{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"id": "2c5deafb-2eb5-4ffb-8188-9e1183203658",
"metadata": {},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt\n",
"import datetime as dt\n",
"import pandas as pd\n",
"import numpy as np\n",
"import statsmodels.formula.api as smf\n",
"import statsmodels.api as sm\n",
"import scipy as sp\n",
"import yfinance as yf\n",
"import os\n",
"\n",
"from dotenv import load_dotenv\n",
"\n",
"from statsmodels.stats.stattools import durbin_watson as dw_test\n",
"from statsmodels.graphics.tsaplots import plot_acf\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "d0955884",
"metadata": {},
"outputs": [],
"source": [
"\n",
"load_dotenv()\n",
"fred_api_key = os.getenv('FRED_API_KEY')\n",
"from fredapi import Fred\n",
"fred = Fred(api_key=fred_api_key)"
]
},
{
"cell_type": "markdown",
"id": "b8bc7241-3c4a-4731-9c5c-fa2438a97ee4",
"metadata": {},
"source": [
"# What is Autocorrelation? "
]
},
{
"cell_type": "markdown",
"id": "3358f1df-afd6-4e71-860f-7c448db3cb4b",
"metadata": {},
"source": [
"Recall that a classical linear regression model \n",
"$$\n",
"Y_t = \\beta_1 +\\beta_2 X_t +u_t\n",
"$$\n",
"\n",
"has an assumption\n",
"$$\n",
"E\\left(u_{i} u_{j}\\right)=0 \\quad i \\neq j\n",
"$$\n",
"i.e. disturbance terms are independent of each other. However, in many real situations, this assumption will not hold, especially in time series data. Many economic or financial time series data has a 'momentum', for instance, if we see a boost in consumer confidence in this month, it is more likely continue the momentum next month unless something unexpected happens. \n",
"\n",
"However if this assumption is violated, we have **autocorrelation** issue\n",
"$$\n",
"E\\left(u_{i} u_{j}\\right)\\neq 0 \\quad i \\neq j\n",
"$$\n",
"There are many reasons why autocorrelation exists, but for now we don't care about the exact reason.\n",
"\n",
"If we say a series is **positively autocorrelated**, it means correlation between successive values are positive, vice verse we call it **negatively autorrelated**. In financial context, we say that positive autocorrelation is **trend following**(momentum), the negative autocorrelation is **mean reverting**."
]
},
{
"cell_type": "markdown",
"id": "1beb4b8c-7883-497b-ba8c-c437fafca609",
"metadata": {},
"source": [
"For instance, weekly return of Microsoft (MSFT) has a negative autocorrelation, which means the possibility of mean-reverting trading strategy."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "0392e99d-27b3-463a-aedf-e4c674b6f1c3",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[*********************100%%**********************] 1 of 1 completed\n"
]
}
],
"source": [
"start = dt.datetime(2012, 1, 1)\n",
"stock = yf.download(\"MSFT\", start=start)[\"Adj Close\"].pct_change()\n",
"stock_weekly = stock.resample(\"W\").last()"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "9d85488d-0375-444e-8273-5de5dce4e68a",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"-0.07145398624533127"
]
},
"execution_count": 4,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"stock_weekly.autocorr()"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "e057d0ce-ab54-407e-8e80-734b5b66628b",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"g = plot_acf(stock_weekly, lags=50, color=\"red\").set_size_inches(16, 6)"
]
},
{
"cell_type": "markdown",
"id": "58168352-5278-4f25-906e-849210c70bc8",
"metadata": {},
"source": [
"What about interest rate, let's try with 10 year treasury yield."
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "3727e4ba-5b92-4be6-83bb-134564c39429",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[*********************100%%**********************] 1 of 1 completed\n"
]
},
{
"data": {
"text/plain": [
"0.06290619628423107"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"start = dt.datetime(1950, 1, 1)\n",
"tr10_yield = yf.download(\"^TNX\", start=start)[\"Adj Close\"].dropna()\n",
"tr10_yield.diff().autocorr()"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "deeeb654-2d60-4afb-8499-249b7e76245b",
"metadata": {
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"/tmp/ipykernel_215000/2352089167.py:1: FutureWarning: 'A' is deprecated and will be removed in a future version, please use 'YE' instead.\n",
" tr10_yield_annual = tr10_yield.resample(\"A\").last().diff().dropna()\n"
]
},
{
"data": {
"text/plain": [
"-0.18313492055652775"
]
},
"execution_count": 7,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tr10_yield_annual = tr10_yield.resample(\"A\").last().diff().dropna()\n",
"tr10_yield_annual.autocorr()"
]
},
{
"cell_type": "markdown",
"id": "99b81047-f3f0-4d46-8a31-2d4a373a4442",
"metadata": {},
"source": [
"We can see that interest rate has considerably high negative correlation at the annual change rate, but not the daily change rate. ```alpha``` is significance level such that only $5\\%$ of chance an autocorrelation falls outside of blue area."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "8861efca-6003-4eea-936b-bc0462383a18",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"g = plot_acf(tr10_yield_annual, lags=50, color=\"red\", alpha=0.05).set_size_inches(16, 6)"
]
},
{
"cell_type": "markdown",
"id": "e45a5cae-909e-4f5f-94f3-ef3774727093",
"metadata": {},
"source": [
"## Does White Noise Have Autocorrelation?"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "b3bcb88e-f165-4140-b8ce-09694ba25a3d",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"white_noise = np.random.randn(1000)\n",
"g = plot_acf(\n",
" white_noise, lags=100, title=\"Autocorrelation of White Noise\"\n",
").set_size_inches(16, 6)"
]
},
{
"cell_type": "markdown",
"id": "d902f758-6dcc-4a5a-8b2b-e93ef443a8f0",
"metadata": {},
"source": [
"Stocks price are random walk, but the returns are usually white noises, so we can't use any models to predict returns of stock prices. "
]
},
{
"cell_type": "markdown",
"id": "dff63e44-eac6-46d0-a5c2-dbadab5cc83f",
"metadata": {},
"source": [
"## Seasonality And Autocorrelation "
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "e4969cbb-5d86-4423-bab0-4cb0747eb058",
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"[*********************100%%**********************] 1 of 1 completed\n"
]
},
{
"data": {
"text/plain": [
"array([], dtype=object)"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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AkCeZhIurV6+WJM2cOdO1fubMmZXHvNavX6/R0dFYz5GkT33qU5o0aVLl39y5c+tsPYDINj1k3e5aWd9+qFzMt31eF/xYz/h4+yrQLRoAAAAA8iSTcLGRLr/8cm3ZsqXyb/ny5c1uEtB5dtb5d1egcjHXeieHPJY0XCRoBgAAAIA8yCRcnDVrliRpzZo1rvVr1qypPOY1bdo0dXd3x3qOJPX392vixImufwDyhsrFXBvdGfxYz4R4+yqUx1xktmgAAAAAyIVMwsX99ttPs2bN0k033VRZt3XrVt1999069dRTfZ/T19enE044wfWcYrGom266KfA5AJqoZFQZ1j1bdMHeaZ37QVOM7gp+LG63aMZcBAAAAIBc6Un6xO3bt+uZZ56p3F+yZIkeeugh7bHHHtp77731nve8R5/85Cd10EEHab/99tOHP/xhzZkzRxdeeGHlOeecc44uuugivetd75IkXXbZZbr00kt14okn6qSTTtKXvvQl7dixQ29+85uT/w8BZCPN8Idu0fk2ElK5OPGgePtizEUAAAAAyJXE4eJ9992ns88+u3L/sssukyRdeumluuqqq/SBD3xAO3bs0Dve8Q5t3rxZp59+uq677joNDAxUnrN48WKtX7++cv+1r32t1q1bp4985CNavXq1jj32WF133XVVk7wAaAGphj90i861oMrFsXOlvinx9mV3i+a9AAAAAAC5kDhcPOuss1QqBVcZFQoFffzjH9fHP/7xwG2WLl1ate5d73pXpZIRQAtzhYuFwM0ioXIx34IqFyceGn9flfcC4SIAAAAA5EHuZ4sG0CRphotULuZb0IQuScbiZLZoAAAAAMgVwkUACWUw5mJINTRaWFC36I33JdgZYy4CAAAAQJ4QLgJIZnibs9wbd0ZgL7vykWq1XArqFj24If6+GHMRAAAAAHKFcBFAfCO7pGv2cu4ffnl9+yvY3aKpXMyd4qi06/n09ke3aAAAAADIFcJFAPFtfcJ9f8IBde6QSTxya8tj6e6vQLdoAAAAAMgTwkUA8bmqyuqdzEVULuZZcSjlHRI0AwAAAECeEC4CiM8MFwtphIv2oYhwMXfS7r7MmIsAAABAfKO7pT+fIN33781uCToQ4SKABMxwsTuF/dmViwRK+RPyOzv20/F3x5iLAAAAQHzLfiVtekB66qvNbgk6EOEigPjM7suF3vr3ZwdKu56na3TehIWAfVPi748xFwEAAID4Rnc3uwXoYISLABIwAqWunvp3ZwZJO5bUvz80Tli4mCR4rlTCUrkIAAAARFYabnYL0MEIF1GfrYuktbc1uxVotGW/dpa7UqhcLBofhCM7698fGigkBEzy3qBbNAAAABDfaNoTLQLRpVByhI72x0Ot25c/KU08pLltQeMs+qKznEa3aDNcLI3Uvz80Tlj35a6+BDukWzQAAAAQG9dRaCIqF5GOLY81uwVoljS6RZvhIt+45UtYhSGViwAAAEBjFOkWjeYhXEQ6mISjs/RPdZYLaYy5aHzLNrqr/v2hcVIPF7tr7xcAAACAW5EiDTQP4SJSQrjYUaae7CynES66xlzcUf/+0DipT+hifywRLgIAAACR0S0aTUS4iJQQLnYUs1K1qzt4u6hmvMhZHmVCl3wJq1xM8N4oMOYiAAAAEBvdotFEhIsAEjDCxUIK4WLvBGnGmdYys0Xny5q/hjyY4COGbtEAAABAfHSLRhMRLiIdjLnYWczgJ41wUXLGcRylW3RujA5KT3wu+PFCko8YJnQBAAAAYivSLRrNQ7gIID6zy2pa4WL3WOuWysX8qPXtaJJw0X7O6O74zwUAAAA6VYlu0WgewkWkhMrFzpJB5WIP4WL+1Pq7ryNcXH29dNdb4j8fAAAA6ETmF//0AkKDES4iHXSL7iyZVC6Os27pFp0ftU5aElUuGu+nZ78f//kAAABAJzK7RS/+XvPagY5EuIiUEC52lCzGXKRyMX+yCBf5WAIAAAAcpVK0Yp41NzvL97w9u/YAPriKAxCfq3KxJ5192uHiKOFibtQMFxO8NxIFkgAAAECb+ut50nUnSMWQMRWLw9LO5Y1rE+DBVRxSQuViR8myW/T2pdLutensExkLCRdnni3tcXz8Xab1fgIAAADyrlS0xiLf9KC0/s6Q7UaDHwMagHAR6WDMxc6SZbfoNTdJv5kpjdaYiRjNV3kfFNzrj/+idM7N9c0WDQAAAHQ6MzQc2hKync/1ONfoaCCu4pASDlwdJZPKxbHu+8Ob09kvsmOHi95AsGd88n0SLgIAAAAW13VX2HmyT4+iFb9LvTlAEK7ikBLCxY6SZeUi8sM+2akKF8fVsVM+lgAAAABJ0cNFvyrFVX9Ovz1AAK7iAMSXReViV6/nNQisW96Opdatd3DpuioXGXMRAAAAkOQZS7EQuJlv5WJXX9qtAQIRLiIdBEEdxvjw6kopDKqaWbjGTMRovnve4b++nspFukUDAAAAlnoqFwkX0UBcxSE51wGMcLGjZFK56AkXS4SLLW/rk/7rCRcBAACA+hWjVi76hYu91euAjHAVhzoQKHasYgbhonc/pZF09ovGo1s0AAAAUD9XUUdIuOhXmEHlIhqIcBHJUbnYwcwJXbzdmRPy7sc1vghypZ7KRe/4jQAAAECnMq+JQoci83ns0U9IN7zIU/0IZINwEXUwD2BhJdpoO1l0i/aGi3wI5lc9lYu7nnffZzxXAAAAdCpXwUXIeXHQOfO626V1t6XaJMAP4SLqQLjYscyye7pFQ5KO+5yzXE/l4rj93PepYAUAAECnclUuho1JH/IY59NoAMJFJEdFUedqyIQufAjmypi9nOXugeT7mTVPOvFrzn3eBwAAAOhU9VYuAg1CuIg6GAewsMFl0X6oXIQk9U6ybk/6tjS00Vlfz/GgUJD2f5Nzn/cBAAAAOlU9Yy4CDUS4iDpwAOtYjRhzkYq11mf/jma+WJp7kbU8/fT692u+F4qEiwAAAOhQrmsin67Pq66Xlv7MKf4odDkFAEADpTTNKzpSiTEXO1YjukUTKrW2oU3SyHZruatHGjNbuniL1F3HeIs28z1FyAwAAIBOtHWR9Nj/c+77XR/9db51O+/28oqCNONF0vN/cLahyzQagHARdeAg1bEa0i2aUKmlLf2ps2z/7nonprNvV7hIyAwAAIAO9KejpOKwc//hy6W5F/pvu3u1dVvoEoU/aAa6RaMOVC52LDP481YcJlXVLZpQqaUNbXaW0wqYK/srOPukghUAAACdyAwWJWnrk+77vhWJhXLACDQW7zokVwqZ7h5tzvjdzzwnnV0yW3SOZfDlgh0u8j4AAAAAqvlejxMuojl416EOzBbdsezA56RvS3MWpLNPb/VbXirWRnZKo0PNbkUTGH//xQz+/3YlKxWsAAAAQDXzS/jhbdZtoSB6FaIZGHMRyTGhS+eyP8jmLEgvWM7jbNHFYen3B1jLF63srJDd/EZ07F4Z7J9u0QAAAEAg83rp7rdYt6O7fSoXmSsB2SNcRB0IFztWpQQ/xeLnPHaL3rXaGTx5cL00ML257WmkkV3W7UH/mk3XC/v9kIf3AQAAANBogefJdFBF4/GuQx34BqRj2R9kaU7kUTVbdA4q1rp6neWhTc1rRzOM7LBue8dns3+6RQMAAADBgsJFxlxEE/CuQ3IlxlzsSK7fe4qHkKpwMQ8Va6WA5Q4wutO67R6bzf4rE7oQLgIAAKBDFEektbdZ3ZtrCbxe4tocjUe4iDp0WJgCi/khlmrlYq/7fh7G2jNnaOu02dOf+ZZ125NRuGh3N9/0UDb7BwAAAFrNw/8l3XimdMc/1t6WykW0EN51SI4JXbIzvE268Wxp0Veb3ZJqZoiWZrjY3SeN3dt4nRxULnZquGj+7e9ane1r3fXmbPcPAAAAtIonP2/dLv9V7W2DrpeqxrKnKAjZI1xEHThIZeZPR0lrb5Hu//dmt6Saq3Ix5UPI9NOd5YVXSJseSXf/qSsGLLc5V6iagxAYAAAAyIUY19iBlYu9/uuBDBEuog6Ei5nZ8VyzWxBs+2JnOc3KRUmu99S2p6Q/H5Py/lPWqZWLZpDalfHJy9i52e4fAAAAaBVxqgyDxibP+vwc8EG4iOQ6KkxBxSMfdpbTrlwcu2e6+8tap4aLrq7xPcHb1WP/t1i3e12Uzf4BAACAlhMjXCwOO8td/dbtaT8hXERTEC6iDh08U24ne/4PznLalYtHfrj2Nq2k1Kndoo0uGF192bzGmNnlhQ76uQIAAABBvKFhcchZts/Pu8cQLqIpCBeRHAPDZqPVK+AmHekspx0u9k5Md3+ZM/4GWv335mfF76XbXy0NbYr3PPP/utf56bbJZr+3GNMRAAAAkIoj7mtwV7hod5Eu+Iy5yHU7ske4iDqYwQoHrNS0epgyfj/rdtw+6XeLzpu8d4u+7QJp+a+lRz4S84nG/9UMm9Nkhou71khPf8uaRR0AAADoSCWpOOjcHR2q3qRQoHIRTZHRYFnoDASKmdj+bLNbEM4OPxvVhbk4KnWlPXFMWnIeLtp2rYy3vWvMxYwC5q7yx1NxRLrpbGnrE9L6O6RTf5DN6wEAAACtbnSX1D1gLZeGfTYgXERzdHjZEepSYszFTDz7/Wa3IFyxXHKf+kzRAYJmQWsF7TLmYtzKY9f/O6OPEbNycesT1vKKa7J5LQAAACAPgrpFVxAuojkIF1EHAsVsFJrdgHB25WJWswRPPsbzejkJF3M9NEAd4WJWlYu+Yy62+N8GAAAAkCnjvN23W3QXYy6iKQgXUQcqFztSKePKxYP/1X2/6Ffu3yrapHIx7t/vutuc5UJGgR/hIgAAAOBmFjTQLRothHARyeW6UguJ2WFPV0aVi97QspiXysUch4tx/5bvfFMmzXBhtmgAAAAgmF+36EJB6uprfFvQ8QgXUQdmi86GUZ01MKN5zQiSdeWit7t1brpF5zhcjF153IC/d79wMasqSQAAACAXanSLpnIRTUK4iDoQKGbCDFBaMbDKekKXqsrFVu4Wbf4NtODvKqq6JnTJiP0+WP5rc2X2rwsAAADkgW/lYhfhIpqCcBHJuQIGgsbUTDrKWW7JcLH8IdbVn83+vd2tqVxsgBauXAQAAABQFmHMRe+ELvQyRAMQLiI5DlLZ6DZCu1YMrIqD1m13RuGit1t0K1cuusLFHI8NGPd91sjKRdc6KhcBAAAASSFjLlK5iMYjXEQdmC06E6UWn4F4yxPWbVaVi95QqZUrF9Um4SKViwAAAEDrKzHmIloT4SLqQKCYCTOkarXKxdHdyvz37u0WnZfZolu5nbVECUZ3rpCK5e0mHZFte6TqClZrZfavCwAAALQs41rMr3KRcBFNQriI5ErMFp2JVh7Hb3i7szyyPXi7elRVLualW3QLt7OWWu+zVTdI18yV/v46637fFOv2uM9n1yYqFwEAAIBgftcfTOiCJiFcRB0IFLPRyt2ijfbMODObl/AG1S1dEdgmlYu13mePf9q6Xf4r63Zkh3U74YDsmtTlFy5SuQgAAIBOFqFbtHdCF67b0QB+/c6AiBhzMROt3C3aDtAK3dlN6OL9Bq6Vx1w0g9BWnnimllrdokd2uu+Plu93j82mPRLV0AAAAECYoAldvMMLtdo1JdoSlYtIjov/bLRyt2g7hPIdDy8lo4Pu+y0d2pm/qxYOQWupFS6OesPF3dZt90A27ZGkoQ3V65gtGgAAAJ3MNTSZ3/WH35iLXLcje4SLqAOVi5lo5dmi7Q8w76QrafJ+A9fKoV2pXcLFGu+zzY+479sVrFmO57J7nc9KwkUAAABAUkCBAOEimoNwEXXgIJWNFq5cNLtFZ/YaOapcdM0W3cLtrCXKbNGu7e33QYYh86TDfFYSLgIAAKCTmZWLPteKha7qMRfpcYgGIFxEcswWnQ1v0NNKP9tGdIueerL7fpSJUpIEe6WSdNtF0l1vjv/cyj4aPKFLVmFz3P02ooJ17qukcftlt38AAAAgd2qEi1QuokkIF1GHFquqaxfeD4lWql4sNaBycfKR0vx7pHH7ul8zyHNXSz/vk5b+LN7rbHtGWnGN9OxVUjFm5Z4kbX1KWvxt5753Ipq0PfAf0m/nSLvWpL/vuO8xO8zNMmQudEkHvsOzjspFAAAAwOJXuegTLrbS9STaFuEikisx5mImqg7+LfRh0IiKNUma+gJp3D7Wcq2qxL+/1rq94/XxXsMVWiZ4//7xEGnF75z7WVcuPvkFafcaadEX09933G7RxQZ0i5asgNG9ItvXAwAAAFpZqVa36G4qF9EUhIuoAwepTFR1i26hcLFRoZL5GplNlJJyON6wMRezCNhC3mN+779GhcxZVsgCAAAAeeZXIOA35iLX7WgAwkXUgcrFTAxvcd9vpXBxdLd12z2Q/WvZ37hlVRGY9pihDZstOoNwMaxy0RuaFkcbM6GL7/6pXAQAAECH6Z1o3IlSueg5h26lMfzRtggXkZx5kFr60+a1o9088mHPilYKF3dZt91jsn+tSuViVhWBdYTju1b57K5B4WIW4w7GCRf/eq4TMmddudg3Jdv9AwAAAK3uVRsCijsCwsWq3j+Ei8ge4SLqYByk1tzcvGa0u5aqXGxguJh15WLNmdZCjA5Wr8uiW/TOldJ1J0mLv++sSyvIrzVei6045L5v/q139aXTliDecJEJXQAAANBpXF/o1zqH76oOF1vpehJtqwEDp6FtUV7dGK30YdDQcLF8eMpqLEPXzzXme9mvTVmEoA9fLm28V7r7XmfdjqXp7Nv8/4dVLtpVin6y7h7fOyHb/QMAAACt7ISvlBfKX7JHmdClalJErtuRPSoXUQcOUo3RoeFi5Ald0qhmi/le9uuqnUX37eGt1evmvDSlnZvhYljlok+Vpq2rP6W2BOgZ777PFxoAAADoJDPPKi/4XPP4Tuji0y2ac2g0AOEi6sBBqiFasXKxp4HdomuFi4nH/aujW3SjKhervnWU1D8tnX2b/4cdS6WHLpcGN1Zv59cF3JZ1t+iqcLFRM3IDAAAArSCkCnHpj6s3L/h0i+a6HQ1AuIjk+AakMYpD0jPflrY80eyWSCNNqFys1S066YzFaXeLzmRCF59vKNOaodk7K/njn5bueUf1dsWQbtFZj4HY6wkXR4f8twMAAADakR0URj3vLnQrNJAEMsKYi6hDC1XUtQu/CrolP5Ye+oC1/PomfzCM7rRuGzrmYo3QruqbuajMysWYP9dV11WvS3tsyJ0rpW1P+zyQ0ntgaHP1urW3Vq8Lq1zMGpWLAAAA6GRxx0/0G3OxlXrCoW1RuYjkqFxMn9+Bf/PCxrcjSEPHXIzYLTpx5aL5/o35Xn7kwz77S6FycdcqqzpvyxPSNXtKmx+p3iat7tfeWaAlaWSHz3bNDBfHue/bbd70sPTMdzgGAQAAoL1VCimiVi52+VQ5cs6M7FG5iDpwkEqd36C8AzOc5eJIHWMM1qE4Ko3uaGy36KizRTdjzEU/9VYubn5U+tNR0h4vkPZ+VfB2S38kTTpUOuI/63s9v/eaHR671gV0i856MhfJGXfTVhqVti6S/nysdb93krTPa7JvBwAAANAM3QPu+7W+XPfr1cUX8mgAKhdRBw5SqfMLuXonOsu7VjauLaZbzpN+O8ea+ENqULjYopWLO58P2F+dFYVLfmjdbrxX6hoI3/bh/6rvtST/cNFPULdo833ZKKWidO2Rzv1NDza+DQAAAECjVMJFuxoxQbjIdTsagHARyfENSPr8Ah+zW+rO5Y1ri61UlFbfaHWZXXmtta4Rs0VHndAlceWiEeTGeS9fe3jA7kLCxVJJ+tvrpAfeF7zNxgec5UaEyFG7V/t1lZaaEy5KnhCXYxAAAADamF3U4Tehy8RDqtdVjdEocc6MRiBcRB04SKXPCLz69rBuzW6pO5oRLhqBpz3mXVdf9q9rh4s1KxcTTujiChRjdIse3uq/PiwE3fKYtOwX0pOft7qY+1lzk7P8xGejtyepKJWLpZJ0xyX+jzUqXDz6E415HQAAAKDVhHWL9iuQ8O0WzYQuyB7hIupAuJg6M/DxCxd3rWhseyT/D6NGhIt2t+ias0U3sHLx2auCHwsLQc0P+eHN/tuM2zdaG9ISJVwc2ugse7vCNypcnHpyY14HAAAAaJbVN0qPf869rqvPqET0m9AlYrjIdTsagHARydEtOn1mkNcz1ro1J9kImlwjS77hYm/1urTZ3Z1LGXWLNv9fUWdEvuvNwY+FVS6arzW8zX+bSUdEa0Nln3X+/UWqXDTaPWZP92ONChdnnmW85uTGvCYAAADQSDe/RHroA+513qpFSe5JKf3CxXLEc9Z14dsBKSNcRB04SKXODHy67XDRCBSjjpOXKp9wsdCAcLEy5mJW3aKN/9dTX022D9f+QtppdyeXgkO9uCGp38zOcUSa0MX4G++b5H6oZ0J9rx9VV6/04hv92wAAAAC0K1e4GLNycc58aa+LrOV7/5mAEZkjXEQdOEClrhJ4FZxJU8xwMeoMv36Ko9KSn0jblyZsk6GR3aLjzBYdZzwR82e5fUn05wUJq1wc3eksP/5p6ZGPVG8T92caNNFKVFFmtzaD3Z5x7scaOaFL35Ryezw/Y06SAAAA0K68wxJJcl+D1+gWbU7usvnhtFoF+CJcRHJc2KfPDrwKXVJXv7VsVqhFCYSCPPt96c43SL/fP2abmtQt2g4Ntz4l3fdvwaGoGS6aFYI1mf8vv28CY9pwt//6TY9IN5zu3F/8f9Kjn5A2L3TWPf0Nafmv472eGVgmERRUDxrjLJrvt57x7u36Jtf3+nEEBc1PfE4aqbOCEwAAAGhFO55zlu3ZomtN6GJGPFOO818PZIB3GJJj1qn02T/TQrdTBu+qXKwjXFx7m72TmE9s1piL5dfYeK/01NekW18WsJ0RLo5GHDtRcs/aXEjpUOj3Af/g+/y33fKEdbt7rXTvv8T/e6q7cjEgXPz765xls1LQ/Oa0Z7x06H/U9/pxVLrIe6tDS1ZQCwAAALS1qN2ijeua6S90lu3x/IGMEC6iDlQups6sXLSDlLW3OI/XM+Zib4wx8jY9LN14lrTuDunZH1Q/3ohu0d5ZoLc8Xnu7xJWLCc08x33fL/Dz7c4gadtT1m3SsROzChdX32BsY7zf7EpaSbpwhTQwrb7Xj6Myc7hP1/M1f21cOwAAAIC0xeoRWKtbtBFCTj3ZfCBmo4B4CBdRB8LF9BmViyuvrX64nsrFOOHio5+Q1t4q3fBC6YH3Vj/eyNmia3HN+hwjXDSfNxKhi7Hfh/45N0rnGOHWHw+u3sY7VqH3NTc+WPu1/dQ7oUuUoNoM83qNbtGN+P2bwsJFjkMAAADIsyjXMAWfcNC+Ppl4mP9zesY4veHodYiMES4iOcZcTF+lq27An2Y9lYvmmHm1xqmrFVw1pHIxaoBlhosxukWblXsr/yhte6bWE/xXzzzLWd61qvrxoMpF+yTi/nfXeN2CdNTHpBd80/P8kAlkoogyOZAZZu9jdJf2VpVmrRA2uQ/HIQAAAORYrN5XPpWLe54fvHmXPeM04SKyRbiIOnBRnz6jctFPPbNFmyHX0KYaG9c4NLRU5aLxMxlNWLkoSU99vcb2Ed/vRc/vqLs/YDu7rTX2u9eF0lEfkea+MuD5CUV5L9kB5ti93eF01N9NWuzX82szX3IAAAAgz4LO64/6uHEnZMzFsHNzewxGzpmRMcJF1IEDVOrMMRd9H6+jctGsdBvaGLydJJVqVMVFriqsg7c6LjBwTVi56P32rmZYFzVcNNowtNmaCdp3u/Lr9YeMXXjM/0infNdaHpjueX4DKhftStmuHmmC0eU7rQlwogoNszkOAQAAIMeCrkP6Jlev85stOuzarHLeTuUispXpFeK+++6rQqFQ9e9f//Vffbe/6qqrqrYdGBjw3RYtgG8/0leqUblYT7doM4wa3FCjHTV+t90N6BbtDZSCuuKaIVmsMRc94Vqt4DbqOCVmGx7+r5Dtyr+Pfd8QvM0Rl0t9U5z75rZ1h4vl/+/sBdKChz2PldzbdPVKfZOkC5ZJr1xT3+smEXbCxPgxAAAAyLPRgAIJ1zWhXbno0y167JzgfVcqFzlnRrYy7dt27733anTUuYB/9NFH9ZKXvEQXX3xx4HMmTpyoRYsWVe4X/AYuRYsgXExdppWLRui1c3ny/UjNqVwMKvc3fyZJJ3SRIoR1Ed/v5snB9iXB29ltDfpdn/y96nWn/UjatVJac3N63aK7+6TeidVt6+53fib272Lc3PpeMykqFwEAANCugs7rzesE3wldytczU0+Sjv20NH5/v524twUykmm4OH26uxvfpz/9aR1wwAE688wzA59TKBQ0a9asLJuF1HBRn7palYv1hItmV+ddK5PvR2rOmItBlYuju53lONV83srFWmFd2AdyV7/THdrsFh3Wfdh+vaDfadDs3qEzJ8dQCbK7q99vxUErXLTb1ugJXLwIFwEAANCuAsNFv2tCn8pFFaTDPxiwjy7PtkA2GjZw1tDQkH784x/rLW95S2g14vbt27XPPvto7ty5uuCCC/TYY481qomIi27R6TMrF/e5pPrxerpFm5Od1Aymanyz1YjZor2BUlDlolkpGGfCG29YWDO4DXm/903yb09QSCw5JxFBv9OeoHCxz/38pIpmuOj5KLD/D/b7pBFhcphCl/wHsRbHIQAAAORb0Ljxvt2iTaWQx2x0i0ZjNCxcvOaaa7R582a96U1vCtzmkEMO0fe+9z397ne/049//GMVi0WddtppWrFiReBzBgcHtXXrVtc/NAoHqNSZlYsH+4xNWs9s0cUY4WKt12lE2FQ1oYtxf9dq6cYzpaU/c38Yx/nQrAoXa4VUIY/3GuGi+XMOG9Zhx1LrNQMrFyf6r7d/9rUm3anFrFz0vh+8VZXNrlyUFPzzJ1wEAABAjo1G6BZtM69Zdq8N3q6yD/t6hGt3ZKth4eJ3v/tdLViwQHPmBA82euqpp+qNb3yjjj32WJ155pn6zW9+o+nTp+tb3/pW4HM+9alPadKkSZV/c+c2aUywTkTFUPoqoV6Xf6BTGpGW/0ZaeV2CfQ/7L/upFT42o3JxtzGRyIPvk9beJt3xene36FiVi95ta3zgesPIQy9zll3hovnNY8ghdtND0v3vCa5cDOwWXf7ZB52ERLH2dunJ/7WWCz1WF2jTcPlLmpGd1m13C0+sxbewAAAAyLMo3aLta6FND1i3O8wx9KNULnLtjmw1JFx87rnndOONN+ptb3tbrOf19vbquOOO0zPPPBO4zeWXX64tW7ZU/i1fXudEFYjBOECZM9qiDkblot83UDufl25/lXTLgvgfEHHGJqzV/boZlYum3euc5aSVi94wMW7l4vGfd5Z7g7pF15iQ6qmvxB9zsVBH5eLIjnLV54ukneWK8EK3NGa2dMJXnO3sk5fdq63bgZnxX6thOFECAABAjsUZc/GuN1u3g2uj7ZvZotEgDQkXv//972vGjBl62cteFut5o6OjWrhwoWbPnh24TX9/vyZOnOj6h0YxLuo5WKXDHHPRL1wcNEK1uJO7DG9zlmt2i26BcDFojEXJXXVo/l/qGXOxZuViSIg17WRjNxErFyv7jTnmYncdYy5ePV76red4ap+0HPJv0pTjreXNj0ibHnYm/hkTXHHefISLAAAAyLGgMRfDriVc1zIh1zGVa0qu15GtzMPFYrGo73//+7r00kvV0+MOC974xjfq8ssvr9z/+Mc/ruuvv17PPvusHnjgAb3hDW/Qc889F7viEQ1ihi31jAUIh2u26BpVb3HDpWFjPNK6w8UGdIsuhASYQe+3erpF16xcND6QvcHfAW93lkeDTg4itsNWq3Kx3tmiK/szvhG1f6/3v1v687HS5vKEWmOCv+BpOrp4AAAAIM+Cruu6QiaHjHwtXr6mpBgIGct8lP4bb7xRy5Yt01ve8paqx5YtW6auLiff3LRpk97+9rdr9erVmjJlik444QTdcccdOvzww7NuJhIhXExdrcpFc13ccMnVfbjOMRcbMcFHWOVi4DdvdUzoUqsCzvwAP/8p92Pj95WmniRtuMdzchAh+LK7oB/+IWn2edJNZ1n3g6pD7fERzW7u9TB/zt7X3HivdTtmVjqvlQnCRQAAAORY4FjqYcUmEa/FK9ePnDMjW5knBOeee65KAZUlt9xyi+v+F7/4RX3xi1/MuklIC5WL6XNVLvoVFhsfMHErF80wrdZzvZWLPeOs8foqzahRVZmGsAAzk8rFWsGk8X4fmFH9cFc59Is7BqQ5I/P0062AceJhwdvb45sObay97yhclYuecLEyocvYdF4rC3wLCwAAgDwLvDYLueYyz4HDzocZcxEN0oDyI7QvwsXUVSoXgyZ0MSYsilO5uH2ptP6O6M/1TugyZo607enor5eGoMq93euldX/3fyzOh6Z321rPdT3u80FfqSg0u0VH+IZw2dXWbVeP1fXh7D+Hb18JF7fU3ncUft2ibXZQ2ogxNhPjW1gAAADkWOCYi6FPchbr7RZdKjWmeARtrSETuqBd5TRcbOUx2iqViwHdok1xwsXf7+e+v/QnIeX38q9cbLSgQOuJzwQ/J9b7MGa3aPNxvw9fv8rFKMHX7vJMb1G7mts/l7gT+gS978MqFythdwt/D5WnYw8AAADglWSiRvMcuJ5u0cVh6c/HSLddFL8NgIFwEcl5w4o8lFrvXm8FbQ9+sNkt8WdWLqY1oYsdXnnZ4+n57rsFwsX+aQEzZod0B44TuMbtFl15vwf8XuyqPzNc9P4cw4SOMWmww8DY4WLA/88MF7vH+G/TypWLaY09CQAAADRD0HVdWDWhed0T+mV7jW7RG+6VNi+UVlwT1kKgJsJF1MEbLuagguipr0k7npOe+GyzW1JtyU+k535evpNi5eLGB/3X94wPfs6u5933u8dK8261lsPGA0xTV6804JmlePNC6dnvBT/n8U9H33/cCV3sSsegD/lKt2jj5CBOABi1m7NdRRgnuLSeEL4/yer+7icv4eLQJmn5b6Vda5rXHgAAACCOJNfRUcPFyjVlhEKDVu7hh5bXwn3d0PKqxqwbldSCIURx2ApQCgW17PhsQ5ukO9/g3O8KmtDFELlycbX/+qDga8ey6nU946QZL5JeuU7qDQkl0zZ2T3fQ+dj/hG+/9cno+/a+f2uFtc982/95Nr9u0XECwAkHRtvODgPjnoREqVwcu6f/Nq0QLu73RmnJD6vXj+5yln+3nzRcDmkvKTJ2DAAAAFpfkh6A5rXgtBeGbFhjzEWz99SK30lzL4zfFkBULqIuOahcHNoi/WamdOsrrPu1qgGbpaprZ1ftbrJRKxcH18d7vt8Hj90temCa1D0Q7XXTYE9eYqvVBfaQd1evG9oiPXuVNLTZvd77fq0V1i68IvxxvwldggLcyUdVr9vndeH7t9nviyy6RY/ZK2CbFvge6uTvSi++QdrzfGm+0aXfDHOHzerPFv0iAQAAADAFXkdH6BY9/YVSd1/wdpXZooPGXzfO829n3EUk16JJC/IhB+Hiit9ZVYEr/1he0apveU+7Ct1Sz4Twp5TqDBevP1Va/N3q9X6zlXWPjfZaaTODL8ldpea7vU8Idv+7pbveLN3+avf6qsrFBAMpm/wqF80AcI8XSHNeLr30UaeLeeWxE6SeiD9j+2eSVrdoczzNMbP9t2mFysWuHmnWPOnM30tTT3SC50lH+G+fhzFgAQAAgDjnrXZYaIeLXSHBorl9lCGSgDq0atKCPKia0KUFw0VvlV1Xt/92zeYNzQpdUm+NcDFqGLZ9cfBjd7/Npy0+4WIzJnSRqsPFjfeHb+/3wbzsF9btmps823rCudHd0pYnk481UmtClwkHSWf9QZp8RPXEKXE+1AtJKxcD/j7HzHKWeyf6b9MK4aLXGb+2boP+X4SLAAAAyIM419F2F2i70KRQ6zy9Rrdo7/UWkBDhIurgCWFiV1I1gN1VtaJF3/JPft59v9BttT0o7JGid4vevS788eFt7vt+XY8b2RXa5P2gDarCrPDr0h0Q0o7scN/f/LB07WHSo5+I3DyXWhO6rL7eWe7ql6ubQ9SZos1t0xpzscv4GwkaNqAVv9GshLlBfweEiwAAAMiBKOf1+7/Fup1yjHUbu3IxqICCoYSQjhZNWpAPOahc7DJCsdU3tu43M+vvdt+3PwRe9Lvg50StXKw1TuGO59z3736rdWuGTs2qXIsbWPu9B6sC5rLhrf7rF3403mvaak3oYv6+CgV3YBurctHuFh0xXLZFGcTZbyxIqTUrF+1vaYP+DqhcBAAAQB4EnrcaxQhjy2Oj272s7HPgmufp9piLQa9BuIh0EC4iubx1i775Je7KrGILtdc7q60dIIUFJFHDpWKNcHHQqGwc2ixtebT8PHPswCZ96EQdV7Kyvc/PK+jbvNGd8dsTprvGmIveECxpuGg/r1Zo7BXYFcJ47UKXtNcF1du0YrjYXaNykXARAAAAeRDpOtq+Xiyf41YqF2ucpxdqdIvmnBkpIVxEHXIQLnoPts/9wlmudwKPVHlnArO/YQr5mSauXPS8llld5+0ibdv+TLTXSlsa1XldAZWLaX+Q2l22n73KeI2QcHFok7Mcp1u03c17y6PS2r/FaGDEQZy9M3RLEcZyaYJalYt0iwYAAEAeRLmO9s76HDlcrDGhC5WLSAnhIuqQg3DR28aN9zrLLRUuekSZeCZq8FYVLnp/b8YHjVnNZ4ZO6++K9lpp658eb/s43aLTfr/6BbNmcBsWZsapXDQn+vnr/OjPCxqv0htsdvtM3hMn/GyUypiLQd2iOVECAABAHkT5UtxTuViKOOaiPKGkF5WLSAnhIpLzHqBacUKXsICh6DMrcrP07eFZUWvgXdURLnqYIduIES6aVXfj94/2Wmk74UvSjLNiPCFGt+i0P0jnvtK6HbOn0ZyIv6MklYtSvPfwtUf4r/eOQ+rXlponLU1gf0vLhC4AAADIsyjDdXkrF0cjjrlI5SIahHARdfAcoHatbE4zQoWFcy1UuTj3Ivf9SGMupjShiwIqF02lJgXH4/aW5v01ergZp1t0YDfhhIdFO4AzZ/iOGv4lrVz0q77ctUq64w3SujuSvfaer/B5zUnR29coNSsXCRcBAACQBwHnrQMznOVCQOVizeGLGHMRjdGCfd2QG96qwOd+Ls08szltCRJ2sBxtocpF7ziIhRQrF2tN6BJUuRi0TTNErZzz+33H7Rad9AO2Eggb+436HosTLvaMD3/87rdJK/8kLf2J9PoI30R6KxVnvVg67vPShnuk3vHSfm+qnnCoFdjf0pZGy78zTxs5UQIAAEAe+F2XHPVxadqpxgrPrM/2c7y9kLy8FY/VL+4smkUSQExULqIOngPUM99sTjNC5aRy0dvOtCoXSyWncvGwD0h7X+yzTYTKxSnH136tLEWdrdjvg7lRE7r4/c6iVi7G6RZda9stT0Tfl+QfbB52mXT6z6WT/0+acXq8/TWKGTgXhxU6ligAAADQqnzDxQ+7v+D3Fp/Y57pRw8U7LpGuPbJ6nHjXOXNBuvUC6a8LGL8csVG5iORyccDJSbjoDUKiVC6WIlQumv/HI//L+jbq+T9Jt77M2E9I5eJLH5Geu1o6/AO1XytLaVUuFkeccC71cNFnhu8sukXXsmNJvO1bcbKWKMzAuTjsc2JFuAgAAIAciHRd4uneXAkXa9WLGQHllsek534hHfg2/9ce3iI9/3treddKaawxljxQA5WLqEMOwsW8dIvecI/7fqUKLuRnPBohHDXHW+wasG73fKm0zyXO+sDZorulyUdJx3zCPc5fM9QcS6RseEv1OrNy0Qz7sqpcNEMt8zUmHxXy3CZ2O671bWerclUuDlV/40vlIgAAAPIgyhBU3eVruZEd5RURw0Xv491jvC8e0CbOpREP4SLqkINwcdGXgx9rldmity6Snv2ee13NWb0UrXKxEi4W3JVeL/ypNPPF5f0EVC7Ov7v2/hslarfolddKPy1Imx42nmuEUCO7nOW0x5H0q1w0nXlt8HOHNqXbljjSrJpsJDMULQ5XnwBxQgQAAIA8iHJdMmaWdbt7Tfk5EcPFHcvc973j0XPOjJQQLiK5PHSLfv4PwY81e5IS26aHqtdFqVyMMqHL8l+XF0rV1XF+YwTalYv7v0na44Ta+2+UqN2ibbe81Fk2/9+uyW2yGnPReF/1T7Nuxx8ojZvr3n7Oy53lwfXptiWO3IaLBc+M0Z7f5xOfk244XRre3vCmAQAAAJFFCfgGyuHijqWe59SIdLbWGo89wkQvQASEi6hD3g84LdJ+3wlHyn+ak44Ifl6UMSPv+9fgx/wq7ewgpntc7X03UtTKRdvutc5yKaCbsr182s+qn79tcfC+97rIf71fWGsvn/m76u1P+5GzPLgh+PXCTDws2fNMeR1zUXLeF9uektbc4n7sqa9K6/4uPfW1hjcLAAAAiMxb9HL0J6q3scPFnSusCRwjj7lY67WpXEQ6CBdRhxYJ5+KYfIyz3CqVl35VeXZQNfGg4Od5Z/qKy6/Sbnirdds7sb59py3sZ1RLrXCx0CXXQMeSf3DbPda6Pf7zQY0s79c8OSi5HzP1TZbGzLGWZ54dsM8Ah3/Iup11jnu9+Z72/nz6p/rvK6+Vi5Iz5szN86RbXx6wTZ1/JwAAAECWvAHfxEOqt7G7RUvSw5cr8piL1S9W436t9YA/wkUk5w3nphzXnHbEURox7rTItzTdfsFZhD/NwbW1twnlM67jiB0uNnkCFy+/ysXjvxDyhFLAshkulkPAQle0btfm9n7sMM/s4lwJMAMmbDn3Dum4z0nHfKr265vs9npPRFZd5yyP3cv9WO8U63bff5RO+k51u9tVqwx/AAAAAPjxnq/6TWbZM95ZHt0dvVu0+Tzf1w64Jm6VQhzkBuEi6lA+4NhBR++k5jUlKrMirVUOmH7doqMEPubkJIlet1yxVjQC112rrduBmfXtO23eD70Ll0vj94//XNd+7OCvO+KYjsb2tey2A8aQykVJGrePdNj7pL6Yfzt2wGnO7i1JK35vbONtZ7ktB/2TtPfFxvoWCdmzQrgIAACAVuY9X/UrrDCLFWadG71b9At9hoByvXbQtUCLXCsjNwgXkZx9ILLDsShjADbbqDGhR6uML9E9pnpdlKC23p93T7k60ew2aneL7ptS377TtuYm9/2ecdLQZuf+yZ7Ztl2MD8agbtF+1aNVu6nx7aD5cxzZJj1/rfPzDKpcTGrzQuv22aucrsGSNMkYg7EqILZ/Dp6Zw9s9fGuVv3MAAADAl+d8NWi8+Rkvsm4HZipyt+juAc9Lec79d62M1EKgFsJF1KEcVtjBTJTZi5vNVemVwrcxWxdJK/9c3z78gqco4V6tcHH7Emd5+gt9XqMcYA5tctaVYlTnNZId0tm6+tzhYtiEL4FjLtofrF3RAqha3aKnHOssb3rQMwZgyuHidmPCmdU3Osu+/z/7vhkuGtWy/dPTbVuraffwFAAAAPlW1S06YEz0yjl8KfmELndc4u65NrwlqFHx9ouOR7iIOtjdonNUuWhWeaVR0fTHQ6VbXiptuDf5Pvy6Z/dNrv28sJ/36G7p90a34UPfV72NPUGJWc2ZeGDgBuvql+a+0lqefnp1e30nVZHcYy4aQaoZsPoJmyil0qZep+J04/3ux9L+eZpB/uB6adND1kmC+f+uCtXK/4dCQerqll6+SHrpo603vmbaCBcBAADQyrzVhIGFE3bBQql2r6qq5xiWXW28dkCBkLdNQA0tniCgpZU8Yy6W8lC5aAZpdX4bM7jBWd5wTx078mnHhJBZom1h4aI37PQbn9D+0HryC9Ltr5JGh2J8SDXY3q913y90S2PnSK/eLJ1zS3ilZaTZomswA6qw7e2fqet9JqVeuWieBNz9NunPx0n3/rMnXPSG557xHyceLE0+It12NZo9a3aYPFRUAwAAoIN5ztuDKhft65BSybj+rHVN63MdYvYAC7ymZGghxNNiCQLyxe4WXa5cHM1B5aJLneHi5ked5fve5S4vr9f0051lvwlfJKk4GPx8b7g15ejw11v+G2nJVcnL67N28rfd9+2u5H2TrCq80PYGjLkYp0rTfF6kcNHzu8myctG2+Ls1ukXXmLk6j8K6w9sIFwEAANDKokzoIskJCovSlvK16LPfr++1g86VGbccMbVYgoB8yWHloqneA2bPWPf9Wl1rA9vhE3KaAdD8e6T9Lq3eJizMLUUIOs1vrKTyB0uLhou9E2tsENJev0BRco+heOhlNfZvhoshVZKF8olAMePKxaCuvn7doksl6dYLpJ3Ls2lLM41GmDE9yt8CAAAA0Cze6sHugOIS+xrRvH7c9nT4vmsVFhAuIiUtliAgV0o5HHPRpc7KRW91WuL91XjelKOlU6+qDtjCft5mFeUpV/lvM7zZfb+rt3UrF2vxC9tGdkoLP2ZNrlLZLmDMxWmneHcYsv8E3aLT/nm+8Kf+6/3CxR3PSc//3mhLG4WLQ0EDUBuoXAQAAEAr8147BE7uaV9TxLjuNCed9BNYIES4iHhyliCgtXgqF/N2EV/vtzHebsn1hqtdfdLUk6VTf+j/+Kxzo7+eXa01/YXS/j5Vj1J1pWVxuHXHXKzFO5u0JD3+aWnhFVa4ZjPDty2PlRe6pD1OcD/XW01aili5aP8tVAXPKQd6018oHf3J6vVh3aKzaksz+f3evZ77WfbtAAAAAJKqChf38N+uUrkY4zq2b4o01VtIYQisXGRCF8STswQBLaXkGXOxJSsXw4KUOisXvf/fJT+Wbn+1NLw95o7K7RizpzT/Lmm/f/Tf7KRvScd+RjrnZv/Xd+2yHC4GDQYs+YeLrdotupZhnwq2TQ9Xr9v4gHW7c6WzbnS3NeHNIe82NvR8YEcec9EOFz3ddbP4eXYPVK/znS3aO0B0zn63YaKEiwAAAEAr84aL3WMCNixf25rFE94iCT9j53hWGNfBhItISRtdZaLxyqFFVznkaMXKxd5JwY/5jXUYh7c67eHLpeW/tirm4ojajv49pMM/4Mz8HKVbdFi4eMz/eNoxko9u0ZMOr17nDRe7ev0/lO/7F+vWbzKcGWc5y95vAyPPFm2Hizs9D2RQLeg30LPfbNFVY3O2UeXiCOEiAAAAcq5qSKWA83X7OuQxowfT0Z+ovf9CyCSIQdeUjLmImEKSB6AG+4CTpHKxVJJUyj7ECv3GJeVu0bbKxBkxRR0Lr9INPULlYlfIn/jMs9z319yaj27Re5xYvc47lsjcVwcMhOw3Tkl52fz5V4WLEbtFV2ZOj3iCUA/f4NinW3TV+7SNwkUqFwEAAJB3VZNBBvE5j+8eW73OK3D2aQUXCBWZFBHxtHCCgJZXqXLrcd+P4q43SdfsLe1em3qzXMLCxbQrFyvro344VBpSvo0ZLpZGpWLA/y9K5aLXyj+2duXiGb+WZr3E6hrutddF0qk/lg5+l3W/NOpfuWgHg34Tu7gOh973snk/5PcU1C06i0Ot30nCiFExWQkXPSF0O03ost8bo23HN68AAABoVeb1Y//U4O38zuOjnNuHhYtBE7rQLRoxtWCCgPwwZtuVFGsMwyU/lHY9Lz3x+dRb5RIaLtYROIwOSpse8H9s2dUx9x0z5LQDLMkdHJlhZ5TKRcnpYu3s0LppxXBx7iulF18vjZlV/VihIO33D9LEw6z7paJ/uNhfHhzZ9b6w/89m5WLQbNGF8A/wwDEXG9Qt+qmvOst2m7OeXKaZDnmP9OIbpb1fE74dJ0cAAABoVfa1wyk/kF72ZMwnR7hu8xaclBhzEelrwQQBuWEflMxuonGrAavGpktZJWTz+7amjsrFW18hLfpy8OPLfplgpzErFyUnXHzw/dLV46XN5RmQo0zoIkkvXSid/H/O/d3r7BeJ1pZWY4eiQZWLB7zdujVD2cp71vg/e8NhOwQP6xItOb+bkQZM6FLrdxtUudhO4WJXjzTrHKlvcvh2nBwBAACgFZVKTuXi7PnSwLTgbf16ziWpXDSrFQkXkZKcJghoDd7KRSl2YBfUtTgt9kGxy2/8vTrCxdXXhz++8b7o+yr5jPkXxvxwGN4i3f0O6Yn/tQLFhR+x1kftFt0zVpp9nnN/ZFv5eTk9NFS6PY/6B8r2z8P1IVp+H09/YfU6SdryuPRkOVws1Rh7pDIeprdrfIMqF032e3/HEk9Tcvq7DVMr9GXMGAAAALQisxCgeyB8W9/htyKc2+93afBrBk7owvkz4mnDq0w0jF3dZXa9jVu5GDQpShrM6jOz2s/v8bQ98b/SY5+KuHHMn1mhywmWFn1ZWvwdY1flfUXtFi1JA37djHN6aKhULhb9AyX75+KqXCy/D/omOT8L872x6CvRX7+RlYu9E8Mft8PFu9/meaCNKhdttcJFTo4AAADQiszAsGa46B3XXdEKVKadJO19sfkkZ5HKRaQkpwkCWkLJr3IxQmC39m/OcpaVi+YB0W/m4K2LsnttSXr4P2OGrTFCH/tDYPH3PA+UXy/OhC5d3dL4AzxNyemhwaxc9Buc2P65mR+i5v/VDuzMcHFrjHFPKrNFez/4Mwj0pp0W/nhQeN5OE7rYqFwEAABAHlXCxYJ/QYzvtgmc/F1neWCG9PwfpbveKg1v9d+ecBEx5TRBQEvwCxejhGlLrnKWg8qw02AeEHetqn78sU9m99q2SGNKxuwWbRre7L6/4hppyxPxKhclqWecZ0VODw2V92LR/1s4v8rF2QuM59v/bzOYM97TU44Nf/3KTN6eMCuLsLZvknT4h4IfDzwh6MBwkZMjAAAAtCJ7OKXugdrXg369/qIWs/ROkPZ8RXk/w9Kt50vPfk9ad7v/9pw/I6acJghoDQnHXBwxArcsD1qtcEAM+ibIFLcreS03nB6vclGSdq913+8PGUi4pRkTuviFi8VhaXRIWvE76/6U46Ru4xtCs1u1Lc7vJ/DbxowCvWNDut4Hvf+zHA6gWegWDQAAgDzaUB6r36/Ls5fvNjHO7e2htQY31N6Wnj+IiXARyfnOFh3h4DZ+f2f5+d+n2ybTzhXZ7DdOOBOrdD2lAGpoY/TZom1jZjvLY/eSxs5Jpy2NZnaLDqpcXPgR6amvWverJkXxCRfNwLxW0NjocDFMULg4bu/GtqMRCBcBAACQR3e8Pvq2fteWcQoh7GvDhy+vvW0rFOogVwgXUYcYlYulkjWmw20XNu5A9chHstnv0p9G3zZSuGj/zFIMoOJ2iz79l85y39T02tFoXXa4WAwec3Hx/xnbe8JA327RcV4/IFxsxhiWQX9nPWMb245GYMxFAAAApGl0ULrrLdKyX2X7OnGGCfOdDDVB5WIUhIuIiXARyfnNFh0ULu5eY43psOJ30uaFmTdNkjSyo/Y2O5bF3++d/+i+P26f4G0jzYZdx5iLga8bs3JxgjGhS7GOgYKbrnxIG9osbV9S/XBpRK4Q1/sB69ctOs5s3n4TB0m1B2fOSjt2gfZjhov2WDImTo4AAAAQx9Nfl579vvS3i2tv2yi+lYuEi2gNhItIzndCl4CDmxmyDa53ljMNXSKEQg9cVv/LhI1PmOVs2EGmnRa/ctFUzyxkzWb/fzc/LK25ufrx4rDc4aL3/ecXLsZ5/aDKxQy7RZtVp16dGC4e+WHpFYul1w1J/eUqXLpFAwAAIA6/CUGzMHZu9G19r9MSdIv2M+Egz245f0Y8hIuoQ5xu0UbIYQ4gWxxKf0ITv9cMMryt/tfpHhP8WJTKxVLK3aJ7J8SvXDRFGUy4VfWMD3+8OOIO+goRKhdjfRvYhArFCQcHP9Yp3ziax6BClzWua1ev8/6nWzQAAABa0QFvt27DesPZ/M7t06pc9F7Tdsp1BFJDuIjkfCsXg8JF4+A04plB2W/ijTREOdDWGqvNyy+kmHhI8PaRKhdTDheLw/EndJGcYG6PF6TTjmbomxz+eMlbuRgQLppjl8T5YG1GuBj2mp1yUuD6GZjhcfn9zzevAAAAaEX2mPGzXpJwBylVLnYPeHbbIdcRSA3hIurgM1t00ICyZtC3e637sTiD2MYS4UAbt9uwXyXipKOcZe/EHZHGXExZcShZt+jz7pMOvUw6+bvZtKsReieFPz46qNjdomNVvXkC4inHSadfHeP5CYR9A9kpJwX9ezjLrspUY/ZwAAAAIInisHTLy6SFH8tg3+Xz1CgTQB79iep1aVUueq+LOH9GTISLSC5p5WKVrMaFixAuxu027DfOxdi9nOXpZ3i2H5TufZf0x8NDJphJeUKXdX+Tnvl2eZ8x/n8TD5GO/7w0ZmY67WiG3snhjw9tcn9wR5nQxax6q/U78lbIveDr0t4ZDwJN5aLUP924Y4bHdIsGAABAnVb8Xlr5J2nhFRns3G+osQCHXy71jHOvizPEWFjhiff1OX9GTISLSM4OLuKOuVj1WIPHXNzn9c5y3MpFv3DRHOdvqqdL8eLvSE9fKW19QnruFwHtTLlbtCnJhC551lejcnHd7dKulc79tLtFe8PFgVnRn5sUlYvucLF7rLNMt2gAUexeL93/HmnTI81uCQCgZRjXqCPbM3wZ+3w9QjTT1W1N3mnqnRD9tbzjzbse84SLnXIdgdQQLiI5e9Znc7bkoECvVSoXZy9wj5EYd8xFO1w0vzGabHSL7vEc3Ff9xVlOs4v0fm+Mtl2SCV3yLCxo82MGUVLtysVazPFDD3hrtIGZ6xVaudghs0Xbs0JLUq8R9ncRLgKI4N5/lhZ9WfrzMc1uCQCgFWV5Tl3pDRg1mvEUpEw7NfprhV0rES6iToSLSG5ok3VrhouBlYshB6esKhfnvMxZnn+PtP+bpFO+q/Ax92qww8XuMdKrN0mvXCsNGN2Iwz4UikE/gwSViwf+c/W6Yz5Vva7TwsW4vN0K6h1z0ez6fvL/pdfVPYzve7j8up1yUmCGi2YlMWMuAohi+a+b3QIAQEtrRLgYsejFe30R53ojTrdozp8RE+EikiuaMxLbYUZQUBh2QM4oXOwpV6XNfaXVXfmU70tjZrvb0tUfb59FO1wcsGYmHpjuzPAlSRMOlvZ/s/9zgw7QpQRjLvaMqV4365zqdXEr+dpBVWAYtu14933fysUYH6wH/bMVdB16WfTn1Mvvd9xpoVr/VOn4L1j/zK4hBWPMxVJRuvdfpcc/F3EWdwAAAEAZVy7GmNClXrG6RdPzB/FQ1oTk7ANhV48VjJVKCgwRA6v2lN3BOuhbIDNY2HBPvH3alYtdA/6PTzpC2uc11ofDYs+sy2lWsXX7hIu9E33W1RiDsB3Nni8t/020bbs94bLvmIsxPljH7mVVszbi5MDmDReP+ZQ12HRppDpcbOdK1kPfW73OHHNx+W+lp79u3X/uZ9KCBxrXNgAAAOSLWTST6Rf2MSsX6xmnP9aELh1SpIDUULmI+DY9Il17pLSpfHHeqpWLldDS8zY3J2XZ/HC8fY4alYumlz0hvfgGafIR5cd9wr9ACbpF++2/b6rPuskx2tEuYvwcq8K28nvlkQ87q+LOlNbIYNH7ejPOlI74UHDlYqz3ZRuojLk4Ku1a5azf9GBz2gOgNc06t9ktAAC0siwrF+2hxpKOuRgHE7ogQ4SLiO/Of5S2PObcL3QbB8MWGnMxqMS86DPjcy3r75E23BscLk46VJo1z7nvF+IEhlRphYtToq3rRN7fl63qG8LyicP2Z6Udy6zlPH2w2u/1wHAx4OfQruyfQ3FEKg41ty1Z2PaM9NzV2R1DgU5hTswGAIBXltcD6++0bqMWNNTTGy60ctFzzZynayC0BMJFxGdOWiGVD1J25WLQbNFh3/Y0sVt0FIMbpOtPlv5ykjSy3VpXK6TxezxJqBm4f59wscunlL4jw0WfD9ygcRjDuh/Ys6HnabwR73ve+3e3x4mNbU+zmd2iS8Ph2+bN0p9KfzhI+vtrmYwCqJd5QUVYDwDwyrJyceze1q09X0Acx/xPvO1jzRado2sgtATCRcTnDbbMbtFBlYvFkAv7zE7k7aAlpFt0FOa4jMNbrdua4aJP+Bf0ukkmdInavbUju0X76A4IF/0CWZsdosftFt1MJc97vjRansRI0tSTrEmNOkmXMaHLqKdyMc8Bwq410h3/4Nxfe3vz2gK0BePzl0oNAIBXlp8N9vn7hIMjPsH4zBqYEe+1wrpFe/F5iJgIFxFfVbhodIsO+lbHrvjzs/aWVJpVJbBbdMzKxc2POMv2/yNoQheb35gZgaFmgm7RYaGYqRMrF8fvX73u2E/7b1tVuVioXnZ9sKY4KU8WKu95o1u0HaKd9B1pzMzmtKtZCsaYi97KxTx/Gzu0wX0/z/8XoBW4Khe5mAIAeLXSbNE+1ytRhXWL9uLzEDERLiI+b9VeV4+7UsrP8LbqdXZZ9h3/IG1+rPrxegV2i45RubjwE9JDH3Lur/t7eR87w5/nV+02uiv668bVM966vWCZNOlwZ31Y6Xu7OvK/rSq9CQdbMzdfuELa9xLpPJ/Zgb3vDb8P9TwFN1XdokflVPC2eDCaBbNbtLd6Om4FcyvxHmfz9B4FWhHhIgAgjPnZkHrvl5izRRfqCRepXER2CBcRn1/lor