{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Regression Analysis\n", "\n", "By Evgenia \"Jenny\" Nitishinskaya and Delaney Granizo-Mackenzie. Algorithms by David Edwards.\n", "\n", "\n", "Part of the Quantopian Lecture Series:\n", "\n", "* [www.quantopian.com/lectures](https://www.quantopian.com/lectures)\n", "* [github.com/quantopian/research_public](https://github.com/quantopian/research_public)\n", "\n", "Notebook released under the Creative Commons Attribution 4.0 License.\n", "\n", "---\n", "\n", "Regression analysis allows us to estimate coefficients in a function which approximately relates multiple data sets. We hypothesize a specific form for this function and then find coefficients which fit the data well, working under the assumption that deviations from the model can be considered noise.\n", "\n", "When building such a model, we accept that it cannot perfectly predict the dependent variable. Here we would like to evaluate the accuracy of the model not by how well it explains the dependent variable, but by how stable it is (that is, how stable the regression coefficients are) with respect to our sample data. After all, if a model is truly a good fit, it should be similar, say, for two random halves of our data set that we model individually. Otherwise, we cannot assume that the model isn't simply an artifact of the particular sample of data we happened to choose, or that it will be predictive of new data points.\n", "\n", "We'll be using linear regressions here for illustration purposes, but the same considerations apply for all regression models. Below we define a wrapper function for the linear regression from `statsmodels` so we can use it later." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import numpy as np\n", "import pandas as pd\n", "from statsmodels import regression, stats\n", "import statsmodels.api as sm\n", "import matplotlib.pyplot as plt\n", "import scipy as sp\n", "\n", "def linreg(X,Y):\n", " # Running the linear regression\n", " x = sm.add_constant(X) # Add a row of 1's so that our model has a constant term\n", " model = regression.linear_model.OLS(Y, x).fit()\n", " return model.params[0], model.params[1] # Return the coefficients of the linear model" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Biased noise\n", "\n", "The particular sample we choose for the data affects the model generated, and unevenly distributed noise can lead to an inaccurate model. Below we're drawing from a normal distribution, but because we do not have very many data points, we get a significant downward bias. If we took more measurements, both of the regression coefficients would move toward zero." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Slope: 0.00907250382269 Intercept: -0.402077440853\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Draw observations from normal distribution\n", "np.random.seed(107) # Fix seed for random number generation\n", "rand = np.random.randn(20)\n", "\n", "# Conduct linear regression on the ordered list of observations\n", "xs = np.arange(20)\n", "a, b = linreg(xs, rand)\n", "print 'Slope:', b, 'Intercept:', a\n", "\n", "# Plot the raw data and the regression line\n", "plt.scatter(xs, rand, alpha=0.7)\n", "Y_hat = xs * b + a\n", "plt.plot(xs, Y_hat, 'r', alpha=0.9);" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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rdPXmC2Xt4j+pz5yf0YV9ZvWthZonFqAccLs9JensmZJelQMGACyMwAMAa1Re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\nX3ynUgTlYrusAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import seaborn\n", "\n", "seaborn.regplot(xs, rand)" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Slope: -0.000569342363105 Intercept: 0.00901176731902\n" ] }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Draw more observations\n", "rand2 = np.random.randn(100)\n", "\n", "# Conduct linear regression on the ordered list of observations\n", "xs2 = np.arange(100)\n", "a2, b2 = linreg(xs2, rand2)\n", "print 'Slope:', b2, 'Intercept:', a2\n", "\n", "# Plot the raw data and the regression line\n", "plt.scatter(xs2, rand2, alpha=0.7)\n", "Y_hat2 = xs2 * b2 + a2\n", "plt.plot(xs2, Y_hat2, 'r', alpha=0.9);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Regression analysis is very sensitive to outliers. Sometimes these outliers contain information, in which case we want to take them into account; however, in cases like the above, they can simply be random noise. Although we often have many more data points than in the example above, we could have (for example) fluctuations on the order of weeks or months, which then significantly change the regression coefficients." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Regime changes\n", "\n", "A regime change (or structural break) is when something changes in the process generating the data, causing future samples to follow a different distribution. Below, we can see that there is a regime change at the end of 2007, and splitting the data there results in a much better fit (in red) than a regression on the whole data set (yellow). In this case our regression model will not be predictive of future data points since the underlying system is no longer the same as in the sample. In fact, the regression analysis assumes that the errors are uncorrelated and have constant variance, which is often not be the case if there is a regime change." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "scrolled": false }, "outputs": [ { "data": { "image/png": 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INUmKZtq4Xup+TEU71sVFK+uE9Dot8dFGPu4zBv7v/2DjRnj//Sobp7i4SBAS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\nQk1T4ywWi15+5GqFO1sOXYzjfSvQtadeWkhOa/ims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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "start = '2003-01-01'\n", "end = '2009-02-01'\n", "pricing = get_pricing('SPY', fields='price', start_date=start, end_date=end)\n", "\n", "# Manually set the point where we think a structural break occurs\n", "breakpoint = 1200\n", "xs = np.arange(len(pricing))\n", "xs2 = np.arange(breakpoint)\n", "xs3 = np.arange(len(pricing) - breakpoint)\n", "\n", "# Perform linear regressions on the full data set, the data up to the breakpoint, and the data after\n", "a, b = linreg(xs, pricing)\n", "a2, b2 = linreg(xs2, pricing[:breakpoint])\n", "a3, b3 = linreg(xs3, pricing[breakpoint:])\n", "\n", "Y_hat = pd.Series(xs * b + a, index=pricing.index)\n", "Y_hat2 = pd.Series(xs2 * b2 + a2, index=pricing.index[:breakpoint])\n", "Y_hat3 = pd.Series(xs3 * b3 + a3, index=pricing.index[breakpoint:])\n", "\n", "# Plot the raw data\n", "pricing.plot()\n", "Y_hat.plot(color='y')\n", "Y_hat2.plot(color='r')\n", "Y_hat3.plot(color='r')\n", "plt.title('SPY Price')\n", "plt.ylabel('Price');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Of course, the more pieces we break our data set into, the more precisely we can fit to it. It's important to avoid fitting to noise, which will always fluctuate and is not predictive. We can test for the existence of a structural break, either at a particular point we have identified or in general. Below we use a test from `statsmodels` which computes the probability of observing the data if there were no breakpoint." ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "7.4485869571761304e-59" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "stats.diagnostic.breaks_cusumolsresid(\n", " regression.linear_model.OLS(pricing, sm.add_constant(xs)).fit().resid)[1]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Multicollinearity\n", "\n", "Above we were only considering regressions of one dependent variable against one independent one. However, we can also have multiple independent variables. This leads to instability if the independent variables are highly correlated.\n", "\n", "Imagine we are using two independent variables, $X_1$ and $X_2$, which are very highly correlated. Then the coefficients may shift drastically if we add a new observation that is slightly better explained by one of the two than by the other. In the extreme case, if $X_1 = X_2$, then the choice of coefficients will depend on the particular linear regression algorithm.\n", "\n", "Below, we run a multiple linear regression in which the independent variables are highly correlated. If we take our sample period to be 2013-01-01 to 2015-01-01, then the coefficients are approximately .25 and .1. But if we extend the period to 2015-06-01, the coefficients become approximately .18 and .20, respectively." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Constant: -16.3503624604 MLR beta to S&P 500: 0.246866260161 MLR beta to MDY 0.0957537082372\n" ] }, { "data": { "image/png": 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iIj1WdtFBAPolRwCQEB3C/ddNwu3x8Ie/b6SmrvGI5yvwiIiIiIhIj+R0udmVVUFybChh\nwQG+7ROHJXDN+cMoqaznw1UZR7yGAo+IiIiIiPRIWzPKqHe4mDI6qdW+H547hKgwG5+sy6auwdnu\nNRR4RERERETErwzDOK7z1m0rBOCM0cmt9gUGWLj4rAHY65189V1+u9dQ4BEREREREb964tX1PPyX\nNUc8xuly84e/b2TL3lIAGp1u1m0rJDIskOH9Y9o857QRiQBk5le3e10FHhERERER8Zvc4hq+3VXM\n1owyHE53u8dt3lvKmq0F/OavawH4cnM+B+2NnHdaGhZz2+vtpCSEAZBXUtvudbUOj4iIiIiIdBqX\n28Mzb6XjcnnonxzRIowUlNbSPzmizQVDzYdtMwyD/3yVidls4uJpA9u9V1CglYTo4KZ7tL0WkgKP\niIiIiIh0mqyCatZsKQBg/Y6iFvvuf/5LAqxm3vjviwiwthxsVlt/qPDAtv1lZBZUM21cH+Kjg494\nv74J4WzaU9LufgUeERERERHpNM09OtddNJxhadFkF9ZQVdPAB6syaHR5aHR5qKpxtAoytYetp/Pa\nkp0AXDa9/d6dZn0Two4YeDSHR0REREREOk1z4BneL4bxQxO4YsYgLjijX4tj7G2Uka6xHwo8GblV\nDE6NYkQ7xQoO17dpHk97FHhERERERKTT5DcFnsODSGJ0SItj7PVtBJ7vbbts+sA25/p8X1pSxBH3\nK/CIiIiIiMgJc7s9LF2bxY6scoJtFmIiDhURsFhaxo42A89hQ9qiw22cNS7lqO47ckAMD1w3qd39\nCjwiIiIiInLC1m0v5C8fbKWqxkFKfFir3pk7rhrrKy9d20bgqa3zbps8IpFbLhvdqqhBe0wmE2dP\n6Nvufr8XLfjoo4949dVXsVqt3HXXXSxbtozt27cTHR0NwC233MKMGTP83QwREREREfGjPTmVvtcW\nc+uwMufMAUSG2vjDPzZSW9/Yan9NXSNWi4lHb5lyVEPZjpZfA09VVRUvvfQSixcvxm6388ILLwBw\n//33K+SIiIiIiPQiu7MrABiaFsU1Fwxr85iw4AAA7PWuVvtq6xoJCwns1LADfh7StnbtWqZNm0Zw\ncDBxcXE88cQT/rydiIiIiIh0A6fLTUZeNYP7RvLs3TOYPCKxzeNCfYGn9ZC2g3Yn4SEBnd42vwae\n/Px86uvrueOOO7juuutYt24dAG+++SY33ngj9913H1VVVf5sgoiIiIiI+Nn+vGpcbg/D+x25jHR7\ngcfjMbDXNxIWHNjpbTMZhmF0+lWbLFiwgM2bN/Pyyy+Tl5fHDTfcwO9//3uioqIYPnw4CxYsoLi4\nmEceeaTda6Snp/ureSIiIiIi0gm+2nGQz7cc5KozYxjTP6Td4+ocHp7+oIDhfYO45uw43/b6Rg//\n868ChqUE8aMZce2e35FJk1pXa/PrHJ64uDgmTJiAyWQiNTWV0NBQhg4dSkyMN/nNmjWLxx9/vMPr\ntNVw6Rrp6el6/3sAfQ49gz6HnkOfRffTZ9D99Bn0HPos4IP1azCZ4MrZpxMZZmv3OLfbAx8UEGAL\na/GeFZXbgQL69oln0qSJx9WG9jpK/Dqkbdq0aaxfvx7DMKisrKSuro7HHnuMPXv2ALBx40aGDh3q\nzyaIiIiIiIgf1Ttc7MouZ1DfqCOGHfCuxxNss7Ya0ta8Bk94SOcPafNrD09iYiKzZ89m3rx5mEwm\nHnnkEUJDQ5k/fz6hoaGEhobyu9/9zp9NEBERERERP/B4DPbmVvLpNzm43AYThsYf1XmhwQHUNnwv\n8Ni9P4f5oWiB39fhmTdvHvPmzWux7cMPP/T3bUVERERExE++3JzHa//ZQVl1AwARoYHMOi3tqM4N\nCw6gtLKuxbaTtodHRERERER6h9Wb8qhrcBIfFcyzb28i0Grm3MmpTBvXhwlD4wmwWo7qOqHBAeQU\nufB4DMxm75o7tc2Bxw9V2hR4RERERESkQ8++5S0KYLWYsFrMPPmzMzssQ92WsOAADAPqHC7fQqQ1\nTXN6wkNPsnV4RERERETk5Od0uX2vPQY8dMPk4wo7gK+wwX++yqR5hZzmIW1hGtImIiIiIiJdrazK\nO1dn1MBYbr1sNINTo477WleeM4hNe0p4e/lu8ktq+eXV46mta+rhUeAREREREZGuVlrlLTIwemDs\nCYUdgL4J4fzxnrP53Wsb+GJzHoXltb75P+F+qNKmIW0iIiIiInJEpZX1AMRHh3TK9aLDg/jdndM4\na1wf9h6oYkdmOWaziWBb5/fHKPCIiIiIiMgRlVY1B57gTrtmgNXCxdMG+H4ODwnAZDJ12vWbKfCI\niIiIiMgR+Xp4ojov8AAkxYb6Xvtj/g4o8IiIiIiISAeaFwrt7MATExGE1eKNJAo8IiIiIiLS5Zwu\nD4XldsJDAgnq5Dk2ZrOJiFBv0AnzQ8ECUOAREREREZF2bN5Twi+fWUVReR1D006sOlt7QoO9Icrs\nh/k7oLLUIiIiIiLyPR6PwXPvbmJ1eh5mE1w8bQDXXTjcL/cKDfL27NgbnH65vgKPiIiIiIi0kJFX\nxer0PPonR3DPNRMY1Nc/vTsAocFNgafeP4FHQ9pERERERKSFvJIaAOac2d+vYQfwlaa+eNpAv1xf\nPTwiIiIiItJCbnEtAH0Tw/1+r9NGJvHWExcRrqIFIiIiIiJyLJwuD4ZhHPN5ucXeHp7UBP8HHoCI\n0EC/LDoKCjwiIiIiIr1SZU0D1z66lHc/3XPM5+YW1xAeEkBkmH/WxulKCjwiIiIiIr3Qvtwq6h1u\n/rUqg8qDDb7tb3yyi2ffSm/3PKfLTVG5nb4J4X7rdelKCjwiIiIiIr1Qfol3Hk6j082/Vu3zbX9/\nxV5Wb8qjpKKuzfMKSu14DEjtgvk7XUGBR0RERESkF8ov9QaeYJuFZWuzqTjYQG1do2//ln2lbZ6X\nVVANQL9kBR4REREREemh8kpqMZnghjkjaXR5+NfKfeQ19foAfNdO4Nmf7w08g1L8W466qyjwiIiI\niIj0QvkltSTGhHDh1P4kxISwbF12i16drfvK2qzg1tzDM6BPRFc11a8UeEREREREepnaukaqah2k\nxIdhtZi5+ryhOF0e3ly2G4D46GCqah0tenwADMMgM7+a5NhQQoL8sy5OV1PgERERERHpZXbnVAKQ\nkhAGwLmTU0mJD/Xtv2BKPwB2ZVcA3l6dP76dzu2//5yaOicDUyK7uMX+o8AjIiIiItKLNDrdvLJ4\nGyYTzJjQFwCrxcwv503wHTNlVBIAO7PK+XhNFvc9/yWr0vMoLLcDMKxfdNc33E+s3d0AERERERHp\nPJv3lFBQZmfOmf0ZmnYouIwaGMu9P55IoNVCWlIEoUFWVn2by+cbcwkPCeSh68czYkAsu7LKmTAs\noRufoHMp8IiIiIiI9CIH7d7S04eHnWYzJ6X6Xo8YEMu3u4oZPSiW+6+dRGxkMABTRid3TUO7iAKP\niIiIiEgvUudwARASdOSv+j/7wVj2HqjkzLF9sJhNXdG0bqHAIyIiIiLSi9TVOwE6rLKWGBNCYkxI\nVzSpW6logYiIiIhIL2JvOLoenlOFAo+IiIiISC9S1+Dt4QntJevonCgFHhERERGRXqSuqYcnWD08\ngAKPiIiIiEivoh6elhR4RERERER6kboGF1aLiQCrvuqDAo+IiIiISK9S53ASEhSAydR7S00fCwUe\nEREREZFexF7vUoW2wyjwiIiIiIj0IvVNPTzipcAjIiIiItJLuD0G9Q63ChYcRoFHRERERKSXqG+q\n0KYhbYco8IiIiIiI9BLNa/Ao8ByiwCMiIiIi0kvYfT08GtLWTIFHRERERKSXUA9Pawo8IiIiIiK9\nRN0p1MOz9sC3PLn6TxTVlBzxOEU/EREREZFeormHJ7QX9/DUNdbz6qZ3+SpnAwCrstbxo7GXt3t8\n730nREREREROMQVldgCiwm3d3BL/yKzI4dk1Cyitq2BQdD8yqw6wuyzjiOdoSJuIiIiISC+xcWcR\nFrOJMYPju7spna7MXsHvv3yJsvpKrho5hyfPe4ABUansK8+m0e1s9zwFHhERERGRXqDyYAP7cqsY\nNTCWsODeNYenwdnA/3z9F6odNfxkwjyuHnMpVrOFEfFDcHlcZJRnt3uuAo+IiIiIyEkuI7eKP//z\nOwBOG5nYza3pXKX2cn7/1UvkVOVx3qDpzB48w7dvWNxAADIqsto93+9zeD766CNeffVVrFYrd911\nF8OGDeOBBx7AMAzi4+N5+umnCQjoXQlURERERKQrZORV8bd/b2dHZjkAA/tEMnNSqt/uty43ncr6\nauYMPddv9zhco9vJE6ufp7i2lCl9J3DzxKsxmUy+/UlhCQCU2MtJIbbNa/g18FRVVfHSSy+xePFi\n7HY7L7zwAsuWLeP666/nggsu4LnnnuODDz7gmmuu8WczRERERER6pXc/3cOOzHImDkvgihmDGD80\nvkUg6CxrD6STXZXLv3d9ioFBcngCE5JHtzjG5XaxZO/nTO4zlk8zvuT0vuMYnTj8hO770e5PKa4t\n5aIhM7lpwtxWzxYfGgN45/cQ2vY1/Dqkbe3atUybNo3g4GDi4uJ44