{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Цифровая обработка сигналов - Лекция 3\n", "# Свертка и корреляция: линейная и циклическая свертка\n", "\n", "## Введение\n", "\n", "Перед вами обучающий материал по основам **цифровой обработки сигналов** с использованием средств языка программирования Python. Предполагается, что читатель имеет базовые знания из области высшей математики, а также владеет языком Python и хотя бы поверхностно знает различные python-библиотеки - numpy/scipy, matplotlib и другие. \n", "\n", "Для пользователей MATLAB / GNU Octave освоение материала с точки зрения программного кода не составит труда, поскольку основные функции и их атрибуты во многом идентичны и схожи с методами из python-библиотек.\n", "\n", "## Свертка и корреляция\n", "\n", "В реальных задачах часто ставится вопрос о степени похожести одного процесса на другого или же о независимости одного процесса от другого. Иными словами, требуется определить взаимосвязь между сигналами, то есть найти корреляцию. \n", "\n", "Методы корреляции используются в широком диапазоне задач: поиск сигналов, компьютерное зрение и обработка изображений, в задачах радиолокации для определения характеристик целей и определения расстояния до объекта. Кроме того, с помощью корреляции производится поиск слабых сигналов в шумах.\n", "\n", "В разделе фильтрация сигналов вводилось понятие импульсной характеристики фильтра. Напомним, что **импульсной характеристикой** $h(n)$ называется реакция цепи на входное воздействие в виде функции Дирака (δ-функции). Она отражает влияние цепи на сигнал.\n", "\n", "В задачах прохождения сигналов через различные цифровые узлы происходит свертка сигнала с импульсной характеристикой фильтра.\n", "\n", "*Корреляцию* между двумя сигналами можно вычислить как сумму произведений пар отсчетов исследуемых сигналов. \n", "\n", "Если взять две абсолютно независимые случайные последовательности, то их сумма произведений стремится к нулю. Говорят, что такие сигналы обладают нулевой корреляцией. Причем, чем длиннее последовательности, тем сильнее результат стремится к нулевому значению.\n", "\n", "Корреляция бывает **положительной** и **отрицательной**. Положительная корреляция - большие значения одного сигнала связаны с большими значениями другого сигнала (увеличение одной переменной взаимосвязано с увеличением другой переменной). Отрицательную корреляцию проще всего понимать так: увеличение одной переменной связано с уменьшением другой переменной. \n", "\n", "Формула взаимной корреляции:\n", "\n", "$$ r_{12} = \\frac{1}{N} \\sum_{n=0}^{N-1}x_1(n)x_2(n) \\tag{3.1}$$\n", "\n", "Нормирующий множитель $\\frac{1}{N}$ применяется для исключения влияния длительности последовательностей. \n", "\n", "В терминах функционального пространства сигналов корреляция может быть выражена как косинус угла между векторами. Следовательно, при полном совпадении сигналов степень их связи будет принимать положительное единичное значение, при полной противоположности сигналов - отрицательную единицу, а при полном несовпадении - нулевое значение." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "\n", "from scipy.fftpack import fft, ifft\n", "\n", "FONT_SMALL = 12\n", "FONT_MEDIUM = 14\n", "\n", "plt.rc('axes', titlesize=FONT_MEDIUM) \n", "plt.rc('axes', labelsize=FONT_SMALL)\n", "plt.rc('xtick', labelsize=FONT_SMALL)\n", "plt.rc('ytick', labelsize=FONT_SMALL) \n", "plt.rc('legend', fontsize=FONT_MEDIUM) \n", "plt.rc('figure', titlesize=FONT_MEDIUM)\n", "\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Приведем примеры сигналов и найдем корреляцию между ними\n", "\n", "Положительная корреляция:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([55])" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# signal x1(n)\n", "x1 = np.array([1, 2, 3, 4, 5])\n", "\n", "# correlation\n", "np.correlate(x1, x1, mode='valid')" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "55" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# signal x1(n)\n", "x1 = np.array([1, 2, 3, 4, 5])\n", "\n", "# correlation via sum\n", "np.sum(x1*x1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Как видно, встроенная функция `correlate()` для совпадающих сигналов вычисляет сумму произведений, что полностью согласуется с формулой.\n", "\n", "Отрицательная корреляция:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([-55])" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# signal x2(n)\n", "x2 = -1 * np.array([1, 2, 3, 4, 5])\n", "\n", "# correlation\n", "np.correlate(x1, x2, mode='valid')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Разные сигналы:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([10.])" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# signal x1(n), x2(n)\n", "x1 = np.ones(5) # [1, 1, 1, 1, 1]\n", "x2 = np.arange(5) # [0, 1, 2, 3, 4]\n", "\n", "# correlation\n", "np.correlate(x1, x2, mode='valid')" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "10.0" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.sum(x1*x2) # correlation as sum of products" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "На практике, когда два сигнала коррелируют, их взаимное расположение во времени - неизвестно. Сигналы могут иметь одинаковую форму, но задержаны друг относительно друга. В связи с этим, для установления максимальной корреляции, её требуется находить для нескольких задержек.\n", "\n", "### Случайные сигналы\n", "\n", "Найдем корреляцию двух псевдослучайных процессов.\n", "\n", "Параметр `seed()` задает начальное условие для случайного процесса. Если установить какое-либо число, то при вызове любой функции случайного числа будет генерироваться предопределенный набор чисел (псевдослучайный).\n", "\n", "С помощью метода `randint()` из библиотеки `numpy.random` зададим случайную последовательность целых чисел.\n", "\n", "#### Случайные процессы с нулевой корреляцией:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "No correlation, r12 = [-45].\n" ] }, { "data": { "image/png": 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8VxRF3+av0n75wHrgXcAOrEDKbnhBFMXIRmxOBzxSc3FAeT3AweltyWZJ6GmR11SGhaUJEpIgI0i6p9eK059idxDqmyxsX5oz67UNZWaOtA2xfVmOn3ctIlyTYEiG/JXQeQDwo7cRIzqH7Nz72AE6rHZ0osgT5/dTmmVi9/2bKTGrPBHU0JiLtQWyKtU9RlqBFBg0Zcl+65H2IT53te/+JSXocXlE3B5xng3ZomDOs3YW2rM2PGy9kDYdgChYDb2nwOPxLQq9CGizjF90WfBSkG6kb1QLYMUDbzT284O7N1z8PdVoYNThJN1oiGGv1GfmOMig1+F0exb/OEil+7nL7cHh9JA6I9B4w4p8vrv3PP+wqwbdYnw2xhOn/wDLdkqLx1Eglk+qW4Fs4OczXxQEoUwQhDFBELy5W0bg/wDdgA14HngDuC/iHrin/K9mTQxJ2zXmE0r2A0RsxVnfbGHb0uxZr21bmk19syXsNhcMbhfopt0+8ldKCvxxhCiK3PvYAdosdpxukUkPON0ibRY79z124PJYAdCIL9QQoJxLehGMhieK1dhrC5hGWpyZTPfwvIrCxYH2rFWe0W7pfATpWZFXG7eZckrQbrHPsuAEyE1Lot+mBSBijWVsEpfbQ/4MN5ISczKd1kV6P5tm7jjIPuW+PMZBKt3PWwbHqcxJmfWaKTGBNSWZfNBiDatNjRARRdj/Q9jyF1E7ZMwCEKIo/k4URaMoioNzXm8XRTFVFMV3p39vE0VxsyiKGdOvLxNF8SuiKNpi0/PLHFGEM8/DiluD7xuBFacoihzrGGZtSeas17dVZlPfdBkEIMYHIGU6yyOzHIbaYtufORxqG6LTOoHbM/sB6/aItFvtHGoLL01dQyNsrC1gVjkAkVYopb7LpG/UQVZKIga9/0eu14pTQyMkbD2XMiBAKsNoeSd2/VGZNqud8qzZkxODXofLs0gneQuIN88OcG113qzXSs0mOoYWd1mZNg5SloZeGzUzyi+83LquiOe1Mgx1aXsfMsvAXBG1Qy7OXD0N9eg6AtlLQ0vRSc0LOwOizWKnODOZxITZp2heupGxSRfjk66w2l0wzBxc6nTS522Pnwhw6+A4CXrf6XAGvY5WbSKlEW3iOAPiSJtv+82ZVOZqAQgNGczMgABYcvWi1oFo85EBAWBK1GOfWuTjgTjnjca+i/oPXkqzkumwLu4AhDYOUpbGnlFqfGQJXrkshwOt1stH/y0W7Ps+bPtiVA+pBSA05HHiKVjj0/10PhGUYPgqv/CyqSJr8UeWx/qkz89LnJVhVOSk4HT7lm5xuj1UzEmj09BQnTjOgAgkQOlFy4DQkMXcDIi8Whg8B57FOUhvt45Tnj3/uVKQbqR3RCvDiBVTLg+NvTZWFWXMer3UbKJzaHGXYGjjIGU56ycDIkGv4+rlubx1NryMao0gDF6QSmdKN0X1sFoAQiN03E5oegOWfyi0/b0ilGGwz4cApZdtS7PZ1zToc9uiYabAGED+qrgKQNSVmynNMs0TzNPrBMqyTNSVhyc8qqERNnMnZGqQXhheBkT7EBuCXBNLclJoGhgLt2calxu2XkkU1YsgSGKUPcdj1ycV6RudJC8tad7r+elGejUhyphxoMXK5oqseQKBJeZkOhd5CcbGskyMBv08V2ZtHBQerRbfQUaQ3DD+cFQrw1CF/Y/CtoeiftjLOwChT/Tv0JBslrZrXKL5LSjfLjlghEKYGRCiKHK6a4RVRb4F27ZWZrO/OX7KEVTB1gtpczMgTsWuP3MQBGFa5TkZAdAL0kO3ItvE7ge2IMx9ImtoqIlrCnQG9R0A0gqlQIcMJl1ubA4XOamB75tFGYtYhFJ71iqPe2r+s3iR2nFOuTwk6ASfKviaE0Zs2dvYx46avHmvF5uTF30GxHffuMAVS3NYkp2CQS+QlKBDJ7D4x0GB7ue6BDj5rOwmRyacpCYl+HWBWlOSQZvFzojdKbttjQCMW6CtHmpujvqhY2bDGRcYjJJdzLRi66E/PEqdsRU+/N/SBabZgs3mxNOwUYb5SEoejA3IPkzTwBgVOSkk+BFsy0pJxOX2LG6Lp7FeqLzm0u9xqHBeYjbxP3es5Tt7z2NyWLAnZfOr+zcv3oeuRvwy3C4JKKmNIVmyx5XB6e5RVhVnBN1PpxNITNDjcLoxGvTh9jA+ufisnYQfXwu3/C8cfAxu+a72rA0H54TvhYAlV8MrX4Ur/jr6fVKRziE7JeZkn9vyM4z0jsi7JjWUQRRF3r8wyN/vqp63LSlBz5TbgyiKi3JM8NsD7RxtH+Zn99WRoBM41DbEkbYhXjrZw/NfuGJR/s0XmTl3evZ+2PHPkLVU2uaehCfuhIxiqNoVcpNne21U+yi/8CIIAh9eVcjLp3q4a3MUnvWXC4cfg42fueS6F0Uu7wwIkC4kYzoY0xnOWAG9p6XftQHRbCbHpNTOsu2hvychMSw7Hqn8wrf+g5fNS7I4sJizIGy9szUgks0waYu7+t6ekUnWlWRyyxIdnUMTaILkGjEhGgKUXvQGWUGIIyHoP3ipyDbRvliF2wxGSUg3qwKK1sNQs/asDRd/5UbZyyTHJPfiWiVss9r9pmZrGRCxo2lgnKLMZEyJvtcys0yJDC3CFeu9DX08daiDH9y9AYNehyAIbKrI4sGrKhmbdC3u4IMX79xptAvyVl6cR5GSC3c9Ca9/HToPh9zc2d5Ragr821QD3La+iOe0MgzlcE1KC8vr747J4bUAxAzceqMUBXKMxLor8cfZl6H6w/JTnHUJsgdD9U0WtlYGDkBsX5pDffMituOcW98LksDeUGtMuuOPrmE7RZnJ6HUCa0oyONq+yMVBNeKTaAhQekkrkK7PEDnSPsT6IA4YXpbkpNA8sIiFKHuOQeE6SEqTVvE9vgXcNIIw6icAIQhScKf7aPT7pCLtfhwwAAoyNBHKWLG3oY+dPsovvJRmmRadE8aR9iH+e89ZfnpvHSlJswMvOp2A2ZSIZewyychxu0D0SIuNM0nNg0/+Gp5/CCxNITXV0GujptB/BgRAeXYKLo9I12ItVYw2J5+V5nVJgT93tdACEHMpqYPOQ7HuRfwhx/1iJik5MB66YKTHI9LYa2OFDyuemWxeksUHLYs4AOG0Q+KcFZ8404EA6B52UDydGrujNp+9jZpKsUYMsDZDVmV0jiVTB6LRj7K3Lxa9E0b3MShaJ/0/oxRG2mPZm4WLrWe2BedMllwFLW9Htz8q02oZpyzLdwAiHkUoRVHkYKuVZw51cLDViijGYWqg0wGO0fk/ztA/y72N/VwXKABhTqYjEiFKBfqoJE0DY/zDsyf48T0b/Wr6VBekcbbXFuWexYiRAKWP2Uvh1h/AU/eEJEbf2BM8AwLg1nVFvHBMvhOVxhxEEQ78GDb/Rcy6cHlrQPiiZDN0HoRlO2Pdk/hhrB/GByB/hfz3eoUo00NTp2/stVGVn+pTbGomGckG9ILA0PgU5pRFJmDmcYPgox7La8W54tbo98kPnUMTFGUmcwG4piqXH73VxD/cWBPrbmlcbkSzBCO9CEZDGwB1D0+Qn2b0q2czl8rcFA62LuLSsp7jUHe/9P/cGhg4C+aKmHZpQTLa7d/xZcnV8MKX4Oq/j26fVETKgPBdgpFuTMDmiJ80/84hO/c+doAOqx2DXofT7aE0yzQt2uw7iBJ1nA54pEay3ptLslmq7w9SGjVsn8I+5Qr4N5VEYsWpQB+VpH/UwUOPH+Hbd6z1ey4C1Bak0dBrY/sy3y5ui4rBC1LZlz9KNsL1/w5P3gX3Pud3pd3jERm2O8kKYSx/0+pC7n3sAJ+/dml4fdaQaH4TcqolrY4YoWVAzKV0M3R8EOtexBenfg+rPh7ee2VacdY3W9gWpPzCi+SGsQizIMYHpcyRuXgDEHFE9/AExZlSBkRGsoH05IRFl3KpsQAY7pBW1KOBjAwIyX4zM+Sml+SkLt4SDFGEkY5LK2a5VVIAQkM+gTIgzBVSiZBMsdR4pmvGc2YugiCgEwTccSBAJIoi9z52gDaLHadbxD7lxukWabPYue+xA/GTCeGe8j2xB+n1ELS73j43wDVVuQH3KclKDn88oEAflcLmcPLg7kP840dqWFOSGXDfmsJ0zvaORqdjscZyQcp0CETVh6Duz+Hp+yS3Kh90DU9Q4ifDaS7ZqUnkpxtp6LlMPmO12Pf9mFhvzkQLQMzFXCEpqmu1qZc49Sys+kR475VpxVnfNBhy5Hjr0uzFqQNh65mv/wBSpNlyIfr9CcCka7Zi/86afN7QyjA0oonHAx7X/DpUtZARgDjcNsSGEPUfAMwmA1Z79AbWUWW4XQoSeQXavBkQGvLxJ0LppWSTlMm5CPB4RNwekcQE/8PV7NT4qLs/1DZEp3ViXjDE7RFpt9o51LZ4NJL2NvSzoyY/4D6lZhMdC9yKc8rl4aHfHOHTW8u5ttp/uYmX6oI0Gi+XEgzLBcheHny/9Z+Gsm3wwl9Jgeg5NPSMUhtimSJIZRiaGGUE9J2RAnhF62PaDS0AMRdBkNJSBrWBESClWCUYw0/TkRGAcHtEmgfGWZ6XGtL+myqyONi6eB7oFxnr8x2A0Bsky7rJsej3yQdjk655Ikw7avM0HQiN6GLrCbnESxHSCyURwBA42j4csgAlSKu56UbD4vQ67zl2Sf8BIKdKe86Gy2iADAiY1oF4N3r9UZE+m4P89MCp9vnpRvpGYx+AaB0cJ0Hvu3zUoNfRukj0XVxuD6e6RlhXmhlwv8IMI70jCzcA4fGIfOXZ42ytzOb2utAy7NKNBsYnXXGRkaM6liAlGDO5+u8g0QR7vz5vU2MIApQz+dCKAl5v6Ls8PmM12P8D2PaFWPdCC0D4pHQTdByIdS/ig5NPw5o7wn+/jBKM090j1Balh2xhlJqUgClRT78tvgSoIsbWA6k+AhAglWH0N0S3P37o9pEWuzQ3lb4RB+OTrhj1SuOyw9ocPQcMgLSikDIgHE43E1PukOpaZ1KZm0KLZXFMVGbRfQwK11763ZQlpVLHS1r6QmJiSKqD90fFVdDyTvT6oyKtg3bK/DhgeCmIEyHKipwUnG7f2bNOt4eKHP/aAQuJQ22Ss48+iFZXgl6HR5Qm8guRb7zSSJrRwEMy9QYqslNoXYz38LkEy8SaiSDAR74Fg+fhg5/M2tTYO0p1fnABSi/JiXrWlmQubiF6tRjrl1ySlu+KdU+0AIRPSjZrAQiQBoZnXoDaW8JvQ0YGxL4mC9uXhqb/4GVbZTb7mxeZaJvNTwYEQN4K6I8PHYiuaQHKuVy5PId3z4fufKKhERHRFKAEMGWDPfjA51TXCKuKM2Q3X5mTQstgfGQ5KYrXgnMmMh1FNLgUsAkUqM8oloIUUwtfj6fdOk55kPrweHHCqCs3U5pl8jkxL8pMpq489GyoeOaNxn521gYvRwDITU1iIA7KY+Ty2HsttFns/PstK0NeFPNSU5hGY88iL8OYskNCEuhkTCN1evj4z+D0H+D0cxdfbuofZ2mevODcbeuLtTKMcDj4M0kIWs73phKx70E8sgh9tMOi85AkFJacGX4bqfkhZ0DUN4UuQOll29Js6psWWRTUnwYExJUQpT9hsJ01ebzRGLruh4ZGRFhbopsBodNJk8AgK/dyBSi9LMlJpWWxCVGKIgy1zXe8yK3WdCDkYrdIQbBglG1ZFILabQEcMLwUZBjpG4l9AEIQBHbfv5nybCkIYdBLP0UZRowJekYdcZIZqE/0n0GTbJa2B+CdcwNctTw0ra7SrGQ6w7HijLCPkfDHE928crqX79y5LmiWhy9qCi4DIUprM2SF4URhSIY7fwPvfgta32diyo1OJ5CU4MP5LQDbl2ZzqG0Ih9Mtvw+XK84JKfiz9q5Y9wTQAhC+STRJkT37IltZl8vJp2F1BOUXID0oJoJ/jk63h44hO0tkpihuLDdzuG2RfU9jfQFKMFbFVQDCVwbEpiVZHGobWrBplxoLjGhnQIAUlPWn0D6NXAFKL0tyUmheJLXiFxnphIyS+av2mhClfEa7Q9M8WSRlGG1WO+VBSjDiJQMCJOvJvQ9fw61ri7hrUxlPPLiV97+6g4euW8pf/vowk644mDAZjJKN5ef3S+fJZ/dK/361I6i9ZevgODmpSaQZDSEdqsRsosMahg6EwQgPN0BuLfz1CfjItyVr2RD6GAn1TRZ++FYTP72nbpbAthxqpq04FzWW86HrP8zFlAV3PgEvPUx74yGq8kPTfZtJgl7HtVV5mui5HI7/FlbcKs1x4wAtAOGPkk3QdTjWvYgdbic0vQnLb4isHe9qYRBOdA6ztiRTdqqb0aDHbEqke3jhCh3Nw9YLaX7UpVPzpABFHNRNdw9PUGKeH4Aw6HXUFqZzsmskBr3SuOyIdgYEBC0dEEWR831jVOWHLqzlpSLHRMtiC0DMFaD0kqsJPssm1LrrJVdD63vq90dl2i12yoKUYBRkGOmLkwAESJkQblHk9rpSNlVkIQgCt64r5rqaXB5++nh8BOcNRpgcBXM5lNTB1Dg47UEn9nsb+9lRE1r5BUgZEGFbcQ40Qlal1MfKa6DnOBjTVQs+NPaO8m8vnOIn99aRYQotwOKLJTkpNA8swjK6mcgRoPRFZhl8/OcUvPoQGzPDe959TCvDCB2PBw7+HDY9GOueXEQLQPij9DLXgWh6EyqukDJBIiXRFNS5IZzyCy+LrgxjahyS/ExcBEFSPx/tjm6ffOBPAwKkMoy9DVoZhobKiOL09SJ/BSUi0osCOmF0Tl8b4aTvmhITmHC6EeMgyKgY3cfm6z+A5DilZUDIY7Q7tABEap6Ucju5cFdiRVFkfGq+29Jc8tKS6I8DF4yZdFjtlGbNfj4+eFUleWlJ/MdLZ+Lj+h7thPRph7NVH4dTvwv6ljca+0LWfwCvFWeYAYgTz8Ca26X/Zy8DS5Nqiy9dwxN86cmjfPeu9T5LS+WQoNeRnKhnbDGLcVuaICcEC85AFKzi+aK/4WNn/z5oRqEvVhWn0261M7xYrauV5MJrkgi0v8XNGKAFIPxRsmlR1E+GzYmnYM0nlWkrNR/GA6dJ7WuysE2mAKWXbZXZ1DcvkgCExxNYXAzipgxjyD6F2c8qwbXVebx1biDKPdK47JgYktI5o01aIdj8BwGPtA+xoSwz7OYL4sRWUDF6js12wPDizejSCB05trPl26CtXt3+qMiw3YnZFLzW36DX4fL4dp+IFcMTTjKSZz8fBUHgazetoN82yU/fbY5Rz2Yw0jU7AHHy2YC72xxOLGNTQTU5ZlJiNtE5FEaGqtsF51+Fqhul3wUBspdKK+8KM2yf4nO7D/H1W1ZRUxC6G0MgqvPTObuYyzAsF6TslAh5ZXw5rm1fgt9+GpzyspgEQeCm1YW8fLI34n4seuq/D9seinUvZhGTAIQgCP8uCIJbEISxGT9PBtjfLAjCbwRBGBEEYXj6/5mqdjKzTFpp8IRXryeKIgdbrTxzqIODrdb4iHaHyqQNek9C6VZl2gtixTnpctNvm6Q0SJqlP9aVZXKsY3hhfcb+sA+CKYi4U/5K6DsVnf74wen2kKDT+S2ZyUpJJFGvozcOhMEW9LWoEZhYlF9A0AyII21DrI9A8b4yN4XmxeKEIYrS9+RrsCoI0v1uXHPNCZnRbskKNhQqroLWhasDEYr+g5fkRD32qfhYcXY43SQl6H0+H3U6gUfuWMtbZwdinz4+2i05poAU1DKmB8xIeufcINdU5co6RF5aEv22MIKpLW9D6RZJtNCLQg51M8cE718Y5MHdh3jo2mVhL4L5orYwjcbFLEQ5MRxx8F8URXpHHGRuuhNqPgLP3i8tKjhGZ/8ECEzcuq6Y545F9zpaEGNKp+PS59dWLz2HM0plB3nUJHBem7rUi6J4ZYj7Pg4kAV7J1d8CvwJuVaNjgDQwyquB/gYoWCXrrZ1Ddu597AAdVjsGvQ6n20Nplond92+mxBwf4h8BaXwJam5SzqYliBXn0fbhiFYLkxL0FKQb6bBOBPULj3sC6T94yV8plcjEkL5RB/kZgeswd9Tmsbexj7u3lEepV/NZ8NeiRmBiIUAJUgZE67t+Nx/tGObhG6rDbn5JTiotg+NsXxqa0nxcM9olBWz8ZXblVkmTnpRF8LdGAzkZEBVXwnuPqNsfFWmzjFOeFdpqe0G6kd4RB5W5US7H8kHnkG99JC9JCXp+dM9G7v7pB+SkJnFliI4SijOzBAOkrNcTT8POr/ncfW9jH5+sK5V1CJ1OQABcbg8JehljypPPzFfrL90Mp38P6++W1YeZzB0TTDjdZKUksrZUvmVyIKoL0nj19CLN7rJbFck8HLBNkpOWJAXq6h6AvV+Hb1TM3zHZ7Fd4tCzbhMcj0jlkj8qYbkGMKZ0OeKRmflnLf5UG/CyjTdyXYAiCUA58BPiyKIqDoigOAl8GbhEEoUzVg5dshk550VZRFLn3sQO0Wew43SL2KTdOt0ibxc59jx2Iz0jZXE48DWsidL+YSRArzkjKL7xsW5pNffMiWEUb6wte35tbI4kzxZCuoQmKMwPfwHbW5PNGQ+wUihfFtagRGGuzImmgskkv9JsBMTHlZsrliUjErDInZfFYcfYc9y1A6SW3RhOilIOtNzQNCJAmCaInrPrqeKDdEnoGRDw5YXQM2SkNMhlJNxr46b11/Mcfz3AqVoLNo92zAxA1N0PjH33qLLg9Isfah9kYRmZXQYbM72bKLtnAV8xZoyzeGJE4vK8xgShKpT5KjwlqCtIXbwZEpAKU0zT02qgtmNY7c0+By0+mzMSQtN0Pt64r4vlj6uuiLZgxpXvK/z0/yGcZTWIZgFgvCMKAIAhtgiA8IQiCv2WsdcCkKIrHvS9M/39qept6hCFEeahtiE7rBO45Ksduj0i71c6htjgfCNj6JJ/xvFrl2gxS57u/ycK2yshWALYtzWbfYhCitPVIAZtAGJKlQaW/m3UU6B6ZCCrUVJWfSrvVzsRUbGzHFvy1qBGcWJVgBNCAONE5zJqSyFbTluSkLB4nDH8ClF40IUp5uKfkiUOXXwlt+9Trj4q0WuwhZzVKuinxEYAIlgHhpSDDyKN3r+dvnzoWvlNEJEzapLILL8Z0yFvhU//sWMcwq0sy5GUxTFOaJdOK8+zLUH0j6ObYYCalgqADR3gBm2iOCXLTkrCMTcXPpFRJBs9LehwRcrZ3lJrCyDU3blpTxEsnelT/rLUxpbLEqgTjWeAXQDtQBHwTeF0QhLWiKM4tfE0HfN1thqe3zUMQhIeBh72/p6SksGfPnqCdcjgcs/bTeabYeu499oXwXi/7ejwIom8xJB0if3zrA6yF8Zt4Ut7zEkLiKlpl/M3ByBxtpXjgMKed89uccot0Drg5vv9tjvt4b6i4PSL7z7l55ZU+2Vae8URl53tMJOXTMxb481/rTqf5hV9iS6mITsfm8Farhywj7NkjCWnNvXa8FBvcPPrMq6zOif45v9CvRY3gbG4+wlHDDpxnrFE/9hUjVt73cc6/0uYh1QB79gQXxvJ33bg9Ig0d7pCeW/HOhobXaKwoxt7t+28xTg6ysul9DusW/t+qNjrPFFvsU9TLOC9yh1PJfuvXNLbFsuI2PI43udiW3MNAw/xn+txrZ6DHQ0sTmPpjL9D87gU3yzIF9oyfC2n/24pF7nr0Tf52nZ7UxOiMXwSPi23jE/PGt7muZeS89C0aKmfb9f2hyU1xqhDWPWliwMOf3u1k9EJoz9v1DY9yoexObD6OVevJo//5n2DJXCO7H9EeEyS53fz2hT1kGeNrTOrvuRMqy9tfZTSlkr4In09vnHFzbbGOPUMN6F12rg+w7+t79+JO8B+M1E+5+fnv9lCapt5nvVDGlJF+ltEiJk8kURRnKuh1CYJwP1KQYTvw6pzdRwFfy0mZ09t8tf8IcLHwsaSkRNy1a1fQfu3Zs4d5+3V+h11X1kFKaCUCWa1Wnji/H5gfifMgcPO1W9hUEQPV9lD56Tfgk49TnR6iyFUoWJfDK/so8fEdvHt+gGsne9m1a3XEh3mm9wDLN65gaRzUgIbNH/fAyhtYs+TqwPsZT1CQmQFrg5/XavDW709y47oitkxbp/q8dgDjkgH2nFbm+5XLgr8WNYJz/l/YcdMngjvHqEGzmV07r4OE2Sr9z/zqEJ+/sZqqfD9WujPwd90AfKfxbXZcfxWGMFYc4wZRhHP/RO4t9/rXFBJFePQ7fj8HjRlYW8BaJe+zcmyFX95E+QL8fL956i0+fvM1PhcV5l47xnMDvNnYz65dK6PZRZ88P3iYW3YuD9lRYRew9FQvP323mccf2EJyoj7oeyJmuB0GfZxLruvgh9som3Nv++533+W/PrGFzBBcSeYydbyb8/1j7LqhKvjO44PQ4iTvY5/zfV8/PkTZUBtcK/98jvaY4IDzDHlLs9lZGz/WhxD4uRMSTz0O135C0iOLgP9tfJd7bt0m2ew6RuGg/32v37lzdrbOHKYKujnZNcJndymYvT2HBTOmjPCzjBbxMrIRp398jSKPAUmCIFwMd07/P3F6m7qUbobOAN/kHOrKzZRmmZhr/y4AZVkm6iJQRledwfOQmCIJhilJiv8SjPomC9sqlVEeXhRlGKFoQADkr4ipE0bX8ARFIXhlb1mSxQfNlpikIXqvxbk3Fb1OiP9rUSM4U+OQYIxN8AGmtW1mZzmIokjzwBjLFAiClmWZYpOWrSS2HkgtCCxoLAiQmBp2WvVlha0ndP0HL8YM0CcuOKcR+5SL5ETfThK+iL8SDHkrjDeuKuC29cX81ZNHcLmjYCk60uV7rJeQCEuugQuvX3ypc8hOSlJCWMEHkEowOkO9l53+A6z8M//39ZJNsrXZvHjHBPo5bas1JqgpSKNxMVpx+nM1koHT7WHK7ZGCDwpwfW0+exv65pVHKElduZnUpARtTKkQsbLhvEMQhJzp/+cDPwP6gHmFiqIotgEvA98SBCFn+n3fAl4URbFd9c7KvNkJgsDu+zeTmpRAgk7AlKjHoBfINBlYoUCtk6qceFpSQVaapFRJVMgH9c0WtioVgKjMYf9CD0CEogEB01acZ9Tvjx/6RhwUBHHBADAa9CzLS+VMT/TFmARB4Eef3kiCXsCgF9DrBBJ0AhXZJnY/sGVBl+poAEOtsXHA8OJDiLLdaqcky4RubgQ6DCpzUxe+DkT3scAClF5yq6UAuEZgRrvDWyCouCqga0s80m61UybDmrsgjkQoxyddpIYxsbpnazk1Ben8y3On1A/aj3ZBRonvbWs+CSefvvjrG439XF+bF/ahSs3JdAyFGIA4+Qys/oT/7VmV0gTYIz9I4x2f56cnoRO4OD5Xa0xQW5hOQwzGPqri8YB7crY9ahi0DI6zNHeGw40+UXJo8IWgl1b1A5CcqGddqZkPmtWbAzx1sIOq/DSW5KRg0EvzO4DyeBtT6hOlxWRfJJul7XFArIoCPw08KghCCjAEvANcL4qibdrZ4gzwYVEUvU/Me4DvA03Tv/8R+EJUelq6GQ49JustJWYThRlG/uXmFfSOOKjISWFjWSb/8LuTfOf18/xtKGlo0UYUoeFFeEClOlxBkG5cM1bCxiZdOJwectNkCGoFYEWRdLP3eERFJgAxYXIMkoKnbpNRJqVQxgBRFHF5PCGnhu+syWdvQz8ri5S1uQqF9y8M8lfXLWPbshx+9m4zy/NS+fKHquPnQaERPrESoPSSVjRPiPJI+1BElsIzWRRClD3HAgtQesmpkpx9SurU7tHCJpwMCIAlV0Hjy7DyY8r3SSXaLHbKQrTgBEhPTmB0wqlij0JjbNIV0arulz9UxVeePaH+WHG0a7YDxkxKN8OLX5ImfcZ09jb087WbV4R9qKyURKzjISjvW5tBlwCZAQzuBEG6Xwyeg7wa2X0pMZt46LqlnOsbY3VxBhU5KdSVm1UZEyzLS+VC/1xZuwVOoPNGBg09o7NLlAxGyR7Sl0ND0xvw7GfgnuekBU0/3La+iD8c7WL7MuVtbfc29PHUoQ4ef2ALpkQ9h9qGaB0c55VTvXxme0VQUfaoYjBC/mq48T/nu5XoE+PCghNilAEhiuItoijmiqJoEkWxWBTFu0RRvDC9rV0UxdQZwQdEUbSKovgpURQzpn/uFkVxOCqdzSiRbK/crpDf0jfqID3ZwFXLc7m9rpRNFVnodDr+35+t5kTnME98EJuJY0A6D0qrUEaVJonJWfNsYQ62WNmyRLl6Kb1OYGleKuf6F2jKm8cjPVxDeRDqdJLFWgzSaoftTswyUjGvrcnljcbo23G6PSJPHmjn09sq2FSRxSc2ljLlFrXgw2JhqCXuMiAOtw2xoUyZNMwlOSk0L/gARBALTi9xYC28IBgNMwBRuhXa9yvfHxWRY8EJ0uq2IAh4VEzBDoXOECw4AyEIQnTGiv5KMKROQO1HoeFFxidd9IxMzF6tlokgCBj0OiZdQRyxTj4Lq28P3mBp+GUYABf6x9lZm39xfK7WmMBo0COK4HDGxglMFRSy4GzstVFbOGexzWCUtAnm/qy8DdZ/Gp75DLj9Bxm3L83hSPuQ4p/3kfYh/nvPWX56bx0pSQkIgsCmiixuryvlk5tKeeNs7OzmfdJ5WJrLFW+Y/1nGSfAB4kcDIr7JXwkylJX96RoY9DoevXsDzxzu4LUz/m0pY8KJp9Qpv/Diw4pzX9OgYuUXXrYvzaZ+oZZhTFilQE2o5K+Evugrfoeq/+AlL0264Q3Yomsb+urpXjZVZJGVIgVLagrSFl865OVMHGZAHOsYZp1CGRCVOSm0DCzwAISlCbJCsGvLrYaB0BwDLmts3VLgSy5JqVJm3ZyAWTzTZh2XFYAAyE5JZHA8dvbUAB3W0Cw4A+EdKz6r5lgxUAkGwOo74MRTvH9hkCuX5UY8SS/OTKZ7OECJjCjC6eekyWYwSrdAR/gBiKaBMZblRUesfFn+IsuCUCoA0TNKdYgirQBs/AwUb4QX/1o6V3yg1wlcV53H3gblAgJNA2N85dkT/OjTG8lJnZ+tfeXyHN6/MBhfdqv134ftX4x1L4KiBSBCoXSzrJtdfZOFbUt9pwCZEhP46b11fPvVsxyOpWes0yGl1zlGwW6FC29IN3WnSjWUqfnzAhAftFjZWqmsYuyCFqK09UJaQej7562A/ujrQHQNT1Asc4C1oyaPN6OcBfHz91q4/8pLE9QSczJdwzK8yDXim6HIhbAiYk4GxPikC7cH0o0GRZrPTUui3xYfNe1hYeuVAs+BBCi9mCskTQ+NwIz2SIGvcFhyFbS+F3AXURQ52GrlmUMdHGy1xnRQ3WaxU54tb9W9IMNI30isAxCSDkykmBIT+MmMsaLi381ogAwIgNwqmLRx4MQZdkag/+ClNJiobvdRKaPNnw7ATIrWS/uHSffwBEUhaFgpQW0cCVF6z6F9PZ7wzyGFAhByNV4AuParUonOG/+f311uW1/MH452Rdg7iX6bg4ceP8K3b19LRY7ve5EpMYGizGSaBuIkyDTcLo2NKq6KdU+CsvCMoWNByWY48BPY/GDwfZHSdb5+q397mpzUJH58z0Y++6tD/OiejdG3jXQ64JGaeSUR/HeldPN/uFH5NJ3UPBi7NAEdsTsRRcJWVfZHVV4aTf1juD0i+oWmAyE3AJG/Co49rl5//NA1JC8DAqQAxPfeOM8dm0pV6tVsjrQPkWkyzLq2BEHAbErEMjZJto9ItsYCI1xBPqVIK5Jq8qc53jnMulLlStgEQcCUmMB4hDXlMaP7WGj6DwA6vaS+P2WHxNj7k8ctE1ap9C4cllw9LTTtO8W9c8jOvY8doMNqx6DX4XR7KM0ysfv+zbIdHZSgd8RBQbq8cYhXiHK1T+f26NAxZOeaqlxF2vKOFe977ABuj0jvqEO572ZqPKjelGfVx8l+6wU23X5teMeYQYk5mc6hAAsAJ56GNXeE1lhiCugN0hg2lIDFDEYdTsnJIEqlmDUF6XzQEvtFsZnXt04UeeL8/vDOIcsF2PKXEfVlxO4k1WiQP0YXBLjpEXjq03DwZ7Dps/N2WVmUTtfwBEPjU5hTwp9f2BxOHtx9mK9+pIa1pZkB991ZI2VdLMsLQb9NbT74sfT9LIBSYy0DIhQK10DviZB27Ryyk5OahNEQ2Me5PDuFb9+xloceP0J/tJWb3VPzgw9eJoZ8i8BEypwMiP0tFkX1H7zodMLCVR4ekxuAWBGTEozu4QlKZAYgVhalc6F/LHgNqEL8/N0WHrhy/up4TUEaZ+NkNUIjAtxOEHTSxDVWmLLBfmlgebR9mPUK6T94qVjIQpQ9x6Bwbej7Zy8Hi+aE4RfvamW4A8sS/5bioihy72MHaLPYcbpF7FNunG6RNoud+x47EPVMCKfbg04QZE9Q8uPACSMcC85AlGWZcLpFOoYmlPtuXFMhKeE35tzAR4T3SUyIfKpQYjb5d8Jwu+DCa7B8V+gNFtdJte4yaeofY2mUyi8AagpjnwEx9/qe9BD+OTTcEVgkNAQae0epLQhzsq5PgE/8XApYNbw4b7MgCNy0uoCXToZfbjbl8vDQb47w6S1lXFcdPPvnupo89sZA52wejlE4/5pkY7sA0AIQoZCQJAl6jA0E3bW+ycL2paHpGqwpyeSfbqrlwd2HsDlir96sKnMCEPVNFrYvU1b/wcvWpdnsa1pYnufAtAWnjACEMUNaxfBEV+BIrgYESA+FLZXZfNBsValXl+iw2ukcsvss76kpTKdBC0AsfEY6AtcvRwOdTpoUTg/elBSg9LKgnTBCteD0klsDA2fV6s3Cx26Rgl7hYjBCSq5P96RDbUN0WidwzxFwdHtE2q12DkW5XLR7eIKiTPlZmFIJRmwDEF1DkWtAzORQ25BP/aSIvhtbd0iLHa+0CRjTc6C/Qf4x5lCaley/BKPlLSjbJi/ztnRzWEKU5/vHWB7FlerizGS6AmV+RAHFrm/XpFQCEWHgv7HXRnW4AQiQMmDufBLe+ga01c/bfOu6Yl441u3jjcHxeES+8uxxtlZmc3tdaBm7JWYT9ikXw3YVFm/lcGQ3rL1TyiZcAGgBiFApCU11V9J/CH2QcE1VLvduq+Dzjx9hyiXf13jBMKcE40CLlU0VymdAAGyrXKBClLY+SMuX9x6vJ3YUCXdwKKWpqS+++ov3W/nzK5b4TLGsLUijcSFmx2jMJtYClF6SM2FCqs9uGRyn0k+daLgszV3AAQi5tcK51VoAIhCj3eE5YMxkydXQ8u68l1sHx0nQ+842MOh1tEb5HAxH/wFinwEhiiIOlztoBqwcVPluRrtDslJ862w/prq7pNXmCCkxm/yXYJx4Wr4IukxtNi9N/dEToARp8SUrJZHBsdhpkyh2Dg21KuI81dhrm23BGQ4p2XDn4/DHv4H+2Q5KpVkmRMTAmiN++MYrjaQZDTx0bQjiyTO4piqXt88FX6RWDbcLjv4a6v48dn2QiRaACJUQbnaiKHK8c5g1JZmymv74xhK2Lc3m7545HnMLKdWYkQFhGZskMUFHmkJibXNZmpsynWq2wAI6Y73yB5j5K6HvlDr98cPYpCus72770hz2NVlUTecddTh55/wAN63x/TlWFaRxtk/LgFjwxFqA0ktaIdh6aRkcpyLbhE5h3ZkFmwFh64OUHHkrZbnVmhVnIGy9kWueVFwFrfMDEBU5KX6fl063x68Am1q0WeVZcHopyDDSF8MAxMiEk8xkZcc1qnw3I11BAxC9I5LeRNq6j0HjS5JNeARkJBt8Z/pOjUuCkuVXyGsws1zKhJOZASplQERXd62mMLaln4qdQ5YLkC1vYu6Lxt5RaiLJgPBiroA/+4lkzzk6O+Ph1nXFvHBcXhbEY++10GoZ599vWSlbI2RHTb6i7huyaXhBCjDL1ESJJVoAIlRKggcgWi12is2msOrlHrp2KZkmA//1yiIdgKXkwLhUFrG/2SorS0QugiCwuiSDk10jqh1DFWy9UqBGDlG24nQ43SQlhLe6k5yopyzLxHkVLal+e6CdT2wswaD3fQ2mGw3TbgWLNNB3uWBtUWQlJmLSCsHWzZH2YcXLL0AaODYvxABEz/HQBSi9ZC0Fa7Mq3VkU2BTIgCjeCJ2H5tnY1ZWbKc0yzdNc0OsEyrJM1JVHd1DbNijfghMgLy2J/tHYrTR3WCcoVcABYyb+vhsBwv9uRrsgI3AA4o3GfnbU5ElClQWroGO//OPMwWjQY59yzX6x8WWo/nBobjkzEYTpsi15Y+YOq13x7ygYNQWx1SW7eA7NmVPLvr4Hz0fsgOHxiIxMOCMSiJxF4Vq48T/hybtgYvjiyzetLuSPJ3pCXvD644luXjndy//euT4sAft1pZmc6hrBFYuFT1GE/T+MWBw02mgBiFBJLwT7oCR+5of6JgvbKsObWAuCwL99dCUdVjs/f0/llHp9ov8oWbI5JHEi+cc0gEd68OxrGgz7cwqV7UsXYBmGY1TSdZBD/qqoBiDCLb/wsqM2j9dVKsNwuj08faiTuzYFFkhakpNCq2UBTuo0LhEvJRjTVpxH2ofYoMIkLd1oYMzhjC+P8VDoOSZP/wEu1a26YlxHG6+M9kjnWyQkJEJm6bxAjyAI7L5/MwXpRgRBmtwa9AIV2SZ2P7Alao4BXtqsdsqy5K/sG/Q6XBGu1EdCx5CdUoUdQ7zfTXm2CYNewJSol/5N0nPTmqLwvpvR4BkQbzT2XbLfXPNJhcowfOghnHwaVofofjGvwU2yyjAmptwY9LqoO6TVxNiK03sOZZoS0euE8K9vBSw41bhGWHodbPuC5I7hkgKQ5pREijOTOd0dPPBT32Thh2818ZN7NoZdPqXXCawvM0ddLweAjg+kMncFslOiiRaAkEPBaug96XdzfXPoApS+0OsE/ueT63j1dC8vykwdkoXBKFltFqyFLxyCr3Zc+lHDgtOLPhFcUxxuG6KuQt0VlW2VOQsrABGuwnnWUrA2Kd8fP3QPOyiWKUA5kx01ebyhUprayyd7uHJZDhmmwCmwNQXpNPZoZRgLmuE2MJfHuhcXrTiPtQ8HteoKl+yUJCzjC2xS3n1MngOGl6zKqN7PFhS2bul8ixQ/ZRglZhNf2rGMuzaXsjQvhf+9cz2vP3xNRPf7cOkcmqA0K7zjGg16JqaiK8zspXPIHna/A1FiNrH34Wt44sGtfP2WlTzx4FYO/fP1fNBsCW+sGKQEw+F00zI4TnX+dJr80h3SORNhcLB0rhPG2ICU+VmwKswG/Tu7+KJpILoOGF6q4sB9q8RsYm1JBt+6fQ11eQKf3lIu//q2NEUcgGjosVFTqIII6Jo7YPkN8Ie/uFgudNv6Ip472hXwbY29o/zbC6f4yb11ZJoiW3zdWZvHG7Fww9j3Pdj2xegfN0K0AIQcgthYne4aYWVRZMIqRoOen9xTx4/eblLXyWG4DUxmyF0OxvRLP2oFHwBScxno6yDNmIApUV1f+9KsZHpHHVGzfYyYiaHw/N31CZJLy2R0Hm5dw3bZDhgzKcxIZtLlwarwhEoURX7xfiv3XxF8Vby6II2zvZoQ5YJFFCWr4ISkWPcE0guZGupEECA1SZ172oLUgRg8BzlV8t+nOWH4R4kMCIAl10DLOz43ne0b44baAj68qhCXR4x65gNI93Kn2xN2qV9BDIUoO6zKWnDORBAENlVkcXtdKZsqskhOTOAn99Tx43fCGCuOdgXUE5Hc3HIuff96A1ReJ1llRkBplokO64wMiNN/gFURWAYWrZeCnSFyoX+MZbnRD0CkGw1MON2xSc+fxuX20Gqxc9u6Ym5ZouPCwJj863t8QHLSiYCzvTZqIxWg9Mf2L0lOcnv+CUSR62vzefNsv9+S267hCf7qiaN89671igRar1qewzvRFqK0Nkv6emVbo3tcBdACEHIo9Z/udaF/jCU5KST4qT2XQ4bJwE/vrePfnj/NmRDSh8IiHNXhSEnN5/TZ86qXX4D0sF5XmsnxjgWiA2Hrka//4CVvpSI2WaHQNeygOEKLseuqc3n7nLJR4oOtQxSkGykLoW64tjBNs+JcyIz1hX+tKE1aIWMDHaxTKfsBYEluCi0DCygAMTYgBVPDsWrTnDD8YwtDpNgXhWsljQ4fZT2NvaPUFKaxoczMkVikEgMDtklyU8MPLuZnGOmNkRWnKunlAcgwGfjJPXX8+wsyx4pOOyT5n4i/3jCj/MLLmjvgxFNh9lSiNCuZzpkZECefgdW3h9+gIVlaNLOHZu99oX+M5fnRD0AAVGSn0GqR78qgFKe6R1lVnIEgCOSZBAZsk75FQf3hGJH0QCIMSnrvMaogCLDr/0mC7vu+i9GgZ32Z2Wc29LB9is/tPsT/uXVV5I4c06QZDeSkJkXXNWj/D2Hr5yP+XmKBFoCQQ77/Eoz6Znn2m8Eoykzm+5/awF//9ujsG7YSiCI0/hFqbla23WCk5tHa2sK2pTlROdy2ymx1s0iUxNYbki+3T6LohNE1NBFRBgTAjtp8Xle4DOOn7zbz4NWhaQJUZC/AFWWNS1ib40OAEiC9CNdwlyoClF4qF5oQZTgClF40Jwz/uCeVyfrRJ0ile3MCPaIo0jvioCDdyPqyTI52DEd+rDBotYTngOGlID12Thg9ww4KI9BICoeizGS+d5eMsaJrMqDOlyiK7G+2sHXuQlHJJhg4J01Ew6TEPCMDwtIknc8ZJWG3d7FfIZZhnO+3Rd0Bw4ukAxG7zMt9TYOz5ihXV+Xy3nkZ42MFyi9AKoOpzFHxO9Dp4GM/hvOvwYmn+dj6Yp47NrsMw+F087lfH+bz1y5VXBB/R00ee6NVhjExJGWz1d4aneMpjBaAkENCorSyY+udt2nfBWUDECCliv/Hbav43O7DDI1PcrDVyjOHOjjYao1MlKzjA8hbIZVcRJPUfKz9Hawvy4zK4bYtJCHKsb4IAhAroiZE2T08QUmEAYg1xRk0dI8qZpPaMjiOZWwy5Elggl5HskEvL/qvET/EiwAlgCEZ5+SEKgKUXipzU2gZVM85RnF6jsoXoPSSvRws5xXtzqLA6QC9giVHS66epwMxYJskJy0JQRDINCUy6XTjcEa/hLHNMh5SJps/YlWCIYoiLo/HrwOTmlQXpPH/TY8Vh+1ByhtHuwOWXzT02KjMTZ0vxicIUPtROPNC2P0sMSfTOTwdJIk0++Fio6ELUbYO2inPjq6lrJeawrSYak/NFcmXPVFWIABhn3Kh1+nCcgqURUIS3PkbqH+Ure7DNLZ2sv9MC3+ob+BQYytf+c273FRj5uY1CmjqzEHSgVBHaH0eh38J6++Rgso+EEVRuXmjCqhbiL8YKZ2241xxy8WXPB6Rc33q1DVtrczmrs2lbPvPN3CLIga9DqfbQ2mWid33bw6v3vDE01I6XZSxCJmUGBrDVpmVS1FmMkP2KRxOd9SOGTa2nvAFxvJXwdv/rWx//DAwNklOBOmxADqdQF2FmYOtVrYrkA3z2HstPHBlpax6xqr8NM712dhYHobuhkZsGWqRsn7iAI9HxOHRUZmp3qO0NMtEWwxTd2XTfQyqbwrvvYkmSejO4w6vhGOxYusJP0DtiyVXwTvfgs0PXnypsddGbcGl1OjVxRmc6Bxh85Lo3iPbrXZqC8MfS+VnGDkTA8tDJZ6NkbClMpsv7ljG53YfZvcDm/2PeYLoP+xt6OP6ueUXXtbcAS89DBvuCauPpsQESSBUFOHM8/DnfwqrnVmUboYjvwq625RLWvBQffLrh5qC9KCCiGox5fLQPTwxK7NoY7mZf/r9SdweMTRXEMv58HR9ZnC+b4zqaJXAGDPg9l+i+94G/ih6YIaJSx3g7s2E7WcV170rz07BMjaFzeEkzRhYED0iXFNw7En4rG9dls4hO/c+doAOq12ZeaMKaBkQcinZDJ2zo60NvaNU5aehU8HaRxRFfrGvlUm3B6dbxD7lxukWabPYue+xA/IjWq4paHkblu5UvK/BODlspCZ1IviOCrKx3MzhGNWyysIWQQZEah6M9/us6VUSj0dEAEXO8x01+exVoAxj2D7F/mYLu1bK0wSoLYytLZZGBMRRBkTz4Bj2xByEMfVWPJIS9Lg9ol8hrbgjXAFKL+YKGGpVqjeLA5tCApRe8ldLWXMzLCul2uxLE/8N5WaOtEf/2dlmsVOWtfBKMDqsE5RG0G8l+MjqQj6yuoAvPXnU//1itBvS/Zc9vHG2n+uq/QQgcpbD1LjURpikGg2MtRyQLAOTM8Nu5yIZpZJAqydwtk6rZZyKnNh9PxXZpphpQBzvlFyaZi7SGPQ6VhZncLxzOLRGFLDgnHuPURvRlIUg+s601TuGEd2Tqhz3mqpc3jmncvn36T9Irh/GjHmbRFHk3scO0GaxKzNvVAktACEXbwbEDOqblC+/8HKobYhO68S8uaXbI9Jutcv3nG3aK6lgJ0RmNxMO+/v1lCZGd9K3bekCseOMdIUrowRGOpXrjw8GxibJTVNmhefK5Tny6g/98JsP2rlzc5ls8VfNinMBM9QSNxoQR9qG0WcWSwNgFSnKTKZ7OLrB27AYt0gDIj8poSGRW6UJUc5lVCELTi86HeTVQv+l0r3GHhs1MzIgYiVE2WaNXAMiFiUYnUN2SiIUaFaCz1yxhMrcVP71+VO+JxojnX4zIAZsk3hEyEsPsCq8+nY4+WzY/Ss1JzN55EnlRNAFYfpcPhNwtwv9YyzPU0n8MAS8pZ+jMSj99LqazOX6Whm26JYLUtAoAhrm3GPU5kj7cETbw0Uqb1GxDEMU4YMfwpa/8LnZO2+cG4QMe96oEloAQi6peTAxPMsPeX+zhe0qBSBaB8dJ0PtecTbodfLVVk88FX33C6SIXH1/Ahnu0NSKlWJrZRb1zQsgABGJBgRIThgq60B0DUcuQOklNSmBvPQkmgfCr22fcnn4/ZFO7qiTL2JVUxhbQSiNCJi0+Yz6x4Ij7UOk55aBLfwVwVBYslCEKHuOhi9A6SW3RhOinIvSGRAg6UDMsOM822ejKv/S5GB5XioXBsaivlo2FmHqcnpyAqMT0Z/kdQ5NRNUBIxD/cGM1E1Nuvv/GhfkbR7sho9jn+94628911UFsFlf+GZwKPwBRnplIUttbsPxDYbcxj9LNkrZZAM73xc4Bw0t1QRrnYpB56W+R9JqqXN4KxZFMFGHKLrlgREBj76hijhOh0B4k4yTY9nDZWG7mWPuwelmLre9KmYKZZb43Kz1vVAktABEOhWuh9wQgees2D4yzTCVl3YqcFL9ifU63h4ocGYI6jlHJrrF0s0K9C502i50Mcy66CBSUwyEvzcj4pIuxSVdUjyubiWEwZob//vyVs1az1KBraEIRr2Qv19fm80YEasEvHu9mR01eWIPVnNQkLONTcZOKphEiE8OQFGXx3AAc6xgmr7hC9QyIytwUWiII1kWN7mPhC1B6ya2Ryjg0LjEagUaQP5ZcDS2SEKXT7WHK5SEl6VLmik4nUJyZTOdQ9DJvRiYir5sWBAFBEPBEuWSpw2qPeQmGF0EQ+MYn1nCwbYinD3bM3jja5bcEY29DP9fXBilnTMsHUw70Bc448Eed5xidaeuVcXTxUrIZOgI7YVwYGGNpbmwDEDUF0bcAdzjdDI5N+hy7ZZoSMSUm0BUsuy7SBTKkRcj+0Uny06OnkxJMzDYSsdtAJOh1rC7J4JhaTkL7vg/b/srvZkXnjSoSkwCEIAj/JQjCSUEQRgVB6BEE4UlBEEqDvOeXgiA4BUEYm/HzjWj1eRYzyjBOd4+yctpbVw3qys2UZpnmicTodQJlWSbq5KivN7woqRjHwC92X5Plkv1mlCd9m5dkcbA1upkXsvB+HpF8L/nqZ0B0DysbgNhRk8frDeGlqYmiyC/3tfKZK8JPxS/KSKY7Rn7xGmESR+UXIxNODHodieYSaYVaRSpzUheGdWwkFpxecpZrJRhzUSMDIrdGEpZzu2gZHKcyd/6gdENZdDWU2i12KhSYFGSnJGIZD+IGoTCdQxNxUYLhxaDX8YO7N/DEgXbenBno91OCMelyc67fxsqiEAK8az4JJ58Ovp8PVgzuoT5FYQ2ywrXSvScATf2xD0DUFqZzNsqZl0fah9gYYJ6wsyYv+EKQAuUX/bZJ8tKTVJsr+WJDEMe9YNsjYUdNHnvDHN8GZOAcTI5CyUa/u9SVm31mY4U1b1SRWGVAiMBngBygdvr3F0N431OiKKbO+PkHFfvon5JNF4Uo65tnW9sojSAI7L5/M+XZJgx6AVOiHgEoyjSy+4Et8i7mk0/D6ui7X4D0OW1fmi2lcE1GWQeiMpv98awD4RiOXIwptwb61U1b7hqeoFjBAVZplonRCRcjYaTL7muyUJGTElFApKYgjcYYqKVrRIC1BbIqY90LQMp+WF+WKa0MqRyAWJK7QEowBs5K96JIMGZIzwgtO+kSkbgk+UMQoGA19B6nocd3anS0hSjbrOOUKWCTWJARfSHKvlEH+YG0E2JAalICP723jm+80nhpNdblkNxm5nCgxcqWJVmhjSlrboLGl2aJmIbE5BjmkQben1ou733BMBilseW4b10pt0dkyu0hOTG2zjrSmCO6499gGnU7a/N4I9hEWQEBSn/3GDUR9Em4/WQWu42ZCEpaG8/hmqpc3j43oHzD+38AWx8KuIsgCHxp53JSkxIw6AUS9Tr0giSEKnveqCIxCUCIoviPoigeFkVxShTFYeCbwFpBEOIjLBOM/FXQewrwruyrF4AAKDGb2PvwNTzx4Fa+fstK/vLapdy2tkje5Gu0RyrByI3MRiccRFHkdNeIFFlPzYexyN0P5LClMpv98awDYeuVPpdI8FoJudRR9QWpBEMpDQgv11Tn8k4YN+mfvtvMg1dFthJeU5iuOWEsNIbixwHjSNsQG8rM0mqiyiUYhelGeuI9W8dulSYBkQhQeskoVl1Ud0Fht4JJBTvM6TKMxl4btYXz67vXlWaql0bsgzaLnXIFyhjy0430RvF68dZ6h2RnGGVy05L44ac38vfPHKe11+K39GFvQz87a0IchySlSlkH7fXyOnP2ZXS1H6FzRIVxSskm6PRdhtFhjcxZRSmyU5OwRrn0c3+QRdKlual0Dk1gnwpQpjx4XgEHjOgKUAJgMKL/8lnEr7Zz+FMnqF//Tfqq7kb8ajv6LytvwTmTTFMiKUkJdA4pqDMxPihpndQEt7l+/lgXjz+wmSce3Mo/31RLsTmZ1/72akWzmCMlXjQgPgS0iaIYLNR+syAIFkEQmgRB+JEgCEHUclRCnwCp+UxZO+gaUiZlMBiCILCpIovb60r5/LVL2XOmT95N7NSzsPoT6nUwABf6x6jMTZGcClLzpHqyKJKVkohbFMNaaY8Ktl5IUyC9VmX1+O4RB4UZyt6wd4aRpna+z4Z9ys2aksyIjl1TkEaDlgGxsLA2x00JxpH26QCEKQfs6lpu6XQCBr0OhzOw1VxM6TkmTUqUILdGK8PwokSJnj8qrobWdznba6Pax+pkRrJh2sYtOhpKbZbxiBwwvORH2Qmjb9RBgcLPRiVZkpPCf9++lq//5nUmTfNr+UVR5P0Lg1yxbL5Tgl9W3yGJmsvhxFMkrL0Tp9uj/CS8dJNfIcrz/WMsV0mnTS7F5ujpqtinXNgcroCuJoIgcMWyHN6/EGCRztIUcQDibK8tqhacFzEYEYwZbKwqZ9uHP03+0BGEpHRVgw9erq8NobxFDoceg42fAV3gTJ4L/TbGp9ysKzOzqSKL+7ZXUF2Qzunu+FpwU2CpIjIEQbge+Dfg40F2/R7wVaAPWAr8EHhBEITt4pw7mSAIDwMPe39PSUlhz549QfvicDhC2g9guSuHc7/7Gbm6Lbz66qshvUdJ0jxufvjMHpZmhDYo2XriFxyp+QpTIf59SvJmpwezCHv27GFpn42x0VfpOxtdQbV8wc2Pf/86a3PiJeZ2iaKBt0maGqUlwu+mcjQJx97f0p2rzmrs0IiLt9943ec2OdfOTDyiSP1ZNy//qS/k1aNfN7rZmC2EdbyZON0iR5vcEbejET02NR3huO5qphqiK2Y7F48ocq7TzZmD79AgCFwxZuP9V16RPUmUc90ku9w88cJrFKfG3yorwJKu55hKSKdLgeupZMCNvvd52prjOOASJQzOUdZPChxQ4z4lilzReYazk900HrJwzsf5m42bn//+darM6p93xy64qEvswXI2+LECXTt9/R46x0RyR6LjpnJuWEQc88T9s+TGjA5eafXAS69gTLj0GXePiyS5PLzzpu/nuy8Ej4srzrzK+4Y/IuqCC4cmTg2zoaeJ/cc6EKZc/O6Pe0hLVO6cSpqcYM2FPRx0b5u37ZU2D2mJsGdPu2LHCxejw82Tf3o7KmPR0xYP+Tpx3nk599rJHPfwq9fa8HT4nthu7zhF/cFziLrmsPty6LyL69J66TsT2+fXBqeRs8//gvFk304wSpI0LvLUBQ/5o5EH03WeKbad+CX7V/8n7iD3GV9j5CWCh+88188dy2NbhjQLURRj9gPcDAwDHwvjvRVI2hFVwfYtLi4WQ+GVV14JaT9RFEWx8WXxyE/+Unz6YHvo71GQPad6xK89dzK0nfsaRHH3bep2KAB/sfuQeKprWPrlwM9Esf6HUe/Da6d7xa+/cDrqxw2Jdx8RxaO/ibydxpdF8ZV/irwdH4xMTIm3fP89v9tlXTtz+JvfHhUPtFhC2nfA5hA/9MjbosvtCft4M9n1P2+LE1MuRdrSiALfqxNFjzLffSQ09oyKn/3VwUsv/PR6UbRbZbcj57r5xp8axD+d7JZ9jKjx1D2i2H1cmbZa3hPF57+oTFsLnZ4Tovj0fao1P/nUA+JX/ucnfrc/daBd/P4b51U7/kx2fvst0RPi9R3o2jnUahH/7uljSnUrKM8c6ojaZxQRx54UTzzxz+I9P/9AnHS6L778w7cuiLvrW+W399LfieKZF0Lbt/6Hovjed0RRFMW//e1R8Vj7kPzjBeN7daLocs57+W+fOioeaZN/f1aDZw91iN/bey4qx/rPlxvEl07Mf2bMvXYmnW7xum+9Kbp9jatcTlH8/uaI+jHpdIs3PPJWRG0oxgc/uXgeqo3H4xFveOQtccwx/5yUzeHdovjqvwbdzd8YeWLKJV73rTdFp8vt553qAHSKfubmMVsOFgThbuA3wCdFUfxDGE141W9iE04r2URq/1HV9R/8cW11Hu+dH/RrtTKLGIpPejwi5/ps1HrTO1Pzo16CAbC5MosPWuJUB0IJDQhQ1QlDcsCYk7LmdEi6Io5R9C77xf/jlJf6urM2j70NoaWpPb6/jbu3lilWa7ssL5UL/QvA3lADnBOgT4qJi89c5imLpxeqrgOxJCfOhSj7GyGvVpm2cmsktW8NdSw4Z9CZsZGdSf4zBTaUZ3I0CkKUDqebRL1OEYG0aJdgdA7FjwVnQEa7WF27kk3lZr76uxN4PB4Otlp56kAHOSmJ8ssi1nwSToTohnHqWVgllQGXmJPpULI23kv+Sug7Ne/lpv4xlsZJCUZ1FK049zdb2BqCSH5igo7q/DROd/soSR1ug8zyiPrRPDhGZU58fP5U3QjnopOpJAgCVy7L5f0LEZZoiiIc+Als/lzQXf2NkY0GPRvLzOyLI0H+WNlwfhH4PnCzKIpBzwRBEIyCIHxCEISM6d8rgJ8Ah4HzavbVH45EMwnucUpSYxPDSUzQsXVpdnABP49HUiuuvTk6HZtDY6+Nqvw0dN6LIQYilADpRgMJeh3WKFtzhYStN2KPZQAySlUTbptnwel0wCM18F+l8F+lXH/wMxf/zyM1soIQVy0PTS3Y4XTz4vFuPrHRt4d5ONRqQpQLh6E2MEc2EFKKiwKUXtKKwNat6jErc1NpGYjTAMTEkCRMpw+eih0SKdmSrobmhCGdV0pbcM7gSMIaVjlP+N1emZNK88C46sJ50iReGYG0vDQjAzb1BJnn0mGNLwtOv4x0QUYxX9yxDLcosuE/XudTP91Pm3WcL/32KDsfeVueaF7xRkmgcGI48H6WJkgwSuKyQEmWiQ6rCjoIJZvnCVGKooht0kW6UaF7U4Qsy0vlQp/6ix6jDidOt4eslMSQ9t9Zm8/eRh+Lg4rpP0RZgNIfmaUwNSYJ+0YBOQtsfmnaKwX3MwKXjTicbl4IMEb+2PpinjvWFVlfFCRWGRDfA1KBPwmCMDbj5yrvDtO/3z39qw74a6BFEIRx4G2gDSmAIdMHSBmOtg9jTa8N6j2sJtLJFGTQ2/GBFBVOis3Fv69pkO3LZkRgYyBC6WVrZVZ8umGM9SkjQikIYMqGMeWtf+Y5YLinpEmHLyaGpO0hkpFsIDPZQLsl8MDnuaNd7FpZgClROema6nzNinPBMNQSNwKUJ7tGWFOScemFKGRAVOak0BKvGRA9x5UToPQSo2B13DHao8zzwQ+HR9LJdFv9Bo11OoHSLBNtQe7PkdI6aKdcAQtOkBZoQsoOVYiOITul5oWQAdEN6dIk5mTnCCMTTpxuEY8oaSK1Wezc99iB0INNggArboWGFwLvd+JpKVtimlKzSVl3gIsNb54nRNk94ogr5X+jQY8goLqg8MEWK5uXhO6cc211Lm+e9TF2tFyA7KUR9aWhxxZ1C86ALLseLuyNyqE2VWRxsNWKxxNBALf+Udj2haC7PXe0ixsDjJG3VGZzrGOYian40FaKlQ2nIIqiQRTF1Dk/787YJ1UUxd9M/98uiuJVoihmiaKYIopiuSiKfyGKYm8s+g9Q3zSIvmwLdB6IVRfYWGamsWeUsckACtUnnpp144828yyAYhiA2FaZTX0cpR9dxG6FZIUcaPNXQr/yZRhdw+o+xHfW5vGGr+j7NKIosru+jfu2Vyh63JrCNM72aRkQCwJrfFhwDtunSErQYTTMEHNKKwKbugEIc0oiQ/Y4zOAC6D4GheuUbTO3GgY1JwwpA0K9EozG3lH0ZfNXjmeysdzM4TZ1yzDaFLZKNBr0URtoW8YmyUkNbaU5pox2QXoRh9qG6ByaYO6UyO0RabfaOSTnu15zR+AyDFGUAhQrbrn4klSCoUIGRMEa6JmdzXO+z8bS3DhJ/59meX6a6qWf+5oC22/OJSc1Cb0gObrMwnJBAQvOUZ82vzGj6kY490pUDpWYoKOmMI1T3WEKZ/edBrczaIA/lDGyXidwfW0+r8l0nlOL+LMEWCDUN1soXXstdMQuAKHTCXxoZT57TvmJw7imoPU9WLojuh3zHt7toXlgnGUza+8MyeCKXmrkTLyRyLhCaYs1lXQguobnZEAojJT+53+1861zA9QUppEfwE4qHIozk+mKkiWWRoTESQbE0fZh1pfNCRimF0qriyqTnmxgxB6HdsJKWnB6yanWrDhB1QwIj0eyp05adi20vut3vw1lZo6orAPRbhmnQqEMCICCKOlATLk8JOiU0a5QHZcDDMm0Do6ToPfdX4NeR6ucTKvspVK7/so/uw5DznIwXsoYK8ww0juiwnM3IVFazJmROXWhf4zl+fEVgIiGBfiBFitblsjTqNtRk8ebc8dhlvMRByDarXGWIVS8UXpmuaNjL7yzJj/8Moz6H8C2LwbdLdQx8q3rinjuaHyUYWgBiDDweutmL1kH/WdiWqd627oANT0XXoPKa5Wry5XJ6e5RVhZnzH8wCzrwRD8FKCUpgZSkBPqjKE4VFMcIGBVMTctfCX1nlGtvmu5hdWtcl+Sk0D866Teb5+fvtvDZKysVP64gCGSnJka1XlgjTKwtkKX8OSCXI+1DbCifE4BIK1Q9AwK8QpRxKJra3wB5K5RtM1cLQADTGkHqBCAulg4suQpa/Acg1pZmcLxzWJU+eGmz2inPVm6Skp9hpHdE/Wd9z8gERXMFmuMR54SkwwBU5KT4LVFxuj1U5MgMBK36BJx81ve2E0/NE0FP0OvwiESWlu6P0k2zFgYv9I+xLM4yIGoK0lTVnhoan0InQIZJ3tjf50JQhAHQYfsU6UbDJR24eECnl/RC5pTrqMW11bm8dTaMAIStTwqULP9Q0F1DHSOvKEynd8SBZSz2Y14tABEGh1qnFdB1eik1cqQjZn1Znp/GyITT96T6xNNSelyMqJ9bfuElJSdqAjBz2VaZTX086UCM9SkjQOklr1aVEoxh+xQZyeoGsq5ansN75+fXIJ7pHkVEZEWROjWENQXpnNWEKOOfkU5IV06ANFyOtA+xoSxz9ovpRVHJgIhLHYiJYSmzLUHhFPTcahjw785w2eCeBIM6E9xGrzhcehE4hmHKd11+mtGAx0Pgcs8I6R6eoDBDub+zIN1Iv039AESHdWKBOGBc0n+oKzdTmmWap5Sv1wmUZZmomxtgDcaqP4NTv5v/utsJTW/C8hvmbcpNTWJAjUlQyeZZpdFSBkQcpf8DNYXpNPaqlwHxQYuFLTLKL7zUFKTRPDB2SZ9ialy69+jCnyo29triq/zCS9UuOPenqBwqOzWJBL1OfkD04E9h0wNBP385Y2RBELh5bSEvnVR/wSQYWgAiDOqbLWxfmiP9UrI5pmUYALesLeKF43MGv44RafWoZFNsOoVUg7bdl01pah6MxUa+Y/vSONOBsPVAqoIBCGOGNIhUMLXM6faRYqpPhAQ/GRGCHpzyJ0k7a32nqf38PXWyH7xUF6SpOhjQUACPGxBBr5wAaTi4PSI9vvRQolRatiQnNf4CEL0nlC+/gKhllcQ1rknJelYlGntmWGSXboGO/X73XVuayYmOYVX64faIiKK0Mq4UBenRyYDoHLIvDAeMaf0HkCYhu+/fTHm2CYNewJSox6AXqMg2sfuBLfLLSVLzpJ/eORaYTW9CxRWQMP8cLs1KpsOqlhClNCYXRRGrfSpkJ4hoUZRhpGdYvXOzvsnCNl9j7yAIgsC2pTMW6azNkes/9IzGlwCll6U7pPMzSuyoyeNNOVkQU3Y4/RysuTPornLHyLesLeL5YAYGUUALQISB5K07rS5buiWgeFM0+OjaIl6cG4BoeBFqP6qctoBMnG4PXUN+UipT82MmRLmhXP1aVlnY+iAtX9k2s5dKDw6F6B1xUDB3ZUqnh4wS+JtT8NUOXt/0S/hqh/Rz66Pw7GdlWXEC1FVIQmcz0zL7Rx2c6RnlmqpcBf4S39QWqpsOqaEAI50XV+9iydlpW2GfA3RdgrTipyKVuSk0x1sAQg0BSpCeXcnmmGXLxQW2HmUz5ObQ2Dt6yR5vyVXQ8o7ffdUUouwenqBQYY2h/IzoaEAsGAeMaQtOLyVmE3sfvoYnHtzK129ZyRMPbuX1h68JX2x6zSfh5BwxygAi6KVmEx1qOGGkFUj3DNcUA2OT5KSqF8ALF0EQyElNUq3080DrEJsqQnfAmMnO2nze8C4EKSJAaaOmIA4zIIzpUja2pSkqh5PsOGXMe44/CSs/BomB7y19YYyRS8xS9lObJbZjCS0AIRObw8mk00O296ZWUhfzAER+upE0o2G2qu6Jp2JafnGic5i1JZm+B+qpeTGzVzMa9JhNiXQNx4nw4JgK9b15K6DvVPD9QqRreILiuSs8p5+TrIwyS8GYjjvBJN3Qjemw7i6o/jD8/kFZWh8GvY4VRemzao1/Vd/KvdvKVa0frMpP00ow4p04EaA80j5dfueLtHypXl9FKrJT5AnERYOeY1C0Tp22c6ph8Jw6bS8ERnskgVOVaBoYozJnuj6+4ipJtNoPG8oyVQvet1vtVCio/wCQn540X9FfBRZOCcb8IK4gCGyqyOL2ulI2VWRFJqRZ/RE4+yfwTGtLTNqg9ySUbvW5e0lWMp1WlcZhBauh76RUfpEXX/oPXtTKvBywTZJs0JGaFF62oLdMWRRFRQIQDb1xZsE5k6ob4dyeqByqOj+NlsHx0OxXPR44+HPY9Nmgu+4Oc4x827pinjsa2ywILQAhk4Otc7x1TVmSuI8zthPaW9cV8bxXjHK0W0rfyVkes/7suxAgBSyGGRAA25fmxE8Zhq1X2RIMmLbiVE6IsmtoYvaqiCjC/h/A1r/0/6btX4TMMnjlq7JEWq+vzeeNaREk+5SLV0718rH16q58pxkNTDjduKLoG68hk7gSoMz0vTEKVpzJiXocTrc0OIwX+s4oL0Dp5XIXorR1S+eVCkxMuUnQ6UhMmB4GpuZJWWsO35OiJTkptFnsqpx7bRZlLTghuiUYCyIDYoYGhCokpUqZUG3vS783vgQ1N/mtX1ctAwKmyzAOxnUAoqYwjcYe5Rc+9jeHV37hxWjQU5GdImWFWpoiCkB4PCI2h1O2GGbUqNoVNTtOQRBCn3uc3wNF64NmR9unXPwpzDHyTasL+dOpnpiOJbQAhEx8TqyL1kP30dh0aJobVxXwyqle6WQ6+Sys/kRM+iGKIgdbrTx/rAtTkt73yR3DDAicDq4oMfDa0fP8ob6Bw+faEB0jsssFFMPWq3yKbf4qRa04u4fnBCDa3pcyH8wVgd94w39IqZDv/U/Ix7p6eQ4vnejhmUMdPPLqWW5aXYjRoA+v4zKoyE6hNcbpaBoBsDaDOXYZEN772vsXBnE4Pb7va1Gy4izIMNI3GnsFa0DSGkpI8lnjrQi5NZd3AELFDIhzfTaqZtoTOh1SRmfTXikI4f2ZfjYKgkBFjjolQG2WccoVtOAEyEg2MDKhvmXtyIST9OTYatOExJwSDMVxOqSy32OPS+fNsSekAISfsVVplokOtTIgSjZB5wHJASMvDtP/kcSv1Sj93NdkYVtlTkRt7KzNkxaCBs9HFPhvt9opj+fsoKxKsFv8Bl2VZmdtHnsbfSy+egO/3p/3/xc2fibovOR3hzv56JqisMbIGSYDZVkmTnSOyH6vUiyAu2Z8caDVyl/tmJNZ4BW9Kd8em04hreJWFaRxuG2IutO/h089HfxNCtM5ZOfexw7QYbXj8oj8zW+P8e2sc+y+fzMlM1cIYpUB4XTg/nY1dY5h6gBm2Fa7jZnov3xWNbVxv6gRgMiqVLSurWt4Yrai8r7vw1VfDv5GnQ5u+wH85napzGTdXQF3954/LYPj/Ovzp3A4PZRlm7hjU+ns80cFvDoQ8TpYuewZaoF1n4rJoWfe19wekc/84gClWab597VoWnEOjM3XZYkFPSegcI167edWwQc/Uq/9eMfWAzlXq9K0pP8wnRrtdMAjNTAxBId/MXvHZDM83AgGo1SG0TbEUoVtDdssdj6+UVmHG0EQEAQBj0dUrYTP4XSTlKCPrHQhWqiYTTPr/AE4/lvp35/tnHX+zEQ1FwyQSjB6T3I+cYwvXBefGRDVBWmc7VN+4nukbYh/vTmyjLQdNXk89PhhvuAakrK8w2TWPSZeWboDmt6Albepfqitldn8xx/PIIripXvG3GvHy8+v93vtgJRd8psP2nn8s1vC7s/H1hfz3LEu1pZmht1GJGgZEDIYtk8BPrx1SzbHXAcC4GPritlX/y4kZ0lZBlFEFEXufewAbRY7TrekaO10i7RZ7Nz32IHZK4ap+THJgBDdk+gdwz636R3DiO4YrCpOWKXvS0n0CZJwjUJR3VkaEIMXpD6XhuiukpAEn3wcDvwYLrzud7eZ548ITDg9iEDn0MT880cFagrSVUmH1FCIodbgGTcqMPe+5gl0X4uSFeeSnNT4EaLsOaaOAKWXjLKY2lzHnNFu5TWCpmnomSEO556aPwD2MjEkbUc9Eed2q/IlGABZKYlYxqcUb9dL59DEwnDAAMlRRa0FlhDPn5nodAI6AXVKH/UGMOXgGukiLy3+RCgBUpMScDg9iv79PSMTZJgMJCdGljWan24k2TWM0xjZ2HTWPSZeqboxamUYRoOeytxUGmaONcO4dgBeb+hjXWlmRCKr19Xk8fbZgZiVH2sBCBnsb7ayZYmPCzK3RvIrj3Fd7tVVuWQ3v4Br1e1RP/ahtiE6rRO4PbM/A7dHpN1q59BM9WxTNowPRrmHcKR9OKLtiiOKIHoi8lj2S94K6G9QpKm+UQf53of4/h/A1ofkNWBMhzufhFe/5rdUSdb5owI1hZoVZ9wiitOD5+gP9GWdl1HKgKjMSYkfK86e4+oJUIJ0bzQkw+RY8H0XI7aei9aJSnM2DHG4tSWZHO9QNmVXFEUmXW5VSu0K0o2qClF2DNlVz85ThCk7JMRBxtQcCjKS6VFJp8NRuJE6/YW4zk5ZovC9vL7JwrbK8PUfZnJzsZ1OfWRZSeHcY6KO18lQhmB6JOysyeMNX2UYMvn5ey3cf2VkZalGg55NFVm8HyNNPC0AIYP9zRa2L/VRW6XTQUaptEoXQxJ1cIPuEO/qwk/JCZfWwXES9L5v9Aa9brZyu04vTbyjTLslsOBRsO2KM2mDJJWiw/krFXHCEEURt0eU/NntVmjbJ9V5yiW9EG7/FfzhL31ahMo6f1RA0oCI8vevERrjg5Cing1rIFoHx/3GB+edl+lFUs2+yig9aI2IvjOQt1LdY1zOThh2ixSwVxhRFKXAcrq81bOUpAT0OoFRh3LaCpbxqUuuYgpTkKGuEGWn1U5p1gLIgBjtlmyz44xSczKdQ+roQHSmrGKrIToWi+FSW6CsBXh9k4XtEQhQzuQK8wjH7ZG11TQwRmWustouiqNPkHT8ug5H5XA7avIuCq2Hy4nOYYwGPVX5kc8fbl1fxHNHuyJuJxy0AIQMDrRY2eQrAwIkHYhYl2G016MvXsuzp4ejfuiKnBScftJ4nG4PFTlzbkIJSVEXfiwLYvMVbLvijPWpll4rBSAiF6K0jk+RlZIo/XLo57DxPimAFA65VfDR78JT98DYwKxNss8fhdHrBEyJekUH1hoKESMByqHxKd5o7GfSGeJ5acoBu/qZXSXmZDrVUo+Xw6RNGryprZtzuTpheDMqVVjB7bdNkpeeFNbq8NrSDI53DCvWlzbLuGpCdfnpRnpVzYCYWCAOGPMtOOOBEhWdME4K1VS7GlVpWylqCtMVzbw82jHMurJMRdoqcXdxdDyHKVd4i4Xjky4SE3QY9Atgmll1o2QhGwXy0o24RRiMQP/kZ++28OBVyriCbV2SzYnOYexTLkXak8MCODPig8GxSZICeet6hShjycmnydp6N+d6bdiiPJGqKzdTkD5/IKrXCZRlmagrN8/ekJoP49HVgdgQ5MYcbLvi2Hqkz0ENFHLC6B52SA4Yrkk48TSs/3RkDZZtgev+GX5716y06rpyM6VZJvRzxML8nj8qUJ2fxjkVVKk1ImSoBbIqona4SZebn77TzO0/rufq5TksyUkJ7bzU6abLqtQtxUvQ6xAQ/AbsokbPCUnsTW1yq6USx8sNuwr6QNM09IyGnRq9sdzMYQVL4tosdspVCv6rXYLROWSnZKFkQKhUyhMJpVnJdFrVCUCcGkkiTRyXxi5xSnWBclacHVY7+elJJCUoU8okWC+QWVrLgRZrWO+XXHbiXP/By7KdATXKlOa66lzeDDMLomt4gubBMa5Ypkymi04ncH1tPq+dib4xgBaACJH9zUFqq4rrYpsB4ZqE1vcRlu64aMkZbXJTkyjKNGLQS6vJBr1ARbaJ3Q9smb/SkpoPtuie8II+Cbcx0+c2tzETQR9lsSKbihkQKTlS+m6Ek6GuYTtFmcmStWvVjcqUjNR8BNbdDc98BtxSoEwQBHbfv5nybFNo548K1BSm06AFIOIPa0tUMiBEUeSlEz3c8r33sTmcPP+FK7hrSzm7H5BxXhozwI/QrZJIFnYxzoJQW4DSS27N5VmCYetWzYKzsddGbeGMe7k+UVJc90WyWdo+zYYys6J6SVIAQp0Mt4KMJHU1IKwLJANipEvdEgwZ589MSs0m1UowzvePQeFaKVAap1Rkp9CikP23VH4Rmf3mLKzNrF69zrdtZAhI+g8LJACRbIakdBhuj8rhrq/Nv1SGIfPa+dW+Vj6zfYmiY+Lb1hfHpAxDs+EMkX1NFj68KoBdYnImeFwwNQ6JMah5Ov8aLL0O9AZuXVfMv79wmtvrSqN2+D+e6KEiJ4XfPbSdQ21DtA6OU5GTQl252feFkpoXfStOgxH9l88iTgxh/8Vt9KXU4Ky+mW+cNvPQ9Supi7oFZw+kqZQBAdKAY6QDMsvCbqJr2EFxplFysbjzCeX6Vvfn0t//4t/Ard8HQaDEbGLvw9eEdv6oQG1BGi+dVL+GX0MmQy1QtUvVQxxtH+L/vdxAaZaJX96/icKMS6uass7L9EJJB8LfgEIhKnNTaB4Yp1JhO0RZdB+DLX+h/nHMS3zqxix6RntUs00822vjvu0Vl14wGCW7N6/i+pnnof8MXPuP0gB4xrOxLMtEp9WumL1lu9XOzlp1XLukEgz1VsDHp1yk+MuKjSdGO9W1iZ97/sxkzvkzkxJzsmolGF1DdpJXboPOA6G7dkUZvU4gNSmBkQknGcmG4G8IwL6mQe7ZVqFMxzwecE2yvaaEb+59f7ZtZIg09tq4ria6bnwRUbULzu2BzQ+qfqiVRemc7bMx6XKTZDDCR74lWYHe+F+zd5xz7dgcTl5v6OPLH6pStD+1hen02yYZHJuMyFVDLloGRIgcaRuirjxIOmTReug6Ep0OzeXEU7DmkwAsy0vF5nCqGvmfyfiki+/uPc9XP1KDIAhsqsji9rpSNlVk+b9ppeZHPwABYDAijPWRUryKylVbqU4a5qsf28L/eaUp+lY0ampAgCI6EF1DE6x0HIGcKuVXUK79R6m++c3/e/GlkM8fFahWWBBKQyGsLZClTgZEh9XOXz15lG++cpZ/++hKHrlj3azgg5eQz8u0oqg4YcSFEGXfaekeozb6BNAlRF0zKObYelTLgDjba6Mqf07wymCUHIuM6VB7M7S+K/1/zuRREAQqc1NpGlDGmUTSgFBn0SYvzUi/SuMgm8PpvyQ33ohGCcbM82fmT4CFnayURKwq2KSOT7owJSagK4uD0ugg1BSkca4vsnGHKIqc6BphTUmGMp0a7YSMEkyJCRRlJod1rTf0jFK7UDIgIKp2nIIgsGVJ1qXyloM/gyv/Nui18/ShTv5sfbFiZTYzuXlNES+diO4CnBaACIHeEQfpxhC8dUs3S9HWaDMxDJYLULzx4ksfXVvEi8fV96QH+N4bF7hzcxl5aTIyCFLzYCy6GhAXGTwn1RXnVMHAWary09hUkcUTB6KTfnURNTUgYFoHIjInjO7hCZY3/RK2fUGZPs1EEODm70gpkgd/rnz7MslOTWJofAoxxna6GnNwDCueUTDqcPKff2rgwd2HuGVtEU88uIVVxQoM3tIKohaAaI5lAGJyTBKjjZY1avYy6Rl3OWHrUSVAPeXy4PJ4MCUGmDwnmyEpA4bafG7eUJ7JkXZldCBGJpxkmCJb/fVHYoJONa2UzoUiQAlxqwEhCAIGvY5Jl7IWiE0DYyzNTZEcevrPKNq20tQUpNPYE5kQZfPgOGVZJuUEHy0XIGc5INlG7m2QN1YXRZEB2yS5aVEua46EnOXSdRIly+cdNfnS59pxUCrdnP68/eFye/jtgXbu3lKuSn9uXVfE88eiW4ahBSBCoL55kK2hWNuUbpFOpmjT8ALU3jJLLfuWtUW8EIUARNPAGO9dGODebTIvilhlQIAkaJZbPV1bLKmr/831y9ld34YlAmVa2dj6pAmLWuSvkGzyIkA/2IBRcEnZPWqgT4DbfyFl8DT8UZ1jyKBYRVswjTCYtCla0uZ0e9hd38rHHn2fooxkXvyrK7lhRb5ymTZRsuKszEmhZTA6AyWf9J6EgjXRO97lKESp0qSxeXCMpaGU7lTfKKUk+2BjmTJClGOT6pcwJCXocTiVneCClD21IAQoQSqNSIjPyWBxZjLdw8pmqZzvG2N5fpo0vkjNh5FORdtXkpqCtIi1p+qbgmjUycXSJAV9gR21+eyVKZjYNzpJfroxqhmsESMIUHkttLwdlcNduSyH9y8MItZ/P6QFvj2n+9hSmYU5xbeeSqQUZSaTmKC+5f1MYhaAECS+LghCtyAI44IgvCMIwqoA+5sFQfiNIAgjgiAMT/8/Mxp9DdlbN3u5tLoe7RXUE0/DmjtmvZSXbiQj2cD5CFO7AiGKIv/+wmn++SMr5EdeU/NjlwExcFbylk8vkgZ5QJrRwBeuW8o3X4mi3Zt9ULLuU4ucyO3rbrL/Af32LyrUIT8kpkj6Em/+X7iwFxyjs3+imHpdW5iulWHEE2EIUIqiyMFWK88c6uBgqxVRFBFFkb0Nfdzy/ffpHJrg9w9dwX3bK5S3CEsrlMQDVSY3LYkBWwzV3XuOQdE62W/z9d2ERG715SdEqVIGxNleG9WhpEYHSEleU5LJic6RiPvSZhmXJ0DpdFx8Luhd9pCeEQUZRnpHlH+GLJgMiKlxMMRvP9UQ1D3fPyPIFg8OdQGQnDDmZEDMOM9DGQvVNyssQGm5ANlLASlAZJ9yMWwPvVSmoXeUmsIFVH7hpWpX1Ow4kxP1rE0bYXKwBSquCrr/Y++3cP8V6opx37aumOeimAURywK2vwPuB3YBF4B/BfYIglAtiqKvpZ3HgSRg6fTvvwV+BdyqdkePtA/zH7f5jY1cQqeTapWtzRcvXtUZ6QKXw+fxvCfT3++qUeXQe073kmlKZFsowZm5xEKE0ou1GbIqpYinMQMmhiDZzG3rinnyQAdH24dYX6a+7SOiKJ0zauGtH3M6AtZh+mPC2kOt54I0EFWbxFQY7YLH/2z+tmSzJHAVBZHQ6nxpMHDDChVLYzRCZ6hFulZDpHPIzr2PHaDDasegl9Kv89ON5KcnUZCRzI8/vZEylSz/gKhlQAiCgCkxgfEorCD7pPsYbHpA1lt8fTelWSZ237+ZkmATuZxqSRjxcsLWo0qGXEOPjXWlmcF3zF4m9WFyDJJmZ0wkJ+pJStAxYo+sfKLdYqc8K8Tr0emAR2qk5zVwPYA34TTAM0ISonRQkaOszkTHkJ1rqnIVbVMV1HbAiBA1hCgv9I9xe93031yyWVrVXuVjbBEHZKcmMTzhvCTqOuc8n4WP81wURRq6R1lRFJ6trk8sF2Dr5y/+ek1VLm+fG+DWdcUhvb2xx0ZtmDa/MaVsO7z0d5IIp5pj82keSNjD++mfYGeQTJHDbVbMpkTVRac/vLqQO35Uz1/vXB6V7JVYlmA8BHxLFMWToihOAF8DEoGPzd1REIRy4CPAl0VRHBRFcRD4MnCLIAjhS/yHgGxv3ZIoR1tPPQurb/e5adeqAvac7sPjUT4jY2LKzbdfPcc/f6Q2vAaS0qT06mjjmgQESJhOY8qtgQFpZU0QBP79oyv5+otncKvwmc1C4dRyv+TVhJ26PLHvx7xvvjUqN2LcU+Dws6I2MeRbXVsFagrTaFQxa0hDJjIEKEVR5N7HDtBmseN0i9in3DjdIp1DE/SOOPj+XevVDT5A1DIgIMZClH2nJI2ZEPH33bRZ7Nz32IHgmRDZy6S04MsJ16QqGhuNvaOzLTj9IQhQeR00v+lz87rSTI52RFaG0Wa1h35Nuqd8T8og4DOiIN2oiiB3h3WC0lCDJ7FktCsu9R+8lGYpb8UpCZtOfzclm6AzBqXRMigxm+ganv4MZJ7n5/rGqMxNRa+AI81Fhjsg45KL3kW9ghBpXKgZEAmJkrByzzH1j+UYYdnoB/zMui7orj97t4UHr1Lfijwj2cCSnBSOK5DdFgoxCUAIgpABVAAXZ+qiKLqAo4CvYvN1wKQoisdn7H8cmJrephr1zTJrq0o3RVeI8tTvYKXvyG5qUgK1hekcVkgsaiY/eOsCH99YQkFGmKvS3uhatMtVLE2QPWNFNadq1gR9RVE6a0syeOpgh7r9UFv/wUveivBEmJwTGM89T1uJ6glGccWyvFQu9MWwtl5jNtbmkEswDrUN0Wmd8Bk87LdNckiBmvWgJJqiVjIUMyHKqXFAkP7WEPH33bg9Iu1We/DvxmAEjxvczjA6vABxTc7zf1eKDqs99NKBql1+yzA2lJs50j4cUV9mTRRVoiAjSZUSjK7hCYozF4AGxGgXpIe2ch0LSszJipZgOJxu9DqBBG95XUq2dM+KYxedmoI0GsIUotzXNBhaiXiouCYlgWHdpUXXdaWZnOoaCdkp7lzfGMvzFmAAAqZLz3xr3yjKkd0YNt6NzSUELG9pt9jpHnGweUkQF0aFuG19Ec8djU4ZRqxKMLy5OcNzXh+asW3u/r5CMsO+9hcE4WHgYe/vKSkp7NkT/IRyOBzz9vvdGTfXFOvYsyc0H3K9y87mhjepN6h/AqeOt1M1oePI+/6tP8s9Hr73Qg93Vytn29JvF/nDaTf/uFHPnj3hK5NvdogcefkPuBKikAkwTb6lnrRxAxemv+fcITtZIwc5O3gpGLBOL/LNPW6SBs6QalAnDck8coaCYScNIZyXkZA7NEVWw0uc7ZP3gCrpe50B1jI00B/2tSMHvcsupdT64fW9e3EnRGe1aXzMxYsvv0KifgEJKC1S6i4c5iTbmDwbPCi0r8eDIPoeIOkQ+eNbH2AtVD/mvt0+Qf2fXkLUBX+8RnLdjPV5eK0JknpPhvX+cMm0naXEk8UpGf1W4rtZ70rh3Iu/Zjw5fidTSpHs6Kd2MoEjCj8fxp0inkk3r732akj7Cx4XVzTs5b2kP4Ew+/sZmxB57ayHlZ6WsPtz5JybtQndDJ8Pfq8N9xnRafFw2ipS4VDORUUURYZG3Lz9xuuKtakWlZ1vM5FUQM94FCZVYTDhEjnV4o5o/DCTzjGRFLdnVnurxBw6n/sxw+nqlCNHinPAwx87WhE7dbLP8+dPuvnoEh179oSukRPouZNi72S5M4Vjc7bnJ7j54TOvUmUOfK26PCIjo27eeTP+rw1fGJwJbGx4hv1TG1Q7huBxsf3ED/lg1X9QmmDju8/sZUuB7+ffU+fd1KULvPpqaPfsSHG5Rf501M1mQ4eyWTU+iFUAwhvqy5zzuhnwFXoZBXx5pGXOaOsioig+Ajzi/b2kpETctWtX0E7t2bOHmfuJosg3T73Ngx+/Wp5YWce32XXtdqnMQE1e+zfY8RC71vj/23a4Pez6zjtct/NqEhOUGXzf/8uD/OcnK7hqeYT1j8O/ZufmVZBbpUi/QuKto5D1EZZ6PzNrFbz8d1TMOT+c+R0c6Rzm/968Wp1+nLSBZRNl1wY/LyNieAW88MV5f19APB748f/hR1XfZEd5JbtWBxdCm3vtyMYxeqme1wfX79wp+SJHgZesR6lYU8lqpTy1NcLn/Ne49uZPhlQGlNVq5Ynz+4H5GRAeBG6+dgubKqKwitD/Iz60bQ1klgbdNZLrprBzmMfea2HXLpUcavzxQSuU3kTxltD7rch3o68nrzgXalW+Z8YDbfXA6sjuqT7Y32xh61QXu3bJcDCxPc2uVXlQsnHWy6Io8vNH3ub6G64Je6D636ff5o6br5Zq34MR5jOivHeUpr3n2bVro493hcfQ+BTFLYfYtWu7Ym2qxgsvwdoPs6Y8fvv6vca32LXrWkXaeuF4N1ekj7HrhhnjyuwuiifH4Ir4vHeUdo/y6JsX2LVrg6zz3O0R+cbJt/nzj10T2jU0TcDnTsMfIfUKdt0we7u7qIdjHcPs2hW47LqhZ5R1VmWvt6jT9zN2bVutXunSyWdBvJmdH/k45vYhfvF+q8/n+IjdyX+f3seP775KecHsALw3cYLkygKuq85T9TgxKcEQRXEEaAU2eV8TBCEBqZziqI+3HAOSBEFYM2P/NUiaEcfU6merxU6JOQxv3eKN0HVYnU558XgktdaamwLuZtDruHJZDm+dVcZx4vUzfSQl6CIPPsC0E0Zv5O3IYeCspKjuJbMMhtvn7faJjSU09to4qVYtlK0X0qIgdJhRIt+C6sJrULiWc/YUiuImxTR6pTrVBWk09Ebmy62hAK4p0BtC1iCpKzdTmmVibuKKXidQlmWirjwKwrIAaUWSeJ/KxEwDovsYFK6T9RbvdzN3jCzru8m5jKw4bepYcDb2jFIjVxyu+sM+yzAEQWB5Xirn+8PTzJlyeUjQCbImTuFQkK68C0bHkJ1Sc7w8G4MQ5yUYIIma2qdcirR1oX+M5XlzxPpKNke3NFomS/NSuNAvv/SzoUfSWlD0GrJcuGjBOZOrlufwzrmBoG9v7A3jHhNvVH0IzquUcSCKsP+HsPUvAVhXksnprhGcPspbnjzYzu0bS6IafAC4bX0xz0ehDCOWIpQ/AP5OEIRVgiAkA18HnMAf5u4oimIb8DLwLUEQcgRByAG+BbwoiuL82aNChF1bVbIZOlQWvWnfB4VrQxIyvHVdMc8fi1wYzeF08997zvIvN6+IuC0gNlacg+chZ/ml33V6SDBKSt8z0OkE/u2jK/j3F0+rIuLJWK8qFmvzEARIyZP3Odd/H7Y+RNdQFGtc9YmSwrPPbQY48LPo9AOoLUzjrGbFGXuG26UAYYgIgsDu+zeTYTKg1wmYEvUY9AIV2SZ2P7Alep7k6YUX7X3VJM1oYGzSFbqVpVL0noSC0AUo4dJ3k5igI0EnYEzQoROQ993kVl8UDF70jKpjwdnYa6MmFAvOmSy7we9gfEOZmSNtw2H1pXPIHtz9ZCaBnhGCzq9Na0aygZEJZbVDOocm5PU9ltiiNNaIgJJM5YQoL/TbWJ4/JwCRVwv9jdHXHAuRpAQ9giCJu6NPlNzZfJFsnqUNU98kU6MuFPwEINKMBnJSk2gNEvRu7AnR5jeeqboRzvrWvomY9nppjDDt7qXTCWwoN3OodbYOktPt4ZlDHdy5WVWfBZ9srsjiZNcI45PKBAX9EcsAxLeAXwKvAxbgKuBGURTHBEEoEwRhTBCEmeao9wCDQNP0zwBwr5odrG+yhGcxWRqFaOuJp2HNJ0PadUNZJuf7bYw6InsI//jtZj66tlC5SWm0rTjdLvA45yuL51T5HLysKcmkuiCNZ4/IzCAIBVuvFICJBvkroO90aPv2nJAGcwWrsIxPkZ2ijhDaPAxGyV7qqx3zf/7ugqTEfuKZqHSlpiCdRi0DIvbIEKD0UmI2UZGdwg/u3sDXb1nJEw9u5fWHr4muWFxaYVQyIECycLOMR8chBoApOyCG5eAzMuGkrtzMk5/byr9+dAUl5mR5301OFQyelX3cBYmtR50MiF6b/NXJlGwpSO8jqLah3MzhMMVd2yx2yuW40hiM8BfvQv5q+GoHr2/65aVnxGffgOe/4DObURAEdIKg6EJCh9VOadYCyYBwT11y/YpTSrOS6VTIirN5YJwlcy1XdXrpehpRWVw8Aqry06RsIoMRNn4GbvzGpfN73afg9l/Ns+Csb7awbWmOsh2xNPkMQADsqMljb2PgxazG3gVqwTmTvBXS+MOprDsLAPWPwrYvznppZ00ebzTOngu9dKKHq6tyyUgO3+Y4XHQ6gRtWFPDaGXXnZzELQIgS/yqKYoEoiiZRFK8WRfHk9LZ2URRTRVF8d8b+VlEUPyWKYsb0z92iKA6r2D/OdI+ysiiMOnCvZZgnNMVY2Tgd0LYPKq8NaXdBELhxZQGvnAy/3KHDaudPp3p48OrK4DuHSmp+dAMQw21grpj/em6N39WTv/9QNT9+u0nxFZSorkrkrww9AFH/KGz7K9weEQFUT4+dhcEo1TbO/UnOhE8+LmVmNL+lejcKM4z0DDuiv7KsMZuh0C04vQyOTeL2iOxaWcDtdaVsqsiKXuaDl/TolGAAVEa7DEOm/eZMfv5uC5+9qpJNFVl8aks5qUkGJpzu0BtISpUGhGo9V+MJm/IZEB6PiM3hJMMUxoDWjxvG6uIMTnWFV6bYZhmXF4AAaHwJ1twOxnRJiM/7jCheDzd9G357N9it895mTknEGkBpXi5SCcYCyICIlt13hJSYTXRYI5/sOd0ePKJIUoIP0fXSzdARv2UYNYVpNPbYJMeOs3+CjfddOr/XfRoaXpwVfHC5PbRaxlmaq/D3O94PKb6DGjtr50+U59IxZKdkoZQn+UMQYMnV0PJu8H3lYGmSspFLt8x6+crlObx7fvDi76Io8ov3W7j/CvWtN/3xsfXF/EHlMoxYZkDENef7I/DWFYTpIIRyqsuzOP8qLNsJ+tA1RG9dX8xzx8I/mf7jj2f4hxtrfN/YwyVVZmlApAw0Sqtoc8n1X1tsTknk/iuX8D+vKZz6Oz7o9yavOPmrQgtAjHZD/2lYtpMB2yR56Unq9y1UkjPhrifhT1+VsjRURBAEclKTGBibVPU4GkGwtsjOgHjr7ADXqiycFJS0QimFPgosyUmhZSCKAYjuY1C0TvbbekccNPbauKbqknZQbWE6Z7plZhpllsGIalWX8cOo8hkQ7VY7ZeFaXvqxpjMa9CQn6hkKIwunzWqnPFvm5OnUs7DqE763VVwJVz0sBSHmrFwqrQOxYEowRrvjXv8BpAwIJaw42yx2yrL8nFOlW+I6AFFbkE5jrw2OPQEr/2x2pm7ZNqn0bfJSaejJrhFWFWUoG2CfGIakdGkO44Py7BQsY1PY/GRTW8enyEw2RHfhSi2qbvRrQRw2+38IWz8/7/NNMxrITUu6uJiwv9lKsTmZUpUtigNRXZCGZXySAZt642AtAOGHsMsvQMpQKFwDLW9Lirben3B9iJ2O2e0c+w1U3ySrvaW5qYxPucN6CL91th+PCNfVKDywj3YGxMBZKdthLkFqi+/cVMbRjmH5g+VAiJ5ZPsuqklcL/WeC73fgJ7D5cyAIdA3b48/jPL0Ibv8l/P5BGGpV9VA10dSBmHt9R3q/WCyEkQHxRmMfO2vjIAARpQyIJTkpNA3KFy8Lm57jsgUoAX5V38p928tnDZZXF6dzUu7qeU61dB9f7NgtYFK2truxd5SawjBTo/NqpYDg1PxJ4vqyTI52yC/DaLfYKZczwLY0SaUgGQEm1Cs/Bituhd99FjyXsmsKMoz0jSp3P+0ZdlCYaQy+Y6wZ6ZSEqOOcUrMyGhAX+sfm6z94KamDTpW12SKguiCNsz3DcOgXsOmzszfqdFDzESkDaJp9TZbwNOoCYfVffuHlmqpc3jk36HNbRPeYeKPiSmh9TzndELsVWt+F2lt8br6uOpdfvN/CM4c6+ParjTHNfvDy0TVF/PGEenpWWgDCD/uaBsMTd3E64JEaeOe/4eW/g/8qvfTzSI38SYW3vZntnHsFdn9Udnu3ri3ihePysiAmXW7+60+N/NtHFRKenElKLowFV9VVDH8BiKxK6cbrB/0MQUpF0vKnxufrUKhJUpq0IuQOICgzOSbZL62+A4CuYUccOWDMIK8Gbv4O/PbTMG5R7TA1BelSOqTa+Lq+I7lfLCZkilBOuTw09tpYFU7ZnJKk5MJ4dO5rlblRzoDoPQEF8qyJxyddvHq6l1vXzZ44ri7J4FSXzKBu7mUQgPA+YxQuHWroCUOA0svFlOR35m0KV4iya3iCYjmp2qHqXm39S8heKo2/pj/LvLQkehUKQIiiiMvjiboyfViMquOmojTF5mQ6hyPPgLjQb5vvgOEl2QyuSXXq+hWgMMPIEuu7iMUbIdWHy9yaT0rXwDT7myNYJPVHAP0HL5IOhO+Fw7PhiNzGKwajJFjfd0qZ9g7/Ajbc6zNzvXPIzi/3tfHr+ja+9vwpDrcN85XfnVBMFyVcbllXxAvHtQBEVPF4RM73jYV3IbmnYMLPasDEkLQ9Ru3dvLaQF4/LW5n72bst7FpZoE4qUEKS/M8jEgbPznbA8KI3gKAPONnbUGamItsUURnLRWy9kFYQeTtyyF4WMMjCsSdg9Scu1hhG1QFDLuXb4JqvwG8/5XNFTglqCqNkxan0/WKx4PFIK5j60OvVD7RY2VyRFfv0T51OmvhEQUOkNMtEuwKpyyHhnJC+kyQ/A3w/PHu4k1vWFmM0zM74WlGYQUOP3ABEzeIPQEwM+Xd7iICz4QhQzqTad0ryxjCEKD0eEZdHDH0SL4rQ8AKs8L16OI+d/y4F+t/5FjCdAaFQCcbA2CS5aXFUnhiIBWDBCWBKTJAcICLkfP8Yy/wFIACK1kP30YiPowaCIHCX50Wsaz7re4e8WikzytbHlMtDz4gj/JIqf1guQE7gAMTGcjPH2odx+xB1beyJ8B4Tb/jRvpGNawqO/xbW3zNvkyiK3PvYAbqGJxABh9ODiFROdN9jB2KqRVaYkYwxQa+azpQWgPBBQ+8o1QUKe+t66T4KnYdC/1HwZpmXZsSckhhyann38AQvHOvm89cuVawP89DpA6/MK4XHIw1IjH5ujtlLA0/Qga/cWMOjbzb5rX8LmbG+6Acg8lf6j+R63FJ0dkbaX1yWYMxkxS1SwOTZ+1U5f6ryNSvOmGLrlqyqZLC3sY8dSpeJhYsxHRzhifPJISlBj9sj+hwMKk7faek+IgO3R+SJD9r59Nb5mSzJiXpEkDfxyK3yq9ezaBjtVuX50DQwRmUkgnXlvlOSizKT6bc5cPnwsfdH76iDgnQZJQxdh6XFA3/2hHPR6eCW70t25UcflzQgFMqA6LAuEP0HkEowFkAAAqQ6+EjFvpsGxliaGyAAUboJOj6I6Biq0XUEgzGF084AGSurPg6nf8+xjmHWlmQqL7Dsx4JzJgl6HatLMjjmo+yqcXrutGhY/iGf2jeyOfU7qS0f849DbUN0WifmPcPdHpF2q51DYboMKcVt64t4TiUxSi0A4YN6NWqrvBx9XKrxCvXn6OOKHv62dUUhr+L/35ca+PKHquatXClKSg7YfdeTKcpokAdxbk3QgW1OahL3bC3nf18/H1lfbD2QGosAhB8hyrMvQ8mmWaKY3cMOeemxsWDzg5LF6EsPK77anJqUwKTLg1PGoFpDQawtF32yQ0EURd6/MMiVy6Mk7BqMKOpAFJuT6R6OQlpx91HZApSvneljQ7mZ7FTfK8a1hWmckZMFkWyWAjuL2aFGBQvO8UkXiQm6yMoGDEapBKb35LxN1QVpnO0LPWAr24LzxFMXywNDJiER7tgNhx6j3Po+vaPKiKl1LhQHDJCCWYE0M+KI0ixTRCnnHo/IxJSblKQA4uylW6AjTnUg6h+ls+b+wBbgqz8BJ5+NTKMuEJYLkBV8wXFHTR57G2YLyLs9ImOTrpjYRqpGWoGk1xaJWL4owgc/gi1/6XNz6+A4CXrfgSSDXkdrNF2ufHDjqkJeOdWrSiaGFoDwgWoXN0hWUbc9GvrPTd9W9PC7VkrersE8sd87P8j4lIsbVuQrevx5REuIcuCcb/0HL0GEKL3cvaWMD1qsnJMx2JqHLVYZEH6EKOt/ANu+MOul7uEJCjIWgMjWjq+BxwVvf0PxpitzUmJ+879sGZLngNE0ME5RZjKmxNCdgVQlvUga/EeBJTkpNEfjPO05JluA8rH3WnjgSv/fY1g2junRC+7EhNFuxS04z/XZqM5XYGXSjzL8hjIzR9qHQ26m3SrDgtPthKY3YfkNIbd/kaQ0uPNJsuv/L5lWZdyTOqx2SrPiPDjvJZp23xFSYk6OyIqzaziEzJScaqkUN94CmCOdYLlA5sobAmtPpRdBoomWs0eVn6OIolTSGkKJ3bVVebx9brbOUXs4rjYLgeW74Pxr4b+/5W0pwzqz1OfmipwUvwtdTreHipzYfqYZyQYqc1M41jGseNtaAGIOLreHlsHxwGlcC5iUpARWFqVzsHW+V7aXKZeH//dyA//20ZXKp3jNJTVfmpCrzUCjFGTwRwArzpkk6HX860dX8O8vRCBIaeuJfgDCn9Bm52HpgTPns3G6PcparqqFIMBH/1cqVzr8S0WbrilMp0Erw4gN1mZZDhh7G/rYGS/lFxDVDIjKnBRaBqLghNFzQnJ3CpFjHcOkGhMC1mSvKs4I0wljEZdhqJABcbbXRk2hAgEIPynJ68vMHJWRKhzQLnEuTW9CxRWSZlQ4pOWj++TjfNn+P5LIXoQsGAtOAI9Tlo5OLJGcMMLPgDgfSIDSi04nCRur7KIlmw9+BFv+guqC9KCZRM6Vt1M3+rryJbIytMkyTAZSkxJmfV+NPaOLR4ByJlW74Nyfwn9//aPzFvhmUldupjTLhH5Oyb9eJ1CWZaKuXHk9ILnctr5YlTIMLQAxh1Pdo6wqjsBbV5/oX0Aq2Sxtj2V7wG3rinnumP/VuV/ua+G6mlyWRCPyFrUMiCABiOxlUvpZCGyqyCI/3chLJ8OcYMRCA0Knh8SU+XXp9d+fd3McmXCSZlwYgxZAGmDd/kupXOlsBA+KOdQWpNEoVyRPLipc34sCq7wMiL2N/crbBEdCehGMRsuKM1X9DAinQ8o0Sgp9gPmzd5v5bIDsB4AVheny7Y1DzFZbsKiQAdHYa6NaCXG4tOmMyDkpyauK0znVHXogSVYJxskQ3S8CkbOM76T8LZ6nPh1ZOjXQMbRAMiAco7Ku11hTmpUckRXn+b4gApReSjbHlx3npE0K6q36BClJCUwFKf08YrqK6zmgfBaH5YK0Uh8iO2vzeKPx0rXU0GtbPBacMylcC/2NkoOKXAbOStpzxRv97iIIArvv30x5tgmDXsCUqMegF6jINrH7gS3qLwKHwLXVubx7YVDxkuQ4yVeNHyIuvzAY4eFG3+r1+sSLLgMxaw+4cnkO//HHM0y63PNWuftGHTxzqJPnv3iF7HbDIjUfRjrUP85gkBIMQ7I0wHa7fNrkzOUfP1zD3T/7gOuq8wLXHPrC1ht9DQi4VIZRvk36fbhdWmlecs2s3brl2qPFA0mpcOeTsPtWMOVIYlMRUl2QxjOHOxXoXAC81/dIF/z+Qbj3OWkC8rsH4LOvh3V9LwqGWsFcEdKuw/Yp7FOu+FqVTCuE9vqoHGpJbopqKtUX6ZcnQNk5ZKfdag/6LE1JSsAjijic7tC1hnKr4dTvQ+7LgsPWI1uANRgNPaM8pJSYdNUuOP8qrP/0xZeSEvSkGQ0Mjk2S40fvYybtVntoCv6TNklzonRrJD0GYCR7LYOrvkrek3dJ99kwJ+d9o5Pkpy2A+/ICccDwUmI20RGBo8+F/jHu3Ow7zX0WpZsl3as1MjVF1OLo41KALUFabKicvp9X+SmZerdjipLsKimIUrpZuX6EIEA5kx01+fzHH89w77YKQMqA+OiahVHuIwtBgPLt0PY+LN0h7731j8LWh4LuVmI2sffhazjUNkTr4DgVOSnUlZvjIvgA0v19y5Js3js/qOhCj5YBMYd9TYORC1AajJLa6dyfcCcTCrdn0Ou4ankObzbO96r/fy838Lc3VEWvljo1L+IViaCIItitYMoKvJ95iVR7HgJ56UY+uamU770RWtbELMYHIMWHz7Pa5K2UJhJePvixJIwz5yYX1xacgUjNhTsfh+e/AIMRCoUC5dkptFmiUFtvMELPUVh6rXRd59VIwbL2/eofOx4RRXCGVosK8Pa5Aa6pisH1FIgoZkAUphvpUchi0C/dx2TpP/zy/VY+s70ipAFUbWG6PDvO3BopoLxYsfUomgEhiiIDNgWtI6t2+cw0W1+aydEQdCBEUcQ+5QotcN/4ElR/REqdj5D8dCMtWVfCxs/A0/dJ2hIycXtEBIi91W8oLLAARFGmka4IxHTP94+xLDeEoFJJnVSyGQ+4XXD4V1B3/8WXqgsC3w/3N1tIqbsLTjytbF8sFyDbh029H5bmptAzMsH4pORC1jI9cV6UVH9YvhvG+KAUJKr+cEi7C4LApoosbq8rZVNFVtwEH7zIMTAIFS0AMQOXR1THWzcOuW19Mc/POZk+aLZgHZ/iw6uiuDofjRKMsX7pOMGQafF23/YK3jk3QJPc+muPO6QsC8WZ6YThGJFWsVZ9fN5u3SMLNAABktbFx34ET98rZZpEgF4nkJqUELE1WEi0vgsVV136fdsXpPKYy5GJIUgOEiycwd6GfnbUqCyWK5e0QslKNArodAKJeh0Opww7S7n0HJNSUUPA5nDy5tl+bl4Tmo7BKrlClCm56getY4lrUsrIU4i+0UkKMozKDWgL1kipxXNSkjeUmznSHlwHYtjuxGwKsbTshALlF9NctOLccA+UbYUX/kp2GnvvqGNhiDODlFW3QBwwQFpldbo9YWlriaLI6ISTDFMIpaPGDGkMNhUHAtONf5T0TWYsjtUWpNHoR3tqfNLF2KSLzDU3QfObYQXR/GJpkpUBIQgCVy7L5b0Lg8q47MQzS66B5rfk3S8O/kwKLOkWgJZaCGyqyOJ09+jFgJMSLNKzJTxaR2FNSQT6DwuIdaWZNA2MXZxcudwe/r+XGvi3j66I7t+fmq/+YDKY/oOX3BppYBUiBr2Of7m5Vp4gpXMifDGtSJkZgDjya1h758W0v5l0DU1QtFADEPz/7d15mFxllfjx71vVa/Xe6U530t3pTkKSDlnISsK+ExAUVBRFFgVxBJkZZZzfzDiuM+MMOg6iAipK1CAKKoICQiBhh4TsJIF09u70nt636rXq/f1xu5JearlVfWvrPp/nqSfpureq3u6qe+vec897DlC0Aq74T/j9p415sBNQXpjJwUgUojzxrtEizKNohTHv/uSB8L92rAmiAOWQy83+2g6WlWSHd0zBSnIY71+ElOU5qGoJPX05oCAKUD65vZqPrywmKcHc4cWSYAtRKgWOacYVpslmqN/yui8HGjpZYGVxOKWMk6bKt0bdvWJWDjtNFKKsbOlhlpn6D12N0NtqZIRZoDArmcbO4W3ywn+GhBTY/J2gnqO61RlbU7386ayzvJhpuOWmJdHa42W6cQCeIJtpRcuhdlfQr2O5rQ+PS9Evn+H7mGN7ZSury3KN47ayC+DIZuvG0lYJOaVBPeSyhdN55cBJDjZ2WbuPiTVJDqN4qdnzg8E+2P8ULLspvOOKIJtNceWZBbz0wcQu7I16TsueKY5prdle2crL1W5mZKWEpd9prFFKcdWiQn762hH+uKOa/3r+AOfMyeWM6RHeiaTmGAcZ4dR00GQAYkFQAQiAc+fmkZWayIv7G9he2cofd1SzvbLV92coWm2xBvuMA9vuJmM6yo5fweIbvJ4k1bbHcQaEx7zL4ew74YmboKfFCESMvJk8OVxQmOG/L7cVOmqMKyBJYw5sz7nbmEM41QRRgHJnVRvLZ+WMqyAdE2wJ1l6h8mN2XhrHmy3uhDHYZ2wrPc1GezZUwG1nyOXmye3V3HT2LNMvc+bMTN4PqRBlcPvquBBEJXqzKuq7WGhFAcqR5l89rh1nYVYKLd39AQuVnWh1UmqmA8b7f/aaoReqgswUGjqGszaUMlqcNx2Cdx4a//3g43NudMCIk+/GzhrILI72KIJSkuOgOoRClIdPdpkrQAnG+1qwxMg6DOGYwDLV24x6VWMKP87Kdfic+rnl2IgadUtvNAq0WsE1COigO6asKs3hzSNN/HZLFelJCZP73MlHC2Kv9j4J5dcahd8nkeuWzeTX71QFPs8xacoXoaxpc3Lr+m1UtzoZcmnef+MYL+xvYMPtZ8dPpDsENW1Ont5TS01rLymJdnoHXczOS+PWc8si+3vbbOHvydx8EBZ+OPB6efNDmlt8+/ll3PhzY75+ot3GoMtNSa7D+2eoq+F0JfFIGeyD+8uN1HaA7w+f3P1oqREAurdiVD2RSRGAAFj0MXjuXvjfOeOXefm9vSmfkcFze8M8l//4mzD7wvH3z78aXvnu8BSiGOrwEG5tx01nQGyuOMllC2P0b5M+3ZhelhX+kwDLO2GM3WcA3Ddc4M3PtvPC/gbOnTuNbLMp9kB6cgJDrhAKUTZVGFfiJxOL6z8AVDR0ckeAbiRBm30hvPxN47t7RMbkwhmZVNR3saQ4y+dDq1qclOWZOMbY9ye48TErRgsYAZJTGRBgpEZf9yD8YB689LXxD/DyOa9udTLX7IlutMXZFAyA4lyjFWewGW1HTnYHbsEJ4/drr3/v9DKTxwSW8dKBDIanfqYk0uEcP6Vk67FW/u7C4YBFyRp47stGodaJdjtpPwHZwWU/eM6d6jv6eGZPLTaleOto8+Q9d5q/Dp66E87/sv/1tIbtv4Cb/hiRYUVKTZuTux7fxfGmHr7Z0MWQ2895jklTOgNCa82t67dR1eJk0KXRwKBLU9Xi5Lb12yZtNM/ze9e196GB3uG5wydao/R7J6aGdz5e00H/HTA8kjOMcbjNt5rRWvPVP+5lyK0ZdGmcAy7/n6HuKGRAuAZGn0iM1Ns2rsNKZ+8gmamTIDbpGoAhH1dTvPze3pQXZoa/FefY+g8eNhus+hxsfzS8rx9rWo8btTxMeONQExfMywvzgEIU0VacaRxrsnAfGuQ+A4x94fq3j/O584I/2S2f4Xves1f5CyZnIcowpM0fbuxmntWZjUkOo0vNmJpJK2YFrgNR1WKiA0bzYePqoYV/i1M1IEayJRjdr7zx8jmvbnNSEi8ZEN2N0em2NQHFOalUt4aSAdFtLjAUwn4tLNoqjQBR6bleF5cXjM+87OwbZMjlJjdtOLhrs0H5NXDguYmPJ8gOGCPPnbQGtzZq6E3qc6esYhjsMTKI/TmyCQoWW97JKJpGvd8Y54xWnCtP6QDEjqo2alp7cblH//Fcbs2JVic7TMxnjEcx93uHuw5EV4O5IpQA2SXQccL0U3v+lmO3P59/y65G82OJgoEhN4l225Sog2JGbloS7b2DuN1h+kLV2qiUXLzK+/JlNxmpyIOhVwePO23mpmBUNvcwLT2JjJTg0kYjJoKFKOfkRaAVZwA7q9qYnpEcUiX0JcEWoswvD6pgcNywOANiYMiNy61JTQpDIbQF41OSzRSiPNHaQ+m0AJ+RvX+wvE1iVmoi7c6JnWAaUzDi4Oqu1kZgJRrFrifAmIIRfC2bI+EIsoXT1p/B2rvGdSDz8BaQ3XaslTWzx3ToW/JJI91/olqOjJsK4k/MnUNEyhlXGAEGf7Y8aKr1ZjwJ1/s9pQMQlc09JNi97wAS7TYqo3xAFy4x93uHsxWns9VIrTN7Qp1fbswLNSnov2VXveVzfK3U0NHHjHip8h0hxTkOakKYl2pKW6Vxlc9XYdKkNGP6kBUHGfHC2RK4ZS7wSsVJLou17hcjZc6IWAZETloSbRM8uZqoX7x5jM9fYC5zZaygO2FkFhlXECebzjpLAxBHm7qZOz1M85DnrRvXmu7MGYHrebT2DJDjr1uB1nDgWXPTJoOglEIpNaFgckt3P3np1hYJDYv+Tki2uO5HBJTkpob0XdvcEyfvC0Bvu9HB4szrfK5SXpg5LgDxztER9R88ppdDX/uEO37RcgTyzLfgjLlziEhZML72zSgN+439l8mCzfEiXO/3lA5AlOWl+SyYNOhyT9qetjH3e2cUGlMTwqHpoNFe0yzP3GKT/P0t+wZdpI/tdd7dGNMBiJp2Z3x3wAiDhYUZHAhXIUpf0y9GWn0nbPtlUFOD4tZAjzEly0TAcHNFY+zWfwDImBmxDAiAbAuu8IaqqqWHk139rCrNCenxi4ItRKmUMWWuL4igRTzoqrc0dbeioZNyqwtQemQVGZlZPS2n7kpKsJHjSORkl/eCfs6BIVKT7P4z7Gq2G9/DKb7rSIQq15FEa4jbSFxlB8Zh/QcYnibTEVwAoqW7n1xHUny8LwC7fgPLPuO34GO5l+LX2ypbOHu2l8D84huMjgsTEeQUjJg7h4iUmSug/j3fxaW3PATn3BPZMUVAuN7viAcglFK3KqXeVkq1KqValFKvKaX8VpJSSn1WKeVWSnWPuL0z0bGsKs2hJNcxroK63aaYlesI+WAq1sXc7x3OKRjNJus/eOQtMB5jkr+/5fSMZB7YdIgfbDxIt6d3bld9TM/LrGvvoyhe5rhGSPmMjPC14jz+ptFj2p/MGVC4JHDq32TQVmnMLQ+gq2+Qlu6BwKnc0RTBDAgwClFGaxrG+reOc/t5s0M+CchISWRgyE3/kMv8g/IXBJWtFhc6643AlUUq6rsoD2d7vHnjU5JXzMphV1W719VNdcDY+wejwn8YFGSl0NARWreDuvY4ak/dWRt3HTAAEuw23JqgslSOnOxmXkGcFAZ1DcLux2HFrX5Xy0lLomPE1M/WngHsSpGV6iVosfjjRsHWiegMbupXzJ1DRIrNZhT/PLF1/LKuBmjYB2dcHvlxhVm43u9oZEBkAP8BlAKFwDPAi0qpQHvLOq11+oib9+otQVBKseH2symd5iDRrki2Q6JdUTbNwYY71sRPRDVIY39vR5I9ur+3p1p8OJgtQOkRZHs3f3/Lp+4+j2f//gKyHYlc/9Db/O7dE+hodDSwJxnTULxJzRnVd762bZJ0wICgfm9/jHTIMGRAaA11u2HmssDrnnO3MbdwsjNZgPLNw81cND8/AgOagIyZRsAxQubkW1gHwp4EiT5OFMdsOx3OQd452sLViycWWF1QGGSgLz+4YHFccLaAY1rg9UyqaOhi4YwwpuLPvxoOvTDqruWzctjtow5EVYuTWdP81FBwDRrp6WE6iC/MTB7dCSOI74j4asFZa3kx00iZnpFMU3e/6fUPn+xmbr7JAIS/99ueaHRGCaf3n4G5l0JqdsBVR9bDePdYC2vn+NgvZM6AlMzQg7FBZB16xNw5RCT5ase57RE4+/NGkGKSCdf7HfEKNVrrsY3tH1BKfRtYDdREejzFOQ4233sRO6raeO61d7n24jWsKs2Z3BsQo3/vyuYeyvLSovd7pxdAd5iu7jYdhDVfNL++I9eohjymvZg/gf6Wn79gDjesLObHm49Q3dzFsSNtXLwggkGIxBSjvZS3Cs/2pFFtp+raeznvDOsOgKNq7O+t3fDIJXDnZkh0mG63NTc/nSMnu60fX8sR42q/md7bhUuMz2P93kk3v3AUkwUoNx1o5MZVJREY0ASk5UNPU8RebnZeGges6tiSkGzMCb7uIcieNXrZmH3G77ad4MbVJSTYJ3bgtbgok321HSwtzjb3gPxyqHp7Qq8ZU7QGtKUHsNVtzvAGlGcuN676uQZP7cdWlGbz6FvHvK5+osVJqb8OGEc2Gy0+E8Izn78gM4XGzhEnt2O/I4b64NF1Xr8jjA4YcVCAEowpGAVnRnsUISnJcVDd6qQg09z385GT3VxSbvJ4yt+x0KvfhU3fgau/F9TJuGlaw7s/hRvWm1rdU4iydFoaW461+P8dl3wS9v0BLv168ONqORpUAUqPmDqHiKS5l8Br942+b6DHqFvzd29EZ0wREI73O+qhGqXUGiAdeC/AqtOVUnXDt78qpSw7CldKsbosl3Nn2Fhdljv5N6Bhnt/7E6tKovt7h7MIZUc1ZAV5opIxI+iiPoH+ltmOJL551RwKcjN5Yls1tzz6bniuqvuSmGJEycfexpyE18ZTmqkZI3/v1Gyj7VXj/qB6fScl2LDbbPQOBJEebsbx142DbbPOuQe2PmztGGJN6zHI9R+AcLk1e060szLW0zxtNuOgM0ItySxtxVn1NuSUQuFiv/uMgSE3T+2q4ZOrJx4MMgpRBrFPzJsfVLZazOtt8311NgStPQNkpyZis4Xxe91mg5K1cGLLqbumZ6TQ5hxkYGj8nOHKlh7/GRD7/mCcTIVJYZaXVpwjvyPSpxvfEXW7x31HVLc6KcmNk+/GzjqjUGscKs5JDaoTxpGT3cwz04LTw9ex0Lr/MTKQ3n4g+EGbUfW20crRxBRDgIWFmVTUGxlh2463srrMT2HmhR82ToBD+a4Jsv7DSDFzDhFJyRnGfqL5yOn79vwOFn3MyCSZxKx+vy3LgFBK/Rq4zc8qr2utLx7zmBLgSeA+rbX3kLnhDWAJcBjIBf4NeE0ptURrPa4UtlLqXuBez89paWls3Lhx7Grj9PX1mVpPWMvu6mN17WG2Wvy3t7t6Wd07xNaXXw7qcQt7U2l84be0Zlt7pTml7yRnDiXx0enNHGrX3LX+TYrSFB+ZbSMrOTZ23Efrhnhv6+vsC3LHEi/bznRnITkv/YyDZcEVuspwu9jwl5cpy7TufTrr0B85PvN6Os3+3bSbcw6/w65nf09/UuAuEfFo5eEdvO9eRd8h33+Tox2aaTY3mzcFt11Hw5o+Nzv/9jRDCd6nM1i53Qy4NHuPuyx5vuUV3+dY0fV0BHiurQ1uSpM0W15/ZcKv2TukeeeAi40bTRbu1G7Oq3mft+Ngv2NGek8Vc52K9yz6fQ62uUkf0mHfLxv71J+P2qfmKhfrn36J2WP2l7sOuVhsq6XryPj9qN3Vy9qj7/J2+iegIjzHa1Xtmp0Nbja6j/tcJ3dgDjM3PsD+o0Oj7t/+gYucbhsba/cG9ZrRsPL4e+y3HaH/g/hrh9jW4ObwEXCcfN/U+ofrhtgbwjGLNyrto6zcfh+1lc3U5wdxccAEs/tUj5ZuzeuVbmY4jzLodPH2a5v9rr/UncOJp35Ce8aCgM89ctuZU/Mivcn51E+S/WgkzHKXop79EVUzrwXt5tz3fsSOM7/BgPwNg6O1tuSGkcWQ5+eWNWb9M4DjwPdDfL3jwBfMrFtUVKTNePHFF02tJ8LgJ6utf86aHVo/dWfwj9v6c623/sz68VRt1fqZu0/96HK59dO7avTl//ea/vGmQ9rZP3Rqmdvt1tuOt+g/bD+htx1v0W632/rxjOF2u/WlP3g1pMfGzbbT16n1Q2uDftjDrx7RT247Yd04XC6tf7xCa5fxnpt+v3f8WuuXv23dOGLNg2cbfxs/vv/iAf3M7poIDWiCnrhZ68YPfC62crtxu936nP/ZpJ/cNsF9RtNhrX95panX+/BP3tTVrT2hvY4XV9z/mu4f9P/+j/LT87Tut+71o+rQS1q/8K+WPd36t47pDe8ct+z5fPKyT/3128f1o28eG7fq5f/3mna5fHwud/9O603fMf2yoWw7J1p69K2Pvut/JdeQ1j9eOe5zdf1Db+n2noGgXzMqHlxz6rsl3uyobNH//Mc9ptbt6B3QH/nJm9YOoLdD659fpPXhl617TpP71JH6Bob0+fdt1l/78179lSd2B96fV/xN62e/Yuq5R207T31B6+odQY1tShvo1bpur9brrzI+K3v/aJxnDPRGe2QxCajRPs7NLcuA0Fp3A6YmSg9Pn9gIPKy1/s