0u6IJ9ZKu9sflEZ3HTQyk1zhBltuhaFn7Efd8e22zNzeHP8+sGnmbloteC8uy34+ZKs+Yn30876J0gzb9bOn+RNDBdGruntX6P46zQ0RRauVh+/+Tpg7W3HDKb4aL9XozTDaJd2BW+pRHpcU/1ap7DRe+XF3nqug+0JDNc5O8JACC5hvty9c5LOVyMXbloiFs8UAioXLSHUTJxfomYCBcRn7dycWC2M2FGUEWfXbk4/XRnXdaVAlFni85i7DW/ySPSHHPRa8KBzvKh77V+H3tfnHx/7cr7gRr2DaHdpThX4eIk69YMF4NmOO8EBWPMRa88h4vetoeNaQugNioXAQCm4oj05Bec+67KxZS7SHuHNaopg8rFSUdVr+PzEDERLiI+b0gxZqbUXZ7dyjuTtM0OFycfLb3k79LLF8l1MFz05dSbGXm26CwuzGNVLtpS6rY6bq70yjXSC3+ezv7aiXecEe97w/zALRXz96HaO9G6dVUult/v3f3NaVMzmWMuemU5TEHWvF/itNtM2EDDGZ+/xZwd9wEA6XvWMwmiGSimHi4G9LYLUk+36KCeTAf/i6oqMvN2HYSmI1xEfH4VUF191m1xqPoxyZlluXeiNP00aeLBcneL9hkPr24Bs0X3jPVslqCCae4rwx+fNa96Xc1u0SnqGZestL7deT9QveHieKMCtDSanw/VA95u3R7+QevW/t0Xh5wTlk6sXOwyxlz0ynO1nzcYLQ7le/ZroJXk5bgPAMjOzuWeFeZ5VgtVLsbt+eY3oUtXv7TXBT7tols04iF9QHxdRgWUXbFYmdAl4AJ3pFy52DvBWZd1+FW5QPC8zknfdt/3VjJGccR/hz8+6yXV61b+MWDjFMZcRDS1Khennewsl0bz86F60rek1+yQJh5i3bf/X9uXOtt0dWLlYvnn4NctOi+/Wz8PXOa+v/w30m9nSSv/0pz2ALlnjqtFuAgAHa9q8rwsu0UHFMQESrlb9GuDevPwxTXiIVxEfOZFeeXbEvs24GBrd4vuMcLFrMO0oAP1xEOk1xkVlknGXjNDUj+FgnT+09ZEN2aos/i74c9Jwqy2Q7iqykXPe2Puq53l0mh+BjIuFNwVuXaodtelzrqODBfbtHJx29PV63avlW45r/FtAdoC4SIAwOANEDPtFl3HhC6xu0X7VC4GXYOm/f9E2yNcRHzeMSik2pWL9hhh9sQvUn0TmEQRNOaiZH1r01OeWbeYoHLRHtsuzIQDpVetd2ZylqS73+bTzoTfCk053ro97H3Jnt+JvJWL3p99V7c09ZTyYznqFu3l+56P2tWijXSFjLmY18rFJ7/Y7BYA7cd10ZjT4z4AID2hlYspf06EXbP6KdTTLTpgzEU/DLmDmALmIgcCjAaMqVircnHEDhfN8Q492XapmHJX6Rol5iPbrdvda92zLUcRJVyUrP9vzYN4wm7R8/4qbXxAmvGieM/rZFW/C58PzS5jMpSqAConXdcjj9nS5uxvZx/5cPVjea1c9HaJBpACKhcBAAZv7yVXFV+zKxfrmdAlTvxD5SLioXIR8Qxvcd+fPd+6rVQuGgeh4qi0/h5p93pnFumwysW0u6AWIx6o73tX9bpHPiL9copz3wwTu3rjdTGN+g1R3G+eeidKM89i4pY4qj5QfcJFc6blJONxtgLCRUvY315eKxc7cWIeIGtmdUZejw0AgPSUPF9Cm188bUxxItLiqLTlUWs56vn76huNOylWLnorFalcREykEojHGy6e/H/lBfvAZhyE7n6rdP3J0u0XSVufsNZ1G5WLQ5s8O0/7ABaxxHzLY55mFKVHPyENb3bWjZ3rLPdOjBcE2jNpB+LA3TDeD1S/D017XMbRoWRd5lsBgbOlJ2Rs1LxWLvZNbXYLgDZEt2gAgMF7nmjev3leeueR6//uLEcNF83r8bjFKaGv4b0uonIR8XAFiui2PSMt/Lhzf+4rpb5ydZ9f5eKSH1q36/7mdEF2dYv2Sjlkq7Ql4G0+5+XW7f5vdq8f2ly9rRmKhgUWfryTiHjFHWcDyUWpXOybbN1uekDa+lTWLcoG7yVL2MRLeQ0X+6c1uwVA+ynRLRoAYPCeJz71Fff9tHo3mcU2e5wQ//lxCwqqrhFCwkkqFxET4SKiKY5IfzhIWvojZ515Al45sJkHIZ8DUndIuJhkRqpnfygt+ZH/Y7XGr5h+qnX7zLeknSuc9YPrqrc1Q9Go4y3aan2jVPl/52Q8vzyrNaGL5IQ3y66Wbn1Z9m3KAuGiJexvNa9dH/v3aHYLgDZEuAgAMNQ6T0zrs8Kel2DmOe7hwyKrs3LxpQ+HbEzlIuIhXEQ0D76/el3/dONO+cBWKyAMO2jGDRdHdkl3XSrd+UZpcGPw/oKCFnPcxDvf5Cz7/V/NdtuzTEfVN8V93xtoPfU165aurNmr6qLuEy7u94/WrT1OqOmY/0m9Sdngm0ZJ4eFiXisXvccTL75lBuJjtmgAgKnWeWJaX1JX5iUI690Xps5wcdw+wdtyTomYmC0a0Sz6UvU6M2jxdosOmpwl9MAZM1w0B9rdtdKnoqfGbNHmwXXr487y83+o3tasuFx/R6xmVr1+adTpnrv2dmnd7eUHCBczFyVcHLOndTu621lX6JZetd7pMt3q1t/Z7Ba0htBwMaeVi7W+hCkVqVwFYjM+C4qEiwDQ8WqFi2mdRw6VC2R6Jyd7fr1jLoaeM1K5iHhIM5DcgE/lon2CPrLN/zmh3aJjfjtiHtQH1/vsr0a3aPNgWmscxbhdocOY33TZs4NJVC42gvdEwe89112uaDUnc5l2an6CRThCu0XntHKxVlVVXrt7A81E5SIAwFTrPDGt8y37GtZ1XR1D3Otnb5gYNvFokiHL0NFIM5AOb+XicEC4aFYuHvsZz4NxKxeNCwC/cRJrdYs219sTPzx3tf+2Y+bEa5vXpCOd5V2rnOWuAWc5r90082T3Gs8Knw9ku7u8+YFK8JtPfidMM8+2bnNbuVgj+OA4AiRgjrmY02MDACA9NSsXUzjfGtokPfE5azks5AtjzhwdRVW4GDbxKN2iEQ9XzEjmlB94VnjGXAwKF80D2OEfkE75vnM/7rcj5kX27rU+j9eYLdqc3GPj/dL2pdLfX+u/7di9nOXD3henlZaX3O4s/35/afNCa9kMW0d3xd8v4vGGi72TqrfpHqhel7fJdma8qNktaA0TDvZZWT4ePPfzhjYlNfZxbfLRAY8TjACxMVs0AMBU60voNM63lv3SWU46pM2Qz7wDYczXGTvX85h3KC8qFxEP4SIi8oQr9oy6lYfLb6XR8qC0w5urdzHzxdXr9rvUWb7/vdJjn47eJFfl4obgx6N0i5akPxwQ/FpmuHjwu6K1z+QNsZ75TnXbuKDJnhkuHvhP0p4+s0GbE/1U5CxcnJPTWa7T5jez8pqbrNvV1ze2LWlZdZ11e9C/SGddV/3445+xvgkHEF1xyFnmsxgAUKtbdBo9YMzr6bgViLa453xdxvWvNzwseKbjYEIXxES4iGgGZrrve4M5u1Lxnn+ybv0OdH7jn5mD0C79kfTw5dHbZH5j5DfGY61u0d63f9i3MwMznOX+BGNiVA22W6p+Tb4dyt6xn7VuD71MOumb/sFzV3f1h2veukWHzcre6cwvCvJs+a+knjHV6x//tHTXmxvfHiDPRnc6y4SLAIBa4WFxd/jjtm2Lpb+cKi2/pvoxsyv09mcjN80l7rwArutiT3hY1UWaa1PEk7MrZjSNt2y6yxO+bLjLfd8vXAwaSyJpCbZ5ATC81WeDGrNFx+mGPP4A6ZB3S0f8d40ZryMq+YWLXNBkbq/zpVeukY773/Dtur3VizmrXPTOOHf0J5rSjJbQN8V9/8SvW7f2rOB5Nbo7+IuTFb+TRnb6PwbAUipJ6+6Uhre7/174LAaAzlYcts6zwuxaJT3xeem+fw+v8Lv7rdZ18u0X+byOWSiT8Lwtbo+6OOEilYuIiXAR0Yz1XIh7K7tMxRFp0Gf8h8ABYz1vw6hl5sUa4WLlAiHgbR40o7Wf3gnSCV+Sjkk5pDEvYhgrrTEGZvhUknp4u0bX2r7VeAO1I/+7Oe1oBfNudd8fW+fkTK2iq1ehH+EPvLdhTQFy6dnvSzecJt14hvvLRsJFAOhcxWHpd/tIG+8N327n89KD75Oe+qq06cHg7cLGRHR1vU5QJdg7OX5vJfMa3hseTjvVszGVi4iHcBHRdHu633krF03FQWnX89XrAysXPcFN1JCtVuViqUblYtCkM35CZ9JKgsrFllZVuZizQ6UZLp5zc/Pa0QomHyVNOty5b39jm/e/t6M+Zv3fJP+JiRb/X2PbA+TNkvLEdJseols0AMCybbFVlViLea2btOrQnHE6yfBYSYZtCqtc3P/N0gu+KR3+ofLDVC4inpxdMaNpvCfbPeODtx0dlJ74XPX6oICu6BkwN0m4uGulz+M1xlwc2R7tddLiHbdSkusbIcZcbCGeQ2OeKxcnHta8drQK8xiQ93DRrqodt6/UO1569WbpIp+TYI4nQHR0iwYASIpcrWcGkEmvE1zXwDGCvPH7W7d7nh//NcPCxUKXdNA/SZOOtBsYf//oaISLiMZ7st0dMu5gcdB/fSFi9Z83bAxskxFC7l7n83iN2aL7pkZ7nbQc8m7jjl/lIt2iW4b3JCGo6rZV9U027uQsGM2C2QUk7+GifZywq8f7JvlP7CK5h44A4GZWZAxvdpbTmAEUAJBPUav1XGP3h51rhzyWtHJx3u3SiVdKJ34t+nMqzTHaE/R/ta+dqVxETISLiMa+EB+YZQ0cO+HA4G1HB6Vpp1nLZtXU+juivVbUE3tXOOBzQK7VLfrQBo9JZs4ybbfN/D+M7GhsexDC8545ImdjFpqVi90DzWtHq/CtXMzht7GlkvGlScjQFLZV12XbHqBdbF3kLOf1iwcAQP1KEYtcRo1imtDuySHhollYEue8dOwc6eB/sXqw1KVGuEjlImIiXIS/xz8r3XaRdcL9+wOkFddY64/+hHTiV6sru6af7iwXB52DpTmzcq1Zt2xRD+quyVD8Dn41ukX3jpdO/5X/Y69cE60NcezzGmd56U+sW7PdfjNsozm87+8xs5rTjqS6+6UX3yCd+Uersq3TuY4B9rexOQwQzJPQsHFvbUFV5ACC5fHYAABIR9Tr1aK5XUiAGNZlut4xF+sWVJlYbvPOFQ1rCdoD4SKqlYrSQx+0AsU/Hyttf9Z5LCioO+vPzvLobufk3Ow+HeViWEpWueh3QK6sC3mbzz63et0Bb7NmFJ41z7q/7z9Ga08tvROlPU6wlivjPRrtLg6l8zpIgfc9k8OuxbPmSXu+rNmtaA3mBD1dOe4WbZ6ERqlczFt3fqCRgi748nhsAACkY9Tzxez+bwrYLmIIGcY8r5twUP37iyso0LQLXrY93bi2oC0QLqLajueCHwurArQt+ZETELou6iNe6HrHHiwOVx/oJU8I6Rcu1hhzUZJ6J1SvsydMOP1q6dQfSi/4emhzYxl/gPt+HrtmdoK8TeCCcJOPdZbzPOaiOQN0z7ja2xMuAvHl8dgAAEiHNzSc9kJp2qnh24Vez4V1izbCxRO+HKl5qQoaU3GCcb3KOMSIgXAR1bY+6Sx7D7BB4aLpmW87AaE5iUuSCV1KJemGM6Rr9pKGt7q3q1m5GCFc9GMHon1TpP3+MYXxLAzHftpZLhW5iGlZOZ8tGm4Hvs26HbtXvsPF+41JoaIc17oiHnOBThR0UZXHYwMAIB1Fz7VvV6//+OVm4Uvo50aEbtEHvE0amBa5iekJ+BwcmO0s33ZhQ1qC9kC4iGqVLrs+olzQjmxzDrJmV2hzkgnTqT923zcrF4c2SRvulgbXuwdcl2qHi3Yw2h0wk2qQrv7a2yTVt4ezXBxytztuCIrsVIWJhIu5Nvko6aULpfn35TtcjKsYcfxaAI5OODYAAPxVFdb0+PcEMUNIb6871/PDwsXy85r2ZXCtCV0krby2MU1BWyDNQLViyIn1lseCH+s3vnGxD5bmuGBHBsy4O/Ukz+uXL4hLJWnNzc76kZ3u7Vzhok+b7ZC0p0bl4Tm3uO9nObuuue9HPuKecGH+Pdm9LmIiXGw7k4+Uxsw0qq9LwZVLedYzTtrjRGuZcBGIj3ARADqXN1zs6vUPF13dohN+btjdoqP27ktb0HlwlJ6KgA/CRVQL+/YlLHgzuy3b+zArF6efFrBPzwHbDiaf/730t4ud9SPbPO2sUbk4ssO6rTU22cwz3eMqdmdYuWh+OD3xOWfA3EPe40z2guajirSNGb/bvIx5WipJW56svZ1U/oa9fJJaT7g4tLk9w1egFsaXAoDOVfSM8x8lXAz93AgpULALZ3pi9rJLTYTKRSAG3jmolnjcCGO2Y78xF4N0e8I/+7krrnGvrxpzscaELpXKxQgTH7hmtc4wXPSWxtvhYlCXcTSJ5/fEmIvto8v4NjYvFUrPfl+69rBo23b1OBXjYV8UhVl/j/SrKdIdb0j2fCAP1t3uvz4vxwUAQPqidovesdRZTnrtPLTRuu2bGrV1jUHlIhIiXES1sANk1EqfYTvYi/BNzMA06YzfOPftahvvWInDSSsXI0zIMnZPZznLykXJac/EwwgXW1XVN3aEi22j0OLh4rNXSTe8SNq93ll391ujP7/QXX/l4hOfsW6f+2my5wOtbueK4Mda8bgAAGgMv27Rg+v9t7Ul/TLXLoRJc/LQOPxCU4nKRSTGOwfVwg6QUU+6hzdbt96qxCBzL5KmHGst292fvRfG3spFM2z0houlUvRu0ZI04SBn2RwnMgun/si67ZsiDdrfWO0RvD2agDCxbbV6uHjXm62KqkcCxqiVpCnHh+ygq/5wcddqZ9n7pQ7QDrwXj6ZWPC4AABqjKlzskTY/7Nw/9LLq5yQNF+3Pm2ZVCgYW1BARIRneOagWemIdUrk4/oDqdeYkL7VMPNS6feA/pJ0rqw/u3jEXzcoDs80LPyY9daUq40hECRfHznWWB9dFbnIi9rdExSEqF1sVlYvtq9XDRduulcGP7efTXdk+/h74T85wFKWE4aJriIsW/hkBSQVVa0i85wGgk1V1i+51D5/l9+VU2OdG6GzRTQ4Xg4YCo1s0EiJcRLWwQWknHBz82Fl/ql530D9JM18sHfM/tV938jHW7banpL+eK6291f146JiL5ZlfNy+UFl4h3f9vzkPmB0IQM0yyu3RnpdsIF4e3WMt9k7J9TcTEmIttKy/hol157Wf5r6vXnXevdMJXpEPf60yklcZs0a38MwKSCrtw4j0PAJ3Lr3LRHGKrf3r1c5JO6NKqlYt0i0ZCmb5zrrjiChUKBde/Qw89NPQ5v/zlL3XooYdqYGBARx11lP70J5/ACtkKOrGevUDa9/XBzzO7FtsGZkjn3CQdcXnt1x0zy1ne8pi0c7n78bAxF60V1dt0j3FP4BBFV8bdou2qouJQvIlv0DhULraxnMwWveZmq4Lbz8iu6nV9U6RD/s36oqLSLTppNx3j55JGQAm0nJCZ0AkXAaBzeWeLLvTK9ZnR41O0knRCl2aHi1QuImWZx9JHHHGEVq1aVfn3t7/9LXDbO+64Q5dccone+ta36sEHH9SFF16oCy+8UI8++mjWzYQpaNyIIz4U/k1GoeAZuzDmgalWhaG3W7T3wrlUrB4vcdTnIjzIcZ+XphwnHfLu6M9JwuwWbV/Exw1AkTHCxLZlHsNaPUS4ZYH/+q4aX0bU2y3afB7hItpR6BcLIcEjAKC9ea8du3rc54t+18L1jrnYrM6kgeGi0R6CRsSQ+Tu5p6dHs2bNqvybNi14DL4vf/nLOu+88/T+979fhx12mD7xiU/o+OOP19e+9rWsmwlT0AV3KcIJ98sXOctBB6wg3tmhvaq6RY9W36910R3msMukBQ9I/VOT7yOKbp9wkREKWguVi+2rUHB+v60eLm5+xLr1vh9rHefsbi5hk1aEMQPFpCfMQCsLCxejnOsAANrTs9933+/q9RS0+FyzhfUU8Rtaac1fpW2LVZnLoOW6RRvtqefaGh0n80Tj6aef1pw5c7T//vvrH/7hH7Rs2bLAbe+8807NmzfPtW7+/Pm68847A58zODiorVu3uv6hToEHyAhdCM0DaOAMVAFqHbzMSQak6mCgOJiPb1cqlYvDcj5UCBdbGmMuthf7ONFK4WJxRBra4v+Yd9iEWjPa95bHcB0O2F+UtlSWqVxEOwo7n2nh4RIAAI1V8FYu+lxrxukWvelh6aYXS384UNp4v7WuWT3YggqBzC/gGLoLMWSaaJx88sm66qqrdN111+kb3/iGlixZojPOOEPbtm3z3X716tWaOXOma93MmTO1evXqwNf41Kc+pUmTJlX+zZ07N3BbRBRYuRjzhDtu5aJ5sJ54WPXjxWFp44PS4MZyezwh6MjOfIRAft2iCRdby8b7mt0CZKkVw8UbXij9arL/Y94vXmqNC2vPPm/PRh9X0ah49I49BLSDsOpEKhcBALauXmn8/s79uN2ivdemdq8UyemV12qViz3jnOW+yQ1pCtpDponGggULdPHFF+voo4/W/Pnz9ac//UmbN2/W1VdfndprXH755dqyZUvl3/Lly2s/CeGCDpBxw8XugXjbmwdWv5Bw3d+k646XrikHyN5gYHRXa4UFQfzCRbpFt7gchNaIrhXDxQ33BD/mDRdrfYtsnwgObU7WlmkvdJYHNyTbB9DKQs9nqFwEAJQVeqRTvifNfaU073b5XhPEOZ80g7vKa7RY5WJ3v3TKVeVt+hrWHORfQxONyZMn6+CDD9Yzzzzj+/isWbO0Zs0a17o1a9Zo1qxZvttLUn9/vyZOnOj6hzoFHiBjfpsft1t01IkWRndat97u2zuXt/bsrzY7KBjdJQ2us5apXGxteaiIRXT2+K5JxyRstKrKxVrhol25uDnZ65njzg6udz+28QFp/V3J9gu0DMZcBABE0NUrjdtbOuPX0ozT/a8JwsZc9IaR3S0QLtqTlx79seBtJh5i3bbSF/FoeQ1NNLZv367Fixdr9uzZvo+feuqpuummm1zrbrjhBp166qmNaB5s9gFy+gvd6/c4Id5+xu0Xb/vJRzvLo0PB21W28czmdeOZ0q7gLvQtw/4GyDWeBeEi0DCVcHFnc9sRxdrbfcZcrHES2jvZuk3SLXr9PdLTX3fum+FicVS67gTp+lOTB5dAK6ByEQAQRZQJTeKMuejXs6/R4eIJX5Jeu0uafFTwNpVePnwmIrpME433ve99uvXWW7V06VLdcccduuiii9Td3a1LLrlEkvTGN75Rl19+eWX7d7/73bruuuv0+c9/Xk8++aSuuOIK3XfffXrXu96VZTPhZR8g7QtUSTr2M9FnUT75u9bB6qRvxnvd/j2kF5SfM7g2fNtnr5Ke/V71+ltf5r6//5vjtaERfMvLCRdbG5WLbaVnrHXr/YKiWcK+8V72q+pjxtg9w/dX6RadIFy8/UL3/d3rnGVzLMbd7l4GQK4wWzQAwMvv+F9rEj0pfMzFqi+s/F6jCd2iaw1fVil8IVxEdJkmGitWrNAll1yiQw45RK95zWs0depU3XXXXZo+fbokadmyZVq1alVl+9NOO00//elP9e1vf1vHHHOMfvWrX+maa67RkUcemWUz4WUfIO2udZI0ENw1vcoBb5Fe+og0bp/4r22PQzGyI3y7uyKGhmY1ZKvwCxepXGwtB73Ts4Jwsa10l8PFkRapXLzjDcGPlUaqvzU/+uPh++sZb91u9x+CJJQ3NFz4EWnHMmvZ7EYe2gUIaHVhE7pwIQUAHcnv+O89BxvrM3ms95yoVLJ6ggxvl9b93fOYT5XjpCPitbMhytemdItGDBGi+OR+/vOfhz5+yy23VK27+OKLdfHFF2fUIkRiH0Rcs0M16GQ7SSAZphVDO8LF1nfildKyXzpdQhlzsb1UukW3SOXisl8EP1YcrP5G2/zix495jNm8MLzbi5ffifXv9pFeX/KEizkYr7JUku56U3kw9u82uzVoJaEBYkjwWByRdq20xt8C0Hp2rZGWXS3t94/Mcov4/II0b+XinufXft7Sn0p3vsH//MvvNWr1SGkG+9qUL9wQA4kGqtnfvpjdohs18cGEA6vXxR270aUF3+J+pe+Ei62lUJB6JzW7FchKj6dycdeq1q3EGx1UXZNpbX4snXYUR92fA7Wqy1vB+rukJT+0htAYaZEgGS0irFt0yGP3/osVtq++KXgbAM3z1/nS/f9ufbEExOXXvdlbuehXcOB93pIfWrebF/ps6wkX97ogevsaiTEXkQCJBqrZBz1zLIZGVfh4Jy6QpFcsrmN/LfgWLxR8PqiaMNYGwnWZ31RSudhW7G7RozuldXdIv50TfaiFRpt2avwuKebx5dEr0mlHadg9Ac7w9nT2m6WFVzjLpeGmNQMtKGnl4uLvWLc3z7MqpAC0ls0PW7crftfcdiCffCsXI1yjxTlP837+xBl6rJEYcxEJtGDygqazv30xD6b9Mxrz2t1+XYbrCHZaNbQrei90+VNsOa6gm3CxrfROsG7veYd099us5aU/bl57wiz/Tfxvjc3tty5Kpx3FEXegOJqDysXV1zvLVcdcdLSk4aLp4f9036c6FgDyzaxAHH+gtM/rol2Hhk7o4t3WE0RGmTCmKcrXpkXGXER0JBqoZh/0unqks/8iHfIeae4rG/PavjMp1zBmdvBjrVi56IvZKVuOt7oU7aN/mrO89YnmtSOKNTfFDxfHeMbuSSNYKw27A8Usu0VnMVvvrlW1t0HnsP+m/C7qgv7evEH9oDGT+pIfS1ePk579YTrtAwA0njlEzvmLpBf+zH+7M35rXR9XnhcjgHv+j+77XS0aLlK5iATykrygkYpG5eLsc6UTvij1jGnMa/t1i65l/n0h+8vJW5yqmtZjXnQyoUt7McPFPIjbLbq7T5o1z7m//s7621AcdlcuPnR5/fv0s+E+6bezpMXfT3e/WbUXOVUOsHsnBj9mev5P0h8Pda8bHXSW7/xH63l3XZpWAwEAjVY53yqEX0POvdC6Pj7iv8rPi1i5OLLTGV7D1qqVi4y5iARykrygoewDazMOdl3d8asXwyoX8/IWz0sI2km66BbdtnI3WU+CE7s5L3eWe8an0IRhd7Xi7tX179PP3W+Rdq+1buPYtcoKJIc2+z++Y2m9LUM7sScn6tuj+jG/C6ln/cLucgi5/Vn36jxMdgR0guW/dX8JANTy9DfKCxF7UNjXylHDxavHVa9r9cpFwkXEQKKBan5jLjbSmDnxtg+rKstDaFfolsbt3exWwIsJXdpXnsLFOS9LdmJnVjsmPZZPO81Z3vRgtuMslkpWKJP0JPbh/7ICyetP8X98aFPytqH9DK63bgf8xpP2uajc47jg7e56q3v1+rvraRmAtNz+SunBDzS7FciTRz8eb3v7WiFuDxPT6FDy52apEi4y5iKiy0HygoYzx1xshhkvql7newEQQXeDunPX48SvNbsF8JOkiz7ywbcrZItaea00kmBm5kmHO8txBho3mVXkz3wn2xmib3+ldPX45BWR6/5u3drj4nmrVRjaACb7b8qvqveZb0v3v9e5PzooLfUZd8se23R4q3v90MZ02gigfk99pdktQDuzv7wtJjzPkqSdz6XTltQx5iLiI1xEtWKTKxf9qoqCxkg7/erwfU0+qv72ZOGojznLVNS0JrNbNMFEe8lTuChVhxdRzJ7vLKcxpuvQJunB/6h/P0FWXGPdDm5I9vyesc5yqSSt+J378cnHJNsv2lOtL1EXfUna9LC1/MT/Slserd7Gfs+NmeVen/Q9DADIl0IKlYs7V6bTlrQx5iISIFxEtWaOuShZ3QC9Dgvo1jDjzOp1+73RWZ5wcDptStveFxt3mCm6JTHmYvua+oJmtyB7hYJz/Iv6jbp5Ajl+f2lgpnN/3e3ptU2yZlbcuii9maHNL8OKQ9LoTvfj5sy+QOU8J+RL1GW/tG6f/4N7vf3lxOigNQHRyj+5H6dyEQDyJ8n5SCWAq6Nysdjq3aIJFxEd4SKqNXvMxdnnSqf91AoZzyvPBL3fG6WX3CGd+Uf3tt5uz91jnCBy8jHWBDGtaNJhxh3+DFtSj8+gy2gPvROkiYd4VrZhgLztKet254po25shpH3sDVLvjNv3/rM1++6ikC5rcU70zc+r0d3VgeruNfHah/YWJVzsm2Ldmr0pDvpX6agrrOXR3dJffL6oIFwEWsuOZc1uAfJgdFf856Qx5mKrh4sqpfdFMNoeqQaqNbtysVCQ9r1EOuuP0h4nOOumnyr1TXZv6w0XR3dLk4+QXrFYOveOhjQXbcrVPb8Ng6dO1z/dfT/uLPV5csfro21XMrpPd/VJxd1hG9fVJC3+P+t24UeDvxVPMtakZF0gDK61lmeebd3uXsvJMRxRwkX7QnOsMcncyDape8BaDvr7oFs00FoI/BFFkiFk0hhzsZTC0DWZMGIiqhcREeEiqtmVi61Y9eedZKNqvKTyxeP4/d1jcLUyv67daD4zXGTMxfbjDRO7+5vTjoYoSUNbam9mnhwXeqwva4KkNrthSRrZ6f9Q0Ho/5kVBcUjaVa5UnHiodTu6y9lmza3Sfe+WtjwZv7loD2a4eOoPpUlHuCdBkqRdq6XVN0pDm511S38idZWPFct/47/vZ78vbV+SepMBJJTGuMNof0mqDytjLnrCxTjXDftdGv91G8HMAZgxGhERLqJasysXw3S10Qy+F66Q5t1mVWSi9biqZAkX2443XCwO1ffNc1JZVtOdZsxw6zchhZd5AdbVKx30zpBtUwoXS6XgCsXioP96322NtpeKTuXi2LnGNuU23/N2awbRO98Qr61oH2a4uN8/Si97VBq3v3ubp6+Ubn6JM9mQ/Ty7cjHME/+bWlMB1KlVu52itZgB4QVLoz2nMuaiJ3yLc2532Pujb9tIXcaX7nHOx9DRCBdRrdmzRYcxKxVbMfyMY+ye0owzmt0KBDHHXCxwqGw73oBgdLe0e3Xj25FlV5OJBznLXREqMysn1gXrPb/XBdKLfu+/bXEopWA0JFwMq5z0a09ll6PS7vIELmOMLq32yfG2p63bjfdH3z/ai1+3aO+wK35O/VG02ebTvBArDkvDCYcIAMDfD6KpfC50SeP2ifacoHAxqkPe69MLr0WY58lJxqNER+KKGdVauXLR7BZ90D83rx3oAEa1IuFi+/ELEgbXN7wZUkC4OOvc+nc95XjjZSKEHXb1n1khPuVY9zaz55cXSul0kxnZHhwurvt79P24KhdHnf9vzzhjTCSqVzqaGeTb713zou6Y/xf+/FOukvZ7gzRmdvVje57vea0Uu5D98VDplxOiDW0AoNot50nD25rdCrS6KGPxegWFi1G6Rc95uXTMJ6O/VqMVupyAMc4wNehoXDGjWrNniw5jXggc8HZn+fRfWren/KCx7UH7mnBws1uALB32wep1UcPFUlFa+zdpeGv97QgKIV78l/r3XShIk4+xlkd2RGiLfew3jrPmpFn906TTf+XcT6s6K+iib+Wfou/DVblYdAeldhf4Ubr1dKRSSfppl/Szbun5a8vrfC4ix+0tnfSt4P2M29u6HfAJF0/4inTBc879Z6+SiikFjNuftW433J3O/oBOtGNps1uAVlf0OQeqxb4uTTKsztyLWn9+APsccJRwEdG0YGkams7vG/1WMf4A6eB/k8bvJ0052lm/96ul1+5u80kZ0FCzz5WO/5I05ZhmtwRZsIMC0+6I4eKz35fufptV1bfgwfraEbfC6dhPx9vePnGN8q2zfXJsVi6a3WKKI+UTzYKkkhUKmsMHROU9CQ+qXNy5wto2ymeRt1u0HS4Weq0u4aO7/MPQUokJm9rdxvtUmezt1pdLlxSd4M/7JeqB75B2LJce86km2eME63ZgRvVjY/eqfn9teTTdz49W/MIXyAsqr1BLmpWLkV4vBzMw20Pq0PMDEVG5CLfRQWnzQmu5FU9kCwXpxK9Ih763+jGCRaSpUJAOfbc086xmtwRZ8JuUYSRiJeKSH1q3mx6qvx3mCener7Vuj7rCuu2f5t725Yukwz4Qb//d5XCx1rfOxWGpZFf7BVQuFoes2QP7plj3BzfEa4vNrsSy7Vrlv92Gu6Snv169fni7tPwapxJx3Z3S4Dpjg6Lxf+mVuvuc9nsxi2h2RnZJCz/R/Fm5n/m2+/5TVzpBYMFnkrigimR7rEW/sLurpzpoH9oYr51eq2+S7v2X2u0CUBuVV6jFr/dGLfWEi7tWxn9Oo9nX1vT8QESEi51sx3LpnndKW55w1j3+WWe5FcdcBIA0mONoDsy0biOPyZTiR6d5QnrK96Rz75aO+G/rvhl8dY+RJh4cv8rOrlxcH9Klcv1d0tUTpMc+Zd03A5cu40sm++Ksf6p1O5QgXFzzV+mPh7jXbXo4ePtlV1eve+TD0u0XSb8YsAKXe//J/XhpVNpVnpynq9c5+X/2B9KOZe5t6WqanbvfKi38iHTtYdIjH21OG7Yukhb/n3vd45+W1txsLY+dU/2cYZ+xDWe8KNrrHfUxZ/mB/4j2nCA3z5Oe/oZz//ZX1rc/oJONMCEFalh5nXUbJ4iuJ1yMM2lds1QqFwkXEQ3hYie7/VXSM9+U/nKydb9Ukp43ZgZtxcpFAEjLJUXp1ZukvS6y7kcNF9PsRmuOy9Y9IE07yQn0zJDDHjcwLjsUWX198DZ3vtE6cVz64/Jreb5YMqsXJaeiMknl4r3vrF7nHevSfD2/WT6fvtJZfuQjTrW9rTjsVDIWh53KyCc/L/3OMwPk09+M1m7Et/ZWZ/nRj0vbnml8GwZ9qgd3PS+tv9NaHuszI6hfV+aoXSoPe7+zvKnOIRMApKeUYEw8dJYH3mPdxukCnCRc7Jsi7fEC6ZB/j/6cZukK6fkB+CBc7GSb7rduR7ZJmx6RfjtH2vyI8zjhIoB2VihYs0b3TrDuj2yTnv+jtOp6awKUW86Xnvab4CGjykXvrOQnfNlZTjrsw+zzrFtvgFcqSXe8Ubrv36RtT7sf81atzzzHfb+vXLm4e2389vh1Q7XbdsDbpdeX3N1L/arIxu3nLG9+RBq3r/txV7frUnh7tj0V/jiS6xnvvt+M2dhrnceM8wkXD/oXacZZ7nXeChPzPdg/3Vnu8QTxAFpDmjO4Azb7fCnO++ugd0rn3SONmZVNm9JEt2jERLjY0Yzqm3veIe1e7f5mYuoLGt8kAGi0nnK4uGOpdOv50l/nS0t+LK38o3TvP1dvH2Xm5ajCBhA/+N+c5aSVi317WLdDG92Dh29fLC39kfTU16qf451Vs38P9327AuTef44/ILnfWJd26GSHvObYcpOOrN7eDASHt1uTtZj+/jpneda88PaMRO0Kj9i84eLudf7bZalWtYVfuNjdLx354fDnnXqVtM8l0n6XSi+53f3YtNOsW3sCmDSVaoTlAPwRLiILlcrFOJWxOYpf6BaNmHL07kZqnv6m9NOC+4PWe9DY40Rm0ATQGexQy6x4GwwJQjbcld5rV8JFn49j8xjclbBy0R4fsVR0h3beQC6MPYGLbdV1zvLuNfHa4xcu2j93e8KMw97nPOY3Jp5pZFvw/2WPE62fq99r9k62biOPs4nYej3h4tCmxreh1vt8zGz/9bVmQZ/xIumFP7VCxomeMUQPL0+6lMW41UxABCRDuIgsdCXoFu13vteqKpWLdItGNDl6dyM1fmNeeTG2AoBOYYeLZvjRsC6c5cq/Wt03k1Yudvc7z929Rrr7bdLzf4p3Inzoe62gZP83W/fHH+A8Fjdc9JsZenizdTtU7gJ92PulqaeUH/MZc9E0tMkJkLyB0JRjrdtzfcLgiQeX90+4mBlv5WIzLu7DwsVD/8N/5mdJmnRY8tesjEmawTGEczMgGcJF1GKP9zzx0OjPSTLmYpfP8DCtqjLmIpWLiIZwEZZND7nvD8xoSjMAoOF6fMLFbYujPXdwg/TMd6Rda6zZYdfeFu+1w7pFm5KOuSg5FVSPflJa/F3p1pdJi74a/fnj9pFes006+bvW/fPucx6791/itWV7yM913N7Wbd9k6YC3WMsjNcLFwQ1ONZc3XLTHwvPr+jrhYGf/dDXNhjdcVFFa+nPpmr2l9fc0pg1hE7HY7zc/dhWtbe9XR3/NNMLFoPck4SKQDOEiarHPC8zxrmsJChfDzum8k+S1MrpFI6YM+mygPdAlGkCH8BvrzxzXr1QKHibi9leVZ8V9h3X/yS9Yk5JEVawRLk4/Q1p3uzUAeFJdPdKopC2POuue/V68fZhdi/smO8v2rLtpmHKcs2wHU95wseg5gXeNc+T5HQ2Uw0W/E3n7IkIlawxNbxde1G/X8+77pVHpjkus5dsukF7pU8WatpGtwY/V6vr8imel1TdIvZOcGeWjsMPF4S1W8J2kSiVoLFPCRSC6MXOsv9+tTxAuoraoX/aa7G295yaTjpBW/sn/OX5DtbQqukUjJioXYRnjGddqjxOb0w4AaLSqCiu5x18Mm7Rk7a31vXatk9mz/yyde6d0wNuSv4a97yGfmZf9nBVwQlyPNX+Vbr0gfBszhAkMFz2z9pq8vyd7Vmu/LuXj93eWvTMBo36rbpDW/d29zry43726Me0wZ0KfvcD9WPfY8OeO30868B3SPq+VumMMS9A72RlTa3Bj9OeZgiYHoHoEiO7CFc4wHnEnH0PnsY+7ccbLrcwWPeK/3k+uKhfpFo14CBc7TTHghNV7UDzyv7NvCwC0Ar8TPfOYaIYiaV+g1AoXe8ZJ006pbwBw+yQ3rIrLVGuGZUk67WfWrXcyiyA3vVh6/vfh25gn470B4WJYN9cJB7rvV362PlWndlWjJK24JrxdiO/xT1Wv8/7tNCLU3VUOMY/9rPSi31ozPNt6aoSLSXV1O7O0J+0aHRQuUj0CRFcoJJtwA52pnspF7/urFDL5Vq7CRbpFIx7CxU4yvF1aeIX/Y+ZJ/pRjszvpBoBWs8cJ4Y+7wsWUL1CSnMzGZc98Pbgh2vZRvrW3xzFMM+zwq1z0Tuiy9CfOsndcvHH7uu+PGJO17HepNOlw47WMMSzveXvspqIGezZuk/dvZ8mPsm+H/d4fmG5179rndc5jtbpF1yPuuIsbH5B2G9uOBExEQ7doIJ4kE26gc6z8izUWsJRuuBhUzCPlK1y0P3Me/q/mtgO5QbjYSW48Q3rs//k/Zs6o2FXHxAEAkDdB4ylWGBVXeQwX4yh0Rfh5yBmnMmo1pNdhH3BmhLaZM/cGdYs2Ayl7Ih7blGM8L2L8P069SlrwsPFaOZqtMY/6plSv8/7tNGLcqS1PWLf25D5mcF6rW3Q9diy1bm97Re1tN9wnXXeCdK0xQ7UZjJsIF4F4CBcR5pbzrLGA19/lvEe64nSLLr+/dq91ry+2SeWi+YUuEAHhYifxzghtMg+C+7w286YAQG6YFyVh30bH2ca771YJF6NO5lWZBCcgBAkz9RTpuM9Ud/UuRBhzsb/c3fTAdzhtsB3yHqtCscIzsY55wTAww/2YOcYm6rPlSf8Jg0qj9XXvj2tkl7RzmbVsVxK6AuwMw0W7N8jwVmlXjYlr7EH/zSrHoL8rwkUgHnvMuOGEX4ShfZlDdaz8s3PulqhyccR93A7rFt2To3ARiIlwEW6n/lg6+N+b3QoAaB1xu0X/4eDoYzNWwsVW+TiOGi5Otm6LQ9Vdl2uxqwa9Y+6Zk2bYYy4Wh9xdr+2f14yznfH0JOm8+6xur6deZWzr8zs47afSCV+xxmc8+y/O+t8fEC8URrBFX3aW+6c5ge/ooPt3kvWYi+akMXaY7KpczLBb9AFvdZYf+3SNjX3+5ryhuo1wEYjHHi5j5/Ohm6HDDG+Vrj/Vub/q+oTdoo3jtzmBWLtULtLLAzG1ytUMmsk8cOzzWmfwYwCAVDTDxQgB1I4l0cc3tMOWlqlcjKhvkhPYbC13PR3ZKZVKwc+x2Z853gHCx+7jLJvBz+gOZ9kOALu6peHNzvopx1W/ztSTq9fte4l0yL9Zy/1T3Y8NR5xNG8G2L5WW/ti5f/C/O+/ttbe4t818QhfjvTh+P+vW/DvLsnLxxCudZbtq0jayS1pzi/NeHjUmKbIvSIMqF8MmNAJQzf68oVs0TI9+Utpwj3N/w13GbNExzsdGjfMYu0p2ZFf7hItxZs4GRLjYOUIH3S9/61LoiTfOBAB0hARjLpqVR6WitO5O/0kaGtEt+rD3R982Snhqm3SEdbvlMWnHMunX06Q7L63ebucK9337Ys/8GU053v3FllnFaActpZJx8u/5rDIrP1/xrPTiG6XppyqUd3zhnSukG8+SHvsf6//DzLzx3Xim+/c6stV5b6++0b1t1uGifXHnmlzG+FvOMlzs7pfG7mUte2cxv/ut0k1nS09+3ro/YoTn9s8kqHJxd40u1gA8yp8NhIswrbmlet3QJus2TqBmfo4VuqWnvyX9cqL7SzavXIWLOfviG01HuNgpBtcGP2Z3s2nE4OoAkDdxx1yU3OM73XC6dMNp0s3nBO87yxO44z6bzclsJVx8XHr6G9bEYEt/5K7a3PqUdM1c9/O2PmXd7v9mZ93Zfw5+nVV/kf58gnTry42fl3HyP/FQ9/bj95Nm+fysvbzdfR79hLT2VmtWxN/tY02ChnjsMQ5tpZK08lr/bUcDZkROix0umr9n80Iwy27RkvP34a1gee5n1u3jn7Wqou0ZrSVpyQ+t26AJXXYs818PwF/lS6uIQ5WgM+xeU70uyfnY5KOc5eKw9PB/+n9Ja36ZmadwkaIjxES42ClGB2tvQ7gIANXijrkoubvYrr/Tfeu376y/He6bHG27cfvU3sbWX+4WPbTZfbJ87ZHO8vO/r37ejiXW7eEflF50jXTxluoJVkxLfihtesCa+MIOagrdVnXijDOlM34bvc2mrj73/eW/dt83u0whme4xwX8zz34/Wjf6pOwLPPPiyOxu3O35/afNnqAobGD/G06Xnvu5c//h/7Ruvd2i7S78O5en1z6gHdkz1e9ziXXLbNHwUwypnI8zPFjveKl3orVcGpaGNvpvN25vZzlP19t0i0ZMhIudYsdS9/3xB0pneC6k8vRNCgCkadKRwY+VYo65KElDEcfva1S46O0C7PWCb0gzzrJuo7JPkIuDck1KYU6kEfa63QPSXhc4J+Zee11k3a77m7POHp+uq8eqTpx3izTp0KqnRsJA5embfIz7/qHvkc6733/bHUul9Xdl1xZ7FmZztubJIX/naauMLVoOF7c+LW16xHl8aKM1zpfJrnj2doseX+5avTukFwoAp2J471eXV5QvdYuEizCEDcsRN1DrK3/5EzbO4pyXO8t5ut6mchExES52ipvnue93dUuzznWvy9M3KQCQppfcJs27VZp8dPVjpQRjLkadHMQeby3r42/Qt+m2yUdJ8/4qzVkQfZ/d5eBwdHd1GLL5UevWWx0oSYf+R7T994yvXmf/vNL4Nt2vbUjugfdJmx927k88zKq4G7tn8HMe+3/SrRf4j0dar4f/q3rdpMOlebdJr1ic/ut5meHilselPx4s/fmY8OfYvJWLEw8p7ytCLxSgk1U+r8uXuAW6RcNH2BA3cb/stY/1y34VvI35JWierrdP+GqzW4CcIVzsWF3Vg5nn6WAHAGnqmyLNeJF/NVuiMRcjhot2ld/ArGjbJ2WOAeknSZcxuypx2dXSE591P/b315W38QnwvLPnBunxGRPPnhwmjW/Tk1Qubl5oTfhiTsIBiz1BiS1sTEX7vbPyWqvr/JIfZNcurxlnSOP3z/517PfvzuXS3W+P91x7zMUxc6TD3ifNeal1P8oQN0Ans8PFgidcpFs0TEE9JqTk4eKz3w95vUnG/gvB27UauxLYHm4AqIFwsVNtfcL64DUrQ7oIFwF0OPME0JZkzEW/2V4LPh+5dtecLGeujaI7wet3h3R53vKYdesXLkYNBsMC2jTC2J4J8bYf3S396WirIm55wnEeW9nWp9OtIAwaQmDS4dK0U9zr0g5rzcq/lz2e7r6jmnS4dbtjmbT+jujPe/5PzvHjkH+XjvucE8ZSuZgPWY4lihq84SKzRcNH2JdfscPF8nlOWA+R6eUJ4vJWyGP//QxtkgZr9IABRLgI8wK4J0djQABAFsbMqV6XZMxF3wojn49ce3+FBo//96JrpP0utZZnvUTa44T4+6g1jmOQqF2azVkYvSYclOy1TV090gXLnIH/a9lljCVZq5t53qy/2+q2e/3J6QUjQeNKnXVd9Xsg7XB95/PWbe9EadJh6e47qjF7WbfmGKRR3PoyJxy1vwC2L16LQ+m0Ddn522ulaw8LH9MN2al8XlO5iBD2+M1+YveMiFCJOHaO9Iol0oXPx9x3k5lfiv894rkSOhrhIhxrb2t2CwCgucb4VMQlGXPRr8LIr3LRHgC8kZOL7P8mac9XSKd8T3r1JunF1yfrphNWuShZk0/4zZQbNVw88B3Bj6XVrWjcXOmEL0Xb1hysvd0uVO1K080Lo3fpNw37VOqe+kNn+VXrrbE2X7HY+pl73+9pD3Bvz6o8dq909xvHmNnWrTmhTFSVcLFcXVsZ35TKxZa37Gpp6yJp1Q3NbklnCuwWzZiLKCsOO5/n3slNJf/xnsN3GG2z8ftK/XvE3HeTmeetq69vXjuQG4SLnSDqia09rgIAdKqBmdXrkoy56Fe1EhouZjwjn1mdd/wXrXCu0CX1TU6+z1pDadw8zz+E8/s5+OmfKh3ynur1fmMx1mNghnT61f6PuYJl43cfNitkHpm/p1rjc/pZfaP7/nkPuLs+90+Vjv9fZ6xDb7iYdli7Y6l1O26/dPcbh/1Fxban4j93tNxN3H6v0y06f6JWuSNdlXCxHCranzebFzanPWg95jAc5izOknT4h+J/2dtuXza6EBUhHt4xnWBRxJme5r4q23YAQKvzG8svyZiLfhVGfuP4NKpb9Cnfk065Sjr3rvoCRVOtysXNC/1/Xquui/4aR3+sutvyxEP9t63H3hf7r//lZGnt7dayGSi2W7hojj+VJFwcMcY4POGr0h7HhW+/5QnP843Xj1NhNDooPfNtacdy9/rtS6zbcftG31fa+qcnf+6IJ1ykcjEfzCEF2jpwaGUBlYvbF0sr/tCcJqG12MfXQo/U3ScddYXzWNQJ50ztXBWbp8ln0BIIFzuBX7c023n3O8tpd0sCgLzxq1x8+L+ck8eo1SjF3daF5sYHjZVN7BbdPSDtf6k07eT09hllzEW/C+w44WDvROmFP3WvO+5/oz8/jpO+U779lrNuZJt044us5VIbh4uDG5zlNbfEf75dqbvnK6RD3lV7+4EZ7vvF8vMf/rD0q6nStsXRXvfRT0j3/JN02yvc6+3KxfH7RttPFuJW2J7xW+d53nDRHnNx5zJp9U3ptA/pS/JFFNLl7RY9bm/nsdte4Z7sCZ2pcnwtj/V7xH85j+37+vj7sz9v2pJ53krQiNoIFzuB3wfpMf9j3e5xvLMubHBbAOgEEw+pXrfqOmnpT6xl+4Kx1myCo4PS4u9K1xnHWG934OKo9PinreWsu0VnoVblomT9HyX3rNFHfTT5a46ZI808K/nzwxz4NuniLdIBb/d/3AwUH/1YNm1ohlJRevTjzv37/y3+PuzKx6hfUp7wZfd9u3LxsU9Kw5ul+/412n6e/rp1u+kh9/pK5WITu0X7zZRus8dS7BknHfQv0pEfluacZx1XRnZI254uP16++DWD/JvnOdW0aC3mhDuEi81RqSIrf97Omud+fHBdQ5uDFlT15U2P9LoR6eKtzli5cYTNPJ135nkrRUiIgHCxE5hjS9h6J1avm5piRQsA5NG4va0JT7w2PmDd2pWLtar2ioPSoi95Vnq+9X3wfcZDDZ4tOg3dPmMuLnjYfd++wN7rIum0n0kvfzLZmIkzz7Fuj/jP+M+No3ei1Q3o5O9VP+atVmyX6sUdz9W/D7ty0e894cc727d3EpmwsaKHNjs/e/N5ZvXlzvL/adw+0dqTBW93Mvscq2+K9JK/WRMWvXyR9IIrpaM/bv3sJnpmtu72dIu2Lf9NNm1GcoMbCBdbgqdy0WuUGdc73vPl7vH2lzyS1NUt9U7w376WsG7Rp/9SetnjyfbbCsy/ox7CRdRGuNgJ/MYcMr99eMVia7asOS9tWJMAoGXt+4bqdWtvkVb8LvoELKO73ReaUvXFjhk+NnK26LR4A9ZTrpKmHO1eZ19gd/VI+77OvzI0ihf9RnrxTdKB/5zs+XH1Tale5+0S/+gnG9OWrD1wWf37iFu56A2Yn/y89OcTnPubH3GPX2fbuVL67WzplvL5Sp8x8+aavzrLQ5ut2yTjZ2XljF9bvUZevsj6OznpW9LYPd3beIcM8KtclKRdz2fXTsS38BPSr6e5xzhvly8f8sYOD4PCRe/nMjrLxvulheXeE37D4KRt71dLkw6rvV3LMisXxzavGcgNwsVO0Depet2UY53l8ftLc1/JoK0AIPkHfZsekm670Ak1gia9OPaz1u3ooE+4GNKVOpfhotHt88SvWWM6ekXtRl5L70Rp1out6oJG8IaLmx6SNnmqMs2uxHk1tFna9GD1+rgD1FcqFyOGi37h/KYH3Pe91YyStOQH1mutvlHavVYaXO88tvzX1m1x1Ak7055ZPK6Lt0mzXmLNQDp2T+mIy6WBkIlevF3y7Is5bxdru9s3WsPCj7hvJWb2boadK6Ud9t8G4SI8SiVpyY+d+40IF/PODOmjjLONjke42Am8H6TH/a97rEUAgKNQx/iHdjfM4u7q8W7DvsCp5zWbxQw8zHEK9zzfWbYDn3rDxUbzVrxd/0Lpgfc2py1Z2bXKqgL06xZ95xvj7atSuRixW7QkHfVx/wpRmzdcXHW9tOSHzv17/8X9+HM/l9bfLY0aQ8E0O1zsHS+9+Hrp2E9F294bGnpni7ZtvK/+tiFbI208DlurMr+gmHS4/zaEi53ryc+7e4z0T8329Q6KOHZwK+ub7Cxvf6ZpzUB+EC52Au/4Iof9R3PaAQB5MGZWvO0nHGRNULHgYSdcGdosDW10b1eMONN0XoydIx33Oemkb0vdRtA499XO8oa7rdu8hYuTDnNPBOA34dnko6XHPyM9/8fGtStNy3/jVBx62RMYRRW3W7QkHfVh6YKlwY/bXZsla+zov86Xtj7prNv2VPVz1v3N6R7dMyH/A9DbxxMqRvKnnSd5aFV2V/Spp/j32pIIFzvZg+9338/6uHriV7LdfyN09bp7OwI1EC52Aj5IASC68ftLJ31HOv1X0gu+HuEJBemQf7fGUbNPVjc/Ur3Z0EZpx3L/XeS1C91h75MO9Myu7Pd/yVu4WOiSzvxD+DabH5Ee+pB06/nSk19sTLvSNOIJTGe8KPm+nvm2dRu3UjAs/Bva5Cxv86mY8H1uwRq+QJJGtuVvuJcj/8t9326/37AJTEzRGsz3qYlwsfHscXG9lb4mromQNrPr8JEf9l+fZ+bYxn5jIQOGNnnXo8quVdLT35KGt0slBpUGgFgOfJu096sihmLGyVbYRY0krb/Tf31QBVkerbmlel0eu33H6eKbxqQojTKyU1p3pzVuoalnfLL9bX7UWd7juHjPDXtfmN2in/1B9eMb7qle92DOe2ZMO8V/vV9IOrI927YgmnVBx3TCxYazKxfDjiuEi7CldX18zi3SHidK594lTTg4nX22EnMoNXscbSBADs/2EcmNZ0rbnpY2L8xfxQgAtIpNPhWIXuaFTK1umCM7/NeP5rRy0c+Uo6Xnfupex+dQayiOSn8+1jo/8Eo6PuHWRc7yzLPjPbdQsCqFtz9b/Zg5Zt2iHFaGpm3iIe6fNSFJawj6uyFcbDw7XAybII2/m8407PNlzPgD09n3jDOk8+61lv2G68i7Q/9DeuJ/reXSqIiPEIbKxXZlXzisvJYPUgBIqicgLDzC6L5oXsiEzQQrWRO9+PGbPTevDv636nV5DRcHZjS7BenavcY/WJRqVy7uWuM/S7odmM+en6xNZji/92ukGWdZy50aznhnhrbNXuC+X2qzMVzzym88Vqlz37/NZP9NhFUuMpxAZ9q10n1/xpnSwRlMuFIqpr/PZjPPDR77n+a1o5anrpSW/KjZreh4hIvtrmc84SIAJBU0vszs85xl80JmYHb4/oK6P895abx2tbKesdIZv3Wv68ppuDjznOp1p1zV8GakJmxsz7Bwcfda6ff7Sr+Z6UyYYrPDle6xydo0fn9n+fRfODN42uHMrtXhz9/romSv26rMiYRMx3xSOu7zzv0iQ960hKBqdGaLbryV11m33lltT/+VszyyrXHtQesww8WTvyvNu6X2MDZJtGO4aH45/OjHm9eOMDtXSve9S7rzje03eWLOEC62u57xnIACQFKH/Yc0di+pd6J7vTkTpVm52DNG6g2YpVIKDhdnnpW4iS1pYKb7fl4rFw//oPv+/m+W5r7Kf9tWP6Ed2SHd/+7gx6cc475v/n+2Lbbeu6O7paU/c2+37Gr7CcnadfgHpaknSWf92brfO8G6tcdc/G2NwH7GGdKCB6vXTzm+el0eHP8Fa3iFQ97jXt8zTjrsMudY1Orvt04RONQF4WLDLS+HiOas8pI1fvKEg8rb/LqxbUJrsMPFmWdLB7wlu9eZe6F1rE5ayd+K8nD+Zo6f6dfDAg1DuJhXYeNzmTNA9lK5CACJjZktXbBMmnaae32X8Y33+AM8z5kTvL92mrglTK+nCi4PJ6d++qa477/gG9aFg1+3u6GNjWlTUo98VHo+ZAbscftJZ13n3B9c7yybk4d4QxO7knHF75K1a+ZZ0vy7pTnlamC7+nfXKv/t977Yfb+rX5pyrDTZCEfPvNaqTMmjiYdIr94knRAwzqT9ZQaT9bWGjQ/4r2/HcPGJz0s/LUiDG5rdEn/j9rNu93ld9WP2MXv8AdLOFdL6uxrXLjTfzuet27DzszT0TZFetdH5sqwd5OL8zYi01t7avGaAcDGXNj8qXT1OevAD/o+vut5Z7hkvDa5rTLsAoB0VCtLcV7rXdfVKs15iXaic8CX3Y2OMSqupJ0sXPCcdWp5NuB0vOP20S+Wid/y77n7r/eANHSVpy+ONaVNSfrMrmyYdJs2Z7/zudhvdkc2uhGbX6p2ecazSYF/8ecfIkqQzfi0d8Hb3OnucUzNsm3OeUwGZR2Hd9QrlcJFeKa3hqa/4r2/HY/2D77Nufz2tue0IMr4cLu55fvVje11o3Xb1StfMla4/VVp9U8OahiazP0+yDhclqbvPOk9oF4UcxEXmRDp/9/lyAQ2Tg3cLqjx0uTVb0xOf83/cvOjpHiNtuNu5/4JvZts2AGhH3nHQCj3S2X+RXv5k9SQuZrBW6JbG7e3MIt0plYt9U9338xou9hjjCM58sbPsFy7edmHmzalLUNhx4D9bY2TaofjALOv2wQ9YVUp3vMFdxWi+h28xJxlJ6WJqrBEumuPWHfB2K+SfeqLUX/6bO+idTmhgtisPF0NJ2ZM/MaFLa2vHcLHVlUatW7/Pm8rfzaiz7uaA8U3RfoY3W7f9U0M3g488BKXm3zI9Npuqjaan7BCPf05a+cfwbcxKi92rrfFg/j97Zx0nN5n/8c/Mal2oUlraoqWF4lIcirs7BxxwcHAHPzju4A634m5FiheKllJ33erWbbvb7Vq77jaa/P7IZPIkeZJJxmf3+3692ok8SZ6dSZ48z+f5iiMNuMEd9aD6Xyzfgx3lTXjtmqPgdKZA40MQBBEOTo0lkTND6nDx3GNZiylZ5EjLlj47i7iofdekqriY0VNyhfbUq+Mv8sRFOUZgsmKU1Xb4TcCAM5T1LoOAhk1AxTxpveh76Z8M61rdsFlZPtPE5doOsmVJzUpg1wfK9rEvSZ+ZfYCrK6TA+WyW9c4i5sh9PMp6m9xE634UxdQY3CcDZuKivI1ilXZO5Nio4SYeIxRqVgH9Tk50LYw56K+JrkGnpgNP7XZQ2MQBRrCzcnJQ07QuMcnW+cL07fgltwwrdteELkwQBJGqaN0UzdpiNutu9fLA8Rxxccjl0ufIGAYXTxZSVVwEgEPuA0Y/obaG44mLyY5R9lptsiLZctGMpVcBdZokKkMuCa9eWtjrb2QE3SzGFdPhVAuLAHB8QIgc/d/o1CNZkSc6zDJ/E4mncXvgOTGIyWiFZdcAc05MPiG569BE14CPFXGRHSMRnQc5H0F6t8TWoyOw4JzQZRJJevfQZYiYQeJiqmElhhDrKlOXK32ywdhjQKubZgIJgujAaC0XeRaLMrxEFM6AuCgw4qLcye19VGR1S1YGMy6zqSwu8mDDjaQKHqMkDJquYBeOuKiNoVk2FVhwtmJFN25ypLVT6HYgsyIqi6Gst4ZeDVy1DzjqxejVJRnpbFbQyU663C/n3J9lU4HZx5knYTRCFIDS34C6dUDNikhqGH16jU50DfiYiosct2ii8yBbLpK4GDnJ5iUgiup1n4GXBhEXSFxMNax0UOjFSRAEEV3sWC5WLeYczxEEREH67Kjx4Q65X1nuaOKip15ZPvhe6TPZReKMXsry6b9JgqEzE+hxsLqcVkgE+IMJb6My4RnNv93hAPoeH96xXQZ3fBdSslxMLroFrPgO/Ydxmd8GAe2V9s4riyEA4KqyX69ooxrAi4bFEooly0UyhuiUyGFByC06PE76ItE10CP4gflnAnNOUG83CgFDxIUOOqLpwPQ9LnSZBMQT0U4aEARBdCi0loraLMIsWZxMmlxrI0E+eSQ1S17kvxnoeOIiS/eDQ5dJBmR34wOuAoZeBVy+B7i6Sp20hi3HIodY0eKukz5593wkZPZWrw+7PrrnT2XIcjH+iALQXMDv7MpZu3seZny8twHI/8jeNb1Mhvb2CuNy8YI1XJAnxpINcotOTlbdBSy/ITGDRVEEtrwA1K6R1slyMTzkhG/JRO0aoGqp4qUpQ5aLCYXExVQje0DoMgl4cZK2SBBEh4a1hkrroo/3xnLks/ptndFykbX2ZIXGjgDrutt9pPSZ7BkK5YQzhz8sfaZ3ATJ76cvZGkQE3v5ZfSOpmZ5MzfmOfiW6509lgm0JWS7GjfWPAH8eok4wJNOcL32GEi1CuRJu/C+w4TFlnQ1ntP5hoGGbparGDLZ9SyZx0e8BKhZK71a72aK14U6I6ONrBQq/BEp+Alr3xP/6VUuALU8r69rJNMIayThBvG8mfztr9W1EMrVhHYwOOqLpwFh5EdKsHEEQROzodYT5/qFX67dxxcWAlXlHFRe7DFGWUzEBihnHvKEsy9mNk13skV25M3qbl8vqz9+uTfzCbreSbM4OA87U1Gm/6J4/lZFFe4EsF+NG3rvS54Z/qbe7mGSGoUR5s765txnYPgHY8YbiPu1rVpeZOSaxbkKyhSaApDIp2PAosPBcYM3frFkuFv+obEv2CaGOgKdRWTaygI8lssWiDFkuhgf7TCVLn9VlYNEdyi0692Hg9yGAqzrqVSJIXEw9tHG/eFA8EYIgiNgRjjtiGiehS9te6VMWpzoaPQ4CxjwjxeMbND7RtYkuQy4H+p0CHPqgkgCldY/iJpxs+N2AO9CRDnW/9Twc6H2ktNx7rLI9g2PlCMQmFMvQq9TraTQgDOIkt+iEoRWj2vcqy92Gmx9rJi5WLGCu4QYatgCVi/TlmnaErGLMSEbLxaZ8xZp0zzdShm6ALy5yPb+SSCTtqLiYBHeJiB3aslu9TjEXw4P93pLFilE14cEQyi06711JmMx7L/p1ImDi10UkJWldQpcp+j729dBAMRcJgug0yAMYO8htty/gGud3SVlAAX18uY7EUc9K/zoaaZnA+TnSssCIBitvA86akZg6mcG6CYW635xpwMWbpeVl1wANm6TltlJ++VgET8/UWCo6k2QwkwyQW3Ri8Xuk5x9QBrHdR5rH4QXUSaC0FExUlluLpCQF3HM0WK1l9GHFxWSx+Ft0AX+7nGSH5YArY1oVwoC2MmU5EeKitp0ky8XwYMX5ZBEXjYyp/Bbcos2OJyKCLBdTjfSuwKh/K+usublM6a/xq08AkWb/CILo6PQaHfgM4RYNKK7RJwYGjVrLxW0TlLIU9ym1YYWvpl2Jq4cZbCfazsDAoXF31rorx4q0EEJNZ0b2YJEtF4smA/UbE1adTkf1UmWZzUDbdYgkMKb34B/nrjU+J5uhfe3fjcslwq1UpmGLspwMVrN+j3EMPzkOLoszw/i3IWIHa7GbCHFR68JL4mJ4ZLDPTpLIR0ZeE1YTulAYuZiQJHcHYYujnleWqxZbO+aMP2JSFYIgiE7D2bOBg+4GTv0xdNlTfwQuzQMOvldaT+8ufXoagLoNwD7Guq2jJTvpjMjC84hbE3N9X5skSlQs5O+X3Ycc6erkRKHQWmOdOQ04SxNEffBF1s8XDvtfGtvzpxpOZqKicgmQcwsw65jE1qkj49dY6TmZ9lq2CE7vJolX1zYA11TxnwmPQciE1mJgz9fKeqNJ4hYvx6AgUlzVwOq7gZpV5uUWM3+TkARWs1ufs39MtGPDEqFhBRw2SZFVKhYAM8YA1TnhVkC9Sm7R4aHqpyZJWATRwC3aqjcFiYsxgcTFVCQtC+g2Qlq2aiVxwOWxqw/ILZogiE5A1wOAkz4Deo8JXdaZAfQ8lDk24KblawFmHwvU5TJlyXIx5RlwhvSZqFhkG/4F5H8sJTbgIVsummU556HNrJnRE9j/ImDY9cq2Y9+yd06rnL8SGHkHcPKk2Jw/VZEtF7e9DGx5NqFV6RRoYx+ywppsISM/J+ldpEF4Rnf9eWpW8s9vx9rZzPoxXDb9F9j9BTD3FGmdZ5VYovGIMhNA48WuD/nbtZnmWXjiokACQ0xhv1+jGHlmLBwv3W+LLwnz+pprUoiN8GAnVcL5HWOBkeWiuxaYbuBhxPbRYhEvmiBxMWUZcbv02Zyf2HoQBEEQoUnvqnZ9Y7GSqItIbmQLv63PA1XL4nvthm2SsGiG3InWujmHYsyT/O2ypSYAdDvQ3jmt0u9k4OQvgWyD7NWdFdbawqr3ChE+DZvV6/52ZjlguahNOMTGR2etf1nXYhmjLOw83DWhy9ilbr2yvO4hYEoXoH6TukzOTfrjeGGZ4kk6R8AFgBF/MT7GwZlc2fxUdOpD8GHbq0hi3IVrtcvGB02WLMepCCvMJ4vFn9n91LQDaOGETSiewhyfJH9HB4OeslRF7my7KtXbyYSQIAgiOTHKJkqWi6kP2/Gef0Z8r621iNK6cQKKpYFdy8WuB/CzrPqaleV0C4nmiOix08BSlCywYoM2eQkrLmotF2VYcfHcxcoyz9rOjrVzuOJi5SJg+6v8MQI7ubUrkD11i8blOLOP/rhEJ0Mwip13lIm7NM9ycfsE/TYiekRLXAw3fIz87ht6NXBhrnlZwhg2nErPUYmrB0soy0OepXdTnrKc6Dasg0LiYqoiW8A07VBvj4XLhAVI0iQIgghBmoEIQ5aLqY82NmE8rXq0HWTebLxchme5ExJOjMbD/g/ofhBw+CNhnI+ICKOBndUMmYQ9tOKij7VctCAusnHBCiYCzbvNzy/T7UDg7DnADe3AMW9K24ziNoZiwTnAxsf5CR9d1fptWguvnofryyTaNZK1aB58EXDMG8DVlZrEExoo5mL8ESN0i5axIy6KgiKkl02VPodeC/Q5OvzrE8CZgVjhyfIcGcVclOElr2NFUrJcjAkkLqYqvQIxv9rL1dtdFdJnVj/grNmS28C4yTGvjkgWkwRBEOYYuTBSQpfUp8dh6vV5p6lFiFji11yH12EOWi6GMSiQYzyzdN0fuLwAOPZN++cjIuPoV/jbvWEkSyBCoxVEVv0FqF4hLfuM3KJN2vTWYvV6+Sxl+eC/KcuiAAw+PxDDMSCYyQkxBD+wbzbgClgyuixaNNZv0G/jWkNqJhS6DNEXSbS42P3gwOdBwJl/AqMe5VtZs4Q1uUJEhEpcjMBSzKqHh+AHZh8PzD8TWP+ost1KrGzCHHkSxWhCJN6EdT8x0hdZLsYEEhdTlS6DpE9fizr4cjBoeyaw/wXAdY3AcE6sFIIgCCI5ILfo1Gf4Ler1xq3Augfjc+3ater1aFsunvq9lLF5/BL7xxLRxyhhRTiZWInQ8AbS806TPo3cog8M9Lt7Hg70P029jw1NsG+W5K4MAD0PA078RNnnqlKW5fiCsoC8+3Mpe/P804GCT4Hf+gP5E/X1bMpTn8enyaIqeAFvg/44bUZ5uf046gUl224oq6FYUr1CybB96D+sJ+lIFourzoTKLToSy0WL/aSWAklEr16mDiHR45Dwr01IyB4aiZ5YkAklDvKy2rNW2YlKwNfBIXExVcnopZj7umuVB0TQDCBiGLyWrBUJgiBscMj9/O124+ARyYczDThnnnrwWhinLMfa8Chsh9vvBmYdB6z+q7QezuC6+0jgrD+VjNhEYtG64MuQuBhdGndKsQfNvldPvfSZ0Uu9vc9RwBVFwIXr9f1w1iCg8EtlmY0FBqgHxrK46GuWxMi19wWO2QmsCVg7yttkGrYB0w8HfmMSieW9AzRsVdbdBm7W+2Yry3u+BUp+lpaz+ittSCIzrc5jBFs7YUVIXIw/0bJctBpqxM8RlACaxI0GwWc/WSwXQ4icvHuBrTu1BzGBxMVUxeGQXJ8BoHE78PsQIPf/GOsEi7N4EUDaIkEQhA16kVtOh2bQeOD4D+J/Xe37nh3MVS8D6tcrWWpJyE59jAZEJC5GlxmjgC3PSnESjZBDEcneRCzdDlSSHQ2+QNkui4tlfyqiHQCkB1yf+5+qP1dGQFysXSPFTrRCxVz+9oXjlWWjBDFywibBD6y8XdnuzGAEhihYLwn+yGPF2wkrUkcJPeJOPZONvHAS0LQrvPPwLGy55Zr427XWuIR9OoLlIvueNJqoIyKCxMVURhYXNz8tdXDy3lFmheIwgGC1RRIaCYIgQkCzpB0f2cJIJh5J1nyaRB6suKiNBUcxx1IfrQuuTLgxFz2NwKKLgFV/VVvVEWq0cQdFEXBVSsvZHHGR5TRGRPQGhLull6vLnDNP+hw3GehzDHDyV8o+bbtihcz9+NtdlZLFouADPIH2yShWYfs+9bozU2lDouEWvXA88Gt/YM934Z+DLNKSl5rVwO4v1NumH8YvyyMct1WeCHnecvvnIfQYWS4WfAbs+T7+9QllCcuzXGQToiXS+roDQ+JiShNQ9GpXMZsCg4o4DCBYt2iR8kUTBEGYQ+Jixyddk6lU6+oYC8zERe27me7B1EdOZKEl5yZFuLLDvplA+WzJqqiyg8fVLPwaqF0X3rHZA9Xrghdor+Dv05LRAzjwZmlZtnbU0u8k6bPbMOCi9cDIvyj7jOJs8ij5FahbD7TuMS7z+yBgShaQc5u03v1goNtwfbnWIvV6tC0XqxYDEIENjwLtlfwygl+KK2t0PTZrNJFc7J3O327VIkVrjW3k8sziadBv41kDE/bhWS62VwJr7gVW3hp/sY5nuXj+amWZZ7nIGl/RZFpMIHExlWncrt+25l7pUxuDKQaQnEgQBGEDBwk7HZ5uw9Tr4Yg9dhAFxXpKZu8MZVnbuSbLxdTHmQaMflK/3dsE/D5YWhZF6wN41tLHXR1x9ZKWigXAqjuAOSeEd7xOXHQpzx7PLVpLl8Bv016u33fQ3ebHdh8Z+vwAUPA5sPxaYPZxkku3EYJXajvaSqT1rP0UbygZX5s+s7UzM/KYi34XsPRKYAWTbNJVJcWH1OJplJLWzDlRyv4LAI2a8c2As8OrBxF7jCxii39UJxoyQvv+NGuf2iuARRcDK2+zXj/CHvKzz1otswJwtN2l3XVA5SLjdxnvet1HSiFqAIOYi8wxPPGRiBgSFzsazWHGsggDgXyhCYIgrJNG8V06PH3GAqf9oqz7W43LRsqe7yXLI62L0tr7lM64X7OPLBc7BoPG87f7WqXfftH5kigjcDKH846RyXvXeh20FrPJjhx31AqNO/Xbuu6vXm8vVyxnsgxEFBYzcXH/i82PdTiAC9aEvsaae0KX4eFv11tHepvNLRfDdYueeRRQ9ockMKmu16Beb68EfukN1KyU1uXPhs1KmdN+sp4pmog/2kRHMjk3A7OOMT9WFIHKxeptLhNx8ff9gfJZ+u3dDzK/DmGdoOUi069QZV+Osrg462hgwTlAEcflunwe0LJbvz2zD+AMxGH1cpIAsZOxJC7GBBIXibBhtUUHKFAuQRCEKTzLxa5D418PIrYMuwYYdL60HG4cPCusvBUonszfJ080aoVHslzsGPjbTfa5gIr5QPUKoHGbdA9u+I+xOzArEtYZlGnZA+x4Q7EkWvdP4KfuQI0FwStpYPqpoSbHN3MsQ7UihWzVl9nX2sSRLC4WT9Zf30iEYdnvBOCQv4cuFy5y8hkZT63exdSRobQh4Vgp+dqB5nzj/Wx7Wb1Mvz//EyD3IWV92HX2rj8i4Gre/SDgyr2BjQ4KHB8r5PcPL2yANp6nlj1fS+84FtOkLga/4cmTzK9DWEfuw4qCMnHFiovaycxIaSuVPkt/1e9bdL6ynMbEIXamAV0C99u6B/SCdFuZsmzFzd5SPcuA5TcCax+MzvlSHBIXUxnWOiLBUBIugiCIEPCsxva/JP71IGJPWiDJQKxmxkNZjclxF7XXJ8vFjoG/zXgf+5vv+RrY+hyw4zVjd2BdXDMXUPgVUPCpMoCccxKw4THg556Sq+qu96XtW54J+0+IO6xVjdH3V71SErB4g1k2EQAAtAZciq24RANqMa5xm3pfmsWkJGNfslbOLs5MvZVr2R/6mGRNOyKLudi41Xw/aynJa+PW3q8PA2GHEycC45cAl+4E0uVkV6JatBKF5MmGm+rIbVGPQ+wfm8/J0h5OmJHswfaPIfiwkyhye8oK89rJzHihbc/ZSXut1SMrLkarf+auAUqmAGW/R+d8KQ6Ji6lM9+HG+waeE/PL00QfQRCEDXjCjoNewx0SOYNprDrbbSGsPuTBsfb6ZhZvROrgNLGUY60xdr4F1G8yL7vjDea8WcDqe4BVdwJr/gbsCyRkYGOdrb1PWU4lS9gNjynLnkYpnlfuw1JML0CKWTlvnCRgyWQPktrto1/Rx4+TLRdDJXORGXKZsrxY4wbdkxNvkEdmb8DBcQO28h652MQtfMCZ+hAOXYfqB99DLlWsl8IR4FpMkswAkrWtDM99nKVPCLdaHmlZwIAzpKQOGT2VOJMthdKnKAJzTgamZAP5H0v/iPCoXgmsC1hyZRlkLq/OMT6eZw3sbQp93ePeA47/UFnvYvH5JELDet/Izz+bVCXabtHKhc13j/qX9HnEf6TPrgco+7QTN6zFbLQsF32BflVadnTOl+LQqCaVYc2AtRz2cMwvTxmiCYIgbEDiYudB7tBGq/OqRWttBgCDL1KWBa9k+ZNzi7qMHLeMSG3Y31qLzhrDZGC2b4Z6XXADRd8p60uvVFt6AOpYeaka787bJFlf5r0rxfQCgPI5+nIXrQeub5UGrZm91fuC4qJFy8WsvoqYJbv7AZIVnZH4wuOyfH04jaCLr4YTPgKG3wqMmwz0HsNPBDT8FuDQBzlZ5wV9+9V1mP2Yi6IonQsAVtyg33/8h5LQB0jCtZyxfNcH0ucR/+EnBhl+q36bHRwO5byyaFU0GahbK9V37d+lfx5O3LZ4UDoV+P0AfdzBVGEpI6ZnGtzfO143Pp6XtNRdY1xeFpT6jwNG3ikJ5sOuU+4tInLYSS154lJkLJ6j7RZthDbEx5hngHMXA2MnSOuZfZR9aZpwD6yVYzSyRbuqlElbEhcBkLiY2qSbiIsZ3WN+eYGNuUh+0QRBEOZws2vSa7hDEgx8HiNxsZVjATSOEYUWnA0sujA21yYSjzMNuEnQb+95uN51sGKu8XmsuKBMNYkLm0qWi2zGZW+jYq0GAEU/AG0aga7LEClOoiymaeMiygKhVctFQIm7yNLzMOvHA0D3EcCVJWoPpS6D1ALc4Y8CN4vAIfcD474FhgcyMx94o/pcR78mtRvpXfXiYvGPUkZsFmeGIoTKbuGhWHIZMH0U0MTEWhx8kVS/m0Xg0L8DI25X9m34lyT2tQd+jx6HAQdqJknkukRKekB48jRKbuHaGH9AiDh/MWTZVdJ3sOTyxFw/Uty1ynJaluSSrsXM+pUnJK7/P6DBwLU+KPB0leKHjl8sJfwhooczTZkQlyceWHExZpaLGrQhPjK6AwPPVGK0dRmi7Ft1p7osKyhG2j8r+QX4baCSSMtJ4iJAo5rUJq2b8b702IuLItMpJWmRIAgiBDyXHoqB1zGJtVv0xsf127KYbK++FqB6ub7MYf8Xm/oQ8Yc3qSv4lHiIVlh+bWR16DossuPjSa8xynJzgWJFCEjZa92awP/a71druVi1WPq009/O6B2yiGWO/wDodiBwwifSuquKuY6BtVavI4A+x0oWNmfOAEY9quzzaeKWlc/SJ6RyOBQx1Iq4KIqSdWzzLmD6ocr2IzWxOmWLI0BKKsQKSyP/Ahz1LND7SPUx0Xh3ZgYEY2+TZLHIo2595NeJBF8YcQYTjdYizJkFHHyv+hkE9BnKjeh+sLKc+zC/jHz/ai3ViOiS3kP6lL0n2HYnkv5Oyx5zsVkUlEkAlr6cWML7naheb2aySrPW2JF6lmwMuGHLE1VkuQiAxMXUhu3oDL1a6mTIxENcZJbJcJEgCCIEvMD/PQ7WbyNSn1i7RZtlXDVDO6gnUhtt7MWWAqCAYyEk05SnLIscy0e75L0d+TniBRsbbOWtaosbwDyrKGAcisiOyKXtm8vCYDj0GgVcUQQc8jf9vm4Goq/DAZy3DLi6EhhysTosx7Fv6cv7OBNicoIMV4Wyra0MWH4DUPCZ5ngDYazfSep1rbdVwedMnZ2SWHrQ3Zq/JQpWs7II6200dpG0EuePUCieAkzRCHzy+1DrcSe4JMGo6AfzJGUHXq8s8+IGi6Ky3cyrj4ic4DMTeC42/U/ZF24ipBmjgWkjgUUG4T7KfgdW3QX80hto2Kjex8sG7nCoraHlEAtAdC0XtZC4CIDExdTGma7cyL2OVM9UxsVyMeaXIAiC6Dj0GyfFl2Ld86wG8idSC9Ytunol4KmP3rl5g+CD79Nv45HRI3r1IBLPOQukieWjXrBWfu44Zbm5QL0v3EzEcriHoh+BvdPDO0esKZoM7Jup3pb3rnpd+4xqM9wazqLb6AxrRTSeMBguQxkr1IHnGpdL78q3bBx6JXB1lXob62J/1izpU54kK/5B+hRFyXW+5Cdgzb3q4+VkOSyXcGLpAcCRzynL2yfo97OWpkB0LBdZocRrEFuRFeSJ0Ky4Ub+t99HSp1Z88buA5ddLlsPrHpSsDyuXqK3TRt6lvl95kyLB5D8OirEYa7TiYgvzHgnHclHwKvE1KxdI1tIlv+jF5j1fS58b/q3ezktwBajfZ9n9meu5+cvhoBVCzBKtdSJIXEx1LtkOnPItMOoR9fbMXvzyUUTtFk2miwRBEKY4HFJ8qf6nK9tIXOyYyG7R+2ZJGWhnHx/eeRp3AgvOVVvy8BIMnGghq2l6N0og1NEYcJpkvTbUonuzp05Z1oqL2piCWowGTtteBlpLgZybpPh63NiyCUab2IhH0071+rDr+eW07PnWej1iOfF/6g/AsBuAI58HupnEyTQju78Ur1GmYbP0ecZUYP9ADFfW7dTv1ieXaimSMpSX/SklBNJi9M4b9Rh/u8yg8ep7NBpW/+mMUCK7Yg84U51tlid0xhqtaBErC/h4MSzQPmlj0gk+JSZs4VdSrOAFZwHrH5HeVwAw5n/A4AuUY1gvPSAgbssx9kSyHos1WnGx/xnKvmhkkF9wNrD8OuOY0ZUL1etGFsxdD1DaMnfgvSeK6snZSJ8rbezr8tmRna+DQL3MVKf7CGDErdLD3lKkbI/DzA377iO3aIIgCIu0MbGq7CQDIFIH2Q2saYf02VIYXsd7wVlSZ3rNPUDdBmmbWYKB/qfytw86H7gwwbHDiNiRZsNiojEgomndPUMNyrP6ASPv0G/f8gzwB+OG66q0XpdkolGTKCJoDRUCbaxGM2IpLjrTgdN+BI58KrLz8EInyJMlADDwLGXZ26iOuQYA00YAs44GlhokIjEaMKRzYuVdwMRBzB4AXNcAXFkGXLTRuK2zgxxeylOnuMV3Gw5cXihln5Up/Bpoj+N9rbWiZJOjJBvNu5U2xQhnQABKy1Jv14YmqF0jfe56j0nQ0gXoczRw3HuBYzSTF6na3qQqcsxF+f3BZq4Px3KxeZd6vS6QCZoXM5qH08ByEVAsFusDfSfRB5WlubdRmgAmogqJix2JOAf9VcVcjOuVCYIgUhjW3YNmZjomPCuvpl2SyOi30QFnB04NW6RP1nJx+C3A6b8r66f+yD/PoHOAnofy9xGpj1mCPy0zRkmCEBu77LzlequiQeP1rqi9xwauZyJEehqs1yWZaS3Sbxs3Gdj/YvU2O0la4hCyKGJ4oRNYa8XMPorA4KqS3Fmt0ucY8/3nMYLCeTnAfhyL765DgD5jrV/TDNlCce80oOh7aTlrP8nleuCZSrlVdwC/D4qfVa42c7mcPCjZEAXgz4OlNoVnUa9l75/qdW02cu25AaWtyewjfZb+CviYtovN+m4UF5WIHrLxkhxGgp3sDEdcjPR9YeQWDSgTH7K1Iy+kzOKLgeqcyOpAqCBxkQgblVs0jY8JgiAsQq/eDk86R+wpnw1MOwhYYdHdUovciZYtpZxZwLjvpFhpMl0PAK7hWLnYEZ+I1IONKWWF3wYCq++SlodcJlmBaQXDY15Xx+DrPgI4+G9SluJLTSyV8j8E9s403p9oeh1hrRwvBt/wm4AzNQLJOfOsX1sbczFV0Gbgld2u90635gp40N3AAVcAx71rXq7/qcBl+cAN7UD/U8Krqx26DZc+XVWK5WqWybPEWre2VwBLrpDiw4VLyc/Ab4OBqmXq7RsfV6/n3KIXHJMBVmzVuohaoWpp6DLyvcdayMlZegGghckEPOpf9utA2KPsN+lz/cPSJ9tOrn9EVzwkkcY9NEvslD1AvW7kBi1bSxJRgUY4HYloBDe2AeVzIQiCCAOajen4dOXEPMv/SPos+8Oe9aKM7FomW2poLahksvoCg5msi72OAEb+xf71iNTB4QSGMG6oI+8ALtoEDDxbWh/ztPGxct9RKy5m9ZfaqrPnAAPOAk6aJLmuHvqAFPfspM91pwIA5H8MLLkk3L8k+gga18uLNpqX7zVG+jzkAf5+bdxSOxbBrOXiWSnkjqd1Wc4OJHXZ9IS144ddJ8VtHHB6yKLocXD84uZ1H6HfZpZtuDEQ5sLTAPw+WLJ4XH5d+Ndffr2UdXvR+ert+ziJkaYeoN+WaFi3Zm+LcTmZcLKjyy75/ZlkVLveB9b9Q5qsa2bExSM0yT6I6NP9IPU6a3nYnG//fJHGPTSzXNTGIja0lA1DDuMlFiIAkLjYsbiyDOgyBDj6tbhcTmAsFylzNEEQhFVIXOzwaGfMAXUiAzuuhCzuWiD3n9Jyj4OMy3VjYuBdso2yRHcGRv9XWXZmA32OAs5dCFxbz4+VGCwbcOHXWtvKLtGDzwfGL9KLaEOuMK9Psgy+2Bi3h9wvialsKAGnJg7cecslAdLsOwsXVlzssn/0zx8ttGEdtHHctd8ZoLfolOl/miJyJxva5CCAOmv4aRqrxMatUiKkTf9Vb4/EehHgu2umAqy4WLMidPlwwgLIk7HODKBbQAwecBaw6wNpom1rIMv46Cf5HgNEdDk00P844ErpMxK35vZKYJ3BJI5VzBKRyTE+ZetGWcjUus+bxW00oqOE/4gBJC52JLIHAFeVAUeEyLgWLUhQJAiCsA9l7O34aGPVAeoZ9t2fWXMJY/G3AwUTlfVuHKsbGTlRAdF5YC2uWMuvzN58EUVGFpL6adxQtckXtGT3Ay7eKlmkHfGE3t2YjemYKBp3ANNGKusnBKyHh14J3OQHbhYl8ZQls5cU08+KhfmJE0OXYWHFFaeJO1+i0b6jtPeP9t4Y/V9gyKXKujMTuL5F+o7PWxZ3zyrLOJx6K8mD7lGWh10DnLdCiTHZnA/8eYhkncuy/LrILLC0YsfIu/jlwrF4jyWsuCgnY9Eii1GAeYxFK8gTKP42/T7eO5eIPrIVs/zba8NHuGrMj2efkx1RMIbiJYKSkd9tog/Iew+YMTpwjNY6OYw+OTsJIWPmot2JoBEOETakLRIEQYQBiYsdH17cLp/GbWzFjaHPIwexBwBfmzrjdGZf4+MOf1RyXxoTYeZYInVIZ6xTtTHyHE4phiIP2QotLQsYZXNyuvdoKZbe0S8Dw25Q7/NxBIB4k/eO8T65HdY+l1a4wQVctEEtRFmBFRSzONbNycLpvynLwzhuv9p32JHPqdd7HCJZkaXCu461GhxwBtBVY1HafxwwLpDspeRnk/PYvN8rFyvL2QPV+4xiqPIEjUTCZm4u/U2fgR4AjmfibLLvr3CQxXmekNl7dGTnJqwhT5Lu/ROoXKJO6AIA6/5ufGzdeuCn7sCmQL8k0gRJ58w3389aYOc+pMR31FpeazOQW4EXKzJZJ1HiTExb/QkTJuCEE05Ajx49MGDAAFx55ZXIy8szPearr76Cw+FQ/cvOjlPsDcIWrCs0CY0EQRBWIbfoDk9GT/0sdvVy9bqVjjVr0eJrVb94M03cgbL7A5cXAEc9H/oaRMeg6xBlWWuNBwCH/Z+UkEUL6/J62MOSBdBhD9m//uAL1Ou+VvvniDY8910t1Yw7Z8/DrJ03LQvoc7T9+LmsK13WfvaOjSf7XwScv0pJ4KOFtT5yZiqi6bHvSBbVp/8al2pGHaNs1j0ODn2sXTF9xU3KstYSVLZQ1IrXnjp714g1oiaeqZxx24gDb5TCAYQrwpg9M11NrLOJ6MH2axacJYVqYTHLvLz7c0nI2/aitM5OnrJhY0Ix7Abgmhpg0Lnm5bThHWS0z1s4IicvM3acwtIlOzEVF5csWYIHHngAq1atwrx58+D1enH++eejtdW8w9GzZ0+Ul5cH/xUXF8eymkSYiCQpEgRB2CcVrDmIyHA49G5aWqsNXudUC2sN074Xqqm8eCU9IFIDZwZwzgLJ6mzgWZz9acAwTqZyVlzsuj9wdSVw3Dv2r7/fier1/I+AigX2zxNN2FijF23il2ETFFy4Ibb1GXKpNOAdcEbyJ/bqdxJw4if8+LGDL1SWD3+UWX4IuKLQukibbBxhkKCmq4VkKnbDALgqlGVvo3riSLaK6jJIfYyczCtZ0IqLoSYUMnsDV5YCRz7L3+9Ik54NGasWnUByi/UdiVCuv2bCsVaAz2K8L4bfCnS3IOID0nNh5ffWWvDLuDUifTdOAr5QaEMUDDgTOCzMWNodjJiOcGbPno077rgDo0ePxtixY/HVV1+hpKQEubm5psc5HA4MGjQo+G/gwIGm5YnEIPiag8tiOCbFBEEQnZIkH1QS0cFsIASEFhddNWo3uKY8TZIMuo8IDYPOAYZeZbyfZ+2qTfYT7uSHwwHcJCB4X+54HVg4PvJsoJHQPRBvMa2rlOCGx1kzgP0vkRK5mMXvigbZA4Crq4BzFsb2OrHmkPuAkXcCQ68Gjnoh0bWJjHPmA4POBy7fDXQxGG8aJSJh45TatVzsMlhZbi8HypgkQ0bum/uSLMN4+z71uq9dHz9Si8MJOAwEqD7HAn1PUNYvWKvebxRKoNcYtVBFxI5QsWJbi4z36cQ+5l3jawZGP64/pseh+m1W+z4Oh9ROadFO/GpFcito+29n/M4v1wmJq/lEY6MU9LNvX/MGoKWlBQceeCCGDh2KK664Atu2bTMs63a70dTUpPpHxAfRzwx6SFwkCIKwRi+KDdQpCBVgfv+Lzfev0MSwa8qTrMFkuJ1ugjBBawkEAK6q6J3f4dBnlY40k24kyAPA/S80LtN9BHDWdKD/qfGpU2av8LKTJhPOdODkSZL7c6r/LYPOBc6ZowjRPHhWpke/JiV76TZcWrdruegNxPrc72Tps5SJcylbRaVlqa0mwxFBYskaTZgFf5vahbzrMP5x2gkNdjs7KacVDI3eqcmceb2j4YjgeWe9LURRLdB5GoGh1+qPYS3LZXobTBTxyOit33bYP9XrkbpF9z5S7eLdyYmbuCgIAh5++GGceuqpGDNmjGG5ww47DJMmTcIff/yB7777DoIgYNy4cSgrK+OWnzBhAnr16hX8N3RoGKatRFiIrAk/WVAQBEFYY+yLwKH/AM4ziU1DpD6hxMXSEHHJKjXWTa1F6phb2sQDBBGKrgcAp3wDjJ2gbOs9NrrXSOumXl95q9rl04i9M4A196kTbERK2TTps3l39M5JEBdtBI54TBId5cyz2oQuoqixNGfwuyVLLQAYfov02Zyv7A9aLmYC45cqrqbJZshRp/FEFDzqRGO8eJ0AMPIO/nZnJlTjSa0VZJpBDL1QsfeI6BFJRmTWclFwAyITKmbwedLEy/krgbPnMNdzKNnTT/hIeneNuN36NTN767cNv0UtkoYj2svvqZ6HAReut398ByZu4uIDDzyArVu34scffzQtd8opp+D222/H0UcfjTPPPBO//fYb+vfvj4kTJ3LLP/HEE2hsbAz+Ky0tjUX1CS5KZ9FKv5EgCIKAFOPs+PeA/qeELkukLlGfyWZetL2OiPK5iU7DiNsk97PLdwMnfw0M41iLREI9Z6Dlrgl93JJLgYKJwPYoBsVv2BxYMBB5CMIqZzEuyWycUlkw0bpF/+AEfkiTwlto8TYqy70DBjdssh/ZKsqZJVnWjn1ZWi/7PfKMy7FE8KndZo3i7xnFC/Y2QSUu8ixGD/2H9Mn+Hslm0dmRyTAIEWAF9nf3tigWut1GAAcEwnn0O1lKSDb2ZSCjF3DM68BJnwHX1AKH3C+9u+xYS/P6YWlZ6snfcER7fyC+aPbA0K7inYy4iIsPPvggpk+fjkWLFuGAAywExWXIyMjAMcccg4KCAu7+rKws9OzZU/WPiA8iKYoEQRAEwSfUIJCNuWUXebBJEOHSfSQw8vb4DIzsuIzWrYvedWX3yzHPRO+cROdk0LlA3+OBQeOBbkxmYtklt55JBlTwqbK8i2O9x4YKkBNTsPF15edFFmPk2IvuWmCRiYt/POGNAT31aqEvVNxhLTU5+sRQWo5/D7hZlEIdHPaw9P0fdLe96xDhw3NTDoXAEX9bChQRfcgleiF59BPAtXXSRKrDGX5MTZ7lojNLHUc1HLdoOXlRqBijnZCYiouiKOLBBx/E77//joULF2LEiBG2z+H3+7FlyxYMHhxBJ5yICQLzYhHJLZogCIIgFIwC/O9/ifQZMutiwAWMlxWRF0eIIJKB496XPoffqmwLlUWWpb08OvVw10lxSgHJGoYgIsGZAVy4Fjh7rjrpkWy5uPkpJTs6G4uwaaf+XGzMQdmyylOvCHayFaMsjLAWX9pwGYmCTS4ji3tF3yriYq8xQN/j7J934JnAaT8DF28NXfa4t4Ery+yLmET48PojZhmiPQ3AH0OBnNvVFoJzT1Hcop0G7u7hJhdjYUXE9G7AEY9LE2oDz1K2h2P5Kr/T0ruZl+uExFRcfOCBB/Ddd99h8uTJ6NGjByoqKlBRUYH2dmUG8/bbb8cTTzwRXH/++ecxd+5cFBYWYv369bj11ltRXFyMu++mWYlkQzRZIwiCIIhOjTYGlzMLOHM6cOxb0jobP1FLe6Uyq3/+av3+aHS6CSIWHPaglDV63LeMVVYDUDEfmHMysPlZ/TFNTLw5V2V06lE+V1mmhA9EtNBaWA06T1leOB7YPUlTnuPCKcdiHHwhkBl4RkSfYr0of8rCozZrdDLAZorOYLLQy1ZgobKIDxovfR75vLLtgCulz2HXAr0tJr7juU4TsYNnqZfWFbgoYLmrdUMu+l6aMCr6FqjVWKXLbtFm4mSksM/OhbnA0YF4w8e8rmwPxy267A/p09cSft06KDHtnX788cdobGzEWWedhcGDBwf/TZkyJVimpKQE5eXKLGV9fT3uuecejBo1ChdffDGampqQk5ODI46g+ELJBnlFEwRBEIQBWsvF0f+V3H+yBwT2twLrHwV+HaDP2Pv7IGWZlxgmkoyNBBFr5AG/nJ16xQ3AwvOA2tXA1ufUHcimXcB0JsO0URIMu8hWMdkDSIAgYseQS9XrG/+ttjQUOAmKgm7PXYD0LspzsjeQgEgrLhrFKEwk1cuUZdYKrCaQqC7UO+qMqcAp3wKHP6Rsyx5kWJxIEhwO4Po2oP9pyjZnOpAesMb11Ct9n53vAuseVMqVM9auAJD3duB4A8vFaMAmAWKF0cw+wIE3SsvhuEVXzJM+y+eYl+uExDTQipWYfIsXL1atv/3223j77bdjVCMimoiqhC6kNBIEQRBEENYV9NxFSmecTQawM2DFuOl/UtByQB+rkXWhkyFxkUgFZJe0Nk2yRVcV0CUgqGjdPKNllettkj77nxGd8xEED62llrtWve53649pr5A+5ThyWf0ki91VdwIb/g24q6XtcviLNI3l4mQHMH4JMCCB9/aeb5RlXvzgULFc07sBI25Vb7MTm5VIHOldgBM/A2aMktYdaerfe829wLjvgPUPWzufI4aWi2z4mfSu/H3JloU9xSG/GiJs1HoiiYsEQRAEEYTtsA48S+l888QTNo6RdoDFK09u0UQqkG6QWbR9L7Oi6T860iRLEq1IYxdZXMygRI9EDNEKf1r2zQBaitTbGrdJnz0DXnmsRZUsLALmbtHzz7RVzZjSa4x+W6iYwjxIXEwdWGtaRzqQxsQeLPre3rnSu0SnTjzYSd50zUSt3CeLJNv42AnhH9tBod4pETaiwCZ0IQiCIAgiyPEfSO5uJ38Vuqy7Vpmx83EGWOctV6+T5SKRChgFu599nHGSF4cTWHAW8Gs/oLkg/Gt7G6VPEheJWHPCR+b7556iLAs+oDSQLbpXIK6gkUApPz9Gk0nFP1mvY7SRM2afv5rv1hrOO6rHwZHViYgfaYwg6EgLP5szAPQ6MvL6GMFmt07T3KfhWi42bleWh14VXr06MCQuEmEjkqRIEARBEHz6nQRcVQ6M/Evosrs/B8pnS8t+jujS/1T1OlkuEqmAkeUioA/uL9NSCFSvkJb3fBv+td2BhElyxl2CiBWH3A9cWWq831WhLMsZzAGgd0BUMRLi5FihRjHhVtxgvY7RRq6TM50f0zSUWzTLeSuAwx4GjngiZFEiSdDGAY2kTxLLjMu9DpfC0lyWr98nP3d2Yy4W/6gsZ3KyZ3dyqHdKhA3FWSQIgiAIE4wSSYx5Sr+t6Afps53Jlnvwvcoy2wEny0UiFTATF+Vss4KJS1okbpKy6zVliibigRwf0QhXjRRPl72nuwbuTZ4LcZ+jleXB5wHDb4u0htGjfqPyfMmZfrWu23bcovuPA457G8gwaS+I5ILtjwgee8ce9Ff1Oi9mZzQZeBbfKtYRpls0GxdbG3OVIHGRCB91yEUSGgmCIAjCEkc+B1y0CTibyTQoW3q4ypVtxzIJ7o57nzkBdd+IFMDMIiXnZulT4CS8kIlEXGyTxcUh4Z+DIKwSyvrqt/7AH8OBOSfo9x10t37b/hcry84MYNw3+jKJYtYxyrKcjONcTWKmaGV9J5IT1jKV1043bDU+lo0xOvgCoMdBxmVjiTNMt+jejBu3kyZ6tVDvlAgbgV4cBEEQBGEfhwPocxQwgAnK7wm4ccqZRA+4Sp3dsOehyrKZIEMQyQJruXhFkWLlxGLWl/S1hX9t2bKqK4mLRBxgrdSdmcCFucBFG9VlZGtdLQfeoJ5IGvsSMPpJfbkj/qPflnM7UPKL7eqGjdaYRBZotLFNI0mSQaQWvHZ6pkkcRdaF+pQEiuZhu0VPiX5dOhBhpHIiCAn2/UIu0gRBEARhEzaQf9kfgLdZic+ldRXqN05ZNkqGQRDJBOvm6EhXu5MBQM0ateDozFIL51YtF0URWHWndP4ug4ChVwPuGmkfWS4S8eaIJ4C+x5qXYcU4hwM47CEAIpDVHxhxK/+Yo1+R/k1mhMyib6V/l+yQ4svFmvoN6nX5+dWG6rBrDUakLvJvPfQaoPRX/f4DrpD6N4DUxrczMUiz+se+fkaEm9Bl77To16UDQZaLRNhQQheCIAiCiJADb1KWK+YBnnppWRvLx+EARvwF6Hs80O/k+NWPIMIljY0TyrFnyHsH8DRIy4fcr85ACgB+l7XrNGwG9nwNFE8Gdr4FzDtN2u7MArIo4D4RJ0b/D+hxCHDog6HLnqERKBwO4PD/MxYWQ1G9PLzj7CKHG5CRXVy1zzdZLnY+jEIDsH2ZM6cBLiautFFc6njgDDPmosyw66NXlw4EiYtE+KisFUloJAiCIAjbtDODNUc64GuRlnnJME75CrhwLd+9lCCSjXRGLORlj+1+kCKmZ/RWhwEAgLLfgZ3vmF9D8AOzjubv6z4isYNXonMx9kXgsl1Adr/QZXscEv51LuRkWrebVENmzX2Sa7VlDzRNuazA36p9vklc7HwMNxDGWbfjwecDRzwuLR/2cMyrZIosiNtxi/Y2K8snfBTd+nQQSFwkwoakRYIgCIKIkF5MbKLS3xSXZ7NMuwSRCjizlWVHOjB+CTDsBuCge6RtnjrA2yAtZ/bmu6et/z/za3hqjffRM0QkmrSu+m1nTFMyRYdD3+P02aO9TfbP42sDCiZKbtVtZdaOYUMVnPGHIt5r3aIHnmO/PkRqM/g8/nZ5wlRm/wuAqyuBY9+KfZ3MkO/ZthLrx8ixsdOyySreABIXibARBJIXCYIgCCIijnpOWd7zNeBplJZDZR8liGQnjREXnenAgDOA034Eeo2WtrlrFLfozD6KFaMdalYb7yMLXyLRnPaTev2IJ4ADLov8vGNfkBKCdT1AWvc1m5fnwYr5VuPOyaEKBl8IHHC5sp11i84eoI4nTHRuuo/Ub8sekHir8tZi6XPvn0CbQbIlLfL9z06cESpIXCTCRp3QJXH1IAiCIIiUJWs/YMwzyrqc0CWDrK6IFId1jWQHY3IMrpKf1JaLJ01SZxK1wpp7jPfx4jwSRDwZcol6/fBHonPebgcC4xcDI+6Q1sOxXFQlWLI4kJPFlTSNuMK6RdNz1znoNsJauTFPAQffC4xfGtv62KVqsbK85Vlrx/gDCce09z8RhMRFImxEcowmCIIgiMg5khEX28ulT3LpJFKdbsOVZSfjNtl7jLLcvFv6zOgtJbO4qhwY94O184sC4Koy3l+9zGpNCSJ2nBHIlHvks9biMdoho4f06Q3DcpGN06jN5G6EkbjIukX72uzXhUg9zvxTskY/d5F5uczewIkTgQGnx6ValmEtKmtXWTtGDltD4qIhNLVAhI1I5ooEQRAEETkOhxQY310DuKulbeQWTaQ6/U4ETvlWn7yi77HKspzQKLO39Jk9AGjcqi4vinoXOlEApnQFTW4TSc8BlwM3emLjpp/RU/oMy3KRERdli6xQyDEXtZnd2feVbI1MdGx6j5bi6KYqJ30O/DFcWs6yKPqvvF36bC2KRY06BGS5SIQNa7lIXTuCIAiCiAB3jXqdLBeJjsCIW4F+J+m39zpCvS6LJABwwBXqfdqEAH4P8EMaIGgEkTFPh19PgoglsYr/mS5bLmrERSsGIH7WctFitmkjy0Wy5CIA4LycRNfAOt0OlJIrAYC3xbysTEtB7OrTQSBxkQgb9XuL5MXOSlWzCxtKwgjCThAEQZhA71WiA5M9UL3Oiuk9R6n3yRk6ZfLe0Z/viCek5EjnLIhK9QgiJcgeIH3KsXoBIPf/gD+GAa5q82P9jPuyVqg3QqCEFoQJ/U8BbmgHht8irZ/8ZWLrEwp5UiuchEgEFxIXibBh3aLJQ7rzcuJLC3DVRzlYTwIjQRBE+Bzzunqdl2GRIDoKXfZXr7Nuleld1fuaGWsRUQSa8vTnky3DBp0DnPCRZEl12s/RqStBJCtdh0qfbaXKtrx3gLYyYNeH0jpvkOZrA2Ydraxbdos2sFwkCJm0bGDcd8DNIjDyjkTXxhxtWIGGbcDv+wN5HySuTikOiYtE2KgNF0ld7OysLqwLXYggCILgM+pf6nU5oy5BdES6DFavs+KiwwlctEFZXzhe+hR8wKxjgMJJ+vM5M5XlQ+4HrmsBhl0bvfoSRDLSLSAuepuAyQ6gbZ+yz9sArL4HmHaQPuHLT5qYvlYtF/PelT61MRcJIhXJ0IQVWP+IlFQv9x/6soI/fvVKYUhcJMJGZbmYwHoQycPUDXtRUktZ4giCICJCdnUjiI6K1nJRG5Ouz9FAVn/1tqY8oGET/3zdD9KcL41fjiA6EtrEX1ueUZb97cDuz4HWPcCeb5Xtjdv157ESc7Flj7LMe75YgZ8gUoGgW3SLJB5qQ3CwsImKRvwlptVKZUhcJMJGNFkjOh+/ri/Dw1M24ozXF6GqyZXo6hAEQaQeg86XPg//l3k5gkh1tOIij9FPKMuiCEAwLtt/XMRVIoiUp7VEWXZVKctsTLnWYv1xfjew/XVg5V+kTOwsNWuAliL1dp4VlzMrrCoTRMJgE4l56oC6dfoy7jpg8aVA0WRlW7LHkkwgJC4SYSOQKzTBUFClZNo68eUFqGgkgZEgCMIWp00BzpoJHP5IomtCELEla7/QZUbepSwLbn1Gz5F3Ase+A5zyDdBtWFSrRxApw3HvK8sVc5Xl5nxlecuz0qenHmjerT+Hvw3Y+G9gzzdABZMUqWkXMPckYNoIdXnRpz8HxWEkUg1nlmI1X/iVfn/zbuDX/YB9M4DcfwaOyQAcjrhVMdUgcZEIH0ZbFEloJDSsKaIYjARBELbI7A3sfxG5dBIdn4xeyvJBd/PLsBmkvS2Aq1y9P3sAcPhDwIjbol8/gkgVDnsQGMqJL9q4TVmWE7H8sh8/nlzVMmV5F5PMonatsszGZeSKi2S5SKQYDoc+qQvLat67ieQzM+jbIcKGBEXCjFS4P9w+P7x+EzcrgiAIgiCiDysuGiUvYkX2kinA8uvU+3scFv16EUQq4mu1WNCgb84mSdo7DVhxE+D3QBWKQCU0evXnGH6L9DnwbIt1IYgkICsQ49rXrN9Xs0K/zWryo05KeqIrQKQuIsVZJExIdm3R4xMw9rm56J6VgbX/OxcOMnEnCIIgiPiQ2VtZZoVGI9Y9KGWRZtn/4qhWiSBSlhMnAn+ECA2gDStgRvGPwKDx6izTq+5gCnA6+aP/B3QbLlnfE0Sq0G0Y0LRDHUYAAFpL+SI6YQpZLhJhQzEXCTOSXXwuqWuDyyugpsUNIbmrShAEQRAdi4zeyrLZ5F7vI5VlNqFEr9FAl4FRrxZBpCTdhgJX7VPWswfoy/DcPs1w16gzRLPw4gJn9AAOuQ/odqC96xBEIpHv130z1dvnnxn/unQASFwkwkZUZRMjdYZQk+zacyq4bRMEQRBEhyQtk1kxGY6cs1C9ntkHuHw3cP6qmFSLIFKW7EHKcs9R+v12xcWs/sCu9/j7ugy2dy6CSFa6DuVvbzUQ1glTSFwkwkakhC6ECcl+S7DVo/uXIAiCIOLMIX+XLBAPvse4THY/zfoAoPtIIKM7vzxBdFYcDuDM6cBJn/OtB3ni4oCz1OvdhivL5XNBEB0eK2E5CMtQzEUibEiQIcxI9ruDbl+CIAiCSCAnfGj/mKz+0a8HQXQUhlwifRZP0e+r1Vj79jgUOPUH4HfGCnG/E4EBZwB7vpHi0PE46sXo1JUgkoGMHomuQYeCLBeJCFDUGRIaOycen+Ian5GmjpmU7DE52fold00JgiAIohNz5LPKspELG0EQCu5a/bbch9TrB92lF+uPeQ3oebi03LBZ2d6Tycx+6IPRqSNBJAPpIcTFXqPjU48OAomLRNgku3hExJ7qFndwuVeXTPXOJL891G79iasHQRAEQRAmDL1GWR5AQfYJIiTHvgE40oCjXjAuI/oBZ5p6W7cDFXFRVZbpKKdTSAKiAxHKcnHg2cBZs+NTlw4AiYtE2JAgQ/j8iuWiNtljsmeLZuuX7HUlCIIgiE5LejdlechliasHQaQKA88GrmsExjxpXEaVmJOBTQwj032ksqwVJAkildFaLrL3OgA07wb2vwA49J/xq1MKQ+IiETZstmiSZjongskPn+zic7LXjyAIgiAISK7Q3Q8Geh8JdOEIHwRB6GFFeR6iX70uiycOjXg48k7g6FcBZyYw6l/Rqx9BJANay8URfwFO+ERZb9gofR5yv/Q5+IK4VCtVoYQuRNiorb1IqemMqOIWam6BZL8jyC2aIAiCIFIAZzpwyTbA4ZT+EQQRObL42HUY0FaiCIe9NG7Rzgygz1HAtfVAetf41pEgYo1WXOx7LDDkUqClENjxGjB2grS91+HAVeVAZp/41zGFoDc0ETYkzhCCielissfkJFdogiAIgkgR0jIlkZEgCHuM+16/bcAZwMH3ScuX7pREk26BZEkZPYGrK/XHkLBIdES0btH7Xyx9Hj0BuHw3MOJ2ZV+XQUBaVvzqloKQuEiEjTpDNAk1nRG1tqi+B5JcWyRxnCAIgiAIgujYDL8ZuJnp6PY8DBi/BMgIJGZJ76IPN5A9QFl2Zse+joSKJpcXny8rRFWTK9FV6fhk9ZVc/wHgpM8V63iHU4q/qE0qQJhC4iIRNmT5FT3cPj9qmczLqYLaLVojLsa7MjZJ9voRBEEQBEEQRFQ45nXJxfnET+0dl0biYrx54Pv1eHHGDjz2y+ZEV6VzcPIkSYA/6K+JrknKQ+IiETYqyy+SaiLi7NcX47gX56MyxWaoVK7PYrt6Z5KbA6qEUbp/CYIgCIIgiI7KqH8B1zVJLtF2IHEx7izLrwEALNlVneCaEIQ9SFwkwobNFk1Exr5GSVRcUVCT4JrYQ2BuAVHwqfYlu1xn1y16fUk9vlyxR2ehSRAEQRAEQRBJTzhCIYmLBEFYhCIjE2HDWnuR3hIdnCkW18EsaYvL649jTcJB5CwZc/VHOQCAgT2zcfGRg2NUJ4IgCIIgCIJIMMOuA8qmASPvSHRNCBN8fgHXfrISQ/t2xfs3HZPo6hCdHLJcJMLGLJkHER5OZ+qKi9o7oL41uWNIhiuIF1S1RLciCUQQRNS1ehJdDYIgCIIgCCKZOHUKcF0D0IUm1JOZTWUN2FjagD837Ut0VQiCxEUifJLdPbS+1YMbP12Jn9eVJroqpvgZlTbFtEWNwKymobUtfhUJA0HlFp3c93KsuP/7XBz7wjzkFtcluioEQRAEQRBEsuBwkEt0CrChpCHRVSCIICQuElEhGcWZdxfkY1VhXdJn2nL7FPfhtBR2ixahrnt9u09bPCbsa2jHq7N3Yl9De+jCDKKJ1WVnYc62SgDApOVFia0IQRAEQRAEQRC2eHHGjkRXgSCCkLhIhE0yCoosTS5voqtgiRa3IsJlpqfWIymYmC7Wtcbn+7/jyzX4ePFu3PnlWlvHxePubXZ58eTULVizJ7ktA1PNHZ8gCIIgCIIgCIJIHlJLySCSCnUyj+QWGpOZZpciLvrM/IyTEMHfGFzWas1N8t/VMgfwlsSsDrsqpRiIeZXNto5TWV3a+NrtyHBvzduF71aV4PqJK20cFX9IWyQIorNTUtumClNCEARBEKlEshv+EB0fEheJsEn2BszByEBVTa4E1sQct1cILvv8yf2dahGbfg4uC6JGoRIBtMwGyi4Edh8Y34pZIQ7aeFFNa2xOHGVSLUs5QRBENPkltwxnvL4I/zdlY6KrQhAEQRBhkeRDc6ITQOIiETZiClkrvjE3L9FVMIT9Hn2CgDfm5OHv3+eauhwnC35BEUadDk5925bEsTb2UGuLsfmuU0W0S5FqEgRBxIQPFuYDAKZRtk2CSGmKa1vx8swdqExiowKCiBbaePPJP3IkOjrpia4AkbqIIn85GXH7hNCFkgCfX8QHiwoAAGtOqcPJI/dLcI3MYV2Ls9L86p1JLljF4551pIhq50j2H4sgCIIgCCIE136yEtXNbqwvrscv949LdHUIIqbUtLhV64IoIo369EQCIctFImzEePiVRgCr66QlcVA5VuTyMZaALq+fUzq5YI0rs9J52aGT776QCTfmoh2S+LZTkSr1JAiCiAWpMhFEEIQ51c2S2LKuuD7BNSGI2KN1chOS3dqH6PCQuEiEjcgYAyZ7U5aeIuqJ1x97wSuasPdA3y6p5YISrjRuZwyaKm7RySy+dwZK69qwPL8m0dUgCIIgCIIgokyzyxuT82rFxFQYOxIdGxIXibARIajWkplUEU98fuU7TYXZJz+bxEVT3WT/xkWV5WKMYi4mcQvb7lEsY8lqJ7Gc/toi3PrFaqwtqkt0VQiCIAiCIIgosTivCkc+OxcvTN8e9XNr4/PzhjMbSxuwcGel5XPWtLhxyXvL8HVOUYS1IzojSTz0JZKdVIq5mMwWZKLgCS77mJdEcFFoBcrvkTIvJxmsAKrLFp3kxOOWTeZYhguYjkaKaO8dnvXkxkUQBEEQBNFhmDBzJwDgi+V7Qpbd29CO3GL+RPPu6hZs39ek2qZ1iy6rb8M783ehlonFeOWHK3DXV+tQVNNqqb5vz9uFbfua8My0bZbKEwQLJXQhwibZs0Wzekkyu0WLbQsBdAegdosOCne1rwGNn0v/Dk+u75wVlYUkFtJ4qCwXQ5QL17IviTVtleCezOI7QRBErKEWkCA6FtStIVKRU19ZaLjv3DeXAAA2Pn0eenfNBKD3crvl89WoanZjdWEdfrj3ZNW+vQ3tGN6vW8g6NLt4MfQJwhpkuUiEjao9S3LTRWcSi4sQlUbcw2S1DopfvtJ418gy7IyZkBoJuYOw9TW6fb+f+yqOeGoq1hRWGZ7H5fWjoc3D3ZfMoh37SCTz49GZSO5WlCAIgiBSA+rWEB0J1iCiokmJca8VF6sCCY1WFtaGfS1fqg3oiKSCxEUibASLll+JQpUtOolFHva94PYpcfAU4c6JWlfPpHQ79rOu8dyuXDLeGRLq+5dfz/8tHIN2Xyau/3St4XlOeGk+jn5+Hupb9QJjMot2rDVmWjIHhyQIgiAIgiCIDozL6zfcp3V/ljGz7Wl1h2eByHrREYRdaERJhI9ouJJ0pKUlscrDoLZclD63VPXFcT9Oxp3zn0lQrYxRWS5qE7ok+Vdu9KJm6ZPVqNumdZGW3Qc2lTXoyia35aJSt6wMehUQBNGJSd6mmiAIgkgScovrUFrXFpNz13KMFGSMknz6TQYzje3hZahmk4sShF1oREmEDWvtleRe0ckdc5FZdjPioj/wpX6/ZQQAYMne4+NZLUv4BeV71VtWSvVfVzkKu+qHxbFW1lBliDa4fzOc1mf9kllI5JHGtP7J/Hx0JpK9HSUIgiAIgugMNLu8uPjdZXhvQT4AIL+yGdd8vBKnv7YoJterazEWF436h0aiIxD+uMRnxfqCIAwgcZEIGzGFRsLJ7RatfI+8mIvZ6ck7g/TInKOCyzy37fLmTFw763Wc/8dH8ayWjjrObOCTU7cGl43uZL6rN5+0JBfomlxe7ChXssyxj2+4CWsIgiAIgiAIoqPxzcpibC9vwlvzdgEAtu7TezMZ0e7x4615u7B1r/VjalvdhvuMRESzoXi4EY+8ZLlIRACJi0TYJLu0yDa4SZ3QhfkmPUyDLr9IumSkRiMvasRFB4DSxuzEVIbh65wiHPvCPHy2tDC4rbLJZep+IKP9m8xIdn3u3DeX4KJ3l2FVIMhzZrrS/O/XLTNR1SIIgkg4Sd58EwRhE5o0JSLFrYmBaMem5t0F+XhvQT4ufX+55WPqDZJDml3bzC06bMtFirlIRACJi0TYWEmIkUjYBjeZ3T4NE7oENMUu6cn33fLg1dLpSHzdn5m2DQDw0swdwW1ur1qwFQV+EOVQlous1SnvJZ74v16hOpBBbs62CgDq+rJCI5E4aCxEEARBEASRePwaRc+Ot/B2xlPIKvWtxjESjSwXzdyitV1Kq11ML7lFExFAI0oibJLdK5ptHJPZcpH9Gj0+ZU2xXEzyLzoAzy06WcUS7cvY0C06hOUiK2CnSsxF+U83m+0kEkOyt6kEQRAEQRCdAW03OdxwYFYNcMz65UZ7zMTFcLuUlNCFiAQSF4mwYRvZZIy/yDaOyWy5yDb/fkGpsxxQlxUXk1kQ4mWLZi0XBUHE5rIG7G1oj2u9eD+9Tlw0mhHkzPOV1Sv196ssF/XHJ+NzIf/tftXzm6jaEARBJB5yoSQIgoicbfsacf3Elcgtrk90VSLGqiFCrK5nZZ/ZsDDcvj25RRORQOIioUMURWzf14QWd6hMucnd+PhSxaqMaf3Z9pwnLq4tqotbteyitfITRRFpjLiYX9WCyz9YgVNfWRjXemWlp+m2WdVoeZaLP6wpwfztlQDUYm+qDE7lDorA1D0Zwxp0FpJRgCYIgiAIgrDLLZ+vxpo9dbjm45xEVyVidN0zG921cEYEpkIhY0zoYM5u1oW007f3CyKu+yQHj/60CT6BLBeJ8CFxkdCxNL8GF7+3DJeFCEKbxEZ0APhm3T6/gLnbKrjZgxPFxNXdg8us4CPHyMtKV8re+OmquNXLjGaXFzkFNaptodyiN5U2xLhWfLIz9M2cVtAxegEbxVyctGIPALW4yMsWnYyPiPxYsM9vPPWt3dUtKK5txZwkew4Thep3SMo7hiA6Pu0eftxdgiBSk9SY7u14NLQZxw1MNQTB2liBRzj2BuFYLja2m3zfovkE9gcL83HPN+vgF0RsKmvA2qJ6/Lq+TGWcQxB2SQ9dhOhszNxcDgDYU9NqWk7VyCah9c2ivOrgstwof7qsEK/NzsOB+3XFksfOTlTVguQW12FuvpJRmZ0tem9BPh4571A4knAO4O15+UGBTUbrQuxwAA7WLTpB90h2RhoA9ctXH0eFf2yTpzt3uywqspN7Se15zyB3NPwqy8X40NjmxblvLgmuj+zfDQsfPStOV09OkjnUAUF0FuIdroMgiNiSIs4kRBKj7Z7Z6a45VMvWbkYzIZC3x+X147+/bzE9xmzo9cbcXQCABTsqMaCnMhb1+MhykQif5FMtiISTxbH04pGEeqIh8gth5hZJOC2ubUtgbRQqm9yqdZ7QICbhY/pLbqluG++lq4q5mKD7RRIX1ejjqNirHC9uYVK73jMESnj2CQAAzXFJREFU3aLF+E8OlDepB/CF1eYTGJ2BRInuBNHZaXJ50Roy/AtBEATRGdHHZ7d+bDihkszGSWxd5DHLd6uKdeWG79dVdYzqlAZVcvkEZKQpO0OHRSMIY5JPtSASDk+M4aHSJpLcnU9ulCsa3SFKxhfti4pvxZR8jynvHtHFJxQB5l2lEuLiSVa6/vuLVNAJWi6GOE8y6kayW3QiLObSncl3Lyca1e8g0mwxQcQDl9ePo56di9HPzKG4pwRBEIQOto/f2OaN+VjXqlu0vPjijB26cl0y01XlrLzfRFFEZprSP2+jMCFEBNBIj9DBE2N4JLugyCK3rTUtySUuatEm6KppcUN0hPeY8mJORguelZ425qLDATiYe0QbuyReZHGF0FAbzJH/FPZlz+sUJOMTInIsF+NVT3ZmNBZs29eIz5cVxvTejzaq2DauDdwy0zfvw9UfrcA+ct0kiKjAPkueFGovCIIgiPjA9pNPe22hPctFZjmvstni9fjbRVHEvgYXt166c2hCHqlKCsZjYHZYR+F6iEggcZHQYVlcTKHZ/mStq1ag9WsydO2uakE4j2l1sxvHvTgf//5lUyTV4+Ly+uHlDMZ4CV3YhCiJelllc+5nbV3CdYu2FXa0cbKta0QLj09AWb0SBoDnFm1Ud1EUcf93ubjv29yoPEOxdh2/5L3leHHGDvywpoS7f0d5U9JNMKhEd5EvHj44eQPWlzTgP79ujlOtCKJjk8FYafj8Ii45cnACa0MQBEEkG2z3rNnlw8+5ZbG9nsE46cNFBbjywxXBdbPuuF/VtxfVZT3buMeIYvInaSVSBxIXCR2syytPRJJJQMi2sEmU1Vwo9G7RmnVRDCvm4pS1JWhs9+KnddF9EXr9Ak56eQFqOVl+ueJiEnztrOWiLJDpMqHZrKjiFs2cIsQx4r5bbF0jWtzw6Uqc9uqi4LpcZ/ZeMxIO61o9mLW1ArO3VaDeZgbAt+bm4ad1SmzOwuoWuLzxcbXYXt6k25Zf2YyL3l2G41+cH5c6WEXVEQwR9HuXxdlvgiDMSWMycHl8gmqdIAiCILR9402lDZaPjWa2aDnxiozoreaWAzSWi6LWeMK4UhT/m4gWJC4SOljLRbO4C1rbr0SwZk8dVhXWhiwnenbGoTb20X5rWhFUMmS0/4bixUT0+AR8sXxPSIGitsWNhja9eAgApXVtaGzni0x6YURUvdREf715pWMEa7noDmRA02ZCs/tOlcVF1d8X4iT/XPqYvYtEiQ0lDar1oOWioDzbRjVnLTztjL03lTbgvYUF+PcvkqXdwp2VOOfNJbh+4kpu+d3VLXh55o6YWhWutNBOxBOvX8DUDXtRzrq6COZfsjYBFEEQ4cFaUXv9AmWWJYgOhtUMvQRhhBBRxAz+/Xf/d7lYV1THv57FsYgg6CfQZbTGE1bHN5H9rQShQOIioSONSbrQbiYuJiBmG0uTy4vrJ67EjZ+uCmkRJbi2xqlWkaFNeuIXRYii/ce0S6ZeXJy0Yg9emL4d57+91PA4l9eP416cj6Ofn8e19mw3+Z55xoCqTZ7CUNWOCazlYrvHj5zdNbjps1WqMuG6RYeyXGSfkT/3nGnrGuHi9vlR2eQy3C9XSXBt0W3Twv59djrqta2KCOb2+fGfX6VrGVk/Xvrecny6tBD/+jn6bvwyWkE50Xy6tBAPT9mIyz5YHtzmE53Y29COGZvLDa2tkzXEgxnztleisLol0dUgiCBsm//r+r2q1i1ZPR0IgrBDcr3zidQjFtZ8s7ZW4NpP+BPtVvt3PE8xGb/GclEN/7gXZ2zH6j3JNQFPpC4kLhI62Ma0zWOcjj7RMdDL6pT4ZKHExXBcixOBNhagIIhAGAldujLioiyqbNRYsPEoq1e+Uy9nGqvFZXw/8N2iEz9zzFrcuXx+PPD9el0Zu/0H+WdSCeyccyRiiHrhO8tw0ssLUFDFF3Pk59vvNxYgtWW1y6HwMZmJHpmyCdXN5hZ3smhtx+XELl5ttqQosbaoDld/tAJbyhptHbc4r0q3TRAcOPO1RXhg8nr8YhDb54SXFmDNHv6sdzKycnct7vlmHc55c0miq0IQQdhX7auzd6qSqZF7GEF0AER7oVwIQovW4MMO0XSL1mJmdKJO1iiq1o2qVNPiwXN/bufua3Ubj/sIgkdqKC5EXFGLi2aWi/GojTFsPd0hrJLMZnkSiXaWSisuSuvKYzqyXxdL5+3CWOvJLwYrLzq3T/m9J68u0Ym2DQYu0YDeLVqXpSxBqKwLRcDB/SJsWi7KbtGqcyfDXwvsqWkFAMzfUcndP2trBQB9Rjke7P0YqpMll61tcWPiUsVKdcaW8pB1jgdm8WPtUlDVgr9/n4vt+5pw3Scrsb6kAbdNWh3xef2iM+jSsiSfH1OnpsWNu75aG/G14sWWvQ2JrgJB6NC21+VM9mgyXCQIgiC03d4hva2NwQB7Aa1EjjeUaXmTs2stF9V/g/2xMImLhF1IXCR0sA2TLvEFW06TkSoUUtaq6PXa2XryXB5PHNGXuXZyiotadOKiqBYXh/TONLUmlWEFtBYbLwb2e3zuz+14Y06ear9RvEVAL+CKghto/E5Zt1yL8Eg3CAqonsXjv1prWvgxJo2Qz6kSF3kFEzhITQuhJlt5ftn70WxGdVl+NY56dg6mbtiLv32bi9xi6/E1WZGTL/yq2VHehBemb9fFBa1SuYLrz2PXLdrrF/DstG2Yv10v0t76+WrM3FKBO75cE9zWYDPhDQ8/8wz5TMRQXwyD4+RXNuOqj1ZgyS7jgOF2SHdSN4NIPrTNWUldW3CZLBcJgiA6Ly6vHxOX7EZehTpG/dihvSyfw6rlYkObB6e/tggvz9yhGwMaYWYwI/iU/nc0jDxC9cvbPD6sKqw17bMSnQvq9RM62LbNbzKItTO77/MLuOjdZfjr1+siqJkav8pyUW9hmZmm3N5CGHEL44E+W7TecpGdoVpW0Igjnp6Dr3OKTM/LCjYtNiwXtQLMIo3rZqOJgKITcH2lcbUY5SWxAdTCmSCI3O+h2WVPGPIHZxnN3aKjaS0XitziOswOWCUCCJn9VLAgULEillnx275Yg1aPHw9P2Yh1NoRFAPAw35GVu+Wid5fhi+V78NRUdRzV3zbsZdb0P4bd3+LHtaX4KqcId3+jb7MqAkJmVQh3bzN4MSz9TEIXMzE0loHq//ZtLjaUNOAvk9aELmyBjLTUmNghOhdaAZF9lklcJIiOAD3HRHh8vHg3Jszaie3l6sQpvhiE1/l+dQnK6tvx6dJCfBVibCdjZjDjF7xMOY1RTxjdsVDJHP/+/Xrc+OkqfLJkt/2TEx2S5FRciITCClNmccpYsUH0m8cA27avCTsrmrFwZ1XUrBfZerq8+oE4KzgKKdLJ0FqKGg1ynpm2zfQ8rPBqx3JR616uvbqZ5aJfa7ko+lXCaLg/e2ldG56dtk3KVN3mxW1frMZUlZAkkZ3Bb878vlbNFk5sSJt1ku999jjefR1PcfGaj1fivu9yg+vpJqKOKIohhVFA/fzHasAdKqSBEVtLS1TrrFujx6evq93r7GXijxphZC0bLuwzZNb2tnv9psm2ImFvQ+i/2w7p7CQP+ZsSSYJZc2bVeoQgiOTF4aDnmAgPI+8bwa8dT4TPNyuLsKqwNqwxsWAi3/gExdAiHpaLi/MkLxerwijR8SFxkdDBighmszSq/nfTd4blALUVlZmrtR3YAQBPOGh1M4Nv946wrrFgRyUe+H69qcVeJGizFGsFHL8ghiXKhXIZN0L3PYrAm3PzcNG7y9Di9qGh3dh9WGsdKsX6iFx8ueXz1fgqpwh3fbUWb87Lw7L8Gjw8ZaOuXFY633JRaFOysokifxbOrnAmW/RqXa5ZJi3fg0V50XEtDQczy8V2rx+sJ7hRtmxVzEXNPTVrSznqW+25k/Ng7087AbAFvzqBSrZTmeDgWVzbFXqt3BO9umQEl0NZiurg3YeC8gyFcn3+xw/6xETRIFyx1whWgI32uQkiXMyeb9IWCaIjQFbzRHgYTTD52qz3uxyCudHN039sw42froIzjElqs4ladiw2Y9O+iGMuWoUm5QiZ9ERXgIgfBVXN+GRJIf55ziEYtl9Xw3Ks1ZvZANdOO8JaUbl9AjLSIte12XryBLQ2NxugPbwGVXbj7tstEy9cOSasc5hhxS3aEca8E3te+ZxWXCm1rqYA8P7CAgDAj2tKTBP8cGqhqXl4Lx45FlZ+VQtG9Oum2scKRkaWi6KgzDSKEOHkKFjccabp4NOnK8IuryqsxfPT+ZnX4kX3LOPm/Yin5wDoGfIc7PfL/n0fLCrAewvyAQB/P+ugsOsIqN2i7XR8tM+0s2kSgOsASBMYbp8f9a1eDOqVDSAMcdFCA9erSwZqAwJrNIwYfaJ1S9/5O/TZppMRtu1v9/rRJZM/CUAQ8cTs8UqW5FwEQRBE/DFKYOj3u7jbeTjc2wEcErJcqPjofMzyIShjobfm5+Mv40aEcX7mShbfh9EyHIqEnRVNyEpP040VifhCloudiBsmrsIvuWW462vzTKNsO2JmuehXCSvmjSPbeLq90XHnY3VPXszFVpcSKyPSmIvljfoXiiiKeP7P7Zi8uoRzRHhoxUVBDE+S41qcWXh/VTQZvzg9fsG2WyN7X4RyIbaCSyMitzP3klHMRVaEEkS+dRzfisW4jm0eqR6iV3HPZqXUMgsutdGEN2PYLdP63JHRz8F2FtjO1q+5ZcHljxZHFmfFbqIVGZ246FDO4xdEXPTuMpw8YQF2VkjtgJmbMQ+jziV773bNUu45nmhtF8HgeUll2HZam32eiC9ri+pw2qsLuUmKOhtm7yCywCCI1Mftz0x0FYgUxWis41dNAJu/J6y65dv2egEgiGaGP+qxkNrMw/ha5x8xkLvd6tsw0e/NScv34MJ3luHsNxYntB4EiYudCtnCpqCqxbScOlu0cQNmRyBiYyJGyzWOrRvvnG1eRVyJPLGI/m9dWViLSSv24L+/b4nw3Ao6cVEIL2KG2vo0Og2+KKoF5dDlHaqYiyzhVsmlsZxk486lG1jDssKyKBrUSBSxLL8a57y5GGuLZFcG40q2uKV9Qst89hSq6/CIlXs9zyrPSBzjYVSSPS8rwEZTJArbLVozYcBa+PoFEYXVksXqzM3l0nVsWi4afX2tzD3HCrjhdBC1sAld1uypC4q40Th3OETDgou9D9tJXEwo132yEmX17dwkRZ0Ns3dQsmiLb8zJw62fr45r7F6C6Ay0e/yo4BgNEARg3H/2Cex4wvwcVntt4YmL1iwXAUC0+ELrmW3g/eW3lrgw0ZaLrLeYmSGMKIqYtaUchdXmWggRPiQuEjrU4qK0XN3sxoeLClDVrLyMVZaLIZrRyz5YHlyuanbjkveWYdLyPRHVk21cteKiIIgqcTFU/ULBa8ejIRTp3KI1G3yhYi6KfqDuLcCljgMicCwXIzW8/zqnKGoJGSyJFt4y6e9jKG9SWwSqkloYnFNrDcYLTiwKLbjtizUorG7FzZ+tCl234PmYmIsGLtIsW/c18ndECG/waUcYMirKtgVijMTFudsqQhfioJ0wYMVGtm2Qnym7FpK8uI2AOnEMG97BzLWl3ePH5rKGkL+JT/M3PfrzJuncCRIXH/lpU8TnYP/mWCWhIQi7mD2KyeIW/cGiAiwvqMGCHWRpmkqU1rWhvDG+3guEPc5+YzFOnrAAxbXRS9BBdByMLRcZcTHkWWJpuWgmLoZnuejx1HC3i/5aS3VKhOViq9uHedsrdd6LZsYVi/Oqcf/363HOm0tiXb1OC4mLhA62Yy0v3vvtOrw+Jw/3fKNkozVrR6qaXJi7rYLbQH+wMB/b9jVZiklXVNNqKAqweoq2jMunzlS8pfbgkNcCgNoWN0oDMf5Y7DnNWkd7Du3fITWQJldq/AKoehQoOo5zXGBZFhcjdNusanZj4U7rcd5EONRu0cyfYXTviKKI275YjdsmzoBYMBTYe5VqvzYrOBsDUntOvyBi275G1YtWNHKLrrg/uKy4z4b+hdXCpchs5x9r9AvkFtdjWwTCIy98gZ33vFFCF/a87POmdU+PhDfn7QrrOL24qKz7W5cp233S92o75mLLbO72JpcyqcB2pswer79MWoPLP1iBaZv2KeV51xT4J4l2Vmqr/M7Jym4X9j4kt+jkYFDP7ERXIeGYD86SQ1yUaXX70er2JboaMUMURXy+rBArCviD21Sixe3D6a8twikTFiaNSE3okUMALbLRpyU6PqIoYtLyPdhUxu+Ps94loZ9va89/OEYb9owHrJWdtjUyg5lEiItPTt2Ke75Zh+f/VOsJZnVRvNOIWEHiYgfF7fNjQ0k9BEFEi9uH12bvtHws27EWvGVA6aXYUNIAANhU2qDsMxgIA8C5by3Bvd/m4rqJK3X7mlzWOslLdlXjrDcW4/9+2sjdz844amctVJmiAeRWHWHpmse9OB+nv7YItS1qM3Be42w3wzCPUI2+EMpy0bWJu59tVzeXNeDUVxbiT0bYMEIbc0NbPztujSIAr8DE/Wudzezj/1G1rR4sy6/Bsj1ArasX0PKnaj/7Et66txHtXuVe0p7zl9xSXPLecqwoP1pVK54IxI8Zav7b7KpsNrRWtHNn1LV6cM3HObjkveWm98P87ZV4aupWrtju5VjZ2XnRG12WFeTY5Vh1IgxbFF8l0DITYOLMaK2RReZ15vMpbYPg2gzAvuWix8UX1liNUtVWipJIzPtu1gQ6M1/nFJle0yjsQKLExWjAfh8ur4BmlxcltfoJHCJ+9O+RlegqJJxUyhb96M+bMPqZOaqJjY7EsvwavDhjB275fHWiqxIx7OS03Ti/RPyxGy6F6NisLao3NXxRGSuEOJfVmIvhuBPbEhfBT8xo9RyhcirIJKKbKk+Af6/JfWA6eZhsL/gOCImLHZR/TN6Aqz7KwafLCvHyzB26pAvXfZKDKoPkHexzJ9a8BrTOCFlOS3NAQMwtrseSPPXMoNUGTRZEZ2wuR10gXiQLKyC6dRZt9mf5WeFqd7XaVYJruRiF9inUOUwbQVFEVWsmTvtlEt7ZeJNqF/u3TFxaiL0N1lx0tA1yUQQigMefgZvmTFCq61dmAsP57hwQVGLOpe8vV1suCmrh84c1pbpzCCI/azY/4Y95JSfM3AFRUERotrTh3+cAvl1ZhHlMQgU21MC4VxYaWm/c/c06fLuqGFPW6hMI8QYx0RC/2U7PrspmALGLGwmYWP8VjgLKLgGavg1u0lousn8uK2pLxr8iWlt22KpLnasXdzv7TLLPWYvbh2s+zglm0Vaur5Rh2yze3/rndn4SngyDeKKpAPv3ewUBZ7y2CGe8vigu8W6W7qrG58sKyYJIQ3ZG6t5P0UIUjN9t0Qr/EW02BiZ5OxrFHG+RVIW1zqZYmfFH12euuA/wGk+skwBMsDzx22bT/T5B7QkVDXZWNNs+ZkeFtTiIgPGY2+przupYIhHhe3pk8/vMZmNneuZjD/UwOyhzA+LFlyv2YHm+XqxYW1SPn9bpxRdAE6/PV294DavPZ84O9Wy01QZtR7mS7fnYF+bBp+mopacpDRk7++jxCWgJw4WojekUZqZrAuJyrQPVG/c1tGN9ifH3xSNUoy2IoqGVHyDi47UHYW/rALyz8RbVnnBnZvy+6MWfKW7e33Cf6s/21QC7DwFqnlOX0YiAaQ5B93exMdwEr1rE5gnSosifXQvn2/K7tkKs/0i5vsqKjX/GzWWNeOqPbbgnkFDB5xdw1Yc5wf3lja6Q1hvVLfq/S/tsmNWBh9H9wg6UHvlpExbsqMTY5+daPm/UEALPVfMfyiatWzTzOltVcRRTDoBQh1aXveDtta6e3O1sR43nPvkuIy5+vqwQI56YqRwbuNOaXV6IvmrLdUlUzMVoIPiViQ1BEFEfEKdXFlqL4xMJt09agxdn7IjLtYyobnZj8uqSsN5JRhRWt9g+H2vdr32/dUZEr3Ecw2hMzEQKb0CYyu2AKUnwfUfCD2tKcP7bS1BW36YK3dJRxMXpm/fhyxV7El0NS/y6vky1Xl0+Bdh3s2F5ux4NRMdGa1iiRZUgMtCfW5e/BfM26r30rI4sfsktC11Iw+sLrLv2qkOdMW7dgjVPNKutcyLeTyP6deNuNxsCmyWqtUtjmxc5BTVJOyGZKKiH2cHJTHcautSx8fNyCmrwt2/XocXt04gkJsFfVbk0jMu53OqBndWOu/ZZrWpWZmpcXj9W7lbO6/YKaGjzoK7Vg5Neno9L3lsOu7AxjbTJGdiqfLioAE/8tkUVj25zWQNu+2I1rv4oR1WvUPjdBab7zWdY/DoBTibUd2w0k+VvXWp6XCSoLPvYtbrXAW8BUPOsadIZp1PQNeDtjIWq9k/qkqEOaixfl5vQhekwOB1+QGgNOeARPPtUghb7Jxkd+cosdXiCoto22xl0szjCANdy0cb7kydOAno3+L9+HdssszyrUjXK793uy1TtMWqr/AHLxTafvThzdW4Dy0W2fTTpUDS2efHiDLW1pAMObCipx5HPzsXqEv39aUQ6UjerndD4XXCZvU+z0tV/f3lje8xirpU3JC4r6G1frMZ/f9+Cp6dujcr5dlY04Zw3l+CCt+211ZtKFctx7XffGTFr3pNhnMD2d2QiDJuctMTq+27z+PDVij2WPTfC5YnftmBXZQsmzNqpCtXSESxkBEHEg5M34Lk/t6dE8pOd5WorsIeWPga4jROTebyp+24l4o9P1FsuXvtFCe75sQ6lVUWqssnSXLPJCVXjsJaZ+sIcrHp+mCU1DJd52ytx37e5aGjTG1UAxvGjzfrmDVH0vrr64xW4+fPV+GW9fYG4I0PiYgeEtUjMTHMaWimsZ1xsbv58NeZsq8Tjv26Gv10ZBIlwwuXL4B7f7rF2+2gNLFQPvb8e8Khdto1obFcahH/9vAnLmYFoQ2sDjn5+Ho59YV7QMkbLj2v07qQsrCWINoad3LiKoojX5+ThhzUlWLBTsXzYVNYYnPHaXNZg6e8BAKH2TdP9fkEwHgSJfjgNYnqEEheNLNX47sHRR3V5UfneHS7Fak/7J6Q5RJ2lWLu7QSnvUJvH9+qqv2+NErr8sOsC5joC4C1BqPk6v+hUieqCanbQ2su4OYwYWpkcF1neTJxfFKXnywJeQ8vF+M7qVxiEagAgtUOi8n25/Rkqy1WPn99OiSIAhxMt3q626mLFLdos8UNF1TLdNofowgcLzScUeKSJBhMWta8Ce44C/NZnsTeU1KvaUkD6mwxdZyIc+Qsu5X1y33dKQrB35qsT+ZwyYSFu+Xw11sUg2HYiRRnZ5Wnm1vKonG/eNum9Y0cwEUVRZVXg7KgqlQ3cfuPvIBliMmknJoDYDN6SgVhZir48cwee/XM7rvs4J3ThMFGFffAJwZBAQMewXKxnBvVfriiKaViUaMB6NAHAmorRpuU/Xhqddjna7ChvwpmvL8LUKCRViwW5xXWWsthv29eoa08b27x47OdNIQ0x6lo9+NfPm2LSJzBi1GC+x4qMXzCemNtXW6xaT4LXCADN2AQOoPk3oC0Hoj/07ycdYw1nGJaLXr+AScv3IM/ANfyeb9Zh9rYKvGWQ+NHIWtKsbx7NSWx53D9zS3K2I4mCxMUOxqbSBvz7FyVmRGZ6mi1T5Q0lDWhpUgaAm2oOweHf/a4rJ4oimtxsYFsTy0WtuMhaeO3qCxQeDHjVjTIPN+O+MH2z+kEuLl8f8vjHf9ui3lB0CuBVhFjWclHrKiF3En/IWRvctreeiROkSexgFX8IMU+a+TY6oaBy8X173q5gRzdUn9YogLAQwyZBnTna4G8qu4xZUd9TTocIwa+evWp3KZ2O/JpMXPHhCswPhATo1cVAXBT1FiGrK49krirXLZS4mKayllPd11GOZcLCmyzgZYsWRREQmtErM3Q8FyPLRZcnOWJhfbn9Mhz+3e+Yv2eoavv2csUa67u8S7jHSrqrA+0+JomFJ7SLl0tjGRk8H/ObmYmv2b41+o3+fbaFLlEUJcGbR/XjgHsLUPu6pXMt2FGJqz7KwVUfrQhu8/oFnPf2Etz6xWqukOiO0G1MNGhTyuoVcYxtD7bta+IVj4hYaTI+v4D7v8vFx4tDT5BFyxPHbgdeFEVc83EOrmEEFn8YlWlx+zB/e6UueVqq8ssG4/ssETE6l+fXqATjvAp9/cIZvKUCsRqEzw0I8fsao2i5LLQCrYsBUXoO2KyypfXt6knqDiAuVjYp/aWvcorw8JQNCaxNaLSeWj4xHf9ZfnfKuS0+OHk9imvb8PCUjYmuio5Wtw/XfLwSf/16HTf8EMsl7y3H63PyVNten7sTP+eW4abPVpke++y0bfgltwzXfsJzOQ6PFrcv2N+dvbVc5+4fqollx2xi9bPwse9Dh7qvU9XaPaw6ZjrNv1MjxuzHn7gWWMtFbymw9xqg5FSIFvsBVl+H4SQenLy6BM9P344L3jH3xKjmWPID6roN6d0luGz2vNeGuGdD4fML2FBSr9IJ8ivJApqFxMUORpHGbSEr3WlLXMzOcOKnXWcE17/Pu1hX5rf1ZRjxxEys2Ws+wyPj9mliozGtQdDEvH0V/ti4F4vk5C+iPp6U28R91Am+FUfPTJMH3rUKqPp3cLXFZMa5qV3a998/lThpbIISlbDEiFJNLi9yi+tMAuqaP4I+QTDWuEQ/0hjLxXcX5GNaICN0KNHKSFz0CzEUF8EX4lhYsU4rWLd6s3XHtbnqVeU3lTbg7m/WAb4KZDr0AwpBFOHwmgtLTiMhh1NX9d8UOuYii18QQ4rAbR4f8iqaVTO/vAEmL+OhXwAgCuiZGdqV6bNlezBxCSOQNH4H1L0Ptydx7qQsz635GwDgoXkXqbZbce+UvhlR3Snce5NR8dDnY77qgirj9oV3jzuY/63i8QuGTcDyfWOlBdFaZ+nndZLrRmF1K3x+AXWtHuyubkFhdStWFNRyY/9oY75WNrmwz4bVnNkEitzJZzuOg3qFdl+vbHJxLfeMLM5Cu9tbZ/bW8qDFxeK8aszaWoFXZ+8McZT5TLoR8nuDFf9570G/IOLbVcXYzUmS09TuU3kpSHWxXRXc/10u7v5mHV6dlRe6cJLj8voxZb2xuBhvHSJndw1u/WI1Tn1lYXBbs3ZWFsYWp//7fQuu+TgnZcWsWIm5kU6McCm7DCg9G6h9BQBUVlU7yptU/cgWtw/b9jWmdEIprSv0orxq/GwQrz0Z4IWZmbLrLGzd18gpnbzwnv9kgRUUrXjffLJkN678cAX+MmkNBEHE3npr/YfCGuV9ZjQBbofyxnac9upC3PGlZCRy33fr8dyf21UWlKGs1tn+zBXfDEarqo8c2Nf8B7z5h2FtxbCw6rl/t/As65zQf0f9suvhFxlx0aeEQ7PeLll0i7agNVQ1uXD/d7lB68FtFp9Lo3cf269ii1jtb1WaeEsZ8fb8Xbjqoxw8++e24LZYh95INUhc7GB8uaJItZ6Z7gzpAsU2MF0z+ZmXWB75yTh+CY8Wjfs023bL1kFljQ489ONG3Blo9CHoB0kuk46ix88XGZo8IWaORKVBYGec2zx+lDcq+1o52acdgtKpVLlK+kXc+806PP/ndtwwcRWu+XilztISkGZWJuddaFo9qYNhbLmo/Wlnb63Q1YeH32B0GS+3aPZPanKn4bqZr+KrHZeqxDpeHE+fqL4/243Er4LBEFv4Wc4dIcRDxUrM/DtcVzUaDe4ewXV10GTTQwFIwnGo3+mKD1bggneWYj7jfvLU1K14So7fJoqAv5lruSgJnMbClJYJs3bC7ZLuH5TfBlT9E+2uBCTCMHHl9gnqeyLb0RD6dIIDENW/uehRZ3ReXViL2hZmZlQUDa2xWddts76UX+DtdMBhEMrACJdXMHwub537Et5cfyt8AqR7oeJBoP5jw3OxLm6P/LQJx74wD1sYy5t//6rPlMjeooIg4qSXF2DcKwvRxmkTeZjF7T311YVocftUWemdDofhLDVbh1NfWaiyNv9qxR4c+uQsvDxTcifdWNoQ3Bcty8XqZjfu+249bvpsFTw+gSvqG9bbhsDg9vkx/i3JmvSX3DKMeXYOFgcm3prr5uvKT1y6G09N3YobP9VbgvAG2yrLRV9N0ArLjGWBxHDfrTb2MhAEUf0cJQkrCmqwda9yn09ebR4iJd5u0cs4SfcOHqDvu/DaG5fXj+9XlyC3uD5mMUtjDSsCumzGIDYjmucSRVFql9oWSRsaJgLQu6+zotDdX6/DJe8tx89hJGxIFu7/Xu8V9Ngvm5GzOznvNe0YSCaDE04mmeF53iQLdS0NwWUjQwUtG0sbsGRXNaqa3Ya/hdvnx9xtFWjiCJZjnp1jyQ3bjIlLCtHQ5lWF1AKkOMYyoZJ9sNmidzUciP/9rghMQS+NvVfiq03m7vhm9MqyaAXn3qZaNernqNyiG39QlqsetnQZMxGStRC0Ii4+/cc2zNpaEUxcyWoO364y7lvwjCq+W1WMeduVe4J9j1h9hX+4qED1+1s7RjLECNWP6MykVmtLhIQdUAFSfDajmaXzjxgIQO3aF+77zMwtellxX3VZpqFq8nSHy5eJ6hbt8fqWwayj6AvX4s6pxGFjBcS/fZuLUyYoVgRejrDp8yoiCPtC2ljagLnbKzFpxZ5gxus/Nurjpvy5YTsKGs1ntr5ZWQyx6QeDvWrLRUB5uYQaHBm9QEO5aUcL9m/6PHcY1laNxrOr71MJilbqYhDjFwAgcO5JUQxtNyZZLpq5oyv8dcEzyvVU1quh8fmN49yV1behqtmF/IBlnGxxJhN8CZffDuT3hK9dbzklyuKijd9UrLhfJcS5vAmwXCw6Tvp0bwP86pe+WxtXseQ0oNU8e7X0FYvq+JiCIoDM2VaBGz5dhas+YuNyGf+CTzKJOcyTQui/d4cDIS1ntbi8flOB7v3NN2Ly5iFA20JMXF6Ocz52Gs6isrEWZSvnx37RC4oscsc0b/tzOOXlacHtrLuc+fHG919lkxsLdlSitE4RFz9ZshsnvDQf36ws4h7D/g2sCPnNqmL4BRGfLi0EAFz54QrdsTJFNa2oCUMEY2N87qxoUrkBhXK7s2O8VFTThoKqFqwoqMW/ft4El1cIWlu0tiqxh+T249uVUnvAE2X54mKgMq7NQEF/oEzvoWCEmQXJ377LxXEvzsemQD/E5fXjm5VFqt83XqzZU4fTX1uIz5cV4pbPV+PS95Ukb6Esb+OdLZrXt2nlZAPnDd7+yFWeX7uiqMvrx4XvLMU5byzWWXDE0wqSFX7ZRIORwrNc3NvQbnliREYQRNzw6Sqc8NJ8fLXjUny38yI0ebK4ZWsbFau+8oA79meBNqkjMYMzYZ6K9MhMTmvfnjEUFwVBhM8vYOaWcqwqrIUgiLbajtenKxNcbm1omBAhrmpa3MhgQvvk7K7Bwz9uQF2rB/d/tx73fpuLBwKCtuitCJZzeYWIEwpWMOER2PcY+470uc2tcv2i2pBl+hbFm62iCcF33ZrKI8Kup6nHHcueMcHF7hltcHAsFwXRqXaLhoAV+8bikWWPoMFtzW1bFyPflRuckGQnWHl9wsY2L6Zv3hd8x2n7pl0yle/zqalbg30HLU4HkFtcj/cW5Ad/uyc1SfJYrw6rYRC+WVmMC99ZFhyrh0QUkZmWvFbFyQKJix2c5QU1wYCjWspqq/D0N//C5vzpwW1ZKMcRfa0lWAkXdoB23tSPMOq7X9DQrh2kRUdc/OfYyeaVcSjiYpvH+Pwev18nBLEvGTb2QrtbH+OOZz26IW+abpsdBL8fS4r7qbbJmZBFwXzg7BNEVDW7dA2wVXHxsWO/tlFTPULFP4LLrV7le2SFCDNBRWZTuXEHjGf5KEIM6fZslCQnFILgDQpzohDaYsIniIaxz855c4lK3DYSIX0NkzFl13koyP9At09K0uHH3tYBVqovHdO+CYBS9zDyzUSOdw/QvlLqOBUebFpUhAOonaCyvtMiW3CyrC4/JLj801qpM1lS1wavX8D1E1cGhZxQGN4p5XfBz7n/HA7AYTGItozLa5wVXmZHdXfAX4MJ6+5CYdMBmB4QDrXUm6nxBogCANcG/N/0PqhsUWaZrbrU8J5DljJNnLLcYmnS5uk/tnHL/+MHJeYX26wWMu+5dpO2vKrZhbPeWIzjX5xvOw4XOymzs7xZZYFhJet7i9uHV2fvVIkpPLQJd1havUpcodV7JOv5cpOYcrz3ZnAg2fAx1lSORsHe7ab1YTH7ymQrgq8DwvC7C/Lx9B/bcPF7SnKj3OI6vD5npy6ucbS59fPVKK1r5yZGCfWzhyUuCi1A81RAsC+k8kQwnlWs06OPqeVp3RhctlvtXZXN2FnRjMKa1uBzB0iToaOfmYO52ypMjrbO8vwaXPdJjmEYifUlyrXNnt1IWV9Sj1NfWYi7DUSKnRVNuO6THKwuVFvsT99SjjWBZ+3Z1ffhyVUP4IJfn+aeI690o24bTyi2yrRN+/CVJi5ctFldWItPluy25b79fYpZ7Rj9aUN6JWcM2Z7Zyrs22m3lHV+txcH/m4W/f78eN366Cpe8vxznvb3EssC4rUp5B1383jIMf3wGHvtxsXT/NE81Pba62Y0s5r1582erMXXjPrw2e2dwYkG25Ba86vbHTogvHmy8cjbxZz3j5u3zm/eRzPozD/9Wh9NfW4RGd7ewxxEA0DXd2qT+b7vPDi7/9/gvuNcU4NCMMxy4Ze5L+G33OXg19w5L11GdtfJhoOj4YEgx7SSUdvLx3m/X4cHJG/BS4D2s/Qm7ZKjFWiM3ZafDgWs+zsFb83bhOwMLR49POdbuRFsO4xr/zvxdulicQby74UBythnJBImLnZjtlSK+2X42bviWdTUVjJMHmKB9cRtlqAbUg7A2XxeIcGLxbqWB8YuiaqZFxu1tB0rOBure1e0zEhcznKEaAdZKy8Tt2uvSiY+sebyn/idlu58f609LmmDNrcRIWPAJPmyt6qXa5gjEXvO3mye4WbSzCie+tACP/qx2cbfqFj1+KCdZhQ0Mw0iqlkN3JHL38q0HAL44KVkumr905O9AFO09B0L534DiE6XltuUhSksdRn/LHON9zMvRqMbf7LwU/8l5CE+vvEVfHxEoqbNnneUXBFW803ZvgmJFNU/D+qrDUNtqXn9BdAKOLrjsA+PvW7JgFVSJRW6Z+yKKaiQxaieTpS63uB5r9tRh8a4a3Qy1LRq/hN+vFxmk2H/2vlOv1x3yufxh6xAUVCu/m5FVYX0YmT6FsiuB0ot02ba1bZooithc1qATs0IliXp9Tp7O4t4M1qXp6xypkxmM1RvAq3l/OBgVks1KyIsxaQb7TLZ6fCpXHbPJKZn3F+bj48W7VVZ0PMxE4BZGXLzx01WGWRYByVLjonf1Wcvlv6Ok3onrZ72K8VM/sW29YkZW4P2/PDBIZF1Fr/l4JT5ctBufLYuONZcoilyRmCfOyeKJNo6oFvl0oihiS1mjNXFo3+3A3quAintDl9XAE4C5gkL5jbpNqnAcNq/LXoNdfujHjfD4BNz7bS7vMNvc+sVqrC2qxz3f8EU9tr2KSZzEANM2SpMuOQZZau/7Nhdri+pxw6erMGNzOR77eRPcPj/X8ra8tS/3N1pfPUq3rdWkbTC0EHVvA/x1+OcPG/Dsn9tRUBU6MVu43PDpKrwyaydmcDKennFof+4xh3Dc9pMZwd8MVD4CtEdm/RZNtu5tRE5BDbfd7ZaljMvCmRQ0Y+muatX6jvImFFa3qkJBmXH94Rt1237e2IqymqqQRgHVLW7u+FCbLwBgYvIHyAzTtd3nF7CuqE419mTjRm4qbcT2QCI5s2zQVslrGI7NNYeELmiA1TH4I8seDS47HOCG3BFEJ4SWWcF1tttW1mLN8EAlqDZ8KH3WvyWdX1NVrbgoT4BOMYjT2jVT/X0bucyzBjrPTd+ujhEfwO1TjjWKuRjKIr+0rg3vzM/Hc39uD/YrRJEJ9+LINPQG++/vW1I2NEm0IXGRUOHypWNLbfiNokzPDGMT43aOSwobS01KdMFJ6NK4EGhbDHDiRBhZ3BkJSVlpgYai8Uvl/CZZMJvcabpGg3VpzvQprkm8GCS8xBhpDmuzH0Yim8dVpNvm9Ehm4n6fuYn3+wslC4jfN6jdta1aLlqtO4vKLZVNrsHGdFNZLkbWPPG+N0EUQ8a8a/Z2Ayofsm0GIgrtkrsAANFCNuKmvJMh1L5n/dxaGr/BmkrjuC4zN27ElRNDJ5pgETTiYqJiiq8q64WrZ76JcT9/aVrOLzpVoQ14CIHENlr2BDqzrJtGNF0BeUapDofddC6AWHKOJSveG75ThHaj2DvhWEAIbcsBf6Wu062djJmythSXf7ACf9MIElaSRGnbIatMCswua+NsaWOQpjFfSLpTqY9WlAyFlzlvu9evsgiYuz20lVcBk1GQtRTTUm+SzVAr8uqyLDLxE9+Yy0++sr6kAb+tL0N+rXLPXPbBcpz08vywnwFW5OzbTYqlnJ5mfN9uLmsI6zpa/vr1OlzwzlJL97a/8RcAgOiyFgpgUV4VLvtgOca9shDnvLEAc3NeRWXVBl35ikYXxObf4RecaK75LWQ9qppcmLutIjh44VoucrYJogMen6By6efpwSsKaizFJ2Ov8fCUjYahCKLFnprQycVCxTxjqW52BwezzS6vaXKJKWtLdKIKPLuB4tOBQHzmKiaswAOT1+Pn3DL8tK7MMJngWiaZixlG4vT6knqMfmYOPtEOlF1bMH3hffjk9/uDm/Y26PuQVU0utLh9mLWlPOjq7fL68ersnabtCwsrTm/d24QVu8rx6JTVQRdSozAIY4f24m6PB16/gGf+2Br0OmA5ceBWzhEA6j8A6t8Gik9QbU5UEumVu2tx6fvLcfPnq/Hrev0kFzt5V9sSXXHRiCd+24Inp24JWS4rjf+cebw18PjM3/c1LfyYi6wFm9MBbCipR37DgaoymWnmbcOGknpMmLVDN1nz+fI9uPaTlar4fGxs4DVFdbj4vWXILa6HVzDPO2Dldrl+1qsob+OL8lawG5cbkMa6Tk7tRNEBv5s/kWd1Al307ASEdsCr76cJ/gbVusfPn9iW3zVOv3oCQ2uNmuZ0YNHOKhz/4nxV/4wtJopSjHhdPRlJy8grpSHEBHu7R3nWXAFN4N0F+TjuxfmBUEJOw3Hy5NUlwViSnR0SFwkVa8tCZ+oMiShAMHEL5bmPsf1oQRTh8+vLuDzGL1iv30BcNGikWeHK1bQKb/7yHNbuNrekMJvF75bBJH9xc8RFt9JIyo2eMwyBjqV0+826bU7vTqBgOIR2/QCIJTuD/31ZFfTCefm9seH24LKRbsdujjT+I292SURoy0UAQNt8iF57GRFlAaiwugUTck4MWb6hzWX5bxRa9dZHKP+L6THryjJR7+pm6fwy0gy6cl+6PbGzljBj8Z4+0vX9xpapALCu8ggA5rGJ5JiLWtI5LjYhswrzRF4D/Jw20Omwno08eB5/gyUr3tr2LiHLhIPcJmjd61WCSNV/8NUyyZV8iWYAb6Xudjisd5Fum9bNWCuQPTBZseRmO7O87MqGiD7Vb+ry+OFtV+ryv9/5g9r9e2UGl9k4Wk9NNRgEA3j8N+MBHusWzWXvtcFFs9iCj/y0CVWtykBq274m1LR4cP3Elebn15BbXIczXlukypjdr1sW0L4WGQ7lnS1bhsgYWnr664C2ZcGXxJxtFbj24xxVvKy8imbUtLjh9QtYuLMK+VUtlmImrdv4PARBhNC61LSc4JcGINM3SQOhxnYvCmtcuHfaGJz01j78uEZyCd1Z0YRz3lyMkycswPubb8RNc17C2B9+RFWIDJQXvrsM936bi5/WleLbVcWq+HVy/4AnLopw4LqJK3H8i/NRuHczUHwW+qVtVI4VpXAnt3y+Gn/9eh2qmqV6uLx+fLS4ALsqlfZcFEW4Nc+JUSgCQBJab/x0pS57cKRoB4FWJ0B2VTbjhJfm4+bPV8PrF3Dks3NxzPPzVGKYLHIDwH9+3YJCrbhZfgfQvhwouxQA32qmsc1jaE3ZYtHd2SeIaGCsz0RRxOTVJbj6oxx4fAJembUTBVXNwd8LbfPw4JLH8co6pc+kFSiX7KrGiS8vwJhn5uD+79cHY+d+s7IIHy/ejWs+VmIIC4KIDSX1XAtZ9m9rdnlx25fr8OuGGrwzV+pDGrmJpok22s4oM23jPny9shj//nUz3p2frwojYdSnMprw1WoQ7R5/VCYZ/YKIb1YWGbZLU5kJtSV51br9Po8ihBm6aJrwx8a9ePSnTbrnycz1fVl+Db5bVaIT6T9bWojHft4U/F7afXwBTmpTzN/3Pr+IzDR9HXp3VZ7Vbpnp+DsnkVCm0/yeu+qjHExcUoj3FigJ+16fsxOvcISoOo416K/ry+IWd96c0GOUg3vpwxLwklUKogMC403H9sc8/tAJXAFALL8P2NUV2H2Abp/fp7bq9nnN+8gVTep7a3OJWlgXRBH/99NG1LS4lQSvME+eyEMbcqqmxY2bP1vFFfKBwHPhr4ez9MzgNjlExzvzpftJ6rP5I/Nq6iQkw1NE2MVXKZn3uyWrhLpWDxpamuwH3IkiqgFk6yydOTsLr5/GbvMLIh79JV9XxuUDNtUcglpXT87x/M6A0UCedWmeOPNdvL/ueCzKDz/AHDvb1dSuf2mVNEj7J8zcgeNfmo+KRpdlkcHoZ3X7M3XbHBABX3FIV8QuGcrvlV/ZHBycW32xRhJPRILJCq3KEK1c3+3PDD9RD/ivZ1G0kTlWtHc/yCKMkcig5ZqZb2B60RmWyi7Ze7RuWywed78oBi0X/YITJXXWxbRowlq5uhtmG5Z7evX92FTZ2/RcAgB49BZcaU6HLj5ayHuj9pUQBSTuXfg/CB5+J8aSuM3gF5wh4xbqrxE9BNGJ0uaBuu1BS29PPlD3GjIFfgwuK1aXofALIh6cvB7PTtuGdKd6kD1lbYnKxQkAmkxiFrLiossrxdJ99KdN5hYbog9fTfsbfpj/cnCT2yfAZ2ARwLJ/ljLR4/QqyVjCzWAdckDQMjW4WBFC5Kpq0b9DNpQ0AM2/Az5jS0x2gHrTZ6tRUtemSsThac0Fik9EukcRKi9+b5lKBNaKJaIo4sNFBXjxh+cw4bdJcNVLFoB/+zYX64rrcfKEBahudqOgqhkXvLMUZ7+xWCWeWonHdePsV/BVTlHIJ1AoOQdo/hNds/j9mOf+lES4C99ZFoz1+daGW7Gm8kgIYhrm7zC3iJXv1/k7KnUis+zO7fHphStBdAQD3k9d8QXQvgRd/cp37PUJ+GiRYgVXHrB2+2BhAV6bnYfz35ZE1comF059ZSFem61vF40sPu78ci1WFdbpguhbgZdoQEYr3Jk9uyy/BkIarNlTF0xk5BNElQu+2YS0NJhUizrdMvW/d7PLZyguhhKRWY5+fl7QvXrDzt/w39/V7c34t5bixJcWAG3Lue92rZD5/gJ1H1kWqPcxFo7yc/r96mJc9VEO7vtOmiBv8/gwYeYO5BbXq0T+dKcj2I9ZWyTdw752/u/Ny94aL+oblXv87fm78E8mDq/PwK1V8CmWnEahBNo9fpzx+iJc9dEKW/Enefy+YS+e/mMbNywFoP49u3DuO1+rYgEVTrbxh37ciF/Xl2Hqxr2A4AZ8gd/TgqkmO5zyeN14aeYO/JxbhplbyvHjmhJ8tulU/nEi4BXM7wtBFNEb+gmsLMZVOi3NwRXCeaIkjw0lDWhs96Ku1RPM7KuFFyLG5fUb3j/xxMr46qwD1MYuDoNpXAFOQ3HRK0SSNMiB/PIaXPWJWgT2FRwKtK2QJgk5yX3KWxWL5w8W5uP3TZqkjT6Bm0DV6dNrAma0VH0hTVIGeGf+LuTsruUKzTJi4/f4YMN5wfU2j18VRmG/7pkqzxDCGBIXU5F9t0jm/SVnwOX149w3F+KUV+bBXXpDYuvVGsgg5quw5ArH8usWpZETBGDmdv3s+IqSXrhi+ts49edJun1GrhtGrzkRzuCgN7/BPGOzFVhxsd6lfzlVtKRjeX4lJi4tDLzwCtAlzV48PC28l6CSLTqEuOhQZk3Pe3spLn1/ORpa2y3/bk6TwYIVjCwk2VfqxdPex8HfhJ/0hvf9bMhfps84rGHc4E2ButjrXMr3U5ONLCh/FJ5l6xosZgJ+uAh+F1AlxXF5YMl/UNy8f9SvYZfX//zTdP8VP11qut/vbwdKx+u2p/vygV1qy05H22LjE4kihHZriV7mlpyCyjr9wN0RhqL0au4dqHH1sXVMuMIVD0F0oKpdf/3ggFv0wONPV1+zYGiwYxdJeAPZ1W/prgpM31yOr3KKsK1OneTnP7/qRcHvV+kTXwDA58sKg8IQAAzp0YzqZjd+XV8mWWy0tQL7/gIw2ewBoK6hAM+uvBqTd54V3Ob1iyo3aSNYq/bmJsUd18xCK8skZnEocqsODy5XmiR6AYB6l0FbuPdquAuOwSPf/oRpa1fo6lTDuOnx/o4Ji7rg0G9+Q075WNX2WZuV36XN44fPL2D44zMw/PEZmLW1Aq/PycPnW8/HxK3X4pMl+sHEyzN3YOYWSfRsdvmwt175brWD0X7d+VbPz0/fHvKe9AtOYO/lyDSI2dw3qwLw6a2NZAb3suYBwhMhZXHR7dEn/WEnGZraA26rbGK5slvR6lZ+m4d+3ICpG/big0Xq52HS8j3Y1+jiWlU1hBD3QrmV8eiTZWwB3+5SuxYvC4Sf2VTagO9WFetEnnaPH43tXmQxbpRtzcoAV26XfM2LYFZVWWRx+TKCYp6Lcy9PXFqIrWV8sbi60ZpbtMy0QKKtkkJ9AjaZxTkPweXTN+BaMd5rIBIN66uETVheUINTX1mIpwIWqYvzquEtfwKfLd6MiUsLcc3HOarzstY+Pr8D8NXAb+DmaCaALNxZiQ8XFVgS6FxePxoNfqhWtw8/rCnRJbjKanpNtc5ayxtZFYneImWZqRb7TO2saEJ1sxtb9zah1iA0hRCwSDRLyrV0V7XKkltXF1FUxbfkCWnNHr3XSV2rB//4YQOW5Ru3PfL5ZdrdbmDP4XDtPADwlulChvBg49W2Vn4YXH7ox42mVvXFdb6QbWtRTSvK6/X1d7kVq8Q0hwM+n95KUSsuTlq+B89O2waPT8AqJglTXasbY5+bi2NfmGdYjwbO7+sXxOD9s+Cqv2FIt+hlrreDlQlo3oQzz2Cl3ZeNdSWsxbqyzxNiLBQ8hjuSTsc/vp+H0kb1BKVHSAdKTgPy9wN2D1ft01q9vzF3F7R4fAK6ZOjbHKfPPAu5lmt/OAy3fb44OFkWMrSAKCJ3bzamFipJciqaXMC+m4Lr/bplAZTMxRIkLqYibQukT38ValrcqG/zo92XjcKytdg/QY2hKDqA0vOAsquByn9EJHwILfO521eV9QUAuPz6jrvR9cysA9/ZeBNyqw5HpkH8EDuwjbTLwGXg1i+UGRCf348B2day7RnGXOTEBmnydMM9C/6HL3dcYXrObKe+U1xV9hkEi79bpJaLRkdHGmdR5vX1t2HpvuN021+cn6aL42KE3YQucryPTJM4Y9GEZ7kaKT7RCTR9AwCYXcyfnY4HImNROHX3KRGdS/A1cLenVd6l31j7ArdsZZML57w6GR+vsh7Evqa9t26bAwAEfjIBI3j3cSjsWkeakVs1CtfMfEO33R2IuejxZ2D81I+xqeZQZaevDCg5A3DviMhysahGug/W7bA3ydDNt1i3zecX8OKMHdjMZBZvc7tU31TV3m9x2y8H47O5P6uO9XBm+H1+b2j3OdGvatPYQO1mIs7hg/XW+YAcp9H8+2R/K7NEEgDw1ZbjDff9tPNY/LatG/75awPgb8aIHkrnfn4gnl/e3iLD4z2Cvn1auVuxhmz1+JDPZKn+r2bQ+vP2Ebrjf9+wF2/NUwYk369SluV4fnkVzXj8182quIQshw7sHvKevGnOBFz+51vIaNInjwMAty8DIiexnAxPHF6UV4VxExYEBSYjPD4BENq473e2L9DkkdoiQWPt3zNdES2Katvw8JSN6pMIraZWntXNmu+tdbFqVRav8iub8cmS3VxhBKKoGsWy/TBtbGtX5auq9Q0lDViWX40rPlyBJ6duxUM/bghaeoqiiOsm5mDsc3OxvUSZvGks+mdwedV2SVBoqTO2eJfqIaCsuS+O+/F7/HflgwCgs4CWWVfCzwDeUPGZ6TW0yG52LpN39x3zn0dejV4Yb66ZCuy7Vfpeq5+F2x06puLrc/JUMYUB4J9THdhRtCS4/uw05bnzepR+oU8QgYL+8BpYcpkJh3d9tQ6vz8nD3O2VEAQRd365Bv/+ZRO37A2frsKxL85TxcCT+WFNCZ74bQuu0CRs48X8Lq0uDtTbwHKReeb9rcrf7/fWBK20l+5S4qo3GCRRmbu9Ak//sc0wKZfoq8ftk9bon6MAda0eVVIyAJi+uRz5lWoBnvXQOuswKX7fq7N24M9N+3DbF2sATxFQMh5o0d/nrFVeT3ENvth4FA7/7ncs2rxYl+yMx/9+3xIUfFuazePTsvy2sTFk2zp14z5M3n60bntdneLG73QI3Ik7rYHn89O346ucIvxl0hrc+Omq4Pa8ytAu+7w4zz6fC20+KexIl3Q3d/xY7459rFErk8O8p89oXPbi6uuZ45jY9xZ9XHjjMrdfxM4anhdhOrxCGq6c/gYeW/6Qat+Zry/GAT3MJ2TcPgHdnHodI9NhPwzDsn3HYus+qb8XciLYsxNNbvUNtqe6FX4mLMSaojrUt0auF3QGSFxMQUqbB2Dcz5PwyZZr4GNmWl9ed1cw2Pvp+5tnC44ZLb8DYntEIlF5wQO2jzHqUJg1ne9tuhnXzHzDMDixHUIFAdaVb10d0nU59DX1A975pSdhXmloMSZT1M8cOpq+s+wWzYvtYQfjhC7REeY+3By+FW+wPu0rbB0n193h2R6iZHQIZYEZDuE+t/8c+4PhvstHLLZfD7fiihVOfE8Wn4HlRTrHKumPwjM5JYEPFmxHYUNvvL7ePM4lS42rN2erA07EPjj75vw/8ed6jYVBmO4c/1vJb4/dbUUAgNKSH1DSPJh/cNEJEb0LLn5vGVburkVNnb1nam+teuDggICaZr01fElDlsoF5491y7Fs37F4ad1fgdo3UVOXjxenb8f6Er3lldfnUnVYD9+PEY1dm4Gya4D21aq/f23lEcHlxrZ2wxiebg9fzCiv3mEphqVYcCge/NI8GZIZp/3yOZ5a9ffg+k85C1HZpgwknvhtCyC4UJL3T97hhrDhjto9fgheRWzUiq17m7uHFG9nbFUEFjnm3KXvL8OPnEQPMr2zvIbZHlk21x6KiVuv5e6rcfXBlFXGVsx+t8ZyVnDhzi/XYl+jS+XCycPTMB2i0Ma1KlFZLgYsm9i+j8efgaOy3jE9P3b1Qnf3FMPdOlGk/i20uxRBvlfXDBRWt+C8t5filVk79clIRA+WLrsam9bfwz3/YU/Oxr2ffwNUPwkAaGvXD/Inr1Ta/2mbyvGXSWsAAAVVLdi6V7K2nJ+v/IbPr741uPzwH07c8806TM8zz4Tq9voxZedxaPV1xQ+7LoSveZFpeR717h62ysvxxs3ERQDYVK6fQH9r5aEoKFkC1L8H1D6H2ma9uPjT2lK4vUrbUdGob0dmFZ+K2YXKRNCCnYrQxebokkMNGWXP1cY047GqsBaP/rwJi/Kq8dO6MvzflI0Y/vgMHPvCPHy8eDdEUcSm0gb4BRFztukTEP22Xro3imrVf8ecEn0f9/Q3t6KwusVwLMC2mzW7lOe6S3p70Drp7fnKZIWRpdMuRrj6aHGBzqK0fe+/OBf3A+V3wVX9Bc54baEkDmq4fdIaQHDhjw1lGP74DBQ2DQ3uc7lb8e9vPsSUdUwDWn6HZGhSdpHuXBVM1mev348X1koZ7P8zqxda20PHpp27vRJf5RQBAFpd1kPjCC3zIfj5765QLC1Tsqx7vc1cC9TMdCZcDjNJsbLQ3oQtAH38VQDrmCRI6Q5/xH3PcLHiGaa1XJSSBdqzeOQlgOEew9n21obbuGVbvF2ws244NtYcjp8LztPtL2vua3otT9tOdE3Xe1yEG7tbtlBvbzdPcCb6alQZqQGgsKYFe5rUiXlOerMorHp0NuIiLn744YcYPnw4srOzcdJJJ2HNGn3DyvLzzz/j8MMPR3Z2No488kjMnDkzHtVMGT7cfAP2tQ7AK7l3wtuiBCZftu/Y4Gz24X2KElQ7iUjiVlw87f2oXc+KCJbpjILlos3YFX5PqeV4gkbx1iL5jnlxKz1iT8tCQKwsF6Od/CEc5DqIVY/YOi4oLorG7jLRxO3PjPq39ffFT+DZ1ffinY03qbaP7MkfrP944eOYfMETeOSY7w0ziB/Wx7o7Q7pD6qirOkAR3mt+IQ2VbfoOjQMiChvVbt9T8i/gnsNV+43t6/KESkF04OBe9hIFhcOqiiPxj59KsHXd9VLs0No3gPze6J0VemChpYnjngUA7sqnAQBiw+fc/dvrRuCKP1/A0n3H2r4my9fLc+EV7SUmkl1bTh28UaojnGjNO0JXzicAHpdyf+5uHKLsq/w3vp/7ND5fvgd/n8KxcvC7UVs1I7g+po8yoSfuGYvZ28pRsu1q1YQN695+YI9SoOZZ/LSuFFd/OB9VpROleKeiF+0B4VZLRu2jliZgpucPCimumFHWMki1/u8Z6TqLjcve/ASLi4ciXHw+F9q95gkxfF6bCaWqnghpodDYlIdpe6zFujXjqVX3G+4TKh4AXAFLrZqX0brNelgDT82H8Pk9qsyXwfMy2+Q2rd2nWLl5/BnwmSTTA4B3N16HbeXGgoE24d4nKzNx6yeKJW+6f19Q7AOADXt2o3RfDoSym/D14rm4+4s/cfvMu3HFz1ehpsUdtNZjmVuwH3K2TgPc21Bar9+/t65Btb4l4IJqZA2mspoGMG97JZ5ceDi3rIyrfS/6ZCjeI8/9+otpeR5/7pHa+EuG8+PqaZmauw1v//EpXD6+y75MdQu/b/fXBU8DnnyIIlDr0ltQ/fvXzXA3Kq6gmajRlTHD42MSowhASfNAlLbo4+0CkmgFSC7Qx74wF8Mfn4G/frUWnmbFou/LFUUqCzF5ua7Vg1dn78SirYqIXFavt0zazrjty+EXWtw+LNnLt7i+/uMFqON8L1r2tmjaRk44lBs+XYXKQDZuFp9f+Y5em52Hv369Fo/8tBGP/7oZoiiipYkzedD8C9D4JSr2PIUWN//5LG90Afn74aEpegvPVUVt+Gn7cNW25xYfika39F7c29CuEtsqGxSR7KWFigBe1eLEKa8qFn5mbNsrWUC3uqzHFW3zZcLfHPl4vcHdxSAeoAPwlgKti9FS9mTE19FS2ay8O9KdfsviW7SxZrnISUhooa/MHmdVPOWNQafvOZ1b9tI/38Ojy+2NnViWb12AHfUjddt9HuMY0GaIgvT8trfuCFlWa9A/adlOjP/lOdU2j8/8O4s0UWtHwZ65VRhMmTIFjzzyCD755BOcdNJJeOedd3DBBRcgLy8PAwboO785OTm46aabMGHCBFx66aWYPHkyrrzySqxfvx5jxoyJdXVTAvbW9pY/CEAvxnVJjyyen13YOgmig9sxjiU+A8tBK8JENNyivRazbgXL+zyWXZAXlPEzD9u1lmTZWKPveLtce60ndInwpWskmNpNXBFL7NZFFmaj6ZJqhssXfbforbUHY2vtwbrtd4yajqdX6wfTJw7cFnzGjP5uO9+H3Nlhj4j0+6xx9cZJP+nFQUF04pFl1jpBvBnYUPDiVYpwIDs99paLMmW1ZRhTdiXQKnX4w7EiNGrLZctZnhXOI8seQW7V4VGJ2elrWQ5PWngdtl6ZyoC11au3BvKLgLfxVwDHAABmMAmWQsV79TfPxZsFyuz9LwXn4TVBxLrietQWj8P9i/8LADh+AD8D77kHrEFp8Wz8+1fpmh8tXI9nL/dCzDjE8HvbL7vRUhv9jyX/CVkmUrbUHoIttYeEfbzf3462lgIAhxqWEfbdDeAOS+frm9UI1L0CYLppubyG4VaraIpZMHxBdAJFRwOH1AE1/8Po783rxOJp3w1P1dsAztLtY2Mib6k9BH9b+F/MKRkX3Pbephtx35HmItnbG2813e92lavWX8m9U7W+Znc+SusVl/UluwWc/l497jqiOyZt9wJQnrNTX1mIwwfxrftunjMBH/aohrtN/2xvruC/27TCZyTc+VUudtXeG1z/dufFYZ/r1MEbkebwY9qes0zL1bZ3xbsru+LY/ieblmto54vuxc3746YfqyHiZcP+IxvDsqzZngtnfasLss1Jkws449cvDMv6vTWAvx53faWE+1mwswpzN5cCsDbp8P2SXwBI/dv5m5bj4XNHItPpAtqWorKxBYBS/1dn70S3DD/eW2QcTqimLV11DAv77tvbqow9g+3pvtvQK/MSNHqU+/WklxfgqEEu/HF7Db5Y1w2FzYdKyaqgxGlfVah83xsLN8DjVe4pGXHvjXA4gM+3XWlYdwDw+Kz3Db7ccQVG9d2DI/oW4tKvFqJvt0zkPjkeDvcGlBR8BOAqAECjOzwPF8FbBUEQ8X6u9fA47b4siG6TxGgRUtfSis2rz8GhvYvx1lq+ZXS0SHP4LSfdjD7h9HlFS/WtYwxLzBJtqc/MEzKNj91lMfQUj5nFp3G3hx0Gqvp/wNA30OYzj4MswgGnpmvFC+0SikhzKXQUYq4AvfXWW7jnnntw55134ogjjsAnn3yCrl27YtIkfVIOAHj33Xdx4YUX4rHHHsOoUaPwwgsv4Nhjj8UHHxgHQO5ssKKSkcAUDWu8cBBFYEr++XG/rlFcGCvCRFRiLtoU+nxiWkjXGJlFZSfwrxllt1i3P9NGtujIXrpGForJYLkoc9+i/9oqL9c9Xn+B258ZNTfyUBg9I+zzZTQL2r9L6NhQMrI1rtpyMbJ7TWvVIiOIDq7IHksEX3XcfjMAUsiHgLDY5OkatGyPBhVt+6FxU3dup++33ecYWjzaxSekWY7hq5017pmpuD61eLvoyvsFAd66r8Kql9evHwhOnXUurp+4MigsAkAr57qANNidXawIQ1lpHqDyH9i5+T7Da+ZUjNVZFaYqPjENbbU/m5ZpbVhg+Xx17l64ftYE3faTB1mPGRYtgu/RfHMXMB5ufwY8tRO5+/61/GHVOissAkCzt5ut0A3c6+971HT/TkZYZJm0/Ur9uXwCNpU1Gr7XH/ilNZi0KSSV/4f2sodCl9PQJ4vvSbCrtit3eziMH7oG+3czT7LBkt9gLr41NOoTHcisrBiLVRVHGe6fuPEky/XQUlStWDqGGlj72tbDl9dPt33yOutJbtiJ8131Q/DC9/8H5PeBWHYFTvtI/ft8sXyPqbAYCvYefHqV0sbKbt9/bipWCYsymyuy0VDyGF5c2AeT11ZjXoGxFfLO2n4qd2aZeaUn4YNN1+O7vEsMj810evB4jr0wE3uahuCdjbcAkKxBX/v9C5z82hY8k3OVrfPwmF/QBSP/OxOLy0ZbPsYrpBsm1IkGe1sH4PLp7+CG2a/i+7zwJwOs0COzDeGJfOHRL7se9x/5M2Zd/mDYfV4rPcv/rvxHcHlfa3+Tkgq88KptBv2aWGHFIpmHt3UlyjYczA2DxLJ8VzGE9gSFk+uAxFRc9Hg8yM3NxfjxSqZOp9OJ8ePHY+VKfSp6AFi5cqWqPABccMEFhuU7I6yoZGQxl5FmscMWNaRm7X8rH8ATOf/glsiIoeDZ7OUPmq1YLs4qspe4gifclhm4jhjhE9LR7ImscxuJ5SKPdl+W4UBYS6SxSFjxSG31mvgwsLLl3kIDi1EjcsrHYlvtiLjFaXH7M22744dLVhp/Rp113zDq2EidNGvIWdxVrhuWj7ZHIoRsQXTE1TqX/d2OmvxTVM/94eYbMPaHKYbtmJE1uV38otPSrPUlw5eqEqYAQNeM9qC7vhyPmEUQnfDYtDqXafZ0wwkaq8Svd1ymK5ffMEy3DQCavV1V4Qcmbr0WTZ6upu36WxvMrc5SiXZfNhpCxKwrabYnpK6pPFK37ccL/4szh6zjlI4dfsGJdl8WGtzdsabS+uAckEKsGLXre1vt9TPCwe3PwJBu5vGp7FLLjT8r0e61KEbUv4N2lz03XwDondWCEwduDV0wArLT3eiWYd191Ki/KrOqQn8fxwPWoi8UPiENazn3tjZDvB2+3XkpttQchBFfTze1DA7FUyd8qtvGCiSsiChPXJlZe/+HEf14AmQo7l34FN7YcLtu+zH9lYzS/bo04Lfd59g678dbrsP8UkVM/njNYFS06QXfeCGITpV1dawwmjCOJk6HGHFIHjt8Mf55/Oe4rzGqb5Glnqku5qJFy0UWXnJU7rU4NWr3m4d2iDZGHnyhuGfBkzjtly+5HlksS/cdi6lb7QnjG268CZ+c/ZJqW7y9NpOVmH4LNTU18Pv9GDhQ3SEaOHAgKir4/vMVFRW2yrvdbjQ1Nan+dWjaclQdz4q2/bjFMpzxFhclJu/SBxeWSUSdnA4Bo/sWmJYpbDrA1jn7ZutnwpfZjCvmE9LQHKFljx1x0cpgIa/+wGCmtFBEak0mwCnFF9OQmAgnalq8XYOxbOwwq/hUXPLn+zHJ4szD7c+I27WyDcRFFiM3CaNYjABwWO8i3TZtLNFIkwcZEYmQHa5luCA64ypqvrXhFgz/ajo+2xq5JYMRe5qGcLc3e6NnuWglBMCzJ32qa5f8QlrQ6pYnLvpFZ9gC/eK9x2NtlXpwzYtp6RP57fQPuy5Cq09dp6Mm/4Qnch7UlR3aPbx4Q8lOKEsdNmHGUfsZW3OFIsPAamFgV/uJAKzw1Y7LMOq7X3H0Dz/i+lmvhj6Awe3PiLpXgh2q2/vERcSUaQsRf1BmUdnxmFdq7k7MY0/TENS0xzbDa4bTjy6cJAThwsZmTVb8Yho+2xb998pl042zsFvlqH76Pn9x82CcN/VDfL3jUtV2v5AWcoJpLieBTDQ4a8g6PHmCFLPY6sR+MqOdGE5V7hz1B4DIjSjsMLzHvuCy3diJMrESQ2Uhc+LWq/HjLskzsT2Em3GyEGoih+W33efaOnef7GZ0zwgvgVFHJ+Ul1gkTJqBXr17Bf0OHhh9gPCXw5Kk6nkauZ+lJEFRU66IWyiw5NoiWguPaoU8YSRG0FDcPRjNnsGsHI1dwHkf3Dz0w+z7PWBge2099fKRfqSgCcOlN0JPBchGQBljhsq1WH4w4FhQ3D7ZkJTCsRzlOGaQPEm4HI8tFFqMQBFprMpZ3z3xdt80vpsXFui8S9+SuGdYzKOqvG797fF1A/Hpp3V8tH2M3ILVRwP9oUdI8GCsrQt/nWWke3XvPLzqDQnALx8JSENOiKuREo3O/rU4/wx5J8q54onVB7pWpT8jSI0OfpdMI2QrnyP3yMe2yR4IJn6xy62FSwp10g4lNK1k5w8HK/WrEY8sfxo9RCC0TTvImIHRMxmhT1S65jofybLlz/rNhizxH9tsduhAH1rLMjAynl5vhNBT/OS78jO6JxiukBY0bPjprAr4//3+Wj+1r4KoeLYZ210+mTys8E/kNB+KZ1eqwEz4xTWdBHWtLV5lhPSpwbH8p0UQ4FpGJhNen3FZ3MFaWG7vspwpyHy2eCV2ymTwJVq7LLxGb+s4oOg0r9o3FhHV34fGcf3LjVyeSUX0KE3btxMXlTG5iOsrp168f0tLSUFmpbugrKysxaBDf3WXQoEG2yj/xxBNobGwM/istjX0mzsTiVVla8FzP0h2+iG94u24xPDGgV2aLymopEXEgnQ4x6gk2+mTbzGDJYU/TkCi4RVsfFFuxGjWzVtD+dlGJudg6X1pmfp54xqMz4/Lpb4d9rJGlUrT594qHLZU71uIAyYwsC3FJjUR8s1lYnkWkV0hTzcqKMRLjIhH5rFhyGl3TalzTRGG3nebFWosmPFe92w/XJ8jIdHp17VK604/uASG4zt1TdwygJKaJBpFMShgxsmcZytv0sZGmXBj7pC1Weev0N/H5uc/jtVPVVke890Szt5vl2f6nVv0dgBLD0KoliQMCcm+8Gc+f/Amw3zOGk63RiLccbfa2DsSHm2+I+DxW2uxkQI6dxhOEosUzJ35q2fL1LMaFXhv2gIcDAtIcArqGkUSxbxQmquONPNEsWfxJbWff7FaceuhBlp7rnlkeLL/pZUvXuumwJfjfmfbHdAO66uM+Li8/hlvWLzhVoStG9izDRQeusH3NcNh/4EmWJm6TkZMGKQLscyd9ElzmJf6LFCuW++cNXYkHjpqC3y8JP1OxzKxALOR4Wi5mMmM03nW1yVd0btExdOP+ZOt1uGWu4v47+nvzpGF2eef0N/Dl+GfCPj7a7/GRPa23OfF0nU8lYjrKyczMxHHHHYcFC5Sg3IIgYMGCBTjlFP4M5CmnnKIqDwDz5s0zLJ+VlYWePXuq/nVoRI/KhJ8XpD7NGXmWq0uGL7d9zKKy41Tr3bNE1Wx0YtyiYyAuRmnWNVK3Qatu0acO3hjxd69tvB3D7N8fLKLoANrk51ydGzgZsOIefuR++XGoSeTcdcQfEZ/DSgfYyArIzHKRJ9L5hTTVHRFNdzOWSMTFLmEMJKVrOoIB5JOVzLjH67XPv4/7WrWe4fQiK82rs45Pd/qDYSz+KDyLe64HFj8etXqFiutjlyVX342fLuKLiP26NOCGQ+ZE9XrXHDQ/rOMuPDwL44euQf/BN6m2G7nIje5rz5Jse91BAIBTLCZnEeHEftlNcGYdDvR/1vD9F+4kQSoQb9Ei0riWVx+00HLyHTuWZZ+f+zz6Zjfh8eP5VoJaQawfk4AsO139HfKsbkU44XCE955iE04BwPihq2yfIxrsvv1yy2UvHb4MgNT/lMOyZI5cCAz5BekWXqlN7kx0HfwYVl+vj0GoZcKdr+Gei+7D9L/zhUGZ4wZsV607M4eHrkiAGlefoHBy3tCVmH/dy+iV1WL5eDOuPsT89xx52HPIGvCE4f6sJM48e98YRWCyk7QvFMcPKlat/3zRv/HbJf/ilmXbgX79z8BjFxyFY/YXsfqRPqr2aMplnyDTqTzLh/fZY1oHOYxGtMeOZqgn5/XX1b7DuBmckyKwlH2G9SjH2Qfkhn18ZpS1BTvxc7Xjm9T8BaJPzE0oHnnkEXz22Wf4+uuvsWPHDtx///1obW3FnXfeCQC4/fbb8cQTSuP60EMPYfbs2XjzzTexc+dOPPvss1i3bh0efFAfh6hTkjVW5cb12vo7dEXSHf6I1XS74qQI4M75z6m2dc/0qwaqPOuLWBOLxvaIvuYvJquYZfy7+qDQWTKtuMrdM/o3fHHu8xHP7GiPd2YfEtH5RDiA9hWA0A6RMV1MFstFK9x2+MxEV8ES0ZjVs+QWbfDTmYmLvPP6xDRVt6mgkZ8QI1KECITscAfuguiwnPk4UYSyXDRyFbzlsPg9D90z2nHdwfOC610zvHAMna2719IcirhoFBsyVFZULT0zozPwDMXInmU4sGcF+nXhT2alOQTccMjcqF7TSvgMHl2G/wwcMB3Zg/XZmnmkOe31L0b2ywAOmIHzh/EH64O7cwYDB8wEhi0BAKT34MdS0opH4TL9stBZXk8fYc0SLlrY6fs8d/pi3bYDmRhgMv0MRISzhxVg0kU/4PrDN1q+ppbumW06y1cjzjxcyVi94+/TsOTqu/HAUVPQI0P/bI4/+X/AsOXYL5tvJfjjhU9gcFcl0/P+3ZikMb3uxC1jK5h9Bhmhhy1FVxsDUhlWkHz3jNdw4sDo3x9WrHDSelxo+XzZgTr7RSdKA5nrs9KdgMOBgb0VK/P5j5yBf51/KIb1qFAJOwCALmdiYNc63DnqD5y+f+gMrWOG7Y8hvdXt9KG9S/HkCZ9hdN8CfHyW1hIyvHfskO7VcPa4GBn97Gcl1/LXU3rhlAP57dxzl4/Gx7cci/49spCVaRwTbkTf+Hs57N/d2vstO92L+Vfeh6mXPGJJXBzSrcrSeXt3H6Cy0tsvu8GwT8LGv/9hvRfY71/AQbswcMA49MtuCO479MhPwRou/HlPDzx2RgO6ZfL7gPJ5E+XyyquVdtJXn9AlOlZ08erfsMhJH68+aGFYx0d7Io03UTSi5159wUMa4UxTG7T9Y+yvUa1LqhLzluuGG27AG2+8gaeffhpHH300Nm7ciNmzZweTtpSUlKC8vDxYfty4cZg8eTI+/fRTjB07Fr/88gumTp2KMWPGxLqqqUHWkSED0HuEjCiIi5E3Ut0zPBG5QpslgrCK0yHi0WO/i/g8LKNGXoDXTw3fbdYKw3uWhyxjJVbYeYdlITvdE7nlos4tOjIRUBCdgOgG2leohkCpFAzaF4eseNEgGnFjLLlFG1zHLCELb3DvE9Li0qkTRGfYsZ/CtVwUEZ9sipFg1laM2b8H/n4kP+t07x7DY1QjDn3+T+WKlZ3VG+h+ge6+yepxWtQD5b91+ltRPZ/Rc/PpOS9KC2n7cRMfZfb/lyoEQzRc+bSWVIDaTdTIssyR1h3ofgkcaepYTOnp+jhio/oUmr7bR/bR1+Glq44Dul+MCw/M0e0bP2ogrjl2f/2Jul8EpEsTmulZ/Fjc0bAMunv07xizX+iYT+eMHhWz5FQ89rYOtlz21gsn4LHx6sR2Jx56gq7c8SMPwz9P3osbD12C9TfeHNx+1bhrkHbwTqT11GdLt0rXdLdlS9J2pxLTssvQD3DgUbPx2E1f49vzn9YX7nE50PVUHHb0z3j3HHVfcM4DwzFmv90qD6AjhimTvpsqeuCRy27FDccPxZ8PnoY0p8G7tOvp6Nr/b5bqzpLZ58bg8sGjXkQWR5w/PkxBemT/bph0x/G4+WgLrtdDZ5juvvnQWcHlrr0lIbLRo4hiPbKkvuiAnsrzf/CAHnjwnEOw5PHrsePZU/D8FaPRNTMNX991IpA5HBi5G8/c+hq+vWIB9vzlUrxw8keqa06643jV+l/GqWNZ33FiFu4e/Qdm3LYFA/Y7CvsFxKR7zwg/5nVWmgdIG4jeffSZae878yDV+ie3Hovf/j4OF43hh+zqkt0fu5r1zxAA/GXccFx0pPR8ZvW62LA+T11+qtWqR41RQ0K3G4f2kSYeDj7kIRx98jw4B7wY8pjT999g6foZaYrYBABZ3Y9HVja//e7Z5wzD8/gcStbsLtn9VePmjL5/wQMX34LNj/N/u2dPlcKuRDtevyUyDub2f7UxaXktUTT6zbEwyHnt1HdU69r3rmw9Hu6Yyo7V+JlD1mFo9wrcf+TPhmV4lpB1Hs5zkdYTaX3/rtp0/5GRe4p1BOIyynnwwQdRXFwMt9uN1atX46STTgruW7x4Mb766itV+euuuw55eXlwu93YunUrLr7YuPHtdKT1hstvHqvPK2QAGcrM7hn75+rcBk4Yqm5AtA1Xq8Zld8K4921XNTPNh4z08NPVR2M2QhSBo/vlRXweluzeV+CC486L6jm1WPnbrbhFDx7xBND7PmT2NE7WYgWt4OB0RGZ9Fbz7WhewaylluTisR2pkcI1Gh4M3M31Qr71AmpKt3ig+jW3LRSEtLu4dHn866tzhZRHNytLHAbSCmAKWi870fob7sjLSDH/P9F5XWL7GmP0KIsuyN/AtZByguDl2yZDaQq1bdFbPM7mCWbh8ds7zujbKrkB13Vj18beepL+X0p0OHHzYk0D3K4Ahf+AfY3/Ulcnq/4AqXuSHV1n7O/96xFTdtp6ZLbj/5FbuZOBwxnrmtrNCZ4dd+tjZweWMdH3g94eO/sHwHhrRqw4L/32NbnvvrtLf2e/QX7Dln7vw1CWjgvueunQUunY194rISOO/V8KJS3jawernIz1zKHDgypDHZWWkm7aF0cYnKH/zsB7l3ERN1x03BNueuwBpaem44ji1N8LI/oowfOKIvjjz0P54+eqxeOTKe/HKXa+hd5YSe9oTOLXXr2+3+2YrA7+XrzrSsL7ZaW7LSf8y0pihiyMDyB4LOBw4uv8u41ikXU7AFef/oNrUv+8hwEHFaGXCoJx/ymPB5WaXF/t1z8Kr1x6FIw/ohe11/9/encdHUd//A3/NzF7Z3PcdcpEECATCEQIECPcpAiqKiKCgiCiiolKpotb6tVVbba36rdbjV1v7tbXaerVW1Naj9ahWvKgX1SrgDXKGJPP7Y7O7n9mZ2Z09kt0Nr+fj4UOyO7s7e8zMZ97z/rzfVQjkjaflucM/ZtlzT8fNi524ZkE5hlS1wWHXXwg5ZUJkTWy2XjAZUxoK0ZGyKOhyQ0tDl5JSZf9v3mX3/K7e/WaA77aKXM85ycgB+pqzkpIOxVGE5a2VeOvKWZhU17OtOqoBJQso+ikkJQsLxkzB6rYqXDSrHj9fPgpTGrQ1wFeMq8KVs/0BTVv6VKB6O1D0v0D+1Xho3gZcNeUtnD+9DpFOTnQ4i4HcCzG+tggLhpdg1YQqlOekYOaQQqwcX6lZdlZjMZorsnHLspEYWqofR7jsMj49oJ91Mbleu69yOozP5167bDrGD4xstldrdS5+tbrF9H6z/SEApLrSce3ioTi7vcZ0mV+sXgIM3OvJFLRXQHZPNl32hIF/xh/nrUdJmknWbwCbrM2ec1b8Gg678Wf0yif+48uIcu0y+2zT/M9hV1CW6dn3Vuf7z20Vh8FFKQA1VZ6at+E2EAvH7+ZcaDx2sA8wHEvrL/rqay7GYlLuoa7wZnJYccLAv2gylAPHGak9dbGPKA0RPX9KhvUg/IZJKfjbysfNs9ABNOTs0N02b5j2t+KNiSjQZnrGJSCdgBI7hYIM7e8uC7mMrPgPdorcDRXaQFRzVQ1OHeyfets24GvM7bmStqi5FP/8XLuRhxoU//T1E3W3SfYBsCuRD6ZD1b0bU7gNm0f/POgyH+8rjLqG2LDcf2syR1wOBXLWqqieMxQrGZ9fHQodGCnKKQWKboHdbX2nrRjsFQKn1tqMFgpDN3oGtAe0wcW3DQbviWp8cXQdmPuKJEXXMf26CTcg2/WtrvNrbpoTqNrm+cNeaRgQXFTzZNB9h1GGdJeq9EkG6+qtBlkuFjlS6iLKrO6GhGc/1daP8k4ZCyfL++H564NOIQks/h0Oh928FqzLrphOabXJkq87byjH1f4Fry9dglSbtQDjwHx9kMqW5T/muOyegG1gIH1cTa4mCBIOo2mh0xsHoipT2yxAlsNrCLPpmGkYWewf2G7frf8d3bBkOJB9JlD2IOAej6xSfZF6l13BEaH+slxkPqX03Kn+wNFFU9Pw8GkHUJPpny752tJTcfExxxh2VU7NO97377pi/dTyhgLtY7yBBgBQZP1xQrGXmAaRPtyTAxhcuKrJ7wkqpE5DeskGTYaU06bgmwPBt538NOOLnOFewPzTeRNxz2ljkCtMx7NnnwikjA35WIdN1ozL+lKx+ws8c9LNutvTXQ6kOj2/obJsN04Z7Q80FaT7P7OTWypw92ljkJPqP/GUi/yZZt09pU3Ex3jNHuifDtlSnYNst/HFFZftsOV96qnjBmBISQY2zqzX3lHyW7RUqJhW7xk7KrL+OLJ59O2+f2el2AF7BbqFCz6y8Jiu7tAn63cs8bznATnhn9grsoS5o6fhpFZPtuT0wZ6AWmGGE/WFniAPHJFn4gHGAV8AKM1KwaLmUtxxqnF2nUhNm+v7d0qQa9prJtVgaUuFLuswKGcjMPBLZJRcgEvnDsbaybW+z0HksMlYOqENrdU5qM5LRWtNHuCoAyQZcE9A2Yj3ccqMjb5jQSQe+3gmIKdBliXceOIIbJ43GH/d2I7bThml+W2fNVkbeEt36T8Up03B+mn68kG3nRJQm95lQ2WuNjD2+HltyHKHDvKU5+jPkRaOKMWvzxiLsVX+C7/5AdvlO1eZJxv84V+fYsnoCixu1p5nnjmxGieNKccvT29BWU4GoPgvPkgG25lXQ/YODM17H1KQcIMYZLNJhzWjP6fdDrn0HsPHHTvcfzyaXK9d393f+vftkiThztMm4/iRZbh7pZCVajPOXHRmnwS4xsb0wmSgFNth4+dXDxuOfq3MPot0xmFt5ke+fx/uijwhKJhOm/8cNHAMmVp6LeAchiM27f78sfVt2LFiXsjnzs4wzmw1ouScCRT+NOixZmLTcZq/bzxxOC6d58+WT7fvx0l1nnrXUnf0DV77IwYXk9C50+pDLiOeZCkpI/UZYRJw0QR/DYEj3Z6rs7ec3IzvHduIPR2pAYuHf7Iq2XJgN5tGEgMzGwdg+ODVQZfp6LIbnjCFQ5a6US5kqblsChTZekfgY6ufCvs1rdTJu+/dmQCAwTnvY1r5PwyX8V7ht4cRDOwy+KoDMzxsBieN4VBTeq40HXoZUP2ZDd954ZyonlfUWvQvNMU4a7UifSeW1j2GLS23QpKAhdXmAZ7xxa/F9LUjJUuqpiN3uBbVeH6/gYMbp9IN2IqBgV8AVW8bBhGb898Ju+OelVqi8eawmWfwBdOtSvi3kPEBAE8tOhO3tX8PS+sfM3mUXmPu+7h+gvn03FEFb4e9bl6KIuO+pV/ApeinmjhtiumgzKbIuGrsLfjXSaE73So9dYHF7OsNw83LV5Rl+4NJ3vMYSYiYe08obcJ3csMJTRhRkY1soTi/Q8jYuGaRcRZVun0//nfKVVAlfUATJb/EwOan8PAy/1TFLoPu8OdNG4hjBhsfd3JSHfjtuhN8f7+44ys8tr4NP18+CneuGI3zp9dhTsBUu6zcKbrncdpkjKvJQ2X6p5hbH2Lqo7ADcJTcgMa643HTcf5pPnLd14Dswn6bPiP/20P+91Geo88gsdlzdLfNb/Jc5T+7Xd/gRi6+GR2O4NlY507xP+7/nT4GjoBOEU7hb4dNRqdJAMXr9LYqTBukD1jMr/pr0MeJJtblo74oHbIs4do5/t+U1WOhwybDnWmeTSQaX5uLqxYMwaPnjAy9sIkr5vs/w686ilBefyN2/M9cbJhW57v92BHabIzyfP/f5TlubJxZj8n1+ZhlNPUze43vn966ySvHV2m+OwBwOfzbh12W8fUB4/2HM+8sKEU/9f2d5tQfB86cVI0nNkxEltuBR85t0/++MhYD1W/ixqUTsX7qQDy+vk3/OkIgQw4SFAGATgvBxdHeII5kfUzoZQt4/bw0J964Yiaeu3gK/rRhIpaMNq43fObEarTXm2e1PX3hZN+/CzKMgwX3rmrBDScM9wXqHzzbPPsnL90fdHaZ1KkDPPvh7y8cqss6DEmytg3ZFBm/PqMVWy+crN8XKfoSDOH64HN9vTnvcUaSJAwvzwIAHNOk3W6GlWXpHueyy6jJT0NJpktzm9Om/V0rsoTHz9NO720ostaYNHA9ACCt52KBLEvYPHcQijNdePRc/3aQk+owDLoHKsrUHv8y3XZcs2gYJgzUz2w4YnTS0MM7bpQV89qSTpt/O7NJB3y1PD33KYBziOHjpg8p9AVmZwzR/uY+26vNChxYmI4fHt9keAzTrY8jFah8IeLGPguqnw65jNt2CJ8f1B874RxuONso8BxMX3Mx8m7Rvd7xuO4AumR/8NcWMIZUctcBVf/S1b+2et6aa3Lx0IgsA7AVYtvXzabLlJe0we3wb6cLhpfC7bD5kjQaCw8BFZ4yNErghdK8yLte9ycMLiahU8YOMLxd2BYgp/ivztgcJbodkSxJmgLU+zvTkea0YfbQYrgdNhzq1G7kityN26deGfa6mnWPm1/1TNjPFWj80Lkhu8KtGvKgbkcWytSyF/HYav+H+enhoZoaaykOBbJsHADZNEFfHyeSHXc4GRWypBpmMa0f7z/htLqTvuXkZlx/fJPudjGrSpG6IUUZXPzsUCXgaMChThse2t47DTtsche+7Qg9kAiHInXj++NuxopBnposW1puC7JsdDVDHVFmh3pJUKPKBJQrnweK74GiaPcJDqXnd63kArLLcECkyN3Bg3ByuiaDCvA0dAncXyUah03SDyoMpDm0Aab/7tOfpJekfo6ZA/5uufs7ACBlHKTiOwzvkiU1qqnw3aqKsRUdaC3eprvPaZNNv0+7IkGSgExn6Kv9NqcnQ1kcTGamZpkuXyhkqhkFc1J8mYv+76S1xnPSn1robwbndvo/48HF2hM4p03GExsm4l/nf4MZzXPQJRs3gIG9FI2NF/n+NMpuWjGuEo6UStP3Iyna/dKg4gxMH1yI9oYCnDt1oC4zPDNFnx1pU2S4qh7C1vPbcPPKk3T3m752zwh5yMAFOHdKrSc7SvZkwHSk6zPyxQsTRllBl8wapLvtRyc04S/nT8SJo/UZBbIsYcfXBoFbwHfsyRYy5Izfu3//4LTJOL2tCil2BU3lWRhYkIZbl2mDcm6HDbefOgqPLdd2GR6e92/8cV7o5g3nTKnFT070Zxy7c/xTTb3rcmqr8bjMy6FImNLgmQK/aIT/t2V0nn/+9Dqc0lqJ0mx/9lE49WFrC9JQlOXPkiwrGAw4PZkjp44bgIaidKxuq9IFRSThOFGR48bZ7bW4a+UYXUAkkHcTyE934vwZ2ovfLrv/u1QCpmP+dKn/M3VmzYMt5xTf3+I2DwBzhhZh0+xBGFgYOoiU6rRhw/Q6w2UX1TyFprx/Y8PI0M2QAoPWy8ZqxyqypAIu73sI/6KY0b4szWnTbP9GY7fq/FTcuXIMGoUpzd7zggfWjkNlnj854LiRZTi1dQCuXuivW//7gGUAYHh5luH0XkCbIWdXEv/iX6RuOil4V+p7V7XgqQsnY1DAscMoY7csxw1FlvDIuZ4LRzX5qfjZycYBDZddQaojvM912qBCnDt1IH66dATuONWfKZoqHONWtVXjhU1TNZmLges6pCQDx9T694s/OM6TRet22PDQ2eNRmetGXpoTJ5kEugFg/2HzBA5vlrqUucx0mQy3fzq9DdrZDEZTuNdOrsGty0aioSgDj65vwzMb9d+J1YDTTSeNQH3AfsJ70SGSzEW7fATrhv3G97dZYo6ubnfVNiB3M5B/tcnzBnaL1ou0nFCvlyGStRm2Npvx7JgjnYGflQq49RdWAW1WuphRX593MOiqeC9MHlLNa4s6bLLmOb0eOGsc5g0rxnXLjgfc4zzrnOofez1xdimQs1H3uKMRg4v9xK3LmpHmEqaspPqvQiqyftchS4AE/4nYgS7toCIwNVqGimkNWWGtU0lmCsSx0wmj/FcuggVlrCrOSIFiEuTzKihfB0nS15QMpqxsAQbV+Lvn7T3UpQmuuewyFJOag9lF+pO8j/eH31nZqKCsGRndGJyjLSi/aXYDNsz3r0uGwQmakdqCNCweWYbXt8zArHr/jl7MpLQFpLSHU0zX68VPs9GdMhUbnzsP33aYT8OMhk3uwt4O86ulkQgcKGQ692N5w8Omr29F4MDGq6YgNusuS92eBjqRShkLZJ4CW0AWsi+42MPo/SrZZwcPsqYvwb0zNuPSUXfAbfMMCjq7lZCdnAOLv/eFv5w/yfdvmywj0xF6Sq/LFjrI570aOrXsRUvroUhdQO6lQNZpWDXk9wb3A4oty9JzGVIBZJyEp/6rny7nmRZtvC9RZAko/QOQOlcXgDx/3Ie4ZYr/O1PyLvLUbBIfn2se5HE5XKjuORkeV5uruz+l58RMnG7jPXEXa1qlCllUgcfEqYMKMLAwHXL2GUDeZZqgoSwBd640nj7Y1a3qpp1luR26bDszGQZT6gJluk3235IDckrwkhfHNJWYnjqcP6Nekx1lVFB9zeQa5KY6cOYk7fTMKQ0FeH3LDMNMFpsio7YgXZNd6iVLEj7+2njbGVrmGYdkuPzv1yi4KN7vsMkozUrBq5dNx4Nrx+GJ8ycZZ9oBGDToAvx6mX9/lGI7hMoM/fT3QOdPr9N8B+IJvPfkd8sxQ3CXyW/Eu54njanAq9+djutP8F/AK8lKwXXHN2mmgo4c4MloEcdPjbnvhVxPr4MdXZrA2BXH+ANLWW4HHj9vIi6dO1j3uM/3+U94jQImZgKnhXozqo5pKoHT4R9b2gJOCPOEAEB3t6o5YSxI9wcXf3jcMHzvWPN6jeFIdRfhoXnnY/0k/ZRS78t7sy8vn6/9jNJd2t+i2yH+HUFwMUjtOy+ji4zebUIRtq8rFwzB61tmoLlCW/fQrsi4YkEjTm4ZgF+tbsGW+YN9GXiBOnQn90CqQ8EI4TkDSx2cNMb6lMS+E1mwZEyVQSaZINVpQ1Wefry6eGQZSrNScOLocty+fBQumlWPST31ErNTHZg+uBBP9tTANLO2JwtXvPCgee2AWMf3FzbCaVMwb1gJBpf4A2vuEEFKb9D+tlNG4trFQ/HIuW2or/bX0hWPZU3lWXh6Yzv+8Z2pmgs+unVzmh/DvHULZZP6hoB2H29LqdOMiQOPIRkuGy6a1eDbx7sdNgzI1X8nP14yHJPq8vH7teNMXxfw7KP+tMH4QlgkwcUj3XbNWNioaSFgcN7kbATyrwKUDMNgnz2wW7TBGDnSDMRwZxeF49ZlPQF1YXUVm/FFjJNatAHszBQHUKof4wLA9EGFGFqaiUXNpZpAYGV28BrYaT3Np4zGJl5Om4zNPcfH5cJFwxEV2fjp0maUZvmPHQe6/L/V2rImFl3sweBiPzGuNg8X9lwxPm5kGSqEna0iS1AlbaBCggQUXOf7e3+Hdse1cbr2IChL3UD+tbh0Ri4mGJzcBZo1pAgXz27AnkP+g0aFkI6uVFnrHBaM0y5DDjWdIt+TbWk10AMATodnx1HcMy1gdGUO1DR/U6EUuwLZZFq00YlQqKk3Rnc780NnU3hJkorKjJ24ebK/02DgiW1plnGmSCBvEDLDZYcrxR8MFoOLRwKmrbpsctjT5r844MQPX5qBP37oD9hYqTkXToFlm9Sp6WgYC0YHb7MsMavZY12qiqYC/QnuZfMGG07lC5cENSZTjQM7hDts2s/CKKNNThlsOnDxFN5XUZT6JVY3/h7ZTk+wqbPbFjRzsSxtl6WAQDis/PbEbfufH32N3IzQ+0G7Yr0eX3vZy6EXQs/JXc/+SLxC7iVJKpSU4aaPf/fq2fjge1NwycwgJ4Wy8XbjtMk4lGd8YSjVaQPS5wPlD+M3x7/iu/3WZSNx7jHr4CjzZ1rabYpuGltZrvmJXVe3ihuWDMfi5jJsma+fIuU0COR5T8rF+8R/l2enaLJFxlZrv09vltKE2jy8ccVMtNebN/ERM0cCX9+ruSILf7uoXbfcmoD6XUZSAjIGfQP2IM6aXIO3r5yFG08cHnJZr1SDqailWSl4efM0bJqtzVDcd6hTE+QzE5ghKkvAgBBT08STVaPXaK7IxhkTq7FxZr0vs8tlV4KeMAAAJBu6nP6TzRTbYd3FMlFtQRoeW9+me17xc/IGsSVJQl2QrDrvctmpDs3zdXR247iRZbht2UhcNm8wHhKmp4qZbeGMYQ4HBIkqcq1l8HsDD6VZKSHHLYCnQcuiEaWYNUQbzP3+oqH46dIRuGbRULhS/YFNRZbQ1hOMXjOpWjMmbCjO0ATLxOm8IwdkG2aSRGTAC0DRnUDeFt1d3uDm+TPq8faVszAuoHlP4H4mRQzkmNTdHFSUir+cPxHPXzIF27bMwNhycUp96M/YaBqnd5wmZjVKkhRyexxXk4cV46tMt5MOg+mt/29VC+oK0/Gzk5vx69VjdZmLF8wIXaYpWWSlRPYby0yx49mL2/E/i4dh2uBCrJ1ca2n7EZ0xsRq/Xj0W3w8o1/Hr1WOxtKUCl8/3dzHfesEkTd1ZsabsoSPG+4nlrQMgScDFszwXo2YOKfJdWLIJ36lRFmKoadSjBmRjrclxzJa7Bqh6x1Pf1IQmuOiswAkGgT6vkPv4HvVF6bj7tDGawHgw1ywainOn1GpmbmXk6I/XVojnKW6T5IuUkmtNH290nqHLXNRNi4681rYYzMxyWugub1FLVQ5mNRb3vIaf2UWV+cOK8fA5E/C7s8bhvjPGegLdinGJgHSXDX88ZwJuOGG45tiQnRI8JmA0xgnktMmY1ViE5y+ZYjjeFI0ckI3h5VlY2lJh+bd5NGBwsZ+wyzJOGlOOx89rwzWLhvrqbgCeAYxq12YdyBJ802QA4NAR7U5pWdsk3L/GXxfJ24lq9ZSx+OWq0MXLbz1lJHJSHWgu8Q+kxNljsjP01c4Vw4MHEJw2GbLBtJLTDLphWimG6+XNWPnNGa1YM6kG1x/fhE6I3fI8wcUzhvxO91ij4GKoi9NG014crtBNe7y8gc4JI9aaLlOcGbw5zozBhbhwRp1mKpI4BU4MvgTW70yxA6rFXYl32uL9b+Thluc9z7+m8X4AQEd36BPVcKb32uRuT+f0GDIKlJlNKbB6MtjdreK2FbNw1phdaMj+0Hd7TUEqbj91FPLSojupkiUVXTHoUBwYvwnMXDScFi0ZT6NdVPMkWoq0JQS8n1eXKgfNtFSk7qinnAfKtND0QxxgTx9ciLy00L8tm82NzVOtNS2xOi6RhAsqStpk3f2yrGj2i7MDsrjsigzZloI17cMCHwogeM6H0yajUzHed2cLBehHNZ2HHet+jm0XHPJlGMghpvoZdRr16lZVDC/PwvUnNOmm8wH+Czji78Y7gBWnfjrtCp7ZOBmPrW9DbpoTT5w/CYuby3DSmAqcGDDta82kGty7qgW3nTISbkfw7MJhZVm6EzBxOldVXioeWDteEyjwTjWcYdC8IJAYhPifRUN9A/ZgLppZjxSHJ+DWbbHo6pyhxs9rNGjee8jabID717SiPM1fs1iRJNx92hjDCyfe1RSzOY2aJciyhO/MGWRY0zGUA8KF1FT7IcMuygBw1bGNeGLDRN10OwCa34P4PQdmsIoCvwHv78X7/LIs4bQJVWgSssrE4U04pQ72HT6CqYMKMKg4w7SMjpGTWyqwcWY9fmwxIL20pQI3LBmum8af5rRh3rASpDptmsCFXZbxs5Ob8cvTW3D6hGqUZKXg92vH4c8bJiIn1aEJyIiZkzHNq7EVAVkrAFl/wVUM0qQYZIAFZoVpprI6jTOIM1NsqC1IR0lWCtJddhw71H/csNJ8pL7I09hFrBHrHWd+b2EjclIdugzLSBllLnozIecMLUZrTa4uc9EeZYmcRGI129xItIEFuyKjtSZX95torcnF9xcORYbQSScwU1Dc/vaZTFG+4pgh2LZlpibL0Ut8zVD1a41IkoSLZhn//m2p4wBnfdDMxywhK1yC5KvhamTPQeuz0MIhSRLOn1GPxSP9516ZEQYX7Sn+2WpG+22brMKetw5ji143WReD4KJTm/lpOC06BpmLWUKn7miJTYHE5ARxPCNeTJMkCY2lmRg5IFt3sReApl6w+JsVg4uZWY0IdNp4f6NQb2wkeOai57lLLFxksysyHjx7PL6/MDaZ9f1F/zkqHOVsigRJktBQlAG7IsNl93+1siyhO7DovKS/6hFIrL9y4IgLUMM/oXfa/M+cKwRJFAsHYndm8CCmJEmG06J1z1z+RFjBxZXjKwF4rvZfMrsBBRkuHBSuBjptMiBJ+M68Fry1/i2Mq/HvBI2Ci7mpwT83o6uC4vcXimIvAQZ+hYwC/zTowKuPJVnBg4tnTqrGuina6dua4GKQBjNWpn56Bda/PG/U0ziu9kmTpfWsBjEBhGzkc9bQ+7Fk4J8sPx/gKQ+gu83kgG41ANbZraIopxwXLzodZfn+k2Vv5tP+w9EF0mSpW5dtasVl8wbjV6v8DQgCD7KB516GmYuyceMTo/qC3uBiZ7cS9GTSE1yMvKagkTwLWYjiPmtVWzXyUkPvw+yKjFXTj8d9x1ub8mxmbrU/E1DcdSr5V+iWlSVZs08Rgwtjq4NP+wIQdGDfrQIdncb3iycIULKAsgeRnr/Yd5MjRHAxw2XH9xcOxQXT63T33ffSx7rbRN6Bq3g13xtcFKe6Vea6MSA31RfQKclKwfUnNOGaRUN1J5Y2Rcb42rygU75EgbUXxefb8aV+etWfz5uEZy9uR21B6Bpy4kDYKOgR6jGVBtPGjNgVGR9eM8c3rbUk0zzjPVggTZTqtOHEOv9+VpIkDMj1XDhZMa7Sl8kGAGrPlj+6KgdzhxVj89xBusBVtMSsPllSNU2ARBLMT0DE6fXiBmlX5J7Mi1ZMqtM23Ajcrh45dwJObqnw1TgzIu5zlLSppssFOnSkGy67gsfWt+GqY/UnW2ZcdgVnt9didGXo/YRVYvBVUSSku+yYMDDPt48aUZFtmPEpTouOpiGZFXetHI2GonTcdkrwLsfBgjpmAi9MuDP89dCNMq6NLBldgTnCBQXvczYUZeCVzdOwUjh5jsaFM7X73lKDcWNgox27LbqgWryMK3lf83ehSeObRCEeXoIdA8xqkkqSpEk6EYm/w8lBGgVFwrv9G9VO9BLPmw4e6UJ1fu+USgqX1e0zkK3gKt+/c136Wrkpds+XaXbuYJSw4Aj4/HSZi4U/iXxatPB6GTEMLh4nBGrFQ+mPlgxHhsuGqxYM0VxMC6U0O8UXmGxv8P9OxeBiVZ5+yvXSlgq4HQpOn+DP2h6UZ56hGc1FBvLgJ5ikfrRE23QjcHqFOI2qu1vV7aoCU9SNxtBicOmbjnQA/mCN9wQwP+WroOspHlAWN5dheesA/Hz5KN0USyM2JXTGllFwUbd7dTWHNaWoLFs/DWWvcLXMd8KRfSbcxRs1mSdGWRYnjQ9+9cso0JrutD5gk3EYULI1J0L7AgJSoep6GZ/s+x/jzJylu993n836AU1s4LC4uQzr22xhXm2zvqzNETw79pSGR8I+GButq1lGSbDpdiIxKKHK/iCX98Sl2OKUdjMSgK4IgovLWwdopoUF7mMCky6MGpzIsgLZoP5fR5d3/yN2CfRmLiowvtzR85z2PNiyQncktuq1y6YDcugAj7gXddlkw67qgbwBruyilRGvX7rLhptXXeBfDzED3KUPTMiSpNm/5ggXdRaa1HMSBdsilowuR2e38RvPNqsL2EPMijY70VjaUoFzpupr1Bo1TQHgu7CzrKdWj5i5aJRRMzBGdUwBYPNczzRhby3hrID3L+5TjYIjKQ7F8FgTSr6FQvWBgb9jhpfgktkNePicCSEfK0kSLp8/GBfNqseD6/QdZO87YyymDSoI60q9knWy79/ibmTLMUNwz2n+YIvb7jnm2BUZNy9txqo27YyLWJg6qACVuW7f92Ze1sJ8HySe3Adme3kyL3Jw67KR+NVq/8WZwN9AQ1EGrl44VNe4RCReJFBs/n1Umt14qh3guTB52ymRd5mONUUztdv6uEbb5bh3o4uT6wvw+HkTfTU/zQQGZ8wuxMwd5L89JSC46LAJ4yoLmYtebqdxpk4sp+ItHFGGZy9ux8+Xj8LAgjTD31GOW/t6Vrul963Qv5eCVO0FHwuNweNK7MjsNvjdPHzOBFwyu8GwdmAojUIiSZY7RuUHenh/H8GaSoq/oUNHutBeX4DL5w/WzJ7z6suZp5G+lj3Nf5w1Ci4qPecRsmyc9GE4LTrg8zvQGfBYW7Zh8oMV4vuszbU208YKMSHBO4OlKMOFYWVZeO2yGTiltdLS85w4uhxVeamYM7QIz148BfecNkZTvzQ31YFFI0qxYHgJRhvUTa0tSMNrl83Ad+f5M7wXD/4kwndFVoTRnpISycIRZWivL8Dtf/sQw8uzdAMMcYra3z/4UtfQoyxbu2OSQkw33XM4DVD9wcVzpg7EqeMrcdP9Z+H2NxeaPk4cTLrsCq5c4LmKblYXRCTLEmYMLsSf39rtu21wcQauOrbRV8fJaFq0nj1kQ5e5Q4vxyLadpvfvPWSeBafN8NOvT3pqCYAPdLd7BXZQBIBwLqJK0J9oHAiooSlJEjbOrMcP/7Td8DmMBoiTGwpw01ZPEXlHxnQAno5ygfWVwslcFF2zaCikw19Awj2WHxNOF2Fb2kQA/zW935P9FmZwsVcyF8277wLAbctG4nuPvI1BxRm49Zn3DZcNRpa60RnBtOjArAzZlgsInfycTu0VbqNsQkWSDE/ejTIXvcHJI9023dR77XIK5MxTAOg7s1sxodqFZz/wbzOyLOGdXaHrzGS5HVg4ohQSPJ0IH9wWvHA04N+uPJ+dibqDwAcNQOd/jNe3Ng+QjHcIRpkzsqTd7zoUGb9YMQovvP+lZpqKGW8WwZmTqnHbM9r9VnGmy7AGGBD6pEQ85oSbjTu/ybgY/F0rx2D33kO+depW/MsZTWcxKvweqdMnVGHaoELfa9+1cgwu/f02XDrHE3R8/b/6k4po/OSkEfj37m99XbCDmT9M+3k5bQrWTApd29ErN82JtZONpxyPrc41nLIUzN7uegCefdfBgGO/N5j5zYEjlmsDRsPtsOGpCyd7xkzvmJ9ABjuxFDMbjKaSAp4A5LgafVZmOMRxnfjv9JRU7Ov5HB02GfedMRbfffAN5KU58YsVo0PWSOtL4udoND4yM0rIngxV1qWvBAYXxe8XAJ69uB3//Ogb5Cqv45G3Pd9P4FRq8SKMK4wMGbsi47drWnGkSzWcIRMrZdlulGW7NQ2GRE5XEQD/eDpYRlo8PTj3fDzxcQumTrgRi372vO7+wE2kt7NjoyXuZ4yO+42lmZogYTgaSzNxx6mjQs5wCmVdey1++pS28ZT3Amuw2Wri+eChI12QJMk0G3fh8NAXSOPN5fB/P4XuL3X3e39qkmsUAKOxZ+jg4uEu/T4g4mnRUHHP9O/i6U9GYvaQAjzwb2uPU2TJ9MJvoJNbBqA4MwUjKrIAhO5FIPqfxcOgqiokSYLbYUNRwIwKSZJww5LhAID/mjSLC8xGDCzvAAA3njhcc9yhyCXiJSeyKMvtwIUz6zHNYBAgy5KvwO5pE6p0J4SBGROhrtDUZP4XQGA2nIWaYw6zGk4hHwpFknD9CU2agvBv79qLkQOyhe6gBk/k1GZ1QrLBHiJzcdOcBgwqzsAPFhtPUdobpM6HuNO3KTKevbhdMzALlWJ927KRSHUoKM3wdxVz2a0fJP6zx1+r7JSxA5Bi96R/Bzq7vRZFJlkSRgPExhL/QOWr/f51C9wnB2YuLqqxNs3ZYZOBlHFhXR1UIeGFTVN0DQ2MChmH6sQoS6F6EusZ11w0y1y0FkARM+DEZ/dmXg0s9BSmbu45KIdLktSIMhcDKYr2xGpMnbZsgVEQUZZlwyCrL7iYdZbn/+5pvm20q1sOWltTkQCbLfIpTFJAt2NZknR1Cc38aMlw3yDGCu92FXQqq+wCTBpTZbs9U4UhiV2OhWwmg/2fLEua22VJwpSGQlw6d7DupOSqsTcDAO46yf/Lm9wznXO6QU08myKbntiGOuEVL8IEBphCmVxnPFXLYZM1x7ZuyfjkaOGIUtQVppnWFIyEJEmozEv1fdbDy7PwyLltvmzfl3YEz+oP1/ymElwwoz5optJdK0dj2dgKXDQrsZosjKr0H6OMaoKtHF+FDQbT4XuL7zP07n+MlrH4XIc7g/+W6wvTIUmI+qRF0QQX/b/z/z1lJJorsvHwORNw18rECiwC2s/Rygnlsxe347H1bZ4O4N+djhcvnWq5NEFvE9ejqSwTF8/W1pkry3Z7OmTb/BdatB2lPb+D40eW4coFQ8Ke8j+qMsfSxYXeZEubpvk7UZsYDM//NzY2/z80V2Tj7Hb9hRXZre3sHph5nmiORFALMRxTBxUa1pcNx4Uz9ccdb3dto2ZBXgeE8UCnSbDqlpOb0TYwD5vmDDK8vzdEEnAeU/gGnDYFT14wCVtXfwKnQUkpX2BQNr4ga9gtOuA88uXP9HVWzeq/hyJBxcTSV3HZmNvRbbOe+RossDi1QdsAT5GlnlrlkY3dre5nAi8ALRll/H4UgzF3c0W2YSkICl9iHLGpV2ycWY+FI0pRmZeKY5pK8NbHO/DJt54Np1SXuWjssfVteOnvS3Fs9dOA+h1Lr1ssXFXwBBc/1C0TKlMS8AxE0112LBldjsv/4MlSCtzZK7JBpoO7HcAO4cXsIWsulmW78dj6NtP7gxWvF4NYNkVCWbYbg4rS8URPxmWwK7ttA/PQUp2L17fMxA8ffxO3/tWTvRTOdN1d+/w766uObcTmeYN8BWkD1RakYddefaajYVMZi1fVAzMXb2j7ER5432J9KDkl7ANicWaKLpMhxXZYN00g1HSdSOr26b4X9/SoMxe7hMxFcZpV4ImY2TS9360Zg8W3mtf0s1pzcUxlDl4MEhAR64z9YPEwTAkIPhkFUxXZOHPRNy06ZRRQ+xmg5ECWfgwA+GhfUYjMRRWKEnlwUZZdAPwNXBRJwnfnDcaj23aZP8iATZZMB8Je3vtDTn/NWgN8frHu5svmDw5aCN1owCVLkua3EyzYcMroTJwy7EKg8jVcfWgXnn33C5zVk7E2qjIHP18+CoeOdOGcX78KwL8vc9pkX+26S+cMQprLFnTak9dFs+rx9DufY94wT5DvgbXjcNpdL+FHIQK2oS4UeJmdDPxoyXDfle++ctuykVh6+z/67PUAz/TOyUG6WseL2Gk7sHlcXNkrTe+y+lMJVc/ykXMnoKOrO2RToFDE7ThduLDr3e4SNcgT7mqJ+8pg+754EE9cz5hYY1rDzm5zADgIQH9hSZEl/PD4JoNHJQcpIadBB2eUpSTb8iHObLl5abNumUSSFqK0USK657QxvtkCgR3sRQeEC05mpQZmDy3G7BheHOwt3vOZmvw0wNZpOJb1HgPNAlnG3aK1+5G9HfoSL+E0/RL5kiayz0cuTgTwXETP4/W3i9pNZ7j0NnEGzSWzG0xnbBjNekzQQ2hSSr6jBFkmSRIGFqbDrsgoyHDh3sUv+e4LzDIxG5gOKs7A8kGPQJG7AckgDdsgMPRT4SBtdmXWysV1b0OZY4QpcWLxdwCQbfpMPP0aKSGbe4RyQs/Vj8Ai7YD2s/Nmm2luC3LS7S0YrMgSirP8B4todnJmgUUAuNakeLzZyfu1i4di7rBirOhpcmPEZYuu4UhxvvWC82aMGs6EyuBQpK6wpxFIinDinjoXqPhzkJqL1hu6eAVbG7Mx/cjK4AW4ZVjrFr2w2T/dxCgLTSytMHtokW6fYTgtWgZkg8xOTWdwWz4gKb7Pccs/1uDVz407DwKegZcih84ySLUdQEnqZwaP1/4tSZFNuwv8fVXkuHH/mlZNXZc3PzWebq37aeZcAFT8zWC58HcEsiRpGjoFzRYq/TVQ9RYgO3FyywDcsmyk5mR4+uBCX+YBIEzzFtZr9cRqnDRG22nZzNrJtfi/Na2+QEtzRTZeu2yGJvgUqLYgDTOHWMssDdYVua+DL+LU4dVtxlO8jhbiZx+qNmffCvJ7CXEB9JFzJ2Dz3EGYOyz4Ca9NkaMOLALaMYFY2znRMhUDWbmQnCzEzMW3d5qX0rA7/cfSWHz3FC7tdm00JVc8hm1oO4j6otB1l+NpTmMRFo0oxf8IXcMT3UThfClYcFGc6p+IF8fCoWhqrauaOtCBLp7VgNmNRfjFCm0jKaPzEpsSfAwvSZLucTdO/EHoFYZwHl94PWoLsyw9Jph4BRYDdQbJlpVl/X45US/QJSMe9Y4ilVkHcGv71Shyfwlgrua+oNtU3hbg8DtASuhi8IC22LRZ1l6ojfjGE4f7DkzZqQ5s/94sPLP9c93UIitdpyFJQadFn2ah097GmfUYW51rOCVFvNLmDRZqOroGDP6/M6cB33/0HQDa7MD5TSV44q3dOG5kGeQgtQKjYXalzKwW0pLRFVgyWhs4CDx/d9k6ke3cg68PR1bvxVl+L/Jcf8IXh7JDLywoy07Bf7/2ZAcYFTIOVQtIkbvDzpqU7cWAcziQNhfIu9Jzm2nmorWriN1CcDGw0ZLI6oFv84xUfO/P/mLlUtkD6FRDT9FUVU99v2ff+8Lwap9YBsEoK9RwWrQkBZ8WLS4rfBfv7wk2NUO1dEK9v9ONLKe+811gtmEkATwAWNVWhZuf8tSRW9pSEVaDi8rcVHzwhVBQXlIA9wQAj4R+cIifrCxpu8WH3EeGuF8M2HlrOfZ2POOqBUPw3YfexC0nN2NWoz6QbSZYcLGviUFdo6nAR5ufLx+Ff338DaY0JNLJY5DfS4if3JCSTAwpieyYFwnNtGhN5mJinxDNGFKILX9U+kUtK3G8tiRI4wyH038RPLDmIvU9o+OVuH922xMom9qETZHDKsmSaCbX5yPdaetpeJWNpvIsrL7nZQCeKdOPn9eGV/7zNWY3Jn52YqAJxa/i2Z0jAAReTFeDzsLJTnXglmX6pkmG06IVBTApweQVeB40suBtzB7wHB77j74xm+b1EvsQErFgM4uU3AsAvKy5LcGv0yUVBhePJrmbMKt6BJB5mu6u4MHFy03vMtoJik9lNjU11Ea8IKBor9OmYIZB9krg01+5YAg+FE/afetkvlPOTQs99cZlV0wLXHcKtVC8Axbxar3YXOGFTVNQnJniDy4KQb2cVAd+ucrTXXLPVx+FXKdYCmz4Ew5F6kamY3/EwUXY8pHh2Bd2cPGMidW47CHPdHmjwNYX+zp0t4nctkPhZy7KdqDqVe1tJieoVoOL4gGwvaEAj27bZVh/zMpxr74wHTMbnJrgYkpWO7qkJyEWYTfzs2XN+Od/vkbbQH02pJjNaLRZGwURZZOGLh1RFKOWLAYXPc+pf+2/vfuF5u/A58pNdeDL/cF/O4Anm9kbXEwXMlpCrZrboVgOaRvFygIbQzx/yRQc6OjEtBv+2vP6EtZMrsE/PvzK0vqEoqnf2PPvS+cOxnd+vw0rg2Q0R+OU1kocP6pcU6fRikTt+FmUwTo+0wcXmh5D40Yyn9KcKOcZE+vy8cYnezCpPh/3v+K56ChmLiZmt16/LLcD//zudN+F12RWnOFCS1VOT6d3821a/E7C3YdR7Bll74s3uVL7rt7r0SrDZcdLm6fBaZN1FwuPdHWjODMF84Yl53FSHONqxruqCjWCCaJGxx5PzXPzcakEQHL6m7BNL38BZWmfW5oqHWmtxkQXrCakbNdf5OxPWfbxxuDi0cReAtTuNG0eECtdYqZLhJmLVolX85vKMrG8tRJb/qDvIhushmG0q5KdGjwwJw5sAk8ETOsaRlg7w4ragjS899k+FGe6sHOPp/5iNANg2VEJl8O807YVGQ59QDgUTVBX0dcf+SpEgEiWgrUNMWb0W4l2WrR4AFwwvBSzG4sNfxdWMuy6VRWS8HsrSFPgtCkhawN6ZbjsptNSMlKEqXgG62IUTJUkbYAvw2XD3kOdmF7xd/2y1kNumoB9MP/dp70gcWrrANz9wn80t3mf6q8b2/HSjq/w0VcHcOOT74Z8brHkg1h7Syy8fqvBVWmr3fWsLhvY4VGWgBJhmnc4XfmMDC7OwNyhxSgUmkEtbanApPp8lGQaN4iKhUj2SakOBZ/3wrpE6ndnjcNj23Zi1VE+LTphZZ0O7HvQ8K5EmSJ198rR6OxW8dd/+3/ZOUJdKac98YN2/SXAJssSfnNma8jlxOYL/eW9G6kt0I+7EpFh4zNJwugBmXjpP3swa1jfNQk5mpltC8neREM8v5RlsR64GlFTGKOL4lYuIkmpMwF4ElM2jbrTc5uFcXWkXaYBT+a8OOZNpDId+enmtdmNxsUJcsjvFxhcPNqYBBYjnRpo9LAOobaG1SAA4Lka/+2h8KaPiTsyb20bowFPsKs3lqZWBzG5rgArx1diWJk/c6/L5IgS+HGY1WM0muYbK39YNx6ffnMIP/zTO77gYjRkWx4cKQ4Aezw3lD8FILxgYabB9NVQxOlgnuDiYc39kgT8fu04/PLvH+GtnXuD1kiyymg7Mdt2lNxzAXxieN8Da8dh0c+eN3y8WcDZaGrl0hbtlPUuVYUi+QdwJVmef1sJUgVmxAUSMxeNBhDaWjMeEiQge53v7wfWjsMb79yB2bm/1i0bbBvNce3FV4e8nQytZy6K/rBuPIaVZemCi94gQkWuGxW5bvy/F3ZYej7x9ycWWxcbWhllamWk2C0PYiKZ5ivLkrYsQ5T7N0mScPPJ+mL3iXhCUJ2fhh1fHoj3aviMHJCNkQPCy8imPiS7gYonYVSOIFHOMyRJ6jmB8+8fxc62Kf04eJWsxGNDf8jYNDM6Saa6G06LliTcd+Z4HDrSlTDdyI82v1rdgnv//hEum6/vfJwIrI6+NJmL7jGa+7pjlLkY6ogkSdrGRVL6YgA/sRQ4jDRzMcttx7xhxfjl3z9CS1UOLps/OKL65bH2v6eMxDP//hwnBpT0CiVRjvn9Qf896pEl69o9adRb5g+J2XOaDYJDuXlpM1qrc7EljAONGJzz7ldPHF2OC2fU4Xdn+a8wi1eWbJI2SBNpYNX/uhIunz8EC0eU+W4TOwCL62i3WctcDDaNO5xO0kbcDhtqC9JwMEZdO2VZ0g6gUyeH/RyRZC4uHlmG5oosXDC9zrAboKoCIyqycf0JTSgwuYIV7kHV6JdiVBgYALJTMwxvBzyNLPyPt/baRoHgMYGDexVQhK5yxRmedbOauRiMWOfLKKvHaFq0JAHI8gcXc1OdOLZRhVPRB0qDbYbPn7BO+EsfXHTZQ2/DxoFh/XLHjyrHhNo8fGeOeVMZwN+8CdDW1RqQm4pfrW7BXze2a9bz7tPGoKEoHXecOgqF6dYy/iK56i1L2skd0WYuJpNZFhu/EIWSaLONxewQ8UJPYDdiij+x3E2whn7Jzqyzb9wFrJfRsf/Tbw5CkSUGFmMsnBqj42rycPPJzSiwOB5KVJrMRUVsDKStueiQQ5fbASLPJBQzQ6XMFcDAbyA7as0f0CPSc8qpDYXYPHcwbl7ajP9dPgpDSjI1PRfiZcaQIly9cKj5zEAzR89Quddxr3qUu3BmPdZMrtFM64vW4GJ/UGXhiDI88dZutNbkBXmEZ/rgxLp8TXcxK8Sr9t5psjZFxropAzXLiUEkSVI1l6R6IxVabFKVmWLHptkNkCRtUwzAvLOzbC8BsN339x3HfY3Tf+sJSCmyjO6u6Ad1hzoi6/IcOJ6UpeAdqq3IdISfueh22PDAWk+h4t+8/LHufjGm0tltHEi1chAvzHBi997DPc9pkEpvElw8ZngJ3vh0Dx567dOgz281s2zesGLc8Oft2C98b0YDOUk4K3baPM8drGuaVVMbClCU4cKUQcbTpo0yDyXPCmlvzDoLOPi8p9u2+PggAXVFmGKuqvrgYqrDjkNHgg/cjLMt9be57Iqv9qm3NqoRseRD4HSfcQb7u0l1+b5u89csGoqTb/8HzpxUrVnm2sVD8d0H30RHz/dllAEd6nxOlrTB36MotojjR5XhcFc3RpRnxXtVKMklWv0l8QKeeNLEbsSJRyyZ0Z/3v+GU+Igno3HbZ98eNliSonXXyjE4775XseWY2CWsxIvVmSNiMoh2e9cGF63UP/QsF/64T4KkudAkSQCUTEiyeV1hcT2tctllHOpJTJElz9h37rDka8JjJNpEI/Lrv5fUyLLoAovanVJBmqQZWDlsMm4/dTROn2BecyrT1Y1ZjZFlnIhZOcGys8SdeuDuQ6wlFitiwXUAOHNSDc6YqO/A21yRZfh4yaH9vFLswpWxGO0A01zhfe8XTK9DttuOi2drM7pkSYp66k8k06JFZjV1vPYejLxb61MXTvb92+ijVyTjz9GhyLjxxBGmz1ud7znoW21yUJjhwivfnY7jRvozZI2yVhRNMM+zwrE4B8hOdeCFTVNMuyLbDGsuSsjuyV6WpJ7tQnYBpfcDWSsClg3S2S3zJP8fqj4g63YaB7fbBvqDfN7fg1gnMJqsBTEjJdzff2VeKp67ZAqWt1Zqbl8yugJvXTnT97dR4DnUV+lpouP/O5Fq4PQ2SZJwytgBaCztuy6+1D8l2nlG28B8lGWnYGx1jubiAadFJx5xWnR/3v8mbmxRu2JG38HnDC72ijFVOXh+01TDBpzJxmrwXAwGan9rKlTVPzbsVq2NE41mVFlZlVTNhaaeZBubcSbhOVP8GY1Wm08C2jri/S0Y17/eTXzxkifFVCTjqFjVIz8SJDtLcyVI2CGeNKYCc4fG/qrLinGVeGnHV6bT9J7YMBFv7dxrGlgK3GcrQYIFPznJPIAVzJb5Q/DV/g6cObE69MIAzpk6EGe31+qmWcpS9EXlI5kWrV0Ho+K8/tv2HNR2Sq7LOwwUXA8xO9SMmBliOLXWJHPRrJmR169WjcWj23bi+FFlQZcTuewKTm6pwG97uoZW5uqvSsrCtGjv1c6fndyMtff+E2e31/g6HEciWJOD3Qf19ZckyZPF8daVMyFBe+FBt2yQsJlUcD2ApwB4akMqAZ9tqkn2jni796X/d/kozPvJswD0mcTh0AYXY3eCL35GkZyYSrrMRQ6ZiJJdikPB0xdOhixJeGSbv4Fafw5eJSuxZEZ/LksRSU3geDD6ChhcpFDEhBUJ3aadnzXTosXxln0AujUt5qztCwzHwhbGceK5imTzzDBKsRsHF4cLszusNp8EtCUfXEnQTIzig8FFikrgTlAMbFgVq/PyziBThTXp6JID6Elj33LM4F4Z/KU6bbhr5RjT+wcWpmNgYbrp/YHHEcnZAOAzANpsptVtVZjfVBLROlbkuvHg2ePDeoxxhy3JcnBFkSXDq4EOl7UAp+l6GRbs9v977yF/cPFHS5rQNjAfSHNCwhlhvY7R8V2SjTNfQ3V3K8p04bQgGb1mRlRk4x/fmYpdew6hPMetu1+WxSulnv/PGVqMd66aBZddQUtVLgBg+S9e1Dwu2vOEN77U13bxflxWpu4F7eiuiO9T3y3arM6P+BV4A27hZGrPGVqER7ftQoZBlq94Ut9bHVtDBaiN2BUZqUImJ4OLROFLxO3Ge+Eh2x3/ulZkThwnJeLvKFaSJbgoXlyeO6wYj7y+EysnVMZvhSgpiOWEZEmF9xTTYZM1jUs1DV3EsWnaQnTbD/r+FKdIB2M0iydUfVNJ0s7gkWyecb7L4QKgn7ml6QUgW5/ZpcgSWqpy8Mk3B7GqLbrztkRj1oiVwsfgIsWUJIWfCZSTFpspbGZ19YCAmovC7aECQPESOCCVnDXwBReFgEOwTLC+osgSJtbl4fevGndGFskSYHSNTHaPi2odQnVx3id0IRcb74RbONnwdTJOAPCl/vZe/GoKM1yG0/lVALIwLVrcIrx1ASfW5WuCrb0pWKajbll3G4CDIZdTVVX3PZhNbxaX8wblxaDgR18F7yx8zcJhKMxwaaaiGzHqUB8LRr+3UINMuyKjIN2FKxcMgdMmh1/Umoh0dVQTyfjaXJzaOgANxeZNwygx9Odp64k7LVpr115/M7zrj2/CspYBGFWZHeQRRNpp0bLUjS7Vsy27AoKLKWlDheWEJ5AkqI56ALsBwDTz0QrVQtaj0UV2T3BRX3ZKvHAdTuaiTZFw3xlj0dWtJsT5ZywFCSFQmBhcpJiKJKAybZC1mnOhHAmauSg2dBFvj8lLx1zgaol/i5mLgRlc8eCwyTh2eCnsioymsqygy3qCJfrvSQps+hEmoyBMe4O/OZBZPU7JNTyq1wUA2V4Io+CiN3AtS/5B+PqpA9Fakxv1awajSPpp0fp165vfTThJG54uexaCi9Cvv2nmohhc7HmM+JmE6myY6bbj8vnmhcmfvnAy9nd09lq3w4YifXZzqPM5b/3HwHqORGRdOF1P+5okSbhiQWO8V4OCOHfqQHzw+T6MGtB/g1hjq/WlUBKD9ij55T5/szeXXen1MRj1D2KGuHiO4rIr2CskLLQ1TsZv33gNgP5cRLwY3G0xuNitlIa9rhICpkX3rIYrpRjAu7rlNR3tZQlIP8HS68iSBEmSIppVk+iYuRg7DC5SVPS1AcPf4aRHUfdMFLTmoss/EBe7QIaTWdWXgk2lEa+YxbPe0oUz6vCHf32KMydWQ5IkzBsWenq22fpG25lTnIrwu7PG4Yt9hzHdQtC6O2UygB2m9xcFZAcaTek2m1bvvfm+M1qx8bf/whXHDMHkeuNOy7EkK/pp0fp1C79RSCTC+VatbouqKul+R2bTrsXFvE/f0eW/ShvYeClclXlWOvGF7y/nT8TuvYeDlk4wk5vGKZNE0TJqlkVk1fnT6+K9Cr3mbxe145X/fB1xSZ6+tm5KLZ7a/lnQxpJEgRYML8ErH32NsdW5uPi3rwM9Y8fAcgDiDLjAsbU4Brcau1IzVwP4UHubCjx6bhte/s9XuOyhNw0f59Z0i/ash8tufH4tZh3aMhcCJdZq9yfqbL9oDSsGinuhuevRisFFiqlI6svEKr6Xm2p+Ui3ZK+CdVpyg8UQNXc1F4e9vD/uvmNnjmJa+bspArJsyMKzHmAWfJVsmjFL3rRKDSGXZKRhpMVvg0JHgefBl2Smav42Ci2ZBMe/tY6py8MzGdkvrEwuy0L1aNanxkoiZi1aXVW1Fus/crFuzUeZiWba/fmOiTn2sLUhHbUF4gcUbTxyOu57fgS3HmGdaEpE1/Xk6K1E0ynPchvWeE9WQkky8fvlMlgihsNgUGd9f6JnyvOl3r/tub6nOxSOv+5tqicPpwKF1JHVJVRgHBAeXZKCuMM0wuChJxhfZzZquiOcANkWxPADvj7HF5a0DsGX+kH7dfKuv9cOfCfWlwIYukQTuos0evPu0MRhdmY0blgw3XeZQpz9bKRmKUFv9TJKtU+SMnu7ZmSnag6fkqPT9O1hjDzPixxVO4OzwkeC1RgKDT0Zp84n2FSgGDV0C2RQZNy9txvXHN/lu6523Yf1ZrX6O3oGX+Bsyy1w06posfqeRZFrHm9nua8HwUvx+7XgUZ6YYL0BEliXytGgiCg8DixQN8UL1VQsaNeNPcRi5v0PbHMUoISEUo3NU7y3Bzg3FQKJ3KbOLZJqm1mFMce6PmYsORWZgMcb636+E4iqSzMVot+lJdfm4f8041OSbN1V47j1/TbxwusUmjvhmoMXK4uZS3H3aGDx5wSTN7eLvJiMl/GmdYiFeoyLDOT1ZrYUZTs3tYtDZSOCA1Kh2Y6J1gxRrwwQb1swdVozFIRqVRCucn6flKSM9C7546VTfbdluO86fXocLptdpXlP8KYjfk/f3MLHOX5cz0W2a3QAAuE4ICBNR7+C0aKJklfgJBJRcxGF+TqoDG6YNFO7z37l917eax0WSy2LYtK9nFlKwIbVYR9FXc9EkuKhoMhetD9T7WQ8XAICdFx5iLhmjLJTAIgsu9m1wZlhZFra+81mfvmY0KoJMP0m24KIiSxhXm6e7XXwXwX4PY6qMC4iLV/ocBke/X61uwU1PvosN07R1kA52hAguBjxXnsHU+0T6ClRVhWShoYuR3tgOw8lKDvcCr9OmHTSdO9Uz2Lv+iX8bLi8Oph46ezz+9OYuLG2pCO9F4+jMSTVY2lIRsxq1RGSO06KJiAgwr60OaMfOgaWW1AgC3cEeYT6kljSJFd6xv9m0aHGdw8lGVPph5mI8y4v1V/xEKSpSwBTWSFKL+zK2mOGyGV8VSmAHOrpMP6Nku+JiNo072sDWO8LVQqOrcA1FGfjZySN1DTJC1VycPtjTFObOFaPRNjAPVx2r79CZCE2B2gZ6ArantFYCYuZiGL/13ngbNfnWG55YXVejxczWvVPoIC9moZbnuLGqrdp0OnWiYmCRqG8wuEhEREDwEjriPYcCSi11Bz/FMGSYuOh9rSDrIU5v9k7HNstcFE/FwpkW3R+PixlRNnYkPX6iFFORZHH1ZXDGrshhZ0jF2/7D2hoep42vQreq4r9fH8CMwUVxWqvImH7Xws3BgkxWfinhZHOK06LPnVKLm7a+5/v7FytGYXKdp7tze0MB2huMOz3HP7QI/Hz5KLy9cy+ayrIAdY/v9nDqi8byfWzbMgMdnd1hBcOiqYVq9rs6LHSQdyVZIJ6I+saPljThZ0+9jy5VxQef7wdgXF6DiJJA0f8C/50D5H0v3mtC/UTgGFNTz1s4VBwMDC5GMK41ekyo81ZJ0mbgHekZ+5oFF8X1DycbsT+VC9k0uwFb3/kMJ7cMiPeq9DscPVFUAhu6xKPmYjg8wcXkii4ePNKlCfyMr83FlmOG4PZTRyM/3Wn6uERkIbYYdEqAlW8unGC1mLl4/ox6zX1TGgotZeKKrzcpTjX8XHYFIyqye9Y3dEMXI7GM8ae77MhNC++3abauN544XPN3ONNMOjr93y+DBURkZOGIMjxx/iQUZ7rivSpEFK202UDdASDv0nivCfUTgacCBcK5lyScwQRmLi5vrQQAjKvJtfxakZ6haoOLnmcxyzQUz9WP1szFMyfV4DdntvargGmiYOYixVREmYt9kPvVUpWDf3z4FZa2VOAfH34Z+gEJLJm73pkFn+PVFCVwIBCthKiBGem06DjnYBoF/X+1ugXjarQ1OsO5NpDKQQMRWRTJFDYiSkBySrzXgPqRwHOUmUOKcPqEKjRXZGtuD7xIPndYMeqLJqEix426zY9Zeq1g06LNSNCWnfI2r7QyLTqcmovJfP5JfYfBRYqpSGou9kU85o4Vo/HqR1+jtToXL7yf5MHFJM7AMvuqxeN2XyaWxjy4GMYVwN6jL+psSZxX3Si4aDToMXpLZrHp40eV481P9+LEMcnTuIWIiIiIEkPgeaosS/juvMEAgKe2B28QWluQFtZrRdMXYOsFk3DwSBey3J7mk2YNXcRkgsQ4b6H+hMFFikrgLilRu0WnOW1oG+iZstqVZNOiAe3U22S4ciRJ4TXeEH8DfdlwJ/aZi4nw3QjBxTAeFe/hhdHXbtYAKJBZ1uX42jw8cf6kaFaLiIiIiI5SwRJnYj12NrrQrqrBX8V7jlidrw1kOm1mNRf9/w5nWjSRFYlwJkz9SDhZiEtGlaMix425w4p7b4UMJEu36DSncew/GYKLdpMgm1kQSJO52BsrZCKw+HIkxHcUSeZuzEn+wURf1hddP3VgVI/vMii6aDToSZbtl4iIiIiSm9UkmMAa4ZEwnBYd4bjXrMu1eHNiJEVQf8JfFEVFktSAv60HV649bhie2TgZqSZBtN5iFMRIRGIQUfxUnUkQXDTLODNt6BIiupib6knxn2LSsTlSYkOXWEiImouahi7Wf+vRZhDnpjmierzVzMVQ06KvXDAEALBxZr3BkkRERERE1gQb2ovnL5Proz9HMRrjdnVHlgghmZwuShE2dCGyIvGjFJRU9hw4Etby4QQjYyVJYoumqfYOJfGbVIQdXBT+bfT1PLa+DT9dOgKnT6gyfPzY6pzwVrDHguElUT0+UFVeakyeJzritGjrv5VoN8VoEwqt1lwUfyClWZ6i7dMGFfpuW95aiVc2T8PZ7bXRrRARHVXi1FeMiIgS2MzGIgBAeU7wRkGxyC8wGgt3dHYGfYxZZqN5E03/v21JXMefEhNrLlJMbd/9bbxXIaQkiS1qAq/i8SEZpkWbBhdNQqahai4WZLgwb1iJ6etFmnV39cKhmDgwXxOcisbK8ZX4+kBHzDMswyJ+logumzAc0U5XNhpQhcpcfPKCSfhqfwdKsrQDvtw0Z1TrQkRERER0/vQ6NBSlY0JtftDlYpEwYzSU7ugKnrl4qNN4FpZZsFPT0CVgIVlKniQcSkwMLlKUknAPlCQ128T9vbijT4bgolmavfm0aP+/I/l2OiM8EqY5bVg8siyixxpx2RVcPn9IzJ4vWuF8LGXZ7t5bEQuM1jVUzUWXXdEFFomIiIiIYsFpU7BwhPG5gmTy71jqCDEr2ux1zRIvtA1d5ID7TDpyElnE4CIddZJllykeFI50+a9KJUNw0Sxz0fRAJ/w7kmNad4JcZuuLzufhsFJz8Zent+D9z/dhTFV0U8Oj/QaMMh+t1lwkIiIiIupL4rA/FqcAhtOi1eygj4kmocOm6DMXo291SUezxI9SUEKTJZ7q9xZx539ESHl3JEF9DLFW3qLmUt+/rTR0GV+bG/brdSXIVbbECi1aC7pOGJiHU8dVRv1a0ddc1N9mVHMxQb5qIiIiIiIA5qWfwmE4Ldpk2jMA1GX917SRjHlCh9jQRTa9jygSiR+loIQWGFxMiGa5/YT4UR4WMheTobOXeCVMPLiZrbl4/KvKS8VfN7Zj7eQay68X6w7gTWWZET0uwRIXEyboaoX1movJ856IiIiIqH8Sg3G9lrnYZRxcdCmH8KfTd8NlN27eaGVadOBsuEQ7j6Hkw+AiRUWGdodXkRPfum1WJEu8RczmE69axaPDdrgUk4Ci2bqLB0BZklCR60aq03rVBivTf8NRGUbXZ+2UiMT6bjq7+u7HHu0rGQWIkyGQTkRERERHt1icAhiNpY90Go+wJdkFKe9S0+cyS/gRz7nsATOEEq28EyUfBhcpKlJA5mKiBVeSmbi/P2Jy1SpRiRlnVuqRSAZ/hDP9O1Yfz63LmtE2MA+Xzh1k+TGRNpPpC7HO6Awm2m7RRg83zFxM3I+biJIYhy9ERBSpXpsWbXqSowCScdYiYH5OLt5qVHORKBps6EJRkRAYXIzTioQhWaZVyiaZi8nAJgQGNVMGTJYXA6ne9720pQIPvvYJpg4qDPl6sWroMquxGLMai8N6zKEjiVv6ONmnRbPmIhERERElolg3dBEv1NcXpmP77m8xu7Eo+ifusWX+4KDdopm5SNFicJGikowNXZIlOCHu3kdUBO8UlmhsppmLoYsLe/+V6rThkXPbLL1eYaYL23d/G/Z6xkJCBxcTOKsykNWai0REREREiSQWI1ZxKHzfGWPx/PtfYtpg44YtkcQBl40dgP0d/vOWwFlijC1StDgtmqIiS8mVUZdMxEBcVV4q/nTeRLy8eVoc18g6s2nRprEizTLhH9muWTQUUxsKcO+qlrAfG60pDZ6Dfkmmq89fO5Q+rbkY5UsZPd7G4CIRERERJSArdeXDIV5oz051YO6wYjht5lOfwyVJkua8TDctmuNuihIzFykqybgLSpbMxYJ0Jz78Yr/v7/qi9DiuTXi0jTjErEQrDV3Cf73SrBTcsWJ0+A+MgdqCdPztonbkpTnj8vrB9GXm4vymElz96Ntorc6N6PFGmYtGg5xoazsSEREREUVNMvxnxMIZ4Tpt4eeISdCuZ2DjxGQ8r6fEwuAiRUUKyFxMhp1SsoQmrju+CRf/7nWsnlgd71UJW3QNXZLhV6RVnqBd0vuy5mJRpgtvXTkTrgivsFqNgybL9ktERERER4fY1Fy0vmwkSRWSpE3oCKxtzpqLFC1Oi6aoJGfNxeRY5/IcN361eiza641rbSSyqxY0Isttx3fmNFgKOIsHMx7WYqevay66HbaIp1QYZS5GsxwRERERUV8INi36+uObAAC3LmsO+hxWz1HtsormCOrxS5KkGUfbbYE1F3kWRtFh5iJFhTUXycjAwnT8c/N0yLKEzQ9u891uFngSj2WOCNL8yVhnV/Jsn8nUfIaI+h+zsh1ERERGrB43Fo8swzHDS3TdmQPVFqZZe90oDlfieVa22665jyUXKVoMLlJUAvdBvOJBXt5AopWsRE1wMcSBl6xLpoDdEYuBUCYuEhEREVEyCRVYBIDTJ1ThYEcXJoeYtSZFMXPQaVPw8DkToKqeGUcio2nROakObJxZH/Hr0dGFwUWKCjMXKRRtJzWzZfx3MHMxdjqTKLjY0WkxuNjL60FEREREFEqsc2qcNgUXzAgdyIs2w7CxNNPwdqP38+cNExOyaSUlJp7FU1QknupTCJImc5HTovtScmUuBl/Xxc1lAIBzpw7si9UhoqOMyvEMERGFIV7z9awGF8uyU8J8Xv0Tc04ihYNn8RSVZMxc5LTK+DE7GIoHMyeDizGTTJmLoYLKPzxuGJ66cDKWtVT00RoRERERESWW/R3WzpX+dN5E/GDxMMvPa5S5yJJnFA6exVNUArtFJ8Puh9kJfUtzTDKbFs3MxZg6Z0otAODKBUPivCbW3XHqqKD3y7KEqrxUDnKIiIiIiEJIddrQPCDL8vLMXKRoseYiRSVwWnQynPczc7FviVOhzaZFy2zoElPnT6/DKWMHoCDDFe9VsWxUZQ52/M9cXPXwW7jj2Q/jvTpERERERKby0hO/FmFtQTrOmVKLfAvrapy52AsrRf0Wg4sUlWi6VcXLqMocvPvZvqiL4ZI14kHJ/ADFhi6xJElSUgUWRRfMqMPbO/di2qDCeK8KER1FzC5+ERERGanJT8NVxzYiP8EbnlhpEgOYZS7y2EjWMbhIUUnGmovfmdOA0iwX5gwtjveqHHWMDlqe2/3/ZnDx6OZ22PCr1WPjvRpEREREREGdMnZAvFchZgxP0xhbpDAwuEhRCay5mAzSXXasm8KOs/FgdnyS2NCFiIiIiIgoPgxO6zktmsLBs3iKiq7mIi9vUBBmByhtzUWlb1aGiIiIiIiIDFue8syewsHgIkUlGTMXKX7Mgs8Say4SEVEcMTuDiIhIS+LBkcLAs3iKSmDmIlEwkskeR2LNRSIiiiOW5CAioqOZqurP6xlapHBwJEVRCWzowosbFIx5zUX/vxlcJCKivsZjDxERJbK8NEevPr/htGie21MYOJKiqEicFk1hsJJaz+wRIiLqaw6Fxx4iIkpkvRvp6zbIXJQZXaQwcCRFUZEDrnHYFO6ASEs8TskmP4+ubv9CzB4hIqK+VluQFu9VICIiSihM+qBw2OK9ApTcAjMXrzu+KU5rQsnArKHLkS4huMjsESIi6mOr2qrxxb4OTBtUGO9VISIi6nMGiYts6EJh4Vk8RUUuvM7370fPbUNDUUYc14YSndnx6UiXv3Yng4tERNTXXHYFW44ZggkD8+K9KkRERDrzhhUDAOoL03vl+c+dOhAAcOzwEvxx3QS8sGlKr7wO9V/MXKSoyI4aAC8DYMFXilynkLkom82dJiIiIiIiOgpdMrsBTeWZmDgwv1ee/4RR5WipykF5tpvnYxQRBhcpKmJAkcFFMqIKdTnNigKLmYtERERERETk57IrWDiirFdfY0Buaq8+P/VvDC5SVNhBisJh9nNprclFSaYLA3spzZ+IiIiIiIiIegeDixQVTeaiSbMOOrqJvwuzX4jLruCvF7VDYQo+ERERERERUVJhcJGiwsxFCkewjmM2NnIhIiIiIiIiSjo8m6eosOYihaKtuRjHFSEiIiIiIiKimGNwkaLCzEUKR7DMRSIiIiIiIiJKPgwuUlS0NReJiIiIiIiIiOhowuAiRYWZi0RERERERERERy8GFykqYmiRcUYyoqqhlyEiIiIiIiKi5MTgIkVFZocOIiIiIiIiIqKjFoOLFBVtbJGBRiIiIiIiIiKiowmDixQVdv8lIiIiIiIiIjp6MbhIUREbujDOSERERERERER0dGFwkaLCeCIRERERERER0dGLwUWKiiZzMY7rQUREREREREREfY/BRYoKp0ITERERERERER29GFykqGhrLjLSSERERERERER0NGFwkaLCeCKFcqSrO96rQERERERERES9hMFFioqYuagw0kgGOjoZXCQiIiIiIiLqrxhcpKjIQjxR5q+JDHSr8V4DIiIiIiIiIuotDAdRVMQ6izIzF8mAy87dDBEREREREVF/xbN+iooYT1RkBhdJ77iRZQCAhqL0OK8JEREREREREcWaLd4rQMlN2y06jitCCWtERTaeunAyijJc8V4VIiIiIiIiIooxBhcpKmI8kQ1dyExVXmq8V4GIiIiIiIiIegGnRVPMsOYiEREREREREdHRhcFFihmZNReJiIiIiIiIiI4qDC5SVFTh34wtEhEREREREREdXRhcpKioqj+8yG7RRERERERERERHFwYXKSrazEUGF4mIiIiIiIiIjiYMLlLMMLhIRERERERERHR0YXCRoiLMimbNRSIiIiIiIiKio0yvBBd37NiB008/HVVVVUhJSUFNTQ0uv/xydHR0BH3c5MmTIUmS5r81a9b0xipSjKQ6Fd+/mblIRERERERERHR0sfXGk77zzjvo7u7GbbfdhtraWrzxxhtYvXo19u/fj+uuuy7oY1evXo0rr7zS97fb7e6NVaQYKc5MwXfnDUaaU4HM1EUiIiIiIiIioqNKrwQXZ82ahVmzZvn+rq6uxvbt23HLLbeEDC663W4UFRX1xmpRLzl9QlW8V4GIiIiIiIiIiOKgz2ou7tmzBzk5OSGXu/fee5GXl4fGxkZs2rQJBw4cCLr84cOHsXfvXs1/RERERERERERE1Pt6JXMx0HvvvYef/OQnIbMWly5digEDBqCkpASvv/46Lr74Ymzfvh0PPPCA6WOuueYaXHHFFbFeZSIiIiIiIiIiIgpBUlWx329wl1xyCa699tqgy7z99ttoaGjw/f3JJ59g0qRJmDx5Mm6//fawVm7r1q2YOnUq3nvvPdTU1Bguc/jwYRw+fNj39969e1FeXo49e/YgIyMjrNcjIiIiIiIiIiI62u3duxeZmZmW4mthBRc///xzfPnll0GXqa6uhsPhAAB8+umnmDx5MsaOHYu77roLshzeLOz9+/cjLS0Njz/+OGbOnGnpMeG8eSIiIiIiIiIiItIKJ74W1rTo/Px85OfnW1r2k08+QXt7O0aOHIk777wz7MAiALz22msAgOLi4rAfS0RERERERERERL2rVxq6fPLJJ5g8eTIqKipw3XXX4fPPP8euXbuwa9cuzTINDQ148cUXAQDvv/8+rrrqKrzyyivYsWMH/vCHP2D58uWYOHEihg0b1hurSURERERERERERFHolYYuTzzxBN577z289957KCsr09znnYV95MgRbN++3dcN2uFw4C9/+Qt+/OMfY//+/SgvL8fixYuxefPm3lhFIiIiIiIiIiIiilJYNReTAWsuEhERERERERERRS6c+FqvTIsmIiIiIiIiIiKi/o/BRSIiIiIiIiIiIooIg4tEREREREREREQUEQYXiYiIiIiIiIiIKCIMLhIREREREREREVFEGFwkIiIiIiIiIiKiiDC4SERERERERERERBFhcJGIiIiIiIiIiIgiwuAiERERERERERERRYTBRSIiIiIiIiIiIooIg4tEREREREREREQUEQYXiYiIiIiIiIiIKCIMLhIREREREREREVFEGFwkIiIiIiIiIiKiiDC4SERERERERERERBFhcJGIiIiIiIiIiIgiwuAiERERERERERERRYTBRSIiIiIiIiIiIooIg4tEREREREREREQUEQYXiYiIiIiIiIiIKCIMLhIREREREREREVFEGFwkIiIiIiIiIiKiiDC4SERERERERERERBFhcJGIiIiIiIiIiIgiwuAiERERERERERERRYTBRSIiIiIiIiIiIoqILd4rEGuqqgIA9u7dG+c1ISIiIiIiIiIiSj7euJo3zhZMvwsufvvttwCA8vLyOK8JERERERERERFR8vr222+RmZkZdBlJtRKCTCLd3d349NNPkZ6eDkmS4r06lGD27t2L8vJyfPzxx8jIyIj36hAlPG4zROHhNkMUHm4zROHhNkMUPm43kVFVFd9++y1KSkogy8GrKva7zEVZllFWVhbv1aAEl5GRwZ0KURi4zRCFh9sMUXi4zRCFh9sMUfi43YQvVMaiFxu6EBERERERERERUUQYXCQiIiIiIiIiIqKIMLhIRxWn04nLL78cTqcz3qtClBS4zRCFh9sMUXi4zRCFh9sMUfi43fS+ftfQhYiIiIiIiIiIiPoGMxeJiIiIiIiIiIgoIgwuEhERERERERERUUQYXCQiIiIiIiIiIqKIMLhIREREREREREREEWFwkfrMNddcg9GjRyM9PR0FBQU49thjsX37ds0yhw4dwtlnn43c3FykpaVh8eLF2L17t2aZjz76CHPnzoXb7UZBQQE2btyIzs5Ow9d87rnnYLPZMHz48N56W0S9pi+3mXvvvRdNTU1wu90oLi7Gaaedhi+//LLX3yNRLMVqmzn33HMxcuRIOJ1Ow+PH008/jQULFqC4uBipqakYPnw47r333t58a0S9oq+2GQBQVRXXXXcd6urq4HQ6UVpaiquvvrq33hpRr4jFNvOvf/0LJ510EsrLy5GSkoJBgwbhxhtv1L3W008/jebmZjidTtTW1uKuu+7q7bdH1Cv6crvxYhyg7zG4SH3mmWeewdlnn42///3veOKJJ3DkyBHMmDED+/fv9y2zYcMG/PGPf8T999+PZ555Bp9++ikWLVrku7+rqwtz585FR0cHnn/+edx999246667cNlll+le75tvvsHy5csxderUPnl/RLHWV9vMc889h+XLl+P000/Hm2++ifvvvx8vvvgiVq9e3afvlyhasdhmvE477TQsWbLE8HWef/55DBs2DL/73e/w+uuvY+XKlVi+fDkefvjhXntvRL2hr7YZAFi/fj1uv/12XHfddXjnnXfwhz/8AWPGjOmV90XUW2KxzbzyyisoKCjAL3/5S7z55pu49NJLsWnTJvz0pz/1LfPhhx9i7ty5aG9vx2uvvYbzzjsPq1atwp/+9Kc+fb9EsdBX240X4wBxohLFyWeffaYCUJ955hlVVVX1m2++Ue12u3r//ff7lnn77bdVAOoLL7ygqqqqPvroo6osy+quXbt8y9xyyy1qRkaGevjwYc3zL1myRN28ebN6+eWXq01NTb3/hoh6WW9tMz/84Q/V6upqzWvddNNNamlpaW+/JaJeFck2Iwrn+DFnzhx15cqVMVlvonjprW3mrbfeUm02m/rOO+/02roTxUO024zX2rVr1fb2dt/fF110kTpkyBDNMkuWLFFnzpwZ43dA1Pd6a7vxYhwgPpi5SHGzZ88eAEBOTg4Az9WII0eOYNq0ab5lGhoaUFFRgRdeeAEA8MILL2Do0KEoLCz0LTNz5kzs3bsXb775pu+2O++8Ex988AEuv/zyvngrRH2it7aZ1tZWfPzxx3j00Uehqip2796N3/72t5gzZ05fvTWiXhHJNhPNa3lfhyhZ9dY288c//hHV1dV4+OGHUVVVhcrKSqxatQpfffVVbN8AUR+L1TYTeAx54YUXNM8BeMZv0R6riBJBb203AOMA8WSL9wrQ0am7uxvnnXcexo8fj8bGRgDArl274HA4kJWVpVm2sLAQu3bt8i0jBkm893vvA4B3330Xl1xyCf72t7/BZuNPnPqH3txmxo8fj3vvvRdLlizBoUOH0NnZifnz5+Pmm2/u5XdF1Hsi3WYi8X//93946aWXcNttt0WzykRx1ZvbzAcffID//Oc/uP/++3HPPfegq6sLGzZswHHHHYetW7fG8m0Q9ZlYbTPPP/88fvOb3+CRRx7x3WY2ftu7dy8OHjyIlJSU2L4Zoj7Sm9sN4wDxxU+c4uLss8/GG2+8gWeffTamz9vV1YWlS5fiiiuuQF1dXUyfmyieemubAYC33noL69evx2WXXYaZM2di586d2LhxI9asWYM77rgj5q9H1Bd6c5sRPfXUU1i5ciV+/vOfY8iQIb36WkS9qTe3me7ubhw+fBj33HOPb3x2xx13YOTIkdi+fTvq6+tj/ppEvS0W28wbb7yBBQsW4PLLL8eMGTNiuHZEiam3thvGAeKPwUXqc+vWrcPDDz+Mv/71rygrK/PdXlRUhI6ODnzzzTeaqxa7d+9GUVGRb5kXX3xR83zeLlJFRUX49ttv8fLLL+PVV1/FunXrAHgGtKqqwmaz4c9//jOmTJnSy++QKLZ6c5sBPB3cxo8fj40bNwIAhg0bhtTUVLS1teF73/seiouLe/PtEcVcNNtMOJ555hnMnz8fP/rRj7B8+fJYrDpRXPT2NlNcXAybzaY54Rs0aBAA4KOPPmJwkZJOLLaZt956C1OnTsUZZ5yBzZs3a+4rKirSdWXfvXs3MjIymLVISas3txvGAeKPNRepz6iqinXr1uH3v/89tm7diqqqKs39I0eOhN1ux5NPPum7bfv27fjoo4/Q2toKwFMbbtu2bfjss898yzzxxBPIyMjA4MGDkZGRgW3btuG1117z/bdmzRrU19fjtddeQ0tLS9+8WaIY6IttBgAOHDgAWdYeDhRF8a0DUbKIxTZj1dNPP425c+fi2muvxRlnnBGT9Sfqa321zYwfPx6dnZ14//33fbf9+9//BgAMGDAgyndB1Hditc28+eabaG9vx6mnnoqrr75a9zqtra2a5wA847dwj1VEiaAvthvGARJAvDrJ0NHnrLPOUjMzM9Wnn35a3blzp++/AwcO+JZZs2aNWlFRoW7dulV9+eWX1dbWVrW1tdV3f2dnp9rY2KjOmDFDfe2119THH39czc/PVzdt2mT6uuwSRcmqr7aZO++8U7XZbOrPfvYz9f3331efffZZddSoUeqYMWP69P0SRSsW24yqquq7776rvvrqq+qZZ56p1tXVqa+++qr66quv+jqsb926VXW73eqmTZs0r/Pll1/26fslilZfbTNdXV1qc3OzOnHiRPWf//yn+vLLL6stLS3q9OnT+/T9EkUrFtvMtm3b1Pz8fHXZsmWa5/jss898y3zwwQeq2+1WN27cqL799tvqzTffrCqKoj7++ON9+n6JYqGvtptAjAP0LQYXqc8AMPzvzjvv9C1z8OBBde3atWp2drbqdrvVhQsXqjt37tQ8z44dO9TZs2erKSkpal5ennrBBReoR44cMX1d7lQoWfXlNnPTTTepgwcPVlNSUtTi4mL15JNPVv/73//2xdskiplYbTOTJk0yfJ4PP/xQVVVVPfXUUw3vnzRpUt+9WaIY6KttRlVV9ZNPPlEXLVqkpqWlqYWFheqKFSsYkKekE4tt5vLLLzd8jgEDBmhe66mnnlKHDx+uOhwOtbq6WvMaRMmkL7cbEeMAfUtSVc55IyIiIiIiIiIiovCx5iIRERERERERERFFhMFFIiIiIiIiIiIiigiDi0RERERERERERBQRBheJiIiIiIiIiIgoIgwuEhERERERERERUUQYXCQiIiIiIiIiIqKIMLhIREREREREREREEWFwkYiIiIiIiIiIiCLC4CIRERERRWTFihWQJAmSJMFut6OwsBDTp0/HL37xC3R3d1t+nrvuugtZWVm9t6JERERE1GsYXCQiIiKiiM2aNQs7d+7Ejh078Nhjj6G9vR3r16/HvHnz0NnZGe/VIyIiIqJexuAiEREREUXM6XSiqKgIpaWlaG5uxne+8x089NBDeOyxx3DXXXcBAG644QYMHToUqampKC8vx9q1a7Fv3z4AwNNPP42VK1diz549vizILVu2AAAOHz6MCy+8EKWlpUhNTUVLSwuefvrp+LxRIiIiIjLE4CIRERERxdSUKVPQ1NSEBx54AAAgyzJuuukmvPnmm7j77ruxdetWXHTRRQCAcePG4cc//jEyMjKwc+dO7Ny5ExdeeCEAYN26dXjhhRdw33334fXXX8fxxx+PWbNm4d13343beyMiIiIiLUlVVTXeK0FEREREyWfFihX45ptv8OCDD+ruO/HEE/H666/jrbfe0t3329/+FmvWrMEXX3wBwFNz8bzzzsM333zjW+ajjz5CdXU1PvroI5SUlPhunzZtGsaMGYPvf//7MX8/RERERBQ+W7xXgIiIiIj6H1VVIUkSAOAvf/kLrrnmGrzzzjvYu3cvOjs7cejQIRw4cABut9vw8du2bUNXVxfq6uo0tx8+fBi5ubm9vv5EREREZA2Di0REREQUc2+//TaqqqqwY8cOzJs3D2eddRauvvpq5OTk4Nlnn8Xpp5+Ojo4O0+Divn37oCgKXnnlFSiKorkvLS2tL94CEREREVnA4CIRERERxdTWrVuxbds2bNiwAa+88gq6u7tx/fXXQ5Y95b7/7//+T7O8w+FAV1eX5rYRI0agq6sLn332Gdra2vps3YmIiIgoPAwuEhEREVHEDh8+jF27dqGrqwu7d+/G448/jmuuuQbz5s3D8uXL8cYbb+DIkSP4yU9+gvnz5+O5557DrbfeqnmOyspK7Nu3D08++SSamprgdrtRV1eHk08+GcuXL8f111+PESNG4PPPP8eTTz6JYcOGYe7cuXF6x0REREQkYrdoIiIiIorY448/juLiYlRWVmLWrFl46qmncNNNN+Ghhx6CoihoamrCDTfcgGuvvRaNjY249957cc0112ieY9y4cVizZg2WLFmC/Px8/OAHPwAA3HnnnVi+fDkuuOAC1NfX49hjj8VLL72EioqKeLxVIiIiIjLAbtFEREREREREREQUEWYuEhERERERERERUUQYXCQiIiIiIiIiIqKIMLhIREREREREREREEWFwkYiIiIiIiIiIiCLC4CIRERERERERERFFhMFFIiIiIiIiIiIiigiDi0RERERERERERBQRBheJiIiIiIiIiIgoIgwuEhERERERERERUUQYXCQiIiIiIiIiIqKIMLhIREREREREREREEWFwkYiIiIiIiIiIiCLy/wFWpTK1KnqO+gAAAABJRU5ErkJggg==",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"electric_gas = yf.download(\"QG=F\", start=start)[\"Adj Close\"].dropna()\n",
"\n",
"# Calculate the differences\n",
"electric_gas_diff1 = electric_gas.diff()\n",
"electric_gas_diff2 = electric_gas.diff(4)\n",
"\n",
"# Plot the data\n",
"electric_gas.plot(figsize=(16, 12), subplots=True, color='orange')\n",
"electric_gas_diff1.plot(figsize=(16, 12), subplots=True, color='gold')\n",
"electric_gas_diff2.plot(figsize=(16, 12), subplots=True)"
]
},
{
"cell_type": "markdown",
"id": "e56b19b5-b5e7-4cc4-af2f-23eef8be2831",
"metadata": {},
"source": [
"If you have seasonal data, first order difference won't work, have to use the fourth order difference."
