{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "#A tutorial on Markowitz portfolio optimization in Python using cvxopt\n", "\n", "Authors: Dr. Thomas Starke, David Edwards, Dr. Thomas Wiecki\n", "\n", "Notebook released under the Creative Commons Attribution 4.0 License.\n", "\n", "---\n", "\n", "##About the author:\n", "\n", "Today's blog post is written in collaboration with [Dr. Thomas Starke](http://drtomstarke.com/). It is based on a longer whitepaper by Thomas Starke on the relationship between Markowitz portfolio optimization and Kelly optimization. The full whitepaper can be found [here](http://eepurl.com/4Pgrv).\n", "\n", "## Introduction\n", "In this blog post you will learn about the basic idea behind Markowitz portfolio optimization as well as how to do it in Python. We will then show how you can create a simple backtest that rebalances its portfolio in a Markowitz-optimal way. We hope you enjoy it and get a little more enlightened in the process. \n", "\n", "We will start by using random data and only later use actual stock data. This will hopefully help you to get a sense of how to use modelling and simulation to improve your understanding of the theoretical concepts. Don‘t forget that the skill of an algo-trader is to put mathematical models into code and this example is great practice.\n", "\n", "Let's start with importing a few modules, which we need later and produce a series of normally distributed returns. `cvxopt` is a convex solver which you can easily download with\n", "`sudo pip install cvxopt`.\n", "\n", "## Simulations" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import cvxopt as opt\n", "from cvxopt import blas, solvers\n", "import pandas as pd\n", "\n", "np.random.seed(123)\n", "\n", "# Turn off progress printing \n", "solvers.options['show_progress'] = False" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Assume that we have 4 assets, each with a return series of length 1000. We can use `numpy.random.randn` to sample returns from a normal distribution." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [], "source": [ "## NUMBER OF ASSETS\n", "n_assets = 4\n", "\n", "## NUMBER OF OBSERVATIONS\n", "n_obs = 1000\n", "\n", "return_vec = np.random.randn(n_assets, n_obs)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYkAAAEPCAYAAAC3NDh4AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/wOuKbkbO3+r3AAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(return_vec.T, alpha=.4);\n", "plt.xlabel('time')\n", "plt.ylabel('returns')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "These return series can be used to create a wide range of portfolios, which all\n", "have different returns and risks (standard deviation). We can produce a wide range\n", "of random weight vectors and plot those portfolios. As we want all our capital to be invested, this vector will have to sum to one." ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[ 0.54066805 0.2360283 0.11660484 0.1066988 ]\n", "[ 0.27638339 0.03006307 0.47850085 0.21505269]\n" ] } ], "source": [ "def rand_weights(n):\n", " ''' Produces n random weights that sum to 1 '''\n", " k = np.random.rand(n)\n", " return k / sum(k)\n", "\n", "print rand_weights(n_assets)\n", "print rand_weights(n_assets)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, lets evaluate how many of these random portfolios would perform. Towards this goal we are calculating the mean returns as well as the volatility (here we are using standard deviation). You can also see that there is\n", "a filter that only allows to plot portfolios with a standard deviation of < 2 for better illustration." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def random_portfolio(returns):\n", " ''' \n", " Returns the mean and standard deviation of returns for a random portfolio\n", " '''\n", "\n", " p = np.asmatrix(np.mean(returns, axis=1))\n", " w = np.asmatrix(rand_weights(returns.shape[0]))\n", " C = np.asmatrix(np.cov(returns))\n", " \n", " mu = w * p.T\n", " sigma = np.sqrt(w * C * w.T)\n", " \n", " # This recursion reduces outliers to keep plots pretty\n", " if sigma > 2:\n", " return random_portfolio(returns)\n", " return mu, sigma" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In the code you will notice the calculation of the return with:\n", "\n", "$$ R = p^T w $$\n", "\n", "where $R$ is the expected return, $p^T$ is the transpose of the vector for the mean\n", "returns for each time series and w is the weight vector of the portfolio. $p$ is a Nx1\n", "column vector, so $p^T$ turns into a 1xN row vector which can be multiplied with the\n", "Nx1 weight (column) vector w to give a scalar result. This is equivalent to the dot\n", "product used in the code. Keep in mind that `Python` has a reversed definition of\n", "rows and columns and the accurate `NumPy` version of the previous equation would\n", "be `R = w * p.T`\n", "\n", "Next, we calculate the standard deviation with\n", "\n", "$$\\sigma = \\sqrt{w^T C w}$$\n", "\n", "where $C$ is the covariance matrix of the returns which is a NxN matrix. Please\n", "note that if we simply calculated the simple standard deviation with the appropriate weighting using `std(array(ret_vec).T*w)` we would get a slightly different\n", "’bullet’. This is because the simple standard deviation calculation would not take\n", "covariances into account. In the covariance matrix, the values of the diagonal\n", "represent the simple variances of each asset while the off-diagonals are the variances between the assets. By using ordinary `std()` we effectively only regard the\n", "diagonal and miss the rest. A small but significant difference.\n", "\n", "Lets generate the mean returns and volatility for 500 random portfolios:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "n_portfolios = 500\n", "means, stds = np.column_stack([\n", " random_portfolio(return_vec) \n", " for _ in xrange(n_portfolios)\n", "])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Upon plotting those you will observe that they form a characteristic parabolic\n", "shape called the ‘Markowitz bullet‘ with the boundaries being called the ‘efficient\n", "frontier‘, where we have the lowest variance for a given expected." ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAcgAAAEZCAYAAAATw7VgAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n7OQAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(stds, means, 'o', markersize=5)\n", "plt.xlabel('std')\n", "plt.ylabel('mean')\n", "plt.title('Mean and standard deviation of returns of randomly generated portfolios')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Markowitz optimization and the Efficient Frontier\n", "\n", "Once we have a good representation of our portfolios as the blue dots show we can calculate the efficient frontier Markowitz-style. This is done by minimising\n", "\n", "$$ w^T C w$$\n", "\n", "for $w$ on the expected portfolio return $R^T w$ whilst keeping the sum of all the\n", "weights equal to 1:\n", "\n", "$$ \\sum_{i}{w_i} = 1 $$\n", "Here we parametrically run through $R^T w = \\mu$ and find the minimum variance\n", "for different $\\mu$‘s. This can be done with `scipy.optimise.minimize` but we have\n", "to define quite a complex problem with bounds, constraints and a Lagrange multiplier. Conveniently, the `cvxopt` package, a convex solver, does all of that for us. We used one of their [examples]() with some modifications as shown below. You will notice that there are some conditioning expressions in the code. They are simply needed to set up the problem. For more information please have a look at the `cvxopt` example.\n", "\n", "The `mus` vector produces a series of expected return values $\\mu$ in a non-linear and more appropriate way. We will see later that we don‘t need to calculate a lot of these as they perfectly fit a parabola, which can safely be extrapolated for higher values." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAZcAAAEPCAYAAACOU4kjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "def optimal_portfolio(returns):\n", " n = len(returns)\n", " returns = np.asmatrix(returns)\n", " \n", " N = 100\n", " mus = [10**(5.0 * t/N - 1.0) for t in range(N)]\n", " \n", " # Convert to cvxopt matrices\n", " S = opt.matrix(np.cov(returns))\n", " pbar = opt.matrix(np.mean(returns, axis=1))\n", " \n", " # Create constraint matrices\n", " G = -opt.matrix(np.eye(n)) # negative n x n identity matrix\n", " h = opt.matrix(0.0, (n ,1))\n", " A = opt.matrix(1.0, (1, n))\n", " b = opt.matrix(1.0)\n", " \n", " # Calculate efficient frontier weights using quadratic programming\n", " portfolios = [solvers.qp(mu*S, -pbar, G, h, A, b)['x'] \n", " for mu in mus]\n", " ## CALCULATE RISKS AND RETURNS FOR FRONTIER\n", " returns = [blas.dot(pbar, x) for x in portfolios]\n", " risks = [np.sqrt(blas.dot(x, S*x)) for x in portfolios]\n", " ## CALCULATE THE 2ND DEGREE POLYNOMIAL OF THE FRONTIER CURVE\n", " m1 = np.polyfit(returns, risks, 2)\n", " x1 = np.sqrt(m1[2] / m1[0])\n", " # CALCULATE THE OPTIMAL PORTFOLIO\n", " wt = solvers.qp(opt.matrix(x1 * S), -pbar, G, h, A, b)['x']\n", " return np.asarray(wt), returns, risks\n", "\n", "weights, returns, risks = optimal_portfolio(return_vec)\n", "\n", "plt.plot(stds, means, 'o')\n", "plt.ylabel('mean')\n", "plt.xlabel('std')\n", "plt.plot(risks, returns, 'y-o')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In yellow you can see the optimal portfolios for each of the desired returns (i.e. the `mus`). In addition, we get the one optimal portfolio returned:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[[ 2.77880107e-09]\n", " [ 3.20322848e-06]\n", " [ 1.54301198e-06]\n", " [ 9.99995251e-01]]\n" ] } ], "source": [ "print weights" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Backtesting on real market data\n", "This is all very interesting but not very applied. We next demonstrate how you can create a simple algorithm in [`zipline`](http://github.com/quantopian/zipline) -- the open-source backtester that powers [Quantopian](https://www.quantopian.com) -- to test this optimization on actual historical stock data.\n", "\n", "First, lets load in some historical data using [Quantopian](https://www.quantopian.com)'s data (if we are running in the [Quantopian Research Platform](http://blog.quantopian.com/quantopian-research-your-backtesting-data-meets-ipython-notebook/), or the `load_bars_from_yahoo()` function from `zipline`." ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "IBM\n", "GLD\n", "XOM\n", "AAPL\n", "MSFT\n", "TLT\n", "SHY\n" ] } ], "source": [ "from zipline.utils.factory import load_bars_from_yahoo\n", "end = pd.Timestamp.utcnow()\n", "start = end - 2500 * pd.tseries.offsets.BDay()\n", "\n", "data = load_bars_from_yahoo(stocks=['IBM', 'GLD', 'XOM', 'AAPL', \n", " 'MSFT', 'TLT', 'SHY'],\n", " start=start, end=end)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfEAAAE3CAYAAAC6g3jUAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzsnXeYVNXZwH/vLp1dehFEBAQpNqwgio6KRo0loqhRwfZZ\nYiwkmlhShtFPTVFTNNF8VkABsaHGStSrEls0IgIiFpAiIJ0F6ft+f5xzZ+7Mzu7O7O7szN09v+e5\nz23n3PvO3dl57zlvE1XF4XA4HA5H+CjKtwAOh8PhcDhqhlPiDofD4XCEFKfEHQ6Hw+EIKU6JOxwO\nh8MRUpwSdzgcDocjpDgl7nA4HA5HSMmZEheR3UTkDRGZIyKzReRqe3yciCwRkY/tckKgz40i8oWI\nzBOR43Ilm8PhcDgcDQHJVZy4iOwC7KKqM0WkBPgI+BFwJlCmqneltB8ETAIOBnYF/gXsqarlORHQ\n4XA4HI6Qk7ORuKouV9WZdnsj8BlGOQNImi6nApNVdbuqLgS+BA7JlXwOh8PhcISderGJi0gvYH/g\nPXvoKhH5REQeFJF29lh3YEmg2xISSt/hcDgcDkcKOVfidir9SeAaOyK/F+gNDAaWAXdW0d3lhHU4\nHA6HoxKa5PLiItIUeAp4VFWnAajqd4HzDwDP292lwG6B7j3ssdRrOsXucDgcjkaFqqYzQ4Oq5mTB\n2L0nAH9KOd4tsP0zYJLdHgTMBJphRupfYR3vUvprrmS21x+Xy+s7uRuO7GGV28nu5G4ssodV7lTZ\nq9J7uRyJHwacB8wSkY/tsZuAH4vIYMxU+QLgMivhXBGZCswFdgBXqJXe4XA4HA5HRXKmxFV1Bult\n7i9V0ec24LZcyZQhvfJ8/5rSK98C1IJe+RaghvTKtwC1oFe+BagFvfItQA3plW8BakGvfAtQQ3rl\nW4Ba0CuTRi5jW0Vm5luAGhJWuSG8sodVbnCy54Owyg3hlT2sckOGsucs2UuuEBHVygz8DofD4XA0\nMKrSezn1Tq9PnNd65riXIIfD4WgYNKjp9Hx7E4ZhKUREJJJvGWpCWOUGJ3s+CKvcEF7Zwyo3ZC57\ng1LiDofD4XA0JhqMTdwez4dIoUJE3HS6w+FwhIiqbOJuJO5wOBwOR0hxStyRd8Jqtwqr3OBkzwdh\nlRvCK3tY5QZnEy8YevXqxWuvvcYjjzxCcXExpaWllJaWsscee3DffffF2y1cuJCioiIOOOCApP6r\nVq2iWbNm9O7du75FdzgcDkeB45R4jhGR+HLYYYdRVlZGWVkZTz31FL/85S+ZOTM5nn/z5s3MmTMn\nvj9p0iT69OmDSMM1Y6uql28ZakJY5QYnez4Iq9wQXtnDKjdkLrtT4vVEaojX4MGDGThwIPPmzUtq\nN3r0aMaPHx/fnzhxImPGjCnY8DCHw+Fw5A+nxPPEBx98wPz58znooIOSjp977rlMmTIFVWXu3Lls\n3LiRIUOG5EnK+iGsdquwyg1O9nwQVrkhvLKHVW7IXPYGk7EtDLz33nu0b9+enTt3snHjRq666ir6\n9u2b1KZHjx7079+f6dOn8/rrrzNmzJg8SetwOByOQqfRjMRF6mapDUOHDmXt2rVs2LCB5cuXM3v2\nbG666aYUOYUxY8bw8MMPM2XKFEaPHt3gp9LDarcKq9zgZM8HYZUbwit7WOUGZxOvgGrdLHVFly5d\nGDlyJM8//3yFcyNHjuTFF19kjz32oEePHnV3U4fD4XA0KBqNEs8n6UbSq1ev5plnnmHvvfeucK51\n69a88cYbPPDAA/UhXt4Jq90qrHKDkz0fhFVuCK/sYZUbnE28oPBDzN59911KS0sBaNWqFSNGjOAv\nf/lLUjuf1Hjxhhxi5nA4HI6a4XKnNzJc7nSHw+EIFy53usPhcDgcDRCnxB15J6x2q7DKDU72fBBW\nuSG8sodVbnC50x0Oh8PhaPA4m3gjw9nEHQ6HI1w4m7jD4XA4HA0Qp8QdeSesdquwyg1O9nwQVrkh\nvLKHVW5wNnGHw+FwOBo8zibeyHA2cYfD4QgXzibucDgcDkcDxCnxemLKlCkMGTKEkpISunbtytCh\nQ7n33nsBuOCCC/jNb36Ttl9RURElJSWUlpbSqVMnRowYwdSpU+tT9JwTVrtVWOUGJ3s+CKvcEF7Z\nwyo3OJt4QXHnnXcyduxYrr/+elasWMGKFSu47777eOedd9i2bVs8t3plzJo1i7KyMubPn88FF1zA\nlVdeyc0331yPn8DhcDgchYizieeY9evXs+uuuzJx4kROO+20tG0uvPBCevTowS233FLhXFFREV9+\n+SV9+vSJH3vqqac477zz+Pbbb2nfvn1W8jibuMPhcIQLZxPPI++++y5bt27l1FNPrbNrnnLKKezY\nsYMPPvigzq7pcDgcjvDhlHiOWbVqFZ06daKoKPGohw0bRvv27WnVqhVvv/121tds2rQpnTp1Ys2a\nNXUpat4Iq90qrHKDkz0fhFVuCK/sYZUbXD3xCkisbmaQNZrdlH3Hjh1ZtWoV5eXlcUX+zjvvALDb\nbrtRXl6etQzbt29n5cqVdOjQIeu+DofD4Wg4NBolnq3yrSsOPfRQmjdvzrRp0xg5cmSl7apybEvl\n2WefpUmTJhxyyCF1IWLeUVUv3zLUhLDKDU72fBBWuSG8sodVbshc9kajxPNFu3btiEajXHHFFagq\nxx13HK1bt2bWrFls2rQp3m7Hjh1s2bIlvl9cXEzTpk0B8B321qxZw0svvcS1117LDTfckLVTm8Ph\ncDgaGKoaqsWIXOnxguWxxx7TQw45RFu1aqWdO3fWIUOG6P3336/btm3TCy64QEUkaRk+fLiqqoqI\ntm7dWktKSrRDhw569NFH6+TJk2ssR2XPL58LEMm3DI1Jbie7k7uxyB5WuVNlr+p324WYNTIKMcRM\nRCIawmmvsMoNTvZ8EFa5Ibyyh1VuSJa9qhAzp8QbGYWoxB0Oh8NROS5O3OFwOBw5Q4QTRTg633I0\nRpwSd+SdsMZyhlVucLLng7DKDRnJ/gLwmgiHitC9HkTKiAb+zAGnxB0Oh8NRe+bb9TXA0nwK0thw\nNvFGhrOJOxyOukaEp4BgIowNQBdVtuZJpAZFXmziIrKbiLwhInNEZLaIXG2PdxCR6SIyX0ReFZF2\ngT43isgXIjJPRI7LlWwOh8PhqFMEWB3YbwMsy5MsjYpcTqdvB36mqnsBQ4GfishA4AZguqruCbxm\n9xGRQcBZwCDgeODvIuKm+xsBYbVbhVVucLLng7DKDVXLLkJr4AfAoymnKmSjEmFPEVrUrXSV01Cf\neZCcKUlVXa6qM+32RuAzYFfgFGC8bTYe+JHdPhWYrKrbVXUh8CXQMPKKOhwOR4EhQjurgGvLGUAr\n4FZgP2Bzmnt1E+FV4PN05x01p15GuiLSC9gfeB/oqqor7KkVQFe73R1YEui2BKP0HQ2csCZjCKvc\n4GTPB4UitwhXiqDAWuC5TPpUI/uuwO9VWanKLODKNG2uAo7NVtbaUijPvCZkKnvOlbiIlABPAdeo\nalnwnPVEq8obLe05EXlERMbZZWwhT5ls3LiR3r17M2nSpPixsrIyevbsydNPP82SJUs499xz6dSp\nEyUlJQwZMoQXXngh6RpFRUV07dqVnTt3xo9t376dLl26JJU4zZTg8xKRiNt3+26/8ezD9BhxXupX\n++uNPxBYntiXr4HdgcWB9stNDw/wEKFtoTyPQty3yzgxuu4RqiLHuV+bAq8AYwPH5gG72O1uwDy7\nfQNwQ6Ddy8CQNNdMm0OWAs6d/sorr2jnzp115cqVqqp6+eWX6+mnn65r1qzR3XffXS+66CJdsWKF\nbtmyRSdPnqxt2rTRJ598Mt5fRHTAgAH6/PPPx489++yz2r9/fy0qKspKlsqeXz4XQprfOKxyO9kL\nX27QItCi3Mihz4G+B6qgr9dWdtDHQX+ccqwT6OrA/vX2fivs+tlCe+aFtpBh7vRceqcL8CAwV1X/\nHDj1HHC+3T4fmBY4fraINBOR3kA/4INcyVefHHfccfzwhz/k6quvxvM8nnjiCf7+979z11130aZN\nGx588EG6dOlC8+bNOfvss/nVr37Ftddem3SN0aNHM2HChPj+hAkTGDNmjP8HdjgcDQQRBBOiNa6O\nr9tbhFFAb4yPEsC7dXDp3sDClGM7sTO9IjwN/M4ug+z5U0RcPHmdkMO3iMOBcmAm8LFdjgc6AP/C\nJAd4FWgX6HMTxqFtHvCDSq6b9o2EAh6Jq6quXbtWd9llF+3UqZM+8sgjqqo6ZMgQHTduXIW2X3/9\ntYqIzp8/X1XNSHz27NnatWtXXb9+va5Zs0a7du2qs2fPVjHxgxlT2fNzi1vcUhgL6Cl2tPoH0Nag\nAvp/oO1red1/2utuBx1nt2/L8hp7gF4C2sbuC+ha0E4p7dqCrgftYO+joGPsDIO/r/l+1mFZqvrd\nzlk9cVWdQeU29xGV9LkNuC1XMuWTdu3asddee/Hee+8xcqTJibB69Wq6detWoa1/bNWqVfTr1w+A\nFi1acPLJJzNlyhTKy8s59dRTadGi3iI1HA5H/fGsXZcAG4G7gUuAKcDrtbhuT+Aj4EBgKhCFrHXA\nl3Y9GPgp0Mnur05pV475/d8rcGy+KuXiUk3VKY0nDlukbpYa8uijj/LNN98wYsQIfvnLXwLQqVMn\nvv322wptly1bFj+fEF8YM2YM48ePZ+LEiQ1qKj3o2BEmwio3ONnzQXVyiyAiPGN37wA62u2r7LpD\nLUXoCPwJQJW5wLVkqMTTyH6gXZ8GtFOt4ITsK/Ff2/3rSZhH+9n1+kwFryk1+a7UZxx7VWQqe+NR\n4okZnNotNeC7777j5z//OQ888AD33XcfU6dOZcaMGYwYMYKnn366gjKeOnUqPXv2jI/CfYYPH87y\n5cv57rvvOOyww2r8KBwOR0HSjkTejEnAmYFz24DONb2wtbN3xPgejbKHd5D9SHwTJtpoiAjHAv+o\npJ2vxI8DUOUPqpTbcwuBycC6LO+dc0QoATZnq8hF6G771j/5nuuvK9sABWwTHzVqlF566aXx/Qce\neEAHDBigK1as0J49e+qFF16oy5cv182bN+ukSZO0TZs2OnXq1Hh7EdGvvvpKVVXnzJmjc+fOVVXV\nL774wtnE3eKWBrKA7mlHC/+2+8ERxDOgT9fi2q1BN6ccuwL071leZzPogNTRTZp2zUG3VnG+K+h3\n+X7maeTyP9MBoOtAm2TQp6Ptc08l56+svT8DFZ6hvzSekXiemDZtGu+88w5//OMf48cuvvhiunfv\nzt13382MGTPYsmULgwYNolOnTvz5z3/m0UcfZdSoUfH2EpjGHzRoEAMHDkx7zuFwhJqOwPuqpJtm\nexE4OJuLidBThDcDo/BUu/UOTBhwNjQBvkk5dnOadv5IvDI2QSJbnAhtRGptLqgxIvRPKaHaE2gL\nlGbQ3Z892Ra43i0itLTXvBu4rM6ETSXfbz519UZCAY/EC4nKnl8+F0IayxlWuZ3shSk36A9BXwzs\n3xQYGQ6z60syv5+eZPvsC3oG6Msp5y8CfThT2a0numLj1+0IU0HvSnPvYtCdoC+B/rCS8+WBa/3X\nXutH+fiupLGdXmXXu4MWV9P3Kdv2Xrsvgev8qaae+OQ7TtzhcDgcmSFCP+CfwGL/mCq3YbzIwcSN\nLwX+L8PrXQQ8b3d3waQ8fTml2Xays4kXAeWasG3fa9dfpGnrj8Q7AytTT6qyE9gKtLSH+tr1MyIF\noZd2s+tHMeHRaRGhM6YE63bMcwZ4PNBkLIG/aS4ohIflaORoSPMbh1VucLLng2rkvt6uH045vsOu\ny4ArIO6khghDRFARjk5zvd8Gts/GKNNUZZKxY5uVvUlAHl8RNwfuq9g+7q3ehTRK3NIC2CjCEZgC\nKj47UxvafO9nZSJrGrmz5U3gF3b7cGCfKtr6U/BNMZ8VjOPgNhLmixEAItkV9MpUdqfEHQ6HI/8M\nsOtURetXfFyhGi9W8hO79kt9HhHsYEeyu5OI4b4QM+JNrR62A2giwt9FTOhZynV2EaGrCJ4IMYzS\n3RFso8q2gMJOpRxT4KoyJe7zJlBstxdV0uZuYGI116kLXgaGZNF+d7u+Guhqn/0GTFGYrpgy3P7M\nxfsiFfwJao1T4o6801DjfgsZJ3v9U5ncItwMcWe274LnVHkV6KfKlsDhv4mwH2YUDBVDtf7H9l0N\nrLLHWpNeiTfFvBT8hIq8gZkqPxJevRyTcTObVNhFGOW8qZLzC9IcO5QUpR9weMvWCS/r74oqJ0CF\n8LLv0rUVoZhEYp7ngD2AZ4A2qqxSZacq7wNfYcLywDjMZYSLE3c4HI5w4Hud/1mV7aknVeNZ0oLM\nBHrY7cNF+M7W7B5Ccuy2P4U7nIrKdDvQ3243t97s7UQoEuFqzOyA9c5u1gWTMe55smNFFSP1A1P2\nizFmg9Qa54PtepNvSsicpmK9xE+vpuFiEl73x9n932LKZW+opE/QtPAN8DVwSmoj+/krtavXFqfE\nHXmngdo4Cxone+ZITNpKTNKmis6GKuQuAk5S5WcZXCY4SrzHrk/E2LwPBd5LvmfSaPeTlGttJDGN\nD8Yx61vgCeDc5KYRf2NeBjIGWV7FuaSZAesw9z3QMsW5zX8RaQ1cnN3tt51mr/mkSDwDXhwb2tYE\nUOAaK8d0VXqqcgtwENBXpEq7uG+2KLf9071o/DnNsSpxNnGHw+GoG34DTJeYtKy2ZQARikXIpE9L\nzAi0WlTZCvw7Tf/gGpJHhJcBZ9i+QWan7Le21xhJYvTrswkzUs22smS6KXMArIngDMw0dGt7bCcg\nVgafJiR8A+4lO/oGto8NnhChFJP6dSJmmntumv5+athZIvxAhG+t4i/GKP7drdkCYE1lQqiyiYSz\nXJ3ilLgj7zQ0G2cYcLJnhW+T/V5iUsEBrAq+wYwCgWS5rYL/gQi/wEx1V+f8FeSXlRyPK3HVxLS3\nKv+nGrfJEji+KrA7jYSjHEAzjIIdY3YPPFeVXil9MqGqkTiqPKXK16qJ52R5IrDdAlN4JQbclemN\nRTgHvBMCh9qnNOlt12fbdQWzhSplJBT5y0A3268lsFk1yRHveSqfege408q1Z2byO5u4w+Fw1AXt\nAttjs+i3axXnRmKUwh+Ah1Xj9b0zwVcUL5JwboPkMK1MWQjMwYRDXWePzbfrp4mHe/23psVKapLv\n/TcQ97IHo8S3AGuBFiKUiiSN1CtjeMp+s5T9YDw3Vdjuh0PSy0svzMxB6ovHraq0rUyYwPVHVdam\nJjglXo9EIhE6dOjAtm3bKpxbsGABRUVFXHHFFRXOFRUVUVJSQmlpKT169ODaa6+lvNxELfTq1YvX\nXnst57LnkrDaZ8MqNzjZsySoxJFYdrmOrc01LrcIQ0kkcTkTuDJLeXwlPkuVbcCewO0kl/3MlAMx\nnvEPY2zqAH8z8qKYEfHAWjzzjL2xfVT5X4xHuJ88xfes/xYTyvUS8JRIwltdhMtFKpS4vjxgywfr\n3S5CKxGeItkfIK0HupXnU+Btu/sUZtbiOira9DOpkPUW1vZeHc4mXmAsXLiQDz74gC5duvDcc89V\nOD9hwgT23ntvHn/88bRKftasWZSVlfHaa68xadIk7r//fsDkTnf50x2OnNIuZb+Cg1Q17J6yf7dd\nT1TliTRTydXhK/GtAKp8gQlx8sPUhmZ6IVXWqLIeeCcg2z+AE+z57apZO7P5HAicV8O+i4ClNpSu\nE2Yk7Dvt+Z+zGOLJb+4lUfYUkfisRNDT3Vf6D5Owufve+cdUI88lGNu9/6JwHYnY9mw4glpUo0uH\nU+L1xIQJExgxYgSjR49m/PjxSedUlYkTJzJu3Dg6duzI889XHsXRv39/hg8fzpw5c3Itcr0RVvts\nWOUGJ3uWpJaYHOZviDBMpMK0LSLshnF0mo21xQbkXgSg6tubs8ZX4sHR43JM9rCNNjY5KwKjyDWq\nbFVNTtFak2euyn9V+SrbfpZP7fphjG1+gWqFRDi+EvVjtb8NnOsJfAVyCMa57f9IhOT5oWFjSNjB\nl1YljCqrVfmaZLt598ra1wXOJl5gTJgwgbPOOoszzzyTV155he++S/z/zZgxgxUrVnDiiScyatSo\nCkoe8JPgM3fuXN5++23233//epPd4WjkpMYtPxvYfg0zRQqYqXIRzsB4Qk/HjCDbpPTfB6jxP7AN\nxWpOsqf2eszLQsVpvOzIxsEul1wG/IzEc5pl19MCbXwlfrJdB73z+wOfA9gXiR9j09ZintNJqky0\nz7KvKmszlOtIEpXN/ifDPkHOrb5JdjglXg/MmDGDpUuXcsopp9CvXz8GDRrEpEmT4ufHjx/PySef\nTIsWLRg1ahQvv/wyK1cm/y8dcMABdOjQgVNOOYVLLrmECy+8sL4/Rs4Iq302rHKDkz1LUpV4kPiP\nvw07ehdjR26JcRbbgJ1OV1XPOmv1I6GUakSadKf+6DzVAzsbTgUeTH+/+n3mNumN79n+20DGut8H\nmh0swq8xoWH3QJJT2UDgs4Dcl5N42Uoqy5rNbIEqm1TZCBSrpn9W1fApFUP7KrlXZs88mwo2oUY8\nr06uo5FI1n3Gjx/PcccdR2mpeYHzR9tjx45l8+bNPPnkkzz8sKl7MHjwYHr16sWkSZO45pqE/8PH\nH39Mnz596uQzOByOrAgq8T8Cv5CYDNOovoNR4t1EuB74XaCd71FdBjwkwluY39sFwI5AJbA6QZWd\n1jWmxg4ygdzshcITwCcpnvtLAttXkqjlfRbwhghdVVmBcfS7MdB2BYnCKmkrq2VDLf5+W6iY1rVW\nNBolXhPlWxds3ryZqVOnUl5eTrdu3QDYunUr69evZ9asWcyePZsNGzZw2WWXxT3T161bx/jx45OU\neENGRCJhHBmGVW5wsmd8r5gMIfl30lcoL9mc3oPs/u/Y/0FovwBe/9+vSVbiAF+CB0Rak1JEJAzk\n4/tiE7+kht4FnQCDCXLmYhzglpN4kXk5IPcqTEESMNXGKvVGzzEZK/FMn3mjUeL5Ytq0aTRp0oRP\nPvmEZs1MmKKqcuaZZzJ+/Hhmz57NxRdfzK233hrvs2TJEg4++GBmz57N3nvvXe09tm3bxpYtifoI\nTZs2pbi4Jo6TDocjhfdS9v1QozYkSk8ajrwF2n0D/714N9b1LsEonNSiIx2gYn50iUl/jerndSNy\n1dgQuaM1qmGMTfWV+DoChV9UKfeDdEToZQ8vJRFZ8BnQW4SzMTMrG+tB1nTU+Ujc2cRzzIQJE7jo\noovo0aMHXbp0oUuXLnTt2pUrr7ySu+++mzfeeIOxY8fGz3Xp0oUDDjiA448/ngkTJmR0jxNPPJFW\nrVrFl1gsluNPVbeEdUQYVrnByV4VIkwTSRvze5RG1fdOXoTJ3gX+NK3an9NzTgbog/nBDqQ6jWD7\nJI3EJSaPkX1O8nTsR2aVvg4A/iUxyfhNv4C+L1sxDn2bqTwszE/1ut6X28bTtwQmA9MyjOnOBRkr\n8Uyfufhez2FBRFRVK9h97PF8iBQqRIR0z8/hcBgCCrw54ySYb7ybRnW5xORS4GDG6TOYFKhDbVvT\n6svjVvPoKx2B6zFZ2T7BVMQ6024fp5oYxUtM/PsVaTR3P2ISk5GQlH71Uo3q/bm6Xy4R4VvMC9Er\nwI2qfGwdC4OVxSSlj/9sx6ryl3oTNlmGJph0rVmVVa1M74EbiTsKgLDGLIdVbnCyV4NvLw2Wyrwc\n4xwFZjTYHJNRbJHZDujeVqv96fLLVeNe6Ivhn8WYEKPOEpPTJSZT7Dl/ijjXv8dBBf44JnY6Iwrw\n++J7op+hasp8Wht6UthXitx+ydfV5AlVdmDGUtWasl2cuMPhcNSM6XbtezeXaVT/ERgl+1OibfBD\nzHq/4fc9jmYbd3DiT+FXrbpITJpi0qKOh2jQW/pq4CyJyW6YeOdyapYBLBuCTmE3AEhMkvK7S0wG\nW5kKnVbAThvuFScQ9pVadhUSyWAqrTZWT2whOed9rXBK3JF3CsjelhVhlRuc7NVQjFHOJ2NsqQem\nnPdH4qX4HtLnx82zm2i6cQd9XoOmm1sDf1XlC1VU9SOTJKbl6scw6TfBVL5aaK+ZM0djiUkpsBhT\nmzuiUV1oTy1JaepR0ZkvjN+XYqggtz+Tsq5C6/plC1RfotbFiTscDkfNaIKZPr8HpDXoipTzO1jd\nbw9Mze4bU85tpe3SXnz0P9Dpc4DUUe2JXHLIchKZu/az643k9vf4ZUwWs9Ua1f/YYzuBYuvgdj4m\nCUpb6th7Okf8F+Ogl45hULFkqo2lH2X75pM69VB3I3FH3ilAe1tGhFVucLJXg3GQKt7aGZXmJMcj\nA+xgQ4897Hbw3Av4nupN4v5w8VGfifvlJTp83Zpku+xnmPzsXbKtkJYFvkALAsd8Jfhn4D5MWVSA\n5hKTpFSxBfh9GQGkjb9V5V1bFKaC3Ko8Gcj+li8yUuLOJu5wOBxZIMJeItyHGRHvpOUa2N56axqP\n8Z1Q7tuvN1K0bSXGqepkjepMlO/p/+wiez5druxS4EPM728bjaqfMOYLsi9LmilfAZelfBa/yMiV\nJELT/Dj4lyUm5+RIllqjylpVwloFyo3EHQ2LENrbgPDKDU72SjgNU3ijCbCDDl+8RHlxusIYO0h4\nF6/lt837InwfV5BCK1ps6IkJP4vnSA/IXQJs1KiqRjV1lP9DiUkLiUldT60PJLX+dcWXk8OA0zFK\n/VDgMV+OsH5fClTuCkpchGYiJDkZunriDofDkR1+wY0TgJ2ULitme6tNFVq9Me4wZKeZ9i5Zth6T\nFSxdTfDppLdzl1B5xrCdwHzgkWwErwqJySiMgk5XdKUP8Ce7PUujupJkx7Z4PXCJSVOJyZF1JVcj\nZgvQUgQR4VUR7sX4YKQ6GWaEU+KOvFOA9raMCKvc4GSvhGCM8UeULG/CtpKKSvzrY2+haCcUbYfr\nunvANyQr8WB960RSl4TcD5Eo3OFzuF0XY5zhzpWYHCExGUTt2R24S6NaIexKo7qARAW07+2xjzDh\nc/cAu0hMnpQfyF2YMqeexKS9xCQMzm+F+j3fgvmOlGNK1p4HNAMQYbRdFzmbeIHQq1cvmjdvzurV\nyfkF9t/UetMiAAAgAElEQVR/f4qKili0aBFLlizh9NNPp3PnzrRr14599tknXlN84cKFFBUVUVpa\nGl8GDx7MiSeeGN9v1qwZzZs3j+/7hVQcDkdW9MfYsKOqrKTrrK6s2aO9CCrCIBEuEqGE8mIo2gFt\nF38Y6BtX4hrVH2lUBeO81i44NR5QfqkhRh9hErDsETj2JjDHKs3LavKBJCYHYSqvVcjXHmAq8BON\narwyl53mX4BJaHM63fiZPbUZE2e9OYdOeA2dLSSXjC3B/I0AJtjMcjvhr2dlcjEXYpZjRIQ+ffow\nefJkrrzS+Kx8+umnbN682U+ByujRo9l///1ZtGgRzZs3Z9asWSxfvjzpOuvXr6eoKP0714UXXshu\nu+3GzTffnPPPkwsK1G5VLWGVGxqn7CL0BPYCdlHl4TRNWgNPqVpP7gMe2osd8ZwclwNXAf+ivAl0\n/Byu3mMXjHd6KWlKgGpUd0pMNmMSk2xQVU9i8hN7ultK2y0Sk9+ByT6Wwi+AGyUmEzSqqQVVqmOU\nXR9cWQON6lxMFbBUVgJ3AtA7fmwVibC5PYAvUzsVEgX6Pf9hYPs+zHcrDVddDvwk/bkEbiReD5x3\n3nlJxUzGjx/PmDFj8HO9f/jhh1xwwQW0bNmSoqIiBg8ezPHHH5/VPVzeeIejWt4DXsTU907Nq+2P\nkLcl9Xjxbn+rr123RouhxQYQemAUOJj0q+n4HqPE/YQrfwfu1qimyxoWvPdfA9v+j/yeldyjKloD\ny0iEj2VDm5T9U4FHgXcxswS/rsE1HXAOcBfGfHMtcBPmO+Lnc99WSb+0OCVeDwwdOpQNGzYwb948\ndu7cyeOPP855552XdP6KK67g8ccfZ9Gi9L8FDVlJF6jdqlrCKjc0PtlFKCJ59Jvq5NUTWJxU3Wp7\ny1V8GX+Z7m7XndjYlTRUVkY0rsR5kjPssYmVtF0CvAO8RiKu+ysSU68fputUDZ2B6zSqr9Sg71Tg\nx0BzvmYL8IpG9SaN6jCM094PanDNeqUQv+eqTFblWlUeVOV7VW5XZTPwJGamYwlwIHiIcHF113NK\nvJ4YPXo0EyZMYPr06QwaNIhddzXRBCLCE088wfDhw7nlllvo06cP+++/Px9+mPz/2qlTJ9q3b0/7\n9u2566678vERHI4w0zNlf28RThYxDkUY26+fWxuJye9ourkTO+L+W74S78zGXYLX+V+7rmz0tAlf\nifflRODtQMa0JDSqGzSqh2lUR2Aqo6FR7QvsCpyNSc/qy9dZYtJdYnKHxKS1xKQkcG53iYn/uTph\npsWzRqO6UqM6RaO6jQmcoFENVnSbRNV2dkf2bMP8vRaTiOGvdgal0djEPfHq5DoRjWTdR0QYPXo0\nw4cPZ8GCBUlT6QDt2rXj9ttv5/bbb2f16tVcd911/OhHP2LJkkTEwerVqyu1iYedArVbVUtY5YZG\nKfuAwPbPMdOZz2GU5fsYJb4cQGLSHVNGFDZ38Pt0tus7QF4FjrP7D2JGyO9Uct/vgY8lJn0YzBlU\nHlqWypcYr3I0qt9KTN7D92COSXNMpbW1mFH608C/rdzLMcr+AYnJ0RgHuqUZ3rNS0jzztVScbi84\nQvY991+KNqqy3U4idBDh91V1ajRKvCbKty7p2bMnffr04aWXXuKhhx6qtF3Hjh259tprGT9+PGvX\npssz4XA4asBLGG/rl1T5kwjHYxRxJ3t+NxLKzqx/t3o3tHhxynV6Y5zPPsDkIV9IYISchi2Y39lp\ndv+2DOW9hOSZ0g0klKbvbedPs/v2+t4kXhL8cLl11nGtrtkElEpMJgMfaVTvsHXRr9Oo3pmD+zUG\n/Nmc1JwDv6yqU8Mc2hUoDz74IK+//jotWyaiS1SV66+/njlz5rBjxw7Kysq499576devH+3bt6/i\nagnCbi8vRLtVJoRVbmhYsqc6qVVsH1fUJ6jyU7t9MsZJq5sI/YE7gKUSk3hcN1s6VDaC3YRJnnJy\nBuL61coO4HNma1Rvz6APGtWdGtXgdHUZJlxtT4K+4jATk2UOoAeJlxIw4WBvZXK/6qiQg9zINh0z\nzf/TQEnTOyQmP6RACNn3/PvktZdRp5wqcRF5SERWiMingWPjRGSJiHxslxMC524UkS9EZJ6IHJf+\nquGlT58+HHBAovCO2DDLzZs3c9ppp9G+fXv22GMPFi9ezHPPPVehXWWITf3jcDQ2RBiISZrh798o\nQupU1xcAqgnnMzUlRj8H7sekGgUzot7Xbt+c5ORmGGjXmzSqOzSqO7MSdjvLq2+UHo3qDrv5OcTD\n4zy7DLP7j5PssNcNyCjWuIb4znJNMM5YfnGVSTm8Z0PGn/WxP+Z3nEf6LHtJSC5HcSIyHDO9M0FV\n97HHokCZqt6V0nYQ5o9/MMaR41/AnqqJBAS2napqBY1lj+fmgzQgbGy60/iOBoEIw0mMNvtiQp92\nVTUpGoCLgF8BqFYIK+tAoprYVcDfGCeXAEM0qhfbNsEflVaYUdIdqvwiI/nMFPNsTMWtP2pUq5wa\nreZaTwEj7e5ijWpPicnjwJkpTbcAvTWqNX5pyFCen+PHkRvOB/6DjTm3CW8cWWC/b2+ocrTdt46J\nlf9u53QkrqpvYxwgUkknzKnAZFXdrqoLMY4dh+RQPIfDEX6OCmyfAElFJL7CKnCgk8RErfMXAKqs\nweQpB5hlR969SS7XuTCw7Zew/DoL+T7BTDtDcvnRmhCs2uUnXNndrn0P9NOAvrlW4JZgdjkPEzq3\nLn1TRxa0DWxXGzOeL5v4VSLyiYg8KCLt7LHuJCeAX0LyP6SjgRIyu1WcsMoNDUN2EUqBGPA7e+ru\nRJt4SNiVwP8wTvzkKgcmXWycDKfpxue4oZ0fEL4vMM8/rUpvTLIUAtPrz5IhGtXBGtWfA/Bucpa2\nGpCu9Oapdj0T2EWjOk2jWmtv9FQq+b68h3HwK9aoHmWroiXqp8ck7z5XIfyevwFMhnj9+Q2YIjWV\nko+HfC/mbXcw5p+jKk9GNz/ucDgqY2/gK1VuxEzlBrnHrh9S5UESpR/3B5CYtJGYvA+s4Felh9Fi\n/Y02x/kRwOsp14pH8agiqol48qxYW6UXeyb4maA6Y3/YNaorMA5tZ9rtekOjOlGjOiQl53owLWxq\nfnhHNahytCp3pBxbUFl7yEOImap+52+LyAPA83Z3KYkpIjBfzLRvlCLyCIlprnWYt1BHhpg3PBM/\n6b+p5ns/KFshyJPJvqp6hSRPY9q3vAOvbxc5JpJ43/fsOtIdeAhkiAgwzjq1zWKIiEQYxzDgEPvz\n2NH6e/flK7YxkX2JErjfv1rBMdRSfiFa688/nwXAePbO9/Ovcr8pI/gVTwNN8y2Pf6ygnk8G+5aI\niFxANeTUsQ1ARHoBzwcc27qp6jK7/TPgYFU9J+DYdggJx7a+qd5qzrGtdjjHNkdDQISWGCez7ao0\nE6EVcAXG8asbJob6alUmAEhM9sZkwfoSOAXjfDULE2b2B0xlrrHAxRpNTiphnY2+VXXmvUyRmKwC\nBmhUV+VbloZAZXoPch9iNhmTyai/iCwWkYuA34vILBH5BDgSTIk7VZ2LydU7F5OY4QqnlRsHIbRb\nAeGVGxqE7H4C878A2BzUd6gyDOMh3RZry7acY9d9Mb8xKzFOcQ9jPNNbAhNIb3f+EcZpri7kDiU1\nkH0H0DQHomRFY3jmVU6ni8jZwH9U9SsR2ReT3q81cJWqPlndxVX1x2kOV5quTFVvI/OMRg6Ho/Gy\nC/CfSkK9/JjqOQA2QcqNKW3eDlQSu0di4jvFVSgFqpq5I5sjznYaUUbQfFLdSPwXJDzG/xcz3XQg\nEM2lUI7GRcjyG8cJq9zQIGSP5zpPw0DTLu6A9nPgj2Biby1tU/oca9c5q4/dAJ55NhTESLwxPPNK\n35REZBwm7Ot6ESnGpBn8GKPE24hJ2oKqxmorrMPhcGTJHVReRSsekiMx6YTxs7mKRK7xn5JS1lOj\n+i+JyUhgRt2L2ijZTgEo8cZAlY5tIvImpkpPJ+BAVT3XHn9HVYdV2jGHhM2xraSkBLEpUTdt2kSL\nFi0oLi4G4B//+Afz58/nq6++YuJEU2L48ssv57HHHgNg27ZtqCrNm5t6B0cccQQvvPBCreQpRMe2\noPdomAir3BB+2UHvBh5RrRii6mdZU0UkJt9hQrIGYJTKp/nKJBb2Z56N7BKT2Zha5GuBrRrVGpVD\nrS0N5ZnXxrHtJ8BJmNjKX9iLDQJqp0kaERs3bqSsrIyysjJ23313/vnPf8b3zznnnLiC97nvvvvi\n52+66SbOPvvs+H5tFbjD0YBYicmGlo7PMUkzIFFCdJVGdbZLBVpvbMHE5i8GvpNYHdWCdlSgSscD\n6zF+ZppjuSht1yipavZAVUNfoSwTwvqmHFa5Ifyyi3ArsLWSJvsD5RKLvyEvw4SQ5ZWwP/Msu2wh\n4WcAJhKp3mkMz9x5DzocjjDSnBQlLjHZFxjMOCZj6nd/A6BR7V6xuyPHbCWRJc+RQ/Ke29bhCGss\nZ1jlhvDILjHZW2JyUWC/l8gRZwC9SBT98PkHMB54FzgRYw4sGMLyzNNRA9m3YCIAXsOksv1vXcuU\nCY3hmTeakbjn1Y0pLBJp+NPbDkc+kZgcAMzTqH6PSQA1EHhIYjIQmEvJubPZyNo0OaX9qlrBIid5\nmcZ1sAUT0VQEvA/0lZh0zpeDW0MmIyUuIodh3nz99qqqE3IlVC4oVOWb6tiW6bmGRFjtVmGVGwpX\ndolJc+AjoAxoA3QJnL4fgG677c0XjE/pdzzGiW0qxo/nW+BgjWrNipXkgEJ95plQA9m3Yl+mNKrb\nJCb/BQZLTGYCazSqO6u7gMSkFdBRo7o4W3l9GsMzr3Y6XUQexSRKOAw4yC4H10Y4RwJVpby8nK1b\nt7Jlyxa2bNnC1q1b4+ccjkbGYXZdatc7ASQml7Kj+fsANP0e4MWUfocAaFTPwjiyvVVICrwR4tde\n9/OIrMbE6X8H7JCYHJTBNX4GLJKY3FNty0ZMJjbxA4HDVPUKVb3KX3ItWGNBRJg8eTItW7akVatW\ntGrVin79+sXPNYbReFjtVmGVGwpPdolJTwDmn/gjAMq6rZXSb68mMRL/B022mrrcB4+CcbJnyiVG\nAT+w2wcCl+VY5KwptGeeDTW0iQP81a7XQtLsSWrGvHQMseuTsrx3nLA/c8+Toz1PflpVu0yU+Gyo\ndTF7B7BgwQKOPvropGPRaJTy8vKkZdGiRfFzEyaEymrhcGSNxKQ78I3E5Ads7rAr21vC10c357pd\n/wLA0sCgbXW/t+3W6RKTItu/DdAb40SFRnWZRnVDPX4ER0V80+tau95Bsrf6vyQmP6Bq/Bnf3e3f\nuDHyGlDlTEQmSrwzMFdEXhWR5+3yXJ2I53AQXrtVWOWGgpPdT8hyCkU7SynrXk73/7YCoLwYHngP\nZp4Pt5YdTccvfmZrfw8GzrJ205eAWZnYWfNJgT3zrKiB7F0ANBq3CbZK02Z0ZZ1tjH9bEoVrjq2s\nbVVkIrfE5BqJSXFNrp9L6jJOfFytJHE4HI6qMSONLW12YZ/JiR/r5fvBpOdBizvpM4+sNgcVickQ\njMdzM+ApYBhwez3L7KiagSn7vo/DLcC9GAU+tIr+5Xa9wq5HSEzmaFTn1Z2IIDFpB/wZkzP/o7q8\ndm3xvPjsw++B6ytrV+1IXFW9dEsdyelwhNZuFVa5oXBkl5j0BQ4HoMWGkQCUF08BYM0eb7FhN0jN\ntjaOVsDfMD++x2NKjv6qfiSuOYXyzGtCDWRfAqwK7PvFUO7VqC7DvIR1rtArmacwNd6fBS4HPk2S\nKVa9w1AGcve060Oru1Z9M3Mm64H1kYjeUFW7SpW4iPzbrjeKSFnK4uxNDoejLihNPaCxHT8GYMC0\nScDZqqQL05gKtLPbxwSmbR2Fwckk4vYBLgUOsgocjLd6h2AHOyr2WQn81JpIXrHHUmeOv5CY/Kmm\nAkpMTiKRf79nVW3rG88T/6XnmeraVjqdrqqH2XVJHcnlcKQlrDM7YZUbCkr2YWxvuZjJz+3GmGNh\nZX/fq7mUovLvVePTqnHilZ1iZiCmUV2R2qYQKaBnnjXZym4T9QT3l2FC/3y2YcwhQdZKTE4HPsCM\n0n2nuHh6XYnJwRrV/9jEP3sA+9ZEblui9vnAoQovk5lgnTKX5eAlsu3gwYBJH1wlLu2qw+HIJ/eA\nduPrERDbAX+btxeARnWjRrWCAk/DUzmWz5EbkuqNB6bGn8KUv0ajui3Q1ucD64S2n92vaeTUBYHt\n/8NM1/uypNrzKyAxaSUxOQVYCpxaQxmqYiDwfiSiz1bX0ClxR94Jq60wrHJDYcguMdkLpZw7lm8G\nZqDFqPJ1tf0Ssl8CRHMpY11SCM+8puRA9h0kzwS3D2wfl9L2uzR9JwMLgYESk19WdpN0cktMjsEk\nMAOTlvf39nhnicnJwFw/fDHtNWOyJzAdY6sHqDKOOxs8T/7geXISsN/06RU+d1oaTe50h8NRcPyV\njd3eZmvbEuCHZFn1SqP6QG7EctQDSSNxoAfwGfAmZlR8WuDcq3Z9ChAMb/4T8BeMEv5DFvc+264H\naFQ/h7hp5iqgvz3X2k6VHwK8oVFdEuj/GWYA/LCVaYTE5Frgnxhnywc1qk9mIQ8Qt4P/AvPZ31y7\nli8z6ZfRSFxEeonICLvdSqTRBt47ckBYbYVhlRvyL7vEpCUwjHvmFgHNVNmgmtnII9+y15Swyg05\nkX070EVi4g8kI8By4FG7/1n83sbe3BqjJINMBvYCKg07q0TursD1vgK3PAKci8m7D2Zafx7GO36x\nzUfg8zgwRqN6EeC/SN4BPIaJlrgjE8/5NAy2677AxWeeacwK1TnvZZI7/VLgCUyZPzBvTNV6zDkS\nzJgxg2HDhtGuXTs6duzI4YcfzocffsgjjzzC8OHDK7Tv1asXr7/+OnPmzKFdu3Z88cUXSeePOeYY\nbrrppvoS3+HIBd+wo/k3bG03nJS64I5GwQ67PkliMgAzoj4K4qPPTcHGGtXvA85jvoPcFkwc+QCJ\nyf1Z3Hsf4PWUY48Bfez2PVRMLrMpkBCmGYm0ssESqwdilPl24BKJSbB4Tyb0CmxvjER0jsSkPTC2\nqk6ZjMR/ionj3ACgqvNJrizkqIINGzZw0kkncc0117B27VqWLl1KNBqlefPmleZF94/vtddeXHfd\ndVx88cXxcw8++CDLli1j3Lhx9SF+vRBWW2FY5YbcyC4x6SExqTYntsSkKdCZR1/yw3vOrqp9hf4h\nfe71IbfnSTvPk1vq+ro5kN1/cTsSMwoHM22+EjOlnLZ4jUZVgHV2d4tG1SYB4n8kJr1T26fKbUf+\nuwMzU5q+Ztf/Bq4D3sLkH7iRROGWATb9635YJa5RnYrRo/6oaqr9bP8gMauQKbvb+wPcY2X/UXWd\nMlHiW1U14eIv0gTSxm060jB//nxEhLPOOgsRoUWLFhx77LHss88+GVUpu+GGGygrK+Pvf/87K1as\n4IYbbuChhx6iWbPU6AyHIztEaCpCvxr2bZ20H5N9gcXAutSpRBGaiODnOb8VE14ESw49Ezhfla9q\nIoMjLScAv863ENWhUd2C8RDvgPHNegI4XaNarlG9o5rIhH8D/9So+l7rM+z6SACJyS6pHewLpmKm\nyT/VqO4Inrej/I7AURrVrRrVIzWqe2tUf6dRXYd5wRgKXI2Z7l6X0vd3QGeN6n8w3u4Ax0pMdg/e\nx/OkiedVTPHqebIvZoZgIrAn8Ft7agR1kDv9TRH5FdBKRI7FPOznq+njsPTv35/i4mIuuOACXn75\nZdauXVt9pwBNmjTh4Ycf5je/+Q2jR49m9OjRDB1aVbbC8BFWW2FY5Ya47DcD8zPtIxKI6x1zzEYZ\nPH4MgMTkdhKeumCce4J8BLwrMTmNxIgFdjQHaJ6d5OF97nUlt+dJsefJ+FRl4HmyC3CD3b6oLu7l\nk6Nnvhk4EWMLXqhR3ZiRLFG9RKN6cuDQsZiwtBI70l5m48BRVU9isheJ790pVCxj6193TeDFIJX3\nMFXVDsFkC5wRPKlRVY3qKrv9V8D3G/sg5TrvYEbrcTxP2mKSzowB3o5E9ItIRLfbZ96FZGe+CmSi\nxG/ATHF8iinv9yIheNMrFEpLS5kxYwYiwiWXXEKXLl049dRT+e4748Pz3nvv0b59+6TFr2LmM3jw\nYC6++GI+++wzbrvttnx8DEcDQYTmIqgIH2J/8DPtB2wVseU++7wOe0y/RGLSzF6nV6D5GhH2F6HE\njvT3pfOcQ4Cn7fmujNPzQTxsTLAjK9pifvCP8g94ngjGVuwnPwnDc90CdAIuJjlFa1bYUf1G4G4S\nMeXdIR5/Phv4SaBLTZ7Ne5iQxpOBP1SX3EWjWoZ5QemSMjN1MDDywX9Kn8CxIYHtz0imLdaUXRmZ\nKPEWwIOqeoaqngE8BLTMoF9B4dfmru1SEwYMGMDDDz/M4sWLmT17Nt9++y1jx45FRBg6dChr165N\nWnr2rJgBcNCgQfTq1YsWLbKKwgkFzsaZWyQmfSUmvqPOCLPyDszyMr6H7MsiHADAvo8djo2xBWDG\nL2HmmK8xNsH/YkYc5q3zxKv8VgcxTjdiaks/li4jW3WE5bmnUody+9nFgmlND8bkmF+PnV3xPGMj\n9jw53I7cq5z18DzZM91UL+TsmW8JbH9aaavMeCxl3/hbzOPDlON/1ahmFLqVgu/AdrtGdVGVLRO8\njMk6NxDA86TjTjWfuWsLZnie/NjzZAzwygq6vAkcGYkkXg7sM2+D+ZtWSiZK/HWSlXYr4F8ZfoiC\nQVXrZKkt/fv35/zzz2f27Nl18Kkcjoy4A3hVhNMxTmTBKfRKw7pEaCXCr0UYTDCG+4Srg9WejOfs\nvFM/51+/h66f9gFuZ5xA+69PAA6k3wv30/sNuH0dGtWPMFXHAF6oiw/XCPGnatt7nozzPLkNuAK4\nLxLRdpGI9seM6M6w7Y7AjNz3r+yCnicjgM+BazxPWnienFlZ22zwPGnpedK+ktPBUdE7tbmPtUXv\nlXTxmAjN7Qsn9AP6a1SvqeH1VaMqGtWMw4LeOBIwTnFz7KFpxUKL2+dBSRO6AZMwL7OMZuKRR312\ndFuJycHxC+xNH0zcellV98lEiTdXTdgqVLWM9LVhHWn4/PPPueuuu1i6dCkAixcvZvLkyRx6aMEV\nzckbjd3GmStEKBahC4mX8CeB84DTEw7Byf/Ldrr9ORF6Y8J8bgE+Bi4EFgAwIBBhqvI9c0aVMWVa\nf+BvdPs4cW6vxwHtzbknXQLA1raIcCYm29Xdqkm5tDOm0J97ZdSh3L4Svx2Tse5G4HxgVqDNVOAP\nnid9gFvtsR7Wnn5KoMCGz0XAFOBOjK36cc+TeCrSmshu7/EuqVXoEvhK/HyNapWjzQzxX05/iHG+\nvsrWnj9Zo/qlRjVj/4/a4nnyJuZ/52CAA/8iChz+1kp4dQUdz3mf9Vt2MguYOpY/sZ1msG3dXQRt\n6GfEM8FVmT8hEyW+SUTiU28ichDmj+zIgNLSUt5//32GDBlCSUkJhx56KPvuuy933nknQMZT9LWZ\nznc0DkQYKkKPwKHb2fP5FVRMY/m5KgIUA63inuPCHzBTnCdD3GN8OcYeCDBEFeG7vTcx1frmbOqy\njCemlmJ+qJ/gwX8n7jLiJrggMgFTG/pgzGjLn1evcnThqJLKkm0FY5995+OX7fp9TEKTfTBOiKs9\nT+7xPOlklW0HEs6JfmKKez1POniejMpGOM+TaZ4niolC2K+KpkUAGtUJ2Vy/MqzHebFG9UXMC8Jf\n7PHUJDE5w/NkX8+Tv2FmP371xpHMAe4fZf8rn/mWv