{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Tutorials" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "0.4.2\n" ] } ], "source": [ "import os\n", "import sys\n", "import time\n", "import numpy as np\n", "from scipy import stats\n", "\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "import pyblip\n", "print(pyblip.__version__)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Introduction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In many applications, we can tell that a signal of interest exists but cannot perfectly \"localize\" it. For example, when regressing an outcome $Y$ on highly correlated covariates $(X_1, X_2)$, the data may suggest that *at least* one of $(X_1, X_2)$ influences $Y$, but it may be challenging to tell which of $(X_1, X_2)$ is important. Likewise, in genetic fine-mapping, biologists may have high confidence that a gene influences a disease without knowing precisely which genetic variants cause the disease. Similar problems arise in many settings with spatial or temporal structure, including change-point detection and astronomical point-source detection.\n", "\n", "*Bayesian Linear Programming* (BLiP) is a method which jointly detects as many signals as possible while localizing them as precisely as possible. BLiP can wrap on top of nearly any Bayesian model or algorithm, and it will return a set of regions which each contain at least one signal with high confidence. For example, in regression problems, BLiP might return the region $(X_1, X_2)$, which suggests that at least one of $(X_1, X_2)$ is an important variable. BLiP controls the false discovery rate while also making these regions as narrow as possible, meaning that (roughly speaking) it will perfectly localize signals whenever this is possible! See [Spector and Janson (2022)](https://arxiv.org/abs/2203.17208) for more details.\n", "\n", "``pyblip`` is an efficient python implementation of BLiP, which is designed so that BLiP can wrap on top of the Bayesian model in only one or two lines of code. Below, we give concrete examples of how to apply ``pyblip`` in three settings: variable selection, change-point detection, and point-source detection." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Variable selection" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1 Generating synthetic data" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below, we generate synthetic data of highly correlated covariates $X = (X_1, \\dots, X_p)$ and a response $Y$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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cgjWA0+2kwJFek95rRLBG4QQvIT4WM/V4/7qY3RZWJxfjWqwxQLxojb4vMynLJMId8TgMPYyRPjeIiccqGNHgLOnAUyZI6F9DCPEYB/gibcsD0iwhK0CE3JaY4BDvMSYjiyuDPNBDHRK3hdfjinkwZvNmliHbtmG4M4PJ2JxJ9bBN/x7iNjRDDv1x+RAwPM0dbrIhYMbXWj0VGALO5BAntDSJptelTNV5g8kMBKeBm5QxGw24XY0RhXZE6Fc9ImC9wjm4RoNVyryD10wbMFmpmXS7RoKPcEQBrtMgu5lZG4u49kgWLZ1uGz9kwqD7e+3klTJyNieRdO43gq9CbGaYBJ9OXOtatCcF/TWUvpc00YY4aejueZ0lN7cnw/UdTBa/Z92Ha6+Rj6LxU8A3i8i/Aj4V2I+K2ec1PmyYdwjhp1GJ8HMaYuxTZsPgHb7VC1XhEYeLv9PzwQcN1qBLsZRZemgjnNJnmH7jgvThyCy+mSno/3oDD8HwaCavGerG670mK085D/G1KauFCJFsvubabD8EgjH945tPJyxZg6PBkzDmuKomfY6Asf0qw/mgE5ehx7HTZ7sAlqD7CfigKwjiUjdl4enGQ0wMnHpDJ9gibOx/+u3jGUxL5v7cbS6nN85Vfw7ixPJsQ0Su/yoR3UbaZzgCBXBNEBcj+I3rIy5GjgR7iKuX6wwXIDMmZqz6ftk4ThuDUH9BiRBkmGbCRjb8LAc8/N1fIE8NyimgH3lfekzMcFxHAqcZAvozjWs/L43r3ADXigAleD1WwtHvZRM+2jhHiMEwJBI3atzIzFtEkt/6CRF5DPgbqBEcIYT/B42Dr0OtkpfAH74Rn/uCKFju3vOJdKs5ANuzkp27Xk7wjv1H3sn0k+/m6rKNcIjFxincZAW+a7CZoV61FGVG8CEGFb0RWxdwnedw3dH5wLIZspHc6IWjODVgTL9ET1g36P/GSL90tkbIrdC6wDjXC2Cc2x42mRYJo8sos7TUE1zw5EYwAUYxu07ZsvND9msjrCOuwUqOjcvFlMGl3wUp89b/q8xEHFz6QqO0K8psC7sBJbQRAvFx9bEZC1JGXDsNuUYiFh33Eehv/BS0hWGSufYGS1lXsLlm2L6LWZ3utw+BlEh5kaE4KbryMGI1g42wSnIwNkKcFOKknSbvAR8hcy2SIIGNZb74TgNX8Bgj4PW3hEAeOoJk/flyPvSwScgK8I5Va9jNdJuWVHAM5NkIgkNcS5YVuo12SZZXBBFMV2NNAU6vwQQJ9PsVPMF3SLtSHNt3A8YdfMyw5ehMH3w8luF1RwJhH6Clf/2R76dZgC3Ad1r8jM97m2M2JgAbg6hNE2rXQAnSrfX9AK7pISGDwneVOFbhmiDpXYSycqRdIcWWwj4m1p7i/RhSzSKuwJJ/9Y2K4TcyeIcQvupZng/An7hhHxjHCyJ4r/aepF3sY7KC1bqj3r9E8I7pLXdx4YFfgtf8AS68+9cxWcHV5b0cPvFgn31fqLQS37UO16z6ScAWFa33XL244OLhGufh8t6KvVXLE/tr/O2B84c1RWaoCtuzKzRLz3sGSeMC++uO3ZFjXncYIxzWelMsW8dulbO/1ps4t1qsvLxs4/sLZiOLkUDng7ZyCYHSaTBedYEy06w9hEBmhyw5ZCXNyiEeMhOO4OSk7WSwaj1lZlh3nsZ5Wm+ou5hh24JVo9hr59M2NIB3HiBsFIGUbRICZCbi5j70GHQbAtiMYHM6DK0b4AUXAp0LdCaw7gKFTbCJfr9lltF0gTzP8UH3I2HeiZUQQqDzEhkonsJaVq2n9YLzWuStMkvddRTW4rxn1QUKS48ngwb2DsiKCWsXyEzW3/CFLWii826WlbQuYL3DG11dGJPTdB4rCsOEEMgjIycDsDmFNTijcEnPNiHVNgymmNK0WqPYyiuWXcBIIDMFTRcoc71ee+ZHCpIR0gnp+b4wibJCxCD1QrNbk0Xs2io8IsJTWL+p+JkCPPTF1YSnh2LSwy7SrhRyQVcMTxmp0O8ayEfxGArF0m2B2BYvlsY52vi9rk2GC/r9ptqKy0a0PuhKOiu1ngIgeo1mtoAAG7wDWj/UPm5UCv6/GPP+sIwPOXiLyO1oi6tb0Anx+0MI37Px/LcA/xdw8tnMeLbP3EPX1Jis4Nh2yfbZFylE0qzIqimXLi2xZYXJilgssn3w9s5jrOlx8vS4yQtapxBL02nBMXgNuKvG9QwLayRm4Z7cGKxoZmpiBtA4r4yNmC1nMbNt3fWXjopP068QukidO6wdW6XFeWV9QLzhnf7u8dUNqDfBGSFoQJeNIJVFKtrVtCzfWB08/XfGxmsS80ZvLiH0OGXnI0YbKRciYBCkUepWVmZgDdnGx5WZITNCYRXfTmtfKyDBUdgMExw+Uu3Szdi4QG5g0QbGuYnHZyisocziTStQWs3UEwPGBYZ6QdyO9CsnodsIGD1jJfj+3g/xcdnIRn0YJqS0XYzps0Bvc1w0R0xwUPrdeY+1gvUtLuiOtSHCWYB3itl2QfpsPO2HsQHaFRiLRwZIzRht3OadBtYY8I9k474jyEjZL23dM4B6FknwQwUgwSY2QjQpY+/hGn1Pvw8p83Y1hID1SnPss3vX6LZDAN/10GP6vFI8TVCmVGJEGfRazk1k1eQFvhjjfGAUqZUmTpzO5D2F10gsFN+oiuXHwHg+mXcHfEsI4a0isgX8moj8bAjhgRjYvwBt8/TsO5FbvC90GYsG3uAdtqxYXn6c+dU13WrO8vITnL/wiSwvP0FWVri2oV0vNajXGli6GGBksc+86ehWcw7XncIBay10Xl40OA9X5g1V5AY3nacqLE3nmRYZi6brA/uydSxbj4+sinVuaZ3+Pxtl1DGQt16524e1U0qhESaFLisToyVxH1KelIp6CQ9PEEB4mkCcVs4u6NIUhmJQKmZKwuo3YKYUBNO1nyCTBBulVYfIBs87Pl9YoXOBUE40W8IcYeWkrL7Pwj09x7cDcvE0PtCJUGXCKk6maWgA13PngTpm7/PG9auGVDBbtXpeGzesJKwhwhxETF/BZV01DHzjYLI+kF+bwHVeVzbpXCbGiTQLpJghzRIbPIYptl0O30cM/lUxxQRHMBlVpu/P8UimsIshEDrIROEssbnyx2PxUSEli/UDDVacwichK3VlsNwjZGXPEQ82HzJ4m0M5IXS5FpVTZpmKnDZXlorvlOsuBrPeJ+Tj4fOzAqkXNM6Tp4BuMhYhZ5wJyy5QFFvkvmHtharcwpmc1gfKMtdrwMCqC9Sdrks2rwe9RoTGKwQyFhOvOY8RSxeDtHU1mc2wrsaKoTCWUWZuGNMEQOxHf+b9ISssQwjnQghvjX8fAu9kUFF+N2qB+ZzWOCZS/yQFn43ipRiL1zU+5dYxLj62j+8aunqFa1aIsX3gds0K3zb4tiF4Rx4zcg1M9MXMwho2CGQ0naeJn6GFvSEbc/3NHvqKd8JrNRvYZKFo4EvMk9zq861X6qDCI0kko393Ead3G493Eb5w8fF+yekTvS8JbqTPFlNfOxgCdDDZU75g2cz44Mh5OPL9xtemOcQDdA3i2j5ztkbIZJg0rBGUHzPUDazoh23yc43oZxuGY0yTgTJiOPJ6iUXNhMM/JfBGAVKIReT07fVZ9saGrn0s4febY3OZDwP2TaRCSrj+qgsxShcMQRH5jaX5Rv7bc6MHkU7og2xPEfSeYDP930emibGajUPMfsNTMPAe43etsj9cq4+5VhksXYO0K0y70v2NjBdplki9QFyjdYbIipF2rSwm3/XfN0EhRiK+bUQnsVQU1+Mdrtk0XCyIW4lUVJPpOY4F8CQeCybT1Wk8LyG+t/VHCEjPaxhjn/PPC3XcEHm8iNyF9hL8VRH5UuDx2J/wOY0UnJ+yXWNZ72kDlvX+JVzbcPrO3b5YabKCdrFP8I5uPcd1Da7RoN6u57TO0zUrVrFQ6TpP6z2r1hEC1DFou4gzpx8YAnodsWTQ17cuMG86XIBV62i9j5m5/iwaz7zRvw9rhycMBT1CxIo1w00XerpOB+pbfP21wYfhf72Yhws+BZvOB5r4uPiOdSz2tF4DW3of0GPcCd9O+5HYOQl/71w8L0YLSOm1zge6frJR/DzdYC7ili6gmWMY8HHnQ39zp+P2kdXST5IRSuo2vhMbJ83cHM2cM3uU/5uOKZ3bzd+BgQbpg2K4WicbNrCZfWOU9x0y5VrnRlSRGbNezYQ1+/QIzqrwpHYB8a7/ftL32a+oIgyjYhfbF+2CSHxsKDaGRHE8Qv9LBxvvHe+GLHtzctkQ6Rwp3kKPnW9ORj1nfIP5YkW3b0WvqXTOkojIioBrIx1UKa9W9HeisppYXLcivW5AfKcQW/BkG88jRuExY/t9EIbV0M2h43kH79gt5SeAP4Oukv8qz8EsXkT+mIi8RUTesv/Az6THaDp/pJhgixHOqXAHYP/ysse3UwCHpxYgxFjyCIpaI302ndgY6R6y5ukvh2tx5PR3viGf72GHiCenrNtK5H5fc7lZEzP1+Hd6b8KYhQHL7R/vtx+FJQzCFBuz2HRMCepIwSw30rNYsv6mkv7z0mvzPpumz6yzjbqAEdGCl+/64+tXHOkzZDgms7Hf+p7I+2UIlAm6SdtI59ggPf87fQ5oZp0y7yMBdmOYfpvxOkjnPWaMwzbjazaocmbjvD3lsnCaofpNZgf0v62gvPcYYDIjRwJPv28b9D5JmPtGAA2Ba4KvvqYPsP6aAJzedC2z5NnGBiMlbFIHn25sbjcJl66hHKaJKtUZ0iTuj/wcha26uKrxSExCEnzIkYkoxPfcoMS7X90/l58X6nhebBNRRv5PAP8ihPBvReQVwN3A2+INehvwVhH5lBDCZtPZIwrL73jDe8P+smU6yrhjd8zLz8761x2uX8qdJ8b81qfeTpEZXnZ2m7e8cuhle8/JKdNRxrvOHXJmNuLCYa24dZlx7+6Yr/q638mn33OM3Srjj/+eT+C1d+5yalKwW1o+78UnKWOk9CGQW8W3z0xLDncqrAjHKssnn51xelpwalIwKSyHtQaw3Biq3DAbZT3NbloY7twZsW7V92RWqoS+sMLOyLJsPWUmjHNDm1gUDAW3PBZ3DKpI9HqeySLunILzVmkZuRWzctRnqLNSWTMnKqvVet8yK5WmlzLZ+M2R2SiLl9DL9dPNUVplwhiBaa7y+8IK+BHB5j1klIbzgVmp59G1gSKPwZYYuIJus3YqF7cCWzElW3SKNXde/VMa5xkZxU4m+fBZIiDekVWW2gV2RvbIMbUmDAIngSJ02Dw/ygpxwoQoavFelYiUCv0IHDSOaaHWCH2QX1zG7kww9SGy2sOM7+6ZGSEqCwGKYkzISsSprYEmDKGfKMU7pQ9ucKgliW1SRh2ZLxZoRrvqlWILnMnJqDXbz0ckZaRyykVhqfUBIR+BdErfsx0hHymbZUOKL65Tqp/NaIotMjxrL4xzT8hHSLPUgJtXynwJntoFctHVxNwbdm3OovVsC3ixCmtlJRPgjm1l5CQ1ZBFnw1y0GJm7mlk50iC9bhiXU/BOs0hRzN+bXBlL0XOGLtUjjmozns94IQfl5zqeD9tEgH8CvDOE8F0AIYS3s9GRXEQ+ALzm2dgm//FNj9FFat7nvupW/ttbHlNxTec5uLzktvuP8/63P4rJCh565a28580PAcoseed9t/GbP/VjfMIX/T4e+sWfwxYj8smMYjzj93/Srfzbf/trPPl5n8AnnX4J//Rn38v4dS/hLQ/vcdfOmP/+7ovsjHOqwrJqHLOxUsX2Vi1X14rtLlvHI/trHjvIOXeo+N+szLECa+e5d3fMI/uqjrMCrzi9xYOXl6xax/FxAdsjss5zsHY0LuAJVF6FB1fXjnE+CGz0Qvd0LuBzw37t+4Rn3nhGVnnXAG7tmJUjLi8dZabZ9MVlx1ZhuRKpi1s7FY9ebRhZ0392HvH/9PeiUTZNZqGLMWRaGBaxMOgJTHOddKYjg89K6taTciCJf+2vdD9CCBw2A6vDGtgpMg5rNeGqvRa0lpELVuWGw9rR+sDeWllAjzaOW8YZe7VjZLXoNc1Nb751vLIc1no+C6sF1cNGJ0X9HoQ8TgSZEaUlApktejZDKvxm7YpgMrxYZrbjoBUmeVJygp9oxzM/3lX5ehO04JdXGkRj8F5LQWnUB6SOhddZqedN0DrLvHFImfWrL28Ub1dlr1O4AMDm5L7ps8515xkXE+U52xwX1a3BWMQ7OgxmegrrW4VxTIZk5cBIadeQjyIVccjQkyFUlUypIh5eTk9imoXWDoyhjBLbKjNMuzXSrtkaFUjTYZ2abJlmwRUq9mvH6UnOqvNxMo62DvFez7KSvbVjlAl5NlLmSVeroMwYLDrRgWDW+yCGotiKFFZ56oroQxxinjfo8BEfzyfz/kzga4G3i8hvxMf+alRWflCja13vErgppCnKjGZxSJafol3sY4uKsrC4ZkXwDjG2D9wP/Ocf55aXfzbz8++n3te54qG9JfX8Co+fX3BYO9bLhgfOHfDY3hJrYF53NM6zVWb9564aR5EZLh7UVIXl1We2ufR4zYlxjvOBwiptMPHAB1Mq3eeLi4ZVfG6/7riVQOcUtvEY1q2KHladFjGtMT2+3HpRXnNQif46Mla6yKwANewB6Ixm8mvnyYzp8cJRNLuyMZAkYyxrAK+Bzknizg7yfNDXKI6uN9w4NyzbAfM3tXLoM1v1vHjQzLvM1BhrDRRGNgqMyq4o7IjG6cpklAk+qnPW0XavsKYvuE7jiqPKVBiSIUwL5VYvIoSTMjoN3oatIkEm8QaPr0lBWgSkUdEMBMR1Uc7eIFkLmeKrVaZZuvgOTE6wObmggbBbU9gSaQ4Hil0MsKMCAgWj0GByhfKMa6kyZYNY3zLOLaX4XqxkoC9ORs4grWTkCbsGcA3jYqI4cz2HfKQBrqt7VWYRaYHSLLUwaVUAA/R4d6gz5Yt7RxhtAZpdm3alTBWvgd5PjrPsAtNigp8cx6z2lLqXsHBjCcWENkARRTQeQXrfl1g/8XpN153qELrIXlrEhYfzAfENtYxwVrntFlh4ZZYs245Zplh/6wJ5NtBKbw4dH3LwDiH8Is9SPwgh3PVctnV4ZUUTBTBP3rbN3vn5EMwvP86lJ06xuPgoYiwXzt3G/uPvIUSl2uTk7Vx+9AKj2UmWlx+nWR4QnMOu5uTG9KIdFwJd45mOsp4dARo0Eq6bfqrcUmSmx3qTK+EmLpv8UGAI3Jk1bBUZe1lL3UVFJYPfiSGyUExyCDRRVUjPg51E+9ZRNryuzAxFhExGPY5P/39hTXQdHFSXIjCii1Q6XcJ2CceWdOxC6we3w8SRzoziyslrJS1Z6Zy6AuYV3QZO3QlqBWsE444yS3p8m+vDsZtS+v4xoqIyKEiezLmSAlPFSDoBKbfb90XYHm+Pmfemt0Yhhjbi7tbqZGxsFguqAbE5Lk6SJlLgsmZBOyoou4aQFdTOE4pi8ASJmHWyXfVZiY/bCFGkIqDUwA0W0xHxTI+j63eYCoE6YWxAK/3r4rmKn69yc8BmiHcEm4HTx3pV63Uw7d6NMOHKUQhkp1vq0dIsEKc0Wxs6vGTK/3Ytkg2hQ2I9wcpR8gsM90xh9ZoqrESIUDHzTZWwD7qSMkGLo8mOIXBUUXsjxsc1bHIjR1FlmMxgM+HYtKQc5f1ztqyopgXZaIItK0bjgnK6e8TfZH1wEYDV3vk+K7d5gQ+Bbr3ARaGNc55V41g2TlkjERoBZY6k59Lfzqu6ctUoz3u+VrpUmZmeNeIDHDbqTGgjzbDuPOtklhUClkjpixdf4wJVNmTeoBmvCD1/ed0NrBBlvISNC39gTyjXWd3ZahdiUIvQiimoXUPWM0cGnnh6jWbVpvfz1uWpvn7RehIRqHGhZ0W0G+wUGDKt1g0sklRUlJhRJnFSopOlm7yIUFBinVijx7jJiumvBaMUs8xIvzrYxFUhFXl18sri5Ntj9Mb20nfxDmtsX4RFMiTSLY0xffEXq86JIR9FMyl6JkbvTSJGWSJYTGTdCIAZqIlZYtlkFrOx3Om3EaTPYq2x0RtFceg2QGFzxbhtoVhwog5uGjWJ0Sx6M1hvuPYB9G6BEn1Y2pi1uza6IhY9EyREfD7ojaY6jEB0A4z4vbcRvulwUvSFcFWVykAd3Cgyb/4t15nRvVig6ydIa4uBkvhcC7LPMm4GbyD2q3wLSg/8EhH5PODvoSSIOfD6EMKDz7gTyUQ/Zr35yEZ1cCArKrLcklVTsqIiLy3FZIbrGiTyMG00q7erOb6b4ruG+vCKQg71CmvNEb6pNcJh0/V/p7FJE0zNBuroSmgF5uuO2TjHR651E58DDVxYxSfXzuN9YI3vaXDOQ9NpcJ8Y05tEiSjW7HwgmMH8ari4ByhgYHNIz30urBxhh+RGGzq0PmCCi9ADuHgjjawGQHHJwXAoLqkkPH4ncQdk43OTt0g6YzbuQ4ofWmh9Kq0r2KKnF7iN7SfTK1VEhp4Zk/xgdEUwfD+Jm167ayTX4Sh10BKQ6zETXAsm7xkfIaD0x8QK8R2ZSRmrA2Lg69/fYGSknh7pPMSsNTVtUPqbbsOjQSwdwWbgCfFci6DBE44EXAlRrLOhkAwRt1ZIx/avJVm4wkAxTPt2DSvmCN0whCHQx0wYm/dc67SaGPZf3x/EqOgonasQegdLxfM3GUfDMfswXBM+EGsGCrD1LJONwB7yiiCGptVM/drJ/PmMm8Fbx59GBTrb8f/vA740hPBOEfn/AX8deP0zbeAfvP41PQwxKSxf8+rbaH3iVL+G2Sjjyu/5BOrO8dKTUx78ghf1mOuFec39xyc8tLdkVmY9/zo3wuu/4Vv5M9/2LfzA9/4E7Vd+Itu7FW979CrHpyW3TMqBQxy/xyJic/vLljLCJvfujvnl91/h+Ljg5HbJpMgoM8vZcc7jB+s+cCba4IVF03fnAbi0bCOzxFM7/f/EOGe/dqw7zWDmTaeNI7zHxeYOq1ZYNA6XqfHTovFc9VGqbwxbpaGs9/GM1W8jpKYNBhecfk41wgfPvAlU+WBu5XzoMUgrilWDnobUsCIlhyYo9t3UjlDNaCWLjBnT+5J0cSJKUAaxQJgUj3Wtr5sWhisrDYYpiN9eefbJmBZahAT6jkOg0E0bFXof2G+Y5KbHyVedJwShcWoIdnXtepxbRJWcPfwClFnFqlFmg4jgguN4s6Ib7eok3nkcSRka96Gc4XxgYbcprFB2nlU2GyT3m7RM3zH3NjaZgG1WtLaKvjVajzDBKc4s2rxBulahj9jcIl/t46YnCUWmrBYx5F67Apl6AXkZ4YT4oTFjJmQDLg2ESlWhwVSEfKwTTgy2iSVjFpcJlTK72q3TWKddcnKJ7w+ekI0iTdQptTHh6/VhZNe0vUw/LyvuqjzSLnSlEAwFLW2myZURwbZLJvmIwhpo1KStjqwc61tyYOUs08KwRtRsDl111s9idvjxNp4vVfA24IuBbwf+XHw4MATyGfDEs23nb/ynd/YZ7Fe85jZ+/E2Pqitg7dg7P+fOFx3nod+6gMkMn/Gpt/OLv/Rwb9/ZrFaMZ1MWe/sAuHqlqsqi4vO/8Y/wj//Bv6baPQ3Aw297gFOnP4UHH93n/KLm/MUl83VHkRlWjWPVdCwbx/FpyeV5zbiwvP/qiguHNU/Oa9517pDjEw3i80a7+ty1O+agVjilsIbT05J53W20RtMgltgVpTXaJSQz7K+73plw3WmHnkoM3sdMIxZospiRjyJcA57DGk7s7LBarjFo8Fp1nkXrWXfqeFiJ44lOi4m9lNxKjykDvaTZivSMlE2OeOsH9oiZX6IYbUE+iRaoui0jkQ1TCBBXCQwCjSpT9sraBXZHdgMmgbVkeHSlkzLTw8ZxepKxXnvaGHxzq+21DmvHdmni9aIFxkQRnBbDKsKIkBdDdiUCpqvJi1KDewh4DKxNZHZE+p2nX6JjhAyFGCa5IWvmHLoRld/vBS5AdOUbQ/CUWRYbZaAwUxi8xtddIM9NzwjxSPQGV+jGZyWMtnsKoWzg6b0cPsEd6bONjYE7Hxz7xGBW+/12We0P9MLgISt1xTHa6h0MM9cg60MQwyLbZnu1j5+ewMwv0W5XWJv3jSKkWeDLLUyz0Ozb5kg047pUW26ZjFh3npE1tKhasrQR6spK2g6sCWSuIcgUNQLTSSUYSxavud0igFFKbReFXTcqX/5YkMfLtX67H9SbRX4c+D+BLeDPR9jktcBPAivgAPi0EMLBM23nwYuH/U6cqCxX1q7P6FJ22sYgM8m1R6PysvWmGGVKN5sU6kRnDVGWHvHnzvO7v/Iv803f+mf58lee4ZH9NZ9224xff/KQWZn1Fq+pUcNulTNvHEbg7p0R77q05MxW2QfbwR5WrWU35fSpr6QRoYpZdGJtVJkG2GlujiwBkxFUHQMtwO1jeGSh0Ma0MMwb30MbyZP7uKy4QoVhoFHJRlDetmrJmfjbqRdlCIFVp/uVWCxGBuhhWuj+bvkldT4hF2gDjA6e0IBUThVOcJ0u08Xgqh3s6qpS6NLSfHM57h2tVd5ugF5xuep0gnKBeIPH3oURX084bLJy9ZELnIIfxLqCRLodDIKWhO1G5z0zv4Qf7/bPS7OknZ4iqw+0hdlqH1/N+kwSk7G0Y8ZuySqb9JNZpLRrMIsTwUHjmVltQzaXEWWsT6TvJER5d1KHJsircQqrjOK1ks5LFkX+Zr1PVx3rqYQQ+eEpUMdJxCz3+ixaT8pgTLVZrEwF0CBGPVCg531LvSCUE/xohp1f1F6Yh+fpjt9D/uQ76U7eq4XMxeWeuZKwd+lq1jt3sGw9O26fUG71cI6ZX6LevjVa7prB2dB3OJNzadUxyQ1To9drmRmurLQfqw+BeeuZ5IaDWu/t07PJ8wa+T37p33vOge/iv/8LNwZov8Hj+fC8vwS4EEL4NRH5nI2n/izwuhDCr4rIXwC+C/gj13l/38PyM/7IX+P+z/1yAD73xSf5b+88j/Pqv/3kk3Ne+aIT/Po7LwDw2k+6lTe+9fGejeI6T1nlrJcNwUPXuB4/296teOyd78d3Dd/0rX+W7/u27+atX/21XDk357u+8VP5Wz/y68yOj7GZ0NSO8bSgax27sxGHyxYxwjf99nv4vv/xPn7XK07zxndf5NT2iOOTgiIzXF22vPrOHd726H7vu/2KszPeff4QUBjmvhMTqtyyt26ZFhmr1vHyU1u03nNp2TIrM/aiYZYR4cQ4j0yVEe+8NGdaWE5OCp44qPsbfJQZpkXGzrEpHzi/ZGeUMc5Nz7G9sNDM/2UnKx6/2vRFysIKq1iEXDtP1epkkmTNqZB4da1Z0oEtqdctW4XlsHHca3N8OWWdqF0ySOub2jHKt6NXhRacfcSoSyPq69wNrdzSRDHKhEWrE3OCQy52OScqy96iY5RluMaxVWbUrWfVdeyMMuomWcJKxOfVAEn/tmzl0YtcBGyGDzAa7x5pMCzFhPzgHH68q5lpVmhTYjHgNEOugiNkZb+s32sMozwW0tLF7FrKrAIMbVbQNMp+2SkMh20AQjxO37tZpprAtdzl1LQ4cbgxmdZMMJTNQkVSUbzifIheI55u56y2L4uB0SS823t6t5esUL+UbDRI5cUQyinSLjWLdx2LLrCNcspDPqYLICfv1XPjHX56EmBgy8SOPsmgzFe7rF1glGfagHn7VmoXcCajFFh5QTxUq32YnODkOBaLyRhB9M8xvTGVwZAL/Sr05tDxfHnev0dEXgeMgG0R+U/AS0IIvxpf82PAf7nemzcVlj/1wJMhUehu3S5V3BLHk4drTm+N+G137gLwilumvPi0Br/cGB66MOcVZ2c8cO6AqXbn7b1M3vboVV5632t47yNX+fJXnuGtX/21/Oq//Of83j/9x6md5677jnF8Wsb3dJzdHTOvO3aqnMO6Y6vM2K1yXn3nLndG5edsnFNkhpOTksf3V5wYF9x5Qp3ZisywW+Wc3a00yFpDZg25NYxz5a8C1M5RWtsXM5Msu8z0denxxN1exOMpY2Pj0mqTAlvPmRQ5VdxuyvR3RpYyE9adduxOdDUXdGVQd4HMJGvWKPUX6X28FVfWbuxFpC2GYIiu1tGvW+GFLMILk2iqVHsNQCkr1hWFZk6rzg+ZZSxYJhtZFz1LlK5pEJG+G3xqRmFzg0dXIOPckBmteyRxTOK4a5OHozxvXaTlfeAGzWBDrswNZ0ZkYRBFYSxeLPsN7IwsFxedcvwNzEMeIa0k1bfgA43N+kJrlRnE1UyLsocEt0sNQunc9OdP7wgN6LFomtqiJd+PLrBRWNUsXBkfrXqkbOSRilUrHt0H8OhLI8GrJ0vwSLPoM+RQbhGylpBX+Dbgx7usyRhNT7BsPYXNaVvPJB/3ytE0Vp2nzItoHyxxwtJjSrUNK6n/qk7WEBgVY+aN6x0tM6OOg87reTarfYLNcGaGWVxGimNHmEXPZ3xcFyxDCH8F+CsAMfP+88CXAU+KyItCCO8BfidazHzGkWTnTcykbtsujzx/986Q6d2xXfb4sRE4s1UyK7XgdazKOYyBbpwbXnvPcZato37ZLZzdLvmTv+vF/J3f//f4wN6Kl56Y8CWfeCs/8F/ezWs/6VZ2Tk6YrzVwT0dZr7a8datkNs65bbvk3M6IW6YleytttnB2VrHuPCcnZT+ZnInPt95zYlxQRh75KCuUGigwKzUzncXJIXWnTxzraaFy+91K5eE7o+wIa6UVz7axqraL1LvNBsfz1tE5DdRPLjqqTOi8npN5s2FCdIS2F/qsJr1Ga3iRKeMDfrJLG2BRuyM3L0BpM1atBuC10+3BABE0boCNrBHmjSezQzExeausnWastR+saY2AdTXeFGwXlqyZE2xOlmnDXtPMKYuJ+kNHdkhXTPV1SXHYrpBujS1VoJKW/PbCQ4TtU5i8wiyu6HGv9lU1KIasuoXs4EmOT2/pIZ4qNISiPALlgO5jawrGuWLyWVcjRkU3jWQUocOJSsuN6Epjs96Qron9tadxNvL3C+qVI7NCYVToFDpt0KHqTkMRfcqNWFpvY4aa4aQg2PERJz5nykigMeyWW9EESyGoloxChK0c2qBZsqwO2XXRLrZZwVrIQyDkpUrtvSOPBU0zO8vIOOziktrPtspVD9mI1laM3YJaJsxKo9L/ADOpWcmIcWmx9RxXTjHNUrn3mSZsW2JARkwLc/1GER/CeCG7BT7XcUN53rHx8B8FfkJEPLAHfMOzve99V9QfufWB19w64+3nYzccgccP1sybjg9cWVLEjjHv31vSdJ4iM1yZN0xHGfN117sCdj7QdJ5xYXn48oKry5bx59zL9/7se7jjlim/8suP0qxWzJ98P2It7/2FN+KaNbYY4buWycnbWV5+gnyyDd/8ZXzvP/xJfumLP5vf/IV3MrvlFFlhGW+X7J2f87JPPM273qGQjskMX/Tau/i5t6jcf+fkhHvPbFNkhv2lWtNeXbZ81SffziNXV+wvW05ulzx8adnzx++/Zcph3fGSE1N+9ZE9TsbJ6cl53dMat8qMs1sjbt/a4oELl7l9VmENXFl1fMqtU0Dl786H6H+tSkwXBh+R1PeycyoutBs0QfXcVp63UiI1CLdh4KHXXehhEx8SZKEZ/CaPe3N7szKwX/u+MApw96zg4rJjnBsOG9dj/6AZXcqEbxmrgGbeODJTYYG6VnbJOJ8wX3uM5FhRL5cqBJZ2jCCKGtiKkRgaiSItq/7T42O34yfH1T/EZvjRTPFclOKYu4DbuoVVq4nFYe2wozI2uYmWuwmr9o5cOuat1dVJXtExUBFXwSJxMhIG2qcRmESbBC18C4W1PUzQRZ/4Y+aQerTLKiYvGrpjnSNi6nof6bYLqy3kzHofX2713HQTxTnelph2rc6A9VyDclHhqh2K1RVCpj4qfryrWfpoS2X0rlOFqs1UOpMVSLvmoFG3zmPllJUZkUWPGyMRrrNjJNayagq2wpJDM6aM3H6bT3Au0DDCtYFdUR+aVbBkxYT92lEYYfRsAeU5jI/rzHtzhBB+Hvj5+Pe/A/7dB7UTVkUixnk8WkhzQYs40zJjVmbMYoY6zi3bZYaLyEoz8uyOiz6Yuxi4rVFl5DLK3c9ujTixW3Fya8RoUnDb/cd5sG1YH1ykWRxg84KtM/exvPw4O7fdgesayukxzZq3T2pw3dohH1msNWS5IS8ztkY5+ShmXtZQZIYst4gRsqTUjGrEqsi4PG9YO1V6nru67s9BmnjaDSHLZsNkINIA9bFl6+iCYte18+RBqDunFLlWVwGNC9TO4YKeF4Nmt60PyIaXSQjgGLjPIgYXlIa3OVJRd9ivCFGgWX3tfF/0TW/VICWIaHDRRYb0gSZlhWk5vOnCuMkRTq+/1hTLh4H6mDq2W5IT4TVZmsiRSQrA1IeEcoqVVqXyXT2wPVxLlZVIUzMpprgQqHJzxLUxjVwCOFVV2pD8vLVfp6T9Mfp3F493U6iSencmtW3rtVO6C+ncGEI20UnCqONibmLAj+c7Te7JT/wpWWpQiy79UEPdeUZZSRNKRs2SkCnd0LhWA7ex4CPcEm1pBVTB6X0/GZCOlaiVyHOVyUeWSRMTBxPUNXSrMMxbhXbaTovotRrjR+fIeL4CPatGrWftDfM2+VgYLwiFZd15OtFA5PxgWtQ5z5VFw6lJwZWFdr05MS7YW7V9ALky1xstqR/rzh8JehcP11yeN+zXLZf2VmyNcpYHa9Y7I5aXH2e1d169wBvb/z+/dJb13nlcrV7gq70nWTUvZrV3gaI6G4O3pVm1HK5b6shdznLtxNPWHV3r6VrHfN1SZJZlVGzWEdZJPuLNxv521wTrJnqJu0A/IWkLqaNS5wQtbHpHK0uHOBkQ2TqDZ3cIQ3YOps9wQyDKzwNlzKgTfJLaol07EjMoPZXYJJv7l+LIYBsajgTq3vM6uqJsKlINqdvQ9a+fVCyGIZP11wYu6F37Eu59JBCktmAbQpkgRr1GpD3igV5xdBLxUW2TxcYBSTyUB1Vu9q/hqL946wcVatpbQzhynAqFRbVp0JnAxwDvrjnEa5ljQbSx8tFjEiT+nxlVSeaRkSMARimLxjUECm3AkalJliRXwsQmSg0kQKX2uXqr4xrthCP0NRET7R0yk5pvK9SSG63xCDoJdXEyaj3XWAhot52bCsthPC+q4I0a9cGVkL4o6dY66wPSrfHVrjqcRRe3JBJIX+rSCeNMWETqW7IJbV3oMcp1lJZ3LrAVnd60zZbv6VkwYKwuwENXVsybjled2eIdFxacmhQsW7X1nI0ydeYLgRPjjEvLru+aMylMlL3rRZboZSNresn87Vt5/OyYsUYNuvSqQt2fa4NgspM10ItkgJ5iBdqxex3n5E2OsY2ZmXFa4DJuUPAlV73UgmtNRimeOpge27auZi1Fb7faxqCkk0HoOd+bBbk0kvNc3yXdZCwi7DJZXsBPjiPtimU27WliIag5VxLpJFOiBBW4MOhU0jnuXOgDeaLhJRVo+n43mS5GYKs7oBvtkNUHXJEJk9woNm3UTvbSyrEzshw2sfjrA5U4vM3VRyQGgXpjclUV6zXnwLd6XmNxFehFRGnkBvZrH6Eg04vIDhqdiAsjfZaejj+EgYGR2vEJ9HbCqSlCmih8GOiKo1iDSAVhF9SWYds6DpylyoQ8dHqsIRyxs9X7U+GXkJXgVIyTh643xwpiMO2KpR333vCHEeoqrLJJfFYO3ZO6msZon9oqNMpdB1KD5CRkKqez5x3Bb/2D3/ecA98TP/ZNL8h8//lQBV+MsknSuAdtwnAW+N2oC+RDwB8OIVx9pm396weXvcXqJ5+d8RsfOOzZFo9cfYx7jk9478UrVIXlRSemvOfSvM9Er8wbZuO8z8CBPvsuMsPje0suzxv+6he+mG/7Dw9w+8kJb/rVxwC4/IF30S4OaBb7AJRbuzSLA3bueClXH3knxWSbP/anv4rv/54f5TVf9oW84w2/xuzWOzGZYboz4uqFBS971Rne+Ta1Ks9yy+e/9i7e+JbHaGvH8TNTTh8fUxUZV5cNZWa4dFDzdZ95F+cO1py7uubMzoiHLy+VpZAZXnx6i0XT8dKTU37p/Vc4uV1yrCp4fH/VG2RNiowzWyWff/cO/+aBi5zdHpEb4dKy4dNum3Fl3dB0gfuOlfzm+SXHxzmr1lNEs6vG1b0hljIHHNa4PqhVWceyDYxz32PZtRNOTwKLLnCpBRe6HvO+dv7f7B6k27OsupZZadmvA63X/QN48fFbeOywZauYcOWwxYr2uXRBXRn1WoOTY+0/maxxQYuohVGF6LwLPWSSGtamzLo34vIN3hT9hNQ4j1ntY/MKX0w4ttzD57vgWmyk0W2VGXlIHes1IbBFFs2nDCauOKwRCq+cdPUo1wa8Leoa2aL7X3vp1a1ppKDaejheWeatZxWNzcrMUHnd11N2zdKOWTu9cVPQG1mFoYoN4UlKAowIWX1AV2732X9iuNQ+MDVauDUHV8iNpSzGeDNh1uwTUJ69yas+UG+yYEJWaCbuGqStmY9KQjAcM4rvWxFsMUXiajpZObgAi9YzCy1znzOJCYw1Rb9qOQgF29GG4IAR28Zy2AZyk3OUzvChjdTE5aN5PB+2ybuBTwKSv8njKNb9YuCvxOLl30EZKX/pmbZlBarc9svAgX0Bu+OCY1XOLVslZWbJjfTsDlB63s5I6XsJ805wxP6y5fRMmSrj3LKzVXJmVnHszBbGCE193+A62KyoD68w3TrGpfe8mVte/tmsDy7ySbfNmN5yN/ecmvLYbXcxOz7GZIbtnRHBB05tj3g8UgWtNdx2rGL7WEVTO86enHBya8S4UOy7imrKPOLxW6OMqrBslfo1VIVVgyszuBkmC9rkdpiOZZxbGud7Oh0MHX6muWHfO0rxbJWaQRkxPaUwM5od6tJ9uMlTJjctDEZ8dD4kusERLQNSsTPEHpia3e3X6qOS8NrN4D2OUsutmLm6AI3VYNt5XRWNMmGaq4PctLAxwOkEHYIWPRNWPsn1fKy76L6Ip80Hd0TtuejIU2/UmDHK6pBRNYNWVxiVzXU10CwgsVWS3Nzre/NyG2lqxuUU8Y5ypKyII51nEoWvWyNdzaTc0u5B88vIKIqNU0sv71SAZLI+G1W1Z5TON3Nmo+2ewy2uoRwVHLaCrA6pKkNR6PWWKKB56CjywcwNYibr2r7zju3WWJS7bdZRh1DtQKsCJj89oTazYrQOEAVSRwyugvbVTHa6/Qo4qj5zI0ylRdqGyuZIG10LiyllDhIci6CUWUOAVcN0PMXWc2xWgtN9ccnlcb0GMVRlhdQrJqPySIPmj/dxozDvzwMeCiE8DDy88fivAL/vuWygd8LzgS7ivFZgb9lwpcq5tGgoMsOpScHFRd17m+wv9cu8eFBTZKbHkJOP8MXDNYfrjnnjOFy2HNYdB5eWmMywuvw47WpOuzwgeEcx3WW9d55bXv7ZnH/HG7FFxf983xWuvO9tPPD+e7jw7rexuvU+iqpifnXN4ZU5Dx0fc+Wc3gzGGh6+tOTK+QVd63jEGg7XHePCcnXZUmSGg8Oa1gdWjeNq7B50ddWq1wNqxtXT/zrtt1nG49r3bZ99H9baGX6/7tit8rjk9XHprZnn2qvv+CiydECX2HW30eDYD/ayaaiU3VPEqqONDJW6U9ghydvT8EGX9bXbMFFigHyaWOjcr1Ui37jQQz52ktE4ZcUso1hn3jg6nyYBfZ02ekh+5lpQdXGfVIHqIlddFaiajSbnQVWZTooxazJstDOtXWAWvDZXMJmyKYyNLAtRpkPnmeTaZCA3wrp2TGLH9YQ9p1HlQmuKSJm0jLZuofYDfKVGXJau0/qDqoEH3rkBxsUWh8q1jHBGznzlaHxge3JMOeaNO2K0Nsosbedig+vQM1Yyk4HAyKq61QX9YvLRjt5zLlBmSnmUWqXxYjLcaFvpenmlvuBHHAqHAmIwUS0ZsW8f4CDkzExLIxk+U5hIayhCbjRBS3z/mcmYN54im9D5QGmjtUCk1OYRPq1dIM9G0RY4uyGZ98cC5n2jgvdXAj96nce/gaPQynWHMU+t3qf/NzuVb/6k55LvdlXY/rkEqSSGxzJK3cUIW2VGUWVkhboR+g1rWbEWW4xYH1zEFhWuWR1xHbzeSB4r3gd17Hya16cVgfdarOuLkWmlgMd20isWfRiKma3Tv6tCC6JVL+QhOhxC6zboY09TsBvcAyPrwwvWcqR450Ns0hAZMiH+H2SQ5udxH1NASgXGJDZKKygh9I0Tmt7FMDEirvm8GHS14KhMEf3OhtcmbDeP+54YFqlHZ8J3hwJm6B0ZJYDEoJCy3a6faULvnx0vBojrisJmSNDCWlqJFNZc9/wSTGykG4uB7Yo8H0OU0TdOnwscta5NuLcRlcX31/vGdS9pshNw6O6lXUiPOXhKQc8IveNgwv9NrAKo9WvMZKOp1SaVUFw7SOzTeTHRe+I6/uA6UQIRyxfUyEqkoLCpEBlXCwboOqwd/LxTcdO7qDnww/ERnnpsH+/jRljCFsDvIQp2Nh7/aygr6l88zft6efzf+r++h6/5+j9MAG6dZGyXtlcEzpspo8xwx6xS6GNkuWVa9O5386Zjf93x6jPbXFl1PQRQxxZlv3VxzqzMuHtnxDf99nvYrXLuPTVlnFse/LQ7KDLDPLYNS3zxV9y6zf983xWsEb7v276bP/Nt38KLbpnyHQ/v8YWfdx+NGwqSdx4f89jtO5FGZvnSl5/m+LRg1ThO74zYKjPGuWVvpVL4/brjM27f4dVntjk/b7hlWnDlTr2BbBTmtE4LoSfGOeNcxRqLM9uMc0vrPc5DEc2mPvH0tgqcnGfWul7skeCU0tpI14qGUUawRjsCdd73UEligVhRTrELIRYJ9ThdCFSdFo6zSEPUYCBHiqpp6LZMT/3aHalRlgtGs+JMb/YQAlultoU7Xg0KzpSZr2PROfmwzEobG1cASK+w3C5M3+DYiHqmWElMF81GD8148JAFDmrH1BasTUnVLQjFRMU0tCpDF0sm4ELOxARlQljBdmuMzaNZlBZi114wNmdv7dR7pguUdqR2DemcbBQNZ6VhktOvMCtRhaq4lnFe9BMn6LHPSos0c0ZFQZkNhflcNAseFVoEhsF6tTT0+5hBLyrq4Yx8PEAl84t6LEUFtkDqOSEr1D/cFqROP9LV+ORrEpWawRZI0eC9nlM73mLVuEjvzJjkgUWrq61k41Dlhqrcom