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "803ce381-2a49-4560-a91e-95b88b31efdc",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"g1 = plot_acf(electric_gas_diff1.dropna())\n",
"g2 = plot_acf(electric_gas_diff2.dropna())"
]
},
{
"cell_type": "markdown",
"id": "c67f3ca8-bde5-494e-93a6-9c0f5b1801e0",
"metadata": {},
"source": [
"## AR And MA Processes "
]
},
{
"cell_type": "markdown",
"id": "4d1c15bf-31b9-41d3-a171-5e4544fc0a10",
"metadata": {},
"source": [
"If the disturbance term is generated by the process\n",
"$$\n",
"u_{t}=\\rho u_{t-1}+\\varepsilon_{t} \\quad-1<\\rho<1\n",
"$$\n",
"we call it a **First-Order Autoregression Process**, denoted $AR(1)$. And **innovation** $\\varepsilon_{t}$ satisfies standard features of OLS disturbance term as below, and $\\rho$ is coefficient of autocorrelation at lag $1$\n",
"$$\n",
"\\begin{aligned}\n",
"E\\left(\\varepsilon_{t}\\right) &=0 \\\\\n",
"\\operatorname{Var}\\left(\\varepsilon_{t}\\right) &=\\sigma_{\\varepsilon}^{2} \\\\\n",
"\\operatorname{Cov}\\left(\\varepsilon_{t}, \\varepsilon_{t+s}\\right) &=0 \\quad s \\neq 0\n",
"\\end{aligned}\n",
"$$\n",
"If $|\\rho|<1$ we say that $AR(1)$ process is **stationary**, we'll get back to this topic in more details."
]
},
{
"cell_type": "markdown",
"id": "a28451d8-e858-456d-bc6a-15ca281ee29c",
"metadata": {},
"source": [
"The main alternative is **moving average model** which is a weighted sum of current and previous values of $\\varepsilon$'s, for instance $MA(2)$ is\n",
"$$\n",
"u_t = \\lambda_0 \\varepsilon_t+ \\lambda_1 \\varepsilon_{t-1}+ \\lambda_2 \\varepsilon_{t-2}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "51672ee1-63d4-46fe-829f-4d6e8f87ab55",
"metadata": {},
"source": [
"# Causes Of Autocorrelation"
]
},
{
"cell_type": "markdown",
"id": "173573ea-7c53-4942-9850-485d48257b46",
"metadata": {},
"source": [
"## Model Misspecification"
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "be6c6f57-0b93-428f-b26c-5a65165de57c",
"metadata": {},
"outputs": [],
"source": [
"df = pd.read_excel(\n",
" \"Basic_Econometrics_practice_data.xlsx\", sheet_name=\"Mortality_NI_WB_2019\"\n",
")\n",
"df.head()\n",
"df_mort = df[df[\"Series_Name\"] == \"mortality_rate_per_1000\"]\n",
"df_NI = df[df[\"Series_Name\"] == \"NI_perCap_2010constUSD\"]"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "a1ff877b-cbe2-4d8c-a02b-f8b0b793c1d9",
"metadata": {},
"outputs": [],
"source": [
"reg_results = sp.stats.linregress(df_NI[2019], df_mort[2019])\n",
"Y_fit = reg_results[1] + reg_results[0] * df_NI[2019]\n",
"residuals = np.asarray(df_mort[2019]) - np.asarray(Y_fit)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "6d99cc57-fcea-4528-b5c4-65ed0a207a20",
"metadata": {
"tags": []
},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(nrows=2, ncols=1, figsize=(18, 22))\n",
"ax[0].scatter(df_NI[2019], df_mort[2019])\n",
"ax[0].plot(df_NI[2019], Y_fit, color=\"tomato\", lw=3, zorder=0)\n",
"ax[0].set_xlabel(\"National Income per capita 2019 (Unit: 2010 const USD)\")\n",
"ax[0].set_title(\"130 Countries' Infants' Mortality and National Income\")\n",
"ax[0].set_ylabel(\"Mortality Rate of 1000 birth\")\n",
"ax[0].set_ylim([0, 90])\n",
"ax[0].grid()\n",
"\n",
"ax[1].scatter(df_NI[2019], residuals)\n",
"ax[1].set_ylim([-100, 100])\n",
"ax[1].grid()\n",
"ax[1].set_title(\"Residual Plot\")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "dff0f659-7152-44ae-b9f8-a35608a369f2",
"metadata": {},
"source": [
"## Omitted Variable Bias"
]
},
{
"cell_type": "markdown",
"id": "01351cdd-64d6-4d48-af38-9437c657e3b4",
"metadata": {},
"source": [
"Be aware low $dw$ test might signal the omission of variable, but not vice versa, we can demonstrate with Monte Carlo simulation."
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "61eda220-dc75-4799-b417-1c743fce812f",
"metadata": {},
"outputs": [],
"source": [
"N = 100\n",
"beta1, beta2, beta3 = 3, 4, 5\n",
"X2 = np.arange(N)\n",
"dw_array_omit_X2, dw_array_omit_X3, dw_array = [], [], []\n",
"for i in range(10000):\n",
" u = np.random.randn(N)\n",
" X3 = np.random.rand(N)\n",
" Y = beta1 + beta2 * X2 + beta3 * X3 + u\n",
" df = pd.DataFrame([Y, X2, X3]).T\n",
" df.columns = [\"Y\", \"X2\", \"X3\"]\n",
" model = smf.ols(formula=\"Y ~ X2\", data=df)\n",
" results = model.fit()\n",
" dw_array_omit_X3.append(dw_test(results.resid))\n",
"\n",
" model = smf.ols(formula=\"Y ~ X3\", data=df)\n",
" results = model.fit()\n",
" dw_array_omit_X2.append(dw_test(results.resid))\n",
"\n",
" model = smf.ols(formula=\"Y ~ X2 + X3\", data=df)\n",
" results = model.fit()\n",
" dw_array.append(dw_test(results.resid))"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "32303dce-7c6e-45b4-a90e-3c457347fc82",
"metadata": {},
"outputs": [
{
"data": {
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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(nrows=1, ncols=3, figsize=(18, 8))\n",
"ax[0].hist(dw_array_omit_X3, bins=100)\n",
"ax[0].set_title(\"Durbin Watson Statistic, Omitted $X_3$\")\n",
"ax[1].hist(dw_array_omit_X2, bins=100)\n",
"ax[1].set_title(\"Durbin Watson Statistic, Omitted $X_2$\")\n",
"ax[2].hist(dw_array, bins=100)\n",
"ax[2].set_title(\"Durbin Watson Statistic, Correct Specification \")\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "18b419a5-3314-4026-9166-94dd1a063473",
"metadata": {},
"source": [
"# OLS Estimation With Presence Of Autocorrelation "
]
},
{
"cell_type": "markdown",
"id": "79a06d41-5f20-4a56-a72a-f1f9c30b92cf",
"metadata": {},
"source": [
"As in the case of heteroscedasticity, in the presence of autocorrelation the OLS estimatorsare still linear unbiased as well as consistent and asymptotically normally distributed, but they are no longer efficient (i.e., minimum variance)."
]
},
{
"cell_type": "markdown",
"id": "37158a0b-aa91-45e2-a592-360ed9abd59d",
"metadata": {},
"source": [
"First use a $AR(1)$ model to generate an autocorrelated series as our disturbance term\n",
"$$\n",
"u_{t}=\\rho u_{t-1}+\\varepsilon_{t}\n",
"$$\n",
"choose any $\\rho$ fits your preference, here I use $.98$ "
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "944c3721-318d-4c3c-836f-d49765a4c5d9",
"metadata": {},
"outputs": [],
"source": [
"T = 100\n",
"epsilon = 10 * np.random.randn(T)\n",
"u = [100]\n",
"u_current = u[0]\n",
"rho = 0.98\n",
"for i in epsilon:\n",
" u_next = rho * u_current + i\n",
" u.append(u_next)\n",
" u_current = u_next\n",
"u = u[1:]"
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "070d3d4e-57ed-4fff-8442-6574e7fa6476",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(18, 8))\n",
"ax.plot(u, color=\"tomato\")\n",
"ax.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "5ab804ec-f9d8-493e-b5ee-7b6c5da82c70",
"metadata": {},
"source": [
"Then assume $X$ fixed at $1, 2, 3,..., T$ and define a true relationship as\n",
"$$\n",
"Y_t = 2 + 3 X_t + u_t\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "c3e6e632-2803-4b70-9ab0-2cf297f86149",
"metadata": {},
"outputs": [],
"source": [
"X = np.arange(1, T + 1)\n",
"Y = 2 + 3 * X + u\n",
"PRF = 2 + 3 * X\n",
"df = pd.DataFrame([X, Y]).T\n",
"df.columns = [\"X\", \"Y\"]"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "8deaaaed-e453-4488-94ba-f30288b08770",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: Y R-squared: 0.854\n",
"Model: OLS Adj. R-squared: 0.852\n",
"Method: Least Squares F-statistic: 572.5\n",
"Date: Sun, 09 Jun 2024 Prob (F-statistic): 1.04e-42\n",
"Time: 19:36:44 Log-Likelihood: -435.37\n",
"No. Observations: 100 AIC: 874.7\n",
"Df Residuals: 98 BIC: 879.9\n",
"Df Model: 1 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"Intercept 94.0287 3.830 24.550 0.000 86.428 101.629\n",
"X 1.5755 0.066 23.926 0.000 1.445 1.706\n",
"==============================================================================\n",
"Omnibus: 4.242 Durbin-Watson: 0.237\n",
"Prob(Omnibus): 0.120 Jarque-Bera (JB): 2.845\n",
"Skew: 0.239 Prob(JB): 0.241\n",
"Kurtosis: 2.327 Cond. No. 117.\n",
"==============================================================================\n",
"\n",
"Notes:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
]
}
],
"source": [
"model = smf.ols(formula=\"Y ~ X\", data=df)\n",
"results = model.fit()\n",
"print(results.summary())"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "b1ecba49-9de3-48bb-bf14-c4a71fdce465",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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q69P82B5Bzc8X0O7nS0RERERERESkV9pbBCvmw+Y3wBekRWNiP8i7HXJvhaR+YSuvt2tXWH3fffdx0UUXkZWVRWVlJYsXL2b58uW8//77pKSkcNttt3H33XeTlpaG3W7nRz/6Efn5+f4+v+effz5jx47lxhtv5NFHH+XAgQM88MADzJkzp9WV0+FktVo6dBPCtvL5fET76rEnxWpl5UlqXjF9bJ90Caz5+QL8PapFRERERERERCKOzwtb3zFD6t0rg48dMN5cRT3hKojq2jyzN2pXWH3o0CFmzpzJ/v37SUlJ4ZRTTuH999/nvPPOA+DPf/4zVquVK6+8kvr6ei644ALmz5/vP95ms/HOO+8wa9Ys8vPzSUxM5KabbuKhhx7q2EclEam5lcyRI0eorq4mMTGxzcempaVhs9nwer3s3bs34Lhgt/U0x7becblcjBo1qgurEREREREREREJs7oKWPsPWPU4lLmCjx15oRlSDzkDtO9Up2lXWP30008HvT0uLo558+Yxb968gGOcTidLly5tz91KL3bsavJg/a+bxwUbc9pppwHmiuF3332Xq666qs11xMTEcMopp7B27Vo+/vhjbr311lbH/etf/2rznN1dXl4eMTExNDQ08PbbbyusFhEREREREZHI4C42A+o1/4CGysDjouJh0vdh+izoOyJs5UUy9Z2QLmW32/1fl5WVnXBcsDEjRoxgxowZAPzyl7+kvLw86H2Xlpa2uHzNNdcA8PLLL7Nt27bjxh86dIjHHnss6Jw9SWJiIt///vcBeOSRRygpKQk6/pvPl4iIiIiIiIhIj2EY4FoBL94Af5sMK+cHDqqTB8I5v4G7N8O3/0dBdRgprJYulZqa6t/QcOHChf5NDr9p/PjxAFRUVPDSSy8FnO9///d/SUpKYvv27UyfPp0333yTuro6/+179+7lH//4B+eccw733ntvi2NnzZpFRkYG9fX1XHjhhXz00Uf+ldyrVq3i3HPPxefzndTjbVZVVcWRI0eCfhzbU7qz/P73v2fQoEEcOXKE/Px8/vGPf1BZ+fUP6sOHD/Pqq6/y3e9+l+uuu67T6xERERERERER6VBeD2x4BZ48CxZeCFveBiNAvjNoMlzxFPxkA5x+NySkhbdWUVgtXe+uu+4Cvg6as7KyyM7O5tprr/WPGT58OOeccw5groC22+1kZ2eTnZ3NX/7yF/+48ePH895775Gens7WrVv5zne+Q1JSEn379iUhIYGMjAxmzpzZajsPu93O66+/TmpqKsXFxZx77rkkJSWRnJzM9OnTKS4u5vHHH++Qx/yjH/2Ifv36Bf3YsGFDh9xXMAMHDuTDDz9k5MiR7Nu3j5kzZ5KamkqfPn1ISkqif//+XHXVVbzxxhsdFtSLiIiIiIiIiHS6Wjf8+8/w14nw6m2wb22AgRYY/W245T24/WM45Xtgiw5rqfK1dvWsFukM999/P3a7nX/84x9s3bqVPXv2YBgG2dnZLca98sorPPTQQ/zzn/+kpKQEl8tsfP/N1iCnnXYa27dv54knnuCtt95i06ZNlJWVER8fz5gxY8jJyeGiiy7i8ssvP66W3Nxc1q9fz0MPPcS7777L4cOH6devH1deeSUPPPAAUVG975QZM2YM69ev55lnnuHVV19l3bp1lJaWEhMTw/Dhw5k8eTLnnXdeu3qAi4iIiIiIiIh0iSNfwqoFsG4xeGoCj4tJgsk3wrQ7IW1I+OqToCxGsB3ruqmKigpSUlIoLy9v0fM4mLq6Onbt2sWQIUOIi4vr5ArbzufzUVFRgd1ub7HZoIj0fjr/5Vjd9d8p6Rwej4elS5dy8cUXEx2tVRsikUTnv0jk0vkv0okMA3Z9avah3v5e8LEpWWZAPeVGiEsJT31E9s+A9mS5vW+ZqIiIiIiIiIiIiPR+jfVmP+qVC+DgCdqpZk6D6bPNlh82RaLdlb4zIiIiIiIiIiIi0nNUH4GCp6HgKag+FHicxQbjvgPT50BGTtjKk9AprBYREREREREREZHu79AWWDEP1r8E3vrA4+JSIOdmmHoHpGSErTw5eQqrRUREREREREREpHvy+WDnv2DlPPNzMGlDYdosmPR9iE0KT33SoRRWi4iIiIiIiIiISPfiqYUvlpj9qI9sCz42+3TInwMjLgCrNTz1SadQWC0iIiIiIiIiIiLdQ+UBWP0kFP4daksDj7NGw4TvwfRZMPCU8NUnnUphtYiIiIiIiIiIiHSt/V/Aivmw8VXweQKPS+gDubdB3g8geUD46pOwUFgtIiIiIiIiIiIi4efzwvb3zJDa9e/gY/uNhumz4ZSrITo+PPVJ2CmsFhERERERERERkfCpr4J1z5v9qN27go8dfq4ZUg87GyyW8NQnXUZhtYiIiIiIiIiIiHS+st2w+nEoehbqywOPi4qDidfCtFnQf3T46pMup7BaREREREREREREOs/uAlg5Dza/BYY38LikdJj6A8i5FRL7hK8+6TYUVouIiIiIiIiIiEjH8jbClrdg5XzYUxB8bPopkD8Hxl0BUTHhqU+6JYXVIiIiIiIiIiIi0jFqy2DNs7D6CSjfHWSgBUZdDPmzwXma+lELoLBaRERERERERERETlbpV7DqcVj7HDRUBR4XnQiTr4dpd0GfYeGrT3oEhdUiIiIiIiIiIiLSfoYBrs/NVh9b/wkYgcfaM2DaHTDlJohPDVeF0sMorBYREREREREREZG2a2yATa+bmybu/yL42MG5ZquPMZeDTVGkBGft6gJEeoJFixZhsVjIzs6OyPuXnm/58uVYLBYsEdIDrLi42P94i4uLu7ocERERERGR3qGmFD79E/z1FHj9jsBBtcUKY78Dt30At38E469UUC1torBa2m3u3Ln+EOjYj7i4ODIyMrjssst46aWXMIwgf/ohgBmozZ07l7lz53Z1KZ3i2MDw2A+bzUZqaiq5ubnce++9lJSUdHWp0o01v25663kiIiIiIiLS7R3eDm//BP5nLPzrt1C5v/VxsXbI/yH81xdw9TOQOTWsZUrPp7c05KQMGDDA/3V5eTl79+5l7969vP322yxatIjXX3+d2NjYLqyweysuLubBBx8ECBrEpaSkMGrUKAYPHhymyjqe3W4nPj4eAI/HQ2lpKUVFRRQVFTF//nxeeuklLrrooi6usvdKSEhg1KhRXV1G2ERHR/sfb3R0dBdXIyIiIiIi0gMZBnz1MayYD19+EHysIxumzTI3ToxNDkt50jtpZbWclAMHDvg/qqur2bhxI+eddx4A7777Lg888EAXV9g7fPe732Xr1q189NFHXV1KyP7617/6XytHjx6lurqahQsXkpqaSlVVFddddx2lpaVdXWavNXXqVLZu3crWrVu7upSwGDx4sP/x9uQ3eURERERERMLOUwdrnoUFp8I/vhs8qHaeBtc8Dz9aA9PvUlAtJ01htXQYq9XKuHHjeOuttxg+fDgAjz/+OI2NjV1cmXRHCQkJ3Hzzzfztb38DzJX5r7zyShdXJSIiIiIiIhKhqg7Bx7+HP4+Dt34Ehza3Ps4aBadcA3csh1uWwphvg9UW1lKl91JYLR0uLi6O733vewBUVlYet5Jz586dzJo1ixEjRhAfH4/dbmfKlCk89NBDVFRUtDrnNzeHKyws5KqrrmLgwIHExcUxfPhwfvazn1FWVtbq8c19tmfMmBGw7lA3oPN4PLz11lvccccd5ObmMnDgQGJiYujfvz8XXHABL7zwQqv9u7OzsznrrLP8l7/Z1/nmm2/239aWDRY74nn98ssvufXWW8nMzCQ2NpaMjAxuv/129u7d267npD0uvPBC/9ebNm0KOO6f//wnV155JYMHDyY2NhaHw8EZZ5zBggULaGhoCHicYRgsXLiQ/Px8kpOTSUlJYdq0aTzxxBMYhsHNN9983PPdLDs7G4vFwqJFi6iqquLXv/41EyZMIDk5udWN+/7zn/9www034HQ6iYuLIyUlhalTp/LII49QVVUVsMb333+fK664goyMDGJiYrDb7QwdOpTzzz+fP/3pT62uOF+1ahXXX389Q4YMIS4ujsTERJxOJ2eeeSa//e1v2bNnT4vxbXl9HzhwgJ/97GeMGzeOxMREEhMTGTduHD//+c85ePBgq8d8cyPDgwcP8l//9V/+ugYMGMC1114b9hXdwTZY7KjXfUNDA/Pnz+ess86ib9++xMTEkJ6ezuWXX867777bWQ9NRERERESkYx3YCG/MNkPqTx6BmiOtj4t3wOn3wE82whVPwKDJ4a1TIoJ6VkunyMjI8H99bFD60ksvMXPmTOrr6wFITk6moaGBtWvXsnbtWp566inef/99xowZE3DuN998k6uvvpqGhgbsdjuGYbBz507+9Kc/8fLLL7N8+fKgoW5H+89//sPll1/uv2y324mLi+Pw4cMsW7aMZcuW8frrr7NkyRKs1q/fH+rXrx8VFRW43W6gZf9vMPtUt1VHPK8ff/wxl112GVVVVSQnJ+Pz+di7dy9PPfUUS5cuZfXq1Z3STuHYIN/r9R53e21tLTNnzmyx6tput1NeXs5nn33GZ599xrPPPsvSpUtxOBwtjvV6vVx//fW8+OKLgPmGQGpqKoWFhaxevZrly5cTExNzwhqPHj1KTk4O27dvJyYmhoSEhBa3+3w+fvrTn/pXiQMkJSVRXV1NQUEBBQUFLFy4kPfffx+n09ni2EcffZSHH37YfzkhIQHDMNi1axe7du3igw8+IDc3t8UbLc888wy33HKL/7mLjY0lKiqKkpISSkpK+PTTT8nMzGw1gA/kk08+4Tvf+Y7/DZ/ExEQANm/ezObNm3nqqad46623+Na3vhVwjk2bNnHrrbdy6NAh/3N06NAhXnzxRd59910+/fRTJk6c2OaawiHU173L5eKSSy7xv8FisViw2+0cPHiQt956i7feeou77rqLBQsWhPshiYiIiIiInJjPBzuWwcp5sOvT4GP7jIDps2DidRCTEHysyEnSyupmPh9UH+mSD0vN0c69D58v7E/nsSsZ09LSAFizZg033HAD9fX1nHbaaaxfv56Kigpqamp46623GDhwILt37+bSSy8Nugr1pptu4tRTT2Xz5s2Ul5dTXV3Niy++iMPhwOVycfXVV7caenaWhIQE7rzzTj744APKy8spLy+noqKCo0eP8te//hW73c7LL7/M//3f/7U4rqCggNdee81/+dj+3wcOHOCvf/1rm+6/o57XK6+8krPPPpstW7ZQUVHhf16Tk5PZt28f9913X2hP0Am89957/q+HDh163O133HEHr7zyCkOHDuX555/3P8c1NTW8+eabDB06lJUrV3Lrrbced+wf//hHf1B99913c/jwYUpLS3G73fz+979nyZIlvPXWWyesce7cuVRUVPD6669TVVWF2+1m9+7d9O/fH4Df/OY3/O1vf6N///7MmzePo0ePUllZSW1tLR9//DGTJ09m27ZtXHHFFfiOOR9dLhePPPKIv769e/dSXV1NZWUlZWVlfPbZZ8yePZvk5K97ftXU1PCjH/0IwzC44YYb+PLLL6mrq6O8vJyqqioKCwv52c9+5q+tLXbv3u0PqseOHcu///1vqqqqqKqq4tNPP2XUqFG43W4uv/zyoKuNb7zxRkaMGEFBQQHV1dVUVVXxwQcfMHDgQCoqKvjRj37U5prCJZTXfXV1NRdeeCGbNm1ixowZLF++nNraWsrKyigrK+N//ud/SEpK4rHHHmvzeSwiIiIiIhIWDdWw+kmYlwcvXBM8qB46A77/MsxZDXm3KaiWsNDK6ma1pfDHYWG/WyvQ9vWzIfrZTkjs29n34ldRUcHzzz8PmEH1yJEjAfjlL3+Jx+Nh+PDhLFu2zL/y0mq1cumll5KRkcHUqVPZuXMnjz32GP/v//2/VucfMGAAS5cuJT4+HoCoqCiuvvpq0tLSOO+88/whcHMrks42depUpk6detz1aWlp/PjHP2bQoEF873vf429/+xs//vGPO/z+O+p5nTRpEq+//rp/9XdMTAxXX301Bw8e5Mc//jGvvPIKf//734mK6pgfGzU1Nbz88sv85Cc/AczVwdddd12LMZ999hnPPfcc/fv3Z/ny5WRmZvpvi4uL47LLLmPKlCmMHj2aN954g3Xr1jFp0iTADBSbVyzfdttt/H//3//nP9Zut3PfffdRX1/Pgw8+eMJaa2tr+fTTT5k8+es/cWr+64Hi4mIefvhh4uPjWbZsWYuVw9HR0cyYMYNPPvmEsWPHsmbNGt566y2+853vAGYrD5/Px8iRI1vUB+bK+m9961vHrWTeuHEjlZWVJCYmsnDhwhbfj8TERHJycsjJyTnhYzrW73//e8rKynA4HHz00Uekp6f7bzv99NP58MMPGTduHKWlpTz88MPHvfHSbMCAAXzwwQctzs1zzz2Xxx9/nMsuu4zPPvuMPXv2tPjLi64Wyuv+f/7nf9i6dStnnnkmy5YtIzo62n9bSkoKP/3pT8nOzuaKK67gv//7v5kzZ06HnTciIiIiIiIhKd8Lq5+AokVQVxZ4nC0WTvkeTJ8NA8aFqzoRP62slg5TVlbGRx99xNlnn82+ffsA+K//+i+sVitlZWW8//77APzsZz87ro0CwOTJk7niiisAeOGFFwLez89+9jN/GHasc889l1NPPRWAJUuWnPTj6SiXXHIJYPaUPnDgQIfO3ZHP6/3339+iTUmz5hYntbW17NixI+Ra/+u//ov09HTS09Pp06cPiYmJ3HzzzZSVlREdHc0zzzzDwIEDWxzz9NNPA3D99de3CKqPlZGR4e/93fxcACxbtszfguaXv/xlq8fec889rT5n33ThhRe2CKqPtWjRIrxeLxdeeGHAFhfJycn+gPrYGlNTUwGzt3t1dfUJ6zj2mIaGBo4ePdqmY4IxDIOXXnoJgLvuuqtFUN0sIyODu+66Cwh+bt1zzz2tnpsXXXSRv93Khg0bTrrmjhTK6775dXn33Xe3CKqP9Z3vfAe73c6RI0coKirq4KpFRERERETaaO8aePUH8NdT4D9/CRxUJ/SFGffBTzfB5fMUVEuX0VIvOSnBNmu74YYb/CHhmjVr/P11zz333IDHnHfeebz00kusX78ej8fTahB09tlnBzz+7LPP5vPPP6ewsLCtD6FDVFZW8thjj/HOO++wZcsWysrK8Hg8x43bs2dPq2FgqDryeZ02bVqrxw4aNMj/dWsb/bVVRUVFqxs9ZmVl8f777zN69OjjbvvPf/4DmOHg4sWLA85dXl4OmG01mq1Zs8Y//5AhQ1o9Ljk5mZycHD777LOgtZ922mkBb2uucdmyZUG/t80tWI6tcerUqfTp04f9+/czbdo07rrrLs4991xGjRoV8NwaNmwYo0ePZuvWrUybNo1Zs2ZxwQUXMGHCBGy29u++vGvXLv/39USvoUcffZSjR4+ya9euVp/TQK+hqKgo+vXrx969e0/qNdQZ2vu637t3r/97eNtttwV9zo/9nge6HxERERERkQ7n88LWf8LK+VCyIvjY/uPMftQTvgfRceGpTyQIhdVyUo7dFDA2Npa+ffsyefJkrr/+ev9qVzA3WWsWbJO+5vYAjY2NlJaWHrfp4ImOb77t2PvrbNu3b+ecc85hz549/usSEhJITU31r9g8ePAgQJtXz7ZVRz6vx/ZFPtax7QtaC+DbauHChf4N/yoqKlizZg0PPPAA//nPf7jlllv44IMPSEpKanFM8wr9QEH3N9XU1Pi/Pnz4MNAydGxNWzaNDNb/ubnG6urqNn1/j60xNTWVp556ijvuuINNmzb5ezqnpKRwxhlncPXVV3PNNde0eHPBZrOxZMkSvvvd77Jr1y5+8Ytf8Itf/IKEhAROPfVUrrjiCm666aY2rRiH9r+Gmo9pLawO9BqCr19HJ/Ma6gztfd03f78BjhwJsEP2Nxz7PRcREREREek0dRWw9jlY9RiUuYKPHXG+2epj6AwIshBRJNwUVjeLTzN7O4eZz+ejsrKS5OTkVv8UvUPEp3XOvNDhbS16oltuuYU9e/aQnZ3NH//4R84++2z/ppIAXq/XH3w1r4KOdHa7nRkzZrBs2TKmTp3KypUr+eEPf8iiRYtajGveKHPBggX+NhTtFWz1f1sFWz3bXOO9997LH/7wh3bPPWPGDHbu3Mkbb7zBRx99xOeff86OHTt4++23efvtt/nDH/7A+++/3yJInjhxIlu3buWdd97h/fff5/PPP2fTpk18+OGHfPjhhzz88MP885//ZMKECe1/sBLUsZu3btmypdW/CBAREREREQkrtwtWPQ5rnoWGysDjouJh0nUwbRb0Gxm++kTaQWF1M6s1rJsQ+vl8GN4YSLSbNfRSx65M3bNnD8OGtb6ZZfPq5KioqBaB77H27t3L0KFDA972zftrng+grq4uYI3NrSTaY/fu3Xz++eeA2Q96+vTpx43pzEC/I5/XrpCQkMD//u//cvbZZ/PMM89wxx13+PuOA6Snp+NyuVq0zmirfv36AS1Xwram+TUTqvT0dLZt2xZSjc0SExO58cYbufHGG/01Pf/88/zmN7/xr7h+7bXXWhwTExPDFVdc4e9HfvToUV555RXuv/9+du/ezU033eRvhRLMN19Do0aNanXcsX85EGyleW93bKsXl8ulsFpERERERLqGYcDuVbBiHmx9Bwxf4LHJA2Hq7ZBzCyR0n0xApDW9Nx2VbmXKlCn+leMfffRRwHEffvghYK4cDbRx2ccffxzw+ObbcnNzW1zvcDgAM1wOZNWqVQFvC+TY+QJtwNf8mFpz7Gr6UFZdd+Tz2lXOOusszjzzTAB+8YtftLituVf0O++80+55p0yZApiBYnFxcatjqqqqTnrzu+YaP/zww6BvhrTH4MGD+fnPf84999wDwAcffHDCY/r06cOdd97JI488AsDatWvbtAHjkCFD/G9gtOU11KdPn4A9wCNBdna2f5X722+/3cXViIiIiIhIxPF6YMMr8OTZ8PcLYMtbgYPqgZPgiifhv9bD6fcoqJYeQWG1hEVqaioXXHABAH/84x9b7eH6xRdf8OqrrwJw3XXXBZzrT3/6U6uh4Mcff+zf7O6aa65pcdvEiRMBc5Vta6H0oUOHePLJJ9v4aL6WkpLSov5vqqys5L//+78DHm+32/1fl5WVtfv+O/J57UrNG3F+9tlnLYLZO+64A4CNGzeyYMGCoHNUV1fT0NDgv3z++ef7n9/f//73rR7z5z//+aT7Cd96661ERUVx5MgRfvOb3wQd29DQ4N90D6C+vj7o+Pj4eKDlmxptPeabxwVisVj858vjjz/e6l8C7Nu3j8cffxzovq+hcLr99tsBc+PPtWvXBh3b3TaUFBERERGRHqrWDf/+M/x1Irx6G+wL9Je0Fhj9bbjlXbhjOZxyNUTFhLNSkZOisFrC5r//+7+Jjo7myy+/5IILLmDDhg2A2bd76dKlXHzxxTQ2NjJs2DDuvPPOgPPs37+fSy65hG3btgHmpoGvvPIKV111FWCuqG1ujdDs1FNPxel0AnDTTTdRWFiIYRj4fD6WL1/OjBkz8PmC/MlMAGPGjCErKwswQ8tjV+muWLGCGTNm4Ha7Ax4/cuRIYmLMfzSeeuqpkFZXd9Tz2pXOO+888vLyAPj1r3/tv/7MM8/klltuAWDOnDn89Kc/5auvvvLfXl9fz8qVK/n5z3+O0+lssVlgYmIi9957LwBPPvkkP//5z/3BYWVlJY888ghz5871r7oP1bBhw/jVr34FwKOPPsrMmTPZuHGj//bGxkbWrVvHQw89xPDhw1m3bp3/tkcffZSrrrqKf/zjHy3abNTX1/PSSy/xxz/+EYBLLrnEf9uSJUs47bTTePzxx1s8F16vl/fff9+/Oj0/P7/Nj+3+++8nNTWV0tJSzj33XH9rG4D//Oc/nHvuuZSVlZGWlnbc6vdwqqmp4ciRI0E/jn3DorPcc889TJgwgbq6Os466yz+7//+r8Uq9rKyMt59911mzpzJ6aef3un1iIiIiIhIL3bkS/jnPfA/Y+HDuVARoJVlTJLZi/rHa+Ha58F5qjZOlJ7J6IHKy8sNwCgvL2/zMbW1tcbmzZuN2traTqys/bxer+F2uw2v19vVpbTZb37zGwMwQnn5LFmyxIiJifEfb7fbjbi4OP/lzMxMY/Pmzccd9/HHH/vHvPHGG0Z0dLQBGCkpKUZsbKz/tqysLOOrr75q9b7fe+89/3GAkZCQ4L/vESNGGC+88ELAx7Vw4UIDMJxO53G3vf3220ZUVFSLeRMSEgzASExMND788EP/bR9//PFxx992220tjs3KyjKcTqdxzz33tOn+O+p5DSZY/cHs2rXLf+zChQuDjn399df9Y9955x3/9fX19cYPfvAD/22AkZSUZDgcDsNqtba4fs+ePS3m9Hg8xlVXXeW/3Wq1Gg6Hw7DZbAZg3HjjjcbMmTMNwLjzzjuPq8npdLapdp/PZ/zqV78yLBaL/77i4+ONPn36+O+r+ePf//63/7hf//rXLW6Lj4830tLSWswzZswYY//+/f5jml8LzR+xsbFGnz59WjwXgwYNMrZs2dKixhN9r5cvX26kpKT4xyQmJhqJiYn+y6mpqcann3563HHHfo937doV8Dlq63PZmmMf74k+Xn/99RPW1RGv+7179xrTp0/3j7FYLEZqaqpht9tb1DN8+PA2P87u+u+UdI6GhgbjjTfeMBoaGrq6FBEJM53/IpFL57+0mc9nGF99YhjPX2MYv0kxjN/YA3/8z3jD+M//GkZtWVdXLScQyT8D2pPlamW1hNU111zDpk2buPPOOxk2bBj19fVERUUxadIkHnzwQTZu3MiYMWOCznH55Zfz+eefc+WVVxIXF4dhGAwZMoR77rmHdevWBeyne8EFF/DZZ5/x7W9/G4fDgdfrJTMzk1/84hcUFRW12DitPb797W/z6aefcskll5CamkpjYyN9+/bllltuoaioiHPOOSfo8fPmzWPu3LlMmDABgJKSElwuF0eOHGlzDR3xvHa1yy+/nHHjxgEtV1fHxMTw5JNP8vnnn3PzzTczbNgwvF4vVVVV9O/fnxkzZvDrX/+a9evX+3sJN4uKiuKll17iqaeeYurUqcTHx9PY2Ehubi5PPfUUzz77rL/9Smpqasi1WywWHnroIdavX8/s2bMZM2YMNpuN8vJyHA4Hp556Kj/72c/4/PPP/T2uwWwn8Ze//IVrr72W8ePHk5CQQEVFBQ6Hg9NPP52//OUvrFmzpsVr87LLLuPZZ5/llltuYeLEiaSkpFBeXk5ycjJTp07lt7/9LZs2bWr3xn9nnnkmW7Zs4Z577mHMmDH4fD4Mw2DMmDH8v//3/9iyZYtWCR9j0KBB/Pvf/+aFF17gsssuY+DAgdTU1NDQ0EB2djaXXnopf/nLX/j000+7ulQREREREekpGuth3WJ47HR45lLY/i7mOphWZE6D7z1jrqQ+9YcQl9L6OJEexmIYIfQd6GIVFRX+gObYnr/B1NXVsWvXLoYMGUJcXFwnV9h2Pp+PiooK7HZ7m/rLRqrly5dz1llnAaFtRCjSGsMwyMrKYs+ePTz77LPceOONYb1/nf9yrO7675R0Do/H42/V1N02vhWRzqXzXyRy6fyXgKqPQOHfYfWTUH0o8DiLDcZ9B6bPgYycsJUnHSOSfwa0J8uNClNNIiLdTnOv6KioKM4999yuLkdEREREREQiyaEtsHI+fPEieOsDj4tNgZybYOodkJoZvvpEuoDCahHp1a677jquvPJKZsyYQd++fQE4ePAgCxcu5De/+Q0AM2fOZODAgV1ZpoiIiIiIiEQCnw92/gtWzjM/B5M21Nw0cdL3ITYpPPWJdDGF1SLSq7377rssWbIEgISEBKKjoykvL/fffvrpp/PnP/+5q8oTERERERGRSOCphS+WwMoFcGRb8LHZp8P02TDyQlDLSIkwCqtFpFf729/+xrvvvsvatWs5dOgQVVVV9OvXj0mTJnHttddy4403RlyvKBEREREREQmTygNmL+rCv0NtaeBx1miYcJUZUg88JXz1iXQzCqulR5gxY4Y2VpSQzJw5k5kzZ3Z1GSIiIiIiIhJJ9n8BK+bDxlfB5wk8LqEP5N4KeT+A5PTw1SfSTSmsFhEREREREREROVk+L2x/zwypXf8OPrbfaJg+C065BqLjw1OfSA+gsFpERERERERERCRU9VWw7nmzH7V7V/Cxw86B/NnmZ4slPPWJ9CAKq0VERERERERERNqrbDesfhyKnoX68sDjouLMFdTTZ0P/0eGrT6QHiriwWn2PRUSkO9K/TyIiIiIiPcSeQljxf7D5LTC8gcclDYC82yH3FkjsG776RHqwiAmrrVYrAF5vkB8iIiIiXaT536fmf69ERERERKQb8TbClrdg5XzYUxB8bPoEmD4Hxl8BUbHhqU+kl4iYsDo6Opro6GiqqqpISkrq6nJERERaqKys9P9bJSIiIiIi3URdOax5FlY9DuW7gwy0wKiLzFYf2d9SP2qREEVMWG2xWEhOTqasrIyUlBTi47XTqoiIdA+1tbVUVFSQmpqKRb/UioiIiIh0vdKvzIB67XPQUBV4XHQiTL4ept0FfYaFrz6RXipiwmqAvn37UltbS0lJCXa7neTkZGw2W5cGAz6fj4aGBurq6vSn3yIRRud/ZDMMA6/XS2VlJRUVFcTGxtK3r/rYiYiIiIh0GcMA1+dmq4+t/wSC7CtjHwxT74CcmyDeEbYSRXq7iAqrbTYbmZmZHDlyhMrKSsrKyrq6JAzDoLa2lvj4eK2mE4kwOv8FzDZVqamp9O3bF5vN1tXliIiIiIhEnsYG2PQ6rJwH+78IPnZwDuTPgTGXgU0t/EQ6WkSF1WAG1gMGDKB///54PB58Pl+X1uPxePj0008544wz1KdUJMLo/Ber1Up0dLTerBARERER6Qo1pVD4dyh4Cir3Bx5nscKYS81NEzOnqh+1SCeKuLC6mcViISYmpqvLwGaz0djYSFxcnMIqkQij819ERERERKQLHN5utvr4Ygk01gYeF2uHKTPNdh8OZ/jqE4lgERtWi4iIiIiIiIhIhDAM+OpjWDEfvvwg+NhUJ0yfBZNvgNjk8NQnIoDCahERERERERER6a08dbDhJVi5AA5tDj4261TInw2jLgar9pMR6QoKq0VEREREREREpHepOmT2oi54GmqOBB5njYJxV5grqQdPCV99ItIqhdUiIiIiIiIiItI7HNho9qPe8DJ4GwKPi3dAzi0w9XawDwpffSISlMJqERERERERERHpuXw+2LEMVs6DXZ8GH9tnhLmKeuJ1EJMQnvpEpM0UVouIiIiIiIiISM/TUA3rFsOqx+Dol8HHDp0B0+fA8HPBag1LeSLSfgqrRURERERERESk5yjfC6ufgKJFUFcWeJwtFk75HkyfDQPGhas6ETkJCqtFRERERERERKT721sEK+bD5jfA1xh4XGI/yPsB5N4GSf3CVp6InDyF1SIiIiIiIiIincnrhXdfApLMz5dcCzZbV1fVM/i8sPWf5qaJJSuCj+0/DvJnw/irIDouPPWJSIdSWC0iIiIiIiIi0pmWLoGlL8JFt5mfLcCl13d1Vd1bXQWsfc7sR13mCj52xPlmq4+hM8BiCUt5ItI5FFaLiIiIiIiIiHSmHRsBo+mC0XRZWuV2warHYc2z0FAZeFxUPEy6DqbNgn4jw1efiHQqhdUiIiIiIiIiIp1pxHjYvqnpgsW8LF8zDNi9ClbMg63vgOELPDZ5IEy9HXJugYS08NUoImGhsFpEREREREREpDNdfK25sNoALr7GvCzg9cDmN82Qet+a4GMHToL8OTD2OxAVE47qRKQLKKwWEREREREREelMNhtcdDUsXWp+jvTNFWvdULQIVj8JFXuDDLTA6EvMkDorX/2oRSKAwmoRERERERERkd7A6zU3c9yx0Ww1cvG13SsYP/IlrFoA6xaDpybwuJgkmHwjTLsT0oaErz4R6XIKq0VEREREREREeoOlS+DN5wADNq8zr7v0+q6syOxHXfwZrJgP29/j640mW5GSZQbUU26EuJSwlSgi3YfCahERERERERGR3mDHRr4Og42my12ksR42vmqG1Ac3BB+bOQ2mz4bR3waboiqRSKafACIiIiIiIiIivcGI8U0rqg3AYl4Ot+ojUPh3sx919aHA4yw2GPcdmD4HMnLCVl6P0d1buoh0EoXVIiIiIiIiIiLt0V2DxIuvNT8fW9eJdNRjObQFVs6H9S9BY13gcbEpkHszTL0DUjLafz+Roju2dBEJA4XVIiIiIiIiIiLt0V2DRJut/XWczGMxDPjyI1g5D3b+K/jYtKEwbRZM+j7EJrWvxkjUnVq6iISRwmoRERERERERkfboTUFiKI/FUwvrX4SVC+Dw1uBjs083+1GPvBCs1pOtNnJ0h5YuIl1AYbWIiIiIiIiISHv0piCxPY+l8gAUPAUFT0NtaeBx1miYcJUZUg88pYMLjhChtHQR6QUUVouIiIiIiIiItEc4gsRw9cVuy2PZv97sR73hFfB5As+V0Adyb4W8H0ByesfXGklCaeki0gsorBYRERERERERaY9wBInh6osd6LH4fLD9PTOkLv6s5W0GUJkB9ckQWwlDkyB/FpxyDUTHd0xd3XUTSxHpVAqrRURERERERES6m67qi11fBesWw6oFUPpV62MqM6AiA7BAfSpk3QA5N3RsHaGE9aEE3ArFJczqPV6io6O7uoxuS2G1iIiIiIiIiEh3E+6+2OV7YNXjsOYZqCsPPC4qDmJHATVfX/flpo6vJ5SwPpSAO1wr2CUiVdR5WONyU+Rys851lKv6w9vr93Pd9CFdXVq3pbBaRERERERERKS7CdcGe3sKYcU82PwmGN7A45IGQN7tkHsL/Ov9rwPezgrSQwnrQwm4u2oFe2fQKvEuZRgGe8tqKXK5KSx2U1BcyraDlRhNL69Ym8FV/WFtSRnXTe/aWruzdoXVDz/8MK+99hpbt24lPj6eU089lUceeYRRo0b5x8yYMYNPPvmkxXF33nknjz32mP9ySUkJs2bN4uOPPyYpKYmbbrqJhx9+mKgoZeciIiIiIiIiIp3aF9vbCFvfhhXzYc/q4GPTJ8D0OTD+CoiKNa8LR5Aeyn2EEnCHewV7Z9Iq8bBq9PrYeqCSwuJSCptWT+8vrzvhcWt3u8NQXc/VrnT4k08+Yc6cOeTl5dHY2Mj999/P+eefz+bNm0lMTPSPu/3223nooYf8lxMSEvxfe71eLrnkEtLT0/n888/Zv38/M2fOJDo6mt///vcd8JBEREREREREROQ4deWw5llY9QSUlwQZaIFRF8H02ZD9LbBYWt4cjg0mQ7mPUALucK1gD4fetEq8G6qub2RtSRmFrlKKXG7WuNxUNwT5a4QASkprOFpVT5+k2E6osudrV1j93nvvtbi8aNEi+vfvT1FREWeccYb/+oSEBNLT01udY9myZWzevJkPP/yQAQMGMGnSJH77299y7733MnfuXGJiYo47pr6+nvr6ev/liooKADweDx6Ppz0Podtprr+nPw4RaT+d/yKRS+e/SOTS+S8Subr0/He7oHAhrF8CDVXmdda448dFJ8IpV0PurZDW1FO3sTF8dXaEC682PwB8PvOjM47pjoaPh+2b8K8SHz4e9O9NyA5W1LOmxM26kjLW7naz7WAlXp/RYkxsG7qsxFitjBtsJyfTDo27+Pju07HHWiPqd4H2PFaLYRjGiYe17ssvv2TEiBFs2LCB8ePNP5OYMWMGmzZtwjAM0tPTufTSS/nVr37lX13961//mrfeeot169b559m1axdDhw5lzZo1TJ48+bj7mTt3Lg8++OBx1y9evLjFqm0RERERERERERER6T5qamr4/ve/T3l5OXa7PejYkJtE+3w+fvKTn3Daaaf5g2qA73//+zidTgYNGsT69eu599572bZtG6+99hoABw4cYMCAAS3mar584MCBVu/rvvvu4+677/ZfrqioIDMzk/PPP/+ED7C783g8fPDBB5x33nlER0d3dTkiEkY6/0Uil85/kcil818kcoXt/G9sgG3/hNVPwoH1wccOmgJTfwAjLwKbfia12bsvwdIX8a9gvvgauOjqrq5K2qGuwcv6veWsLXGzdncZX+wuo7I+tL8icKYlMCnTwZSsVCZnpZLdJxGr1XLcuEj+HaC5S0ZbhBxWz5kzh40bN/Lvf/+7xfV33HGH/+sJEyYwcOBAzjnnHHbu3MmwYcNCuq/Y2FhiY4/v4xIdHd1rvrm96bGISPvo/BeJXDr/RSKXzn+RyNVp539NKRQtNEPqyv2Bx1msMOZSyP8hZE7t+DoiwZcbzTcFjr0crY0Mu7NDlXUUFbspdLkpLC5l074KGn3fbDZxfMD8TVFWC+MHp5DrdJCb7SDHmUa/5Pb1no7E3wHa83hDCqt/+MMf8s477/Dpp5+SkZERdOy0adMAs2XIsGHDSE9PZ/XqljvNHjx4ECBgn2sREREREREREWnFkR2wcj6sewEaawOPi7XDlJkw9Q5wOMNXXzOvF5YuabmRoa0NDX+7oxHjYfM6/CurR4w/wQESTj6fwc7DVU3BtJtCVymuozUhzZUcF0WO00Fedho5TgcTM1KJj+mhr9seol1htWEY/OhHP+L1119n+fLlDBky5ITHNPemHjhwIAD5+fn87ne/49ChQ/Tv3x+ADz74ALvdztixY9tZvoiIiIiIiIhIhDEM+Gq5GVLvWBZ8bKoTps+CyTdAbHJYymvV0iXw5nOA0RT0Apf20NXIF19rfj42eJcuU+fxsmFvuRlMF5dSVOKmrCa0zQsz0+LJdab5A+oR/ZNabekhnaddYfWcOXNYvHgxb775JsnJyf4e0ykpKcTHx7Nz504WL17MxRdfTJ8+fVi/fj0//elPOeOMMzjllFMAOP/88xk7diw33ngjjz76KAcOHOCBBx5gzpw5rbb6EBERERERERERwFMHG16GlQvg0KbgY7NOhfzZMOpisHaDlaA7NmKuRMb8vGNjV1Zzcmy29gftvWlleRc7WlVPkctNkctNQXEpG/dW0OD1tXsem9XC2IF2cppaeuRlpzHAHtcJFUt7tCusXrBgAQAzZsxocf3ChQu5+eabiYmJ4cMPP+Qvf/kL1dXVZGZmcuWVV/LAAw/4x9psNt555x1mzZpFfn4+iYmJ3HTTTTz00EMn/2hERERERERERHqbqkNQ8DQUPg3VhwOPs0bBuCvMkHrQ5PDV1xaR3jqjN60sDyPDMNh1pNrfzqPQ5earw9UhzZUUG8XkrFRynWnkZjuYlJlKYmzI2/lJJ2l3G5BgMjMz+eSTT044j9PpZOnSpe25axERERERERGRjtedV7we3AQr5sOGl8DbEHhcXCrk3gpTbwf7oLCV1y6R3jqjN60s70T1jV427q2gyFVKQbGbNS43R6uDvPaDGJgSR252mn8zxNHpdmxq6dHt6e0DEREREREREYlc3W3Fq88HX34AK+bBrhMsCOwz3OxHPfE6iEkMT32hCqV1Rm8S6SvLAyiraaDI5abQ5aao2M26PWU0NLa/pYfFAqPT7f5gOjc7jcGp8Z1QsXQ2hdUiIiIiIiIiErm6y4rXhmr44gVY+Rgc3RF87JAzIX8ODD8PrNbw1CcnJ9JXlmN2bCgprfm6pUexmx2HqkKaKz7a1tTSw0FOdhqTs1Kxx0W3f6Lu/JcVEUphtYiIiIiIiIhErq5e8VqxD1Y/AYULoa4s8DhbDEy42lxJna5VuT1OBK4s93h9bN5XQUFxqX/19OHK+pDm6p8ca66Ybuo3PWagnWhbB7xR093+skIUVouIiIiIiIhIBOuqFa9718DK+bDpdfA1Bh6X0BfyfgB5t0FS//DUJhKCijoPa1xuilxuCopL+WJ3ObUeb0hzjRqQTE62g1yng7zsNDIc8VgsndBvOlx/WeH1wrsvAUnm50u0gjsQhdUiIiIiIiIiErnCveJ127uwej6UrAg+rv9YmD4bJnwPouPCU5tIGxmGwd6yWn8wXVjsZtvBSgzjxMd+U2yUlYmZqeQ1rZyekuUgJSGElh6hCNdfVixdAktfhItuMz9b0AruABRWi4iIiIiIiIh0pvpKKHoeGAiv3Q6+usBjR5xvhtRDZ5i7xol0A41eH1sPVFJYXGpuhuhys788yOs4iD6JMeQ0rZjOyXYwflAKMVFd1Hs9XH9Z0V164/cACqtFRERERERERDqD22X2o17zLHgaYOITrY+LiodJ18G0WdBvZHhrFGlFVX0j60rK/Bshri1xU90QWkuPof0SyXOm+dt6DOmb2DktPUIRrr+sGDEetm9qutAFvfF7EIXVIiIiIiIiIiIdxTBg92pYOQ+2vA2Gz7ze2korj6R0mHYH5NwCCWnhrVPkGPvLayksdjdthFjK5n0V+EJo6RFjszIhI4Vcp4Pc7DRynA7SEmM6vuCe5uJrzYXVBnDxNeHrjd8DKawWERERERERETlZXg9sftPcNHFvUfCxAyfC9Dkw7rsQpSBPwsvrM9h+sJJCl9ts61HsZm9ZbUhzpSZEk+t0kONMIzfbwYTBKcRFa+PA49hscNHVsHSp+VmbKwaksFpEREREREREJFS1bih6xmz3UbE3yMCmtgfXvwJDv6V+1BI2tQ1e1u0u8/ebXlPiprKuEQCb4WNObSF5nn0URA9iXnwuXkvg/tHZfRLIcaaZmyFmOxjaNwmrtZu8lr1ecyPDY/tPKxTucRRWi4iIiIiIiIi019GdsHIBrFsMnurA42KSYPINkPMDWLEZsqYrqJZOdbiyniJXKQXFbgpdbjbtLacxQE+PObWF/KRmFVbgNM9uAP6WMBWAKKuF8YNbtvTolxwbrofRfkuXwJvPAQZsXmdeF45+1NKhFFaLiIiIiIiIiLSFYUDxZ7BiPmx/D7MBbQApmTDtTpgyE+JSwOMBNoerUokQPp/BzsNVTS09zH7TrqM1bT4+z7OP5nXUVuD86CPEXjCKHKeDiRmpxMf0oJXJOzby9TlpNF2WnkZhtYiIiIiIiIhIMI31sPFVsx/1gQ3Bx2ZMhfzZMPpSsCl2kY5V5/GyYW85BcWlFBW7KSpxU1bjCWmuzLR4quyjML7ajQUwsDB+xqmMP2t4xxYdLiPGN62oNgCLeVl6HP3UFBERERERERFpTfURKPw7FDwFVQcDj7PYYOzlkD8HMnLDV5/0eker6ilyuSlyuSkoLmXj3goavL52z2OzWhg70E5utoPcps0QB9jjwHsmLB0IOzZiae7z3FM1135sz+rOoN7YnUphtYiIiIiIiIjIsQ5tMVdRr38JGusCj4tNgZybYOodkJoZvvqkVzIMg11Hqv3tPApdbr46HKQfehBJsVFMzkr1B9OTMlNJjG0lBrTZek9f53A9FvXG7lQKq0VEREREREREDAO+/AhWzoOd/wo+Nm0oTJsFk74PsUnhqU96nYZGHxv2llPkKqWw2Fw9fbS6IaS5BqbEkZudRq7TQY7TwZiBdmxWbeTZKdQbu1MprBYRERERERGRyOWphfUvmpsmHtkWfGz26TB9Noy8AKz6s39pn/IaD0UlZjBdWOzmiz1l1De2v6WHxQKj0+3kZZvBdG52GoNT4zuhYmmVemN3KoXVIiIiIiIiIhJ5Kg/A6ifNntS1pYHHWaNhwlUwfRYMnBi++qRHMwyD3aW1FBSb7TyKXKVsP1gV0lzx0bamlh5mMD05K5XkuOgOrljaLFy9sSOUwmoRERERERERiRz715v9qDe8Aj5P4HHxaZB7K0y9HZLTw1ef9Eger4/N+yoodLkpbAqoD1fWhzRX/+TYFhshjhloJ9pm7eCKJWS9qc93N6SwWkRERERERER6N58Ptr9nhtTFnwUf23eUuYp64rUQrdYK0rqKOg9rXGaf6cJiN+t2l1Hr8YY016gByeRkO8h1OsjLTiPDEY/Fon7TEpkUVouIiIiIiIhI71RfBesWw6oFUPpV8LHDzobpc2D4OWZTYJEmhmGwt6zWH0wXFJey7WAlhnHiY78pNsrKxMxUfzA9JctBSoJaeog0U1gtIiIiIiIiIr1L+R5Y9TiseQbqygOPs8XCxGvMTRP7jwlffdKteX0GW/ZXUOQyg+kil5v95XUhzdUnMYacpmA6J9vB+EEpxESppYdIIAqrRURERERERKR3cK2CxX+EPXshtgKSy6G1RdKJ/c1e1Lm3QmLfsJcp3Ut1fSPrdpf5g+k1LjfVDaG19BjWL5FcpxlM52Wnkd0nQS09RNpBYbWIiIiIiIiI9FzeRtj6NqyYD5v3QUUGkAL1dvN2+56vxw6YAPmzYfyVEBXbJeVK1ztQXkehq5TCYjeFrlK27K/E62t/T48Ym5UJGSn+zRBznA7SEmM6oWKRyKGwWkRERERERER6nrpyWPMsrHoCykvM6+rH8PVSagvUJ5ufR15ohtTZp6sfdYTx+Qy2H6qkoNhNUXEphS43e9y1Ic2VmhBNrtNBjjONvGwH4wenEBdt6+CKRSKbwmoRERERERER6TlKd8Gqx2Dtc9BQ1fK22EqoT8EMrA0YOhJufh76DOuKSqUL1DZ4Wbe7jCJXKQXFbtaUuKmsawxpruw+Cf5gOjfbwdC+SViterNDpDMprBYRERERERGR7s0woGQFrJgHW/8JBGjZkLwHYpMhahhMPgsuvwVsWvnamx2urPcH04UuN5v2ltMYQkuPKKuFcYNTyHOawXSOM41+yWoVIxJuCqtFREREREREpHtqbIDNb5gh9f51wccOzoHps2Hs5WCLDkd1EmY+n8FXR6rMYLqp37TraE1IcyXHRZHjdPjbekzKTCU+Rm9siHQ1hdUiIiIiIiIi0r3UlELRQlj9JFTuDzzOYoUxl8L0OZA5Vf2oe5k6j5cNe8vNYLq4lKISN2U1npDmynDEk5dtboKYm+1gZP9ktfQQ6YYUVouIiIiIiIhI93B4O6ycD18sgcYgm+DF2mHKTJh6Bzic4atPOlVpdQNFLjOYLnS52bCnnAavr93z2KwWxg60k+N0kJedRm62gwH2uE6oWEQ6msJqEREREREREek6hgFfLTdD6h3Lgo9NdcL0WTDpeoizh6U86RyGYbDrSDWFLjdFxW4KXKV8dbg6pLmSYqOYnJVKrtMMpidlppIYq8hLpCfSmSsiIiIiIiIi4eepgw0vw8oFcGhT8LFZ+ZA/B0ZdDFb1Fe6JGhp9bNxXbq6aLnZT5HJztLohpLkGpsSRm51GblNLj9Hpdmxq6SHSKyisFhEREREREZHwqToEBU9D4dNQfTjwOGsUjPuuuWni4Cnhq086RHmNh6KS0qZ+026+2FNGfWP7W3pYLDA63e4PpnOz0xicGt8JFYtId6CwWkREREREREQ638FNsGI+bHgJvEFW1MalQu4tZj9q+6CwlSehMwyD3aW1FLpKKSh2U+QqZfvBqpDmio+2MSkzlbxsBznZaUzOSsUeF93BFYtId6WwWkREREREREQ6h88HX34AK+bBrk+Cj+0z3OxHPfE6iEkMT30SEo/Xx5b9Ff5guqDYzeHK+pDm6p8cS262gxxnGnnZDsYMtBNts3ZwxSLSUyisFhEREREREZGO1VANX7wAKx+DozuCjx1yptmPevh5YFVI2R1V1HlYW1JGUbEZTK/bXUatxxvSXCMHJH3db9qZRmZaPBaL+k2LiElhtYiIiIiIiIh0jIp9sPoJKFwIdWWBx9liYMLV5krq9PFhK0/aZm9ZrX8jxEKXm60HKjCM9s8TG2VlYmYquU4HedlpTMlykJKglh4iEpjCahERERERERE5OXvXwMr5sOl18DUef7sBVGZAYxoMHws3zYWUgeGuUlrh9Rls2V9BkctNQXEpRS43+8vrQpqrT2IMOU3BdE62g/GDUoiJ0mp5CYHXC0uXwI6NMGI8XHwt2GxdXZWEgcJqEREREREREWk/nxe2/tMMqUtWnGDsZKiIM79eXwKf/gsuvb7za5TjVNc3sm53mT+YXltSRlV9K28wtMHQfonkOc1gOtfpYEjfRLX0iAThCJKXLoE3nwMM2LzOvE4/MyKCwmoRERERERERabv6Slj7HKxcAGWu4GNHnA/TZ8Mby2D/2qYrDTPkkrA4UF5Hocts6VHkcrN5fwVeX/t7esTYrEzISCHX6SCn6aNPUmwnVCzdXjiC5B0bzfkB/cyILAqrRUREREREROTE3C6zH/WaZ6G+IvC4qHiYdB1MmwX9RprXjdwHW9Zhhk8WczWmdDifz2D7oUp/MF1QXMoed21Ic6UmRJOT5TA3Q8x2MGFwCnHRasMghCdIHjG+KQjXz4xIo7BaRERERERERFpnGLB7NaycB1veBsMXeGzyQJh6O+TcAglpLW+7+Frz87FtA05EPWtPqLbByxd7yszNEF1u1rjcVNSF1tLD2SeBXKcZTOdlOxjaNwmrVS09pBXhCJJD+ZkhvYLCahERERERERFpyeuBzW+a/aj3FgUfO3Ai5P8Qxn4HomJaH2Oztb9NgHrWHudwZT1FTS09ClxuNu0tpzGElh5RVgvjBqeQ53SQm+0gx5lGv2S19JA2CkeQHMrPDOkVFFaLiIiIiIiIiKnWDUXPmO0+KvYGGWiB0ZeY/aidp0JnbKoX4T1rfT6Dr45UUVDsbmrrUUrx0ZqQ5kqOiyLH6WjqN53GpMxU4mO0Sl1CpCBZOpHCahEREREREZFId3SnuWHiusXgqQ48LiYJJt8A0+6EtKGdW1OE9ayt83jZsLecwmI3hcWlFJW4KavxhDTX4NR48rId5GSnkZftYGT/ZLX0EJEeQWG1iIiIiIiISCQyDCj+DFbMh+3v8fUq5lakZJoB9ZSZEJcSnvp6ec/a0uoGM5R2uSl0udmwp5wGb5Ce4AFYLTB2kN3fbzrXmUZ6SlwnVCwi0vkUVouIiIiIiIhEksZ62Piq2Y/6wIbgYzOmQv5sGH0p2I6JEMKx+WEvajVgGAbFR8wV679+cyOrXOV8dTjICvYgEmNsTHE6yHE6yMs2W3okxireEZHeQT/NRERERERERCJB9REo/DsUPAVVBwOPs9hg7OWQPwcyclsfo80Pg2po9LFxXzmFxaVN/abdVNXV8+hUeG3tXuq9bW/JMTAljtzstKZ+0w5GpycTZbN2YvUiIl1HYbWIiIiIiIhIb3Zoi7mKev1L0FgXeFxsCuTcBFPvgNTM4HNG+OaH31Re46GopLSp37SbL/aUUd/YsqVHbBsWnlssMDrdTq7TYbb0yE5jcGp8J1UtItL9KKwWERERERER6W0MA778CFbOg53/Cj42bShMmwWTvg+xSW2bP8I2PzyWYRjsLq2l0FVKocvcDHH7waqQ5oqPtjEpM9UfTE/OSsUeF93BFYuI9BwKq0VERERERER6C08tfLEEVi6AI9uCj80+