2lU1yzbwucnzOCySETP+oTBn7Nt3XZK9+wL\nZgbBOugdAPyxCmc7IDMlPhaYKiIzRGQGJlvNVdX0cVi6d+/O448/zpIlS9i4cSNLlizh3nvvpaSk\nhPPPP5+33nqrQp8FCxZw9NFHJx2rrG1DoD5snHaEWadvQQVom30X8/+JCO2BX9B5bvD8ZswIeLuI\nRKw9egsmgxXAboG2AhylSjdVDgXaqrJSYjKEfi+3jg+i5p/k22V3qPImi4e9xK1l23jlj8Zprtdb\nY4BnNaofYqbRD7ft76zphyzA554RdSG358nNmGmUFzBhTcdjQpJaRiK60m8XiehHGEevfsC1mN/s\n1hhHMjB29Z9iwpe2AT8AFmGiBfpjZl7ApEGdmqXswYIgizCOZen4APt9rSsqhKYtqPdEQqMwpg2f\n/d44ksuGdjQ7M9fhp2NdA3SQV57cD+hPs3ZN6XOZ32cMcKud96o21rza3Omq+h8RGYj5wyrwuWrV\nbwYORz4Q4Qngt6rJHp4iXI/5wfu9CAOBi1RZne4aYcUqbTA/muB7Kfd78UHgYja3WwP0U60wtdkK\n+FaEYzG/B9cC9wLfY2ykAKjGPWTNqHzZ/vDAu7B6T7+JnwCqjO0lzXj3ug9ZNfBNzj3pSCBmz83H\nKJzfpZHDUQ3WA/03dveFSERvrKaLX6J1aSSi//E8WY8ZIU4hkWDnrED78kjEVA7zPJmKyQ2+N0CP\nHsl5ATKkK+YFYa3nyc8iEU1KH2pDsrJK9JMFs4BLeZUKMeO5wPMkhvGQ9yO3RmNesKYB1wNcZjxJ\n/KmqNUAHNsx5ms5HwtJpsOuPoNXusHXlI7TsAczfoVENmkjSUnmlFpFj7Pp04CTMP19/4GQRGZn9\nx3Q40lNbW6EIZ4swDOPIMzc1EQmJ8KfrMXGix9fmfj4FZps9xK79Qg2DgXvZ/a3d+PK4u2ixrphx\nAXvMON6SmLQjEW4zHTgGmKzKZqDIt1lLTEokJmqTZcDkZ9eydg9YMhQ2dwCTKtPPsOVPk6/n3JN8\nm6rv2ONPJX1Tmw9aKM/d85ITeVTSZhfPk41QJ3KXBLZ/kUF7f9TtK47VmJcAP3lIMOf4EAL22EhE\ngy9x/5k4kZ2eJ597nkzxPKlu8LfTv18kouswkQ0/zEDeOkOjup9G9X39tvpSnrXB86TImg5+S6II\ny2Q4aicAACAASURBVI2RiD6KSWbTHmPGYP5GigJT42uAvSgd0JwlT8OXfzFHD34EepwBB/4D+nf8\nM4B4np9TPS1VTacfYdcn2+Uku/j7Dkeh8GNMDKfPrjau2WcVybGWj6acbwj4Ly5+QpbBdP3kS4Qh\n9H01hokLPyTQ/lfAWppuDHrbtvcVt2pSVsZkr+ZFh/k/4s0xP14DSIQ7+f4yn2lU5wHtAtmxbgCO\nJpHRKpR4nrTyPOkLLPQ86Z/mfFfPk0F2dwTUaBSbjoOB9yIRlUhEU+OJ0/FXYFQkEq/A1c6u34lE\nVDCOVxuAzpGIfhCJVMiSNgJTK2M28BJmIHcWge+D54napcju/xjja1EciaivzB8FjvE8+czOJoQO\nz5NLPU/SVSY7KGX/OEw0CJGI7iCRXrZDSmz5UuAGyrfBtpVnJF2hl7VkHPrka+J57TGOpZVSqRJX\n1aiIFAEvqeqFqUtVF3U4sqEObIV9MG+9/sjhc8wPmE8JCecs30ic+s+XNQVmm/XDa662oWQHc/Sv\nOwPTNaobMG/+L0pMTEjYAm4G4KY2wWJGzwBITFZJTEYEjvcjkWv6ezZ3HAWMVGWbKreoslM1HvP7\nKvCCqilgEfQ6VmW1Km/UJDY8SAE893EknL86pjn/CInZh+sBPE8mjBwp13iePOF5MtHzZD/Pkx5p\n+lbFcZgZk4yIRHRBJJJUErMDsMaPRY5EdFIkom0jEU2baCUS0SWRiC4Fes80f/0/YpwTd7efKag/\nRnieXI0JmyLlhcBXQgNItpfnnNp+VzxP2tqR9qnA6Ta7Gp4nT3ueLME4DIJ5ee4fieh0q7x9zsWY\nFNaRzN9Mr/awbd2XwFWUb780cH4DM2e+hPFrqJIqHdtUtRyotOC6w5FvRBiKtdsBXwdOXSoSt4d1\nxiSD6EXiR2SGiPnBCSs2jvsJEfYCq5QNTwJ7set/epOYwvZHbiOTMkiJDsPMrB3KkePGSky6YhTT\nrXYKvT1wDfB3jL28pyqvqKavZKjK86qcVIcfsxAJhuV1S3PeH5XuSuK7OXrwYM7CmHwGYV6KMq4G\naRXm9SReRmvCEyRs6tlwzVtvMTYS0V8C9wFPWMW2ExPF8DeMJ/Vf7LGkhDH2pWG53X3GV4SFjufJ\nP0mE7Z2I8RO53n7204BdMSaKgyIR3R6JVAxhi0T0+UhEmweTuIDN6FbUDIqawYDrZ2lU76GoqV8Q\n6I8kshueW52c1Tq2AdNF5DqMF2G8PJyqOscUR52Qra3QhkRNwITUBFMoDgZ+RiK72DIRxgLDgYmq\nxhZrHd1+j5mGP6e+5M4BB2KUwhmYH+iv8FOpNt8AJSvOIvEs/NHQQmCwjZ89HHiEcTIbMzUetFX7\nU+8nY6ZhH6gu1WR9UQDPPTiq6g7gedIa4+H9TxIlLYNeyhxxBH5yCH/w1M32LQVOiUQ0NeuYr7x/\njFEikLBvZ00kojVK4BKJ6KxIJK7MpmD+93y+xOQPuMPuD04zLU8kot08T3xv+HWeJ4MyNAnUihrG\nt7fF/I18O/4izMvwBkxMfpB3bCRA9nT9wUKkeBeNRPz/Kz8efBOwlcFVmsLjZBJidjYmFOEtTCGD\nj6BCKjuHoz5pj3lD9RX4TzHVhQZRcXTzZ6AnyQkTapRkJJ+I0FOEESLcJMIUEZpg4oXftk1GYaZa\n/xeAvi/5P6r+VKkfLzwak0LyIcyUcDuMvTPo5BQs2jAe6FkoCrxAWBHY9kfiozAVss7BTFu/TbDY\nS4KVJEwfu3qezMP4CDxqR3hxrH35Y4xN+RxgeCRSJ0lRakwkotsxIVADMc5wo0iYsU6MRLSqVJRT\nAttzPU9S8xfkHc+TfTAvaf4g9SPgX5GIjgauxLwwX4h5yT0Hk/c9a8TzDmfPn/dCioOZ6vyX6C4k\nokyqJZMQs17ZiZc/XDKUcGJilrN6Y26H+THsbPc/VY0rs3XmklyNUfT+iDKoxB/FjGi+EqGopjba\nGshdI2x8e6pH9zMYG+MnmJkGgPdVeR34jcTOfh+jpBeAKRIhMdmMn73tQ+Ag1mM8mDslX5qZGMUe\ntft1koyjrqiv514FQadIP8bO98p/GPN0g3bRXYCtd9zBOdddx/34pVgN/e0CgOfJsEhE/R9239zz\nCeZvWavUpLUh+MwjEZ0YPOd58gImTn1Lur4+kYiuti8mk+2h32N8KHJGpt8V66h4KNgCP4bTIhGd\n5jvj2SnxpwLn/1ML0fwImfiLjEYiKp4HxplwGjNnYkfjnxP4jqRSrRIXkZaYaaHDMXHibwP3qlb9\nB6tvVLVONHgB/EDUiLDKXUPaYrw7fSWezk74Csn+HH4IlO95/bUIi4DeGGV+NTBXtSDrAqRmzHqd\nxKhmf8w0+p98ZzKJSRHm5aVHSvKLvpjnBl/xpj6vWyUmkzHTtWBejIYDyzSqGyQmE+y1L8MRxE9j\n+zZwlC0a0jVw/nGMorockEhEVwAcddT/s3fe4VVVWRv/rTQSepeOCqigiG3swg6KfRRRx4q9jDoq\nlnH0s4TYx94dHTs6dsU6FiQb7AoK2AWkSO89kJCs74+1T+7NzU1yAwESh/d58tzcc/Y5Z99zz91r\n77Xe9S758e23tdh7ibwi8amOURjoahLSsZzT1PyqmwjBuKVkD5zTF7wXj3nDUvEE1xqCMR4GnOGc\nFnkv/bBV70jMUEb9uQ+4LvJ6JMazawlXA8+qcyUJ2ycABZSftP9OFUZcqivqISIvY7GAZzGZphOB\nZqpaIym+2oKIaG0Z7M2onxAhl1heZqkq7ydp04xY7LKrakX3lAhvY8/2thgxZ7Iq3TdYx9cBImWq\nWhMx9+zLWHgg+jzpiZ6EQEabonnanARIvgwGhodSiUi+pBNbNf6qebptXFsBDtA8TZkR/b+AUHCk\nEUYSS+be7uCcVhuyCbHwLGwF+C62CrwYM/53YXHw9s7p4lrqep2B99IBC+s8Box2Tjfoijxcsw/m\nZdreOf0xMXwRh2zndIMqvYn3K4Ed1bnJlexPx/TwewDvkps7ujK7lwqxbXtV7RX3fqSI/Fhp6/iO\niDyBzSrnqWrvsK0lNlPtipFs/qKqS8K+qzAh/hLgItUN/8VuRu1ChCxMK/t4YIIq1SoOpXjeO7FV\n58EYc3OUKv+trL0qS0N05ZFkBjxgPOXjlk0qabcpEQlz7KBKEUFGP2y/Ot6AS778GYu3DqeS+sya\nV94VqnlaEsqUfkj5AhqEOPhmA14RDYFpzuky78uNqw87p+dXckwFOKeRC/5tAO9lGeZlmhK2T/gj\nGvCA+Zj34mpga+9lGkYaOzcVAxoEZ54HrnVOf06hfUtiaZI3eS/JZH8vBxZsBAN+EuEZqqxNWKE/\nUXZMFedLxZ3xjYiUldwSkT2xYH8qeJKK6lhXAh+q6jbAR+E9ItILExLoFY55KOSpb1TUgRzUdcKm\n7LcIe8Tpkn+HuWyHYVKnKRxfdd+DpOilQC4WL2pOas9uQ+C8Kvb/kPC+rUj59Jiq+7Vh73ncPf17\nMOCAhQNUuTBOChXJl78Bb2KVrT7CXHBVnLtc30eHY1NRAdvk2FTPuveyV1i9XUyMzPVQXJMqSWcp\n9HspsGfc+x1r2scNhdq+54EgF6EdRqw8Fcoqd1WHQzGSWZUM97h+R7oHHwEDiRFCwQq/dHVO73RO\nn07p6iINE943Qcor2YXVdDL0Am5Q59ZWsj+x71UilYFwN+BTEZkmIlMxcsVuIvKdiFS5ylLVj7Gi\n6PE4glBDNbwODP8fCTyvqsWqOhVLXdidzagzEGEfkfLfpwh9sJj0CBF2xIg+kY72b6wHRDhYhL6U\nL2U4KrxOSXJIOahSmKA8lohEAQaIKZ7VBTQAilTL0neqwtHhtRRLe0qZ3ap5WqR5eqTm6dSad/F/\nCvHEsrEAzukFwICwbX1XzfHekyKqUer6A2AUFsrJjdt2p/eyyns5JbFxUIb73Xs5BDO834Xtj1V1\nEe+lFeb9/cQ5PQDjHwzCxqkDgLOd05R/L4gMJEq3FtkLkQewsNxtZU28/1P4bIj3bcT7XePO0IkU\nxq9UkYo7vVZ0puOwhapGKRpziRFCOlCeoDQDS6bfqKiv5LCN1O+BxKQbIxwVXvtj7ukI9wErQ/3o\nj6uqHV1F35O5yyOVq+uT7Kspkj3/WaRYancj3PMcUi/7uwRj47+KkYyqrA5VX59z2Ph9D8S1crwD\n53RO3P8jglu9SiNeXb+d0zneyzBiFcbqDHl4Q9xz59R5Lz2wwjgFmKz3Suy5v8h7aYCl32UD0cq9\nE8YfAEtxmwWc6b0MwAianzunGo4tKihgFLHv7rxw3XviuvFRlZ0UaQfMR4OErEgHojRWkeOJMe0h\nKNmJ95lgBFnx/pC4/kaetbaUT1NMilTvebUrcVWdWtVfKhep4twKVa6UNuem1hEE1+7l4f94V9KW\nUK4i2D7YKmUiJr7yIrEqVjVF/MC5P0H1SRWppSpk7wOHhP+jH3NdWolnU81ALvkS6XI3AeZrXlk8\nb0Ylh2xGzfFfwGNVqvpixiMZkpKUaohTgUHO6Szn/icEtSYB2zmn/UPRlfHYfdyVmBDTn4kZ8Ui5\nDue0kFiKVhcsbbTUe5mJTQaeIZbBslM1OewVYdyv2cBaRD5GpDlRdoch3oCfTazwy7XEar5HBhzx\n/mrx/s7Qp/nUEjZ6zBmYKza7QUTaE8vfnUn5esadKH/DyiAiT4nI0PA3JD52ICJuPd/X9vk2yvto\n2wa8XqZteX8u3H2LCBlm2N/dF668A0tDug0kC+RyLL53iI19/uxqzj+kkv1jwIOMgKGyDOgAkltb\nn0+VNSCrrY+UALOgb7/qjr/xRhnjvQy/4Qb5egN/vznwvla2X/LlIKawQo6Wd7C44kIRcQwlNyph\nuAmflw35vrLnpdbfN2kiB4wdy56Y8c457DCycnNjk9i49i2c05FVnS/x3ie7Xm4u/XJz6bexPt+m\nHl/C520f935Ibi5nhbd9P/qI98eM4VHMVj0U2n9FkL49+mhajIvoasC4cTBuHB0w6deTX3mFuePG\ngXM6vkb9E2kB9BwJxd527Qss9sD1VjhmGMDlcMWWFp+fDzQQESdffnl28+XL84DfGTcO3n03yve/\nkXHjLuWbb3oTFj5V3W8xO/eUiDxFFag2xWx9ISJbAm/FsdNvAxaq6j9F5EqguapeKUZs+w8WB++I\nuSO6a0IHZQOnmInUz3zrDd1vEZpik6r/EstbPg+rPb23Kp8ntD+O8gpNjVRZlfzcyfsuwjvAVhx3\n1CJ6Dt9H8zbM9y7CNOxznAv0V606XhWlpowbB0OG1F6fRLgE+FWVd8L77YGXVemVtH1+hRSZrLhS\nh9Vcq34+57Bx+56YhhSqf60TNt/z1BF33/8CvBT+751sNe297ICFZddgk9lWmBfv0XHj4OSXOaz1\np/pu4nGVQuQMYmqQ2Zgq22RM9fBnVHtiWVZ7o/o2wKt9+548YOzYYdlFRQtavvlm65nHHkvzt9+O\nztiH8qFGgGx1rkoWfPw9r8rupRITX2eIyPNAP6C1iPyO5fbeCrwkImcSUswAVPVHEXkJqzK1Fjg/\n0YBvDNTXH9lG6Hfk2o0XoohW2PMqNudnjDm6P8Z12II4MocITbDv+nxVfauSazZiqPRcz35XC9UQ\nyxJOpxp3elx89Niddgo65QmQfPkW+F7zdHCqfRBhNCa0Mg7MiFNFTFzyJSLRTMJEXEjVgEP9fc6h\n/va9vvYbNknfT8WIz8OxvPmRzunEZA2DYS9v3EXSgUedvXsHkSw05d/H8eF1X1TXEGUgiHQhKuRi\ntUPKrPQx118/7BjvOe/NN1v3mDGjqNnKlfHjSORm3wn4HMipzoDbJVK75xvUiKvqCZXsOiDZRlW9\nGbh5w/VoM9YDDTEjXkSsitMuwMWqFWOBqozHUikQYSmxGBEidMFEDDphBLXkRrz5lLZJt9cQki+9\ngR8S1MuSoYjqY+KNsdjoOGIs/PhrZWA/1pTLTMqOzzbnqPf3Y8x58Pve24vQKsT8qyK2XYrF9Adi\nXqsLU73eZmxGXYdz+gwxud9H1uEUielbvyDSo4yglgxm+NMw8afuqJYf11STpm2K960BChs0wO+0\nE+N69Lgd1WsWNG16wOoGDT7ssGDB9+6ee9yoiy8eL97PAroh0hjz/G0HnAX0Q3V0svNXh00RE6/T\niI9P1CdshH7vg62uj8ZW4xFzPJW0mjUEvWkRdsZEDqJqQDuVjwnxgAh9RBhA58+6xZ9E8qXGpLNQ\nWnMCqeWfpmLEm2LpJPO/+YYtvBfxXrLj9kdEmipn/SI0EaGdCI3ZcvTZ9HkWztwHzGX3gwinUIkR\nD0pqChyhebpa83RfzdMapSPV1+ccNl7fvZd4T4tbH1c6bPp7Lt7niPf/Cuzpmh1bn54XKSui4dMt\nfW01sBVVVSwU6YoZ/iKMJDe12st4nyXeX4SV/uWdvfYqvOGUUyYSvAKtli8v6LhgAQKMGjLkuHDY\n85iA0rtY5bco/n8UCbnnqd7zzUZ8M8pQmdCJCMMw2d3vVPlClXexdJAbSE3Raw3QIDDc9w7b9sdq\nExdCh/iCEhdgq9wPaDkpCzNWHTHDWV5gITVEOaj3pdC2JkZ8BeZWf47yghM9wnnmAEi+tJV8SZam\n+SIwG0q/YmWb2+K2D8dCD08TZ8QlXx6WfLklrg+rNU/jC2nUeXgvrbyXG72XztW3rhOI7jfO6aiq\nGtYTHImt/s7Z1B3ZwLCiNKq5pfaag2XW7FbWQqQTImMQ+VfY0oNYfYWFVa7YY7gBq6HeD6s1nhPO\n81a4fgkmoHQxcB4ibTQ3N1+dO5BY0aIIQ4jlnj+NyC6pftjNRjwB9TVuVUv9XivCviLlqjSBpdTc\nTZxEqSqlqlynyhyqR7QS70FMRhQsDWouzJwIIBIn+9lsGuQOBThd83QW9iNZLPnSWvKlueTHVAQr\ng+RLW6A3lu6G5JdbMSdDykbcOdVdduEnLDd1S+8l8hocj5XybBXeX0pCvnuYzFhqW9sfe9I3LoJ0\n+RbxPJBd2XHYzoHA9lfgSsmXpVhOeONq+lklNtFzvgCT2bx6fU6yCfp+Zm2cpA6MLYdilbcqS5Gr\nFHWg76lBpBGx6nvx/Z4K9CamAjoCS2M7F5EB2ELhE8wmtqv09N4fI95HYbSt43Z9gnkpL1XnVpZt\nVb0Dymo7zAOKEYlXRuxAfHETkR5Yqddray1PfDP+NyBCj/Dvx8Dq4OpVEV4CugFXqa6z+EQR8Cdi\ncfH4hzq+pGhvGgdNmB2fjY6NdPoj47YdZhTLlWWsxEB/TKxoyPy461eGQqpf7bchJq8ZL2ATzfLP\nw3K2m0m+nEbI15Z8aRPXtiylhmbTYH5PuO/X6cDLNJ43hLy04zngimLSV1/MoFMSY+vRZ6jcNVgH\nkRhy8F4yvJcc7+Ui7+WMTdaxFOCcPlF9q7oN8b4/llXyCTBYvN+gfKiNCpGWiCiW130XNrFO9Lwt\nxbxyl2OCLdsSY6B/ADwFdEZVUU0qhyqm6PMycIF4n4N5EyNV0cfUudfUubsrHKj6CxYmixB53tJQ\nnU35kOQx4XUgIpMRaYFUWqglnGQzyqFexX7iUAv9/jXh/d/C67FAmuVUrzNaYoTFSGUtKm1ZCvwJ\nnrsWgIOHwOUdoOto2G74LyzY5m7N06hmb+QduJjy+tIRCiVfyirrSb40IFbreRlmfMdU089pmHhN\nUngvt2Jyjx8CfPRRlDvPE9NXsaXky07YhGUwpq39JJQx2OdJZuFDIrQl0j/IWA0nHQ7T94FFPXpg\n+uU7IvoC+96eSc/hkcGO3HxR3/I0T+OFJmqMTfCc/yXu/0Hh/QuYO/Jx71N3H27Evk8g+bO2TtgU\nY4t4nyber8bEjLIJXiliUrGpnWdD912kFSI3BsJXTRF5wXoSCxWENM2yfkcpXq2I/SZvTDiPo2qc\nGl4vxwp1jcGErfLVuZerOfYyLEvntfB+D2LZV/Hyz/tjobZrvK30v6vmvJuN+GaACNEqKUoVu4WY\nC1FZ/1VfxAo/BECVaZhr/VngXlg+V4QH6RDs9en9oOOYbWn968i4c7QIr9FMFcmXHpTHNXH/dwmv\na4mln3QOtbYrw2Qo7VbF/n+E1wcBbr6ZWzFRiaWj53M2pnWdhk0GosEyJh2ce915xOQWl3Do32yF\nt/MTz4UCJ2+Wu9oxJ8CKtm9ghYGO0TydBnTWPK0NydmNjaheQrSqfQ6roxChLrLrm5I8fbI+oQTK\nhccihnXqedMbBydjYZZUuCsxGKM8H0tfjSrI9SKxAqbqfGxMa4eVkT0b1alY7nV3VAWtlmPSP7w2\nxMKCr6tzperc0Gr7qfpj6N8gzGj/ELcvIsEOxzJ6lhGTTa5WenyzEU9AvYn9JGBd+x3IbA9hbuuO\nGPM8G3vY78DqVa/Xqo8kz5kqk8LqfgHNDt6G/tecT7MKNQi+jvv/dWJu7LOAewgTDcmXKIbVVPKl\nTWBvtwHGaJ5map6+A2V1woeQBJIv+3BhjyMYmn6Z5Fedm+6crgYoKVHvnJYCy1wbWmfbp8wAlmP5\n2xHMQKUFL92RZ8Du961ll8fPAL4grfQqAM3TZdikYAd+PewgABrPe0Xz9BPN01dDm1qRU90Ez/kk\nLMPhaspXj9sRGxx7ey99vK++cuHG6Lv3IpgRX1ld21SxiceWqEDO+1W2qgS10neRnEq234D9nvMx\nlnbvGpz1Fmxx8ACqDwdjXEY0Tej3FIyl3hwjpkaNqpXLFe8HYR62CzFZVbBsndShZRkkY1FNfK52\nwOqrt8fGjykutu/PVZ12sxHfjO2B04E7VFkbmOfNwr4Pq6kCliqiVfStmLsoHivZ57Ze9L0Jms2A\nWI3d3zWvrFAOmqdHEzPAT2Cuzii2fBqW5tEMWzldi+koF8cdPxlz326V2DnJl8bAJ7SatE/YVGGw\n8V6aYDHzCgz+qSvJ6tSQZvu3LbuWEicEwVDtxsjrS1gbHB47PwmHXtw67HWaF8s/1Twt1Tz9gW3e\nGQ1chKkY1ht4L1neS/vw/2neS2YQyOkOfBsKh5TpRzin32GhnF2xrIQF3ssRSU69IfqaGYx1/LYM\n76UpxnFYQiV12esDxPuIh7GnOvcaphJWjHE2yBwxok/zt9/eOJkCJmO6CpHvEGmLSDYi0cT6Goy4\neicWn66WtBoHWx2r3pVC2ykYK3wQFRXUqkM0CfpInbsRKwy2LnndrYhV7oxB9QdiQlrLUC0JXoJF\nVJPuttmIJ6A+x8SDnnl1DOxEjMcGq6fitl0C9FDlg6RH1BxzgDdVuUqVkQn7RrPil5Zx76MVZxcq\nIjPs09DnUyRf+mJG/Gtik4Wo4ErijP4RTAIxEV0T3if7XXQDJoeVNxB7VkbMszSwBunM692Ui0If\nx2Cu/0uAIUOPfj39wIOeXsTQcjZjfFzBknII+d/3pyBQs07YgM/5t8As7+V0jBMwABs0o4IVkeE+\nlBgrd1bc8S0w3kGlqMW+FwFjQolL9V7aYQIjS7GY6qfx3/f6YhOMLd2AMerclwCRSpg6tyJnzZof\n12ZkjGu4enVKJTjXq+8iOxLzTO2AhZQKgYmIbIdNvDuiuhxzKT+CyHFJz1URK6m4MIi7dLl+x3ux\nkqq/VYH+wPXq3E8A6tz76lwqaWjloboI1RWV7L08vC6H0HfVVmjVhVs2G/E/DPq3xVaeI0VIE2GM\nCL1FaFndkcD+8StuVZaplnMHry8csZKliRjPVmV2/QSMdNKikrbx5LuIpDYKMwbJmPPXJbxfBuwn\n+ZK4mk6cMCQTw+hOnItc8qUvR3ExwPPTzXsweIumc+7bmfu8l1+9l0YF/VipeXqPSCn9dvyWPbrO\njv8u1hATevgjIZpERrHvdzDt63h2Ls7pf53TX8P/iqX2XRrtD6vkTO8lZenaVOG9PO69RISheELd\n4cS8BG1IoVzkhoR43yowotcV5UteijyOyAJEvits0KAXwOzWrVnVoMEeiOwZJ5JSSYckA5GlVbKl\nRU7BJLXj8TpGbh1JxTr3HwGPoWrkLtXnMRd5eSMusj8ieyRsS8Mm6qlVJzPW+WPAkZUx0JNBvG+C\neS82tJpoxL/YsiYHbTbiCaivMXH4KNL77Yyxp3fFXM4LRajKZbaEFNSJ1gchpzz5imaoDGIr4PFP\nAV7VPC3WPF2SrKnm6aioCEq8CzogHUtji+Lo22ueJqZ7RMckutTPJT5GltyIbwdMlHwRyZdTgVH0\nYaDkyzalkD2zkPnNmyzbMbTtEc73X+/l7pEjbc6we0v4Z2/o3pj5mqfZYbW+SVCbz7n30sx7aey9\n3IsxaqPJSXzd5mMrHhmDc1oc2kd8hG2wlfIziW3Xte/ey5beyxyMWbxD2BxVSjyVmOGIUgdfXZfr\nVIaa9Fu83x9z5e+7Hpe8gvLlfHMxd+4O99x/f5m+w9t77/0FpuldaYZA6PtNRCmOlvqUFURTLkfk\nUkQGYQTGxxBpjEjDYHi7AEOBg4hxU6JQV2sqGsdbgQMQOQyR2Yjch+V1f5bQ7kOgBaqVkg8r3HPV\ns1F9M3nrSnEM8EMqeufriYnYc3gr1BHt9M3YOBAhi9hKNw1z/fwdeyCWYT/eCoOhSBlTszL3zsaA\n9ev3vTvUpIBHwGOYwbgWmwBMD+51p3n6Y2JjzdP5ki9fYauseE/DkQlNyxlx7+UeLLXtKGx18xQ2\nOKZhqWSfTZjXuLRj16S3sYxI1zjDDPnuLWmTrGF9g/fyOhbfm4sN7jnAx87p497LrhiJ7Q3gR+cq\ndSGWIazIf/ZeFhO3uvJePnVO96n8yJQxAFPDA9jZOR0Xzt8Q41c8HfrRwXuR0J9NhRHhdXdM76BG\nEO97YERCS7MUOQibvP4I7DS6T5+c7jNmPDupU6c/l6SlocBqaFAksvtMmN4KtmoBnxXBv2+Dv18M\nF+XAFdNgQGf4UGGRYqkriX+F8IPA8tXweXaIb3ey32pbzFXcuDE0mAcLc+BRVFeKscwbYR6ZiLiT\n+wAAIABJREFUzEXweTN4O6wyLwRYBkuGihywBWQeDe8uBb6EGy4Q2Q/zAGWHLqzAJoBrw19UtKgN\nxpsRzPY1xEInv2Ms/kZxfUhjt9160rp1Tzp0OJTPPx8uP/10PZFgi/32lRjzvwibIGWFfdFfetz/\nWZjQTissN3xm6EdOeJ0X2u+GSDGwMxb+a1Tld70JCoWtFzaXIi2PoK4WamK7vbHZ6ghVywMVYRBw\noWqZ/Cgi7IsNsAcDqLLB7mdVCCzyz3iPV/RzvXMdjj8dOEnzNGlBnUqOeR14TvP0lbhtiT+CmzRP\ny9LVvJcZGHO/a+4omkFQlptCMVsFg//e3Tw4+AV69fqSGTN6/NSp08Qyhvvvv/fg6afz/u+aa05e\njbmMOwGHO6fvUAvwXg7DiHR9nNMJ1bWH9XvOvZfemHjO7CS7uztXPdu3mvNfDtwevy3SLfdets7N\npUtVffdezgKaOGeeGO+lEWZEji8q4uLp0xl79tlMwsI2zaO/nXemwS+/sGrVKtpgg2lTbNBtSvkV\nbRpWD3o15snKCn/RIB61jQbw9PDXHIvhRv8XYkZtORZeKQXW0rJlOr17H8WSJYUsWLCCmTPnYgYj\nLbQpwQxRWngVzCA1Cq8ZZGdnk5lJ5vLly4qhtCE0ToOMFXZ9xQxHdHwZpJK/8AMpKYaicLEcQNNA\n1kLxGljdBBoXwqoSKNoiISQ2y3gPaeFeSvi8mcQKlTQK93M1sDYDWq6FrHBjS1bAqkzI7gTpa21b\nWiHMmWVx7tVxf2mYmmEmZhibEzPoi7HnVsP7VZhhbxvargx/ReTkZLPXXofQsCE0bAivvHIjpaUl\ncW2jSfyacL6s8H0uDvui76k04f0PGEeoETYOFIVrrsXGmLWYN7VBOOYZ7Bkr3CSlSDdjw0IEBxTY\nu9xc0O+wASG+XOjPBBa3CN2wles+VNTu3XD9NBGUXzVPE+uJHw3syVwqqhylAM3TJzHyVE0wBdhK\n8mVvYJbm6dQkba4W4VosBv9oQQHjsB/YcmICMrCE1zHRknl8cXHbC74oW3T7I4988Jlddx3xzH77\nDZ/566+7MWLESbfASQB3ey8LMX3l2gpnDQuv42GjTMgmYOkw5WRqx4+n75AhtATpRMygNMDcqdnY\nwF6IrWSiwap9OEdm+MvKyKBR374wejQfNmpE6733ZufbbpOvO3Rgt7lzoUULvhORceG4hRijuU1O\nDjusXcvOu+1G39JSaNVKLl2wgJ+XLqV3URFbLFoES5dyFzbwrsQG3CXhb9m339IhnG9W6OMabBBd\nlOQetA6frVlc20XEDIlgg3Y0kJdgq6ox4f9l4fgo3toASEekNYMGXUCHDrBw4Wtst91fWLToWUaN\n+oCRI2cQmxCUEr8AfuSRG2jZ8kiys2HFisto2vTO2YcfTiY0jZaBc+C47UztUIBC3n67Dzk5XyPy\nsfbvn42Fo+JxP7YKXu6hiTNFs/ITN5EdgCkVUqZEnsUe+F2BHFQ/TbyBItI0fJZMYLHGlwoVyVwD\nB3SDgpl2b2QyrO4cKwjUH9WCJN9L4jXWabIq3g8mkkaG5/XFF6+tqv064qsq+2B9nxP+r7zd5pV4\n/YII6aqUiHA35qqdhq20k5bzFGELzOV7C5bnuH3YdQPmhv5dtQKxq3b7bCvdW7EY43LN01/C9usw\nZnm3wDjf4JB8+UfoS4Q0jHz1GJDJ+3e+wEGXwdCSbyFtZ+CjggL5CYuXtssdxRBsknQuxiUopiRz\nITcURVrpF2MqZAAnN2q09EbQd1esaF5WRc172Q4TdtkW6OhczXK/Q1rU58CB2AA3O5xvB0w0Y2xu\nLqVAu7Q0ehx2GGdNncoX333HNOBXVQ1a9ZKNxfp7YQZ1AWaQ2mIrlhXh3BELtwPQ+ogjePS332De\nPJg/n8WZmTQqKipblfyKrXCWYwNuJubCXYMZrkbhnmeG+zcr7CvGJgXFaWk0OuggTn3vPT5p0IDC\n44/nubVrYelSEIH27aFJE5ZnZdHkiSe4bc4cdkpLY/Epp3CcKmy1FSxdyqfLlrGPKqSlwerVnPLs\ns7wHLFTdMIz/dYZ9D4JqoXh/CSYdChaLjTxGb6pziWGf2Cm8r/D70dzcPGzCfmDY1A3V3xKO2wN4\n/teTTz69x8yZHot7P419Pz9j4ZDDgR6opk52FTkB+A+1PVaLdMNChZdXwfJe/8t4fyk2+bxEndvk\nRrIqu7fZiNcjiHASpnL2b+DssLlBUPuq7JhMKLf/IGCJKl8F5vqq9dBEr77P5jIvBb7EXJOjMW9A\nN2wS8cD6SojahWQ3tHqimOTLjZQvwLEVJnbzQEE/3jvppIkls87YHm5ZBiUNAO78aKQ0u2ciZ701\nlv2Yzd3M4mvG8jzQnjN4EQWeHAu0WQ737gh/nWI2cfV/If0Q2OkwmDwXW+W17tiRouuuY/yqVbyx\nfDlHvv8+Qz79lCmYLON8oENGBn179WLghAn8hkkvTsRWjIeecAJ5c+bQYtUqWL0aFi9mxaxZlOTk\n0KxZM1i0iOJVq0hLS2Npjx7ktGtHzsSJLJ41i8nYJG4itkruBEzGJnlLsQlBFma4Izdzd2LPzzQg\nffBgDtpuOzIaNuS9Sy7hasy7sRIo1g0woHgvB2Hs9ocxbfpEpGO8htfitjXGcr2fB9qvbxnRWoNI\nJvZb+DeqD4dtb2DqdZPPuOKKbk8eYgvAGx5/fPC1Z545DKD7jBlMHDy4QTJVMfE+rUFR0Zo1mZlF\nR48e/f2r/frtfuVzz3HLY49lo8lTGBOOV+BJzc195ZihQye92q/f1cCZ6txaRKIxJ436ZizWA+L9\nfcCUpFromwBV2b3N7vQE1MWYeFhN30dMfzoy4BmqtkqqrN+qFMd5Yi6Nz/1WTeomrB2IXAnMY2hZ\n6lqUHtKbkCq2/CZoXMzeMlRm1+ieW2rJv4CvUf03Iu2ArxHphOrMao6+hZgRfxXYZ0Bb2q0upSVw\n4rPP9qD/+81p0mrKtOXz6Ap5/U8eTLc5s4HSQDDKIg3oC2zPG+krycpsZKnQ07KBKbaQUoi5417D\nVp1bAYtnzqTwqqtY0KgRR3boAIWF3ENczXVgddOmjO3enX0WLmTCzJnsjrG2cwYMoHlxMeyxBzRt\nCtnZ8N57nCbChLw8fl29GhYuJHP33SEri9EY8ewdzFXqcnMpxty6vYD/lHNhpoCgqLYYi23erKrf\n1OT4dcT3wJfO6fneywUDBuA+/JD22LP0V8wLcRj23V4FPOacrgRGeS/nANmItMQmUW1Q3fgCLiJp\n18LVN5gI0c7ARWWu6KBdsLhx425PHnIIdz34IJe88gqTOnToeu2Zlq01qVMnVmRnb9M4IZ3q+Ouu\nu/DRb77pd8uJJ2b8dtJJGV/07Ln7q/36kV1c/H4qBjzgSuCvUlBwJjahPQXzlgzGfiO/CPRTI97U\naQQ3+HIsle0YcnM/WMfxfFvWUd2utpCqLdpsxOs4RBgAZYb3Z4x5PgsgMuAp4iHVdYs9x3XGGJlV\nzchFbsLIJrcAvw0ex9bD+hAfqW0B0H4ZNA7m4xFzqfsa9KQHNpE5G5FCYrnJPYilDCWF5ulKyRcw\nb4Y2TOfZhu9Du3Zcesjl7LR6NUiDJSxf07OrSCtUu2yxb39WjGtA04nteIkM+gJ/1jydJfLRKpbs\n14j0NcOgyQ8gd1lfSl+CVQfbonbla9D82EQXrvcS5fB+APTJzWVrbNAc8fbb7NWokZVsvfBCCoDn\nVPlq1Sq6NWpERBrbBUshOuWSS8wQB6W0PsRysgdiK+lV2DMzr6CAV5zTU0WkkaoWey/bY27ynpjr\ndgHmJZmCSe8udE6Xx3X9NcyAt3Fu4xhD53QmoRCJc6pr14o6p/8B8F4uAw6jlOL9DuWqj9+jATH3\nP85pUM6TB8OmY7AJ4MaDyMnAsDhFkn9hz3yk9X0vqkPmdumiAMd6/xzw29azZ+8af5pnDjro7+fD\nqaGC1s5AT/r3v+/F/v05f/hwAErS0r4Bdhl62mln55EytsJyk7cmVi3QqvmprgbGUH9EsKIsnJuA\nqzj33EzWbfLRCAv/1HlsNuIJqGurcEx6E+A4VV6CMhd5uZrf1fS7HbUjHzkW07quID2Kdews4mqO\nlwgdnxkO72zDb4saxmrv/vtNFp71Da3mNeTbtqsYd44dmxEJMIixOCIm69+x1VUh9gMt2hua3Q4z\n9oJOCsMK4a6Qg9GhYpekA8aknY35uHfiEGA83VnA8vad4Q0zizsD3HQTDP8NLhsAs2b1oGPHmY3b\ntqXp2WOZywpaY0SmpSKkwf45Rl3KKgHmhVVtsQhFsYqmzRZVEoNdgJGGPgPGFhQwzzlt7L3kYES1\nD7CV48XAaSLQqBFRpaS+zum3xMmXAgRJ0zlBNnQ7YFXEFPdeovjqKcCpqurjWO0R1mIu9Jsw0s3u\nGHGyf4jD34i5rT/fWAY8GRKe9VbAtD0GMzR9Dfe6XBajao+DlIVyhmIGcxLla0Anh9V0Pgu4spZc\nyAMBnN3XzoSVb9x+DzChW7d/5axZ07fT/PknI9IoTXXFYZ9/zjt77UXG2rUrRPWUoszMf27x4osX\nzW3Z8tz4C0zs2HE60OWIm276C/Y5k2UOVIa7MI5HEyx+fhcx7gxQJ8fFChDv4yuzmbft+OMvF+9n\nY5KuL6lzqSrBZUHlYcqNgVTv+f90TFwEqSVt8A0GERRoq8r8TdyRDCKBhmT3X6Qj5WUNPwP2BliR\nya1NruZ9oGfvuXSe8DBXhTYPAsMUvngdRh9tA/IsypdJ/ALQ3XZDfvuNGYsWkd4LukyF3qsCMzrT\nUl/S21ImeTQSG8T6YXHfCMXAWBoxn5V8e8ABND/sMC7q0QMyG7A6K4Ps1atzhmdnF1bQNs4dxddE\n7N2hpYC0JjYxGg68pmoscRGmEpNyfUy1LPxRASH9KSLoHIl5MHphqS/nUrFc4gjntEZlJOOu1R2L\nh4/FWMNg+ci/Y/r5Ef6LhQJGYCvgc7Hay9mYO/dPURGYOgGRoUD8wvNgVN9H5FPCM4gNyOcAB6A6\nOByXlbRylUgeZvhTYkCn0L8xwK1oLK0xCJj8CdgftawN8d5hZS37hTY6p0UL2r8WC/X/85FH+Me5\nMft950MPcdn559Nr6tTnfzj99OukoGAy0F6di5eyrb6L3n+GufovxzxCZ6pzuVUfVbcg3t+CTZB6\nAj9hpY+vwyq2HRqabQkcENptE5HWxPuLsNX3MHVuhnj/LXYPNka4qFpUZff+ZxXbRHgMKA1GMm57\n3XEbhRV3CSmsojdCv6srStEZU0vrAvD3AUx7bTvb0biYK3UoYxlKwc4Ps+AVjKk1DBamwUHtgb9l\n0LdPHzQjg8ex1dIWk2ByMXxYUMBBt9/Onq++yjEfDyf7wQJ2nbIbD3o4fzIwH9L/D859HAv+ZoDL\nNuN9IjGhhdZAA1Xdq+BtjiooYOzVV3PRJ42Z/s4iyMogG/gqO7vwWoAHP4stRMJEL24SJQBbxnnp\nBhLLdwVLv4oQP4mogBC7jZCPGfB3w0r3qSSHHJNkW0pwTidhJUB3HTeubPPhzukZmNcjireejqUg\nHooRxJ7DDPiBzmnvTW3Ay551kXRE5hIz4DlYHv6RiByOGfCbwr4sLD/3JER2QqQTsAaRbePPjUik\nLgaxOtWpdKp5km1piDTABGa+LvcbVb0I1b0iAx7QhKCbHfD3dosXR5OQwZlr134Ub8AfveMOLn35\nZTQ3lx9OP/0cVCepc1pTAx6wEnMfFWL8jaz4nXVpXKwCTYGL1LmfMcP9DPagHxrXpjXwTyzM1Ea8\n7yTeH4tllNyMScQCFQjBGx2p3vP/SSMuwhVYGcubw/vk7uFNj27A4jriLYgkKCvTk/4TMB3V32Uo\nze/YhxOOPg6+acUbzwGdjdn80zNw57GYT/4UuERh+66deXzYe3DPPezw4Ye8UFDABQqNt4Zuaekc\nTJyO+9pmRhb77VIa79iHR7cGmsEXN6k+ejjccShQbEIQ/RRGTzyP0oICxhUUsCKOOT0NS5157NWZ\nrH50CmDpegOc0+/733nupW9MbMOkFXDGl+kcknerEOm2Lyvz2O8Oy+JJRvH8hLMwd+QqkucYJ+Kj\n8LpTeH0CymLBadig0wvo6ZwurXh4jXAG0Oujj7gAONk5Iz+FuPcuQCPndK5z+kmQQm0NPApc7Zx+\nuJ7Xrm00xdLhAKaG+G0hxmB/C5tM3YSxq08HfsNmYN8Sk+CNGXGRT4hV0XsaC0OlisWIxPQZjEhX\nguWNtyG1cFYL4o246h2ofg60UOeeLc7I+DdAo8LC2SX9+3P2O++ATVrSaiHdalcs5PASFhePJg+I\n9+8zZMiJ63n+jYHOBG+gOneYOjeZsWOj/O6bMO9gY2Ievxux5+Cl0OZFYDfx/iDs91u3UhErwf+k\nO12E8cBUVY4U4UfgbFUqiBFsaojwEDBPtWxlsOlgRQ/uwAbD3kAjVCeJSLN94Pzj4eoP4J9v7clg\nhI6spYQxZKE0aA/sD4Xn3EBOyb7Q+mO+7X0dTlWXeS//ISG2C7DNnRTmzCJnfNBxa/dfkBIGN/2R\nYb8O4XzN4iHMSD6PedGX/elUJjSazjsAJdnw6WtQGisqOgBbaUQVsrZ2TqdIvvwA9Io02QHkqNOO\nY6enXyg78qejoOfrt/HKf0qZuceVLN4azOW8DPM+3AFcrko51TkRGgPFoW56pfBeImWp+cDzzml9\nGDA3PWw1/SWwbZkRE7kCm/RAsrQokdOICQSNwdLQbsG+x9cw/sUTwPHANqj+LYV+HIgxmR/CPBh7\nYXn88VX0qkzREu9vwPgKN6pz/66kTRdg2r4TJtz48cUXXwM8gWpisZF1Qlye+b8wh9ZbwDvq3OFh\n3wR1LlkFwE0C8T4NmyQNwQzxDdjK+Wx1bkxcO8Fkpz3GMxmFaT5kYsJNkav9JUymupAYtlPnftnQ\nnyUVbE4xq4gWxLTGX8SKrn8qQlOgmyrfVnokIEIjLL96Q8+AtsN+UJsGUcxQJGLR3jAKLhoN42ZD\n24dFVgPZn2LLtbe25kLSaEMOMIexKBfnw9xrYWJJDjmfhFIOC/Zj54IC/ua9NMBc0a/2/gcHNh/P\n8TOOJmPK2bwx5Uxy1jZiLeEZ7fYvyFzGMOD3X67gKWzVeg7mUQFgzGPMb/0JSAkD2n3Ah6UN0J0v\nRGYcDfMd8avIYc7plPD/kyTWL97p6e/Kve/5Okw+oB/fl801FmAx43tVuVOEC6CMNV4G1dQ06Z3T\ntVgd7aeouQLd/zKaAisSVqF3Exnx5EbzGey7+wZbbc+GMo7Gz6iaEJDIHOCviKSjWl0WSJSKFP1O\n3sQmCBMxmc2MFAhykczvJ1W0mQMwu1WrqC5Ahbr364FB2CQmh9jnOUy8j4qTLE961KbD7uH1noTt\n8ZUOCTHvkQDi/SpMJ2MEFjJZjPFQstS5iJfwD+z5cXXFgFeHeulOF0FEeE2EXJEKFamSte8uYtrh\nIvwDc7tMDbunAtuJkAOcCf4bEc6prC63CO0xItLfRFggQhsRuopwnQi7SK9XauKCSzx3hggviXBh\ncPn3xmaOKRxbefxERNJEJEtEmolIFxHpKSJbicj2IjJIRE4UkZNF5AQR+YuIHD1Q5JKHYU0LkWcG\nwZ2HAgK/HgtZI6FtMfAknBMJEQ8HOIU2HIitRY7lYFX99DrVSZrBzT9eB02/hz1OKBPkuAkjnbyR\nm8sDrb6iSfoa3un6H97ofh+/FzcHzSQjfQUr+gyBzFiyR+dQl/qvWFzrKkzecR/NpM38XJh3AB9O\nuA2klBubfQ9dQ9JJ9ixmZS5ioHN6SnQyzdM7NE+PTrhlFY3vyBv3APYQSjmAD8NAe/5kAFW2VrVb\nsD5wTk93Tkev73lSQT2JcSaFiLigcvYD8TK4AJYhMJ7ywi/x+0tRPQ7Vf2KSlnvG7Z0T9/9wjN9R\n9e/ZCouAhRwi9MdWeiNQvQ7V/yvrd7JTeN807u3Uyi6lzhUBTO7YcQpmxK6prG1Noc5FseB56lwx\nMS6BTXDGjdtHvN8x2bGbCInckCXAG+pcubSwhHteiIX9flTnlgAt1bm1kQEHUOduAzLVuZTG3Q2J\nVH+j9XUl3hpbSR8FIMILmBtodOLqWITI1YUI/4fFwa+KK425CJuNrSJW6u4RjNjxQJJrR6SR+8Lr\nc0Rs6l0fzefP5yKi26lSo1mcpSxxNVayMSrb+LfE1VxIv+qIhZWjFBoFdhSRFRgBKQ1Lt+qGSXEO\nDNsLQ/uZmPu2GFsxRNvTBdK7QqdJ0DITOBS22B+yn7FVxjtzYVqcT+cZgOI0bhi9DReGc6YBmZqn\nRUFe9Hg+tLSzvQdB1iI9Gi/TiNXwrvAMdniDzqvb886MY3lz17/SueFMrgFuA/6DkX+iileTiZNQ\n9V5uxpTH/gmgGdwIPN94Cl+5XG4I2+en4D+xH/WSLmtoPt1S+WaaVs1RvD7lVY4ZKGj3pjy8pXlQ\nN2NjooOlV0Zuz2SGbNck25JD9UtEtsM0GFbGbS9C5BfMG1aV9kCUk/855hk6A3PLHkXqYiFHYFkY\np6hzhdW07YV5DDaEF7ArsdS0+ymvbAgwXrxvFG/0NhTChKGDOveeeL8LMCnBQG+LhTzeAjqnuGou\nxMb1MQDq3OJkjdS5lGuN1wXUVyMe/XB2xIoxHB/+DhfhI6CLaplbJXoQx2MG/FPsAY3wNiYcsg9w\nGrgbsBjJ4SLcj7lflmO50RFbcVusytJi7Adr6PPML2HfQSIsBeZXJ8hiRtmfBaWPmk1djS2+f5kC\no7qLrLgHEzHZCjPaXTAj8xO2YoyvZnQisSpFi7Af5EfYhGMs1cliitwK/CNh64HANWfEJCKj9I0y\nvHwb23bYleaXzOLuu05U9V6KvZc9sIEJgKyF9MhaXDYh2TLcpxxgkapOQ+QeLL51WlopT3V/iGHd\nH9QXmSmRzOZVVKN57ZxeDeC9PITlSJei/BQYwlGcNCt8DgE6oRXqkqN5ukCOOu0Yhj81husy7uTn\ngUfvwlgm0oPmLJkBbKXIdGASIiehJjyCSGugFNUNp4RXS6gPeb+VYWYo6AMMRfWmCg2qd38ntv8F\nkzV8PGHPRGLEuYqw5wosHrsmnOtJTJugH6YZH3eZSu/5MOB0dW5itV117qfq2qwr1LnpcW/Le6N2\n2ulmwAErxfv26twcNizGA4j3QzHX92UETXnxPgtTTDw9TCgqNeAJ93wRtlj5eUN0uLbxh84TD6JC\neapcH9zg71OxKlcLbNb6IEZaeAkTQbhZtcIMM5yb1tjDewiVuePgTVWrPx3qcc/GYqpfMlSepYQT\nufsrWCHAbx/DcedhxKstMQ9CF2x238f+z+gKzdOgR5rxrkZ7SPsY1izCmJSrMMbsEszdN72ggBVA\na+c0pdxxyRcp6Ed6iL2WbcOKfnwOvNywiJyVN1cqELENoWgGIp0xSUMAVrdh4BcvlbmSi7AUjeMw\nXfTtsAnETwmqX0k6KU2x1f5MbIXfEtXFiDQDdmZ9jI6UKzV6MDaxGQnsV5bzboSohagmDuSIWLXW\nNziCI3kz2hyt3q5F9cbQcBSwB6pJQzGbUUsQeQKYgGpiPLS2r/McNhF9Cg3Pr03+dkP1a0S2B15H\ndRusHvZ2qP6AyJ+x30HjwJiv/BIxQlkbdW6TCegkg3h/KFbrYE+M9R1NILqocxUmv7V43YbYYuRn\n7HcGNja8iI2Dp2AEthrVmA9kuLT6ttKGqolt9dmIZ6rGcnNFJvdIT5/9a0nJeMxe6gTovKPl75++\nE3yyDLZJg7lrYGl2aJSDkWM6YTPuxpQVfGjcAvp3hzat4P3/wt77wvzF8OlsKOpALG+4AdASaEwG\nTSgFMtNKWNMz3bzL30yDwibYLPA3zB3/CzAOmAIrfw7qXltj1cgurerzey+Z2IRkIMasPMo5LapM\nZ7fNLfLWy3txeNymY5zTVyVfjgDeSAO6l8LXL0DTX1mKTYZWY7m3V2JeixNQXS35clbLUr77YiFH\nd3+QQ9e0YfsvQnJG3g8clL99mftwDhZLPNc5jY8VJkW5vos0xozrf6s7LmWI3Bb6Mxhjwn9LbDae\njU3aXgdmolohr1uEn5WEfGI43sMLzv5/AwvJGOpSgR4zOlmJOtp1sUZAShC51sP1DvZNVt6ylq8V\nPzjOxMJYV2Px4m+wlLyK37dIG+AmVM8pv7n8PRfvywSU1Lm688wkgbRtezAvvRT9Jrupc79VecD6\nXMv7DpjnMB8regOm3BhfY/5gda7acEW9fc4p3/c/IDu9ObB0uQgrMIPTCGjcogVss0368s8+azgB\n+uwDS0rh59mw9jUgHX6NavGWYK6yQmxG8CtmeKZgzOPPYUUJfNoRmreAGUvgpVcxl9kMbPXdJJxr\nFbCUczmNVuSTTjHppeN568K9GHtuMTHlLoDOqmSLIFge4nRs9dpHlSlYzmdUtWkO8Itzutp7aYXF\n/g7EvAu/YTHiK4A13su4u+9mJ+/lIuf0foChL0va7EKOfnw3M+CqPC5Cc+CVZ9+Vz3o2Ye8zO7Ns\n1zY0BfgmF1Z+x3cTO/PjJeM5A7he83QGEe8gXxqkwb+H7UfpzAzSpg1CM9Jg4RrGnvAlLYu1jIA3\nwDkd4b2UFTqpEYxpXHsG3M55BQAiS7CUtHich03CADoi8mdU3wrtBaAlC1okHDMPyk2MKi0RWQdw\nEXAPIiej+tym7sx6QSQHuHaWTV4/q655LWAEpu4FZsAhRvjaJeF9DKrzsfh4dYhIcX3XsX8bDwsX\nRh6FVSRIPm8ANMO4LY8AH2Mr7/YJbTbG918vUC9X4m++CcuX8/CSJXw7ZAjv3X8/p3bvzlnp6TGD\nee+99zNy5PEsXdo6pRluIEXtgxnxQZh2dD8shtoU+8G9E/SpK/YrX54KbT/E8kyPYqi+Xq5R65/h\n9L6fcPu857AZ5pnA+arsFtePfsSkwF5zTo/2Xh4mprV8P3Cpc7p2zL+lx4puHE8a/wgK5H28AAAg\nAElEQVT97gqwpoSLSuHmnHQaA/ztW/hhGZ2BVt0bM+7YjnBg4Ny2fxvaFsDPxbDmPlhSROEnC8l5\nfAr/XlLM81s04LO+bWj76gymX9sL9mkFb86CozvB90spHTKetBLlIc3TsnrZdRYiDxJLA/oE2LeS\nlhmolgT3+NJ/cOuAf3Jl5CL/CfPgbIlxFaI45nIC6Q7IjHTgNwlE+qA6HpHdsPxnQ13yENQE5p3Z\nCUIVOfMs1Kj62jpedz/MnVwV+qA6YZ1O7/01QCt17pJ1OX5jQ7z/EAsH/gWb3E9X557YANfZE7hX\nndsjvB9ObKL8JKbKtsFqiddF/OHc6cOHt/q5WbOFUaxkHDGlqzaYO/zzuENKCTW0nbN606GYQ2Ns\ndjcTU3QaiMXBB4X3x1JxxvmZc1ohDiP5koWt0g/CFEUjBnsrhuoyzLj35YB/PMm+t7VjaCkcfh60\nHwtPj7yj