okn2LBhAzNnzgRg5syZrF27\n1p9NEBERERHptSoONhBgNfP4T89gwrAEv4Sd1Vnr+NO6v7F413IsZgsmk4nXN/8Tl9vV4rgN+Vt4\ne+ti7l32BMsyVvPnb16nweU47vvuLNnHBzuWEh0UydVjLm3z2UIDQwgOCKKsrrLd6/g18OTn51Nf\nX88dd9zBddddx7p162hoaPANYYuNjaW0tNSfTRARERER6bWqax1Ehtn8EnQAthTt5K8b3yQ0MITb\nJ1/L4zP/i9mDZlBYU8LSfataHLu3bL/vtc0SSGVDNUv3rjyu+5bYy3l27QIA7p56MyEBwe0eGxcS\nQ2ldebv7/TqkzTAM37C2/Px8brjhBgzDaLFfRERERESOnWEYVNU2kpYY5pfrZ1fm8uyaBZhNZh46\n6w6Gxw8GoE94ImsObORfOz5m5oCphNu8999TnonFbOGBabfTL6ovD376O/69+1POGzSdCFvHbXR7\n3Lyx5UPGJo7gna2LqXHUcuukHzEyYegRz4sPiSG3uqDd/X4NPHFxcUyYMAGz2UxqaiqhoaFYrVYa\nGxsJDAykuLiYhISEDq+Tnp7uz2ZKB/T+9wz6HHoGfQ49hz6L7qfPoPvpM+g5uuOzcDg9NDrdmDyO\nTr+/w9PI33L+RYPbweVJs7AfqCb9wKF7TA4fxaryDbzx1T+ZEj0Wp8dFVsUBEm1xGIWNZBdmcnr4\naD4v+4b/W/V3ZsWf0eE9ix1lLM1d6esVmhAxgtjq0A6fzbC7j7jfr4Fn2rRp/PrXv+anP/0pVVVV\n1NXVcdZZZ7Fs2TIuu+wyli9fzvTp0zu8zqRJk/zZTDmC9PR0vf89gD6HnkGfQ8+hz6L76TPofvoM\neo7u+iyKyu1AAWkp8UyaNLFTr/1t/lZqM+u4eOgsrp3ww1b7hzUOZ81Hm9nZsJ+fTbiRPeX78WQa\nTOw3lkkTvO/FWPdYtn2yj801u7BFBhEaEMKtk3/U7j23F++BXO/rUQlDeWDGz7GaLR22NXdXGZu3\n7mp3v18DT2JiIrNnz2bevHmYTCYeffRRRo8ezYMPPsj7779Pnz59uPLKK/3ZBBERERGRXqmqxlsQ\nICrM1unX3lW6D4BJfUa3uT8sMJSz+p3Oysw1bC7aQcHBYgCGxPb3HRNgCeCaMZfxwjevsebAtwBH\nDDx1znoArhgxm2tGX4bZfHTlBportbXH7+vwzJs3j3nz5rXYtnDhQn/fVkRERESkV6uq9QaeSL8E\nngwsJjNDYge2e8yFg2ewMnMNy/etJizQWxN6YHRai2POTJvM2txNfJu/BQCn20mApe01OJsDT1JY\nwlGHHYDUiD5H3O/XKm0iIiIiIuIf1X4KPA3OBjIrDzAopj82a2C7x/WPTmVY3CC+K9rJluJdhAQE\nkxgW3+IYs8nMg2f9jKmp3mFutY117V6vOfCEBAQdU3vTolL4nwt+3e5+BR4RERERkZNQcw9PVHjn\nBJ7sylx++fGjvLd9CR7Dw8iEIR2ec+GQGQDUOGoZEJ3abnns8KYeoBpHbbvXOhR42i9B3Z4B0ant\n7lPgERE4RkF6AAAgAElEQVQRERE5CVXXNgKdN4fn04wvKa4t5eO9nwNwdv8pHZ4zJWUCUUERAAyI\naj90hNlCgA56eBqPP/AciQKPiIiIiMhJqLqmeUhb+8POjkWxvdT3emT8EPpGJHd4jtVi5fxB3qrL\nQ+IGtHtcWKB3HZ7aRnu7x/h6eAI7N/D4vWiBiIiIiIh0vuYhbRGhJ97D4zE8ZFTkAJASkcRVo+Yc\n9blXjryIAdFpTGynohtAWGBzD8+RAk8DAKGd3MOjwCMiIiIichJyujxYzCYCrEc3aMveWMfiXcvJ\nrMwhOSyRH4y8CJs1EKvZSnFtKfXOBs7uP4VfTLnpmNphNVuYnDL2iMeE27w9PDWOo+jhUeARERER\nERGX24PFcnRhZ29ZJs+uXUBlfTUA24r38On+L1sdNySm/WFpJ+LoenjqCTBb2y1bfbwUeERERERE\nTkJuj4HF3HZVtMOt2P8Vr256D4/hYd7oS7hk6Cw+z1zDtpI9mAC3x43T4yLQEsiU1Al+aWtzlba9\n5ZlsyPuO0/uOb3VMnbO+03t3QIFHREREROSk5Okg8DS4HLy+6X1WZq0lPDCUu6fewtikEQBcPGwW\nFw+b1VVN9S1Muqs0g12lGSy84hnCbKEtjlHgERERERERH5fbg7WdIW21jXYeXvE0hTUlDIhK5b6z\nbichNLaLW3hIaNOQtmbVjpo2A09scHSn31uBR0RERETkJOT2GJjb6eH5Nn8rhTUlnN1/CrdN+jGB\n1s4pXX28LGZLi58POmpIIcn3s8vtotHtJCQwqNPvrXV4REREREROQm6PgcXSduDZVZoBwCVDZ3V7\n2GnL96u1NVdoC/bDkDYFHhERERGRk5Db7cFqbvvr/K7SfYQEBJMWmdLFrTo6Bx01LX72V0lqUOAR\nERERkV7kLxve4GcfzWfZvtW43K6jPm9TwTbWHvjWjy3rfO0Naausr6aotpRhcYMwtxOIusM9U29h\nSEx/AA46alvs82fg0RweERGRJp4jjIcXkZ7BMAx2l2WQV11Esb2MktoySu3lDIhJ48oRs/kqZwMu\nj4uFm97jP3tWcO3YKzgzbfIRr+kxPLy04R80OBs4PWU8VsvJ8RXZ7W57SFvzcLYR8YO7uklHdGba\nZJLC4vnVZ39Q4BEREelqO7PK+dVLX/Prm07njNHJ3d0cEWnH5sLt/OGrl1tsM5vM7K/MYcX+rwC4\nYNDZWC1WPs34kj+te5XUyD6kRvZp95rZlXnUNH0Bzz1YyIDoVP89QCdye7xD2krt5Wwr3sO24l2U\n1VUSbgsDYGT8kG5uYWvNbatpFXgaAAUeERERv3n+3c0YBnz0ZaYCj0gPk1GezSf7VjFr4DRWZq0F\n4KYJcxkU04+E0DjCbWEs2PgWq7PXATBjwBkMiR1An/BE/pb+DvvKs3G4Gnlx/ev8fMqNDIkd0OL6\nW4t3+V5nVuScRIHHoDZyOz9f8l6rfYGWAAZGp3VDq44swhYOtBV41MMjIiLiN3UNTgrKvBWDkmJD\nOjhaRLpSrcPOM2v+SkV9FV/lbAAgNbIPFw2Zicl0aDjXTRPm8lXOeiJs4QyK6QfgCy7ZVbn838Y3\nAFix/+sWgae64SDrczf7ft5feYCuW47zxLjdBo22EkwmEzeNn8uwuEE8vuqPNLgcDIkd0COH5tms\ngQRaAtod0hYaqMAjIiJywiprGvhiUx6Z+dVkFRwkt/hQtaCausZubJmIHM7j8fDi+tepqK/ivIFn\nsa14N8X2MmYOmNoi7ACEBAbz8qW/w2N4MJu8E/VTI5IxYWLZvtW+46obDh66vuHh0ZXPUlhTwqiE\noewtyySzIqdLnq0zuD0e3JY6ooMiuWjoTABO7zueL7PX97j5O4eLsIWrh0dERMSf/v7xTj7fmAtA\nUKCFIalRDEyJZOnabKprFXhEeoo3t3zIpsLtjEsawa2TfoTL42JnaQZjE4e3eXx0cGSLn4MCgkgM\ni6OottS37UB1ge91qb2cwpoSxiWN4P5pP+O/Vz1HVlUutY12wgJD/fNQncTjMTAMA5e5jtiQ/r7t\nlw07n+KaUqb3m9J9jetAuC2UgoPFLbbVNSrwiIiIdJqDdm+oef7ec+iXHIGlqTLbmq0FHLQ7urNp\nIqe8r3M24PK4cXvcLNn7OSnhSdwz9VbMZjOB5kDGJ488putZTBYAUiKSiAuJZkvRLuoa6wkJDCa7\nKg+A0QnDsVkDmdJ3AhkV2aw98C0XDJ7R6c/WmdweAwIcYDKIDYn2bU+LSuHJ8x7oxpZ1LMIWTpY7\nF4erEVvToqhah0dERKQTNTrdAKQlhfvCDkBEqE09PHJSKbNX8OaWD6k6bJjWyay4tpQX1/+dlzf8\ngwXpbxMWGMpDZ99JaODxz62bkjoegMuHX0Bq0yKcB6rzAchpCjz9ovoCcHb/KZhNZlZlrjuRx+gS\nbrcHU6C3sllccHQHR/csEU2V2ooP63k7VKUtqNPvp8AjIiKnHEejG4vZhNXS8n+DkWGB1NY7cbk9\n3dQykWOzZM8KPtr9GY+v/CMVdVXd3ZwTtnjXp3gMDxaTGTMm7p92G0lh8Sd0zR+MnMNTsx7gnAFT\nSWsqTb0s4wsq6qvIrvQGnv5R3iAUHRzJhORR7K/M8YWhnsrtMXyB5/AenpPB5JSxAHyw8xPfNvXw\niIiIdKJGpwdboKXV9shQGwA1dvXyyMlhc+EOTJgoqCnmsZXPUmov7+4mHbcyewWrs9eRHJ7Acxc9\nxu/Pn8/IhKEnfN1ASwBD4wYCMCF5FPEhMaw98C2/WPIIW4t3ERkUQdRhc39mDjgTgFWZa0/43v50\nMgeeM/pOZFBMP9blppNRng14A0+A2UqAJaDT76fAIyIipxyH00VgQBuBJ8w7lrxagUd6uA153/F/\n2e9RWFvCpJSx/HDUxRTby3h05bMU1ZR0d/OOy+Ldy3F73Fw54kKSwhPoH9230+8RGRTBn+Y8zu2T\nryU+NIZGt5PBTSWsm03sM4ZIWzhf5WzA6XZ2ehs6i9vtwWzz9orEhcR0c2uOjclk4vpxPwC8hSkM\nw8DurPNL7w4o8IiIyCnI0ejG1mbg8fbwVNeqcIH0bB/v/Zxql7ec+sTkUcwbfQk/HnsF5XWVPLby\njxTUFHdwhSMrrClh+b4v2FuW2RnN7ZDD1ciqzLUkhMZyVr/T/XqvAEsAswadxXMXPsaj59zDTyf/\nuMV+q9nC9P5TqGm0k16wza9tOREncw8PwMiEoUxMHs3O0n1sLtxOnbNBgUdERKSzONod0ubt4Tmo\nwgXSw5XaKwCYmDyaM/pOBOCKEbO5YfwPqWyoZvGu5cd97R0le7l/2ZO8uuld/rTu1U5pb0f2lWfi\n9LiY0ncCVnPrf5v+YDabGZ04jJjgqFb7Zg6YCsCqLO+wtp5YFMLtMTAF2TEbFiKDwru7Ocflx2Ov\nwGQy8daWRdQ22hV4REREOovD6W5zSFtEcw+PSlNLD2ZvrKOsroL+wSn86uyfE2Y7tF7MnCEzCbQE\nkF2Z2+75hmG0u6/e2cD/fv1/ePAeU1ZXQVlTuPKn3WX7ARjeQxbLTI3sw5CY/nxXtJMPdizltn8/\nxIa877q7WS3UNNgxBdcSbkr0LbR6skmLSuGc/lPJPViI2+MmJLDzK7SBAo+IiJxiDMOg0dnekLam\nOTzq4ZEeLLdp4cwEW+t5G2azmbTIFHKrC3h2zQKW7l3p22cYBgvT3+PupY+xKnMtD694mrK6ClZm\nruFgg3d43PaSPdQ567l02HncMP4qAHaXZfj9mXaVeu8xPG6Q3+91tKakTsAwDN7b/h8A1h74tptb\ndIhhGOyvysJkgihTUnc354ScM+AM3+tgP/XwaOFRERE5pTS6vCWn2xrSFhbsDTz2hp47UVl6n+qG\ng2wv2cOUvhOPajhXTpV3DZn4wLYnqveP6ktGRTbr8zaTUZ7NRUNmYjKZWLZvNcsyVgPwl41vAPDa\npvfZmL+FSFs4t592LVsKdwLeoXJWs/dr4u7S/X6dV+PyuNlbnkXfiGTCm9Zn6QkGRKe1+DkqKKKb\nWtLaH756ic2FOwCINvfp5tacmIHRh4pGhAYc/3pLR6LAIyIipxRHo3fR0bZ6eEKCvP9brFPgkS5S\nai/niVV/othextxRxcwdfUm7xza6nXxXuIOVWWsAiG+jhwcOLaIJUF5fSVFtKZX1Vfz9u38RaQsn\nOCCIoqYFH/c0DSWrdtTw9Nf/h9VsJSQgmCGxAzDwlnRelb2OHaV7CbYGkRKRxO2nXdep82y+K9yO\nw+VgTOLwTrtmZxgQldri58YeUrHNMAxf2AGIsSZ3Y2tOnM0aeOi1JfAIRx4/BR4RETmlNDrbDzzB\ntubA4+rSNrVnzdYCqg42cPFZA4/53BUbDlBUYee6C0f4oWXSWf69+1OK7WUEWgL4cNcysqryiAmO\nJC4khhn9zyC6aX2YRTuXsXjXcupd3qpcA6PTiAtsPdkeWgYegC+y17Fi/9eYgP8686cEWgL4+3f/\nYk/Zfg46agG4b9ptfLjzE7Iqc5ncZyyWpkBzybBZfJ2zkYOOWopqSsioyGZ6v9MZm9R5v1crMr0B\nrnn9m54izBZKfEgMpXXeOUzN71V3szvrfK+d+YOwDbF1Y2s6R3J4AoU1JZTV+We+mAKPiIicUhzN\ngaeNIW0hQd4F73pCD49hGPzfB1upqnUwflgCKfHHNtTnzWW7KK9u4LzT0kiKDe34BOkW+8tzsJqt\n3HvmT/nz+tf5Nn+Lb1+ZvYJbJl1Dib2Md7d9RIQtjPMHn820tMn0j+rLpk2b2rzmgOhUEsPiGRTT\nj7UHvuXDncsAuHni1YxMGALA3VNv5s7/POw7Z3zSKCb1GcuGvM0tCgdcM+ZyrhlzOQBbi3bx1Bcv\nsKlgW6cFnvK6SjYXbmdQTD+/rLtzogZEpx0WeGq6uTVeVfXeinGT4ifz9YY4LMNN3dyiEzcxeQwf\n13zut2GDCjwiInJKaR7S1laVtgCrmUCruUf08BwoqqGqaT2gRaszuOWy0b4eqI6UVdVTXu3tCfhm\nexFXzOg5E8FPFS63i++KdjI0biAR7cxLcbqdZFfn0T+qLxP7jGHhFc9Q22invK6KX6/4H/aU7ee+\nZU+Sd7AQgBsn/PCo5tLYrIH8+eInMAyD0toyiuxlXDDobGYPnuE7JjooEpPJhGEYRNjCfMOKzkyb\n3O51R8YPIchqY+m+VQQHBHPVqDknPLRtVdY6DMNg1sCzTug6/jIkdgAb8r3V2YrtZTy7ZgFDYvtz\nYVM1vO5Q2VANQKjVW4raYj75a5BdO+5KEsPiOLvfFL9cX4FHREROKUca0gbeXh5/Bh6ny43ZbMZi\nPvJfZbdklPpeL/8mhy835/Pg9ZOZPCKxw3vsOVDpe/3N9sJWgaeuwclfPtjK3FlDSEvqOROxewOn\n28mqrHUs3rWcsroKooMieXD6HQyK6dfq2NzqAtweN4OaJm2bTCbCbWGE28JIjUwm67DS0mGBob71\ndo6WyWTit+c/hGEYmEwtf98sZgsxQVGU11cSF9L2XKDvs1qsjE0cwYb87/hg51KGxQ1kfPKoY2rT\n4TweD6sy12Cz2ph2hKDVnS4aOpO+kcm8tWUReQcLWZ+3mfV5m1m27wuuGXMZZ/U7rctLQjf38IRa\nwwAnFsvJ38NjNVu4cMg5frv+yR8JRUREjoGvaEEbQ9oAgoOs1Dv8M6Rt0eoMfvDQEq544CMuf+Aj\nfjh/CTf+9zJ2ZJa3OnbrvjIAfjF3POdOTsXt9vDb19ZTWlnf4X325HgDT1CghV1Z5b5hfM3Sd5ew\nelMen2040AlPJc0KDhZx19LH+Fv6O1Q7ajij70QqG6r5++Z/tnn8/grv+z+wjTB0eIWws9JO41fT\n78RqOb6/U38/7DSLCfHOATrawAMwb/QlBDT1bNQ22o+rPc22Fu+itK6CaWmTCQ7wz/orJyrQEsCk\nPmNa9NJNSB5FdcNBXlz/Oq9ter/L29TcwxNs8Q5V7eiPJ6LAIyIip5jmL/+B1vZ6eKx+6+HZsLMI\nkwnGDo5jWFo0STEhVBx0sG5bYYvjausa+W5fKX3iQpl9Rj/+60cTuX7OCFxug62H9fzkFB7E4zFw\newyee2cT9/7pC+7+42qWf5ON2QRjB8fjMbzXO1xxhXfSc0HpiX1hlZY+zfiS8rpKzh80nZcufpJ7\np/2UMYnD2V22n4KDRa2O31eRBXgLEHzfwGhvhTCTycQtk65haNyxF67oSGxINABxTf89GmlRKfz8\n9BsAsDd2HL6PZEXm1wCc10OHsx0uwhbue33LxGv405zHiQmO4uucDXg8ni5tS1WDt4cn2OINYb1h\nSJu/6R0SEZFTypGKFgCE2AJoaHTj9rS/Gv3xMAyDrPxqUuLD+O0d03j6l9N55q6zMZsgI6+qxbGf\nrj+Ao9HN7DP6+7aNGRQH4OsN2riziF88s4rXP95JVkE1K7/NJTO/msIyOxaziXMmpRIf7V3Er6au\nZY9Vc+DJL+0ZVad6ix0lewkwW7lxwlyimqqrnTvQW3lsZda6FscahsG2ot2EBYaSFtl6HZX+TSWR\nB0X3IzTQP2uTxAU3BZ7Qo+/hAQhpWivl8Gphx2JfeRbX/+tuNuR9R7/IlDaH+/U0h/fwxIXGEB8a\ny4Tk0did9eyvzOnStlTVe3t4gsxNPTy9YEibv2kOj4iInFKOtA4PHFqLp97hIiy48yYlF1fUYW9w\nMWl4pG9bkM1KSkI4mfnVeDwGZrMJt8fg4zWZ2AItXDDl0F/++/eJJNhmZWeWN/A0B59FqzOIi/QO\nB7rr6vGcO/nQOW9+sguAmu/18BSV233/dbs9WCz6++eJOuioJac6n9EJw1pMZj8tZTxWs5UdxXta\nHJ9fU0R5fSVnpk7C3MZf6AfG9OPM1EmckXps83aORUpEUov/Hq2wpgBmbzy+wPP5/q9xuL2/k3OG\nntvukLue5PAFUZvn7IxLGsHnmV+ztWgX/el4bl1nae7hCTJ7PwerhrR1SIFHREROKY2uIwee4ObF\nR+udnRp4sgq8f5UdkBLZYvvgvpHkFtdQUFZL34RwNuwooqSyngun9ics5NAifBaziRH9Y9i0p4Sq\nGkeLim07mkLQyAGxLa7dfH5tOz08bo9BcUUdfY6x5LW0trNkLwCjEoa22B5oCaBfZAo51fm4PG4s\nJjM1jXa+ztkAwNikkW1ez2q2cM+Zt/q1zTMGTCUhLI7RCcOO6byQQG/Pod157EPaPB4P6QXbiLSF\n878X/sZvZYg7W2NTQDu8QMHohGGYTCa2l+yhf4T/Ao/D1chfNvyDcFsYE5JHU15XSXhgKHi8bTHr\nDxYdUuAREZFTSkdFC0KaFx91dO48now8b+AZ2Of7gSeKVel5ZORV0zchnCVfZwJwyVkDWl1j5EBv\n4NmZVU61/VCvzdZ9ZcRGBpEY03LoU3NgO3wOj9tjUFp56C/z+aW1CjydYG+5dz7OiPghrfYNiE5l\nf2UOv1nxNIW1JdQ7G3z7xnXiAp7Hymq2MCZx+DGfFxrgDTx1xzGHZ19FFtWOGs4dcOZJE3YAX1GF\nITH9fdvCbKHEBEVRYi8HPz7KtuJdrM1NB2B5xhcApEYk+4bdqmhBxxR4RETklLFlXykrv/WW+g0M\naPuvoqHBnb/46Huf7eH9FXuxWkwM/F4Pz9B+3nkUG3YU0T85gq0ZZYwbEke/NspFN/fg7MyqoKrG\n4dteW+9k4rCEVkODwkMCfPublVfX43Ib2AItOBrd5JfaOa1zHvOUlt+0Vk5aVOv5OM0V1zIrDxAV\nFMGo+KEkhcUzPH6wr3DAyST0BObwbGsa2jexz5hObZO/XTrsfBpcjVwybFaL7VHBERyoyscwDIpq\nS8mtLmBC0qjjrqjXloyKbAB+PPYKahvr2Fa8izP6TsRd4y2WYNUcng4p8IiIyCnBMAz++PYmKg56\n/7puC2j7f4HNQ8U6q1Kbx2Pw7y8zCQ8J5N4fTyQq3NZi/7C0aPonR7Bma4GvbZee1XZFrqFp0Vgt\nJnZklRP0vR6qOdNa9wg1D2k7fA5P83C28UPiWb+jiJzCg7z8wRZGDYhlxsSet9L9ySK3upDooEjC\nAkNb7RsYc2he1Z2n38j45LaHsZ0srBYrNkvgcc3hya0uANquTNeT2ayBXDfuylbbo4Ii2O/JweFp\n5NX0d9hStIvY4GguHnYuswaexUFHDX/+5nV+PuVGksMTjuve+8qzAThv0FlNv1/edixb593e1hww\naUnvkIiInBIOFNX4AgUcYUhbkLdXpL6TAk9O0UFq6ho5bWRim4uGmkwmrjxnMB6PwY7MchJjQpg8\nsu1J5LYAC4P7RpGZX01R2aGS0oP6RjJqYGyr48Pa6OHZluFd3+eM0ckEWM2s217IJ2uzeeXf23C6\n3K2uIR2rdzZQVldB38i2P7fUw6qwjU069iFkPVFIYPBxzeHJrS4gOCDopOzZaktUkLfH1u6uJ6+6\niEBLALXOOv7x3Qf84uNHWJm5lr3lmWwp2nlc1/cYHvZX5JAcntAqTGtI29FTD4+IiJw0dmaVH/f/\n3DftKWnxc3tD2pqrtNV10uKjzQGjuax0W2ZMSCGvpIa8kloumNLviM84amAsu3MqKatuIC0pnNuu\nGMOwfm1/eTw0h8f7LE6Xh0/WZRMaZOWscX1YujaLfbnektjVtY2s2VLAOZNSj+cxT2n5TWvs9I1o\nPZwNvIUL/nD+fMJtoS0mvXcnwzCoqnUQHd7+gp+7sioIDDAzqG9Uq32hASFUN1ULO1pOt5PCmmIG\nx/Q/KSqzHY3meUjVzhoq6qsYmTCE+868jVfS32Fdbjrbi3cDUHcc4RCgsKaEOmc9k/uMbbXP7daQ\ntqPVM/7ViYiIdMAwDJ5auIFH/rqOOkfbC/1V1Th49q10sgtbfxH7fuBpb0hbSCcPadvaFHjGDm4/\n8FgsZm6YM5Jf33R6m71Ahxt5WE9OdLiNcUPiCQps+1kOVWnzDmlbsyWfqhoH50/pR5DN2uqL7Mdr\nsjp+IGklr2n+Tt+I5HaPGRiTRnxo61647vL+ir3c+N/LyS2uaXO/0+XmwRe/4p7nvmhzf2iAt4fH\nMDper8pjeHh762J+sug+3IanRY/Xya458OQ3lGBgkBgaR5gtlHFN1ffyarxh+HhLeDeH6bSolFb7\nDvXw6Ot8R/QOiYjISaGwzE5NXSP1Dhfrdrf9JW3J15ms3pTHL59Z1arowP68auKign0/dzSkzd5J\nRQv2HqgkLiqYhJjOWTxyRP9Di0RGhbX/13nwDoELDLBQ0zSk7T9fZ2IywcVN830GNRVQCAmyMnF4\nArtzKtn/vUVQpWP7K7wLT6ZGth94epLqWgcfrNqHYUBeSdv/lnbnVB7xGiGBIXgMDw2uQ8UzGt3O\nVgHI4Wrkj2tfYfGu5TS6vb+HvSnwRDctMJvfUAxAYlg8AJFB4QC+inx1h1XmOxYV9d5/j7EhrXvZ\nmgOPWUPaOqTAIyIiJ4XmoVcA6/fUUl3raLHfMAy+3lLg+/mt5bt9rxscLmrqGklNOFR+ub0hbc3r\n8BzvHJ56h8v3pa+61kFljYMBfTqvZm14SCD9krxfpqIjbB0c7R3WVlvXyJ6cCvYeqOL0kUkkxXrn\nAgzq6/2yNrxfDJc0haCla7M7ra29nWEYVDUc5Mvs9UQFRTAopl93N+moLFqdQb3DO1/roL2xzWO+\n21t6xGuEBras1FZUW8rt/36I97b/x3dMdcNBnlj1HBvyvmNUwlCsZu+/rbZ6K05WzT08eb7A4+3J\njbSFtzjueCraAVTWe8vZRwe1EXg0pO2oaQ6PiIicFJoDz7RxfVizpYBFqzO46ZJRvv2Z+dXkl9Yy\nZVQSWQXVLFubzVUzhxATEURplXf8fEJMCHf+cBz7DlS2u/BoZKg3RJRXH/tfZGvrGrn5qU8ZMyie\n+TedRk6Rd2hd/+TOXaRj5MBYcopqiArrOPCEhwRQXt3Akq+9w9UOX99nUEoUc2cN4fSRSQxJiyYx\nJoTVm/L4yaWjOnXR1d7GY3j4JncT7277iKJabzC4cuSFBFh6/ntWVeNgyWFDF6trWweeLftKWXPY\nHw/a0mItnhB4ffM/sTvr2dG0ACvAi+v/zr6KbM7uN4WfnXYdtY12NhVuZ2QbaxWdrJoDj9vwBsjm\nHp6IoJaBp/4Y5/DsLcvk91++6BsGGRMc2eoYDWk7en4NPBs2bODuu+9myBDvL/bQoUOx2+1s376d\n6GjvBMtbbrmFGTNm+LMZIiLSC2TkVWE2wZ1XjWPr3iI+WJVBQZmd//rRRIJtVjbu8v6F9ZxJfTlt\nZCIv/nML7362hzuvGkdppffLRnxUMBdN7c9FU/u3e5+4qCAiQgPZ18bQrpKKOkqr6tusiAaQU1RD\nvcPNhp1F/Pn973xDxtpaU+dETBmVxCdrsxmQ0vpL0PeFhQSSU1TDl9/lk5oYxrgh8b59ZrOJG+Yc\nKpF80dT+vP7xTj7feIDLzx7UqW3uDfIOFrKvLItl+1aTVZWLxWSmf5S3lPcFg87u5tYdnX9/uR9H\no5vzTktjxcYDrXp4qmsdPPrXtXgOG5nmcnuwWlp+qQ4N9AYeu7OO9IJtbCrYBnjfI8MwMJlMZFbk\nkBgWz8+n3IjJZCIqOJJzB07z7wN2scjvLZ7a3MMTYWu5mK/9GBdpbQ6Q9qo8AKKDNaTtRPi9h+f0\n00/n+eef9/08f/587r//foUcERE5aruzK9iTU0laUgQRoYFcc3YcX+52sm5bIbV163nsp2ewLaMM\nkwnGDo4nJMjKotX7Wb4um4um9qe0yjucJD46+Mg3wlsmekhqFOm7S6iudRAZZiN9dzEul4fPNhwg\nfXcJ7zx5EUG21v8LLSr3looODLCw8ttcNuzwTjju18k9PJOGJ/Lmf19I5FH08DT31Hg8BpeeNfCI\n1bHOOz2Nt5bvZvk3OQo839PgcjD/s//B0TRn5ay005g35lKSwuI7OLNn+WZ7IUGBFn4wc3BT4Gk5\nNGXTe2sAACAASURBVDQzvxqP4V0fymIxsTOrgoZGN2HBLQNPSNPio5X1B3ln62LMJjMpEUnkVhdQ\n7agh2BpETaOdAdFpvaYiW1ts1kDf68SweF/p6CCrDZvV5vt9OdYqbdGH9eiEBgS3uE8zDWk7en7v\nAzua6h0iIiKHc3sMVqXnUlvXSGZ+NY+/sg6PYXD9nBEApMQG8j8/P4upY5LZtr+M3y5cz+7sCvon\newOR1WLm1stH4zHglcXbKfH18Bxd4YAhqd5RCM3D6P7ywVaef+87CsvtuNyeduc9FDYFnnuunkBK\nfBi19U4sZhMp8WFtHn8ijibsgHexUovZxLRxfTj3tCMv9hgZZmPUwFhyi2uw13dO0YbeYk/Zfhwu\nB6eljOOZ2b/hrqk3n3Rhp7SynrySWkYPivMV8KiscbBtfxlOl/fLc1aBd87IlTMH+/69NDhaz2fr\n07SI5sJN71JsL2POkJlM6jMG8FYWK6+rACCul6y3cyRnpE6kT1ACD5/9ixbbD+/lOdY1i8IPO7et\n3h3QkLZj4fcenv3793PnnXdSXV3Nz3/+cwDefPNNFi5cSFxcHI888sj/s3fe4W2W5/7/aFqWvPde\niZ3E2ZsECBmEJkApq1BaCNADHUBpTzn9taWcHsqhBVpoSwflQEuZKZRRRhmBLLKXHSdx7Hg73kuy\nZcva0vv747