{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# 関数近似 その3 \n",
"
"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"\n",
"## 関数近似とデータのばらつきの評価"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### ある固定された設定の下で複数回の実験を行った場合のデータ整理\n",
"\n",
"次のようなデータがについての分析をしてみよう。\n",
"\n",
"固定した$x$の値に対して複数回の実験を行い、データを取得した場合、データのばらつきはエラーバーで表すことが通常用いられる。\n",
"\n",
"次のように、x=[0,1,2,3,4,5]に対して測定値が与えれたとき、y軸に平均値とエラーバーを引いてみたい。\n"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 53,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# データの準備\n",
"import numpy as np\n",
"import random\n",
"\n",
"def make_sample_data(x):\n",
" # y= ax + b を計算し、ガウス分布に従うノイズを加える\n",
" y = np.array([3.0 * x1 + 1.0 + np.random.normal(0., np.random.normal(2.0,0.5))\n",
" for x1 in x])\n",
" return y\n",
"\n",
"# xのデータ列\n",
"num = np.random.randint(10,20,5)\n",
"xi = np.linspace(1., 5., 5)\n",
"x = np.full(num[0], 0)\n",
"for i in range(5):\n",
" x = np.concatenate([x, np.full(num[i], xi[i])])\n",
"\n",
"y = make_sample_data(x)\n",
"\n",
"# データの描画\n",
"import matplotlib.pyplot as plt\n",
"plt.plot(x,y, \"ob\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 平均値の標準偏差の計算とエラーバー表示\n",
"\n",
"$x$の値ごとに、$y$の平均値と標準偏差を計算して図示してみる。\n",
"\n",
"numpyの配列でできないこともないが、できるだけfor文を使いたくないので、pythonのデータ分析でもっともよく用いられているpandasというモジュールを利用する。\n",
"\n",
"もっぱらCやFORTRANなどで数値計算している人は、pandasのデータ構造は最初はわかりにくいがデータ処理には大変便利なものである。\n",
"\n",
"ゆっくり解説する時間はないので例を示すので、それで学んでほしい。"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {},
"outputs": [
{
"data": {
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" 1 | \n",
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"text/plain": [
" x y\n",
"0 0.0 -1.492749\n",
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"4 0.0 -1.601253"
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},
"execution_count": 54,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# (x,y)を2列のarrayにし、それをpandasのDataFrameに変換する\n",
"data = np.stack([x,y]).T\n",
"data\n",
"# print(data) # 内容を試すときにはコメントを取ってみる\n",
"\n",
"import pandas as pd\n",
"\n",
"df = pd.DataFrame(data=data, columns=['x','y'])\n",
"df.head() # 最初の部分だけ表示"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"data": {
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"\n",
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" 78 | \n",
" 5.0 | \n",
" 12.442383 | \n",
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" 79 | \n",
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"text/plain": [
" x y\n",
"78 5.0 12.442383\n",
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"82 5.0 14.570702"
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},
"execution_count": 55,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df.tail() # 最後の部分を試しに表示"
]
},
{
"cell_type": "code",
"execution_count": 56,
"metadata": {},
"outputs": [],
"source": [
"# xの値ごとに平均値と標準偏差を求める\n",
"mean_y = df.groupby('x').mean() # 平均値\n",
"std_dev_y = df.groupby('x').std() # 標準偏差\n",
"\n",
"# あと結合するために列名を変更\n",
"mean_y = mean_y.rename(columns={\"y\": \"mean\"})\n",
"std_dev_y = std_dev_y.rename(columns={\"y\": \"std\"})"
]
},
{
"cell_type": "code",
"execution_count": 57,
"metadata": {},
"outputs": [],
"source": [
"# データフレームの結合\n",
"summary_df = pd.concat([mean_y, std_dev_y], axis=1, join='inner')\n",
"summary_df= summary_df.reset_index() # マルチインデックスの解消 (必要ないのだろうが、以後の列名指定がよくわからない)"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
""
]
},
"execution_count": 58,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"summary_df.plot(x='x', y='mean', fmt=\"o\", yerr=\"std\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### 多項式フィッティング\n",
"\n",
"scikit-learnのlinear_modelを使ってデータの多項式近似を行ってみる。\n",
"\n",
"\n"
]
},
{
"cell_type": "code",
"execution_count": 62,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[-0.08240333 3.60996296 0. ]\n",
"0.14157642979750662\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"import sklearn.linear_model as lm\n",
"import matplotlib.pyplot as plt\n",
"\n",
"# べきフィッティングの次数\n",
"m = 2\n",
"\n",
"# 予測の範囲\n",
"x_max = 6.0\n",
"\n",
"# 説明変数の作成 (x, x^2, ...x^m) 行列\n",
"# うえで作ったxから「計画行列をつくる」\n",
"power_matrix_x = np.vander(x, m+1)\n",
"\n",
"# 関数フィッティング\n",
"lrp = lm.LinearRegression()\n",
"lrp.fit(power_matrix_x, y)\n",
"# 予測\n",
"x_lrp = np.linspace(0., x_max, 100)\n",
"y_lrp = lrp.predict(np.vander(x_lrp, m+1))\n",
"\n",
"# データの描画\n",
"plt.plot(x, y, \"ob\", ms=8)\n",
"# 近似曲線の描画\n",
"plt.plot(x_lrp, y_lrp)\n",
"\n",
"print(lrp.coef_) # 説明変数の係数を出力\n",
"print(lrp.intercept_) # 切片"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### (x,y)がセットでばらついている場合の関数フィッティング\n",
"\n",
"データに載せるノイズを場所によって変える部分を変えたmake_sample_data2()も作成してあるので、それも試してみてほしい。(17行目の関数を変える)\n"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[0.01309437 2.93969279 0. ]\n",
"0.7379904902535381\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# データの準備\n",
"import numpy as np\n",
"import random\n",
"\n",
"def make_sample_data2(x):\n",
" # y= ax + b を計算しノイズを加える (ノイズが両側で大きくなるようなケース) \n",
" y = np.array([3.0 * x1 + 1.0 + np.random.normal(0., 3.0 + 0.5*(x1-2.5)**2)\n",
" for x1 in x])\n",
" return y\n",
"\n",
"# データの描画\n",
"import matplotlib.pyplot as plt\n",
"plt.plot(x,y, \"ob\")\n",
"\n",
"# xを[0,5]のランダムな値とし、y = ax +b (上のままだとa=3, b=1)にガウスノイズを加えたデータとする\n",
"x = np.random.rand(100)*5.0\n",
"y = make_sample_data(x)\n",
"\n",
"# 計画行列\n",
"m=2\n",
"power_matrix_x = np.vander(x, m+1)\n",
"\n",
"# 関数フィッティング\n",
"lrp = lm.LinearRegression()\n",
"lrp.fit(power_matrix_x, y)\n",
"\n",
"# 予測\n",
"x_lrp = np.linspace(0., x_max, 100)\n",
"y_lrp = lrp.predict(np.vander(x_lrp, m+1))\n",
"\n",
"# データの描画\n",
"plt.plot(x, y, \"ob\", ms=8)\n",
"# 近似曲線の描画\n",
"plt.plot(x_lrp, y_lrp)\n",
"\n",
"print(lrp.coef_) # 説明変数の係数を出力\n",
"print(lrp.intercept_) # 切片\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"このように$x$がばらばらの値で、それに対して$y$の値がデータとして得られる場合は、$x$の値による誤差の大きさをどのように評価してよいか難しくなる。"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### エラーの評価の仕方\n",
"\n",
"データの分布を踏まえた評価\n",
"\n",
"図のように、得られたデータへの最適なカーブ(赤線)は、あくまでも得られたデータに対するもので、データは曲線の周りにガウス分布していると想定されている。\n",
"\n",
"一般には、$x$の値によってデータのばらつきは異なる可能性がある。上記のデータはあえて$x$でのデータのばらつき(標準偏差$\\sigma$)が変わる。そのような可能性も含め、得られたデータからばらつきの範囲を決めて以降等のがベイズ的な考え方である。\n",
"\n",
"繰り返しになるが、以下ではフィッティングの係数を${\\bf w}= (w_0, w_1, \\cdots, w_M)$としている。べきフィッティングのばあいは\n",
"$$\n",
" y(x,{\\bf w}) = w_0 + w_1 x + w_2 x^2 +\\ \\cdots\\ + w_M x^M\n",
"$$\n",
"として、データより${\\bf w}$を求める。\n",
"\n",
"模式図 (PRML 図1.16)\n",
"\n",
"
\n",
"\n",
"\n",
"**[注]**\n",
"\n",
"ここではデータがガウス分布しているような例だけを扱うが、一般にはそうではない。特に、生物・生態学とか医学とかではガウス分布にならないものは多数ある。典型的には成長や減衰を示すような例で、上限や下限が決まっているような場合である。このようなデータについてはポアソン回帰やロジスティック回帰と呼ばれるものが用いられる。どのような統計モデルを利用するかは分析結果に大きな影響を及ぼす。\n",
"\n",
"たとえば、\n",
"https://stats.biopapyrus.jp/glm/poisson-regression.html\n",
"のようなのが見つかった。"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## ベイズ的予測に向けて"
]
},
{
"attachments": {
"prml3.8.png": {
"image/png": 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6U7dan+AIoYZ2cT2XQb67rDBLXLgtyveelgWaWcupL1mO0gjk5OiFeiYNxVbIVXWkknmqDQtMEq9fA3FxKo2V5qmaVDNVPMQVCbQCSCEiSnTsVQpqGl/tzfeKClJFEyAxaAVXHWXhtTi+5qoodBoTJAMQoISEBFSpUkUzO6ey+d6aiX3SxPgWEyJVBGi7w34MT3kblUTSqfhTpw1YGT+3fEEyEAbaunUrFlMCoxKINYvHAftTeD9pdOnZ3yQLo2rMw+Gg7zSzvqGB8VV5OuPrBwc+xZTkYWV+jhegAvjkeCHQItSgpzBlBEg8Vi55TlIFiLdDRFaFfU63xHyO96t/rr6DLqPorMpClMNZP7S00KJFC7m/aOnTCNmBj4T6ygoiMPQUSQzO+EagB/cwdh3I0rshsoMeKzxWvKAlBWCQ+xwctj6h2kGQg17aWo66hMjCwkIhAaJFQRIgVdEjoDaWVZ0ptF03QoiXuEmAVMHhFxv5m66f7zwc4x4KIyam7N5Q2pzOxHeUiRrTUMQCdM76BrpltjEaAdJEp55jAevxW6WvMTZlQNGLVFa3chm+4rAw+Tq5akOIrljfUfmOKgskQPZ1myM1+K7BC1CKSZrGqi6JBSjEPBx1ct0ElqGNoKOyfMWE6K233sKn1ItPAlQqxfFOCPiyGCH/Fb1BEZ0UFk/B0OT1TEkpeo/WgGmJlYptNGkiFAWif9NqnkTQ0MHTdhjyVhr++Nsew/ukCgJE3mnylZASKP4N2l69Ev5dkpY9PAQHHaUUSi7rSq4cyrPcq6Al9NVXX2HBggXFXvuJs1Df5QyMUhYqefwXLQL++ouqFlGXWcX1Kj9PZI+aCHwuKNokQKWqZelIrywmRKcLmib98ccfha9RQSJ4NdfIj5MAEUiACkGCxwna3kaPMTJ1qlYG4bFFEBoq+J2OHTuWeu1dWRYq+XvWrhU2JZHt/5z7v4Sl9sknEK14hOv299E2q6nmB4lu7o0bkb3zJ1jmiNRr4msKVBjPyrsRsoIeaew3HloGoHG2LxrmKO4fkyZEWkWBQIoFKGpIR9Q8eFn5/d26RUElwP37Up2cX1T/Hss+/hiW3KZ2P5HKKCMwWZMCZOPdBBlBDwxH0aJ2MKQ2yKiRSgJEjWbr10tDZIwZ4g9dAN5+WwhtowZAFMdKAkLlHPbv5wbApvgOWrWiEFKp+27hPgh3XhxWj3WmVlDtLXGBMhIkSj2kBUgZMPOph7xA1cP687iHGfcwGAGS1NUkl1lkNeI9Glbwr9rAA9XOMcYsDtXznMsUIN0JkbR1IQqBIAVYRgqWWIBuWz1Gy6yGSv3sPOfVWB+3yHDYp7xkQ94UTBEC60ugrdswXKfESCWx1WEPZiSPVr+fSG0MJGthkaiXrK2wMJlfFwvQyipb8WnCDLl+UrxuZzQCJAnKzqhUun3t9QBBgFy9OiMy9KLcPzuixhzsi94otwBpX4iodaVFOT3vyFSnxB1x6QFZglEgQOQVpmr96UH3C9vHfVjtSzjnVcGy1x8KAiexbqcurFu3Dh9LUTK1KkBy6JqSAiTNAZrLTe/WPo2RW9CTngRIJRNfo3B2FprEygMSIlIg5WgoS97zkmUk/vfqM42fjl4LkAyjRZoD1JzTD8UCpBY/kUYZSF4BkvwOTXuv9anxlZ5MYWqyftUFzQsReY7NlfwZMXtpKITB6AVIS4JU7tVNS0+HnbKhmuoYGBJAfesEa0gCJPkbqiZdKCJEhZkeHOxo7auiDLQSKJY5qKfHWMy1YpDTWQVBHmcIiEQijjgr3pAyIVITzHSZOa9GJCcnw8HBQWEhcmQiIDdMjP0EFRUgxkQMapvOElEiFz8zMxMXL16ssIPSUyjWSQwtmYtfKg+/b9++aNq0aYUdp1VCSzMTqUz0008/yV9DpTzTW5NJeDoGdQ5Upq4LFfrJexpQbFjaDHVDbLw5nj/LlLoWZpyKtbw+B/ocjZaGu/sYiNbKh/qKpIRf3zgQLjyhBXlaldd3d4HKQqSo44+ETR86EegSJcdsxgxKoy3+GtUZevKk6PM1axoEK5lrXIBKflfTgiTr+NT4uxs2bMDcuXO5e0NOJpb83PffA9On8wKUmZOPY1VOY1izERBdSioUoDF+t7DbvxVq1rFBbl4uXr3WP/uH/GJit4b8R1dAxTLneTnyrN50nYh/A3ZqRpCSkopSZ8oSLjX8NgkQwbQsXY+yYAqq3pv4+ULk6YUHZzej4fSpEHuUrGtUw1CnWRDFcv94kVVYIXFfxCfYHf0noi4XrBkGQO9YXNIvZq7wnVQCu+2PYkxqf7nyrP6N3Mn/tcm3RoZppubZR9tsKKNg1NuxbYGEU7jwc2U0Gs0Jez0pvy9RCCw34D9uGgNsvZsi/eRBQZ/UY3VAaZ50qdMesSFXeQFSFEJ8cwBcfDshFrHaEyDJ79DyhJxVLcW4ffs2WrZsKddxjJ5fA2Fnr+DynTo4niDUOmzW0wWm9aqX/0MFC84UaAdOfppyj/vcg/+N8jJeDUGInlgGoUG2Ny9AqiI24BKy8AhWPg2ll23XpH5GxQ3o+wrEOskUIPHNwZGrjTVg1cgb1hkOSAq+U0wwOilCJCRIdIwhIbwAxY55Cy67TxdmvB719+U7lH35pZ4LEVmaTjnc4KSboHIlEarX6YCYkCvy3LJU+FG406kJQxm6gxUsgcBAeHr2wPPnZ+RThKlhlkRPKNUkOVbYVJgqzp0DuncvKLLOIesRpwKIBUiVKUgiDIYXIJEIY2p+zOlLX6O/XwD699fy9CZjSi1TiMjCBHe9LCsJzlq5BEi4ZamZi+z3/fz4NieSIAHa6LgTcxInFmeZkoVD9TCuqFs38AJE2cKUdq5ua7AwnopjaxKgLlF+uFDTX3iNYtYp+UGTEPczlIeJ5syZAxsbG7hK9Ced7rIM30cvU+9BFQhQVjbwz2U7vPVZW1hePFMoQOLcMB7iwqEaBFlPzZsDd+4o9r0TJ04UeqwnVP8EiWGc3uJbR+3HRzNCLbLwAgKxbV8lfFiJs/reaQRcvy6kN2tQ6R7WOwX7N0fh54OVMHrQa9TzFNID16xZg4ULF5YWoo0bN/J/CxswkVvDYTfgoBkGsOJmsn7dOaq7KDGNNW4Ms4cP4VynLeJCrqvvxzp0ALp0ERrZlQA/DSlxEd6mDNMC7Kp8WGPVwGlGELpt+WDqojwhN6+PMDaDa87EoahvhetDK/Di1opqmr72bxaezp5ZC5Oj/AvzS8UCpJhiLR5kTU8nBam8JEDfOG7H/Jpf4+DGcOw45IBjP7wsn3bJ63vqlJC/Jokrpafi5u7v4O6LP2FQIP+MRLgwCVD3CD+cre2P5j0cEfUqF9GvVHROksQGBgrPOab7o8q/SInyV6OJr654Z8k7X0bB8/mJU4CnU9DQ4gGO9ZJjmiAFXs4Oatsc/jA8ASo5fpye8tGqqji70B/BgXm4+mcgrDlThXdOUtoV33hLeYv39OwGeGvTEwxP7SO8ICPWyFzpE1BWkKRNG2LFUEY+fr2cOmjo0RePw46rPPaLndbz/Q6nJg9XvwKsbXh74+uf6cLHoa4P6ZBmqFnJD1Ep/kLyJ21K1g7nM2E3PSlivzJqPJmrdCcQe8jbakuelXzKx5c8afL+FuSdiQXIqW4bxAffUM7IgKh4N1FjWRCWuKl5AeJUAu/+8xD0/J8yl3voclB+aNyVIuERF84Yvmsb8numwbRe+WOk2uRJ5qU8rKTsxaK8M9ok5ur4QEGA5K2J+MgyAA2zffhMWVNxdCs5NqnEijFBQmdttextdNr9Jmf61oZJciqu7g9DO5S+RkEniqzTajlOiLV4jbwCy3lIrzS5r5u5Wk9AcjpSJWlRpi1uUii0kgK0qur3WFtlG9bGfYwTdudw2vYyMoMEBb1Rtm9pwS/DrxITE4Pq1ctemjh58iR69+7Nr+ZrtNmYktfi1qECgVlzGyLSj2/+D2g2la9b0K/Wezhhfx79U7vjyMvvhXvzwEGAViD8BYHKCouGpXvZVh5FdR4/flyNQiRrOtLkXUfOk4I6kYtfT+c33q+VNFL29+RQNssTIAIJEEG8mq/PrMRjqlC20OTIURy/yp3/8sfAnj3Av+OBX37h3SqShhlQvptALEDqFyJtgpwntMmr4NP0ZWL0yRqlhUmiBHFOnwGwGFBQvnj8eGGTk6E1P53piVKpdp3MGFDgLyM32cXDr/DJ1ARUaVUXCbcKiolR5CS/vqU8yhWiVq1a4RYVhTQEpbJg1ZuHMpVIjBjksO/QoRr3rBoSkvlBU9u+pQqRZKbH77//bjgjJV711hIkler3338fW7ZsMWpBfPbsGerVq6c4E6VIFjk3YJSXHhwZGVls4VlRkKVm6NjDKdvp6el49913pb4vTYDkEiJFGsfoM8pLD1ZFgAhWVCbQwDF69GilvkfdqCtQKTKFUJUNgfw6URU2DHKBAj0S2