{ "cells": [ { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAASwAAAHMCAYAAABvOZX3AAAABmJLR0QA/wD/AP+gvaeTAAAACXBIWXMAAB2HAAAdhwGP5fFlAACAAElEQVR42qz9d7xlx3EfiH/r3DtvcsIgDNIgExmMAAEGgVESkyQqkgoWLcuWLK1lW07rdVzv57f+2XK2dy3ZCqYCLVGiRDFHEYQYkUgiY5AGcZBmMDm89+6p/eN0d32rus99D9q95ODde06f7urqCt+qDkd+9Ef+lUIVACCqAAQKBVQBHX5huJ2+KyACdc8AogCGJwFVCPyzwHCNf/PzgAI9/CffE031p3rKZXtAyn+10CF0pdADelbTc2J1SH5WPSm5LwK4+ks/XD2ZQKH+SaFdRSBQiKZ6pDxa+i18IY2DlF725Zvvk/p6RCEqhU4RGq/QpkCGNksd9F8xXuYx6ajDIsSD9KXjcSH+FjlIny7yjMvRwyq+DBz99KxY/5gmoXES8f0XUSoX22cOcfvq6jZS29cz70TydZN/K2O61FFfkGRFqG0I0CnzrG/wEJA+tSVJpjNftA+8Sc+qyXnn6lP7q8RLEI1UvnP6qkURrR8KNg+SlF96GlfVQnP+24E6XVS9GCgeLqpd1f2VzEQaJDNOVH8wAmBjRfeUmEJVZwKDSXIV2n+LzSUGMUkaHtNAhtgN7rtWDwYJ4R+uaIN/zY8Nbv7XUkymRkN/TFaEe232nwsFWbVrahW733FstdzT8NvkhDmTpUMCK+JY2vhpkI98s9xrjIgS/1oVO/JUoCokW2HI1CTON2TcVX64KV/M6JokyWNNTtGVEz+W7AhqHkcpkcHiQ1EJywg9QTTcNcFf4OP6grEfK36mSLw0q+atqEdZrBXqLGEkrOpYHG1tfU/sJcUqTItGVE2EBDVjRcbaY0Z5s1eQlaC6nh8RV5WE+hVMjau3fPdCK/S4ZC9U8UzjBddWLbeaBDR5aapTJBoKj5wqbuZ+SWwDTSSYqyjU5TK52yLOgZSmRb1hLoPf8J6BNi1oSTwvHau4X6EzDA2TMpSS1Rg0iAkyw33OtJVmtNXuUCcjFs3frXONvrc+Qk66SWbDXgWEnH+UMWM+hPr/whZs5U81hACmxVhFD0AD1fTM5XvDawQEoaopRIjIyZ5V+p0Nh7qK5xtIviDN79YHob4KS1sSfvRtY9Py8vVN87Qq1QMVMUUwc3VaSVMpk/lRQgVt1+8MkIaBdwpoAe4oigtWuzwl9bg3MNJgKFihtfdmo/IK0axkLzGOZsWE2Fci1jd1pAyhsnmLBhERJDt7NdTZJ5npyv1ohBPpbFCDDrTGr7pWgYVQpJDvR1HC7erDNlzD7xGy5tmmzOP2s9Ls91iTvv9W6bSNjtS8QmYWGxCHuhqMDfUUrxOYn41URYIboKSE5r6MO9EgNaWrNRJRaDxy5Muc+2jW3UCUxQDU+mMXZVxuVY1mCc+Jb9Zwoo4Jk7Z1nXlZcYskj5xI5IAz6gZO6vZjrq1uEIaUzFLkep19Zm+/YkjEFzXRJ96QEX8dQnKVSeGLOdM0Hi3IQuMUILkHTFqqh+nEwC3OI0LHPOjYMLbNgITrFTgaUYlYXcV2RZ2HzbW3SHF64XNfjRrcp4SERflDfooC+fK7IiwYqlGD4x5T18woHYxBVB0C8XWyYVHkJGkxuAGv+Txb5npjJApbQ3vVII6PSi0msbnWs0GwaPQMJfgxaA1wi2QGFhKeMUdV86sJ1fKNjFCVLFcJcfsGZUy7UN/UteXdBfWTNVXM5HRW0oFAZxiiDxMtPLWpDddkYB51PXgDRz/nLavum1yLq3c8pAPVa6F1VWXtOQhe5gmfUWwzSm/dTPt6RpHjhXyIudrPUGHnjA0nSRUD5nWhom9Fc/KSqvDZzvSP6igWmZmT2i6zKq4Zl8kqDzSjLdYhqJMXri0/78OjRJdayKghTHa94AQ04LHwCPQNlTT6FcpoKKIDTRIT+IFfWrPL1ePs3DzPGT8NclWNruxwiiiV8mJ0unDct8YIVfNsVRahBi2liZRBj4aXvwmkqksb/HBMImdXyTnzu+pvrrtO/NWzzw3HSXydNzBaP1b/pdIq/gGbzCIMPy9fJlx9mPAI8mbjMlafC5JbA9e80Y3cbQusjN+rPIXOMdFUHf8rzwka0+48GKFXjllaOxj2WVloR/vCUiyVkrYQDDtTrQS+VpBCirb+NfimroGioK2QMs6aNTUdlg/Lhll51k3b/TRj3eBEg0e+30KCbKPiu2h9NMxkVqadOoCrN/OmHk/v8v2MKMoyHfax3hD5xpXKNOtsfbgJ9QXJNpYf2WgV59pyQiMfoYZc3R6sUn3j49kmsnXPljuNMcBLXu266k7457uxigG4dTBcAyfzXGKP3Yd7rGCn0Y5YWV9HqMaVL53Nc8GSCsnwI3pZe1aKUghLEQvQSG6ihhi5BU3orB54aQhbjWwinIJpReXTQ+Nq7cQwEWN1N0SlNCV+2r/0w2C0GUyHAIkWp9VmEKECqEB78XyIhoEnZOi6ht8eaXreed3J8ECqIRzEpxGgB8PsDZQ0yzhPGBjI66zMoBC/Wp/Urca0gIWkxRi3a+GeidZ1u4431EGq2gy1lnpkXL/d0hV2Di/hk2ufRitvNiGudGLPG5W2MtflSc5LqRN4HoEADN1XpeKZ4Rbn5+rqhF+mogVLG4aByJKc/6pZD85x5IRhe+Y9JJsdaogRZMFpKwybzXgx10q+SbxgN8U3Tbkb2pNyrdTI0qo2mn5GOX+qbKsfX5+7h9MCDcn6MfjK4yRS3Uo2Fl4gfC6llI/rDHj6MHSn1Btoq3g7Oo0eWMK5G+pAQbVi1UgxYtLmC0g/ackGp+lizpt1t9EtGhQ/7lVXCsto0SvL00jc4kVsPoSJT+epiClbb2FBjQ05o0AS3xwfz8Aoq/6GmldqICjVtBra2R31hNWjaX+dZJPxkLFBm8/M7Mcq+1z6pG7cc331GDTcfINRpgs1OqoVmun3giP8hceyLA5tCVqgnBWfe1cQSnB+df6dNEqozxJEI3c6aI0Cw4yZONryL15DZzmtCGUZkRAPsgjyPQlDEg1cEBLH0zLLCi9/DSRSJfljvWyEHUsIjUqjvpbY1WS3CzU+EvSw5dDh2Ecy4WzLSs55/P60NalQPdMAVDWAZuWYY8wat8bCsiJ0I3TMBySV1fCeuMnweYw0Ilz+wZFrkN93Nqm4qONSRJUyDypnZQxjlafYBaTEzcWPadmAitvmYoA3VBxRY8Wa6NgI8YpfxuB8+jxHU6EOb9SE+mezhIS2s6cX37Yw7xraHG1idYPHW8SjJB6IaATLAFHihO1nnC5ryrmWca23XjFw0BFLZANX+u/GdiVU77vk2FehTkcyVKLjz/SuZKzGr061JYSU/OTwyYUfMFnyMJeSfNEQzRH4mtyAKHR1DC4OsHID6gSCvRSLrkFb9uBKz5HJaSBSlDqJ5gCxvQJ7JCrWUFUj2xS3MkitTeZfy7jlQWuBs/ZU8zwkjWGanJDNeKjkh8IvPPeaOoxhC/dGgtOY8RCLhvCw0dESZhnvh21MRlhBkSU1IsTnEBLRkLWiY0OMLfqJxdJWVx8yRwMXUEwAf/xsvKbpxmj+jOlk9Fo+q0ljRN6v/kaLF9O6iLM+Vb3+KluAAINDmVjbeKRrZaMzrCmKg+eNQNW3oJFVLogqM280stF5lKZGx9QXHn1+jgEsgh9yX0I1RAjeAExGf2mbYc248CmkbPMBDDTwbgUzzlo3xH2NeavK61FhRlkNhc2TIz5MFdeXOkembYZUnGqgMGcMY3xtVcecnIRmyoLT2FyMVMWYOLDJt1nJ34hczgsTR6S44oK4v2Lh/pi6hVqyoV8NcBmjsGPM7yeaZbQPJlq0IjfDmqr9YahkpI65PHRtrdCbKgSp72deRS+xmp0SClOLIquECFY98REIMK/HN2gcXPkW/rS8xtiSBseeXF+ZwZOKpnzbV6XO7rbqKksKQsFqlrQn2spzuQ0JNDAyNuRf+ttYk2ZLS+LAjOQeucOu/sAD8ayrxsLZaakraDQdNaE9s4lm6Xat7RLNlHMp3lD0MW+HAVVzn91adQOi7ejvJQCy1oNToGXtQ6DLVt0pWzAnYTtHgZshWVkgNiOWVrvEkCrRzTQ4ugJsClPdMRFe4HLThaprJ+64i4lmfy9/cabF+ON2BPP9kCOLI11YG2KK4AYtHFTjuXP9FhC7PDhsqBkt5O06LaDTYoDx13JrtvJcKJEc+gctW2PGxrtaKc0QOax+57qb41VQGvyMIOcU6H4UNXX5uoYbdsMU2g4JoVGg56410PqcTx09NCttPDFSVNo3Vkzkx0eDbqzYBAbn1hVL6JCQl4b6EA9DHO0mS4FiNF7KJGapRUlZmiWIrrQISUAGOPwzE5QFWEtD6pa+j3kqLf1xSikWPrJQxjSMuhtUF3wuRFrthn6b8DZccBmCrI15d1ojC8ggZQw5hMKqc0Y/6q6SscqTD2P8ba7GpMsa86OEpCritTYUjeU3fJQRA8aKAOOoffKRSmMQm0PiFrSbg54yRboaHs9Bc/ONVcs8qb8p8Y7Wyf9WuyOTGy/l0ypfclg2G89GSxsKRMo259rAKPaz2h603Dmt12p50OAP/mJhVbAqSiU8/n6qk9wkb2ZtsmveffVYItNboUbHxyBxpb+EAbRuj7Efg9lx4ZGq77x9humNC1nZsFcIhIfBoVAbT4fQGJaNQLSoWBpqbwJgIspxLyEft75MOYfSgibqichDI+YAs0w3nhwBHo6Lda6y7O+L0YrMrTguLwhJST8rSgPaaAEcvbiclzbqnjteY3I4UsHox3i2QtLdlMdoJdHNSNtxioxOhKulhMItMUJDXmkVszdKGNESr/DOWLW6r9q6GHteysaEaUV3EzWTwCsZW1ttSWyrN5Ab/9oDWwlIKsqhKofNPgldH3Pn7zexFw+NtxGhZD7upiSJW0ORlSi2o0QPT+81x98MkQ+HKsjBHjgzKowVPe3y2BTCtlkSDERok+mICFsZdZsbFtUSWvK6tebAcyqlFWo2WZGhyHhX4mdu/1fxsfDfZbpX/zx/pxOOwyyhVn/GI1o2cOMHhrUXJHo5snFnwQfVj8LwWik9goqobB7ubh0DU+fhar6I1niLj+HJZZpTKKrt70R/7fxNAbwgeV8ZAYI/DC5XEbingWfRM1O3KgRVk1eAQx7EygvPOSOs7IqQ6o6jt7oWapKR+iu2Fn4I9atltIOBjIaqSQ3c+LI823iRKmceNlbyEzRM/x9bihByryLpZJpxGD6OjML9KjR8KZ/M6XpBc7Nog67Ml6kvSGt32OMzoqr0WMNfP1gu6adRgWI4x7jVew2HACisKWUrw8CsbW+IHh5llEahg6sb7nptFMeQXWZ2rqYeDU+XXzpQqZQjgEOhmifiTJMt6zQHH7cUOQhUjwEHEbVldDyoloQI1UCdKb2T2EzYFp2cIsTzsLnmiuqZ79EjGhOrs9QvLqQq0EcjWsq8ErRnA9qtF52gbH6cj6kfYJ552SsnnQY+eGlY7Yf1Ys4nyGPr9iqbcpGwu01yOHUei0pWoZ+Tq2CcxgwNN18hC3tmbkpefe6qPtIiV8JRuQl1e+y1CXzi9peiUPldF4w+HN0egVXITpmf6opUYY0zRsNz4hBnPJuriUNGrxfZGAM6zmBIc1ycMfYMNDEPdpzpYoOGhmFT+i8j7IL0Sk7NaXEjClXqQzZEdcGC9oVxaUD/rTxR88MS541XFXa3FmEHumqdY8fJwVYDmowAq4atG6G/gfTg0xCNR8gpAu1TW4yBNRnzc15TZpwrF8q3jVX6Tgfct/hQQiiNiXPU7QIQbRChrbKti+qMT3vQG98jOaplDyNdbNPDFwKyaxaOCJHrDsoQz4DPY8Ei41Fq/uMVk/falWdcpp0Ok4vEthSUpJ7TRc1cWGW8WDut324TcB4eqcfYJ4rDoXsNS1wQEzgkjRjfO1ZvrNhSkqWu5Mf6NYK53bPGggaDq0vzYFeiuYo7qU91aLDCh/LX6ZfMMYSjS0byeLe8RObTCvTwrofpmD9oNVzCAbpYhIZXFoNzUl7hatLjJtW28WjlHdkfsgI3Nwq7rz5EzM4+FvTwvGU42kbP+emYC2NU6fYQlc5W4HVwVJwo18oj23epUhlO8MaEtjEt3wphTVgb0qIY2V5C4WcwQA7xuTTVyBjO47XrpBBqog6PQkxPPxsrMywVrGSu27iWvjZIFrhwMiJ7Q3sNHqZv5Qz5UEhJqL2+rHCK6dhnFIVlfas72HwkCEV2No6dc4jzISH3qzBsDCmt2I8GLEcdmjmlz3ghePw5dfrrWYHZ+0kR+rgNt4LQjaFw7cVV2+FWE8JTqIPcO4LTXIFDJdpQwFyveitUp9g9Gpg3RnEM8m9BbEOayydYKRVa3i04XCjx2hy+UrjN9oQnAIRQuYdv1T5jz/x2B2tEKtVzNk6SDJW0DXxE3ZIdEFbH+7HxIL0eO/7bWFHFDuO8WalpZyBb6LgGBbFs0w82Y+r4maeL9adzKawAIpTrDNQ4Bw60XIKnqfGTQXmuI29/GO40zV9bIsSuVY6QajNDVjN9LvNdrzOz7J8jKcJWbbelfK1Js8B1rCKFBi1eymSOD0MpaAuH60aUKi4nk2qjmviMI4i6yIswizejA/6qf4y4agVp/uDUAyl7o+uJxFh3prklG41IoLHvRZtPwxCqK5BOXxv3oaPX1dUr88tH2vxAzY2wWFpbvJ+fefJlRmLmVX26yrT7mpsXihoVy9NoPeI8IYY2GeehdTuJmlqWhgUtgqnlnyenhZXJZMgQdo3ykmWhsuS+Sn+Kg7pOtdSuPoGRjZRX3kZz7dvCtGaBDMZAfDtcwhpohYotOqwufmPxcMH/1up6/m4U2HqkSNGYYWNkOFf9rB7xuU7PyEBP+R770eKPNtyMt2Yv6SUMbpw4IKf25wntCnekOqGXCynmghHMSY+NObKaHeEzzpxO3Tu76+4UxkgSykYZZqwTnWK0vNhVx6myDXJtJJEQqVtkoyBWgQqbrDGREUebI0SZdvrS0rEmS/3AZDKbK+Ub8t7CYB4yeVTVRop8X+tbbpDU5ZW8Arepan1Ea2U3+tiY1Eqft9x4JTQT0fTe3C2xeiVbA6cQvna7EYyf1qXahseOD7L+t7kkSm96CsZfMG64HAWMxPKkQJh9m3s0UPg6D23WN0Y+Eos1bMbIZ0VpmlNgGoFVa8B8XVL+O+/Tum85ZnVm2acoeHEZZaBc8jtnRvNftu/jaERSbmIV+ucGMKZoxr0jK2PmEyc8GVvFNVcjoxUiDy8WUZX4HCe70lqDw3mzsfrG7ihQJZarp8sFRgBZunrH13zUtNGMkfVE479LJlRYjvK9YPIUYbbdxqt1xefY6U6ow3ZsGlMiG+bxtf1RX1F5Pbi130Q3sY28VWm0jXkkZJ2bV05XrOovGAW6j1vWYB1vGKVsY+YtOQj5lIFBQePsZiibv4t76/PghZgLAW1p9aXJoMEJ2HsKeSaqQ1IakiC3NIK+e5b4t1G3UUk0pjW5tfEYMQDUKuf/qnVCEVLJeL0eztsaKeHCinp1ezaFOoSADqQ7GjQ0rFQD/aUTGlozZDXOCuua6tv2dMsyOJHKnpTGO/DMk6COQfVK8tWZotWXrBPT46vd5z/fMm6VM3pJdPjclCLoSiunPprwmsOJNAidE6iG4XEVq4/Nzf7o+DNUd023jHgfemN0g3LbGsNE0/vhrObhDmFeO9eJ37CbiRtLWrYNjZFAkL+c2cQ8oQxI0a/WKNpIhuDaPeNfcppOmihjEOIUodNPtbZrZU9iOMmAT3BoRv+BIe0wQMvG9uFePggrGwYlPo3npvi/1rgT2EATylibRW8j70qOtOVAtHqC+2/jGnOnilYNPDzWvK5cUAPI8eJP5aXck1alrmvR0Y4ZDd6xGupY4aNzfr3Uz7S6EtdT0S8HnLVVxjNkrOviagwdCULCsDzLnlcCFI8nzQRxQHXOISdVyEUkhG4jENpPkatvp+qkhidZ6OZ5q3iHykisFxQK1TUYGiMHIRG3SDu3KvluTZF7/Txpn4g5CX/OWB6DbGRZBgIvWnMkTR45qSypSSFl5dCwzow1uF1SnFwnWfAclVUWUryClIZl/nn9pRUdvTe2bk/G6mmF6s0mTOLLC4RjvY26eFjLko6qzuo92vbwvM+c+9MKvbXC84o52rhWlx211WPhcBWa+l6UPLlLOrMXj0MA6FgYqlrnkHprv1oLpeEFX+oT2rZbLw9kQEYjg8Br21YaLbO59Xoyb8iyhEUJ1aLRTaPpyjPa9Mcn5nEobbb2+eRZv6K0Dk4g5vWGujIKniNXzVyWjmgT/cyOLvBZXEVNeDPQqpxzZEPtnYDn6UvJ2gR4G15OEeeAVqqqMlShidH2W6TTtdbYtDc0i2dHiEFbPtcVqAgeJLDjMsq1NSrRFctQe/PKNlcMo8wGVrhjhUEqhqxObFnYFxTGssZ2Lc8eu6WmaidglmcZ3blkcoPnK3x43Vn9SCOMaSQW3VuyC/2BxhDtjk3JN5sSroMaC3LleMT3y5KFfvgnvY2B2P3IT+sj9UdpiYEL9cL4jnz3izf8/SbiR5+QRx+uh5+jaiOmB80xHPmoL2/YZ2yQ4uUG3pZ5z7Xi/gBRCqCQFetx0rVKkCUryKQAmGq4wCGSo1vnKZbx2Dae5y951kfBhkrBXSP/ls4F4kP1/DYUDs59wnZAiNELeljPxkfpunmlxiJQG7Em+uIwoLaZYwGIR11+PX4l4rA4LiK3RuyUL9VOr0aaNMZ+JbMPX40fibbEM1tRQteRw+toDKJAWljYTrS3+pVzj56rRTay4UhhZzlLieSltVFFeAxKlMn0CtHJmrACJHQz2DS6VZQR0G1jb2Fs2dHaKDsnwpxzI/BgtD8oUcaofANQlZrTI3Wzxo6ROK2hsPhH1cTK8SICHwfBPbzMIVGEgawQzhDoHMEOtBUjERPxVHnxC0qCnbdUaDAWqm68fcjmjYyVbWWP1Pd/9EM0KiCtWLk1MxsMsh0/bOPBetdyhPEcq9ZYxpBrUOzaSDpsTItAhcYi5vtszL0BbfXBh13qiK4Rtn3XNOXnFuc2jE50oKU5kpHWKOdL0iChrXg2u9fcd9mMlYKBbH20fcHRUIkR33WCbX6wtd+19IPHov2p+TEf1Y9wuDxvr6rXmlGDdTQjUZYCOMWPDam7HhGN57nnYOvlA0Wgg9IaXRFR5XqysTUjyKKYE8MF6jZkwS8S5Q3Tuc2xqWWl9nwyhf1sXITKCWi7J3Xd4XollMFRdq3nxgBMqSPtz0zWQCXt43KHNWVEQ5WFMK1GVspNGBLP/WZCmOSwUc9FpaW8kDES+xsdoAZjof5xh6KUTsPPeaxEQH4xR53DCpzlkzBiuZajkDmGqfXRVV6b+1kZlmVcmqnjXHTL4A+/Godk/gUJFVVeOGqDHFMUFVx10BXIc+Dzz7VCGNDa0OSksaU+xjwNJ72DkktGThrqCHUVY1VV3W7TGSuPqzh0DSz2YQazQetBzkjRsysgyshDEOLhs7Lc7oAWMmuYwvRcVk4+IUJsgAJflAxVvt42WCEoSghmTGBX0sIW0qGIIGwH8ieLElqiN0ub44TPC1ajmiZgRvNHqI6BktxGQI3tKrRVI9EasVG9ZrKc0ECYop0cf8mWLTxRh5EtZDlvwTW5FoxznZ0vaMyoEnepgfxqNfBPOW/FBAdPJLXalk7WzOE2xbXJz1ut4tqRumdmuDKAiD11HW1xgfugdK1+vryDSNxQ+8CogKAI+bgg93YkjFRFM1E7H8VboepFfA3rntZ6Ddd62FabIcnOa69y0t2YHesMaEzoel4Y5pjK6Fsb9HjDqYk+8NXs2Pi16gU9cUlQqOuHJI+rm+WmwWwlXZjF0XLVIzaOehqEFKPB17OcjOtwe2XgSld05Pr8Lkjz1ihmoM80l2DvbgilmXVzHqImQZpnnudC2Rk3fX5AXGPIrqzy1ew3swcKolGm6QnuOuMhdsxu6UTA69lA8dEnFWNj4lGI0pUGL1ynLrSeFQl6Hj0597gCw61V2Z5FEvkVCg71ZgJDTpERMHpUs5WxToabsdP017UJlAPdPC3iKtXQlkTmFjSZjVDj/PkkU34ZScttpsyeeKLb57XSkyMgbc7wVHeiHfBIK+tF+9mBZtQh81i7KbruMCJ+ldBRRa3KV9dJV/3UHWSXk5PZSTkP5rnsz0L3DRsIV4PClCeqaWND4sPS2Bdv3EC5jWicEARNoU0DlkxvvSAq6JZXCGeulP2T76RtAZIR4ZznV9q5jBLxOTkzY9JqKSKxyKlWUscLo7q/kq0mGxzJiCWEgzHP5Sr3/bNtMZkGoytiab7eXmHe0IoiAmI0MtoN/JPqC/M7IesVlM2N10qfMBT+tXuNeh1x44s+K26vcAJD3QY93exvJZBttjU+q6NkqHnqYnudr7T1FC0oXMhltXo27s1qUSLcBI1u8l1oKn04FzrqQOUPndBwilsLQIv+WbitaC2rrop/LvJOWnQwX/l2LRyZhK6qPBWtTrWwNsvIRcOk1mI1tqmMhLqkvLSWOWihmS1paKGvxuDTt1oPvCOQEUGqjjpu3jd36FbpxzEt08mU2mjRxvyrwtWOvtt9oUvjn9FkwZyyLSfjueyCU008kfk4UKpf2i6gaPYrXjL94ohpnB3x3hRqeRXTg4ysygX/p7WWacRY8Y941nrsb77AyxsikCoV1dW/hI8f4HgeVdx6Q2k463V21g1DFj1iZUhzhU4X56GfwhjEVfNeT7RaTzUCZIjZRIRb/+AR1WAsmCbbXmOIqicnom4co0chN+n60d7Uy6GNRxHDGJiRz7O5rovN8U/GKGSC2yvXPeKSNIb8Nu24NcXsnYeHY1uOyhC0haBGv0UfGqhntWgO44biJT0cAc5YaNisoBlyNekTpLfmOFVJTCiWsDJE0VhQmSpeq5nLMzCj3Zln/OZFTk3U0v7L6MCf3W8K1CV6edtNm6HUT67H2YOASiPt3L98PC8rZ1SsBvy312m1Q0IDU62XxcYxI+NLeyyHvz3YkA2U9OlXPjqGFkhiJKfZMurSuMY/hG2f5Z44mR7rdwg8pzRoTD0C4LHMCGtFSOSZXBrjwI7HNw5KYIeEuriI+MebvHoJn5V6tsqeY75irvDMKhrIdEzdQWRxj15SvCIcVf2tt+CMoawakUjVZsJ64vShDj1ACqvte2OGCiyotNg08sxW16/kJbxRjpFBRBI+YdKoO3inKgJiKNoIA4TNg1IFQnTkCMXiROJb6EBGdcJ8jcsV4lmlCbELk+GNtOtmiLe4z9W4xB8V2qT1fqE8j7V7qzmx3eaW20TQWZFjDbgb/E7I6rMKXQ6da4eUI+B4lG8rNh5L+rdcNlEdM2iOe4qsc4CsVOGjDf5MGR35t9Mo5cmTQOtgcEzYuWIyPM0zs1Z1aC2Fm/BKXYVt+UB6H5YMRUfOGtVADym/M05OCdjLDt9MgVEwflFKZ1Cs+azAvOm38FEMecZzubK4NDhl/ltQzbwOA9/gsdoaIkbRprAUTgon8jN6ykbKeG7JdRqPkTyb5Dbt5YLunv8vShnejuOdTMBW7Dhb4UnpaDxUsbaYPqLjALBlAAwW8eu2Kty3WigUw9E4KTRilHxvvOJ7W9IKS8Y+DWP1UvoSqIxrsl6K3bMXqap/hZfSX35DCui7X9jpc2BeXtuoazRMj9eYR/6ldavnUy5f3lTTUWokW+a4JGMo6VXI467i0YmeFjKLB8Ll00+zca2OjCkelWAKkdF6zZdf0e4Znr2ky3dVtGlh+IAkGg6Bz16X7GDoxAwOJbP8tIaptV8oQKsx45ARUnGmmRFqvXVsjPYqO2jOb8UV7OPmsxqjKBtMZ8t/2aWKsKazbDVZNS0t/fZaz9JsitwoIw1iAg2FjfKStNA3zayJofIIKp3a9hQiuDKiHpnUrKxDQj7Rs1VP+yys2rCZwCfxHDvmlQyGvZrKTwpXglj2TOXRDrjbnW/EPVHPdGJ2ace5O3VyWV52EeNHl5+BoVLxxSCg1dp+aGIei/M9KHWFcSkbmbPxrNdXWRKdjFg6xcCMFVdah6sA4iEE1UeaFxrC20KPAudwKr0b845V+Cjt68KV5tgwVERWxIWCWtc3lkeb/xkPuQoJK4GmFapwW9UkXK/KvkR6G23X/R/nxjQWsd350YjYX1YoI8AMH0P38k7LeFxyhbqSIkRUNpo8RykvZeCV6vJl6uf5EDkONNTzoIUSS0kLb6pDRLSlYCa8ORcSDbCJuhRD0PLEHjIra4G72VSGoDiC4WywPHtp66CYZ7ZK3O4peH1WzEU0oVH+Kg0hjUotZRRKGMttaPwObxAZLRTw10Q66b8NY8p/3abv1ShqdgRsRVrPytyfoUP2XaU1ozpOXzsMG+mIQzzSNlZz6Bw1wlU1LTSnIw/qYLDMieVmWEEyojCTqzzLRHbFPFoQrmB7XBK3SFpKtouWTdcu/GRDQ8wuK5XVwrN4OFyLGSXvojRwjk8ezUUDEfc9WlfNQLb11Sejbbz8IJXZNhnq7KgOCYpvexs16J2HFqzsxcBywl3I8DtElRFdnglU1w8PHzXZHhPEKgwBr6wz41XQoZiCc76rDrzm5EVzFR52+r/jj1o4nhfnUcO2xatV4WqtT7vI6Es90jB3+YCAlxiHFX6vqu/k8HTlZ1bdwaBi1Zldq3AC/ojkLPiFI+Rlo9V2Zby3rhtnBSDkBTMymTsFF8RNzamRkvhnxOZOKu0buYwQv1WnUtSvuS/1Z+/CxrNiLLVWrafK4VaD/408TnMNFQZj7k5bBDIzwpA2Rj68JIKNlJVvoCdYQl0b5Zzj4AZ4gOt4iw5KRBRZtIyAYMwkeBmtIhiAjGA9YtJ8KtccQ2r/MCcXqlCSxyCGo2NKKbHemt768frXmG15aWFnqD3TNYK0YmbDX18NMss16Irlpwz32Jl4M85cH7SvyiVVMJQp91tkKk/JIZuaZx8cdjA2gEv286kMhUpVp/hwjKO/jXDPbzky3sQzvtp8b9RdSXyI52PfKtpi+GS8qcNf/4lIy9BMaIs2C5uQ2dmc/iWnnp8map7eBnNcm6piuckVw0jqiVsflseIsZaM15WvcSARkFJrK5DP5zRNWN06M+UlvDV1JaMS4p+V6UAwKGPtVMaoEW7qeH0xxIxOpWHKqxpWY1CnMfktRUlbxNZhU/mr4S/9Metr+Q73GKGe5syjxW0oHpVmN4v/D8sc2ICBrsYlGXWuyiyJqqKaYi2/R/oJ+MR/ZqlQ2OjZUBsXCt0cyxvunsNWadxj3YxhXpnlq1BWojNbRrWQs0mHGg01M4L1jZ0pxssjrhIqVu2J0VUPSgO1hjrIqjQu1R+tg8BMmdhAt/nhKq1V9S8SbhXRW8WzqzaV1bFGI4h19RTGnmI8hJcq2jDD61udxplrfyxxDmeCQieOlVyGk3N1jfmXHfgQLho4e3twCw2FkKXQF0KWVB9bex/yUb0VQokGyJcrvmJs72TqmltPlRkuGnRsJGSIISEprdB9c/qjImBlU25J4EM7oXG0lfNhSYtniGfVCBoaU0LeB+j2BJK14DBunh93rMxvpUmeYZB9y4P5vuQooSLO+CyClFANNAjiaPj+8OkHje7xBUWzzKhRSDfGAlhfcOQjUWbahtTd5VC1hIYjlaMIv9mRZlFigNPXlT/TIY8akFFAHHYkthkTO9EzF/OLTp3xahKlVZ0RPbnkeXgFUUZTEgyZ1UnXmjiZhJkMVDY2vn2rLSLA+JVDOg6vuGhEPR7twSEy/xkxqOnBGOq5kzOFlyaEsQb1mXkXFKvtN0lQQzlJ7XJFRUU0Cr7Q5nOpV5SXtpCO6TLuWmKetzLFJ7VFXWggjYr6dziLu8/jJDQKWqPLagzZiOYigo6PyGHL4MZ2nilS2IRJa4zmfeY7PD6TnY1VPX6Bv6Hv85aNt3bQ2Gh76qfQ3j9FDXIo59ovyxni1hxvzNC450M2b3DKupQShnEuSpP3ZA2yqXYWndInZjxCsjyiIxKULPqd1uJdG604/I2kvMbBQPHojiWhzNgEF4dmPm9gvHRj4HJUVpadTSJpfqjlKElDIixa7I7r8rUxkfR/ziH5b/VSBB4R39agUHkzTI0aMkJu5m8Kb0ei3tp6hjGq45lcq2LYl9oQAaItj0vbvGT6RyLxFT8vKfIsQ96gZlVxYXB2q2x8NSHoNJ9/BSAYjzS8RbEJBSihrhxOsAGIb3Zx1/i3usECt6V12QqN0SJW21sYe0D1BNpQ3fPl7RDDWiyy4QrqYz/cBX/ooVZ0aF05kBZwEjoplXgDVYxWCIEsjLU8lYQSTHK92De1QJpVhwP+fT85FMvoqvzmLUzUaMEw2QALhZRhD0cxjkX4/P22T/bWwYXZCcpKuW//LB+YjKoLD7PEkXkNY8WEWPhOsoNs7BryOO4f3CUPIqjtlieMBkRbN6gtaVczLgcm1+XFHVKP96DeTULI/7Qs3FB2Kj0FQBwalWNus46EcKO0ELx73K8H+Pvg9U1hvVRJoNehoQ1kTzN50XjFMI4MXDBGXhZafioiQ/bSIwYsVMfinfOB5UUH7pm6Pks4W9/cqQkxV8IhX6nYHEIfkpqV8tAdn9nwRqCAaynNttGUAF3BNHbL0IjHCxYGSqiOQ848a9lS2TFUKIUXdQiZ6xJ0kJJa8XgrfacXckDod8zFBT/UUuyWOvI4FAM6iuRJrR3NdnseZ1YNy1plR2NTwq8hgT8OyuYQQkCKP1NbNuDDOa+cSnpvYZMd+s+GiwgZQRED0/pwbxxBlZbzkgdeo0X3iEJDXI6e8AzTUzFWq0GX1v43V0cN+/PdgoaoUm7L+27mkyadM4NsewZJMMrheVZfuas1TREDs/BndRhCrMHKDt8b3RerhfklsUD4LfRtQFW8zCEGbmMqPnY/mGHNCCmaX365hiS5HgySp5+MFV8OoV3sppcvj4A8GtTq2flGpQG7wp1q+9VofTr3UulDI0Bq57DGW/Eh9pxtdlXEYXI+tfxUnNHLuuJRShVeURg3f7kA3/PPMRe8kWQuqT/LPF3j0IcNnMb2YAbAb9hsM9qMQLxmvlohBdLne9Z3FCX3KI0MftM9Mn9y3zxKKUiKXhprNFF9NGy+idCgSjOiGCD9SFal6TY1AievWwU1SjESA6IiM5fhW7GOLT8dGw/oiRrnk8Wk+bwYuqPlFSWyQD4nwhu3gnGc7WA582PffstOiZHsOYZ5c42MNDniOWPaJK1m6x9jElIVK4cQrCwU7YqKbLbXe3ngbqG7Ow/LTtdkVBOFgBEYI6l63VMlQG45QzBWhCCcfWQFbx3hbJSSJxkzQlZGSZA00OCeSa7E24BoeOOAtVxUK9nrDWkmztCOn7V0J7EKaBkIcd8JIlBdHskPtDBK6WK2L/yEqGuKOeidgYRWMoJphX58Uqf1OCIUWmBCFbQQVwPziRmhbCB80lyq72oPUk1sZBtyGS2Ezw8YfbTHsNY1Gg9GNC0oW4WP8yzeChCuFUsWehFkTFdXJ9cxr7hTqbrAlFFVWSFOSl/4HmYGVUOlRVdD3soZt4zcRpbgU52ZjjI287yNIyF63mi9PZSwrjY2GavjAH1aZ1A2pcjdV9j2mrLROJd2e+fSs2zACi/NqVQhR2UnpcE3aX71yja+lsrl74KXnZuvKftxWNE5DKyDSTQQT/WrCCP/TvzUkcCS2jSsZGEfvyJuQMnRYlcxPVzjDT6sLMepXAi1CovHgEsYt1KJYwbGDQTpedaWlTASRsvxG4bafV+VPs+5Po3hWZy0cIQpG5xAAa8daeSu6kQ7E2fKGu0gC1nZFE1lvAemB9Wrs4FPRjXRQwDDtqMQDjrsHVCUtIo10vIxZgR707yhNfLN0BPji3j6B+Ovsr3QwR+ijPMnsYvcl6w4o9LLo6hmjxw7SeHLZeNzWWyJmDPiUeHRZWQVNLsYCil2msPy+L20VkLSgLCEv3sDFnoy+vEuLMIvb+gJiFcsXg1ueamfKuQCnN42DRLxVbgg/I8Yquaca1Un68QqLKUiJd1HLZ4Lr9T9tjwKP2tlTL+zYispTu/qce2U5327vLDRmNFawZ7rE1qhXzMyC5zf2chj5r2FtiYVSre1hBoemZpRq5+rv8ejoBnJ2pHDOS8RzH5CE3kdsCfRuOTeOQE2CHXw1Z52Z6ukpW8S+mrIMddpKKWTjsLCaBXbUqvURvXqq8rSRjrTSFPol18iIZVEMKRjHrtXTlTg1NHjyGLjF3hJ3jjmfx3dWP2nhULr51vhdB6fEShW+DFmWRh5+0smZ80dnxVlUgtwekaHI5KzMJjB8w/4MLERr+cLGhmWSHAxZG/GDvl6CHeQZv0K7xQ+AZ+7FmgECbbUdMRIoh48Hmg7XSKOQ4sBlunwqImPYLE8sq0dyxVXCzqVr6XSpTg9rZ4SjUdAOiAS0Yvz841r6QrH5hzRlQZiLdEYmjKIdBDpQkXSoGEgvPLoebQltJbXbEkeu4zeqsC5oCo+7NAZIoKWtGGnGu3qDDRmQjBa7oW9sazrJSOvGvHIWBWhnLtaRQExQsiyNAfLOVTjTfSY5IzVI/7BRqd09Pc0IhvDIj4BXwaooAmE67FD+WzyiLAye9S1kzfi2ixaDDHp2VyvM4TUuQp32vVijjjdUI0tW4EolHYmenz7jKA38XZK7JEgbzRuH1dTUQP26po7gvyumkiy+Asx6k1lfBiinjnlQD+r0r+kQqtTT33YZciCw646qyRw56flViS+JoKUtrENSD0FJBvimiq4SqKeJF4nWgcW5NnBqJz0lENtWZcIZjrUnx/wsTifZeJujMiDs6Fl2FojgarGbh5cYwCl86prz1Ay1U1Q2SKrAp3+Qtn1kj7TuCHWZDJsi8m+n4wEGzQ/CBzuRSOV79vroLiM28uG+jvTwAi2fpUUr8ZHLmQDXGHT+PKLmnlAFkql72ZWMqJyZ6dzPXzel++RwwJF6xthnbejjDDGpCCGqYNS8hgqcj4prJBX+CigHOZITkvoVkUuGSoRAB2hl4wSySAIKV5BKD6Dx6ir/vh+u21Nhc5opihLVrQsnoZl2Kag3obytXBHgykjn9bLXVfoo0tWttuUke+ltHssOLqq5fnhqTZ4MtzQNnUavo9UzremWnx0UkSxsNDH1T7UGVB4iDVpTdfQ/1Yd2TByqObDvHgUb72vMD8HiyjCzKOPmP21GuC3vqu70HpTsKEp4ks1Cu0RMmNqTzlxGHb4JqMvZL+kXXW5ziGFUeqWIThjxX8J06jZTGk04346Sx8LmMKzEZC0ViLuHnShj3PT4tqpMpmFLY2ZQXeEtaEr/yovxsCZ2d5YNYE7X2hujwHp1PyPtx0hPOT/NEM3b478uI410qJg5E6j7cqANbpuV+YxQFegyW5OgeVCkKj6+htThj656hFDNFCVsarQU3ieURcM5eVn2FDk9ovmR+SHRqgDUCjQQlTE3xKaeraboTKUUZ2S4Mipz7MSSCGrHm/y0RQueEQVH2KFsvxKGU7BkNtyNBiQA0CTI/QM9TP3xPEolSknoeYjWkqOKFOUCkuXjG/2MsFINPnB59tnIexIhqzv3B8QTaWFxrRnfZSNjejYMcj1FZP/fMcrcprAYX8UKDH7lK1blI56VrJ+R8IYjYp4w9A280Hgd6DUoxE63my/hcTKvs2q44hDmZyZ1cnFp4plxLPJI7RtoRWOTXx5b4ENkVnIWSfdc+lwjpUzNjRzxu2x1XEOjn5XR3qgfmNNYl6NJiwEKMgT1gZ/zxW3HKB1I4iZusbIaKmfsRRHTqic/CmhKm7cT6QpYo7I+8ABLXTSFtJB7yk0gqE5y1/l3FWHMhunvGo8GzEKt3hMaqswlJFa2iVqH4WPQykpfRRae5UBg8hYo+EvM2mF8KU2pf4jrjydA+aYYO58xYP+Vro/99nUZklFtAXYUGkbLc3DUXl2v3otmDJLV4ahU9GTntuBhOJrirL6HEJ9hjsxeaDUrsR8VkBg5mV8GJpXANfISJ0sAShvlvZGtB4fRtyjB85xPzUqrxko6zCLa5TtelbP1CjkXhAQEVXWAr7D9XC6KOHfSg+EOKOsEGq8qcIKdQwR5lvmRw7xaMmCZGQ1DA4ZKD9TWCQrvvZbM5fEIrVkZEoCIuUz/T5kWzXvwj9FSqx7XhRtsta8fw/Gyjv4geaWMo/ZN4fFvPVy+tXEUB4s+1RB6tMgJ0FQxNfDKpvXAHaZJ/NmDBufQfr6eLHRi5pHBZcF/BEBigKYCpYD5dx3ce2Z8jYMenRugWADi1yIISIZsKRhZXBaC1Hz85GMaEQA1+nIwHHHND8nJaUxaljFC3miu2/UIBDakB5nxMy4ga4ZB1vinNmn9vqnsGy6HNOsjouD8mcE7FBHFCxtKkyqJN0zZOVNfv6dlxGGPYTerNjRPkKmmLo+ksYt/SljqBiWUhSEFUC5INDJffPXogw5H9BwWK0xqutxDTae8SapdahkLSNehZ16Sd1Co6maYP4xzvoVP+2QMEcHvi2WtczeKXS5yk00Qw9Hp3/nIOh6RV3AyKIR+tWnKkRDMRh8RmcsYm0EVbdgRaM9rn1UXJCarrm+shC1hFko8DWkWNdqdHFwHMNCofzI2AsxSmK+KPvQTq8+bOopzOXJjLzEQjo/51p+FZvhJxwKlnKrxsM/TcZKk2Gi0z0hUhTeGfx6ZE2mo+yVKM/fkDiSFg26ev33FkKOg82JfM+rWI9HXg3ZYmhRtiPxZJj/2C4EqpdiLXYi6nK8rV5au4ZyQpuZPOEYy1MXw7zxT4zA6IFGhBd1c6q6PFJvtPLWnrNBasNUi1k+H4eoIWM6/Nba8KkpT/b4RkX0KYEBgTUdxiJjm09q+dYiWDlUanC0nG2p6sQ8r5MqIqoSnvJVKQaDHAPKIhrqe9p8lZqY3JdwyQgoPehSQrdX2HE5GtfnzJE4AfElXRJvrNjgKASihLaaRo0HNODh4n0Fjqmjz5BB0NZ6K0JFbImcnbEn5s6UlsGyMLYth/M2anuWMyiwvgjslBEyGCuGbVqTOjLCcZdTk2HVTX90QN1KdoNV1OuKOHut0cD754YjkkOI4Goiihm9oUFAC+35vXdsICL243oaswmNj8MpWtds7LILNchv1Vl7mPp8ZSmzgL6oOOHzOubvmTGyci1k6HN49Wfgly19GHI6ORfmj4eexTO9KGzt5mx6LuiSEEo5cI+XLrh1VhwW1v/8sTJDSN1yIbw4M0YnRXZSGTZGndatxvHzM3e0dSmG/9WPaDxpdpaLjg9anYCuu2Xj6+62y0Uyc8kOK38cKBgLDcc+o+Vj5NJg40p3Qt1TnTEH4WC/5259wD8bquwEWQiU/sNLDAanSI1VQ523p3iPGaP0Mn+pdl1agh1onW8HWSDqM75ckbwNRDFqTrz8G0bKv/0BrTlUk+phDcphedFUJyNXMUNlQ9uDX0nlNoKTEmaj2T4HS0ukWf4F/lq4xHfa/yzRnp4hq8LgJUIaCVrl90Gmv8r0jI31Clts5j4/pqU+pGy+ACUwjJto1coyP25IYlKC7jBgHWWHd5wVmSPPtNRjTnHkiZX5elhjthIS9j0nt1GEvq8KZ7apyxE5RmdFYMUjxfSOnUIbIQPpNDyGYJFZdYigjeGWRh3ea1rS2fl4jkYc15O1UAfQ61Cv3KDzOJVoVN9di+DUtVv4mscjhdGeLMsz1e8xN16a4e5pcKUSDHYAbJwMG0Uj4aBOftKHf2GVOw2+H6GG1mbD0t6szfEprdPTWoUrM1xCysYnhCtESC1Q8y+V51YIGpoFXJOON2Ph5TxDyoa+8fScCGqlq83PSPTrAIT6iz5C8p+pPZSWaXI8mT1agFbVW4lCI6Xv1fouY1R8Jp4GIzy9nf/kAW8MiPMKFVJcAYBW53P5hEIhreSSMsLj0I6NT1LaeEQNipm139mAaYb+FBgzTE9fWNWNCgsbCuoSVBMVHGpHw2RN0GYV8Q2KQ0G2SLSMISQNUgoF3TKGOjDLhFS4wCxvCZ2MOqCK5UBGysmoEmXiSreVsJaOeWuD2ggqnIK7is9YWJjvSVVa2zajscynqrE6cXc+G8ZpG+tfpk8Cc2r9KqvnCwKaj7kE2WCx10dGV+INQ1EeGfId4PRLXhwqVQMebpMy5l9hzxyfVmpGIaIvM3LFaEa5cha7FVaGe8xfoq824DBIK/Y9V17qV1MM5cGIqIq7lo1WIqi8NZr6jEBTn8orEdxCno6BqWzXUIU8JJafqityUVrTKCH8bhgqQlKsQD7st2IgSaiTsh49+JxNNtJCW7haH6ozK9CcUCfT4UJKcgZ+fR3XHYfD96U+Kx2G9Brx1woRb+XcI7opbfKQjSEsvrdakNWyVfPi33xjZC/T1E+1c65E4b+JU7a+NNYKEY2SPEPmwz8rVT3r1tDwqw0CNAjQLholaEM2QAtfS7hl/HHhryIdCdL2scoDXRkq+s7tAOBZizwzGOyIz00ZvEOc8Shj0Q/fyoaVllKS4gu9faflbhk55d8dhYWlzKhx6tK9kaS7+opcS0ERIoJZIRqbP1kT+FwuOyPRTnC321NXKubWWk/5c9VQQvnmLF20LKOOaN5H3HM1YnPg0D8TSwWDOR4uttrODqeO/ay7FDO0QjYAU1KfYD2lbj+WadzmL4x8lIjviJBiXBgpCYNxny/J055Wt7mH7O0YibSGxvbWWczXcgLRWJntMIrcgoZirOJJXX6sfaI9laHMqBOXaIWpVuctdViqwG0SiEFcXqL8zsAc3kHSTKHlrSBBmZy7DartjJ8k1loWS+fGIvRcCzJzfBwNbDZmI96/9aKDWtlWsATzpsfjpXjPlWvDCkaWykorQS2Z1qqfKMuMMviQRrsW/ZjMzgE1gTu8rGJeeR1ngcPJdRTnTF5oY5qnwKtpzaL+fFqPmPqF8M9+1IJhVQ4C20MhvVXBoZfZIAoKRVotpSviKDPDVXOK67eOepDsnFmhz4yaR8XRgwQq8+3MslTWOwitIm8WK07j1SteOHTVWpHJ+DtBksyxzN8BUXUi1dIGGfln9+lq5mky6B1di7jFvKi6rTKSCW8ovcQKJNJRtUASEXjj8LTWdwj6OyMBoMHqRv2VNIyR58rLijVTaQdFuGqtZDAaq/mfeZaoda8OfxtbPuf2f7WfaZ5W9oeUSbtetSEe64jSdzvoroHiGnwZPISTEo+kAJfoL7/JYOSD5vwpB5FTDcguqIxwOSOQysXqqmUUObwgAzVcVpfzGwwZmRytvZIzZuIpsPbU7/kNIEZTR0o4SGGXhXreWAlqdOUXYJp6+XlVLuFcTj3mI0IbZ6HHPrKKa4EtdH0O2pI40uKkxklIsw8hBAHg15y0P3lUWyZ0vM9tI+R+1wCmzVx3zetIC/DGh0dpaINBrDzCFGKTEkz5GJHWFG5NeqrEndHepiMmf1mAfDLbwpJ8IlZ5R1y1sMszIM/c+YWNY5KRwhSVku8BUojqHYQ3ejBDGfvjME/MSfVeSLIxz9f6CmWNHNRffTzSCiBx7ixQ3tIhCWmJDOcpFGNFiXZ/wiiHkTyaue/5ibCQtDUG4DCNTEDtqD2YCIIk/mdQVJ2jxS2KmLXaFGuH2nV+PVmn2sFQ+7e450bCxipfsLLizys7XkPrzktBaX8BEt1IDnoq4oV7KiJhdixiCsIQDeSw0scpcPrvYGi8IeTBKOFOQSskxZWbaPidrGdS6XJ5oqdYvxdDBEJt2eJKoaS5HwS3sV2zMVb6nZmvJclekuqay2qraq+I6hsrzscz1203yY9wOJ6f7UTQdYys4jYWTfadFwE4nAaHqsrK+iB+bhYRKVQkvvAIhjweD+08JYmIGzS2skL5+o6jfrzBqInB8pgj8aYrhrXlkdoalfV38z+rtQi6ihqyLMp4Idfcqi1Rk5qqlaortZ2ZSguNRJRUarOrnPdyrUndTr0soREaOgvGu/ZJgUVX7KgzUJmcVsgf4n8NIsXArvLAtJ7CkuYo6MnSBlrCPvtN5WEGq0JrEW3l9kL9hSjhr1LCuWJi8m/xaCobLDvsxQyiGQ0tY1LyebT+ik+B45xWXP0Ugy1/BPMKwp8VXLQk7/PzkirLMhkRTDWG7aoLmx1PVZwwVG/eo4fd8oBUGZ/9Vm3tDuMZHWukjWUjXkG8Qt7D10FHncfGVkRhUh9Z0/yI04V5fHe/dSwYts+UGcwhWenoqJHhN9zMoYKvxzyXSHp5KyjPKvZ+vhge5K+0JiH4ZDNQkbHZK4p5+YpmOnyvrNIf20ZAoR2jTlvAmdBU34fHwjHS8Kir0CZWPiOrehV/TqCDpJLXlyeeiAVoGU11AkyKwcr6GGnLH9/G3EAnwNo81k3HGGO6WFdLiBQ+4g+aLjJe1uxOXuPmQ978g1MVfjHvPMxWoyeeyapC91bXI2KjfmTL7oAYKahbmhHGqMlNHRvHSF3KkfZ2zdxOjMbGhq1hZM3nNygYGWekhaPVYJVNgXUHqRu1K8DYXI35JTZWzghV9XpJG8bfTi/ohOXCmBaP1c7RV6R57jrkOo51XpT8Ta7Voace2QCrK1/KgQ1bbsaYmXNbFi6oM9IWSmQXk/lLs3zlBNC8Ih0pBOzQdYa2mAv5JFGL4LQt9MJfpIR9Wo5GaYTppUpCK43wOkpOu5LWdbrB+hGe0cRPV9wgPI+U7yrb5Dli00RDjWejIQysqZhtMtA3EVPT5hdHF2+S7giDEraExpP4nGtvJRhVfch6x2d53EbqpDc/M1nZH6u73klWMCG0bCvFNcBA72SkMeDqBontBEtzWTMJm0Eqq+15v2L6zmcSVQDEWi49tJX65D9inJ4XsboQQMH8GwyUIa18rfylOt0K9/xcppeQTOF9XPuQYFMJ/5DPSrfxKeEf1EI/GfJXbhwELLWVAogvWDHUB9NGe5RFRz5WkvUcA8LJ55ySeZi8020UFgevTUkNsEgWhqqFoW4evKDcKQ0Qg+GCGBr64JyoDmFvsXUBFFT7Wt2YZJr9yjPrRtMievYSUvcSaHW1QtDWOe7xWUdPXXWzXFxoO7UCpphjcWxWKI0QX9vlY44iHoFqx9xWDTloVARJiLxsxDQKG9elvj+8742lSFmJtFKSoQgxvgidGadcXebl0LQ/MYG7BdTPWX3Gn2zceknrx4txMn4J/bXNypyfYuNmPLDnzKi2BTIOkdDGdrs6jEEr5vFBhFsoUIyvx9nGbBaIGrEw3wy1i+/E3ChTDY0ghMQJfuTcSvX+wADpVzTCCqxq7SzJyFiYRsytn0vyOpYWjEuH7NFgdHxHXyKYGvcyI83XvdRap6eGpEbSXXEUiiLlODS+VIGssQBxBXe5kQe5oCLupKBAqRDrGpqD036HTCjbzhuuPRMzYtKaLuVu87lXRndcre6XZhhp9SJDPuO+NhJOKJISlm0xCQF2HQXfpADZSEGG18FnNNVlY9bRwcVmu6gxCgGlGrV2XFiUdkR2iEfR+TACdvuciBF5ljiGau3P6jccx56XvnLUkGrsgqradLv1w7s0NDQqBmZaG/cRkyBwkjf8N4dyUcBIkDyvRzpetWTQx4Idj3LmMLA5Ik3LwiCA3wZcaA7PJaWaqs4RgorfgbKMnBm5FMSStdWMQHypSdUHQjtxiNrewnvigUQv8Ej5il7hEn05sc3PmKEb7nXB2ysrtaYV+zmsLPzhAVfqvoW/Fh5q1ZsOQL2Pzy87yEaJgeOQv4KtraLvbjMzQHsJR8K2Eh83XtZAfeVjZZqRhOuZWDWs626qr/VEi8CxS4yDGkiZ6K8QKssL3IIWoygSxSiosj0aIlqK8XgvZ/VpHMU0l6/5Zu8vy8hP1bFicz/j9K700RXv2CSCR0ct+qYaBtTDNRdNoilVoVcmB2k7RjYGBTQZsgp+ywty6olPlNcCandqxpSjixvhWC/akmn/wpZkkhx/uG7Jxip4pWKwmRb/F6GezDMRf4pCCQHzwOZwLBFrRihtN07GKe4JzKFYNjFStJT+Emgqa61yKFkG0Upki1+WuKTEu5Mlfr4lM6tSGT7oj2QlI7amNjc13LXojyEy4tzx3Kug0BxqjfC08a35rIz1wxM+koay7hKbVg7tG/S0QtYVyGoj2xXQSVWtn9nWkTqnHnUF61YtPY40tOY6qHqhgLNsISGw7eJ0SWtsfM15g65LgmfPn4REaRTNi9KsJCPAMFCmVPZcM02Q2ogTCw5RaWA0oSvnyVOfslHvsiEqPAuD6LbMDHfLM2nt02DoCEmJ4Z/8Lj7H/sKWHHfXw9wec9Zicf84tFrNkseVhLmMY2v+u1kPvRZK6yKVMs4lUOyh6Hl4gZ5LZ/gKR40LPTs/LGtfb6UZxrji0ONY1wOhTvTZ2Y+FdyOf+ca+kb8uzxjK9Y8ops5mhKyFEYmkeH6HtcSWqos865VgdoHeKElz2/xqg8IoI+46j6yN0/M5DGwkhEa8hzYHqbg0CGzKO9em5Z59bw9QVJJhK5CFSCz/nFB3KCcZrU6sDCMr8PWCtpJhjAe7kaGyZ0GhI6My3wtFNpq2edpyHeLbCWJYh4y2HKM6jUE9ikVpa14+JYSEUZLVtx/PmBsmSmhd/0r5HyrAVZfnK+sYcjIkf+TdiOzs2GD3SAOLzjTSC20JtBSLNu7yAHmDHz14K5oZHxPfYeaL2C0+ZqdcFi+vCkyBzq22LlUXI+PDmIjCalY1fGs2VsX4aX2Nh53jbBbk4LGE/iOurFQC5UMI64uMqRaHHpnmMGRenv12X/KHzUFmo2TdCKEfzCjltVO5rM38BQRWngEJO18DnOklA9WCH7GPftuAf6V7ZHn9iUZkZN1eTA0UpitMqqPKaTnw0NM/fnhji7QcCdQyjFpPQ6qihd6LJIxM2TEiLF0r9+xoouZLuDWVaXXK8Wk+YlsBao5/dPTH/F9N5EkGew5JU80Sm2rS9NdNsY8B/CBYA2LyIhhz4MMD2Vh15RiPvrUaOnVMyfp6Bz0n6ielz2UdHxyUbz07znCrmVFKg/Z8vayx4vPuOQrLaIvRkhlOv8jT1lS1yC7HGGdYncPBUmeml96WLLThOYRN7viYdIUyYY2ZLmNANEf86gs3cmVpQc11j3hHxmxECAYJmzOuc0BJZairsLBR4dxzZ0JIR350fuDU6pUDQ1X9dXCXvyb0NMY2bddZY9W6AjfSjFznMXiFwZDGrSlDSn9mEXVOPSwvtUUU2xovlktEZUj/LaFO9AeGgdxzWke/bAjGeCCgXvJKezIkqbJyv6J51EL2RCmHpOKeFdduRFi21ipXUOeibAaQl0SwQcrGkQ1UMVK56mIIPXKMX/h4Pzfw5bXu4RHwsxFPUdkRuNO+rPPvN/atufTDivVHvKdFUiTmNFdRkb8VjHL1+EheiFI0XE/McrREsUVaTl7YCGj7ofkWbC4Wsxz1KvNcraItR0DkTLV3JZGTwfmaWgFfv7bYSV1kJ2RVe/jM0UXJ6ViStb2G1WqI75Bz7QYmlB4xIggoJfK7JP4NgPpRK0fg5OrY8FnIppRQK4gmIJCuPML5qa5UZcsdjNOVscprVwS0PzAPli1pKKBaHKnEJwoHKVTR/N7A8nA2XjUvS8tqRrfStqDWXGaeiSrKp4A0kHORN5nTZGmnjeybIheLNEKbUTvGYhfkqLlWKTHDSUlw/shIJveF9Kxpralr88yKjO0SmPMpWik6B11FpJrk3UKpcV6mDk9nfRb8off5HXvmH+3kKJ81aJ/jAGB0diRkccJpCpb/ydYwh0R0Aku7TZZ2h+byDylGYoxmXsCaJwOisar6JNQ2GS2Uti1nZ29GtnJmL2w2MKMzn3xHeI5zZeEIPRFHpy2LUIes8j2u36m+ciGPqKo8VbBGFSINAxWzV+X3S1SS9odTGdFhJy9IRiv7APGa0ajW5NL3x4/NXNgT6jOOhZeeCLeZGY6aPyuyawS5iZ+6aL2a3v5yyXkxdIs/zJxMvzG/QvTZaI3KgWKqfdqs6/IcHDoN/8nK4LbuaigLeMZHgksZMpL5iWJhnRUDkeAbaA2KZlRjhspAiQXbplYtrxbRhvGyniagJG8M/dAVJnTCbxnmEM9+g38zIuQ6aXyGazaDVL2Sy/3LY8vJoDp7YpMiZFQI8bQWinJYGytsOxW6lIeexkJGyuYiYwgmtiMsL+0inkpnicfzmrF9l4+ifM54WIbxNviZpt3zz1Us0vk2zNmLMfsyJ1R3I+2OkE6vCBzhd9ULgYuOVhxT0t1pfuOKCtCplCOGJRaG5UwYwg7RgF+f5IddiTG1B2YoKKG1iqvB+1g6iFBZ7psmeJoBAgmT7xfR7GBpe0MnGzN3FA2NdkcFPWqyIY+ePRqo/L3kqooRU6ozGLfchhg6HIwVGeuGoWoKVTB5zbGzLtu9skwl7+/Mg2Ian9nsuMahIDuLhpLVVgNt2tAyTiy3ocAcZc29Z6TRClbrx01jzBlzwNt4d6e2eF0buSYbxm3hUEuwyXXYNd7eWLsrfcr4anzaa3wdg8VaytacQVJm6F04IlZuWKjIa6Yo6ZtPcMinFeT7jgxFmRHMyjx0pM5WlCvxRQANwbIFZqQ11R7CGJpQVRoWatiNipHxNRc+rIOjoYNQ9DEyvELBkTNo6uuWwXDZHqv0142Vf5moZGMN+wuqz/FUmcYoJu1j+Gphkjm/7ScrpNMUGX3SjyNdaZ1nxfkTF1kEQxHSgURSO56rnHQgP9IfkVQkpf6lVrzKA61gheYwbuWRYdSd+aY1j+IzLhU1JxQMfZDqykvr0tSf75RCyLQvyVZM6zAHxiuOk/LYVhsfGpQd7sny5WNXytiIVkS5v1VvzIDkpQ4GT2vlyEfOR2+eGSyuLlTMNDXVqomYM6qOKQ4oyskDoYcOft6G27Ez161GFxZKrstm/ko+SxiR1djfGSEXJeaxYloakjginAWlVgX9KvjK8YwiHXNhzYU1wZlVqbVUb51dC/v1Ghodo4VyWwEZ0eQ6z6n193CpOVeRaXbHnRixfr3ZnPobw+YBatBB5ZIrVBZKtCIR5UKNcNsWuAxU1XUoIg3TfIRvLUypM3Te1bDS2gtPUZ5mZznECh1VEzT4J8ZSS8iSpFEnWgaeks+G8jh35svl9xSa4UihbJ6p45XsbjwN7o9tw4iLXcs/qY1ivm6IC+5e+Z5+dOLrbW+sdV6miIJ1JT9RLyKpsVXsXLgV9jppo3aC3J4812aUm3pLlHJP8tYpVBIY2lBrWkZ7VT/XmPqyYEG98Uky2qw3AKrA5PaYcX3cXaLB93U8lAuEN/gcSArIND/S5ltb38twNzpbI2d17cTPtNceefOqlrVE1ErunxpaKk2nUKVrCjjcuozaT5jhLfmEEUqdcoUe1gaE9UAofULhV6OVfIKpSYTlyIQrhSlJRqA5zCmhGhu+UnEI85AW57rQr5FwJ8PF6KpVzv6wgcpfTaPqDQBKVKHkwOx+HNnwcW3X5arz00Y/Ro20b7Wa9X3kr3MM0kjTNSVFUOYHMC8prxPAUDvX7y801SMuBeB0S3zzUfVwrWPjzmk1wVsuZ2VrEAEH8cpWLo31eGfNHwsJ2XrkhxurmPOqrAK3kyHrxA7lKMiGGdtkRj2dO7ZXzC/qG8HRebBK38OABzQiQRg9uqCNtK7l4YQkplGSgBh6Et+WUO0UqvH2HDN2pihCdDujFY0VQMf+BoFsSLqfLTfzGle5+z6OiC0ZQlNycaZHxoauESrE9lsoaUyYy5iG8o629Ks4szmf/AyT6e2uoCXDw3hJgUERgErdCEbtygjrrOiYMSEoVORxvMPN3U4jTOEXCK/ozKq7wVo3jFXrSq5jmuN5AECvBXraUIBQRGAwSdJM/TEnZVsJAH8qo1RoqiAbZ3GtbXcGfEo+sy0tAjWY7VJvy8I3rT4rC/XLFMM2fcdMChutwhbXDq04l/gM/DVephB4xeCWy+R73kBnjgaDXY1dCxnXuSIZ+Z6vVDmvmJsJzqOCxCF89eNgENxV6SJKj+Bb9Eq0DHOOCy4iJCiyy6mRunyqN/+RmqbKCs07yqFlrFphpnIeyB5k8l2YzN0PXfGi4ZWrLqdzwsLA/D48vOJnPpqbcm4nM1JTR81CZ0/Jb7ihlBkLT14kKfYyVO9hxbVXTEGVzzBBKQNMAxcNi/+ic2Wh4STtZ1aSWDcIPRGhNtlg9HFuSoLIcjulTMhldalARFjDXzKursKo/I1BF28HsnbZ9hxpKpITZmlVK/WNMtZEZ/lN+IvD06LsHCZ7jMse3RQzaKIbS7DN84Pe2Czt6g1bLbxhDnXRg47znuHEmtiTxqcJxVpGQlH13xk41uWqukZtak4ni0QMNRC+jwQ9K37G7FNjqROQXvPVF8NA3VNbcZ1Pc7AZEsBWxbtuJjs3HMSr6NHlmacGKmVhkUykcG01/Dc0NdJJCV+rQaeLhF58qWQswgkN5b9i09w2Y0h8QTzzPqIjj7i8MNZBUea7P8SuerQ9e1S0j4S2DTOre5G8BrnEVf/2Hs3840WzDinXRsuQFa3hYpHNZCYgPXYyRMuwRvmqJSJAj1FB840KgoxWSecWNCJeVHBKRtqVCu0Ml03g6/RFrj+g23zk0JgHCs2OidRK117Sp4EkWktMOnW3smHqoVD02qPX3q2WVwA97JoZs/Svz3+HMr1qqiMfcAfkmcnhXnr7Gxm/oUoTAw1yUIYgffFDEuI5NpDRHKzk2BI8jFtdzKywV26EPEmpJNbLMZOL4aWy0J5EKQrPPCltryKx7cPRwI+RWTv3USFjTLyunmHtCjcDGmw57NHmV1N2xUHWRjli8eiTid65Z5yPBNTaKFFt4ie+aruvdfk5Y07RirYsT6OTFeDMOibzx0ZWuh4dxSoHPd6a5vVRvj6jTrPWDXEi9YMH3aarBxSd351m/kfTbGSX9yam+krcT0Em5zzcgr2Amoq4a7hYlHre0a3hkdxfmSsCPsKp2Mp4fDWjm7wd8cHFFeJ/DnbOPCnbA86ZzLVbFZgyZFfQRg1Nax44dz4SrjiUwh3yheIZ9kAOrUe6QHP6rYjEby6O4ePIYFa/G3CzvAUaJustToUhjN1uh5bh+QYJNYrRqhGOQFW0PYo6T0Da5Kz4xDy0u9KzBATjqwXjp4MmRFUBhMYrqhxaImTUa1EalHuAFoSmBY3N+h6zjKwq5AW40yPUEeS/FtJslqscd1Y9l4zmCBMkfm8VLIjNpGk8q0BISRqNUA6ltnU57OTnaEQ5BGwSOuIyw+79ppEozqUxBgoz/wSFXWt53Fcy3PoSf7fGKlvwkXU/Wl2RuZa8xnqwsGmMppeyWVvGy68ceIa+r6IWw4BjcH0cR9YyrasaIlFdgWcGclrRcFNVwmfa97NUSri+9JetdniRaGis91WUdVsCoNc+PWJ5GKWpb4HQK8NyzF+sZNL/RAu/eoeRYdElv5FEwbkoO9zOoSquoqAVX4uw8pbSbLL877mM13nDn41v2HLEXnvsoDgeF4owfTv1+WIx8xG/OrrdBrxoQEfOdorZb5KGaE/HEUQ9VkWx4g5kaSm7tvtUcaf1O0sqoxfLi81NUcXhbZSZm4sDIFRZy++t9hSHFhod5Ue9+XbFRzynmMC6UGt5x2re2djN+llCQX3aPhMnwzM6IajmLGhGWj36PtdhBa3OAT5ldJaRV99bLqugMWioR6hd859RuIp48Xk07n5ANaUu+zeEwOJe2FovrUehT6OFCJCW9NOflVXcTEA0rp+wtuKYO3ChngRXm3dArWivwa66vfI3viOQ/46FwqEBibWtQICOX9TmTW4r/Yf833jRdpLH1tVpcyyyfEe3I8RYL3IRhaQyI+PcSj74H+L7yHTpKvjbqLs8patDV47dY4VaC/1WR1r5TPs+bXiWDnndT5deHYmcXyhH/Ga0MdzTwtEcxqQD/0QotLGZIDd0LsZmxVV6RVXjMLCmmzDE7fJdifa4ZguOHnG5ZqFCsSkWuogEKnQRH06Kw3k43sOosWgGBNWeS82pryqWNV421nzRBRYqW2w64uILM4lozs846jPjmMAGbskOSOCPMA4aP2+p0tjHlvI1UHEhZcTzE3kVQmuhGI5rGuNRlLFKnIVyjcvNsWABGQOMq1R+J+usH2V1wHhlY6GqxWPzWWzPNODzCvBt2i8vAyKYTIYB0GRIOrcIgyesA9dSGT5SubwqK8hrTNlLOs5Ge2KSDOFlRwNi/yxUzM8WpYtykw1lFIgWHuawptSX+23XuaKhbg6ZR5zKiDzH4XODzb4+hw1h4BCEahTZI725uKn8vJxy0NTSX8lPBwtXkwFoXukfQ0uTD0joYSUbgW6ml1FSYGgJxVshJV1bTbhRnHHWuUa/4zn1K35aMVxz8/RKb63W5lejvNG/EImvOvobM+yj9pmtc7O4J3y1RrpR23R5aWlAQX2PbtINSKvs/8j5ji559ZyXsrxNRqyehvrtta0xM/mzdwuaPNpWmZzc71j2+UWolPOyvZAkdUpGpikK/rXhquadnYKBFCQbaon01sNVBY18rIwLY1F7N/Ht0xPht/2oA1j67RBEgyMVMqrNMecbzalkx2X3CtorcFJC/1rxgRiCBLwcFXKIZwWlaVA0T3kXlcP53XziRQjpbcDAZ9+PC7e2L7UW9Ta6v5LR4fARJHfDzxq5MepfPVDlY5/a/WzRWThHtqu2qw1Dvar8mz03XV5aTidiKrQXSNeh6zpo16GT/G6p3nNOuiKK7Yq9EhrM1oKMukB8PjImM4tfvpBZP4PSLr4xT6fegIbFn+0FpWHD7ag7rjdCxNAwMrg0RZdsyp4OdkPt0d0uAQrFAXYatVczr+DHxYlu5j+fcRa7Uk7V45AwVxEQVTYkSg6gLA6NSC00g5HrinwQW+ihj7X82JEzxLxPG+VUhGWHmn9mR9lC7OrrHaWBTwYZKTQCapttFhtedYlRj/gUwJykumuWkW65aLLHIuaOuxslPt1RONmfOyz0mc4Wl9B3HSaq0EkH6RQ6UUjfQ7sJJpPOVlpLF0SkL7mRLJrVG2gcBLaXjpbzteIgSt68XLCa42k2nQLKf4g3IuzNW2MS4ay0BBXtZ+eqQYSb6Sc7/tZLTaVV8xyJbR1cl8tySOxvM68DX8kIqUMTjCbh0Ff9Eq9ad/0r2OH+a/0ITi4/l9uoNlfDa1MjfKkW1DfoMyc68CpL5+gwuzPL52lVG/k2jXIjTF/Z0IJOv1AjpQlYJTLMOVw/xu0PP25out0XEL//v/2Yq53O+h7oh/VS034CmUyG8LDrgIkCmFhSXhQiHTrpK04Lw/TYlJuGouNzhwdTuexxkujQvp/saG2bEEoI2aWQr1dvAJQWu4KuG4NT6BHj/2AovGK2IC09E8K5gqIYsZW/g8bY9h4bFN7w7JqOmLbh5SU8qGwgK+WuXKcFcdmAFYMuzsM2p+JLyBJPYrXCLRTLp0UUZ0Pmo3QzhHxzPfgIeZURd9vBRpAT4v1VaCXb4qrO4CCt8/VRMy4soMfCJXbyowtuYXpTE/dSHHmMrcYii/br6Km7TSrbC75TSDhLKzV1eVDwbtZDJx00GS5VRdclYzWxULDLCElZfEzQTegoLISWlJJIenlqCf9I1WmfIm+qjknRHoph36K6M5wEsNAz7/tTLxsKdRC2jgJNmM37yqgmxCNfavRChCfjKy2tJ2PFulmQ/JhAsjJnhFJ4Z30caNXx56u4OYZ1JIJBEX2w2ugUoxr/g+oTV3UW4coqa3wuKnUdnDTsvwv75iMbXflyCMHHeSygBFldkc6tpfnxDqK1Ho4P6hxlU1WrzuNLAKTu/DBFOZOLKag2UUu70jGypsuq5dRKnc3QiWCS1kcN4aAO+axJB9Ee3WQCSIc+Lz0AhlwXQKghBSdsiJJByetChNlKxmg4u9xehlEvTfFopEePjIMYJWfk0sOrXY4VynILmLxb9TmWEa9ceRD5qJF2HFd4H1eU13A8txnEU+FnQaOMNUc0II+RyDGHFE2VLqF44wQyflNEMKRljyUtcPRLVCVWxiLTGl6idyjoDpdMORB+RVybFyM8yNcDwokFHKCLyKfRptNHHdXH+icBH+cQtDHeYc9nIZ1CQAufmYhUMO//JR60/XA7moi5p3kGba4TaKFYbagVfaYqQz4pd0Qh0Jmi63to32HST6CTYVNzl/JZXTcgpa6bAJ2klez5f4DPn2S/m5GQeAtcUAOFlEJM5LpKbmP49OxJQk8532EnhFLei/IcjoHOcwc3Lg0lzs3TDx962l459zZtN0p8trwJS9MeehQ/OuCtEa8ByLgrF6cl4+jSI76WNnPIOwb0WxeSi1FSyIyMa1jWZgQaCG5OuFTfj0t5GiFSuFUA6ny4FuLPuo6mkRzrshKKBlp+ZS6vIlidS3pElCtAwKgn5cE525rmtT/tE5LJyGhGK1t1Nmzb0b5PifkJOlVgosPRvxgWmQ7rtwSddOjFUC9PoWe/m9+0a30NC1HzAPCYUdLVdYhX4QbmcThqiwgFMxnMXBdCSM8wO2KW5wVFx4fT6YX4ujzh0tYljgxIYpX+M3ezrNTPRmmqFCmPDzG+cEVSAp76JNWDHklJWjAsHB8TTU54s0KNTum1EFILCtDAu5BZfPNNraT8TTYWjiGtkHX+x4dQLOXzkQjmja0rt8pAMTreSofE3W+fc9ZqiTymxuv1w3OizRGjNb9/U005nj7hlYnm87HSQcAzDNPeKWybaAftO0jXQScKTADpBiHtEyO6IXkU4GNAFxGFhcEwWK0urMvPcvdsDRALmjqGDWzuy+8eKDNQ2aD2ml56CnWKVeaQsodXu+lfIiu1PLHx4rQNfTd5TcE0e8umJazfAcmpkEHntC3cHKY20KgTNmf3aq1qhVnRy/swKRgRzDum2LunTIKQoLfIap4IryPViwAaJ5BG46N2p5ll43DRM1ZNygUaeG+NN/Gq6nz0FmlfETJxsZaszKlrBdtZ8tWrKFs/0y48tWnfAVXMMKyRyjmgmfboVTAZuDW02yu6LuFQHQxW13XoOkC6Dr0oOqVzz0u+hDTAoEPpvMM7wsXUKRczsjqIVhuxt1joqCTlPEjZKPYkdV3JdwE2m2f1d2RYFEDH5ktIiIUHjV0Pv5zW6BK0BMifkz70RUuVtX5JLXDE3qYAGofp+YahkmhoqIz4hvIJou1PQwMaYVmQjJHAk0q5zdBj7QLz5h4qNDpP4bKchpltGe1LQL6RdalolaGI7PXqM/4ZNaQNh9vopFRfRtpdrZ+YE1fOM1YAMJWQqFMZEFanMOMlOix9EAGWh+IzEaxZuyY12Q2zfukt0l3XoddhaYQjrSRkxQRZUzjaJUUtyxZQZiknk4mhjnQsTTfprLON3BJHb5JQYzl3vRRIcKSjtWMeKROiSoqap59hJ1QUhJcVWXI/DHGZndKgcPNdD++XrqKsoLLspA0d2QsyCoIrT7a+ZXLYNdJfRonlTjagFUlJkcE6UsJkf7qHET42MzUUacXTjjzb/ypGW7YgqnmyiHhOY9+031mOPBx2HDBnw+GSjy5KlTnqdFCax6vievlehbcrfubh4JVmRlu1iKd7hFf+p1b1zDtwpFFV+XRTHWblRIdQLitnL8BMFL3oECJiOE1huZ/h/MsuwHVveg2mkwlmy8vol2foZ30xJvnEUlU7iQEIIVsS2p3n7sR7fvLd2HnOzhKuZMN27kXn4jXf9WqsW7+2JOMvufoSXHXd1egmE1pJTyeecmiYbRI4T6ZFQDdv34LNp2wxI4l8bld6jkIPDW2U01IJ0fG5XiAlZjBZhk5znXzfD5FbvkZIuPpofV2j5FhBZo2diqGhOE9ZSa04LnXE7StCfa0TIhjt+v5qxShmBDkVrYlWX70bQ6N3GOA5wIs6adfHFLu5LovEvFDZGAMuK1pX0yZmXlhO70qYV5c0miq8YYLbi1Tmf6KJGudz0a4xvjc+XScdJiqYqKQQxz8xw2CwZkm5+l7x9h98K37pf/9FbNy8EbNkrGZLy/Z9NivoyB32V4zWQOGahTV494+/Ey+75hIcO3JsQEp5KYQCr33La/Gz//CvYOuObYAqum6Cd7z/Hfixv/6jWLturdONKN/WJooRyrrZq2K6sAbv/5s/iR//2z+FNWsXyHjYIXRKdXG92bh4I5YNnlETZbS9RANOwVrC1fRT6cxaj2CygCXEx6Cx5Q3NZ4c8EP1tYf4Qk0n5Z4XtSF0lhSUH0Oz0iJhHEhuRJFVc8V+DUiiXHbc1rlKNTGp+wpGK5hW8kYjGO/jxCB6d9Ql+yOu6VFWWsu7CiFFpObax2bxRixRuyHi5ZqipOvLg8Hu6ZjLBrM8ng+bkOgqqGmRfhkWaiZ7JmulgMFTR9z26fkjZ65ICvaKbdqWN4VDkDv0sLUBNs4t93+OcC87Bpq2b8If//Y9x8MVDmHSeyOmaCRbWLpTN2CKDkcuhaO5ghtC9alkTVitJ9hjDZzabYe9jT6ObTAZ02Oe+AvndRF0JNS221J43ynohzOvM+B2EuYz0KRQQCcpaT/qXY2fKMT05xlPbdiKwt7owomsJAgt5sYGa4ye0LIAPD+cJnr0HsqxzK51I4SgziTelc6wcSRkNvxzXS1NsYFqzoc6tS/XVlVXrFXjiwo+WkR95ZdlGdba0FeYh3HfsVvh5k5Xyj41yrf3GZUV8PZTk+MgczoFLCrOn3JZgjshEPrq2x8oP/51O1kzRFVSU0VRfiGGD1+ckbzkYDNAemC3PsHb9WmzashEnjp/E8vLMZg1FsXbjWmzYuB4njp7AbHlWkoyHDhzCn/zmn+KpR59MG7BpUIPHZ+Qw3Bd0Akym06H9dQtYWLuAY4ePYdbPIBB03fCvn/VYv2kjtFecOHocEGB5aRmf+t1PAgCWTi5CJh06GQzZhk0bIACOHzkGhaTV8gMNGzZvwmx5GUsnFzGdTkooDFVoJ9iwaQMmkwlOHjsOnQ2LWteuX4uFdWtx4sgx9Msz5HW2WZFUTER8MNd4tYV44baDf5SeanjpfI21uYWqch5OqcFKcLKmNjSIQkhJOaPhsn9FV/VcMCLegCfuNJMe2hT0nLzNvB1TCM4tjm8hGCqUmMiX0F40hNSJanvm/6vPUEl7G1EdZzNwmjfDaK81GzmupvVhPxDe+DMGhKt7c8Nh74ymIoBMhkWdPRQddEADqphlXKUwhAVTo157zPoZdl18Pn7iF9+Pi6+8CE8++hR+/9c+jD27H8Nkqrjmuqvxgx94L07beSq+/Y078Ye//hEsnVjENdddjXf82Pdi6/bNuP0r38LnPvx5nDh+Anle05Ao22oTWu17nH72GXj3T70bex7Yg6uuuxpnnrsTt3zpFnz6Q5/C8SPHcdV11+DV3/Vq7H1sL67/7hvQz2b42G9+FHffcjemC1O886fejdnSMj71u5/ANTe8AldcewWef/p5vOZN12KyZorPfuiTuOOmW9GrYmFhAd/1/W/G69/1Xdi39wU8sXsP1m1cj8/89sdw/MgxbNi8EW/4vjfjFTe+GuiBT/7GR7D7jntx8TWX4q3vfydO2bkDe+55GF/80Cdw4Nn9BWmaS4/eLIhLRCZhSN1eTK46y5CYgePnpNRpyXBWqtrIGLKU1jXSIgN+nl7uQa0YmobZi7ftN2zngMZEvQojlfgyUkkmuRg7QukSG2+80GE8MU4ErOLjjDbzaczoCVBm+sZt6winMGr8x6wXa+b8zJU4w7kS+uJ2Y7luMpmim3ToJhNMphN0XYdJ+jf8b1iPNfz1Qzzre6zftAF/7R/+LC647Hx84vc+hXMvPAd/9e//DDZuWo8t27bgL//yT2My6fDxD30Sj+5+FIuLizhz15n4wC//FA7sexHf/sadeM9PvAuvesMrC1KBWMg1wloogA2bNuDGd9+I7/vp78cTDz2OvY/vxXv/yntxxauvwGw2w6k7T8X3vv8deMM734i7b7kLW3dsw4//rZ/E9tO2Q0Rw1XVX4/LXXAkRwelnn453/tR78Jo3X4dvf/VbWL9xPX7kF96H7aefgtnyDNe8/hX4wZ//UTz50OM4uO8A3v0z78XVN7wck+kEk8kEb33fO/A9P/UePHr3Q7jtC1/HgedfxI6dp+GH/tZPYrJmils+/VVc+bpX4G0/+R5M10xRBFeE8j1enH3agUKt6K0NBDS41VDGkpHxoYHDcyP8d+oaZxRKsi48EUM2IlaojDcF9qsIOPd9JAHjF+2GgmPKGFRIuR4+nihU1RqKgQZJMtzgheN4IIVCex5TrRpt57RWZQfH2BHQdJW61MZ1xEIrmCGtvlCwPfJIuDWVrgM0bVnpgL4XSC9DTgeD4BRDUuL7gbBZ3+PSa16GV73+lfg3f//f4bMf+RyOHj6Cv/uv/jYuuvwiHD18FOecfzb+y7/4VXzxY3+GtevWQiC49sZXo5tM8Ae/9oc4cvAIrnzV5Xj1ja/CN/7sm+hnvc95pD+8QTp/+tkQut71zTvxx7/+xzj3onNx1WuvwoVXXIRbv3QrlpeXISK4+eM34TO//xns3fM0fv6f/3VcfPXF+PZXvuVOflheXob2Pb74R5/DVz55M44dPoq/9Pf+Mk4/+wwceP5FvO4db8Qzj+/FH/zH34Wq4oIrLsTC2gXMlmc4fddOvOH73oSvfeLL+NNf/XDZk/nG974VO848DX/4bz+IR+96EBu3bsIN77kRN//R5/DcY09jknjPJ5d2iB9KEDTkIa5UL38Epc4oSu78CQliWuJOH6q5l0NTHdULO9LCRgONBPFcn4TQ4FjCimhoQTJa+JtveqOiZbnE3O0yoT6+1ByL1qN0O69da61rcsewuL6ncUo52Spkkoa5iyA8JOicyMyHtXRDbYxXMIDsm2SlksW5Uv0rPld/uoyuum4y5IUIbU2mE0y7CSbdBBPpMBGpBv3Cyy/A8tIyHnngUXTdBI/c/ygWF5dw3iW7sP/5/dj//H58zw+9DbsuOhf9bIbJtMNFV1yE2fIyzn/Z+bjiVZdDJh1OP+s0rFm7pj5LC6RgYYU7ZMif7X1sL/pZj+NHjuHksZPYsHlDOhJHcOLYCTy952mICB7b/RiOHz2Bs84/u+KUiOD40eN4/unn0HWCQy8eAgCsXb8WG7ZsxFkXnI1H73kYx44cw+Lxk9j3zAuFxF2XXoD1Gzfgnq9/Z+jjZIJuOsG5Lzsfh/cdxP69L0BE8MTuPVi/cT12nHU6Tbe3Q4QWLmqLS3ieU0tkf1pVudxg5nKBe2Mg37toQVhKwsrfQEHVCZlxuFsIQKtqrAcKLzPKaiBwmj4WSjoHOR6yaUMOx1BbWaC8kpEMfJhnI1oTBPVD/Ko1s0zaqD+LHp+mW08gjLA+XLXlKPOSZNk558Shyd5qP510yUhN07/JpMzmDX+7EiZ2IphIV2bPOumw47QdWFpawrGjxwEojh05hqXFJWw/dTuee/p5fPDf/w7Ov+Q8/JP/+A9xxSsuh4hgy/bNOPeic/C+n/8RvP8X34et27fgqT1Pp7fu5PnJ8aEbFp7a8TVxuwL7SL6/eOIklhYXsWnrpjrklIy2a4+4bv06bNi8EUcOHAb68Bp6AU45/RQsLy3hyIFDyKv6u67D5h1bcfL4CSwvDefmHz9yDBBg45ZNCa2qCXfOrXAfSoSV3yQ0fzDdRvFWQp3/kS67qA6NRD+C8cgEs3RTJ/wsaKJb5yhmyW8YE1wY6B5UcFikVoUpmSKtLWwwKcTc1g5LF0Z4XYdiYyhDeDB99fPHkOiK1+Y9nsNYi3D9yI0au9xGFVo2grUYjkZmrDY/V+ibV7ZtwaddNxwhI103vCuwH1Zsa3pdoYqWLSB5/12Z7Bdglo5YnnTpZNJuOBN+6eQidNbjy5+6GfuffxG/9H/8Iv7qP/gZ/Mu/8yuYLc9w16334D/90/+CfjbMKC4vzXDi2HGUI2h0WPPFxwTnRaV5RtP1H/4E0+gpIFJoW15aHvfaacR5/PpZj9nyDJM1U/NeNHCzWXqrdecDutnS8tBmWsU/hICC2fJyCcVcZBDIyUKfy/qD/QYLmw3P+FHJXvhKm43QyqJAmxUdbmVqtFFvCAddDGmxRT6TrOwFpDC4nPnecCIBKDgGadTsQJMLa8ixe2bYUUYllyYt+eEmNBJiXZWRZ0bhXU197H6zkIz8DB7GF52z9SYaMBeywyzh6IzCSgaI6Xd5DH+rIQZFF5BSJiKGpLpJh66TYZo/hTZDmJh+TzqsW78WJ0+cxGxphmefehZr163D1lO2otce23Zsw9r1a7H38WfQz3r0sx7f+tq38Lv/6UM496JzcfqZp+GZJ57Bxs0bceTQETy393m88MwLOHTgUHmv4YAmehzcfxDThTXYuHUTtFdM10yxZdsWHHjhAJYWlyyv1RL0dGkyHdZyad9j89ZNWFi3Fi8884JDUs6b+aQOpAOOHjmKg/sOYOeuMzFdM4TOa9evK2X2PfM8Ftatxalnnw7te0AVs+Vl7H/mBWzcuglr16+D9oqtp23HrJ/h4PMvuji+Ep7WR+iPJhSRhrP1AgLrT5QI+lNyCl7YKjPHqIolS619fv+2PcmwMaMt7zl94GkQKSJKc/qhQz2qMMQvUG7BHPvZRPIE5ga9VfsxZ2yaF6mfpushwd8mr77KhpBpbNBRDXuIjueSnu/J/PujdWijhHqn6iXOuMDpjCLoVLbzXE0oxBmv9G86wcbNG3D+y87H1ddehSf3PI0Tx07gwbsfwskTJ/G6t12PrVu34Pq3XIejh47i/u88gIV1C9i2YxvWrV+H9RvXY/HkIo4eOoJvff3bOOu8M3Hdm67F2nUL2LB5AxbWrhleY9/P0Pc9elU8ct+j6Gc9bnjb9di6YyuuuvYqnHvxObjvjvuwtLRcjMuAPoR+2+GC6zeuxzWvezm27diGV77x1VBV7Lnv0fTuwwbXS97H6jpx5Bjuu+1uXP6aK3D1Da/AZa+6AhdedXE56+qJB/bg4AsH8MbvfwtOO/sMrNu4HpPJBA9/5wFs3LIRl7zqcmzathlXXP9yPP/4M3juib0QXuBaxm0YuGwAoi1mJKbJYjHabWcEzEDMdf58ZHEOqUalklRMo+C1hDyHvh5l5JeOaFDumLyy46493OLJhnozdgxpagPmzUars2E9/hgqH+NRBFUafhCM05FKm1tjWsZqYFQgIjytCmcP3HN18yulIPgR25Tf8pBK9UlJvxSUHMqPyjAUUyPfHuy6rrwvUNNews2bN+Nn/94H8IrrX451G9bit/7dBzGbzfD4w0/gY7/7cXzfT74br7jhFTjz3J34yG/+CR576HFccuXF+Ov/5Ocwm82w66Jz8dXPfg2PP/Q49j7xDL7xxW/gZ/7OB/Dmd98IAPjk//w0brv5NmDSAf1Aw54HHsUX/uSLePsPvg1XvuZKbN2xFQ/e9RC++cVvDhT3ipPHT2K2PCv9WjyxiOWl5WK0lpeW8fIbXoGLr7oEZ+7aiZs/8WU88dDjmEw6LC0uYXlxCRCgn82weOLkkKOCQGc9Fo8vlvD0zz92Ey6++lL85X/8c3j28b1YPDHc67oO+/e+gM/89sfwA3/9R/GL//bv4sVn9+Fzv/NxPHD7vfjOl2/Hu372h/C697wJW0/bjk/82odx5MCh9N7HIDwuTMpJUCUjGv7mTjeT6lqhuPI9RzHzD//2sZG2y9sbcgys5VAs5kUMyA0/ctghZHiZ4LIhmpZQu/AtKluhB9xYHQKXGC7x1sXlNSpTpoVJrBgrlZZzGF4zuepyUFDUdYUBrQCWA7BknLWuu2mwheUD1fX5n1XkpOaWc7C7eXdy9qbz/3lUgpK8LVtiBF03IKzHH3ocH/7vf4TvfOPOJNeK3XfuxuMPP4GTx0/gk7//aXzp4zdhtrSM5cVlHD9+AidPnMRNn7gJn/jQp3Ds8FEsnlzE3bfdg72P78XS4iJ23/0g7vv2fTh25FgJ8wTDqvMH73oQj+3eg8MHjuDWm27Dpz70Kbz4/IuQTrC0uITHHnwMD939EI4fOY5+NsPTe57Gg9/ZjYP7D+C8yy7AVdddjT/+b3+E5558Brf82S3484/dhJMnTqID8MLTz+OBbz+AF5/fj2OHjuLhux/Ekw89jtnyMhaPn8Cj9z6Mx+9/FEsnF3Hs0FHcd+vd2HPvI7jti9/A6eecgbXr1+Gbn/4KlpeW8PQjT+KRux7EiSPH8exje/H4vQ/jyIuH8ehdD+LgCy/i6IHDuPmPPosHbru7IDNLgGsxTpwQj3mrFoLi12d5REQvgqD8DZ99nx8teSR6t6Pkxktei7JXtGVJqCKbARL6L9EA67Ojj+5bddwvnznL5e13PXsdwxku42jOSyMcL7xBcnwkvlX005gyHcr05AjAEWvXjEYN9HsaYnQsMGMWc1aOTuKlK0/tujqlRUMweg35821y+dygpTIiL0s/KRwokvXanW9SsIFiIpI3zEe9DDmpmc3KJZivfU8ox45BVmhJjgsw5MO6IUeWvf9kkgziZFLCz2HbjZQwT9S+T1KZXGc/69MsZsqG9MNpqNr3+K733IgP/IO/jF/5pX+F+26/F5NJV+rpRErOrJt0QK/pSJxkOlLeouuGMBmpn33fY+Pmjfjb//F/xeH9h/DreeIA+az3wSB0k+EEVu0VwyFxA3tzvwA6h54GVQB0UUiknIdIQks5o5TEdEFmLF+2NJHCOsE0deVF+EXMSDJFvAnpcm/Ei15GOlY/Gyk6/70Ys2Dg3BorOl8/KKITelIenijrSgjNBkudwQLXKbUyGV1eEbPTQTrokl/GIMjDQ4ZDON/n6ZfSrt+iVRmLglRNfgYw6kMqSYdWCtUjVB7cbwFEexIhendBbzR00hfKuoJSY7hN/Uhb/ZAPBRVN4akWVouqfy61yQuMRYGpOqbySOcXFaTzsNBh2gn6aTecxJAqy7OKebZRVYE+n5qpSC+NHipOR1jlNrsuCXEyQNn4STdB2WHfeWXKx9xk8R3OxbJ9jvn0U9M1KYZwMpmQ4AkmE9rUNxnW9bMhyQhSVbFtxzbsOPM0HDlwCFdcexXOufg8fPRX/wCz5WV0YkY2MzsrQJdX5LICFQVGac8pBCuo2CAW8S2DXVkW5K1NbVTNeD/cohmhKkKS+Ii6m+VX3mvKZTO8oK1F4tqMfSDCmgk3aV8PEexY7/3v+gEOmzMTVntWAxcaTdF7NNB4lO41iin9J24g1pG6nZOI4V+sfCRaGz8LDKMi1ayjSZnOL0fgaQpkQTOL1TzJMoVqE0mGrxt6l5c9ZAM2eKx8rhQlSbMSKdJ7wyUZvOQVhkXfwzkJ2qPLitAP/xmOLu6B3tZgiaCgr0yj6rAfEgBOHj+J/c/uLzOK1n+PKFlUXCiigwHs+x7nXXYhfuRv/Di6aYeFhQXc9oVv4I4/+2YyVlaNhStBcEiDNUlXx1otXDBKjjiDkqktoVxrJqklLTm53ryPdh2ueG292Htn2qtEcTZMrbqQD9VrtTHPKCf5kvq0izG9MPtYG0m/Yl8dKW1GjSt+la1Ra8MXj2MdMWMjH5ajnszrikarzzCtH9B6CUzW/fDR8HdVHxl/QOsL7fO2mh51KH/dGTdq9oJ5x3qccaseVDNS2SipKnTWl0WC5QQDZYFOXRI2MkmWO1snNYRNXUFgJTxM5RnRZMPT0dadjHQ2bt6A7adux/5n92Px5EmC1ZJCPy8mhuRqdm3YuB5nXXAOtpyyBYdeOICnH3kSiydOurDGEJHVZaeVoqq3EwtvXB0YD3EY2sOV4VCgtZDW1+MlKEN1G+/orM2Q5zCwlg/Js1R8XfL6KylOz2qhsNC1z6EyyQn3wyXv4fjMYVvhdeFxihjoRboppiEXkJQ+OJ4yriXs4nHLtKRn1RsGl0sSRshJEeEdWA4PS6SCHHB4cxhTCiYHw9/OyXOOHnJIRs9mfqmFeyWMFUD6IgjoEELC0j47rTokFIgL/Yq6ZaBTeJM+OSRMIaeoYtr26Ia68ltuLHcgw1HAeV3/kOAaaqFTQPN6pHjgHY0wCZgUwrNz1X6Gcpxt19mQqABdP6gYJa+L6iWUBQGOHDqKI4eOYpIMoQm+nfSZFVEC2rLXbA21nzh6HA/fuRsKRZfDv7kYWB1Lo89gtR0rwxdbE3o84L5iQwFVKEeJ9FI/0vHOeQii2+ayZDRt9k4IeLExgF++RHsHczt22+8JzE7UTqGYH3DELrWOXslhusEej5Za52ip6PxhBg+zNw75u6lofKNORSIqofFXQhCOSmik/CNH6O5pVPUQ4P+/+FTgM9qVANk061lbUSxDZdHZsKyhk2JczEgR68kwAFlRZMgvqQAq0GS0CvqSiX1Pea2SXO1gkN7HOS4ezlPmwxuikdBVcgIynDEvUHTJj2RYP7w8wpK9fARyTNcqhvBTYC+iKOSIGS6IQCYSputtAPK5T/Yqv9yDAoBiNBVG2pSmY6jmopMsgDmUirakVkKJ96J0ljayoSFe1Ye3WzkgvQpNymW2le69PspU5NX5yUwFhrjQzNHqjZs9YAgJ8V78ROb7k/9W+anjJL+MIvPPh0a532NGwZmvZOk1FhgNzTyqGefCeARRNmq3Pev/dx96F+lYh2y9Xn1/mkqkyiyW14yceG9M6UCGxYRadIIcGiIZqOF62u+XYOjQjH++6wwVkZsvxrNyOoKUqxoMU58RVxqPwfAohsQYr2saKuphpyLkfHAfd5GTdCnzKBMh5sPK/BUtRHLTz2Hcx1JEOS9XC7V6WlB7fcZUjGzE1UUWwCxyFT5F41Pq5de7aHjAVZKNnfWkHJSnsYERFSaYxDzmAsV4tcHGCp8KDkQg6a5Ffjgnk0NCxXC0TOlf4FORC2JgtuncjnPaeZz8K/JcX8N41JxiOZBiNDwfdeWHG/aluXq9CKDRXtOprGyeCY4ehpmCqYgwUqdtCNlLmlLnVoU7l9GEmOcX0eEV8oWrOW4mxILG2plcexZAOuUxLwisAGaCRr30aYaQaU2YiYxgvlnedUghUEZPUXiKjPGMlrru2Xhonl1te7LYXzf0td63pWSssgAYpCXVDUsnje8OGTY+wR7FpxoH5IUHikES+65JhuJZNkxHoL+E7mQR2ZFG6kbHhG251Jcx7xmutzTiGTca9vFdhyTz9iKpnw/gNeeaGMk7Qywjzc4jKTaahzAYrtJdRuqV93NKOUcn1IeIJAqZJ9Oydy411vIymsI59+JPSqBmBvFRtF0662kwNFqMSzFqbmzJKggLX2pfqW6QUSAG9aqQXoA8a0ehhGjnaOf1UkBabZGNdRr64fRV40WHHPYK9ZeVgOlrOOMVBivmo/IUtYxIm/PAQmKtdsb96CwbG4IglCW6yf0YgXKtfliCmJC3uyn2t+hoRoTZ6Q1ayORFUFKjIjZywWaMoi8Osr3R9mUFqExHQCNV5W04Iq0LShWI/YzO0Kj2dVeGrHrEG4v6Mx8RjoYGjU8BEK07RWdaUFBTJETrvmAJek6LTMvMTXrBQlmDVTUZpiA15DC4+3kWMAuwKr2gVD1jS3iVkR2jNSonRMHYlhI1VEjEJKMlVR8yg4ZTKMxo5VmkjMIYMeVNuXnpQjiefVTZnWGjCJ7sqh/DpsTUoQoaz5rstSeNo7DUIWr6r3fZQ43sUhm5jki377cTnlrb3MkJ9nCeEGh1ZuCd+pNGGbhh5Bniu/MJ8yCx41J4v6Sawq40hpnr0irpjBWDiRCqjjiT+rVjSi2uhPR8DyvqBZzmXNXHPc/IMFxnA92S2iwTU+3zu/pSp4qJt9pLRbyWSTCgGWZU0FBeYe3rt/CpkJoPgSuLD8WFthk19SXkGuroJL1vOXWUtxVlY2PrtvJ3Q2xO8SRBnC0AAIAASURBVGWYWs7tuW0M+TeFDZ0I+tT3cmoEWx/1AgdJZ+MXJGED1Qf2eQilZhyQMnvZYynK9zJpQBFYMRvRMo4IqYolXzWcM5/t/3BtYIK9abtliqPwkyUpU+Ns7OyMTp6ZNu/Lzqai3L6T1vOyGqayIJUMQPIKc1XP99IBzstlxzbGSQ0EBgcVEHi+y7wsPA7UJxhe8bbQPWbU8dI+NvEWGhor7/o0x6Ilqy6U07YdB+1m+Bz/6Xe/961ksHoapyCsFLJ5+gkyc2xbHYSnLj+Wk+G2XstfZxrauZ3QqUITr3+xK/kht+6HKw8DlBW/hR2YFRHVmLGkTbi0LYb5ytssslgOdZgDMcNKClXKGs+Mhtq7cn02YsN1s4f5nlB4zH3m0ILVXuCbjYbKQ52BBVF6Mi8NXTv7SjFhJdD8Rh2logBcQlh9bsTa19V/J2Pt2tEQ6iAct5NtSc5PNcqXv+SUrF+ellK32ne3hEF7N/aGwLWMed5K42SmyIEBB+NfT/V1xUJJOTVQgX4WB2fEzunctAlfEudgBdMt27c4gv1aEVpHJWYKTAeVx9A1pNlbMNzLyxzywKR7ZsjspaRmuCjxHmLa2qgKTHazoNRG1h00xwMdmBnhs80KEkPpir9e89K33zAwdN0n7cnwELPz8cT8rBf+1G5BqkSP1gojgZxYLqLCVsg5OEMyLvPeKsOr1N1q91AvIUYHprg+5kvlVE3hHB/zuERE5cp4WTEUCkJlAV1o3oVBBFZel2kWA4Y19HJ95j2AEZELj2kD4dlSCdI3RLnSWjYUyPths66yPhu/otFuEkN4c84nBCtFx244++1a+KhDYOG8a14ACmnHzJlZtDI+bmrlgWfr7pBLTjY31mCwIcoPdHkxV6Kr43atcdvfl+rJv7oc52WDmBFTakTCM3y966zOvGbKn74AOj6GQmrqr4WZqJBdRz+yEfKr4NuIqqy4zjfJs5dnwyBGI+t1qs5PumfDhuZ8zbjMpyRlK5LXbSWe53Cd2nPrtMJzUrXvKYg7DvKnK6G4l0vmLzs2nxym1Xtcr9ii6q6Bov1427h0TcNYj2WHHjZtnVaui00G+RXqtrgyGw+jhTY9Eyp0jqpcp1XsAaFy2CylTG/RAm8fy+syQavYVcmIq7vfkkOootOU6EigcZqFoyiY0uwbNK0ryYbEFpZmQ5H5XBTaKR+7AcsPxW0LBMHMYnOsoLCXj7JQpxeP8badIvpuoWs2XlQH7T/kZ51hoPCkrMinuus8lzihAD1fGSxnjDLv1fWbt6e4gQQ968xLHpcY+kjjO3lqhPFoPZPoA/XHC1iNpFqAovzu4ITXm7c07A2kBOJJuBDKmMWWRjmpygKjuYaRn1JdMyjUxpW0pMdhaA614wvO4NBl3Bso7WbCpZH+ycgDq/6YnDXTJq5Jyq9wFOCu52vi66DPlNc35UWiXdKaIXzr4RVDKqYxdUphWAnLsrznnrkBsucVtMob2bmwFzCDoOqNUoXucv3Fq8buK9239lw7dM2jRjhB9+gNvtyKH19Q+Vn1xmc0sWk2aFwBQx6JpjZWpgfwjUcZG+2r4atmEzIimlLTRj4ts6YYbQ28dyLPdEsokw13sw/mOQq/JCDY+UPpxiBHKC4E4xbKVrdxfspY7Y180Kpm8jjm8naz8Xw0kr5A0Uu6V4eJTKyO1u8Nmv9Mte9heLgre+TytoyJTCzv5CqSwCweBM73pG0rpRMMkvOWHxZQ80HFYJVw0G8PGjMQPixx/7FnGb0QeirwmWcTXRttwxdG01+dY7yqle065xmhPJTm3yjr3PL1/Bb5wtfYAOWLyg4DbTiI5BT8jJGmdjMD6+WNJRlfHKGl52sT1ugwLVOIO/BafBeaOWYqnFywUwUgo3WmwnnjcaFFCm/nDM+IVDARjVPkV3ButQtpFGjkrCxAaTimaLznkhONSTQoWv7J2DMCoDfKJD7fBIGeXwJg2s/68kqvlMFK50L5EMheOmoziX5FqlTCbm1q+du3cgFFuFpDHJKx0TZQLjPTac9QmCFebHJ7fqB8Hxh5WQm7JxV9oGdX96HdPJURdnk+KmdERWXnpHq+3HKX2nTmLmcrNnSuCa46I2repOwkj05dcEcd29/i5IXVK/G1Ycl9KwNT8iRNbkyZacy/xLfs+V06XZn/jVmsRhhW8c8prFijTQvFzOYEbRgYXVmeZJUXxwCgNGm0BL0E2+PraywGbS1UTWMsjRx1k0ka4dHwGRBWbrLLAtGbQtIapvxwfFXj0KaS0TJu27orQX7pgKSYrhCk2VjFRGfYcE0dK8IXQzpKrLNomwFSW49F3tLyVx2FrX4CwQytLbaNouBAGBvXIN02OcQK7PuY9VgdnR415oWCA/skIB4Y4iIZqVACh4uN9Ff8CD3EmDiWIpPU0MM6id48k8rd90sYVKz/fhdGG0HFcMwFMK7DCUWq72usR/JAUkfYmPOfVhjV5pVne6yr5RxbH22UWemAQ15yZBxv3B9tqUFXUpPR94yWsKBVFc1qCqAq2WB16NEnaN2hT6d2dvkcAz7DmZPVbpoU6SgOGrloOaUWo/jWXovMcujhwzWuq3MIqDGjlUmnkC8b35grE24n/0YwaoQ4AWszOESjoYVYEIVRvK1qCK31kXjKyuSsE9yMV2ULcxOCyrDVjaL5mR/ueuvnQ8ERlBJpIZ4hPecXleQrzWDHao48YxMaNZ/kzehrWIgW83gB9MjbW+fuOggfl1ur74JlpObbPMPQClXHjGiDn8QX16arxjsE/8KQmh6uvhJBdbchUExnsxk6HRaDDQfbKYAO6AYjBqAcqOfVNA1EPl2UrxfX1BDDsq+Qc1eZ4L4aWIfGhMIwsBiMGKuMmoTqghkfv76GaiIDGNf0DEgxhTjBX881CA0BcDwjj66l3UEBYtgSQyfz8kTACgLgBcF/KgWY45p9+NVMk1vDzaX8FEqVkD5JRZo15VOIOB1RsCmRF2duY8c9Aqrxkwvr2rGSv0ZFKhaVe61NOPSrceZWNbHF9LNPaI2mO/kkSXewvUM9xBedJ6utT0z/RIhE6JWvVfGtl9WKoOLRhhJTVcVs1mOSBqhXoXVAgl4UUHtxhFt7k4TDXlw5EBBjT79qOsQn1DVXtjA7HSNTrRiXMnpaNNz7YctHmdUSq8AoqpATCUMM5SiL0lRsot15tfi7PG83KqTo4kuSqIZHcwLYtFBByktIGvrbkC+N8Wx4ps4EpropYR2NhwvvArk1CgBZ6zqzkZPuVUU83m6BI00IxSecolgr1ULS4mUzdG5spI7R/tgn73d1HNSRR7UtX/E+dSoE5zRUSUscnW2E79qvrJvWZVofSfx1Ti4UySF+/h50cspGOVfQ9z06VWjXpf1yaS9XOrZY7M0SFYoZrLmtkHe5p+CNTRiyffZJy3KgYOpoDh1cn7My8KK1gHQ888MwEPpK2NLY6CMJPyTlzC6PFAamS9Xl/DJQnn1kTOJV2mbZmlITYZ0otU7dIkVlNGGQvs2LChsV6YnPeLUX6lW0K2XvY9UJ32/jRF4DqF6GHK3qvnvZTspYAHP25HkfWwSObfNQOZWKfi1M8ssrglWZ84ldkTlPxRyjVjWtLsST8PS8ZQy52vJGn2YTI0jUOdYV9l+mtrItipgdoHVY/Ww2GJ5ueHtML4BgONWz67phxXsH9L3A3qMH5BWdZR8YjVFejJoNjpJ3MIPOsTGFOmqIR1XtFFF3QA4L3jDMwzEzqc5kXHM7Npsl9lwx2H5qPJNm4VhUFsAnITP6s+UeeYA84xUt1bc+scpWUabVoArlVzIJyqvOXN9M2mhLkAm2Uyn1fWjgzRUF1W3LqQyNfW+Hjm1+1IY4fxd4Q0phSDZiVXhODPOddzK1IoqZQ+9Qf+RLOyclI/Vp49tYUyt9XNlo08igNCPgjIqa9TXCwGZo2azU7mqUcxqj8Jk6z64AesVMZ8O55egA6YbXanUC0b6EX52kV9iHgSnvHSTSLBTNkmY70yPjx6Bg8eVZqcNDOQ9w2pmnYfPWTVAo9j+7H0cOHAYSCjQ0SWeYO1g/x5i0Iw7nHktIW7x6y8u6+JJOP2joUGvMZRij9Vs24rRdZ2HLqduhfY+Dz+3DC489haWTJzH2KZ67wd9cYrT/o5WOGL9GWOqwVAnRyemQHGejMz8YZcGOiXny2Kkdew3WGF0YaZCVKyPrekhXRB6rsjKG9Jt4KT6vrR+rRFqanYuO09WoRsLfdkiY+W8ItF2pUJlAt7KoDvem0pnn5ThGMbykVPJ+qV4wXTPFeRefg10X78Kpp5+KLds3Y82aNVheWsaBfQfw9GN78fjDT+Dg/oODAnYtiOw9PG9LKfckqDiHNkFSOLicTCb44Z/7YbzxnW/E0uIifuff/Q7+7CNfgEy6dECcrSlxHkyQlmQEZpL2xRwUr52Jm1Z9DsOjnqoLpV5OOCdMVhAk7S4QwctueCW+68fehV1XXoJ1G9cDAPY//Rw+9E//HZ649yFMOgtseW1RJMlhn6B0bl5rJFnueuyOWyFOOh6k6wGJt8KPVlPCpLgBybkHbci8t4J8VEk9YpwL8wt0fdFWjoBD++IZ6TGhZ7mvMajzdTtdmTcEjnlzrAzzm2f/K6PiUaGdmjD2N9M1Eho2L0kor3WZ0M/p8ALUdFeHVen5rJ98JExm9vptm/C//JOfx2ve+GpMpxNMppOyWHO2PMPRI8fw6AN78IU/+TPc9Kk/x9HDR5Py5FBOCpIoh+JlWRKD7wxTC+Yp23JioJLDxuH3pq2bsO3UbVheXsa69etGWeaUmM9byuvJnBWqFcEqZiMcVxHFvX6YI2xBABgNJEFQKC6/4VX44X/w13DqOTuhqsmpDM7hxJFjfklDQ4bcRCKXK+Go52sMk2uq1RuSxKvczbIBl4Bs9fHdrMM3ziPUeDy1xwY2GDMXTJtrrsdjrKced9ZTCNkQxsSGdXDom3oeNFCFa0la4VLglyMz86Mt7VYmUlanHOYBwbKdjxJq/s3PEV15VrqwT71hRxx/tcXFAmDaTaeDoUqvbS8ZbceHHJsKtmzfgnXr10JVcezocRw9fBRd12HTlo3Ysm0zXnH9NbjsmpfhwssvwG/9u9/BkYNHhtfPgzViIMe9KouWQvAqa7d8NF9M68X8AkGtjJkGsYn33Lqvco24xlCZVmmzEooE6YlusIESXNmVkHvRO8W2007BW3/6vYOx6hUPf+sefOuzN2Pp5CJUexx+4UXPg3mC3QoJg9HyiIDD2+CZCbIX4aIxBEyhbT6C5Uwa+RMOvTzyMb76kLuE99T34Ss7PW8cuIYc0pfuNELDfNify9k6++idm0OwdC3m1ri5eOKqH0OuiI0Tt5tDvTDmQZ7Y+NWoPxyNVIiO22rQluEKkfGv+llz+xweZrpNy6eTSYe+1+Hdf9qXl6NWL6NQOGN24vhJ/Lf//2/g1ptvw5q1a3DO+efg7e99C1731uuxbsM6vOt934sn9zyNP/mtj6LvZ2VluTgmEyqRwahlT2mH8JMgKLB1+1as37geL+x9PoSyfmV8/amhDRstf4Jk2LIB0FoZ27ZRZFWMR5aw5o3dLatVD7QhyLghdxiLC195BXZdeQkA4PnHn8JH/+1v4Il7dw+87aS8rqwyKLFdiy4rIRvfDt22vKqcC0RRwlqIWVtrAeZArD2GHPx7vjLvORzLkzHRl1QRHv8lpdfR8pwbGKIHt7sGKHR53kV0WP+KSDWOn6mvmnK3OtSsnUPUsXAwCmVCx2wAs/y49ZZaiC0kjUSnbdqaUha6JJhKN0mJ80F5e+nLLFsJCVXR5/Pe09PLy8vYffdDeODO3ZhMJ7jvW/fjjq/egV/4xz+Hd73vHVi7bi2+54fehj//zFfw7JPPoptM0vqumiR3rDFJJI/dqTt34LVvey1e/92vw6MP7MEHf+WDmC0vW4dGQq1WGDn0jcKVliEj5Vekl1DMkQmD8OreQl3uysjDK8VIqdVuMsGuKy7G2hTmPnjbXdj70B50k4nzhD7k8AfrNgDDqB2tbGr0ujH14E+xQzEkAK2uqKe1nWOIMCsQkndSmJkSG3v3ZHJ60TiG9Vp+oXPkTnJmYPlpDRalNQKqKcaNoaYmY9E8jTAboHRdw6RURP2ODEn8MSvRMpOeQ9FIaW28ym/1OpOXOATDV55ssjSgW+o6c9jz0Bv5zvbVdcOShskEMu3QTdK/riszfzHamEwEMukG7z7psO+5/fjwr38Eex9/BgCw68JzcMlVF2PW99C+R9/P0Kui1778y9PzfTw4UI18VcX1b3stfu4f/zW86o2vwuYtm0pnymvvBc38Fu8F7FzZlrIYSlvJI+f2eBV9B0nGylfA+xDLb6JBsow6t2TrjxSK6cIUp5x5GoBhMuS5PU9heWmZRKYlyFIqrjhTS4Zbi5cBNUVTTrS5ZAHfTs4ZHccnq1RKHmnrv9L3jLYLUX1pcDj+KJ3uVo4GHspo+lvfU98WlP4HQ4mhpy7sakREw/BJdb2QztdTX6LSSqiRpXEeWNHYCN+pB82kpoxVMF6NxoQHzgkITW2M0FBNaeVhrpjVMLFU3/DWHNr/MMDbpOSqULH3C3ZdVy/OU2Nr1wmeeOQJPHDXbpx9/llYt34dzr3wHACKvp+VHELX5bczp/cJBjQjMbekioW1C5iu8e99HTyCGSsH14FizAQooW7ZIN0FDJRhbv6RuZ8HtGznl2L4sqFxhk1zakHNoCkG45x45HJyPChD7Ak/zTy0LV2HhYSu+tkMRw8eTi+rNW9nARA9m0N8IPVZXO6kxB1ZDgsCsNBj4B3KbgeniEL1BM9efyhmjJqaw6tSMu988GGSlgeSKS9hOM/q5ftiv93gsIoFY57Kt9AmMYhH3G4JU7aKSC1yJ+3PzWRagNw2VS0+myQwf8PzBblpu1L4GV9/rpWGf35kBrmZHwe2sCW3bfVk0TTlnBrvTe3suNOurJfBDOimU88iGZSA58kXTy7hmSefHX52gs1bNkFEMFkzxWTSDZurZz365RlE7CibbEzWrFmDbjJkY2azGabT6YDmkrECgMl0gnXr16KfDdeWl5YxW561xUIVC+vW4dSdO7Bh80acOHoc+/a+gJMnTgBd5+25w94DW7fu2IJTTj8F0zVTHDlwGC8+tx/Li0vF4LkTJTrBwtoFdJ2gn/VYXlyCKrBxy0ZsP/0UrFm7gGMHD+PAc/sxW1pqhKpKxnKgvZt0mKxZwNr169BNJo5XCxvWoZt00H6G2eIyafdgpNauX4etZ+zAug3rsXjiBA49tw8njhxN6+uoz0mCJtMppOsgqpgtL0N7xXRhDbadeTom0yn2PfH0QLcjmURP8stgA/QngSnAmWPXFO6Zglr/C/JjG6+wehI/8s1sgjjkcW+sto1ncCvzo/rPi6dA7fKarEgny5Xa8Fb3iiGndYCt/EMhNcRbGgv43oymMBxcJMIZEBCCcuPi6vJhcRlT6kucIa762WRwQPQKTCW/JosGMVszTbNxqgqZTIYV75wDyOHiZHiLRh66IVRJZVL5N7/rRnzXO96Arutw92334E/+x0exvLQ8nL+VBmHL9q348V98P3aecwYOvXgIf/rBj+G73vlGXHTlRdh5zhmlrmuuvxp/99/+3WFav5/h0x/6NO64+XZEm62qOO+yC/B9H/h+XHndldi4eSOOHz2Be265Cx//H3+KJx58rGyC9m+AUWzcshmve+cb8bp3vhFnnn8WJtMJDu0/hHu+eSe++AefxtMPP1EQYw5bt556Ct77C+/DKTt34IHb78GXfv8zuPr1r8Qb3vtWnHXRuVizsAZHDhzCnTffji/9z0/iwDMvDAY/CEMe3L5XnP2yXXj7z/wQ1m/agHMuvQDAYFi+633vwcvf+jpI12Hvg3vwxd/6Q5w8dhxQoJt0uOTVV+O6H3g7zr3iZVi3aQMWj5/A3t2P4pY//Rx2f/129MuzIpyKwVG8/v3fh3OvvBRH9r2IL/3mH0C6Dm/4iR/AZW98LQ49vw8f/if/GoeefQF2XjX784QEszGCba2pcUzDv6qVLWmf1ITl0vm4IqvKLcPiv5WSUocrL9UwVlmh2Ail/lUblsmY+P2TpnUyx/iV/FELlrHxGoevofBK9z39SmewV+FhaZuNF58Zn8dqrG0yxhnBU+vsG2z3QhtZTitjJQgKPBzFUkIcIqLrJkPOS9IB3QkRbN66uZQ6ceLEsLl6OsHr334DFtYu4PSzTsMXPvpF7HtuPyai0B7o+xnOPHcn3voDb8b2U7fjgTt3Yzab4YpXX4FXvv4VjujTzz4dp599OoAh+X/7zXeg732srr3ivEvPx43vuRFXXndVub51B7Bz106ccsYO/Nd/9J+x75kX0HWZcUMfNm/bjB/5Gz+Ot/zQ27F2/Vr0/RAWb92xDedcfC4uvOpifPD/99+w5+6HoITS1iws4GWvvgJnXXgOJpMJoMD3fuAHsHn7ltL+lh3bsPP8s7HllK34w1/5DRw7fNTWpKWxNY+t2LR9K654/auxftOGUkc36XDuFRfjXFwMAFi3cf2AQFUhkw6v/J4b8Y5f/Els33n6EA72PTZu24JTzjoDu656GT73a7+LWz/2BeisL3IhXYdzr7wUV775dTj0wn7ce/M38ap3vw1Xv21wMksnT6KTScnR5NDMomehPBjnE1uol7M1uSZFJcoGPJz8Vu8DCLDGhySM5LIlE09KubLKIE7MHHHKp4W0qq7zrZJcz/ek6lu1di0b6FKEg2TuZ/6q1lTTmGnog3JT5X5J6OdkZQtJRtbFJDtRzLa4C8aJYpaq6qnEVpQGhKM/Bbpu4irp0j7DYfHpYH03b9mMXRefCwBYPLmIZ554Ftr32H33g9j//IvYec4ZOOPs4d8Lz+wbvGYS+rPOPwsbN28EADxy3yN44ZkX8I0vfhNP7XkKF1x6Pq549RUQETz+0BO4+5a7izI+/uDjQzhC3mEyneBN3/cmKBRf+8xX8dQjT+G8y87HK17/CiysXcDV11+D67/ndfjkb3/MTlMFMOk6vPmH3o63/sh3Y2HtAp546HF85WM34eTxE3jt97wel73qCrzsFZfhvT//o/j1f/p/4ciLh8pShuWlJSydXAQA7Lr8Qpx3xUUAgK997Es48Px+XPLKy3HRyy9FN5nglW+9Hnf9+W24/bNfBSZhFPIYdIIDz+3DN/70C1i3cT0ufe3LccqZp2M2m+GhW+/C8088jcmkw3OPPYXlxSVAFedffRm+++fej+07T8exQ4fx7c/ejKd3P4rzrrkM17z19dh86il4y8+8D889+hQe/dbd5cUgOYTNvHvN9303LnvjtRARnDx2HMcOHEI/681QUdK2IA+nMyR2QY7KAyHWy6PQSsg7YBQTTHNf9cwzpWQQaE0Y+/qYvYoq7puiTKCIf6qh1Brpi7OAEf3FLUC5gfKlcaKDa3POkcXlME1+NBuvmONSWxgaYOUoqErl3USOwg4GKG3WrsJHw85TYVpuBs5klFUqlVBOBgM26Sbo0vae2azHVa+5EhcnRd3//It46N6HMZlM8NzTz2PP7sew85wzsHnrJlzwsvNx7x33lgonkwnOu3gXFtYuYHl5GQ/e9SCOHDqCP/3gnwIKvPdnfgCXv+pyiAjuu+M+/Nr/8WslrNFe3f5FYJggWFi3gD/61T/ER3/jT3D86DFsO2Urfvaf/By+6z03Yrpmile84ZX44kc+j+NphXjfK3Zdsgtv+eG3Y2HtAvY98wJ++1/+Br7957cDqrj7G3fiF//V38YFV1yEq254Ba55/Svx1Y/fBE3Gcnk559KAzdu34PiRY/ijf/87+MpHv4jlxUWccd5Z+MD//ot42auvxPpNG3DFDa/EnTfdkvJ5lATOU8YieG7Pk/jov/8trNuwHj/9L/8OTjnzdPRLy/jmn34B3/rczZhMhhNS+77H2g3rcf0Pfi9OPedMzJZn+OqHP4k/+80/xOLx4/jO527G8slFXP9D78D2M0/Htd//djx134NYOjEYWO21GNv1mzfhsjdeBxHgzs/djG996ia8+PQzOJqMc0ybGtSHtyiMuijMs+0/tgjXLVEQWpFeQiwXZDn99MfqVCamnZ6KRq/1PcWWeSKi5HOrkNPSAkP3a/7MyydVn9jB2KOQ5rPVq+q1nY2bGyRz7GWSBXkNpJWxdY7eAOc6BwOU+ameJtAjMYROAyCpL/NfmOERZ2er27VZrBwfA/gksSaKCrwXXHT5BXj/z/0otqYQ6JabbsNTjz6N6Zo1OH70BO6/czdUFWsW1uDiKy/CmjVrkJPW69atxa5LdgEAjhw8gkfue6Qo4vLyslvyMGxJmWE2m6Ffnvl71IdH7n0En/2Dz+DooaMABgN68ye+jONHjwMAdp53JraesrXMggHAK974Kuw870wAwLduvh33fPPOYUnEpMPju/fgKx//MmazGdZtWIdXveU6rN2wbjg1AQOt/czefnv/rXfjG5/88mAIRPDsnqdwxxe+XozazgvOxrqNG5BfHhvHLbO4n/UpLGUe9OhnPWazYbmI9j3OuOg8XHzdNQCGhaW3f/JLWDxxApPpFMcPH8WtH/sCDj63DwBw0Wuuwam7zh7W1yFvrxpyj91kgunCGtz5+a/gY//613Dfzd/Esw8/juWlpbR1y1Kx9Ma74XuWByWjlX5reUuwqYwq0KdXyw084DphdZKc1fFIe7FpdMajRkNRlKcoNn0kVhiy/mMnVzWJGf20sNBqXlih8SEUA+MS5mRFFMVEZUMF/kfrWdySB7fUBP7Z0D5HLX0LiZXfnJASaofNvdXflUvaF8VrMigwqpt0OHXnqdh57hm46PIL8a73vQN//1/9Ml5x/aAwD937CD7+oU9haXEJ08kUUOCB7+zGsWQsLrj0fGxKM4giw5afs3adBQDY+/gz2Pv4M2kZhYTcWaQvDYfWg3v/Hfdh/7P7U2J7MLx79zyNQy8eAgBs2LQRm7ZuKgxev3E9rnjNVZhMJlg8cRJ3f+NOnDxxsnReVXH/7ffg8P7h+fMvvxCnnLHDxrPXwbBgMF6777h3QG+0hGLvo09i8cRwosKGLZuwdsNa5ARmcH7zpLRcSwtKABGcd9Wl2LxjOwDgiXsexIt7n4fkvaLS4bk9T2Lvg48CADafuh1nX36xCVUPLC/aZMnBZ1/A1//gkziy/wBkMpxAW4VIisEQIRiTZFw0v+NSWR0EPfnIEOGk7yx06V9cOCbBeI1+dNQhsKkt6sEHTlGWhFWoORIjYewwGRXQR+YbGXDrUzCQzkimUK58jcaqFVgFXvBIZPoa1mRYXtHX9ehYzXC0tSkYxtG/v9NycFpXWP2clhMCylqsHI4M1eSp2+jF1q1fi5/9ez+No0eOYf3G9di+YysW1i5AVfHoA3vw6//6t/Do/XuGqXIIptMpnnj4CTz31PO44NLzcNZ5Z+G0M0/D0YMD+jnjrDNw6s4dAIBH738Uhw8eoUWfDcFsTLlwqb7v8fzeF9D3s7SXcejjiWMncOLYCQDDuqLJdFqYvfWUrTjz/MFoHj10FHsffcrxous67HvmBex75gVsO207tuzYhtPPOQN7H3kSHR0hDQDLi0vY9/TzZeV7JvD44WMlV5QX5jaG3sSPBrW2Y9biZM0anHnJ+ZhMJtC+HxDR4pItlAVw8tgJPPvIE7j8DddiumYNzrhwF7rpJKEs/3n6gUfw7COPQ7oJOXGxXJPTa8u2l5VDc3WH4oAY/pR6pbZFVfjmBbp5gAOXiNGhy6clNMHPOzojPRaD5FDKzE34Vuv8UL70JcfLo6agMKfklhqhlN9exvysXg3jVrQPzXv0ZOVj9FKHh2XChPpQOYc8OxNSafGrVW1I0NoApihnQ+WYdjhXvQPI69dEdF2H0848Fael38vLMzz/zAu4/c+/hY/97iex++6HirJAh/IvvnAQj9z/KC649DxsO2Urdl14Lh574DEAgnMuPAcbN28c8ld3P4TZ0nJR5l76UZBhUYFnb9/3A5IpeqHp+qygoPjZdur2MqN35OARHD54KJ02YUbr5NETOPjCiwCAhbULOOX0Hc1Fq/2sx8njJ8LAArPlGbRvKKuXkiBzUhXTIEhr1i5g2xmnDmOxtIwDz+2D9gqZ5LVRAp31OPDsC+hnM3STCbaefiq6NWvQ5zwWtbHvyb1YTNdr5nMeKz/oU9dQo1qdfQpGhjxsR2OazyH3BiO1yZs5oxHJWYr8hRLY7HSlUpa88FSoW0pJYp+XAjBMLITlDVKMAbOncSSjEllMvpPpwPZstNSf/FVbgRa2oRxV6Lk72z2GkIWtSvfg85JK/KvobSTPw6fyWZk3kY+aVrqzd0SytnnJfpfX3IQN0UuLS/j6n92K5556DouLS3j2yWfx4D0P47EHH8eJ4yeG5zLzU4OLJ07ige88gDe9+41Yt2EdLrz8Anztc1+HiGDXxcM6pRdfOIA99+8Bb6vpQkiY1051qQzv/K9USwTV/rEWfMewwHNhYQ0A4PjRY1g6sWghqQzPzpaXcfTwgAq7SYcNWzYivzG7WsunnI0JMXnrI75kvhYhO6vegOoV04UFrEtLH2bLMxw/fLT4fatVcOzgEcyWB4O1dtMGTKZTLOli2d2QPyeOHB82xTPv6LutwW54EgUdS5MtSAtm+DB+sElBYxtGfN4nFs+/i/Fjw9d4Cayvo22QV9UwHSq44schy1BnYWgoGAu1Ol1QlNKN4tLLNdN+ylUVox9ftdXK6dU//QJg25OZt5wKW6ZMZz44IPsloEKR05oZQhaTXrAUEvOLJxfx8d/7FG77yh3opEPf98N+OpFirGJ3VBW7734Ihw8cxrYd23DBZRdg7fq1EAC7LhqWQjzzxDPDZumUvzKG+Qo7kQEZCgY8KDn0snJdfl0ZTzkHw9Kl+woMq+rTbONsaXlAYoKC9CTxIId0gmERZ3lb9ipls/2j9XbeHKq0PzYcaU3cNG1d6vuUj8oZmnTGlyKtvh8eLGvogtcHhu0/vMfS3S8eL4R/ajJjSmOhDCsO26Q6RAMs0Gjz0KhSM34uaosBGgO0wVi5o7L9UJTCHsVEWDearDGyiHXOpmQnnKfa8ljrPDnSrNel0YK1VN1MHWt72ZJWOMIGjGhgoeJr1M8SQWcnFPf/Wvajtq/VdytQbI42yiI7MrWXUJRmKqHU4okqW51mqmRiSg1vM1LZhDQ6wd7HnsFTe/Zi245tOPv8s7B1+xb0qti5aycA4JH7HsXhg4cDLo4brzOiETJA0tigLcVo5Zo6V0DKWrLhZ7jXpefpXlchthJtND8c8owZHj/efgA0DWZttGljLK0iZqLyeJXTVBvO2W++CAmQ3LG8H5MGX4RyQk5myTSpVuFC2SMIfi+AX5CcKRnlnFg7w/MtlzbnTYCiADq3Qr59VHU0UgqvL8F4tU4oDPpU2uD8UYGBnsn8noFylEsDCNT94+v0l3ezU9zlTxMlxJaiLHFdzMKoVh3zw71bNPc1kkrvlWSASEJasTl9hjdoZdtL1tFtQ81aE1mlKLNzwywjnaXl+JfrFxw6cAgP3fMQAODUM3Zg57k7cdqZp2LH6aeU9VdLCcE4aBoHKesSX5KuolGK4RneAFRthSmocMjx5PzSmoUpptPpcHa9DDm9wbhNsLB2oZC3vLTURG5G1hzY5bpFIQnJlGpd1pyHYQ1eUtFJh2kKbSNCmy4sFAM9W14eVruP0ViWJHg0l++Z/KcMR5KHPsmAncyhmPU9ZtpXtPuDeKTud8Wd1rWQIWpGUGTUlQyrWljNZX2AGP9qCffnOYGKXrV8kcbq6Qnff3UeId5zfp06WHSWpmm1cMH/M531xk1Dm+w8cy98TRkYcBoB1f5JZRqp72PHbRaEjPxKGVqVKgUyeE74Iyi4ody54aiPvDxCw7qh/FlaXML9396NxZOLWL9pPXZdfC7Ou2QXNm7eiEMvHsaeB/YktCjm6tCoitaT1LF6ILF48hBbg3JcIjh25Ggxlus3bsS6devszTOJJ9M1U2xIx9vMZjMcOXA4CHv7M4J0C+k2VZ3DuLoPVZ0kSEsnl3D8SMqtTSdYt3mjIbMst9Jhw9bNZRP1sUNHsbyUN41LTRdISEng8zIBKJJRyn/VGaeejJcS0QKUt3YPldqxP1nk+OidXJBDQN4aU/AVHVHsogXXLwtvNMiNrUvKjthX4PpRDYcZzVbD44sjjR4v5N5DqRHs+xF0MF/ixaBRf7Xou/eInFJSumY10LKFDFRySyVPBaJhPPTgeqMDwehTZR2WQffSGTdcjbM8SYgLE9QYkgU7n3tlK/sFj9z3CPY//yImkwnOv/R8XHzlxZhMJ9j7eMpfSQcUQV/BEowZKsecrDh2zAs/nxHhwX0HcfjAYQDD2fCbT9mKHl7A129aj22nbgcAnDx+AvueeSEYzqp280AkEF4Y24lrEyWpDHaeFMn1L544iQPPDotCpwtrsH3nacirtPOj3WSC7WeePmxWB/Di088NpzzAFoNaA4ygjI9lTVMa24KkesVMe8x6+82LB00MDcb7XBRcqTba4QL0syXkQTYNcYQBaDxrpzzQwHMZghWEU9LDIwoajR9qcTFjqOVvTBGN4xAzXF4yxu+zvrfoZIfH9lJV0RM99vYdj4b4dzCvjkI6o6Ia5pAZSivd0wUORTKs9p1uDYYxxryxOqNlCGyAt88+/Rwef+hxAMBFV1yIi68aFjA+ct8jOHzwCFaS0IV1C8ORzsGfVUpNjLFZTl+mTwoGAAf3H8Czj+8FAGzYshFnXXiOybgMxm7HWafjlLRebP8z+/D8k88lw6BoLpbIiwMZCbRFrfo3qA4ta2zJX4Ijy0vLePrBxzCbDdt8zrz4PCysWzuITspFrd24AWekyY3FEyfx9O7HwhIPqRqwkH/4l/k1S0ap57+USzP/JeV/WaaEr5WstAYUUmlqqY95li0fn61vnrtWWZZTf8M47VIgDU/k7B7pu/utyrdcnBJHufquni6/QZw76T1l5oyhsdo4GS7yvGbD5arONQQD3WeloHQPJ5NiHitysXJUuR9Ne291d9rPCB3FAXaSgnZVcTaGUBaHAyVOFhw9fBQPfGfYpnPBZefjgkvPw9LiEh749gNYWlxqJktPHD+BfjYo1/bTtmPt2oXixauVv47RSsIzjthEBMePHMf9t9+HftZjzcIaXHXDy8tpDZrOvb/82quwadtwGsVD33kAB8uLH2IIwt6xPoyWx0m9fNm9OeCxiCg999hdu3Fk30EAwK6rLsGp55410K7DurCdF+7CWZecDwDY/9SzePL+R5zBiONc+NonpNwP4d+sH7YKzXTYP5qRVjbOCnEGBMgRPiN1UjIPvEi2PPzhYNkMHxEbsrTFeI5zPvwDvJkhz81ax0noImcsdWy8uPUaAjgDFRFHapcNgCAivxGjx7Ao/ovCpYmvhJ5djk/T7oT824/O8EvZrHBoHh0Et5vpidnI1md4ruv7YV9eP+vhNYf6nBnZMlzhUoGC0iAaQ55rNpvh/u/sxrEjx7Fu/TqsXbcW+59/EQ/f9wgNmz2tqtj3zD4sps25F1x2AV5946uxccsmrN+4oWy+9oITaavRVexG3yu+/ed34LknhyOer3n9K/Cat74W3bRDr4oLr74EN7zrjei6Dof2H8RtX/gGFk8u2fg3Kq3ySBEFal1Wg4FrRTLDs9lQDunIvQ8/gQdvuxsAsOPsM/C6H/4ebNy6BdorNp26HTf80Nuxecc2aK+458u3Yv/TGR020GlCU7M+5aRmfTFUOWcV0VdWblOuGuJXMUI1seaNVLMCrb0zIyolVBsRi5MsNhQVD1i5A/OzYudZvVKMEUxEOGGwqVrvRhvEgnQvhnBpAMR5PEU+7in3IyMoyfQz8oItKa0BgJUcxt3jszqs99MVLu9PmftKXcbWcpiFBgBM+9lsOGVShtkiEcFwABa9gj53pKHxFXLIie2cwSdsWOYQRPDYg4/huaefwwWXng8A2LP7MTz75LN0RJC9OUZE8PjDT+CZJ57BhZdfiC3bt+Bn/7efxfe+73vxzBPP4IO/8j9w4PkX0wyfVgQ2Z928/A1TyJ3giYcew5c+8kX88C/+GLacshXv/zs/jZe98nIcP3IML3/jq3D2RediNpvha5+8GQ/cfi8Bq7jBUwwAldxebl8CfWonAbBg0+ukmuPoZGRYhf+1j3wOF7z8Muw4+3S89vvegq2nbcfTu/fgnMsvwqXXv3zg/d27ccvHvoTlpeWy1q2H580Q6vXIyyO8OCp4iOd98oJbKd+zM6NaJec/6sEphoUS8lmX83kiuUw4xNQ9WwCYZgVoGNO6mfACXd5+EwoWogxFOfSXryr8eilXRuHWQ4m/51dNJAOUOuW215ChEY0vpggH93Hg15j59Cgqhd+qflyBtOKfJ1IS3xlJw3Sh4nfmHQuhFFErfJjq4EqTt0ibjfOWgzInSQKWvWfRGKX6G4bKEWDx7sH9B/H0Y3txwaXno5/1uPuWe3D08DF3PrcNMPDcU8/ikx/6FP7SL/8lbN2+BdtP247tp23Hjp07sGHTBrz43H7HAju7nJO/XlAk3AeGVeKf//BnsO307XjzD74NO3aeiu/+8XeW+4snF/GNT38Fn/iNP8GJYyeGZRJlxtIrglZtKrMBRYsRipAlMkQgHrmEFf65rke+fT8+/au/j3f+9ffjlLNOwzVvuR7XvOX6oepe8cS9D+Pj/+G38eyjTxYBiu+oK7xQ9UMvwRCkv35mCAU1dSQrbFxthDyS5sDJnWUujWUGZIGKEibPndfl+RlGIcKzJmSYJNRGljxr3/rs3wRUwhkJdFVDGYyNajCuvDYtm2KUtVfWP5Mq9720S5itlWMgicwr/83WEpqsJNYMd15m7I4GB9wx1Mr0UbVjvo0nOUh7HS+zHZ/mFepFMDqB6LBSvbxsIa3bOXn8JL70iZvxwJ0P4sTxE3j2qedMioH62FgmKijmmoU12JC2khzYdwB33XIXVHtI2ERcGNcrvviRL+LA8y/i2jdfhx1nnALtFY89+BiOHj4GiKDvFXf8+R04cmjYfrLn/j3VkB0/dhw3f/zLuPe2e3D8yDHse3b/kFBPyedOBIdfPITf/w+/i0fveRiv/e4bcMa5OwERPP/Uc7jjS7fgm5/9Kg7ns6GKgR6M2S2f+xoeu/8RLJ1YxPNPPQdA0BeDIDi0/yBu/qPPY/3mjTj0wv50FlfssRcGxbAl6K6bbsMLTz6L2dIynnts73ASAxsLGXJVt37yZux/+nlc++4bcc5lF2Lt+rU4evAwHr79Xtz6iZuw96HHPG8T9Nt9y10JBfbYc9fuqH9VSj7b22wkxIubf07YEHnklX9Xz5TeB+1hutsA1BBSadMjoDrnGDpXiBiMWj7FoXMFUOr1Lw4ZqcrHeFXOzd4zmJGWkqYzQvKoaOAfvRXIJdCpziKHGuyJGT3bckU8Ci9H5FyVVG93JmBTtmQZIo9yZPtwyZCyH7CeDvS/YusNxQbaynFJYWIiqsu/xbbMBOGoj4ERB874mX42w6tf/yr8o//8v2Lbjq34+he+iX/9y/8Gx44cs4P4QuxmyFuxZs0arFlYA0CxtLg0HOSXWSmmICi8NhiQabVmyIqT0uXBXb9pAzZt3QQR4NihYzh+5NjAq/ACC0Y/kjxRGSBzPmWQOhoQN4CMpDjyEFu7xPC6zv8MkqG9Ys3aNdiwdTPWLKzByWMncPTgYfTLy4BjMa9Gz/zTSpkZDAqMf0VuIg+Q3s8oWSjV5ITLJiZGNGaozMIkO+GAFBw5xKKwksc68BQQ2u1gLxKx1fbOrNI4eEMbx6djdBgiRntOyb8p6Qb1rzzH/aG+WrYJbo9CMljCoR0U3bzEfBl3b1iLI8inxhZkNfyeiI1551CQ2mGLvbXDMtpRSFjGnOSvLK4lQ5brhqbTGpj7RYH7PjmkFCKmHM+AgrJxIuli6JdPf+B3tKntM1u/YR3e8v1vwrYdW7F4chFf//w30ivvmXU06Bni68Co2fJyOWyOhcKFSMlI+sV0SPo8TMtn1JMXSHDiOFd6/OixdO46XL+1Vy+NasEEFOjJSGkw2EMS1JQo88zuc+dZvurkAvla8/SJpsWTSzj57D7LoWTB76mJ4qEz0vJtS4MUPzaNbTWEntx98YoetzS5MJC66Xbt51xVWI7Telmu1RFzTxQW8piQwY7BaUUT8a6Mg1C1bHALkTVVrZeZMk0mQBRmSZ9K9hZK0iw/h5ecoyLAWIyEcjdSW3y8tY2L9amMbUBo6v9jHB9NdtoYOAQ6glQFimkhRKjitLYmr3rPu+ilN6RVTjDoOhqTLPxhwzHMeKgqrn3TtXjd24e8ykP3PIzb//x2oqymdthTFWITJ6R8NEhmgIldeWszGwhIGWhtMJN9cD6ALw9uPge9DD4MSjuB9sMNBa3wFioX2tfRHz5CcKud1YbfTUnDvK1LfYwkK5z/idA8G+YADRl1dAk2lGu5DjFvndG3zxsBfguKlo4q09iwHq299mPmyxypdYRzpREVV5wnC6pjbRH6zIpWu2E7OG9IpdWGxQaFkVFfDJlpWEROyVgRGnWD3Fwjlv8jfswJhVr+yvpvO0G0yCQbH7bT/FdYeCpEL6Euo35aYnRSuYI0EtDNlnR4bf3wQtSS30pMH0JFe/1TX2YUkmHTYenBZS+/FD/xi+/D1lO24uSJRXz+j7+I58vrrtpiZkfCkFYCRDPDmeRfxEfjYchKvSU2jghH2Pvl3/D1ZUMfvHBWWi8NVLUXW/+K7zygSXlsA6wJm+uXqpO4sqylzEzS2460pdgxvKGpg4Cw2FjZXxNocfxgCxgcQHbPlTjyuHrjXB9glY1OJrQWemkwPquaGX3CXSWJLo6mem7QvX4CJJBZdFzF3IZT5vJ0cqElyZ5bsDFnw2R5qZ6Mh1+y4IxAWUaggZ5aP0D3OKSeCN+jSMxB/dosl2FKctuFelqPDAWMfrZpU0CKUHtsaF1TN8BDR/ocGqZ9YL32kC4plwK8SFB1OGH3ytdcgZ//h38Vl6SV7bfdfDv+/NNfQd/36Z2H7f6axMfkwAiDnJUIiwtLORLnaKuKANTHi8T1ZRYG1alm4QrprhtbSoDmwRmQn5lHIeMDsDBnq+Yp98javFXFjwZc8bM/6vpbUBMZoQn12+XqCFG5RHsRLamk1iVlWelL2AeyCJGZ9ID6JqrxZ8NVUHLAx4pKloo9KyeE+qIFuRd9SvUFAxh57mgr7cbjibX+pzRDargaOY9V5CfJjh1sWAbG0GZ2OGo8ixvyJFASu+B6WXgVCtL4ldMaohGDn7k2PZW0rIEoyibKVip7JS/Xim6YpdXelDe/EaXrhjc9v+yVl+GX/8+/iYsuuwAA8NC9D+N3/vPvYd9z+4Yyfe+T3qQcWYFF+F5mtutp+8OCTvG0pAGrUEc0ShEINH4XJESwwL6mMCl9VRKKCMTs6FotoVkePDakw6d3KIERRV5t4dlABk3qTlRT1c4YkQESOlQxIFFn2MgAss4W9Fu+Z/4Zs8vR3bk+msluDXDJkeb35zHwIcNVUCn3nJWmWMVsybJSiZ8IyL3OoaSr0fSCERXTglC+GgvJ4WtuxNCV36KjZQGrC+UByvAkqdEQZIU1UflHnH5wBjHMQEoekxZ2YOPHosf1eYA6ikOy/E6HV52be3en0BLELw+RwoEGUFkTySj0s2GP2ZFDR4rQPnjPQ/i//8Wv4r5v3z+gtX6WBN9mGkVMWKQ03CE4t8SYhAKdEtJpRrl76vvizhuKzGGQVoYvD3wIYFJ3y8nHFGIOl3ozB6qedhKclvBkwaoXDVqRMttEz1giOr9RWAqvokezsI6uM5ilMcn5IjNMSZQkGz2WjegMtDIQ+aqhUUMNrXFxiAeWqZSqDPEpGUYXvcQQB2w47R2XbkGjm5hi5A7ThWzcIjiq5Emt3ihwHALm3FBKvIuO88d2HpBBiaFb/kYoiw1TprvL40cyCPdVqcOhn0U+0uwwOeXOSVmICiLiFpbRoWFLugfLmxeNeqYMXodnzJyIBOkq0+UCPLXnKfzZx2/CYw89gd/7z7+H++/cnU7qTP9oVjJ/Sp4sWQORPtzP74xNnsLlc8jQRSNHyfnsyXvYAOWB75AT89xJdge0yFUN4ma0w2faazJajLwqGc6DytOHrOTUVxReEVr03HeMYMNtFZCRYQNFQhKdSDRWjKg4ihoHvRHZsfCCFGleeoIXF+fcT2a0kMenl+sGY8FGnHntlKaEizapU6qpZv2IVvboXH+JFuI4NcasCgFtAE2WKZ9VbXexVAOLk+Wns4Gy3GNxPnlMU7rBO18tXPXvETFLYcg7R0khjOCHeWxKfb6HLhJ55dYbtABcwrZ5htDCouC1GiIoXVdO+Gx5gK2nbEXf9zh84FA6RtniZpBy+CYbYUoqkxW7tJbqWLdhHdauXQBEsHh8ESdPnCwwuvXaMHagsa3c5y7FQmy8LXw1Q75uw3qsWZhCdNiwvXxykUbK84zXBmXpYtrc6ahQTCYd1m/agIyKTxw5Vg7t4wV43mDbu9wUAJ9fyMYlr50ChrwUyrNmEMvMcK4z9oOUI/IpixavNRrqzcqjhRZU48AV5nVHWtorv3P9YuVsRo0MfQk/UY7HLmOc6XD9MCRQnCDRZoabFdYbACDwjCIC7rtoTyi1t/vlWR8OmvGxvbS8nMHHHBZid2oyk+nqRIbrpV9miroRwylMA/HCZhStHoGi45XOPB7E5bwK32RACrKcqusOMd1hsdShTrBl+1acesYObNuxDZu2bMR0OsXy0jIOvngQLzzzAvY9t394W410ldE7mN4HKOHVVuw1a3vo08WZSYphrVOZncpGTwRv/5Hvxlu+/81QBT7z+5/GZ//gM0XZoFLyL2XrUXE9FEYGSNJnOO48ji3+U+2xsLCAH/j5H8FV11+DpZNL+OivfRjfvunWdGCelj446cnCnaMD1eFVXcDwskDyblt2bMP7/sFfwWnn7MShfQfw4V/5Tex95IlyvlVWzsl0Ul7WasMrpMw84oycxCtefiZpUydoOBQbJ2eAzZW6Mi7JImT2CQX4/Xuw9WHJgJZQgVyvRVZis30VarPnXLqgLFOoV9VbRGiIStQMjEOE3N0ytiTd6mlwGxwLXyw5Lo5XZixCcEehn8KdHxtf/lEMcVitjuyEBO4Nzvmvqi27oMXKlsOSQiIbLV8L4GWhcauRgjFNG3g0dQIcoEZOZOa6Nm7ehF/6Z7+A177pWqzfuB5rFtag64YtMSdPnMS+5/bj7tvuwef/5Au485a7sJxewZ6r7Shmd9PfUsCjCUWzFyGE0GTOypnlg9c6/ewzcNkrLwcA3PblWzHrZ5h0HfJrmWaJlpzTMhpz4pZjbWvahQMN8qQTnHnB2bj4mkuxtLiELadsRa9lcYivrxE3iQguvOoSvPEH3oLjR4/jy3/4WTz/5LNlXKZrpjjv8ouw84KzcfD5F7Fuw3qY+CnWbVyPG77vLdh15UW45yt34Ntf/IbtAiDmVugF2ZhxDorDQKlQh9Vnntd6aUneooAufDCF6sp9E9DqJTseyI7leMkAgeiRgrh4DK0JWyZSDFmWq6r+GKZGubQ2xDdS0GX5nss1tui4Ux08i7NJq+SSbVttcjLVYiGe2DgKTzzl0JVSEMF3FxthaxkzAje0VriUx1X48Rr9VemK7AiYBwCm+bjcemkDhV/Jqq5ZmOKCS8/HGWefDmA4Inh5cRndpMOWbZux7ZStuPDS8/G6t74WH/rVD+Ojv/2xdCSMlC03LNpllq54MG+XXViWR0RBi+zaq5D5DdbZO+dZKF7FO/DEr7JhYWrYFDcaASS1ZCSEBTk0qsNDVWDDpvV4z8//CF7zthvKyRN//J9+bzhuulSfEQWFuBiOgrn0uqvx/b/0k9i4dRMufc1VeHbPU3jy/kfsJRtZQBOdJcwDjXOcGczGosQ5hHiVx0eDoaBp9mRomBOlTGK0pvay43F8VvoBFAPHmSwHefioZAnVBRoBmtmNSR8vFW53gp84qI2bItPo5SiHPAXJhOy8IcxkmjTUSos+JcnBELJFZ5A7SzO19JdDNvD3ggVyK2Hxq3qeCD3LIVzbpbQdQXTn/HQA5PZewrw3DhQOmMkOsB7AyROL+Mj/+Cju/OZdmC5Mcd7Fu/DG73k9XnbVxTjtzNPwgb/1U9j/3H588WNfqsOIMvAWyzHKyZ3mnIAy1Y3u55Idrf8q7Ct5L5qaLh6mZjWHGtFkiVM8jS35mUrWI0ev+ALp+8L6dTj1zMEZSCc45czT0E06zPqe0I7vP+vMtjN2YN2mAXVt2r4Fm7dtqcI8pA3m67dswPKJRcyWl80zdl3xluPG2i8KjWGUCZo5gpJorkLGVFY9jyLbQzBdpNjCNYZdlg8rkKk0GwxAybUy9BKbOBEyPBU9NWLq4R3C8OoxcSiq0AzLsfnXpMGVZalhhG/mZLiTQ0FrSih9YUIfDUxeemB1m7Hi9xQ6n6Gwo2bcDDOBHeK5oU6l0B3Ft/C4Ol1vqOC0vASUBrGUydcLQjHSlhYX8bXPfx3fuOmW8j6/L33iy/ilf/4LuP7N12Hr9i34/p98D771te/gxRdepLfVGHvMeAWDRowtq4B5RqzuRyPZa9fZWOXBE/pta4zMI421Y7wd+pBeO0THeYT2qTzNm1RwWCA4dugI7rv1Lpx54dlYPH4SD9x6N2ZLy64wC45blybAk/c9gmcffQqn7zoTj93zEF54Yq/NtAKYTCY444JduOKNr8aZF+/CZ//r72P/U8/SWOekOqNsblNrZKGsTGPLEUwDM6r14k2LZ8XfETWelR01+Tvst7g1eUJKRtZQbflFRi+9eMPqbZ2fyOBJmWHcLNzJOa6yZqvQ750S91FdmcYY04/clxKqectLJewKbzQvqCrLvhsj2wBfUBxZsbbj4vWAjLDyIIVozZFKsT0NESPH0K0yDpbD4hvREuRZsM5HqJPpFGsW1gxJYlU8unsPfvf/+n1ccuVF2HH6Dlxy1cW45KqL8c0v3YIOnWuAZ+28AjRm8QJjmt9L6BJQDg+exPoMfUlsTdBoSRtXeHV4e2i5TS8oPmRYOrmET/y3P8LuW+/BiWPH8fB37i/G1bxeqDcZmm4ywRP3PowP/qP/gNPO2YknH3gUB57dl7ZMAegVp5x1On7iX/wN7LrqEux78llM16xBtnZZsJu0U8iUQza/XDTxIlqqkE/K/c9hIIeNZRAzwnOviHeZpuFX6x2AqXKVUH9yCNWbn5O8Kcui6xCXtU7aWkBbu5W7UZYDuOQwy02dDnBNlpDW57M0oUM7BbR2CgE8giOKOCMYUX/e5yveQhbeZ8Ns6MyjNd8hb6xyN2z2NuIxz4FopI1eySEhtSoIiMewjoTtM9IJRDpAOnSiEOnw4D0PYfddD+GGt+7Axk0bcMGl5+OWm25znemEScgdGhBc13VFEOJqe5sPMGGNKCi+d1CKQlJdGcqScassu2N2TwiMjI9p34ofTjTmt/4yis0sObz/IG7//NcAAN2kK4Y298MLpb1TEQC07/H43Q/h8bsfshfEJvSloli7fi22nrHDh/ssQJpwhvC4pLai3lZoxMaLvT8vF2njCKrHlYjbNtioNSqUqkqSX0ttqJBBKPdi0plRNgUpZOcyMsub4WPuK4y++zZi093VHgXzDe33ZFrI+nO3yQ2TIwzrrFwIWDwQ5ayKIFCd6vSsy44luC2HxhsDY4dOeHTWsG90i8ECLRy1wbXv7Hla65cGC96VV8SLACePL+Kpx54GMCjc9h3b0jR9QAdZCXU4t2nj5o1YPLGIk8dPFHhfvJcINmzcgHUb1qKf9Th2+NjwsgpBWXyaGdERkiq0o4N0go2bNmBh3VosLy3h+OFjpHAcCibm9sNxOuvWr8PaDWvRSYelxUWcOHocs9kMk86WKrAuuS6mgZCuw4ZNG7CwsAaLJ04OZ2rNQYJIyxTsTdZDRR1huVKenhNI2c8p3H+GT0HJy9IOvkc5i6zwWa0LwlKuKok1ofxQnYVBId4Rvh+EtkYQio6etLkXW7CrElTYbUIkxci5JXJ+MTtl5owMhxrdpW00wqwwk6zCjsEruRuWIlK8al0tiuI6G9auGCgYau4KbXSCrNsQTahNqYFAY5HPsrA8jlk9CcYq0o5cMoKsZae2/2Kvqnf30iCXxZ2Oyd4yVg33ihPHTpYik8mkLH0454Kz8eZ334i16xZwz+334dYv34aLLrsA73jf9+JlV1+Cz/7R5/Hp//lp8hyKHafvwBu+9/V49Xe9GjvO2IGlk4vY88BjuPmTX8Y9t95T3qQzbBkZaHZvgFZg6ylbcON73oRr33Ittp26HUcOHsHtN92Gmz76Zzj04sHBQ+bEqg7v9bvgsgvx8je8EhdddTG2n34KptMJjhw8gofvehBf/eTNePyBR9NgZiFseFcFTj3zNNz4Q2/Hlddfg41bNuLA8y/i1s9+Dbd87qs4efT4ELLRI1e97uW49NVXQqF48PZ7cd837yxSEw1cRlFd2ji4adtWXPeeG7Fx62YcP3QEt37yyzi87wAuec3VuPwNr8Sm7VuxLp3yumHrZrzlp38ARw8eRtd1eOahx3Hn57+GK2+8FjsvPncI8e+4Fw9+8zu0dXQIG7aevgOvfOeNWLdxPY7sO4BvfeomHD901MmG5UTMcHOKyhLalWw7e8ML3p2xVkBo47jVl9eNmToK08MOW/LeQxPmsgQiFyHjHXNiApMbPzLaUGaveCWXloxZ5pkz8ozsYPwyQ2p05wMhY65q+G57N5nFmirjMLAFLBLF3oBkP9fqIxsp8YjQ9u7WqFPn8SzrpgmCkuWU5hMxb8FxcGFiJ1i/cV25s7i4lGJv4PSzTseP/dyPYNOWjfjEhz6FY4eP4hf+2c/j0mteBgC4/eY7IGnBqfaKXRfvws/8vQ/g2je9Jp0wOnyufM2VuO4t1+IP/ssf4PN/9HksLy8bBCZ0oarYuGUjfvxv/iS+9/3fW14xDwBXXnslzr7wbPzuv/kgjh467MKZ8y49H3/jV34ZZ19wdmUkrr7h5Xjlja/BB//P/457vvGdMrMWYyZVxSk7T8VP/W9/Fdd9z+swSctHAOCy11yJHWedik//xh9jeXHZhUyXX/9yvOtnfwgA8Olf/wge+OZdgxAVJGu85y0z2is2bduEN/34u7Dj7DOwf+/zuP/r38bB5/bjvKsvwVs/8F7Xlw1bNuH6H3x7+X33l76Ju77wdZx9+YV48wfeCwC441M345E77sXSycWy5EB7xVmXXYi3/dUfxdqN67H769/CHZ+8yZ9yMyLAfKG17qZe1MpGJJfLGhQVAdFq0IZ0Kxglm+1XNiA2W+036LJhKmvTGh3kPY4ZOghs+cRgXIUjMqK5tFoMiDPIRK+lJiifRLkqISNWD0U4nqjBF37eoXlnvHhBcnt7UI2suNkaMY2FliLAtOSD3FKDdgcq6+tczeBG129Yj7N2nQUAWF5axgvPvID8RprlpeVydvppZ56GH/9f3o9Lr3kZVBXLS8uYLc/SVgnFth1b8VN/6ydxw9uvh6pi9527cd+37scZZ5+Bl7/u5TjtzNPw/l96P55/5gXc9qVbS+4q53oyL17z5mux/bTt2P/sfjz96FM4Y9dOnHnemVizsAZv/oG34PEH9uAzH/oUdUNw7NBRLJ1cxFOPPImH7nwQB/cdwPbTtuPK116NHTtPxfmXXYD3/vyP4ulHnsTB5/eXkJRDgq7r8MYfeAtOPft07H3kKex/dh/OvugcnLLzVKzftAHf/RPvxpP3P4pvfelWL3CR72IeaTRF0hAIvrz/6efw4C13Ye2G9Tjr0vOxJoWmT+9+DIsnTqDrJnj6wcewtLiIx+7cjcXjJ7Cwfh1Ov+BsbNi6GQef3WdpIxGcdsE5WLN+LQDgqfsewYnDx0w8nZemI3qyT2TnRqHmiMB5FJ+2Z7ABySKfv5RURhWq5BaDkeHV58mw9YAt7CxWmNIjFcul0g2lRGBcaMOLMon0smawT4Uk3DfrGRxWUubynivxRiKeCGdI13ip4ZloBhyK9OEYfR2MsyGlHD76TmS+RtDrqqZnmHtTRy0vaYjyglGdMBHoFRdcej4uvvJCAMChA4fx6P17imdfWlzC8tJwtPEVr7oca9ct4MjBI/jq576Ou265Gw/e/VCKkQWv++7X4fq3XgcRwZ3fvAv/9z/7r3jqkSexcfNG/Ngv/Bi+/wPfhx1n7MC7fuKdePDbD+DwgcNl/VChqpP/h7L/jrPrOM/D8WfmnNu2d+wu2qIDRGEB2HsvIkVRvVjVsizbkuPYsZ3kaydOtZzEsaw4ViRLtiSr2aIkqlIUeydBkATRO7DYxfZebznnzO+PmXfmnXMvlPwuP0vces6U933mecu8g1XrV+Hwa4fxtb/4ewycPI/uNd34yB9+DFfctBu5Qg63vOM2vPbkq5gcnTBml8TU6CS++d+/hsnhcYwNjCKKIoRhgN23XoVP/OlvorWrDZsv24qtu7fjlV887/Y0slkNMyF6163Ca4+/hO//r29henQS67ZvxAf+6BPou2QDGtuacf2Dt+H4a4dRXlquGnsuKFwufhVm1ZwZKXDomb04+uIb6N6wGp/4yz9Gc2cb5idm8IM//zLG+od0eZ8oQlSJMHzqPGbHptC5thct3R1o7V2B6eEJs1NAIciE6Fq3ClJKlJdLGDh8CpUoQhDImuVsHJikaARf6xj6CKRNLGEFkbmsHMMS5MvyvU3OJ8lfcS3wIMQ+S6CsP1Qx5XZ+oJTyMgem5wETcDltdH/hm5csuGiVl28BqnKxsR6Qb9JrF2ub6x6Zmwrcr8YzAi0ThHIAyD7nvt0abiVzFxp/Y//X9DWlRrwGLaclzks+Za4BmaZwfu4EC8bXctEo7dNQiT4BuK2zFe/86NvRsUIf5X7wtcM4d/K8jS7GsT5EFQAamxsQRzG+/b//CX/7Z/8Hjz/8BPpP9EMBaGptxI333YBcPoflxWX8/FuP4vxJfbT9/Mw8Hv3Oozh/egAAsO2Kbdi4c6OX3c4fs1OzePiL/4zjbx5FaWkZZw+fxg++/DCmx/WxYKs3rcGGHRttv4UAokoFb73wBi6cHkBUqUBAs8U3nnkNB158EwCQr8tjw85NCMLA8yVxJRnpH8KPv/Q9DJ8eRGmpiGN7D+KX3/gJSktFAMD6XZvR09cLKCd4nizYYWf/r1rdUqtwen6gT/NZmltEcWHZlhJKkgTLC0tYnlvA0twCysslQAjMjE7YU3UKDfXoNkfb01zn6+vQaRj0/OQ0hk/3e2DCncZcpmhjru2YxyeF/S/tq7JJklW5Sr5MkgHn0uHSPIibcDzvUH89gbKHwyZMnW0rDXEXqUmwLmtvKgTcMe76TykgUTpbng4kTSCQgM6A1OcM2HbYawsTSDDQIchPy8eM7VYgVVfuLzF7YO0Ysbmpkh5Gz7xS6Ewo0zmPNkAg3NUVv+avelQtcvQ/yhTwP5dWmBJlhZkExNb9MVdhVj2EAPKFHAr1BbS0NeGyq3fis3/2W7j5vhsghMDY0Dh+8q2f2TpYAgJxJfY25b7+wpt47HuPo1QsacWXEkgUVq9fhfXb1gEAhvqHcXz/cQTs1J6xC2M4su8IAKChuQHbr9yOIAzgpQiYx6mDJ3Fi/zEEQaB/HwY4c/g0Tuw/rpWyvoCNOzfp4IAQkNBOexkEOq3AROoCKRBVKug/fs6atV0ru5DLZS8SQQWO7j2I4TMDCAKpAU1IHNt7EENn9JmATW3NWLWlLyVEF5vPGnlPcFG7qgMkuDZaOpNyEglPCyEgUFoqov/gSSRJgiATomdzH2QY6KPp4wQN7S1o7ekEAIydHcTs6CQoO9ydvm1MG6soNZw1cPd3CbBu9hT7I21L5+Z6CshNOF/8UW3fuLFTSgNEoriyOfMv7cXhxq6yY5v6s2NKZ9y4s24SA1x0enac6L2tMZQ9VVmBHQ3PGk3ySaksJHfpyDj1gcDPjT333vvj5JuYvt+K5ibtz1Wp/3MSV/M2/y8Pzyas9r2Figx2+kDBRBVgaLeLYPDr5Qt5fPR3P4T7338vmloasWrdSrR2tEAIganxaXzjC9/G/lcOeHlRiUrs9SrlCvY+vQ8Ls/PWIU0kcM3mtWhoagAADJ4ZxNz0rFMqw4DOHj2DqBLpDcGb+5Av5FFcNgebsoG9cPYCisslO9hSaKU8fegUrrrjGggh0LtuJXL5HMrFEh147TEbGMVL4gRzU7Pa15aVyNcXEAYhIlTYtOtHHMe4cOq83WtJl5ufnsXgiXNYt2MjwmwG3X0rdTWHWoko3FZg82Pf4YyAzJiLSMlFEvGtyUMfJUrh/KGTKM4voq65Ed0b1iDbUMDSzDygFNpXdaOuuVHPzdEzKC4um+tw1XI31SDi5s59p9oTRKiTWJ+S83UI1lhbnTTlPnHy61+XKyCXaXpu/WK8RdxE9RxmKXOS+02qu+L+5SarBUdqi78/0+KrcFvNLEixcUybpyp1c4/lCv+pYr8lsOJHeblcSTbWqRW5egF1v+HD4aVxUOfYXtgquQED4BTuhCpJ2IALN2IQ5kRoarBwJTWhS5hsu2yLa6zSFRuOHziJ7//9I3j5yVeRxIkHWHx7zdLCMgbPXnBNMaavDCR6Vq9AmNEpYuND4yiXKlUt1++XEWZCtK9oR6G+gKIxtfi4FheLoMNi6f1EJRgbHEWlXEE2l0VLRyuy+RzKxbK/CKkEYSaD5o4WdK3sQktHCzZfvtUpIC7+UHGC4tKynwVtWOb44KiNYLWsaEcQBvrY+BoC4PmAVPXnTD6r2wDnQNav/eWP2pakHLwjZwYwMTiKNc2NaF+1As1d7ViYmoWUEl3rVyFbyKG0XMT5wyc1eAcujYT7W6sTkNm6mVI0AiQFprRpB6oCeORPcLn1bs5uAjcAzmT0PEk++bKmVsrJbg9TFcwFJtxNma+KLzKc/emxdvNATeHdcP0nRkVgpe/ngUyVJLB78dI1KelQYOcMCvg1sKhvwgUq7Bh6vkS+OKYSQfm88lunvuJFWpl6p/1vvPmh9v3UWjGU7YEyiTSJim0joyjCyUOnMTs9h0q5gtELozj8+lEc2HsIk2OTLotcgSWhuvuUS2V73p9rlIIMAjS1NevJTRLMTs2ZQyr8KZqfXUC5WEZdQx3qGuuQK+QcG2SDkiRxalXUAz03PYeoHCGbyyJfl0eYDWErF5nN4Osu2Yjr33YTtl+9C50ru5CvyyMIAy87/leZcipOqt9LEsxNapYWZkIU6gsasMoVXe+96jpO8JMqxGK+CeVnhgOwppnnZ4H/OZ1K7VZ7nW0/ePQM1mzfiPrWJqxYtwqDR88gyIRYsW41hBCYG5/G6JkBry1ph0Pa/+mqgQg7Dz5ZcfSC+0fYgszcX7WcqgxIOCmi/yt/PH0vGjODGNhyX5YGLf9edhHmW3YU+djY+CvUMNHMpZjfTppOSgHLrtKOdEZ+uOq4htldFbx2lQMPupaLKrLSQqI2+DiSVVviHc1JLYqsb76BS1PtO/j/bw97CIVdtYwguzRtJz0JY1il5RL+4fP/iNdffBNSCB0BNGkJ9qxC7txTyjjGzaqeJIiiyFFy83UpJbIm50opZcrTmDWBjUWlVLYO/CCQCMKwdg9tE+zSAQGgXCxrMINmddK0WUFHwm68/2a84zffjZ612sG8MLuA4XNDCDMButf0QgTCu0XNwRbOT+KcoZqJUskYGejk3JRlbq+rUsKdvr79LxXj56Fz549Mgblx9rpz/YQZ2wrOHjiOqx68Ddl8Dr2b+/D6o88j31CPzrU9AICxswOYGZ30/E9kWrgrpVIxmFJZf5MZGyvYaZDh4yt8U0F5LIxH0FKLieIwxRJFVXpXAGsf7bYQDki1KjCbTaS4hTIpCXRn5fvxlEpsO4S9pr8JyG23gjHNhJdTJVMoxbgaCKxE6l0nL45B8e07fC+W4GkebOLseKZ9Q97IV+sC/yStI05ma+1MrX4IUHmZqosLug7AQEwlzgellMLy0rL2QYWBzYqnJYboN1HsRCXWWW0HIUkQJ7FFWgI2nyUktkVuMISnhE7IzAbOi9FQRkFqO6n148rbr8YH/+AjaOloxdzULJ7/8TPY9+QrGDk/gu1X78Qn/+y3ka/Le/dU0MLJHxoQyCxWZhyUNw4UxdErdK3161dMpKoGJK495EyGSqBUgkT5dbXo3jZUbBYppRQGj57GwtQsWla0o2dTHzL5LBo7W63DfeDIaZSWimB4BR/2aJ440/H3pBFqOS7jm1POl5H2iXD/C7uncGCVBqk0eFql9doP65qorZDujk5e3Xf5IkGmX6ISKxfOzGS9UcLlEHrMKuWp4f1PmYD22kZ3uAoppDYtC+b5AYGiG37PFLd4LyAMFCdwJbf9ueZi6S8K3q6DlH5bPnQx2uYTNoTS5Ne4kRRu5fu/gR4DJqc4YHsLaVJ1JnYaJAjEyHxUSiGKI0SRq1MeZkJzCrUym5AFlEoQhKF11idJgjhKXBiX0227KLD3Es2iqPpEHMWI4xhJkqCjpxP3ffgBtHS0YmlhCf/8v76Npx5+HFGpjDhO0Ld1nb0WKbwGIGHD4u7eigGCW/PDbGhXlziK9dgA/gG/bordWFcxMAeW1mRUqc/NNRK2OPKr23+5zSgEJgZHMXp2EC0r2tHV14vG9hZ0rtYO99JSEQNHTkElCWQQ+BngnGEZ+eCVFRzDYP0iBeLFAb2oq++yIFOsllWYeE5sZwaSUlqFZVelPa22NLG9rWdQee3QYybsPZ3K6DmPlZ4RF3hg92IPx6YIrNxzd0fl3ddvlap6P91i98d9YJxdOhBJDyndg5JZaU2pDVSpURLVZjf5xrxN/f8P7IoeIQmHXcNSHk/GuAFiUXzSzA2dJ0xYJy4xLN1XosQ1lJ01vFJRWJib15Mp9aELiUqgYkfnVZIgX59HaEzH5cUilpaWq9kGtdMsgwnohByFuoY6nQoBYGlhCaViGXGSYMOuTejbphNfj+47jOd+/IzdmsJTAOiRJMr19yL2PQk0PeoaG0CVXhfnFlCpRB4tdw/GBi9yXRKkROm2eJyTANzzXfqA6hYRP6N+eW4B/YdOYss1l6KpoxVda3p1xDCfw3j/EMbPXLDhdJ/E8lNt/IJ0Xr+4SXOR1VrhokNS9U0O1sqegeQubB28abaRvo9icMrNJ+Fy7Ci5lNqfGHbjGJUz/ex2N9sQZ2pKCEjpDqN1viphx04IPmsGjBUBAV/hXHoHXZ8PGYGgnWnbJOUBDS2c/vYgX26sFZkSS44V1Z8Jl32gqtOP/l8fobtgiqoi7Y8QzNdBn0uryISebt6F/T8Ay774IzFHe/Hid1EUYWxo3J4G3dHdDhHobT3ExJI4QXNHM3J5vTdwcnQSi/ML2ryEr+CZbGjukdgJUQpo7Wqz+xOnRiZRXCpCCIHVG9cgZ7adnD50Cotzi8zXwp2mXEyqkxuFEAizWa+/OgoaoK27w0bWJofHEZsIYS2nOM9tooRCK0jMnNRgparuR/lRSZrhmvcJMAQTXAiBOI5x7uAJlJaLyNUVsHLrevRu7gMAjJ4ZwOzEFLxN5vy+3J9S9R1f/EWNf604s0Hx/C7sSjxNgF/fru5GplmA2jMtCZm4u8H5d9jqr4RJtzAWhXDgoU3vhPljuXIL77mAPvadwJ58VNYtJqp9PbRQ08LoQljO6CXzVFhWQ+kJbm9h9ThTq9iKJmDBP+2gsH43M3jp1BJ7XWKzfD5pHjxr7mLMivkJU1+hushVd/VyZww/TdNZR82lLrFsnuskSWGKx/G/1G1SbE1Bg9j5UwMoLuuKDyv7VqKuoc5uLSCf0JqNa+xm5v6T/VhaXDLmYOIBR9eqbgSZQGfZJ3r1CzMB1mxai8AkRJ4/1Y9yqQwhBeqa6jXjTBIsLy6xa+m2FuoLlh3xAaPoIilYmAnRvbYHQRB6np18XR6961cBgN7Pd3oQcZzojOfU/CgFxIlCkjifW5rNsDhGtelLgOcxLDPxYQAZBpZFpMQLQggMn+zH7OgkgjDAusu2onu9znofOHoa5aWiBX/m8tU9lQKZXA75hnoIKcD9fFAOSKvdDgyo4AMILds2IRIEEgnzUqXAzXNN+JzEb7NnNHnpN97vyCpQClGiECUJIqX/EpXoTHXKi7NtIXbmEj4DIREKgcC89tXKh2S74Kg0g1dV/XCg7vphAUT481vrwY+yt3445WTPN0x9gfIYU/o0dc5q6XsXSxhMj0GqsdKiX5X3sZpxqfRFDbuiswillLaonzCZ3b4MVhPBlOEJISTOHj+LkYERAMCajavRt6XP+nlUotDU2oTte7YD0Obc4X2HdQa9MWdDFjHcfOlm9K5biTiOoZRCHMdo6+7Aliu2AtAm2cm3TugsfyUQlUwSqJRobmuxUTxAH7/Vt3UdsnmfOdFkShl40cptV+5AS1cb4jgxLCdB74bVWLOlDwAwNTqJ/mNnDFDrzy/qpzLKkt5MoZRz7FZvX1GMvSokUYw40ns583V51Dc1+IjDBUNKzI5NYehkPwBgw+7t6FjTg+LiEgYOnbJlfRxr09K9+drL8dC//hQ++Oe/j7s/8yFk6wssF82DYxDz4ezcLoJc4AT1BVAJLKOx/ebQY8CBb13xJC6tJ9ZqTNUkEAJQwo57bO4ZJ0qDVBKjHCeoxIkBr2oAlJIifhKhlAjMn5RklbDNy9RVxqgVAz8/D5+DlW+q8Sij9PpVpXTgg2z9oIqNNd2pht+v1uVY16s/F7V/W9uJYkbFK3tt5FI5GHVCpdgPGbOSovqWfPVyE+9+7+13Ev7QWXPSMjUNeuPDE3j9+TeglEJLewvuec/daGxpRGyODbv2jmttSZpTh07h6JtHvUz2TM6Voula2YV7P3gfGlsbkSQJ8nUF3PGuO7Fm4xoAwMkDJ3H26FkIKZAkCYbPD6NS1qB1yZU70NnbhbgSIY4TrN22Hrtvu8q1X/rbFaSUCLMOsNZuW48bHrwVmVwWcRShoaURt7znLrR0tQEAjrxyAKPnR9zU1WRIbIVNm6MpsFLVaMemUmB5YQkLM9o/WGhswLbrLkeuLu+2IVHunJnT0tIyzh04gSRJ0NjWjGw+h+mhcQyfPs+m3LEPGYa4/N4bcf3734Zdd1wHGQYoLxU9ieMuYu7bIWVLf5ec2Bo0EsSkwsw8po3NQkjnq6J7pW1Ixib54SRIybFjGfz+BFYapOIkMQw4sUpOMi+FNNtoJEIhERhmFTCgYpTEU18yLRO2WFn3CkWUmaxok08gnRIhUuxN+C/sE2WuqxLFQKvWV2szn5pcifGgiwGdqnmFi3u2BFjiqF83CC4NC6hZkZYGwJpBnifOUVF6Zcv41mgEv7oQeqPx4z94AlfdeiXWblyDm++/CSpJ8Npzr6N7dTfu/+B9qGuow/zsPH7+7Z9jetwdciGksKbi0sISpkYncftDt6OhsR7H3zqOvs19uP7eGxBmQizMzuPJhx/H/PScNl2Q4PibxzByfgSrN67Ghh0b8eE/+jhe+vnzqGuow63vvhOdvV2oVCrIZHQte1vnXul7UyBgdnIGpeUS7v/1h9De3Y7hsxew+YpLcPmtV0IIgfELY3j+kaf0PkopL7K1hgFR4pu6VrCVE/KLS49mrouzC7hwsh99O/Sm7Vs++DasWLcSC9NzeP1nz+LM/uMahM1UJrHeprM8v4h6sx1n4OhpzI5PsSRQc1ulkKvPo23VCgBAaamIU6++hahcgY1E85wjL39LcJywkTU/NYFhDc+fEk5Z9etaPiD2W/D87TS/Z2QRyjrTE6VNdsojtOkiVjH1+YraJwVr+kkhEUhhQOri5YEImIXtqf7zTnkGUzNPe2gsFDu6qzad4Um4PNUEfLG7mCPda8nF8qYcJXYLRy2N99PI1cWuVwN0QpssCuYHE5p6uw+oM24bDyXU6fwePTkETs4x7CbVMixiQlIwhiXc94WADATOHD2Db37hW/jUv/kkOns6cfd778Zt77gNQRAgCAMszi/iB1/5AV785YssPKoTMclkm5mYwQ+/+kO8+zffg1sevBU3P3CL9c8Vl0t49FuP4rWn97I+SQydvYDHvv1zfPBffhh1jXW49p7rsefWqxCEAcrFEp56+HHsvO5SrN64Bplc1h7AYe9tHO3D5y7glUdfwDt/5wO484Nv0yanuff8zBx++pXv49T+Y24XgFGSFAXVuVPkw3YOJ5YcSeNsrs9yegQvsQwgKpWx96fPYutVu9C+sguNbc246m03I6pEGDp2FqffOArIwE6blALj54cwMzKB+uZGROUKTu07jPJyCUF6O45SaOxoQ1uvPqZs4vwQBg6d8vpi+VSKaYP6YqJrtLR5B27y5ZqUwbM1aGyMQgiWL2TdEkZGUspISasKCdt9pn1SAnC+KQNYBKOSzYUQAoF022kCadiUNadIyJg/yOoHATTlyRnAYiyFGJXN0GfX1XlVzlJhdi5s2gCJFt2fLQbcMKt22FQ5gtyg0uJhp0eYBSQ1vt7VqoHp4pwq5SRTQKj00cQWLJRS9iAIk1RF6buolCo4vO8IlheWsbiwhJnJGdt5yqdKvDPcmEmpgOXFZRzYexBD/RcwNTZtInMElMKP7Cvg2Z89h4XZRTzwa2/D5p2bUKgvYLG0iPOnBvDL7/0Sz//8OZSLZWMK0B0F+k/0Y3/rfgydG8IrT7yC2alZvPOT78SqDXpbydiFMTz9wyfx5MOPo2Q2RpNcx3GMJ773GOI4wu3vvgsrVq/Qvzk9hqe+/zheeexFRJUKZsamMHRuyK7E9NtTB0+guLyMk/uP4bkfPY1yuYI7338fOld2IokTDJ0dxOPfeRSv/uJ57U/izFYBQ2cHceCFNwClMHRm0Cmt0PXyj+87hMnhMcxPzWJ5YdHu2ocQKC+XceK1QxjrH8bsxDSKi8t+pFcInHj1IL7zn/8Prn/nnVixbqUG/5l5zE3N+G3x5lC/mBmdwLm3jhGcGIwQFi9XrFuFhtZmAMDp1w5idmzSlhZyJh+8BYrYIflu6Noe62EKTwqYrilOom2PjPX6wX2kNcxTBe9UGjI5Y+XMT8rvIpULDDBBwEb9yOzjLIvfzaUduEifyx5XXr+5smtmZd34th8ScKkKXsVbtw/QHaBSi3yz/D9fZR3V/FWPtKwofvKzlz5q+8I40f/lUfve4rKma5T1I9HFSAkYdyT/Ui6f1dE1laBSrFigsiwKfijb1e8BAimRK+RtDfJSsaz32zHfWhrpVaLQ2NyAntXdaGhuQHGpiNHBUcxMzvhKQBMlgGwuizAMkCQK5WIJSim0dbZhxeoVkFJiYmgMkyOTNnWCBshm5Zv327vb0NnbBQGBiWH3m3w+BxkGUEmCcrFkM9el1OxOF8SLUS6VIYVAe08