VkK5ZXYidOeD7XlSvSu/zofTWe73vf9/cmKir4hRQIBALBF5NP99XyzNtHyc+OobHd\ngtXh5odfX8iSAQ05VSolP7p1Eb968QCH+tLZZg+wfl40Q270eai0laYOCzC6CA9AXob8u1RR18nC\n6Ql09jhwujw4XHKevsXmIljP9FajHEnKzYjikW8v4yd/3kVijB6N+txNSG66PI8bVueOun9Rdkok\nReXt1DZ3D5m690VCkiSOt5Wxv6EIkLvdn69F90XlsjX7/Lx4dFoVWrWSovJ2isrbyc+O4cE7llDd\nKNedTUmN5HCflbstiOBZkDKbzKg0TnY1EKmL4MZZV3Go8SgAjd3NeLzyZyXOEDNo3wuNHy6/m4KC\nApLCA78VIkPCae81AmOP8DgGuN/FjCR4RIRnRCZU8GRmZnLfffexfv166uvr2bBhA48++iixsbFM\nnz6d5557jj/+8Y/893//97DHKSgomMhhCkZAnP/JgbgOkwNxHSYet0fitY/lVLCSGvku8dVLogiX\nWikoaPVv57sWX5qjxmgKoabVQbjSHHCNlk2BwrJ+A4KTVaU01o48ObDa5cnaweKTZEb24OwTOr7/\nC4qK6WwZbAldebINpQLqqktRKRV8a20MCsV59r5xyFGqz/cVY+8cPjJ1Xr2u0+Rg1zG2duz3P7c1\n9FDQNHle91iuwdb98uRb426nsLALnVaBs0/LlNSYuPfXn+H1QohGQX1NKeZOOdpTdLSYtpjBKVXL\n9XNoMrewMmoRpUdL6LbLVtZ/LXgdg0q+uWBp66bAPnnO10Ry6rWQ+r5HQG66uv/QAdSK4GYpp9Lc\n0eJ/7LW6g17n5hb5fJ84UYqpefIbZpxLJlTwJCYmsn79egDS09OJi4sjKyuL1FT5zsiaNWt4+OGH\nRzzOwoULJ3KYgmEoKCgQ538SIK7D5EBch7PDpn21mK2NXDI3BaPZzmXzU7nqkpyAbU69Fgvmeyiv\n62RmTuygeoGm3uO8va2SmIgQli5ZNOpxvLTtU9q7vWRPzQcCHatS0rJZOHdwL5Hfvf8xiTEGliwe\n/d+ZbMQkm/nX3u141JEsXDhvyO2+CJ+Hw83FbKs6gAIFEhKRIeEsX7zsXA/Lz1iugdcr8dv3PiE2\nUse6VUtRKBTEfb6dbqssaq5ZkcP7O6oBmJkTy+JFiyjrKGVfWTlZObnMnjK4ce5CFnIdX/Y/t7sd\nvNmyCZvbTq9Hjmgsyp/PrMTpZ/pSJz3BrsUBTwlVNfX+59NnTR9kcjAU73RugT4n66lpOSycM/g6\n760ugope5syeNSFps+cjQ90AmNAY+wcffMCf/vQnAIxGI0ajkccff5yysjIADh48SF5e3kQOQSAQ\nCATnEW6Pl39uqUCjlmtwfv29SweJnWBoNSpmTYkLWhx90+V5JMTo/XU5oyU3PYoui4PK+sFubT3W\nwTU8VrsLs8VJUuz4NBg9V6QlhKNWKfy1HF9UGszN/H7v31Ar1fxi9Q+5Km8N9110x7ke1mlT02Sm\nu9fJvLx4/+ckwiBHbUK0Ku66ZhY/uX0xoSEq5k+Ta5N0Wvm+eLAanmDo1CE8ccVPWZw6178sTn/h\np7QNha/5qFIhT7fHUsdjHeDqNlStmLvPtGC06apfZCY0wrN69WoeeOABbrnlFiRJ4uGHH0an0/HT\nn/4Ug8GAwWDgV7/61UQOQSAQCATnEVsO1tFmsnL1xdnERo6u3mYk9DoNf/7RKjSqsd3jy02PZs/R\nZg6WtgxaZwlS0N9qkm/HJsUZTm+gkwSNWkl6YjgnW3rweqUvpOVtt8PCEzufweayc/9F32R6/FSm\nx08918M6I3yNROfl9deZ6Pua7EaGhaBQKLh4TgpL8pP8NWehWjn9yu70MFqSwhNYmb2Mg41HAIj5\nApgWDEWiQY6KpUemcLKrIUDEjITFZSUxLJ7b5l7PguRZQbcRpgWjZ0IFj8Fg4Nlnnx20/J133pnI\nPysQCASC8xCbw83GTScI0aq4cc34Nib03akeCz7jgoITbYPWWYJEeHyW1Ekx57fgAUiJC6OmqZvO\nHntQ4enyuNjSvo8IYwy5sdlBjnD+4va4eWr3c7T2dnB9/nouyVx8roc0LhzuMyyYN6APk8UqC/dI\nQ399zkCDDZ/1+mgjPD5mJvRn72jPg2asE8Vl2ctICIujrKNaFjxjivBYidfHsCRt6LRSr0eYFowW\nIQkFAoFAMCn45+ZyTN0Orrts6rhFd86EqWlRKBQEtaDusQ6O8DR3yBGe5LjzO6UNIDFGfg1tpuAT\ntN11hzhkLuZP+17E7RnbZPhcUN5RTa/TOqptP6vaSWl7BUvT5nPTrKsneGRnB4fLQ0mNieyUCKLC\n++3MzRbZCWwoi3N/StsYIjwAek0o35hzHd9ccPNpjvjCQK1UMTtxOgaN/H02WsHj9Lhwed3+5q5D\n4faKlLbRIgSPQCAQCM45lfVdvLO9koQYPdevmhypQ3qdZshC4GA1PP4IT+y5ifA43E68fROgMyWx\nrw6p1dQbdP2mys8BaLa0sbl617j8zYmiqPk4D235Dd/54EHKO6pH3P5wczEAd86/yV97cb5zvNqI\ny+0NSGcDuPva2aiUCm5dF9xUQBfiS2kbu6j9yowrWJe7csz7XYjo+wTPaEW3bztfc9eh8PgjPBfG\n+3QiEWdIIBAIBOcUl9vL028cxuuVuP+r8wgNmfAWcaMmN72//0VynIGwUDk9J1hTTp/g8UVHzhYu\nj4s/73+JO975T7730c/ZWr0bt3dsd+RPJSHaJ3gGT9DquhqpMp0kJUSePB9pKTmjvzXRbK/ZC8h9\nTT4o2zzsti6Pi5L2CtIikonRXzg9AvvrdwKL3+fmxvPub65hSlrw1+qL8ATrw3MusDncE9LQ/u8f\nHOfjPTXjflwfvkhNr2uUgqdvO4N2BMHjr+EREZ6REIJHIBAIBOeUN7eUU9vczZcuymRu3uTqXJ+X\n0V9w/fBdF/H4vZeg16mHiPBYiQoLQa87OzULbq+Hf5V8wvMF/+Dz2n3EG2Lpspl59uCr/OCj/6Gw\nqXjIfSVJYk/dIewue9D1PtEWTPBUGOWJ4eyIPDRKNV227nF4NROD1WXjYNNRUsITidJFUG6sHnbC\nXNZRjdPjYs4FZqNcVN6GRq0ccyNZXZ9pgWOMKW0TwYe7a7jpwQ+545FNNLT1jHn/yvouvvvElkH7\n2hxu3tleyRuby8drqIPwWVF32Uc3bp+5gS8Vbig8wqVt1Eye22gCgUAg+MJR02Tmn5vLiYvUcefV\nM8/1cAbhi/AYdGpS+tLbwvTaQTU8Ho+Xtk4rU9PPXlTgcHMx/zj2HgCxodE8ccWD2Fx23i3dxObq\nXfxh3wu8cO2TKIM4OB1pKeX3e//GjTOvJDs6g+zo9AD74IRhBE+dWe5JlBASQ3RoJCb7YNvuycKB\nhiJcHheXZC6htqueAw1FGK2dxBmCWyUXtRwHYE7SjLM5zDOivrWHF/9dgsXmxOHyYHd4cHu83Lp+\nBisXpGG2OKhp6mbO1DhCNKNreunDF2091xEer1fivc+rADB1OygqbyctIXxMx9h3vJmGNgv7ilu4\ncXX/vr7IrNFsp6PLht3pxmJzMT1z/Oy0o0MjAei0je6zYnGOHOH52V92c7SyAxApbaNBCB6BQCAQ\nnBOcLg+/3ViIxytx71fnYQidfG5O2SmRqFWKgELvsFANzR2WgO3au2x4vBLJZ7F+p9PW3yfn/mV3\nEqrREarR8c2FN+P0uthavZvarnpyYjIH7VvbJTdD3Fq9B5PtIy7JWMz9y77pXx+iUREdHjKE4GlE\ngYI4bTTRoVFUGGvwer1BhdW5ZufJAwBcmrkYrUrDgYYiyo3VQQWPV/Kyu+4Qek3oedUo89P9JzlQ\n0oJCIUdkQjRqunsd/HNzGZEGLeV1nYCcvjZWQk7DlvpMefHfsuhcOD2RulY5ImI022g29jIlLZKq\nBjMnW8Ye4Wlul4VNVUOg6Gjq6K9T+/sHx9lR1IhSAc89uHbc0lOjQnwRntFFQ62+lLYhang8Xskv\ndgBEgGdkhOARCAQCwVlHkiSef6/Yn8q2aEbiuR5SULQaFffeODdAjIXrNVQ7PLjcXr+Fb2O7LIDO\npmFBt0Oe9D102f3MiA+08c6Pz2Vr9W5K2iuDCp6G7mYATH13nKtMJwdtkxCjp6K+i4a2Hv/ddI/H\nS5WxngRDHFqlhujQSLySl25HD1F9d7EnCyZbF8VtZeTF5pAYFk9erNzAtqyjmuUZi/zbHW4upr3X\nRFpEEkZrJ6uyl59XVsqltSZUSgWv//JKf83N4y8fZPeRJn7+3F7/dnNz48Z8bF+E53RMC06H9k4b\nb2+rBPD/P5C7rpnFz57dw8nm0adRVjZ08Xlhg188VTcGNtRtHiB4dhQ1AuCV4P2dVdz9ldljfg3B\nUKvURISE+T9vI9Ef4Qme0uZz1/MRrOGyIBAheAQCgUBw1nlvRzWf7K0lKzmCu68dn0nFRHH5kkDB\nEKaXe5Z0dtv9qV/Hq40ATMs8e00WzX31AL5u7gPJT5AF0MtFbxEdGsHFGYG9ZBrMzQHPmy1tWF02\nv5sUwOL8RMpOdvJfT+/grz9bS5hey0cHT2D32Ih2pgAQo5NFjslmPieCp9dpZX9DEXvrDxEREs73\nLrrTv25P3SEkSeLSzCUAZEenA1Dfl5IHsLe+gN/v/RuSJLEicykgR4POF1weiaoGM9mpkQG9ptYs\nSmf3kaaAbacOYUwwHCE+W2rH2YnwFJa1+h9fNj+NRfmJ/vqU6PAQZk2JIzXeQF1LN5IkjTjRtznc\nPPbSQdoGRCqbOnqx2l3+Wrum9sBo7Q+/voAX/13CZ/tPcssV0/1GJWdKtC6S1t6OkTek/0bEUClt\nHV2j7+cjkBGCRyAQCARnnX9tryAsVMP/3HXRmOsKzjWzc2LZfaSJ93dWc9dX5A7ox6uNKBWQnz1+\nef8jYe6L8ESGDBY8cfoY4g2xtPcaeXrvC8xNyidMK0efvJKXxu6WQfuc7GoIiBTdtCaPNpONT/ef\npKHdwvTMGHaVl0IIGFs1SBkS0X1OZp1286DjnQ4flW/laEspN868ipL2cq6ednmANbRX8vL6sffZ\nUbsflVJFp82M29sffbh93o1E9AnAnbUHUCmULMtYCECIWkucPoamHnlSfaChiKf3vuA3MdjfcBil\nQkle3JRxeS1ng2aTE7fHy/RThPaCaQmsWZzO3Nx4iquMJMXqT6vOQ6VUoFUrz1qEx9fk9/9+ssZf\nM3cqGUkR1LdaMJrtxEUFRkBcbrmI3xd5ffXj0gCx46Omqdtv4NBs7EWhgHXLstColaxckIbRbOel\nD0v4dF8t168anybI0aGRnDQ3YnPZCdXohtzO6/Wy8+QBdOqQIZv6CsEzdiZfwq1AIBAILmgsNhem\nbgd5mdGDJiznA1dclElCjJ4Pd9fQarLicHkor+siJzXyrDm0AXT3RXjCQ4JPDL+96Bv+x+29Jv/j\njl4TDo+TabE5aFUacmOyAKjprA/YX6FQkJ4oiweT2Y7L7aGmtxSAnpYIdpX0YO2Rxepoi7FH4sXD\nb1LYXMyDm5/g1SP/GpRqV9JWzrulm3B5XDjcDlLDE7ll9le4LOsiQK7ZeafkY+q6Gqnpqmdu8kwi\nBpyflPBETLYudtcd5Hd7/4pGpeHynEsAcHicpIQnDpvOZuq2U17XiX2S2DSfaJAnvjOyAoW2SqXk\nB19bwKqF6Xzvpnl8dU3eaf8NXYj6rAgeq91FUXk7ybGGIcUOQGaSXA9Te0pa2+6jTdz+i0381x92\nYHe6OVFr4oNd1aTG96eZJkTL3zeHy9v8y5o7eomLCuWeG+Zy91dmo1AoWLcsi9AQFe/vrPaLqDMl\nOnR0NwcKm49htHZyaeaSgIjrQITgGTtC8AgEAoHgrNLQl0ufkTg2l6XJgkat4rZ103F7vLz2SSkn\nak24PV5mTRl7jcRY2Fq9h598+pi/8LnbYSFca0ClDB4hm5M0g1vnXg9Ae6/Rv7y2qwGA+SmzeOHa\nJ/nukg0AlLYPrpmIjZTvRBvNdg6WNSJFNqN2h+G1RLPlSDevfyQLEpMtcBJX2FTM3wv/OaaeKW0D\nxuijuact4PnBxqMAfH/Zf/DXa3/Db9Y9xHX565iVMA2Al4re4vVj7/PYjj8DsKIvnc1HSrhcK/b0\n3hdQKZT89NJ7WJ1zsX99RlTqoDEYzTbu/c1W/rm5nHue2MIDT+/gnt9s9bt7nSt2HG5gT6mFmAgd\n86cljLzDaaILUdPWaePFfx9nX3Ez3b2DLdnHg7e2VmBzuFmzJH3Y7TKT5O+NupZ+wVNc1cGvXz5I\nj9VJdaOZP791hD/88zAA37tpvn+7yxakYQjVsGnvSbYXNvDgM7sxmu2kxgUKrLBQDWuXZGI029l1\npBGbw82bW8rPSPhFh8pCrdM2vOD5rGonAGunrBhymw6zbCe/dGYSX10zPhGoCx0heAQCgUBwVvEV\nD6efp4IHYMX8NLJTIthe2MAbn8n9OyZy0mm2d/NS0ZtUd9bxZvG/5WWOHn/61lDE97mRdVj7Izyf\nVe0AYE7iDLRqLSnhiaRHJLO/4TAHGooA+ODEZp458DIxEbLgMXXb+bh0DwqVl0sylvLU9y/jykVR\nSC7Zve7USdzjO//MxxXbaLW0j/o1lrTJ5/GrM6/ia7OvAaDF0i94JEniYOMR9JpQ8k8xaUiNSAp4\nbrR1khOdwdK0+QHLUyL6zTHW5a4kPyGPtAH7ZkYOFjwvfVhCXUsPr3xcSq/dzbSMaNo7bfz0z7sC\nCt6D4XB5eORv+9h1pHHY7U6H/cVyWuLP/2Mp4X11ZRPBkhmJuFwe3t5WyS//foC7fvkZH+ys5rGX\nDmAJ0o/qdLBYnbz3eRWxkTq+smL4lMLMZFk4+JzaLFYnT20sBIWCR7+znKlpkWwvaKC+1cJVy7OZ\nmRPLhitlm/GL56RwxdJMuiwOnnqtgGNVHcyZGset6we78l2zYgpKBfxreyV/eOMwL39Uyuuflp32\na4zW9UV4hhE8bZYOippLyIvNISs6Td6+x85//WEHRyr6P0u+CM93b5jDhivzT3tMXySE4BEIBALB\nWaXeJ3jG2EdjMqFUKrj9qnwkCY5VdRAToTst29/R8l7pp9hcdjRKNVuqd1PX1YjF0Ru0fmcg8Xq5\nTsEXPak21XGkpZSZCXlMjc3qey1KfrD8LrQqDX858DJN3S28cuRtttfsRaeX03mMZhsVlmMgwQ3z\nVpGXEc2iXAOSUxZE7UGiMwBOjyvo8lPxer0c6oveLEmbxyV9kZmWnv5J3smuBjqsJuYnz0StCixB\nPlXwGLR67lmyYVD0yxfhAfxiSKfREW+Qz9OpEZ4TJ01sK2jw14TodWoe+fYy7rgqnw6znZ8+s4um\nUyzKB3K82sjBklbe3V418kkYI6Ye+S6/TwBMFN++fg7/ePRKHv32cr66Jhebw81z7x5jz9FmiipG\nL2iH43B5O063l/XLsgLMF4KRFGtAo1Zyss+44E9vHqGjy8YtV0xjbm48//vt5czLjScrOYINV8li\n4MbVuWz83/VMSYvi2sumMC83nutWTuXZn6zhl9+9mGlBeu4kxuhZPieFmqZudvUZQHSd4o42Fvp7\n8QwteD6r2omExBVT+6M7BaVtlJ3s5KFn9+D1yhHTji4bSqWCqPCha4EEgQjTAoFAIBCcVfyCJ3Ho\nPP3zgQXTEpgzNY6jlR2sWpg2od3ODzQWodeE8p3Ft/LbPc/z3KGNSEijj/D01fC8d+JTAK6d8aWA\n7dIjU/jmgq/x7MFX+PnWp/zLnQo5bejwyWq8OSYivKkkhsviQKlQEKrRoXZFUNpRicPtJEStxSv1\n1zxYXSPXGtR2NvD8odeoMNWSGBZPemQKSKBWqmkZECE60HgEgMWp8wYdI1SjI04fQ4fVxP0X3ekX\nTKcyMMIzZYBdd1ZUGh29JrKi0vzLvF6J5/51DICHvrmUt7dWcNGsZPQ6DTeszkWhUPD3fx/nv/9v\nL8/9ZE1QU4CSGlkIVtR30mN1jmskprPbjj5EifosNJ3U6zTMzYtnbl48IRoVr35yAoBW42BDgNOh\n4IRsJLFw+sj29CqlXFtW39LDp/tPsvtoEzNzYv11SmF6Lf/7neUBLm4KhcJ/7mMidPzvd5aPalyX\nLUjzix0g6Ll+a2sFMREhRI7w8Y/Ty8YSzT2tQde7PC621ewhTGvgovQFuNxejlS0B4isX714gKRY\nAw1tPcRE6Cb0O+dCY1SCx2w28+yzz9Le3s6TTz7J1q1bmTdvHjExZ8+NRiAQCAQXBvVtFqLDQ/z2\nzucrCoWC71w/h1c+LuXLl+ZM2N9psbTT1mtkSeo8lqbNZ0b8VH+9zUgRnoiQcLQqDe1WI809bexr\nKCQ7Kp05iTMGbbsqexnH28r8zToBOmxGwvUaLLoyNMBFKYFCwqBT47Ik4dSUc6z1BItS59Bl66+t\n6B1G8NjdDt46/iH/LtuCV/JyccYibp93o+zKpoBEQxzNA1LaDjUeQaVUMS85eApPZlQqRlsn+fFD\nF+jHhkZzxdQV5MZkB7i/bZh3A2tyLiZW3+92tvVQHRX1XayYn8qCaQksOCVl8fpVU6ls6GJnUSNN\nHb2kJ4bT2W3ng13VLJiWwMycWEprZKHpleBoRQcXz00ZcmxjxdTtICL07Dsc3rx2GktmJnH/U9uD\nNqYdK5IkUXiijcgwLTmpo7M2z0wKp7rRzF/ePoohVMMPv75g0OR/PHrTzJkah1qlwO2RIyvGvtoZ\nHy63l1c+KiEp1sC3rhjekj4zKo1QtY7ituBpcfsbiuh2WLh62uVoVRpe/qiEN7dUBG5zvN9dccpp\n2Ix/kRmV4HnooYdYvHgxhw/LBWBOp5Mf//jHPP/88xM6OIFAIBBceHR228ma4DScs0V6YjgP3hE8\nmjBeHG2RndHmJE1HoVBw29wbeHDzE0DwHjwDUSgUcuSj18QHJz5DkiS+MuNLQSeDCoWCuxfeQm1n\nPfV9jUmbLW3ERIbSGteE5FZzw4KLA/YJ1Wmwd8ZDdDkFTcdYlDonwHyg1xl8Qtxl7+bnW56kxdJO\ngiGWuxZ+fZCQSQyPp7GnhT11h6jtaqC2q4F5SflDOlfdueBmrrKsIUY/9ERQoVBw18JbBi1PDIsn\nMaw/JdFqd/HSR6WEaFXcefXMIY+XlxHNzqJGapu7SU8M55WPS/nsQB1vbqkgIymclo5edFoVdqeH\nghOt4yZ4bA43Noeb1JiQcTneWEns6z81HoKntrmbzh4HKxemoRxlxMLn1ObxSnzvq/NIiA7er+ZM\n0es05GfHcrRS7p9jNAcK+BZjL15JNhEYyaBDpVSRn5BLQdMxOnpNxBkCgwZ76g4BsHbKpQCUnewM\nWP/Kw+twujx09zrptjrJSZlcjX4nO6OKg5pMJjZs2IBGI1s1rlu3DrvdPsJeAoFAIBAE4nB5cLm9\nE1pkfaFQ0HSMffWF7O6bCPmiMlNjs1iesQiQIzgjEW+IocfZy+bqXSSGxXPRKYX8A9FpdDy29if8\ndt3PATm6pI0xodA6iHLnEB1uCNjeoFNjM4UTHhJGYdMxvJKXtgHNFYOltHklL7/f81daLO2sy13J\nU+t+HjRqkxwmR1R+v/dvvFu6CYVCwaqcoVOREgyxzEqcNvzJGCWvf1ZOV4+Dr67JHdY6PTu53yK5\ns9vOtoIGkmL1rJiXSlO7Bafby6qF6cREhLDnWDNO1/g08OzsludgYecgwgOyEIgwaGk19Zs2dPc6\n+bywYVSWyccqO7j5Zx9SdtLk770zmnQ2H3l9fYfWLskY16hZMFbM76/rOjXC4zOtcLo82JzB7asl\nSaK+tQdJkpidKJsjHGs9MWi7Fks7Bq2e5HD5fR8T2V+fYwjVEBUeQkKMnqnpUSyYlkBU+LkRu+cr\no67hcblc/jtCHR0dWK3jk7cpEAgEgi8OPlen8epefqFS0lbOr3f9xX/XeH7yzIAIxB3zbiRKFzGs\nePExP3kWR/qiRF+Zvhalcvh7nT7nNrVSTUtPG06D3GNnacqiQdvqQzV4vDAnIZ/d9Qeo6awPMDAI\nFuGp62qipL2C+ckzuXP+TUOmHq3KXobJ1kVqRCJ5sTlMjc3yN08dKydbutle0MCqhWlkJA0fXWxs\nt/D+jioSY/Rcd9nUYbf1O4Y1d/PJ3lrcHi/XrZzKlcuz6eyxU1DayqIZSeh1at7eVsmBkhYumTvY\nCW6smPoET/g5EjwgR3lqmrrZfaSJrYfqKTjRiscrcem8VP7fbYPfKwN5f2cVVrubwrJ2jla25JRB\nSwAAIABJREFUo1DA/LzRm37Myonltz9YcVaiHFcszWTRjER+u7GQo5UdHK1sZ2paFHqdhqYBLn1m\nq4dtBfVsL2wgIzGcrOQI8jKiaeu08vDz+/jvby5lVqosyI+1lQWId0mSaO81BphqDEzR8/UPEpw+\noxI8t956KzfeeCPt7e185zvf4dixY/zsZz+b6LEJBAKB4ALDYpVduwx6IXiGwmzv5um9L6BAQVpE\nEl5J4r6ldwQIg6jQSO6Y/9VRHe/KvNUkhSVQ3XmSlVnLRrWPUqmUa2h6WvGqlOAI4csLFwzaTh8i\nTyPyY2ewu/4ABU1HMVn7m5AGq+HxRYBmJUwfts4iIyqV/1x+16jGOxwf7q7h2XdkB7iOLhsPfGPh\nsNvvLGrE45W4dd10tJrhBUVUeAhR4SHUNJmpbe5Gp1WxaqHcRyY6XMflS2RjhNWL0nl7WyXv76hm\n2eyUMy427+yWC9nPteCpqO/i8ZcPApCTEkmrqZfSmuCOfT7MFgeHSuXC/bKTJkprTExNiyIybPQR\nC4VCQW768DUz44VCoSA2MtQfcfnZX/aQkxLJI99eFuDQ12318NnRKqobzRSe6K89u3xxBiDb8S/O\nn0qkLoLi1hMBpgrdjh4cHqffLRD6vyuBCUvZ+yIxKsGzfv165s+fz+HDh9FqtTzyyCMkJExcvwGB\nQCAQXJhYbPKP+LmK8BxpKcFk7QqaGtXea+SFwje4edaXyYoevvnhROGVvPxp/4t02s18Y851XDN9\nLZIkjRiVGYkFKbNYkDJrTPukRiTR2CMXSa+YspTEmMHRFUPfdcwOn4JKqaKg8RhadX+6YrCUNp/g\nSQiLHbRuPJEkidc+OcEbm8uJMGjp7nVS2dA14n6NbfIkdnrW6IyZspIjKCqX3eRWL0onNGTw1Coj\nKYJls5PZe6yZjZtOcNv6waYRY8FnSX2uUtpATmvz8YcHVpKdEsmjL+xn//EWjGYbsZHBoxK7ihr9\nJgCFZW1IEiyYPvnnlLER/Slm1U1mHvzLbrTq/s+luddDY7uFjKRw7rtxHh/vrWFbQQPHq2UBaLY4\nUCgUzErIY3fdIRq7W0iLTAagvc9FMUDw2AYInhgheM6UUX2DVlZW8tprr7F+/XrWrFnD7373O8rL\nyyd6bAKBQCC4wPCltJ2LGh5Jkvjl53/kLwdf4aPyrYPW/WLb7yhoOsb7ZZvPyng8Xg/bqvfw2I4/\nU29u4vVj7/HHfX/nSEsp85Nn8uXpl6NQKM5Y7Jwu10xf6388Nym4M5pv0ut1q5kZn0dNVz0Vxhr/\nxM3qDCJ4LPIE0NcjaLzp7LHzyd5a/vBGEW9sLicpVs+T969gZk4sje0W7A73sPs3tFvQqJXEj/Ku\n+kCHvtWLhhbK37tpHgkxev65uZy/vleM1yvRZrLy6Av7ufN/Px2TAYCpr5YkXHfu2inO60tBu/2q\nfLL7UsvyMuSoS3ld55D7bStoQKmA5FgDvjr/RWOo3zlXDBSy11yaQ11LD5UN/T116jucOJwespIi\nmJEdw+IZcm+oZqOc9uazlw5Wx+Mz+ogfYGTQaxMRnvFkVBGeX/ziF3z/+9/3P7/hhht45JFHePXV\nVydsYAKBQCC48OixnrsIz8Bi+leK3ubijEVE6iJwup28fux9/6TDOoSz2Hjh9XrZU3+IN4s/9Nsu\n9zgsVJpqAYgJjeLepXcE2CafC/Licrgh/0q21exhfnJwpzK9Tp5G9NpcLEyZzdHWUrySl+XpC3nv\nxKf0ugafy4mO8Ly1pYL3d1YDkJMaycN3X0R0uI4paZEcrzZS09TNjOzg0RtJkmhss5AcZxh12tmS\n/CSef/By6lp7hm0+G67X8tg9F/Pw83t5b0cVRrONxnYLNU2yjfd7O6r41rWzR/U369vkXlbnMsJz\n8ZwUnvvp5STH9Uf+pvUJnl+9eJAfb1jEJXNT8Xi8nDjZycGSFkpqTJTVdbJgegKxETqajb2EhWrI\nTZ/8Fsu+eq0vXZTJXV+ZhVql5J3tlSTE6GkzWalukUVoWoLcXywqIjBFz9wjC55ZPsHTVobNbSdM\na8DmkvdNCEhpcxIZpmXdRVmsWXxuIs4XEqMSPB6Ph0WL+gvQBj4WCAQCgWC0+FPaTrOG54XCN9Cp\nQ5jG8BMAq8vGb3c/zxVTV7AkTW5UWdIm97RIMMTS1mtkf0MRGZGp/OXgyzT3tJEYFk+rpZ3G7pbh\nDn1GnOxq4Om9L9DQ3YxKoWR19nK21uzxi52ZCXn8x4KvEREyOZqy3jz7y9w06+oha218gsfqcLNw\nyhz+fvifACxKncPHFduCRnjae43oNaFBDQg6umyYuu3+SMHpUNUo33XfcOUMrro42x+FmpIa1be+\nixnZMRjNNnYdaWJXUSNhei0/vX0x1U1m2e45fmznPynWQFLsyIYKCdF6nrjvUn759wP+hpYrF6Zx\nrLKDzQdO8vUvTR/xZsCn+09ysKSV7JQIIg3nTvAolYoAsQOQmxHlt+H+2/vH6e518urHpf4bHT5W\nLUzH3BfxmJcXH7Rp62Rj6cwknrjvEqZlxqBQKLjj6nympEWSFGvggad30GuXXdrSEmTnxJgBKXAA\nZosc3U4wxJJoiONY6wkKGo+i1+hYlr6wb12cf3uLzUVKfBi3nmH6o0BmVIInPDycjRs3snTpUrxe\nLzt37sRgOD2nFIFAIBB8cbHY+lzaTiOlrdXSzicV21EpVWRlfWPYbffUFXC0tRS72+EXPMfb5VTs\nby74Go/v/DP/LP6AHoecbnJl3mpumf0VHtvxJ0rbK3G6nQG1KOPFxqPv0dDdzMqsZdw480oSwuIo\n7aikuUeO9NyzZENAHv9kYDhjAX2IPDm32lwkGFKYEpOJydrF1JgsDBr9oAiPJEm09RpJCg9es/Hb\njYWU1hp58edfGlMR+8Dj1zaZSUsI46trAhuQTkmT066