TCUQlL5Jr4qK/bqCCoXLyRqEOt37MC81atVt0ZVGStdpZuXE7VYEjcSE9GmTRvFdCKVQEHl6hAiDWOePixd0IXUhT9LAQEitJFSOU/zzkYKblJ2sbOitTWnBAQ7O+39XhltMBTViTQLkYhpDfKCMli0yUa0YG4QQiRmFEUHp6KxkLbZSI3jyyqlVXQ2MighUoSNKioLSU4zFFZjACxUSoiWLFmCFStWMDbQNUjhNfoiV2WAwlZ/ifoKPdLbYYnzRpyyu4iXIZfkZyMDY6Hdu3djzJgxyrkWnFdjQ9Wd/PPmmQ2KN6cjg0QT8U9qGt9Azur2KbC6iwmRKixk6dMQ2YGPi4Wt7ohZXfi8ct2WSBKnGBsBQkND4eXlpZQAiePDqf9ayR5stb06I4LaS5FrRI/ZyEfCbaMyE1Hcbpj5S16AygIJUDP3gbgXeES238iAWMhLySjAk7YXykwwiCjoT/ajwz5Mw1L1HrQ4IVGfprMsZPNVPTxz5VsBv/fiL2x32I8pWFzh1JxMbrQosbB3ehe5Pj8teQQ6ODTHFdu76jsIDfnslBYiYiC+LIyCmJI8FD9iOabVWFphLDKxACmKKxH70N63Pa5C9VpQZbVEVYsQNW7cGA9ltLOWhWSTVFQWKVfZlO6y1jVa4yb3MDRQpOeoUaMU+k6eSb6UUury4WrALuzw3YFJUHF9ryBYX2NCtH+/Yl2LZ1b7Et+q2CLzZsBuTsE04RnNkFho2LBhCn3+Z4cDmMyxryqYFNIVojoiPgFTKbx8qXkTX1bYY1mWhVqmaG4/Wyp/jvcx2mCESJFWVGobq9xcXHmxFx3dRyn3/dRUzQuRvNhrf1xtAiTG+0mGI0CKgDpiq3OsOma2hJnIlM+Th709UKuWfF8sqyyzLoSosMSImjG8xmz8Eb3JqIRIEx2xSYA+cVqHtfEfy1+XOylJf4TIy/MNhD7/TyMHQQJUtU4bvA65YRQC9K7Lp/gpdqVG9s0LUEmrVlZ2r5Z0TbmEaGSNuRoTIDFIgEjJNjHwvnQ1vDoiOvSyRn+jhfug4ksk5ESkTFfJjBMNWmNKCdHeaM3kVJn4CZ5rkb/gSd1c+VfMThpv0EIktwBRouMmbgqfNo0qrgqFpIrdVa8Bypvv148KJKLlIHfcPvyCf4sEqGvtsTgf8VvR58kPJC6ZI1HXSS+EqE1uS9z4a3Hx3vRUGYlin8WvlXRkkdJXrZpQXUtctV783NOz8GM/fBmDvLwi5iEBsq9dH6m/fCcUtyTQb9BzirOR0vKAvwNpv/SbNjbCa7a2RQUw6b3yFjLFdZYUwC+//ILx44sL/Koq32NxwvTSH6ZyzJMnAyNGAMsKKvG+/76wyULVqsClS4X/vP3EBvbN8pB6T4iJLiZAheaubtwl5QrRDfPbwBDN/Pi0EcmlrdGIp0AP7kmPHlobhD61puJvDJL789Qsb0BBdY0A7qL5Fgjg4jf+BR5uEIqPTpwIDBwofKFdu6IWVMpO99cDkerICVD9+sDTp/xrTd0H4P6LI1oVmCOWpzAAAzkeSYRjQa0DvYxsFNdV1AZ6uk7EP9S4RgEiOnDgALIL4pN9JRmMe11TqOpY0KSnQIBIMO9zDDekxoc4GP0/zQ/UrVuoNGwKUjK42cAOhQKkt0JEAlStTju8Crmm8d/6p6DzkaKw1GTkoTygKfL+fRw8PxToquZ90zQ6ZQoVGKBi3YJ7oVVzpITeB9zNVPMTaRMkQLnI4w5Qc/3me9WajFMvfzZcLb6giXF7h964Gn1I0AWVRceOlIwv9GTp1KlU24zfKh3BhJRBqvmJdIED9n9jZGo/jezby6sHQkPPGIVf6mrySTT3ewcv7C4h/sdDQueA8kDVXlq1orp5QvbtZdlWpalPPeQHPlPNxNcYyBwli0JGFiYJkDrX6sTI4TjO4ASIUtLLWMK4G/4nfvwyCx9dHYyvu3B6y2efAfv2CWxFljKlhpNVTa9TNCZVSPMvf1zDzCPLFCDdChGVFibTmzYqxikjXZoEaGelQ5iYMlhtP01liZtnNzAM4aE0dHExUnpehglvMWUXvhaPEzVCU0MztEr59qqb+JozNyQqt5QhRAR1CpA4FtygGEgSZA2S74xKC5bAJG6cTHw45g5UD3P7er6FgOen9VSIpFXWJ6egpEOzBDY47sRccS80JVHH8w3DEiBZDlAaKxn9ZkmAeteagpMvt6v00xbczZYj51jpRoiklVApJ06HBMjPoxf8w04p9ZOfOm1AiIbX/9SKKlXKZ3LapExvJED/2FxGz4yOSv302OofyS1AuhGiMhqN8HWUy+gVQgJk7d24sFq+vNhR6SBWxs+FQYGUYWXYqkCoSIDCzaPglqtYeeEdDgfxW8zXCn1H+0JkVobfh9awygEJkCLu/tZuQ3Az/KBhCZAqdaVJqGhVn7N6SYDO2VxHt4y2cn11SM0PcTBKce+3doVInmg8WjiNji7zIyRAV63uoW6uG1zyZLdZUKeSqVVUqqTa98l1UsBIJEA16nRAdDn9e1UZq2JCNGTIEBw8qMG71r58c5FvzFaOEBHaZzXj//ZwHY930t7ErERhRT3RNAVVvFvxrgGDFCB5w17lYaQCQSIBOmh/CvesnmJ5/JxiH6NYMXpNlbHSHhMp0gWQFvfIMSYHzkT+Uvyr+ZXU7pwsNj22bo2bN2/q9kZTAkNSe/EbIRvU5VIES+6hjlixYkKkURZSRIiopYKcQqRtaFSA1MVCUthIEpawUOvPaIeJJBvfaYCNjAYaYiFNQztCVFWJuuJ6zEYGwULlsJFhCVHt2qqZutQcj7FQBWciVWJcyNStCEJUp45m969hNjLX+MGrCvJ5aKiujv7cyoZdf1X/j14LLTczsrJgo6vz01Y1NA2ykbnenKQOj0FSgBTt60F+o0IokzCozRZXakhoTM/L4zQUQUURuztYHWsVoVG/kTFMZzY2NrCzs0OctKRBI8KMGTOwdetWlfZx5coVdKBGq0YOaUmbZQpRnz59EBERwehGDjRp0oQfq9qquDSMkYkOHTpkFCcpEok4/Vy2gq4qCxHs7e35zdDxwQcf4LvvvpP5fkkWqjA6kYmJCRjkw6ZNiteJYoo1Q3GBUMJnRd9gt6l8SGJjxZiIgQkRgz4LEeuvKUMfl3juzm1hbEikTvGOUpnon3/+qbCj4unpWayDTllYvFgNPUo03SBPjXj58iVqFcQ9rVq1quzprGfPnvLvuaxFPQNrQ0lo1aqV3OtnkgOpCKiegmlqEn5dJxRo2PZHJUwdnoJ53/ti/fqKphOVtyqsTAPhCoDdywL4oqdiISIBMvHzhcifxtO3AgmRvKGrr17Jn81ZEVBw44kr5oohCJBh3njKC1FsrHyfS0hgQiQvc4tBPWAlquwapxApGtzEpjXpY+bnB7RvD1y/XlTQU6xsa6oHrF4IUX4+YxTFzZri/546ldOmt5WuVEZhwGLLUM97wKomRDJK4+kVG714AWRmFlWY1yXoppNsFUWWb4ELhepU7TzkgHeHF9TzpmOlou+uBe1QqUKKkr1mdSZES5YsKbsjNZ2gIU0b4grzJfteqE0+8mEqrdaSrJtu+fJCASIM+fMJxk3mBD61d+Frhx/7opt9Bs7dsMHfF+zw4z79G+KSoTWKMVFaWplvv+k6Ae8njcHg1LcKXxtQawamJg5D//QemmcjWboatY3QgCCVK0CSx5OXByxdigvWN3HZ5g4WJbyHv4Y2wJ3rzYGGWYg1i0cv1ym4+9afuPneT3j37irE3wjh9hGrd9NaydCaYkJUJguVoUxTJY5nFsH4N3JXqfeOvBQCvrrVHotz0vpRaMvyIUHS5sUoOJ76fTzQuVUGfnzvDiy79+LL/XXJLAju546nRcEhuXCfv/viT3ztuB0f/fAu4rvRSss54U0qF6xquRmd60RlXKBZ1ZZj86ulaFdQ6kUWSICoBbpJwGNY+jbUjemsLb1M4ngeHw/D3/XnYMqPtkX1IqmUXkm3R0FKz0eJU/iWXcnnj6KyeFWTEjgNWojKuEB9a03D8Zc/yv1j4hboz7mHJ9TkB1G017smBUnKWJk2aYSkyNXYHtMfC9Y546s1ItkVUgoEiXq+UafvpPdGofIPv+u9m8RcmK7zYGamWPuD+c5rFBIgSXgGZEPkq6YGecpkxyq56FlmVoi0m+2rrzDuVR/8ygkQv6wRFMwJUN2yf0QiydDhhz20ykuLdEU3jB76jngh6ty5M5/yIi8izKLxTdxClX444cUDVHVvqtrRK5unTx5hJe5qRQL6SWgs8n5BdtAj4fr7B2DnRV9MrCvHlyUY6dHXE9EoG3rtO+KF6KOPPlLoS075jir/cNVMGwzO7odDlseU3wkpnKpMPWq+IDceWGHJBmeM6BqNxpl+aDn0FbAmplAwJiryc6QDcefXKNsX3iZ+CBL5F7kMpNUB17UQDR4sf8X6DrVH4krEXrX8+KHn62Hha4EcvvybhpRpLQrSqUt2OB3mh8xJf2NK2NEiAVLG4UlldQpuEhIgD6/uCAs9KzgvuWnNzt6kPI+LfijWbdoAaa898PgEZx5//z2qrv4Rr63pyP2EkjFUEoU8sGPHKl1fJ4ez1h5YHkWT7IJ9ajv5T97W4HJMX6LxE4AzZxBsEYiG2QWCQ1aYsnqMhH4UtmUBMt/OgrXICjvWRnMCVJNvD3vsmBbHSoZOVqYQURHXjFRB4c6YMRGvw6YD5dXUJKfaQk5fOnKEuxPXAIPKb4vpkVNQJSw9XRg0Ks9XVnU1HfQ5Ldv5Btw8yN1ojT4t3hWJ0m/Kq4xfHsjgoTHt0weXpvvhza3+mDQ4BUH/ZHICpMUlEVpGIlhbKyZEtASFAKHfBpWvbZ/ZXL6TXrdO2MQQd/KT0RqJzFkb7ybICHogvEC5/7RJYwc9rFXEexkCsnDU9kzxyrXqKF5FHQgKbhoSILGQenvkCFU+tFVVhITB3V1JPxHdaar2HJPs5Pfpp8I8KW6yWwASoM2Ov2JW4jjZOkt4uOJ+IS3ijYz2xacidUGiXYVo0kQELQ2Dd66H9rzw5TB/uUL0wjxKvXWhV64sZKe52xshr64PNi95xb/0QeIYvZ+6ZKGw54hkfzJ1wcICFg18YGeTj0t7P4N1T47h/vbXmJVZSqdRRbHm92H2Cu65NdV/cBw7ffeeD0RXcguFyAymqOTdHClBd7UqAKcv2ULE3ei9epX/2eHDh3MKbT++sMGNGzc4Um2DeO7BCxBZYRpwBpJfNDzCBG61TTHu45q4+7d/8dmhjKlGZSQn43GgBTqNdkd8TBZoyTk2NhYuVN1XXiFqk9VEYxcv+7GEfkNRftyURwJ02O4fDErrqUGpOQ18+KHQK/Wrr+DVLQyb1teWS4j27t3L2QqDeCEiAeL9ZtwDvk6aG6cCZ2POy1eFse2i9d8gZmAcquc5C0qvJrzZHMut+r4KfDj9a8GZpejUdTmuXEcxAZJPJyKqpK6IZXRGVAtIZyK/yE8/oc/c99W7b2r/PWEClTUTeoe89Vahjia+o7/9Vr5dUfjHX3/9pZs5U7K2N8eGEcP8UH2vf5HBoc5prWA1YPH0BF6Kcy3HYdH5HH6+UEqx5hcMybTTdFAaeWnnzoX10qWw+O0P5ISqoIvt3Ck00v37b6BdO6mW4ROLII32AdEIJHxHLfeWmNbUqR9JrAZUrt8eScG3ldeJCmFnp72BWr6cE6Dl+G5LY3zQ+meYjx+N3KdymPZUW+fcOeDwYWDiRGErS2ZFdjBIkO+JsmggNFp+ZBGIq7tb4t5Ta3z3XaLQ0kJN1tjCg35IGuKvmmIt6y7QBj54/yHuP7PgBaieXz6etZlAC32C74R6oHL6CbZvF1a5hwwBZs8WNnkMHp8GyAl8YphCRF7wAiEi1H73M3x88zoSb4VwWi9UEyJJteWLL7BmWflMrXigfjkNf+UCeXIlHXFlCOaMnoPxb8AfeOZPdsGvRW/QMsuCBcKmIBY7fWO4AlTihr77xAq/uv8D0SELIEYN05qEEI3akoTfYyT9GNZqEiJVq7+Th5XineVkuCvh++DQqDmSg++obfxXxc8vbj8bUKJgMXDj2Kq+pbAmu8gfb7pOxL+RO5UXJIlrYOrth/wg/+LXSG1MpOq0VlKA5NgnCdBty8doma16WO3GyrswJ2lCoRPPYAWo4IbMe1o0Zv9e+QKvvF6jWn7BuqMiYSMSY/8H95BXgJQXIrGirWgsQnl3Br0vzhkrAXUIULH1OYIB5HQpdENzN2jVJo2BewXduomiKHFSShusArecgFevCl/PQS6G5wxCYV+9uuVH0SkvRJRgpwgbyUutYs8rLS6Sr0LsaePwwNJfCBlRAqUa5RpTWreEIJlxAnR/bBM0/a3gZqHESSm5/ZTYw+nNWDadU3qSkgpfF7VsgVMbg9CrczoGfeiKw6fMNChEikxrdesqvm/SnSRPnPsdEqATtufxdnpXhXZl5lPPMJsKKwLy5RUoxSRAJqOSIfrdQXiPbsQSOtKwYQVTWIH85HKP/JUrYHn7AXohXYiPknOtW/WajSQgwcGy33dzE8JD1HS3kQDRel6lfHvYicrvDWTn3RR5gc+UY0UDFaIPvnBBD/Oa8OhhiRfZSRBdSizTCv7RYR/eq7kUIv/PixgpnyTIREtCRAIiy+wnncNCjU1rCwSpRp6Qs+VYtxUSg6VXNQuweI7nFhFIC7pfYl4z4irCBePz3TKh7E81P0fkPkksM5SHbrJ82zSsWxCLftNq4diPLxUep2JCNGTIEL4jdUxMDKorEs5AZj+dAMW85OQIgqMppVWiiZ5YgGiQxiUNRIfMFphRfRl+jVqHsSkD4JvjKf37ZSBfgaon1LZCkfh0rUBifF75J/ILzaL/+RcyziyXFcgzycdfkVt4VudvMhdunKb8i/hEM7mmsVDuOntJXN9iQpSTIwTMV1c2HkYb1o6UO0TyLpueNLJsi7IclJtfD7Jq/Dnrxk//BEg8PhSrTqHGhP/9T1gGGjQI05JH8FsxDB0K/Psv/3T1/His3uIIaYusxS+zl2wmOkJx0YZm1ipqUaoBJEB6DUp2kBwfcZw7HTcJFI1fkybA48fAgQPFBVAJ/dVwi6F7FISHKvL5igRpN5pkJMOTJwpP9cYnRIoGqGuzTaYeCtK1e9Zo1yyz7M8qCXOju9vUPEDGIEhnfglHj3YZaDvMjXsegX3H7TF5aIraxsfcmO42qdCzlGNdoMd4NzRvkIm7f76AZUMf1HXPLhIiNdxg5sZyt0kVJNKD5LC2KgLuPqEwDl9kh70U3DDu6ksqMJ4uQ5J+KgXvMHU0EjYYSFmMlRfi7BbjFSLBgaHU1yQFSN6+HhUR0gTI+IRIRxg9ejT27Nlj9OcprZ15uULk4ODA5xgFKVu72kCg6nRGAnT27Fl07969Qt5EZQrR48eP+XU0Q8fVq1d5L3NVGZVG6DxVQW5urlEI0KxZs7B582aZ70tjoXKFyM3Njd8MHXQO2RLBbSVx4cIF1e5Ec+PQCvKVbLlRIXSi2tounGWg+FbeNOCSQiQSiRK5v5XZEDLICUcUxkPKBMlTIhsqBjmRJPdsRjqXvZSyjDt++gmT5KiopxE4OenPUGq63oUWcPLSJfQuUXuMcOLECdy7d08jv1mRe1ZXdEi2mpabiKjmvrTey6smT9ZtGz1dr89TJKkeVpFUBqvmz5c6nqepmpOGEBERgUmTJpV+Q5f18fShS542oemxpiRAGQn4xmPf0yBSrIculuqpLnBZuVIMhglxp8WKEISmJwVRjcPRSOt6lCmrRNcgpUE1CAyhlSmDajepsZIRNR9WtTwUIyIpoHoFFGulZHsRhUAFyiSKaDAwMjIoUDoiZxLrE4xr6ZWq8FDebmUNLgISAUlUSmRgZGRQoOLVsbF6d1jGFwMijp7TBBkxEmJkZMhITtZLEjJOItIUGdEFFLdCYKiYoNVRQ11No84IcnSK0ksiWrJkCVZQYcgC0BK+mToq5imJMPNI3LZ6jHyTfPhle/ENmk1kVYIjMqJjVYfPiAiogpIQXXORGvsTbtiwAXPnzjXMwaBxIAevOhppahO0sFLQ58cgiagktEVCIu7R1m0YnltE4kr4XnjnCBWFPHJd+U0allf9Dp85bcY/ETvwZkYH4UXyGVGOio2N8gdDM4meqrPaAF1zEyOqbkk1h/vWnoZ+qd2wO+obOIikT1T77E9gYo1P0DKrES6F/170Bq02UfNYQ8l9okrwBrC6WyYRSWpD2kADj7fxTuqbWBU/DzfCDyj03aWvP+A3Qg73cPRuhQvhu9EyHEJJEGUqW9Hqgp7PJIYGXWhDw2rOQqhFBG69OMRXOJWnsd2I1LcxIujtwn8/tgxEI49+CAs9C/eMWjLbE+gVqKIJ30de/6FzH1EmsmDj0wQ5gY/xJOyEWvZpwT3ENavnOq/C9fz7uJJzQ7E62nq4xMkgP7KQDWvfxkgMvIX9UZtV3l/DbJ/CTgzvuXyGZNNU/B6zXf3dxtUFynag8koGAp0RUaZJFuy9myM38IlGW21siFvM/z1l8ws+dduKW5Cj5BALVjRYFJMrDbX0/SH2S/7vadvj+BBr4Q89axVDviwDK95TjIhkFVBTN0x96iGb04Bytdg0s1dGZ/QK6IzZtd5FNXtPLOEeUqGncRaGjOfPn8NTC+0IxV1LtCVXb6V3gn9AJ3zt+AkCXRLxA/fQCxIywNzHYkT0008/aZSIOtcejZVxc5FfsleUFrHp5QLeee3g5oAY7mEDCUe2ZKVQBvWYSFlZ8NBw+4I6nm/gQsRujWlA5eGjxCl80RN3X3f8xz18oMMlfgNNwC5GRD/++KNGfiTdJBO163TG6+Cb+nHWGRlIDriF5OrxqFO5NaJePwbi4hhraADJycl8pyYnDZRsuW/5DO9VX4qQ5//pxbm+CPgXuXZWMHU1RT50UJFCTxJYVSYiTaCxR38cevk//SEhCTjEpCMq5jxq1PHFo9fH4ZxfhTGHmlGtWjWN7JcaRCYE3cK18P36dUOlZSI/4Bl6uLbD5yZfoIttL0ZCuiSiPO7h4N0SaUH39H4QokOuINj8Bfq6TsN1PRNshuIIN4/CgFozSnfy1TOcifyFX7mz87aRfqwU26auWCQDJyGNEdGsaivQNb21QZCQGHVz3XkSsvBpgBwtOtEZ5Ed9jz58wOrdF38axPFawZInITevrnj6/ATsRXbF3AOFBEJFz5WJ1tazUh56RUSmPn7ID/Q32AEhElpZ5XvUzq2OCSmD2N2vJzDzqYc8HS5yqKTFhZ7HHcvHWOb8Pxx9+b10QhGTkrxF/ihvjJJYjQRqI6IIs2j0qj3ZoElIjE8TpiOXe9h7N0OqAWl1xogD9idxw/qhZkmIiOD2beD8eSH+5uJF6eWPyZzq2FHYBgxQKI+xRXZDnoTEIQYyIY7/Id9alSpGrQXJTUTUkKq6HJGjvWtNwbq4BXispshopUElOlJTgaSkomL2Mkq5LrjUD4ubn4SjXS5ep1pg3f23sLrj8WIDk4pZsFvqh8Q/foQFd/0L1WcSEG0UYKvgcKzbCrHBVzE0tbdyO6CYmn//BbZsAZ5w5razMzByJEA1siWvH5lGbdsKmzIgzWTePJ7ATE3ykf9MWEI38fOFyL+4/4ZIqGvtMdgWsxK+OZ6y90klZypQ8T2ZRLR+/XpubOehW7duOHfuHP/axIkTsXPnzmKfq+PZAyEPxDZ7qvCHSrZqs2yrGEQQtEk6Abt2lfrRryYD4z5egN+OOGBEn2Ts3U4lEiaX+lxa5GR8+/avqJzvgHEpOk50pLQTaTO1mupm/+J0HON9i19fuuYZ5M9QA1avXo1FixZh+fLlWLp0aTkmfj3Z8WakEZDWcvAg4O8v5BFSR4g+fYA33yz6HCXr0usS3SI0AgcHCsLjnzYflIVZK6pBFBWNVrgBfLYe+PLLYh8/H7EbQeZh6FJ7NC5E7AFDGURErScPcheaepiKUZKEeJl4foabXfIN8uR/XRfNb+VhZtI4ZJhkolqddngVck13B2xrK/31pk1V3rWJj5/UVBu65q1atVLL4XckkwZC547yUGbQK2mmtE2YoHcydfuwOMmUKlU4clsBCR0/LmhN9NfbG965HjwJGbpPtTxQmEVadoLyRLRgwQJG05LuAZE1T0LmPvV5h7bMOkgGhlDzCIyuOV+j+X5idOnShf/7ww8/VDwB6ttX2HiW5Sbudu14TS1/pT8ae/TDvxE7UT3P2bDO6f594PffBXKlVsr16wOdOwOdOuH7Lk+RbJMjhC64q+gjYpCiKQY+xWdOm1AzpxpmJI826HOhmk9/RG3C1fB97MJqE7QqduNG4T8fLuiD2xc7Yvr5N3E46jv9OU7yUVEvwxMngBYtBI2udevimjhta9YU+1rlui2REHwTplnyt/hiRKQEvoyfzQds2ng3QUbQA4M8B1mmGIMO8MEHaMlth6MKEncbNeQXW0SHD6PVu83wLMQS9/4Mg4+nBvIgyaG/ezc5hTk7yg749FOgd8HiAK3cbdggbHIgi3u41O2ApODbCh8GIyIlYcY9iIRqe3XG/bCjcMp3NIjj/s3+L9y3fsZISE9Bq2pjrszHjMRP0dmjnbDqdv48BvWtjsNWnAb+/vsAdVdWpKEoVZPYswf49VehKeiIEcBHHwn1ucihP3assKmAsdU/xrSk4UqRUMUmopKBY2S3K1HDJSL0Iu9n6e06BTfDD+o3efL+rccYmzqQ3fHqRqVKQM2axV8jvwn121MQu6O/4TVuyzxLTiYfQdSlKw4/pnfuKHdsLi7AnDnCpgnturzYKEZEMiCtLQyREr2uRN6OV25tnoRohSAx6BZfIVKfcMz2HH5z+At5gU8ZYagbpFV4eUl/j0JYxLJGk1y+/KvLpHFncSTU3m0E9katl1mrXZf4vOpmPqxFHeVXKhYREdmQJlQeSVFNFyU6V9AKQYh5OLq7jUNY6Dm9OGXyBREB9UvvxkhD3XB3B6yt5dfAeRU6QogHkxO0kJBgmiQsg+tRoq86tKCKSUTUgaRuXfk+S72rFJzBxKiT68aTUN9a0zAypS/GpejGDHrDdQLmJE5gviBtatXyoHZt4S/5auQMRK2SX5knoakuS1Anxw2LEt7T2Wk3d38HW2M+V3sRuopBRKQJyUtCkjOYkmREOP5SKDJHQZB3XhyGW25NrZzqjkqH8Jf9v/gvchcjC30joZITY8n9UAQ7pShRzXTyL5XAtlihq45T3ba4+mJf2SkiasauSoc5ufpPY5UPjJ+IaFWgPHOsLDJSsdaLOBLbpU57HIn8Hu2ymmrkNBc6fY0Ay+c4FPUtJqUMZmShzyQkC5RUS5u0YnISk2J88HX+r7V3Y1wM34PWWY01dkg/OxzAUbuzfHyTJqtRGD8RqdoiWEkHdknEhlzl