HOno6EccxxgZGMDMxrSeXEmaN0AohkMmECLMZCABJpE/WBpQ1e7KFrBk/vT0pSRIK9UJKgVw+byNzlaL+3MY0hRPOXH0e9U2NCAKpD8aYW7BnINLYJ3GCy++8Fh/5899HvqEOe3/8FL77Z3+j89LY/JJy3PfZX8Ndv/k+LM3O4x//6L/j+Auv68RSOBPEI5DEoshOseDszD2aY3e8uks65HLjX9/tiyOZIPCg0D/AtqKBfDcU5UuMKaif03d44iUBlI6Gw0T9pHmPtR2KRd+U60OK4dB4uFwpBe98SNPvAAqBaUcgnBksweHKnTolOPsm8y8FCEK5fDnpYRBjc3BMSjJLgJ8gzf8oZ4TGwMoeY8025YTPPfO0CSSOLJpbhtYHkxIou7Ir170kibG8tOyBkRUPWoiFgBKJt5IlSjvLk0QhWlh0Ey+Ey+5OQy5dWwoszC7g+MwJJrzSdtbu3mf2eWm5hJIxEYi2T45OYmJk3IGoMUmtyWUEnK4VJzHGBkcxaqKVkjnYl5aW3Fixdqs4wdJCZJtPfR4ZGMZw/5B1inJnPc9BUwqIyhHicuTuCSb9ULrQnqc8buKUUijZ+XFMl5vo9LvSYhGlhWX7W0nzaV0CCfINBVxx743IN9ShtLSMg8/sRXm5ZPx2zBECoNBYh9XbNwIABg6fwuDhU+40cdJXKLsGOn8cmSukNIyFcWbGTcAqUyW9uLr3ecQxccMA6x8kBgUXcaRgBoEpjY2JP1qwCMkElAIhOdOdxjrjUTGfjX3u/iXQcb3y2QXdXwogYG3gSp8eD98XZofZsTxRQ+VSL+y+Qwt8Tjc5ONrv1lBjJ1AOqFSNO/p9F6ln7gshrcZp04EccR7jYS98ak1lZQ1dh96O4zLoGQCSL0uB+b2UdShyRXb3UO53dEeirKatNe1j7hxlkqygc5toBXMgXWOyzMySjwW2j6na4TQv9nrC73NQK0pqkgHJvDDv8ef6SsITTn9PWlrqfBrut4jGlgmegDfP9KFSwI6br8QlN+wGAJw7cAKnXjtk6o1Vy2Rb7wp0b1iDOIpw8MlXsDSrD/Ygx7UVyFpMCrw9POtbpLSAR9ecULsxcmyPsy63sDOzk1IGTJTVgZXzIykwh74BqcAsltL4rMgEpPu5hZPtzGBCouCc7w5j06rq3tNszmTFA969BB8KXkbCFwD//tUfVy28/gd+W7iPTKR/r+DjBTExL5Ik/Jlj901nx9d6hLVOSgY0s7HV5JVb5VTijly3LWQtd20jTzEdQkDKQTOlnZluv6HyDmh0Mqw/lwYAlH2PbnOR/WfmHk582SCBUfxao6IcCNNFnIWsqq7lfsRpKjuMUwhwMOVR0yCV7uEDkxtm/4UbcwJ6r19MAnnf+RpeBV5MmFWcYO2OTbjrk+9GXVMDSktFvPqjpzA/OWOjiLxvUAprdm5Gc1cbLhw7gyPP79OVPVg2uO1GGoPMtXhqS3rx8UFNeXPqlJbG3lv7LYMlEyw2zMmWegHPYfMVUwpt5gcGPB1AmWx1yQCW+aFi5v/xM/Ad4yITz++g72TWAOVyqmSNsbPrtiePPkDCjIO/VYmNUkoJqsAwNQvW9HPEv/aDE46qjwSXZhArtL8gE9LeUb8IOQuqbZUJv4NU64JsVEaBrZVQo5OkEM6Uo/ec+eg2kap0O/XuMAtelBLnw5GDIdI8n0GIlBKkyJHXLzuxjHHwcXIBgpqQZ+/mIlPmcFTyv0A4vwNvTHq58+SQCZdyysBZBn2Nn3Tq3LVuzqr3nbl7rt2xCe/8o1/Hqq16T+WRF17HoWf2en2z65UCgjBEJp/F/l++iDd/8TwmLox4A8YszbRwwZptdlxYd0X1bxXNKcAiY9R3ZacvHa4nM48AyzEsHvVzNajoEFvyUwWCIn/wPqfx1SdKO9BzOsGcMJyZ0ELNBFCwoQmgQVFIw6z4+HmpGzWAymi6i3im76vfuxhBr8XcHYi56CUXBytOytcLBe6IT1+UgZJnCfFr8PcVxJVdNyseiaLJ9ZQxtYzz2lneANQIV9NDm3+MrXldqvq6vQ/vjE9HJQQTZWkgXzjRZSzAXN32gx9F7jM2n+lUMzPeLm526NfufvzMQP4Z7ca3v1W1rutBY/X3hS+kwiwAskZzuXB5fePvmBVcJQqbr9qJ9/7b38CqreshhMCFE+fwrT/5AvoPnjAZ2j4hoFUxk88iiWNUSmVvLGkBIxalK2iSTDh2n1YCW0iOkxB2HRpbbjbzKGN6D6aASTxNEvCKDpJd326dkZSlTgmfup0UDZTeZJCfyEUSfTBRrH8GGOEzdfpM+6jA7kWyoux+Q8nBh8mKYKYXbcQnWaHvVjvmq007ydpJTNrmeDHQsqEqpdyCwR3qZiQkFKQlAcqetu0BIyWvp2S1ykkPZQ5SJVPMmj1c5BiT4jJe5SshyfT5GoEaN9v4w0tYrbqm/z1491IWoLgDmAMVZwFCuAFRvD9pnmRXaxI44QbYNaZqomHCzOwXdiJ5gODijAxVphM1QQkqUyM8weS/44YSBy+V7o2Z4MQKLWdmOvmzfVU3hBAYOTOAR/7HP6D/0AnGWoSrq8USPKNFPxDB+y2gI8SgezLzrTa7910NNL4WpJg8EFNPWOk8tzMgMfv+YntNXnqImhEY7QmMA903/fRrB7gAqNSRADMlfXcDz5fyBTlFJhhDlEJZENesqtpX6VSfLWxMJnihRru2MQbqkxbSBtaWKrBiQGUBKz1F3qptO1lT0lOkxsu18zqZShbmJiEHAEmCyRsm2A+FG/F0trMDEKa4HkvijMcNXC0fmt9HzmjIHHTCywGVbiNpbfDGMm1CXmQgSeEMcjjHqLDKY1cExWgv90Ux4KNFIC14F7P9BfSiI5CY25g9bVQ2xfj+XFkbYhiuyI9b1FyxFZFuROohpcTZ/cdxat8h5OsL+OnffBun9h2CC17ojpA/hLNUezsm1LYkSwp4uGoL23bef64ZduZTUU9mThnAsqae0ttmlHkvZrsxSIQtMAjGpiSlK0ibBOqBJAgQzf2V75NSNoiTYuQk89atq7x2BPAz5JGSt2qw8W1IW76I/LbW4c/hRLnBY6CV9iRxnRPEniwPEVam0i4Rt8j6ZMHNNPdPER/2/bHegHlIwj66qudW5a3BKfagUkiZzhtK71/jIGWVm7fDCqqPWpoV6EQ3q/g+8apatXlIN+1A90CxVmTDGxQOfjQvIvXddB+Mmjk7LaWobLwouKBUVZud8Q/WxhqVRxn78vwZTI5k1bX1I614dp6YcBFVhwB6NqzC8vwSpofHwUGKjlx38+zPedpcc2VTBHhOFPel8QXHO7nYAzkGYjTaBiwSJFCx3oxMaQjaT6VhjADG+qcsEAm7bUZKt4UmkLQPkBYZAZcQweXV1UAjk1CLGstpsrNh+mzaL435J4VOOg1tsMFFEKUFc59JcVOO5MIDA8D6XQVdx1tEzPWtS4d0xzdXdQoH/61wgM+qAHOm5clWypTTt3Iy4e3OSJl+7hpmnm2/TT0sjpZcMOyeLc9n5VZ8pXSSZqEujyAIEFViFJeLiMoVIxgux4uvxWlU1xFCEg7JHJWk9BwkfGXVAyq99wAGmkTbjZCSza10zRYI2vRrvuwNmPCv57M5DoJVxLhqhaM9l3GsjZJASifEqfQRm1Bp2+8vWEr4dyOWx1c5znAd0Dup5tU1/TI0CgOmgoSXYkL98XxLfgoCd377k+GPl+XajMHy8RdSuJgBsQi4TvJcqaauNuy4/QaE+SxmxyfxxmPPoLy46OYlBVTEqKxfSpIzXVqT0CoZMzur9vrRnAnnt/JdAB4PtPJAuVSBdIuMMwvBrsPmisliWsYIMj3HtmVEfAJUirWmFcZ9TBn86UXRSKYdV8rAT92lVkPTTy7WhKqH91NBJiGFXZA6QskqPf9XF4Pr6u3E1TfvwWXXXIqeVSuQzWWxuLCEC+eGcGDvQbzy9GvmVBymWDWc7VaZ6XPmVBZ2gOBfw5p96fGsNveqWZfQZWIuWYu2zjacO3YWU2OTNZggZ4kMlNjztEuKzAPLnM1YEQnL1xewYecmRJUIZw6dRHm56C0IJIRc6a1JyACQooAXMW49dkctU0bqLSNO/AXDi3C5D9KDB26m2FLYVZ6oGtrlZI4xOwZ8jM7a9ApmflE+nTX5VIwoitDd2YY7fvMDqG9pxsDRkzj0wqtYnF+wUTxKEibQInMvkKw+lX3uA266pAvd37Iq2w1hdYeDsvUPCRovyuXSzMr3DXGfFzMtOXKl5MSNE/dp1Rp7RgAMmFnsImYHWtxq+JRqXYdPs2dt1liwmGAaou5IkqrW8YvdFgoIQfvwJFBT3QVfJfR3rrp5Nz762Q9ixxXbbGUE+7hpN6647lKcOHQKi3MLHtjRAHnSS50UMHE/YkM+cHDaSSsOrWZ+VLO2Pe6QOsGOK3fgd/7zZ9HZ24GXHnsJX/6PX8TCzLwFD2+kuNKbt5wbQNV87V3BMBcZBLj3I2/Hg598F6JKhO/81dfxxHcfdWcC0oKR7gP1Lz01KbD0sv0J4qx/h7qeeAuEAzISYjf2VQEH44C2rgwClqoQe+oVkx+PFVozyPSR+uA5jZX1n6X39cVJjEqlgkocV93T3EAXkpQuLUFKUzjP1qaqPjXZ3ZmXcHGAKVJKy9mhO0DFdxjbvC0Bu3VHCmXsghrOeSsCKQCsAiuVajetlLVZruDXT+mHZXfeAkTy5y7Lr2wPsuDtFaw56QakwJwYGmeW/LdKKHdMqumTdbpbZOc6yk04AahEYfcNl+MP/vNnsWb9KiilMD+3gNELYyiXymhqaUJXbyeGB0YwNTYFWwOerwSxjq5Iqipg+WtqZfBk31/Fq0s1C2+AlGEP3iGu7Ls7rt6J1Rt19cxd116Kju5OzE/Pc3cU17aUGBMxZvczDIV8VdQ3EjKlFOqbG3D5zXvQYMq0XHrd5Xj2+4+jVCqbMXcQbR25F3GQp9/nqznPsNZCkVgQTFN4aruNtXomMQEKy5HyTJUa5nAKRNMCaw8e4D5KM9ZKaEDlcKXNZ72xPgbPSk+sSZgov06rY0zSMqfA81FJ56diAZW0AQf4gMVVjRhTOlnTsRzuRHcgFQhnBvpmVxp43BXTlpU7qVrw5jj+7VkogM5F5O1OyxIzRQHw/YsaDoS/6Cj2Q2/BFlW4Af6SL1uKmaye0pkb1MAA+nrNTHfXAGEFM0kStK9ox4c/8wELVvtfOYh/+rvv48Shk6hUIjQ21eOSK7ahUqpgaWnZMQehQ+FhEKKnrwfbLtuMg3sPY/TCKNzeY9dQl+ynO8NwR0+iEvBwhX0qgwBdqzux9fJtOL7/GIbPDflmW5JgemIalVIZmVwW89NzWDYheSsMyoGgg0naqOvzD/pGrpBD39b16Oztwr6nX0VpuchlCpVyBbMTM7YdMxPTiOPYUnHbPsr4Z/OiRLqXivl4tKBa05M3mpkWPHzMzVonY8IoUxq0qoWn+qVRLWbO8DvQdS3lcK3yIm0q4cX5lHWk60J5CfsVkxNPLzQghUGg2ZRhWIFhVhQNlMyaoGAC+am4/UGMyfPTMGblhlpZPaFh8BiVFF5lBf09ngdl2LGX7Ovk228X05f0XKTkBIDRLx9crflHpignwOYSBFQ++XTCIFL9TTXOjJFbKG3zFFCjkGj1g/fPQoNA6H7l+B13YRNNV0rh8msvxY7dlwAAzp7oxxf+4xdx/MBJyyimx6cxcGYQMgj0Fh7mtK2rr8N7f+NduP2BW5Cvz+Pff/o/Y3hgGFTZgRzinj+L+Q3sOiKcP8fbbKIUcvkc3v6xB3H7Q7ejua0Zn/vdz2HwzICupknfFMBLv3gBbV1tWNm3Ei/8/DmMXRjVQkv8lwQWbqCqebv5fqKwcv0qvOczH8TlN+zGwKnz2P/i6ygtMfNKCBQXl/HIl/8ZS/MLKC2X8Itv/RSRqaDKxzm986DWPjCrIwBgdgrY8xjTScBg9Ylq+Ph0tQoWvfEk1/lGlBHYNOlLZ9HD+Gr8qKsPbVCweVI0yonSx6zFBrSgFKI4tq2g0D0xPWnPCeB2MRDIQJcjDgLDsPR3w0BamRL8mnbKDUu2vVbeSLiFxedixLsFtEFB5p9NMoW/rYYDYMqISIEV2zx9kYe7HvmhhDXvaT5p/jmTAnvu1hBzV2+u2H34kxqNYkNzESRy+GLvmSZh3rfTvlGtu+4g1TTscQYogEw2g517tqNQl4dSCi/88mWcPnLGHd3OtUkpt1PfgFBDUz1uue9GrNm4GtOMaVR3PDVgltU4k8f31+gJUkohV5fH9Xdfj74tfViYW2BCxx17AtMT0/j2X38TYRiYcsipnI9UasfFxEVAK15P30pce/cNKNQXMHhmwLsaTaQQAifePIozh09p1kCnALExS08urfq+KaeAxLXY8mHhxsvLWzNPuKOb+ysALrQp85JERTmB9xcUNxKWtVkF4rKkkFi6oOzCRM5zpfQZlSrRvinuu3LTIey2MGq7MGyKbiSFQCYIEMhAH/RgfFVurTFgyUEnJbeeZyLNBEyIna0W+r7QTMbVxDJsL73OeQyUcSjmqyGzj38z/YIzX09Gvfd4tJPGjdfbYgtA2tpjS2UNpwqcXrm5sfrFXBvulB8rhPYg1TQsVmMdmZt+A0MvF8cag9BLAkWOlEA2m0VndwcAXcL4Qv8Q4jjRZYJNQ32Acc2J4xhxklqTzIELifE3UTiZHokpCZwu9kb1q7iJo+j7SeJ1LkkSc1iCMS1tuROBOIosaASBdPJgo2XC+lSkdAfBSunOZlSJQhLTidap+ybKZpVTJFYpXZ9LDxeJhc9meDE/peIU64QHCG5sdIkc6ztLEl0R1GaX++CUdgAooynWVOBKpVxViticIanTVXQEVEoJEfjakxizHSox86vNXAUNTFEUQRmGkxgWpQTzBXLFYukpSJROT5Ds8FHpx4oDIZCREjKQtg6bnVZiQ2T+MX+Pk1a+iPiDlZApxNiSNvt00mkA57NypJyfzeg5ney9FX+PDMBaUVs7f6pqPunyno8QnFlVFwf0eYZg4KV8BuTbhTVYoar6nt9y5ZJPRYqNpR56WFKLCHuE1HJfiLmhbp5KV2FASol8Ie+csUz1eCqEShRa21vQvbob7Z2tyJvz/sIwxIZL1kMGEkEgsbiwhMHTg4iiCFAK2WwWPWu6sX7rOnSv7kYun8PS/CLOHj+HEwdOYMFEH2mSGlsa0dvXg6aWJhTq6wAAQRigb0sfysUSZBCguFTE4OkBVMoVFOrz6F3bizATolwsY6R/CBVTgwpGcYIwwOot67D18q1oW9GOqFzBhXMXcPKt45ganQSUQndfD5ramrFm01pIqcvk1TXWY8vl27A0vwQh9Mk4YxdGIRKFtq52tJoDKGYnZjAxPAbP/0GCmijIQKKtpwM9fSvR2NaMuBJhbGAEw+cG9cEOBgAzmQxWb+7Dpsu2orWrHVGlguEzgzhz8ARmxiYNiPuS5PLuUqs9Mw24OS4E0NjeglVb+tCzYQ0aW5uhkgSTF8bQf/A4Js4PudOrrQwnKDTWo6tvJUQgMTMyjrGBYdS1NGLzZdvQu7kPMgwwcnYAx155E9OjE9V5byySmM1lsW7nVqy/7BLk6+swNTiM03v3uyJ2RvR0ZNCBVWJLU5sVm8xAA1jEJXyLPzUfNRRSCLh6WGQCcuYjfJCo1m9hwZnfkbsB0guL8ykxsGLMSaZeC3DAonax9BjWKK7H3hywxpPFVNW4lN/LWtRpFijSffJHu+oz4V8HCggdLWaN9S6s36+UI0xNTAPQYLD10i3IF/Iol8uus2yV1itwgsuuvRSf/fefRjaXRV1DAQDQ0FSP3/qTTyGOYgSBxOHXj+LPf/+/YW5qDi1tLXj/p9+L6++5Dp3dHchkM9CF8BIszi1i33Ov45tf+BbOnzpv3996+Vb83p//C+QLeRTq9T3yhTw+9ocfRxzFkIHEmaNn8LnP/FdMDI9j1frV+KPP/zGa21tw7vhZ/I/f+wtMjkzownQJUN9Yj/t+7QHc/f570LmyC2EYanZUKuPYG0fwt//fFzDSP4T7Pvx23PGeuyCkqyO/dksf/uCv/41RDImfff0RfPt/fg1xonD9AzfjXb/1AUgh8Og3f4Jv/8+vIYljT0iSOEFHTyfueO+9uO6+m7BiTQ+yuSyUUpibmsU3/+IreO6HjwNKoaGlCfd+9B247b33oqO3EwG1s6hLKf/9n/41RvuHICTYmlwtKHaWicWSjJjV+tLbrsbdn3w3Vm1Zh3xDnT1UIqpUMN4/hCe/9kO8+uOnEFciWKd5kmB130p87L//ERpam/HEFZoNJAAAgABJREFUN36A137+DB783Y9h+w27kTcLS6VUxvHX3sI/fe6LOHvgmDbhzH2l1Bnn9c0NuONj78WN73sbmjrbIaVEpVTGiZffwOGnX/Z2W1A/3OnjyimkSps5aQXhlgGP+jl/JOV31Y4A+tF266O21ouzYrgj3VXOoGRURgB4x5A26xhoKR+cvMNZDcP1Fyjum4NtWxpg7fvKa4YvQ3wBtF6VWqDrfcWzntKuKGdG+mwvTJIkdWEBfvosXbRcLmP/qwdw9ztvR6Euj6tuugJ7brwcLz7xKmqrg+Z+MpDIZDMWeOiamTDUWyICiTATgAyRTC6DS6/dhZ7VPZiZnMbc9DxyhRw6utrR2NKIWx64GWEmxBf+v/+F2akZwAhRmAkRZkM3CEIfZkorLp1VqKABt7m9GU2tTWhsboQQ+tQaJAmCMMDbPvJ2vO8zH0C+kMfy4jJG+ocRZEJ0dHcgX5fH8uISEpXYvnm9Nm1RSj8XUugKAUmCbD6HlvYWAPpcwDiJkSSxW/FUglXr1+ATf/pp7LntWnMdhagSIQgkGlubUS6VoBKFXCGPt33iXXjot96PbD6H5cUlTJ8fRpgJ0dbdiXxdHqXlYi2yXLUY8U+4qUlC2LN+NTZecQnKxTImBkYQRxGa2ltR19yA3k19ePBffgyzUzN48/EXAQBRkkDFMUqlEnL1dahrakDfrq3YeMUObLv2chQXl7A4O49CYz2y+Rx23ngVolIZf/eH/xULU7PuIF4hkM1mcPuH34W7P/V+ZPN5qCRBcWEJMpDYesOVaFu5AhmWC0j7CElRSaGkpy2CKRlXJhe1pJOwkd73J119KjpkgjvUayupsv4pp5V+LhVPReEzYxcO8hPSMe/MP0aVHixYCaRAjfudfGRQqc/TjbfqlPJ/V3URPBBWO6VZgblAlC+Fvk/Os+N9hpUkcXVkil3MHc+l8NoLb+CtvQdxzS1Xor2rDZ/6o48jimLsfXafDtFLZ6bRIOx/5QD+7DP/FW0dLfjkv/oYuletwMLcIr72V/+I/lPnEQQB5mfnsbigt1NMTUzjqR8/g+cefQGvv/AGZidnkC/kceM9N+A9v/EuNLY04sqb9+Dy6y/DUz96GlIIHNt/HH/+u59DU0sjPvL7H8HqDatRXCriW1/4Fk4dOokgCLA0v4i5mTkdmWIHlurVOEasYiBWWL99A+5+/73IF/IYGRjBN//q6zj0ygGE2Qy279mOOI4xOapru//0H3+MVx5/CVsu24r3ffZDyOVz6D9+Dt/+/DewvLgEKSVGzg9pR3KiPCbAT4mm2Whqa8GH/vATuPquGyCEwMj5Ybz4s2fQf+wMCnUFdK5agTOHTiFRCmu3b8Bt77sH2XwOo+eH8M+f/wZO7DuMTC6DrXt2ICpXMDc1Y/O7KN+KFIdmtVYGvycjCji+9wCe+c7PcOTFNzB06jyiSgU961fjvt/6ALZcuRNNHa247l13463nXsPi3LyukBDFWFhcQmTOeNx29WUQUmLfY8/jyW89gtJiEdc9eDtuft/9yOZz2HbtFbjkmiuw79FnEMrA+DQVNl6xAzd+4O3I5vOIymXs/8VzeOux55Cvr8O173sb1l2xwxvTODHsylRTIDNQsVQGCcUSEi18OEZG5h1cORx9GKpxpBuzi/Zuuj2A3JziY0z3IWOPTt8hMFDwmIrVUw40TrE9BszNP/g+M8+/dRGkcfPvg0RNAE6hkANUZ17TeFzsYWGTNUelQdIbRObThWFYfEWlndTponqAwMTYFL75t/+E1etWYeXaHqzf0od/9V8/i+/+3ffx6Pd+ibmZeT8hFAqjQ6MYHhjGit5OfPDT7wWgc5Le2nsQh984Yk0Acp5WSjG+/w8/RKVcRhIlMP5dXOi/gO413bjvffcgX5fHrmt34ZmfPoM4ijExOoHRoVG0trfgoV9/CAAQRREO7zuE15/bBxkGhs5LqEQfhMkHMIpiRBV9gs3WKy5BZ28nlFJ46geP47HvPmqd6ueOn4UMpMkYFzhz5DROvnVMO5CjGAAwNz2HN557DfMzc9bH5zuG+cwINvYCNz5wK665W4PV0NlBfOlPP483n9tngwOZbAYqUZBSYOueHWhfodv57A+ewHM/eNwq4YVT53UgwZvb1CJkqTtby5kQJUxwzx46gXNHTqFSLNmywoOn+1GqlPHbf/0naGprwbqdm9G2uhsTb0wAQiCJE5RKJSSJHpdMLovj+w7iG//hCxg5o8354TP96Fm/GjtuvAr5+jps3rMLB596WVcvkAKZTAa7770Frd2dAIBjL+zDz/7qq5ifmIYQwOTABbzvv/whVqxfw+bTnGKkfP0iR7vtIsuqd+u+q+1kGZWgfX/skFL6DkeSKsX0+IR+J7VnlIVaal+EdNaCD4v8gcDKmY9C1PLF+dd2W7wIWC6+xcv9xgfOGl8A8VkXgza+Q5Z9UH1+Q8r0ZU41z3XFiJZNubI+DKrImD6402QUv/HyfnzxL76KkQtjAIDulSvw6T/+BH7vP/wO1m5cbU+Q4SHjquRU4XwBVCNc5+DEiJMYpWJRC7pwK97C/AL2PbcPZVMgrndtL7KFLKI4MhUe+JrFZpsiZwKIkxhRko7qKVbUDejs7TQbuSMMnr2AKI50xEmSE9edoiKlgAwDEzl0twyCwP6RM76WIJIJkiQJmjtacctDdyCXz6FSLuPHf/997Ht6L5I4sSczJ+bIeyElOnu7IAOJqBJh5NwFJHFiD7eggIc7vYgcz8Izy/mGbncoq7/9JUpilMplLC4u6lOP4xiVOEEljnHizSO4cKofAFDX1ICOVd06O12Zca3E9kj7JI6x9+fPYPTcBWSyGWSzGSxNz+L4q29ZOeta04tCXcGmJbR2d2Ljnl0AgOLiEl7/yZOYm5iGCHSkduDoKRx68kUvspooHb3kJzZzySCdcSdmJ97uAB15pD2HOvE0lNI42Nm4caBSadnzo76x0mccUllmfRpPyqOUZmggsBKG5TmwBANNV0PLx04lGMSwa3NGbf9NVUt1oOf2TTorjaGHh14p4EsTuirPOgNRFtdIR//T21lDVz7Yjrz7VCX67FQGNnGS4KmfPINysYxP/eHHsGHrOuQLedzzrjvQs3oFvvAfvoijbx23YWxHuP3GKytILMxMyOpFNU2oO0kwMTKBUrGEbC6LptYm5PI5zKk5vVcuFf60w516/2LhYvpuuaRNmDATYu3mtchkMvYoM496e4IlUtdKP6rpOG9Wkihs3LkZfaYk8eCpAbz6+IsujaLGo1J27Vy1aQ3CTOiHta1JIiw74IpkHcO2PYmLopFiJS5nKkpiqCiyAJskCZKZOUyNTph2ZNDQ2mwXO2Iw1M/i4jIGjp7WDmoDBEIpTA2NISpXkMllkW+oQy6bRbFcgVAKXX2r0NqrT5KeGhzB+cMnoOB8VEkc4/yhE6gUS8gW8haIrD/FjAcBBzfRFJTdHiMtE3YVR3mGugOPWgxDVb1WZoIJBBNV4/ssfUCm5IOXmknLnHfcFjPjrUzSwl11vgCTxhr+Im9LjkgxHPj9rhXV4yYkH5Ka3DGt5L9yRHkrFaTOI4rNnyvbQQyL9mvRSkQZyM/+4nn8x9/7HJ559HlUyhUIIXDZ1bvwL/7sd7B+cx/iOPaUoNbEEnDbKImyb+uVyeToZPM5tHa0olBfsCt2EEh3TLy9+q+gttw2Ty0PRP+VSnD68CksmwNIb3vHHbjp/psRhgFDGEfK7V8NUORsxcJxagjo91JKbLp0K+oa6wEAJ986hqmRCZ+5Qa/s0iTPnDty2mz/EbjpHXfg6ntuRGhM3/Ti59gzPMDRJYNjRHGEShyhHFVQjiooVcxfVEGxXMZyuYRSqYxisYTl5SISpZBvqENTW4uj60LYJGK76ZjVPS8vF7E8t4BMGCITBghNgmdszlYETOSNHQ3WvqobWZMKMzE4jPnpWXtgRAJdmG9+dhZRpVJ7zplbxsmyYV1Gk8jsC81WnjCQ3t5DawlwE7CKybv5TBRM2/Tz2LApyul33iufzTgWRdt43L81gcvzkSkNMoJkjAMgywMTPljxa7iu1AYSG/2l63jdF25l4MLNGmv3LIObrLDXs60QF9FhQT6sKDYXpIbo5zGfC0HWcmLLlADAkTeP4nN/9Jf4yGc+iHd+5O0o1BWw68rt+LXfeT/+x7/9PBbnFu2hnrRPjB5E20VsptCsOGTOZLIhNm3bhD037sbWXVuwYmUXWjtaUd9Uz5HBNlKwiEtKjsg5Vy1o6fGVEgde2Y/9L76Ja++6Dp29nfj0n30G3Wt68Yvv/AzT49M6iZRl3Cl18etZQOYvajwyuQx6162yaRoDp/oRV2JrhmrFcpt1hQKOvPIWjrx6AJffchU6Vq7AR//db6F7TQ+eefgxzE3OQAbS+aOI2rMsc+5TUcokwKrEJOAqk7hrRDVJkMQK7T0d2HnDbuy49nKs3LgWzR2t6FrV7cbb+OsCc2+dha4fcZwASYJMGCATmGiuSAyauDGzIC+Axo42BCa6Ozs2iXKphIQ2cxsQiqPIbnbnY28PNIHvT6KqEwHPobJ7DjlgcN1hGsr3vMKxNrsrgcYZxqvj7flTdpwAx8zt2X6CMTqiy2CMCz5o8QijvkQtGXPlotKWAbxrODX51R6t1NWraBYMuIhUW929vO+bSUrjLEUcU5dFGEc6D0hItteKDRQSZVdNdwFXenh8eAJf+ouvQiUK7/uNdyOTCXHDXdfhqZ8+i2d++ixkIMyqnoJfA2JJqhNJkqCzuwPv/sQ7cde77sIK46uJY+0PCZgSpH0I6WtxZyfYc35Siv2imbGp8Sl846++htauNmy9bCs6ujvwkT/4GLZcugXf+Muv4czRUxDuQPSaZqedC6Lsyrkj/cnW/olcLoemtmYAehfB7PgMpBAIA5dVLyFYQEMnnn7/f30TzR2tWL9jE9q7O/Huf/lRrN+1BQ//9Tdw/vhZOwJeO5XJxCdwMtSPdgVYc0YpDQRKIciEuPre6/HO3/kQtuzZibzZnhVXIo/l0p69QAYQUAiDwAvoBFIilJpdkWymzenEsCcpJLL1efv+8sKC3SxOZzn6QqAnkqo5AMJmpeu26VWe/FEEUpJMQQiWS8VCiFySuL+X/euy6J3yJWAHNcA/SMSmKAiW7CnSe/6EPWG5Vu4VM09q+IVUikkJs6i7Bd4NjdF5mJsrhWppJhbF7Qt+W1Ed5PDcD665noLwF94p18L7l18vTOLY+D5SBcmE/4NEJJZaUufILTI3NYd//JtvY/OOjbjqpj1obGrAdbdfjRceexGVSkUDU5J4AJtY57erSqpiXRHid/7db+OOd9yGIAhwoX8Irz69F8cPHEd9Yx0+9nsfRXNbs1thkxiBSWSsWmkJKO1J1Mqat2wcrfJKUw7n2JtH8fk//kt8/I9+Hbtv2oNsLosb7rsJbV1t+MK//TxOHTxpS9fUWo3c9gi3LUcm/mnYutqlLoQbhqHLE0sSROWyZldSgvsoXL/074+/fgR/9yefx/t+/+PYcd1lyOayuPreG9HU0YKv/Mlf48zhE3raBR9vWOe9dgcQvXFboQS7kRACNz10Jz75n/4FOnpXoLi4jDeefgWHX3oDE4MjuPk99+KK264FoM30QAbIhAFEimGBsa9qV4ejWDzpk49XVI5swMH9yl94iFklKgHfVE8nM3tlZgLpVVHgppdno6Tta7CFkPmrPLZjzT++j8459W3ulqBSM8pjURykuO/KNs3mdVXXSeO+JHIfkM5SBgBbLfivPKbrfUUxnx+/Eb8GY0pV/jJWYVrVUhj2gai1+JtrCwCSTLM4iRHHerd8HMVIosSwGs1s4ijWr/m/UWyVYHhgBI8/8hQqxp+wfss61DUUEEeRVow4tsKlzCofR3R9fT0hBN7+oftxx4O3IQxD7Hv+dfzJb/w7/OW//p/4wT/8AK889SpKZi8eOV9ph3/CSpM4fVPO52H2tTELxFOS9G+P7T+Kv/yD/4bv/s23MTM5AyEEtl+5Ex/+/Y+hpb2Z+cTS5XmEZaSBSVqlf9OAJUVg6zbx1SoIQ2f2wEWy4sTMiYnexSrG0X2H8Dd/8Bd45P98F3NTsxBC4JKrduFdv/tryDfUYblYQrFYQrFYRqlYRmm5jHKpgko5QkRzGMeGTYH1S/9v/a7N+OAffRIdvSswPz2Lb/3Fl/A/f+vf4Qdf+AZefOQJjPUP2T4FUiIbhsgEAcIw8Ptl58TMP1xdKzcVfnSPz5MMA+Oa0A+KuPnslpfREbbETMawupAxvNCUReZHjVXpUPq58QNq3xT9ufbGBGIpl62L6FFOl18vy0sCNUxLm4aKEQlCU+X8UQw7fOuVR4O5ZIIBjd9TFwKr7juNp2/j1RiztM2Zel4FReSzVqlrsKd8fABAuoPZ9CgK8y9tRnUdUXYF40BAjjilFE4dPYOlhWUAQH1Dnd5SYk+E8pHCHsOUaBYURzFWrOzCHe+4HWEmxNjQOL78ua/gwCsHNAiq6vxZCgzYaFTNiCDzFdRgjnzybSTQlCeZGJnANz//dXzlv3wJM2Zb0p6b92DPLVeBai9RygMXTnIoSxnYTPsgCGwSLrVFGIduHMUWiIMgQH1TgwVZvXE8QRRHiKLIpBVEiKIKKlGEKIkxdP4Cvv65L+Or/+l/Y3ZyBgBwxS1X45JrLkNpuYRSsYJyqWxAKjIglXiMVEi9K0FIaTL0JcJMiOsfuBWrN/UBAF545HH88huPYHl2AdlMiFwuq/1VJExCmL4bEK6KnpqFw5xmkyTV5jRJXKIUKmZMACBXV9CAxQ9CVa6ig1UrCbtIhDKwf5nAOPoNs7JRP0YuHDdyKkti5YAqBaoKNkWBvuM51YVz7Lva8nRv9x0XhXQgxdvmlff0CZF9jxOmqoXCttEZmNaRrriup1BDcewh5PGRSKS+8aucYPYejM1xLLS6QQuJ8K8pZSAhM4ERVgNagVZEEQb6eegEWQYSItDvC0/ABeI4cnlYNL7mM8EiXg48pN19r5TCuq3r0bu2FwBw7K1jOPbWMe08ho/+XECJ0dQEfApNSwkBaZmPzci3iiatD0/YjbO69nsSJXj6h0/g6UeehFIK+boCdl1zGfL5nCsWx5JyiDlZv4SX75SePS30pWJR15WHTlPoWt2NRChUogiVqIIoiszzCKVyGaVSGaVyRUfulssolyMszi/i0a//CE89/BgAoNBQh+1XX2rmJdYFHdhqRmxeBsLNoTGVwjBAEEo0tjRh655dEFJiaX4R+59+FahEyGezyIYZu72KjzeZw1XVnJi553KR0oDDZEMlOipoosKNHW2QYYg40XlNNrE1lQNnQSqQyIYBi/ppc9QepVXD/cxf8yhwAg1UkdKRybhWP7wruIhumlXREfd2K43w0y1qRe4sBKaBykMprhG/Ciz8qLWq+oHzH9F/HD29UUuBifOcs3Gs7RCzjKs6GJC6T6ozUoaBTn7MhJCZAIF9HSDI6H9lJkSQDc13QsjQfBYGEIEBsVCiZ3UPCnXaUTo3O4dSuQJ7/ZA5YM1+uyAT6KRI83lXbydyZl/Y5NgkoiiGDHSbglAik+UKImy1B0mMhjt5DeAIA0ZBaJI5DevhAGMTPWVgBds9D1ApRzj06gGUlvWK39LRgkw2CxuuTTEnb4FSLiLK5y5JiD3FKBaL6D9+FrHJll+/cxOydXmUyxWUyxGKxZIDqqIGqeJyyZh2mj1F5QgL8wt449nXUFwuAgCaO1ohyY9EQmJYjTCBFhrDIAwQmvnPZEJkwhB1DXW2ukRpuYj5iRmEYWjGi34XVilFrGqZa870Ti7yOY2fgkCigMkLI6iUdaJwx8oVyDfWmTwrp6uNrc0IMxkr7JkgRDYwjEpKZIIQoQEqr4Kq4AqsL0bWUmL/vVjSZypFgZEfe86hdPlc3G/lVXRlbN9TXI/1cd+Ve82ZCQcI+1vhg677E/5zHqFLmaapK1eDCX/hSQBcy38F2xIc8OieF2GH9AhFYA4mFe4jl+7vBkFAuHwZ6eoMwTi7G1uacNM9NyBf0IB14vBpLC8VEVBCo5TWwZvJZlDfWK+BhkWMwjC0rc3mc1oQhYuOrVi5AnUNdVawM5kMwkzGbLlRCGRg7xGGIRqaGxEGIQKTbU4ENp2MqU0IXoiQ7ulC4XEUWwUrl8qIzZYTW9PJfJavyyMIA51sGghbo4tSBeiRqATluGJ8hRGOvH4Is1MzaOtqx8adm7Ftzw48+8iTkFLqqJdZEsm0trW6uGNCAXGlYpc1Si6l3Kb6pgas274RbSva0dTWjIMvvo6R/iHngGYnygAKWTO2gHaoZ3NZVwddAdl8Hm09nZ5g+U6EGhIKchYz7eDCaSO4CqNnBzA/OY3cqh50rFmJno1rMTM+4Y7mymSw/tJLkDUyJ6Rmh2EQmnpYztT3wli+bttz7xIfDlj+YMqzw6KP1C3uRA/oPZAjn/fXOdQle+70zyRECNQsXexe+C+d+WjklnlgXFPNtb0pcRcQcO3RmuKfBMSmEFWwIlSN+/n3tU1X/rXS/fRcbDTU5n1pT3QwsCpMpEzoEopuu0cgsXn7RqzdqLOqyfcEIdHS0Yr3/fq7cPPdNwAAJsen8MITLyNKaFuJruypq4AChUIe67es0/dS5DMKMTM1Z+tS9W1ai7auNmvL1jfU49rbr2WAReaXNHW6JaIoxuKc3kSdzWexfus6kwFuwsrG7PNKQKeGOFfIIZfPafYTxYiiGGEmxCV7diBf0OH8wTMDKJfKdivTwtyC3TLUtqId7b2dKJXL2m8UVVCuVFCqlG1dckCzrnK5or9XjnB8/zG89eKbAICG5ka89zMfwrpLNqJULKG0XEK5WEJUiWyhwlwhh3whj9gUEExiXcFh1/VXIFfIQyUKQ6fPA0ohzASQgcDO6y/Dn3z9c/i3X/0v+MDvfxwNzQ3IhAGymYxL6DTO8lAGSMoVzE/P6TlrrMfqreus/yhOYqy5ZAPWbNsAPph8VeV75xQDI6/Wle8uMXsV9e/GL4yg//AJAEB9cyP23HsrGhobEUCnLPSuX4vtN11jWXWYCQ3ImuPlPYe6qAJR2zZymjNzL6bEWhsAYL8VrCC0TJt/7rUumUxySuafcgBn5ZhHGX0/mqJAg3C9sMrOgIyzJ3cdn1H5vWaA4cf12M2cFaLv55ClFnHiuvSrDu6qXqdq0CqDUuklI+S3so1M/VgphUIhh0/87oex+ZL1ePPVgzh78hwW55fQ1tmKK665FLuvvRSFugKiSoSffe+XOLDvkKv0IIClpSKGzg/j8msuRZgJ8fYP3Y/5uQVMjExg6PwwLvQP4ezJcxi9MIq+TWux8ZKNeOgjD+JH3/wJkiTBLffehNseuMW2idiZW7UESsslDJ3XUSspJe58552YGpvGyMAwRi+M6gMpvClzipQYB881d12Hq269Gq89sxeDpwYQBBJX3LQHd773HggpMDY0htee2YtypYwgCKDiBKNDY5gam0RLewtaOlrx7k+/D/VN9VhaWMKpQycxNzVro6L0SOIYUTmykdaZiRk88pXvYftVO9G1cgV2XH0p/vUX/z0e/eaPce7YWWSzGXSv7cXLjz6H4XMXcMs778Se26/Bq4+9iMFT5xFmQlx157W4+0MPQAiB0YFhvPnsaxBCl9OBCtC3bQM6ujsggwD9x85gcnAMmYxmoG6fnNtgWlxaxtkDx7Hj+iuQyWZxy/vehgunzmP49Hl0963EA7/9ITR3tlkRCmwJn9rmwMVACun5MPNXWlrGW0+8gO03XIl8fR1233ML5kYncfjpl1Df3Iibfu2d6OpbhahcRpjNIghDHWFlgOJ0z3cnu4g1DynBJq1WtcxZjlbh7JYeQac5c0YFx1iYG4i/nx6DqvdqtUNwYCCD1j2v/gVnPiJ1L17Kz3NE2QTlWg/vrItUNQX9VCeZ8zYT66N7WlhT1XBpW+STOwBAKGxKrylrSw5ps0oopYA4RntXO7bu3IR1G9dg/eY+w7Bis8FXmw3LS0X8/OFf4ltf/mcUS2XrTIcQKJVKePnp13DzPTegoakB67f04Y//4vdRKVfwlb/8Gv7pK9/HhfPDePInz+Cjn/0Qcvks3v+b78G1t10NpRTWblqDofMjmJuZx5oNq3X0LQjYqqJQiSrY++xruPXtt6KlrRkr163EZ//TZxBVInz3i9/FN7/wTZP+4CtTYrao5At5XHPntbjtwdtx49tusucqNrY0IcyEWJxfxCN//wMcef0wKpXImonD54fw2tN7sW7Lekgpcd3dN2L3zVdhdnIG//7j/wYTQ2OAENaBDMBGRu2GZgCvP7MXX/9vX8En/+S30NrZhm27t2PTri0oLRchgwBJHGN8aBQzE9O48e234ZZ33IHb3nkXFmbnIWWAxlZq5wJ+8vcP4+zRU8jkMtqXk8lg7eZ1kEGAOIpw+KU3USkWEQahAyli7WZsoijGqz9/FrvvvgErN6zB+ku34rc///9hcngMHb0rkG+ow4l9B7H+0m269lgYaEFTTPzYYm1LRVsFqzYchXFKB4FOQj3+8us49PTL2P2221DX1Ii7PvVBXPeuexHmc2hoadJVR7MZrLtiJ4JMRrsg0tLPru0iYrwelbKJnpS+4NiHkS7aZMzAigAqMGYgUsxJ2u+SqeUqg3JAsYpP7amhqGmgshMlagEUv4CDKao9S64RN0bCARjnK16wyOWFcdPaMwOtXVorPEatd+a0uGhSlruMANg+UCCUmcBF9FgGcfrfpaVlPPfEy0iSBCt6Ok2ULEAcxZhdmMfpY2fxix8+gSd/9izm5xbsUVUkJUIIvPj0K/jOVx7Ggx94G1rbW5DJ6KJ+2VwOEEClUsEPvvEjtHa04q6Hbkd9Qx227NqMOI5xdP8xfPUvv4bb334runo7EUURgmygfUkiAIwzdt/zr+M7f/sdPPSxd6Ctq13vb5O60F6idHpAqVzC4twistkslhaWUK6UNWPKBDh1+BQ27diMzp4OtLS3QkGhuFTE8QPH8dN//DEe+6dHsbyw5AlRabmEf/rbb6O1sxXX3Hkd6up1SkeYDSHDUAcPpESpWMKCGZsSC9lDOD/ZT7/2Q8xOTOOh33gvNu3agrrGOhTqC4gqMWYmpvV1MyH6j53B0NlBtHV3oLWrHUrpdp4+eByPffsnePYHj0MAyGQykACaWpuxenMfAGByeBzHXjugxSh1hiKxVfKLnDtyEt/7H1/Fu3//4+hdvwYdK1egY6XOyfrF3z+MCyfP4df+9DOoa6zTRRpJY5VeCIqLyygtLaO4uGQPmFBGdRR0Sgcds1YplnQKQhjqBFMhUFlcxhNf+Q4yuSy23XAlsoU8WntXIKpUcGrvfjz55W9h1103YeW2TaiUSqa+vEuA5WzOq95ALMG8TrzsdubLZX4w54YgVpViTYIBFfRhqWTyuZOLzGjb5E8Oivp/Qin/3lbRCeh9l4aFh4vREsV8VXDf8V16fo2qdBIRf279ayr1AQcr71rutjUhKn28mXczvxHi0rW3K34zjq5g2dkqSZDJZtDd04U161ahq6cDOXM8/dD5YZw7fR4zJgdISFHVWEq6y+Wz2LhlHdZtWot8XR7zM/M48tYxXOi/YBWlvrEOV1x7KbZfvh35Qg79p87j1Wf2Yvj8MNZuWovO7nZUyhWcPnqGnS7tRi8MJPq2rMP6LetQqMtjYW4Rx/YfxeDZQdCRYxsv2YBMJoOlhUWcOnQSxeWSPnUlm0H3qm70belDW2cbkjjB6OAoTh0+iYnhce1ETzsGjQI0tzVj6+Xb0Nu3ElIKTIxM4MBL+zE3rRM6e9auxMp1KyGEwNjgCC6cGQBVq4AUdhsUALR2tWLdto3oWduLbC6Lhdl5DJ48h8EzgygXi8jlcujpW4m1W/rQ1tWOJE4wPjSK88fPYnp0kimZnscNu7bgX//9f0V7dyeef+RxfOmP/wfKy0WbOc6P+RK+GkAIgVWb+7Drxj3oWNmNpfkFHH/tAE68dhDZfA5rtm1AGAaYGh7HSP+gne9cIYfV2zYim8+iUixj4MQZlJeWPUVsam/Fqs3rEIYBlucWMHK6HyJRxgflHOcNrc3YeOWlWLl1A0QgMXa6H6f37sf8xBQ61vSieUUn4koFY6fPobS0bDPHdVNYIIBtRnfarLwxsCBBAESfC10bizMnap+0vinFttgo/Vvhm3vEtuj+nvOcAQQ9l+6HKZe5AQghvAxxYd8H25vIAEMAUvmZ9MSmeHFDLt+SWCdDR26x2nvyPio3NtwUtCzW3oddy7Je0yebCKyVTuzqu0PZ2EKqXDLfqsFPN3YXdXRNSmmZlFuoUmhLZUcS5d1LmrBzEie2XngSxyZaBbshl/aGEZXXkT1aJPU17e9tVI+iasreS592E9s+6bY75dR5S4k3GZToyR82LG25KxtDcr6GgXXEKqWg4gSQAkHgopWUL0aX0X1Sjgqb/CgaZ9ryok91hlFsYa+TzqpXcYzb3nsvfvNz/wpJHOOLf/jf8MKPnjDnNRqIYmBF9+f0nw54pfG14wbl9zmgLTH6O7QDQUAgCKVzSAthM+HdUfJ6m5KkdADrwKY5TswJRwIwlXLt4mhqogVSsu0fLsHUxc94mMp3YluAEO7QU9prKOz7zmnuAZeN/FElUmVBy4vqkTKzNlqPG4EIi9j5nifz+1SUkoDLAz6muw6wXIFCqajKA/cpuX6A/Q5QkBxw7Wqt7LYbf3+hgDAZ45K+T2OsdHKtSP3GYQx7n2OIeT9UpkieMBnr1HELTIx1KQ/xrEgY/KLMaU7YWPF6IWxmuqt4qT+M4wSJkLpqp1JGCPXmWpUQrdaAJpxGI1Gx7QwAvb0nkOwYJ2qvnsUkTiAqRH0d4Oq66tUPYZZcyUBYcVDmXlhoMBQisADAFUrne5EN4ELGJLg6jSIFHCzBlbb3QCnwZFQCJs8HldqeFGYz2HT5JchkMzjxxgkc2fsWwECUm0A878f6JwyYWINEUNt0+F3KwN7T1UQ3f0HAImUuP4kiu5QBHgTu0FPrvCYfiiAzIbCAI8wi5+YpsGVnFJv/dOk+a4K5qfB8M45ZuYx0y6RE2i8FH7wIiFgyKBPPGvaQf2QW9yvZKeSsxii8O+zUZ8H0ivYm0vcF+w7Y/bS8+ealUG58PGLC9UJwV7/7lDM1OnSXrseLpaQZPMmNGxV/uPihqiF1Xh8j507dtT8l9gKN2tz2d+a4Dge7mygvVYXYjV6Nda0g52cgxmbUQSkggsfm3HUY67G+MdZDpaAqiRUEz01h76PsCSN8O0/6LDeb5kFvCMc+OCuxgkFKzICEfwa4rHeuGPQ+Xc8lFrI6TIKcvPycQV+euQfGjLRWIaXQ1N6KDbu2QCUJXnn0OUyPTeqyP0xALFgxZRCsXUxaraInbAHzTSxhvyvN6cu0VUfSsfHmeUDfkW5sfaASrDeMfbA2UTIqL+3iMSkYpWG+Ir9LwppPmlG5dARiTTodxo8EUqqCV+TPA0ZmfAp/lHxbivWXLRrWh+17kFif2MTz9zigCfZ+1RNjNnInmFfIj30v7eKhVjLA97CVrelpma3uUe0kCJW6IwCEMAxAMeT2hJ+ZdwmNhWKKwaMbIFMG8HYZk9+Asqyt7Sq8xlsQSZWi8U/CJQbIwchQeK1FAISrh8QazCssCCm8o4u80jqCKY8RINrSY+dSuH1hil4zcLHKZh2e7H3zPUrQpO+4SqF+Vja1gyBGR2+Z0CimGKwv9N/KjWvQ0NKEgy+/iVcfex6JYWkUwneC5W5IhoIFb0+IaNHhQqpsXhyZZlqhqcxw4NefYuae/g5SwGiuLSiy5oDe9dbV8+IJp/SMxyP5dbmz3CZ3CjpgwgAWtcHc0zrQUc22BAgQuaJXPXXKYz9zaQVUScHWthJMMzgyMbBVyi+F44ECzSE3FdlvrUxpJuLdRrGmWjxMgTwJQ/o9Dl5cZvRcwoUqyVXjbu9jLzMjedBR7NxyryI/hEpiy5gsyBj/AAGNEDA+KLaC0ffJZcRX3oQdMQ/3WXo3OR2uQMzKgZgElE6M9BGaNioLqFjf2PpXWIed/0M58wwMvKQbEVvig5+YnAIZsPe4T8eBHrEkBz7u967PNoGVASNfrSycM6cjmbq2/DRbKKqUg4FZZ28XOno6MTk8jqmRcSbQTrA5XrlyysKCH33sFMpngNY3YphUIMnvptlUKJ3/SrMY6UXXPGUSKSWxAApr5tmNu7avji/6IKWfBWzuvHIyZGJLWMDywMj4pLhz3Zq4NtconQZRzQ34AREi5T+qOX9VqQG+v8c+dzgGyRYgGjdpTTxhAwO6H+waKb+V7RMDO3pOlpbzM3E/mYMc6yQ3fbHXZ2zOubiVLSvvLC4nl+SyEgBC2mumEBvt1jviLbVOEggEdosJ90V5LCrhRW+YOWcGiHKQLJOhVcGstOSf4ttjkCSmYikQMMdu2o/mL0DCAZ4BRsWe09x7ysIkxgMaOMW0A8hNR8A6nrWiS6fw9vouGMEZlt9+H2SJOtp9ana1c5tW/R+4V271dUAwMTSG8cERe3o3+Z/IlWhXVCdK9qZK+eY1MUfJzF8pU05/01faGK5ZpwRPtCT2JlImCAd+B6LkclC2TbWAirfe+qrgrukWCpaBTg51SSxdWeVz2evOfeFysRzrJ5ZkCZES2vJITwpHZDbzdN6MN5/Cm2gGAxy4hB0fwa7r1RLjFSHg/tLvuaHm/igufilzlsYhLYsCLuXB65OwmOIPhl+Oxy90mbJ3AYSZjD5VWAWBRUJdbM+ZeO4EXfNeHLPPnIbwqJzuE63ScOBGvifebMHmm63oxM4Euz4HLG9wU/410mzP0ch+z9mSj1mMBdUCL/5dI/z8KK20M5wzF2GpsM/ILCu1zU+troq1wXBouzpZ4kEmMODjmICUAGTofWDJmYBxVsMbK5ESUWKUdjuU3foCV1fK1kEPXCVPc2S8NI3lZ+pxzfGVDNYFQRUtCLyrXBCWHThnP5sgf2sMzRn5pIRvHoIigHC1qvR3OIvkwMhMam4eCSfGtPPNyQKtPsL60ixfqXIfCabIZg7YC8qHsixYMbll1/H8qsx09KHgYr4kGlfhtc29Vr6QV/2aAR6BmfeJ37+q7Hou6EohDGyIXDFb0oSqLQARWBk7O1SWcdHd/FNJhDP9mMllt+oop7S2UcyMsrOXKFsT3p4rRwyPmaSWYTGgI/C0aQd8oM1rqraqABOlcueXCCGsCQwwMEoxPMmByYofW3UZiFbl1PHgBn9WwzeQcMVU/Bop4eDrgnd1s48PdJqMgqolHMRSU4JOR19ZliYck3KOcwnPWU311Zig24WXMy0jkLa9ipt8ru6arxaO4VhFYwuDYGDlQMjcF47pWTNNmpOcLbNiGeoeUPkT5LErJ4isHUx+mMT6iao0Lg54+EXS4MJB2fNzitRnVkaZGehWuNSkeILgsUAu0w4gmYVC16AF0HxI5h2XaZ+QMfNPXKwt7vsKQBgGbv8XMRMFpTkyy7niIKNP0lXGXDQ+H3KoC4a+dDyWBRlTa9tSb8ZYuF/L2kDkNFNW4YUAIH3GJwDfpxaYNicuikiHF9D9crksLrlsG+ob61EulXHsrWNYnF3wVitiFZ4AkFmnhAV2V2LGtFPwRD4mgCyPLD03vngwMU4zKfv/GisaJ59spnVABZal0jxJVoLZKoeATacgpgTAAJVMOcwlO8xB+KYwzTMpUrqjpDNGcWmBoZwpp1PKmVdG9uge3DyypqpwbIiXPeapCaRoBEjOia5YrSqeba5sRQc+A75sUFtIwVPRVTYnis2fZ8YD4CFMUUtALJak87MEuyIbk9T4M1LrtcaZle7d9FLDF2V7J+FLoo+DwruuH613A1IrzSE9ZnTNUIaBu1MqMZQ7yEnQC7ksbrn9anR0tgFK4diR03j9tYPWr+VWAwEROKDpXtmFm26/2lQhVXjjlbdw4uhpZ4v7Y2HM0BRT4c+Vz6KUdOYoCWyS+CBrr5AkaGlrwaf/7aexYdt6TI1P4T/+zn/Csf1H3WkzzNntZpH5dJTO/O/q7UJxuYjpsSnPVLVMAv6EclXjbIFuKdxXGEtS4PvGKJ4kICzzovdrTXwCDehBIHHFLdegb9sGqDjGgRffwNnDJ23iLrEi558SvlknTFmXdKIq0w63s5P5LuDAngOugmbKdHyIfieldDRCxF7YSk6ax8HJByyXJmIPHAXfMmNYlQDqmppQ19SIpelJVEymvB19c++aJ8pUITE/L4b3laufS17gaQya1dZQXI9FcRjh0WynC/TcBn/Spp43sCnmyxVROalKf1Qt16x3Qg+azyFR2+Rj0/krjiq0FwqDTMiSRBN3BWYO8tNWmlqb8L5fewCbtvQBAF587nUcP3oGi4tLKbYkLVAkcYzLrtyJ3/y9jyKXzyJJEnzp89/AqRP9JuLlm5MeaNH1qOPEAlXitiww5OZ5ZDJQ3rXsb4XOQM8XcsjmssgX8rZmOE/As4EHk1HORzjMhHjHx9+Jt33oAUyNT+Grf/5lHNl3yPeZ1ZpVoNrP5BDHABADJ0o7MQim7OfCsBGXYcQzqEXq3pR1f8MDt+LWd96DOIpQKf0tzh09ZQoW+lnoMsWcdNjfT0eg6/q5Oylzgbon+Fquy/L4rxX/uX3f1wQH4uTI980/XpeKm3UcuHxQE0qhtbcHN/76J9C5fh3OvfYaXv3mP6K0MM9Ay7E6Tn8sbnq+zRQAeUueb44x4xFVHaV7WkBiQ8wAmzMnm1bDnvuw6RZAfqiFDe6kRNIz/Zh3A941U8LMFtmLBDrtqPhLmqUeVd937hOBUISh27OjXF6QAyz6sYJMEhTqCsjlc/aafetXYkVPJ/rPXfCdf3QrpQv2bd2xEbl81gp5oa5gd9ZLAkbAS+P3TCk4H5sGMGmBRDmbx+wAZzvxLSsSThvixPeZ0KiZrEFB91QJu65TIpUotHd34M53343evpXo7VuJa++6Hsf2H3VmMRt0G41j7MCfaJZFniLi1BTe/oR9w7Iw5j8g0OU5RgBMRVZWsTUMkMlmEIaBB0yk3MSmyEQkIa427wT48NIcw8wNVwg6sYiOZOOmHc2bM3+rTT5n4jGHeqruFLELfr4gT/rkTnckCVZfuhNr9+xGEIbYeOMNOPHs0xg+cticWuT3lc8RmWaurc4cTANENXmoPrLUVUzwUwUs+AsBkSg3Ft5Cz80/Htm+CGpU39xj9i5HC0Y3GXjX6gs7dUurHddDOEywtzdjRfJUjVM1RkchlKF0WkF+IutDcCYVMax8fR55AzwA0NbegrUbVuP84AgCth/ObjJNFBqaGrDBVAogYS7UFyBNZU7uw7BNgZ+GoDiaKTocUjLWRRpb/a8gMLQTIuyeNztXVMPeViNVEEpfX/pxV80OpPAK8sVxDAQ6Z4wyxJ15oP+VoDP1akxLlQmq2Pup9Yg5x/U7Wospr8v2iSJ6AhBCHyrBq60GgS47EwSBNY3oqHa6bsC+zxwobq7AzJSUX4RlTDkzOSX0ChyYXO4YOcg5GPKSLhKw2fHcNyVtyoZiUUA6BMK5C0i59brkouJJHJtjwviqwziAZR0yNR5GCT0PAu8d/G1qRp6tOQRYq4RMJ+tHA28zRVRdArYUwm5OrkHoWfv8rUDE3Fmtgirnt3/sVm0jMDV7/vd56VN7A/q0urWcxfm+YP1hKELjeLWmH9nCcEpErDjWFTkzhhkppauHbt62Di+99CZs5QH2W6VidPZ0YuXqbjuJQghdOTSQ2n9hXTTCwxvbBrfEuNeK+aUMzbAE1oCZlkDHFO2CmCiIIGCDJ8zBGvpwDW5GCsBu7qWfCwSYnp7BT779E9z73nsxOTqJFx5/0Zw6ZFgjN3UZKwns8PBKXmCg60CZ0zNr0tL1lLuuM4tIuDlTctU3M5mMPdQDQp/uk8mEFrBI+LmZwQ8PdQmmoqZiEGtKksSBASg6maqQADcfxIZd+920cke6F/UTDLDsd3k0UGeuu+O0eCliyhDXUeiBt97E8WefQef69Ti791VMD5zXZWoYOHsmkmUFWiEVcwAp4S8uzIj3NmW7dsDbzGwXMwIt4e7nGBdjivQ+34XBR5pF7zkgKKPY1A8rR1YEfbM2