qGsw8tbGAzwsbGNg65c9vHWHroXqAMQue\nsRCu1/LIt5bx57eOUNvczbevnc2n+0/y93+X8PbWCm6/Knj6IMCJkyb+8vZRwkI1PHjHEhprB9sb\nn0v0Og1P/3Alv/jrPpo6enn+3WNoNSrWL8ticX4iapWSmqZuLp2bQmO7BUOohsuXZJzrYY8KhUJB\nfnZswPMV89MAiIkIwdRnJJGWKL93ok+xjfaltIEc5dlSvQuQjT0Kmo8B+HvzuNxe7E4P4cLcZdwY\nleB57LHHeOqpp/jHP/4BwPz583nssccmdGACgUAguPDoPYOUNl8/Go/Xw0lrE0N3ZIHddbJzVIWx\nhi57N1G6CMo7qjFo9cxLzmda3BTKOqpIDk/gu4s3MD1+CiAX6pe0V9DU0zruxgVuj5uS9gpSI5K4\nZ+kG//Ip0Zk097QRERJGnH50hfKTBUNof4QH4KeX3ovb60GlVKHXhtLtsARs73ej0scGuFSBnMJz\nvLoDrwRHKzpYNicZ9Rjv/Ld32ei1u5k/bbD1dGp8GEqlgsqGLmqbu4mLCuXG1bnU9llK+8QOMChy\nMd5oNSr+85Z+17srL87mg53VvLejCl2IivzsWHLTo9Bp+6dppm47j714AK/Xy/+7bSlJsQYaayd0\nmKdFSnwY65dn8bf3j+P2SFx9SSb/cU2/Ycb8abLYzUiK4PVHrzxXwxxXrr1sKi98cBzof++EhqjR\nalT+3ktmi8P/np+dOM0veAA6bWYSw+L9TXX9N4ZCRb+y8WJUgicmJoZf/vKXEz0WgUAgEFzg9Nfw\nDP9D7vF62HnyAE09rXTZu+m291BmrPavr7bWB91PkiT21B+ipK0ChUKBJEkUNB5lVfZy2nuNTInJ\nQqlQ8u1F3+B4WzmrspcFRHJSI+RC44bulnEXPOXGahxuh7+BqI+cmEx21R1kSkzWsNGUyYgvXcza\nl6oYoetvhGrQ6GmxtAcIm1aLXL+zr7CLvxqLuXtAzUphWRvevojLr189RGiIiucfXDumSE9ts1wP\nk5UyWPCoVUqSYvT+bS6alcRVF2ez+UAdn+ytDdj2bNeU6LRqvnXdbB5/+RCvfnyib7wKvnfTPJbO\nTMbl9vKrvx/A1O3gzqtn+kXDZGVgJGRJftI5HMnZ4drLplBeVUdUdJxfpCoUCmIiQmgxylFOj1ei\n1+YiTK9lVsI0FCgwaPVYnHKU+YopK/zH81lSn27qr2AwwwqeH/zgB/z+97/nsssuC/olvH379oka\nl0AgEAguQPpT2ob/IX+56G0+rtgWsEyjVHNV3hp21O6jqrd+UITA6XHxp30vsq+hEKVCya1zr+Pl\norc52HSUucn5eCSvP2UkLTLZbwk7kLQIeVlTz/jX8RxtlZt/zkkKFDwzE/JQIN/1Pd/wmxbYBzuf\n6TU6PF4PTo+LkD5RWdslC1WvNZz3d1b7BY/F6uSzA3UB+9scHlqMvWMTPH0GANnJwRtSpsSH+ZtF\npvWlraXE90dzFkxP4I4BrmNnk2WzU3jx51dQWmOipMbEezuq+GBXjb8WBmQXuOtWTjnrYxsrU1Ij\nCQ1RoVQqhzSIuJBQKBRcPi+ShQvnBCyPDtf5BQ/IaW1hei0RunD+c/ldxOljeHDzEwCsyunvkdV7\nju37L0SGFTwPPfQQABs3bjwrgxEIBALBhY3F5kKtUqDTDl1s/XnNPj6u2EZaRDJ3L7qFKF0kkbpw\nQtU6FAoFZns3u+oOUmduJDMqLWC/fQ2FzIifyneXbCApLJ5t1Xs41nqCBrMsYOJHSBmL0smRgVNT\nscaD463lKBVK8uNzA5ZnR6fz9FW/GHFskxGDL8Jjdw1ap9fKVrq9Lqtf8FSbZFHj7fXV03RRWNbG\n29sq6bW5yEmNJCE6lH3F8vVyur1jGo/PvSwjKTzo+pR4A8i6019cPrBeJysp4pyIHR/R4TqWz0lh\n+ZwUjlV2UFnf3zdo9aJ07r9p3nkRBVSplPxkwxJUSsWY0xIvJKJPdWqzOEnrC85dlC6nND665ke4\nve4AEw+fuYtBCJ5xY1jBExcnu0U88cQT/OEPfzgrAxIIBALBhYvF6iQsVDvkpK2uq5HnDr2GXhPK\njy75DslBitvnJ89iV91BDjcfJzUiGbVSFk9lxioA7l74dZLCZHvgRalz+VfpJ2yt3g0E9rkIhi+H\n3tpnEzteOD0uqjrryIpKI1SjG7TeN97zDX9KW5AIT1if4Om2W4gJlVPEqjvrUCnUSDZ5cvfA0zvw\neCXC9RruvDqfKy/OxuH0AEXsK27x1z+Mlo4uGwoFQza9HChuUvvsgyMMWgyhGnptLtITgwulc8Gc\n3Diqm2THOV9jz/OJ86GZ6EQTHS5/1n3W1eYBxgU+8uJyBi3z9Ss7HXMXQXBGJbszMjJ46623qKqq\nor6+3v9PIBAIBIKxYLG5hr1r+a/ST3B53dyzZENQsQMwN1l2sdp49F2+9d6POdoi37KvMp4kVK0j\nJaK/ieHi1LkAHGgsAiBuhGaX/YJnsJ3ymVBtOonb62Z63ORPRxoLhlA1SoVcUH8qvp4i7Va5v5HT\n46Le3ESMOh7f9EOrUfK1tdN4/sG1XL8qF51WTWRYCLOmyDdcxyp4jF12osJC0KiDT29S42SRo9Oq\niI2UJ6MKhYKUvkLz9MTJYQcOMGeqfA4SY/RkJQ+uSRJMfnxObZl9EcdggicYFpHSNu6MyrTgo48+\n8hd/+lAoFGzZsmXCBiYQCASC8x+3x8trn5ygvK6ThrYezBYnyUP0K+m0mdlXX0h6RLJfqAQjIiSM\nNF0SDfYWrC4bv9rxJ74x5zoae1qYlTAtoGFnTkwG0bpIOu3ynfKRIjw6TQgKFNjGWfCc6JCjT9Pi\nLyzBo1GryE6NpKK+C6fLg1YjR9u6e50onPJ1brW0A1DbWY9H8hKulIXsvTfO5eK5KYQHuYvtO47D\nNfqUNkmS6DDb/A0ig5HSF+FJSwgLiDLOmRpHR5eNzKTJIyxmT4ljWkY0qxamnRdpbILBrJifRm1z\nNyvmp3GwpJX2rtF9r5TWmACICh+7NbsgOMMKHovFwjPPPENeXh6LFi3i9ttvR6MRalMgEAgEo6Ps\nZCdvbe1r+BkdyoLpCVx9cXbQbd8t3YRH8vKl3OBGOQP5StJqsqZlY3PZ+c2uZ3nlyNsATI3NCthO\nqVCyMHUOm6t2AiPX8CgVSkI1OnqDNMw8E3xRqGkXWIQHYGZOLFUNZirqu5iZI0d1Xvz3cbaX1qKe\nITuzSZLEm8f/DUCENxXwMjU9KqjYAQjRyKJVTm8bmXc/r6KkxojL7SUucnDKoI+4KB1rl2SQf0oh\n/YYr87l1/YxJVW+iC1Hz5PdXjLyhYNKSHGfgxxsW09YpGxe0mqwj7AGHSlvZUdTI1PQo8rPOv7q+\nycqwn+yHH34YgJtvvpmqqiqeeeaZszEmgUAgEFwg+FKd7r52Fn976Ap+cfcyFgexqT3eVs7HFdtI\nCU9kZdayQetPJUytJzMqjenxU/nl2h+TEi6nseXFDs6HX5wqOyeFaQ3ogtTPnIpeEzquKW3FrSco\nbisjPz7XX8tyITGzz4K4uLrDv6zZ2IurVz7XrZZ29jcc5khLKXOT8tE5UgCGFDvQH+EZTUqbxerk\nlY9L2XusGYC4Iep3QM5Ouf/m+Vy+JDNgufILXlwvmFhiI0NRqxS0GocXPFa7iz+/dQSVUsH9N81D\nJd6T48awEZ7GxkaefPJJAFasWMEdd9xxNsYkEAgEgguEzh5Z8MRGDD0JtbnsPLP/JRQKBfctvSOg\nL85oSAqL51eX/5hjbSdYkDJr0PqZCdMI0xpIj0wZ1fH0mlA6rKYxjWE43jz+EQoUbJh3w7gdczLh\ni+ocrzLC5fIys8UBXjUGtYH67mZeOvwWaqWaby64mecr5X5Kw3WRDxmD4NlaUB+wXVzU0O81geBc\noFIqSIjW02LqHXa7lz4soaPLxtfWTjvvTComO8MKHrW6f7VKNbSFqEAgEAgEwejqkYt0h8tFf6no\nLdqtJq7PXzcoJW206LWhLE2bH3SdVqXhsbU/RqsanZDSa3TYXHa8kjegHuh0kCSJ2q56UiOSyInJ\nHHmH85DIsBDSEsI4cdKEx+NFpVJitsguU5HaaJqsDQBcn7+e5PAELNYylEoFoSFDT0FGivB8XthA\nRlI4WckRfLL3ZMC6WCF4BJOQpFgDhWVt2BzuoO/949VGPtpTS3piODddnhvkCIIzYdhv8lNzqEXR\nnEAgEAhGg83hZuOmEzS2y/1sTu1H8fyhjTy5+/8obCpma/VuMqPSuDH/qgkbT2JYPNGho7tjqtfq\nkZCwu0fnqDQcvU4rNpedxLC4Mz7WZGZmTiw2h4fqJjMer0RPn61uuFo+5/GGWK6bsQ6AHquTcL1m\n2DlFiN+0YLDgMVscPPlaAfc/tZ2SGhP1rT0BFsjD1fAIBOeKxFjZpn2oOp5/ba8E4P6b56FRiyDD\neDNshOfw4cOsXLnS/9xoNLJy5Up/d+vt27dP8PAEAoFAcD4hSRIOt4ONmyp59/Mq/3JfPwofn/WZ\nCJS2V6JSKLlv6e2oVaMyDp1w/NbUTpv/8enS1ivXtSQYLmzBMysnlk37TnK82kh8lB6fqWukKgE4\nzp3zb/I3H7VYXYSFDh9t0w4jeIzmfgvsD3bK6XE3rs6l8EQbMHQPHoHgXJIUIwueFmNvUJvxVpMV\ng07N9ExhVDARDPvr8sknn5ytcQgEAoHgPMDl9vDbjYXMmRrH+uX9bmuSJFHQdJQ3iz+kvruZ2d5r\n/Ot0WlVACofX22813OOwsDrnYjKj0s7OCxgF+j5jg/EwLmjtEzwXeoQn31fHU21kfl5/tCVLPZfb\nrlpFYl9jVUmSoz9JfXe7h0Lb59LmDGJL3WHuvy67jzaRlhDGrJxYvrFuOgdLWoiPFoJHMPlI7LPj\nr2k0c9Gs5EHrO7psIh1zAhlW8KSmpp6tcQgEAoFgknGivZL/O/Qaa6dcyrrclSgVSjZuKmPXkSZa\nTFa/4KntrOcvB16hpqu/IXW7ugTIAgZHd3qcFv9jhULBtdOvmPDXMhbGs/loq+WLEeFJiNaTEB3K\n8WqTv24LwObw+sWO/NyNxyuN2EE+RCNPT4LV8AyM8ACsW5aFQqHga2un8bW1087kZQgEE0ZuehQa\ntZKNn5bRZXFwx9Uz/TeC7E43FpuL3PQLz8VxsiD87gQCgWASs/dYM3f98jNajMO7+5wpR1pKeKXo\nbfbUHaKj14Tb6+G5Qxtp7G7hxcNv8uj2P7D1+DHe2VYOQEdnvxh4qegtarrqWZ6xiKfW/Tcp4Yk0\nuStALddxnGpYYLb3ALKF9E8vvZek8AQmEwaNHH0YD8HT1msEIMEQe8bHmuzMzImlx+rk2AB7amtf\nx3gfFqv8fDiHNuiP8ARPaeu/Llq1ktWL0k97zALB2SIhWs+v77uUjKRwPtpTy/ef2k5lfRcApj4R\nLxwGJ47JkTAtEAgEgqB8sreWVpOVzw7Ucdv6GWd0rHpzEynhiaiUgQWxXq+XZw68TKfN7F+mUapx\ned1EurKJj9VQ3FZGcVsZmplhaHuy6GpIxOHyEKJR0dTdSrwhlh8s+w8AVmYvY+PRd1FFGPGYkvF6\npYC/12XvBmBecj7zkmee0WuaCHwRnvFoPtrmi/Bc4CltIAuebQUN7Dna7F9msQcKHr+ZwYgRnqFd\n2nyTwxlZMSydmTTisQSCycLU9Ch+94PL2LjpBO9sr+TpNw7zx/9a5U/TFPVnE4cQPAKBQDBJsTvc\nHKuSJ8yfFzZw67rpp+2WWdxaxiPbf8+i1Lk8sPzuANFztPUEnTYzS1LnkReXTXlHDa2WDloaNLSU\n59DmVZM2NYkWqQx1TDtufTHakBaMXeuIidbQaTczJ7FfjPmagKKRU5u6+ya5PnwRnsiQwYW7kwG9\nduganuaeNtp6O5iblD/sMdweN7vqDlJlqiUyJBydemhb7gsFXz+e+tYe/7LeUyI8nX3pbpFhw5+P\nflvqwTU8vpS2X3xr2bDW1gLBZESrUXHH1TOpa+3hYEkrTe0WOrr6+pUJh8EJQ6S0CQQCwSTE5nCz\nrbABl9uLSqmg1WSlvK7ztI+3vWYvAIcaj/D8oY1IUn/U5fNaed0109dyzfQr+K9Lvs2l+q/RVTqN\ni2akEx0RSl2FnsSeS3nmql8RrUpEFdVBRUsTLT3tgNz804fP/lmhlX/ET3UkMjvkCE+kLvy0X89E\nMlwNzw8//gW//PyPdA2Ihg1EkiQ+Kt/KvR8+xDMHXsbudrB26ooJHe9kITU+jKhThIzV7g543tYp\nW/ImxAxvWqBUKlCrlDhc7kHrjGYbep1aiB3Bec3y2bJxwd5jzf40TZHSNnGIbwuBQCCYJHT22Nm4\nqYxDpa10dPVPtlctTGfzwTqaOnqZdhqWpXa3g/2NRcQbYgnXGthas4cIXThfn3MtIFtDR4dGkhvb\n77p2sKQVgHtumItCoeD9nVWsXpRObFg4s6IWsNP4MfubDhESNR2ApPDBgkcV4uTuG+awYl6gAU5X\nX4QnSjc5IzzBang+qdiO2+vGI8kRhwpTLYtT5w7at623gxcPv4lOHcLVeWu4ctpq4vRfDJtZhULB\numVZvP5ZWd/zwRGetr4eJAmjcFIL0SiHjPCIO+GC853F+UkolQoOlLSQnSJ/Z4r39cQhBI9AIBBM\nEh5/6SAlNSaiwkKYmxtHemI40zKiUamUbD5YN2jyOFoKm4pxuB1cmrea9bkr+fmWp3i3dBNx+hgu\ny7oIk62LWQnT/Olydoeb4mojOSmRREfIP8AbruxP4VqSOo8dbZ9y0LSbozuOghqSwvqNB6J0kSCB\nWufgygHW1T7M9skd4TFoZcHT1COLPq/k5R/H3sPj7a8nqTDWBBU87b0mAK7MW83XZl8zaP2Fzs1r\n89heWI/d6UGtUmI55T3ra7qYOEKEByBEqwowLTCabdz/1HYsNhdZKZNTLAsEoyUyLISUOAP1rT3+\nOjRRwzNxCMEjEAgEk4TqRjPpiWH88YFVqFT9GceHy+SGiqcteJqPAbA0bT6Rugh+tvJ+fvTJo7xb\nuom82BwAYkJi2FZQj9cr0dhuwe3xBnSvH0haXAzOynlopxzFqZZTuwZGeNRKFbhDUGgcAft5vV7+\nVvg6n9fuAyBykkZ4ksMSyI5O52DjEYqaS0gKi8PmCrRCrjDWBN3XZJNdl+L00RM+zsmIWqXkmf+3\nBqfLw0+f2TWoq3x7pw21SjHIqjwYWo0qwLTgQEkr3b1yPViwxo0CwflGUqyBhjYLtc3daDWqEd0L\nBaePqOERCASCSYDV7sLu9JAQrQ8QOwCGUPlH8NS75aPBK3kpaj5OZEgEz26s5Uh5OwmGWJakzaPD\namJHn/jYV9DNbzcW8vvXD/PmlgoAFs1IDHrMuKhQvOZ4nJX9EY4jxb2cbOnG65WQJAmvMwSv2hZQ\nK/Rp1Q4+q9rpfz5ZC/mVSiXfXXwbKoWS5w69Rkl75aBtKo21AREfHx1WOcITE/rFFDwAGrUSQ6gG\nQ6gGq13uu+OjtdNKfJQepXJk841TBc+RCrle7IdfX8A31p2ZY6FAMBlI6ot0tpqspCeGnbYpjWBk\nRIRHIBAIJgG+Zo3B7nyH9Qme04nwVJvq6HZYyAubzZFqE398s4i//Hg1F2cs5vPaffy7fAsAPV0h\nrF+eRW5aFEqlgsiwEPKzg9eehGhUzMiKIUyfSH23mw5LN88eOA4cJ1yvITcjGskTgmToxuqyYdDq\nMVo7+cfR99CoNLg8pxepOptkRafzlRlX8E7JJ7xU9Oag9Q6Pk+aeNtIiAzumm6xyhCdWLxoIGnTy\n+9ZmdxGm1+JweejqcZCZO7pURq1GhaOvhsfrlTha0UFcpI6VC9LExFBwQZAYa/A/Tk+cnCm+FwpC\n8AgEAsEkwNQtp0xFRwyOepxJhOdEhxydUFvlaE2rycq/d9Xw5RXTiNRF+OtpojTRfOe6OaO68w7w\n6+9diiRJ2BwLqW4009BmoaTGyJGKDgpPtKHJkoWbydaFQavnhcI3sLntfHvRN+i0dxOFKI4CAAAg\nAElEQVQ9SdPZBnJD/pXsbyiisbslYHlmVBonuxpo7GkZJHiMNtlJL/YLmtI2kIHv2zC9lnafQ1v0\nyPU7IAtrp8uDJElUN5rpsTpZvChdiB3BBcPAWrYMIXgmlAkVPAcOHOD73/8+ubm5SJLEtGnTuOuu\nu/jRj36EJEnEx8fz61//Go1G5CwKBIIvNp3DRHgMZxDhaTDLTSBNrRrUKtBp1byxuZw1izNYn7uS\n14+9D0BiWNyoxY4PhUKBXqdh1pQ4Zk2JY92yLArL2vif5/YiOWXh1mkz09zTxsHGI8yIz2VVznKU\nivMjm1qj0vDdxbfx31ueRKvW4nDL12hu0gxZ8JwihACM1k5CVFq/09sXmbC+egSL1QWx0GIcnSW1\nD3/zUbeXD3ZVA7BsdvJwuwgE5xVJsULwnC0m/FdnyZIlvPzyy7zyyis89NBDPP3009x22228+uqr\nZGRk8Pbbb0/0EAQCgWDS0N3r5PGXD/L+zirsjv4eI519EZ6YiMGCR61SotOq6LWfhuDpbkGlUFJf\nL5GVEsnNa6fRa3Px+mdlfGnqZf7t4iPDTuPVDGZKqmyvKjnl1/F57T7+Vvg6aqWaby36+nkjdnzk\nxeXwwMXf4seXfMffrNXXZDWo4LF1EauPFlEIINIgi15zrywUi/ua6Oamjy7dT6uR3ysNrT18XthA\nemIYS/KTJmCkAsG5YWCEJz1JCJ6JZMJ/eQYWrIIc9Vm1ahUAq1atYs+ePRM9BIFAIJg07C9uZveR\nJp5/t5hvPvoZ//i0jB6rsz/Cc0pKW01nPU/v/Rt6w9gjPJIk0dDdTIwuFrcbctOiuOribJJjDXy0\nu4Yus5fvzr4X+7GLiR2nhneRfY0nPZ2JhKui2XnyAJ02MzfNuprUiPNzsrokbR6zEqeTYIgFYFrc\nFDRK9SDB43Q76XFYRP1OH5FhstWu2SK/t49UdqBWKZiZHTuq/bV9EZ43Npfj8UrcuDpvzFFIgWAy\no9dpiAzTolErSYwxjLyD4LSZ8Bqeqqoq7rnnHsxmM/feey92u92fwhYbG0t7e/tED0EgEAgmDXWt\nctPNlQvSOFTaysZNJ3hnWwV2p+xGdWpK24dlW9hdd4jw6CX0tvS7pkmSxN76QjKjUoMKCYfbycmu\nBqwuG4reOABm5sSiUSu5/ep8Hn/pIP/cXM6S/CQkWzhx493wzqPhkvAbcMWcYFHqHBakzB7f458D\nvjxtLW29HYSotSSHJ9LY04okSf5ojs+S+ovs0DaQCF+Ex+LEYnVS1dBFfnYsupDRTT18KW17jzWT\nEKNnxfzUEfYQCM4/br58Gk6XB5UQ8xPKhAqezMxM7rvvPtavX099fT0bNmzA7e5P4Tg1+jMUBQUF\nEzVEwSgQ539yIK7D5OBMr0NxuZzWszTHy7Ip8RRU9vJ5cbd/fW1VCU0n5eC7JEkUNsg9dJzaViy2\nGA4dOoRCoeBgVzFbO/aRoktgYeRMQpRasvWpnLQ1UdJTRbmlFqckR4S62jVMS9Oh97ZQUNBKiCSh\nVSsormhG45X/ttnYREFB1xm9Nh8pMRqaTC66WrpZETcdqdlJQfP4v3/P9mcimlCiSaegoAC9R67p\n2b5/BxEaOR2wztoEgNNs/8J8Xod7nS3tcmSnrKoOS1cLkgTxBteoz01XZ6f/8aIcLUeKDp/ZYC9Q\nvijvtfOB07kWKfrT31cweiZU8CQmJrJ+/XoA0tPTiYuLo7i4GKfTiVarpbW1lYSE4I3tBrJw4cKJ\nHKZgGAoKCsT5nwSI6zA5GI/r8MzHnxITEcIlyxYDsPwi0L9fzLufVwGwbOli/7ZNPa1YqvoaN4Z1\nIUmQP2sux40lbKvcL29jb6PJLjcmvTRzCTubDgAQGxqD0Sb3hJHsYTzwrUtIjhtggbpzO/UtPejC\n4gAzixfMZHpmcBvqsfJ4np33Pq/ia1dMQ6edmJ+Zc/2ZqCpu4sTxGmKzEpiTJNf09Na6oQlm5eSz\ncOqF/3kd6Rokt1t44bMt6MOisXiUgJH1l80hf5QpbUeajnOwopKo8BC+eeMl/oiPoJ9z/TkQ9COu\nxeRgKOE4oTU8H3zwAX/6058AMBqNGI1Grr/+ej755BMANm3axKWXXjqRQxAIBIJJg93hpq3TNqjf\nwhVLMwOeW502ilvLeLd0EwBKhRKH0gxqJ4/98zOe3vM3tCoNV0xdEbBfpbEWvSaUO2fche3IChyl\ni/F0xROnzAgQOwApcWE43V7K6+S76HGR41PDA3Ja3h1Xz5wwsTMZ8KURNnQ3+5cZrcKSeiARffVc\nXRYHRyo6CA1RkZcx+nMT2pf6du2KKULsCASCM2JCf41Wr17NAw88wC233IIkSfx/9u47vur67v//\n43P2yTkne09IIIQRVgABUcRVrVrHr/Vq66htbb1aWzvs8upl59VxaVtr9Wtbr1qtvVqrVi+Le4EI\nAjLChpC9yN5nz8/vj09ykpAACSSM8Lr/4zmffRLkdp683u/X+8c//jFFRUV897vf5bnnniMzM5Mb\nb7xxMh9BCCHOGo1tLmDkAnM5aQ4+/ZEikuMs/GnHM7xV9X50n17RsXr6CtZVf4AhpYEypR4lHOQ7\nF32JWcn5vFv1AWFVm//T5u7ArkviD389AqpKRE0i4Exi0YrsEc+S2R+ADtV2oVMgwTFy/R9xbFkO\nLfA09bVGtw2uwSNNCwBsFgMGvUJNUx8dPV6WzE7DoB/7v7NetjQHvU7h2ovyJ/EphRDng0kNPDab\njT/84Q8jtv/5z3+ezNsKIcRZaaBhwdDAE4lE+OG6XzM7fSYXzLqcP/9rEwnWOC7Ou4D8xFwKk/JR\nVZX11Vsw5lQAEKyfRZphOg6znesybuGFQ6+gj+sirEbo6oREh5lv3bqEF9dXsu1gC0vnpI14lsyU\nwYpPvMOCfhxfRAVkONJQUDjiHOzUJhWe4RRFIdZmoqPHC8CCmSnjOj81IYabLy+cjEcTQpxnpu54\nAyGEOMs0d7gByEoZXPOmtqeRw53VHHG2kmiNJ6xGuKbwMj5WdMWwc6eb51Ht30u4N4lQyzT+771K\n7vm3RbQ2mom4EtDHafN1TKqNh+9dQ6zNxMyceA5Ud7KwcOQXzczkwWdYPOvEcynFcGaDiWRb4rDW\n1F2eHll09ChxdjNdff0Lts5MPsNPI4Q4X8k/6QkhzlvBUPi03m8g8AydT3OwvRwAV8DNX3Y9j4LC\nhblLRpybr19GsGk6yX0ryEy2s35nI529XvZXd6IGBoejpToSiLVp65+YjHoWzUoddRHMzCGh64bV\nBRPzAc8z2bHp9Pj6cAe0xhKd3m4SY+Jl0dEhBhYfjbebyUuPPcNPI4Q4X0ngEUKclw5Ud/KJ+17l\nL68eJBIZW4v8U9Xc6cJo0A1rEHCgrTz6OqxGWJQxd9QhUZ+4ZC4XplzGTz+/hhsvmUEoHOHR5/fQ\n1uXBbhwML9kJYxs2FGszMSsvgYsXZZGXIV9ET0Zm/zyeA23lPLDx9/T5XSTLcLZhYvsXH50/I1kW\nDRVCnDEypE0IcV46VNtFOKLyz3UVtHV7+PonF2E0TG4nqOYONylJRp4ofQZXwENYDbO/9TBxllh6\nfdp6OLcuuGnUcxMcFr51q9by9NIlOfztjTJ2HNImzF+5eBavtGntqGekj5yvcyy/uufiMa+HJkYa\n6NT27L61NPR3a4szS3gcKq6/U9v8cc7fEUKIiSSBRwhxXho6n+b9XUfo6vPx/TuWYY8xTcr9nJ4A\nTk+QtBl9vF21edi+jxZeitlgwm6ykR2XccJrmYx6rrson7++fgir2cAVJbN45XVt35zs8a1GL8Ov\nTl5WrBYuG4a0prYaLWfqcc5KK4szaGx1sqL4xH+uhRBiskjgEUKcl1o63SgK/Oqei3jk+d1s3tvM\n3986zBdvKJ6U+w0ELJ2tD8Lwn6vvYXpCDnqdnhjj+NfA+ejKaby2uYYLF2SSah9sg5wZN7ZFHcWp\ny4od/iX+Y0VXcNWMS87Mw5yl5hUkM69AmhUIIc4sCTxCiPNSU4ebpDgr9hgT9366hC37XqG2qW/S\n7jcQeHy6TvQRHUUpMzDpjSd9PXuMiT//55XReRFxllg8AQ92k+0EZ4qJEmu24zDZcAbcpNmSjzkc\nUQghxJklTQuEEOedQDBMZ6+XjCQtHJiMepJiLbR0uSftnm3dHiBCd6idnLjMUwo7A4ZOAr8odykX\nT1suQ9ROs8z+eTxZYxiKKIQQ4syQCo8Q4rzT2uVBVYe3h05LsnGwppNgKDwpzQu6nX4Uq5uQGiI/\nIXfCr3/7oo9P+DXFiWXFpnO4o4qcWAk8QghxtpIKjxCCzl4vr22uOW3tmc+00dbDyUiyoarQ1u2d\nlHv2OP3obL0A5CdOfOARZ0ZuXGb/f8fXLEIIIcTpIxUeIQSPPr+HHYdaCQTD3LB6xpl+nEl3uL4b\ngKyUwcCTnhQDaGEoa8iinBNFCzzaHKH8hLwJv744My7LX4VJb2RFbsmZfhQhhBDHIBUeIQTdTh8A\nm/c2n+DIc184HOGdbfXEWAwsKkyNbk/vn8/T2jk583h6XD4MDid6RUduvFQDpgqzwcTlBRdh0E3u\nGk5CCCFOngQeIQQ5qQ5AW4xzqi9EubOsja4+H5cszsZiHixyRys8nR7e2VbPezsbJvS+3U4vWPrI\nnqCGBUIIIYQYGxnSJoQgEApHX9e1OJmWMXVXi3/r0HbMxRspKioYtn2gwtPQ6uRf71dp25JtFOUl\nAhCJqPiDkXHf79l3DrN+RwNutQeLLjwpDQuEEEIIcWxS4RFC4PMPBp6fP7WNzt7Jmbh/Nqh070dn\ndfP7/f8PT2Dwc8bZzSTFWdhd0R7d9ttndhHsD4NrN1bz4ItNNLW7xnyvN7fW8b+vl3Gk3T1k/o4E\nHiGEEOJ0ksAjhMDrD6HTKXzispk0d7i5/4+b6XX5z/RjTbhIRB0Wckqb9w/bPzMnPtqpTqdTONLu\n4p/rKgHYWdZKKAwb9xwZ071KD7fx2At7GFgqRzF7AMiW9VqEEEKI00oCjxACrz+E1aTntqtnc/3F\nBTS0urj/j5txegJn+tEmVEuXm4jRE33f5u4Ytn9mTkL09Y/uXE5irIXn3imnsc1JZUMPAB/ubznh\nfWqb+/jlX7aj1yl85/alACgmrTFEkjX+lD+HEEIIIcZOAo8QAl8ghMVsQFEUPv+xuVy9Yho1TX38