/85xXokH1v44E/GLemTXuwmOR/6INfEfMZIwZBKSZ1IsURg/M+gh/7e76zh45tTGjtjVavs5d69umJ8wCbM5835y8lCNn16ZRPTdd9/hgw8+YIKjJjIibIz7tPB599rjEGDxHEHP/+FTSOTBE4sgtPAYhHmckFAjSkMNqGQkpKR2T8dRwuF9NvJXwbIzyYSDdwusjpuPjxKmKLz7ITU/xBPLIDwN+xsvtLzYUiYRnTlzphgR9e3bF8ePH6+YgqNGMioUoIhfi/072OIFtlb+HUftz/BmFqFNRmMMSHsDsxPG8xX+GuR4F86E2gBd83QFVnnKw8mTJ9G7d1FZDyquT/u3lZXQy0ioNMjhTaVuYmKKa8fcZCZZXfSpRTCG1PoQT62C0TKzIbqnt0PdHHe+lTu13n7IaeZvpLXHichtsIQFDkb9TyuHTwn18fHxxUoMySSihIQEDBpU3CassCSkQTKSBAnJ13Gf8Ju+gK65urLvCWnkiJWAg4MDIyFlULmyEDoQFibzI/Vz6srsnrwG83V26Obm5qXqnMkkoipVqmCsimHfRik4GiYjY8eQIUOYLKkLVIeJgikNqLW0UqYZIyFGRhUW+k5CYogjuw2cjMyZ4DAyYjBQEpIkI+qmW4aZxojImAWHkREjIX0y0yjl5MULRkRaByUVenrqXnApVJ9C9hkMF7Q07uNj2OdAzmsDNdMMl4hktVvRBSh9hLqGiDuHMBjeDezubhznYqA+I5WJqNWQIbi1f7/2b3zK1dEnODkJ3RwM2Gk44/PPsXVPBesqQbV6HB2N65yIjOgeUVN3F1Vx48EDtGnTRj1ERFHW0nDr/n0wSAiAofoYOMgioVu3bmnsNydRjzFZJi+D8pCWVKsjtNG0RuTv78/3vLLmVNt69eqxi2/gGDFiBPbt030hfYq8zcvLgxU5YBkMHqmpqbAvpyGpSkTUunVrPkTf29sbQUqUWWXQL1StWlXnx/Do0SM0atSIj76lnnrdu3dnF8bAcejQIYwfP15zREQkFMzZoYyE9AORkZH45ZdfEB4eji3UZllR02zrVp2fA5HQtGnTeI1o+/bt7KLqGCKRCNevX0dUVFSplC958Pz5czx+/FizphmhrqIFxxg0gmPHjvEqMOWFUVtnQ8aPP/7ILqieYO/evdixYwdWrlyp1Pc9PT2xdu1azRMRg36gX79+bBAY1I5Ro0bxm6ZBROTIhptBzcjktoVsGBjkRBbTiBg0IljctpYNA4MiGhEDAwODzonIk9tM2VAwyInn3CartQnlSYSxIWKQE0kocA0REd3jtspsTBjkhGOBADEwaN80+/bbbzFz5sxSr9NyscopANTL6eVL+T9PEbdUf4VBrZgxY4bUWCK1XOMSoCVhmekdGgK1CqOCDXw3DKrdI6V3mEVDX7RrB1y+rHRLO4YChIaGwktWO25liUgWVBJQBbpdFkNWllAHqEYNIdGUQS3Qh4BGTYFKJMdcEcq1mPj5QuRfmoT+/McWO1e/xJgBqbh+3wpfrayJBZ9aMsFQEvKSkFqISGmoo4ZPdLSwsQRJhrIQGIigk0DlZnXg5JiH3KfSi9m907OoW0nbplnc9pyb8Lh/uLkJjQ8ZdG+aqQ0lmsSpBaQdUVErKm7FwCAGVSvMzOSfVrIDkm4rWRYjPFz4yyY8IyEiaiUTGamxWY8vbmVtza5qRUduLhASov790oRHPcX0uf0RI6JyUKI7pcZmQGMsdMUgPyR6xEvF6dPAhx9Sp0ehkmFJULIwbVRnS1rxPZJjep3lWBogEZUnHOpEbKzge6KKiQwVBzTJEUnIQt++wOzZwFtvUSEt2Z97/31hI/ToAXz/fWmTjOSLuQO0R0RXrlxBhw4dVFdntQ2qHU3qeYluksbg65AKuhlohjbV37hUSpz8/fffNbPzsmSMEjanTKGWtaXeMqvng4yHgdh7vBKOnLHHgc1RxT9w5ozwt2FD4OHD0uPL3AHaIaITJ04UI6K2bdvytUnkQk6O2uo3n7a9hLVVt+GM7bVir7vmVMeYlP5YHjcbliixzEq9wUlwqMi+IUIRpz59VlwTytUVsLNT22HQNafyIqqivJrFSoFiz2Qd27NnwLx5JMSFL92yeoQ3a09AjkkuJiYPRn7nqXiYaonTsckQfXgKHdwO4KrNPcxKGI9Nrz7lv/PzQQc8GR+Dr5+eR9XBXfHqSRzMG9Dyv0B+Qwdm48DOBKBmTcYmmiCimJiYUuUd5Sah8mbwcjCixhycs72OkND/YCeyxVvpnfitPGxy3IW51VZx/HcWHrm1gIQEQVtwdjYuDagsiBcDvL3VoiHRNaeARlUxd+5c9Y1PeQGwfn7A06fIP3EM1eu0w9jkAdgQtxitshohMfh24ce+2yb8/W0a/X8YED6s2G4STJPxwSdN0HLXl0jxHIQU8yowa1QN+c+ewvctTwSFWeDS3nAgJVM4JkNvR6SPRFSdM2sWLlSwkgMFGirZbfKY7TlMrPEJ4kKuY1/0RqX2MTtxAr/xZqX1XfSoPR6ZQQ8Fm94QzDTyo6mr2iXtx9icqomJgg9Q0qXzeTUsmJoAT9dczHo/Bx/5HsFPr97HPoe34f/8JF6FFNeiC9vtlIWCQNsq+Q7ICHoAdOQmZrNXyM32RW7gY5ivWIGAT9oDb7xRXCslE5Et8avfNJMLdNFoBidTTAn0q/UeOmQ0x+KE6TwJqQsdMpsLJMTB1KUmYl/eh3Otxvp7JeLigNev1btPsVNVH9svyQvSDMvoXrrp01ewbOSDd/An/jz6E9q07I4vX8/mt2JQZDVVsgNGgf+pep4zRIGCk9t65z4E3RuK2v37A0ePlvZXGfJ4GywRkR9IiRWxvrWmYnTKABx7+YPmFY3AZwIhiUyRYJKAyvqW46vpTrG0/0qVDMOPoeDihsX4URh+KRZd6k7G4eQNnJkENBvgjk1LY9GyYRYqNffhlRWlQYRUwl/HT3D2nDw9C0CWpR8sHvuXHm9atWUrt8oR0bp16/Dxxx9r9AeP2p7Fuqo/4ULEbu1bPhwhZSEcZr5VkYc8g7zxlEZKirBpyXSgzg3p6ekYO3asZn7g5EncPbwMI65WRsDz/4DkordqVMvFvadWcG7mrp7VddoJjVsJ310+pyGlPcmAYy0/pIU8EJKxxaCVW9Jwmd9IcSKiQtfUq8yPnH1qhoh7mPrU49Xb/um6axFjBUvkBTzFPted2Gv3Fw5zD51AE6ku8hIfterW8GritWvX0JCWvdUISkQ983ssFp3sCpP0DKwIjeVIKKE0Rx3nNHQHwSeo1vA1WqovkahtJ7JBWqQ/ljmshomdPT5//WFpvxGLN1KMiIYNG6aRH3nX5VN+1UtsY+sDRkR2wAh0gIWPBbJNsmECLQpKOX4PjYNWE2mjUioaamL41VdfqczTbl28EHExFGEvzTFiWB6uVeqODr0/xtc/TOBu7K1Y9CxAuimlSYj9RyU02S+yFnETywuYvOkHUUAJOacJhxZLKrOyXxrxEVGA6nernDFzdAJ8vaQ7q018/PSKgEoiJ/Axztr8hp8q/4Hd0d8I2gLZ9poKDiQCePVKP05ecoWTSqpQ/JGOnKy7OUudevDl5/vg6PeR6Nc9HbGvzfCZ3178YjEFv+7Mg+mo55w5RCtV3OZfgoRoJYxWxLQFIiNKhs3IKKYxEQnNP+KH+mOX493k4UXvxcQg/MFrzPzaC3/9JQRsk7YmDuJmRKQkpk4Ftm0DNue8j9Tef2FhjS1Y0/8y0LkzRcHhK8dtcMi3l4+EaMWN1F2KU6JmbDTbPH0qvEetrGmfFBDXpYtGBqF7Rlt+M/EtmM0SEkrPgnXqqK5eUyImRXzrI6icijY0ChkgVxLvVDYxhcl0ER8wmP2YQhlGYpjlHSx0/qZw0aEYqDwHlenQBeh3pSRyfzPAHyKvprBM/wLZgUXNBd2q5+DIERH27zfBRx8pHeliGCB5olVKOaPOlSYiIiEK6TjgtxHj736BNbYkRe2F+9anPnIDn8hv7tBMRoRDmyJ48IC68QH//CNkRVPcU8+eypsDHAnNc16NdplNMTz17aI3yC8g9ueQpkTBgobgDzIgFK5scWq2CEXaTq06nfAk9ASOvyzRdJEmBX1wBJMWScdR4vqa3L+P7Gnr0GK6H445XkStPBfhPP2Fzw0LcuA07xrGeTHFZqsCyecqmWYUmvH+mGROxxSk6JXpa3RzG4u8wKfaOeEmTaiGrfT3njwBJk8WZsy9e+UOaFwftwhZyIa9dzOkBt0r/QHSp8UDXasWUCL6vBS0UXXAGImJe1j5NCqmURRC35y/4lW1kiugH3+MOxkz8bRvM4y63RrnI38rei85WdiMKQCSVgpp07aPSBJ9ak3Fqri5eBx2Qj8GpUEDWrop/hqVfqAM7KVLeVtgy57KWPtjVSz7MB6ThxSt/9LKGpGQnXdTpATdhamsJieSaQaSzkgyvyi+SqUAloqL7Q77EW0WV5yEzM0F81hPMW0acO+eL0Q5OWhcJw0/r45FSLg5uo5tgDZNknHewREmeVIc2URexlC6RsUwFJlERMXN0zj7V1rB/FITgq+UAdZH9O5dWALio7VOWFVrC96P+gxZrc5hzqrG2Lg4rtjH04LuY3PlX5HPPeYkTSh73zExwmbA+OeyLTpqoO6XOCTknXfewZ9//lm2ll2nPV6GXOQEs0A0Nbiyp06Qq0KYdyw4BckR21fF4te/HBB+Xkj8NquXC9GnS9DlLT9scz8JvxyJNBPycdBmgNpRQkI+3FyBn1fZY+TcmsjnTM88zmiwbuzDzccm+OUXYNw4FYgoISEB8+bNQ7du3XDu3Dn+tQMHDmDo0KHFPvfKNMEwSKgEvv6EVMgReNxuHBq4Z2Pj7DCgWUdg9GhgwYLCz81KGodc7lGtTrvSeUvGgKAgPDgZgft/Psf4F6t5k8jTE3j+HIXXPEfJ9B0xfuGkceXKlejevfz4sdiQq2qvIKBVH5f4eb43ls0M4kMPPGrlIu8Z+YYm4AK33Rjhh2H/9sL+6M2ltQpDqo/NWQSHdppi1TwTDH87FT/+kY6IaDO4d6sD61xbZN05j75L26hGRERCZ8+eLSQhQkkSIlSzcxdWvQzUD9LQp6CbAwn+PQmfEC0LkgOSO3+anYmELL0bIivokXZjjpQFtcrZvp1acwjXZ9AgYMwYobaOJLy94TDHBt+t+h5tm6Zj5fAiEhJf8zVr1qh0KERChNmzZ5f/YWPxmdCiBncuHihtsrT5zR/763eHSaQUS4JCAvTFES+HKTZFghL+3RmJ/KBAjoQaIp2ShRu54++/1eAjkmcGK+UELq9SnqFg27ai5xRWMH48sg8dwpLOm9Aguy5Gp/bXj+PcuRNYvVqYSWnV8M03hdepgdeMGcJWBtq6DcPeqPW49nIvsD+cZY+rGzSetJSdnFz8dW6SF52JQONqfjhlW7SqVqhS0Y2u7dgoeVBGhYgNW+vB9pPPBRJSl49IaZCDgQafYisoxsIY0LZtoW9pRXwD5I0fA8dLnyHx4cXyV83UhZ9/pnBlwWfyzTfcbNNIeH3iRGFTAgbj2zN0ULAopdSU7OFXuzYewh+3xzfFpNOtcCpye/H3acGDJhSylfUBslbFOPPdZu6nSJvxDKbJylkLmqtZTXa+Ouvr6As4tdns1z1I5GSkctOWiAu+hpyfD+LNtW/gStv5uDthA7acrY9tK2IV3zfFRf30E3DqlGBCkWlFkd4ECkWgTQ04Y30Nvzn8xUhImxCnhpC5X2I1teWO+zi1/wpMJghZCEIDSMH0GTzNCYe+1YPSIjJWxV53qI8mUdWQEaqaLGm2eH6BnayTutVlgWYn8Q2uQh2gpODbOGNzDT8tvomraz/DF22O4euPquDhMYmQWVLJaSakqGpaGaGl2qpVhXEhspYExUVt3qzRU3eq0waRIRfRI7MdIwddgHw/VMZYYoW1xTvuuPvUFx+eGYiFDapiS/QyNO+2EM9CLXHncIEskQzpIoRBljKRno7Oyc2x9dZRRISqbs5rp4sH3XS6Tm+gJWAya0qCysiKS8lGRQmlMhRAj4x2/PZ7vgk+C3yGZTNLkBq1xG7eXNh0iGizV+jsNhrxITdkf4i179YOKN6MNm6CHji9Jm4ffsH7p89es0FKejgGbPwO7z+1Ka2x0v2jTd+RDPdK9oplsN21H7mUvpUN6fcUTbZ6R0QEYnLSPOLitG5Kyb0CQYXDaCMyiopS6GdIpV7nuB3JZilYHj9Hr+Te1asznj7/G4HP/yn9Jvn0KD2GQfvgJui/fqWbXfhn93biBNpJHAlNwsjbfhjdZQsGpL1R2ncknuA1gTJSkt6MaYIlK7dxJPSFWmVJu51eiSUpglRbfiNlC8hTNUPaFPRxfZw4hf9r4dMAqYH3+AhtXeKG1QPMdPkSkaEXZWuqDDqeJVxl3vh7W3Iax/T5MDnyPp82VSrCn7QjJZN+qTkPRavcvFkiooNITkrcWJh5JNpUfgsxeAxkqF+WzLU+8NrwG9FKFuWBqetYxWoxxXjIEdyXE/gEqSbpqFS3ObKDHmt9iPkidL71eNX+RvgB+c1UBt1AnKsmjQS++Ya7jl8jskc9NHlRGfHBJUxrKkNC9xLFwZX0OZbxc2J/+aRJwvqIWZJsa4VWV/M+no+YqY/h2KouGnpn48pdG+Q+CYBZdcXNMP0gIkkGlRZfoY79agLkKCyr+wNpTxQ/VVBK1F5ky5MQxYh8wGklQdLMIg2AKh9kBN6XvSIm6ahn0C+QfNGER/7UEszh8o8/qtpYwrz3I3ge+KC0PJEvRzy5l7PCJiYh6oC0Y9lzIDhbpiyl23DT2r2nwFRTPAqwxIdjE7B8zms+gnrqOl8+qkQtt5dOB57iKyggUh0lMnSdk0TaE5USlVSbOfRK78wLzQPLZ+jqNg4JwTfV/tM53MPStxGyAh6VXfmAdSXVf9CER5NpiTbtLu3qIuERxSH5wsQqDFFBl+FRpxsyAx+WNtkk45VILsnNIE4gJD8ttf0CX/+/EDcfWqHNUO4ecqGcyRrIv3kdebVcgAfnCz/TyDeb217z+6zdpS5+VmN5MHOdD7xYLVW2J5q+5ubQOUl0u22SXa+QhOzrNsOBqM3ona7alZzssggBls9xKeL38mOCaLHA3Jzd6IYC8m+S2UXuAA4Jt4KRnVNgVlGM0aM4DGx/GqaXTOHl2QPP/+wAUbMV0jV1ChegrQxTvk379pgf3wdfx33C/UY+TG7dwRteQXjcwQox8WZ4cT4EbjXyBB+vi4v6+VfWG5GRkZg1axYOHjyonYEnbUZK6xaZ5EUXSt8LktMSq5QgttTge4UC0NptKCItonExfA+8c8r22xyzO4sBtWZgfPI72BmzBj/HrpZfqDVV+lZOnDx5Er2p+gGD/KAJVsKfaim5Yl+/PsZ9YQcTP1dUsQlE3h2BsA7Zn8awmrPROaMlvo1dhkbZPqVIh1q4T62+FJkmWXgYdlTo2ZZ6Dth7jBOy6RzRfc99shISk0wRfSWEF13HlnUFLtNQUGUhET169AiTyHPFa/Du2iMgWRqSMYHCB6SEx1Py7K1w6eOcZSLY7VaiopW3fmndpZdLLe+3WQcJwwbdD1LabA94I60wApvTGnize/BXX5VpnpPMkbvgRei5ohcpkv/LL4HLlzkh61f48u3D4YW3ZFKqZqO6C4moUaNGuHmzuP9CZ2RkjKCC/OQkljMcQJKAVCJAPSEhpg2pCFoJlpEiwkMckU9tudu1ExKhqeKCLNDnOnYUPjdgANCrl/TPUZBrDc2XtGVOA21CmykvLEbIOEGTi7SVNTHIh/NMQmsmP+WRI0WNITt1EhZ26HOPH+uNDDEi0pWqXaJrqPquqH6XVGVQ0zUmGaLcRdJsygL5KYcMUWz/GnJIMyLSR7i7F1tVUwtIhWb5YhUHRBa0SUxqJn4++G9XBCYvqo5TP0fCzysH5vV94FwlD2ZmIkReLEPedFiQjRGRLiFeVaO4D2pZxEwxBmUnNQ4ZYbFo4peFHu0yMG9SAv6+YIeVW63w6nowqjjk4/vfHfi23W2bZhX/Pq2EURCkLpU8dhX1AGIhUMZ3ZEg1jhk0ChsPF9zn3UO+mPVB6UoS00clF9d+SO50HNbBiEgfIdZqKLAzK6vsz+pBbBCDHkNcSUKHyMsjc1C+ZX+5iciNm3lbt25d6vWgoCDunvBmF94IQEGsrlISJ53F9ZrUCHHMGoPxwkyB4Ee5iWjgwIH8xsDAwKBXplnfvn1x/PhxvtsHtR5iMGzMmDEDW6n9kA6QmZnJb/b29oiLi0ONGjXYBTFwUD+78ePHa56Irl69yv+9J9kPjIFBCVhbW+P27dtwcXGBj7739GLQL43odUHReeoKy6AfuHTpElq1asXf2IpCV9qQGB0p5YBBb9C2bVtcp55+SkJebUhlImLQL+Tm5qJp06ZKkRADQ0moQkJa1YgY9Ey9NTdHJSqCpTtQyYDb7EowyInUQtkViUSv2XgwKICqbAgY1K0NseLFDOqGiA0BAzPJGBgYjIuEJkyYIDXStmSlQa2B/B+WlvoxipTtLKULpqHhZVYWaklpvbRq1SoNDVsmLl68yO7CCghPT8/C0Ay5SYiC29q1k9IfXZd97PUlw1yXY6BGPM3JQf1i3fU0i59++gkzZ84s9Xqrpk1xa/9+3QwCVUAoq02UMeL5cyA7WyO7nvH559i6Z0/pa9yqFW7dumUE5hgVgdJysabS6sNLo5HF+jou+yDGLSpHLNE2R6ugelBUfsXMDBUC1BVEQwRE2MqRkNrMMb0EVaHTJQnRjZKaynRrYwPVgaoodZwK2hLpEobvmKYqhrpSn2XVBmYwDg3B2Gs5RUbqxWEYPgmR+kzFwrXdHJDqAenKZGDQjoZgzNoQya6eLKYYxxI9aSTaFhhlOs4yGBbS04vaMBsb9EiLN544IWJ1Ozvt/FZyMrtBKwIiIoxTG9IzLd54SIjsW20JTHQ0u0ErCrQ5uVVQLd64Iqap2Xblypr9jdcs1a5CQZuTmzZQokA+IyF1IyZG8yQUF8duTKYNGS6iohgJGbQ2RMGRDEwbMlSU192VkZABaEN6ehEZtABjiBvS00nUOLPoNaENMS2oYsPQ44b00Bdk3CSkCW2IaUEMugiKVRf00BdULgmNGjUKv//+u2Hbv46O6tmXrsqVGCGuXLmCDh06GObBU7a5ITYB1fO4Npkk1KZNm2L/zs/P5zdTHbUmzkM+nloG4xm3ETpntEb1PKeyzSdGQipBJBLx19xMjRnlJ06cMFwSogA/bkz4Xu+GBD2Pa5NbtyTy0TYBBViEoo37UOSY5GJi8mAMSu2J9hnNkWaajn2VjuP7ynvx1CoYsxLGY9OrT0vvQB1h9xU4OtqEu9nMNFzSQtUWM8ritO0lrK26DWdsrxV73TWnOsak9MfyuNmwhJSiebRSVru24VxEPSy2R9c8VaL6hLls0tddWPcF65vo6jYWi16/h8Tg29LUIvgmemFWotDjKNYsHu5e3eCU54i7L/4s+pw6wu5ZdLRGoW0CetN1As7b3sS+qI34L2KX1M8kmCZhaK3ZOGp3Bkcit6J/eo/iE5shQU8y5UtecypqVi4JzZ8/X/vaLveoXqcDxiYPgCjQX+7vuXBm2YvQc5zwJMPGuwl+jl6FUan9hDcpT8bKymhmEUNGTEwM3/pZFxhRYw7O2V5HSOh/sBOVrR1Xya+MIy+FppCbHHfB1NUPoaFn4ZFbUPqWCtlJKYOrd6AKEwYAvXH1P7D0RyuPwcgIfAAzKGcCVMl3QEbQA3xVZRunGXXliOm8kCejrDakh7OIIaN69epYuHChVn8z0TQFVbxb4WrYPuyL3qjw92cnTuC3brXHwlxkjn8jdxpOITuqtcVISD5sqrwLW6r8juzAx2rZ34KEqZiQPAhmPvWRF/hUmBGodjDTgioUjtmew8Qan0AU4K/yvs5F/IYr1ndh7d0YmUEPhTAQjlT1FhROYCDQOQn1r/Ueb075Pz+p3lk3zxm5gU9g6lMPCSG3Ubluc6YFVSDMqrYcYeYvEReiPp9Th8zmSAq6DRNfP2QFPIKlPpOQAdW70ikJ9a01DaNS+mFsygCN7N+Ee+QHPuNnr6D8INQ2dZPvi4bmfGQohn7cxNYhozk2v1qq9n1bwZLXrGhyi41+BOcaDfRvACiMgIr1MxIqn4DGJPfH6NT+Gv8tUp9tvX0RhWhUhhyR1LSqxmCQILkazcnVGA3LFU1utAjyFM/gyT30Ci9eGNQ10wkJ0UrF26ldtUJAhcpN0H1u9nJElkk2LFCGf4j5ggyYgKZiNKdVj9GSXNEiiKlPHSSYJMg3uWlLC6IVYUMlIWpwuHXrVo3+IDmhLUUW+CB5jNZPNo+bvUx9OXW6rFbpzBek3jHnzAIzLfTwmu+8Bk2y6vGBhtoEaUQmvo58eAmZ/zqHAcpvIQkdOnQIHTt21OiP3bV8gu+q7EbA89M6OVkSktT4F7BzskMapGg8LFNe7Vi/fj0+/vhjjf7GUduzuGn9EBciduvkHDMDHsLc1xx50AM/jAH6MwtJyMPDAy1bttTYD6WapKGt+3BkBz3S6QnbxWfgutN1NOUe97lH0ZSWzzLlNYDDhw9rlIQizKIxpcZixIZc1dk5krP61esAuFR1QSx0OJEZaDfgQhLat28fHj16hAkTJmjkhyr5tFBLvIY60CjAEu/4voPPCx48goIYY2gAc+fOhb+/P/z8/NTv/uAebnW6KhRdrylUjcvD/xw2YpD5IBzmHjqBgXYDLiShr776SmM/0sSjPyKCL+jViX8ROBbePn0wU/QBnIOYBqQpkD9IEwREsPduxi846AtGhLTCPp/9OGZyDP3QT7s/bsA5jhpfHdvq8Du6pLeGa56eBXaJRAgKOAETXxfuqT9jCw1h8ODBGtnvuy6fYkf0GtiIrPXqfA8FroWFT0Nkm2Rr11FtwNUeNEpCmSZZWFhtHZKC7+jtAMQEXYGHV3eEhZ5ljGEgeGIZxG3B+Cl2pV4eX2rgXVj6WiInJ13xdCGlhDjGoK+nRknI1rspv4Spz3DJd8LQlF74yeEPvJs8nN3hBoCGHn31wg8kC+SoPh3+M8ZUHozdod8ILxIZUZG9KlXU/4NUU52RUGl0qT0GD8OOGsQgfBO3EI51W2JsykBYi6zYXa7HqFq3DZKD7uj9cXbPaItFzl/z1SGaZPsJSdSvXgkbwc1NPd07jCCuTSMk9JAb+Er5dmiY7WMwA5EQfAtWPo3UlsnPoH585bgNq17NRSWRYTQivBa+n092lboqTN07qFKpKjWrKTraCCL8NUJCTTwH6M1yvLwgJ+KJiG0YU+Mj7I7+mt3xeoYMk0x8U3UHYkKuGNRxJwbegqdnDzx/fqb0mxSbFhAglItVpgxxcLBRXFu