6DrqJCoIlwXOcCq044XpYgBtfpZ3c+YG6UwvJjwJjqRmTeXwS8NYRwPj0gIq8HvgT4vPA0dJZNefz/eOhSeGS/jsv4EY8erPsMbL/uODMtOTeve++PS8sB92ojrW3ZOvbrrqfRWYHHDtbsrVoO1i23TAved2XJnbtjfu3hPV52dps3v/9KH7yDD9x6rOLqsuXyouGB9+8B8I/+37/BD73hffz9b/1OPuPrvp4f/gf/gt//x7+SCwdrPvC+K6xefpq3/ZYeelZY7jk14b//5jnqVcc9d8w4PatoImSxap26FeaWx66umK87pqOMCwcqwDk+Lbj3xIT9dccrbpnyhocuc8fumGlhubBoyK128CkzwygznBxnvP/qSi1m1x0HdcdLjlcc1jGrH1mWrWNSmD5Tr7tA5+AwdjpfNb7Hu61ou7ZpbqLzWzzHMZBe9BXN0mMk9O3Y7Iasvu60zVli1SQq4M7IalATxc7nne/ff3qSc3npYoMJpQ+6EBtTdMOlM4tc+v2145ZJRuO1eJmk6K0PvfgIFLe/2vgY5HX/To51mZ5gjNwI3c5t1I2nkTGVKFtkISOMB828I3RiA7XTz1qbks4FhJzQBTTHVFbNiSywNqUGTteAJbZbq3Gjcc86sSYyOTKVtgeE1HMymEJXPF7l7Q05qy4wzUo8go+B2weoA1jJ+u8hXfsJLwewh+fx1Q6IqDw+GoYZArI+JFQz9SuJGHeTTyhc04uVzGpP/VBWc7CKdfdGWK5BZAWuw5bH1FKhW+GzCnGh95gBrXmMYjPuzgekqynsOPrlSxRzATEbl6DF1HVnmObqKZiSk+c7biRsIiJfCHwPWi//gRDCd1zz/B3APwN24mv+8ofSLvLacSOC91exAZnEA/mLwG8PISyfywb2647SKlFfRClxaVl67lCzhMcP1oxzyy2TgguLWmEKIxxGRoKLOHIa83XHye2Sd507pOk89x+f8MZ3X+TlZ2e87V0XeeD9ezz+0GV819BGtsl7IlSyffpWLrz7bQB8x8N7XHnfO/iMr/t6/ucP/zPOfvLr+B9vfD+jccHiYM37zx1wuLci+ECWWx65tOTqxSVd43gktz3mfXmuPPWDQ52EqsJy4aDm5PZgMrS/bJnXHYum47DWbj5XVg0+5Fya10xHmdKocsupibIm9lbaGzGtBOatp/XqpOhDzrJ1tD5jf60TmxpAeaalepwc6QIfz3nn6UUVjkAWM6LjJdQhi8pH03tlu4j95oUu9UfXwAouaFFyVtrez9sQIZioBEzOiyKJneKpsiGgz8ph6Z/FAm5hhMxqoXM/8u+S+MWKrjoU1NH9K8VDYXqF47z15Bfew+zEPcpzbhpMud3L74PJaENgYgMthsIqfjuKVDcYGB+dDxAMK2zPax/ZQjFvHxBb0XUagJzXzkerziDOx5WEFpWLrIyrmoCINitetz5m4Y6WrM+6E+Zuo+FYalJhRM9DGbsAMd7F2QEpTpOCR5DoRCj1vC9A5q5WFkmz0MeKiUIosbs8rgOb92rLkKnrY2+Fa5NfTuRtG/WvCRC7M+n1oM6N9LRIhdgUXrJCzyef5Ba8I7PFU+DVD3XcqOAdyRrfi1qBPAa8WUR+KoTwwMbL/jrwr0MI3ycinwD8NHDX8/3s5+vnPUF3+hs3Hv6HQAn8bMSofiWE8MefbVu187TOU3ehx2/VE8T0tEEY6GMm/j/KFEoorOmbBzsfmI1zJkXGTqUufePccmp7xGycM5rk3HHLlP3LS6Cim03xnWe8XdKsOqY7I1a33gfAF37effyH9Zq3/vuf5uwnv47H3/zTvPorvpqudeyfv4SYk7TrpJSMgbjzNBvO8ctovrNqHE3tWLaOx66smNcdFw9qLsau9McmZX9cuVXsvojq08QhLjLNvF2i+UWGxbLVgJ3oWLnRIKXPiza/jUW/ZJBVWOk56anXZgipt6Uc6a8JwtUW6ijLbFL1i9Q2LUIr2dCpflOEU3eBfVwPaaUCqhvTS/fTvmiTBaV8mrgaULw8sLdy3GLUwGjVhv6YGqe0xjR/b1rzJhw+q2wvABOJbdl2zsYGCpZxWWpxLdOMMxHE10EnmmTfWntwGzbAJm4/t4YKZVQUVo2pSlvgMZpxmyxSNbWwm5TEQA/34RzCMFHpdzl0kblWvQrps6XflhG111XHQYe0K4WwEjMEtDgp9LqKvg+mMdGON+tx8N4iN7JN9AKoNQsHUl9Na3TPxTVYW9KhTJg1WSxIyhFlaTqGPugzCI1ScwxEr6dKhmO9EeMGZt6fAjwYQngfgIj8K+BLgc3gHfggexw8l/G8gncIYQEcv+ax+z7Y7aQbLLKW+izSxIwvyYBz9IJPVDUgmjUFXFQLbv4kP+8kz52vW5rO07Wexy4taVYtXeto10uCczi3TbNcADus9p4keMe5/XtZ7T3J8Rd9MouLjzA+fiuPvP29ANSHV7h8Thsf+7ahmMw4t38nh1cOaBf7zGclNpJqm9glZjWveeLqiv1Vy8OXFjgfOB9l8leXLTvjnAuHNcfHBQ9dnFN3njM7I957ft5L7XfG6lxoRXj48pKRNezXHVcWDY0LLDZscfdWLceqnCsr7Q4kAotGGSjOq8Nhyr4T5DTOJQY+fU0R7WK1/Vo8vxHaAKhdbBgRGSKJ550k92mpq0E23ZzE7y9m4bHoaBgENqNIMSzQYmGGUOXalUZ3WJtbVJlONimDtUYFLcRrJY3EwkjFwhUeWR9SbU+VmtauEFtRGvo2Za0f/GBAg0cRA+hmAc37QIfBaYMwGucZtyucLSPv3NC5YRsSz4UGbZ0QtFm0xTnlsI/Qu37d6fkORUnTDVl3gn9MXP0klas1gxhHxDDKK9ZkBK8Tbmr1hg+YfEyw+RHfdBXZFINlbGShHGkJl/ppQk8VTAwwbbysE423Oa71vYgrbIjiiIrULBYCXJwAUlEz0SstAiZ/ioL0f9XYrM/F8f0R9gXVtTy68dxjwKdes4m/CfyMiPxJYAJ8/o3YrxeEPP6O2ajP8nZHlnt3lYpVZpp5nxgrh3WcW85ulbGbjA6FBWJxa8v3y6p08WzdkbFsHTujjE+99zjHxwUvuWuXKrcYI3Sto2t3tXVZldE1u0y2Csazl2NE+OwXn+TxJ17JZLtkOd+lrTusVV+TX/8PP8Xs+JiHLjxKXk1Z7Z3n0Yuv4OCxd9OtF5Szk+Sl3jRt7bSv5aLhHY/vs79suXpRKYXzGLybacHDl5dcOFhzaqvk/MUl+8uWK4uaR87PmUwK6saxMy2YjpRi976Lc47FAumFg5rGhSMdei4tW+6YBS4vm54fvrdqdcI0SiU0oufZSFKQWvbrliovtSdnvGeVLqh4dx07/4BSzo6PMxrnCSFSHjd8RZL8v7CaVTsfOwcZ9WppvXaDX8cVUhuz+PQ9+xA4NC4aYql4Ze08TRewxrHMlct+Jar3QHH2RO9Lxe8qkyNNLVwIBJvHJsyaHDgf6CL2nVSeq1Y7H80bx3Zh2Kujta0ZJqVFq5BIlQnLqOhtylmvnl15IuNEt5sCXaqfVnGSD5KBUx5+aqBcO2VvdGFQtHqSWj4QXDyeyAByHoxRwChEebySNwaYK8SCdJWXOsGNZnQhYuXtiq6YYn2r9gDdSi1mY9/XviMPkHpghgxmtmMetNvPiI7WZBjXktuMnCiN92oudqKySN0xqRTrz6zpO907E/ejWQAwqXbBD/qPGzHMZvr/LGOzPvchjq8CfiiE8J0i8unAPxeRl4cQ/LO98ZnG84VN/jTwR9HVzz8OIfz9+PifBP4Eyl76TyGEv/hM20lc5DZe9GlJ3UYb01FmmI2ynsc7zm3PjEjDhcC0sD3ml6ASaNiOIpjj44LdKue23YrpKGN/1XB5Q5lpjdCUnjM7FeuVFkVXjSPLLSe2Sx5fdRTbJZfPzcnLjrs/7fN4z6/8Ove+9ncxv7oiyy0vOjvj0XteCcDpu3aZ7Yxitq+Z93rR8sl3H+Pc1TWPjXPOzCrOzVY4H9gaZZyZjZiWGfecmPC+s1tMR7q/RWaZVWoBe3xasDsumBaGl52d8ZITUx4/XDOrcpV8l5ZZmVNY4cxWyc4o4/RWyThXEdBslFHGarv2/Qw9Hm6NcHqSseoKTlSWdRTW5DFr3Sq1f2ZyFdTvSc/99QybkgVAYhqkzu/TIjZG9nCsUhx3d5T1mXPdDSIeQdkzCqfYKFM3QwATWLWe41XWZ6NWhO14PaTR+dDbC4gofZFcucQ+AMaqJ7qPxya6AsjjpFNmBh9bziX/6RQIS6tOgpno8ZYG7MGT5NVMu/R0hzTlTLvJmAxxDYuQs5Vr8KqDUIrHNCtyOz5yDo/F1nGrbpgEXRgw76GhwxDcUuceI9AYnegHz584KaIF51SQbZwWC0z07PaSDX7jsTGE3ig5dOs+wCuFMGMR1O62HJWsukDdOaaFpXWqsEwNsgHOLx23TI5zaeU4VmUsWk/jDIVVdlHtYRQLprUHIxlthLyqG2EreOPG48DtG//fFh/bHP8b8IUAIYRfFpERcAK48Hw++PnI41+OBu5PQaXw/0VE/iN6IF8KfGIIoRaRU8+2reRT7YLeXH4dL1JjuLRsKa3l3GHNtFD63JVV2/OK503X25JuZuTp+f26Zb7uuHu34n2XFpyejXjrw3tsjTLe98g+bd3hnCd4KKqMtu5YHDZcflKFN1dedJK983Oc8xxcWuJilhZ84KFf+E/c+9ov5j3//ScxWYFrVrzzrq/lwgO/TLPYp11/NsuzJ1QWveowIiwOlrz51i2uzhuunJ9z6VjFwZUVAKOJUiAvHNQcnxY8+Mg+42nBfN3yyPk5oyqn6zxbY20QMW88v/noVarCMl93nLu65gvvO87+uqN1gdPTjHOHNWe3Rjx5WJMbwyho78zcaqFs2WomuukpPskNFxeN3tixrRzALUZvzroLfc9N0Mw7oDSxBL1sZt5JcemD9qfUnp6a8d+6lXNxmYrOit0WUWCzyTZRk34N0q23vdBHC5xaF7iy7mIHepgZq57hydcInajq2m903gng1mDHGvy8U0dGKz0skZnU/1N/F1ZYRV+azAxZ8Kr1zEqLi5h9Z4Tp9IS2oXNAto3rArXYKK3X1aTS+5Qp0qIFy9Ylwyrd870o2jkxzlh3sVsNw8S1mbD0XjZG4R0j6kXjjRpFbQqL1OdF6xQE19dLTLPEZxXaXdQqAi8ywCYuXivdevA78R2j0UjhTd9g8lKLpiZCoWL68+qCZ1YYzHqPndFu/A71uvNxRTC2IGu9L/KorBR744ACY29YFv9m4H4RuRsN2l8JfPU1r3kEFTL+kIi8FG1ec/H5fvDzORsvBX41MUpE5H8AXw68BviOEEINEEJ41tlFu5KEAb8OsZOMlx67hiEItD51oCF6UqfnfY+He69NaxNNL42ElRexu3sS2agWIS2D4+9IP0v4sQ9Bu1nH15msYDmvsUVF8K73S3Bt7BPo1GCp71MbAsE7ZZ84jzGCXGf5lkRHaaR9tUZwRvrO9tboc6PMMqfrawVlLGpa0eJkkel7civkVvoMXPdJb2aFTfSxIq5uciOEbHAclMjiSBal6fpXQYaKV4wQC58bWLPoEixPN7KJdY7+f4kwQqIeSgzkwyRsEIKk19B/zmZRNBVd9TuMv9FloQ9DsStl5z4EMAM/HJurUV4M3C4oryswQD8JmpAoIvJIX6xTmF2oGdgS1mYxCOv1lKCDdO1urlSuvRLSpZG+lwTlJP9uPf5r3BEZjj8QYRab4bqjDBW/cX5aHxjFRsvXwsoiRBXlINZJ7oIhJxYr9adv3OwdxsZ99Q4rmQqI4jbTZ4vrjnxXhthkOB3QpkDoBTqiDcg3A/8VvVx+MITwWyLybcBbQgg/BXwL8I9F5M+ip/z1T0eh/mDG8wne7wC+XUSOo82GXwe8BXgR8FoR+XZgjTYmfvMzbajHPd3gCOhDwMWb18cbSX8PQR5D/xzEQLzB6y03LnqItqoRG3TeE+LN4GKGZ63+7X3Ab8jJYQjsQ7AXgldIxXcNYvQ3gM0LuvX8yDGmnptpP0QiX3djXW/MoB7dHJuPpQllCCYDrTL5hrQu0EY8dp1Umn6jE8/GZ7p4N7cuSskjZ7t18VwT2EiiNQAQH/dxAiAQSEVkhSU25dsmixMqGmDdETx8MzAqjhyC6GfE/cUcff1zuer7CSftw0bAv97QZFxx634b17w/QDS8CsmdtWfiJNWij8fpg+5EmghgmBRSEN0cIaXRG8NfG9xFrrv/m9l0GlY29i/4WPw/+rpNX3B8PLbY6NgaQZzvVY7XDaIpcAN4H50UhwNLq4DA8Ln9xBtfYyLfXA8s1gH6WXZj+8F/UDj1s40bua3I2f7pax771o2/H0DbRt7Q8XyMqd4Zjad+BlgAv4EmWBlwDPg04JOBfy0i91w702xWcP/6d3w3X/P6b8B5DZbHY4GyyoRJMUUEdkbq33G8ynjR8XF/wTZOM5CjAQD21x3HxjkXFyW5MUwLy6fffQwjwpe/+ixlZnnZ2Rn7y/aI5B7UIOrKvKHzgc+69zh15zm1XcaC4CBOefPul3HXHTOO3fIVfVa+tVVyz2f8DlznmZ0Y87J7jlFYw5VFTZFZLhysedWdu3AnvPf8nFNbJVejP/m0zDgTMfKXn97myitOc2xacGqr5MxMaY6rxnFsUnB8XLBqPZ9x3wnObo84NSk4MxtRZYZbt8u4BIW7dipmpeXMtORYlUdWB1FhGfpj0e9Ej7+w+h2kLvchvmaam0h1Cz37JGWoZSaUG0vRza97nBua+PpjlaX1qpSUmKmenuZ9sE+8bxe73ved4UVZF8dGNqr0FM7pUnHQBWal6eXwx1iRV2OqSDV1Acp2wcnxtG9S0AUDtXYt9zYHZ5iYkJYOJP/riag6sTUZ1reMc+3Ck3p1+qATjoiQ+4Yqi86FLtnQqtoxsSncxj6nMYqfO3e2V4SmgF5EuGEerWFLKz1Da+0ClY39QDci/eY13cUVSWE2uOHoPZPh+wzYBIcXi7F6+Kk3poihzSoV7thCWSDFWFcqxka1ZUHWzMGMVYnpOzpvwagKNMtMhM5CD89Iu1LM3LXYmGWLsdqEeL1SB0Mx5PMLysMvKg3m1a3PKUZ9rI/nSxX8J8A/ARCR/wOlybwE+LcxWL8ptkM7wTUYz2YF97+992K4smpZd54qH3FxoRnstMh4ZH/FLdOCx2L39MIKD15Z9dnmuvM9bLJ2R2GTct9yZdWwahyve/Ep3vTwHqd3RvzXtz/ZY971qo0YJOSlpWsd1bTk6kWtdJeZ4Wfe+H5mx8ccXlnR1B3GaJec9/3Sf+Hqp/xOHnnTzwLgu4ZXf8VX8uAv/iztYp9Tn/CZLA6USZIaNiz352yNMs7vrTi8smK6M+ox7/FWyT23bfeKy194+5NMtkvuOTXlPY/vM660r+bxacErb9/hM2+f8T8fvMRn3HeCi4c1Fw5qPvvO3b7T/OzUmA9c1SbJjx+sMaKwiWLeemMvY0fzxAcHGGUlFxcNRoqee53431pYCkcsApwPbJc2MjkGvngaLugku1Uarq5VEZuw9JPjnItxAm26QJEJI2viBOH7yXgSi9TrzrM7UqFQ65VLPo7ttlaxJ6RBkLJivnYciGLrPgROjidcXXZ9gG9c4EzoYmd7TxUcCyyFBR8MwUeMuwvkNtPVSab2us4HnBFCbJ6geHiIxlQeZ4RJxNWTFawPaVVJL6iBSAf0OqlObOCq12J98kFJBfzdWLjsvGb3az8kMEboqYhppFBe2kAX1JFRJ+Lhe/FikcxiuppgLDY2LTbWKDQiaj6VdysNrp0GVOkafS6qOHEd3eSEcrO9I+RFH1zaAM75vsDbuEBpA1le0UpGlmsPTYVNlAc/KjNMzLp9tYu4phca3Qgz1+vBlR9t4/myTU6FEC5E+eeXo9m2Bz4XeIOIvAg915eeaTtnYgf3WQmrNnAido8vM2FWqzfIsSrXVmkIszLr8e3WNczGBft1xwgNtnXnWZMUd4bGaPPbIjOMrOHMTsXxScHVZUvduL4IuTUpWK47btkZ8UjMIk/vjDh12zZnT054JNLvQgjkpeXwpZ/G6bt2WC90RRS8o2sd22fuxRYVFx74Je57zdcTfKCpHcEHRuOce05OtW1Xbjk+LTDWYDPD8WnBbbtjjk1KzmyPuO+OGSe3RpyKKszjsaB5bFpw/4kJhRVec/cx7tkdc/us4vKyYXdk+8zbCrzkxIQT4wx/fMLOKKOwws4o6wN1qiOkLBgU8751q2RnZKk7bRTsPMxKe6RJQKLbOa82rVvF0KZqE1tNTS5qFzhe2SilV+hoWhhyo/LvbKQBzHkY5xCCOYILr50GcSsRG48CneR73fkNqmAOYCg2GCGgsvmhQYVH1m3vDx4oyXxsKBEhD+tqclvoiiXTScCKqho3ed6N0yCvPHhY+UBelswb369SUqu23AwTWm+yJiAeVkGDcJ5rsFXGzdH7xTPAUmkCUC44/bacp9cYeFGTrc0u7UCPxZtOm2WEMEj5g0iU0Zv42oh3uw5fTpF6oayT4LWQmRWa3VtRR6PURi9+V2IS5DRk/MGqV7qTXLH1ZoXJK0ZWCFHZCarSNLY8ApE+3/FxH7zRRsPHgRb4EyGEqyLyg8APisg7UBbK1z8bOL9ft2yVGevWc+tWwcXoXWL9sAxPdLXMHHXMm42GTuwJyy0zyzSo38ks0gQbF5iOsh7rurxoWK07VvOGrnWIEdaLFuc8znnm+yuC1zZr+5eXeB+Y769o1458ZMlyy/zJ93Pl1DEOHnt3vz93vuw26sMruGbN7Z/6xbznVx4gq6a0i33EaKu1N5/ZYv/ykqsXFuyfmnD1gmb5l2Yly8ZxcFhz27GKd7zzItvHKu4+s827P7BHWWW4zlNWOav7T/DqM1u88d0X+0YU5/bXvObWGefnDdPCMs0ND1ycMy0y3nt5wV27au51ft70KstUwB1lpqcPWmO5vGoRGZoBgwboRas8700fERXlGBaxpmBi8EgZuCoJldVw2CQ1ZcwWfei71ce6LFVcYq+dp4vCrSpTmKCJuPq12f08SivTtXHYmdheb3A/nNmGucuOZJ5E/nTiN2MrZVAYva7mIadAJ7kmenV0pMw41WLSfguVaBeaSW7Imjl5OdHgI1FZKdJPJAPFL4p/rJAZNW7axLs36c2b0HjajgswyvS7SS/VSTCuKDdWSEnMk95nBSQrMV2NN9op6VpgPUQRjvgohQ/afzLJ13vvb3QSKYzFi9Urw2TRElZ9bdI+1cFQiWFNhgkB7yHPx6TOViPanudtqhLrarDldYuzH8ow8nEevEMIr73OYw3whz6Y7WyVGVVUD+ZGpc0h6MV9clLQdJqNp2LatMh6Bsq4zyCvYZV45QYvWx8LgbBTqUvfy85u8/iVFa+8c5cri5rlhieK89pg4eFSucenZyNuuW3G/bds8a5zB0ew8dUnvIqdk2O6l/22/rFbT0649NJPAmDn5IQHz70PW1RcfvCtHL/v1ZisIPiAtSYyUUI/oYhI789SZJqNpwzBWsO4yllEX/NV4/qbEujft2xdf4McNOoHXjvHYeN6afiydX0WkzxFfBgu6FVretqli5PgVpH1DRxAO733ELdXj5HcSw+bbBbabLRwHTrICFVGz9svM3Uy3MpUpTfJk2uhYS2hl4l3cQJPfuJJydn6QZ5PhB9Sn0wfiG3AgqodW9cXQH2AkBVK+xN6MUvYaPGWrgmghz8kFtdkYwZRQY+FZo0LOlnZaCSVFJdaCPZ9rQCGemBqROH8ZpFW1ZOp8fSqG1Y8m63Q6i5g84G/Drp6StCYiYVAiZXS9Jp1qyVGGxg6skeXwBDorWTbrEKAbJTk8o16ffuOYHNaU5Aby2GtQqpmVLBu1Vt+2Q3tCNNttug849wQslFPv+w2znFmBCd5rwTVlcvRZOPmeIEoLKuIZZu47ErGRlocE2Yj07eFqjJDkwdG4ShP02OOZCVNF6j7mKyTw7TIGGWGSW6ZjXP2l9ocOKndgN74qfdIKTMNlq2jKiyrxvW+2mkkTBXg5NYIa03kjgdcveLiu36F4/e9mssPvpXJydsRI/3zAPWqRozFLA1t3VGvOuZr/T0aew7XLW3dsVypPabzoacSZkaYjtSlbtmokvSw6RhF7vN2qYKc2ShT8Yi1PVUwZc5JCLXpeTLegCe2y6w3GUpFxCwyFdJI7Iu+DyhD5p2KioUV9usQfZ11OzsjtfpMwhf1Mgk9tS9NAgYNSE187ar1qJ/f0K9x1freMMqKFlCNRG9tFzCEIz1CGwJQaCANQTFd6DPv5COSgp3I0Npskz0BUeDltLlBFTQRkbZWEz6bk0uSwKezNgRwGCiNAXrKpFIrhRB8H+SSp7rzgo0TiLUKQ3k26IgBTLy+Cloc+eCHw7BayG38HsPAEzHNAl9MezilCNHrPHYB6psVpxWEAN5R2FyLtqJUcBGhMAMdMU8F8bTiEAuO3ssmixNzJUImAboGokePN3n0ueeGjJuwyQ0aKSNToc5AZTMxUHQbdLLkU7LZId4aYZ1MiCJm2nofBT6Gg3XLKnalAbi0aNiP1q/nrq6oG4VNNjvxHByqc+F+3XFwqAXEg8OapnZ00Xd6Oa/ZqisWB0tCXEI+fHnB/OqC4B2jyJqZnLyd+vAKk5O3s7j4qGLgq452vaRrq/69RgbetzUS6YUx+MT/IWVnobdBbTrfN3dIEvJ1bDywiFn2snUxm3axUa2hDv5IsExDpeAd09IcKRoC/bmvOw0mHrWY9SEKaWJ2v5kgqdVn6LPMTariMhZAU7buInMj8eubWJRMND+lFh41KNL3Sw8JpOxeBTSDD44KSuwRqqGsDym2p4hvtXWZCHgfKXPK8k7GVqDYr4/scuWva2OHdD2K7wjkGOhbpaU2Z1aeasCURoJJUnBPro7ZxiShEnmP8+nY4omOK5/OhacNSiK6n0kFm44pZfJ9EzUxfePfYAvd7w1+d/AR/3YKiRC8duIJ6XtPsFbM+kWPu43H0PphhSddjTHjmPxEQVEM7OK73vjKijbOtiaP5rvPf3xcBO+IYX8JcCGE8PL42N/jaZoMi8hfQeWgDvhTIYT/+myfsVVYRrG5QGmF7UIzqZEdHOFKq+5qVW6OGNUvUmPTeEEkKtvEqCfKvHGc2SqZ5oaXn9qido5bJgWHEXa4sGiOiHs049GA5kLgM27fiWwMFbEsW8fessH5wG/uVrzqzl1+/bbt/lhec/cxikxl4PecnPKmW6ZkmaHrfB+Af+Gf/lM+/Q99He//lf/B4RMjJifvoFvPCf4kYoR61fKuc4dcPXceMacJHvbOz9k+MaZZqSL03P6aKjdcOag1S48BHNR5cZxb9mrHfN1xftFwddXyiFlzalIM3iYbQanMDMtWj/HkWM/PHUZYQT8h5t2KKquou0CVE/1ohIbAJBc6b2IQjgXAMCzxp4UGsk5CFBANr5kW2qZtu7R9gbO0R0UlKatPy+vdWOswhIELPMpi/0kXs2f0uTb2sFx6ZrEHI6h4JeQl+cE5QjnBLC5j80q9qrMCYwsopkqBAxoZK4bbDni9jxlrltSEqwV2tNsHtBCDm/UOZ8uN5sdD42KIdrViemgIBk50mRmyoNCD66/14XrtvNYTOhP67F2h65jhenp7A0B7WwINhrFbanOF1lH4lXa+6RokK5CuwRRjfDHBNAv1gTEFZb2PH80wi8uQFRrsXUNl1IlQ2hWj2KfTrA9htINIoBRPJZ5lK1R+TRDDxMYuRkZT9MLoAUhXI80KRLBFq7TCfJOFf3M8F43oDxF1+RvjZ4GXhxBeCbyH2EUnetV+JfCy+J5/FP1un3kn4iQoErNPkX7Hnk1fFcLwO+GgkAQRMQuPESoJgdT0yKsNbXysdfp7HSlo6f8kaklConWnmHITi3apX2YXf6eKfnquax1d9DZJP0AU6AxYu/eO4JWR4p2n6fR/32kBNQl6kkio6ZzGpk2BTsT9U6u19HgSNQ2Cp6FglR7roiXvESFUYOMcJAXeIJ7ptx1CD4MkFaA+loQ+9EvexJToMWmGVZWPmXPyq3Z+czv0Pwm68TGjRQxerOLLJuvd6PTvTDM4m6mdqcmUyRCbCugFaI8wKzb/9iHo6+P/4WkKXSEMz113aR98/3iC2K6X/G0W0q5t+7V5Xxx9fPP9A0XQbvwNugKQCA8RopQ+CWGSRepmy7MNYU6/irjOc5s7srnPsvGa6x1r/3x/E/ujv2H4Tm7wsJk8558X6njWzDuE8EYRueuax35m49/NJsNfCvyrKI1/v4g8iHqf/PIzfYZPN2T8zjaDixW9Ajs/XMyx/gUkfHDACUUgGF2GrzrlEqvzoO2D+LL1zBvt7HJYd70PeNN5isyw7rRwmKT5VyLvvCosFw/q3p/78v6ac1fXXI0NI4IPXDyouby3Ui64ERYHdY+BA3StY3Lydh58029hixGLi4/SrbWq7uoV+WjMev8ydXcb6/2LNMdO4jtPs1pRrwrauuvVn2unAd15LYgtG+1Ik1nTW61CkqJL7wNuI9/bR8ZIZpVWmNujN0oKsH1AMTb1n+1Vlem7S2OzoGtEemGGtxEL9SG2QUz7FgN6H5AH/DgFehs9RFZd6Itypv/QZEQVosm/xVijYhJiFho7xEizIORVb7AUshJTH+LLqR5bNcOZHCnGhKwkGKVUhryKGT2Id3G1cm1gjcHRdVFcw9EO8zaP3iKhL76mzNgHjgQp5a8Po/PKdClMiK3F0v0Rs3Ef6IwyeNJXuCmbz8X0UFUIgSI1ZvCRNSImdvCJk1t0DQyFTnTiOy1SUmgw89rxR7cRLWR9Eq/Rt1trTUYRhU1NsL0plYheSzRrKCaauUfOeDBZXwjF5mCiJW0/eX54gvlH47gRmPc3MDQZPosG8zQei4894whh6EZuXQ1kMWsOAx6uaTU+SJ8xpjHQtYJ6/wKdg3m0sNxfd5wcF+ytFS64vGy4um4HG9XUGCAuQ8eF7VWPV+5sefjykipyvC8ervv92r+05OFJwf6loWHQ5UXD4d5Kb0xruHpx0XfZqVc1wTsmJ+9gtfckAOXWMerDK5is6L1RUkbuO6UxOufxbfw7ZuKgQThJ+9NqIARdIhtR6l1qaKHeG0MwNyIYK0fO42bWlwJvGj4Etet0WoPo3LBsCyFl3SBosTL07yN+HwoHdB40r9YnUvMGFxRH9yHQeekLcM4HjN/w4HY+qkOHbY8yLSyunfZDPEIFBAqr/PjKFqzJyHOFXFofqKBnTmAyPc7YRaeL16ARsLYkOBeDrO/x9OEajr9t1vuJpAa+qdFBbxmwEUjTPnZBSO3o1NJ1OPdpBbKZvZqI66fJLgXnzfpEnwUHf2Su2cz8fVb2KsqQlT2GHbJyCNDRNVCC1+bEJopzzFEOePLxTv7eRpSv7W2ORGpMg8HglF4oK1WoRrJBIQb16crIiZh3XFVJVqo3+A2qWH4sNDN+viKdZ2wy/Czv7eXx//D//h7+6Nd9NSHPwTuO0erF5jtmeYGJzVCTNHeWaWePYAvWtqIUTx2UsbIZcOaNpdwIDp9ydityiAMXl64XofTeKDHLTL9BmRh3/457+84sVW64vFSaXHvNhRSCCotWn3lXb/w/rz21U7e95MT33stLdqucg3XL2nmmRcaqdfzU257gzW98D8fvvIPMCL/jK1/XrwCO33K/0geNcNvumJed3eb4yPA5rzzN77j/BE/G7N+jhlxWhLoL3LZTse48O6Nclag9iyROej6Qx6Vh3TnKTOXruRGOjYa/R15v2FFW9JawZXyfi5jqzkj9rJvoUZPw17QNgGOVToLpuUmmLdD6DjPxvB8V0+hr99eOk+OMw8ZTZdLj6Y0LTIqjgp6R0eYIaVgjzMOIygwc8dJsBO7g8XlF0S765gS5GGpvmWTC1cbRuYA9eJLR5BZaf41SMcDVxnPMFgiqKszzKk4A+rrU5i0xSdoNdMCFgEQ2DKhatMzoBUQAl1Y6qedG+gzeeaUSFkZogu/hw/RcAIgNo9M4MmE3S5qswsaGyhhLl4+xrtYA3tVcaApOjDL2GnBN4Fh1jL21YzYyPU9/q5oQvF4TKyZqAWyVZlhH58q10/2aFoY2QJtt42KzawDJM5atZ2Y7zjeW7WJbv2PnsSbjYOV63/Ob4/lZwr6epzYZfi7etsBRefzje4twaNQcaSfP2G91KR0EFrXn5PgkV9cOG6KC0kX+aROoXRt9IvTCtpE9ob4X0PqWZeu4Y7vkkYM6FuqE84uG3GgWnm76tfNHGhi7AL/t1m1+49xBr9x0QTP6MjO84/EDXn52m3c8fkBmNFv8nPtP8Mvvv0LdeV59xw5veLe6AmijY83mP/DIPkWVMb+6pms9NtMMen51hRjLuXe+neNnPp3f+vk3sX3mHqY7FXtPXmayO6NrHA/vjLiyqPm9Lz3Jz//mk1gjnNtfc+7qint+14s5WLc8frDms+7Y5beeOOAlZ7Z4+PKSW3cqWq+NGWC4wavcbmTd2uX+8cM1d+6MeGxfe4euO889u9ssasdh7VlED3YRLb5tR7/t1OU99Z70RNP/2DD5kYPmCD99EbuJj2K62LjA8bHlsD66Gkqw2IVlR2GUcphw+ZEVDls1+U/HMRdofdf7srgQ2Ckt5xdtTycsrLCNY2VyWm/ZssK+jLUpQ8T7J7lwtVGaqvMQRlua4Uf5+qbaMTdCCEptsyKY1RXycossQQGZ9hpNxdoyo/dZEd9pobXt2B1pZ59M1Dtlq5ReAr85Wh+wmenhExu54om1kvtYvG0atm0xYMyxYLvMt5GuoUjFxXYFrsFmrk+YCJ5j1RTTzNktKupgyVZXmI12KRcXKfIRRbVNtr5KKCbMW5iGdZ+5G+9wpuwpm50P7Neek+OM0i9YZRNyo7BOHjrGeUYgY5oPBe1VF3r73WUbOHa9gPJBjhtpTPWRGh9S8H6GJsM/BfxLEfku4FbgfuBNz7Y9LYLpzaEXmN5cmdHlct35KEuWHiNN04Xz4E3CCQVMiNziKFgJagS/doErK/V7njdd34H+/MH6KZh36jfpfODeYxVvf+KA6Shj1TiWjesx8Pc+cpUri4Z3f2CvP5ZxYfmFtyskcmVR8/YHLhA8ZLlhvdDP3D9/AVtWzJ98P75rCN7hmjWubSi3dlnvX2K9eA37j7wTMRYxd3H4xIP49g5cswLOcuGgxnmY7694bG/FhYM1h3G/VFSjXiBXVy25MRyuO9ad4vyJq56gFqBvsZb8T7xPHuv0RUPieW9cKljqMTddwJb6f+MGCCyJaBKMk5gUm/4nhphJEhs+RFfCIkE6fgjcVgaoJHVeylGmRx7NthI3GqCIBVHNVGGcCSG2VOuv5aZhlFfKoW6XVFmlkm2b6/uDQjsmTlLKrCDa2aqIBkPv/SLLJYxGSjWEI8W9I23TwuBMCGjmG7u6rxKMZ3R9suqUTjnJTa9M1Ws/4CIjZZNi60XfZ7My4vAqqkkZVqoBtC7SAaPCMsTsWxWUg4OImkc1+r2UU8R1OjHE47OuRroGP5phQ0C8HrP6orT9CkVCiCwYehfGnieflmJAMJbKgGnVFygrSjKBwt7Aju8fD8FbRH4U+BzghIg8BvwNlF3ylCbD0cf2X6PNNztUMu+uv+VhnCwDhBZflIRgmGVdb3pTjUvy0DEt8r4oVGVZb2KziEsyFyyp32Wil61aQ2YVPjg9CuSnJpHzHNivNZDee2zcc6LLzGwwUzSzO7tV8ul3H+PEOOewduRWeHRfTZ7uv2XK3cfG3HNSPRicD3zanbvMIr/7zPaIz7r/JHvLpm+YYI3wrnNnmVU5Fw/vH9pkNY79q2uaWJB860/8S179FV9NW3d84Nd+jVtf/hpMZrCZsLVb8Zn3n2B3ZLn9rl1eefuMK/OKVeO4baug7ia9uu4z7z3OqUnBp9y1y+4oZ5QZTk3LI1TBlAkn4c7OKOMTTk2ZlYY7d0Z95to3P8gFa0wfBD1K4UwddVKrrzQKq+KL1gdOjrMjoqjC6nthyMwEmBZx2/G7TP4gJfRS+3TOXYCKFvKerdzDZaCBofNKSSutdocJkffsqh0kqIBHmiVZXinPO3pTdyj+v4hmVLI+hHy3V0Gm2ox25gnkk+Ms1p61gd1iwiJosM9tRhN7UaZrNAlvQPULKmQqmNcuTk56bcx7M7DQdxhSaCT5wOhKJJ2vwqqYzcX3T4sJazfQNjNT9J+JjQwfVGBTuUOkWeGrGWa1T8hL9jvDrJhoi7PWM61mNKagGG0TbM7aC9V4lzbEVmfZdBBc2aoPym5j39qgASRdU86r6VfTeQoUNtrKIt8cFThtQj/Pd3xcBO8Qwldd5+F/8gyv/3bg2z+YnbhYC4XNaFvHicKz12kBw0rOwbpjWhiWbavFxNywjHQ7FwKL1jOyhnXqQ7hRvEmNePfXHc2xMe+8NCc3ytXer7XbzBNXV33G3USqX/q76Twnxjm//P4rfebddJ4LEV9+7yNXecldu7wrZt4+Mj/e8LZzeB+4744Zb39Ae1FowbIj+MDVc+fJJzMOzz1IcA7fNZp5dw2j7ROs9s7z6q/4at76E/+S2R0vZeeOl/D4b/4qk5OaeS9O38EvVTn7n3o7j35gj9/cHnHhYM3BYc1jrzzDuy4tGOeWV9wy5Zceusyn3XOMtz26zz2nJkxyy/nDmmIj+KXVRoITymybt5+fc6zKefjqmq3Cctg47p9lGIjdXPzgj+KV6VCr21I0ghq+30Wn39HICueXXQ8bgEIei05lL1m0P5iVtlfdtX6Qxxs0UGdGekm/fuewCHkvwxYR2iYVFYfMe5QZahf6jBagqq/gq108gpRTuqDsjCTuSbRE1SEIoZxi4uIwMaFSkbGwglntUeU7jDNBVgsmxSQyKFq8LXrYzsdtpjOR2qGJbzVRAWyE8DIr18280/Ebge1ys8O8TswJ1pL1nFG5FT9J+u43o8xCPJ+Fb/SUGIMvZpqtRwvWWeaRZsXUOq0RLA4pRltIu0Q6Q1VMkPqQbHyMZeuZdiskr4DAKDS0pugbDTuvK+FpEQU4Jp6D+P2q0lqY5LoS0hNQxXrWjQveHwvjBaGwFBn8IoLJMGh1PEmqCyN0Jvolm0GFZgO0Vo444lldk2l2ktu+OFNY6fssugC7oo1d11PNQhL+mzDgVfQIGeeWY9OC01sjLi5qqtz2VMFqWlDltldSeq+Of+n/Y5OSrd0KUIwtL7NIGzzJZLvEmPsB6Jpa2STrucIk1rJeNmydubeHTlZ75xFjcc2abDQl+BNsFYZ61fXB11hDbrRjzrJ1vaez96Fvc5ZbMxS6NiapIjO9AiI3ZsBNTbKLBXEt1hQ9ttv7mBiFNlLDXKW/RfZDgMqayEiBSaYZ+iazJRVXdfIYgpMVpYTmJnqqxH1K2WvKQD26amh84FoWQQgbjBdMhCuGfcNktLHmIa5hFQqyPOt92wfGih5jsHlPl9xsBDxce8q48AiSjdQnRAQvlq5LLKGnuuM5IxgxZFlJs47GVEZXG6vW03kweJrIlzcyMEt8gHkz/N2fG/T/7bxi0Q0CntIm9oveZ6arI4ZlleqYMUA9riO4FlynQTZaxNKukLbuOfLSrLDmgKLYwizmBNcotm6MGkt1a6ReI6OZwqH1HNo1hRhcPibDYZoVWTHBNHNcOe0x+sxEdagRjn67H/r4WDCmek6kSRH5QRG5EJ0Cr33uW0QkiMiJax7/ZBHpROT3Xfuea0cSdST61cD7jeIHEs4dhm4kITwlwzu6zSGAtFF+DQOHvPWhz5Sv/Wmc7/8Ger43HJXnb3bB6Y8j4Y4+vYbeLzz4oLS/KNrxPvSB23cNXbOia1a4eqUeJo0WMEMU8Og29G/nVBgU/CCP9xuioyTMWTWO1geWjWPVONad71cQq/hYev+qdaxap2IkN2S+SbiEsb0sXzu+H+3qkyTtqZCYvp/0uPMqd084evou+vpFel/6LsKA5aZtqj92knan1w46gc3tJhZIOPJZoeem+4BS0XqsNYvGVANkk25xSfuZDJL8ICA78hk9vp0uCq9YrwzbkZgZC0n2zlAL8C5OiEOtIFEItf3aIJXfrAUkFkvaXrqxdZHh+646/SpmQ1DTC5vSuJZLbawG0s3Xmezo6+OPD/RiqCRv93Fi2HxPz9dO29v4zGCyKHpSjndfQwkDBfX5DjHynH9eqOO5Zt4/BPxD4Ic3HxSR24EvQBtsbj5ugdRl51lHFbuKdyaQNXNGG92zU5adsgkj9B1DbIDWCyMrrBnUZRL0Ir669n3neEM0K8o2HfP0M3pP5R6HNb1LX75BuN2kZgGUhbIHylj8y2IGXEbTqK1RRhl9UMrC9vL47RNjstxGjnalgbzzrBdT/cyR/p6cvAMxlmI8631RxsdvRYxa0rZe3QabzvUZ9mSj9+U6ZtSbTmz+mtmuiseQfgqrrJqEc8Mgd28lo3GOzmuz59SyrHWBzg3ddVKhUj8vOQIytAdjKHZmueA7zzhX1wqdMGLgJwVd6QNPEzHxzTZrIWbiyVcDBnw0OQ2m4QK9j3XjAhidEIyAyUraViek1idBi+L1Puj59KXt+ejGxy468RwJSj2sG62hTIylDir7Tvh14wMjOeorovulz5fWUMfCcsqsE95dZRvuiSQ/mkCVSVT46oFlNvQNLXyAcVVSr12/ahEZVLAIPYzSe5VsNFwAlKueFRpwg/pwA4RcBT5JUFPnE5wLhGyEy8d9S7XOBTAZtoyWBgK+GGNTZ570PWYlQYTOlirGukbFeS23/uN9PKfgfT2VZRzfjbJO/v01j/9J4CfQNmjPOtZdYJRFv4dyQtsOhZ10IyXzouRdYtAbIF2wyXUQhot+lJl++ZsaB/jInOic76GEVEDbFAAkSCFl3LkxPdSQ3pNMrJpucAhMWWx6TXIPVIFNfM2q06C7atVhMMnnV3NsWeG7RumDzQrXrDUrXy8YH7+V5eUnaBYHrF5xN1bgwkPv4tw9uywOauZX15yfNzx6ZUlVWJat471PHHBqq+S95w9xIfR/T0f5keOucss4Bv6z2yMe31vR3BF48nDNcpSzt2q1q4vTGsK8Uf8UI8reOTXJOaw75b/BxqoFQCeQolN4xBP6ZsGJoZKCcQhQZUNxtHOAjW3GbGomoBNB8hQXSRYGIHE7qZiXlIYKNej1kZIpI4DvsDZm2aEDsj5L3QwUk+hJbtsl43x0pPDowjBZiVPMuswMwWeUcRNdEHwUKlmjf2/6eadrNNnkais0nRT0kkuQIeCP9rK0JhZyY56Rsu+UkashVTzmjfvOiiizhA17AO8IxUT9XcQgndZ3pIuBVmKHHVv0sIn6eWtNyklQT5SsxLQrghiKGMilqQl5pd9Fs0TaNZJXmCgAkq7W7wvUljdOKtZrd5/MFNwomvcLOaN+ruP58Ly/FHg8hPC2I34GImeB3wt8Ls8xeG9mTGn03iZBb1wXVD2Zlq+Op2aRCQMdhBB6w2m39aHhwDj31J2hzGzPcd40aRpHNWWVW5yH6SijzAxVrqKfnbFWxWfjnJ1x3rNLAHbHBccjjn5sWrAVu9/ABhzgPLvHKupVS1FmCoG0jnWVk5cZzWqLrd2Kxek7sEXF+NhJtYzNCprFAd16TpYrfa1d7NO16onS1h3L1vX+5K0LtLX+X0cbgFXjOIysl2Xj+oANw8pjXnf6nk753Lk1LJqOdae0tf1ag3fCrpM/+GE9uCMOTZEVj25doM0G+Mmh700WstZKP9G2Xo5aJThFa6eFBunCmghvBQpLr6rd7LQS3PB94o86GlpJ/OygASKP16CY/nNTUC6in4shSvNjsIfBWpbo2W2NeqvYiNFuQgHJ8TJEuty1jaZDCH2tQDvtyACDxAKrrgL0sxJVMvWEdDKcP2vUZTBRGa/NVhPmr5OXSt19rrUZcdreDO80nscAir8OaSw2bJZIh+zvx42MWYIKk8RF50HfYY2JwqgQTcTitl2j0IpoUTUZU2E0kGdlphNGVT11Xz7I8bHA85bnWsGNmfd/DCG8XETGwBuALwgh7IvIB4DXhBAuici/Ab4zhPArIvJD8T0/fp3t9QrL7/yef/DbvuEbvgEXlOC/MqMeF+w2smEbq+KNKfriS8Ibk09EavMUgLLex1U7mK5GXIsrp9h6TpNPyENHK1mfeabfqeOJ3aBz5UYzzsRk2Sm0Me1+7dguLPv1sCStu9BLuQsrR8yqIEqy+2YDgzMcRAe56Jw3jdvdKhSKqTvfq/qMwN7a8eLf+ad5989+D9/3y4/wRz/1Dh49WHMyThbbpRZnH9pbcfv2iCcOa2ajLDZrgGNVzmHTcbzK+1Zorff9hCcCV5Zt7wDoQuCVp8YcNI55M3TS8ejvaWGYNz46Duokm2iISbE6LQwHteubH/sQuLWCS41hWqhYx6Cq1toNuHdmhFEmTI3jybVwxszpRjt9g4Ot7qD/ntPsLa7tfTlUHp4yyxiMEgSQjZBujS+3NNDUh4R8jHRrhQ2ih7VZ7uHLKcutWxkfPtFLyAlBYYbgcdtnwOaY+SVCOTnyWcFGpXAxRtaHhNHWkR6QUi/UX2W8qx1kfNTIe6+mWnmln9UudXt5FbPfFSEr8WI1Q4XheNPf0AffFEARo8fc1bhsxKJV1eq89exmnjUZIYQjCs/UEQiSInS4B9PLahc2JrWBTdLF77K0yhTKjDD1S1w5Jb/0EKGY4LZuwc4vsqhOMFmc79kuIRspbTH+Xxy79XlH3s/6O294zvD5L/6lz31BRvoPNfO+F7gbSFn3bcBbReRTgNcA/yo+fgJ4nYh0IYSf3NzApsLysSvzkKCRsqxoWt+LNvbWTjHtGDx3RgVXV0PLq2WbMhK/YTMaRR6MadY1zgdOTys+cH7JpMi5uJizv9Zl/+OHKgRQlZde6LMyY7/u8D7wiae3eeu5/4+9Pw+Xbrvv+sDPGvZUw6lzzjvfWbq6mqLBVmTZZvCEwTFmSgcc44QY20mnSUgIISF5koZ2J9Bx0gTiAJ3AQ4BuQkITBqPEJrTBNgZjbHmSJWv0vbqj3vmMNe1hrdV//NZau86rK+nq3hsQlvfzvM97Tp2qXbuqdv32b31/3+GMg0agg8Io7kc/8Ofur3j80pTn7q8yzfAb3nqVn3jmiG5wvPcNh/zccyd0g3Sxicd8dNbyyOUJv/T8KWUl2Ldznm7TU1SWdtPzyOP7vPDsMdtVz2y/5vxogy0Md57+GP3qlPmNN/HxH/o+3vLrfx9v/+bfzt/42x9ndffT/NH/6LfwIx+7w+G04mvedInv+Us/x/ve8xA/+6FbPPL4Plf3an7ppVP25hXLdc9iVmY4aH8iP/+aN13ip5495l981w3+4bNHLCYFR8uOJw8e5e564BP3Viw7x6wc8yjfc2OPp4/XEUoZnRxBLhTr3nFtVnIU7WjbaBWwVzW8cLblUlPw6fOWwigOmyLfLxX+SWG4MSs463rKZs5m1bPpA5NCsTVzZi5wtNVR8AMhyIrChSKfF5NCs/byORCHnzeGJadmj9AH5lXBXfaYoWlVgTOB+UQuoodXrnDaei77luPmulxIozjHl1LMDqyhdC2r6TVKo3OXD7F41bVAVPNpvHgDWjJsnN0b/VuMpUuipULYJv02cHliOe2tfE8Qff3gS6oARnk2Q0rTsTncBAyN1ay8zwK3RIdfbT1XwhrrB/aUBm+4vL6Dm19lsrpFMAW6W9EdPE558gJq7zpeF9jTm9h6jtqcCmwSL0jr+UNi57s9xjcH6G4F/YCv5hQMKNfi7RwPzIYzsYsF/OQAlEZvxIq3NopQz9HrYynexTDCM8P2VZasX37bqyreIYQPAVfT77udN1LU0+1/Eem