bVS6O5F+pWwGwcSVkTrPNGb805Mnwv0a+BdCsn3YCtakguL+JPIPCVOzPESlEmFpqYjm5gZs2tyHQkMdFheXAUnMzAixBNauX4mW1iYsLi4jiiI0Nzcil89BhNKYoYDHHSFYaQln9/PO8uRQPgS2H/Q80N+V/B5SeQdWQBhzKTRFARUBq2kOS82gyUgS4PEfPYm9z72GcqmMpflFyExohZSXN3HKaRYGEmHuxIfQJigJuWLMhTk/AXdApsu4d9nllFlOddy5wmdYjXZA95lYF/dJ2SxlbuJ5LfBFzPqkGED5Dgy+v4+voHBskUUYyX/m2g+PZblsdWXA009FcJnoMExLA5QlbdQOoeVjYXICz3/ly8gWCijNzyOOKo4lC1/JPBclSzPXi67PJvRaI+0d3QKV8tVY1sgXuOpqC9QWz/Sj71WlyFT7w7y3vfl0DM6bccvC6P7M1VL1SLFmBlZp31eth1L4v30DABCCKghQI43JY/OXPJNXIFeXQyYToFgs4fzAMHY0bcTqNT3o7G7H4rkLgBEUiipmwiw2bVmHbDaDgfPDAIDm5kbkCzkEmRBRkrgJYSyPrwtaiKWdQD8aqX/H99fR/NgQfjoPLEkgwsBb1fTpPaEFFaqGKAJAglgX2zYU6PvOTM3quQ0DRtnJ1+UE3CqscuWYKYXAkikj3IL6wQSU5kXntklT9UA6NmUAKhDCApjHUKAP5vCiTBQRDCTgQZC7MXeP0vM4UQCdCWnpKPXadgDkw9DMmzF4cyO/D9wPxZz6pp3e0QPGDyZMioUrmAebZqEBIbFt4FpJTIWuDyEQFYuoLC/Z8bS+QfPEN96cbCkrW9qk4x5xzRJ4RJiEwZw+TqAj/fxDDlLO6S7cfez7lAhNc8XAyi44KVcCNYM9tX5OBkauPT7gEQGzLLwqgEBuAiZLqbHwRMQ118oYEaZ0c4VSukQy0w9jlTCjgFZ345QvFPK6XG+5gvMDI9i8aS3a2prRt24Vzp0fcg5apaNY9fUFbNi4BgAwMDCC9o4WAEChLo8wl0U5isC30yiVoK6QR3d3J7q62lEo5FAuVzA6PI7hoXEUl4tWsAnK+epD+WBSCjQ0NqClpRHZbAalYgnTk7NYXlxCkmgTkOO+CCTCTAbdvV1YubYXhUIOU+NT6D99HosLS9Y/pJSrGFFXX9DHkimF5aVlFItFrQpKIZvLorGpEUIKLC0sYWF+AZlsBivXrkTPqm5IKTE2NIrzZ86jXCpp5kN9UKw/RjkaGuqwcu0qtHd3AkphbHAYo4MjiKPYHsFOE05lXBwjkxBQuh4Vr+klAATuTEIwVukBrYLNNk9UgrqmBnT3rUJTWwvKxRJG+gcwMTxmDiXhLMNR/rrmBnT2dqOlsx2ZbAal5SImLwxjenQMKk7Y4abCmnuF+nqE2RBQCcqLS0jiGPVNjejZ0IcwE+LCkaOISiXUNTQgX1eAUgqlhXkk5TJyDfVoX70SDW1tSCoVTA9dwNzICBSVJGJaK4IAufp6c/pSgvLioik5pNuUa2xEmMtBJQmKc7OIKxHyTU1oW70aheYWVIrLmBkcwML4uK9gVT4uvbA2dvagddVqhLksFsdHMTvQDxVHyDc1IwgDqEoF5flZCJPj5+/78wsNuhv6qTLctHSI4YCTRx+ty4djKkcWA1zebgzwB2feF2NTggOMfU9xKmYFjiRZ+f0SwpWXgWC79020UHCoNGZVoS6PQGowOj84gsXFZbS1NWPTprV4/qU3fG4Xx1jR3YHVq3sQxzHO9V9AS2sjACBfyCObz6JYKtk8rzAIcPXVl+KOO6/Hxk1r0dTcoA8zjRPMzs7j9dcO4off+wUGzg+ZfXvO9KCFTQmFrq523HTbNdhz9S5093Yhm8uguFzCqWNn8bX/810MDQ7rA0TZ5GQLOdz9jjvwwHvuQffKLsggQHFpGW+88ha++9Xv6Yqo5Cgxcnj/++7DDXdchziK8aPv/ARP/expQ9ASrN+2AZ/4vU+grr6An3/v53j1ub14x4cexLW3XovmtmYIITA/O4+Xn3wJP/j69zE1PmlBizKSaWVdt3U9HvjAg9ixZ6c+FTpJMD05jZd/+Tye+P4vsDAzpxkirdiWYTjfhF5vUqSf1/olKTdClTBGqdcBhUQC2668DLe+523o27oRubo8kijGxNAonvnho3j50SdRZqWflVIo1NfhmntuxRW3XIeevtUoNNTrw12jCDPjk9j/9It46ce/wNLMrGUaEvrUo9s//B5suGwn5ian8PP/81Xk6+pw64feg75dOzAzPIof/Pl/w9z4OLbfciMuu/duVIpFPP/1byCOI1z10EPo3bYV2UIeSaIwPz6Og4/9AkeefAJxqQjyiSql0NjegZs++SnUt7djcXICL/zDVzS4meDMjvvux8brrsfSzCye/+qXUN/ahssefAid6zcgzOWQxDFmh4dw4Cc/wukXn3Nb15hJKZRCJp/Hpltux5Y770HTil6IQKI0P4czzzyO/pefw2Xv/ygau3sxefIo9n/9S4iWFquSPh1pSlEU5oLwauo777llacL7Tg1gsf5nJhOJHwdN45AFG/u2n3vmR/2Zh0x4pJsBln9JMklD0NYXjoDcwW3voN+rq8tbP8jI2ATGJ6bR1taMjRtXo76hgIXFJVegTwn0rVuJlpZGLC4t49z5IezYuRkAkMtlkM1l9KnSQlcBzRWyuOPuG3D99VcgMse3q0QhX8hhRXcH7r3/FnR0tuJvPv81TExMa9CyZqA2wTZfsg4f/eR7sfOyrfqcQ/aIohgidCdV00MGErffdxOuum43GpsaEJvDNXK5LG6550ZAAF/873+HxYVFOx5CSnSt7ML6LeuRJAlaO1ptuEoBCLMZrF6/Cg2NDbjk8kuwY88OXH/79frXiYIMJDpWdOC+970NMpD45v/+R5TLZef0NhO8aftm/Pq/+hTWb12POIpRXC4im8uie1UP7v/wQ8gX8njkaw8jKle833oF/oVxikrhL3/GDrOOYpY0nLDX5Je6/Iar8d7Pfhzt3V2IKhWUlkvI1eWxcmMfHvqtjwAAnv3Ro87/lwANrU24+Z33YeX6taiUK6iUSgjCELlCAd1rV+OOD70b9Y0NeOxr30ZUKhmGrkskt67oRM+GdWhsa8XqrZuw+547sW7XDsCMb2DYYb6xHh1rViMqlbDhqiuxeucOrNiwQW+9ErpSRPvq1bj2Ax9ApbiE48887fqfCIS5HNrX9qGxsxP5hgYE2Zz2MxkVyDc1oXXVGhRa5rHphpux4brr0dLTiySK9FmI2Rw612/ENR/+GIoLcxh4fZ+JNjvzLshksP2+t2PXO9+LbKEOdERcXVsHtr3tIdR3dKJt/SbUtXVgeWrSz4kz6GGd4l7eGzGTFAKlaBAFTIT3TjXSWA4lar/vnDUM2FLX9a4p/DtxM/Nifivu3ve4mwJCIX2mQuagtxZTLpKQOh3BnAE4NTOHgaFRbNnch9WrutG1oh0LZ5fMAaIKYRBi06Y+ZLMZDF4YxdDIuD1MNJvLIpPLGtNMr/blSoRDh04gCCT27j2A4aExSClx+eXbcPfdN6KxqQFX7NmBG265Cj9+5AlvtUkShZWrV+CTv/0h7Ni1BUopjAyP48CbRzEzPYuOzjbMzMxianoGSoIdmgnUN9Tj5juux+D5IXzvWz/C3Ow8rrz2clxz4x6EYYgrr9+N5558Ea88txfCHNoqpL/GGQeKNWkqUcUe67Xn+j3I5rI4dfQUnv/lC6hUKrjutmux44odCIIA191+PV595hUcPXDMbn0BFJpbm/Guj78b67eux9LCEp780S9x4NX96Nu8Dve+7360dbbjhntvwbG3juDg3v2urq+ZMmcySGeeMBOFTjHWiklLG/OzGYVI4gQ9a1fhbR99D9q7uzA9PoFHv/1D9B87iR1X78bt77ofdY31uO099+PEgUO4cKZfH5AbAIuzczi5/yAunDqDo6/tx9zEJOoa6nHpTdfi0puvQyabxRV33ISTb7yJk6/v11VZdZMRR/og2DCTwZ5778TqbVuRxDEWpqYxeeGCNtsEUCmVoJRCkM1ixx23I8xmcPKVl9G//00Umpqw7eZb0bZyJXL1Ddh++x0YeGs/FmdmLGPmkT2bQ03jqBQqRX2SdrZQwI577oOQEkeffhJDRw6hqWsFtt56Bxo7OlDf1o6tt92JkaNHEBVZXXml0LvrUlzytgeRLdQhKpcwuO8VjB09hMYVPei7/hasve4Wm1KjogqESa3gDvcaillb4YX7DTf7qpiahzGuqknapuNbySx3V/4F0i2p3TLhfeabtLVBi3+uFBCKQDC8Es4nxCNTRNsCYXOw4jjGUrGEs/0XoJRCS0sT1q7txen+QS0AEqivK2DdupUAgIELI5iZm7e5S3kDWJAuHA8FPPn0K3jiqZcxP79oQfTwkZMIggDveOhOhGGI3Xt24sknXsbS4rKNXOTyWbz9obuw3TC448fO4O+/9F0cO3oKUSVCJhPqgw5KJSR6YbWPIJAYGxnH337+H3DgjcNQKsEbrx1AU3Mjdl2xHQ2N9di1eydee+VNXQYnkHqvpTcXxm9kCv0lyp30XN9Yj3On+vHlv/wKTh87DQWF44dO4Pf+/e9i7Ya1aG5rxrbLt+Pk0VM2ogcFXH7dFdixZycA4NWnX8JPvv2IPhnnyAmEmRDv+sT70NjShD03X41jbx1BHEWeU90TQAUkgpdj0aAdqRgioRI5zgS0z5UuR3zVnTdh9aZ1iCoRHv/nn+CJh3+COIrQf+I0GpobcetD92HFmpW49IarMDpwwfrR4jjCY998GFGpjFJx2TrIB46fRH1zI7ZdtRv1zU3YvPsynDt4CDqupiOecUUfqpurK2DN9ktQKRbx5i8fx9HnXsDSzDRKiwsG2CLtsggC5BsacOzFF/DMP/w9lqanIaTA7Ogobv/Up5Grr0fb6rVoW70GC9MzjhELX4UVBBLGDGJj4skgRLYgceAXP8Or3/kWSgsLkGGA5bk5XPfhjyHMZtG1cTOaVnRjqv+sXT+ydXXYfOudqGtphVIK5158Fm9+86sozc8hCEMsjg7hsg/9OoJMQc9LVNF1upAypS6OAZ7j2lbEYKzKpk8QaDAnvVIEJMojARw+bPIAfDeln8l/Mf+Vz5pAOWTmBzV/4/XbdVLaSIiJLNkVR8D868ISQkoU8vpY8ChKUI4inO4fwtJSEblsBps2rNFOQyPsnZ1tWNW7AgBw5uwgloslVCq0aobI5jLGchS2INHC0jIWl5Z1bpA5GLNYquCVvQewYEyy7p4uNLc0aZYkNFNYv3ENrr3+CgghMD01i29944d468BRVKIKlFAoVcpYXFrWbbNC6h4vvfAaDh86Dhlq5/v4+CT2vbrfgs6qtb3I1+V1ZC0I9FYenvsiBUSo3xeBNM5q4/9JErz49EvoP3semXwWuXweo0MjOLL/iBYwKbGqbyVyhRxkKCEDibrGOlxx/R5kcznMTs/gpadeRKlUQpANoASw/5XXMT4yBgBYt3UjWjrbTN9g/xIoxMZRHps/TsMTlSBKEsRwn0fmjEb3OkZTRwt2XbsbQggM9Q9g77MvIlG6Vny5XMbrz75kzkaU2HzZDtQ3NehSM1IiCCSWFxYQx2W9aGRDZHIhlubncHzfm5aFrli7CnUNBYSBRBjqCqQqiczY6sXhwJNP4aXvPYyx8+ewPD+HxETakiS2Y708P4/DTz2JpZkZPRdCYPDIYUwODgAAMvk8mrp7DKsSSCBSpokCFdlOzBzyA3DnJ8Zx5KknUVpaRhDqbW0D+9/AwoR2uOcbG9HU1WUjxlBA6+q1WLH1EgDA0uQETj7xc5QWtN8RSYzBvS9i6uwp1gSeMwZGk4zqC+VRJqrBziN+fFeAYyq+zCslbEa62/JGLgAOhBdjUML7HmHMxdiWorbDepg0GYL/R2NQdQHw8jrMZFAQUEJa4ErM5AmpfVgAEMUxYqUwODyGcXO818b1a1BXV0ACHVBes7oHrS06/+rE6fOoxDGK5kj3MAyRzWaNaaaVyppp9r7GNBHAxMSUZl0A6uvrUNdQQKwS+/nlu3egrb0FALB//xEcOHhMJ0maVVRICREIFyJ3yxBKxRKOHTmlM5wDU3pSCgwNjaBc1gDb0NiAXCGvzT76EzynSSLIBAgMaCnhAGt5aRlnTp6FCCSCTIggoz8fHR6zq3d9YwPCXEb7lCTQ0dOJtRv7AAAXzg9haHBI562ZNISZ6VkMD+iTrFs7WtG+okOPl/mLGUhVkhiVJEaUJEjYxp4EQKQSRAagIjMHiVCWhcZKYeX6tVixqgcAcPbYScxMTut+mjyuyZFRTI9PAAA6e7vR1NaiD+QINPgSCMtQAxj5nmbGxxFVtDw0tDQjV1eADIQ5zAMeUMyMjuLA00+jUippRbfsSAMWPebGxzB54YJOAjbzXl4uYt5E8GQQINfYCCWEkVPFzyi2+sEVkgPi9IULmBsfAx1ALIREaWEei5MT5voh8o0N1g0sBdC5YSPyTc0AgMmzJzF7YcDmvkkpUFmYw/Tp4/b+cVS2ey39pAF1UQpDACk5q0obfywQ5zm2VW0S57+fPgMAnPgQHHnf179h4WbUALSqG9euKGv1zJsk+gJrTaJcUQ0ppQ7jA6hEEaI4xtTMPM6a4+FX9XZhRWc7EqUFY/261chmMxgbn8L5CyOIVcIAK0A2l7GHWyY2ryWx5lScmG0SgTaxSiUNHoFRBFtBor6Ards2QAiBSiXCW/uPoFQuG3ByTnYNWuaPmXTlcgVzcwtOwQINbsViSTtuzT1DAzZBGJgDWpnjXkoEYYgwo/+C0GXSLy8XMT+/YBRXaOAMBIrFZVeJVbr3IYAVK7vR1NIEABgZHMbS0pJWHqXBqFgsYmZqBgCQyWXR2NZswIf/xfqP3k8xLMUAjhYH7dei1VCne6xavxb5Qh5JkmC4f5CZnvpixaVlLMzOAgDqGhvQ2Nqskz9D3R8CIWkWCxlK5PJZCKXc+IbaZKf0BqQCBGP9/ZgdH7PjY3OqUubc0uwcKsWSyYnSqZhxkqC0vMy0W0AX8qAc/JTq06INOHPR3GJpZhpxpcySdgWSOEKluGx/buuCmX61rloDquw7O3AOSbnkbTFCkqA4M+V2VLDdGR5YeXBARp9x3fBgDQMqiurRXwLWN/vHz6V2r30nkn9dF5hzKQcW5JXPvACWKeXRRZHqlUr96wMZAISUZ0MRAJ586Y5uSgxgBchls0bJy4iiGMulEo6f6sfN112O5uYG9K3txbFT/aivy2H9Wu2/OtM/iMnpWSRKWcAKggC5bMZu47BhUANaTY312Lh+DTZv7kNvdxfa21vQ2dnmyZUeL4Xm5kasWNGhBWppGQODwyZE7vZmuaxykxXOMt0JHGUQsK0rwg+UCqEZQhhq/4xRQNscKTXrkAJCmTP4zGdRJUIU64gSmZFKAXGSuKkhJZR612F7VzsymYwGgYY67Nh9KTy/khAW0IIgQLaQR6wMBBH4G47vNojwUAOsqaiUdNnkgJd1nglCdPR0QUiJJIrQ2tWBS6/bY/cYCugASr6uTgtUJoOCYUoUQFBQCCTQ3N6GNRs3oHd9H1q6OtDS2YlMzm2kdyaPSMcHMD85gTiObHlnrVbatOd+u6hSNmydfC16GxMBIxd/xXBBpT8jGbC5R/oeUbnkInZMtmjhsV0xwZdMNou6tnY93lEFS5Pj2j9F+YpkkUU12gcPs+2AeHCkKALooneezP8KKEiTNRshTKFMVWAytWXJ/ThtctYihCxlgrEv7jv1ne2uPUIoA1iMr7lDHBLvPaW02VMwTvdSWTOsRCmcODOAhcVlNDXWY9P6NXj8mVfR2tKEVb1dUErh2MlzKBaLEBBYMiudlMKyNVAblEIYBrjiskvwwL23YvslG9HQUOcJpBs0SoIUaGpuREODVpjFhSXMLywhMCkNzpfgpiNRGnz4pjUZSAShBFVgpexxvqDIIEAQSrf1hbVLSs0kIAVE4pSeC5swG9101CYV/jXfoXlsaG604Lnnuitx+dWXs4nWjzDD0jYE9FHwUpqtRaaylGLrqaqxo08AkEbouf/D9DmTzaKxWQOjDALc9uC9uOX+u1KToYGKxonMPhnogEq+roCd112NPbffgu61a5DJ5WzuXVqYFQUdUlNeLpYsUOtbCqc8qe8mRs7JHwPDLHi/LSBdzKNtgVDYhTF9T2om339JbTPDijATImPAPIljVJaW/MjfRQDTaQVLVbHA5NiV276Vit5ZsHKybwkb/YRvfWOZ7u4OroKKxg7BLkItYKzPd3ylp9bdWrH7/z853d3zMIlpb5u7iCtt6m6sSzs4k7BcqSAyZVoGh0cxMjaJpsZ6rO9bibq6PHq7O9DW2oT5hSWcPHPe2qLFYlmHoKXOmhdSC4CCToO4647r8JEPPIj29haUyxWcPNWPU6f7sbRUxE037EFXl16ttJmht8PkclmbG1auVBCZ/BhJR3mZ1cZOvDIMi42HDI2TnzLOhTZduABbc7EGYNEmNiHMAQSpjXiCStfQ9iDjI+ShXjLJANjSO0oplEolFJeLVXNqnfpxgoX5Bc2WEvdZ1arFtjsAMAEEAy5wjlr+PAglMtmM/U2pWESlXIaoEjPd59LSEqKogjCjS9YU6utw80Nvx9V334FcIY/i0hLOHTmK0f7zCDMhdt5wPXKFgh1jIeHYlUj1ldGuixkPZOLEyk572tdsv0Ofp69RAy+rPtdmmPLBx4mKM/noAFyaExN08qNtNaiIWU18Mw92Hu2NbIdSoARhI4EXDzI68HdRPD8/i9kQVcmmrEVwtEel3q2eLIsrKbvRGwLLHOHAKwFCv2a2qtEAd4EgDJA1K2m5EiGO9bo1M7eAs+eHsHnDGvR2d6Krow1rV/egUMhj4FQ/hobHbSXPcqWCxBwpX1efd2aSAnbt3IJfe/8DaG9vwfT0HB5+5DE89+LrmJ6eRVNDPbZfslEDFgmCOWrd+jWgwS/IBNaxy7cx2F1+Sidu8hEKAmfS6Qspb6OwABhgmchVWsiYSUfsLz29XsSED6+C9TmRcNPj6ceeweM/e4IVD1DuO2bupiemDODFdhxIEcgRm66xLqVmlGEQuIhS1T4+B7JRpYJf/NMPcfSNt/T4sn1/Lh1DYXZySvv5hMBlN12Ha+65A9l8HmODg3juB4/g7MFDWFpYRE/fGmzZs1sDlqadzCStho10+oEArE+GP+i0ARvAwcWArcaDSJWoBjpvnlkULi0HzroX/rplMuf9TdC1H7bCKoMFwe5PH7tqGv6p3VZMGCDzwn9VjTaMTFY3wrRVuWuwMfRn42K+JwZm3t5D17iqihD8csxhH1Zf3q+J5cxMhUwmRM6stuVyxYaVy5UIx0+fxx03XYXmpgasX7sSa1frqNKZ/guYW1yClLr2VbkSQSkNELQvUQiBfC6LO2+/Dp0dbYiiGD959Bn85NFnEcexBqEw8JRNMPCI48T6EHK5LAqFvDbdpKiGDJNVT0yJ3ieTjs4ZlEid7Ekmgv1LTTpJqZDQyQT+nGl/kStXE8eRyUlz4BMnifZrKYWi2eIihMDS0hL6z/bzizkhMOaff06gMVnojEDTD12ZgQGWkAhDA1h0bQNAbo+XBioag6X5eYwOXkAYapALhETATEp3Wo5AU3srLr/5RmTzeSwtLOCZh3+AI6/uNXl3iQeGdH1yeKdVmVgRVxSz6HpRPtr3mChyQVWfBKOMLgqGTL717sfXWEDZ9pGSM+20VzEs2LlOzPgJKREacPZ2ltSAT5LVqtQE1gfLtoQwOxN8N4Ni11KGcflXSN3RWFXWr8YuJ7xf+iajHXhyu4jqO1AFF94m/4p+W9Jsjl6GymuNuJinDAp6O00upwGrWCqDiuwpleDUuUHMLy6iubEB27asw6reLiRJguOn+1GJI8NodBRP5zYFqCvkEWZCJEmCrs42bN28DgAwPjGFV/Yd0GYiVSVlUTdiO4FRmuVSEcvLRbS0NKGhoQ5tbc0YHh5jysmjK1oCvU3ANMp0fZ5/xseApJPmx5sQc6it2XwdpxyecZJY8E1UokFWeaqm85+SBEkcY2pySm9sDgO0trdChoFNkNSuBLcE2aoFwpSXYcm47sxAU62Bl5ehw07pBGva0SDNIa9GHhbm5rWwhCFaO9uRy2VtjS0CKD22XPASrFizCh29euEaPnsW544csdUZVOKlsVGL2IJQzVAtCIHMKWWifb6csh1G+FUGnlbManAkGXALgKdKtnnS8JpA+NdwzRdIKmWU5uaMDGdQaG03oMwOfTDpEbXk0W8928/HgkHgmMdE3pd6RlksLSNUSrP9dPkb/Zuqzc+KgaYnyYxXKQdWAKvcq3xzs7YXz1hEwjE7aaNlLExMvg2bEmDey+Wydn9eqVKxlFsEEkNjExge1Xugdl2yEat6VmBufhFnzg9phTIRuJIFLKCuvs4oUYC2thY0NzYAAKam5zC/sKgjciYaR39WtIVmREEgsbC4hInJaQC6oOC6vtV2Y69g1d381Rz+c+H66SuNP4wu9O+vihaUjFkXxzGbSMU+0/1PVGLHwU6yUkiSGHESY3hoBKWSZlndK7uRL+S0U93IG0VBZSARBoE27cLQZPT76RVhqD8PagQKaI4hYMczkAEzFRUmR8cs2HavXolsLusOq5DCxxc2bC0d7TYKODM+gTLtFbTDm1ZS2KTe9IKh45+aXCYKiI0lYM8srKkwF3s4gKnl4HflbgishOdvSTOri5qOAOJKBfNjw/a6Tb2rIY1bRbkbItvQ6E4cN2BI7oyUoJqFRXjg7P0p//RBnSBqB9ixVeUNsKcYHOwUhBlnlhLhOUOFdxm9eOvFxP2r5y1teTjFQg0ml4py6jlxzmTJAMopsDQObKkZkYmiVaLIgJUu1TK/uIQzJh+rb00v2lqbMDQ6gdGJaYRhRju0MyEqcazLkAAo5HVNLBlKrxqmEOQQJuAUqK+vQ0N9nTdIOlIosbxcxOmzOpM5CAJcdtklaGputHk2PBpovbo1VlUlHHXmByMABCYmGTMhhuQ+j+MYSRy7zxL+W1j2pBJl2RZnWEq5jPQECgMDFzA+qpMd16xdjfUb1wMgJ3lgq4VmMxlkshlkTW32MDSAFQTImH+p/AyZ0HwMNfC4BUUnhJoETxM1HRkYxPKiTtpds3ED2ld0aoZggI4y67kmCykQZFz9LYpAEqIpAIWmRpfWwBcLkt8Uc9I5aM7kS5Q7bch7pBGkpo+JRUNr/JxHSrlu8aPu7SGruMhDACqJMd1/GlFJB03a1m9CfUcnEpMqpBQQFurQ0rehusHeKqBfK8VzqIRl9lzW0sE6B2T8M3+xBdLAJ2zCuLJWV6o+v72u8sxzvqgnin5VY/kQqRYwtuy1TjkXiBSWSQV2y4l9Lwjs+zBZ7mFIgBXr3KMgRBBIREmCk2cHEEWRBbWz54ewuFy0SiDN90hRc7msrXhZLJVsVnlbWzNaWpqtWaUAbNqwBu1tLa6nTJDiJMFbB49hdlabLlu3bMAtN11tzE1lwMAc+3Ux9mQ+18CkEMfKAyQF5yuLDAvyAS1BFEdIklj/KT8vJ44TRJHOx4rjSANW4gNWbPPdJKYmp3DogN6609zSjLvvvwvtnW2QUlpQCohZBSEyYca8J70FSMpU4matNczUP7c+G7tgaAAbvTCEwTPah9bZswK7b74emVwWiYrhSuQmtkoD7SIoLi3b/KeWri5kCwWboCrDEGu2bkXWbPXSemAUUDkloAcxKxL9NLOoqQ0WjaoRy6VwVJum7mc+aNFn9gAMMg+r7+DGRQhMnTmNuaFBAEBj90qsuf5WyEwGSRxDJQqdW3agfePW1O8ZkxIEIIzB0B80o0qUS9y0vwcsowL7rcu7vAhYMTNOKT7ewm3dUezPyK//Gva76bGtMSNez1PS6bUzFHREvbVP9Z3ssfDmpxIB8vm8dUqXyhUNZMLYu0LgzOAI5haW0NbShEolwomzA4iSRPtJAIhE2Ax5AMjns1rBpMDE9AxGxibQ2tKEzvZW3HLDHvzgp0+iWCpjXd8q3HPHDTalQkiBMNDbW6SOHePUmX7se+MgbrvlWuRyWTz4wB2or6/Da/vewvzCEurr65DPZXHi5FlUKrEPRma1po3ZxHY4oIDMtTjWw2fGgQNOYhzmsfmefxqMBmqVVLkrdZ9MqoROttSH2L747Eu46to96FzRiatvuArlchlPP/Y0psYnIaC3C61csxKD/QMYGx7VvyNFIvHlyYZSMLIp0LtmNS698gpXkth4W6UQKBVLGDx7DlG5jKXFRex74SWs3bwBhbo6XH37rVBK4cAre7E4N4dAAg1NTejo6Ub/8RNYnJsDIDA+NITFuXk0t7ehd906bN2zG4defhlQwIadO7D92mtc+wKd5hFTaRqVDshroOP1vn4lWNl/VRWhppeSAVf6185x7iqi0oc8Dytd3YHkiYiBEAKLU+Pof/UFtKzpgwxCbLrjfggIjB5+Cw2dXdh094PINjZZnbNSk/Itu/fJK043dmW27b9kQwlXPdfLwatZGgaugqhzArr7Kupz2udVDTe+F4qTqYsb6lXBghpfDaVVPOU1SNof69tJCNQV8gikRKIUypXImhSAFvjRyWkMj02iraUJc/OLODs4ovfGkeJIiUoUIzJZvflcTidqCoHZ+UW8vO8gNq5bg0wmxL23X4+1q3owt7CIzevXoKmpAaNjk1jR1a6V21YM1QJcLJbxk0efRveKTlyybSMaGxvw9vtvxy03XY1isYRCIY+h4VH85ee/imKppMHFG3TlQAew4MOHMjHRPf19/3OdLR8BEJZlwZtI5Qm7VP72ICEEMmEIlcmATrs5d/ocfvbIo3jPh96F+oZ63HrXLbjiyssxNTEFpRSaWprQ2NSIh//xn/HkyKgpIywsaNHDns0nXeRTCIHrbr8JV998fZVQSCkwcmEIX/+rv8X0xASEAI688SbWrO/DdXfehrqGetx8/324/PprMD8zCxkEaGxuRpgJ8fCX/g4n3zqIQAqMDw3j9MFDuPzmG3XxvXe/Cxt27oBSCmu2bAGUwvzMDBpbWqx8xErZwxeqnOmiWmGsX90NpO2frXcu0l/hJZd9isTNRSkBoZgfC877pdi9/ehbDcVNFM69+Ay6tlyC3suuRK6xCdve/l5suusBBNkcouIyJk4cRfvGLRCBPheAb59xdpKLDItqKLD3E9YVghpoIqxWu0IejpgkvPH8aRrAlMMHv43wrlh1JQLbqvuoKpQTNX7O6mE5j79/eIK5kEhQKGh/QxzHKFUqVabV/OIyTpwdxOZ1q3HuwghGJ6dBGelCCIhEIYpilMta6cnnQh1+5qV9WNW7ArdctxuFQh67L9M73BcXl/GjR59GXSGPt997CwSAbDZrmJBbQQeGRvGVrz+Md9x/By6/7BI01NehtbXZtm9mdg75vC51q+DKv1gnuDkEApYtJd53CKT0vwKxyZlKksT+CSHtthj+W8egzB5EmWjwZ76uMAwRh7FlOwLAs088hySOcdf9d6K7txut7a1obW+1111aXEImlzVbjci80X2w5xGaKZLsMA19EnRgM/v5Q0qJbDZr00KkEIhKZTz945+hVCxiz43Xo7mtFa2dnWjt7LRtmZ+eQTaX074WIVAulfHSY4+huaMd67ZtRUNzMy656ioAwPT4OJ770Y+x+bLLsG3PbsgwhAxDbS6aKJrbX0oVUCk0b9TMRPi0OZ/oMvu01Yuc5jCgZPut6+LrY8KIBcHu41NKUWkzW5cMys0hP46O/2t3FiSJ3VBN6RBCSCxNTWL/d76GqFhEz64rkCnUIcwXsDw9iVO//AmEDKxZSP3lzMZqMmNGzinvSoxzuBAsUZjg1pmNnGFxIOL9YqsGuWCU79sVZD6yhlq3vYlgCu+eirU3XcRPfybYK9Zz/e89v/EnbDhYAqlyDaR8lk1rV2Lr+jVIVIK3jp7GwPCYVSxqdG9XO9b0dGFqZg5nzg/ZvYLSTHZ9IY+rLt2GhvoCZucWsG//EZ1zZNIjmhrqcO3uXbh0+2Y01BcwNT2LvW8cwhsHjmJVTxe2bloHpRQOHTmJC0OjdvWj849VAtQX8tiwbjU2bliLttZmQClMTE7j5OlzOHnqHMrlMgr5HPZcvgMNDfUolUp4/fWDmJqaNiF3nVrQ0dGK3VfsQpgJMT09g72vvolSsWip9a6dl6CvbzWSJMHRI8dx+tRZO8AtzY245tqrUFdfwMLCIl579Q0sLy17pteqlb3YeZku4jc+Oo6D+w8hjiOjKJRqoBWuZ2U3tmzbhJ6VPcjmsqiUK5gan8Tg+QEMnBvA8tKS9asAzFXH1lApJTZv34ru3h7QIQg+F3M+mqXFBRx98wBKy8s2QVTXhQ/QvWoV+jZvQFtnJ4IwRKlYxPT4OEb6BzB24QIq5ZIRdq3ErZ2d2HHVlVi1cT3CMIPJkVEcfnUvBk6fwrqtW9DR24tysYQTb+7H4uysZqAAVm/ejO615jyAU6cwfPqMA2FSAZWgc+VKrN9+CYSUmBkZRf+hQ0iSyLZZCIHVW7aga80aKKUwdvoUxs6etiwsX9+A9VfsRraQR7S8jPP730BlccGSgY5169G1YSMAgemBcxg9ftTZfVCQQqJ3xy40ruiBimOMHj2I2QsDnuNeu0QUsvUNaF+/EY3dPYgrFcz0n8Fs/1lsuvsBXPrBT0BIidNPPYo3/+GLQBz77MU85wavPeuQTF+ghhdecYzSv0/8lBqLMXBA4oDDWVzG1LDtkko50GPsSrD20W+FMvWsLHY5NxQdvCKUy/GyxJdYNwBx76f+VBEd8+m2Ymjr7FpiDemzDOxPTLUFEnzL3oiWm+/YQyBTA0bXz2UzCAOJShTprSDGr6OSxFL2wGuDy21R7HvUzsRE6CwjVTHiOLErLq2e2tmYWD+eSigaqOxdQI7HxO1Q0/WfaB8izMlB7Fgq6ZzeLjrlBENIdjQXXdPzjzvQoT4RKxCsOgCZ6NZ34y+QgIrtasz35XHLiKcd2GPdmV+MTtzW7dXA5Noi7FzwjHwBhTCjt1BVyiVX8cFUkHDy4tpLjJba6peAZm01c2Yd4jLVH0CftGOupesvujETRpmoyqdNOLYAkBiZIGAQTknJ55skbI6Eddh7Sac0F0nsA4gAtr/z/dj+rg9CQODoT7+PA9/+mgV8y1hsn81zZg+7ZAXflqbj8nzTDvbkIfemMMzTHbIC777MbWSZm4LkbWSAZY8JUNDXNN+RHqxwwGL9Y3/uOhq0QkviROrUOEUjLNjA6j2AnAIS++JdpyO3nG/MJYy5wyFhab8Tan0FBaBYcocZ8EmgLS9KsTpG1vxxiXXkm0sSdk6eMIBoJlEYz6uWRReT4AxcSImQ0WErPHAOar5xmBgLHeYpIHxFJOUXTtS4j8WuLlw5kQq/my0sMnQbtW1/GJ92bJ4dryToGDCYBYPMRkfcbXuYKFgTRE8CYOdOm1fK2FckyHzuSeAiU2rYqrtiZwk4XfLHwC46fOWlMVMsBSHQY43EsW72ncCcf6mxRJn9kvq0NgfI7tRvbu7psTL2ozU+FJM2kktpFdebL+ovdVUGoKJ7CoAIAtS1d2mgTxIsT0+506eNfNOPU1BpH1TYju8LTj+cmjqCQEmZHJDSfi9XhEexoeEmJey8+/fmfjY68i3VBvaN9KPWtUK7Gdf2SOFiD5Uors66Eew9zUgY0rseex32jsb2rgZ7HQ5e1DSCJGImNoxOt7FHcDE2xNrGYq1wJymnFIsuqJw5QYCYNn8BxzSpeBpFTflUWfCh/vL8HwZIJALekeXcxOO/p/sq1hAGGHaKPbOQ+XRSgOnNBWMQdCUBt0BwRg1h6uNbfxOfUKYEJMzGf+RO2PTFNf3Mpm7Z+XRj55lGzF/FGSrBkJB0QrQy71EelUr1XzF9ZL6dWnph2k9RTdfmlApyH1qqf0olyDY1o3lNHwAgKhUxNzLkgbmicYA7e5Mdv+uGulb7PDLBzDqV/qqqvhBLWXAn8vj6L+xv2GxYBCMCwKhQClQVe9+NDMkkRzj9JASqGZIZGmYisTXFmkzUJxYtU9RJOsHYCQHVJxJC54+kCxrwwSKntajRNncYo2I/0SsmKYy3rYAHETy7nA1OIJAkygIUjwMJBic8RcCBEaqubSNUjBXY8RD+VNkIFFNKz1xjylRtKnJh0GBpT6wBE3RjOhDo+izF5wG2LwJwsOsYlh1jOgU4cdLP83BIkJUiUHfvkyyA/vUkVni6bl8KN8bOdGWs0D5xiizZwiBNrpkU0vIoclrz9pLsMwlLCwzsIpwyYY2h4hrNMEAIqqIaWX+NUvr0pVVXXouWVWsBAAtjI5gZPA9iZCRPirfBg+qLwCn/QQ0ssleqxgQrWdRP36HvxocvoHStdESWt8fjrT7usXH0F3ceMAGsSegGUEGZw0gTi4bkz/EYlbHbXWcZS0nTRdYxlSjrgNdsK6UyyjcnFMjhxjS3Bson9rf++/7gKAYMzs9gE+C93DN/5zpXGrq2JzbCKZ9I3Z/fy5uYqmxr33eSBjiqX8Q4sRUWj82lFneee5U+MkB5r9l1VVph9b8UuXP+LM5UuWngcqUSWkSYT1MZc9TmDKXa7Y+7U0wLUayyg2NOjFUJPX8kX4EZB9r/x2XEvaqtRSrdHqTnki0ipGDcdFQKzT292HDjrZjqP4u5oUFES0sIC3Xo2XUZtt79AIJsFkkc4/zel7E4MQm+bck5wKs3ISl2W9vYixhJvlam51Z5aKL0ZLOxceOVHhRuwlczN/+7PH1B8AtcBOz4/kUoIHQlSlzYHvY9B1xgIGKd0B6joSPYfTXwVMGaVLwDlKdFl7QFnTyTgjMux3mUG39O4dPsjTMJZoI5v5OyvhxvJUkBlJs0wVoPx644OCi3xYnOpOEml1710+YgeM98UbF9Sgkpu7f7h+3vY6zN/YiE0vfJpRMLlRVm7RhP+Fzwz70olGL3ZD5Fb+KVhQ0Hpu7ftPlMz11/XLY57PWdL1AKmA3JLAcN1crARtcfARZk4d/y+JQw5lF6ETBg7H6mF+fOLZdg671vh0oSlBYWEJeKCHN55JqaEYQhkjjGwL5XcOrpx5EksTnb0933V1W1Yk30v+uBF1vgSK9IriyIKO8zd8Hqe6cMBZucKoSTLe8SNL6WWauqua1VocNfnIFQl9RNWB6Ki5yR4HLW46i++07CwMxfsdgYsUZ6okAmBCkevy+9Tg0YKZow4kt9F77WwjrjLYuh062F52fwBooxHvKfeL4Zu4owERfutGY3AYxVETAp5d2DvmxzgUjYlfudNfkYKiko54hmJhOn6DVpORdQJtppxmTvohzLJWCkKC4Hc1IMBza+2Q42R27x8NtOrIngjhiZFVg2h9afZ+xKycDJHWYtbLTWETt2jJXwQ/fVSurYIA2uldPU+BJL5Asa9+tCSshMFqWFeeQbm1DX2gYqWqmiGPNjI+h/5QWc+OXPsTQ1CQgKbHFtgp0DB6qsuXxhU3zkncXjsSh7CQdWCinnPWEwyWhKljxmCSZXDhNte+lWrmwV0xXSFxIFT939pTtUJiGSemAFlNBWwYKVnQDhBoW/TqmG0yK4zvrsp7pkL1OjmvQyzVJcJMXdjkdXavmMLqbMFowBppA1vi8ci/DWXcqfYhekSVWMTjhgSQuNW1U9w42vtp7DvlaEMd0hNzf+Kse4hXJjzn2WUC5507JMYpwKbKFgc4va1D5tQ6WFXQnfd2eXEQJ7myZA+/90fX5n+oFF/Ug2uN3i99OOiKrVTMcJ4PVF2TnmW9eIdTKLiv1Cv3Hi2acwduo4Wlf3obGjE2E+j7hcwsLoCCbOnMTchQtIKhUIIVFTlS7y2jfqWYY7Z4se+6L3lHdBxeUhdUPfUmJlcbi9x2U5deU0S7IgxeSFg5twP/a6KwCE3AxUdKqKh8JkOjhDUwBQpvywUDrhE+TQ9b7v0/r0a5fuoNhptYIxI8ArhkPROrqW+Q7tvXPvU8/ZKmmZkUNQHszhzFeAATGXkpQyOQc9Y3tWsFNC5obPAykfT/1Vkw+dYxWcZQjvu+TX8UEQbN+kW4X5AqRfJm5hSqcn2HFxoE/jY1dOwRYfMoetvVpjNU4953JRlUNlcrAcMLEon3D+KjLT+IJoldGnT5556j5xXKR2QIifYeiWVgGXq0kMll9eASgXlzF28gTGTp5waSXK5fLZM0G9eyJ1dc6QqQVsZbWADPA6Vx4YmfZI3rg0MqTsJD53ngOD35r6TfIAswjxNjGZJSbnLVreJWvcA+TD8iaVmX6m31wt3fuSmW+MGXhRuTRS+0svOYiV8lkEL00MxX1GVQu1x1rA2ypIwJQbKKE8hsChXJlr8Tt54e4U6KbNgvRK4csdY5F8dfSu7y5E4Mc/k+n2gExDVlhNsVXek0B308RUOXWA5ObMjwr7XhPPdFIp3x1c0q5g7YRIj5NjhIxw2k6nc9ScmUf5bM6RTs81mNWqrc5GwK7eDLhUShP42Crqk2/S+PNaa4SVp//+Q2hHug04mTmz9d7h7lStq96i4dwT7HspkkH98LYSkalH/7JZdsPGLR5VJeO+APrj5/nujW1KtogFPvZzjdHKG1w/yl9tYvklkgWYmuir2Gz1VFut74iv1EqZDFrnK6JWOLDy2ZcfJVMpM84JEK1IvoO3xiCa61DmuqOvKSD2hlI/bFlb5cCUt9NG6Szldhnrdv6E1wxvNBUbX6e45prWgcsZByNdqf7ZlT0lNHxpd0/ZXjfltlUQk/JNcDYHzDymvnFD2C0ybFERfE7ZPBqG6xYW2G8IC0our84e4iCEreipq3vyPYLVw12t5Iw1WhnjCuub1ZbUMNOcBsGDKDNcpANcPDm4UHu4j5MkRpPqlMnEdJSCHJ5JRteuMsFqybdrKAdsBd/XbGU3BV7efWuJoS+S+h97YXdfGjnLhEF8QjF1Vu59NpdgMgwBhJooMTE0qQcCghKa3QqeBi/FjD+VgCq5CQGbQKrv5fJirLDbAeDhbLbygASfCUiKLbl8FgYaTODIcej5ZUhNvHQAlg8FOwwu/4V+x+mB7Zdv11nFZiae6zMrjcuuyQ07vbWFqZ7gI+5A1nMGKl0z3hdMl2bimftQ3nikU1Hc8LmFwTpcCdzMBLqcL+H6kjb1GFuiJ7R4eUm3BEocpMz82+02yjHN9NETPPHREQB/5Pwn1cmxdiFQrk9gimTzED1Fgr2Op2j2HikmRrKqHMNxrohU5hsDWX9p9e+ZQDFnOTzmY3XEyoEPEFznAAYorB/OYvn/56HvouerOg2IP1SN99yHhu2bL4TOLJPOTPLsJQXBJ0XxKXaDSMF7GxGU7Bsc8JQvbCniwHpAWfOMfVlTjibTLXMesrNBUNwJZFdNE8kRMJE7Bl7iInPj2QYOJH3/SNq2SF9AjxMpnBMMflMupG4V54OTmM9cTpRhWkrphE6TK6fY53aPJ1thvbMB3XloPjtN94zMNlo0akXvkDJ3aQSEn8wpYEq4QHiVIRyrIjDzTcuLTY+T8ersslq2Gl8oCDh8MVJV1/SQhwGBGxsfoDhx4otJ9dLlForUFTypsBxXMUlnpIKtpt7i7z7x5cu1ze+DcB8wOeWMiS/4jr25JGsj60ilDNm58fidPwgJ74vyxjIUgoBG2oZ46Ql2Vz8sexIpxfdtH38LhQJPKOO/4+OqwA7UMwwN9j2ewGnxiq1SupkpBpUaZAIj+6mnSW7SuC+AF/kzlMI305gwWRPJu2cqogcPNz36nmYFts1c1Phke3lSpvyK3bRNV7VLrr2u/Q2xJ85MBN3jImseZ0w0iIqAyC1IZPI589oxVp4/Je1roUs4w/8ON/tqrcBWTllfhHKmnltM6QvCzbV5WcOW8VgYUmPtLR7K+5aXTmAlnS0QdmyIsZKVQOlBqV9zRm3TcThns8BHMkHvMxOL5MBKGpM98/00eHiMGMzK4SSvBnv1Fizl/I6ialz98UqbxMprCTdgFUIZBCxsTSaGmXIFQARsBWF38JYbToJNX2zEisUoKOJk6pbrMa9OFNW3YmYLaQC3gpQ/0HQvIYTNlXF0T9Rspz98qTVNpX6akiUhyHxzgijZupk2e7kAVnMEZStc0AD6C7xjSXys6D+h4Cfz8vHkCMlYnV0ohBs7V0qIEj2F7auT2Vpmn3Bg7Zl57lqBOa/RRvYkd6ZrRsWZlC3vTqk1wgd4sEVVKOWpIo2LBWvHCfkVqqZBQNhFKm1Koeq3zLEN2ORgLk2q6hrC9seXBbcgpZka6Y1lJ1xH4JIQEsA5sIktCnjf91pnrZ6UnLkQe5UZ5+STvu6AjHaj0PekAKrl3I1HbRPQ/8T2knQfQEgHPyQUXgWZFyIFUGx5UAI21GrRXLGNkS6fSyUsXG62/FgFMTlgjl24Ui9+1JEm0U+4lPDN0yqzoBaAMaVybXXXZ9JrVj8aQ0Yd6Cv00kyy24wteEPAo5PchOPrB7EkeysunPa3vJRH4pmEVWWBaJJToGSJkXKrMnM/+/KTyo2yJYU5g60KTsCCkDRuAQnYE3soNUF/Lm1iZ8AYqGVwfNHgJpC5W8IYhuO0KsWeUsuF7S+7FlNYj4swX5Dyn3iy6XQ49X2lvMitQ/1q5ksKaT/2Rc1e35mcDrRIB4kQcHmSKbDl7Nfez77n5kDrs9MX5rHwdITup/XM7cV1m6X98fEgrNbazRdsklU4XQzJsWxTCaySK52ugCS9wJjTX2In5BZcWB0pYkCUmGrYlK6FpVyZF2IFjDXQNatqbVtHrAEr4SshrUtW2OwAQteMgjArvWNsyiqiKy3ilJR+n2Io1UuNN7gcZLRQ+r48HlLmJoarduFWRtqBYB3ncIzCS9Hg7WNN0g7Z1KpldYQUWlWxJgWeSkFLqM9Q02f3CcaY3GnQwqUiSMmy0V1uVfr0GmX7RA31/Tpe/h7rrzUFmaFg19qUOZJWFKsUdlxJNBkoMvD3fgfmJuHM3wNZbnKyhaiK6SjrPnA9TEOs8hYopSfav7b5cgIHan4irR4gql5h98F6NbgApt5sjOE50i2rYotDmieh6n0ju47uu7EiPfIWDP1cl0jmpgNjN0IoJImLbSmVIJcJsaanC11tzZhbWMCJc4NYWl52gJMkZvIIiNxWH2VKEQulD3kgJU7+f629adNlx3Ee+OS5911770avAAiQxEKIpChKFBeQIkVJ1G7Jo5FMyzP2jLcPMzFLTMT8gIlwzC+YsWP2cWhkjTyyaEuUZJKSrYWCKJKgSAAEARB7o9GN3t7e3/XeU/PhVGY+mXVuE3b4ko33LufUqcrKfOrJrKwqWgoURvq6Y7HGNbjZavQf+cEPYH19DU989cnh7LxaxoED+3Hy+LFhk7lqgZcvX8GdzU1iBQXve+xRnDp5HE/85ZPY29vD2uoq9vaG0218wzjPbF5bXcVsbxez2bzJh4nI7h0Mc1IK6dKg2D3Pptp7AnBL5tXtmX12rZ39dLDR+hSqnwKLwpTFDsYSNp2QopSe0lvER2kCHt5gTzcinFCMitMU8okzbIha3d7ibNktGx2rB42QAAvu+gJhp6vQTyWCQJhZtWvjJFHTzakf3D2MXgc/lGOVWmZwA9M9Bs2FdATkSYTB0wdQqz+zYOtjGuDIW3Cwot9BzEv1p9TteXjQa73P8Rfjd6p52L+NHAaRyrA0yl1yWTSKFRTsX1/FZ3/qU/jQ+96D2WyGre0d/OPf+BxefO3WcI8Ck7ov9XNfmZfte55mWGx9GnVOxxYD9ckJtwuwvLKMn/nxT+LGrdt44qtP+vbDBfiRj34In/2Pfh7b29soALa2t/FP/9m/wAsvvlwNatja40c+/mEcPnQQT3z1SZw6eRx/85d/EX/+F1/Fk998GrFSBWfOnMKv/NIv4I//5Mt46pln0UlXXVpnULwsSFvJU+JhaUzJC8npL9id9oTPYdTUkd58O1NmJkQmK3VZAZOrCCmnjrKkvKxXuoqB3T2d2VOGNOHTpzPDqjEqwPOtVMtc59pE1bxXuKqkxCrCzSgbSRl5R082kqMyJ28izbBZKVal4BtyDeokVwQxjyVJAA19SNsev78QSIVTCdk+A+Cl/rP/jsVX498RPzTo0xCJzGGa4q4fpRs5O0sUjb5iaA4sGpFDaflT302PllyQwgz7Hg3G8mMf/iA++oHvw6/9zhfw/MuvYWVpCReuXKHR33fz7OtxWLYLRO8jmMWxamfnjBitrRtLVFZlV/v3rePYsSN49oUXh0MIJgMpnU4meOhdD+KtS5fxm5/7PGZ7M8z7OS5evGxHjgHA+voqTp44jtfOvoG9vT2srCxjZWUZe3t76ETw7ne+A/v27cOz33kOs75gZXkZS0tL2N3dqwHrCibKQAQooG15AHfphg9D3Mm+G44E41lPj+0pUM1NUUAMQBc/l5qo20nUBHazeotNSGAbfqoM3ZvyEeLmg+rWaYxKMKmbDXYiwzmV5AaGNAYZM8mGqtgvTg548r+YTjRuA9sFmYKEa+rAV0o9z89ZfnCzimujsGYSKDiz8dgZu5V6je/UoXXQwdnZqmk2ARDLx3cDrTE6BVsL4A/X9Iiz6mHwGgFF0fpyGhO9DeASYl8MurSVkPZfoLkFeVY9ttFfmq4T6+gus0D3w9LtkXtFdQ+I6xl9q0tL+NB7H8G3X3oVf/r1b2K2t2fCL6VHqQA1nUywtzczl6+vR7RPRTCddpjN5nYy7KSeODybzQAU2yAOMgRUl5eGLYD7vqZd1M7tuuF49hP3HMWB9XVcuHjZTqQBhuPqT504jpdfO4vnvvsSGZur33TS4dChgzh06ADOX7gIlIJz5y/gn/xv/xSbm5tYX1/Dr/zSL+CV117HU898GyKC186+gX/8v/6f2KoHM/T9fKhLNxmO/yLg0RFWY2Hz2cy6iLdptpN4KHfK1/WJgRfT7Q7APFgpbdWiAFNgS0F4ktROciHFM+Wl5M2cvqAA1UlXgWoApol0lIrgbp/Wk3e0dU5Fg2Lt8wwsHofzYT5fH1YYjPkflIag5RfVV2JB2X1jFtfzgGrxrBw3JBAJZlhqqsJwV0jKTC6ay4XYSJrEGkyVgL5hef6AgDl3S9wMlLqyouQCiziD6ojthLjjSGCvoB46Ebqkt0vUHliOMJ2sTJzDFaVg6sIYjMIZAG0708/RyRQry1Ps7u6i72cQ+n0+n+P08Xvwk5/4KO4/fQrf/M5z+NKfPYHtnR1Mug4feOw9+NRHfhgrK8v4Z//y83jj/Hk89vC78eMf/9jgjn3tG3ji69/AfN7jwx98P9ZWV7G1tY1PfuzD2NnZxe988Y/w1qXLAASHDuzHjz7+ETz67nfi0IH9gAguX71aN/4fmn7o4H4cPnQQ5756AaUUY14oBaurK/jID/0AHnv0YayvrWJ9bQ0X3rqIgoIPvO8x7Ftfx0uvvoYf/9Qn8M53PgDpBD/1mU/jib/4S7zn0UewsryEv/zak+hLj3vPnMInHv8ojh+/B9/5znP48ye+gp2dbTzy8EM4dfIkLl2+jI985IexNJ3ii1/6Q7z6yqvmEg5stLfTpkMMxRgrK6bP4MwBY2UDwLj7bEt8KuJ43IFiVkafCiB+8IWCVNcpSxJjYJ0M7EkPXe0CUMGu14KE1DF5AcEdcI+bwIraNha+NeDSzxq7InfOMCyUy3GfDAotY+vrZ0kgYplqBRY3G0uH8O2EeGG+xEOLrR3FQMvvdUAN144wFo5TqZDiwKTPjO4hw4aCut6nC6QNqKw8GiRH+kUTu9ueoxZWr85mxvOlNKipb1kATIfC1UVTVjWn0X/4t7m1iZfOnsMPvOdh3HfyHrz6xrnKoOY4fvQI/ov/5FfQdYLLVzfw2Z//abz+5pt46jvP4zOf+Bh+9Rd+Dq+cfQPfffU13Nnawvvf8yj+y7/zt/Dy62dRSsHf/9VfwflLl/Dq2XP49Mc/iu97+CG88PKruLO5iZ/45OO4dfs2fvN3fg/71tbxt3/5F/HuB9+Bbz7zHTz8rgdx6/ZtXL9x05hM3xccPXIEKyvLuLJxDcvLS+hkOHF6aTrBz//Uj+MH3v99+ObTz+L73/cYdnd3ceXqVUyXJvjUjzyO7a0tvPLaazh27AgmXYeNjQ30/RyTyQSf/tQnsLGxgb/4yl/i3jOn8Xf+01/FjRvXcevWTfzCL/wcLl66hG899RTe//734hMf/zhefPFFbFy7hg/90A9iNtvD//HKy5VhqivSG4PiXRM4dsH5MlLdBnOxihpDR6zAu1/qzJ6CkceVQPlTFJdScLKs83oSdddBpPN1fCELvWu2GtZYHjv6FmpjozSgKiG8oYbls6keiXF9ZqulxE5mXTprrTZE7LcUIAarqwl6Re0aZ1HkoqDGEvvhu07dTVA7mUUJ7ZBAkWRmnJGfedggRPtSqksTB6sxQhuACukOAYu7kq2r6PoTr7Hr2O0NYFRSmTwY1N/Fuy7PmmtYylzQhsXW7WU0toKie2MV9POZpSAU9JjN9vClJ76CH/y+R/B3f+mv4X/6td/Apasb6AT42R/9BA7sW8f/+E/+V5QCvPeRh3DPkSN46MF34Fd/8efwp3/5dfzm538fW9s7OLBvH371F38e5y68hf/l138Tp08cxz/67/9bvOsd9+OtS5dx6vg9gAC//QdfwKWrG3jPQ+/CoYMDk/r4h38QH3jvY/if/69fw3dffhXvfOB+oBTc2drEEDsS9H2Pk8eP4eCB/fjrP/MZ/NSnfwQb16/jt/7V7+NdD96Pj334B/Hr//xz+Kunnsahg/sxO3MaN2/fwv71NRw7egRfe/JVnD13Di989yWcOnkC/9/n/hUuX76K4/ccxdEjh/HU008DKPjJz3wae3u7+Ke/9uvoOsHDDz2EBx64H089/RSO3XMMS8tL+NIffgnPP/8CTp44gf3796Pv55jN9oa4FcU5jOUOfnmMI8Y+MwCiuRqi/IPWWtIlaZ7u4+QB9M6zz2tcSjAEz6eTriqPsykLsBvriqwsvyz+CbdPXiaUribiJwFEmIOowfZkEHl2zbf1Le52k4GHnRLM9pLRFYDPDggMkSaMmB2G1NVs6CIEVm7wXE8Hd4pLFQaFBFIERoFBk8EPfZjcO6qjgYqWKzFEoL2RKV1cBpfc+PCb/7evv/G2RM3e8OnZY3GzbjinbmBVpZ+j9DP0/QzAHKXM0ZfhOwHw4utn8X9/7nfxnnc9iM/+3E9haWmC40eP4GM/+AH8+Tf+Cptb2/jRj/wwJt0EFy5fxk984nHc2drG7//Jn2J3NkM36fDYQ+/Cu95xP/7tX3wFu3u7w4nLfY+V5WUcPnQQx44cwZ985at49Y1z2Le2iuXlZVy6uoF9a6v41OMfwVPfeQ7PvfgS1tfXcOzIYbxx/gJ2drZR+vlwVLz0uPf0SVy+chXffObb+M4L38V3X3wZ8/kefuSjH8brb5zD088+i5WVJRy/5xguXrqE7e0tHDl8CPv3rePN8+chApw5cxIbG9dw69YtlDLH0SOHsLa6ijfOncPJk8fxfY+9B19+4glsbFzF3t4u9mZ7mHYdlpYmOHH8OL7+ta/hmWeegQiwurqCi5cuYnt7C7P57gBc8xnm9K/vq6wNwDR/rXcXURXE2FJea2uuAACAAElEQVT6pyfRG3sSAy8hd04BZ4j7dRYTnE6Hk6AnXVdPhe4wmXToJp25gI1m2awwjbX1u74MjHde29LXeKiejNwjGjob8nAtLIaqW3OHZxAI9dW9tmfU6+e1DiW42REAra4j/4qBrYOV3WdA1RqeGq/2zcB2/X5to6e7FCuTr+GJKOZhbNk2gHTFVwvYTLCCkf/V956+BMuJI6++oVYqp4KCIj1cI0uoj18PFCnoZfhrXFUBzcqmgTSpF42zAIBp6ef1kFGNqdR0BHgsZSh8oNdPfPNbePDe0/jpTzyOL/zZl3Hs8GGcOXECH/nA9+ND73svDu7fj8998Uu4duMGPvCeR/HU88/jxq1bmE4nQAHe/55HcOPWTZw9fx6T6QQH9q9jaWkJtzbv4MQ9R7GyvITnXnwJBT2OHzuC/etrOHf+Ak6fOo4zJ07g81/6I+zs7eLeA/twYP8+vPHmOezNdi3gvrqygjOnTuDZ55/Hb3/+96177zt9Gu984H78wR/+EXZ2t3Hinntw5PAhPPvcdzDb28WJE8fQlx5vXXwLy8tTnDx+HG+8eQ7b25uY93OcOH4Pdvf28NbFt/CeRx5BP5/j+Reex95sB5NJh5WVFWxc38Da2ioOHjiAp595Grfu3MR9h+/F4cOHcPbs69jZ2w77V/EhsmVklLO4lI6Ixd02zXO1rZhrzzpj6hy0lBV1/luXPk/oHk59sBhZHPsMNDwYrcYPZzE00nIe1MKFr2SYHANz15djXdGdtLSRJvZHxilUJgGNgoYwKgRQc4PNeW9jbhnHe2IBkTGx3Q6rIaKblVm4yw9NJjyzEB2ghrgdaLmThOowOFkPF0R2Xl89uD8jdObLA5BVBhx3zqDkdGg8LUbtcwhE75v2FbDQe7zK0be3CqqRzGYzPPnsd/Czn/oE7jt9CkcOHcLO7i6ef+VVvHHhAl56/SzOvfUWHrz3Xhw5dBBvvnVxUNhJh6XJBPefOY3LGxvY3N4amMzJEyilx8Url/HQAw9gZ3cXlzauAgKcPnkC877HW1cu413vuB/zfo5zFy5g3s9wz9HDmHQd3rxwoW7aPzRq/77BtXvq2WcB9JhOOpS+4OTxY1hdWcG58+dRyhyHD+3H+toq3rxwAQVz3Hv6FG7dvIWNaxs4sH8dhw8dwle++pfY3duBiOD0mVO4fv0arl3fwJnTp3Dt+nVc3biCvdkujhw5hNXVFZw9+/oQ+5pO8Ma5s5jNdnHs6FGsrq7ijXNnMZ/vAZOJGbPSZFZ4lbX68woYfLqQplBo7KkOr34dx6M0YD7pbFZP3yu4GVgB4dkODIOyaCpF40LVi8Lp2YjAZDG2GAhJsSgGqwgajjfkNhVnJxrn8bgTQr5fF9xCKr8BQOqKXDNyJ3N8iuOEgZyUkprYGnw0/JQ0mj2yETdpeL5v9ZN3Q8lt8QRhndbwmdDQRzR5EWOAVU+zoDj2anIu4bTnEH/V26mNQ6wvxdvoNS3khvC+13oyLQqGQ2/rMe9dJ5hUENibzXBg3zpu3L6Fz//xn2Djxg1D8bXVFSwtLWFvPh9GchFMp1PsW1/H5atX0fc9lqYTvO+RR/DmW5dweWMDn378o7h24yZu3bqN6aTD/WdO48bNm7h+4waOHn4fdnZ3cWfzDgTAux54Bza3tnD12rUaFB4EdfzYUexbX8f5ty4M/nulowcP7se8n+POndsACu6/9wxKKbh46SKm0wnOnD6Fi5cv4ebtmzhz+mGsrCzjzfNvYjYb8rPuPX0a5y+cx+3bN7Fv3zq2tjaxvb2Jfr6HRx99BNevX8Mrr76Ejz/+cWzeuYPLVy4CpceZe89ge2cbFy9eGDq0j/EbTYFhEPL0An/fda6CuozK2Y/YEfGQzKKG2b3JZHD9JtIN19JMn6i7Z8pTUGxnA1q/Zirh7pDOQOmJSR4PQaN0RLiSwRqJar7nzxpD6lHiEewhEI0WMIseAusGxfEbDfoqILKVhBiX2YlYeojnm6nB+Sygx6w84Kx9buc60jVmb1lwksGlZXI2EyhevukIMVQtttOdV+wxEh5ZQt9Qwmqtq5cV+7DN0fdhzccqT9MJ4C5DvTJzI0JYg+6M9LTgtZTBL16aTrEyXcL2zg72r6/hkx/6Idy8cwdnL1zAsSOHsX9tHWdOHMeN27ewuryM2WyOO1tb2NndxTtOn8J0OoFgSLDc3NrEwQP7MZ1O8OC99+F9jz6C3/nSlzDb28N9p07hrcuXsbW9heWlKe4/cxqXrlzB5tYm9mZ7WFtZwf71NSydOomP//CHcP3mDWxtb2E6GYLCpe9x5tQJlL7HrVu3sLa6ismkw+7uDmazPSwtLWF9bRWHDx3AR3/4h3FncxPXb1zH+toKTtxzD77xrW9iZ2cTR48eBlBw7foGZvNdHF49gGNHj+Hbzz6Dne0t3Lx5A2dOn0bXCU6cOI6PfvijeOIvnsDGtQ284/4HcOXqZdy6eROTSYcH3vEArm1s4MaN6x47MLDxESec7kPsiF09BjBVXwUqC4wLAZMxqAGUuk7BKgJjNE5SRA+f2FW9Kq6xxD7s202Dsxlzhh9W5C59F9w+NWT9U6fLde+vxuVL93PLgrtFsTAZA8eC8d/FZwp5i+boVrXss0gJv/HsnTeOBBA6Q0aASfWGVyjQewvyw4DGAIaeHdmU15r/+vvo+kalAck3tl0vF3p2dkXDKosRVs4PmobwRCG6VhvV94J3338/PvtTn8HtzU0cPnAAp4/fg9/6wpdw5fo1PP/KK7i9uYm/98u/hO+89BLWV1fxu//mj3F5YwNPPfc8PvOJj+Po4UM4++Z5fPHLX8a3nnsOf+NnfxZ//2/8Ct5x5gxeePllPPGNb2DfvnXcc+QInv3uC5jNZzh44BCOHzuKJ7/1FOb9DK+ePYvp0hT/4G/9Km7cuoWl6QRXNzYw7+eYTKpr1E1w76lTOHLkMP6zv/lZ7O7tYT6f4/e++IUhHrW1hc/+0i/h4qWLWF9bxeUrl7G5dQdnTp7E/v37cfbcG5jP9rC3t4t9+/bhZ37yp/DPfvM3cOjQQezbt46zb5zF3mwXTz3zLXz8Y4/jH/zdv4+jR47i6tUr+MKX/jWWl5Zw5swZnHvjLLa3N7Gysor77r0P5y+cx/b2VmBBOkIaGAGQriPA6iLDIvDy9wo8Ayh13aQmdGowvQKVxb0i6A3GNPR9n5TDBn9VB3OnCjGUOvom1qSzlXqfMRfE2IvAnxvdIWJc7F5Yqo3GRZQtlQZ4irEqBSE3JX2eTacXNzTfkrqFWWc1NJlh9a+bQpKx5mz5aOWlLdxiVUIxS/oL+LIY63v93l1B3X3Uis71pD7geCEAZ6LsWlcqZPFHYsLMQGPvwdheWweNTfluKnngCjBFrHPy8Ec/9j/wrIJtJdLpTJJgaTrFof37cGDfPly6uoHf/bd/jCeffRZAwa07d/DquTexvraKtZUVvPzGG3jp9dewub2N186dw2y+h4P79+PClct45Y2zePOti9je2caxI0fw9PPP4/f+7b/BrTt3sDSdYntnG08//zxu3bqF5ekUu7t7+Hb9fOvObdy4eRP71tfwV888jaeefRZnz53DlatXBxeoAyaTYbbrrUsXcenKZVzd2MClK5fx8quv4OLli7h89TLW11bx7eeew9f/6hs4+8ZZnHvzHKbTDteuX8fTzz6Nza07uHb9OnZ3dyEAnnvhOezu7WFj4yqeeuYpbG9v4fLly7h27RpOnDiBl195Cb/127+Fy5cvYmk6xWw2w1NPfwtXrl7B8tIUfd/j6ae/hcuXLmJSp/E4Y1w0ftQpoHQDcKlrV3OgBhCa1O8nmHSCSTfM6nV1Vm9aZ/i6+l3XTeozCKwUEIlbtYpMClv/Fprp85BqYd2MxpdMMkz7B0OKSs4n9/SV/Q9Y1dtsYVhNQMbPsamefg9pDShwtyrFeoqabwkulW6Jo3loPvMKn8WyR7fMQtsa4l7JsIu60bRagF0/S84VkK06aPFBsaFNXdoZQwdM94ETmKcYpMWdXFZd6lkPHbRMWyRm+NtKC21H/Y4noIL8tE/qjifyM//Nf1f8AWkmRhPrauBw0g15Tv1cx65hKnk+m2PSDQHX2WxWT6318oZlLL01qMMwpT6fzW30VyVU1tGJ1DV6ncXFho7s0Pdzp+a0LQ5QFwnzQQvUNt3NYd7Paza/tq3HfO57c/W6HAZAPx9ifMMz/cSTUnp0XYd+Plzb1faXvretVLhetmuEKi/R9+D2pb+6nKjNLu+sTF3jN+k6UmIqp3Nw8h0onIprbYLRqetF31mGtsRcKaf8tOWy6pMZngbCo/tkddGhtPjz3H0bmflLcRSPqbEn6T5tRzsPcP4P24juPACpRlllNFFWBa97mFlD3PcqlJ9AUXVOGWIANYr9dRzfUTcOeh5jAiV7ZqF7nW35/dGF1rhvAKyelzMxSFFdCdCkRLxQT61T168QYNXvLYm2enTCM8oUoRoyQSrjrPWfykTcnyZXUNvlvVDzYVAgHSwVQrdHmVfDNoTOLkQdEjRfZ1iHR7NakIC6w9+JuU/e4UDXTUKnDYIaFgJPJgKUzoLAlkleG6OAxqM4b+uim+LZZnlV+z0dwRW5lIJuUmtSBjaKiS8GdoNWoHIt53iD78XlYARp33tcqgJWZWkKdrwdjv611IiUIuEG68pqAFXlYa4Xy5oVk8DB3AVTRO//EPtQ9qUDTHFm5zuq+r0YAysMG9P1VixPmxffElwBiMDMYx8Yf0khUKKzEEGGZhIjeWRmkf5GHw3kGycXT59DgNhpvewqn+wwsVbaYTOG5CJan2e59smNyzOAtXC2s4IBzHOkjic4VHamd/ady9VcQlYrrqdhEMV6CzCdTDoLNhjiWifH0koZdmEoKEBfKH+rugy9sg+qvHhjzXTFDXrIBZI65U4Jb/DpzWxkIQHQWDwDjSt6QXUlaKubyK5KvD5sYFaCkSiYah7JADD6myuh26VQh8d8JsszsXKdSdmSF4tBUUwKQoyT4lzkQpiiAPE7AhSLSSmoFAUMQxRivrAYBuuDuQAj4Zj8KvSfCEAFfe91i7k7HvBlxg4A88S0zBVJaRI+I+Wjsj7DGVmcADEXDDGwPtiPeyE+rpeoo+Raol7LdK5lR5G56W+d7fjpeUodSriP7UPjRR6kl7rHPcNL7UsbxKlzVMZCqSChY4tfru3SChRUN1qsqaF94BOPCI+ihgzFcUCro3gmBNNhBC8eIQ2V8Qxh9NVt6ufm+uhfBwv/bB0jElw6c2nU+DpnB75uzfvXR192T2DDegEBpeZO23Y29LcueVF30hW3D+1lw7A9z2tgkM2RXazQpwpqJW7dYn1Ls3wcPAd465bo6rHMmnwpLbMao3D9hBXGAbp39Ag5S6qODTsQGvRISXWbZ5YAj0/aNHPPNSWhPrdXN9PYfZ/KoSUr9tjsGppCqH6zrjM98LZSJcNRYmnGT+x+YhGGzzyQjSE2D6jpd+obO48RnioBcdcJtZft4A5KycjAZ4MnV8FbD4s3FWfFVg7Z7Dj5jC5vCc8ucQC2f1W2PGkQxrc0CjY2VhAKLAVT3Q4rHxahm+4NW8dowNP3veKFuwxYdTVoGK00hqLxlK4GjDWAOKnxnkndQlfzXJK8yN+OLKq3ZSwFHGPiQO1gQZrcSCBrnaWxpuFcRnX7bCKCEgA5BqUHLahB2y4JJmupzLV+UgZlgNX5CC6+EZ65eV1nZfD3ztpyb5dQngFy78DhM218rzMCm0FMND/oFGlsPm1Idcxm9oChzwq8P4DqivsGiOMDhpiB2G4LcCZVLO7pLXCgcVNrQMb6ttR+cFew0wFKvP2BnY28eM8s0xH2UpSBa2xJGGgYKN1Y2SUc2kRrRptrlE0lo1EWXb/hyQiW9zAwu1yDu5Zc8gxW2l4GUIt5FUHX6aBIrFNlFLulkWpwTyGYokNdMDooT28g1NeAsu4WOrfdQvueMuLND9eKe/F68EDePncArLS1rv11oHOXOs8MwdiSAlihWFSpsTbumDyzlH+3UUKGtffcCcpeKG8w6nH90BHrgRmRwNIYoAAFY0oOSGJstNN7OH0hpDHAFY1ASxp5+WSGGo/tp0QgawZm+tPuRxV0ihiw3qGg7GkQFCw3148Yuz5bJyWMSdfyzEZ814LoxoWvrWM45tZX1xJC5YpuCc57y6P2CQG32DvSEzbULJXMP5z1cr8pOHc0sPixZ9GziIeakn1VN1dTGVD7NYZN4AdxFM+fizOAcWaYXVLWp6KDPCIoucz9foDcaPOQgnKRzbh8TAfTxlrZ7Z06C9EgOi22LfyZdnVIvjg0v6jQmiBzY3RJiDMsZREBpGzEU5OJjCDuG9VjXrheA3uyfGa9jkGJDl91dBf7G2IkdZ97jqexYWjAXUfH1qKJEtOiYXMGJcaqAjDZfdJ0duh4t3h7tucr1U/WJgd5Y9dgg9TgN8VqRpRGlUrC80GDATBMIFfm28cFx2GnBIl1pMMFk8C5JvF+NX4DFQVoUfbm8izQbbeJ4VSGBWLRwYUku8on2ZiLCHav3D0KNlJZqO4XNkzjsxuv7Eb7fiSoruUryEj6HsxAmVXFT0FRGZzMKyA2LT5wBfAt3i6fPfQYqrp+7GmYrgh/bKlVdkdF4g9Tjfl4OsAAYGH3UVY0FKCrLIBGSl06wtPqyjqkZlvrk/XgTL4+TocjuGwKqsMo7a6qcPcUByX7q0AF/14Zk4/uPKHPtENHiApOXe3K4gmCQHJdzR3o6Ey+mAA6KBsliIK2N6YZUi3PATXGIJiNlKJg5IHqzgypeCyHRresGIM4KGYQ3ip4BzM1uNA9+VFqyki9r9d4Z2J4pog2exe3sjOHlJFAn0ldFeODbqxSXJams+T22fHpNiBxAJomG2rZdqgEMUjucP2Okz0cqFzHjUnZdwo07hqCBhWuv5Vnkyu+CyjLzFtTwmCR2WCXgENdzowh/DE8W11ben5HOtPolw1MBO4BO7klNNOYcGFa5nN38Wjx87C/FLlMghqLqikFthd8CTtTKvp3Sr3hLp6+wpS/jUZqjD6drkZkm5HoLB4xKA20I3SM96QzP+3xYkBhRsRiYoHqSEdMazhFSIXpLqO6Q5qmYBMNJBt1GU0m0E3q/JwVzpliV0ZB1w9NRRhIzLoqaPUm2/pewZcMqVXOwg+1ekaFd/Ax14+YlMcMAQ2c+TbDypLUyHWGj4mNDy5MeHzyxcGAY4emWwpOPGEiMuQv2QxgGbEoL5PrC6hrOehAHwBXZZlcG5UxDUDB9SMbiLsjlPieyjPmAndzFTR0sHaGTZyK9lSX/Jn1oIKVDlB2fYnP53aIDurwFAq7j7TKhRvb4y4ly6+E0EbuoOm8+C4NTRBa2dJEF9v6zFcYAci145mvLjyKO8J8GJJYoZGyfjY3EMaUdCF2MGJRj4LAigKQ0hFQcH0oBYNBywOPfrX5510xsFLKq0tuLKdKmaUFyb2MHIuSwjUqbpFhQBy+5zV0oa/IdfJteZ0DCb1XuUeXkD+1a8bEquaMm5mTun58sg//Dds9a1pARdHCdYfH3JpzB6FudfQaufYCctsMrED/SmyQ8bsR2wjGBrvWQgKmy74zqklZ+NBZWDwqAlBxOzHga108tjUDLKpw6BPEWFUxGyTvyOya2BXTQfTWbP66I9FZzhcoEZmkomQAJCUTO+k6x7vjRAIPY8xnyxDD4pkP7XRlSAGEiEVYToVoBzlSdrqbpVFAVl5vEPvVtjsEC5xcOwUxPX9Ov9dV79IBUj1Zc4EqkOisn7uALgtd9R8VX9vqLFIv4Bk4V6aUY2UxutwdaP4Or56ucVeIZ9NUMYetgLILQ+ZudRQaYGIb4vl93AeulNZsGYLlKjM9qo1PQQLP0ALgBFB2/XSmNSSYBiig6qQz8dhdHQMY25QQlU3ZEWS8aR2MxXs7XQuV5yq46DO6VDklJBDSbXG5elw2un5qpHHw5hcFroP7F086CozXmBXFcFEQQVSfTfJC7AdmQpJk3wApg6jaM3k1emhKoWuGHyS6nToghr6kuDK5OyrzqTKRItQxhYyR3LkhybRUgKJFtdox5IO7dcCUFQoepTd2Ev3aBGAZtNhFBVPXGnfohuC+C0dHCbdQzsIfKt55ecWNx+BXRxOaEjTA0usMrIf7NfGwTR3QDk3KytPF5NYxkxmOTUOSp5bjzw97tmuNgtuB6AqnwK8qnCl+D5vd6wywnOX5LG2hstW94HQH/12HyLi8h+qBsZcnsbIb6BM6xGZsR4q40FfbpqTWxrH6fI778ymddlCCGqcwyNEsralazatSZiWaZ0X5SMQggnGLtzZuBOj5UnoCuFqA701PTErrUYhZBrfNbTPMN4yc6Ax630lMnwgndDeaLqGvkMqS9KV9lwYj91gLpqLB777YFDuso9XNGxo0mfC6Pj9EM1YtrpMqPr86/DapQ1EpKPp9ge/FTYboW8qqq0SuRQdIL0HY0om7WAQ+PBpbTIanT4OnwDQVdmyjEC3hpM1BNtF59Bi6mUIIPKvhhE5ht6nw5AL9Vhx8woZr9VmdDS7FjEpnnaICsRoR0FTlsxgZsShNIQlgWahvuJyR956nFCm+ykyZTTFji1BfMCQgsmF3Nth4uxk8OrY2VXyqAjPJYu5pdfHsGkXIqBeu/8UXFosnf6oLqnUbA4FcX2dlxWJVHoNVH0OTo5NLGBhVoTJ1EoJ31XC4s/oQ2/EBu9AEgcQ6kuqMvdipc9vTL0u4lyYgk2aQmtWypsMOAkPvaravoZ2QsDV4SU9geuiuTJ58p6URNDpyJAAASjeAps/1jAhB3Rt9zgQGMM4iiS3Re53usTCXuIyk0CwVC5JcQGdDDNLBHui9syTfqM3LLwTqqnTKXPT+fmSZE8i9i8wWNrBwbMTjG9lABJ7IyYDl4BNypoonEms/e8CW2S6xV9YJ/j3JjYE+fleUlDcsw9tek047NiRih4V5L6jtZEocJgAZsagO0WCr4C/VmMUHdJ146ogZOcPyZS4ta3HQ4DWL6koV+KYB7laXIE/VJ2W1AwkkWUu0D9YFdu0AnQwotARIXe3suo0w4cI9z7/HwdGYZOF+J52x+1sUmE6mE+uMTuk0yK1QCkju33C9z2xRXaDHnptgNE1Ko3U8urErjkh6QrlCIKH2pUqiwBS1rL71uI4yk1L0QZScSIbAEo8+Pws9ujIcU2MgjsFRHbudNelvClY2mUBun5pXWLaBOsnRUYdnFzD7TkQv/Ch1/euLwH0lQwEnbZa+DwoUc7piQmKBt9UAopRgjI1aN64b//V4aThRWtMUiM0YoFfXDSSfqKgJ0JyEuqlQWVb3TkJagrJaBipjNtCcKiZpgxJyEN6BynO1UHQG3HWBs6xcSRENiXVTsn2WoA8Sm+zASbo9fPb2s1tZJLIjhpc4pNP34lfk2FWmKSPeJqbTqe6IUIXYua8dAsc02sXeZTSAAYahKQEVs4/g5sE7VX9TBS1GBmhZAtNowJMEq1SdRbnrZ2EsGa7ncqJtu5nZ8fPMyqzqirRu+MPvrCTsytEsaCkpaM0uYQR1bbPGxUzBhY1SlcsTZy3eYw0rdZUOgZKtDPDvbBYSpW4JpO3poytjKqEA27M4yUXJIBVVkmeKxlyIxhURQdfB0hQMHJJOBLUPATwx1hv1rg4+AbjYvRPbE0sZR+sS8vdet1oyMam4i4KEevc+YJkJqxuIaFuF3UDAwgClxMGWYk7WZ9y+QvUoHhENdeZO8hqQ9FpPI9tsmzfmhbZwO+a5yMCwYoBdHbYS9k7y0pj3ReAKhF94YWseGfyawgIQDGkBfe8KaIN0TPakIJnv5EmdN1S1CiqMKgWlY6YopgilysCD4joKc6ck0QYaDmcSgC28VsBSl09P127yqFQyym7h8o+AxY61aiHHNXw0tAXGwc30NISwyL1X911n+Ty4q/LgOrrbRswryCh8eZeXWBv0wjDThhKZjQGI0/OcC2VMn/o5M8y2Z7m84WE2eHcUQBfadkbZlYISpfVwXElFpoyLWVpgLSNxwnDmAlzHInrw8jgChmonHvusAyC7fGgB1Db7467T8b/QtzzYK3aYGJ0sRFhzF523BcrNZFZYMOxeMZ1Op8HV6+h9CIaRe2NB8/q7BAZVO3wIStGsnFULOvTbKKIsoU5TxrjR4JKWPhTieFUlEk4nsViXq2HpUScEhepLSzZoiqinjjfG4ShYfytB2PxbIYAy94oZFWJZbFTmhlcTsgMnxIFg+NXnsQoA3wSqup19rUfvibW+VIbypmzGVmNTnDRJo3k1lEF5Yp9aAmM1kGKGQUq8iGOxyzdYWDUc3VcsMhyx352dGYDa4BHZjUpFiuZMMZd29R6qK7bOL5/76PlUJczGOqtyWXifDoV3iOf+8b5alnZSLFLlSp77gWKGbKd88IWvlKC+65ThKONLmffKqoozWd500ZQwjUUsOzea9FshfQgaX9zjSRGMVlGG66eTSUeGgiBsNcTBbouPZJSFzO5zxQMzRiZghRTeWborc8GwayevaDcjFJ3pKkAP26JEBavfi/hUdURJysWh+tkIEPIPCm1QpsrR2218mpCyyJhQiQEket0MsA8JsDlRlXch9RGuglcX42Eec/M8J3MaON5UYM/taY1o2KWiLm0aDDmyRp4lc/9UCWvWWHUJx+m+zZDKIlX0gUITfMM2xFVG0sUYGE//+8y22HdctgchFrgvBKqdzux1CawQg+gBTBs4proK7QNVnJF5HUgvFLCIQQ1MJIYdjGHZzJ/aJj2/dogCKrfbGRSDk4TvUw97XROR5Yt9+CjpS1KQQoBs/YJUqN+bVwtNJ5NpmG50pVMaww+Do3YFnOqtQWfuovvn/3gENrQXQSl1gUrJihifaV08ATqbsKLRrOZe6Hoslx2NSDS7qYXrVHpziKWUGusiRNbfU7yJY0ClV+YCeFwIppTZUIzt0YyTpyL4LKfKQ91VC+b3ccF3TOzsMe91Dea8AjezQWqf+ySNco7N1mR9dYYSFd48+MAOvf2ajzQAQB3lO0qcDEDOu2+6YSRv0g2htPUR14YmpWBCz5rY5HmpG0sys5KGVfkg7CBgR4F15NrW+vNg46BazB3PrjWzXvGRy0hEx/IlN13gMndwGvbVsnuDuxhUwR6T37A3pU0KfevaaxhhkYbCPWcX03v35Ep67rSrW/raNsbJqKw2cdCyNwWaPxO39SoJ2JiKC1XMDgLVVpQeFq8yPklU1EbiUg9/jewg1NFQEL4Xj3aUfcwA653ddQ5MHgugA9Yrm7KYVF9ndgpCXpmBtbBSSwgcG4AId7yPFMwcOaeLNykECvp5P2xXjeG7vu+dnZoAU2yFZvi8g4hZJUXO+sFtiu6B9qmjhg9K1H5jKaWNXUHC32ZEN9bnLMl/c5bvcSUvwieXYKzK9ypLWyMnVhXX9CUwSPcEoNI+1P+mAUgrH/alsq7wAcfbTt1qTDOBVKqfDQDF66n3x2XoXiFNME1dAH1S0I2UAqCmaNzKCA63q5agsWS2Y3rWdIiRxAWReqPPuFGB5FLRBpEAG0XCGG7IMAL0rtop6BxmG03ohYSgt2kqAzWK6TKAIpqtzuwppjMApW6jQQYdZgCLGXwZiUlZbKjneBGJhBQaiLtCstvDzQezN3j8juN/tvd8ZVS6jq/Qex1Gcha0WP9GA4mAtJhVsZ7wCN7cQ/3i/e/AbcYCpIA6gRDvUaVlUnwl6BfcKAxpaWB1I0/xJ/G9sTivio/0ikAV+21gUWL9q+v3JPW9sSo1VgqiG6MKaECsKsi6mMzCQID43sCzNj6kUhRNuRCSCyzON9KF9MZt0b0zU1kI6ZqWoeOWAXQCo0SQ7U4JvxVMNW40LIHp/cm1Uu761cCz3lrghpyCg0WC2iBsMVzKMBOIfpiBYwrIohKEtROW1yPeEIguHBVjS2Zser9R0mJAYDEwTamosQMh14Vn09jdawLofR+mmyN1d7ag1fR96j3Yyp1VeH/zxP7iltSDu6f76lt8qhqEu3rkrvCJK8yiVPGS0jevlDnoYzi7CDRSBYDiiQTP9fNdLVRevEyIDGpUsQs0bYU1kI3I2+Nsdiw2xW7oREGK6sj38uSHAYO1cXxpS3SCSpDlkE9Xwtcug9QvwXOh7wnkQx2Ky5+3f7EzMbmOSoghAUxs3OC6aL+VWA/vo5iYoThFm7ykl6ZkuE4N/4/INtUtRxRYPFdI4yje+7aCnjFNaSQ/CHWrYR7EucGlOpKlDGknSrasodUAurhPVtgfxwZffb7n0FiaAu2PpcsTdCYssqjep1jDVsswt0oZFAA6LQh+bXIPDFgNpIordG2HxXVUrtR+60bdNFHZlG5N3df4FO20oS6DdoUalm2nwu6+DgSjyBRfMvJeYSaffBKUmUBbDdp/1od7JYwxW5kqLyfcOX2hlN6AkTm5xrksD8oYnackdB3o4BNek+jLnPL2xbzzp86uOfBRfxIKuIHGyZwsT4Ze1dHAfpDdPn9pcufw/ASkVE97VojzkkSVQNSBhzMFvK68Q8XIq44jenIVg3aha0ZvFVOBUSWcitBeTPBYk3RtDhJASzmI3tmoZkIiWhEqWGg7ldp1HcIaMVfMBOnkftqWxUCY0dOLlF147EbRu4dtUwMHJUtRsO2gewKnQrNsSudLJaAFzpSoQztnUt4WVzJLHyiJnerkArE6T43wgP6wMZ5vZc2MU5Wdc3xyp9sARJ8j6LSqKHS9w0Np71IDMQNnN89ByeVGIE7MwOeOqe4EBDbIIupKqLuCJLGkiQKTBs+FtkaCWIDd9njjNsAz0QUD2AFxf3YXs7vxbjLsRnnir2WWS2yHanmndiiE8drSwnE+7Sdnpjwb2JFsIiMqqSsJrOiroOMgD0wNt7qTzeaxaMGRgTC7g4HdBPWV4ah673wJ+SFeWmUEqpG9K2tc7V9LyKCmFVU3sgjFkaA9UCmxVEwo0YWpkUF3v2gJgc5mcgPrCMpbswDKpBTYPLNb3ax+7odrRPdPNzZkxlcCSZAgj2IicIG73HjnCU1k1AXPQyyqTUkwttX7hoZssHd158aUgV/E01tXhJkh4EH7rMzOlAJoMXgykAEILF4kVyjVPX6gaECMKTGTUFbVdfXkZmdVdiKyKAOhswcox6tNZXAwMIBmFsKzgOwh1HZJruNI1/hOE21QO/Sz1YVYlUKT+Ck7XE5hmw4S99lGrrNta1wYK7zbvLdogxsOnkPqzjJxkLPUJm43N47CI/qMqTbYQNBApsaZAGuYpVERNR+e2QVjHAJ3vblstQlh5OR0fXMdC/zEGvYTybiD5AwFiTUhuWjKhIxFFYAW9Qb2UigtwH4vo8/30SwpY6C0PFJQYFVhryf5Wi7XAEp93QnWXMBSQaoul2HF5Y2zPW0hXMBaZSN3jlOYQfAavGBczu99f7SYD90clmE/lZHvK9NLgBtHXB+WS22f56g72ylUVzvWHUNoYlJBSQ8+CW5grbOzLG4T5V6B4ln6OYcBAAOoQrFDTVo1N5VdwuAyJSAjm4w5gwT4Wk/ur5HPojZlesmuqttirod2ubHnVF+17QLUrKYIeOmcCer22MMjuzOPvMoQw1I4sx0EVL9J8T0ng9gQtcrYhY7ApTM/3I5rEoEeB0+aHFW0Y7dxKEvnAgZg83MPI6/14LR0DkbDlsgarNbZMz9oo68xKj1yPuymCU3i8ziK7QVOihCqojOq4i6nKwgxxOIpEJoaobJSt29wTefG7pBGKBswlJzkCKgpowO4fa2Wxn1Hxgjk/k0KRnGnTnJqYisbDfJyDWIXiqXWSHheDXJKXc0AClwYeHlqhC7gd/YkmNb1sQ5efAgIoMOtbkLpbE0BDiYPBqs4zc+hEaciQZ5Q4IC5T2FShuQhFkOO3Zp3IG22GYLEpNAg59ICSPjsAOzdpA2R1u6YN6iG5/IzCgUmqt/Fm3xHU50I82pMbVSGQDfu46OYDKyMT4r5rrwLqbsKEvDHc7tK/VtjZhoAD8paKyqFd2odtkUOZ5pRhrYpSAUiYlqwwzR6+y2cAk2zbJqVHoLhQAW/4YPNrOhIIwmwCgGVMjIO8BNwKWD1BFI+EzmvuzfUU7bRh/utKzACUCODCetmE7cid4jZEbM0Nzj/a3HKzLDsYZKMxQEuujQqO4YiNiaHtLD9Md8vyoD8+DhmUh1974DlB/aGGTRmURagT0mmpNe+PM3b4TGa6P4IvPHs1YRy+frAsPQ6BqQIVuoWdsWf5YvT3U5LlavHkcgjSXWyhjPt1ZCNa3PDrOKL5SDmBTXxRlNn1hCmXoKp9rpt7eaZdsO3GtQTbrSOgkMjiVU6VbcH05pEZSnV9WMlKPpMzTnq4NsXW+/SZwt5KINTkBkASiqAabqGnrzT62xfcP/0n9Y/PUOznqmdWg2deWn3fSokbAKpohvkeRB9cEfnFDvTMx+VTVZWmjc+owCCZvKbeHjQSMrHxqMHY8RJAiU1wsTMR3fxZIMIVy04sdIy2/BnqaNMbdGq8LlaZLh8VqMIDITEAGk4tWhKx8k5UCEE2bUcX1guEagAanPrDkUFToangzUDLN1i8U6VsZPe2E4grghArIvqprM/xhaXYZhxp37xgSG65hwYd41LGr7AlXObbom/6SINsEx8JJYQ5DftREGKJ9TVP/emF7Av78oVUFlH9rD8Q7U/Vlh3OtWJLqPSNWbfeTvMFVLwUDYHZVHGPHzmzHOnKlBRXlVf3CXk2JRQMFljIVrJ7AZSEr2BUeTIyigjiPGJ2fYXDqg6U+ltyvEdYr7MRop/DjEeu95jMLq6wGfpkiHpd3RN3Ao43TMSk7D3jdIjMiSVrytQKMSZgure8P3g9g1XTOpp4ppDlVmWuoLGmhL7swNV6zeczmCMGrHOhE9xOxdyBQECJZNVdLuksOgkfG6YlDJ75H8SkkLVlEqsUqh36Kxq3AacHKciV9Dm4ymmXZpCXQAy+sD0MnCOQGUL6O1o+gpY8UGpEfDZEsX3saDuWONAe1FpI2MHkoJ3BaVpNDGzAlsIXajTPceqAgEfYY8YowpH2pO7xgalmxUGJRVvDjdTNw60nvPuBKuK0mUGS94gr+cTgEAAV4ptTa1i7KTuL15SBwA1+RA2olsbZFLjOuoCiZ8hOaK7sH52F1G/40NjlRFkA0VTM2J09eYxpqV/mP2JXS+WnmCzeenkcHX/JhSnirOBzsgclH1G0EGKWaTXP5vJKNOy+/KOCvX66tkHcOHCa5+jgmcIcCtYCQEZuaIMgACZXrGincWVoDkIMc4CIiTcR6UCVLHyOEQT5RFd4fRVqyOCkO7kRSsDrjf3FbBKLoViIMwooG4HP6xAz3GwoGmoeHBN4nCr+WnEWYMmlMSsSim2eBo1P8mOXq9H5hRy/wwgKFbE7isrGczgGag0qK2y8M5SULG8tARU8bNu5zJvdvXU2NqwXGl43+lZHyQPN17XgsbN6MjYRNlEPCykE4mdx04cDVJx65YYjGeGpAeh5CF8zAUyfUn1t8Ew9A2xO6q/gVJX41C1vgZSzK4q0DkbczCeJHCyzPamHqQP5t6nwYzdHpodFN0MIMlIkt5z9npgfiQ4vdxOjaY6eMwxpikEcK2dxetFhS4qoV6u8whsKi7XVr/MyAP1aO77kt64fsTNCPIrzIiLBt3ZgSwSBJcVjjvTFFZ/42dmVKvPcaT3hoWmBsc3N159xWIUlo3e/keJl+7kOqPiyQ6mokGJoLOVhdiUTg4Mdeqtc6kbtREVSH1XT2J25JsPt5NLEQBK+2R4W6qwO4lX6GsyoWRHdX2qAWsXd03Pxv50OTgTaS9PMRQZU7Q4ivPydzUy7vccvFc2xyyKZ/cmFZy0rdM0M8gTCQbe1L4h9uXti/GqaEhB/8Tz/5q5USuP+5f0iZ9vhKY0AM7/tBz/TuzemKCdvBSlKRw0t1goIjYEt1RVLvoLJZfPhYRBO7E3fhAF2t/eDiCRjQvKkDgK0JQyxafGlVVnAuPKeJt+TAyKGVvcgE6tUBW+jkR9ep4IYIme3BfD9YVc1LB3lDiYWva8GkWIudWSi65xUxCUuiB4+G3I11QXcpAXudewvKaabApiUeb6pZSJEAvUzcQMhF1ZB5YB20KHZ8Vc/oLJpLPv2Fg7HYFHACuAExmw540xsDiA8ogfYVMHhai2TZhe3R7xqzwITqxHuhAkZxdwUt3cJlWBQEkNm5NDra3iOzUALJu4JAYlDjDGTJgtCutzvY4cBgYEIbfLltQYUyrGrkxu9Fz+ngNVLU8gHcrGQ+zK9tMKPah/a5Cl6KOKszSTTUtuGETjOJz/W0aeSnoEt1l91rSQUbQ0jlwi6oTB+Oko+lApKkNAoJViX8UXGzNdLpU5DYIoBgQKiJw9bKfiwGffPH6jyt2hSBmSwwmx43ayxcCIhVn6ep2HvKC1MiXo43Il3+I2nobM6QkG0JWt8XkePnUvZhA6ozq0rQvsQ3Ogus7jOqwUxnrNgGPAWWjNJzMd3ruL43rxGLRiwJPNJRhork993wWFIYAl9zWnJWhi50TGZgCdkYtIA9px6xoCguAJsGPjNsAAJmwHXnuwogaWRD/pR839ymzK3W9asqP/BDU/C8GWSgAt801hgMRYwMt/6NJC96sLqJ8iEWnXQ7q+jcGO61UHYplKOOwiIZnWfrA1kbUtAkytIyjgjFIsOi/8WOqkQCHhLWQDaf5WYzdD1GUDwaXQ3q3GQQ0TfwwMQdj/1zI7VXY/16vrWJnVCN0V62i5kTIqnQywEXgy/Nb3Lmgta55OnQE0vsUTwSNdKllZSQMNVNMMl7pCACZd1wTR2RitT/R+OCvQa9W9dvGnFIlqKFaWhLud3qeAViGrymxcv9dj42w0NTYEAiWf3Zwk1892VFBWBWdQuiWMgmp7IrPX0w2jNcI2o12szo3cLUajxkNxx8L657ZiNljG+9AHWEeqQv8pVE8PsrAb4QyFuzmjTLFr6hKbZumOyq6gieojXUjPyYPkeKxqRAYEzCr3aUNp3T8JnWtLZpjKuR9oYGHS0ex2BZxCiqGXJJRGGVa82zhnyxzASGVGBMiw51UHoBcL/g/lYAhSWKZ9SQjOdHioa6+7g6rdDUQpjLK96R4ngDILdifRdk4oqd48ta2TGGnUVEXlTufZsXCgbQAg6mxY08K1Ekr3G92r8RHNXP/AJlR7qyH1/EMCw1AHB5Ncd2NUnXhg2eJUaMEKYtvUcKIns6dhRpSZSQmxLG2zmXbayVTDIu6C62BbQruEKYn113CBgVVibwDJ1WyIXSjx71Nvxdwn7+jSfhU+5jWg+ru6fRZYL6E05xv1uexGZt4ylnOVgZ1ZDLNH1q0YJ/VnTVmRIB5UVsHYIzRBHWyYcbRkV6sw7aNlBlmQzAQa95BGKO2k0PVCY0/XobPtiOtV6soE4Rb6DQ4wpQC9nT3sIKI9Co4t+T0hnaIG+dVubWZV4zoqaQb0KluVUQaTgSl0IbFxUrO0AWcM3AtaR45n6asbYQZRK1UzxdiJSZw6IPR7R1u1pdGVlSSMtlLX+enZimVY68ezmQ5SXWVcMU3B3GEoWDlgdeGUHUprSECdQSKkIkisszC6EDtn3fLrQLJI3gec5TJ4sfHqtsX8SFdZpyHswOgMvhp8BChlRZHdKED1ClIEWuFetoeGIEUqFNzlEQLmNqq3E5koUX5ZV6c8eobOsocKUvG2ADNNG0TGxXTBNsuP66fCrYU60VIVAF1zFZ6hI3se0UUPhVWQ64MiWafRGkdfnifoJn3NQ1WAc45aes6p8lGI1wBabYJRt0qSW+/xqUGmGWC6zpkGIBF0gtGIf1fY+Ouv4ortp0xX+fBsUu6cCijCSbu5S1S8Yy2k+vq2LbCDHnxbYo4zecKnpiDYnlrGeJxV+cnLKjeEshwMeETM7SwWGnFmVSJQszaWdC8rc9M3rhs2W056Ioj/2Ee3gVwfGgZ5BGB0EkBssHi9dBA1P0ABCmG/zAWv8V94NwdrI7nGYzCJynpNbxkTwk6oPvEF2AZ+PuXsaO3Cs1kzYgbWC8VvMuQvoda2LlAVzGWuTIhZR5KNEEciVwLoqgEN7h5sBm94oBmtsSHtRKtsnb2jgYcXqwEhlsTpEvqdbeJHtxn75Lr22j4hd1AqMHvH6jUD0xju58BycKtGFMf2aiLXaCgjXifVjWaKHg/K1H7hm9iQxLbHdpmTjiQVDS6a6HS85j7RLJ4yKm2jxOTPJlZFYKUgbzsxmB5XGYwZXlJjFFjWOh/qwEH5sM60vukIyMxmePCgZ7YMDyG43jVEqFhXBJfPSIN/ziEWgUQvCc6iBk++mL6y75BjWkFm42gddDJ7CWOETMJ1HEOk3VKNsChuFM3Dgl8o8WEew2CfLCKiOYG1UENcRUb+TKLxzgXZB4WoPRxkQAeBHZEtxYPqMikkCGJ/uo+V+ZRujFKqC2j5WlJHIZ0cKA2jGkTiymFOpwwMRPrq6pWCUmf4FDGYRfk6sjizGY5ir5LinQU8huDGCL4OcWDQ711Xhi/14E/uGasjxSJNLlRPZVtN4oO4keQTiiS1w05ShqTdFfLiY7FJFEvsTAxrOMgUAaj0qRFQQb9GQwtGQpcFdiMlxpWUyWj/uT/mRhjYWbq3+JmGMcZqppdMvh1Ivd/SAFMVxcmW6rBUr6APsbDsIfjMsX9fwhu32TG2b/ZM7Nt11tdPNrlWyrySzLQS07EuzOe6mbdQpx4L+8Ym4Bp0F2ptBQhmOx6rqWpesmE4DHBmbciw73SkKvZPlbKYS1Uq2HbOjJLrVjDMHvaeATo8XlCd+lIXKPtSH0VQrcdwOk5JbizJ0Tax9k7VnVx1w0M7dh7D8VK8zYl3Ioy0+oGwKn8CN5sxFGsGkx6m2rxASoqHBMLx8YUrTgbKlF58JOdBj9MvVGa8LbEvn3H2xQuZDeQgxkQYrPw3YlQ2WCXWPsIMJP1Xzz6Mv7cOw9AfJVzjQEVApvoPHcQcqPQ6Z1eRlaacdRiKIPZnpjFC3xf6QTW314RmsxeMIhEzSC4g7wTcBSlmFharL5AhzzINLCzvxnMw8Kkuoa0VNIXTJM0kEaLJiZsGZqr3KuQokPEhlzxKDX6053YUfqpU2lK3K7bjiCrD8k31HQD6nvbbosLoDIrgwgD9wBbmlMmr6Qjem1Z3X3xcAlNiW1Yl9YmH6B4E16Ya3nTSmW1pBjMrpi1S1/YTw4DeQ4F8YzXKJjHMHWjKgA0wqigd9BBo0hHfZZRdhsAckl6ppNTVs/YSa5robKD4tsQ8qdCNgBWnZAhdx7pqM2tCkwCJMRkpqnJwwBhbTlK8P6ydeaYbaQEzrC7KmgJ7gLucgxy1YtX1KyRYSt61tlDSVVokF9xPrVtfyL70PUVIvLEZZcjBpEGv6BF8DGokV4ZcrbkOJJwe0pnwYPlWCbPDS3+aKtoIBfn0wAZ3AbkOQu1jlyJOq3oQnUYFjd+YEZTGGLTm5mZCanqCP8cTy4qfYlID7DLxhNaipzcasPnyaFWCgEkyMCrTIakThASU6lWqG8jbonjqu+/uwEMhTzY40xi+0xmyhgbDPPB6MrYbrQKB6poea886qOkmw1HpmRUoE4XPCPLsKcUqXSGF3EPvOOHroADTtk+VVQ99UFDSfdYBhNwqHZnH3MU8IZQBR+uslZTUB+r+crzWGuRE0oBBmW6r5zAEYGbC2+MwONrRW/ACGS8sOVpifdw8mDjQoEN25P8YoIp917yMQRJVq7qsOuj4SFvipOfGIkuQoQR5MWVFFGpEvkCEplq5sMunCiGTLAdcmuIkUBJPDA0V17qJj+rcAw6AztiGK/SI1g4+/ayA5cLoAKB09p1hSM9efmUfPV/Af4hRhUx648IuPMVEcwG6enSYAqADuBoXwOfeDX/9MARnPYEd0issIdH34syrlBRcN7xRFzkGe4FkNCrbCoo2klKemVVL/I3tvEmsT3XBTj4WTitIWxgLpSCA5KRlKGB1PFo7wwmGTPrElFegkwqupwxaEhoXdd0YWdJXBmn/Q4MT6X1Tbzag4rgw2LFQPaISOHjqIn5PHRroj98VtoAJe8y3ZWe9WMBUHKBVp/V5I8zIWVUGLmVUSYD0biy2qi9f/GwsiRU49qQRTR09wAF2NA8OcrG+FEJ6hB95vBSJgohTv3q9x69kRGjoiudQBWZQd1XVW0KMC1Z23esjbm2jsFncUFEGxmRKowZBzJXdomGRMm8g57LKgBXATpslLCm/hpmvuaq2mD2u/fRnFAcncVXlOtHAajJwUlFjklQHAyko8fR8K0GNU3Xe8wZKcObU6fXEtMJRVqrY+lyrmyuM9wHAmfrMRoKuso5xu+k5mYAwEHEfjoFrvM51SgcB91oiM2syMYq3n/FNoaxnt08ZVjS42oYS+lTTHqrmtAMc/fMYkkqopL7hNou1I4NRiizEgachggVT5SV2mk14NC321Uqa4KIPq83sSNh63SgEI38nyBLyHT51JHdgVSV1sOsjm1S3rBMNgUVqXP15nQ6GClY7sc4+lU6GNe79YPA2n2hxJt+Vtd4YOspm9kSPhaqLrMUXDtu6vbAcKjKBTiQGfY2aer8YYJk7blbggJIDt9ytRSdOItXg8SsobVIzBx+vs/71jPW0RIba6Yub495UrgNsEG7BfkxYa1wur/w5smzJ5QpCKkQ4omsU+F2mvE9VOAswWUAAPyY1whNJWqabdjjW3XR+uLgvDlwGZDk+lXxaCV6SGUlovdVfEI7ca7XABxoG/3CdIPRlAwMdhfbTvVPvjMFY+wbVvODgNYZp6ygMvTa42oQmxuL0cAGTnVmgsSff5UFnF8lV0y2E9YGkKAW+VEhPzInOKHdrNVKNZ0jtEy2vfskunh7SqvXhsUKDyRA6s05iEDooQOGu5tiNj0Pq1rHb6weyctsL7ZSgSXeRAYDaFsYTVaQ+2IpvIJiVU7sR1B54m9kFNvcX7PJFRsZxr2YXA1Z8p5JwmgvTLx3zheUYjMQBnttjsVtQ+dQH2R4CABKTUx3ya5RhuOYF4VFZhpdkQHnACFUhfCml0O7/nprTvJrmRPDm+lg7Sm1FM+ua9AFCbiMo1uUTY9z88frEAYqrNuXOjrtTEXWTFqXDaIQ4ylm/jyzH8aLFQUrbkJDXDJ3qY3VRATKrYkUzlyj3ReuMsvVpoHrIHKii7gpEurqlMTxnr3aGnexciwkGmkZ3fm4+tptjTbzhHDUHpdAuB+p+1opoRjsf7hEGFepaT03R/1ISa4rRcZ21iM4fP9JnClQYCZQ7s3Qw56PhHdS8dq3sLHBLvetGQzrJ/cw6q+0TcolHrh8+MNuJqSDwr0lfqV+srDEmkBCfy8xGLK0k9OeeB+Oq3pa6ULIMR+qkKJhojYjEmBX93LpyYvJmndB2SKhIalxp+5lDPCyGKXfP8LDhPMJWGYjbJmbleyJxwBx1pFfREEhQAECkqzlMPTEqH9V8VlABjuIWlR4UUZao35LwQ/In/QvMyqWmYSsF1WGX00qd6wykTT0XUnBBjdNUmYRgeuooYoK+XU9kHybzIPZBCfXEYU9LIHkgeO4e72ASom6DsaxiyqnuriApWWJpY1ufaF2YVYaUBMSDHxjUwy6aoOB9cheCBksJdSD1rOpi0Rm6nderuhvUsC0ho1wA3vqFJn86o/AROC8GDjOxzDLcsq2v/WGlcat02B22VfIvzBUknea4fJSN20ioD81Wh9gwgTajibOp6DpamknDThOVG2HpgR8RM53mqJWpXUbdpsMWjBjcOczapI6tpQ9Xm1KXukOQxA3MLKcpCLWYQLzu6eQVeHY6J3zyLgvw2nm99Ugxcw87FPGDEUvRkdNX/vM+9V3HdY8dbRng3MlJcjqjZsqghqOKBDqpp/eyxfW9KoH/ICBwq3E6dSOhLmTVmLypHp9VGeIxBQ0g81o+Sdebq0dsa2LskwfMaOTtltt1BQGljqhR2L26Fs10WEwXA3jTvYWflUCG1x/y6TXtPyHQcgY6PMLRKTymArb2cSBctn2GWB31ZVt+F/c42D3UP01+WWY5BJgBoBgkE6hoX5sea9tRwuf4TKlrNGuBMV40wqRr7dNswXDMV2kvVwMs1AAfcLVjSjR2ftVpvqFdQiO0AhMiimtHa+PCKvrMk7XHW9AM277oaTkMeBoj04FO/JkQWGq4bmw3AFcHjQ2p2isD4el6bbaukQuDCxM5e+ZQAT6RpqPRa3TVO5Eedd2c3ns5WRG64hsNckxGWRx70r6fIK1IAMWwCmwtYmAVQhMl1k6ehICzSHYPeUaPuiIrr7vAfo+73DE9xNtW+1tBLRuTS87vVMAXuja4LYN0lC12QXcrQDaDkZpQ3s00X+exN1t7qr8oLS60JUzWfysD5pIa4SvxOa4j8TmR+eWXWPn6yQ7e4P5r7h8vMLuWuR3239r2KWqO0/Aczc52BQx5HsnfVvYTxMB+MI2ECFcRULF6SV8VL+4kEHKpSpSGk4nBdYw7p5f0KVFTm3evRdOygQLNV/XO5NQA3RyuS+1gt1YVzKChpI5G5/faKERK0fRkBPpMowN9DzJnk0xboNQXB9TtvQ79pV2qEfY1HwGmsN0x3WuHfdL1puCsDyXCig0qpdiGgzZbyrGTANjkMgYACRQkAAoyoGjPUzucURCzIJadSaE3RCcSEnsB21mtQyFORQmf9pfAKmo17UySgEOa8um3APWug/XxJM/oYsfj0NRrCZIbKRe892aqfW5TpI3ToAj6gKT43k6JShV6I7538qebARaAUg+0432dWQFKB0HfTFFb0ZXplcIiC00D90T4VcG1G5JkS6+M0UfDYrlUNRGThsGYUlC/EzY8dS91mhgpoOtKrtWMeyJFACq5s2mXx2EZTVwsq8Bqrk2J6qgXd0KiZCVmY+WcJacc0Q0kBuVr/FzuZtAiQV5u6EkezUoL1jNqBtU5pj2kl8BjKtqHySpG2076YP1kspIA1L6ObpC3cAfyc6hO/L2+9wngEY9B/5WCOQ2AvCh9uDAVShbA8g/hI00TKiRTAhL2EHSSI4AVyQWBvTddMfJKlaG6a5tpgZWVMTU+4c52rWDLihi8mEjZ2zA7BYN3x2UFrz6OTl48fLfrKHcrSd3MnHhXBW20WetrM29pf4WuG6g1KZpl4EJn2nhXBTdg10nORVNJUt3pBCJdHhNZZXzPW/V6YJ+uYbdcLVGNjZROGU9YgQ+vSycujbHgNruBEWzbtXVBacP17C7wCJ6STAv/NuIiUJgAurBdXJlZ9v45ZVYDyCsy7NowiRNfLcDSd03sJdKZQrL1PMeRZMwmSQlGKkoZIhSaCNrTIsCwNK40j6f6U8EhVcO5UMMIQWZtYqMYYerbMBiwDmRM4vqMLO8ad2+5DhbD0gcoV0Drsyv9DnEVXiDJUQ+XYhsM1hF5gBp3qbSnBt9MVMe01KoBPgMooVHB4SMMDsNbVU4zChF0PbhyVqClKmgMS1hh/Rah4Yi3IkmTQZafAygba8eiCBoI1htMupAy6FdOkl1myS00YxNNynQD9tOQvO4BfKSN2bSgFsHLA/DMLJ0VIdxPgESqK/mzKX6aTXXNtc9dMiT1EDpSHAaV8Az4pIrrQwIuBgqhJyfZsWtqwwEzZmISTpiG8EaPEhYw28ErOtAGFpXl07IqbqTnjsGf31wmpucGbjTIUFcGzrSYVaWL6z9tW1MQ4vupGu6gTCWwKKWp4X42FEsOErqPEhlVMIz+NIPjRlNdRuv4Dihz+EEIvjLP35NW5JGLH6izk+gpk1ytsgMmxUFHAVOUObQxkE5dS2Mm6ufrjI1TbM8Xg8XJFJw9gJ2GIO5yS5QlBaluMUDgLayoegmxIHHF6+i6ZnYOCP3WtJ0VNuheBqgxdtZqXxjdyUX2IDztwZXK4XrZZwZhaltQ2wAwUfJoyqL3qU1Z7gGkRkGixAu1H1NCswKVvadlbOxVxHK13sQgR/ImIxMto5hQaufy4Okuf/VwkmytzYnFZRnk3SX8kjLKsCT9BYBpR1WPM3oUU1CDH+HsxoSK0M+JZgcKr84hUXQrrManpMBjX/oADalrxEug2e2sJTbj0dXfuwFUhqn7IefLfUiug6c/aDA9TOMrckC3cknKoi6Yle3swCQTNMRlTsjrnR4YrQNfPqxEauV0eZBKSmgldDiGSyhPiqrDYGPxKcTrDCQIKFByZj7ie+9aCg2MxZPIEc3LiRIby89gZtckc3LWv+Oh9b0xWXijBBiJWbLOiw+wBJJBl1me9owS9Mj9Lz//zxhV72sAVa/MtuhhxuAIQEMcOsijytWYXXyFgVFIDnkAIhzgXRu4z5Shx2dE5Y3hN/1Adyj7Iv4xHaXV4irllFaSwXE1CmAJp36BKhF3vFPKdgRQX19POA4+FQToiV2B4kUQ6LbI7KZQGNxG1gGTKnCJG4jQBQOTAnRjPUnScHAT3/65uhC260RKsTf+GfKjami9RCUzl0ytqRmpYoxEFSX0FYlN+0HLZCDWuvFuBrwwWa+x06P5+woIXa2nZeGzcdoA6Lo0xhbFNLMFNWYHcRDRnD1/BuunAUt6+eqKGOBH4bLpPRstDSCcUDUWr2kHtXFupMto+poEOqeF+GHWncZDoRI4TaV5fEg6je64ljCUmfRGryY2LukBzVjLsh/pC/3gYvGlgJGBj1JUAHUDP/ONuQbBx2cmA5tS5ctN4bgx1h1x6pc34tNRismusMVmey2hKl41jgcIK3AFUm1M1YKO1YWXtpThqDHA//oMiIKV1hFAp3lfVW3q/vKF0RP+eNX1DsNsokUB9WShOvp3Ugz88rmNYUQzqXGOUQUB6pvAjMQVUELdhgs6Ky9OEljqBWJyrAGKcH1c+ZkV+iREZh+IDEhLoJgX51l14FURfI8OUhHoRp9D/+XXAEzF+tjrReERY9lsBKwvzML04dGl0089YGDVl+LBdbUzdQWl1isaGD06KhwzSRW6tkD0Jt78jcCDbSwz7fg9t10Hf65PC1bsBoYCWThj9A016J53TCzw0aDke1Knh9hDUoaYJ0P5Xo0rG9e++ZjrNJEXLxPHgBmmHuNOY495hpYKqY0RWuelC6l9n3P114XqZl1twc5iJzLbHvCkA8NhAppmWkhunM9VQmd6v/k2HwrI3GJWRjsrD+yadGTcxG6JaSowhWskKaJEpQyHJYwor8rcZx6HD5xQaK4Y6bmua1xkGK5PlCxavK+6oE/Dh852H0mKm9668TvYxHSLxDiCXgj1BfMlfkixZjebJlQWNe9LZVU+I9isJClkT2OsZwEpse2ZobrKTE3StaRXoD6hUUeMZpq4vK6F9dllkKNlwQPMVZdQfPMaYlhSDbLwmZhimdFFlwakk3055iLiHc8jdXRbvNIxB1WoaQ5a+gT+x4WpnjmOe2cyQLtvTiVZjo67Hh25Jw4AtYa2lGcouFQv2GQmXpdOCWKhTqR1b/wM33JZ3VWqPPcsid6SNIjxaE6YP4NERe6lGby4ezUwFhpkil9jsQiSZ2BmEEpizLNVCk7iI66+JwS2nRmIdTOLsH2yuA5qtMn3aBhmcsmDizYyWLic3ECtGO2bcC0Xyf5NCUYZr9A0hQGg5sVnAvUqH469E1mvvW7EjMj+2IqsmpnUBPnEPs4kLvZ5/F41klvZcBKQTYQv64BV2rLja6js1KlfNXaalbDxREcrcb7h94Qrg6LZzIJE3OXAnB6WqpWPA0UeNsSMyCWe0ijqTx3d7oFkv1nqwq2O7g/7zmsFqdNtyw44oxmAgzOTqxuh7VaFN6aafNrC9aT2ks9tgFMLyvlB1W9IrMAR1ALadaE5u176viuudIFt6bPoOx1wHMypGcTSTEeSgrrLzkMWXU0M1/cdI+CyPtKGwJWCQZwqZakEySzi012HRON4Jf2tg3tkJ5oYDaOZLc9wBqqsqgDDAScarzKdS6BAesLJuxKub23SGFhp2R0rYWS1POgX2tgg3RYvT6w1sqrc/lCL78Go8ivs1tDURqQCmA63faOAId+DPmupGg9Rg+V+bjs11sMaGEYwoZHNaUBMBlRBOqioQWeXrCNpjbkiCOXFz/w8c2TJKHzdocdbwMZtcZLkk8PsjsBO2+gGW9DmOhmkVkCJ7R0MMacfAL41TcuglIX6DJwNYtSYADjMDKmcQuUPKuXuchMvI8PRfzkXyjSO4xb01iZBiEmCRc3uK3Wr15HYdWIjDJIhbWfsJer+1ThVdQF1ztsqU5SrZNAiNi0lhHbCcWqaqJxcvXCaEzPOnFslmqNWrJwxVoUF3wX7cS8xtDLUq4x/J7ksKmHqlKWFvjgLR1vHJIeTR1OdMVKlswwqpvpGKeJjeTmKo3F0pQL/Mi0bF6xO7w+6xfEpoLOcM+pwbq8ykaKb9bnJFUMRASNxkBgBppbXMUNlRhXSJJzRanuEthe2dgVuMELZSVT5ePrIxGLMxuNanAkvI8pIkGFiiMiet4aJYEizr4ExCMLJNMEFLKFMm0UFGSmlG2T5RD0kRsI6EC5MrwBabdY6P5Axu2ewSmyK15u2cuc+S24zNDZIjF/aei6qn3sc9e7EjJHe+3fkPlMbVXYNg1pQjaBCqU9DUjIraymYOhKOcDvAGEDGfKWMPLIKf+YFzByXiQjVNIppY95jvmE92hB+Sy5gEAL95dva0bFoiCuARiEpDnhS5cLPTLKwdlPahLI8X3nv8SgFbAXFPPpZ3RMziArmI6f+6AmfBE4yFjiPKRxBYZipxGBny1TYJaKxaazOsOeOsyqRyCL9njJaln4ZZq1Z/fheVlDuwwQW8avG9wGs//hnD63Mq9vX9w5Yg01Fdp9dP62rDygl6CtPoBjstmTKn5FYYh4sBFoed5SvjTVwIx0Jr2zaKfpxt2CP39iW7LpUT82JoKBFU3CFoHBs1A2JiOLsqmEkGE495F0LjBCrW9XwxCx6sgCQSyGxib52q7pjKcbjJx8nX7WgBgHjiJ3bwXG8aBeuVGF0UAMiBlrnJ333TgUmrh8bvCopfJ2g3ctKQe5xzNYXmghJMzr2jORCqlkxsFPCbegZTgNYBAACMDvkJMbhMAv4DCBMXBhLIm1cNH5YS+Bp9Ob+0x/T5xL1JWhrZo7FDdQ0ltjUkAyqgXXv/3GK4X81fjTIidMsql5rSCTIpYy6WmaPPAAm8JK2Cv7fbIKQFqCgNtyKqaSy3+4rXx9Ofg7bINf4VUT8OMLlIDUrY1Do3ACB02IkSOKoupUnbtFWgL7rgE53e9B7tKhB8dVN7eqTBJFdmKCDCWsaAwEVhW24ulYXMiaexHCJVfZGYKDgz0tmtAyL+XQxpUDbxrIH9Fm5DRykroAklLA6Vo66CLWurqy1TxPb83o7dNpp1pzDVvszr8HTenVh2VYcWVuAJXOS6CqGiAXVU8J3Cmxx1A/veWxqxszW9xmAyoPo8x7kCg46ZkVmdpbA19w9TQuhlA5eVB8mPFLbbVwnbbL97E32YmsrDfhHD42hQiEYc8j8+f7fxp6olFGelcIh+enT+DEWZeuCg98crZPBitUl8rLUtwZgbYUHeVUBEymJ/M871T8KIH3tlqHmMa/IWcagXb1xrOxGZv7Azy+srMwkCNTV+AoZWdwXLCX/ESCM7YTARo0ALDClL/Zk7R5/Nu+SqWyx2SBRCLzIpfTcx0LjBue7xfif36euZ5vTFAcUb2sXmGEeSLMSkzzTiSfOBBHqll9aP9U1a08xqYTnhb+kL+ra2YLl4gmgpeSUBRp7qf+ZJRq48zY/iWVb1W1AaZ3AYCs08DQ7tZIu8jURRVUi/rlUPdMda1VPhmIZBxxbGLTG6zvOwfTbqX8x0EtvO9FWpsuUXWwUk9Q3PM5Y2bjC5BrlGIOxPHA6g0NXDEwO1/GBnGwgnr3NAsgLkNjV9EbYcpu065kCYDsSuBsZXW12P+O0PNeLy4uLlbWkONx77KPE6ypChdkes0yBLURPQKh9VjgdIOhqrLcxMURjirJ20NX8NWO7YWAhQ7F2MItEKLWwvlCfjW13bPxPkbug7bvQv8V1OGBiCbqtUKGuoC5aph2svWbMBvn5Nptb+5GWKQ0yIqbqzbTGxWU8XrfWA6jlsf0wcNH3o7Op2VuqjW4DBJlhxZqFz0JEqOmtWOaUZ/7yaa6R5nOjVClUAEoz/bfMnnLlx8eCEd+eopmDEXjWejtjpMCkWfXFs9chZKTay7WmxpQkVIz97hB0t+8lxOPcdSEtCq2UUFe6JXRcpNGueDG+pEuEYOgQ3B5yRWPqxtBG3W21UajkRowqWqi/t1ldF4Cez6yh1j/vCxb/RbphQeDQGbFOWU/bZFKXCc+MhV5WQHJaFxmoVoaN39b7+X5VYZM9zirX8sdAkpmlMmCVV82FcoadQaM0HlxgVqTzXZVlmLSpv5fkhnEdmW3HREhaahNWoiwoY+T3srA/eYD2509D8p0JsBY2IgRJSB/cLkV6VpXS9pDzAHU6SyjLe8OQBAowHL+2UVIkzngJ1SvkOmnZLiXhZyiAsQyTXvMe5Lw9dDCaGn8oNEL6lcWVlAzEp/LJ4IUyj0pms8QWlF3pSMUDCbcRbpTKlrVOzl4DbXXDZWDle21nCZdLfmbcRtoNhpldnLGMa0tda1x5Gb+sXeyWcldbuyWwKye9xEb4sdnKSHYGVND91Uv4Lh+e4PYDczl9cIvLYPRvTJStZWSGQw8IBl6fYfl1BFLWbhJDBDlvYwAPyhjIWfl6X+tLkRDzoMP2roMYMW+9lL+fMvkyiaY4VZOYWf92klWq/jfN8Rb+KplvrJyYoOzxpcNwYKoS5p7csGFhswmcaXXoCHfFArCICkfM6AEJ8QZdBOaDvrOgKMy2x/hpTQpI+E7rTnUOncml6aAhdg2fiC2pQ53oePpEKLeostAuGfoc/ly4reOjZzBKkjfLio0wbrGDuBVMUGUHnvb5GV3iKCv5nmQ0ypTu/koBp+IuoG2uVxlWv4CVGtCOHlBBM4EqJw6so9UFBYq7MiJuMwEXC2Fs15RmlpcYaYhPlejltHP//rlQuRnV7JmqO2T/jjrDl1NFkrjPDgOOZm/T6CXxHDmb/dCGhYDb8J0H2ilgS2gesDalEnh+jhumG2xXDT/m/uTZykjF8xOHypeUt2My4PJoaYuzPuZPaaSma5vRVOuRs+05blK/96O/4iSHK3wh8OGHc/wncMc0rsRrTY6LRkVWqrCLKIGU7npBStnMdnJfaB+P9ANPKNgruOOkn9kzEJ14oPYWKyKCX0yNHwVGPYWJmVV7PcIgXwicGYA4+TOcDyDU5gAyCQ7E+zWGHMR1nndlSHYcCEKyrTw4FHjumJZSsKDxC14Ni0V7u+mSXePKNs2Di4lYPFZiDFqFaIrFd437sKob7UgQ+EdqDD1j4HLQDQSbDcO62sEk7FiuYGHFwktX1XubrU6UfR3aUvz3WGCdJEBUUq1WTgS0OmtiZ61yx0ojrGRxZIzzWbpMQ8vImXVpVNXb+gWjtU3EZIF5wD6zNjdKj7mF7WAy8DEwjvXPCFNiw2myzolNcNuTuqVnJV+BR3r7lTfVQ82xyrEkQ9jIUuBM3QccnsBiNuVyYpvgLQHCEpaU1Gz6xFURknsCIqmdJvU5Ga55UxjWJGNNLD4e2AgfGuDPTCrUuwQdEOrxkNbQGLrlFThau3FEVlBCt+p/BLklzLoADoImI6L9rRiGOuKVLvAOHeiA1rDPz0DDh+961ucQv2A6GxigKa+XF5QuU2wdskocYU22EtWBuV6ThiEI9NwTCXlXglgsw6rn8iCAroN4CQo9RtUz8VZ90uBtvoHrr/G+DtxWKtsk74inck6Hu4VYi+tDZD2jsg7uvas1F877VunOsawjdE54WBs35kgy49XVEAxQXEepbomz7eLxvSJ1sNCKlbYvGBBMMF6eWSOxOM6/YkCQUK6YRDNIBlmO9CbVKNRVBI7uAay4jxhJJfSLFjdlA+IdBXj0Y5bI2/62+9xEphUdycVxghAHytoFGkHTLFycFSMBFQn3e8ldGC3iVRoPS2BlR48RbBYXtFjci56WqHEEepaxhMuNsVAf8ARCZ/ydqDuVw88d9K6Y8rmbwCOlg5jnpI24tMYK83o7bp+DrgNUZFUGvqHvOSGSVUXo2XHtPxsXs7+hnEK6VJLqtQjLfWapFiymWp6xKjCARQsQLocSPgMA1j+2hxcdRRaAlAa+sapzefp7WK5EbC6rZf4upyz45FmFPJUB6ULcZSG640EmzL4FDDc0oHthmtbCpIZrPZVUOEIdkmEIF1GMvWRk42sEFMQWMvQRhdHofO4MqUd/+cjZh1F7uJ6OB7MGFGMWw/Kj3qaNYYmdzFKGo5QLsRlrWx2JQ2xMBFIXRwf/P0khgArXOXRFie2B770OFHovtFuq1CaSwZqx+6DScZ11ZFVApq+1zLgLCzMUBpHYFo2b2ZH0rJCZbbJlsPyttT4QsDGM5lvl6ts3xPaDfqfBc3xqy8rXyb6eYlV9rWNkPKTXxnb9udyvbOhxlp2YL8wEybw8hYi1x5NKaQBsBh0fUEB9YANw0CkeHmAgZIOabqfU8BAmFFGn7HtlT0FACGy9dUr9NUV+LZwxEaZgRI/LyG0tYR5AgLdcGRnviNYxC3Ew0HyfahQ2K8jgM7Aiq4NQAqQeGUzCsyxqZpI20npjOZPfv1fQgudDmTvYCtwf4TOTPkslntFMrMNZSpxNjT0jofN5OOR7mwXuBV5RbiMNMIWOJ+tAskoAqwbnf32f16FdRPfznv0jeqAjfG6pARgpEK8gCMu6Wo+iZRmN3jqLUkMtVXZ+4jLJtxbW6UJ4kmVg40CIIQk1wgB9JBUiOFmZCZHA1L205zNi0cG+vnYzsn1+4KIcSt4BOAsvQIyUoP85dDDWF00/i8ufMYEAy0c9XpqR96fhLWeGqXCMvFQYlKOh95QRpUmMwfrSGuMVHphGPVFngVs1KBTtnUqa2zoF3QBaEuRkoGo0Ng3KXEfv3wpgdH3XPI9sShkbBcYt61tU6cXKMeNQ2KuGEd0ShcTkglaGGEDKENQVsQC2eV3oIzMqUiAzvmJHidkCZqL21vcjo5SJMJKtoEXerrzuzs0t4J+k8hNO+6s0740TK1iZKzjC7hKLYWbK5CLoO4OZ3sODm8QplHYJTwtcWX6ZlcRYEA2WWPTKYfZcYGnvJxtwOkJsNw0uQT59fsDYk4fha8rjviyu4sKXOUJSQhxn8HElGlRY1OzVLoUPilAG4lLwxD7xJ0qBHlnTdBBqwJPa5Psj9OFKPW2Hv9GMertWg/Z+RE4tW9cjKrvj+upTk8YhKrDW0sc9ysWBs84wu8f7opObwKatZceUOh/RVQEsBqf1JfeB5ekGSW2TlCskizbZyx8c8OxjGTcfjm2xwZubQkDR1j0BEgnEu9EZiBlpAKtovMYYkhtD6mrA08Un0cBLCaMjOTDWTm2suzPNAB7kpAM+6YzrL4KtRBKSa0CKQ08aY2O58bajRJb/iP5Yn1q/tatE4hIrSxwdm+rmAlwqXk9G0FQR+AyRflWoMpFZqTA7iPT+e6Dcfl1nBseOZaY67TTqMDIL/BQddd0iRQmuXAVS3eVR6Za5njRShXP1AlCNJOdZIDYZtwzBWAdNSntYsKuA91VWNop3UMLsEDCtAFi8VzryCflAjXC/xM85pyhktAd3M8X+ki7rM3mmzC8pnlrh/LmRg6g7WHywal6jthZNK6QtKNMoXASDTL2zDs5aHAM4RmoiynatvSZYX7dKdypjDScs6bNGQDOw4npR3FVj5D5q3/AIAopEX3V9b57JHcmUizY/8IPUukUvt3+u6jR+lTpCgUEYpKzaiKfEqsLHoOIgcGmzqK2R9b8CaJQrCp5YR4BK7wE3/lgHFqLK3SFR2QWxxCQHA90AaIOC+ZUMuoh/w5PRBBYFoDrEZEFBHH3FBguKU3AsjXpPZ3ILeMkSAQLIkgKNd90M7CWteOWZSwfscZXT0rWaAkSDb9wYiS6HuWOup4sUfenASUxXD2J74zX0s11rVTSQpLOIYNW7yS5crjSIRBmCkDHXnLNAImiQt1gTEI54g+uqhHtdHIM+Zhnw9XSD2oMyraLPXiy/oamCUKEgdUTk0HKYUalaSaz3GEB5jifLT9ry08sYFoNATApt1cQyc2m8szmpMBuhEFEAWrTMwpDQCVobXm7jiYcBqTG4ZPowPTxDj5aCvudzCQPLYyWMqq3t14mCANi8tKLA9tryRhO4MJDS71maYjWqe8xHbt50tLkKiIoSHkOG5O4AVbwMJXd1BjXOXKkOkMtYCKS4HqMaMqLY3HwGwXQd4Qh/E3onNLYULO07hkMPfBQrh+/H8qH7sPGd38fmpefQ726h7G6aZzAWGzEmxW6gMXv4QJsdEPurMib9ZAPOgBwMWRaUCQdD1cfw20j4ZqR+7ALmZze3kVuc+Do1QvVfDULiwGzskBecc1sjyGt6ROtauuyyuzqNVctpml6RsRGU9UrIAPiJHuNqJJSew4DZ2YUdvN87Y1ocVE6+NqG8j5RRMUp4x93TGVjmzpUQ/fRn2N3BZVPWlcGfnmfYUYwR+W/jANB0QaDqgCQhx6l21gBncfmZYesbAXg6nI2kMxe5uIuYNWNklzdpBWtycNlFdzDqTX4VdNMV7DvzA+iW1rB3400ceeQzOPTgx7B76y3ceu0r2L15Af3OpithZSMje/B5ztGCp42zBXqfQCJONKRJotjtdv9Y+SFjXiVZ0oMWgaNixbg37jeVt/N9AoNshqIyEBtlpK+39PHCQuXxTqmEh8jj97QHEE5B5sbqt6WRK0CGB/s9X+Wg5Puz62+drWhvZj7IrbKZp/Bs3eMpOnJ2c2knxG24KSZHhlNrexB24p1+3QjYjlBpEHAZiKSRMIBejqw0HaYMLnYDrxEMeq2uQOgOLzAEj1VLaBYpFkiB/9DGsVEWTR1JHCn1yVkpa6lAyNMqsZBEWCfL+zHbvIpbbzwJ6SZYP/4obp39KlaPPIhj7/8l7Fw7i42nP4d+vtuM6sX+xSF9MVscn5ryHSji/XGWz/k9L33Lom5PnE7MKImjqS/bkilCmucMXkMqO9dHq87glNijVSk1Jth2ArZCtHZkUxc4gfKXuYRd+iHTQna1tChvoNh0s5t1bF0ELZ+zM8POQcsEVo1bQbM7efbMOJjAsxtIYayghqQVr6UCV+oBkRgL8liIWMdKqlOUAmDgiOQyagdbdXQmb0Sx6Hp+FwYNZWrWBO2kyrxYqNyORnPq94V/55hB1OKYUxQZkgExVF9aplybPlIHrW4dlErB2j0P4dhjP4ud62dx+9w3IJNl7Fx9BXu3LmHr4vPYvPgcjj72szj00I/ixit/hrK3baXxMK3nCehM9KA4DqScetQREKiuWnIuN6X0BMJuUbr0Jgwc9lv0BsKgUPU+aCT3HY+zY2DSShl8VaAbCdSdEcroNWFANX0cVdhxVWbSFhhpvHY6WlnEgKCEAkv7BHULhI2QKxA5Qg56x4cr46rBdutQv6gkQWn9mg3w8/Q8P49HMBtjmXFpu3yUGMrnJTzKauL74B4Zq6NZu9SZQc7kZyuYN0tigmJExeGyY75SCffGZ1SxjGRrW4kKcJxtbUyneKfQ0q1WOfOWKBKsQarM82g7OvMIoJss49ADH8N89zb2bl+CdBOUvW3s7m1BZAKgYGfjVVx7/l/jng/+TezePI87558GwlTEICjpplg/+QjWjr8b3fIa+u3buH3uKexcO9d6F7WjdHlNZs3a7uWj92Fp3zFsv/UC+r0dv5jdJ2qgMnz9wIeTBObDsl/EtpKjw10fZj2rbTXJnWOz0mP4k/WgXkdcMuhkZnBF+z49r4w+UnxgSBu0IGksuAo8MA/AIuG9XVfEFnEOCZX6r/P3iJ876F/NZCdzDjN2Yv9zDtYs2AntoVu9HUVie2muXoFTJdgp7ZcuPN+GzdBNUsU7NtkLui52LDdVZYaRfmHIs1E7aDwsT6rtUpV9EEgzwgNjh19ETRK6P3yORcdSSlkgk3YwjL0Zh+H1E4+iW1rFnfNPYb5zc2A0AkxWDuDgOz+OyfI6RDrsbLyGzTefwuqxd0O6JXIDvVGH3vU4jv/AX8dscwM7V1/DgQc+hMMPfxJsPoJWu4TqzsxYug6Hvu8zOP6pf4ilw6fhrnxuTWReHf1zEEfUyfA/JQkL5MTSzcBFbaADeBbInvpSdTPpH4lzXBeol5u5pbf1KiNLc6iQwgKrLYzfsZKNUFT7flEQ3w3FWK3RjMgEqKmBAgcUou9aBzf1EDGdwJDER6BhQJe4zccI1/Y0AY+hRbtmYs5MrB1HmkRIq6y6KAj7H43OFrHC5FmuwAiSSiUGF2s2znqCSKwLuO9HQg0yVm5R0ZGM3K0u4XPB8oGTOPTA47jx2hPYfOvbkG5SO2+OpbXDWD/5GDbPfwvAsA5w861ncc8HP4ulc9/E9sZrMCguBZOV/Tjy8I9i59o53Hzpz9H3c5TZHtaOvxvSCTAHCiXEuBeAoOslgdad176B2Y0LmN2+Sm6y9mgheYirj8oiMx4q11337EeR8tqlsawR/yi4xkJI0uzzlZb12LCZPB4E2Yy/ItNe9GoLmY65CRwHUoVBNmy7MjddIhEqpJDWGC07gl2k/h54HcMKhHVRsJqU0g3KVdJNgAczg1FHdxVUjy7FtuJoKgQevYNLKSxC2zPb5FlyINE54r/Lq4l9DY1vlUAQJjLCkwlVI5a3caXMAPN8dHswRqlxpqolPAKPZLX77hegPifGqd1QgG5pDYcf/nHs3rmErcvPAyjYd/p9WDv2MHY2XsXaPQ9jvn0d/d6mlb175ypmWzdsQOUqdN0U3dIKlg+exHTfUezdvoLNC89i9/o5oBR002VMVg+g39tGhw6TlX2Ybd7wlAmZYrK8jjLbxWRpFShAv30LOxdfwN7G6yi724NMJhNMlteB2Q666Sq65XX0d66hzHZcDtMlTPYdhUiH+eYNoB+AsuxtAQAm+49AltfQ376GsrMFQQdMppDVVZTdHXRrB9DvbKHfvkPami1hfCAKerloIqfeLA2YOJFpNn1EHK7VfpsYWX6NBLqmo+iu1Vf2ULICR8bABF5zhBwU+JramuJ5zZJqpiMOg1CiKySeYpSIWZEWVBrBRgma24W8JjIyS2nqSqxF4zcFGOZv9REut9jhZdj+Fu0WPQ6YY8NTpP/1wjDCc3jfs6Jrc3M8K8uDlUa47hzvoqPLLIF2bPM8GBtXcBuelPPS6s8aRyGtkly9qoul9Dhw5gewcuAU7lx8Ft10FTJdxb5T3w8Rwdrxh7F28n24/Ff/D/r5DMCwA0e/t4N+to2lA6ewdfW1UOH5zh3cOf9tHHnsJ3Hq8b+Ha89+AVsXX8DOjQuYrh7Ekff+NPbf9wPYeut5dNMVrJ54CLsbb+DKN34L/e4Wjrzvp7F24mFsnX8Wa/d9APM7V3Hj21/EgUc/henaYVx54tdQ5js4/P6fxsrJR7B78UVM9h/D8rEHsfPmt3Hz6/8C/c4mpvuOYv/3/zS65XXIdBnd6gH0u5vYef0pbH33K1h794ewfPIRyPIaAOD2Vz83zIp+8Kcx2XcEuxdewtqjH8fWS1/Hrb/4bZTeZ5xaslPCu+D6AbDseLNZ0s+G/dGgv4BVxYH0LtSLtLQNeFUSEZHXPdewxxR9PxgA51fF5pJXHuA5TOEH/0J/X+BIW1m1XpA6AkhlvC3sZcoZjJFiQ4FVNXEohN0Thus4/iMj/1pZ2TeFYl6NrBZ1MZrSQm+RyEy/ckBev5fUN9QXYZO9YlL2gkN3UmLgSJ3aejOgIvRx5rcBrLggcjtnOzdR+hmW1u/Bgfs/jAMPfBRlto3rL3wR6Ka4+eqXsXXpRdD+HSilR9/P0S3vj3UToPR72Hj2D7Dx7d/H6tEHcOZT/xVOfORvY+XQafS7m9i7eRHLB0+hzHdx7dkv4vp3/hDr930Ah7/vJ1Fmu5hv3cDqyUeweupR7Fx8ATtXXsfs9lWgn2P56P3oJhOU3U30e9tYOfEQAODWN38P269/E+sPPY6lo/cDAux7309g5b734/ZTf4Db3/p9TA+fgUyWsHP2aazc+xjW3/tj2Hrhz3H7yd/F0vEHsf6+H8N86yYAwfI7PoDp0Xux/fpTmF07H9ZAfm94uNurjLxrNXSQpQQbGn2wu2Zv65W9qzBL2NFvBgGNy5h1zhlUJJBMeeoz1PiF1kzZjXnJyMj0x9tqGhmH0VPzz2z/cX1sXr7i4ie3L7U3xp7Yars62+HDkSQZMkDGEUvrF9vUrPG0/bfiVQ3Lsox86hUNT4wqjKdojOz4nOqAkS9aJR2ImgcAdSM7BSReTTJcwA8qo29FBFuXnsN0ZT8OP/QTWD36Tsy3b+LmK3+CQ498BvPtm7jx8p+gL/PAYAUA+jlmty+NpOgIZpvXcfVb/xK3z/4Vjjz2kzj08KcwWd6HC3/+v2P3+nnM9zaxdfkVbF99HXu3rmD/Az+E1ePvBroOOxtn0e9t4fYrX8WtF/4UIhOUfoa96xdQ7nv/0ITZDmbXL6DfvYPtc89g7/Ir2Fk/jH2PfhLdyj7IZBnLJx5Cv3Mb89tXAQjmt6+izPZQdrew+tBHMNl/D1be9aHBo5jtAJMl9DtbmF2/iLKziTtP/RF2zn8XEF0254znbeKD9VuIhY54L2GZTwmXNzrSqM/brYy0107zEzJMjL03g5Z4XxwKgZDpnIBr+DYq8AJ1bZwY/vZuYD12rdlViJNo58bWdmxZ3FGebBWXtASQjGIIgFycebjbFD35sM6R/N1IrZk6p5y2Me1xlCbSlOIU9n5sVyTqq6TEScetdfx8rmsG48atJN1hYNdY1+1zT2L32lmsHHkAALDv3h/EbOs6rr/wRfR728wPhyd2U0xXD2K6diix+ILpvqOYrBzAzsbr2L78Ei7evDikOZx+L5YPnjKhiciwRXc/Q799G91kCZrXVvoZ5ls3qnD7oGs2gx6WU5FcRID5HmbXzmH1wQ9h+eRDKLNddKv7sP3K14Cuw/TgCcxuXsLO2WdQ9rax+cIT6DdvDG6fCPq9Lcy3bsYTn7QfTK1b9AqDVzI6SUbX9tFIOEO/HhkQwcNH3hn2ri8fzLsgVXNmyOXJLgerWaiYV9njUwxmUWbWUaaSI/NJVDZP4zZ+DqFdbEFMqWAnJbptEu6T9DkKvT6zqMvcOj4ag4ugwsrqbxrXTb9j2XLdBalOfrM/vynUS06jYe5C6zFBe28us1BTxl5l/O67uyDUtY0ekDz6Hru3zuPma38+PKqf4/oLX0C/u1ljmj1K6QeFKz266TIAYPf6Oaj7Msi5YPngKRx57DPopmsABP32TWxffRWln1XwqbUuBaXv0U1XMFk/hK2L30XZ207LadLsXRWEsBWXCga8l3k/w53v/BvM72xg/wf/GtYe/RHcee5Pcef5L6PM5+h37mCyfgjzW1ewc/4FzK5dQJnNhnZqr40cFGIOxiJMyCAV+qjtLf7G3WoHiLd1Ylp4brnrZYF0iGBqCYFoR0g/cklnbzLXad97HNpNQvL1d1mMGkypWYDII7NQbJh2MU3btgDx9BlnWvWaAvBp0tpyyflMqmB52QQrRe754Op6Hb0m7XcyMvIwrHJPxe2dY3+MzcIaKw5B7sx0nIJGfbg70Ni11O6scJpgmqdcdFjmxENviQq7jFRmitWj78D++z6E7SsvYWnfcWD/yeZMg1J6LO8/iW5lP2S6DOmmKP3cpNrvbmLt+CM4/PAncfPVr6Jb2Ye1Ew/jzrlvYu/mW1g5ct/AuM68F/PNG1g79Sjm2zdx67t/hm66hKVDp9AtrWPp0KlhtnBvC5PVfVg6eALd8jqm+4+j37yB6cGT6KarmOw7DFlaxmT/UcjSCib7j6FbXsPqfe+DdBPcfu6PMbt2Af3mTZS9HZT5DFsvfw2HPvmf49CP/QPsvPZNdGsHsXPhJWy/8W1M9h1Ft7IP06NnsHdrA5jthj7Pg8wic7vba3SIVAMsWVPKIniIBdzlmbLg8zSX0KquGmQEHKZ3ccM9d/VcXiOzSaThmYkFYcDN001cNZEz04leh8x6jzNFV00NQaC7OXjOKK2no6U4BnKWb8X1RQDFxr0rAt1dwkBKqVTx9mlFhGZmA8CSAD0nrnXrWo1oVWBsxaU3VdhvTlsct7GwwL/MD/7eznpM1R67wmUQnbwhHWHt+GNDAP7ASRzcdw+BXYyBSTdFv7uFtXsexu7GWcznc9OXvVuXcfPlL2Pt5KNYPnwvSumxffnFISdrb9vY2Oo970Q3WcbutTew8eRvYe/WZSwdPIGlA8exefYbmO6/B8tH78XuxRexfPgMRDpsn3sGy8fuB2Y7mKwexNbrf4XJviOY7D+GyfoRbL32DXRrhyCrByErBzA9ci8O/vAvm1u7+9aLuPWNz2Prpa8DMsHaQx/B8n3vw/bZp7Hz5vNYOnIGEGDr1W9h+fS7sXftLextnIPvb/Lv9tI8wEZzyIOJaxSRx2eyF7Rgpt+9jTiWhxloIP5H/+9vFAWNzo7Boh0Rw0jtG+rxHuug9x7P1GBJqf5n8esEtJ9Qoedw5XpzhkOQm74zYy0Fvikf8dL63FKv8Vwlqrf1TkGHHoK2bVLjEkOHFgIy5sDexrBAOFyX21nsPjZGviZsWFe8TWPJmRIAnvorBUj9UVRGuIa36lHdK6aYnEbiZVbgLSUoL8egTOTw643jpd0a7LfiFhRkZGtPJ035frgp9YN+jwLMZ/AcMZfYZGkV3XQV/XwX/fYdcynXTjyM05/+r3H1yX+OO689iTKfVX3QcMMEUvoK8j3Q9+i6DrCtvFUunT+unwN1+VCpn9ce/CD2v/cz2H7jacw3b2Hp6L3Y955P4eaT/wq3v/WF4XnTZYgI5rs7QF8oYbaadj8fygaBi7YzxEILSAV9wGGvgOXTk+fSk4fUkwQVyNgGrS8F0tP34T7yKgp8Mf+wQZnrWBFNHK0LhZN7YLQkJ446afHr8lCbX5wzVPxZ5kLys78HXQyPzR8M1X1ksFSCsAn6GEtjFkcdB9TlOD34RMrCxpfcUF3gHRy+UXdphJOHQWkRZyf2FcaiMtIvia7n16KuC4ukiXGlbXOsJiaXPGtcQpHjwVqua0FUslia82ZBt7SGrpu6XjWB5aJjJgCgn+1hPr8NHxicu5XdLcx2NqluLGOgzHaHxdMKEvqgfo9c6NrjfY+aIm/VKWXmGlEA9BVA+x7Twydx4IO/gDvffQK3nvqDIcC8tI6lo/dBpstOG/Z2YpnzmUuR+iNC8V1eknQUau/5Mopqjbh77fPcJxq1ZeE/kq7J+uG9Ph1ZSZOAK4FRoIOxmn4yYaKFTU3v4tBKVE+/Ukdbck/AZssgpShvlGD4TWjGDRJiJrGrswtCvwlD7VhHSGAR5PmONl/lP2yi5+4fmZHfqi50OEyihD7J8busAMqmOalWTyzOC97ZbXW3dLzdwSXsKtCZBBbeNlpGfLk2NddPlnHs/f8x1o4/AvT9iEamlkuHrUsv4PLXfh39bNuFH7xx1ZHa190USweOD+Bx8CS6lX1DSoEO9Fo7CjlEEAbpbOXVReogTex5aR2T/fdg6fBpdGuHUHZ3MD3+IMp8hu03vm3qjCjVBZKJeOL1LPBlTgtkzyarzNbFkfpSmR0/WG2NyqLQR/vU0nzj79u2TUs4EbE9c8V3muQV+1XoHBRqDkOgCmnu0F2YU94TzMRMsyuFBcIySPlLaUxHY8jiLXUd8C2KM9rH0T+oafx9RHdYFu6G8jO0LFbB4k8hRhJ53MhuDRbncncrtiQOAXlYGAUFMBdh8MnIC4zFrXjCweRshuyjuSy4X0ffsBWRVb/H3q23IJMl+FYu6RXk3GHv5lsIew41XRefNF07jOVD92Lzzacx3X8PVo+/G1sXniPZwYy5mSNKMvVwDp8kPdy4e+08bn37S9j38OM4+ul/iPmtDUCAm9/+I2xfehWWW7WgN4Mp5r7kuvEYrvXmSnPXEOo1u6TSd3FQSJVY1Kf2t+pHDpwt0DP5R7/xG0Uf5H5sjOPYe6vh8DlsD6wxGmsPHfDN8atUnsZ3fJO+apw6XRtiTgCg/rluPFgQYmT6PsxysWEuiFHla+y5fm3OHRbdM4kg1tpDny0WRM8QO/HHy+PnenkL/qovre1Tb42MwuTOBqSKp35SrFrbjyPAx0FTA0cFo5KuUwDgEbBQWxaUA22f7r/Ee3EV/QxAOi/PROmhBi229CSrfh7EIqHtyVCkQ9dNHGhLGeJE1E+i8gRSm8jy2BSse+IMs3QTLB06jcmBYyg7W9i7dmFYT2igndqex0g+bKQCoZQC6d1tcSalOiy+87HpAsvS26T9GJhWz2TCtKyuwy3WTgDDcV7WDmYo9DzWrZ7qUH8f3a1h8YtaXYhxWbnRQTPXKYBkOwwyWCJR5ZYjxE8cEpF0SWB6lYUJsRDOtreOshZgwZPJsISNifz84Lb6kBbYhkFgYmo2QlnrSO4Snq/ybamz0/KS44/psuw6OiC0cs6q0K4pEwPBpr/ykN9qATF73VBvEQBQMcUnZwzjEhDEXQsSAwz0wBtr2fClR5nPq55llu5lxIX7uZk03BHgZh0v8xl2rrwOXHndQJN7t8SrIy8fE6l1FDduvEtG3/PWJVWE4w5oLH0RUx9TwdCXC75iT2KaSGt6enSFAjWDI25JfFSXjrDN2oJotgZiQUXdNKkKp0po7lBkaAXDFtFtrKbYgRRA4Q2/PFep1Po06QAOZnwQgxYwuMWxDO1YCcFpFlmAuuBeRtbUQiW7G+xeixUf1dnYpNpa6j+vUlkAOItesW6jOldiswexuKya7IUc48iq19Qod/bYlQ7sPAD6BcX7h/p5DMiMMXJMkutZB8CFOJEeHrl5rUYwGx2waO/fekFvj25BV+7y3OGpXbguaot6JXnIEwLt2E/GsgDw7qcLuiXUiOtQ/D8LpSfenSawLqw3ZmkaE5H4VGoQ9T0ZEaqOErLrCGda28KMU/SI6NqZBcWOYCpWZIngFsqJlLyNf9Df4lcbhFWQzRphmw5SS6TKK+6I0P5jYORf2j5XxXXw80XmLBEhQB2RqZXmbWOcRer8sfF3dFQNYhk3GQcQYp1Y/OLmqbTkLuXzTy6bYne6xGNNWOZh7ao1TKoBC4EVlaEDK1VBY59xACgmv948QvpfIR02zS/punrsWPF7Qt+gzu5LaE0jy6gPsX/CmmDJMsojjD/BAjXj5L7pI9zla8Ei5eAVKsNrqkINIxKNRnwAKteqQKevF0umHdv5gjrKZ6KbQMjuUvCyuIt3rdRODVVQFlUf778nCxTTptDhOdAeguIGThEaTbTp7MLYBewqpvJtsz136aQeUxZJG014mLLSFYk5+mSHAOhH6zO25eAgb78y9mp29TMAE4BICWxiTCqLRtr8eEm35L3Fco8tckXiBFBm2gnDzCPgmweWVdL3GovLYQUHKO9f0OOLeEHBVRyPjfy7iHB0MsDbSMnHzf0c6sirM+9WhbtUdkE9hf9TFt/Qpf6u5xoWW/LSVL9wE1TaaOIeYW/wBj3zWO692VtR3lMW7LYjmPj4cB6xCvrCKqy/0YiYOq8dx51ZWDslXhGRn+6Xdr6tNYJwWBYJHUa5Tdl5akevoWc3jFafUWloXKIyzsRGuBA0hkTQFNue28UD5F1AIIwVhUpJBpx3ArHiCppQlK1jSwbPYJUHIvuf0HfN+r8oHUtdQFTp/Jnrx0wpenJqObz9zTAQaW5ls4BYRZUbWM0ic/nBE+hSb7euZMtsx19Rj93gJRUW+w6ke8klS/VpvZDxunRJhm3wLhsr16Nt+sKXyILyqPJDZwTUS73kI76RZ1PiCEw8NIWOGHNxGoDxRnruCwuUF2JnEw4OBFgNDFQSzeXYF7uVYj/KAom9ve/GblbXNmzz05QwnrPDxcroMxY4FAm9kmhDIzIojD6zaftiHRx91kg/8HZCYV29cC9kNGn7QBOx2e1rx/WREAXE9ppbbNvF6iUStcPrrBX3Wfaw6ysicxpnooGWjFaFB/V2KIxDRBDyyFPGwCqX2WHsVXc38JG+jQqZJteWxlBQ28jxKtXOKfF6Pk16TEjuPrZVZ5haaND1P/k0kqDApJsMzjHBIMJWjidpbGsY8TraJHBELrqjRKAFceiKR0DVZ5exIsW2NLG6cLlNqnL8y137PYah0IY4WkvQj+Yuui7v5ZD7zTB1YYXuMnIbE1OQZkPHEDzPZVMF78ZLA7NiZyiwpNqewsGPuiwoeZrDPXGQHs8UjyDAbTLZ53ZmipFJvP5iujPe07kOXkg7TN9Nbly/puS7KF7XFEeGOjbolqAciybUqaplRFz6k/VNGdI5At0fQfaMUDImRv2JDTKJKfFgAxLb5yqH1XM3tUYeAyZjkokMbaTrEJQgPJGbnOok0cCt/BElt/5QCoCFevE2fxkPGTA/GNmC6S6sLRon52aJ3phcTn/rittOM4xWN/UMbDaWe3+4IMDRQgn5jLa7hn1xL8DDJ8OA4a7gOGdrJwVg+YoKRB29/94DTCo90ONWZwL/GqHTeV3zENd+u0+/iyBZpulzl7+woKDQ5TkNnaCxEKuICyZBLlV+iLTP5HvSd637mQWf/tWbcrzCQZC61ww4Qsr3Erzkd5LK49+DP5xjQIkBZQoN1K164iiW2SrHcnwnivQMuiswYuE25CtVriMlJffaNqkj/2BspOWj4bzOubZlaLf4gDcaEyYAc+kS8Ekut9Ge9GkkcASPLPLBviHKasBM00ELlKgwWFFTdFH52J4pjhvkaNGMdUYsGRVY1J02gjTulyzEE1P1ghg5Hr+/WVcrC24IoZH46por62WM/K3EHRQWj5zjqN12XqpzIi2564aRsHbZIhaBwSh09AmMKlhS7GXOXR5LQoiZU2NdzL8vrtvoeFjGLIvbk9sRS7J+Y7mXxBUWlPE9XwuUR78c44XhPprAGCvHloGEnVLRBuNzKRFFF8h8nA9GUWQDjlq56NqCOudKDCnHqhyYSo1N8f0SA+yK9WNMp/j3o24UVT2oNhZfG/6OguuYB9Om9YRrZdF9uQfe3muEYQkoA54GR1432AZig6E29cvr4KNCs58PpI5r2I9QmTXepUIh5iHoGqalbl4QqhlyrE/J3TgCGux5LIrPjcaZwhgjvpi0AT42ycRC9bsm2MIMsY0HxSRK3g22cXyojqoLEVCbQXs06bIFbb5kMYcJDaU6UrRQmH0QLY5+JP0tI30y1n/anHZGRpdauQmkO2nQ9hm+svghxK4CRDLKjOb/ETOFBDfQGyXjGG7ftdlteQjOV2btKKnwZjZTZZbv+Q/06jjIYKyKjEldlYY1BAfWBdzkbSfXJDMqnRGBiHVaDOA34rfV7j4dzbAYHME43Iy5ajwLx88r9D3XoaQy6TeXGQNQ7P7QrgBaXmY7u8KKVhY+H6mu2ZZTmC1dbz6HGcziWBM9hfq9dWR8wGCXvOFjAaTGOKT2+11rMrwrGfJb12wh+eB66GJ90u242DceLcd5VmE7qBzuKAiTTMP4WWgVSNu0oAl36ZD2xMvcLh1U4++tp+KzmqNow+MDqc3dXv+hQKvTTNo+NZYG7gUVIBDjDbhGGq6X+B4Z0QXLMyqRcDKlIeUNngHnJmlvKMOq5Y75nAQHTcBQ4rXO2nInjLU5f0/fSDf8y0yuxr4Y4kacIHfzZASsv4drZACWJkLGs0HEZS6xJP1bqCNGhjTrhqYq+o2mNc0AAAQSSURBVEZJUiKFd31xgJP9rvai0QcziecUhiClsWn3hP4hZSHEolzfU4iNPidgybpJfyysweLhzzZ+LkpU1r+pTXfVldz48eezRDQG14AI3l63hmLvcnEXRwZiWxijdmMj+iJVTS1C679rG8NlId7BLlDgTXRFJK+DwjkgKMhwUDswkESEVaty+gKzmgAOBABj5ScYbX5hVfCF5GRcuVxh+ZCMxOsh1O4AiE3dfMQVANkjGsuQXhg2DD+0me1jo/VdGQNXavQmlUVknG0Mkl1cNn4Zf2ZT6+LMiAY1BauegCgwOcmliAXn+zFkoasZqGKQfYyFhkZR35JFSIcxX3EcSJQyLIhL5gYSY2wb/+/Pq3LOmJbVcZV58BqRe1PgImXjeMzdmsAxrPFy/O6cWW6VILprXZsBROivzSTGdjdhxOKlOp0Yu97rOOZ4+JqrJDDpQh0joI5NYOTnjCuJR32SUS5czh9Zq8cyM2do+6Y56EKDy1hkDPy8slC5yvcwlUWvFgDHAv0CnhkekUITknNWpO8iswh2k/5y0H1MiKnb02wvg1Ssl5Prkmwgy0TCs5J4RqUY1T3hg8b0LD6IdneStplvC7pYb/gf39sBOXeCfVdpqa22P9VinIDDNChlO4w0wkEuN73JDEcXR54RoQ/PSWBFYohB7ruxRImVr5+L1qtJHyAAYs6ewLkFIxoTyTUMbJP6JdYwf46/eX+6heRdxjgY3wbRFw0oKhtprw7NUiN0bq1sth0k2XUFRvNiAl2Tu2FfEIj1dNOkBWgTbnfdLAW+qw2UWS0CM96srwUuboprLeeSjXdFtj+5GyzQQ0wt3zb5WRRXS7/dhS5nn2ZR/9z9NVzUsXZZbESrGoKQSHDnwfIY2klNod5bxEDYXSnhL9WtyfERO/rd1lKFlOU0z5EMK1hV2F4jXlcWfO87ZXYOqHVW03Ng4nu2Yp0RjfgzNr4kmWUGkT63LlE0uHCwQOpjf8Q4SNn3qT3aW2wSi+YiFwzqyB5s237inOK1GS1T/J4My/rfJjxHz+c1htrVo6wK7gY6ICEAsblLdwswcVuiijd14mtiOaGXSXqUhCOSL1/YKaOeOFoGq43ThPJ/P268+JXF1qkAFqtUdu/alpYABgmWJHbkcP14/7WLPmXkb2QdvtwlmRlPwxdxYBUZml06hKFWqFRhg9O6ZbCjRtjqfURtSgy0RHTSFkDdzrwDA/83BOETW/WSFhn8IjeyhN/LmLwDmGbN8P+Eoy+qfMaUN3KYpFfC/NqvchAeaWVSx0V8kOEzGLQQvAdUSB2oNXKlatymzKzyp9AHiQxkoAzxqpCuMzqMRW1lVa3qjk7Aq6QbLWQw44qFoW98/yueirCt0KnP0pMg8abEMJuvw+v/B1zBSj+GD0vGAAAAB3RFWHRBdXRob3IAqa7MSAAAAAx0RVh0RGVzY3JpcHRpb24AEwkhIwAAAAp0RVh0Q29weXJpZ2h0AKwPzDoAAAAOdEVYdENyZWF0aW9uIHRpbWUANfcPCQAAAAl0RVh0U29mdHdhcmUAXXD/OgAAAAt0RVh0RGlzY2xhaW1lcgC3wLSPAAAACHRFWHRXYXJuaW5nAMAb5ocAAAAHdEVYdFNvdXJjZQD1/4PrAAAACHRFWHRDb21tZW50APbMlr8AAAAGdEVYdFRpdGxlAKju0icAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "execution_count": 27, "metadata": { "image/png": { "width": 200 } }, "output_type": "execute_result" } ], "source": [ "from IPython.display import Image\n", "Image('../../Python_probability_statistics_machine_learning_2E.png',width=200)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Useful Distributions\n", "\n", "## Normal Distribution\n", "\n", "\n", "\n", "Without a doubt, the normal (Gaussian)\n", "distribution is the most\n", "important and foundational probability distribution.\n", "The one-dimensional form\n", "is the following:\n", "\n", "$$\n", "f(x) =\\frac{e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}}}{\\sqrt{2\\pi\\sigma^2 } }\n", "$$\n", "\n", " where $\\mathbb{E}(x)=\\mu$ and $\\mathbb{V}(x)=\\sigma^2$. The\n", "multidimensional\n", "version for $\\mathbf{x}\\in \\mathbb{R}^n$ is the following,\n", "\n", "$$\n", "f(\\mathbf{x}) = \\frac{1}{\\det(2\\pi \\mathbf{R})^{\\frac{1}{2}}}\n", "e^{-\\frac{1}{2}(\\mathbf{x}-\\boldsymbol{\\mu})^T\n", "\\mathbf{R}^{-1}(\\mathbf{x}-\\boldsymbol{\\mu})}\n", "$$\n", "\n", " where $\\mathbf{R}$ is the covariance matrix with entries\n", "\n", "$$\n", "R_{i,j} = \\mathbb{E}\\left[ (x_i-\\bar{x_i})(x_j-\\bar{x_j}) \\right]\n", "$$\n", "\n", " A key property of the normal distribution is that it is completely\n", "specified by\n", "its first two moments. Another key property is that \n", "the normal distribution is\n", "preserved under linear tranformations. \n", "For example,\n", "\n", "$$\n", "\\mathbf{y} = \\mathbf{A x}\n", "$$\n", "\n", " means $\\mathbf{y}\\sim \\mathcal{N}(\\mathbf{A x},\\mathbf{A R_x}\n", "\\mathbf{A}^T)$.\n", "This means that it is easy to do linear algebra and matrix\n", "operations with\n", "normal distributed random variables. There are many intuitive\n", "geometric\n", "relationships that are preserved with normal distributed random\n", "variables, as\n", "discussed in the Gauss-Markov chapter. \n", "\n", "## Multinomial Distribution\n", "\n", "\n", "\n", "\n", "\n", "The Multinomial distribution generalized the Binomial\n", "distribution.\n", "Recall that the Binomial distribution characterizes the number of\n", "heads obtained \n", "in $n$ trials.\n", "Consider the problem of $n$ balls to be divided\n", "among $r$ available bins\n", "where each bin may accommodate more than one ball. For\n", "example, suppose\n", "$n=10$ and and $r=3$, then one possible valid configuration is\n", "$\\mathbf{N}_{10}=[3,3,4]$. The probability that a ball lands in the\n", "$i^{th}$ bin\n", "is $p_i$, where $\\sum p_i=1$. The Multinomial distribution\n", "characterizes the\n", "probability distribution of $\\mathbf{N}_n$. The Binomial\n", "distribution is a\n", "special case of the Multinomial distribution with $n=2$. The\n", "Multinomial\n", "distribution is implmented in the `scipy.stats` module as shown\n", "below," ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[1, 5, 4],\n", " [1, 4, 5],\n", " [4, 2, 4],\n", " [4, 2, 4]])" ] }, "execution_count": 28, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.stats import multinomial\n", "rv = multinomial(10,[1/3]*3)\n", "rv.rvs(4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that the sum across the columns is always $n$" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([10, 10, 10, 10, 10, 10, 10, 10, 10, 10])" ] }, "execution_count": 29, "metadata": {}, "output_type": "execute_result" } ], "source": [ "rv.rvs(10).sum(axis=1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To derive the probability mass function, we define the *occupancy vector*,\n", "$\\mathbf{e}_i\\in \\mathbb{R}^r$ which is a binary vector with exactly one\n", "non-\n", "zero component (i.e., a unit vector). Then, the $\\mathbf{N}_n$ vector can\n", "be\n", "written as the sum of $n$ vectors $\\mathbf{X}$, each drawn from the set\n", "$\\lbrace\n", "\\mathbf{e}_j \\rbrace_{j=1}^r$,\n", "\n", "$$\n", "\\mathbf{N}_n = \\sum_{i=1}^n \\mathbf{X}_i\n", "$$\n", "\n", " where the probability $\\mathbb{P}(\\mathbf{X}=\\mathbf{e}_j)=p_j$. Thus,\n", "$\\mathbf{N}_n$ has a discrete distribution over the set of vectors with \n", "non-\n", "negative components that sum to $n$. Because the $\\mathbf{X}$ \n", "vectors are\n", "independent and identically distributed, the \n", "probability of any particular\n", "$\\mathbf{N}_n=[ x_1,x_2,\\cdots,x_r ]^\\top=\\mathbf{x}$ is\n", "\n", "$$\n", "\\mathbb{P}(\\mathbf{N}_n=x) = C_n p_1^{x_1} p_2^{x_2}\\cdots p_r^{x_r}\n", "$$\n", "\n", " where $C_n$ is a combinatorial factor that accounts for all the ways\n", "a\n", "component can sum to $x_j$. Consider that there are $\\binom{n}{x_1}$ ways\n", "that\n", "the first component can be chosen. This leaves $n-x_1$ balls left for the\n", "rest\n", "of the vector components. Thus, the second component has\n", "$\\binom{n-x_1}{x_2}$\n", "ways to pick a ball. Following the same pattern, the\n", "third component has\n", "$\\binom{n-x_1-x_2}{x_3}$ ways and so forth,\n", "\n", "$$\n", "C_n = \\binom{n}{x_1}\\binom{n-x_1}{x_2} \\binom{n-x_1-x_2}{x_3} \\cdots\n", "\\binom{n-x_1-x_2-\\cdots-x_{r-1}}{x_r}\n", "$$\n", "\n", " simplifies to the following,\n", "\n", "$$\n", "C_n = \\frac{n!}{x_1! \\cdots x_r!}\n", "$$\n", "\n", " Thus, the probability mass function for the Multinomial distribution is the\n", "following,\n", "\n", "$$\n", "\\mathbb{P}(\\mathbf{N}_n=x) = \\frac{n!}{x_1! \\cdots x_r!} p_1^{x_1}\n", "p_2^{x_2}\\cdots p_r^{x_r}\n", "$$\n", "\n", " The expectation of this distribution is the following,\n", "\n", "$$\n", "\\mathbb{E}(\\mathbf{N}_n) = \\sum_{i=1}^n \\mathbb{E}(X_i)\n", "$$\n", "\n", " by the linearity of the expectation. Then,\n", "\n", "$$\n", "\\mathbb{E}(X_i) = \\sum_{j=1}^r p_j \\mathbf{e}_j =\n", "\\mathbf{I}\\mathbf{p}=\\mathbf{p}\n", "$$\n", "\n", " where $p_j$ are the components of the vector $\\mathbf{p}$ and \n", "$\\mathbf{I}$ is\n", "the identity matrix. Then, because this is the same for any $X_i$,\n", "we have\n", "\n", "$$\n", "\\mathbb{E}(\\mathbf{N}_n) = n \\mathbf{p}\n", "$$\n", "\n", "For the covariance of $\\mathbf{N}_n$, we need to compute the following,\n", "\n", "$$\n", "\\textrm{Cov}(\\mathbf{N}_n) = \\mathbb{E}\\left(\\mathbf{N}_n\n", "\\mathbf{N}_n^\\top\\right) - \\mathbb{E}(\\mathbf{N}_n)\n", "\\mathbb{E}(\\mathbf{N}_n)^\\top\n", "$$\n", "\n", " For the first term on the right, we have\n", "\n", "$$\n", "\\mathbb{E}\\left(\\mathbf{N}_n\n", "\\mathbf{N}_n^\\top\\right)=\\mathbb{E}\\left((\\sum_{i=1}^n X_i)(\\sum_{j=1}^n\n", "X_j^\\top) \\right)\n", "$$\n", "\n", " and for $i=j$, we have\n", "\n", "$$\n", "\\mathbb{E}(X_i X_i^\\top) = \\textrm{diag}(\\mathbf{p})\n", "$$\n", "\n", " and for $i\\neq j$, we have\n", "\n", "$$\n", "\\mathbb{E}(X_i X_j^\\top) = \\mathbf{p}\\mathbf{p}^\\top\n", "$$\n", "\n", " Note that this term has elements on the diagonal. Then, combining the\n", "above two\n", "equations gives the following,\n", "\n", "$$\n", "\\mathbb{E}(\\mathbf{N}_n\\mathbf{N}_n^\\top) = n \\textrm{diag}(\\mathbf{p}) +\n", "(n^2-n) \\mathbf{p}\\mathbf{p}^\\top\n", "$$\n", "\n", " Now, we can assemble the covariance matrix,\n", "\n", "$$\n", "\\textrm{Cov}(\\mathbf{N}_n) = n \\textrm{diag}(\\mathbf{p}) + (n^2-n)\n", "\\mathbf{p}\\mathbf{p}^\\top - n^2 \\mathbf{p} \\mathbf{p}^\\top = n\n", "\\textrm{diag}(\\mathbf{p})-n \\mathbf{p} \\mathbf{p}^\\top\n", "$$\n", "\n", " Specifically, the off-diagonal terms are $n p_i p_j$ and the diagonal terms are\n", "$n p_i (1-p_i)$.\n", "\n", "## Chi-Square Distribution\n", "\n", "\n", "\n", "The $\\chi^2$ distribution\n", "appears in many different contexts so it's worth\n", "understanding. Suppose we have\n", "$n$ independent random variables\n", "$X_i$ such that $X_i\\sim \\mathcal{N}(0,1)$. We\n", "are interested in the following\n", "random variable $R = \\sqrt{\\sum_i X_i^2}$. The\n", "joint probability density of\n", "$X_i$ is the following,\n", "\n", "$$\n", "f_{\\mathbf{X}}(X) = \\frac{e^{-\\frac{1}{2}\\sum_i X_i^2}}{(2\\pi)^{\\frac{n}{2}}}\n", "$$\n", "\n", " where the $\\mathbf{X}$ represents a vector of $X_i$ random variables. You \n", "can\n", "think of $R$ as the radius of an $n$-dimensional sphere. The volume of \n", "this\n", "sphere is given by the the following formula,\n", "\n", "$$\n", "V_n(R) = \\frac{\\pi^{\\frac{n}{2}}}{\\Gamma(\\frac{n}{2}+1)} R^n\n", "$$\n", "\n", " To reduce the amount of notation we define,\n", "\n", "$$\n", "A := \\frac{\\pi^{\\frac{n}{2}}}{\\Gamma(\\frac{n}{2}+1)}\n", "$$\n", "\n", " The differential of this volume is the following,\n", "\n", "$$\n", "dV_n(R)= n A R^{n-1} dR\n", "$$\n", "\n", " In term of the $X_i$ coordinates, the probability (as always) \n", "integrates out\n", "to one.