9QXxKIjcvGYuKUMtoMWlnApemgUagsWPkL4INnrBuHR3fDqErDNpvi+uVFXLW4kEffOs6HH3yLuy6ay9lludz2621UtzpJtNsYdLkpyXWw4fazKQ7jHNSWngGmpSeH7fljQnKG0Qa1+QjkmU87LJ+RwRuHLJzP33TA6Lhis1PT5uTW9Sbf76U3ws/Ohwu/Ckkx3AEiFK5BUPaA+4DXDjZx5wWBC1XGhMzhQpTTF4b1ZTyfofr2Pr711/cZck9gn7H1YVh7V8DVthxroSTXYek+aX5BBocau1hcZLIFY958aDkMM86ybAxR0xVcJfpAKuq7+PjKCHRC8LJPXTErh5+/cZTbOT2datDlxm5TvqeE7H0SrrrP+zKLFGSmcLIrQIFDmx0WXAUH/wZLbjh1d0fvIFkOE/V6ok1r0K7wF1QMk+IcB9Wt5jIUj5zsZm4w0y/MSMmETz8Bj33UKAg7c/nEn3Prw0YhaZM8+/Oatl6e2F6NAvbUtPvfn8+9DF76BgwNBFdDpeUITIuT79NoG+yD+8uN6XIA942Yenj4JaO+SBDTe6e6aLThPBd4Dfie2eCDUup6pdRMZchWSn0PyAFeCPRYESdSc6Cv3drnbKowTvKClV8enrnFXQ1Gwc0xUhLtfOmSM/j9nWvZUdXK5T98ncrmHgZdGueAi0GXpqrFyW3rt3myf8JiUnXA8MdXFWM/ygszTs3HtMTxN2H2BWituXX9NqpanObe78QU46B4z++sG0us6Kg25sj6UdPmJC05gWxHeIrUWS4j/K04R36GNNA7OIF9hrMVqt4x5hQH8Ms3j1seCFpSlMW+2g7zDwjXvjoaOust7VxQ0dDJgnC24Bxp/tWj9qnlMzLGFUT128ayqwH6OmB6EB2rQpCUYPPZz36UpTca7UCH9Q26SEmIkxP6vnZIyY72KEKWn26+C8aRxm7mTQ/DZzyjED65AZ7+otGZaSI8+9Tya02tPnZ/7nJrhtwm9ucJSUZNqaP+p2qMeTHj82Jh7ZlJzTVwOvgwVm+b9+KmwqdoFKH8LpAN/JdSqnvE7WueFZRSLyilfjbiMeuAnRgZFhXAIuAyrfWJCI5bhFM4WnE2HQquBWc4xwLGQZafK1z5Gcl8bEUxbq0Z2wbb5dacaHWyoyp8czrr2qdKAGJd0AGIwkyjeJllAaDKN2H2heyoaqOmtRfXmDfc7/u96g7YsR7cFhfFjDYTBShfrTjJZWYrnseCjBnQZbKmQYhC+gz5fLJHYeVtAa+eHjnZTXffEMtKskMYsW9BByDy5huB5smgq86yDAiXW9PdP0RWaoSu2M+/ctQ+NdFuIy89mYaO0wUfK1uczPLVAWP/U7D44+EeJQDJCTb6BgPsOwsWG+9HTzNgBD7jpwVnXdy24AQjM9SmYMhEoOhIU5AFKIORNw8+8hN48uZTn4OQmNynnlp9IvvzpTcamURmOVvAkWd+fSEsFPEAhNb6Eq21TWudPub23yPWuVpr/cURP9+ltZ6htU7TWhdqra/VWu+K9NhFGKUXWH/S33bcdMXhUZQyUu96WqwdT1eDEVn3o7K5h0Qf7ewS7TYqmy2qcu/FpOuA4UtOGfS2GzeTlFJGf/JA6btmuF3GSVP+Qiqbe0iwe09J9vl+p+dD8Wo4OMkSwFoDt+DcdOAkly0cn0UUszLDnwER0mfIm6F+46rv8psDrrr+7ePcfn7gdqnBWjQzi/endAaENQGIE61OyqZFcIqWl33qitIcdp04fbJ0oqWHUl8dMCIYgDBacfb5X0kpo6r9+08DUN3aS4m/9qGxpKM2YCZZrCvMSqW+I8B7BBxu7OKMcAUgAErOhkv+HX7/aaPVYrCC2Kd6TGh/XnI2nDwAfSa7CU2gA4YQExX1NpxCAEYAosvCAMRgL9gSwR5imZO8+dBs8YFtd+AARFlems8U0UGXm7K88B1U1rb3UhQvV3km6ozLgktVBBbOyORAgwXTMBr2QcEisNlCf7/X3j35WnK2VUKu75T+nv4h6jt6mZsfR7UvMoZrQISRv8/QwFAQ+4x9fzKmJyX7T2lu6e5nZ2UbV5xpfSAoy5E4PA3JRJo8GJ+XVn8NtOKIhRkQFfWdlM+I0PQLjzH71BWzctg14mptVYuPoEjTIeMzZ1HwJZCCzNGZGT4tuQH2/RGItwyImrhtwelRYrIVZ3VbBAJD5R+CZTfBHz9r1CkKhsl96kgTOgZU6nRLTjNajsC0uabHJoSVJAAhYoPVGRAtwRUZHCe/3PrU3u6TkOY/fXxVaQ4luQ7sYwp12W2KWbkOVpWGb66eUQNiihTQWXA1+Gn16PUhhRlU1Ju8suDP8TeMuZoY73dh5vi/ecD3e3o5JDqgdufExxMrWo/7nYLx9pFmzjsjL756jWfOMFKiw8jnPkMZc94ffvUIR04GCJxpDdt+Dmv+LuDrPf7uCT59dsm417OKpxClKQlJgDIKr8W7oX7L+sgfaOhiQWGmJc9l2ph96vJZ2aMyIKpanczylgGx7w9G6niEFAxPpwsoexbYEqD1mHGiG8YC0JaK8ykYACW5Dmra/BeidA4MkWS3hW0/NMqqzxnFKJ/7srGvNOPUPvWLgdcd+VITPQZc8kljmzJDMiBEFEkAQsQGqwMQTQdDK0DpEY7UXtdgwOrESik23H42pdMcJNoVjiRj3uCsXAcb7lgT1pOvuo4pMgUDjCkMtTvBNRR43WHlhRlUWJEBUfkmlBkBiKbufhLtNoqyU0+93zYF+elJgd/vc++BLQ9NfDyxor3KOOj34ZWKk1weT9MvwOhUMmiuonuovO0zEu2Ksrw0Xr73Iu68YA7/9If3+MYz+2nxVdzt2KtG1leA1O2+QRd/2VPLJ1aV+F1vIhYXZbE/mGkY0+ZA69GwjScihvqNjD2LVNR3sjBSBSg9xuxT89KT6eobon/IqLdQ3eoli0BrOPCc6QJ9Vig0MwXDY8knYO8fqW51yhSMCCrJcVDT6j8D4lhTj/UdMPy5+N8ABa9+19z6x14b3qcGl43ic38+zeQxYP58YwqGmal/LUeMWhfCHHuS74KdqTnGcmGaZW04hZiQ9OlGhoBVmg5OrPVd/nzY8qB14xnqN71zKs5xsPnei9hR1UZlcw/vHmth9ezcsBeI7B1w4UiaIrsEmx2KVkLNdig9x9RDgroy64tr0LjSnzePrr5B7vzNDr7x4TO5eH7+qfc70W7jt1srA7/fsy+Cl78F7dWQHb4TwojQ2qggneC9DazbrdlW2cp/XLc4wgOzgC3BeN/t4SsIOHafUZaXxqrSHJRSFGWn8ue7z+PPu2q48ZGtfHxFMZ87r4yUxBFF0bY8BJd+PeDr/HVPHVecWUhacvj2E0uKsnjx/XpuXG3yAXkLjGy1MLc6DSsT9YGCcby5h9lhnK7nlZd96pKiLPbXdrJiVjaDLjfJYztJVG8z3reUyGVrFGSlcKjRVMd4WHQ9/OoaqofOiaMpGLVxPwWjOCeVTQf8X5A6cjKMBSi9UQqufQCeuAm2Pwqr7/C//pYHTe1TvfG3PzdlyQ1GXZVz7/G/nom6S2KExBSj1aa3bhf2JGnBGSTJgBCxwfIMiArIn0AGRGYxdNRYN57uRiPIYpJSitVluXxiVQl3XXIGf9kT3jRu58AQqUlx0mbMKkF2w0hLTmBgyG1+fro3dXtg5jIGXJq7H9/FzWtLuWTB9FHv9/XLi8hKTWL3iQDdC5Qy0jvf/Zn/9eKBjxa1HvvrOigvzCApIQ6/ssLVVWeMkZ+h1WW5ow5W7TbFJ1aV8Nd7zmNgyM1HHnyLv75XZ3R1OXnACJAG6HevteY3Wyr57LllYf09Fhdlsr82iKlO+eVGHYF41mVdAcqe/iGSE20k+ChmHFZjWhwvL81h94k2Tnb1Mz3Dy8H53idh6ScjOMDhDIgukxkQqTmQO5uSvoNhDbpZqvtkUMcasciYguE/A+LwyTAXoPTGngCf+JXxuT3wnO/1TO5T/fG3Pw9o8cdh/5/8r+N2GyfSctIcnMQUI2A69iZ/x6DF4dGcmJTS8ibW6mislqMTm9tms0FyutGb3ApdjSEXGJubn45zwGWucFaIpkwLzpHmXgZHgitEOTc/nWNNE+hEUvkG7tIL+Jen9rJmdq7PVPbPXzCHX75lov/44o/D4ZfMV72OVW3H/Rag3HzgJJeWx9n0C4/MmWHvhGGWIymBf7x8Hr+9Yw1vH27mhp9tofnl+42ipgG8cbiZ+QUZFGaF90Ar25FEd/+Q+UBf/oL4b8XZWWcULLXAwcYu5hdEePqFx9xLR+1TVwzXgahqcVKWN2YKw9AAHH/d2A9HUGFmCo1BfJf2ln+cq91vhnFEFtIatMt0y8dYleNIpLXHf12Xw40RzoDwSEqDT/0OXvsfOLHV+zpbHjK1Tw2bjEJIyYaTfvaLHdVxP1VHxDcJQIjYYE8Et/n5+H65BkG7faZzm5a3AJoPWzOmrnrICP0E6iNnzeSv79VaMxYvatv7pk79B4/UbOPWauJEf9iCwgwqGiZwsn/8TX5eXURasp0vXeI7QLZ2Ti41rU6qA8yDJSEJzvoU7H4s9DHFggAFKF87eJJLFuRHcEAWyphhdDiIIdMzU/jeDUv57ysKcFZu50s78qlq8R9Y++Wbx7gjDK03vZk3PZ3DZtPk8+ZBi0X76WixMAOior6LhZEuQOkxZp+6oMCom1PV0sOs3DFTQo5uNqaRBaiLZLVsRyLtvea7GVTmns8a166g6gVFTW+b7znqcUQpRaLddqp+iDeVLT2URrLV7EhpefCpx+HZfxxfK6z7JNTuMrKBomnpjf6LUUoBShFlEoAQscOeaE0189Zjfq+mmmbllbXu0DMgAD581kye2xu+q6hGB4wpFoAA4yDh8EumV184I4MD9SHWgRjqp72xit2dWXznI4v9plQqpfjseWX8+p3KwM+78nOwa0P4D5AH+9B9Hew8VMXTWw6w81AVuq8DBkPMzBnsMzI3+jqNlNX0QuP/Y56vsbOPBLuNaekTDChGS+aMmMmAGGtB9ZOUXHEPN6wq5a7f7uK7z39Ah/P0yZnWmu2Vrfx482FaewZYNDMyJ7aLi7LYX2ci+2ywzwg4D/aBs/X05ynUz2S0WJgBUdEQhRacI43Yp9ptitREO09sP8Ggy21M+fHY+2REu194ePa72mQ3g+ouN/XZy+D4a+EblFUmQf0Hj+KcVOravW/HA0NuFCq6U/JyyuCjP4cnb4Gmw6f3PVseNtp2eqsTEEkLr4WK542pFt5MNEtYiAmKk0ltYkpIy4eepqCrBo/TdHBi9R888hf4TrELVlcDzDgr9KFkJJPtSOJQmNJr69p7I3ZyEVMWXA1/+6qp9oMA5YWZPLm9OqSXeueNlxhwzeHHN60w1TrsmiUzeejVo/xj3yCZKX4KGDpyoex8OPBXWPyxkMYW0GAfrv9bgL2vnZXAyhGLXCnZ2P/pYHBzIAf74P5y44rdWKk5RqGn4ed7peIkl5bH8ZzmjJlQbdF+xEqDvfD+06gvvM4lSQ4umJfHE9ur+fjP3uEza2ZxyYLp3P6b7VS3OnFrUMBl97/OhtvPpjjMLQmXFGWx6UAjn/TXbWPsZ+j7I7IzxnyGYp6VGRANXfz9pVGsbD+8T62Zfwu3rt9GZXMPbg3vVXfwzJ5a4/OTOmQEHUvOjsoQcx1JtPYMmApqVrf1osqug71/gDMuj8DoJqCzbuLHTzGiOMdBdavTazHVypYoFFn1Jr/cCPo8tGr8sjd/EN19UHIGFCyC6ne9F9puOQLzr4z8uIQYJhkQInZYVYjSsgCEha04Lahy/tHlM3lmd3imYdS291IUL1W+rTRtrlGfo99cVsOsXAdVgaZFeLH1WAvHtv+N1ZdeP7r7gB9JCTY+vqKYJ7eZCHisvRu2/tR8j/IgaVc/9r52r8vsfe1ol4/2jr64BrwHH8C4f8TVI6P+QxwHIDJnGNt/rHnvCVj4EUgyggkJdhs3ry3l6bvPpbGzjyt/+DqVzT0MujQut2bIralqcXLb+m2mrx6HaklRFvsCteIM4jMU87oaLMmA0FrT3N1PfkYUs4WmzUV3NfB3j75GVYsRvAJGf34O/BUWftgopBsFBVkpNJhsxVnd6iTpjAuhbjcMTKD+TyR01EyqDIhqH4UoDzd2R74ApTeuARjwMVUsFvZB/qZhyBQMEWWSASFih1WtOJsPwjwLrlRkl0Jb5cSfB6B74gGIK88s5KFX3+arVy7AZuIKejBq23unXg0Ij7mXwNFX4cyPBFzVZlNkpCTS7hwg22Fu7nJFQyff/Mt+ns09TvKCfw9qaDedPYsbfvYOnzuvzH9V+2lzjQyi6m0wa01Qr2HGrhPto7Iexmr8y7cozA0ig2bIXMCib9BFZUsP5YVRTCmfqIyZxpXJWOJ2w/Zfws1PjVuUkZLIZQsLePSt46dOHj1cbs2JVic7qtpYXZYbtuHlpCXR1TfEkMsdnW4OkeZsAce0CT9NfUcfM8JcJNSMxvxzmP3edt53j74y7Pn8dG77HVkfeyA6gwMKM5Np7Oxj0cysgOvWtPVSnJtmTC2p+Bss/UQERhiizlqYsSzao7BESa6D3SfavS47fLKLeQUxEICIdXMvhY3/bkxtHltrpaMGsuK8fbeIa1Pgm13EjYxC40R9opoOQt78iT+PPcHo7TsQ/BXvcboa/bYZNCMtOYFFMzPZURWgPWMIWnsGmJYW2WJgMWP+Oji00fTqCwuNwmpm1LX38g+/381PPlFO8kB70FWnsxyJnHdGHn/bb2K7OPce2PKToJ7frBPN/q/8HU89E2ada/5WYi5IsuVoC+fMmRZcC7JYY3WHHysc2QSFS30GRSube0j0ceKfaLdRGeDzYIUz8tM50mSyEGU809q42SZ+OFbR0El5tApQjhxHxnlcat/lddlMezsuZwfkW/AdHaKCzBQaOswFQWs9HaICFfWLBZ11kyYDoiTHdyvOIye7mZsvAYiA7Ikw52Jjfz+Ccg+CLSHuu6WI+CYBCBE70gsmngHhdhlXV5Msmh9oVYV118DEu3IA1y8r4mmLp2G43BqbIr5P8iZi1jnGPElfxZrGKC/M4KCJAES7c4A7N+zg2x9ZxIKB0Oc7f+68Mta/dTxw2vusc4xih63HQnodn2p2cvnuL/ldJal8HSy4yvzN5FzqzRWNXLowjqdfgHGQp11hmx4Tki0Pwjm+39OyvDSfbTAHXW7KIjD/eklxFvtqJtAGueWIdYMJp942o3OEBSoaumIiWyh9/vmcxSEU4z9D6/TbdM+/PvKDGqHQ5BQMrTX9Qy5j2lzhYmOqTHdTBEYYoo6ayVMDIjeV6rZer8uONvVIAMKspZ80Cr6O4Ohr8Nt1SohIkACEiB3p0ydeA6L9BGTPsmY8MNwJ49DEnmNowIhEW+D8eXm8e7zFb3uqYDV29lGQGf203aixJ0LhEqjzfsVurPIZmQFbcfYNuvjCYzv54kVzOXduHhx/E2ZfGNLwSqelUZiZEjjzRSlYexds/VlIrzNO+wn40x2w6Vukf+g//a66Yla2Na85gtaarcdaOWfOxFPToy45E/on0L7VSvV7jc9K4WKfq6wqzaEk1zGuWKrdppiV62BVafhb/S2amcn+QHUg/Hn2H+H5f4q97JOxuuonPD3Po6K+i4Uzop8BsXL2dKoS57DcPrrFsd2m+FjiVkouuDlKIzMUZKbQ2BE4ANHuHCRn5FS7xR+D958O48gmqKcJ0uI8YDssMyWR7r7x7VKHXG6GXG5Sk+TqvSnFq42s4L7T+9K03nqp/yCiTgIQInZYUYTSqgKUHla04uw5aQRXLJBot3HBGXm8dtC6qzB17b3MzJqi9R885l8Fh140tWp5of9WnC635stP7GHdokI+fNZwYbnKN6HsgpCH9/kLZvOLN0xkNpx5HRx7zXdxPjP6OmHTt+H3nzYOuG97lsEZK+jE+xWnHnumMVUpGPYk3/3qU3PAnsSB+i5m56WZLtoZ02KpFeeWh+Ccv/e7ilKKDbefTek0B4l2hSPJTqJdUTbNwYY71kQkW2pJURb76/wEbQJ9hm5/EWaugF99CN76Yey25uyst6wF56HGrpgozqeU4qzLPsVH0/aN+vxclN1MWXExyqKOH6EqzDSXAVHd5qRkZHHmxTfE7jQMC6fyxApHUgLOgdHtpavbeinJDW8XHtNMfI9FnVJGwdcDz566K62vTgIQIuqkCKWIHVYUoWy2OgBRDvv+NLHn6GqEdGuucAFcv7yIR944xrpF1jznlO2AMdK8K2Drw3Dp1wOumu1IorNvELdbjysGqrXmO8++z6xpDu44fzjFsb/bqJ6eEXoNkJWlOTR391PZ3OM//d2eCMtvhp2/hvO/EtyLuIZg16/h3Udg1e1w56unClc9urWegbUv8A8Xl7LrRDsnWpzMmuZgWXEW33i6gnlv13HXxXPNv1ZiitGizFuVcHsSJKbwSkU1l8Vz94uRMmZCVx1ML4/uODrr4OT7cEbgLJniHAeb772IHVVtpz53q0pzIjZVa1p6Mu3OAVxu7b1trYnPEMs/A4uuh3cehEcuhgu/Cos/HrXuC1511VnSgrN/yIXWxEzAbtpZ13Dz3l9SftPa05+fIw+i8j4V7aExfbgIZSDVrWNOdrNLwJ4MLUeNwr+xxNlqtGSeRIpzUqlp6x3VevxwYxfzYiDIBpjbB8WCpZ+E5+81jg0Ah2RAiBgweUKlIv6lZENv+8Seo+mgETSwSu7cic+p76qf0MnnWMtKsjnW1ENH7/j0xFDUtE3hDhgejlxITDXm0JowK9fhtUXYw68dpbN3kH+9asRn8MRWoz7DBCiluP382ax/+3jglVfeBnt+Z0z9MUNrowjnLy6G1uNwx0ZY+8VTwYf6jl6e3l3DFy5dhErJYuX8Uj56zkJWzi/F7sjmf25czVtHmvjzLnN/u1MSUyAlc/xt+KDtlYo4b785UqxkQGz7BZz9BdMn4EopVpfl8olVJawuy414nZi5+ekc9VeIMsBnCDDqAV38L3DL03DsVVi/Dk68G/7Bm2VRBsTRkz2cEUudARy5qMRUVuc4jc/PrGzUwedh4bXRHhnJCXafNU5GMjIgxlxtX/oJ2PfHMI1sAjprIdOaTJpYUZyTSvWYttdHmrqZGysBCDC3D4q2vHlGMfXhbkxpfRKAENEnAQgROzwHtxMp1tZUYU0HDI+EJGM8Zk/mvOlugAzrUk6VUly1uJAX91tzQlPnqfI91QXRDaO8MHPcNIw/7axh67EWvn/DWaMzI46/DrNDn37hcdWiQrYcbaHdGeCzmJJlFHn84JnAT9qwDx673ghYfPIxWPfdcSml333+APdescDnnNvkBDs/vXklv36nktcPWTM1qLm7H5eG6ZOlNoknAyKaBnqg4jlY8snojiMIS4omWIhypMwZcN1DcM3/wWv/DX+41fqCraGwKAOioqGThTFQgHKUkfvU6nehYBEkx8YYkxPs9A36r6VU0+akeGx24JnXwQd/ia2isjAcgJgcBSg9SnId1IwpRHmksTt2MiDiyZIbTmXzJg52Gt2ZhIgiCUCI2JKcDgMhtl7T2pi/blFF8VOmTTALoqthwi04x7p+eRHP7LbmhKZWAhCG+VcFEYBIZ3NFI3/cUc32ylZerWjksS2VPPyZFSQljNmtVr0NpedPeHgJdhs3ri7hd9tOBF555eeMtPO+DmOb8Nw88+A76+EvX4Ln7oWL/w0++RuvVbHfOdpMZ98Q6xb5//xmpiTyi1tX8d/PH7DkhPHVipNcsiB/ws8TM2IhA2LP74zpB7F0ZS6AxcVZ7JtIIUpvCpfALc/AspvhyVth47+Prpky2Dd6mxm77YRAa832ytZT+4tRHW066y0JUFc0dLEgBlpwnjLYZ9S9OfC88ffb/ZgxFz1GanEUZCZzstN/K85xUzDACNBOmwu15ooWR0xnbdBtnmNdSY7DawZELNQ5iTvl1xqZO+3VDNlToL9rwvs1ISYi4jUglFIXA68CIxuJt2utfe45lZH3+W3gTiAL2AncrbXeH7aBiujwtOIM5SpJpzVXksbxFKIMdf52VwOccYWlQ5qdl0bfkIv6jl5mTLCAZENHH4VZ8XNSEjb55dBeZaQqJvkuclXT5uQHLx2itr2X5/fWMzDkRin4013nkJEypttJbzu4hyDNmk4ON64u4aMPv8Pnz58zPtDhMdgH6680TqruG9MRJiUbVt9pXAm/8KvwkQd9puMPutx89/kD/OTTy02l3hdkpvDQZ1Zw12938uhtq5k1LfRCYa9UnOTuiydRimjGTGMqVrS4XbBjPdz2bOB1Y8iSoiweeiUM7TSVgvlXwtxLjbonj14Jq+4wakY8sMR7EdfUHGO+d5ABnJo2J7eu30Z1q5NEu41Bl5uSXAcbbj+b4hzHcAbExFPnD9R3csva0gk/jyUG++D+8tN/x/tKjH/3PB7y39Fqnlac/vZTxverl3EuGW5tWLwyjCMMUkctFK2I9igsVZyTOmqqo9ut6e4fGv89K/wb7IOfX2Bsjw8sJhtOb5Mxsj2KqSeaGRDZWuv04VugsO1XgduBdUAe8DawUSklYdDJZiKtOJstrv/gkV9u1JYIVVeDpTUgPD5y1kz+umdiWRBaawZdbt8ns1OJUjD7ImPKhA9aa25dv436jj60BueAiyG3xu3W3Pvke6OvbAJUvQOl51k2xIyURC5ZkM9ze/28764B310w+trBngBfeM1IyfQTWPjNO5VcOD+fOUH0Wz9jejr3fXwJX3hsBy3d/q8u+jIw5OZgYxeLZsbQ1dyJypxxav5tVBx8wWjHFmdpt3npybQOF6IMC3sCrP48fH6TMVXul1f43nZ627wXm/PDs7+oanEy6NI4B1wMujRVLU5uW7/N2F8M9Rv1Zyaotr13/HSBaPG3Dwrh7xgOBQE6YWitcbk1CXYv343zroSjm8FlTR0mS0zCKRjFOaOnYNR1SLZmSOJgexRTT7ycddwN/EBrvU9r3Qt8A0gCPhrdYQnLTaQVp9UtOD3y5hvBjVB1W9sFw+PapTN51t+JqAmdvUNkpcrVhFPmr/PbjnNHVRs1rb3jTohcGk60OtlRNeZLfoLtN7357Hmz+fU7leODHWatvTvg1Y6TnX08ub2aey4JPgthZWku/3TlAu7csGNcCzUz3j3ewprZueM6jMS1pDQY7A28XrhsfRjO+VL0Xn8C5uSlc7w5xGl5ZqVkweXfhhvWW/q0PvcXbs2JVic7jzVa0qqvpbufXEdSxIuExrPCzBQaO3wHIJq6+snPSPa+MDEFSs81Wh7His66SReASE0aXafjyEmZfiHEZBHNNpzHlVJJwH7gP7TWXi87KqWygDJgm+c+rfWQUmo3sBx4zMtj7gXu9fyclpbGxo2B53b39fWZWk+ET3FDC7aq1zlRE3z69plHN1Gfdx5trda+hzZXP2uO7WRLiJ+N8zpaePsV31fVJ0L3ulj/1IsUpYd24FndpbH1uSf8uZ8s245yD3Lu+y/xduKLXrMD3ql3o7T36uk2NM+99i6tM07Hdc/Z9wLbXasZqrL2b5M84OLHT75Iec74GLJ9yMnlfh67afNmXAn+t6/1H7i4OF/x1mubQx7jwlQ3n3zgJe5eYvPeRtGHJw+7KM9RbNwYA10jLHSus5ctL/4NrU4X84zEdpPZfYQzOpzs2lUJVIb1tcIhtdfN4y80sbYw/NdLrNh2Rgq0v3jj1Zco67Ozc4KfgYo2N2mDOmb2wVb/Hb2Z6LZT2+Lmg1bNrN7DXpcf7dDYnL6/G3P65lC88QH2HQvcTSMSzms8zttv7wIVL9cVzXH3D/H0cy/iSFS8fMJNsh02bgyy49IUF4ntUYhgWRaAUEr9GrjNzyqva60vBiqAZcD7QCrwdxjTKdZqrfd4eZwnD7d9zP1tI5aNorW+H7jf83NxcbFet25doF+BjRs3YmY9EUYHBqF2JwsvD+F9WP8AJR+6BdLDULzu2H+x7orLwRZkj3XXEBzNCtvnqnd6LRUNXdy+LrSpJy9/0MjKtFbWrVs4oXFMqm2n8wnWnTUDZpw1blFuZSu/O7wVGJ994EZx7cVrWF023Iu9pwVO5HLZNR+zfIgFZ7bzo02H+MdPnT1+YV8nbPf92Msvu8xoE+bDtuOt2E8c4ms3r5nQFdV1wP0vH+K1jl6+9/Glpp5La80P3n+DBz9xHo6kaMbHw6Dxp1x5zlmQdfoqZUS2mz89CR/5NuvmXBze1wmTxIpG3jrcwrp1Z4b/xSa47Yzlb38xpBVXLSkkr2HJhD8DNW8d5/IyG+tipQaExX9Hbya67cyq7+TYq0dYt8573YS/7KllTa6TdZfP8/4E7ivg4d8x8+LzjOLZ0aQ1HE5j3VVXR3ccYfBc627mr5jDoplZvPKnvVy3spizZ+dGe1jxJQLboxDBsjJUeg+Q7+d2HYDWukFr/Z7Wekhr3aW1/gGwFfDVG6xz+N/sMffnjFgmJgtPEcpQ9DSFb45zTim0VQb/uJ6TRl2LMLlyUQGbDjTiDnGOdG2bU+ZUjjX/KjjofRrGqtIcSnId467o222KWbkOVpWOaGFZ9RaUTbz7hTfLSrLp6Xdx5GRX4JWDMORy85/PfcB3PrLIknTur1w+D4Xihy8fMrX+0aZuinNSJ1/wAYxOB5EuRNleDS1HjdomcWpxURb7re6EESGrSnOY6WX/alcKR6KdF97ZRb2e+MlURX0MtuCMcYGmYFS3OinJ9fPdaLPBgg/Bwb+FYXRBcraAw5pCx7GmJCeV6lZj+pp0wBBi8rAsAKG17tZaN/u5+TuCcANej3aHH1cJrPbcp5RKwMii2G3V+EWMCLUIZU+zEXwI1xzY/AWhFaLsqg9L/QcPR1ICi2dmsq2yNaTH13X0SQBirHlXwuGXvC5SSrHh9rMpneYg0a5wJNlJtCvKpjnYcMeYjIHjb0DZhWEb5h0XzObRtyrHL7AnGZWtvUnN8Tvn/PF3T7Bmdi7zCqw5mVFK8d2PLub9uk4ef7cq4PqbDpzk0oXWF2yNCdEoRPnuz2DNF8O3X4yA6RkpNPf0hxxkDcoEth1vegZcOJISKMxKGb2/yHPw4lcu5NMLE3n+uObvf797XLvBYBxq7GJ+LAUgLP47hkO2I5E2p+/ie15bcI61dLgbRrR11IzKrJpMjEKUTrTWtPUMkJsW/c9O3ImD7VFMPdFow7kOOARUASkYrTXPA/6fn4c9DHxVKfUKcBT4OjAIPB3e0YqICzUA0VQRngKUHnkLhgtRfii4x3U1Qkb4AhAA1y8v4i97alk7J/grILVtvcxcLgGIUdKnGydsXY1eu5cU5zjYfO9F7Khqo7K5h7K8NFaV5ozPGDixFS7/TtiGefnCAn748iFauvuZlj6iWFpiitFWy1tla3uSzwKUzd39PLa1iqfvPtfScSbYbfzkpuXc8ug28tKTWbfI9/bwyoGT/PBTyyx9/ZgR6QyIvk4jkHbZtyL3mmEyJy+NY8094b/6OXbb0S54dB3c9KTx/gXRqm5gyM1dv93J7eeVccPKYu/7C1sbd1x9Li+7ZnDnhh1cvGA6d18yl8wg2gy63JqeAVdQjwm7EPdBkeTZX2utvWZ71bQ7A3cVKVhkZF52hzfTMaBOa1q5xqKS3FQ2fdBIU7efoqDCvzHb46bNm41pFxAz26OYeqJRreZs4HWgCzgBXA9crbXe4VlBKfW+UuprIx7zA+DXwCagBbgAuEprHebS2CLiElONtmTBaqowggThEmorzu6GsAcgzj8jj3ePt46qFm1WbXsvRbHSui2WzFsHh30XOFNKsbosl0+sKmF1We74A9iuRqPzQRjnBtttipvWzOK3W0+MX5iYYszpHHvzc6Dx/RcruOeSM8LSY92RlMAjt6zkgU2H2eEjW6fdOYBzcGjyZuRkzoxsBsTux+CsT0FC/F/dWlyUxft1EZqGMXLbSc0x2nTu/UNQB+lut+ZfntrLmtnGPsLn/qKzHpU5kysXFfLs359PYWYyH33obR7bUsmQy1xxw8qWHsqmxWABuRD2QZGWm5ZEa4/3LIjGzn4KMkyMddHHYP+fLR5ZkDprITNQN/v4VDLcivNIo0y/mJAR26MrwRGT26OYWiIegNBa/6fWepbWOk1rnae1vkRr/cqYdRZprf97xM9aa/1NrXWh1tqhtb5Qa70v0mMXEaJs4A7yZLrpUHgzIPLnG0GOYHWFPwCRYLdx4bx8XjsYfO2Mrr7B2LpyFivmr4NDE6goH4b2m97csLKYv75XG1LwaaRdJ9qobHFy3bLwXUWblp7MI7es5N/+vM9r7YrXDjZx8fwoXkUMt0hmQLiGYNcGWPm5yLxemC2emcW+mijVgVj+Gdj/Jxj0XS9grO9trCAt2c6XArWx7ao/deU60W7js+fN5s93n0d1Wy8ffvBtNh9oDNhut6K+i/JCKSAXioLMFBo7x1/wcLk1Csy1Al5yg/H5iKbO2kk7BWNmdiq17b0cPtnNPAlACDFpTK5+PWJycEwDZ5A1DcI9BSMlC/q7jGrTwehqCGsNCI/rlxfxzO7grq72D7lItMsuwKvCJdB8KKiTjlGOvwGzw1f/wcORlMCViwr5y57akJ/D5db8x7PWFZ70pyTXwQ9vXMaXHt9NY+fov+3mipNcunASByAimQFx4K9GAMwxOarFLynOYl+0ClEmpUH5NbDvD6ZW/9Xbxzne1MN3PrI48PbU0wyO0YWTs1IT+dqHFvLzm1fy51213PLoNj6o811v+2BDJ+UzYqj+QxwpzEwZtx8CqO/opTDL5JXhrGJISDGKvUZLR+2knYKRlGBj0OXm8Mkuzpgun3MhJgs5+xCxJ5Q6EJ11kBnmKwBZxUaxp2B0NXitI2C1s4qzON7cQ4dz0PRj6tv7vFZoFxg1IMrONzpZhKJ6G5R4aZEZBp89t4zfvFMV8EqpL09sP8GykmwWzojMVdTFRVl8/dqF3LlhBx29A2yvbOWJ7SfYWdnK0qKsiIwhKtLyjRPOcBjsM2o+9HVCXwe88yCsuCX0AFqMKchMoak7QoUovTn7C7DtkYAB6Of31vPCvgZ+/Onl4zrljKM1oI1uCl7Mmubgoc+s4CtXzOMbf9nPP//xvVEny1prtle2srniJIMuHfL2P5UVZqXQ4CUAUdPWS3FOENNaln7SmKYTLZN4CobWmiS7jZc/aKRnYEg+50JMEhKAELEnvSC4AERvuzGXLdyV3k8VogxCd2QyIJRSXL2kkBf2m0/xrmvvnbzz7a3gpx2nXx01RhZPYmT+tgWZKZQXZvD6oaagH9vWM8Cv3q7kK1fMD8PIfLtgXj7XLZvJmv/ezE2/2Mq3/vI+DZ19XPnAG9S0hd4NIKbZ7EZRQ6sPoAf74P5yuK9k+DYL6nbCzy807p8kQYiyaWlUtvRE58UzZ8L0RXBks89Vth5r4eHXjvDIrStJSbQHfs7eNkjJDrjaytJc/vTFc7hwfj63PPouP3z5EIdPdnHZ/a9z0y+28kF9J//vT+9x2f2vT95tJ0wKMlNo8NKKM2ALzrEWfgQ++Iv127ZZni5gk0xNm5PL7n+dg41dNHb2c8/vdsnnXIhJQgIQIvakTzeqSpvVfCi8BSg9QmnFOdgHSZEpEHb9siKeCSIVv6a9VzIg/Jl9oTGVItiDyuNvRmT6xUhGS87jQT/uf186yBcunENWamTrgGitefzdE/QPuRl0afqH3Lg1VLU4uW39tsl7lSs5E/p9p9OHxDVgnMx609vmvRNBHFpcFMVpGADnfAm2POh1UUVDJ9/8y34euXUV2Q6TRT+76o3WrCYopfjwWTP56z3nk5po40M/epPK5p7hzAcYdOnJv+2EQWGW9ykY1W29lASTAZGaDXnzoGZHwFUt53YbF1/iuNWuN1prbl2/jaoWJ57EJ/mcCzF5SABCxJ6MwuAyIJoOhrf+g0d+eXCFKN0u46pnhJTlpTEw5Ka2vdfU+nXSAcO/xFTInQMnDwT3uONvwOzwF6AcadHMLFxuzYF68ye3+2o6ONTQxQ0rIp+6u6OqjZrW3nGxHZdbc6LVyY4qHyfU8S5zBnRGsBXnJLKkKIv90QxAzFhqZLA07B91d117L3//u9386FPLg8so66yHjODm7ack2llZZtT1GDsbZdJvO2FQmOlrCoaJFpxjLf2k6TohlnK2jKsjMhl4viNcYz7o8jkXYnKQAISIPcHWgGiqMIID4Za/wOi2YVZPU8TTIq9bVsRf95grdFfb1ktRtrRg8mv+OjgUxDQMraF2JxStDN+YfPh8EFkQbrfm28++z7c+vMhcpXeLVTb3kGD3/rqJdhuVzVFKtQ+3jJmR64QxyRgBCIuzR4J1zj2w9eFTP3Y4B7lzww6+c92i4GuoBJEBMVJlc4/P4sGTetsJg+mZyV67YNS09lKSG2Tm4rwr4egr4DJfh8kSnTWTsgDllP2OEGKKkACEiD3B1oBoOmi0yQy3tDxwNptPye+qN1rvRdA1S2fw3F5zAYi6jl6KsmOwf3wsCbYdZ1ulcTCYkBy2Ifly8fzpvF/XyUkvV/TG+tPOGsoLM1hSHJ2ij2V5aQy63F6XDbrclOWlRXhEEZIZwVack0xBZjKNnX3RTb0+4wqofw+6GugbdPGFx3bwxYvmcu7cEALNXcFnQMAU3nbCIDnB7vVv2dzTz7Q0k1NpPBKSofQ8OPqqRaMzqWNytuCUz7kQk5sEIETsSS8IrgZE+wnILg3feEZKm25kNpjR1Wj8LhGUl57M9IxkU6n4Jzv7yc+I/IlyXMmcCa5+6Gkxt34Upl942GyKW9aWsmFLld/1OpyDPPLmMf55XQSmLfmwqjSHklzHuE4BdptiVq6DVaU5URpZmGVEsBXnJKOUYtY0B1UtUSxAZ7PB6s/jfvcXfPmJPVy5qJAPnxXi1efOupAyIKbsthMmSXYbfYOuUz8PDLlJsttCa0m89EbY+6SFozMhEh3AokA+50JMbhKAELHHMc18u7qBHuPKQ6RqLeQvMF8HoqveqGcRYdcvD1yM0u3WaAjcKk4YqbVHXja3buWbMPui8I7Hj4+tKOKF/fX0Drh8rnP/ywe5/bzZ5ovlhYFSig23n03pNAeJdoUjyU6iXVE2zcGGO9aEdvAfDzIKrc+AsCdBgo/56qk5xvJJYkm0C1ECeumNtGz/A3Oybdxx/uzQnyjEDLkpu+2ESUFmMidHTMOom0hx5lnnQMNe6O+yaHQmdNZMygCEfM6FmNwSoj0AIcax2UF7T70bp/kw5EWwhWB+uTHlw0yXg+5GozJ2hF1xZgE/3nyYf1lX7nN+f0gpplPV/HXw9o/hrE/5X09rqNsDM5ZFYlRepSTauWbpTP60q4Zb1o7PCvqgrpP3ajr45ocXRWF0oxXnONh870XsqGqjsrmHsrw0VpXmTO4Dy8yZ1hehdLZA9iy47dnxrV/tSZA4eeq8LC7KYldVW+hZBxb46Tt1zEm/hK8W7ASWh/5EnXUhT9GbkttOmBRmGYUoZ00zpiNWtzkpCbU4s80G5ddAxfOBvy+s0lELiydfAALkcy7EZCYZECI2JSSZ61/fdDAyBSg98uebb8XZVQ/pkc+AcCQlcFZxNu8eb/W5Tl17n3TAMGvGcmh8H4YCtDNsPgy5s8Ee3bjuLWtLeXxrFe4x1cO19hSePDNmMl+UUqwuy+UTq0pYXZY7+Q8sM2ZAl8VTMF7+Blz2DcgogJTM0bdJFHyA6GdAPLWzhneOtHDpLV/DtmO90QIxVEMTa9E85badMJmeMboTRnVrL8XBtOAca+mNsDeC3TAm6RQMD/mcCzE5SQBCxKb0AugxUQeiqSIyBSg9gmnF2dUYlSkYANctL+KZ3b6nYdS29VIcaprpVGOzway1cGKL//Uq3zCXGRNm+RnJnFWczeaK0dvPM3tqmT0tjeWzZO5s1CSnw4CFNQyOvwG97VB+rXXPGcNmZKXQ0BGdQpSvHTzJhi2V/PTmFSRlF0LR8uA65Iw0NAC2RGsHKEJSmJVCY8fpAERNm5OS3Al8N05faGQldQVRSHsinC3GtFUhhIgjEoAQsclsIcrmQ5HNgMgIoop9d0PUAhDnzZ3G9qrWUcW1RprQPNepaP5VgbthHH8DyqJTgHKsOy6YzaNvHTv1c1ffIA+9epT/d1X0Ck+KYTY7uIYm/jyuQdj473D192CKXBVUSlGS66C6tTeir7u3pp3/+VsFv7h1FRkpw4GDc+6BLQ+F9oTdDUbGioi6wswUGkdmQLRNMAMCYPHH4f0/T3BkJrjdxrY/RbZ/IcTkIQEIEZvSp5trxdlyFHLnhH88HkpBSjY4fU9vOGXACUnRaRWVYLdx0fx8Xq3wHsSpbe+VKRjBmHMxHHvVdwtWt9uYplG4JKLD8mV+QQZJdhtPbDvBH3dU829P7eOWtbOYli5dT6LO7L4tkG2PwNxLo1JnJpoWF2WGfRqG1prtla38cUc1z75Xy71P7uHhm1cwPXPElJbpC40CyHW7g3+BztBacArrFWSOnYLhpCR3AgGIwT4jYP3eE9DXefpmZkppsHqaIC3f+ucVQogwkyKUIjalFwQ+SB/qB2UDe4RTWfPLjcyLWWt9r+N2GWOLoo8uL+LBV45w9ZLxhc5qJQMiOMnpRvZLyxHvJ3xNB4zPRaS6sQRQ0+bk8Mluvvb0PpISbPQPuvmgvpPLFhZM/OqemJiMmUYWVdYE5m13NcCuDfD5zdaNK04sKcpiT3UH1ywNrYBjIDVtTm5dv43qVicJNqNF48zsFJITvOzPzx3Ogvj4L4N7ka7QWnAK6xVmjc6A6OwbJCs1xGOKwT64vxx624yf7ys5vSw1B+6tsLYuyyTtgCGEmPwkA0LEpvTpgadgtByFaXMjM56RzBSi7GmGtLzIjMeHJUVZnGh10u4cXzyxrr2XIglABGfB1b7nfMfQ9AutNbeu38bJrn7cGvoG3WigqtXJbeu3RWX+vBghc4ZROG4iXv4WXPT/jMDYFLO4KIv9YcqA8Gw7VS1OBl2a3kEXGmjo7Pe+7cy5xAhGd9QE90KdobXgFNbLcSTS5hwEoHfARWriBILIroHTwYexetuM5VbqrDM66wghRJyRAISITemFxlU+f5oqID8Kc9o9rTj9iWL9Bw+lFB9aMoO/7Rv/d+wbdJEykQOtqWjelb7rQBx/MyYKUALsqGqjprUX15guGC635kSrkx1VPg6QRWQEU0fGm6otxuMXfcy6McWRouxU6tp7wxJIC3rbUQrO/jt49+fBvVCXnDjGCk9XBa01NW1OiuNpamJH7cQyqYQQIkokACFik5kilJEuQOmRNx+aAwQguhqM3yHKrls2k2f2jO6G0dM/RFqyzL4KWk4p9HWMv8Lldhmfh+kLozOuMSqbe0iwey9Klmi3UdncE+ERiVEyZ4aeAeEago3/Bld/f8oWnlNKUZSTSk2b9YUoQ9p2ltwAB1+A/i7zLyQZEDHFkwVRY0UBykjqrIXM4miPQgghgiYBCBGbzBRqa6owggGRlj0L2k/4X6erISYOMEunpeFyG1d2POrae5mZFUdXeWLJGZfDkTHz7hv2QsHimDkhLMtLY9Dl9rps0OWmLC86hVHFsIwZgbO7fNmxHkrPg+lRCLzGkCVFWWEpRFmWl+azc5DPbSchGZbeCLt/a/6FuhokAyKGFGQa7V2r25yUxFMGRGetfI6EEHEp4gEIpdTPlFLdY25aKfUjP4/5tlLKNeYxv4/kuEWEJWcEvqLU7KMgYLjZ7JCYCv3dvtfpboz6FAyP65bN5K/vnb7iWiMdMELnrR1nDE2/AFhVmkNJrgO7bXRAxG5TzMp1sKo0J0ojE4BxwtAVQgZEdxNs/yVc9C/WjynOLAlTHYgD9Z2kJNqD33ZW3Q47f21kQ5nhbAZHdGsEidM8rTgn3AEj0jpqIUsyIIQQ8SfiAQit9Re11umeG3Du8KLHAjx0y8jHaa0/HeahimjyXE32Nc/XNQTuQSMQEA15840pIL501cdMAOKaJTN47r36U3Om66QDRuiKV0HdLuPz53H8jZgKQCil2HD72ZROc5BoVziS7CTaFWXTHGy4Y82pOc8iStLyjWBCsDZ/Gy74J0jJtHxI8WZxGDIgXtzfwF/31PHXe84PfttJmwal58KBZwO/kNag3WCTBNRYUZhltOKc8BQMe5LR7cKbpHRjuZV6W32/nhBCxLBYmAh+N7BNa70j2gMRMSYly5hzn5o9fllbJeSURXhAI+QvMApRFq3wvryr0SikGQOmpSdTmJXCgfouzpyZSW1bL0uLs6M9rPhks0PRKqjZZpxwuAaNz+K0M6I9slGKcxxsvvcidlS1UdncQ1leGqtKcyT4EAtsduMENBjV26H1OHzkwfCMKc4U56RS22YUorTiM729spUfbT7M459fQ25aUmjbztovwV/uhkXX+1+vr934bhMxoyAzhSMnu4cDEBMIziemGK02x3a7aKuCp79g7TQ9twuUPWam/gkhRDBUNFuyKaUygVrgHq31b/ys923gnwHn8O1t4N+11sd9rH8vcK/n57S0tKKnnnoq4Hj6+vpISbGwR7OYkGUHf8DhWZ+mJ3V8lef81u3kdB3kUOnNURgZTG/ZRlb3YQ6Xfsbr8rV7/43ti76Jyx4bmQbbG91UdWluOMPOox+4uLzERmmGdQcuU2nbKWjZQlb3UQ6V3kxW1yFmNbzIvnn/EO1hiTiyZt/X2LHw6/QM2QJvN9rNmv1f54M5X6ArrSwi44sHD+xxcUu5jWkpE9uP1fVoHtnv4p6ldvJSJ/Zcyyu+x7Gij9KR4bs2UbrzBHOr/8h7C/5pQq811Vn5nXOkXbOlwc3hDs1/rAnPdbm51X/AbUvieNH1ljxf0kAbSw//hB2LvmnJ84mpYyodr4nouuqqq2q11l7niVm2p1VK/Rq4zc8qr2utLx5z361AP/BkgKf/E/Ar4AQwE/g+sEkpdZbWetxEfK31/cD9np+Li4v1unXrAv0KbNy4ETPriQgZ3EjBonkw+4Lxy97cD+lXMXt5lN6vptmw6VvM8fV5OfwNLv/Q9REdkj8XDri49idvcvkVF/HL41u44epV5KZZlw46pbadvrXwq2uYvW4dvLEP5tzIzBVT5HcX1mjbwOVnn8nGXZWBt5sd6+HMyzj3Q38XmbHFid3uCnJLsli3OPRivw0dffzf+nf5xR3LWFxkQVbCfAfTt/8C1v2973WObIKU5RROlf1lmFj5nbOwxckrf9hDYa6bdevOt+Q5xxm4AH5xKfPX/rs1dRtqdsLQkqnzvSssM6WO10TMsnIS4j1Avp/bdV4ecxfwK611n78n1lrv11pXaUMtcDtQxOn6EWIySi/w3QmjKUotOD1yZ0PrMe/L3O6YS4tMTbKztDiL37xTSWVLD0dOdhHN7Ke4Zk+GlAyo3wfHXoWZK6CvEwb97saEOM1sK05nK2z9GVzytfCPKc5MtBNGR+8gd27YwTevXWRN8AGg7HxorzamZfkiLThjTn5GEu/VtKMxpuOE5bsxyQGXfh1e+ro1z9dZA5njs0OFECIeWBaA0Fp3a62b/dxGHSkopS4GFgI/DeXlhm+xdZYnrJU+HbpPel/WVAH5UWjB6WFPNOZfejvpdLbEXIXzmjYnW4+18l/Pf0Bz9wCf+eW7XHb/66PacwoTBvvg/nKoegd+fj5UvgU/Ow/uKzHulyCEMCNjhlGoNpDN/wHn/YP3OjhTnBGA6Azpsf1DLr742E4+f8Fszp9n4b5aKVh7lxE08qWrXlonxpCaNifX/OQthlyaD+o6uekXW8P33Vh+jdHd69hrE3+uzjrIkgCEECI+RbMM893ARq21j8vIpymlPqmUyhv+fwHwS6AReCe8QxRR5SsDwu2GQafRqjOa8s6AliPj7+9ugIyCyI/HB601t67fxsmuftzaKMI+6NJUtTi5bf02yYQIhmsAetu8L+ttG198TAhvzGRA1O6CkwfgrJsiM6Y4U5KbSk2rM+j9l9utufcP73FJeT7XLQvDCdyij8LRV6C33fvyzjrJgIgRnu/GqhYj2DDk1uH9blQKrvqekQXhGpzYc3VIBoQQIn5FJQChlCoErgce9rH8faXUyJzTm4EDSiknsAtIBC7XWneFe6wiijJ8BCA6a2Kj93V+uZGJMVZXQ0wdYO6oaqOmtReXe/TBlMutOdHqZEeVjxNqIUR4BMqAcLvhxX+Fq++Tdo0+KKUozEqhvsN81pHWmv98/gMKMlK484I54RmYPRGW3QS7fNTVlgyImBGV78a8M+CMK+BdP1kyZnTWSQBCCBG3onJko7Vu0Fonaa29Ns3WWi/SWv/3iJ8/orXO11o7tNZFWutPa629XHoWk4qvDIimg5C3IPLjGStvPjQfGn9/V4Mx9hhR2dxDgt37bKVEu43K5p4Ij0iIKS5zplELwJc9j0PBIpi5PHJjikPB1oF45I1jNHX18/VrFoa3Je3Kz8Lux71f5ZYMiJgRte/GC78Ku39rHCuEqrNWAllCiLgll1ZE7ErLh+6m8fc3HYT8GAhA+M2AKIz8eHwoy0tj0OX2umzQ5aYsLy3CIxJiisuYAV0+pmD0tsE7P4FLvxHZMcWhxUVZ7DcZgHh6dw2vH2ri/z55FjZbmMtHpWbD3Evgg7+MXzbUZxQkFFEXte/GpDS4+F/hpQls473tkJpj2ZCEECKSJAAhYldCsvc59U0V0e2A4THtDGg5Ov7+7tgKQKwqzaEk14F9zEG33aaYletgVakcxAgRUcnpMOCjyN2r/20UMnTkRnZMcchsBsSbh5tY/1YlP7tlJckJ9giMDFjzRdj6sFF0x2NoAGyJkXl9EVBUvxvPvN7I8Kx8O/jHul2gbDHXbUsIIcySAISIbTY7uIZG3xcrGRCJKeAeGp9m29UA6bETgFBKseH2symd5iDRrnAk2Um0K8qmOdhwx5rwpiJPNvYk31edUnOM5UKYYbOjtGv0fQ37jOKTK26NzpjiTOk0Byda/Bei3F/bwX89d4Bf3LqKzJQInvznzjbm6FeNqJXd3RhTBYqnuqh+NyoFH/pf2Pi18cc4gXQ3Gl3ChBAiTiVEewBC+JWWB87m0xkFWhspyrFydTB3DrQeH90SNMamYAAU5zjYfO9F7Khqo7K5h7K8NFaV5kjwIViJKXBvhffMHHuSsVwIM9KnkzQw4uq91vDCv8DV3zMCryIgpRQFmSk0dPYxIyt13PLqVidfeXIPP715BYVZUdg2z7kH3n4Ays4zfu6qhwyZtx9LovrdmL8AZl8A238Ja79o/nGddbFRiFsIIUIkAQgR2zyFKD0n9N2NMVXg0ShEeXB0AKK/K/otQr1QSrG6LJfVZTESvIlXiSkSaBATlzGTlIHW0z/vfdIIaBavit6Y4tCS4iz213aOC0C09gzwhcd28j8fW8IZ06O0P561Bl5ugeYjRveDzjrIlAKUsSaq340X/Qv84jJY/DHzWQ0dNVKAUggR12QKhoht6QXQffL0z7Ey/cJjbCFKrY3USsksEEL4k1FIsicA0dcJb94Pl387qkOKR4tmZo6rA+EcGOLODTv48uXzWBXtgOvau+Ddnxr/76qPuew4EWXJGXDhP8Omb5t/TGettOAUQsQ1CUCI2JY+fXQrzqaDsVGA0iN/PjSNaMXpbIVUyTAQQgSQOSID4rX74Ow7jSlnIihLxnTCGHK5+fvf7eajy4tYtygGTvbLPwyVbxnfDZ11MgVDjLfkBmirgupt5taXKRhCiDgnAQgR2zxTMDyaKkZPd4g2zxQMj656KTImhPBtsM/IeEjJIqWvEWp2QOWbcNanoz2yuFSa66CioZM/7qhm2/EWvvbnfZw5M5Ob15ZGe2gG9xAsvRG2/hTaT0BKpvH+D/ZFe2QiVihl1H558V+NDheByBQMIUSckxoQIralT4e63ad/bj4UWxkQyRkw2AtuN9hswy04ZY6vEMKLwT64v9wopAvMBvjl88ayBxYbBU6lvohpNW1Obl2/jfr2Pr75l/fpH3KRlpzA3/7hgmgPzTDm/Qbgg2eMf1Nz5P0WpxUuhuLVsPNXsPrz/tftrJMpGEKIuCYZECK2pRcaXSU8uupjqwglQFYJdJww/t/VEHvjE0LEBtfA6JPRkXrbvHdXEV5prbl1/TaqWpxooHfQhVuDc8DFZ3+1zW9rzoiR91sE4+J/g3cfgZ4W/+v1dUBKVmTGJIQQYSABCBHbRhah9NRXiLUCj/nlRm0KGG7BKRkQQggRTjuq2qhp7cXlHh1ocLk1J1qd7KjyceIvRKxKzYbzvwybv+N7HdeQ0aY31o6DhBAiCBKAELEtNQd6hwu1xVoHDI/8BacDEN2NUgNCCCHCrLK5hwS795OwRLuNyuaeCI9ICAss/ZQx1bR2p/flsdaKXAghQiABCBHbbDajtSUMF6CM8QBEV70xbUQIIUTYlOWlMehye1026HJTlpcW4REJYQGbzShI+cK/GrWlxpIWnEKISUACECL2JabCQE/sFaD0yJtvBEcAuhqlz7sQQoTZqtIcSnId2G2jsyDsNsWsXAerSnOiNDIhJmjGWVC4BPb8dvyyzlrIkgCEECK+SQBCxD5PHYimCuNkP9Y4cqGv3cjUkOJQQghf7EnGtDJvUnOM5cIUpRQbbj+b0mkOEu0KR5KdRLuibJqDDXesQcXCHHl5v0WoLv06vPOgUftqpI5aacEphIh70oZTxL706UYAor3a6DgRizJmGK2xQIpDCSG8S0wxWi8Odz/YtHkzl192mbHMniQtGYNUnONg870XsaOqjcrmHsry0lhVmhMbwQcY936PIu+38MeRC+fcDa9+F675v9P3d9bC3MuiNy4hhLCABCBE7EsvgJYjkJRmzI+MRfnlUL3V99UuIYQA46Rz+MTTleCAlMwoDyi+KaVYXZbL6rLcaA/FuxHvtxBBWX4rrL8S6t8zpmWATMEQQkwKMXo2J8QI6QVQ+VZsFqD0yF8Ax16X+g9CCCGEmLhTBSn/5XRBSpmCIYSYBCQAIWLXYB/0dUJyBhx7DXLKjJ8H+6I9stEG+4ypIcdehdRcY4yxOE4hhBBCxI+ilZA7B3b+2jiu6G0HlBxjCCHimqVTMJRSZwH3AcuBAuAKrfWmMevkAA8C1wIaeB74kta63c/zLh1+zEqgA3gE+I7Wnv6MYtIZ7IP7y6G37fR9r3/PuKXmGPNqYyGtdew4d643bhBb4xRCCCFEfBnsg4rnYc/j8PxXjPvuG66FJccYQog4ZXUGxADwZ4zggi+/xQhOzAXOGP7/b3ytrJTKADYCbwN5wDrg88CXLRmxiE2ugdHBh5F627wX9YqGeBmnEEIIIeKLa8DosuWNHGMIIeKUpRkQWusDwAHAaxVqpVQp8CFgmda6efi+fwL2KKVmaa1PeHnajwF24Bta6yFgn1Lqf4F/AH5o5fiFEEIIIYQQQggRHpHugrEM6Ndav+e5Q2v9nlJqYHiZtwDEMmD3cPDBYzswRymVqbXuHPsApdS9wL2en9PS0ti4cWPAwfX19ZlaT4SffcjJ5X6Wb9q82aggH2XxMs5wk21HiODJdiNEaKbKtiPHGMJqU2XbEbHNVABCKfVr4DY/q7yutb7YxFNlYtRwGKt9eJmvx7SPua9txLJxAQit9f3A/Z6fi4uL9bp16wIObuPGjZhZT0RAX6cRZvLh8ssui432dfEyzjCTbUeI4Ml2I0Ropsy2I8cYwmJTZtsRMc1sBsQ9wFf9LB80+TydQJaX+7PxEkgY8ZjiMffljFgmhBBCCCGEEEKIGGeqCKXWultr3ezn5i2rwZs9QPJwVwvgVIeLpOFlvh6zXCk1MliyCjjmbfqFmCTsSUaFZ29Sc4zlsSBeximEEEKI+CLHGEKIScjqNpwKSB5xV6JSKgUY0loPaa2rlFJ/A36glLppeJ0fAM/6KEAJRleN+4DvKKX+C6N7xleBB6wcu4gxiSlGeylvFZ7tSbHTdipeximEEEKI+CLHGEKIScjqNpylQO/wDeBvw///+oh1bgGagaPDtybgVs9CpdRnlFLdnp+11l0YrTcvBFqATcB6pAPG5JeYYsxtHHuLtS/ceBmnEEIIIeKLHGMIISYZq9twVgLj+2+OXqcVuMnP8seBx8fctxe4wIIhCiGEEEIIIYQQIgqszoAQQgghhBBCCCGEGEcCEEIIIYQQQgghhAg7CUAIIYQQQgghhBAi7CQAIYQQQgghhBBCiLBTWutojyHslFL9GN02AkkHugOuJYQYS7YdIYIn240QoZFtR4jQyLYjIiVfa53sbcGUCECYpZSq0VoXR3scQsQb2XaECJ5sN0KERrYdIUIj246IBTIFQwghhBBCCCGEEGEnAQghhBBCCCGEEEKEnQQgRrs/2gMQIk7JtiNE8GS7ESI0su0IERrZdkTUSQ0IIYQQQgghhBBChJ1kQAghhBBCCCGEECLsJAAhhBBCCCGEEEKIsJMAhBBCCCGEEEIIIcJOAhCAMnxHKVWnlOpRSr2hlFoc7XEJEUuUUp9SSr2plOpUSmmlVMKY5UuHt52e4W3p20opFa3xChELlFL3KaX2DW839Uqp3yulSsasM0sp9ZxSqksp1ayUelAplRStMQsRC5RS31JKHVVKdQxvFxuVUsvGrCPfO0L4oZR6eviY7fIR912slNqllHIqpY4rpe6K5hjF1CMBCMNXgduBdUAe8DawUSmVHtVRCRFb2oCHgS+PXaCUygA2Ymw7eRjb0ue9rSvEFKOBz2JsFwuHf37Ws1ApZQOeA1qBImAlcCHwv5EeqBAx5glgldY6C5gJvIRxbGYH+d4RIhCl1K2AY8x9pcDzwKNANsb3031KqY9Genxi6pIuGIBS6jjwgNb6R8M/JwD1wL1a68eiOjghYoxS6mLgVSBRaz00fN9tGCdMM0fc94/AP2it50ZpqELEnOEruLuBXK11m1LqImATMENr3Ty8znXA74BpWuu+qA1WiBihlEoG7gJ+CEzXWjfJ944QvimlioF3gPOBKuAKrfUmpdS3gOu11stHrPtDYKnW+rLojFZMNVM+A0IplQWUAds89w1/ke0Glvt4mBBitGXAbs9B4LDtwBylVGZ0hiRETLoSqNJatw3/vAw45gk+DNuOcdVqfoTHJkRMUUpdo5RqB/qA+4Efaq2bhhcvQ753hBhneBrSeuC/tNYnxixexohznmHbkXMeEUEJgVeZ9DxfUu1j7m8bsUwI4V8m3rchz7LOiI5GiBg0PAf3W8DHR9wdaNsRYsrSWj8PZCulcoHbgJoRi+V7Rwjv7sLIcn/Ey7JM4NCY++ScR0SUBCBOf0Flj7k/B6iN7FCEiFudQPGY+3JGLBNiSlNKXQv8FrhZa/3iiEWdeP/+8SwTYsrTWrcqpX4EtCmlDmmt30O+d4QYRyk1F/gGsNbHKr6+c2SbEREz5adgaK07gEpgtee+4RoQyzCmYQghAtsDLB/TGWMVRmq5fKmJKU0p9RngceBGrfXTYxbvAWYrpaaNuG8V4GT8VSohpjIbkAjMG/55D/K9I8RYFwDTgJ3D3WM80/ueUko9grHdrB7zmFXIOY+IoCkfgBj2MPBVpdRipVQq8B1gEBh7oCjElKWUsiulUgBPe8BkpVTKcBX/PwMu4DtKqdThNrZfBR6K0nCFiAlKqXuAB4FrtdYbvazyJlAB/J9SKkMpNQv4D+BRKUAppjKl1D8qpQqG/5+Pcaw2gNH1AuR7Rwhv/gDMwbiQ6rkB/B3wr8CvgXKl1F1KqSSl1AUYnQBluxERIwEIww8wNshNQAtG9PAqrXV3NAclRIy5BejFaHsG0D3884Va6y6MFmgXYmxDmzAKIP0wCuMUIpb8BEgHXlBKdY+4XQCgtXYDrX7o8gAAAOFJREFUHwbyMbov7QbeAv45WgMWIkZcAexVSvUAe4FC4HKtdT2AfO8IMZ7W2qm1rhl5G17UrLVu1VpXAR8CvgB0AI8BX9Na/zlaYxZTj7ThFEIIIYQQQgghRNhJBoQQQgghhBBCCCHCTgIQQgghhBBCCCGECDsJQAghhBBCCCGEECLsJAAhhBBCCCGEEEKIsJMAhBBCCCGEEEIIIcJOAhBCCCGEEEIIIYQIOwlACCGEEEIIIYQQIuwkACGEEEIIIYQQQoiwkwCEEEIIIYQQQgghwk4CEEIIIYQQQgghhAi7/w99ZU2f0DqL8QAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N = 48\n", "# No correlation. Seed for all random process\n", "np.random.seed(2)\n", "x1 = np.random.randint(-10, 10, N)\n", "x2 = np.random.randint(-10, 10, N)\n", "\n", "# correlation\n", "r12 = np.correlate(x1, x2, mode='valid')\n", "\n", "# plot results\n", "plt.figure(figsize=(16, 4), dpi=80)\n", "plt.plot(x1, '-o', linewidth=0.75, markersize=6)\n", "plt.plot(x2, '-s', linewidth=0.75, markersize=6)\n", "plt.xlim([-0.5, N-0.5])\n", "plt.grid(True)\n", "\n", "print(f'No correlation, r12 = {r12}.')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Случайные процессы с ненулевой корреляцией:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Correlation, r12 = [-69].\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N = 48\n", "# Correlation\n", "np.random.seed(1)\n", "x1 = np.random.randint(-10, 10, N)\n", "np.random.seed(2)\n", "x2 = np.random.randint(-10, 10, N)\n", "\n", "# correlation\n", "r12 = np.correlate(x1, x2, mode='valid')\n", "\n", "# plot results\n", "plt.figure(figsize=(16, 4), dpi=80)\n", "plt.plot(x1, '-o', linewidth=0.75, markersize=6)\n", "plt.plot(x2, '-s', linewidth=0.75, markersize=6)\n", "plt.xlim([-0.5, N-0.5])\n", "plt.grid(True)\n", "\n", "print(f'Correlation, r12 = {r12}.')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Фильтрующее свойство **дельта-функции** в процессе вычисления корреляции позволяет найти значение сигнала в момент, когда дельта-функция не равна 0:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Correlation, r12 = [-8.96717793].\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N = 48\n", "# delta-function\n", "x1 = np.zeros(N)\n", "x1[4] = 5\n", "# random signal\n", "np.random.seed(2)\n", "x2 = np.random.randn(N)\n", "\n", "# correlation\n", "r12 = np.correlate(x1, x2, mode='valid')\n", "\n", "# plot results\n", "plt.figure(figsize=(16, 4), dpi=80)\n", "plt.plot(x1, '-o', linewidth=0.75, markersize=6)\n", "plt.plot(x2, '-s', linewidth=0.75, markersize=6)\n", "plt.xlim([-0.5, N-0.5])\n", "plt.grid(True)\n", "\n", "print(f'Correlation, r12 = {r12}.')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Автокорреляционная функция\n", "\n", "Автокорреляционная функция (АКФ) - показывает зависимость между сигналом и его копией, сдвинутой по времени. \n", "\n", "АКФ находит применение в кодировании информации. Выбор кодирующей последовательности по параметрам длины, частоты и формы во многом обусловлен корреляционными свойствами этой последовательности. Наилучшая кодовая последовательность обладает наименьшим значением вероятности ложного обнаружения или срабатывания (для детектирования сигналов, для пороговых устройств) или ложной синхронизации (для передачи и приема кодовых последовательностей).\n", "\n", "Автокорреляционная функция помогает находить повторяющиеся участки во временной последовательности, с помощью АКФ можно находить несущую частоту сигнала.\n", "\n", "Поскольку АКФ есть произведение сигнала и его копии, то физический смысл АКФ - энергия сигнала. В частности, в нулевой момент времени (`n = 0`) АКФ равна энергии сигнала.\n", "\n", "В numpy нет встроенной функции автокорреляции, но её несложно написать самому на базе функции `correlate()`.\n", "\n", "### Свойства АКФ\n", "\n", "1. АКФ это симметричная и четная функция.\n", "3. Имеет максимум в нуле.\n", "4. АКФ периодической последовательности - периодическая функция.\n", "5. АКФ суммы двух некоррелированных сигналов - сумма АКФ этих сигналов.\n", "6. АКФ бесконечного во времени белого шума имеет пик в нулевом значении и нули во всех остальных.\n", "\n", "### АКФ прямоугольного импульса\n", "\n", "Пример: Автокорреляционная функция прямоугольного импульса - треугольный сигнал. Ниже будет показано, что корреляция и свертка сигнала с самим собой даёт одинаковый результат." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Auto-correlation function\n", "def auto_corr(x):\n", " res = np.correlate(x, x, mode='same')\n", " return res # / np.max(res)\n", "\n", "# Signal\n", "x = np.concatenate([np.zeros(5), np.ones(5), np.zeros(20)])\n", "\n", "# ACF\n", "cfx = auto_corr(x)\n", "\n", "xl = [x, cfx]\n", "\n", "# Pot results\n", "plt.figure(figsize=(16, 5), dpi=80)\n", "for i in range(2):\n", " plt.subplot(2, 1, i+1)\n", " plt.stem(xl[i], linefmt='C0', markerfmt='D', use_line_collection=True)\n", " plt.grid(True)\n", " plt.xlim([-0.5, x.size-0.5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Поскольку вычисление АКФ прямым методом - трудозатратная операция (большое число операций умножения и сложения), выполняемая за $O(N^2)$, то во многих задачах встаёт вопрос о снижении качества корреляционных свойств в связи с уменьшением длины последовательности. Однако, с помощью быстрого преобразования Фурье (БПФ) можно свести вычислительную сложность к $O(Nlog(N)$. \n", "\n", "С помощью теоремы Винера-Хинчина, которая связывает АКФ сигнала и его спектральную плотность мощности, можно вычислить АКФ через двойное взятие БПФ сигнала.\n", "\n", "$$ \\Psi(\\tau) = Re[IFFT( | FFT(x) |^2 )] \\tag{3.2}$$\n", "\n", "____\n", "\n", "## Свертка\n", "\n", "**Свертка** описывает взаимодействие сигналов между собой. Если один из сигналов - импульсная характеристика фильтра, то свертка входной последовательности с импульсной характеристикой есть ни что иное, как реакция цепи на входное воздействие. Иными словами, результирующий сигнал отражает прохождение сигнала через фильтр. \n", "\n", "Как правило, выходной сигнал является запаздывающей (относительно входа) функцией. Кроме того, выходной сигнал может быть усилен или подавлен относительно входного сигнала. \n", "\n", "**Чтобы найти импульсную характеристику цифрового фильтра, необходимо подать на его вход единичный импульс (дельта-функцию), который равен 1 в одной точке и равен 0 во всех остальных точках** \n", "\n", "### Свертка и корреляция\n", "\n", "Связь свертки и корреляции достаточно проста: свертка эквивалентна взаимной корреляции двух последовательностей, причем одна из последовательностей обращена во времени относительно другой. В случае с корреляцией, последовательности должны быть одинаковой длины. В случае свертки последовательности могут иметь разную длину, тогда этот процесс называется линейной сверткой. В случае, если длины последовательностей совпадают - это циклическая (круговая) свертка.\n", "\n", "### Свойства свертки\n", "\n", "1. **Коммутативность**: \n", "\n", "$$ a*b = b*a \\tag{3.3}$$\n", "\n", "Из этого выражения вытекает следующее утверждение:\n", "\n", "$$ \\sum_{m=0}^{N-1}a(m)b(n-m) = \\sum_{m=0}^{N-1}a(n-m)b(n) \\tag{3.4}$$\n", "\n", "\n", "2. **Дистрибутивность**: \n", "\n", "$$ a*(b+c) = a*b + a*c \\tag{3.5}$$\n", "\n", "3. **Ассоциативность**: \n", "\n", "$$ a*(b*c) = (a*b)*c = (a*c)*b \\tag{3.6}$$\n", "\n", "\n", "Существует два типа свертки - линейная и циклическая (круговая).\n", "\n", "## Линейная свертка\n", "\n", "Линейная свертка двух сигналов $a(n)$ , где $n = 0, ..., N-1$ и $b(n)$, где $n = 0, ..., M-1$ описывается уравнением: \n", "\n", "$$ s(n) = a*b = \\sum_{m=0}^{n}a(m)\\cdot b(n-m) \\tag{3.7}$$\n", "\n", "где \n", "- $n = 0, ..., N+M-2$ ,\n", "- $N$ - длина сигнала $a(n)$ , \n", "- $M$ - длина сигнала $b(n)$ ,\n", "\n", "Вычисление свертки - итеративный процесс, в котором сигналы сдвигают друг относительно друга, затем перемножают и складывают. Предполагается, что сигналы равны нулю вне заданных своих диапазонов, то есть $a(n) = 0$ при $N < n < 0$ и $b(n) = 0$ при $M < n < 0$.\n", "\n", "На следующем примере вычислим пошагово свертку сигналов:\n", "\n", "`a(n) = [1, 2, 3, 4], N = 4`\n", "\n", "`b(n) = [3, 2, 1], M = 4`\n", "\n", "Простейший алгоритм (через циклическую свёртку):\n", "\n", "1. Дополняем нулями слева первый сигнал до длины N+M-1.\n", "2. Инвертируем во времени второй сигнал.\n", "3. Дополняем нулями справа второй сигнал до длины N+M-1.\n", "4. В цикле от 0 до N+M-2 сдвигаем второй сигнал вправо (или первый сигнал влево)\n", "5. Вычисляем на каждом шаге цикла произведения элементов и подсчитываем сумму произведений.\n", "\n", "Сравним полученный результат и значения, вычисленные с помощью встроенной функции `convolve()` с параметром `mode='full'`." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "a(n) = [1, 2, 3, 4]\n", "b(n) = [3, 2, 1]\n", "\n", "a(n) * b(n) = [ 3 8 14 20 11 4]\n", "np.convolve = [ 3 8 14 20 11 4]\n", "True\n" ] } ], "source": [ "# input parameters\n", "N, M = 4, 3\n", "\n", "# lists of data\n", "a = [1, 2, 3, 4]\n", "b = [3, 2, 1]\n", "\n", "# signals\n", "an = np.concatenate([np.zeros(M-1, dtype=int), a])\n", "bn = np.concatenate([b[::-1], np.zeros(N-1, dtype=int)])\n", "print('a(n) = ', a)\n", "print('b(n) = ', b)\n", "\n", "# Convolution with 'same' mode with list comprehension:\n", "ab = np.array([np.sum(an * np.roll(bn, i)) for i in range(N+M-1)])\n", "\n", "# simple way:\n", "# ab = []\n", "# for i in range(N+M-1):\n", "# br = np.roll(bn, i) # shift second signal\n", "# sm = np.sum(an * br) # calc sum of prods\n", "# ab.append(sm) # append new value to the list\n", "\n", "# Function convolution:\n", "print('\\na(n) * b(n) = ', ab)\n", "\n", "# Convolution with np.convolve method:\n", "cv = np.convolve(a,b, mode='full')\n", "print('np.convolve = ', cv)\n", "\n", "# Check conv method:\n", "ab_check = np.all(ab == cv)\n", "print(ab_check)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Пошаговое объяснение линейной свёртки\n", "\n", "Важно помнить, что второй сигнал сначала инвертируется слева направо, согласно формуле вычисления свертки!\n", "\n", "```\n", "Step 1:\n", "a = [0, 0, 1, 2, 3, 4]\n", "b = [1, 2, 3, 0, 0, 0]\n", "\n", "sum of prod = [3]\n", "\n", "Step 2:\n", "a = [0, 0, 1, 2, 3, 4]\n", "b = [0, 1, 2, 3, 0, 0]\n", "\n", "sum of prod = 1*2 + 2*3 = [8]\n", "\n", "Step 3:\n", "a = [0, 0, 1, 2, 3, 4]\n", "b = [0, 0, 1, 2, 3, 0]\n", "\n", "sum of prod = 1*1 + 2*2 + 3*3 = [14]\n", "\n", "Step 4:\n", "a = [0, 0, 1, 2, 3, 4]\n", "b = [0, 0, 0, 1, 2, 3]\n", "\n", "sum of prod = 1*2 + 2*3 + 3*4 = [20]\n", "\n", "Step 5:\n", "a = [0, 0, 1, 2, 3, 4]\n", "b = [3, 0, 0, 0, 1, 2]\n", "\n", "sum of prod = 1*3 + 2*4 = [11]\n", "\n", "Step 6:\n", "a = [0, 0, 1, 2, 3, 4]\n", "b = [2, 3, 0, 0, 0, 1]\n", "\n", "sum of prod = 1*4 = [4]\n", "\n", "Convolution seq = [3, 8, 14, 20, 11, 4]\n", "``` " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Свёртка прямоугольного импульса\n", "\n", "Свёртка прямоугольного импульса с самим собой вырождается в сигнал треугольной формы. Как было показано выше, для автокорреляционной функции результат аналогичен:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Signal\n", "x = np.concatenate([np.zeros(15), np.ones(5), np.zeros(15)])\n", "\n", "# Convolution\n", "cv = np.convolve(x, x, mode='same')\n", "xl = [x, cv]\n", "\n", "# Pot results\n", "plt.figure(figsize=(16, 5), dpi=80)\n", "titles = [\"Signal\", \"Convolution\"]\n", "for i in range(2):\n", " plt.subplot(2, 1, i+1)\n", " plt.title(titles[i])\n", " plt.stem(xl[i], linefmt='C0', markerfmt='D', use_line_collection=True)\n", " plt.grid(True)\n", " plt.xlim([-0.5, x.size-0.5])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Циклическая свёртка\n", "\n", "Циклическая (круговая) свертка отличается от линейной тем, что входные сигналы имеют одинаковую длительность $N$.\n", "\n", "Циклическая свертка двух сигналов $a(n)$ и $b(n)$, где $n = 0, ..., N-1$ , описывается уравнением: \n", "\n", "$$ s(n) = a*b = \\sum_{m=0}^{N-1}a(m)\\cdot b(n-m) \\tag{3.8}$$\n", "\n", "где $n = 0, ..., N-1$ , а число $N$ - длина сигнала $a(n)$ . Как видно, результат циклической свёртки имеет длину N.\n", "\n", "\n", "На следующем примере вычислим пошагово свертку сигналов:\n", "\n", "`a(n) = [1, 2, 3, 4]`\n", "\n", "`b(n) = [3, 2, 1, 0]`\n", "\n", "Алгоритм:\n", "\n", "1. Инвертируем второй сигнал,\n", "2. В цикле от 0 до N-1 сдвигаем второй сигнал вправо (или первый сигнал влево)\n", "3. Вычисляем на каждом шаге цикла произведения элементов и подсчитываем сумму произведений.\n", "\n", "Полученный результат не совпадает со встроенным методом `convolve()` с параметром `mode='same'` в связи с тем, что для этого метода в библиотеке numpy используется дополнение нулями." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "a(n) = [1 2 3 4]\n", "b(n) = [3 2 1 0]\n", "a(n) * b(n) = [14 12 14 20]\n" ] } ], "source": [ "# Input parameters\n", "N = 4\n", "\n", "# Signals\n", "an = np.array([1, 2, 3, 4], dtype=int)\n", "bn = np.array([3, 2, 1, 0], dtype=int)\n", "print('a(n) = ', an)\n", "print('b(n) = ', bn)\n", "\n", "# Convolution with list comprehension:\n", "ab = np.array([np.sum(an * np.roll(bn[::-1], i+1)) for i in range(N)])\n", "\n", "# simple way:\n", "# ab = []\n", "# for i in range(N):\n", "# br = np.roll(bn, i+1) # shift second signal\n", "# sm = np.sum(an * br) # calc sum of prods\n", "# ab.append(sm) # append new value to the list\n", "\n", "# Function convolution:\n", "print('a(n) * b(n) = ', ab)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Пошаговое объяснение циклической свёртки\n", "\n", "Первым шагом инвертируем сигнал b(n) и начинаем с -1 отсчета\n", "\n", "```\n", "Step 1:\n", "a = [1, 2, 3, 4]\n", "b = [3, 0, 1, 2]\n", "\n", "sum of prod = 1*3 + 1*3 + 2*4 = [14]\n", "\n", "Step 2:\n", "a = [1, 2, 3, 4]\n", "b = [2, 3, 0, 1]\n", "\n", "sum of prod = 1*2 + 2*3 + 1*4 = [12]\n", "\n", "Step 3:\n", "a = [1, 2, 3, 4]\n", "b = [1, 2, 3, 0]\n", "\n", "sum of prod = 1*1 + 2*2 + 3*3 = [14]\n", "\n", "Step 4:\n", "a = [1, 2, 3, 4]\n", "b = [0, 1, 2, 3]\n", "\n", "sum of prod = 1*2 + 2*3 + 3*4 = [20]\n", "\n", "Convolution seq = [14, 12, 14, 20]\n", "``` \n", "____\n", "\n", "\n", "В связи с тем, что в библиотеке numpy отсутствует встроенная функция для вычисления циклической свёртки, можно использовать свойство преобразования Фурье.\n", "\n", "### Свертка через БПФ\n", "\n", "Из предыдущих курсов, посвященных преобразованию Фурье, известно правило: \n", "\n", "**Свертка двух сигналов во временной области равна произведению их спектров в частотной области** \n", "\n", "$$ a(n) * b(n) = A(k) \\cdot B(k) \\tag{3.9}$$ \n", "\n", "Используя это правило, можно вычислить циклическую свертку двух сигналов. " ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "circular convolution = [14. 12. 14. 20.]\n", "True\n" ] } ], "source": [ "# Convolution with IFFT of FFT(a) * FFT(b)\n", "def circle_conv(an, bn):\n", " \"\"\"\n", " Calculate circular convolution via FFTs. \n", " Signals an & bn must have same shape.\n", " You should import fft and ifft from scipy.fftpack.\n", " \n", " Parameters\n", " ----------\n", " an : np.array\n", " real 1D numpy array\n", " bn : np.array\n", " real 1D numpy array\n", " \"\"\"\n", " return np.real(ifft(fft(an) * fft(bn)))\n", "\n", "\n", "# Input parameters\n", "N = 4\n", "\n", "# Signals\n", "an = np.array([1, 2, 3, 4], dtype=int)\n", "bn = np.array([3, 2, 1, 0], dtype=int)\n", "\n", "# Calculate circular convolution\n", "cv = circle_conv(an, bn)\n", "\n", "print('circular convolution = ', cv)\n", "\n", "# Check conv method\n", "ab_check = np.all(ab == cv)\n", "print(ab_check)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Вычисление свёртки через БПФ имеет ряд преимуществ, одно из которых связано с количеством выполняемых операций при вычислении.\n", "\n", "Например, сигнал $a(n)$ имеет длину $N = 2000$, а сигнал $b(n)$ имеет длину $M = 8000$. Вычисление линейной свёртки потребует $N*M = 16.000.000$ операций умножения и сложения.\n", "\n", "Однако, если дополнить обе последовательности до $N_{FFT} = 8192$, то для вычисления БПФ потребуется $N\\cdot log_{2}(N) \\approx 106.000$ операций комплексного умножения (или в 4 раза больше операций вещественного умножения). \n", "\n", "Из формулы для вычисления свёртки через БПФ очевидно, что требуется три звена БПФ: два прямых БПФ для входных сигналов и одно обратное БПФ для произведения спектров сигналов. Комплексные умножения спектров вносят несущественный вклад (8192 комплексных умножения), поэтому результирующее оценочное значение количества операций $3 \\cdot 4 \\cdot N\\cdot log_{2}(N) \\approx 1.280.000$\n", "\n", "Полученное значение в **12.5** раз меньше, чем если бы пришлось вычислять линейную свёртку по формуле из определения.\n", "\n", "### Сравнение эффективности\n", "\n", "Ниже представлена таблица сравнения эффективности быстрой свертки и свертки, вычисляемой по прямой формуле. В таблице сравнивается число действительных умножений, требуемых для вычисления свертки.\n", "\n", "Как видно, для длин БПФ до 64, быстрая свёртка проигрывает у прямого метода. Однако, при увеличении длины БПФ результаты меняются в обратную сторону - быстрая свертка начинает выигрывать у прямого метода. Причем, чем больше длина БПФ, тем лучше выигрыш.\n", "\n", "| **N** | **Прямой метод** | **Быстрая свертка** | **Отношение** |\n", "| --- | --- | --- | --- | \n", "| 8 | 64 | 448 | 0.14 |\n", "| 16 | 256 | 1088 | 0.24 |\n", "| 32 | 1K | 2560 | 0.4 |\n", "| 64 | 4K | 5888 | 0.7 |\n", "| 128 | 16K | 13312 | 1.23 |\n", "| ... | ... | ... | ... |\n", "| 2K | 4M | 311296 | 13.5 |\n", "\n", "____" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Список функций из пакета signal:\n", "\n", "Ниже приведен список основных функций из пакета **scipy** по тематике свертки и корреляции.\n", "\n", "**Свертка и корреляция**\n", "\n", "\n", "| **Function** | **Description** |\n", "| --- | --- | \n", "| `convolve(in1, in2[, mode, method])` | Свертка двух N-мерных массивов |\n", "| `correlate(in1, in2[, mode, method])` | Кросс-корреляция двух N-мерных массивов |\n", "| `fftconvolve(in1, in2[, mode, axes])` | Свертка двух N-мерных массивов через БПФ |\n", "| `convolve2d(in1, in2[, mode, boundary, fillvalue])` | Свертка двух 2-мерных массивов |\n", "| `correlate2d(in1, in2[, mode, boundary, ...])` | Корреляция двух 2-мерных массивов |\n", "| `sepfir2d(input, hrow, hcol)` | Свертка массива рангом 2 с характеристикой фильтра ранга 1. Функция может использоваться для поиска изображения по его B-сплайновому представлению. |\n", "| `choose_conv_method(in1, in2[, mode, measure])` | Поиск наибыстрейшего метода корреляции или свертки |\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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O8EXEWqDdW1FKaUqnRSRJUi/lLrqSpKPlGnySpK6Uzwi+z7Y5rgA+CXy388KRJKn3asz5RuYmG5KkfLgGnySpK+WzBt8P2pZFxK+BrwBf68ygJEnqjXJ30XUEnyQpH4WFjuCTJHWdY10ifClwaWcEIklSb5e7Bp8j+CRJ+Wg9gs8MnySpc+WzBl/bZOAQ4E+ATZ0akSRJvZRr8EmSjpa76EqSulI+a/A1cPAmG3uAD3deOJIk9V7uoitJOlruoitJ6kr5JPgub3O8B1iRUqruxHgkSeq1GpyiK0k6SoVusiFJ6kJ5jeBLKT3RtjAiLkopPdmJMUmS1Cs1usmGJOkoOYJPktSV8tlk4zeHKL+/MwKRJKm3a2h0iq4k6eg4gk+S1JXySfAd9FUmIko5eF0+SZL6JXfRlSQdrSITfJKkLnTEKboR8RiZJF5ZRDzapnoK8GxXBCZJUm/jLrqSpKNVWHhgbIVTdCVJna0jI/geBH4PNGWfmx+/A74CvKejLxYZX4yI9RGxNyIejYjTD9P+4Yioi4jqnMdn2rR5d0Qsj4j9EbEsIq7taDySJOWj9Qg+M3ySpI5zBJ8kqSsdcQRfSumLABHxakrpx8f4ejcBHwPmAiuBzwPzI+KUw+zG+79TSp9tryIiLgDuAK4D7gOuBn4UEZemlBxZKEnqVI7gkyQdrUI32ZAkdaHDjuCLaDU84ScRUdDeI4/X+wxwc0rphZTSfuBzQAkwL//QAfgU8JuU0l0ppfqU0l3Ab4FPH+X1JEk6JHfRlSQdLUfwSZK60pFG8O0Chmf/buDQG2oUHumFImIEMA14urkspdQQEYuB2cDthzj10xHxp8Am4F7gyzmj/WYBP2vT/hng3YeI4UbgxubjwYMHM3/+/COFLg1YNTU19hEpx3ObDyT4mhrq7R/SYXgPkVp7adOBe0htnfcQ6XC8h0j5O1KC7205f19+jK/VnCjc2aZ8R05dW/8ALM+ecwZwGzAdeF/ONTt8vZTSLcAtzcdjx45Nc+fO7UDo0sA0f/587CPSATVLquClJQCUlhTbP6TD8B4itdbw/Aa+//IiAAoKvYdIh+M9RMrfYRN8KaXHc/5+5Bhfa3f2ubxN+Uig6hCv/2TO4dKI+CvgwYgYlJ3iu/sQ19uNJEmdrKExd5ONHgxEktTnFDpFV5LUhQ6b4IuIN3XkIimlP3Sgza6IWA2cByzIXr+IzDTbQ03Pbat5XHvz3XFJ9nq5zgUWd/B6kiR1WKObbEiSjlKRm2xIkrrQkaboPtiBayQ6sAZf1reBmyLiD8BrwGeBeuCetg0jYjyZtfkeA/YBp5KZXntfSmlfttl3gYcjYh5wP/AO4CrgDR2MR5KkDnMXXUnS0SosdASfJKnrHGmKbj475HbEzcAwMonD4cCzwJUppeqImAK8DFyVUnoMKAP+GTiFTAJxI3A38KWc+BZGxA3AV4E7gdXA9SmlZzo5bkmSWu2i6xRdSVI+Wu+ia4ZPktS5jjSCr1OllBLw+eyjbd0aYGjOcSVwfgeu+XPg550YpiRJ7XIEnyTpaBU6RVeS1IU6PEIvIgoj4u8j4tWIqImIlRHxDxHR0em5kiT1ablr8DmCT5KUj6KCA1+9nKIrSeps+Yzg+yrwR8DXgVXAdOAmMrvY/m2nRyZJUi/jCD5J0tFyBJ8kqSvlk+C7HrgspbSiuSAiHgIexgSfJGkAcBddSdLRar0GXw8GIknql/LZRKOQzMi9XKvo+A66kiT1aQ2NTtGVJB2dQhN8kqQulE+C7/vAP0ZEAGSf/x74r64ITJKk3iZ3F11H8EmS8lFU6BRdSVLXyWeK7qXABcCfRMRaYDIwCngqIh5tbpRSekPnhihJUu/Q4CYbkqSj5BRdSVJXyifB92D2IUnSgNR6DT4zfJKkjit0F11JUhfqcIIvpfTFrgxEkqTezl10JUlHq8hddCVJXSifEXwARMQwYFhuWUppfadFJElSL9XoFF1J0lFykw1JUlfqcIIvIuYAtwEn5RYDCXfSlSQNAPWNbrIhSTo6juCTJHWlfEbwfQ/4LfBBYG/XhCNJUu/lCD5J0tFyBJ8kqSvlk+CbAvxVSsnbkSRpQHIXXUnS0SoqdJMNSVLXKThykxZPAjO7KhBJknq7RjfZkCQdJafoSpK6Uj4j+D4B/CAi5gMbcytSSj/s1KgkSeqF3EVXknS0nKIrSepK+ST4/gi4DJhN6zX4EmCCT5LU7zU2Hdhkwym6kqR8tB7BZ4ZPktS58knw/SMwL6V0X1cFI0lSb9bQ6Ag+SdLRcQSfJKkr5bMGXwHwy64KRJKk3s5ddCVJRysiWpJ8JvgkSZ0tnwTfz4BruigOSZJ6PdfgkyQdi+YEn5tsSJI6Wz5TdEcBP46Ix4ENuRUppQ91alSSJPVC7qIrSToWRQVBHY7gkyR1vnwSfPuBn7RT7u1JkjQgNLjJhiTpGDhFV5LUVTqc4EspfTT3OCKGAh8BPtXJMUmS1Cs5gk+SdCyKnKIrSeoi+YzgAyAizgA+A1yXLfpep0YkSVIv5Rp8kqRjUViQWQLdEXySpM7WoU02IqI4Ij6YXX9vCXAFUAicnVK6saMvFhlfjIj1EbE3Ih6NiNMP0XZcRPwgIlZFRHVErI6Ir0ZEaU6baRGRsteqznmM6GhMkiR1VPMIvsKCIMIMnyQpP47gkyR1lSMm+CLiX4C1wH9nn98MnALszj7ycRPwMWAuMAZ4Apifne7b1lDglezrDc8+vx3413banpVSGprz2JVnXJIkHVFD44EEnyRJ+XINPklSV+nICL6/y7a7OqX0gZTSQymlo70lfQa4OaX0QkppP/A5oASY17ZhSun1lNK/pJReSyk1pZRWkkkyXn6Ury1J0jFpHsFXZIJPknQUigpN8EmSukZH1uD7OPBp4DcRsQT4LvBj8tw9NzttdhrwdHNZSqkhIhYDs4HbO3CZtwKL2yl/JDt1dwXw9ZTSPYeI4UagZUrx4MGDmT9/foffgzTQ1NTU2EekHLv2NACQmhqpqWmwf0iH4T1EOljN/sx9pKEp2T+kw/AeIuXviAm+lNKtwK0RcR6ZEXjfBL5BZuTdDGBzB19rePZ5Z5vyHTl1hxQRnyOTCDwvp3grcBHwHJk1Ad8N/CQi5qWUft3Oe7kFuKX5eOzYsWnu3LkdDF8aeObPn499RDrgq88/BPv2UVZSTFlZkf1DOgzvIdLBvvHyI2zaV00TYf+QDsN7iJS/Dm2yAZBSeial9FGgAvgnYDXwUET8toOXaF6vr7xN+UiOsJZfRHwJ+GPgspTSupyYqlNKC1JKdSml/Sml24E7ges7GJMkSR3W0LLJRodvn5IktXAXXUlSV8n7G0pKaWdK6ZaU0inAVcC+Dp63i0xSsGUEXkQUAbNof9pt8667/wF8ALg0pfRKB16qCXBxJElSp3MNPknSsXAXXUlSVzmmIQgppQdSStfmccq3gZsi4vSIGAR8EagHDlozL5v8uwO4jExyb3U7bS6NiJkRURgRJRHxAeCDZEbxSZLUqQ6M4DPBJ0nKX+4uuke/b6EkSQfryCYbnelmYBjwIJl1954FrkwpVUfEFOBl4KqU0mPAxWSSdbXAqxEHvkyllIZm/zwFuA2YkG23ArghpXRft7wbSdKA0jKCr9AEnyQpf7kjwJsSeDuRJHWWbk3wpczPVJ/PPtrWrQGG5hw/whGm2qaUvgd8r5PDlCSpXQ2NTYAj+CRJRyf3/tHQ1ERhQWEPRiNJ6k9cJVySpA5yDT5J0rHIHQHe6E4bkqROZIJPkqQOchddSdKxyL1/NJjgkyR1Ir+hSJLUQY7gkyQdi9z7R6Nb6UqSOpEJPkmSOiCl5C66kqRj0noNPhN8kqTOY4JPkqQOyP0e5gg+SdLRaDWCzwSfJKkTmeCTJKkDGpqaWv52BJ8k6Wi03UVXkqTOYoJPkqQOyB1pkbsLoiRJHeUIPklSVzHBJ0lSB+SuleQuupKko+EuupKkruI3FEmSOiB3t0PX4JMkHQ1H8EmSuooJPkmSOqD1CD4TfJKk/BXmLPHQ0GiCT5LUeUzwSZLUAa3W4DPBJ0k6Co7gkyR1FRN8kiR1gLvoSpKOlbvoSpK6igk+SZI6wBF8kqRj5Qg+SVJXMcEnSVIHuIuuJOlYuYuuJKmr+A1FkqQOcASfJOlYOYJPktRVTPBJktQBubsd5u6CKElSR7Veg88EnySp85jgkySpAxzBJ0k6Vq1H8LnJhiSp85jgkySpA9xFV5J0rHJHgOeODJck6ViZ4JMkqQMcwSdJOlauwSdJ6iom+CRJ6gB30ZUkHSt30ZUkdRW/oUiS1AGO4JMkHStH8EmSuooJPkmSOqD1CD4TfJKk/LmLriSpq3Rrgi8yvhgR6yNib0Q8GhGnH6b9yIj4UUTsioid2b/L27R5d0Qsj4j9EbEsIq7t8jciSRpwcnc7dASfJOlouIuuJKmrFHXz690EfAyYC6wEPg/Mj4hTUkrV7bS/AygFTsge/wT4AfAugIi4INvmOuA+4GrgRxFxaUrp2SMFU12f+NMfLzq2dyT1Yxs3NnLfNvuIBLBpV03L34WFAQ09GIwkqU/KHcF3x8I1PPrq1h6MRuq9/B4i5a+7E3yfAW5OKb0AEBGfAz4BzANuz20YEVOBtwGzUkpbs2V/DSyJiCkppTXAp4DfpJTuyp52V0RcD3wa+PiRgqlvhF89v6Fz3pnUX222j0htlRS6woUkKX8lRQfuHy9U7eKFql09GI3Uy/k9RMpLtyX4ImIEMA14urkspdQQEYuB2bRJ8AGzgNqU0tKc9ksjoi5btyb7/LM25z0DvPsQMdwI3Nh8XDh09FG9F0nSwDWsGMq2raAmapk/f35PhyP1WjU1NfYRqY3G+sTIUthR29ORSJL6m+4cwTc8+7yzTfmOnLq27dv7SWtnTvvheVyPlNItwC3Nx6PHjElP/N2bDhOyNLA9+sgjvOGNb+zpMKReZczQEkqLCpk/fz5z587t6XCkXss+IrXv6qua+Pn9D/gZSzoMv4dIB5v0r4ev784E3+7sc3mb8pFA1SHaj2invDznWrsPcb3ddEBBBBXlgzrSVBqQRpXZRyRJkjpTUWGBn7GkI7CPSPnrtkWEUkq7gNXAec1lEVFEZprt4nZOWQKURsSZOe3PBEqydc1tzmtz3rmHuJ4kSZIkSZLU73T3KuHfBm6KiNMjYhDwRaAeuKdtw5RSJfBr4OaIGBMRY4CbgV9mN9gA+C7wtoiYFxHFETEPuAr4Tne8GUmSJEmSJKmndXeC72bgNuBBYBtwKXBlSqk6IqZERHVEXJrT/gZgK/Ba9rEF+FBzZUppYbbNV4E92efrU0rPdMN7kSRJkiRJknpcpJR6OoYeExENwMaejkPqxYYC1T0dhNRL2T+kw7OPSIdm/5AOzz4iHWxsSqn0UJXduclGb7QxpTSpp4OQequIWGcfkdpn/5AOzz4iHZr9Qzo8+4iUv+6eoitJkiRJkiSpE5ngkyRJkiRJkvqwgZ7gu6WnA5B6OfuIdGj2D+nw7CPSodk/pMOzj0h5GtCbbEiSJEmSJEl93UAfwSdJkiRJkiT1aSb4JEmSJEmSpD7MBJ8kSZIkSZLUh5ngkyRJkiRJkvqwAZngi4wvRsT6iNgbEY9GxOk9HZfU1SLi/RHxWETsjogUEUVt6s/M9oe92f7xhYiInHr7jvqtiPhaRLyQ7R8bIuLOiJjcps2UiLg/IvZExNaI+FZElLRp86cRsToi9kXEooh4Q/e+E6lrRMQ/RcRrEbEr+9///IiY1aaN9xEJiIh7sp+13pxTdln2vrAvIlZFxKfbnFMaEf+R7V97svebyQdfXep7sveDxoioznncmVPv/UM6RgMywQfcBHwMmAuMAZ4A5kfE0B6NSup6O4BvA3/ZtiIihgHzyfSHMWT6xyfatLXvqD9LwEfI/Lc9M3v8y+bKiCgA7ge2AxXAOcAbgK/ntHkP8C/Ah4Fy4PvAr/2Cpn7iJ8C5KaURwETgATL3gELwPiI1i4gPAYPblE0FfkXmvlBO5n7ztYiYl9PsFuBSMveXCjL3m/uy9x+pP1iQUhqa8/gAeP+QOkuklHo6hm4XEauA/5NS+rfscRGwAbgxpXR7jwYndYOIuAx4CChOKTVkyz5MJlExMafsL4A/TymdkD2272jAyI5MWgyMSintiIg3Ag8Cx6WUtmbbvAv4MTA6pVQTEQ8BS1JKf5VzncXA3SmlL3X7m5C6SESUAp8GvgmMSylt8T4iQURMAp4ELgEqgbeklB6MiH8Crkkpzc5p+03gzJTSFRFRRiah94GU0i+y9WPI9I83pZQe6+73InWmiPgC8OaU0iXt1Hn/kDrBgPs1KCJGANOAp5vLsv+ILAZmH+I0aSCYBSxuvqlmPQMcHxHD7TsagN4KVKaUdmSPZwGvNyf3sp4hM0rj5Jw2T9PaM9hH1E9ExNsjYidQQ2a00TdTSluy1bPwPqIBLDud8L+BL6eU1rSpnsXh7w+nAINo3T+2Aquwf6j/mB0RWyKiMiJ+HBHTs+Wz8P4hHbMBl+ADhmefd7Yp35FTJw1Ew2m/XzTX2Xc0YGTXTPon4FM5xUfqI4drYx9Rv5BS+lVKqRwYDfw1sCCn2vuIBrpPk5kh9Z/t1B3p/mD/UH/3P8CpwDjgIjJLoTyYnWLr/UPqBEVHbtLv7M4+l7cpHwlUdW8oUq+yG5jUpmxkTl3zIrfl7bSx76jfiIh3AHcA16eUfptTtZv2//tvrjtcm91I/UhKaXtE/BuwIyJWpJSW4n1EA1hEnAB8DphziCZHuj/kfkfZf4g2Up+VUnox57AqIj4G7CKT7PP+IXWCATeCL6W0C1gNnNdclp2/P4vMEF9poFpCZth8buL/XDJTEnfbdzQQRMR1wI+A96WU7mlTvQSYHhGjc8rOBfYBK3LanNf6NM7FPqL+qQAoBk7KHi/B+4gGrkvJjGx9LrsLbvNyDndFxH9y5PvDK2QSe7n9YwyZaYn2D/VHKfsIvH9InWLAJfiyvg3cFBGnR8Qg4ItAPdD2y5zUr0REYXYR55JsUWlElGV3Z7sbaAS+GBGDstvO3wT8R84l7DvqtyLifwHfAt6RUprfTpPHgOXANyJiWERMAf4Z+H5KqSbb5tvAxyLi0ogoiYhPk1mf77aufwdS14qIv4iI8dm/x5L5772OzE6G4H1EA9vPgOPJJByaHwB/AvwdmfvAjIj4dPb+cCmZHUH/AyB7H7kV+OeImJLdVfQbwMsc6GNSnxUR780mrcneS74HbCKzKY33D6kTDMQpugA3A8PI7IY4HHgWuDKlVN2jUUld7wYyHx6bNf83f3lK6eGImEvmRrqNzHD475DZIbGZfUf92b8DDcBvMuukt7gqpfRYSqkpIt5J5gPmBqAWuBP4m+aGKaWfZz+03kFmjZllwNtTSmu76T1IXektwD9k10vaTWYB9DenlDYApJT2eB/RQJVS2kdmRHeL7L1ka0ppO7A9It5Gpj/cQiax8Q8ppbtzTrkxW7cYKAUeAd6ZUmrq+ncgdbnrgf+IiCFk1s57lMw9ZA+A9w/p2EVKqadjkCRJkiRJknSUBuoUXUmSJEmSJKlfMMEnSZIkSZIk9WEm+CRJkiRJkqQ+zASfJEmSJEmS1IeZ4JMkSZIkSZL6MBN8kiRJkiRJUh9mgk+SJEk9IiI+EhHrejoOSZKkvs4EnyRJ0gAQEdMj4s6IWB8R1dnnX0fEcT0dmyRJko6NCT5JkqSB4dfAHuD0lNJQYDbwUyD1aFSSJEk6Zib4JEmS+rmIGA3MAL6TUtoOkFLalFL6QUppY0QcFxH3R8SmiNgTEc9HxHvaXCNFxF9ExIKI2BsRSyPijIh4T0S8EhG7I+J/ImJozjmrI+KLEfGH7KjBFyNi7mHiLIyIv46IZRGxKyKei4grcurPiohHImJnROzI1p/S+f+LSZIk9S0m+CRJkvq5lNI24AXguxHx0Yg4MyJyPwcWAv8NnACMAv4N+HFEnNbmUh8BPgiMBF4B7gXeBpwLnERmVOCftTnnM8DngHLgm8B9ETH9EKF+DrgBuCb7Gl/Otj8hW/9t4PfAGGAs8HFg55H/F5AkSerfTPBJkiQNDJcDvwE+DTwNbI2ImyOiNKW0LqV0d0qpOqVUn1L6PvAy8KY217glpbQqpVQH/Ag4HviHlNKelNImMtOAz29zzg9TSk+klBqy110CXH+IGP8K+P9SSq+klJpSSvcATwIfyNbXAVOAqdnrLcm+riRJ0oBmgk+SJGkASCltSyl9PqV0PjAC+BjwSeDvI2JkRPxXRKzKTrXdCZwGjGtzmQ05f+/NXrdt2bA256xq53hy2/giYjwwHPh5dgruzmwcFwEV2WYfIbNm4B8iYl1E/J/cKcGSJEkDVVFPByBJkqTulVKqBe6NiAeBs4GvkVmj743A2pRSioilQHTCy01r5/jX7bTbCdQA70gpPXqIuCvJJCWJiBOBX5BJKv5jJ8QpSZLUZzmCT5IkqZ/LjtD7WnbtvdLsZhZXkJm2+yiZEX37gG1AcUT8GZkRfJ3hQxFxYUQURcRHyKzT96O2jbJJx+8A/zsiZkbGoIh4Q0ScnH0fH4mISRERwG6gIfuQJEka0EzwSZIk9X91ZDam+DmwlUwi79+AfwW+AXwWGARsAlYD44EnOum1vwN8hcwIvb8B5qWUXjtE25uAO7Nx7szG8vdAcbb+cjLrB1YDS4EF2fcgSZI0oEVKqadjkCRJUj8UEauBL6eUvtfTsUiSJPVnjuCTJEmSJEmS+jATfJIkSZIkSVIf5hRdSZIkSZIkqQ9zBJ8kSZIkSZLUh5ngkyRJkiRJkvowE3ySJEmSJElSH2aCT5IkSZIkSerDTPBJkiRJkiRJfZgJPkmSJEmSJKkPM8EnSZIkSZIk9WEm+CRJkiRJkqQ+zASfJEmSJEmS1IeZ4JMkSZIkSZL6MBN8kiRJkiRJUh9mgk+SJKkfiogPRUSKiDPalF+dLf9hO+esiIhfRMQXIqKmE2P5bUQ83FnXkyRJUmsm+CRJkvqnx7PPl7QpvwTY17Y8IsYBJ2XP+x7whq4OUJIkSZ3DBJ8kSVI/lFJ6HVhP+wm+/wamR8TEnPKLs8+Pp5TWpZSe7oYwJUmS1AlM8EmSJPVfj5OT4IuIMuAc4MfAOuDSnLaXAPuB59pO0Y2Iy7LTeudGxG0RsTsiqiLiqxFRmPuCETEnIp6OiJqIeDUirmsvsIi4NCIei4j9EbEzIn4WEZNz6r8TEc/kHJdExN6I2NDmOisj4mtH8z+OJElSf2GCT5Ikqf96HJgSEZOyx+cDTcBzwJO0Ht13MfB0SqnuMNf7f2RGBV4L3Ar8HfDx5sqIGA/8jsxnzA8Anwe+AJyZe5GIOAd4EGgE3gf8GXAR8EhEDMs2ewSYnXN8HlAEjI+IU7LXqQBOAB4+4v8SkiRJ/ZgJPkmSpP7rsexz80i9S4Bns0m8J7LHRMQg4GwOrNt3KPellP4hpfRgSumzwFPAe3Lq/4rM58srU0r3pJTuBK4BJrS5zj8C27Lt7ksp3Q5cDUwHPpJt8whQyIEk5BuBBcALwGU5ZY3Z9yJJkjRgmeCTJEnqv54HdnMgSXYJB5JhTwBnRsRwMiP7ijmQEDyU+W2OXwYm5xxfADycUtraXJBSeglY3ua8S4FfpJRqctotAl7J1pFSWg+s5EAy7zIyI/UeblO2KKW05whxS5Ik9Wsm+CRJkvqplFITmVFvl0REAXAhBxJ8S8msuXcRmcRfY7bt4exoc1wHlOUcHwdsbue8TW2ORwIb22m3MVvX7BHgjRFRlI3zkeaybP0bs8eSJEkDmgk+SZKk/u0x4HQya+yNILP2HimlBuBpMsm9S4AXUkq7j/G1NgDj2ikf3+Z4RztlkJnKm5tEfITMpiCXkVl/b0G2bEJEvBE4GRN8kiRJJvgkSZL6ucfJfOb7W+CVlNK2nLonyIyCu5AjT8/tiKeAyyJidHNBRJwGzGjT7jHgXRFRmtNuFnBKmzgeIZPY+0cyG4DUZON/iczmHU0ced1ASZKkfs8EnyRJUv/2NJmptG/n4M0onuDAyL7OSJR9k0zSbX5EXBMR7wfu5eDpuF8BxgC/joh3RsT1wH3AKuC25kYppTXAag6sv9fs4WzZ0pTSzk6IW5IkqU8zwSdJktSPpZT2A88BwcEJvgVAyv59zAm+lNIm4C3Za/4U+BLwT2Q2+8ht9xzwZqAU+BnwLWAh8MZ2Nsx4pM3zocokSZIGrEgpHbmVJEmSJEmSpF7JEXySJEmSJElSH2aCT5IkSZIkSerDTPBJkiRJkiRJfZgJPkmSJEmSJKkPM8EnSZIkSZIk9WFFPR1ATyouLk7jx4/v6TCkHlVbW0tpaWlPhyH1GPuAZD+QwH4ggf1A6s19oKqqqi6ldMjgBnSCr7y8nHXr1vV0GFKPmj9/PnPnzu3pMKQeYx+Q7AcS2A8ksB9IvbkPRMSWw9U7RVeSJEmSJEnqw7o1wRcR74+IxyJid0SkiDjsCMKIGBkRP4qIXRGxM/t3eZs2746I5RGxPyKWRcS1XfomJEmSJEmSpF6ku0fw7QC+DfxlB9vfAYwHTgBOzP79g+bKiLgg2+YfgeHAZ4EfRcS5nReyJElS/5ZS6rUPSZIkHVm3rsGXUpoPEBGXHaltREwF3gbMSiltzZb9NbAkIqaklNYAnwJ+k1K6K3vaXRFxPfBp4OOd/w4kSZL6npQSO/bVs3rbXlZv3cvqbfuo3Hbgeee+Rnj41z0dZruGlRUxbfQQpo4efOB5TOZ57NBSIqKnQ5QkSepx0RO/jGYTfA8BxSmlhkO0eRfw05RSWZvyWuA9KaX7ImIx8LOU0ldz6v8BeHdK6ex2rnkjcGPz8eDBgyvuvvvuTnhHUt9VU1NDWVnZkRtK/ZR9QP1FSok99bB5H2zen9i8P7FlPy3P+9v9xNW3lRbCuEEwdlDkPAdjB8OIEigw+ac8eD+Q7AdSb+4DV155ZVVKadKh6nvzLrrDgV3tlO/M1jW32dmmfkdOfSsppVuAW5qPx44dm3rr7ihSd+nNuwRJ3cE+oL4kpcTmPbWs2rq31Qi81Vszz3vrGvO+5sQRZZSmGkaWl3d+wMcoAVura6nasZ+mdn6Trm2EtdWwtjrlnJFRVlzAtNGDc0b+DckcjxnCccPLKCgw+afWvB9I9gOpL/eB3pzg2w2MaKe8PFvX3Ka8Tf3InHpJkqQ+pakpsXF3TZuptHup3LaP1dv2UlPflNf1CgIqRg5qM801k+yaPGowZcWF2Q+zF3fROzp2dQ1NrNuxLzvFuPX04rU79tPYTvavpr6J5Rv3sHzjnoPqSooKmDIq879Fc9JvWvZ/m4nlgyg0+SdJkvqY3pzgWwKURsSZKaXnASLiTKAkW9fc5rw2550LLO6eECVJkvLX2JRYv3M/ldv2sWrbXipzknmV2/dR15BfEq+wIJg8ctCBUWqjhzBtTOZ50shBlBYVdtE76R4lRQUcP3Yox48delBdfWMT63fuZ/W2fdmk6IFk6Nrt+6hvPDj5V9fQxMrN1azcXH1QXXFhMHnU4IPX/Rs9hIqRgygu7O496iRJko6sWxN8EVEIFJNJ0kEmgVcE1KWUWn2STSlVRsSvgZsj4oPZ4puBX2Y32AD4LvBwRMwD7gfeAVwFvKGL34okSVKHbKuu5cnXtrFozY4jJp4Ox8RT+4oLC5iaHZX4xpPHtqrLTaS23WDkUInU+sbE61v28vqWvQfVFRUEk3ISqWdOKueSk8YwfnjvXKtHkiQNHN09gu8G4Nac4+afTS+PiNeBl4GrUkqP5bT/FvBa9vh+4E+bT04pLYyIG4CvAncCq4HrU0rPdNk7kCRJOoz9dY08vXo7T6zcyuOvbuXlDR1fOaSkqICpowa3Wi/OqaNHr7AgkxSdPGowl5w0plVdy1TonBF/q7cefip0Q1PKjBTcto9HAKgE4KRxQ7n4xDFccuIYLjh+FMPKirv+zUmSJOXo1gRfSuk24LbDNGk17yKltB344CHaNrf5OfDzY41NkiTpaDQ2JV6o2sXjr27h8ZVbWVS5k7rGQ0+xzWz+0GY9vDGZvye4+UO3KSgIJpYPYmL5IC46oXVd82YmuQm/ym37WjY3abuZyaubq3l1czW3PbmawoJg1uTyloTfrMnllBQNzNGVkiSp+/TmNfgkSZJ6nZQSq7buzYzQW7mVJ1/bxp6ahkO2P23icC45aQwXnTCGGROGMW5YKREm8XqziGD88DLGDy/jguNHt6pLKbG1uo5XN+1hwevbeHzlVpau3dmyy29jU+K5yh08V7mD//v7VxlcUsgF00dlEn4njeGU8cP8/1+SJHU6E3ySJElHsGVPLU++lply+8TKrazfVXPItpNGDuLSk8Zw8YmZpN6oISWHbKu+JyIYO6yUscNKuejEMfz1W09h1/56nnp9W0vS97Wc9fv21TXy0CtbeOiVLQCMGVrKJSeO5uITM/+NTCwf1FNvRZIk9SMm+CRJktrYW9vA06u28/jKTEJv+cY9h2xbPriYi08Y0zIlc8rowd0YqXqDEYOKeetpE3jraRMA2LBrP0+s3Jadtr2NrdW1LW23Vtdy75L13LtkPQDHjx3CJdlk35zjRzNikOv3SZKk/JngkyRJA15DYxNL1+1q2Rhj0ZodNDS1v8ttaVEB5zdPuTxxDKceN9x189TKcSMG8e5zJvHucyaRUmLFpuqWZPHC17exL2cNv+Yde3+4oJKCILMzbzbhd/bUckqLCnvwnUiSpL7CBJ8kSRpwUkq8tqWax1/dyuMrt7Hw9W1U17a/jl4EnFExoiWhd87UkZQVm3RRx0QEp0wYxikThvHxS6ZT19DE0nU7W6Z7L167k8ZsMrkpwZK1O1mydiffemglZcUFnD99dMuU3pkTTCZLkqT2meCTJEkDwqbdNS1rpD2xciubdtcesu200YNbEnoXnjCa8sGuo6fOUVJUwHnTRnHetFH81VtOZk9NPU+v2s5j2YTfq5urW9rW1Dfx6IotPLois37f6CElXHTimJaE36SRTgeXJEkZJvgkSVK/tKemnqdeP7COXm7ipK1RQ0qyCb3RXHTCGCaPMnGi7jGsrJgrZo7nipnjgcMnorftreOXS9fzy6WZ9ftMREuSpGYm+CRJUr/Q1JRYtGZHy0io3KmPbZUVF3DB9NEta53NmDDMqY/qFcYPL+Pasydx7dmTjjiVfPW2fazetoYfPbXmoKnk508fRXFhQQ++E0mS1J1M8EmSpD7tlY17uHvxOu5bsp4Nu2rabePmBeqLIoITxw3jxHHD+MjF0w+7GUxK8Py6XTy/bhf/7+HXGD2khHeeNZF5sys4c9IIIkxgS5LUn5ngkyRJfc6m3TX8YkkV9yxez7INu9ttc/zYIS0JvTnHj2bEoOJujlLqXEWFBZwzdSTnTB3Jn19xEntrG3h61YFp6Ms37mlpu21vHbc9uZrbnlzN8WOHMG9WBdfMrnD6uSRJ/ZQJPkmS1CdU1zYw/8WN3LO4iide20pqM/u2sCB448ljufL0CVxy4hgmlg/qmUClbjKktIjLZ4zj8hnjANi8p4YnV27jgZc38uCyzdQ1NAHw+pa9fON3K/jG71Zw3rSRXDO7grefcZxr9kmS1I+Y4JMkSb1WQ2MTj63cyj2Lqnjg5Y3U1Dcd1GbW5HLmza7gHWcex+ihpT0QpdQ7jBtWxjWzMyP1du2v5zcvbOCexVU8tWp7S5tnVu/gmdU7+OJ9L3P5jLHMm13B5TPGOWVdkqQ+zgSfJEnqVVJKvFC1i3sWV/HLpevZWl13UJspowZnEhmzJnL82KE9EKXUu40YVMz7z5/C+8+fQtXO/dy7uIp7FlexMrubdF1jE/Nf2sT8lzYxvKyIt5+ZWa/v3Kkj3XBGkqQ+yASfJEnqFdZu35ddV6+K17bsPai+fHAx7zjzOObNruDsKSPdNEDqoIryQfzp5SfymctO4KX1u7lncRW/WLKerdW1AOyuaeDOp9dw59NrmDRyENdk1+s7cZzJc0mS+goTfJIkqcfs2lfPr17YwL2Lq3h69faD6ksKC7hi5jjmza7gslPGUVJU0ANRSv1DRHB6xQhOrxjB3181gydf28Y9i6v47Ysb2V/fCMC6Hfv51kMr+dZDKzlz0gjmza7gnWdNZIzT3yVJ6tVM8EmSpG5V29DIQ8u3cO/iKv6wfDN1jQevq3f+9FFcO7uCq844zt1vpS5QVFjAG04eyxtOHsuXr2nggZc3cs/i9Tz+6haashvYPL9uF8+v28WXf7WMS08aw7zZFbz11AkMKnG9PkmSehsTfJIkqcullHiucgd3L67iV89vYNf++oPanDhuKPNmV/CuWROZNHJwD0QpDUxDSouYN3sS82ZPYvOeGu5bsp57l1TxYtVuABqbEg+/soWHX9nCkJJCrjw9M1X+whNGU+h6fZIk9Qom+CRJUpd5bUs1v1hcxT1Lqli7ff9B9WOGlvKuWZnF/U+bONx19aQeNm5YGZ+49Hg+cenxvLppT8t6fVU7M/13b10jdy1ax12L1jF+eCnvmlXBNbMqOHXi8B6OXJKkgc0EnyRJ6lRbq2u5f+l67llcxdJ1uw6qH1RcyJWnT+Ca2RVcfMJoigpdV0/qjU4aP4y/vXIGN731FJ5evZ17F1fxqxc2sKemAYBNu2v5z0df5z8ffZ0ZE4ZxTXYE7nEjBvVw5JIkDTwm+CRJ0jHbX9fI75Zt4p5F63j01a00Ni/ilVUQcPGJY7j27MwaXkNK/Qgi9RUFBcGc40cz5/jRfOHq0/jD8s3cs7iKh1/ZTH1jpq8v37iHr/1mOf/62+VcePxorpldwVWnT2BYmWtoSpLUHfx0LUmSjkpjU2Lh6wd24ayubTiozWkThzNvdgVXnzWRccPLeiBKSZ2prLiQt51xHG874zh27K3j/uwu2M9V7gAgJXjytW08+do2Pnfvi7zl1PFce3YFl540lmJH60qS1GVM8EmSpLy8snEPdy9axy+WrGfj7pqD6ieOKOOa2RVcM7uCk8cP64EIJXWHkUNKuGHOVG6YM5XKbXu5d/F67lm8jtXb9gFQ29DE/c9v4P7nNzBqSAnvPPM4rj17EmdOGuF6m5IkdbJuTfBF5k7+BeCTwAjgOeAzKaUX22k7BXi5TXExmZjHp5S2RsRlwEPA3pw2O1NKkzo9eEmSBrC6hiZ+8+IGbl9QybPZkTq5hpUV8fYzjuOa2RWcP20UBe6sKQ0oU0cP4S/efBJ/fsWJLFm7k3sXV/HL5zewfW8dANv31vGDBZX8YEElp00czocunMrVZ1UwqKSwhyOXJKl/6O4RfDcBHwPmAiuBzwPzI+KUlFJ1bsOU0hpgaG5ZRNwNlKSUtra5bnlK6eB5QZIk6Zhs2LWfHz+1hjufXsvW6tpWdUUFwWWnjOPasyt404xxlBX7RV0a6CKC2VNGMnvKSD77jlN5dMUW7llcxe9e3kRtQxMAL63fzf931wv8y6+X855zJnH9nKlMGzOkhyOXJKlv6+4E32eAm1NKLwBExOeATwDzgNsPd2JEVADvBK7u6iAlSRrIUkoseG0bP1xQye+WbTpow4yTxw/lugum8s6zJjJqSEkPRSmptysuLOCKmeO5YuZ4dtfU89sXNvKjpypbdtfetb+e7z2+iu89voo3njyWD104lctOGUehI4AlScpbpJSO3KozXihiBLATuCiltCCn/AHgxZTSjUc4/5+B64ATUzbonCm664AS4EXgn1NKjxziGjcCLa8zePDgirvvvvvo35TUD9TU1FBW5sL3GrjsAwfsb0gs3Jh4pKqJDfta1xUEzB4TXFZRwEnluH5WP2M/UHdavTvxcFUTz2xOZAf1tRhdBm+cWMDFxwVDS7r33xn7gWQ/kHpzH7jyyiurDrckXd4Jvuw6ehNSShvyPG8ysAY4NaW0LKf8p8CelNInDnNuMVAJfDOl9PWc8gnAeOAlYBDwJ8CXgTkppSVHimns2LFpy5Yt+bwNqd+ZP38+c+fO7ekwpB5jH8hsmvHDBau5Z3EV++oaW9WNG1bKB86fwgcvmMJ4d8Htt+wH6gnb99bxs2fXcsfCStbt2N+qrqSogHeceRwfunAasyaXd0s89gPJfiD15j4QEYdN8HV4im5EDAa+CXwYaASGRMS7gNNTSl/pwCV2Z5/L25SPBKqOcO68bLv/zi1MKW0ENmYP9wA3R8Q7gPcCSzoQkyRJA1J9YxPzX9rIDxdU8vSq7QfVXzB9FDdcOJW5p02guLCgByKU1N+NGlLCp954Ap+89HgefmUzty+s5OFXMj++1zU0cfeiKu5eVMWZk0Zww5zMsgCu9SlJUvvyWYPv68B04ArgV9myRcBXso/DSintiojVwHnAAoCIKAJmcYT198is3fezlNK2DsTZBDhvSJKkdmzaXZPdNGMNm/e03jRjcEkh155dwQ1zpnHKhGE9FKGkgaawIFrW6qvctpc7Flbys2fXsWt/PQDPr9vF3/zP83zl18t437mTuX7OVCaPGtzDUUuS1Lvkk+C7GjgrpbQ9IpoAUkprs5tfdNS3gZsi4g/Aa8BngXrgnkOdEBGnAm8E5rRTNxdYQWb6bhnwSeBi4G/ziEmSpH4tpcTC17dz+8LVzH/p4E0zThg7hA9dOI1rz65gWFlxD0UpSTB19BD+8e2ncuNbTuGXS9fzw4WrebEqMxFo5756vvvo6/znY69z2clj+dCF03jjyWMpcFMOSZLySvAVc2CaLQARMQjY337zdt0MDAMeBIYDzwJXppSqI2IK8DJwVUrpsZxzPg0sSik91c71zgf+CxidjeOF7PnP5hGTJEn9UnVtA/csWsftCytZsam6VV1hQfCWmeP50IVTufCE0W6aIalXGVRSyHvPm8x7zp3E4rU7uX1BJb96fgN1jU2kBA+9soWHXtnClFGDuX7OFN577mTKB7urtyRp4MonwfcMmamy/zen7CPAwo5eILv77eezj7Z1a4Ch7ZT/2WGu9yXgSx19fUmSBoJXN+3h9oWV3L2oiurahlZ1Y4aW8oHzJ/PBC6Zw3IhBPRShJHVMRHD2lJGcPWUk//j2mfz0mbX8+Kk1VO3MjDFYs30f//Lr5XzjgRVcfdZEPnThNM6YNKKHo5Ykqfvlk+D7G+DRiHgfmQ02HgRmAxd2SWSSJKnD6hubePDlTfxwQSULXj94ydrzpo3khgunceVpEygpctMMSX3PmKGl/OnlJ/KpN57AH5Zv5ocLVvPYq1sBqG1o4ufPrePnz61j1uRyPnThVN52xnFuyiFJGjA6nOBLKS2PiJnAh4ClZHav/WhKaW1XBSdJkg5v8+4a7nx6LT9+upJNu1tvmjGouJBrZldww5ypnDpxeA9FKEmdq7AgeMup43nLqeN5fUs1dyxcw8+fW8uemsyI5SVrd7Jk7U6+/KtlvPfcyVx3wRQ35ZAk9Xv5jOAju4vtN7soFkmS1AEpJZ5ZvYMfLljNb1/cSEObTTOOHzOE6+dM5Y/OmcSIQW6aIan/On7sUD7/zlO5ae7J/GLJen64oJJlGzLLhm/fW8d3HnmN7z76GlfMGMcNF07j0hPHuCmHJKlfOmyCLyI+1JGLpJR+2DnhSJKkQ9lb28C9S6q4fUElyzfuaVVXEHBFdtOMi0/wC6ykgWVwSREfOH8K7z9vMs9V7uCHCyr5zYsbqG9MpAQPLtvMg8s2M230YK6fM5X3nDOZEYP9AUSS1H8caQTfV9ocjwcKge3ASKCJzFRdE3ySJHWRlZuruWNhJXc9t449bTbNGD2khPedN5nr5kylotxNMyQNbBHBudNGce60UWzZcyo/eXoNP356DRt21QCwets+vvyrZdz8wCtcM6uC6+dM5fQKN+WQJPV9h03wpZQmN/8dEX8OzAL+MqW0OyJGADcDz3dphJIkDUANjU08uGwzty9czRMrD9404+wp5XzowmlcdcYESotcRF6S2ho7rJQ/u+IkPn3ZCQf9e1pT38RPnlnLT55Z2/LvaVGb5Q4kSepL8t1F9+SU0n6AlNKuiPhLYDnw710QmyRJA87OfXX85Jm13L6gkqqd+1vVlRUX8K6zKrjhQkecSFJHFRUWcOXpE7jy9AntjohetGYni9YsYVgxrChawfVzpjBuWFkPRy1JUn7ySfANAsqB3G8bIwC3pJIk6Ri9umkPtz65mrsXraOmvqlV3dTRg7nBNaMk6ZidOG4oX7j6NP5m7incszizpukrmzJrmu6ph//7+1f5fw+v5J1nTuSjF0/njEn+mCJJ6hvySfD9AvhlRHweWA1MA74A3NvZQUmSNBA0NSUeXrGZW59YzWOvbj2o/k0zxvGhC6fyhpPGummGJHWiIaVFXD9nKtddMIWnV21v2ZSjKUF9Y+LuxVXcvbiKc6eO5KMXT2fuaeMpKizo6bAlSTqkfBJ8fw58E7gLKAVqgTuAv+qCuCRJ6reqaxv4n2fX8oMFlazaurdV3ZCSQt5z7mQ+fNE0po8Z0kMRStLAEBFccPxoLjh+NHf+4resKZ3GnU+vYee+egCerdzBs5U7mDiijBsunMYHzp9M+eCSHo5akqSDdTjBl1LaC/xxRPwJMBbYklJyJVpJkjpozbZ9/GDBan72zNqDdsOdMmowH75oGu85dxLDy5yGK0ndbVRZ8IG5M/jzN53EvUuquPWJVazYVA3A+l01/Otvl/Nvv1/BvNmT+OjF0zh5/LAejliSpAPyGcEHQDapt7kLYpEkqd9JKbHg9W3c+sRqHly2ibY/jV10wmg+evF03jRjHIVOw5WkHjeopJAPnD+F9583mSdWbuPWJ1bxh1c2k1Jm9907n17DnU+v4ZITx/DRi6dx+SnjXEZBktTjOpzgi4i1QLsj9lJKUzotIkmS+oGa+kZ+saSKW59YzfKNe1rVlRYVMG92BR+5eBozJgzvoQglSYcTEVxy0hguOWkMq7fu5bYnV/M/z62jOjsC+/GVW3l85VamjW4egT2ZoaV5j5+QJKlT5HMH+myb4wrgk8B3Oy8cSZL6to27arh94Wp+/NQadmTXcGo2YXgZN1w4lQ+cP4VRQ1zDSZL6imljhvCFq0/jr996Mj9/dh0/WLCaym37AFi9bR9f/OXLfOOBFbzn3El85KJpTB3tGqqSpO6Vzxp8P2hbFhG/Br4CfK0zg5Ikqa9ZtGYHtz6xmt+8sIGGptYD3mdPKeejF0/nqtMnUOwujJLUZw0rK+Zjl0znwxdN46Hlm7n1yVU8sXIbkNlA6dYnVnPbk6u5YsY4PnbxdC48YTQRTt+VJHW9Yx1DvhS4tDMCkSSpr6lraOI3L27gv59YzdK1O1vVFRUEbz/zOD568XRmTS7vkfgkSV2jsCB486njefOp43ll4x5ue3IVdy+qorahiZTgwWWbeXDZZk4ZP4yPXjyNa2ZXUFZc2NNhS5L6sXzW4Gs75GAI8CfApk6NSJKkXm5bdS0/fmoNty+sZPOe2lZ1o4aUcN0FU7h+zlTGDy/roQglSd3llAnD+Oq1Z/I3c2dw59NruH1BJRt31wDwyqY9/N3dL/Cvv13OB86fwg0XTuW4EYN6OGJJUn+Uzwi+Bg7eZGMP8OHOC0eSpN7r5fW7ufWJVfxi6XrqGppa1c08bjgfvXgaV5810VEakjQAjRpSwp9efiJ//Ibj+e2LG7n1iVUsWrMTgB376vn2w6/x3Udf56rTJ/DRi6dz9pRyp+9KkjpNPgm+y9sc7wFWpJSqOzEeSZJ6lcamxIPLNnHrE6tY+Pr2VnUFAW85dTwfvXg6F0wf5Rc1SRLFhQW886yJvPOsiSxdu5Nbn1jFr17YQH1jorEpcf/zG7j/+Q2cNWkEH714Om874zhKilyfVZJ0bPIawZdSeqJtYURclFJ6shNjkiSpx+3aX8/Pn13LDxasZu32/a3qhpUV8b5zJ/Phi6YxedTgHopQktTbnTW5nP/z/tn8w9tmcsfCSn701Bq27a0DYOm6XfzlT5fwL79exvVzpvLBC6YwZmhpD0csSeqr8knw/QYY3k75/cCozglHkqSe9fqWam57cjX/89w69tU1tqo7fswQPnLxNP7o7EkMKT3WfaokSQPFuOFl3PjWU/jM5Sfyy6XrufWJ1by8YTcAm/fUcsvvVvCth1byrrMm8tGLp3PqxPa+dkmSdGj5fDs5aN5RRJRy8Lp8kiT1KSklHn11K7c+sYqHX9lyUP0bTh7LRy+exhtPGktBgdNwJUlHp6y4kPecO5l3nzOJp1dt59YnVvPAyxtpSpmd2X/+3Dp+/tw6Lpg+io9ePJ23nDqeQu87kqQOOGKCLyIeI5PEK4uIR9tUTwGe7eiLRWZxoi8AnwRGAM8Bn0kpvXiI9g8DFwF1OcV/m1L6dk6bdwNfBqYCq4F/TCnd3dGYJEkD1766Bh6pauJ/3/IIr23Z26puUHEhf3ROBR+5aDonjhvaQxFKkvqjiOCC40dzwfGjWbt9H7cvrOQnT69hd00DAE+t2s5Tq7YzaeQgPnzhNN573mRGDCru4aglSb1ZR0bwPZh9vgD4fU55E7AR+Gker3cT8DFgLrAS+DwwPyJOOcxmHf87pfTZ9ioi4gLgDuA64D7gauBHEXFpSqnDiUdJ0sCycvMe7li4hrueW8ee2ibgQHKvonwQH75oKu87dwojBvtlSpLUtSaPGsw/vG0mf3HFSdy9uIrbnljV8qPTuh37+cqvl/GN373Cu86q4IYLp3J6xYgejliS1BsdMcGXUvoiQES8mlL68TG+3meAm1NKL2Sv+TngE8A84PajuN6ngN+klO7KHt8VEdcDnwY+foyxSpL6kfrGJn738iZuX1DJgte3HVR//vRRfOziabx55niKCt3NUJLUvYaUFnHDnKlcd/4UHn11C7c+sZpHVmSWjaipb+Knz67lp8+uZdbkcm6YM5W3n3kcZcWFPRy1JKm3iJQOvYReRETKNoiIQ37bSSk1HfGFIkYAO4GLUkoLcsofAF5MKd3YzjkPA2cABcAm4F7gy82j/SJiMfCzlNJXc875B+DdKaWz27nejUDL6wwePLji7rudzauBraamhrKysp4OQ+oyO2oSj21o4vH1iV11reuKC+CcMU1cMaWYKcNc40gDl/cCqXf2g417Ew9VNbFwY6Km9b5PDCmCi44L3lhRwNhB3sPUOXpjP5C6U2/uA1deeWVVSmnSoeqPNIJvFwd2zm3g0BtqdOSno+br7GxTvoP2d+cF+AdgefacM4DbgOnA+3Ku2eHrpZRuAW5pPh47dmyaO3duB0KX+q/58+djP1B/k1Liyde2cfuCSn63bBONTa1vX8ePGcJ1c6by7rMnsfCxP9gHNOB5L5B6bz/4MLC3toFfLFnP7QsrWZbdfXdvA/xubeJ3axt548ljuWHOVC6fMc5NOXRMems/kLpLX+4DR0rwvS3n78uP8bV2Z5/L25SPBKraOyGl9GTO4dKI+CvgwYgYlFLan71me9fbjSRpwNm1v567nlvHHU9V8nqbTTMKC4K3zBzPDRdO5aITRpPZ90mSpN5vSGkRH7xgCh84fzKL1uzkjoWV/Or5DdQ1ZiZSPbJiC4+s2EJF+SA+eMEU3nfeZMYMLe3hqCVJ3emwCb6U0uM5fz9yLC+UUtoVEauB84AFABFRBMyi4+vvNU8Fbv5WtiR7vVznAouPIVRJUh/zYtUubl9QyS+WVlFT33rViLHDSvnA+ZkvRceNGNRDEUqSdOwignOmjuScqSP57Ntn8rNn1/GjpypZt2M/AFU79/P1+a/wfx5cwVWnH8cNF07l3Kkj/VFLkgaAwyb4IuJNHblISukPHXy9bwM3RcQfgNeAzwL1wD3tvPZ4YDbwGLAPOJXM9Nr7Ukr7ss2+CzwcEfOA+4F3AFcBb+hgPJKkPqqmvpFfPb+B2xdWsmTtzoPqLzx+NDdcOJW3nDqeYjfNkCT1M6OHlvLpy07gj99wPI+u2MLtCyt56JXNpAT1jYn7lq7nvqXrmTFhGNfPmco1sysYWnrEPRYlSX3Ukf6Ff7AD10h0bA0+gJuBYdnrDgeeBa5MKVVHxBTgZeCqlNJjQBnwz8Ap2etvBO4GvtTywiktjIgbgK8CdwKrgetTSs90MB5JUh9TuW0vP3pqDT97di0799W3qhtWWsQfnTOJ6y6Ywknjh/VQhJIkdZ/CguDyGeO4fMY41m7f13KP3L43s7PU8o17+Oy9L/K13yxn3uwKrp8zlVMmeI+UpP7mSFN0O3XIQ3ZH3s9nH23r1gBDc44rgfM7cM2fAz/vxDAlSb1MY1PioeWbuX1hJY+s2HJQ/czjhnPDnKm8a9ZEhjg6QZI0QE0eNZi/u2oGf/nmk/jNixu4Y+EanqvcAUB1bQO3L6zk9oWVnD99FDfMmcrc0yZQUuQod0nqD/wWJEnqtbbsqeVnz67lx0+toWrn/lZ1JYUFvP3M47h+zlTOnlLu+kKSJGWVFRcyb/Yk5s2exEvrd3HHwjXcu7iK/fWNADy9ajtPr9rOmKGlvP+8yXzggilUlLtOrST1ZR1O8EVEIfC3wMeAycA64L+Bf00pNXZNeJKkgSalxLOVO7h9QSW/eXED9Y2pVf2kkYO47oKpvPfcSYx2h0BJkg7rtIkj+Oq1Z/D3b5vB3c+t446n1rByczUAW6tr+dZDK/n2wyu5YuZ4bpgzlUtOHENBgT+aSVJfk88Ivq8CfwR8HVgFTAduAsrJJP4kSTpq1bUN3Lu4ijsWVrJ8455WdRFw+SnjuGHOVN5w8lgK/eIhSVJehpcV85GLp/Phi6ax8PXt3LGwkvkvbaShKdGU4Hcvb+J3L29i2ujBXD9nKu8+ZxLlg0t6OmxJUgflk+C7HrgspbSiuSAiHgIexgSfJOkovbJxD3csrOSexVVU1za0qhs1pIT3njuZ6y6YwuRRg3soQkmS+o+I4MITRnPhCaPZtLuGnzy9lh8/Xcmm3bUArN62jy//ahlfn/8K7zxrIjfMmcpZk8t7NmhJ0hHlk+ArJDNyL9cqOr6DriRJANQ1NDH/pY3cvrCSp1dtP6j+nKkjuWHOVK46YwKlRd5mJEnqCuOHl/EXbz6JP738BB5ctpk7Flby+MqtANQ2NPE/z63jf55bx5mTRnD9nKm888yJDCrxvixJvVE+Cb7vA/8YEV9MKaXIrGb+98B/dU1okqT+pmrnfu58ag0/eWYtW6trW9UNLinkXbMquH7OFE6bOKKHIpQkaeApKizgytMncOXpE3htSzU/WriGnz+3lj01mZH1z6/bxd/+z/N85VfLePc5k7jugikcP3ZoD0ctScqVT4LvUuAC4E8iYi2ZjTZGAU9FxKPNjVJKb+jcECVJfVljU+LxlVu5Y2Elv1+2iabWe2Zw4rih3DBnKvPOrmB4WXHPBClJkgA4YexQPv/OU/mbuafwy6Xr+eHC1bxYtRuAXfvr+f7jq/j+46u49KQxXD9nKm+aMY7iwoIejlqSlE+C78HsQ5KkI1qxaQ93L6ri3sVVbNxd06quqCCYe9oErp8zlTnHjyIzKFySJPUWg0oKee95k3nPuZNYum4Xty+o5JfPr6euoQmAx17dymOvbmX0kBLeedZErj27gjMqRnhPl6Qe0uEEX0rpi10ZiCSp79uyp5b7lq7n7kXreGn97oPqJwwv44MXTOH9501m3PCyHohQkiTlIyKYNbmcWZPL+ezbZ/I/z63jjqcqqdy2D4Bte+u47cnV3Pbkak4cN5R5syu4ZnYFFeWDejhySRpY8hnBB0BEDAOG5ZallNZ3WkSSpD6lpr6RB17exD2L1vHoq1tpbDMHt6gguOyUsbz7nMm8eeY4ipzGI0lSnzRySAmffMPxfPyS6Ty2cis/e3Ytv3t5U8uovpWbq/n6/Fe4+YFXmDN9NPPOruCq0ycwzCU4JKnLdTjBFxFzgNuAk3KLgYQ76UrSgNLUlHhq1XbuWbyOX7+wkerahoPanDVpBNeePYl3nHkco4eW9kCUkiSpKxQUBG88eSxvPHksu/bX85sXNnD34iqeXrUdgJRgwevbWPD6Nj7/ixd566kTmHd2BZeeOMYf+iSpi+Qzgu97wG+BDwJ7uyYcSVJvtnJzNfcsXse9i9dTtXP/QfUV5YO4ZvZE5s2exInj3F1PkqT+bsSgYt5//hTef/4U1m7fx72Lq7hncRWvb818Zaypb+K+peu5b+l6xgwt5V2zJjJvdgWnTRzuen2S1InySfBNAf4qpZSO2FKS1G9sq67ll0vXc8/iKpau23VQ/dDSIt52xgSuPXsS508bRUGBH9YlSRqIJo8azJ9dcRL/600nsmTtTu5ZXMV9S9ezc189AFura1t24T1l/DDmnV3BNbMqmDDCdXkl6Vjlk+B7EpgJvNxFsUiSeoma+kZ+v2wz9yxex8OvbKGhzbp6hQXBG04aw7yzJ/GWmeMZVOJKDZIkKSMimD1lJLOnjOSzbz+Vh1/ZzD2Lq/j9ss3UNWbW63tl0x6+9pvl/Otvl3PxCWOYN7uCK0+fwJDSvJeJlySRX4LvE8APImI+sDG3IqX0w06NSpLU7VJKPLN6B/csXsf9z29gT83B6+qdXjGcebMncfVZExk7zHX1JEnS4ZUUFfDW0ybw1tMmsGtfPfe/sJ57FlXxbOUOILNe3+Mrt/L4yq189t4XufL0CVx7dgUXnTCGQmcFSFKH5ZPg+yPgMmA2rdfgS4AJPknqo1Zt3cs9i9Zxz5Iq1m4/eF2940aU8a5ZFVx7dgUnjx/WzhUkSZKObMTgYq67YCrXXTCVym17uSe7Xl/ltn0A7K9vbCkbP7y05fPHjAnDezhySer98knw/SMwL6V0X1cFI0nqHjv21nH/8+u5e3EVi9fsPKh+cEkhV51+HNeeXcGc40f7C7okSepUU0cP4S/ffDJ/ccVJLFqzg7sXVfHLpevZnZ1BsGl3Lf/56Ov856OvM/O44Vw7u4J3zZrIuOGu1ydJ7cknwVcA/LKrApEkda3ahkYeWr6ZuxdV8dArm6lvbL2uXkHAJSeN5drZFbz1tPEMLnENHEmS1LUignOmjuKcqaP4/DtP5aHlm7lrURUP53xWWbZhN1/ZsJuv/maZn1Uk6RDy+RfxZ8A1wD1dE4okqbOllFp+Fb//+Q3s2l9/UBt/FZckSb1BaVEhV55+HFeeflzLbIO7FlWxZO1OAJoSPLpiC4+u2MKQkkzbP8rONihwtoGkAS6fBN8o4McR8TiwIbcipfShTo1KknRM2lvXJte4YaVcM7uCebMrmHmc69pIkqTeZeSQEm64cBo3XDiN17dUc+/iKu5eXMW6HZn1gvfWNXLXonXctWid6wVLEvkl+PYDP2mnPLVTJknqZu3tTJdrUHEhV54+gXmzK7j4RHemkyRJfcPxY4dy41tP4S/ffDLPVu7g7kXr+NULG9iTXa9vw64avvPIa3znkdc4vWI482ZP4uqzJjJ2WGkPRy5J3afDCb6U0kdzjyNiKPAR4FOdHJMkqYNWbd3L75dt4vfLNvPM6u00NLX+zSUCLjphNNfOnsTc0ycwtNS1aiRJUt9UUBCcP30U508fxReuPo0Hl23inkVVPLJiS8tnoBerdvNi1ct8+Vcvc/aUkbxpxjjePHM8J48fSoQ/bkrqv/L+phcRZwCfAa7LFn0vj3MD+ALwSWAE8BzwmZTSi+20HQd8HXgDMBbYCtwJfCGlVJttMw1YBeyj9UjCipTSrnzelyT1BQ2NTTxbuSOT1Fu+mde37G233cnjh3Lt2ZN416yJHDdiUDdHKUmS1LXKigt5x5kTeceZE9laXcsvl67nnsVVPL8u8zUwJXiucgfPVe7g6/NfYdLIQVwxYxxXzBzPBcePorSosIffgSR1rg4l+CKiGHgPmcTehcBrQCFwVkppZR6vdxPwMWAusBL4PDA/Ik5JKVW3aTsUeAX4ZzJJvOOBu4FBwF+2aZtvHJLUZ+zaV8/DKzbz+2WbefiVzezOTkdpa8qowbzl1PHMm13BaROH+yu1JEkaEMYMLeWjF0/noxdPZ+XmPdyzuIoHXtrEq5sPfMVct2M/P1hQyQ8WVDKkpJBLTxrLFTPHcfmMcYwZ6lReSX3fERN8EfEvZJJy5WR20P0c8DCwHtid5+t9Brg5pfRC9tqfAz4BzANuz22YUnod+JecopUR8d9Aq6nCktQfvbalumXq7bOVO2hsOni504KAc6eO4oqZ47hi5jhOGOvUE0mSNLCdOG4YfzN3Bn8zdwZrtu3j98szn6eeWrWN+sbM56m9dY389qWN/PaljUTArMnlLaP7ZkwY5ucpSX1SpHT4PTIioonM9NjrU0oP5JRvIDNybnOHXihiBLATuCiltCCn/AHgxZTSjR24xq+BzSmlj2SPp5EZ3bceKAVWAF9PKd1ziPNvBFpeZ/DgwRV33313R8KX+q2amhrKysp6OowBr7EpsXJXYunWxAvbEpv3t99uUBGcNio4c3Rw+uhgSLEfQI+VfUCyH0hgP+jv9jckXt6e+Zz1wrZEdX377UaVwhljMp+1TikPigsH1mct+4EGut7cB6688sqqlNKkQ9V3JMH3UeDTwDnAEuC7wI/JJNNm5ZHgmwysAU5NKS3LKf8psCel9IkjnP85MiMAz0sprcuWDQXOILOWXyHwbjJrAs5LKf36SDGNHTs2bdmypSPhS/3W/PnzmTt3bk+HMSDt2FvXMvX2kRVbWnaCa2v6mCFcMWMcb5o5jvOmjaK4sKCbI+3f7AOS/UAC+8FA0tiUWLJ2B79flvkc9sqmPe22G1xSyCUnjmmZyjtuWO/80t+Z7Aca6HpzH4iIwyb4jjhFN6V0K3BrRJxHJsH2TeAbQAkwA+hQgo8D03nL25SPBKoOd2JEfInMjr2XNSf3srFVAwtymt4eEVcA1wNHTPBJUndKKfHalmoeXLaZ3y/bxHOVO2hn5i2FBcF500ZyxYzxXDFzHMePHdr9wUqSJPVThQXBOVNHcc7UUfztlTNYu30ff1i+md8v38zC17ZR19gEwL66Rh54eRMPvLwJgLMmjeCKmeN504xxrncsqdfp8C66KaVngI9GxF+RWZPvT4CHIuJ3KaUrO3D+rohYDZxHNikXEUXALNqsv9csu+vut8hsynFpSml1B0JtAvyXVlKvUNfQxNOrtres/7Jm+752240YVMxlp4zlTTPGcdnJ4xgxuLibI5UkSRqYJo8azIcvmsaHL5pGdW0Dj7+6ld8v28RDr2xma3VdS7ul63axdN0ubvndCiYML+NNM8fx5pnjuOiEMZQVuyuvpJ7V4QRfs5TSTuAW4JaIeCvwqTxO/zZwU0T8gcxOvJ8F6sls3tFKNvn3AzIJwEtTShvaaXMpmfUBV5CZovtHwAeB9+YRkyR1qu1763ho+WZ+v3wTj67YSnVt+1NvTxg7hCtmjueKGeM4Z+pIipx6K0mS1KOGlhZx5ekTuPL0CTQ1JZau25mZyrt8M8s2HNhjcuPuGn781Bp+/NQayooLslN5M6P7xg/v/1N5JfU+eSf4cmU33XjgiA0PuBkYBjwIDAeeBa5MKVVHxBTgZeCqlNJjwMVkknW1wKu5w59TSs3z1U4BbgMmZNutAG5IKd13DG9LkvKSUmLFpuqWUXqL1uygveVNiwqC86eP4k0zxvHmmeOZNmZI9wcrSZKkDikoCGZPGcnsKSO5ae4pVO3czx+WbeL3yzfz5GvbqGvITOWtqW/iwWWbeXBZZvWqMypGcMXMcVwxYzynVziVV1L3OKYEX75SZkePz2cfbevWAENzjh/hCFNtU0rfI7OphiR1q9qGRp56fTt/WL6ZB5dtYt2O9re9LR9czOWnjONNM8bxhpPHMmKQU28lSZL6ooryQdxw4TRuuHAae2sbeGLl1pbRfVura1vavVC1ixeqdvF/HnyV8cNLedOMTLLv4hPHMKjEqbySuka3Jvgkqa9qbEq8unkPz67eweOvbuWxV7ewt66x3bYnjRuaXZNlPLMnlzv1VpIkqZ8ZUlrEW0+bwFtPy0zlfaFqF7/Pju57af2Bqbybdtdy59NrufPptZQWFXDxiWO49KQxnDt1FDOPG+bnREmdxgSfJLWjuraBJWt28lzlDp6t3M6SNTvZc4i19IoLgwumj+aKmZmRelNHO/VWkiRpoCgoCM6aXM5Zk8u58a2nsGHX/syuvMs288TKrdRmp/LWNjTxh+Wb+cPyzFTeQcWFzJpczjlTR3LO1JGcPWWkG61JOmom+CQNeCkl1u3Yz3OVO1oeyzfupqmddfSajRpSwmWnjOXNM8dz6UljGFbmhzFJkiTBcSMGcd0FU7nugqnsr2vMTOXNrtW8ec+Bqbz76xtZ8Po2Fry+raXspHFDWxJ+50wdyfQxQ1zDT1KHmOCTNODUNTTx4vpdLMpJ6OV+2GrP2GGlnJvzYevMSeUUFvhhS5IkSYc2qKSQN586njefOp6UEi+t352dIbKDRZU7qNrZeh3nVzdX8+rman7yzFoARg4uzn7+HJX9DDqCsmLX8ZN0MBN8kvq9bdW1LFqzk2crt7OocgdL1+1q2fWsPQUBp0wY3iqhN2nkIH89lSRJ0lGLCE6vGMHpFSP48EXTANiw68AskkWVO3hp/W4acqaR7NhX32qH3uLC4LSJI1o+o547dSTjhpf1xNuR1MuY4JPUrzQ1JVZuqW413XbV1r2HPWdYaRGzppRzbvaX0bMmj3DKrSRJkrrccSMG8Y4zB/GOMycCsL+ukaXrdrYk/J5bs4Od++pb2tc3Jpas3cmStTv5/uOrAJg0clCrab2njHfzDmkgMsEnqU/bW9vA0rWZD0HPrcl8ENpd0/5mGM2mjh7MOVNGcvbUkZw7bSQnjRvmdFtJkiT1uEElhcw5fjRzjh8NZNaKfm3L3palZZ6t3M5rW1r/eL1ux37W7djPL5asB2BISSGzppS3TOudPaWc4f54LfV7Jvgk9RkpJdbvquHZ1dtbftFctmEPjYfZDaOksIAzJo1o2ZnsnKkjGTustBujliRJko5ORHDiuKGcOG4o7z1vMgA79taxeG024bd6B0vX7aSm/sDyM3vrGnli5TaeWLktew04edwwzpk2knOyn4enjh7s8jNSP2OCT1KvVd/YxMvZhYibHxt31xz2nDFDS1pNUTi9YgSlRS5ELEmSpP5h5JAS3jRjPG+aMR7IfGZetmE3z67O/AD+3OrWn5lTglc27eGVTXv48VNrgMxn5uYfv5s/M7t5h9S3meCT1ONSSmzZU8vKzdWs3FLNys3VLN+4h+fb/BrZVgScMn5YZqpt9sPJlFH+GilJkqSBo7iwgDMnlXPmpHI+xnQA1u/c37JT73OVO3h5w+5Ws162VtfxwMubeODlTUBm1svpFcMZ2tBI1ZBVLaMGjxtR5mdrqY8wwSep2zQ2Jdbt2JdJ5DU/tlTz2ubqI66bB5n1RGY3r503dSSzXE9EkiRJOsjE8kFcXT6Iq8/KbN6xt7aBpet2tiT8nmuzbnVdYxOL1uwE4NH1L7eUDykp5IRxQzlx7FBOGDeUk7KJvymjBruRh9TLmOCT1OlqGxpZtXVv60Te5mpWbd1LbcOhR+S1NXnUoJZ1Qs6ZOopTJrgZhiRJkpSvIaVFXHTCGC46YQwATU2J17ZUZzfuyIz0e33r3oPO21vXyPPrdvH8ul2tyksKC5g2ZjAnjhvKCWOHtjyfMHYog0qc6iv1BBN8ko7anpr6g0birdxczZrt+zjMvhcHqSgf1PLLYPN0gBPHDWXUkJKuC16SJEkaoAoKgpPGD+Ok8cN4//lTANi1v54f/fL3jJl+WsuyOSs3V7N2xz5Sm8/2dY1NrNhUzYpN1a3KIzKf7U9s57N9+WA/20tdyQSfpMNKKbGlOrM+3ms5ybyVm6vZtLu2w9cpKgimjh7c6iZ/4thhHD92CENK/adIkiRJ6kkjBhVzwohgbna33mY19Y28vmVvy3eA13Jm59Q1tp6dkxKs27GfdTv28/ArW1rVjRlayonjhuQk/4Zx4rihjB9e6jp/UifwW7UkIDNMf92O/azcsqfVtNrXtuxl1/76Dl9nUHEhJ4wbctAvdlNHD6HYdTokSZKkPqWsuJBTJw7n1InDW5U3NDaxdsf+dtfXrq49eH3trdW1bK2uZeHr21uVDy0tanc2z+SRg1znT8qDCT5pgGhqSuzYV8fG3TVs3l3Lpt01bNhVw5MvNfJ/lj/G61uq81ofb+Tg4pab7wk5N+OJIwZR4Dp5kiRJUr9WVFjA9DFDmD5mCG85dXxLeUqJTbtrs0m/PTnTffeytfrgGUDVtQ0sXbuTpWt3tipvu87fhBFljB9WxoQRZYwbXsqYIaV+75BymOCT+oHq2gY27a5h064aNu2pYeOuTAJv854aNu6qYdPuWjbvqaG+8VAL4+0+5LUnjijL/KLWMq028zx6aGnXvBlJkiRJfVZEMGFEJhF3yUljWtXt3FfHa1uqDxr1t27H/g6v89esqCAYO6yU8cPLGD+8lAnDyxg3vIzxw8uYkC0bP6KMYaVFTgHWgGCCT+rF6hqa2Lwnk6DbtLuGTbtrWkbgbcwm8zbvrm13CHw+CpvXx2szLP6EsUNdH0+SJElSpygfXMI5U0dxztRRrcr31zXy+tacNf62HFjn71CDFBqaEht2ZWYlHc6g4sJMsq85+TeijHHDSjMjArPJwLHDSikrdvdf9W1+c5d6QFNTYtveupak3abdtdnEXXMSr5bNu2vYtreuU15v1JCSdn7ZKmX8sDLWLl/MdVe/lZIi17eQJEmS1P0GlRRy2sQRnDZxRKvyhsYm1mzfR+W2fS2DHTZlvys1/71tb+1Bo/9y7a9vZPW2fazetu+wMZQPLm75rjQhJyGY+z1q9NBSCp0WrF7KBJ90jBqbEtU1Deyuqc889jewp6aePdmyPTUNbKuuzYzC25OZRrt5Ty0NTYe5C3XQ4JLC7PDzA0PQxw9r/mWqlHHDMutTlBYd+teo+WvD5J4kSZKkXqeosIDjxw7l+LFDD9mmvrGJLXtyB0zUZpN/BwZTbNpVw54jzHraua+enfvqWb5xzyHbFBYEY4eWthoROHpoCcPLihlWVsTwQdnnsuKWsmFlRW4Wom5hgk8DWkqJfXWNOcm4TIJud5sE3Z6cxN3umpwE3v569tY1dnpcRQXB+OGZ5NyEdn45ah6BN6ysuNNfW5IkSZL6iuLCAiaWD2Ji+aDDttvbvG55dn3y5rXK2y6FVNd46I0HG5sSG7NtYVeHYxxcUtiS+Msk/YpbJQMzzwcShMNyEoTDBxUzpKTQdQR1RCb41Oc0NDZR19hEbX0TtQ1N1DY0UtvQxP5som5PdiRdcwIuk5A7kMBrnbhroLETRtLlY3TudNkRZYzL7gSV+yvQqMEl7gglSZIkSZ1kSGnREUcDppTYsa8+Z/Rf6+WUmqcFb60+/LTgtvbVNbKvrpFNuw/eRbgjCgKGljYnAHNHCeYmBZuThQcSg4NLCikpLKC0uIDSokJKiwooLSpwRGE/1a0JvsiknL8AfBIYATwHfCal9OIh2o8EvgW8A0jAr4A/TSntzGnzbuDLwFRgNfCPKaW7u+xNDHAppWxSLZtYyybZ6nISbbUNTdTWN+aU59TVH/i77hDlR6rr7oRcewYVF7Yagj0s+49r5peY3F9hMs/lg0uYMKKMsUNLnQ4rSZIkSb1QRDBqSAmjhpQw87jhh2zX0NjElurMxoc79tVlB5FkBpgcGHTSeuZX80CTfUcxA6wpkbl+TQOw/xjeYUZhQVBaVEBJNuHXkvzLSQQeqq7D5xS3aZdTXlJY4ICWLtDdI/huAj4GzAVWAp8H5kfEKSml9va+vgMoBU7IHv8E+AHwLoCIuCDb5jrgPuBq4EcRcWlK6dkjBVPXmPjl0vUkMokrgJQgkTLPiZa6BJCgKft3q3bZE1vKc/5uau+6bY5pfo2U6biJRFPKbMTQ0JRoSomGxsxzY3NZU6Ixe9zY/Hdj5rnteW3LWs5pc41W57VT1tiUiauvKy6MVr96HDxUuugwv4pknov9xUOSJEmSBqSiwgKOGzGI40Ycflpwexoam6iubWh3aajWCcIDs87aLh11uGnEHdHYlFpGFfaUiMzSVAURFBbkPNoetykriKCosM15hyjLvUZBROb1CoLCAigqKGhzLSgsKOD1VU0sf/BVIjIjJ5unRkdAENnn1seZ+si0z/7d3I6Ig9q3HLfU5bRp57oBFHRginZ3J/g+A9ycUnoBICI+B3wCmAfcntswIqYCbwNmpZS2Zsv+GlgSEVNSSmuATwG/SSndlT3troi4Hvg08PEjBbO3Hv7szsWd887UqYqyvyiUFh/I9pcc4leC3F8Ccoclt5eoG1ZWTFlxgesXSJIkSZK6XVFhAeWDSygfXHLU16ipb2ydADxEYnB/XSO1DY3tLnF18Oy6zHF9Y/eM6kmJ7Gv1wlFEq1f0dARHJZpHrnX5C0WMAHYCF6WUFuSUPwC8mFK6sU37dwE/TSmVtSmvBd6TUrovIhYDP0spfTWn/h+Ad6eUzm4nhhuBltcpHDq6YtKf/qBT3l9fEUBhNitcEDl/d7C8IKC4IJOAKy6g1aOo1XMcVN767ziorvm4KHDr8W5UU1NDWVnZkRtK/ZR9QLIfSGA/kMB+ILIz+qA++8j9O3Oc2hy3/TsdVNf2GvVNmRmMjdmZk03k/N2B8sbUK9OCXa7yX99RlVKadKj67hzB1zyBfWeb8h05dW3bt7ctzc6c9sPzuB4ppVuAW5qPh40ckz779pmth0Ny6OGUBW2GVpLbnoOHU8ZhhmLS6jg75LLgwHVbho92dLhqYea5IDvUNPfvggJaznPkmtqaP38+c+fO7ekwpB5jH5DsBxLYDySwH6jvSCmzhFhDUxNNTbRatix3SbLmZcca2yx/1l5ZY1PimWef5eyzz2lZUq2pzTJsHGLptZbl3Y6w7FvbpduaWuraX/Ytd0m5T/7r4f836c4E3+7sc3mb8pFA1SHaj2invDznWrsPcb3ddEBZUfCJS4/vSFNJkiRJkiT1AhFBYUBhQWGnXnf/qgIunzGuU6/ZWT55hPpu2ykgpbSLzC635zWXRUQRMAtobyG8JUBpRJyZ0/5MoCRb19zmvDbnnXuI60mSJEmSJEn9TndvBfpt4KaIOD0iBgFfBOqBe9o2TClVAr8Gbo6IMRExBrgZ+GV2gw2A7wJvi4h5EVEcEfOAq4DvdMebkSRJkiRJknpadyf4bgZuAx4EtgGXAlemlKojYkpEVEfEpTntbwC2Aq9lH1uADzVXppQWZtt8FdiTfb4+pfRMN7wXSZIkSZIkqcd12y66vVFENAAbezoOqYcNBap7OgipB9kHJPuBBPYDCewHUm/uA2NTSqWHquzOTTZ6o42H22JYGggiYp39QAOZfUCyH0hgP5DAfiD15T7Q3VN0JUmSJEmSJHUiE3ySJEmSJElSHzbQE3y39HQAUi9gP9BAZx+Q7AcS2A8ksB9IfbYPDOhNNiRJkiRJkqS+bqCP4JMkSZIkSZL6NBN8kiRJkiRJUh9mgk+SJEmSJEnqw0zwSZIkSZIkSX3YgEzwRcYXI2J9ROyNiEcj4vSejkvqLhHxhYhojIjqnMedPR2X1FUi4v0R8VhE7I6IFBFFberPzN4L9mbvDV+IiOipeKWu0IF+kCJif5t7wxk9Fa/U2SLiaxHxQrYPbIiIOyNicps2UyLi/ojYExFbI+JbEVHSUzFLna2D/WB1RNS0uR+8o6diljpbRPxTRLwWEbuy/9bPj4hZbdr0ue8HAzLBB9wEfAyYC4wBngDmR8TQHo1K6l4LUkpDcx4f6OmApC60A/g28JdtKyJiGDCfzL1gDJl7wyfaayv1cYfsBzne2ebe8EL3hCZ1iwR8hMy/9TOzx79sroyIAuB+YDtQAZwDvAH4encHKnWhw/aDHP+rzf3g/m6MUepqPwHOTSmNACYCD5DJCRVC3/1+MFATfJ8Bbk4pvZBS2g98DigB5vVsWJKkrpBSmp9SuhN4vZ3qa4FC4HMppf3ZhMbXgf/VnTFKXe0I/UDq91JKf59Sei6lVJdS2gn8b+CsiBiZbXIpmYTHjSml3SmlSjLfEz4REWU9E7XUuTrQD6R+L6X0SkppR/YwgEZgHDAqW9Ynvx8MuARfRIwApgFPN5ellBqAxcDsHgpL6gmzI2JLRFRGxI8jYnpPByT1kFnA4uy9oNkzwPERMbxnQpJ6zB0RsS0iFkXEJ3s6GKmLvRWozPmSNwt4PaW0NafNM8Bg4ORujk3qLm37QbN/iYjtEfFiRPxtRBT3RHBSV4mIt0fETqAGuAX4ZkppS7Z6Fn3w+8GAS/ABzf9n7GxTviOnTurv/gc4lcyvFBeRGZr/oNPUNUANp/17QnOdNFC8GZgOHAd8FvjfEfHpng1J6hoR8Wbgn4BP5RR7P9CAcoh+APBh4AQy3xU+RWYG3Je7Nzqpa6WUfpVSKgdGA38NLMip7pP3g4GY4NudfS5vUz4yp07q11JKL6aUKlNGFZk1KSvIJPukgWY37d8TmuukASGl9PvsNJS6lNKvgX8DbujpuKTOlt0s4H+A61NKv82p8n6gAeMw/YCU0iMppT0ppYaU0uPAF/B+oH4qpbSdzGee70XEWdniPnk/GHAJvpTSLmA1cF5zWXYXuVlkpulKA1HKPnr1rkBSF1lCZsp67o6i55KZptVrb+BSN2jC+4L6mYi4DvgR8L6U0j1tqpcA0yNidE7ZucA+YEX3RCh1vSP0g/Z4P1B/VwAUAydlj5fQB78fDLgEX9a3gZsi4vSIGAR8EagHOvKPm9TnRcR7I2JM9u/xwPeATcCTPRqY1EUiojC7QHpJtqg0IsqyOybeTWZh3S9GxKCIOJ3Mbuv/0UPhSl3icP0gIs6OiHMioiQiiiLirWR2iruzxwKWOllE/C/gW8A7Ukrz22nyGLAc+EZEDIuIKcA/A99PKdV0Y6hSlzlSP4iIkyLi0pz7wxwyI/i8H6jfiIi/yH4PJiLGkskR1ZHZNRf66PeDSCn1dAzdLiKCTFLvj8nMn34W+NPszihSvxcR9wEXAkPIrCXwKJkdglb2aGBSF4mIjwC3tlN1eUrp4Yg4k8wN+xwyw+6/A3wxDcSbpPqtw/UDYBiZnRQnAw1AJfD/Ukrf6bYApS4WEYnMf9+1baquSik9lm0zlcwXvTdm290J/HVKqe05Up90pH4QEecD/wUcT2aGTxVwO/D1lFJ9twYrdZGIuJ/MrM6hZD77PwP8c0rp2Zw2fe77wYBM8EmSJEmSJEn9xUCdoitJkiRJkiT1Cyb4JEmSJEmSpD7MBJ8kSZIkSZLUh5ngkyRJkiRJkvowE3ySJEmSJElSH2aCT5IkSZIkSerDTPBJkiRJkiRJfZgJPkmSJPWIiPhIRKzr6TgkSZL6OhN8kiRJA0BETI+IO+P/b+++w+wsy8SPf+/MJJn0BBJKmvReggKW3QjYgl1WXFdFRF1X0XVdkS32xbK6u4jrb5XFtRewsCAiglGUtogCGkIJRUoIqaRNMpNk0ub+/XHeSU5OMpMZ5sycmTnfz3Wd67zleZ/3PpM8eXPueUrE0ohoLd6vj4gDax2bJEmSescEnyRJUn24HmgBjsvMscBJwI+ArGlUkiRJ6jUTfJIkSUNcROwLHAVclplrADJzRWZ+JzOXR8SBEXFdRKyIiJaIuDci3lBRR0bEByLijojYEBHzI+L4iHhDRDwcEesj4n8jYmzZNQsj4qKI+E3Ra/D+iJjTRZwNEfGhiHgwItZFxB8i4sVl50+MiFsiojki1hbnj6z+T0ySJGlwMcEnSZI0xGXmauA+4KsR8faIOCEiyv8f2AB8EzgU2Af4EnBFRBxbUdV5wJuBScDDwDXAK4CTgcMp9Qp8f8U17wU+DkwEvghcGxEHdxLqx4G3Aq8r7vGZovyhxflLgV8Dk4EpwDuB5r3/BCRJkoY2E3ySJEn14QzgBuB84E5gVURcHBEjM3NxZl6dma2ZuTUzvwEsAF5UUcclmflEZm4BLgcOAT6SmS2ZuYLSMOBTK675bmbenpnbinrvAc7pJMYPAv+UmQ9nZntm/gT4LfCm4vwWYCbwrKK+e4r7SpIk1TUTfJIkSXUgM1dn5icy81RgAvAO4F3AhyNiUkR8LSKeKIbaNgPHAvtVVLOsbHtDUW/lsXEV1zyxh/0ZlfFFxP7AeODKYghucxHHC4BpRbHzKM0Z+JuIWBwR/1k+JFiSJKleNdY6AEmSJPWvzNwMXBMRNwLPBj5PaY6+04CnMjMjYj4QVbjdQXvYv34P5ZqBNuBVmXlrJ3E/SSkpSUQcBvyUUlLxo1WIU5IkadCyB58kSdIQV/TQ+3wx997IYjGLF1MatnsrpR59G4HVwPCIeD+lHnzVcG5EPD8iGiPiPErz9F1eWahIOl4G/HtEHB0loyLihRFxRPE5zouI6RERwHpgW/GSJEmqayb4JEmShr4tlBamuBJYRSmR9yXg34AvAB8DRgErgIXA/sDtVbr3ZcBnKfXQ+wfgrMx8rJOyFwI/KOJsLmL5MDC8OH8GpfkDW4H5wB3FZ5AkSaprkZm1jkGSJElDUEQsBD6TmV+vdSySJElDmT34JEmSJEmSpEHMBJ8kSZIkSZI0iDlEV5IkSZIkSRrE7MEnSZIkSZIkDWIm+CRJkiRJkqRBzASfJEmSJEmSNIiZ4JMkSZIkSZIGMRN8kiRJkiRJ0iBmgk+SJEmSJEkaxEzwSZIkSZIkSYOYCT5JkiRJkiRpEDPBJ0mSJEmSJA1iJvgkSZIkSZKkQcwEnyRJkiRJkjSImeCTJEkaQiLiZRFxXUSsjIgtEbEkIn4YEX9W69i6EhHfjoiHah2HJEnSYGSCT5IkaYiIiE8Cc4F24G+BlwAXAk3AbTUMTZIkSX2osdYBSJIkqfci4mXAvwD/kZn/WHH6BxHxmv6PSpIkSf3BHnySJElDw4XASuBjezqZmdd2bEfEuyLiwYjYXAzhvTgiRpadPz0iMiLmFENn1xflPhcRDUWZ6RHRHhFvrbxXRPw0Iu4s258ZET+OiOaI2BQRt0XEn3f2QXpY9/iI+H8Rsbj4PPdHxF/u/cclSZI0dJjgkyRJGuQiohGYDfwqM7fspez7gf8BbgVeA3wJeD9w+R6K/zewFPgL4FvAPwPvBMjMxZSG/b65ov5JwJkd9UXEOOAW4HnFfd5IaQjxryPi2XuKsQd1Dwd+Cbwe+DTwquJePyx6NEqSJNUFh+hKkiQNfvtSmmdvUVeFit53nwB+kpnvLg7PjYitwCURcUJm3lt2ybWZ+ZFi+8aIeAnwBkoJQoArgC9HxJTMXFkcez3QAPyo2H87cBAwKzPnF3H8CngC+GhRfk+6U/ebgVOA52TmPcWxX0XENOBTlJJ/kiRJQ549+CRJkurHUcBkdibIOvygeK8cNju3Yn8BMKNs/0oggfIhsW8GfpOZy4v92cBDHck9gMzcBFxTnOtMd+p+WRHT/RHR2PECfgU8u2M4sSRJ0lBngk+SJGnwWw20ATP3Um5S8b684vjTlJJpkyqOr63Y30KppyAAmbkG+AXFUNqIOBA4jV2H+07aw/06Yqi83w7drHs/4Dhga8Xry8Bw4MDO6pckSRpKHKIrSZI0yGXmtoi4DXhpRIzoYh6+joTd/hXH9wOC3RN63XEFcEVEHAScRSkJeHXFPY/dw3UHdON+e6t7DfAAcF4n1z+9l/olSZKGBHvwSZIkDQ0XA1MoLTaxm4h4FfAQpZV2K1eZfWPxftszuO+1wAbgTZR62/0sM1vKzt8GHB0Rx5fF0gS8thv321vdvwQOBlZk5t17eHW54IgkSdJQYQ8+SZKkISAzfxkRFwGfjIijge8Dy4CpwNnA6zNzWER8CviviLiU0jx4J1JKCv5vZt73DO67MSJ+Cvxtca/PVBT5FvBB4GcR8VFgPfAhYB/gs72s+3uUVvW9OSK+ADwIjKM0bPegzPybnn4eSZKkwcgefJIkSUNEZv4LcCallWYvBX4DXEJpXroXFGW+DLwbOAO4Dvh7SnPWvbUXt76cUgJuLXBDRUwtlObOuwv4CvBjSr9kfklm/rGXdW8BXkppQY4LKS0K8jXgRcAtz/zjSJIkDS6RmbWOQZIkSZIkSdIzZA8+SZIkSZIkaRAzwSdJkiRJkiQNYib4JEmSJEmSpEHMBJ8kSZIkSZI0iDXWOoBaGj58eO6///61DkMasDZv3szIkSNrHYY0INk+pK7ZRqTO2T6krtlGpN0tWbJkS2Z22jDqOsE3ceJEFi9eXOswpAFr7ty5zJkzp9ZhSAOS7UPqmm1E6pztQ+qabUTaXUSs7Oq8Q3QlSZIkSZKkQcwEnyRJkiRJkjSI9WuCLyL+KiJui4j1EZER0eUQ4YiYFBGXR8S6iGgutidWlDk7Ih6KiE0R8WBE/EWffghJkiRJkiRpAOnvOfjWApcCo4BvdKP894GRwKHF/g+B7wCvBYiI5xZl3gJcC7wGuDwiZmfm3dUNXZKkvrVteztPrNrAg8tbWNq8ida2bbRu3kZL2zbatm3ftXBW7u56ICvOV0NEFeqgl5VUJYZeXl+FH0TvY+h1CNX4UXb5s1i6dDu/aL6nz2Po/V+pKvx51v6vdRViGAA/hwHwF2LU8Ab2GTOcqRNHcdQB4zlsv7GMaHTQkyRp4OvXBF9mzgWIiNP3VjYingW8ApiVmauKYx8C7omImZm5CHgPcENmXlVcdlVEnAOcD7yz+p9AkqTqu3dxMz+66ymuv28ZazdurXU4UvWsWFLrCKReGTeykZcdewBnP2c6zz9031qHI0lSpyL74lf8e7tpKcF3EzA8M7d1Uua1wI8ys6ni+GbgDZl5bUTMA36cmZ8rO/8R4OzMfPYe6rwAuKBjf/To0dOuvvrqKnwiaWhqa2ujqalp7wWlOlSN9tG6JbnqsXZ+u7z/n8WSpJ6ZNTn4q8OHMamp910N/T+W1DXbiLS7M888c0lmTu/sfH8P0e2J8cC6PRxvLs51lGmuOL+27PwuMvMS4JKO/SlTpqRLb0udc3l6qXO9bR8Llq7n3G/+nlWtO4feNg0fxmlHTOGE6RM5aN8xjB/VyNiRjYxramRkY8Muw9fKh0aWf9XcpUx1BkACuw8BfkZ19LKKaqRBe/uLzRr8XrRPYuiPP8/bbruN2bNndxFD7/X6z7MqMfS6hprHMBB+DgPi35iETVu3sap1CwtXbeD+peu5+aGnadlc6o9wz6rk0Zbg6287mecd0rvefP4fS+qabUTquYGc4FsPTNjD8YnFuY4yEyvOTyo7L0nSgLNg6Xre8vXf7RiOO25kIx962RG84eQZjBk5kB/NUvc9PDo4aPKYWoch9Urb1u1cd+8yPn/Dg6xq3ULr5m28/Vt38c3zTnHIriRpQBnIM8beA4yMiBM6DhTbI4pzHWVOqbjuZGBe34cnSVLPLWnetEty76SZE/n1hadx3p8dbHJPkgaYpuENnP2c6fz6gtM548gpAGzaup13fPsuFiy1T4EkaeDo1wRfRDRERBOlJB2UEnhNEbFbHJn5JHA9cHFETI6IycDFwM+KBTYAvgq8IiLOiojhEXEW8HLgsr7/NJIk9Uxm8o//O39Hcu/ZMyfy3Xecyn7jnGNGkgayCaOHc9lbn8OLjtoPKCX5LvjxPWzZ1l7jyCRJKunvHnxvBTYBc4v91mL/hRExMyJaI2J2RflVwGPFayVwbsfJzPxdUeZzQEvxfk5m3tXXH0SSpJ66/PeLuP3R1QAcOKGJb739VMY1Da9xVJKk7hjZ2MB/n/NsjjpgHAAPLW/hyzc9WuOoJEkq6dcEX2Z+OzNjD6+bM3NRZo7NzNvKyq/JzDdn5oTi9ZbMbK6o88rMPCozm4r3q/rzM0mS1B3L17Xxuesf3LH/b68/gQmjTO5J0mAysrGBi99wIo3DSosYXXrTozy03KG6kqTaG8hz8EmSNGT8z62Ps2FLacXcN506gxceMaXGEUmSnonjpk3gfWccBsC29uS/fmMvPklS7ZngkySpj61u3cwVdz4JwKjhDfzDnKNqHJEkqTfOP/1QJo8dCcD19y3j8ZWtNY5IklTvTPBJktTHvnX7Qtq2liZif9OpM9lnzIi9XCFJGsiahjfw17MPBiATLrvlsRpHJEmqdyb4JEnqQy1tW/nOHQsBGN4QvOuFB9c2IElSVbzluTMZ39QIwNV/XMKS5k01jkiSVM9M8EmS1Id+Nn8ZLW3bADjrpGkcOGFUjSOSJFXDuKbhvO0FBwGlufiuvPup2gYkSaprJvgkSepD18xbsmP73OcfVLtAJElV95bnPosoLajLNfOWkJm1DUiSVLdM8EmS1EeeWrOROxeuAeDw/cZy7NTxNY5IklRNB0xo4gWH7gvAwtUbmfdUc20DkiTVLRN8kiT1kWvnL92x/bqTphEd3TwkSUPG62ZN27Fd3mtbkqT+ZIJPkqQ+kJlc/cfFO/ZfO2tqDaORJPWVM487gJGNpa9VP5u/lK3b22sckSSpHpngkySpDzywdD2PrdwAwKkH7cP0SaNrHJEkqS+MaxrOS47ZH4C1G7dy259W1jgiSVI9MsEnSVIf+M1DT+/YfrW99yRpSHvNiTv/nf/1g093UVKSpL5hgk+SpD5w88M7v+C96Kj9ahiJJKmv/flhkxnRUPpqdfPDK11NV5LU70zwSZJUZWs3bNmxkuLh+41l2sRRtQ1IktSnxoxs5JSDJwGwpHkTj61srXFEkqR6Y4JPkqQqu/VPK+novHH6kVNqG4wkqV+cfsTO3to3P+w8fJKk/mWCT5KkKrul7IvdGUc6PFeS6sEZR+38hY4JPklSfzPBJ0lSFbW3J7c8UvpiN2ZEAycftE+NI5Ik9YdDp+yckuHOJ9awYfO2GkckSaonJvgkSaqiB5auZ/WGLQC84LDJjGj0UStJ9SAidkzLsGV7O3c8trrGEUmS6onfOiRJqqI7Hl+1Y/uFRzj/niTVk/J/93/3uAk+SVL/McEnSVIV3fnE2h3bzz3Y4bmSVE9OLZuW4a6Fa2oYiSSp3pjgkySpStrbkz88WfpCN3H0cA6bMrbGEUmS+tOkMSM4fL/Sv/33L13Pxi3OwydJ6h8m+CRJqpLHVrayduNWAE5+1j4MGxY1jkiS1N9OKXpvb29P5i1qrm0wkqS6YYJPkqQqubNsONapB0+qYSSSpFopH6Z75xMO05Uk9Y9+TfBFyUURsTQiNkTErRFxXCdlZ0ZEa8Vrc0Rsj4jJRZnTIyIryizuz88kSVKHu8q+yJ18kPPvSVI9OuVg5+GTJPW//u7BdyHwDmAOMBm4HZgbEbtNUpSZizJzbPkL+DlwQ2auqig+sazc9L7+EJIk7cldC0sLbDQNH8ZxUyfUOBpJUi1MmziKqROaAJi3qJmt29trHJEkqR70d4LvvcDFmXlfZm4CPg6MAM7a24URMQ14NfCVvg1RkqSeW9K8iSXNmwA4acYkRjQ6C4Yk1auOXnybtm7n/iXrahyNJKkeRGb27IKIAA7IzGU9vG4C0Ay8IDPvKDv+S+D+zLxgL9d/CngLcFgWQUfE6cBNwGJKicL7gU9l5i2d1HEBsOM+o0ePnnb11Vf35GNIdaWtrY2mpqZahyENSJXt464V7Xx9QamXxisPCl5zcEOtQpMGBJ8hqme3LGnnikdKz4SzDx3GS2fu+ksf24fUNduItLszzzxzSVejVhu7W1FEjAa+CLwN2A6MiYjXAsdl5me7UcX44r254vjasnOd3Xs48NfAF3PXjORDwCzgAWAU8G5KQ36fl5n3VNaTmZcAl3TsT5kyJefMmdON0KX6NHfuXGwj0p5Vto87r1sAPAHA2WeczBlH7lejyKSBwWeI6tn0peu44pH/A2Dz2AOYM+ekXc7bPqSu2UaknuvJ+KH/AA4GXgxsLY79EXhTN69fX7xPrDg+qexcZ84qyn2z/GBmLs/M+Zm5LTNbMvNi4HfAX3YzJkmSquLexc07tk+cPrFmcUiSau+I/ccxspiqofz5IElSX+lJgu81wF9l5u1AO0BmPgVM687FmbkOWAic0nEsIhop9cCbt5fL3wv8ODNXd+NW7UB0JyZJkqph2/Z27ivmWJqxzyj2GTOixhFJkmppeMMwjptWWmzpydUbWbthS40jkiQNdT1J8A2noqddRIwCNvWgjkuBCyPiuOLaiyj1BvxJZxdExDHAacW1lefmRMTBETEsIkZHxAeAPwOu6kFMkiT1yp+ebqVta2mupRPsvSdJAk6YvnM19XtdaEOS1Md6kuC7i1JPunLnURoS210XA98GbgRWA7OBMzOzNSJmRkRrRMyuuOZ84I+Z+fs91HcqcAvQAiwCXge8PDPv7kFMkiT1Svnwq1km+CRJwKwZE3ds3/tUc83ikCTVh24vsgH8A3BrRLyR0gIbNwInAc/vbgXFAhmfKF6V5xYBY/dw/P1d1Pdp4NPdvb8kSX3hnqd29swo77EhSapf5T265zsPnySpj3U7wZeZD0XE0cC5wHxgOfD2Yh4+SZLqVkcPvmHBjjmXJEn17aB9RzO+qZH1bdu456l1ZCYRThUuSeobPenBR7HIxRf7KBZJkgadtq3beWh5CwCH7zeOMSN79GiVJA1REcGJMyZy259Wsap1M8vWtTF14qhahyVJGqK6/BYSEed2p5LM/G51wpEkaXB5YOl6trcnACfOsPeeJGmnE6eXEnxQ6u1tgk+S1Ff21s3gsxX7+wMNwBpgEtBOaaiuCT5JUl1asHTn/HvHOzxXklTm+LJ5WR9Yup4zjzuwhtFIkoayLhN8mTmjYzsi/g6YBfx9Zq6PiAmUVsW9t08jlCRpAFuwbP2O7WOmmuCTJO10zIHjd2wvWLq+i5KSJPVOT1fRPSIzNwFk5rqI+HvgIeC/+iA2SZIGvI4vbBFw1AHjahyNJGkgmT5pFOOaGmlp27bLL4QkSaq2YT0oOwqYWHFsAjC6atFIkjSIbNvevmOBjYP3HeMCG5KkXUTEjl58y9a1sWbDlhpHJEkaqnqS4Psp8LOIeEVEHBMRrwCuKV6SJNWdJ1ZtYPO2dgCOLhuGJUlSh2Om7nw+PGgvPklSH+lJgu/vgD8CVwH3F+/zgQ/0QVySJA14u86/Z4JPkrS7o52HT5LUD7o9ligzNwB/ExHvBqYAKzMz+ywySZIGuF0SfPbgkyTtQfnzwR58kqS+0pMefABkydMm9yRJ9a68J4Y9+CRJe3L4/mNpHBYALrQhSeoz3e7BFxFPAXtM6mXmzKpFJEnSIJCZOxJ8+44ZwX7jRtY4IknSQDSysYHD9hvLQ8tbePTpVtq2bq91SJKkIagny/19rGJ/GvAu4KvVC0eSpMFh/RZYXayGePSB44mIGkckSRqojpk6noeWt7CtPXn06dZahyNJGoJ6MgffdyqPRcT1wGeBz1czKEmSBrqnWnd2and4riSpK8ccOJ6rWQKUpneYUON4JElDT4/n4KswH5hdjUAkSRpMnirrgOECG5KkrpQ/J5yHT5LUF7qd4IuIYRWvccCHgBV9F54kSQPTYnvwSZK66WgTfJKkPtaTOfi2sfsiGy3A26oXjiRJg0PHEN0RjcM4ZPKYGkcjSRrIJo0ZwdQJTSxd18aDS9eTz9rj2oWSJD1jPUnwnVGx3wI8kpnOEitJqisbt2zj6Y2l7SP3H0djQ29nvJAkDXXHTB3P0nVttGzexuq2hlqHI0kaYnrUgy8zb688GBEvyMzfVjEmSZIGtIeWt+zo0u78e5Kk7jjmwPHc+ODTwK4LNUmSVA096XJwQyfHr6tGIJIkDRYLlu6cP8n59yRJ3VH+vDDBJ0mqtp4k+GK3AxEj2X1ePkmShrTyCdJN8EmSuqN8oY3FTnIkSaqyvQ7RjYjbKCXxmiLi1orTM4G7+yIwSZIGqvIefEcdMK6GkUiSBosZk0YzdmQjrZu38VSLfSQkSdXVnR58NwK/BtqL947Xr4DPAm/o7s2i5KKIWBoRGyLi1og4rovyN0fElohoLXu9t6LM2RHxUERsiogHI+IvuhuPJEk9tb09eXh5CwAz9xnNuKbhNY5IkjQYDBsWHH1g6ZdCazbDuo1baxyRJGko2WsPvsy8CCAi/pSZV/TyfhcC7wDmAI8CnwDmRsSRXazG+++Z+bE9nYiI5wLfB94CXAu8Brg8ImZnpj0LJUlVt3D1BjZt3Q64wIYkqWeOOXA8dy1cC5Sme3j+ofvWOCJJ0lDRZQ++iCifd++HETFsT68e3O+9wMWZeV9mbgI+DowAzup56AC8B7ghM6/KzK2ZeRXwC+D8Z1ifJEldKh+ee7QJPklSD5TP2/rA0nU1jESSNNTsrQffOqDjKbSNzhfUaNjbjSJiAnAQcGfHsczcFhHzgJOA73Vy6fkR8T5gBXAN8Jmy3n6zgB9XlL8LOLuTGC4ALujYHz16NHPnzt1b6FLdamtrs41IFX7+2PYd25tXPMrcuY/XMBpp4PIZIu2uef3Or1O//sNDzNj4pxpGIw1cPkOknttbgu8VZdtn9PJeHYnC5orja8vOVfoI8FBxzfHAt4GDgTeW1dnt+jLzEuCSjv0pU6bknDlzuhG6VJ/mzp2LbUTa1RXfvBNYCcBbXnk60yaOqm1A0gDlM0TaXdvW7fz7vLlsb0+aYxxz5syudUjSgOQzROq5LhN8mfl/Zdu39PJeHWOaJlYcnwQs6eT+vy3bnR8RHwRujIhRxRDf9Z3Utx5JkvrAg8tKj5jRjTB1QlONo5EkDSZNwxs4dMoYHlnRyqNPt7BlWzsjGnsy45EkSXvWZYIvIl7UnUoy8zfdKLMuIhYCpwB3FPU3Uhpm29nw3ErtHaEV7/cU9ZU7GZjXzfokSeq2lS2bebplMwAzxga7TlUrSdLeHXPgeB5Z0crW7cmjT7fuMi+fJEnP1N6G6N7YjTqSbszBV7gUuDAifgM8BnwM2Ar8pLJgROxPaW6+24CNwDGUhtdem5kbi2JfBW6OiLOA64BXAS8HXtjNeCRJ6raO3nsA08fWMBBJ0qB1zNTxXHPPUqC0kq4JPklSNextiG61+4tfDIyjlDgcD9wNnJmZrRExE1gAvDwzbwOagE8BR1JKIC4HrgY+XRbf7yLircDngB8AC4FzMvOuKsctSRILyhJ8M8bZe0+S1HPlK7AvWLoenlPDYCRJQ8beevBVVWYm8IniVXluETC2bP9J4NRu1HklcGUVw5QkaY8WLC1L8I01wSdJ6rldEnzL1tUwEknSUNLtHnoR0RARH46IP0VEW0Q8GhEfiYjuDs+VJGlQ6xiiO7whOGB0jYORJA1Kk8eOZOKI0vaDy1oo9YGQJKl3etKD73PA64H/AJ4ADgYupLSK7T9WPTJJkgaQtq3beWxlKwCH7zeOxmEb93KFJEl7Nn1s0LwmWbdpK0vXtTFt4qhahyRJGuR6kuA7Bzg9Mx/pOBARNwE3Y4JPkjTEPby8hfaik0VpQnQTfJKkZ2bGOLh/TWl7wdL1JvgkSb3Wk0U0Gij13Cv3BN1fQVeSpEGrfIGNYw50xUNJ0jM3vWwe1/L5XSVJeqZ6kuD7BvDRiAiA4v3DwNf6IjBJkgaSB8sTfFNN8EmSnrnyhZrKny+SJD1TPRmiOxt4LvDuiHgKmAHsA/w+Im7tKJSZL6xuiJIk1V55D4ujDxzP7/5Uw2AkSYPalFEwekQDG7ds36WHuCRJz1RPEnw3Fi9JkupKe3vu6GExfdIoJowaXuOIJEmD2bAIjjpgLH9c1MyiNRtZ37aV8U0+WyRJz1y3E3yZeVFfBiJJ0kC1aM1GNmzZDpR670mS1FvHTB3PHxc1A/DQshZOPXif2gYkSRrUejIHHwARMS4ippa/+iIwSZIGigddYEOSVGXlvzByHj5JUm91uwdfRDwP+DZwePlhIHElXUnSELbABTYkSVVW/gsjV9KVJPVWT+bg+zrwC+DNwIa+CUeSpIGn/IuXPfgkSdVw1AHjGRbQnrjQhiSp13qS4JsJfDAzs6+CkSRpIOr44jWuqZHpk0bVOBpJ0lAwakQDB08ew2MrN/Dwiha2bm9neEOPZ1CSJAno2Rx8vwWO7qtAJEkaiNZu2MKydW1AqfdeRNQ4IknSUHHM1AkAbNnWzuMrHSQlSXrmetKD76+B70TEXGB5+YnM/G5Vo5IkaYAon/jcFXQlSdV09IHj+Nn80vaCZes48oBxtQ1IkjRo9STB93rgdOAkdp2DLwETfJKkIeneJet2bB/rAhuSpCo6tujBB3Df4vWcdVINg5EkDWo9SfB9FDgrM6/tq2AkSRpo5j/VvGN71oyJNYtDkjT0nDh9Z4Jv/uLm2gUiSRr0ejIH3zDgZ30ViCRJA9G9i0s9+MaMaOCQKWNrHI0kaSiZOHoEz9p3NAAPLF3H1u3tNY5IkjRY9STB92PgdX0UhyRJA87Kls0sad4EwHHTJtAwzAU2JEnVdcL0iQC0bW3nkRUttQ1GkjRo9WSI7j7AFRHxf8Cy8hOZeW5Vo5IkaQC4t2y4lMNzJUl94cTpE/jZ/KVAqdd4+bx8kiR1V0968G0CfggsBraXvbb1QVySJNVc+fx7HT0sJEmqphPLfoFU/tyRJKknut2DLzPfXr4fEWOB84D3VDkmSZIGhPmLd66ge8J0e1RIkqrv2KnjGRbQnrs+dyRJ6ome9OADICKOj4j/BpYC/wr8sgfXRkRcFBFLI2JDRNwaEcd1Una/iPhORDwREa0RsTAiPhcRI8vKHBQRWdTVWvbyW5gkqVcyc8eKhvuOGcH0SaNqG5AkaUgaPaKRI/YfB8AjK1rYtGV7jSOSJA1G3UrwRcTwiHhzMf/ePcCLgQbg2Zl5QQ/udyHwDmAOMBm4HZhb9AasNBZ4GHgJML54fyXwb3soe2Jmji17+asvSVKvPLVmE80btwKl3nsRLrAhSeobJxbTQGxvTx5Y6lcZSVLP7TXBFxH/CjwFfLN4fwlwJLC+ePXEe4GLM/O+zNwEfBwYAZxVWTAzH8/Mf83MxzKzPTMfLWI4o4f3lCSpx+Y9tXbHtvPvSZL60gkzdg5AmreouXaBSJIGrcjMrgtEtAOrgHMy85dlx5dR6jn3dLduVBo22wy8IDPvKDv+S+D+7vQEjIjrgacz87xi/yDgCUrDhUcCjwD/kZk/6eT6C4Ad9xk9evS0q6++ujvhS3Wpra2NpqamWoch1cQVD2/nlqWlZ+QHThzGMfvs+jsx24fUNduI1LnK9rGkNfnUXaWhubMmB+cf31Cr0KQBwWeItLszzzxzSWZO7+x8dxbZeCdwPnBDRNwDfBW4Aug6M7i78cV7c8XxtWXnOhURHwdOAk4pO7wKeAHwB0pDhs8GfhgRZ2Xm9ZV1ZOYlwCUd+1OmTMk5c+b04CNI9WXu3LnYRlSvLllwK9DCsIB3/cVLGTty10em7UPqmm1E6lxl+2hvT750/69Yt2krizYN52Uve4lTQ6iu+QyRem6vQ3Qz81uZeSrwPOBe4IvAMmBf4Kge3KtjOO/EiuOT2MtQ34j4NPA3wOmZubgsttbMvCMzt2Tmpsz8HvAD4JwexCVJ0i6aN27h4RUtABw7dcJuyT1Jkqpp2LDg5GdNAmDNhi08trK1xhFJkgabbq+im5l3ZebbgWnAJ4GFwE0R8YtuXr+uuGZHD7yIaARmAfP2dE2x6u5XgDcBszPz4W7cqh3w112SpGfs7oU759875aB9ahiJJKlenHLwzufNnU+s7aKkJEm763aCr0NmNmfmJZl5JPByYGMPLr8UuDAijouIUcBFwFZgtznziuTf94HTKSX3Fu6hzOyIODoiGiJiRES8CXgzpV58kiQ9I3ctXLNj+9SDJ9UwEklSvSj/hVL5c0iSpO7o1ZijYtGNX+614E4XA+OAGynNu3c3cGZmtkbETGAB8PLMvA34M0rJus3An8rnoMjMscXmkcC3gQOKco8Ab83Ma3vxsSRJde7Osi9WJ9uDT5LUD46fNoGm4cNo29rOnU+Y4JMk9Uy/TiqUpSV7P1G8Ks8tAsaW7d/CXobaZubXga9XOUxJUh3btGU79y1eB8AhU8YweezIGkckSaoHIxqHMWvGRH73+BqWNG9iafMmpk4cVeuwJEmDRI+H6EqSNJTNe2ot29pLC8Wfau89SVI/OtVhupKkZ8gEnyRJZW7706od2889xASfJKn/PPeQfXds3/rIqi5KSpK0KxN8kiSVufnhlTu2Zx8+pYaRSJLqzckHTWL0iAYAbnlkJe1Fj3JJkvbGBJ8kSYXl69p4cNl6AE6YPsH59yRJ/WpkYwMvOLTUi29V62YWFM8kSZL2xgSfJEmFWx55esf26UfYe0+S1P9OO3K/Hds3PfR0FyUlSdrJBJ8kSYXy4bnlX7AkSeov5b9guvmRlV2UlCRpJxN8kiQBW7e383/FAhsTRw9n1oyJtQ1IklSXZuwzmsP2GwvAvEVrad64pcYRSZIGAxN8kiQBf3hyLS2btwHwwsOn0DAsahyRJKledfTia0+49U+upitJ2jsTfJIkAdfdu3TH9ouOcniuJKl2yp9D181f2kVJSZJKTPBJkurelm3tXHfvMgBGDW/gpcfsX+OIJEn17LmH7Mt+40orud/08NMO05Uk7ZUJPklS3bvlkZU0b9wKwMuO3Z8xIxtrHJEkqZ41DAteO2sqAFu3Jz+/b1mNI5IkDXQm+CRJde+aeUt2bL/upGk1jESSpJLy51H5c0qSpD0xwSdJqmvr27byqwdXALDvmBHMPmxyjSOSJAmOOXA8R+xfWk33roVreWrNxhpHJEkayEzwSZLq2lV/WMyWbe0AvPrEqTQ2+GiUJNVeROzSi++KOxfVMBpJ0kDntxhJUt3asq2dr936+I79N54yo4bRSJK0q9c/ezojil88ff+OJ1m3aWuNI5IkDVQm+CRJdeuae5awdF0bAC8+aj+OPnB8jSOSJGmn/cc38frnTAegZfM2vnfHwtoGJEkasEzwSZLq0vb25LKbH9ux/74XHVbDaCRJ2rP3nHYIw6K0/c3bF7Jxy7baBiRJGpBM8EmS6tKP7nqKx1dtAOD5h+zLs2dOqnFEkiTt7ln7juHVJ04FYM2GLVx2y+N7uUKSVI9M8EmS6s7itRv57M8X7Nj/uxcfXsNoJEnq2vvOOIyGohvfpTc9ygNL19U4IknSQGOCT5JUV9rbk3+66l42bNkOwF+dMoPnH7pvjaOSJKlzR+w/jvedfigA29qTD/14/o4V4CVJAhN8kqQ60t6efOLa+7n90dUATJ3QxEdfeXSNo5Ikae/+9kWHc9QB4wB4aHkLH/jhPLZuN8knSSoxwSdJqgtbt7fzsZ/ez/d/twiAYQH/fvaJjGsaXuPIJEnauxGNw/jCX57IiMbSV7gb7l/O+6+Yx6aiR7okqb71a4IvSi6KiKURsSEibo2I47ooPykiLo+IdRHRXGxPrChzdkQ8FBGbIuLBiPiLPv8gkqRBIzO547HVvPL/3cYVv9+Z3LvkL2fx54dPrnF0kiR137FTJ/C1c0/ekeT7xQPLeekXb+FXC1bQ3p41jk6SVEuN/Xy/C4F3AHOAR4FPAHMj4sjMbN1D+e8DI4FDi/0fAt8BXgsQEc8tyrwFuBZ4DXB5RMzOzLv78oNUyqzuA7XK1VHN6qr+WataW1/87KpXYbVjq7bK+LZsz179Vngg/+yq//du4LaLqv+9G+BtbOPW7axp3cITqzfwwNJ1/PKBFTxRrJYL0DAs+MIbTuR1J02r2n0lSeovpx0xha+dezJ/89272bytncVrN/Gu797N1AlNzDnuAI6fNoGDJo9hfFMjY0cOZ2xTI02Nw4iIXeqJinorTu9WXpI0sPV3gu+9wMWZeR9ARHwc+GvgLOB75QUj4lnAK4BZmbmqOPYh4J6ImJmZi4D3ADdk5lXFZVdFxDnA+cA79xbM2rbkoH/+eXU+mTRU3fqLWkcgVc3x0ybw2bOO44TpE2sdiiRJz9hpR0zh5383m49dcx+/e3wNAEvXtfGt2xfWNjCpmm7yu7rUE/2W4IuICcBBwJ0dxzJzW0TMA06iIsEHzAI2Z+b8svLzI2JLcW5R8f7jiuvuAs7uJIYLgAs69hvGumqiJA11ARwxMXj+AcFzD2hl2QO/Z9kDva+3ra2NuXPn9r4iaYiyjUidq1b7OG9mcuKoYdy+LFmwNnGUriTVr/7swTe+eG+uOL627Fxl+XV7ON5cVn58D+ojMy8BLunYHzlhcp40c2LnEfdQtTuxV7tbfDVrq3aP/aj2T28AVzfQf3bl8a1evYZ9992navX1Vl9+1oGomv8GVP/fpyrXV8W6moY3sM+YEUydOIqjDhjH8dMnsN+4pireoWTu3LnMmTOn6vVKQ4VtROpcNdvHmcX72g1buHfJOh5ctp7l69po3byN1rZttGzeyuatu662W5kHrJxqZPfzVQlV6rZ165qZMGFircOQBpQn93K+PxN864v3iRXHJwFLOik/YQ/HJ5bVtb6T+tbTDeNHBD957591p6hUl0r/+XxercOQJEnSXkwaM4LTjpjCaUdMqXUoUq+Vvof4XV0qF3/b9fl+W0U3M9cBC4FTOo5FRCOlYbbz9nDJPcDIiDihrPwJwIjiXEeZUyquO7mT+iRJkiRJkqQhp98SfIVLgQsj4riIGAVcBGwFflJZMDOfBK4HLo6IyRExGbgY+FmxwAbAV4FXRMRZETE8Is4CXg5c1h8fRpIkSZIkSaq1/k7wXQx8G7gRWA3MBs7MzNaImBkRrRExu6z8W4FVwGPFayVwbsfJzPxdUeZzQEvxfk5m3tUPn0WSJEmSJEmquf6cg48szd76ieJVeW4RMLbi2BrgzXup80rgyiqGKUmSJEmSJA0aUbliUj2JiG3A8lrHIQ1gY4HWWgchDVC2D6lrthGpc7YPqWu2EWl3UzJzZGcn+7UH3wC0PDOn1zoIaaCKiMW2EWnPbB9S12wjUudsH1LXbCNSz/X3HHySJEmSJEmSqsgEnyRJkiRJkjSI1XuC75JaByANcLYRqXO2D6lrthGpc7YPqWu2EamH6nqRDUmSJEmSJGmwq/cefJIkSZIkSdKgZoJPkiRJkiRJGsRM8EmSJEmSJEmDmAk+SZIkSZIkaRCrywRflFwUEUsjYkNE3BoRx9U6LqmvRcRfRcRtEbE+IjIiGivOn1C0hw1F+/iXiIiy87YdDVkR8fmIuK9oH8si4gcRMaOizMyIuC4iWiJiVUR8OSJGVJR5X0QsjIiNEfHHiHhh/34SqW9ExCcj4rGIWFf8/Z8bEbMqyvgckYCI+Enxf62XlB07vXgubIyIJyLi/IprRkbEV4r21VI8b2bsXrs0+BTPg+0R0Vr2+kHZeZ8fUi/VZYIPuBB4BzAHmAzcDsyNiLE1jUrqe2uBS4G/rzwREeOAuZTaw2RK7eOvK8radjSUJXAepb/bRxf7P+s4GRHDgOuANcA04DnAC4H/KCvzBuBfgbcBE4FvANf7BU1DxA+BkzNzAjAV+CWlZ0AD+ByROkTEucDoimPPAn5O6bkwkdLz5vMRcVZZsUuA2ZSeL9MoPW+uLZ4/0lBwR2aOLXu9CXx+SNUSmVnrGPpdRDwB/GdmfqnYbwSWARdk5vdqGpzUDyLidOAmYHhmbiuOvY1SomJq2bEPAH+XmYcW+7Yd1Y2iZ9I8YJ/MXBsRpwE3Agdm5qqizGuBK4B9M7MtIm4C7snMD5bVMw+4OjM/3e8fQuojETESOB/4IrBfZq70OSJBREwHfgv8OfAk8NLMvDEiPgm8LjNPKiv7ReCEzHxxRDRRSui9KTN/WpyfTKl9vCgzb+vvzyJVU0T8C/CSzPzzPZzz+SFVQd39NigiJgAHAXd2HCv+EZkHnNTJZVI9mAXM63ioFu4CDomI8bYd1aGXAU9m5tpifxbweEdyr3AXpV4aR5SVuZNd3YVtRENERLwyIpqBNkq9jb6YmSuL07PwOaI6Vgwn/CbwmcxcVHF6Fl0/H44ERrFr+1gFPIHtQ0PHSRGxMiKejIgrIuLg4vgsfH5IvVZ3CT5gfPHeXHF8bdk5qR6NZ8/touOcbUd1o5gz6ZPAe8oO762NdFXGNqIhITN/npkTgX2BDwF3lJ32OaJ6dz6lEVL/s4dze3s+2D401P0vcAywH/ACSlOh3FgMsfX5IVVB496LDDnri/eJFccnAUv6NxRpQFkPTK84NqnsXMcktxP3UMa2oyEjIl4FfB84JzN/UXZqPXv++99xrqsy65GGkMxcExFfAtZGxCOZOR+fI6pjEXEo8HHgeZ0U2dvzofw7yqZOykiDVmbeX7a7JCLeAayjlOzz+SFVQd314MvMdcBC4JSOY8X4/VmUuvhK9eoeSt3myxP/J1MakrjetqN6EBFvAS4H3piZP6k4fQ9wcETsW3bsZGAj8EhZmVN2vYyTsY1oaBoGDAcOL/bvweeI6tdsSj1b/1CsgtsxncNVEfE/7P358DClxF55+5hMaVii7UNDURavwOeHVBV1l+ArXApcGBHHRcQo4CJgK1D5ZU4aUiKioZjEeURxaGRENBWrs10NbAcuiohRxbLzFwJfKavCtqMhKyL+Fvgy8KrMnLuHIrcBDwFfiIhxETET+BTwjcxsK8pcCrwjImZHxIiIOJ/S/Hzf7vtPIPWtiPhAROxfbE+h9Pd9C6WVDMHniOrbj4FDKCUcOl4A7wb+mdJz4KiIOL94PsymtCLoVwCK58i3gE9FxMxiVdEvAAvY2cakQSsi/rJIWlM8S74OrKC0KI3PD6kK6nGILsDFwDhKqyGOB+4GzszM1ppGJfW9t1L6z2OHjr/zZ2TmzRExh9KDdDWl7vCXUVohsYNtR0PZfwHbgBtK86Tv8PLMvC0z2yPi1ZT+g7kM2Az8APiHjoKZeWXxn9bvU5pj5kHglZn5VD99BqkvvRT4SDFf0npKE6C/JDOXAWRmi88R1avM3EipR/cOxbNkVWauAdZExCsotYdLKCU2PpKZV5ddckFxbh4wErgFeHVmtvf9J5D63DnAVyJiDKW5826l9AxpAfD5IfVeZGatY5AkSZIkSZL0DNXrEF1JkiRJkiRpSDDBJ0mSJEmSJA1iJvgkSZIkSZKkQcwEnyRJkiRJkjSImeCTJEmSJEmSBjETfJIkSZIkSdIgZoJPkiRJNRER50XE4lrHIUmSNNiZ4JMkSaoDEXFwRPwgIpZGRGvxfn1EHFjr2CRJktQ7JvgkSZLqw/VAC3BcZo4FTgJ+BGRNo5IkSVKvmeCTJEka4iJiX+Ao4LLMXAOQmSsy8zuZuTwiDoyI6yJiRUS0RMS9EfGGijoyIj4QEXdExIaImB8Rx0fEGyLi4YhYHxH/GxFjy65ZGBEXRcRvil6D90fEnC7ibIiID0XEgxGxLiL+EBEvLjt/YkTcEhHNEbG2OH9k9X9ikiRJg4sJPkmSpCEuM1cD9wFfjYi3R8QJEVH+/8AG4JvAocA+wJeAKyLi2IqqzgPeDEwCHgauAV4BnAwcTqlX4Psrrnkv8HFgIvBF4NqIOLiTUD8OvBV4XXGPzxTlDy3OXwr8GpgMTAHeCTTv/ScgSZI0tJngkyRJqg9nADcA5wN3Aqsi4uKIGJmZizPz6sxszcytmfkNYAHwooo6LsnMJzJzC3A5cAjwkcxsycwVlIYBn1pxzXcz8/bM3FbUew9wTicxfhD4p8x8ODPbM/MnwG+BNxXntwAzgWcV9d1T3FeSJKmumeCTJEmqA5m5OjM/kZmnAhOAdwDvAj4cEZMi4msR8UQx1LYZOBbYr6KaZWXbG4p6K4+Nq7jmiT3sz6iMLyL2B8YDVxZDcJuLOF4ATCuKnUdpzsDfRMTiiPjP8iHBkiRJ9aqx1gFIkiSpf2XmZuCaiLgReDbweUpz9J0GPJWZGRHzgajC7Q7aw/71eyjXDLQBr8rMWzuJ+0lKSUki4jDgp5SSih+tQpySJEmDlj34JEmShriih97ni7n3RhaLWbyY0rDdWyn16NsIrAaGR8T7KfXgq4ZzI+L5EdEYEedRmqfv8spCRdLxMuDfI+LoKBkVES+MiCOKz3FeREyPiADWA9uKlyRJUl0zwSdJkjT0baG0MMWVwCpKibwvAf8GfAH4GDAKWAEsBPYHbq/SvS8DPkuph94/AGdl5mOdlL0Q+EERZ3MRy4eB4cX5MyjNH9gKzAfuKD6DJElSXYvMrHUMkiRJGoIiYiHwmcz8eq1jkSRJGsrswSdJkiRJkiQNYib4JEmSJEmSpEHMIbqSJEmSJEnSIGYPPkmSJEmSJGkQM8EnSZIkSZIkDWIm+CRJkiRJkqRBzASfJEmSJEmSNIiZ4JMkSZIkSZIGMRN8kiRJkiRJ0iD2/wHNwVfItQTW2QAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from scipy import signal\n", "\n", "# Signal\n", "sig = np.repeat([0., 1., 0.], 200)\n", "# Window\n", "win = signal.kaiser(32, beta=11)\n", "# Filter by using convolve\n", "fil = signal.convolve(sig, win, mode='same') / np.sum(win)\n", "\n", "# list of frequencies\n", "f_list = [sig, win, fil]\n", "t_list = ['Signal', 'Window', 'Convolve']\n", "# Plot\n", "plt.figure(figsize=(16, 8), dpi=80)\n", "for i in range(3):\n", " plt.subplot(3, 1, i+1)\n", " plt.plot(f_list[i], '-', linewidth=2.5)\n", " plt.title(t_list[i])\n", " plt.xlabel('Samples')\n", " plt.ylabel('Amplitude')\n", " plt.xlim([0, f_list[i].size-1])\n", " plt.grid()\n", "plt.tight_layout()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.9.7" } }, "nbformat": 4, "nbformat_minor": 2 }