHpNFnYETIorgRwmaLPGl83X+2Ysr3GyM2Ow5vLkxoDd2yaip+Nsj0yaPHSvRHLh0LI+N3pjhOMdU3sDUZWaLWWZKWZ4ceTwyU6A5dFnpWNzbGVIvZKiaGndb9j5/+N4zf/5EhVuNETlV4vs3d/DDiIIuY2ryvu127YB6Br7+SB1ZEnlpqQskVE1tn798n3t9l4f8vYTxDm5/dXNA1/b3Mw0PUmL9IHb+y4ij8f7jx/uxscNiXfDODOthkcjDY/l7LeTfz3U8bE55P3odB0tL6wWdjY7FOII7TQsruP8+997Pg6Wpe5jWYOtttth3ICOxX0pULhm8uNRhpWNTMFSePJaW3OzYHierJrW8wcmamS68NYkf397h9GSOvu1xpznip7d36Ns+L692eW2tR0G3OFPPMZk3WKjmsIOIggadscftpkVr5HJ5ZcBTCwVA4Kd3W5yYyFHPG1xe7e8KNMrUchrPLJaYLaf9cQd/o2Mlg08dK/DkQonr2wNuNwcUszIlQ2bkeGQUiZWuw53GCEkSURWJ9c4YSRJpWR47I5c4Sjg7nWe2lKFj+ax3bf7yTpv2yKWW0xm4ISVDIYpiogRqWYVtIS0TimKBkRtwZ8fiRmPEsbLJ6brJbDlDGMW8ttanOXAYunE6l4vpebf7DiCgyqntPX+iDAK8sNThtJ9nrS9yr2lzp/mwhtZ31484wseLj71n4AgfL2bLGT5zqERnDx8mKvqRNiDv1T9W3+aadv2Qy8sdLh0rMVvOcKKW5WcrPQoZhWo2FRdb7bhIoggkWE6Iqkicmk7VaKM4pjF0qOcNhDp0xwHdkY+mC1yaKzJwA45XM5yayHF1e0Q9Z/CZkyIbfYONrsfJiQxn63l+cGuHW80+oijyxEIJEYHm0OXCdA4nTFjtWPQcn63eGEkUOVUX+N61BqIk8cxCibWew63NATcbQ0xD5KnZCn03RNdlaqbG7a0+QRgykctyfavPasehaqp89cI0GV1GkUXiKGZrAzq2RxQnlHQVUxWZKuhkNZH1gc0Pb7RAEpnKaVzdiHGHDptdm7MzBZ49UaZr+7y41Gbkh0iCwObQ5Y2NAfWCzkp3TM/2kRSBjuVzcaZIxdR4bC7P//XmNqWszkxRJ6MqVEwLUUgwDZkkEZnMvf3Mvnp+koKh8NlTNUwjjf7vicV9ajFtDH5ttcf/5/t38IOYT5+u8uVz9f3J/7BNPb1YYbllkQCOH1E1DU5NpD0oFVPl/HQebznVH1jpOqhywrmpwm6db0hz4NKyPLq2TzmrMnDC9xTGawxcrm0NiKIYBIFaLi1P+KiVWI9whI8SBxfqe5oAhzOsh0Uigfuywx9FydvD5pSHKQ8fPv9eaakipRnRSR1MVQIhSUtbDowPewr0B8eOyYLO6AG06SJvqw9PFUSiQYwVwfW1IbVMFkOWuDRboJxTOT5h4vgRv/noNKahMnJ93tocEoYRCALLrZTF5/mTZTpOwIv32hiKQFaS6NguE/kqzx6vEEYxS+0xZRVqBYO5XY7kaj7VVfjjt7a52Rhxp2XzjUeneHKhSHPgsNRyOD1p8tRiZb9M9vW1Hl3bp6DLvL7eJ68rrHUdrm2O2Og4OF6TWIDGwOdzJys8f6JMEMd0xwFC8nZG9sJMge9fG/PKUp9aTmOxmkbZH5kpsD0Y88bagJKZRvWTJB0D63mNC1Mm21fhwkKZ5sjjThPmSganJnJYfsSFmcK+kns5m6rZTxYMmgODalajNXIZOKlA2URO49JcnkvHSry60sENIgxdpjvyCGNw3Xc2fbzbOuYIfzU4cgZ+wfFu0Zx3++7wxHB4kH8/EaAHRZ0OKkUervUMw5AoTiex715vsDVw6do+X7kwdZ+a4aVjJTa7YxoDB1OTyOsSYZIgRTEVU0WRRE7Xc9xujNjoeTx7vAzAS40RpiZzt2Vxu2kxXTDouwELlQyyJNIdB2z302t87FiZ2XKG/+8rK1zfGlHNaWnTclZloqhxaiqHIorEcUIcCwxdnwlTZzD2eXG5BbHEZ05UcP2YSl4n37WRJIHNkYupKjheSJLEBDF0bZ8EAS+IESQBO4iJ4gRNEshoEqNxTJxAJaOyMXB4ZSVlu/jMiSpjP6TRdylnVS5OF9juRxSzCnEENxtDJvM6A9tnqpjh3FSeRt9lFAQMXR9QOTuRw5AkXrzX4o3VHroiY5UDggT+4U+WubI54NJMkf/7pxcZOSFn6iYvL3Xpjz0kUWKlN+Y7b20yDhOeWShzZrp43zM+nN5tDMZYY4+yqXG8mmWpNWaqYOwzCF3bGrDRtakXDGbLGWbLGb756PR+NDOM4v3jzZYM3hJTe/nhrRabPQddlvnCucn9bVNla3W/J+G9nNd6QWd7kDZRT+Q0Ht9t8Dvc83KEI3zScTjDerAuf8+e7ysv+ghK3h42pzysof9h59+jGgV4c3OIJMlIu04+vDOrtzd2lLMq9SyM3vY7ANABWUp57jcGMeHuelNI4PRklpvbYzRZxAvhsdkitxsD3lzv8fVLM6x3bVpDj1JWoZZT+PMbbZojjyePFbHHIY2hS9YQ0TSZ2PXJGyrbAwc3DCGBnAqKLOxep8tCOUPfDRi7MYsVA0WSWGqNWajmmC1lWe04hHGqCDxZ0Hlzrcf1xpCsJHK7kTbuLp6qYXk+Z+smU3mNvhNiahKjCZ9a3kBXUkKPw/1YHcvn1ESO9Z5D1dRoDFze3OghJFDKqnhRzErL5tr2iLWOze9/9ng6BsYRkgiL1SyKLLPRczlVz/P6ao9CJj1upiwzWdA5MWEyUdC51Rhxp2nxo0GLE7UsILI9HFPMuDwyE/PmWo+l9pi8rtAdeLhBRFYTeP7MOyl9f9UzsJ8EHDkDv6LYqxvck4o//DIeTNfu1XM+rK4a3q75W6gYWH78ju9blsfOwKHvp5PYV87XubE9IBGEfZn0T5+s7qdMe07AatdhuDUkryvkdYn2rkT8pWMlSobCTDFNUe41WdVyGjld4u6OzXLLRpdEliQRVRKpFwwagzF/cbPJhZkCz56oEEQx5+pF3qgMmCsZ2F5E1RT4tZM1WpZPYzDGUES+frHOlY0hP72zw2Y/jcRldRlBhOlihtOTJn6YsNIZMXB8MorMasdmszvC8xOkJGEsBSiqwjPzJeqlDGtti+/falEwZKbzGgLwmZMVrjcs7nVGRCGQQGfoY2gieUWhPfJoDH2OVUzEOKFhefzg5g4DL+KJY0UemSnStnxyssJjFwu0hgFZXaaa1/mdp+Zoj3xEEWZLWb5/vcHQ8emMPJqWmzaz7dLRlbIyt1sjSroCKKx20wbu/WfdG/PqSn/fCYOEMIpZblnEUUI5r3N2Mo8hS2yN3P1a2b2F+O3GiJWOw2d2be5gjeidxpCu7RFG8T7bSDmr8KXzk1zb6NO2ApoDl8Waed+iR5FEMuX3Hs4ORxzfqwH5CEf4pCIdsx9Am3pgLH+33q6P/lre2Tf2sPOvd8cp+0wC8xWDyWJ2v6TlIAPd3ntaMVWiKKY18nhAYoCItHoqBLzobUahqarO/ITJvXY6x2x2LcZ+xJ9ebaR9CIpILafzbz0xQz2n8dpqF00WmCnqDNyIcRgy8gOcUECTRSo5jWvrfdb7DtWsysWZAkUNCoaKAGz1HKJYI4qhXtaYLaTaMScnzP37OlHLcnm1x1LbpprVaFs+OwOPnp2WvOYNhfmyzRsbAwxV5OsXp5gpZei7Ic8cryJLKQtboz9GQeHySoepvEFzEO+TfXzrsdl9Zr44irnesHhmscjzJyo8Mp3jH/10FctLGeQaA5dKRiKKU+a2ck5noZLhx7d3+IubLZ5dLPHlR+oAdCyfgRNyqzGiNfLoWh7LLRtVEpkwVbqWRy2v8Mb6AF0WQUiomRqN3hhdU/D8kNuNEV88+1Fa3xE+Chw5A78iOBzR33up9zz+wzjY8PmwDMLhOtEojgnit2tC97Dctnh5qcOFaZNi6nugqzKfPzuZytzvNjIV9LevozXyyOsyTy6U0GUJ1w/5V29sQQKSJHJvx6ZlO0iI+3WXnz8zgaGKtEYes2WDQlajaMicnyowW85QyeqM/Yib20O+e63BqYkcpqHw24/PMPZjWiOXQlZltpxluW3zZ1ebJMC3Lk0RhBGW41PLKXz29ARdy8MNE0xdppjV6NptSoZGOZc2aH332oieHaIrcKyWZTJvYHkh7XGAG40ZuD4CEaqscHN7yNiBV9cHnJsuMlfJYGoy610XJ0x48liFmqny5zca9MchQVZBlAQuzRaJooTrjSGT+QyTOR3LixCAnaHPC0td7uxYlLIqn1oskTcUbjQGXNkcMvICdFlElQWaA5cf3Giw2nXY6js8OVdEJiFIYnKKyPGJPAhwZbOPJIrEcUzLdlJ5+nKGExPpYv6lpS47ls+jcyWmchorvTGqnKaW92zq8WMlTE3iTnNE3pDftRxtj22kawecnsyjiCIvLXUIDzCSPGhxE0TxvoO551wePMfDFkVHjBZH+CRjP/uakd574128Xwfg58n4ftDzHzzHHqHE+nWwvRhDkcmo8n1z0cHAUxjF9MYhJ2oZwgeUloewrz8wYQp0rAQX0GWJe02boRPuZqM9jpV1yhmF6YKB5Ua8ttbkq49MMvIjtkcepqZQM3UURWSmWOLSXJHr633udm1m8gZBmDB0PKREYLVjkxHSQFYYw1w5nbcQBLKqyHLb4kQty2MHWJGqpkaUJARBRJTAXEXH1EXmilWW2mMkUeBkNcutpsV6d8yPb7b49fOTnJ3M7Y9n3726zcvLPV6Iu3hhzMmJLL9xcXq/RHIvE3urOaKYVXn+RJkojuk5AQki/6/fOMfVzQElQ+Ha1oCCJtJx4VZjRGHopX0BfQ+BBEGQ9tcJ+1n+KCaKYsqmwbFKRNGQ6bkh8xNZqlmdjYGL7fpsDjxkEVbaNnldohPFTOSPAi+fRBw5A78ieK+yoIfh8HaHozt7x5wtZzhdz9GxfeRDzA/tkcfOyEMWc0ji27Wupiqy0nG4NJfHD0Je2OyjKCJfPz9FLafRsX10WUKWRBIhjcYfr2U4U88RRTH1vMJm37vvul6822Kl5fDosTxCAsvtMeem03rHL1+o07EcVrsOqiTQHHksVrNEkcZav48TxFhOgKGKiCI8vliiqMkM3AjLCUGWuDRbpmCo/GwlreuczGl89+o2W0OHhWqWuZKBKkrEcYwmCYQkIIjECBwrZRGIeXGpje2GiLKEIYtM5nVkyeF3n5wmTCR2drMoIzcga0h8+dwkzYHHOIgRxYS+5eJFAt+4MMPJSZOvxVNMFTK4bsB230aXJS63hzhBwPYgwo8ibm4pTBc12kOf3thlsmBwYbrA2IuwvIBG36WS1RBJeHGlTWfkU8yoKKKAEyU4XozlhZysZWhbPm3bxw2j/Sbcmqnx7PEyYVSkbXncaIwY9V2mCxquH+6zXDQGLm3L45WVHgJwdrqwn2WYLWdoWR4FI2VLCaOYSZ19leG9utK9muiHNUo2Bu5+s/Fndj9/WK30YVrbX2Ua0SN8svGg3iv4aJzYh9n+3ucFQ76vhOf94t3er9mSQUWDMw/p8TmYvW4OXCQxXUjnNAGs+z2Cg1XoO1aynz04VyvwpfOTlDIKS80RRV0lq0l0LZ+m5dO80cDUZf70jU0WajkenStQMCRApGDIbPY84iRGEkUkRKp5neE4RJFkJAWGfogep2NVkKRR//MzBW41Riy1LO40bTRFYrVjc6cx5NREqsWjiCKiKCEJEMXwkztdfuuJaZ45XuWlpS6mofIbF6f447e2GLnRfpmRIokstyzaVsCT8wUWKlnu7dgUswpOEKJEIhvdcRr82s2mjNyEWk7jdsNi4KSECc2BS83UmCzotC2P280hUQLHa1k2Bw5+HPHZMzW+/MgkB/WC9uzr5ZUuMwWNUxMZTk1muNO0CYKAR6fzjNwYP4hRJIlqTkUVRDYGDs2eR9+LWWodqvE6wicCR87ArwgeVPbzfgb1d4ssHTxmY+DeV7d9EI/MFOjZPuem8vz05tu1rq4fstIZ0x8HDN0Iy4vAT1mEHp0r7WcN7rZssqqY8s/nDW41RvtUZwvVtynVFEmkampMFFVEBK5sDdgapLRupyfzZFSZi3NlxkGHW40RQZygSgLXtoYslA1KdQ3Li/gnLyzzl3c6ZFSJ0xMm1YLOKAiZzOuEScxP7rUYBwGPTOUZOB7Xt4fMFXSOV7O8sT5AlQWemK8QhjG3W0MyioSuiHhJwtKOxUrXRxPh0TkTO4gYWCHTErgBVPIKN7cH3GyMaI1c8obKta0+33h0Bkk8Scdy+ZevrpEECRttm6Eb8Mh0nqvrPb5/c4etnouuCgiCQF6Xsb0QWQRZFjHUtInuzfWEKEpYrOWo5jRublt89mQFTZX4ozc2ae1K1muKiO3HKCJMVA1KWQ3bCbmzM2ajO+bG9oCsphJFEWEUs1BLm4gXdhf+Wz2Haw2bMNnZbzi+tjXA8UJ0VaQ3DmmPPPZYJJbbFq+u9rg0lzYJ39oesbe2OWize+VBBxslD5e47ZUwHa5hPowH1TQfLo07whH+OvAwmtzDmYGPszH44DvxoLH9vfBePQuSCLMl4x16M4ez13uBgJHrc6tzvyOgABLg7v59sIxo03bp2z73WhZXt0c8vVhEFCROTuTxgpC3tvpsDxwsL+KSH3FxrogqK6z1bEpGjoKhkFGFVI1eEzkzaXJhukjL9ojimLX2mJ0evHCvw3rf2WdDu3SsRE6XmS8bnK3nubk14J9d3uDCTJ5/75kFfuPiFBs9m9WOiy5DHCdsddPGXsvzubE95OSkyVw5S8/20SSBlfaIiqkSRjEDz+NYOY8XJnhxwo3GiJeXu8RxQtFU+dojU/THwT5JwoWZAjVTI4xS4o031geUMiqfPzNB1dT46R2P1Q6cbFtsDgNUUeLkRJqJaAzc+37vMIpZadvca42Yr2Q5PZHj1GQWVRa5OFMiiGOubQoUMyq6LNEYeTh+hD32aNsulv2gQq8j/HXjyBn4FcHDyn4+ymMeZmPZG9zDKCYR4IW7bfzw7VrXg6rDUwWD+bLB6+t9VjsumjJi4ITUTI2TtSxhFDO1q4TYGnmQJJRNlVuNVO2wZXk8fqzEQs3k2eNVbmwNkUSRmVKGMI653Ryy0Rvz+mqPMIrYGrh0LJepvEZGk9BVldlShpeXOtxsDsnqEl4QcWVrwOTIY+AGxEnMW+s9Rm7Ayck8uiphOxFFQ2FhIkccp7RqSRJzqpbF9iJUWSJOErwwpprTEOKEO1sjanmFJ+bL3G1Z1E2Iexb/+s1NpktZMorEyAkZOAF3mkNuN0cUDI2FSpbm0EGUZBLP5257hNiTeH21ixcn+GGE7XqISOQyGudnyry03GEcJNxu9Lm5BW4Y4YQJthvw6mqXL56doGWnYjAAp+sFioZKY+SR0SROVrNYfsy1zRETOQ/bjylnFGxPp5rTMDWV240RP11qc317wLnpAotVk/MzBbYHDs8aZebLb7MJRVGMJIl86UwacZos6MyVs1RMle9fa9AYuDw5nzJMkcQP1KXYw2ThnWJ3e3Z5mKv6vRzagzXNH+U7coQj/Lw4vMjfbxAO7l9MfZyNwQc/fz89OYfxQa7t3bLXe9fxwl2bw7Jjhgx+yAMxcnz+xWsbzJQMzk/nOFYyGXoB5YzCI9M5vDDhXrNHqIg8PV+mZmpEUUx37LHec3n2eJmqqbHRdylmNM7U8/SdgKqpoYgi9ZzGX6xCRpHIqDKWG3KvNWa2nMXUFExDQ1dlTENmrmzw+LES2wOH0/UcvY0APwyZLmX43JkKr6+ljsnpiRxLLZsojnlyvsjr6wPutiyub1vIokgYxwzHIW9sDKiZ6byZVSSWQ5u+69MauPzr1zY4sbuY39NpWKyZrHfHrHZcEhLmKwZhFOOGEde2Bqz0oLrU5YvnJiF5m/GvM/bZHuhcmCnQHLg0hqnTkyRQMhQGbsjZ3cBcvaBzebnDT+/1mK8aPDZTYGlnxI7tMlvOMA4STk8VPrAdHeHjx5Ez8CuGD0I3+mGPeVBSPY5iXlzqUrbe/v7gRLNXC1kvGCRCygJRM7X9yMQeJV3FVLm+NQBB4FZjtC9Q07F9NrpjZEnkwkwBQxEJooj5apbNnseNbYv2KE2HHq9keXyuyJWtIbIk88h0nlP1HLIgoMkCa+0xOUNmupTBDxOmCxlOqiKlnMr/75VVQGDk+lxe7ZHEqUNTy6o8d6rGX95q8sM7HW431wGR5xbLlLIqnZFPo+tghz6CBLomszkY44cxCxMmlxuwujXA8UOymsLO0KHnuIzdCEnweWO1wxvrfRRAUyTCOKY5dCmbGoIgUMtoWI7HQARJlokTgdWeQ5QI+GGIIMp4foQbhFyYLiJLErWsiuVFDMchr672cYOYz52p8ukTFf7Zz9YY+yFPLpSx3JDNvsNa1+FMPcszixX+4sYOj86WKBgqJUPhJ3davHSvy1rX4ZnjFdwg5I21IV+/OMmpen7fHkRJpKzL+2xCe2jufvf8icp+fe1syeB1uI+b/KBdvRsV6Pu15Qctgj6KxdURjvBh8X7t8ONmYvkwZUgPKyt9N0aid8teP7bL/nUQbgj+oc8E0nzj2A253RyhKyLHygYbfQdTE7nX8Tg5aXJmKsvra210VSEII+61bSZyKr2hR1ZTKGTSksWn5ktUczo3twb8xa0WuiwyXTaoGRI/3oYvTHs8d7xC0VDoOwF5Q6Zr+fuBrBtbFscqGYIg4jtXmtzaHrA58FI6U+DUpIkqSoiJyELF5HY7JVm4MFPkaxcMNno2sphmvl9Y6pAk8NhcgYVKSrW92nV5bL7ATt/l31zdxvJCqqbKNx+buS/rUjFVnj5eSoU6dzVgHC91bqQi/PZj0+iayvduNPGjCEkQmS8bdGyfq5sD7u287aSEUQJCwkwpy2RBpzlwU0Y+Q+F4LcNs0eDK5pDrjSFbfYfnF6rMlky+eH7iA9nQEf5qcOQM/Irh/dKNHuSHfi/hmvdDNxdGMSsdG/VAUGvvWHlD5ie3WyQCXJpNB/u9xZ4ipWJQpiri+iHNQYwoiRR1GYWERs/m649OE0Rv82ufrGV5fbXHq6t9KlmV47UspaxKoz+GJME0FM5N5ZjIpc5Gc+RzpzEkQaBvByiSAIJAFMIXztRoWQEFXSGvy3zuVJ2bzQGNnkUha2BmVKI4vab+2OdOy2a7a9O3A4pZhbstm+G6hx/GDJ2QmYqBIkIURUQBqLLE9sDFD8FJQq5vDVOFSUlEk0RECURRoO9GnJ3MMnRDZko6uiyiyCI7A5fZSpbJgsZad4Qiyzx/ooLlJzw1X2KjZ/H6ao+NvstMUaeYyfG3nprjytaQG41RmhUQRXJ62iTWtwOm8mna3g0S3ljrUzY1tvoOHdvjFFl+eGuHP7vWQBTh0ycnkCWRWsGgmFFwg4gX7rY5P5NjsqBSNdMM0ErLYqNnYyoihYyS0oeSUnruPbNLsylt6UZvTHvk8ciUSd9P1T0fmX27Ae8wE9Z72fIHXSgd0dwd4ZOAT4odflS9NO/13j4sMzf2Q65uDjhTzzF0QiZk2DmQCTicKYC35auGjsvChEHF1OhYIVe3+jy9WKJaSMcq149RFAlDEYkFgYIu8xfXm7yw3OHkZI5rG31uNEaYuszJmknb9omjBFkRuLU94JVxwLqV9sWFcYwki1h+nJayOiFn67u6OMTMmjqmIVPNKzw2W6Q/bnGzZzPyIgxV5OnjJS7O5vnsmQmONTKpiJnlMVUwiGKRUxNp5L1teUiCwEIljfz/bLlDlERYTsS25SEIUNBULs0V94kUAG41R5SzKsWMwmrHoWZqnK3nMFSRMIzY9NfR1XRJmNcVsqqO7UecmyrsZ/D3So1alsfrG13aA5+vX5TpjDxeXu4gSgJfPz/FNx+dwXJ8vDDiVM1Ek0TatosTxtzYHlEv/PXb9RHux5EzcIR9HFy8v1dD2eHPH4TDvNdfPjfBT9q30vp+5e1j+UHIla0hF6fz9wnnuH7IncaQtuWlCrn9HT59oszZXen1//2VVW42LSRR5G89uwCki8uR69OyfB6by2MaMkttm08XDJ45UUOWRFqj9Lw9K6Riaqz1bLb6AtY4YLU/pp7PoKtpOrZre1ycLiJLAr1xiKGKDJ2AvptQLQiEcYIgCARBxJX1HmsdG8sJkEQoZBQkKWHoRpiqQFaTKBsyMWC5MQ3LpWQoNMYBVgCSJCBIIO6WvmiKzMTYI6epzBZ0zs7kmMzpfOfqNm0rQJUEju0yD91tjeiO04gUCBQ0CVVJRcOeWBB5NIooGGrKahREFLMazx1PVYtvbFs8f7zKbMkhEQRkSeRbj03z59d3MA2FruWyPXDJqhK9ccjPljsst23+5Rsb3N2x+PzpGo9MpdH/f/XGBje2Rlyay/Otx2YxVJH//aUVOrbPanfMqYkcjx8rEsUx2wOHx46V3sGA8f3rTbYHLmFY229qOxgdfS8mrMO2DA92Yo/Yg47wy4QPYs8fZNuPKlP2ft7bvfPsMdYEUczVzQE/ut2iNXRRFZmMDuxmmGs6TJdT4cOtYUzC/Tq2W0PI6B6rHZt6LlWwbw995ioGLyx1WGpZJFFCEieISUzV1DB1ldmCwSP1HKu7GdFKVqGSNZjM6Tx9vIIbBKzcHuMGERKwPXD5569u8jtPznCylsX1Q6IoJm/IrLRH2G7EauywPfR57FgRJ0pStjvdJU7gxaUeEzmVUkaja/vUd0ti+27IVIH7hBTrBYNiNtU6COKY3q7wWJgkzBZ0tMVKWgrqR7y1tcN61+HZ42XGrk9z6HK8miGK0wX9pxZNGgOXcRBxawD5ex1O1fN8+mR1P9q/90wUSWS2nOH1tR4ty2O2YHC+nqcxcOk5PpYXkdflffa4P7rSYGfoMl3SMWSRa9sDLDdiqzfmCJ88HDkDv8I4PCE8jJ/6IB72+btR0+2rK2oiTSetAV/Utf1j5A2ZWl7fVzkMdiMPt5sjBmMfU1fo2z7NgcuVzREnJwvUCzq/9dgMLy21yRkqL95rIQD1vEFnT5U2k2W969AceIQLMR3LZ6Pn4kcxc0WDmSKYhoypyjT6Ls2Rw8AJiIKQ6apJGMa8tjogSgS+/sgUPXuAnyScny7y5IKAkIis9my8IOKNzT6WF9GzPIoZiWJW4/FjVU5MZhk4AWtth6EXEIsJpq6QUUUEIaEz9ihoMoEKtQmTjKoiSGCqChVT4cZWzNANeKXvcrVh8fhsntbIY7VtE4QRxyommz0XhIScJuP7MZdXu5SzGhv9MU4QM1/WkQSRf/PWGserWRZrJguVDBd3szDtUYBpqHyhnufNtR6W4/PySputgUNGFfeb4mZKWU5NZpkq6uiqyJurHV71ewiiwEI1x2RBZ6GcJUkgjBI2ujZbgzEvLHd5aq7I7zw+QyWX1toKpBNdx/L3o38/W+5QzCh84ewEPdunpEv82GHfNt/LBt/NFh/kxB6xBx3hlwkfxJ5/3qDOh2ms/yBlT3sZw72yT0hZh7qWz8aBUtOWC0nPI4kTZNIswcH2gUkNjlez6IqE48dcOlbgzraFqkgMxz4nqiaiAL2xz8hPg1aPzORoWR6aKjOTVXniWImpnI4ki7tqv7DRs+nZIVvdEcEQRBH8MCXBaAwcbu+M6Nk+N7YH7PIpMF8y8EKQRZGW5SEkCf/us/MoskRr5BJFCZt9l/bIY+iGZNU0Az5Z0MnsRuz36EJ3Bg7bQ4/PnqpSy2kkgJAkbFs+17eGzFdNEiCvSbRGHi/f65I3ZCRRpJ430HZFyza6Y8IoZrpocJzou8oAAQAASURBVL6Y2sKeUGRGle97DvWCnjoCIw9ZEJAVma2ew0bf5cJ0nqcWytzaGnCzMcByAmo5lVO1dP57a9yjZ3npsxUFjvDJw5Ez8CuMd5sQ3k9D2fs5VmPg7qvEnpnIcFVnP+Kzh4wq8/Ri5R37zJcMkrJBGCdEEXz2tM5UwdhXIT5Zz6OrMo2Bw+XVHnebFhVT4fSEybGSTphATpUY+wF/cbPB7zx1jGePV2gMHO61bHpjn82Bw0I5w5fOTdIeefzplS1evNuiYqg8cabMvbbF2A25sdXnR3fbqKLI8Ykss+Us/+atbU7WsozciBuNIb2RC0mMqilkMypbQxdEgedPVujaIZW8hiELtPoePculPw6I4pisKlPRYaGaRZYURCIur/XpjlVuNYeQgK6JBE7Ia+sxx2smJ6oZltoWsyWVR2eLbHQ9EAWqWYWMKvHWxhBVFOl5Hje3Q1Z7I7Z7PhBRymq8OOiy3nP44rlJsqpIezDmhzcbhInA3Z0ROyMHXZG5vWPRHftUsxpnp0zqeYPLq33qOZ3LiQBCev3hbgRPVSTOTOa4ujVktT3mueNlfuORST5/dpKCobLcsnhpqctT80VmdxuHl1sWr692+NGdDicnTL7x6DRTBQPH8++jFn2YDQZRzHI77Ql57FiJjuW/g3r0YQqphz87whF+UfFB7Pmjcqj3tt0rR5ks6A/VI/ggZU8H+wf2aDAzqsxQCinI0Dmw4m87DxAe2EUswO8+PZfSDd/toyjQHvvkDYn+OCROEvIZlYKmslDO7AtYLlYdMqrA2E94/JjJbDnD5eUO99o2x8oGWz2fSk6mNZKZysIzC1VeXunxgxs7HJ8wafTHRAls91wmCxrHyhkemyujqzJ5Q+ZfXF7j9o7N2ak8z82VOTdVYOyHvLnWo2goeGHMD262yOoSYRQzW07r8i3HZ7tnYxoqF6a1/f6qvUX99mBMZ+yjDRx644CLMyXqhQylrJou4KVUpFMeuBQzCtsDh6WWDcToCsyVDJqjtzswDj6Hv7yzw09ut3juZJWFssn20GGrn1DJyOSMtMz0+zda2H5AyVT51LEyjx0rcaMx4uxEDi9MCTVOTZoPelRH+GvGkTPwK4yHCYh9lFGf+z7flTy/17LRtbRu9HCPwh512l4p0K3mCD+IUGWB2VKW7tjn+9e2OTdVIBHgleUu00WNC9N5qqbCa6t9fny3g5DAySmTkiFzfXvIm+sDqjmNpxdrnKrnaI08JvNqumjtptLtC1WTz56dYKk95uREjjs7FnES8dN7Hf7y7g5eEGMoEs2hy/mZgI3emIohs1DSeWujjyKLFAyDxarJwPVxfJ9XliwKmsRMSSeOY/puyFwpSxjHFAwZy42YyhvYTvq7FAyNu80+az2XYxWdE7UcYZTw7IkyiiTyFzebhFHMqckCO5bPcttGURRaQ4+FapavXZxhe+BwbdtCEuBMvcBCNcOdpsm/fn2VeiGDKgvc3rHJaBLLLZvLKwPatkPL8nlmvkQtp6EpIlM5ja2+R5KB6VJad3tls8/2YMyZmTy2F1IvZnjsWBGA2w2LE7UMl46VyGgimz2H9YHD7zw+R2GXWjSM0tIrYL8++Kf32iw1LcpZhcdm0yjgS0sdojhtrmsOPWYV5R0Zp4P1sHulRfKusNneuQ4uXt6vw3uEI/wi4oPY83tt+6CF/7sRRezpepyYMPf1CA72ne1t917zy8F5aG98OKgZUi/oVAsynQPewF6zsMg7+wfKpsxL93o8uVjkRD1DTpHYzLqcmcxj6A5RmCCLIrGYsDXw2OiNUUQxFRGLYi6v9gijmJ/c3uGP39okp6lM5FUGjs/iRJY7OzamAk/OF8lnFNpWwGDsszlwOVnNUihqJIJI0ZCZKOh0LZ8313s0Rz59x2fkB/uBsaubA27vjOjbPkEY0xw6mJ7CK6tdfnSnxZnJHDe2hzQsj0/NFfnNRxcIopgf3GhyfMJko+fy6RM1bC+iZwUMbJ+Jgo6uyvc9g+bA5VZzRBTFIAgcr2WpZhVe24DG0OHJhZTN7bBGxI9u7vDKcpeJvAqIZFURyw+4u22x1BlzvJKhlte4mMtRzum4QcxGz8bzQ3puSJyI9MchnfERtegnEUfOwC8hfh4mlZ+HTvFB6pR7ZUEXZgpkVPm+FPNGzyEnp+nevYjPHkvMxu6gv1AxsPyY+YpBe+SRUUXCOOF0PceZeo5//doGNxojVrpjFspZurZHz/apmhqzpQxbA4/W0GHghtRzOlGcMJs3EGSRJBa4tjUgimJu7Vg8u1hioZzhrc0hl9d6bPQ9ZkoaXzg7QRwnXG8McFwfxwswFIF8RsMLY2w/pN1PqUl/uuRTyeggwvnpIr/7qVmubAxY7wrc6wS0Rz732jYnxTQq0+ynugePzRf5s6tbuGFEa+QydMHQY2QhndBUEcIg5ng1Sy2v8vzxGj9darG8Y9OxfH797CQXZ/K8stzlrbUOxaxB1VS50xoSxlAzFRpDl8gJOF7L8mfXtogSgfWuzaRpkJUVpvM6syWdMMohiAW+f73J0ydKbHU9VqOYGBFJEXiiXiKrSTSGDj9b7jF0fSw3YGHCpJpNm8qAfVGgjuUzW8xyrJKBRNhXDK6Y6n2iYnufnahmiaKEuYoOQkpp99R8iSSJ+dFqqoopy/J9i4uDC5Cn5ktcnM5zcSa/X2p2sFflKPJ/hCN8MDxo4f9uRBFPLhRpj7z9Jt/DfWfwTuG/IIrpuOz3kMGD6UX3NEPyhszl5c6+s7EHDagVJWI/YvNQOXoErHdtdEXAD2O2uw59N+Bey2a+luGp+ZQtzYlirm0NuLbRx9AUHpkuUDZV8rpMEMf8+E6La5tDLswW0GWJgqHgeSmF9HIvdUa+9MgUHctHkeAPX1kjoyk4fojtBeQ0heubA15b66f3bXkMxwFX1gcUDY2amYps5jWZ65tD4jjhqfkyz5yocGt7xF/c2GE49tFVmZwiEybwnSub3NuxuNMa842LUzw+X6Ze0JmvmfzgRpNkl3Hv4O91szFioWwQRTFRArWsklI85xT+2IHVez2+cE7d79+6tjVge+BwYabAIzN5NroOJSOdN1ojl3pO53ZjhCYKJIJAEEV4UYII3NgesNq2SBLY7I/R5ZQ1bqvnfFBzPMJfAY6cgV9C/Dy10D9PycSD1Cm3Bw4/ut3CDUJ0Rd53CjZ2I8COn4rMbPTTxdyTC8V9LQJIqJoadUnkyi6Lw2dPVbk0m9t3GMIEjtcMTk7ksP10wKzmNIQEtocOiiRQyxkYWsBa22a971DJqSyUs6iKRHmXXQjA1GR+dKtNRpGYyGoMHYczkxl+4+I0OUPmRmPAGx2LkxMm56ZLFA2FH91ucrqWI2eozFdcTlRNZElCFBM0WWaj53Jle4gsCCwUM3h+TF6RuNUcUVBldkYer6+nLEc7Q4+x5zN2Q8YWnCkJ+EmEoSpcOGbQGnlsjxxadoATJiRxzOJkljP1AmVTx/bSLEM+K1MvZLjdHPL9600yqszjCyXOTeUZeTF/frPJnYZFQoIbRARxxJMLRUZBxI/vtFEkiemCRtnUuL1t8YNbLXZGLucnc8xWTN7c6BNECX/j8SmeXizx2mofL4rxg5B7nYChF3FptoDrB6x0bKIETlSz+89GFkWubQ3wg5CeE3J6Ik0T/+j2DieqWS4dKzFbzrLetfnOlQaTBZ1vPTZDJSMRJZBRpX1hu4OZpL1FAoAbpU12e7W18OEi/0fNxUf468InwfY+aJbBUGRs32HohO+aSTj47+bQY2v8dg8Z3M84tPc7zO5qLLyy3OFPrzRpH1rwB0DXjnhQwDmKIhDgx7d3cIKY2VIGRRAYeSFXN1J2HcuNCMKIJIKl9phTE1nyhsyPbjZ5eaWHoYmcrGbZ7Iy5MFOkpCv0dZ9wt1u568ArKz1ymTSbcbs5RBRFTkxkmStmCJOEnu1TNBQKhsJ82eDSbJ6frfZI4nTOrJkaF6YLWI7P7YbF0E0bjU9N5lmomkiiQNv2OTmRpV4wuLbR54+vbBHGCY/NFPn82Yn97KsiiXzlwtQ+U9+rq11+ttzm+ZNVCkY6Pu5RPIdxzE/vtXl6vsi0AZl6ljP13P6z2h44dHb79R6fK6PLEqIkcacx5MWlDkVdSbM4RZNSRqIx8LD8kNsNi/bQRVdkFmtZLDdCleK0r243M3yETxaOnIFfQvw8C/sPMvgfzAjscf/vZQb2aOPcIORHt1sAPL1YIYxi2iMfdzcStFcu0hw4uCGcrGX5zKna/qK/Nw45Vzd57FiJjCoTRCn7jOUHFDQVWRSpZETOzxToWj6NgcPIjXh8rogbRLyx1md76JBRJS5OF7D9hJqp8vixEo1Bykqx3nUYBxEzRZ3ljs2VzSFdO+Lfe26BjCozX0np3Z4/PsEjswXeWu/RGPoYqkPVD1FEkVOTOTqOj5QkXN+28PyQUkbF8kJuNIcMnZA7bYuW5XNpLs/YD7m340PNRBChkNHIGRJ2OOazpypc3RgRJwnLzRF9N0QR4Avn6kgivLLSRxBEzk6YaIrEyNM4LgmMvYiu5bHUGmN7HrOlMo/OFhnaPkPXYdLUOTWZxwlSlqWrmz3CJNV2yCgiIy9EkTPMFDWSRCAmJkpi7CRGEqGW13H8CEkUOTmZ46WlLroi4gRpo3Br4PJmkvCd6zucn8rxlfN1WpZHd+wjAEVDwQ9C2naA44f7TBmDsc/tnQRpt0nQ9UO+fH6CesFI7aBjsTwCszdm8YD66d4iaU9Y7GAG4KNaSH2Y5uJPwmLuCB8vPs5n/IvQ2P4wdeR3yyQcvpfJvMZ05v6eoIOMQ3B/NuHCTIEoivnhW6usHQguR4AY3s8itIeBnfCNx2b43tVtoggmTJXNoUM5o2D5EYYmc2VryHp7zKW5Aps9l1JW4c31HpeXu/RsHy9MWO44hAJc2+yz0XOYK2WomiqSKCIIafCjYqrcbg750c0mG70x8+UMC6dMNrrjlMpzXuPzZyb2x6m7OyNeXx9QyEhMnq+jSCI/69p0HI+V9pjvXG1SzRnMlTN86ZE6VzcH+83Ub671MHWFnKbw5GJ5P5J/mAxkvTvm5XtdbjVHWG7IVCm773iEUcxP73YYOOk4PY6hKMsMnZCCkWYH9ubLMIq517ap5tK+PdcPeeFeh7btc6KWoZgRWahmWe+5nJ3OIcYJmiywY3msd1NtAj+OKBgKE7mjTO0nEUfOwC8hPu5a6AeJPu1RxSmSyNOLFcb+25kBSCk/RRE6XhoJAgiiiObA5dFjpX0Bqo3umI2ejSTCxdnSfqS3MXAZuCGPzxRpWx4vLXVxw5ggjtnspdLwp+s5SobC//nqBh3bY66Y5dfPT9B3AtY6DoWMwutrPc7Uc5yt58gbMjlDoTlwuDRf4nTd5MJMcZ814V7bQVclXlntsNyxqOY0vni2huvFLHUsmiOHje6YHcvDiyJGbsi6EPO5kxN0bQ/fjyjpEc2RjeOH9G2fJElAAEkUUEQJQxWpZTSiAWz0XFZ7Y1w/QFIEjFBEkEXWuw5ZVaKY03DGIS+tdjlWzHBuOs+1jSGaJLNjOeR0CUMzeOZ4hbWWxWvrg1SpOaMy8gN6VipP7/gRYZJQ0GS644DWyGOz77AzdAmSBNeLmCroLBQz5AyVExNZ2iOXy8tddFlk5AXMV/Kcm8pzb8fi8vqAjCrxyHSeE5UMjYGDKInIgsDtHYvNnsNMyeBcPcee6nBz4PKV83Xalkdr5PH9a9v0xgGLtSzyLqNUGMUsmvD0Qnl/ktsr/1lupZQie1HDD1Pu9iB8mObiX4TF3BE+HD7OZ/yL0Nj+MHXkB+FB5aR7C9aKzkOZwoIovi9L0By41AsGyQNWLaOH9BB7IazsDMnrCuem8mz2XTJ+SN8NsLwQQxZ5dLpAZ+BjOSFjP8LUJHYGLnc7NpoosNay0DWRZxaKDJ0YJ4iYq+hM5QwyikhQhicXSjQHLv/Hz9bY3u0XQBC4vNwhjGP8KKQxdJgtZRn7IX9+fZvr2yP6ToDlJfvOz8AN+fqFOn07YKGaZaU9wnJ8+k5AZ+zz5lrM1mDMj++0qZkal+YK2H5K3rCXnT/4HOoFnb/x+DR3mqN0Xug6lE2V5tClMXB4cqGILktM5hSKalrCezCoshfcmyzou8QbKdPQyXqe33tugReX2nTHAetrAwbjkHJWxVRlVjtj6sUsCPDySpswSRASQCAtBz3CJw5HzsARPjDez2R1mCFotpzhC6er/B/Lt8jpEiMvYexHvLE2ZKaUQRFF1ns2r632cMMYTRTJ7aY0g13NgaIuoyki/9ebWwwcH01Ov3/2eHmfOcYJQjRFpJpVMHWZlbZNIgiUMgqNocMPb3RwHwlZrKaCZiutEX9ypcFkXuP/+WsnaVseS+1t7jSGHCsbZGSBzb7DcstCVxX+H59eYLZs8P/+7m3iOOF2e0R76GG5PnOVLFlVIY4TXlvtk9MVTtR17Chk7Cdomkwxp2OqCnlVJKtJLFZM/CCm7cJLSy1iRKqmytPHq/gBxHGE5YYkCDy7UObVlT47I5fAT9AVkdfWe5iqxHw1h5AICAIMHI8rmyO6lstCxWSjPyaKEzRVZLFqokoyC1Wd9Z4LJBiqhO2GLFZNpgoa91oWPTugPw7JGgGWE7LV97i5bTFd0CjoKuMg5kbD4rMnKkwVMzxzosJSy+bHd3a4dbvNVx6Z5PxcifzAgQSOVzLsqQ4fVJR+atHk8nKHl5ZGWEHA0A3Z7LmcmDDZGTiM/LRB8CAO9gt85oCDcDhb9WFoED+MQ/2LsJg7wofDx/mMPymN7e+W/fgg5BMPKid92P3tZRk2umMag7T3a2+h/NJSBxAY2e/cTyBtIN47+17FUAL84FYbTRa5OFNgMq9zrKzzxq7ielZN6TZ/7VyVrhWBKFDMqrx0p8tc0cAPY7wI/CDhuXM1Vtpj2raH5US81O6y2bOp7Z5re+CQUWQm8hqX5ovIosgL99pYXsT5qRxvrA9Y7TiUMgo/utVh6PmcnjDxgwhFgop5v0199+o2Lyx10BWRoqEyXza417JpDl0MWeK5E2VmixlatkdOlcjpMnebA25uD9AVkXPTBZZaNhdmCpyfLnK7OeTyShc3CHlzfcDSjs1vPTnNYjUtC5LENEuzlwnYazKWJJFHpgtUTY3X1vq7Jb3QdwJAYKGc4Vg51c45VjGomWkPhCyJvLIE373eIIkiQgS2ez7fu9rgs6en3s30jvDXgCNn4AgfGA+brN5tUlAkEcuL2HLghbttvnRhhr/55BzbQ2e3QWuH1bbN0A0YeyEjN6KYkXnmRJWb2wPWuw4VU8fyPN7a6HOsrPPFszUuzZUY7k4wd1s2ugxjPyIME9a6DrcbI54+XkY1VLwwoWenHM4/udNmpqTRsgJEISGO4dXlLq+u9bm62cNyQybyOlVTw5AlHp0pMwh8umOfH93eYWfoECUJWUVkrEpYvkAUwUzRQJMlSMANAkY29G2PMA7Z7Do8Ol2gaqr8+Y0GvXHAU8fSxjs5AVEAWRIoZDQemysyckJutyzUJKFgqAgJZJR0suzaPm9t9vD9iKbnI0sCXhAjiQJDJ0IgIaMpFDIyY0/l6YUy52aK1HMaPSfgxXsdNnsOX70wQTWn8cb6kEtzBUqajCQIZHUZx08QhJi27XNptsCT80WqWQ1EgZtbQ0ZeiGmo/OaxtHa/YKhsdG3W2w6yKHKvbZPXZZ47WaE98rjVHN3X0Pt2iYFBLafxVKXIZMFAEVP6uzfDkB0XXl7uomvq/qI/jGKeXCiiiG8f63C26t0yBB93Gc8nZTF3hI8PvwjP+MPa+fulnn6vbNxBesqO5e876pWM9NDzpmxicLpu7u//7PE0uHQ4ODBhgGmohFEaNNFkiWbXZ5SAIoEsQsFQuLk14plTFSZzGi8udemPfb57tUHbDvjNS1OUMwKFjEh36OEEEZokstodY3shTyyUWWmPSQSQhVShniTBdiO0MM12D9yQZ09UEIDuOCCKAiwvoj3yGBR0spqEJoGqCHz5kQmubQ641xqx2fco52QuTJeo7pIxLLctbjRGzJU0TkzkaA783UzBmKqZBrIkSeAvbrWIk4RSRiWOY3621kvpTPMak/kdZDn9jZ9eTMfg7YHLuSmT6aKGH0V0Rj5jf8DxikHHhY2ew2rP42QtS0YV+dnygMWKsUv4EVPOppmCl+62+MHuuYuZ1FFRZQFZFFnpOsxXDFqWx6lJE0MVubPtEiQpOcZK1+IInzwcOQNH+MjQGLj77AOP7/IfH5yQzk/nmcsAiDQHLroqM1fKcrM5omSo9IyAnK5wcTrPes8hQeRfv77Fes+GBD53SievqVSyKlOFtKTnVmNE1/Y5M5mW/rh+SN5QCMKYge3RGLqEcUwcxQxdn6EbcG29j2HIVHIyXhjz6GyZMIr4wtkaUZyw2beQiDk1kaVrB7SdgOmiQVY3+BevrZPE6QDYt31eW+3zxHyZx+dKIIg8NV/i3HSBkRuwPfB4bbXN2A3RFZFCRuFm22Zj4GI7AVEYsdIZc3VzQM+F6RyowMWZAvWcweur22z3HT41X6Ka1/mzKw1alocoxKy0bcZBhKmK6JpKY+TSt30KhsLF2SKnJ3PcaVqs92yOlU3mK1nu7gzQxTwbA5daVsGqpo3Y610HU5NYao641bRoDF2+eGaCk5Mmf3mrlWZoKgbJ7jTcHrr0xj5FQ8b1Q5Zb1n65ztcuTjNbznK8luXlex164wBZEumNA0iSfY2Ig8xAs+XMfi3twUXLpbkiVwvwzGL5vkX/XlbhcDr83f5/2E7/qst4jvoIfrHxi/j8Pqydv9/sx3ttd9BxyJTlfefhZNV46PH2Fv574wqw3yMkHuIQFYAgiNixYgwZBFOgXlJwugGKBKoost61eWujT8Ny+e0nZxAS8IKIu12LKEgY2D7NkcfdnVRH4DOnqpQyEle/M6QTedxpjBAQUCWo5NKepudPVnjhdpPxvVUm89o+4xnA5eUOt5s2nztVZeSGJIKAkMS8vtGndy/g0myekRNTMw3O1gvMV03++Mo2WVXmbz19jI2ezZtrPR47VuRkLc/JGlzZ6HN1e8hUTqOcVREAP46YLejUCwZtK2C+mGG2kEESwPbT7/ZKdR+ZKbA9GNMe+aiKxKmaSW8cUS/oCMCGDZs9B1NNhc62Bw4bXQdFSufrMIpZqKTP8fJaj7XumE8tFPGihKEbc246x4WZAh3LZ6U94jvXmlyazfPEbInNzpjebt+wphwtOz+JOHoqn2C81wT0SZigDl7DQfaBxsBlbrckZJ8BJqfwSAlKGYWNno3tx5yZzHFhurBPNQrc1z/gBCE/vdPirY0ht3ZGFAyVf/upWS7OlAjimJeXOlyaK9wnnf61C3WaA4drWyNyhkwUJ/zkbotzk3kWqxmyhoIAKKKAaUj0hh5bI48f3NzhifkiOyOHjV7aXDxVMGDoEMVQL2mokohHxKXZEtuDMQMv5HjVxFBEFFminje40xghSiITeQVDkxAlgZyp8/hciZ7tI4kiI9dF9iVmChnWOjbtQZpBCDQNU1P4yd0Wq50xTcsl15CpjX1alktGEVnuuMRRQhRGuAmYOjx/okZr4OIGEW3LY6vvcmdnwNiL6YwCVlpjVjpjvp/dwQ1ipgo6U0WDl5fbrHZcJkyVxtAjThIuTOcIE7jXHKb1sWWDK5tDlttjajkVU1OwvBDLi9getihkFE4Msvv9AFMFg5ET7kfPztRzRFHMvdaYuzsj1jvjfV7sg8JgwDua4CYyqRjbnn3XCzrhbnYg2P3vzbVeqhNRM/e3e7fI7V9HGc9RH8EvNn4Rn9+HtfP3m/04rFB8eCw/rA8SRjEna1kmc8pDj7e38D+IvblmeD+zKE0HdCICwAvA7oVEpP5Cz4Xhbua0qEuYuowXpg0GFVOjklEZ+RHHa1lO13NIYsLxiRyfOTnBqysdJos6UZh6HivtVCSsXtB5/FiJje6Y7jiktctudPC3qpoaP1vrkgga56byyJKI64e8sTagZKo8NlvE1BQEAT5zusbt5oiL03lWe2NeX+tiaDKaLHGsnI6pb671aNs+NVMmQeRELUvV1HhzY8CN7RHFrIYkJByfNJEFWKxk6bkBU3ljPyh3qzFiq+/RGLg8s1giZ8is9MZUzTIzRQ1ThrXuGFVRmC2nv8cjMybzFRMnCPnhrRZZTSKMY+aKBkkCp+o55oppn1fZVLm6OeBMPYcbRPRtn5X2mKyhMlPJILXHmKbK/+O5xYfa0odZ0zyIqvYI7x9HzsAnGO81AX0SJqjD17DHPvDACG0cMQrB645BkDhdN/cX/gcp5PawNyEsVE0urPVwwpCtnsfjxyos1kz+8naTuzsWs0Wd1Y7Nv3ptk7KpYMgS56ZyrLZtqnmVthWQJHCvY9F3Qs7PqOQMlVfu9UBIU8yPZFUSJP7s2g7bA5+25TH2Y05Wc6iyyHLbYrKgUi8Y3Nga8r0b20yXMjy7UKFje7y53ufTJ6usdGx+eqeFKAr81mMzZDSZ719t4EQRNxtDFEmillUxNJWe7XC3Y1E1VTaboMsiM+UMthvwwnIPkghJgI2+Q3vsY3khuqoRxTGJmJBRZbKGwrGyiaEIjKOIkqlycbrIpbkY/UbCrR2LMI4JkohTk1lmCjrNYYAoJURJwlbXxQ9jKqZKRhVJSOXiLT9AkyXqBY3Pnqrww1ttvvrIBJWsypvrAz5zapKclo64bcvjXstmpeNwYiJL1/bJ6zLljELfDXd5xw1u74z4F5fX2Rp6+7zYrh/y0lKXZ4+XkSXxoQqnjdHbTsLedrIksj1w+NMrTSYLKt96bPYd/QOH1VD/uhzooz6CX2z8Ij6/w4v092vzD3tHPkhvwL0dCxD2e3oObrOX2fsgxz54/OkMrI7f+f1e+VDA270DFQOKWZW8pmF5Pn3bY2fg0nF8NElgrppho+uy2hkjiQIrHZe2FZBTFUxNRhRgppylXtR4+kSVnKbsz1NhFLPRG9MawfevN/j8uSm61tvqvSTwk9ttiuaQb16cQVdljk+YnKhlMQ2VO60dhq7PZt/BDRPO1XPEEby62ufxuQLHJ0wuTBdpDlwur/aIkpj5Uhbbj/b7r+ZLGf7NeoMoaVHJ6ixUDIZuzNXtEScmTFa6DvouCUfH9lNRx7kCCbDcHiMhMPIC/vCVBlUNnlooMXAjKqbKm2s9rm1ZjIOYrCaT1xXyusxqJ+01m68YXNscMVXIkMQx//zyGut9lxfvtgiiBDcMKRoyp+o5Rk7IXUXlC2cnuLRQfajtfZg1zYOoao/w/nHkDHyC8V4T0Mc1QX2QBdPhazgcTXqQ6Nhji2VkWd4fVJdb1r7mgKHI71i8dSyfp3abkfdUZ4MopprV0BSBpfaYII7ZGjg0+jbtccDd5ogEmC9lmMzrVM1Jljo2f/LmFq4b8ePbWyy1LJ46VqJaMPjy2QkkWWS1bbO0I1PP6wy8gN+4OMXt1ojtgUvL8vnUQhmSGNuPmczreGHMbFHn9fWEnuXzz19dZ3vgslDKcKM5RBEEYgRaQ5ehIpFRZOqmhiYI+GFId+RhGgqaBIkgMF/O8tRCiZ2RxziIWO+OGfshOU1hrpJFjGO6Vkp3Z6gCJwp5SqZKs++hCCIzBR1Dk7m+1eNnq0OyqsBkLq35vNu22R6MeXSuBLHAYjXL1Y0BcZLw4zsdHpnJU8lIrHTGmJpEMafw2o71/2fvP4Mkye/7bvCTPrO87aq2093jze7s7qyHWSwBLAyNJIoP7znGg5MiFBTv+IQYDJGhCIXeUC9IhSj3XJB3ETqF4qgTqYeP7kAnGhALEASwWIfZndnd8TPtXVWXN1npM+9Fdvf2zM6swy6wAPobMTFdVZlZVVm/v/m575d/+9c38KKIp+QyA9vnq1e3CaKQZ05PxNL2kkhpp2GsktU5v9zilZUOHztSxB34DGyX2VKKUlJjWRhxspJirpjAdmOGjSAM72pLu6j3HW41rb0swm6T8C6VbRCElFLaXi2yH4Tcaph7DYv7sw93ahXs2tOdjugHjR+GGvMD3Bsf5d9v/3wNb1X6facN1p3z/b2Ov/P5e9GLFlNvChHeOZZvazz2vL1IbmvgveMmcPdc5y7MQfYdj0NAAabLKWRRopBUWGsPccOYYEEMI0JJQBZEHjqUY6VtkdQkSgmFruXxwkKThCbieCFdx2VWTZPWlFiVeKnF2R2V84QiYwZwcb1PfeBQH3hMFQyeOjrGmckMf/VajaQeb7MKKZWEKmB7Pl6oMJkzKAcyRDJTBYm5YqwOv9YeMV9OYvsRHcujLInkE7EAmiiJHCsk9uarM5M51joW1ayG68PJ8SyRAM2Bw3w5yWLD3CvN3L2HtZ7N6+tdcobMk/NFnrvZ4H+8XmdOgsclkeXWkFxSZaMzIq1KTGR0Tk9mGc8a+EFIJLCP8KPHi7eadCyPN9a7ZDSZoSUxWzIoJDT6bkAppfPgoSxHK0lWmhYrLZOT49m3/Y3fz57mblS1B3j3OHAGPsJ4pwXow1qg3ot3vv8z3Lk4eEG4t9mCWEl24O+UfbwljxfRHDj0bZP1tkk1a5A2ZP7ytU2yCZX7p3LIOxParYaJLInoqsxULgGCQD6pklRlEopIz/ZRFZmHpzLMlpJ880aT05MZtjojtgcOz16rU05qTGQ0HjhUoDtyubk9ZLac5Pxyh0pW4+mTeUppDUUUeep4hd7IozFwee5Gg5bpIggCSc3njY0+E1mVclIjm1DYGFiYtstaN+LLrzjMFhIIUbwZdTwfVZZ4Y7OL4/lkDJW5UoqB65JUwBdEgjCk5wT4gcCDMzkemskRRQJJVeSrV+qklNiJ8sIIXZWYyqV4YCrHUtPE8i3aIw9VGjFbSpNPSJyayHGimiOfkGiZLrcaDjdrfTRVQRbYoWA1EAQ4MZ5hNp8gCEM2+y66LGG5IU3LZSypkTbijbcqwrVan5EfcriYRFViTYZLq21Sukx3p0zstdUui60RG12bLygyxyrpnbKtkL+92SQSIgqGxrFq+i0UobsIQvbKCgAub/YoJNW9nhRFEnniSMznsVeLXE7uUcderw32nAO4fbHZbVS8WwTzAAf4YcE7Kf2+0wbrzvl+v/DXftx5nbejF71bmQ+8yRZU69lYjrsXyZ0qpvaufa9g1O71x0satbXbhas04myAw5vtBB6w3jEZBQIJTWSymCSpSGQNlWJax/F83tjs8fEjJcIw7hswNIWFponp+CRUiWxK5RNHy7QHDp2Rw19c2mK757DeHiFLAkEUQgSGLNK2fBp9h/smM0wVEmz1LCRJJKvJWJ7P1y+3+MqlOoYm8XPnpjhWSTFwPS6v9RGQeNXpstmxGTo+pZRGRpfojDzKqXiO3FV33hVgrGZ1Zssp/t5D07dlQWs9m75t8vzNBn0noJzSmCunmC4kGLk+a20zZvSzoWN5PH2izOL2gJTZZr1j4QY+37mxzWubPVRZYqvvUO/bdEceW10LWRR4+mSFSlana7o0hz6aHCs8J9ISkSAyN5amM4qF3J69XGPkhXRNh5eXOxwqGfd0Br6XPc3dqGoP8O5x4Awc4C14L7Rx+3Hn4rCfAvLx+SLHq2lGC28ev+ss+EHI4/PFvdrIl5baiBKkFYmXVro8ORez1exu9I6Uk/hBSCGl8vBsgXxSpTGwOTmeIaWLJAwZywk5UklzfavP6+sdOqbLWEYjo0k0hzYhMLR8XlnuYHs+fhQhXgNBFKlmNB6YydMaury23qE9cCimdQQEan2V2mBEZ+CRScjosoDth0zkk5ybL5BJKHxl5NIZ2SR1nRu1HnYQ0RrYhFGEgEDaUHGiiLSughTRHfloEqQTKh3H4+JKh2xSpj10aAxcsoaK5fkstU1OVVL8nbOTNIYeludzbjbPoXwCPwhojxxWmiabPYsz1QzHKjkOl5KYrsuRSpZ/9PE5vvzqOr2RS4TA0PXp2x4bA5BFia++scXpiSyPzhcYa1s8drjI4bEkX7+yzXjeQJUEHjs2hiTChdUenYHLRdPnUyfL3KwN+G/fXScKA05PZnlsLs+j80VeXmxzdEfRcrltkVJFXlnt0B/5PHGkSEqNtSjuLOMpplTqXYuWDQsNk+M7i0dWl2/rSbmX3e6K8PQsn3JK28sk7F9sdhsVvfDNHoSDheQAPyzYLZ/bnynbxduJf92JOzf5+4W/dvVj7nad9xvF3V0nZvNxJLeQVG5bY/azE+1ubvdvdjVJId72vwmHmHwhI4OqwPaOKNlgGPHk0RSzxSQrLRPTCemMfI6MxYEfP4iQRRHT96n1LNKKTGvkkNUVDFVGjmCra/L6xhAn8OkPPRRR4NJmj67lc3wsgRtCiMCjh/LoR2ROTWap9WxOT2bpmC71vsOfXthEkQXG8wbTeYNSUuPieo963+ZWYwhixFNHyzxyKMdyy6Rj+aiSyLFqAlkS6Vn+niPwjat1IgEgz3Qh8Ratn91saXPoYXkBlufz/K0G+aTKzVqfS1sDjpYSDB0fPwypdUcM3IC1NpSaJqIA26aLjEBRV0hqUsyIZPu0hzYL2xZpQ2aulOZIJc1ap8HcWIqO6XN4LIHrg+OETOR02gOHrZ7DRFbnWt9iu2eztH3AJvRRxIEz8GOOu23234+I027E4VDRuG2ReHw+3shPFRIQBry+b6+1RyEXRRyrxNHhatYgjCK2mjZ/96FxJFHki2cnUCQRd7NHIaXSt3wub/YINmMOZIG4/jGlixwrpwmDiJWuxfWtPp2Rz0whxePzBdbbI7wownRCHp5JEQoCvh+w0bexHQ9BEDg7lSObjCfcxw4XaQ8cFhsm+ZHL3z83RXNos9SSSCbg3HSeIBLojFx0ReC11S7TOYP5QpqVNhwupVjvjxiZDildomf6KKrIkXKKtunihREPzhTQxR6vtjo8MZOnmNFZa9oUMzIvr/RpDmzmS2lapsPIDrixPWR74LLWtRGiiKHrk9QVTMvDUGQMRUaSBR6dLTCeM7i5bTJwPS6u90jIIsutEbYbMJ0zECM4XsmS1CVWmyZXtvpYQUhEhBdEXK/1+czpKicms4RBCILA1Y0eI9tn5HlM5RMsNUYIwFMnxqj3LVZaFjlD5b6pPJYb0nd8GgObnKEwclxKyQSmFZBNKKRUGdMNb9t07K87bg9sggiyhowfhCy3LY6Uk1SzvIXF6G7YbTbe/ftudLdz5dSejcsH2YED/BBht3zuTmat92rDd2sAvtO5uNd5+1nB3s6R3u/k728gLurQNj1uNa29z74/M3E3jQI3CO/6Hi7g+lDax1h6bCbBo3MF3ljvoUoSR8oGnzxR4fJ6l5blcaaS5uPHSogiBGGE5waEQUTZ0JAEsMKQ7a7DdFYjIcvIksjjczkyhsLzC20yukpCielCZ0vxGvbirQYX13t87kyVjx8r80fn1yilVY5X0yiiSNf20VWZx+eLLDeHsRilEKGIEut9m4EXcCilct9kntlyipHr4272yBgylzZ6vLHZ576JzG1aKsDe/b200QNB4MR4mlJa49pmn5eW2qQ0mYmcwVRWZ73rsN23OSmKPDidY66YZGjDsbEUiy0L349w/Iie7XMmGZd9jWcNZvMGI28biLO0luPhhgEjy2ciF7MSDR2Xej/uHwtCaJoeHz9a4o3NDgKgKnenlD3ADxYHzsAPAT7Mpsd3Kgl6t9GfSxs9vrPQ4qljZRRJZOT6e/LpuyrCXhjsHb8rJDaV1yGCxsDZUwfOGwr1vs21rSHlrM5iwyQIQi5t9gnCkJPj2ThCPPJIqHGNa2vgsNYK2OjZBEFEq+9SMDSOVpKcHE9TSmk4QcQT8wWW0hY//cAEHgKrrRG5pEohpXJr22QsrRMEIRc2+1zZ6uIG0DFteo7HH7y4zFbfQRFlDo8lODWVZbaQ4o2NDn/+2hZdy6M/nqGSURm6BhN5g1fWunieTyWfoJoXSSsKWUNj6PhMJHV0UaQzcun70LZ8Do+pLDMirciYtkc+oZJWJBZtj1xCxvZ8RBEO5QycMGAinWC1a9IcOEzmY42DIAqQFYlSWmezb9MZONQsi5XOkLbpkEtoLLdNdE3m5Fiao+UkU7kESU3hxHia5xeatIY2Izcio8t88kSFjY5JZ+hyfrvPdxc7DByfgqFSSCkM3IDXVzt8/EiZp06IsdIkcXlPb+TymukytH1GXoCAwHQhQVoXyRsK41n5rhHNYkplvSXxhgct06OUNsgaMeVda+jetbznbmUL+5uNP0rsQgc4wPeKO+ksv1fcTVn+3Z4Db++E3Lmp399AXMloIIh72bnW0KVtunvrx66I4G5mQH2HvWRzX9IgCmCtbbHVc8gkZOoDl2bf5nglzXwpiSiI3KgPMDSFTx8bo9a3ySU1iCIsN0QWQ17f6qPJIo4fcayS5DOnxtnu2Xx3qYvp+ozp8PlTcdnM+aUW37jeoDGwOVRI0Bo41Icu901keOJwee9e7P5mWz2LmVICIQJJiufEzshlpWORT2g0hw62H/LSYoe0IVNOahwrJ5jJG7y22qFn+1iez83agEiAsbROy3QpJBSyCYWrmz2CKKZnPlpNxxoJgO0HnF9qk0tqpAyVn3lgggvmdc7N5qnmEqR0kfGsQSWjcnI8y3I7djoPlVM84gYcr6a5XhtwqWOx3XXIaioCEV+72mDkxoGppCYiiQKHy0leWWmz1BgQhLxVKOJ94qPApvijhANn4IcAHyZr0L3qQ3fxbqM/u1zGu/9f2ujxzRsNIBY82W0gdv1Y2ARB5PxKBxB4fL5AY+jQMl2ubPQQRYkjYwkiRMIgpGW6HCklOTORoTl0Ob/S5fH5AlOFWK795eU2xYRCJauRM2SCIML3I9Ja/FlbIxfb83Fdj6OVDBlDR1Yk1naaq0zXoD1yEIj46tUaU3mDY9U0Ly+22B64jKU1dCmgM3Rw/JDT4xmWWyZXN/t0TZftvk05peHtRKxUReHwWIpCUiOlixQKGX7uoUluNEd0hy6W46HKMqIIK10LQRCYSIIiwF+8sYHlRWz3LOo9h2fOVPn0iTK9lwIm8wbnl1uUUwkUEVY6I15Za5HXVcIo4spmD1kSSWsK37m1jSxIXNvssdIa4QUhbdNBV0UUSWAURaQVibWuRdpQUWWBfEqlPXSwXJ98SiYbikwW4wXtG1db5FMyUzmd/JkK9a5FNqHRNh1eXYpp746OJfnifRM0hs6e9sMX75vYK8PpjjxOT2a5Xhtwozbk4nqPjx8t37UuePdvK4CMLlPrW6y0LcopjalCgocP5WkOndvs9m6b+nez0f8oN4ce4AD3Qmy3H1yz5Ptxit/tObvrzG7d+y67HLxZ4/2dhSaHe0nOzuQpJFVapktr6L6lDOba+l2ohPZBJc4SACzXR3z+jMTPPzrF8rbJGxt9Lqz1+MypMSYyOls9m9bA5cREhpu1AaoicWo8gx+BEIWMpzVeWe+gyXFUvmXJtIcusiQyU0iQUKAuga7ItIYuN7aH+FHIoULcy1ZKaTx5uIAfhtzaHiALwl7vW61ns961uLrZ56HZWEvlzGSW11Y7vLjU4itv1JAVkYdn8lSy8Tx3cb1P23RY6VqYVsAnj5eo9yxeuNXm0fkc8+UkW90RQxG+fq1Ob+QxntX5/H3jHComubTRo226FJIq1XyCYlKlktVZ3u6z0I832Loqk9BUJrIJcoZCrR+LiO1mHbYH9h5pw2zZoGu5aCL07IAjYymm8zobHYvzKx1SqspDM1nWWg6mHWd2PC+4y6/23vFRYFP8UcKBM/BDgA8zcnmv+tD9eDeDLqHKPLrD+ANvdQ5qPZvrtQFrJqRrA46PZ/eEZSo736uc0uJykNaIuXKWjY7NyfEsuirvNUstN4asd0asd0xOTmRpDlw0WQRBpJLW6NvxptcLd0qF6iYnJ1LcrFtc2ewzntGYKyW5utXjG9eanJ1KgwC9oUsQRGx1TRp9i5ymUEzp9CyPY+UUD0xneX2zv6PyG5dPDWwPXZHY6tkcG0vhhCF5Q2G6qHN6Mscba10sJ8TWQgZWgOcGbA9sUroci8YIIvPFBFlV4ny3Rt/x2R7YRACRhO0FREHEUtOiY7lUUirVjIEXBAQRuH5Aa+hgJ0NySYXN9ghNFUkoMldrfRwfiCKSelxmgwiHS2nun87y6lKXUxNpvn69ztBySRoqlYwCkcxMwcVQ43P+9NUN7p9I4wUeaUXh6taQlC5jqAqnx9NUs2N4YUitbyMQsd4xaY88ZEGgktX3skIj1+e11Q6b7RF5Q+HR+fxtCsLw1khPJaMxlYTxrM5Lyz16VrzEKzvN4z3b5NJG77Zm4rdTSj3AAQ5wb7yfsfJ25+wfz7vrTN/y3yScCG/fFPZGLgsNgalC8i0U1fuv2b1DZ+BO7CP3JG0IyLKM50WUMjoPSSKPHS7SHXlYfsRU3kBRJG7W+ryw2Ga2YDBfSZGWJUopja9f3SYSoGIouF5Eo+vE4lvlFE8dH8OQI5avgKEILLZMpgsG2z2b7YHFubkik4UEV7d6fP1ag3xCwfFCjk+k+fSJKoYq8rdX66y1TSayOo/PFVEkkbMzeRoDB0ORkMRor/T21GSWatam1rNYbY24st7ADwtM55KM5zVOjme5WRvwN9caqBKMZQwMOWChafL1q9s8fMhjoTFiMq9jez6zxQS6LFHv2Xzt+javteHKZp9TU3nCICSly3z5wgaNoc3//PAMhhL3a4VBuNfX9+BUDk2WeG2jR33g8OkTYzw6V+JPBxtkNZWj1SSlrMEbm32OTeSodW3OzRfv+du9FxxkdD9YHDgDPwT4MDc072ZAvZ+G4judg2pWx/fTDJJwfB97DMBSYxhHhUpxVEhX40zFXMl9y/voqsyVrQH1ns1Sw2Sz73CokECRJU6OZ/GjiMvrXVKazM3tAdeaQ87N5ZktiHRHHgPH49X1Lo/NFpjJ63x3tYPvRZSzOodLCea7abpDh3LOYHxn0++FEa9u9rmx1Wcil+DB2RIvLrQJo5CRExKEIbW+ycCOuLTV55W1Llt9m6yuMp1P0Hc8nl9qcW1rQCGl8MhcniOlFH/y6gaDbJxRaFrwD54c4/p2kpeWWiBALqlQHzpc3OhQ7zkUkzJz5WScWQkEfvL+cf7gxWUEIWI6Z3Aon9hpkHPpDj1KqR0lTwFeWmxTzeh88ew4zaHDctOiN/IYOAGvb3XJGzqfPjGGoYk8Nn8IXZX501fX+fatBpfXuoiyxJXNHoWUzhPzBWRZojF0qOQMxjI655faWF5AY+ByciKFrCh7YmCyFNPQ/fGrmxRSCnOlFIdLsUjZftxJ+1nvO+RUmMwbfEyW9+r/vSDkbgJ3+3GQQj7AAT4YvN+xdOd43v//7nV3qUWnCgm+eN/E3jH30kio9WxSwG4LqgS8XZz5vpkCR8tJrtUGdC2HfEJnsz1is2shE/H3z00RITK0XC5tDtjs25xf7XComOSpY7Eifdd0KBoKp6dSCIhc3eqTT6ls9SwUIeBWD/7kwiY9J+TJwwUkEbb6DgPLo96zWWyOyCVkDFmKm3b9ANv1ubDSw/IDJnMJTkxmuF6Pyxn9IKRvB5TTKqsdi7+8VGO2mGKqkMRQZEZuiO0GaErch/b4fIKfeWBqr0dKlQRUReRIOUlnpKN2TR6YypIzFHqWiypHXFofct9Umq2+w8nxNCcraawcHK2k+Oa1Oi8td3D9gKQmEUX6HnVzMamiyxqvrncRI4GsoXD/ZIapvMG1rS73TWSAWPW5mNYJI5HXVrr4YVwhsNGymcl/MHuZg0DPB4sDZ+DHHHcbUHdO/vsn5gurHdpmHHu5F6Xova4xlTd4XY5rRO+sm2ybDkRxVGg/g8R+Hvh4YTD55LESQ9vnaDXNYiOWj39psYXtB9ys9fnWzSaGKqHLIoIgsNEaMZ5P8PnTVWzf57mbLTa7NjdqQ+pDm5QmM5bWOFJN07M9FhsmrhdwdDpLdaOP58fMRbIoQASO5zNTSuK7PpEskDJUcrqKJImoQsR3Vzr8xWsWwk4dbEREOaWSTyocKaY4M5HlX//VNVbaFms9izPVNKYfs+b8xMkK9b5DUpVRRYHlrklrYKMrEqqgcHoqx+WNPn3bp2+59O0ABI+tvktWU3jgUI6Nro0mEYvn6DKaKnL/VJqL6z1eXW5zejzDA9MZEEQurncQBAjDgO+utglipjweminypSdnESBWMR46WL5PPqnx8GyBr1+r8+0bDVbbI7K6zN/eaHIob+CGICKS1iXOr3SIhIhyUmcyrzNXTnBmMoOyUyKWT5h87EhpTwPgTtrP67UBLftN6sFaz+byZo/G0OHBmfw9o4fw/lPIB07EAT5K+CjY4/sdS3eye90pJPjaWpd1c0ckaiymv3wnzYNqVidjwNC6+3sawP6Xrm/26Iw8NvoWrb5Le+hzrdbjwkqHhKagyCI/9cAkE4UEnzhSZKM7Iggj/ACyhsKhgsFqy+SrV+qUUiqllMbrGz2u13uEkUhWE1kdQqE14sH5AhEwV06TTygcHUvh75TTzJeSRILA2MCiPfL5qytbPH2kzCePlGiZPtt9l5M76sbLjSE9y2Uyn2KjY5NQZTJ6HCDzgpCtjokfRpybyaIo0m2UopEA2YSKJomAwBNHCshCcc/JKCRVSmmVUsahPXRZqA9pDW0UUaCswsAO6IwCkqrEiWqGB2beJACp9Wx6lo8jg4xIKiHTszwubHRZrA1Z71mIosQDMzkSisQT8wVsL0RXRF5b6xL4AQvNARs9m/un37UZHeD7hANn4IccH8ZisTsB7xdr2p2YW6ZLbqfsZLdG/m4Owt0WkN1I0HrHYqXzZpdXz/Z5+FCB8axxmzBU1pC5URvQtz2+cGacxtDh2zebnKymODmeZWD5PDiT58Jqh5eXOjy/0MSQZRRZpJzWeehQlqHlE0QCQRCQ1HS8MOTvn5vi6laPRt9hMq+TNFRSqsTzt9oYiogmyTQHLiPLZyytcaNhktAUPnV8DEmUSBsqtutTSqmEkcChCQM7gIwm0hx6TBYSDB2XZt8hCAMUWY6dHURatst//+46jh+gCSEPTeU4NZXlxsIqt1omqdU2fcvjxnYfGRFdF6nmk1RTOglNREBgKmtw0x2SSyoUkxrzY0kqGYPFhglElNMqWx2L9c6Iv77m4XkR7cGIW40RSw2TW9Nxvb0iipRTBrOlBGEES80BhqxwcbXLpY0+nzw2xk/eP0HDdDBEgVfWOxwuZ+jaHlc2B/GCldM5UkpxvW7y0/ePs9qzWGmPSBkyQRQxmdF4YDrPZCHBXCm9t9hF6z0OFePMwH472XU6bdcnqUoEUaxPsdsoudWz9prNH5zJv6um4Ls1s7+T7e+32wMc4AeF74c97teDuRs71/stx3i7QJMfhLRNj5R8u0jUndmEXeah/cw5+/tP78wKuEBGgb4XPx45Ps9erXNsLMmJcoqcobDRd2j143LM9a7FX1+qcahgsNg0iQQ4PZHlZn3IG6tdbjSHhEQYSsz5TyTQH3n4uQSTOY0TlQTPXwRRERlL6/TtIKZgPlzi4lqfs9MZjlXTewJgx8pJ/vJyjY2mBccEjlTSdFc7TBeMPaE2WRIpJFWmcklmi2lqPYuuHZfybvUsFrYtErrI33tgkoEbkDHkvTU4o8vMFpN4fsD17SGThQS5hMJfXdriE0dLHB5LcbyaxpBlrm4N+dTxEl4YcmG5i+bHv8Unj5WAEoWUyvXagOPVNLWeTcaQyRoyaVVitpTkcDlJKaVB2MP0PLojh+VGn4VGH9OJy2kVRWZou7yy0sG0fWo9m9XGW6lFPwpO7487DpyBH3J8GIvF7qTvB+FtTkExpXJmInubiFNj6NAYOJTT2js2bu7KhQtwV17s/SqJwB4N3a3tIesdk1JS48hYgsXmiOXOiHJS5+OSyPFqmrmiwULDxN9RBE4oAqd2HIarWz06ls/l12sMHZ8nDxf5zKlxpgsp0qrEs9fqLDSGtIYuTx4u8oVPzbPUMGmaLild5ZNHNQ6XM0zlDCRZ5BtXajSGLm4YMpYyWGyPiIKIBT8kn1AxVImsnuR4Oc3N5gDfjxc+WRToWw6FtE5GV+iYccnSpVqfoQeYHpIgocoCluUhyhJuKGCoMpt9m82+zanJDLIqoSkiihSL1yy3LHRZxPMDEprCdmNIfWCjySLzhQRXtwY0hzayGDFXTJAzZM6vtBnPanzxzARPHCnx315cIa2rHCknubVt0hhaDO0NUroCApiOj+WG1AYu1ZTGZN5gtpTigek4cjRR0LHDiIyhcnmjjiJFiKKA48eLW2vo7lEFemGIJAhUMwZThcSew7nfps+vdAmCuDh4t8FdkcQ952+/Q7B/8di/qOyOhwurndua2d+N7R/UoR7go4Dvhz2+k/je3aL673Xjtt8JuNUwOVJOcmoig7N0u0jUrgPg7zgotxomJ6ppWkN3b51LawJYd5EhJnYOdh0BgEJKoWM6LLYiWkMPy/fRJImBG5LURY5VkhSTKjcaQ9pDl47pIEfQMl36lkt3FOvJPH64RG/ogghPn6pgOR4DO6DnBEykIKOrlJIasuhxY3vIyPGo922ub4GhKQRByELTZDKrkdUl6gKcX2ojSiKSIDC0fC5vxVnPM5Nv9tNNFRJUsjqXNnpxmc6OhkDOUOhYHn3bjzOopksxqXJmMst0IbknuHi8muab17ZZbY94aaGJrimUUxrVrMFya8QDMwUqWZ3pnMH66ytxBn8nC3Blo8dzCy0afRtViR2BtuniBzKPzhdQRBFDFUmoAudmCnRHHps9Cz+E+yeyPDCV4/mlNvWuzcD2mcpojOcSPHm4dFcbPAjC/GBx4Az8kOPDWCz2lwXtphf3U87tf75lupTT2ls2ZXeLClUyGhU9XhjkfTRyd1Oa3GUuOD2ZRZZEbtSGrLQskqoIApyoZkipMoYq8s1r9Vh1WBZpDlwW20OCSECUBJoDn0pW42Q1w32TGf7mSp3NrsVm12LouNzYsiCKEBExXZ/G0KdrxinbWs9iRRKpZDW+dqVGOWVwrJIkFATySQVNFoiEiN7Qw/R9PD9EFaA5iCfP5bbLYmNETpc4Xskw8gJWW0McP+Lzp8fxwghFFglCkERQJYGXF5vcagwJBZFHpguIooChSURByLbpUUprCBFc2uhyfXuAACy2RziuRyRIXFrrECEynU8giiJJXeGTx0okNYlLGx1GfkQprVFOaswV01SyBksNE8uPODWe5lA5VhQeuS63aiZt00UWBEoZjbGUSG/k8sZmn/sn0pyazDFZSLCwPeDW1gBDksgnFGwvwHQiHp7L0TNdlpsDnAAKSZW26eJ6ASk97jmYLCT2Fv7dqOSuPoXv+/ztKrc1uO86BOeXWtyoDffUNXdxt0Xlzmb2d2P7BzjARwHfD3vcFd/b/fud8H42buvtES8utnn4UO7NQNAdujPAbXTAu0ridwaNRFFkf05AJQ4wCYB95xtHkNVVdElm6PhYbkChoHGimkGRRE5N5LhRG7JQH5BSZTY6NoWEytmpDCfH03z7RpP+yOfCSoerW31URSKhiVgu9JzYedgcQsLxiOIqUnq2S9uPGHo+K22Lx+YMSimNV1c7tIexiOTJago/gqImMl3IsNZy9lTi6z17j5FNlkQsz+eFWw3WW0M+f/8kTxwps9Yesdyx9hyA3WDL/v/PTGa5tNHD8UN0SaA5dNG9gKXWAFkUOT2ZYa1jYvsBWUPhkreTvR94vLbewXZ8DhcNHjtcxHLDvTV5q2dxqz6gkNZoDxy+c6tNQpFIqQoDG2RNQBRFltsjPnmszGurHZZaQ9YHDkfLSca/BwrzA3x4OHAGfsjxYS4Wu9ceuT6NO2gcIWYB2l9GBG8fNVIkEUmEV9e6SKLE4bHUnpDMnd9hPzXpgzN5yimNrZ7FzfoQUYTe0OH6YMBGZ8S3b7UophTun87SGwUYqoAmiRi6zMXVTRQR5u5L8pevb7LUHjHmB7x4q8nzt1qs92zyCYkojDBdn4XtPpos4AURP3V2HE2VWdjuc3mzR1I1ySZkKmmVjKpwrdbnsXmDqSmDpfqQQIBQBF2RsD0fRQgJfQijEF8EVZZI6DKCIBJG8PMPz3CzPqTVt7jZjkVvEqrM/dMFpgsGjhtgByGtocd00eCBokHX9Fjr2EhC7CQMPY/W0MZ1A0RRxHEDTM/j08cnSCU0nr+5zeWGjeUGyLJMVpUIA0gZCrmEzDeub9Md2kzlk4yldS6udJkqJEhrBtc2TXRFZLKQiDm5JRHLcTm/1KVp+vz561v4IXRNh67tI4sCpyeybPZsHpzOIUkif7vap5RWePxwaW9x2h44lJIaPTsu31nYjsubHoc9e5orp/A8j6IWN5zf2by+G9m6E3dbVO5sZj/AAQ7wJnbF994t3v/GLbpN78MLA4IwLhudKkpvyQzfuYbsBqLa1u3FQS6gALoEbhA3Fe8mB5pDj2LWJ6mKnBrPYPtx2eaTR4tUsgaBH/Ky2WJ76KHnJE5MZLh/KocXCjQGLn0rwA4DOiOHIPTRZZmkokAUIAsyrg9BCClNoTV0WGyOGE9pZFMq212Hm9sDho5PKaXxzKkqXhjSGjj0HZ8/v7hBOa3xieNjDB2PR2dzpAx1L8iW02Vs1+fyRly2easxRFNknjkzvtfMu1v6mCjI3Kj3+dqVOmcmMzg+pFSRhcYIz/dwvQikkIqm8/pan5bpcrSc5GbDJKFIJHWRtR68ttbl7KEiYRDyrVst5soJbtYGVLMG3k7Gxg8CVttxZ8YzZ6rkEgrVrM6F1Q6dkU8+IbHWsfnzN7Y417VYao2w/YCu5eIFES8ttPjJs5O3/YYHQZgfPN5zcda3vvUtfvqnf5qJiQkEQeBP/uRPbns9iiJ+4zd+g4mJCQzD4FOf+hSXL1++7RjHcfgn/+SfUCqVSCaT/MzP/Azr6+u3HdPpdPjSl75ENpslm83ypS99iW63e9sxq6ur/PRP/zTJZJJSqcSv/Mqv4LouB3jv2GVt2O0D2I/99KPwZmSo3ntLHGbvtdrOa7vXHbk+y00TN4BzMzkeny9yZjLLkXLytv6D3XPyhsLHD8fH7C5Wj8wV+eSxMo/MFFjvOtyqx6nd+VKSnzg+xmdOjXNmKsvfeXCaz98/ie2E6LLMSsfiy6+s8eyVOpIgMJkxMFSZw2NJfv5clcfnC5yZKvDYXIm0KlPvWax3TK5u9bhRHxCEEYWESj6hUknrnKxmqQ0ttno2f3tjm5u1ATfbI1ZbJtt9l/7IYalhMrBCDld0jlTSZBSJI+UUTx2v8MhsAccL2exatEYuL660WRvGyppPHCnyv/7EEXK6zLdvNal1Rnz6ZImUKrHSsPirN7ZwXJ+jlQxPzBWZyqW4byLHY/MlZgoJltsmLyw2+S8vrrHUGHJpa8CVzT6jICAMQ5Y6I17b6DKW1RhLG7xwq8FXr2zz7LUa37ixzaurHV5abHG9bpJPKPzsuQnOTmUwVJGsJnG8mmG8YGDZHgvbQ759Y5uUIfPYXB5NjqNYj8wWODdX5IGZPF+4r8IXzozz4EyehCrz4Eye0+MZjlXSHC4nyRsK52ZzPHwoz1bP4vJmb892IM6YTOWN25oJaz2bqUJiL5q533Z2F5XvR93p242ZHxUczPfvHT/qdvFux9j++zBVSPDxo+VYiX4fum7cE7R/zL/d9Ws9m85dmoc9YBBACIynBcZ3iMoKCYmmafPKWps/ubBJbeDg+iHFlMbN2oCXV9pkkxpPzOb5zMkKP33fOPdP5XB9n/X2iNOTGZ4+UWEyl+ThQ0VOjGcYOAFbPYvXN4d88+Y2TggnJ1I0By7tocP1usn1rSHLLZOtnsNLiy3Or3TjcsmBwzdvNvjalTrX6wNuNob0dvrtdh2lqUKCMxNZqlmD8ysd+nbIF++r8smjJeoDh/NLLeo9e0+YbdfO6j2Lm7UhQRgyldd5ba3DVm/EVDHBF+6v8tSREqIocXYqyzOnxnhwOsczp8b4ybPjnKykUQXYHsTaDkfH0nE5UVrj+YUmf/DSMl+7ssW3bzYREbl/KkPKUHhlucNnTo+TS2o0Bh6qJHJyIsfpiQy2F3C1MaAxsDlaTPFLHz/ME7NFzs3m372xHeD7hve8YpqmydmzZ/nd3/3du77+27/92/z7f//v+d3f/V2++93vUq1W+exnP8tgMNg75ld/9Vf54z/+Y/7wD/+Q5557juFwyE/91E8RBG96/L/wC7/AxYsX+cpXvsJXvvIVLl68yJe+9KW914Mg4Cd/8icxTZPnnnuOP/zDP+TLX/4yv/Zrv/Zev9IBYI+p5cJq5y2L2J3CZNWszolqGuC2jf/+YzOGzFp7xFJzyHM3m7y22uGlpTZLg1igZaqQ2HMurtcHt71vrWez3LaoZg1aQxdvx1mo9WwqO1Hhz52p8LGjBYZuwNnpHFP5JO0dp6Xes/na5S1eXm5zrJLkyFiKrunhBCGGLLLeGdGzHEIEJFEmoaoMbY9SSmGhbXJlo4euyEQhLGwPuLYxoJDSeHA6y1MnxtBVmXMzRabzOkldYjqf5KfOVJkvJAnCgCAMEYgQiAgjqPVcrm71WW4PaQ48dFkiiEJubA9QRZgrJ5lMwNmpPNsDD0UUeWyuSMaQ2eiO+Jtr2yw2RzRNm67lstG3uL41YK1jMVdOcHwig0iEJAr0Rg4QIctguQHHxtKcqGR4cDLHQzNFJjIGaU3hY4dLHK+k+NSxMmcms/zMA1PcN5klpclosshW12SpZfLiQpvvLLT5s9e3+Nq1On99qYbjBoiCyCePlcgnFL5zo8lyy+TPXt/i/3t+g+XWKC7rUWUeniui39G02xg6LDRNuiOP5baFocjoqkxn5BEE4Z7tjFyflh1rFCw1hgwtl5QqkjHkPZu71TBZb4/2Nh3fz43YnY7vjyIO5vv3jh8Hu7jbOLvzuf33Yb945e7rXhASRHCoaOAHISPXv+c43n2cMWRSytt/tuYwYmvHYWiZAfdP5jk1nmU8p3Oqmub+yQyXNrp868Y2lutRTMqUswbL7RHrXQddlRGI+JubDS6udzEdj9bQwY8gn1QZOT5EAjlDIopCFCGOqL+w2MRQBZKazIlqiiePFvk/PzbD339oinOzObZ6FufXOjR6LsfGUnziaJm/9+AkpyeyFJLqnhiZss8pePhQnmOVJD9xqko1a7DRG3Gl1merZ5FQ4/LZpeaQtfYo7qmrJKmmDV681eBr1xosN03qPY/ZclwSutkdUcnqzJbSbPQdNEUmrSnU+w5uCGNpFUMVee5Wg6QmUc3qWG5Io+eSMRTGMxqSJHLfVB5ZgOduNfna5S1WWiYrLZOEJjCwAxRR5FAhiSaAIop0XJ8bjSHXt/tc3Rq8za93gB8U3nOZ0Be+8AW+8IUv3PW1KIr43/63/41/8S/+BT/7sz8LwH/5L/+FSqXCf/tv/41f+qVfotfr8Z//83/mv/7X/8pnPvMZAH7/93+f6elpvva1r/G5z32Oq1ev8pWvfIUXX3yRxx57DID/9J/+E0888QTXr1/n+PHjfPWrX+XKlSusra0xMRHzE/+7f/fv+If/8B/ym7/5m2Qymfd1Q35c8Xa87XcKk93ZU7A/XbwrJf/cjQaSJJLRZSCilNIoJRWslTepRXfrQnfVJncZLTojh/XWkGpGZaNrs9WLlWdvNcy9JqZCUmU8a/DGxoCu6fBiz+HsdIasIcfy7NsmQRTyyFyBrZ5Dd+TRtTxE4Gp9yJnJHONZgebQx/U96n2LXEJmNm/ghhHzZYOLqx1uNQdU0wksL6A2dHl1uQ1CxONHCnzm1BjfutFAlkS2OhZ2GCFIIqEokk8qlLIJkppE6Ee0TIeZQoJySqcxip2g5sBlKp/goZTGstNCkSClSwwdj1uNIU/OFfnGjQZrnRGfPVXhcLnCt240uLDcZKNr0RlZfPLEGG+sdfnWrSYIEVldYSZnIAsC/+P1LVQRTC+gkFbI6jJHS0kalkfPdNns2giSyEwhyVwpyUsLbRRR4pHZIocrKV5ZauOHEAoeUxmdpdaQ63bAeFrDCUIyCZmVzgjLCfmJU2WenI9LvwwlTm8vNYZ4Ycgry13OzeYwlPi3uVEbMlPUyRsKuYSCH4RUsjrltEbLdLleG9CzfFIKbI5iIZzltkPbtCkkdSRJpGf5zBYMsoZ8W0M78H1rRPtxqHM9mO/fO34c7OJufQN3PndnEOnO1+t9h7oF3ZHHsOfRGDp7ZaNw+zjezzDX3tcgDJAQwQvj7IAOePt6i5O6yKGCTigk0CWBs1N5Lq732OzamE6I6UQMlJBcQubB6Sy9kYft+lTyMbtPMaVRSmtMlxJoskRWk4kEkcNjSQRJYK09QvWgNfSQJYlj1Qz1noskCbyx1mMsrSELUMkZdEYeU1mdQ3mDTx6v7NXh13s252bz+EHIUmNIZUekrbpThrvcij2blZZFVlPJGzLXtvq4gY/lRLy2EuGE8NhsgZ95YGqHzlpktpTgwaksMwUdQxX52uUWrZHDSwstfvbhabK6zI3akPycwmNzBawVODud4xvXm3z7VovJrEE1bfCxIwU6I5epbAJ3R8iyktWx3TTPL7SpDRzEvoOmSJSSBmld4mZ9QGfkst42ySUUKskES40Br652eWw2z9MnKh+wRR7ge8UH2jOwtLRErVbjmWee2XtO0zSeeuopnn/+eX7pl36JV155Bc/zbjtmYmKCM2fO8Pzzz/O5z32OF154gWw2u7cwADz++ONks1mef/55jh8/zgsvvMCZM2f2FgaAz33ucziOwyuvvMLTTz/9QX61H3nsNmbejbf9zsVtN0p/Zw/B7jFbPYvtgUNhH7vBbsPYWIKdKJGyd/wue4EfhLy42OKN9Q6bPYdiSqOc1vYmrN2SItvzubrVZ6ag88UzVXKGwiurXa5vxfz7hirSt1wSssRKa4QoiWz3LURB4OxMlsePlnhsvsjLi20gJtbv2h7PLzTRVZnPnCwzW0rxl29s0R66HC2meehQhm9cb9LsOoz8gMmsTj6pkjVUXlhocmWrT9aQeXA6Tzmr89JiC1UU6Jk+j80X2RrYbHQdEEVUUWJ6PIXlh2R0mb7pcq0DVn0AgsCXv7vGt242OFmNm9jqfYfj1QyPzZdZaQ65tBWzCeUS2k69vocqCRyrZiGApU7M+awrMo7n4QWgSiIhkNEVDFWmN3Q4OZElpUhsE7HSMKlkNUopmZQhoSsS/6fHDsXibq0hz11vcqiU5rgkosoS17b6pHSVTx2Pew1OTmRZbJgcqWRoDV2eu9kEIg4VE0BEvWex0rZIKiJBFNA1PUZuzHu9uwEopzTKKY1CSuX11Q6tocPIg7lSgmouucdqtbtYxvSE7h794N3YrN4P3i1byo97nevBfH93fFB28VGmW7ybw7OfBW6tPcIPwtuCSHeeU8loTCTg1ESGvhPtNb7u9gfpEtza7jF0YkXzI+UklazOnTxCXhj3CSQV0BWo7WslkiSZxW2Thuny6HyRjuVxZjJD33KYLhk8NJND26ENXWtbNE2H5261MFSJk9UMD07nKKU0HpsvcrPWZ6lpoikSnzpWZr0b19tPZeAnHhinlElAGGHIMl3b49s3W8gyVDMJfv7hqXgtMz2CKOClhRYf32muXWjGWjmXNvpkdIXD5STLLYsHZrJcWu9wsz7g9ESKjx2JaUA3OiYvLrUZOQEJTWJg++RSyl6ZkReEfOJoiVxCYrk5omV5dEYuG10bIYK1jsVzNxocq6RZbo3wwpCeGQs8KpLIx4+V8cOQo5U0uiKz0XNojxzKaZ1CQqFrx9n3pulQTquIRKR0lVJSYXvg0Bk5ZAyZTx4r8d0lCV2WuG86w1+9vsHICVmsmxzgo4cP1Bmo1WoAVCq3e32VSoWVlZW9Y1RVJZ/Pv+WY3fNrtRpjY2Nvuf7Y2Nhtx9z5Pvl8HlVV9465E47j4Dhv8tv3+30APM/D87y7nvNesXudD+p6328UExLrrSGVjHY75VtagTDACwPWOxbXd6I0PcvH99NM5d9Ukz0znqKeVEjrEq+ttDg1kYnP3XdvFOX298poAq+vDzg+ZpDXBPpOyJOH83RMjxs1n1rP3OPST2oiPcthtRnyxOEiAjCT17leG3C9PkATBewgJKkp1PsWluMjCAIDyyMhCxiKyJfPr3Jre4imSIhRxERao225SKJAXlcoGTKzpRSGOCKhydyqmWx0LPxsyFhKZ6ltcqMx4IHJHE8cLmD5AboIXdtnMguTOZ0btR5bPQdVFjhRTeO7AZNphVtNi+lAJfBDNtomF9c6mB5sDxyCsE+9Z9Ec2iw2IsoZjQgJwpD/48VFLC+gpGnkKgr3z+QI/Yj+yGc8Z/DAVI7OyKPnuFi+z3w+FUevOhZz+SSGIdIdumz2R7SEmK1bFGC+aJA1FBoDixcXW/zBS2ucnUrzvz59lCNjadbbA4aOx+F0gicOF2maHglF4FApyXTeYDJv8Npal29cb1LrDHnySImpbEyDN5k3GM9odE2bN9Y6zJeSjGe1WE04CpiZTLHk+1iOy2rb4ng1TXtgc2Gtw8W1Lv0u3Kj3eeLw/vkgoppW4s1SV6Q9dBjPaBAGt9nqyPOo95232PI7Yde+fT9NJaO9r2t82Hi/88wHOS991Od7+P7M+d8rvCC8q43tt8P98+v3Y42512faj/1rwv7n1jsjrtcGHC4nOVIyKCakvc962zlhQFEHRYjH8+64Jgyody0urHdYqA0pZzRmi0k+dqSEIkRUZKi/mUDYaxi2Pd7sHN6B7fqs9yyGjs/5xQZCFGeplxsjkrpEJR0HtDZaQzqWT0aXkAUopWQqaR3b9/nq5TZdy2O1OcIKAo6U06y3Tbww4uR4ikSnzv0Taa7UTK7VBgxcn6KhkFYF7p/Oc99kmrwuMZE3SKsC37nZ4EJzRBD4dCyfjumhixG6JHCooJHTJYLA59pGh2/daDByQhbqfT53Zpz1jsXFtS7FhMaDkxqCINC1PSopjcLOffaCkObAomN69G2PrKgwldVoDeKA2sB22eiMUCSopBUur3W5Uuvit+H4Rhtd0/jY4QJXNwckVRGJkHbP5qY82GF5C1hqDFhumgxsH6IIxwtYapssNuLf68x4ms+erFJKqXz1Up2VZtyDVk7JfOJk6UOx3R/2vRd8ON/h3V7rQ2ETEgThtsdRFL3luTtx5zF3O/79HLMf/+pf/Sv+5b/8l295/qtf/SqJxAcb4Xv22Wc/0Ot9WAjCuIkrp8bNmi07Ls2YSEDxHsHV3XMGMgx8GC3wFoo4gIUeXO3CyRwc3sfquHtvakO42IasGk/oNQemEyBL8ft/pwauD0sdWLoOk0mQBEjLoNmw4cD/+zJYIZQU2HZg5IMTgCGDpMKLK9C1IK9BzYb/x9omkgBhCJYPmhgzAM2kICfGUaW/eL7B4RSYAzAiuLXYJanAhAT3qUMaPRj0QBXg5qjFFSAtgiZBrw+vNGDDAsGDvAj1WoutrRayAsMmbIxgWANVgvUR1DtQMaAU9jFMmJLAEqHf8dlqmUgC/NvtBl4EkwloOjDyoN1qMJOEjBDfswtvtFk140HdsMDrD6gYMLDgxqjDoRTc7ENzBKcL4AUNVoagF8EU4UILXqnDCHCGJoeCGoczsGWB24VrLVi8CUeyQAQvL8Jf2XAsG9uP24FX63DrEowCqOixTeVUWOjDShPcBmTLsDKApSG88HLMBlLWYnsbLcQ2otpwJAKKcOXCeeqXY1vbtdM7bdFZeqsNvhtbfjv7Hi3E/2+Obv8uHyGf4D3PM6PRWxmYvld8VOd7uPec/41vfOMDn/PfC/bPu7s2dqed7rfDu82vH+Ya837HDtz+ud9prAQh/OH/ePa2cRWE0HJA9mHch0wPLBMu1OP7YPq3X+NunRkSMfmo6sJk0GTThaU2bNYafHoSRAciGf7s2UVaDgz9uIFyOgWrQ7jsxexEwwBsF+aycEgCMwRrq8l/XlrCEGEsAYk0/Pc//zpbFtg+dJz4viUcMNoNltrwbB+O7FSyXetCQoaBDRvDeH5dAqaSkG7ANQ+IQJZh3Ia6DRcu1ugsvEYQwWYPxnQY9mFrBF4ACwE0b8a/1UIfNs14fRJF0JLwSis+1hDj+7Lch+eD+HMYCvg+dFz4f/7Zi2Q1UEW40o3XkpwKdgh6F/52FV5ugCzGc3YkwiCMj1vfjtfAtAWvt2Br4SpbJqwNwU7BzS7Uh/DHf/Mq7uJ7s6n3gh+Wvdfb4YP8Du92zv9AnYFqtQrEUZzx8fG957e3t/eiOtVqFdd16XQ6t0WLtre3efLJJ/eOqdfrb7l+o9G47TovvfTSba93Oh08z3tLBGkX//yf/3P+6T/9p3uP+/0+09PTPPPMMx9YzanneTz77LN89rOfRVHeodPpI4Dd6NPxahx9eruIkBeEbHQsIt5keHk7jFyfK5t9Tk1kSKgyI9vhy3/5df7+Fz9NQtd4cbHJ+RdWaYQhpyayPDaW5MkjJQZ2sPf+6x2LxGaftC4zntWZ3HnfpabJfz+/Rq/nkNIkQlVCdwJOlxLMFBMM7IDV9oiV1TaGIfLY0Tx//kYNTYBPnagShiHPL7U4U8mAKFJOq9ysDbH9AZEsM3FsjN6WyWOzORqmS0IV8XyBbEKmvtjGd/tkEgrlfBLHDzg6lqKaSZBLyHx3scXGtW0cOaSYVOmYLuN5nSPlDJ8/PcZLi20sL6I+dHj4sIGz0MDtdkmWqhQTGumEQrZrsdIaUs0lWWwOKKQUBCRmiwmkrsVWz0KQRIxKhlJaY7vvcnOpSctxOT2VZS6hUs0abA8sbix3SSV03FyCnOrR746YnC3zk/dVGbghZ6djT+07C22mrm2z2BzymZNjfPxoGdv3eem7Gxw7YVBK6pTTKg8dytM2Pb52tUZn2+Tcw5OkdZUTnk9j6FJOqmiqjABcrw8pJhU+WUlx/FYTELlvKstkx2Tz/CZaQiYhi4wXEnzyaHkvAuoFIcuNPn/x9ecZP3aWsYzB9tBBiCKeOj6GIonvGLl8N9HNdzpn97EfhCw0zL1x8oPG+51ndiPjHwQ+6vM93HvOf/rppykWf3B0s/vn3bfLPt3Nhr8fa8z7GTvv9Voj2+H/9eWvU5w/yZmjY8yVksCb92a+HD8WYG/eB/inL3z1bd8vKYEhxZvbbDmFVMrwQErluBfQt3ymZwuoA5sghHxS4dG8gSBANaMzkTN4fb3LrbpJWpd4faPPatuEtM4Tp8a4VhvSHDhobYtcSiWfVnljcYH/6089TiphYLs+r6x2OTcTUysLO99fWmqRNxSOjKUw1vs8NJOjOXRZuL5NOHAZy2n85AOT9CwPw/Q4VkmhSCJnPZ+XlzvMFAyyusxiw+RL1TRHxmICj5WWyWtrXbZ6Dh87XUGWRFYubZEd+YhEmF6AUkry2FxhpzEabtSHHPN9eiOf2VKSUkrhb6/V+dqFW3zu0ZM8cngMx/X576+sM3R8TlZSXNjo8eknD2H7EZdeXiciolROkU+olFIK+aTC4tdvoSsSHz8zQWPk0Bm6eLLDRCbic2fH6b20wvKoR6Fa4YtfPPs92dRd7eyHbO91N3wY3+HdzvkfqDMwNzdHtVrl2Wef5cEHHwTAdV2++c1v8q//9b8G4Ny5cyiKwrPPPsvP//zPA7C1tcWlS5f47d/+bQCeeOIJer0eL7/8Mo8++igAL730Er1eb28BeeKJJ/jN3/xNtra29hair371q2iaxrlz5+76+TRNQ9O0tzyvKMoHbjwfxjU/DEwVJWRZ3qtLVRSY0996jwBqgxHnV3uAgKGpTBfuftwusorC2UMKlzZ6nJnM0rZCNkfQtkKyaYVzc2VAxAoCxBA0VQJRomHaVHIJFEWmkhNomB6GIvIXl2pMFwy+cN8kiiwzXUhxvJKmmNHIGyov3GpyvTFkve9QTGpMFgz6dpZj1RRX1ro0By6FtMqpqSwXljqM3BDbj/jMmTJt0+GNzT4JQ+ZYKc2t2oil1gg/jGibHmMZlVCIUwr5hMZ42kCQIG+orHdtal0HSRTxI5XJUppHZ0MKKYWF+oCRF3DuUIlH5wqkEyqhIOKFcR3s40eKrHdG/M1ml+Zql0cOlTg5leW5Wy0Wtk22+g4JTWYylyKhKgwsj7Sm0lY9eiOXpZZJhMCnT49hOh7fvtGg1hmiihnyiZAj5QyWF2E6HrYf8uChPGEksNa3+fOr23zmeAVFUXhttcON+oCxgsHPPDRFNRsvit+6sc1Gz0KTRNxAwA3hiBMxVUxRySRYatmsd11M16IzcokiqCc9zs3mqfUsRl5Aq+FRzSX5wtlp1ndqiUspg597ZIpSWkcWhL1egPXum3G+F5e7XO7AwwmVs4eKfONqnTc2+1TzI8azBreaFrIs39MO386W74XaYHTbdXev4QUhuqZ+5Oq33+s880HOSR/1+R6+v3P+e8Gd8+7bzbn3svMP8zu8n7FzL9zrO7Q7Fts2aG6IIst732WqKIEgst4xubjWI59Q+ZgsI++IUe5G/XehAzGHWgwziP8BrDaHbA9c8gmV/8sTsxiqzHhWY3PgUMmqVDMGsiTQNj1GrsVEIcVUIc1UIU0hpVLM6Ly40GK1PWKxMSKb0DgzmUWSRHIJlctrXW5FgBh/ZlmWOTdXpGO6lNIyCw2TjC5TSulcqQ2p5JI8daIaNwuv9vCBUxNpTo1nUGSZrhP3ytUHDitti4mcxtAJkSWJv77S5Hp9wP+kqdw/U8ILQhabFq+u9RGEiNrQQRFFCgmdhw8lyCZUvna5xq3tEVYY8fhcrPUiyzHpQiRA4Ic8t7DN5foQBdBUhali7Ig80rZ5fqHF1W2T1bbNK2s9Tk3k+NSJMXojn0JKJp9U2ey4bPYHmG6A7YcktZgtMGcovLHV58JKh4urXZwwoJJR+LlzUx/q2PtBj+0PAh/kd3i313nPzsBwOOTWrVt7j5eWlrh48SKFQoGZmRl+9Vd/ld/6rd/i6NGjHD16lN/6rd8ikUjwC7/wCwBks1n+0T/6R/zar/0axWKRQqHAr//6r3PfffftsU2cPHmSz3/+8/ziL/4i//E//kcA/vE//sf81E/9FMePHwfgmWee4dSpU3zpS1/i3/ybf0O73ebXf/3X+cVf/MWPFLPERx3vpdmtmtV5+FCe5l0EyO6F/eJhZ8ZTTCTixrHd954tp/GDkL98Y5PNns2rKx1sP57WH50r0hq6bA9srm70eHW1w2JDZ7qQ4sGZPD9xsrLHJDNwfN7Y7HFze0g1oyFJAmenM4CILgu0HI+JvMH9U1kaPYfFtglRxPXtAdkljY8dLTKeS1BNGUwVdW5smWQ0mblymulCwPFKkr+93mLkRiRyEumkQnvocWIyS8qQeX29x2rXQhIEpvMGhi7HTEICJDWF19a6+EFEFIW8tt5n5HmkNYWVlkUuqZKO1xLWeyaWnWE6q2O6LkoU4oYR5ZTKiWqG19Z6DG2PyUwCTRYQBJFyRudEJUvxYwprXZN232alNaA1sHlopsjRsSSLTZPD5bgJzfJC2qbD0PT4o1fXsP2QW/UBryy30GSZk2NpUrrM+eUmK22TUkJjIp/EDUPmy0mKKZVaz+apE2OU0xopVaJre5yezNAbuVQzBo2Bw1cu1fH9kMmisfd7A3z1Sp1sQuGpY2O32d5ae8R3bjXp2x6fPVkhbyi4IciiQEKVefpkhXJGj/sKhu5bmoY/CNyLCWb/OPkoN3Z+0DiY77833MtW3u28+6PATHRnY/HuvahkNI5l4VOnq7fpD+yqEK+04iz0/A5xxIuLbWaLBtId11fFuIzlbvA9ODRuMJFPYPsBuiZj+xGiAAvbI7a6DiM3oJJVqPc9bm0POFxJc3o8y6vLbb5yuUYhoZE1doJBUcR903ksNxbgcsMQUYBrW0O2zBaFhEbeULi02edkNU0uqXBze8hMQeepoyVOTWZp75AfTBcM1lojvABqfZfZUpozE1n8IOQ7t1r0LJfJXLxWlpIaf/ehSa5t9pgvJffsKhIETlbT9GyfyxsD8gmVkxOZPTKQI5UM+YTNbClBy4w1BGRJ3GPm++5SmyubfcRIoJqEazUT42qdp09WODqWot4fMbRDsrrCZCHJ1y43+OzpMrMlmZbpoogiPctlqpBEkUSGtseXX13j6VNVPn2iymwx4PJGn62uxcWVIQjwp2/UePhI9UOwtAN8L3jPzsD58+dvY27YTcH+g3/wD/i93/s9/tk/+2dYlsUv//Iv0+l0eOyxx/jqV79KOp3eO+c//If/gCzL/PzP/zyWZfHpT3+a3/u930OS3hzmf/AHf8Cv/Mqv7LFQ/MzP/MxtXNeSJPEXf/EX/PIv/zIf+9jHMAyDX/iFX+Df/tt/+97vwo8JvtdNjCKJ6KrM0LX2GCLe6brHq2kafZvj1TSKJMQNYzvH7KcXfeZUlatbPfxIQJMEzkzGpSvVrM7ra7DVt5FFOFJJkVZjO9lPb7rUHCAK8QJjKCJREJEzVEZOyFhaJa3JCGmNet9le9AkIcucmcxRTKh84ew4h4pJmgObxdaIyXyCpCpjuSkaA5u5SoYgEjk1mSWpiaQMBdML2OxavLLUxnR92qZDOalRSGoYqkIhJbHWtLG8kIwqsd4dEUUR6YRCQpYYWA6ZrEJ76LDYMJElkBSZRt/mLy5tUc4YPH6oRNfx2eiYnF/psNAw6Yw8/BBSCvQtH1UUmc4bNAcW//vLa6iShCiKhGGIT0RtYGP6EilVJYrg1ZUOlh/QtTw2OiaWF5HVZBAFlhpDEEW+dq1OManTGvlkVZVzs0VOT2YYzxp7zE+XN3sUkirFtMZXLm8hRAIPH8pj+6CrMg/MJFjvmLy+1qdgKNxqDFjrmJRSGllD4XAp+RZV4Ywh4/kBiiTQGDp84liZpStw/1QOeFNJeK094lbD5EQ1/YFvxt/NJu1utIo/qjiY7783fK+28qPAWLX7Hdbao9vuhSKJjCVgtpR8yziuZnU+dqQExEr3F1c7uIGP7fs4d1y/f4cjsD9zMPQha6h0TJ+XFjt89tQYeUNhOmewLTksbw+oD10emptGk+JovBCxE6Da4mqtzycOl/gHT8xytdbj1eU+Sb2O6ws8fCjHE/NFtm7ASneEJIkcLiU5Wk2z3bdomi6GJnFls0drYPP3Hpqmb/m8uNgmCEOSqkjSkDg9niapKaSNuAzoeDXNx47EJWx+EFLrxRv4eF4tcKthIslDaj0LTRY4VI4pq7umSzGtYSjy3j0sp1Q6o/j8E6XbgyfFlEpKk9AkgSAKaC5tcWI8jROE/P++u0oowNALqQ8cjlZT+F5EKaNQzRiMZXWeu9Ega8Tz+XpriKaKSJKKokh0Bi4ZQ+b0ZJZad8SriwGGDKom8Ojh0gdiVwf4YPGenYFPfepTRNGd5F5vQhAEfuM3foPf+I3fuOcxuq7zO7/zO/zO7/zOPY8pFAr8/u///tt+lpmZGf78z//8HT/zAWJ8EJuYu0Wq1tsjXlxs73HJ76eI61s+qiLTHrq0o5D9WlDVrB6zygCz5RSz5dSe1gCwF0V6+mSF7b7Nq17MnHNxvYeuynsaB7uc1rIYp5afu95CkSSWmyYXVvs8OJNhppDE8SPagxGbfYfTc2mCMI44v3BzmxdugShImLbP31zdxvUDLm30CMKIZ4DJXIrDY0m6psfXL2+zuN0nqSsYikhvFGK6PglN5qFyAj+Ele0RbhiSVGXSqkTb8jhcSnCkmuXKWpflzpCh42H5Eacn06xtbpNPSiw3XEQRkoqELEvcV0pwZCzFpfUuIpBUJdqmw61uTMU6XUyhiAL/96/f5LW1Do8fLvLgTI6tjo0bhAgiWG7IWEphe2Dzt9e3+dSxElM5g9XWEM8PuNkcUkrq5JIaCBGfODbGsUqaxsAml1AZ2j4PzOTjHo72CNv1MR2Xet9mvpQgCCL6loft+xwpp/d+//GswfMLHV5b71G/Uief0Pi5hyc5Vk3vOXsXVjt79KBXNnts9R2mcjo922dgBxzOxk7AnTboB+GecvVeLfX3KWL/oxCtfbc4mO+/N/yo2sp7HWveznh9t9m8XdV5iNeBnu1TSmpsdBzuJSeYkSCbgOYQrB2TVUQYzxqsd2weny9wdCzNN240SKoyhiLR9fyYjloW+blHZnhpsUXXdLH9gHJap9l3KKR1dFWmlNYpZS2iUMANfJZbJv2RS1KGTFLjWDXDw3NFaj0bUZJY7Zh4ns/ICehrPusdk2rG4NxsjubA4WbdJArgtdUuxZRGc2BzfdskCEKmCm/eJ1kS2epZ9G2T45U0J6ppbm73+MMX15AlSOgKKUVippRElkQWRyZXNns8fbJCNWvw6mqXlZZFJWtwfqlFSpXo2B62a2AoMpPFJJ7rUo/g/qksV2sDLm/2mS8ZTGV1sppKMakgSRKPz5eYLCT4xtU6lzb75JMqx6ppvnXdJqto/MQDZUw71vn5+uUtymmd17f63GgPmSonOFxM88ihwruysQN8f/GhsAkd4KOJD2JhulukKuZ7d6j3LGyfPcrR3feyPJ831rtEhHTd268lSyLXaoM9juTdx/sFaKpZncfniyR1iYwqkzQUho7Ht282+cypCnOlFOudEX4YcqKaYTxjUExr1PoWhbRMypB5MJ2DCF5YjFjvOsyNpcnpKq+vt/mTi1tIIjx9bIzxjMZrfYeu5TCwXGRZJAoBIaQ1cNjuO6y3h6x1TKZyCfwgQpZFjo1lSKoKrhex0R1xfrVNxoijKH4UkdZltgYuQ6+LLgo8c6rKfTM5NtoWl9b6+AEM7YAwjJBFgTOTOa5s9XB9lWu1Hs2hSzmjMZ41CIloDCzyaY1zMwXmy8kdqj4oGSpDKySTUGmPbFRJJKXKmJ7PRnvEatvkwrrCeFZHEkUOlwwePJRnrpREkQSu1wfc3OrzqeNj6LJErWfR3+GVrvUszq90CKKQ/shDkAQePZTn4UN5vn59m9fW+swW07SGLtdqA2YLBj//8BQ9y+OlhTZnJtNUMwbLbYt6z6YxdGgMHMrpOBUeCQJnp7J8/FiZvuVTTNxeELB/A7JrJ14Y0h15nJnM7r0vfLgR+x+FaO0Bvj/4UbWVtwsseUG4F9SZ2skA1Hr2XbN5QRg3DE8VpXtTmO4rM6r3bAzAustxPjByIZ+I2YcAiKAxsmmOHDa7FuN5nZQmc2QsxenJLCldYqExojVw2WiPGFguz17bxgsDyikVYzbP0PLojByWmiOymowoCQguPL/Q5GZ9SNmD/9vhIpVcgu8utcglFOaLCXojD0WWefpECRBYbIxY7zg8Pl8gbygkVFh2XJ6/1eLMZI5/+MQhAGzf57X1Dls9nTOTWRpDh87Io5zW9sqpzi+1CKKIckJHEuD1jR6WH/KJI2Xapstr6z0Anj5Z4Yv3jeMHIVc3+7y01MYLA3qmz+mpDD99/yQnKmlsx6VuxI3afggvLLQZuCFJX+DMVJYzk1nqO1pAr612CCI4WU1RTmlMFhLkDYW12RxBEBIGEUEUcXPb5KXFDhAhiQIpRaLv+ryy3OEnz/7ojYkfdhw4Az9GuNvC9G4iPO90jCyJFJJxM5au3p4ZUCSR7sjj0mafclLG8+BWfYCkyChi3DR6opreqyctptQ9cbFySqOa1Vlvj3j2ep3+yIsZfJJ6HFmpDTkxnqLetfiz1zZoD11OT+WYzhlcr/cpJHXmi0neWOsx8kL+zgMTzJUMhpbH0vaApK4yU0pxspoll5DomC6dkcvpiTSKlEOTRMopjePjWVQJbjSGLNSHWI6L60e0TYe1jkXakHnkUIH1rsnXrtXJGiJTGQNNkVhsDrA8HzESOVJVGLkBm5bDl07MkVQluiOHju0zlYYnz07xv7+8wmDk8cpKi7bto0rQNj0c30dXEhhanC5O6AqT2SSqImO6AbOFFK2hy8DzuVEfMl9K0rd9oijA0yNSukI2JVNIqpydyiEKEkPHJ6Wq+BGsdmzyaQ29ZbHZt/ij86sMvICsrnJyPIMfhHx3uYMXhqQUkXYUkdcUdFVmSpUpGHFWYTdin1JFJgsJjlYzLDWGdEce52aLVLI6zaHDesekbweU0xoPzuT37GjXZrKG+hZ+5P0bkN0Nwlrb5DsLLYC96/yoRWEPcICPGt4usFTr2by42AYiPr6z5tzr+K4L12uDnebiu28Q969bc+UUuhjTSd+JUQB2AKV9S1RSgQdnChzKu9R7Dpc3BpydzhKEIds9m8/fN8lfvbHBV96os96z+OSREkdLCUw74JXVDrIAlh+R1iUaQ49KRkcWwI/gRCVNOalw9eo2lza6bPQc/uzCJvNjST5/usojkkg2odAaOtysD8knFE7vlDw+e63OpfU+IT5+EHK4nEBXZVbaFn4UcriYpGW6sShZY8ThcoIHd7Kza+0RiiLxk/dVyadUTCdgFIR86ngZeUc0LAhDmsO4B2K5YZI2FBAEHp3Lo8oiLy91uG8ys1f2udAcMfBiBsBrtX48Lx/KMplPoogiiiRi+wH/n+8sc3gsxf3TOcopjctbPV7f6JA2FJa2h7yw0KZnucyWkhBFhETYjsdyY4jrBRyvZvfY6w7w0cKBM/BjjndTOvROx0wVEnx8ZyO3e/x+x+HMZJZG36bes3itC/61bQRBJBIiHpkp8PBcca/U6PH5OIV4fqW79/dWzyIIIxKKzFTW4L7JHH4QstmzkUWRC6tdmqaDLstossAfXVynb3k8cqjAF+8f5yuXtrC8kKtbPdbbFmudEfWhTSGhUcnoFNMqGV3iuZtNWkOHI+UU1byBLEromowqwdGxWK2xktaRBIGErpJQZSbSGtdaQzw/xCdkYLs4voiuKoSOy1hSQ5Z1rmz0WKzHqr2SJPCtKzV6boAiwclKGkNpUDBUiimNjulhBwHjKZ2kpuAHAZW0juP53Kz7aLLAWMpAESMWGgPGUgr3TeVY71jUBjaWG+AEAUfLacIARr6PLgl4osKRsQyPzBfQZRlJhJ7lMZ7WqGQNICKrK9S6NiM3pD/yeXAyx4MzedbbI7KGQhiGRAiUkjoPTmf3Nv8PTmepZg1kSeQ7C016I2+vfrWS1fn40fKeY3dhrUtSlfca3XbtZLcHZLc8zAtCWnbsjCLeXmawu0EoplQEIG8od73GLj3oj0vD7wEO8H7wTmPkztfvlfHYLQc6N5tDEd9cE+51fE59s0H4nUr+dp9TZWJxkh3oQLjvKUWM6UgjIJWUyWoqnz89zp9f3GC2mMQPQ/704iZ5Q+GhmTwJTYFQoJLWWGmNWGiO6AxbdB2fx2aLzBaTPDid47urHYIgQJQ0rtX6HBtLU0rpbNvwwmKb2WICQYwoJRW8MGS5ZTEZhpxfarPQMHloNo8iivhByERGxx+PKKdVZgsjPnGkTGPoEIQRkiBycjyLrsrYrs9ya0Q1G5Mw7AbMTo9n2OpZLDZM2qbLXDFF1lC5Xh+Q7cXZ8OXOiOdubPPXV7Y5O5nlsfkiHz9e4fW1DpmEjCzG97Wa1VnSZbZG8M3rTV5abmM5IZ89XaE78mib8Z198VaTlfYQTRb4uw9N0hm6NHoW313psto2KaZUwigiiiJC4j6fU+PpWPl4uY3pwNWtHn97fZv/5YnUezXRA3zIOHAGfszxbkqH3umY/RP9/iaxalbfm9CfOTPO8nYfbw2eOFri+vaQK7UBN7aHTBWSO1eKI8u1vkXDtHaap2w6I4/5YpJCUqVvBzuS8lm+uDNZ3jeVYTyjMfIipos66x2LN9Y7LLSGnF9u4/gR+aSKiEjfiWv7ZwoGiiyx2hjS6Dv4noKhSARhQMt2mZNTPH2izFrX4vX1PlOFBNWsRimt8mS6yJWNAT3bpT10GIxcoiCkNYz56McyOhCx0rBR8hJnKzm2eg7tgYWuKUQe1Ecerb6FqspIgoTVBac14sGZAgPLJZvQMGSRl1farLVtpgtQlDVyCYXPnCjz0mKHFxYbWEF8z4+OJdEkEUWRyJczVLMGx6tprm/2Cf0ISwgpJDWOj6u0By6fOpknCEO+eaPJet+mNfJ55lSFkRtrSbyx0eXUZJbm0GG5MWSykGCunOClhRYJTeK+yexO83CNnuUxXTDQVJnj1TRpTcJyfL55rY6iSDx5uLTX1GZ5Pm3T5cR4iuPVNBdWO3vsQLu41Yhz/L7vszmCet9BloO7lhkkVJlq1uDFxTbyTp3xnc7ru3F4DxyGA/ywYL+T/EExKL7TGHm3Y2i3B+j0RPZdlUdJYrx+3GqYe6Wi93q/3efsfaJjIrETsJsoCAFRFBCIiABVFGgOHV5ebLHUsqgNXE5UUmQ1haVtE8sNeGAmRykTkyGsNEc0BhZDN6ZwPjWe2ctornYsvnmjwfOLLQxFRhJg6PrkNTg+lqRlBTT6Dpt9G32rT20wQhEjurbHyPOIwthRemmpTWfk8sR8kbMzeVo77ELr/QGPzhXIJ1UaQ4djVZW1tsO52TxThQTr7RHfWWjukC8Y9Gyf+XKsISBLIoWUyjev1Xmx1kOIhJiwI6lRTmlM5Q1ESeR6bcBKy8J2QhYbIzSlw4MzeUoplZEPc0WDnp3mZt1kqWGiKBI5XWarZ5FLahwbS2O7Ec/fbNC2PJZbFmlNIp9QeHS2wNFqmiubA6ppla2Bw2QxgaFIfOxIhZdW6tR7AYv14TvaxQG+/zhwBn7M8W5qWu9Gq3hnKdAu9jsOd5Z1yJJIORGzzdT6Lhld4dhYaq8W9PH5mEFhpWUhIe6VjWz1NBqDmMe/kBBvo0i7uN4HIh6fjxkKbNfncCnJWnfEyAlIajIzpSSlpEzf8XlsvshKc0BCkVlujUioOvdNpTlUTPFppcRfv75NLqmw2DJJaBK+H7LVs3h5qcmry300VeSzJyt87kyVi6ttnm0Ocf2QXugQChGFjM7//NgheqbLn15Yp5LRmC2laA4dbggRAiGapqBLApmEii5JRIRkFLCDgPWOTRhGWF7IVD7ByUpcojOW0qgPbFKaysgN0VSZUkaHKGKtbdIZ2kiSiCQK/OT9ExRTOltdiwsbXRKqzDMnxzg8luav3qjx0nIXVRbJJ1VSusxkVsPx4zKdp09WeGWlzVbXggiubA549mqdn3t4Goh4fb2HqoiAgB9FXN3skk+oZLR0nNZe67DattAVuF4zcb2AmYJBEMY20ho6tAYxJd312oCvXa3znRvbiKJALqlydCy9F/33PG+PinaXK3nXvvZv3mO82eS622Bsuz5LjeFeKdrbObw/TgxBB/jhRr3v7DnJH5QWwN0CPvtr/9/tGGqZLsWk+pbrvJ2jXcloe5oLb/d5dsd1b1+J0O6f2s7fHrA2eHMuqPU9GkOHjx8pYfsB313q0LY8ZooGjaFDIakQBhEDx6PddwjCAF2RmMgmePJwgbGszuWtHrWexXwpyVpnyNDyeWg6y88+PE29OyLYgP/pkRleWulQ6zmoosBCy8S0fRa9kKQsMZ5Jst62We+YTOQ1mqaDH4Z7a+suK14xpe41517f6rHUtPnCfRWO7awDa60RQRCRTSiEQcixapqB5eOFIa+vdlhsxr/XuZkcxbTGRnfEF89U+OSJCgMrLkl66FCOQwUDBGiZLuvtES3TQRVgoWnywHSOUkrjyaMlLDeeR19a6jBT1PnYsRIvLrWZKybxGwM2OhaVjMpkLsmTh0sMHZ9zO+e3rm9zfWuIH4aYvo8uiaSNaK8x/AAfLRw4Az+C+DCjnLubpt0mYX9nErtb+riYUskacQ/BblTDssHxfHqWx5NHCpydyXNpo7cXTapmdR6bK9AcOlR2rvngTJ4Lqx1apsuJSppqNm5armT1vVKiqUKCpeaQP7m4SSGp8sBEnkiApKqQT/jYXkTPsskbMtdrIzqmjSpLjGwfWRLpjAJM22V75JJNKgwsnxcWWuiqREqJOZa3eg66LLLVs2kObVqmx3bfoTV00BWRKIpQRQlz5HP/VI7nF1p4YcRmz2S+lKLRs9kajPCCOGIjAseqad5Y7xKa8IAq84nDeTRVYb1rM3R8uq6HrkiM5wy6to/leSy1R2x1RwQBtIcOQRBRLqg4jk/b9Gl0bc7NFkjpyo49RPhhhO0HFDMqRysJjo6leXmlw8gJODKWZq09YmDHEaqfvm8cQxVxXLix3aPWs3nuRpNH5gukNJlHZ3PMjqW4stljvWOjSTIgMJnTeXmhxUbX4tMnywysII7qiyJHx+K+kKUmzI0lqGYMJgsJrm32uLIxIGlIzJVS9Gyf8WxsZ8WERE6F5aZJzw44u6+kaP/mfaqQ4PF9tg/QGDrcqA1AgGOV9G3lSHfDjyrrywF+9FDJaLfptXwQUHbm8P3rxv7a/8fni8jvUD60fwztH2vv5GjH763sBZnqvVh4cLf5+E7iABHuyihUSUFtGDcS7yKufowwVJHeyMN0fdKajEicVbTckK2Bg65IvLLSpZzRmC0lmczqlNIaAzsg3InmixLcN5HBDeDYeIaEKjNXSnJJI14HBi7NgYUhCQQRnD2UZXHbZGD7SELEte0RERFPnSgzcgIWmyNmS/F3vrTR43g1zaWNHk4QMp7ROFFNsdV3ye2UQMqSyGTeIGfEfQhXdu5p3/bpjOK5WxQFHj5U4JG5IhdWO3z7eptKVqVtulzd7NGxPA4Vklzd6vP4fIGOOWK5OaAxcGg58PJyh1sNi9lSCssNmS4kuFnr07NcBHTqPY+srjBwA05Ws6y0LZKKhCAIfOPaNo2hw3je4OGZAs+cqmL5AS/cbCBEEAgi1ZzMifH0W367A/zgceAMvE98lMsKPogo572+3+4G/3g1TX/HGbjXe7WGLj0rZqLZ6lkEQQQCdC0Pxw/RZZnW0L0tmnQ3LYNdh2D38+zvL9hNjXaHNi+ttFhqDal1RY5XMygytK24br81cgCBQ8UEn4gitvoWz91ssdwaktYUxjIaIHB0LMHH5wtkDImJQorhyGOzb2OOPBRJQpIELm90MRSZo9UUaUMmbEWEQUAqqdEdebyy0uZarc9kLkHTdKj3bCJErChAV2QePpTnVjNuqq31Riy3TLo9WLqwzumJLE8dLTNT0EnrCn99eYswjCgkYgo32wlZa44oZ3QyqsyyDFGkc6iQYrHZQxAkzCDgykaXQkrj86ernF9p8+y1BvJCg0omwU/fP8GRSobm0KE5sPn6lToN0+WFhTbjeZ1yyuDx+RLnVzucmymw0h3xyFye1caQpuXhhCFXNoeYTsSxappSUuVqbcDA9qgPXU5V01TSOpfFAY/O53l4tkhClVlrjzDdkMfnS8yWY5XLv/PQFLlEnaNjaQ6VU3sp82u1AUdKBi0b/ujCBpYXIUkij87F2aM7Nx77WakgjnjNl5MIO3/XevbbjoU7M2Qf5fF9gB9tvJPtKZJ4m17LB4U7143qvmALcNd5/s5z7jbG3o2jvXudlCpyYa1LRld46vjYW8r8qlmdQxlY6sfnycQ5QQdwApgdU9nYdvfYhtb78Oevb7HVteg7PoYs0x+5LDZNbDdgLKWR0xUmcjqvrcTaKbOlBM/damP6IR87XEaXBb5zq8VYVmMqlySpqTQGDueXWiRVgQtNaN3Y5lptQBBFpA2ZoRuSMVRkcUQ1rbDciSP2kiAiiyIzhQSHdzKgF1Y7fPNGg1p3RN8Oyegi5ayBHwnM7dCFrrVHFFIqOUOmY3kcHUvx1LHyXomlF4YEfsjWwMYP4/6LM5NZgiAkZyhc2+zz4kLMcJfVFLZ6Nq+tdllqjiilNdIqCAIcLiU5Pp5hspC8I7sTUO/Z3D+dYaEucHN7yCOzeY6NpRm5ARdXWyy3R4xnDAgjLq50MFSRqWKSy1sD+o6HKouAxFbvTqWIA7wTvh/r0YEz8D7xUS4reLdRzrczsHt9v3rPZmHbpJzSmCun9tKbd3uv3eds1+fm9hBDEbFCODmeQVNVzkxm9953/2e41+f3d9LWsTZB3F/wR+dX+YtLdWQhIpdUMW2fhhcwtAOOTaZpDBwGlocbhMyXU9h+REJXOWYoBBEEQciJiRxCEPLczRadgcv/eKPOwPEpJHR0JY5EXa3HombzxRSllE4pqfLUiTF0RWSh1mdgR1SyEoWSztDxuLDW5SdOjHGikuL19T5Hx3QGtksyJ3N4LM21+oCCodIaOQRBQEKMlTRvbffZHjgUkhrHKkkMRSaTVOk5PoYkcGm7z3JzyMmJLEfLGT52uMxiw+T19TZd02d+LMV4Vufl5S4CcGVjQM6QKRoSzVHA9fqAP3l1jZ86O4kfhmwPHMIgYiJnkE2qzJUMZEHED+PYW2fkkU+qyJLIRseilFAYzyV5bbXL0bEkTxwu0B75yAI8drjIYsPkzGSWizuZnHOHcnuUdBAzcFT2RSDbQ5e+E4ugHdmXMgewHJeWA5VxnbFsrDy8vzF4v13eq6xg15bfbizcbRx8lMf3AX608V5s74PcJNw5hvZz/d9rnn83a83blaLuUotWcglOVNPYrk9GV/aUzpcaw7cQB/T38YruZgFUIKlJBF50W2ZAAiQxwhVC+rZHqEWEgsCJaoYggq7psNA0eeb0GNnjKkEErueTN2Smduacb17bBgEKhspkIcGsJHJ+qcWLyy02WyPW+nAoiqhmEoiCyAOzeXK6yuWNHt+82UIVQ3JJjZ84VubpE9W4/6r0ZontruZKWpW4uN7bax7OGPJecGPXUVpuWSBG6KrMoXKK11Y7lHbW4vX2iJcW2vRsj4Hl8/TJCjlD4bmFbcIgZhI6PZWjktGZLCSYLye5utHDD0NSisCtq3B4LI0TgKHIe/YkSyIDx+fbt1pEwPXakKQmcas+RJJEhrbLrYbJRsei3rVZ61qEYYjjhXzuTIWsrmC6Lo8eKnJ8IstTJ8bewRIPcCe+H+vRgTPwPvGDLit4u0Xg3XJbv52Bvf33e7Mm8+1YJfZH8oe2RzsI2OzDzfqQh+fLew1n+52Ce32vO1PW52bzXN3sY3kRIhGCCHPFJD9xcoxXVtp0RgEpVWQ7iLDdgHJG56ljZR6YyfPaaoevXq2x0jDJJ1UOFT1OjGdpv7HFGxtdqhmdqUKSF5aa2F5EMaGQ1BRsL86EzJYSjKd1tns2Y1mdE+NZrmx2ESSopHQ0SaCU0pgtJqkPXKp5nal8kqWmhaHKvLLaJpfQeGg6x0JjyJpikc84eAmVge0REtAd2by+GSALApM5g5u1PlYQ0jFtHC8CIhqmTTGtEIYRs4UkUVEkr8lM5xJIooTj+Vyv9emMfNK6RD6hUu/0+Is3tlhqmKQMBSJ4dL7ImfEMQzeglNI4v9IlCEPmi0kWIxNJEOmZLpt9h+migecFrO9Qqj5+uMxUzOhJQpUZzxooksgDM3kEYs7sP76wRr3vcHIiw6dPVG/TAwBojxzayy7VfQrHAK+udWk58NRkhofny29rr3fa4b3+vhvudt0f9Pg+wI8v3ovtfZCbhLdbN+712veqo3AntagXhOiqvFey9OJiCxB4fL6wty5kdWjdzjqMLELfCnD8gP0vZTWYKSZ4aCLP1/rbhGFEJa3y+fsmubTR48WFJqutmN3s40fj0pqrmwM0RcLxBa7XBoiSyIlKClGUqPds5sopqlkDCZFSSsPR4fREhstbQ0Dn+taQhw7lODuZ4eJah83eiGJS4/HDJTqWx1hwe5GTIomMZw2KKXWPQWi9bZJLqixsmzx8KMeJapqhFZMsnJmInYfzyy3+6JUNihmV/+XRWQAm8gbVQNtTEV5qm1za6HO4lOSZM+N7AbxySqPRs+mMXFqmx3rXpO3Apa0ej8+VbrO9qUKCp46VubjWRUDAdHySqoQfRUhRxNnpHMsti5mCwVJrREqWGHkRkSLSNX3GcxoX1jsM7ZBcQn1HmzjIyr4V34/16MAZeJ/4QYvJfBhqwu/UHAxv0oju6gLca8DeWdP9xfsmsByX/7F+gxvbQ6q5JI2hwzdvNG5TXNx/3m4t5ZnJ7G0p60pW5xtX67y+0SOpSDw8W6Q1dChnDCJEPn1inL+6vEVr4DGZT/DE4SKVjM7903nWOyO2eha6JOEEAZc3Oiy3Rpyb6XN2PEOjb3P/VJ4T1RSvr/do9E2GtsupiQxhBH/6+hbjWYOcISNIAooo0rY8JEGkO/QgGoEQcd9ElnxKZXNgc6KcYiKnMpGL7+tCfcBUPsmDM1maQxtRFmn3wQ4cwiBEikT80EMceYgSVNIahiqhRRLVqTxvbHSwfB/VkfjbGw10OU49F1IymwOH1q0GD03nGQiQ0XXGcwI9yyerKaiqhGU6rDQH6JpKOaOhyyLfutUioUoUkw6nJ9MMbZ/Tk1nu32H5sV2fzb7Ng9M5SkmNzb7NA9M5KlmdSxs9tgc2VzZ7SPtoQqcKSf7mWp1bdRNBjOk/d21tl5K0ktV5ZKbAwg6D0G4J2MOHcjw6W8BagbPTub2a5v32ei+8l8XkXsqoP+jxfYAfX7wX29vfl/Vh48PYpOVUOL6vMXn/d4/n/Lgs0A/CvdLQwV2qTKwQAgdyOrgBew6BG4DphDQGDpYXUEgZ5JNxX8J8Ocn/8fIKLdPh8kafR+fLzJeTvL7W5uxkloyhcLyappzSWFYF3tjsY3n+XsnOI7N5LNenuQ5/fXWbjY7DudksbgCvrfUQBSimNTojl9lykpcWWzRMj1p3hOlGPD5fYKqQuI2BCeDLFzao923OTmbQ1TfpoiIBJDEmTf3OQhNdEsinVAxZYqtn8cBMnp84UaGYUvna5S0ub/Y5VDD4+XNTnKjEzsSfXVjjaDXDS0stXl5sExFxuJiknFRpSpDVFEopbS8DL0siU4UED88W0RWZ+XISQ5XwIxCikM7IJ2PIHCom2O6LlFIGRPD/Z+9PYyw58/NO9Bd7xNnXzJN71pK1s7gvTbKbavUmyZIty2PPte4VPIDH9icDgqX7wfAXGRBk2B8MAxf3g2EYI9mGl5nxHXskS61mt1psNtcmm1vtVVmVe548+xL7ej9EZjKrWEUWySKb3V0PQBQzTpxYTvzjfd//9jw7povthix3LZ7MVfjlM5P88FqHb5/fZraS4W8+vnBHm7iflf0gPo/56L4z8FOKe+Ep3mpgtzYHw80v463R/r3B+XbsALfWdB+q5wiCgIoBkiAA7Nc0BnHM+a3hTd87yKoA8MSh6k3y9IkgMF82KGY16jmVUkbh6k7aCFXPaSkv9EqfQ9UMZ2ZKrPQcLmwO+d6lHXZGHg/OFlisZGkOHVpDixeu+CzWU67miZxCMasiyyIVQ2V96BBEMLQDgjAiDCP6VkxEQhSkbAu6KvHUkTqWG+ERkzNUXlvu0hy5rHdSLuidscfSRI7pokEiJXznYhtRECnqMoELsi6jSgKiJLLZcfEjkEWBjYHFA7Nl3DCtCxUFkWbPpSMFjGyfmapBHMdMFDTyqsjFnTFRBE8frhBVNOp5nTfX+szXMjx3vM4Pr3Z5tzlgKm/wrTOTHK3nWOnbmEOPKztjgjjCDwWmisb+b277IY87ASVDQZZEfu3szD7d3btrfW60TfIZhScP125i8Tk2kSOKEmo5hedOTH5AQViWRB6cLyNJqQDdZs+mZ6Wz/WzZQBI+aK+36gjcittNJh+WcbodZel93MdPA/b6svb6qz4uPs4C/9Mu0m53LklM3/Nbz723714T8Y22SRSnzG62f/NxFdLFvweMvYN5a6gVJAxFQpVEpos6syWdGx2b5jCgoEvkVYUHZkp84/QkN9om372wxXcutKnlVE408iQCCAm8uTbAdkMub49QFAkhAUkSOVI1OFYEvZZnvedSNjQeWaiQCGkA5S8v79DUFVoDl6EbcmYmjx8m+FGIE4R859w2XhijyeJ+83RWk9EUkZblUxcSNvoWXgQFXaZoKAytkJ7lUdQ1vnlykjCOudoyEYDHDlVRpJSw4ZXlHooisVDLkTNU/tPrq1zaMfnKEReEtA/AdAKysyWmCypNHU5O5fe1Ym50TUq6yq+enUaWRIZOiOPHfPXkJOc2h+iywItXu9SyRW6IFpdbYwxZ4ivHJpgq6RiawlbfolHOUM+pXG6abHYdvDD6UDu5n5X9yeC+M/BTis/CUzy4EN/LDBxEc+hyfmvI9tDZFXlKbnOUD7++qgYPH63tD/KzlSzntoZUsyrVnLqfmXhnrc/O2OPoRCp1vldH3hy6GKqIkCT8yoPTOH68v//ACTlUU3GCkPbYQwDW+y5nZmChanB+Y4gmS9TyKocncmQ1mcvtMWEQMl8p8PhimXc2h2yNPEZezNAOqOQVNFVirWMx9HzqeY3TM0U2Bw7LbRNBTEgEEAUBL4rJGgpfPVSmnFX403ebdO1Ui0CTRRzPZ3to8/BcDdMLeHShxPmNEY4f0rXhgckMXzvTYGCH/MfXrrNUzpCVFGIx4c21HjPFDA/Nl1luj9mKQsLQxwqgO3RwYqjnHaYLGRCgbTq8eLXDlY7J2ekCgihiehHFrMb/+twh/vClFb52qo4kygRJQmvgkVElRo6P60UkQiqOs7foXu1a/Le3N5EFAU0R+erxCWYrmVSefn3I9e4YQ5GoZVU2+84+i8+D82VmK9n9LM+egM0eTWAYxWz07f0+lD01a1kSb6JQnFWU/YXEQTu8HUvQ7SaTOy1k7k889/HTjE9rvx9ngf9Jz7W3sA+jeF9D5ANBpvHNzv2t1zVbyXCskdIXWweOLZAuYgLSvoFKFjYO0NgnCUwXDa52TEwv4kbH4cx0iYfmK+QNma7pUcpqbA09zm8OeX2lhyqCKgv0nYAf3ejRGnroakpS0HdCZDeklNWoZ1VmygYTBhxbKLE+cHBD9sucvnNum6s7KRVoXleoFjQm8gaXWyYPTBcY2AHvbY2YLmhoeX0/C/7rD82w0bd44XKHcxsmQzeiaijMLFSYrxrcaDtphjav07d8sprMpa0RYfx+hr3vBJycLpDXJK40TcqHFP76QzO8er2DGyW0Bx5H6lm6ZoAuiTx9tMbOZajlNCaLOkdqWdojjyCKeW9jwHMnJvapZZtDl57l4wcRhiJysTnizEyBy80RF5ojho7HL55oIEsi+RN1Xr7aJq9KnJ0pcnF7SN748CzW/azsTwb3nYH72MfBl1Apih+I4qSc/w5dy6ee0/ZVZe+Eu4kE7S0KIW1Ovta2KBoyy20b0wuoZVWWOxa6mprq+a0hraHD9sijXtB54lCVG22TH630QUyQxRzfu9ji2o7JA7N5dCWNZLdNj/PbIzRJ4GQjj+MnNIo6k1mDOEn40tEqlhtSz+mMPZ++6dExPW60fFISpITD9TxfPznBhe0xeUViuqAzVcogLsBq22K+nCWjiuiaRGfksVjL4nghigglTeZ6EuP6MZ6fytr3TJ+R43OyUeTceMxUJcOTh+t859wWCSKGJHGokeNKc8T1pkkYwtmZEpoqo2sKuqEydh3yWYXYiRgHIX0vYLGSJavIdEyHoenTHjucaJRZ69j8++4Kp6cLbI08/tPrG+wMPZ45WsH2YkqGjCxIbIxcpvJ6qqK5OyFfbY5ZbplIQkLOUHhrfchiPY0iPbxQZraiM/ZCBk7Ek1MFZPF9PYi5Sob1nr3PGmWoIt85t83hiRwbfZesKu5H/R6aL/PQfIm313oslHUm9ZRC8aADcGamSCWr3pEl6HaTyZ0WMnfT83I/Y3Afnxc+rt192oXTx1ngf9Jz7S3sj9azH9AqiGJ4Z33A0EvngFt7dvaaiN0wwg1CjtSzNx07gX3mIB8Ibgk6z9dzlLIqbhhzdiaLGyZkDZkwirmwNSQRBOo5leONPC9dadMxffKqwkw5y1I9RxhHtIYeMyWdQ/UcYzdAlmRKmfQYI8dneQjPFDT+5qNzdExvn0p7Z+xxZjpPJauhqjITOZWSoVDNq+Q1meWWxUOzBVRFREDkStOklFEwFHlX6Mxgs2dxZWfMjzcGDLyQxXKGvu0SxBpXmyMuNk0mdkvExAQKhsxba33apkc1q3K4luWV611+eLXNbzw2x/+rcZg/fXeTjZ7Ds8frmE5I347oWQGSCMttC1mWqeU0Hporstwac25rRKNk3MTktj10aI09BBJeuNxhrZ5hvpKlNfIpGSpvrA546nCFq80xf3GpTbUwRIgSHD9mo3dfdOyLiPvOwE8In+di45Oc63YRo1spPu8mrXwwgns77NFCnt8aklVFcqrI8UaeUialQ0MQqBwQsdkeOnhhTCmjkFclrjZHNEcOOV2imlU5PVPE8gJWOiaGInFqOuXxf+JwhfmywfnNEU4Q8dBciWo2y5HJHBlVYGT7/Hh9yOGaQWvk0rF8sqqU1uYrMmIscqie58L2mLc2Bgxsj5Ed8uSRhDNTRRplg9WeRc/yCK52KGdUDFnEi2NkUURSJI41ikwWdEREmmOH1Z7F5e0RTy5WeLAGX16qU8mljBVFXWG5NWJ77JHXRAxd5tH5tCntRtvEckN2BhZBytbKyakSDy2UGJghCJAICSM/oJpXiYCO5dI2PQZWwEzR4ORkju9f2mal65BREhqlHF85XmO973C9ZbHWdzhU98ipIgPbQ5RSlc1GOcNMSeeBmfL+M/nqiYldtWiHq22TvhXw3IkJRk74gcVGNafyf/5ojRevdTjZyPOrD80wW86kDtvY49zmkObA5v9+Z5uFaoZCkNqv64f4QUh7nNA1/Zvs8G5s/uMuZO7Xrd7HTwKft93dzXvxaeeqO+kPQNpALI1TAcmCId9U/rdHu3mlOWa9Z2MHEb9ypvGh59pxICOAIkA2J/LLp+d4cLZIc+zRGjpc3B7z0tUOr8k9MrKEFyY8vljmcnPMYj1HQkJGVZClhJ7jM182ODGVI0jgjZUBk0WNWlakO/a40rI4vyHx4w48vDlEV5TdMssYATD9gKKm0ijpyGLabLzScygaMt8+t8Ol7RFHJrJoiszJRh5IOL8xYOSGHJvM89ihKoYis9bzqGY1MrLI9Y6NHYS8uz4iTGJKukSjrKOrEjsjjx+vpiWbQ9vn8GQeXZWRRYGXb/So5lQeXqjyzFIdWRR5dKFKa+jynQs7hFFMXobirqP02kqP9a7NZEHnwdnMPuOR7Ye8s9Ynp0oUdAlJMCj2bDKKSDmn8eVjNU5NFXhnc8RKZ8xW38H1QzRJp5JTMTSJ2cpPh+jYz1tA6L4z8BPC5znof5JzfdxI6p2OsZdJaA5dGnnlQ/e7uD1i6O6VkRgoSrrAP1gKstdn4AYh373UIiGhkkmpPkduzM7IxfFj+k7A9y93aI3SQXt7aFPN6pyayfP26oAfr/bJGTKiCCttm7lKlhOTOapZlVeud/d7D0qGTiWj0LE9ho5Hc+hRMVQKioiXSZgrZ2mb6f2tdU12Rg5H6nk8P6RjBURRQklX2Rl7zJczPH6owivXeqiCSJBEOEHA1fYY3YP1vsXKj0wubZuESczQjXADh+p0kfmyxMbA4d+/toYfJ5yYyHNmpkhn7PHgbJGxHzNXMqhkYqZLGu+spenYh2bKZDUZywuZKhksTeSZKGR48nAJQRR4/sI2A9tHVX3W+w5vrvYZOmkJUwJcaY25vD2iPfZRVZGJOOFrp6YoHkj1ypLItbbF0XqWkRvy3m4kaW/BfrDsbKNnE8YCM0Udy48Z2AHHJmXOzBT5/sUd2mOPpYk8f/3haQxF4pXXr/PO+pBz22N0RaSWVRnYHus9i4c+REjsk9j8nQSUbvf5z8PkcB/3FndjP3cadz+ouP354dPOVQd7ffaoQmVJpJKRiBIoZxSsMOHC5pCVrrPfh7anaHy4nuXRxTJ9y6eW0ziSh+Xxnc9nJyAnkElEXriywyOL6Rj43sYIKwqxXB9dkTk+maegS7y23KWS15gpG3zrTIN31vq8er3HyHXZ6NsUdZX5io4ADCwfP4xpDhzqBQ1NFsnJ4IYxL11r4YUxF7eGHJnIs1DOkDdk3l4fUjDklMJzN9iV12VeuqLgRaDKCXMlnfWBQ8cK2BzaDJ1wn13ticNlgjCgY/m4UcxzSzVkIdVjaJsBm4M+h2oGXctnYPlsDh1aI48jEzkmizoPz5WI4phD1ew+RWnfCbiwOaSW06hkVRRJpOdCc7XPL5xQySgCqiKyWDeYyhu8udJlsmjQHXv82Xs7KArIgoiuiqiShOUnNCSBTF5n7EccqWd5daXL69dTOtKKoaDKIpIoYnvBnR/eFwg/bwGh+87ATwj3qlb5bhiAPsm5Pkn5xO0+y6sSzUHKOPBhxzozU2R7YNOzPZbbFo2iwZldReKDKpRhFLPcsVhujyER+NLRCoYkESYxI9djZ+jQt0POzhS5sD3EUGQO1ww2ew4vX+txqJZh5AeM3JDe2CenSAQR7AwddEXipZ0OxycLPDYnM13WcIKYK60xIyfivY0Bh6o5BBEu79gookjX9BASgb7lpQ2+UYIoCPRsn7Hno4gSjbxEEMfookR74GG6AVGSsDVyUCQJTRSYzoLrRby22seNIn7hWINXr7cY2T5xHLPRcxjYAQVd5shknsVKhnJWoaArGKrMtc6IrCozWzbQFQk3jBGihIHvc2gyx4XtAWMr4ktna3Qdn+WWSTmjcapRojv2+NLhKuWsSmfkU8goxBFc2zEpZxSOThY4OyOw2rVZ79u8cGmHXz47c1tdiMmiTiWrUjYUNno2l3fGRFG8zzIEYKgi//Pj87QtDzcIsf1UmK5vhxypZzjaKHBypoTteqyfh3pOpaArFHSZkRvyJ+9sYwcRAuzXyN5KTVvdbQD8ODb/UQJKP2+Tw33cW9yN/dxp3L1JeOsOQZXPCndinfsop/jW/faoQnuWTyWrsVjR2HHgF4o6uqbi+iErXfu25z34fidSyqhzJ+QAE3C8ED+OOb8x4Gg9x+nZAtdbJr2xh+X6BDXIayIrXZuRG/DM0Rpd06eYUUBMqOVU2qM0OHV0Is/6pRaml9Yh9a0Ix3cQBWjsPq4bHZN6TiFBRBYFZEliaKVjfUGTud62sfx0kX9yqkiSJPzhyyup/k7QpWioVLMKs5Uq57eGXGuNWelaXGsNudqyiBMoGSqzpSyLu/SmGwMLEClpEtWcytNLdap5lbfXByzWsvzZe5uc2xyxUMsiySJ+EJLNGwxtn+X2HgV22vvV92E89LjRtrB90GURRRT5v97eYmfkcryR56vH6jw0l2fsRVxujigYOicXSlzZsVisZVnvObRNj7wuYcgijbzGpeYI048Qg5CcKlHMqh+wjS9ioOXnrZ/svjPwE8K9apL5KAage3mug+e73Xlu/aw5dPmLy212hi6NUoaHZwvA+w1jBxvKAGRJ4nA1y9JkKld+cKDYo187UsuSUQTiOCGvKWx2HURJQBIkjjXy6LLAWr+DEMesdW3GbsgTh6ucrGTIaBJ5Q+PYVAHbDRm5EYqsMFFQeWu9jyKKOGHMUj2PqshYAfhRgixIFHWJKzsmXhDx1JEJipqLGQTYXsThiQwt06GWU1OKz6xGzlAoGyV2xg6yLKAnMusDi1EQMLJDjk3k+MUTE7x4pc1bqz3GEeSmQ5I4ZipnUM7IqKpMMRF5dL6GF7YQhBhVFvDjiJ2Rx87YoTn2KWgSsigydnx2JAFVNpgpaZiuz8WWR0YasD30EAWB5eaYcRghIQAxc1WDbz3Q4Omjda7tjKjlNOZrBtfbNqIo8LefnMMNE3KaxPbIRxIDdsYef/ruJieni8yWM2z0bTrjtFY2o8rMVrL8eLXH9sBCEKBeyDBb0PfZMh5dLKOIIooT8MPlLgDdsUd75LBQ1d9f0Gckqjos1LLkMu9/3w2j/SjhpeZ4P9J4kJr2RCP/kUxCe9j7vGDIH0rT+PM2OdzHvcWnsZ+bKUTThfDtGm8/Lu5mEXYn1jm4M9vc3uL/g4rG1ZsyAxczMFM2yOjaTRoDt573oJO/M/igI1CToROmImOaBraXliCNLJ+O5bM+bLPeseiaPo8fqnBqukAtp7MzctgZOQydkD99Z4tiRqVnpuQTQQSVvMqZmQJvrvQZOiFzZZ3HFio0zbTsSAKiBIZmgBdG5PQs85UM3zzT4M2VPm3Lx/YiTjQK9J2A621rn5ihOXLojX1mygYPzZVSmmo7wPUiJFHgh9faXNgaU82pPLFYZq6a4eK2SRCnv4UsiYSxSNGQudSyiOKY622LxxarHKrlWe9Z/OBKF8sLeWiuRNf0+OG1NkdqWb56YgJDSZd/K12HKAop6fD06UnqeR1JFhES2B451PMqlazE8cm0R8yLYL3nsNqz2Rm7SKJAnCQst0xURUYG3l0fsdw26Y1dOqbPe6t9MoZMkqQMebdbK3zRAi0/b43M952BLwg+qWf8UQxA9xoHJ6Vbr/nWya5R1PnmqUk6pseZmSJBFNF1U8XJ1b73gYayjZ7CcjtgaAds+h5BnJaRlDIK7XGq1LvRt7jRsZEEkZwucKk5ZqFiUCuI5FWJjuXRNX0KisSZ6RJnZouEYYzlxYSxQERMo6jx1sAhq4k8d7TBu2vw4nKXR6dzzNYyPDZf4a3NIXGcUmK2Rz6nGkWGbpDKrRPzlRMTnNscMFPOcHK6yHrPJREERARaZpqdGGVDlho5NvoOuiQgqBKeH6OpIhtDh2JXIY4jwjgmjsHxApwoAREa5Qy1rEY7cSlmZOp5A1kS6NsBthuyGphkNRnHC9AkODGTZ61vszFwWGlbCBLMlHSGXo6x66NIAllN5tzOCFEQUAW40bMJI4HFapau6dOxPNwoppbVqOc11vsuyy0TQ1MII5l6XuOxhRJ9O+CV5S4Xtsb8wvE6b60P2N6dnJ44VKWaU1npmLy43KGkqfz1R3KcmSnuswkVdZmVrsNDswWePVKlOXR5/UafBLjesRk5IZIkcnwibRZMB2UN4CYa273FQxjF+04B8AHNgI+aaG51qO9E03i7xckXKZJ1H18sfNq+lYM4SCG6lxnYGXlc66Tts5/0uJ+0hHSPCSyI4jsyAN06HxxUNAYIgoCqzv73P+z32aOyXqwa2Lf5PNilIFYFqOQVurulKG+vjfkbj8rkVYlzTh8/inG8iFNTRf7s3S3eWh8yX82wWNUoZjV6Y4erTZvHD5c4MV1ke2izvGOyPfRYrGZ4fLHCa6s92iOHtZ7LkVqWwIa47zBVNDjeyJEzNNZ6DqIkMpnXyCgyuirzeKPAXCWL64f88GqHRlHh7FyRB2aK1HIaHTNldFvr+pyZLnJ1e0x76PHIfJm/8dg85zeHVDIqAztgc/D+/GmoItsDm7yh3UTaUDBknhvY5DIKhyo5wigmShLe3hxxeqbEqaMlgijmKcB0XP7HFfDDkDfXBzxzpIYsiVh+zGReY6XrsNq3kSWB2bLOmZkCx7ezXNgaY3kJXhjRd0KKJKiKhO37FDQZQ8ww9EKGgU/TdPCimCj+oGP8eQZa7o/dt8d9Z+ALgk/qGR8cQD8Jz/THxcFJ6aAQzKF67gODuSKJLDUKLO3+faNls2WnAjJFQ2ayqJNRZWw/5NzmME3PkuCGIbokcn5jwJWWxdNHKpAk9J2Qla6D6YVIosh8LceNjsO1jsnFHZNrLZtfPdvguaUqeU1moZajbXr8xaUWYRgxU8lwZrpIEMdcbproqsSp6bT0qKLLBHGC5cf0vYAgiHhva8SXDlVZrBn0rZBfe3CGdzYG/PBqG0OVmKtkeWi+xKMLFQTg3Y0hKy0bSYaeOaDveHTGCkGQMFfP4AcRuiKTUUXeXh/wl5fbDCwXWRbpWfDaSh8AK6Pwwyst2ruOzZXtEc2hixsEVHMaEgJbfYe26eCHCSMnICvLXOuYzJQzdEwPP0qYKek8d7RG3lBY7ZpkNYULm2OudUYM3IDFao7FqoEoivzRy9d5dLHCZEHDCmJqWRVFFhi5EdW8hheGLFQMHj1UpWe6vHClhaFqbPZtjtWznJjK7VPAdk2fxXqejCZydCLPk4frdE1/n02obCisdG10VWbWUOnaAU8dqXBsIs/ACejaAZWsymQhdQBujYAeHMz3apFlKaVCvbwzpqin78Eefe1HTTSfxKH+Ikay7uOLhXtpIzfZcJyWqkwWNGRZ/lQLqLtdhN1uAfXq9R5P8b6DfrvF/633/WG9Dx+9SEuo5TQUUuaggxjulqHHCThBQhawAEOE5fYYP0yQRJGMIvDW5hD51VWaIw83jMip0j5N9cA0WOs7RHGCJApc2jZZ79qcnMrzKw9O8/LVDqsdi52xhy6JGDJIEoSKwFTJQBYlFqsZZEGgntOo5FQuN8dM7t7TXCXDjbaJH4UMLIEvL9V4e23AW+sDuqbPoaqBHcUcFg1mqtlU5PNYnQubQ662TI5N5Dg1U+TC5pAwipmtZHjjRpfXV/o8Nl/i9GwJ1w+5sjOiO/ZQVZkgSFjuWByfzPP1Uw3+/N1tVjsmD86Xyagyh+o5Xrlqca4H/nKPat646Tm6fkjH8umPfa7GCYaisFjL8+uPzPPQnElz6FDMKFxrjXl3fci5rSEJAqcbeSRVopxR6YxdTC/A8UK2+/Zt1wqf1zh6f+y+Pe47A18Q/LSUIBy8zo2ezYfVbt6KSlYhI0EUxyy3bOo5jUP1HOc2h7xwpc0zR6oca+S50hzTczziCE42ctSyGtc7NnlN5PHFCTqmx1rXIafKzJQN/CChmBGRBJmVjs3IC9keeRyZLHCskec757YZugELApyaKdIauvztJ+fZm29eWx0QAW6csN13AYGO6bLStUAAPwgx/Zi/cmaKiYzGjfaYwcCnZ/rUcypTRYPNvsdGz6bv+ORVkelyhiRMsPyQo/Uc+YzCj1bGJEk6oemaxGRep59RKOkK510TURao5wziKKJnJSyVsxiigCgKxCTYXsRDs1mmSjqvJz38JEKXJMZewMZgTE5XMSQRL4iI44jNoZPSoOoSqz2XalZBEBI6I4+B7fG/fnmJB+dK/H++d5WNvsOJyTx/+4kFNnoWF3fGkIATBHhhzIuXu0wWVRbreb5/scWNrg0JXG9b1Isazy3VeWN1sC/SM5FTeeZoleu7ZWAHF9x7pUJ7f5+eSsvHZncH5tSu3setEdDb6QzsOQVt0+NKc8xK1+HZ3e0fNdF8Eof6p+V9vY+fHO6ljdyUldp1Bg5mzO7FcT8Mt19A3Tz2302f2Yf1PnzYIm2yqHNkIsdMJYPGB50BmVR8TBJhaIX7WgSJABsDl6mCwROLVbww4WpnzGTBYKaS4dLWmNWuw8tX25ycKtK2PcZuyA+udqjkVU428kwVNH7xVIN31vt871KLxxfLnJ0p4YQh760PyHpwqmzgR/DmyoCYGD8UeOpwhZET7gfP9ui6DVXk2s6ItuVTz6q0xgGPzhcp17N4UczIDgnjmNNTBWZ3x7srOybrfZvpos4Ll3boOQHLbYu+E6ArIiMrbTAe2AHLLZO+7ZNVZQSSfU2E2UqG7aHD2I14+Uafw5OFfbrQU9MFHqzCLz08jaa9XyY5V8lg+yGyIDB0AhISHjtd2c/CypLIxsBDlkTGbozlRRyfzFPKKpQMg+bI5oGZMu2xw/fObeNG0By4H2lvnyXuj923x31n4AuCnxa+84PXOVvJ8KyUKid+mCIspJRk37u4w7oJl7ZNdscSgH3asjMzRRRJJKdJvHy1g6gKnJwq0hw5rPVTHv+8rrJYy6GIKb3ZnvgKccLV1hgEgbKhIgkhYRTz8tU2bTt1LLpOwAuXdhAlkYm8zvFGnjdXuzw2X2ToZKhkVPwYFqsZrjRFNnsOYRgxdELCKEEWBTRNYaqYpWs7NHsOP7zWZaqYYbaawbseY3o+QSJR0FR0TUxrSy2PGx2Trb5NKaeiiBJm4BOpMlNFg0fnC7S21plsFMlpMj9a7TF2Qvp5n6Ku8sBcCUEQeGejj+0F7AwFhl5ANaNxeqrAC1dbmHbE0qTMtulCApP5lPd/e+zQtgSiBLZHAUGUgJAwMAN2hg7dsgFC6qgVswqTexzSI4+LW0O8MGajY3Nmpsip2SJhFPOLJyfo2z5PLJT47pUOqiRycXOIE8bsDDU2+h6Q0LN8LjTTBuI94bF31vosdyzmK6kD9dThyk1qxI2iTtv0UnGyJC0TyusSfhBiqCLrPZtqTt3XGdjo2fvf26O+refSBdLd2OW9eA/u4z5uh592G/kwdq29sf9uIvw3OQAHjhMEAV033V9R0vc1p4q4fnhT+RGkGeme5XNuc8jt9GslQBDAjIEDc4sswlOHKmRUiROTBSRZRJMFrrVNJgoKC7UM2wOb5thjvd8kiBLiJEYRBVoDl+bYQ5QEeuau+5GA60fU8jrVvEpn7LHdTRWKT00ViZIYTZHZHJps9C0eXaxyopGnmlP3+95aQ4fzW2N6lsf08UmeOVLg8cUKK32HIIjwo4TNvsfRieJ+ZnNpMkff8Xn+/A6SlDoa9bxO1/IJgoisLiMLAscbeeo5jSCO6Yw9enZANaOk26KYsqHwjdN1ylltn5pblkQm8wpHCpDTVRBSdri9cfWdtT5hktKOWn7Mmze6KIrMM9TY+1FqOY0EiJOEnCpSK2iUDJVrLYmcLvP8eYsggpwm8OXj1U9hlXe2tbvFT/t7+VnhvjPwBce9TmndbTPl3Syg9l6q9Z79odcYRDHfv7jDq9f7bNmwOrB55kh9PxKcUeV9GsqCIfPGjR5bQ5fFaoaxF/Anb29TL2gcm8jRKOpca435b29vYCgyi/UsIyek7wSQwJG6Ti2n4YQRP7zaxvRDkghOTeXx4oTlts2Reob22OPS1pDLOyZxnGCHIZVswJnpAmGcMHIDHl8sc7iWZeCEbI9czs6WODVT5LVljUSA75xvslTLUspqrLZNWmOXIIqZz+d4YrHMxsDj6GSOKztj1noWsgRPH66z2k7LmiRxzKOLNa61TM73wNEtpssGCxM5BmMfMwgIo5ih47NQz9EcufS8gO2xS1FXKGdUlqYK9E0fJ4w4M1vkv7yxjhv4xHFCFCdoksqp+SokMT9Y7uJ5AQVdwnIjVnsW3zo9xSPzRTb6LlsDj3fW+lxv2zxzpMrZ6Tz/5Y11zjVHaIbMdDXDX17pMFPSOD5VpFbI8LUTk6la5tU2OVWhltWYLaeL+Mruoj2IY85vDalkVZbbFkMngIrBXmSxUdRxgpD1noUThPvlRHtlQld3TC7s2peqyJxo5PftZa9fYM/2DtYl32qXd2PbXzTn+z7u417a5Mc51oexa33YgurDegcOfm+j+77C+CFdo2v6rHSd/RLCW5XC92iqVSGlD92DTDqShLdJUueNlNntT97t8dhCGtSo5nU6lstfXm7jhQlTRQNNlvnaqQm6ZkrPOXYDzm2P8IKYRik994NzZcZOiB8lRFHMg3NV5koGf9q6TJDTMd2QRIBmP81iXm/baMr7c9veuPbYYpmdscO1Vjre/0+PzwMw9iMO17PUm2NqOe2mcqvHD1URgIvamFpO4eunpwBSzv+CRhBHmG7CzsjFUNISXEUUqeU1OmOP89tDLmwN6dsBkihSMFTe3hjRszyKhsKRmkHXhcvNMcenihytZ1N1+J7NctvC9AMeXCjRt3yutS0832Eyr6ErIg/NlwCo5zTCiZgfXO7w5vqAyZzG1bZF13QxHZ9YgLGbcHl7xJePTX2o7d0tfpIsWz9ruO8MfMFxr1NaH8UEcatk/J0mjw+LGt0uMpQIAl86XKZkrVHPajSKxk3H2yv9aA2dXXq5NL35ztqA7bHLialUhEWRRK42x1zv2CyWMxQ0ia2BgyAkPH20jiKKvLzc4VprxJUdC1USMDSZ6x2LRl6jUlRZmshzvWNhaDJH61kenC+x0jG53rE5vzli7KZpXUORyBgKTyxWMHbGJAL0LZ+1nsvJ6Sxn50s8Nl8mCGPsIMGPY0qGytF6hoVqhnfWRzxzrMZKx0ZVJbKKguMF9B2fUlZGlSXiJOFic4wZgOP6rHYTfuOROWbKOn/yTpOVnsWfvL3Jg3MV/tpDM/y3tzYxMhIiAmtdk//0mk05o5EkMe9uDDg9medHqx3aI4d8VsUOoef4REEMSYIgpCJvJ2dSRclEAMeHvKFQMmSymkTPcVmo6iAIJIJASVdYqmVpDV2uNMd0hg6H6lnmKwYjN0QRJSq6hhtGOGHE2I843sjT23VS3l7ts1DL8NhimTCKKWdVZEFgrpzdr+sf2AEvLXd55kiVE7tsUns4NV1AkmWON/L7QmYHS4PkO0Qob7XLu3Gs79eT3scXDffSJj/OsT7p3HM3vQOQ9jxMZ9h3+lO2ocodz1nPadRzGreSCVU06HipQ6AAGQmGu+kDP04Yjn12hjaXmwKljMpUUeOh+TKXtkwmczI5TaI5chk4AZoiUcqpCAIICFSKGmVDoW8HjJyQZ4/V+f+9sUZCmi2YLGhIAjTKBrEgMHJ9OqbHQjWLrqRCintljycm8/sBsF9/aI53N/vpAn6XfGHohFzdLXHcmx+D3QU5pCWukiRyZqZIRk0F2pY7FkM74OR0juZuNmJnGLBYNRi6IVEUgyAgJJAIAofrWaaKBpNFnXpOwwlCru2YtMY+0W70f7Ko0zV9LjXHLFYMFqoGUi9lCDo7V0Du2qwOHf70vW2iOOGBmTwDN6I9cnlkvkwtp+L3Qyw3ojN2GLshlYxG3nRpWgk/Xh98LHv6MNyul+Y+PhnuOwNfcNzrlNadBvg7ScbfafL4sKjR3sJ+o5fqBUwWdR6cLVHNSISr7zA7mYqh3Hpde+rCc3FMmAiQxPzy2SkmCjrPHqvvOw/PnZggjCPKGZVqTuP1G+vEScxEXidnyPx4tc+V5hBJFok0mWwCnbHH1sDhoQTObQ2QRAnHC5koGuR0hVpex/Zj3lrtUy/oTOZ1WmOPgiZxbcfk9Rt91noOUwWNhJgbLQtVFvmLiy0mChpjO8D1Y7pjm4ym0Bx4XG2NieMISRB5dL5CXpU5v5OW03zjxBSaKnCjZfPO9picDIcn82wMfSw3oJYp8thiCdfzeb095pUbaTlOo2DQKOqoisR3zm3SG3k4fogbxIyckGOTWWRZIqvJPHOkzhNHaigi/OByh3pOJ6dJjNwQVRQQSJu0e6bLVFEDQWClk/YCXGmZ5BSJZ49UqWRVrCCmb7vMljTa44ArOxZHJ/P4QZqVWagaXO86/Hilx42ew2JFx4nScqSNnoMiS1zYGnJuc8TJqQLNYVoidFBMbu/fvYmIJG1ky6jyfm3rQbGzj6t5cTeLm/v1pPfxRcO9tMmPc6y9EpWPm5U46Kh/WJmeIokfYBM6yDZ0EM2hy7W2xYlG/gOftbz3/18WQRRhr5ZoYEI1r7NYyzFwfF5ZbvHM0QmOT+X5X55dJIwSXl/tsT1weeVql6VGnkfnSoRJTBQmtC2frYHLYj2H64e8tdpNxyZBYGkyRxBq3BiD4gSIAlhezObAJoxhsZajUVTY6Fus9hyeOFRho2fTHDoM3ZCpYoar3pi313qcaBRYqBps9i3alrNfk59qM/SAhCMTOYZOuO88VHMqR2pZltvWLqV1Sm0NCSVDoWf5eFGMJok8eSTt3zpcz3K9bTFZ1DlUz7Hes5EkkShMO7CHTshG3051dyRww4gXrrTpWT5RDA/OFagYKtcREYWUVvXFqx1kUWCla6GKIvWChh1G7Jgek3mdh+Z0vnGqwZ+fa/Jn57b4hRMfriL9cXC7Xpr7+GS47wz8nOFOzsWtqdzbbYeb+Z73Uom31nfuLeyvNE1WujbPLtXTySEIGPjgdSyqBQNDkW9yOs7MFJkqGrh+nj87v81qL+KB2Zhvnplio2fT2h0EJ4s6U8UMyx2LRIDJgk5OF+jbIas9h4HlYwcRXztUI5dRmClnWW4N+eG1Nq+udNkaeTwyV8SLEna2+gzGLq+vDZClhJET8eSRDA9Mlxg4AbWcxsXmmEZepdm3IUlY71p0LY8HZovYfsRyy6SWUVmqZXl3o08Ux4iigCjActckiATCKKZkyDRHLhlNom15LOUKaLJLCJR1+PrpKTb7Dutdm//v+jW8MCGnizw6V6XruHRsjwdnS3ztxAT/2w9XmC4aNEWXvukxWdRxwwjTDxASqOd05io5lup5wijmK8ehb/pc7Vi8tb6N6YbkDQVNllkbOICAKksUsxqLlSxhHPGjlQFJAlldTRWenQA7hOmKwdF6llpW4+31IVESc3q6wERBZ65ksG16rPVSQbXHD5U5OZUjp8lc3Byy2rWRSPCSZH/C22Mg2msGVoqpLVUz0ofa8h7d4B6b1UHczom9G8f6fj3pfXzRcC9t8uMe69NkJW7X6P9JcXAeKgLDWz7fZRbFidP/9jCRh9lqFkOT+N7FJsKuIJjlx5yZLuL6IT+41qZnuqx2TUQxoZ6vcW3H4r31AaWMytiNWJrI8VrfoWN6HKpn2Bp6vLk64GvHq9Q0mC6q/OBqj/W+xTdOT/HEQgVEgavNMW3Lw/JCLm2NGHkhJHCssacg7/Ldiy3ONUd8/fgkaz0X04lww4hXrrXJqRKzJY1qXkMRxf1+qD0tlccOVZmtZCkYMroy5ngjz6Fa2i+HIGA6AVpe53rbYuiEvHy1zRsrQ9wgZK6cxXR8tvpm2mkNHG/k2R55PH++Ta2gkFdltnbZlb52apLZUpaxG/PYYplHD1X48/e2uXZlzNFKloVKjqwmkdEUjk5kudK06Fk+GTtie2jz1nqfSk6nlLlfzvNFxH1n4D6AO08SdxKcOdHIf6Dx82AjTz2nUTqsoIg3l3BECfRsfz+debCBdE8oKohiHluo7DPRbPRs/vvbG2wPHU5NFzlUy/KDyx2ymkRWkajkFOYrBrIoUsvrPHmozA8utzk+U6BnBkyVNCShyKXtMSExSxNZZqsZ/vzcDpe2RygSGKrMfCVDISOQ0RS+e6nFyckcph+yM7K43re5uDli3vQwVInQSliq59E1me9farI5cjFUgZ4TstpJxckmizoSIrKU8NbGgChJfws/ShCSVP3yG6cmcMOI5sY6f/zWJo8fKnOxOSZOYkwvxFAkJkoGYQJXmmO6ZsBKx+L1lT55XWa+mCGvKciyAAOPkeVTL2T4nx+b5dRMyvrwnQs7FDMKj8yXaJke02WDnulTzir0rYCJnIqhygyciEImZuTBo/NFZFGkYwYcm8jx4HyZt9f6XN0xOVzL0CgabPQtoiShkdd5bbnPbNXggdkyXz8+yavXe0hSGskf2CFvr4/oWSlTUywIECe0TY/FXefyYIPhvh3dVaTn9mxWd4qA3suemfu4j88Dn9YmP833P01W4mCdf3PofiqH5mCWImPA0Ln58ztx2kURrPctDtWz/JWzM2mT7WQON0p2mc1iyobGdDmi2XeJBYHrHZvNnk3b8pgpZfjGqUlOzhR5+WqHOEmYq+hsD9ps9m2a4xxeDG4Qc3lnRHPoEQQRJ2dKvHKtzevX+5ydz1MxFDqWz1I9y2wlu1+Ks1jLoigivhfhhiGHqxlI4LXlDu9tj6jlNY7WCmiqTM9yKOoytZzGQtVIFZvbJrIk0jN9WmOX9sjlqycnUSSRtunhhRGtoc10XkUgzdTkDYmtns1fXm4xdEP8MGIir1Hf/c2ONfI0BzbxbmnRRF7D9mOmijqyJFLPqSQkrHdt/vaT89RyKmemCmyPPXZGPlsDm8m8xpGJHNHWiIHr87//aJ33NsbMlDR0+cODPPfxk8F9Z+DnCJ9URv4gbjc53EoZB3CtbbFQNWjvRq33jiOJUDFUBKBneYRRzGRR/4CQ2emZIgKpJkEQx2wPXEw3omyouGHEStfiscW0hlJIYK3rkggJIydkqZFnppJlpW2TkNAdS4y8kLOzJda6LiMnYmfo89hCifWuyWY/HfgcP6Sey9DsO1xvWVzvphzTGUXkcCXLVEFj5AfICBQ0lXPbQ5YmcyiSTMGQODmZp2cGhHGMIEJz6HCknme6qBMJAo2sQUaFS9tjuqbLj270cfyItZ7Nehf8UQ9RFDBUkZ7pEYQxXhBxfLLAXEHn/NaAjZ6FocKXDlWYLOl0RwG1YpoGzyhturZHydAwdIW26ZHTJFRJ4FprxGvXWiQICInAL52Zwg0S1nojcoaMLgfUC1nqeZ21rkPfCXjuxCQXNofUdqNRU0WDWl5jZ+jw7fNN/CjCDxLkooDlhYRhhOkFBHHM105NMLR9yoZCfaHMg3NFXlvust5z0CWRM9MFhm54kwP5UdSDt+LDGE3u5NzerQDZnT6/7yzcxyfBp7GbT9sz8Gm+/2myEnvsXh+X7eVO2LuPWlFh2wluu48AN+kQdG34H29vMl3KMFFMleG3Ry6WHzJwfIZ2QCWrMJErMq7nqGZV6jmNvK5QzqrMV3PIu2xpfSfgUC2DF0S0xi6iIBDGCXYIoiTy5WN11roOTx6qEuzOWxMllUbRYK3r4vghs5W0T+qttT7bA4ee6TFd1HH8mLWuy9JkjvlqhhcutigaCo8uVHC8AEVMKa4vDGwsP2SxnKHnBGz3UyfrmaM1hATe2xpRL+g8cajKw/Nl2iOX5ZbN9shn6Hhcb9s8fbjC9shjtWNTMhS+cqTG6ekCL/3wOpebYyp5HS+CKIZyRuLhxSqyALWsxkvLHRYqBkKS8N72mHpB5+unp3lno08UJ5QMiY1+kl5HVgUZdtoOURiQJCAQMV82PrUt3Me9x31n4OcIH1ZWcRB3O3kcnCgaxfdVKSeLOicaeVY6Y54/38YNQg7V8lQzElUNHj5aI4xhs+/RNj0SAZZbFvWchiyJnN8a4gchK30bQ5YZOz7ztQwZWeK5ExO8s94npyvM13J0hh45Q6FR0GmPXd7bGlHOqjy2UGajb9M2Xa61TOwg4umjVZ44IlHPavvKtUM35N21PgkCjx6qUDbSCDpCwtAOWO9ZjC2P73ctsppElEAlq3K8kedqy6SS1Tk7kyeME7q2jyKJrHYs5qsZbD/iWnvM0PF5aLbIRMHgStvkSttkYHtUczqqIJDRJUoKUNCYKWV4Y7WP5cYomoQhi9heSNv0iQWB6bLBVCHLZCnDc8dqvLnSI0wESobMfDVHy/Qp6AoXt4YM3ZjHF8tc2h7x6koX14tYrGWIAdMJ+eUHpzk7V+CtlT5t06doyNSzGp2Ry6XtEZ2xS98JeGt9wMNzJUw/RpPT/gNDkzhcze0rPj+yUML2Y/7725t0xwFfPVHD8hM2+qmmgOlF/NrDM7y23E1/lx2Tp47WPsAwclDh+nbxvtupXn+cRdZHRTo/6vP7Dcb38Unwaezm0/YM/CT6YG4VBrzdZx9VBngr9sYGWZKAm50BQwAnFW+/SYMgq0Ilr5LTJcoZDVkScLyAi9tjNvoWmwMfTRZ4YLbIw7MlFEWmUTTQVJmvHKvx2nKXC80RG/1U9f5wLZOyDIUJTx8po8siF7rw7ovLPHeswd96bI6cobLRsxm7EYuVDGVdQahAo1hmtpJho2dzcXtEb+xi+TFnZ4ssNfJc2hpyaXtEHMfYYcSxySyeF/LK9R7/450mxxoFajkZP4xZbtvMlDVURSSrilRyKscm8+QNmbKhYPspCcazx+pUsiolQ2G1a0HS5qkjFZpDfz9L/dihGrMljUtaWiY0WcrslyNNFnV2hqkugOkFnN8Y4oURjy+UGdgBh+tZiobKu+vw+kqfrCpzfCqPtdpHEgUsO8CLIrIZlZLhsdoP+cOXrvN7v/7Qx7So+/iscT+09TOGvaat4CCR/01IPnL/xu5i/naTx0bP5odXOx8QhgJomx6Xd8b7cuiNgkGtoNAd+5zfGrIz8pBEmC0bLNZzHGvkGbohnbHHQZrJSlalb4cQC/RMh5eud7G9gImiwYXNIfWsxm88Mo3thFxsjpEFePxQlW+cnuIXT0xweqZIc+jw0nKX1a5Dx/RBgJ1hQKNoMHACTMenOXLIqlLKxZzXqGc1MprCm2t9fnRjQN8JOFLNI0gSQ8snSRJkIaE98vC8kJKh4voh4yDmwo7JjY5JzVDRNIkHZkpM5HQOV7LkNRU7SBh5ESVd5lA1lYqfyqn4cYTpRXhAQZFp2R6VvMJ8Ncf/9PA8eV1jx/LRFIGlWpEHp4tMFDS83V6FMIZrrRG6JjFbMQijhBtdizdXBihiwvWdMZsjl8VKhq+fmuRrJyaREHhna8ArV9vokkR5d+DvjDxeW+2xMXDZHDlc79gUNJmcJu+qQkNr6DJyAwxZIIpj/DDi5etdvDAmjmNOTeVQJYFaXkWTExoFlY2+xZ+8vc3V5phvnpnC8UNeW+1zvWV+YAF/UOH6dthbVDV3J6i9uuS31vofYvPvY8/xuJPjcNDBuN3xPuzduI/7uBM+rt0cHJc/ymY/Cp/2+3eLg9d863t6EHuf7Yy82xzlztgbG3ZuEa3KSeDuTmsCN0c4VRFkRHqWT9/yUCWBsRuSkPD4oSqPzxVRZfD9iKWJPCcm8/s6J9fbFqIkUsuqFDSFgrFLnVzUma9leOZInUfmy1T0lF8/o4okwPntYVpCGUX0nZAfXOuwMUiDXm+t9XGCENMNKWY0zs4WODlVQJcl+k7Am6s9dsY+UwUNUZQYuRE5RWLg+mz0TBRJZqmeo55PGfl0WcLyYy43xyx3LAaWz2srPd5Z63OpOWbkhHzpaJ2jjQKFjMoDsyWaQ4/XV7pYbsCXjlSZLOrc6Fi0HPb7uPagSCn73LW2xY3dsl0xgaETsDF0+eO3Nlhpmzx5pMrhuoGupXSmJUOj5wQ4cZxSmWoyOV0iAq61xnc1Vt/H54v7mYGfMXxYBOp2ZRV3arS8XcQ1iGK2hw5R/MEXeY9HuaTL+03Fi/UcTx2u0Rp7VA7wxu+d4+H5Mhs9mzCKmSoa+zSTD8+XKRsKqx2TV5e7FFSZB+fLlAyNK80xYRKTRDFt0yejS5ycKu5fYz2n8e5aPxU4G9g8uVhhIl/kcD1DLa/zg0s7vLs5QlVEoggaeTUV4ooTEASKuszQ8nCCED8Q+cXjk/y1h6d48UobgJeutZEVyGc0DC1m7AU0ZI2JjMrbG32O1ws8dajO4XqOrZFLKadwplFge+QxkVe5tO3jhTFhKDDwAsZuSBi4jF2Ixg65jIIiCiiqxGRB568/NM17m2OeWqryzkqP71zYQVdETk2XEEQBzw/Z6Dm8szZkrqQzX81Q1BRGQYgfwaWdMScaOY7Wc2iSyF9cbjO0fSRf5C+utNgeujRKGnGc8O72kK8dn+DJhQrntgZsDj2OTORY76WOQWvoMVnQOdnIcX5rzKsrA545VOHoZI4brTHntk0eni8gyyKvLvdomx4FXeWpI2Umi2l0qjl0+ZUHp6nmNJ49Vt+nzgviGEVMm8MPNqZHMWz0HWar0r5dhlHM2PV5+ZrF6ZnivgDZQZXTD6PC/bj86gdxv8H4Pj4JPs/G3bvFpyldut137yQuZvsh5zaH+9TA1ZyaCnHdJjNwu+MeJK040chTyUhsWe/3E5kRZIBcBnKGxFY3Itz9bNuF+Siia/vsjF2uthSqeY2pgkFRU9gQBUwnxo8S+k7AlCozdENKuowhCQRByJOHq7t6KQnNkcPmwKOSUdFVmYwq8+gE9PJ1Tk4X6NsB7aHD5e00c3GoluGJhQl0VWajb/Ht8zs8Nl9KhRstn3pOY6Xn7BMyiILIwPbRSjolQ+LEVJFH5oo8OFfiyGSevKbsR+vDKKZx2sALIi5tj0gA04tw/JCSUUKSot0MaxrEu962OVLPUjIUXrvR43rL4ex8gKH4vLzc5fUWGMtdjlkBP14bkFElJvLpOH2ikadgyEhiSjfdKBhM5VXeWO+z3nc4OVVgo+ciigKKKDBfzVDJypi2Ty/yCEN4cL5K12wxX8x96h6S+7j3uO8M/Izhw1LCt5uQPopqFN6fjJpDl6EbcqzxPl/yrcfZ0ymQd891U83obRpC96Iwp6dTask9KjpZEvnepTarfZsnF8s8e3QCRRIpGwovXNnhzbUBWVXirz04w+JuydNGz+ZP3t2iO3YZeyFzlSxfOlzD9CNKhsKFrQFvbQ7QFZnH5yvsmC6PzRcZuT5+GOEGIcVMlvXrDl4Qcn7Lw/QTfvsbx/jrj87zr//yKqos88RckfmSwY/WevSsgJiEOEoZKgoZhV8+O8XL1zqEYcy1HYu1vkvP8nnE9tE0mb/xyAwvL/fYGtn4cUJGNtjY6uN6EVe2hyxOFDhaM5gtatzo2xR0mbXOmPW+zch2kXMa1YwCArQtDz+K2ehY+GFMa+zh7Ea5+qbHleYYRRRoDjyymkhBk5go6UwVdIIgYeSH5D2VgqGQF1OKVV2VGXsR2wObS80RmiIjJlDOKggkPDRfpmuFHK5nODSZ5aRc4AdX2lh+wInpImICO6OAjCbiBNDIGyw+kGd76LDadzg9XeSvPDgDwI22yZ++t02cpCqWzy7V9xvKSQwGfiqEI8vyfnRTlkT+8lyb7V12qTMzRd5Z6zN2fTZ6FkM3vMlu72TPn+Qduo/7+Dzwedjgp3E4bi05DaIY1w/JqSnl5cG55q21Pi9cadMeufuigXvscndzTQdJK+YqGVa7H5xHFAUWJ/J0Rh6yFHFQpthQZR6byBNHMU4Uk1dkgjjhesfixGSek1Opam/fTq/nSD3LztDhv7/bwvEjJFFk5IZ0TI+e7UEi8OVjVVw/5NVlk6oCv/LkApW8zg+vtAkTaI08MrqE7SfkDJVqTuXV6216lkfH8hm7Ie2xx4XNAUcm8lRyKienCpSzCp4f8eqNPn0n5NrOmJEX8cyR2k2lvbIkcn57SBTFtMYOL17tc2wix3PHakiSuF96W8ooGIqME4T0HJeZQCXJKHzt5ARjJ+B4I09GlTlSy/KeTho0y2kUDQU3CHjlWo+8ITNXztLbLTu63BwzU8nw7NIEq/1UR+DdjQHLbZOZUoZG3iCrqZzbHCJKAlld4fR0EcsJQBCIhOT+2PoFxH1n4GcMd8vxfOv+t+JOjcJ7/956zDuJQN3KA3ww0rtXO5nTREzH543dhVy4m4E4MpFjaTLL33gsVWh8a61PKaOgSDKGLCEkQkq5tnstYRTTs3zaY4+hG/DIfBldlTm3bdKz+lheCJHAtx5q8OzReqp42UlFXtpjj5EX4vghyzsmc5Usq12Toe3xFxe2KWY0elZAPa+T0zXe3R5yYWuMLCZYfsDDMyVOThZpWS7/6UdrXNgcUc4oHJ7Is1Ax+MHlNgPLJxMlROUM9aLOSs9iOpdJRV3MPm1ULC8kiCIkUeL/fq/J+a0hYgKCBLIoUC3q1DIalheSUSUsL0ARBK62x4xcH0MQcMOQnC4SxRpZTcIOY+Ikxg0EKhmZiqFTzeu0hi6WG3D6ZJ7Jgs73LuxwcXOEAJQNBddPWO+5VDIyiSAiiQlXWiZeGCJLoEoib60O+fJSjeOTOVbbNkVdZrGaZ3StQ1bNMPKCmyJu1Ww6Md5omwRxzM7QIafJzFcMNEXaX0hASi1aUtM61kZRvylC+PVTk3TG3r4uwUrXpr+e9kscu005xsflV/8kUav7zcU/f/isnvnnkYH69A7H+yWnzaHLG6sDIGG2kiVTeX9psachclA0cA+3y/zdek23bktuU2FiBfDjlTGaBMEtvsKj82Uemi/z+kof0w84UsvxzvoA0w8JYnjmcI0wirm4PaRvpwvty02TzZ7NV47XefZYnZ6ZBhreWB0gCGA6Ed9ea3Jha8jhCB6NYn682udyc0RGFTkxVeDoRJZGIWX9+fa7bb57cQdigVpWpWwonN/o8+K1Li0zIKsrDJ2QE42UCro59snrEn07ZOj5bA8dKjk1VQhu5HH9kPbQ4WLTJCNLfGWpwtNH6xiKzLsbA15d7pA3FC5tjRAlgSCIGNkhb28M0ZomYRwjiykLUbGu8uhimatleHShgqIo6KpMe2Sz3NrEDaMPaB10TZ+ZSoaleo4fXGkxVSxypA6yJCFLIg/PF/D8kBvtMZIgklFlfrzWhSRhvpq9Pz5+AXHfGfgZxa0Rlnsxad0LnvaBD+e3RrStgLKhYLoBIweawxZFQ+NYI41+DN2Qs3MlDtezvHBpBy+IudqxODNV4PFDZYIoYrll0TW9m7IJRUPh3Y0eax2bnCbxxKEqTx1OKTbfXu+x3nfSCMUualmNh+fLrLVN+l7Ady80cYKExYWUF/tya8TzF9sUdIkwTvjVs7PMVdNrcv0YTUpYHbgMvJByXuG755vIAhiaQtFQmC6qaJIEgsDqwEYWRCRBoJZTOTpRYGfkcKVtUtTh2OwEG2OHyaxBMatgOj6toYMiQTGjM1vPMF3KMHR8LjZHXO+I9GyfU1MFNoc2K72AmXKW2UKWtZZDLqvwVx+awfQColgEYhw/wvIiJvMalzZHjP2Q7YGLH8a8vTVCRUBWRJYmcvy1R6bojj3Wei6KLHByKs/1lkPPCRnbIdl6jpONHPVcqtLZGvvMllK2jGONPK2xR1mEqy2TKI73FThTIZ0uHdMjSeDxxTKNosHlnTHnNof7iwdgv8dEkURutE1eWu5wpJblsUNVjk0WUpsrijy2UKY5TJU7F+u5ffXOgzb/Ubb7ad+R+83FP3/4vJ75Qdu8V/iwd+Kj3oVbS06rOZXFqkEtp33gGm8VDdwLVBU0gZUxqFujmzJ/tyvN2yv/2yt7uRV7ZUFVBRwB/N0Nh0siRxt5ECCOE0wnYGh7SKLIA9MFZspZnCDk+fNNhk7IE4fKbPZs/DDE9EIsN6Bn+sxWMlRyKi3TJdotKc1rMooksmnCn7yzzcbIpjnwODqZ45dOV3jsUJUbHZP//Ufr+H7K6//gbIkTjTxvrA54cK5EQuosuUHIQtXY/+2eOz6BoYq8eLmFKmlcbI64vD1kc+jxyrU2xaxKmIAuCWQMmeeOTbLUKBBEMS9eaXGpZXJyIocqyZQzqVMRxQlzJYPTsyXaY5e1rnPb33Lv937jRgc7iFBEYV8Zeo8StVHU0/7Ba23e2xxh+SHPHq2R0VTk3bG3bwcUdBVZkljvWby7OiZIoDv+eL0i9/H54L4z8DOKW6MpH3fSuh3z0L2gJi2pUM0qdC2fnCYxV86wWM9iyGlEYa/8aC+78J1z2/xfb21xqJplrqLTsXy8zSEDJ+SRhXQwPb+VStBMFnWmS2mKs1pQKRgqF7dHfP10g4yamvqlHZPrHZv/8fYmawObubLBE4crVLIal3dG5FWZMI756ok6f/xuk4HlIUkifSsmjAS+/d4WTx+ts9F3SEjQZAUBl67pI5IQhhGaJnO0lqOUUTm3aaLKqZqy44aYfsTQ8XnycI25kkbf8rmxM0YNQLJ8Fss5FisG2yOXel6nlteoGApn58vU8xoJAm+u9jD9VIOghIoiCNTyOp4fsFQvsDmwudoyaRR1ZkoZzs5WeH2ly5XmmK2+gxWE2EGAFYUcn8xRyess1bN87VgNO4gZWQF9O2CqaLDV9xEEUHebh+t5jbmKjunFVLMqRydzuxNbgUfmy/vPea90xw0FlrsWvTUPebcnwPVDZss6tZzCxW2TWk5jtpKhbXq0xx7fv7iDJIkcn8h+wLaGts9yW2C2kr2px0VXZdwIdFW+bQ3z3dj8p13Y3S8v+vnD5/XMPw7l7r0+393oz3RNH9OPmT3w/n3UsXMKmGE6H3zU77dHFBBF8f7C/yBqOnRcMDSBrvt+xmKykufNlQHTZZ0ojlgfOCiCyPFGjjPTJZa7Fu+u97i4PUIUBS5sSVzr2PzisTq/eKJOzw75wdUWJ6eKRFHM2+sjJvIaTx7O88ShMn3L41IX+rYHkUg1q2G7EcVdYa1LWyO2Bza6IvHMQolfPDXJ+c0hfhSy0XeZLmdpj30uNMc8e0TEUGQMVeRH19tsj1wuNU3KWYUgSDhcz5HX0qbiuYpEywvYGDgsyGnpJKRz72zV4Fv6BMfqec5tjzk5VaRteph+iBsm5DSFoxN55sppv96NtsnYcflxGx5rjSnnIpwgFfCs5VVmS9mbSpSUoshGz2ajb7FQzdMau9hBxI/XB3zjZIPJos65zSHvbg5xXJ9EEIiiCEMFKYLZ6v1AyRcR952BzxmfVynBrYP13UxaH4w+3cw8dKcJ4tZ7+qiJpJbTqBZELm2NUnXfksHZ2fJN++x978kjVbaGFovVHLOlDH9xucVG16bnpGJYlh9T0mVcP+SdNYvVroPtR3xlqc6hWo7Xr/ep5zUenC+zPXI4VM3yzvqAvu2x0rE4tz7g8UMVanmN/+dTC6y0Lc5tjWiOfBpFDV1VWCgZOEHElZ0hb60N8KKEckbF9gJ6VsoSkdUkNFGmWtAp6AqjIOBkqcCpGZULm2OUUoYj9TwjL+T8Vp9L2ykftOV6DGyPighLk1lkSeQ7F5us9WwmCwZz5SwjJ2Bn5PKj1T6TBZ2pUoZT0wUemyvz2mqXV5Z7abNXTk8jWn5AVkuf/1xVJ69K2E5Ae+xSMRQkCbb6Fk4sMFfOMJFTWajnWKjn+C+vrXCjY1LKyDxztEYUxWRVgb+80sF0g5R7u2IwWzG4tD0mZ0j4UapsOfJCZFnk1x5I+wF+vDYgp8scrmZZ7dpcaZm0xy4rfZtKRmOhYiCJwr69npkp8v2LO0QJ1A80nAdRTHNsM1nU+eapBs2hg+uHNylf3015we1s9SA+7cLufnPxzx8+r2d+k23elRjfzfi4887HfRc+zvyyp17vej5TBjw4V7ptJu/W42/0LK7sWFR12LyFpEgAVGBjmNzkLIxtj5myQVYTeWvo0Bk51HIaAy+kY3k4XsgLV7qoUhqN/5Wz07x0rU3ekKnkFaSeS16TuNI0eXS+yC+faVDOqsiCwEvX2qz2bIIEzs4WGfsJnbFL1woY2AHNoYsoiTy2UGHgBvSdkP/6xhpxki6Or459Hj9U5thkka7poSsiP7zawfV9vn2hhUjCTCXDTMFAlAQm8xpPL81wtTkmiNPePC+MOTWVZ7Kos96z2ehZvLk65LljdU7MlCjldBpFncV6bl8jZmC6bPQsSlmV719qUdAVskqatV9umRijAMcLiOOEpXqO7ZHDTCWzH1BrDl1eutahb/s8c6TCowtF/vDlG1zYGFDNqKiyyKFalpmixo+GDq2hQymvstTI4wQxjZ9inYGf5VLQ+87A54yfVCnB3UxaB6/tdsxDH9ZsfFB2/uB+tzoYAx+W2xaVvI64Kz51ZqZ400Sxl4ZUJBHHj8lpOjsjn6ym8NUTE+wMXWRJ4OxcmZ6Z1lP+8FqHG+0xfdNDkUTCUKCU1QiSIX034NvvbvLC1S6ikNAae/zymQYnGnn+7L1tvnNum3JWR5clnjhc5fLOkPc2h2RUkYVKlvlKFjcMyRsaOU1EEiSudUas9x2IIyYKGR5frKJKArEIA9ula4U0By61vIYowsD0GIkiZ6YKBGFCx3KwvJAoBi8ER4S1rk1z5GG5PioCI8dltqTTc3wmixqaLJFVZHKqyPbAgwUBEoEkgaV6lnJG41pnTBQLTBYMxm56/B9c63CpbWL7IWdnioiCxGrPZLGWRVcVLrfGbA1TqtgwAUWUEEUplbB3Q0pZhS8tluk6Hs2hx4vXujwwnZYBPSgWqWU1fnClzdgNWZp6P4JUNBQWKgaNosHSZJ6rO2M6ZgCxwJFallpOYyPr7qeVz20OQRBoFNLSrb1Fz87I41rH4UQjn7JyDFxW+6kw2sPzaTnXR5UX3I2jei8Wdj/Lk8V93IzP81nf2nv1cXG3886H6QPc7fXd6Zh75BJ76vWrPQdJ5K4yeem7bLDStcnowC3OQNuFjAjhLf0EvZHLRF4jEeDC5gDXT2jk01Kjt9aG1PMKGVnmkUMFvrw0QcFQ0WWZv7jYJqfKfO3kBCVD4S8ut0mEVHixOXRYblvsjFxUSWLKgPmKwbnttNdsshBxeqZIRpUJowLjss7l5oj22OOdjSFeEFLKaiSxwJeOVFnrOeyYPqWeAyQ8tlChaCjkDQVZFFjreZQzEooi4fgxs5Us724MqBgqTxyucrxR4Lvnt+lYfioMmZE5XM/e1Me3R/H67saItuUyMAOOTWRpWwEnpnKcnS5w4wJ8+VidC02T15dHxGKCuRPw2vV++kzKaaa2klPJqiIdK6Ga1xjYARPZ9He53h6zOXQ4XM3z3Ikac9W0GXuta/GeGxIHMfJuAOinET/LpaD3fAT7vd/7PQRBuOm/RqOx/3mSJPze7/0e09PTGIbBL/zCL3D+/PmbjuF5Hv/wH/5DarUa2WyWv/pX/yobGxs37dPv9/mt3/otisUixWKR3/qt32IwGNzr27nn+CLzlB+8tttxUx/ctlf3aftpw29Rl/fpHQ8uwjZ69k1803sNoWdmijw4W+KbZ6bIqPL+S3Zuc3jT/o2izlOHKyxUDa63bXZGHhebYyaLBhlVpm16NIcuqx2TyztjNscehypZChmFgeXRtwLeuN5jtedQz2kcm8hTzenMlA0Kuookioy9EFkR6Nshb670udGx+csrO7x4tY3lBcyU099loZLhxFSRakHhaC3HRE4hSRJ6tscbqz0ubptcbo7ZHrg4QcjWyOHtlQGtsUdWUdjqO7RGHllNwFBTWr3O2CajiYQxeH5IVpVolDKU8io7Q5++65PTZJYmCzw0V8RQBbb6Luc2h/z3tza51BrTMdPf5MVrHSw/Zrqgk9VlOpZPa+iiSSIPz5WZyBlEkUA1L2PIKl86UuWrJyYoaBLffm+H711sIyQJ3zw9yeOHymlGwfX58eqAqz2LnK7xyHyFw/UsM9UMD88WqGc1njxS5ehkhoV6hsfmUmGd2V1VTEkSWe5YmF6ELEnUciq/9ECDxw5VWazneHapvt9H0LV86nmNMzPFm3j+Jwvavl2m9lDlSC27b29wZ32NW/nOP+v378P41X8W8fM83v80Peu7tfuPe08frWtz8wLq4Ht8vJGndKAF4MOuce/4Tx2uMrhF4qa4WzUli3yghGi2kccKIl690iYIExRZYGQHVHSZiJhiVmW+biALIhe2R3z3/DYbPRspidFkkVoudSRGTsDmwOFP3t3i5eUOqgzTRY28LjP04c/Ot3lrfch63ySMEy5sDgmimLbp8cKVDi9f69MZ+8iCCIJISVd57niVek7jcD3L8YkscyWdyaJGx/I4OVXk6ESByaKB6QX7GghhFGOoIq2hTRQnHKpm6Fgez1/a4Y0bPb53scm1js31XU2Ag79/Z+xRNBROTOSQJYEr7TE9y0cRxVQgLZ/2dMiiiBfFnJ0u8uWlOofq6aL31etdXr3e43IzZTiyvYjmyOF62+ZXHpzimcN1hk7Aattks2/z1uoA20sprttWgCRAfTfo9tOKL/L67dPiM8kMnD59mu9+97v7f0vS+w//X/yLf8G//Jf/kj/8wz/k2LFj/P7v/z7f+MY3uHz5Mvl8HoDf/u3f5o//+I/5z//5P1OtVvmd3/kdfvVXf5U333xz/1i/+Zu/ycbGBt/+9rcB+Pt//+/zW7/1W/zxH//xZ3FL9wxf5FKCj3NtewNM0ZAZOiFH61lmKymt3HrPxglC3lwZ8NhC2jBVzals9NNRfLZsoCjyfu0hsK9avJcZ2DtOo6gzWdR5b2OAH4Zc2R5ycWtEPavQHXv07LQhzPUTvnKsxlTBYGkirZUsZmWyqogoJDxztIrpR4RxzInpImEU8d7WEJGEgqEwWzCYr+icnC5ycWvEwPZpj12Gjs/bGwMqhsbA9Xn5epuBE1LQZRZKOR6aryCS2viFzT5jx2O2nLLobPVT6Xg/SkjCiIEd8PbGgFxGxvNitgcmIzeiUdIZeD4DN+Roo0Alo9HsWax1LUzHJ69pXGkOeWO1Tymj8tShGr9wvMbQiTCCiDiJ2BmG5HQJzRcp6jJPLFbRZYntgcMrN3o8dbjM00sVokjAD0MkOcEJ0zKwoxN5ZitjGnkVRZZpjnyyusJyy6I9djG9CCGBmZJOTELGEljtOCy3xry7OeT0dBHTjzFUidnK+0wRsiTuMwjt9RBc3B5xaWvIbDlNOx9UsN77dy/TVNREonjPLt/XqDhUz+07EB/VE3NrNuuTqBZ/HPw89g38vI73Pw3P+uNG+j/uPd1NpPROLHSzZYN3D7x+t5t/bpdVuJVNyAvShYwfwt5HKV0C7HRt3lvrsTq0ma/mGLs+b6wNGXoRlYzG0kSezsjHdANUWWToRmwNbcZeyMA1udGzGJoeWwOb6zsy/i7T3cgNkASRgqFgFOCxw2VevN5jZ+hiuTGWn2ZvBm7IQ7NFTs/kieIEIQZJFpgpZxESeGN1wExZY2Pgcr1rsTPwsIOQWkGjmtF4YKZAJZtqGgC8er1HVhVYbtn4SYS5G0AqZ1SIIWvI1LMqxxv5/d9nT7n5cD2LALhhyGReZ2tocbieYbNvc3l7RLcPK51Uu0WWRA7Xs1xpjvnG6QayIFDOqFzdGWFIAjMlnfWuTRgnSOLuHFIy6Jg+LcsFEdZ7DgPLRxQFlltjChmF6aLGsck8P634Iq/fPi0+E2dAluWbokN7SJKEf/Wv/hX/5J/8E37jN34DgD/6oz9icnKS//gf/yP/4B/8A4bDIf/23/5b/v2///d8/etfB+A//If/wNzcHN/97nf51re+xcWLF/n2t7/Nq6++ypNPPgnAv/k3/4YvfelLXL58mePHj38Wt/UzjTulvO8kAhNGMUfr2X26s8miTkaVWd/NBGRVEUj29Qau7Iz48/e2UA9EdfZYZUDg2aXafkozjGLeWevv04xe2BpybmvEVEHF9GNUVeLitsnYj6hlVWarGYZeyKnpIrOlNJX56GKZd9dSQZTVvk1WlRl7IV0r4NmjVV653uW9zQFRFCFJIhd3xsRCOhgu1LKYXoChiJhuyJnpIiMnZLFmYHshUWyhyOBEETlNoaArrHTGCIKIqko8uzTBm6t92raLQJqqdvyAuVqe+XIWyw8oKgpD26aU0/mFo1X+j1dMdFUkK0s8c7TCzjhLIsCO6eJHMVdbI7wgpGxkqBcMVBleWW7ylWN1toYOQZJQy6q4YYztx2nzcDnLpeYYP4zY6rscaxQRpITzqyP6pscLF1r0TJ/pkoYkChyeyLFYzSFLqby954c0igokApsDF9uL+ItLLUw35MhEhmstE00WEBHJGhIlTaFygO2jmlOp7k5MO0OXMI5TZeOWRaN0swbFrYwhlaxKe+gwuL0Q8V33xNxu8L4Xqd47vS+3nu/noWzo52W8v/VZfho2ns8LH9fWP+5i526ch0+zgNq7/qP17L4YYTULneH7+7iki/+sCloMmgqt3Xlm7KQR7LEb8thsiWJOY7Nnk5ElzDCm2XcwVImJfDqPSAOP09N5fnSjy1sbQ/7PH60ymTcwNAlRkqjIEkliMHZCEuDh+RIDB55eqtNzQ/783A4L1SxRkuCGITMlnZW2xVIjz9trAyBl5pElkbHr07YchCTCj2Im8xpBmHBIN5it5bi2Y1LLaizW0iDZ22t9ojhmaaJEOaOyObB5c3WAiMDTS1VOTRVpDh1Wey490yejymz0bNb7Fms9BzcIObc5IqvK1HIqGz2XjZ7D1ZZFEIR0u1C50uLB+SoPz5d5a63Pi1c7TOQURFEkjmOudWy2hx71vMpaz+aJI2WeXaqjSPCdcy2eOlxJ59PmiNbIZWvsQBKzM3LojGw2ew4PXWnzNx9f+ET2cB+fHT4TZ+Dq1atMT0+jaRpPPvkkf/AHf8Dhw4e5ceMGzWaTb37zm/v7aprGc889x8svv8w/+Af/gDfffJMgCG7aZ3p6mjNnzvDyyy/zrW99i1deeYVisbg/MQA89dRTFItFXn755fvOwCfAnSaNO4nA7EVpRk64zzucqcg3Uc3NVbL7f3fGab15aTePu7fof2yhjCy9n1EIo5iXljv0TJ/HF9Om4kQQeHC2yHzZ4PtXOzy1WMb2E8oZhZEbsTPyGNkBl5sWryz3ma9mOFLLstK3mS1lmCgoBDH4UYwuicRxQmfsAQkPzZWZKma52hoxsALesPrMlzJkNIVDtRw3OjaaJCJKoMsStazGSsckJmEkBOiKyM7Q4aXlLnEcASI/Wulwdr4CSYFrTQvbCxk6AVlNxg5CqhkdXRXo2BmmSga2FyMI0DcDXhp3GDkBQy9i5LjYfowbRgR+RM5QWJoocKMzwvVCupbHuxt9Tk2VsPwQMU64Mh5jaArLLZuxE+F4EUEYkyBQzig8vZTWcV7cHGAFMQtlAyeKuLw9QpNEipm0TOfc5pDrXYuRE/LQXJFnjtbIGzLbQ4v1vktOlZkqGpyZyXNyqsjA9rncsrjcHO8v8p0gZLllEUUxK12bKIZfWKoji+J+KdBB27rRMfnuhR2+fmoyzSSEIWPxZh7yu12Efxj2ImV3oim8G9ztIutnucZ0Dz8v4/3HeZZfhOd+MGjzWWUvPo0mx0bf4XbVRQff8b13dU9196XlDtYBrTKBlOYiBsZ+SkUsRe9vt33YHruIgoAfwUIlgx/FXNgc8cShMk8eqlDOKax1XVY7DqokMFPOcG5zTBjFtEYeU8Usv3qmQRgnvLs+5JGFEoqQ9jzMlQ22A/gvr6+SNxSGjk8YJyDCextjJHHEd87v8K1Tk3zj9BSyJO7PcVklHb+2Rx6SLKCIIm4UMaHqlHSFSkal7wQs1HOc2xzStwOONfIcbRTQezZvrg0wNImHZ0t84/QUABe3R/hhyPYwpQ196VqHlY5FIZNqueiKiB+GPLpQZrGeI4gjumOfV652sHyIomS//PLMTJHmwOZqy8IOQhoFgyO1DI8tVri4NSJJEhRRYK6S4X978Rr/+UfrTJcNfu3sNAPLp2JoFHUVN0rXCCoJbdPH8T9+z8t9fPa4587Ak08+yb/7d/+OY8eOsbOzw+///u/z9NNPc/78eZrNJgCTk5M3fWdycpLV1VUAms0mqqpSLpc/sM/e95vNJhMTEx8498TExP4+t4PneXje+xy3o9EIgCAIbquG+Emwd5x7dbzPC9WMxNGaQTUj3XTtt9t+cBvwgc9T6rsk/TeOsIOAsi7x9RMVOpdWCIKAjaHF6ys9nlisMFsy2OjbXG6OOVLPMl1Q2Rk4mJ7P2BbIyjBZSBkIKobMmakCuiqT1yXe2xjy2vUxK12LjCxQyShYjkfXFBlbAXMVg0cWiqx3HSZzMu9tjlDEhGP1LLYfYrohQ9nFCyJyqozjRfTGLh0rZKGsQ5wQRRH9sYfrRtTzKvWcyuFanjBKaA9dek5AnMSEQUTfCfGCARM5ndPTRZZFi6P1HFNFgziOGTs+cQzzukFRVwmDiE3fJa/AQlXnrbUhI8+jOfBwwpCpgkEpY3BpZ4wqirx+o4OXQFYVGdguGwOBqYJOGEW8vT6ga7qUMyrNikEURmiywGRBZ6ak07c92kMbkojNvoPthzizBVw/wPQDHM9npT3m/HqXrK4S+AF+EHO1OUYWYGAJXGtZyKLA9sBmoaLzpUNldsYBJyZzNAoaxycybHTT3omsJuIHAW4gc2Yqy8AOOTtTIKPKBFHE2HbRxYSCJqQ20bW4vD3kxGQO4pjLOyPaFuQ2B0BaVrDRd7jcHBOGeWY/ISvFzsChN3bZ6KYORiWr0LMCJgvaXUdx7/S+fNL9Pi4+6Thzr8elL/J4D/d2zP84z/Kzeu5w87MPopidkXeT7e5tC6KY620rLRmJo0/UePxZYaPvcH5zwMD/oE3uveOOl6VrenStgJ2sguOH3OiM2TqQXT7IdycCfgye9/52VYJTE1nW+i5+GKLIAroooMkixDHXuyZiklDUJfwwZLllU81KZJSEX3ugQWsUMF/NUM8obI882iMX4gKNssZkQaNsiLzYhO2dJnMlnaEbsNwa88B0EUUWsVwfJwzZHjjIIkzmFd5c7dEeufi6zMPTRWo5lY7pc7E5Jo5i5koap6dyCElMa+Ty7Xc26TsBSxM5zkzl0rGyNyaKYoqaQi2nEAQBL1xu8e7GmJmSSnvk4vohmgj1vExBS5WN86rIj1fHuEHEg7MlVnsOWUWiUVJobsPZ2RxhLNAf2wzGNq4fUTBEHpmvIAupErPlBlh+yGzZIAwTrmwPOFLPMFvW+eqJOmEYszV0eXRO59cemmKz7/CS2mVjaNIa+3iB/5msj35a114H8Vncw90e6547A7/8y7+8//8PPPAAX/rSlzhy5Ah/9Ed/xFNPPQWAINzcTZ4kyQe23Ypb97nd/h91nH/2z/4Z//Sf/tMPbP/Od75DJnNvozfPP//8PT3eZ4UoThl+SmoaVfksjtd1YcuG6Uy6/T//8fP4ESyPYeMyVLV0+zgEexm6HlzvwpXLMAhIBzQDGrvfP7ednmPgQ8uFMIKyAFPmDle34MowbSYjgaoBN67BkTy814erA7ixukFWAd+DrQGMFQhiaDVBlCAyIEhgbURaOnRxh/cGKblNLQNxCAkdOjbsOHCiCNUEugFMKTCph4yaq/yonUamnAjiBNZNUEWYzcK1Hgw8GPnpBKYI8OJ7TdwEznsOIx+yCpj+mGIGJBvyCnR9MB0YC2B6UE48rvkDNq00OpYJIbB8LlwxCRJQRDiUA3djmx+2Yf0ibDlwpZ8yB3W2N5El2O6B1euzsQY3hnCsCPUsGCKshLByGZo2rJhQUWDbgYoGYmeZqg727vNuXQDHh0tDWCqk6fpz56CmQi+ASwWYyKTb3+qk9nGpBlU9fW6BCVfe2WRZgGsjOJSH7Utvsb1rJ5A+d3uZm+qNP4mNrl9In19GAjtK7bP6xS3/vi0+7jhj2/ZH7/Qx8EUe7+HOY/73v//9ez7mf954/vnnbxpb92x3b9ukAZLw6d6VzwoH54k9G97blpfTuWD9AmzbkJPBv5HOC6NhSiF6u/Zml/czAvvbIvj+O6tkNOiLsLW5jgyMAlg24WKqH8a0ARkVRn34s+YayyN4ZHdcemsD3nkvHYuqAVx5Z4WX3fQ3B6gZgNNnLoGdELY2xvi9bZYKqf7BogRVa8wbL66yYsKGmX7vaAHOb6TjZkmBoQkDC/5y5wat8+nct26mTEki0M7D5bfTG9x2wNhtzfn+FvxITu+JBAwPrlyHG2MwlPT3fNtJf9MzZSgmMDbhxTXYtNJ9MhLM5eHbL7yBE4EdghXCyIO5LERVyEvpuF7RwQnADeG/rl4nr6bzmjOA1rUOeQ0UG25c7/Hn/etkJbi8DVd6YCXw2luXmRhevscW9T5+WtZeH4Z7eQ93O+Z/5tSi2WyWBx54gKtXr/Lrv/7rQBrpmZqa2t+n1WrtR48ajQa+79Pv92+KFrVaLZ5++un9fXZ2dj5wrna7/YEo1EH843/8j/lH/+gf7f89Go2Ym5vjm9/8JoVC4VPd5x6CIOD555/nG9/4Bory2YrD3C4q9HGxF4U53vjkkdaD17Ez8vaPt/f3XuS1Yoj81z/9HtWjD1LJaZxKBG50LCRJ4MHFCookMlnQsP2Q4sU22wObN9bSptljUwUapQwnp/J0TQ+zOUZ2A745XUCXJM7OpVRuQ8fn+xfb2GHIjZbF1tBhpetQnipT1iIO5zyeO16nb4ecmMhwbmvMztjjsYU0XXyjZRHGCaokcGY6x7ubY7woJisMGLkhQ0VkbjKDoMv0mmOcyCc3UyMvj/FMj998cp5fOzvNatdiuWXy+GKZ6x2HkRfw0tUOhiSSN2Te3hwRmC6JFHCykmV5o4OgyhRViWxWodd3mZjIo+kKY0kgr8Q8faTMi9f7dFsjxCSmnlP564/NM/ZDNs5vowgCc0WDszNFSlmVt1YH9GyP/HSByZKB7LcoLpRZyGos9iwuNseIYsrwMJTHjJwQT9eIPY/Tp6b55bMzhFHMlR0TN4iYNj0eF2CqbPBn7zY5OV3guaNVNFXeVwkGeGOlx/XLHYzJHI9m0/Kv+arBZt/lkfkSsiRS6DsMVns4fsQzj85iqDLSxpBTxDx3PI0Cv7PeY+f8Gzz4pWe5uJOWG52cKrBwj+Ts90sVohhJEm+6hy86Puk4sxcZ/6zwRRrv4c5j/le/+lWq1eonvs+fJA4+e0SJjb6DAMzs2u+9mBc+DwRBwLf//HkOPfQUQzemltNY7Tr7c9He+7l3b5DOVy/965fYugPZkcbNjkLZACGjsdgo8OThGitdkzdWe6iGzNRimayusjV0eehIhUZB49SueNqPV/v82gOT5A2VMI6RRXH/9x06Pi9f6/D00RqKkPBf//R7/L//H19DURTeXOnzyvUephfy0FI17TXLmTx5vEajaGBfabOzOcSLYqaX6jhhBAk8drTGXylofPdCk3NbJspkjmDoUK4k1ERYqBiMvQhJEDg1lePN1QEPzRbI6qnibyWrcHXH5FAtw42OzWlN4q21IbOVDFMFjTCO08zsXJGeFfCDK236ts9vTOfRFImlmsF//B8vMHf8ASRJZLGa4eqOycVtk7whkyvo6IrE+FoHKaNSySloQYLm+ByfylPKaNSbY751aoJ6QUN7a4OBHVHMyERRQj0ecGXYIQyhNj3Br/zKQx+0h09pt5/n2uuzwmdxD3c75n/mzoDneVy8eJEvf/nLHDp0iEajwfPPP8/DDz8MgO/7vPDCC/zzf/7PAXj00UdRFIXnn3+ev/W3/hYA29vbnDt3jn/xL/4FAF/60pcYDoe8/vrrPPHEEwC89tprDIfD/QnkdtA0DU3TPrBdUZR7bjyfxTFvRXNsc63j7Eq5f/C+7gazVSltALylQXiP5Wf2FnrRO13H5ZZF2wo4M1NEltN67HObQ3qWz+npIocmCgRBQEmFiYLBwIs5MZljrvo+L/21toUsy2wPXc5tmchiwnQxi6HJ6JrKVDmDIssMPAddlWlum5yYEtgY+sxWI4pZg/HAo2UF2H6IFcQcm8xTzGr8ygMNLu1YhElCQVcwgxjDUFEVhUI2oV7QcPwIRZa4uD7E0ETWew6vrvSYKuk8NFOmmlM4tzHmK0tV/AimSwZvrQ04NVeibQe4YUx77POd8zt4Ucyr13tsjjyqGY31gY2IwHtNk7mKzlwlS5LEOEEEokCcwNFGntMzZa61R3TtiKmijuPFXN4e0jJDFFHg1EwRWYC26dLIZ7jQMoniBEkQcMKI1tjl7Q2BY408ThgxcHzeXBsysiLOzBRxQri+OkSRBNwkwbMjpgoSxyYKXO9aTBQN5ms5Hl+sgiAyU80gyzLrfQsnTHjmaI3Jos5EIUPZUHhjtU+UJAzciOONPJebY5amirRNnyttE3ng8uShCg/Ol+ma/k09IUcn8lh+jKGpqQKxFdC1fHp2RNv0GLkJ4xBmKzmutl1eutbjjdUB/8uzhzk2Wdi31U/aqKkoYGgRl5pjTjTyZPRP9g79JPFxx5nPekz6Io338PmO+Z839u5hz4Z1TWWuoqEocOgnbMsf9V4GUcyO6dC24cK7LZwg4a+cneL0bPn9Bu3d9/P81pC+G/HwfBlDi+7oCAAogCpDFIIFLExkKBk57Chka+wiyyIRUNAknlmq44UJbphwsWlytW3jRxGmE/HVkxPousrzl9o8u1SjM/Jojj3OzpV5ebnHKzf6IIg8d6xGlMByx2Z94PHMUh1Zlnh1pctrNwZMlw0enCvx4EIVRRJ5/HCMG6ZsQ6emi0iySGfsUcnrdO2Q505OUS8MMf2A9aHLowtFZnf5/RMBFFHkvY0BL1zr8tJyj4fmS/zK2Wmud12GXszrKwPeWBnyjdN1vnpqijCKubwzpqjLNEoZenbEZCnDUqPA9baFpips9D0mCwaLeagVM9zoOWwMPHIZnW8+kKecVelbPnlVYnPkcrKRR1ckTD/iLy+22Bp6mLt9b/VShqvNMcsdl8WKjhuk431OU9BUkEIA6bbv3r1Yz8DP1rt9r451N7jnzsDv/u7v8mu/9mvMz8/TarX4/d//fUajEX/n7/wdBEHgt3/7t/mDP/gDlpaWWFpa4g/+4A/IZDL85m/+JgDFYpG/+3f/Lr/zO79DtVqlUqnwu7/7uzzwwAP7bBMnT57kl37pl/h7f+/v8a//9b8G/v/s/UeUJHme3wd+TLu5lhEeOlLLqiyRXVWtp6e7B9MjABAgMBgs93F5WYEDjzzjvgccwNu+t4/7Huc9kgsS5EL0oMU0WpeuyqyUkSJ0hHu4NDet92ARUZFZmVVZ1T3dNd3xvWSku5ubufvP/v+f/H4zqrk/+7M/+70aHv51UNs9jW3lkOXnGQbE2pUcu4bLwA4YWEE2DNqzWOlYnGrlH7k+ScwUJwdO/AgtZKOoHg4Se0HEty61qOUUxm5ItaDSNz38MKJeLHFZqvDGgx7rI4eHexNAwg0jVnsWWyMbXRWx3ISh49Msajw3W6FSzDHlJQxMj4kfIyEgiyL1gkopJ/Lze332nICTtTyX5stYXsja0EIgpa6rzDXy3N0xQMyUdVVVpp6XiBLIqxLfeW6Gv/rFKj+6vYcVxkyXVPp2QHeS0eKFScxSq8hCPc+ry3USUu52jH0qT4+RD1frBdpVnZ7lk9c8Xr/fZ75VpKgr7I4jqgWZ1042GEx8UgRaZY1dw0WRBebKeewoxI+yz73WFzC9kLEVUCkK3NozeF6p0SpJtEoyXz3b5N01gxvbBjlVxPEhp4hUCzqlnMSbGwaVvMPZ6RKtooYdJJxtlw6DwxcXa2wNHa4u1egYLisdi844CwoBLsxUuL41oahnYkEHDkG9qFLSJFxfBAReOVlnft++arpCvD/0OLADGgUFV85Ex1491eBuZ0J34tM3fc5Of2irv8qg5t8FesjPM47X+98+Po82/En3ZcfwMr76CKbLOWRRPBTqepxh7GBvOdgnPg4mUJOy1hfbhSgRqRdkXn84JggT/umrS6wPXIa2zy8eDvnT52b5giRS1RUkWeT6xoifdocIQGfi8v76iInjszvxEREZ2VmSw3BC7u3ZlHIS7/XhvZ+uMQkSDCfkT67Mcmd3QlGVudAucfVE47Bic79rsjZw+OLJOqfbZTqGhx1k1fmhHVDJZS7ZzjgjuBg7IbLoYocJl2YrtCs5vCDiynyZB30Hy4/pGi7rA4/FRg5VlmmWFdplnYV6HieI+GBrxBu7E0QR6gWNU80CraLGTEUnihO2RhnrnSTCTCXHBzsTSAXOTudoV7KKjB0kzFR0/vjyDHd2JjhBwtDyScnEJUlTbu2a/Lv3tlhuFcipIrtGwI5hM7BDXlys08qrrA5s/i9fWX7ib/d5tOPfJ/zag4GtrS3+8i//kn6/T6vV4rXXXuP1119naSmjkvrv/rv/Dtd1+Rf/4l8wGo149dVX+d73vnfIOQ3wr/7Vv0KWZf7pP/2nuK7LN7/5Tf6H/+F/eIS/+q/+6q/4b//b//aQheLv//2/z3//3//3v+6P87nG3xbnbbuS4+pSjb7lPxPjyoFzeJT3HbLF5cARDOOEtb59SPl2cN0HVKTn26VDCtIf3M4YZRRR5NrOhJ7pcbNr4gUJmiLzyokGY6vEcqPAyakSYzti7IRcG0yIk4RmQaVvBlRyKmEc88bakJwqslArECcpaZpw8XSTWlHlQdekbwVMgoiCLFHJa8hiiplCTdf49sU8lXyOuzsGm2OXkibRtSLOTyvc252wNbL539/e5E+vzFHOaYRJSiKkuEFEVVe4NFPmdtfAGIcQpVxcKpLTJHqGR7WgIgo+/UlACph+xGbfJq/KpHGME6T4QciVmRpjJ2Kulmcw8fDihPMzJWw3QlUkdFnCE2LCQECVRWZg1/2gAACOQUlEQVQLOao5lYHtY3oReU2kXimgKyJvrY3ZHrtU8irbY4/diYcdhYgxGH5EXhH5zuUZwiThXtekZ/rUdIVqTqamZxkGJ4j40e0uUZIyVcpK0EPX48pci3Y1z7l2ieubIxRJxA9CTC9gawh3uyZBGDF2I2QR7u5ZzO0HF5tDh7fXR4BAu6JzebZCIy9x+1242zGpl3Kcnalwrp3ywuKH7SSNokpRFfGCiDBOPn114HeYN/o3geP1/rePz4sNH1WR/yQWo3YlRxSVMIswP1tm7CdM3IiJGz0SRDy+tzyLGJrlZ3NmAKKQIABRktK3PIZmwHI9Twos1DNHd23g8tpJnfl6nu2RTbOqUNRk3nw4wPRDDDvk0kyJ0+0SMyWdBwMbXZWYuAGdsU+SwnKjgCZLVAoabzwY0LUCnpstc/VEAyeI+JtbXbwoZmPg7AuHSdzZNbjXNbkwW2G2qvPjO11e7xjU8xpnp4r0TIU3Hw6ZquR47VSDRlHl7dUBD/o2f/bcHCM3pFnSiKOE97bGFEwBURI51Swyt28PAytg4sWIosBzcxn730rX4kHf5lSzQCWvsNzIM1XWuEXWjvVHF9v0rSyRdr9nP0LremNrxFvrY062dECitU87+sJ8GTuIiRKB7VHAi/M17vUsCo7K5TmVIIj45eoQP455b2vC+bn6R363z4sd/77i1x4M/E//0//0sc8LgsC//Jf/kn/5L//lU1+Ty+X41//6X/Ov//W/fupr6vU6/+P/+D9+1ss8xsdAkURyqowVuIeUoc9yzNEbeb6e5yv7mZ0wTnhvY8Tt7TH3J1mm96CM/TjNY9/02TU8uoaLJIoMHZ9elFJUFK7M5rk8VyGME8wg5sJsiYIqc366gq6K3N2dcPVEnZwssTZ0qRc0gjDLnNzYNGiWNPwgYnWY9Z+X8io/ud8nCBPKukxFV5hv6OyOPbqWT1GRmKnkeWN1wPl2hZOtIs2Kxvdu7DEwA95cG9MxAjYGNnP1PP/8tUWKqsTra31++XBIf+KjaxJBmBClAj0zwI9gZdcgiFMKikTXi7H9iDNV8KOY9zZHvHqyweX5OuWCgyKJCLLIiwt1klTk3XWDnuFR1xU2xi5JmlDUZOqKxq7hMQoi8opMraDwnUtzvFccIiuQlxUQBPKqQBiH3Ng2ODddZntk0x17TNc0Xm7X+daFKZZbRbaGDqaXcKqVQ5ZE1gYOd/dMVromJV3mg50Js2WNsRuyNrCQhMxmzreKvLcx4t6exb2OwdiLSVKRf/bKIpWcfJih+vb5aXq2jxdGOEF0qCwMmQDdwMoEBqoqmViOINIqah9pWxtYAWsDh7VB1jr2aQTFPi9c8H+Xcbzef77wm7Dpp53jcSHK8+3SU69B2Z/RuS5nleKuGRLFyaH45McFETUBRumjjwtkg8UxmVNj7VOW3tx0+MNzs3z78gzvrg74/u1dpks6F9olvny6xZsPh7hByNbIpmO4POxn2ap31oY87DvUCxqqKuHHMF8r4IcxQRCjSxKilLVmnirDP3hpjvlGkYEVUNZlWuUcl+cqKJLIj+90+X//cg2FlGZRQ5YErm8b/M3tHrsTD02WKGoZTbaEyNmpIldPNAjjhFZJo1nUWG4VWe1bfP9Wh0SAV5frfOFEg47hYcYBEyfiQWRztlVElKVHqL5fWqpyc3tMd+xj+RHlvIyQwutrA9IE/DChuj+NHMYJK10TL07oGC7VfBbYyZLIG2tD7nUnJGnKcrPISsdClmTcIMaLUs7OVJBF2Bo4vHKyRS2vkJJSUkQ2hi5xHGE7ET3T/RWs7xh/W/hbnxk4xm8fn2WDeFrJ7uPe6/Hnjmb/B3bAyVaeoAzT5Q/7AQdWwNAOuLFt8OJijRcWM92Bmq6wsmexVMtzdqqEJIso4v6A6uqAe3sWNV3BDrKF6p21EW9tjCnnZWYqeb59cZo0Tbm+OcIOI6IEvnt9lzg92LQmnGoUGFo+QRiyNUqQRJmpUo4Ls2XeXg1RRZGfPdhjve/w3HyZv3xtGcMN6I5clppZK9TACCjlJKaLOtsjh0pB5YXZKm89GGE4Af/5VpeLsxVquQBBFtgeWWwbHrYX8cJCjYEZMHYDhl5ISxIpaDKVnEJRV7myUOPttSFXl2p4ccLQDrjfc9kaOVh+QL2Yw/JiFmsyBU1EkQQEIaVr+ph+TJKApklsDF0ahZSR62fUcG7Eve6ENIFmWUOWRL5zuc3Lyw3u7pk8HNioisTD3oS5qsr0vqP+3saAn93v8/JilS+dqlPLKdzrmRQ0GVUSkSWRjuExsAOaBY1XT7cQSPnS/pzBruFSL6icnipyul3G3Bjx45Ueuf1qz4GqcHdfx+J0U0cSM8fhft99onNxNIg4CAT+LnHBH+MYv078Jmz6k9S+D1Tkn7XdQ9lfO+50zEORyqedr13JYaYffY/zreycfgSVvMSmEZMCzWJW8ZQBURAAgZImc6JV4s2HA958OObUlM7DvoPhhLQrKmkMPSvgZFPn5FQJWRJY7Tv8za1drm8bdCY+y80CF8sFri5VubuXBSNdw6NeVLm+MQIh2w83hw4nGgXOtYq4YYThBoiRQFGR+NpLs1zbGrNY02kUVV49UadjuDSL2f6YV2W+eLp1+Bn7pk9n4pOmCZtjG1kSud+zKagiZT1TRw6ihFo+a7c92I8NJ+QX90eYfkC9qFJUZVIBCpoMMUzckF3DZ+DBuxsjfnl/SKUgsjXyaZZUFup56rrKbDVHx3ARhRhZFPiji5nQYCpAHCXEccLdzoR3NgwaRZVaQcX2IgwrQRQEXl5scK8/4cTU310F4t9lHAcDvwd41g3icWf+SVnWJ73XUcn4u12TXcPlxcXa4TGHm0ReYniHRxy6diXH1tBmpWNRzSvoisyL+20gfcvn9q7L7digVcoxdEIGdzwGdogXx7yyNE9RV2lXcpT1bNFUFYH/8MEury7XOD9boTMJKOUVWgWFd9cN2mWNK/NV7DBClrLB2SBK0BSRMEqYLuv88l6fzsSnosnokkyjkONsu0wYJ/y797Z4d9NgfejiRgmVosTFmQof7Brc2BozVdapFRREWaBZ0jDdENOPUFQRP0jwgoidscNyo4AoplxZrNOzPbYMj+Uo4UtnWnywPaaVz+HrmWrytS2DkRMRpQmL1QKaKLA+cqjnM/XjubrGvT0bP4yp5BQERII4ZmXPpJpX+ca5JlVd4d99sMtm3ySIUoIoxgxDTrQqvLBQZ3G/tHx71+B7NzvYfpzR9AmQU2SunmgQxQl3OjYjN8QJYh6kMPYClqo67apOvaiyM3SwHJ9qQeXr51qcaBYP24BGTkhVl2ntb3aX5yqP/Ls1dHj94ZCrS1XOt0uHOhbTZe1wyP1J9nq0WvBxfadPsu+nvfYYx/i7iE+y6V9H5eBZ1L4PqsnPer6Pu+6jz20NHaInHB8nCU6Y0WF6+4EAwFKzTG/iszW2qeZVSprCyVaJse1zYaaElhOo5hTe2hhSyWlUC0VEUSBIEpw45XbX5MX5Ks2Cyvduj3D9hC+eaHCiWWRlz2KtbzP04Lu3OtQLOWq6wl/f6jC2Av7+C7NEicCVhTL/+OV5tkcOP7rTAwEESeT2rokiS9zYtagWswrs9e0J93s2K12Tb1yYJq9+6KK9sFjj7u6Et9dG/OLekIVqgfPtEmU9e03HcHhrbUxOERk5AednK6wPXOYrGl8726CkyUiywLXNTDDsZKsAgsgFAWbKGr9w4AQwU9M4OVXAi8a8vFylO/K4sTPhD861ePVEnR/e3ePa5oTlRjZD9t7GiGubY65vjLkwW+aV5Sq6JvH2Rtb2mSawMbaJ4hjbT0jjJ0Rzx/it4zgY+D3AsyquPu7oP8nxf9KiffC65bpOHCf0TJ+toYO873AdOF5bA+sjipPZczprA4e+6WMH7uH52hWdH93t8d7WiGZRo6zKbBselh+gyhI/XunyX35h6bBP9eJshbWBiSIKvL9hoCgS2yMHXZFoFnJcmoOyJlMvaUgCnGgWMoabJMH0QuJE4PauwcANcIKQkR9Sy2t8bbZEK6/x3Q+2eXN9hJDCdEnFqOep51Xma3lWehOqBZUr8xUSAQZ2wHeey4atDCvETRKKKqz2LTpjjzBMCMKEYk4hr4rIItTyCtsDmzs7Jm4z5qJe5VSzwMlWie7ERVMlbu1MuLNj0LNCSAS+fLqFYUe4QczpqQqzlRzVgoofRbyxOmBoBwhpSlVXKcgiJU0krym0KzmGdsT52SqyINCzfK5tjNBViSTNGDnapTwFVeZBz2G+XmCqkuN8u8DexGPD8GmWZDpDjyRJsaOE1Z7NwA24vW2S1yT+4uoCupI58dkgoMZKx+Tt9THyfjbwaNCYIT3MDh6IpWROhnaYaTvIPD4p+Py4vtOO4XFzx3jk9Z8mOD7GMf628OuytafZ9NGEzf1eNuT/WSsHz9Lb/aTzPSm5FCcHCuPFp77n4+eb0WD3Qx05GhoosoSQRqTAkae4vzfh1VMtRlZAkqQMvaytURRF+pZPUZH5t9e2WRs4nGwWeOVUjcV6nqImUcsrfLA9YWXPoq6r/IMrs+QUiecXauwZHoKY0rdDRgHMaAqnmgUuzlXYNVze3zTwo5jNocd0RSGIYKqS45+9skAln1GQbgxdnp+v8Nx89TDQKWoyvYnLStekXlC5eqLxCLPfX7y6RDWvsD50CZOEHLAzdnl/c8zVpSoPejbbY5dfPhhSK2TzVH3bR9cUzs1WMqIOQQQBLsxWeNizs2RMEjOdg3Ypx3KznJE4mCFRmNIoZUrQB0mcSk5hZPu8tzHE9EPeeDjA8gJ2TZdLYpFzM3Wub41Z2Z1wea7MT+8O2Rp72G5IKgjc3fcpjvH5wnEw8HuAgRVguNEn9v8/7ug/yfF/0kZw8HwUJ4iSSKOQBR2PBxY3dyasmdlGoSgfbhjTlRxfOdP6SHl5vp7nn7w8z/sbQ27sTggTOD9dZHPk8cH2iLWejRsknJkpI6QwckNIM8n5+z2b7YGDFyS4QYQdZANtfTvEsH0qeY33N8ZESUp34jNV0Rha2UCtTCbL3hl7iAjsSiL/+wc7aKJImqRoisRyq8hcLc/m0OUn93ooksB3LrX5hy8v8JO7Xd7fMHh/w2C5oXNt2+Biu0SzlCNJI3YNh5wqUNI12iWVi+0CqWUwCWKCKGK5WeClhSo9M8CLI0w/oG/5lDSZ/sTF9UPSGOaqOVZ6FttDl7myxkunGsSpwIlmgQddM6MbDSK+f7vHQt1hfWSTJiKvnWjQLGv84E6XX9zt0qjoVDSZ+10TK4hYbhQxXA9NlViq6VxZyuj+3l4d8NN7Q2aqGnNVjbwqsyZ6LNXyjN2Ae12bq8tVXpirIIsZQ8fP7vV5ebmKrsica5fwwwhSDp2Eg37UdiX3yJzJ4ziYOxnaAfWCiuFGnG4VqBfUQ6aRo3Z5dJjxwKYeZyY5biM6xucFf9u2dvD+p1uFp/bkPx6Q/CoBypPO96TPOA7g5s6Enh0+ITHwUczX83iPJZSGPgRDHzPOdAZmKgJrRpZ9jkJwooSLc2XOThdxwoSSLnN722DiRlR0hdPNEiMnoF3MvpMzU0XGXsR8rYAsZVSeP9oY819enee1Uy3eXh2w0jUp52QkQaCkwtnpIlcWa+RVmX/+2jLPLxgYrs87awZRkmL7Ibd3Pf70+Rl0RaZV0Zkq5/jK2RYTNyM/ADjRytMxXZI0paor+8x+QyDlNUCWRM7NlNk0XO7uTtA1hSCM2TU8bm5PGFohiijy4lKFFFjZMxnZISeb+cO1cH3kYjghsihiBQlbI4fBxCVJYH3ocm4m27/LOQkEgXYlR2t/mHi5rnOqWeQ9d8w762MMJ2TP9Lk8UyZF4Gy7zMgJ6YxduqbP6vvb7Iw9JKBRkFlqlvjLVxc/lS0d4zeD42Dg9wDP2g5x4OgfZGDbldxHHKwn6Q8cPU4+4swd/btdybFVULCiLBOkyCEdw8XwIi7NVp5aXl5uFZElkS3DY+JGnJqu8uWzU1zcKPHm2ohiTkNIIU6hpGUtO7WiyhsPBry8XGOqnGN34hLEIY4vZDMKE5eBPWC6qnOyWWC2qqOrAtc3HXbGDi/MVHhluUlRlxEEgYHlM60rzFZz3N8zWetb/PLhgH/2hUXu71kEUUy9kOPsTJmdscsbD0bYQcCO4SMkCZYb0bM8/Cimb0fUixqCIKCK8P6OQV2T8SOYLWk0KjqtosbEjVl52GfshFRzCqkA9/oWYZLs99gmrPWtTG9hbBOEEdK9AbWiSl4RududMFPO0dI1uo6HKiaUcypBFFPSFc7Nlnl/Y8zN3QnJ7oSz7TK1vEY5p1DKSdzp+JieRV6TeE3JfhPLDxFJKSgioihhhwkXZ0pcmq3wy9UhgiBwebbKhbkqAPc6E4a2T9dwsYOsp7Q78ehOfP7Bi7OcbhXYNVyGTsCukePFxdrHZvUzulH1UM9gej+AOMpi9XhG8mCYETIH5EmsV7/qfXOMY/yq+Nu2taPv/zSH+1kqw5+l7edoC1+0Tx184PxWVWgUlGcO0BVJJAgffSwFzP3HfGBgfdiG0qyoTBVUfv5giCKLnJkq8dN7PeIo5fR0gSiB0SBgrponElKubU64Ml+mmpMJk4QPtid0TR8vyK53a+jwywd9HvRsrixWOdPK84NboO+atKsFTrSytsiZik5JlTg9XSAnS9wdW6wPHLqGy3ytwKWZMvP1/GFr5FxNY2PoUlBEJFFA1yT6ts9Sq8hrJzPmnWhfu2a+piEhMvFi5uoFTrYKSKLAy8s1qvf7rA6yPXq17yAJAvc6JkVNPkyKnGoWeNCzaRY15lWZzaHNT+8NCF0QhzZRkvD+1oSZao7n5qpcnquwPXSQRfhge4wkifzhuRaSJHKyVeCdtREvL9eY7eTwohg/CLk8X6OsK0yciBu7YzRJoDvxKOZVnPCxaO4YnwscBwO/B/i0lF0Hm8DRrK2yPxz6cfoDj5/n6N+KJHJxtswv5WxRe2djQJzA2XbxiRvg0Y1oupLjVLPIw4HN9shnuVHilZNNXlqqHw4v3d41MPeHid0gIRXgnbURXz8/xc9Wevz1jQ5eGHNuusjdns3QdDC8kP/6i4v0rJD1vsXuxMdyQ273LL59cYpGUWetZ3F6qshUScMPYww3m1dI43Q/MyPz6ok60xWdH9zs4IQxN7YNBBI0RSGfk3huroTpxqwNHXKKRLuY42Hf4X5nwvJUhVpO5MEW7EwCxl5Kkgj4YYgfRkiygKRIvDJbYWvscmN7zKlmEdOJ0HUZ2wnZkRxyOZGYmF3DhSRhbIV0LQ/SFFWRcKOEvCqRJAkjJ+AXd/qUcwpjx8+y+JrCl07VGTsBrp9QySvZpjVXZrVvcn/P5JcPhky8EDdOWcgrFHWZnZFPlKYkSUyjqNK3/UOKz0wZU6VZ0BjZJn07JIgjdsZZVuvSfJV7exZJHBMnKWzw1OzgUeeiY3iHla6Fev4RO3s8I/l4telZ74XjFqFj/CbxpETMr9PunsXun6Uy/KwVjCed7/FB4XZJeaLuzCfhSeSiMhzOEpjxh487fsyO4UIKU2WNk80CmyOLa5sGYzukZwfsWj7np0q8crrOO6tj3tkck1dkzs8UCeKEs60il2fKtAoaUZxg7wcGYRTzxsMBdw3wdgyKukwUZ3vPz1d6xEnCH16YZqlRoFXKsdQxaRY0bu4aWavp4edNiZOEjYFDs6TS0FUkQWB94DFfe/zTprTLOs0LOe51TM61M7pQVZEJY3hhsc7m2OWDLQM/Tlmq55h4IaYbHrYJtys6jZKGLGZ7u0CC6weYPqzcH1DSFGRJ5Lm58qGezPdudRk5Pm6Q8KVTDV473SKME350u0sqwGrP5mf3B2yPXQqKxB8/P8OV+TmiNOWb5hTvrA35N+9ssDvxHtGJOcbnB8fBwDE+gqNtP0dZHKI44epS7ZGM/6fB0A5x4mzYq6BKnGmX9lV8R1zeF5w5wMGcQ1mXubFtkApwopHnzHSJrZHNw57NiVYBIYX3tseZCq8osGu4vLBYyx7fHDOwfP7kyixOEHJz1+JrZ5u0qzm+e30X0wv5Dx90qBRUbm4azJR1SqqM5UeEYUocJ/QnIaVpia2xhxtGlHMKeUUiTDLp9IEdEMQJf3O7w9rQpapJjG0fTRQ50SyTpCI7Y48widFEmTRNaZWy3su+G5DXBPwoRgQWqjqztTxLzTw/vdsjr6l863SDqYLGjW0Dww0xvRhFkvhvvn6Cu7smlbxKKa9Rz8t4YcK9vsn1bRdJFIiiGEEUEWPYHXvUSypBlLAxsOhMAmarOa4u15mv5tA1hYEV8De39wjThGZB48XFMnEC/68fP2S+liOIU56fr9IqqvRsnzhJiNOYt1eHPNhzSEh5b8NgvpZlyOpFlYIq0pm4jJxsruHCbJmhHTPxYvqmj+VFSAJc2xjhz2bVg3ZFPxQiO8BR5+JZhw0PnKlnocZ9HMctQsf4beC3aXePO/Af1xL6WSsYjxyfxEfO8/GKs0er0k+CBE8cLJZFgSuLtawCYPu8sT5kqVnirQdjupbHaycbnLbz2H6KgECSpuiyQFGTiZKU3bHD2JKolzSirQmvnazzz76wwK1dg2sbBrc6E0ggr8j8/P6Qnhnw4mKNG50J93YnmTN8vs3YDlAViZya0Xp+sDM5pB+dq+XYHGTV3aqeJ6+pnJ4uIosiUZzwxmqWhPn2henDdtof3e5yu2PSruq8uFgjijNyCoDLc2W+23fwooQz7TIlTaVS0OgaHh3DPdQYsPaTZz+6vcf1bZN2Cl89U+eFhTpemK3DYZywa7gUNZmLMyU0ReJsu8R7GyO8MOKDnQnPzZYpaBJhnDBbVZm4CT3T5YNtg5myhhNkyZ6cKpOXRBb39R2O8fnCcTBwjI/gSW0/nX26xwNxsMeHOY86X0/Lqk6XNaZzcH/P4vaegyQKjO2Anz0YAPDKPrfyQZuH4Ubc7ZgM7ABZEBBlCcuPedh3uL1r0rd8bD8mFVK+eKqJ60eHg7AnmwV2DJs7OxYLDQNZFCmoEq+vDlkbOJyfKZNTRb52usmdPYuhE/CN81NAyvdvdnk4sJkq5yjmZZabRR70bB72XGp5lZu7Eww/ZrmZZ6qo8MG2Q3fiogopLyzUiGOBYkHiOxfbdC2f65tDhm6IkIYgCPTtgFcW69jbY5I4ZaVnE8XQMz2mq3nGdkCcQCWvUFUV3lgdstq3aRRUFAkcP+QX9wb0nQBNEinlRHZNj6KmcKZV5t6eiaIIFFWFL59uMHFDNoeZJoGAgB/HiEKKKMDtjsnYiTH9iOmySjmvsNjQGZgh6yOXvOTjhjGOF5OIAkM3YOgGOH7E6akSmiRS1BXOThdpV3Pc69qHbQA/W+nxxtqIZlHlVLPIF083mC7n0GWZZlFjrp5npqLzn+902TI8KrpCEKasDZxsdqD0ZBn1j8ty/rqEa45bhI7x28Dn3e5+1fvr6PFhEn/Cqz/E0ap0U4Ou/+jzPqAAj3UQUc4rWE6I5UUZb76uoQgCiZDSKmo8N1tly3D5X97cxAtDemZAFMeoskhvDHsTn4qucHmuwvOL1UMNlG9fmuHMdIlf3FN4eLfPlYUyjXKe9n6iZ7ma40HX5G5nghclSILI5f3h4ldPNQ4DgYEVcGN7wrtrIwQx5cpCjUsz2QDvLx702RzZaBIUNfmQWGFz6JAKAhfaxUMhSFkSD7+f+ZrGVDmHQMpLi3Uq59RMj8AL+OHtPYq6xKvLddpSFmz80eU2cRwxXh+iqxmt9eZwzFvrQxZqeZww4UQrz0xZR5ZEbu0Y/OBmj29caPD1M02aRY3Nsc3IDvmDCy3WehaaInNtvcMNGUp6pvczMLPK+/dvdvhvvnr6s5jPMf4WcRwMHOOpOEov2iiqhyqEBw77UYEZ+DCT9bTsliKJSCJIosR8JUcqCFR1hYvtEufaGffw4/SSZV3m7pFyaKOo4gcRQytgvqaxNfaQBJGiKhMnkMQJK10LO4g40SrycM+lYzjc3DIx3JA926U38Xlpqc4fnJ/lZtfCsD3SNMVwfHpmQFaKzbHUyHNvz6ZZ0Pj5Sp/bHZOX56t8+VSTnulxbX1MlIIXxeRUGUkUOTdbZs8M8IKQ797qYnsBCGC5EaokUM4rkMLNXYMgSRFFgflyjn4P1gc2Qzfi4myVjZGN5Ue8sTbkbtcgpyoIIuQliZyiMnEiposqr68OURUR04n4s+dr+9chUC8obI0dkihmY+gwtkI2xg4XZso0FJXdoYPlR2iqxGxVY9tIaRY0ojTbJAdmwMgMqE8VePVkjdlqAScIyMty9p0Uc8iCQLWQMTMVcwqVnEy9ENKzfGRJJBUEXl2uUS2o2EGCrshM3AgrSJhXZfKqzIlWkZKeXfMfXW7j7pfg25UcYRgy8D4cOD/A02ZXjj7/qwqPHathHuO3gU9rd7+pdrZf9TxPGuj/NOc7qidSL4p0/Y/2nT+pMrDZd/nJ/QG6IrJQ01EkGcMJkAWRMIJ3NsZ4QUScpPh+ygvzZbYNnxtbFtVCtkZV8pmeTcdwubE1wnAykoecIvHHl9r8q1t3ECWR0/v8+T9e2WPkxJyeKjFT0VmqFbCDmLHt8/bGmI19BePFus79PYOaLvOPvjCP54coioS8//1ujBw2+g7nZ0ucny4fthVl310V0wv4/u0u3xLgRLPI1aUafcunqivYUcT2wOXWjsEXT2W02wMrEx2bq+aYquS42zHZMz2mSjn+4pUl/mrnNqRwZ8fguze6uEGE5cY0SiqyKB4qxM/VNOolmbEdcX42z9vrYxolmXpZ4c62wdrQpaDKNIo5uhOXigbnpopsDW1cP+T8zLHOwOcRx8HA7wj+tjaFAzrGekE9ZBQ42ib0pMX947JbVRWem68wXc0f0kOqiszQCpi4EW4Y0bNdNscKC9UCW0Mbw8tk6g82yfl6ga2xxwsLNa4uZ5+1XlQPg4ab2wb39yy2Bw6iKDBdybHcKFLQJK5vjXnrwYjFeo6JE3Jtc4QiCrTKOawgwfZjWuUcrVKeXSNbPN9ZG6KqEovVAq2SRkLCG6sDvCBmrp5juV6kXdDQVIU4geubQ7ZHHkESU1BkpksZ7elsRWepmedhz0FTJCQhwXYTFCWmpkGtqGEGETtDEwSysqqaCeXMljWsIEISJaYKImGaMjADBpZPOSdjuhE/WdlDVyQGTogiCjhRysruBC9KmamqTJU1TrUKRElCXlOYqerkNQVdkYgTGDoBThCzM3bIyTLbY4e1gcV0OcfJVpE01dizXGRZ5HSrgKLITJU0TrYKvPFgwMlWgZEd8LBn8b0bu/yDF+e4PF87tKNGUaVreJxuFWhXcjhBxLWNEV4YI+7PehwMBEOmVL3jPKpYfcAqtNIxkUTxibMrBwHlayfrnGgVP9G+j9uBjvF3Fb8p+/0099ST8HjyKIoTSJOPUE0//nrIPpciiYdrw+3Bkw86yl6vkVULCirUcjL1Ug5JFDC8ANuDb1+e4rn5GiM7oGcFfPVMEwSB5abOqakSkOLGKW/cH3Cmle0db60Oub1rUiko3NqdECQJZ1sFVk24GkSHCspLNZ2e6fPVcw3alTw90+NUXmVl10SVBd5ZG9GzA9b6Nitdi+7E5S+uLvJHz81wfWPE/T2D6bLOV043uJZTmK/kGDkR3X1NlYN9fnNos2sc9OCXyakyVuDSrsg8P1thZIbEyYcsbKeaBb56pkmcws9WekRpytD0GFgBJVUgSKAqC+RUiYuzZeZrOpfnq+RkielKjplK1t4zXclhupn+zdgJUGQJRRSQESnqMufbEn/2wiymG/HB9hjTj3llqUbfCfjhzS4rXYurJ1rHM1mfMxwHA78j+CybwrMEEEfpGFtF7ZAm7kkCMwf4uOyWJMJ8TUdRZPJ1+bAV6WA+oaCKSAjc3Da5vWNS0TXOtos0iurhYN0BBeXRQKRjeAztgLsdM5sZAN7bGCMJUNNVzs1kJdkrCzV++WDIe5sGG0MXw86CjK+ebTKwfOIoBRKmizKNkkY1L7FnB6iySLMo8zd395AlCMOIdiXHnz4/z09W9kjSlLmqyC8e9DD9iLwmkU8z/msvTumPPaaKOfZMH03K5h8aZZUf3tqjllOoaWCHEVsDm+HE5Q/Pz/LV803sIOZh36Vnedh+QhynnG6WuDJXwvYi9qyAl5dq7BoO17fHWEHMyAxISJiq6Miqgmv6JIi8vFDDCRJefzjgZKvEKydqPNhzECWRK/Nl2jWd733QYWvskJdFnChBlUQGdki9oLK8WOJOd8J/vr1Hs6Rwv+uwVNe51zG51TGJk4SJl/De+oh3N8fUCiqX52uHWfxDZeFWgY7hsTW0+e4HXVQZaoXM2T/qdEyXNWbzjypWH7AKnWwVmKnoH2ER+jAAfTZhm897W8YxjvFx+M3a79PvqU/aSx5PHkVxwt2OyTh48vs9/rmOUgt/EhQ+1BrYsQABzreLbI9cJEFhe+wzXytweqrEWi+rInuqhCgIbAw9VEnktZMN3t8Ysjt2EUU41SqzWNeZeBE1XWa1byOJInlFIoghSeHnD/qcahZoV3TaZY/5aoGVrsm1bYOCImIHCS/O1zjRKnCvO2GhotMzPFYHEW+uDpmv57m+PWGlY9Iqq3zpdINXl+tUdYX3twwgWx9//qDPUk2nWdT49sUpWsVMg6VdyeGGEZsjm+VGnvRcVknZNVxkQWCunme5VeS9jRF7pp+pMosylpdRV98cwrs395iv6by8VONbl2bIq/JHxB37lsfu2GWxniOIBE61ClR1BV2boEkCy80ybpCQU2X++LlZBlZAo6gSBQlelLA79o6TMJ9DHAcDvyP4LJvCs9yQyr4w1CcFDc8SWIRx8pG2j8fnExpFlZmKjhfF9EyPdkXnRLP4EcGohXqe1Z7FT1b2KOYkLrYr5FWRlY5Fq6hRySu8uz5k6PhEScKfX0kwvIitgYXth9nnWqjSqujokkijpHFty+DenskkiNg2fPKayNAKma/pzJRyeEGMKAos1fIUVAVNFRlYHtOlHHlVppxTcIKIekFjaPtMnJSztTxuGCKJAqKQ8tbqgIkb8vrDEf/Xb5yiWVB4a21ExwQh9EjjFCOKGPoBkiji+gELtQJ7loPre/QcnzfXe9SKMvf3bCRJ4NauSSUn4QYJZ6dK/JOr8/zwZm9/eEzA9GI+2BlzarrEet9i4vn4gYobxFh+iO0FLDeL+H5MJa9wby+mZ7g0Szm+cq5FEKdIosh0Jcd/urHNrd0Jjh+ya/rc2jX4k+dnePVEDduPWBtM+AcvzrDYyPMXryyy2rf4X9/eYraW42tnpjjfLhHFCTd3DPKqyDcutEhJmKlk9hfFCQdOhyKJNHIfVaw++Pfo40dt+eP0Cp5k38eb0TH+ruI3Zb+fdE990l7yePIo3K8MOA+efL7HP9dRauElHdbdp1+rKkC4H7dEQNcMuL0z4Y2NMfNVlednq1yaq7Dat/hf3t5kZ2TTsyMuTBep5VW+fr6VkVT0HWZrOqebBXQVTk+V2TV9NnoOhh/RKmgoksRiKRMUW+k6h5Sdp6ay6kkqCMyUVKJEZL4ucWGmzFw9jxsm3Nw1qBZz/OG5aap5DS+KuDhTZKqksDn0+MW9IcvNAl8+3TxskYriBMMJedv00GSJy3Nl3l4fkwqgKzID0+f7t/bIKxKVvILlJSRJjChJdA2PE63iIUNQFCecaYOQQhRFzOXBK+ew/IiHfeewEnEQhB2wC/7g5g7fvdXlC0sV0lTktVM1coqMKIAVJKiywA9vdUgFgcuzZa4s1ri2MaJV1fnamRb/1ReXHmt5OsbnAcfBwO8IPsum8KvoDzzu8D9LYNGd+GyY8INbHb51ee6QPejxQOJEq8jm0OFBz8J0TeZrmWDKgbrxat9i7IQUNYntsUt34rM99liuFzhwJAeWT06WOTel0CzqVPcHrd61A0izmYAUkZIq86Bv07d8wiihnJeZKmsISTbQiyjQLGqkQpYB2R45+EnKa6cafLBl8O7mmIaucrJVwAlTXlmu8P7WhCRVaRQ0IKZjeBR1BcPPxGUEEizf59+/v4Usi0RxTDMHrz03S4rAva7FUk3nb2516Zo+DV0hKegMJh5hBH3D4d+9t8W5mQpfOd1gYId8cblGKS+TpiI9K2Br7CBKMF8r8GBvwsbQ43s3dvnqmRa6qnB/z6RjZkxIpCnrA5evn5/iynyVM1NZq9VSU+fPnp/lezc73NuzUEQRy0/QZAEEaBRUklhgte/QLKi8tzVmaIXIksy/+MOzbA0drq0P2RzZtIoK05UsaHKCiPfWB9zZ9biyUKVrhOhygLUvDHew8YVP6CF4ZADxiN08yZZ/nSJKxzjG7wo+6T74LPfJ0/aSj5vJma/pXH/G27BRVGkUVC7PVUg+xmupyKCKcFBAWCzBH1+aRpFFVvoWxAJ+nPL/fWsDJ4hY2Z2gyPDiXIlqQeX6jkmjqJIKAk4Qc2W+wsOBzZ17E/7wfMp8JYcuyZwTEiw/xg4iZBGiJOUPL0yRkyWiOGGlazJX0WjkFeYqNf76RpdT0zXWhi67E5d318foMrRKGl861aBv+by1NqJeVPnyqSbtis0762OWGvojegRXFsq8tFjFDEJu7ZjsGR5uEPGTO10UWeKV5TrfudymlJPpmz5902NjFKHI8SO/R5gkvLM+5rWTdWRJ5OaeyVQezl+e4s11g7EXsDWyCZOElY7FqVa25t7cMZhr5Pmzy9O0Kjl+eLPHwPJ5ebnIcr1A3/b5YHPMextjavmMOvZe18TyI95dG2StsH7M/HES5nOH42Dg9xifNoB4Wt9ouC8ks9TQ8YKI1Z51WFJ0gogb2waX5ypMlzXiFH75cEirnOeLp7PBptW+xQ9udfnWxWnma3mubYyo6gpJnHCrY9EqZ/2KoiRSzcnc3Brz9saYP740zT95eYGtscvA9NgxXFRJoF5UieKEC3MlLsyW2By63NuzOD1dJImhoKksNQu8tFSlO3G53zGJ04zuNIxSwjhCkyT6dkAQJYiCwMWZCuWaznRJRxAFzrZLPOjZ2H0L0w0ZuiHNgsaDbsL60OHMVJF2WePdzawnfrqiMlvSieOEsR9xd8fgfteklFNQZJEghZ2xh58kzDfyJKmI6cXYfoiuilR1melqnnJRpTN06Jk+7VqIJAjMlDU0TeZ0q8Tb62NcPyWIY2bKOdIUzrarLNYLzNR0JFHk//G1kzzo21RzCnlN4t9f28VPYlJidE3hxcU6p1pFVvYs/sP1HX5+v48AzFZ0/ujSNMWciOklLDd0nCBFVwXe3zDQNYmvnylTUiX+3XubbIxcojSlklMRRenQDm5sG6yPXTb6Lkv1PJAeCuAcVSoNI+2JA8QHeDwAPbDlzaHzxOH2p+lnHOMYv4t4miP+SYmbJz3/aTL/n/Ren+XaB1ZwqC3SLGlsmv4Tj4sA80gnUaWgsWN6BFFCTVOZruRw/Ihfrg6RhJQkAT8FXVd47WQDP0w408qzaXjkVZFiTqaoSIRhwk9X9nhpqcF0WeXMVIlUgF/c67IxgX/z9jb/4IVZvnVphvc3RvQsj3udCYoscrpVpDPxGJoBzy/WuLllcH/PZKqY49uX6ofCmvVCRvk5vd+a2yxqtMv6IbsepHQmLnd2LU60CnTHHnlVQhHg2vaEqbLGl041WagXcMOI2x0TJ4xwg4QvL2XCZat9i3fWxkxXFIa2jxtG6MicbBUwFWiXdV5ZEnlv02B94CKJGelHJa+wa7jk1azd6VuXZvGCiPW+Q7us0zU8+pbPwPZQRJn5So7z82VI4Ucre+iyyIOehb055sWFKhdmKs9sC8f4zeA4GDjGp8RH+0YPaEcrusyDPRtIDwc7b2wb/HilB8CL82XmihBUs0z9QZWhb/qHg1BjJ+S7H3SZrqj84bmpjKGnXTqsIphewPdvdlFlgXZZZ7lVpG/5bAwdVjoWUZJwerrEF0+1+PsvzNMoqljuLm8+HFErKPzTVxZ4f2PIzthne+zyxoMhhhvStVyWqwU0WYRUoFVUMT2NrbGN5Yds9G1sL8L0Ql47WaeSU7D9kHJOYXtk0zNc6ifqWGFCKSfjhBFvrdk4UUJeE+lbIT+3++RUkaV6gXQ65VS7RFGRWOlO2BnBrukSRCkLNZ2cIqBrIufLFVRRIKfKLDR1yprKz1b67FkujYLCX9/qoogCtzomSQKL9RyqKDJbtTk5VcRwY15cqPD8Yo3/7e0N3tkY8cWTdVolHRBwgggzjBHSlGZB51SrAGSL/1rfYnNksW04yAi8/rDPqWYRVZbR1IhmSSMny5hByMAK+YP5Bpfnqvybd7bYNByKssx3npummlf50Z091gY2vYkHgsDVxRqvLTc40y5x74iWxQFziBtG3NwcsmFmitW6Fn/EqTnQojgQ0znA04bbn6Sf8VmyU8cVhmN8Gvy27OVpjvgnVYSf9PxnaUM9SBIdEAZ80muPfkcH1+6GEWMn5Fy7dDivFsUf7kEq2RxanEBOBieCo/XEzb5P3/BRJQFICeOYv/jCAieaRWwv4G7HRpDhhbkK6wOH1YHDrpm1fvbMgGvbBkIqsFjPY4cxA9NlZ+zQtwKaRZU0FZkvQrWcY6Vnwc1dJEliqaaz3rfZHXukSUI5p3Brx6RRyjFyQ5YbeYqaQs/MRBqnKznO7rPq3dg26Fk+tbxCmCS8fa/PuXaBMIrxo5Rdw0MixQlimgWFM60SW4bPqydr9CyfiWdTzskUNRlJ2K+UT3x2xj5LdR1IkUWRiq5wd3eCHSa8slRlHMDPHww4NVXkj59ro+y3hi7UC/sqxX0utEs8N189/D3//gvztCs5toYOG2OHOzsGqigSJil9N+B0s0jP9ClqEqKQEMQp28OP6fE6xm8Nx8HA7wh+ExvO0/pGjzpfraL2iOT85bksA5D9mzKVgxefnwVB5OaOwdbQpqYr/MnlNlcWM+aZOE5oFjVkSUTdp6Os6CoL9Ty/uG/j7CsJz9XzrPYtvn+rw9AOcIOQ7YnL2A4Oh1YVKZOgv7GTqT/O1/L8fKVHZ+KRpgnvbgx5frZMRS9j+iF+kjJf1RhaPq2iTiGnECcxayOHoeOjyBJbE4/1gcPO2KeQE4nTGC8CL0qo6hrVmsy24SCIIlMlhTBOqegKcZIwsAPyisiLi3VmKxo/vtfjXsdi4sBCKebsTFaWNrcMzk2XmSqqDO2Qe50JThBzdrqErktYg5i314acm65wdblOTpH46xu7dAyJqZLOmXaJgqogiRLtis7djkmYQppmA9x2EBPFKUUlh3thioIm07d9/ue3NhjbAX94fgrLixhaEZWcyldPNclrCmsDh4WazotzVdaHHpIYMFfLcaqdp1HS8KIYL4xZKGtMVwosN0u8uzHgl6tDXoxi8qrClYUq87XCYfn7rY0hQirwZ8/PcqJVRJFExk7I7Y4NZM77z+71P1KROpotPDrE/rTh9ifpZ3wWHA+/HePT4LdlL09z4D+pIvw09eBPe+1HtWk+aU96vOp8cM2bQ5ufH9GhAVAV6fC4AGjIoCgCPTvlceWCmg5uGLM1DtgzXUREpkoaf/HqMu9vjIgRWWjojO2Au12TMEmYK+osN/M0iznyqsDdrs1Co4gmC+yZPoOxx0INRk6MHcTMF+GVCy1u7GQq69MlkQvtCje2TNaHNvf7FkvVAm4IYzvADSLqxRyG7fPLhwNaJY35euGjujr762CcJPznO3vc27P55vkWr52oM1vW8JOUZilHTpU53SoiiwJvrg5ZrOX44qkGsiRyY8tgMMmcb12WaC/XWW5mlN0dw+Mn93tUcgovzZdBgIkf8rDn7KsT64e/e1mXud81QRCQJfGw7TLap3meruQ4US/w07tdZss6uiIiAOdny6RCyu1dk4vtGp2Jzx+cbwLHSZXPG46Dgd8R/CY2nKdtCEcfP+j3P5Sc36ckUyQRkhhJzNhhumZIXs24i8u6zIlmgfc3Rlyaq9DepzCrF1Uqlv9I5veFxRp906Nvh1zbGOFGEetDG0UUCNOEKEr5YHvMzR2TmVqOb55vI0tZFkSWRK5tjLjXsTnXLmRCNBOPelHmW+dm6FkePTugmlO4vWuyVJWoF1VUUaKgKnztTAsvjinpKm+vDWmXNWaKKooIIyfifLvGwPKZqea5vFDB8QLeWTco5xW+enaK6+sj+uaAe32bE42Uke0TJymXZoq4io1WzTO2fVY6JkVVolXW2Bn5RHHCjuFyf8/kTsegWczhhRGiKKDKcH/PZM9wMb2QMI4p6xpfWKgw8SOqOYnVoc2760PGdkBN11jpWtzcMdgzfabKOaZKOc7UdP7t2zt8sDPCDRJ0SWSqnGNjmAmiVQsarYqOKguI+wHGfL1wGPgt1/OYXszANNkxHOYqeU5PZ1UGXZPJSdl8xp4dMLZ9Xjd8Xjv4UROBOE3ZNdzD9rLLcxXiKGLLv7+/UXy0IvVZmVR+1aHLYwaiY3wa/Lbs5bc9HP/pP/eH9/jBtTeKKvL+enCAoek9ctQgADFIeRLhqBvBxdkyM/u8+rd2J/hxyo9ud4nSlFpeZjDx+On9AbIkMF3McbKe52K7Qk6VieIEN0zJKQJ5VcZwfV47VeXbl2cw3YitockPNyFOU2YqWvYRhKyS+19+YZ7pisr22GOqnCMIY+ZrOZolNePzT1K6ZkBBkw4rKAeiZkf1dWRJJK9lQo2XZitsGT7VYo4vLNV50HMOB5ZtP2C97yAKMHEjLs9V6IxdBKHEXF3HdkOifdahraHDO6sZRfNSPUuwNDS4fLFN1/R5e31ELW/z9XNTLNTzDK0AUZRoFdXD37NjePz43h67I49/fHWeMEqIY4hJKcgiIy+j5Z6r6lyeqzKaONztWnQn3uHxx0mVzw+Og4HfEXzSwvu0KPxxSsanReofd/xq36Jv+rywWEPZpwk9KA0f7dMmTQgiuLY5xvATyjmZWl6lnJO5tmlkmaSuSSqA7ce8uFDFChK2Rg5jJ+TyXIW8KvPcfI3/+MEuD3o2iw2duVoe24344+dnGZk+rUqO/3SjS60gYblB1n4TxtzYHrPcLFDMy7y8XKdjelzpVKjpGm9sDOmOXc5Ol1lsFtgzfVrlHEGSsFjTeX5uPhu02jV4uDehO3bxwoibvRA3CDnVLNE1bDbGLrIMLy/P81evr/Hm6pC5Wo6SJnOnmw2rycDbawOWGgXCMMFNU8oyDJ2Qjb6FKotUixoj06NjBVxolzCcPCVd5sJUGU0Vma8XeXd1wK3uhDceDoiS7Le/ulgjEUSqBZXt0YS3Vidoisx638YJYk5MFeiYDtc2x9h+yHPzdVolDVkUeXG5RruisTGymakXyCsiXz83hRfEfPvSNDuGz1xF469vdAmTKmfaZVZ7Ft+9tUsSw6sn6lT1PDd2TPKqxNgOcQKToirzhZN1zs2UuKoqj1Dlzdfz/PmVWXYNF8OL6BgeC/U8eVXm6nKdvVswV9PJaeoTM5wHNnY8JHyMY/zm8HH32dHnntXJe1rVOa/KhxWBA6waH00MFAWYpJm+QMKHSsR7LtzaMVhuFtkdu5xsFkmShLdWh5xs6XywPUGTJBoljVPNPB9sTXjQd7i7Z/Gl003a5RxFVeT6lsGNHYMwSnntVBM3SDjRKjJdUnjrDbi+aXC3a3N2psiFaWVf98anXc0zVcqxN3G53bPomh4XZyucbBao6BKtksqDPQtRFJH3NXEOVIYNN9PXeXGxdkijHMYJZhAfsvGsDbK9ceJFaDJ89Uyd09MZY1vX8JCkrBIii/DjlT43OhP+q1eWATg3W6ZZUmkUs/caB1mirm+HVHSFk60CjaLKas9idWDSt1yWGrlD0ccoTsgrWUvXg55FKafwj67Oo4oSP17ZQxRSJn6E33eo5xV+/qDHthHzwzt7/BcvLx8nVT5nOA4GfkfwSVmgp0XhRx8Hnhqpf9zxP7jVZdfwkCWRmYr+SGn4aJ/23Y7Jpg15O6RV0Q9Fql491eC8HXBnZ0IqCAhpiiREh0Olj5eK5+t5/uS5GSw/5O7uhHZJYzNMaeRVXl5sMLI9CqqM7af8zd09vDDm1taEzn65tKIrGG5IGMEfXWxjBzF/c2cXy4uQBXjz4ZDNscNUSWOppiNJEiM361vdHtr8pxtdkhRyqpT1qXoJY9dHU2SqmsqrJ2p8sDlmoabzZhqTkHB9e8zQDpiv5imrMisdk9UkY2vwwoRXy3C2VWDgeJxrlXgwsHl3c4QqSQwKKmGa8MJ8DdMNubVhocoSS60iu6YHUwWCMEVRsmyM6ycoooCuCjzcszg9VeLCVJFUFGgUVd7fHCEIIAsCy/U8XzndZL3v8MVTDZYai6z1Ld54MKCYU8BLyckSb6wOsLyYMIqx/KyP1wkiPtgaE0YJinRQLcjzF6+I3Nwa0514TJc1vnhqmpwiM7AD5utZkJhTP1x65vftqVn6sL3swMGIk4yFar5RfKJz/7hd/iayTccZrWN8Gvwu2svHfabP8nmfxhL2pECjCFhHHlOBelmmnCbsTBKOHlFT4cpClYHpsTl2CZMUy5e427EwvID1oct0UeOfX14kFeDWroWQpqz3HJKkT7Ok7a9JKbKUzZL9wblsj3lrtcfpZoGFAlTnylh+wlItI7q42zHpmT6GHZAKAmM/xvFiFuoFarrK+sBl5AT4UabN4oUeb6+NyWsy3zg//cg81NH2xhvbBkM7YGAFTFdynJoqHoo+3h+4dPerJqoqU8+r1PMKYy8iSlLCOEFMRT7YGvOlM00utEtUT9SzCkgUsePArZ0Jhp9kBBiVbDD49YcD+paP4YX8+G6fFNgeeYBAu6IxXcmx0bN4f2vC+XaRBwOT1Z6JJIl8+8IMzaLKu2tjBEGgoMLXzk1/5Dc/xm8fx8HA7wmeFoV/3LDYsx7/rYvTdA2Xmq7QKKqHg17waJ82aYJZyMq2841M/ORWx6RVzmVOfi0bOD7XLjFxo8P38IKIr5xqcK5dYnPo0CiqhEnC9292eHdjzFRZ5UK7RJQkXNsaEYYxzbLKYi3H5dkqtzoGu2OPdlnndKuIF6W0yzqy6PPGqsnm0GZoh0iSQNfxGUw8+laAAMxN8izWc8Rxyp0dg62RSxAnXG6XeX6+Ss8JeP1hn/lqkfm6xvbI4z9e32XL8HH8AD8VaBY0zkxXMO2QhVaeRjHH+sjhuXYVIwgYmB67loccxoQhbI8dTCckCCIKusobawOmSzrrA5sb2wZuGFPUJGq6QquYY2D6hFFEGIOYpqiKwK1tg/lGkUYpR16VmIQxF2ZKXN/KgpILU2UURUbXFN5ZH/CL+yPsIOSX93voisTuxGdeFBBFmY2RxdYQBBnmynm+dKrBpbkKP7rd5fq2wVwlx5fPtg5bfHRFxg5SepaPrioMrUywrlXUaBTVD6nt1sa8nCSMnZA900NIQZJE5CObxDiAux0TWZYf2TgOHIYDezsQpXvc/p6GX6WC8LTB5WMc43F8miHaX/d5/zYrZEf3g8fP9STBsE9zLZ8UaESPvT4C1owPHz3aLqQoYPkxiihyspFHEiTOzWZ6ArW8RhInFDSFRkljrpZnbAcoioiqSpxvl3CCiDNTJd58OOTtjSGOH/Pm6gjTj/lgy+DCTImCCc8lKYKQUs2rnJ4qMV3JcWPbIAUaeYW8IrAxcGgWFb50pslKx6RWqCELAqkAP7rVxXBDxvucqF3DY6VrEscJV080Doeqe6YPaUqjqLI1cnh7bYjhBtzbs3C8kNWBhSKLTBVU9gyPM9NFzk+X2BzZVPMqmgS/fDhgYHmIkojtx3zn8gxzNZ3ZfLY3T/yUKE4OBSKvLtXoGC7dice7m1lF97WTDcIkoWO4zNVyTJU1nCBmuqLTKKqs9y3W+zZbA5sz00X+5EobNwpZHThU80+ghjvGbx3HwcDvCZ6l3x94anbm444/O11GV2TudMyM9eYJmgSHvNLyvgLxkT7Qy3OVR7IeB4HAAaXa2tDlfLvE0Ap4/eGQuZrGz+8N6O0Lfk2VNaww4ca2yWxVY2PgYXsRu0bA1WWZr5+bZmvoMlXRud+zmK/mmKrk6ExcDDdEVyUuz1Yp5xQMJ2DTj1FEGFoeYydAFKskKdzYMbm6XKOSU4gF2Jp43No1OFEv8tJSBdMJ+dn9Hp4XcnKqxB+cmWd3bNMu61zfNpgu5xlYIdc3xjhhTCQkPL9YZ6Nn8u5oiOWFxGnMzshn4qWUc9Au5/CSBEkRuDRbZaaSSd07XsyN3UzFcrae5872GE1J2d5Xi765Y/DNc1OcmykxtDwGVshaz2RoBzSKGpcX68hCihUmzNcLnJwKuLM94Z2tCct1ne881+aVkw1+cb/HmWaBgRviejEvLFao5TWGVkCcQkERSQUB+LDFrF3J8eXTDV6Na0RpyvsbQyZexNfOTu1nmoaH1HZbI5vNoUcQhUiizIWjjn1eoqrCuSc49wcOw/l26bCsfvT/BzZ8MEh+EKg8fvxRm39WPG1w+RjHeByfZoj2133eX4XS8ygT15Ou++h+cHDvHZzrSYJhn+ZaPi6YaFdyPE4qKpMNEj8JpZzK2PHZGng0SrlMLbegZmQIPQsvTtnpWawPHVZ7NkM3RPZEXl6qsbI74UHfpl7IcXK6wP/5tSVsL6JVyVPTJc5NFRhbHv/+Ngzv9uhaIbuGyz9+cR7I1i3I9rdmUeNO12Jkh/zbdzZQZZmvnZ3iRKvIas9CkWW+c3mar55rsbnfgmM4Abc6MUM74BsXpmlXcuwaGj3T59rGiI7hsj1yUUWB9b5DJSez3ChyplVk7ETc62bZ+eVmiSsLNUw3Yras8d1bXVIkypqE4Ub7tKUf/q7tisLW0GGpoRPFCX3Lxw4TzrZLOEHMxdkKzWKO1Z7FxsCjpivsjD3sIEESoOdEnGqWGHkhqyOb/ttbvLhQoVbI8aDnfOLvf4zfDo53st8zPClL86THnnUBfzxDe3T24EnHx0lGFTnfkA77QQ+k5numT6ukPTJrsFzXD7OwXcPjYMisWVLxw4jzMxXyqkROk7iza1LSFSTR51SryIOezerARJdlTD9ma20IQEGTeHttSDGnUMkrLNbKVAsKmwOfE608eU1h4vi0qjqGHWYMQbqK5Ybc2hohyzKSAIYTsmd4nKhngmM/WNmjOw5IUsjnZL50psHYLvO/vb9Jz/LQFQldFnHjGD+M2DVdakWNekFlOp9xPG9NPIZRQiUXc2m+wZ88P8v/+s4mOwOb92SZIE6wg4hKTqGuqwSkLFRzOF6JK0tVNEHkzdU+9/YserbHF0+2eMsOKespnUlAnKS8slynXpBZ7zs4YYwsCJyfLnG3Y/HCfIlCTiVKUj7YNvhPN/Y4O1NETOGDHYNKQaKo5bi6VKVVVFnZg9U9k6HpcaZd5sJs+XC+Q5FEvndjlzfXRpRy2TBez/KJkwRZFKkXVGRRxPJCwjhFkSLaFZ2BFXCnY3K6qSOJHwaPwKFuxVGqQXhypjKKE15/OOQo1e0BfpV+1eNe12M8K35btvJZz3uw7j6u0QFPz/B/FqpSJ4i4tj4keDzNz5PVh4/uJVURRkfS/weBgMKHswJHz/PScp0kTvlgy2C+nmfX8BmaHoIgEscpNV3lxuYYP05pFmUaBY3u2OVe10YQBcZ2wMqexeXZMv/o5UUGVkCjqHJj2+AXD4fs2LAYhJyezvPW2oi/en2Dr55rMV3OIe1rJCy3inzz/DQ/vN3l2rbJdEU7JEyI4gQrDHhupswHWwbXN0c8P1/hG+eneOPBgGtbxmH1/MXFGu9tjFjpWMRJwqsnapxoFDg1XcILY7wg4qvnpljpmEiiwNmp4uHA8MSLOTut8k9eXqBv+VR1BS9KkSWR7sRny4bXHw6w/JgUAVkU6Nk+IyfgVKOA4Yp0rYB7HRO3nmD5IZtDmz++PM2e6dE1PRbqOltDh3OzZUIyB7M78XHDlCSNUWXh4w3wGL81HAcDv2d4FkGZT1PafjxDe4CjdKOrvazDs56XWDNB3Zk80vZxIDXfKmmca5d4b2N06Ox5QcSDPZtWUTscMmsUVcZ2wGrXwQ1CKgUVXRZJkoR7nQl+lFHV7Y5d/s3bW/z5lTmmywoTO2SqrNI1fe52Tc5Nlfja+Sn8KCUny6hywAsLNSwv4v2tMTlN5gsn6pyfLeP7Ef/xxi5vPBxQ0GXOtau0yjplXeZPL7cxo4RaXqGaBwEY2QGbAwddk3llqU5FVdgxXWIjIUoSoiRmvWcR+jGhIOB78FxeYUrXiOOYK3PT/PNXl/jRSh/bjxjZAVtDm5QUy4vYBc5Ml9BliecWakiCxIOOyVRZ4/R0kVJORUwFBpaHLIu8MFUhBXYMn74dMHJCEgFkQeTGzoSdkcPQCnjlRJ2eHfL6wyGqAEEUMVvJ0ShpGG6E5ycYto0sJjRKGiRwuzvB8WMMLyCvSfz07oA4zioOThCjSSLfuZyxOhlexNl2ictzFU40s011oVYgTBIUUTycHwAoa8JHRMeO6lYcHSx8UqYyUzOuP2KPT3r9p8Vxr+sxnhW/LVv5rOd9mkYHPD3B81moSm9sG/zk3gDFfvIxH6cuPluXGPUfJxHN2oMEsiHiA74hL0g4US/yN3c6fO/WHmGcsNjI8/rqkDRNsYOI2YpOSVepigm7o4DbuzYLdZ3zMyWunqgjCwKSCKkgHH4nv3zQ4/WHA+arGqdKIEkSp5olJEFgre8RxBF9K+TsdOGwNfLSXGV/7U8R0pSHPYeZio4siZDCz+8PSdKEzaHL2At5bqZMKghcni0dVtEVSeTFxdohhXfP8tme+FRyMr98MMAOIubqBb5wosHC/nzWh4Fb5vjLkogVuLQrMl8508raevYmhDG8u2EwtkPOtovUSznKmsTWIGbkRFyYqfD1szKKCP+fXzykllew/Ih7eyYbAwffj7ixNWR16HGymeeFhRoj22Nt7GC4PnEiMPEiniAsf4zPAY6Dgd8BfJqezGcRlHlSafuzZoW6hsfP7/eZeCGXZ0pYETQKyhPP3yiq/Oh2lxs7EyBz9m7tjLnXNYCEq3GduXqegRVwZqrE5sjl6lKdkReyPrC52zFJSVHFrG+9oEmsDx3eWRvxtXNN3DDl8lyZmq7yb9/Zwg5iIKWak6nqCsW5Mrd3J5ybKXF9Z4IiQd/K6D9XBw5zFR3DCZit5skJAo6fzRl891aXC+0StbzGbLWAGUTsjl2+e2Obr5+bQpVlKrpKUZMo5XOMHR/DCdgZubh+RLuaJ4lha+wgqCJRKtAoa7yxOuSLJ2sIQsLf3OpQKSjU8hp5Wean9zs83JswUy1yZ3vCyPH55f0+uiZxZaHOQj3Hje0JLTdHs6DQnQTM1/MsN0S2hh6aLNEoqrx6qsHuxGVtz8KPY/p2wMlWgZ2hy67hMV3J067k2Bh6VHSZtaHD9sjl1q7E8ws1GgWVvCozdkL6Vsh6z6ZZVmjuzwdsDW3uD2xu7jNxvHyizoWZrGqQr8vZLAkcBgIHtrVQz7O6N2HLztinrp5sfaS17Fls/FlbM45ZiI7xdwFhnLA1cv/WHKqnaXTAr7fKcUgd7N77yHMHleLhfv/8UXVxgPXBo4HAAfFwYV907JHqQAJvr49RJQmEhJEdcG3LYHvs8PxMiSvzFaqFHHGScHG2gizazFSzhMrEi3lvfUS9pPHcfKaBE8UJ9/dM/uO1HdaHLrWCTFGFqq5iBwlnpyvomsLZdpmuEdAsalzbGLHSNanlFURJZKqUo6YrbI997u+ZWF7IhZkyOyOPxbrO2AlYG7isD11UWeLC6eZ+VfzDdsf5ej6rpls+QpriydAqqbQFlXNHyDvWehZ9y+fiXIXXTmbJk7IuU9Flpis58qrM5tDhzbURPRcuVXK8eqLOhbkKD3s2JTWPE6ScbBVYbhU5I4n8/97b4oPtCRemSnzpVANdE9keZZUBK5QRAUUWmavpTBwfywu53zUJkhTLDRkeUY8+Xnc/PzgOBn4H8Gl6Mp9FUOZJi/5RitAD/YCPmyU4EJG5ulTlZKvA/T2LOE2Y0TN2B+CRmYKFep7VnkXfCjk9laemK4RxNly6NfTYHLoM7YAvnGhguBFzVY3lRgFEgZ+s9Li+OSaMY75xfpqzrSJulPDcXJl/d63Da6dqhAk8N1dlY+hg6RHLrRIbY5uHXRtZEdEkCcv3+cGtPlfmyiRxws9WesxULe7tGkQIXFmostTIszvxeHttSC2voqtZ36XhBlxdriMJIoOJy9ooo/LcHnrM13VGbkirqHF1ucqDrsnI8uiOXYI4RddE5BBOtUr4UUwUxNzpGGyPfNaHFmeaJaYreRoFlVZFx/MjVFkmjCP8MOKdzRGvLdU5P1fOWn7aRSo5hXtdm0ZRwQxiNscmRU2iXFBJSZl4PgPH5+xMCc9PsPwYP0lZ6Uzwg4RyUeHLZxqcmS5zd3fCet+iUch4tAs5CVWSuDRbYr6aZ7mVJ05gZPuYXsoLC1mv7LWNEbomU9MUNvoOb2+MmXjhI1L0W0OHf399h1RI+fPn5jjRKh5uEKWcRBjDrV2TdrXAiVbxiVSDz2Ljn4TfRcaXY/zuoWN43O2YjJ/WJP+3iF9nleModfDj2Bo63N6dUNtvD/3IgHIB7h+hE5LIAoDJE1qOzi8VCeKIIEo4P531uvcdjySJ8VKQJQnXj/jWpWlOTZVQRJEHPYf5aoGVrsnm2KOxX5U+2NMkMcH0Y56bLVPMy/xsd5eLM2XmGwWGTshrJ5tcnqswsAJML+CHt/ey3ntdoZ6XERCo6Qq1vMIvHmQtnS8tVPnO87Pk5Ezb5vrGiChNmKsVkEWR1x8O8MIY0pTXTjeRRIHbuxM8P2R77JICiw2d6UqRoZXN3blhxP/ydtai+s9YZL5eyFrALB/DjQ4DjChOWKjneUMAP05YbpUw3YiVrslSXefLp5vM73cMvLcx4pWTdbwo+7K/crZFGCe8OzNmuVXAdAPudU3++kaHuZoBpFxsl7ndndA3XKJUJD2iJ3G87n5+cBwM/A7gs2ZsnhaVP2nRP0oR+uw3b3bTz1R0BGBv4jH2YXvkIssh93v2I+/jhhE7Y4dXT9VYG7rIkkhNV/j2pRa1gsZSvcBUJcetbYNrm2N++WDAxZnMQazmFZIoaznpuxGGEyKJJhFwr2vTtQLOTRUZOj6rexZnWgWKssTWyGWpkefyYpmf3u0hkLJn+QwdP7teN+ROZ8JcvchLS1U2Rh57pkNMiqqINIsafphg+zFD22emkmXKRUlkuC8q9tJiDSdMuL4xJr2f0DMDJn6MKArM1fN8YbHBzbsjDCdgZAf0LJ8vnmhAAvf2bN5eG6GpEl8906KYk7G8mMWaztbYxfZD5uolLi5UWGzm+fHdAX074GHfRpEEWqUco47JbDlPQVeY2AGmH2H5IZooEycJoiTyp1dm6Jke728adC0XWRZ5bq5G3/L5yb0+qiIyVVZRRInTrSJhDFEKP1rp8a2L05ydzjQHfn6/z9gO2Ri6kMJsRSevyjTLKooikFdV7u+ZmF50mN1PAZLMtg6G5+73bIoKeAnY4RN2+V8zPo4d5RjH+E3j4yqxUVTCefBbvLjfACwvQtpvy4EPKa/blRzhY7ekyofVABkeYRvqj7LMtOUn/MH5Jl8+3eL/+d076IpNGCZossCNHZNqXiYnS1hBxL09A0lMuDRboV5QuXJEP6c7cVBFgVZJQ9eUbNYqD+fbRXRNJY4TSqpE1/CYr+fZHNpYfkSjoCBJmWBjq6QBmVDll043yKsie0bArZ0xQSSw3NDZGvtAyumpCo2iynwtxy/u93hjbcStXYMvnKizOXTww4ibOxN0RaJRzNHap0J9/eGQ+ZqGrkrkJOkjwmZdw2PXcHnYs4nShIoqcrkGX1iu4QURm2Ob1YFFnKQsN7NKw3sbI3680uPrZ1ssN0v8eKXHrX3SjyBJma/mWI9SNFWmmJPYM132JgEvzJVZrOTxgxAvSCjpH7KwHc9ffX5wHAz8DuCzZmw+S0UhPFIZ+Dgc9PcfpSgjTfiZB2+sDvnymamPUECOnTAbaBVFzkxlwimZOJXIqVamxDi0AtYGDnd3TXbGLnN1nS8s15mr5BAFga+ea3F9a8yDPYsTU3lePVGjllMYeSG1nMKe6bJimqz2LQo5maV6HsOLuLM7YWvo8eJihRiBnCIysLIFeWxHIKT0TI9yTkSTCvhhQlPXqOQUFk8X6Fk+/+H6Drqq8vJSFVkWEGWRIE4ZeyG3tse8tzFib+Iw1ygyW1bZGSsUVJmUlPtj2F3poWsSQzvgpw/6lPMqsghBGKLKIposoioygeWTCCKCIBDECZKQcL9r0Spq/MOX5tgzXP7Ne1uMbJ/og4SxG/PSfAXbDemaHtWcytnpAk6Q4gQJu2Obq0sNzrSKiCL0JiEjJ2BtYCNLUMkpeGHMfL3I0I5ZqOd44+GQn9zqMAkSZsoaJ5pF5ut5zrZL7Jn+vj6DyKW5Cnc7JgM74Munp1gfONzrmNzdy1J7Ly7W+PPnZw9t4OjQ+MlGjlMluDRXPRTZ+SQ8KxvK0+wbPsqO8knnOg4ajnGAX5dNfFx//nxN5/pvwNyeVVjs123705UcLy1WaRa1w+D8gESiY3gMP5TFQQZyCjhhllR4PG1gehF/c6eLLIgs1nVWezYvLdXZGjkIkkCtoDJXzeHHKd+71WVgedzcNrjbNXnQs/k/vbpM/ogmStfwSZKUM+1s/WyXVF5ugiyJfP92F9uPWO2bNAoa377U5spCjZEdEKVQ12UQoKYfUGumFFSFv3dphv/j+g5RlBInKc2iRiEn88aDPiM7I0LYGnnIkky7pKPKEnd2LMp5hTOtAiDQKqmcnS5i+QGWHxAnCe2yzpdOijzo2RhuyM0d63CG6taOQZRm7T8dw+H1B0NUFwQBvnerixdGCInAyUb+kN3tXLtEHCfUdIWpSo44TgiTBCeIKahZC6fhxfx5exbLi3jQs+hOAjq2T1FViBOBMBXoGR8qSB/PX31+cBwM/B7js0TlzyoO86TgYbqkcKMCLy1WD897VDX20lwFAajqClGcUC+qLDXyh8Ivrz8ccmWhnD1WVCnrCgv1HIYdcH1nwmwlhxsk5GSJkRPyoGvz6skG2xMfxwv4yUqP6XKO5YbOW+tDcorEcqPA9e0JqgiaJrDcKHK7Y3J9a4Trp5yYyvOV00WKusI76yPCKOHiTBkvTrjXNylaCi8vVFndM+mbATklZLUvc6pZZrqUI0VgZdekkleZrWrMVQs09EyOfr5WoG+5/Ox+Hz+C2A348qk53oz77PQdJBGaRY2cpjBVzjFby3G/a3NupsTG0ONMq8Bb60Nu7kyYeDGqLPH3LreZqmg08gqOH7FYzaNJAW4YM3QDiqrMf/HyHLIg8G/e3+LfX9umZ4W8v2HQruks1grUiynXd8b8z2+sM9/IM1fXWOt7bA9s8qqIImY83FsTFwmBnh3w+v0esiRyca5Cq5gxZUy86BGNgUxds0BZl2lXdc61S3T2M2gHdiDvB5CGG2F6MaoEdhDT3Re1OzrX8vjfB1zcT2NDOYqPs91nvS+OS9zHeBy/Lpv4VTOmvw5n/bMKiz1rEPG0xwdWgBUkzKvy4T19QOXbruSyKeH9ThMVGOyXBY48fAhNEhgYHnld4eaWwTvrQ2RRYLaWy9a6ksZba2NOtorkVYmTTZ0kBsMPKWoKbhjx5uqAc+0SPcvn5FQBWRC4ulTjxq6JLImHwog5RaQzCtgYuGyPPMIooZpXKesypNCu6Pz8YZ//vNLny6frLDZ07u1Z6ErGsGOHCRfaWdLr3vaIH9zusWN4fPtim6tLNdLlGkIKq0OLX94f8vxCmYVqga7lM3Ei3lgbsjVwWajr/MH5qcP1WJJESqrE1igLLH50u8u1LYMr8xW+cKLB/Y7C66tDrBC2xi4jO+DkVJ4kEZivF9gaOfynGx1emK8wXy9wv2eTU2Xm6wVu7Bi4QYQbpewaPs2iRhDF9OyARkHl1ZMNzrfLpPukJLYb8wfnmp/JHo/xt4vjYOD3GAdDRp+0aTxtcT/ooXztZJ0TreInH5eITOVBV2Xu9+xDcamO4XFzx6BeULMF80Efwwl5br7M9sinVlAzOrMgUxy2w4SXFqu4QcSDgU1BlTnVzPPFk00aRRXLDXj1RI04SejbPrYTcn1rzM7E5dJMmVNTBe53HNrVHPWSyulWHidI2Jt4SAjsGQ5BFFMtqMxW8iw2yszVVG5sGEyCgIImISNi+gFJkvKzB326hktZFSkXNQZ2QFP3KOoq97oGqipxqlHkT6/MstK12RzZzNfyzFVzrPdNXD+ipUOxXiBKEroTnwgo5RR2Ri5hktAu5bi+NeZHdwZcGZaplRS+cbpFvaDywztdSqqEE6Xc2p7QKGl857k2760bfPvyNA96LrM1jZXOhJs7Fn0rQJNF8opERVP2s2syQ8vndKOIoCiYboCDgBPHXGiXmT2Vp2sGbPVshqbPqbpOUZUpaTLTJY23N0es913+UZKQU2RGTnhYDj+oDB3N1L9yosFqz3rEfg4CSCeI6Fk+9YJyqDMAH7YKPO3vhXr+I2woB1mtx23345yZp2WrPklc6RjH+CSbeFYn/VfNmP6qOgNPYvE5io977lmDiHZJefLjj73342q8p2ZV3t/K2oeOstY/HghANt9Uzhf50pkGSZryv7+7Ra2oMVPO882L06x0TBw/wnB9VjoR377U4r/+ygncMGJg+dzcGvP+9oSXFitYfoIsQL2kYQYxLyxWubEx4q0eGOsjGkWVi/NVFFWiM3bwopQf3OwwcEKmyxpXJZGyJtEzfa5vTjjZLGC4ASMbKprChXaJdkXn5q5BfxJktKDlHCMnZKFeOPwue5ZPlGQMeMutIi8uVHl7fUy7rOJ5Mff3TBaqGtc2Da4sVJh4EZ045eXlGrIoHjIUnWwW2Bo6yJLIpXaZPRtkUcCPE+ZreU40s8r96w96fLBl4McxCJCTwHIDojTF8QMuz5WZqYUYdkizqHBzx2O6rBAlAkM3RBEEPuhahyQSP7yzx+l29ePM8Bi/BRwHA7/neJZN42mvieKEoe0/IlryLMdNlzVkWX5k0d/dF8tqFTVONQusdC0GZkAQR7x+v8/uxGemrLI2cEFMud+1MopM02eU+rywlMmq39g2ssGvQSYiIwiwUNcRRZFaQaNaUHhpqYEiiPQsn82hy8SLiaKYOEl5Y61Pb+IRxwkXp2tcmiuTkrA9cslrMuVYJYhSGgWVszMlpooq630XN4yZ2AGOHxNGCW9YA2ZqBdI0ZaM7YeJGXF2uEUUxiiIxciJmqzlOtEqUcjLBcJdiJU8SpxR0mRcWqkznc7xuBRRzCkVNZqqcxw522Z64zAgCkixyfrbMtS2DsR9yopbnCydqPOg79CYBe3ZIzwz5+rkpGkWVoRlgeyNubY/QZJk0TlE1CSOMeNA3mTghcSxQ0SUqOZWLs2XiRMAOEhYaBfKazLtrQ/phTJJCNa/y9y63WWwUiG91ENIsw7VruAxNj5ONPNOV3GG2/07HxA0jxk7IuXaJXcMlTj5qOweiXkM7PNQZQJQ+0p72pL8fZ0N5WsvPZ3HkH7fn4xL3MR7HJ9nEb6qa9KvqDMBHWXyO4uM+5zMHEUn8xMcff+/HRf7yqsrTZcYeRTGvMFfXaRZVinqWbLo0W2a+XsTyYyZeTLOocXKqRJiYbI0cwiQhSTLOfQGBke2zPXSIBYG6riGkKff2LCwv4Gf3+gQudE2PejFHXhGxnIiBE7FQVVhsFFluJAiCyMgJeW6uRruSJ44TDD/mxYUqfhDTtwKsIMQNFZI4oe+EnJkuUi1okKaUdZl7nQkdw6WqK/zJ5TYX5ypZ4FbWaZc9Ls2W+OX9Pve7FlGSUlQVZsoaqixyq2Pta/jonJ0u0jd93tkcIwkCr51s8MVTDX68Bc/NVSjktEOdmI7hUdEVFup5lmo66wMPw/UBgYkb0jV9upMAXRb4yb0B59oFukbINy9N8eb9PrsjBy+OGU480jghjBNyivRMv90xfrM4DgY+x3jWLNKvUhJ+lk3jaa+RpX3hqCP0o0cVX5903EFJdbqaf+SaL89VuLYxIooTrizWkCSRPdOnJkLfirg8W+JEo8CPVvrM13KIkkizoHF312RjZCPLIudnSgzsgFPNAi8tVulOXFIEWnmVa9sGP7/f437X5vRUheVWieE+zZnhhRR1hcV6nq2xhSRAsaTRKqvc6Zjc27My3vxanouzJd5YHTB2Iv6g3OKLp5oM7Q7fPD/NtQ2Dk808722P2OhZVHSZuq7hBwmbAxs/jBAliUvTJcp5jaVGjtlqnt7E4cebUMl5pGWVc1MVZkoab60PqRc07DDmbnfCxjALbhwvZCD6fP9Wh52Ry8bQwnQiREFkYWgTxSn5vMaXTtZwggjTC7ISbZAwXdZxQ1gfmbhBwtfONBjZAf9b16Bv+fQtmzNTLURB4Pm5KjsTh7ySBU5D06eYk2kWVcwg4va6RaOooCkSTpDy6ok6F+cq/B/vbnFj1+TddYN/8c3TXJipHFKIfrA15nbHpDfxECWRU63Coe0c2G67kiOKE6IoIogOROo+FM85sC/gE+3+8L32N6KD130WR/64EnCMXxW/KRv6tPb9NPHIX/XcT1KyP6hGH9URySvKE48BPqJ5YzmPS4s9HRs9h5Ke5we3e3zzQovL8zX+/Lk21WKORlElThKsIGK5ViCJs355N4ip6FnC5kyrQBim3O1ZXF2o89JSlftdi5Hjs9636Nses3JGknFmukC7rNO3Q9qVHEutIvM1nVZR4/r2mIHpMXWmyZl2+XCv3DVcbu2NubFpkKZwslXkH74wS7ua51y7xK1tgwc9h2ubI358r8dG3+G5hQp//twcdzuZovypZoHlRp4HexZ+klArKpxvlYmAWzsm//Cl7P1qusLdrkkQRozcKJsHKGUtnTVdouuC6cWHbG0fJlISLD+gmKtxZaqIsF+CidJsjq5d0fH9iN2Jz/OLVVY6Jj+/2+WDnQm1gkpFUSjUJTRBZHVkZQHOY3b365g9CePkI7o0x3h2HAcDn2M8axbpV8k2Pcum8aR2ogPn7uXljH/54KY+UHx9DR6hID3AOIC7HZOeHT7S0z2wMm7lBz2bs254SM3mBRFvr48OeZ5bJY3TUyXud01KeYV/9soC//lODyuIGTsh56ezlpL5ep4z02W2hg5bQ5s314asdEyem6scDqUZdkDH9HD8hEpBpVrQqOk5NFlmvlZAViQ2+9ni6QcJtbzKqVaZOBXYHdnIkpR9FstnsVbly2frzNULqIoMCEwsn8VGgXPtEvVijtNTRTYHDi+dbGA4AdW8yti18IM4Y94pa0iihJeG7FhZe5Aoprh+xEYYQgKpAJYksdYfsjG2GZs+2yMfVQbSlJEbsbI74b6ucKKu88bqiJ/e6/F//4PTnJku8uJSla7hca8j4MUpl2errI0cGkWdck6jpCk4UYKmSPzkfo97XYuT00WenymjqwqlnMyF2QppmvD26pgUkb7pI4lZT+zQCkgRKcgi3YnHvY7J6alsNgAAQWCmrPHqqQZukBwOmMtH7PDAXt5YG7JrQqljwn4lZ6VrIgkCX9l/zSfZvbIvsnOnYz5yjs+C40rAMX5VfF5t6Gnikb+u94WPilwWFdhxsuTQvKIc7i9HjzmYFXvtZP1wXbjR8Z98sieglpc52chjuDE90yOniIy9kFPt8n4boYYkCKQCnGwW+OJyDUEUKGgS721O+Nq5Jo2iRk6VCOKUn9/vcWN7wuXZEn/vQpuqriIOLKZKGu2yDsCZVoHmiTqSnM1X1Ysqhh2wNc5oYV9crNExPMIk4WHP4Xy7TLukkcQpfpLtmwesdO2KzsqeyQebI/oTj7wqcb5dZtdw6RgelheyWNdZGzgEUcq3zk8zsH0kUUYgYbXvYvkxXzjRYGvoUMnJrBg+hhcgSUUMJ+TnDwa8vFAhL0G98KEXfRB8/eRul7fXhrhhwl9+YZEri7XDls8DmmjDDbgyX+X52Qr3dk16TogsiZyqF9A0EUVS2LM8/Ag6ow+bu36dlbLuxD+0pxM57ZMPOMYjOA4GPsd41izSbyLb9PhNeyBMdjCoeeD4v7xcpW/6h07ewesPUFXhZKuAIIi09tkiIOsLXW7oREnCwA4YWAEL9TyGG1DOydSL2eL4FUlkc2jzk/sDhFTgL19b5P/2jdPc2DY41y7x1uqA793s8PXTDWKynsWB5bPZN3GCbCjsoPypqzJpAudnSpQ0maKusFDX2Rg6tIoKRVViaIVsDx2CKOHW9ohWUePybBlZFDJ5+2qOnCLyzuaQnhVwtuXx5bMtdscO7xguN3YmqKJAOZ9DFgW2Jz76psGF2SI/uLnH2A3YMWzMALqWTxSBqohEaZbJ7pseoixT1yXyiooowcB0cYKIZTnP2eUGf23tUM4rvLxUQxYEDD/ECkK+cXaKG1sGYzfgP32wy/n9Ae231kaMHZ/LsxVSAX5wc5c90+fcdBFdVWjoKq+crHNrZ0KaCBRkibGblfQlSSKvSHzjwixfWM4GwerFrDp0QFmnygL/5OoCGyOXr5xtHdrOQXZPEgVubxtANiB9ulV4cm9/CiXtw5mBg6pPc199c7qS43SrgBdErPasR0TL4FfLdh4zBR3jt4Xfhu39Oqh1n8Tk9aT3Pbgfy5rA7XzWNvq0mYGsEvjoNEAFGD3D9ajAbKvM1sTHc2OGro/txeQUkdWeTb2kUc+r1AsqYydkfeAydEPqhRyV/cdXuhY/udfjmxem2N5vfxw7AW4Ii60iQRxj+vCl002iBL5/u4sfxwgpVHIyrYpOI6+SIh4qCa/2LX5wq8v5mSKSCEVVRkDkdKtw2FJ5c8dg13AzBqQ9i4cDGy+Is3bPic9u4pHEMV0r29+WGnmKOZm1no0sxuyaLlcXa0yVclzabye62zUp52S+eLpO3/QZOSGKDI28TE2XcGIY2iGVQhbUHCQBB5ZHEMT0Ji6vrw0AsIIkm6swfYqqxI/v93hvY8zWyMYKEr6wWMP0Y27sjnH8hD+6OMWrS01MJ+T5hQ91Zn6dvst0WWN2356O8elxHAx8jvGsWaTPWhL+/7d37sFxVGei/3XPo+c9o5nR03paFtjGEBsZE8BAuCROSOrevJZNKgm3kpuk1hWSDcsfm7DZKlgqBVXLPqjNFmzYrcpmH+xyc1NUsglZ4k0WSOw4BmMMtsG2LMt6S6OZ0bx7pl/3j9bIkixjBWyNHudX5ZKnp/v0d86c/r7+zuP7fhdlv1Cpz41ZPHdjqNflpFAp0eyQZ1/AZo2Az0H1dr8dSNEd988u96hGkKgqxOp1vz6V4NholvqQh11dMdqidqgzwzBBmp+JdiKr8tPXx/jVqUmOj07TFQ/yPzbXE1YC7JcT6IZFKl+mWNHRDZPpkspY3o4CUQl4CPmcxAJeTk3kOTqcRXFJuJwS4aCL5LTKcLrI6ak8t11Vz3imhNspI8t2Ap1UwY4eMZ4tcXosCzI0RXwUyhXGp1Xa4zq97XVUDJOKbnJ2qshYtoSMRUHVcUp28hzFI1Mf9JAv6yQyJXTTorctjCTJdMQ9DEyViHjcGFYWU7bom8oSCyk0hr2YlkS6pFHWTEDi1FiGeMBDTtU5myrS1eBHM51EfS4qmkHA62K6qOF3uwl6nDSEvJimnRJmuqRRrBhsaQ7QHPbw8kCahkCAW3tibG2xl3TFAwqd9QHGMyqTOZX/flPlxu4YnTEfHreTPduaZ5cGBNy2kdu2IcyxkQz7zyR4ayTHNa0hPr6jjWS+Ms/ZbI36uGVTnFfG7NFBJNjcGKR1xhF9azyHZpqcHs+RKJRRHA52L3gO3s1op4gUJKgVteh77yS07kIWRvKq7g+qrj+vllt9HjVNI+ax7x0LOGY3Cc+lGqJ67suivCCZgAOo7j5wzznmdEC2oNEYdLKtPczAZJ6EXmE4VUAz7BCe12wI45AtvA6J1ojC9tYQHrfTDufpVzk7mWMoVWQkVSLsdeGUZDaE/bx/awPJfJnf9KdxZuDjIYWBmcSY3fU+Tk3m6UsU2BNQiHhd5MsaN3dH8bmdTGRKnB7Ps6U5wO6eekJeJyfHc7MZgTXDJJEvk8iV2X9qkqMj0wQVJ9tbI4xnKpyayBEJutnWEqK7UUbV7CSVTSGFo4NZOus9hBU76WR90EO2pNMU9nB2Ksfhc2nev7WR5rA98PbSySlKmkFPg58Wnz0zUB2UATjYl6AvWSDod1Ef8ODAzq3T6nYyMJXjB68M2/lximWmixpbmoJc1WAv/awPy3TEvGBBJODmudfHyKg6Q+kSNy3S794tLoc8258EvzvCGVgnzHUALmVsFjoLCz8PpYr0JQpsbgriczvxRW0FNpQqzhuFrT6UVSOwKW6POEhApljhTMIOXTY3Cszcex4ZTGNYsKUpQNDt4NREFsmyp1Hfu6l+9ryfHxvj2GiWW3vidMd97O8DrVLBsCy2NIWpD3v4r+OjjE+XOJsq8MpAkv6pAhXNoiVsK7ihZJHOqJetzQHKmk5fIs9wssDVzWE6I36GvUUmCiqtIQ8D6SInJ/K01fmIBu2oDQ1+Dx1RByfGsgynSuSKBh0xPwF3iGNjGTbVB5gq2onWXjuXxjJNDAkaggpBr4tS2Q5nZ6oSPsWFw5IJ+tyoFYOueICe5iCHziTJlDRiPifXNEU4MpxifLqET3FhWSb1fhfXtYXY3h7mt2dSFEo6Fd2it6OObFnn5FiO0xN5JAsKFY1MocxtV9VjmCY3b4pybDjLWLZEXyJPnc/FYKrISLpEb2eYkWmV4WmVLzYE6U8U+NHRESRL4gu3dtEVD3DorM5Lp5Kouk5FlxhI2lEqqiNdA8kSA8kiHreTHe11lDUdyZLY3hYhFnAzkVEvmCForfPy37qdl8LhcLK7Jz4vis9QqsAbo1m2NAW4rrXugtGl6ueQ1zkbHrBqGC9lMMT+AEGtuJJ9b7GBoKXs9VoKCyN5DaUK7D9jjyTv6oq9bblzNwkDF2xirtqXprAHacG1zX6YLNhbiudtKzbg+EgObYNMd2OQba11ON0Ooj43r49k6E8W+FXfFI1BD2/G7eWHt/fU09sVYCRVZEOdB59bZjBVoi3qo7cryumJHG+O58mrOhbgcTnIzuxrOjmWJZErc8umKE0hD7/uS9HTEMQzk4TrzbEsG6I+mkJeNjX6aY3YM6UH+xK8Npwh4nPRFQ8wnCpS53WhajolwySkONnSEmHXRjsaUMDt4OhQhpxq0BBw8lL/FIl8meaQh+Y6hevb6ziXLBLwuOiIn99rMV3QGM/YSze9igu/W6YtZu8l6GkI8HIZziULHB8r8t6NUZwOmYP9Kc5M5OmMBrimJcxtmxvonIn8li9V0EyTnKYhyxJup0Q6X0HVTcamS2yqD/B/butmIqvy9MEBxjMlvC4HdX43gpWHcAbWAEsZ6X+70G1vd27bnDTs1RCQi12/cBR2rvKeNRI+O4rAhjovH762ZV4Z9uiQmyODabZtCDORUTk1nqe73kdT2MvB/iRT+TLTaoWQ28n17XW0Ru0RCEuS2NTgQzdNbt4Upz9ZIJOroLhkxrMlpksaZQss00JxOFF1g1fPpnC7HNzWU09nvZ8DfZMcHZqmqJlUTIPtbREiPjdxn5tksUJZt6jze8iqBv91Yoyjw9NsbQphmtih32JeehqCnJnMo1sGm5oDbG4IUNQMXjo9xc+OjXF0aJqgx4lu6JQrOrLTQbFs0BRU6PTCpMfPaKbIRE6lzutia0OYoM+Bx+1iYCrH4cEUpYoOUgAJaI/78XuclHWddF7jP94YZUtTiHhIoT9ZIO5zs3lDiI2Nfgam8jx/PAmWHV2prJtYkszp8RzD6TJO2eJcukhLWKGiQ6qk4XXKmJZFRzxAY9DLqfE8x0cyfOjaJhoDtlM5lSvTWudjKlsmW6yg63YIO5d8fk3/pnr/bLKbauKg3s4YnTOh66pT2NEZI1FdXhbzOTAsOy+FV3FfEDEoNrM8aduG8OyI2tylRtXzDp1N8uKpBImsOrOfY+lJ9gSC5eZK9r2LreE/2J8EpNnZtaXcf7HNwXMjec19Pi9Vr8VsytyBgblye9zMmxkYKYBPtkNeVjRwOSA3M1UQcsOujggfubaJF05O0RH18epgioph4nM6kCSLjqgPJxIj0yV+ey5F32SOZEFnIlfE63Qgy3BoMMWmxiAfuKaZ5kiGoNvB4cEMt/bEOZ3vZyRd4vRkHsUl0RT04nE7Gc9WZuLx2y/ch/rT1AcVdnbF+PC1LeTLGv9y4CwTuQr9iTzb28J4Xc7ZfXcdMR8Bt5P3tEcJKQ6GUiq39dSTyJeZmAmbrOo6HkXm9uYYd17TRLakMzCV44XTCeoDHjY1BNFmcguUdZOrGwPc3BOnVDGJBdy0RW1n4ZX+BMdSYB4bpz7im/0tfIpEWTdQNY1EoUJOtRv+bCLPWK5Evc+NaVq4ZIlkocJVzSHKmkGyWGE8U+YXx8cYz6i8NjyNZIHHaQf+uFgfEtSOVe8MPPHEEzz22GOMjY1xzTXX8Pjjj3PrrbfWWqxlZSnTym8Xug2WEl/6/LrNxa5fGLWlKpM+N2PxTCg5l0OeXe4xl6ODaX72xgSGYdIU9gIWummX+Z62MG+OZSgmdM4liwymirRHfXz42hbao17+36EEqm7yP7e38PHtrTz72jDjWZVXh6a5oTNKo1/hrNdJzO9iPK1yLlVgR2sYr1tmKl9meKrEkZE0G2NBYiGFgNvJdKFCZ8yP1+3EsCxCbhcfuraRQ2dTvDaY5kwiz2tnU4Q8TrpjAaJBN/VhD+lChal8jvc0hxjPqCguiYlMCV036GkM0hD2YmLREPAwmCrQnyyQsMDpK9BS56ct6iWr6jgdEt31QbKqTqls4nU5sSSLqM+FS5Y5PZVHrZhE/Qpep5PhdJHDg2laIh6SRXtT78BUgcFUiQ1hha3NIUqqRl3Ai9ct0xm3f4NSRUPTTWQkehpCqLpJ0OPAKclUsPA4ZTbFg0wXK+zvTzGaKbGlOUws4OaamWU/fYk8xYrO0cE0TqfEXddumKfcq+v5Fy4VqPaduaFlNzcFiQXcHD2XZKxo56VYLI+Fz+2cjXyx2HNQ7Ycb6/0ksurspmUx2r+6ETr/nXOxl+5qcsffZc/ApezOwufz7VhoU9qiPoZSxdm189s2hGdnnEeL86+VAacMTREX6YJOuXLeVukmFMsGzx4Z4fWRLF6XhMfh4I5tjbidkp0J3YS8arKjPYJhWhw6l6aoaliAz+0iHnTjdMqous5wukh9QCFf1hhI5mkMRpBlGEwVqRgWrRF7iWRj2ENnzDdrD4NeJ4rH3pg8nCoyninxi7cmODWR55qmIC1RD7ppv6BXB06iM9GOEjmV6ZJBXrWjKFWdqzqviwNnkqgVE5/HxYtvTXL75gaaQl7ifgW/Yr/eHRvJcPhcmkyxwpbmEKlCBe/MoIhumAwk8vjdDvwOODWVxwBKmv3Sv6UlzH+/NYXL6aS9zk4UeWQwzZtjGYaSJXBIbAj76GrwMTBVwilLHByeJuh20Frn4eWzKY4Op5FlmbDPxVi6xPHRLDs6YkvqQ4LlY1U7A8888wz33XcfTzzxBLfccgvf/e53ueuuuzhx4gTt7e21Fm/ZWMq07tuNylSX5KQK9iTrwpGhxrCH7oYAjTPlL2YsFkZtmRsWbmGSGc0wOTacJVWozHMWIl4XHrdMxOuiNeqju97PywNpQr4C9X4Fj8vF5sYg5bLJQKpA0KuRyJc5Mphi31uT9DQEaAp57agxdX7CXoWOOh+DSZWP7mihIezhpo1R/vHAAIlchWNjWYYyZaI+F1lVw7Ig6HFyQ0cd/3hggLGMSnNI4fd62/ivtwwmcmWOj2RwyjLNIQ+SJFPSDfKqzuFzaZzDcOfWJl4dSPLCyUmefmWQoMfNpvogXfEAiVwZv9fFluYITREPR86lCfncaIbKRBIUS+OaFhcSMqPTJVoiPoanVVwO2N8/haaZMyFXVTqjfnriAd6cyLKrK8Z7O6PsOzlBQTW5uTvGaLZIKm/gdEhYpsmrw9OMTpdQyya/d0OA929p5LdnkgylS4S9TtpjAeIhN3V+F81hH5gW454SQUXmt2fT/Cw/zm1XN7Ax7uPkeI6I34VpSrw+mOa69jqubgoykC5wdHSavGbSFg2wqyt2QSSfWMBNwC2jVnSKlfNZRasRNqp96mwiz4mxHJoBQY9j0cRhb/cczO3TUb8bt8tJqWIKg7PKETr/3bGYHUjmK3YuEZdznsMOXBBFbi6XeznTYiFFfW6ZU+N56gPK7IDA1mYHx8bO5ygwAEm2gxv43RaTxfPTBhkVTk7mCSgyLSEFVTMxJQmvW2YiW+G2nnrqfW7OJgv0NAQ5NJDGrziJ+xQ2RBVAxilJbGwMMJgssb8vScjnoi3sZTxT4ucnynQZ8L7uGJYsz4bd7JvM8R9HR9jUEGRba4SRdJmoVyFfNjg+mqKiG1zVGGBTfQAJidFciZF0eTbTeizg5thIhnPJEoZlEfO72LopPrtHb0d7HZphEhqZxjAtnj82Tn+iwES2yGdv2sjn3tuJNjOQFnQ7CCoOTk6ouJx2VuKsWsAwTBKFMkPpIkGXg4Abpssmb43lMa1RPr3LyXs31gMS04UKd25tIpWvcGo8T0hx0hbzEVQcFCsmDWE7B1CyoDKSLpIuVFDbLTKFChXDojHgIl8skyyUmcqdHwQUyzFXDqvaGfirv/orvvjFL/KlL30JgMcff5znn3+eJ598kkcffbTG0i0flyNbZXImffil1nP6os5FR2CHU0V0w6Qj5p0dDQFmk07NnRmYyJZn7wfMmf510hX345lJQx8P2NOJIcWBJUnEfC4iXh8hj5ObrRi5kk66qCFZEkGvkxs668iXNQ6dTbGlJURHzE8ipzKYLJEs2aM6B8/CttYIIa+LnKqhlk0qmsmNXXHiviyqYfDiyUkmp+2U6xIyL5yZIl8xKFQMxrNlXLJE2OuhMeRhZ3eUE8MZziRyvDmYRS3r3L65gf1nkjhkiYKqgQxbG0NsrA8S9Mi4nS7Uio5TlrkqHuKkaZFPF9jeFmHrhgivDKXIVwz8isxUXiVVUJnKqrgcEo1BD6fGswynVBqCLjTDYiyt8oaSI+hRCHgsfIqD7oYgXVELh8NOGtaXyOFzSeSKOpl8md+emeJcsgRY+BQXsYCLZM7k58cn6I77UHWwsKgYJkfOpUkWVCzLYlN9AFW3KKoGw9MlxtIl4iHbWWwb8+N1OujtiHB1U5CzifwFMcKrIWQHkkXSJY3JnMrrQ3DHlsYLEtqNZUoUDTg9kSc/E1p87oj/wheUhZsgq32sGqZWGJzVj9D5l5+FL2Rz/76TTN1vx8IX/rnMvRfYywU9Tjts5dzElhGvF8jPuzZbgfy4ekEW4sYQbGsJ8tpwlqhXorM+QHe9n4DXyRsjObbLEvmKQbZs4HTI3NwdI+hxMF3S2NQQYCKj8uu+JB31fup8LpIFJ4ZhEfA6aYt4GEgWyRr20teR6TJvDKfJlQ0ypQqvnkvTWudl24YwAcXB6YkcVzUFaQ57GcuUyKg6pmHyxmiWqxp8NIV9lDSdo/1ZOmNeplWdjpiXVKGC02EnXTw2kpkdtNMNk6G0SsDjxCVJDKeLvDIwze6rCmxqsEfwT4xlKKgGt19dT8Tn4j1tEYIeN2Xd5OhYlsaQgq6bJCs6Phf8713tZEomBc1AN0zOJfL0jWfJV0wmsurM8k+LWNDD9nY/0YCbV8+l+U3fFGcmcvbsQUOAQwMpHJKdm2dHZx1F1eDlc1P4XA4agud/e7Ecc+Wwap2BSqXC4cOH+eY3vznv+J49ezhw4MCi15TLZcrl8zGKs9ksAJqmoWlLT2TydlTLuVzlLQcxn4PNDX47JJdpoM3JDFn9flPcS8znoKiWUcsVOuoUYj4HmqYxnC6x/8wUWNBd7ydT0hmfLpAsaPaIRkuI4WSeqNd+cYt6ZTY3+In6XUxmy7NlgYP3dtUR9Tk4O5lF03WiPieb4n6mSzpqRefQeBaHQ6I77qdckYh6HfRe30xjSCHkc/Ivvxng5XNptjWH+PSudnKqzoaIm18cG+fgWXs96Odu7GRLU4AfvDJC2TQwVDg3lUdCIpEtI0kmyBIddV5kJzT5FQzdRNMNBlMFrm4I0BXzcPvVcc5MFumfyqHrOplimSNDaQKKk7DHSdjtpKSbTBUq5IoVfF4X72mNcXwkQzKn0hHzsr0tTNeYm1f0FDe0h+hP5LmxPcJNnXVousl/vD5OUasQcjuoSFAxDBSHxOYGH5mKTiqncrCk0hRRuKrez0CqxCsDKQZTJTxOGb/HQaagU9ZMPnLtBoamCkiSzFtjWeIBBbVi8PKZKUqVCg5JIlfSmMza6e5v6o6TKZbp8zpwOTw0BD3s6ojQHFa4vj3Cz46Pc3K8wP6T48iyg5awl/Y6L1uagkxMFzk0kAILbtkUn+1XMZ+D7a0BxjJlXJbB8FSe/qkiQcXBTd3nlxRouo7XJeNUoCuqcDZVxuu0ODuZRdV0Dg9O09seweNy0hhSZjeTT2TLNIaUeX3aJVn2rNQifXu18k71zGrSSwtZqTp/ubkSNmbh81H9PFf3L7zf3OdtsRm7xb4/O2XnfNnVGaUx4CSpQlEt4wNCikTAZf91OWQ66hRGposE3DJY5uz9+8byF9zLnPkXksGSITczOeB1OemKBmjwK1zXFkI3YUtziNF0iWubA+RVjeOjORyyBJY9S+2QJCTTIJ2voOsmRbXC5HQR3YLtrSFcDon+qSJIMj7FQVCH4VSe/zyR4K3xPEHFQUPAjYGFrtty941neG04SypX4hO9bTQGQ0xky3hdEmpFJ6i4SOXLGIaOYeh4HBZapUIk5CdbtO2crtsR5qJ+FyFF4vXhHAG3TMTnRkJGrVQ4PWXrYwcWw6k8U9NFAl4X56by1Ac9lDWDyWyOUkUjkVVpDLiRJTBNi6wGHVEvrdEAE1k7PPj/fWWIA2cS1PnchNwSH7u+le64l1RBg4jJxHSR/3xjhFMTOZyyhGF6aAl7aQn7MICMqhH0OJgqlGkIKsT8bnrqvVfk2VuN714LuRJ1WGpZkmVZC53pVcHo6CgbNmxg//793HzzzbPHH3nkEb7//e9z8uTJC6556KGH+LM/+7MLjj/99NP4fMI7XQpJ1U4U0+KD2IyDb5j2cSSIuGxFHHTCUAHyOgScUDTmX3OxsuYeb/SCQwLDgr6MrewbPHaugojbvk/EDQ7Zvma4AHkNTqSgyQc7G8A9893rSShpEPHYx2NueD0FWQ38LlvGt9IwVYI6BeJe+19Wg+6QLcfZHPRnIOSyp6bb/DBWgv4s+B2QVaEpANc3wpkMhN32vcs6tPpBwy5rJA/HU/bmNr/Ljq5kSeCRIeiCa+rsug3moaLDZBkm85CpgCJDyYSeMIwXYVq118vuboGMDmkVNgbt8hIlUHVbVpcEm+ugYtpt4gB8bnhxBIbydp2vjoAsg1eGsgVXhe3fcyBnn+uW7N+pavcrOhxP27/LzAowJkt2GZtC2NtMJIgp56+p/r4np+2+oRu2TDc2QvOcR3CyBH1ZuxyHZPcHn8PuR4oMU2WIK1A2z/efi/UnwXmKxSKf+cxnyGQyhEKhWovzOyF0/sriUs/bYt8v9lxf7Pmt6vSAEzqD53XIt38DiUXk8QBtXuiJwXgezk7Dpii0B+0wo40eW3/4HDBRsm2FCWDBxpCtm8HWd1nN1vOKE06kbZmymi13TLFlS5btf1eF7WOTqq2zy4Ztl46n7EhHbX772vGCra+ujUJ3+HwbnZy25Wj22ufmdPv4qcxM2TM2D+yknRG3/bfaNtVrFAleTdo2pS1g25lzeYgqEHTb9ame65NhtGTXbyBn69KoZ76uNkx4cxreTNu2ycCWvTN4Xo5k2W6fXBkkCSoWRN0QcEG9DxJFe9ZmMA+qBg4n3N4MV0Xebe8TLJWl6vxVOzNQRZLmBxqzLOuCY1UeeOAB7r///tnP2WyWtrY29uzZc9kMo6Zp7Nu3jw984AO41mBO7EuNBi12btTvIlXQiHplXvjlL2bb5mJlLTyuGSbD6RIS9nTs241CRf0uJrLleecWKzonRrP0NAbIqcZsuR+Zcx+ww6qNZ1WaQh46YnakorlyVMvpivs4O1WkpzFAIltmPKcSUZzkKvZGZ5dDnpVlMlvGwk6EkipoNIYUNMPk9eFpIl4XDllGNzQOHDjI7btvpqM+dMEot2aYvDqYRjctIh4nw+kSN3TWcTpRoKzpKC4n124Ik8iWSeQrszKMpEvopgkWOBzyPBmq97h1Isfx0RzxkJsdbRFyqjH7ey3lN17Yhpf6naq/1XC6hGGYWNihYlsXnG8vPctz7Le/5s7330mqZJ7vRwv+LjYzsNYjU7xTPVMdGV/NXA6df8cddxCLLW1z60pjpdiYdzIzME+vaRo/fO4XfPLDd+LzKIvq/cXK79g2xZ/+5E2aQwqbGkO8MZRmc1OIa9vqCHldXD+znv5A3xS7uqJkVQMJaJjRf1UboRsmErZunKt/tAU6ba4NW1iXqo760Afn27S5dqh636DHwemJPFtbQvjczvNlLKIzq7Zm7rlLafuPL7Abi9m9xcpZaJurfGjm+8Vkn3f9TH0Nw5zXntX6lTWd8VwZpyxxfXvdonV6t6yU5+LdcCXqsFSdv2qdgXg8jsPhYHx8fN7xyclJGhsbF71GURQU5cLsdC6X67J3nitR5krA5WLJqb7nnhv2n58arLbNxcpaeNzlgqua3/6eC+81l7DLxU099rF4aPFrALZsUNiyYX65c7+fW05TXXCmPD9bFpFnMVnm/v/Wq8//X9M0zvpgU1Nkts8slO2OLefPv2Hmb2v8fMK1xWTpWaTN5srgcsF1HQrXdcTnlHHheW/HQjkv9TtVr1nS71kv86YMPo9CeGbqoSrXwr+LybIe+F31zGrWSStd5y83ta7DpZ63xb6fe0ybSRLl8yiL2oOLlb+9u5mffL35kvL9r+vtAZ2mOccW0xuXkvtidmWujlrMpi2m++Mh/wVlLKYL59qapch4seOL2b3Fzl9omxcrb6HsC79frE3n1u/ai9bm8lLr5+JycDnrsNRyVu3wmdvtpre3l3379s07vm/fvnlTyAKBQCBY/QidLxAIBFeGVTszAHD//fdzzz33sHPnTm666SaeeuopBgcH2bt3b61FEwgEAsFlRuh8gUAguPysamfgU5/6FMlkkocffpixsTG2bdvGc889R0dHR61FEwgEAsFlRuh8gUAguPysamcA4Ctf+Qpf+cpXai2GQCAQCJYBofMFAoHg8rJq9wwIBAKBQCAQCASCd4dwBgQCgUAgEAgEgnWKcAYEAoFAIBAIBIJ1inAGBAKBQCAQCASCdYpwBgQCgUAgEAgEgnWKcAYEAoFAIBAIBIJ1yqoPLfpusCwLgGw2e9nK1DSNYrFINptd9SmxLzeibRZHtMviiHa5OO+0baq6rqr71hvVeudyuVXbp9bKc7EW6rEW6gBrox6iDouzVJ2/rp2BXC4HQFtbW40lEQgEguUjl8sRDodrLcayk0wmAejq6qqxJAKBQLB8XErnS9Z6HSICTNNkdHSUYDCIJEmXpcxsNktbWxtDQ0OEQqHLUuZaQbTN4oh2WRzRLhfnnbaNZVnkcjlaWlqQ5fW3SnR6epq6ujoGBwdXrTO0Vp6LtVCPtVAHWBv1EHVYnKXq/HU9MyDLMq2trVek7FAotGo75JVGtM3iiHZZHNEuF+edtM1qfQm+HFSNYTgcXvV9aq08F2uhHmuhDrA26iHqcCFL0fnrb2hIIBAIBAKBQCAQAMIZEAgEAoFAIBAI1i3CGbjMKIrCgw8+iKIotRZlxSHaZnFEuyyOaJeLI9rmnbEW2m0t1AHWRj3WQh1gbdRD1OHdsa43EAsEAoFAIBAIBOsZMTMgEAgEAoFAIBCsU4QzIBAIBAKBQCAQrFOEMyAQCAQCgUAgEKxThDMgEAgEAoFAIBCsU4QzsEyUy2W2b9+OJEm89tprtRanpgwMDPDFL36Rrq4uvF4v3d3dPPjgg1QqlVqLVhOeeOIJurq68Hg89Pb28qtf/arWItWURx99lBtuuIFgMEhDQwMf+9jHOHnyZK3FWnE8+uijSJLEfffdV2tRVi0//elPufHGG/F6vcTjcT7xiU/UWqR3zGq1MavZHqxm3b0W9exq1okjIyN87nOfIxaL4fP52L59O4cPH162+wtnYJn44z/+Y1paWmotxorgrbfewjRNvvvd73L8+HH++q//mr/7u7/jT/7kT2ot2rLzzDPPcN999/Gtb32LI0eOcOutt3LXXXcxODhYa9Fqxosvvsi9997LwYMH2bdvH7qus2fPHgqFQq1FWzG8/PLLPPXUU1x33XW1FmXV8sMf/pB77rmHL3zhCxw9epT9+/fzmc98ptZivWNWq41ZrfZgtevutaZnV7NOTKfT3HLLLbhcLn72s59x4sQJ/vIv/5JIJLJ8QliCK85zzz1nbd682Tp+/LgFWEeOHKm1SCuOP//zP7e6urpqLcays2vXLmvv3r3zjm3evNn65je/WSOJVh6Tk5MWYL344ou1FmVFkMvlrJ6eHmvfvn3W7bffbn3961+vtUirDk3TrA0bNlj/8A//UGtRLgtrzcasBnuw1nT3atazq10nfuMb37B2795dUxnEzMAVZmJigi9/+cv88z//Mz6fr9birFgymQzRaLTWYiwrlUqFw4cPs2fPnnnH9+zZw4EDB2ok1cojk8kArLv+cTHuvfdePvKRj/D+97+/1qKsWl599VVGRkaQZZkdO3bQ3NzMXXfdxfHjx2st2u/MWrQxK90erEXdvZr17GrXiT/+8Y/ZuXMnd999Nw0NDezYsYO///u/X1YZhDNwBbEsi89//vPs3buXnTt31lqcFcuZM2f4zne+w969e2styrIyNTWFYRg0NjbOO97Y2Mj4+HiNpFpZWJbF/fffz+7du9m2bVutxak5//7v/87hw4d59NFHay3Kqqa/vx+Ahx56iD/90z/lJz/5CXV1ddx+++2kUqkaS7d01qKNWQ32YK3p7tWsZ9eCTuzv7+fJJ5+kp6eH559/nr179/KHf/iH/NM//dOyySCcgXfAQw89hCRJb/vvlVde4Tvf+Q7ZbJYHHnig1iIvC0ttl7mMjo7yoQ99iLvvvpsvfelLNZK8tkiSNO+zZVkXHFuvfPWrX+X111/n3/7t32otSs0ZGhri61//Ov/6r/+Kx+OptTgrkqXqINM0AfjWt77FJz/5SXp7e/ne976HJEn84Ac/qHEt1oaNWQ/2YK3o7tWqZ9eKTjRNk+uvv55HHnmEHTt28Ad/8Ad8+ctf5sknn1w2GZzLdqc1xFe/+lU+/elPv+05nZ2dfPvb3+bgwYMoijLvu507d/LZz36W73//+1dSzGVnqe1SZXR0lDvuuIObbrqJp5566gpLt/KIx+M4HI4LRpImJycvGHFaj3zta1/jxz/+MS+99BKtra21FqfmHD58mMnJSXp7e2ePGYbBSy+9xN/+7d9SLpdxOBw1lLD2LFUH5XI5ALZu3Tp7XFEUNm7cuCI2gK4FG7OW7cFa0t2rWc+uFZ3Y3Nw8TxcBbNmyhR/+8IfLJoNwBt4B8XiceDx+yfP+5m/+hm9/+9uzn0dHR/ngBz/IM888w4033nglRawJS20XsMNo3XHHHbMjcrK8/iap3G43vb297Nu3j49//OOzx/ft28dHP/rRGkpWWyzL4mtf+xrPPvssL7zwAl1dXbUWaUVw55138sYbb8w79oUvfIHNmzfzjW98Y1UYvSvNUnVQb28viqJw8uRJdu/eDYCmaQwMDNDR0XGlxbwka8HGrGV7sBZ091rQs2tFJ95yyy0XhHU9derUsuoi4QxcQdrb2+d9DgQCAHR3d686D/xyMjo6yvve9z7a29v5i7/4CxKJxOx3TU1NNZRs+bn//vu555572Llz5+yI2ODg4IpeL3uluffee3n66af50Y9+RDAYnB19C4fDeL3eGktXO4LB4AXref1+P7FYbNWt8601oVCIvXv38uCDD9LW1kZHRwePPfYYAHfffXeNpVs6a8HGrFZ7sNp191rQs2tFJ/7RH/0RN998M4888gi///u/z6FDh3jqqaeWdYZMOAOCZefnP/85fX199PX1XWCwLMuqkVS14VOf+hTJZJKHH36YsbExtm3bxnPPPbciRidrRXWd5Pve9755x7/3ve/x+c9/fvkFEqxJHnvsMZxOJ/fccw+lUokbb7yRX/7yl9TV1dVatHXFarUHq113Cz27crjhhht49tlneeCBB3j44Yfp6uri8ccf57Of/eyyySBZK/lpEwgEAoFAIBAIBFeMlb0wTyAQCAQCgUAgEFwxhDMgEAgEAoFAIBCsU4QzIBAIBAKBQCAQrFOEMyAQCAQCgUAgEKxThDMgEAgEAoFAIBCsU4QzIBAIBAKBQCAQrFOEMyAQCAQCgUAgEKxThDMgEAgEAoFAIBCsU4QzIBAIBAKBQCAQrFOEMyAQCAQCgUAgEKxThDMgEAgEAoFAIBCsU4QzIBAIBAKBQCAQrFP+Pxnwz2ujRc7RAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 30000\n", "plt.subplot(121)\n", "plt.scatter(data[:N], range(N), alpha=.2, s=1)\n", "plt.title('Input')\n", "plt.subplot(122)\n", "plt.title('Output')\n", "plt.scatter(f(data[:N]), range(N), alpha=.2, s=1);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The data itself appears to be Gaussian, which it is. By that I mean it looks like white noise scattered around the mean zero. In contrast `g(data)` has a defined structure. There are two bands, with a significant number of points in between. On the outside of the bands there are scattered points, but with many more on the negative side.\n", "\n", "It has perhaps occurred to you that this sampling process constitutes a solution to our problem. Suppose for every update we generated 500,000 points, passed them through the function, and then computed the mean and variance of the result. This is called a *Monte Carlo* approach, and it used by some Kalman filter designs, such as the Ensemble filter and particle filter. Sampling requires no specialized knowledge, and does not require a closed form solution. No matter how nonlinear or poorly behaved the function is, as long as we sample with enough sigma points we will build an accurate output distribution.\n", "\n", "\"Enough points\" is the rub. The graph above was created with 500,000 sigma points, and the output is still not smooth. What's worse, this is only for 1 dimension. The number of points required increases by the power of the number of dimensions. If you only needed 500 points for 1 dimension, you'd need 500 squared, or 250,000 points for two dimensions, 500 cubed, or 125,000,000 points for three dimensions, and so on. So while this approach does work, it is very computationally expensive. Ensemble filters and particle filters use clever techniques to significantly reduce this dimensionality, but the computational burdens are still very large. The unscented Kalman filter uses sigma points but drastically reduces the amount of computation by using a deterministic method to choose the points." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sigma Points - Sampling from a Distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's look at the problem in terms of a 2D covariance ellipse. I choose 2D merely because it is easy to plot; this extends to any number of dimensions. Assuming some arbitrary nonlinear function, we will take random points from the first covariance ellipse, pass them through the nonlinear function, and plot their new position. Then we can compute the mean and covariance of the transformed points, and use that as our estimate of the mean and probability distribution." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import kf_book.ukf_internal as ukf_internal\n", "ukf_internal.show_2d_transform()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On the left we show an ellipse depicting the $1\\sigma$ distribution of two state variables. The arrows show how several randomly sampled points might be transformed by some arbitrary nonlinear function to a new distribution. The ellipse on the right is drawn semi-transparently to indicate that it is an *estimate* of the mean and variance of this collection of points. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's write a function which passes 10,000 points randomly drawn from the Gaussian\n", "\n", "$$\\mu = \\begin{bmatrix}0\\\\0\\end{bmatrix}, \n", "\\Sigma=\\begin{bmatrix}32&15\\\\15&40\\end{bmatrix}$$\n", "\n", "through the nonlinear system:\n", "\n", "$$\\begin{cases}\\begin{aligned}\\bar x&=x+y\\\\\n", "\\bar y&= 0.1x^2 + y^2\\end{aligned} \\end{cases}$$ " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Difference in mean x=0.254, y=42.846\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from numpy.random import multivariate_normal\n", "from kf_book.nonlinear_plots import plot_monte_carlo_mean\n", "\n", "def f_nonlinear_xy(x, y):\n", " return np.array([x + y, .1*x**2 + y*y])\n", "\n", "mean = (0., 0.)\n", "p = np.array([[32., 15.], [15., 40.]])\n", "# Compute linearized mean\n", "mean_fx = f_nonlinear_xy(*mean)\n", "\n", "#generate random points\n", "xs, ys = multivariate_normal(mean=mean, cov=p, size=10000).T\n", "plot_monte_carlo_mean(xs, ys, f_nonlinear_xy, mean_fx, 'Linearized Mean');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This plot shows the strong nonlinearity that occurs with this function, and the large error that would result if we linearized in the way of the Extended Kalman filter (we will be learning this in the next chapter)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A Quick Example\n", "\n", "I'm soon going to proceed into the math the Unscented Kalman Filter (UKF) uses to choose sigma points and then perform the computation. But let's just start with an example so you can see the destination, so to speak. \n", "\n", "We will learn that the UKF can use many different algorithms to generate the sigma points. Several algorithms are provided by FilterPy. Here's one possibility:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "from filterpy.kalman import JulierSigmaPoints\n", "\n", "sigmas = JulierSigmaPoints(n=2, kappa=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This will become clearer later, but the object will generate weighted sigma points for any given mean and covariance. Let's just look at an example, where the point's size indicate how much it is weighted:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from kf_book.ukf_internal import plot_sigmas\n", "plot_sigmas(sigmas, x=[3, 17], cov=[[1, .5], [.5, 3]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You can see we have 5 points centered around the mean (3, 17) in an odd pattern. It may seem absurd that this will do as well or better than 500,000 randomly generated points, but it will!\n", "\n", "Okay, now let's implement the filter. We will implement a standard linear filter in 1D; we aren't quite ready to tackle a nonlinear filter yet. The design of the filter is not much different than what we have learned so far, with one difference. The KalmanFilter class uses the matrix $\\mathbf F$ to compute the state transition function. Matrices mean **linear** algrebra, which work for linear problems, but not nonlinear ones. So, instead of a matrix we provide a function, just like we did above. The KalmanFilter class uses another matrix $\\mathbf H$ to implement the measurement function, which converts a state into the equivalent measurement. Again, a matrix implies linearity, so instead of a matrix we provide a function. Perhaps it is clear why $\\mathbf H$ is called the 'measurement function'; for the linear Kalman filter it is a matrix, but that is just a fast way to compute a function that happens to be linear. \n", "\n", "Without further ado, here are the state transistion function and measurement function for a 1D tracking problem, where the state is $\\mathbf x = [x \\, \\, \\dot x]^ \\mathsf T$:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "def fx(x, dt):\n", " xout = np.empty_like(x)\n", " xout[0] = x[1] * dt + x[0]\n", " xout[1] = x[1]\n", " return xout\n", "\n", "def hx(x):\n", " return x[:1] # return position [x] " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's be clear, this is a linear example. There is no need to use a UKF for a linear problem, but I'm starting with the simplest possible example. But notice how I wrote `fx()` to compute $\\mathbf{\\bar x}$ as a set of equations instead of a matrix multiplication. This is to illustrate that I could implement any arbitrary nonlinear function here; we are not constrained to linear equations.\n", "\n", "The rest of the design is the same. Design $\\mathbf P$, $\\mathbf R$, and $\\mathbf Q$. You know how to do that, so let's just finish up the filter and run it." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from numpy.random import randn\n", "from filterpy.kalman import UnscentedKalmanFilter\n", "from filterpy.common import Q_discrete_white_noise\n", "\n", "ukf = UnscentedKalmanFilter(dim_x=2, dim_z=1, dt=1., hx=hx, fx=fx, points=sigmas)\n", "ukf.P *= 10\n", "ukf.R *= .5\n", "ukf.Q = Q_discrete_white_noise(2, dt=1., var=0.03)\n", "\n", "zs, xs = [], []\n", "for i in range(50):\n", " z = i + randn()*.5\n", " ukf.predict()\n", " ukf.update(z)\n", " xs.append(ukf.x[0])\n", " zs.append(z)\n", " \n", "plt.plot(xs);\n", "plt.plot(zs, marker='x', ls='');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There really isn't a lot new here. You have to create an object that creates sigma points for you, and provide functions instead of matrices for $\\mathbf F$ and $\\mathbf H$, but the rest is the same as before. This should give you enough confidence to plow through a bit of math and algorithms so you can understand what the UKF is doing." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Choosing Sigma Points\n", "\n", "At the start of the chapter I used 500,000 randomly generated sigma points to compute the the probability distribution of a Gaussian passed through a nonlinear function. While the computed mean is quite accurate, computing 500,000 points for every update would cause our filter to be extremely slow. So, what would be fewest number of sampled points that we can use, and what kinds of constraints does this problem formulation put on the points? We will assume that we have no special knowledge about the nonlinear function as we want to find a generalized algorithm that works for any function.\n", "\n", "Let's consider the simplest possible case and see if it offers any insight. The simplest possible system is the **identity function**: $f(x) = x$. If our algorithm does not work for the identity function then the filter cannot converge. In other words, if the input is 1 (for a one dimensional system), the output must also be 1. If the output was different, such as 1.1, then when we fed 1.1 into the transform at the next time step, we'd get out yet another number, maybe 1.23. This filter diverges. \n", "\n", "The fewest number of points that we can use is one per dimension. This is the number that the linear Kalman filter uses. The input to a Kalman filter for the distribution $\\mathcal{N}(\\mu,\\sigma^2)$ is $\\mu$ itself. So while this works for the linear case, it is not a good answer for the nonlinear case.\n", "\n", "Perhaps we can use one point per dimension, but altered somehow. However, if we were to pass some value $\\mu+\\Delta$ into the identity function $f(x)=x$ it would not converge, so this will not work. If we didn't alter $\\mu$ then this would be the standard Kalman filter. We must conclude that one sample will not work.\n", "\n", "What is the next lowest number we can choose? Two. Consider the fact that Gaussians are symmetric, and that we probably want to always have one of our sample points be the mean of the input for the identity function to work. Two points would require us to select the mean, and then one other point. That one other point would introduce an asymmetry in our input that we probably don't want. It would be very difficult to make this work for the identity function $f(x)=x$.\n", "\n", "The next lowest number is 3 points. 3 points allows us to select the mean, and then one point on each side of the mean, as depicted on the chart below." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.show_3_sigma_points()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can pass these points through a nonlinear function f(x) and compute the resulting mean and variance. The mean can be computed as the average of the 3 points, but that is not very general. For example, for a very nonlinear problem we might want to weight the center point much higher than the outside points, or we might want to weight the outside points higher. \n", "\n", "A more general approach is to compute the weighted mean $\\mu = \\sum_i w_i\\, f(\\mathcal{X}_i)$, where the calligraphic $\\mathcal{X}$ are the sigma points. We need the sums of the weights to equal one. Given that requirement, our task is to select $\\mathcal{X}$ and their corresponding weights so that they compute to the mean and variance of the transformed sigma points. \n", "\n", "If we weight the means it also makes sense to weight the covariances. It is possible to use different weights for the mean ($w^m$) and for the covariance ($w^c$). I use superscripts to allow space for indexes in the following equations. We can write\n", "\n", "$$\\begin{aligned}\n", "\\mathbf{Constraints:}\\\\\n", "1 &= \\sum_i{w_i^m} \\\\\n", "1 &= \\sum_i{w_i^c} \\\\\n", "\\mu &= \\sum_i w_i^mf(\\mathcal{X}_i) \\\\\n", "\\Sigma &= \\sum_i w_i^c{(f(\\mathcal{X})_i-\\mu)(f(\\mathcal{X})_i-\\mu)^\\mathsf{T}}\n", "\\end{aligned}\n", "$$\n", "\n", "The first two equations are the constraint that the weights must sum to one. The third equation is how you compute a weight mean. The forth equation may be less familiar, but recall that the equation for the covariance of two random variables is:\n", "\n", "$$COV(x,y) = \\frac{\\sum(x-\\bar x)(y-\\bar{y})}{n}$$\n", "\n", "These constraints do not form a unique solution. For example, if you make $w^m_0$ smaller you can compensate by making $w^m_1$ and $w^m_2$ larger. You can use different weights for the mean and covariances, or the same weights. Indeed, these equations do not require that any of the points be the mean of the input at all, though it seems 'nice' to do so, so to speak.