\n7tldU6qJQXVjL4rZi75/+mK7u2vY/pk5WhjR6RTm5Cdx143FhMIRfvGX7bi8QQAqGnpOOOTvsX/u\nwesP8Y1PLubC+ZlAJBp4EiXwCCGEEKeVBB4hBD5/GGt/xzJFUfj3m+YzNz+Jrftb2LJv6rSqLjvS\njKKLMC12OgDt7s5h+wcCT3aqHbNRz4riDJbNSae+xQmAw6r9lVnev47PsdS3OslJs7NifhoPb3kC\ny+J16GKcmHUWTAbTRH8sIYQQQhyHBB4hzlMbSht57p1yALz9FZ4BOp1W6QGtjfNUUdWuhbf8pCzi\nzI4RgcceY+KemxfyxeuLAS383XVTMRaTtsbK7BytdXV797ErPB5fELc3SFKCiQc2/Z4P6negGEIo\nxgDJMQnHPE8IIYQQk0PaUgtxjnnqlQOkJ9m4asW0Ufe7vUFs1uHrvITCEb736CbmFSRxx7VzeXlj\nNY+/tA+AjyzPwx8IYzUN/+sgzm4GtJbVe1oO0upqJzkmkXR7Cim2JIzn4FoyzX0dYIWc+DRqepOo\n7WkkokbQKYP/9nPFBXnDzklNiOHujy9g4+4m5maG2Vbuou04gae92wv6IM2x6+hraSElJpF2jzZ0\nLtWRODkfTAghhBDHJIFHiHNIr8vPC+srMZv0rFqYhf2oYPPqBzX84cW9ZKXYKClKY8nsNBYWpnCg\nupPD9d1UHenBoNfxbH9lB6DqSC8AFvPwleKNBi0E+ENB/nvjU4Qioeg+BYXZKTP4wSVfR6c7NwrF\n/mCYvmA3BiDVnkyKLYnKrlp6fH0nnFdzSUkOl5Tk8N6mbQBUNvbw67/t5JariqLr9wxo6/Zgyt9H\nH22syCnh43M/yr1v/BSARKtUeIQQQojT7dz4piKEAAbDiT8Q5t3t9cP2ef0hnnmrDJNBR2evj7Ub\nq/nB41t4YX0l2w5qncVCYZVn3yknMdbCDau1hTerGrXuY0dXeIwGLQD5wm5CkRA6Rceniq9nzfSV\nJMckcLC9gmbXuTPc7UibC6zaXJwMRyoptiRg5Dye47FZdBgNOg5Ud/JeaSOvflAz4pjWbje62A7i\njUl8bfnnyHKkR/clxUjDAiGEEOJ0k8AjxDlkIJyAVs0ZWDMG4O1tdfS6Anz80pn8/adX8193rcRm\nMfCv96vYsq8Zq9lAYqyZ5DgLv7j7QpbOSeu/5kCF5+jAo/314Iu4Abim8FJunHMVX1p2G9fMugyA\nmu6GyfuwE6yuuRd9bCcxOjvp9hRSbdrwsrL2qjGd3+dzUu6uITneEt22u7x9xHE1nUdQ9BGmxeWh\n0+mGVcDiLbGn+CmEEEIIMV4SeIQ4hwxUeBbMTKa5w82u8sEKy0BwWV2SjdGgZ0FhCpctzaXH6ae9\n28vSOWn87t41/P57l5GZbCcrxQ5ow7OAaJe2AUZ9f+BRtcCTYI2L7puekANATffwKtPZKByOUH2k\nl3UHD6AYg8xImIGiKCzMmIfNaOXv+15iU932E17npUNv8q+WdQSztwFa0Kxt7qO7zzfsuEantjDp\nzOS8oy8BKKf6cYQQQggxThJ4hDiHVDX24Igxccc1Wge1VzYNDqlq7/aiKJASb41uu2bVdGIsBhYV\npvDFG4qJs5ux9A9dS4y1YDXrae3SFuI8eg6PTqeg1ykEVG3/0MAzLX4g8JzdFZ6nXzvIp+5/ja/9\n5j32t5YBsCxH68CWakvi+6vvwWIw8+iHT7G1oTR63rP7XmZt2dvDrlXRqf2s3aZGdLGDw+B2Vwyv\n8nQEtOGD8zILott+fOk3WZQxl5W5JRP46YQQQggxFtK0QIhzhMsToKXTw8LCFGbkxFOUl8DOslaa\nO9xkJNto6/aQ4DBH594AZCbb+d8fXzVs2wBFUchMsUcrQ0fP4QFtWFtA6Q88lsHAYzVayHCkUtNd\nj6qqKMrZWbl4c2sdqgoXLYtnn66BkKpnWd686P4ZSdP4/sVf5WcbHuHhLU8QioSYlVzACwdfw6Az\ncGn+SuwmrSlBj68vep4+oRVjTgWB2tnsLm9nTUlOdJ+bDlAhP2Fw2+yUmcxOmXkaPrEQQgghjiYV\nHiHOEdVNWjApyNKCxzWr8lFVeG1zDeGISkePl5SEmBHnjRZ2AA62VWBJbQElAoycw6OdqyOkaC2Y\n44dUeADyE3JxB728XrGe77/zAPU9R6L7GnqbuPvl7/PK4XdP4pNOjGAoTJ87wIxcO21xG/FHvHy+\n5N9GzKMpTM7nvou/glFv5Hdbn+TuV/4TgFAkxLbG3drrcIg2Tycxem3+jj61AZ2tF+v0cnaXt6Gq\ng3OpwkYX+rAdsywwKoQQQpwVJPAIcY4YqMQUZGudvi6cn0m8w8w72+pp7/YQjqikjhJ4jtbp6eah\nzX/iR+t/Q7VhA+Y5W0CJYDWPDEZGg46QbmSFB2BRhlYpeWrX81R01vD9dx/k5xse4Yfrfs1/vvsg\n7Z4u/u/g66f0mU9Fd58fUOlK+JD63iNcWXAxlxdcNOqxRSkF/PKK75HpSBu2/d2qTQTDQdrcHaiq\nSn5MDkadgYGClhrTRU+kmfpWrfub1x8EfRATlqNvIYQQQogzRAKPEOeIgeYCBdla8DAadFxakoPL\nG+T1zbUApCZYj3U6qqryWvk6vv76j9nSsJOZidOY7ihAZ3Ois3ePaFoAYDDoieh8mA1mrMbhX+IX\nZ85DP2TBzmA4yO6Wgxxqr4xucwbc9PmcJ/2ZT4Yv6OO+t37JX/f+E0NmFd1KLXNSZnLH4puPe15m\nbDo/uOTrZDnSuSx/FSWZxVR01fKT9b+NfqZEYxyZsVqbaVP/wquGzOpot7aOPheKTsWkO/bvQQgh\nhBCnl8zhEeIcUdXYi81iIGPIQpeXlGTz4nuVvPie9oV8aMOCo7106E2e2fcvYs12PrfoZlZPX87m\n2t38blsVxvx9/E95GU7rNVxRcHF0To5RryNi8JEwSjtlu8nG3NRZ7G09xJeX3c7y7EUoig6j3oBO\n0fHiwdf5x761HGgvZ0XO6Zus/9yBV6nqrqOKOgxZYNM7+ObKL2DQjT60b6jEmHh+c/UPUBSFQCjA\n77f/lQ/qd1De37AgwRRHxKyjrqeRksz5dLh6qKCKLZVlXH9xAe1ObZ6PVS+BRwghhDhbSIVHiHOA\nPxihqcNFflb8sAYB0zJiyUlzRN+nJI4+pM3ld/OP/WtJsibwyyvuY03+SnSKjsXZswHQmX24Qk7+\ntPMfPLTlT3iDWqtlgwHQ+4d1aBvq5nnXcmXBxazMKcFitGA2mND1V33mpc4CYF/r4VP+/GPl9Lt4\nrXwdjv5GA4oCH8m6gViL4wRnDhr4+ZoMJu5Z/jk+Wfwx1P421InGWHJiMwAoTJrOzfM/CkBVYCfB\nUIR2pzbsMMYogUcIIYQ4W0iFR4hzQHN3EFUdHM42QFEUPnvtHH7yxIcAx5zDU95Zg6qqXDJ9Bcn9\nC27C8C/mcxLmEtH72NpQSkNvE99YcSeupJ2gQJYjfdTrFibnU5icP+q+/IRc7dmdrWP/oKeorqeR\niBrhsoJV7K/s4mClkwXLik76eoqicNOcq5kWn83B9kpSgonMyC+ky9vD6mnLsZlicCgp9MU3s+nw\nYbrcWoVnoLObEEIIIc48qfAIcQ5o6gwAMDMnfsS+pXPS+a+7VvLxS2eSmzZ6JWNgDZnC5Okj9n1i\n5ieI06XytVW384M13+CjM9dwpK+Fb735X3hiaoi4YvnU/BvG/cwGvQGHyUaPt+/EB0+Q+t4mACIe\nB966fMKt00iMO/UGAoszi7l1wY0oikK8JZbPl3wSu9mGoiisyV6DosAb5Rvo8bgAiLXaT/meQggh\nhJgYUuER4hxwJBp4Ekbdv6AwhQWFKcO2ba7fwQsHXuO2hR+PBp4ZidNGnPuJxZfyicWXRt/fsfhm\nZiRN48nS59A502kpm47lJOekxFvj6PR0n9S5J2OgNfZzrzSjerXwlxhrntR7XjV3KWsbnqPd20aC\nMRmAeIsEHiGEEOJsIYFHiHNAU1cAR4yR9KQTt532Bn08Wfoc79VuAeDV8nep6Kohw5GKwzy2L+Kr\n8pZxYe5SfvLEh7REWgmGwhgN4y8Ix1tiaehtIhAKYDoN69LU9R5Bp+hQfYNDyo61DtFESYq1oQbN\neJU+nP7+Ft42CTxCCCHE2UICjxBnsZZON999dCPdrjCLChOHNSwYTVNfC7/c+BgtrnbyE3LxBL3s\naTkIMO5OaYqiRENOMBQ5qecfWLunx9dHqj35pK4xVhE1QmNvM3YlEbeqPbfdapzUe4L2c9KHYghb\nenAF3aBAsn1kVzshhBBCnBkyh0eIs9jLG6vp6vMD2lyd4wmEg/x68//Q4mrnY0VX8l+XfXtYyPno\nzDXjvv9A4AmFTy7wxFu1L/49vsmfx9PY24w/HIgOZfuvu1byq69dPOn3BbAoDlBUnOFOAFIco3e1\nE0IIIcTpJ4FHTGlN7S5eXF9BeMgX9sbeZkKR8Bl8qrHxBUK8u6OBBIeZ+z6RyXUXjd4NbcAbFe/R\n0NvElQUXc+uCGzHoDSzNWgDAsqyF5MZnjfsZRqvw+INhnnz5AL97dheRiHrc8+P7Kzzdvt5x33u8\n3q/bBoCzJZ7sVDsLClPISjk9Q8vseu1zutECT7JDKjxCCCHE2UKGtIkp7eWN1byytRybQ2VFcSZr\ny95ibdnbfHbRzVxdOP6Kx6nw+UOYTfrjDkt7d3s9z75TzoNfvYjtB1txe4Ncc3khZqPnhNcfmLB/\nXdHl0W0zkqZx/yVfi7aIHq+B+S8Dgae2uY8H/3cH9S1OAK5fXUBe+rG/3Mf3L1h6ok5tETUSXb/n\nZIQiYTbUbiXGaKWzLZnpC05vhSXBHE9bBFSDtn6R3SxtqYUQQoizhVR4xJR22LMLa8m7PFH1EHe+\n9G3Wlr0NQFlH1Wl9jqZ2F5/+weu8+kHNcY97b2cjzR1u9lZ08MaWWm3hzAvyxnSPTq/WDS3ROrx1\ndXFaETbTiZsdjGZohefd7fV887cbqG9xkp+pBYqy2q7jnj+wYOnxKjzbGndzy/Nf5dcfPE5td8NJ\nPefu5v30+vpYlLIIVD32mMmfuzNUsi1p8E3EgEE3uY0ShBBCCDF2EnjElNatalWPcHcqC1KKWdk/\np6XP7zytz7GjrJVgKML7u44c85hwROVwvRYg3thay+H6bkqK0khNHFtY6fB0E2eJxaifuC/7Rv1A\n4AnzP//aj9Gg4/7PXcA3Pr0YgEMnCDzRCs8x5vAEw0H+svufhNUIHzbu4jtv/Zz/3vgYba6OcT3n\nuhqtI928hEXA6WlWMFRm7GBLcAOT341OCCGEEGMngUdMaT6lFzWsJ1CxiCzPar6+8k4SrfHj/kJ9\nqg7WaMHgcH03Lm9w1GPqmvvw+rW5RXsrtee7euW0MV1fVVW6PN0kWUcuTHoqBio8bl8ItzdIYW4C\ny+amk5vmIMZi4FDNCSo8A13avKNXeDbWbafd3clHCy/lPy7+KrOS8tnZtI9XDr875mfs8fZS2rSP\n6fE5xOm14BFjOb2BJzcpFTXS3xnuJKtpQgghhJgcEnjElNTnd9HQ20RY70IfdOCIMfHO9nqCoQhp\n9mQ6vN2EwqHT8iyqqnKoRpvMHomo7KloH/W4o6slyfFWSorSxnQPp99FMBIiKWb0hUlP1kDg6er1\nAhBn0xbx1OkUivISaepw0+vyH/N8q9FCojWeA+0V9A6p8oQiYfp8Tir7F0RdM30FCzPmcO+qu4Dx\ndXV7v+5DImqENfkro2HSdporPGnxsfgPXUCoJY+b5lxzWu8thBBCiOOTwCOmpNgG+ekAACAASURB\nVEe3Psm9b/wUdBEsahyXLsml1xXgwwPNpNlSUFWVds/I6oQv5D+pFsoeXxCXJwBAQ6uTF9ZVRDuY\ntXR66Orzk9Y/NG1/5ejVpcN12vPMzdfmg1y1PA+97vjr7gzo8GjzdyYr8HT0apPxY+2Dw7VmT08E\njj+sTVEUbpj9EfwhPy8efCO6/dl9a7n71fs50FaOoihkOrRg5zDZUFDoHeOQQ1VVWVe9GaPOwKq8\npbgHAo/l9PZjSYy1oLrjCNbP5qrZy0/rvYUQQghxfBJ4xJTT53ext7Us+t6ui+cjy7WJ/29urYsu\ngNl61LC2Hl8f333r53zrjZ+Oq221qqrc/8fNfPO37wPw/d9/wFOvHmTr/mYA/v6m9iwDz9DRXy05\nWl2zE5NRzxeun8cli7P56IXTx/wMXf0NC5KsExt4DAOBp2egwjMk8ORpgedEjQsuz19Fmi2ZNys3\nUNlZC8DelkP4Q36aXW2k21Ki8470Oj12s21Mc6wiaoQ3KzfQ5GxlWfZC7CYbHt+ZqfDE2kzcdvVs\nfninhB0hhBDibCOBR0w5O4/sJaIOrhsTZ0okJ83B3Pwkdpe3E3Brw7La3INDy1wBNz/b8AjNzjb6\n/C7eq9nMP/atHXadY9lb0UF5fQ/NnW6cngDdTm2IV3VTLxtKG3mvtJFZuQncsHoGep1Cj3PkELBw\nRKWhzUlump2C7HjuvaUER8zYJ79PXoVH6zbWOVDhGRJ4CvMS0CmD85OOxaA3cNfSW4moER798Clc\nATf1vYPNG7Jihy+oGmd20Oc7fuDxBX386oPH+XPps5j1Jq6bpbXidp+hIW0AN19eyJLZYxuCKIQQ\nQojTRwKPmHK2H9kz7H2yRavoXNNfMfnHK43R4yKRCL6Qn1++/xh1PY1kOFIBeHzH33nx4OvUdjee\n8H4vvT/Y4rq5w01M/3CqnYda+f0Le7CY9Hzz04vp9HYQazfQM8qcl5ZON8FQhNzjrGlzLG3uTp4/\n8Kr2WSc68PR3aevsr0rF2s3RfVazgWmZcVQ29hAMHb8iNi9tFh+duYYmZyu//uBxwkOC5IjAY3Hg\nDLgJH6fK9kr5OnYc2cO81Fk89NEfkp+oVc/cPm1elu00Ny0QQgghxNlr0gOP3+/niiuu4KWXXuK+\n++7juuuu4/bbb+f2229nw4YNk317cR6q6W5EDZjxVywk1JlOliMTgIsWZvH9zy5DdcdhC2Wwp+UQ\n/7vnRX616Y+Ud1azKncp31jxhWHXanUev3rR2OZkx6FWBtYSbWp3EepfpLOysRe3L8Sd1xfTRwv3\nvPZDdFllo1Z46pq1eUN56Y5xf96nSp/D6XehU3TRwDZRonN4ekZWeADm5Sf1r9Fz4vVzPjX/BjIc\nqRxoKx+2PTs2Y9h7h9kOaI0YjqWqqxaAr6/4PMkxidHtZ7LCI4QQQoiz06QHnscee4z4+MFWud/6\n1rd4+umnefrpp1m9evVk316cZ4LhIJ3eLiK+GCLd6QSrFhJvt0b3L5+XQXaqA9ehYtLtqbxS/i57\nWw9RklnMly/4DLlxmZgNg1WM8uam495v7cZqAK5YplUYyht6CIQGqxfL56Vz5QW50aqTx1GBLxDG\n5x/eIa6uRRvCdTIVnpr+xTofueYnxFnGf/7xmIzaXxHO/oYMcUcFnpvWzCDGYuDJVw7Q7fQd91pm\ng4mvXHAHSn86XJK1AAWFgsThC6vGmbXQ1+t3EolEUFV1xLUae5uJNduJtQwPiAOBJ+Y0Ny0QQggh\nxNlrUgNPdXU1NTU1rF69OvqlZbQvL0JMlDa31v5Z9Q+uhXJ0VWLhzBR8Xh3X5/wbhMzgTMFzeAFr\nN9RQdaSX/Pjc6LHNfVpjg1A4wvqdDdGhXaCFgHU7GkhNsHLjJQUA7OvvwDZ7WiKXLc3hK59YiKIo\n9PbPSTGoFoARw9rqWgYqPOMLLK6Am05vNwvS55BiSxrXuWMxMIdnQKzNPOx9UpyVT11ZhMcXYv2O\nEw//m5k0nc8uupkVOSV8bfnneOAj/0F23PAKT1x/iGl1dfDNN37CI1ufHLbfHwrQ5u4kJy5zxPXd\nviAGvYLZqB+xTwghhBDnp0kNPA888ADf+973AKL/qvu3v/2Nz3zmM9x777309PRM5u3FeajFpTUi\n0AXt0W1xR31JX1CoLU65bZcL767VhCuWUHqogydfOcA3f/s+zfvyoHUmAO39AerF9ZX85u+lfPan\nb3Gwf02dN7bU4g+Eue6ifDKSbOh1CrX9Q9MumJvO1z+5mLj+OS+NfVrHNqNOC19HD2urb+kjxmIg\nOd4yrs/b0KtVoHJH+fI/EQbm8AAoCjhiRg4Vu3RJDnqdwobSEwcegKtmXsI3Vt6J2WAiLz57xP7Y\n/grPH3f8jSZnK5vqtw9rHnGkrxkVdcRQONAqPDarMfr3jRBCCCHEpI37eOmll1i6dCmZmdoXMVVV\nuf7664mPj6eoqIjHH3+cRx55hPvvv/+E19q5c+dkPaYYgzP9849EVAIhFYtJ+/Ld6wmxdms3q4tj\nyU0ZHmY+aN8LQJLRwcBgtOqqw3i6Bqs8fp82Gf7D/c2g6rikOJZ5eTHUtfn54JCT5gaAfCwplXS4\nO9i0ZTvPvaMFFlWFF97aRdscB8/XrsVS0ss/W9/lny+ApTARd9kiAJzdLezcqYWfsBqhrr/5gT/i\nAVS+//tNXDjbweriWEJhlcY2F9lJJkpLS4/5cxjt91Dae1D7GXUHJ+X3VNc2GMwsRh27d+8a9biC\ndDPlTb186eevowJ6HayeF0tBxvgCHECHqw0YPofn3a3vkWiKA2B/XwUAau/Iz9zj9GDS6yb1z+yZ\n/v9BDJLfxZknv4MzT34HZw/5XZy9Ji3wbNiwgcbGRt566y1aWlowm838+Mc/pqioCIDLLruMH/3o\nR2O6VklJyWQ9pjiBnTt3nvGf/wvrKnjq1YOsKcnmtqvn8OJ7FVS1tNDrdfLIt5diHzJB/bU3tC/k\nS2YWsfjyGWzZ18zVly5Ad9QCnn96+41oleWCxUUsm6N1CrO9W87Trx0CFNSghaDRS3W3jYDiZtFF\nQXZtjiGk2Hh+ZwdkdGFWLGTFpdDq7iAQ2wq6MET0LF00J7qAaG13I+EqrUIRUUKgDxEIGVm/r49F\nxTOYnhOHqh5hzowMSkoWjvozONbvoXTHYWiHixdeyPSEnFP7QY/CUd8N72hVs8S4mGP+WVBsbfzs\nqW00dQfRKQrhSIQXt/Twu3vXkJoYM+o5xxLTHstLLe8CkJ+QS3V3PdZMByV5JTQ5W3l5u9bsZOW8\n5cxJnTns3MDzzaQn2yftz+zZ8P+D0Mjv4syT38GZJ7+Ds4f8Ls4OxwqdkxZ4HnrooejrRx99lOzs\nbJ555hkSExOZNWsW27dvp7CwcLJuL6aQykZt6OP6nY18sEer2+gU6Oj18cTafeQv6KLD3Y1ONVPR\nXQ06WF6YT/H0NEqKRl8XZVpGLLud2hf57NTB4W/5WXHR16rfQsjUzcsVb2CZX0WZP4I1ZyZ7K81E\nYjowZ8DVsy7mlgU38j87/s7bVRtRzB4IG6jxHmCOehGKovDiodcBsBoseEM+FJMP1auFtEef38N1\nq7R22eOdv1PdVcfWhlIMOsOI1s4TZaBLG4ycCzXU4qJUXvjltdH3b39Yx++e280TL+/nvs8sO+Z5\nnb1e1r5fjdsX5LarZxNnN0eHtAHcsuBGfvrew5Q27WNv6yHer/2QiBphVnIBM5OmDbtWMBQhEAxj\nk4YFQgghhBjitH4zuPXWW7nvvvuw2WzYbDZ+/vOfn87bi3NUt9OPosA9Ny/kb2+U0dHr49arC3mj\nah3rK5v5gCHr7uiAoIU5eccPANMyYtld3o5Br5CWMFiBmJ45JPAErKB0o6RXYNXZ8KkejHHdeGsj\n6M0eANLs2nygdLvWDvqOm/J4s+Ztnt6/gbR47VpbG0qZlZTPgow5PLf/FRSjH9Xr4BufWsxDz5Ty\nwvpKAPIyxt6Sen/rYR7Y9Hv8oQBfXPJpTPrJacM8NPAUTUs8zpHDXb4sl1c+qGHrvmbauj2kJoys\n8rg8Ae7/42YaWrWha+lJNj5+6UzS7SkszVrABdmLmJk4DQWFTfXbAa2F9c3zrmVZ9kJ0yvApiB6f\ntKQWQgghxEinJfB85Stfib5+8cUXT8ctxRTS4/QTazNx+bI8LlqUTVlNF05zLe7O/Rj780myewnJ\n1mSstjDL581Crzv+pPVpGVo1JSPZhn7IxPwEh5l4u5kel5+YYBr+SDPm3gJ+95l/55cbH6G6qwF0\nYRSz1q0ttb8zWoZDCz46q4fukFY5+rBhF/vayjDoDNy17FYqO2sBUExa++ZLl+TQ1O7i2Xe0dWnG\nWuHZ1rib3255AoBvrLyT5TmLx3TeyRjape3C+SObBByLoihctyqfh5/dxeuba/nMNXNGHLN2YzUN\nrS4uXpjF+7uPUFrWxscvnYlep+fbq/49etzS7AU09bVy05yrWJmzBJ1u9F4rLZ1uQBYdFUIIIcRw\nMvZDnPV6nD6S47W1dMxGPQsKU/jN5pcArXNYjNHKw5+5HeM4qhwDgSc7dXhVRVEU8rPj2HW4jSXp\nS3h3eypf+tRi4qw25qYVUtVdh87eHQ08afZkYLDC0+JsI8ORSrOzjffrPgTg5nnXkR2bQZdHG5q3\nZkUy/1Z8OQCf+kgRTR1uel3+aEe34/GHAjyy9UktFFx4F/PTZ4/5M58Mg34wOM7MSRjXuasWZvLw\ns7uoaOgedX97t/YzvOXqIpo63Rys6cTjCxJzVGD51oV3nfBeqqryl1cPAbBy/uR0rBNCCCHEuUkC\njzirBYJh3L4QMx2D3b78oQC7mvbjMNvxBDysyls6rrAD2lydW68qYnFR6oh9X7h+Ho1tLmZPS2Tp\nnHRWFmuVjTkpM1lb9jY6ew+mGB+qopAUow3zSrUno6DQ4mrHFxrsbJYTm8ENRVcCkGjVFuC12sOk\nJ9kA0OsUvnPbkjE/96H2SvzhAB8rumLSww5AvMPC4qJULpibPqLxw4lYTAZiLAZ6XYFR9w8sZuqI\nMVEyK5XKhh72VnawfN7YK0kDNu4+wr6qDpbNSWfJ7NHnbQkhhBDi/CSBR5zVBjqpxTsGqx/7Wsvw\nhwNcXbiGywsuIt4yvsn+oFVy/u2KWaPuy051RCs/Fw6pFmQ4tC/SitmLzuIlwZqAQacN+TLpjSTH\nJNDkbKWvv52yxWDm35fdhkGv/W9mN2nzWNwBz7ifd8DeVq2KMT9t8sMOaIHsx19YcdLnx9nM9Ln9\no+5zegLoFG0I2uKiVJ59p5zSw23jDjxef4gn1h7AaNBx5/XzTvpZhRBCCDE1TerCo0Kcqh7XyMCz\nv+0wAAvS55BqS5q0CftHS+qv0OitHkI6L6n9w9kGpDtS6fH1EVEjXJC9iKdu/A0zk6ZH98cYtWF5\nnqD3pJ9hX8shjDoDRckFJ32N0ynObqLXFUBV1RH7nJ4ANqsJnU5hVm4CNouBnWVtox471KubqvnK\ng+vo7f+z8ezbh+nq83HTmhlkJNsm5XMIIYQQ4twlgUec1br7tAn+CUMCz8G2cow6w7AwcTqYDCZi\nzXaMsU5gsEPbgJy4wWpQgiVuxOR6o96IXqc/6cDT4+2lrvcIs1NmYjIcu0X02STObiYcUXF7gyP2\nOT1BYm1aWNXrdSwsTKWty0NTh/uY1+vq8/HUqwepa3Hy1od1VDb28K/3q0hJsPLxS2ce8zwhhBBC\nnL8k8Iiz2mCFR5vD4/K7qes5QmFy/mmr7AyVFJNAKBICIMsxvPV1blxW9HW8deQwO0VRsBmteAIn\nF3j2tpYBMD+96KTOPxMG1u7pdQ+fx6OqKk53AHvMYHAbmE+1s6z1mNf72xtl+AJhAJ5+7RD3/b9N\nhMIqd91QjMUkI3SFEEIIMZIEHnFW6+6fw5PgMBOJRHjh4OuoqMxNPTOL1g40KQBGLPaZO6TCE2+J\nYzQxRutJV3hO9/ydiTDQeW5gLtYArz9EOKLiGBp4ZmmBp7SsbdRr1Tb38c62OnLSHFyxLBeAUFjl\nO7ct4YKTaHQghBBCiPOD/JOoOKsNfFHWmwP8dMPDHGgrJ9WWxCXTT34i/alItg62Zs6KHd4NbNiQ\ntlEqPKAFni5vz5jv1+Hu4vfb/0q2msI+ZxmxZju58VknPvEsMRB4jm5c4PRoQ9wGKkAAyfFWctMd\n7KvqxB8MY9Dr6HVpazAZ9Dr+vHY/ERU+d91c5kxPZNncdIoLkmWhUSGEEEIclwQecVbrdflRrH38\nbtfv6As4WZq1gC8vux1bf8ez0y3ZpgUeo95ISkzSsH3mIfNqjlXhsZmsBMJBQpFwtMPb8fxj/1r2\ntZaxD2042yXTVqBTzp3CbJy9f0jbkNbUkYhKt1Obm2WPGR5WFs9K5aUNVewpb+dPa/fT3OFm8axU\nrr+4gF3l7SwsTKGkKBVFUU6qfbUQQgghzj8SeMRZzR8MY0ivpS/g5Jb5N/KxoitQlPGtBzORkmK0\nwJNpTx3RlAC0ZgXdvl4SrKMHHuuQTm2xZvuI/YFQgHZPF1mx6Rzpa2Fj3TaMOgPZlnQW5M3l+v41\nfc4VcTatwtM7pMLz0DOlvFfaCEBszPDmCyVFWuD588ta2AEoPdxGY7sLRdGqO2fy9y+EEEKIc48E\nHnFW8wfCKBYPOkXHNbMuO+NfdpOs2hyeo+fvDHjwI9+n3dN1zLWBbEatMuUJeEYNPH8ufZZ1NZv5\n2eXf4bXydaiqyj0rP4ehNULJ/JIJ+hSnT+xRFZ5tB1uiYQfAYRseeIoLkklNsHKkXQs7112Uz8sb\nq2nr8nDFslymZ44eJIUQQgghjuXcGRsjzkv+YBidxUNKTOKYhoBNtoLEXFbmlHBZwapR98daHBQk\n5h3z/BOtxbOuZjMALx58nc31O5ken8OyrIWn+NRnTnz/HJ5elx+fP8QfX9w7bL/DOjzw6PU6blg9\nA4CMJBu3XT0bq1mP2aTnlqvOne50QgghhDh7SIVHnNW8QR+KMUC6I+XEB58GRr2Rr6+886TPjzFq\n7bXdowQeVVXRKToiaoSdTfsAuLn4ujNe1ToVA3N4uvp8/OPtw7R1e7nygjze+rAOAIdtZMOBKy7I\nZVd5G6sWZGE1G/jhnVqDiqQ46+l7cCGEEEJMGRJ4xFnNSx8wcpHPc9VAs4XRKjy9vj4iaiT6fkbi\nNBZnzDttzzYZjAY9BdlxHKju5FBNF6mJMXzhhnnRwBNjGRl4LCYDP/j88uj7uflJI44RQgghhBgr\nGdImzkqvla/jmb3/IqBogSfdnnqGn2hiDAxpc4+y+Gh9bxMAVqMFRVH4ZPHHzunqzoBbr5qNqkI4\novKlm+ZjMRlYOV/rsJaWeGa67QkhhBDi/CEVHnHW8QZ9PLXreQAUwywA0u3JZ/KRJszx5vDU9x4B\n4ItLPs2clMJjdno715QUpXLVimlYTHqWzNbWLvr2rUvw+kPDFh4VQgghhJgMEnjEhFBVdcKqEduP\n7Im+Dse0o2PqVXhGDTw9WoUnLz57yoQdAEVRuPvjC4ZtM+h1EnaEEEIIcVrIkDZxylpc7Xzu/+5l\nbdnbE3K9jXUfRl8rtm5QFVKnWoUn4Bmxr6G3CaPOQMYUCXdCCCGEEGcDCTzilL1c9jbuoJfnD7xK\nj7f3lK61/cge9rQcir5XdCpm1YFJP3Jy+7nIZhqo8PiGbY9EIjT0NZEVm47+LGi/LYQQQggxVUjg\nEaekz+/ivdqt6HV6/CE/Lx9+56Sv5fS7eHzH3zHqDHxxyS3R7VYSJ+JRzwqxZgeKolDX04iqqtHt\nre4OAuEguXFZZ/DphBBCCCGmHgk84pSUtVcSDAe5vuhKdIqO8o7qcZ3vDwV4aPOf2NW8nydLn6PX\n18fN864b1o7ZoUydwGM1WliauYCangYqOmui2wcaFuTGZ56pRxNCCCGEmJKkaYE4Je3uTgCmxWeT\n5UijvrdpXA0MPmzcxZaGnexq3o8v5GdG4jSunXUZiqJgUAyE1BCxhqm1DstVM1ez7chu3qh4j8Lk\nfADqe/oDj1R4hBBCCCEmlFR4xClp93QBkByTSE58Ft6QL7ptLDbX7wDAF/Jj1Bn48gW3o9fp0Sk6\n4s3xACQYp8aiowPmps4i05HG1sZdOP0uABp6mwHIiZMKjxBCCCHERJLAI6KGzikZq4EKT6otibz+\n6kR9T+OYzu1wd7Gn9RA5cZlckL2IO0s+RXZsRnR/ti2XiN9ConnqDGkDrU3z5QWrCEVCbKjdCsAR\nZwtWg4VEa/wZfjohhBBCiKlFAo8AoLnDzSf/+2n+sX7vuM5rd3di1ptwmO3kxWuBp65/eNbxdHq6\n+e7bvyAcCXNFwUXce+EXWZO/ctgxl2Veg3/fKqymqbdey+ppyzHoDLxTtYlIJEKLs40MR+qErWUk\nhBBCCCE0EnimEFVVKW3aj/eolsdj8fSm9ajTt/JCw5OU1laN+bx2TxfJtkQURSG3P/DU9zad8Lxd\nzQdw+l18rOhKPjJj9ajHhIJAxIDZNPXaNDvMdpZnL6LJ2cqm+u0EIyEyHWln+rGEEEIIIaYcCTxT\nyP62w/xy4//j2f0vj+u8cDjCrk5tLo1i9vHA1ofZ11J2wvM8QS/ugIdUm9ZUIMmaQIzRGp2AHwgF\n8IX8o57b5GwFoCSjmH+uq6C+pW/EMf5gCACzceoFHoDLC1YB8My+fwGQ4ZAFR4UQQgghJpoEnilk\nT8tBAD5s2DXm+TiBcJA/fvB/hG2txJJGuutCwmqIn214hHerNvHPpjf5zeb/GfXcDvdgwwLQ5qbk\nxWfR5GolEArw682Pc/+7vxr13Ob+wOPsMvL0a4f4x9vlI47xB8IAU7LCAzA7ZSaZjjQ6Pd0AZEiF\nRwghhBBiwkngmUL2tWpVmU5vN1VddcP2uQJuery9I87ZVLeN95rfAVXh6oIr+M511xOuWEYkrOeP\nO/5GlaeBrQ2lRCKREefW9jcnSLENto3OjctCVVUa+1qo7KylrqeRUDg04txmZxs2UwwNTQEADtd3\nR/epqsqv/ncnj72gzSeaqhWegeYFAzKlwiOEEEIIMeEk8EwRLr+b2u5GzAYzAK+VrxtW5fn1B49z\n39v/TUQdHlwOtVdqLyou5GMLl5Od6uDGpRfgO3ABNmWwY1int3vYeU6/i7/t+T/0Ov2wRUIHGhdU\ndtXiDLgB6PYND1rhSJhWVzuZjjQqGnsAaOvy0O30oaoqazdWs2HXYKe3qVrhAbi4v3kBSIVHCCGE\nEGIyyMKj57AuTw//2L+W0qZ9zEyajorKdbMuY2fTPjbVbyfDkcon5l1LIBSgrL2SsBrhvZot1PY0\nct2sy0mxJXGwtRI1ZKA4qwCjQQsWN19eyIbSRjq2L0fJLMeYWU2rqyNayVFVlf/Z+Qzdvl4+VXw9\n6bZ0nnnrMKsWZEYXztzdP7wOoMvbM6wK1O7uJKxGyHCkUjqksvPW1jr2VXWwp6Jj2Oc0G6fuH9NY\ns52Pz/0oHe4urEbLmX4cIYQQQogpZ+p+k5zCfCE//zr0Fi8ffptAOAjAzqZ9pNtT+OjMS7my4GL+\n890Hef7AqyRa48mOyyDcX9l5fMffiagR1ldv5tpZl9Pu7SDiSmbRnMHhVGajnrtuLOYnT3yI3hcD\nQENPK/PSZgGwqW47WxtKmZWUz/VFV/KH/9vH65trOVjdyX98fjEA+1sHmx50HzWUrq5Xa2qQYEyi\nvduL3WrE5Q3yv29o5yyelUpGso1XP6jRnmcKV3gAbppz9Zl+BCGEEEKIKUsCzznozzuf5b3aLSRY\n4vjc4uvIi8/mzYoN3DDnI9jNNgD+Y/VXuf+dB3l8599ZlD43em5EjZAck0ggHOCFg69p21zxZKbY\nht1j6Zx0PnvtHP7yvtaY4Mndz7C54UO+dMHtPFH6D8wGM3cvv4OWTg9vbKkFoLHdhdVoIc2WTKt7\nsErT5e2Jvt7dfIDHtj0NgCmQDLTxkeV5bNh1hHi7iTuumcuCwhT2VrafN4FHCCGEEEJMHgk855hw\nJMy2I7tJiUnk11f/AEv/nJ0vX3D7sOMyHWl87+K7+fH6hyht3j9s3+ppy7mm8FL+vvclNlTvxNed\nRnK8dcS9blozk4qGcnb2vz/cWc3333kAT9DLXUtuId2ewjsH6xiYKtTZ68XtDZITnzUi8KiqyusV\n6/nL7n9iUPTcs/yzlO2OAdoomZ3GHdfOHXbv7FRH9PVUbVoghBBCCCEmnzQtOMdUdNbgCXpZlDEv\nGnaOZWbSdL6x8gsoioLDbCcpJgGA4rQi7GYbX1x6C4XOm1G9DpLjRgYegNQY+7D37oCHksxidD15\n/Psv32XjHm2R0bn5SagqVDb2kNc/j2dAl7eXNys38NSu54kzO/jRpd9kVd4yDlR3YNDrKMxNGHHf\nBMfgZ5MKjxBCCCGEOFlS4TnH7Go+AMDCjLknOFJTklnMf66+B72iY3PDTvY0H6QwaXp0f0ePF6tZ\nT4xl9D8K8XYj9E/BCbVlk5oVZJb+Eh56phRVhSPtLgAuW5LDgepOyuu7ySscHni6vT3s6q8y/fSy\nb5FmT8HjC1J9pJeiaYmjVnAURYm+lgqPEEIIIYQ4WRJ4ziHd3l7erd6EUW9kXmrhmM8rTisCYE5q\nIaqqDgsTnb1ekuOtw7YNFW8zENhbhM7qIlg7F2+XhSc+qMARozUaUFVIjDWzuEhrenCotosLl2mB\nSlEU7MYYujw9hNUwcZZY0uwpAJTVdRNRtcrQsfz8yxfS2ObCJIFHCCGEEEKcJBnSdo7o87v41Qd/\npM/v4pb5N2A5yRbGQ4ONLxDC6QmSdIzhbAB2q45w6zSCtfMAha4+P/F2M7/48iqmZcQCkJsWS1Kc\nlYxkGwerO0mJScakN5JgiSM5JpEWdztt7k6yhqwzU9uklY1mZMePdlsAiguSuXrFtJP6nEIIIYQQ\nQoAEnnPGg5v+QEVnDatyl3L1zDUTcs2uXh/AMefvAOiGBKT/b80M8rPiFzYJZQAAIABJREFU+PmX\nLyQvIzZanclN1xoMzJ+RjNsXorapjzsW3czypDWYwvHRBVAzY9Oj16prcQKQ1x+ahBBCCCGEmAwS\neE6jUCRMpH89nPEIhoOUd1ZTkJDHV5bfcczhZ+PV0esFICn++NWimy6ZwcLCFD5zzRwe/uYl5KRp\nAWf53AwA5hVowae4IBmAfZUdXF6wis0bdBzaO/hHLHNIhaeupQ+jQUd60vB22EIIIYQQQkwkmcNz\nmnR6uvnx+ofIik3nuxd9eVzntro6UFWVvPgsdMrEZdSOHi3wpIzSknqoz143eoOEBYUpPP3DjxDf\n31GteIYWePZWdnDjJTNo7/ESUhKx9vdIsKpxqKpKRIWGFic5qQ70uokJb0IIIYQQQoxGAs9p0Od3\n8V8bfkeLqx13wDPu85ucrQBkxqad4MjxqWzU5tFkJttPcOSxJcQOVocSYy1kpdg5WNNJV5+PUDgC\nDLaXfvjpCl5JdbNqfiaBUITcDMcoVxRCCCGEEGLiyJC2SeYN+vjFhkc50teCQWfAGXDjDwXGdY2B\nwJPhmNjAU1rWitWsp2ha4oRdc/6MZLz+MB8eaIluuyzxZhI9C1D9Vqobe3jq1YMA5KXL/B0hhBBC\nCDG5JPBMkjZXB76Qnwc2/Z6q7joumb6CVXlLAej0dI3rWtEKzwQGnpZON0fa3cyfkYLRMHF/DAaG\nta3f0RDdFu5NxFs/ndSEGP543+XcsLqA/Mw4ls9LP9ZlhBBCCCGEmBAypG2ChSJhnip9jreq3sdm\nisEd8LAseyF3LbmFFw6+DkCHp3tYx7ITae5rRafoSLMlT9hz7jykhaiS2RNbNRpoXFBW1x3dVtHY\nQ1efj4WFKaQn2fj8x+ZN6D2FEEIIIYQ4FqnwTKBIJMIjW5/krar3cZjtuAMeitNm8bXln0Ov05Mc\nkwBoDQzGqtXVTn1fE6m2JAz6icunO8raACjpXzB0osQ7zNE21QMqG3oAyEyWjmxCCCGEEOL0Oqcr\nPKqqoqqgO4OdvkKRMAadHoB/HnyVLQ07mZ0yg/suups2dyeZjrRoUEmO0ebKdIxxSFtZexUPfvAH\nvEEfN86+asKeORAMs7eyg5w0B6kJMRN23QHFBcnU96+zMz0zlpqmPgCyUk6+OYIQQgghhBAn45wO\nPN99dBNGg46ffenCM3L/P+14hrerNpIck0C6I5WDbeUkxSTw3VVfxmK0kBufNez4pCEVHnfAgzPg\nJt2eEt0fCofY0lBKSVYxpU37eGzbX4moEe4s+RRXzrh4wp57f3UngWB4wqs7A4pnJPPqBzUA3Hx5\nIf/99A4AMiXwCCGEEEKI0+ycDTy+QIhDtVqlpLKxh1Aowqy8hAlblPNEQpEwG+u2YTKYCKlh9rWW\noSgKdy25lRjT6OvaRAOPt5s/7XyGHU37+P21P8Nu1oZ6bW/awyMfPhk9PsZo5Zsrv8D89NnHfI7O\nXi8VDT1cMDd9zJ99Z1n//J1JCjzz8rWFSGNtJlbMy4huz0yRIW1CCCGEEOL0mvTA4/f7ufbaa7n7\n7rtZvnw53/72t1FVlZSUFB544AGMRuNJXbe5wx19/Y2HNgAwIyeej186kxXzMiZ1mFuXp4f9bYfx\nhnxcNeMSPlfyb/iCPrwhPwnWuGOeZzGYsZtsdLi7aXK24Q/5OdhewbLshQA09bVGj021JfG9i+4m\nO04LDKqq8ou/bKer18fPvnwhnT1eXlhfybodDYTCEe77zFJWzs8c0/OXlrVhMemZ2x9MJlqc3cyV\nF+RhNRvQ63X8xx1L2VfVSUaSBB4hhBBCCHF6TXrgeeyxx4iPjwfg4Ycf5rbbbuPKK6/koYce4oUX\nXuCTn/zkSV33SLtr2PuMZBtVjT388i/byUmz84Xri1k069QqGC6/m19vfpwbZ18VrbJ0uLu455Wf\nEMIPwOJMreOYxWjBYrQc81rR57SnUN1dT1iNALC/9XA08HT0NzP4ZPHHuKLgIhzmwSFgeys72LKv\nGYBvPPQeR9pcRFRIirPQ2etjZ1kbs6cl8tM/f8itV89m8TE+e2uXh8Y2F8vmpGM06E/mxzImX715\nYfT1iuJMVhSPLYwJIYQQQggxkSa1S1t1dTU1NTWsXr0aVVXZvn07a9asAWDNmjVs3rz5pK99dOB5\n8KsX8dh3LuXypbkcaXPxg8e38OBfd+D0jG+Rz6F2txzkQFs5T+56jkh/QPnt5iejYSfGaGVOauG4\nrjkzOT8adgD2tx2Ovm53dwJwTeFlw8IOwN/fLAMgOc5CQ6uL/Kw4vnv7Ev70/StwxBjZVd7Gxj1H\nqGjoYUNp4zHvHx3ONntyhrMJIYQQQghxNpnUCs8DDzzAD37wA1588UUAvF5vdAhbUlIS7e3tJ33t\nI21a4PnRF5aTmhBDnN1MnN3M1z65iGtXTeexF/bw/u4jVDT28IsvX0hS3OjzanaWteL1h1i1QGsw\noKoqfX4ncZZYanu0xTOP9LWwrXE3xWlFlHdVEnbGE6xawC++uQqTfnxD8mYl5/Na+ToAFEWhsa+Z\nHm8v/397dxoYVX3ucfw7M8lkJyvZCFlIWEIWQiKyiIAYAfG6gBuoVbFWa+WiLWoVq1AqilprW6Eu\npbZcxYobilBAyqZAICEgEPYECITAJGQjkH1m7ouYkbi0EJZJht/nDclwcuY552TynOf8twAvf0pP\nleHj5oObsfU+dx8sZ+eBcvr1DuOR2/tSWV1PdLifY8xOn+6dWbu1mIVf7geg8NiJH33/bfnHAX60\nBUhERERExJVcsILn008/pV+/fkRG/nBXJrvdfsb7ys3N/d5rew+WYDSCtfowJacMlHynUWPcIB++\n8Gpiw56T/P2TLK5K/f7YmiWbKtm49yRgp+HGIvx93Miu2Maqsmzu6HId28p3Oradl/sJw0MGAGA7\nGYC9wYv8vCIqO1m+t9//pL7p27FH0e5dKWw4xOcbl5Ho241jJ49jPenHzDkrGZUR4Nhu/lfNLT9J\nETby9+QBcLz4232GeNUCzd3VAA4WV5GdswnTaeOYahtsNFnt7D1Yioe7gaIDuzhy8AwnOfiB8y8X\nn65D+6Dr0H7oWjifroHz6Rq0H7oW7dcFK3jWrFlDUVERX3zxBRaLBXd3d7y9vWloaMBsNmOxWAgN\nPbNWhoyMjFbf2+12KhcsITLEl8v7XfajP9ezdwMbnl1CVb1nq300NllZv+0oG/cW4R67A1PIET4p\ni2CAfxLrq7YCcNitlDJbFaE+wcQHxZJ1OJfd1oPN71/TCYDIrgmkJISczWkB4MOSZZTWlFOwPQK3\nnoc45dNAt6QE7AU2bPVebCg4ydMPXA3AipxD7DpcRELXAMZeO/AHZ2JLS7Ox5eBqCr9Z+8Zqg4jo\nnnQN+3YB0AnTl3G8qg6T0UBC1wAuu+zHz9vpcnNzv3f+5eLTdWgfdB3aD10L59M1cD5dg/ZD16J9\n+LGi84IVPK+++qrj61mzZhEVFcXmzZtZunQpN9xwA8uWLePKK69s076Lj5/iVG0jfXt0/o/bdfIx\nExXqy55D5Vhtdurqm1i0dj+fringZG0jbibwCS+lrslOSX0xC3cfAcBkMPJVYTYAiZ0TGJM4iqzD\nuWw5tgMAW01zIVF2oq5N8f8k7WZe+3Q9tVUBeBs82GHZQ0nsQADs9c1d70oqaigpr2HWh1/j4+XO\n5DvSf3TaaZPJyMyHB7Pwq/00NFr5eFU+B4tPtCp4jlc1x2q12Yk+7XUREREREVd2UdfhmTRpEk88\n8QQffPABkZGRjBkzpk372bn/my5eZzCtcmJsEMuzD/H6x1tZu7WYU7WN+Hm7k9kvmoQeMHdfHb71\n3Sjf2Y0nH+pOk6GOI9VH+WTnUgB27bBS7GckPbJ5MVC7zUiEbxjFtTWUV7Wt4OkdlMyJg83jg8z1\noVjsh9nxzeQFLQXPvKW7ydl5DLsdnrqnH1Gh/7lI8fU2c8fIXmzdV8rHq/L5V9YBosP9iInoRGOT\nrdW2XVXwiIiIiMgl4qIUPBMnTnR8/fbbb5/z/nYcOPuCZ9mGQvy8zdw9OpHrrojD29Odz3f/G4CU\nsB6s2g4nS/y5pn8qJ+tPYbPbyckrJT8/gNePbOOxBzKbC54aX5LiQiguPUR5G1t4Dh6tcnxdecwX\nt2hYvGcVAAkhXamwerNyU3NBNPHWNPp0/88tWd893sTYIPIKypj4+1UMTIlg9KDYVtuo4BERERGR\nS8UFnZb6QrDb7ezcX46Plzsx4Z3+6/YDUyIYmBLBPdf1Zs7Tmdx6dQ+8Pd2x2+1sProdgFEpzX0u\ns/Ka17nx9fDhis7Dyc8NxWzwpPJkPTmbGujjNZzGw73oHddcaG3LL2XDNz/zXSdONfDLV1fz7Jvr\n+WRVPgeKq7DZmidqOFjcPItabEQnmqqCADjZeBK71US/2J48dU8/gjp5cvs1PRg5IOaszo/Z3cSL\nEwfzzH396REdQNb2ozzzZlarbdSlTUREREQuFRe1S9u5slpt/PWzPI6WnWJgSgRG43+fZczX28yU\ney9v9VqjtZG3N3/AjpK99AyJp3dUFLER+9iyp5Sauka8Pd3ZXdi8COh9NyTz6Zp8Pl+7n4SoUGzV\nZnrFBgJwoPgEM/6ezaPj+nJ1v+hW77Etv5T8ouaWnC17S/n7Igjw9WDsVQkctjRPLjBuRE9mzq3C\nze5Fk6EWW3UQ3dODSYgK4B/PjvjRMTv/jcFg4PKkcPr1DmPyn75k3+FKAEKDvImL6ERIwA9P0S0i\nIiIi4mo6TAtPTV0jz/09m8XrDhAb0YkHbkpp034qa6t4dsUrrNi/lhj/Ljw++OcADEiOoMlqI3d3\nCQDHypqnj46N6MTPbkzBZrOz91AlRgOEB/u02udfPtpKQVFlq9fyvykyHrszg1/dkc7wy7pS29Dk\naO1xdzMyICmcqFA/GiqaCyjbiSC6dWmePrutxc7pDAaDY38AP7sxmd/c1/+MCkUREREREVfQIQqe\nmrpGnpy9lk27LKT3CuXFiYPb1EpxrLqEZ1b8noKKQobE9ud3mY/TycMXgEGpEQCs3HSYDXlHOXq8\nueAJD/amX+8w0ns1T6EdEuiNm8lIaGDz+0+8NY2GJhsvzM1h854SZvx9IxUn6ij4pnUnIzGMqzK6\n8svx6fRJ6EzlyXoOFJ8gOtwPk8nIwJQIGi1dsJ3yw68xhgA/j3M+X6eLi/i221/Ijyy+KiIiIiLi\nqjpEl7Y1W45woPgEwy/ryqTb0jCZzr5O219+iBe+nEVVfTW3JI3m1qT/adWKEhvRiaBOnmzaZWHT\nrubFRM1uRgL9PDEYDDxwUwoTX17lKCBe+MVgauubiInoRGllDfOX72XqW81jZfp070zBkUoign3w\n9XJ3vEdMhB/ZO49htdmJ/WY/A1Mi+HBFMPU7rqBP7/A2n6MfExv5bQtPcIDned+/iIiIiEh71iEK\nntxvCpDxI3q2qdjZdmwXv1/3JvVNDdyfMY4RCUO/t43BYOCay6OZ/++9jtfCgr0d3b+6dPZl1uNX\nOQqY0CBvx3bjR/Ri36FKNu9p7g6Xu7uE6ppGUr8zu1r0aZMsxEY0FyIJUQGEBHhxvLK2Vfez8yX2\ntBYef5/z23okIiIiItLedYgubV/vKyUq1Pd7Y2fORH7ZQV74ajZNNiu/HHT/DxY7LcaP6Mmrv/z2\n/8OCWr9fl86++Pt+v2gwGQ08PeFynvv5IAwGHIVP96iAVtvFhH87O1pLS5HBYGBQSnN3uu5dW29/\nPvic1sKksTsiIiIicqnpEC089Q1WLksMO+ufa7JZeSPnXaw2K1OGTCQtIuk/bm8yGUmICsDLw0Rt\nvRU/b/f/uP3pzO4m+nTvTGSID0dKm8f/pPVo3cLTpbMvRqMBm81ObOS3LS/jR/YiOtyvTcd4Jt79\n7agLsl8RERERkfauQ7TwdOnsy3VXxJ31z2UXbeFQ1RGGxw36r8XO6eK+GffSlhaRmG9abgL9PL7X\nRc3sbqJ7VMD3Wop8vdwZOSD2grXA+Pt6/GDLlIiIiIiIq+sQLTyv/3p4m6ZpzrPsASAz/sqz+rnJ\nd2QwZ2Eed41KPOv3jI3wZ/22o6T3Cv3BmJ+9f4BjAVIREREREbmwOkQLT1vXpNlRuhcvN0/iArue\n1c+FBnkz5d7L2zT1dUavULw8TFx9WfQP/n8nH/N5n3paRERERER+WIdo4TlbJ+qqWZq/hqPVJfSN\nSMZkNF209+4RHcgHz//PRXs/ERERERH5cR2+4CmutrC//BDuJjcMNLcEfZC3iENVRwBICu3uzPBE\nRERERMSJOnTBY7fbeWHNLCynjn/v/y7vkoaXuydDYwc4ITIREREREWkPOnTBU1hZhOXUcTzdPBiX\ncgN2e/NkAAFenRjYNQOjoUMMURIRERERkQukQxQ8xSeO8dya10gO68n4lBsJ9Gqe7nlT8TYAft7v\nLgZFX+bMEEVEREREpB3qEAXPygPrOV5TzuoDWWQd3syYxJH8T89Mcoq2YjKaSAs/8zV2RERERETk\n0tEh+nx9VZiNp5sHP00fh4fJnfe3L2TK8hc5UHmYtPDeeJvPfvpoERERERFxfR2i4KmoreKyLn0Y\n2X0ofx49neTQno5Z2K7vmenk6EREREREpL3qEAVPZ+8gRiUMBcDb7MXPL/8Jnm4edA+OI7Gzpp0W\nEREREZEf1iHG8My+fkar70N9gnn12ql4unlgMBicFJWIiIiIiLR3HaLg+SHB3oHODkFERERERNq5\nDtGlTUREREREpC1U8IiIiIiIiMtSwSMiIiIiIi5LBY+IiIiIiLgsFTwiIiIiIuKyVPCIiIiIiIjL\nUsEjIiIiIiIuSwWPiIiIiIi4LBU8IiIiIiLislTwiIiIiIiIy1LBIyIiIiIiLksFj4iIiIiIuCwV\nPCIiIiIi4rJU8IiIiIiIiMtSwSMiIiIiIi5LBY+IiIiIiLgsFTwiIiIiIuKyVPCIiIiIiIjLUsEj\nIiIiIiIuSwWPiIiIiIi4LBU8IiIiIiLislTwiIiIiIiIy1LBIyIiIiIiLksFj4iIiIiIuCwVPCIi\nIiIi4rJU8IiIiIiIiMtyu5A7r6ur48knn6SsrIyGhgYeeughli1bRl5eHoGBgQD89Kc/ZejQoRcy\nDBERERERuURd0IJn5cqVpKSk8NOf/pTi4mImTJhAeno6jz32mIocERERERG54C5owTN69GjH18XF\nxURERABgt9sv5NuKiIiIiIgAF2kMz7hx43jiiSeYMmUKAPPmzeOee+5h8uTJVFZWXowQRERERETk\nEnRRCp7333+fv/zlLzz22GPceOONTJ48mblz59KzZ09ee+21ixGCiIiIiIhcggz2C9i/LC8vj+Dg\nYEdXtuuuu4533nmHoKAgAAoKCpg2bRrvvPPOj+4jN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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Get pricing data for two benchmarks (stock indices) and a stock\n", "start = '2013-01-01'\n", "end = '2015-01-01'\n", "b1 = get_pricing('SPY', fields='price', start_date=start, end_date=end)\n", "b2 = get_pricing('MDY', fields='price', start_date=start, end_date=end)\n", "asset = get_pricing('V', fields='price', start_date=start, end_date=end)\n", "\n", "mlr = regression.linear_model.OLS(asset, sm.add_constant(np.column_stack((b1, b2)))).fit()\n", "prediction = mlr.params[0] + mlr.params[1]*b1 + mlr.params[2]*b2\n", "print 'Constant:', mlr.params[0], 'MLR beta to S&P 500:', mlr.params[1], ' MLR beta to MDY', mlr.params[2]\n", "\n", "# Plot the asset pricing data and the regression model prediction, just for fun\n", "asset.plot()\n", "prediction.plot();\n", "plt.ylabel('Price')\n", "plt.legend(['Asset', 'Linear Regression Prediction']);" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Constant: -28.5210310926 MLR beta to S&P 500: 0.176425363423 MLR beta to MDY 0.203681925802\n" ] }, { "data": { "image/png": 