1k1CtOp2QEHjTIAfjzYwOWOC8Di/NYlErz4Xd+XoEe+/mfGkWQ0NlUSUMTu2JP+xPYHjq29I/RAnTTk7CJjcrZwgkxkioOI7ankH/1B5wFDkY7IDcCT8sW4Vm0AmmuizBpfA9+pGbpQTWxy3iM+6HBfWRfQ7U0YWIRd4i+mTOGQnURkIUvTrE9UOj8Kk8CT2Brq5jcT7yN8YAOsYr09e4YnMH22JXGPR5JAbdQiVOm0sNuif7Q5T3FRIC1KlT9s4CA43qGquNhKrUbcUPtDGgfk5diExECDIPg3euB2MCHcLFu73mtVLqTnrxInD2rJC+I6sej6cn8MYbQLdu1JhPoZ+gZfsVcXOw2fFXzEocJ/uDVJaV/EQ+PtL7m1EDRpGIkVBJbHfYj49fvwtbkY3BnPi0pS6499SKv56NfbPw8+riiYeUkc3MMt2iT62puPNczXlYN28CVK7m2jWh+mDfvgKhdO4MDJcjToxIgr47aRK1kwW8vIDPPwfatePf3rKnMtb+WBXLPozH5CHFo5jnJE6EnXdTzEwcA1OYlq/tSPqJyP9DjmgjI6AySSguLg7Ozs5ymWEfuHwpFP/WNcR2Mqm0hIQE4PVrqR/d9scaiD4ROj9YrF2On31+Li0HFqPR9ZMxOP/7NGE5lWZCgpsbYwgN44V5FOLNEtA8W4XyqdRtglqZ798vmDq9ewPDhgE//6zCHcPdMp06CZsYtP/Jk3HBexICW69C2LlQzFpRDRdvWaNzq8xiX08OusuZZS2QVpZZJuknqgDdf6WS0I0bN/g20GPGjMHu3WXXaKE+YalfLeXY6KDwAlV1kxVAJbmkKCYKjuxAZFdWYW5xr6q6dYteEz+XtJ9pViKycHUVeo0RaXjIMKfWghccfnJba1H4XBIUwSEyGQN/n3z4xVcVZieaPU+eLH0ekudGz+lz5GgsC3Re4plO8jwkz1MSsnwFsj6vKNzdNSpsO3bsQFpaGmbOnFnuZz3qdFNMC6XcKSKcAwcEc6pmTWDqVIDKiCxerNm7iIiN246sdcLap4M51foa1h07jU92Ny5FQmacBrT61XxsrLwLc5ImgEEGCVFG/QHuYvbq1avwteXLl/PC06dPn8LXUrnH8JTeMH/rbemkocd4eSkYlg19kJNrgqjLsuMtLkRyZlk3PTHLpJVqoAhcNSQvZpvkcMKQX8xICOc0y6VLl2Lnzp1qOfz79+9j48aNWLRoEVavXi3zc9NdluF62H7pb5JGw02SOHJE8OHQv4mER44Exo0D3ntPZ5dn5dx42Dc/h0PfvsSgt1yQZlEFmPFfqVSNWUnjeCf1h0ljle6xZ/Qk1KJFC/5vjERiHAljuwK7t5BruMe3r5bRE4NDzWp5yH4s3yrD9bA/MKzGLOyP3qzbg5ZG7moifEfvpkjNfqfYa26c2akuAhIULUHTunq1qAAZTXZDhw4t9rnlv/ig2tFtgpYp9oNQ3hV1Pe3ZE+jaFfjmG+mOWx3CyhK8TD0OtET2s1Du8O4Ac+YIviM6Z4kytwlBN1GjTke8Crlm1ATD+1VLlFOma54j0R1WKgnRTPXbb79xJnUoGIA2WU3hbxWKGLM4vp+ZseEHh334PH4mTCuZavR3Ll++jHnz5nFW0tTC10oSEKFa77HAW6MNdjwb+mQX/YPT/HjTnMiTUjR+/LHgxjPH1KThOGz3Dwal9TTK+6an6yQEhJwGSngR6JqvWbOmbBIy4WaYsWPH8huDgAdhR41ytYwKtM91WYn0oAdAJc3+1sGDBzkL6izva6xQIA3ozBnB/1mvHvDJJ/zq2qr4ebD0boisoEcGG4hZClSn/dIlPA8+g7SJV+AzYGS5znVzRi/y41bYIQyuOROHor41mnOqXLclv2KjLXTv3r3iChAtwDx7Bvz1F1C/Pn+zJuMOqtVpp9ZOsdqZvfKBP/4A/vwTuHtXWAiiRhkF5rLXwkXChC1H6W9GQgqgZVZDBFo8N5rcsg2OO/H1q084IWDOUa1i4EBhGzUK1ikpmH5lJPbYH9VqHz6FQQsg5B/86SeBcChOijt+fkGgBNq6DUNIyL9y75qRkIJ4+OKYUZhlOdzjc6f/ISn4NruougKFFGRlYUXt1rBIycKo1H76Y5bRYsDhw8C6dUK83axZwLRpQshDGXhiEcTX5PLKlT+WjpGQUmbZQfRynYJTkdsN9hwcvFsiTY+KxFdYkFbx4AEyD99BlbfqIfGbJUKogU5mphxOPd4AbN8uRJGT7+qqYq2UGnr1VXiCZiSklFnWiC9k/sgiEI1yfAzu+Bc6fY1d0WthaizOUCOAWbMWWJq9AN81vIAP/FZQryQc9PoII+bURO8uaTj2g4Z6ilEZkeXLgXPnaNlK0HQWLFBqV83d38GLkHMKf4+RkJI4G/ErTHz89LrWsTS8Nk3Ebw5HsCb0I3YR9QzzE6eg8rAtmNbiEXJuB+Kb0aHIbTsYd9/bialLamDbCjU1Vvz7b4CWyKlN0MKFwA8/qLzLM9bX0DyzPtxyazIS0iYSgm+iruebCH7+r8Ecs1PdtgZHnBUJ5KMz96mP28+CMH2tNdB3O5rPn4OLpzYCce9TEJ/sVCRpIN/Ov5x8bttGIeucutJc0HbOn1frcfdym4wcJYvOVVwScnAAatQQnlMph5QUhXfhmO+AYSm9sbXyHsxI0v/gus61RxtM8wGDBBWuJ7nKzFSpA8bpiB1Y220Wfh94FKERFvj64nE8PBMGuH5PrZIFJ/Gzgi42tNRvaSmkrojzFx8+FJbQKdn2nXeAAQOE5XRNTWx12iAlUPkwj4pJQtbWRQREoGRHEhyJUHJ5sSb+Iz7WZlLSEFhDfzt1nLa5hNo5NdAo25eRhSZA0dCmBRHnlSsD1asLibSZmQrvqkdGOyxx3oCnISfhnlwXy2ZKVIIYMULY9ASLnb7BmriPVJL9iklC0rLFKQOfikkpqULr87J9NnLwdu1pBlmj2SAgqwAZyRktb4vb/CiAK+H7eJ+j0LdPPxcQos1eYX+lkwh8/o9K+6l4JFRWuQqq70urBUrgUegxvOk6Ef9G7tQ/xc+nMfICnzKy0ATIDCorkZYy6EnzVqImdHrQfSGiXU87GNes20ktE2/FIiESFusyepcr03alAA1zfOCcVwVH7P7DgLQ39OaUiRjPROwyntwkfQKlYZjJEW1OviLStBVMCLcRWWNp/AdY6rQRy+Pn6NWpu3p1RlKgegJdKxYJkSCUByocJi5UpiD2Rm9AzTod0f55c1TLr6rz06U2M055juiW0ZYRhiZQVYFrTG2gyW9ENawVwMeJU/i21++k9ETL7IZ6cdqLndbz5ZwdROopI1NxSIhmLHM5Tpc+QxqTkrV8o0Iu87Y8mT/l1hHWIMLMI/GhywqDaxZoMFCmcyo5rn19FfY9Pg47DgufBkgNvMcXzNclblg9wL+2V3Aj/IDa9llxSEgeLUhSG1KhuyU5gM186ussHicHufD06sHigTQFO7uilTBlQESkYFgIxeDoevEjyTQFXd3GIoPKvqgRFYOESLtRRGhIa1JBG6KSnREhF+BUtw3ig29o/XQtfRsiL+AZIwuNOURcVd8HhYVQmAgthJRXi7wAFItD9Yeyg7Tf24+qIzp6t9IICVYMEvJQoncYaU5K+oZ4Oc2rjjPhv8DbsyeCVFzCVIgAfeohK+ARywvTFBRp1VweaKITd26h4EIKcExLE0hJygRoL7LFrReHdDK5mXJypamJzfhJiDQgMyXq5ZirPjRNs+thU+ynWiMiMgHTAx/AEhaMLAyBhErKKS3nSxbFJ2KipX3qYFOAJtl+2BP1jVYnN5KrrMCHGpvYjJ+EPFTooEoxRbK6ccqJvundUD3Kme9QmxCsmQ61udzDgjPBSANiBKRBSEbZa2sCJfkl3xH5kArQK70zNscu4VdiaSFEkyYY5bFlcASkSbkyfhKyUGHwyoopUgCtshrhyfO/NbJqRsX3a9bphHxOVWaxQBoG5YXpApUqCZq5RMDj2+ldcSpiOze5teYTqdUNKnpn6dtIKxObcZOQhxr6yKsQRS2JmnnVkMsREKm2tGzukqe6Wv+jwz4scd5YENrPoFHUrKnb36eAR2p7lJgoYZrVw9PnJ/hVM1q+t1NTG/ZHlgFo6z5MaxObcZOQlRoSSlWIoi5lW3MaEC2bN/boj/pZdfBH9Cal1WTXOp0xOrk/YkOuMoLQljaia7i4CI0uyVckthC5yY1WrOzrNsOBqM3ond5FpZ+Y7LIIAZbPtVp1UyYJPXz4EI0bNzZcoXFRYyF6Cs+ndi1qApXTuG/5lJ/BNsUs4Ttyyov3XT7HLofDiA2+praZj0HPtSBJUK5aYOmmnanB97DI6RuMrDkPUSGX+JQPRRBg8Rx+Xr14E++t9E5aPSWZJBQZGWnYJESqq7pA4flqJCFC0+z6/Ax2yP40b6J1zmiJtXEfo21m01Jaz2nbS5hafSn//NaLg9gS+7lBXhKSqVmzZvH9x5gWpCRoWZ9W0Cg7vwRWx8/ne5m1dhuKSItoXAzfA++csl0Sx+zOYkCtGRif/I7OAiHlNseoc+ZHH32EwYMH67/QOGugSyrViFGhUJUsDE59i3dWE8GQQPStNQ3/2V5Flmk2PHJqoUmWH6YnjsKL0HNaH0bqwDtz5kwcP35cLftzlRLkR63Gq1PtHX0FtZ7WN1SrJpWEeI7iHrfCBZJfVfV7fOq8AQ559hiY+gY6ZArt3U/YncNR+7OwyrfETzErte5TpGueL2FSyk1C69evL9WLXm9RVQPJo3SjaICEJIWnf1oPftMXeHl5qURAjx49wiTqTwWhD700DUivCYhgb6+fx0VBjuWUB1n8ejq/iZFlIrSnnp40UqeHTtfcVCKDQSYJZWdnw9/fH35+foalOjtrsFd8idUJhrLRqFEj3LxZfPk4R4nqlUwLkgIbxf2BViJLvTwVmSQ0gOrSGiKqarCEBjm7GQmphCNHjhjOweqrFlSkqipco8igSMggoUktiGlDFQv6rAWJYWEc0fHGRUJVtVBIjGlDFQP6rgWJ4ekJPH/OSKjCaEFiyFgiZWBakNZB7X7IySux2sRIyJi1IDHKWCJlYFqQTrQhFcrOMBJSB3QR0UpEpEQrFwY9h7i+j0HdxYZ9GxsHCekiopVMMkZCxgcbA02FoWTtsDBGQjobfF3Omkr0k2LQY7PGUGFlZbCHbtgkRA45XQ4+zZoq1KJm0DNYWhr28RuoNmTYJEQZxbqGip05GPQEdB0NHTQhG+CkaLgkRH4gEz2oJEj1q6nmUHo6u5EN1h4wN3jnbjGT0sCiqA135PWpxgtVX1SwoR2DHkGRnnT6DoqiNjBtyDBJSJfOaFkwAid1Xl4ezFDBQHWjTYysNreBuQgMj4TI/NHHlQByUht45Ortx4/Rpk0bnR9HqyFDcGv/fu38mLY7aGjrHqGNm1R0jRmff46te/aoh4Rk1hKilrYMApTpT65H0Db9uHHaY+vWrUu9HhwWhtZDh2phCjZXriedIYDMsexsnR9GZGwsbkm5xs4SaVbmjDkYdIWBAwfyG0PFBiMhBgYGwyWh0aNHw9HREVu2bGEjaeB49uwZbty4gfHjx+v8WAIDA+Hj48MuCiOhspGZmcmTj729PaKjo1HDGB18FQj16tXjSUjX6Nu3L1/Xunv37jh79iy7MAaOGTNmYOvWrZohoZCQEDRo0IB//vTpU0ZCDGrBxYsX+b/hLCePaULlgQjo8uXLcHFx4WctBga1CGRB5HJ8fDwbDEZC5aNt27Z8gBuD7rFnzx5cu3YNTZo0wbvvvqvUPvTBH3T//n3cuXMH//zzD7uoeoCrV6+iYcOGyM3NRVUlCgc+fvyYb3opreecWkiIZi1zc7bApg+gRYJNmzZh8+bNBn0eFDvkZoiFxYwU7du3x6VLl9CqVSulvn/hwgXNakIM+oNx48bxgX9//vkn3nnnHTYgDCojKCgI1tbW6NSpk0YXnxgJGQl+/fVXNggMaoW3tzdvhqWkpGh04YmREAMDg2yCMDdHJQ2XT2YkxMDAoFui4zYTNgwMasZCNgQMTBNi0CXWsiFgYCTEwMDASIiBgYGBkRADAwMjIQYGBoaySKgOGwYGBRBSxnusCySDIjARkxDr3MegsOAwMDBzjIGBoWKRECutUHHRs2dPte6PKu1JK1q2Y8cOTJo0Sbsnl5srdNwwYQqeOnHy5En07t271OsnTpzAvXv3lCOhiIgIzQmIot1LqQe9mRm70moGlXfVRt8xqkG1atWqUq9TqeDFixdr7HdTUoTu4UhKAmJiSr3/x8lKmLiwJnccAIn6WhZyqTQaNWrEl5cpidOnT+uhORYYqPh3qLsk63emdui68aGmCIjab1Fvyp+25WPyFFPkP4uRqviMmF0DIn9uQrS2hn0Dd0ZCKkAaAalsjmkEoaHK98wm7YkREYMcmD2bs7rSsmDyIgx9Lpvi658d8fGURCmfLGCmzExkpIvAfPDage5IKC4OyMlRbR/PnwOenuwqMpSJnt2z8c2yJHw0Bfh6e1WM7pcs9XOPj4fCxE+Y2K7uC+Mmuiw20RktCZEz8PVr9ejZ6emArS27kgzSkZaGwc0iseAfZ55gVs59hRYNpbdHbuCdI5hjJd0FrAeaEZJQSIj69hURwWYrBunI4jSZyEj+6Vcfx/GbwiB3QRinFXl4sPE0GhJ6+VL9+2RCwiCLPNRFZrSiVrkyG1eDJyEyw1JTNTPj0b5Z5w8GSTNKnaAlfQcHFk9k8CSkTjNM2r6ZWcZAoFVXTREbkzEDJqFXrzT/G4XRaAwVFrGx5a+6RkUBgwcLiyPt2wMJCcCzZ9TNE/jll/LdCbVqsXE2SBKiC61pkHAxEqq4oNXSxMSyP9O5M9CsGbUWLf1eZibQsiW1ohWCi6SB3AnM9DdAEqJ4Hm2Bepg7ObErWxFRlpzRJNiuHXDnDmBnJ/0z1tbA7dvA3r0A5T2dPMlMf6MgIZo1srMZCTFoFmXlHwYFAQMGAP7+8u1r5EigRQugQwfgyhXpn4mOBjTYEJCRkDqhSWd0WX4BFxfjulJkZtB5SYJMz5o1mRRLycgvNimNGAE8eVLqrd+P2ePUJTt8/0UsrK1KpA+RprN/v2wiSk4WZMzUlI2/pkgogVNfq1SpotreteGMlnXDGgsJkRYpy8wgRzxtpPnpsfZHPc137tyJFStWaOZaZ2RIf498POQDkkJAC75yQnXnPOxcEwPLhj7IfixlSd/VFVi2DJg8Gfj5Z+kaFjPLNEdCJDRz585Vfs8ULKYNZ7QsGIO6LKPkhNTZnshIT/PoqKd5SVA5DzNVy7HQKlhJ7VBS/po2FVa9pGDdP6nYf/UvHOCeL/4uEmEv3eFRK6/0bt7qhRmfucD9f/ZY/KEQ42ZW3wdzJybgh72OeHA9BV6N2GKIPKBrLpKSsC63ObZ8+XJYWlpizJgxWjXDMpGFxc7r8Z3jbmSbFl96bZ7ZAKvi5qF3emfp6rIhkxAl+CqSX0cak5rznAK5/Y0dOxbXr19X++mpTEAkzGXFA9Fy+927hcGFIu4xz3k1NlbdhXYZzTDj+8nY+XEvrPkoDsP+TMKrPZ/hZ4eDqJLvgL8it6J1VmP+e6b1fJF+3wT32oxGs39PYv+mKGxZFov3Ribh60/i4NXDE6ERjGDkveYmUoI95SahpUuXyk9ANCvn5al0wCdsz6Nv7Wnol9oNu6O+wfq4RVI/t8/+BGy8G6NlViNcCv+99I3s7Gx4V4uScpVJ8KUbk2otUdE3NcCHIzRNEJCaGFL2ezNmABs28InNRD5t3YbhuUUkbr04iA1xBTWLuCF6MsYC/x70Qf6GRJjELsN33MZPuFW/Qxv3ofgnYgd6dXKFjbUI7e//gPv1rOFeKwc/H3TgSSj4hTlaN+ZMvhCOheqwfhFqN8cyODs7lJtpvLy8FL8RKF5HScSaxaN63Q74LmYZRAHlr2aMSH0bI4LeRqZJFmp7dUbrzCY4HPWd8CbdyIZGQjR+ESpMrUT+ephLp1Z/UFkrYUeOAOTL7NgR2x32Y0b1zxEfdAOVRKWX5SlrvoF3YukJ9/UH/Pap0wacOjYbj67dwn8XHPF23WewWr4MH47byGfkd22djnO/cdcqt0AT5SwFBjWSkNJV7lTI2RlWcxZCLSLkIp+SsBZZISL0Ih5bBsLExw9hoWfhnlvL8Jbs1ZHzRLl0RMBVqxqfxJYYn/+u2uDNiW7887TzN2G7fDlw8yYaeLyNd1LfRHbg49L7oBUtmlxLmoRpaYVZ94SV8XOxEnNh17MJvso8iOMTvIE+tzB2wUuM9U8p/l1aPGBOavWSkFIIVr57kK13Exx6+S16p3dR6RAaZvtAFOgPV04rWhY/E9PiRxgOCakr61tsilLCpTFF9krRgAZMdy2sAWTh1wzZ/jdg5lMPIaH/wTPXtfQ+SEO0spK+fwpiJCIhTT6liGTSgu6jzVtDcSfLF9v//hvw85Mec2SMoSEGRUK0XJmfr/ikjWxY+zZGYuAtVBapb5UhktOK3nP5DKNs5+H3lz/qf74PaS+0qRPGEtlL4yKDoOu4FQTCduiAXKsImHIElMNpP+bSRJuc9vJkwVPsFVW7l3Ar3Ag/gLnOq9DBbQSu7NoFfPkl8Nlnxb9H4QLVqrFMe62TkLQgOjlBK1/2Ps2UMr/kwQ+xX2JL5T3o4NgXV3C34mhBJc0EQy2BS/4xCkSkeB8ZqF0jF826VEJIylOYZdohN1CGLMlLQGJQICh9XqL+FTm1tzscgM/IpQicw2lKixZx6pdFaeJX08IAIyF5oSwBmXAE5N2cE5qnGj3B95NGwzvHHX62fvCHv35ehRcvNLdvcphSuAKZZoYCSvUh34wcmuHfc04jc/mnsI8KLJSl5FQTLNngjLe7paF353TltUHShsi8kpDxKclDUTunOlpFbsCtqq2A+/eLf4cWBsi3JCs/jUHDPiFFNCCegJ5o5ffeSu+E1ZHpaO/aHldxVf9uuDJmerWAAjfFM7s+Q1GTnrvZRaNGwiYzh/cDipUnj2518PpmMOasckaEyBXvqmKROjoKmfMUNlGAXhmdEZb0EgN//wx/kY+oT58SvoBI5qRWloSec6q7pxZUdxvfJhozwWRhcNpbCIkNx3su7+EH7qE30FZuHS0aSIlc1hS00kixRQuY5ZsgR2IyO3rWDns3RvF8u2m7A5q1MsG776r4O7Vrl3KKT0segcddg7Di6zlYgj7SzWtWclhxErp69arGScjSuyFSA+/p5GQ/SpyCQTYfYEelHZiESbof/fJq36gTpGFoKVwhJycHU6ZMwa5duzieaKGZH6lfH5acApkQdJMT4qKl9v7d02DRwAfRzxIxYaA51BaeRD6lEuEBm159itZL7qDDh33QY8HfxT9PpiSLHVKMhLK4QRtJJQw0iDqebyDk+X+wE9no7IQpkNHd/g10MukEH+i4lYuS/jSlQSRExdo1vGxvYWGB9u3bq52AklJM4dy2LnLzgPaPnPBvzIZSK6qkAWUHPseOs17YuhVwd1fTj9OOS/iHCDfDD8LhhxaIufoCNi4lfozFDilGQhs2bMBHH33EyadmBHSGyzIseT0DtXN1n8/1IvA/mHDCkc89THTVZVOTzujyzD8t3Bjz5s1DWloa7NTooHVsVRcir7r4YUtzTD8zHF16tZb6OdM6XpiiiSwK8g8RkZdISUoOvgOTTn7SXQwU/U7mHEP5JETqc1JSEqetq19dv2/5DHetnmBr7Bd6c+I5If4wq2PGE5HWoQ1ndFnQQkO/evXqqbyPLmNq495TK5z+ORLtmtF4mSB9xadY1HMeqo3hyKBXiHSzSZOg5XcpQZNJh3ehZr+OiAq9XPwNcmhTtn/JpXyG0iRUjYKsNABKIGzmOVDrjuhyT5zjgYsvdqOfez8c4x5a10Z0CTUnumoCrQa74++fIlCtaj5qdvRC1GtrfDPpPuxGv4sGPplo3C699JdI49DGCiAFvpbon+fQsB2mfZOKLZP28GEhxUDZ/swsK5+ENAV772bICniklyffMbMl0tM24YLFf+hi+YZ2fjQ5WT9OnkwKPW5xfPuxFU9AtGw/Ju4vJN96ih2N+iMg9BR8jksJ7KQQBG21A6f4Ico/KxFO8EXvq6ghao7hpn3gnF9FqllGFUZICb540bBCt/SWhKjonGOOI+ZOTJT6/ofVvsT26FWwhP6qomcif+FzjXIDnsLEwlJwPmoy0IxidvQFpBGRaUHnS9UGaCVHR7FE5IqsWc0Dr16bIfNhEM7sioBbMye8m7Ebm80/R6uaG9EhvTl8cjxLf5kSUbVd5pbCHUqaZRwJRs8cApMD7Upr/pxZZmMjQmKiCZ+6RsMspb4XIyFFQCYuXYPMZ2mwb14XqXeDhdUAqj/z+DHCkx/j0opH+F+HA0DWvOJfpI3qr9CM0ry5kFbQsKHOZuX0wAe8xkaJipJZ1Lxgq7OFkOS+9QkU4UsbLSVRxwktgyYz8tPXSg/DnYfm2Nz7GGZFLsKLS5c4dWEMlpg8g0ONT7nrc0+2n0YXIP8pOaolsWoVguocRNvHw3A9fH+xtzIzTQpzZ5s0MXJmUaAtktIkRJMnX2qII5NcZADz5wv1fLt04QuLu/sWrBY8kGNnZF8/4ky2U6eAa9eEmsB0U9jYCG1aunYFevbUWG0gK05X+yFmOT5xWoe18R8XvUEJjLSRdkQrI6qaP3RODFJliSrZ1po6ETGX7WG3YicwrF/huqWNdxNkBj2U/mVdmpPSSIg4ccc5eBzphnPtb6BbZlHA5uQhSRgx0Ap1GlhL+5pxQYFVWHNV7qlz5zgt4sdwVFvKqcPffFP4Xn2PPggPPi//zsjRR9tbbwEzZ5Z+n8pSHDwI/PefkKtDs/Xo0cLm5qaWMRubMgBuXl2x9PX7sC9ZAItiQ6hoP6ngyporKpQ5MXYsWCDUlH/58hJqVc9B5LCisq2zqq3A71HrYQopXS1Ig9Z1Kgpp9CUXGjgN+o+ZjWBxZxxyQovMsu2rYpDBaUNJ9q5YvdrWeC9oWUXn1ElCVG7l0CEgI8kM4ReKhOa0zSV0zGiB2nlqjAciDei994RNDFr2pAP49luBJIYPF6RZBfMpPPQ8XxBNJC0Tmwx4cuQqY6KVWElhkGGplsgdizNNwFG7s9j8aknpL9BKmD5EI5PJQRp7yY4f3KSZ5OCHqilt8DrkRuHLVCrWJpcqZxrpapkSPk+VHNPUzhsBxSvM9an9LvICn2n+ZMmvRP2kaCOQEGzcCFCtF/IzUY1hJQrd3w47hP61puPoy++lf4DMM7Id5A1Ao/D91FTGMkrApW475EubEKpX195KmDwgbVzK7G/7+2HM/2wQdn14GBNSBhV/U49XJpWGuGKDNkmoJGp4dURi0G3dDADNRlTfhTbSWoiEfvgBoLZF06fLvZsW2Q0RaR6DEPNw1MmVYepRABrN2uUlhNKsrqk6QUaOkTXmlm5cwAtZDf1c25YSO4QGDfDpTFfYL1qI8SnvFI/OJxk11EYMsqBku3e1kdAB+5P8QEsrKK51kJ9g3jxhIyc3LUVQSc49e+SKXL3z4jBMfP3KDrAkgqHZj7zz0vaZL8S4MCiOCLNoPLTyR4fMFoZBQARa6ZW27n7mDBKr+KFSdnOkllzdozrgVJRf1fZH+oCy2i9pi4TG1ViAjKAH+jc43GyEBw+EJUNqWURBY6dP80syLQe58zb6pd9LtxH2Dz2FrrXH4nzEb+UPPq27kkoubgmsaM8whuLWTZ2upf1yOgofUGTe+/RTH6xcKUL+s0D+3xMXVsfl2zY4sPwYVs7ph42f7sKcpAnFv0gLFoYeTU3uhpwc3ZKQY91WSNKVGSb3mXKnum9fga4/EqZ3byL/SQA/C1H7FnGxdDF8+aA4EQIsnhc8L8fvw7QetaB3rSl4EHak+Itk9upxz3daD6FmwxTFMW9sDBavd8Ldp1bYtPgV/OrkwKlNL8S7+MBu9Sp8kDQGFiVvO0Muwcsh9lEM7G1NYGstUi8JffXVV5z2WwPjx48vcwc/OezHgtfv6nVUdCns3QtzvzygWzegTRvY2fwl9WPnI3bLXi0zMsQlmCIyyQRNW6t/3126dMGFCxfw8OFDNG7cWObnEk2T8dosCY2z/YQXaPXLAG5OSsX44w9g2jRunjtbA80bvMSaH504AhJ8RB9NTkDssL+RZu8N+9zWSA0uUe+cHLqkTZBJZ2Co45mHcf0qc5aDJczNRPjt6xgsWOeMdT9V5S1nWsNRioRWr16NRYsW8a2fy8O06kuRr43VMDWjcYN8zGr5DKKwF6ifcQv4+2rpMp0cAkNPo0vt0bgQscdoCWjJxqp4FmyFce+aoHlbpZqmlIl33nmH/zt79mycOXOGf75mzRosXLiw2Od8PHviVVBB+V1y9BrITTlkCDBunBBBQou1e39xRhWHcNTv44GF015j8YZqWDSdU5U4Il4zqwt+XfIXxqUMLL4TcmobmlmWnAw7Syt8MUtwPZBFsfWLWDwJssCul19hoO0CvPkm8O+/KLzmWVLqhkslodu3BdPKQ6I85a1bt9CxY0dunIoPlMxQej3H7cMv8DqRU/FN7FC1sg3wvyDBf3TzZrHcMe9cDySZpiLWNB4u+U7GxT5kx3M3xsqtM/DZT24wGfItpk8vujkSExM5AfoXQ4cOVeln0gvqM7u6FvUBK0lAhFch1zmJNDXIlsq//ipsBSocenbPw9OOYXjx0rzI1K9eHTNfvgNLpwWlSYif8Qxo2Z4c8NHReBQo8AEFYZImlJZuAp/Owfj9/kKM772gmL+arvmBAwfkI6FZs2bxfy9fvlxojrVq1aoUARFsRNYGew9WdZSY8j/8UNgoaptulh07Ct+6/+IITDmzLN+QzTIKIqO7hISAysrSSlOHDnzUecsG6fh6UhzSsnth0A/Ali3CVxwdHVUmIMKLFy/w6NEjbN++vRzdvo5e+34UApmRAQFwr5Vb/PW1a5FU+U9US2nHke610jc2aUT63iOPUBAlnvkwAE36e6BypTxkPxYc8hu/aI7eXVNg+jbkSk8xl2XDEwH973//K38PZPiRPZufbxzCQytn5CikJX2KxqacNQ5XX/yBITU+xMHo/xnGeVzlzJqff+Y1HV6oJ04UUmI+/rjUR/0fuGD8pDB0CbbUSKWRH3/8Ub4PGgsBiUEBrbQaW3LivngTU9e2xt5JxzEytW/xN+le0vfa1JQuUVBd0oo7zAdHi2LhesY2wyOL42j400vVc8fI9JIL4qhkY4qLoVmM2vx+9ZUQ7Hj9OtqiKQKsQhFjFofqeXoYYEam1bp1QsQ4BcAtWQJs21bu176v/DuWxs/Agk857cjdQa+XwQ0OFNVNMUAlysHSxL0q6WOYu8zDiNS3S5cY1vfa1BKdaSURumgUUn/zQ8Nwxbq6qC9immYxGjiya42lUAqtvdJGDutq1fDwl2PlBzFqE5Rw9f77wLNnfNgBPvoIWLxY7q/ncY+Fzl8jMfg2IwxNQUY5WOpDlF5tC1xetS9tlumzf0hWBsCJE6hz8I5S94b6KyvSwCmYRav3oAZ3lEXfoAFuLeyDQZ98wHft0AkoIIWWYaiawAcfAH/+qXQmedW6bZAQfJMRhaZBPkYptaQsr9/BjJV+2PreHsxIHl3aP0Tr29QdRV9AK1vSuuKmp6Ntu7l4HnJWqd1qpryrlB5NBg+qwf3kCVpypln0w/GIuvwDag58Tzu/Tf3YaTXp1i1aNRCCLlUsYfFF1f9hc+wS6SUyGNQLWm2l1B4pUcVfNjoAqypDMTV5RLH+aTxiYoSKDfriK5OhBT0c2xyO1zrC46VyDnXNkBDdIDLY3+DRti2uwh8mH3NmmdlGUCCEaNMmtBrqiWchlrj3Zxh8PHNU/52HDzmm+EIo9kZRcL/9prbaOVncY32VnUhiZpj2QDmG0iyExo2RPuAN2P/dvDDtieJtVsyJw1c/VcG9v57Dq0cdvSUgjBqFJpyoigJ/VnrXmit0Xwb7GwOeh5xB89QPcPfZGjjXd0G4iTNsly+CVb9FyHqkhIOe1O/Dh/klXH71gXxRUmIq1AEbn6YGGWBq8KAFDymZ5mb/24Id4xpg8eb1GH7pE/yyNgrj3knBpzNeo15vbnI781y3keNUmV+aGcZNkF777/BdcFWBZrttyGJ/I4BHrisa5NTFJadneI3msH12h9de3q50EfDrJpT+7N0b6NRJqJ8tWTyfxuQsZz/fuSOYWLQcO2gQMHmyUKNbgxhb/WOcC/+VEYIuQNeZ5EBKmd+RSx7io4wGeL/uFHy3rBFPQg8DLNGuWUZRnR5dVRCQ0ajzt4NDMLTbZDjGOegxCRH0zSyjRFZxVT7KrKcBzs1Vale7o7+BhU8D/LC8Gx+w9VYnZ1zIcxCW98XaDZlVVLBdErRiQqtaNtpthx1mHoknVkHoktmaEYKuQPeDxMRMRNN0gAcsLURI+HITbD9pgz8mRcKyoQ/e7pqGP7cU1CiiYFMiMG2X/ZBRoiOnZ3dMDbXiTMhPVL8lNX4SNHBSejTpBEQ+khX5iJAoSpeqMoaHK6epBj6E7WIPZA1/xHPO15/EFb1JPhyqZaQnrRU86/TQuyaUFdY/VHBzNx/owZf+4M2y+h8i5NxWDD/UC9l9Dpb+nrbLfpDGJs2dcuUKrINfIifoqezvKhBeYK6Vk6EbXdeBjKR9yJpFSCOhchFKHKMZ9/g+5kvMrrYCm6TVQtYTONVti/igG7I/QBOFuTkjCG2AfKVU9yMxEfXrFvla8vNN4LXpL7Tc6Yed7xzCxJTBpb8rT0VPdYBmVBkWTK8ak3Ar4rDslVUFiVI7UkcCLsMW1jkBSR4jDZ4SPqxJnLC0d9zHmzvkK9I3fF51M5bEz0DVfBkxJ5SoLG6IxaAdUBspjoTsbEXoNq42gsMssPXzGP6t71tcg51DO4xJ6Q+LkiVyyKKgiGVNN3uUEWJz7JeRqLLgbTSPbqAWAtIeCUmxhbVng3gqZkcrSURXw/fpZe0hSjPZ43AMAc9PS/+AnhcMM2pwJsu1P6Tc7FWqIO2DCTDb0Vh60whaPaUyJ+pszCkJGRpQXvhzDF7+ENmBe2XLkl76hEr6ZKQk9GkMFGCoTCIgERFlCSvosH4dfAN23k2FTq56ghp1O8r2AxlT1rohoqx4usWLEdjoD3jc64aw0HOl3ydtiLRXdSe6irvxSiOLHr04UnyqdlnSLgnJSujTlN1NRcSVBQ0qrUgokFZehTN3/orcypcoPflyu+5dDz4NkRYogxApyZX5gHQPclNQ0jDF4pQUwcP3MOdjP7y/7HNsefV56e9SzBE5gBUMYqVGx2+/DfTqxad8FTf1ZGhBdTzfQPj9ozC1NZU+2asgS9qXQlkJfeoG36NaVTWihkBkCrTteTOjA/ZVOoHVVX7AooT3dCbbzd3fwcUXu2Errd4TzVhVqzIC0BdQEX8Z98Tc7n+i7+V38GvL5mUXQpOTiMjfTIUhSA8gDqOqkAfFC3EyFmbecJ2ATV86ofZ4Kf4eIh9VJnudkBCBnHLUNVWDtrbaQCovmWfUPSMuTq6vbItdgbZuw9AqsxF6ZnTU+vCOrf4RpiUOR7usZrInAgb9gqzV2fr1cXzu2/D7ZgEa2HijZVZD6UQkz+ILhEgU6oRFIHcplZviIYMEP3XagKbfX0P/8f44ddEGA2bURhWHPPTpmoYdq2PUUgVTNyREy5N0Q2sidohWejTRn5w0B9rE2c1UspQ2GedwPXw/vyx+9cW+8rt1qBG7Kh1Gumlm6axsMSgrW9f92xmka6eyJucNG+Df7CyqxY3FnegTcMuVsjJGMUTEKuX4iEjpolREKq65ejVHQuc5eQ6QvhK2o9IhPL7wPf70/pP/d+933QpL1Xr18FSPtaEzEhIzv7rNMiIJTS810w1MJEqbJMh3VKIPd3zwdVh7N0bg89PSBUfN2OFwEH/ZncGfZZUZoRbKDPoJkimqhyrFZ7p6Rhjy7M3hnl4TYZGn4J5XU7qPiEwj8tGUAZo3qSLMR7OyZXZN3VHpII5EbsGf69oDO+uXej8+kdO6LMwMnIQI1DBQyUhlqWaTLlvqUl4PbeTYk1hdyAx6yBPRxfA9aJ3VWGM//7PDARy1O1s2Abm6shtd3yHFZ3rmmg1i4s3w+t+7mGWzFh4xw3AjY6t0eSJ2oY3uLVlpQZw2XyUpDHiVLfXthU5fI8DyOQ63jgD8/yva9a0gPsOfsH+/+k5ZtyREg0Q3rqqFjUmVlegMolPQjV6iAysRkatXZ+yO/hrdMtqq/SeH1PwQ5iKz8gut2dmxm9wQIJHWQTh6xh7rFrzi7tbaWPXhP6gy6TjGHxqJaUnDMTdxkmznD4Hiieg+IwcyuQ9kNAKr84YnQiMsYXW1M2Y71cMhnwelkqkdK+UL5pis1ucGSUIEWoGi5cnsbOUJSBth7IqANDLKuaGgsgJEhl5Ed9dx2JXzJ3bErlbbT7l7dcP8hEmYnTihfMFmMAzQDS4xOa/9+BXsmvpg85JYzPjfKuTUb4zpP32F2nkXMK/hdFQa+A+S7wRL3xcVzqetDOw+Yo9tK2LQb5wPVvyzC5mtuN8dXam0y4FAPicL9TY61Y9AEXKokWNN0fgh8s/oGwGJQWH1NPNInNPZyF/xo8M+1KjTAdEhV1TafbJJKip7t0RY6Fm459Yqn6gtLNjNbUigybmAhCy5S0ftdEIjqIcZOZEPobmfA/JueuCKSxA6ppjj2Z1rqFdJuaXy274nsaH/FGQEPsQrKxv8YH4T6RNmwM7PBx61clDJLh8Pj4UV3atqhv5Eq5EtTE4yeTUiuqn0fXaXYt9PSx7Bx3tQCZDVcfPxUcIUpcyvJ5ZB8qeI6EEr5e+++w4fUE1sBvlRokyyV+2iCP5mnezxqnUfdPC/jB4dUjHjvx4IsHiOoOf/yN0L8IlFEFp4DMI8p0mwss5D9/pZuHXfHDn+eajR0bNwJWz2SmekppnA3k8zPkWZJLRu3Tp8LKVHlcY1InnicUjL0FTejCbOqcQKBAlJTuATHLQ/xXfvoOTS5fFzytxNLvIwtsZHOFDpFJ4+/xs+OXL6wCh2RA8io6n9MyMhBUGavozFm5PbX8Kt60tE+Flg/aJYzI34FSLuQYGFZ22vY9OrTzE9cRQsSyTAJpqmYKnTBnxbZTfmv57M+ysJqx4GCb32nlJahimcHPOQnSNoYS9eWsDOwax4GRxtkFDjxsU978mcakjtfG01dCCFEMfjULwEBTNIgqoVOhlYK2ayoWWE5Q9J7cXndT21CEYDj7fx1CoYLTMbont6O9TNccdzi0icsD2Ph9b+eCOtPU5EbsPe6A2K/b4KwWS5ubmIj49HdQ0s6/ft2xfHjx9nRFMeyKlMG9W8KoHw86GC75Hu1YnP+P5lZyJ/4d8LtniBRc7f4Jj9WX6li9AmozEGpL3Ba+D/e/VZ8Z21bg1cvFiY//Xo2AtYNPBBXr4Jxg1MgkkdL7Vcc3FLcKkk1Lp1UbW9mzdL14x1cHDQPAFJggK3aDMGlBGWT6ifUxdPwoqSeLKRA5GJCNx/WIP5yv8ukZ8KgYnmnAZVXUNxRYyAFABpQ7Lkh9wS1AyBtBiq4lkQrEiT2DdxC/mtXFD54UOHit1vJDa5TwOLLA81BLjSNad28jJJqCTxpOmq9o8xC5KcMVG8Cq2O/pFEfnqAhIQEDKIa2gxq8w+VmC2EBpjNmwObNgFdu8q3T9LOmzYVyg/LCnAkktOw60OmOTaEMtsY1KtWk7AoWc9aYehR07wqVapg7NixTAZU9Q/RpCKj6Dz//r17Qn+6Tz4BLl8uO5eMcjYoc9W/nMUNLSz+sFoO2gT5Z7RV2I2lZxgfyLwuL7h3zRohLKRvX2GRh0hpwADhPdKWNmwQNB9qoLlokV5o0oyEtA1NVxAQ2/AMxgmKHyJXSVkxdaQBnTwpPKcyNEQ44olpu5x1rsR1jhgJGSEoCpX62otEmvsNQwlfYFAOitTkonQmZVKatJhnyEhIF6Aob1lORnUIKIPxoyxHtarQZlshRkI6AjkRKd6JyjaoE7pojsegOxmSQkRxCaaIiTNHQx8lczF1MIkxEtIViIQoGFOd9bZZqY6KR0REGsFC8urkxS6cmW+CDi0y0GmUGxJuBWPFlipYvsUJ2TmmeHIiFPXr5sjeH4WR6GASYyRkKLY9M8MYpIFIo4CIdhx0LMz3+v2Y4BfcsscRWY+EsrFUC0j8vtQJTMttyRkJ6QtK1I5RWqtiZljFJiLONKvunMubY06O+ThzTagdlZ0jGeksYzGkZHt0RkIVDBSRSkunMTHKfZ/C9A0tn45BI6ZZ9CtzDBvghsiIfGQ8EHxFX3wYz+eA5eaZIOifEOkatI4nMEZC+gCKbqZIakUd1eQT0IMyHQz6g/1HrISk1lBB6/lgbBK/lYIctagZCVU0kDZDpCJnW6FCXwADgzTtmpbZqaI9RU2LI6ypDjvJmZaCEBkJGSKohAnVBJbRAaEQFLpPkbNGBkqatmN1sNUHKstBpYZ10AAiIyMDNnI6uhkJ6RvIx0OzGJlmJc0zmsloGVVD/eNv3LiBNm3a6OzUu3btilu3bjEZMALMmzcPW7duVS8JrVy5Elu2bGGja8SQVbROWn0pVTBz5kyprzMCMh7IIiBp11huEgqS0aeagYGBQRUwc4yBgcFwSYhqEOfl5cFK062XGbSC1NRU2JNjXAfw9/fnnZnW1taoV68euxgGjhEjRmCfuISIJkmIHJnVqlWDDyXSMRg0srOzcejQIYwfP14nv9+sWTOehJydnREnb5gCg96iKq30aloTevToETp06MA/P3v2LLp3785G3oBhWVAgXVewKGjO6Cit6ycDM8ekoX79+rz6Tuoz04QYVMWbb76p8AzKUMFJyMzMjI8FIJ/QdnlLRjJoDCKRCNevX0dUVJRSnS2eP3+Ox48f6+z4yRQMDg7mTXwG3SMyMhK//PILwsPDlQrNkTdGSCUSIvz444/saukJiEB+/fVXrF+/Xqnve3p6Yu3atTo9h7osDUVvUKtWLcyePVsrvQbZEr2R4OHDhwgMDMSDBw+KNbJkYFAUx44d410tTk5O6NmzJyMhBvlALXaHDRvGd01lYFAF/fr10+rvMYk1ElCbbgYGQwQjIQZ14jYbAgaFSUgkEiVyfyuzoWBgYNAAHLktSQ37obogG9lwMjAwaAAZzCJjYGAwBFBU/zQ2DAwMDBpAktqVofj4eNy5c4cNLQNDBQKFvLIkLgYGBkOF2pWhzz77DOPGjUO7du3k+nyrpk1xa//+ijXq1PaAikabmDAJFINaRLx4QcVF2FjoAWZ8/jkmzZkjd/HxVq1aGVydXkp0ozDxphwHyYMdP/2ESUokaBo8KIdHR216GbSIjAwq9m1wh33y0iU0ad2azzmTBydOnMC9e/c0rwwpilsHDwoTYUVCZiYQEiI0MWStnIXGfdTySCRiY6EvigKnDMHd3ajPkaqBDB06FJMmTZLr8/acnC6eOrViCgQ1zaTmmQzGCeoGnpRkkIfeyNcX7QcOhJe3t1yfP336tNTXWcyQ7phYUIjIQ6RnDTK1CrJEIiKYPDDoPRa/917FM9zEePVK8NpWr84EwZhA8hwWJhikBorR/fsDtWurvB+mDOkS5AmhpSEimMoVMKFPWt9ZBgYG/QR5DsiIk3M5gkHPQQoQKUIVVcFnypAeglyUJJjOzhXrnA3ULcvAUGGRmioYcCzm0fCv48uXbByYMqSHeP2aWt0CNWoY93mSNywy0iAD9RgYGCDEPNLSNi1NMIXIMOca1niWKUN6jeRkwQ3t6mq850hWZVYWu9YMDIYMyjwKDzf6IHujQ3S0MM8wMGVI75GWJqzjEskYk9VFHiHKGDPgQD0GBgYJkIeIjBumEBkGyJvHPPJMGTIokOeEFCIPD+NQiMjbRYoQ/WVgYDA+hYjFEOm3IUpePLpWDEwZMjhQGmtoKODlZdgkQ5kKTBFiYDBuhYgmW6YQ6Sf/smK2TBkyeFBANSkSVJzREEmGjp8UOlZMkYHB+BUiyk4y5nhHQzVEiYcZmDJk8BBXZzY0hYgpQgwMFQsU70iZokwh0j3ENeyYIsSUIaNTiAxpyYwpQgwMFVchoowlYy8Rou+KEMWcsqUxpgwZJQxlyYwpQgwMFRuUum1qCri4sLFgipBxK0MJCQl4+vQpOnTowEZQm9B3DxEFSTNFiIGBITFR4Chq8MrAFCFjVYZ27tyJ+Ph4pgzpAvrqIRI3/GOKEIOeICgoCEuXLkXdunWxYsUKNiDaBmc08x4iJyc2FkwRMk5lqDxMmTIF9vb2mDVrFsaMGWP0g5iJLFywvYmTthdx3/oZLlnfRrZp2cUFXXOqo2lWPbTKaoT2Gc3RI70tLLmHXCAPkThQUR8UIpa1UCERGBiIsWPH8s9TqdeRnsHb2xtt2rThDTfZopuPvLw87jYy4eZt0wp3DfOQjwjzKARZvECCWfFegX7ZXnDJc+a2qjCBkjxDY2/J8VqlSuyG0aQiRAUVmSJUxhCJ+Htd/FxrytD27dvRrl07ox3YE7bn8a3jb/jH7jL/795pnTEpeQg+j/8QDiJ7xYwn0ySctr2MobVm4x/bS8g0yUbHzBb4JH4q+qf3kP1FqiRKNwDV9tA1WNZChYSPjw+uX7/OP2/VqpVBngMpQGZmZsY9EXCP21aPsbvSEeyofBBJZqmwzbdGE84Ya5HVAO0ymsEttyZvlImRZprOK0hnba/D3zIUd62ecNtTZJpmoWZuNQxL6YOxyQPQOqtx+QcQFQXQGNvasptGE6B5gNqjMMgEGTvi+9xEhgNBYWUoJiaGG/cM3vMTGhoKL4pfMXLEmsXjw2rL8YfD33DJrYplnNKzP2oT7ESq39xV8itjROrb/CZGpkkWfqi8F7Wrd8ZL81gMTH0TG199Co/cWsW/TDcA1faoVUt3FglzzTLoMcTWYIWygrnHRetb+KjaWty0fohqeVUxN2Ei5iZOxIa4xfLtJA/wzeG4PV02JxJHDan1IcLNo9Asqz7WvVqANzM6yJ6wyXCzsWFCqU7QCgFThNQChZWh6tWrY/HixUY/MImmKZha/VMcqHQKLTMb4tuYz7AveqNWfttaZIXZiRP4jfDYMhB9Xafxf99M74DtMSvhLlaMaHlCFwoRc80yGADmz59fMZQ+7rHD4SAWOn+DJLMUfJAwBv9F7EIlkZ1Gfs8lzwlLX3/Ab4QE02R8XWU7+rtOh6XIAivi5mB60khYcI9CUJVqajFkZcUEUx2gEgZUyoBBN8qQseOY7TkMrzULtvk2+C16HfZHbdb5MTXM9sGjsGP88yvWd9HebQTizRJ5pWhMygBBIYqJIU1Vu4oQs0gYGHSKB5b+GFlzLoIsw/DR6ymIDrkMM2h/2a9KvgNWxs/lN8LXjtvh6N0KTnmOOPzyO7TMaiR8UNxzkSlEquHVK9Z9nilD6kcWsvFxtbX4X5Xf0D2tLaKCL6OySD8D/jpkNkdk6EV+KW1YjdkYW+NjjErpi53Ra4Xwa20oRKzpHwODzkDLYMuqbsYKp63wyfHEqYjt8MzVr6rPHyVO4bcYszj0rzWdX66bnDQEP8R+CXOKMaRsWAsLdjGVwevXQqYeA1OG1AXKAhtaaxZO2l3Al3GzIQrwN5hjp6W0o1Hf88+3VN4Da5/GaJfRFEfi9sLZ2Y8pQgwMRshXwzi+OmZ3DpOThyA78BFH4PpN4dXznHEj/ACvwM1zXg1Ln0Zol9kUf7/4GZXdGgqZZgzyg+o3xcWxcWDKkJpIxSQLQ2p+iFN2l7Arai2OvfzBoM/n/aTR/Hba9hLcajWFOzxwint4cg/1maMipggxMOgA5LkeXGsmx1cXeQ/wUQPkK0rNp+Bt2rY7HEB1r3Z8BtvZ3HOobe7JLrI8oGWx2Fg2DkwZUo9lNYQnlcvYxZHK8Zc/GtX5vZXeCRlBD3DI7jTq1KqDtiZtcZJ7VOYeTBFiYDBco+2XKOPhqynJQ/ntlM1F+LrWRwM0xH/cQ2WeMmZQXCgFTDNoXxmiQmTh3ATo6WkcWvt85zVYX3UHFsZP40hlm1Ff1MFpbyE/8JkQxOjiiGnc43vuoVThNJY+z8CgVdCS0sgac/FHpb/5LFZjM9rE6JXRGelB9/Gjwz5Uqe6I/iYDcIB7FMtAYyjKGGbQjTK0fv161K5d2+CVoaO2Z3lvULvMZkgNvAc7UcWpc0EBjB+mT8FIjwUwNzHHT9xjEveQG9RrjCpL018GBj3FjRs3sGPHDmzdutXgz2VT5V2Y67IaY5L7IyfwCUfQZkZ//aYlj8DU5OGYU20VLKtYYjn3WMI9GFBUS45BN8pQVlYWDh8+jMuXLxvsiUWYRaOL2xikmqYj5Pl/qJ1bo0JeYKts4HDQOrz2+AHNLFvjE+5xmXv4cI9yb0JaGmNg0FPk5OTg6NGjWLZsGT755BPcuXMHLVq0MMhzuWv5BG09hsMzpxYSgm7qbTarpkBe602vPsWqpE/QzWM8VpusxlHu0QM9Kq6Ac/Mw42AdK0MbNmzA3Llz+aWy4OBg+Pn5GcwJkYv5fZfP8X3lvXwdnsnJQ9lVFolQ9XkSXjjdxT6nf+HLPd7hHoe4h9SlM6pZlJTExo1Br2FhYQEPDw+0b9++sEeaoSHVJA19XKfiuvUD/Bu+A10yW1foa2qXbY6bgXvwyC0ZHWx6wIt7XOMeNqhglatJEaLwBAbdKkPUaPXixYvcfJhkUIrQfctn6OA+Ao2zfPm1aBuRNbvCkoiPx4jXLTDENRnDbSfwxdmOcI9+3ENg5lShjxDrPM9gINi3bx/mzZuHXbt2YejQobCzszOYY//BYS+m11jGV4u+GLGHXUwJNAp3QLL1IyyrvR22prZYxj0+5x5MEWLQqjJUrVo1DB482HAcH9xjqssSbHc8gH0vN2J4ah92ZWUOlgjmEVE4hDW4bDMc3WoPQq/0zjgauVX5ztQMDDrCV199xf+tV6+ewRxzukkm2rkPQ4R5NCKCL8A1rzq7kNKQmYkvgsZgvt0otKjVDz+Y/ICH3MOZexgtcnKExtcM+qEMGRKeWAahtfsQNM2sj6yAR7BkmQhyo2NGC6QG3kUf13dh6dMQ/4XvqvBuegYGTWKrw+94v8bnvDfof6+WMgNEDjikmSIo8ARfdbuaczV8xz3e5x5GqQhRwgrzzDNlSFF8WO1LfOu4G79HrcfI1L7saioBK059PBP5C87aXEd3t3EYmdIXv0V/zUiagUGNoJpBrd2H4oV5JAJCT/FtNBgUwxevZ+GDxDFo4tkfa0UrcTvsEJzNXABaGjXnpjJra6HnmakpYGJg/MUUIaYMKYNw8yg09RgIj5xaSA66o7HOzBUJ3TPaIj3wAbq6jYG9dzNcffEHmmT7sYFhYFARe+2PY3TN+ZiaOBwPXx1lA6ICXPKdEB1yha8bV827HbZFL8e73LiWCWr5YW8PVKqknw1iKUaIlsaYIsSUIUXwleM2fOLyNbZGf47pyaPYFVQjyEt0LXw/fqt0BE09B2BB/LtYG/8xGxgGBiWQxz261x6P29aP8TDsKBpm+7BBURO+iVuI9xNHo6XHIGyrvB/nI37j+zVKBRWMpeamtIlBilG1aoJHSZdITwciItgFZcqQ/MgwyUQL90F4bZaE8ODzqJ1Xg109DWFsygD0T+2ORp79sK/S33jEEbk9874xMMiNh5b+aOk+GD3TOyIl6A5MuQeDelE31x0JwbcwosYcOHi3wOnwHeiW2Ua+L6ekCJtYMXJxAcy0XOCSypdQGRMGpgzJi9M2l9Cn9lRMShqMbbErWDyLFkBF38JDz/OdpitxRLMvagOGp77NBoaBoRzMqrYC/6vyKw5EbsaQtF5sQDQImgv+iN6Ef5OuoKfbRAxPeRu7o79WbCeSilENzsh2cND8gbNabkwZUhSUMv9z5QO4FP472mc2Z1dMy1gftwhjkwego/so/Jp+BEdeshR8BgZpiDNN4IN7rfKtkBB4E44iBzYoWsKbGR2QFHQHnWqPQtU6bfAo7Bhq5bkoviNqhkobeYuqVxeCsdWJ/HyhhhAFTDMwZUgevDJ9jcYe/eGUXxmJQbdZkLQO0SK7IXcNbqG9+whU8m6OB8+Pok6uGxsYBoYCHLU9g4GuMzA1aQR+iP2SDYgOYCuyxp3ww1hZ5Xu41u2MnVFrMCFlkHI7E3uLKEOtVi31xBYlJ7PO80wZUgwH7E9iWK3Z+Pj1u/gqjgXw6gMouPrOi8PY6LgTdeu8iU2xSzArcRwbGIYKDSr4OqrGPByqdJr3XnfIbGGcJ5qbW/Sclnfi4kp/hjwplLVFoNR2M900mf00YToGp/bkSxn87HAQ5yJ/Vd6bnZkJhIQI50JLaMpUOBcXUmQNr5kypAj61JqKc7bXcef5YTTPbsCukIawZU9lbN9fGXEJZnCrmYvJQ5MweUhyud+bkzgRb6d1Q3OPgThofwpnI35hwaEMFRLUDLqRZ1+45lbnPae2IgPpn0VZVY8fA4GBwP37QFAQ8OpV8RiWKlWEjRQcZ2fA3R1wcip638ur+BJSWhpw65bE4EQICgBtsbFAYqLwOnlaaJ+tWwONGgEdOwr7VjPq59RFYvBN9Kg9gfdm33v+F7xzPZTfISkykZHCc1L4KOC6PG8RNbsmTxBbEmPKkCJ4YR6FJh794ZvtiaSg26yStIZw4ZY1uo11w+zxCbh9uKjs+6wV1WDi54sLu1+gc6vMMvfhm+OJ5KC7HNGM44Or74b9yb/GwFBRsN1hP96tvgQr4ubg04QZ+nFQNPn6+wsKDv0l5UTc44om7po1gaZNgYYNhb9DhgCTJummQCHV1KFjPHUKuHgRuH1b8D7RktSAAUCvXpxGUx/TPquObX9URuvGmXirUzpOXbTFrUfWmDQ4CdtXxZZ56Obc40LEbmyq/At86ryFDTGLMSdpgurHTj0caSPQAdjaCh4jek6p8qQYUmwQg/EqQyJOgJctWwZPT09OObbHs2fP8Nlnn6l8ED9xxDK1xhKsfDUXixOma38USOsXu3RJiCUFmdzByclFn6MqobKsLbH1Qzc6uValgawk8Y1UVh8aIgZ5bigFXdFH8tfCXPQh1v7Kkc5vRa7vdSIL/IxXODj2MDqbzi//Z7ntPLdt/kAEv429sGEOMGdzOccp7VipCFrt2sVfI9K2KWFlW1gUtyDJMhO75ItJNCfSHhIWIJGrtYyGvWTZmjKvFoMCHMg9+tR6F+dsb+BB2BE01lZhUvLaPH0qKA1PnggKD3lzCBTsW7cu0KqVoOS88QYwYYJ+DyQpDtRPjrapU4u/R82iOSVpwdTX2BY3GQkuvnDs3BMYNgwr5tTC6yRTVG9fF9Wd87B6fny5PzU7aTz6pndDU87YPlzpH/wbsZMztdXkByCuJ+WHNoaKowwtXboU2dnZmDx5Mv9vapI4e/ZsbNq0SekDmGTxHna5nMH1NkCbmxu4VzZI/yBNfKSBKwKaZEtWHKXJz7McLwa9L5646a/k5ErPnZ2l39xUxEvPsTIbODsiH/YBGZg+KhFvdeSsrUu2+P53RzRrlImv9vbhFA/5G93O4ra3Q8PQfMM7OLS6Ps5G/MopShqOFaCKrbLSUl++BOILCJLW+2/eLG45kwIqTp0lq1kyFoKeS1NOKZCSlFhFkJBg2O5xio8IDTXYw/f39+fm2Km4cOEC/+933nkHy5cvR+PGjZXeZ6JpMnw9e8IzxxWpQXd5z4PKckzGFi1TkXJDy1Z37xYpOVQ5mThP7M2hpaVRo4CqVY17ViJjaOJEtK1lB3wI/DHzAqY1v8VZXpy1dfw49mVPQi6+R/PaNE7yGTPeOe5IC7qPLq5jUKVua9x+cQh+OV5MA2BQThkigmnfvr0EX9bAiRMnSn0uJCSEM1YqoXr16pzeUHaH4U2532BLsClsfrNmV0MLsOL4Vbw89jrRFFGvzPHFrHhsXvJKaW85rcUnBN3ki8zVqNMRj58f58vma+4krATPkDS4uLCLrCKoIeaXzt/hr/xTGICBMj+XySmbwcHB/PM8PQsOJcONFCAxBg8ezBtuZ86cKfY54q+YmBj06NEDbdrILtgXzz3qcYrQ2yldsCtmbekPkBJNyrX4LynrpEDTc1JuqAqyGBR706SJoOCQwUYG1rvvKm7sGTmGvJWGl5eCseCrapj5ZV/k5PbjXx/RJxlRE8+hxv7vOGE9KCiNw4cDM2cCjo5l7vNC5G58W/lX1PPqjV+ivsK4lIFsoA0Y2cjB3krHMRYzy1SLY7l78eeffy6wQbJUV4YWL16MRYsWYd68efy/T506hY8/Lp3tVadOHe4+byjXPh1E9oCIra/qAlUd87ktW01atTnuvziCxU7rUaNuBxx8+S0GpfVkg2xg6Ok6CVds7iAg5DR8anUGyrBRrK2tC+9zMx1lDsmCj48P0il+owAJCQlwdXUt9bm3334bkyhuphw4cY9Xk/sDR49yBDdGWMYlD4Z4mZf+3aAB4OfHFHJ1Oomq5eHXddH8Vhy1gGYrgZUrhX/euwdMny541ii4m5ur0KmT1GXwmUnj0CazCTq5j8YRu/+wP3ozG2gDRJh5JOp7vo2u6W14ZagsuHD35MKFC/nnBw4cUF0Zat68OU6ePMlbUmQJ7t69m10RhmJYFT8PA1PfQGe30eif2gMHOKJhRRr1H885YqG6Xo2zfJAQdMvgExhoSWw6Nzleu3aNj28kj9D+/ftV2+mSJcIky6B/aNYM2LtXeE7xO7t2AR9+KCxV09Li++8Xy4Zrk9WUT9Rp6z4M1eq044s0Vs9zZuNoIPjBYR+mV/8Ma2PmYcHD3kBn1WM/lVr0puUvBgZZaMsRTXLQHbT2GMITzeOw44xo9BjfV/4dM6p/jrWxH2FB4lSjOCdTU1P8+OOPhf/+66+/2IWuKKDMLlJ+aCNQPBYtod25IwRsr17Ne/FsRNZ4EHa0wJvdEb+/XI+RqX3Z+OkC5MWlJCRxcoB4uZmC6ZOLSr7kW1uh15EsXH7DCo9WjUbDCO57DZ4BHTroRhliYCgP1rDCQ87aWlJ1I080u19+jdGp/dnA6BGoq3oHt5HwtwxBSMi/8GJVxRmMERSA/vvvwnPK+F2/Hjh4UMgynT8fq0bOwZDUXmjrPhR/pP6Ng1H/Y95sdYISVyiR5epV4NEjQdkRx+1Qooa45EP9+kL83KxZpROfOISaR/DldxplN+OM7T0wHyaxNK+GZXqmDDFoFCtez+Fjh9q5D8P+1JM4FPUtIxo9wBOLIL69SrOs+ngdfJMVzmSoGKAA6y+/FDYK+j95EujRAy2jopDetQNabr8MlzrtcT/siHK9zSoiaCmSiniePy9sz54JY0sKDSk5VFiTsjhp2VLJJIENjjsxz2U1vo/+Au8lj9TIaTBliEHjaJnVEJmBD/kmipTW+vT536iZV40NjI7wRdX/4XPnb1Xr3cTAYOggb0LfvsLGwTImBg8/Wo/Pmv8F1886Y8uNiZhhOZtl+YkVngcPhAKZtJGHh0DlZEjZ6dxZKOA5e7Z6f5Z7dHIbjWeWIXgechYeubU0dopMGWLQDu9wj6sRf+Abx+2oVbcTvo35DB8kjWEDo0VkcY927iMQYhGOFyHn4JZbkw0KA4MYFAu7di2+xFoMDHuEDq1G4s/TO3G8HzdRVqshFLKkYGwbG+MdA1rSovIT5DG7dk2I16FCtlRShyqWjx8PzJmjlUN5aBmANu5D0SW9FRKCb8FUwysKTBli0CrmJ07B0NTeaOIxgK88fiN8PyxY6xWN44z1NbzpNhETkwbh7os/2YAwMJSBllmNkB50H292mYhK2fdxM+wnNDoVLtSDun0b26w+wLTM/6FZjWgMHWmOl7Hm+O1IJdhYi3B13wt41c7V35OjzgZU4PO//4RSEeJuCW5ugoeHKph/841Qv0lHWOj0NdZW3YZ9URsxPLWPVn6TKUMMWodHriuSgm9jTI35sPFpgnPhv6FTZks2MBrC2OofY5/DcW6cf0WXzNZsQBgY5AB5s6mi/l77Y2js2Q+Lhr2HVT12495TC0x7xwu/LHyMcdk/A/v28U1cv6tUCYOzD6HP+HZ49pe/0CZFV6Ain5cuAVeuCDE8VH+JKuyTV6tLF6BdO2DQIGDGDN30ppOB16aJaOkxGDnI5Qv5OooctPbbTBmqqKDgNirrTxkV4rRGLbeP2B39DaYkDUN3t3EYltIHv0WvY4G8agQVJWvhPohXPlMC7/IZfgwMDIphZGo/9A7ugkYefbGv0gmczz6IypXc8N3fdTB453TYvfce/7mHAZY4Ptgdo5qFCgHalCZOFdqpfxnVOKICpRRITF0ZvL2Ftk9Vqgh9F+WBuMUPpZ2LU88pcJmUHXELF+J1Kv5Jv0MV1akospVh3Pe/2f+FcTUX4KOEyVgX94nWf58pQxUNZK1QOqOkNVC5srDRTctZOJCo3Ktp9MhoxwdXU5FGG+8mfBZHvZw67DqpiMVO32C104/4MXo5piYPZwPCYDgg5YDid8iLUdJrQUs81OqE+g9qsTO8Y74DIkIv8ss3bo3aYEvgMjjvnYZOo9zwOMgKZmYi9OqUjnt/haF+XWpNs076jijLKjpaUGYoNof+RktU16Z+gOLzoorp4ibT1E+RUtCpWTVxeLduAmfrWeV3ZUBeoB61x+OW9SM8DDuKRtm+OjkOpgxVFBCpkCVSlhVCn6HWAhREFx6utUMjd/SV8H3YUekQ6nv2wazEcdj46lOWgq8Eos1eoaFnP1TNc0B80A1Uza/MBoXBMECTO7UyKWvZhtprkDeFNjLeqP+brKbNGsCa+I/wXtJINPMYCN9pB3G1zx7FPK6kvJCSQ5tEn8+KitM2l9Cn9lQMT+6D8xG/6XRlgClDFQHkJiWLQt61YbLIyI1LVkt2ttYOc1LKYIxMfZuzEiagct2WvJVASzwM8uHzqpvxhfN3WB+7CHMTJ7IBYTAMUOp6rVpS+4iVa+CRB4m21FTBw6IFb5FXbm0+5nG6y2ew8W2CHVGrMZHjLgb5QQ1W+7u+h/9sr+FW2EE0z26g82NiylBFsLaUaZ9CxESeJFo2o14/WgKVyL8avg/rHLfD06sHlryegeXxc9h1LAMxZnF8bJCdyAZJgbeF5scMDIYAMtKsrVXfj729YMBlZgIREVpRir6P/RIfJoxDG4+h+M3hCP6O3MYyY+XAMdtzGOA6HcNT+iAn8LHerAAwZciYQa7kaioWNyR3LllcEv1htIGPE6fg3eShfMGt9VV24MKLPWiZ3ZBd0xKgvkqrnX7AhpjFmJM0gQ0Ig2GAFCBK5VZ3JhPtl5QiCjQmQ07Dnu2GOT5IC7qPkTXmwtqnMQ6//A4D0t5g11cKqP1PL9cpuGB7E2cidqFbRlu9Oj6mDBkrSAkiZUgdoIBrWuumbAZt6nL5lfkmr//aXEE7j2F4I609/nq5FVawrPCX94bVA3R0H4XmmfWRFngftiJrJvMMhgHKYnXWcONmio0kz7aW4or2Rm/Aqrh53D05Eh+KluNW2CFUy6/KrnUB/rA/gRE15/LeIEqY0cesYaYMMUVI/n0StKwQEd7M6ICcwCeY6rIE1r6NserVPCxKeK9CXtok0xR0qz2OL09/8cVutMtqxuSdwXBAsUH2WlzGlYwroizZmBiNlRCpk+uGqJDLfB8tl7rtMSNxFL599VmFLhdC5T261x6PNNMMhIecR+28Gnp7rEwZYoqQQShEhG2xK7Dh1WK8UXsCljltxvHIH9Ezo2OFuKwi7jGu+sfYXfkotkQvw4zk0UzWGQwHpJRQfJAua95QoLaXl/CcFCOqzSPunq5GUPICZcQOqDUDZj718Uv0VxiXMrBCXW5Kl+/tOgVnbK/hyMut6J/WQ++PmSlDxgRyP2tKEdIThcheZIvr4fvxwNIf3d3G82rC1Rd/wDfH02gv665KhzGxxkIMSu2JvIBnGu/Rw8CgVlAyBikh+lQThxQjDw+J2TtHyEgjJYk2Wl5TAVQu5PjLHxFpFsPX0JnjshKnI3bwTauNHZ86bcAqp+8x9/VE/BO502D4iilDxqQIaXodXlIhEhc/0xGaZPshPvg6TtleRBOP/qidWwNnI34xquajOxwO4t3qS9A/tQeyAh/CksVKMTBFSDOgGCNx/aKyQAHZ1NaCFCfacsvuQeaaVx3+Yadw3/IZ3qw9EZXz/9/eWcBVdbdx/Ec3SCNIGFizxWbWnM4O7O7pdPZ01tRZc3N2O2fM+dpu5mbPmAG6WTNoAQEB6a73POd4nTqEexG4wfO9n/MZw3sv9574n9/TZhq3Tr1ar8wOY6TDLGm9enJfWK3Uq7KOxZAmQOXzJSWEZFAMngRRYqJSv3q7lA+R5ncPJ43/gLtbW1jmmONo2CY0SK+ploeSwmEkgkYJIqhL0kdI9b2rdosKw0h3F13J+6IBXZJfQcNLaSPPEjWIFC/aXKkjNo00ege1M6oiKuA6ThhfFNcpMt7Oh+yCS7b6i6LtZoLR5kDrVWukCOuVuha4sBjSBCFUmD5CRQG1hydBVIJ9iN5Fh5QWoii6K1hg7Z1GIUrnBX6K+BZ9kjqqxWFM0UrFIIfpOGx2WuzGmip6glgEMWosGqiaqzRA+VBkjNJG3fuppP8dfY46prQU1ykfg/vwoIGkWpli+EzdjLcs4THHehWWWW9F98SPNcJoYzGkzlBVhrKEkAzqQ/TsmeQyVgFqCRZYWOBlQVykoU/ZiejrOAVD43qIVR3UlFDVuK//BB2cRiNGJxZrn3+FQ+Fr+bxm1F8IvZ6PU5qQde8nj3l4+Duf5pFeA88DriFcJ0rMKfLXf4plUdMwMW6ISlefUYPXXsK6etnYB9NjRiLnySONGZvEYkhdMTGRylRVAfIQUddXsopUBOq7c+zZZvHnLeb7YF+hiZh8/U30NAxO6K7UpL4ErSRMsl2M7RaH0Sy1Hq6E7IFLliOf04z6o+joH02FhqmSsVrAulg22xYPg08hGzmYarNUrD5rldoIe8NXwi7bWmW+Dq2hE+0WwyzHRPxsrUMba9whYzGklkdNV3WEECEb8EoTlwtIKFQGoxP6iFuWsOTMtV4FA/cPYJJjLI76GBc3QBwBUtw80QvCTJvvxTBY1fQKWB01Gz8+X8rnMsNCSFOh/UBdtuPipMaP+aAjmGeromeL25+Gt9HIuReC9MLQK/ET0atd0sKIchd/MTmLcfYLRO/V1NjhiPXzgaEGF3EoLIbCwsKwZ88eXL9+HYcOHeITXhlCiGLxqrbg0Och1zgJohKYC1S4k10HS2Omihtd7IdNT+PDcgNwy+g+HLJsMDK+F4YkdEelzPdz8ZPo+s3kElaV2Sn22SC398CELqJXisNgJcu9e/dw6dIljBs3jndGcUKhMRZCeVOmjJRwHRwsV8l+07R6CAw6L/58R/8h+pSdhIvGN+GYaYcZL0ZjVEKvYjHg/tHzwzrL3fjR/JAozibGDoFv4BmVTC9QCTHk5OSEmjVrimLoXbx48QKRkZEwMzMTzgFjvhiKUghRmaqqLjhUNUKfLyDgvft0FLt2Ex5eSe3ETcZDPX/sNzuF3WZH8dDAX/ydUY4hqmdURPX0SrDPtkHFTBfx95GCtRSrk4AAvRAE6T7DPcPHknGcow/P1PoYmtADJ8O2anQSdFZWFmKoigakf1VTAJPxdv78eRZDxQl7hOQTixUqAEFBQHa23C+rnVENF0J/euWtOWJ6Bh0dR+MPY2/kCI8WqQ3QI6ktWqc0QeUMtwLXG3qPeO0k3DD8G8dNLuBX0/MI0QuHbZYVBid0w7yY8djwfH7pvL2+/Yv79+9j2LBh/3mii3Cyy+sJsrKygr2yE3s1DRIa5HlR9QVHJojIQ6TiguhtqmVWRLUXFTHrxZg8/z0DmcjV+vc76efqaUzyYOG0ue6r61xbWz1HDqxcuRIHDx7EiBEj0KNHD15nWAgV79pIgigkBEhLK5QBR8KHttfFDRlk54yuiS05aEyPn34wggUDLV373yG1urm6qJdWTTToGqXVRt206lgaPRVro74qFbs+ULgfjR8/Xvw5hZpqyiOGatSoAW9v73zfODk5GZnFNN+FecdFRKExdenXIfNgqaEgyte4I6srl09HTWLy5Ml5Gn+MnEKotFaNFRbZWBIqvy+CliQkkMhbLfNYM3lTXrgfnThxQvzZw8NDPjEkD15eXuLGlJAQImGhbpa3hgoiRn2IjY1FRkYGunfvjsePH6NKlSq8U4pSCLnwDbjQUEuSiAggIYH3harcsngXsBBiQcRoIpaWlujSpQvviOISQhwaez8cHKS1narNGBZDjIYKIRZEDMNCiMkfGulBxQfsIWIxxGiwEGJBxDCaJYQ4R6joIQ8RiUslDr5mWAypHrIpz5oihFgQMYxmCCHOESo+qCqTjOB8hr0yLIZKD3p6qtlQsSgFEZWWqnBjRoZh3oJ6xVHCL4fGihca9EpV2jTXjGExVOotL01fcMj6qVhRaj7G7RkYRvWFEI3aYUoGmvNInnMVGXzNYogpWWjoKllepQUSfOQBe/oUSE/n488wqoi5uZTPwpQsNHfy2TMWRCyGShk0t4YqCkobsuZj1GuD3cIMo1pYWgK2trwfWBCxGGJKAIoRW1mV3u9PgojcwpRLFBvL5wPDqALkEWIhpBqCKDycjUUWQxoOhcUoPMZICy/lTJGXiGEY5WFtLW2MakDGIlUWc9k9iyGNg7whVGKuy7v+P9aooSEQHMyl9wyjDKi828KC94MqHhe6b3CnahZDGgPd7J2duUT1XejrS5VmlFidkcH7g2FKClqXjIx4P6gqlFdKHiLuQ6S5YsjDyws+Bw5o/p7mygz5oAueKs14iKFSGTt/PoZNmoSGDRvyznhJckoKTMig0cTrjT3Vqg/lmBIsiN4gNT0d+tnZ0FE1MeTi4oIRI0bAmPpTyIF/cDAa9Oyp2UeLeuvwYqM41IeImzMqhbDnz3Hpzh25r2Mb2UKtwbQYNEizDDeeM6aegojuJcL1yUhMWbq0SAy3Ir9Dz5gxQ9wYhmFUmfHjxyv0fB9BHDKM0qF2LLQxIhv37FHsOvbxKRkxxDAMwzAMo04oVQxlZWUhMDBQDK0ZkMuWYRiVISkpCaamprwjGIZhMVRcdOzYEbNnz0bTpk3h6+uL0aNH48KFC3xEGEbJZGRkYOLEiWjSpAkGDx5c6vfH48ePsWDBAkyfPh1btmzBhAkTULVqVT5RGEbJPHr0CPPmzRP1xPuuVUoRQ/fv38fly5dFIUS4u7sjJCREFEOtWrXiI8wwSkSfWhwwImlpaahTpw7Cw8NRpkwZrFmzBg4ODuIa5sDVoQyjVMgosSqiKQ5KEUPVqlWDrq7uKzc8hctiYmJEUcQwDKMqBAQEQE9PTxRC4oIprFv088OHD1kMMYwGoRQxpKOjgzt37mDKlCkYM2YM1q9fjzNnzqBcuXJ8RJhST25uLq5fvw4tLS1Ur14d586dQ4sWLYrMAiqIoKAgPHjwAObm5ggLC4MTjY4ppdD+b9OmDa5evYpmzZqJIX06DuzBZhgWQ0WCs7OzGH8ntm3bxkeCYV5CQoTydcaNG4d+/fqhQ4cOokAqKdzc3HDp0iU+EC85fPiw6L329/cXiz1u3rzJO4VhBPbs2SMaasuWLUPZsmVha2uL27dvY8OGDSX2GTZu3KjeYohhmP/i5+eHe/fuiaEY8kJ4enrC29tbNB44LKNEq1FXFxVpVAzDMK/o37+/aKjduHFDzPmVt0mrSl7jfDgZRnWoVKkS7OzsxEXl5MmTSExMRIMGDXjHMAyjUhw/fhz79u0TK7lojaJQcnJyMrp168ZiiGGY94dydWSYmZnxDmEYRuXo1KmTuBF9+/ZV++/DYohhGIZhmFINiaE6wqbNu4JhmGIgkXcBwzDqIIaCeDcwDKPixAsbj1dnGKbYxBDDMAzDMAyLIYZhGIZhGBZDDMMwDMMwLIYYhmEYhmFYDDEMwygTQ2Hz5N3AMEwxkCVsF98WQ3HCZsH7hmGYYqAMpEowRbETtjO8+xiGKQbiX65Nb4ghhmEYhmGYUguLIYZhSgVpaWm4fPky7wiGKUW4ubnB3d295MXQxo0bxQFutWvXluv527dvx7Bhw1Rjr6WkAKmpRf++WlqAhQWgo8NnJqMW/Pbbb6hVqxYcHR3lej4Nlf37779V+jv98MMPMDExkXu98fDwgI+Pj2Yd2NxcaY1LSAAyM/+73ukKtwR9fcDUVNzuPNDFtm1AaChgawv06QO0bs3XB6M8xo4dK17DDRs2LNLruMjFUHZ2Nnr27Cn3gmMqXHCzZs1S7t5NSgKePSv+v2NgAJQrx6KIUXlq1KiBJk2aoHz58nI9//Tp0xq3D9RRCMXGArSc7t8v2XaWlsCIYTmYNzwEutnpBb9BVpa4RYWmoWIbM7g4puH0jgg4VjVHgo4lRo3WQps2wIULQIsWfJ0wJQ85XIoDpYfJlCqEMjKAp0+BnJyS+XvpwmLk7w9YWQE2NnxWMypL//79eSeoGf/7Hx03YPNm4YaxVhA14eHITUnFhEW20Kvkimv7gtG4Trpc77XrF3MkpWjD+2AIjAxzgehomCMa+5bo4I8Lbli9WofFEKNRlM6cIXIVkycoOVk5f//FC8mEc3MD9PT4LGQY5r25dEmwsaxzMaqlHxCQK/6OIvQzP43But2WuPqXkdxiaPzAOOw4bI6ynhWwYmYUmtZNxT9++pi0xA5ZmbnYMFUw6uKsgTJleMczLIbUkpIKickjyAIDpcXEzo7PRIZhCk9KCtZOfIaHtxyhU6US+nRMRKPaaTh+wQTnrplguFccpg6Lk/vtDPSBe8efik5zn/sGuPa3EdwcM/HotyAYG0pCC8+fA1FRAOWVmZjwMWBYDKkNYWHK8wa9i7g46TO5uHAuEcMwikEJ0JTdLBhXutrAxd2h4q8zsyh/UwsTBsVBW7vwb0+vbVgrXdzeadTRukprl6urlIDNMCyGVBSqmggKki5cVf18lEvk7AwYGfFZyTBM/lCiM4kgynvMAz1d2kpwvcvOBgICpCq0smWl+BzDsBhSIaiENCJCPT5rSIgUMuM4PMMw7yImRtpUEUpDkBl2VD3LMCyGVABVDIsVBMXhqerM3p7PToZh/oXWBTKYSqr6tbDQ5wsOlur6qTkRw7AYUuLFSCXz73Ahqzzx8dJnp55E7G5mmNKNLC+HGgcVBWlpwI0bgJ8fNVOSvOeUAG1oKHl0qLdU06ZSYvT7QBWziYlSPiTnEjEshkoYEhFklahqfpC8UGIkfQ9KSmRBxDClExIT4eHv9x4kdrZsAXbulNZHEjr9+gG9egHDh7+5vlD+4sOHwL590kaCxtMTmD4dqFJF8b9NuU2US0SebgueB86wGCoZyHIKDdUsYUfl99SP6H1KQhiGUS8oIZm82yROCgO9butWYPVqydOzYAEwbVrBr6O+Z7VqSdvkydLvSIwtXgycOQM0aACsWqV409jISCmfiLxNbNwxLIaKEWpkGB2teUdIZlnRgsal9wyj+ZA3hvr3FHYdHDJESmKeOlXy8ryvIUXVYevWST9fuQK0ayclR+/aBVSqJP/7UP4mrWVcgs+wGCoGKBxGlgtZHZoK5UDJPES8iKgPZJ2Td4/+K7PwyfKmjVoosLePedvwodA4eYUUxdcXGDpUygdau1YKhRUHFDK7dUvKYRo0SPp7O3YAlSvL93pZCb6TEzdqZFgMFakQov5BhXUlq6MgIg8RCyLVhBpoUsmzojczEkaUU0HTwpn3IjY2Fg8fPhS0QFP1+uDkCSKPkKLQ+TZ4sLQ2kKfGw6PAlyQkaaHLWCf8cdMYtpZZgjbPxbPnuqhdNR2//RAGB1s5zl8SM+fPA3fuSPlHdP7+9BNgbS3f5yYxxdVmjDqLIT8/P8ydOxcVK1bEokWLlPfJNSVRWlHxJ/MQ8Uwz1YBc/+SZfJ9yZ0qWJ1EvE0YUlmDBWyh27Ngh6IMY9RFDhc1zpPNtwgQpj+fbb4GuXeV6Gel097bl4VEjDbmPn7zxb6Pm2MGlVXlEX/eHuamc62rt2pKniIQQ7fMRI6Rk6zy4eMMQc1fZ4FGgPgwNctGqUQoWfvkMro24SSOjhmKoUqVKaNiwobjgvPs6zREuumzh/NaCdnGEAlS8kWI2chCqGw4/vaeI1Yl/49+qZJSHXbaNsFlBC4VYAGSCiDxELIiUJ0rp/Kf8jKKGhBGFESg/jForqHDjulxhP+S8FIG5amKULFy4EJs2bRJ0xAQMGDBAeR/kfdp/nDsHfPYZ0K0b8M8/+eYSpiEdl4y98ZvxZdwxfIQrhreQEZ2Jk8K//Wf12S/9p3qmvbA+WePjlKZoldIYrVMaQR95ey1zhMM+7Et77PplISwt5sPpQCgebnMSnT7ndoSiVtUMZAtf1a1leZib5eDavqevhBbNPKvW0hk9OyRh134jNgCYIsPX1xcDBw4Uf06SM4WmWM4+EkA6xZXsqyKNFHOFxy2DB/jZ7Ci2WxxCvE4SjHMMUSu9KuqlV0fj1DpwziqLJql1/3UiaKeIAumC8Q081g/EXwb/CNtDpGmno2yWLXoltsfAhC5okF6z4A9AXjFOqi553ie5VSFFnS0dY7KYqU+LCooiMnZk17mWmlj25NUeNmyYcj8ENValkGphjEAvL+m/x47lmadz0vgPrLD8EedMrkM3VwefJH+IYQlemB/zOcxzTV9p+WnLbLBqh6W4fGhp5SIjUxsDu8Zjy9fPYfRyEGusdjxOG19FT8eJOGN8BWlaGWiWVg8zYkahc0pr8TnthjshMFQPWQ+fQEdm9+5dgh/nBaJ21+3wPhQEC0H8hEbqYeeU8Dc8Th410tHloySc/9NIMgDII2pmxmsM8964u7vjBvXSovNMjtBxocVQjjI6oFJeEN0clNR9lcTPZUMfTLNdBm/De7DNtsLk2KGYHDcUK6NnyesyQuVMQcC8o3fac50YbLbYCy/HzxGiG4466dXwXdR0tEltmrdlKfMQsSAqfsiCp+6/hUlufV8vFJ33PAizQCIjI5GamgpTU1Ph0ggULo3yqvUBC+vRpnOAQmE//ghMmgSMHfvGmvG57ULsNz8FuywrzBNEz6/PNsIk1zgfEQt8/2W0uOWHZY4F+iR1ELdXniatdHGNKmf/IZ7pPofh7K4wmrkCcQnasC7zcm3u2xe+YdbQ2pIDo6nj4P7rUuxcFo4hM8ri+x8tMbJXAuKTtLHh5zKIT9TGjYNPpddRuJmuM3nzjhimCCnUyjqVSjZLEiqZL46QREGiT3hsNz+EL22+R7xOIsbFDsC50J0wyy2eKghyTc99MU7cJMssAcstt6Gz0xjo5+phUfQkjInvCz3osSAqSTFCPVLoRqZMZFU45uZSsirnWPwHe2G/zJo1S/U+GOUFkUc7n1AiXcoPfPVFkVDJJRP2NtnSIX70COjfX/IO3r0regjjtBMxyn42Dpr9jvppH2Bd5FfYF7FKsc9EuWmyrtMUbqf1g6rZSIzQ56Vmj3kIf8NcA0yMGyJuxIPqvhh3rS9sjLyhff4j6IzehswAF3zcNAXhVwNhv1Y4X+vUweANGzD4cWsxrJaWJp27c8bmsaZT+JlCxRQiZhhVF0MlBpVtkjVewvkId/Ufo2/ZyfDTD8a0FyMQEXAVOih5sWGZY47FMZPFjVheZhvKVPKAdXYZHHm2HvXTa0irKPUU4RyioodmQVFehyrlw5Aoo41uFsbGfIxUGTpOJKTzOX8eB+qhTldXlLXNwuwxL+Bon4V5a6yxZb8FBpsexs6U3sDmzUDz5jhufBG9HSfAOMcIuyO+w4HwNfJ/Fhr+TB6X/IwmqmakjSbP08BomTFAaQkUGs6javeDDHdcDN0t/vyn+1/o9aghYnTi0PP5HNgn9JGaPVJfIgpN9uoF7UWLYGyUW7B4pDWNCkXYyGNKtRiimxBVWJRgSILCYPOs1mCR9Ua4Z7rh99BtcMtyUqndMi1uhLhF6kSjs+MYMVw3PN4Lm59/DV2qRuIqs6KjsHkdJQVdHySGqMSZvUSqA4kHCoWRZ0UOxn9th2b1UnF2R9ir37XXPYuhBzajadI1dNnshz+8vsJay1Hoktga4f5XYZErZ14NeX4cHN5PUNC5ReKINvpulDP3jua2TdPqIizwMtKRgQl2i6DlUAV9EzpiZ9Nl0P/rL6BTJ6BFC+D48YJzg2SeUF7TmFInhsjDQS5SugGVoCVO1Ra9BGvruMlFDE/wQobvfWGnqLbDzD7bBjdDDooCborNUui710DjtNo4FbwNFs4fqHQFksqjTkN+yYKmYZs0XJPCHYzyBBANVybviYJrV/c2SRj3tT3W/2yBcT0ixEaGUffCMVr/JHCwE/p0OoWvoyci98lj+d+UPEDFkXdDwsjKStqoQufZszyfZgB90UCjbYPFHhi610Tj1No4evEQbKYtBRo2BPbulcryC9qvlAZAgo7Cwwyj0WKITnYlNE0k66WH43j8bnIZOyKW4dizzWp38Kg0n5K3adtmfhD2FZrAOcsBFzIuopx+eT67FVbGaZIQUrcbMX1mstzLcr+WEtvndK5QHuN7VrZ+NiAeI3vHY8WEILT+WhfRFU7h3rHR0OnYBLvDl2GA7wr534zmhZFQKQnofKNqtgIGyX4W31/cThtfgXOFFnDZ54jfN0+EW+/e/0kGfyfkaaP9TOc3w2isGCrh6hyqhvAq+7kggq5gl7DYnHi2RSMO5IiEnuL2u9FlVHaqjur4AOeEhwV4UrRckEeSQmPqClnqZFhQxRnnWRSdOJYlFMt+LmoEIaEvCINJWUm4/NgR/7gHYncEiaCVbzzt/hN9tB3uhPAoPZRzyERSijbiEnQwqnccNq/NhJadkjo5U7iLtgI6aLdN8USq310cNjmNCp9PQKMONvit/ipYXL4M7N5d8GgaEl10DOj85jE2jEaKoZIy5oRHX4fJ2G92Sqy+0BQR9DbtUj9Eit8dbDHfB0v7Muis1QUHhcerCjQmzxuSvDkeKg1VA1HiqYaHFaiha0hICNwon6Q4obys4mrlQUYgdWo+cQJTt1pgxYgUfBnTGid8/1upS0nWNTu7Ye3cSIwf+G8T1yw9Q3zwiTM+6qslTsZQKjRWgzotkpeSzsN30CO5LXJ8H0nFIPHfYvSmW9jUvDm0KI+IkrzzgyIIFBYmQcSpAExJiaGbN29i+/bt2Lhxo9p/ydUWOzHZbikGJHRGpu8/wpfWfMt5dEIfjEoQLE7bJdC31MdC4TFHeDCvK+SXISZK2NckKKxAlUwamly9YsUKlCtXrvjFUHFBoysWLcKxPqbwytJG47RKSPL9ASa5Rnk+3fhlE8TnMa+tW8L3z9QyFg9zhQqqcjfRlT6MHK1QqBDk87hB6DtgMnRHncUPo5pgWPNt8g2Ypb5bJRkSZEqnGMoU1PexY8cwb948zJgxA7dv30a9evXU8sv9pf8PGrn2hlumI2L9vOWvwtAQKKdoddRsLImZipbOg7DUYCmOCY/WaM1nvpKbeBY7FNqhSeYaNh08XRCuR44cwdWrV9XmM0dG6+Aff33YRT3AB3O9EFrREM0jTZBkpY+AoBMol+WQ7+udy2bh+TU/eH3uCK0qNq9+T1XwS5ZQ3zcV+8IkVCwspHl7+SSUU6L1kfD1eKEdjzqbu2JG7DBcPTQF7h99WvDfIMFF5zhXUzLFJYb09PTg6uqKJk2avJrtoW4kaSWjvdMo3DC8i7Mh29E8rUGpPsgmOYbwDj6A+9bhaGrdGeWFx3XhYQSj0rlDCjscUx2hZn8aVIK/cuVKTJ48WQyV+fv7o0qVKir7WduPdMTZP00w5aO/0ePMWJyy6Y4G6wYidegWrAtegnFxXnK/l611Li5d0SEFoR5QOXylSlLFWQFJ5lY5FngaeBH7TE+i8pjJ6PbCB4djthQ8u1HWj4jCZlx+zxS1GCL27duHKVOmYOfOnejZs6dgWKqPZbnZfC/GOMwTu0VfDt3DR/g1asSURULcX5jnvA3G+saYJzzmC49SRUnNFlM18UdeIupcbaHeCfUjRozA5cuXER8frxJCKD1DylfXfSvy/v2PZfDbZVP4m9REhSsBuLNvCuZ5zUet9MqIdI/HhYpaGLc2XL4/QseMjp26QeKbRHg+ZfivQ2M/vP5pjd7Cf3UaVsPRsI3olNIq/xfJuvBrwLnNqKAY+pbm4AhUrVpVfdZ7rTQ0dumFUN0IhPpfglO2PR/dvBAs6gVBQzFVpzfqOXfFZv3NuCc8bGCj+d9dlktTWqFuyCQEqS+Rmiag2traokePHkr9DJe8DdF6sDPsbbIwuFsisrKB3UfNERuvjQu7QtEk8TR6rlmOubiNz2r+AYfjn2Kn9SL8L3QV/v56IJb5m2PpuILFgaiyaAyHuns9qAy/YkUpbFZA9bCuniEOW57H1W+/QMvJY9AuoyWOPdtUsJeIzm0qguCwGVOUYkjd2Gj+P3zmMF/0Bq2NmlvwhcPAPNsYfkFnxK7btja2WC88PhMeGgslSlNpbmmHLGnZ4Ffq28IjPRQiNU0LLQa64Kvx0Vjw+b9Jwt+NCcCXY+PQqm8zRDXYA9eLu+BjdxH1nHrCOrgGKjRMwiozbQzonICMB0+gV9DKq2kJwnS+kSAiDxF5igqgWffvkPSlM9p3XA/91h/gXMjOgtMdZGEzNRb7DIuhQkE9gxq49MRT3TA8CfxdHKPBKMaCFxMwLm4Aarl1xrLcxbgVfhw2xs6Sy5mqQ9TdypJ1sc2n3LdUQha6LG+KLHe6+VJGLoPHj4E9e4DYIBuUd8pAxxbJqFxeagxrZJiLxrVTsXWfBSYOiIHVT2vE2WHPsm3xM26idi3AbPcmfG77NdaV+Rn/C1+BvjkdgVNh8v1x6iROc+c0tZeOo6PcPb0MxkzA+T89cKHVMLQ6NxB9kzthd8Ty/I1dmdi3tcXqXZZiX8caNcSxaLh2DTh9GvDwAC5dYr3EqIAY+vlnYMgQ6T7laOeK0AhdGOjn4uCaZ+jUKkWu99hregL9y07FqLjeuBd2SBrlgXfE4KnnigZV1BQ1djnWiAj4E1NtvoGtSz1sjViIkYG933wSLc6ySde0qYPrnirGCqhoYSBZ6nlZ6xSiKUVjPmgUFqUh1a1LeZNA+exoPPTVQfdxjggO10XA2UDYvXiMa2Un4sKddHRovx434tZDR3sdPBukYuf4GLh73oSVa1e4Zjoiwe82zHIVWHdKy/Bd6idEa4k8Q5CbNkWrKn8ipVwntDhyHKYNz+La0/2olZF/vtie7amYNNUSf/4JNGnypg1AjbN79gSOHeNLn1GiGJo3D1i4UDJKyUiAX7CYy3H7aAjqj+mH1ZXXYULmCsmafx26eCwskG1jhVabn+BWJT3c+3YQPoggV/I2qelXXo3mZAl2MihvhNyplEhLG10ddMOk573db4YEAE2Dpw9Kf596aFBogaoXqlWTFi4Nsqa/j/4Sn8X1R33X7thqcQB/hO6GYa7Bv/uRqkLergwh9ze588mTpErWrJxJmwwjY+lSSeffvClzEWWj2rM/cMPlF9j4H8CK1ifwTfcbwNy5aLXaBtfFJz159fpvy2zFR3bLsTFiPsYk9FNMHND6VZpyXcgtQ2Ez8uIUNI7J2hoGF67i+pgx2O30B2r/3AXTY0ZiWcwX73xJzcoZ0EIu9m+JQ5PaBq9E5h9/SH9y2DA+39USul+TiKb7cBEbaiUuhmixkc01FMXQyZPil4vMkKoGTAYLkr1X2zxfe0//Meq79MDHKc2Q6LcJ2t1L+OZLYomS9OhgnDkj/ZeuLPovqTtZF2PymlB1A5WW0kGjgYT0s7u7ylvaFbNcEOvvgz4Ok2BeqR5Oh2xHy7SG+Z+clJQrq9CiRY6+uzK/JyVTxsfzwsEoxNdfS/NDySG2axfQ9K8zOPuHHobcOgRbey3MPNEBMGv/n9elaqWhnkt3vNCJR4j/HyiX7SC/ICBvUGkdnyIzNuXpAE/P3bIFA4UD09liMWrc+wH73E7hfvAxmObhfSMxlHzHD4s3WcHIyhBp6ZLWbNMGePhQWooZNYPWdFrbNcUzRB3oaWgxnZSS4T5B/L2jfSa8DwXDo0be3YAn2C7CWsufcDBsDbyS2ynPmqGN8isUaURJZc3URp5azt+9KyUlyDwsNF26ZUvJP9+8ubQSK3lxpJj8/ojVOBv/Jz52HoreiR3wc8Ry+QWjbNgpWWMkjEoqpEbCjMQp5wcxhYDsFronUzrLlSvADwm9YeGZjcD5wTA1zjucc9roCtqXG4Vh8T2w9fki+Yo36K5MSb6lKARZ4I6ntUKeG93gwbAQbiAh7r0wZUkYzKbUw77wlWI5/ttQfteiSTHi9spIVYH1lVEQWR5YMQ90V0rOEN37w2T5hCQS8ukCHK0dKyb3GuQYINbXG2Vy1XDmEpkhtLVvn/e/y8ZCkA+XBhd6ewvmZqp08VLAu3FjoHNnwM6uRD92m9SmiPe7Dc9y/WBVoaFghR2HY7YCn4HCkbIQJYXSSPgVVyiASuYpBMow7wldZmL1fq2EfNemUXZz8KPFQVwJ+R+apNWV783JHU4J68ybUJidxCHd9AqCWr74+GCFcJAG7vZDs6uT8ZP5URx9tjF/MUo3U6o2455E6kMJDtBW6WqyY8bn0dVpLEbF98Hm519r7gEngUB5SILVI25v8+iR5Le/eFHyMpHLuFUrSVy1a1eseUvGuYa4HXIEiy03wanih9gR/g2GJHZX/I1oVhFtJPAoNFBU3iLyAoWEFLvVwDAyorRfoKZrZ1jnWCDO75Z8SdI8S6tgyOtO6QTyeAHouSdOoN733yPOcgua/HkBZnXr4m7QMVTIcs7/tbIwuiZX7ak75CCgdb0E26GopBiiCfP9HKbgsNlp0epqmlavdJ8YZAnRNm3av7+jkNBvvwFDhwK3bkmLQ8eOQL9+QM2aRe6BmR07Bj2SPhZbGfxofggXw34qXD8nWuSKwltEFju5F8mDxjAlxEHT39DLcSK+eDES30Z/UfALHBzyLuxg8obECQ3gpTwiOfoR0WA2gzZtcLtxf6z6LBUVV7fB6udzMCFuUP6vo5ssRSVKSwWfOkHHRpZqUYKonBgK1YlADbeOcMqyF6wuHxjnGvHJkRcU9ybxQ9vr3peDB4EJE6TFhPz9n38OdOpUJBd8tcyKiPP3RutyQ2BWqS7+DvoVlbJcC/+GMm8RiSH6rHTTKEgY0YVC3409QUwJ095xFC4a38DtoCOom1H93U+kc5jyYDgcVig2bNTCtm2OiI7IhLNDFob3jMdwr3w6x1OBirc3Jnl5ocPJANT9exEOmf6OC6G7oI0CPD9U+ELHiY4Xd65WPkosflEpMbTN/ABG2s/BouhJmB07lk8MRSFPy+jR0kaQq5Gmew8fDvz1l5SvMHAgRvtPx9ZDVmhQMw1tPVPw+2Vj+Nw3xLAe8di25Hm+a4Ku8LgU+jNWW+yCe4W2WBk5C5Pih7zf56bPSReBLIGSPgCJN/J20b+RAGIPEKMknuqGo5ZrZ1TOcEO83y3o4x0hXjpf6RrjoaGFghohUj7pxImSsxu0n5MzMGGsAbSqVMaln5/iQ480PA7Ug0cPF9GJ1KFFstjN+5ezptDWeoIzdaYiwXw1Wp/zhlnzevgr+BdULqgZL3mguHO1cpG1uClgXIvGiyEKi7V3HClYXTdxN/goamZU4ZOjKCBR4ekpbS9Fx/QZudj6qzViYYEymcLCXXcKFk1qgRfx2rBvUhH2NtlYOjWmwLeeGD8YHVNaorZwkzhidgZnQ3cIS1cRnU4kgPLqacQw+bB9+3ZERUUJOtoY5ubmGJxX/p2C/CAYaKMc5mBx1GTMih2T9zVGPYIoIZc9C+/F0aNS0/tly177pYkJvttkiB8P5uDQaVN41k9D7S6uGN0nHmvmvDlwedb31mjywwpE/fwJ/mjXFWtGp6LKmnZY+VwOg01WsaSuQ3HVmODHaRgyKAeXb1UQDoMWDA1yMKpXPJZOi4aJ0ZtVnNGx2vjrH0PYxWvB/YOijXAqdPd6/PgxRo0aJSj4S+L/d+vWDQsXLkRNylEpJHHaCajs9jHcMp2Q5PeX6Hlgik8cNWpjCvwK7P/6MUZ3jgBWrQLGj8e+jGHIwibUrSy/AKmU6YJkvzto7jQAlhUb4NbTw6iSWZ73s7oaZ8L9YOb3Nli5wxJZWdKNnSKX69YBgwap9mdfunQpIiMjhdN5lfj/tC7NnDlT/H1hGWM3D1vM/ocbwQfQML3Wm/9oZiaFdrlMu8hYvBi4cEGKWo0RdGfbtsDvvwObNumgTh3g27nC2pQF1KuejuMXTDBvfAysy0jVfkkpWjgm/M7VKROW9SoAf/+NCSNHokOlP1H37yU4bEZhs5+ggwKOF4VoyFOkCQNy1YCFX2Vg3iIDnNsZilaN/vX+f7ncGqZ1KuHO0WDUqpKBOaussHijDbzaJopCOChIC8M+FQ8zTp2S6ohKVAzNnTtXFEAyaHr0xIkTcf78+Teed/LkSXFhat26NRo2fHfDvhjhUVUQQh0Sm2Nn5DI+M0oAr7bJeHbFH9O/tcX4r2sjM2uH8Nsd6NM+AeHt9sJhzWxgWoBUrTZjhtQUrQAuhf2MdRY/oWr5T7Ar/FsMSuzKO1rNSEzWgkvLCmhWLwWJ9/7BfosTGGg5HonpxmJKxs6dwNmzb77m+fPn+PHHH8Wf09PTlfr5b926haZNm776f1dX11ef7XV8fHwEHWOGWrVqoTLNZchvoY6ehJWRM2CUa8gCqASgCJUUHpNSCSk1cMECYM0amdPNWRy79Oe+EJy4aCx6iMIipVuYS9ksLJ0ajX6dXjZvpGO0fTsqHT+OWKupqO99Cw41muFB0Alx/FD+VkG2VORBxR3W1nxgisXyksJi97xt4WSnBc/6b6ZB9G6fiGVbrXH3EVVK54pCaNeycPgNX4x2Nuvxa84vuN2rKz77DPj0UynC9oaTJS5OWK+kBStTzvxShcSQu7s7UlL+nR0WGxsLJyen/zyvQ4cOGCZHv3Nr4REVcCPfXh5M0VPWNhs/fRchbm9SD2h/SvqR8neWL5cG+FDFxaxZUkD/HaWo4+MHoWFaLXi69MdRk3M4ELGGd7SqQGFHGj1DrXep4SdV0VBI4J9/pF5QAsmwQzzC4R7yNaxclqNFemMMxHgxakCTZ548+e/b2gnC4MsvvxR/PkiJ+0pkwoQJWL16NaZMmSL+/9WrV0Uv9tt4eHigJw2mkgPbHEvAwlwqi+cS7BKF0h/z7ERA4sTEBB1bPkXopcCC36hTJ+g2aYI7rTti1tRYOMxqikPP1qF78scFv5bmXZKniNqesAAuQssrUVK6AruXR6D14HIwrOGOFg1TUcklAxdvGsM3WB/LZzzHwK5SRWH9D1IxuM5gGBudxZN1E+E+sh32/SrOSMbYPNKLy5Qp8+o6/+abb4peDJHrecyYMbh+/TpMTU1Fj9CBAwf44GoiFDf/7jtpo+Rlmq47daokXEmKjxz5n/5GDdNriwmmjVx6wbZCY7FJo322De/L4oQ8MiRq7twBbt+WTGtaxEkA0ewbWshpTDdVy1APFy8vycPx1s2dBkgszl2KWZWXQ3eWsHhcHQ/PdANc95Ze7uOj2ruhefPm4kYiKCMjA2vXrhVOz/fsv0X7i