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Last active September 4, 2022 19:26
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Causality // Controlling variables"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Basado en curso: \n",
"https://www.youtube.com/watch?v=eBij0BFc-RM&list=PLcTBLulJV_AKmUTH-nUsxxFyRQoWnUzxU&index=1"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"df = pd.DataFrame()\n",
"df['W'] = np.random.choice([0,1], 1000, replace=True)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"np.random.seed(42)\n",
"s1 = np.random.normal(0,1, 1000)\n",
"np.random.seed(43)\n",
"s2 = np.random.normal(0,1, 1000)"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"df['X'] = df['W']*2 + s1\n",
"df['Y'] = s2 + df['X'] + df['W']*2"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"<div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>W</th>\n",
" <th>X</th>\n",
" <th>Y</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1</td>\n",
" <td>2.496714</td>\n",
" <td>4.754114</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1</td>\n",
" <td>1.861736</td>\n",
" <td>2.953254</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1</td>\n",
" <td>2.647689</td>\n",
" <td>4.269185</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0</td>\n",
" <td>1.523030</td>\n",
" <td>0.988114</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0</td>\n",
" <td>-0.234153</td>\n",
" <td>0.623920</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" </tr>\n",
" <tr>\n",
" <th>995</th>\n",
" <td>0</td>\n",
" <td>-0.281100</td>\n",
" <td>-0.199370</td>\n",
" </tr>\n",
" <tr>\n",
" <th>996</th>\n",
" <td>1</td>\n",
" <td>3.797687</td>\n",
" <td>6.021496</td>\n",
" </tr>\n",
" <tr>\n",
" <th>997</th>\n",
" <td>1</td>\n",
" <td>2.640843</td>\n",
" <td>4.389198</td>\n",
" </tr>\n",
" <tr>\n",
" <th>998</th>\n",
" <td>1</td>\n",
" <td>1.428821</td>\n",
" <td>1.965806</td>\n",
" </tr>\n",
" <tr>\n",
" <th>999</th>\n",
" <td>0</td>\n",
" <td>0.572583</td>\n",
" <td>0.378277</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>1000 rows × 3 columns</p>\n",
"</div>"
],
"text/plain": [
" W X Y\n",
"0 1 2.496714 4.754114\n",
"1 1 1.861736 2.953254\n",
"2 1 2.647689 4.269185\n",
"3 0 1.523030 0.988114\n",
"4 0 -0.234153 0.623920\n",
".. .. ... ...\n",
"995 0 -0.281100 -0.199370\n",
"996 1 3.797687 6.021496\n",
"997 1 2.640843 4.389198\n",
"998 1 1.428821 1.965806\n",
"999 0 0.572583 0.378277\n",
"\n",
"[1000 rows x 3 columns]"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(6, 6))\n",
"for name, group in df.groupby('W'):\n",
" if name == 0:\n",
" ax.plot(group['X'], group['Y'], marker='o', linestyle='', label=name, color='orange')\n",
" else:\n",
" ax.plot(group['X'], group['Y'], marker='o', linestyle='', label=name, color='purple')\n",
"ax.legend(title=\"W\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"([0.0015931609016947965, 2.0365122453911257],\n",
" [0.010236827080753587, 4.034998352182664])"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# Now we're going to find:\n",
"# X_exp = Part of X explained by W\n",
"# Y_exp = Part of Y explained by W\n",
"\n",
"X_exp = []\n",
"Y_exp = []\n",
"\n",
"for w_value in set(df['W'].to_numpy()):\n",
" X_exp.append(df[df['W']==w_value]['X'].mean())\n",
" Y_exp.append(df[df['W']==w_value]['Y'].mean())\n",
"\n",
"X_exp, Y_exp"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(6, 6))\n",
"for name, group in df.groupby('W'):\n",
" if name == 0:\n",
" ax.plot(group['X'], group['Y'], marker='o', linestyle='', label=name, color='orange', alpha=0.5)\n",
" else:\n",
" ax.plot(group['X'], group['Y'], marker='o', linestyle='', label=name, color='purple', alpha=0.5)\n",
"for w_value in set(df['W'].to_numpy()):\n",
" ax.axvline(x=X_exp[w_value])\n",
" ax.axhline(y=Y_exp[w_value])\n",
"ax.legend(title=\"W\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"# Now we are going to close the back door for W computing the residuals\n",
"df['X_res'] = np.where(df['W']==1, df['X'] - (X_exp[1] - X_exp[0]), df['X']) \n",
"df['Y_res'] = np.where(df['W']==1, df['Y'] - (Y_exp[1] - Y_exp[0]), df['Y']) "
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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MqaSzAhT3zwXyc1YEhU1CF0QYyENCrjIW17i3kdu7Bv3R7Us/cPAJ9JsS6N1F6P8+SDO1b6sK469A9q5zrzWfz+zPU+raWhuYRgw1fjJwn5ci6DLPHb0eCAN5SMg8Lmnb/jlywRr32YA69uLJIC7I4NVAUoISyIp/vfwnfEpdu/u90Pc3Nggaiuef3T73Cl3n64kwkIdcO1ziRpH8njzP/+HzVMYqODWHsX1jnHj9BA/+8YOXNcicafLOGQPgbEC1DVD0QPboOTNB3Yf6VHDNlptTNj71VQa9n6iQ2/d+jKHime1zL8Es0RuRUEcecm1wGRpFdn91N1OHpwDm9NVTh6fY/dUL35i/kCn2S2ncm29uPvPU+tkmIjEKghS4JwoCSDFAgNb3XZqSxWxd263B8FMw9iJ6d4Tt/59NPPyNh9n+2PYFAXpZZomGLCAM5CHXBpehUWTo1SGiqSgRNYIgCETUCNFUlKFXh878wCUGFM9mnksG3iVYajD0+N7xMwfA2YDaeBvYUyDHof1hWPEhSG+EDb917hfjDEOXl8StQssD0P7RYDFZYqE9p6HNIedFWFoJuTa4gEaR867D+iDMc6mql+uUR8rYps2Ox3Ys/vgzeI7knpi6YGOuxdQkO7+88+y188wWuOOrC8tQ0bbzU35ciI/KeYxtO6ehzSHnRZiRh1wbzGtFn+MMjSIXkg133NVBrVTDNm1qpRrTx6epV+toq7WlH3+GO4XlzjzPyx8msyWwu73rG8Hf51NSOc+7n/yePDv+3ODJLzaw46uB5wuw5EJ7ye0RbkDCQB5ybbCUCdUSm3dnq8MuVrve9lvbaFzbCEBpuIQgC8Sb43Tc0bF0HfcMniPLbcx12QLgefiozC2Ypka6uYZZDIy78gdZcqFdqnQUbnReOGFpJeTa4DwbRc4k4VtKNbHhoQ2kO9NMHpqkZtSQVRklrZz2+AWcoaV8QQt81MA6kcOaqtDzqQQUGs974/Gy+MPAebXJzy2YyiaYeAU1Afgxcj+x0H9t6bFtV8Qe4TomDOQh1w7n0ShypjrsYg03lfEKL33xJbKbs8gxmagWxXM8nJrD4CuDdN7diRSVTs+mzzB3Us/MBN5vvYCxdxdau0zPx1T0VRfu3X1ZAuB5zNKcWzBFFbJ3Q3E/imJgjGkX1VYf6szPj7C0EnJdcqYyxGK16/JwGdd2KZ8oI6sy6Y40AgLWlIUUkxh5Y2TxMsaSdrUnp/1s/6X9PPx/OGz/rIq+cfGa84XIFC8ZZ3lN88935M0RDv/4MOV8OWjHT2/CqmmBg+LgExckD71Qtc+NTJiRh1yXnKkMsVi2XhmvEG+OYxkWsXQMQRBIr0xTHi7j1T2Apeu4Z7tTOIvi5rI0yBT2kH/uCXJPGxgTGtrGTXT/0gNLH/8Mr2n++bbf0U7/i/0cf+E4K+9IIptvY1VUej6WWqh2gXNu5rrkY/iuQ8JAHnJ9MU92p8e70H/nEchsX/Aji9m3imKddHKcUsnCnlKIpLNIcoxsd5bWW1tRM+qFB5Gz1JwveeAq7CH/T39O33daULQ06ayFeexV+v6kQu8XPnzez3Hq+a7avoqRN0YY3nmc7vuj9Hw8GgyLZub1HvxKoDE/RznjJR/Ddx0SllZCrh/OsfvzNNWEUuT+nz+ISJ1kawzHcjHHTmCXS6TaUxevDDmL4uaSNsgU9sDuz5F72kCJjqHGKwgRBbUhhiINXFA35annm2xNsu6D62hbV2b7b8dmgvgMEQ0mXz0vOeMlH8N3HXLRGbkgCJ3AN4FWwAe+5vv+n13scUNCzpvzaEpZsGm45zGoR2nqjpJ7DmxLolb0iKWLNK1vuviNtswWaH8IDv4FmMOgtsOGz86d0yVrkJld2KwxjMmNpJsqUB2CeAfICZSYMbdYnM/m4pLn25lcfCAFwnmNhVty4MU8062QhSxHacUBft/3/TcEQUgBrwuC8Izv++8uw7FDQs6dCx0TNvM4fQMns0lfAnMA7tp+8udONe3SbgZj71nrvvmXXyT3Ny9hjPWitUfpfqCEnngK0hsgs4Xmm5t56Ysv4dou8QaPdGYS0btwmeIcB78CxQNQn0LTTmBWGlFTQG0CRDnYlFyvLRhIkY4ZmIc0+v7k6JJll0UD7egIPR+dhBP/DNEmaNgKshLceWTvCgL6OU79uWwyy+uIiw7kvu+PACMz/y4JgrAfaAfCQB5yUZy3BG2pWrQQDbLupQLuueimT21bLx2CY9+EprsgtW6ujJP3foPcs97cOTff3MzBv3seJREnvSKGWYK+x9P0/iLoySfID7Zw8KmDZDdnKR/PUxkZwRqXuP/fXpxMkcIeGH0Woo2gttN950H6nuoBP4oSr2DValjiBnoe6Sb3rRdQvHdQ0zEQ06iyBdPvkPtWAn3LJ0479GmBttmi58OvoG9MgPvewC537LnApGt2o/Nc55TOe44wcJ87y1ojFwRhFdAD7Fzk/z4tCMJuQRB2j4+PL+fThlyHXJAEbbFadOlIUM44U938XLpGT21brw6DnAbzxFzdN9+fpe8/Pb/gnF/84ot49QpqQxRBBDUdTLrPvZCC6sDcxqGiKVCfQIpIyIrEsddOryWfl0Rx8IkgM0aASAr9phS9D+9FVSYoFhpRV981l3EbB/ajpGOBZ7kggKSgpGMYB/YveXh9i872x7YH7oa/tD8YQxfNgNoWeJ6v+BlQ9ZPql7PIGUMujmVTrQiCkAS+B/yu7/vFU//f9/2vAV+DYGbncj1vyPXJeSs5ZssedhEqAxBtgMxWSHQGTnyn1M3zzz1Bbu/UyWz/fb+BHn1+6a7RU8s2tgGR9AL/l9wLKZR4acE5e7ZHcSJB00orCJSAkgRjuA7xLowBAzEiMvTqELJTJ5aKYtfgaN9Mm7uvkfuxwcjEt5k+Nk3z5maa1jWdXaJYHQhe/8SrwddyAn2TiL7uINz3pwtem5Y1MKtp1HllbKsaC7Tg58K5lLTCqT+XlGXJyAVBiBAE8W/5vr98vqIhNyznpeSYr1Zp2AKZW4Mg2/lIMB3nlI22/DGNvq9XFmb7X5skz28ubTJ1qmlXRAsWjXnHNobrKA2pBQ9LNCeollPgmuBa4PtM9dcpDHk8+Z9WUjhaYPCVQWRFJqJGEXAQBFAbYPd3oO9vHUxTwypYIMDEvgkqY5Wze3jHu4KFo/nuYLCEXQyybf39p7227g9pWIaNWQxuSMwiWIZN94fOcbP1PA3NQpafiw7kgiAIwNeB/b7v/5eLP6WQG4YzeF6flwTtTG59iwSZ3DM1lMbE+Q02OLX8Em8HpwjqirlyjNZSxWLtgocl25NISgJT3oYvKEweqzK0N0py7XrSa1eRXJHEOG5Qr9Txo03Ypotr1tA7hxl6vYAiDaI2t1Ar1lA0BUmRmMhNAGeRKM4fMtFyf/AnvRHWf+a0H9Xf+wi9nxhDTZgU8z5qwqT3E2Po7z3HaULnaWgWsvwsR2nlHuCXgXcEQXhr5ntf8H3/R8tw7JDrlbN4Xp9JgnbaJui6EfRbWhcef/bWfuPvnrbRZgzLpG9aqAs/q277VNOu1Hro+NkFqpXuX3+Qvq9NQsGcO2dJlrjvj+5jfO84xkCaUq1A+/1JshuyAGQ3ZBldOYo1WUJyLJSYSVvHMJIggpBGacxA6QBKfD22JSEr8twCd+rCdtp1ed9voHvfhuF/AvxgY3aJ16Z/9HPoW+d3Xn7u3Esh52loFrL8CL5/+cvV27Zt83fvvvDxWSHXJgsCTexNuu8vom+e18E3qxzZ8tjpPz+jWgHm2sPnAvzRnfT+4hmOdYpscMe3NmFa6QU66Fld9PbHtp/fi5p/bDFGfl+J3LMOxlgcbVUj3b/6EPq998/9+JOffDLwcRFPDrAoHTvOsecOsf5eD0UawSq5WJUIES2LpMZRExblaYXBA60ggKqptG5txSpY9H66CT39PPk9I/R9pw1lxVqU1o45SWDvh18JNiLnq0XCjcZrFkEQXvd9f9up3w9b9EMuC6f5iRwo0fd4it5fnafdPmWDbDEJ2o7Hdpy+CbpiLblnd6OvLywubztlo62b/PI0nMzcVeQPiuSeqWEMF9GaCnTfb6BvEMEpgXMA+sfmMnct1oU5uha1rXPuMLJznDV3uqgZhZE3Y9RMhVi8TkQtUJiIQ0eMRNKg5eZbGN87TiwTQ82o9PxcAl38a/L7sjz9ZZ3KRJ3E8Z1k1+wkuSILfoXcy03oW2cWrFMbpC7xMOuQy0cYyEMuC6epUBpTINTIPTevpfscNsgW8+FwaCD32mqMyWm0rEH3hzLo7z3zrX1EKtL/47fBq9OxNUrv5x48f93y4BPkD4r0/Z2PolQQJZ9Db61hz8sJ1rxnmm0fGUJv3w+7fxtiTSCqdN+Uo+8f18F0K0rXe7DqGtZUhd5PqiBA4bBAg26gJMAqeyCAW6tRrGo0bW3inj+4Z0FHan5flr7H01QmbdREEbsuMfhOhE65RkI+gnFi3dzp5g9C7tkGjKEy2ubv0L35mSBbP9dxbiFXLWEgD7ksnBaA05tQrFcwhgA/ck5NInB6e3h5tEz/i/3E0gnSW27FNCz6nrLo3dCCnjn98XNdjN47bLw3hlWNYRl1OPpN2NxwfkGsOhBsnMYt3JrA0KF25KiDmqwwcjBK33c76P3AAfS1duDXXe1Hb4Pen4XcThfjXQ/t5jvoel+C3DMmuRdVJKmRtpXDCPEaaloBtYaaMNn+pV88/dyqA+Re6ERJQyJVwa7LRGIANhP9SaSONFrDMLCe/MFgco+SqJNuT2IO7advbwu9vz5jcHVKth76gV9bhIE85LJwmj+H2ooV3YbWcSRohT/HDbJTN0FH3hiZO37/i/3BBmNUYvdXdvORv/rIaY/PPZFDkQaCLkZJCbTTQnSmBHG6J8ssiwa2eBfGif2ksy79x5qRow6RiIPvQ81SUGIT5HZtQN94BOqTIMYA0DtOoK81oSVLPvcSfY8nUKR+qK/AV1QGD66gc8MJiCQZH4pRnm6CP5ui+5H8yWBa2AOloxiHXdKtAtkVNkMH2wAHKSJQmQKrpZWe25+Depbcsw0oiTpqogoNW1HdV8FPk3vu9NJWfk+e5//weSpjFZyaw9i+MU68foIH//gC7lpCLgthIA+5LCyqQjGT9Hz+N+EsweHUILrhoQ0zKhADt+bSvLmZqYNTSIpELB3DMR2O/ng/+f/xNLr2LNSnA011NIuxs5d0wwR47SAFx1eSYOSVhQ0s8+rH+aEu+r7bhdLattAv/NMPomV3YlZVSoUEji3iOjKC4JFsKKOoJsZkA0SSgb+JFAts5dwKRFaBY5H74ThKeiNqsgOlv45tGcgxjf4jW6hOe7i2i5KWmTg4cbIBSHsZ9n4R7CJaYwKzmCaZLtGxASaGG6iUMySaoPeXbfS1t0M0gzFUJt2eDDxQ1FaIaChxC2NknlZ/prS1+6u7mTo8RSwdQ9EUHMth6vAUu7+6m4989fTFMeTKEwbykMvChRohLTZ04eBTB+c6Gnc8toND/3wISZGIqJHgQfUp1Mggue8fQH+0H4QI1ApgTaAlmzGNKO7kMSbG1mBZCaQItG2onazPnyKNzP3ExJvax+hgFasqo2gKqfYUu79VhPp6Dr4qUy2pyFEHWXZwHZm6pTA5rpNtK4EgBX88J/gjiJDuhsKbGJO3kF4dAzFGdiMMveXi1iSmhqpEU1GkiEQkGWFi3wTZzVly33oB/f4/AYRA8nhfgb7vpcFTSKQMpO5mLEsKVDwrJ2B9UPPWtu0I7ohUlXK+zMQ7WSonTpBotMkfkNBXnyxtDb36CtFUlIhcg8owEa+GL8UYetk5eX3CTdKritCPPOSyMevPcefv3gnAzi/vPKtnyPxN0sWad7of6cacNPF9H9/3sUsGjpFHXzmKMaEBInhBVyReje5t71IYy3B8Xzt2uYQo2tRKLsW8R7744Jx/d373IXb8ucGT/6HG3p+oDOcS2MUJYukYtmkz/Nowh35wCEm/nUSTRCTmYltRPE9Ga7GQkynGR7rovr8ADTeDooNTBlzI3hdk5/XJoPGpHLzWZBY6topYhouAQDQRJd2ZJpFNICkS5eFy4H/i2RDVQBDQu6P0fnwctSlBsbwaNdtA7yfygRRz3sbl7Oi7iYMTDL4yiFmREOJZUnqEvm+Y5I/P8z/xQXDMwPLWd0CMIfgOWKPQ/91z8nwPubyEGXnIZeV8x5qdbVqMvkVnzfvXMPLGSND9KBVo655AEl1UrQSiDE4dcAEBfdUk6cYKlZKGW5MRhQrRRAOFiVae/oM9fOjfvgVGjb6nbkVJWqQT/dSqQTOOkqgjCAIRNcJ0cRpRFlHbOvFjk7SsG8ecKlG3YvhSCiUpoCQc9I/+TiA9lGKQvQN8H/w6+eMZcj/+GCMHoxh5aF4PjR0gSXUEKUasIYZdsTExERCIJCJMD0xDyeLJv7gPrblM933T6Gsq6Ots9K5d0PXxOQ3+qczeET39uafxHI9ES4Lspk6SrUnMgklur4r+aBD0O+7q4PiPd0NCRo7JODWoVWVW3eYEnuqZW8/J8z3k8hEG8pDLyvmaYZ3L0IVtn9l2skmodACrEMMqePQ88FbQMi6I4LsERXEB14myridPpSAweFDHB+qmQ+lEiX/8YhtNK6KkMtXAu9uXiUZruHWV8mSUTIuPYzm4dZeYFmxeKk0N2GYCtb2GODVB970GpqmhdtwCKx8FHl3wmvJ78vQ91YeiltHX7iaiwtihCPWyTaqxhpxoJCIrWNMWtmVjDBrIikytWCN1k0K6OYY5VaXvH1bQ+3PD6B0ngvLRbEv8EqUPfYtOZk2GlfevXNCQdGpX67bf2kbxnZeoFBVqZZCi0NgJ234+GjhJtty/4PWck+d7yCUlLK2EXFbOd6zZbEnALJj4no9ZME8bvbZgdNuUhppR6f3ZQ+irp4LSgA9BvQAQImgtJlaxxsRwIz4RqpM+TrVMLF4DUeLYm1mcmh88VpBINZRJZGw8YtSKNSJqhFR7am5xyXZncS0XqyoRa12JmfgAlttF9+37F/WRmVvM2joRWu4muybKqp4ybTdFSW64kxV3riaiREi0JJBjMq7tYk6adNzdQdPNmxAkATWbQUn55HYkwKkGPioHvgyvfQbe+sKSpY9z8bDRt+g8+JkK6289TFvXAOt7jvPgpyeCOrraHhpkXYWEGXnIJWe+6qRwtIBt2XNeI3DmsWbnukk61wVaaAwCl78epl2oHiXfnyL3+s0YY0m01jrNXRMcfH01FUOlXlfwBQEBgXi6RjQhUZJk8gPtpLInwK2QXRmlfKgJbXWadR9ch2VYFI4UQAha+xMtCbKbs4zvGw8CtFIMBi2sSkDk9GabkbdGsArWnBFWdtM2EhsTGENFGIemdWmUtMJEbgJRFsmsylA4VqD9Pe0gCpC9G4r7UTISxlgTaFbgAx7RYPAfwRoJBl+obcGm6qyB2Fk8bOYo7EFvfQf9Y/uCRVCKBeZbpc3BiLrhp4KfO8chESGXnjCQh1xSTq2JOzWHob4hAJrWNZ1Te/x5TYuZb+AkxcibH6XvzS6UtjbSKw3MEzkOvn6MDfeUMaZXUDokEUtCPCOCIzM1CL7nMTUYYaJjBU0rKkgd22gUJNKdaYpDxWAx+ZPgfHd/ZTcHnjoAAnTe3cm2z2xD56+gnli0jpwfbGH62DQIoMRd7MnjDD5ziJaNEZpu3gRqK2bBJKknSepJIFgsEIIFT82ogXxQbcUqmGixnZBcEzyHNRqUPoQIuLXAOneiLzDLcgbmruVZF8ZDXwVrLFgI6kVwq4EdsBwPSkXpDaFB1lVGGMhDLimn1sSb1jcBUBouEVEil2Ye4zxvldxjO1BaZ2vsKur64HnGR00+9IUY//gFQIB61cHIx3FdAVnyESWP47ujlDa1sfp9nfT89umdjfk9eeyqzcoHVs5lt31f6mND9zjjA1mMPGht0P1e0NcHdeTc0zmaNzcz8fYgzvQYsiLh1COMH3S55xPPwJpfoe9rQeljfsZ8+2dv5+BTB0/7fs8HRiAy4/xo7A+8x30/UOpIM/sK028FU3tmOOvCOPEqyKkgcEeD9wunGmT5p1zfkKuDMJCHXFIWU500rm1Ejsk8/I2Hr8jzKyu6Md7dhb6qwP2f1nj+z3ymRyUQBERJxEdAiMnEsglqpciS7emLbdxWJ6q8+LfNrLqtRro1hjlVoe+/luh96G307hjGoWM0rVuFYu9leK/E5IAMPsRSEkTS6Onn6f38b56WMQNE4hH6X+gHIVCW9H6+Fw6+zY6/NDHGVLSETvc9oLfsneki9YOgbk+d5g1+5hb8mf2E+QgEx7oGuRHsBsJAHnJJORfVyWV//rqGdvMdEN3P5nsHOPZaF+8+F8O2PERJJJqMggCO5SBK4pKKGuPQMcR6P8dfqmFVYyhNWWpWBE9IoSYKYJdRpTFQo+T6utBvk9GUtzBHZXBK+G4SrdXGd0wEHPq+Xqf3F0+gf3Jhxjy/PLXxoY1z2fjkwUkOfrcLxXuHdFbAnEzS97219D5cRV/nBVOBxOhpU4GWkoDOdczu/iBa6kggb1xnB9m9XYKWBy7tm3UJOF+567VKqFoJuaSci+rkijz/Lz0QaK7v+gZusoeWm9uIxCMoGQUpKiHKInbVJt4cX3K8XG1kH+/+xGfsWAxr2sY4cpyxPcNURksc39tOedQC30NJSRilVZBaT/f7JKwTRxg5GEOiAPVJ3JpD29oiSrxC7ln/tOaapZqidv3FLpTWNtTVdyFEFFRNRknUyb11J7R/eMmpQIsdz3M9Xvzii8H4u009mLVm+p5YTf7QTBaeXAsbfmvBcc5rGPQV4mwNZdcLYUYeckm50Nb8+ZzPrXH+5RfJfet5jMEyWmeS7l968KzPr3Vp2JbNRG4Cx3KQFRmn5iCKIumOdHD3cIo2O//OJKOHGvB9AVl2qVVd6mYcAB8Pu1RgaKKRjttWIEUFtJnZxPpNSXp/Nsf3/6QL3/ZQkx5tq/Mkk2V8VIzprtOaa5ZqiioNl1h5/8rAWVEN6uRKcx7jUA7MwCMmt+tujL8+htY1NXfdFjtecaiIZ3vz9hK2w9B+cm8m0e/TTmvDv1Yy3bM1lF0vhIE85JKz1ObauQToUwPG5KFJvv/L30dbrdG2tW3BY/Ivv0jfHz+JokVJt4A5cpy+//2v6f1kmu2/82nIbF/0/GYlea23tTL6xii1Ug1RFmm7vQ1REul+n3jaWLrcD4YR5TQN7RLWlE3NlhElHznqgBcDUUaSK4zsj5BdLdPzszNPZhvonXm6H1yJOTKJmjDBcygbSUaOt+GSZsefG3R/7qTT4VLlqVR76qSSZfb7dQ1t63by8e6g6SijkO5QFgTaxY5XHa+SaE6cvChqK8ralkASueX0vYzzbey6Ulzp0t7lIgzkIcvGeWXO55jRzQ8Y5dEyY3vHQIBaoXbaY3J/9xRKbBJVKEPZQo0nAIXc0wX0NYGOe99zErv+Yhel4RKp9hS3f/Z2Nj+6eS5rl2MytekasYbY3ELBwb9ix0/agg3FNuh+bwZjskI8WcLxUjRkp3BqDYiyh2NHaWiHiCJhmhEE36X3F6vo65NQn9FcRxvofn+Mvq9pIMVw6hH692dwaj5qxmXf8xq5Xd/nvj+6j82Pbl5S+73+o+t555vv4Nou8eY46Y40oiTS86meMwbaxY4nRSSS7ckF79GZAt61kumek27+OiAM5CHLwvneas8FGqUI4ztRbQNcjdy36uhbPjH3c/MDxsT+CWRFDgYQF62FWaD2MsbhAdLZCjguIIJTQVEljFEFoin2feMJnv3LDNF0lERbAnPa5Nn/7VkANj+6ecm7hr6vV1AycdKtYBaDAQ0RJU5aG2Vs0IWIgBRxsCoxPE+kVnGIqtDSrdJ08yb0zfuh8FZgpxttgPo0+ooj9P5aI7kfjPPOrk6sEjh2BNf1SHY04OHz4hdfpGlD06Llqa77ujj41EGym7OUh8tUxitY0xb3/9H96Ft0dn5555KBdrHj3fdH93HwqYOY8wZHnyngXSuZ7nKU9q4FwkAesiyc7622MWAgugWO79mPVY2ipNI0ddYw9r4GhU1z9dj5AcMyrMBv3HLm2vwVTcE4dAz2fhmtuQOzoqCqRcrTChMnmqmU4iQaBfLH0uz6lkU0HUWURYoDRRzLwcfn5T99mc2Pbl76dTUmUBMWiApqGqhN4hZPIArQ0jFKcTKFaydw6jLJxhqJlIVZTGJMJuj+9ZuhcxOUj0JiZdANWToME33oKzbBXWPs+ZcuBMkjGnEBmeIJk3SnimM6c9fv1PLU/Nmls12yZsFkfO84+Q15CkcLDL06FHSddmdJ6skFgfa0cldhD028Te5pA6NfQ9u4iZ7PP7BkwLuWMt3zaii7RglVKyHLwvl6qEhRif4Xj2PbEWJJCbsm0P9WDEmJBJt9M8xXncTSMSzDwrVcst1B8LIMCy3dD55N9wMVrEqUiZEMgwdXYFYiCIJDKlOh76sDFAZ9BM+iNFTCsz0k2UV0K0ztHyb/3ccWtWI1BgyUFd1Bl6RrgV1GEY7g1gV6f2YnMdWmZimARLrJIJE2qZsiassK2u9ezbHnjrHjC0/w5P/Zzo6vZ8gfEoPOyKa7YHofuZ2rUBsEbCdOvaZSq8jYlRrGoEGiObHk9Vvqeo+8NULfl/pItacQZAFz2mTwlUEmDk4srRaa8V/XVxXY/u9SPPwfCmx/+IfonWNLvt8L/G2GioG/zVW20XkjEWbkIcvC+dxq5/fkObH7BKVxj1pFJpkFcWZaD2KM/J4Rck/sOG0ikJIJHAGzm7MkWhJzUsKeD4xArBl9rUnvI8d5+qs34bkCiXSVbPskyYyNWVURxDZKQ1NIsQSiKIJdwvMkYgmR3E9M9BWnDx8OXlcUNXs3TO6CYg6rLKBlDRAk7HqMlZuGOfTWKpxalKnRGJnOCNlbVuH7PkefOUr72grFiQRD+yD3HNz3b2Hz+9bB1C6Myk2kOwRGj828fFnAd32saYvpoWksw2LHYztO229Y6nrXpms0rGxAzajE0jEm9k9QGatQPlHmQ3/+ocUD7eATwUbueVrT3giZ7rVCmJGHLAvnqhefraXbVZtMpwh4TA8FLrMrt0FpzKbvO22BnnneRKDuR7r5he//Aj/733+W7IbsKVlgGyQCNYm+4hCZtio33XWEVTcdJ6lVQJBRUhEaWqZxTA/HNPBrU9h1AdcWaL8VjDH1pLnUYq9ruo7