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bAWVbTQsa7x9CdZ0To9nqo6WV9USEWQkLsbZ57ZX5a6hz1bfY/unmL/f5HG1R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\nrQKAmxZcG1S/NBVIksTXlt1Ml7Wb/XVHANhetZdjTSe5c8W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UeRlRSBpF8PTvR5IRmeJ7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sj8oqy07n1yMkb2i/2cwnT+vvYoAB+6ooBPXFMct2DmaLvtA+c2z20sig5pSzQn8I3ln+9zH5c3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\naNEifvOb3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WCMzQESQgghhBhKEniEGIDymu65Kuu2VcYebztQh16n4dt3L+LRb1zF5Nxk\nTlSpE/nnFqVz7dI8/uueJeRnq+2WXZ4AZlP8ejUGvZawNlrhMcZez7Sl0eRuJayE4/Z3+d0cbiwd\n2jc4ALtPnQSNQrJBHXqm1+n56mWfJdmcyFP7XuBv+16iqkMNgzWd9fiDftq8alDMMI2PO9emyh0A\nseFwhPSkSuARQgghxDDQn30XIURZTQc6rYbpk1LZf6KZyrpOJo5LpKndTWqSBbvFAMC1S/J4pGov\nKYlmvvaJ+STZTXgCXk4oGzEW1RCsm4TZODHu3Hq9FiUaeCIVHoAsezonWivYWLGdZHMSJr2Bzad2\n8daJjQD8vyu+xKysqcP+3l/fVMZbOyqpta9HmwQFSZNj2xyWJL562Wd5cMP/8OrRt2Kv+0MBvrf+\nlz3eSyblkV4FYa+VHdX78AZ9uINq4NFrjZgM8UFQCCGEEGIoSOAR4ixCYYXyuk4mZCXwweX57D/R\nzNptFXz6xhm0dfmYlt89XOvqxRNIT7ZQnOfAajbQ4e3kpxsfodxZhS4ZQIPZMynu/AadFnRqRzdT\njwrPpJQJbDq1k0d3PNnnfR1vKRv2wKMoCo+9dghNWgW6pBYy9Xncc8UH4vYpTp/Mb677ASW1B9hY\nsZ3bZ61hU+VONlSobagNWj0zHbPZVLGLYH0+WlsHAfNJSmr3k5M4DgCL3jys70MIIYQQly4JPEKc\nRW2TE38gRH52EgunZeFIMPFuSTXXLc1DUSDd0T0US6PRMK84A4BGZzM/fu+31DubWJazmE0Vu9FY\nujCH40eS6vVaNLogFr0FraZ7W0FKfCVoZf5lLJuwgOzETO597buUt1UN47uGdm8nte0tBHVOLLnH\nsRqt/PDaz5NkMfXaN8OexnVFK7muaCUAs7KmsiJvEX/Z9Qwp1mTmTM7G/8xiVs7PYcOhoxjGn2RT\n5U6uL1wNSOARQgghxPCRwCPEWZRF5u8UjE9Cr9OyetEEnl9fymub1An6fU22d/s9/OS931HvbOKW\naddy24yb2HT4JNrEZk6YnmZblY0lufMAdQ4P2gA2gzXuHPnJubHH31xxL/OzZ8aeJ5kTqRjGwBMI\nBfjWWz+j1dOOcYoVRRPkM/PuwmFJGvA5ZmYW8z/X/wBFUdBqtbz80I1otRoO/qQFpyeRvXWHmZM+\nB5DAI4QQQojhI00LhDiL8lo18OSPV7/sr5yvBpG1WysASOsj8Lx+/G3qnI3cOGU1H5u5Bo1GgxVH\nbPuvt/w51srZoNOi0QewGOLPYzZ0h4Bp6YVx2/KTc2hyt9Llc57fmzuDtaXv0epRmy9ozW6yDJNY\nNmHBOZ9Ho9Gg1ar/zOh0WjQaDTML0gh2JhNSQpS3VgNgNUrDAiGEEEIMDwk8QpxFtMKTn60GntzM\nBCZmJcS29xV4KtrUL/Jrpl4Tey3FnBq3z9snNwHg1beg0YVwmByc7qGrv8v3r/wKFkN8BWR8ZO7L\ncK3Tc6T5RNzz5Wmr0Wg0Q3LuWZPTUALqsLg6ZwMAdpMEHiGEEEIMDwk8QvRDURTKajvITLHGOrEB\nXLVwQuxxX0PaarsasBttJJq6F97MS8wDINzlIMFo4y8lz7CxYjt12n0ALM1e0us8eY4cZmRO6fV6\ngskGgNPvGtwbO4smZzMmvYmrkm/Dd3QBeanjhuzcMyenofjVwNPkVtcZspus/R0ihBBCCDFoEniE\n6Edrp5cOp59J4+Pnrqy5vIBrl+aRnWZjXJot9nqLuw1/KECDs4nshMy4Y25fsRDNsVV8cd4X+H9X\nfhmrwczvdzxBM+WEnUnkJxQM+L7sRjUgDEfgURSFRncLqeYUaitNhDvTcCT2blQwWBkOKw6Lui5R\nq0+tUCWaJfAIIYQQYnhI0wIh+lFeqy6cGR3OFqXVarjvI7NRFCU21Gtt6QYe2/0sl+ctJqSEewWe\njBQrz37/1tjz717xJX604Td4g3785TMIhpQB35fdqFaOnD73oN5Xf1x+N56AF5xaTh5rBCAlcWib\nCkzKyOAAECYEQLLV1v8BQgghhBCDJBUeIc5AURSOVqirZRaM77s7WTTsvHr0LR7b/SwAGyu2A5Cd\nmNnnMVGTU/N46JrvsNx6K4ongWAoPOB7G84KT6NLHWbW1db9+5Ak+9BVeAAyE+PnKzls9jPsKYQQ\nQghxfiTwCHEGT7xxmGffPg70rvD09PKRdfxt30ukWhxxbZtzErPOeo1MezppRnW/QPBcAo9aEeka\nlsCjDjML+9S5STaLAb1uaP+pyEh0oPQoaKXYJfAIIYQQYnhI4BGjSlEGPoxrJHn9Qd7cWgHAstnZ\npCX3PaSr2dXKswdeJdXi4MFVX2V6elFs24zM4gFdS69X/xr2DDy+QIi65jOHGfswNi1ocKoVHsVn\n4WMfmMLvH1g55NdITbRC0Bh7np6Q0M/eQgghhBCDJ4FHjJo3Npdz5w/W0tTmAUY//CiKwptbK2hs\nc7P1QB1ub5CPri7iW3ctPGNL5tePvU1ICXPbzBvJsKeRHKnwJJkTMesHNgzMoNcBxIa0VdR18uVf\nvcsXfrGeqoauPo/pHtI29HN4oi2pFXciC6ZmkJo09C2jHQmmWKc2gGS7tKUWQgghxPCQpgVi1Byt\nbKXD6Wf9rlNcf/l4vr/+lyzOmcvts9YMy/V8gRC/e3YvVy+ZwKzJ6b227zzSwKP/3Me4NFus1fTq\nHu2n+3Kk+QQGnYHlExcBcH3RSspaK/nk3Fv7Pa4ng04NU4FgmINlLt587j38kWrPwbIWcjN7Vz8s\nejM6jRanr+8Kz4byrbx29N9MTS9kXvYMZmQWY9QZ+ty3p2AoyKHG45iVJDx+S59rDA0FR6KZsNOB\n1qYGOqNB/ikSQgghxPCQCo8YNU2eJgwTD/Fa5T958N2Hqe1q4KUja4ftejsP1/Penmq++79b+txe\nWad2ZKtrdrH/RDMzC9LiWk73pcPbRbI5Eb1WrdKkWVP4waqvku/IHfB96SMVnvLaDl7Z1obBoOOu\n66cCcKyytc9jNBoNdqOtzyFtXT4nT+x5nqrOOt46uZGfv/8ov9z0hwHdy7GWMnxBHxa/uu6OzXz2\nkDQYjgQTgaoiws4kdK6zz3USQgghhBgsCTxi1DRoD6DPrCKQUE1VRy0A6daUYbtetMU09N0goLSq\nPe756kX9V3cURaHD10Wy6fzmnxgic3iiw9duXVXILSsLsZh0HD/VdsbjzhR43qvYhivg4eOzPsQP\nVn6VBKONms76Ad3LvvrDAOjdGWi1GkxG3bm+nQGxmPQQ1uM7vIQF5huG5RpCCCGEECCBR4wiL+oX\nfO/ey1nC3eQl5wxL17GoaItpoM8g0fM1q1nPZbPG9Xs+l99NKBwiyZx4XvdliHRAa+30ApBoM6LT\naijMdVDd6MTlCfR5nN1oxel3x819qnc2UR0JN/PGzWBaRiEplmScgYHN9dlffwSdVofiTMVq0p9x\n7tL56j6vhvlT+m/fLYQQQghxPiTwiFET0rnRhEyk21LZtq+JBGMC3qAPX9A/+HOGFd7ZdQqn28+O\nQ/X8/Imd+AMh/IFQXKA5fahYW6eXlg5v7Pnlc3MwG/ufV9LuUytG5xt4ol3aotdPsKndy4omqK2b\nS6v6rvIkmBMIK2Ga3Op7Odp0ki+98X3eKdsMQLotFQCr0Yon4CUc7r/tdae3i/K2KorTCvC4FayW\n4RnOdro5RRkjch0hhBBCXJok8IgR5/S5eLzkOTC5MCo2Vi2YgMcXwudWh091+PruTDYQ/95eycPP\n7OFfWyr40WPb2by/lu2H6nl63VG8/hCzJqcB0NblizvuVGQ42YeuKOCOa4v5+DVTznqtDq96TPL5\nVnj0vSs8oAYegGNnGNa2IHsmAO+WqXOSDjUei22zGa1YDGorbZtBbTzgDnr6vY/9DUdRUJidNQ2X\nN4jNPLyNBB7+zyv47qcWkZwwtIuaCiGEEEL0JIFHjLhHtjzDmyfeBcCiSWDVAnWC//EydThbp3dw\ngUdRFN7YXA5ATZMz9vp7u6t5acMJMlOsfO5mNSS0O+MDT3Uk8Ewan8RtH5iCI6HvdXd66vBGKzzn\nOYcnMqQtOjItwaoGnikTI4Gnsu/Ac9mEBVgNFt4u24Qv6CekdFdw0nrMhbIaI4HHf5bAU38EgBkZ\nxXh8QazD1LAganJOMktm9D9sUAghhBDifA17L1ifz8cHP/hB7rvvPrZv387BgwdxONQvcp/5zGe4\n4oorhvsWxAWmtKki9timS2Rcmo1bryrkpUNlGDhzhefVjSfJH5/EzIK0PrcfLm+lItJpraHVjU6r\nIRRW2H5IndPy5dvmkpmirl/TcYYKT18toM+kPRJ4zrfCEx3SFhWt8KQkmkl3WDha0YrXF8Rsiv/r\natabuLbwCl48vJY3jq+n2dU9TC/Fkhx7bDOo79kVOHPgURSFfQ2HSTDZybSoXdOGq0ObEEIIIcRI\nGvbA8+ijj5Kc3P3l6+tf/7qEnEuYP+inK9wGkTnrCUY1YNx1/TR21O2iEWjobINsdbuiKDy+5zmc\nXi//fiWZmQVpzLy378Dzry1qdUen1VDb5KTnMqY3LMtnZmQ4m9moo8MVP0+oulGtCOWk2wf8XqJD\n2s67wnNa4LFHKjwAq+bn8uzbx3n27eN88oZpvY69qfhq/n1yE68ceSs2ZwcgFA7FHtsii5S6+lmk\ndEP5Vto8HSybsACPTz3WapG1cYQQQggx9g3rkLaysjLKy8u54oorYp2kenaUEpeeQw1loOkeemUz\ndQ8dm5ylTl7ffrSSj3/vTR747UZ+9tqLrC3dwOaq7ehzjlPrU0ON2xtgw+5qvL4gAG1dXrbsr2VC\nVgLT8lNp6/IRDqs/a9MnpcaFhSS7iQ5n7wpPRoq1VxXlTHbW7IutGXTeXdp6BB6LUYtO290Z7SNX\nFZKaZOaNzeX4A6Fex1oNFm6dfgOeoJdTHTWx13Xa7nPG5vCcocKzv/4If9r1d2xGK7dOvwG3V/1M\nrQP8LIQQQgghLmTDGngeeughvvWtbwHdbWj//ve/88lPfpKvfe1rtLe393e4uAjtrzwFQKBmEoG6\nfCZbZ8W2TZ+glnUOnKqiy+3nWH0Ne5zqXB8FBUN2Ge7szYTDCn986QC/+nsJX/zVu3j9Qd7aVkkw\npHDDsnyyUq2xc665vICf37dcXfclIjkSeKLhu8vtp73LR27GwKs7u2r2A5CfnEumre+K00DpdT0C\njyn+r6TZqOeKuTl4fEF2H2vs8/jVk5aTZU8HINXiYGbmFD4177bY9miFp66rkV9u+iNlrZVxx//v\nzqfQaLR8Y/nnyU7MirXBto1QlzYhhBBCiOE0bL/Cffnll1m4cCHZ2eqXWEVRWLNmDcnJyRQXF/On\nP/2J3/3ud3zve98767lKSkqG6zZH9VoXm5fWbkGv05CdYuRIlYfXd7Zx++Vp5KR1D9Hac6IUTBB2\nJhPuyKAxs56SEnU4mdHvQwkY0KVXE2odR86McppCIbQeB2FL98T9l9dt5d2SJgDqW9w8+/pW3ixp\nx6jXkKxtJuTrbljg6WqO+zOt9TYSCocIhhTWPPAqn16dHhv6ZsQ94D//svoKAG5OuYq9e/YO5uOK\naXMGY4+tRm2ve0g1qcPvfvrXHWg0YNJruXmpg6Lxltg+i+2zeMW5nnH6NK5PWEHNsVPUoIbLOqe6\nqOsrh9bhDLnBFWJl2mIAfGE/Le42JllzcJ/qpORUCcdr1EpQW0sDJSX9Nzq4UMnf46Ehn+PgyWc3\nNORzPH/yGQ4N+RwH70L47IYt8Lz33ntUV1fz1ltvUV9fj8lk4sEHH6S4uBiAq666ih/84AcDOtf8\n+fOH6zbjlJSUjNi1Ljbbd+zib++24A+GWTk/h/LaAC5vmPUHvTz8lcXoIlWM3+97D0zwvTuvpLQ0\nzK1XFcZVOP66tQLX+PcxFpXQFAqxJHcewcbx7PK9Ftvn3cNeFEUdqnaorIV/blYn69+zZgaXLSkg\nKaOFd/ZtAmDWtMnMn5cDwPHmMp5a/xeSs8dD9UwUBV7d5eSDy/KBJhbMmsz8+RMH9H6fqH+FJFMC\nSxYuPu/PrqXDA6+qjRWsJm2vn8F5ikJF214q6jrRajWU1XTw+q4uHl21kCS7KbLPPCaemkhR2iQy\nbKl4/UEUBSwmPebGBF6qf1sNO4A+wRi7RmV7NZTB5HGTYq85NdVAC0UFecyfn3/e72+kyd/joSGf\n4+DJZzc05HM8f/IZDg35HAdvpD+7M4WrYQs8Dz/8cOzxI488Qk5ODs888wwpKSlMmTKFnTt3UlRU\nNFyXFyPM5QvhD4bRauDdkmoA9DoN5bWdfPcPWyjMTaaxzU2HvwOdDaZkj2NBfu8hZJOSCtjbfgRd\ncjMOSxKfm/9x1u8uZ9ep7n0qGlrJzXTwoSsKOFTWAkDeuETWXF4AqEHo8jnj2bi3hrzs7vk1J1or\nAGinBlDbUze1eXjqTbUd84QBdmgLK2Ga3W3kJeec02d0Jj0DX4JV12u7RqPhS7fNjT1/8d1SHn/9\nMGu3VnDbB6bE9lk+cSEAb2wu588vH0Cn0/LHb10Vm8MT1eLurpY1udTPr2fDA7dXHdI23G2phRBC\nCCFGwojOSr7jjjv49re/jc1mw2az8dOf/nQkLy+GkcurNiK4/rJ8Jo5L5J1dVXzimmJ+8dRODpW1\nxIKJeboXnUaP3Wjr8zzpDguBvYVozR6+tPLT2E02ZuTmQI/AozF6uW31FLJSu88xISs+rHz9jvl8\n+qbppCZ1f9nv8rni9pmcm4zVpGf/iWYAcgYYeNq9nQTDQdJsKWffeQB6Ni2YPO7s6/9cuzSPf/z7\nGGu3VfKRq4rimhycrG7nTy/tJ6yondpKjjYyd2Z3sNSgodnTHXgaI4Enw94deJwyh0cIIYQQF5ER\nCTz3339/7PGLL744EpcUIywaeByJZq5dmse1S/MA+OZdC9lzrJGF07LITrPxjXe2YDE4Yk0sTmez\nGFBcSRhOrGJ6hloBnJCVgO/wYvRZFehSGkhP17B8znh8/u65L6dXZzQaTVzYAWhwqcHGoDUwpTCd\n+z86B4Ney5d/tQGLWY99gF/wo1WRjB5VkfPRM/BMyjKddX+r2cDSmdm8s6uKU/Wd5GcnxbYdP9VG\nWIEPr5zMC++eYF9pEyvmqd3vHJYk0qwpnGitIBQOodPqYoEn3aq+l2AozDu7qtBqIOccmjgIIYQQ\nQlyopO+sGBIur9oyOTkh/gv77MJ0tre/xW8O7GdW5lQ6fJ3kJJ15KONNfLaGtAAAIABJREFUKyZx\nuLyFO6+bGnvNoNdx98rl1ART2NjyJlddloFOq4kbcuU0l/O7bVtw+d0EwyHumH0LeY74IWd1nQ0A\nmPRGfvT5y2Kv/+ZrV8ZaWA9ETac63ybNOjQVHr1OS4bDQna6HZNhYI0To9Wt09trR6szMwrSeG93\nNftKmzDrzdwy7VryHRPYWrWb0pZy2rwdpFlTeoW3ddsqqW50cu3SvLgKmhBCCCHEWCWBRwyJaIUn\n2d4deJpdreytP8TGyu34QwE2Vm4H+g8KSXYTP7t3ea/Xb75yMnvr/GzcCHX+cl46vBYFRV3TR9Gw\nvv4NguHuis+Wql1xgUdRFGq71MDj8rsJh8NoI2vVpCSefRhZ1I7qvTy2+1k0Gg3FaQUDPq4/Go2G\nv3z3AygK7Nmze0DHJNrUznedpy2g2uVWA0+C1cDsonTW76yioq6Tj81cA0Bpi7qO0brS9yhvq+JA\nw1HMejMJJjtOT4Cn1x3FYtLz8WumDMl7E0IIIYQYbRJ4xJBw+dQKT5K9uwX1r7b8iZORNV9WT1rO\n6oIVHG0+wbzsmYO6RkZkzsz26j1sr94DwGXLrqf0GDjDQeaNm8Hts9bwwLqf0OppJxQO4Ql4sZts\nHGg4iifoBdQ1fbr8znNeMPTN4+/y1z3PY9Qb+ebye8lz5A7qffRFo9FwhlF+fYp+zqcHHqdbfZ5g\nNTKnUA08e483MWm8Ouwt1eIA4JWjbwFgDKSibywkrMDzbx+n0+Xnruun4kgYeAgUQgghhLiQSeAR\nQyJa4Ym2SVYUJRZ2AKamFzIpZQKTUiYM+hrZiVncv/hufEE/Hb5Onjv4OoVFWj56xQy+/e9/kWVP\nZ1xCJgCt7nb+uud51p14j99e/yB/2/ciGjRMTplIaWsFnb5zCzytHvV8SeYEvrXivvN6H0PhTBWe\nng0HZheqi5HuK23ilpWTAViUM4f9DUcoSMnD7Mrlj8+WAfD4a4d4Y3M5GQ5LrNudEEIIIcTFQAKP\nGBKxOTyRwFMXGT4WVZw+NF+iL89T171pcbfx3MHXqWyvYULSeADSbCkYdQYSTXZaPG0cbDwGwP9s\n/T8q2qu5fOJiMuyplLZW0OHtIjfpjJfp5URLBQoK1xWuHPWwA5BoUz/n3kPa1Od2iwGdTsvErAQO\nlrUQCIYw6HWkWh18c8W9hEJh7vvvd9BoQFHglY0n0eu03PeRORgNvVtjCyGEEEKMVRJ4xJBwecOY\njTrMJvVH6lBjKQDXF61iavrkuHVehkKKJRm70UZlezVT09XqRapVHa6VanFQ29WA1WDBHfBQ1nYK\ng1bPbTNvpKT2AACdPuc5Xa+sTa1WFaQMbGHS4XbGCo87gM2sjy30OrsoncqNZRytaGPm5LTYfm/v\nrKKmycV1S/PwBUK0d/m47QNFTMsf2j8nIYQQQojRJoFHDAmXL0xij4YF5e1VAFyZt2RI57pEaTQa\nJiaP53BjKdWndU1zWJMpb6/CYUzCHfAAcF3RStJtqSSa1PbVHd7Oc7reyVZ1IaD8YXgvg5FgVQNP\nry5tbj82a/c8qjmF6by6sYzth+p5fv1xappd3HPTdP7x1lGMBh23faCoV/tuIYQQQoiLiQQeMST8\nwTAppu4fp6qOWrQaLdmJWcN2zfGJWRxqPM7hxuNAzwpPMgBtno7Y6x+aeg0AdqMVIBaEBkJRFMpa\nK8mwpZJgujDWpjHotVjN+liFp7ndw7d+v4nmDi8FOd1j9aZPSkWn1fDKxpOx1375txL8wTAfXjlZ\nwo4QQgghLnoDW/RDiLMIBBWMkTVkFEWhqqOWcfYMjLqBLeY5GA6z+sW+tqsBnUZLskltQhANPqAO\nQfvdDT/CblTXlDHr1SqUN+hjoJrcrXT5XUy6QIazRSXZTLHA8/jrh2hodQPELaBqNRtYMDUz9txi\n0uEPhrGZ9Xx4VeHI3rAQQgghxCiQwCPOWzisEAqDyaBWeFo8bbgDHnKTsof1usk9uqylWB2xdXWi\nrZcBEow29NruSfiDCTxlkW5zBY4LK/Ak2ox0uvwcKmth456a2OtmY3zhtmfXtU99cDoAt6wsjA2L\nE0IIIYS4mMmQNnHe/AG1Q1u0wnOk8QQAE5KHN/D0bCud1qOqk2nvnpxvP20Imtmgri8zkMDjC/pp\n93ZQ1qbO3ym4ALqz9ZRkNxEMhfnts+qaRHaLAacnEKv0RM0oSOWO64qZnJPM3KIMstPszOjRwEAI\nIYQQ4mImgUecN18k8JiMOk611/CX3c+g1+pZkD17WK/bs8KTGmlYAJDRI/AkRIayRZ1Lhef/dv+D\nDeVbY8/zHRdW4Lls1jh2HK6nttnFqgW5pCaZeX59KTpd/AqmGo2G21ZPiT2fXZQ+0rcqhBBCCDFq\nJPCI8xYNPBh8/Pz9R/EEvHxpyafJc+QM63WTLX1XeKJze6C7SUHUQAOPL+iPCzvT0guxnXau0Xbl\nvByeX19KW5eXT94wDatJj9MT4Mblk0b71oQQQgghLhgSeMR5U4e0KZzUrafT3crHZt7E8okLh/26\nSZEW0xAfeDSa7grH6V3VDFo9Wo32rIEnul7PzMxilk1YwGUTFgzFLQ8pnU7Lz+5bhj8QJiVRHap3\n74eHt6omhBBCCDHWSOAR583nD4EuSCcNTE0v5Oap147IdQ06AzajFZffHTekrT8ajQaz3nTGwNPk\nasFhSWbzqZ0A3D331mFvvnA+HAnm0b4FIYQQQogLmgQecd78gTAaoxeAnMSsuArLcEs2J6qBp0dn\nNgCbwYLrDGvtnCnw1HY18JV//YC542ZwoOEouUnZF3TYEUIIIYQQZydtqcV58wWCscCTEln0c6Sk\nWNT5Omm2+MDzo9UPsGrSMlblX9brmDMFnlPtamvnPXUHCYaDLLsAh7EJIYQQQohzIxUecd78gTAa\ngxogHCMceD4640Yuy10QW1g0KidxHJ9feEefx5j1Jlo87b1e7/Q5455fiPN2hBBCCCHEuZHAI87L\nWyc28lbZdjQmdRjbSFd4pqQVMCWt4Ow79mDWm/AFfYSVMFpNd5Gzxd0Wezw5JY8su7RvFkIIIYQY\n6yTwiPPyl5JnANDaU4HuIWYXsmhral/Qj8XQPem/Z+BZNWnZiN+XEEIIIYQYehJ4LhKKovD7f+4j\nw2Hlo6uLRuSa/lAg9lhr6QIgxTqyFZ7B6LkWT1zg8aiB59Ebf9KrCYIQQgghhBibpGnBRaKspoN1\n2yr529ojnKzuPT+lL63udt46sZGwEh7UNaOT/AE0Rj96jR6b4cJanLMvZ1p8tNndRpI5kTRryoh2\nmhNCCCGEEMNHAs9FYsPuagAUBf78ykEURTnrMb/a/Ef+UvIMGyu2D+ga4bDC468d4sCJZgBOtlbG\nbU8wJo6JoNBX4FEUhVZ3G2lS2RFCCCGEuKhI4LkIKIrCpn212CwGFkzN5FBZC5v21fZ7jC/op7S1\nAmDAgaespoMXN5zgufXH1WtGFueMcpjGRlgwG6KBxxt7rcPbSSAcJNU6Nt6DEEIIIYQYGAk8F4Ga\nJifN7R7mFqXzuQ/NRK/T8vjrh/D6g2es9OytPxR7fLDxGJ3errNepzQyVO5EVTt76w5xrPkkmoAl\ntj3Nknqe72RkmPXqvJ2eFZ46ZyMA4xIyRuWehBBCCCHE8JDAcxHYe7wJgDlF6YxLs7Hm8kk0tXm4\n6wfr+Pj33qSlw9PrmKqOOgCy7eMAqHc2nfU6pVUtGPIO4jbV8MTul0EBb9nU2PZ0W9pQvJ1hFx3S\n5g50fy51XdHAkzkq9ySEEEIIIYaHBJ6LwP7InJpQQg0HG47y0dVFGA06PL4gTk+A0qreTQzavR0A\nnDqpNuprdDWf9TpHmk6iz6jGVLSbWlcNwdYswp3dVZ1M+9gIPOMTswA42Xoq9lptJPBkS4VHCCGE\nEOKiIoHnIlDX7MJiVXjy0NP84v3/pT3QypdvmxPb3tLeu8JT3aoGnLBTbSPd4Ow/8PgDIRr9Vd0v\nKHBz8fU8eM/y2EvZiWNjoc4paQUYdAYO1B+JvVbX1QDIkDYhhBBCiIuNBJ4LmMvvHtB+LR0eEjI6\nCSthfCE/j2z7K8tmj+Pn96lh5L09NbxbUhV3TF1HG0pYQ9ilLhTa6Grp9xqlVe1g795nWe5i7ly1\nkAlZCbHXxieOjbBg1BkoTiugsqOGdm8nAPVdjVgNFhJNCWc5WgghhBBCjCUSeC5QO6r38qmXvsau\nmn397ucLhOhyB9AmqmEkLzmHE60VvHRkHekOtaHAkYpWfv30btq6vBwpb+UzP36LFnc7BI0oPnWf\nsw1p23GiFK29nXRTFj9c9XW+sPjjAKQkmgl1pKKEdDhsYycszM6aBsDuWrWFd72ziSx7+phoqy2E\nEEIIIQZOAs8F6tWj/wbg6f2v9Ltfa4cXbUILTlMFZr2J/3fFl0i1OPjnoTdoDzbE7fvCOyf4rz9v\npbHNjcbgg6CZgvEpKH4Tjc7+Kzwbm9ei0SrcPPVaitMLMOqNAGi1GvzHFuItWY1WO3bCwqIcdcjf\n9urddPq6CISDpNlSRvmuhBBCCCHEUJPAc4GKVhpaPe2x1tL+oJ8vvPod/r7vpdh+rZ1e/n97dx4Y\nVXU+fPx7Z7LNTLbJnpCV7KwJCauGJAgIAhalbqBUUVut2OqLWqS2WtufWCy1KC4VAVEUhAqIiLII\nxKCEJRC2iEBYQgiTPYHsmcy8f8QMRBbJQibL8/nHmcmdO889Ds+9z5xzz7EN+BGTUscjcffh7ODE\n7wdPxWQ2MW/nQhTdxQkLPv82i5paIxqNGUVlwkHRERGox1SjoaiyBKOp/oqxmM1mKpQCVNUujIwc\nfNnf33wmmQdv6RzD2Rr5OHoS4hrAgbwjZJc1rFkki44KIYQQQnQ9UvB0QCaziezSs0DD1MkH8hpu\nrs85b6CoqsTyHCC/tBxFW47e1ovhwQ3FSF/vKG6LGEFBRREOvdNQHMoBUCnw9OQ4evSwbXhe70Cv\nEHfMNVpMmCiqLKbkfDW1dU0Ln9zSYlCZ0KldrhhvsK8zwd72bdsI7WBwQCz1pno2HEsBwF0rPTxC\nCCGEEF2NFDwdUH5FEVXGarwdPVErKuanfUBRZQm5P80kdrLkDB/sXUFm/lFOFZ9DUZnw1fk22cfU\nmEn09Y4EQHGoZPpdMbz822EkDfDHz7dhKmpXB2d6h7hb7uM5WWjgofmLeGHxxib7ysxpKL70Dq43\n9Ljb2xD/WAB25zbcJ+Wu7VrHJ4QQQgghwMbaAYiLqo01bD+9i4N5PwIwJiwRlaJi8b4V/Pv7BfT2\nirBsu/7YVr46tg1XpaHQCXb1b7IvlaIiMXgoB/N+ZNLoAG4dHARAjbGWPIc9UAMTB8fiqdfgZONC\nNbDv7BHsQg9yvKgQs3kMNbX1ONjbcKLAAICvc+dYZ+d6+Tn7EODix5mfhrS5a2VImxBCCCFEVyMF\nTwdQa6xlw/FvWXtkI2U1FwBQq9QkhQxFa6vhWPEptp/exbGik03ep9e4UFzVcLEe7RNy2X5dHZwB\n0DqaLK99dWwr2WVnGdHzJpJCBwIQ4uHDD0BmXhYAim0NaYcMvPLBLvqFeXBemwMOEOzu3ebHbm1D\n/GOl4BFCCCGE6MJkSFsH8P7e5Xy0/zNq6+sYE5aEp86dh2LvQmenRVEUfhc/hUCXHpe9b86oFzAX\nBmBT7UH/HmGX/d3FoWGa6LKf1pqpqK3k8x82oLPTMrX/JMvECP0CG3p/8mvOAaDY1JJ2qOHxgeOF\n5JQUABDu69fGR259QwIGAA2TROgdrnyPkhBCCCGE6Lyk4OkADhqO4OLgzFvj/8G0uHt4a/w/GB2W\naPm7vY0d0wf/psl7XB2cOX22iuoTvUlyuRv7n6aJ/vk2AIbyAsqqz7P2yCYq6qqYGHUrWjuNZbuB\n4UGYTQpmVS0Aim0t6Uca7hf6x++G4e3TUBgF6j3b9sA7AH9nX0L1QQS7+KNWqa0djhBCCCGEaGMy\npM3KzteUU1RVQqxvHxztdVfdLlgfwN9veQadnZYfC7Lo79uL9dsa7q2JibhyIeJk54hKUbHfkMmj\nn/8Je7Udrg7OjAlParJdgJczilELdhUNL9jUUVZeg05jh+JcSIVtLhrFAWeHzrOw6PVSFIW/Jj9l\n7TCEEEIIIcQNIgWPlZ0uzQEun3TgSiI9QoGGXgmAjKMHUasU+vR0v+L2KpUKja0DFbWVANTU13J/\n/zsv6w1SFAUntQsXqPjpuRls6nDxv8Ds1PUoKEwfOg2V0jU7BDW2DtYOQQghhBBC3CCd8gq2tq6e\nNz7dx7EzJdYOpdVOlfxU8Oh/ueC51IXKWo7nlBIZpEfrYHvV7RqLHQA/J29u6XnTFbfzdmw6A5ta\nb6DE9XvsVLbMGj6dwT9N4SyEEEIIIURncsMLnpqaGkaNGsWaNWswGAw88MAD3H///Tz99NPU1dW1\naJ87DxvYtCub//efbzlbUI7ZbG7jqNvP3nMHAQjRBwKQk3+BiqpfbpcDxwoxmyEmwuu6PufRuMm8\nOmomNuord+qFejVdx0ftbgAFnhj8G/r8tJ6PEEIIIYQQnc0NL3jefvttXF0bFnScN28eDzzwAEuX\nLiUwMJDPPvusRfs8X15jefzYq9/w1OsppB061+kKn0/TvuNw/lGi3CIpylfxl3e/5/F/bmH+yoxf\nfO++o/kAxF7l/p1Gt0eNBmCwfwwO1xi6FenbdBY4G13D9Nj+Lr5X2lwIIYQQQohO4YYWPCdOnODk\nyZMkJiZiNpvZvXs3ycnJACQnJ/P999+3aL+5RRVNnp/MLeP/Fu9ixrxvOZlb1uq4AY5ml/Cbv23g\naPYvD5szm818vH81i/Z+et37N1wo5LOsTzGbISPVjZlvbSfjWAFqlcLeH/P54WQxD//fJk6fO3/F\n9+8/VoDOwYbwANdrfs6UfhP55Ndv/uKEAz6OTQsns7qhl8lNc+39CyGEEEII0ZHd0IJnzpw5zJw5\n0/K8qqoKW9uG+03c3d0pKCho0X7PFV4seO4bHclbz44gIaYHx86U8vTrKaz85mire3tmL9lN8flq\nVm09/ovbbju5g8+PbGRTVup1f+7nGd+BTR3GM5GYK1wYEOXFnOkJjBwUSGW1kefmp5JfXMmKb45e\n9l5DUQWGokr6hnmgVl/7f6GiKFcdxnYpL93lEx9obTU42Nhf1/EIIYQQQgjREd2wWdrWrFnDwIED\n8fO78mKVrSlIzhVW4KS1Zc6TCfTwdERRFJ57IJ6RAwN5c8U+Plz/A2qVwp3J4U3ed9pwnvfXHCIm\nwpNJI8KvsveG2ApLqwDQO1/7gj/n/DlLz069qZ7Kuip0dtom26QdOsePp0uYelu0ZbHPvVnZoIEn\nxyUT6x+J3rlhuFlhaRUb0k5fEszln/nj6YZep76hHpf/sYWc7B3p7RWBg4096bkN9xW5S++OEEII\nIYTo5G5YwZOSkkJOTg4bN24kLy8PW1tbtFottbW12NnZkZeXh5fX9d1wn56ebnlsMpk5V1iOj96W\nvDNHyTvTdNvfjNDz+ufn2PD9MYKcLw4Hq6ypZ/66PCprTGQcKyDAqQy1SrniZxWUXZw04NQZA+np\nV55EoM5k5MOcz6mpr8XVxolS4wW+3bWDzbuMDAjVEeXfsLjn/33SMBObu10Zvm52nDBUU1BRgo0G\nlPOlnDh2+OJOa0xNPuPo6XzL8ZvNZr5KL+V0fsMCodXnDaSnl/5S81238c7DMZlN7OUQZsyo61RN\n2v6XNGdbcXXSjq0nbdg2pB1bTtqubUg7tp60YduQdmy5jtB2N6zgef311y2P58+fj7+/P3v37uXr\nr7/m9ttvZ8OGDSQkJFzXvuLi4iyPzxaUU286S3iwd5PXL7V2Twonc8vo2y8GY72JL7afYO23J6i8\npJjQuAVf1kOSnp5OXFwc3+3PBfIAUGx0l31OzvlzvLPrI06VnKHOZGR06HA0tg58fmQjZic9R8+e\nQVFrmPKrOOrrTfBTwXPepGdQz0BeX5uCKqAaBYWEQTdjo1I32b9Gn8fsJbupraun+EI9MbEDUKsU\n8oor2bVsk2W75JsG4KnXXFcbNof7uTUUVhbj5eZ51Tb+uca2E60j7dh60oZtQ9qx5aTt2oa0Y+tJ\nG7YNaceWa++2u1px1a7r8PzhD39gzZo13H///Zw/f5477rij2fs4cqoYgMhA/VW3iQzSY6w38/7a\nQ/x29maWfnWEyuo6hvTx4S/TBgOw67ChyXs278om5VBDj1Be8cW1a0ouVDfZrtZYy9zt73Gs6CR1\nJiMBLn5MjZmEs33DpACn8xvuSzp6poSSC9XkXnK/0fb9ucz+YBdl5bU4u5pwdXC+rNgBiI/2ZsUr\n40iO86fWaGLnTzPQlZxvGou7y41ZMNNd29C2xVVt13skhBBCCCGENdywHp5LTZ8+3fJ40aJFrdrX\nDz8VPFHBblfdJjJQzzpO8tX3p9A62DBlTBS3J/RE62BLbV09DnZqdmcaePj2PgAUlFTx1v/2Y6w3\nkfRjPvkllxQ8PysyvvhxM2cvGOjrHYmn1p2J0bdiZ2OHs70jAGdLigEtZjPsyczD3u5iQXMmr2Gq\n5xED/dltrsBb23Qq6EupVQpD+viyNT2H2Ut207unO71Cmh6z6gpD8trCpF638cq3bzI+cuQN2b8Q\nQgghhBDtpV0KnrZiNpv54VQx9nZqQnydr7pdXLQ3/cI8CPV35dcjwnHW2Vn+ZmerJibCk7RDBs4W\nlNPD05HVKccx1jcMd1v8xWHcfuo5iQh05Wh2KR+sO8yUMVHUmKpZc2QjLvZOTAq5j9eWZJC77zgD\noi6g82xoyoLyMqBh0oKdhw0EeDf0/Dz/m4F8suEIzjp7Hhgfyo4vjbhrrt5LBTCsnx+vP5XIxxuO\nsOeHPA6fKGpx2zVHjG8vPrzzdexlhjYhhBBCCNHJdZqCp95k5t1VB8g2XCA+2vua0zE7ae34v8dv\nuurfB/XyIe2QgV2HDdyRFMax7BJUKoXegRoOnjpPtuE8Oo0t/l5OHC87xhfndnFkTU96hblSY6xh\nUq+x7D9SQmFZNYVl1ew7WoCiLcOhD5RWnaeHZxigkHGsgKoaIwB9Qj2YNyMZlQInSxpmWrieNW7C\nAlx58ZEh/H3hTnZlGn46PluemRLfjNZrvmstUiqEEEIIIURn0a738LRUbV09//xwN1/vOEVPPxf+\ncHdMq/YX38sbRcFSQOSXVOLhqmFUjAt2tmpMZvDWa7lQWYuNdzZq52JO1O9h3Y+bsVHUDPMfxMmf\nFgSd+8fh/OHuGDwcXQCooxo/H3vie3lRU1vPgeOFuLnaUK+qQq1SqKirZOHe5QD4u/hed8zBfhd7\ntF5/OokBUdc3w50QQgghhBDdWacoeD74MpMdB8/RL8yD2U/cZFmzpqX0Tg5EBOg5lFXE1Je+pvh8\nDT5uWpy1au5ICgXAy03DuGHBqJ1KcbJxof5ELBQHUHkykiVrsjhxtgwXRzvCA1wZNTiI+LAAAFTa\ncn7QrKDaNdPyeXbBmfxu7Uy2ndzB37a8zrGikyQEDeKWnlfvhfq5IB8ny2O3X1gbSAghhBBCCNGg\nUwxp+/5ALs46O158ZAh2tpfPatYSA3t582N2CSUXagDw0msBE3cmhXEm7wID+upYnDUf1HXE9ogi\nzC+Jt/63H4Bv888CEBPuaVlINNhXj/mUGpX2AvVAbs0pHDV9Ka+qo8zuBABv7/oQgNGhw5kWdw8q\n5frrzSCfiz08tjZt0wZCCCGEEEJ0dZ2ih6eorJqYCM82K3YAbh0STEy4p+X5Bd0RNhZ8h8behud/\nM4gTxr3kVzRMEhDh0ZNbhwTxwNjoJvsI6eFieRzg5YS5Rmt5frrsLHHRDfvXqhtmcBsWGM+DsXfx\ncNy9zSp2APw8HZt3gEIIIYQQQojO0cMDEBvRtvesuDrZ8/LvhnL7M2sBOFGbQXnlebKKT9PD2Yfv\nzzQsXNTXO5JB/jEoisLdIyMoLa/hi9SGHpvel0wTHeDthKlKh0rbMPV0XX0dNw12RqVS2GWqJNIj\nlKeGPtzieG1tVLz4yJAmM84JIYQQQgghrq1TFDzBvs4M6Xv9N/hfr8bhaKiMlBsbJiHYlJXKYP8Y\naow13NlrDPf2/VWT9zROMw3QN8zD8tjF0Q6t4kotFxc0rVIVMe2OPqR93rDIaGvFR3u3eh9CCCGE\nEEJ0J51iSNu8/5eEo8a2TfaVU3aO06U5mM1mThSfJn5MDoMGXew1+T57Dz8WNvTg9NQHXfZ+Pw+d\n5bHW4WJMiqIwdcSgJtueKDlNaVVDIaV3cEEIIYQQQgjRvjpFD49KpbTJfmqNtcza/E+qjTV46zzI\nqygEoKf+PJSA3taZkrrzfHVsKwD+zj6X7aNXiBtD+/oyIj7gsr9FeF18Ta1Sc6I4m1K/MgBcNa3v\n4RFCCCGEEEI0T6coeNpKznkD1cYaPLRunK8pt7x+oiQbgAS3eL7M30a1sQYblQ3ejp6X7cPWRs2s\nBwdd9jqAn1PDfUb9vKO5UFvO6dIcCitLAHCVHh4hhBBCCCHaXacY0tZWzpTlAvCrqNG8P3EOc0bP\nQmNzcU2fIK0fg/xjAfBz8katat6scHY2dnxw57/5U8Lj9NQHUWcycijvCAB66eERQgghhBCi3XWr\ngie7rGH9nEBXP2zVtgTrA4j06AnAyJ43o1U7MCr05oZtXPxa9BlaWw22altC3QIBSM89CMg9PEII\nIYQQQlhDtxrSlv1TD0/AJcXMQwPuIT33AGPCktifsZ/eXpE8OfghIjxCWvVZPfUNBU9NfS2KouBz\nheFxQgghhBBCiBur2xQ8dfV1nCg+jbtGj6PdxZnWfJ28GB850vJcURQSgq98j05zBLj4oaBgxkyg\nSw8cbB1++U1CCCGEEEKINtVthrSlnt7NhdoKbgqKb5fPs1VfnLI6RH/5jG5CCCGEEEKIG69bFDxf\nH9vG++nLUCkqxoQntdvnNk5F7aZxbbfPFEIIIYQQQlzU5QueA4ZCOu3pAAAgAElEQVQfWLxvBTo7\nLf9v2KN4aN3a7bOfvekxYn37MC5iRLt9phBCCCGEEOKiLn0PT2FFMfN2LESlqHju5scId2/dRATN\nFeYezPPDn2jXzxRCCCGEEEJc1GV7eOrq65j7/XtcqK3godi7273YEUIIIYQQQlhfly14Fu9bSVbx\naYYHD2ZUaIK1wxFCCCGEEEJYQZcsePYbMtmclUqQqz+Pxk1GURRrhySEEEIIIYSwgi5X8JjNZj49\n+AUATwyair2NnZUjEkIIIYQQQlhLlyt4zpXnc7z4FHF+fQmW9W+EEEIIIYTo1rpcwXO6NAeA3l4R\nVo5ECCGEEEIIYW1dtuAJdOlh5UiEEEIIIYQQ1talCp5TJWfYdjINgGBXfytHI4QQQgghhLC2LrPw\naHltBX/dMpdqYw0Azg5OVo5ICCGEEEIIYW2dtuAxm82cLDmDk72OcxfySTmVZil2bgqMt3J0Qggh\nhBBCiI6g0xY8e3IP8Nr2d5u8pndw4Z+3zsLZztFKUQkhhBBCCCE6kk5R8FQbayitKsPHycvy2nen\ndwPg6+TFYP9YQvQB9PaKxNleih0hhBBCCCFEg05R8HywdwVbTn7PmPAk7u9/JwB7zx3CW+fBf8a+\nhKIoVo5QCCGEEEII0RF1ioInw5AJwNfHtnGk4DjDg4dQbaxhVGiCFDtCCCGEEEKIq+oUBU9xVSkx\nPr1w17rxzYntnMr4HwCD/WOtHJkQQgghhBCiI+sUBQ9AX+9oJkSNRFEUNmelAhDmHmzdoIQQQggh\nhBAdWqdZeLS3VwQAd/cZj6fOnbv7TECldJrwhRBCCCGEEFbQKXp4Xh4xg55ugQC4Ojjz1vh/WDki\nIYQQQgghRGfQKbpIojzDrB2CEEIIIYQQohPqFAWPEEIIIYQQQrSEFDxCCCGEEEKILksKHiGEEEII\nIUSXdUMnLaiurmbmzJkUFRVRW1vL448/zoYNGzh06BB6vR6Ahx9+mMTExBsZhhBCCCGEEKKbuqEF\nz5YtW+jbty8PP/wwubm5PPTQQwwYMIBnnnlGihwhhBBCCCHEDXdDC57bbrvN8jg3NxdfX18AzGbz\njfxYIYQQQgghhADa6R6ee++9l+eee45Zs2YB8PHHH/Ob3/yGGTNmUFpa2h4hCCGEEEIIIbqhdil4\nli9fzttvv80zzzzDr371K2bMmMGSJUuIjIzkzTffbI8QhBBCCCGEEN2QYr6B48sOHTqEu7u7ZSjb\nuHHj+Oijj3BzcwMgKyuLl156iY8++uiq+0hPT79R4QkhhBBCCCG6kLi4uMteu6H38OzZs4fc3Fxm\nzZpFYWEhlZWVvPjii0yfPp3IyEh2795NRETENfdxpaCFEEIIIYQQ4nrc0B6empoaZs2ahcFgoKam\nhunTp6PVann11VfR6XTodDpeeeUVS4+PEEIIIYQQQrSlG1rwCCGEEEIIIYQ1tcukBUIIIYQQQghh\nDVLwCCGEEEIIIbosKXiEEEIIIYQQXZYUPEK0s6KiImuH0GXILYjC2kwmk7VD6NSysrKsHUKXIfmw\nbUg7tkxpaam1Q7imblXwVFdXU15eLl/mFvj222+ZOXMmO3bs6PBf6o4qKyuLJ554ghdffJFFixYB\nklhboqqqis2bN1NeXo6iKNYOp9OqrKwkJyfH2mF0SoWFhYwcOZLi4mJUKpX8O26hNWvW8PTTT/Pd\nd98BUjy2RF1dHUuXLpV82EqN55Xa2lppx2ZKSUnhscceIzMz09qhXFO3KXg+++wzpkyZwr/+9S8W\nLFgAyMXm9TCbzcyZM4ePP/6YqKgovvrqK3bs2GHtsDqdvLw8/vOf/zBhwgRmzZrFO++8Q15eniTW\nZvriiy+4//77WbNmDf/4xz8oLCy0dkid1lNPPcXs2bOlx7EFiouLycnJsfxwIZqn8dzr5OSEra0t\nGzZsoKKiApWq21yStJnt27fzxhtvsHLlSkCua1pi5cqVPPbYY2RnZ2Njc0OXp+xSCgoKmDFjBkuX\nLmXatGkMGzbM2iFdU7fILqmpqaxfv565c+dy9913s2vXLsrKyuRi8zqUlZVRVlbGf//7Xx588EFs\nbGzw8/OzdlidjkqlwmQyMWbMGPz8/LjllluoqKiwdlidSnFxMVu3buWdd95h/vz5ZGVlkZuba+2w\nOp3GX9GdnJwwGo0cPnyY2tpaK0fVOTS2nUaj4d577+Xrr79m7969KIpCfX29laPrHMxms+Xce/bs\nWcaOHUtAQACrV6+2/F38ssZ28vX15eabb2bbtm0cOXIERVGkp+w6VVVV8c9//pP333+f2bNnM23a\nNCm6m+H48eMUFRUxY8YMBg0aRE1NDSUlJdYO66rUL7300kvWDuJGKC8vx87ODoCMjAz69u3LwIED\n2b9/P9XV1dx8881SyV/F6tWrKSgoICgoCAcHB4qLi4mKiiIlJYVFixahUqnIy8ujV69e1g61wzpz\n5gyTJ08mJiYGLy8vHBwcGDZsGBqNhueff57s7GxSU1MxmUz4+fnh4OBg7ZA7JIPBgFqtxtbWFo1G\nQ0pKCmPGjKG4uJiUlBSCgoLw8PCQ9vsFl+bDxovNI0eOoFKpMBgMRERE4OTkZM0QO6xL82Fj26Wm\npuLl5UViYiLvv/8+d9xxh1woXcPP82FdXR1qtZozZ84A0L9/f1JTU1Gr1Wg0GhwdHa0cccd0aT5s\n/C5u3rwZT09PYmJiWLduHSNHjpQfc39BYz5UqVQUFRXh6upKYmIiZWVlfPnll9ja2uLu7m7tMDuk\n1atXk5+fT3BwMAEBARw7doyioiIOHDjAG2+8wcGDBzly5AiDBg2ydqiX6ZIFz6effsrcuXOJjIzE\ny8sLZ2dnBgwYQEFBAX/9619xcnJixYoVmM1moqKiMJlMkiB+UlJSwsyZM3FwcMDT0xN3d3d69+6N\nSqWioKCAqVOn4uTkxNatWykuLqZPnz7WDrlDyszMZNOmTZw7d45bb70VlUqFRqMBIDIykmnTpuHr\n60tKSgohISF4enpaOeKOJycnh3HjxuHq6kp0dDRqtZpbbrkFtVrNkiVL6NGjB3v37iUzMxNHR0d8\nfHysHXKH1JgPo6Oj8fT0xGg0UllZyZYtW3j++efZtWsXFy5coKSkBD8/P7lwv8Sl+dDb2xs3Nzeg\n4b6Jo0ePcvfdd7NgwQIWLlxIWFgYgYGBVo64Y/p5PlSr1UDDxfqQIUPQ6/UsXLiQHTt2MGHCBCl4\nruDSfNh4TgY4f/48ZWVl3H333axYsYLdu3fj5OQkIzGu4tLrQx8fHzQaDSdOnGDJkiVs3rwZW1tb\nFi9ejFqtplevXnJ9eIlL86GHhwfu7u64ubmxatUqKioq+NOf/kRERARbt26loKCAfv36WTvkJrrk\nme3UqVNERERYusgb/+F7enqycuVKZs+ezSOPPMK///1vgG5/gj9//jxVVVUApKenExQUhK2tLRkZ\nGU2GacTHxxMYGMjw4cMZOnQoJSUlMvzgJ3V1daSlpVnuh8jJyWHu3LkcO3aMDRs2ABeHw3h5eQEw\nZMgQiouLMRgM1gm6g8vOzqZPnz6kp6df1kaPPvoov//973n22WdRqVQytO0aGvPhqlWrALCxscHR\n0REHBwcURcHW1pY5c+awceNGObFz9Xy4d+9eSz788ccfyc/PZ86cOWi1WgBuuukmq8Xc0VxPPgTo\n0aMHzz33HM888wwJCQn07duX/Px8a4XdoV2aDy/Nd9nZ2Tg4OLBjxw6ys7PZuXMn0dHRVoy0Y/v5\n9WFQUBB9+/bFz8+Pp59+mhkzZvDss8/y1ltvAXJ9eLV8uH//foxGI9HR0dx33308+OCDBAQE0KdP\nH5KTkyktLe1w14ddoofn4MGDZGRkEBISgtFo5Pvvv2fs2LGkp6ejUqno2bMnZrOZ2tpa1Go1KpWK\ngIAADh48SO/evXF2drb2IVhFfX09c+bMYcWKFaSnp9O7d2+ioqKYOHEiRUVFHD16FCcnJ3x8fKir\nq2Pjxo24urqi0+lYtGgR4eHh9O7d29qHYTWNY9F37tzJs88+S15eHp999hnBwcGMGDECHx8f3N3d\neffdd7n33ntRFIWSkhJWrFhh6QZOS0tj5MiR0jsBpKWl8b///Y/S0lLCwsIoLi5m8uTJZGRkkJ2d\nTWxsLGq1GqPRiMFgwMnJCUdHRzZs2ICXlxdRUVHWPoQO4XryYV5eHuvXr2fVqlXU1tbSq1cvoqKi\nCA0NtQx9626uJx/qdDp8fX0xGo0sWLCAoUOH8sorr7Bjxw6ysrIYMmSItQ/DapqbDwFOnjyJj48P\nL7zwAsnJyRQWFlJeXi7/lvnlfBgTE4NaraakpMQygcvMmTMpKirCYDAQGxtr7UPoEK6VDxVFITQ0\nFA8PD+Li4ggKCgIgICCA/fv307t3b1xcXKx8BNbRnHwYHByMm5sblZWV2NnZsXjxYiIiIjrc9WGn\nLniMRiOzZ89m/fr15OXlkZGRgV6v59e//jXe3t5UVVXxzTffkJSUhI2NDRkZGXz55ZcUFRXxySef\ncP78ee68805L93p3k5qaSmZmJnPnzmXfvn0cPnwYgMDAQFxdXTl8+DAlJSWEhISg0+n48ssv+fzz\nz1mwYAGRkZFMnjy5214cwcV7IT7++GOGDh3KU089hclkYvHixSQnJ6PRaAgNDWXTpk3k5uYycOBA\nNBoNNTU1pKSkcPjwYaZPn97hun3bU+NF0jfffMN///tfkpKS+OijjygvL2fo0KG4uLgQEBDAxx9/\nTEREBF5eXiiKwsKFC1m2bBm7du3izJkzTJgwodsPC7zefJiYmIirqysnTpxg+PDhPPHEE0RHR7Nl\nyxZiYmIsPRbdzfXkw9LSUkJCQggKCmLSpEkMHDgQgGHDhhEfH4+9vb01D8GqmpMPz549y8CBAwkP\nDycuLg47OzvMZrP8iNaMfBgZGYm3tzf19fUkJSXx8MMP4+3tja+vL87Ozvj7+1v7cKzqevLhli1b\nSEpKQqvVoigKKSkpZGVlsWzZMioqKuT68DryYWhoKPb29nz66acsXbqUt956i6ioKO67774Od33Y\nqQue+vp6Nm/ezN///ndGjx5NSUkJS5cuZdy4cajVanQ6HYcOHcJgMNCvXz8cHBwoKipiy5YthIeH\n8+c//7nbfZkPHz5MXV0dzs7OrF+/HkVRSEhIICwsDIPBwJEjR+jVqxfu7u5UVlaSnZ2NXq+noqKC\n4cOHM3r0aIYPH85tt91mOUl1t2Ew+fn5LFmyhJKSEnr06EFOTg7V1dXExsbSq1cv0tLSKCgoIDY2\nFkVR6Nu3L/PmzSM2Npbly5dz0003MX78eMaMGYOXl1e3bMNLKYrC+vXrCQ4OZvLkyfTp04d169bh\n5uaGr68vnp6enD17lj179jBixAgURaFfv344Ojqi1Wr585//3O2LHbj+fJibm0tMTAwDBw4kLCwM\naJixbfjw4d2u2GluPjx9+jTu7u6UlJTg6uqKjY0NZrMZjUaDvb19txzv39p86OHhgZubG4qiWCYS\n6s45sTn5MDk5Gb1ebxm2bzQa8fHx6fbFDlx/PszLy6Nfv35UVlaSlZXF559/TmRkJLNmzZLrw2Zc\nHw4YMIChQ4cyYsQIxo0b1yGvDztdwbN27Vo2bdpEZWUlfn5+fPjhh9x5553Y29sTFBTErl27OHHi\nhOXXNnd3dzZu3Eh2djbHjx/nnnvuYeTIkcTFxVn7UNpVeXk5r732GsuXL+f06dNkZGQwadIkli9f\nTmJiIp6enpjNZrKysqitrSU8PJyePXuSmprKggULWL16NcOHD8fX1xcXFxfMZjNms7nbjW/dt28f\nTz/9NEFBQezcuZOKigoqKiowmUz4+PhYfll79913GTt2LA4ODuj1epYsWcLy5cuJj48nKSnJ0m4m\nk6nbtSHA119/zezZsy3d4nq9nmPHjtG/f3969OhBYWEhhw8fJiwsDGdnZwYPHszy5cvZv38/8+fP\np0+fPgwbNqzbT5rRkny4efNmcnJyOHDgAD179uyWvRKtyYfvvfcea9euJSEhAQ8PDxRFsZzUO9LJ\nvT20Nh8OHDiQUaNGXbbf7taOrcmHb7/9NiEhITLhCK27Pjx27Bh33HEHY8eOtfTcdhdtcX2YmJhI\nYGAger2+w14fdqxorsFoNDJ//nzWr19PZGQkzz33nGVqvHnz5gENayPcd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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Get pricing data for two benchmarks (stock indices) and a stock\n", "start = '2013-01-01'\n", "end = '2015-06-01'\n", "b1 = get_pricing('SPY', fields='price', start_date=start, end_date=end)\n", "b2 = get_pricing('MDY', fields='price', start_date=start, end_date=end)\n", "asset = get_pricing('V', fields='price', start_date=start, end_date=end)\n", "\n", "mlr = regression.linear_model.OLS(asset, sm.add_constant(np.column_stack((b1, b2)))).fit()\n", "prediction = mlr.params[0] + mlr.params[1]*b1 + mlr.params[2]*b2\n", "print 'Constant:', mlr.params[0], 'MLR beta to S&P 500:', mlr.params[1], ' MLR beta to MDY', mlr.params[2]\n", "\n", "# Plot the asset pricing data and the regression model prediction, just for fun\n", "asset.plot()\n", "prediction.plot();\n", "plt.ylabel('Price')\n", "plt.legend(['Asset', 'Linear Regression Prediction']);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can check that our independent variables are correlated by computing their correlation coefficient. This number always lies between -1 and 1, and a value of 1 means that the two variables are perfectly correlated." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "0.98870295660403051" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Compute Pearson correlation coefficient\n", "sp.stats.pearsonr(b1,b2)[0] # Second return value is p-value" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "*This presentation is for informational purposes only and does not constitute an offer to sell, a solicitation to buy, or a recommendation for any security; nor does it constitute an offer to provide investment advisory or other services by Quantopian, Inc. (\"Quantopian\"). Nothing contained herein constitutes investment advice or offers any opinion with respect to the suitability of any security, and any views expressed herein should not be taken as advice to buy, sell, or hold any security or as an endorsement of any security or company. In preparing the information contained herein, Quantopian, Inc. has not taken into account the investment needs, objectives, and financial circumstances of any particular investor. Any views expressed and data illustrated herein were prepared based upon information, believed to be reliable, available to Quantopian, Inc. at the time of publication. Quantopian makes no guarantees as to their accuracy or completeness. All information is subject to change and may quickly become unreliable for various reasons, including changes in market conditions or economic circumstances.*" ] } ], "metadata": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.12" } }, "nbformat": 4, "nbformat_minor": 0 }