1E9qDmjbK6ZPN3mSUAJ96wlgnDv2ugIPrw8Hp3N2uKgYLAV2B6E3p+Sq8kjSDPkmPfjrdEr+nrAlf+F5vuSoLvH8Pj6F2iEOqj7WSQG/W0G/b36aNde6rVbVDPYFRJD2sICumXLllf//+uvv77/J3h9wZENA6XFXFjQGBWBhtSS+KGNoOaPXbpIixHNVZk58+WgOYghhbvBxzDLegUcKjbD/56tQN+kjrwPC4tsMCFND6Xu5NeuSTkNFFOg6hfqTk7bRx9JPacKQY7waOc0HFeNbuN+0Al8MEy4JoeFvZxar14WcbNmzficKQ2Qp4YGZ1N3YupSLA/ffINGN7ojwWoYGlw7DdvqjfEg+IR8Bhv9HfIS0TXHXsLCrWOKVou9eIFNJ7pg7MIoLHs+DdPjRgGz6VjHvVyb1HxQawFqS7JaaSPIhU+N9XJz+WRSJShcRhtBN2rKfKT4LFXVzJ8PtG6NJTFT4JXUDo1cemJ/0ikcCl9buCaNpQE6v2mUCGWPkuARrFjx3KcETqoE/OQToEYNoFevIl+IA3VDxbLxGhmVkSAWMHA4gFEjyGNDJUXSoMuCadQIhj73cG/IEMzp7A2Huc3w87Pl6J/UueDXkheWQszkZZXdo5iCobUsNFQx7fTdN2g6cjsezzdFQMBZlC+oq7jGiaG3oZOcZnqxKFJdSKGvXy/9TIlq27cDlEeSmor63bsjZdJ51K83CnYVmuBO8FHFZptpIjROhaaAyrw85A2lIb00e468O337lpjlubLMDkyxW4pNEQvwaUJfPpcZ9YTKzxQJm5FXafduLDp2DN3rTUPjG9NwwOw3HA5fJ5/BJgv1cKPGgqEoT0yM/M8XxOY/X/VCk3MpqKPXAC/85WicWSrE0NuiiEoMoqP5BFNVyJPxetPHhw+hP20m7l3zxVfzAad5H2JDxDyMTeiv+fuCxDt5eiiUfPeu9DsaqULhRaoDlaPAoLjIFB6ezv3xSD8AQQEX4JrlyOcuo94UJmwmGCD1BQMkrUZPeG4/C8tGDfAw6BTKZtsW/FoKVZOXiMJmRRyu0QjIyKPZYopUmc6fjwWV/of5Pij8DEyNF0MyqLyAGp+QBaDETpWMnFAZ0o4d4o9fCxdH1xsX0LTBRPzy9wKcGGQJ3R69pFlqjmp8M6aqu+PHgXPnpC7ftAhQHhwJHhI+/furVI7BPf0naOjSE81TPBDr7yPYXGzZMhoEhc3IUyRvWEYwtHWOncS1nTvx/aElcPzeE+siv8K4+AFvPI2CEodPm2LJZivceWgAA4NctGqUgpUzw+Fey0gqOGEvkQQJILpHy8vTp0jv0x2NzyQhoLYpngYch3NW2RL/2OrX4ZBalJJLVIkzTJhCIAiC+pYfIcXvDto0HwqzyDvwvloXNX7YDhw5Irqdt7otwuig2ajj8gI9e+Tg2XNd7D5qBiPDXFzb9xTly2Up7+K+f18KbVEXuIAA6TysV0/MQRCFz4gRKn8IvrRejmVWW7EvfBV6J7Xnc5LRTCiSQAYJ5TPKW4gzZAimRnVAT4/uqHXua7Hz+M2QA9ATHimpWnBuUR5VKmTg8s8hMH7ZFfmvf/RRo5MrBndLwNbFflLKQGkf50GRG4rgyMvmzTh/ewXaRAFDE3rgL/+lSvvo6tvumZQ4eYnIFceoDdQBljrB7jU9jpqeYzGz+qdYMtsHfz/Uw+hu5bFr3HUM0vkfcOCQGGpaL1hbPZIOor1XMzz6codU5019j4rKCiOTjy5eEjtUnk4blarLLmjyRlKFUvPmUrXWpElqt89faMehvmsPZCILsX7eKJPLU9QZzTe+4OYmhcwodCYPtrZw3XMF8V+uxIBmm2A0oBYuhuyG2aPGeBGvizF9o14JIaJu9QxxNtplH2NpHSFvSGkd+krfn8SnvGExqhr38sLABYHYt1xH2M870TytgXL9LGp9AKjkm7xEdBB4irl8kOVCCwUlGipxn/VN6oRP/JujhmtH7DM7iT8yDsHCzBnrr9RGjx3WMBk3TnzevSf6ONHDBf0+jJVyAmgUDOXg0DGnrTA5ZNR/hroJUjM9aq9cvbrUj4daBxTlsBsVYLfprxhUdjqmxQ7Hd9Ez+PxnShfUG4gECnWULqAAJzxKB0nJ2nAaOwU/x/XDiO5d0OpAf/Qq0wmbF27BkBllsXybFbzaJSJReN7mvRbQ18vFrSNP/30TWS5RafIS0SBtckrIW+B06xaCZw5APZ9cuJpWR6LvXhhC+ftK/QeBUeIcWQBUmvxaMycGknVCiwHd9POzVCj/ijwh1KW4JNepHHOEBl4WwzfONRpig+882OwdDc9+znjgZyAc2ly080zB378Go1pFEm61JfEyYAAf2wIgL1DrcoPhY3gf94KPiaXzDFMqoZA2FeBQHtFrExSIkHAdeHi5ivfxyUNjUcM9A3NXW2PfyUoY2iMYaYNG4sMJB/H5LFc8HHAUVTMriGEzCt0vnxH9bi8JeYmoGyDlQ2qyl0jRdJWlSzGr0g4sDQK2RCzEqKe9Ff+bFBF634aqGimGZDd9ck1SVn9UFF/8ZJHQmBRdOQ8vCUrqEUQbeYyodDQ1tcQ+7jcx0/BpfF/Uce2KyqMP4Vr7PSphKagrp42uoH25Ueid0B5/hO4usdJUhlFpKLxOLYsj/h1D9Nl8e7iUzYT3oX/TLTq3Tsb0UbGo390VbZavxp8xg7F9bC9U29QeE+IGYVXUbPlK8CkURK00aC0uqjbJqgLdJ6iJoryjtNLTETG8Az44FQorcxfE+B2EVY6FYn+TjHpLy2ITl5o1Ip52FJV3y9uASxNFEF3w7zNHhwQUlYuSdUP9IRRJhnsPymeVQ7z/LYyx+wpGlWthe/hSDE3swQu4AmQgE52dPsU54+vwCT6EuhnVFTcq6BqiPCnusstoIuRVoLDZy7Jvyvn5bIE9NuyxwGf9JQ9HUooWJiy0RRnzbLRvngJYVMGwynfQt9sEtJ7xEywaHRa9ra5ZTvL9TWqzQYY6rc2acF1RBEERp8PNm5gfMAQLvHOw4vlMTA4aqrgIynNQHYuh/KETnSatk2otLU0aZQKGhGBRQTdGOglpU/Tkfw82Pf8an8cOQkPXnthtfhSnwraKFR1M/hw3voguTmPQO7E9Mn0fKNbtm/KkyJ3PAogpDdB5TjmCgqE3tn80hveMx/c/WqJRL2eEReqieqUMzPz0BTq2THljPTT6bi2ueXvju1+HwO2b1pjzYiwWxkyS729SXg3lEtFN3UZN5zXKRgMpkGsaeWon6nktgUlvV8T7HoZ5rqn8f4/yOqlVQgmFGXU18mQnUUCllSSIND2xmkQQJZIXJ+QtoI3cvhRCk9c1Wkg+yHRHsp9giTlMhqF7TRx5th5dkj/iRTyv9Ul4tHMagUvG3jgfuhMtUxvJ/2LZfDMWQUxp5GXfOgPhBj9rTKy4FUiDBvii5m2M9OwHz80bsaL6dlx6ugf1Mz6Q72+Sp522kli3ixJFO0kLwmnW00FYOvEWVkbOwqSgIfK/lvKBKAG9hNclXY090UlNUmI1JXhRnFjToMRoyvEpyeQ8inuTyCSBSXH3Ys4r2huxEkuip6CZS198nrsQPsGHYZtjBUZiv+lJ9Ck7WfQGpfnekz83iM4Z7pzLMJJXnapUyfMtbwGJcN1Ybj+CB0eO4OykL9H4VA98lO6JX59thAHkTOylMB39bbrp65bsbZgK3iiTQi4tRqXylHiuQJPjmwZ3hTW7H+q6VUOy7x0Y58q5ztC6RPlVSqro1dXoE512roODdBMnj4amfCdl38jI8+b8cnAe9fGghaSYQpIVspwRHnBVnKNlV7EJxsb1w7qor0p1UnCwbhhalRuMZO1UhAT8gXLZDvK/mFZAZ2cwDPMaZFhSWIbCQPJ6vrt3R5uPP0bmB30xatoVGI6uiSVRUzAz9lP5Xk9JyNTAtQR6E1Ff2549Ja1B05IoakcjJemr0lxoGhbwBrSeU67TW9V3+RGvnYiW5QbhUe5DXN49Do0bTZD/A6pAfybdUnGi04RhEg9U7ljMIZ5ixdpa2lQJ8lDRRhcPCSPq+1MMwmhy3FCxkqOL41jouFfDrohvMSixa6lar6lc/hOnEThvfB1HBSu0c3Jrxd6ghBIRGUYtofAMeb4VmW9GN/Hjx7H1p5+w0nQRPjq7AvMarsGJsC34OLWZ/K4aqjorJkFA+q5HD2DLFmDUqH9/v2iR1Ee2RQvJV/Cq7kbBHNFc4THI/gv8bHEMG8ZpY2ybw0AjKWz4OFAP2w9ZiP3iTI1z0K9TIjq3Sn6zxoe8YyrgpdYtNSc6eTOoQaOCaldlLlIlxFAVQlaJRJvMsqCLnDba30UwS466V594tgVhOpFiD51JdotxOnQ76qd/oPGn72zrlVhivQmTXwzFmbAdis8UU5EFh2FUHkralU03kNewGzQIpp0744agOu5ahqHVheGAowWuPd2Pypluiokiuk7JhfM+VcGvQUVspPHWrJG8Q7Ilmr7e0aNSc30dberEH6twE9udZkcw1OFLdBf0T/ZX1aB94KAY9kvPANzbloexYQ5ObAlDRZcsZAm3gHEL7NB9nBMOrA5Dz27ZkpdaRfow6Zaqk5x2Op0Z1JxRXcJmZCmQZ0sd9zV97oI+O+UfkVCi5Gzy3VIeUgHeO6dsezwO/h139B+hTbmhsMgxw4XQXUoZ7lfcbDc7jJEOs9A5qTXSn9yHvqKVdbKmpEW0sDJMqYAECSkIatNCa5M8kIf8/HnU2rsXMbbz8PtIC9Ta3BnlshwUW59oHfT3l4xfGjv1nus/vQ1prMOCYPn4Y+D2bcm+btgQuHghB7VsI4QnJCm2Lpkfwkj7Oej8Sw7S+wjvN+kL4MjIV/++/6QZQsL1cOtwsCiERLEhLEGbv34O3yA9bDrqhJ4TVOuQ65bKE51OLsojomqzrCzV/YyU76TpM27IY0fb214LWdiNKi/e4VWqnVEVUQHXccL4Itzd2oqLzvmQXXDJVn9RtN1MWGwc5qCLIIJSfO/Kn5j5OrTiUQkxT9NmmMIZdOShIQNNjhmYtGT1n2qPvSfmokWDafC8+huq67jir08i4XKkHRx0zXA0bBMapNeU7++TUUhGO22UZE0eK7pvFfJ6plAZbeIHpa7RslxPOXUQhcNIBI0SRFCX2OZIreYK/chY4LdDkpPhNQZ2TcTOX8zRtK8z5nwWg3H943HrgQGmLLXD4yAD+Pio3uHWLbUnOsllqiIowR468h2RYugZpK4LkSzsRhcsHaN3xPE7prREmt89+BjchwcNJNXKFMNnci86KkKW8JhjvQrLrLeie+LHSBVEkH5heyxRRcZbCxTDMIWAig5k4zzyqaD94lsbnLhoiuQ7fjA2pPBaDSy6ehXPR3wJe6M0eH5xBd0WeyFFOw1Hnq1TrA0GGe2vNxMmUUQGM+UZFZQ+QcYkRUNIAMkxSDUlTQuXfYzwOEAfDjZZaN8mDkNdJ+Ow2Wmxq33qrs3QHz4G6NwZ+OWbPP8+Ld9nd4SJSzeJoIs3jaAlfOarPgYqG+jQLfUnOt1sqYqATjRl5hLJQnjq1HuiJPcNWUVU8ZFPV2yP9Bp4HnAN4TpRYk6Rv/5TLIuaholxQ1S6+ixSJxq9yk7EZWMfTI8ZiZwnjxRrmvg2lO/g4MDnDcMU5RpERmo+KRa1q6YjMVkHP/1ihk/7vmzn0qwZfpxyD/geGPndQhywmYoIr2boKfz3qvNguJ0eAMOpa1HLWQeLJkXD3U3OSAWF7uQN38lJfKIW6nV3RXKqNjbMi0STgT74yHY0Eg1joffVYoT3WA+HOaOAS4IQ2rlTirPJsds8aqTDo6WggKzKqPQhZjEk8xKREKH8FUq9L4JkX4X+NrliWQTJtyBRRRRV1JHbmmLreVA22xYPg08hGzmYarNUrD5rJVhhe8NXwi5bdarxtpjvw0S7xTDLMRE/W+vQxu//purc4ZZhVB1ya5DXlSqT30qxGNQ1Ee2bJ2PGd7b4fKE9MrO0xATiAV0SkPiXL0xjpgN9+2LWDGvc1L2G01tCEdh+B6b87YRHUebYP3QH6oa0xO0jT5Xy1RZttEZAXBr6+A6Hl90hNEuth/sRu+Ec7Qi3veUxf8U2bGqRCzx4gLRMHRz41RQXbxoLy3IumtVNQ9+OieIA2/+gJsUbLIZeR1ZxVohGUwpDCa00AoFFUOFEEV1gZBlRdeC7djG0sSp6trj9aXgbjZx7IUgvDL0SPxF7FZW0MKKY+y8mZzHOfoHovZoaOxyxfj4wRBFNYCYvJwshhileaO2mFIs8ujLbWOZg25JIcfsPxs7A1avYX6ciBqb+iI9XrQE8dmN0Qh+kaqVh+LdbsLdaZ5TRNhJHfYyLGwCj3OIXEU/0gjDT5nsc/uE0MLUq7i34DkG9voWrUxaex+ig3UhDhD/XxdgDHwG1WmP2Siss2WSNNXOeY8vCSOgI9vzh0yawbFARHzdNwbHNL8N5lPJBxRtq0uG+UGLo3r17uHTpEsaNG6eZJzuNKSBRRMqfOlgXpTuSQnJ0w+LqnveH4uYUy8/HSySjaVo9BAadF3++o/8QfcpOwkXjm3DMtMOMF6MxKqFXsSw8/+j5YZ3lbvxofkgUZxNjh8A38AxMcotYBKtiD6oSJkwQxnv27MH169dx6NAhvj6Y4oWuNwpJKxhNOLbpGdqNGI4rdz0xs9Y3MOzdBTuetcXpK+vw3fSvMHVELA6bnsaH5QbgltF9OGTZYGR8LwxJ6I5Kma7v9ZGzkI3fTC5ht9lR7Dc7JaYPDEzogm+ip+FQ+FqyIOHXQxfbD5sj5NfbMAl5hMVjTNDgyIev3uP7H63E2W2fD4p/9bsebZOx7ItoTFpsh3/89FHdw1hKbVAjdAu76Jw/f15zxdCrvaMrhbCIjAypB0OSYiWIoheDktxIAOnxwNFi8xJRHpGcPTJqZ1TDhdCfXnlrjpieQUfH0fjD2Bs5wqNFagP0SGqL1ilNUDnDrcAkZnqPeO0k3DD8G8dNLuBX0/MI0QuHbZYVBid0w7yY8djwfH7x7QPKpZI1DynFOAnXas2aNUUx9C4SEhIE+yYSZmZmMFZS239Gg5BFE2jteUcu49u0apyKjAe+gq2thbDncxGzZAt++XMgjBbNAnr1okUNXkntxE3GQz1/UbyQiHlo4C/+zjzbFO6COKqeXgn22TaomOny6vnkAf9H3xdBus9wz/CxZOPn6MMztT6GJvQQm9bSuKO8qBR9E/M3DQIqVwb++vk/4zHII/TpVw7wDdLHwknRol2/emcZrP/ZEl+MjEH1D62V3g4mKysLMS+9djlyNlouljDZypUrcfDgQYwYMQI9xFo+DYDKlCms9eoOmCsJpLc9EiSgKD5KrkEuaS45KFeGRCe1S1BESwkPEj60vS5uAvRCcM7omlhK+kg/AH76wQgWFpZ07Yx/D3WuLuqlVRMXokZptVE3rTqWRk/F2qivSu57U6I0WadKIDAwEOPHjxd/TimB4oP79+9j2LBh//m9iyCG5fUEmQv7yp56tzBMUULGLnn9FZhyQLcKV8csuK4bDmQK4mPKFGDOHAg3TuCLL964f1TLrIhqLypi1osxeb5XBjKRq/Vvvg79qK9o+P3uXelvk7qhpkRVquT5tNF9EsTt6TNdXPI2QkqaNsb0jcfaBbHQcnNViaiHrrBzZde5tpxhumIRQ5MnT85z0dI4jwSF02hjVEewUtiMFqSMjMIfWuFBVtbrlpaKukKkUKGSKF++PE6cOCH+7OHhUex/r0aNGvD29s73OcnJycikQgiGUYaXiBo1KuAleuO1a9dKqRmrVwNVq9JFBSxdKnm+C1r6yHtd2ClINLiMRBj1JDt5UvI0y4GLIOSon9BLK0PtK1gVFkOxsbHCfSYD3bt3x+PHjwXxWIUvAka1RCol7RVmQVIneLxGnnh5eYkbwygN8hJR2JpyiRQV5uQumjpV2p48AYYPl4pEBg4EJk6UvN9FgZ8feS2kv0HvTW2pC2vYK9koU5oYshQOcpcuXfiEZ1R/QSKx8HqjMk2AXL7ly3MCPsOoMnR90nVKjQ4jIwv3HpSzc/as9PPNm8CQIRQrlkbM9+sHdOokvwiJiAD27gX275cq4Khh4qZN/+bEFgbyZpE3SU2qxYpcDDGM2kBWFJXAUh6RnHF81b5a1atUlWFKPZRHRMnEVPEqR/fnd0INDl/Pi7tyBZg3D7h0SRJc+UE99GgoGXlMJ00qmu9FlWI0i02DYDHEaDYkICiOT4tRPq30VR7qR0UdcBmGUS/IeCEPChXb0DqUm/v+7+npKW3KWE9dXTXSM81iiCkdkJDIo0maWkD5B3ImNTIMo6JQ2J4KPBRoA6JSaHgLDxZDTOnB+mX/C6o2KwrrrCRQYuk8wzDFALUBIVFBeTyJiar/eckrTblFGh6eZzHElC6o/F4WNiuga7VSoYWH8oN0+RJlGI2Dql7LlpVyb6haLI+1iKrsJy22xQ8HLZCeIQkRN6cM7FwWgeYN3nz+rfsGOHbBBFEvdFG/Rhr6dEiEidF7GnwUCqN8o1LSPoZXWqZ0LkRUmk7dxFWx2owqRKjBJzftZBjNhgQHrUU0zuM1UeQXrIsqn5THiJ7xSLvn9+rp/k91Ub1DeQz3isfGBc9x/KIxOn/qhN7tE8X/tzTPwe9XjOHoWUEQTpn465enijt0aN2h9UcDyuVZDDGMPFC1GcXwqR/I+1R6FCVkifGYCIYpvaJIMNDCo3KRk6OFLq3fHP9U3jkL7m4Z8A2WRgTNWWmDFg1TsW9VxKvnfPJhCnwOPUXlduVx6pIJOraUc7ZmKRVBLIYYRrYAUHUEVZqFhiovl4iEGbnN2RvEMKVbFDk748P+wD7tHHQbWA7mJtn40CNVEEg68L5nJPycghNbwsSnfzc9Cu1GlMMnIxzxw5JI2Fll4+Bvphg1xwEeNVLlE0KyUVP6+qV617MYYhiCkgTJS1TSFWeUE0QWIecGMQzzGr37agub8EOOYCC9SAPi4v7TL+3jZqnIeeQLv2A9nL1qAv+neqhdLR3RN/1hZJCbv+ii6jAuzmAxxDB5QhVnVO1B5a/FKYpKuUuaYRg5oaQf6qhPG0FzF6nRYkKCFFYTqOSaKW75Gl3UAJIaJXL3ehZDDCO3UCFRRBuVvlI7/aLqYE0t7EkE8YBfhmEKA4WzyKvDvcc0SwzRlGkTto4ZVYX6EtFGuURkjZHHiGpeFbrKdKWFi95HTUhNTRXWXH3BiCy9VqSHhwd8fHz4GmAYFWLs2LEYNmwYGtKIEk0SQy1atOAFh1F9yFtELmbZPB4SR1SBRqWwNJlaNp2aPD/k9aFus/SzmiZET5kypVgWHGXi7OyMqVOnYsOGDXI939/fHw0aNOBzn2FUiLCwMFy6dAnGclbd2sjCiyUthsaPH6/Q81kIMWorjkjw0KaBbNy4UeOu465du4obwzBMsYshhmEYhmEYFkMMwzBqTFZWFgIDA+Hi4gIDTnZnGJUiKSkJptSbTRPE0OPHj7FgwQJMnz4dW7ZswYQJE1C1alU+ygyjZB49eoR58+ahY8eOGDx4cKn7/vS9Z8+ejaZNm8LX1xejR4/GhQsX+MRgGCWTkZGBiRMnokmTJkW+NilFDKWlpaFOnToIDw9HmTJlsGbNGjg4OOD+/fvifxmGUR5klFhRr6VSCK1Bly9fFoUQ4e7ujpCQEFEMtWrVik8OhlEi+sXYJVspYiggIAB6enqiEBI/hK6u+PPDhw9ZDDEMozSqVasmrkcyNzyFy2JiYkRRxDCM5qIUMVS9enW0adMGV69eRbNmzURXNFmibHkxDKNMqK/SnTt3xNYCY8aMwfr163HmzBmUowG6DFPKyc3NxfXr16GlpSXex8+dOye2xykpT3JQUBAePHgAc3NzscTeyclJvcUQcfjwYdHqol4elKR48+ZNPtMYRmDPnj3iArNs2TKULVsWtra2uH37ttz9cYoCRUvrNQnqR0R5jMS2bdv4hGSYl5AQoXydcePGoV+/fujQoYMokEoKNzc3scdQcaDUajJyR1esWJHPMIZ5jf79+4sLzI0bN8RcFXmbizEMwxQXfn5+uHfvnpjSQtEcT09PeHt7i8aDJqS3cGk9w6gQx48fx759+8SKJup+TKFkGlnTrVs33jkMwyiNSpUqwc7OTjTOTp48icTERI3q0M5iiGFUiE6dOokb0bdvX94hDMOoDJSrI8NMjWYtshhiGIZhGIaRQwzFCVsO7wqGYYqBwmZXPhU2Ld59DMOUBP8HjeFBv0OzfnYAAAAASUVORK5CYII="
}
},
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"metadata": {},
"source": [
"\n",
"ベイズの考え方は、端的にいえば、データが追加されるごとに予測の範囲が狭まっていくというもので、モデル(例えばべき多項式)を選べば、モデルに含まれる係数がある確率分布をもって決められると考えるのである。\n",
"\n",
"イメージとして、PRMLの図3.8を引用する。\n",
"\n",
"最初に1つデータが得られたときの、データの存在予想範囲(各$x$での$y$の存在確率の標準偏差の幅)をピンクで示してある。赤の実線が予想曲線(存在範囲の中心)である。緑の実線は、データを作るときに使った$\\sin$カーブであるが、これは伏せて見るのが良い。\n",
"\n",
"ここでの予想曲線は、ちょっと複雑で、平均値が異なるガウシアンの線形結合としている。(時間があれば詳述:この図の描き方が、https://qiita.com/naoya_t/items/80ea108cebc694f5cd63 に公開されている。このページを読み解くとどのように推定しているかがわかる。)\n",
"\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**(注)**\n",
"\n",
"詳しいことは、上記のURLにある記述かPRML本を参照してもらいたいが、ここでのフィッティングはべき関数ではなく、「ガウシアン基底」を取っている。つまり、\n",
"\n",
"$$\n",
" y(x, {\\bf w}) = w_1 \\phi_1(x) + w_2 \\phi_2(x) + \\cdots + w_M \\phi_M(x)\n",
"$$\n",
"$$\n",
" \\phi_i = \\exp \\left( - \\frac{ (x - \\mu_i)^2}{ 2\\sigma^2} \\right)\n",
"$$\n",
"\n",
"として係数${\\bf w}$を求めている。具体的には、$M=9$で、$\\mu_i$は$[0,1]$の範囲を均等に並ぶようにセットしている。\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"[ベイズ統計の基礎へ](BayesApproach.html)"
]
}
],
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