\n", "\n", "We want an algorithm that satisfies the constraints, preferably with only 3 points per dimension. Before we go on I want to make sure the idea is clear. Below are three different examples for the same covariance ellipse with different sigma points. The size of the sigma points is proportional to the weight given to each." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.show_sigma_selections()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The points do not lie along the major and minor axis of the ellipse; nothing in the constraints require me to do that. I show the points evenly spaced, but the constraints do not require that. \n", "\n", "The arrangement and weighting of the sigma points affect how we sample the distribution. Points that are close together will sample local effects, and thus probably work better for very nonlinear problems. Points that are far apart, or far off the axis of the ellipse will sample non-local effects and non Gaussian behavior. However, by varying the weights used for each point we can mitigate this. If the points are far from the mean but weighted very slightly we will incorporate some of the knowledge about the distribution without allowing the nonlinearity of the problem to create a bad estimate. \n", "\n", "Please understand there are infinite ways to select sigma points. The constraints I choose are just one way to do it. For example, not all algorithms for creating the sigma points require the weights to sum to one. In fact, the algorithm I favor in this book does not have that property." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Unscented Transform\n", "\n", "For the moment, assume an algorithm for selecting the sigma points and weights exists. How are the sigma points used to implement a filter?\n", "\n", "The *unscented transform* is the core of the algorithm yet it is remarkably simple. It passes the sigma points $\\boldsymbol{\\chi}$ through a nonlinear function yielding a transformed set of points. \n", "\n", "$$\\boldsymbol{\\mathcal{Y}} = f(\\boldsymbol{\\chi})$$\n", "\n", "It then computes the mean and covariance of the transformed points. That mean and covariance becomes the new estimate. The figure below depicts the operation of the unscented transform. The green ellipse on the right represents the computed mean and covariance to the transformed sigma points. " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.show_sigma_transform(with_text=True)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mean and covariance of the sigma points are computed as:\n", "\n", "$$\\begin{aligned}\n", "\\mu &= \\sum_{i=0}^{2n} w^m_i\\boldsymbol{\\mathcal{Y}}_i \\\\\n", "\\Sigma &= \\sum_{i=0}^{2n} w^c_i{(\\boldsymbol{\\mathcal{Y}}_i-\\mu)(\\boldsymbol{\\mathcal{Y}}_i-\\mu)^\\mathsf{T}}\n", "\\end{aligned}\n", "$$\n", "\n", "These equations should be familar - they are the constraint equations we developed above. \n", "\n", "In short, the unscented transform takes points sampled from some arbitary probability distribution, passes them through an arbitrary, nonlinear function and produces a Gaussian for each transformed points. I hope you can envision how we can use this to implement a nonlinear Kalman filter. Once we have Gaussians all of the mathematical apparatus we have already developed comes into play!\n", "\n", "The name \"unscented\" might be confusing. It doesn't really mean much. It was a joke fostered by the inventor that his algorithm didn't \"stink\", and soon the name stuck. There is no mathematical meaning to the term." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Accuracy of the Unscented Transform\n", "\n", "Earlier we wrote a function that found the mean of a distribution by passing 50,000 points through a nonlinear function. Let's now pass 5 sigma points through the same function, and compute their mean with the unscented transform. We will use the FilterPy function *MerweScaledSigmaPoints()* to create the sigma points and `unscented_transform` to perform the transform; we will learn about these functions later. In the first example in this chapter I used `JulierSigmaPoints`; they both choose sigma points, but in different ways which I will explain later." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Difference in mean x=-0.097, y=0.549\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.kalman import unscented_transform, MerweScaledSigmaPoints\n", "import scipy.stats as stats\n", "\n", "\n", "#initial mean and covariance\n", "mean = (0., 0.)\n", "p = np.array([[32., 15], [15., 40.]])\n", "\n", "# create sigma points and weights\n", "points = MerweScaledSigmaPoints(n=2, alpha=.3, beta=2., kappa=.1)\n", "sigmas = points.sigma_points(mean, p)\n", "\n", "### pass through nonlinear function\n", "sigmas_f = np.empty((5, 2))\n", "for i in range(5):\n", " sigmas_f[i] = f_nonlinear_xy(sigmas[i, 0], sigmas[i ,1])\n", "\n", "### use unscented transform to get new mean and covariance\n", "ukf_mean, ukf_cov = unscented_transform(sigmas_f, points.Wm, points.Wc)\n", "\n", "#generate random points\n", "np.random.seed(100)\n", "xs, ys = multivariate_normal(mean=mean, cov=p, size=5000).T\n", "\n", "plot_monte_carlo_mean(xs, ys, f_nonlinear_xy, ukf_mean, 'Unscented Mean')\n", "ax = plt.gcf().axes[0]\n", "ax.scatter(sigmas[:,0], sigmas[:,1], c='r', s=30);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I find this result remarkable. Using only 5 points we were able to compute the mean with amazing accuracy. The error in x is only -0.097, and the error in y is 0.549. In contrast, a linearized approach (used by the EKF, which we will learn in the next chapter) gave an error of over 43 in y. If you look at the code that generates the sigma points you'll see that it has no knowledge of the nonlinear function, only of the mean and covariance of our initial distribution. The same 5 sigma points would be generated if we had a completely different nonlinear function. \n", "\n", "I will admit to choosing a nonlinear function that makes the performance of the unscented tranform striking compared to the EKF. But the physical world is filled with very nonlinear behavior, and the UKF takes it in stride. I did not 'work' to find a function where the unscented transform happened to work well. You will see in the next chapter how more traditional techniques struggle with strong nonlinearities. This graph is the foundation of why I advise you to use the UKF or similar modern technique whenever possible." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Unscented Kalman Filter\n", "\n", "We can now present the UKF algorithm. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Predict Step\n", "\n", "The UKF's predict step computes the prior using the process model $f()$. $f()$ is assumed to be nonlinear, so we generate sigma points $\\mathcal{X}$ and their corresponding weights $W^m, W^c$\n", "according to some function:\n", "\n", "$$\\begin{aligned}\n", "\\boldsymbol\\chi &= \\text{sigma-function}(\\mathbf x, \\mathbf P) \\\\\n", "W^m, W^c &= \\text{weight-function}(\\mathtt{n, parameters})\\end{aligned}$$\n", "\n", "We pass each sigma point through $f(\\mathbf x, \\Delta t)$. This projects the sigma points forward in time according to the process model, forming the new prior, which is a set of sigma points we name $\\boldsymbol{\\mathcal Y}$:\n", "\n", "$$\\boldsymbol{\\mathcal{Y}} = f(\\boldsymbol{\\chi}, \\Delta t)$$\n", "\n", "We compute the mean and covariance of the prior using the *unscented transform* on the transformed sigma points. \n", "\n", "$$\\mathbf{\\bar x}, \\mathbf{\\bar P} = \n", "UT(\\mathcal{Y}, w_m, w_c, \\mathbf Q)$$\n", "\n", "These are the equations for the unscented transform:\n", "\n", "$$\\begin{aligned}\n", "\\mathbf{\\bar x} &= \\sum_{i=0}^{2n} w^m_i\\boldsymbol{\\mathcal Y}_i \\\\\n", "\\mathbf{\\bar P} &= \\sum_{i=0}^{2n} w^c_i({\\boldsymbol{\\mathcal Y}_i - \\mathbf{\\bar x})(\\boldsymbol{\\mathcal Y}_i-\\mathbf{\\bar x})^\\mathsf{T}} + \\mathbf Q\n", "\\end{aligned}\n", "$$\n", "\n", "This table compares the linear Kalman filter with the Unscented Kalman Filter equations. I've dropped the subscript $i$ for readability.\n", "\n", "$$\\begin{array}{l|l}\n", "\\text{Kalman} & \\text{Unscented} \\\\\n", "\\hline \n", "& \\boldsymbol{\\mathcal Y} = f(\\boldsymbol\\chi) \\\\\n", "\\mathbf{\\bar x} = \\mathbf{Fx} & \n", "\\mathbf{\\bar x} = \\sum w^m\\boldsymbol{\\mathcal Y} \\\\\n", "\\mathbf{\\bar P} = \\mathbf{FPF}^\\mathsf T + \\mathbf Q & \n", "\\mathbf{\\bar P} = \\sum w^c({\\boldsymbol{\\mathcal Y} - \\mathbf{\\bar x})(\\boldsymbol{\\mathcal Y} - \\mathbf{\\bar x})^\\mathsf T}+\\mathbf Q\n", "\\end{array}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Update Step\n", "\n", "Kalman filters perform the update in measurement space. Thus we must convert the sigma points of the prior into measurements using a measurement function $h(x)$ that you define.\n", "\n", "$$\\boldsymbol{\\mathcal{Z}} = h(\\boldsymbol{\\mathcal{Y}})$$\n", "\n", "We compute the mean and covariance of these points using the unscented transform. The $z$ subscript denotes that these are the mean and covariance of the measurement sigma points.\n", "\n", "$$\\begin{aligned}\n", "\\boldsymbol\\mu_z, \\mathbf P_z &= \n", "UT(\\boldsymbol{\\mathcal Z}, w_m, w_c, \\mathbf R) \\\\\n", "\\boldsymbol\\mu_z &= \\sum_{i=0}^{2n} w^m_i\\boldsymbol{\\mathcal Z}_i \\\\\n", "\\mathbf P_z &= \\sum_{i=0}^{2n} w^c_i{(\\boldsymbol{\\mathcal Z}_i-\\boldsymbol{\\mu}_z)(\\boldsymbol{\\mathcal Z}_i-\\boldsymbol{\\mu}_z)^\\mathsf T} + \\mathbf R\n", "\\end{aligned}\n", "$$\n", "\n", "Next we compute the residual and Kalman gain. The residual of the measurement $\\mathbf z$ is trivial to compute:\n", "\n", "$$\\mathbf y = \\mathbf z - \\boldsymbol\\mu_z$$\n", "\n", "To compute the Kalman gain we first compute the [cross covariance](https://en.wikipedia.org/wiki/Cross-covariance) of the state and the measurements, which is defined as: \n", "\n", "$$\\mathbf P_{xz} =\\sum_{i=0}^{2n} w^c_i(\\boldsymbol{\\mathcal Y}_i-\\mathbf{\\bar x})(\\boldsymbol{\\mathcal Z}_i-\\boldsymbol\\mu_z)^\\mathsf T$$\n", "\n", "And then the Kalman gain is defined as\n", "\n", "$$\\mathbf{K} = \\mathbf P_{xz} \\mathbf P_z^{-1}$$\n", "\n", "If you think of the inverse as a *kind of* matrix reciprocal, you can see that the Kalman gain is a simple ratio which computes:\n", "\n", "$$\\mathbf{K} \\approx \\frac{\\mathbf P_{xz}}{\\mathbf P_z} \n", "\\approx \\frac{\\text{belief in state}}{\\text{belief in measurement}}$$\n", "\n", "Finally, we compute the new state estimate using the residual and Kalman gain:\n", "\n", "$$\\mathbf x = \\bar{\\mathbf x} + \\mathbf{Ky}$$\n", "\n", "and the new covariance is computed as:\n", "\n", "$$ \\mathbf P = \\mathbf{\\bar P} - \\mathbf{KP_z}\\mathbf{K}^\\mathsf{T}$$\n", "\n", "This step contains a few equations you have to take on faith, but you should be able to see how they relate to the linear Kalman filter equations. The linear algebra is slightly different from the linear Kalman filter, but the algorithm is the same Bayesian algorithm we have been implementing throughout the book. \n", "\n", "This table compares the equations of the linear KF and UKF equations.\n", "\n", "$$\\begin{array}{l|l}\n", "\\textrm{Kalman Filter} & \\textrm{Unscented Kalman Filter} \\\\\n", "\\hline \n", "& \\boldsymbol{\\mathcal Y} = f(\\boldsymbol\\chi) \\\\\n", "\\mathbf{\\bar x} = \\mathbf{Fx} & \n", "\\mathbf{\\bar x} = \\sum w^m\\boldsymbol{\\mathcal Y} \\\\\n", "\\mathbf{\\bar P} = \\mathbf{FPF}^\\mathsf T+\\mathbf Q & \n", "\\mathbf{\\bar P} = \\sum w^c({\\boldsymbol{\\mathcal Y} - \\mathbf{\\bar x})(\\boldsymbol{\\mathcal Y} - \\mathbf{\\bar x})^\\mathsf T}+\\mathbf Q \\\\\n", "\\hline \n", "& \\boldsymbol{\\mathcal Z} = h(\\boldsymbol{\\mathcal{Y}}) \\\\\n", "& \\boldsymbol\\mu_z = \\sum w^m\\boldsymbol{\\mathcal{Z}} \\\\\n", "\\mathbf y = \\mathbf z - \\mathbf{Hx} &\n", "\\mathbf y = \\mathbf z - \\boldsymbol\\mu_z \\\\\n", "\\mathbf S = \\mathbf{H\\bar PH}^\\mathsf{T} + \\mathbf R & \n", "\\mathbf P_z = \\sum w^c{(\\boldsymbol{\\mathcal Z}-\\boldsymbol\\mu_z)(\\boldsymbol{\\mathcal{Z}}-\\boldsymbol\\mu_z)^\\mathsf{T}} + \\mathbf R \\\\ \n", "\\mathbf K = \\mathbf{\\bar PH}^\\mathsf T \\mathbf S^{-1} &\n", "\\mathbf K = \\left[\\sum w^c(\\boldsymbol{\\mathcal Y}-\\bar{\\mathbf x})(\\boldsymbol{\\mathcal{Z}}-\\boldsymbol\\mu_z)^\\mathsf{T}\\right] \\mathbf P_z^{-1} \\\\\n", "\\mathbf x = \\mathbf{\\bar x} + \\mathbf{Ky} & \\mathbf x = \\mathbf{\\bar x} + \\mathbf{Ky}\\\\\n", "\\mathbf P = (\\mathbf{I}-\\mathbf{KH})\\mathbf{\\bar P} & \\mathbf P = \\bar{\\mathbf P} - \\mathbf{KP_z}\\mathbf{K}^\\mathsf{T}\n", "\\end{array}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Van der Merwe's Scaled Sigma Point Algorithm\n", "\n", "There are many algorithms for selecting sigma points. Since 2005 or so research and industry have mostly settled on the version published by Rudolph Van der Merwe in his 2004 PhD dissertation [1]. It performs well with a variety of problems and it has a good tradeoff between performance and accuracy. It is a slight reformulation of the *Scaled Unscented Transform* published by Simon J. Julier [2].\n", "\n", "This formulation uses 3 parameters to control how the sigma points are distributed and weighted: $\\alpha$, $\\beta$, and $\\kappa$. Before we work through the equations, let's look at an example. I will plot the sigma points on top of a covariance ellipse showing the first and second standard deviations, and scale the points based on the mean weights." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.plot_sigma_points()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the sigma points lie between the first and second standard deviation, and that the larger $\\alpha$ spreads the points out. Furthermore, the larger $\\alpha$ weights the mean (center point) higher than the smaller $\\alpha$, and weights the rest less. This should fit our intuition - the further a point is from the mean the less we should weight it. We don't know how these weights and sigma points are selected yet, but the choices look reasonable." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sigma Point Computation\n", "\n", "The first sigma point is the mean of the input. This is the sigma point displayed in the center of the ellipses in the diagram above. We will call this $\\boldsymbol{\\chi}_0$.\n", "\n", "$$ \\mathcal{X}_0 = \\mu$$\n", "\n", "For notational convenience we define $\\lambda = \\alpha^2(n+\\kappa)-n$, where $n$ is the dimension of $\\mathbf x$. The remaining sigma points are computed as\n", "\n", "$$ \n", "\\boldsymbol{\\chi}_i = \\begin{cases}\n", "\\mu + \\left[ \\sqrt{(n+\\lambda)\\Sigma}\\right ]_{i}& \\text{for i=1 .. n} \\\\\n", "\\mu - \\left[ \\sqrt{(n+\\lambda)\\Sigma}\\right]_{i-n} &\\text{for i=(n+1) .. 2n}\\end{cases}\n", "$$\n", "The $i$ subscript chooses the i$^{th}$ roth vector of the matrix.\n", "\n", "In other words, we scale the covariance matrix by a constant, take the square root of it, and ensure symmetry by both adding and subtracting it from the mean. We will discuss how you take the square root of a matrix later.\n", "\n", "### Weight Computation\n", "\n", "This formulation uses one set of weights for the means, and another set for the covariance. The weights for the mean of $\\mathcal{X}_0$ is computed as\n", "\n", "$$W^m_0 = \\frac{\\lambda}{n+\\lambda}$$\n", "\n", "The weight for the covariance of $\\mathcal{X}_0$ is\n", "\n", "$$W^c_0 = \\frac{\\lambda}{n+\\lambda} + 1 -\\alpha^2 + \\beta$$\n", "\n", "The weights for the rest of the sigma points $\\boldsymbol{\\chi}_1 ... \\boldsymbol{\\chi}_{2n}$ are the same for the mean and covariance. They are\n", "\n", "$$W^m_i = W^c_i = \\frac{1}{2(n+\\lambda)}\\;\\;\\;i=1..2n$$\n", "\n", "It may not be obvious why this is 'correct', and indeed, it cannot be proven that this is ideal for all nonlinear problems. But you can see that we are choosing the sigma points proportional to the square root of the covariance matrix, and the square root of variance is standard deviation. So, the sigma points are spread roughly according to $\\pm 1\\sigma$ times some scaling factor. There is an $n$ term in the denominator, so with more dimensions the points will be spread out and weighed less.\n", "\n", "**Important note:** Ordinarily these weights do not sum to one. I get many questions about this. Getting weights that sum to greater than one, or even negative values is expected. I cover this in more detail below.\n", "\n", "\n", "### Reasonable Choices for the Parameters\n", "\n", "$\\beta=2$ is a good choice for Gaussian problems, $\\kappa=3-n$ where $n$ is the dimension of $\\mathbf x$ is a good choice for $\\kappa$, and $0 \\le \\alpha \\le 1$ is an appropriate choice for $\\alpha$, where a larger value for $\\alpha$ spreads the sigma points further from the mean." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using the UKF\n", "\n", "Let's solve some problems so you can gain confidence in how easy the UKF is to use. We will start with a linear problem you already know how to solve with the linear Kalman filter. Although the UKF was designed for nonlinear problems, it finds the same optimal result as the linear Kalman filter for linear problems. We will write a filter to track an object in 2D using a constant velocity model. This will allow us to focus on what is the same (and most is the same!) and what is different with the UKF. \n", "\n", "Designing a Kalman filter requires you to specify the $\\bf{x}$, $\\bf{F}$, $\\bf{H}$, $\\bf{R}$, and $\\bf{Q}$ matrices. We have done this many times so I will give you the matrices without a lot of discussion. We want a constant velocity model, so we define $\\bf{x}$ to be\n", "\n", "$$ \\mathbf x = \\begin{bmatrix}x & \\dot x & y & \\dot y \\end{bmatrix}^\\mathsf{T}$$\n", "\n", "With this ordering of state variables the state transition matrix is\n", "\n", "$$\\mathbf F = \\begin{bmatrix}1 & \\Delta t & 0 & 0 \\\\\n", "0&1&0&0 \\\\\n", "0&0&1&\\Delta t\\\\\n", "0&0&0&1\n", "\\end{bmatrix}$$\n", "\n", "which implement the Newtonian equations\n", "\n", "$$\\begin{aligned}\n", "x_k &= x_{k-1} + \\dot x_{k-1}\\Delta t \\\\\n", "y_k &= y_{k-1} + \\dot y_{k-1}\\Delta t\n", "\\end{aligned}$$\n", "\n", "Our sensors provide position but not velocity, so the measurement function is\n", "\n", "$$\\mathbf H = \\begin{bmatrix}1&0&0&0 \\\\ 0&0&1&0\n", "\\end{bmatrix}$$\n", "\n", "The sensor readings are in meters with an error of $\\sigma=0.3$ meters in both *x* and *y*. This gives us a measurement noise matrix of \n", "\n", "$$\\mathbf R = \\begin{bmatrix}0.3^2 &0\\\\0 & 0.3^2\\end{bmatrix}$$\n", "\n", "Finally, let's assume that the process noise can be represented by the discrete white noise model - that is, that over each time period the acceleration is constant. We can use `FilterPy`'s `Q_discrete_white_noise()` to create this matrix for us, but for review the matrix is\n", "\n", "$$\\mathbf Q = \\begin{bmatrix}\n", "\\frac{1}{4}\\Delta t^4 & \\frac{1}{2}\\Delta t^3 \\\\\n", "\\frac{1}{2}\\Delta t^3 & \\Delta t^2\\end{bmatrix} \\sigma^2$$\n", "\n", "My implementation of this filter is:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.kalman import KalmanFilter\n", "from filterpy.common import Q_discrete_white_noise\n", "from numpy.random import randn\n", "\n", "std_x, std_y = .3, .3\n", "dt = 1.0\n", "\n", "np.random.seed(1234)\n", "kf = KalmanFilter(4, 2)\n", "kf.x = np.array([0., 0., 0., 0.])\n", "kf.R = np.diag([std_x**2, std_y**2])\n", "kf.F = np.array([[1, dt, 0, 0], \n", " [0, 1, 0, 0],\n", " [0, 0, 1, dt],\n", " [0, 0, 0, 1]])\n", "kf.H = np.array([[1, 0, 0, 0],\n", " [0, 0, 1, 0]])\n", " \n", "kf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=1, var=0.02)\n", "kf.Q[2:4, 2:4] = Q_discrete_white_noise(2, dt=1, var=0.02)\n", "\n", "zs = [np.array([i + randn()*std_x, \n", " i + randn()*std_y]) for i in range(100)] \n", "xs, _, _, _ = kf.batch_filter(zs)\n", "plt.plot(xs[:, 0], xs[:, 2]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This should hold no surprises for you. Now let's implement a UKF. Again, this is purely for educational purposes; using a UKF for a linear problem confers no benefit. `FilterPy` implements the UKF with the class `UnscentedKalmanFilter`. \n", "\n", "The first thing to do is implement the functions `f(x, dt)` and `h(x)`. `f(x, dt)` implements the state transition function, and `h(x)` implements the measurement function. These correspond to the matrices $\\mathbf F$ and $\\mathbf H$ in the linear filter.\n", "\n", "Below is a reasonable implementation of these two functions. Each is expected to return a 1D NumPy array or list containing the result. You may give them more readable names than `f` and `h`." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "def f_cv(x, dt):\n", " \"\"\" state transition function for a \n", " constant velocity aircraft\"\"\"\n", " \n", " F = np.array([[1, dt, 0, 0],\n", " [0, 1, 0, 0],\n", " [0, 0, 1, dt],\n", " [0, 0, 0, 1]])\n", " return F @ x\n", "\n", "def h_cv(x):\n", " return x[[0, 2]]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next you specify how to compute the sigma points and weights. We gave Van der Merwe's version above, but there are many different choices. FilterPy uses a class named `SigmaPoints` which must implement a method:\n", "\n", "```python\n", "def sigma_points(self, x, P)\n", "```\n", "\n", "and contain attributes `Wm` and `Wc`, which hold the weights for computing the mean and covariance, respectively.\n", "\n", "FilterPy derives the class `MerweScaledSigmaPoints` from `SigmaPoints` and implements the aforementioned methods.\n", "\n", "When you create the UKF you will pass in the $f()$ and $h()$ functions and the sigma point object, as in this example:\n", "\n", "```python\n", "from filterpy.kalman import MerweScaledSigmaPoints\n", "from filterpy.kalman import UnscentedKalmanFilter as UKF\n", "\n", "points = MerweScaledSigmaPoints(n=4, alpha=.1, beta=2., kappa=-1)\n", "ukf = UKF(dim_x=4, dim_z=2, fx=f_cv, hx=h_cv, dt=dt, points=points)\n", "```\n", "\n", "The rest of the code is the same as for the linear kalman filter. I'll use the same measurements and compute the standard deviation of the difference between the two solutions." ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "UKF standard deviation 0.013 meters\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from filterpy.kalman import UnscentedKalmanFilter as UKF\n", "\n", "import numpy as np\n", "\n", "sigmas = MerweScaledSigmaPoints(4, alpha=.1, beta=2., kappa=1.)\n", "ukf = UKF(dim_x=4, dim_z=2, fx=f_cv,\n", " hx=h_cv, dt=dt, points=sigmas)\n", "ukf.x = np.array([0., 0., 0., 0.])\n", "ukf.R = np.diag([0.09, 0.09]) \n", "ukf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=1, var=0.02)\n", "ukf.Q[2:4, 2:4] = Q_discrete_white_noise(2, dt=1, var=0.02)\n", "\n", "uxs = []\n", "for z in zs:\n", " ukf.predict()\n", " ukf.update(z)\n", " uxs.append(ukf.x.copy())\n", "uxs = np.array(uxs)\n", "\n", "plt.plot(uxs[:, 0], uxs[:, 2])\n", "print(f'UKF standard deviation {np.std(uxs - xs):.3f} meters')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This gave me a standard deviation of 0.013 meters, which is quite small. \n", "\n", "The implementation of the UKF is not that different from the linear Kalman filter. Instead of implementing the state transition and measurement functions as the matrices $\\mathbf F$ and $\\mathbf H$ you supply nonlinear functions `f()` and `h()`. The rest of the theory and implementation remains the same. The code implementing `predict()` and `update()` differs, but from a designer's point of view the problem formulation and filter design is very similar." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Tracking an Airplane\n", "\n", "Let's tackle our first nonlinear problem. We will write a filter to track an airplane using radar as the sensor. To keep the problem as similar to the previous one as possible we will track in two dimensions. We will track one dimension on the ground and the altitude of the aircraft. Each dimension is independent so we can do this with no loss of generality.\n", "\n", "Radars work by emitting radio waves or microwaves. Anything in the beam's path will reflect some of the signal back to the radar. By timing how long it takes for the reflected signal to return it can compute the *slant distance* to the target. Slant distance is the straight line distance from the radar to the object. Bearing is computed using the *directive gain* of the antenna.\n", "\n", "We compute the (x,y) position of the aircraft from the slant distance and elevation angle as illustrated by this diagram:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import kf_book.ekf_internal as ekf_internal\n", "ekf_internal.show_radar_chart()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The *elevation angle* $\\epsilon$ is the angle above the line of sight formed by the ground.\n", "\n", "We will assume that the aircraft is flying at a constant altitude. Thus we have a three variable state vector:\n", "\n", "$$\\mathbf x = \\begin{bmatrix}\\mathtt{distance} \\\\\\mathtt{velocity}\\\\ \\mathtt{altitude}\\end{bmatrix}= \\begin{bmatrix}x \\\\ \\dot x\\\\ y\\end{bmatrix}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The state transition function is linear \n", "\n", "$$\\mathbf{\\bar x} = \\begin{bmatrix} 1 & \\Delta t & 0 \\\\ 0& 1& 0 \\\\ 0&0&1\\end{bmatrix}\n", "\\begin{bmatrix}x \\\\ \\dot x\\\\ y\\end{bmatrix}\n", "$$\n", "\n", "and can be computed with:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "def f_radar(x, dt):\n", " \"\"\" state transition function for a constant velocity \n", " aircraft with state vector [x, velocity, altitude]'\"\"\"\n", " \n", " F = np.array([[1, dt, 0],\n", " [0, 1, 0],\n", " [0, 0, 1]], dtype=float)\n", " return F @ x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we design the measurement function. As in the linear Kalman filter the measurement function converts the filter's prior into a measurement. We need to convert the position and velocity of the aircraft into the elevation angle and range from the radar station.\n", "\n", "Range is computed with the Pythagorean theorem:\n", "\n", "$$\\text{range} = \\sqrt{(x_\\text{ac} - x_\\text{radar})^2 + (y_\\text{ac} - y_\\mathtt{radar})^2}$$\n", "\n", "The elevation angle $\\epsilon$ is the arctangent of $y/x$:\n", "\n", "$$\\epsilon = \\tan^{-1}{\\frac{y_\\mathtt{ac} - y_\\text{radar}}{x_\\text{ac} - x_\\text{radar}}}$$\n", "\n", "We need to define a Python function to compute this. I'll take advantage of the fact that a function can own a variable to store the radar's position. While this isn't necessary for this problem (we could hard code the value, or use a global), this gives the function more flexibility." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [], "source": [ "def h_radar(x):\n", " dx = x[0] - h_radar.radar_pos[0]\n", " dy = x[2] - h_radar.radar_pos[1]\n", " slant_range = math.sqrt(dx**2 + dy**2)\n", " elevation_angle = math.atan2(dy, dx)\n", " return [slant_range, elevation_angle]\n", "\n", "h_radar.radar_pos = (0, 0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There is a nonlinearity that we are not considering, the fact that angles are modular. The residual is the difference between the measurement and the prior projected into measurement space. The angular difference between 359° and 1° is 2°, but 359° - 1° = 358°. This is exacerbated by the UKF which computes sums of weighted values in the unscented transform. For now we will place our sensors and targets in positions that avoid these nonlinear regions. Later I will show you how to handle this problem.\n", "\n", "We need to simulate the radar and the aircraft. By now this should be second nature for you, so I offer the code without discussion." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "from numpy.linalg import norm\n", "from math import atan2\n", "\n", "class RadarStation:\n", " \n", " def __init__(self, pos, range_std, elev_angle_std):\n", " self.pos = np.asarray(pos) \n", " self.range_std = range_std\n", " self.elev_angle_std = elev_angle_std\n", "\n", " \n", " def reading_of(self, ac_pos):\n", " \"\"\" Returns (range, elevation angle) to aircraft. \n", " Elevation angle is in radians.\n", " \"\"\"\n", " \n", " diff = np.subtract(ac_pos, self.pos)\n", " rng = norm(diff)\n", " brg = atan2(diff[1], diff[0])\n", " return rng, brg\n", "\n", "\n", " def noisy_reading(self, ac_pos):\n", " \"\"\" Compute range and elevation angle to aircraft with \n", " simulated noise\"\"\"\n", " \n", " rng, brg = self.reading_of(ac_pos) \n", " rng += randn() * self.range_std\n", " brg += randn() * self.elev_angle_std \n", " return rng, brg \n", "\n", "class ACSim: \n", " def __init__(self, pos, vel, vel_std):\n", " self.pos = np.asarray(pos, dtype=float)\n", " self.vel = np.asarray(vel, dtype=float)\n", " self.vel_std = vel_std \n", " \n", " def update(self, dt):\n", " \"\"\" Compute and returns next position. Incorporates \n", " random variation in velocity. \"\"\"\n", " \n", " dx = self.vel*dt + (randn() * self.vel_std) * dt \n", " self.pos += dx \n", " return self.pos" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A military grade radar achieves 1 meter RMS range accuracy, and 1 mrad RMS for elevation angle [1]. We will assume a more modest 5 meter range accuracy, and 0.5° angular accuracy as this provides a more challenging data set for the filter.\n", "\n", "The design of $\\mathbf Q$ requires some discussion. The state is $\\begin{bmatrix}x & \\dot x & y\\end{bmatrix}^\\mathtt{T}$. The first two elements are down range distance and velocity, so we can use `Q_discrete_white_noise` noise to compute the values for the upper left hand side of Q. The third element is altitude, which we assume is independent of $x$. That results in a block design for $\\mathbf Q$:\n", "\n", "$$\\mathbf Q = \\begin{bmatrix}\\mathbf Q_\\mathtt{x} & \\boldsymbol 0 \\\\ \\boldsymbol 0 & Q_\\mathtt{y}\\end{bmatrix}$$\n", "\n", "I'll start with the aircraft positioned directly over the radar station, flying at 100 m/s. A typical height finder radar might update only once every 3 seconds so we will use that for our epoch period. " ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import math\n", "from kf_book.ukf_internal import plot_radar\n", "\n", "dt = 3. # 12 seconds between readings\n", "range_std = 5 # meters\n", "elevation_angle_std = math.radians(0.5)\n", "ac_pos = (0., 1000.)\n", "ac_vel = (100., 0.)\n", "radar_pos = (0., 0.)\n", "h_radar.radar_pos = radar_pos\n", "\n", "points = MerweScaledSigmaPoints(n=3, alpha=.1, beta=2., kappa=0.)\n", "kf = UKF(3, 2, dt, fx=f_radar, hx=h_radar, points=points)\n", "\n", "kf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", "kf.Q[2,2] = 0.1\n", "\n", "kf.R = np.diag([range_std**2, elevation_angle_std**2])\n", "kf.x = np.array([0., 90., 1100.])\n", "kf.P = np.diag([300**2, 30**2, 150**2])\n", "\n", "np.random.seed(200)\n", "pos = (0, 0)\n", "radar = RadarStation(pos, range_std, elevation_angle_std)\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", "time = np.arange(0, 360 + dt, dt)\n", "xs = []\n", "for _ in time:\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " kf.predict()\n", " kf.update([r[0], r[1]]) \n", " xs.append(kf.x) \n", "plot_radar(xs, time)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This may or may not impress you, but it impresses me! In the Extended Kalman filter chapter we will solve the same problem, but it will take a significant amount of mathematics. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Tracking Maneuevering Aircraft" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The previous example produced good results, but it assumed the aircraft did not change altitude. Here are the filter results if the aircraft starts climbing after one minute." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Actual altitude: 2515.6\n", "UKF altitude : 1042.1\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from kf_book.ukf_internal import plot_altitude\n", "\n", "# reset aircraft position\n", "kf.x = np.array([0., 90., 1100.])\n", "kf.P = np.diag([300**2, 30**2, 150**2])\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", "np.random.seed(200)\n", "time = np.arange(0, 360 + dt, dt)\n", "xs, ys = [], []\n", "for t in time:\n", " if t >= 60:\n", " ac.vel[1] = 300/60 # 300 meters/minute climb\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " ys.append(ac.pos[1])\n", " kf.predict()\n", " kf.update([r[0], r[1]]) \n", " xs.append(kf.x)\n", "\n", "plot_altitude(xs, time, ys)\n", "print(f'Actual altitude: {ac.pos[1]:.1f}')\n", "print(f'UKF altitude : {xs[-1][2]:.1f}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The filter is unable to track the changing altitude. What do we have to change in our design?\n", "\n", "I hope you answered \"add climb rate to the state\", like so:\n", "\n", "\n", "$$\\mathbf x = \\begin{bmatrix}\\mathtt{distance} \\\\\\mathtt{velocity}\\\\ \\mathtt{altitude} \\\\ \\mathtt{climb\\, rate}\\end{bmatrix}= \\begin{bmatrix}x \\\\\\dot x\\\\ y \\\\ \\dot y\\end{bmatrix}$$\n", "\n", "This requires the following change to the state transition function, which is still linear.\n", "\n", "$$\\mathbf{F} = \\begin{bmatrix} 1 & \\Delta t & 0 &0 \\\\ 0& 1& 0 &0\\\\ 0&0&1&\\Delta t \\\\ 0&0&0&1\\end{bmatrix}\n", "\\begin{bmatrix}x \\\\\\dot x\\\\ y\\\\ \\dot y\\end{bmatrix} \n", "$$\n", "\n", "The measurement function stays the same, but we must alter $\\mathbf Q$ to account for the dimensionality change of $\\mathbf x$." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [ "def f_cv_radar(x, dt):\n", " \"\"\" state transition function for a constant velocity \n", " aircraft\"\"\"\n", " F = np.array([[1, dt, 0, 0],\n", " [0, 1, 0, 0],\n", " [0, 0, 1, dt],\n", " [0, 0, 0, 1]], dtype=float)\n", " return F @ x\n", " \n", "def cv_UKF(fx, hx, R_std):\n", " points = MerweScaledSigmaPoints(n=4, alpha=.1, beta=2., kappa=-1.)\n", " kf = UKF(4, len(R_std), dt, fx=fx, hx=hx, points=points)\n", "\n", " kf.Q[0:2, 0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", " kf.Q[2:4, 2:4] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", " kf.R = np.diag(R_std)\n", " kf.R = kf.R @ kf.R # square to get variance\n", " kf.x = np.array([0., 90., 1100., 0.])\n", " kf.P = np.diag([300**2, 3**2, 150**2, 3**2])\n", " return kf" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Actual altitude: 2515.6\n", "UKF altitude : 2500.1\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "np.random.seed(200)\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", "kf_cv = cv_UKF(f_cv_radar, h_radar, R_std=[range_std, elevation_angle_std])\n", "time = np.arange(0, 360 + dt, dt)\n", "xs, ys = [], []\n", "for t in time:\n", " if t >= 60:\n", " ac.vel[1] = 300/60 # 300 meters/minute climb\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " ys.append(ac.pos[1])\n", " kf_cv.predict()\n", " kf_cv.update([r[0], r[1]]) \n", " xs.append(kf_cv.x)\n", "\n", "plot_altitude(xs, time, ys)\n", "print(f'Actual altitude: {ac.pos[1]:.1f}')\n", "print(f'UKF altitude : {xs[-1][2]:.1f}')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A significant amount of noise has been introduced into the altitude estimate, but we are now accurately tracking altitude." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sensor Fusion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's consider an example of sensor fusion. We have some type of Doppler system that produces a velocity estimate with 2 m/s RMS accuracy. I say \"some type\" because as with the radar I am not trying to teach you how to create an accurate filter for a Doppler system. A full implementation must account for the signal to noise ratio, atmospheric effects, the geometry of the system, and so on. \n", "\n", "The radar's accuracy in the last examples allowed us to estimate velocities to within one m/s or so, I will degrade that accuracy to illustrate the effect of sensor fusion. Let's change the range error to $\\sigma=500$ meters and then compute the standard deviation of the estimated velocity. I'll skip the first several measurements because the filter is converging during that time, causing artificially large deviations.\n", "\n", "The standard deviation without using Doppler is:" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Velocity std 3.4 m/s\n" ] } ], "source": [ "range_std = 500.\n", "elevation_angle_std = math.degrees(0.5)\n", "np.random.seed(200)\n", "pos = (0, 0)\n", "radar = RadarStation(pos, range_std, elevation_angle_std)\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", "kf_sf = cv_UKF(f_cv_radar, h_radar, R_std=[range_std, elevation_angle_std])\n", "time = np.arange(0, 360 + dt, dt)\n", "xs = []\n", "for _ in time:\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " kf_sf.predict()\n", " kf_sf.update([r[0], r[1]]) \n", " xs.append(kf_sf.x)\n", "\n", "xs = np.asarray(xs)\n", "plot_radar(xs, time, plot_x=False, plot_vel=True, plot_alt=False)\n", "print(f'Velocity std {np.std(xs[10:, 1]):.1f} m/s')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For Doppler we need to include the velocity in $x$ and $y$ into the measurement. The `ACSim` class stores velocity in the data member `vel`. To perform the Kalman filter update we just need to call `update` with a list containing the slant distance, elevation angle, and velocity in $x$ and $y$:\n", "\n", "$$z = [\\mathtt{slant\\_range},\\, \\text{elevation angle},\\, \\dot x,\\, \\dot y]$$\n", "\n", "The measurement contains four values so the measurement function also needs to return four values. The slant range and elevation angle will be computed as before, and we do not need to compute the velocity in $x$ and $y$ as they are provided by the state estimate." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [], "source": [ "def h_vel(x):\n", " dx = x[0] - h_vel.radar_pos[0]\n", " dz = x[2] - h_vel.radar_pos[1]\n", " slant_range = math.sqrt(dx**2 + dz**2)\n", " elevation_angle = math.atan2(dz, dx)\n", " return slant_range, elevation_angle, x[1], x[3]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can implement our filter." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Velocity std 0.9 m/s\n" ] } ], "source": [ "h_radar.radar_pos = (0, 0)\n", "h_vel.radar_pos = (0, 0)\n", "\n", "range_std = 500.\n", "elevation_angle_std = math.degrees(0.5)\n", "vel_std = 2.\n", "\n", "np.random.seed(200)\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "radar = RadarStation((0, 0), range_std, elevation_angle_std)\n", "\n", "kf_sf2 = cv_UKF(f_cv_radar, h_vel, \n", " R_std=[range_std, elevation_angle_std, vel_std, vel_std])\n", "\n", "time = np.arange(0, 360 + dt, dt)\n", "xs = []\n", "for t in time:\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " # simulate the doppler velocity reading\n", " vx = ac.vel[0] + randn()*vel_std\n", " vz = ac.vel[1] + randn()*vel_std\n", " kf_sf2.predict()\n", " kf_sf2.update([r[0], r[1], vx, vz]) \n", " xs.append(kf_sf2.x)\n", "xs = np.asarray(xs)\n", "plot_radar(xs, time, plot_x=False, plot_vel=True, plot_alt=False)\n", "print(f'Velocity std {np.std(xs[10:,1]):.1f} m/s')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "By incorporating the velocity sensor we were able to reduce the standard deviation from 3.5 m/s to 1.3 m/s. \n", "\n", "Sensor fusion is a large topic, and this is a rather simplistic implementation. In a typical navigation problem we have sensors that provide *complementary* information. For example, a GPS might provide somewhat accurate position updates once a second with poor velocity estimation while an inertial system might provide very accurate velocity updates at 50Hz but terrible position estimates. The strengths and weaknesses of each sensor are orthogonal to each other. This leads to the *Complementary filter*, which blends the high update rate inertial velocity measurements with the accurate but slowly updated position estimates of the GPS to produce high rate and accurate position and velocity estimates. The high rate velocity estimates are integrated between the GPS updates to produce accurate and high rate position estimates." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Multiple Position Sensors\n", "\n", "The last sensor fusion problem was a toy example. Let's tackle a problem that is not so toy-like. Before GPS ships and aircraft navigated via various range and bearing systems such as VOR, LORAN, TACAN, DME, and so on. These systems emit beacons in the form of radio waves. The sensor extracts the range and/or bearing to the beacon from the signal. For example, an aircraft might have two VOR receivers. The pilot tunes each receiver to a different VOR station. Each VOR receiver displays the *radial* - the direction from the VOR station on the ground to the aircraft. The pilot uses a chart to find the intersection point of the radials, which identifies the location of the aircraft.\n", "\n", "That is a manual approach with low accuracy. A Kalman filter will produce far more accurate position estimates. Assume we have two sensors, each of which provides a bearing only measurement to the target, as in the chart below. The width of the perimeters are proportional to the $3\\sigma$ of the sensor noise. The aircraft must be positioned somewhere within the intersection of the two perimeters with a high degree of probability." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.show_two_sensor_bearing()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We compute the bearing between a sensor and the target as:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "def bearing(sensor, target_pos):\n", " return math.atan2(target_pos[1] - sensor[1], \n", " target_pos[0] - sensor[0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The filter receives the measurement from the two sensors in a vector. The code will accept any iterable container, so I use a Python list for efficiency. We can implement that as:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "def measurement(A_pos, B_pos, pos):\n", " angle_a = bearing(A_pos, pos)\n", " angle_b = bearing(B_pos, pos)\n", " return [angle_a, angle_b]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Assume a constant velocity model for the aircraft. For a change of pace I compute the new positions explicitly rather than using matrix-vector multiplication:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "def fx_VOR(x, dt):\n", " x[0] += x[1] * dt\n", " x[2] += x[3] * dt\n", " return x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next we implement the measurement function. It converts the prior to an array containing the measurement to both stations. I'm not a fan of global variables, but I put the position of the stations in the global variables `sa_pos` and `sb_pos` to demonstrate this method of sharing data with $h()$:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "sa_pos = [-400, 0]\n", "sb_pos = [400, 0]\n", "\n", "def hx_VOR(x):\n", " # measurement to A\n", " pos = (x[0], x[2])\n", " return measurement(sa_pos, sb_pos, pos)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we write boilerplate which constructs the filter, runs it, and plots the results:" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def moving_target_filter(pos, std_noise, Q, dt=0.1, kappa=0.0):\n", " points = MerweScaledSigmaPoints(n=4, alpha=.1, beta=2., kappa=kappa)\n", " f = UKF(dim_x=4, dim_z=2, dt=dt, \n", " hx=hx_VOR, fx=fx_VOR, points=points)\n", " f.x = np.array([pos[0], 1., pos[1], 1.])\n", "\n", " q = Q_discrete_white_noise(2, dt, Q)\n", " f.Q[0:2, 0:2] = q\n", " f.Q[2:4, 2:4] = q\n", " f.R *= std_noise**2\n", " f.P *= 1000 \n", " return f\n", "\n", "def plot_straight_line_target(f, std_noise):\n", " xs, txs = [], []\n", " for i in range(300):\n", " target_pos[0] += 1 + randn()*0.0001\n", " target_pos[1] += 1 + randn()*0.0001\n", " txs.append((target_pos[0], target_pos[1]))\n", "\n", " z = measurement(sa_pos, sb_pos, target_pos)\n", " z[0] += randn() * std_noise\n", " z[1] += randn() * std_noise\n", "\n", " f.predict()\n", " f.update(z)\n", " xs.append(f.x)\n", "\n", " xs = np.asarray(xs)\n", " txs = np.asarray(txs)\n", "\n", " plt.plot(xs[:, 0], xs[:, 2])\n", " plt.plot(txs[:, 0], txs[:, 1], ls='--', lw=2, c='k')\n", " plt.show()\n", "\n", "np.random.seed(123)\n", "target_pos = [100, 200]\n", "\n", "std_noise = math.radians(0.5)\n", "f = moving_target_filter(target_pos, std_noise, Q=1.0)\n", "plot_straight_line_target(f, std_noise)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This looks quite good to me. The beginning of the track exhibits large errors, but the filter settles down and produces good estimates.\n", "\n", "Let's revisit the nonlinearity of the angles. I will position the target between the two sensors at (0,0). This will cause a nonlinearity in the computation of the residuals because the mean angle will be near zero. As the angle goes below 0 the measurement function will compute a large positive angle of nearly $2\\pi$. The residual between the prediction and measurement will thus be very large, nearly $2\\pi$ instead of nearly 0. This makes it impossible for the filter to perform accurately, as seen in the example below." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "target_pos = [0, 0]\n", "f = moving_target_filter(target_pos, std_noise, Q=1.0)\n", "plot_straight_line_target(f, std_noise)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This performance is unacceptable. `FilterPy`'s UKF code allows you to specify a function which computes the residuals in cases of nonlinear behavior like this,. The final example in this chapter demonstrates its use." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Effects of Sensor Error and Geometry" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The geometry of the sensors relative to the tracked object imposes a physical limitation that can be extremely difficult to deal with when designing filters. If the radials of the VOR stations are nearly parallel to each other then a very small angular error translates into a very large distance error. What is worse, this behavior is nonlinear - the error in the *x-axis* vs the *y-axis* will vary depending on the actual bearing. These scatter plots show the error distribution for a 1°$\\sigma$ error for two different bearings." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.plot_scatter_of_bearing_error()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise: Explain Filter Performance" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that for small angular errors the positional errors are very large. Explain how we got such relatively good performance out of the UKF in the target tracking problems above. Answer for both the one sensor and multiple sensor problem. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Solution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is very important to understand. Try very hard to answer this before reading the answer below. If you cannot answer this you may need to revisit some of the earlier material in the **Multidimensional Kalman Filter** chapter.\n", "\n", "There are several factors contributing to our success. First, let's consider the case of having only one sensor. Any single measurement has an extreme range of possible positions. But, our target is moving, and the UKF is taking that into account. Let's plot the results of several measurements taken in a row for a moving target." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ukf_internal.plot_scatter_moving_target()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Each individual measurement has a very large position error. However, a plot of successive measurements shows a clear trend - the target is obviously moving towards the upper right. When a Kalman filter computes the Kalman gain it takes the distribution of errors into account by using the measurement function. In this example the error lies on an approximately 45° line, so the filter will discount errors in that direction. On the other hand, there is almost no error in measurement orthogonal to that, and again the Kalman gain will take that into account. \n", "\n", "This graph makes it look easy because we have plotted 100 measurements for each position update. The movement of the aircraft is obvious. In contrast, the Kalman filter only gets one measurement per update. Therefore the filter will not be able to generate as good a fit as the dotted green line implies. \n", "\n", "Now consider that the bearing gives us no distance information. Suppose we set the initial estimate to 1,000 kilometers away from the sensor (vs the actual distance of 7.07 km) and make $\\mathbf P$ very small. At that distance a 1° error translates into a positional error of 17.5 km. The KF would never be able to converge onto the actual target position because the filter is incorrectly very certain about its position estimates and because there is no distance information provided in the measurements." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now let's consider the effect of adding a second sensor. Here are two plots showing the effects of different sensor placements. I used a square and a triangle as a symbol for the two sensors, and drew a distribution of the errors due to each sensor using the same symbol shape and color. I then computed the $(x, y)$ coordinate corresponding to the two noisy bearing measurements and plotted them with red dots to show the distribution of the noisy measurements in $x$ and $y$." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "with figsize(10,5):\n", " ukf_internal.plot_iscts_two_sensors()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the first plot I placed the sensors nearly orthogonal to the target's initial position so we get these lovely 'x' shape intersections. We can see how the errors in $x$ and $y$ change as the target moves by the shape the scattered red dots make - as the target gets further away from the sensors, but nearer the $y$ coordinate of sensor B the shape becomes strongly elliptical.\n", "\n", "In the second plot the airplane starts very near one sensor, and then flies past the second sensor. The intersections of the errors are very non-orthogonal, and the resulting position errors become very spread out." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation of the UKF\n", "\n", "FilterPy implements the UKF, but it is instructive to learn how to translate equations into code. Implementing the UKF is quite straightforward. First, let's write code to compute the mean and covariance of the sigma points. \n", "\n", "We will store the sigma points and weights in matrices, like so:\n", "\n", "$$ \n", "\\begin{aligned}\n", "\\text{weights} &= \n", "\\begin{bmatrix}\n", "w_0& w_1 & \\dots & w_{2n}\n", "\\end{bmatrix} \n", "\\\\\n", "\\text{sigmas} &= \n", "\\begin{bmatrix}\n", "\\mathcal{X}_{0,0} & \\mathcal{X}_{0,1} & \\dots & \\mathcal{X}_{0,n-1} \\\\\n", "\\mathcal{X}_{1,0} & \\mathcal{X}_{1,1} & \\dots & \\mathcal{X}_{1,n-1} \\\\\n", "\\vdots & \\vdots & \\ddots & \\vdots \\\\\n", "\\mathcal{X}_{2n,0} & \\mathcal{X}_{2n,1} & \\dots & \\mathcal{X}_{2n,n-1}\n", "\\end{bmatrix}\n", "\\end{aligned}\n", "$$\n", "\n", "\n", "That's a lot of subscripts to describe something very simple, so here's an example for a two dimensional problem ($n$=2):" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[ 0. , 0. ],\n", " [ 0.173, 0.017],\n", " [ 0. , 0.172],\n", " [-0.173, -0.017],\n", " [ 0. , -0.172]])" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" } ], "source": [ "points = MerweScaledSigmaPoints(n=2, alpha=.1, beta=2., kappa=1.)\n", "points.sigma_points(x=[0.,0], P=[[1.,.1],[.1, 1]])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The sigma point for the mean is on the first row. Its position is (0, 0), which is equal to the mean (0,0). The second sigma point is at position (0.173, 0.017), and so on. There are are $2n+1 = 5$ rows, one row per sigma point. If $n=3$, then there would be 3 columns and 7 rows.\n", "\n", "The choice to store the sigmas in row-column vs column row format is somewhat arbitrary; my choice makes the rest of the code clearer as I can refer to the i$^{th}$ sigma point as `sigmas[i]` instead of `sigmas[:, i]`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Weights\n", "\n", "Computing the weights with NumPy is easy. Recall that the Van der Merwe scaled sigma point implementation states:\n", "\n", "$$\n", "\\begin{aligned}\n", "\\lambda&=\\alpha^2(n+\\kappa)-n \\\\ \n", "W^m_0 &= \\frac{\\lambda}{n+\\lambda} \\\\\n", "W^c_0 &= \\frac{\\lambda}{n+\\lambda} + 1 -\\alpha^2 + \\beta \\\\\n", "W^m_i = W^c_i &= \\frac{1}{2(n+\\lambda)}\\;\\;\\;i=1..2n\n", "\\end{aligned}\n", "$$\n", " \n", "Code for these is:\n", "\n", "```python\n", "lambda_ = alpha**2 * (n + kappa) - n\n", "Wc = np.full(2*n + 1, 1. / (2*(n + lambda_))\n", "Wm = np.full(2*n + 1, 1. / (2*(n + lambda_))\n", "Wc[0] = lambda_ / (n + lambda_) + (1. - alpha**2 + beta)\n", "Wm[0] = lambda_ / (n + lambda_)\n", "```\n", "\n", "I use the underscore in `lambda_` because `lambda` is a reserved word in Python. A trailing underscore is the Pythonic workaround." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Sigma Points\n", "\n", "The equations for the sigma points are:\n", "\n", "$$\n", "\\begin{cases}\n", "\\mathcal{X}_0 = \\mu \\\\\n", "\\mathcal{X}_i = \\mu + \\left[\\sqrt{(n+\\lambda)\\Sigma} \\right]_i, & \\texttt{for i=1..n} \\\\\n", "\\mathcal{X}_i = \\mu - \\left[\\sqrt{(n+\\lambda)\\Sigma}\\right]_{i-n} & \\texttt{for i=(n+1)..2n}\n", "\\end{cases}\n", "$$\n", "\n", "The Python is not difficult once we understand the $\\left[\\sqrt{(n+\\lambda)\\Sigma} \\right]_i$ term.\n", "\n", "The term $\\sqrt{(n+\\lambda)\\Sigma}$ is a matrix because $\\Sigma$ is a matrix. The subscript $i$ in $[\\sqrt{(n+\\lambda)\\Sigma}]_i$ is choosing the i-th row vector of the matrix. What is the square root of a matrix? There is no unique definition. One definition is that the square root of a matrix $\\Sigma$ is the matrix $S$ that, when multiplied by itself, yields $\\Sigma$: if $\\Sigma = SS$ then $S = \\sqrt{\\Sigma}$.\n", "\n", "We will choose an alternative definition that has numerical properties which make it easier to compute. We can define the square root as the matrix S, which when multiplied by its transpose, returns $\\Sigma$:\n", "\n", "$$\n", "\\Sigma = \\mathbf{SS}^\\mathsf T\n", "$$\n", "\n", "This definition is favored because $\\mathbf S$ is computed using the [*Cholesky decomposition*](https://en.wikipedia.org/wiki/Cholesky_decomposition) [3]. It decomposes a Hermitian, positive-definite matrix into a triangular matrix and its conjugate transpose. The matrix can be either upper \n", "or lower triangular, like so:\n", "\n", "$$A=LL^{∗} \\\\ A=U^{∗}U$$\n", "\n", "The asterick denotes the conjugate transpose; we have only real numbers so for us we can write:\n", "\n", "$$A=LL^\\mathsf T \\\\ A=U^\\mathsf T U$$\n", "\n", "$\\mathbf P$ has these properties, so we can treat $\\mathbf S = \\text{cholesky}(\\mathbf P)$ as the square root of $\\mathbf P$.\n", "\n", "SciPy provides `cholesky()` method in `scipy.linalg`. If your language of choice is Fortran, C, or C++, libraries such as LAPACK provide this routine. Matlab provides `chol()`.\n", "\n", "By default `scipy.linalg.cholesky()` returns a upper triangular matrix, so I elected to write the code to expect an upper triangular matrix. For this reason I access the result by row, so that the first sigma point, which is the center point, is affected by a full row of non-zero values. If you provide your own square root implementation you will need to take this into account. You will find UKF algorithms in the literature that take the values column first. This is fine if the cholesky is lower-triangular, or if you are using a different algorithm that computes a symmetric matrix so row vs column order doesn't matter. " ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "cholesky:\n", "[[1.414 0.071]\n", " [0. 1.731]]\n", "\n", "square of cholesky:\n", "[[2.005 0.122]\n", " [0.122 2.995]]\n" ] } ], "source": [ "import scipy\n", "a = np.array([[2., .1], [.1, 3]])\n", "s = scipy.linalg.cholesky(a)\n", "print(\"cholesky:\")\n", "print(s)\n", "print(\"\\nsquare of cholesky:\")\n", "print(s @ s.T)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So we can implement the sigma points with this code:\n", "\n", "```python\n", "sigmas = np.zeros((2*n+1, n))\n", "U = scipy.linalg.cholesky((n+lambda_)*P) # sqrt\n", "\n", "sigmas[0] = X\n", "for k in range (n):\n", " sigmas[k+1] = X + U[k]\n", " sigmas[n+k+1] = X - U[k]\n", "```\n", "\n", "Now let's implement the unscented transform. Recall the equations\n", "\n", "$$\\begin{aligned}\n", "\\mu &= \\sum_i w_i^m\\mathcal{X}_i \\\\\n", "\\Sigma &= \\sum_i w_i^c{(\\mathcal{X}_i-\\mu)(\\mathcal{X}_i-\\mu)^\\mathsf{T}}\n", "\\end{aligned}\n", "$$\n", "\n", "We implement the sum of the means with\n", "\n", "```python\n", "x = np.dot(Wm, sigmas)\n", "```\n", "\n", "If you are not a heavy user of NumPy this may look foreign to you. NumPy is not just a library that make linear algebra possible; under the hood it is written in C and Fortran to achieve much faster speeds than Python can reach. A typical speedup is 20x to 100x. To get that speedup we must avoid using for loops, and instead use NumPy's built in functions to perform calculations. So, instead of writing a for loop to compute the sum of products, we call the built in `numpy.dot(x, y)` method. The dot product of two vectors is the sum of the element-wise multiplications of each element. If passed a 1D array and a 2D array it will compute the sum of inner products:" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([410, 520, 630])" ] }, "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ "a = np.array([10, 100])\n", "b = np.array([[1, 2, 3],\n", " [4, 5, 6]])\n", "np.dot(a, b)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "All that is left is to compute $\\mathbf P = \\sum_i w_i{(\\mathcal{X}_i-\\mu)(\\mathcal{X}_i-\\mu)^\\mathsf{T}} + \\mathbf Q$:\n", "\n", "```python\n", "kmax, n = sigmas.shape\n", "P = zeros((n, n))\n", "for k in range(kmax):\n", " y = sigmas[k] - x\n", " P += Wc[k] * np.outer(y, y) \n", "P += Q\n", "```\n", "\n", "This introduces another feature of NumPy. The state variable `x` is one dimensional, as is `sigmas[k]`, so the difference `sigmas[k]-X` is also one dimensional. NumPy will not compute the transpose of a 1-D array; it considers the transpose of `[1,2,3]` to be `[1,2,3]`. So we call the function `np.outer(y,y)` which computes the value of $\\mathbf{yy}^\\mathsf{T}$ for the 1D array $\\mathbf{y}$. An alternative implementation could be:\n", "\n", "```python\n", "y = (sigmas[k] - x).reshape(kmax, 1) # convert into 2D array\n", "P += Wc[K] * np.dot(y, y.T)\n", "```\n", "\n", "This code is slower and not idiomatic, so we will not use it." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Predict Step\n", "\n", "For the predict step, we will generate the weights and sigma points as specified above. We pass each sigma point through the function f.\n", "\n", "$$\\boldsymbol{\\mathcal{Y}} = f(\\boldsymbol{\\chi})$$\n", "\n", "Then we compute the predicted mean and covariance using the unscented transform. In the code below you can see that I am assuming that this is a method in a class that stores the various matrices and vectors needed by the filter.\n", "\n", "```python\n", "def predict(self, sigma_points_fn):\n", " \"\"\" Performs the predict step of the UKF. On return, \n", " self.xp and self.Pp contain the predicted state (xp) \n", " and covariance (Pp). 'p' stands for prediction.\n", " \"\"\"\n", "\n", " # calculate sigma points for given mean and covariance\n", " sigmas = sigma_points_fn(self.x, self.Pp)\n", "\n", " for i in range(self._num_sigmas):\n", " self.sigmas_f[i] = self.fx(sigmas[i], self._dt)\n", "\n", " self.xp, self.Pp = unscented_transform(\n", " self.sigmas_f, self.Wm, self.Wc, self.Q)\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Update Step" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The update step converts the sigmas into measurement space via the function `h(x)`.\n", "\n", "$$\\mathcal{Z} = h(\\mathcal{Y})$$\n", "\n", "The mean and covariance of those points is computed with the unscented transform. The residual and Kalman gain is then computed. The cross variance is computed as:\n", "\n", "$$\\mathbf P_{xz} =\\sum_{i=0}^{2n} w^c_i(\\boldsymbol{\\mathcal Y}_i-\\mu)(\\boldsymbol{\\mathcal Z}_i-\\mu_z)^\\mathsf T$$\n", "\n", "Finally, we compute the new state estimate using the residual and Kalman gain:\n", "\n", "$$\\begin{aligned}\n", "K &= \\mathbf P_{xz} \\mathbf P_z^{-1}\\\\\n", "{\\mathbf x} &= \\mathbf{\\bar x} + \\mathbf{Ky}\n", "\\end{aligned}$$\n", "\n", "and the new covariance is computed as:\n", "\n", "$$ \\mathbf P = \\mathbf{\\bar P} - \\mathbf{KP}_z\\mathbf{K}^\\mathsf{T}$$\n", "\n", "This function can be implemented as follows, assuming it is a method of a class that stores the necessary matrices and data.\n", "\n", "```python\n", "def update(self, z):\n", " # rename for readability\n", " sigmas_f = self.sigmas_f\n", " sigmas_h = self.sigmas_h\n", "\n", " # transform sigma points into measurement space\n", " for i in range(self._num_sigmas):\n", " sigmas_h[i] = self.hx(sigmas_f[i])\n", "\n", " # mean and covariance of prediction passed through UT\n", " zp, Pz = unscented_transform(sigmas_h, self.Wm, self.Wc, self.R)\n", "\n", " # compute cross variance of the state and the measurements\n", " Pxz = np.zeros((self._dim_x, self._dim_z))\n", " for i in range(self._num_sigmas):\n", " Pxz += self.Wc[i] * np.outer(sigmas_f[i] - self.xp,\n", " sigmas_h[i] - zp)\n", "\n", " K = np.dot(Pxz, inv(Pz)) # Kalman gain\n", "\n", " self.x = self.xp + np.dot(K, z - zp)\n", " self.P = self.Pp - np.dot(K, Pz).dot(K.T)\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### FilterPy's Implementation\n", "\n", "FilterPy has generalized the code somewhat. You can specify different sigma point algorithms, specify how to compute the residual of the state variables (you can not subtract angles because they are modular), provide a matrix square root function, and more. See the help for details.\n", "\n", "https://filterpy.readthedocs.org/#unscented-kalman-filter" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Batch Processing\n", "\n", "The Kalman filter is recursive - estimates are based on the currernt measurement and prior estimate. But it is very common to have a set of data that have been already collected which we want to filter. In this case the filter can be run in a *batch* mode, where all of the measurements are filtered at once.\n", "\n", "Collect your measurements into an array or list.\n", "\n", "```python\n", "zs = read_altitude_from_csv()\n", "```\n", "\n", "Then call the `batch_filter()` method.\n", "\n", "```python\n", "Xs, Ps = ukf.batch_filter(zs)\n", "```\n", "\n", "The function takes the list/array of measurements, filters it, and returns an array of state estimates (`Xs`) and covariance matrices (`Ps`) for the entire data set. \n", "\n", "Here is a complete example drawing from the radar tracking problem above." ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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T+DKFSzaJiIiIqPsY8ogucLbMOIsX4ukMTxeFTWtZPG4QBAE4kFONguomm9ZCREQ0EIiiiOyKRnyVUogt6SVo1uptXRKRTTjZugAiKTljo03QOxPq5YKrY/yQnFWJzw7m4y/zE2xdEhERkaS06PQ4XliHlLwapORVIyWvBjVNOvP9bionzB8ehBvHhmJilC9kMut3zSayBYY8ogtIoenKhZYlRSA5qxKfH8zDQzMHw1XFtywRETmuioZWpORV48i5GqTk1+BEUR10+o57yiqdZBgZ6onS+hYU1jTjy5RCfJlSiBBPZywaE4rFY0MxOMD2P8wl6k/8xEh0gbPm7RPcbFyJ0awhgYj0VeNcVRM2HS3EHUmRti6JiCSqTW/AR/vz0NqmR4SPK8J91Aj3Vdt86XlnRFFEtUaLnEoNsssbO/xe0dCKa0cE4f+uHQIvtdLWpZINGQwizpY3GGfpztXgSF4N8ju5fMHPTYXxEd4YH+mNsRHeGB7iCaWTDAaDiCN5NdicWogfjpeguK4Fb+/Kxtu7sjEi1BOLx4bi+lEh8HNT2eDVEfUvhjyidqIo4oxpJi9QGjN5cpmAFZOj8LdvT+K/ybm4LTECci41IaJOvLMrG//edvaS273UCmPg81Ejwlfd/mdXRPiqEeTh3K/L17RtBuRXa5BdoUFOhQbZFY3IqWhEdoUGdc26Lh/3vyOF2HGmAusWDsO1I4IgCPx3zxFoWttwrKAWR/KMgS41vwYNLR23ERIEID7QHeMivDEuwhvjI3wQ5uPS6feITCZgQpQPJkT54Onrh2H76XJsTi3ErowKpBfVIb2oDs/9eBrT4vyxeGwoZg0JhLNCbq2XS9SvGPKI2pXWt6C+pQ1ymYCYAFdbl2N287hB+PfWszhX1YTtp8swZ1iQrUsisistOj2+OFyA95Nz4KNW4vN7Jw64pdEniurw2vZMAMDMhADUNmmRX92EykYtapt0qG2qw/HCuksep5TLMMjHBRE+akT4uiLEU4WKagGx5Y2IDvDo9gfeao22Q4Az/Z5f3QS9Qez0MYJgvPY42t8N0X6uiAlwQ4yfK/SiiHXfn0JWeSMe+PwoZg0JxLOLhiHY06X3f0EkScW1zTiSV4OjeTU4kleN0yUNl3y/qJVyjAn3wrhwb4yL9MGYcC94OPd8dtpZIcd1I4Nx3chgVDW24ofjJfj6aCGOFdZhx5ly7DhTDneVE64dEYzFY0NxVaQPr9+jAW1g/S9G1I9MTVei/VyhcpLOT/LUSifcmhiOd3Zl4/3kXIa8AU6nNyCvqgk5FcalaTkVjcip0KChpQ3rbhiGidG+ti7RYTRp2/DZgXz8v705qGhoBQAUVDdj7Xcn8c9bRtm4uu5r0enxyBdpaDOImD88CG/fNtY8q6FpbUN+dRPyqppQUN2EvGqN+c+FNc3Q6g3IaZ9lAyrazyjHfzL2AQACPVSI8HFFWPssYISvGionOXIrTUHO+H1c29T1rJyrUm4Mcv6uiLng9yg/1y5D5I8rJ+Ptndl4e1cWfj1dhgM5VfjL/ATcOiGcH7wHsILqJuzPrsL+nCoczKkyb1l0oVAvF4yN8Mb49pm6hCB3OMkt2wze102F5ZMisXxSJLLKG/FNahE2pxahqLYZXxwpwBdHChDq5YIbx4TixrGhiPGXxiUcRD3BkEfULkNCnTUvtjwpEv/Zk4NDudU4XliLkYO8bF0SXYYoiqhs1F4S5HIqLz+zcdf6w1h/11UMev2soUWHj/fn4YPkXFRrtACMHyxvGB2Cd3dn48uUQkyL98eCkSE2rrR7/r01A5nljfBzU+G5RcM7LFtzVTlhSLAHhgRfugS9TW9ASV2LOQTmVWuQV6nBiXOlqG1ToLG1DWX1rSirb8Whc9VXrMM4K2cMcDHmQOeGQA9Vj5dbqpzkeGR2HK4bGYw/bzqO1PxaPPXNCXyXVowXbhrBD90DRFFtszHUZVfhQE4VimqbO9wvlwkYFuKBseHG6+nGRXhbfcZ2cIAbVs+Nx6Oz43DoXDU2Hy3ClvQSFNU2482dWXhzZxZGhXlh8Rjj9Xs+rrxOlAYGhjyidqaQlyDBkBfk6YzrR4Vgc2oRPkjOxWu/G2PrkgjGGRTjjIbmfKBrD3UXX0dyIbVSjmh/V0T7GWc1ov3d8FVKIfacrcBd6w/jw7uuQiKDnsXVNenw399ysf63XNS3j0+Erxr3T4/BjWMGQekkg1wm4I0dWVjzdTpGh3lhkLfaxlVf3oGcKryfnAsAeHHxCPj2oIGEk1yGMB81wnzUuHqw8TadToctW4owf/4caHRAXnUT8qo0xlnAqibkVTehRadHlJ/x+zcmwPh7lJ8rXJSWXwERF+iOr/44CZ/sP4eXfsnAoXPVmP/qXqy8ZjDumxYDhYVneKhvSutasD+nsj3UVV/SJMVJJmB0mBcmRvsiKcYXY8K9oFZK46OoTCZgYrQvJkb7Yt0Nw7DtVBk2pxZh99kKHCuoxbGCWjz7wylMjw/A4rGhmBrjbeuSiS5LGu8sIgk4v0eeNJquXOzuyVHYnFqEH46X4M/zEhDixetTrKWqsRWnSxqQU9l4QfMIDYrrmiF2PikHQQAGebt0CHIxfq5dzmzMGRqIez8+gr2Zlbjrw8P48K4JmBDlY4VXZ/+qGlvxQXIuPt6fh8ZWY7iL8XfFgzMH4/qRIR2Wgq28JhbJWZVIza/FI1+kYeMfkiTb7KihRYfVXx6DKAJLx4dh1tBAi51bEAR4uyrg7arE6DAvi523N+QyAXdeHYVZQwPx1DcnsCujAv/aehY/HC/BP24aiVE2rs+Rlde3YH+OcZbuQE41cis1He6XywSMCPVEUowvkqJ9MT7SWzKh7nKcFXJcPyoE148KQWVjK75LK8bm1CKkF9Xh19Nl+PV0GTycnTDcQ4bQwjqMi/Rlc6CLNGv1yCxvQHFtCxKjfODNGVCrk/47jcgKdHoDssuN2ydIcSYPAIaHemJitA8O5FTjo33nsObaIbYuyW6JooizZY3m/8zTCmq7DHOeLooOs3Ix7YEu3Efdoy5tzgo5/nPHeHPQu3P9IQa9Piqvb8F/9ubg0wP5aNbpARjf3w/OHIz5w4M7DW8KuQyvLR2Da1/fi8PnavDWziysvCbW2qV3y3M/nEZhTTMGebvgqQX2/+/BIG811t95Fb47Vox135/CmdIG3Pj2b7jr6ig8NiduQISHga6ysRUHcs4vv8yu6BjqZILx/6qkaF9MjPHFVZE+cBtgTYwu5uemworJUVgxOQqZZQ34OrUI36YWobiuBftaZNj33kEMCfbArRPCcMOY0F41hRnIdHoDzlVqkFHWgIxS46+zZQ3Iq24y/7/p6aLA6jlxuJUdwq1qYL/ziCwkr0oDrd4AtVKOUAnPkN0zORoHcqrx+aF8PHRN7ID/z1NKtG0GHMqtNge7wpqO145Et8/CGUOcq7kjoI+r0mI/we0s6H20YgKuimTQ64ni2ma8tzsbGw4XQNtmAACMCPXEQzMHY9aQwCs27gj3VeO5RcOx6os0vLY9E1cP9sW4CGmNwfbTZfjiSAEEAfjXLaPg7iAfLAVBwA2jQzEl1h/P/nDKvIT9l5OleP7GEZga52/rEu1KtUaLg+0zdftzqnC2rLHD/YIADA32MIa6aF9cFeUjyX0ZLSU20B1/npeAx+fE47fMcrz2/SEcr3XC6ZJ6/PXbk3h+yxksGBmM3yeGY0yYl13N7hkMIopqm3G2rAFn2oNcRmkDciqMn5864+OqhFopR2FNM/767UlsOFSAdTcM4/9pVsJPiEQ4v1QzLtBd0p3bZiYEINrPFTmVGnx5pAB3XR1l65IGtBqNFjszyrH9dDn2nK1AQ+v56+iUTjJMHuyHa4YE4JqEQAR5OlulJlPQu+ejI0jOqsTy/zLodVdBdRPe3pWFr1IKodMbf4Q8NtwLD10Ti+lx/j36wLVoTCh2ZZTjm7RiPLwxDVseniKZn9BXa7T486Z0AMA9k6McslGPj6sSrywdjRtGh+DJzSdQWNOMO/57CDeNHYSnrhti90vDajRaVGlaoW0TodMb2n9d+GcDtHoRuraOX7ddeJ/eYL5fe8Fj2/QitHoDCqqbzP83XighyN18TV1ilI9DblhvvH7PB9WxBkyaPg0/nCjD5wfzkVneiC9TCvFlSiESgtzx+wnhWDQmdMAF38rGVpwtbTg/O1fWgLOlDdBo9Z0er1bKERfojoQgd8QFuiO+/Xd/dxXa9AZsOJSPf/6SgVMl9bjl3f24cUwo1sxPQICHdf5fdVQMeUSQdtOVC8naN0d/6psT+O9vubgjKZJLH3pAFEVklTdi++kybD9djiN51biw0aWfmwrXJATgmiEBmBzrZ7PlXxfO6CVnVeLO9qA3nkGvUzkVjXhrZza+SSsydy6dGO2DlTNjkRTT+2tlnlk0HCn5NSiobsbfvjmBVyXQ8EgURTy5OR2Vja2IDXDDY3PibV2STU2PD8DWR6biX1sz8OG+c9h0tBC7Msrx9MJhuH5ksF3NpABAbqUG7+3N6/C93t9iA9zM19QlRvuyu+RFvNQK3HV1FO6cFImj+TX4/GABfjhejDOlDXj6u5N44afTuG5ECG5NDMPYcG9JfU82a/U4XVqPs6XnZ+fOljWgslHb6fEKuYAYfzdziItvD3ShXi5d/oDcSS7DsqRIXDsiGP/amoGNhwuwObUIW0+WYtWsONx5dSQbKPUThjwiXNh0RdohDwBuGjsI/9qagYLqZmw7VYp5w4NtXZKk6fQGHMytxuZzMrz86m/Iu6jbW0KQO2YNCcSsoYEYGeopmZlcF2X7jN7Hh/FbVpV5Ro9B77yzZQ14c0cWfjhebA7rU2L9sPKaWIvMfHo4K/Dq0jFY8t5+fJNWjGnx/rhxzKA+n7cvvk0rxk8nSuEkE/DyktE9uu7TXrmqnPD09cNw/agQ/GXTcZwta8TKDan4NrUIzy4abhdNqjLLG/FxpgypB34zf697uiigdJJBKZdBIRegkMvgJJdB2f5nhVwGhVPHr53kQvvxpvsv+vqCY73VCoyP9IG/e/c7tjoyQRAwLsIH4yJ88LcFQ/FNWhE2HMrHmdIGbDpaiE1HCxEX6IbfTwjH4jGD4Km27uyewSAip1KD1PwapBXUIjW/Fhlll24+b3wtQISP2jwrFx9kDHSRfq69DmS+biq8sHgkfj8hHH/79iTSCmrx9y2n8cWRAqy9fhgmx/r19SXSRRjyiCDtPfIu5qKU4/bECLy5Mwvv781lyOtEXbMOu9qXYe7KKG9vly8D0ASlXIaJMb6YNSQAMxMCJN0i30Upx/t3XIW7PzqMfdnGoPfx3RMkd32YtZ0oqsObO7Lw88lS822zhgTgwZmxFu8EOS7CG6uuicW/t53FX785ibHh3ojwdbXoc3RXSV0z/vrtCQDGLqAjBnnapA6pGhvujR8emoJ3d2fjzR1Z2H6mHAdf2YM/z4vHbYkRkvkBTk+cKa3HGzuysCW9BKJo/HA9a0gAHpoZy66iEuapVmD5pEjckRSB1IJabDiYj++PF+NsWSPWfX8KL/50BteNMF67Nz6if2b3ajRaY5grqEVqfg2OFdSat465UIC7CvFBHZdaxga498uWKAAwcpAXvv7TJHx1tBD/+OkMssobcfsHBzF/eBCevG6IpP9PHmgY8sjhaVrbzHv5JEh0+4SL3ZEUgff2ZONIXg1S82swJpz79Zyr1ODX9mWYh89Vo+2Cn056qxWIdW3FsmvGYMaQoAHVsMZFKccHyy8Meofx0YoJGBchnTEXRRF7MitxKLcKckGAXGacMZDLBDi1/5LLZcbf27+GaMDxKgFOp8rgrFS0327cp67jY8+fq7KhFf9vTw62nyk3P/f84UF4cOZgDAvpv8Bz/4zB2JtZiUPnqvHwxjR8+cckqy8vMhhEPP7lcTS0tGFUmBfunx5j1ecfKJROMqy8JhbzhwfhL1+nIyWvBn/99iS+SSvGP24agcEB0v9BHmD8QcYbOzLxy8ky820jfQx4ZukkjI5wvGswBypBEDA23Btjw73x1+uH4tu0Ynx+MB+nS+rxdWoRvk4twuAA0+xeaK+vJdW2GXCmtN48Q5dWUHvJdhYA4KyQYWSoF8aEe2F0mBdGh3tZffN5wHjpyZLxYZg7LAiv/noWH+/Pw08nSrEzoxwPTB+Me6dGc5WCBQycTzpE/eRsmXEWz99dNWCuNQjwcMbCUaHYdLQQHyTn4s1bpfOB31oaWnQ4mFON37IrsedsxSWtvGMD3HDNkEDMGhKA4cFu+OXnnzBvWCAUioH3z54p6K348DD255xfuimFoJdV3oBnfjiNPWcrevFoOT48e6zHj5IJwPWjQvDAjMGIC+z/D+1ymYBXfjca81/dg7SCWrz2ayZWz7XutXCfHsxDclYlVE4yvLxkVIe9/ehSsYHu+PK+JHx6MA//+OkMUvJqcO1ryXhgxmD8aXoMlE7S/Ps7VlCLN3Zk4tfTxh9kCAJw7Yhg/GlKJLKP7sWwkIHxg0i6lIezAssmRuD2xHAcL6zDhkP5+O5YMbLKG/HsD6fwj5/PYP7wIPx+QjgSo3y6nN0TRRHFdS1IyzfO0KUW1OJEUR1a2y7tcBnt74oxYd4YHe6FMWFeiA9yl9T1b54uCjx9/TAsvSoMT397Egdzq/HvbWfxZUoh/rZgqEX3/nREA+/TDpGFDZSmKxe7e3IUNh0txE8nSlFY02T3Sxy0bQak5tfgt6xK/JZdhbSC2g7XEjjJBEyI8sGsIYG4ZkhAhyV1Op3OFiVblItSjg/uHI8VHx7GgZxq89LNsTaaxa1r1uG1XzPx8f5zaDOIUMgFLBwVCleVHG0GEXq9aPzdYGj/XYROf/7rNr0B5RVV8PT2hl6E8XbzY0S0GQwXnMP4uyAAs4YE4v7pMYj2d7Pq6w31csHzi0fgwc9T8dauLEyO9bNaV8vcSg2e33IaALBmfgJirPzaByqZTMAdSZGYNcS4ifqOM+V45dez+DG9GE9dNxSJ0T5QOUljtiAlrwavb8/E7vYflph+kPHgjMGIDXSHTqdDto1rJMsQBAGjwrwwKswLT143BN8dM87unSyux7dpxfg2rRjR/q74/VXhuGncIKicZEgvqkNqe6hLK6hFeUPrJef1dFGYZ+jGhHtj9CAvq1/311sJQR7Y+IeJ+P54Cf7+4ynkVzfhno+PYEa8P/52/TBE+dlmifxAx5BHDi+j7Pz2CQPJ0BAPXD3YF79lVeGjfefw5HVDbV2SRRkMIs6UNuC3rEokZ1XiUG61eUNrk0hfNa4e7Gf+NdDaVPeUWumE/9551fmg98EhfGTloKc3iNh4OB//3noW1RpjB7ZZQwLx5HVDevQfsU6nw5YtW3DttROgUAyMcVswMgR7zlbgf0cK8cgXafj54an9/iGqTW/Ao/9LQ4vOgKsH++KOpMh+fT57FOLlgg+Wj8f3x0uw7ruTOFvWiDv+ewjOChnGRXgjqX07gBGhXlaf4TuYU4U3dmQhOasSgHHWeNHoUDwww/o/yCDrc3dW4LbECNyWGIH0wjp8figf36UVIadCg79vOY2XfjkDvUHExb1RnGQChgR7tAc6Y6iL9FVLqnNnTwmCgIWjQnBNQkB7z4Ec7MyowG9Ze3Dv1Cg8MGOwzTpeD1T82yKHN5CarlzsnsnR+C2rChsPFWDlNbEDfkPkguomc6jbn12FKk3HNs5+bkpMivHD5MF+mDTY1+5nLztjCnp3rT+Mg7nGoPfx3ROscl3mgZwqrPv+FE6X1AMABge44a8LhmKaA21A/fT1w3D4XA1yKzVYs/k43rp1bL9+sHpvTw5S82vh7uyEf948akA2D5EC0wfIKYP98K+tGfjlZBkqG1vxW1YVfsuqAgC4KOQYH+lt3i5gRKhnvyyLFUUR+7Or8Nr2TBzMrQZg/NB+09hBuH9GjM0a+5BtjRjkiRcGjcCT1w3B98eKseFQPo4X1gEAQjyd25dcemNMuBeGh3ra7TVrrion/HleAm4ZNwjrvj+F3Wcr8NbObHx9tAhPXTcU144IGtBh1poY8sjhDdTlmgAwLc4fMf6uyK7Q4IvDBbhnSrStS+qRao0W+7OrkJxVid+yKs0NcEzUSjkSo3xw9WA/TI71Q3ygO/9xhzHorb/rKty5/jAO5Vbjjn4OeoU1TXhhyxn8mF4CAPBwdsIjs+Nw+8QISV3fYQ2uKie89rvRWPz2PmxJL8X/jhRg6VXh/fJcJ4rq8Mq2swCAdQuH2cVWALbm7arE328cgecWDUdWeSMO5FRhf04VDuRUo1qjxd7MSuzNNM6quamccFWkt3nj72Ehnn3al1QURezNrMTr2zNxJK8GgHHfsSXjw/Cn6TEO+UMrupSbygm/nxCO308Ix7lKDZwVcgR5Ot6m4dH+bvjwrqvw6+lyPPPDSRRUN+OBz48iKdoX624YNuBWX9kCQx45tIqGVlRptBAEIHaAdF27kEwm4O7J0fi/zelY/9s53DkpUtINGZq1ehw+V22erTtVUg/xgmUoTjIBo8O8zKFu1CDrL58aKNRKJ3x4UdD75J5Ei24h0KRtw7u7svHenhy0thkgE4BbE8Px6Oz4AdOkqD+MHOSF1XPj8eJPZ7D2u1MYH+lj8evkWnR6PPa/Y2gziJg3LAg3jgm16PkdnSAIiA10R2ygO5YlRcJgEHG2vAH7s6uwP7sKB3OrUdesw86MCuzMMF4n5+7shMQoH3PoGxLk0a2ZVVEUsTOjHK9tz8KxgloAxi6gv78qDPdNi2F4py5FOvi1aIIgYPbQQEyJ9cN7u3Pw9q4s7M+pwvzX9uLOSZF4eFYsPAb4Cqb+xJBHDs00ixfp69pve8L0t8VjQ/GvrRkoqm3GLyfLcN1Iae2bV1LXjE0phUjOqsTRvFpo9R07gCUEuRuXYMb6YkKU74Da3sDW1EonrG9funnoXDWWfXAQn96d2Of9s0RRxHfHivHiT2dQUtcCAJgY7YOnrx+GIcHs7gcAf5gSjT1nK7AvuwoPb0zF13+62qI/kHhl21lklDXAz02Jv984nDPY/UwmE5AQ5IGEIA/cdXUUDAYRp0rqcSCnCgdyqnAwpxoNLW349XS5ufOlp4sCiVE+xuWdMb6IC3DvEPpEUcS2U2V4fUcmThQZlzg7K2S4LTEC902NRoCH483OEPWGs0KOh2fFYvHYUDz34yn8crIMHyTn4tu0YvxlfgIWjwk1v/dEUYReNP5QuakN0OkN0LYZoNMb2v8sGn/XG6Bra/9dL5qP0bYfd/F90+L9bdborLf4aYoc2plS43+88QN42t9ZIcftEyPw+vZMvJ+cI6mQV97QgoVv/oaKCzqBhXg6m2fqkmJ8EeDODzp94aoyLt00Bb3b+xj00gvrsO77k+blZKFeLnjquiGYN5zXQVxIJhPw8pLRmP/aHpwoqse/t2ZgzbVDLHLuQ7nV+H97cwAALyweCV83lUXOS90nkwkYHuqJ4aGeuGdKNPQGESeL64wzfTlVONw+07f1VBm2njLuZefjqsTEaB8kRfvC3VmB9/bkmK9fVSvlWDYxAvdMiYa/O8eTqDfCfNR4b9l47DlbgbXfn0ROhQarvzyGdd+fBERA2x7SRNEJOLDdos/t4aJgyCMaSAZy05ULLZsYgXd3ZSM1vxYpeTWS2D+tTW/Ag5+noqKhFVF+rlgxOQqTB/sN+A5gUmQKeneuP4TD52pw+wcH8dk9iRg5yKvb5yhvaMG/fsnAlymFEEVjE4r7p8dwU9rLCPJ0xj9uGok/fJKC9/bkYEqsPybH+vXpnI2tbXjsyzSIInDLuEGYzX2iJEEuEzBykBdGDvLCfdNioNMbcKKoDvtzjMs7j5yrQbVGiy3ppdiSXmp+nJvKCcsnReDuydEOvcSZyJKmxvnj54enYv1vuXh9eyYaWtoue7xSLoNCLkDhJGv/swxKJ+Ntxt/bb5N3vM10rMJJGJB9GxjyyKGZNkIf6CHP312FRWNC8L8jhfggOQfjIsbZuiT885cMHMqthpvKCe8vH8+9vfqZMehNwJ3/PYQjeTW4/f2D+OyeiRgxyPOyj9O2GfDhvly8vj0Lja3G/ygXjQ7Bn+cnINiT1wpdyZxhQbgtMRyfHczHo/9Lw08PT+nTzNvffzyNgupmhHq54G/X29e2KPZEIZdhTLg3xoR74/7pg6FtM+B4Ya15pq+4thkLR4dixdWR8FIz3BFZmtJJhvumxeD3ieEorWsxBjInGQSDHrt2bMe18+bA1UUFJ5ngsD9YZsgjh2UwiDhb1ghg4Ic8ALh7cjT+d6QQP58oRUF1E8J8bNep7ecTJXhvj3G52T9vHsmAZyVuKid8uOJ80Lvt/QNdBj1RFLHjTDme+/E0cis1AICRgzzx9PVDMS7Cx9qlD2hPXTcUB3OrkVXeiD9vOo7/3DG+Vx8qdp4px4ZD+QCAf90yasBvieJIlE4yjI/0wfhIHzx0TaytyyFyGB7Oig7NV3Q6HVwVxh98Olr354s59qsnh5Zf3YRmnR4qJxki7WBfovggd0yJ9YNBBNb/ds5mdeRUNGL1l8cBAPdOicL8EdK5RtARmILeuAhv1Le04bb3DyC9fa8lk6zyBixffxh3f3QEuZUa+Lmp8M+bR+Kb+69mwOsFF6Ucr/9uDJRyGX49XY5PD+b3+Bw1Gi2e2GR839w9OQpJMb6WLpOIiBwIQx45rDPt1+PFBrr1ae8jKTHtk/fF4XzUt+is/vxN2jb86dOjaGxtw4RIHzwxL8HqNVB70LvrKnPQu/2DgzhRVIe6Jh3WfX8Sc1/diz1nK6CQC7hvWjR2rp6GW8aHcaPtPhga4oG/zDd+vz/3wynzUvDuEEURT31zAhUNrRgc4IbH58b3V5lEROQgGPLIYZmbrgTaT0v4qbF+iA1wg0arxxeHCqz63KIo4snNJ9rbvqvw5q1jHH6phC25Oyvw4V1XYWy4F+qadbj1Pwcw49+7sP63c9AbRMwaEoitj0zDmvlDuCzQQu66OhLT4vzR2mbAyg2paNHpu/W4744V48f0EjjJBLyyZDQb3RARUZ/xExg5rIwyY2vrgdgxqSuCIOCeKVEAgPW/5aLtoj3p+tNnB/OxObUIcpmAt24dwz2gJMDdWYGPVkzA2HAv1Le0oVqjxeAAN3y0YgLeXz4eUQ6+0a6lCYKAf90yCn5uSpwpbcCLP5254mNK61rw129OAAAemhl7xUY5RERE3cGQRw7rjJ1sn3CxG0aHwtdVieK6Fvx0ovTKD7CAtIJaPPP9KQDAn+fFIzGa1xNJhSnorbg6Cs/eMAw/PTwF0+L8bV2W3fJ3V+GfN48CAHy47xx2ninv8lhRFPH4V8dQ39KGUYM8cf+MGGuVSUREdo4hjxxSi06Pc+0dBe1pJg8wbo6+LCkCAPD+3hyIotivz1et0eKBz45Cqzdg3rAg3Nt+XSBJh7uzAn+7fiiWJUVyCa0VzEgIwF1XRwIAHv/qGCoaWjs97tOD+dibWQmVkwz/XjKaY0NERBbD/1HIIWWVN8IgAl5qBfzde7+nlVQtmxgBpZMMxwrrcCSvpt+eR28Q8fDGVBTVNiPKzxUv3TLSYfejIbrQn+clICHIHZWNWqz+8hgMho4/bDlXqcHzP54GAPxlfgIGB3CbESIishyGPHJI55uuuNtlKPF1U+GmsaEAjLN5/eX17ZnYm1kJZ4UM79w+tsNeNUSOzFkhxxu/HwOVkwy7z1Zg/b5z5vv0BhGP/i8NzTo9kqJ9sTwp0mZ1EhGRfWLII4eU0d7e3N6Wal5oxdXGBixbT5Uhr0pj8fPvzCjH6zsyAQAvLB6BhCD76VJKZAmxge54asFQAMA/fjqDk8XG/Qrf25ONo/m1cFc54V9LRnHrCiIisjiGPHJI55uu2G8wiQ10x/R4f4j9sDl6QXUTHvkiDaII3JYYjhvHDLLo+Ynsxe2J4Zg1JBBavXFbhZS8Gryy7SwA4OmFwxDq5WLjComIyB4x5JFDyig1bp9gb501L3bPZGMTlP8dKUBdk2U2R2/R6XH/Z0dR26TDyEGe+Nv1Qy1yXiJ7JAgCXrp5JALcVciu0OB3/28/dHoRc4YGmpdUExERWRpDHjmc2iYtyuqN3e7sPeRdPdgXCUHuaNLqseFwvkXO+cwPp5BeVAcvtQJv3zYWKidu3Ex0OT6uSryydDQEAdDpRfi6KvH84hF2eT0wERFJA0MeORzTUs1B3i5wUznZuJr+JQgC7p5svDbvw9/OQdfHzdG/SinE5wfzIQjAq0tHY5C32hJlEtm9qwf74ZFZcXBWyPDPW0bCz83+uvoSEZF0MOSRwzF11rTnpisXWjg6BH5uKpTWt2BLekmvz3OquB5Pbk4HADx8TSymxwdYqkQih7DymliceXY+ZiYE2roUIiKyczYNeXv27MH111+PkJAQCIKAb775psP9oihi7dq1CAkJgYuLC6ZPn46TJ092OKa1tRUPPfQQ/Pz84OrqioULF6KwsLDDMTU1NVi2bBk8PT3h6emJZcuWoba2tp9fHUmVqbNmXKBjhDyVkxzL2zdH/08vN0eva9bhT5+loLXNgGlx/lg5M9bSZRIRERGRhdg05Gk0GowaNQpvvvlmp/e/9NJLePnll/Hmm2/i8OHDCAoKwuzZs9HQ0GA+ZtWqVdi8eTM2btyI5ORkNDY2YsGCBdDr9eZjbr31VqSlpeHnn3/Gzz//jLS0NCxbtqzfXx9Jk3mPPAeZyQOA2yZGwFkhw4miehzKre7RY0VRxOovjyGvqgmhXi54delotnwnIiIikjCbXpA0f/58zJ8/v9P7RFHEq6++iieffBKLFy8GAHz00UcIDAzE559/jvvuuw91dXX44IMP8Mknn2DWrFkAgE8//RRhYWH49ddfMXfuXJw+fRo///wzDhw4gMTERADAf/7zHyQlJSEjIwPx8fHWebEkCaIo4qx5uab9bp9wMR9XJW4aOwifHczH+8m5SIz27fZj39uTg22nyqCUy/D2bWPh7arsx0qJiIiIqK8k23UiNzcXpaWlmDNnjvk2lUqFadOmYd++fbjvvvuQkpICnU7X4ZiQkBAMHz4c+/btw9y5c7F//354enqaAx4ATJw4EZ6enti3b1+XIa+1tRWtra3mr+vrjS33dToddDrLtKLvC1MNUqhlICmqbUZDaxsUcgFhXkqL//1JeVzuSAzDZwfz8evpMmSW1iLS1/WKjzmYW42Xfj4DAHjqungMDXKV5Gu7EimPi6PimEgTx0WaOC7SwzGRJkcYl+6+NsmGvNLSUgBAYGDHC9QDAwORl5dnPkapVMLb2/uSY0yPLy0tRUDApQ0iAgICzMd05oUXXsC6desuuX3r1q1Qq6XTUXDbtm22LmFAOVEjAJDDT2XAtl9+7rfnkeq4DPOW4WSNDOs27MUt0ZfvtFmnBV46LodBFHCVvwEe5enYsiXdSpX2D6mOiyPjmEgTx0WaOC7SwzGRJnsel6ampm4dJ9mQZ3LxPkKiKF5xb6GLj+ns+CudZ82aNXj00UfNX9fX1yMsLAxz5syBh4ftl/npdDps27YNs2fPhkKhsHU5A0b+7hzgTBbGDw7GtdeOtPj5pT4uPgnVWLb+CI5UO+GVFdPgpe68Rp3egGX/PYJGXS3iA93wwR8S4aIcuPvhSX1cHBHHRJo4LtLEcZEejok0OcK4mFYXXolkQ15QUBAA40xccHCw+fby8nLz7F5QUBC0Wi1qamo6zOaVl5dj0qRJ5mPKysouOX9FRcUls4QXUqlUUKku3cdIoVBI6ptGavVIXWaF8acfQ0I8+/XvTarjMjkuAEODPXCqpB7/O1qMB2YM7vS4F385hZT8WrirnPDusvHwcHW2cqX9Q6rj4sg4JtLEcZEmjov0cEykyZ7HpbuvS7L75EVFRSEoKKjDdKtWq8Xu3bvNAW7cuHFQKBQdjikpKcGJEyfMxyQlJaGurg6HDh0yH3Pw4EHU1dWZjyHHcbZ9+4R4B9k+4WKCIOCeKcbN0T/adw7atkuXbP54vAQfJOcCAP61ZBSi/K587R4RERERSYdNZ/IaGxuRlZVl/jo3NxdpaWnw8fFBeHg4Vq1aheeffx6xsbGIjY3F888/D7VajVtvvRUA4OnpibvvvhuPPfYYfH194ePjg9WrV2PEiBHmbptDhgzBvHnzcO+99+K9994DAPzhD3/AggUL2FnTwej0BmRXNAJwrO0TLrZgZAhe/OkMyhta8cPxYiweO8h8X1Z5I5746hgA4L5p0Zg7LMhWZRIRERFRL9k05B05cgQzZswwf226Bm758uX48MMP8cQTT6C5uRn3338/ampqkJiYiK1bt8Ld/fwH9FdeeQVOTk5YsmQJmpubcc011+DDDz+EXH7++qHPPvsMK1euNHfhXLhwYZd785H9yqnQQKcX4a5yQqiXi63LsRmlkwzLJ0Xin79k4P29ubhxTCgEQYCmtQ1/+jQFGq0eiVE+eHwOfwhCRERENBDZNORNnz4doih2eb8gCFi7di3Wrl3b5THOzs5444038MYbb3R5jI+PDz799NO+lEp24Eyp8ULVuCD3KzbvsXe3JYbjzR1ZOFVSj/05VUiK9sWar9ORWd6IAHcV3rh1DJzkkl3NTURERESXwU9x5DAy2jdBd+SlmiZeaiVuHmdcpvnB3lx8ciAP3x0rhlwm4K3bxiLA3T4arRARERE5IoY8chimkJfAkAcAWDE5CoIAbD9Tjmd/OAUAWDM/AVdF+ti4MiIiIiLqC4Y8chhnSh27s+bFovxcMWuIcRsRnV7EtSOCcPfkKBtXRURERER9xZBHDqGhRYei2mYAXK55oT9Oi4ZMAGL8XfGPm0Y6/LWKRERERPZAspuhE1nS2TLj1gmBHip4qZU2rkY6xkX4YOsjUxHg4Qx3Z/vcNJSIiIjI0TDkkUM433TFw8aVSM/gAM5sEhEREdkTLtckh5DRvn0Cm64QERERkb1jyCOHwKYrREREROQoeh3y9u7di9tvvx1JSUkoKioCAHzyySdITk62WHFEliCKIjLKuEceERERETmGXoW8TZs2Ye7cuXBxcUFqaipaW1sBAA0NDXj++ectWiBRX5U3tKK2SQe5TMDgADdbl0NERERE1K96FfKee+45vPvuu/jPf/4DheJ8R75Jkybh6NGjFiuOyBJMSzUjfdVwVshtXA0RERERUf/qVcjLyMjA1KlTL7ndw8MDtbW1fa2JyKLOtoe8BHbWJCIiIiIH0KuQFxwcjKysrEtuT05ORnR0dJ+LIrIk00xeHJuuEBEREZED6FXIu++++/Dwww/j4MGDEAQBxcXF+Oyzz7B69Wrcf//9lq6RqE8yyozbJ7DpChERERE5gl5thv7EE0+grq4OM2bMQEtLC6ZOnQqVSoXVq1fjwQcftHSNRL2mN4jILGsEwD3yiIiIiMgx9CrkAcDf//53PPnkkzh16hQMBgOGDh0KNzd2LiRpOVelQWubAS4KOcJ91LYuh4iIiIio3/U65AGAWq3G+PHjLVULkcVlmK/Hc4NMJti4GiIiIiKi/tftkLd48eJun/Trr7/uVTFElmZqusLr8YiIiIjIUXS78Yqnp6f5l4eHB7Zv344jR46Y709JScH27dvh6enZL4US9UZGqanpCrdPICIiIiLH0O2ZvPXr15v//Oc//xlLlizBu+++C7ncuLm0Xq/H/fffDw8Pfpgm6TjLpitERERE5GB6tYXCf//7X6xevdoc8ABALpfj0UcfxX//+1+LFUfUF81aPc5VaQBwjzwiIiIichy9CnltbW04ffr0JbefPn0aBoOhz0URWUJmeQNEEfB1VcLfXWXrcoiIiIiIrKJX3TXvuusurFixAllZWZg4cSIA4MCBA3jxxRdx1113WbRAot5i0xUiIiIickS9Cnn/+te/EBQUhFdeeQUlJSUAgODgYDzxxBN47LHHLFogUW9llRuvx+NSTSIiIiJyJL0KeTKZDE888QSeeOIJ1Ncbuxey4Yp1ffDbOWxIlyN4eC0mxPjbuhxJyqkwhrwYf1cbV0JEREREZD29uibvQh4eHgx4NnC8sA55