HabPhpEXgLWd/aZ7+eaHx/J4fWzeV0Ghy02Ry1w9faiyPuT5zhszgMnZfcl1Ohg7yE60WnqIiPgprBYRERERERHp6SoPmL2oC56G2tLA46zRMOEqmD4LBk4M/f560eaH31RR52FtSZm/3/S63WXUerwhzTVyQBI5TrPf9JQMO+tXfsyfr5lEdLRWT4uItEZhtYiIiIiIiEhPtX+92Y96wyvg8wQeF58GebdB3g8gOT189fUAe8tq/cF0QXEp2w5WYhgnPu6bYqOsTMxobunhYEqWg9SEGP/tHo+H9R1Yt0iP4vWaG7Me+9cYtnb+RYdEBIXVIiIiIiIiIj2Jzwfb3zND6uLPgo/tO8pcRT3xWojWRn1en8GW/RUUucxgusjlZn95kE0ng0hLjCHH6SCvqd/0+EEpxESppYdIq5YugTefA4ymfvf02r/OkJOjsFpERERERESkJ6ivgi9eMEPq0q+Cjx12NkyfA8PPAYslPPV1Q9X1jazbXeYPpteWlFFV3xjSXEP7JZLrNIPpXKeDIX0TsUTwcyvSLjs2Ym7Iivl5x8aurEa6MYXVIiIiIiIiIt1Z+R5Y/QQULYK68sDjouLglGvMldT9x4StvO7kQHkdhU2bIBa53GzeX4HX1/6eHtE2CxMGp5CXnUaO00GO00GfpNhOqFgkQowY37Si2gAs5mWRViisFhEREREREemO9hTBynmw6Q0wgmzwl9gfpt4OubdCYt+wldfVfD6D7YcqKSx2mz2nXW72uGtDmislPpocp9lrOi87jQmDU4iLVj9dkQ5z8bXm52N7Vou0QmG1iIiIiIiISHfhbYSt75itPnavCj52wATInw3jr4So3r/qt7bBy7rdZRS5zGC6yOWmsi60lh7OPglN/abNlh7D+iVhtaqlh0insdnUo1raRGG1iIiIiIiISFerK4c1/4BVj0N5SZCBFhh5oRlSZ5/eq/tRH66sN4PpYjcFLjeb9pbTGEJLjyirhXGDU8x+004HOdkO+ifHdULFIiJyshRWi4iIiIiIiHSV0l1mQL32OWioDDwuOgEmXW/2o+4zLHz1hYlhGOw8XEVBsbup33QpxUdrQporOS6KKVkO8rId5DjTmJSZSnyMWnqIiPQECqtFRERERESke/J6YemSlj1Obb0gdDQMKFkBK+bBtqVg+AKPtQ+GqXdAzk0Q7whfjZ2szuNlw95yfzBd6HJTVuMJaa4MR3zTiuk08rIdjOyfrJYeIiI9lMJqERERERER6Z6WLoE3nwMM2LzOvK4n9zz1emDT62Y/6n1rg48dnAPTZ8PYy8EWHZ76OlFpdQNFLjeFTW09Nuwpp8EbJKQPwGqBsYPs5DrTyM12kOtMIz1FLT1ERHoLhdUiIiIiIiLSPe3YCDT3KDaaLvdANaVQtAhWPwmV+wKPs1hhzKUwfQ5kTu2x/agNw6D4aA0FxaUUFbspcJXy1eHqkOZKjLExxenwb4Y4KTOVxFhFGSIivZV+wouIiIiIiEj3NGJ804pqA7CYl3uSIzvMVdTrXoDG2sDjYu0wZabZ7sPhDF99HaSh0cfGfeUUFpc2tfVwc7S6IaS5BqbEkZudZrb1cDoYnZ5MlM3awRWLiEh3pbBaREREREREuqeLrzU/H9uzurszDNj1CayYDzveDz421WlumDjpeoizh6e+DlBe46GoxAymC11uvthdRn1j+1t6WCwwOt1OrtNhtvTITmNwanwnVCwiIj2FwmoRERERERHpnmy2ntOj2lMHG1+BlQvg4AnalWTlQ/4cGHUxWLv3hpGGYbC7tNbsNe1yU1hcyvaDVSHNFR9tY1Jmqj+YnpyVij2u5/fjFhGRjqOwWkRERERERCRUVYeh8GkoeAqqDwceZ42CcVdA/mwYNDl89bVTo9fH5v0VTaumzdXThyrrQ5qrX3IsedkOcpxmW4+xg+xEq6WHiIgEobBaREREREREpL0OboaV82D9y+ANEubGpULuLWY/avugsJXXVpV1HtaWlJn9pl1u1paUUevxhjTXyAFJ5DjTyMt2kOtMIzMtHksP3SRSRES6hsJqERERERERkbbw+eDLD82Q+qvlwcf2GW72o554HcQkhqW8tthbVkthcSlFLjcFxW62HajAZ7R/ntgoKxMzUsnJdpCX7WBKloPUhJiOL1hERCKKwmoRERERERGRYBpq4IsXzH7UR3cEHzvkTLMf9fDzwNq1LS+8PoMt+ysocpkbIRYVl7KvvC6kufokxpBzzEaI4welEBOllh4iItKxFFaLiIiIiIiItKZiH6x+EooWQq078DhbDEz4nrmSOn1C+Or7hur6RtbtLvP3m15bUkZVfWNIcw3tl0iu0wymc50OhvRNVEsPERHpdAqrRURERERERI61by2smA+bXgNfkLA3oS/k3Qa5t0HygPDV1+RgRR0FxeYmiEUuN5v3V+ANoadHjM3K+MF2fzCd43TQJym2EyoWEREJTmG1iIiIiIiIiM8L25aaIXXJ58HH9hsD+bNhwtUQHRee8nwGOw5VUeDvN13KHndtSHOlJkSTk9W0ajrbwYTBKcRF2zq4YhERkfZTWC0iIiIiIiKRq74S1j4PqxaAuzj42OHnmSH10LOgk1ti1DZ4+WJPmT+YXuNyU1EXWkuP7D4J5DjNYDrX6WBYvySsVrX0EBGR7kdhtYiIiIiIiESeshJY9TiseRbqKwKPi4qHidea/aj7jeq0cg5X1lPkKm3qN+1m495yGkNo6RFltTBucAq5Tgd52Q6mOB30Tw7P6m8REZGTpbBaREREREREOp/XC0uXwI6NMGI8XHwt2Lqg9cTu1bBiHmx5Cwxf4HFJ6TD1dsi9FRLSOrQEwzDYebiKwmI3BcVuilylFB+tCWmu5LgopmSZwXSOM41JmanEx6ilh4iI9EwKq0VERERERKTzLV0Cbz4HGLB5nXndpdeH5769jbDlTbMf9d7C4GPTT4H8H8K470JUTIfcfZ3Hy8a95f5gutDlpqzGE9Jcg1PjzWC6aTPEkQOSsZ1sS4/u8kaCiIhEPIXVIiIiIiIi0vl2bASa21oYTZc7WW0ZrHkGVj0BFXuCDLTAqIvNftTO0066H3VpdQNFLjeFTW09Nuwpp8EbZBV3AFYLjB1kJ9ffbzqN9JROaOnRlW8kiIiIHENhtYiIiIiIiHS+EeObglADsJiXO8vRnbDqMXPjRE914HHRiTD5Bph2J/QZFtJdGYZB8dEaCoub+02XsvNwkPsMIjHGxuQshz+YnpSVSlJsGP7b3hVvJIiIiLRCYbWIiIiIiIh0vouvNT8f22qiIxkGFP8bVs6Hbe/ydfjaipRMmHoHTJkJ8antupuGRh+b9pX7g+kil5sjVQ0hlTwwJY4cp4Ncp4Pc7DRGpycTZbOGNNdJCecbCSIiIkEorBYREREREZHOZ7N1TmuJxgbY+CqsnAcHNgQfm5EH02fDmMvA1rb/DpfXeFhTYgbTBcVuvthdRn1j+1t6WCwwakAyudkO8rLTyM1OY3BqfLvn6RSd/UaCiIhIGymsFhERERERkZ6n+igU/h0KnoSqg4HHWWww9jKYPgcy84JOaRgGu0trzV7TLjdFxW62HawMqby4aCuTM5taemSnMTkrFXtcdEhzdbrOeiNBRESknRRWi4iIiIiISM9xaKvZ6mP9i9BYF3hcbArkzISpd0JqZqtDGr0+Nu+v8Lf0KCx2c6iyPqSy+iXH+tt55DodjB1kJ7orWnqIiIj0YO0Kqx9++GFee+01tm7dSnx8PKeeeiqPPPIIo0aN8o+pq6vjnnvuYcmSJdTX13PBBRcwf/58BgwY4B9TUlLCrFmz+Pjjj0lKSuKmm27i4YcfJipK2bmIiIiIiIh8g2HAzo9gxXzzczCOITB9Fky6HmKTWtxUWedhbUmZuRmiy8263WXUNHhDKmlE/yRysx3kONPIy3aQlZaAxWIJaS4RERExtSsd/uSTT5gzZw55eXk0NjZy//33c/7557N582YSExMB+OlPf8o///lPXn75ZVJSUvjhD3/IFVdcwX/+8x8AvF4vl1xyCenp6Xz++efs37+fmTNnEh0dze9///uOf4QiIiIiIiLSM3lqzRXUKxfA4a3Bxzq/BfmzYeSFYLUBsK+sloJicxPEgmI32w5U4Auy72IgMVFWJmWkkpPtIC/bwZQsB6kJMSE8IBEREQmmXWH1e++91+LyokWL6N+/P0VFRZxxxhmUl5fz9NNPs3jxYs4++2wAFi5cyJgxY1i5ciXTp09n2bJlbN68mQ8//JABAwYwadIkfvvb33Lvvfcyd+5cYmL0D76IiIiIiEhEqzxo9qIu/DvUHA08zhoN46+E6bPwpk9k64EKilbtpqDYTVFxKfvKg7QJCSItMaappYe5cnr8YDuxUbYQH4yIiIi01Un13SgvLwcgLS0NgKKiIjweD+eee65/zOjRo8nKymLFihVMnz6dFStWMGHChBZtQS644AJmzZrFpk2bmDx58nH3U19fT339133DKioqAPB4PHg8npN5CF2uuf6e/jhEpP10/otELp3/IpFL5/8JHNwEBU/BpjfA1/QcWeOOHxfvoGbCTawfcDlrj1hZ+56b9bvfp6qhscWw2Dbmy0P6JDI5K5XJmQ4mZ6Xi7PONlh6GD4/HF9pjCjevF5a9Cju3wLAxcP6V5gaK0uV0/otEtkj+GdCex2wxDCOEP4ICn8/HZZddRllZGf/+978BWLx4MbfcckuLYBlg6tSpnHXWWTzyyCPccccduFwu3n//ff/tNTU1JCYmsnTpUi666KLj7mvu3Lk8+OCDx12/ePFiEhISQilfRERERERERERERDpZTU0N3//+9ykvL8dutwcdG/LK6jlz5rBx40Z/UN2Z7rvvPu6++27/5YqKCjIzMzn//PNP+AC7O4/HwwcffMB5551HdHR0V5cjImGk818kcun8F4lcOv+P0VANG14xV1K7d7W4yWdY2GkMYo1vBOuM4ayxTmBvY1KAiYJLiYtmcmYqk5zmyunxg+zERvfilcb/9yBs++Lry6Mmwg9/03X1iJ/Of5HIFsk/A5q7ZLRFSGH1D3/4Q9555x0+/fRTMjIy/Nenp6fT0NBAWVkZqamp/usPHjxIenq6f8zq1atbzHfw4EH/ba2JjY0lNjb2uOujo6N7zTe3Nz0WEWkfnf8ikUvnv0jkiujzv3wPrH4CihZBndlass6IZp0xjCLfKAp8o1jjG0EFiSFN7+yTQI7TQa4zjbxsB8P6JWG1Wk58YG8xfAxsKgIMwGJejtTXWjcV0ee/iETkz4D2PN52hdWGYfCjH/2I119/neXLlzNkyJAWt+fk5BAdHc1HH33ElVdeCcC2bdsoKSkhPz8fgPz8fH73u99x6NAh+vfvD8AHH3yA3W5n7Nix7SlHREREREREvsnrhaVLYMdGGDEeLr62c3oWt/d+9hTBynmw6Q2O+BIp9I2k0DeKQt9INhlD8ISwlirKamHcIDu52WnkOh3kZDvon9xKj+ueKpTv5cXXmp+PPUZERKSHaNdvA3PmzGHx4sW8+eabJCcnc+DAAQBSUlKIj48nJSWF2267jbvvvpu0tDTsdjs/+tGPyM/PZ/r06QCcf/75jB07lhtvvJFHH32UAwcO8MADDzBnzpxWV0+LiIiIiIhIOyxdAm8+BxiweZ153aXXd839eBsxtrzDzs9eoHBvHYXGKIp8j7LLGBjSXSbHRTEly0Gu00FudhqTMlOJj+nFLT1C+V7abJ3z/RYREQmDdoXVCxYsAGDGjBktrl+4cCE333wzAH/+85+xWq1ceeWV1NfXc8EFFzB//nz/WJvNxjvvvMOsWbPIz88nMTGRm266iYceeujkHomIiIiIiIiYK2oxmi4YTZfDdz/1jV42fLWPwhXLKdx5gKKGTNzMDOkuBqfGk5ftIKdp5fTIAcnYempLj1BWSYfreykiItJNtLsNyInExcUxb9485s2bF3CM0+lk6dKl7blrERERERERaYsR45tW4Tb1LB4xvtPvxwA+YwB/+99/sX5fNQ2GFUhr+mgbqwXGDrKT60wze05nOxiYEt85tXeFUFZJh+t7KSIi0k2EtMGiiIiIiIiIdFOh9Cxu46pfwzAoPlpDYXEpa2rHMqrvaQwrd1EQPYh5B4fhtdQC1jaVmRBjY0qWgxyng7zsNCZlpZIU24v/ixrKKmn1nxYRkQjTi38TEBERERERiUCh9CwOsOq3odHHxn3lFBW7KXSVUuRyc6Sq4ZgDJ0PK5DbdRXq8Qc7wdHKz+5CXncbo9GSibG0LtnuFUFZJq/+0iIhEGIXVIiIiIiIike4bq353rVjFvfuG8sXuMuobfe2ezoKPUZbd5PZpIG/SZHKm5DHYEY/F0kP7TXcErZIWERE5IYXVIiIiIiIiEcgwDHaX1lLoKsXe2I+zMRt4+IDXqxys3lXa5rniqGeS9UvyLNvJid3N5MlTSfnWbeDI7qTqeyCtkhYRETkhhdUiIiIiIiIRoNHrY/P+CgqbWnoUFrs5VFkPgM0YwZyEcvI8+8z+0/G5Qefqh5tc63ZyrNvJs25jrMVFtCMDpt0Fk/8H4uzheEita2P/7R5zPyIiIhFEYbWIiIiIiEgvVFnnYW1JGYXFpRS63KzbXUZNg7fVsV6Llb8lTA041wjLHnKt28i1bifXso0syyH8HT2y8mH6gzD6ErB2g7A2QP/tHns/IiIiEURhtYiIiIiISC+wt6yWwmJzE8TCYjdbD1TgM0583DfFWH1MtO4i19joXz2daqluOcgaBeO+C9Nnw+ApHfMAOso3+m+bl3vw/YiIiEQQhdUiIiIiIiLdVYBWE16fwdYDFRS53BQUuykqLmVfeV1Id5GWGENOuo1czxpyD73GeGMbsZbG1gfHpULOzTD1DkgZHPLD6lQjxjetdDYAi3m5J9+PiIhIBFFYLSIiIiIi0l0d02rC2LyWlTuPMj95GmtLyqiqDxAon8DQvonkZjvIzUolx7KVoZv/D8uu5V8PsLRyUJ/hMH0WTLwOYhJDut+wufha8/OxAX9Pvh8REZEIorBaRERERESkmzlYUUdhsZvRn69iWFOrCQvQuG0Dn6UMa/M80TYLEwankJudRq7TQY7TQZ8YL3zxAqxcAEd3BJ9gyJmQPweGnwdW60k8ojCy2cLTOzpc9yMiIhJBFFaLiIiIiIh0IZ/PYMehKgqa+k0XFJeyx10LwI9rHPwEsAI+oCB6UNC5UuKjzVA620GuM41TMlKIi27a9LBiH6z8AxQthFp34ElsMTDhe+ZK6vQJHfEQRURERNpEYbWIiIiIiEiYFRSXsnZPJQXFpaxxuamoa72lx7z4XADyPPsoiB7kv9zM2SeBHKeDvKaV08P6JWG1fqOPx761sGI+bHoNfEFahyT0hbzbIPc2SB5wUo9PREREJBQKq0VERERERDrRkap6CovdFBaX8kXJUW4YDLcsKqDe21pz6Ja8Fit/S5gKQJTVwvjBKeQ6Hf7V0/2T41o/0OeFbUvNkLrk8+B30m8M5M+GCVdDdID5RERERMJAYbWIiIiIiEgHMQyDnYerzHDaZQbUxUdr/LfH2gwY3La5kuOimJLlIC/bQY4zjUmZqcTH2IIfVF8Ja5+DVY+Buzj42OHnmSH10LPAcuLgXERERKSzKawWEREREREJUZ3Hy8a95RQUuylymT2n3TWekOYanBpvBtNNLT1GDkjG9s2WHoGUlcCqx2HNs1BfEXhcVDxMvNbsR91vVEh19kpeLyxdAjs2wojxcPG15gaKIiIiElYKq0VERERERNqotLqBIpebQlcpRcVu1u8pp8Hra/c8VguMH2wn15lGjtNBbraDgSnx7S9o92pYMQ+2vAVGkDqS0mHq7ZB7KySktf9+erulS+DN5wADNq8zr7v0+q6sSEREJCIprBYREREREWmFYRgUH62hsLi0qa1HKTsPV4c0V2KMjclZDnKz7FC7nRX3nUNqYgjhNIDXA5vfhJULYG9h8LEDJ8L0OTDuuxAVE9r9RYIdGwGj6YLRdFlERETCTWG1iIiIiIgI0NDoY9O+cn8wXeRyc6SqIaS50u1x5GabGyHmZqcxOj2ZKJsVj8fD0qXbSYwJ4b9itWWw5hlY9QRU7Aky0AKjLjb7UTtPUz/qthgxvmlFtQFYzMsiIiISdgqrRUREREQkIpXXeFhTYgbThcVuvthTRp2n/S09LBYYNSCZ3GwHedlmW4/BqfFYOiokPrrT3DBx7fPgCbKyOzoRJt8A0+6EPsM65r4jxcXXmp+P7VktIiIiYaewWkREREREej3DMNjjrqXQVWpuhljsZvuhSgzjxMd+U1y0lUmZqf5genKWg5T46I4uGIr/DSvnw7Z3+bpFRStSMmHqHTBlJsSndmwdkcJmU49qERGRbkBhtYiIiIiI9DqNXh+b91dQWOymyOWmoLiUQ5X1Ic3VLzmWXKeDHKe5cnrsIDvRNmsHV9yksQE2vgor58GBDcHHZuTB9Nkw5jKw6b92IiIi0vPpNxoREREREenxKus8rC0pMzdDdLlZt7uMmgZvSHON6J/U1G86jdxsB1lpCR3X0iOQ6qNQ+HcoeBKqDgYeZ7HB2MvMTRMz8zq3JhEREZEwU1gtIiIiIiI9zr6yWgqKzU0QC4vdbD1QgS+Elh4xUVYmZaSS07QZYo7TQWpCTMcXHMihrWarj/UvQmNd4HGxKZAzE6beCamZ4atPREREJIwUVouIiIiISLfm9RlsPVDR1M7DTVFxKfvKgwS7QaQlxpDjNIPp3Ow0xg+2Extl6+CK2+Cr5bB6Aez8KPg4xxCYPgsmXQ+xSWEpTURERKSrKKwWEREREZFupaahkXUlZRQ29ZpeW1JGVX1jSHMN7Zvo7zWdk+1gaN/Ezm/pEYinFta9CDjgxRvAFyRwd34L8mfDyAvB2gVhuoiIiEgXUFgtIiIiIiJd6lBFnT+YLnK52bSvAm8IPT2ibRYmDE4hNzvN39KjT1JsJ1TcTpUHzV7UhX+HumqY+ETr46zRMP5KcyX1oElhLVFERESkO1BYLSIiIiIiYePzGew4VEWhq5SiYjcFrlJ2l9aGNFdKfLQZSjdthnhKRgpx0d1oFfL+9WY/6g2vgM9jXmeNO35cfBrk3gp5PwD7wPDWKCIiItKNKKwWEREREZFOU+fxsm53WdNGiObK6Yq60Fp6OPsk+Ft65DodDOuXhNXaRS09AvH5YMf7sGIeFH8WfGzfUeYq6lOugZiE8NQnIiIi0o0prBYRERERkQ5zpKqewmIzmC50udm0rxyPt/0tPaKsFsYNsn/d0iPbQf/kVlYldxcN1bBuMaxcAKU7Tzz+6n/AyHPBau382kRERER6CIXVIiIiIiISEsMw2Hm42h9MFxaXUny0JqS5kmOjmOJ0+IPpyZkO4mO6UUuPQMr3wuonoGgR1JUFHmeLhYnXQO6dULAThp2loFpERETkGxRWi4iIiIhIm9Q3etmwp9wfTBe53LhrPCHNNTg1ntxsh3/l9MgBydi6W0uPYPYWwYr5sPkN8AVpa5LYH6bebvakTuwLHg/QhpXXIiIiIhFIYbWIiIiIiLTKXd1AkcvcBLGo2M36PeU0eH3tnsdqgTED7eRlp5HjdJCb7WBgSnwnVNzJfF7Y+o4ZUu9eGXzsgPEwfTZMuAqiYs3rvF549yUgyfx8ybVg6wGrx0VERETCRGG1iIiIiIhgGAbFR2v8K6YLikvZebg6pLkSYmxMyXL4g+nJWQ6SYnvwfz3qKmDtP2DVY1BWEnzsyAvNkHrIGWD5xkrxpUtg6Ytw0W3mZwtw6fWdVraIiIhIT9ODf2MUEREREZFQNTT62LSv3B9MF7ncHKlqCGmudHscOdkO8pxmW4/R6clE2XpBP2Z3Max6HNb8AxoqA4+LToBJ34dps6Dv8MDjdmwEmjebNJoui4iIiEgzhdUiIiIiIhGgvNbDmhKz13RhsZsv9pRR52l/Sw+LBUYNSDb7TTvTyM12MDg1Hss3VxH3VIYBJSth5TzY+k8wgjxHyYNg2h0w5SZISDvx3CPGw/ZNTRcs5mURERER8VNYLSIiIiLSyxiGwR53LYUuM5guLHaz/VAlhnHiY78pLtrKpMxUfzA9OctBSnx0xxfd1bwe2PSGGVLvWxt87KApkD8Hxl4OtnY8Fxdfay6sNoCLrzEvi4iIiIifwmoRERERkR6u0etjy/5KfzuPQlcpByvqQ5qrb1IsuU29pnOz0xg3yE50b2jpEUhNKRQtgtVPQuW+wOMsVhj9bTOkzpx2fD/qtrDZ4KKrYelS87M2VxQRERFpQWG1iIiIiEgPU1nnYW1JGYUus63Hut1l1DR4Q5preP8k8rId5DjTyMt2kJWW0HtaegRz5EtYOR++eAE8NYHHxSTDlJlmuw9HdtjKExEREYlECqtFRERERLq5fWW1X6+aLnaz9UAFvhBaesREWZmYkeIPpqdkOXAkxnR8wd2VYcCuT2DFfNjxfvCxqU6YdhdMvgHi7OGpT0RERCTCKawWEREREelGvD6DrQcqKHK5KSh2U1Rcyr7yupDmciREk5ud5m/rMX5wCrFREdh6orEeNrwMKxfAwY3Bx2blw/TZMPoSsEbgcyUiIiLShRRWi4iIiIh0oZqGRtaVlFFQbPaaXltSRlV9Y0hzDe2bSI7TQV52GjnZDob2TYyMlh6BVB2Gwqeh4CmoPhx4nDUKxn3XDKkHTwlffSIiIiLSgsJqEREREZEwOlhRR2FTMF1Y7Gbz/gq8IfT0iLZZmDA4hdzsNHKcDnKcDvomxXZCxT3Qwc1mP+r1L4E3yEaTcamQewvk3Q4pg8NWnoiIiIi0TmG1iIiIiEgn8fkMdhyq8gfTha5SdpfWhjRXSnw0OU3tPHKdaZySkUJctNpU+Pl8sPMjWDEPvvo4+Ng+w2H6LJh4HcQkhqc+ERERETkhhdUiIiIiIh2kzuPli91lFLrcFDZtiFhRF1pLj6y0BH8wnZftYFi/JKzWCG7pEUhDDaxfYvajPrI9+NghZ0L+HBh+Hlit4alPRERERNpMYbWIiIiISIiOVNVTWOymyFVKQbGbTfvK8Xjb39Ijymph3CA7OU3BdI7TQX97XCdU3ItU7IeCJ6Hw71DrDjzOFgMTvmeupE6f0HH37/XC0iWwYyOMGA8XXws2rXQXERERORkKq0VERERE2sAwDHYerqawuJRCl5sil5tdR6pDmis5NoopTge5Tgc52Q4mZaaSEKNfzdtk3zqzH/XG18DnCTwuoS/k3Qa5t0HygI6vY+kSePM5wIDN68zrLr2+4+9HREREJILoN2IRERERkVbUN3rZsKe8RUsPd02QcDSIwanxTS09HORmpzFyQDI2tfRoO58Xtr1rhtSu/wQf228M5M+GCVdDdCeuTt+xEWheRW80XRYRERGRk6GwWkREREQEcFc3UORyU+AqpajYzfo95TR4fe2ex2qBMQPtTaumzbYeA1PiO6HiCFBfCWufh1WPgXtX8LHDzzND6qFngSUMbwSMGN+0otoALOZlERERETkpCqtFREREJOIYhkHx0Rr/iumC4lJ2Hg6tpUdCjI0pWWaf6bzsNCZlpZIUq1+zT0pZCax6HNb8A+rLA4+LioOJ15n9qPuNCl99YPaohpY9q0VERETkpOi3aBERERHQZmm9XEOjj037yv3BdJHLzZGqhpDmGmCPJTc7jbymlh6j05OJslk7uOIItXs1rJgHW94Gwxt4XFI6TP0B5NwKiX3CV9+xbDb1qBYRERHpYAqrRURERECbpfUy5bUe1pSYvaYLi918saeMOk/7W3pYLDBqQHJTv+k0cpwOMhzxWMLRZiJSeBthy5uwYj7sLQw+Nv0UyJ8D466AqJjw1CciIiIiYaOwWkRERAS0WVoPZhgGe9y1FLpKKSh2U1TsZvuhSgzjxMd+U1y0lYkZqeRlp5GT7WBKloOU+OiOL1qgtgzWPAOrnoCKPUEGWmDURTB9NmR/Kzz9qEVERESkSyisFhEREQFtltaDNHp9bNlf6W/nUegq5WBFfUhz9U2KJdfpMFdOZ6cxdqCdmCi19OhUR3eaGyaufR48QfqERyfC5Oth2l3QZ1j46hMRERGRLqOwWkRERAS0WVo3VlnnYW1JGYUuN0WuUtaWlFHTEKSfcRDD+yeRl+0gx5lGrtOBs0+CWnqEg2FA8b9h5XzY9i5f/xVDK+wZMO0OmHITxKeGq0IRERER6QYUVouIiEjv1N4NE7VZWrexr6yWQtfX/aa3HqjAF0JLj5goKxMzUshxppHX1NLDkag+x2HV2ACbXjM3TTywPvjYwbmQPxvGXA42/TdFREREJBLpt0ARERHpnbRhYo/g9RlsO1BJocsMpotcbvaW1YY0lyMh2h9M52Y7GD84hdioIG9QSOepPgpFf4fVT0HVgcDjLDYYexlMnwOZeeGrT0RERES6JYXVIiIi0jtpw8RuqaahkXVNLT0KXW7WutxU1jeGNNfQvonkHNNvemjfRLX06GqHt5mtPr5YAo11gcfF2mHKTJh2J6Rmha8+EREREenWFFaLiIhI76QNE7uFQxV1TS09zI0QN+2rwBtCT49om4Xxg1OaNkNMI8fpoG9SbCdULO1mGLDzX2ZI/eWHwcc6smHaLHPjxNjksJQnIiIiIj2HwmoRERHpnbRhYtj5fAZfHq4yg+niUgpdbkpKa0Kayx4X5Q+lc50OJmamEhetlh7diqcW1r8EKxfA4S3BxzpPg+mzYdRFYNX3UURERERap7BaREREeidtmNjp6jxevthttvQoavoor/WENFdWWgK5Tgc52Q7ystMY3i8Jq1UtPbqlyoNQ8BQUPg01RwOPs0bB+CvNkHrQpLCVF7L2bsoqIiIiIh1OYbWIiIiItMnRqvqmlh7mqumNe8vxeNvf0sNmtTBukJ1cZ5rZb9rpoL89rhMqlg51YAOsmA8bXwFvQ+Bx8Q7IvRXybgf7wPDVd7K0KauIiIhIl1NYLSIiIiLHMQyDnYerKXKVNvWbdrPrSHVIcyXHRjG5qZ1HbraDSZmpJMTo19AeweeDHe/DinlQ/FnwsX1HwvRZcMq1EJMQnvo6kjZlFREREely+l+CiIiIiFDf6GXj3nIKi90UFLtZU+KmtDrI6tkgBqfG+1dM5zjTGJWejE0tPXqWhmpYtxhWPQZHvww+duhZkD8Hhp0DVmt46usM2pRVREREpMsprBYRERGJQO7qBopcbn9bj/V7y2lo9LV7HqsFxgy0N62aNtt6DEyJ74SKJSzK98LqJ6BoEdSVBR5ni4VTrjb7UQ8YG67qOpc2ZRURERHpcgqrRURERHo5wzBwHa2hoLjUH1B/eagqpLkSYmxMzkr195uenOUgKVa/UvZ4e4vMftSb3wBfY+Bxif3MXtS5t0JSv7CVFxbalFVERESky+l/FiIiIiK9TEOjj037yilyuf0B9ZGq0Fp6DLDHmiumnQ7ystMYnZ5MlK0Ht3qQr3kbYes7sHI+7F4VfGz/cZA/G8ZfBdHaDFNEREREOofCahEREZEerrzWw5oSs51HYbGbL/aUUedpf0sPiwVGDUhu6jedRo7TQYYjHotF/aZ7lbpyWPMPWP04lJUEHzviAjOkHnKm+QIREREREelECqtFREREehDDMNjjrqXQZQbThcVuth+qxDDaP1dctJVJmWZLj5xsB1OyHKTER3d80dI9uIth1eNmUN1QGXhcdAJMvA6mz4K+I8JWnoiIiIiIwmoREREJL68Xli5puYmZzdbxx/QSjV4fW/ZXfh1Ou0o5WFEf0lx9k2KbNkI0N0McN8hOtFp69G6GASUrYeU82PpPMIKsuE8aBHFnQ208GJPBMTR8dYqIiIiIoLBaREREwm3pEnjzOcCAzevM6060qVkox/RQlXUe1paUUehyU+QqZW1JGTUN3pDmGtE/iRynw99z2tknQS09IoXXA5veMEPqfWuDjx00GabPgV218PYLgAHbNpm39dLzTERERES6J4XVIiIiEl47NgLNPSuMpsudcEwPsa+slkLX1/2mtx6owBdCS4+YKCsTM1LIcaaR19TSw5EY0/EFS/dWUwpFi2D1k1C5L/A4ixVGX2KG1FnTzX7UH95Hbz3PRERERKRnUFgtIiIi4TVifNPqaAOwmJc745huyOsz2HagksJdh0kBzv/zp+wqrQtpLkdCtD+Yzs12MH5wCrFRkdEaRVpxZAesXABfvACemsDjYpJhyo0w7U5wZLe8rZecZyIiIiLScymsFhERkfC6+Frz87H9pzvjmG6gpqGRdU0tPQpdbta63FTWNxJrM3h0KuwrrwXa1pZjSN9EcpyOpnA6jaF9E9XSI9IZBuz6BFbMhx3vBx+bmgXT7oLJN0KcvfUxPfQ8ExEREZHeQ2G1iIiIhC6UjQ9ttvb3wQ3lmC5wqKKuqaWHuRHipn0VeEPo6RFtszB+cErTZohp5Dgd9E2K7YSKJew6YrPQxnrY8LK5kvrgCVp1ZE6H/Nkw6hKwneBX/x5ynomIiIhI76WwWkREREIXQRsffpPPZ/Dl4SozmC4updDlpqQ0SPuFIOxxUf5QOtfpYGJmKnHRaunRK53MOVN1GAqfhoKnoPpw4HHWKBj7HTOkHpxzkgWLiIiIiISPwmoREREJXS/e+PCb6jxevthttvQoavoor/WENFemIwGo5NffHkve0H4M75eE1aqWHhEhlHPm4GZYOR/WvwTe+sDj4lIg5xb+//buPDzO8rz3+FejXZa1eRe2JbPa2OBFsi2HpEnDTkJDIIsJTQgQSLHJCeG0vZKekya0aXO6nJ6U1DZLQiABl5CmhJAQGhfSbLVsSbYBG2xsQPK+arNka505f7xCYPAMlizNSDPfz3X5EjO69eoeW88Y/+aZ+2HRbVB4xlB0OzIMxW50SZIkjQqG1ZIkafCS+EC2I22dfSM9gl3Tm/e00N078JEe6aE0ZpcWUFlWQmV5sHO6ODedp59+mk9UTiMzM3MYuteIdaprJhyGV5+FtSvgtV/FvmbJWVB1O8z7FGSNGeKGh9hggucUfgeHJElSqjGsliRJg5ckB7JFIhFePdROXUNj37zpJl4/3D6oa+VnZ7Cgb5xHZXkx86YVkZd14v9ydXcPbke2ksC7rZmuY/DCY8E86sOvxL7WjD+AquVwzmUQCg1Pv0NtMMFzCr2DQ5IkKdUZVkuSpMEbpQeydfb0snlPC7X1TdTUN7FhZxON7V2DutYZRblUlBWzsLyYirISzps8lnRHeiTeSB0dEW3NtO6Dmgeg9kE43hTj67NgzseCedSTLxi+PofLYILnJH4HhyRJkk5kWC1JkpJe87Eu6hqCYLquoZHnd7fQ1RMe8HVCaTBrSgGVZcVUlJdQWVZMaVHuMHSs0zZaRkfs3RTMo9787xCOseM+bxxU3gILPwdjJ8WtvSE3mOB5MO/gGKkvVkiSJCkmw2pJkpRUIpEIDUeO9R2E2EhNfRM7DrYN6lp5WenMn17UP2963rQixuY4Y3pUGMmjI8K9sO0XQUjd8PvYtRNmBfOoL/wEZCbBCyODCZ4H8w6O0fJihSRJkk5gWC1Jkka1rp4wW/a2UNfQ1D9v+nBb56CuNakguz+YXlhewszJY8lIHyWzgHWikTg6ovMobHwU1t0LTa/Hrj37EqhaBmd9ENKSaKxMvEYHjeQXKyRJkhSVYbUkSRpVWo53s2FnE3X1TdTUN/L87mY6ugc+0iMtDc6bNLZv3nQJFWXFTC3OJS2ZgsFUNpIO/2zeCevugw0/gM6W6HUZOTB3aRBSTzgvfv0lo5H4YoUkSZLe1YDD6t/85jf8wz/8A3V1dezbt48nnniCa665pv/zn/3sZ3n44YdP+JrLL7+cZ555pv92Y2MjX/jCF3jqqacIhUJcd911/PM//zP5+fmDfySSJCnpRCIRdjcd75s33UhdQxPbDhwlEnn3r327nMwQc6cWBcF0eTELphdTmOtIj6Q1Eg7/3LUe1q6Al5+CSG/0uvzJsOhzUHEzjBkXv/6S2Uh6sUKSJEmnbMBhdXt7O3PnzuXmm2/m2muvPWnNFVdcwfe+973+29nZ2Sd8/oYbbmDfvn2sWbOG7u5ubrrpJm677TZWr1490HYkSVIS6ekNs3X/UWrqG4OZ0/VN7G/tGNS1xudn9Y/0qCgrZnZpIVkZjvTQMOvtgZefhLUrYU9t7NrJF8KS5TD7WsjIik9/qWIkvFghSZKkARtwWH3llVdy5ZVXxqzJzs5m8uTJJ/3cyy+/zDPPPENNTQ2VlZUAfPvb3+aqq67iH//xHyktLR1oS5IkaZRq6+xh485g1nRdQxMbdzbR3hVjB2oMZ0/Mp7KsmMryEirLiikbl+dID8XP8WbY8DCsux9ad8coTIPzroIly6DsotE9j7q3NzjI8K27l9PTE92VJEmSRrFhmVn9X//1X0ycOJHi4mI++MEP8o1vfINx44K3NK5du5aioqL+oBrgkksuIRQKsW7dOj760Y++43qdnZ10dr55UFJraysA3d3ddHd3D8dDiJs3+h/tj0PSwLn+lYoOtHawYWczm3Y2s2FnE9sOtBJ+20iP7FPIurJCIeacUcD86cXMn1bEvOlFFOWduDO1p6dnCDsfWq7/AerthV/+GF59Gc6aBZddN3JC0cbXofZBeOFx6G4P7gvlvLMucwxc+EmovAlKZgT3jeCf0VPyi8fh6R8CEXhlSzAe+spPJLqrEc/1L6Uu17+U2lL5OWAgjzktEhnM1Me+L05Le8fM6scee4y8vDxmzJjBq6++yl/8xV+Qn5/P2rVrSU9P52//9m95+OGH2bZt2wnXmjhxInfffTe33377O77P17/+de6+++533L969Wry8vIG274kSZIkSZIkaRgdO3aMT33qU7S0tFBQUBCzdsh3Vi9d+ubhJRdccAEXXnghZ511Fv/1X//FxRdfPKhrfuUrX+Guu+7qv93a2sq0adO47LLL3vUBjnTd3d2sWbOGSy+9lMxMD3mSUonrX8nmeFcPL+xpYePOZjbuauaFnc0c7RrcztHycWOYP62I+dOLmDetmBnjk2ukh+t/gP7lbtj2/Ju3z5sLd3wt/n30dMHLP4Wa78CBzbFrSxcEhyaeexWkn+b/co/UneVv3VlNGlz1SXdWnwLXv5S6XP9Sakvl54A3pmScimEZA/JWZ555JuPHj2fHjh1cfPHFTJ48mYMHD55Q09PTQ2NjY9Q519nZ2e84pBEgMzMzaf5wk+mxSBoY179Gq4OtHdQ2BPOmaxsa2bK3ld63z/Tg3QPmzPQ05pxR2D9vuqKsmPH57/x7f0Q6zZm9rv9TdPYs2FJHfyh69iyI5+9b+xGoexDWPwBtB6LXpaXD+X8EVcth2sKh+/7PPA4/fQSIBL8PaYyMwwM/tDToxZnVg+L6l1KX619Kban4HDCQxzvsYfXu3bs5cuQIU6ZMAWDJkiU0NzdTV1dHRUUFAM899xzhcJjFixcPdzuSJGkQwuEIOw61BcF0fSO1DU3sbDw2qGsV5GRQ8ZaDEOdOKyInc5QGXE8/Bk/2hYgvbQruGwkhYrK5qu+de28NRePh0DaoXgnPPwY9HdHrsgtgwWdg8eehaPrQ97F9M0FQT/Bx+7vs6o6X9HR/3iVJkjSkBhxWt7W1sWPHjv7br7/+Ops2baKkpISSkhLuvvturrvuOiZPnsyrr77Kn//5n3P22Wdz+eWXAzBr1iyuuOIKbr31Vu699166u7u54447WLp0KaWlpUP3yCRJ0qB1dPfywu4WauobqWtooq6hiZbjgzsIZFpJLgvLSqgoL2ZheQlnT8gnFEqSkR4jNURMNvEMRSMRePW5IKTe8Z+xa4tnQNXtMO9TkD12+Ho6Z07fiyF9O8vPmTN830uSJElKoAGH1bW1tfzhH/5h/+03ZknfeOONrFq1ihdeeIGHH36Y5uZmSktLueyyy/jrv/7rE8Z4PProo9xxxx1cfPHFhEIhrrvuOu65554heDiSNEr09gazPskPPn7oFN46fZrjBqRYjrR1UtsXStfWN/Linha6ewd+BnN6KI3ZpQVUlAXBdGVZMRMLcoah4xHCEDF5dB+HFx6H6lVw6OXYtWUXwZLlcO4VEIrD83CidpZLkiRJcTbgsPoDH/gAkUj0f7z+x3/8x7teo6SkhNWrVw/0W0tS8nj6seBQqitvCT6eyvxRxw1oiEQiEV473E5dfVP/zunXDrcP6lr52RksKCsO5k33jfQYkz3sU8ZGDkPE0e/ogeDAxNrvwrEj0etCGTDnOqhaBqXz4tYe4LgNSZIkpYwU+tekJI0ggxkd4LgBDVJnTy+b97T0HYQY7J5ubO8a1LXOKMrt2zVdTEVZCedNHkt6soz0GAxDxNFr/4uwdiVs/jfojbEecouh8mZYeCsUTIlff5IkSVIKMqyWpEQ4Zw68sqXvximODnDcgE5RU3tXMM6joYm6hkae391CV094wNcJpcHMyQVBMN030qO0KHcYOpbiJByG7b+E6hXw+m/e+fkIcHQqdI6F4iz4o88E86iz8uLeqiRJkpSKDKslKRGuWhqEIhHgqk+e2ugAxw3oJCKRCA1HjlHbN2u6tqGJHQfbBnWtvKx05k0rCkZ6lJcwf3oRY3Myh7hjKQG62mHTalh3LxzZEb3u6FRonRb89/40OJBrUC1JkiTFkWG1JCVCejpc+Ql4+ung46kclOi4AQHdvWG27G0Ngum+sR6H2zoHda2JY7NZWF7SfxjirCljyUgPDXHHUgK17IH190PdQ9DRHL0uPRsu/AS8FILWV/rudNySJEmSFG+G1cmutzc4lO2tOzFPJRSTdOpcZxpGLce72bCzibr6JmobGtm0q5mO7oGP9EhLg3MnjqWiPJg3XVlWwtTiXNLSUnjedKL09sIvHgfyg48f8jljyO3ZANUrYcsTEO6JXjdmQjCLuvJmyJ8AoUfh1e04bkmSJElKDMPqZPf0Y/DkI0Ckb9Yt7syUhprrTEMkEomwu+k4dQ1N1NQ3UtfQxLYDR4lE3v1r3y47IxSM9OgLphdML6Ywz5EeI8LTj8HTP4Qrbwk+puFzxlAI98LWnwWHJu6qjl07aQ5ULYMLPgYZ2W/e77glSZIkKaEMq5Pd9s0Eu4PAt7NKw8R1pkHq6Q2zdf9RavpmTdfVN7G/tWNQ1xqfn9U/zqOirJjZpYVkZTjSY0Qayc8Zo/GdIh2tsPERWLcKmnfGrj3ncliyDGa8P3i7wdsNdNzSSP79Gsm9SZIkSVEYVie7c+b07fT07azSsHGd6RS1dfawcWcTtfVN1DU0sXFnE+1dvYO61lkTxpwwb7psXJ4jPUaLc+bAK1v6boyw54zR9E6RpgZYdx9s+D50HY1el5EL8z4FVbfD+HOGtoeR/Ps1knuTJEmSojCsTna+nVUafq4zRbGv5XhwCGLfzumX97USHsRIj6z0EBdOLaSib6RHZVkxxWOyhr5hxcdVS4PXtiLAVZ8cWc8ZI3nXN0AkArvWwdoVwciPSIz57WNLYdGtUPFZyCsZnn5G8u/XSO5NkiRJisKwOtkN9O2skgbOdSagNxzhlQNH+4Pp2vom9jQfH9S1ivMyqSgr6Zs3XcycMwrJyfTt+0kjPR2u/AQ8/XTwcSSNZhip7xTp7YaXngxC6r0bYteWzoeq5TD7Gkgf5jntI/X3C0Z2b5IkSVIUhtWSJA3Csa4eNu1qpq6+iZqGJjY2NHG0s2dQ15oxfkzfOI9iKspKOGvCGEd6KDFG2jtFjjdB3UOw/gFo3RO9Li0EMz8UhNTTq04+j3o4jLTfr7cayb1JkiRJURhWS5J0Cg62dvTvmK5raGTL3lZ6BjHTIzM9jTlnFFJZFgTTFWXFTBibPQwdS4MwUt4pcnhHcGDiptXQfSx6XdZYWPBpWPx5KC6PW3v9Rsrv18mM5N4kSZKkKAyrJUl6m3A4wo5DbSfMm97ZGCMwi6EgJ4OKsmIqy4NZ03OnFTnSQ6mttzc4/O+tO37T04N51K//BqpXwivPxL5G0XRY/Ccw/9OQUxCfviVJkiQNO8NqSVLK6+ju5fldzdQ2NFHX96vlePegrjWtJJeFZSVUlBezsLyEsyfkEwo50kPq9/Rj8OQjQCSYqRzugekZUL0KDrwY+2unVcGSZXDehyDd/42VJEmSko3/ly9JSjlH2jr7g+ma+kY272mhu3fgIz3SQ2nMLi0Idk73HYg4qSBnGDoepGg7WKWhMpifse2bCQ79I/j47Heh5Pno9aEMOP+aIKQ+o2KIGpckSZI0EhlWS5KSWiQS4bXD7cE4j/ogoH7tcPugrpWfncH86UVUlpWwsDwY6TEmewT/Vfr2HazgDFsNrcH8jE2ZBC+9cSMCGUdOXpdTBBWfhUW3QeEZQ9GtJEmSpBFuBP8LW5Kkgevs6WXznhZq65uoqW9iw84mGtu7BnWt0sKcYNZ0eTEVZcXMnFxA+mga6fH2HazbN8eudye2BupUf8bCYXj1OaheATueg4Kp0DkWso/C2N0n1pacBVW3w7xPQdaY4exekiRJ0ghjWC1JGtWaj3X1jfNooq6hked3t9DVEx7wdUJpMHNyAZXlbx6GWFqUOwwdx9E5c/p2u0aAtOB2LO7E1kC9289Y1zF44TGovhcObwvuSwMK3hZQA8z4A6haDudcBqHQ8PYtSZIkaUQyrJYkjRqRSISdjcf6g+na+ia2H2wb1LXystKZN62oP5ieP72IsTmZQ9zxEBrMruerlgYf3/o1sQx0J7YU7WesdR/UPAC134PjjdG/Pj0LLvh4sJN68gXD368kSZKkEc2wWpI0YnX3htmyt5Xa+kbqGpqobWji0NHOQV1r4thsFpaXBIchlhdz/pQCMtJH0e7Nwex6Tk8f2M7oge7Elt7+M7bveVi7Ejb/GMLd0b8ubxxU3gILPwdjJw1/n5IkSZJGBcNqvZMzSyUlSGtHNxsamqitb6K2oZFNu5rp6B74SI+0NDh34ti+kR7FVJaVMLU4l7S0UTRv+u3iset5oDuxJYBwL7zyTBBSN/wudu2EmVC1DC78BGSO8jE7kiRJkoacYbXeaTC79wy4JQ1QJBJhT/PxvoMQg53T2w4cJRJ59699u+yMUN9IjyCYXjC9mMK8JBvpEY9dzwPdia2Rbbj/bu5sg02PQvUqaHo9du3ZlwQh9VkfDF5NkiRJkqSTMKzWOw1m956Hckl6Fz29YbbuP0pNfSO1DU3U1Texv7VjUNcan59FRVlx/1iP2aWFZGUk+UgPdz1roIbr7+bmXbD+Pqj7PnS2RK/LyIG5S2Hx7TBx5ul/X0mSJElJz7Ba7zSY3XseyiXpbdo6e9i0s5navoMQN+5sor2rd1DXOntiPpVlxf0Bddm4vNQb6eGuZw3UUP/dvKsGqlfASz+FSIy1nD8JFt4KlTfDmHGn9z0lSZIkpRTDar3TYHbveSiXlBxOY2zA/paO/nEetQ2NvLS3lfAgRnpkpYe4cGohleUl/QF18ZisgV9oJPM5U/EwFD9nvT3w8k+heiXsroldO/kCqFoOc66FjOxBNCxJkiQp1RlW650Gs3vPt6dLyeEUxwb0hiO8cuAotfWNbHj9MLM3/YLzju5ke2YpP8itpDft1EdyFOdlUlFWQmV5MQvLi5lzRiHZGUk+897nTMXD6fycHW+GDd+H9fdDy64YhWlw3pXBPOry9zqPWpIkSdJpMazW0PDt6VJyiDI24HhXL5t2NVPbN296w84mjnb0APA/jq3n5mPrCAEXdQeh1j15i6J+ixnjx1BZVkxleTEVZSWcNWHM6B7pMZjd6D5nKh4G83PW+BpU3xscnNjVFr0ucwzMvwEW/wmMO+v0+pQkSZKkPobVkqQ3vWVsQAT4dXgi/+9ffseWva30RJnpsbB7L2/sow713X5DZnoac84o7BvnEeyeHp+fZOMBPGBW8XAaI3reVSQCDb+HtSth29O8+YLVSRRMhcW3wYLPQG7x0Hx/SZIkSepjWC1JKS4cjvDqoTZqG5qoa5/JrHEXcW5rAzWZpaw4dDa9aS0xv74ms5SLuncRAsLA4cln82d/cB6VZcXMnVZETmaSj/TwgFnFw3C8KNLTBVv+HdaugP0vxK49oxKWLINZfwTpmaf3fSVJkiQpCsNqSUoxHd29vLC7hdqGRurqm6htaKLlePebBWnzoXD+KV1rWkkue+b+ES82T+Ts5gZyZ1/IRz90/dDt+BwNPCxR8TCUL4oca4TaB2H9A9C2P3pdWigIp5csh2nRR/tIkiRJ0lAxrJakJHekrZO6hiCUrq1vZPOeVrp6wwO+TnoojdmlBVSUFVPZN9JjUkFO32crhrbp0cTDEhUPQ/GiyKFXoHolPP8Y9ByPXpddEIz5WPx5KJo+yIYlSZIkaeAMqyUpiUQiEV4/3E5tfRO1DcFhiK8dah/UtfKzM5g/vYiF5SX9Iz3GZPvXxjt4WKLiYbAvikQi8NqvgnnUO9bEri0uh8W3BwcnZo89rXYlSZIkaTBMHSRpFOvs6WXznlbqGhqpqW9iQ0MTR9q7BnWtM4pyg13T5cVUlBUzc3IB6aG0Ie5Y0qAM9EWR7g548XGoXgUHX4pdO/09waiP866EUAqN8JEkSZI04hhWSzp9vb3B4V9v3fGXSjOL46j5WBcbdjZRU99EXX0Tm3Y309UTfaRHeiTM8uO1LOzeGxyYmFtJb1qIUBrMnFxAZXkxlX07p0uLcuP4SCQNi7aDUPMdqPkuHDscvS6UAbOvDQ5NLD21GfWSJEmSNNwMqyWdvqcfgycfASJ9M1UZnrEIKRaKRyIRdjYe6xvpEcyb3n6wbUDXWH68ljuPrSMEvLd7F1VnltBz1aeYP72IsTmZw9O4pPjbvzmYR/3ij6A3xrsrcouh4iZYdCsUlMavP0mSJEk6BYbVkk7f9s0Eh34RfNy+eXi+T7xC8QTp7g3z0t5Wauob+w9EPHS0c1DXmjg2m4XlJXxyawuhY8F9acB7wvvh3AlD17SkxAmHYfsvoXoFvP6b2LXjzoGq22Hu9ZCVF5/+JEmSJGmADKslnb5z5vSFxxEgLbg9HOIVisfJ0c5uAL793HZqGlrZtKuZ4929A75OWhqcO3Fs30iPYirLSphanEtaWho89TI8uY1h/7ORFD9d7bBpNay7F47siF175gegajmcfQmEQnFpT5IkSZIGy7Ba0um7amnw8a3jOd7NYEZ6xCsUHwaRSIQ9zcepa2iipr6R2vom6g+38ncL4b7fvEZn76kfZJiTGWLu1KL+YHrB9GIK86KM9BjMn42kkallD6y/H+oego7m6HXp2XDhx6FqGUyaHa/uJEmSJOm0GVZLOn3p6QMfxzGYkR6jKHjt6Q2zdf9Rausb++ZNN7G/teOEmuxTHLc9Pj+LirJiFpaXUFFWzOzSQrIyTnGH5GD+bCSNLHvqoHoVbHkCwj3R68ZMgIWfg8pbIN9xP5IkSZJGH8NqSYkxmJEeIzh4bevsYdPOZmobgl3TG3c20d418JEeAGdPzKeyrLg/oC4blxeM9EgmKXZYpjRg4V7Y+jNYuxJ2VceunTgbliyDOR+DzJz49CdJkiRJw8CwWlJijOKRHgD7Wzr6g+nahkZe2ttKOPLuX3cyC6YVMbdsfH9AXTwma2ibHYmS/LBMadA6WmHjD4J51M07Y9eec1kw6uPMDwTD6yVJkiRplDOslpQYo2ikR284wisHjlLb0ERdfSM19U3saT4+qGsV52VSUVZCZXkxFdPGsvfFtXz/lsVkZkaZOZ2skuywTOm0NdXDuvtgww+g62j0uoxcmHc9LL4dJpwbt/YkSZIkKR4MqyUlxgge6XG8q5dNu5qpawiC6Q07mzjaEWNObAwzxo/pG+dRTEVZCWdNGNM/0qO7u5u9Lw5l56PIKN9ZLw2ZXeuhZhVs/TlEwtHrxk6BRbdBxWchryRu7UmSJElSPBlWS0pepzgX+eDRDurqm4KDEBua2LKnhZ5BzPTITE9jzhmFfeM8gsMQJ4zNHopHknxG0c56acj1dsNLTwKZ8Mi1EO6IXls6H6qWw+xrID3F3oEhSZIkKeUYVktKXieZixz+0Kd49VAbtQ1N1NQ3UtfQRMORY4O6fEFOBhVlxVSWl1BZVszcaUXkZHpI4CkZwTvrpWFzvAnqHoL1D0DbEZh7f5TCNJj5IVhyB0yvch61JEmSpJRhWC0peb1tLvKWX/83n9owgZbj3YO63LSSXCr75k1XlpVwzsR8QiFDJEnv4vAOWLcKNq2G7r4Xx0I576zLyof5n4bFn4eSGfHtUZIkSZJGAMNqSUnlSFtncBBiQxMzmgr4JBACwsB/dI0/5aA6PZTG7NKCYOd0X0A9qeAk4ZIknUwkAq//BqpXwivPxK4tnB4E1As+DTmF8elPkiRJkkYgw2pJo1YkEuG1w+3U1b850uO1w+39n0+PzGFfXgcLu/dSk1nKitzKqNfKz85g/vQiKstKWFgejPQYk+1TpKQB6umEF/8tCKkPbH73+o/eB+d/GNJ9vpEkSZIk/2UkadTo7Oll854WavsOQ6xraKKxvStqfW9aiHvyFp30c6WFOcGs6fJiKsqKmTm5gHRHekgarPbDUPNdqPkOtB+MXpeWHhyWuPB22LQ3mE1tUC1JkiRJgGG1pBGs+VgXdQ1BMF1b38jzu1vo6gkP+DqhNJg5uSCYNd13GGJpUe4wdCwp5Rx4KdhF/cLj0NsZvS6nECo+C4tug8Kp0N0dhNWSJEmSpH6G1ZJGhEgkws7GY327phuprW9i+8G2QV0rLyudedOK+oPp+dOLGJuTOcQdS0pZ4TC8+iysXQGv/Sp2bcmZULUM5l4P2fnx6U+SJEmSRinD6tGmtxeefgy2b4Zz5sBVSyE9PdFdKZnE6WesuzfMS3tb+2dN1zY0cehojF2JMUwcm83C8hIqyopZWF7CrCljyUgPDXHHklJe1zF44TGovhcOb4tdW/4+WLIczrkcQj4fSZIkSdKpMKwebZ5+DJ58BIjAS5uC+66+IZEdKdkM089Ya0c3G/rmTNfUN/L8rhaOd/cO6lrnTsqnsjw4CLGyrISpxbmkpTlvOun5Yp0SpXUf1DwAtd+D443R60KZcMHHoep2mHJh/PqTJEmSpCRhWD3abN8MRPpuRPpuS0NoCH7GIpEIe5qPnzDSY9uBo0Qi7/61b5edEeob6REE0wumF1OY50iPlBSPF+sMxPVW+56HtSth848h3B29Lm8cVN4MCz8HYyfHrz9JkiRJSjKG1aPNOXP6QpoIkBbclobSIH7GenrDbN1/lNr6Rmoamqirb2J/a8egvv24MVlUlhf3j/WYXVpIVoZvoRfxebHOd68o3AuvPBOE1A2/i107YWawi/rCT0Kmh7ZKkiRJ0ukyrB5trloafHzrrj9F5y7JgTuFn7G2zh427Wzunze9cWcT7V2DG+lx1oQxVJaV9AfUZePyHOmhk4vHi3W+eyV1dbbBpkehehU0vR679qyLYcmy4KPPV5IkSZI0ZAyrR5v0dHf5DcRgdkmmesB9kp+xfS3BSI835k2/vK+V8CBGemSlh7hwaiEV5cUsLAt2ThePyRqixpX04vFine9eST3Nu2D9fVD3fehsiV6XkRPsoK5aBhNnxq8/SZIkSUohhtVKnHiEwoPZJZniAXdvOMIrB45S29BEbX0wb3pP8/FBXasoL7N/13RlWTFzzigkJ3N0/r5oBIjHi3W+eyV17KqB6hXw0k8hEuOdIfmTYOGtUHkTjBkfv/4kSZIkKQUZVitx4jEbdjC7JOMVcI8Qx7p62LSrmbr6Jmobmtiws4mjHT2DulbZuDwqy0pYWF5MZXkxZ47PJxQaZW+RT6IXHjQIvnslufX2wMs/heqVsLsmdu3kC6BqOcy5FjKy49OfJEmSJKU4w2olTjxmww5ml2S8Au4EOXi0oz+Yrq1vZMveVnoGMdMjI5TGnDMKqSwLgumKshImjE2CQGcUv/AgKYrjzbDh+7D+fmjZFaMwDc67Mhj1Uf5e51FLkiRJUpwZVitx4jEbdjC7JOMVcMdBOBxhx6E2auubqG0IDkNsOHJsUNcam5NBRVlwCGJFWTFzpxaRm5WEO45H0QsPkt5F42tQfS9sfAS626PXZY6B+TfA4j+BcWfFrz9JkiRJ0gkMq5U4I3U2bLwC7mHQ0d3LC7tbqG1o7D8QseV496CuNbU4tz+YXlhewjkTR+FIj8EYoS88SDpFkQg0/B7WroRtT/Pmi08nUTAVFt8GCz4DucVxa1GSJEmSdHKG1UqcZJoNm6DHcqStk9qGIJSurW/kxT0tdPcOfKRHeiiN86cU9B2EGByIOKkgZxg6HgVGyAsPkgaopwu2/DusXQH7X4hde0YlLFkGs/4I0jPj058kSZIk6V0ZVkujRCQS4bXD7dTVN1FTH4z0eO1wjLe1x5CfncH86UX9hyHOnVbEmGyfDoDkehFFSgXtR6DuQVj/HWjbH70uLRSE00uWw7RF8etPkiRJknTKTKekEaqzp5fNe1qprW/s3z3d2N41qGuVFuZQWV7SdxBiMTMnF5CeCiM9JCWvQ9ugeiU8/xj0dESvyy4Ixnws/jwUTY9ff5IkSZKkATOslkaI5mNdwTiPvpEez+9uoasnPODrhNJg5uS+kR7lJVSWFVNalDsMHUtSnEUi8NqvgnnUO9bEri0uh8W3BwcnZo+NS3uSJEmSpNNjWC0lQCQSYeeho7Q98ShZr73Ef4cm81fhC+lNCw34WrmZ6cFIj75gev70IsbmOINVUhLp7oAXH4fqVXDwpdi1ZRdB1TI470oIpcenP0mSJEnSkDCsluKguzfMS3tb+2dN1zY0cf2B33LnsXWEgLPYzpG8Lu7Je/c5qhPHZp9wEOKsKQVkpg885JakEa/tINR8B2q+C8cOR68LZcCc66DqdiidH7/+JEmSJElDyrBaGgatHd1s6JszXVvfxKZdzRzv7j2hZmH3Xt6ImEN9t0/mvEljqSgvprKsmIXlJUwtziUtzXnTkpLY/s3BPOoXfwS9MWb15xZDxU2w6FYoKI1ff5IkSZKkYWFYLZ2mSCTCnubj/cF0TX0j2w4cJRKJ/XU1maVc1L2LEBDuu52dEWLutCIW9u2cXjC9mMK8t4z06O2Fn62G7ZvhnDlw1VJI923ukpJAOAzbfwnVK+D138SuHXdOsIt67vWQlRef/iRJkiRJw86wWhqgnt4wW/cfpba+kdq+3dP7WjoGfJ0VuZXkZabzB2kHOFY2iz+8eil3TC0hKyPGSI+nH4MnHwEi8NKm4L6rbxjU45CkEaGrHTathnX3wpEdsWvP/ABULYezL4GQ448kSZIkKdkYVkvvoq2zh007m6ltaKS2vomNO5to7+p99y88ibMmjOmfNV1ZXkL5uA8PbKTH9s3AG1u2I323JWkUatkD6++Huoegozl6XXo2XPjx4NDESbPj1Z0kSZIkKQEMq6W32d/S8ZaDEBt5aW8r4XcZ6XEyWekhLpxa2DdvuoSKsmJKxmSdXnPnzOnbUR0B0oLbkjSa7KmDtSvhpZ9AuCd63ZgJsPBzUHkL5E+IW3uSJEmSpMQxrNbo0tsbjMIYopnNveEIrxw4GozzqG+kpr6JPc3HB3WtorxMKsuKqSgrYWF5MXPOKCQnc4jnSV+1NPj41scvSSNduBe2/jw4NHHn2ti1E2fDkmUw52OQmROf/iRJkiRJI4JhtUaX05zZfLyrl027mqlrCILpDTubONoRY2dfDOXj8qgsD4LpirJizhyfTyg0gJEeg5Ge7oxqSaNHRytsfCSYR93cELv2nMuDkHrG+2Eg45EkSZIkSUnDsFqjywBnNh882kFdfRO1DcGvLXta6BnETI/M9DRmlxZSWRbMmq4sL2Z8fvbA+5ekVNDUAOvugw3fh66j0esycmHe9bD4dphwbvz6kyRJkiSNSIbVGl1izGwOhyO8eqiN2oam/pnTDUeODerbFORksKCsmIXlwazpuVOLyM0a4pEekpRMIhHYtQ7WroCtP4NIOHrt2Cmw6Dao+CzklcStRUmSJEnSyGZYrdHlLTObu888n43nX0btf+2grr6Jup1NNB/rHtRlp5XksrCspD+gPmdiHEZ6SBp+QzznXifR2w0vPRmE1Hs3xK4tnQ9Vy2H2NZCeGZf2JEmSJEmjh2G1Ro0jbZ3UNTRRl76AmpxyNte00lW9fsDXSQ+lcf6UAir6gunK8mImFXiIl5SUTnPOvWI43gR1D8P6+6F1T/S6tBDM/FAQUk+vch61JEmSJCkqw2qNSJFIhNcPt1Nb30RtQyO1DU28dqh9UNfKz85g/vQiKsuCYHretCLGZPujL6WEAc651yk48ipUr4JNj0J3jFFLWWNhwaeDcR8lM+LXnyRJkiRp1DKx04jQ1RNm894Wausbqa1voq6hiSPtXYO6VmlhDhXlJSwsL6airJiZkwtId6SHlJpizLnXAEQiUP9bWLsSXnmGN18AOInC6bD480FQnVMYtxYlSZIkSaOfYbUSouVYN3U7g2C6tr6J53c309kT4zCuKNLSYObkgv5gurK8hDOKcoehY0mj0lvm3PfPrNap6+mEzT+G6pWw/8XYtdMWQ9UymPlhSPd/LyRJkiRJA+e/JjXsIpEIuxqPU1MfjPOoa2jklQNtg7pWbmZ630iPIJieP72IsTke0iUpivR0Z1QPRvthqH0Qar4DbQei16WlB4clVi2HqRVxa0+SJEmSlJwGHFb/5je/4R/+4R+oq6tj3759PPHEE1xzzTX9n49EInzta1/jgQceoLm5mYsuuohVq1Zxzjnn9Nc0NjbyhS98gaeeeopQKMR1113HP//zP5Ofnz8kD0qJ1d0b5qW9rdQ2NAVjPRqaOHS0c1DXmjg2m8ry4v5507OmFJCZHhrijpNYb29wwNxbd5Wmpye6K0kj1cGXg13ULzwOPR3R63IKoeKzwTzqwqlxa0+SJEmSlNwGHFa3t7czd+5cbr75Zq699tp3fP7v//7vueeee3j44YeZMWMGX/3qV7n88st56aWXyMnJAeCGG25g3759rFmzhu7ubm666SZuu+02Vq9effqPSHHX2tHNhoZgznRtfRObdjVzvLt3UNc6d1I+leUlVJYVs7C8hKnFuaSlOW960J5+DJ58BIj0ze3FXaaSThSJwI5noXoFvPpc7NqSM4NRH3Ovh2xfYJYkSZIkDa0Bh9VXXnklV1555Uk/F4lE+Na3vsX//t//m4985CMAfP/732fSpEn85Cc/YenSpbz88ss888wz1NTUUFlZCcC3v/1trrrqKv7xH/+R0tLS03g4ioc9zcf7D0KsqW9k24GjRGKctRVNdkaIudOK+oPpBdOLKcxzpMeQ2r6ZNw9Ci/TdliSg+zg8/xhUr4LD22LXlr8PliyHcy6HkO9ukSRJkiQNjyGdWf3666+zf/9+Lrnkkv77CgsLWbx4MWvXrmXp0qWsXbuWoqKi/qAa4JJLLiEUCrFu3To++tGPvuO6nZ2ddHa+OUaitbUVgO7ubrq7u4fyIcTdG/2P1MfRG47wyoGjbNzZzIadwa7p/a0nvjU86xRzi5K8LBZML2L+9GLmTS9i1uQCsjJO/OKR+vswap09B17ZQhBYpwW3/T0eMUb6+leSajsAdQ/Dxh/A8abgvlDOO+tCmcE86oWfg0mzg/t6e4NfOm2ufyl1uf6l1OX6l1JbKj8HDOQxD2lYvX//fgAmTZp0wv2TJk3q/9z+/fuZOHHiiU1kZFBSUtJf83bf/OY3ufvuu99x/y9/+Uvy8vKGovWEW7NmTaJbiKkI+OAY+ODM07nK8eBX8z72NMOeF4aiM8WWD1fe8ubNCPD00wnrRic30te/ktEcOPfvTq20rgFoGNZuUpnrX0pdrn8pdbn+pdSWis8Bx44dO+XaIQ2rh8tXvvIV7rrrrv7bra2tTJs2jcsuu4yCgoIEdnb6uru7WbNmDZdeeimZmfEfgXGgtZONu5rY2NDMxl1NbDtwlN7wwGd6ZIVCzD6jgPnT3tw5XZyXNQwdS8kj0etfKSAchh3/CTXfgZ3/Hbt2/LnBLurZ10LmSXZaa0i5/qXU5fqXUpfrX0ptqfwc8MaUjFMxpGH15MmTAThw4ABTpkzpv//AgQPMmzevv+bgwYMnfF1PTw+NjY39X/922dnZZGdnv+P+zMzMpPnDjcdjeWOkR21DE3X1jdQ2NLG76fhJKt/9QMOivEwqy4qpKCthYXkxc84oJCczfeibllJAMj2XaYTobINNq2HdKmh8LXbtWRfDkmXBRw+0jTvXv5S6XP9S6nL9S6ktFZ8DBvJ4hzSsnjFjBpMnT+bZZ5/tD6dbW1tZt24dt99+OwBLliyhubmZuro6KioqAHjuuecIh8MsXrx4KNtJece7etm0q5m6hkZq6pvYsLOJox09g7pW+bi8/mC6sryYM8fnEwoZakjSiNKyG9bdBxseho6W6HUZOXDhJ6FqGUw8rflOkiRJkiQNmQGH1W1tbezYsaP/9uuvv86mTZsoKSlh+vTp3HnnnXzjG9/gnHPOYcaMGXz1q1+ltLSUa665BoBZs2ZxxRVXcOutt3LvvffS3d3NHXfcwdKlSyktLR2yB5aKDh7toK6+idqG4NeWPS30DGKkR0YojdlnFFJZVszC8mD39ISx79zZLkkaIXbXwtoV8NKTEIlxAGL+JFh4K1TeDGPGxa8/SZIkSZJOwYDD6traWv7wD/+w//Ybs6RvvPFGHnroIf78z/+c9vZ2brvtNpqbm3nve9/LM888Q07Om/MvH330Ue644w4uvvhiQqEQ1113Hffcc88QPJzUEQ5HePVQWxBM1zdR29BIw5FTH1b+VmNzMqgoK+4f6zFvWhG5WY70kKQRrbcHtj4Fa1fC7vWxaydfAFXLYc61kOGLj5IkSZKkkWnAYfUHPvABIpHou3XT0tL4q7/6K/7qr/4qak1JSQmrV68e6LdOebX1wTiP2vpG6nY20Xyse1DXmVqcy8LykiCgLi/m3IljHekhSaNFRwts+D6sux9adsYoTIPzrgxGfZS/13nUkiRJkqQRb0hnVmt4/dm/vcDrh9sH9DXpoTTOn1JARVkxC8tLqCwvZlJBzrt/oSRpZGl8HdbdCxsfga626HWZY2D+DbD4T2DcWfHrT5IkSZKk02RYPYpUlBW/a1idn53B/OlFVJYFwfS8aUWMyfaPWZJGpUgEGv4bqlfC1p8DMc4hKJgKi2+DBZ+B3OK4tShJkiRJ0lAxxRxFFpYX8291u0+4b0phDpXlJVT2jfSYObmAdEd6SNLo1tMFW56A6hWw7/nYtWdUwJLlMOuPID0zPv1JkiRJkjQMDKtHkcryEmZNKegPpivLSzijKDfRbUmShsqxRqh9EGq+A0f3Ra9LC8Gsq4NDE6ctch61JEmSJCkpGFaPImdNyOcXX3xfotuQJA21Q68Eoz6efwx6jkevyy4Ixnwsug2Ky+LXnyRJkiRJcWBYLUlSIkQi8NqvYO1K2LEmdm1RGVTdDvNugJyC+PQnSZIkSVKcGVZLkhRP3R3w4o+gehUc3BK7dvp7YMkyOO8qCKXHpz9JkiRJkhLEsFqSpHhoOwg13w3mUR87HL0ulAGzrw1C6tL58etPkiRJkqQEM6yWJGk4HdgSjPp48XHo7Ypel1MElTcF86gLSuPWniRJkiRJI4VhtSRJQy0cDuZQr10Br/86du24s4N51HOvh6wx8elPkiRJkqQRyLBakqSh0tUOz/8rVN8LR7bHrp3xfliyHM6+FEKh+PQnSZIkSdIIZlgtSdLpat0L6++H2u9BR3P0uvQsuOATwU7qyXPi1p4kSZIkSaOBYbUkSYO1ZwNUr4QtT0C4J3pd3nhY+DlYeAvkT4xff5IkSZIkjSKG1ZIkDUS4F7b+PAipd66NXTvxfKhaBhd8HDJz4tOfJEmSJEmjlGG1JEmnoqMVNj4C6+6F5obYtedcFoTUZ34A0tLi0p4kSZIkSaOdYbUkSbE0NcC6+2DjD6CzNXpdRi7MXRqE1BPOjV9/kiRJkiQlCcNqSZLeLhKBXetg7QrY+jOIhKPXjp0Ci26FipsgryR+PUqSJEmSlGQMqyVJekNvN7z0ZBBS790Qu3bKPFiyHM6/BjKy4tGdJEmSJElJzbBakqTjTVD3EKx/AFr3xChMg5kfCkLq6UucRy1JkiRJ0hAyrJYkpa4jr0L1Ktj0KHQfi16XlQ/zPw2LPw8lM+LXnyRJkiRJKcSwWpKUWiIRqP8trF0JrzwDRKLXFk6DxX8CCz4NOYVxa1GSJEmSpFRkWC1JSg09nbD5x0FIfeDF2LVTF8GSZTDzakj3r0pJkiRJkuLBf4FLkpJb+2GofRBqvgNtB6LXpaXD+R8J5lFPrYxff5IkSZIkCTCsliQlq4MvQ/VKeOFx6OmIXpddCBU3wqLboGha/PqTJEmSJEknMKyWJCWPSAR2PAvVK+DV52LXlpwJi2+HeZ+C7Pz49CdJkiRJkqIyrJYkjX7dx+H5x6B6FRzeFru2/H1QtQzOvRxC6fHpT5IkSZIkvSvDaknS6HV0P6x/IJhJfbwxel0oEy74GFTdDlPmxq8/SZIkSZJ0ygyrJUmjz77nYe1K2PxjCHdHr8stgYW3wMLPwdjJ8etPkiRJkiQNmGG1JGl0CIfhlWeCQxPrfxu7dvx5sGQZXPhJyMyNT3+SJEmSJOm0GFZLkka2zjbYtBrWrYLG12LXnnVxMI/67IshLS0+/UmSJEmSpCFhWC1JGpladsO6+2DDw9DREr0uIyfYQV11O0ycFb/+JEmSJEnSkDKsliSNLLtrYe0KeOlJiPRGrxszERbdCpU3w5jx8etPkiRJkiQNC8NqSVLi9fbA1qeCQxN3r49dO+mCYB71nOsgIzs+/UmSJEmSpGFnWC1JSpyOFtjwfVh3P7TsjFGYBudeEYTU5e9zHrUkSZIkSUnIsFqSFH+NrwXzqDc+Al1t0esy82DeDcE86nFnxa8/SZIkSZIUd4bVkqT4iESg4b+heiVs/TkQiV5bcAYsug0qboTc4ri1KEmSJEmSEsewWpI0vHq6YMsTUL0C9j0fu/aMCqhaBud/BNIz49OfJEmSJEkaEQyrJUnD41gj1D4INd+Bo/ui16WFYNbVULUcpi1yHrUkSZIkSSnKsFqSNLQOvRKM+nj+Meg5Hr0uuwAWfCYY91FcFr/+JEmSJEnSiGRYLUk6fZEIvPYrWLsSdqyJXVtUFhyYOO8GyCmIT3+SJEmSJGnEM6yWJA1edwe8+COoXgUHt8Sunf4eWLIMzrsKQunx6U+SJEmSJI0ahtWSpIFrOxjMoq75Lhw7HL0ulAGzrw1C6tL58etPkiRJkiSNOobVkqRTd2BLMOrjxcehtyt6XU4RVN4Mi26FgtK4tSdJkiRJkkYvw2pJUmzhcDCHeu0KeP3XsWvHnR3Mo557PWSNiU9/kiRJkiQpKRhWS5JOrqsdnv9XqL4XjmyPXTvj/bBkOZx9KYRC8elPkiRJkiQlFcNqSdKJWvfC+vuh9nvQ0Ry9Lj0LLvhEsJN68py4tSdJkiRJkpKTYbUkKbBnA1SvhC1PQLgnel3eeFj4OVh4C+RPjF9/kiRJkiQpqRlWS1IqC/fCtqeDedQ718aunXg+VC2DCz4OmTnx6U+SJEmSJKUMw2pJSkWdR2HjI7DuXmiqj117zmVBSH3mByAtLR7dSZIkSZKkFGRYLUmppKkhmEe94fvQ2Rq9LiMX5l0Pi2+HCefGrz9JkiRJkpSyDKslKdlFIrBrPVSvgJefgkg4eu3YKbDoVqi4CfJK4tejJEmSJElKeYbVkpSservhpSeDQxP31MWunTIPliyH86+BjKx4dCdJkiRJknQCw2pJSjbHm6Du4WDcR+ueGIVpMPNDQUg9fYnzqCVJkiRJUkIZVktSsjjyKlSvgk2robs9el1WPsz/NCz+PJTMiF9/kiRJkiRJMRhWS9JoFolA/W9h7Up45RkgEr22cHoQUC/4NOQUxq1FSZIkSZKkU2FYLUmjUU8XbP5xcGji/hdj105dBEuWwcyrId2nfUmSJEmSNDKZWkjSaNJ+BGofhJoHoO1A9Lq0dDj/I8E86qmV8etPkiRJkiRpkAyrJWk0OLgVqlfCCz+Eno7oddmFUHEjLLoNiqbFrz9JkiRJkqTTZFgtSSNVJAKvPhvMo3712di1JWfC4tth3qcgOz8+/UmSJEmSJA0hw2pJGmm6jwc7qKtXwaGtsWvL3wdVy+DcKyAUik9/kiRJkiRJw8CwWpJGiqMHglnUtQ/CsSPR60KZcMHHoOp2mDI3fv1JkiRJkiQNI8NqSUq0A1ug5l548d8g3B29LrcEFt4CCz8HYyfHrz9JkiRJkqQ4MKyWpEQIh2H7muC/H7wcwjEOTZwwM9hFfeEnITM3Pv1JkiRJkiTFmWG1JMVTZxs8/6/BPOrmPTD3/ui1Z10MS5YFH9PS4tejJEmSJElSAhhWS1I8tOyG9fdD3UPQ0RLcF8p5Z11GTrCDumoZTJwZ1xYlSZIkSZISybBakobT7jqoXgFbfgKR3uh1+ZNg4a1QeROMGR+39iRJkiRJkkYKw2pJGmq9PbD1Z1C9Enate/f6D38LLrwWMrKHvTVJkiRJkqSRyrBakoZKRwts+AGsuw9adsYoTIPzroSFt8OWJrjgY5CRGbc2JUmSJEmSRiLDakk6XY2vBwH1xh9AV1v0uswxMP8GWPwnMO4s6O6GLU/Hr09JkiRJkqQRzLBakgYjEoGda2HtCtj6cyASvbbgDFj8eVjwGcgtjluLkiRJkiRJo4lhtSQNRE8XvPSTIKTetyl2bekCWLIczv8IpDvmQ5IkSZIkKRbDakk6Fccaoe57sP4BOLovel1aCGZ+OAippy2GtLT49ShJkiRJkjSKGVZLUiyHt0P1Stj0r9BzPHpd1thgzMfi26C4PG7tSZIkSZIkJQvDakl6u0gEXvuvIKTe/svYtUVlwYGJ8/8Ycgri0p4kSZIkSVIyMqyWpDd0d8CLP4LqVXBwS+za6UugahnM/BCE0uPTnyRJkiRJUhIzrJaktoNQ812o/S60H4peF8qA2R8NQuozFsSvP0mSJEmSpBRgWC0pdR3YEoz6eOFx6O2KXpdTBBWfhUW3QeEZ8epOkiRJkiQppRhWS0ot4TDs+E+oXhHMpY5l3NlQdTvMvR6yxsSlPUmSJEmSpFRlWC0pNXQdg+f/NZhHfWR77NoZ7w9GfZxzGYRC8elPkiRJkiQpxRlWS0purftg/f1Q9z043hS9Lj0LLvhEsJN68pz49SdJkiRJkiTAsFpSstq7EdauhC3/DuGe6HVjJsDCz0HlzZA/MX79SZIkSZIk6QSG1ZKSR7gXtj0dhNQ7/zt27YRZsGRZsJs6Myc+/UmSJEmSJCkqw2pJo1/nUdj4CKy7F5rqY9eefWkQUp/5h5CWFpf2JEmSJEmS9O4MqyWNXk0NwTzqDd+HztbodRm5MHdpMI96wnnx60+SJEmSJEmnLDTUF/z6179OWlraCb9mzpzZ//mOjg6WL1/OuHHjyM/P57rrruPAgQND3YakZLZrPTz+GbhnHqz9l+hBdf5k+OBX4a6X4OpvGVRLkiRJkiSNYMOys3r27Nn853/+55vfJOPNb/OlL32Jn//85/zoRz+isLCQO+64g2uvvZbf//73w9GKpGTR2w0vPQnVq2BPbezaKXOhajnM/ihkZMWnP0mSJEmSJJ2WYQmrMzIymDx58jvub2lp4bvf/S6rV6/mgx/8IADf+973mDVrFtXV1VRVVZ30ep2dnXR2dvbfbm0NdlF2d3fT3d09DI8gft7of7Q/DmnYdDTDxtVQ9zAc3RPcFzrZgYhpcO7lsPBzMG1xMI86AozgteX6l1KX619KXa5/KXW5/qXUlsrPAQN5zGmRSCQylN/861//Ov/wD/9AYWEhOTk5LFmyhG9+85tMnz6d5557josvvpimpiaKior6v6asrIw777yTL33pS1Gveffdd7/j/tWrV5OXlzeU7UuSJEmSJEmShsixY8f41Kc+RUtLCwUFBTFrh3xn9eLFi3nooYc477zz2LdvH3fffTfve9/72Lx5M/v37ycrK+uEoBpg0qRJ7N+/P+o1v/KVr3DXXXf1325tbWXatGlcdtll7/oAR7ru7m7WrFnDpZdeSmZmZqLbkRIrEoGd1VDzAGxfQ7A1OoqCqVB5U3BwYk5h3FocSq5/KXW5/qXU5fqXUpfrX0ptqfwc8MaUjFMx5GH1lVde2f/fF154IYsXL6asrIzHH3+c3NzcQV0zOzub7Ozsd9yfmZmZNH+4yfRYpAHr6YLNP4bqFbD/xdi10xZD1TKY+WFIH5ZJRnHn+pdSl+tfSl2ufyl1uf6l1JaKzwEDebzDnvQUFRVx7rnnsmPHDi699FK6urpobm4+YXf1gQMHTjrjWlKSaz8CtQ8GO6nbDkSvS0uH2dcEIfXUyri1J0mSJEmSpPgZ9rC6ra2NV199lU9/+tNUVFSQmZnJs88+y3XXXQfAtm3b2LlzJ0uWLBnuViSNFAe3QvVKeOGH0NMRvS67ECpuhEW3QdG0+PUnSZIkSZKkuBvysPpP//RPufrqqykrK2Pv3r187WtfIz09neuvv57CwkJuueUW7rrrLkpKSigoKOALX/gCS5YsoaqqaqhbkTSSRCLw6rOwdmXwMZaSM2Hx7TDvU5CdH5/+JEmSJEmSlFBDHlbv3r2b66+/niNHjjBhwgTe+973Ul1dzYQJEwD4f//v/xEKhbjuuuvo7Ozk8ssvZ+XKlUPdhqSRovt4sIO6ehUc2hq7tuy9sGQZnHsFhNLj058kSZIkSZJGhCEPqx977LGYn8/JyWHFihWsWLFiqL+1pJHk6IFgFnXtg3DsSPS6UCbMuS4IqafMjV9/kiRJkiRJGlGGfWa1pBSz74VgHvWL/wbh7uh1uSVQeTMsuhXGesCqJEmSJElSqjOslnT6wmHY/h+wdgXU/zZ27fjzoOp2mLsUMnPj058kSZIkSZJGPMNqSYPX2QabVsO6VdD4Wuzasy6GqmVw9sWQlhaf/iRJkiRJkjRqGFZLGriW3bDuPtjwMHS0RK9Lz4YLPwFLlsPEWfHrT5IkSZIkSaOOYbWkU7e7DqpXwJafQKQ3el3+JFh4K1TeBGPGx609SZIkSZIkjV6G1ZJi6+2BrT8LDk3ctS527aQLgl3Uc66FjOz49CdJkiRJkqSkYFgt6eQ6WmDDD4JxHy07YxSmwXlXBvOoy9/rPGpJkiRJkiQNimG1pBM1vh4E1Bt/AF1t0esy82D+H8PiP4FxZ8WvP0mSJEmSJCUlw2pJEInAzrWwdgVs/TkQiV5bcAYsug0qboTc4ri1KEmSJEmSpORmWC2lsp4ueOknQUi9b1Ps2tIFwTzq8z8C6Znx6E6SJEmSJEkpxLBaSkXHGqHue7D+ATi6L3pdWghmfjgIqactdh61JEmSJEmSho1htZRKDm+H6pWw6V+h53j0uqyxsOAzsPg2KC6PW3uSJEmSJElKXYbVUrKLROC1/wpC6u2/jF1bVBYcmDj/jyGnIC7tSZIkSZIkSWBYLSWv7g548UdQvQoOboldO/09sGQZnHcVhNLj058kSZIkSZL0FobVUrJpOwS134Wa70D7oeh1oQyYfS1U3Q5nLIhff5IkSZIkSdJJGFZLyeLAlmDUxws/gt7O6HU5RVB5Myy6FQpK49aeJEmSJEmSFIthtTSahcOw4z+hekUwlzqWcWcHu6jnXg9ZY+LSniRJkiRJknSqDKul0ajrGDz/r7DuXjj8SuzaMz8AVcvh7EsgFIpLe5IkSZIkSdJAGVZLo0nrXlj/ANR9D443Ra9Lz4ILPhHspJ48J379SZIkSZIkSYNkWC2NBns3wtqVsOXfIdwTvS5vPCy8BRZ+DvInxq8/SZIkSZIk6TQZVksjVbgXtj0dhNQ7/zt27YRZsGRZsJs6Myc+/UmSJEmSJElDyLBaGmk6j8LGR4J51E31sWvPvjQIqc/8Q0hLi0t7kiRJkiRJ0nAwrJZGiuadsO4+2PB96GyNXpeRA3OXQtUymHBe/PqTJEmSJEmShpFhtZRou9bD2hXw8k8hEo5elz8ZFn0OKm6GMePi158kSZIkSZIUB4bVUiL09sDLTwbzqPfUxq6dMheqlsPsj0JGVnz6kyRJkiRJkuLMsFqKp+PNsOFhWHc/tO6OUZgGMz8UjPooe4/zqCVJkiRJkpT0DKuleDjyanBg4sZHobs9el1WPsz/Y1j8eSg5M379SZIkSZIkSQlmWC0Nl0gEGn4fzKPe9gsgEr22cFoQUM//NOQWxatDSZIkSZIkacQwrJaGWk8XbP4xVK+E/S/Erp26CJYsg5lXQ7rLUZIkSZIkSanLdEwaKu1HoO5BWP8AtB2IXpeWDuf/UXBo4rSF8etPkiRJkiRJGsEMq6XTdWhbsIv6+cegpyN6XXYhVHwGFn0eiqbFrz9JkiRJkiRpFDCslgYjEoFXnwtC6h3/Gbu2eAZU3Q7zboDs/Pj0J0mSJEmSJI0yhtXSQHQfhxceh+pVcOjl2LVl7w3mUZ97BYTS49OfJEmSJEmSNEoZVkun4ugBqPkO1H4Xjh2JXhfKhDnXBSH1lLnx60+SJEmSJEka5QyrpVj2vwhrV8Lmf4Peruh1uSVQeTMsuhXGTo5ff5IkSZIkSVKSMKyW3i4chu3/AWtXQP1vY9eOPy+YRz13KWTmxqc/SZIkSZIkKQkZVktv6GqHTauDedSNr8auPeviYNTHWRdDWlp8+pMkSZIkSZKSmGG11LIH1t8HdQ9BR0v0uowcuPCTwU7qibPi1p4kSZIkSZKUCgyrlbp210H1CtjyE4j0Rq/LnwQLb4XKm2DM+Li1J0mSJEmSJKUSw2qllt4e2PozqF4Ju9bFrp10ASxZDnOuhYzs+PQnSZIkSZIkpSjDaqWGjhbY8INg3Efzzti1514RhNTl73MetSRJkiRJkhQnhtVKbk31sO6+IKjuOhq9LjMP5n0KFt8O48+OW3uSJEmSJEmSAobVSj6RCOysDuZRb/05RMLRa8eWwuLbYMGNkFcSvx4lSZIkSZIkncCwWsmjtzs4LLF6BezdGLu2dEEw6uP8j0B6ZlzakyRJkiRJkhSdYbVGv2ONUPcQrH8Aju6NXpcWgllXQ9VymLbIedSSJEmSJEnSCGJYrdHr8A6oXgnP/yt0H4telzUWFnwmGPdRXB639iRJkiRJkiSdOsNqjS6RCLz+a1i7Erb/R+zaojJY/Ccw/48hpyA+/UmSJEmSJEkaFMNqjQ49nfDivwU7qQ9sjl07fQlULYOZH4JQenz6kyRJkiRJknRaDKs1srUdgtoHoeYBaD8UvS6UAbM/GoTUZyyIX3+SJEmSJEmShoRhtUamAy8Fu6hfeBx6O6PX5RRBxWdh0W1QeEa8upMkSZIkSZI0xAyrNXKEw/Dqs7B2Bbz2q9i1486Gqtth7vWQNSY+/UmSJEmSJEkaNobVSryuY/DCY1C9Cg6/Ert2xvthyXI4+1IIheLTnyRJkiRJkqRhZ1itxGndF8yirn0QjjdFr0vPggs+HuyknnxB/PqTJEmSJEmSFDeG1Yq/vZuCedSb/x3C3dHr8sbDwlug8hYYOylu7UmSJEmSJEmKP8NqxUe4F7b9IgipG34fu3bCLFiyDC74BGTmxKc/SZIkSZIkSQllWK3h1XkUNj4K6+6Fptdj155zGVQtgzM/AGlpcWlPkiRJkiRJ0shgWK3h0bwT1t0HG34AnS3R6zJyYe7SIKSecG78+pMkSZIkSZI0ohhWa2jtWg9rV8DLT0GkN3pd/mRYdCtU3gx5JfHrT5IkSZIkSdKIZFit09fbAy8/CWtXwp7a2LVT5kLVcpj9UcjIik9/kiRJkiRJkkY8w2oN3vFm2PAwrLsfWnfHKEyDmR8KRn2Uvcd51JIkSZIkSZLewbBaA3fk1eDAxI2PQnd79LqsfJj/x7D481ByZvz6kyRJkiRJkjTqGFbr1EQiUP87qF4J234BRKLXFk4LAuoFn4Gcwri1KEmSJEmSJGn0MqxWbD1dsPnHQUi9/4XYtVMXBqM+Zv0RpPujJUmSJEmSJOnUmSjq5NqPQN2DsP4BaDsQvS4tHc7/o+DQxGkL49efJEmSJEmSpKRiWK0THdoW7KJ+/jHo6Yhel10IFZ+BRZ+Homnx60+SJEmSJElSUjKsVjCP+tXngpB6x3/Gri2eAVW3w7wbIDs/Pv1JkiRJkiRJSnqG1ams+zi88DhUr4JDL8euLXsvLFkG514BofT49CdJkiRJkiQpZRhWp6KjB6DmO1D7XTh2JHpdKBMu+Fiwk3rK3Pj1J0mSJEmSJCnlGFankv0vwtqVsPnfoLcrel1uCVTeDItuhbGT49efJEmSJEmSpJRlWJ3swmHY/h+wdgXU/zZ27fjzgl3UF34SsvLi058kSZIkSZIkYVidvLraYdPqYB5146uxa8/6IFQtDz6GQvHpT5IkSZIkSZLewrA62bTsgfX3Qd1D0NESvS49G+Z+EqqWwcRZcWtPkiRJkiRJkk7GsDpZ7K6D6hWw5ScQ6Y1eN2ZiMIu68mYYMz5u7UmSJEmSJElSLIbVo1lvD2z9GVSvhF3rYtdOmgNLlsOc6yAjOz79SZIkSZIkSdIpMqwejTpaYeMPYN290Lwzdu25VwSjPmb8AaSlxac/SZIkSZIkSRogw+rRpKke1t0HG34AXUej12XmwbxPweLbYfzZcWtPkiRJkiRJkgbLsHq0aD8M366EcHf0mrGlsPg2WHAj5JXErzdJkiRJkiRJOk2G1aPFmPFw3hXw8lPv/FzpgmAe9fkfgfTM+PcmSZIkSZIkSafJsHo0qVr+ZlidFoKZHw5C6mmLnUctSZIkSZIkaVQzrB5NplfBjPfDpDnBuI/i8kR3JEmSJEmSJElDwrB6NElLg8886S5qSZIkSZIkSUknlOgGNEAG1ZIkSZIkSZKSkGG1JEmSJEmSJCnhEhpWr1ixgvLycnJycli8eDHr169PZDuSJEmSJEmSpARJWFj9wx/+kLvuuouvfe1rbNiwgblz53L55Zdz8ODBRLUkSZIkSZIkSUqQhIXV//RP/8Stt97KTTfdxPnnn8+9995LXl4eDz74YKJakiRJkiRJkiQlSEYivmlXVxd1dXV85Stf6b8vFApxySWXsHbt2nfUd3Z20tnZ2X+7tbUVgO7ubrq7u4e/4WH0Rv+j/XFIGjjXv5S6XP9S6nL9S6nL9S+ltlR+DhjIY05IWH348GF6e3uZNGnSCfdPmjSJrVu3vqP+m9/8Jnffffc77v/lL39JXl7esPUZT2vWrEl0C5ISxPUvpS7Xv5S6XP9S6nL9S6ktFZ8Djh07dsq1CQmrB+orX/kKd911V//t1tZWpk2bxmWXXUZBQUECOzt93d3drFmzhksvvZTMzMxEtyMpjlz/Uupy/Uupy/UvpS7Xv5TaUvk54I0pGaciIWH1+PHjSU9P58CBAyfcf+DAASZPnvyO+uzsbLKzs99xf2ZmZtL84SbTY5E0MK5/KXW5/qXU5fqXUpfrX0ptqfgcMJDHm5ADFrOysqioqODZZ5/tvy8cDvPss8+yZMmSRLQkSZIkSZIkSUqghI0Bueuuu7jxxhuprKxk0aJFfOtb36K9vZ2bbropUS1JkiRJkiRJkhIkYWH1Jz/5SQ4dOsRf/uVfsn//fubNm8czzzzzjkMXJUmSJEmSJEnJL6EHLN5xxx3ccccdiWxBkiRJkiRJkjQCJGRmtSRJkiRJkiRJb2VYLUmSJEmSJElKOMNqSZIkSZIkSVLCGVZLkiRJkiRJkhLOsFqSJEmSJEmSlHCG1ZIkSZIkSZKkhDOsliRJkiRJkiQlnGG1JEmSJEmSJCnhDKslSZIkSZIkSQlnWC1JkiRJkiRJSriMRDcwGJFIBIDW1tYEd3L6uru7OXbsGK2trWRmZia6HUlx5PqXUpfrX0pdrn8pdbn+pdSWys8Bb2S4b2S6sYzKsPro0aMATJs2LcGdSJIkSZIkSZLezdGjRyksLIxZkxY5lUh7hAmHw+zdu5exY8eSlpaW6HZOS2trK9OmTWPXrl0UFBQkuh1JceT6l1KX619KXa5/KXW5/qXUlsrPAZFIhKNHj1JaWkooFHsq9ajcWR0KhZg6dWqi2xhSBQUFKfeDKing+pdSl+tfSl2ufyl1uf6l1JaqzwHvtqP6DR6wKEmSJEmSJElKOMNqSZIkSZIkSVLCGVYnWHZ2Nl/72tfIzs5OdCuS4sz1L6Uu17+Uulz/Uupy/UupzeeAUzMqD1iUJEmSJEmSJCUXd1ZLkiRJkiRJkhLOsFqSJEmSJEmSlHCG1ZIkSZIkSZKkhDOsliRJkiRJkiQlnGG1JEmSJEmSJCnhDKsTaMWKFZSXl5OTk8PixYtZv359oluSNMS++c1vsnDhQsaOHcvEiRO55ppr2LZt2wk1HR0dLF++nHHjxpGfn891113HgQMHEtSxpOHyf/7P/yEtLY0777yz/z7Xv5S89uzZwx//8R8zbtw4cnNzueCCC6itre3/fCQS4S//8i+ZMmUKubm5XHLJJWzfvj2BHUsaKr29vXz1q19lxowZ5ObmctZZZ/HXf/3XRCKR/hqfA6Tk8Jvf/Iarr76a0tJS0tLS+MlPfnLC509lrTc2NnLDDTdQUFBAUVERt9xyC21tbXF8FCOLYXWC/PCHP+Suu+7ia1/7Ghs2bGDu3LlcfvnlHDx4MNGtSRpCv/71r1m+fDnV1dWsWbOG7u5uLrvsMtrb2/trvvSlL/HUU0/xox/9iF//+tfs3buXa6+9NoFdSxpqNTU13HfffVx44YUn3O/6l5JTU1MTF110EZmZmfziF7/gpZde4v/+3/9LcXFxf83f//3fc88993Dvvfeybt06xowZw+WXX05HR0cCO5c0FP7u7/6OVatW8S//8i+8/PLL/N3f/R1///d/z7e//e3+Gp8DpOTQ3t7O3LlzWbFixUk/fypr/YYbbmDLli2sWbOGn/3sZ/zmN7/htttui9dDGHHSIm99aU9xs3jxYhYuXMi//Mu/ABAOh5k2bRpf+MIX+PKXv5zg7iQNl0OHDjFx4kR+/etf8wd/8Ae0tLQwYcIEVq9ezcc+9jEAtm7dyqxZs1i7di1VVVUJ7ljS6Wpra2PBggWsXLmSb3zjG8ybN49vfetbrn8piX35y1/m97//Pb/97W9P+vlIJEJpaSn/83/+T/70T/8UgJaWFiZNmsRDDz3E0qVL49mupCH24Q9/mEmTJvHd7363/77rrruO3NxcHnnkEZ8DpCSVlpbGE088wTXXXAOc2t/3L7/8Mueffz41NTVUVlYC8Mwzz3DVVVexe/duSktLE/VwEsad1QnQ1dVFXV0dl1xySf99oVCISy65hLVr1yawM0nDraWlBYCSkhIA6urq6O7uPuH5YObMmUyfPt3nAylJLF++nA996EMnrHNw/UvJ7Kc//SmVlZV8/OMfZ+LEicyfP58HHnig//Ovv/46+/fvP2H9FxYWsnjxYte/lATe85738Oyzz/LKK68A8Pzzz/O73/2OK6+8EvA5QEoVp7LW165dS1FRUX9QDXDJJZcQCoVYt25d3HseCTIS3UAqOnz4ML29vUyaNOmE+ydNmsTWrVsT1JWk4RYOh7nzzju56KKLmDNnDgD79+8nKyuLoqKiE2onTZrE/v37E9ClpKH02GOPsWHDBmpqat7xOde/lLxee+01Vq1axV133cVf/MVfUFNTw//4H/+DrKwsbrzxxv41frJ/D7j+pdHvy1/+Mq2trcycOZP09HR6e3v5m7/5G2644QYAnwOkFHEqa33//v1MnDjxhM9nZGRQUlKSss8HhtWSFCfLly9n8+bN/O53v0t0K5LiYNeuXXzxi19kzZo15OTkJLodSXEUDoeprKzkb//2bwGYP38+mzdv5t577+XGG29McHeShtvjjz/Oo48+yurVq5k9ezabNm3izjvvpLS01OcASXoXjgFJgPHjx5Oens6BAwdOuP/AgQNMnjw5QV1JGk533HEHP/vZz/jVr37F1KlT+++fPHkyXV1dNDc3n1Dv84E0+tXV1XHw4EEWLFhARkYGGRkZ/PrXv+aee+4hIyODSZMmuf6lJDVlyhTOP//8E+6bNWsWO3fuBOhf4/57QEpOf/Znf8aXv/xlli5dygUXXMCnP/1pvvSlL/HNb34T8DlAShWnstYnT57MwYMHT/h8T08PjY2NKft8YFidAFlZWVRUVPDss8/23xcOh3n22WdZsmRJAjuTNNQikQh33HEHTzzxBM899xwzZsw44fMVFRVkZmae8Hywbds2du7c6fOBNMpdfPHFvPjii2zatKn/V2VlJTfccEP/f7v+peR00UUXsW3bthPue+WVVygrKwNgxowZTJ48+YT139rayrp161z/UhI4duwYodCJcUt6ejrhcBjwOUBKFaey1pcsWUJzczN1dXX9Nc899xzhcJjFixfHveeRwDEgCXLXXXdx4403UllZyaJFi/jWt75Fe3s7N910U6JbkzSEli9fzurVq3nyyScZO3Zs/8ypwsJCcnNzKSws5JZbbuGuu+6ipKSEgoICvvCFL7BkyRKqqqoS3L2k0zF27Nj++fRvGDNmDOPGjeu/3/UvJacvfelLvOc97+Fv//Zv+cQnPsH69eu5//77uf/++wFIS0vjzjvv5Bvf+AbnnHMOM2bM4Ktf/SqlpaVcc801iW1e0mm7+uqr+Zu/+RumT5/O7Nmz2bhxI//0T//EzTffDPgcICWTtrY2duzY0X/79ddfZ9OmTZSUlDB9+vR3XeuzZs3iiiuu4NZbb+Xee++lu7ubO+64g6VLl1JaWpqgR5VgESXMt7/97cj06dMjWVlZkUWLFkWqq6sT3ZKkIQac9Nf3vve9/prjx49Hli1bFikuLo7k5eVFPvrRj0b27duXuKYlDZv3v//9kS9+8Yv9t13/UvJ66qmnInPmzIlkZ2dHZs6cGbn//vtP+Hw4HI589atfjUyaNCmSnZ0dufjiiyPbtm1LULeShlJra2vki1/8YmT69OmRnJycyJlnnhn5X//rf0U6Ozv7a3wOkJLDr371q5P+m//GG2+MRCKnttaPHDkSuf766yP5+fmRgoKCyE033RQ5evRoAh7NyJAWiUQiCcrJJUmSJEmSJEkCnFktSZIkSZIkSRoBDKslSZIkSZIkSQlnWC1JkiRJkiRJSjjDakmSJEmSJElSwhlWS5IkSZIkSZISzrBakiRJkiRJkpRwhtWSJEmSJEmSpIQzrJYkSZIkSZIkJZxhtSRJkiRJkiQp4QyrJUmSJEmSJEkJZ1gtSZIkSZIkSUq4/w8wP0fapK+DBAAAAABJRU5ErkJggg==",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(18, 8))\n",
"ax.scatter(X, Y, color=\"tomato\", s=5)\n",
"ax.plot(X, results.fittedvalues, label=\"Fitted Line\", lw=3, zorder=0)\n",
"ax.plot(X, PRF, label=\"Population Regression Line\", lw=3, zorder=-1)\n",
"ax.grid()\n",
"ax.legend(prop={\"size\": 18})\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "4af9e927-0917-49b3-8ed9-65b87a489e4e",
"metadata": {},
"source": [
"You would be surprised to see that true relationship (Population Regression Function) deviates much more than fitted line, it is exactly due to autocorrelation, as $\\rho$ getting smaller, the generated dots will be closer to PRF, therefore fitted line will be closer to PRF as well.\n",
"\n",
"The point is that with presence of autocorrelation, the estimation results will vary wildly from true relationship, hence all hypothesis tests are invalid too. This happens very common in time series estimation."
]
},
{
"cell_type": "markdown",
"id": "b8f369d4-04e9-4044-a322-6d0b02133fc0",
"metadata": {},
"source": [
"# Detection of Autocorrelation "
]
},
{
"cell_type": "markdown",
"id": "26719b7b-a126-474b-a43a-f4df3ecf6db1",
"metadata": {},
"source": [
"## Graphical Method "
]
},
{
"cell_type": "markdown",
"id": "e2828f12-0285-43dd-b645-ebe01ae68c5e",
"metadata": {},
"source": [
"Though the non-autocorrelation assumption relates to disturbance term $u_t$, which are unobservable, we can instead visualize the residuals $e_t$. Very likely residuals can provide useful information when demonstrating a visual examination.\n",
"\n",
"Here is a simulated residuals from example above, though graphical method is subjective and qualitative, you can still draw to a rough conclusion if you see an patter presence in residuals."
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "060c6415-77ec-46e1-b477-b51893d22979",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"fig, ax = plt.subplots(figsize=(18, 7))\n",
"ax.scatter(np.arange(len(results.resid)), results.resid)\n",
"ax.set_ylim([-200, 200])\n",
"ax.grid()\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "da3d57e8-c5eb-4a14-82d0-3f0effb11517",
"metadata": {},
"source": [
"## Durbin-Watson Test "
]
},
{
"cell_type": "markdown",
"id": "a61c5e2b-e22c-427a-9c39-a58681bbe34c",
"metadata": {},
"source": [
"The standard test for first order autocorrelation is **Durbin-Watson Test**, it is one of standard output of OLS estimation. It is calculated by the formula\n",
"$$\n",
"dw=\\frac{\\sum_{t=2}^{T}\\left(e_{t}-e_{t-1}\\right)^{2}}{\\sum_{t=1}^{T} e_{t}^{2}}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "a96372d7-6102-488f-ba43-26b8309c7a78",
"metadata": {},
"source": [
"where $e_t$ is residual at time $t$. "
]
},
{
"cell_type": "markdown",
"id": "ad0e47a6-b1b6-45f3-832f-84a1ca32fed1",
"metadata": {},
"source": [
"As an example, we can reproduce the OLS estimation of disposable income and house price in China. "
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "cb4cd440-4d44-4f81-895a-81e09e90b34f",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9255117521586897"
]
},
"execution_count": 23,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"df = pd.read_excel(\n",
" \"Basic_Econometrics_practice_data.xlsx\", sheet_name=\"CN_Cities_house_price\"\n",
")\n",
"model = smf.ols(formula=\"house_price ~ salary\", data=df)\n",
"results = model.fit()\n",
"\n",
"from statsmodels.stats.stattools import durbin_watson as dw_test\n",
"\n",
"dw_test(results.resid)"
]
},
{
"cell_type": "markdown",
"id": "becca321-aa54-44c0-8d74-cc4f41e025d8",
"metadata": {},
"source": [
"Or we can write our own Durbin-Watson function to verify the results"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "6102455b-3688-438a-b797-aed4bcfb62e3",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"0.9255117521586897"
]
},
"execution_count": 24,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"def durbin_watson_test(series):\n",
" nomin = np.sum((series[1:] - series.shift(1).dropna()) ** 2)\n",
" denom = np.sum(series**2)\n",
" return nomin / denom\n",
"\n",
"\n",
"durbin_watson_test(results.resid)"
]
},
{
"cell_type": "markdown",
"id": "609b6635-fccc-4cbf-a74e-f449c7c07a8d",
"metadata": {},
"source": [
"But how to interpret this number? Some mathematical manipulations of Durbin-Watson's statistic will bring some insight\n",
"$$\n",
"dw=\\frac{\\sum_{t=2}^{T}\\left(e_{t}-e_{t-1}\\right)^{2}}{\\sum_{t=1}^{T} e_{t}^{2}} = \\frac{\\sum_{t=2}^{T}\\left(e^2_{t}-2e_te_{t-1}+e^2_{t-1}\\right)}{\\sum_{t=1}^{T} e_{t}^{2}} = \\frac{\\sum_{t=1}^Te_t^2}{\\sum_{t=1}^Te_t^2}+\\frac{\\sum_{t=1}^Te_{t-1}^2}{\\sum_{t=1}^Te_t^2}-2\\frac{\\sum_{t=1}^Te_te_{t-1}}{\\sum_{t=1}^Te_t^2}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "4c306308-95d9-489b-939e-d68b64821fe2",
"metadata": {},
"source": [
"If $T\\rightarrow \\infty$, the second term approaches $1$ infinitely and the third term $\\frac{\\sum_{t=1}^Te_te_{t-1}}{\\sum_{t=1}^Te_t^2}$ equals $\\rho$, because it is a simple OLS estimator of $\\rho$. \n",
"\n",
"Therefore $dw \\rightarrow 2-2\\rho$ given $T\\rightarrow \\infty$.\n",
"\n"
]
},
{
"cell_type": "markdown",
"id": "c6280b36-5cd5-49cf-88bd-78d7257eb1ed",
"metadata": {},
"source": [
"If no autocorrelation, $\\rho=0$, $dw$ should be $2$, if $\\rho > .5$, i.e. strong positive autocorrelation, $dw$ will be close to $0$, or if $\\rho>-.5$, i.e. strong negative autocorrelation, $dw$ will be close to $4$."
]
},
{
"cell_type": "markdown",
"id": "9dbc2740-4f2c-4b56-9e32-18bf3b419612",
"metadata": {},
"source": [
"Because $dw$ statistic doesn't have critical value (due to some technical reason, critical value can't be calculated.) However, it is possible to know the upper and lower limit of $dw$, go search _Durbin Watson table_ on Google and click any of image that shows on top, or click here.\n",
"\n",
"In the data of flat price, number of observations is $25$ and number of independent variables is $1$, here are upper and lower limit from the table.\n",
"$$\n",
"d_L = 1.055\\\\\n",
"d_U = 1.210\n",
"$$\n",
"Our result $dw=0.9255$ is lower than lower limit, which suggests a rejection of null hypothesis $\\rho=0$, why? Because it's too far away from $2$, if $dw$ is larger than upper limit, we fail to reject null hypothesis. If the $dw$ drops between lower and upper limit, just forget about it, no decisive conclusion. \n",
"\n",
"However, keep in mind that autocorrelation can also be attributed to model specification errors and we almost only care about autocorrelation issue in time series rather than cross sectional data."
]
},
{
"cell_type": "markdown",
"id": "ef3d5ec0-2cd3-4864-80f0-fd80431391b2",
"metadata": {},
"source": [
"Here is an example of exchange rate $EUR/USD$."
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "fc671261-eb89-4bad-9c26-289955951216",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"start = dt.datetime(2005, 1, 1)\n",
"end = dt.datetime.today()\n",
"EURUSD = fred.get_series('DEXUSEU', start, end)\n",
"\n",
"fig, ax = plt.subplots(figsize=(18, 8))\n",
"ax.plot(EURUSD, color=\"tomato\", label=\"EUR/USD\")\n",
"ax.legend()\n",
"ax.grid()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "2038561f-cd09-4a04-9146-86ead4a87529",
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"3.12645076860537e-05"
]
},
"execution_count": 26,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"durbin_watson_test(EURUSD)"
]
},
{
"cell_type": "markdown",
"id": "76a3ec0f-2c32-4177-a10c-ab26902e7e70",
"metadata": {},
"source": [
"The $dw$ statistic is literally $0$, which means $\\rho=1$, this shouldn't be a shocking result. Most of time sereis of assets price will show a strong first degree autocorrelation, this is why we like trading the trend or momentum. "
]
},
{
"cell_type": "markdown",
"id": "596a4817-529b-4372-869f-5a5b70f75fe3",
"metadata": {},
"source": [
"However, $dw$ test is mostly for testing residuals, here's another example that demonstrating highly autocorrelated residuals."
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "76bdb929-868d-497f-b50e-d3b9f88c39f7",
"metadata": {},
"outputs": [],
"source": [
"start = dt.datetime(2005, 1, 1)\n",
"end = dt.datetime.today()\n",
"\n",
"\n",
"real_GDP_perCap = fred.get_series('A939RX0Q048SBEA', start, end)\n",
"priv_resid_fixInv = fred.get_series('PRFI', start, end)\n",
"df = pd.DataFrame({\n",
" 'real_GDP_perCap': real_GDP_perCap,\n",
" 'priv_resid_fixInv': priv_resid_fixInv\n",
"})"
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "c88ed04b-9e78-45cd-b719-73ef6a6df10c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: real_GDP_perCap R-squared: 0.685\n",
"Model: OLS Adj. R-squared: 0.681\n",
"Method: Least Squares F-statistic: 163.0\n",
"Date: Sun, 09 Jun 2024 Prob (F-statistic): 1.72e-20\n",
"Time: 19:37:11 Log-Likelihood: -707.73\n",
"No. Observations: 77 AIC: 1419.\n",
"Df Residuals: 75 BIC: 1424.\n",
"Df Model: 1 \n",
"Covariance Type: nonrobust \n",
"=====================================================================================\n",
" coef std err t P>|t| [0.025 0.975]\n",
"-------------------------------------------------------------------------------------\n",
"Intercept 4.836e+04 840.787 57.516 0.000 4.67e+04 5e+04\n",
"priv_resid_fixInv 14.0669 1.102 12.767 0.000 11.872 16.262\n",
"==============================================================================\n",
"Omnibus: 23.388 Durbin-Watson: 0.089\n",
"Prob(Omnibus): 0.000 Jarque-Bera (JB): 31.697\n",
"Skew: -1.377 Prob(JB): 1.31e-07\n",
"Kurtosis: 4.514 Cond. No. 2.34e+03\n",
"==============================================================================\n",
"\n",
"Notes:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n",
"[2] The condition number is large, 2.34e+03. This might indicate that there are\n",
"strong multicollinearity or other numerical problems.\n"
]
}
],
"source": [
"model = smf.ols(formula=\"real_GDP_perCap ~ priv_resid_fixInv\", data=df)\n",
"results = model.fit()\n",
"print(results.summary())"
]
},
{
"cell_type": "markdown",
"id": "96366bad-0d43-4091-a60a-fce2bfdce21b",
"metadata": {},
"source": [
"The drawback of $dw$ test is that it assumes nonstachastic regressors (or independent variables we call in previous contexts), i.e. the regressors are fixed in repeated sampling. Then this drawback would invalidate the power of $dw$ test in time series modelling. "
]
},
{
"cell_type": "markdown",
"id": "ba7216e9-e73f-4ae3-ac12-a80e427fd7c5",
"metadata": {},
"source": [
"## Breusch–Godfrey Test "
]
},
{
"cell_type": "markdown",
"id": "1884e0b8-b880-490f-8d5c-354cfd2085da",
"metadata": {},
"source": [
"The Breusch–Godfrey Test is more general than Durbin-Watson that it allows for higher autoregression schemes and higher order of moving averages of white noises. "
]
},
{
"cell_type": "markdown",
"id": "6988ceb4-196b-4b3b-bc00-b5c18986ca1a",
"metadata": {},
"source": [
"Suppose disturbance terms are generated by an $AR(3)$ process\n",
"$$\n",
"u_{t}=\\rho_1 u_{t-1}+\\rho_2 u_{t-2}+\\rho_3 u_{t-3}+\\varepsilon_{t}\n",
"$$\n",
"and choose whatever $\\rho$'s you like. $\\varepsilon_t$ follows classical linear regression assumption."
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "6d6f1751-6bfc-4313-b056-c89a9249eb56",
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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",
"text/plain": [
""
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"T = 50\n",
"u = np.array([0.5, 0.45, 0.4])\n",
"rho_array = np.array([0.5, 0.4, 0.2])\n",
"for i in range(T):\n",
" u_new_element = np.dot(u[:3], rho_array) + 100 * np.random.randn()\n",
" u = np.append(u_new_element, u)\n",
"\n",
"fig, ax = plt.subplots(figsize=(18, 8))\n",
"ax.plot(u, color=\"tomato\")\n",
"ax.grid()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "03b628c7-284c-440c-8729-c97877445b14",
"metadata": {},
"outputs": [],
"source": [
"X = np.arange(1, len(u) + 1)\n",
"Y = 2 + 3 * X + u\n",
"PRF = 2 + 3 * X\n",
"df = pd.DataFrame([X, Y]).T\n",
"df.columns = [\"X\", \"Y\"]"
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "5a847adc-c543-437e-916b-8cb8bd39fe01",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: Y R-squared: 0.949\n",
"Model: OLS Adj. R-squared: 0.948\n",
"Method: Least Squares F-statistic: 957.2\n",
"Date: Sun, 09 Jun 2024 Prob (F-statistic): 1.02e-34\n",
"Time: 19:37:11 Log-Likelihood: -319.97\n",
"No. Observations: 53 AIC: 643.9\n",
"Df Residuals: 51 BIC: 647.9\n",
"Df Model: 1 \n",
"Covariance Type: nonrobust \n",
"==============================================================================\n",
" coef std err t P>|t| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"Intercept 1604.3103 28.779 55.747 0.000 1546.535 1662.086\n",
"X -28.6921 0.927 -30.939 0.000 -30.554 -26.830\n",
"==============================================================================\n",
"Omnibus: 1.124 Durbin-Watson: 1.021\n",
"Prob(Omnibus): 0.570 Jarque-Bera (JB): 0.547\n",
"Skew: 0.219 Prob(JB): 0.761\n",
"Kurtosis: 3.238 Cond. No. 63.0\n",
"==============================================================================\n",
"\n",
"Notes:\n",
"[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.\n"
]
}
],
"source": [
"model = smf.ols(formula=\"Y ~ X\", data=df)\n",
"results = model.fit()\n",
"print(results.summary())"
]
},
{
"cell_type": "markdown",
"id": "ed675090-11bd-43b0-821c-21bb4b68fb37",
"metadata": {},
"source": [
"Once you have residual, run auxiliary regression\n",
"$$\n",
"\\hat{u}_{t}=\\alpha_{1}+\\alpha_{2} X_{t}+\\hat{\\rho}_{1} \\hat{u}_{t-1}+\\hat{\\rho}_{2} \\hat{u}_{t-2}+\\cdots+\\hat{\\rho}_{p} \\hat{u}_{t-p}+\\varepsilon_{t}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "5d540e6f-e19b-4b1e-a0aa-4c0b6d2f315a",
"metadata": {},
"source": [
"Use the coefficient of determinant to construct the statistic \n",
"$$\n",
"(n-p) R^{2} \\sim \\chi_{p}^{2}\n",
"$$\n",
"where $p$ is the number of lags, $n$ is the number of observations."
]
},
{
"cell_type": "markdown",
"id": "069c0d72-9f47-4637-90e2-f68cde8091f3",
"metadata": {},
"source": [
"Fortunately, ```statsmodels``` has Breusch-Godfrey function, the first value is the test statistic and the second is the $p$-value."
]
},
{
"cell_type": "code",
"execution_count": 32,
"id": "adbfec38-daa7-4d8c-832c-64d3c61daa7e",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"(15.395020146240233, 0.0015083813366996376, 6.5502048744008805, 0.000839352599895712)\n"
]
}
],
"source": [
"import statsmodels.stats.diagnostic as dg\n",
"\n",
"print(dg.acorr_breusch_godfrey(results, nlags=3))"
]
},
{
"cell_type": "markdown",
"id": "e9097f42-d33d-4a54-8760-802eb3d2eeb8",
"metadata": {},
"source": [
"# Remedies For Autocorrelaton "
]
},
{
"cell_type": "markdown",
"id": "84998e0a-2f82-4829-8f90-f24182b36136",
"metadata": {},
"source": [
"If we know $\\rho$'s, it would be easy to convert to a **generalized difference equation** form\n",
"$$\n",
"\\left(Y_{t}-\\rho Y_{t-1}\\right)=\\beta_{1}(1-\\rho)+\\beta_{2}\\left(X_{t}-\\rho X_{t-1}\\right)+\\varepsilon_{t}\n",
"$$\n",
"such that disturbance term now is $\\varepsilon_t$, which satisfied classical OLS assumption.\n",
"\n",
"However, we rarely know true value of $\\rho$'s."
]
},
{
"cell_type": "markdown",
"id": "a9f87f19-c200-45de-90f7-8ab5361a163d",
"metadata": {},
"source": [
"If you have no information of $\\rho$, the best guess is by check $dw$ test, if \n",
"$$\n",
"dw < R^2\n",
"$$\n",
"We assume $\\rho =1$, then generalized difference equations becomes\n",
"$$\n",
"Y_{t}- Y_{t-1}=\\beta_{2}(X_{t}-X_{t-1})+\\varepsilon_{t}\n",
"$$\n",
"or \n",
"$$\n",
"\\Delta Y_{t}=\\Delta \\beta_{2}X_{t}+\\varepsilon_{t}\n",
"$$"
]
},
{
"cell_type": "markdown",
"id": "9e0ae51b-74ba-4f19-bf1d-fd204db52dff",
"metadata": {},
"source": [
"If you don't want to guess or simply using first order difference, the best choice is to estimate $\\rho$ in model\n",
"$$\n",
"e_{t}=\\rho \\cdot e_{t-1}+v_{t}\n",
"$$\n",
"where $e$'s are residuals. \n",
"\n",
"Because $\\rho$'s are estimates, we usually call these procedures the **feasible generalized least squares** (FGLS). "
]
},
{
"cell_type": "markdown",
"id": "3ec231cb-5cbc-4030-9ba6-f4e23a635cf3",
"metadata": {},
"source": [
"Instead of using FGLS, we have **HAC (heteroscedasticity- and autocorrelation-consistent) standard errors** (some textbooks call it Newey-West standard errors)."
]
},
{
"cell_type": "code",
"execution_count": 33,
"id": "ac6f430e-9c0a-4616-b4cc-7b8e97de623c",
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
" OLS Regression Results \n",
"==============================================================================\n",
"Dep. Variable: Y R-squared: 0.949\n",
"Model: OLS Adj. R-squared: 0.948\n",
"Method: Least Squares F-statistic: 549.4\n",
"Date: Sun, 09 Jun 2024 Prob (F-statistic): 5.72e-29\n",
"Time: 19:37:11 Log-Likelihood: -319.97\n",
"No. Observations: 53 AIC: 643.9\n",
"Df Residuals: 51 BIC: 647.9\n",
"Df Model: 1 \n",
"Covariance Type: HAC \n",
"==============================================================================\n",
" coef std err z P>|z| [0.025 0.975]\n",
"------------------------------------------------------------------------------\n",
"Intercept 1604.3103 45.544 35.225 0.000 1515.045 1693.576\n",
"X -28.6921 1.224 -23.439 0.000 -31.091 -26.293\n",
"==============================================================================\n",
"Omnibus: 1.124 Durbin-Watson: 1.021\n",
"Prob(Omnibus): 0.570 Jarque-Bera (JB): 0.547\n",
"Skew: 0.219 Prob(JB): 0.761\n",
"Kurtosis: 3.238 Cond. No. 63.0\n",
"==============================================================================\n",
"\n",
"Notes:\n",
"[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 1 lags and without small sample correction\n"
]
}
],
"source": [
"model = smf.ols(formula=\"Y ~ X\", data=df)\n",
"results = model.fit(cov_type=\"HAC\", cov_kwds={\"maxlags\": 1})\n",
"print(results.summary())"
]
},
{
"cell_type": "markdown",
"id": "6e14b4a1-3e36-4651-bf1d-d7a2d55269d2",
"metadata": {},
"source": [
"In small samples, FGLS and HAC are not better than OLS, by small samples, we mean a sample less than $30$ observation."
]
},
{
"cell_type": "code",
"execution_count": null,
"id": "6557ff5b-b1ee-4381-a925-daceae554965",
"metadata": {},
"outputs": [],
"source": []
}
],
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