8v/9z7S/7DiOe0VDlL5wkrIihf20VtW+ZFGU6DojBqnbXyQfy8E0SVwSG2a9t9DYpWVTFBX+IInYEyV3voCnwAaal4bFFTWV1Tpe5PCnpnef6fs2NWcWVGBAMkp/5rkcXlEbzxoMJp+s+F79ZbekGz3I7cH2/ZtGUGbZYd8L0uLGoOd8OvPHqlF/Yq6WoNgV3zlu6wXHzjQcZJvnvfuJ53v7Nv52P/O2/xtd893fxwsflGA+nFY9fnvDwXs3ikoiInr484Y1XZBB6+aDhySszbp5uuLFoaAfB/5tSEoRmleWNV6ZsB8/htBQYaSZ86kKrDCtNCinedUxCmhQmUwtry4UotUkxKhunpcmDYIU8fl5pFn1iJ0jBX3U+rwYqK5hvujD3XlHFKLVpIZTG2U4Actp8IAf+VkZhlM4CJgXQW+aFovUK3a3ZK+Wzrm3kd6/uwuQK1fI2h3vXwXlm1uzsXy4umiDCn36gLgqU70EX2W/cKc0kxr2VYcApk7vSANT43D07baiNyoIb0JRekmjmlclS+eQZk326i/E7kN4GrUAHsTIoIo5vYgFcBivOgpWYPinvGBYPofwgBVUbvBauuJteyiwQ3yyEJdIscr4ljabSsv9QTGRlkix5lcaZChONp2qjCLomqBVBabQbxFvd1ijXsXWBiR9yoU4eK6qcjEPU17j9cjAnfEXF++VUliGEzyrU+UI3yVcUSGI6qzleDxcm7Ye15bR1bAaFnVScruN0PMIavXcXOuckhKjsKDV+aGq5tRporHwh7q07FlUhDIIQ6L2iHVx23Nv6sfCse8e6l78t3UjFW24HTguT6XZGKw6bUrBlHMvpED1Nhhyrlu633A6iqvM6u8aBwD6b3lFbQxe9w/ebIv/ctwNd69Ba8dveeZ0f+JFn+Od/x7/C6qzl9kd/mt69l4/dPONo1fK2KzPuffqMX3hhyv2bSz4cWTJnxxtOlh3rZcfNPfmClLF4py78F144oSkNz9xZsT8pON8ObAbBtY83PXfXHfPKZn/xq9OSm+dtHgLDWNgeW9QcbXouTyzOi3hKcHJ4m63ZDp7BBe6teyYxbONkO+Ti3+IpbcGqDyy7gc5J93m6dexVhlUvWPpp63Knm7Iu5XyIF4TacH/jYpyY3O+GW7M1E7YuUNuC7RDwQWAhD1TlhM3gaaoZm14w3nU7YE3CnMfh6KzUDHpC30u7UGi/YyvgMxd7qy0wwkIAHUr89ZRcEE9bCQvp/Dig37rAqg8Z1huzSrnwutNcIF3IVKHzPEJgqOSq6AnVjE5ZTIDWK1GqKp2rf7C14PcxKV7HYp2GlwBOFxjgvBcvGLRhi6Uy4gi4jdbM6CLCf4GyrFH1XOCfiHWHookYudjw+igs8s2+PI+tMXZslF7L9iWFef8fuR2dr4OJE/baKNpI00owQxkzLQEsngGd47sKLdLlaSE5l7u+FSNXWHDZzgUWlWYTB28Jz0uy4cRIaeyYmWn1aAqU8PVkRrTLMkgY4Kw0+QTVStFY2ccyHqMwa5SkbJsxGUapi0ntlZVYq0107xsin7lzAWvkwrVfG+6vHdbIY62W52td4FPHG9770Jwfe+6EG/OK0+3AjXnFdvBZoZq63xSokLDtQusMc7x41rKoLMtu4L0PzTltHadbCTWujMmPTfvRSuWimz6zg6bgdDvwyF7J7VXP6Xbg8qRk2Q28/cqETx5tOIywyaQw7NeWVSdujAk6OWwE/tg6z2FtR4/rKCBqCsHTE2wyLQSDT8NJjfy/m+BjjWK/gLNe3td5ZTjaDJQxHFopxaVac3/rOahNtKt9cEgu+zNKVo1Hvoorg52B7Y7fSqGhUQ6niwvulTJ3iIwZxtSg0mhWvahFJWFq3HdK0DnrHIvK5GSf9LfSXJzbpGzLNIcowoDqN4InR5qg7tcZC0++LH5+DXPyEm5+BeUG9FaSdHbvg9L4eo7qW/TmFIzJVrihnIJ36G4pXirNArO8i2sOMJtjeb5+M14MFg/JjKHek2NaH+P2rotxFlAuLr/myvt1f+Lvv+LC96O//2u/KCv9F4XC8qR1VEZofTemlvPWZR+EVe85qGHZSWG+VMFpdJwLIbCNHNhTozK9DEbBQhtpaFenlvubgc5pzjvP86dbLk8K7kQzp8SaMAoWdaS9AY8tGp4+FpmuDyLs2cbu+9l7K67v19w62WZM+50PL/j47XO6wfNljyz4+J0lpdXcOWvZnxSZP2604k7MxgTYdAPn24FLs4qTdcd7Hj/gHz99n27w3NhvePFIjuHk7go3ePrW8ad/z1fxu//LH2X/ypSTuytOnv0Q3/N/+w7e/zMvobTiD3zjU/y+7/3bvPWr38KnPnybR566BMDR7RV7hw3bVUczq3KhsjGq7H1vuszPfOqIb/nyh/jJp+9zOKs4XXe86ze/nZfOWj5055xbJ1sOI6umGzzvvrHHJ+6vmEYoZfeC8Oii4Wzbc9gUvHQWl+zdgAvwzqsT7q17FpV8FgJNietjSvZJq6Ebs5LnTjtmhabzgePNwLy0Oby4deI1DtA5ly+GSXm4F4eiCWbABQ7DBsc049PjQA4ZELqOzmlM37KiprGK09bvSNTHC/tBPWHiJVFJsGcFOl7s4wWtc0BhcEOS948rvHTOrnvPaSuvu7IhdvxyzoiIaoT7lp00Cs6PPiGJcdV7lWGmVR/QKkSbADn4c6e5NHQCkSA8b7X0hKIeB79Diy8adDkh2JpgkSFpOQHXx465Qrcr2vqAsuyk4E8OMl88DYNDPyUUDStvmM01qt/iZleEhlhOCUWN6rdsgmFiS4lZAxkC9xvhk78c6+VLdHtVGZbx9n8H+LcR1t4PhBD+oFKqAP4c8J647/9PCOG/+HzPsdvMBKWimEOcBoXnHUZTGmUY/DiwHHzIIoscXIyiKNIXMWRxT9qMUhw2lv3IvgDpQhNeu6iKzBnvvfibGKVy7mUbFZg+BC5NSmpr2A7CojAKru/LEOr6vOLuumNaCL55MClZdQOn656H9htJe480Q3H662nifW8saq7uyX6uziuc95TWMPSOvnUMlaglJ7OKqimYzCrag+v8lb//KV786AtcevQqp+3A3Y/9Yw4evs6dj/wE8NUUleX+s59g+8ibWN27xfTy9fFkiPj704uaOy+ecffJSzz/6XPu73VslnKR2w6eWydbbp5uL6pQA9w62Wb8f/dvB3Fg6ZHCZo2OkveQ1X6CaY+BEbWV1VaiAabfdSywuxFsLtLhklmU1MwHqKfq4v/pZ9VvsdUsfq5yntn82Uf6YGLAhUDrxkGlURf9RVwI1AwM2mSudhGP30UkIjB6dIssXyCcTcxiLcKAqSybwVPu4tmIu6FRImJKFEsQ4U/yqU+rSIFz5LGlEUhm93d5fQ7drXDlJLNvQDpl1UrqkOo39GiMKQR7Tl12OcVE46pga0IvfPBel1TpvhEOGdAyk7IVTksDMy2F7he0RfXbzKBh6OS9s7VI8nccDsUj5vUp3q9nGEN0Wf0+xGDiz4UQvvdl7vOtwPcgp8AHQwjf/lqf95V03n+RB9SVSqmvRyLP3h1CaJVSaXj5O4AqhPDOSCf8iFLqfw4hPPu5nsCoxHO9GKaQTkJItqRS3Hs/djvOR79mP+J9SdzQR9pgmuwbJUPMzjuuTsWj47CR4llozWEjzoUyHNU5kWReWjyBRW1zh947GcItasthMyZ8LGrLpa107VemJe+8NscoxcN7dfYEP970XJ9XFDtDvt6L+AXkovTEfkP7xEFmWjxxWRwRr84r1p2jspprs5J3vOsaV+Y1d8+3fPrGjH/vX3gLv/N/+cs8/JZvp3eBxWNvA6A+uIYtDPW0oJodYktDMV1QVjYrP5Mc+NKsomosj12aUE8KZrXNIiSjFbPaMttaFpHvntJ6FpOCaTIcUuKPXhsZonofmBWavbpgXhoKo9gOAgdcm5ZMC81ji0YohZWmLjTb3udivqgk9V3gE+ke55XN3jdpxpG6Z+E/6zyUlkZS5QIo5xSovqWciK+I+LnIvnsPyoHq19Rmgt6eMZldywZLIAW79BFu84GCpJKU1PchiCBHu55eWyxeMN3tSkJ+q5kUuOCZ1At0vwY/0GhLVTTxd2jslEqD7pYYU1BbKxBEHAZOykp40f0qQxihaFCD0CX16oxpvSdtFuT/a1PHwOEdRWWkVirXQS/0SoXgzl4ZUAZVz/EodDWN3XhFCD46L8Kl2RXOOs+kWuACrOPqoDSWMDhCCNzrNI2dEYDZxOBtxdHGsTe5xFnr2asqKtsRghfnR+84HxTTYlRfv5bt9cK8o5r8TwO/HkkO+4BS6v0hhI/s3OcpxIn1V4cQjnfq5WvaXlWGJfB7gO+NWZWEEO6kuwNTpZQFGiRd/uzzPcdeZXJXYnzPLC69E1ZYG8WiMtJBeMH30raOQ6GE4yUzpcoqypAm9iEneIQQmBXiktdYHZf5FznXwlSR/bsgGDMo2rgEVcpkgcSkEIxbx4vDaRTAJBZA7wIY6VhThmTq9ttBmBQ+YvMp3Nh5kZ8vWxl0FkZxFoMc7q86ltue0hqONj23jzcMPnDveMNm2fHTz5/w+K/6zRir+TM/9Els2XB275R+dcr5nZt07RWWtz+FLkrW918CHsvvZYphe/Fozem9NZ+6u+L8WHDG8+NNNMN33DzZcvd8pGxVVlKCjpYXmQDOB5ZacdAUHG17jjaO++uOZRexdh9w16bcXLbs1YYXz7YYrXhzOeHuqqN3gdYl5WzFtanldDuwVxk2fWDVOXRp6XWAwbOJ7oRGByojw2qlEBfAuG2ddLQgF6JgK5wPGS93QSC6JPgJVqxcQ1HjYre9G4zg/JgbOaDR2ojyNp4DzgeCLiBIsk9QGtvso13PFktZTlAhsB4Ck3Iq1DgtjBJTTKVbdoHWQ5WsXYMSO9YQsXIXUMpS1Pv5dW4Gj42fZzGf0Dmf9Q8x5yAOVhHow1agrXDMk8BIieiodYHSDxc0CelxKCWFHDn/m1IENjbGoEmG7LhqqK3m9qrnsDGjBmB1iionNHZC6VpqW8oxxpVA4u83topc9vqzVJJ/Ktv7gF8KITwDoJT6K0hj+5Gd+/wbwJ8OIRzDhXr5mrZXi3m/Gfi1Sqk/CmyB/yCE8AHgryEHfhOYAL8/hHD0+Xa26n0+0ae1DBTTYEgGiCb7O1SNydh0wlbHnMvkZQEM4xBx8KM/RBm7ouQSB+PStYond1b9aUUIo1pQ22hb6qEqFL2zIjbI9pZQRFaKUYraaB6KMMKiKiitohvkQnN5UrJeiK3qLi+695IUP68MV2dVptkxLWkHz9V5xayyPH55wuVJyZsfXvDGK1M+OVlyc7rh4cOGsrIc3V7y0BsOmFy6xvr+bWbX3sDm+BZDtyF4z9mLHyd4z8ZKcITWBh+XpMdHB6zu3eL+6gmOby/ltttLeh843vTcOt1w+3hzwU7gpatCPRwiW8Y8oPi7e9byzqtzXjzZUFrpwHsvuO/pdkCjON6KyOTheR1DomUlIgERkoj00tmWWWk5bXuON31e/Ty2V3F72aHVuIo62vQYPeLYlycFx5shvufShYdqwrofHQTbIYCNKt4Q0O2Szu+ju1N0taCNhTuVsET304pRWUmycZCCGdG7kbfeyfyiNqBaGfqV5Vy64G5FKKdUWjIwU1iEYL2GOvqKqLgPbSskpFdh1kd56DfLFwJRJdZJQemH7O5UGrvjV1LKcwRPHhyFIHTBAMEU4mdjlQwdQ5DHvlwwcFReGtfiTJXVqqlYN4XOcGdllGDnriNooRgqLQk+GTYxpbBdHnye17B9IfL4XUFh3P5s1KmAZPS+sPO3F4GvfGAXb477+XEEWvmeEML//oUe84Pbqy3eFjgEvgqRwP9VpdQbkauQQ1J0DoB/oJT6u+mq9Nm2EKSD8YBXhhCGKBNWbJIfiBs7nOSzHIBNL14Zu3Jqo+QIkw8KjHh49vrupQOTlPLRa0M6aBl+2UBOUEnwi1Ky3HdB4JPCKFonMEqCAkAKSOdCHnyue4kI613gzqpjUVvurNrsD9IOnrsrwQ2dF0reSey2excudN6bThSd/onAzZMNTWE4WXecnba8dLQRyKCyTGpLv91iyoZhu+T85tNcetN7UFpTL67Qnh9RThYAKG3wQ4e2YmlbTBcsmoJmVlFPSupJGbFpTVNaJk1BU9qMxc9LQ1OKjYDVKqtCrVbs1QXLrcjpkxEWcKGL280DTZTPREMk8svnlcEaTWkVtRN7g0kh/zxi6lQYlXnhk8LkgAkf5eXTUlZw0qHL7tPxjIwQgbEUEGyJ6aUD9bHz3s2vTJuKkJ8eWrQqL+wPRmdAncq+NmPxU3q0KN0xakpFNETvj8Te8ChMtGIN0ZVPhSAd9M59lesEpnHdiFfD2NHqKFvvNqioNFV9G5Wc23xf3Yhni4mdvG6X6KhCJXh0Kc81qEqGoc4RVBwumnFGAORAibJUo0WAGuGZoHQMwdCUWguZJR67C9JkvB7bg/YEn2vbFRS+ys0iqWJfhwgaf0wp9c4Qwslr2OerLt4vAn8jZlf+lFLKI2rKbwf+9xBCD9yJV5r3Ap9RvHevZt/7x7+Pf+07vztPf1RcbiXMGsiUsMJL5l4azFDIBF+65ZEOloZCKU6rsWOAMBC//BrTewzJDGhsOlIEm0z144AqnoSFiWkghcnilBirSWVMLj7JWD5R8ipjAMHbexc4qAuKWEGkYET+rQvUEdIBmFWjtebVecWmc8zisDUNNa1WKC1+KlVjsYVhf1JQNg2hrlHGcOlN7+H+L/1sdiYM3qF2vgzp5z5ygm+dbujbge26o4sXIe8D3eDYbAc29SCUvUiNXG5l4Jq9sOPnmQIvnA9ZtJSGfelzLWORleCDiD+bNKRUWVhj1OjdDuT3N62k0nstBlCjdapPJlWoXEBLrcB1lMWEjRc6XcLN0YoChV4fU9YzdLumNIrz1l8IeJBjiLYFwUmh8SNNMpJW5P31DpUk8Q4op1ker1N3LR7CEokWf8/5lnSx0Me/4bIHUK8sZbpvKtLRUlVpK0Xey23pPgUiwQ+mIPlyo408Xo9dtUI6fVNMRXSUpPZ9K/vvN6iho6plFaKGLU0zQZ+fxX0UoryMM595qWX1g7B5lOugg7reR5+fYWdNzN+UGYFuzwmmpDZEp7LXDpt8IcX782yvJLf3ReAnY138lFLqE0gx/8BreeJXW7y/HzGe+hGl1JuBEriHWMN+A/CXlFJTpDP/b15uB7tXs+fuLz+DcxkiH9W5EP0TBG8LWoaHOvKt09DSqbEj13o0HgoQi6/QyNqdTr6N2YCQ/JljDqYlx00ZHaJIQrrq2upsxHRv3QElx7ErTlvC4Pdry3GUea97J/i4iwPLWcWt5dh5935M6OkGz415xe34+9Z57p7F9J7b55xvB/YnBV//5GV+6aVTLh803L675vT+mmfurrj/wh3qvQX3b8y598mfp5gu2Nz/NKasszNhCniwzewzCvjQP0J3fiRWrr0TWtuOB6uLnORdznPyON99HxL0NKstR8uOwqjRlXGnE0tsouy17kbnR8GZowVtpbJHd9p8kJXTsAM7FVpnOif4yEQJ0Xkw5NR25QDloz/5GGUmnjrxfJocsOk8vl7klUQXjzfpAlx8PdoaNJH9FC82PohtFYBHQ4DCRkm8LjDRs2QIUEQhTIip87YQ/+xeWUxZoOL9QO4r3wU1+oyYMvtjDwFs/LsyhVxAtMmwDkrTBk3hdrI2x5NAbtrxXnlZuGK34CMXKhdAAikCtpqBNpjI/Ennw6r1FEbgp2DK7CfuQyDYUuZdKfQh+YgD3hToB2xivwi2DwBPKaXegBTtb0Oa2N3t+4HfCfyFmHvwZl6mof1Ct1ebYfnngT8fwxk64DtCCEEp9afjAf4icsH+CyGEX3i1ByceFaMJu0eMdULYAR3hAnadAb10/OPriIb2Yxedbkv7UEFFzFS8xdOyXjpwKMLFpbYUo0Rxk+ffRnFPWq4nY6feh0x3KyI7o4hDLWs0DOTCBnIM6fdCj+rHprS0g0AVhZH0nElpsKXGFlqUdUWJiY+1zQxjS2wtOZup206hDsFd7L7l9niBG3yGLnym5pFDINJ93ANdzIMFfHcIu/t3F8bB30UKX2RzxIt3YgZcuEC6kSqYmCTOQxE5zCEkSiEXzonkUpk+dzW0mFLlTj1h1yCDQTV0WD3N3abRipCUNA9sfuf1KMjUvQvvjSwWxy2Ei4Xzs2zKO+lCo7gnd+S6GM/x4POujBVzLq2tdO0xqX63M9dCRo8PHjvtB7eQ9v0Zf/AXjj1DSTH8IVMPd5a0PozfVxkv+LzvtH+5/87TxEIePuMAXv32enXeIYRBKfV7gb+D4Nl/Pmb5/mfAT4cQ3h//9huUUh9B1lz/YQjh/mt97lebYQnwr77MfZcIXfAL2lJH5OP0POUXqog3uyAZiYWGbWXZuh4dO47t4LOUPjWHRoOLMV0J0+6c7Ncocawro5dJN4QMh6g49LRR9GDMeG5vIm0tyem7QbL4ztshJ80kXPa8dax7fwHHnUS4RquocjMqd5+71rYXUmQiJDGrbKbkGa2YlIZL05JLTcFiVnJj0XC+HXCD58Z+zd7lBbbQXJqVzK69Aa0VJvJqlTbYZsawWTK/8STnN5+mXlzJBT0dT3suc+Zhs8S7Ca7bxLSXz/z8UsCFqB4vQibyeQhfv4iD4OV2oCmFlWHiimnVifKz0DrOEDzt4GM3ruP7q/NnUVkN7Yiba5U+d3leE1cztR1tXne8snIhCNVUziMXqBFWUFL2+gChmdBtAtEHNntkpy0pN1PAg/IDPghbKjlTBoTh0SasPHgwBca1YyFVipSvplyHNWWk8bVQRhzcOwzkgowWdpZXNl/wVE5tj7CNUuhY+BSJKy2+I/0Ql6nGyirAOHw1k9dQTCLlUKh5oZT/E97uQqCIbonimmgvWCNYBQwdmBJh00GKyFunhiwEjDX4agra0rtAacVR1OkCZWVwKe6NUbC1OxP4ItlCCD8I/OADt/3hnZ8D8O/Hf6/b9kWhsEw4pgtQaRExZGGESfzsERsttYqTe3Bek/x4Ck22KLVaXZC/wyhOqIwsfadWs3UXh1fpeKQzH+GbIaaxpCu2T4PRB7b0JSoihp6ognlgGYtaup/NTxyy/0l6/O7vqXA/CM84L/BPilzLx6El4R2I/O2xOCttMGWDLkrqxRW2p3dR2jC59BB+6OnbgeBd7vy9DwR3URzhhjGMIjkEPrjtpsTLe0Z+TYXWmCK9Vzrj1WngWBjxBtFBVjE6Fs302YCmiu+dUaOdb9qXuFLGv+fzYzyWXICDjzQ3SWhKYq28BRHPqH4Dzfi5ZQviIAU8e9IH8SdJ6l4b2ShDLFYOJZBHTKBJHTVIYcW7DIdoU0Jc7RhjctH1KBHNxIFliKsiGOGNoJRQ/0IYX28K34zP6UKRX2OCJVMXnC4CIbE8dAypIBCMFQjTjHCGUTo2ONCYUsyltBYqZucz02ZUgY78eKO0mF5BZpXsbip4YaRYO/qLv8btdcS8/6ltXxTFO6WL4GVZp5TGkIrWOBBKVKwUnqCUwpqLa6mwY2KfHg/RXY2U3QcmdkaJZbLLfEj7T1/OBLfAuA+QjjMN0xK3u9AyjEme2JPCZHm2wCbkDiUN5oBctJJLohy7oilNfn+MVjRxiJmEJ6XVeX9p1esHj48GT7vbBWw7dpJKm1zYXbcdu+9BaHu72ZlCxbzYVQMZEkmrg1TUnZdVUfo93RdGdWLybU8wVHovQC5sOsJMRo15julzTepMoy/6luzeZ9dW9sHwDpChmylUVMcqrBlFOAAMHYWWrnP0Mdk9v8b7yjlMPobd5wuMnTjEghTGjkGOUacPSh6jdnImw3i7KE/ZeWx8jsxeGS9mAtPZeCGNmLdScfBJFvokPvmDEI6sJAB8Xk2kY8j32f155+ImBxXpovGzMxpwD8BJQaATyZ/2kL5vuzDO62wD+CVRvF9OHq+Uejfw3wMz4FngXwkhnCmlfj3wvcgAs0OwnR/+fM+RIqx8CDhdMPghf+FyuGwAfAwo3qEKCs3wImyCFrxSh3EQ6UOi/CWzoB2aYBgFOh45sXzEPD3yRAmmQclx1jt4tFGehNjtntQJ+95lmyRlJkhST2EiTWxwsWhJR5osbZ0OkvgTKXbz2jKJ1q0uBPYnJU0pEWbrylJajd5ZvhqrpUssSlwrghv1AN1qcukhXLelPT/ClA1KKYZuw8m6x3UbuRgMHSq+9pQGlCAeo9UY0Dx4usHln1Oc3KYfw49NpOJtekfnxCumG3YxcTmuNLBMW4KstlHc5Hygxed8x94nRabOAimtxiFm2rdWIrtPH1WC7db96BGSAiqwWkQ6Vjxgku+8eaCWpG49mBLXeTrn85CcCMNkOb0e4Qt5kCep+dWwJdgqMkqEeVIViMVsvK+Nf1OAch6jIvc74dIBtFEYL5i38gPWVijXZzYLWnjeahCFp2mXwh1PYQ2RZhji8FEhn/egwPj4uSRKJ6JQ1SqGp2gjKxFTiioTFwe8IVNvCy1DVllSSefde2hM+pyCcNi9E7tabRlcQL9MZ/5qNvulULx5+fDhP4cIc/6+Uuq7gP8Q+EMI4+Q3hxA+rZR6BwLUP/z5nmDM7ZPfU1f9YKOklRhVxQUqcHEAsrsZJbSvFGU1LTRNXqbHAaJJKjh5jFKjJ4YmJXFHCMeEPDUXSbsWippV6H7sGC9PLEebaHIVoYDSiv90aRWTYOi9FHCJZUtQQdqHqBWvTiW4YHCeS5MyU+dS6vuNRc2s1FydV7zl6oxu8FxfNOw3BU+86RDnhVZ4/fGDmFg/k4I7eLrNVbp2oKws62WL6zYEF1Ppuw1VU1DUUyalRK+12x7bzHLXPCkNPmZ1ushrH5Poxxg2gKFzedjau7Ez3/Rio9sOnpNNL6KbdSdCrVJnq4CUlXneORa1pY8wTV3L8LfW0jFv4uyjDx5vAgudVijgE9th53zyxIahWTAMMhOpjQhrku9K2lwQbNjHbkGr0S1QWE2xs3Q93hRYrSLfPeSVXlIHB23AudGRL27WiglUsDXKD/S6lCJtCokx0wV2ewJFg7fVhXmpi9DebiK7DpFmmJJ6dhOEVBh51VayKBOHXPkB1a4kpxKgaOK+iwxXKj/IdzSKa6TIDrKKilRCa0twgsk7r6mj57pxLY2V96h2G5yeiBhHD9RFBc5Ra/C6QMVmQ/eymqhNGS9iX1QKy39q26uVx78Z+LH48w8hRfoPhRB+buc+vwg0Sqkqyeg/2+YjY8AjmNrIMkn48Hi/xip2VdgRbeHBC6kLY7CtQ4aVnRNFV9qvZxSHqKCyqi7EjtuF1DGpbAGbGCWmHLvN3bzG82hlKh0qtE6UcQIriLw82bImQU/yEj+NXOreiW/18Ua6LWuG/LejZcc6dq+r3nN/1fH8yYY75y03TzY8cthw66YklNzZb7h/S37u24F+K8KL7vwIN3QYW9KeHxG8E6x7I2rKu5dusL7/ae6dtazuPk85P2R15/lo9+q5v+zyhcA7T9dJpzTEgrwbwGy04mjZ5Z9P1n0u4N3gsRFymhQmd+mrTgaSSWHp8nmgLoihXBxwewKV1hdWPUJBlDNq7MiFg2+0zlxv5TqUqsRxj1FM8yC1YpcqlxqGvNCLGG4qgJ0P6Hh8il3cXxMGLyrJlNQexvdKmRIVWolMQwzaTDy/jFaZVieQiM4wiX4QDcrTWIFI8rHv8MZDsOiiQHWb0Zs7eHAO6iSwseCEBqvocarMb0yADL8kSEMr6HZRl9i5G+3ZuoDRAUxFlxTSxSRqOeS1dC5QakOnLMqPw8mUKt8OnvJ16ry/JGCTz7L9IiKD/36EXfLoy9znXwJ+9vMVbhAv5tR56m7FtJjgA9mzeVLIMCSla5dG78AkIzvA7ERLJ1e3xqqM05ZGxeiukMUNoTRR+SYDK+dhWijKQWUv6BAuKgALLaKDQlfMo2IPpFsvo4DHBfEOV1Ftd9gkwY3mWtzVpJhmLN15MaZKzI3DpuDtMflGIsBEZn/QFCzbgTceTqiN5ssf2+f6rOLhRcOt8y2PH0x47NEF3eB545Upzz15SJ9UnsuOoXOE6/v0W4e2mqF/TGARH/BO/m9mFVff/qt5x6P7fLCZsbg84exFMh+6bwdsYdBa7ANMDHIwRtSXgx+92EG+KGWcD6QinnDwOhbv/dpmXB8EMvE+MCutFFwlF7UqhkjDSE1zPjArZf9J+n5Qy+dcGx056OKvcSmaj2klIp1gSuoItTRW0u3T5xeCKBAbq1GJuRLC+Hln+lvAKmGT1KGlseVFIREh+n/ImlF3K3AXfWCKcipil3ZFqOeoqJBEWwoLqm0l+7KoKIoJql/L5UdpKi0y9ySZB1BFPT6H9xDVkcm4KnXioWwgDj+xpbBqvAMbi+QD8vfBB8rk8ldOoihpACN+JE6wEHlv4oVpURmONk4MrnYass7F4AVbC/smyPP4uJJgB95L59Lu9/C1bF/Kxfu7gP9WKfWHgPcj+HbelFL/HPBfAr/hs+1gV2H5//ivv4/v/O7vxnmYa9gOIYceSPccslugJgpE3LhkdXGC3e3kWCbqXvqwr5SW09bHUIM0gY8Ch7BjuBZgM5DFGttIK0ziHqETCoa+6ny+sEjHJl/SwQnO2nuTxT6JWy7YnzzXshtyoEHvhRaXzJika/fRqtTlLj8JWJKvx2kUAR2vO1482nDQiOVm2zmW24HVWUuIGLUfPNt1n5PmbSEWsyCMkn51GgeUh7TLI77/f/0Q559+mvv719me3ZP8zVVHuxk4vb/O+ywqyzN3VixPtryoVb5YeC8c7ccvTbl5suFs29M5nz0/2tidLrcDR5s+d+jr3rF1nrN2wG2kU6+N5sa84njTs57FtPrOER11aeOqJs1KVr1h1TmcHVdFy15ohmlQ7QxQFWxaOY4urq5SsLFWAis4JwyLJESCsfvOzpcmGpH5km64mJIjw7pxSFfbCmwlvtixW0dpKWJR4o42ArGkjt54KBuSGRRJ3BJFPbsQSerqM7vE2AucbDV0whhxrUAmiZbYycWDYiL/x47caOG7G9tgVUD1LUXt5T5+EKinW6NsRWULUVZWHtVvUaakNY2EQSixwa2tXKQT7qw6wd1tMUX3awY9odIRlgEI0pE7U4why69xS0ysf5a3V5th+TFiYY4Ky29Jf1NKPQL8TeBfCyE8/Tn2kRWW7epcQBPvoN1yuS7yFHw9SJrMrDTUVhzMZjE0QCnFUIymVLsex0opjjYDlxuJyfIhMK80tVGs4uefsEv7wOeoVJTHa7gSE0quNkpsLgvNsk9ey5q9So9iHp1eG4BhUkjARGnGZaVgtiF27ip3qM4b5lVUkQaJ1LoWw4ELrZkU8sWrY2e+7h03ZiXvuL4ngp/LU+5dnvLE/oTqfSbmMGoeuyRMiU3vclxb2naDIdKWFJGn67fz699yhf/tF9/FI4cNf/3HH+PKxPL1T17ih37hJr/5q99KU0oEnPOBb3nrNd54dUppRvZLgjiuTiu+/NF9vuzGHtZoBufZq0VsMgtbvu6Nl7g2LfhVTxxSGMWlSYHR0/x4gHlleWyvpNAHXJ8J9v3wXkVtxJvdh8C7r08zPXTrAgd1HUMWhKlSGfHsTqiIAuy9T3J1/2E2dkrtNiwW4vJHkEzJk27O9drgw0IYQ0ZFCEDltCcXoOzO8dWcsjvHltPIla4yFdCbAu16nC5wSPffYTMLo/eBoAy2qKJnj6c0BmNEqKRUSW1cVl9qE33TgwxfPZqijEKspE60FVkiHyX2gAQqBE+vS9TeVUI1Z+UNk3ohqffA0CwEx+63UfLeESpYO8WsqMRBsZrupOVM6JSl2p4JJ9wU6PYcX+9FUZqHvkXZRii/rsXrGrM+in4qnsIU6PUx1WIqkvh4UQIZ8L5ehfvBc/6f1e1VFW+l1NUQwh2llAb+rwjzBKXUPvADwH8cQvjxV7y/biXYWz3HTw4wq/t5mTat55izT+NnV6Dz6M0pha0uYJChnKDbpZi2By/DFqV5qFmgl7eZFBXqbCMm8cZSTQ7jxFtl8QyQB1WpK1RK0QwrumLK/a3nUgUnsXCnriqlnKQLwaVas4oDsEIrHip7ettEf+f4PMNGTkwSd7cQXi4y9Ara0ge41ohKzhclemjpdUlAViZGSSH/yofnFBpWfeBNhw2zUnN9VlBoEQadtvJ3ETuN73myRk3L+0SJ3B0SuxD4PV/9OErBt7zlCje+5vdSTBc88b5v4P3nHUe3l1RNQTMv+eALJ3zsw3c4uDZjebq5QAX7ll/zBH/np17g9/+Wt/OPnjniaNXSlJZucHzVw2/jb334OX7j267xv35YHA7f8/g+P/vcSYQohFXyFU8c0A1zfuqlE37N4wc8d7Ll/rpjr7Isasu1acXH7i0zPe5d1+b8wu1zcW/sheZ4Y1ZxvO2zGvZwUnCnfgOrM09hOm7Mak7Pe9a9j0NGx5XG8vxZx2N7JcvWUZuW0768kAwvA8MJsyFw3DeYwWO0Qce0oN5DoYfIZhoyRDe4nfAEErQ3XvA3UcRk4yB1KGr6zscVpb8Q7SaxZyPMsB00IBbITaHYDpZC22wLiwLXe6gPRD/gPCedZ6/ex7iWDQV1qWjLBfPlLfzsMvX5Lerg8fOrVOe3cPOrqKGV7145kcYpuRQqTX/5TejtKb1p0EqjtKHszqnaFX52WbD7ah5XHOLpzfwqy95zoC1qcyoXvhiblkIZmM5faWn5Zb29Wnn8TCn1b8e7/A3gL8Sffy/wJuAPK6WSwug3fD7/2pSaEbSNE/cyD0J6XWK0xUcTn6B0VnulAu7j7ykkNXGTe2Up67mIIYYOXwmGnOxh088JAw9GTPhrO9LBfNHE+3vaYGkHh4v1ft17GivOh6lWbZ1i08uAZlJonG3yUt2HZHHbiMjFx+WgC7ggUElpTGZwaMDokr51FLpgs3VsXcrf1MyrwN31QKFVzny8Oi15/nSLUYor05LnTjbiWuhkSJrk7qftwKy0FwpQkpvXRvxb9uqCZ+6vWDQFR6uOYrqgX51y5+mPcTJZsL7/EraZ0Rxcp6oL7jz9MYb+KVZH9y/QET/80gFHN8+5u+746EuntJuBqrE45+k9fOL2OV/9hkOeu7+iGzxPXRd72V2q4eOXJyz3G56/v+bk6pyzbc+dZStKv4hrH296KiswVOeiAjaHHQdaZzlvh2wGNikMTWPzYNNFEUkfP/sBoXr2PkS8muzBceH8DTsCovh+psIK4zBdKYWOw0ejFCNZO6UAyeoxZBuGKNlP54ICr0T0k1YTKsI7abUoxzPi8i7I7aUZtRJp80GM3nABrcQ10vRrVPDUZYnuVtS2IhQVuD6KigZhyihhx2SoxnUoK107Q4cqGoiMmhACg9JiC6C0pO9om4fCEkhhCaaKq4OR+ihD1ov2s6/H9iXReX8Oefz3vcx9/wjwR77Qg3C2FkaHqTCuJZhpXvq1LlBML7EeAqUpKWaXcWZMkO59oOs8tW0iTm1QRqh1694TiqnQz5TGFRPh83bSWW2GnXg15Ms2OGGb9D4VWhP5L0TJ9EhUFBGOZjO4C0UQ5IvivBgUmR14BEbOr4s6jV0cftfUwQX5ciZ/DvVyNAhGnjsOTrcuM2K6WLAT/XAZsWitVf7b7paKUhsf2/vAzZMtpdU8c3fFE+/7Bs6PTnDthtnlq1ngU01n7C0qJpceppmXeH+IsTqn81yaVcwPG5wPzCcF3gcmdRKOwH60m51EvnptDY8cTLh1uskdutES6tCUhnllmFWWvbrg8qTksJFEnYOmyLz5Wam5Oi25PBHv6XXvWFQFlTEZ3moKfSHYo464ta3HgagPMCvEOc/oKj8uUQXT57SoDMb39HEgnlZnu2wogfdUDgzZ7d4FzoneOqWO3fxYkCeF+IBUVoQ2aaW2y8qqfeQGKEVVVnkVB1CpIEXXRdqg0pTVDH1yT4aWRUljNfrslFBN0ZtjVN+i9JpgLHp7Js+nLWp7DkocFyHSC3sw9QH0W4FLbCmYePCUzSHG94Lxm1LcFPsNhSlk1R1j0IzSEl5cX90p3Du4fWLY/MoGfJEoLOUk1pGKF6WySolHxCCTb+ekyBVK56RtGIvlGGYARgVC7DIk61AGT53zNMrhg87GSruDJZ2ORUunapRi2Tk2g9znrHXRbU6Wruvex6GmR8uYndKEfFGobeB8J5UludUlxWU7jEnwznPBi8Oai2Iia8j+4Oeto7aaa6Hkl+6vKWKnfLzpeee1GT/14gnOBx7bb/jQp8+yhH3ZDpysJSPwfCspPek9Sv+6wdOUhvNVx5sfXvAzH7rFj2txF5wfNpwfndCtT7n90ecJ3tNvlihj2L/6zRw/80Hg3azuPn+h8/6lxxYc3zqhGzy3bi0JcZA59I4Q4GTdMSk05zsxcLdON6w7ly9sp2sJX7i/7HjxrGU7eI7XnfD5Y9TaaTtE0RTcWw8cb/sLeaOV1dxZdVlBu6gts8JwupX3s3PioZOYJkYpHio3LHuDMh2FrdmqkrGnHrfN4JkUBV2cI3TxIjtEkVmhwRiVPT3gYueXiniCTYj3SDLyzgVstBZIlMm0ucjKCpVcXIISJbKPboI6OLwy6KIRmC6ySyRPtABtqYywYZQfUOtjYZEMW4k5q/dk+JmCIPqNJMV3wsNOHuJWIYyVLnbJ2iD0zAC6wGQflBKlhuinUkp6va1k5ayErcWAPH7nrU4D2tdj++XQeX/ey5hS6lGl1I8opT6ilPpFpdTvi7f/jvi7V0q994HHvEsp9RPx7x9SSn1OVr1RiOlOWor5AeWdnExKodrz3IWo9pxKi8Q8Bf6m5aB4pIw+IIokoUawcKUi7zQuJ43KX+QkDDJ6lMun/SYBUcKHd208Ml0M4Runrs4zQilyv/H2cd/peeJz6p2f1Y6fhyb7UEuRH5kv6echJq0nmTqIqCcJZjo3Kh+HB4p1ou11gyd48VgJO6sBF/H/5cmWzfEt+tUp7fkx29O7DNulpPAMUsj71SnDZnnhnxuEyXK67oUL3g60G/nnI9vkeNOz3vSsVp2sCqLo53Tds9wOcoxBVJnp9W46d8ErZnQajO91fA3ptt5dDEzWEW8GuXB2LozBIEE+zxSTFmyd6aaJ85/w7EShTPvOjYUfDZg8F0VCaQvxX7YeiOyV1FSkx+8+dAxiHs+trBgMXgo3nylyA4EaEwTR79RBF6ToB1sRioZgS/m/qKSIGhstZ2NkWvQ9kQBi+TcEKbDBVqMnirFZsZqKs/IDPvG1Y1hxKGp6ZQlFLa6VNq6uldrhk6vXDTpJ37tX8u+LdXslnfcA/IEQws8qpebAzyilfgj4MPB/Av7M7p1jfuX/CPyuEMIHlVKXgM85JpYlovmMzltEMx5MmeXxpbbZ5Menkxs52TPwEKTzHna+qKho8qST5D7gvMpf7CS0cD5grMYHD6jMN7ep4GvpplT0mN790oLALum29CWXL2D6+9iV9X78Wx99QDSJNrjLiQ6UVrGN0WAJ7ng4ChfqmI0p+G/EOiNVcje1prQmF/Z0gUsG+WI3O/5dG01pNTZK+Z3z2NLQHEja/K4fSnt+hLaacrqgWlyh3y4f8AiHcn7IrJaQiBSEPPQxU7S2zEpLFUMnEjunKUcfl2SS1RQmq02bUlg1u54o6WLcutEh8YKyMowmTuveoZTKwp00ZE2KW60QqCH2OJ4RUkpb+lzlsyZ/rnlfsYu3cvpGmE5opQk+G49t/D64AAbx707zkuTdLc8b8mN0PNelKJvRITNf2KKASansnyLfLy/mUkp0FioEMYAyBcoNEALKDfhoSpWSe5JsXoctWTERohAqeXwjhTt5cYcgdEvlpeO+cDV6oCDL9zSyZtLzmlI69l8xpsrbK8G8byKZlIQQzpVSHwUeDiH8EPAZfsUIhfAXQggfjI/5vL61561jKAyb3rGoG1Y7Mq1N7xmmMzYbkd+qcs6yHf8uZP9AZVUMTRiPyWjBEn0A1+zTtY6pd7QufZF8tqnclUOfti5ilTtL0/wlgXmlxfy/Nln4k7ZJoQU794ppIc5+CZMO8WIzLQRTH7yOVLNAiLJ5ketrmkKzjZTC9EXtXODqVCh2p61jVmrec2OP0ijuRzXmjVnJVz9+wPGm521XJMC2j8Wmjda1LgRONj37TZHpeL0LbAfpdq/OK+6ctxxMSvabQjpOq/nozTOqusDYR1kvO4IXX29tNR/8/r/Ck1/325jt1yxvkyPVgnfsL2qej0PkqrGszlrc4Bk6n2GbpCAdYlDz/qTgPIY5gxhwLXdk92cx77IdPLfOW67EjE8f5YbbQYaV2yj2SbDVvXWfxTa9s6x7z83zlhvzipOt4+ayFZjJeSqjecui4fZyw9sWQksUM7JxoIwaO+YQArVVpMNMhTt5iA9BVmbTYvTvSCtEFcaCXEbsPUS2TYYz2iV2l/qXi2RBXVr0+mj8UimNjXxuTEnpOqHkMUrlF3vXsXefJww9/vH3Ys5uodul2MQOPcp1+GaBcgv05hQ/0eAHdHsuz+161I5qUyO4uupWKGPlAjB0lLM5hULof9pih1a6dlPKPrqVSOorgWIm84XQFNMqfIiEBG9eN9jkl8P2BWHeUSb/5cBPfo67vRkISqm/A1wB/koI4b/6XPtNkIc1skzZVad1Wgx2jNZ50FPb0Z0Nxi5TTIdGWGP36qpdTxEjnkptMld3vOarbPMJIcMh8roTrDJyudPwMAVA5FVr3ls8BqVAp+ML2UlPRBuy3xDAK+KFRx6XOqq05N5lL7gwdoeelCh0sdOHuJyPghMRAoUdP3LxFQHB3gVWifhwhFB8CKwjj7sdPMvtQLsVUVDfDgydwCxFLYPLbtPTVZZhsyR4hykb/CCZm67dCM+8dQy9wzuPczIzSL7ewyC3Jehnl5PeDT4rNDNNM8bB5bCGELI3ze6WXv/4+8WfUzfu4+fYvxzeoDTekx30koVqZpSw4+4Xb9vdTfo802P1A01PWiWmIj524bFj1ha1a9GaYIQQJBA4W8j6cbAXlZe73bA8mSKZQaEtKk1etZHCnX4OsWveERKlfQcjAclywn5+KONCPNtOAVZZrj/+zQUovIvc9PgPwP8K5r27veLirZSaAX8d+PdCCGefZ5+/BgkmXgN/Tyn1MyGEv/dZHxBxZeNluGK1zl2IBrk6q0oKs++FURIfG2AH3070uuihHDHK3ss+UEau9lFPmQaUEZGJ7IKQu8HdL1jnA7WSC0RSW7aDuKPtqihnRchUxL1ALpBpVbDdWcML5U9lV0UXAnXQcdktlMDdC9nWCS676lwU6hjurjpqq7m3lnT1eWV4+mjNdnAs6oJP3lvJ88fie549UloWk9HY3vnAphtwPnB90fDM3SVvu7HHzz9zHzeI9cDp/TX3nruJHzq2p3fxg9DEiumCvUfezM0P/n2mVx9ldXcM01bacHp/zfnNpzlZfwVn99Zs150IrHqhCp6dtrSDl47cySDy3lnLdt3nVdT9aGhz93xLOwjWfb4dpHhPVTx+h6kSdBKhlGiz6z0xdX6g3qEKysrJSlpRTD2aFOMqKGibHSQTNOEjBu12CqxRQitcRSA5PHABCCHkxPIM0zEW/PS/UUnpKb9rH6TuKiXFO4rXdnMqPZG5YqIniZbzPMRCnqPEtEjfQ4xhaz3Yep51BapZRJiIHIEWbD0muKct/Zzoe8GB0hLlZit5blsDW4izBGUsRczpDPE+Kfotx6ApgzGFDPvHE0iOvd+CGb1gXuv2y8FV8BWh/0qpAincfzmE8Dc+z91fBH4shHAvhLBGEibe8zL7/D8rpX5aKfXTf/Ev/A87f9AXTnyfb7t4oqdBzy7une6ffn+5IZGPhj8hRN8SdvYbfw87+0tLX3neEO1lY/fFzmBrdx9hhEgSfhl2/oeIAe4cA+mY4u357zud4YVhWhClYGbZJHjAk/3F0/m56w/+4LbLNPlsm9pZbSR64IP/gneYovyMPMwUq6a0vtDxAgT/mdaq+XP6HMeTi+bOfXYvtImvnmwH0myij6uKfuefD6MlbMavQ5K3h4wzSwjCzvHtnhNhPO92//Zy2+659Gq2C8Vrp4jLUH7cp/JD7mpJissQ8j5UkNVOgjyMUiM1zw+RNDBkwc2FjnfHyvYzuukQ8v6VG/Lz6LR/yM+jd58zxAG/d5G/7sf9/x8AlaSZzyv598W6vRKRjgL+B+CjIYQ//gr2+XeAP6iUmiCeJ18L/IkH77Qrj79/vg4ZN1Sa3WmGhnhyFYJDm4LkZRwgqgelY9lGbFkrgS2K1JErUP0WU9bCIw8GGzFooxQK6aSMUtlXOTFCGqtx3mO8mB6FOCBUChovg57ZjkpTI1a0VqdEdB1l8cRBWmBeajZDoLKJ+yuvfXAhK+9cEPxcq0SlVIBHqZHeZ7RiUVsmheGg8fgApVUsKksdwwWuzit6F9irC47XXfYF32+KPARM8ERipjwSOdlPXp1x57xl0wmt8FNDoL92meAD28Ul3DCIaq6yeB/YnFyhmu+P70Us7PWkpFudsekczbxku+5kKOxCXsUAGKtxEQ9qaptT7AGOVq34mWwHhuiPsunFv6WNLo2bzmX6I0RIZKeSpg46Z2Q+AF08aHp0gWmQ8xhfjmlPtjswhcxDKpsUkioOEGU1kKiLiTaYtiQU00oTGKmwvVfZvkH5AR9ZHTpGi0mocVT0RpOooG1e4fkApYIhGKyRuDTjWlDxHCynYgurkI69kLi8YKz4nuxI4X3kZ4uRVEmwI32QwUhykK3w1ZShnFF0a3yzYDNIK1UWkwwZiX+MZ1o0sq+ioh08pmwiu6fCTw4geHlebfHl5ELww5f69kpgk18N/C7gQ0qpn4+3/SdABfxJBNf+AaXUz4cQvimEcKyU+uNIqnIAfjCE8AOf8yC0omYAa9FDS23KzFXtzNg1Wq0EuzbjYfdOhkQQDW/i900pxbLzTIsYulAvcA42qgBE/NPYMZBBCnnIyspUMOeI2MdGibkPsIr87nYQjHTTj7TAppDbey9sgmUXHfHiMnwzjGyUFJMVYvHuI8wzOPE2OY/FNEEyvR8hEx8CB7XlNBevMVuzHbykp/uQYZIEm6Qu+2TT0xQm+5AMXmh46cKw6R2fPtlw52yb3+uhd7SbHu887fmJBDRoQ/ALwbzXp/KZrE4vfL7L0w22ajjf9ixPtgxdy9A3DJ2jsiOUMMTXW1rNetPnAqaUoinlM5/X42ffFBJSURjFvJQgitpKUVtUBZPCsKhsNsAqtGJW2RyfNinE62ZRWXm8Eehjoo3Y/moZatdWM6AxeU5xkV6qd1ZUww7TRIoxMfdR7p88Z0DOt91GAwQ2VDvzF6vH5KZgK+lkzZgCrxEPFqNCVCrKisxqi0VgE+UHrNbihZ2wZKXRepI73xCXnKGcoDanUNSgB0kamihww6imBJKdbYjdNd4xtUoMrvoWU2wFetme09SH1Eahhm3u8OuikWR712YcvzQa4hBbbU7zwBIQ0ywnBlY0Da91+2LuqF/p9krYJv+QBxUF4/Y3P8tj/keELviKtkIrApYCRR/Ey1gCbGTZchomMacPnDLssl5Tt+SIMMl4FKx7j1Y6Cigs28HnAu/8KI2HxMkNOUFncBD0mLmXnssFyb4EoQvOCs12cBRa7eRnypfahzF42MT9zGOH1rkgkmU90secl4Se7SAGWClpPnXjWyfS9XTcjVVcm5VMI0brQuCwtkzLvczY+cpH9nPG5NFmYF5KYVp2Io9f9xJyYJTivHORK+5546Up16Ylj1+acFAX3FmJIOb2ecvNky3zqJAcfGB/UnB/2bFsn6QpDKebd+dPwfnAlz9+wP92acK3vOsGt++uOblrOL51AsDJ1rE83dAO8tzLky2fvL3EFobj2yt0ZF0st1N657l9vGEbOd5Hq5b9iTBmXjzbcrru83PeW3fcOW8ztc/5wNVpyfGmzzazPgQ2Q82dVSuGX15xb91T6PG9uDErefGs5bApMErlRmHZeSaFqChFeatiRqnMMlLmaZ+ol14xKLFESHVj03usH4fmsjpT+aKeYJ2kxiw2p7jpJelQ46rSBVmtaMUF5fHgPE7puEwQKbrRJdqMfvZTPKGo0NtzrPdjVqQ2EsgQBT2dCzTG0uuSQg2EssHVexKErI2sll1P66FxPb5ZCJtkcoAaWhoVLUAjYWBrGvKReicXlL7FlC3KDdhKEeo59FbojLYWIQ/TV1pSPu/2JVG8/0lsq95LKkmQznMz+AvT9lmh2Qzp94tsgeTyluTnY84gPDaFpVcsqoLOSRdutaKxllnp8/7Sc5VGxUgtxflOxzwthCNe69Fi1hpFE7/IjZXuyAWYF4rBSwGeF4qTWEQTJXBwIUqyo+mQVrR65Ps2yuEqSRYvGxkMVcrTWsNCyUqj8yG6zikOasuk0BxtB4KTorNfS4E+qC3LzlNbMTqaV5Zt75mVMoSbFCI1383k9EFSfk63A+ed4/KkzKk/iV9+Y1HTxjQcoxW1Nbzh0pS7qzZ29mNnlDr93/TeR5gUhre/4YAXFxXrjZgLXWoslx/a43jTM3SOq4/ssd8UtJue/SsTisoy9I43XplxdVrxtkf3eXheUxvNpnM8etDw8F7Fw3sVT12bRf9ueHy/FuOq6F7YO8+8MrzxYJK534eN2LweNAXzSlwg760NlycFk+3AorY8VHuePJjw8LxAkaL0FPu1ydJ3SUwSE7PaFAyFZVEZsSiOK5k+yumVklWm04XAYlHCroaWUBQo31OXFhWcmDsR2VYgye5DS2MKGISPXaQBYIRn0jB1GwVJiX3lSSuG8eKxdrBXL/IA0keBjd4cE6q5+JkUjSQNVQsCcNRrDsspRxvH5cLQ6RIfoCosTbfCF03GvPEyyOyVxcYViFJQDy2OSnzOy4kMRouGTpeUzUK+g0Ei25QbCBb87Eoc1v6zX3Rfr+2LoninZPikeivNSK1adtLdpQ641COGGEKIJykMyBfERJ5vCHC7VxQ6sOkH9mvDeecpjXCAT1uXXQR9XPZOCul6KqNY9wKfHNaG08w7T+EQUqjPo8ObFHrpvFdDYNV72kF+znmMYbxYrHufPcutGb3CxwvVwKQooogkXVQkBzAFVKx7R2k0L523LKqC07and4Frs5KXznpeOt9y3hYcb3uWrYQ8nLYymOqjV/ZeZVn1jmkMVlj3Lnb/huN1x9V5xcdunnM4K7lz1tINnmfuLlmtZPns4nEnk6nVWYsxmjZCHukzuvzQHs999C7f9A1P8vd++GnObj5DvzrFDz0n/8p7+PhP/hLvenSfW594mhe7Dbb4Ku6+eMbpp1/AlA3BO/rW8dS1Gf/op1+SkIl7az707BFvuLHH6nGBkn7kY3c4nIoiclFbfvLZYy5FW91N5/jKJw742J0ls7hquDKt2H+o4IXTbbTdNdw8bznd9iw7h1aK67MDPnL3OIdpLCojn5/zOejBB7mAT2YzOicpSD6M9L+0pWbgoBbzMbkQmGwM1feBWVGy7L2I1rxgxaaUC1A5nBOqOVssRSG3YSTbESInXMXAZUSOD3LREIHZCCsGoFIK3Z5KAEQlxm96eybsLjdI8S63qGKfYtjQ2YZ5qVHdilk5B+cotActzJSumFIMGyEYxMxMFTza1hBcnF95nKmiOlisYfXmlNBvKebXxNukugwg+ZrRUlev7uObRZw9LF5zzfmS6LyVUo8i+ZXXkM/8z4YQvm/n738A+GPAlRDCvTjg/D7gNyJUwd8dQvjZz/Ucgw8k3VShVfaXACKEYLOB/2nvYqeY8FAiBW9kebggBe9aFbjXSZcE40Witora2hjikEQyxL8lFzYp3mkpLMeWBEFaZPhqhEVSoZpph68MrfHMtMMURmhxXjq2zgWmVjG1itaPXXXGPsPArJTOu2lK2nj/bRxiboeQB2F7lWZRFcxKjVJFxs0fmhe0znFlUjKvDOveZYgksVNS0EMKgCiMyl7h1yJUUBnNw/OawoiSs4qUxHbwma6nM7XOc94OOSVnd7s+q3j+n7uG84F/93d9OZ+89RQgF6vSKL7s176F/UnB/iOP8fCTh7zr0X3Wy47rT7wTWxiCD7z78QMente898tu8PjBhFlUYz51fcaNec0bDxre+4ZD5pWld4HLk4K3P7THJCoyex9Y1AVPXZkJ7KAQc6toYHVpUlBbxZOHDZUxtM5RGcN+qXn7lRnXpgXbQVY7lVWUJiUwqdzV6n5LZaSjPqgN9zaSwpNea20SXCZ00Mqo3JGmlB3lOvbKSrIfbZFZM0UYMruktArTLjOHu4hccHoXaX0Fk6LMKyrjWpytstgnDV+PnaXRllBNCeUUNbS4RqCO3RQb52Cja4grCMq5GLhFb3EJPK6w0U5AuOAKsz3DTw7YDJ653+CLhl5ZihiyXK/u4uu9HMOW8O15oVBn55kJw+ZUMPrt+cg5f43bl0Tx5rPI40MIH4mF/TcAz+/c/5uBp+K/rwT+u/j/Zz8IPXbekGwx5Q3u3Lj0A5iV5oIToNEyIKxihFUKQVUKbm0Ffz7aOg5rk5e8nQu5897dV4JNKivQjUbBRBSXLuLP28EzK6UgHG0ch41EPKVYNqMLjjYDvRfTH/EFH2mALjIFtoN00XLc0cI2QjSdG1hUBcfrIRr1qyikCdE8KWHWmturlnVvOYoKy4f2Kp47bXn+VAaNL561bHpHUxiON33GO49WHYfTMv8NyLLveWW5c95+Rue9bAeevnWe03e61mGMjlJ3x+qsFSZBe1HCPNuvufP8Ke/7ykf4R//wOc5vP8f5p59GacMf/Lo/yk//0M9w43f8Gl78mR/j5odq2m/6dTz/oafZnt7FVNJ5n7zrnTx+ecKP/8TzvPHKlF986ZRPfuqY5+7P+aonL3F5UvB3f/E2N/aFrXB5UvAzzx1zKSovu8Gj33DIx2+f50Dka3s1pwcTXjrbSqi0UTx7vMEayc8stOaJ/ZKP3F1yfVaw7j2HjWHZeTa9DDI9Ak/MSoOL4Q/nXR/93WXuAolNJCu2ysZh9pCG7WOgyNTYCCOO1sBWK7QuKIZO0um9JKvnIIRYpFUYp0GbPohBG2B1yZC8wbXNE6wyBBgG6XC1FfXk9hS9PsZPDsRjv2zQdo9aB3o0VosfPbZB9RtsLNZq2NKbCguizDQVoZqBd5S2xEe7WKMU21BhAvTTK5QhXUwMThcoW3Lcei7VcxmcAqFZoFb38fXr5+P9y6F4qwfFBJ/3AUr9LeBPhRB+SCn114D/HPhbwHtj5/1ngB8NIfzP8f4fB74uyuxfdrt7tg6JKpVENalgn3U+pt/4uCy86ARoFFlKnry1U6r3gRk4djZCESFP7zsX2DOOpTeZMZC29H4kP4mRsjUuP3ejzGC0ZHVeuvo+8q1npc4Y+mnrmZU6OxGmTj29Dh+x/Gl8LXuV5nQrRXJRG85an5+jNNIxH1jP0otgqYuFX44ncLx17FUmv4d7pawg0gUKLqpRk3Nden89QpPcvbiFEPI+kvgovY70fhU6Dt527AAevMDuKgyf+sZ/l2/8N/913npjj3/zqx/j/R+9w7e+4zqr3nOy7fnInSUHTUFlDfPScLTpuTwp6b3ndCve3IWWwe2njjeR3654y6UJzxxvJHHeCd/7sUXNnVXHpBCcX+YfimXvOdkMvOvahJvLPgdDa6W4OrXcXQ88NBObgH02HNHk1zO4kRFzUBuMa7nVGoHpWkdldYb30ns/KwSXr20aOkLTHuObA/T2FF/NL/C5zemn8dNLqE7sWeWEEbgi/R9sjTm7ie42+JiGk3Mq7ZhnqdyQ99FffhJ78pIIfSYH6M0JqlvRX36S4ug5oes1++jNifx9fSyMlCIZU5UjAyV4QjnlXm+5bMX7Owl3OjeGMFcajlvPPNrewsi0SWInuz2hrRY5t3ZeSIKW8T29sswmzWuuvN/7I598xYXvP/76p74oK/2rlscrpX4r8FI0n9q928PACzu/vxhv+6zFW6uUYiPF1e90EIMPmHiyJ5VakjunIWFKs1n2IcMmRilOsdJlexlWrnpheGwGz7pX9N7tiGvEgzlZtoo3uGJeaZadz9FlW+cj/KI43ToOGsPxxmV/kOuzgpOtZE4Wuoj4t8AeCa+elZre+QtQSqICghS62ipWER4xnWcTXfVSpue6dzy+qHnhbEttNUcb8ew4bArOW8fTx2ueOpxyc9lyvOk5aAqON32GEM67gXlp44pC3BnXvUNrRaE1R5uOG/OaT95dspgU2d3vE7fPM4Y8DB5rdcaQT85bbGHYxpy5pO3YW1TcfOGUr3nvI/zwTzzP8mRDe3qX4B3f+G/+6/zdP/PnOPu238Vf/as/ydEzH+RHvuPbeOajdzn99At0q1N0UfLIO97Bb/maN/A/vf+j/Obf8BTP3V/xzNNHHF6b8Y5H9/maN13i//UjT7M/k+Hbt3/Fo/z1n3uJRw4m4lDYO37dW67w8y+eMot0w2t7NV/5yIKfeOGES5OSRW35uZtnuCB0S60Uv+Utl/nJF0745qcus+49s/mM+yfdhfevd4FpKVBJr0vOuo7SyOeX1LMyt1F5dTX4wFk7hiYUzSGbwTMrp6ycwsaUeIDp3nW8rbCbUygnOZhkV/IetMXPr+FdJ0Zu1QztRj+45IeiXJ89sde9Zy8qKVPSO7bGnt6Uwjy0qGGLm18Tjvn0kkAZQysXmH6TeeHK9QRTsqeBwRO0QXdrClMwqBEWDEoumAEyu6pY3iEUNa6cY7sl53aPmWupQgdugFBitueEsqHUFvjiogoqpf4FBCo2wJ8LIXzvZ7nfvwT8NeArQgg//Vqf91XJ4xEo5T/hcwQMv4L95QDi//r7/iTf/h3fSYpz6uJJ6y/InMf/ByX4IIxDoNJI4koRB5pDkKXsZnCUMUFerGAlHTxJ51NnGELq+iMfOwfVpg7aSTJOkCIPIohxXv5Pv0u4quCYyQe8QL4ogk0Ljp+6jjHJR8yIdgWHGoFvUgDypJDnM5FlMislDX1eiTClsSLxFiaE4trUsqhlwCZ5mmP3l/jLq046+sSKkPdYc95J13ZjVmX6IsBXv+Ew+6UMTnDwJDv3IVAZnW1bgQgTaI43PQ/v1bzx6pS7cfiZBnpn3/a7+Km/8pf47b//9/DS3Sf5pnde5+f2au4vr3J0tKGZlbz1xh5vuz7na37tEzx1bcYjhw1X92qhMk5K3nx5yte+7SqLiXTIb7485WvfcpUb84reCQ/+3df3aApDEa2EF7XloLa8+/qceWU5qAxPXZpQGZO91Ve9570PLzLEpYNjUWkqW1AbldlPisiWak+ZFlPmcdWVzpnUDFgdYoOS4MHIXtqeMK0XbL1lakH1G7FL1RZ6hx5ayZeM0IacIAJ1pOBi1S7jmz6gbSWGT0rMpFS8kkrAgpE4wLpBDVuBTZACrFyHm1+TKMJoAas3xyKTH7bCTIlhx2rYjheQ4FGDpQwe3S7FqGpzip8cYIupJPaEgNquaSoZdhobRXNFDUpTOpHmz528jk0xF6gnzrUIfrSKfY3b61W8lVIG+NPAr0ca1Q8opd4fQvjIA/ebA7+Pz+0L9QVtr6h4PyiPV0q9E3gDkLruR4CfVUq9D3gJeHTn4Y/E2y5sDyos0wiyNBoXl4yCA4b8v9h3XrT4hNGXORX4JKRY5sQcz6ISnLm2MhBtnc+MgIRJV0bRxeKdvmz7tWHZSoe+iZ1Uxuh9wBbg+hRIKwPFtFVWoZwsqeelzoPWWWmycEQ6b3m9YjUrdqHpdUwLTWkUTSGrAunQhS1iVMnddceqFzjBKMXlScl28Dx9vMboCS+etZxte2aV5d56FFmct0Me7iVL1dRtFkZx57zl4UXDx28L5n33rOV8O/DJ2+fZQMoNHq0VdVMwDJ71sqOsDOvoQ5KYD7NFza3nTvhVX/ko//DHn2N57w7r+y8RvOM//UO/m5/9/r/JV/+r/xp/92/+A06e/TDa/G6e/cgdzl78OK7boLTh9pe9j0uzkh/+4aeZffNbeO7+imefOeJjV2f8c4/uc3lS8MMfvsV8Kp33I4uG/98v3uKRg0kMX5Y5xAdfOGUSVaYPHzTMSssHb51zdVry8F7NJ++vL3Tev/Wtl/l7zxzxzU9dYjN4tt5y3A6sOsc0YueiYJULZlctWJ12nHdyriw7l20RjI7mYYVcsJfd2Hm31YJtH+G8wVBawe5xgdpWeGUoz27hJwfCsU4pOcm/BPDNfh5GOl2ga2FlJMGbSoVe7Xi1mDFyMBRSGKVwF9JZ+4ahOUQHl0VCqhfGiLEum16poaU31ehvn6IKTSGrZ1tJMERUiGIs3eCZGIvuTwm2xJUz7PaEU7PHnupo2mOxpK1mqNh5i/fKF1WG5fuAXwohPAOglPorwG8FPvLA/f5z4L8E/sPX64lflTw+hPAh4OrOfZ5lxLzfD/ze+CK+Ejj9XHg3jHhvCLDpRxtQE3m0m0i5S+6BCV4IsWte9Z5ZTHXXUc1mYycq6khF7TbcHQqMlqSSSaFl6BQhGR8Ce7HAl0ZlqlhpFLVRMa/SZLOoWZS4C89Z5wsApAGsyvi0iDtMTABS0fJT9iWrAHXBda7Q4mOcIrq0gnkc1DY20HtJrp8UApP4AI8t6ozDGq15w37DQzNhSDyyV+E8XJ2WmVFy3slQtHWOQosndqI19t7z7mt7GC37XdQyEH32ZMNT12c4H5iWllUnn1VKjL95uuXyrOJ45yLhfODavOITT17i4cOGq//Cm3nx+BFevPdWQgh86zuu8yPf8W180zuv8z+teiZf+15+/P/9F/nyf/F3srrbcP2t7+L09h0uPzSntJq9wwlPXZ9x63TDdK/mcK/ikcOGJw8nXFrU3Fg0dM5zeVLwyMGERw4blttBTKuU4vHLk8yG6ZKDofMsaqFmHjQFy0ip1Epx3nomhXxWg4PbayncKRczvWfbpQQ6a6VYdU6CM+JFAMQE63wj+02rH2ksiOe6Ydk55lPL2WYQOmHEi7cKjPLYeo6v5iw7j1Yy0HQBKiPwQxLpOB9wsdEwkXorEJ0FM+aWqgChnmeHwlBMCOV0xLLVJVyE/rRKcn4Deka3ddS2lou/VqAnNEoyMDvb4AYvTBZtaXxPCKXg+EpWvbUOLD1M1SCZtWn4akppqMI24uriAZ4uLNlX5TVuryNs8nIw8QWChlLqPcCjIYQfUEr9kyvefBZ5fAjhBz/L/X8QoQn+EkIV/M7P9wR7us/dgNMFGsno067HBc1hET094om/6wiWuNEechEFMgSTaIJow+VGaHtyISBj5gljTzxqraQLBvl9NYwdfCrQm95nDHvXE6PQsAyBwUnuoI7HmOKwBh+oYlSaVvKcKakexuHerBTIJCWKpzSSIQ5D7607DmrpuA+bIocOX5+XOA/Pn26YllIQbp63ItAZRuHRsh1Ydo7e+RzIC2JwNSkM552L+90wKy1n256ff+GUm6cSfZWi1NKXYH9ScPNky2JScLLs8F6izpzzXDtoePHWkq9553V+9IM3WZ5sWZ9tUVoG0c989C4/t1fz9Ad+hvmNN/Hl/+Lv5Of+5v/M5Td/BauzNUobNkthxwDcPWuZ1QUqDh3LCOtYLYrcEj2yPPw4gN7G9zNtpdHsVYb9Wuh9lTFCpaySGldzZWKYlYaDymSaqEbk+LsRdpVVXJlYNoOoMpNwar8usv3Bfl3JhaKS4fHuoLc0ikVlUP2Gg7qmNjKkK03I0KHadujtKfN6IcXVRntWrdF9lJ5H2uASgXWUGi2W08A+ZWCuWydWFDFYGCU5ssXyDsP8Kjo6DCaM2urRbbPQQiQYwkh3NP2aUDQUwVOqKM13PUtKpoCPfixb57Fas1+CVxWm34wUQG2wKLydZ3OqnG2rraxAPl9BeQXbF1K8dyHeuP3ZiBy8ksdq4I8Dv/sLOb5Xsr1WeXy6zxM7Pwfg3/7s9/7MbRkkWcMHKIKPvOqAVoZV7yiNFKHELEkDSpACvHXSwSb+M5CXo4lBsV+WHK+GSDX0Fxz+HvQ2Sd7X6fPVCHe5sTHQoNCoOKCkgG4ImQnSOSncvfeEoNm6aHgVwoULBaTEleicGGQQWe8OoUJyPxttRNPFqdrJM1x1PnfUnQts+9FpLnWI28Fztu2xRjM4z2k7oLWwRgrtsUZn/nMfB6IAJ5GCeG/VCXY7+GwAtdkOGCuJNufbIQ8qt1GmrpQU7/NmYHW2FZOrZcvyZMPq7vNCAdx+LaeffoH7y6sE5zh78eOs7jZcfvNXcO8TH6A5uE57fsTs8m/kYzfPuffci5ysH+Xpm2fcffGUEAKLScmbL8948daS+zEk4uvffJlPpuFq7zhZd1zfr3nu3no0rvKBk+3AiycbZqVhURe8dL7NwRSl0Zy2M14633LWzWiHwL5SnLWO07ZnUhhS9NyitmwqGcwdbwd8MAwOlt7nFeJ2cJlR1EXefjKdKrSsMCdVxXLrUZVh8OniHec9QbjVoiiWdKngAyoEimjzqmP6DnH/yQMlxKIegthOEM8t1a9RPdn61bqeYEtMuwQ/YEJgQ0m1wzCqrMqsIxeSqZtAJbpbE2wlfO4gUvvG6OhJL8fSWIEQV4NnpgfJwgwebI3qN3RYtDsfRTr1XGCTopIkoOb6F1JeXnb7QuLNdiHel9k+H0w8B94B/Ghs0K4D71dK/ZbXOrT8olBYTq3K8l7NeLLq4OhLTWVUxn6nduwkUscyeLlP53QscBfTuV0Q7unlSUnpO6bTceixa81ZhCFLeZMrW2V1FO0I/p3SVBqrslCmsfrC0LMpND5SwToXotf4aHWrlOJy6Vh5kZ3vRnXt8t3TqkEraGzy0JD/55UMJl1IfYjNw9ZZoSnMBKsVjy3kSy3DV5nS996zHXzGbHeLWcKpExxwY1ZRGMWTBxMe2284f3Q/M322MdW9NprCaO6vO/abIhf8NAS9NCl58anLfM0bLvHUtRk3T7YcrZ4QJWRV8DXf8j5+07seAr4BgOW655HLE569+VZsYTi5u+Jtb7nM45cnvOm9b+bdjy64NCv5xYOGhw8mvOX6nNpq3vuWK0xiqtGThxN+9VOXeexgwrp3rLqBG/Oa/bq4wLCpC82Tl6c8dWkq+HxcraQVyaTQPHU45XJj+PRyyBa26XPTSkQ7695lc7Dehegaubt6Mmwjn3/ZiyumjqtDH0TV6kLgfhuH6wq6EFWIcfGY6Hdqp5caB83RsyTOVRIsmBoQpRSFQsypQDpab6VwmoKhmWC7ZfTNtuA6lBtwzT6VDxS+Q8cOmD6wpxUMARMxdhU8JzQsjEENLbqY5GO0m6MswQ/aUkdBEaqOPvvx+04ApZkVGrXcxBSfDhUDipV7fSCT13n7APCUUuoNSNH+NuDb0x9DCKfA5fS7UupHgf/gnwjb5HMpLJVS/w7SZTvgB0IIf3DncY8hoP33hBD+2Od6jtWQ/KpTeEKUjmvBnou4vN4O0Pux805LuV0WRVYqxrM2QRo3piVHa8ekKFhu+0hVkq4bpPAKr3mImLewMC41lqPtwNlW5On3Nz2XmoK1UdxZ9Sx7w9nW5aJ3bVaIqMcHLjc2p9Gn5frgpSgvnWbwns6PtqjyJdZZCLSLuyd4JsEnq85hVMVL5y2F1tm3+nBSsO09N5ctbzqc8KljgTmMVizb4ULnfdAUWTlZaJU56EmkMistN8+3zCvLyabnuXtrXjxeC36sFevtkKmCVitu3V9TNwXrKJ/XWuGGwLUrE555+ogXv3zDBz50i+PbS9b3b+KGjm9776P8yN/6h5ysv5Kf+6GfZNgsaQ6u83TVcOcXfxxtS4btks3yt7KYlHz8H32Qn33ikA8+c5+bnzrm2etz7p5vufzuh/jHH7pFMy8JPvDlj+7zIx+9w+OXp2y6gfPtwNe/7Sofu3meMzIvzUqeujTlE3eWFFqxqAUm2vVteeNBzcfuLXnjQZMhK1GTSvBFGymck8LIvEFpbq/67NEDRAvUMY+0ijBYCv6ISY2EAItac3c9yHPtNBbSgPSZYodWY/oOI+Ml3bftffa1T913rxRK2XGo6ByhbMB7gSWURhW1/B8DGPTQsg4FmDKmGYmV8Kr3cQXhc7M0iTzdUDTxvDcS9FAfXPi+Dz6gTImP96VdigdKgEoJNbepphLJ5p2IdGLn/XoFED9oB/xqtxDCoJT6vYgVtgH+fAjhF5VS/xnw0yGE978uT/Qy22sJIL6GTFXfHUJolVJXH3jcHwf+9is5iJnqRXAQ8a1GSXcQlKaYyiFemdjMiy4jthmi5Fjc9lQ2zk82q8+edjw8F8UjwdNYFW1gNdNCHpeWTyF2XUmGn7B1o+Awuu4tKpMl82LvaphaTahkGZZM/AstJ/PWBfYiZWyAeNyCIS47EdEk9org38lhULaL7BmhCCorq4snFiVlGCgPG8HZO6EUKiXmVJXVLCrDO67OMjc9XfSMVpy3g6gKtcwJtBpta5US3H2/NhxtJrkz754Q344qmlTtDlmXnWNSCD58L8ImZmef5+99lDfsN3z9m6/kEGXpvC2/5//yG3nb9Tlf/7arGZI5nJZ87OaXUVnNeTvw+KUJf/jf/y/4td/5nfz8L92n3fZM92rWy45PPHPM8m3XWJ5s6VqBclIyz50Yqrzd9Nw62XLzZCPBylpxuumYvvshltshmnGJ46D3PUQhz35lKI1g32edXOD2a8u0NOIkGeG3yir2ShMH3zbSCKPHt0oUVI0vxNskwRtWCRvEtEtmVYFeHXFjdgW9PWWidKzMQvfzzQK1OWUWRTni0hdZJKoQX5DgKZQW+l3yIE8DyIEL7JSDogEXLwohCPVPW7Z2StOdEooGZypsnO0A2e0wMcDS5kLYUUuKGMchMv+NU1mQ1LnANGxxxYS764FpUcDsCkEpvAsM5Ywr3RJX7aFtBd7R20Zek339ird5fWo3AHH+94MP3PaHP8t9v+71et5XHUAM/BvA94YQ2vi3O+kxSqnfBnwKWL2Sg9hQ4D0EDA2w8obE5D7vhF+dBlBN9PmQ54RthCa2O8rBVJBrq6K0XYYlWzeQUrs3g/CtU8ccIKaDy3J3FZec81KGd6dbwdzPWpd53qtYMFedzyIdGx39AKaFiUb0AvF0O7BH4pKXRtHGDqr34YKq0cVVcEomTxcHoaAJY+ZkK0vJ9Jx7lcwJXjxrKU3Di2dtHr7dW3dZDJWEO8l2tjA6DzRBsP1ZZbl53jIpTPYyef7+GoDz7UDnRPVaRvz9dNOzaAruno8e4M4HrsxrPvz8Mb/+XTf44V+8zen9NZvzDh8Cf+S73sv/9P6P8lVf/Sgf+MBLtJue2X6D1op7z70o78t2iS0b3vmbvpUf/0t/mff+9n+Zkzsr7n3y55leeQz7xEOse8fp7Ts0+4dorThtxTu8rAxd6+g2PSebnvOVRLBprdiflZy1A3fOW24uZTh33g6Zh15GPcDz99csOzEzu9xYfuloy2kr9rqJUTIrhXdvlOLuqkOrks4FNmHsvkFcIZPFg3h8qxhKMBVlbb3HSefZrxck1qkVhIJyewxFjatm+b0FCKYSmK5ZiJOfKfCmyDCkct04AIyWr4TAMhTsuSEaBBkJRVCa2m0ih9xh/BpdNAxKBpP5eJSiCFGtmby9tY1UQhHv2PaMoC2lsRSkC4kmqAaNiNWMazHndwQWmV1Bb47o6gPKzUnkjncUE4Nul4QYNPF6+Hmn3NN/lrfXEkD8/wR+rVLqjwJbBMf5QBTz/EcIaf0/eEUHodWFdJJy57IoJkDSxQikp6K1ZpSjx/vWO49JHWvr4lDFj0W9sYo2nq/SZao8uCy1IhjZV6tVDDyGymhKKwWwdeIEWGglBkFK5S+h19GHJWHyBGyM/0rDR8WIMdvYKYvJv8rxXRCVpRH/3vUvT8fdWMWi0lnEk943q2WoOy8NRikO6oJlJ51lUrSl57g8GdPjJbsxZJvTde+4MatyQV9EFWWhpfCdbPqMlxut2HSOG/s1i6Zgf1KM3frgefigwYXA5VnF+568xCdmZfberqzh2mP7PH5pyvOPLehax96+4PRFpEoOvaPfOm5+4lNcetN7OL69ZOgdpmpw3YbNsuN009OtT1HaoAtZ4m9XHe2mYugd21XP/WVLu/lM3PR82+eAC+cvhjMnRSvAqnMcVNJdt4OLQ2IffbdDZhYlg7Dd2QF6tARwYSzcEHNXlThg4mXoLgEK8vUUJojNAhk9SBKO2jFp6gFcNKbyDpUKabRmVZAd+tJBGVMSihrVrUXQE4TVFYoGui0qMlFA4JeglKTFP9j9JgFQDIMAsgJUBS+RfsagXY9Ho3xH0NEN0Wp8Pc8ZmcHWFL7D1wt0t5LMUFsJnLPj5/Ir22sIIFZKWeAQ+CokbPivKqXeCHwP8CdCCMsHZPMP7i/Tb/7Un/yTfPd3fzcg3W+6wnvG4AJ5TBzoqai4inzuIhbGMow4+OBFCVlohTMazZi4Mys1p63fiRmT59NqTEcxEUpIKEbyDalioatMWhIL5UwuBDrGrgkMohlxyWw9i6wobBrKqtFbJQXnBiWFeJMEQRqUlzdHEQhpKBuG+PwyNNOKSOMiBg4ESquovPC4J4XJz1PHsN2i0NGPWudB3s1ly6KyVNHzO18MiaIco2kKk+9fGOF6d9GpMKkcdx0G55XEtZVWc2lWZbqnUVBPpdjvzSvWxZAx9FUMSB56hy0cPPwIznmG3nHvY/+YanGZodvQbnqBgj79NO7SBmUMy+0/z+bkiO2iot861kvppjdLkfAn06d28BydtfTe5477/qpjue1pSotSipunmwx7bKLjZWL/uDB2wMn/xsTP0TFmdDoPZRHPv8g2CRBVvuLbUZoCNQyUhZJiakowhUAh7KSohwDBZd500BYFUfXYgY30P9fvJLBHr4Ld5HY7jYU3jOELSe4+dDB0hGZfcl8TJOgHwcKV4kLHBfioftRDK5zzOODsPTRDKwXaS2iE8T2VNQQVoNwJWTBFXB3sHKd3UrS9y3zw17p9IWyTL9btVSks480vAn8jUgN/SinlkanqVwK/XSn1XwH7gFdKbUMIf2p3n7v0m9PVJiQoRJKQUqhCyEKD1MFoI1+EoORLM5gYFhvPpd4nqbLcXzBJCZJNePbWCTSSvoTOj9itZ/wZUgxV8vEei3natycaMEW64eCT4EhhRlfNC4+xamSmpAVDscNWCXH49ODFT+6rcue29AZwtMPo6eJVUu8NHDYVRxufO8DEjkgMm9SBewfO++jHEqIN7hh03EYhxlikQlaFmh2rgvT3B/+vIga97l2GWMaLmtDdktPfbuZkCPJ78CI60VbTtQOXbsw5u/YEQ7fh9PmPMrv2BgAmlx6imh9KrqbVFNMFRWUJHsrKMikNRbSSLStL1cgFajYpqCP8A2SXRRFgSQTbrEx+8ONFp3eyOupJmoHAIkbL1Vax6cfcTPCxOVA7tE8VWSeMhfBBEUoK6NUQigbVxSKrNCiTu+ohGEptCRaRygcfU25U7pRVDBdOW+ciNbWMuZUxtQZTgLbSdXt3gZGVOmQXAuaBYmo2Jwz1PoSQczLxjtKUBF3GLFqxd66NRfswBg3vbGOOphxHj6ZUmmCKzBV/rdvrNbD8p7m9lgDi7we+HvgRpdSbgRK4F0L4tTuP/R5g+WDhfnAzaWijxNdY6dG4ptTiEZI4pbtduFIqMgd89kg2KqXWQOekC3VmHGRWGnQhnOj0RUwFuWbAFpL9Jz4kcv8Qh5yzQkdWiqLwHdPCUBrFpIgDSiXDqDOBTwVaidCI3+H3EvwFsVEdXTrTKaziFzw59MHY5SkFJq5I5sMZWzNnWiQrAJV9Ug6aQmxKA3ROaJapw/ZIEV9Eg6YE/SRLAJCL0V5pgDpGhAXurrpMn7s+q2idpzLSed86b7k+qzhsCm6vRoWlDxI/1g6et16ecrspuDyrWHVDhmHe8eg+B5OSX/3UZW6ebHnksKG0msWkjDCG4/6y4/6dFftXJmit2Lv+CEorZtfewEsf+EFm3/Ve6sWVCBkYZrVFa4UtDD4WfhN/11rli4SP3HUXoCnHwrBLnwSBsY43PZcasRQQvxhpLlrnOd723HAlRRgy5JK77rhCSYrb3S0QFcY6hiuouIobdtz6bJ0Hd7a22a0vbUk/MJQzkbHrkQKqQhAOBIizYIRBAJwLYAxBxeFnTOUBCIWOsEebv6PJ3kH5AaOLUXQQj9PXCynawYMen6dzgToGFGqlqI3c3yglgeK7WzTKksg1+W4ryGlB/W739CW+vZYA4j8P/Hml1IeRlPjvCF+ov2zc1juimwe7zWTotOrTEFCzdZ4QY/G2g+e888xLsntbSuKZlTqKUJLBVaCNT3W0dSJB9iEXyFZrPD76oghVbC9CLL0PnLaSh+gDFNoCIXJpd7i5buxuq4gv6xAVljuvbxc2SDBIHSGY0gTq0LEKBZWVC0jrxyxDiMW82GcWu+LKym2lESrljVlBY4UDf1CrLPuXgGNRpe5a7HqES54oZy7Ia1jEmLSZAk1FClBIIcqpg7kylULbFJpFvUNHC3JbbTWP7VXMSku759gOPgc/fM2bLvHmy1OO1j331h1PHk7YDp43X55lsVAdza1cCJnCmCLWZt/1Xn7f7/nP+Jf/wL/Fx54+YrpX8fC85i1fdoO33tijGzxHq5ZvfPs1PnYwyaylpjTcmJX8tvc8zI15xaycUGjNC6cbtFYxaELzTW+7SmUUbzpsMBoeXdRcm5WZqSNBC5rD2nA8yGsySvGG/YrzVo6/KTSnrUj0xWohxvYhBbyKNsa+XsiKaHYV42NEWr8h2Ipo/f2yeLg2imJ5Jxb7ElUvGLzOnjsa8THJYQxRsbwMBZWR1+qVxQbP7U3gUmPY9IEQCrz3DJHqKI2RBhxGFZKfKWc0M6PYhAJPgYuWFtOiRgfYYoUdFhzngzRdSolXfmKMidAODv0GV5YU0RVRGwkvxlZUrw/Z5HVlm/zT2l6rwvJf/TyP/Z5XchALG6tn8EJbild/p4s8tGtiek36Oe4/L0trO2KuqfMWJzgdI7mkk62dTMIXlWFqFaAYQsSbfY83Bdr1NBOL0aIquzKxnHUuYpWKiVXoboW3DYXWOeShHTyVSR4QipSeAjCvJKncadD9mqKcZSaAjp4U2yFk9eept5RGXuNqkJNt1QskMjgpiOWw4XwosWa0lU3c4ZPtwGFtWEVPDqPJocQAp23PoioylCIKQE+h5f3svWdeWk7bPmdfnrYDp1vBKtvB5QuWVor7a/HJvjQpubVsSd7MvfNcnVW8dCZRY5+8v+Jo22csfFEf8NPPn9AOnpfOttw82fLM0ZqmNHzs0+cAbHrHnbMtZ+ct2mjK0vDsR+9iC8PQO+4/+zG+97/9T/kTf/YfsD27i9KGj3/ZQ3zoxz/BzceuMfSe5cmG2ydbjm4vc+ddNQXf8KbL/H9/4jl++1c9xktHwol/8Xid2Sa/+tEFf/3nXuK9D+3x9PGGNx02PHO84c6qzSZgm+iJ8u5rMy41ho/cXXN9VnFvPVx4L3svTpUPzaK0f+dbFftLdLdCFVPs5kiCd7tVpPr12RgqKB3vD17JV9j5gJtdEUhF25jOIxzvDNP0G1JwAgBmj1nYojp5jHUdvppzvXIwdBSRleKLWqwBNBmy8Uq8yzPO7Xq6oIX2S8CXNco7lO9Fqh/ikBLNnpHnaz3sl/H7G6m+tfWE0AiUlAahauy8d+0NXsv2Jcc2+T9qSyebUkJ7SpsPYg+brszBCcdaDKh26HPhgYFgxLkT/t35QKN6em+wtoFA7Mh1jiiDQGMLusFT2YJlTNqRouk5b+XCcNY6tDKU5Yzlss8DVaWSQ6HKK4mUCAREpZ1cSGbxQmO1wpoyCx3Sa02S6LQiMHGo6hJ2TVzOG4NHOvJlDEzWKrFy0jAtCpH8xZN19ztgdBp0yhdp2Q3ZabCPcnsXQs52dEEKau88lTW5i1n3jqaXrnpXhXm6HThadZy2A7eWbXYo7Jx015+4fc6VPUntuXO2ZdkOlEbz0ZdO8T7gnadrHX074AZP1RSc3xGvM6UN9d4V3v/TL3L6wkdpz48I3vHM3W/g6FMfxFRfxbBZsrr7PKvH9jm+fYaKEV+TWcV55zg/2vCxT59nHP+FuyuCDzLYDIGbR5sMKbk4CxAJvWdwXhgnTt6jzSCQSrLcTSuHNF/YXZtqlQQ2oiYWDDs5VUUjp4QpKyWOeiH5/Mj9DBGH1grdnov9qykhBgEn3jfO5XCGhDEbJYNJNXTZh0THUIXE+Q6FuBvK3EhLYnyQz9cwCoAgriY9kToYpMCHfscIy8u8R9uMf+caoBTGjSuNwshrJpAdEVXw8DpZwn5JYN7/JDblOswOxUhsKhXW9TQxPknk6PKmJ+aHD3LCzK0HpShiKyMWmGTMuggKgqS5ByXFdr82mT9r4rLRuJbKVigvSzkb8fbGKoZSZ2+VZE27V2q2TqTqaRP8WH7fL+B8UHE4pSN0IzSwjQ8cVOMJlCxt06qhspo+dsqFUXkZajQEJ/L9fXpCiHS6qJhJaT2zQke+Otm/fFGbKB7y1LYaKY5xWpbw2NqWKCWwU2WrDDNcaoo8c0i8coDWuZg1apiWhsOmyJ23C4HDpuDGvOKgLviqR/djjJvLiTff/hWP8ubLU950acp2EEfAde/5+jdfFmtWLfLzpCS9PCn50Fc/Jhe5qPB8eF7zE2+6zHkrWPpf/C/+W975m76VZ3/mZ5hdfwOXn/oylFa0p3fHz8o+xLw0eC9GXU1p2HSx2IpBCBroYwyevNbAvXVH76XjXsdM1UkhMENjE6wldgqeQDck4Vj0qfECtyUbhRACg1Y471hE5sVQzsaBcoA6dDuiGzGS2oVB9AODPHN+Jzvxqf5iJqXswzLf3kOvjkApfL2H7pawPWO4NMWc3iLUc9TpTfy1t1Cu70uaTnuO6rdoG3MnUzffbyHyz/X2jOA6VBQH1XWFauMA0xSRbeJEhg+sozdQpS3rITApGjwK20WZSGTcSNF3/Mom26uWxyulvgz474Ea0W79WyGEn1JKLYD/EXgs7v+PhRD+wud6jqBtnog7W2dXQWVKun704NYqinSGkY9caEXrVcZhQRgQAel2dYwVK7XPUVRGib/ErBh9jUWnUMbloY77ChnHXnaeyhixkY3UuLux2126FB8mK4NNLmzSaftAHu4FASDFkD8Gzyb4IQ1cfSDCIIJFd27s3JJgR7Dy8aLhvNyWuv5lDJNI3SCQgxd6Fy7EiRVa59tBCrN04wUn20G44R6ePVnnYId1L+yUOk7lzjtJE7o8Kbl53ubOu/eeq9OKZ+6veN+j+3z83opbp1tO1sITL95xnb/+cy/xtW+5ys+/cMKdsy2PHIgvxidvC2zSdo6hd3Stww+eZl7y7C/eIniHtiVaK97yZTf4wN/+cdrTe7ih452/6Vv50P/2V5lceoiTZz/M9vQu1df/Vra7xbtsOG0H1mct59ueTTdkZaYfPLYQBWy77cf3Ja5Qlts2Uy9X3cDxpufxfWFJrGNRt1qUrPK+2vxe79cy6FaMw/omDoXVsCEUVsQrO9+PoEsUMTRhRyUZlGZALA9MpAwGpQnTw/jgQCinwkpJ6TuxA+9nVykg+4sEW2fI0k8OpPhPDggBusklLDI8DaYUCGcnqDjELl0EOjWhaLJop/VQ5xWEjh4msXEJKd5QoVxLbSuUa1G2ymZZIVJw0wXr9di+JDBvPrs8/r8C/u8hhL+tlPqN8fevQ7xOPhJC+M1KqSvAx5VSfzmE0H22J5Chi+BbBqL5DnEiLX7VRkWRS8SuIeKtiGWq5mIYgwopuUREMEFbbIRmiEU/DRZFPMO4lIuTcKVGCCM7uyUBTsSzdyXlSWqU7pOcDiVeTUXzKlkFCCsk5Nch/6tMkUx88+BHOtruPLiPNCsfLw6ekFPMey+Mk7TMTwyTMpp6aRWYR6m/0fGLs3Mypy6uNCqbV5VWcXVaRUhFU5jRvCkl6yRe+Lw0+X3pvdx2EDnbs9JyfVHTxECEw6bgjVdmPLxXc3xpwryyPHZ5ktkSaSh5uukyTn5lXrNd9QQfhEViNO94eMELb3k73abHOc8zP/kTzK49wfL2s1TzQ8rpgr4d2J7ey6+zmC4A6Noh+7VsOsfQOYbei62tUvQ7gcrJcTGFMGziz1qrOMwWGEmKvMoMjfT5JgZK73fqV5BZR++hNnK+B1PmYOGQYJXUde5Y+MrndfHzA0aeOOzww32cKwlubfq1dM5+EJhm2MrP1QzdLfHBo8IKX0wpBpkVKT9IlmaiHXphpeC6XPjHQGMHfojsmbhqCD6HQ6SzWXqGgFGJMRapjTGeTSVGSsrV+5UNeG3y+ADsxbstgE+nhwDzSDGcAUfIBeCzP0fqvFNHEf9XfiDEQjtE3E09QJEKSoZPSgs+5iNVLqDkREk4uB9wqkQHLnyhgHxxSJuKadYwcr6TRWxiKiWGiVC95If0t8SLTZSxZELkEu7sBkx8QsEhTS7aacumQ/E5NSNTRREpfUGYLkkQpJHiL8ccIh9cHqMReCTxt5OdrfOI+o+RS986gQKcN2x7H4MaAqftkNWa697Ru0AVDzlhuxI5JlL6xO+eDeLq54Pc72jVZYXleTdw83TL8abnzlmbpfVGK567L8vmTedy9+2GwMm65/5N6cq1VmirefHGjPvPPU+3PsW1Gy4/9WU8/49/EFvPcH3HsF2itMJWo7Raa7EyCDtL8eSZM54bI3SRrASM4sLgLBXylOjUewk87uPt+T33nigviyub+Bwk2miI8nbks/Wx64xJNw9CH7tbPua0GtvpUC+wTOKmgsfvdMfBVgJNxMf5YiIyext53cVEIGhtJRXeFOK5ko5p5xiDLS+oIeU8tLGrErot2sjcRWuCl5V20BYdIJDuY8djisf+evG8iwcugP8sbq9FHv/vAX9HKfXHkDPyV8W7/Sng/UgxnwP/cgif+3Kp2/NctGVY0uYuYVY00DtmSicVDk3kpGIKkfEWjXQDRYMJg9zP9VS2wXZLJtUMfXKPenIAiO/DTPWEYDFDK0tHpdHbM8qihqFjWk5Qg+dcT6h9y5VJRaU8tolFPbgLLBQp4kSzovHEKMIQfSbEjEj5AbX27Oke1fXgB5o4nKptlRk2RRC4YkBHs/vRghTgeCsyZQkRkJXBPNrTnrcu+2wkaAhilw0xBNdgI3tHjnk3Xm78ghw0iQsOblbROlFKpqFkKvhGwUFTcGVaRrhECl3rPE8eTEQGPyuZlYab52WGuB5b1Py6t1zh3delD+ijPHw7eK7v12PnvRaGitGKK3sVP1aKGEZel+Ib336N2yfvoN0MDL1DaUX19b+Vvh3QVgrEMz/2t3jDr/kttJtW3Av3D4V/vzfh8ctTltueWV2w3fS4IWBLoTjuX5liNNyYV2wGz/V5jdYpck6cGR/eq5gU8nk8tqg5bApmhUYrSTOaFoJ/a1RWWCZbgl3GT9AVFR4dAwqURr4XUfAibn8FhJDhE600jXKjCCcV7vgdCtUc1XY5OT7BftHP7gAAvm5JREFUbarfjKpMbQW3Dh6z7GTw2S7xkwOKchDcPNWBbi3pNyB+osmqVRvB0KMnSVopqHkzdvzaYiKrrCgLVL/G2EZWncMWW9T4YC4Ig8TAS2fjuV/ZZHst8vg/Avz+EMJfV0p9KyLk+Ubgm4CfR8yZnwR+SCn1D0IIZw/sb5TH/zd/nH/9u75zHMgkfCx4Ol1i7UgRsngGtCjOEK9jwceLC49VxIw+WwlToJ5n5RZAr0uZfBfNuIwrJ9KBaCuCCAW+F9rTpnUjfm4UWhvOuqRujF1BGD28QfDvzhuC99m2Fgx7wFZJJBlO566mcwETYpqPKaKSMUTP8jHWaogKxWB0jGUTPnlOjwmC988KzbofMzohYI08T8pgBNjE9yR9L9IXZ1oY4dQHWfKftn10D4zdtRuNvU7bIYpF4M6qy/hu7wXrf+lsy6TQ3Fl13Ft3LKOh1psvTfjIrXMOmoJP3V+x3A4czoQzfvNkm824TtddtGQN3F/VvPSSnE7GaIzVfPLSlFvPntC1Ury3x7foVqdsjm/nbnv/iXfwwk//MME7/NAxu/YE8D7O7t7nuXuXAPj00YbT+2v6raOoxUDq/s0lzsPRpufatOLW+Zbb5y3eB1YRNqmsRNI1VnMz2vQaJZTNdvBZ4VoYcaMcfIINBPZqrMwcSu3plKU0xdgFx9mISOFNPseDNsLqQOGUpVS9+J1EXDsbRUUvlGDSbMmLi+fOFpRGxdt8OcVsjqVAeyfBCpbMBBH5fZnNqDA+49GhnkcIpc4Xk1Rug7agjQwsiatZW0WLW9Dxu1rJMlNERYgiWSi1paywX4ftS4Zt8lnk8d+BpCED/C/An4s/fyfiNhiAX1JKfQp4K/BTu/vclce3q/P4+Zrs0yB3kqJ9QVIcPA6dB5ZygoYLwzt5qOBnwWhRkkEu0hABip3Bz8ttQQk+HMJY2FzskhJerdRIu5PhpMq/p+dRPCDXjzl+aOLyUWCXEAJaayAV3MRcGPeXKJFGJXjnM7eXOy+VGvej+cw7aMSLA8islrSfB/eX96PElApPphmKBBy8UhmrB7mtiPi6DEhVxLRjoEAg35aw7rRvNJlzv+uNDuCcDBYf5P+mAh28Y2g3mKKkXlzh7MVPXIBJ8n7i40WOL4X2wbc3DXR7L6rM3gc2nRTvwUmBTp+ZC0HmEGE0G3MhUHzuUCqh4cFnnJdy7nqhzqVhJUY6Wm1GODHJzR+ASNjdp96Ry7/c+Z+687ga1kqBlwKt/ABukIuEH8ZXE/8WtEV3azB+hxK485ozLBQIBBQepWyecel4PHoHQhTIRzQRr5e3yS+H7bXI4z8NfC3wo0iX/cl4+/PArwP+gVLqGvAW4JnP9Ry7TmHpBADpOHz8kjgvhky9tuJ1Ebs8EmtD6ZzGI8NDLS5tycXP69ylaO9wXmxQpYCbjLmli0fy3EhYZzqGwQW8laLUOemMEzLhQ6CCHHmWPEqyj4eXoSJa5yKenov4v+ClUIeQud2KNLiT4phw1RB9QvJ7AeLUhuwn7TexaRJE0vsEecRBmo54+I6/TO/Gi5ZSMhBNobxpy0HRWtEO4iHuw8i/10FdOBbJ5xyf2/lA61weRKbCnIaZldWsY3Cw0YpLs4rltufStMQWBmO0FO9Ss5gUlAnisRq/uJL53NqWKGOopjPqxWWC9yitKePAUhdlvlgk8caDnVkIIgQzWgazs1p8URZNQefEPtcHcZxc1AXz0lIbzaIqmBQ+Ju/o7Ajpwkh9BSlWptCo9Yq60uJhEguoToPGKJkPJkFZqRhbdIT9CGGcjfQyPwhFLT8/cNEK1kfYpBWa39CjtEf120gvHKCoMb4XFokp835CPI/pt6A1aujwjUW5XtgrO8esCWLpqrQ8ppgIRFJVqG5DWe+hhxblxJwrv+FJpDPEoAjvxy7qNW5fKmyTzyaP/zeA74vuglvGgM7/HPiLSqkPIU3nfxRCuMfn2JTrREGmLcFW2QrSAHUxidLeeEV2PcYWqCBm9sp1GaFV3pG8iqVdLND9hqKcxQ9/EJEBRE8UwQ2V8/nv+GhKtPPhBkZVZxU504lRkJgh0iCOw67EFtHx4uFJXhMg/hXj/pNYowtj55a8KxI1MBlm+fiz0erCACvtQxJcBFsdJfgXz9TdopuKKIx4c6E0Lvicr9gNwjaZlVZUo3b0V08Ux8qayK