jQL2ZFbauhTJyq4wNl2J8XezcSVERERERNbTq5m8qKgoCILQ5f05OTm9Loi6Z0qsH7acKMOerEqstnUxEqRtMyC/ugkAEBPAkEdEREREjqNXIW/VqlUdvtbpdEhNTcXPP/+Mxx9/3BJ10RVMHuwLAEgvqkeNRgtvV6WNK5KW/GoN9AYRrko5AthZk4iIiIgcSK9C3sMPP9zp7W+99RaOHDnSp4Koe4I8nBGsFlHSJGBvViUWjgqxdUmSYl6qGeB22VlnIiIiIiJ70+dr8i40f/58bNq0yZKnpMsY4ikCAHZnVNi4EunJbm+6Eu3HpitERERE5FgsGvK++uor+Pj4WPKUdBkJ3saQtyezAqIo2rgaackuZ9MVIiIiInJMvVquOWbMmA5L4ERRRGlpKSoqKvD2229brDi6vBh3ES4KGSoaWnG6pAFDQ9jl1CSnsn0mjyGPiIiIiBxMr0LeDTfc0CHkyWQy+Pv7Y/r06UhISLBYcXR5TjIgMcoHu85WYk9mBUNeO1EUkd2+EXpMAJdrEhEREZFj6VXIW7t2rYXLoN6aEuuHXWcrsTujAn+cFmPrciShSqNFfUsbBAGI9GXIIyIiIiLH0qtr8uRyOcrLyy+5vaqqCnK5vM9FUfdNjTVupXAkrxqa1jYbVyMNplm8Qd4ucFbw+5GIiIiIHEuvQl5XTT5aW1uhVHK/NmuK8FEjzMcFOr2I/dlVti5HEszbJ/B6PCIiIiJyQD1arvn6668DAARBwPvvvw83t/MfovV6Pfbs2cNr8qxMEARMi/PHpwfysSezArOGBtq6JJvLMW+fwJBHRERERI6nRyHvlVdeAWCcyXv33Xc7LM1UKpWIjIzEu+++a9kK6YqmxQXg0wP52H2W++UB5/fIY9MVIiIiInJEPQp5ubm5AIAZM2bg66+/hre3d78URT2TFOMLJ5mAvKomnKvUINLBNwDPqeRyTSIiIiJyXL26Jm/nzp0MeBLipnLC+EjjeOzJdOzZvBadHgXVTQCAaH/HDrtERERE5Ji6PZP36KOP4tlnn4WrqyseffTRyx778ssv97kw6pmpcf44kFON3RkVuCMp0tbl2ExeVRMMIuDu7AR/N5WtyyEiIiIisrpuh7zU1FTodDoAwNGjRztshk62Ny3OHy/9nIH9OVVobdND5eSYWweYm674u/F7lIiIiIgcUrdD3s6dO81/3rVrV3/UQn0wJMgDfm4qVDa2IuVcDSYN9rN1STZhbrrCpZpERERE5KB6dU3eihUr0NDQcMntGo0GK1as6HNR1HMymYCpccZgt9uBr8vL4R55REREROTgehXyPvroIzQ3N19ye3NzMz7++OM+F0W9My3OHwCwO8NxQx5n8oiIiIjI0fVoC4X6+nqIoghRFNHQ0ABnZ2fzfXq9Hlu2bEFAQIDFi6TumTzYD4IAnCltQFl9CwI9nK/8IDsiiiJn8oiIiIjI4fUo5Hl5eUEQBAiCgLi4uEvuFwQB69ats1hx1DO+biqMCPXE8cI67DlbgVvGh9m6JKuqaGhFQ2sbZAIQ7qu2dTlERERERDbRo5C3c+dOiKKImTNnYtOmTfDx8THfp1QqERERgZCQEIsXSd03Lc7fGPIyKx0u5GW1L9UM91E7bHdRIiIiIqIehbxp06YBAHJzcxEeHs4W9RI0Nc4fb+zIwt7MCugNIuQyxxkj01LNaC7VJCIiIiIH1u2Qd/z48Q5fp6end3nsyJEje18R9cmYMC+4OzuhtkmH9KI6jA7zsnVJVsOmK0REREREPQh5o0ePhiAIEEXxsscJggC9Xt/nwqh3nOQyTB7sh59OlGJ3RoVDhTw2XSEiIiIi6kHIy83N7c86yIKmxvkbQ97Zcjw8K9bW5ViNaSaPyzWJiIiIyJF1O+RFRERcctupU6eQn58PrVZrvk0QhE6PJeuZ2r5fXlpBLeqadPBUK2xcUf9r0elRVGvcu5HLNYmIiIjIkfWo8YpJTk4ObrzxRqSnp3dYwmlqxMLlmrYV6uWCwQFuyCpvRHJWJa4bGWzrkvpdbqUGogh4uijg46q0dTlERERERDYj682DHn74YURFRaGsrAxqtRonTpzAnj17MH78eOzatcvCJVJvTGufzdtztsLGlVjHhU1X2PWViIiIiBxZr0Le/v378cwzz8Df3x8ymQxyuRyTJ0/GCy+8gJUrV1q6RuoF05LN3Wcrrtgsxx5w+wQiIiIiIqNehTy9Xg83N+OHaT8/PxQXFwMwXreXkZFhueqo1xKjfKBykqG0vgWZ5Y22LqffnZ/JY8gjIiIiIsfWq5A3fPhw8755iYmJeOmll/Dbb7/hmWeeQXR0tEULpN5xVsiRGO0LANidYf9LNrlHHhERERGRUa9C3lNPPQWDwQAAeO6555CXl4cpU6Zgy5YteP311y1aIPWe+bq8TPsOeaIocrkmEREREVG7XoW8uXPnYvHixQCA6OhonDp1CpWVlSgvL8fMmTMtWmBDQwNWrVqFiIgIuLi4YNKkSTh8+LD5/rKyMtx5550ICQmBWq3GvHnzkJmZ2eEc06dPhyAIHX797ne/s2idUjQtzg8AcDC3Gs1a++14WlrfgiatHk4yARG+aluXQ0RERERkU70KeZ3x8fHpl66G99xzD7Zt24ZPPvkE6enpmDNnDmbNmoWioiKIoohFixYhJycH3377LVJTUxEREYFZs2ZBo9F0OM+9996LkpIS86/33nvP4rVKTYy/G0K9XKBtM+BAbpWty+k3plm8cB81FHKLfUsTEREREQ1Ikv5E3NzcjE2bNuGll17C1KlTMXjwYKxduxZRUVF45513kJmZiQMHDuCdd97BVVddhfj4eLz99ttobGzEhg0bOpxLrVYjKCjI/MvT09NGr8p6BEE432XTjq/LM12Px6WaREREREQSD3ltbW3Q6/VwdnbucLuLiwuSk5PR2toKAB3ul8vlUCqVSE5O7vCYzz77DH5+fhg2bBhWr16NhoaG/n8BEmBasmnP++Vlt3cPjQlg0xUiIiIiIidbF3A57u7uSEpKwrPPPoshQ4YgMDAQGzZswMGDBxEbG4uEhARERERgzZo1eO+99+Dq6oqXX34ZpaWlKCkpMZ/ntttuQ1RUFIKCgnDixAmsWbMGx44dw7Zt27p87tbWVnOIBID6+noAgE6ng06n678X3U2mGq5Uy4QIT8hlAnIqNcgpr0OYt/1ds5bVHvIivF1sPjbdHReyLo6L9HBMpInjIk0cF+nhmEiTI4xLd1+bIEp8p+zs7GysWLECe/bsgVwux9ixYxEXF4ejR4/i1KlTSElJwd13341jx45BLpdj1qxZkMmME5Rbtmzp9JwpKSkYP348UlJSMHbs2E6PWbt2LdatW3fJ7Z9//jnU6oEVlF47IUdOg4BbovSYHCTp4e6Vp1PkqNUKWDW8DVHutq6GiIiIiKh/NDU14dZbb0VdXR08PDy6PE7yIc9Eo9Ggvr4ewcHBWLp0KRobG/Hjjz+a76+rq4NWq4W/vz8SExMxfvx4vPXWW52eSxRFqFQqfPLJJ1i6dGmnx3Q2kxcWFobKysrL/oVai06nw7Zt2zB79mwoFIrLHvv2rhy8sj0Ls4cE4O1bR1unQCtp0rZh1LM7AACH1kyHt1pp03p6Mi5kPRwX6eGYSBPHRZo4LtLDMZEmRxiX+vp6+Pn5XTHkSXq55oVcXV3h6uqKmpoa/PLLL3jppZc63G9qpJKZmYkjR47g2Wef7fJcJ0+ehE6nQ3BwcJfHqFQqqFSqS25XKBSS+qbpTj0zhgTile1Z2J9TDcjkdtWBsqC8CQDg46pEgKd0rsmT2vcJGXFcpIdjIk0cF2niuEgPx0Sa7Hlcuvu6JB/yfvnlF4iiiPj4eGRlZeHxxx9HfHw87rrrLgDAl19+CX9/f4SHhyM9PR0PP/wwFi1ahDlz5gAwLvf87LPPcO2118LPzw+nTp3CY489hjFjxuDqq6+25UuzmuEhnvBxVaJao8XRvBokRvvauiSLyals3wTdTzoBj4iIiIjIliQ/pVNXV4cHHngACQkJuOOOOzB58mRs3brVnGJLSkqwbNkyJCQkYOXKlVi2bFmH7ROUSiW2b9+OuXPnIj4+HitXrsScOXPw66+/Qi6X2+plWZVMJmBKrLHL5m4767Jp7qzJ7ROIiIiIiAAMgJm8JUuWYMmSJV3ev3LlSqxcubLL+8PCwrB79+7+KG1AmRbnj2/TirEnswJPzEuwdTkWY9ojj9snEBEREREZSX4mjyxjSqxxU/QTRfWoaGi9wtEDR06FabkmZ/KIiIiIiACGPIfh767CsBBjB57kLPtYsmkwiMipNM3kMeQREREREQEMeQ5lWpxxNm93hn2EvJL6FrToDFDIBYR5u9i6HCIiIiIiSWDIcyBT20PensxKGAwDYnvEyzI1XYnwdYWTHW0LQURERETUF/xk7EDGhnvDTeWEao0WJ4vrbV1On5mbrviz6QoRERERkQlDngNROsmQFGPcI2/32XIbV9N35qYr3D6BiIiIiMiMIc/BmK7L23O20saV9N35mTyGPCIiIiIiE4Y8B2MKeSn5Nahv0dm4mr45P5PH5ZpERERERCYMeQ4mzEeNaD9X6A0i9mVV2bqcXmtsbUNpfQsAIIZ75BERERERmTHkOSBTl83dZwfuVgo57Us1/dyU8FQrbFwNEREREZF0MOQ5oPPX5VVAFAfmVgpsukJERERE1DmGPAeUGO0DpVyGotpmZLeHpYGGTVeIiIiIiDrHkOeA1EonTIjyAWCczRuITDN53COPiIiIiKgjhjwHNW2AX5fHmTwiIiIios4x5DkoU/OVAzlVaNHpbVxNz+gNInIruX0CEREREVFnGPIcVFygG4I8nNHaZsCh3Gpbl9MjxbXNaG0zQCmXYZC32tblEBERERFJCkOegxIEAVPj/AAMvCWbWe1LNaP8XCGXCTauhoiIiIhIWhjyHNi0uAAAA6/5yvntE7hUk4iIiIjoYgx5DmzyYD/IBCCzvBHFtc22Lqfb2HSFiIiIiKhrDHkOzFOtwOgwLwADazYvpz3kcSaPiIiIiOhSDHkObuoA3Eoh27xHHmfyiIiIiIguxpDn4Ez75SVnVaJNb7BxNVdW36JDRUMrAM7kERERERF1hiHPwY0c5AUvtQINLW1IK6i1dTlXZGq6EuCugruzwsbVEBERERFJD0Oeg5PLBEwebNxKYSBcl5ddzqYrRERERESXw5BH5iWbA+G6vJxKNl0hIiIiIrochjwyN185XlSHao3WxtVcXnY5m64QEREREV0OQx4h0MMZCUHuEEVgb6a0Z/OyuX0CEREREdFlMeQRgIGxZLNNb0BeVRMAzuQREREREXWFIY8AnA95e85WwmAQbVxN5wprmqHVG6BykiHUy8XW5RARERERSRJDHgEAxkV6w0UhR2VjK06X1tu6nE6Zmq5E+blCJhNsXA0RERERkTQx5BEAQOUkx6QYXwDG2TwpMjddCeBSTSIiIiKirjDkkdlU83V55TaupHOmmbwYPzZdISIiIiLqCkMemZmuy0vJq0Fja5uNq7kUZ/KIiIiIiK6MIY/MIv1cEe6jhk4vYn92la3LuYR5+wQ/hjwiIiIioq4w5FEH57tsSmsrhdomLaraN2rnHnlERERERF1jyKMOpkp0v7zsCuNSzWBPZ7iqnGxcDRERERGRdDHkUQdJMb5QyAXkVzfhXKXG1uWY5ZiWanIWj4iIiIjoshjyqAM3lRPGR/gAkNZsnmkmL8af1+MREREREV0OQx5dQopLNs83XeFMHhERERHR5TDk0SVMzVf2Z1ehtU1v42qMTMs1uX0CEREREdHlMeTRJYYEu8PfXYVmnR5HztXYuhzo9AbkVTUBAKK5XJOIiIiI6LIY8ugSgiBgaqx0tlIoqG5Cm0GEi0KOYA9nW5dDRERERCRpDHnUqalxfgCAX0+XQRRFm9ZiaroS7e8KmUywaS1ERERERFLHkEedmpEQAKWTDNkVGpwsrrdpLeamK1yqSURERER0RQx51CkPZwVmDQkAAHybVmTTWsxNV7hHHhERERHRFTHkUZcWjQ4FAHybVgy9wXZLNs8v1+RMHhERERHRlTDkUZemxwfA00WB8oZWHMipslkdnMkjIiIiIuo+hjzqktJJhutGBgMANqfaZslmtUaLmiYdACDajzN5RERERERXwpBHl2VasvnziVK06Ky/MbppFi/UywUuSrnVn5+IiIiIaKBhyKPLGh/hjVAvFzS2tuHX02VWf/7znTW5VJOIiIiIqDsY8uiyZDIBi8aEAAC+scGSTVPTlRg2XSEiIiIi6haGPLoi05LNXRkVqNZorfrcbLpCRERERNQzDHl0RbGB7hgW4oE2g4gf00us+tzcPoGIiIiIqGcY8qhbzHvmWXHJprbNgPzqJgBcrklERERE1F0MedQtC0eHQBCAI3k1KGgPXv0tv1oDvUGEq1KOQA+VVZ6TiIiIiGigY8ijbgn0cMakGF8AwLdp1pnNyyo/v1RTEASrPCcRERER0UDHkEfdZlqyuTm1CKIo9vvz5VSy6QoRERERUU8x5FG3zRseBJWTDNkVGpwsru/358suZ9MVIiIiIqKeYsijbnN3VmDW0EAAxtm8/nZ+Jo8hj4iIiIiouxjyqEdubF+y+d2xYugN/bdkUxRFZJe3h7wALtckIiIiIuouyYe8hoYGrFq1ChEREXBxccGkSZNw+PBh8/1lZWW48847ERISArVajXnz5iEzM7PDOVpbW/HQQw/Bz88Prq6uWLhwIQoLC639UuzC1Dh/eKkVqGhoxb7syn57nspGLepb2iAIQKQvQx4RERERUXdJPuTdc8892LZtGz755BOkp6djzpw5mDVrFoqKjM0/Fi1ahJycHHz77bdITU1FREQEZs2aBY1GYz7HqlWrsHnzZmzcuBHJyclobGzEggULoNfrbfjKBialkwwLRgYD6N8lmzkVxlm8Qd4ucFbI++15iIiIiIjsjaRDXnNzMzZt2oSXXnoJU6dOxeDBg7F27VpERUXhnXfeQWZmJg4cOIB33nkHV111FeLj4/H222+jsbERGzZsAADU1dXhgw8+wL///W/MmjULY8aMwaeffor09HT8+uuvNn6FA5Opy+YvJ0rRrO2foJxd0d50xY/X4xERERER9YSTrQu4nLa2Nuj1ejg7O3e43cXFBcnJyVi6dCkAdLhfLpdDqVQiOTkZ99xzD1JSUqDT6TBnzhzzMSEhIRg+fDj27duHuXPndvrcra2taG1tNX9dX2/sJqnT6aDT6Sz2GnvLVIMtahkZ4oZBXs4orG3Bz+lF5pk9S8oqM/59R/m6SOLvu7tsOS7UNY6L9HBMpInjIk0cF+nhmEiTI4xLd1+bpEOeu7s7kpKS8Oyzz2LIkCEIDAzEhg0bcPDgQcTGxiIhIQERERFYs2YN3nvvPbi6uuLll19GaWkpSkpKAAClpaVQKpXw9vbucO7AwECUlpZ2+dwvvPAC1q1bd8ntW7duhVqttuwL7YNt27bZ5HmHuspQWCvD+78eg6ww1eLnP3BaBkAGTWkutmzJsfj5+5utxoUuj+MiPRwTaeK4SBPHRXo4JtJkz+PS1NTUreMkHfIA4JNPPsGKFSsQGhoKuVyOsWPH4tZbb8XRo0ehUCiwadMm3H333fDx8YFcLsesWbMwf/78K55XFEUIgtDl/WvWrMGjjz5q/rq+vh5hYWGYM2cOPDw8LPLa+kKn02Hbtm2YPXs2FAqF1Z8/rrwRW9/Yh4w6OSZOmwkfV6VFz/+vM3sBNOOGGYlIjPKx6Ln7k63HhTrHcZEejok0cVykieMiPRwTaXKEcTGtLrwSyYe8mJgY7N69GxqNBvX19QgODsbSpUsRFRUFABg3bhzS0tJQV1cHrVYLf39/JCYmYvz48QCAoKAgaLVa1NTUdJjNKy8vx6RJk7p8XpVKBZVKdcntCoVCUt80tqpnSKg3RoR6Ir2oDltPV2BZUqTFzt2i06OothkAEBfsKam/7+6S2vcJGXFcpIdjIk0cF2niuEgPx0Sa7Hlcuvu6JN145UKurq4IDg5GTU0NfvnlF9xwww0d7vf09IS/vz8yMzNx5MgR8/3jxo2DQqHoMG1bUlKCEydOXDbk0ZXdMDoEgOW7bOZVNcEgAu4qJ/i7XRq0iYiIiIioa5Kfyfvll18giiLi4+ORlZWFxx9/HPHx8bjrrrsAAF9++SX8/f0RHh6O9PR0PPzww1i0aJG50YqnpyfuvvtuPPbYY/D19YWPjw9Wr16NESNGYNasWbZ8aQPewlEheH7LaRzNr0VelQYRFtrPzrR9QnSA22WX1BIRERER0aUkP5NXV1eHBx54AAkJCbjjjjswefJkbN261TxVWVJSgmXLliEhIQErV67EsmXLzNsnmLzyyitYtGgRlixZgquvvhpqtRrff/895HLuv9YXAR7OuHqwHwDg27Rii503uz3kxfhxE3QiIiIiop6S/EzekiVLsGTJki7vX7lyJVauXHnZczg7O+ONN97AG2+8YenyHN6i0aHYm1mJb1KL8NDMwRaZectp3yMvJoB75BERERER9ZTkZ/JI2uYOD4KzQoacSg3Si+osck7zTJ4/Z/KIiIiIiHqKIY/6xE3lhNlDgwBYpgGLKIrIbp/Ji/bnTB4RERERUU8x5FGfLWrvsvn9sRK06Q19OldFQysaW9sgE4AIX+lsOk9ERERENFAw5FGfTY3zh7dagcrGVvyWXdWnc2W1L9UM81FD5cTGOEREREREPcWQR32mkMtw/SjjbN63fVyyaW66wqWaRERERES9wpBHFnHD6FAAwM8nS9Gkbev1eUxNV6K5fQIRERERUa8w5JFFjA33QriPGk1aPbadKuv1ebK5fQIRERERUZ8w5JFFCIJgbsDyTR+WbOaYt09gyCMiIiIi6g2GPLKYG8YYl2zuyaxEZWNrjx/fotOjqLYZABDNPfKIiIiIiHqFIY8sJsbfDSMHeUJvEPHj8ZIePz63UgNRBDxdFPB1VfZDhURERERE9o8hjyxqUXsDlt5sjG5uuuLvCkEQLFoXEREREZGjYMgji1owKhgyAUgrqMW5Sk2PHptdzu0TiIiIiIj6iiGPLCrA3RmTY/0BAN+k9Ww2L6eSTVeIiIiIiPqKIY8s7sYx57tsiqLY7cdduFyTiIiIiIh6hyGPLG7O0CC4KOQ4V9WEY4V13XqMKIrIqeByTSIiIiKivmLII4tzVTlhzrBAAN3fM6+0vgVNWj3kMgHhPur+LI+IiIiIyK4x5FG/MHXZ/P5YMXR6wxWPN83iRfiooXTityURERERUW/x0zT1i8mxfvB1VaJKo0VyVuUVj+f1eERERERElsGQR/1CIZdhwchgAMC33ViymV3OzppERERERJbAkEf9ZtEY45LNX06WQdPadtljcyrZdIWIiIiIyBIY8qjfjA7zQoSvGs06PbadKrvssaaZPC7XJCIiIiLqG4Y86jeCIJgbsGy+zJLNJm0biutaAHAmj4iIiIiorxjyqF+ZlmzuzaxARUNrp8eYOmt6qxXwdlVarTYiIiIiInvEkEf9KsrPFaPCvGAQgR+OF3d6jKmzJmfxiIiIiIj6jiGP+t2No0MAdL0xumkmjyGPiIiIiKjvGPKo3y0YFQK5TMCxwjrktM/aXYh75BERERERWQ5DHvU7PzcVpsT6AQC+Sbt0ySZn8oiIiIiILIchj6zC1GXz27QiiKJovt1gEJFTyZk8IiIiIiJLYcgjq5gzLBBqpRx5VU1ILag1315c14wWnQEKuYAwH7XtCiQiIiIishMMeWQVaqUT5g4LAgB8e0EDFtNSzXAfNRRyfjsSEREREfUVP1WT1dzQ3mXz++Ml0OkNALh9AhERERGRpTHkkdVMHuwHPzclqjVa7M2sAHBB05UAhjwiIiIiIktgyCOrcZLLsGCkac88Y5dN8/YJfmy6QkRERERkCQx5ZFU3jjF22dx6qhSNrW2cySMiIiIisjCGPLKqkYM8EeXnihadAZuPFqK0vgUAEOPHkEdEREREZAkMeWRVgiCY98x7c2cWAMDPTQlPtcKWZRERERER2Q2GPLI6U5fNsvpWAEA0O2sSEREREVkMQx5ZXaSfK8aEe5m/jvFn0xUiIiIiIkthyCObMDVgAbhHHhERERGRJTHkkU1cNyIYcpkAAIjmTB4RERERkcU42boAcky+biqsnBmLw+eqMTHa19blEBERERHZDYY8spmHZ8XaugQiIiIiIrvD5ZpERERERER2hCGPiIiIiIjIjjDkERERERER2RGGPCIiIiIiIjvCkEdERERERGRHGPKIiIiIiIjsCEMeERERERGRHWHIIyIiIiIisiMMeURERERERHaEIY+IiIiIiMiOMOQRERERERHZEYY8IiIiIiIiO+Jk6wIGClEUAQD19fU2rsRIp9OhqakJ9fX1UCgUti6H2nFcpInjIj0cE2niuEgTx0V6OCbS5AjjYsoipmzSFYa8bmpoaAAAhIWF2bgSIiIiIiJyZA0NDfD09OzyfkG8UgwkAIDBYEBxcTHc3d0hCIKty0F9fT3CwsJQUFAADw8PW5dD7Tgu0sRxkR6OiTRxXKSJ4yI9HBNpcoRxEUURDQ0NCAkJgUzW9ZV3nMnrJplMhkGDBtm6jEt4eHjY7TfxQMZxkSaOi/RwTKSJ4yJNHBfp4ZhIk72Py+Vm8EzYeIWIiIiIiMiOMOQRERERERHZEYa8AUqlUuHpp5+GSqWydSl0AY6LNHFcpIdjIk0cF2niuEgPx0SaOC7nsfEKERERERGRHeFMHhERERERkR1hyCMiIiIiIrIjDHlERERERER2hCFvgHr77bcRFRUFZ2dnjBs3Dnv37rV1SQ5j7dq1EAShw6+goCDz/aIoYu3atQgJCYGLiwumT5+OkydP2rBi+7Rnzx5cf/31CAkJgSAI+Oabbzrc351xaG1txUMPPQQ/Pz+4urpi4cKFKCwstOKrsD9XGpc777zzkvfPxIkTOxzDcbGsF154AVdddRXc3d0REBCARYsWISMjo8MxfL9YV3fGhO8V63vnnXcwcuRI8x5rSUlJ+Omnn8z3831iG1caF75XOseQNwB98cUXWLVqFZ588kmkpqZiypQpmD9/PvLz821dmsMYNmwYSkpKzL/S09PN97300kt4+eWX8eabb+Lw4cMICgrC7Nmz0dDQYMOK7Y9Go8GoUaPw5ptvdnp/d8Zh1apV2Lx5MzZu3Ijk5GQ0NjZiwYIF0Ov11noZdudK4wIA8+bN6/D+2bJlS4f7OS6WtXv3bjzwwAM4cOAAtm3bhra2NsyZMwcajcZ8DN8v1tWdMQH4XrG2QYMG4cUXX8SRI0dw5MgRzJw5EzfccIM5yPF9YhtXGheA75VOiTTgTJgwQfzjH//Y4baEhATxL3/5i40qcixPP/20OGrUqE7vMxgMYlBQkPjiiy+ab2tpaRE9PT3Fd99910oVOh4A4ubNm81fd2ccamtrRYVCIW7cuNF8TFFRkSiTycSff/7ZarXbs4vHRRRFcfny5eINN9zQ5WM4Lv2vvLxcBCDu3r1bFEW+X6Tg4jERRb5XpMLb21t8//33+T6RGNO4iCLfK13hTN4Ao9VqkZKSgjlz5nS4fc6cOdi3b5+NqnI8mZmZCAkJQVRUFH73u98hJycHAJCbm4vS0tIO46NSqTBt2jSOjxV1ZxxSUlKg0+k6HBMSEoLhw4dzrPrZrl27EBAQgLi4ONx7770oLy8338dx6X91dXUAAB8fHwB8v0jBxWNiwveK7ej1emzcuBEajQZJSUl8n0jExeNiwvfKpZxsXQD1TGVlJfR6PQIDAzvcHhgYiNLSUhtV5VgSExPx8ccfIy4uDmVlZXjuuecwadIknDx50jwGnY1PXl6eLcp1SN0Zh9LSUiiVSnh7e19yDN9L/Wf+/Pm45ZZbEBERgdzcXPz1r3/FzJkzkZKSApVKxXHpZ6Io4tFHH8XkyZMxfPhwAHy/2FpnYwLwvWIr6enpSEpKQktLC9zc3LB582YMHTrUHAb4PrGNrsYF4HulKwx5A5QgCB2+FkXxktuof8yfP9/85xEjRiApKQkxMTH46KOPzBf6cnykoTfjwLHqX0uXLjX/efjw4Rg/fjwiIiLw448/YvHixV0+juNiGQ8++CCOHz+O5OTkS+7j+8U2uhoTvldsIz4+HmlpaaitrcWmTZuwfPly7N6923w/3ye20dW4DB06lO+VLnC55gDj5+cHuVx+yU8eysvLL/npElmHq6srRowYgczMTHOXTY6PbXVnHIKCgqDValFTU9PlMdT/goODERERgczMTAAcl/700EMP4bvvvsPOnTsxaNAg8+18v9hOV2PSGb5XrEOpVGLw4MEYP348XnjhBYwaNQqvvfYa3yc21tW4dIbvFSOGvAFGqVRi3Lhx2LZtW4fbt23bhkmTJtmoKsfW2tqK06dPIzg4GFFRUQgKCuowPlqtFrt37+b4WFF3xmHcuHFQKBQdjikpKcGJEyc4VlZUVVWFgoICBAcHA+C49AdRFPHggw/i66+/xo4dOxAVFdXhfr5frO9KY9IZvldsQxRFtLa28n0iMaZx6QzfK+2s3uqF+mzjxo2iQqEQP/jgA/HUqVPiqlWrRFdXV/HcuXO2Ls0hPPbYY+KuXbvEnJwc8cCBA+KCBQtEd3d389//iy++KHp6eopff/21mJ6eLv7+978Xg4ODxfr6ehtXbl8aGhrE1NRUMTU1VQQgvvzyy2JqaqqYl5cnimL3xuGPf/yjOGjQIPHXX38Vjx49Ks6cOVMcNWqU2NbWZquXNeBdblwaGhrExx57TNy3b5+Ym5sr7ty5U0xKShJDQ0M5Lv3oT3/6k+jp6Snu2rVLLCkpMf9qamoyH8P3i3VdaUz4XrGNNWvWiHv27BFzc3PF48ePi//3f/8nymQycevWraIo8n1iK5cbF75XusaQN0C99dZbYkREhKhUKsWxY8d2aLtM/Wvp0qVicHCwqFAoxJCQEHHx4sXiyZMnzfcbDAbx6aefFoOCgkSVSiVOnTpVTE9Pt2HF9mnnzp0igEt+LV++XBTF7o1Dc3Oz+OCDD4o+Pj6ii4uLuGDBAjE/P98Gr8Z+XG5cmpqaxDlz5oj+/v6iQqEQw8PDxeXLl1/yd85xsazOxgOAuH79evMxfL9Y15XGhO8V21ixYoX5s5W/v794zTXXmAOeKPJ9YiuXGxe+V7omiKIoWm/ekIiIiIiIiPoTr8kjIiIiIiKyIwx5REREREREdoQhj4iIiIiIyI4w5BEREREREdkRhjwiIiIiIiI7wpBHRERERERkRxjyiIiIiIiI7AhDHhERERERkR1hyCMiIoe2a9cuCIKA2tpaqzzfsmXL8Pzzz1vluVavXo2VK1da5bmIiEg6BFEURVsXQUREZC3Tp0/H6NGj8eqrrwIAtFotqqurERgYCEEQ+vW5jx8/junTpyMvLw/u7u79+lwAUF5ejpiYGBw/fhxRUVH9/nxERCQNnMkjIiKHplQqERQU1O8BDwDefPNN3HLLLVYJeAAQEBCAOXPm4N1337XK8xERkTQw5BERkcO48847sXv3brz22msQBAGCIODDDz/ssFzzww8/hJeXF3744QfEx8dDrVbj5ptvhkajwUcffYTIyEh4e3vjoYcegl6vN59bq9XiiSeeQGhoKFxdXZGYmIhdu3aZ7zcYDPjyyy+xcOHCDjW9/fbbiI2NhbOzMwIDA3HzzTeb7xNFES+99BKio6Ph4uKCUaNG4auvvurw+JMnT+K6666Dh4cH3N3dMWXKFGRnZ5vvX7hwITZs2GDBv0UiIpI6J1sXQEREZC2vvfYazp49i+HDh+OZZ54BYAxJF2tqasLrr7+OjRs3oqGhAYsXL8bixYvh5eWFLVu2ICcnBzfddBMmT56MpUuXAgDuuusunDt3Dhs3bkRISAg2b96MefPmIT09HbGxsTh+/Dhqa2sxfvx48/McOXIEK1euxCeffIJJkyahuroae/fuNd//1FNP4euvv8Y777yD2NhY7NmzB7fffjv8/f0xbdo0FBUVYerUqZg+fTp27NgBDw8P/Pbbb2hrazOfY8KECSgoKEBeXh4iIiL666+WiIgkhCGPiIgchqenJ5RKJdRqNYKCggAAZ86cueQ4nU6Hd955BzExMQCAm2++GZ988gnKysrg5uaGoUOHYsaMGdi5cyeWLl2K7OxsbNiwAYWFhQgJCQFgbHry888/Y/369Xj++edx7tw5yOVyBAQEmJ8nPz8frq6uWLBgAdzd3REREYExY8YAADQaDV5++WXs2LEDSUlJAIDo6GgkJyfjvffew7Rp0/DWW2/B09MTGzduhEKhAADExcV1eC2hoaEAgHPnzjHkERE5CIY8IiKii6jVanPAA4DAwEBERkbCzc2tw23l5eUAgKNHj0IUxUsCVmtrK3x9fQEAzc3NUKlUHa79mz17NiIiIhAdHY158+Zh3rx5uPHGG6FWq3Hq1Cm0tLRg9uzZHc6p1WrNQTAtLQ1TpkwxB7zOuLi4ADDOThIRkWNgyCMiIrrIxaFJEIRObzMYDACM19vJ5XKkpKRALpd3OM4UDP38/NDU1AStVgulUgkAcHd3x9GjR7Fr1y5s3boVf/vb37B27VocPnzYfO4ff/zRPBtnolKpAJwPcJdTXV0NAPD39+/WayciooGPIY+IiByKUqns0DDFEsaMGQO9Xo/y8nJMmTKl02NGjx4NADh16pT5zwDg5OSEWbNmYdasWXj66afh5eWFHTt2YPbs2VCpVMjPz8e0adM6PefIkSPx0UcfQafTdTmbd+LECSgUCgwbNqxPr5GIiAYOhjwiInIokZGROHjwIM6dOwc3NzfzjFlfxMXF4bbbbsMdd9yBf//73xgzZgwqKyuxY8cOjBgxAtdeey38/f0xduxYJCcnm0PeDz/8gJycHEydOhXe3t7YsmULDAYD4uPj4e7ujtWrV+ORRx6BwWDA5MmTUV9fj3379sHNzQ3Lly/Hgw8+iDfeeAO/+93vsGbNGnh6euLAgQOYMGEC4uPjAQB79+7FlClTujXrR0RE9oFbKBARkUNZvXo15HI5hg4dCn9/f+Tn51vkvOvXr8cdd9yBxx57DPHx8Vi4cCEOHjyIsLAw8zF/+MMf8Nlnn5m/9vLywtdff42ZM2diyJAhePfdd7FhwwbzrNuzzz6Lv/3tb3jhhRcwZMgQzJ07F99//715Y3NfX1/s2LEDjY2NmDZtGsaNG4f//Oc/HWb1NmzYgHvvvdcir5GIiAYGQRRF0dZFEBEROYKWlhbEx8dj48aN5o6Z/enHH3/E448/juPHj8PJiYt3iIgcBWfyiIiIrMTZ2Rkff/wxKisrrfJ8Go0G69evZ8AjInIwnMkjIiIiIiKyI5zJIyIiIiIisiMMeURERERERHaEIY+IiIiIiMiOMOQRERERERHZEYY8IiIiIiIiO8KQR0REREREZEcY8oiIiIiIiOwIQx4REREREZEdYcgjIiIiIiKyIwx5REREREREduT/A0UN0bO0iKTyAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "dt = 12. # 12 seconds between readings\n", "range_std = 5 # meters\n", "bearing_std = math.radians(0.5)\n", "\n", "ac_pos = (0., 1000.)\n", "ac_vel = (100., 0.)\n", "radar_pos = (0., 0.)\n", "h_radar.radar_pos = radar_pos\n", "\n", "points = MerweScaledSigmaPoints(n=3, alpha=.1, beta=2., kappa=0.)\n", "kf = UKF(3, 2, dt, fx=f_radar, hx=h_radar, points=points)\n", "\n", "kf.Q[0:2 ,0:2] = Q_discrete_white_noise(2, dt=dt, var=0.1)\n", "kf.Q[2, 2] = 0.1\n", "\n", "kf.R = np.diag([range_std**2, bearing_std**2])\n", "kf.x = np.array([0., 90., 1100.])\n", "kf.P = np.diag([300**2, 30**2, 150**2])\n", "\n", "radar = RadarStation((0, 0), range_std, bearing_std)\n", "ac = ACSim(ac_pos, (100, 0), 0.02)\n", "\n", "np.random.seed(200)\n", "\n", "t = np.arange(0, 360 + dt, dt)\n", "n = len(t)\n", "\n", "zs = []\n", "for i in range(len(t)):\n", " ac.update(dt)\n", " r = radar.noisy_reading(ac.pos)\n", " zs.append([r[0], r[1]])\n", "\n", "xs, covs = kf.batch_filter(zs)\n", "ukf_internal.plot_radar(xs, t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Smoothing the Results\n", "\n", "Assume that we are tracking a car. Suppose we get a noisy measurement that implies that the car is starting to turn to the left, but the state function has predicted that the car is moving straight. The Kalman filter has no choice but to move the state estimate somewhat towards the noisy measurement, as it cannot judge whether this is just a particularly noisy measurement or the true start of a turn. \n", "\n", "If we are collecting data and post-processing it we have measurements after the questionable one that informs us if a turn was made or not. Suppose the subsequent measurements all continue turning left. We can then be sure that the measurement was not very noisy, but instead a turn was initiated.\n", "\n", "We will not develop the math or algorithm here, I will just show you how to call the algorithm in `FilterPy`. The algorithm that we have implemented is called an *RTS smoother*, after the three inventors of the algorithm: Rauch, Tung, and Striebel.\n", "\n", "The routine is `UnscentedKalmanFilter.rts_smoother()`. Using it is trivial; we pass in the means and covariances computed from the `batch_filter` step, and receive back the smoothed means, covariances, and Kalman gain." ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Difference in position in meters:\n", "\t [-1.4166 -0.2815 1.2679 -1.2405 -2.1863]\n" ] }, { "data": { "image/png": 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Ms, P, K = kf.rts_smoother(xs, covs)\n", "ukf_internal.plot_rts_output(xs, Ms, t)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From these charts we can see that the improvement in the position is small, but the improvement in the velocity is good, and spectacular for the altitude. The difference in the position are very small, so I printed the difference between the UKF and the smoothed results for the last 5 points. I recommend always using the RTS smoother if you can post-process your data." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Choosing the Sigma Parameters\n", "\n", "I have found the literature on choosing values for $\\alpha$, $\\beta$, and $\\kappa$ to be rather lacking. Van der Merwe's dissertation contains the most information, but it is not exhaustive. So let's explore what they do. \n", "\n", "Van der Merwe suggests using $\\beta=2$ for Gaussian problems, and $\\kappa=3-n$. So let's start there and vary $\\alpha$. I will let $n=1$ to minimize the size of the arrays we need to look at and to avoid having to compute the square root of matrices." ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sigmas: [ 0. 3. -3.]\n", "mean weights: [0.6667 0.1667 0.1667]\n", "cov weights: [2.6667 0.1667 0.1667]\n", "lambda: 2\n", "sum cov 2.9999999999999996\n" ] } ], "source": [ "from kf_book.ukf_internal import print_sigmas\n", "print_sigmas(mean=0, cov=3, alpha=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So what is going on here? We can see that for a mean of 0 the algorithm chooses sigma points of 0, 3, and -3, but why? Recall the equation for computing the sigma points:\n", "\n", "$$\\begin{aligned}\n", "\\mathcal{X}_0 &= \\mu\\\\\n", "\\mathcal{X}_i &= \\mu \\pm \\sqrt{(n+\\lambda)\\Sigma}\n", "\\end{aligned}$$\n", "\n", "My choice of $n=1$ reduces everything to scalars, allowing us to avoid computing the square root of matrices. So, for our values the equation is\n", "\n", "$$\\begin{aligned}\n", "\\mathcal{X}_0 &= 0 \\\\\n", "\\mathcal{X}_i &= 0 \\pm \\sqrt{(1+2)\\times 3} \\\\\n", "&= \\pm 3\n", "\\end{aligned}$$\n", "\n", "So as $\\alpha$ gets larger the sigma points get more spread out. Let's set it to an absurd value." ] }, { "cell_type": "code", "execution_count": 46, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sigmas: [ 0. 600. -600.]\n", "mean weights: [1. 0. 0.]\n", "cov weights: [-39996. 0. 0.]\n", "lambda: 119999\n", "sum cov -39996.00000000001\n" ] } ], "source": [ "print_sigmas(mean=0, cov=3, alpha=200)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can see that the sigma points spread over 100 standard deviations. If our data was Gaussian we'd be incorporating data many standard deviations away from the mean; for nonlinear problems this is unlikely to produce good results. But suppose our distribution was not Gaussian, but instead had very fat tails? We might need to sample from those tails to get a good estimate, and hence it would make sense to make $\\kappa$ larger (not 200, which was absurdly large to make the change in the sigma points stark). \n", "\n", "With a similar line of reasoning, suppose that our distribution has nearly no tails - the probability distribution looks more like an inverted parabola. In such a case we'd probably want to pull the sigma points in closer to the mean to avoid sampling in regions where there will never be real data.\n", "\n", "Now let's look at the change in the weights. When we have $k+n=3$ the weights were 0.6667 for the mean, and 0.1667 for the two outlying sigma points. On the other hand, when $\\alpha=200$ the mean weight shot up to 0.99999 and the outlier weights were set to 0.000004. Recall the equations for the weights:\n", "\n", "$$\\begin{aligned}\n", "W_0 &= \\frac{\\lambda}{n+\\lambda} \\\\\n", "W_i &= \\frac{1}{2(n+\\lambda)}\n", "\\end{aligned}$$\n", "\n", "We can see that as $\\lambda$ gets larger the fraction for the weight of the mean ($\\lambda/(n+\\lambda)$) approaches 1, and the fraction for the weights of the rest of the sigma points approaches 0. This is invariant on the size of your covariance. So as we sample further and further away from the mean we end up giving less weight to those samples, and if we sampled very close to the mean we'd give very similar weights to all.\n", "\n", "However, the advice that Van der Merwe gives is to constrain $\\alpha$ in the range $0 \\gt \\alpha \\ge 1$. He suggests $10^{-3}$ as a good value. Let's try that." ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "sigmas: [ 0. 0.0036 -0.0036]\n", "mean weights: [-999999. 500000. 500000.]\n", "cov weights: [-999996. 500000. 500000.]\n", "lambda: -0.999999\n", "sum cov 3.9999989999923855\n" ] } ], "source": [ "print_sigmas(mean=0, cov=13, alpha=.001, kappa=0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Robot Localization - A Fully Worked Example" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is time to undertake a significant problem. Most books choose simple, textbook problems with simple answers, and you are left wondering how to implement a real world problem. This example will not teach you how to tackle any problem, but illustrates the type of things you will have to consider as you design and implement a filter. \n", "\n", "We will consider the problem of robot localization. In this scenario we have a robot that is moving through a landscape using a sensor to detect landmarks. This could be a self driving car using computer vision to identify trees, buildings, and other landmarks. It might be one of those small robots that vacuum your house, or a robot in a warehouse.\n", "\n", "The robot has 4 wheels in the same configuration used by automobiles. It maneuvers by pivoting the front wheels. This causes the robot to pivot around the rear axle while moving forward. This is nonlinear behavior which we will have to model. \n", "\n", "The robot has a sensor that gives it approximate range and bearing to known targets in the landscape. This is nonlinear because computing a position from a range and bearing requires square roots and trigonometry. \n", "\n", "Both the process model and measurement models are nonlinear. The UKF accommodates both, so we provisionally conclude that the UKF is a viable choice for this problem." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Robot Motion Model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "At a first approximation an automobile steers by pivoting the front tires while moving forward. The front of the car moves in the direction that the wheels are pointing while pivoting around the rear tires. This simple description is complicated by issues such as slippage due to friction, the differing behavior of the rubber tires at different speeds, and the need for the outside tire to travel a different radius than the inner tire. Accurately modeling steering requires a complicated set of differential equations. \n", "\n", "For Kalman filtering, especially for lower speed robotic applications a simpler *bicycle model* has been found to perform well. This is a depiction of the model:" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ekf_internal.plot_bicycle()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here we see the front tire is pointing in direction $\\alpha$ relative to the wheelbase. Over a short time period the car moves forward and the rear wheel ends up further ahead and slightly turned inward, as depicted with the blue shaded tire. Over such a short time frame we can approximate this as a turn around a radius $R$. We can compute the turn angle $\\beta$ with\n", "\n", "$$\\beta = \\frac{d}{w} \\tan{(\\alpha)}$$\n", "\n", "and the turning radius R is given by \n", "\n", "$$R = \\frac{d}{\\beta}$$\n", "\n", "where the distance the rear wheel travels given a forward velocity $v$ is $d=v\\Delta t$.\n", "\n", "With $\\theta$ being the robot's orientation we compute the position $C$ before the turn starts as\n", "\n", "$$\\begin{aligned}\n", "C_x &= x - R\\sin(\\theta) \\\\\n", "C_y &= y + R\\cos(\\theta)\n", "\\end{aligned}$$\n", "\n", "After the move forward for time $\\Delta t$ the new position and orientation of the robot is\n", "\n", "$$\\begin{aligned} \\bar x &= C_x + R\\sin(\\theta + \\beta) \\\\\n", "\\bar y &= C_y - R\\cos(\\theta + \\beta) \\\\\n", "\\bar \\theta &= \\theta + \\beta\n", "\\end{aligned}\n", "$$\n", "\n", "Once we substitute in for $C$ we get\n", "\n", "$$\\begin{aligned} \\bar x &= x - R\\sin(\\theta) + R\\sin(\\theta + \\beta) \\\\\n", "\\bar y &= y + R\\cos(\\theta) - R\\cos(\\theta + \\beta) \\\\\n", "\\bar \\theta &= \\theta + \\beta\n", "\\end{aligned}\n", "$$\n", "\n", "You do not need to understand this math in detail if you are not interested in steering models. The important thing to recognize is that our motion model is nonlinear, and we will need to deal with that with our Kalman filter." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Design the State Variables\n", "\n", "For our robot we will maintain the position and orientation:\n", "\n", "$$\\mathbf x = \\begin{bmatrix}x & y & \\theta\\end{bmatrix}^\\mathsf{T}$$\n", "\n", "I could include velocities into this model, but as you will see the math will already be quite challenging.\n", "\n", "The control input $\\mathbf{u}$ is the commanded velocity and steering angle\n", "\n", "$$\\mathbf{u} = \\begin{bmatrix}v & \\alpha\\end{bmatrix}^\\mathsf{T}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Design the System Model\n", "\n", "We model our system as a nonlinear motion model plus white noise.\n", "\n", "$$\\bar x = x + f(x, u) + \\mathcal{N}(0, Q)$$\n", "\n", "Using the motion model for a robot that we created above, we can write:" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "from math import tan, sin, cos, sqrt\n", "\n", "def move(x, dt, u, wheelbase):\n", " hdg = x[2]\n", " vel = u[0]\n", " steering_angle = u[1]\n", " dist = vel * dt\n", "\n", " if abs(steering_angle) > 0.001: # is robot turning?\n", " beta = (dist / wheelbase) * tan(steering_angle)\n", " r = wheelbase / tan(steering_angle) # radius\n", "\n", " sinh, sinhb = sin(hdg), sin(hdg + beta)\n", " cosh, coshb = cos(hdg), cos(hdg + beta)\n", " return x + np.array([-r*sinh + r*sinhb, \n", " r*cosh - r*coshb, beta])\n", " else: # moving in straight line\n", " return x + np.array([dist*cos(hdg), dist*sin(hdg), 0])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will use this function to implement the state transition function `f(x)`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "I will design the UKF so that $\\Delta t$ is small. If the robot is moving slowly then this function should give a reasonably accurate prediction. If $\\Delta t$ is large or your system's dynamics are very nonlinear this method will fail. In those cases you will need to implement it using a more sophisticated numerical integration technique such as Runge Kutta. Numerical integration is covered briefly in the **Kalman Filter Math** chapter." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Design the Measurement Model\n", "\n", "The sensor provides a noisy bearing and range to multiple known locations in the landscape. The measurement model must convert the state $\\begin{bmatrix}x & y&\\theta\\end{bmatrix}^\\mathsf{T}$ into a range and bearing to the landmark. If $p$ is the position of a landmark, the range $r$ is\n", "\n", "$$r = \\sqrt{(p_x - x)^2 + (p_y - y)^2}$$\n", "\n", "We assume that the sensor provides bearing relative to the orientation of the robot, so we must subtract the robot's orientation from the bearing to get the sensor reading, like so:\n", "\n", "$$\\phi = \\tan^{-1}(\\frac{p_y - y}{p_x - x}) - \\theta$$\n", "\n", "Thus our measurement function is\n", "\n", "$$\\begin{aligned}\n", "\\mathbf{z}& = h(\\mathbf x, \\mathbf P) &+ \\mathcal{N}(0, R)\\\\\n", "&= \\begin{bmatrix}\n", "\\sqrt{(p_x - x)^2 + (p_y - y)^2} \\\\\n", "\\tan^{-1}(\\frac{p_y - y}{p_x - x}) - \\theta \n", "\\end{bmatrix} &+ \\mathcal{N}(0, R)\n", "\\end{aligned}$$\n", "\n", "I will not implement this yet as there is a difficulty that will be discussed in the *Implementation* section below." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Design Measurement Noise\n", "\n", "It is reasonable to assume that the range and bearing measurement noise is independent, hence\n", "\n", "$$\\mathbf R=\\begin{bmatrix}\\sigma_{range}^2 & 0 \\\\ 0 & \\sigma_{bearing}^2\\end{bmatrix}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implementation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before we begin coding we have another issue to handle. The residual is $y = z - h(x)$. Suppose z has a bearing of $1^\\circ$ and $h(x)$ is $359^\\circ$. Subtracting them gives $-358^\\circ$. This will throw off the computation of the Kalman gain because the correct angular difference is $2^\\circ$. So we will have to write code to correctly compute the bearing residual." ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "def normalize_angle(x):\n", " x = x % (2 * np.pi) # force in range [0, 2 pi)\n", " if x > np.pi: # move to [-pi, pi)\n", " x -= 2 * np.pi\n", " return x" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.9999999999999774\n" ] } ], "source": [ "print(np.degrees(normalize_angle(np.radians(1-359))))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The state vector has the bearing at index 2, but the measurement vector has it at index 1, so we need to write functions to handle each. Another issue we face is that as the robot maneuvers different landmarks will be visible, so we need to handle a variable number of measurements. The function for the residual in the measurement will be passed an array of several measurements, one per landmark." ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [], "source": [ "def residual_h(a, b):\n", " y = a - b\n", " # data in format [dist_1, bearing_1, dist_2, bearing_2,...]\n", " for i in range(0, len(y), 2):\n", " y[i + 1] = normalize_angle(y[i + 1])\n", " return y\n", "\n", "def residual_x(a, b):\n", " y = a - b\n", " y[2] = normalize_angle(y[2])\n", " return y" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can now implement the measurement model. The equation is\n", "$$h(\\mathbf x, \\mathbf P)\n", "= \\begin{bmatrix}\n", "\\sqrt{(p_x - x)^2 + (p_y - y)^2} \\\\\n", "\\tan^{-1}(\\frac{p_y - y}{p_x - x}) - \\theta \n", "\\end{bmatrix}$$\n", "\n", "The expression $\\tan^{-1}(\\frac{p_y - y}{p_x - x}) - \\theta$ can produce a result outside the range $[-\\pi, \\pi)$, so we should normalize the angle to that range.\n", "\n", "The function will be passed an array of landmarks and needs to produce an array of measurements in the form `[dist_to_1, bearing_to_1, dist_to_2, bearing_to_2, ...]`." ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [], "source": [ "def Hx(x, landmarks):\n", " \"\"\" takes a state variable and returns the measurement\n", " that would correspond to that state. \"\"\"\n", " hx = []\n", " for lmark in landmarks:\n", " px, py = lmark\n", " dist = sqrt((px - x[0])**2 + (py - x[1])**2)\n", " angle = atan2(py - x[1], px - x[0])\n", " hx.extend([dist, normalize_angle(angle - x[2])])\n", " return np.array(hx)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Our difficulties are not over. The unscented transform computes the average of the state and measurement vectors, but each contains a bearing. There is no unique way to compute the average of a set of angles. For example, what is the average of 359$^\\circ$ and 3$^\\circ$? Intuition suggests the answer should be 1$^\\circ$, but a naive $\\frac{1}{n}\\sum x$ approach yields 181$^\\circ$.\n", "\n", "One common approach is to take the arctan of the sum of the sins and cosines.\n", "\n", "$$\\bar{\\theta} = atan2\\left(\\frac{\\sum_{i=1}^n \\sin\\theta_i}{n}, \\frac{\\sum_{i=1}^n \\cos\\theta_i}{n}\\right)$$\n", "\n", "`UnscentedKalmanFilter.__init__()` has an argument `x_mean_fn` for a function which computes the mean of the state, and `z_mean_fn` for a function which computes the mean of the measurement. We will code these function as:" ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [], "source": [ "def state_mean(sigmas, Wm):\n", " x = np.zeros(3)\n", "\n", " sum_sin = np.sum(np.dot(np.sin(sigmas[:, 2]), Wm))\n", " sum_cos = np.sum(np.dot(np.cos(sigmas[:, 2]), Wm))\n", " x[0] = np.sum(np.dot(sigmas[:, 0], Wm))\n", " x[1] = np.sum(np.dot(sigmas[:, 1], Wm))\n", " x[2] = atan2(sum_sin, sum_cos)\n", " return x\n", "\n", "def z_mean(sigmas, Wm):\n", " z_count = sigmas.shape[1]\n", " x = np.zeros(z_count)\n", "\n", " for z in range(0, z_count, 2):\n", " sum_sin = np.sum(np.dot(np.sin(sigmas[:, z+1]), Wm))\n", " sum_cos = np.sum(np.dot(np.cos(sigmas[:, z+1]), Wm))\n", "\n", " x[z] = np.sum(np.dot(sigmas[:,z], Wm))\n", " x[z+1] = atan2(sum_sin, sum_cos)\n", " return x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These functions take advantage of the fact that NumPy's trigometric functions operate on arrays, and `dot` performs element-wise multiplication. NumPy is implemented in C and Fortran, so `sum(dot(sin(x), w))` is much faster than writing the equivalent loop in Python.\n", "\n", "With that done we are now ready to implement the UKF. I want to point out that when I designed this filter I did not just design all of functions above in one sitting, from scratch. I put together a basic UKF with predefined landmarks, verified it worked, then started filling in the pieces. \"What if I see different landmarks?\" That lead me to change the measurement function to accept an array of landmarks. \"How do I deal with computing the residual of angles?\" This led me to write the angle normalization code. \"What is the *mean* of a set of angles?\" I searched on the internet, found an article on Wikipedia, and implemented that algorithm. Do not be daunted. Design what you can, then ask questions and solve them, one by one.\n", "\n", "You've seen the UKF implemention already, so I will not describe it in detail. There are two new thing here. When we construct the sigma points and filter we have to provide it the functions that we have written to compute the residuals and means.\n", "\n", "```python\n", "points = SigmaPoints(n=3, alpha=.00001, beta=2, kappa=0, \n", " subtract=residual_x)\n", "\n", "ukf = UKF(dim_x=3, dim_z=2, fx=fx, hx=Hx, dt=dt, points=points,\n", " x_mean_fn=state_mean, z_mean_fn=z_mean,\n", " residual_x=residual_x, residual_z=residual_h)\n", "```\n", "\n", "Next, we need to pass extra data into our `f(x, dt)` and `h(x)` functions. We want to use `move(x, dt, u, wheelbase)` for `f(x, dt)`, and `Hx(x, landmarks)` for `h(x)`. We can do this, we just have to pass the extra parameters into `predict()` and `update()` as keyword argument,s like so:\n", "\n", "```python\n", " ukf.predict(u=u, wheelbase=wheelbase) \n", " ukf.update(z, landmarks=landmarks)\n", "```\n", "\n", "The rest of the code runs the simulation and plots the results. I create a variable `landmarks` that contains the coordinates of the landmarks. I update the simulated robot position 10 times a second, but run the UKF only once per second. We are not using Runge Kutta to integrate the differential equations of motion, so a small time step makes the simulation more accurate." ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [], "source": [ "from filterpy.stats import plot_covariance_ellipse\n", "\n", "dt = 1.0\n", "wheelbase = 0.5\n", "\n", "def run_localization(\n", " cmds, landmarks, sigma_vel, sigma_steer, sigma_range, \n", " sigma_bearing, ellipse_step=1, step=10):\n", "\n", " plt.figure()\n", " points = MerweScaledSigmaPoints(n=3, alpha=.00001, beta=2, kappa=0, \n", " subtract=residual_x)\n", " ukf = UKF(dim_x=3, dim_z=2*len(landmarks), fx=move, hx=Hx,\n", " dt=dt, points=points, x_mean_fn=state_mean, \n", " z_mean_fn=z_mean, residual_x=residual_x, \n", " residual_z=residual_h)\n", "\n", " ukf.x = np.array([2, 6, .3])\n", " ukf.P = np.diag([.1, .1, .05])\n", " ukf.R = np.diag([sigma_range**2, \n", " sigma_bearing**2]*len(landmarks))\n", " ukf.Q = np.eye(3)*0.0001\n", " \n", " sim_pos = ukf.x.copy()\n", " \n", " # plot landmarks\n", " if len(landmarks) > 0:\n", " plt.scatter(landmarks[:, 0], landmarks[:, 1], \n", " marker='s', s=60)\n", " \n", " track = []\n", " for i, u in enumerate(cmds): \n", " sim_pos = move(sim_pos, dt/step, u, wheelbase)\n", " track.append(sim_pos)\n", "\n", " if i % step == 0:\n", " ukf.predict(u=u, wheelbase=wheelbase)\n", "\n", " if i % ellipse_step == 0:\n", " plot_covariance_ellipse(\n", " (ukf.x[0], ukf.x[1]), ukf.P[0:2, 0:2], std=6,\n", " facecolor='k', alpha=0.3)\n", "\n", " x, y = sim_pos[0], sim_pos[1]\n", " z = []\n", " for lmark in landmarks:\n", " dx, dy = lmark[0] - x, lmark[1] - y\n", " d = sqrt(dx**2 + dy**2) + randn()*sigma_range\n", " bearing = atan2(lmark[1] - y, lmark[0] - x)\n", " a = (normalize_angle(bearing - sim_pos[2] + \n", " randn()*sigma_bearing))\n", " z.extend([d, a]) \n", " ukf.update(z, landmarks=landmarks)\n", "\n", " if i % ellipse_step == 0:\n", " plot_covariance_ellipse(\n", " (ukf.x[0], ukf.x[1]), ukf.P[0:2, 0:2], std=6,\n", " facecolor='g', alpha=0.8)\n", " track = np.array(track)\n", " plt.plot(track[:, 0], track[:,1], color='k', lw=2)\n", " plt.axis('equal')\n", " plt.title(\"UKF Robot localization\")\n", " plt.show()\n", " return ukf" ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "Final P: [0.0092 0.0187 0.0007]\n" ] } ], "source": [ "landmarks = np.array([[5, 10], [10, 5], [15, 15]])\n", "cmds = [np.array([1.1, .01])] * 200\n", "ukf = run_localization(\n", " cmds, landmarks, sigma_vel=0.1, sigma_steer=np.radians(1),\n", " sigma_range=0.3, sigma_bearing=0.1)\n", "print('Final P:', ukf.P.diagonal())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The rest of the code runs the simulation and plots the results. I create a variable `landmarks` that contains the coordinates of the landmarks. I update the simulated robot position 10 times a second, but run the UKF only once. This is for two reasons. First, we are not using Runge Kutta to integrate the differental equations of motion, so a narrow time step allows our simulation to be more accurate. Second, it is fairly normal in embedded systems to have limited processing speed. This forces you to run your Kalman filter only as frequently as absolutely needed." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Steering the Robot\n", "\n", "The steering simulation in the run above is not realistic. The velocity and steering angles never changed, which doesn't pose much of a problem for the Kalman filter. We could implement a complicated PID controlled robot simulation, but I will just generate varying steering commands using NumPy's `linspace` method. I'll also add more landmarks as the robot will be traveling much further than in the first example." ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [], "source": [ "landmarks = np.array([[5, 10], [10, 5], [15, 15], [20, 5],\n", " [0, 30], [50, 30], [40, 10]])\n", "dt = 0.1\n", "wheelbase = 0.5\n", "sigma_range=0.3\n", "sigma_bearing=0.1\n", "\n", "def turn(v, t0, t1, steps):\n", " return [[v, a] for a in np.linspace(\n", " np.radians(t0), np.radians(t1), steps)] \n", " \n", "# accelerate from a stop\n", "cmds = [[v, .0] for v in np.linspace(0.001, 1.1, 30)]\n", "cmds.extend([cmds[-1]]*50)\n", "\n", "# turn left\n", "v = cmds[-1][0]\n", "cmds.extend(turn(v, 0, 2, 15))\n", "cmds.extend([cmds[-1]]*100)\n", "\n", "#turn right\n", "cmds.extend(turn(v, 2, -2, 15))\n", "cmds.extend([cmds[-1]]*200)\n", "\n", "cmds.extend(turn(v, -2, 0, 15))\n", "cmds.extend([cmds[-1]]*150)\n", "\n", "cmds.extend(turn(v, 0, 1, 25))\n", "cmds.extend([cmds[-1]]*100)" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "image/png": 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KdxERERERJ6DCXURERETECbhVpvMHH3zABx98wP79+wFo3rw5L730En369AHAMAzGjRvH1KlTSU9Pp0OHDrz//vs0b968ygOvKrdPXcexrMKTKwyDnFxX3tm1Bkwm++pwPwuzHuzkgAhFREScl37OilSdShXuderU4dVXX6VRo0YAzJgxg/79+7Np0yaaN2/O5MmTeeutt5g+fTqNGzdm/Pjx9OrVi507d+Lr61stJ3C+jmUVkpCae9paEykFeQ6JR0REpDbRz1mRqlOpoTL9+vWjb9++NG7cmMaNGzNhwgR8fHxYv349hmHwzjvv8MILL3DTTTfRokULZsyYQV5eHjNnzqyu+EVERERELgrnPMa9pKSEWbNmkZubS6dOnUhISCApKYnevXvb+1gsFrp27cratWurJFgRERERkYtVpYbKAGzdupVOnTpRUFCAj48Pc+bMoVmzZvbiPDw8vEz/8PBwDhw4cMb9FRYWUlh4cuxbVlYWAFarFavVWtnwKs8wzrpfjcRzETuRX+W55in3jqG8O45yX4P0c/aCoM+845ya+/PNf6UL9yZNmrB582YyMjKYPXs2Q4YMYeXKlfZ20yk3mkDpDaunrzvVpEmTGDduXLn1S5YswcvLq7LhVVpOritw5vhO9stlwYIF1R6PQHx8vKNDuGgp946hvDuOcl/99HP2wqLPvOPEx8eTl3d+93aYDONsfxWuWM+ePWnYsCGjRo2iYcOG/Pbbb7Rp08be3r9/fwICApgxY0aF21d0xT0mJobU1FT8/PzOJ7Sz0vudNSSk/XMSY4O9WDLiimqP52JmtVqJj4+nV69emM1mR4dzUVHuHUN5dxzlvubo5+yFQZ95xzk19/n5+YSEhJCZmXlOdW6lr7ifzjAMCgsLiY2NJSIigvj4eHvhXlRUxMqVK3nttdfOuL3FYsFisZRbbzaba+aD9Td/DTi9nz7oNaPG3nspR7l3DOXdcZT7GqCfsxcUfeYdx2w2U1xcfF77qFTh/vzzz9OnTx9iYmLIzs5m1qxZrFixgkWLFmEymRgxYgQTJ04kLi6OuLg4Jk6ciJeXF4MGDTqvIEVERERELnaVKtyPHTvG3XffTWJiIv7+/rRq1YpFixbRq1cvAJ555hny8/N55JFH7A9gWrJkyQU7h7uIiIiIiLOoVOH+ySef/G27yWRi7NixjB079nxiqlHhfqcN0zEMcnJz8fH2LvdENxEREakc/ZwVqTrnPcbd2Z3+eGWr1cqCBQvo2/cKjQETERE5T/o5K1J1zvkBTCIiIiIiUnNUuIuIiIiIOAEV7iIiIiIiTkCFu4iIiIiIE1DhLiIiIiLiBFS4i4iIiIg4ARXuIiIiIiJOQIW7iIiIiIgTUOEuIiIiIuIEVLiLiIiIiDgBFe4iIiIiIk5AhbuIiIiIiBNQ4S4iIiIi4gRUuIuIiIiIOAEV7iIiIiIiTkCFu4iIiIiIE1DhLiIiIiLiBFS4i4iIiIg4ARXuIiIiIiJOQIW7iIiIiIgTUOEuIiIiIuIEVLiLiIiIiDgBFe4iIiIiIk5AhbuIiIiIiBNQ4S4iIiIi4gRUuIuIiIiIOAEV7iIiIiIiTkCFu4iIiIiIE1DhLiIiIiLiBFS4i4iIiIg4ARXuIiK1jGEYlJTYHB2GiIhUMTdHByAicrEqLraxemc6f2StJSYsgJuvaoq3p/t57fOHdbuY9MVq1m47DMCUEX15+IbLMJlMVRGyiIg4kAp3EREHKCmxcfekuaz+/SjJmfsAFz6Yv4F3hl9Lh2Z1zmmf2xKSeebDeI7nZoJbFpS4M3nWWtKy8nnx7qvOK978QisAHu5u+iVARMRBVLiLiDjAFz9tYdOeJDJLUsGrEGyuHEj24Jn/xDNv/O2UFOWRmppqfx0/fpzc3Fzy8vLsr/z8fGy2k0NiVm85wKHE4+SW5IGrCVzcSUr24909ayg4tJHOlzYhJCSEkJAQgoOD8fPz+8ciPL/QynMfLWXhL3vYdTgNgBXvDKFr6/rVmR4REamACncRkRpWUlLCD8t/If3gJorS94JxEDJNJOUVkVyYR9C/78cwqmaMesFfrwm/fluuzd3dnejoaOrWrUtMTAx169albt26xMXFcckllxAZGcmEz1bz/dqdpOWlgFs+FHvx8Fs/8NVLA2nVMLxKYhQRkbNTqcJ90qRJfPfdd+zYsQNPT086d+7Ma6+9RpMmTex9hg4dyowZM8ps16FDB9avX181EYuIOAnDMDh8+DC//fYbv/32G9u2bWPHjh3s3r2boqKi8v2BkhqMr6ioiISEBBISEips9/X1xeoeiM3Tj2IfP/APAO9IMnJ8GP3fZUx98nrCg3xrMGIRkYtbpQr3lStXMnz4cNq3b09xcTEvvPACvXv3Zvv27Xh7e9v7XXvttUybNs2+7O5+fjdbiYhcCL5dsY1pizaz4Jc9AGz95CFaNIiwt2dkZLB27VrWrFnDxo0b+e2330hNTa3cQdy9wd2PPldeah/ScuK/Pj4+eHl52V+enp64urraN1237RATPl9NRn4K+YUZ4JKBS5EXfq6+NInw59q20aSlpdmH3xw7doxDhw6RkZFRYSjZ2dlAdrn1SR6+zF8ZxfwvP2HVjDG0b98eDw+Pyp2niIhUWqUK90WLFpVZnjZtGmFhYWzcuJGrrjp545PFYiEiIuL0zUVEnNaspVsZ/d/lZBfmgEselFi49YVPua9zAHv/3MyaNWv4448/MAzjb/fj7u5OXFwcdes35PfEYtKLzeRbTODpjdk7kEjfWAZ2a84bw66pdIxt27blz+Nmfli3kwOpR8G1CH8vf4K9Qhj7eF+u7dCowu2ys7M5dOgQhw4dIiEhgV27drFz507+3LGDhH0JlP4t4BQF2VCwE9J2ctVVS3F3d+eyyy7jiiuuoGvXrnTt2rXMxRwREaka5zXGPTMzE4CgoKAy61esWEFYWBgBAQF07dqVCRMmEBYWdj6HEhFxqHdm/0Jm/nHSEn+H5IOQeog/V6bw1KwzbxMaGkq7du1o27Ytbdq0oXXr1sTGxuLmVvrVu37bAQaNm0VCSh6Yion0CyY6xJ/n7zz3GWBef7gXFrMrb32TBSUQHBrEPddeesaiHUqHxDRr1oxmzZqVa3tg8nf8sOxnUo5tpSTrMGQch8zjUGK19ykqKmLt2rWsXbuWyZMn4+7uzhVXXEHv3r255ppraNWqFS4uZR8bcjQ1m637jlE33J+m9ULP+XxFRC4m51y4G4bByJEjueKKK2jRooV9fZ8+fRg4cCD16tUjISGB0aNH06NHDzZu3IjFYim3n8LCQgoLC+3LWVlZAFitVqxWa7n+1e3EMR1x7Iudcu84yv2ZZWdns3DhQn759h04vqtMwXoqFxcXLr30Urp06ULnzp3p0KED0dHR5WZtMQzDnudWsaE8fV19Hpm+Awx3bu/WnBG3dMTX0+2c3ws3F3j1gR48c1snDqdkER7kTXigzznvb8yQ7vxv5zFc/cI5knkUMIjwDSfSYvDglSGsX7+On3/+mT179ti3KSoqYtmyZSxbtoxnn32WyMhIbrjhBvr370/Xrl2Ztngrb32znn2JGQAM6NKY/3vsWiKCfM4pxnOhz7zjKPeOobw7zqm5P9/8m4x/+rvuGQwfPpwff/yRNWvWUKfOmeccTkxMpF69esyaNYubbrqpXPvYsWMZN25cufUzZ87Ey8vrXEITETkvOTk5rF+/nnXr1vH7779TXFxccUffEAhoAoEN+PK5vnh6etZsoDXkUFo+H604wpZDOQA0CPPk4R51aBxxcjhMRkYG27dv5/fff2fTpk0kJydXuC9PL28IjsMIb0hBUBgYFkI8gogJ8uaFG2Jxc9UDvUWk9srLy2PQoEFkZmbi5+dX6e3PqXB/7LHHmDt3LqtWrSI2NvYf+8fFxXH//fczatSocm0VXXGPiYkhNTX1nE7ofFmtVuLj4+nVqxdms7nGj38xU+4dR7kvvUq8aNEivvjiCxYsWFDme+kEF3cvjNAYjLBQCIvA3RxNpHc9nr61Ew/2a1fpYzpT3g3DYNehNLLzi2jVIBx3s+vf9t2zZw8//fQTixcvZunSpRXmE3d3iGyAe53WRER3YOQtHXhkQPtqPIuTnCn3tY1y7xjKu+Ocmvv8/HxCQkLOuXCv1FAZwzB47LHHmDNnDitWrDiroj0tLY1Dhw4RGRlZYbvFYqlwCI3ZbHboB8vRx7+YKfeOczHm/vfff2fq1KnMmjWL48ePl2uPjo5mwIABdO/Zh4k/HiQpM4ujmYlg2AhwDyXI14tburU4r7w5S95bNKz4e7wiJ8bMP/744+Tk5LBw4ULmzJnDl19/ByV/FfFFRXBgB0UHdnDQYzEj/ncpN3f67G//ilvVnCX3tZFy7xjKu+OYzeYz/wX3LFWqcB8+fDgzZ85k3rx5+Pr6kpSUBIC/vz+enp7k5OQwduxYbr75ZiIjI9m/fz/PP/88ISEh3HjjjecVqIjIudiWkMzPfxzEzdWFvh3jiAjyJS8vj6+//poPP/yQX375pdw2YWFh3H777dxxxx1cfvnl9hsrGzRL5Jmp8RzdWFDazz+IsUO7EV6DY7OdkY+PDwMHDmTgwIF8eWQ0pO+D1F8heS+U/DVzfUEG7F9BvXr1uP7663n44Yfp3bt3mekuRUQudpUq3D/44AMAunXrVmb9tGnTGDp0KK6urmzdupVPP/2UjIwMIiMj6d69O1999RW+vnpIh4jUrI9++I1XZ65h39HSK+kNQ1yob93BxlULy81d7unpyY033shdd91Fr1697DO/nKpN40ji3xjMtoRkcvKLaFYvFF/v8n8xlDPb/9VIBoz+isNpl5CacxCS92I6ugcj5TBgYLPZmD9/PvPnz6devXo88sgjPPjggwQEBDg6dBERh6v0UJm/4+npyeLFi88rIBGRqnA0NYt3vl1PVmE6FP0BCZvZu3Ife0+bk7x169Y8/PDDDBo06KzHGzaP1fS256peRCCj7riCFz5eSmpGKIT6EhR7Fb4mF9r7H2Nt/DyOHDkCwIEDBxg1ahQvv/wy9913HyNGjDirIZoiIrWVbt8XkVpp4S+7Sd23mbQVU2HdbEjay4kHCbm4mRkyZCjr1q1j06ZNPPzwww65Gf5idXuPFkx8oAcYFij2JyYkguG39eTLj//N/v37mTdvHn379rVPpZmbm8v//d//0ahRI2655RY2btxYZn/FJTZKSmyOOBURkRp1Xg9gEhG50BiGwQ8//MD9gx6CnMSyje4eUKcttoguvP1/4wj0q53TNzqD27q35OarmpOTX4QJ8Pfx+KvFhRtuuIEbbriB3bt38/bbbzN9+nTy8/Ox2WzMnj2b2bNn06dPH0aPHs3PBw2mL9rMtv0pACyYdAd9OjZ22HmJiFQnXXEXkVrBMAzmz5/PZZddxg033FC2aPcJgM6x0HMgNOgA7t7/OPRPqp+bqwsBPh6nFO1lxcXFMWXKFA4dOsT48eMJDw+3ty1cuJDOnTvz0hNDObT3f2DOBFMRj/17EYt+2VPh/kREnJ0KdxFxeqtXr6ZTp07079+f3377zb4+JLohwZ2HQqch4N8HN5cAIvxDuapVvTMWi3LhCQ4O5oUXXmD//v1MmTKFunXr2tvyj+0ma/UM2Pgl5GwlMz+Ll6Yv50hKpgMjFhGpHircRcRp/fnnn/Tv35+rrrqqzLSObdu2Zf78+Rzc8ydduvUGayDkBxPlXZ9gX39GD74KVz2h0+l4eHgwbNgwdu/ezccffwwegScbjyfBhu9JXT6FDevWUGfg244LVESkmugnl4g4ndTUVB566CFatGjB/Pnz7eubN2/O/Pnz+fXXX+nXrx+eHmamPnn9X62u3N2rNXNfuY2e7Ro4JnCpEu7u7tx7771w+aPQ9HrwDjjZmJEIv38Km6ezcuVKh8UoIlIddHOqiDiNkpISpk6dygsvvEB6erp9fVRUFOPHj2fw4MHlHtgTHuSLsXxMTYcq1cxkMjHxwV785/tAEhs0pChxC+z+FbKzSztkHqBbt250796dcePGceWVVzo2YBGRKqDCXUQuKDabjY9++I3Pf9rCmq2HAPhx0h0EGmkMHz6cTZs22fv6+vry7LPPMmLECLy8vBwVsjjIYzd2YPGGvRQfKeZIMBB6Cd5pxyjatQZrVjIAy5cvZ/ny5fTs2ZNx48bRuXNnxwYtInIeNFRGRC4oH/3wG69/tZadR46Aaw4UZ3PH3ffQuXPnMkX7XXfdxc6dO3n++edVtF+kfLzc+fBf19EiNhKKAqAgjPC4rrw6dTafffYZjRo1svf96aef6NKlC9dee22Z+yFERJyJrriLyAXlkwWbyCzIIKMoBTL3wtZVZBXm2ttbtWrFe++9p6EPAsAl9UKZN/52ft52iKMp2bRrEknTeqHAFdx+++188cUXvPzyy+zbtw+AxYsXs3jxYvr06cPVV1/t2OBFRCpJhbuIXDCKS2xs2HkUbMdg7yI4knCy0cUMDa5m48bvcXPTV5ecZHF3o0eb2HLr3dzcGDJkCIMGDeKzzz7jlVdeYf/+/UDpPPALFy5k2bJlvPLKK+S4BjN2+gqWby5tnz6qP0OuvbTmTkJE5CxoqIyIXDBcXUyQtgvWzyhbtIfEQPthUKejinapNLPZzL333svOnTuZOnVqmXngFyxYQLt27eh3Q3+2/rER3LLAVMDYGSt586u1DoxaRKQ8Fe4ickHIz8/nscceg60zoSivdKXZAq264d7hJurHxvLvx691bJDi1Nzd3XnggQfYvXs37733HsHBwfa2rIO/k/rTv2HrHLAmkJGfxn++38gv2w45MGIRkbJ06UpEHG7Tpk3ceeed/Pnnn/Z1HpFNKWjYDTy8CPUKIyLIl3v7tHFckFJruLu78+CDDxIeHs7Ro0d54ukXoeivaSSPJcCxBDIiGpJRpycdHz2u6URF5IKhK+4i4jCGYTBlyhQ6duxoL9o9PT15dfLbPPDsG+AWDsW+XNqwDp883Q8vD3cHRyy1idlsZtiwYdDhcWh0DVhOmZ0oaS/8+h/Y/m2ZXyhFRBxJV9xFxCFycnJ44IEHmDVrln1dmzZt+OKLL2jatCkA7zzaB8MwcHXVNQapPsvevZd7J4eS0qQ5ufvWwb6NUFhU2pj8B82bN2fQoEG89NJLNG7c2LHBishFTT8NRaTGbdu2jfbt25cp2v/1r3+xfv16e9EO4OJiUtEu1a57mwb0bBtLsHc01OkAVw3BrdlVuFh8gNK/DJ34hXLIkCHs2bPHwRGLyMVKPxFFpEbNnj2byy+/nB07dgDg5+fHt99+y1tvvYW7u4bCiGNMevBq2jepA0X+UBRJnZY30vXBtxj38nj7Taw2m41PP/2USy65hHvvvdc+N7yISE1R4S4iNcIwDF5++WVuueUW8vJKZ41p1aoVv/76KzfffLODo5OLXYi/N1+NuYUFr93J68N68+Lgrsx/bQgvjX6BhIQEJkyYQGBgIAAlJSVMmzaNJk2a8MADD9jnhj+VzWbDai2p4bMQkdpOhbuIVKkiazGvzlyNqfs4TN3HMWf1dnJzc7n99tsZM+bk7Bx33XUX69evJy4uzoHRipzk6upCnw5xPHVbF+7r2wYfz9K/APn6+vL888+zf/9+Xn75ZQICAgAoLi7m448/Ji4ujoceeoiDBw8C8P3anXQa/gnuvcdj6j6OD+dtcNQpiUgto8JdRKqMYRgMnjSX/3y/EVwKwWTl8Te/pWGzNnz99dcAmEwmXnvtNT799FM8PT0dHLHI2fPz82P06NEkJCQwZswY/Pz8gNICfurUqTRq1Ig7h9zHU+98y4GUZDBngks+r81ay6sz1zg4ehGpDVS4i0iVmbVsK7/8eYTkvKNgyYTifRxZ8ibHDu4GwMfHh3nz5vHMM89gMpkcHK3IuQkICGDs2LHs37+f0aNH4+vrC4DVamXmp/9l1+wxpGz8GmzJYMkmPT+VTxZsYv22gw6OXEScnQp3Eakyg8bPYX9iGnnWXLCthV++wcjPKm20+LNu3Tr69evn2CBFqkhgYCAvv/wyCQkJPP/883h7e5c22Eqw7d8CK2bC3h/IzD7MniOpdHp0mmMDFhGnp8JdRKqYqfTpkz9tgaLi0lU+odD2fpo3b+7Y0ESqQXBwMBMmTCi9STWmC7iYSxtKDNh1EFZ8DnsXQlGOQ+MUEeenwl1EqsyKt4cQbk2A3xZBiQ0AU0gdArreQ4tLGjg4OpHqFRISwtK5n1Kv/0uYG14OLn8949BWDIc24Lrh3zzzzDOkpKQ4NlARcVoq3EWkyuz+9SeS130OGKUrIhrj03EQgX6R9OvcROPapdbr0bYB13RpTWS72+CKe6B+a3BxBaDEWsjrr79ObGwszz77LKmpqQ6OVkScjQp3EakS77//Pg888ACG8VfRHnUZNLmdUN8oerZtyDO3dXFsgCI1ZOL9V9OxWQyYoqBef+r0G01Mm95YLBYAcnNzee2114iNjeWFF17g+PHjDo5YRJyFCncROW9vvvkmjz76qH155MiRpO9YxW9TH2bVu/fw4cjrCfD1cGCEIjUn2N+LL0ffwuLX7+KNYdfwysP92bnuB/bu3cvw4cPtTwjOyclh4sSJ1K9fn9GjR5Oenu7gyEXkQqfCXUTOy//93//x1FNP2ZdfeOEF3njjDQJ8PWnTOJLoUD9cXDRERi4uLi4merdvxJO3dWbotZfiaTETHR3Ne++9x549exg2bBhmc+lNrNnZ2YwfP5769eszduxYMjIyALDZDBb9bw/PfBjPpC9Wsy0h2YFnJCIXAhXuInLOPvnkE5544gn78ssvv8z48eM1ll3kb8TExDBlyhR2797Ngw8+iJtb6U2sWVlZjBs3jtjYWF5++WUmf7aUYW//wOuzVvH8R/EMHPsN0xZuOjkcTUQuOircReSczJw5kwceeMC+/OKLLzJ69GgHRiTiXOrVq8d//vMfdu/ezf33328v4DMyMhgzZgwvPNifY1vmg3sSeB4nJSuN1778mV93HnVw5CLiKCrcRaTS5s+fz+DBg+1X/v71r3/x8ssvOzgqEedUv359PvroI3bu3Mm9996Lq2vpLDS2ojzyty+HlZ/CoeWkFxwlJz+Pt79Z7+CIRcRRVLiLSKWsW7eO2267jZKSEgAeeugh3nzzTQ2PETlPDRo04JNPPmHHjh0Q3hr46/+poiLYtp2SZTM4svkHvoz/jaycAofGKiKOocJdRM7arl276NevHwUFpUXDoEGDmDJliop2kSrUqFEjaHojXP4oRDTjZAFfAHtWw/p3ePfdt8nLy3NonCJS81S4i8gZ/bL9MKbu4zB1H0f8z5u59tprSUtLA+Dqq69m2rRpuLjoa0Skqh377knuvflqoq+8B64YBFGNTjZa83jpxeeJjY3l7bffJj8/33GBikiN0k9cEanQxz/+xqDxswEblBRwfb8bSEhIAKBVq1bMnj3bPh+1iFStsEAfXrm3OxGBfuDWAJr1x+/qh/Cp28b+F67k5GRGjhxJgwYNePfdd1XAi1wEVLiLSDkJR4/z5tfryCxIB48U2P0NRemHAAgMiWDhwoX4+/s7OEqR2i0qxI/PnhsAuEKxL1HRLRn23Gts2rSZgQMH2vslJSUxYsQIGjZsyHvvvWcfyiYitU+lCvdJkybRvn17fH19CQsLY8CAAezcubNMH8MwGDt2LFFRUXh6etKtWze2bdtWpUGLSPVqcOe/2XEwlbT8NDi0ApL2lja4upMeexOBwaGODE/kotG0fhjG8jEYy8ewbdojTH64F61bt+Lrr79my5Yt3Hzzzfa+iYmJPPbYYzRq1IgpU6ZQWFjowMhFpDpUqnBfuXIlw4cPZ/369cTHx1NcXEzv3r3Jzc2195k8eTJvvfUW7733Hhs2bCAiIoJevXqRnZ1d5cGLSDU7the2/XlyudU14B1GYqr+fxapaac/gbhly5Z8++23bN68mQEDBtjXHzlyhOHDhxMXF8d//vMfioqKOHgskyf+vdB+z8ov2w/XcPQiUhUqVbgvWrSIoUOH0rx5c1q3bs20adM4ePAgGzduBEqvtr/zzju88MIL3HTTTbRo0YIZM2aQl5fHzJkzq+UERKSa5CbDlp9OLjdpDyGlN8i5ummUnciFonXr1syZM4fffvuNG264wb7+0KFDPPzww8TFxdFn8L/4btVWcMkHihny6lzmrdnhuKBF5Jy4nc/GmZmZAAQFBQGQkJBAUlISvXv3tvexWCx07dqVtWvX8tBDD5XbR2FhYZk/52VlZQFgtVqxWq3nE945OXFMRxz7YqfcO87puT/0xcNc2q49aSV/vRcRjfFodCXBnuG0aRRNuL+n3qcqoM+849TG3Ldo0YJvv/2WjRs38sorr7BgwQIADh48CAenYfL0g4btILoxx3PcGT1tOa0bhBId6lejcdbG3DsD5d1xTs39+ebfZJx49GElGYZB//79SU9PZ/Xq1QCsXbuWLl26cOTIEaKioux9H3zwQQ4cOMDixYvL7Wfs2LGMGzeu3PqZM2fi5eV1LqGJyHkwDIO3336bVatWla7wDoc29xEW6E14gIX7ukZTP8TTsUGKyD/atWsXs2bN4rfffivb4O0NsR0hqBO4uDF3xKUOiU/kYpSXl8egQYPIzMzEz6/yvzSfc+E+fPhwfvzxR9asWUOdOnWAk4X70aNHiYyMtPd94IEHOHToEIsWLSq3n4quuMfExJCamnpOJ3S+rFYr8fHx9OrVC7PZXOPHv5gp945zau6nT5/O8OHDAfDx9SWn6VDwCuaHCbfRsVkd/Lwtjg22FtFn3nEupty7dxgG+5dD+r6yDZ6BUK8reb/NxM3tvP4AXykXU+4vJMq745ya+/z8fEJCQs65cD+n/1Mfe+wx5s+fz6pVq+xFO0BERARQOjXVqYV7cnIy4eHhFe7LYrFgsZQvBMxms0M/WI4+/sVMuXecP/74g5EjR9qXp/33v9xyyy0OjOjioM+841wUufePgdaDIW8bJKyGlKTS9fnpsGMul156KS+99BK33347rq6uNRbWRZH7C5Dy7jhms5ni4uLz2kel7jAzDINHH32U7777jmXLlhEbG1umPTY2loiICOLj4+3rioqKWLlyJZ07dz6vQEWkehUWFjJ48GD7X8Aef/xxFe0itUDG/FFc1aouETFtoN3N0GEAppCTF9127drFXXfdRYsWLfjyyy8pKSlxYLQi8ncqVbgPHz6czz//nJkzZ+Lr60tSUhJJSUn2p7WZTCZGjBjBxIkTmTNnDn/88QdDhw7Fy8uLQYMGVcsJiEjV+PTTT+3PZWjbti2vv/66gyMSkarg7+vBpAeuJsQvAAoCwacxUd0fo2Hff9GhUxd7vx07djBo0CBatSqdJ95mszkuaBGpUKUK9w8++IDMzEy6detGZGSk/fXVV1/Z+zzzzDOMGDGCRx55hMsuu4wjR46wZMkSfH19qzx4Eaka8fHx/PjjjwB4eHjwxRdf4O7u7uCoRKSqdG5Rly9fvAlwgxIvrmzZgK/eeor1a9ewbNkyrrzySnvf7du3c9ttt9G6dWu+/fZbFfAiF5BKjXE/m/tYTSYTY8eOZezYsecak4jUoLS0NO6//3778uuvv84ll1ziwIhEpDq0aBCOsXxMufXdu3enW7duLF26lDFjxrB27Vqg9J6XgQMH0qpVK8aOHcuAAQMwmUofApWQmM6uQ2m0jYskNNC7Rs9D5GKmp6iIXOQef/xxEhMTAejdu7d9RhkRuXiYTCZ69uzJmjVrWLx4MR07drS3bdmyhZtuuom2bdsyd+5cXvx4KVeP/JRrR31B2E1v8Ox/4s/qwp6InD8V7iIXsR9//NH+VGMfHx+mTp1qv6ImIhcfk8lE7969Wbt2LQsWLKB9+/b2ts2bN3PjjTfyxqh7SN6/Fiwp4JbNVyu28cpnqxwYtcjFQ4W7yEUqOzubYcOG2ZfvueeeMg9OE5GLl8lkok+fPvzyyy/88MMPtGvXzt5WePwQueu/hv/NhPQdHM9L5cuftrL7UKoDIxa5OKhwF7mIFBYVs/NgKnuPHOe5557j0KFDAPTs2ZMePXo4ODoRudCYTCauu+46NmzYwPz588En4mRjejps/JGslR+zY/N6Gt/9nuMCFblI1Nyj0kTEoZb9lsBzH/3E/3YchcxDsOm/AHh5efH+++/z559/OjhCEblQmUwm+vXrB+0egtRtcHA5ZKeVNmYeg61fgF8d4uO70LNnTw25E6kmuuIuchFIycjl6Q+XcDAlBdzSYM/3QOnNZI+NfLbcw9RERCry0dP9qN+yC5aug6FdD/DzP9mYdZjevXtz5ZVXsnTpUt2wKlINVLiLXARmLN5MWlY+xwuTIflXyE4GwOwfwR5TIwdHJyLO4u5erWkQGUioZyQEt4BOd+J7+UDcAyLtfX7++Wd69uxJt27dWLFiheOCFamFVLiLXASe/vAnDiSlU5SfDTs32NdbG13F7NW7HBiZiDgTi7sb058dQOM6YVAYCAUhhDW6gg+/+IFZs2bRtGlTe99Vq1bRvXt3unfvzqpVmnVGpCqocBe5aJhg1wYoLC5djGoAgXWAs3u4mogIQEyYPz9MHMSyt4fw32cG8P3EOxjapw233XYbW7du5YsvvqBJkyb2/itWrKBr16707NmTn3/+ucy+DMPgUHImx7Pyavo0RJySCneRi8Dhr0bQro4ZDv1RusLVDbemXYkODOeGzo11I5mIVIqnh5nubWK5p28bmtYLtX+HuLq6MmjQILZt28Znn31GXFycfZulS5dyxRVX0LdvX3bs2MG+o+l0GzGdure9Q3D/13nwje/JySty1CmJOAUV7iIXgegwfwJT13LihlTqdiE6pCWh/v6Mv0/TQIpI1XJ1deWuu+5i+/btzJgxg4YNG9rbfvrpJ5599lk6XXU1f277DcwZ4JrN4g17ePKDxRRZSxwXuMgFToW7yEVg7dq1/LR4QemCuw/U6cI9fdqw8NU7adkg3LHBiUit5ebmxuDBg9mxYwf//e9/y8xglX7wD1KWvgebZ0P+ftLyj7Hk170s+EX33YiciQp3kVrOMAxGjRplX5763lsYqyYwZkg3IoJ9HBiZiFws3NzcuOeee9i5cyf/+c9/wHLKNJIph2DtbHLXz2L/rj+4cfTXjgtU5AKnwl2klvvxxx9Zs2YNAE2aNOGee+5xcEQicrEym82l30EdHoPG14PHKRcPUg7Ab5/A1i/ZvHmzw2IUuZCpcBepxQzDYMKECfbliRMn4uamByaLiGNNuK0J9dtcjefV90OrjuBlOdmYtpM2bdpw0003sWXLFscFKXIBUuEuUov9/PPPrF+/HoAWLVpw4403OjgiERFoFuXDJfVCCPaOhqjL4IqhuLe8GlfPk0No5syZQ+vWrRk4cCB//PGHA6MVuXCocBepxSZPnmz/9zPPPKNpH0XkgmAymZjyRB8iAv2hIBiswUQ1v55bnv6At95+m8jIk09i/fbbb2nVqhW33XYb27dvd2DUIo6nwl2kltq+fTvff/89ADExMdx+++0OjkhE5KQ6oX4sfu1O/v14H4b168zTt3VmxgsD+deIEezdu5d33nmH8PDSWa8Mw+Drr7+mRYsWDBo0iB07djg4ehHHUOEuUku9+eab9n//61//wmw2OzAaEZHygvy9ePTGDkz513U8MuByLO6l9+B4enryxBNPsG/fPt58803CwsKA0gL+yy+/pHnz5tx9993s2lU6dWRufhFT5v6P0f9dxrLf9mGz2Rx2TiLVSYW7SC109OhRPvvsMwD8/f25//77HRyRiEjleXl5MXLkSPbt28fkyZMJCQkBwGaz8fnnn9O0aVNuu+NOej/6f0yetZbxn63g6ic/48E3v8cwDMcGL1INVLiL1ELvvvsuVqsVgEceeQRfX18HRyQicu68vb15+umnSUhI4NVXXyU4OBgoLeC/njWTtdNGcXjtR2DsA7dMlv62n2kLNzk4apGqp8JdpJbJzMzkww8/BMDd3Z3HH3/cwRGJiFQNHx8fRo0aRUJCAhMmTCAwMLC0wbBRcmg7rJoJOxaRefwAM5f+QXJ6jmMDFqliKtxFagGrtYTZq7Zj6j6OgLYDycrKAmDIkCFEREQ4ODoRkarl6+vL888/z969+6B+d3D7ax54w4DDf5Ie/y5Lv3yX8L6jHRuoSBXTk1hEnNyx4zncNXEOe44cB1sxHC6dt91kMvHkk086ODoRkeoTEOAP9btCvRaQuA72b4QiAwwbJP4GSZsZNqyA559/npiYGEeHK3LedMVdxMk999FSdh9OISn3IKT/DEXZANS5pD116sY6ODoRkepjMpkY2LUpUaHRuDXuCL1uhEbtTrkCb+PDDz+kUaNGDB8+nMOHDzs2YJHzpMJdxIkVl9iYtmgzB9KOUlCSAwd/sbcd8miJT99JDoxORKT6PXlrZ/y8vAlwD4XiKIi9kjrXv0jXG+6235hfVFTElClTaNiwIY8//jhHjx51cNQi50aFu4gTsxaX/PUvG6Tsg8y80sXASPDXn4VFpPbr0KwOz995FcHeQVAYAtYAOl3ahB9nfUxCQgLPPfcc3t7eQGkB/+9//5uGDRsyYsQIkpKSHBy9SOWocBdxYhbzX7epFHvAnm0nG+q3c0xAIiIOcHfvVqx97z5mj7uVn/99D7NG34y3pzvBwcFMnDiR/fv3M2rUKLy8vAAoKCjg3XffJTY2lieffJJjx46V2V9hUTFHUrIoKdGDnOTCosJdxIm5uJiY+8qtRJvzIT2xdKV3IOGxHenQNJqkb3VzqohcHIL8PLnpqqZ0blEXF5ey5U1ISAivvvoqCQkJPPXUU3h6egKlBfxbb71FbGwsTz/9NCkpKUz+cg0e10ygzq1v023EdH7eetARpyNSIRXuIk6u/xVNCc3+/eSKOlcSExrKm4/0JjzYx3GBiYhcYMLCwnj99ddJSEhg5MiReHh4AJCfn88bb7xBTN16THh5DJSkgDmDvUnJDH93AUdTsx0cuUgpFe4iTm779u1sXr+8dMHdB8Jb8eOkQXRpUdexgYmIXKDCw8N58803SUhIYMSIEVgspbPQFBbkk7VjGaydCvtWkJK1l+PZuYydvtzBEYuUUuEu4uQmTTo5c8wbE8dirHyFsEBdaRcR+ScRERG8/fbb7Nu3D6IvB5NraUOJFfZupnjpDA7971s+mvuzYwMV+YsKdxEntnfvXr788ksAgoKCeOihhxwckYiI84mKioK4vtDxCYhpDSfGyJdYYf96WP8uY8aMISMjw6FxiqhwF3Fir732GiUlpVNCjhgxAh8fXWkXETkXid+O5NLmcfi37QddB0FTPzCdKOALefnll6lfvz7jxo0jMzPTscHKRUuFu4iTOnjwINOnTwfAz8+Pxx57zLEBiYg4sYhgXzo3j8HPEgAWf6h/F249BuPTsCMuLqVDaDIzMxk7diz169dn/PjxZGVlOTZoueiocBdxUuPGjcNqtQIwfPhwAgICHBuQiIiTe+7OKwny9YaCQCjyIiywKbFXDWb52l+57777cHUtLeAzMjIYPXo0sbGxTJgwQUNopMa4VXaDVatW8frrr7Nx40YSExOZM2cOAwYMsLcPHTqUGTNmlNmmQ4cOrF+//ryDFblQ3D51HceyCv+xX7ifhVkPdqry4//555/2q+0BAQE8/fTTVX4MEZGLTZ1QP7548SYmf/kzuw4fJzrElzGDu9KyYThXdfiY559/nvHjx/Ppp59SUlLC8ePHefHFF3nttdd4+OGHGTFiROl4+VNs259McnoubeMi8ffxcNCZSW1R6cI9NzeX1q1bc88993DzzTdX2Ofaa69l2rRp9mV3d/dzj1DkAnQsq5CE1FyHHf/FF1/EZit9ot8zzzxDYGCgw2IREalNmtcPY8ZzN2IYBiaTqUxbgwYN+O9//2sv4D/77DNsNhvZ2dm8/vrrvPvuuwwZMoSnn36a2AYNeeCN+UxfVPqcjVYNw3lzWG96tmvgiNOSWqLSQ2X69OnD+PHjuemmm87Yx2KxEBERYX8FBQWdV5AictKGDRv47rvvgNKpzB5//HEHRyQiUvucXrSfqlGjRkyfPp2dO3fy0EMP2eeBLyoq4qOPPqJJkya069KTxctWgTkTLGkkZx7nqQ+WkJqRV1OnILVQtYxxX7FiBWFhYTRu3JgHHniA5OTk6jiMyEXHMAxGjhxpX37ppZfw9vZ2YEQiIhevRo0a8eGHH7J//36effZZ/Pz8gNLv6i2/LCdxyduw8StI30JqfiIZOfm8+bXmhJdzV+mhMv+kT58+DBw4kHr16pGQkMDo0aPp0aMHGzdutP9GeqrCwkIKC0+OFT5xh7bVarXfeFeTThzTEce+2DlV7g3jrPtVxflk5RaSkJjO9g0rWLNmDVD6A2Pw4MFVsn+nyn0torw7jnLvOLUx98HBwbz88ss8+eSTTJ06lRfGTgTrX8Mpjx+F/x2l2HMTB6Iv49Ujybx8T7caj7E25t1ZnJr7882/yTDOtgKpYGOTqdzNqadLTEykXr16zJo1q8LhNWPHjmXcuHHl1s+cORMvL69zDU2kWo3f5EpKwZn/jHpCqIfBi21Kzvk4RdYSvvwliXW7M0k6ngP/ew8KS3+5ffHFF7nsssvOed8iIlI9Bry5AY79DofXQF5G2UZXd667thfXXXdduRtZpfbLy8tj0KBBZGZm2v9CUxnVXrgDxMXFcf/99zNq1KhybRVdcY+JiSE1NfWcTuh8Wa1W4uPj6dWrF2azucaPfzFzptz3fmcNCWn/PE4xNtiLJSOuOOfjTJy5hk8X/05afiqZW+Jh3/8AaNamE5t/WXnO+z2dM+W+NlHeHUe5d5yLIfd/7k+m/+hvSM49Sl7yJjj8CxzNLtevV69e3H///Vx//fXVnouLIe8XqlNzn5+fT0hIyDkX7lU+VOZ0aWlpHDp0iMjIyArbLRZLhUNozGazQz9Yjj7+xcwpcv83Ny2d3u98zuXHdXvILMggJ+sQ7N/41z5dsNbvRXJ6HtFh/ue874o4Re5rIeXdcZR7x6nNuW/RMIqWDcL5dVcBecGNIbgxlsZ5WA7vouDQbxQVFgAQHx9PfHw8kZGR3HfffTzwwAPUrVu3WmOrzXm/0JnNZoqLi89rH5W+OTUnJ4fNmzezefNmABISEti8eTMHDx4kJyeHp556inXr1rF//35WrFhBv379CAkJ4cYbbzyvQEUuNoVFxWzYeZS0rCxKti4F219Dbuq2Yne6C3Vue8eh8YmISMVcXEw8eVsnvCxekO8PhV6EhbWg44BhJCQc4NVXXyU2NtbePzExkfHjxxMbG8v111/P/PnzKxwLvWXvMb6I38LGnUdr8nTkAlLpwv3XX3+lTZs2tGnTBoCRI0fSpk0bXnrpJVxdXdm6dSv9+/encePGDBkyhMaNG7Nu3Tp8fX2rPHiR2szdXPqEPhL3QMqR0n97eEGDjo4LSkREzkrX1vV574m+9O3QnE5NL6HP5Y2ZNqo/UZFhjBo1ij179rBo0SJuvPFG+xNZbTYbP/74I/3796dOnTqMHDmSLVu2APDiJ0tpff+H3DVxDgPHfsOYacsdeXriIJUeKtOtWzf+blj84sWLzysgEWcQ7ld+eNf59KuIyWTilbs7MOaRN7CdWNm0G2GBMTSKDOebMbec875FRKT6XXt5I3q2a0BxiQ2L2bXM3PAuLi5cc801XHPNNRw9epRPPvmEjz76iEOHDgGQnJzM22+/zdtvv02jJs047tUEfCLB20R6gZWZP22lY7M69OkQ56jTEweo9jHuIrXRrAc71chx9q35GlthTulCyCXg156IwCDGDOlGVGjVjm8XEZGq5+bqgpvr3w9wiIqKYvTo0Tz//PMsWrSI6dOnM3/+fIqKigDYs3M7sB1MLhAWSVZkMyz1uvDBvF9VuF9kquUBTCJy/hYuXMi0adMA8PL2gbi+YDLxxfMD6N2+oYOjExGRqubq6sp1113HN998Q2JiIu+//z74Rp/sYNjg2BFsm+M59v14vv94PLNnzyY/P99xQUuN0hV3kQtQWloa9957r3357bfe5MEHH3RgRCIiUpOCgoJ45JFHGP5NCuSmQPL/4Ng2KPhrKmJbMaRs55ZbbsHHx4f+/fszcOBAevXqpefg1GK64i5ygTEMg2HDhpGUlASUPo34gQcecHBUIiLiCMe+e5I2l7bE/9JroPvdcEMkpnotMbmfLM5zcnL44osvGDBggH0mvxkzZpCWlvaP+7fZzvlxPuIAuuIucoGZNWsW33zzDVB6xeWTTz4pc0OTiIhcPMICfejcPIaUjGwyi46D9UbMrdyI6jiYDpEl+GTvZvbs2WRkZACQn5/P3LlzmTt3Li4uLlx11VUMGDCAa665psx+12w9wITPVpOckUez+iG89mBPokJq/sGXUjkq3EUuIAkJCQwbNsy+/MEHH5zx4WUiInJxeKR/e+J/3Qep/uBaQIh3OIG+vrz94iAig32ZMmUKP/30E3PnzmXevHkkJycDpdNLrlixghUrVgAQGRnJTTfdRPN2XXhryVH2HDsOLoWkZGYz5NV5/DDxDizuKg0vZHp3RC4QRUVF3HbbbWRmZgJwxx13cOuttzo4KhERcbRm9UP5cOR1jJuxksS0bGIjAxl/Xw8ig0ufkePu7k7fvn3p27cvH3zwAb/88gtz585lzpw57Nmzx74f+w2vvA8ubhAUCaF1SS5phNm1DfN/3snA7s0ddJZyNlS4i1wgnn32WTZs2ABAw4YN+fDDDx0ckYiIXCi6t4mla+v6FFqLsZjdcHGpeAilq6srnTt3pnPnzrz22mv8+eefzJs3j4ULF/Lzzz9js/31ZBBbMaQegtRDFP75M/sts3n6j284PvxuevToQaNGjSo9TDMrt5Dlm/cT7OtBl5Z1NcyzGqhwF7kAzJ8/n7fffhsovXLy9ddf4+ensYYiInKSi4sJT4v5rPubTCaaNWtGs2bNeOqpp/jmm2+4c+I8OL4Hju+Ewlx7X1thDge2/szDD/8MQHR0NN27d+eqq66ic+fONG3aFBeXM89psm7bIUZOWUJqRuk+r2xVjykjrsPDolKzKimbIg62d+9ehg4dal9+8803adu2reMCEhGRWsnb2xtCm5W+zGlg2gJZf8BeHzieCCVF9r5Hjhzh888/5/PPPwcgICCAjh072q/mX3755fj6lg7VyS+w8vSH8RxITiEx+yjYXCnebOP9uf/jyds6O+RcaysV7iIOcDglk4zsQuoEedC/f3/S09MBuOmmmxg+fLiDoxMRkdrqj08eoP/ob0nOKSTb1gjqBGAOqUu4RwxdG1hoEZjH8uXLWbNmDXl5efbtMjIyWLRoEYsWLQLAxcWF5s2b065dO/LdQ9ifUMxxt2IwF0CJOzlFWcxZs4ORt3Y6ryEzuw+ncTA5k1ax4YQGep/3+Ts7Fe4iNejPAyk88vaPrPj9ABg2Qo78SOqebQBccsklTJs2TWMCRUSk2jSOCeXKlnWJ/62Q7OwsyI3G1xKIj5cnrzxxJ7FRgTz77LMUFRXx66+/snbtWn7++WfWrl1rn60GSmes2bp1K1u3bj1l7yYIcAffCLL8GrDn+CWs/F87ul7e6px+tr325Rr+u2AzNpsNLw8zbw2/hqvbNqiCLDgvFe4iNaSkxMbwdxew+2gymDNg33pS924EwNfPj3nz5mlcu4iIVLtRd3Rhw86jHEkJApMNP/8g7uvbltioQHsfd3d3+7CYp556CsMw2LdvH2vXrrW/tm3bRklJySl7NiCjEDIOUMQBjrGc7h0/IDAwkBYtWtC8eXNatGhBs2bNiIuLIyoq6ozj5n9ct4sP529kf+phcCsg3CeSpz6IZ8XbQ/D38ajmDF24VLiL1JDP47eQkJhBWsExOL4V9q7/q8VEv3ufo3Hjxg6NT0RELg6X1Avlx1cH8e7sX8jOK+KmKy+hT4e4v93GZDLRsGFDGjZsyN133w2UPuxpy5YtdLz7Zcg5DDlHITcVbGW3TU9PZ/Xq1axevbrMek9PTxo2bEhcXBxxcXE0atSIRo0aUa9ePd795mcKinPBnAemEjIKk/HJ82HOmh0MvfbSqkyHU1HhLlJDhr42DwwDChNg87KTDQ2uYubmQr5wXGgiInKRqRcewFuPXPPPHf+Gp6cnHTp0YNgjw/h+7Q6S8g9QbEqG1BJ8CkvwteXRJLCE3bt2cOTIkXLb5+fn88cff/DHH39UuH+TxRs8PSCgiCJTA5J99zBtxgHquh8nPDycsLAwgoOD/3a2m9pGhbtITco/DpsWQolRuhzdBGK6ODYmERGR83DPtW2J/zUB7yJ/Mots4ONOSL36jBvajcHXtAZKr7pv376drVu3snPnTvbs2cPu3bvZt28fVqu1wv0ahbmlU1ZmgMHvZPM7q7b8yNWz3rL3cXV1JTQ0lLCwMEJCQvD39ycgIMD+OrHs5+eHt7e3/RUSEkKdOnVqIj1VSoW7SA357d930rFzZ4qsBaUrguvg02YAIT6hTHrgascGJyIico7aXxLFHT1a8Fl8CZmZLoArHZpGc2fPlvY+gYGBdOnShS5dyl6sKikp4eDBg/ZCfu/evbz12SIozILC9DJzzVekpKSEpKQkkpKSKhVz//79mTt3bqW2uRCocBepAdnZ2Tx07yCKslNKV3iHwSWDCPGJ5MYrLuG27i0cG6CIiMh5GHdPN9pfEsXve45xSb0Qbr6q6VnNJOPq6kpsbCyxsbH06tULgMHDnuaml74iOTeRnJKjUJKCW6YP/jYLHRsF0Dzam+TkZI4dO8axY8fs/z7TlfuKeHs759SSKtxFqll+fj79+vVjw4YNAISGhZPSYBCYvZjyRB+uuTxOU0CKiIhTM5lM9OvchH6dm5z3vlo3iqB1wwjW78gnJzcbTL74h4cRExLOJ6/dRXiQT7ltDMMgLy+PjIwMMjIyyMzMtP87IyODrKws8vLyyM3NJTc3l8svv/y843QEFe4i1aioqIiBAweycuVKAIKCgli29CdatNAVdhERkTN59Mb2/PF2MqQGAAa+/v7c17dthUU7lP7icGL8enR0dI3GWpNUuItUk5KSEgYPHsyPP/4IgI+PD4sWLVLRLiIi8g96tG3Af0Zez9QfNlJkLWHQ1S258cqmjg7L4VS4i1SD4uJiBg8ezFdffQWAh4cH33//Pe3bt3dwZCIiIs6he5tYureJdXQYFxQV7iJVzGq1cuedd/LNN98AYDab+fbbb+nWrZtjAxMRERGnpsJdpAoVFRVx++23M2fOHKD0kdGzZ8/muuuuc3BkIiIi4uxUuItUkfz8fG699VZ++OEHACwWC3PmzKFPnz4OjkxERERqAxXuIucoN7+IlMw8Arw9MIrzueGGG1izZg1QOqZ93rx59O7d28FRioiISG2hwl2kkoqLbfzr/UW8N7d0XnYKs4g6Oo+jB/YCpbPHzJ8/n+7duzswShEREaltVLiLVNLrX/3Mgl92g2sO5CfDprkcLcgCIDQ0lIULF9KuXTsHRykiIiK1jQp3kUpISsvm8/gtpOenQfZu2LQQrEUAWPxCWBy/nDatmzs4ShEREamNVLiLVELkLW+V/iN5Lfy5DAyjdNknhMLmQ2g74luM5SrcRUREpOqpcBepDMMGe+Ph8LqT60JjoPkNgK/DwhIREZHaz8XRAYg4i/T0dK7x+F/Zor1eS7i0H3VC63NXz5bkLHjOcQGKiIhIraYr7iJnYdOmTdx8880kJCQAYDK5YDS6FqLbQZEL0SEBTH64F96e7g6OVERERGorXXEX+QfTpk2jc+fO9qI9ODiY7+bOh+jLAVcwmfju5VuJDNZQGREREak+uuIucga5ubmMGDGCjz/+2L6uffv2fPvtt9StWxfjhuscGJ2IiIhcbHTFXaQCmzZtol27dmWK9oceeojVq1dTt25dB0YmIiIiF6tKX3FftWoVr7/+Ohs3biQxMZE5c+YwYMAAe7thGIwbN46pU6eSnp5Ohw4deP/992neXFPkVYfbp67jWFbhP/YL97Mw68FONRCRc7PZbLzzzjs8++yzWK1WALy8vJgyZQpDhgxxcHQicq7KfVcaBjm5rryzaw2YTPbV+q4UkQtZpQv33NxcWrduzT333MPNN99crn3y5Mm89dZbTJ8+ncaNGzN+/Hh69erFzp078fXVGOCqdiyrkITUXEeH4XSOHc9h854kAn09aX9JFCaTiYMHD3L//fcTHx9v79e2bVtmzpxJkyZNHBitiJyvir8rTaQU5DkkHhGRc1Hpwr1Pnz706dOnwjbDMHjnnXd44YUXuOmmmwCYMWMG4eHhzJw5k4ceeuj8ohWpAmOnr+Dz+C3sPZoOQL9OcXQLP87Y0c+TnZ1t7/f0008zfvx43N01U4yIiIg4XpXenJqQkEBSUhK9e/e2r7NYLHTt2pW1a9eqcBeHm7tmB1/Eb+F4fgp4ZEBOLks++YLvk3fb+0RFRTF9+nR69erluEBFRERETlOlhXtSUhIA4eHhZdaHh4dz4MCBCrcpLCyksPDkuMOsrCwArFarfYxxTTpxTEcc+5wYxln3u9DPqSZy/+G8DeQU5ZBVmAZHV8O2HRSWFNvbhw4dyuTJkwkICLjg81WVnO5zX0so7zWoFn1XOjt97h1DeXecU3N/vvmvlukgTafc6AOlQ2hOX3fCpEmTGDduXLn1S5YswcvLqzrCOyunjnO+kOXkugIV57Zsv1wWLFhQ/QFVgerM/eJf90H2Tti1GLKPn2yw+EHjfgwYMIC1a9dW2/EvdM7yua9tlPfqVxu/K52dPveOobw7Tnx8PHl553dfTZUW7hEREUDplffIyEj7+uTk5HJX4U947rnnGDlypH05KyuLmJgYevfujZ+fX1WGd1asVivx8fH06tULs9lc48evrHd2rTmrm6t8vL3p2/eKGojo3FV37pOTk2HHWEjaXLahTguodz2YPejbt2+VH9cZONvnvrZQ3mtObfqudHb63DuG8u44p+Y+Pz//vPZVpYV7bGwsERERxMfH06ZNGwCKiopYuXIlr732WoXbWCwWLBZLufVms9mhHyxHH/+sneEvGRX1c4rzoepzX1BQwLvvvsvEiRPhr6FYAPiFQtNuhEVdSsPIcGa+eKPT5Ki6OM3nvpZR3mtALfyudHb63DuG8u44ZrOZ4uLif+74NypduOfk5LBnzx77ckJCAps3byYoKIi6desyYsQIJk6cSFxcHHFxcUycOBEvLy8GDRp0XoGKVJbNZmPWrFk899xzHDx40L7e08sH72bXkurVFEwuhAUE8sawXtSPDHJgtCIiIiJ/r9KF+6+//kr37t3tyyeGuQwZMoTp06fzzDPPkJ+fzyOPPGJ/ANOSJUs0h7vUGMMw+Omnn3jhhRfYsGGDfb2Liwv33nsv48ePJyG1iE6P/heA78YNJC4mxFHhioiIiJyVShfu3bp1w/ibu/NNJhNjx45l7Nix5xOXnKVwv/LDjM6nn7Nbvnw5L730EmvWrCmz/tprr2Xy5Mm0bNkSgPBwMJaPcUSIIuIA5b4DDYOc3Fx8vL3LPTlVRORCVS2zykjNuVgfzX3qTEWGYbBy5UrGjh3LypUry/Rr2bIlb7zxRplnC4jIxef070qr1cqCBQvo2/cKjfcVEaehwl2cxsrN+5nw+WriN+4DYNTtHWkbmMWbb77B//73vzJ9mzZtypgxYxg4cCAuLi6OCFdERESkSqlwF6dw4FgGT7y3iOTMDDClwdEdvPnUexTnpJbp17hxY8aMGcNtt92Gq6urY4IVERERqQYq3MUpvDpzDceO7id552I49CdYCzl1QqXWrVvzzDPPcOutt+Lmpo+1iIiI1D6qcOSCVlxczI8//siHrzwJ6XvLdwhoAHU7s2nTp2d8Oq+IiIhIbaDCXS44hmGwadMmPv30U2bOnFn6xNNTuZigTgxEdwT3pmAyqWgXERGRWk+Fu1wwjhw5wnfffcfzzz/P9u3by7W7eQdhqtcKa2QsuHsS5B5KeEAo344d6IBoRURERGqWCnepViUlNo6kZePjYSbIz6tc+86dO5k3bx5z585l/fr15Z4R4O7uTr9+/RgyZCg/7rSxeOM+9ielQL4Lfv4BPDmwE83qh9XU6YiIiIg4jAp3qTZT5m5gyrwNbNufAsAzt3dmwn3d+fXXX+3F+o4dOyrctkuXLtx9993ceuutBAYGAtC3r43/fP8rw99dCMCrD/bk1m7Na+ZkRERERBxMhbtUi4W/7Obtb9eTkX8c3FIgNZEpry9myqjbyck8XuE2zZo1o2XLlowZM4amTZuWa3d1deGRAZfzyIDLqzt8ERERkQuOCnepFpM/X0rK7jVkHfoNkvdDSTE5p/UxmUx06dKFAQMG0L9/f+rVq8eCBQto1KiRI0IWERERuaCpcJcqc+jQIebNm8e8efNYsXQZGLbynVzcILAhn0x+huuvv56wsJPj061Waw1GKyIiIuJcVLhXoZISG7kFVnILisgtsFJYVIzJZMLVxYTF3Q0fT3cCfTxwdXVxdKhVwjAM/vjjD+bOncu8efPYuHFjxR3dzRBWH4IvAb+W4OrOvffeW6OxioiIiDg7Fe7nqaTExrH0XI6kZpGcnovtr1lRiotLsFqLwGTC1cUVNzc3XFxMuJhMBPp6EhrgRUyYPx7uzvUWFBcX8/PPP9tvLk1ISKiwX2BIBCVBjbGG1CHf1w8wE+lTh8uaxPDxU/1qNmgRERGRWsC5qsYLSHGJjd2H09iflEFxiY2cnByOHz9OTk4OBQWFFBeXH/bh6emJn58faX5+JKf7setQGjFh/jSKDsLLw+yAsyiruNjGe3N/4V/vLwFgxrP9ubNnKwoLC1iyZAnz5s3j+++/Jy0trcLt27ZtS//+/RkwYADNmjXnuY+W8u2qP9mfeBwwEVUvgP97rA9hgT41eFYiIiIitYMK93NwJCWL7QdSyC0o4lhSEimpqRQWFGB2c8HP040AP1csZjPufw2JKTEMrMUGOYXFZBxP4dixY7i6uhIeHk6h1crB5EwaRgXSJCYEFxfHPQF01NR4vlv9J1AERXk8OWYyr71wiITtG8nPzy/X39XVlW7dujFgwABuuOEG6tatW6Z98sO96NgsmlvGfgvAFy/eSP2IgBo4ExEREZHaR4V7JRSX2PhtVyLH0nM4fjydgwcPYrUWEeJrJjjIB18PV0ymMxfeobgDUGi1kZxVyLGkRJKSjhEREU5JiY20rHzaNY7E01LzV98X/rKLrxasIXX/Oji6HdKTSMUg9bR+Pj4+XHvttQwYMIC+ffva51iviMlk4uauzTGWa651ERERkfOlwv0sFRQV88v2wxzPymPfvr1kZGQQ4GWmboQPHmbXSu3LYnYhJtiTyAAPkjILSUxMJCsri4aNGrHy9yLaN4ki2L/8U0armmEYbNy4kblz5zLhnY8gN7nijmZvHhg6iAEDBtCjRw88PDyqPTYRERERKUuF+1koKCpm7R+HSM/KZceOHViLCoiL8CbQ+/yujLu5mqgT5EGAlxt7k/P4448/iGvUiF/+NOjUvA6Bvp5VdAYnFRUVsXLlSubOncv8+fM5fPhwxR39PCCkKfhdCv4xTJ06rspjEREREZGzp8L9H9hsBr/uPMrxrBx2/Pkn2Kw0r1P5q+x/x8fDjebRvuxNzmPXrt00btKY//1p4oqWdfH2dP/bbbfvT6b5PR8A8OOkO+jbsXG5PllZWSxatIi5c+eyYMECMjMzK9yXJbgetrB6WEOiwScQLzcvwryjGXdPt/M9RRERERE5Tyrc/8GOg6mkZeaxd88ejBIrzaJ9cHer+nnY3VxNxEV4sSsxl927d+PerDkbdh7lqlb1znjD6oYdR7h7whwwDDAZDH93IXdtP8LL93QjMTGR+fPnM2/ePJYuXVrhw43c3d3p2bMn/fv357rrrmf05xtYtjmBAylHoQhC/CJo3ySaO69uVeXnKyIiIiKVo8L9bySn57L36HEOHz5Ebm4uTaO8/7Fot5bY2LQ/iz8O55CVX4yLyUSDME8ahXvTONILl7+5edXFZKJRuDfbj+SwZ89uLM2bk5CYTsPooHJ9jx3PZtTUn8jIzwbPVMBGyrEk3ns3ns9fe4z9u7ZVeAx/f3+uv/56BgwYwDXXXIOvr6+97cOR1zNm+nJenVl6Rf7a9nG8+kDPWvPAKBERERFnpsL9DAzDYPuBFDIzs0hKSqJusCc+Hn+fruSsQmasPsrR9AIKjSKKbVZcTC7sTbGwbPtx6od4cmvHCCL8LWfch5uriYbhXmw7nE1ycjJmN1eiQ/3KPagp4ua3wLBB3g44vh2S95GbnQdAxmn7jImJsc+vftVVV2E2Vzw2393syqQHejLpgZ7/mB8RERERqVkq3M/gWHou2XmFHDlyGB8PNyICzlxsA+QUFDPlp0Ok5eaTZk3Dais7NMXiasGaHMg7iwq4s3MULWN8z7An8La4EurnzuEjRwgKDmbHwVQubRQBQH5+PkuXLoWd8yF1J1hzK9xHq1atGDBgAP3796dNmzZ/O02liIiIiFz4VLifwZ4jx8nKyiInJ4fGkd5/29cwDL5an0R6XiEpRSmYPDMJa/QH7r7p2KzuFGSEkHWoEccKiggygpi26gj3XhVNi78p3usEeXA8J5ukxCSK8nPZ/PNivp8/n8WLF5ObW3GxTlAUPnVa06r91fz88ZPnc/oiIiIicoFR4V6B3MISbDmFHE1MxMviSoDX30/7uC8ln21Hcki3pmO45RPe/H+4WgoBcHUvwjvsKF7BSRzf05Lko664Fhs8/9VOKM7nqf6XcFXT0HL7TE9L5Y/1a/ht4wYO7N2BraSkXB83swVzWGPy/aMgvA7+fuGEeIdz/81XVk0iREREROSCocK9Aln5xVhsNrKzs6kb9PdDZAC2HsqmxCghvySfwAY77UX7qUyuNrwj95N5KI7ikkJwLwIXM5/9nERhiYmezYNJSEhg/fr1/PLLLyQkJFR4rJCQEG644Qb69+9P167dGfXJSv7z/UYwINgrkD4d4hjcu/V550BERERELiwq3CuQnV+MR042hs2Gn+c/p2hfcj4FJQVgAq+gY2fsl3W4PiaXIrAUAAa45nI88SDTPvmRLzJ2cTwttcLtQsIjuaJHH/718FC6dOmMq+vJOeQ/HHk9j954OYeSM7mkbgixkYGVPl8RERERufCpcD+NYRhkFZRgycrC7OaCp/vfP2ipxGaQlFFIkVGEm0cuLubSm1JtNoN9R9PLdj7uCUW5kJEAOashoRir1Ur5GdYhLi6ODh06ENWoNcF1GtG0aVPatYktU7Sf0CI2jBaxYed6yiIiIiLiBFS4n6agqBibYZCfn4+P5Z+fjmoYUGwzMDBwMRdV3CnPBvuKYNsySDkGtvLj1TG50ObS1nTo0IEOHToQHBwMwOHjBaTmlu43J7/oH5+kKiIiIiK1kwr30xQVlxbVVqsVT/d/nkLRzdWEh9kFF6sLNqs7NpsBQGFaIWzMh31WSCz+q3de2Y3NrhASizmkFT26dGB436bl9m8xu1BUlEeJzUZuQUXX5kVERETkYqDC/TQlJaWFt62kBFeXs3tiqLfFFZd8F2zF7ieHx2wqgJ/zy3e2eENoA4ioC0HRgCcmWxCXNgqvcN9uLiZ7PCU2W6XPR0RERERqBxXup7EZRqW38ba44oILNqsZbK7gUgINzLD6rw5BrqXLDd3Bsz4kXQklblDsjsnwwN3dheZ1fCrc94lwTCYXPURJRERE5CKmwv00nu6lKXF3t1BUfIYx66eJDLCwN6V02shIr0Z4BiVTEmHjwNXFEO0GAaVj5etF+OPqkktRzGpykxqQeywGk9WVMB9vCq0V/8JQYjMwmUy4urrg7vbPY+5FREREpHY6u7EgFxFPixkTYLFYKLBWcBNpBVrG+GJ2MePmYqYgLQoXF1PpMJvmFnvRDuDq4oKLiwkP3zyC4/7ALzoBN0shLi4u5BRWfKzCYhtuZjMmkwl3swp3ERERkYuVCvfTuLiYsJhd8PCwUGi1YZzF0Jm4CC+83F3xcfUmLy2CkqKzm/nFxc2KzSgdt55bUHHhnpVfjK+PLwABPh5neRYiIiIiUttoqEwFPM2u+Pj4cNRmkF1Q8o8PYTK7utChoT9Lt1vJLM4kI6EpwU1+p1GdoL/drrjQA1dT6VV0H4/yV9NLbAa5hSUER/ji4+mOh3vtertun7qOY1mnPGXWMMjJdeWdXWvglPH84X4WZj3YyQER1l7KvYiIiPOp8kpw7NixjBs3rsy68PBwkpKSqvpQ1SbIxw0fH18sFgtpOUVn9fTUKy8JZN2eDAJtQRxPMfAITME77OjfblOUHYjZZAZKx8mfLiu/GMMw8PPzI8Tf69xO5gJ2LKuQhNTc09aaSCnIq7C/VB3lXkRExPlUy1CZ5s2bk5iYaH9t3bq1Og5TbQK8zLi6mggODuZ4jvWsZpoJ8DIz8PIIvF298HL1In1vc6z5Zy62i3J9sOb64unqSUywR4VPaE3MKMTHxwdPDw/CArzP65xERERExLlVS+Hu5uZGRESE/RUaGlodh6k2ri4mIgJ9CAkJxWZAUkbhP28EtKnvx2WxfgSaA3E1PEje0omCjPLDZWwlLhzfdSluLmY8XTxpFeNbrk9WfjE5BcVERUXh62UhLFCFu4iIiMjFrFoGTe/evZuoqCgsFgsdOnRg4sSJNGjQoMK+hYWFFBaeLIyzsrKA0ieXWq01/6TQE8esG+bD0bRsgoNDOJxyjABPF9zd/vn3nBvahHAgNR8jM4w0axopf3TAK+wwHkHJmD1zKCn0JPNgY6y5voS7BxHu507nhr4UFxfb92EYBgdS8rBYLPj4+FIvrGx7rXG2c+YbhkM+C7Wacn9BOJFb5bjmKfeOo9w7hvLuOKfm/nzzbzLOZtqUSli4cCF5eXk0btyYY8eOMX78eHbs2MG2bdsIDg4u17+iMfEAM2fOxMvLseO696fmk5Sez/79B/B0LSbS5+xSVVgMyw+6cjTbRIGpgHzyKeHkrDFuuOFj+GBxcaNfo2KCPMtun5YPxwtcqBMdTYCfD61ifGrlw5fGb3IlpeCfzyvUw+DFNmc3NaecHeVeRESk5uXl5TFo0CAyMzPx8/Or9PZVXrifLjc3l4YNG/LMM88wcuTIcu0VXXGPiYkhNTX1nE7ofFmtVuLj4+nVqxcGLizfvJ9jyans3buXmCALERXcRFoRm2GwdncmC7ekUlRsUGyUUGIU42JywWwyE+Jr5q7OEUQHlp3iMSu/mJ2JeURHRxEdHU3HZtEE+9W+G1MBer+zhoS0f74ZMjbYiyUjrqiBiC4eyv2F4dTvG7PZ7OhwLirKveMo946hvDvOqbnPz88nJCTknAv3ap9f0Nvbm5YtW7J79+4K2y0WCxZL+WLYbDY79IN14vhtG0ezERNFRYUcPXoUi8VMqO/ZzdPerVkIHRoFkpCSz+5jeeTkF+Pp7krDcC+aR/vg5lr2imdOQTEJqYUEBgYQExND03qhRAT7V8fpXRjO9q8IJpO+ZKqacn9BcfT33cVMuXcc5d4xlHfHMZvN5z30udoL98LCQv7880+uvPLK6j5UtYgK8SUnPwQAa3ExCcnJFBXbiAqwnNXwFU93V5pF+9As2udv+2XkWdl7LA9PL28aNYojLNCHRtF/Pw+8iIiIiFw8qrxwf+qpp+jXrx9169YlOTmZ8ePHk5WVxZAhQ6r6UDWmcUwwRcWl43zdze4cPXqE7PxiGoZ5YT6LG1b/TonN4Eh6Accyi/D396dhw4aEBfpyWZOoWjmuXURERETOTZUX7ocPH+aOO+4gNTWV0NBQOnbsyPr166lXr15VH6pGNa8fisXsislkwtfPl71797LlUDbh/hbC/d0xu1augDcMg7QcK4eOF1BiMxEdHU1kZCRRIX60aRSBayX354zC/U4bImUY5OTm4uPtXe7pnVK1lHsRERHnU+WF+6xZs6p6lxcEk8lEXJ1ggnw9+W13Ip6eLUhMTORYcjJJGYUE+5oJ8DLj6+FWbuz6CYZhkFtYQlqOleM5VqwlNoKCgompG4OnxULjmGAaRQddNFfaZz3Yqcyy1WplwYIF9O17hcbfVTPlXkRExPlU+xj32ibY34uurevz54EULGYzUZFRJB1LIi01lZSs0kfIe7m74u7mgqurCRcTWIsNCqw2CottGIaB2d2d4NAwgoND8Pb2IiLIh+b1w/DyUMEkIiIiIhVT4X4O3M2utG4UQeOYYPYeTcfd7Ead6GgKi4rIysoiJzsbq9VKYUkJ2AxczW4E+HlgsVjw9PLC18cHVxcXwoN8qBfuT2iAnooqIiIiIn9Phft58LSYaREbRpOYYI5n5ZOamUdqpi9ZeYXl+rqYTHh7uuPj6U54oDcRQT6Y3VwdELWIiIiIOCMV7lXA7OZKeJAP4UGlUz4ahkGRtQRrSenQGDdXFzzc3S6asesiIiIiUvVUuFcDk8mExd0NzcchIiIiIlWl9s85KCIiIiJSC6hwFxERERFxAircRUREREScgAp3EREREREnoMJdRERERMQJqHAXEREREXECKtxFRERERJyACncRERERESegwl1ERERExAmocBcRERERcQIq3EVEREREnIAKdxERERERJ6DCXURERETECahwFxERERFxAircRUREREScgAp3EREREREnoMJdRERERMQJqHAXEREREXECKtxFRERERJyACncRERERESegwl1ERERExAmocBcRERERcQIq3EVEREREnIAKdxERERERJ6DCXURERETECahwFxERERFxAircRUREREScgJujAzidYRgAZGVlOeT4VquVvLw8srKyMJvNDonhYqXcO45y7xjKu+Mo946j3DuG8u44p+Y+Pz8fOFnvVtYFV7hnZ2cDEBMT4+BIRERERESqXnZ2Nv7+/pXezmSca8lfTWw2G0ePHsXX1xeTyVTjx8/KyiImJoZDhw7h5+dX48e/mCn3jqPcO4by7jjKveMo946hvDvOqbn39fUlOzubqKgoXFwqP2L9grvi7uLiQp06dRwdBn5+fvpgO4hy7zjKvWMo746j3DuOcu8YyrvjnMj9uVxpP0E3p4qIiIiIOAEV7iIiIiIiTkCF+2ksFgtjxozBYrE4OpSLjnLvOMq9YyjvjqPcO45y7xjKu+NUZe4vuJtTRURERESkPF1xFxERERFxAircRUREREScgAp3EREREREnoMJdRERERMQJqHA/zZQpU4iNjcXDw4N27dqxevVqR4dU66xatYp+/foRFRWFyWRi7ty5ZdoNw2Ds2LFERUXh6elJt27d2LZtm2OCrUUmTZpE+/bt8fX1JSwsjAEDBrBz584yfZT7qvfBBx/QqlUr+4M3OnXqxMKFC+3tynnNmTRpEiaTiREjRtjXKf/VY+zYsZhMpjKviIgIe7vyXn2OHDnCXXfdRXBwMF5eXlx66aVs3LjR3q7cV4/69euX+8ybTCaGDx8OVF3eVbif4quvvmLEiBG88MILbNq0iSuvvJI+ffpw8OBBR4dWq+Tm5tK6dWvee++9CtsnT57MW2+9xXvvvceGDRuIiIigV69eZGdn13CktcvKlSsZPnw469evJz4+nuLiYnr37k1ubq69j3Jf9erUqcOrr77Kr7/+yq+//kqPHj3o37+//QtbOa8ZGzZsYOrUqbRq1arMeuW/+jRv3pzExET7a+vWrfY25b16pKen06VLF8xmMwsXLmT79u28+eabBAQE2Pso99Vjw4YNZT7v8fHxAAwcOBCowrwbYnf55ZcbDz/8cJl1l1xyifHss886KKLaDzDmzJljX7bZbEZERITx6quv2tcVFBQY/v7+xocffuiACGuv5ORkAzBWrlxpGIZyX5MCAwONjz/+WDmvIdnZ2UZcXJwRHx9vdO3a1XjiiScMw9BnvjqNGTPGaN26dYVtynv1GTVqlHHFFVecsV25rzlPPPGE0bBhQ8Nms1Vp3nXF/S9FRUVs3LiR3r17l1nfu3dv1q5d66CoLj4JCQkkJSWVeR8sFgtdu3bV+1DFMjMzAQgKCgKU+5pQUlLCrFmzyM3NpVOnTsp5DRk+fDjXXXcdPXv2LLNe+a9eu3fvJioqitjYWG6//Xb27dsHKO/Vaf78+Vx22WUMHDiQsLAw2rRpw0cffWRvV+5rRlFREZ9//jn33nsvJpOpSvOuwv0vqamplJSUEB4eXmZ9eHg4SUlJDorq4nMi13ofqpdhGIwcOZIrrriCFi1aAMp9ddq6dSs+Pj5YLBYefvhh5syZQ7NmzZTzGjBr1iw2btzIpEmTyrUp/9WnQ4cOfPrppyxevJiPPvqIpKQkOnfuTFpamvJejfbt28cHH3xAXFwcixcv5uGHH+bxxx/n008/BfSZrylz584lIyODoUOHAlWbd7cqibAWMZlMZZYNwyi3Tqqf3ofq9eijj7JlyxbWrFlTrk25r3pNmjRh8+bNZGRkMHv2bIYMGcLKlSvt7cp59Th06BBPPPEES5YswcPD44z9lP+q16dPH/u/W7ZsSadOnWjYsCEzZsygY8eOgPJeHWw2G5dddhkTJ04EoE2bNmzbto0PPviAwYMH2/sp99Xrk08+oU+fPkRFRZVZXxV51xX3v4SEhODq6lruN5/k5ORyvyFJ9Tkx64Deh+rz2GOPMX/+fJYvX06dOnXs65X76uPu7k6jRo247LLLmDRpEq1bt+bdd99VzqvZxo0bSU5Opl27dri5ueHm5sbKlSv5v//7P9zc3Ow5Vv6rn7e3Ny1btmT37t363FejyMhImjVrVmZd06ZN7ZNsKPfV78CBA/z000/cf//99nVVmXcV7n9xd3enXbt29ruAT4iPj6dz584OiuriExsbS0RERJn3oaioiJUrV+p9OE+GYfDoo4/y3XffsWzZMmJjY8u0K/c1xzAMCgsLlfNqdvXVV7N161Y2b95sf1122WXceeedbN68mQYNGij/NaSwsJA///yTyMhIfe6rUZcuXcpN87tr1y7q1asH6Hu+JkybNo2wsDCuu+46+7oqzXuV3DpbS8yaNcswm83GJ598Ymzfvt0YMWKE4e3tbezfv9/RodUq2dnZxqZNm4xNmzYZgPHWW28ZmzZtMg4cOGAYhmG8+uqrhr+/v/Hdd98ZW7duNe644w4jMjLSyMrKcnDkzm3YsGGGv7+/sWLFCiMxMdH+ysvLs/dR7qvec889Z6xatcpISEgwtmzZYjz//POGi4uLsWTJEsMwlPOaduqsMoah/FeXJ5980lixYoWxb98+Y/369cb1119v+Pr62n+eKu/V43//+5/h5uZmTJgwwdi9e7fxxRdfGF5eXsbnn39u76PcV5+SkhKjbt26xqhRo8q1VVXeVbif5v333zfq1atnuLu7G23btrVPlSdVZ/ny5QZQ7jVkyBDDMEqnqxozZowRERFhWCwW46qrrjK2bt3q2KBrgYpyDhjTpk2z91Huq969995r/04JDQ01rr76anvRbhjKeU07vXBX/qvHbbfdZkRGRhpms9mIiooybrrpJmPbtm32duW9+nz//fdGixYtDIvFYlxyySXG1KlTy7Qr99Vn8eLFBmDs3LmzXFtV5d1kGIZxHn8REBERERGRGqAx7iIiIiIiTkCFu4iIiIiIE1DhLiIiIiLiBFS4i4iIiIg4ARXuIiIiIiJOQIW7iIiIiIgTUOEuIiIiIuIEVLiLiIiIiDgBFe4iIiIiIk5AhbuIiIiIiBNQ4S4iIiIi4gRUuIuIiIiIOIH/B3tPE4wG2agIAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "final covariance [0.0013 0.0043 0.0004]\n" ] } ], "source": [ "ukf = run_localization(\n", " cmds, landmarks, sigma_vel=0.1, sigma_steer=np.radians(1),\n", " sigma_range=0.3, sigma_bearing=0.1, step=1,\n", " ellipse_step=20)\n", "print('final covariance', ukf.P.diagonal())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The uncertainty becomes very small very quickly. The covariance ellipses are displaying the $6\\sigma$ covariance, yet the ellipses are so small they are hard to see. We can incorporate more error into the answer by only supplying two landmarks near the start point. When we run this filter the errors increase as the robot gets further away from these landmarks." ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "final covariance [0.0026 0.0657 0.0008]\n" ] } ], "source": [ "ukf = run_localization(\n", " cmds, landmarks[0:2], sigma_vel=0.1, sigma_steer=np.radians(1),\n", " sigma_range=0.3, sigma_bearing=0.1, step=1,\n", " ellipse_step=20)\n", "print('final covariance', ukf.P.diagonal())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Discussion\n", "\n", "Your impression of this chapter probably depends on how many nonlinear Kalman filters you have implemented in the past. If this is your first exposure perhaps the computation of $2n+1$ sigma points and the subsequent writing of the $f(x)$ and $h(x)$ function struck you as a bit finicky. Indeed, I spent more time than I'd care to admit getting everything working because of the need to handle the modular math of angles. On the other hand, if you have implemented an extended Kalman filter (EKF) perhaps you are bouncing gleefully in your seat. There is a small amount of tedium in writing the functions for the UKF, but the concepts are very basic. The EKF for the same problem requires some fairly difficult mathematics. For many problems we cannot find a closed form solution for the equations of the EKF, and we must retreat to some sort of iterated solution.\n", "\n", "The advantage of the UKF over the EKF is not only the relative ease of implementation. It is somewhat premature to discuss this because you haven't learned the EKF yet, but the EKF linearizes the problem at one point and passes that point through a linear Kalman filter. In contrast, the UKF takes $2n+1$ samples. Therefore the UKF is often more accurate than the EKF, especially when the problem is highly nonlinear. While it is not true that the UKF is guaranteed to always outperform the EKF, in practice it has been shown to perform at least as well, and usually much better than the EKF. \n", "\n", "Hence my recommendation is to always start by implementing the UKF. If your filter has real world consequences if it diverges (people die, lots of money lost, power plant blows up) of course you will have to engage in sophisticated analysis and experimentation to choose the best filter. That is beyond the scope of this book, and you should be going to graduate school to learn this theory. \n", "\n", "Finally, I have spoken of the UKF as *the* way to perform sigma point filters. This is not true. The specific version I chose is Julier's scaled unscented filter as parameterized by Van der Merwe in his 2004 dissertation. If you search for Julier, Van der Merwe, Uhlmann, and Wan you will find a family of similar sigma point filters that they developed. Each technique uses a different way of choosing and weighting the sigma points. But the choices don't stop there. For example, the SVD Kalman filter uses singular value decomposition (SVD) to find the approximate mean and covariance of the probability distribution. Think of this chapter as an introduction to the sigma point filters, rather than a definitive treatment of how they work." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "- [1] Rudolph Van der Merwe. \"Sigma-Point Kalman Filters for Probabilistic Inference in Dynamic State-Space Models\" dissertation (2004).\n", "\n", "- [2] Simon J. Julier. \"The Scaled Unscented Transformation\". Proceedings of the American Control Conference 6. IEEE. (2002)\n", "\n", "- [1] http://www.esdradar.com/brochures/Compact%20Tracking%2037250X.pdf\n", "\n", "- [2] Julier, Simon J.; Uhlmann, Jeffrey \"A New Extension of the Kalman Filter to Nonlinear Systems\". Proc. SPIE 3068, Signal Processing, Sensor Fusion, and Target Recognition VI, 182 (July 28, 1997)\n", "\n", "- [3] Cholesky decomposition. Wikipedia. http://en.wikipedia.org/wiki/Cholesky_decomposition" ] } ], "metadata": { "anaconda-cloud": {}, "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": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 4 }