v2phWGsvM0H37AXKvrUdJVHEdiXo1huuJRCI25YLCUN8QAy8eRBamGDvo4lSmiWt1fAFe/K+Qf7cMajtaq0VxFFItIIrguz4IAr7vUzfqtN/ZPrffMF+nvdT1jjXE5jL1ZGuSVdtX0XVfF9a0tfQgj+pAUPKZT2hNe00RBvKQZeFcb7Vna+mJlgRSPENTe53GLpdoHGSpRq3ooqxYu2QDx+yUoYe/8TDbH9seHL/zkWCUmhgDIYqWNbCqERCiICdAlLBMhVWb+lnbM4AsedRNkYhcY83tFumWwBNlseClb9HZ8NAGRl8/wt5n04z2t7DhrjH0lVMYExpKvM7EcCPxdBUQ8RHx6xX86iDloQKi5CDHVSKyjWAbKPE6nu2Se9aFDZ+l+95JzGkXVYOmlS5KysX3JdQGlXhTnFRbatEmlqWud9vWtgU2teX+fvp/8jqSPUA68ibmyOBpiwLxrtCa9honLK2ELBvncqs9q0LJdmcZ6rNAbkOKFqhM1rHaYsTadJTWjgWPOausbdbxsO9XQG2h+70Cfd9pBNFEiVtYVRGr6tLzkQG67zxK39PbUZIOSqyMVUtiFTsCnfdM8Jovo5SiEsXhIq1rS6y8LYllRDi4q4MmfSNa1sCsRClNx3HtGL4LTj2KGBFRFAM3LeNaMWIpE3yfWlWgbDj4RMm9topu4170j25gzQ+eYGRfHY8oTRuylCZ9lLRCJB454zVY6nrPbUJGDUZe2w+eSNvqcYTSNCo5iN2zcBO685FAJw+hNe01ShjIQ86NZRq4O1vbTepJOno7mMhNUBmTSaxM0PvHHyL3RO6MtfYlteqZLeSrHyP3k8BAKhIfxnU9ihMCWnOVnn/1Gnr7MOCx4fYhdv1wPaWxJKlMidsfeQe9TYG6RN76X3j+Pz1PZayCUylRHS0giRbpWwcQJBE11Ul1upmnv343sdgUE8NNlItJJNlBinh4M+dsjMWIp2rUKh6WCAIixfGg4SbRFkWKJ+n7kx/R++gA2x4aoc9sQ1mxFqW1g8M/PkytWKPttrZFr8GZWCC3e2snbh1WdveTTJTACc5OcXZgHEoC24MHzbf+Da1pr0kE/wo4mm3bts3fvXv3ZX/ekAtk/lT5+RnbKRuD58J8vfl82Vrv53uBwN/76LNHUZtU9K16oBmf9/9nemzfn/wIpb4LRSlhlRysIvQ+tBd9vQuVoyAI5Ee30vfkJhSlgOMo5I81YZYV9LUG8ZW3cOx1kep4iVRDFTU2wfiQhu9LZForbOjJUS41cnTvWqySQzpTolhI4tQjCIKPFPXwHBFBjiBSY/UtAxQnVCpGErMcQ5Y9lKSFIMl03rMKqX4ctSHK9t+OkX+3TO5ZF8PaipRupjhYJLM2M/c6C0cKpDvTuDX33B38Xv0kO/5vE3PaQk3OaOvxMEsC6or1bP/rL53vJyHkCiMIwuu+72879fthRh5ydi5Q1XAqs9m0VbQwBoy57slZ7fFskF793tXk38pz7LljrHn/mrla+3ztNJy0jX36c09jTVtIUo22dhFBJJi3KUjkdm9E37A3kPzVDHI/bUaJTeDWRYYOZZFTGpIf4fjeBPHhAtXpCAIW1SkXuVEiGrOx6z7FyTjlciu5na2YJQE5IiBIMiAiyQ7JdAm7HqPuxYioEIlKZPVJEskorltk6FALvg9qSiDbMUFSKOCndYwxBQTQN6fR1xfIH+8nt3c1pZESo2+PEmuIkdJTIASSzURzYslmq9PuVm7uovu2v6fvn94Dgo0Sr2NVoljVGD09ry3HJyPkKiEM5JeZa9IbuToQeIzM5zxVDfMzcX2LPpdNz77+U4N0qi01V2KZvT6ntoWXR8uMvjOK7/h4rkd5qsDUoSyZjmYaOqAyCeUxF4DueyfRmwcwxmKkG6fp71+JHLWJRKE8CQgisXid4ijEEgJ4PtWigpqqYeZjODWZN59dhecERt2OIDM9lkCWbTwEzEqCpFZEy07jeCkiqgJSAiVRoTgVp/uOIUxLQ025IAQ2tpa7Mthknb1GxzT6vlFB2WAuuEYIkFmTWdhsZU2Q++pfof/qjIlX8UH6vja5sLP2u130bnPp/egb5HZtwBiLo2WL9HzoBPpq83w/BSFXMWEgv4xcCce4ZVk44l1BKcWtQTEXlFbEKGRmuvjOoX6+VOfn7q/sJqkneedb75BckaT5pmaSrYHnx6kbfFJM4vCPD+PWXRRNoV6uI4gCclzGGDTAdZEViek8TA1BosEhpRmYBYu+7zTT+1AbWksNs6RiVRVicQecCraZRhTqlMc9PFvCKolEYiIeMhHbxnUlPE8AT2BmwgKeK1G3QFCChcIXPGJqDauqIODQtiYPje/BGtqPpIiUK0mOvt6ImrbQuyVkUcaq2/Q8Ej15jZ6pBV2kp1yj/hf72fjRjScvpjmKUt+NMRE/aeL1N99DUbehZjJgjqLW94NfIvfGVrZ/7Bn0lRMgxSGaBs+B7Pbz+wyEXNWE8sPLyOX2Rp5dOOZrsk+Tnp0LnY9A6QiMvRDMbxQiwdACcxj6vxvUz5eY2j7LYp2IjuVw8IcHOfTPh7BKFhO5CY49d4zyaJlyvszhHx9m5M0Rdjy2g33f3UdxsEitWEOKSNSrdSYPTeJUHWrVWqC7rojUSg61koNAnVrRIbviBGqyjhKvsPuf11GeEjn0xhqqRoxqScW2HHzXxq6JOE4MJekgSjZ1U8ZzBaxKFElykWSfiOIiSj5z43N8AbseIRKzaMgaKEkLEMh2jJFoimIadQrVrRQnFCShyuqeAohRDr8SYXBfGmtygtyPJskf8KBewBh2gi5SAHMURneglH4CZh5rdOjkhSvuxzLjaB0xEESIZjDG4igcCR438Qq4FoqWxJjugEgSFD0oiUlxSK07zaM85NomzMgvI5fbMW7ZrEYzWyDRCbVx8OpBWaXpPUFWfvAvIHPrXN08fzxD7icKxtgTaFtnPLA7x9Bib2IeKKE2piAdDBkefGUQ27QBSLWnKPYXqYxXOLbjGMJMsFx5/0rMgslLX3yJ7OYsqx5YxURuAsuwiCajuK6LNWERiYEXc6lXRHxPwKl5RJM1kqlpEAKHwWP7VrK+5xCrb+5n8FA7xriGlp0mnq5QMZL4nkBal3DNMuVCHLVBIiJbREyb4mQax5bx3dkg7uO5Ar4v4vsSK1aPsO39b4MokXttHcYJCa0rj7tuG5LfgioeATOP4I9zvNqOEIujdzuYEwX6/lqg939tRLt5E6aVRhVngrGkYllpOjZbWANvAaC0dmBNlbCqSXoePfkWae1RzEIJVZyZ2ykpWEXQVmrQfD+YJyC15qIURyFXL2Egv4xcbse4i104FpRlRIXuD34QfeO8mzjfC7LylvuDnz8YOAMqKYV0oxHcAfzJj+j98Ct035+m7/EUCDUU6xWs6DZKwyWSrTIRd5iIX0NoiVGeUjCOG7RuaaXttra5Motru5SHy2Q3ZOemy4/uHeXgDw8i+AJO1QFPRpJ9wMNHwHVkxgazVCsNjA1qyJKL68ikMiY33XWcyRNJSlMpSkaSjG4i4OHZUeLJKp3rjuL5cbSVjby7cx3+ZAXf9UDwYZ7QK6rUWH/rIaSIR9+P7qL3I6+x/effAb8ODVt48tv/mkRHB+WxDBN7dzNx1EEQXHynhOAWUbMNUGskt3c73b80Y0Tl7kdRVayKglWC3l9VwK6Te/EIxlAarTFFz8eK6BtOvrfdD5ToezwNlFC0JFYRrCKBPj61DmQF7vrGub/f18r+TQgQBvLLyuV2jLuYheO0ev4Rjb6/rdP761H0DTM/ZBugtoNtkD+e4ek/hcoUJDIu2bUayS4VJgbIvdzE9s+q9P4q5J6LYQyB1vo28ZRC1JmGughykpjqIGYMnFqKdR9chyCenAAcb45TGa/MfT22b4z+Hf3gghARcEwQBFDSAiBRKwtIUZdj765GlDxq1RioNY7tW83qzcdJNvo0tvvI0TKrbjMxKypqbAqcIogxzEocVYPura/yzo4OwCMYZjx7BsE/IorM8NEuBMHBqsY4sufjJBsqdKwbYtu/PoTm/CMTP00zMdiIJJbwvQg+ArVqjPKUSFIbQ5Hthfayf/4ixngabUUQiPUNgJ9EXz0Adz0GhdUz5Sx3Tg6qryzQ+wcfC6YjDdXQOmInH1s/2aW5VLC+Vib+hCxOGMgvI5fbG/liFo7TyjIdm8B+ldxPXPT1sZNa8g2fJf/s/6Tv21UqYynUtINdjTH4bhOdTWUSMQNjNMgc9Q0zgaU6BWPPUR65j+N7GkFykb0ijp+mZspk2uqBy2HdZXjXMKWhEnbVxrVd3vq7t1AbVQpHCiCA2qTiez5e3UaUwKmBkoREh4dZkKhbEeKajZoygxuIcpwT/WvY0DqKVYmitdl03zVA3/e7oeaiKGCZMSwzQc/73kZf0U82e4jqVCeOKOC5AoJI8Dc+riuBJDM1ouHUJSTZpTgZ542hLby5YwtKqo7niMQb6sRSJUSpAdeOkGiqMTGYJqlVsUoO2q3z7GU/p0G9EJSpnoOd/wO0lhrdH+hChyUbePTMFvTNDQs1/7PDLNZ+6ozB+lqZ+BOyOGEgv8xcTse4i1k4TivLqK0oK++cmwc51/0H5F5sQEnWSWg1bDtCJOaBLDKxfwKpXUNrNYGTdwVMvwXRJrZ9+CjFyQSV6Si1ahQpatHYleLWD43zdl+B0b2j2CUbz/ewLRtBFCiPFCkOTeN7PmldIJ7VKI26iBEJwbeRowIRFeSog1mJIckOqYYiPjKlSRVEMCbTmJXpoPTwaCP6+jS94gFyz4Ex0YDWYtHz4F70lRUgSduqE5SNOEQ0ImqgMjnxLriOgOf4TI004dZtfMCxZTxXwvcEfAHq1SjgU5n2wUuQaihTsxLIUQ+rLGKWZaxanJ755mKdj5D/pz+n7zsJFC1COlvDnK7T992N9G7Iz3WyLlrnPkOXZu7PTtfhA3Ofj2th4k/I4oSB/DrnnBaOReSDi5ZlZuZBctf2k4/d8xjGVBPpFTGyERh6G3AdJKlAZUzG0rvoufcVqCfmdYVOQut7QR4i3VShOKGA4NO2ZoJtvwz65maODaQZeWMkEIg4EE1EcS0bwbcRJB9EqEwIxBMnSLWuAEHFnPCRFQ/PsfDsGoIQRYyKGFMNaI1FUk0m5YKCYzuomQQ9HxlD79bAtdE78+g/1x9sFHp18B0gA36d7nvGODGwhqkTdRCi+ATbA54LgiyCI+PjzzgX+vgICKKP7wl4Lvi+gIBHLCGwoWeI8nSCkaMa+BHUjELPRxsXvkeZLez+l/uYGDhGrWjj2ApSPIvS5LL7K7v5yF995Mzv5xJBfkGwNkehuB+ldnKQhGlEr/qJPyGLEwbyG5357ffz5IPd7/sN+r4WuOidsSxTHUBr78QsQTILHbfCxDGJyqQd+Kd84UPonduChWJ23Jkgk3/9CH1P3YwSnWTjHXmsqoRVFAPP70ITbh4SGY1YUyOT+0exqxYCNr4PgiAgq4GXeXlSoLFrnERrJ1JEwnM8zCL4ySiJZhG7AogylaJKsskmpqlsvK3G9v+1BO2fAGMvDD0JkTRk74HC7pkgLgVlCSmK/p71PJgV2f0/TjB0dA0IEkrSR5RdPFLUp2x8D0AISufz/viAKHq4nsjkcJzSShlZlcmuhN6PvY3eOQRb/68FlzS/J8/RlwwkpRnTrIIAdslHjNU5+uxR8nvy53dXN7NQa6KBeURDbW6B0oE5VYzWYtKc2sGLP9yA50VJNCdItieRZOmqnPgTcjphIL/RWaL9Xo8+T+/nf/PsZZl4F90PFGcUE5BoBEkKnAx7/3h2kMHMY2bHnTkbyX1rFEXqR1V9cD3UqAfxJLk3tqLfl0FrMRk7ZOEYdWSxTM2REABR8ImqdVxXJqZY+K5HdayIFy2grdIxJ0wyLRO4bgzTAFTw6jZ1KwJ+ncZOgW2/oARNMQf/IpDk4UPDVoi3BTM1888EE4HECOjvB+0m9O4CH/k/0qDKUB3g2/++i4mBNFXDJZqOUivV8OuBxtzzfPAFEDwk0UOQfOSYhyTZDB9bS/fd4/R8cD/IKXY8+TMYf7MXbWt2buMx90QOtSmwpxUlF0mw8GwXa7xCujOzZN160Y3MzrG5hbq5W+Ol/+riWkeINymk2xVEEbreo3LweYmWlQbF8sq5+Z/3/dF9YX38GiEM5Dc6Z2i/1+86h7JM5yPo5S/R+4uQeyGFMVxHa5qk5yNR9OoXYM+Mbnn+guGNYoynSTdOBSlrtAEcEyXbgjHVCAJ0f0DlxH6bqf5JIvEYfkHAc0Wiio2SNPFsASniIUou3e85QLl4Aqn1PYyK7diTMSJRh3pUpl4NYrYU8Whba7Dt4cPo0cMwOh14lbfcD+I+GH+RvPFecj/djDG4Bi11hO77pkHsJvffTYxhGW39Rrpv34+eeZO2FVWm+tciR1L4voySUjANExyCIE4QzB1HQvR91AaRde+ZplxugsQq/uW7qzCGoXmdT2M2j3loB31/8EN6P5XAOLQSfavO1IEx5IiFLwt4SLiWh97Zj3EozZxz4QxLbWRuuPVtxg+0MXJIZXoYkq3gTptUCgmsKtz/b2H8MChaBDVu0NSxGjg5/5NHCbkGCAP5jc5s+/1sRg7nN1RgZnNNTz4RyOPEGFROQGotROZ1etpFaJip2xr70draMSs6arwS6JyNfVhGFa2tEQjULQ9+TmL3148xdGw9ySaolR1isRrxRIV0UxFRhN6f6UNfXeTJv/oZEtbLZBu3MDQI9WKdajFJvSYRiUIkYjO4X2P11in0llpgN+CUYeB/gpwkf0Sh7wc1lJZgE9Wcaub5x9cBNTIrVdJrm5ncu5/vPymhtd5FqsmkVrRJZyfwlHamh1xUTUXNqpSGS9gVGwQBKSIQVT0k2cEYFSgX6jS0xyiOQmkSjLxPpiXGiltrKJk4uZ+YaMpbmGwj025TGhdwbRFRhHSniKzEUNP9p70Ni6lOqhNVXvxqnVV3BM1BCFAZg471NqvSxzHFzYwfBmME0tnagilB4UbntUUYyK83ztM3PF98kNzffA9jrIbWHqX7gRL6yvMcKpDZQn6whdzTOYy3dqC1pOn+gBpIDWcXiMpAYNX6Yhrj8BqkmEhxPAIrEihJsEwNy3Do+aWTh9VXG3zk909AphmiGfb9oMqux+uUJpIIgs/tH9iNvqoAcgatuYJZFElmh+m4bS2HX5Kp1zwETyDZJKEqJpYZ46W/X09T47vo7Sb7dt/Krqe3UppK4DrQ1FEg0zEKER11fQ9Dw0UAVqxfT/ndHYwdjYLgU6vEaGizkWMetuVRnTCQYymSbUlEScS1XMQ2kXqhgtZcDBQqRYf8oTirbzmGW2pkergFKeojR2qUjBSD78h0zIycu/MTNn2PH6Gpo4JTTyCIgA+NK8GqROn5yMhpb8FiqpPiUBHPj6ImLWoVBSUJTh0mhjMktRKKamGciKG1BqPs1NUn6+HhRue1RRjIryeW2Lhk0+eDQHtK/RQIHPPUbaRXHMEsBN2BvX/wMfT5wf8si8O+7+7jxS++iGd7JKIWdk2h7++g91dndOMRjfygTt8/CChajXSLh1U0wY3hmjbF4yNordDz3iPoqzTwtQU6dYafIn9I4mBfA62bplnp7ceqRDj41maauhz0zjzNbcd48dX78XyFRIsAciCDTGZF4u1rYHoviuhQnYbcznVMdmg8+/jdRBWLhFZibDDL8ME2Yg02LXcEFgJurYA/0/gzcbiGHHGQowJWVUZNOqxYN81Ev4qqGqjN4PrBRCA5JhNvjVOpTxGJeljFGmrCwypHaGyz6d/nIEdsBCGCIEvULZnqNOx/FlrWAnKS3k+MkPtpG3WrTq0SJZaC7Erovr+EvnmeZeIMi6mMquNVEq1ZcA+hJGTsuowccbDKErTcjzU+htZs0P0Bjb7vbgQrjRLzL3mjWsjyEwby64klNi7zzz1B31O3nlY/jcQjM7fjGaATtQ0omOSe9dDvnTnmGRYHMlvI78nz0hdfAiHovrSnFCYOu2TXS+SemwnktkFuVzdK19rAc6QioCrToGuomRjbf35n0FG57rfBLZ0+pSa9gdx/fwIlXkJNRaDeicpxAHKvdMDtZQ6+sZGWzjGKUw1UJhUcM4YUEVCTNerlOtWxJPWqT0QVGOlv4/jeNqJKDTVep16LzhhgSRzdKRBPPEdy83uRpFrweocOYhkSMdXFsWWUhANenaaWMUrjKzAmmygd8lASY6y4cyVVI4k5bZJqrLFq8yj4DmZFAVHEsjNYZpxEc4RyIYljlnFrPqIs4NahMg3/8/d81vS2se13HmS7+NenD/To/LXT3vrFmr+kiERyVRayzWTX7mfwDRunHkHN6pj+aiypjZ7PBZ2bvRvmjbeLSUTiEXZ+eeflb9VfpklUNxphIL+eWGLjMve0sWgjSP8L/Wx8aOOCHz+tNnqWoRK5J3K4tku8OY4gCETSWXCHKed9IhEpkBvWCxjFraTXdoDYCaM7QE6hRIsYeTHY7GzYHATxLY+d/royWzBqx0i3DsHES4ALkTRK3MCYSJPbtR4lUUNN1mlaYYIwyqRxM0d3RSkXYlSKU7iWhO/a+L7P+GADri2gZQvUazGMyTSS7OA4Io4tM7A3Tnq8L/Ahd2Ic2qkhiBWssodT8/BUl9wrjbhOI54XpfOWOqNHXARsJvccJLl2DfWiTcumGH69glXXsMoytz80xMG+DFJMxBfqqFkV46iJFKnj1AUcR6Qy6SFJPv17U9hfm6T307+B7n0bhv8J8MlP3Uvuyf0Y48eQYhL44NaDqUEbHtrA+N7xubuu+/7oPg4+dRDTSpDofoCWyBTje8eJtWioGXWBCmm232D+pmmiZekhFpeEsyQNIUsTBvLriSU2Lo2JDOkVCy1kFS2YTGMZ1tJNIIU9MPT94N+RBkh3g6ovGCphDBjEm+M4lkNEjUAkidywgsroJKtuM4JzWfsptPVTmAUTt+Yy8ZqFVckgRRtp6wZau4IOmzMMqtCaLcz9r6ImASkBooNluGjZCsZkI+nmOhAJhjb4Do1NQ5RWtTN6NI1t2khRiUhcAqeO5wm4rkjNilOrxAKJn+jheSK+D3UrRv6gyOqtk0SbVpDfX6c6LeA6SeyahFQJpIT1WgxVE4jJ/XRtsJkYaqAy7eNOHOZ9//t7Gd9fxnijH625TM8Hi+irJmlqHWX3M+/h6BtR1BVRUp0NCH6R6eM1orEakYiPJyQpjdq4jkvun0bQH65Ay/3B4IlvOyiJVxHjt3J8Rxk46RB58KmDpwXcpg1Nc5l20/om7vmDe84YkK9oq/4yTaK6EQkD+fXEEtPQtY13Yy4SsDvu6ggm0LBI089sdiTGwPcDXfVEH2R7QYrNqVq0Lg2n5jC2dwwgmLFZlRGTrXR/7jdh5pe/+5E8z3/heaaOTBGTFBzbpTgqUR6HH/xH2PazZfTNSytlum/fT98uCaQYStzBqipYVZeeB3aT230TptmImvLBqwEiVslh1XtcShNVIpEInhBBjivEs1kEC8rjFnUzilWNEFXq2HUJ34c1W4aomiuoTNZpWlGE9ApS6gkmh6Icfr0ZOeqCpCIIAggikajJxGCcVTePkmzI43tQLGTYfNMP4Ne+Cv0S7P0i+DZIzehb2/nIbVPkvUfIPeuR+96bVPImUkwimowFDoxWDd+G488fZ6KhTPfWLPrmNLnnQWmIoiY8jr9xnFi6HYDJA5Os2r4KgNy3XkBn/1xpQu98BP2x7ef8EbqYVv2Ldk9chklUNyphIL/GOe2X532/gR59fkGduTvZsqh5Vu/ne6F4MHDMe6OM1pmk59MPBrfY3/0rcj9pwxhpQ0sdD0alrfGh8CakN86pWmZrsy03t1AcKlIdryJFpNOaSfQtOunOdNBsMpmgNl0k2eQiqxIj7zr0lQR6//BBlvq11zsG6P34GLmXMxjjSbRsiZ67d6O3j4IQoe+f7wHfxHFS5Ad0zGmRNXdLCKJMssUlGp2GeAdEotS9BtTEce77uXd45hu3YlViKHGLlWsGaFkxxb7X24hrFjhVKB4Au0RxfDW+C9muCoJogVdncjhOpSBjGhmsqoISr5Fq9mlqr8DEq8GJr3w0mBd6St1Xz2xBvxe6b97B//w9AZ+gnd9zRGpViMQdPNdDkur0PZ6i91dnZIKtgBDDKtaJtQW/vpYxsxhHDYy9u6DukB/sIPeMiTH8d2g330H3Lz1wTkH1Qh0zl8U98WKlsDcwYSC/hln0l+drFr2f/030u+YF0QyLm2d1jsH+v0b/1OxmWgHqf03+Zej7egUlEye9QsA0VtL3jxl6H34XfU1pQc1yvjGXHJNZ/a9WL5mJuTUXfavOkR9X8IQ4dbOGFKnjEUXp2rpwk/VU4l3oG0fRm5+dMToJBlLk+1eR270BqywzPriCihEnmSmz+pZpJCeKbzdTnRAQMjYyIzjRVdRNmVW32Gy+6zBNzf08//idVIpxpsayTIxkMSagNJZicqgbJWERjaWZyifw8agWRRINHogy0YTH9IiKkrSIKjammcQ4EKH77jwLTMuXMrgiWKDW3NXJwFtQGvVw6j4CPnZFQJADSaiSqJF7LobWBmYR1EQNJa1gWw7A3OQl60QOrV0mfzxF3zdBSauk2yzMof30fSl6TkH1Qh0zl6Uks8Qd5XlJYW9QwkB+DXM+vzyLmmft+atFa5K5rz8fzI5MWCAqqJk4SHFyezT0+9XTgtK5OjpKUYnjLxynXqkjJ2K4bhRjwqWhI4rCEYzdb8OeHYsrFbSb4dg3g41R24S6wb7XunnpqQ/i+jHiqTKO4xOJ1WhbY5BsApxx2tbUGTnaDr6PNV1GbqzSuK6Zbb/cHHR2ytFg0pEgU6/JlA0Vz5UQZB/bBnNUQ5RcPFdElDwK+TROvUq6sYRVziDH6miNBnVTQlWLNHfYjB+LwcN3ndN7SLyLbY8UsSsR0to0x95uBQEkERIZi6nBFKpaxKjAnb8Soe9vHbBrNN3cTf/OoEaub9UxCybWVIWej6nkngMlDWoa8GOoqgEJ5ZyC6oU6Zi6Le+IZnBtDzkwYyK9hLuqX5wwbmcZgmfSmbTAVZGaIMRS1hjHsBEH2QpmZEyFFpcApEAKDKquAZYDWkVhaqWDshaa7gpFlkkG+v4kXv38/iB7xRhmn3kBpyibZZDEx0kKy4SgIMk16BduaoG31JMZ4HK3ToPvTnwQ62PGV/eReySJFAufFiaEG7LqK59gIoo9Tj4Ig4DoRoqqNJNk4jk+5oMxMIJJYsXoQ35OwTBVwicmTGKNJ0N+3+DWfH6S0m8EaRU88Q+/7FJ7+xgPE4g6S7JJsjhBLCNh1i/zQStbfUUDvHKD317vI7boVY1xh1fbsnGpFbVPp+VQCfVWBnSOZoAQDwZ5BRDuvoHohVsvLNv3qDHcvIUsTBvJrmAv+5TnLRqbWmcGsa6jZu6G4H2wDy9TQbu6Z+yWbq80fOoaW7qf7nhH0LW0Ls+lTApdbXMnK+1dy4vUTTB0KfFYE6kyPSESiZZo7TvDkHypo7RrNm59gvDR1sva/bgR9fQrM4NC53ZvwXIF40kIQUkSiDnLUxizHkaIzpRchglWVaesapPvOIXKv34Zxwmf3//X3FKfSZJrT+L4PvsvQAR3blvE9ASnq49kCcszH9z1cV0SO+KQbTSpGjJqp0NDqEF91grHBJmJKjZhSo1qOM7brJtSkxY7/70t0/3oL+r33L7zms9K64sHgDiPbC63vRa8/QSY7TlNXlaFD7YgROTBQdOtYhkD3Z4KNYx3Ql/I/KTTC/i+htSiYJQU1WQve20zPJe/UvNzTr0IWIp79R0KuJvJ78ux4bAdPfvJJyqNlCkcKmAUT3/OD2+uCNde1uSSzMq/G22ZUHgRKlMKbUC/Q/UsPYhUsTCuN3/wAZuIDWNKtdH+0DV77DPm/fIC+3/tDzL3fIy32BQOE/04g/8KP4ZVfhv7vngxc9cKcJlhT3kJmmvbb20m0JoimouA72BacOJBkYH8WUbKZPFrh2f9cY+LgxMna/+MN5Pteg9IhMEcwRnwSqSqOLQevQZBJNgnYVQ9JKOMjY1YkrJJIc9cUfT+6D7MaI91sM5ITmep3cOUVqA1K4IkS9XCdKIIs4zoR5IiHLFm4Dgh4OHWBYiGYAiRIHqNHExzf10G5kKBej1CvRSkbKTxPIqramJU4ff/pefJ78guveTQDghjcWchpqA6D2gbaZrQVInJMorNHJhKDWslFEGDNbVMzBmSPBdd1KWZKE90fULEKVcyKgt/Yi2mlz+1zcRHMlmTUTODaqGbUcEzcZSTMyK8hTt3ctAwLhGATsThUPPcJQLMyL0GE5rvB2D/jEy4EBliZLfSmF6phen4uge78/6BwmNwrPSgpJ+jSrEmoUhQSKXKvbUBf83Ygt2u+e2H93avT/Z5D9H2vzMRYJ0qyATmmYhtTRBQHzxGYzscojbciR1wiikk5t5uspqCmN0G8Su6nLegdJ0CMoWWL2HWPiXwjRNYgSxaeO0gyY9K2zqBYaETL5Ol54AC5t3qD841bIIi4bpSYajNxTECMpxk/kMR1QJRBVkQ8VySeMvE9C89NACBHXWw7Qr2igh98LUoiIFApJPEBOeahZSv4vozaEAW/dLIufaq0zjYCD3R7ptyR7qb77r30PbEORfdZubWGNWVgVWS2/WxkYYNM+0NBqWmx7sfMFvRHtyzo1NS61Es6UnCWyzn9KmQhyxLIBUH4EPBngAT8te/7f7ocxw1ZyKKbm2uCv7efh1Z4gcxLaQ3+zH49T42y4Jdyz2NwYgwiaYyJFOnGEtg2+DXw6igRD2NQDgYWIAQBavWvBI+1RmH8FfTVMXofOcT3/6wNrFHqVoZUc53yuIjrSICApNSwqhFsW8SsKlhlFyXxJk0tUxiuPjPBx6K79wR9/3Qr2RV5JicUxodr+G6E1dtsVt9WZvyojDHaRm53hJGBJPpaOwiG5jBK3KZejzA9AlYJpJiI5/u4toTrgpqu47kQiUVJZyuYpSi+J+BYEiCC4IMg4XsiUqSGLDt4vkRj6zROXSSSjINXQ2lInaxLnyqti2jB4hltCL5WdfStRXoj4+R2ZTAmNLRmh56f89A3z+yDRDNQmwgWytbtZ+x+DIPqjcVFB3JBECTgL4H3A0PALkEQnvJ9/92LPXbIQi54c3OxTbbhp4L/O1eZV3UgsH6NamjZEua0harO+m67WOUaWlOJYC33g9LB1OuQ6IIT/xw8h+eit0bpvr0DsyTSv88iFqtS8hrxfZBlF0lywY9hWxJSFGIpCbsG/XuzrNpaJD+2mdxPmzFGY0SiVWzTpTrpIcke0aTN+DH48bubWHm7RGNXGXO8xnReIRop06S/C75NVq9x/OBGKhOASDC82RGIpCLIMRnRKdGxfpTej77Jzh/2IMaiHHmjGbvuIQoyouwj4CFHXRwrAj5IkotVjSJISdrWCuBWseTNJ+vSp0rr1BXBNW3YHMgpbQNEGf3j/yf6v50JyK9+8vQGmcpQ0Fx0rt2PoXfJDcFyZOR3AId93z8KIAjC3wMPA2EgX2YuaHNzMf+K4adOvz0/m8wr3gXT+8C1gi7L798E+CixIlY1glVR6Nn+dpCtSgnwHPKvHyL3uooxcjtaU4HuOw4AEcpjVY6+sxK7JlCLRnFsEdeREQQXuy7Pzb0UZz+dggSCSLUAff+wAiXlk26qYBkVRgfWgCSSztjIEYepkTh2zWPyiEdTuh81JdLcOcl4fwPxxDRK3EWSLOLxMaacdkQZfBdEyce3qviCi2OLKPEKudfWo2WLmJUISkLD98C0VHzPR5SkoCTkSkRUmYhSA8Elu6pKItuIyU1YZpKum5vZ8diOoMTR/DM0t+xnfL+BMbEBbdW9dN87ht6xxHswm8W7NSjmgmBfHTq9QWap7sfQu+SGYTkCeTswOO/rIeDOZThuyClckDJgKf8KY+/iBlVL0flIkGGXDqO3j9P7UZvczi6MiWa0zCg9299C75oAPwpOifzwavqe2ozSmCDddAKzqvL8P7wXPIdMyxSrNx/n6N4ujIkGBMkjqlp4nkytGkOOOqhpl7olMXYYYnGPtk0xRg+3osQt3LqAkoyTbbMxK4lgYIKXwKnZ1E0ZKepQHJ3ROvoeTS1T2FUBNVELShbZIi3t40znG3B9GbsWQxBc8Hzsqk8iVUNRShhjWe58+AB9/7gRSawSjYNl1nEdkUjMw65LCJKAvgke/HcxsGvsfqKRAzt1cCeJJ4/w/O/tRoxEiOtNlEYzvL0/Q/tdN9O0pQnTsOh7qi1o4FqsDNL5CLz1BSgfgUgKhAjgQ30KzJlN1GIOamMQawkC9/wAHXqX3DBcNtWKIAifFgRhtyAIu8fHxy/X015XXJAyoDqwYPILcGH+FZktcOsfB7VZUUZfOcr2Xxvj4T/NsP0XD6CvnCLQE4oQaSC3cxVKwkTNZhGiadSUT8WIUzFU1IRJqqGE1limodlAVU0EEdSES+OKMrLsUKtGSbVCy1qHRKPNyJFGyoUUvtxATFOw/UYGj67HsQVqFfA8CSkWRRB8bEvGtb1g5qZTwarGaFuVZ/v/8jIP/+YP2f5oH64t0b5hCNcR8Vwfpy5Sr8s4doSMXsCqKmhNU+grBun9cB9tq0Zx3SRaq0uDboHr4Luw+g548N/N2PXKSexyhZV3JmhfO8DIuz4VI4IUdXCME4zsGkSMiJRPlBFEATWjomSCRp0lr3miM9gU9WyQ49D6IEgKjL8ME68EdXZkiLcH2fZ8VctyvfchVz3LkZEPA53zvu6Y+d4CfN//GvA1gG3btvmn/n/IuXHem1gX4l9R2AMHvwKTrwICZO+C9Z8JAssdXw3+PXvLHtGgsScYWCwng6Dj1jDGk6SbnSBoeA74Lq4NvhdsaiJIWFWFZEOVuhKhY+0hJvJtWGYSjxiKJhKN1UGIgtJMfbSGpEYQEi0IaoQIQMnAH5xEEMBHQMBDirrYlRiCZONbk1gVEasSoeeBXYANvgh4aFmDaCXOirWjDO5fgetKIPrElBqlQppIDHr+1b+AV0NfWeUjv7WLfLWT3A4FY2AarSFP93YL/T3rgkYqIPdMLeiIFY9wfDCOIArIMljTAmrKom5I1Es1aoUK2e4sST159j0OrwZtHwwWyFmiGRh6EqKNoLSAtunkhvX8bPt83vuwln5NsxyBfBewXhCE1QQB/OeBX1yG44YsB+frX1HYs/B23ifwD68OBRn5bOfd/FbqptvBHA0UFW4JpBTaqixmUUT1DgXH8WykiAeeC0C5EMeqqhiTaWJKDUSFVbcWMJ0E/fuztN+9lskDk1iGhaIpKI1FBARcK3i8rMggxUEsEk+7+K6LU/OQIiLJhirRaI3ihIqWnaZn+xvoXWMzL9ADoPv2HH3/fB+1qkJz5xhOPUK1mCAWN4kpFrJcI/faWnb+aBtac4nuewvoq3+C/hCB0qRuBMF1bBia7wdZwRiWSd/UDYWdWGWNqAKO7VGvOjiWgij6OC6Ifpmhlw7Rcd96pJh05j2OxYKxpATa8/aPLgzwp2bb5/reh7X0a56LDuS+7zuCIHwW+DGBZOEbvu/vu+gzuw65aJvP82U2y7KLUBkIAlBm65k3NgefgNp4kFlLM5uqggDW2Jlrq03bgqaimYDT/TPQ91fDEG9GiclYVoSEVgd8JkYaGR/WkSIuXiWGFPUYPNRGs2sjtdxCx70tSFFpzpoV4NA/vQ31KdrWlJgYTGFNNSDFEzTf1ErTxiZKwyWsEwdRYiVSDRM0tU6y/ZF/IT/QSG7XJnb+cy9adpru2/ejd42hr6nS+5FdfP8rPxPowiM2qUYD35PwPInhw22kMkXS2SqmmaTv+1l6P/om+urSTMBrCzLhsZdh+ElQdbS292EWbdSIhpJ08DyZ+qiD40jEVDtQu7giimog2SVGdolkN3edeY9jqWCcvSv495my7ZkFN//cE+SeDnzptY13051sQZ/3sLCWfu2zLDpy3/d/BPxoOY51vbIsNp/nw/wsq2HLvDFhZ7llrg4Et/PyvCxRUqBukN8zQu6JHYy8doDayFFiKYm2mzrpfqCI3jYctPtH0mAOoyvjbNiSYNfz2ylNJUi1wPoHoDDgk3s20Gk3tFRoXWdQLaWoTEF5OsGHPrkTlDb6vtsFtAWbuqNDJJRhiEeQ1CQrt1pYxX4s8RY2PHonB586SOutrSgbj2MNDmCVY3Rv20t+oIm+H96NkqiRbipiVhL0/fAeen9mJ3p3BH1Tgu67J5ns9xgbyCBHHWTFZmK4Ed8Xcb04ghJFlYIR9Lm+TvSuN8G1gq5YAISgdh3R6L71p/R9fwra1tLUWaT8VoKoauNXZZw6iJJH16YTeI6MWZYRvGF6P32WRp2ljKRgyWx7fsIgxSSKgxvIrA2Gi5iGdfrnLvQBv+YJOzsvE5d98sqFZlnxLvJvDJB7pRVjPBmUQ3yH0pTC9GQrqXVDFA+NIAhRzIpEJEkwsPkX16N3DIGxDzyb/PAqDr7dSmvnMCvf085UPsHu70D7ZptkSwwx0YBbniaeLdOy0cO3DIrTTei3tIJdoPfDQ+T2vR9jqI4WO0LPZx3wTHI/LmH0i2itNXr+9Zvoj37y5BScfRk0tUTX+uPkdnWTe30DkuTStnoUQQBVk0Dyyb3Rg751HMQY3dv28/2Xe0GUkCN1nLqM60qkMkHmn2yuzYyVq2KMpYK7jua7g5r06I5g0XMq4FroGxV6f/YwuVcqGJG7WXVHAcpjDO1PIckubavHSWpl8F3MioqaUdDTzwP3n/m9XMpIatPn4dBX58bA0XQX+X3T9H3tyFzCcPjHh6kVa6Q70nMbrHDK5y70Ab/mCQP5ZWJZbD7PhwvMsvLFB+n7/iRercT4sMr0SAJR8og3eEjpNPk38qhxm3hjBNu0KQ9VaF09Re5HAvrH9wQbc9EMuR+BkplEFUehZFAaXE9UUSmPeSjZLLYTQ84kmJiKUC0fZ/AtFacmUvgU3P4LGTY/APrW/YFE8oW/gcogVI6hf0yd2VyUwJ6Cwh70LVuCoLRnB/l/KdL3vfUocTPoVQIGD7bTueEESa2CokgYUzp4eXAm0FdV0XSbWsnFMuMo8RqZlmkE0cMyFbDHINaMVZPQ2qpBJi5GgyYeawzsaYg1z5Wh9I2gr3wHVm4Kzr2wh/w3P0nf99YgSTV8z5uZbhSn572vQ6F+ce+zE4yBm83Kc1/7Hoq6bWagduCMGEvFmMhNkNSTwCKfu9AH/JonDOSXiWWz+ZzHGWvuF5hl5Z718LRbGXvrONWCTURx8YgyPSbT3JzAcw3MUgS76mBbLoKo0tQRw8g7QSu+G0yrMYZM0olxEJJBl2MZYmoJq95Bx52rGOobQopJTB2bYmTCQ5BEGtrBLMGz/3/A19h870BQIiofC3TTszX76lCgm5ZU2P05SK0JXlfhLXLvPICiDaPGJZSEg10TkaMOEyeyJDM1LKsJTbfBrUByLYgybbekmTwwTP1EIxPDWiBJ9AS0bAnfqWFVTSwzQc9vfQxuvRUGnwjKTD+5A2PYQVsh0X3vRHD9XmrAGO8O7HI/lw8Wmd7b6a39mNxra4I6dYtJz/v3oq8szcgHL5BF7rqMsRrpFUeYFZIpmkK9Wp+bIgSLfO5CH/BrnjCQXyaW2+bzrDX3C8yyjAGD4piE3LgSvxTUWEWgblYp58uIsog1JaImbUQJEAT639FYdfMYqO1QeAvUNrTMKGZRQU06IMdRGhswiy5q2iKpJ+no7WDkzRGs8QqRmIPWVCYaEYNhDz7s+maRJvUwua/8F4yxe9FSR+m+axB95WSQBdfGCfLtKMSyIBegfAxjZA1pvRPq42RXOQzlGpEkF9NOY0pNWFaRng/tD2r5iU5QWmleV+aN76+kbgrIERtRBNeJUKvGyA+uoG2DQ88vJJh841We/g9HKOTjOPY69FsSNMg7OfSaxptPtyFHXdrWTdG0OoZpaiffj/WfQR/+Afrqt2aGWAhBSUbKnPRauRAWuevS2qOYhRJqW/B1dlOW4zuOE0vH8D1/6c9d6AN+TRPa2F4mltvmc37NfdHmktksK5oBcyj4+xzkZFqXRnW8iqzIyIqM7/h4jkdMi+GYDm6tDnh4DtiWgGv7lKdinDjeSX76gcBj5cQ/073lp1jTNua0gx/JkmqFelUk2VShNFJi5M0RzLFpBKFOqtkjqnrUTZgeqlMadRg5nOL5b9+NOV0nnc5jVhT6nuwmf9gHP1C/BDgw8mOongisYLVhrIoMiZUkO3Q6tgCihOBVUaUBeh8dRL/9JmjYGniwF95ifM8gsZRPJOoAEpGYi9Zqkmys07auSvetr/LiX9V46j82MX7Mw6mW8BybgZ0FDu9dD4Dr+ljVCBPDLVSmZVwhw8Sbb/P9R/+MHV94Irg28TbACzwB4qug+Y5ARXQ2CnsC07JXP7nQyjbeddI9cYbuB0pY1dSctbEUlWhc10hbT1toL3sdI/j+5e/N2bZtm7979+7L/rzXE09+8sm5DaxZfM+nOFTk4W88fP4HnJEq7vvBOP/8n5tx3AiSEsW1XERZJKEnENwaxeECsTi4dQfbEompDvFsBNeWWbGhSO+/fhl9owDl4+T7G8ntvgmjtA6tU6V5ZZljryc5+mYjapOK3jXMwRc8bEsk1eRQnfYQBRvPFbDtGOkmi1WbjoFnc3x/F8ZEGnxobh/jnodeZvOdM06LYhRirbDmV8i/fpC+f+xGiZdQGlJY9SasgTfp/dnDwXm5FtQKgB14wsSaePJPOxk50kAsbiMIBM6GSFgVkYbsNErC4ejeTjwHxGgU0xBR0lCrRhAlkbZbUkzkJvB9l4Z2CV9QcKtFpJiE54is7KljTZXp/cQo+q1tC++Qzra4zlcfnfo4WPT/8t5vkHvWu3wy15DLhiAIr/u+v+3U74ellauQc9GbL2vNfSZY5PuzHOzLom+0ObHfDWZOiBKxhhiu5bLmtiLcZCMpCqP7HexKiUjUw7ajiNEoE0dMvv/lu+i+r0j3v9qA3r0HvfsIRCeCzLNeYLxwO+tXpIPzHnqXzlvTHP4pTA7KiBIIiIiij5qyiMZtThxppTIdpWwEm66+LzA11siP//uHACkI5r4Dbon8u2Vyu7qxpI0YozVitRhtbQfo+WUPvdmAmgt2GWqjQWNSfAXICbQVEmNDIo4TIaLGQFZxKlXkqEOtEqFhBTi1wCRLFOqIskK94oFv49g+1GoIUQVBjCA3NjL+dj9SVMa1RaIquG4MpRFyfTHQkmfWdJ/KmdRHWx5btLatZ7YsPcQ65LokDORXGeeqN7+QmvuSC8RMsMi9mEZJQ6YjQlStc2K/TaUI5oSJ3qOTTB+juTvFwRegYsRQUwK2ZWEVfRAcYnEJxAhmEfr+R4Tef7MFvX0gKLekN4GcwNi3i3R7EsxNENGIp2uo6RjFGfsdUQIlbhLXfAREjMkE9ZqMKHmIAggRl0jUwXUldv3k9plA7pEfaKPvGQGlay36Fn3uenTfM4J+SxcYFRh/KShrCDOe4k4Z/Czd905w4lCKqaEoyAq+K1MvQ2OHhyDIKAmLWNzFrkuIEZeo4mKVBBB9ZFnAtlxEr0y9Fif/Zh674hNNiEgyROMw9Da03xJl5IBLoX5r8N7O03RveGgDx549xtCrQyBAx10dbPvMtsUHUsBC9VFY2w4hrJGfH0vVKpeRs9a+ZzjfmvvsAmEWzAULRH5Pfs5cyRgBJQnlCZgajBBRbKKJKIhQnawyOaJx8F8cNmyHRAbMYpRIIk4sKaJkVAQpipKwUVOgpDxy/yJB49ZgELFbBTGK1pFgqr/O8Z+8Se4FhQMvSNSrPpEoqJpHU2edZKaGgE/NlPE8Ac8RQRDxfWFmMo8HPpQKaYKWe5HcO/ejdG1FbetceN1+2haUHGrjkFgJ2uZg2LQoBj4utQn0NRUe/JUcq24t4joeXkRn1d1pHvydKG2bk1hlgRUbCri2gG2L4NtEFD/wUlEJvNNjIvF0Hd/zQRRw6z7xBog3BNLz/AGXmhk/7b31XI/nv/A8x184jmu7VMYq7P32Xv7h0X9g33f3LVoHDzXeIacSZuTnymXyozgfvfn5GGid1pCkFKG2m9x/+g76Izsg1oyW/SBmOcnEMZCiLlY5Ejx/WiGiRihNZ2ltP8L4AZcP/UGMvr91UBImx1+PIiPhuipt7UPguygJCeMEwXWS4nPlgeb18PYPokTjLoJkUS1G8X2PdLNDvSozPdFAuknENU0aW/IIXgNWJYrvikSiLoIg4nkSCJDKFIMO1M1/iPHsOtKti1y3IyuhfjSweo1mg2HEUgI8K8jOXQtcE32lxUe+0AqpGGz5zZPv93uz9H1zBammUVbfMszQkU7qZWhaJXLPp6BpJTz9p1CZEkg0WBBrIqo6GMemsMoC8YyI77lYhk9yS9CpOp/iUBGzYJJoTWBOmIiSiByXsQyLl774Ek1/+SC6+NfBD1+oxjs0xLruCTPyc+XU4bmz/x58YlmfRuvSFmh+4eL15hAsEHNBxByF/HMoHMcYTwbyvWo/3Tc/hzVlUpl0kSSHei2G7/vEs3FkRcaqyigr78QYU9E7h+j99Sjq6rsQIirg0LE1QrK9GQQZq2SjrRCChc6vz9mpjh+G9i2gpkXKYy5STCaaViCapWHdCqSoSHFUIqHZ3PrBApkVNnHNQpQ8PF+kWolRt2JIssjtj5bgzq/B5t9f+rqtXx2cQ6wlMPWSVGh7L7Q8CLgzUyUUaLg5GGDR+Ujw4BnVj745zYb7yowOrWJs7GaablrLQ1+U+PQ3p9n8/sC+NtMBNz1YY9WdCqm2FGIsiba6Cd8TqZXqCKLEmg9soO2OjaedY3W8iiiJ1Mt1RElEjIhIkWChcm2X3LPeBamP5lhkCPZpdrch1zxhRn6uXCI/ilPr1s03N3PwqYPA8ujNZ1mwOVrcHzTp1BJouhMEckFA7xqj9yN9PD3+IJVSA9GURDQVJZqMYpt2cD51DW3rdrhrOzqgPwrdH32Rvj9+EkmK4osJLDtCYdLBzd7Mk79/DC3WRff9RfTNaYwRaOqEbEcNq6xgCylKgyVK5RJOzcGzLFxHJt6S4qffXY9tCaSaHGTFp1KI4tUdXEGm4zaZppu6gmlH6Q0L9wyiBtaJHNZUhZ5PJYBHYNufL1R4iFFouivQknu1xTPVzBbygy0c3PMjWjcOsDI2jFUrc/CnDTQ1D6HfBEQ0tJYa5nQddXUP2e4EQ31D+EKMps0r0bfqWAWLbb/bC3DavoYUkVCzKpXRCpF4cAfkOR6iJBJvjgd3YpntF55Bh4ZYNwRhRn6uXIJa5WJ164NPHWTDQxuWTW8+S/cj3VgFK9AX1wzMkoBVkuneuhumdkPpGDgm+s2NfOgbv8mKO9fQcXcHgiBgTpvYpk2qPRVsID7SveDY+r330/uHD6NmYhRPVHDdGKTWIqVagtflraXvmwL5fUU03ccyauCaCDENc9zEl3x836cyVsEq+siqwNgxlckTaaREClHRkGSfdLNLW7dL0yqBVItA3+Np8v1ZGHzi5J6BUqT47i7UhEnvJ1X0VUEGmt83zY4nf4Yn/2OGHf93ifzxDGz9k8Bf/a5vBAqQmcCW35Nnx2M7ePKTT/L0Z76LN7UPNWEFAzISForcT+6N2+ay5O4PqFjiLZhWmkRLguzmLPjMlbLmv3+ReIT+F/o58E8HcOsu9/3RfWRWZcAHx3JwbRe35hJNREl3pM/9Tmyp/ZtwuMQNQZiRnyuXwI9iKSOt8b3jbH9s+8WeccBMfVSvDtD7UBe5XZsw+jW0xDA9972CvuIE+DMDk90qTL+LvmWM3k83kfvW89halZoZJ9bSRtP6piU1yfq996PfG5g/7XhsB9I8aaTaFrSL5148Qve9I/R9p42Ks5bS2DSWYQUbhAAC+J6AVfSJNwhE41CZhKZOh5IVwfddlJSPqkyjMgpygtxzGvrqICjpW3R09kPdgWhq5swy5A9J9D3+PMqaO0lveWBmxJpF74aF0r/8njy7v7qbo88cDXTuW3Uq+QmqQpxYg0SyCZAUlDQYx8fmRuXpQO+GmTurQ8fIav3c+/8eQd/SBp2bIaMvUCNtfGjj3J1W04YmHvyTB3nxiy9y9Nmj+J6PtlIj251FlMTTFs0l3+Ol9m9CQ6wbgjCQnyuXwI/ikhtpnfILrq8qoK/4YTB4+e3HoTIMSEHLuO8FdrVSDA59FV2soH8qQ/6YRu4ZE2P4IJgNwMnAkt+TJ/etFzAO7EfLGnR/SEN/7yOLv67WDoyhNPq/eYwNyj5e+uJLOKaDIAv4dR88EGQBMSbg1lzMaY9Ui8j0kI9tubh+HN+2cKoV2rqnwDVxyja5t2IYJ9Jod+wIFplFSmC5F1Io8dIZnSdnA+3EgQmUxmAvYfjVYSKRGq4fY+IoQSAHrGoMLbvwPdK36OidY7D/GzPlm9YFATX3xNSS7pfbH9vOx//h4xfuV3+m8kloiHVDEAby82GZNbvn2tSz7L/gxl7QbiJ/wCe3c1UwkLjFovuBMvrqaZh4FVruJ388Q983QUmrpNsszOO76fvD/fR+YiTwDH+8AUXuJ93gYE6a9H2lQG/+t9HSv8DkEYfScIlSvhRM9RGhoauBfd/dx66/2IVruygNCk7eIRKP4FgOvufjOQIgYpU8tKYCmRafiOjj10Uk2aFz/QmSqTLlqST9764gFrdIJ/OYI4P0falA70NdQTllXgZqDNdJr0gtuDSnLpizd0du3SWWjiEIQcesZ8fAdqlMSYHhYRksw6bnkUVKHmcIqMZAz1kX7fMe4zfLmfZvQkOsG4IwkF9BzqWpZ+6WXC2TjhzB3F+i7w930PsHD86VMpZk/i+4NQrGfjBHwDbID6+k74d3oKRBjMc5tCfFnpcl1vRMsO3DR9DbNXJPl1HkaVQqYArB34mbyL2sg2eiOEdw7ST9+yWsahpJdtn9ZJbVN32Ft599H6IsUymncOoSvuvj2i4//t0fI0UlUh0pmAqUGb7vB+UVDxB8BMnDtaFSiLC2ZwQ5JhJV6+A5SHId3xcYOdYEArSttxAkEdV9G9wkuR/kYds+cm9sxZhsRGu1kCQbi5tQ512aUxfM2bsIRVOwTZuIGkFWZGrVBpo7BilPKhTzMlqrRc8HJ9Hf+7klr3f+IOSeA2MENL2B7ntH0Lq2L7poS1GJHY/tuLh2+rOVT8KmoeueMJBfQWY36OZn2z2fWjgxJvdEDkUtozq7QVJRM0kQauT+5nvomxvOOiSCegG8Ooy/EpRP6pMgyOReaUdJ1CiNRRnINeH5IpLk0P9uM7bfQm9iAKNfIN1sgxgLpHt4KEkHIx8DVMQ6DOUi+ESoV2VqZoSpoQ1UizJN+hQDBzqw6y6iDHI8Sm26hiiLRLwIbs0lkU1QTBepG3UEUUCQfUTRxfMhotrEk2U8y0TV6vT88lFwquz+0WoO7F6DMZGmQTdnujQjUDmKktjAyOFWCvk4SnScdIONWdEpWqthWALFXHzBLOxBi72JeaBEtiXF4LsakAQfpHgCqXEzH/r0AHrHrA77c4tf93gX+X1F+h4POmTTrWBO1+n7ThsbfvV0NVLhSAEEkGLSxU2NCssnNzxhIL/CnO122hgwSEeOBPpnKajdKlosaLY5m4Rs9he8eCAIxuZw8H21A2OqEVF0GMjp+L5HJOrhEaNUUHHjLeR+chytWcA0k6iJoHmmXM4yssfFJegArUy0IngWpUIMzwHXBUHwOfz2epINZXw/aOJB9HHrEngQTUVxag5uuQxVg0xLndFiFFGGSKSOHLWJRGqsvmUIz4aHP/MMAPmhdnb/ZCtH32lDTZo06CaeC0PvanR0OyA2MLJXCbLgtjRtG2IIiRhq63bImrh1FzWjnr5gFvaQ/6c/pzzWzNHXkqiaQ2PzMMViJ6YhsOZ9a9j2W9vOLbB2PkLuz76OkqihpqLg1XCtOhMndEb/+CU67urArbkUh4poXRpup4sUlS5+alRYPrnhCQP5VY7WpWHuLwWZ+AxWOfCdPquEbPYXvO9Xgq99F9SVEEmi6TaHdjbgoRBRXQSlCWyXqGxTPjZEpEHmzo+8S98/bQEUHLOV/n1N4MPKXv6f9t48OI77vPP+/Lrn6J4ZTGNwNoiTNyRSlCBTBySLoiXbkRXbshklTuLsxnGq/NqblJO34ko28Xqjt/LG+27F3jgpZ9fltZ04u3LWiUObiu34kGVGtgUdlCzBojm8L5AYkCAGM8Cge47u3/tHAyBAgsRBnNTvU4UiMJzp/s2A/PbTz+/7PA+lMej/eQzQqZQ1NC3ohRKKVHAKJs6ogRAShEQTPhKBj4/0JLouadl8lsGzMUqFMIlUBSM2gq5LjCqNusYz6HoJ0yoDkDmZoufbtzF4PolZVQYEpbEglx6Kljl3OEa5HAe9QiQeAgl9P4vQsm2ERGMQAef78jM6gQ5+aS8/+lwT7phOpQiFXIhLZ2JsuCfLu/72w/MW1Jx7B0nrNFRyjOYs+o42osdjSK+CHtFxs+5kxL3vg/uI18enHWLBm90qffKGRgn5KqdzTyc9H98PoohhRYPNtjx0vXNkbhay1A5oeQ+MHIXiMDhnoByn8+4yvU+/GS1UwS974F3C9wTJOpfCUJSOW0PYWyTd7zlE+oVNpF+rJ2oUaNo0RqI2Aakilq0xeDqKHvLQdZ9QuIzvB6UJxTEDPVzBK2uEQhJECU0TFHNjCCQHf5ggFNVItcAdbz3Jz77fgFeWSOlTHItSHIvhVXLs++8Pk71QTaKmgFcJEY1LhB6FcAhZGiNsCi6cqqFm3ShNGwcZPN9A2fXQRZlzr4eJXnidQlYQb4iT6c1g77AnN4/7XzxM33MuQpMUxyJIqSG0oKz+0smFjWCzNq/HydqYKZPBY6fQE8HFyKw2r4q4l2JqlOKNiSoIWuXYO2y6/+ghzPgY+fNFzCpJ96/nse0jwQbmXBp4WduDIQpaJMgpVwrYDQfZcOclYrERKqUQCJ1k7Qh+uYgW8ul8JEnmWIT0j2rI9UsQGsk6l8GzCdJPu5x6xaD2tnY0DSJGiWishO9rlIpR9FAFNJ9ItAQIfCnQQjJoQ+t7hCIVhK5RLkL/IXjuH1vx0QlFfMaGNc4db6DoRtBDPsnaPIV8gotnG9B0QYVqCCcI6UV8rRp7Rw1Wk2BT1wUSyVHqGk5RKULRCZHNxHEunEf4earip+j5o09z8NNP0PPJb+Oc/hnumZ9RKQkKw0bgvgxVAElhSFIqRq5qVDYXphZeucMuUkoqboW6W+qA6RH3tCItXwavmaHgSqGYDRWRrwHsN+8KNjYncqAiAs7EQIX62Rt45V4PytGd88HrvCKENXY+/DLlylto1HXyGRi7oKGHBA/86mGIbqfnqR0YRhZ3TOPSuTgDJyxCUYm1TlDWmxk9UiTRqFHKa5RLOp4nCEfKSF8gtArVDTlipTLumEk4XMF1TDRDQ9d9ED4IjYoPpWKY6sgYXjlC+22D9B81qJTDmImgD0q8uoRTiCDDFn45DBpIt4Ju6Lh5aLk9jCtbMTlKwirQum2Uwy80ooV0zESJuqY0ieYmnNEYL32lTGP7S3i5PJfOtVIuhoMhzT4IQNM8vIqOj7mgFMfUDWwAIQSt97WSaAxSY1Mj7rlsdisUc0EJ+RKwYN/39ZiaA+19IijcmWv/jLEzULUJkluCIcb5NJSHsVtO0/0bRdI/gVAY1m+7FMzF7Bhi/79sx0iUGBmq5eTr9fh+CDSolAXZsxJLc9DCGut2rqNy7kUKwyGG+qvRwz5Ro0hj+0XGRhJU/DDx6goP/MoRnvrMDsJxga4FQ5Z9D5AS6UFYHwNg8EwMzzOQ0oNoLZTz1DUPc+bIOirlMG1dkElXcAtxNuwosvOdZ2H4ID3f2AqxCkbCRA/7hEMuW+7OUVU9CrIcVGRWwcjFMLWNRfp+nkLoAqFJpC/wPY1ySYKvIYWGc8kh89zz7HvPT7G23kLn+x+c8+9wYgN7wl6qR/RrzsuccbNbdStUzBMl5IvMXAdD3BDzbeA1YUP0ikGKRTeCqF43sa1nsD/wIJg2OAZcOA9aktx5STLuc7jHQo9o+H4w9MEvg9AEY4NjbHvfNvyyz64PP0j6y98g3aOjh32aOgZI1ArQCziFMmYSLvaliJhBDl2EIyBCCK2MX5LoUQmRGkKeizsi0KMVCCUgmYLyKAn9NI3rxxgZsfCLJTbfM0bnL+/EFp+HXC9UGXS/u0z6uUZyF8JYTUNseNN4qqQ0BJEaINgkrmqAzPEEoUiJqlCe4mg1vi/B1/ErOkFc7lN2BaNDETRRxDn5PD2fLND9J4/O7Xc4U1uEvtLcIu5lapesuLlQQr7IXKt/yjUtZQuJvubbP2OqDVGPkjlRRfrHteSG78Oy+uh84Bj2myRkXw2m5uhxrNQAjruOohMmbJTwRAjP1whHIZJKUHYgZIQwm0zsRx7Dvud2On+wl54vFtCNMtKI4TpR3JFLdL39DC98vYOWzmFO9jaCFkXoFfxK4GYx4w5lxwM9gR7ziCeGwajCyUmMWAjXTaJpPo/8u29j3xqHLb8L7Y/Dv/5V0IJWCOyNo9htmWD9QifTv5meb3SCqWMksrjnT+COxbjrlwy++2kDvDCer6PpHloljNR8pK+hhSRSCsIGVEqC/iNRttwvoXBmbrbAa7VFmKsQq26FigWghHyRmVf/lIVGX/MtAJm0If4mmRNV9OzbhFGbJNkawxkO0/O1i3SXX8beqkPToxAy6HyoQM831hGKXsAra2ghj0pZQ4+W8MYKhKKxq9MEW6D7/XnS/1ZN7qyL1abR9S4Tu24Eq26IiNzEhroWzr8yTLlQACTV9WOsv+0cmVM1OHmdDfdq7HxXDpJNwWzLgQhWjU7XrySwb31H8F7PPUXmbAPpv28jN/QmrMYinfecxq59iczpOtIvbaL/dAsjQ0lKbj2hSJmWrTm6H/kx+A7h0C/iliMIfMKRClGjSCEfh5AkUeNTckKETfAqkB8AtChGNDe3nPlMQlwchAMfhaoNs1+sl6hdsuLmRgn5IjMvS9lCo6+FFICkdkDLY6S/4WA0mJjj1xrT0qEUIn3wYey3XF6zfSt0O9+nnNvB8Z4IoUgRq9HBHQlTcX023jFI94fumyyqmbgg2bc1YnfmYPQ0mM3BUInYO+j8nYfo+fwlqhoNbrfP4w70ke0TJGsLeJUwm7vO0XnvySDiXvcOaN2DvWUv9O0DLUKmfzP7Pz1Erl9Dj+jkc98mVVtFMnkOZzBMz1fr2HLnRo68vBHP0xi+mAo87CGobx0OIn4qpF/czLqNfVw4axOKeITCFdyxCIWRBKnmCvGaCMPnfDxPQwASwC/iFi2szXOwBV4pxO4AZH8GVKBh1+wXa9WtULEAlJAvMvMainwj0ddCCkBa95A792WSTS7IaDBQwXMwqkLkzksyPS+RfrYqaKLVmqDztgv8yn8LB42u9jUxcsmkvn2MzTv7KOubeOFTz2A97dO5fT92xxUXpMSG4M+prV6T45vAB0axLJeu38pg24dAhIIvdxCGveD9H/0fUH0nSEnmiE7PP5cxLEmyIcyxly2Koy7JpEBEypixEsgoL333ThrbMwycaSYU8QiHXMrlMCOXYjS2XyD9yp3kLpapabyEV4lw/kQTRSdKxCgSNceQvklZpjCTGXKZCL4UVK+r4AwXcbUtdM3FFnilEOcOjU+Uarg8WQqufbFW5faKBaCEfJGZi6Vs0tXyahtWg0Pn203sLeN/uZTRV2oH1va7cfoOYZq5QChSXbinX0avnKfnn9ZhVEmStQWcgRF6Tt5Od8Mo27qPs+2BiyAEmaMher6+CaPeIFmTCzZzv1ig+4MW9tbx93cE0k9Xk+sbxdq5f9K1M+nQ6N0P508GT5atZA57pH9cR+5iF1ZDkc7u89ht52HoeYg2kf5xK0aijGkWQavGK+tEDZfBviSJN8Vh5CiG6TCSTdK+LYPrmESNYKRaKOLjFgyMWJlcv49Ve4nB/jqGMjXEk6NYdXncsSiVkk4sKfEAGW4g0ZCj4paxmsKY6++l7a7tpPemeeEzL1zfiXSlELsXQAtBcspF4HoX61VSbr8kzivFkqGEfAm4Xv+Uaa6WzZ04p1+g5291uj8Qwl6/9NFX5/sfpOdTEYgbl+8Y8oIwMhDLBCDBTJQhapJ+2sP+5QgH9yd56V/aGDhZRTjq03JrBnNrVZBCqomT/r6DvdUkcwR6vgx+uUz+YoK+fzxI+utpHvjEA2x7fFuwiNY9cOkADB8kczJOz77tGOYIyboxnFITPU9V0/0egd3SD5VhchdNknUOSAmyghErUXJ13FENjBqoFHBHoKoR3GI1RsKn7IYIRwSVko4RL+K6May6ETrvPMzXP3cL4BOKeFTKYUCwbtMQhVIH+bNZnNEoZk01d/3+Xdz/B/fPz4l0pRAbDWCuC1xBE8x2sV7hcvtlcV4pFhUl5MvMdFeLibn+Xug7RPq7OeyPppY8+prxjuHXh3nh/zQTj18I0i1aFOI2hu+Rc3dw8BV4+ks6EaOEFoKKp3Pip7WgF2ioHcBY10nu5y9BKUv66WoKQ2X6D+lIEUGLOFTcIt/84D9x8itfYv39VVy8cAu5E2/DCkUZvQRGooRpFEELBxcQzyP9XCv2rw6BX8BaF8IZDmPGSyBC1G2Oc+olj2i8EvQId6pwhwe56+HnOPLKVhL1GhePCyqVMFKGqFnn4o5G6HroKHaHpLo+hzsSoejEMOIlmjb0Uyh1cO71ENXrSiQ3tVHMFznwNweobq/m4usX5+dEmirEU4cfr5FUybydV4oVRwn5MnOVq8VsxNjYQK4vDzseu+brMr0ZDvz3A/Q93wcCWu5tYedHrt+V78rX1GyuIVYTwyt5WG0W9/z+PZOpDutZB6fQMbkJiufiOgmszet56XuCSPIoplGhOObj+zqeHuL8YYuGWw7hRu7B2n43RA7R//Mx+g/FIBRF08MUhx2kVyEUlZzureL4iz4tt75ITYvAGdvCiUNR1t8D6K8GhTveGEZVjNxAHHwH9Co63x6l5+90iLVimNXo5RI1LUWS9aWgk6B1ga73nsRuOUNtu0f6hc2US80UHZNoMkxtZ5LON1/Crj0Ffoim7UmcCwOYsfOBp95s5si3koQMH9OKgKZhVgfi9dJnXyK1ITU/J9KVdtJVkCqZD0s+uUqx6CghX2YW0igp05vhmT95hqHjQ0Srokgkp/afIt+X56E/f2hGMc/8+NngNWfKRBNhSl4Vx7+Txaw12birGufoT3nmP/wrySYTjxR6OU9+KARNJQy9H3ekguu10/VWjZ89OUJYSIYHayiVoFKEUBTcAjhDI7hRl66PPQg73kdR+zs8MkTNKMVcEaF5CAlSajjDEIlrnP1ZnIvH8xipOHoUzr4Gsfhm3OExjFiRhB2irvEiyAok1mNvbKe7cSPpfcfJnR3Fak3Q9bvvCNoWHPgoFC9AtAGS78XebGPfnw3mj3qD42PXLChrUNoKt3yMzpYGej75bfB/hpGI4o5FKRYkqeYyRJsnP8NoMsrIuRE6dnfM7Xd2PTvp+KbvWkA181p7KCFfZublahknvTdN4WKBaDJK2AwDQQ+PwoXCzLe72V7Sf/vPFIaqiFaFCUcqFM5lCRlxfNflUu8h6jZoDJ0zKQxX2HTXCVw2weA5vNw58n4sSLk8XMbWvkAk1kX2ZIRI1CdsaqBBqQBhw8esqaLrI92TXQVHMiNUChVKIyVkJZj2o2kSXfp4JUGx4iN9sFJjlMcMSgWDsSyI9jjRKh9nRCP38wi33D8Id//PoPAHsHeA/cgMH07VhsDWJ6b0fwtbUOm7ZiRsp6D7Tx4l/WR8ct5oTbuFr9VD+HK74GK+SFVz1dx/ZzdJMc9C/o0qVhYl5MvMQhol5c7k8IoeUSs6+VjICOHm3Jlvd8/uJXchhlcOEU0AIkSlLAlFilRK4I5FGDytE4mDVwkhwiamfgnaDcxoLbsf7wGnLzjWUD2puiaGTlbheUVCuo8QGnpYsv5NY+z+5L+fNiVeD+uIsEA6EvCRXjDBLaz5hPQyFS9M1PQReoSwzFEphgjHdMyEh5uPYjavp6GjiYv6u6B99+X3dK0K2Ov5rq+zaRhsSL9v8uf6rx3k6T98GoYdoskoxXyRUr7Erv+0a+6/s5ukmEc181p7KCFfAeY7ZNdqs7hw8AIVtxJE5OVRKvlBQn4JKzoA2fXTBWvsDFZzKxdOQaUE4SiEoiLo062DUaXhjoIeCib9oEWhnMPQHXKnCzB2CkQUkOD2E5Vn2fCWB+l/JUcxP0bULNF26zDRqB6IK0xOiZdeMHtT1308JPgCTfOJJQv4FR03F0HTNAbP1SB0n7IDVfUVOu4OQ/IWMBuRvgwuUNnewE8+8Exg4zObof7+6SmLRfJdTzhqXvrsS4ycG6GquYpd/2nX5ONz+p3dRMU8Cx4ErVgRlJCvATr3dHL+wHmGjg9BeQzpZiiNhahpD9O5K391pWCsjc4H85z/eZKhs4CEsOHh5HXC1VDbWiRzLEpxFJpuIXCqhC3cSyNYtdlA2LUghYPnY9WNEAn30/jbu8EZgMHncAoWZnVkUlRzR9+Clqgj35cH6QWNqBBousRqKEBFYMZdKmUddBPfA+FXEEKgay6UdQBGB0bpf6Ufb2yU/f/3t+i8sxe7eSRo8uVmIPNDaHo4EMuze4Pc8yJtJm57fNtli+RCUMU8ihVCCfkawN5h89AnHwocKM/0gFek49bz7HxsEHtjG2ip6XnY1j3Yo5/ioY/Agb1V9L3moYc8Nj7cSqwminehl6YtkL8YQddLyLKDK7bhjg3R9bbDgV8bCX4FpKTz/gF6vlOArIPhHsItxHALUboeZzL6tJKn6X16hLJTBt9HaKDpPgLQwzq33neM0eEop9JVRKs8QgxTKfoUQjEqZR1n4DyVgWc5fXgD6FHat+WCwcVP3Ub3O/LYGwrB5qdXCKolk1uD8v2Zmo1le4NWv3NpRLaYLWNXSTGP4o2HEvI1gr3D5p3/pQ1+9PsQroGQCZ4LF/ug7t6r87B6DNt6hnf+lgj+fvNHpgvd2b1kevtJ/6SJ/tPtFMc8oqKG9CtdoP0cu30QECAkdvNJut9TT/rETnLHR7Fa4nQ9zuVq1LBFfetFcmd0hCbwfZC+hvAleqTCyGCUzjdf4oW962i/o8ylUyXcEQ0jVmLjpiFG8wlMS5DuiRKNjdB0/1YSleMw5oIIkX5pC/b6l4Iyfr8YRObuAISTV7tDYO6NyJaiZayanalYAZSQryXO7oVI7fgPAnQzsNmd+yYY9UEUam2Hc08F4tT8bijnyPy8QPqfD5G7eHJKufUT2DuAHRmyn+qhOmVgRAyc4wP0fHMn3e89gt10JBjYHKnD3l6Nfdu3YE8M9PJVeeCLZ+sJmSGkJ9HEeGpFgkAQMYukX1xP/7kW9EsmTc1HSSRzEE7ijMVoahhl92/0kRuIoCU0BtOD9GUsjIhHbcsoudHaIBr3K0G5e3kkEPFU19X9S2DuzpGbxGWiUKiZnWuJsTNQfUcQiXtOIGhj/eCNQs09QUT5+p+Ni28KhEbmVIqerzbg9B2aVm6d6c0A06v4RNzG3Lwbo76e9I9qAAGJjdD0VqjaTOZ0Hfu/kGDfn4bY/1mHzGE/OGcpSy7fTs3GGkLREGZ1iITlEEu6QZZGi3D0lTYct4YLx8L0PruZ9CubuXQ+gTsaovPe0zB6DF3kOX1AUB7JEa2po1yOcrq3Gj3iQ6Qe8ALhDldB/a7pZe8T7pCxM8H3U7mWc2Q+z1UoVjEqIl9LTLgi6rqDcW2FdBChmh1k+po48FXoe3k3iBAtb4KdvwLpHxD0UOEknM9hhi0wN076z2esNN36KLlXJGy+c9KfnTkCPV+pwogMkmw0cQbO0/O5CN0fjGE/+jGszUOU5SClbJ7SiIvvRZDSQ9M8hKxQ9muolDRCsRCVgsdwJo70JLve93Ps+p+B5wE64MHIUfAtiNYFM+HkpcBi0/o4bPkPQcRcyk7/bKa6Q2ZwjmT62kg/sX96E6ibyGWieGOjhHwVMWvHuQlXRCQVFMGMd9bLDN3LM5+HC8fBd2OUS5D7Hlw8AUbMxW46FdgJQ0nwXIzyAXJHK8Dua1fxtSagfFnk0j8Aw8hhhi9BqAOzaQMMl0g/M4b96OUikqbOAqMZKORCaHqIYgHCRoj8uSKe56NHdMJVBpqI0HFPiYsnIrBTQKQJzzdo3z7Mpb44bt7BSFawH7wFT78LHv3y9A9rJndI/QOQeRoGng5SUKk7yJyIc+CrOidei2M2HMW+w77cBOpDD2FrX7j6OMplolhjqNTKKmGioMbJOjOmQIDLrohIKijYMRrA2k76J3UMnyvj5MoUxzQqJY1K0SdzGC6dLHHspzbpF9s5dUAwmjVwnRhW8jQQCLCbdXGyDtKXDB4Z5NT+U/SfbmL//4DMwTxIn1xfEUPPBLl4PRivZlhRchdik7npcDzM4LESbkGn/U547ydBD8PooI5XlmhhDd/zKY2W8D0NY8s7yI11BhuxZgOW7REyNDruGKHz3n467hKEKqeuLg2/8nOY2A8491QwlLrh4eAzff5lev5XmP6z7Zj11QD0Pd+HV/IwUgbpf+mHUBwuPBu81iuq2ZiKNYmKyFcJ1+w49+S/YXNouj1uom/HuOsidzrH6AUDrxRC0yVaSCB9n1JBkC/HSDZCpCpE2YVTB6CmNULXO/uB6VV8/a/2kzuZo2F7AzUba3AGYvR85Tjd7+vHamnCuVCLOT7IGIJhxlZzhExvPz3fC9qebn1LBDdXxC0EVaiRGBSGJJou8D0fTdOCsTsCjn33GF4uwf6/cei8XdL55iw9/1wVtKqNR3FHo7jZwswDHa50h/Q+cXnjMgLEmkjvdTBSJl5/lGgihBACgMFDg7TfZZB7/SX45Qg0v+tyNK5QrEFURL5KyJ3JYVjGtMeMSI7c6y8GAjPVHpftDZ4wHpladVnKJR0hQNN1hKaDFgiXJETHTo+IEcygjCYgWV/C3tE0eR57h83uJ3bTdEcT7bvbqd1ci9AEZlMrxoZ7SB/7NTo/8mHcUj3OcAnpg5MHNw+dD46Q/knT5Q3T6lsw42MY8SLppyXJuhIxq4IeiyIrEt/zERFB2S1TzBdpvqcj8It/fQv4Rbrfewwz5pDPN2ImXLp/Oz63CsMZNi5zAwZGNIema2SPZRlMD1LIFBg5N4h77Gks6wxkXwtSVBMXgQnnyxQyvRn2P7GffR/cx/4n9k+/S1IoVgEqIl9urlGAMmOu+nwaqzkEkarggZnscakddL49ynNf0/G9wMPt++CXQUqJLzXwi3TcKUGLIitFMoc99j95B7nP7JuWi79e+1J7h033Hz3EgU9/g8P7dUCnZXsRynly+dtIbhy/CJmNUHcfRugQub5RmrYlCKcsRs/lGL1YplIO4xTCRCyDjgc7SNgJcEwQB0j/yGL3b57DftNG0N3gwjXhDb+Cq/YTNsWw674LfonM2XWkX7qF/rRBn2dRKhWoFCvoUZ3S2BgMO2TPaXR9cDRw/wz2BBvIRsNVjhU1ZEGxFlAR+XIydcjAFRH2lblqJ+vgDhXofFt0+jFmsMfZO5rY1F1GDwfmD78MWihIsYQTUc4ebWV02IBKnqF+g+HsOhw3OSlMz3z8Gb754W/S/0o/x757jNGB0cljT2tfmtxCObqd9p0htt6fRzcMer59H3qyHjfnXl6Q2Yhr3IO18510vv8h9FIfjZuKbPuFEFt3FYlXjbHlrbWBiI8/39j6KDntXcHgZVkGvwR6DA5/JkibTNyFMMN+Qv9Zev6XIHNEkDlm0vMP1Tjnj9LccZLCJZ3iSBGzPrhAylKJRD0kGyR2x1DgxdeNwAU0g2Nlmj1TE5gpM8iv703fyL8EhWJRURH5cnKdAhR7xxMzdJyLY3dkgVnsca172PWbf02l1Ej/4TBeyUcP+2iRBKF4HEIhLg5UozfZXOw7Tf2OusnI3yt5DB0bonChQPM9zZx+9jSn9p+ifVd70GFxSvvS9N40RmMTZmoDACZA1sErerjZQMintj1te6CN9JP/hDsqyJ13iJpDNG0psmFnNe7FU1w6DaP9o1TGxkCOUd3gkjliYN/16OWipnADmYN50n/1RXLuHVib1zOaGZ2+n6Adh1SC9E/vhMIZjPgYZtyHUIVY0sEthihmi9R11lFX00+8Lk6+vwaKWfD6At+99CCUgDs+Oe2jVUMWFGsBJeTLySxtTq/qOJetmVsTptQO7Hd9lIf0/8k3PhECJEa1Sd3tTRCtZfDQICPnRzDfYmKtt6jdVDv50sFDg0SqInglj6qmKjoe7KD/p/2ce/EcnY91Tmtfei1Ry/flr7oItT3QxpGnjmAULmI3D+LWmrgFg857+7h0JsPTf9+FVjWCc2kEWXaQvkaoI0rP35bozvwVdlcbRFLj/vUkRrxI0jqNk7U58fQJ1j+8/vIiyjmMZJLcaQ+kTbK+Etxr+kUSdRrRYhEvnKJjdwcMnMLJFrEaveA5HkHFqB6F8c3QqaghC4q1gBLy5WS+BSjzaMKUOThM+hkNwnH0iE7d+hIJ7RWw7kO/o5GOt3Sw+4nd7H9i/zRhcnMuuihi6FnoO0wibLFpVyf5Sya7n9g97RwTouYVPQbTg8FrIzpNXU1XXYT2P7E/iJplATyBWQWICumfNEA5T8vG05w9HoWKTzQmiCQEFReM9gjp52zsLX1QtZn0D4Kc/8CxKG6+hLFugJAZIvNqhqqm8b2DsIWbLWLV5UCL4oyGMeMuaFHqNuiceqlMtFFH+hLX34ibe5WuXa9BuBrCqaBStv4+0CJXledfa8hC2wNt7L+ywEjlzBUrhBLy5WQhbU7n0IQp05uh578+gxGP0bwjxOkDcOqVKPXrBfkXD+E4NWx46wYyvZmrhEnXihQvDdD0JjlZMOSefgFr/b1XnadzT+e0kXNaWKOYL5I/lyfTm5kmZJPRe84INhRlBSNaInfeA+LUrCtxccDDSg0ioimkiOCOBv3Rc6dqoHgQgP40ZPsgHPWIVkUoO2UqboXicBEn6wTiOiHO7xoEJD17N4AnMOrrg/mebVGS25qC+Z5trbR115D+/jle+HorejQEkRSeH8OyJZ1v7g960Iwz05CFybsNtQGqWCUoIV9OlqjNaXpvGiM2glmdAAEdd8GZn8KpA2FqWousf3g9elSfFJupwtS0MUs+JtCNCFKCWzBwCxpddx266jz2Dptka5LCxUJQVGMZrHvTOvSIftXIucmUhGkHvc3LI7gjeaz6MoRMHKcaI6lTHo0SroxSkTUYicvedLQwlLIUR6oRwiccLoPRSDgcphKvYFhBjjwQ13Fx/rEgd2qAcLSCp9vkL4SwGsbo+uQ7sN+8C5jiQqETLVHk1KvBZnL7TgIb5Feb6N4x/aJ0zbsNNWVesUpQQr4IzFpaP5XFbHM6bmXs/8EYxWEP1y1hWFHq1oOZBFnx2bwrCo1Vky9J701PpkzSe9PkDoyStON4JcgPgNUEXe8JYbfM3DjKK3ps+oVNCO1yPnlyos8UJiN/cyOGzOKWm3Bdna5fOATlLD3fuoeq5AADQxaV4hiEPFItGu5wma73ObD9E5B7nag5hpOPUdbqCIXiVJwy+FDVUjX5Pi5bBB8m2ZXDPZ/GHSrQ/dtR7Id/bdrnPelCMW7h1PdeIRqvgAhx6USFjjvGwLp1VkFWG6CK1YYS8htkxXzG41bGzOk6cgNVSF/HiA5THrPoey2KO+pT3VCC5J0AjGZGJzc9RwdGyZ/Nk9qYItmcmKzE7P7N8R7jpRxEZs7bT9v8cwYgf4ihEwVGLsXZ9/4hrM3rJy9kk5H/0QpW6jRd9xzAbjgKepTud71G+qXNlAplisUU0ZROXXOOzkcs7Ic/Oi6+j9P08H7CRwYZPT+Km3MxLIPUxhR1W+om1zS9KtbE3GxD1iH9uon9+I5p3v3cq20kN3eCaeNWmohGh8Efr0Stuw8j2jCrIKsNUMVq44aEXAjxF8C7gBJwHPgtKeXwIqxrzXDN0vqlvs0etzKmn01SvxkuHI1SkRYh3aVS1qgUIyQ2bQazkdHMKH09fUghSaxL0P9KP8V8kWRLMqjErDwXrPnpCHbH8HXz9pORtjuIUTrAUH+cvoMxmreVSEZexekP0fOp7OSFzN5hk+ntJP3kv/HCt05gpZrovLcPe/0F7NazoFdB8yNw919c93yNtzdO22zsnFK2f1WE7AxguIfIHRiFF78KhbNQtRHMFqwGB+f0C5jr78WorabsxAEwrHDgf886swqymjKvWG3caEHQ94HtUsodwBHgj298SWuLGUvrl+M2e7wkPdcPNS3QegeEYwbFYgxj3WbqdnSgx2pxsg6DhwaRIhj0UH9rPd7YKFF9kMEXfwz5Q1C1NWiA1VcIHDXXaRw1EWmb2nHygzFGBiM07xDUbYggwiamdnxawcxk8U7fIZK1Dk6pkZ5v3kHmpBXMBo3WBFN/rsHk+VIm+b48Zsq86m7HarMuFySNzxR1c0WsljgMvQKjx4OGWEKj8+0mbsHE6TtE7dZaivkixXyR2q3BZ3XlRWKha1IolpMbisillN+b8uPzwOM3tpy1x4rdZo9bGa2mFE4eErWQqHZBN3AiNmbKpHNPJ+m9aUbOj5BYl6D+1noSyQJGaIBSKRykEzwXRg7jhnZi7WyFHbtnPbW9w8b+zcATv+9PIdk4/hdaNPB011++kE3csXhnRzl9rJmRoRAlN8y5Y01s332BzruPYLdcv//3bBPdp0XIV84U9UvBIIp8Gkwbewt0fyBE+rs5cmWfjgc7QAS5f7PJnOabv5E1KRTLyWLmyD8IfHURj7cmWNTb7PkMAh63Mnbu0un5ShV4JQxzfIhy1qXrl+PYfA77kTMw0IbjV2M2JmDgAHUbBKde0YkmQAoDtyBwC8fp+p23zbrEyY3dV9uwGhz0iIk7Gmyu4hcDT/fEhSzbS+7V/WhilL7XwJdR3NHgJnA0G+XS2RA952+hu+shbkQSp+XjD1wxU3TAgspYYPWceP76HPZHU7DjsRs4q0KxephVyIUQT8OM/88+LqXcN/6cjwMV4MnrHOdDwIcA2tpW8QSWeU5Vn8lnPNeo7qrzzmMQcOZsA+l9v0ju8CHCoRE8v4p8aQtWeytdb9WCgQml4Fidu/L0/P2rABjlHHo0SU0bJBvGnSp20NZ2tjVP29jd3Ilz+gXy/aFgSlFTiYpbInO2CSd3lA0PWGT+5X9jNdRytCdByHApDFbQQzoSiaaXGblk0rhzK+mnfew3z+/jupLJCLl3//SiK+sWGNgfzPiUvhoeobgpEVLKGzuAEB8A/i/gYSnl2Fxes3PnTnngwIEbOu+SMFVMpxbsLMewgd4nrq76nPh5ov/4OAe/dpBn/+zZ8QENPkIIjKTBA594gG2Pb5vxWJmDedLPJsn1g64XQYvilQO7YeeuPPa25PQ+5zNczK6sCsUZwOk7hDc2AuEqTrwUx2yoxr7DJjT6Mu5wiS0PRfjBZ8C0IHe+AsIDGaLK1pG6xdZHmsgfTfPYf5zbhXNWZvodjp4AsxlkaXHOoVCsEEKIl6WUO698/EZdK48Afwg8OFcRX9Ws5FT1WfqwTJDpzfCjP/tRUN04UpwclqCFNZ79s2ep3VKLPcOx7FsT2OvPkKl8gJ4/34dhQTwVwcmW6Pl7QffHx9Mb17kzmNE/nYB8TmDZsPntNmZTa/AXfTmQSS4egw33BhWaCB1Ng0R7K0IXhEPFoIq0ITKnu5A5MVPR1e1/fu3jzfMOTKFYjdxojvyzQBT4/rigPC+l/PANr2qlmKOYLglz6MOS6c3wnY9+h+ypYJJNKBoibIbxyz5eyUMPjVdY7rn2sdJ7fYy2O4KOgeUcZsoKimAm0hvXuZhZbbtx+s8Gr3UyUBrGLdvopkX6BxWQP8doyFF3WweJsIURc8n1G9zzG9DzZUitK3PxZASv4iFLkprWQdyCSdevRECweBfOuRZdzTOdpVCsVm7UtbJpsRay4mR7YeQEXHx+fBbmLWA0Lt9U9Vn6sEzkpwsXChiWQeFiAb/io4U0tLBGuVAm1Z4K3CLXOVbuzEmSLS2gtU6e2phamXmdi1nnWzV6/vxVsCIYuos7GiabcSBiokejSF9Qzg/S1xOiZXsKfeQAVsLFti7Q/UvrSf/Ioqy3URwzQMBIv0s0GSX9g+A09haW78IJK3sHplAsIqqyEy5HZuY6KA1BaRgu/ARSt4HQl2djbJY+LBM2vnhDHKELnCEH3/cpFUqEjBCappFoTgRukescy2obuirP7fYdwjJz0PvTSQvhTNG8zTN0/3tJ+tkouWMali3xvBJ65CKhWAunX9aRnoduDHN6JMe6LfV07UqDexG7fhj7P38C2h+/vGm6zsAwXZy8Qc+XCSpLO5b4wjk1lTL0CtTcE8z4nGA5LyQKxSKhhBymR2bhZOA5Ll6AsXOw86+XLzq7TkpgIj9d11lHX08fCTtB/nyeilshbIRpvLMRPaRfLmaZeqwJ8Tr8GTq3t9HztTagCSOSwz39QpDeeE9VELUXzgZ9uRMbrr4zOPwZ7FtbsLcBAyfAc9j3l3cgvSJDpyBe7VEc0yk5LiNjYbb8ThT7vruBu4Nj5F4HHp/W74TB5zDjMJaN8p3/UiFlh7C230InmcX3aV+ZStEOwsVnoeFBMMfPtVx3YArFIqJGvcH0wb2mDY27ofVxqNqwam6xJ6oXE3aClu4Wki1JqpqqqGqqorm7mdZ7Wq+uLsz2wosfgR/tgfP/CoSxO7J0P/ocppEnfzSNWR2h+7ci2Fu1QOCqNgYOj0gKnL7plZ6xtst+7GQneC5WbY7MqRr0SIVYskxqQx01zSVq2zUuHpvyBqZEupPVsOPzPUeHDQYOVygMh0neeheOm6TnUz3XH3Kc7Q3cOc9/8KpRcNdk6gVbaFBz5/ixfhpYE0vZ4Kt1z5x/LwrFakBF5DD/gQ8rwNTCo3hDHD2qY7VZ1y4Nn4g+84chXBM8dul5qOvGvjUOsUOkL+XIDSSvzlFX+qZZHjO9GdJ/tZ/c0XYsI0vnW/PYtzaAtY3O+87S+2/rMVIhpGlTqUSplCO0bC+S658yb3TK5zmtGtZsZPCCg6hyiFWbiLiNGbQ/uXa/moVuUl6R/8+caST9nUfJnc5itY/Q+UgK++EbbyusUCw3KiKHIAKbiMZWY2SW7cXmc3S//TuYpRfIHz81e3+PiejTL0HInDZkOHPSoueLBRzHIllfxMkHrpLMEWZ0ykwOOt7YgRPaSc9XkmR+NgDJLdjv/xs2vPt+RLyZohO4aFrfvJ5QyMVqcMgc9tn/WYd9fxpi/5O3TA63mDpounChAD7UdV7uaHjdfjVXRtYT35/de/3PccodReZI8J6d0QjJDW048bfT89TtZM42zOc3o1CsCpSQw+XNwZnSCSvNRPRZymLf1sju387y2O/8kN2/V3P9HPJEuihsBf1UADQDyjnS3y9i1MQxW25BSAcz7mJUSdLfc666gF01Rb6pFWPDPaSP/VoQtad2sPMjO6nbWkf7rnbad7WjVzXgardRv9Wk50sOTsGcljIBpjWdijfEqd9eT8JOTJ73uv1qpqbCJpjLJuWUC3b6aYkRL2LGx4IOkClzWrMvhWItoVIrEyzmwIfFZKEWuVhbUM35zE5ypy5hNZbovC+DvSFC7lyF5K2dkzlq8ocwjBy5C9ZVF7C5DFGYuU3Bo8FFYMtlh8zUlMnu36vB3rMfxs6Q6Qs2YJ1sfG79ahaaCpvi5sn1jZJsTkD1HcHnMMP7UijWCkrIVzsLLFLK5B+i5+/3YVhhkq21OEOD9Hytme4PJrG2343jJgNhNRun9OE2r7o4zLW740zdAF/4zAszXwSOnoRDX5rMcQcbsH2kD76NXF9p9n41C5l9OsH4BdvaOd5uwFTDIRRrH5VaWe1MdYpMMIfoM/30eAVnKorQPMymDozNbyN97HE63//gtBz19fpwX5nPnmvPbriiT/g4bs7FSp6evMvIHNXY/8UUL/xTPeQPcc/v38PuJ3ZfFvGZ3CmLkAq7kfelUKw2lJCvdha4EZs7k8NobAmslC2PQeNujMYWcmdy8xqMcCNDFK4plvf3Q9i6vOGYh2RTBGdoZLrtcMr+wDR3yoSY73gC7v3SZK5+PqjhEIqbCZVaWe3MUvF5LWZLicxnMMJChyhcs8Uvr5E5mOc7n05SyEI8BXXtJRINVRAxLtsOl7iEXg2HUNwsKCFfLm6ky94CNmI736rR819fgNgIRnUVLhtxncSyz5WcSSwP/t1d/Oj//QnZjMRICAQefcOClgfWE58yXWhFm5gpFGsIJeTLwXJ32cv2YmtfoPvX60j/WxW5c0WshgN0feiXljUCnZwmNB6NT+Sfn/3LM2DUYVTlqRQ9vLJOrCHF4EmJnpyy4bgGCrUUitWAEvIpzCQ8iyJ8y91lb+J84WTQHlaPgu5D5hlg1+KfbwamTRNqSeJkHXo+1UM4FrTdjdWn0I0EubM5pIBiQSAvFKbbDm/EnaJQvIFQm53jTKtgnCI81+33MVcWWsByA+fLnLQubyQ2gjNq0PPFwoLeT6Y3w/4n9rPvg/vY/8T+OR3jqkKi8YKbvuf7iNfHqbgVIokIVqtFKBrCzbnEG+LTNxxXc6GWQrGKUBH5OFOFB5j885r9PubDcqcIYm2kv+9gJM1gKDJgJoog4vN+P9eKrGdzeFyrkAgBieYEgwcHAQjHwxgVA7Pa5JG/fuTqY67WQi2FYhWhIvJxJjvyTWHRKv2Wu5dL6x5y5yoYpgtSBiX6noOxrnPe7+dakfVspezX8pC33NuCHtKp21ZH2AgzdnEMJDzwiQeWJ3+/kK6JCsUqR0Xk48y1gnFBzNVCmO0l84O9pL+TIzdoYW29hc73Pzh/gUvtCKo3+w5hmrkgjRNrwz2fvjxAYo6umbmU6M/E1G6NU8vuuz/WDQQXiLARpuMtHYu3FzEbarSb4iZFCfk41xKeRbPrzZYiyPaS+Ze/puerDRhWkmSdi3PyeXo+WaD7Tx6dt9B1vv9Bej4Vgbgx8wCJOQrY9S5w19scvqaHfMrfLztqtJviJkVIKZf9pDt37pQHDhxY9vPOxpxdK0sxeb33CfZ/NugUOJHXxnNxCgbm5t3sfmL3vA85+X5e3Y/V4ND5djPoOQ6Xc/ZT+o5f6xgTOfKpF7gt797CkaeOTHs8ezxLsjWJV/QW1/WzWDz/wSASF1MyitIPNlLv/dLKrUuhmCNCiJellDuvfFxF5FOYU6XfUt2ej50hN9BKcurptShGNLfgPP3Ee0n37Zt5gMQcXDPXiqyv3Bz2ih5Dx4coXCyw6Rc2zXlTdFlRvnTFTYoS8vmyVLfnsTasRgdndEpE7hdxixbW5oXl6Sejac8iWb/wIcdz6Ww4mB4kWhXFK3mTm6KwANfPUtztTKB86YqbFCXk82UxysZnEqvWPXS+OciRI8MYsSJuvoirbaFrvCJyTqmfKcdOf7kNw9yIWX15yDEySvp7LvYHbkzArsyduzkXLaxNc/7M2/Wz1JuRC+xbo1CsdpSQz5cbvT2/QqwyB/Ok/+qL5Nw7sFrexpaHDnHx0IRrpYuucdfKnPzcVxw711ckWXcAuG/WARLz5crNYT2iU8wXWfemdZPPmbfrZzk2I5UvXXETooR8vtzo7fkUscocgZ6vJDHiRZLWaRz3Ho68djvdH6rFTj4DY98FDkF2D+m9Q7MXLF0hhFZLFCcLZv5Q0M72OgMk5suVufOmriby5/LoER3py4W5flSTLIViQSghny83ens+RazSPwAjCWZVBCq5QJzdQdJ/ux/7I0xLL+SOvoXkxo5ph7oqdXGFEHY+DD1fjoAcwahfoLhehytz51emfq475Wcm1GakQrEglJAvhBu5PZ8iVrn+oA8KfnGyF4vBcXIXYhCJBs+fiK6Tp3Fy9vULlq4QQnsLdP/6COlnk+T68gsT13lww/291WakQrEglJAvN1PEyrKrcYZLmHEHUkGU7A6PYDUnpr8mbNF5fz893wtK3q9ZsDSDENrtWexPfmDR88JL0ilSbUYqFAtCFQStBOPOkkxvPz1fbcJYtxGjsSUQ5xMv0P3reextU8rix6PsDB+el2tl0e1741yrSGhVecYVipsQVRC0mhgXVpu9dNNP+ieQO17B2ryerj96CFv7ApS8q9ILdmoOqYtlcGUsaadIhUIxb5SQrwRTbIL2bY3YnVkonYBb3hSIcLZ6VacXFtpIS6FQLA1KyFeC2fzSixRVL9XEoyXtFKlQKOaN6ke+EizDxKClnHjUuacTN+viZB2kL3GyDm7WnZzJqVAolhcl5CtBrC3IfU9lkf3SCx0IMRcmioHMlEm+L4+ZMtVGp0KxgqjUykqwDH7ppc5j37BnXKFQLBoqIl8JUjug+d2QfQ1O/0PwZ/O7F3VD81qj1lQeW6G4+VAR+RJx3Y3GbC+cewpSt0PDriAiP/cUJLcsmpgv+cQjhUKxalAR+RIw60bjVNeK0C5/f3bvoq1B5bEVijcOKiJfAmYtmFmmLn8qj61QvDFQEfkSkDuTmzZgAa7YaFwG14pCoXjjoIR8CZh1o7F1T+BSKWWD4b8T37fuWYHVKhSKtY4S8iVg1oKZiS5/kVQwwT2SWrxxZgqF4g2HypEvAdeaPD8tX61GjikUikVCCfkSoTYaFQrFcqFSKwqFQrHGURH5TcRSdTtUKBSrGxWR3yQsZbdDhUKxulFCfpOwlN0OFQrF6kYJ+U3CrEVICoXipkUJ+U2C6naoULxxUUJ+k6Cm9igUb1yUkN8kqG6HCsUbF2U/vIlQRUgKxRsTFZErFArFGkcJuUKhUKxxlJArFArFGmdRcuRCiD8APgXUSykHF+OYitWDKv1XKFY3NxyRCyFagbcDizunTLEqUKX/CsXqZzFSK38J/CEgF+FYilWGKv1XKFY/NyTkQojHgHNSytfm8NwPCSEOCCEOXLx48UZOq1hGVOm/QrH6mTVHLoR4GpgpIfpx4E8I0iqzIqX8PPB5gJ07d6rofY1gtVk4WQczZU4+pkr/FYrVxawRuZTyrVLK7Vd+ASeA9cBrQohTQAvwihBC7YLdRKjSf4Vi9bPg1IqU8mdSygYpZYeUsgPoA+6UUqpdsJsIVfqvUKx+VIm+YlZU6b9CsbpZNCEfj8oVCoVCscyoyk6FQqFY4yghVygUijWOEnKFQqFY4yghVygUijWOEnKFQqFY4yghVygUijWOEnKFQqFY4yghVygUijWOEnKFQqFY4yghVygUijWOEnKFQqFY4yghVygUijWOEnKFQqFY4yghVygUijWOEnKFQqFY4yghVygUijWOEnKFQqFY4yghVygUijWOEnKFQqFY4yghVygUijWOEnKFQqFY4yghVygUijWOEnKFQqFY4yghVygUijWOEnKFQqFY4yghVygUijWOEnKFQqFY4yghVygUijVOaKUXMGeyvXB2L4ydgVgbtO6B1I6VXpVCoVCsOGsjIs/2wqFPQSkLZkvw56FPBY8rFArFG5y1IeRn90IkFXwJ7fL3Z/eu9MoUCoVixVkbQj52BsLW9MfCVvC4QqFQvMFZG0Iea4Nybvpj5VzwuEKhULzBWRtC3ronyIuXsiD9y9+37lnplSkUCsWKszaEPLUDbvlYkBd3+oI/b/mYcq0oFAoFa8l+mNqhhFuhUChmYG1E5AqFQqG4JkrIFQqFYo2jhFyhUCjWOErIFQqFYo2jhFyhUCjWOErIFQqFYo2jhFyhUCjWOErIFQqFYo2jhFyhUCjWOErIFQqFYo0jpJTLf1IhLgKnl+FUdcDgMpxnMVBrXRrUWpcGtdalYba1tksp6698cEWEfLkQQhyQUu5c6XXMBbXWpUGtdWlQa10aFrpWlVpRKBSKNY4ScoVCoVjj3OxC/vmVXsA8UGtdGtRalwa11qVhQWu9qXPkCoVC8UbgZo/IFQqF4qbnphZyIcSfCSF6hRCvCiG+J4RYt9JruhZCiL8QQqTH1/t1IUT1Sq/pegghflkIcVAI4QshVp0jQAjxiBDisBDimBDiP670eq6HEOJLQogLQojXV3otsyGEaBVC/FAI8fPx3//vrfSaroUQwhBCvCiEeG18rf/PSq9pNoQQuhDip0KIb87ndTe1kAN/IaXcIaW8A/gm8J9XeD3X4/vAdinlDuAI8McrvJ7ZeB3YAzy70gu5EiGEDvwN8A7gVuDXhBC3ruyqrsvfAY+s9CLmSAX4AynlrcC9wO+s4s+2CDwkpbwduAN4RAhx78ouaVZ+Dzg03xfd1EIupcxP+TEOrNoNASnl96SUlfEfnwdaVnI9syGlPCSlPLzS67gGdwPHpJQnpJQl4P8Aj63wmq6JlPJZYGil1zEXpJT9UspXxr8fIRCd5pVd1czIgNHxH8PjX6tWA4QQLcAvAl+Y72tvaiEHEEL8uRDiLPB+VndEPpUPAv+60otYwzQDZ6f83McqFZu1jBCiA+gCXljhpVyT8VTFq8AF4PtSylW7VuAzwB8C/nxfuOaFXAjxtBDi9Rm+HgOQUn5cStkKPAn87mpe6/hzPk5w+/rkyq10ci2zrlfxxkQIkQD+Gfj9K+58VxVSSm88tdoC3C2E2L7CS5oRIcQ7gQtSypcX8vrQIq9n2ZFSvnWOT30S+Dbwp0u4nOsy21qFEB8A3gk8LFeBL3Qen+1q4xzQOuXnlvHHFIuAECJMIOJPSin3rvR65oKUclgI8UOCvYjVuKl8P/BuIcSjgAEkhRD/W0r5G3N58ZqPyK+HEGLzlB8fA9IrtZbZEEI8QnBb9W4p5dhKr2eN8xKwWQixXggRAX4VeGqF13RTIIQQwBeBQ1LK/7bS67keQoj6CfeXEMIE3sYq1QAp5R9LKVuklB0E/16fmauIw00u5MD/N54K6AXeTrAjvFr5LFAFfH/cLvm5lV7Q9RBCvFcI0Qd0A98SQnx3pdc0wfim8e8C3yXYjPtHKeXBlV3VtRFC/APQA2wVQvQJIX57pdd0He4H/h3w0Pi/01fHo8jVSBPww/H//y8R5MjnZetbK6jKToVCoVjj3OwRuUKhUNz0KCFXKBSKNY4ScoVCoVjjKCFXKBSKNY4ScoVCoVjjKCFXKBSKNY4ScoVCoVjjKCFXKBSKNc7/D+UcUCzcOBgCAAAAAElFTkSuQmCC\n",
"text/plain": [
"<Figure size 432x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(6, 6))\n",
"for name, group in df.groupby('W'):\n",
" if name == 0:\n",
" ax.plot(group['X_res'], group['Y_res'], marker='o', linestyle='', label=name, color='orange', alpha=0.5)\n",
" else:\n",
" ax.plot(group['X_res'], group['Y_res'], marker='o', linestyle='', label=name, color='purple', alpha=0.5)\n",
"ax.legend(title=\"W\")\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [],
"source": [
"# If we compute the correlation between X and Y, we'll see it's a different value\n",
"# if we control W, than if we don't do that."
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.8637995074698627"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 1. Not controlling W\n",
"df['X'].corr(df['Y'])"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.6869890857793172"
]
},
"execution_count": 13,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"# 2. Controlling W (real relation between X and Y)\n",
"df['X_res'].corr(df['Y_res'])"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.5"
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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