6Q98g4SeQxsV4URlEZQxHdGGcx4EIr+fnypKApDYezkkkhdraLHWtZkLT3ppTPr2rsWLwLKfZlJRJsPWiGvsb3M4qhw0R8tp6WlPPD3HnbeiY8clvSbnouHTScDx4XLzA+XvR8pk5GptFu559XRyoOdke2Ub6PJwdX7DJMjNEjVBVzJTMF0JTj0D7CDbIkiMKd5Cboh9GPJOHQD7IydpqS+OTxRLDgomOfKSRVJ7oMYosYbhwhGltHaCTux8YhYm6AhPOtOvF7V/12tKHtN9FAy4EDU7bi010Itp4KN5F1poat4PZOhDnytsRO/3Vim3xJwCafRx7/z7/M/T8N/IYv5CCCKel1KZ2P6xnK2Q5POFApT0DghaCL/OWJhAk5MXfkwyjpaisUAZsHhSGqyLLtpR+EUrWDE+Lk5CnKKYSAMxWla9mEgkZ5nDLMtEMNLaqUQVaSwLtAHB7K8YknicIQsFGm31iN2mww1QLdLQnaUhTyJdRFgfE9dSEfy7xQtEaERqYQL/HkLLgZAqrfMCv3mFrF0oooZ1JoKit4u1FgJoZ0nXCBzIffKw2TInqvIIV8uxOkfKmxGC0XudYJt/ulMwndPWjsBQvZPgblXouFNzEsUqTb5YnI8Esr/uJaKaoUWFEaDqclPgTmlaU0kpyzXxccAYtJwaZzXJqVwjoZPOvOMWmk2HeDpxs8i6agiN2vMR5bNIKHVw1KmwijeJqD6/heOtjt2V3+m7/xYV76wA9y7bFv56WXzujbgfvPPYsbOop6RucCxy+9yDa6IjpfsOodd8/aTC3sBs9hU3JjVlEaxe1VFxWqBffWHdvBM4/e5JPC0EYs3cfC5EP07Bk8M21laJ3mP7YaIYxCmpJdrnOgGl0Gi8lYSIetGFolT++iHqHCLPYp8Y2ch6rfZGbH7uo3VFPJdbUWR40OToapiZ2SZkxDK7eZAmIYQ764aIuPjUbq4P3kgE0wVJNDmfUU42vScQZk4vsTikZWDUXzGfDoq92+kPT4L9btiwZASrLuLZYyU98irpygDcZOJ731mWaojXQjOx9ufnGJbqQUwcqAcpyi7Ezoo3k8psyT/SbKhI0uUd0KWy7yslAGkDqzNdLzlUaYIcp1MQ0+ArcK8UguKomMilsysTeQLT7TF7bQIl6wpnxgrSf5fzqQ/ZZ3r7F6B+NOboM+wjKDG7HYNqr/QKiYg0u0SPH8HiKdJMEx8vPFz84ocShMmHZKVQcoSglZXlQWjYr88hG3Pm8lK3NSGJ7Yb7h13tIUhnkl5lbt4GAqF56DpuB+TAN65LDJ/iPOi3Ph+976/2fvz8Nuy+66XvQzmtmt5u12U7WrTyWVnggY2ugBBJGAArag4qHVK1yVo9hefTzKkefo9RyURr0qit31oqIoYgSvSuCABhIIIX1XSTW7du327VY3mzHG/eM3xpjr3alU7aTKh7qE8Tz72e+73rnmmms2v/Ebv9+3ucDxumex6WkHz9FpK+7qWjF0nvPnGm4eznJSauxDDL3n/s/5Ct7x73+Ez/na38NmqVlc/SjTC/eLsYOSsgvI6iGZQp/5/lomzaTMuFvZSNiK2XhQWz0BuSjL3uODvGdwIQtVpV5Nr0pZyUQxteADVSEmFWlhmdGBUY9nW3QqqxK6QUoV3kumHRFdeCcZbmq2T8/lrJmhlUw71piTBotxI+IEYvBPz6k20kzFSFlSF1lYKyiVa9W6W6OKRjRRBp8blEMstwnsVarh2/h0FRufojz9/Mevgth9RzXvGvhpoIrb/3AI4X+Nppv/C4IouZBKI0qp34846SjgFPjWEMI7nutzshO3ZuzEx7JEksv0gaywlwNTYl0lbeF4M6rg2WCpEWxosbomWcZwStBWEB5DG2/qWDIZOihq6XKXUwKGjZ1GajL4ai5BPy5hQ0R1mC2oIKSmJploEcL4/bS2mMV1+skBpj2NHfsmHreRCUbpnMl4pHzkEcSJilhiHySLcdrmSS6VWDoXcnNPkC+jKw+oWJMe/TKlhq5y0E4Iks6NeufKKKalpveKplD0XlEwNh23pTrTxJDo8SlrBWGArnrHok1ok10+fGuNVorL0RRB8OSO68sxu113jvc8dZINHt57+ZgqZt7BBw6mJf/93VczSSd4WByt6Zan6KIkeMeN3R2Wtw5x3RqlDevDp/mKr/tyfvlNb+J1X/HVPPH+G0x2appz9zDEbRTgunXO1G7e5sSTa/dbMrCLbhBzYjdCKdM5VUrYtfu1yWWtYAJWifQCg9zjOlLDg9LUERqr2ojeMM9QHrmd/q50DpjZwzI9G90yll8kQ1ftEr28ieo34n2JUNzRGrU5hQTfVUqOo1sRlEZ3y1yGpN+gayAE9OoQVU2lBLo5FvhvorpHtIzZnFBWO9hugS+nFGEQFcHUp3C9uMVvcT8yQ5TdZwohn3LjTjLvFvhN0RmnAH5GKfUfgZ8FfgxpWG6PjwBfEEI4VEq9EUGUfM6zfUDCbwYC/VY/wqioDKihj/XgIajcEPQBfFEJA81WUjdMIH5lBL8dK+KhnktdzxQ5Oz9TB1Q6ay3kul/w1BFIp5TUz7GStaQHIZVM0n4ySiIOnWQttUX5Pq4CitFO6vbuuXfSqNIGFTw6PrjajExQlMLoQNA1FpWZeGLoEKI0rIqMS3LAh4SICTlr62Mx1sbFyGjUIEEmiW4lLfXeCTN0O1i7rWTodr3lbRzzNkY3YbSPWyeEFhfYrS03Vh27lWVW2WhyHKCU7Pb+/YYbUSv8dtTJbmV54J45NxcdQ5woysYydBOM1Qy9Y/fchJNZOSJC7r+Xj1w+ZXbXQ3zoLT/Pzn2vYL1oOfrou7D1jKKZ4QKsbj4VJ2ApRx2vek7bgWbVCyMzNmQ3ERLY+8Bp6zg3KWidj2qNLp+HEAInrWNajMJoVifZ3oLWgymmUkYcWjpdgoZCMZZI0n0KY2lk6zWxQxtiw28z/s1JExLtc42Z2Gsat+nGbD0aOmSp5rS61YZAmYNtYkkHYwllI+We7fKOlUkhO/YkGn45FT0jbQnlJCoRDviiwXSr8RlJx/pClU0+RWreAVjEX4v4L4QQ3g58jP52COG/bf36FuC+5/qMBGNTjJWBEF8fjRpChO4JmUGQdiHSbEXsCV2M8DbvGNC5dpjq2SkoOh3/ps/eECOjTUoiSQRIw+jnZysYUoYp00OGC0J27vHb+PMA6ELE8m3JgKaINldBW5Qacq1zG22zHjzToqH1SStcPmtwAeU3tKqgTslP7B/1PkRzYx1Nj8f3oVV2+3F+RMLAGIRVnDSTH2MIMikpRaTUf+w1bKOqXvJvdD7gdYLgRd0OJQFuETHh+b2D6KQsWsFEJ5LOJtZnUl077ddolTN3IKNEVp0Ttp4PuCHgBy80dyfNRzcE+la2AbFXq6cFbuiY3f0SjNUcX/4wtp4xbBZ5//16kSe1zkXzhriPlHGnCUircQIbHKMKYWwGC9In3pLxxvBhvG9CIqPFeyaYUhaHSlZaaCOEmhTEY2YqZbY+HzO2HIPeNiQwlk7OvBZ81j5J+G28j/R2NwI8lCbZrwUSMsyMyUz2yBxQupd9xRVkVjTUJqJW1mgTznhdqnQDhjBqmmw3KG8ri36qjzvFeRvgF4CXAX8rhPBzd7j/bwb+451smLDLQC5BJBhcFmkKIqWQAo7fasChRcmOkLJgHTMa8XK0MbvwysTVXxjVylKmC+MNHWvVXhlMZPcHbSEg5AgtLjWKs1Tp9KOJ5IuQtknfTxm0KaODvCwhRdlQzIC1KSOjbEtGVCWqf8irFA+oocOZGGBJWbWKzuTiIrTqwWqiGYTgjFP9extiCGQGYBq3oyZKoxiiPkySjDUJYWJ0LpMk1Mm2vsd2ud4ajRtGCdtUX7dRoCj9XhqdKf6l1RlXXkZXnKYwrPvRoaW0mrUWtxxw4qLjQ9bvtqXGlmcf/tJqinpGGR3JbdlQNKKON2wWdC4wbBYcb0TL/OK0FHr+Qmrzx+se5z2n7ZAntVXvaJ1MSG2Ui22HEWaZMvUUq9KqpnMBX1phkqaJUpGJWtZWo0tOdIdPK03jR1f4PLaDdCqZuEFQKVtNy2ArCaLpbdqifHe2FJPQLURUi9I5u1Z00ieK97OyW8bFyVg4rQiQpMRoI//fnjgFD0ocduw2Xn2rHPpCjMKo597oRT7uaBoLIbgQwqcjWfRnK6Ve+1zvUUp9ERK8/8zH+fsfUkq9TSn1tn/4Az9w5kFOGfj2zyo+uCZm4+mfJuQmh4LoCRj3E4kNuT4efBatki/2cW6EnMmMpydliqKvMpYgtsd2Npmyqe2syoWxLJE+B9Lf2QrOqQlJngASXDBlwiPEjLxdOibN2Wc4jWci53wiIwSyV6fz6V/YKrXcfj5CnCie4WDSKVDPjLl1PnzM/p5tP9v7SFm2lIeiD2a6Zl7kXtPf5TX3Mddy+ztDLIlsbZKyb+d9/lkc6Le/wzixb197z3i9Q0gmGmc/d5sI9Qk315Q6gyrJEEN/BwSe24g8Z7ZNWXz6F0scqcR4Zpv4t5RxZyf7eHjb3pjhGTLqTLy7Hfb4ayMP9Yk6lyml/iKwCiH8H/H3jwKv38ZyK6VeB/wI8MYQwgeea5/djSdDusihqEcyQqTh6vXxqGGchHSMzVoN+QKbUup18UY4NjvssGFjJKsqtOL6auBcYzjaiP5HPN68HA9BqM7H0YxhahWth0p5+jjXidKgPqMHIm49KtfnQTLPzo2swFRiaoYlXSFNGoLHmQodpMyTmoguCNVeIZlagvJNC1FQPO0DB4cfZH3h5VSLqzkbWhU7TNc3IqpgQiJKhKJGbU7R/Qpf72bYJNrIchwyJMs3u4I8iA9wwvgO1U52/8nnPEMeFCgtVOoQoWYx69u46DQUIYQwoleaKDkw+JDldNeDZ78ynHQ+riKgjE2+ZR8ySUks46RmXBnFURvNeP3ZiUSpkTWaJh4Y9cuXvSgKJvOMLqJxjjcDf/Kf/SJ/5Ws/nd/2tX+W3/7tf5j//be+ip/40E3effmE+w4aqX9vBi7t1XzRS89xcVryHz5wnbtmFZdmFY8fS715v5Gm+6IdOBcVFtt4IFop7tupuLHquW+n4kO31pyfFLkkI9h4UWc8bvt8/IUZ+wnnmoKb655Ca1rnuHdexXvwY0ubQIa49l7OQ83AOshqclKIPo6N5+Tm2nF35bjaiZRt8pXdreR+XfUChSz01qouQkU752no6XWZ1Q9vrR3TQuWVKxClLsSjMiU96V5v/QhUANidNs87bX7LY7fuOPB97oMHL8o0/U7QJheAPoRwpJRqgN8M/LVn2f4B4N8Af+BOAjeAn+xLN9sUqPYU3+zGPzh8OZGgXTTQLSUQlROZlc3YfVfD5mwD0nWimdxuqGK5xPie0miKYU1la2qjRAg+lgESDV95l40RhiBBfzkoSpNMepODetT7TkxFFcsTsURirDgAFVs1Y4BOTTAusPIapQzBudi48jnIi0yolD5SGUSyP8msl71nr5px3HoOdu5mEY0bgguY6YUskrXsPWUZm2LzOaURmnku4wA0Zx9w5wNUEXWgxsblepNKFDZ+FxG68kggWPeB0sj38viohCgwuNMYiGelPPCLXmrApZGHv7KK085FKGNCzEQlPgc3e4fRFYvOMy00V5c909IQAhyue1520PD0ossaIsAonhW/66V5xdVFl3XTJ4Xh7nnJ1YVYuN09K3nidJOz4ONNzyMv2ee4Hfjt3/6H+ZHv+X/x/b/j+/n+f/lOrn7w3UwvPEC/PKY9vcX+Q6+i/JrX8bq7d/hXP/MYL7l3zmvu3eVnP3gDoxW/7v49rsRAfmm35mBWMi0MV08Ffjcp9nn8eM2lWZXhkKveUVvNTNl4lg2nrcvHX0QP0t6FDM9MtfeTzmVIYW10ngRh9E8dYlM7BIUuLItWJrG5O2E5NBw0NjeunakwysUALffFehh7HJ2TCXimHUtv6HwgxMlnrQqO144qShIbDcet39LQifdEJ9fpMDZz04pjMwTWEVLpgd3pnUSVX/3jOTPvmEX/Y6Qvp4F/GUL4TqXUHwP+NHA3cA14UwjhW5RSPwD8TuCxuIshhPD6Z/uMxWodVtE8wOfyAdlt5LQVw1YQk4EkZO/CSG4ojczygbF0Ulkx21VKHGYWnc+O7KmBl1hvzkum64M4yNxaO2qrqIwErpRF+DAG6yZijEsjSt5GKXRwWbYyY519x0aVVMqPYj7btcjE7oSRNNRvCNXsDNzK6UI0mONktsFS+zbXGoMa9T9S8yyVbeSckP02A0St8xF7nOB9hxuXz7d8LznXs7DJn+WVyaYZ7eDFbDlCDUcWofyfgs2il8DrA9l8d+ZX2fV8EyVzr64GDmqba72dC+zXhsunPfNKx6AeosG0fB+B6Al802oioWlUNwSBdco9MX7Xu2eWpxcD5yayGiuN3AMpGL1kr+QjRx2zUjMvDfd+wR/hF970N6iNzqJdjdU0kSA1sYonFwOzUjD6mxjgypgcpBUakAOqUYod3bNRZS6zlGb0YU3vlfs0jHILgbySSedVznvIATqhfNLUbBUZvmq7BT5qdNvDx/HFhNDs4sspen2YESKumGRIH4DeHOPrXfT6EIzUt1W3xNe73GzhfDHkpqQvJ5hEjY918BNnmBeS2NRG0FIJfRWUEPU2WCYrMc7wk/0IBRaIbjXbfd6Z8FsfP7zjzPuzHth/UWben3DZ5H/ESMJUyfx3W+ukD1DGZbjyQ7wh5CZSwctNU83R7amQD7a63iszYdKf4Jo92a/StEFnZ/aJVWe67qOwzpKVmYzQPDjjIGO0BPXEeExekyDoAxuXlqkMY/UIB0t43zYGptSUTUvGNBGkILuNBln3nlkp8LJF57nYX+eovsg0OpOniSehUhqrOdy47ESUJq7tkYIHjGgWpSTLSXDDUou/ZjI5Thm7QBFVrsPDSJdPQytZwSz6cTXTDoGN82gUu5Xm1sZxrrEct45172mdY68uOGkHtv0i55Vh1Qtj8z3XFpyblBxH1MlL9ye84+pJRnrcWEhGe7zqM3TzofNTPnxtkc9pZTWf95IDfuxdT3NuWnJhp+KXnzhm3Q2sOsdi1fOXftur+V9/9N383s9/iH/0Xz7EH33jK/gTf+Vfo23J0K1x7Zpm/27uftl9/IEvfYTXXJzz5/7523n4wT0+48F9fvK912jbgdc+sM+tZUtTWh65a0ZpNXdHY2ajFZ//wD7vv7Hkc+/f5e1XTrk4LfOkmEhQTaE5XA+5nAJj421SGKHmx5XVTm2ivjvZZzW5SCWYZspsGyvGDK6Y0DnPpD9hVexQG1l5rnqf7fnSKrV3W2YZQRyuimGd0SQEn1e7To+2eMb3rINg3FcxOcsJRbyJUhlzqgXF0uuSIgz00fNyNnn+ZZNfeOLojgPfr79/71k/Tyn1ZcD3IAnuD4QQ/uptf/8TwLcgvgbXgW8KITz2MTv6BMeLgmGZdUdcL5lnDM64HmXFWomiEbGedhlFqHQ2WFVDK/jVIDrBiTVpiqkI47joCj+0rJ2lVo6gpIbeK0GQSGNIZ4EqIGc7KiIeUiCCkXRh1LhS0IA1ZzPWtZPfXCrkxZ8VI0kmZXq9F8NljQTZQkuWljI0ybRAK3FeUa7PjjxKCQ44PaTpQSh0UvSTCaKyyWk+nCmVGDXWgOWF2CQmqv0FcD65XarM8EvCpiMJaDw3KQuvrWI9pOZzxKgP4FX6/oE2ZrHp/QIHlcCdluYHTQH01FazUxciqYvgwWeVZr8usvFBbcXh52AqBs+l0VyclvgL02w0PK8s+3XBa+7dYV6JD2YiASUN8f/6oRt85sPn+PmP3OJdP/4f+dw/9Nn06wXL609QTncZ2jXL608AcPn19/GS/QndeuB0M3Br0bFZ93gv1+s0ysMer3qa0nDL6mxKkazT1r3neCOs00U3MPGGymjYDBhdcLju8+RYaIUe5FxXxmTj6M3gqQsdrzGEWDZJVy+9P6GAfIDGNpy2opA4wXO4cRxEoa/OBZpCs44r4HSvmkBm6Wql0cVEVlBO1nqij2MZBp+llEtj2TiP6+WcJGvC1PcwCk5iaaxopDy36D2FNnnlO5t8ItHlmccL5cUQkXh/CyknPwm8VSn1oyGE92xt9nakL7hSSn0r4jr2Nc/3s18UoMkQZ+te2VwecLqIRIAIZ9J2FORJJIEE4NcmE2yymI7SeQmaM/lIN9/2/0tBOf09OVWnoYc2O51kZEtEt4BQ4UWAihxo4Sw8UMWHRG2RHVKgS2WiNJIVmkiyShC+/UbLTZ64DB3CiEhJAVhFrPT2Z6VleJpstpt6gREdMh7LmGVnxE46L8QeZVyCp+2faaTyVMqAcxBXChubcaWWQF9alctNSeyp0Dpbzen4vpRBFkbo+IOTGrCJmaYLISsEpmucPj8LcbnkcCQMyeNoh7bYDLkR+fkPHbBoB155ac7FV38ei86zuPpRimbG5vg6fugomhlKG1adrC6GaGI8eEG6DL1n3Q1ZBwVgsRGj5IRhT83tVe/YDC47EqV/6VqKO894XRMrtnVnNQu24atKjSih2xfaPh5n4btx8lY6PxNm67onxJSgvNL9oXJGn+jzVm+LosWGqJX+TaXl+tRWrkkqCW2vClKSUfqOwrXURjw+K6OYFi+6CsZnAx8KITwarR5/CPiq7Q1CCD8ZQojaA3fGfbmT8Xzo8f8AeD1yXT8AfEMIYRHf83uAv4TEhHeEEH7fs31GWgYqpQjK4qInoqIguEBHCUPAqwnznSmnfYiaHgV1KU25ptyNy/7Iqyxqah1YNucpUVxfDlRWUxtwpsZ1DqyouqXa7eBj/bdoMFEv5LC37Ee463IYM2UfgpjuajHfVfHLJpeUNm+b6uVjo7MpJBitY/3eAyo+WJ0f0RWdjzKsMUueFFtZvZZUNwSpY1qdyheybe2FznyiCmbascAwtUJm6o3NZRwXRqTMpBBs/LL38rDoUd2wVj19YQWBYwIbP05EIYRcvyzNaMCcsvGpCdRWatjSQ1Ds12Ss+YWJofdw11RuxxtGcVBbpnF53/vA4GU7oxQHtYGDCY2Vc3faei5MDJWd5JLIvDQct1IyWvdyTuel4VXnp7kmX0Q0xf27FbtROOozL82pTZIQCGyGwJ/+opdybdlhfv+n8/L9ku/923+Bk02fdVWcD3z/Pxa5+sN1z4MvP8eD56c8eH7C9dM5R6uehy/MOFr1XNprstnEXl2wnrncK5hXlhurXlx3EqzQBzDxvtk6H7NSJq5F5+IqTbMZBibasIoa3CmAyupsqyEdr+lOJcc/Kw2LQeUMe7B7lDELX8f7dR0z51mpubmSmv7hxkU+gWLZB7wtwMkqIiUeiw72asMimnW76Px0FPsqy9gHWQ/JPm5EgW1UmWaN3M+6HVL5yY5PRFVw2zgmjr8X/QhALCGf2Prbkzw7o/yOuS/PNZ4PPf6PJ3ccpdR3A38E+KtKqUeAPwe8IVLkLz7XB5QxtfQhUIQBZwRWZRWshsDEKvoABR69PmLe7GdBHOU6TFlhhg1FUY9iVkNLR8XELfFmym6lM1zN+D5iIeQzE9MtXVDlejpKrJaabNL5kEAQA5ORbBHGmrFSxCUjuYnmvDxESo1lFaGMjyWWNLZvzHVS+AtJx1uOobFSlO6cfHcfiBNPZO4ZCaa9EaiYc6Lx0nvPxoFSli420cxW/TvtP+GO14PHbTU2BwrWvWMNbIwmhK0JNySXe0GbtEPIZRMAU0lN3oUIB+w9bTxPs0Jz2IqV3GknD/D1SIE/XI81bwkIE66cdkDJ+2+uOD8pRCelk7996NYqZ6g+yHu8Dzk7fWC35vHjTT62SWF46UHDO54+Zbey7DcFH4i+mc4Hbi06XnvPDu948pjSan7w//NWftsrvpr/x1/+Z7hO4JV+6NG2oFue8MHXP8hnPbTPe972BIcPn6cbPO98zzXcIKYNxzdXHB5uYlnGs+4cj14XJuer75rzwasLLj58jo/eXKEvTLm57JhVNvuBrmJJJfmHFkZlhU2R6ZXXF93ArDRZcjepO5b27P2aAup68NG93rEZAnO/oHM1jVXURnHcenYrzXEbMFp6OhLMdURFBSqrYhnr7EqvSqtHJfe7jTDDdI+Lcuj2fSj9nNIodkp5bhad9Gu24bbPd3wiu9k2jnl+n6m+Dkl4v+D57gueHz0+BW4FNJB1+v4gwsI8jO+/9lyfYbw0E03w4HqpnyF7LIyINNmiRg1DpgbrLRJNsgfbRhYYJTXWhMJQSizUWhR4h1FGTImxGXGRa4G2wvqR3VZbzawcM5Nl78/cjGOgHlEs283BmCRnre0mYlyTi0wI8iAU2o8wLj9qmSRoVoYgRpSIqy6wG7O//RJ6dG56QvTBNIK/DfFYXTw2HdTHNEQFljiyVreZrFqRH9baSqYlZCBZSq8HT2UUKy+TjWc0qUg1UkHnjNK5wJZUqmbRS6354Nwk4pB1vibrwXO+MUDJ3VPLqq+Zl5rW2YwJfun+JJr8EmVpRVekHTyTwnAwKUbfSyX65AAP7TXcu1MzK3XMgCMk73zgJXsNs9LSO88XfMmrKI3iS37Pb+Z0M9CUJjvpHN9as1p2NIXh0z/3Qe7bn/DFr7hAaTW3Fi2f/8h53nfllIvzigfPTehd4N6dmgfPTfA+cGle8dkP7jMvDb/+/j12ayvqhEF0W3Zry73zglU/4dqy4/ykyNj11MQ9bQULXhjFvNxq+nsJ3EVEc9nIwE+6NqlRvIg37PlGc9IJzrvQo0HIxnkaL43GUgtaZBtRNI0XfBWfDwCngEg86+P+BxdYD4G9WhA+VqsMNwS5/3TcZ0ilPD/q7LzIxmXg/q3f74uvnRlKqS8B/jyi+9Te/vdPZjwverxS6geBLwfeA3xH3Pzl8W8/i3Rf/1II4cefbf9LL9KbvTfMC5vLE6kjPSkqht5jdUldaNbBxKkiYHVJ23t0If8PMfiVphTAv6no4k2zcuJ52ZmKMsDCGxQBqRaO7vBV7M4XWsoYZRh1QNK9sw3X2h4pO0jJhNHkm1MpRWNHxqVWY/BLzRsTJ431EPK2aVJKaBN5DabrY4aplId6xtKMtIugU1aYfz6M8DylzkDMUmAm7lMpxUnraAqdtVJmViad1Oij9xnfrSE2zLZ6BzqgwviUpXrm4CVDA3LmfbRxnHQuarBIkF4uey7NSg43Q8Zqb2Jd+OZKmrQ3Vh2LTkfZWI+elTx5sjmDdElKhsljszCKw3Wf67bH7cC985rTzrHoBhad+G8eblTO9o2CyycbNoPjI5dP6X3g/R+4wRBx9ckMYrPs+G1f+ghve+yQN/2tv8fuA6/i0Te+gZ//Dz+Na9e8//Wfw/WPPEkx3eXuh85hrGZ3r+bWDSmFfuNvfoQfe8dTfPnrLvGmX77CwxdmPH285mBWcW5acvdezap3/MLlY45XPbPa5rJNaTUHjWiiN4XhZNPnzBzI5hmVEQnatTEYDecjjnuvMrl8Ny00alixX83Yr414oUYE06wwQqpyIWrB+zMkoHQvpWRmcInZmpjRKjoJaTyyYgJ5T6Gld1JENNKs1DEJUdEPlaze+UKM58s23hpvBR5RSr0ECdpfC5wpEyulPgP4u8CX3Ukye6fjjoJ3CMEBn66U2gN+RCn12hDCu0II3xgD+/ch3dMfjPt8BPhCZBb6aaXUp4UQjrb3uV1H+pvf+338wW/5FqJUD9UWbtqHEeqkFah2ial2b9PkODvSZXFBlgnOy82Wsj8fRKlQSAxnERcqCGSw0AJnCnFpZ6OXZWk0YRBp1oTgKE3S8pDMNTEj117qwIVW6EIgX5pIIVZb0Egjq4mylHq9RlAnEysYWJlIZJ+VlaYqVhGqqTRMfU+hwKm0ClDZ8s3GY+wYXeJ1DKbb8K+08tAK2kGWy0ufdEoUhY6IG2TFkYJ3vJZy3Cnbuu2ClEbTFJKpp8w3+T3OY+CYl1L3FFad1N99MOxWhsFL9r5TagpdMq803bSkjsGIeK/cs1Odkd9NwbuPaJ2DpjhT6zRKsVMZ7tupMoPx4nRs/LXOMystl+YVq97xknvnzErNS192Lhsod52jLA2Lk5b7Dhr+6Y9/gN0HXsXx4+/lkbu+jJ9dnqC0pqiSRZv0dACWy44+Qh37SLM/Xgu0MWm2GKVoolF0G1EwZzw+t8bolSkBO6F2dAyaiYiWzv+s1By3An1dR7SHgkxH11FK2BiF03FFqRJiaFxxpn56dpjS28cUz3XM+lMDUwNlhN5K41tWBFarnAwAMaBDcqV6ocYLlcGHEIYoj/0TSLL6D0MI71ZKfSfwthDCjwJ/HZgB/yo+K4+HEL7y+X72JwQVjCzLnwS+DHhXfM0ppX4IIez8IFKw/7kQQg98RCn1ASSYv/W2feU60ma9DhByIDJGbM5Uv+KgmaC7FTumIKAJ5ZRCJmQAlOvYrSq06ylKm02GPYod1gQqSt2zdCV7pUa5Fq+jLZZRGVmSoIdWW/TpTer5Xah+TWVqTL8CbahNiXIt8/YUtCZUc/TxVXZm5+WG15qNsdQM4B1FVVEOa1TfYcopqm/z5wRTZPKCcj0qeIyKdPWhZd9WqPWSYGtqQA2eqSkIXpA0PgB+yKJc0uCKD2/E3iaJ2HaQjHs7K01SpCb2AZLyIES51bhpas66QA7YIXBGuheShrk0oG4XtOq9sChV/Nx1P0oGnLaOZRTlT8fnQuDWZmBwZEiiJ7AcPO0QRZyGAHi6VgLzS/YqDjdDdm3fi3rZhVZsnGTts0Kghdu49sYqdquC3UpHlE8dce7RFk5LbXzRDbzm3l0KrXjphVk+/nbwTErDtdOW1929w1//htfz3f9ll0fu+jL+znf+DV76hV/NdKfi+hOHPPyZj3B6uObCXTOa0nBpt+Gxm0ucD5yflDx4fsr+pORiLKdcKwyX9oQoI16Yht2moLRaxLmUAkOcdEquLTsG53ONu7aafgjsVgXHw5Cx1ru1mEUcbmTFsx4UB6wp6gnLPjCL120IkUUZ7xNJfoysFmNjXSMBWsXEZ2pVFjwrihFlNfq8ikzyrDRsXGBeGmqrqE2IjVdhfJpY0lPxfizw2Y3nhRj6BQreACGENwFvuu21v7j185e8cJ82jk+WHv//VEq9LITwoVjz/krgffEt/xb4vcAPKqXOI2WUR5/tMxLjS37xET+sUOWEReeZF43gQbXGdktctQNIULGmjI0y0YJI9TzpbIv/pbM1xgsiQqmS2nfi5AFn9LSD0ngUqtkTlIVtCC6AKfCmiI7vJctin1nMGpr53Sz7VECAdnBYrSmNod04KltTlo0gCowAVJMuStBlRqkkGVQCaFuwcYGm2s+syITztkFF8+0AXpQGTZTDBSH/zLTDagtI0E76HzZm5EMsoaTMOzEtYVQaFF2LuAxWMKgR922fIeMzqIjeMDkIJ0ZhoRXz0uRSVKJDay1QwTpIM7myKqN0divDaevzvk7bgQd3a9ph4MLE8OjRQI2lMFIeOW4FTrcKkrFeXbbZjk3MkQ2XZhWXTzc5+66tpvcFjx9vREO8tHz4cJVRQd4HXnF+xnuuL+i95z+/+ypf9+su8X+98+msGe4Hj7aa01tr/vN/ei/f+gc+i7f/l1/kAxfu4Wu+49v46f/6AY6efJz7XvtyHn/vFerphJPjllMNk9JwFCnzx5uBdcRpJzhh5zy3Fp1gwtcdj5wTEk3CiZe5QRhoWkM7OCaF2YKIpl6QpzDSUEyrIhOfkyYirm6phuPVIAgfpVn3gZlPOuPSQFz7kFEhnQ8sOp+lnNM1G4I0Qrd7N7NS+kTOC1P2xBkWnSBVFp1jt5LyTDre2ki5dB5LhJ0LOKVItnEvAMz7V8W4k8z7EvCPY3lEA/8S+A+IO/wOcu3eAXxr3P4ngC9VSr0HcMCfCiHcfK4P0UhQMWFsSuihpY4WVKURkZpgKzTRBV6JRZjRJXrLeVouuTz0yXQ4hLEB2KkS78KZJiDxHT4kB5jYuOs9wVp0t8KbhpoBW8nKoDSKcljT63o0B7BkdmXnIr5VwSZIpu9RmGEDthZcbDaS7altRNngMVpT+g6nKyaFBN1NrGknynMo5TbeYHGDp/PiTdkHKXwXYWDwJhMx0qQovQL50gkOGBiNJBLRJ5WCUsN3iM3AZyI4hDDqiKfMe9gihST4YB8bT0liwCN17kmh6XqBBBolD+82c3NSyAOuFFxfieaHR1YM89IyLXR0d5dEYK8ekUGtcxRas1MZfKhyLdh5ua/OTwrmlY0TchWPUxqdhVHsN3JfveGR81ijePXDBxlHve4GZnXBtZMNX/66S3TOc9cjD1NUlv/rzR/G9x31/t2849/+EC/9wq/m6MnH2Tkv1+3JGysWRxK8N4PjqVtrjtY9V47W7DayT7PbCEXeam6sem4tOk43Q7aAA5jVlrbyLHuHC7Dshih6pelJJhd9/D4av5Fjv3decm05cHFq2TEO542soNbHmFJKcsvIjJV7b8ygEzZ7u3y26D0HxmTiWirJ+SCootbJPbxTyueseyH9JJEsFySJWA6eWWFyX2kTa+CD878iaJMX67gTtMkvA5/xDH96w8fZPgB/Iv67o9HGGvLgA9ZWtIPA3owu4wXWOXDMlMAHE7fPqILFRjKOdedywFFKAufGGXRshi17z06lM7U3NXUkaEvwCiAlkRDonDzgQwBdTIQppi2nqyFjopUVL8XENlvHtZ+J2e1mCPiIG249GCWmxioEOgqsEhsxo2yuaSbMtjclbosKHRAd8mxG0S5wdc3EKtowBspKQ5LtNMqIemEUk1Le4bPWuSgmpokNRqRM2pcxCt1vQFdbhCOVG6PpPUPMsHWhP6YHUTOwNqJDIgw9qcWHOEEOXvaptVzV0/XAXl2xGVw2l0iu7GvEG3LVS7270HL+jqOoUhchliGojDzZDB6slF5670mekr337MSluIvZpNGxRh5hdqlp2fvAleMNRimunWwyvnsYhDl5/eqCt+3ULDY91z/yJAAPf+YjvO9n3oa7/jgv/cKv5sNv/rfsPfRaTm6soq+m4/RQIIeXb605vrni6aMNt64v+aBWnJ62rDvHvJbG8+F+z5OHa45WHZPSUFo59lmEOd5adMxqy61Fx92zij4G93qjaQdHYSTUVpHQJjo4ktmeYOS7anA7d9MtBe+f4K7b7J6k2ijluBEJNTbTQ66JrwePNZKlu7hNH7P2EJIkg5TCNs5TG83gQJfjCjUJwr1QgRte0Iblr9h4UdDjG3pwTgx1N8c0RRMpig5TNNgIU1MhoJanTCb78sZIq1eVpVKSVShGAL4ODluanLUWWsXGnrw93XRpJNge3uExAqlLdWDfAwK7mxQ6B/1KQ6dGgad2K7htlxf6rTJFEeuHz+RgrZRkvJ2P1mGM6JGEOknwqVBOcLGe7PyW4w1OHL9NiR8CzhRStgmgolNLqmsbBS5qh4/HCmUiiQRgC8utQ5LBHUWWclnHhxy4Q9iqV5uCoZX6fCK/pMZi59K5CTEgjlK6yaQAJHv2wdANgcEQA7MEp1H0adskgmz6W1txuZdG6Fg3NVoQDZPCUGjN1GoOlWJWmhz4E8zw8skmfq/ApDSZWNZpaShOZiX37TfcXBiK6S7GWk4PxQfTNjOOnnycvYdey9FH30U1OxANcX+O5fWnALi5fAmLow03lx2nt9ZUdcHp4Zq+dXR7NavO8Wn37nDlaM1q3XNcGJpSjBnOzUqunrYcrXq6wXO07sXpPl5T8RD1VAF6tS1EJn+bFTpzLRTCkYAao6AdRtnj2/XUlTrLwHVeGpo6NuZTyQzIGiZpJPldpaCyEY2iR+6ETPI+Pw/Z7/O2Y/hkx6dE5v0sDEsF/BXgdyPlkb8TQvje+Pr3IBDCFcK8/MVn/xDpfGTp1/QaDotn46QeqvxAaHYzvhsEx11IyCZ64eSgofwgCn9KxRlcMs00g2/rh2wv85ytIWb/iXnndUGjY1klll8UiJ2TqnMgbiINWCnFtEiZ7Ig2gUhGitm1PEiyz0msSSs/YApLGQZsUYzSniGaTvgBZS2BipmWGnOC6hnfY46fQjW7BFsz8wOsO7nQ2sLQUZooNRDldIt0MrUB5yjqCaZfUVWiCKc2pzSTfVxR5kmp2BILQ4smeRIhSqiA1DxWQ8tBU3G4cVRKGHXp2dFK6q5pxdR7OYeV1TTFWKPtnOGeylHbItZITUYkdE5EjM41ZUba3Fg77p7aSJoqchA5aEyWJEjqipOi5Gjj2KsNLpSxeWvHRq2Cg0nBuYkQt37r6+7BKME9g+DRL59sePhgIkH9ja+ic56HL0x5+8vP0w6evUnJtZMNq/WvZ29e8XM/8TYuPbzPbK9ms+x5+MKUX5gWPHhuwrsvTHnFg3t8uNSc2625b3/Coh3YqQseuWueESlNnIgmpWEWvfCa+PO5SZkRJ3fNyjypFVrnn+elZuN05g1UVkp/wZS5dLhbm3ytAlC6lr26ZFrofF+WtyUhs1LnoJ6akCoilhqrhddRGmqjOO1lNTaY8fmrLDRhNExOaoRqaLMkxK+N58ewfBUCTn9lCMFvMSnfiKBLHkFoon+H5zAgFmGpTkT/o6hUkksNRUNDJygL79CrQ5GIhCja4PC2wfgOjNTD8R4VHdi1thHlUedMuQ9jrdsFMIxZpg/QqB4XDPiRbi5wRZ+zc601ksIW4MeMQDRDZJ+JpJMICBHxFfHk0QGeZGGW2JRi2da5gLFijZZKHKMyoRWp22FJV+xgtIqQK8W0KFDllFA0QlAyRfbRxDuU8aL6lkhOUScmDy2NstpWDD6gbQXlANqw6STDrpFJ03vR9nYhYEPAKSu2Y/HBTT+X3tERpXyDYzzj4xjxwrJKagqBXWYrOBDv0JiRp3Dh4ipi4Y3YvWUXd2HupVo8yCTRDj6vDlJfI6FOijBIgzdm7IOHG6uei9OCp05a3vbkEa+/Z8Z7rpzI+7fQJk8ertipCz56Y8lb332Vrh148v5dPvL+G/jBM9mpOD1cs7z+FMvrTxC848O/OOPGB95K8I7/dO+cp977Pn72vl0ef+cHWS86jq4dcWU64fHzE4zR3Lff8JZ3Pk276TFGo2NZZLpT8dJLkpXPa5sz8FltMVpxc1VxfdVRxzLL+UmBC3DfvOTySYvZrbFacWs9CKRvVnPz1gqr4bQjE3KMgp1K6uS7lZCqUqIEIj8wsSIpbBS5Vr4tN7DoPLMoXdBE05N5abIxRXoOy0mVoa2ti9DBwsoz/GzB5A7HC4k2+ZUanzTDEmlQ/r4QedJb4POvAv5JfN9blFJ7SqlLIYQrz3k0SnI2tR1YYHShTmud7TVPFK8S+JykAlkd0JTiNxkDrI/1Bx9Gkk1imcEYKLwpGHqHizdgak4KiSWRWWLQ1Vb8MG8b6TOMGgNzusk9W27uKrrs6BHilwyNk41XPL9bWudn7zzFWbx6EunK2uHx/BDpSCTT2DRBRj0YtUV5V0GafNk66/ZLddvvqW/A1v/55whtDCFku6u0TWVGCOMzLYnTGistm7dLUWnVkspK6dhldRCX9HrkChRaMWiFipd8e8lvjYLgMMpGLW3ZqxgHj64323BLGMW2SiuNOrmWYoic/paCbD5uW6B0zfL645lm37UO166l9DR0YuXWrvFNI4bKRNs153ERJqm0yobLAG1EcAyDUO/N1jF0W72TdjBnyGXJbFo04KWcIWqOo4/pyFwmi6Yl1c1YWfuYe3P7rkmNS6PIq1Yfth7prW1D+NjgGrbe80KMXwWx+5NnWCqlXgp8jVLqtyMatX8shPBBnlmo5V7g4wbvYCvBQCSrs+TeHm+GhC7BVOikF5zeq0Su1OsCHcbXUtlEXvDMtARl5XoKXeR6t2JU4kuawqZdMCmmEgTSzdWtmBYTqX0bS6VjHd71TIsY/FTU844PjVY+Q/FqyOUWiycYcYHRwWGt1OV1pIMLPllQJ9qYXKohmk7oqBBH8FtNnfgdukVWX1RDK1c4BPD9mQkRbWLwVjloB21RrhPmpxJj5EIJtt6bglXfS3brBOKX6NnJ0iypIQ5bkcEDoSw5beW8LJ0aRYoC1NZEZqgIcQ0uOeiITGxKyESESoyYN8MYeFOAcSqcabwm2FkIybz67CSRPEJdhKYqJUnCej0A+ky9PenVnJ9VOA8XdqrRmzIiQZrScO9OzY1lx8H5CW3nuLTXcOOCyBvXkwJjNba4n+mFe3CDpz2+jm1maG3Y2asxVSOY5sku9bSgmu9RNQW2MJjIprSFIfiAthpbGIbeZQLQ+Z2KphTm5cGsZDeiZHbqgo3zEQNPLrcYrSJ+XNNYnTXAje/Za2wWwtJbUVMp0bI3Wsosab6VpEZ+SfVsafqOZclkNVeaUVGw9tJ4LuM5l3KNFx2jOLGRLAMhQmB/bcDzYFgiq5dNCOH1SqnfAfxD4Dfe6QdvMyy//29+N3/wf/69UstNetxKg+tE70QbrBPdY7xDt6fjNkpLHSw7bWwFjnKazR28Ekp9yvw2Q8gY6hRrEouzrqasOyF21FG/uLKNoGIQyNpgUx3dsu5GNpw070ZN7sEHfGzWFHF2MVqxaUWRUEgvLlqN+ezluOo9rtT44DM+ehP3kbJPNXQsOnF/2Tj5TFNMRRQfmRR7ZSmUJ9gG5ToppSQf0KSJDmP9euv8FUHIRqpfoZXGRnRHku1MK4teqazzrBVntGF9nLyETh3yw5uCd6GEkToxklsVWoJ4bRSDU/iISkkB1AWYWPnsrLwXhODV+7GckpxltCIjHyrl0UbjU0asoFAq497V0LJblVkPvXOBw7VmJ2qeCFY69jZKIyijWHu+Fe3VUsCcxBp0WRncEChLg0pNNx8Y1guK6W7Msh1HN1b4oaNtB66+66exzZdz9NF3Ukx3ae95CSEEjl52jsOrC9anpxT1hKKymaF5rTRcuXxCUVm6tTwre9Erc3Fp4INXF7G2rbgYJ5/XXpzx+PGawkzYKTXXFj3zyuBNzfXlqdSnFVmXfYjlPxFNC5y2PqNNlJLaP5BRKCK3Cy7e92kyrOxYSkyiVgm9krgFXhlU5GK4ACibdeJfiPGJqAq+WMfzYVg+iXhVgpgN/2D8+Y6EWrYZlt2tp4Lq1rmJlgyISQHblNBvxDnHD9CtMpwhGe+qYSPbbWlxJ7YiSmOyO7ZCG52DpPPbzMKP/c6Fgo4oBuVD7H6HHJ9SbS8tCSFqHWtFMmXTioybdret+4ySqrdW41LxmcoHo47Ilg630jmz7+JkkyQBgrY5KBlb5Vo62jKgsVozBMlkvJLsXusCHWvZPWBNgYqZjjcFRg9RG0Xw2C5Gx/x7OFs+2R4pk23sWWw9W9unt00iVtGaaGOnJXgY31MZQ6WjTkYYsHECcqoYIZLAQJK0lTJJoRXKDVhbbc9P4gakxzKaUSO23QSh8xstBBdBpKgog6oxhXz3IiJOtFLsVpa9SYHRilllqZsiI0JWy46hc5I57+yitcL3uwDcurogOMd8WjK9cD/d6S25l7Rk3Snwex9Q2qCNUO6DDxgjx1hUlrKSzFx0wiWpSLrhTSmGBrPa0kXM/KQwkZ6uMk6+jezMECDke/Ls9Uy/x+pS/l0Hl1EoQs8PZ7Yv9EgIa6xi0QdKnewKoxY4YifodJR3DqOxxwsF8ftVELuflwHxvwW+CPgIInGYzIZ/FPgjkTL/OcDxc9W7VXTBwQ8xgK/HZb0pJUMsaoLrUP1aAnYa2YxBvPRyWSDXc2PdPDEqg49B6+zVMwp8uqJJ20HJzwrx2FNK54fbxrqLmAOMNN4QhGBjlATA0qgznyXaDhqFH9UBgzqzX2miSUOni9rmtVFsGOU8tQJcj60UVqUJI74eG5BWie+SCqk+b9BOyic+knWCNjlqpp6BiQ43Ok2eETXifCDEh9IHsg550qBJiJ1U6xwJHNvL6HxfoQjobklhJrHEVeTzlmrXLtZY8Uqa2sqIe70u82ph2zYvXf92kNJCkso1ClRswqaMPJWwPEZ6Bsrg3FmjDKulJ5FWHATPQVPma5ngm7Pa5tXE7qTMAXtvUrDqHLO6oGoK+tbRtw5bavqNi2UTxdV3vwWAxaqn2b+bcn5AtzqmmOxSVBZbaOaVpYqZfT0tqaLTTT0tBPddGWxh8D5wblZlEk9TGmaVzRBHoxVlDM4pGxd5Ak8VRCYg2ckZldQoA1ZFPe+1TLBJ5S81Fo0C3Z7S2HleVYKKXImQnwWrxlJlHSeeJIyV3qf8AMacCdgq1bdegPEMedr/341PimEZQvgxpdTPAP9vpdQfRxqa3xK3fxMCE/wQAhX8xuf6gFDUseZdZt0PAKViEG0XOWAHWwmaJAbmYEcHHfwoKqT8gC+nKL8WREjwEryGHm3rXOvsXMAirby0NBf9hlROMAQnfnzBS+CX5V8S9PE5c3ROsvlAgkipXJ5JsrXiViO0b72Voio1urq7IEYHm8iadB42SD14YGRBzm3FevCRcJIaTIHCljmo9R5q7fFBi8lrHNJHSIFdapA6OJT3OCX6H14LkzT1EMooBGW2HqAUsMtCjyJEW9c226jlhtUo5AWKYCoUCpyjjNe4RlBBadUipRlQrmNaN6j1ksK6jEzSQ4efXURvjnMprSlnGNdSm1Imazy6XQt6BqQRC7Iq8wObUACO2tqc2xklvqHlzFJZzW4lq5bdelzCOx8oohnxflNw2jkxpPCjmw5InbmMdep6WmCMpplVuZn5mi/9Um5cPuFgp6LavcDlt76JnfteTvAOY6UB2g7SpDRWjy5BVjF0nlUn2uXOeYZe9MJLYzOCqXMeukgkizK2VgvOO63k+hiMQ4awChxyqkZYYBvVHVOT0zAKmiml6KpdutUQExKV69gwrjqV63BeGLHHrYtNUBGBU0rRGEXQpSDHQiyv+U7iw9Y9/Kk+PmmGZVQJ/IpneD0A//dP9oCCtqgI1cIFCeS2PNOkTKgUnql5kTJuUwgVPbqdKz/QOg26YhikEXajkxsniy3Fm+u0Ex3ozimm0e0DRrlXF8j6xrU5q2ucshQgqwEet6J/vHCROm5F/yFBqJIKnugXy36WvScECYhJK7vzYcsAAvzkHGbjJUBbLZhboyQzVVrMmwWDR6GUNID8QFE00riNgc4oFXsMkpUbW0hjNj4o2g8EUzD42GQ1ZDNlkABdM0AU5fJRWCy58JjFDWbT85K9bY6YV/NcqiEkJENBoQSJ02fUQqppi0b0TlGyGgJ1c4AOLk7I09yY9vVuvg2Soa5xLUGX8nnlbGx+IxOYeCgWhMHnFUvCGxdGcdAYjFbs1ZZpabAKLk7LjwlMIrCkOWgKvvgVF+id5+K04iUHkzypfdq9OzxxuBZ/y2XHxXnFY9H84XNeeo6f/eANXn7XnKce2uezP/8Pc+OkxUYRqp/+oX/Pd/yOb+Pp4zXXjjasTlp8COyemzCdluxNSo5OWzEJqQy7TZnLN/ftNrkvs+4cu40YAgcYm5W65555JeJTfsOkMDRWYWMtMfW9E6xSKYFeqlgKTNZmRRhoYtkrySzMUkLjRBs/ULJTBcywYacqxdHeSFafxMSUa8XPVmmKcoranEpc0BYm048bP+50vJBszV+p8eJo3QafM2u9OSGUk5hV16A0bbVLgWTbDJvRJT4ukZ0u0NpJkyPW3zQhPrgSuJ0uKIiNFQaOHdw9tdHNQw4jZcmTrWZX68dscekDhZIue20U6yGWOba+yr71LLzJ8rPHrYu6DIHdSpatQ9JVie9JMCxlRmGmEMsPqcnjgjDYVi4AUXukW3K0KTk3Edys1XJciTCT4F5GyQqhMBPEUguMLkYBL9klKJFntUo01qcqYsK9TIC71Yh5/xi2Xd9SlALJVCFA8HJzKU2o59JUdC3B1nhlJKtSCtW36GJExhigNFaUHAvRADEKLkwsenGLaWOy2qJyHbrf4OZ3YXwvJI44oSvXYRD4YxGx/mm1Zrd4BHU1R7mWxlao9RGmOaAMPQSp86emqlGK5eBlv7F5qb3KfZLjhZgGX5yWfDAG5OPIKu2dsDRPYnMx6ZJcOV5nTZwPXl2w2AzsTgqqxopZ8XqgBY7agU//ii/lnU+d8N/+y3tw3Zr5xUvM9moee+9V7nvkIvPasjxpKStL1w4crzuO1x2lFSbmo9eXGWWyOykiE1dIO50LXN5o3n9zxUv2GlwxoXVLXLBcPel5YLfk1mZgv5Ly0nrw7FnNcTtQWYVGMvHeO2wjxsnp9lj1ogQppKZAoUXH5mjjqGYVi7XDakEcLTrRkT92gQuTimQ0vvGKanY+Pxfbz9un8ng+DMsvRnRqNVI2+YYQwoe23vc7gR8GPiuE8LZn/ZDgpUmpLaGopTkJKNfjpwdUw1IeyrzdWoJ3RE7oGKCNOotH3kZV6ODo0agAa28wynN9JQ9TxsLGQCl2aZKf7VYmN9tSdr7uPYNTEdZnsgASgPOpzipNPBWX3karvERsCs1yGJXXkldlH5ei201Jo6HrOaMFYrXUnYMpmBRCRU6wLpWwt0pn556kx90g2XRVTtBbgS5oyaiNl6DVeyvZ0xBrjzEjP+kE0VKaET8MkUVqJWvT2kpmu5VZl/0aqpLOVFTdKdhaMmwvJSsxoBblxhDkfOlCFPR6L5PoundctCUbVVJXsY+hNKFoYh+kykw8QEhKsYHdoymKRkphadWGBPjWQ2VKoYmbUq6BslGdQa556+FoM4guiplya31CYVTWyNFKyg/Hbc+q91xZiFHKblXw2K1VbhZeO2l59PqC02VH3zrK2rI43gj65ME9rj55zE8Cj733Ogd3zTi+ucIYTdcOXH7rm/j8v/InmZ0/YHHjFstbN1kdGXRRcnq45skQOLmxoqgs7brnqf2GSW0xeuA19+6w2PSsuyGTigYfWPViarHXWC5OCq5NCk67ARPdcjoX2K1NXkFuItHME3L5JARwhJjgSJM4IXzSvTEvdTYCaawkQq1V2XvVxGa9wGAFKaSHFtWvUUpTV3P0+miEujb1s4aTOxkvlHv8r+RQz6UVEOnu022GJfDtwD8BviqE8F6l1LcBnx1C+Ib4njmiPFgCf+S5gnd//fGAdwRTEMoJuo2coOAzBDBnVaYYUSipGVnPUVt1ceUGqaO3S0JRofoWt3M3ulvmBqZygmgJRQMhbOHLtbA4pwdxu35sdsYyQm+qrF43YlNjJhMGemVzrXM9hLwaUDGDS3ThRLxJ9cLBCwOtsoKF3q8NmyGw6B2zmDUlA4jKanS/oTMVhUJMmRXMtMvnZ2MaydDj7wnHnUpQyg+RrKNyJnqGvFM0AsuMsM3TYg+joNZBgqDaMn1oTySQDm0+x+n66OVNQrNLsBXm5Gl8NZVrlKCKridUU3ADulvi67lM0iEQygbVb/D1juxy2EjWPWxEEree02tZeuvNcb6eRIgpQZQolesE9rjdU3E9XTGlcK1s06/zPZEmhI+eOh6aGz58LNf+4f2SDx1KcM748PgIzUthHV5fdlkT5da6p/eBSWE4XPe0g+Pq6eiClcg0D56b8L4rp7z04oxfeuKI0kiz+uK84oNXT3nw3JT/8y/8H1z6jC/h9b/hpTx9bcl9d8+4uei4tFez25R0zuf3PRzx5c4HHrkw49Gby9yonFfChP1dr77A08sha2o/teiZFZpZKfZkpVGcawRF08USofJyf1vFmeufSlANfaxND2wQPkQb+z9Sw/a5H6OCl1VzcON9YCuBDG9OoahFwiFd75jAlXsXn3fN4+nj5bMHvq1x9+70RVljeT4MywDsxNd3gae23va/IYiUP3VHR+FdRniobjUGlPjwoq0EZu8lONgqPoR2xHkX9VgXNxFlUlSCQknfJWVmSnOqaiaFzk0gbaqcec+aXRZBkA91WcaMQ9NHv8v1MCqdlUYai4lGrwvRFd/2Xqyi96NSiiF4nFEMkWqfepZGS0Oy9wHjBC2xie4myYKtc7HJ5BTFEDjnVxz3lnkl+siFVlS1aFynAN4OnkaJJVoRv/sQBInidCHa4Kl3EGI1WGmCKjIuXMUHqPcBrxQ2ijwl81tBImjZn/H5wYSYHZcNvmgE5VI0hHIqcEiloFtCOZGHtJrhbYmv5jkQO1Nhyl6giosbhDIiU0wJfoPqltg6+sXd1rSWay1uRAryKmzEufkz2+hhQ6jmUa/FELRhM/QEXXLcbjhtHQ/uFjx2tBnLTXEcrnse2mtY9Y5ffvoEFzHfH7m+jNomBU8errlytObkuJWJ24eM0967MOXq48fc//A+H3znVeppyeJojbGabrXk7fu7XPqML+HK2/8z//XJ96NtyZN3v4Tl9ce5/LJXM9urOb21zjjvDzy8j4np5c0HO375iaPsyPPwhRnOB77goQM+dGvNg3s15xvLY0cb7tup2K0MT5xsuGdecWUR2K00J53YoZXacNRKwD/aDCTyqI7ooLopubZ2aBQuwgaLCPUUCV5FY0uOW89+XXC4iWVFr3BBowbpf+yUk9y7SQE9rb5fiPGrIPF+XgzLbwHepJRaAyfA58ZtPxO4P4TwH5RSdxS8/fRgzHBdf1b3IkEG00OppRa+vfQNpszvV8FnpIhv9uUGsBW6PaUr51m8ad37XJ4o9Iifdh5s2bBuXWQMqmjiEDJ7chXNF7LPZX6KA1r5LGGaMmsY9U4SXjt5WqaxjYNVSmHNlqJhvNOSEqGUSRTe7FN2srydRs9JrRQMPZiCpj+lLecw9BSFzdmnBHcnzTbvRuRs8FKqKpo4OZaoEFc82qBd0mWBwLhqyLouIWQ8/Rn4npGGIYAqJ/iIOx98YIKQqVS/JpgCZ2tOOsdevcvGBdzg8cGgvWfW7LIOhtoGmRziiqhHGl1Z1CzJAsTVweADRZzYgynHhqWtpGxjSqnTI5NcGYacCDRRgCmRdJLrUFKOTM1NsdkbdVVMbLyZCDFMrzWlYWkVxGMYesF9X9ypOGos52YlHykNs72a4AXjXlSW1fGC3/Jlr+Ynm4bFtcscP/kBTq98mNldD3H4+Eeomke49fiHqWYHtItb7N/1ukzTT5+zjv8vdga6weFC4HDdMy8Ns0Jzsum5VWge2i25seo5PylpB4fRlnYIhCBmJ9eWPZ0LHEUrOLEtM9y7U9BGed7SKGqTvDNVzN5DlP/VnHaOnUqzjkYPnRN1zCRN0EwabNHgEcBAU0yz5vwLoW3yq6FheUcTUAjBhRA+HSHcfHZkWP5x4MtDCPchBJ3vVkpp4LsZzYjvbMTGRAoSOWDHv8n/asR4nhFVEuuzVPIIW39T24SdbSVCpbPUZD4Rt/18+9/lEFQ+lI83tsknH+8G2c4dsp5KSKJWIVK6R30T589ul9AuIP+7EPL/gtUeA6gQaUysQ28F1nSOtZFzH89/roPHwHf7uUvn55mIOB8zUpa0lS0pP4gUgFLj+fSDELCCRxOyz6eKGXPCwBN81F2Jeivxn2TVYXztGY55e2xflvQdtzU58jkIZ8kpt3/nhBRy4WwWDkkYS16U1VPIZBnvA26QzDtpk7SDxw0R8jd4+nagbweG3jF0Dt93HK86uvUaN3QEn5x8hKHpUqPbu/w3EFKP2/ocOEsUG/Vdoh6L2rbAGyGDamu7hLAx8efklZn2p5EmZnpkt/eR6tsmXlud9zs+4mn/ynUY32c3J8XH8jM+lccntHqI8MCfRJQDf11ykQf+BfD5wBx4LfBmpdRHkWz8R5VSr799X0qpP6SUeptS6m3/4Af+Psp18q9fi6djCrzpRkz/x3rsdmBWsU6bgkB+gFNtPFLkrZKmnGTnkVRw5vvF/W29VjxDgC9ikyoF+USOSVnp9rbpZ6XGYJ4MXNO+0jaJQQlkTQ+tVL7Z0/Cxgar6tSj/MQaIeHLBO3x02kmiXd4UECGUQVthsCktDcOkLBh8lNHVkdCjMrLHx+PbZqX6cFtQSyig7eVt6jMocjacz1HCW6eeQxCse1BSakr1OUHExAlsm4wVX1MJQZI+ywvxS4UtU918j4QsrZuZgcikt70K2b4OyeOzj8SsVCZI/6cGXh01SLa1T7aDpQRSWa30rWTd3gv2um8d687RxaDdtQObZcfm5BhdlNxcdCyvP8765lPoomRy7h5WN5+imh1grMLYEl2U2LIRPLjR2AjbU1rl12QVMHIDqmjKnUZmD2tFG1doLoSI8ZfvnLLpKjJPjVactl5WJoixQoIW+iB9HxdGKQph5Y4r0+17KE8aMalQkJ2zXqiRntc7+fdiHc+HYbmrlHp5COED8bX3hhCOgfNb730z8CefqWF5uwFxGNot9cD48Me6qNRdU9lEssYQtEQD1zEUU0rX4e08PrDS/FCuE/ZN8AI7DF4c2/sNTSHazInJByNsrggDdVSJU36gsVLrNhGXbcPIvMsTwNY+vFL5985F+roLGAN4WcaHIO9J1mNKycNSBPl/UoyZf8o2mkjNTvZTwVZUEYHignxW60TGVRPQ/YY+lDSGbDYMMUOXq4BXQrEWAo3GlBPJ1gCUSIpiYkbkfJ6wEgMv3eAhwursFtokDR0/0yArpBTMfAB0YsDWogAZApUJBC3mG0k81oUYkLW4EHlTCOs1Bntua6IRPAM61l4DWht0UjREoI5WaYEkmiI2zrZWCnnb9D23WYfk1zIqSAkufLNlTzYpRFvbdI5ZbZlVUhZJCn9NaTg5bfE+8MpLOyyXHedmJQd3zWhmFcYILd4NU7wLXNqrufyyV0tAP3waN3TML72Mq+/6ac4/8LuZnLtEPSlZlU1mWyqtmJSGSVNkWGK6D3ZKucf72NOpjGZW2nzshVYcNIXcd8pg4323W8vfdqoIzbVS2tutDFOr2K3k71XUsUnch9KIhjfItrVR7JSaaaEpTaC2KgvFKYWU9JTH6HKEAL9AAfxFHJPveDwfhuUfBP61EhrkIfBNn+xB6G4JrotQwM1IvklNTNfL300JrstZFRG/W1QDqt+gUqMs0exTgyOiLDAFyknW3lNQRQEiF5l8KjVJlc4ZpVcCFZwWOjqjp6xhFJ5KJYyknJZq52kp6UIU/o814iaK3gtFeMxC+zgZpGBdGpVLJ1Jrl+xviI1S5XoGZ3Ep+KcJpF/lLLMwJbiesigw6yPp1hdjM2g7UMnBduhiEpuUFapb5+tgrGiHV8oLIDt+RtAWtV5S1RbdLbMeSl4ldStKU6CGFtVvRKnQVpLBtku8KaVRnVFFAmUsTAUx0BqAvqMqp+j2NCJIZGVVlAV2fYtga/SWJIKQkBTalHJfxetrtBlZoPEYbbcA7yl8J/2TqIdTG4NxQogpzFbJYGvyrqzGmtGxPU38AGXMxI1WzGtL5zxN2TOJzcN11CdJUrIH0ypmyeMlGXrP0Dua0uIHz7Be4IYOY0tct+aBz/utAFx7z3+nOXcPi6c/yt6FN2LjZ1w7P+XWjRVFZRh6z7y2Gdm06h2r3sXfHVcWLS87qLi2bLk0k+pyXvVF5FSCzaZejydgvOJcIwSxzgnxaxUfjMYqdBC2sddj2U35AR/XviGELDWw6D0HrPHlFI8ShESEsp7ppTyP8WLOqO90PB+G5Y8gglTP9t4vvJOD8EWDMoXobxfNGSnXVC5RCefdt4JA2WJSOl2gjMAIQ6yBJgyw7pZZ8yQojVcGY2G9Fm9MF8BF5MdmSPrZgkKxMbgKzltoxDqIiE4RM2AR9CFqe2xl3tE1JGUgKfP1gfy+0qjsm2mUYhocobKoEKitpYgJ/LQwkRwjjbGEGVf9ioPmAE2gD4qNikEAL+gOF3VVVHS3ieYMwZQZ/tgHMrNRSgmiRGhtReuhLpocvFM88VtZNVpMk4vImqSaj7VyYlXDFBGm2OObXYH2BY+K9XbgjF6N1QqcQ1kpiSltMJuTCBlr87Gn/41rcZMDdL8547SShI1kp7WwMqOui1Kgh5aNrqiUZxEKZnXBRknpIX2DSeHptaUygd2qoDSK+3brrNXiozzvPfMqY+2dlyz8/KTg2lIgqXt1wdFGJpvj2OjTSrHo5Od7d2q++BUXeGC35vUP7rPohkzBL7Ti6mnLr7tnl4cvTDle9Rwl5cCm4GjdM68sb/jM/5l171hseh65a86105Zu8HzGg3uAUPQTjND5wGYQSn8fE4n9RuRhb60Hdish29wzr7IS5LL3uWa9cT5q7wScC5SFotLgqDCqz6ddKRXhr3Ju1tFjdPABpwsGNwjrNQi+v6gMGmiLKYbbzBi0MEOfP8r7V8d4UTAs7eHjEfJXCi476fgmnG7EaqOjKFEbsaIxozLVDL0+llKAF8SECh7MQsonQKimqG6FNha9OmR/90GaYUmwFcFolO9p6jEYVLUEk4TbLlxLVdVo19NpHQX+R8OFJDBl9fjA6Rh8k/LftvRsep8LY03cI56ERcxMUCPZAeRBaGN3bK+AYKaRUj8WDGelITiB+XlbicZ5QsZt14NdD9oIW03p6DgkgmD18eP46TkmEbYZygbVrVlXFynNiNnNAV8r9MlN/M7d4D3aDSMIOn7mEIBiKmJZLtAFhRs8+/E4VS/M1GkpcrzB1PjeU9tIgjIz5v0RQ3OQSx3pOwRTxjr81rlqTzFpBRF13NOKLE1CQVsqLffSvD0FrWX1sDnOq7bOTSnbU+6Zz7m1drlHkVZS6efeB5TzaKICoVHcWPW5Zn60EQLPZvBcW7bsVuLonsa1ZcfxukcrxXuunDCrRWo4lVjawfPEdM27Lx+LT+Wqp7Saa1YzKQ0feOqEdj3gnCf4wH/9kZ/i5MkPYMqGd/ymN/Lhn30zthbs94VHXsfQOz7vT/5PvOndV3nlpTmfdnHKzz56k3sPGh7Yrfm5jx7y6fftcvlkw2fdu8vl05Z5JZo3jx6uOT8p+Eg0T56VhtWJ53xjmVq4sug4aIoo6SCmwrc2A4MTi7TSaNaD43DjWA+Bo05YmK0LnLQR8mrJZiQKCfqFHmvmz3f8akCbvCiC91jeMGeaTkDMvmMT0jPWtOPfzmTpcKZhGYxke3l/0bsxGMFuNzFr90FkU7soMjWxpWgSA9oWDM5TRApvaQpcO0jmFlINeYQapiDtYuxK99r2TWeUqP1t10yTYpoK8l1CkKw/BeYkxZqghAOKwjupMCmV68i9D1jXR2MLR1AmnycVvJyabXrZdnMxYqBzZlvUqH4Tr1GUDn2Gy6ciwkWFMF6b7RE8xkRlRu8B0QsJPoxEIT9gC1l2a2y2fUvlIKsV9GRCR9j+nBABmN7Jd4ulMpQ6s+pS2o5oJDmp48+JEKJNlmUgeIIDtGXR+izitOxcNjfuvQiD+RDQGIwO3Fr3OYAfRxy3aLRLieI0vrbshjP178VmoB0cp5uBVedY9y6XXI5XHfcdNNxcdLSdY7XopCFZam4C7Vqamz7CK40tMWWDMma8h7Q5g0Tp3RYCJoyImBDIXIVZafAIFDAEsqRCct3xQRx4thFBSb41jQStdCr1L2KfIJ16reiSkuXWG3VcEYYwCl+p8AJF718F447RJkopo5R6u1Lqx+LvL1FK/ZxS6kNKqX+hlCrj6w8opX4ybvvLSqkvf659j5hcfdbyLAe2FIyLCA3UWwG6zKSNxNrL70n72kJSpJp5HWvGINmtdn3GdSvXUZqoX8FofpAs0axRWZd4+18RG5MQM3E/WpeF2F3PDxKc6fB7VBa6HxDMtic1IkeyzsYJrGyIgW8TIWIbF6KgvZRMgilZOmmg9bpkg2UoZ7hiQq+s/K9LOmVxpmIIcn59UWfvSxIRKv6fHt7bdU0yVHMb6QNkpqN38qM2WyiOeG4iXFE2l0kgyYUaLQFfKOhKehdp/9soJKUFSpbKbCFAZGgmc4/UC1Gxr6KGjazQ+rXU4jenqEG0UnS7QPUrVLeiMhrVLmisZNQKmJaGphBVvPRzMvXdRgmdti4GN5+z7hQwbx8py5br7Vn3Lps9pJGCq9IKW0jgVkqxN6+oGouOtXJjNdqWNPt35du+Xy9w3RrXbSL8sM3nGCS5WHVjYO+c/5jmoI+IExfGwKvjM+OC3IPKDzFjZsubdbRa24a8pttoM4R8P8izICNJCJuYNKSSzQsxbn92n+3fi3V8IlDBbwfeu/X7XwP+RgjhZUjD8pvj638BaWp+BvC1wN9+rh0LeWSITjrd2Vr3Vka9/XMemTUnAeYZM7/8QToH9M6NfooSWGwOsgkf7XzIARQSSkP0ifutRmXKtFMDa/s1OAuDSjdyF2FaiTmZpDuTxKqLDZz0Ob0fA7hk9dGjM2zD0saHMSgVlf/kc1NpJp8KdRazK4gNIaSgRwz99v8uHo8LUgbpvSgHOh/AiFyqt5UclykItpLfi2Y8/shkTd8bBPonDE6pU2+flyGSodYxQ/WmkInFFBL0I/QR0uQuPAEV/NkvHO8Vbrt3zkBL0+ovDS2aHCgddcrTeR4DUfo5ZeUpqJ2ZmHPAEs3sdedoo89k+gdE0TLPYtPjfGDdDRyvBN99FEssXedo1z2bVU+7Hug2A6ernuVJy2rRsVn2rE5bji9/gG5xiO+7zIQdHwOFjj2GbSij0SpOGJxZyYUwfgfnz34fv3X/JXXKEV45XoL8PxJ0Qhgb8wK1VXmf6dT1fgzqqfr3DPPep+y4o+CtlLoPkX/9gfi7An4TIjwF8I+Br44/Bz4+bf4ZR8q8z5JvBJ+2nWXLxh8bnNMDqNxw5veUaeUszQ2CWvFDzrA1QZbirsvek8r1Ihofa7smwpaMEnZm0rROzEyRsRyZdVpJPbyInfX0elr+JwGeIn6G1YpCkRtDlRbzhUqLc3cdVQxLEz9HjecirRbSSF18FbbcfnSkh3uXg7aK2Fu5nltL3i1+6zbhKV73nA3prf/TsaT9pqCYjiP5Yho1rmRMPGek44rbpM9PEM7t85Zx2/1a6t1edFzye9Jrt3MD0n1zO3EnSSsk+GnSjI+yC+ncBKXjvSDfNU16Ca8v94IgLLYnUEiY+HHlVmjxu6yi7+WstjSlaH0nBMqsLrIOSVNaZnXB3iS6ylhNWVmquqCsDEVlqEpDPSkoKxvddCyTc/fgI2FndbLBdWu65Qn9ekG3WmanHhdx9iGI+Je8RpyofT4HWf5XJ56DioJnskJNPR68E0eeLX5Ckc+Rypl60nQ3WoJQWrmmZyJlvUrJ/qWIePbcPp+Rjv9O/j3XUEp9mVLq/bEK8Wef4e9VrE58KFYrHnohvsOd1rz/JvCnERIOwDngKISQmDLJZBjgLwH/SSn1R4Ep8CXPufeYTQUbURBbkp25FKI0oZxkoSp8fOASQ7CcnnnoACmx2GoUSrLivhJsLcEqsjMVcf9bh5Roz0L+sDl1CDE73fYsTzT4VCIB+dloKf0kw1sXyE70t09BYngwHkFqqGRYlVJZRwK2scajZGlQYSsgDmhdYLR8pkxKsW+gjUx0OhoPeI/RBjXIeVduIHiXIZlJq6QwY/05oS3OSLs2YYRxbpe8QmzCxuMqTGJ+qnysBJEeUH7Aait/UlI2sXrr2jzT6iuJbaUeSIaYCtJDvuMg38vYs+8rp1FaoUQl5uLWPbQd7lNWXZotowHiz3YMbpWRMooLgTqMeyiMpgowLW0mtqRglIK1TSQapaC0+ed1N2R6vfOBoXcZx220whYSyAHc4CnqGUU9xdiSnXMTbD1j2CwwZcPJk+/HD1KXv7noOJh2KAWLTc9iM4g866bntB2ojdzvrXNM4qpkE2vk7eBygGudyDRQGFZ9y6QwWGBwsbccV5JVvC+Sf+VmCFRGSi7S9I1Q2jDe4wmRlVa3L6YRIdR/C+G6PAm8VSn1oyGE92xt9s3AYQjhZUqpr0WqFl/zfD/7OTNvpdRvBa6FEH7hDvf5e4F/FGnzXw7800ibv32/mWH5A//knz/jkjZvu5VJf8zfY52U2x66nHWlLHCIpRnXoYLfwmaPNdu8RItws0AM1mcOXGe2ZFrOpW3zR8fXU5mhi3XOVHKAsTaaSzVhXBLeHshD3G6kzoc4EfhIq1dZSvb2LnreZ9pdbCwCZ1mqYasImc7vbdckr0xCiDT2cCZbH5uPbiuQjgHd+B7iqiZl1MoNsfbcysMa+xA2Bi3lBTJXxJWBYP6H8djidxgnjY9lduavtD25JwmFVKbb/pdWcG4YLbnSOXiWRMwTG6z6LHVcdFH0Gf9Go0QCNY1U387Nva0GYuc87Rb5J1PsI7LE+YB3ggWXfz43JoOX3wFM2eC6NeX8gGKyw2YYz1UIUFoJzqnnkI4v0fw3W4Jr6b0C5fP0zufVEZxpWeX9Awx+xIenz7ld2TTd49sjlRRfqNCt1J3/e47x2cCHQgiPhhA64IeAr7ptm69CqhMg1YovVi8A3OVOMu83AF8ZG481UhL5HmBPKWVj9r1tMvzNiEExIYT/HvXAzwPXtnd6xoD48OkQIkLA2woTTYMhNbTEmDiUU8mOijojR/L+6vm4/fZ7I0Vc9SIliikIQ8c8OgsrhdDAg6eKKAu9PqWo9wQG17cUUWbU+ATt0rkcktQCDWFLe0FuMatV7s4rJWQDEz9vWoghQWkEqWB8H3Gs8ncb1fxKU2TZWRU78iGiTsQVB8ywoYn+jJXyMdpLDTaZ8ppUWrodnbMlCyt08XE7NXRjpup9fnA+xjeSrQAXITbbiCBgFA5LmhxppWJsRIIIAgUl/p/Jni1Nlj4oYUhqk2vyIQXfrc85M8Gnn123JUE75CasGjqGeg/br2MGLn0XCmHjBlsKKzSWU6wW9cFEDU8ToyytdcZ8VyaaHtQWNuPxVMaO1Hqt2DjPbmUzRf2w7JmVlkt7dSYBJZf6vaZgXtmsCHhr2VJak7N3t9fwWCWZ+jB4jH2YxdE9uMFz/p45x6/4LE6efD/l/KUcffRdAFyaVxntAnAaceiJuu5CwBpNbTTXB89BU2QjjklhuLHqhaRkdG7KNk3JZmhZ90JYOu0GKlvgA3SDGFALtNJzuHF0zrNxYkLiYhJjlBDgJLgHWj8S1l6o8YmgVpRSfwj4Q1sv/b0Yv0AqDk9s/e1JxLt3e+RtQgiDUuoYqV7c+AQP+8y4E5LOnwP+HIBS6gsRuvvvV0r9K+B3ITPN1wP/Lr7lceCLgX+klHoVEvCvP+tnbDnjmHaRoWqqWxIqobyHohH8Lci2sfHoiwbdr/P/SUKSENDLm/jJvnhgFrU8mMOGYEtO+8BOFP/vlXTqE1SwafboIxEnubloW2VyR+FF/ax3wrrLjbewheHWAvvrvVDNU8ZiNHRoKqs47aUNoxW0GIhmuZ0yka1n8M5n5TUYO/BXlz2XprssN55FsFgjDj2gURTZLGATopem00wLS4GnDeJFGYhwsSDEiKqQc1raDUO1gy6nqOBFTtZWuF6y+w6zhX0U0+XdnbvZIJ6JxpQYNTaYjBLa/hTRQl934/fpz79UlOemDavWUZoSFcSBRTJRQxgcHtgvGpbeoMu9fO/01Dgnk5uOQcIomLsbggkfNhkuqPq1FLsSUslLJmlMiV4dSlKQsvlYtjvXaFjDtFCEoDDtgkLXWxo2ck9UVnoZu5Xh5mpgVmoON44LsVZdmtGjNE3mWkXUDeSm4ODhZQcNlREjjZN24FxT0LnAvXPLb3xgn43z+T7ofWCnNFw+bamMwWjJihdbyJFJoTl94yup7RvZDJ5L8wofAq//ij/OX/3eP8+j15ZUVvGNn/cQb338kAd2Su7bn3BxWlFbTWMVh+ueu2ejnl+hNecnRda6qaxht9JRwVFRWsW80oDleOPovawepqXmo0ctp93AXdOCyydtDvLHm4F5ZZgUJTfXA0X0YD1uz5pxn5vz/MezARtu33Qr0XwxjeeD8/4zwA8ppf4K8HbgH8TXvwP4+9GYOCAOO88+zUUdkmCiI3jKvE0pjDpToPs1oZgQSpXhXygtVGlTSuCOD1125Wl2BRNsR82UUM3Rq0OmtUa1rRjkKg3eY3UpDcd+Q2UrVLLWMgV6eQvV7KKGDbbap1Bgo+OHiVoiSSfbb1WjBi2ZWhcDvfOBiVuxChN2tGQ63lboIQr0B4caOmamzLWYXePPQiC9Z64HwjDhQlhFcae44ug9en0MwVMXE4G8uYG5lu+I1hTOCfFp6EZtEW2FHBUp7+b46UzO0c0uen3M5K5XCX18c5q/X9JVt9cfR88uCO29W44Ph7b4ek7Vb2RyBsqihiHW3Jen7CiNGjaUswuoxTGhnlObMsL1oktOUUPXMR86/PSc3CORqIUxwpAMgklXQ4de3hLbu2TiEfyYpadz2W8opufRCzlf6Ttvw1CXxR677ZLe7okwV9GgvFzndFcnDH5tFEcbhwtw3Ip5dBJ2OtqEHFhPW5d/BpngZqVh1Tvu36n5wM1VbpS1g2PRCTbc6CkfurXm5qrLZKE0Gdza9Bm14nzg0evLWCfXvPLSnHdfPubmQr5/yrb/6vf+ef7sH/suXvVbfhff8QUv4Yfffpn3PXqLN77yIj/x5kd59+VjXnPvLhenJY8drUUbvjD8y194ki985UXe/vgRICzPK8drPv2uV1JZzY+9+yqvf2CPu+cVT5+2PLTfcNq6zDadlZZry467phVXlx2V1dxY9YLGWUuDd6eyLDqZXMUa0GeDkxdiPCsq7RMbl4H7t37frkLcvs2TSimLADluPt8P/oSCdwjhzcCb48+PIvWe27d5D1JqueORFOGyy4lPeKv4cCZUQHxaktJYUBqskGWDKVADUhaBsbYZvFDr+w2hmkW3jhLTr87gyxUjCiOVENJnEQK+2ZXf4+d5FDoeT6r9ytI51i21Qg8tVpdZMlN6cApfTjEBfBRZCkECuAguKbStska1HloGM4kWZZ6AkRJENcfpAusHQhV10IuG5RCYKy1Br2zEZWhzmgNxpo8bK7XdWEJAaYhGBHp5S75vIrjYCt/sSlnDBUI1G4Xy43vDEPXYjc0GDrl8FUXBUvkrlSyC9rnunHsSUV0wmILEsk6kHNXLBKdXh2fvOVVTGYVarcBY2ZdSEZEyKk3mySqhKPq1SI524jWS8N+JNBZsxWyyEW2WHcm8pQZvZeXlR90PoxTLPjArNZWR678eVA6yaVU2K0SFrym2OQFCs9+rLRcmhs1+k7/bsnPsN5bOlcxLw4N7NQeNzZC9ymp6F7g4qzjOZQ/RVEnB/OK8ortrzsG0O3PeHr225FW/5Xfx3p/4YY7/6Odzc9GKVIQSAhXAg+cnTEvDTmU5NymZFIYHz02ZlZZXXpqLofGkoCkNe7XBBXjkrhn37zbMYwNVK8VubXO5xWjYrwuUgt3KsldLGDreDJyflOw3Bh8SPFZWNRAF2F6wmPuCjbcCjyilXoIE6a8Fft9t2/woUp3470i14r8+Z0J7B+PFwbBUOrLb7JnArLSVhyk2lUIxyctbNXTyoEbLM9puJGLELC+UE1S3kn0NLWid9+F27xG7s3oHnRpqsXyjuiWhmOTab9BWSi9WEA1O1Zkw0GtxEg+R2g6xKekD2IoQl8owVhpUvwbbSLadqemRNBFJJEW9i24l2KbJIRGYEjHJdgvJBIdWsNQBplbBgATucip/KyUYhKIaJ7Vt8ajUvBs6gi0lcCfijCklwA8tp7Gs0ShH0I2c13h+zHRPJsc4wlbmPTrfSLYdkpuOtthbH8U3u4L9LaeS3ZZC4w7VHCJmPDMeo/FwnnBiHXzwgdLGid7GWnpiipaNnN+EWkqZuC1FTbCax9q6ztc9jRuu4q6iFuGm3rMb9TzGUplAJJOo2LWlz3KoViuONn2E1IlZw6p3HG8Gaqs5XPfZnb22mkU7cO9OzTuvnZ6RlN2pLCftwIN7Db/81AlHq/6MOuCkNFw53nBz0eagff3qgtWxCGrd/eAeT31YfC9tM6M9lirmn/pjb+Q/3Frx63/37+c91xZ88N3XOH/PDqve4X2gtJr3XTnlNz18jhvLjouxbHJz2eFD4NFry3wM105bFr3ondxadhy3QtY5XPccNEVmlxZGMSsNT/pwxsg6/d86x0krqoM7lRh5r3qfJ0mlX6Ds+wXKvGMN+48AP4HItf3DEMK7lVLfCbwthPCjSFXinyqlPgTcQgL88x53HLwjJOZtwOUQwm9VSv0D4PVIQvkBpDyyUEr9CeBbEAb4deCbQgiPPeu+u9UZpIDqVhHe5aJ2hY2ohBNBL/Qb+T+WRJJXJV0btZsDqDFDF/edKn0RkR81pQT9bXGkrUAj9HKpkbMNN0REh4owEJSl8B1BlajgSS4yo1+fYJpjPM10YuU6iqSKF+v3OZNNgdQPGR2DdVnrnNhUC0WNr+aY5U1CUaMX19FGYJB6dShMt2oTGYQSlCWAxQ5/gsalOu9W80+txY9SIIU93s3Rm1Ps9JIwU7tWmoC5HDEIVHBzIteqW+fMO2iLn51Hdct8jkl67VGqAO8z1C+VN5ypMJE2LwE6Xr7kPWrKbGvmTYHr4z5UbHKmVcXQRlikyfLACZmi26VsHhEuqm9F+KyoMqywmUpjeDNEBqDr8UFWL2ky3sZAHDSGk1audecC5yZFLq84L4zMQusYxGw0cwjMS8uqstw9L3FhRm1FpXDVey7NKg43PQ/u1uw3BYfrURMFoLKGa8uWNpZDOud57NIqMjYD9+03PHr3nMXmnviOlwDwcx++Sb885umPgjWac5fmfOSXPkjxNa/j6rvfwnT3C8RUwgWuHG14YK+ByvLhKyc8cteM66ebSKbyPHZjKVjxwfPo9SUP7E8otMgDPH68wfnAtWXHpDDsNwWXTzacnxQ8fiylrhsr8fecFIZHzk05bh1thA92Q6CMSpzOp6N/8YwQwpuAN9322l/c+nkD/O4X+nOf04A4byhB+fXATgzeOyGEk/i370bghH9VKfVFwM+FEFZKqW8FvjCE8KyYxs16HYISinqnopqeH0R0n+1mjqAzXMYNC/17YhWrITAxgR6doVaFipRdJYSX5RByQ6spdDZxSHBCbwqBwbWnuHpHHKyjTkivSwrXZtlSiCWVKJCUAokrJhiX6tdBtu/X4ssYFQ71+ph+dhG7viUZ6RZMLdhaoI2b05wBp2NQERURlJZ9bSv+xVLH033J3ZWTYBnx73p1iK9m+btu/3/GbWgbOhiRJjmY9W22qxOik9TPEzFKb47xpWTeaeIZyyZV1B2JYlKmEI9KbenPvQR7fEWy7/Uxyg8Me/dhFtcF9x+DNP2GdXOO2q1ztu/LCToabVxdOe6uXLTE2yoPbBF1zOJ6PKexfOMG6ZWkY3Q9ul9lY+SgLW73HszxU/TnXoLZnGR/zTQhAuAG4SBESQHVjzK6aRLQm1Pczt2ooWVlZzT0bFSZyypdhNoVvsvaOwlSmQykT5zJuuEuwk4T9DDzChA00qLzbOLskmQbkudqoqg/sFPyy9dWGKWoC81TJ5Kpf9Xv/XP8m3/+v/On/t7P8Q++/Q1sBs9d04p3Xjvl/KTk2qLFGs1BU3Br3WfzhP/pwV1KrfhvT55y0Fj26oLBB+al5rh1OD9qgZ90jntnBU+e9uzVhlXvcZEUe++84Gjj2K1EJiKR4eT5V+zNJs8bZteeHt1xCl/N95735/2PGHfqYZkYlt8F/AmArcCtgIbYXgsh/OTWW98CfN1z7T+ruPmBMpYBCF40l7dsuQpAbVbYWL7QwKTeRa8PmTT7mMUNVKzHmuRBGJuRquuYlVN6ZSn7JcFVEuD0WPPVkOukulvFzLuLxBInK4QIUVTdCsqJkFlS8NV2xIWGVAc345I/LfODj6zOIdfn1ZACzkYCYhAd7NxYiYE2bRdsyToYputD/GQ/OxFNihq1OZJGbtGghg7Vnoq1WELjbB3HmUAes381bKJVnJagHebodoGfnc+Ztkw2esR0t0tUbDgTsfTpuoViF9Uux8+D3Jy2p9eEXbk6lPLGehNXDbP8neQm0dRB9qvaJRRVNMGQ1dWkMKh+AYmtuTnNJSVMIa93a9H7jgFeDR1u9xJ6cX28hkOP0ka2tzHDHzox0yjnlN2SttrFNlE4i5Rle3oHjbXYWu5Pr8xoItDssxwCxhbcWDsaa2ndkIW+Bi9IpAuTkhvLgYTg8wSmVouQmpUSwraOtibJtbpcD26d48mTNjMm95uCG6uOo3Wf9cUBLs1r/u6bP4zSiq/97Pv5N794mff/0hVe8hu+kv/l+36WJ37uP/KPPu8BfsurLvLzTxzl+va/+/kneNm9uyw2PTdOWvZmJUeLjv/p6z+Tzgf+xS88wW945AL37tRcW7a8dH/CjVXHtWXHw/sT7tmpeOvlY+oH9nn7lRNecX7K5ZMNi84xKw0wo3MepWxGbylF9IxV7I3VuU9+vHANy1+x8ckyLAFQSv0gQsR5D8/sW/nNwH98rp1n49iU4RZjiSIoLdmRKQTSV0wyNjtEhqSvdwXGN9mPDivVCA2zlQTzw6v0F14ms7cfUH3McrcyxJylpWwvsTpBlt1FbFYWjdRos2JdfARDiJjxkbTiiwYsDGiKJPZUzdCtZNYiw2oJZgzSwZaClHE9IUnfBo+PgVW5Ab0+pq53JTjFZiXA3uoKfnaeEDz97CLFyRX8/C7wA77eQfWr/Dkp0896HmklkiJOOge2InRLCczbWtp5gopfv57nRt/Z4N3kvkYqSYXpuXzepfnr6NGoej/KfxqUGRt3aeVUFiW3hpqD2owNvyC6IKfFjtiU6Yq9GhZ2h8lU0cZDrKcHsRzT5xLZwhuqg7ngpSNMNa3AhCwF3V2voO5W2VZOQdRNl5Ey2R3V4VTNjfUQNdujBjzRDkxuEQotgb+MmXLvA3tb36cpRB9EK0GkrAfJOKeFQnqQsf4bV5izUkfMuI68X8OFSUnnAtZAbc7W6XsvWe6NVcc3/8aX0BSGV12Ycve85sOfdjdf/cqL/Ov3XOWe/9vn8P0//gG+87c8wtd9y3fxMz/8XQD84L9/H7/5Sx7hb/779zLdqTg3q7j81ClHG0dlFE9cX3L1rjmTwvDBqwuuHG94YH/CR64v2a2kVPTBqwvunde8+6kTCq34yK0Vi83ArLZcnFYctwM7lZyTJ4433DUruRXLRa+86/YI8omPFxBt8is27sQGLTMsI847jxDCN8Za+PchdM8f3Hrf1yFlli/4OPvNwPfv/77v5Zu/6Zs+dpsY2Hw5lew3DJJr+LE2SoIJllNZ9m5lqmgTxa56hv37UcFTmgI6n7XAcyYbCT25GUZc8k72x7JDykzjklr1a3y9O64cQAJUQqpEbHowJeVwGs0EosSqKdHr46zdkpbhucloylz6kJ1F+SVT4m09GiNM9nNpJkRDCrwTJIWTGrfanEq5ZjgZr12sdet2Mb6WegtDO9beU41ZW1Qqf/gBvVp9zKSXUS1bUE6FQ0Xoop/so5e3JGt2Q24Am1h2qOJqg9ldFMP6zESi+o5pLD3d0x/jy3NUW25AZbOD3RzJccRa/nx1FbShifV9vJPzFjNrgFmzi16cjCWuzSkmyQLYipPmIjurqzxlL1AFx0GIHptb5UYfYNF7FljW655JoVkPgcqKwcDocxlV+WJ5oAtksatrywFrBFFxtHHZ6ACELt7HBmVpNIP3eALDQHZenxZ6rMEHWPaixrjuBQN/0rqsVdIOckz379b83OOHvOTclKPNwLVly/uunPLmuuB9V0752Q/e4A984cNcWw78+D//y/zUR29yblISfOBnPiRIt8XRhke1oo2BNbEy151j0Q04H3j9fXt89GidiUnJHm5eyf8PH0xYxeM9Py1Z9Y55abJgW0KtmKhz8mtDxifFsFRK/bMQwtcBhBCcUuqHkMz8BwGUUl8C/HngC0II7TPt9HaGJREbXJTT3NwCYv13DI66W0ngSQGyjiWMohFESDnJEMMUZHMNM4gmA6bMDay0PZBhhmrYSIaotCznI4pBpYDjxcUmZe5ZxlYbwWxvBa8QJxVf78q2EWfumn10v8llmOAFv60iXt0sVvJZbkCn+nNkCerYqN24wKTfjCsXpVlNLtCsb0pgXh/LcXenoKa5MZcbudta54yNuwyv0xbVb/DVDN0ucLv3jNtsTSoEj4mEKPpWJkU/atL46Tkpq0SzByDitN3YQ0jN56GlCMP4eirrpEZjPtZuFDTThmXv2YV8LVS7jPDRNmfIenNCKGpCsFnBUpAo6zhZbtDxfXKNN1Szu9CbEyb7d4lujJPvnfTGQWrNjRX3pQsTk4XAABorRspWK1Qr5KSb64EmZsM6Z9GpPi1BKgUuH6AMisHDcTQv2MT6yKh6qbLcbGEUq17KJkPcbqeWJudx22ftcRcCl2YVP/3+67zF3uS3ffo9/NtfvMz73vYYP3N+l8XRmqd+4SeYf8e3cmle8Z6rpywiW7SeFtxatkx3KjZR7bBqCmaFMI8nTcHBrOTitGQRUScpYM9KuxW8LbuTgnbwFEYzqy2F0dw1K6OvppybeWXRSIP3BQvenwqZ9zMxLIE/oJR6WQjhQ7Hm/ZXA++I2nwH8XeDLQgjXnnGntw3X7ElNUUExrGkrwVQbNWKmXdQIMROBkSWYkVXQzy7Ksc4vbhEnENx0dHshIhjWvc/uMcT6bJI8zTXwLRidn+wLYiNNDE4wxMoNoLozmTYIKGJ78vHNPjplst6hgliB6W4pmOhUotGaYGtpwvUbTouSWdiglKYt5xSuJdhYigAwBVYpQrObjzMhaobpefT0HIetZ7/SbJrzlEZnOFu+tvF/BTmbTM3d1kPNgNOFNNN2FNXJ01LyKCeEqjiToYd6Ptazz1bXBPpXTtl4RV0rkXBtDgSnvLgqjbz2lK7ex9a7nA6KWVnQMprmNn7D0hsmRUNrpxRaSgap5jz0jrbaFYejYiLwPyBEGKHVSsyVIwwRZAJYU1Ae7GH6Fb1tRBc8IX+0hQDD+YdZt55OKep6yunanfl+KmrRrIfAQSPMytIo1oP0ZZRSDH5EgiRT3uySjrAgxcdRat8i/iXfsbLC4jzfGI46j0qKAEG2nRSawWkWEVJXaM38gs1wwkIrNoPcG8lnEyRL/qY3PMS5ScmrLkx49YUZlz/vQXREmDx++Dp+w0MHfPnXfxd///u+g2/4pr/IhVd+Ll/x2z+bn/jx9/D7fuen8+Z3XOEj77rKfY+ci+UdObbrJ61k/p2LZiWB41XPunfcWHU8fSQr0MdurLhvp+bKyUY0zSeex483bAbPS/f3WA+BRw833D0r+chRy/nJlrXd8xmfCsH74wyFmBLvxJ/fAXxr/NtfB2bAv4raK4+HEL7y2Xamh5Zqyzm+yAEmYHwHQbJNTJnpyNr16NhQMzH7SrZYSahKuQ6VzBqCx3jHtJigjw4Zdu9BR5svdMwStYZ+MxI5dMSHJ0x5t8ruPNuszfGsSJ09/+oGhgBFmgy0IXjodCkTSKyv6qEFW0mgHDylrWEQSQBcJ1IlsXaf68SmQAfwWqBoylZi64WnDxrjOyaFfPfKSg03Qxi3RprcJEhGopLvMcqiNqfoZn+UnU24dxgblUiAzOiSBNHbGkOAYmhRphknU0Dprdp6yphjkzc11RKxCW2kRqwUhVKYYYNO8M8oM1vg8Vo0Y8SkWDwvS1NAbN7pbnmGrSqu8fFvSklPQGkITnJiJQ3t0tiMDCmNyn6kSaE0ac/Y5Q12JucoFDTW5Ps1wfhgZEXK3+W1JnRR+2WA0lBo+d6dC3kb5QdKPTqwp/1owBpF5dODI6p8GhVVDhUJa5mCeRpNYZgU4pKTstrzE6kv705EZuHiq99AZTUXXvm5XH/fW9hr3sD68GmaGKnFMFkxKYTCntQPL0wraXJWlnaQZuesNMxKybgbqzk3K5mVlv1JyayWkkoqMwUkoUiKhX0U6HpBxqda8N5mWPJxWJQhhOeWgH2GkZbEvakottiNIwtSBHcqK8tVawrRSi4mudlVmtF0Vsd6bcjwrQ2UI3IlCzKlzw+xdx98lvwLHoKNE0ck/qi+jRT+hDf2I1IkNhvz714kM0dssSjsFfjsUK6T9CpgjFD0NWK4KuiSlrKIk4l3CFgZzNDSFlOq1EiMrNCNipovtgIXBAPtR8uq7VtWuESSjSdTB6VAmQLngmT0Ep5lRWMKqavHCTKELaIPnEHujCdWarGFNnm11Meg43wQpTtToU0p2izasupdzDrBKDnmWktmW1uF857aVhkGCtIQ7K3GOdE4b9xAqCspiSTp22GTGbvp4RURLA8x6J8R3QqKoOQ6Om+jb6ceFSUjGxcYVSrreZa77Z2QtpLTTO+leZlEl1JNWytQRcUwBKbW0nU+Bt/AJtWzvfQdnAs5kx082BzkfUao9BF7veqjXVtlOI01796FbAZcaM3Ti5ZF59hrLE+etPzSk8d85gN7vOupE64cbyi0Zu/ClA/eWDI5uMDeQ6/lrR++ycmTH+AdT7yB608es7z+FNdrWaF1PvD0lVMenRRc2Kl435UTXnlxxnE78Oj1JXfNZcJ97OaKK6cdj15f8uq75lw92XC06rm4U3F+UopZRS/N2lXvsgztqj+76vlUHi8KhqWKyBGCRxcFDFJH07H2LKJTLY0pCEFR+g7V98JMjIGvjMHaJmpz1PJOOF7l+rFMECQQhrI527BMULctwhCmGNUJnWTgvpqjI+Sut41AD2OdlOgKI9lksYX5HvUyBBY3kdp6zvA70fqu5wIRjMgQ1YuGxxmiTWqoFlNpBja7sak6ZeKOCeUEfXQdvXcf+ugaViXTAZ2NnPMEpvQZjWvlZFKzMSgV3RWK+LObXZAa8lZZCB/daFwPKpKAwniMKE1TA67DlGC7Zc6yk+2d6VeoYUNTzWHomZU1U6uyEFgI8jm1kmufnOibEGQGUorOFJRhIGgxk8ZIQzmxbpPUbIYEpjq6lck1mBK9vCmrrnhfBW2ykt1uJU1Iu76FKfYixFPOi4/kFIBjZ1kPPmK0ibocxOx7NMBY9SOoZ3TiAV8ZjjaifSKUes+ql+B90BiONgNHmyELj4kOiLi5pzJJNwSuLNpclln1htPO0Q5R+yR+p/OTgrc/fsQrL8156qTkly8f89jNJV/6yov84mOHnJuV/J1/927+2te/nu/4+z/P7/ryV9CUr+Zv/PV/zm/+g1/Pv/++v0u9e4G7XvO5PP62n+Lq8g2cnxRcfs+HqeqCWV3woceP+eULM043Ax+6fMxr7t1hVlkevbbgg7eWfPjKCZcf3MvaK+dmJbuNKGk+edqx6ISRChsO12Li/IIM/ymWef+PGtnHMBr6ZujaNjU6mgWDlAg05IyT9DNkogSMk8I2gkQ2jn8futy0U8oTkiZ0Ckggmhp+IERZUdlv1OEAgf+lBh9SQtjWiJY69G2OLnaEImbYiNIEHYOsjQzPIaIttCVYcnMOBC0R4rlKWiAJ2hiSFZm2mRq/HTAzTXy72RqPATPkPkBmrkZquxraM6UbUq2eSHhK100xXssINcwTRZTlTRNswqOjNE4XmCDZ4RDrvcmMwniHU5LxD2iZpLcyfOd8XmVYU+bmaIgZq0wwjEzZ2MR2PuTJK5STnIWH6Epv4oojNRAxJYM/u4LJx+ADVWXonDvjEJNq4krFFUdM2LUCKRIlx5Zo5KvHMowJKssMqxCwmjNNu8LEMiIKx2ghtj0qK+bHafW1TewBQYYUsRS06hy31kK/v3bS0swq3vSeq1SN5c3vuAKAtiXvettl6t0LbI6vc+ODv8TQrpkU0l8YujVDNE9OGinOB7rWsdgMrBpHG02Y+1a2W3UON/jso7nYDOxUNh5niD2OZzjpn+T4lIAKpvEM9Ph/hMAAj+Mm3xBC+KW47Rci2PACuBFCeEa4YB6Joq40mnBGKzqYUvC2psjmreI6UuUHFWLt1laZGCH2W/1YNonehutBGpa+nAhMTpvx89KDbXTW5sjL7FgSkWgQ8mtnNDZghMkB+IFOTSlsDDiRORoS07BoYhMzrhS0pdcltrJsvKKJzTVfzSPyQo0NTtfJ0r2cyHcoatEM0VbOQTWlD1AWE3lfasomxIfSECTgb+OaVQioIa5aEqHHFOB0hhWKIFiZTQvkRc8zRrTgctYr56cbJ+vt8gpI7VmJaYGNNU9pSMp5UwljDpnRmt8LZzWab9s3IMebVkXx+mSjmxi06bsRbklHGwoKHKte4HqhLuj7sbmbIIPpo7PcK5wJNp6xPj54KYtJk1jggpXVJBVXE+vk4tKzvY+zSAsXxLk9Va9SmUYc7RWQLMo0ldXZ8aaKGvLOB/aagt1JwW5VcPduzcWdGh8C9x1MWGx6ZrXlLe98mp1zEx5/33WUVuzc9wpOnnw/d73mc7nxwV9ief0J5pdeyuPHG+mraMPypOXmoqVdi9rhoh3o1j03F53or5x21Ebnv687R7cZWFvNupcgXxrFpBB5ZPlf6PO/NmR8Ipn3tyMGxDtbr/2pEMIPb2+klNpDTIe/LITwuFLq4nPu2TtUDIQCtRu2Xh/wushekiYK4YuruMnBUsfGpNYIDpyxtp2suAgRfqR0RoCoxJBkRF+k7Dv/vP06RJzwyBRMdHn5vYj6Kj43X5UborlCwqfHYOb8iFQJPlqNCYqjqmaodiXllH4tGW9Cx0BeBRDlb5MMrnI9lFNUu8TUe2dw5Rm3HbbgkxF6CGRdmLRyUJtTKBsJlq47C6uMWfeZsW3eexvefvt85e22z63ScdXiIwROx2U/Z92N1Jai5NZnfMy88YzX7TY5gLivdB5GqKTLfzcAQbJX5QLKtRhtRWFQQYgrDOe2rLpCyIHXIYFekwyiifINZw93iImJ7EPe70lu6/IZtzebTVSrhMi2jL+7IEHa+UDhNZNCGn3JCaePPZ1ZaTla9xxsBhbdwK1lx7UTuV+uHEm58fS05eUP7/O+D99i/64ZwQce/+V3Mjl3Lzc//E5WN5+imh+wPrzKQSMwwKFbY4vRkxOkUaq0orICCdRWiEXJxg3I/YtkMNE5qXEbNcrn9i9UueNTJfN+Jnr8s4zfB/ybEMLjAHcCF3yiTRommgsTz421zr/3PlDoXmCC8UZNjtZKDdkE1vleXEScy1ZUDzWaJ9aa882Erm7o+oAaPJvpvXR9oCwPgJEhl5TLdnTPiS8oNByuHDv1+TPaCt6Bo8EoRbt2VHZGiJDGmd+wttO87fHa0RQF642nsoYQNKUpqI3osZRFRAak8oCCwRisD6z0BDsRWFxvGmk8GmH51UYxDIF2ck6O2xR4U2DaBTfWjguTfQC6aheLZ+WikaupznxeMgkQOJsccydYGOa1pysk+9fFBNstRrmCqAUifzRkv9CkLZKaed6J1nah6ZUlWDvWrYPnOnN2tKbUDj20OFOxq1YEGmonzFqQoF/HVUMXCgodsc5a+gpFLKklqJ8IXkXyULJK61t8Nc9aNIRR8RGlcdUsM3cTjrwOHoKhVood47jeNZyrdZ5sU/bfS5jHB9ivBS1TG8UQRkGyXciaPJrAcgg0qXl4fJnQ7OLtlGou3yXpnKTtleu4NC05P7E5B29dYBqNPRo7BkLtivw9VL8mHEQmbfD0Wq7v4AOfeenllEZRh47Pued+lp99Hwr40of3cbGWb2LGnqC7nf98dOxHDD7w2NGGB/dqfuqjh/zRP/yX+Zrv+DYeffKES7sN74smywB7F6Z82r279N5z/vyE3cryypce8IoLM7pXXeTdl4+5b3/CXbOK0mj2a8O00NxY1VyaV9xcdcyqF6jS+/wVWX/Fx/OixwPfpZT6i8B/Af5sJOS8HCiUUm+O239PCOGfPNvO752fRUTcM4uIkWhwIIFbZZ2D5NbuQrIdk5paaaLehBKXEdUvuXtaUbiWiVvhm31O+8Bee4NhfjHrl+SyiTYk1cJd3cPgMZM5VXcq2xjJXIdqJ+tr93UUrDIml0CaIcLRBtitm+gMbyIEUsVM2jNVGtUliF1snJZTStfj7IzZsEavBF9uE/FoiFmxGzDNearNYZa5VbEBe24+w9y6TL/3AOVKmnAzUxKCHvWqIWcfzRbJSPU9VfqszSllyvijCiBDl8s22ygb1S3HrDqVgmJgm032UesVRTWTz1catJRIzlsHgzA9/WQf06/obEOR+wWyf92eSvmoX1MXlaB/kFo4weMpxnq8d5mQk8W+0mqiPR17Gt5RzkaJAh21ZBI5StlSBMrWp/hyl6U3nC96ulDig0YrPdaNB6Gc11axSUzKQP55iAp5ST42iUUpFfVHppfYDIFmCNzauFgu0Qx+wGpZFd4zLbm2dpy2Pjc7PYHdynAaNQASg/O0G+hdR2EUe/WE01PHKsoOb+JKsTCKH3v3VR65a8bn3b/Hzz15jV947JCv/LRL/PDbL2O04gNPHPEVr7+PH37zo1y8JDICb/v//gL3vvoRnnrfowzdGq0N3fKYb/v2383XfMe38S/+z7/N7gOvwvvP5KO/+A5+ar9h6B0f/sUP82OzkgfPTXnPLz7F+156jv/2M49xabfhp97+FEfXl3zgQHo0R+ueNzywz+G6511Pn9AOjvc8fcrur+G883g+9Pg/BzwNlAhT8s8A3xn3+esRK7QG+O9KqbeEED5w234zPf57vu/7+Ppv/GZRAtSj6lkfRpdprWRZuYniNEJiiP6R8YbtfGCIgV4MXgvWQ8CUNVqbrLLmJ/sct45ZZCaOtOKA0oq6NHTKRtduh6l2RhszU0WpTUNjLaveMytreSBtgRk2Yx09eDZDwGmBh7kI66q1ISANMQZBfyTjg15ZrCkFtlc0hAR3VKJYmLDNqVTjm33RUIm6HcXiGset42AqpAk7PYdHRWH7QNNMMrkFJFPdhtwVpWh/9MpSlt2oS0IsWRTNaLpcjg+AinK0zxS8MQU+HoeIjZmsGKm8k3JJ0nM3BW7wlMrTK7k9nYd6S//GhzCeBz+ALnBDwJnoQaqtnLfYUxCIYyGInXKaMeoZAVQ0smqJ2XYwBUpLv2TwAR2vR+cDk1Js2oB8DlPdO60McynjtuTOaKmFeyVJRyKmAdHcYVQKTNuK/0UYzZgjdlvuf/LzMCnGUozVnPE+nRQ6/i/9oHVEbJRW8foH9rh/t+GuacHr79llt7YcNJYvfdVFNs5z337DpZ2az/q0u5lXlqY0nHzua3ngrhn1pGToHcuTlsms5Id//AOcuzRn94FXcfz4e6m/6HPwfYdPmP1YLmtKcb13PlBElmU9LbBHhnoiblZ7TUFlVcaA70fW5rR8UWAsXhTjedPjgTYKVP3J+PuTwM0QwhJYKqV+Gvh1iOZ3Htv0+NV6E5IYu2BpZWg10oUBtFWYQTJvnbJYJCsptDxMJgL8k1GCDoF28NRa0hcXBPs8VSE3xNIkkDJ2gjx4Kh5Lcm0HIZyEeGyBEd+bRwxM0tM0aCUliUKn0gyEtGwNYKM3ZqpnSjalCHHVUaSGqSYunfssudpTMxlOpVyhrQgulRM6FwhWpHOHIF9o8EmYyG8Z50JLwh+PgaOyVjQ59Bzlx1XO1CpBfMT3pOzS+UAdGZMBCU6pLJOadH3MQH0s25gYqAavwHlsMQcPgxeY3QZLiMeslAJjGYZAZSzrITAvNK2HwlRCDFHRLzQ2tOsi4ccFV64AO7sg59zEpqcf5HpE9TpT7VIMaxGvihNP1R4TioYpPdoUBCVep1qBYyuBiCUEG4NSlnONx9UUmkXnqQqpnU8LMVRODU6jhGIv+9GZGp7w5KVRBBWyq4w1Erwbr5iVohRYxgaq0UKXr7TOYKbGKpr43mkUfruy6Lh/t2GvsfgA01JzaVZxblKw6uU7PrDbcGvd85p7d+gGz7S0fP4rL3IwK3n4woyjVc+Thysu7tQ0heF43eOGz6B97Wt5zf173HrdZ3DjqVOMVfSrY566vuThCzPa0xMWm4GhdxyverrWsVq07Jyf8N4rJ+xNSta957jtef/Tp+w3BU/eWp+poz+f8SmBNvk4BsRfp5S6FEK4EunxXw28K77l3wHfH73aSsRJ+W/c6QH5HI7HzCbVaHtPJpKw1XnXivzAhIia8AEsng4R81HDBmOEuKL7DU6VlEajg0ObVK+MdOWhpyikSTq4gK1UppAX8cHQamwY6WgiLGgvL01QJZOFYtRTzo2ZuLwvAHw0cYj146JoUL7HKUsRBmF11nNppmVykUAai9QFCyFqhZeodkFTT9DrY4rJXVLSUQpTVDQWjGtHdigSwJwVSyrnQ64ZF2UVha3S4y9QOxMZkUYb1NBn5IhaL7MeTMZSp4zdVpTKE3TULlEK0FilKaxkg6YVV6DK6jyZBaWxcdIrfIez8Zis1NVrJUuuWlt6L7R+r+Waqm4tWb53YnzhB1S3FO2cLQ2XodihUI4q1YeDl89IRiBRm6a3Df0QqH2C3I0NxCTdkCaRjQtoF0Sgqvd4pGySJk9ZxWlWvSeWvPn/tXfmUZ5c1X3/3FfLb+lfb7OPRkiDWCwjFrFJGOOYY7yAiQH7eMHnEPBOnBiMYzsmwTaOc2wDOcFbDCfEdmKDHTAmjrHN4gAOq5CFJYVFEhKgZSTNjGbp7unlt1XVzR/3varq33S3umem1TPod8+p09X1e79br+pXdd97937v9ybOvpc6YXlYMPTZkoF2tpsJjYmYlWFmfujMPg8c3Uu1ajNg/Cf1DMtQ2ACgNyxKpMpdp5fZN9GgtafNvfM9vja3QhJN8qWHrE7pA6e7HNrV4h9uf4iZdkqnEXPDrQ+y/9AUDx1dJBvmdBcHxEnEk5+6n+NzXe781GdwScrHhwVHbr6Bw9c9l2EvZ/nEEbR4KvfPrbB84j6y4lmcOXoP892rWDzdpXvqAc50GuzZ0+bUkl9Z+olGlhd0h3mZYHTe8mgw3hvIn4nIXsw+3Qr8SwBVvV1EPgR8HkNI/aGqfnFdLVRE9LlCLFZtPTyGIlLyJWR+BgMVCb3VEbSovpMqYm0zwIhcPS1nVPnK1GcfhpdIiypgB0onSjyfsPgCqLbfzwrUvwixMxxud1gwkRjJUKHQcDFDXAlWWRpa4dRejWinFaeW0agQu9hmb5H9zTMlEgt4DYmYaE4afNBDAKPID2/henygsEiaBvcLhnkVMiYvk0HwroUwUInHRovWoG3O3AREjZIcKXJUTH9Rsqr+ZyERUZyXMQN1I7OjQEAVcPQuKeMMhXpyJo8KMvRLXhJjKR6d4fsSZsQl9wh46tbc+lIoTlzl1w+QRPEkYQET73U0YmdJYVqUBFklc2SBxTnUWPgC5j9yKYTJgl2EDaS4srYlmE85LoTMZzX2fDBdtXK1hHs+yL3Lzz+HId4b/kaOWum1gBfX8rvBboe/obp8vcZmToVKMVx5YanqjbiM34U6lTPNhMSzGE43Yp58aJpWGtFKI+59zDRX7e3QSiOWehnLiwMarZir9nZIY8eJJz0dgMsOz7By5um0Og1OP/ggcXOC3sqA6VZK1Gixu5PS6BhoIGlEJO1p0lZczq5DKn8jduUKL9AmjOX8ChB/2wbt/hPGcbIpqQwnlpxR+4FyP3sND3kgZi/KWUb1WUnV6WdGUC3bRQsKX2UHqhcgEu8KKREnVb/M/SJlKajAZ5FGFWtcGjnvrvHfFUeEIP4lSSPx3M7hZYKGFGhkfBJO8wrCJjB0MbEYMVQaCdLtkqQ2M5e0XSEohl3y2GPYg+HztTAzp9437DvpjWleKHFcVWHBk/kLdp25N+jOF/ZyhHvpVw113u9QAg1PRVCyCErVJsD5AmIkJMuE50TCb61GyuXdTQ5DkThs1lmokmhG4XlGMlWjGAgoEiwgLEVOLDU4YLhXkpXGOVT1CauDrFDKdUhtYFhrZlb4z4YeFkhhA1twn9mAXLlSQtmu8NyWpyknGbWEmfBTeX94ePbCIBuJrSxib9AiB6KeTyUSXCblrQ9+clUBp8TYbxvoZ/H3tJ8ZhHBpkBG7lCQST+NKmdRzenlAJ405utBj94TdqfmFHktTTU7OdRn0cwbdIcN+xqnlAUfneywcfwhxEfMzTRaP30vaSujOHWP5xBGiyGp19uaOc++pFVZOPcBS7xpWzvRtf2qaU0sDtFCWBzmLg5z57pCVYc5Sb3X5t/OSR/nM+4KJGT3v1xYpl5IKFDViHvXNwqwCKiNceL8jTkpjWmLDxRzU4aFGFaXSUeJL8f5VtSoeoW8CJbtd5GygcbUXZTOyalDxRsJeTF/MYSSpRMPL52eY4mfPSCDcrwaL9aTetxBTCIkszhsHqbxUVXs1x0VIbjL+D13tQmHk3FpUhrsuIdEHqoDlWlL/rhjGuySugpLhz7DZ5napY9WLIpzLD6yh6HFdAp49vLha+f/Lz+up8+HWFFnVPZuOn9X9sJIq1Cfk1PDZVZv6ph7HLeVnBcHHbV8ttBpkcx8LydVjv71bJQwOBYrz2PP6NYX9Uq+XMFAD5d/qO6tnt1a8weImljXp6Wi98qLQMuknzwrUD5qFKurdTLHP9JXaQxk5KdvWJY0d/cHZx8N3Loh8HRjvTTuQRCQSkVtE5G/9/y8QkZtF5FYR+ZSIPN4fb4jIe0TkKyJyo4gc3ox+9VsIepUIEOzBCy9GqE8Jqx/McKxKdPAzO/U6XVy2D8v60RVYCA4Z6ZIPvlHatpLlrNCqbehb2IZKiRqwB9r3vX4dVLPfsF+IpWSHY1DrNzbrLVQ9ptpw1blSZmbaFqF+xq2RUYKGz8L9W31PtexH2C+82yMr7D7U+0k9e/SsH7BYbZ3KYwbLEy3Osu2rMiLD4LLOuylFVpJ8Vd8vKgM+2p2a4S5RL6N99wHDoKueKVsfdHBxuRpU78opdY+c1wklDexaUpRGG7K8ul2jxnXVtVC7peUAoX52XYY9KHx6fPlb+v+1/J6WG1QJLwHCWF1D9Y5ByNys3BYWaihwLgw8Wq5QnRPERSWypP437N9/eqXcD3pHJRj50eryF8ptIvXn8mG2i1XOJ8Py7cBLvY/7XwG/DPwIVvpsTlUfLyIvB96MVdlZV5KsW5XOqtG6yqBLkk5U9RjzYVWXMMzCPFNcx1dxb2tmDnBx0IfJYc9cJu1ZWt0Fmmkb6Rd0XIwM7LtJfamtlvXY9tjm/Y1JpDdX8nsAFd45z2i1pnErC6URCYULwAzonsak9/Oa4ZWsjw4dSX/J6jT2e6sMRqMxiWQ92oVdhwxWLMCZZ6SRFUcIjtDJBkZyJVbwwPUXkaxPsyGQ+ZTowTJFOmEc3X5QSAQWM0vqCLj4+jthQTBn9Khxq8TPF3FVlsxh/vLyHW/N1twgq2dzIVCWDY01UVUZDu1YYNdzcRPUMukGhTKTOpa987hQyKOYE0tDdjUTTq1kHOwYQkSBSCJiZ+XOVAvjPYk9zFBBC0UkJWk16GUFkY85xM4Cfc0oQRAaPp5SSORRT76CTRLTzy2+0YwiusMquScEegONaezEo0ukhKaKSJkh6ESYiM2PW19FdtKqck47sQQVS0azY83IqHr3thNmisrdkhWWDJRGQjOWsiBDoRUNbRoJeaMKbs71cpxAK26wf6KBiJ3z8EyT/RMNDnZiIjfLRBJxYmXAvomUg5MNHjvbohU7vmFfh8OzLe44uez7Zsl0BzoNlr4x445r9pMXynMP7+LG5x0GYGHlKua738TVByd5/O4JPnroFbz913+b73nNq3n6lbNETjhyxTSX7Z3g0Gyb2An7JhIm05irD05y1WybweN204zH6fFBzifDUqkM+TTwoN9/KfBrfv8vMeSJ6AZl6odxyyNKHEUUV+6MdJJ+rrRbM/SzgsIlDIZKJM2S7zdKUntxpUmjlqSjag91P54wmJUCE3tYGuRlmaoksdlZroCrZmrtpsG6ogj6Q6URWOQ8HDErlDRtEzlhaVAwObG3hIk5EfKkXfppFzJHFNjpcnCuzUSkDH2bOKk4rktjETXIxPCuqbhVVdIl8KFkPfKGVWINiA9NJ5CB5xPXwlYPJUNebO4Pn304kVhgMIor7mzPYF3C7iJn3MoByePKtP6hH0xrqea5Fe51gaAq+LwBSZrW/zguy6q1IpvZ9lVoxq5kX2xHMROSUUiDjstK3zdacFknsSzPVpsk96gVz82y0M+ZjQvyKKnSyLUgdo4C48yR4QrNpG0JVgIy7ONoeV4RxQ27FjBNWlb3VBwSJbh8yMC7SpqRMPADThoF3mzLMSjUBx4LWBkWTKYR3Twv3VwhsNj1AWybLRflADgsTKcVGTbDmxXQiIVlEWabCXO93Gc9ViuoqdR56tTq5xiUA4cNDCtDyzmwz0z3kYU+x5cHTDdiJpI2x5YG3DPXJd8/yc1Hz5A4x92nltk/1eRTd51g72ST3Z2Uv7/1QR5/aJqvHj3DsJ/T7w5JGjEvevbl3HV8kc986l6SRsxHr5jmvi+fZM+hKU4fXWT+vju46vpn89Rv2MtfvuO9fM9rXs3f/P5/5eQrXsltn7iJ4fICd0xM85wXP48j98xx7eXTHFvq8/7P3c91j9/DJ79wjEYr5tXXX7meKdm8PIpYBX+HszMsfwL4gIh0gTPAc/zxQ8ARAFXNRGQB2A2cXE95OvQUoyGLzy+3NUpJXESuDSOg14KWJ6YJS+6h4rG5VgUljnylFoR+oWWx17lezt52XPImTCRmMIdqNyEE6jI12FpaVmspaMfCmUFhFUsKg4BB5TMOfrjIiXGmuBgnjlwSIleUQc6urx0oRUbhnH2vyCmwQF+u6pNCLMApQJ60LVgqVgrKef+35BnJya9aXchQns2vRDoyRIZ9JobHy9l+kbRo5MMy7TvCB3EbE4bgqPGEWM1NWxHEoY5mLVNRhj3oL636TlmFaISrRaMUl7QgH1J09uCWTlbGHUimD5EsPYQmTeNSiRI0TomGXav27pfXGsXQmsUtnSCaOQxqmaqhBFwoUBB8+CuZrR4yT6swKJQobnm+bx/PSGLamKFrSFGScNWZE7vDgrbPuplIvE9dhDjyv3uh4ISG2My3EQlZarPqZiwE/7j5mA2nHRAkjipPYDJ19L3BnWw4OokNQcPcXCyt2Io0d1Ln9VZusInEUZCTevRLgCtGfhLTSSMc0IjMxdHL7fvN2FZnM82YmWZErlZ+bKYZ8bjZNkkkHJw0Arjk6n1MN6yM2Z5Ogz3thKNXzpAXSneQ00ojrr98hmsPTXNwusV0O+EJezvccvU+Dsw0+dpDy5xYvILnPmEPBzsNll75Mp5+5SwnX/FKbnjXnzJ1+RP5lh98Mbd8/Dau3D3B0sqQfR1DRj1m7wS7Oil79rSZuWAZlhfG/bKTcj4Zlj8HfLeq3igivwi8FTPom5JVBYh/5638xI//mEHDoqRi5gs1IdVmpXgIXUBHFN7nXCdEqvuLQ8WQSISJxCHeF6hawRMLDcveasaexI0SHZCr0i+kRMTkfrpjyBMt/Y3hOHGjfC7CkrrAZlDBXxkInQxX7ar24Rp8n3BCTE4kZuhFdTVao4S+1Uq3gb9nha8duWQGLoqt3cDul8ZpSWoVUCBlSbOQvZgPLGsSfCZjBOohgkmNnQ9KOCBFXGLcwuuxypWUtmzWU8Oaa9KsIIhxWvbJkCqeydEHI9VnO4KuCpj2cqUVUwaVI1cLyOLJjrzFDPc5pmAxs+SVDI+7D6gdf21Gv2rXMsjVqG+xqkORWCwjL9S7OIRIXDnDbkZVxXZVLTMqB2ElQ+VSGuRSFmsY5ErfVTN5J9DPIXEFWVGl34fnKY3sORz4Oz4k8IhbP1JfiSa4cQLH+OIg46Sfrs80I5YGBSdXBuzvpBxd6pM44f4zPXa1Ur74wBn2TTWYbad87PbjXH1wijuOnmHFMwKmsWNvO+Xu0yt8/JYHaU4k3H/lLLfccYIDBzocfXCR+RPLLPYynv3YXdx8k6Xf3/aJm5i6/Imcuf9Obrv5CZz6ys3cP3cNJx9c5KGlPg+c6XH3A4tMt1KOHV1kfpweX8q5Zlj+HXC1qt7o27wH+JDffwB4DHC/T9SZBk6NKq1nWPYX5y0KEvC9PokD7MUIMDEnVUZlEDNyzvMyuzICniskamnesVQQwIKzg2IBH254cZvhRxKV3ymDWiJEZ4Wo6nrMwIbkc/GQsYhAFVrpqnzC6kt9eT+yT/jJa+e1+2WNBAj8HRV/dmXEpMjMhRNge4H5LxRilh7qa2cGQ0WUlBS4xtAnRFECgYekFigsDbyrXCBlH6OKMAnNPSbOu3RCMFBclT9edtqV36/OUUPg+OCh+oE6ZMEGfVJDLITfIC+qwTsYdBEbN4LLYVXfz/o1/anxwS0/g7Zg99kvvhJ4uqsJg/Xn7MB4kHpQvjyfn0CEgHJAseSCPd/heF71woLKWiJQoArwWaLO+sFTsIo6YTVgx6vnMy/Mh54XShq7kks8HUmWCdWCFlaG5HlBnoU4hy8AkRfVu+l9+cFd15zay3J6hKJQ8uD2w5gcLZXer2pFyiDpWM69APHLgGMi8kTPWfIdWDAT4P3Aq4AbgO8HPraRvxug5zwBkYtpDRboptPgDV0skEtCjKfjJCAJlEgz4jhG1dGM7QGMPOeDE+jmVvewX6in9BySF34GrpQcFf46DbIHlhCSFRQ+cSKP7YWpo5csQm/ukF5WlEiUpjM603ogKZT/akmVfh983IbvjkvMdzsC0RyJbLBygy5xOoHkfUv3tx+C4dRBBnlBM7LAWMjgnEraLPRy4umDdIcFUWO2vD6AuNPyaenG+VKiIsTaRCL2EknMcjRNipS4a0MdWFJQjEDULLNb25PTdDMtnyhXqTWj29hFjDCIpkrIWa5wsDfPYjzFZL7EQjwD+DRzhAEx6tPjO6mjNVii19lPKoIMsrKYsOQDdhVdyGIisZlkO2kheR/nYhvAtKDQiDSqfPdFlNCKK2x7SUzmS9YhwkpWMB0VKBFz/Zy9DWVxYAiPfl6hRCJnro/AxVN4qOfArxSNd8fuiXHxKH3v2gj3K8sVosr3vTSoJiKRs4AlJKW/PSBI0kiIskADa9wmgRsFYGngS8PFPn1ezDi3E6sJO9uKyoDq4Zk2hyYT5nsNdrUSDnl+79kn7aefm9vvO560nwOTTXZ53Hd3mBM5Yd9EyjOumPHXKDzp4BR5oXQaMQdnWtx1bJFvPDjFMx8zw01PPcCh2TbPefHzuHL3BPfPXcP8Yp+nXfdTfOAP3sHrfv3nuWZfh0NTTY49+QAHZpp0h3tLrPn5ysWMItmsnBPO2/uyfxJ4n4gUwBzwY/7jPwLeKSJfAU4DL9+Mzm5mBPL9xjSDrFpq9nJlbzvmVLcgcoYwcOTe6DhyzWnFjpVhVpL7hIe2kzoW+rmhCgYFkXMkDpaz1UvSamZkO4VSIge6mRnfzCdORB5HHotBEfuZGdCKtnNIIo7Y2Wyx4dReOpcQi5Z1KYkhzvpolJCQQWGzYKNujellxn+RNzqGcgjVg8QCkPFgiaS3iDYnaXt0jKpDW9NMxhEuHzIhBRRalkDL1NLME3HkcUJUDKvqRFJhhp2Y0Z2NMoq4QT8rmIjFfN1ghj5pVQgdBxQZiWiJ/qlzquOLT6hr0dQhokM0tYIH/Xiajg9WTudnzK+uPYp4EpcvWum3fIBqi7zRoXnmGGda++iIK33eQ5eSp2lZ7b4cGH3BDuddboXHzTnfLzdYYUEbTDciCvXxhBr8sIisso9GKcXQakn2iJlMLcEljsRDQc0VlxXKVOrICkcjEj+RsGetmykupaRtDa6/AMlLsy6tRsJQIjqJFe5oNAya6LI+kCO9RabSNp3JNqJa0s2KwFTD3D7BKA0kWkU+lmmVxBYSik73CqYantfE+9gdynwvZ7IRMyyMT7tQWPCVb8yfXnCmNyRXZamXsdTLmG4n7GolfG1uhfnukJlWwsowpzvI2D2RcmyhixZ2344u9jmz0Cc+JBy5Z46llSEnH1xkenebr955itf9+s/zO7/6n7nibb/CfSdX+JuPfZVDj9vFHTd8mcl9e/mtFz9pMyblohAR2YV5Jg4D9wA/qKpzI22uxdB7U9ii+zdU9T0Pp/t8Miz/CvirNdr0gB/Yil6oCKUSgUF46kRo+l2bwVbLUaj4TgzKZrPcuqsBKEmsEp+dNiiUhquqcgu1WaJfsoaXKsITWYUlXt3S+wSSevIE3kVihZOj8gWLosQSGbB0eMHSsDW4P7wbQYqMJEp9Fp35K13WJ4lSnHr2PV9jEi3MfxzSyOOGBQlXzpC5NkjgFll7hhEShKrfjRIVUbbxxg8oKxWVn/ngaRArFhGVLIR1N0woAKwi5psXK3lGBIl6909mAVFjUBTDrCctW2XVGQiTZlVAwZ8/lBAjz6u6ps6qA4Xlf3BL2cVWuO5g4kSwAScfIr76ks3QfVo/kQU2HSwNKp6QgJE3Ha5kwhSxMlJhf5AHeKFDxLNnFkX56yRpi6EG/7kZ06E6NDN4ZSwYhULSYmUYiLiwIGgknr1SKNTcSgNP6QCUUM/Q5+DzzgtY6A+ZbiQkTlkeFiz2Mzppg9MrQxqxY2lgZcrmurZaacaOB053iXYL951coZ8VLHSHzK8MOb5vkoXukHtPLnOqGdNpxhw5scwgKzh2aoWFUyvc2044ONNk7vgSd+5usXi6S9KIWZrvMuxn9JZ7fPCT99Cc3ks7icoK9VrNsC6MPHIz79cDH1XVN4nI6/3/vzTSZgV4pareJSKXAf8kIh9W1fmNFF8UGZaBp1sVWpIz9FVXHJ6UKh/iZG1851pZRsEI28NdEQeBp47N1WeqlavjUuwZKcqgYSs2F0i92kdWGBdIfaAIfuvy/+BzFFvexmIGTwWKdMIHAxuVEdKCDCMyijxWuNCCyKUeXyzkufni4ygmCSiSdKJEduRRA3E2a4+ShNT7u41Iy3OpxGlpJHIxXpdAQTD6ekyI3X+jjFVag8UyqEwUlTNvdTFF3PAoGIMElvwg3ofuxBH1zlA0Jm2Gp1WKeiCKCtwnkg8s5X7YNVhkYS4Sw1+v+qH9M1BlvBpxV04hMVExgKjhoYYwKIwkLCTfiBSrcyVDjkHtxW7UHOTtxK6lGQuRc2XCWF4EP7dNPjqp8yn71WoN7NyNyEq8WS3TWqwitxIYRdwgDJENKcjEkWgG2bCs2tSKmzisnmWYeacRNBwlTUEzspVWCHSnkSvdLM0oDDxKI05pxY5BXtCKHYkzKtb9ndRfc8TRxT5XTDdZ9H7DJx2cop0YUiUY7+lWwsFOgwfaKU97zAydZszV+yc5tTTgyj1t7minnJpt8YwrZzm8q82BwzN88xP2cOzYErv2tNFCmd7d5sxcl+c+9SDvvfcwYPSxWigznZTlE/cxuW8vF0QeOeP9UuD5fv9PsMnvKuNdp8tW1QdF5CFgLzC/kWJ5GHf0IyILy13NCi0f9MAdEXx7Ab+dj3S1UJj0yRDhQQovSi8zg524emDHqpwsDXLSyOB/wTjn3i8ONkvveurZaV3hNBUcbdknlwQ0ykI/ZzJ1ZLXs8DAgqFLCC42/2Xzj7cQx38utukxhPNFhRWH0nlUfggEYFpQIgzQyPvNWtsxK1KYlOV2tzFDLE/y7lTn6E3tJh8vkjU6ZfReMTiIeain20tddDgBxb56sOVPxe/cXqplwUQUkc5esMsajkkeNkqlPk9aqsm6naTGT+iBpbjBLCRznqmXx4hB4Rgui5VOstPfSxAzVYmZVbspsVCDun6lqf3rkUtBdlr2TigGxaEwSz91HNnsFrrdQoneytEM0XKHrmuWMWITyWRMqd0Sr6CGDlTJhKhSPgGpg0ijFdRcoWtOrj3v2QvvhrLxfwO+7lTm00TGGyShelfZfXkM+KLndVVx5naXbKlyzi3G+T0uuTad/mmxiD6e7mQUIYym5dRoh1t2dK2GiWXOmxN331TJUQ5Kd6y9WNV+1MBda0mahSJiO7fw94nLSkxQDljUpVwZp5Mrn88RKxqfvm8c54Sn7Jnn7Z+7h+552kFuPnuHffMvjzjtqWdz56U0bvugbnvdqPDLOyzs84OJhRUTmVXXG7wuWwDizQfvrMCN/jerGI8xFZbxjZ66PrucSztWCN7NxwVJh6I9CK4pYqNwieS05R6RyiwQptHKdgEcHlJA/yow7gESzqhCAVjSwISkD7MEuMPrOycTKXYXZtQily6Suo1BPueoJkgJaQ339zcKT/4dZfxpVtfzC9xP1PvN6Lcsip5jYZbPUwQqD9m7L+CuG5ew8JOcEY6I+UzUYx8AOCJSVXuLBUmn0RSDqnSmRH/VEHI2Scsbrugto06cDeNz+IJkgHS4j3QXyqQOrDGiRTuB6xpldYsW1IGvOEHdPr/rfobjuHP3mLKlnOMzjZnVfQ/kzWF0hCXPZhMmAy/qlgelJSkN8KvRguSrggLlWiqSFG3bpxhMs9nP2pjldknJVBxUcNPiqlzP1xUBcGdguCyB4DH8wYOF5SjwaxuUVQioMWolmhNJtGiUMXLpqpSQ1PWArgNItGFBU/hmvr7Lmenn5bAXWwuVBwWNnUu6eH9BKHPO9ITPNhCMLPSYbFtg8stDjQKfBMU/bGtxGz7l8hq+cXuG244vMtlOu3jPBp+45zcAHQ48u9HjC/g67J1Lef+uDfNeTD/CeG+5l/2yLB44vMzvbZH6hxzMev4cPfOQrtCcb9JYHHL/9c0Rpi8HSHP3F0wxu+ePzNt75HZ/cvPG++ls2PJ+IfAQ4sMZHbwD+pG6sRWROVWfX0XMQm5m/SlU/+3D9uijcJnUJY8moiyvcvdE7Hh7M9bgkguSqRCqr8OEBcRKCSkG/iisLE9iAsXogyAslEyuY0M8KWrFxgaj3Y4YXJiBAgv7M+80TF9nMxhuafgFJieag5FUpseZFFVh1LjFaWC2QYc98wIMVQsEGPEpF/Cy1Xqi3QIgCrwuGew5ETuYDts/Ka/UDhLEMihljcYiLDXrtOUVCgec64dOqv34/fC6eggAskJaKq354cVBkVZakBKSI/w3EijqHwSMkWiWaVTrCues8KLiKYEsVKKDIiWI/+xVnlXaS1qrrKGfptf6dDVjF3zdB8j6QVIlb/l6GWbpRHEvZ1SreEvpmnCHiy+w5J5ANq9JzQORdQUXNX+/8qir8dHV44GhPw8QoEs5K+Eljz37p8BV6IlqxMNmImGzEQEYnjZhsRCz0o/Iac78i7KQReyaM97udROzpNDjTG5LGrkSedNKYfVNNphsxkxMph2bbLPYyDs7YCnffVIOJ6YaH9wvt3YdYOfUASXuKYXfprPu+06Kq377eZyJyvFb74CCwZk1fEZkC/g54w2YMdzjxRbEBP3Uh221X250+/6XU150+/6XU150+/6XW10tlw6ixX+/3Xw+8ZY02KVYH+HVb0r3TF1e7gM9dyHbb1Xanz38p9XWnz38p9XWnz3+p9fVS2TBqkI8CdwEfAXb548/CCtUAvAJLjL21tl37cLovOrfJWMYylrF8vYiqnsKKsY8e/xyeTkRV3wW8a6u6N83nPZaxjGUsY7l45GIy3puC3myh3Xa13enzb6Xto/38W2n7aD//Vtru9PnHwkUCFRzLWMYylrFsTS6mmfdYxjKWsYxlkzI23mMZy1jGcgnK2HiPZSxjGcslKDsCFRSRqzHClkP+0APA+1X19vW/NZaxXHjxlJ2o6umLWedW9O70+Xda56NFHvGApYj8EvDDwLuB+/3hyzHe73er6ptqbaexQhAvA/Zhmb4PAX8NvEk9ZaKv2PPjwPcCl/mvP+Db/ZGqDreqc6t6v55FRPZTG2hV9fg67QS4jtWD8j/qOg/ZdujdjE4RuQJ4C4a/ncfYF6aAj2HZcPdsVe926NyK3p0+/3bqHMs6sgMZR3cCyRrHU+CukWMfxugTD9SOHfDH/r527H9iZObPwQaCy/3+24H3nIvOreqtfWc/8Ay/7d/gPghwPfB9frseP5ieq94LrRO4FvgsViXpI367wx97xkjb7wS+AnwQ+EO/fcgf+87t1rtFnTcAPwREtWMRNoH47Ln0dTt0bkXvRXD+bbn/42397ZE/of2gV65x/ErgyyPHvryBni/X9u/coN2d56LzHPRu5eG94IZum3TeCly/xrU/B/h/I8duBw6v0faxwO0jxy643i3qvGu03XqfbVbvdujcit6L4Pzbcv/H2/rbI39CeGHNyIQixMHIvHCk7d8D/5barBCbLf4S8JHasc9i1Xtc7ZjDRvcbz0XnOejdUUO3TTo3esm+MvL/XUC8Rrt0rbYXWu8Wdb4beBu2MrnMb9f7Y39xLn3dDp1b0XsRnH9b7v94W397xAOWqvohEXkiZ/swb1LVfKT5D2FMXB/3vjQFjmNFjn+w1u7lwJuBt4nIHOY+mAb+gbNraG5WZ13vH4jIvD82s47eCVW9cY3r/ayITIwcjqn8/XV5AKuedS56t0PnB0Xk74A/BY74Y48BXokNuHX5Y+AmEXn3SNuXY3VN63K+eq/Afse63q3ofCUWy/gPjATNz6Ov26FzK3p3+vzbdf/Hso5c9BmWHplyOeYLW6odf6Gqjj4UiMhuv/u7qvqKNT6/HrhDVRdEpI0Z8mcAXwJ+U1UXam1TLLj6IHAztmr4Zt/2Hbo6EPp7wONY++G9W1V/ptb232EDxVqG7i9U9be2qncdncHInZNO3/ZFrI0M+sAa9/ZJwEvWaHvbGm23ovcb12l720i7717n/Gfp3Ipspa87qXOnz7/T1/Rok4vaeIvIa4F/jbkErgV+VlX/2n92s6o+w++/f42vfxsWvUZVX1LT+SXgaaqaicg7gGXgfVjk+2mq+n21tn+GzWhbwAIwgRVdfgF271410t8dNXSbNXK+7bYYunMVEdmnqmsS1a/RdrcaW9u5niugiF7G6uu/oCgiEblTVZ94njquAn7Z9+/NwG8D34S9E7+oFdrkEbkmf67zuq7NXtNYHkZ22m+z0QZ8Aej4/cPA5zADDnBLrd3NGKXi84Fv9X+P+v1vHdFZD3LdPPLZrSP/f97/jTHXSuT/l/DZDt2XfZtst/s8zzMNvAl7qU4Dp/z+m4CZkbZTwG8B7wR+eOSzt438v2uN7R5gFs93XGv7JmCP338m8DXMD35v/bcFno25s96FrSL+DwZDuwl4+ojOraCTIuDVwH8Enjvy2S/X9heBM/5v2PJwfOR7P1O7pscBnwDmgBuBp4y0/QTw09gK8YvAL/jr+3HgY9t5TVu5ru24pvH2MO/nTndgw87Bl0b+72D+s7dSM7RYEPHn/At7rT/2tXV0vhf4Ub//34Fn+f0nYn73etsvYoGxWf+wBiL1JmcHAXfU0LFJI+c/35ShY31Y5es5G1b5Pt+Hl2G+y/cBDf/Z6CBZAHePbEP/92sjbb9Q2/8H4Nm13+tztc/+EXgR5uY6Any/P/4C4IYRnVtBEf0h8OfA64B/At5a++zm2v7vYW6oeiD87od7rrHSV9/r958PfHqk7S21/fs2+OyCX9NWrms7rmm8bbzteAc27Jy5Pa4dORb7hylfo/3lmHH+L6MPRa3NNPA/gK9is4IhZug+jrlN6m1/zn92L/BarCLGf8NWBG8cabujho5NGjl/bFOGjq3BKm8d+f8NwKexSiKj1/Tz2CD8lNqxu9c5z+14tAln45Xr13xLbX9Dg8DWUESfr+3HGDrqfwGNNfQ+0z+zr/X61ptA1GGuoxOGz4/8/0/+N7wOOEk12Xj8SN+25Zo2e13neE3P3uiaxtvG2453YMPOmTE+sM5n37zB916MBR830j0FPM0/mBsl01wGXOb3Z4DvB65bo92OGrrNGjn//y21/Y1mc1uBVd5eNxz+2I9gwd171/lt34utoiY3MHSv8f34NuDXgN/F3GH/AXhnrd0NGNb9B7DB9mX++Ldy9uB1GHgPlll7p98e8sceO9L2jjX69Eb/e50Fj/PG7bXAJ4EH17mm38AmEFcB/x6bAV8J/CjwtyNtXwB82d/f52ED/V2+vy9d45pO+OsJbc77mjZzXRfwml620Xs73mr3cac78PWy7bSh26yR8203Zegw18ybsQSeOcwddLs/Nuqbfgvw7Wv064XrGQT/+UuwWeOxDdo83xuhW7BVzweAn6KWqYsNxB/G8geu9tc/7+/pc9fQeT02m92NIYh+AfjuNdq9i5H8A3/8J4DhyLHrqFY83wL86lo6a7/3jdjMcxG4DfhNYHqdvga916zX11r73X571zqfb/qa1mhzEDi1zmc/utlrWuO7fzv6Toy3jbeLGm1yKYmIzGIukpdinClQ4cffpKpztbZvwVwpHxnR8ULg91X1Ceuc4yXYrOawqh5Y4/PnY4GgJ2LL4SPA/wb+WFWzWrunYca2wFxDPw28Cov+/6SqfqbWdtNQTd/2ELZMr7d9kap+cL22WADscar6xS3qXdXWo20u20S7N2Juoxjz918H/F/gO4APq+pvjJz/OkBV9SaPEnohNnv9wAXSeY3XebuejSDalN6tIK7WEhH5U1V95RrHz1mviLxTVf/FhdQ5lprs9OjxaNjwAdIL0RaDLT55K3rP9fzYMvnL2ABwD6uX6aPunddsoe1W9G6qrW93xyZ1fgFDXLQxJMVU7d6O+mffiK0MPocFmT8G/AqGmHjDBdL50bV0bkUvW0NcvX9k+xtgKfw/0nZTetfQ+f4NdN6y2b6Otw3e1Z3uwKNhY53g6SPV9lx1skmo5sXQdos6b1lr3/9/6xrn34zxvOA6t6KXrSGuNm08N6uXrQ0em+7reFt/2xE+769HEZHPr/cR5vve1rbbdH6n3v2gqvd4t8xfisiVvi0XUdut6ByISFtVV7CAtV280QUXI20zNdqGFRH5qqqe8efoiki97Xbo3LReVS2A3xaR9/q/x1mfr/+ZwM9igfJfVNVbRaSrqh8fbbgFvc/aBp1j2UDGN+zCyX7gu7DAXl0E+Mwj0HY7dB4XkWtV9VYAVV0SkX+O8Y08ZeS7O912Kzr/mar2fbu6sUww339dNmuUt0PnVvWiqvcDPyAiL8Zm9WfJuRjPh9O7HTrH8jCy01P/r5cNI9R53jqf/fl2t90mnZuGau50263o3OLv2ljn+B5GMgd3Uuf5bGwCWnsx6Bxvq7cx2mQsYxnLWC5BGRcgHstYxjKWS1DGxnssYxnLWC5BGRvvsYxlLGO5BGVsvMcylrGM5RKU/w+N6ifZ34SM/QAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# generate synthetic data with 10 signal variables\n", "np.random.seed(12345)\n", "X, y, beta = pyblip.utilities.generate_regression_data(\n", " n=300, p=500, k=5, sparsity=0.02, dgp_seed=12345\n", ")\n", "signal_variables = np.where(beta != 0)[0]\n", "# X has strong local correlations\n", "sns.heatmap(np.corrcoef(X.T), cmap='RdBu', center=0)\n", "plt.title('Correlation matrix for X')\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2 Linear Spike-and-Slab model + BLiP" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can apply BLiP in two steps. First, we fit a Bayesian model to $(X, Y)$---in this case, we use a spike-and-slab model for sparse linear regression. Second, we run BLiP directly on top of the posterior samples from the Bayesian model, as shown below." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Step 1: sample from Gaussian spike-and-slab model\n", "lm = pyblip.linear.LinearSpikeSlab(X=X, y=y)\n", "lm.sample(N=2000, chains=5, burn=200, bsize=3)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "BLiP ran in 1.03 seconds.\n", "\n" ] } ], "source": [ "# Step 2: Apply BLiP to detect signal variables\n", "t0 = time.time()\n", "detections = pyblip.blip.BLiP(\n", " samples=lm.betas,\n", " q=0.1,\n", " error='fdr',\n", " verbose=False,\n", ")\n", "print(f\"\\nBLiP ran in {np.around(time.time() - t0, 2)} seconds.\\n\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Since the data is synthetic, we can check whether the results from BLiP are accurate." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The true signal variables are [ 54 68 148 184 272 306 383 409 426 471].\n", "BLiP correctly detected a signal variable in {54}.\n", "BLiP correctly detected a signal variable in {68}.\n", "BLiP correctly detected a signal variable in {184}.\n", "BLiP correctly detected a signal variable in {272}.\n", "BLiP correctly detected a signal variable in {306}.\n", "BLiP correctly detected a signal variable in {383}.\n", "BLiP correctly detected a signal variable in {426}.\n", "BLiP correctly detected a signal variable in {417, 421, 407, 408, 409, 412}.\n" ] } ], "source": [ "print(f\"The true signal variables are {signal_variables}.\")\n", "for x in detections:\n", " true_detection = len(x.group.intersection(set(signal_variables))) > 0\n", " if true_detection:\n", " print(f\"BLiP correctly detected a signal variable in {x.group}.\")\n", " else:\n", " print(f\"BLiP incorrectly detected a signal variable in {x.group}.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see, sometimes BLiP will detect individual signal variables, but often this is not possible due to the high correlations among $X$. In the latter case, BLiP outputs larger clusters of variables." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.3 SuSiE + BLiP" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "BLiP can apply on top of nearly any Bayesian model or algorithm, including variational algorithms. Here, we show how to apply BLiP on top of a SuSiE model [(Wang et al, 2020)](https://www.biorxiv.org/content/10.1101/501114v4). We do this in three steps: Step 1 is to fit SuSiE, Step 2 is to create candidate groups based off of the SuSiE outputs, and Step 3 is to apply BLiP." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [], "source": [ "# Step 1: Fit SuSiE model\n", "import rpy2\n", "import rpy2.robjects.numpy2ri as numpy2ri\n", "import rpy2.robjects as ro\n", "from rpy2.rinterface_lib.embedded import RRuntimeError\n", "from rpy2.robjects.packages import importr\n", "%load_ext rpy2.ipython\n", "\n", "# Import and run susie\n", "susieR = importr('susieR')\n", "R_null = ro.rinterface.NULL\n", "numpy2ri.activate()\n", "susie_obj = susieR.susie(\n", " X=X, y=y, L=10, coverage=0.9\n", ")\n", "# Extract output\n", "alphas = susie_obj.rx2('alpha')\n", "susie_sets = susie_obj.rx2('sets')[0]\n", "try:\n", " susie_sets = [\n", " np.array(s)-1 for s in susie_sets\n", " ]\n", "except TypeError:\n", " susie_sets = []" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Creating cand groups and running BLiP took 0.36 seconds.\n", "\n" ] } ], "source": [ "# Step 2: create candidate groups based off susie outputs\n", "t0 = time.time()\n", "cand_groups = pyblip.create_groups.susie_groups(\n", " alphas=alphas,\n", " X=X,\n", " q=0.1, # FDR level\n", ")\n", "# Step 3: run BLiP\n", "detections = pyblip.blip.BLiP(\n", " cand_groups=cand_groups,\n", " error='fdr',\n", " q=0.1,\n", " verbose=False,\n", ")\n", "elapsed = np.around(time.time() - t0, 2)\n", "print(f\"\\nCreating cand groups and running BLiP took {elapsed} seconds.\\n\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can compare the detections from SuSiE and SuSiE + BLiP. As we can see from the smaller group size, SuSiE + BLiP localizes signals more precisely than SuSiE alone. (All detections are true detections in this case.)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[{68}, {306}, {426}, {184}, {272}, {54}, {382, 383, 384}]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[set(x) for x in susie_sets]" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[{54}, {68}, {184}, {272}, {306}, {426}, {382, 383}]" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "[x.group for x in detections]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As the number of signals increases, SuSiE + BLiP tends to have substantially higher power than SuSiE alone, as discussed in [Spector and Janson (2022)](https://arxiv.org/abs/2203.17208)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.4 Probit spike-and-slab model + BLiP" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can run BLiP on top of nearly any regression model, including various models for binary responses. For example, suppose we only observe a binary indicator $Y^{\\star}$ as an outcome. We can apply BLiP directly on top of a sparse probit model in this setting, as shown below." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [], "source": [ "# Step 1: fit probit model\n", "ystar = y > 0\n", "pm = pyblip.probit.ProbitSpikeSlab(X=X, y=ystar)\n", "pm.sample(N=1000, chains=10, bsize=3)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "BLiP ran in 0.91 seconds.\n", "\n" ] } ], "source": [ "# Step 2: apply BLiP to posterior samples\n", "t0 = time.time()\n", "detections = pyblip.blip.BLiP(\n", " samples=pm.betas,\n", " q=0.1,\n", " error='fdr',\n", " verbose=False,\n", ")\n", "print(f\"\\nBLiP ran in {np.around(time.time() - t0, 2)} seconds.\\n\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Once again, we can check that BLiP makes (mostly) correct detections:" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The true signal variables are [ 54 68 148 184 272 306 383 409 426 471].\n", "BLiP correctly detected a signal variable in {68}.\n", "BLiP correctly detected a signal variable in {263, 264, 265, 266, 267, 268, 269, 270, 271, 272}.\n", "BLiP correctly detected a signal variable in {180, 181, 183, 184, 185, 188}.\n", "BLiP correctly detected a signal variable in {306, 308, 309, 310, 313}.\n", "BLiP incorrectly detected a signal variable in {417, 418, 413, 421}.\n", "BLiP correctly detected a signal variable in {53, 54}.\n", "BLiP correctly detected a signal variable in {424, 426}.\n" ] } ], "source": [ "print(f\"The true signal variables are {signal_variables}.\")\n", "for x in detections:\n", " true_detection = len(x.group.intersection(set(signal_variables))) > 0\n", " if true_detection:\n", " print(f\"BLiP correctly detected a signal variable in {x.group}.\")\n", " else:\n", " print(f\"BLiP incorrectly detected a signal variable in {x.group}.\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.5 Purity thresholding " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In some applications (e.g. genetic fine-mapping), it is common practice to only discover groups of variables whose purity exceeds (e.g.) $50\\%$, where the \"purity\" of a group is defined as the minimum absolute correlation among its variables. To enforce this constraint, simply generate candidate groups and use the ``min_purity`` argument:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [], "source": [ "cand_groups = pyblip.create_groups.all_cand_groups(\n", " samples=lm.betas,\n", " X=X,\n", " min_purity=0.5,\n", ")\n", "detections = pyblip.blip.BLiP(\n", " cand_groups=cand_groups,\n", " q=0.1,\n", " error='fdr',\n", " verbose=False,\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can check that this only outputs regions whose purity exceeds $50\\%$." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "hatSig = np.corrcoef(X.T) # correlation matrix\n", "\n", "def purity(detection, hatSig=hatSig):\n", " feature_ids = np.array(list(detection.group)).astype(int)\n", " return np.abs(hatSig[feature_ids][:, feature_ids]).min()" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1.0, 1.0, 1.0, 0.9999999999999998, 1.0, 0.9999999999999999, 0.9999999999999999, 0.8065878127309256]\n" ] } ], "source": [ "print([purity(x) for x in detections])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.6 Hierarchical priors to ensure error control" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "BLiP can wrap on top of nearly any Bayesian model, and in practice, it is fairly robust to some degree of model misspecification (see [Spector and Janson (2022)](https://arxiv.org/abs/2203.17208) for simulations and a discussion of this issue). That said, if the underlying model is extremely poorly specified, BLiP will violate FDR control. For example, in the following problem, the prior indicates that $50\\%$ of the variables are signal variables, whereas in truth only $4\\%$ of the variables are signal variables." ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "scrolled": true }, "outputs": [], "source": [ "# Sample from an obviously bad spike and slab model\n", "lm_bad = pyblip.linear.LinearSpikeSlab(X=X, y=y, p0=0.5, update_p0=False)\n", "lm_bad.sample(N=2000, chains=5, burn=200, bsize=3)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "BLiP problem has 2292 groups in contention, with 500 active features/locations\n", "LP had 431 non-integer solutions across 454 locations. Binarizing with deterministic=True.\n", "The false positive rate is 92.0% due to the mispecified model!\n", "\n" ] } ], "source": [ "# run blip: FDR control fails because the model is very badly mispecified\n", "detections = pyblip.blip.BLiP(\n", " samples=lm_bad.betas,\n", " error='fdr',\n", " q=0.1,\n", " max_pep=0.25,\n", " verbose=True\n", ")\n", "sigvars = set(signal_variables)\n", "fdp = np.mean(\n", " [len(x.group.intersection(sigvars)) == 0 for x in detections]\n", ")\n", "print(f\"The false positive rate is {np.around(100*fdp)}% due to the mispecified model!\\n\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To avoid this situation, we recommend using **hierarchical priors** on unknown nuisance parameters like the sparsity level in regression problems, with a conservative choice of hyperparameters. The samplers in ``pyblip`` automatically use relatively uninformative hierarchical priors which empirically control the FDR well in a variety of settings. For example, in the previous examples, the prior was quite uninformative, and BLiP still performed quite well." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "When using MCMC algorithms, we also recommend **running multiple MCMC chains** with different initializations to protect against convergence issues. As discussed in [Spector and Janson (2022)](https://arxiv.org/abs/2203.17208), even when each individual MCMC chain fails to converge, often using multiple chains will overstate the uncertainty in the location of signals, leading to conservative but valid inference.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Changepoint detection" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given time series data $(Y_1, \\dots, Y_T)$, suppose we are interested in looking for \"change-points\", or times where the stochastic process changes. Often, we can tell that a process has changed, but we cannot discern exactly when it has changed because each observation $\\{Y_t\\}$ is noisy. The following synthetic dataset gives one example of this:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Changepoint series with 5 data-points\n", "np.random.seed(123)\n", "T = 200\n", "_, Y, beta = pyblip.utilities.generate_changepoint_data(\n", " T=T, sparsity=0.04, coeff_size=5,\n", ")\n", "mu = np.cumsum(beta) # true mean of Y\n", "plt.scatter(np.arange(T), Y, color='blue', label='Y')\n", "plt.xlabel(\"Time\")\n", "plt.ylabel(\"Value\")\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To detect regions where the true mean of $Y$ has changed, we can call the function ``detect changepoints`` which will fit a spike-and-slab changepoint model and apply BLiP on top of it. This only takes one line!" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [], "source": [ "detections = pyblip.changepoint.detect_changepoints(\n", " Y=Y, \n", " q=0.1, \n", " sample_kwargs=dict(N=2000, chains=10, bsize=5), # kwargs for the sampler\n", " blip_kwargs=dict(max_pep=0.5, verbose=False) # kwargs for BLiP\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Below, we plot these change-points on top of the raw data and the ground truth. Each output from BLiP is a region which contains a change point with high confidence. The detected regions are shaded in the plot: true detections are in green, and false detections are in orange." ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Plot data-points and ground truth\n", "plt.plot(np.arange(T), mu, color='red', label='E[Y]')\n", "plt.scatter(np.arange(T), Y, color='blue', label='Y')\n", "\n", "# Add BLiP detections\n", "changepoints = set(np.where(beta != 0)[0].tolist())\n", "color_counts = dict(orange=0, green=0) # for legend\n", "for j, cs in enumerate(detections):\n", " cs = cs.group\n", " if len(changepoints.intersection(cs)) > 0:\n", " color = 'green'\n", " cstring = 'true positive'\n", " else:\n", " color = 'orange'\n", " cstring = 'false positive'\n", " # Decide whether to add a label\n", " if color_counts[color] == 0:\n", " color_counts[color] += 1\n", " label = f'BLiP detection ({cstring})'\n", " else:\n", " label = None\n", " \n", " \n", " plt.axvspan(\n", " min(cs), max(cs), alpha=min(1, 2 / len(cs)),\n", " color=color,\n", " label=label\n", " )\n", "\n", " \n", "plt.xlabel(\"Time\")\n", "plt.ylabel(\"Value\")\n", "plt.legend()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see, in this example, BLiP does a pretty good job both detecting change-points and quantifying our uncertainty in their locations. The vertical, thin green bars are change-points which have been perfectly localized." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. Point-source detection" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose we observe photon counts from a telescope, and we are interested in detecting point-sources (e.g., stars) from the image. Since most images have some blur, we may not be able to perfectly localize each point-source, but BLiP can still help localize them as precisely as possible. Below, we give an example of how to apply BLiP on top of outputs from a pretrained [StarNet model](https://github.com/Runjing-Liu120/DeblendingStarfields). Note that the StarNet model is described in detail in [Liu et. al (2021)](https://arxiv.org/pdf/2102.02409.pdf). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To start, we load the simulated $20x20$ image data, which was generated using code from [Liu et. al (2021)](https://arxiv.org/pdf/2102.02409.pdf)." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Load simulated image data\n", "npixels = 20\n", "image = np.loadtxt(\"data/sim_image.txt\").reshape(2, npixels, npixels)\n", "true_locs = np.loadtxt(\"data/sim_locs.txt\").reshape(6, 2)\n", "\n", "# plot one of the two bands\n", "def plot_starnet_sim():\n", " fig, ax = plt.subplots(figsize=(6,4))\n", " sns.heatmap(\n", " np.log(image[1]), \n", " cmap='Greys', ax=ax, \n", " cbar_kws=dict(label='log(Intensity)')\n", " )\n", " # Plot true locations\n", " ax.scatter(\n", " npixels*true_locs[:,1], \n", " npixels*true_locs[:,0], \n", " color='red', \n", " marker='x', \n", " label='True Sources'\n", " )\n", " return fig, ax\n", "\n", "fig, ax = plot_starnet_sim()\n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we load the posterior samples from the pretrained StarNet model. See [here](https://github.com/Runjing-Liu120/DeblendingStarfields) or [here](https://github.com/amspector100/DeblendingStarfields) for examples of how to fit pretrained StarNet models.\n", "\n", "Note that the posterior samples are an $(N, n_{\\mathrm{source}}, d)$-shaped array, where $N$ is the number of posterior samples and $d=2$ is the dimension of the image. If ``post_samples[i, j] = (x, y)``, this means that the $i$th posterior sample has asserted that there is a point-source at location $(x,y)$. Since there may be different numbers of point-sources per iteration, NaNs are ignored. See API reference for more details on the data input format.\n", "\n" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0.07279399, 0.34460315],\n", " [0.05383444, 0.83722878],\n", " [0.12657177, 0.60644835],\n", " [0.54421228, 0.45192835],\n", " [0.76564646, 0.75837231],\n", " [0.87883556, 0.64780414],\n", " [ nan, nan]])" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Load posterior samples from StarNet\n", "post_samples = np.loadtxt('data/post_samples.txt').reshape(996, 7, 2)\n", "# Print the location of sources according to the first posterior sample.\n", "# The NaN means there are only six estimated sources.\n", "post_samples[0]" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([[0.07735128, 0.33859724],\n", " [0.04566601, 0.82996595],\n", " [0.19049473, 0.56281787],\n", " [0.59320527, 0.43181294],\n", " [0.87796324, 0.6558165 ],\n", " [ nan, nan],\n", " [ nan, nan]])" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# In contrast, in the 8th iteration, there were five estimated sources.\n", "post_samples[8]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Given these posterior samples, applying BLiP is as easy as calling the ``BLiP_cts`` function. Note that ``BLiP_cts`` is useful in problems where the set of possible signal locations is continuous, for example in this problem, where a point-source could take any location in $[0,20]^2$." ] }, { "cell_type": "code", "execution_count": 25, "metadata": { "scrolled": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "BLiP problem has 44 groups in contention, with 9 active features/locations\n" ] } ], "source": [ "# the grid sizes determine the resolutions at which BLiP is applied\n", "grid_sizes = np.unique(np.around(np.logspace(np.log10(4), 4, 50)))\n", "detections = pyblip.blip.BLiP_cts(\n", " post_samples,\n", " error='fdr',\n", " q=0.1, \n", " verbose=False,\n", " grid_sizes=grid_sizes,\n", " deterministic=True,\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot these detections on top of the image to see the detections." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.patches as patches\n", "\n", "fig, ax = plot_starnet_sim()\n", "for j, x in enumerate(detections):\n", " center = npixels * x.data['center']\n", " # since rescale=False all radii are the same\n", " radius = npixels * x.data['radii'][0]\n", " if j == 0:\n", " label = 'BLiP detection'\n", " else:\n", " label = None\n", " circle = patches.Circle(\n", " (center[1], center[0]),\n", " radius, \n", " edgecolor=(30/256,144/256,255/256,1),\n", " facecolor=(1,1,1,0), # make interior transparent\n", " linewidth=2,\n", " label=label\n", " )\n", " ax.add_patch(circle)\n", " \n", "ax.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As we can see, BLiP makes four true detections at various resolutions based on the posterior samples." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 5. Inputs for arbitrary problems" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "So far, we have reviewed three major problem settings: variable selection, change-point detection, and point-source detection. However, in principle, BLiP can apply to any problem where one is interested in jointly detecting and localizing signals." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In generic problems, there are main types of inputs ``BLiP`` can take." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.1 Posterior samples for discrete problems" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "``pyblip.blip.BLiP`` can take an $(N,p)$-shaped matrix where nonzero values denote the presence of a signal variable. Here, $N$ is the number of posterior samples and $p$ is the number of locations at which a signal can exist. So if ``samples[i,j] != 0``, this indicates that for in the $i$th posterior sample, the $j$th location contains a signal. We call these problems \"discrete\" because $p$ is finite." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.2 Posterior samples for continuous problems" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In some problems, we may be searching for signals in $\\mathbb{R}^d$. In this case, since there are an infinite number of possible locations for signals, we cannot automatically apply ``pyblip.blip.BLiP``.\n", "\n", "In this setting, ``pyblip.blip.BLiP_cts`` can posterior samples in a different format as an input. In particular, ``pyblip.blip.BLiP_cts`` assumes the posterior samples are an $(N, n_{\\mathrm{source}}, d)$-shaped array, where:\n", "1. $N$ is the number of posterior samples \n", "2. $d$ is the dimension of the data\n", "3. If ``samples[i, j] = (x1, ..., xd)``, this means that the $i$th posterior sample has asserted that there is a point-source at location $(x_1, \\dots, x_d)$. Since there may be different numbers of point-sources per iteration, NaNs are ignored.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.3 Advanced usage: directly specifying candidate groups" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A ``CandidateGroup`` object represents a subset of the locations which could potentially contain a signal. For example, in variable selection problems, each ``CandidateGroup`` represents a subset of the covariates. Alternatively, in the following example, each ``CandidateGroup`` represents three circular regions of the globe." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [], "source": [ "from pyblip.create_groups import CandidateGroup\n", "cand_groups = [\n", " CandidateGroup(\n", " group=set([1,2,]), \n", " pep=0.01, \n", " data=dict(\n", " latitude=41.0,\n", " longitude=74.0,\n", " radius=1,\n", " name='big_region',\n", " )\n", " ),\n", " CandidateGroup(\n", " group=set([1,]), \n", " pep=0.3, \n", " data=dict(\n", " latitude=41.5,\n", " longitude=74.0,\n", " radius=0.01,\n", " name='sub_region1',\n", " )\n", " ),\n", " CandidateGroup(\n", " group=set([2,]), \n", " pep=0.2, \n", " data=dict(\n", " latitude=40.5,\n", " longitude=74.0,\n", " radius=0.01,\n", " name='sub_region2',\n", " )\n", " ),\n", "]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Each ``CandidateGroup`` has three attributes. \n", "\n", "1. The ``pep`` attribute specifies the posterior error probability, or the posterior probability that the candidate group does *not* contain a signal.\n", "\n", "\n", "2. The ``group`` attribute is a set of positive integers such that two candidate groups overlap if and only if their ``group`` attributes overlap. For example, above, the group attributes suggest that the ``big_region`` overlaps with ``sub_region1`` and ``sub_region2``, but ``sub_region1`` and ``sub_region2`` do not overlap.\n", "\n", "\n", "3. The ``data`` attribute is a optional dictionary that contains miscallaneous metadata. BLiP largely ignores the ``data`` attribute." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "One can directly apply BLiP on top of a list of candidate groups." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "BLiP detected the candidate groups named: ['big_region']\n" ] } ], "source": [ "detections = pyblip.blip.BLiP(\n", " cand_groups=cand_groups,\n", " verbose=False,\n", " q=0.1,\n", " error='fdr',\n", ")\n", "print(f\"\\nBLiP detected the candidate groups named: {[x.data['name'] for x in detections]}\")" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3.9", "language": "python", "name": "python3.9" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.16" } }, "nbformat": 4, "nbformat_minor": 2 }