\n", "\n", "$$\n", "\\int f_{\\mathbf{X}}(\\mathbf{X}) dV_n(\\mathbf{X}) = 1\n", "$$\n", "\n", " In terms of $R$, the change of variable provides,\n", "\n", "$$\n", "\\int f_{\\mathbf{X}}(R) n A R^{n-1} dR\n", "$$\n", "\n", " Thus,\n", "\n", "$$\n", "f_R(R):=f_{\\mathbf{X}}(R) = n A\n", "R^{n-1}\\frac{e^{-\\frac{1}{2}R^2}}{(2\\pi)^{\\frac{n}{2}}}\n", "$$\n", "\n", " But we are interested in the distribution $Y=R^2$. Using the same\n", "technique\n", "again,\n", "\n", "$$\n", "\\int f_{R}(R) dR =\\int f_{R}(\\sqrt{Y}) \\frac{dY}{2\\sqrt{Y}}\n", "$$\n", "\n", " Finally,\n", "\n", "$$\n", "f_Y(Y) := n A Y^\\frac{n-1}{2}\\frac{e^{-\\frac{1}{2}Y}}{(2\\pi)^{\\frac{n}{2}}}\n", "\\frac{1}{2\\sqrt{Y}}\n", "$$\n", "\n", " Then, finally substituting back in $A$ gives the $\\chi^2$ distribution with $n$\n", "degrees of freedom,\n", "\n", "$$\n", "f_Y(Y) = n \\frac{\\pi^{\\frac{n}{2}}}{\\Gamma(\\frac{n}{2}+1)}\n", "Y^{n/2-1}\\frac{e^{-\\frac{1}{2}Y}}{(2\\pi)^{\\frac{n}{2}}} \\frac{1}{2}=\n", "\\frac{2^{-\\frac{n}{2}-1} n }{\\Gamma \\left(\\frac{n}{2}+1\\right)}e^{-Y/2}\n", "Y^{\\frac{n}{2}-1}\n", "$$\n", "\n", "**Example:** Hypothesis testing is a common application of the $\\chi^2$\n", "distribution. Consider Table [1](#tab:diagnosisTable) which tabulates the\n", "infection status of a certain population. The hypothesis is that these data\n", "are\n", "distributed according to the multinomial distribution with the following\n", "rates\n", "for each group, $p_1=1/4$ (mild infection), $p_2=1/4$ (strong infection),\n", "and\n", "$p_3=1/2$ (no infection). Suppose $n_i$ is the count of persons in the\n", "$i^{th}$\n", "column and $\\sum_{i} n_i=n=684$. Let $k$ denote the number of columns.\n", "Then, in\n", "order to apply the Central Limit Theorem, we want to sum the $n_i$\n", "random\n", "variables, but these all sum to $n$, a constant, which prohibits using\n", "the\n", "theorem. Instead, suppose we sum the $n_i$ variables up to $k-1$ terms. Then,\n", "\n", "$$\n", "z = \\sum_{i=1}^{k-1} n_i\n", "$$\n", "\n", " is asymptotically normally distributed by the theorem with mean\n", "$\\mathbb{E}(z)\n", "= \\sum_{i=1}^{k-1} n p_i$. Using our previous results and notation \n", "for\n", "multinomial random variables, we can write this as\n", "\n", "$$\n", "z = [\\mathbf{1}_{k-1}^\\top,0]\\mathbf{N}_n\n", "$$\n", "\n", " where $\\mathbf{1}_{k-1}$ is a vector of all ones of length $k-1$ and\n", "$\\mathbf{N}_n\\in \\mathbb{R}^{k}$. With this notation, we have\n", "\n", "$$\n", "\\mathbb{E}(z )= n [\\mathbf{1}_{k-1}^\\top,0] \\mathbf{p} = \\sum_{i=1}^{k-1} n\n", "p_i = n(1-p_k)\n", "$$\n", "\n", " We can get the variance of $z$ using the same method,\n", "\n", "$$\n", "\\mathbb{V}(z)\n", "=[\\mathbf{1}_{k-1}^\\top,0]\\textrm{Cov}(\\mathbf{N}_n)[\\mathbf{1}_{k-1}^\\top,0]^\\top\n", "$$\n", "\n", " which gives,\n", "\n", "$$\n", "\\mathbb{V}(z)\n", "=[\\mathbf{1}_{k-1}^\\top,0](n\\textrm{diag}(\\mathbf{p})-n\\mathbf{p}\\mathbf{p}^\\top\n", ")[\\mathbf{1}_{k-1}^\\top,0]^\\top\n", "$$\n", "\n", " The variance is then,\n", "\n", "$$\n", "\\mathbb{V}(z) = n (1-p_k)p_k\n", "$$\n", "\n", " With the mean and variance established we can subtract the\n", "hypothesize mean for\n", "each column under the hypothesis and create the\n", "transformed variable,\n", "\n", "$$\n", "z^\\prime = \\sum_{i=1}^{k-1} \\frac{n_i-n p_i}{\\sqrt{n (1-p_k)p_k}} \\sim\n", "\\mathcal{N}(0,1)\n", "$$\n", "\n", " by the Central Limit Theorem. Likewise,\n", "\n", "$$\n", "\\sum_{i=1}^{k-1} \\frac{(n_i-n p_i)^2}{n (1-p_k)p_k} \\sim \\chi_{k-1}^2\n", "$$\n", "\n", "\n", "
\n", "$$\n", "\\begin{table}[]\n", "\\centering\n", "\\caption{Diagnosis Table}\n", "\\label{tab:diagnosisTable} \\tag{1}\n", "\\begin{tabular}{lllll}\n", "\\cline{1-4}\n", "\\multicolumn{1}{|l|}{Mild Infection} & \\multicolumn{1}{l|}{Strong Infection} &\n", "\\multicolumn{1}{l|}{No infection} & \\multicolumn{1}{l|}{Total} & \\\\ \\cline{1-4}\n", "\\multicolumn{1}{|c|}{128} & \\multicolumn{1}{c|}{136} &\n", "\\multicolumn{1}{c|}{420} & \\multicolumn{1}{c|}{684} & \\\\ \\cline{1-4}\n", "\\end{tabular}\n", "\\end{table}\n", "$$\n", "\n", "With all that established, we can test the hypothesis that the data in the table\n", "follow the hypothesized multinomial distribution." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.00012486166748693073" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy import stats\n", "n = 684\n", "p1 = p2 = 1/4\n", "p3 = 1/2\n", "v = n*p3*(1-p3)\n", "z = (128-n*p1)**2/v + (136-n*p2)**2/v\n", "1-stats.chi2(2).cdf(z)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This value is very low and suggests that the hypothesized multinomial\n", "distribution is not a good one for this data. Note that this approximation only\n", "works when `n` is large in comparison to the number of columns in the table.\n", "\n", "##\n", "Poisson and Exponential Distributions\n", "\n", "\n", "\n", "\n", "The Poisson distribution for a random\n", "variable $X$ represents a number of\n", "outcomes occurring in a given time interval\n", "($t$).\n", "\n", "$$\n", "p(x;\\lambda t) = \\frac{e^{-\\lambda t}(\\lambda t)^x}{x!}\n", "$$\n", "\n", " The Poisson distribution is closely related to the binomial\n", "distribution,\n", "$b(k;n,p)$ where $p$ is small and $n$ is large. That is, when\n", "there is a low-\n", "probability event but many trials, $n$. Recall that the binomial\n", "distribution is\n", "the following,\n", "\n", "$$\n", "b(k;n,p) =\\binom{n}{k} p^k (1-p)^{n-k}\n", "$$\n", "\n", " for $k=0$ and taking the logarithm of both sides, we obtain\n", "\n", "$$\n", "\\log b(0;n,p) = (1-p)^n = \\left( 1-\\frac{\\lambda}{n} \\right)^n\n", "$$\n", "\n", " Then, the Taylor expansion of this gives the following,\n", "\n", "$$\n", "\\log b(0;n,p) \\approx -\\lambda - \\frac{\\lambda^2}{2 n} - \\cdots\n", "$$\n", "\n", " For large $n$, this results in,\n", "\n", "$$\n", "b(0;n,p) \\approx e^{-\\lambda}\n", "$$\n", "\n", " A similar argument for $k$ leads to the Poisson distribution.\n", "Conveniently, we\n", "have $\\mathbb{E}(X) = \\mathbb{V}(X)= \\lambda$. For example,\n", "suppose that the\n", "average number of vehicles passing under a toll-gate per hour\n", "is 3. Then, the\n", "probability that 6 vehicles pass under the gate in a given hour\n", "is\n", "$p(x=6;\\lambda t= 3) = \\frac{81}{30 e^3}\\approx 0.05$.\n", "\n", "The Poisson distribution\n", "is available from the `scipy.stats` module.\n", "The following code computes the last\n", "result," ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.05040940672246224\n" ] } ], "source": [ "from scipy.stats import poisson\n", "x = poisson(3)\n", "print(x.pmf(6))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Poisson distribution is important for applications involving reliability\n", "and\n", "queueing. The Poisson distribution is used to compute the probability of\n", "specific numbers of events during a particular time period. In many cases the\n", "time period ($X$) itself is the random variable. For example, we might be\n", "interested in understanding the time $X$ between arrivals of vehicles at a\n", "checkpoint. With the Poisson distribution, the probability of *no* events\n", "occurring in the span of time up to time $t$ is given by the following,\n", "\n", "$$\n", "p(0;\\lambda t) = e^{-\\lambda t}\n", "$$\n", "\n", " Now, suppose $X$ is the time to the first event. The \n", "probability that the\n", "length of time until the first event will exceed $x$ is \n", "given by the following,\n", "\n", "$$\n", "\\mathbb{P}(X>x) = e^{-\\lambda x}\n", "$$\n", "\n", " Then, the cumulative distribution function is given by \n", "the following,\n", "\n", "$$\n", "\\mathbb{P}(0\\le X\\le x) = F_X (x) = 1-e^{- \\lambda x}\n", "$$\n", "\n", " Taking the derivative gives the *exponential* distribution,\n", "\n", "$$\n", "f_X(x) = \\lambda e^{-\\lambda x}\n", "$$\n", "\n", " where $\\mathbb{E}(X) = 1/\\lambda $ and $\\mathbb{V}(X)=\\frac{1}{\\lambda^2}$.\n", "For\n", "example, suppose we want to know the probability of a certain \n", "component lasting\n", "beyond $T=10$ years where $T$ is modeled as a \n", "an exponential random variable\n", "with $1/\\lambda=5$ years. Then, we have\n", "$1-F_X(10) = e^{-2} \\approx 0.135 $.\n", "The exponential distribution is available in the `scipy.stats` module. The\n", "following code computes the result of the example above. Note that the\n", "parameters are described in slightly different terms as above, as described in\n", "the corresponding documentation for `expon`." ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.1353352832366127\n" ] } ], "source": [ "from scipy.stats import expon\n", "x = expon(0,5) # create random variable object\n", "print(1 - x.cdf(10))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Gamma Distribution\n", "\n", "\n", "\n", "We have previously discussed how the exponential\n", "distribution can be created\n", "from the Poisson events. The exponential\n", "distribution has the *memoryless*\n", "property, namely,\n", "\n", "$$\n", "\\mathbb{P}(T>t_0+t\\vert T>t_0) = \\mathbb{P}(T>t)\n", "$$\n", "\n", " For example, given $T$ as the random variable representing the time\n", "until\n", "failure, this means that a component that has survived up through $t_0$\n", "has the\n", "same failure probability of lasting $t$ units beyond that point. To \n", "derive this\n", "result, it is easier to compute the complementary event,\n", "\n", "$$\n", "\\mathbb{P}(t_0t_0) = \\mathbb{P}(t_00$, \n", "the gamma distribution is the following,\n", "\n", "$$\n", "f(x;\\alpha,\\beta)=\n", "\\frac{\\beta ^{-\\alpha } x^{\\alpha\n", " -1}\n", "e^{-\\frac{x}{\\beta\n", " }}}{\\Gamma (\\alpha )}\n", "$$\n", "\n", " and $f(x;\\alpha,\\beta)=0$ when $x\\le 0$ and $\\Gamma$ is the gamma\n", "function. For\n", "example, suppose that vehicles passing under a gate follows a\n", "Poisson process,\n", "with an average of 5 vehicles passing per hour, what is the\n", "probability that at\n", "most an hour will have passed before 2 vehicles pass the\n", "gate? If $X$ is time in\n", "hours that transpires before the 2 vehicles pass, then\n", "we have $\\beta=1/5$ and\n", "$\\alpha=2$. The required probability $\\mathbb{P}(X<1)\n", "\\approx 0.96 $. The gamma\n", "distribution has $\\mathbb{E}(X) = \\alpha\\beta $ and\n", "$\\mathbb{V}(X)=\\alpha\\beta^2$\n", "\n", "The\n", "following code computes the result of the\n", "example above. Note that the\n", "parameters are described in slightly different\n", "terms as above, as described in\n", "the corresponding documentation for `gamma`." ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.9595723180054873\n" ] } ], "source": [ "from scipy.stats import gamma\n", "x = gamma(2,scale=1/5) # create random variable object\n", "print(x.cdf(1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Beta Distribution\n", "\n", "\n", "\n", "The uniform distribution assigns a single constant value\n", "over the unit interval. The Beta distribution generalizes this to\n", "a function\n", "over the unit interval. The probability density function \n", "of the Beta\n", "distribution is the following,\n", "\n", "$$\n", "f(x ) = \\frac{1}{\\beta(a,b)} x^{a-1} (1-x)^{b-1}\n", "$$\n", "\n", " where\n", "\n", "$$\n", "\\beta(a,b) = \\int_0^1 x^{a-1} (1-x)^{b-1} dx\n", "$$\n", "\n", " Note that $a=b=1$ yields the uniform distribution. In the \n", "special case for\n", "integers where $0\\le k\\le n$, we have\n", "\n", "$$\n", "\\int_0^1 \\binom{n}{k}x^k (1-x)^{n-k} dx = \\frac{1}{n+1}\n", "$$\n", "\n", " To get this result without calculus, we can use an experiment by\n", "Thomas Bayes.\n", "Start with $n$ white balls and one gray ball. Uniformly at\n", "random, toss them\n", "onto the unit interval. Let $X$ be the number of white balls\n", "to the left of the\n", "gray ball. Thus, $X\\in \\lbrace 0,1,\\ldots,n \\rbrace$. To\n", "compute\n", "$\\mathbb{P}(X=k)$, we condition on the probability of the position $B$\n", "of the\n", "gray ball, which is uniformly distributed over the unit interval\n", "($f(p)=1$).\n", "Thus, we have\n", "\n", "$$\n", "\\mathbb{P}(X=k) = \\int_0^1 \\mathbb{P}(X=k\\vert B=p) f(p) dp = \\int_0^1\n", "\\binom{n}{k}p^k (1-p)^{n-k} dp\n", "$$\n", "\n", " Now, consider a slight variation on the experiment where we start\n", "with $n+1$\n", "white balls and again toss them onto the unit interval and then\n", "later choose one\n", "ball at random to color gray. Using the same $X$ as before, by\n", "symmetry, because\n", "any one of the $n+1$ balls is equally likely to be chosen, we\n", "have\n", "\n", "$$\n", "\\mathbb{P}(X=k)=\\frac{1}{n+1}\n", "$$\n", "\n", " for $k\\in \\lbrace 0,1,\\ldots,n \\rbrace$. Both situations describe the\n", "same\n", "problem because it does not matter whether we paint the ball before or\n", "after we\n", "throw it. Setting the last two equations equal gives the desired\n", "result without\n", "using calculus.\n", "\n", "$$\n", "\\int_0^1 \\binom{n}{k}p^k (1-p)^{n-k} dp = \\frac{1}{n+1}\n", "$$\n", "\n", "The following code shows where to get the Beta distribution from the `scipy`\n", "module." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "1.0\n" ] } ], "source": [ "from scipy.stats import beta\n", "x = beta(1,1) # create random variable object\n", "print(x.cdf(1))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given this experiment, it is not too surprising that there is an intimate\n", "relationship between the Beta distribution and binomial random variables.\n", "Suppose we want to estimate the probability of heads for coin-tosses using\n", "Bayesian inference. Using this approach, all unknown quantities are treated as\n", "random variables. In this case, the probability of heads ($p$) is the unknown\n", "quantity that requires a *prior* distribution. Let us choose the Beta\n", "distribution as the prior distribution, $\\texttt{Beta}(a,b)$. Then,\n", "conditioning\n", "on $p$, we have\n", "\n", "$$\n", "X\\vert p \\sim \\texttt{binom}(n,p)\n", "$$\n", "\n", " which says that $X$ is conditionally distributed as a binomial. To \n", "get the\n", "posterior probability, $f(p\\vert X=k)$, we have the following\n", "Bayes rule,\n", "\n", "$$\n", "f(p\\vert X=k) = \\frac{\\mathbb{P}(X=k\\vert p)f(p)}{\\mathbb{P}(X=k)}\n", "$$\n", "\n", " with the corresponding denominator,\n", "\n", "$$\n", "\\mathbb{P}(X=k) = \\int_0^1 \\binom{n}{k}p^k (1-p)^{n-k}f(p) dp\n", "$$\n", "\n", " Note that unlike with our experiment before, $f(p)$ is not constant.\n", "Without\n", "substituting in all of the distributions, we observe that the\n", "posterior is a\n", "function of $p$ which means that everything else that is not a\n", "function of $p$\n", "is a constant. This gives,\n", "\n", "$$\n", "f(p\\vert X=k) \\propto p^{a+k-1} (1-p)^{b+n-k-1}\n", "$$\n", "\n", " which is another Beta distribution with parameters $a+k,b+n-k$. This\n", "special\n", "relationship in which the beta prior probability distribution on $p$ on\n", "data\n", "that are conditionally binomial distributed yields the posterior that is\n", "also\n", "binomial distributed is known as *conjugacy*. We say that the Beta\n", "distribution\n", "is the conjugate prior of the binomial distribution.\n", "\n", "## Dirichlet-multinomial\n", "Distribution\n", "\n", "\n", "\n", "The Dirichlet-multinomial distribution is a discrete\n", "multivariate distribution\n", "also known as the multivariate Polya distribution.\n", "The Dirichlet-multinomial\n", "distribution arises in situations where the usual\n", "multinomial distribution is\n", "inadequate. For example, if a multinomial\n", "distribution is used to model the\n", "number of balls that land in a set of bins and\n", "the multinomial parameter vector\n", "(i.e., probabilities of balls landing in\n", "particular bins) varies from trial to\n", "trial, then the Dirichlet distribution can\n", "be used to include variation in\n", "those probabilities because the Dirichlet\n", "distribution is defined over a\n", "simplex that describes the multinomial parameter\n", "vector.\n", "\n", "Specifically, suppose we have $K$ rival events, each with probability\n", "$\\mu_k$.\n", "Then, the probability of the vector $\\boldsymbol{\\mu}$ given that \n", "each\n", "event has been observed $\\alpha_k$ times is the following,\n", "\n", "$$\n", "\\mathbb{P}(\\boldsymbol{\\mu}\\vert \\boldsymbol{\\alpha}) \\propto \\prod_{k=1}^K\n", "\\mu_k^{\\alpha_k-1}\n", "$$\n", "\n", " where $0\\le\\mu_k\\le 1$ and $\\sum\\mu_k=1$. Note that this last sum is\n", "a\n", "constraint that makes the distribution $K-1$ dimensional. The normalizing\n", "constant for this distribution is the multinomial Beta function,\n", "\n", "$$\n", "\\texttt{Beta}(\\boldsymbol{\\alpha})=\\frac{\\prod_{k=1}^K\\Gamma(\\alpha_k)}{\\Gamma(\\sum_{k=1}^K\\alpha_k)}\n", "$$\n", "\n", " The elements of the $\\boldsymbol{\\alpha}$ vector are also called\n", "*concentration* parameters. As before, the Dirichlet \n", "distribution can be found\n", "in the `scipy.stats` module," ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0.26430564, 0.12853028, 0.60716408],\n", " [0.19141157, 0.29026109, 0.51832735],\n", " [0.2200943 , 0.13789725, 0.64200845]])" ] }, "execution_count": 35, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from scipy.stats import dirichlet\n", "d = dirichlet([ 1,1,1 ])\n", "d.rvs(3) # get samples from distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that each of the rows sums to one. This is because of the\n", "$\\sum\\mu_k=1$\n", "constraint. We can generate more samples and plot this \n", "using `Axes3D` in\n", "Matplotlib in [Figure](#fig:Dirichlet_001)." ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from matplotlib.pyplot import subplots\n", "x = d.rvs(1000)\n", "fig, ax = subplots(subplot_kw=dict(projection='3d'))\n", "_=ax.scatter(x[:,0],x[:,1],x[:,2],marker='o',alpha=.2)\n", "ax.view_init(30, 30) # elevation, azimuth\n", "# ax.set_aspect(1)\n", "_=ax.set_xlabel(r'$\\mu_1$')\n", "_=ax.set_ylabel(r'$\\mu_2$')\n", "_=ax.set_zlabel(r'$\\mu_3$')\n", "fig.savefig('fig-probability/Dirichlet_001.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\n", "\n", "

One thousand samples from a Dirichlet\n", "distribution with $\\boldsymbol{\\alpha} = [1,1,1]$

\n", "\n", "\n", "\n", "\n", "\n", "Notice that the\n", "generated samples lie on the triangular simplex shown. The\n", "corners of the\n", "triangle correspond to each of the components in the\n", "$\\boldsymbol{\\mu}$. Using,\n", "a non-uniform $\\boldsymbol{\\alpha}=[2,3,4]$ vector,\n", "we can visualize the\n", "probability density function using the `pdf` method on the\n", "`dirichlet` object as\n", "shown in [Figure](#fig:Dirichlet_002). By choosing the\n", "$\\boldsymbol{\\alpha}\\in\n", "\\mathbb{R}^3$, the peak of the density function can be\n", "moved within the\n", "corresponding triangular simplex." ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from matplotlib.pylab import cm\n", "X,Y = np.meshgrid(np.linspace(.01,1,50),np.linspace(.01,1,50))\n", "d = dirichlet([2,3,4])\n", "idx=(X+Y<1)\n", "f=d.pdf(np.vstack([X[idx],Y[idx],1-X[idx]-Y[idx]]))\n", "Z = idx*0+ np.nan\n", "Z[idx] = f\n", "fig,ax=subplots()\n", "_=ax.contourf(X,Y,Z,cmap=cm.viridis)\n", "ax.set_aspect(1)\n", "_=ax.set_xlabel('x',fontsize=18)\n", "_=ax.set_ylabel('y',fontsize=18)\n", "fig.savefig('fig-probability/Dirichlet_002.png')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "
\n", "\n", "

Probability density function\n", "for the Dirichlet distribution with $\\boldsymbol{\\alpha}=[2,3,4]$

\n", "\n", "\n", "\n", "\n", "\n", "We\n", "have seen that the Beta distribution generalizes the uniform distribution\n", "over\n", "the unit interval. Likewise, the Dirichlet distribution generalizes the\n", "Beta\n", "distribution over a vector with components in the unit interval. Recall\n", "that\n", "binomial distribution and the Beta distribution form a conjugate pair \n", "for\n", "Bayesian inference because with $p\\sim \\texttt{Beta} $,\n", "\n", "$$\n", "X\\vert p \\sim \\texttt{Binomial}(n,p)\n", "$$\n", "\n", " That is, the data conditioned on $p$, is binomial distributed.\n", "Analogously, the\n", "multinomial distribution and the Dirichlet distribution also\n", "form such a\n", "conjugate pair with multinomial parameter $p\\sim\n", "\\texttt{Dirichlet} $,\n", "\n", "$$\n", "X\\vert p \\sim \\texttt{multinomial}(n,p)\n", "$$\n", "\n", " For this reason, the Dirichlet-multinomial distribution is popular in\n", "machine\n", "learning text processing because non-zero probabilities can be assigned\n", "to words\n", "not specifically contained in specific documents, which helps\n", "generalization\n", "performance.\n", "\n", "\n", "## Negative Binomial Distribution\n", "\n", "\n", "The negative binomial\n", "distribution is used to characterize the number\n", "of trials until a specified\n", "number of failures ($r$) occurs. For\n", "example, suppose `1` indicates failure\n", "and `0` indicates success. Then\n", "the negative binomial distribution characterizes\n", "the probability of a\n", "`k=6` long sequence that has two (`r=2`) failures, with the\n", "sequence\n", "terminating in a failure (e.g., `001001`) with\n", "$\\mathbb{P}(1)=1/3$.\n", "The length of the sequence is `6`, so for the\n", "negative binomial distribution,\n", "$\\mathbb{P}(6-2)=\\frac{80}{729}$.\n", "\n", "The probability mass function is the\n", "following:\n", "\n", "$$\n", "\\mathbb{P}(k) = \\binom{n+k-1}{n-1} p^n (1-p)^k\n", "$$\n", "\n", " where $p$ is the probability of failure. The mean and\n", "variance of this\n", "distribution is the following:\n", "\n", "$$\n", "\\mathbb{E}(k) =\\frac{n (1-p)}{p}\n", "$$\n", "\n", "$$\n", "\\mathbb{V}(k) = \\frac{n (1-p)}{p^2}\n", "$$\n", "\n", " The following simulation shows an example\n", "sequence generated for the negative\n", "binomial distribution." ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "([1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 15)" ] }, "execution_count": 38, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import random\n", "n=2 # num of failures\n", "p=1/3 # prob of failure\n", "nc = 0 # counter\n", "seq= []\n", "while nc< n:\n", " v,=random.choices([0,1],[1-p,p])\n", " seq.append(v)\n", " nc += (v == 1)\n", "\n", "seq,len(seq)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Keep in mind that the negative binomial distribution characterizes \n", "the family\n", "of such sequences with the specified number of failures.\n", "\n", "## Negative\n", "Multinomial Distribution\n", "\n", "\n", "The discrete negative multinomial distribution is an\n", "extension of the negative\n", "binomial distribution to account for more than two\n", "possible outcomes. That is,\n", "there are other alteratives whose respective\n", "probabilities sum to one less the\n", "failure probability, $p_{f} = 1-\\sum_{k=1}^n\n", "p_i$. For example, a random\n", "sample from this distribution with parameters $n=2$\n", "(number of observed\n", "failures) and with $p_a= \\frac{1}{3}, p_b=\\frac{1}{2}$ means\n", "that the failure\n", "probability, $p_f=\\frac{1}{6}$. Thus, a sample from this\n", "distribution like\n", "$[ 2,9]$ means that `2` of the $a$ objects were observed in\n", "the\n", "sequence, `9` of the $b$ objects were observed, and there were two failure\n", "symbols (say, `F`) with one of them at the end of the sequence.\n", "\n", "The probability\n", "mass function is the following:\n", "\n", "$$\n", "\\mathbb{P}(\\mathbf{k})= (n)_{\\sum_{i=0}^m k_i} p_f^{n} \\prod_{i=1}^m\n", "\\frac{p_i^{k_i}}{k_i!}\n", "$$\n", "\n", " where $p_f$ is the probability of failure and the other $p_i$ terms\n", "are the\n", "probabilities of the other alternatives in the sequence. The \n", "$(a)_n$ notation\n", "is the rising factorial function (e.g., $a_3 = a (a+1)(a+2)$).\n", "The mean and\n", "variance of this distribution is the\n", "following:\n", "\n", "$$\n", "\\mathbb{E}(\\mathbf{k}) =\\frac{n}{p_f} \\mathbf{p}\n", "$$\n", "\n", "$$\n", "\\mathbb{V}(k) = \\frac{n}{p_f^2} \\mathbf{p} \\mathbf{p}^T +\n", "\\frac{n}{p_f}\\diag(\\mathbf{p})\n", "$$\n", "\n", " The following simulation shows the sequences generated for the\n", "negative\n", "multinomial distribution." ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Counter({'a': 3, 'b': 2, 'F': 2})\n" ] } ], "source": [ "import random\n", "from collections import Counter\n", "n=2 # num of failure items\n", "p=[1/3,1/2] # prob of other non-failure items\n", "items = ['a','b','F'] # F marks failure item\n", "nc = 0 # counter\n", "seq= []\n", "while nc< n:\n", " v,=random.choices(items,p+[1-sum(p)])\n", " seq.append(v)\n", " nc += (v == 'F')\n", "\n", "c=Counter(seq)\n", "print(c)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The values of the `Counter` dictionary above are the $\\mathbf{k}$ \n", "vectors in\n", "the probability mass function for the negative multinomial distribution.\n", "Importantly, these are not the probabilities of a particular sequence, but \n", "of a\n", "family of sequences with the same corresponding `Counter` values. \n", "The\n", "probability mass function implemented in Python is the following," ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [], "source": [ "from scipy.special import factorial\n", "import numpy as np\n", "def negative_multinom_pdf(p,n):\n", " assert len(n) == len(p)\n", " term = [i**j for i,j in zip(p,n)]\n", " num=np.prod(term)*(1-sum(p))*factorial(sum(n))\n", " den = np.prod([factorial(i) for i in n])\n", " return num/den" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Evaluating this with the prior `Counter` result," ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.015432098765432103" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "negative_multinom_pdf([1/3,1/2],[c['a'],c['b']])" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.7.3" } }, "nbformat": 4, "nbformat_minor": 2 }