4P2m+RirdQEWS34Dm/HmY96BrTDi3jvO6QrJlzbjH+KUHedxB0b4ujV8rr2LSsnLSuPA\nqSth/FKmP/Ib0wpL2A8jhQwAemet5fKZwylsNp0HQ+pWAxlKZotMVpy2JRzRAZ6YAi/PgGM6UXzm\nVmRGnzXvBx4ZvYBXMAW3phg79C+aV4e0tCuDyLFYKOIVbEW+iuSr/qaoLk9wp0boibn6GqIqcW12\nxzxbnwEDUB2xDv1rCBSt1wRA5Aus7Ou2GOv5diyE8DAWr6+5d2Rjw2pYg+pzIb78BkbcvBMjs22c\nAVxkG8qTpo7Cwi4PAH/DnoPcsnh5TU/v/e3A/JDWVC8g3n8NXICJ7BSoc/1r+fzbYITAEercwWHb\nl4S88LoedthQ+MO50wcOXHBMQYE0xtzoHwFvO6d/DrsXeC87YDHuEzDm+btApvcyAHPxTqbiZz/L\nOX28TRs56OWX+QDTrT4HI7aswFxr33lfNmjPcE47S760JRgCzdMPACRfovjZQFWewHS135MzPvsa\n+DPHnEBOnxdpnQX/93LTJsC0UmU5kJMmLAMed04nei9LsFXfCuf0xXDuRgdNZN6O88r6fQsit+wP\nx32k+pLkS+GWDeH3QihR9tU8/V3yZQXBVb//b3Qc8QwPEZvZ7oVqkUKR5Eva3RPZo1kmR56xFVee\nYRn4ZQYc2HXUBVY/WvJlG6C55ul6CyJstLiV6ssQVxTVjGaE97FJ2FrgRkQuIhlUf0bkZqBQRJwa\nh6Apql+Hc4Kt8GtmxEW2xiaAnxBzs0b7JKWUIpFDidVtvwursX0sqq8gcjZmkCScsi7HCp8FQGQe\nJpxyL3BnlEmwEfseLzH8LKrDASkTP1LdLelRlSBJvzuQUB+8riKu70XESv/2Ee/T1bkSAPF+S+Ag\nde6Rcsd6fxiwVJ2rSsgmwplYmDJeCvtILIR5xnr0u94h1b7Xy5U4aHYkZem9pAOlIW+4AoKk5blY\nXGX3uF37YfrApwBnOKdfhfNXeuNC6cYHMBflscDZ+4+isDQMOuWkO/NF2zaAF/ekr3P6seTLvsDH\nWzSAPVvBMR3RTg1tQH3pdwY8/BtPh3N0rHBhO98umJv9sptG8Oj/JfwcTtmWT4edwKXAl12XcOOU\ne+grphE84pr+7HZTX3oDe+lQ3sXc7scC76BaIS81kOeKAJ6bzjW7t+DpHk1Y4tyGWQFt0h9abCV9\nILbKKsE8DMmwHRqbtCTtt8gFWIzz1OqYyZX0AyJ3vm2P8vsPLSP7ifREtWKqkcj92OA3APNIAbRD\ndS4iuwBjI5d6nR3crADJD5inzJCwAtmofbfv5W+oPhi3bQtgbzQhXFbtqeKISiYHOgE4R537vMoD\n6wCivov3H2O8oOPDrpvUuWvC55mFEUgbRMI0UI6B3wTzfharc1OTXsf7iKd0mjr3Utx2BY5X515c\nl37X5Ji6glSJbfXSiK+LdnqQ+NwFcyue5Jz+sD798F5OBJ77ZTmj751I3/lrmDn/Ku0UXPVbvTmL\n44/oUEZ6aXXRt7yS25bco4KJnryCj1+byfOFJTxUEEsU+13ztEvitSRfGjRew+rRT0LBlrD/FD6d\n0ZSWs5rQs9MymN4MtljB2qNOIOP6kXBtQhRPYWHaULrqUJpi6WpHl5G3Kv982wNTnNMNLuywSWHu\n2v2BK4LAR2U/iFJUqy+UI5JLkHmMS19rBTRD9beEtq2xtMNJGEt5H8x1fB7wcTC+fbCQ0WMYL2Jv\nLE47CCPX3Y3q9+F8r2HiQzMwD1JO2UTCSHoLMZ3x+cFl3byccUoFIu2AuRtIbASsJv3+2ERzL+BM\nVGs97lqD/lwPPIxqTepzV39a72/E6sm3qk8pT+L9Eox4BrY4eoRYsZBoYtk1yjkX79sTCy+eQIxY\nmhaVAY07dwssi6e5Orc0Yd/BgFfn6n7YbgNgsxHfQPBeLiEIEAQMw/K/dwT4ehGLOuTwScecWBnP\nGYUMPv8bHl++li6ap3MlXyIBEwHmap5WkHmUfNl+32l8/3FQ1VZYWSoMysjjSOD8i77ggHvfY0S7\ny2BOrARHPlZPtyfwMqq9goHJR7Xus2E3FSo34qkRw4xBHU18zIjGznkVcEdZzDu2fRLQPcTYr8HE\nQ8BEfH4klit7DRZCirS+I8zD9P/fwlKvkouGWJWuf4fzXRm23oZqosBP4nHNsHz/k7CV/guoViha\nUysQeQCYjOrdG+T8dQBxxuo8de5fm7o/NUHcqhpgZyxdUzFX94GYB2iIOvdZaP805u38HlOPjPCk\nOlfOPS7e/wKoOrcdm1EOm+uJ1wA10ZTOHcW7h38C903kr9jKZzBmwIcCA2/+mQdO/opVi4u45M1Z\nFAFdTj5En112tTbQPI3ibVnYwNgIyJZ8aSP5cprkS5TatT1w5AfD4nLioVG6Mhm4GMi59z28p5wB\nvwP4Z1A4WwlsgchV2I+ozqkV1Vcd76T9tvBERJZrjEi8BOgtmGAFlK8/3T3u//jUmeaYgX4AU8u6\nETPg94b9g7CVUFuMaPRBpQbcMBbjelz5nPFEzsWq0iX7cN0QOQGRnYkJbESeiOMRqV0+jUgHRG7E\nSFNjq25a75+XCwHqkwGP6/tM7Pu5RJ0bhxH8xmOs8SVh35Hi/UNBXOWocExkwLOwmgmni/fnl53f\nGOnbUH5RVJv9rnf4o2unb3JEYikrS+D1WTz52tn6SHClt3dOZwEsGSXLgH6DPmcCsPiuE5NKfK5F\npDGqKyRflmAD9RlAhuTLaShPaX5Z850xI9wa1RlhSryWPPAiQ51NHt5D9e9xl5iO5UFH1YiG1OJt\n+KNjGOYq3AVzRaeK47AypU2I1WGPMAiRLbGsAzAi2pfY9w6mufs7tnIpwAiSR6G6CJH3MMW5VzGX\n+buovo5IAfAC5nKvCn/H5GfXnAs7nWQThvuwwaI5NghPxVLnPkg49i/huplYjL5d6MP6QySN8vrk\nH1fW9A+CeZQvmFKf0BnKqoOByVhHNSYWYqGfV8L7z7BneBhGTvtKnSsOoYRzMInnh8T7wYQ6DKyL\ntsT/ODa709e1H/llrtDOQRQlWZu9iFtZxRPfrIFsg+Ubvw/8RYZyMRYXBVjZqIifrvPsdoWd4QNU\ny7OWy5+rAbArqhVFECxWGpVe3QrVqVV/uv9hlHenv4fqISGmnY7qvMoOS3KezzEVvkh7e1diRTae\nBU4uO3/y4/tiBv01NFRZk7JUxo6ozoprG6VCxQhxqffzd0yxMBEvY/H1Jpj7fG3cMd9iaZ3t0eS6\nCTXswwPYCvx24PYglvKHQyB/OYwz8aU6t2fVR9R9xKnOfYB5hlYRI7iBTfRy1blJCcd1JKbK9lBo\n1wkrAbrJK4jVNWx2p68DJF9aS76slXw5M7zvKvlySvhfMBZzt8oMeEA88/vE8heQ9tjAG0kHXjbw\npzI36bNAo5PHmwH/pRW3VmnAAVTXJDXgtm9QiOembTbgNYKJB6kurJEBN/xOfPEM1W9QXYURK08O\nW49IclyEceE1ZqxVizBDPatcS9VfUZUaG3DDqQnvx2OFQM5E9Q1Un02St94jvP6l3NZ1cbGbFv8F\nQBdUr6hvBly8v0y8V/E+s/rWTCYiPUKN0tPqKgIp72DgCHVupTqn6lx7YuJUTbHPnYjZWHjm4PC+\nH2b4N0op3j8SNhvxBEgbOVzy5QpMGz0deEzypQnmZnxa8qUZMYJPdYzVyIjfqnkak/v8//bOO0yK\nKuvD72GIKioiGFCCIAJrADGugTtixJzTiogRw+euugrqShDFtGYF04pxDSgYMCA414ioIIi4RsQE\nohIUBSWd749zm2mayam7Zu77PPMwXV1V/euips69555gkcL3YUFGYPm8O49+nCeADWbfwLVXj+fl\n21/gT+DsrX7WzECmNXWXZf0kR90uObxuNbikN0vR3SP8+xChOH4g5fLerMSqY6q/YmunQzK2V8RQ\nr0Ga9gLMiPYAGqPaFdXTSilgchkWRHdhcIWDyC7AsuBBSP+gNoi8jqxRez4V6f4NsJAiusmVQXtW\nEO/PEO9TQVlbhH/XL27/cMwGTJnSCssu6I5lJSSGkq65OveyOvdnxuZUXMOSzCj0cMxKbPZ+CNBL\nnZupzs0tat/KkO17pTLENfGKcgD3U/gHdj4WRJTex3Zh+PcyHbhmjnUGnwO9daA+lLH9eGyWdihW\nJe5lLGBpmA6iJ3DdgDdpF/aNa0TZQrVcOakZnAGMAYatlouvOgWRLVEtqUd1at+i+tlXLTawK19T\ndNVbgFsQmQf0D1kPqRrjW7P6bGpfrCbDy8HAtw+fNx8zaGBu2JxCvN8Z+CQz1SlwV9jnEQrr7v8o\n3n8FvKfOHVvEud5h3rznkpATXkWknpmTSthnAuahfLf65dResrYmLiKzsP/oFVif651EZAMsercN\nNvM9RlUXZhxXbWvioaBKagR5EBa0kWocfzi2ZtcBOBJ4RwdmuDXL9CFSH+uHPhzVpzLey/zPGApc\nkasz6FpJ6v+gsveYyJbAZ5U+Ty6z5v16G7Ac1QvC+52xFLkHseh2SKXTWRTyN8AdlSozWw2EteuV\nmL4tUhXJwnurCiFhpZovJ8M1nioNGs7TABuo7451/ypPgGRiEe9TbZr3UeeKrF4o3m8IXJaU2vHZ\nJFfLrirgVHV+2rb+wCuqep2IXBJe9y/y6NIQ+SvwVWlFGoLhXqAD9SsKDXieDtSV4f2tgF10oI6R\nwVIAtNaBOj3tc+phA5H+2MDjJVSLGr2DyH6YAQfL683kWQrXSdug+k0R+0Sql4WU4hotI19iD/na\nzNXApWmvXwVOwxqW3ERhad9R2Mz775gBPxbVJ8hdUh6C1li54uvF+06YIf4Ayxx4Cuuz3RELWJyB\nxTFcLt5vi0Vqp8fLbKDOLaDuMBdLX/TF7RD6p0cDXkmyORP/CthBVeelbfsE6KGqc8XWy7yqdso4\nrvSZuMhB2JodQMvigmVksKQiK/+DjahnM43n9Gk9JJwnr9Q1yMIo4hQe1fwi9kvvKDUQ1SFr7GP7\nbYxVBytXIFVtKS+YJJKqG6pIu8V2HIhFFT+PzVA/xoxZz7DX9qh+EPa9HGul27vEeIDSP7Zar7t4\nfxm2LHAc5jFogJVsTtWlvweLJTgT2Eadax6Oa0qhG/k8rA3slmCz8zp/v2SBpOqG1bXn8kx8vIis\nAO5S1XuAjVRXFUGZC2xU7rNac4I7sGIW3bD1uKeL2Tv1oGmH/dE9zGjuC+c5GHgWkcLSlbbdOpup\n/onIv8JnzMaaGTwAHBm8AE2Bj1H9FpE2FBrwZmQsEaxGVaTsRCI1gc0Anl9tm8h7WMTxOVjt/qlp\n+15JMmiLNaL5BKu9kMlozNPSI32jOrdIvH8B6IUtLdyHxbtUSTBiJFIU2ZyJb6Kqc0SkBdaD+zzg\nWVVtlrbPfFXdIOO4NUckIk2x1pHpM/CtgXxgW1TPWOPzB8s2WAOCcyksVrCdDmIukG5I52Ou7/Wx\noJyjsYFBOvsA00Ot67exms+GldJM9QjfqAKpSpFIchA5EmsOcmG2pVSEsI49i5AxwuoFdE4HxgQ3\n8KoSpOntMdPW0wEOVudWH+REIml48WsDi52WHJWfk3niGtaq1VzdozF3VcqNjlgedZEGT0RGisgg\nERm0ncg1Hn4NQTTPeGAAXIrqDOD7UdAlPVRfRJzsJhf3e5cPt54LB1zF711fZTIwUwfqhwUw2xd+\n1MseNvAW4DYWuNXDHi/ATKwQxt4C+WLBPHOxjfPTjmeAyIBr4ACsleGPIuLW0BNfx9e15TXMk8KB\ndM18/sknXxFytRvLmWdeJ3l5FTqfeC+MGXMXU6ZsiK1xf8nUqTA1OBOcu5f8/K3Tjm/AkUful34+\n8vN7cP/9g8L+z2f9/yO+ztnXXvymU5n621SmrvTid/PiR4qI6yydD28gDfLFbNxIERlJCWRlJi7W\nxzlPVReJyNpYvuBgLE1lnqpeKyL9gfVVtX/GsSnFBdhMO8XXWFT7yag+GHb+K/DWCuGrPKXb5E34\nvfsc6u3el7ff/A/dVzvvIBrrIPp6uNNZMMvnmEvtPCyYpUf42RFoFApvFPsFUVVWj97tj+q1Zb9K\n5UOkdqz9JImk6obao128b49FvIN51M4FfsaC09oBr6hzGrpgNcDc28uKykcW79thA/Sf1bkW4v0W\nmNv8GWAzda5SBVpqyzVPErms24ufghW42SRt876YPXzwaq5+41IufcKp+1VycE18I2C0iKQ0PKKq\n40TkfeAJETmVkGJWwjnSDfhCUtW14N1QUW1ls4th/nWQp7TrewgLD/4Mus+BcyfBD2vz8Ma/8zdC\n+osO4kLg8nnwVkYHpdQ63vOY4HqlBrsVjoxSnaXA1ukjkUhlOf30/cX7IVhg2ctY843tMQMOVudh\nOBbzcox4P4bCpjQAT4n3R2PG/wx1bkLYfg4WSX9OeP0VsBclRFhHIiXhxR8PPIoNBE8GGjl1P3rx\n+2AGvBO2bOOwWIxx2DJv71706g309uK3Lekzklk73VI7RmAz4wMwV/d6wGxUVQZbr28AUcasHLxm\nqs+vDem67lJmoLockV7hHADrllKtqjxiW2ItHPuGkpuRSKQSiPeNgMye0u2Am7GUtrWA8dhM/AOs\nqNIArPLdKVg8yxAsBaw5UKDO7RXWsn8DuqhzX9fAV4nUcrz44yjsn57Odlh543FO3X5p+6+N3YNT\nsTixVY2s8smn1vYTD7PuPbDRyy/Y6PsVYG8dqBMAVoo8Wy/kZfc7kOdue4FH6yuPr1ZEReQGzE1+\nXs19m0gkUh7E+6swl+NybDB/pjp3dygc0kqdm5bW83odUoNo+FCd2y4j8GwSNguahT08twbqVXXp\nz0jtxosV9XHqlobfl1MYb3Yc5snpS2EnyRexyWcrp252xrlmAk84df29+LOw+3NlPvl9cy6wrSoI\ned43Y3naC4D/YelkT5GWu10PTgMuBloPf14Pqb9SH1ujCprqRaiet1qQSoJIqm5Irvak6oZkaRfv\nu4r3J4j3bwGXMnToCCzYdKI6dzdY4RB1blo45GDgInXud+BCrBbETWE/BRphLV7/irnj22IGvE91\nGvAkXfNMkqq9unV78fWxdOg/vfimwFGYXX0SuAEY49TNdeqGYVlLP2AG/L5MAx5oj3mOyCf/E6fu\nFCxdulgSWTtdBsv+WODZ1di6+a3Y+sIxQD8dqCNWO8DSuq6vYZmRSKSMiPfXYMGqKzBP2omYZy2V\nojUXeB/4OxMmfKnjx99X3LlCWtfz4feFQMOM95cSusOJ94dhD9b11LkHqvI7ReoEm2H37GtYoZ/F\nwClO3cgi9v2Qwhat/Yo6WTGpZpnNZVYjke70tPILv2P9vBcAyGDZBJibKpkaiURynwwX97tYumk6\nbatznVq8bwP8RZ0rccYTicAq9/npWHXCHbBeGidgtfZ/BzZ16n4t5thjgLZO3XXl+LzO+eR/XKvW\nxBlEV6CZDszN1IFIJFJ2xPt1sVn3x1hZ1r5YKWSwGXKRD8RIpCrx4jcC/nBaZOc6vPidgUuwGKz0\nVrLHO3WPhX2ktMItFaGkFLNEGvHq6mIWzp+zeYUlkVTdkFztSdUNuaFdvN8MW68+B6u/cARWEfEh\n4CRgvLo11w1zQXtFSKpuSK72sugOM+uzsToDX2Oz7EVYc5ZLsUFldyAVST4T6Iq5zus7XaOXepVr\nz8U88UgkEnkN2CL83kWdW4LVbSDt30ikujmLwtLbbbBc7RTptUruxYLVZqUZ7qzXxY8z8UgkUuOI\n99thAWwtYPX645FIRfHi/wV85dQ9XIZ9OwKbA//GcrfPwzIX+mIZTa2Bx8I+s526rMVaRXd6JBKp\nNOJ9E6CbOvd2Ee81w5oFHaHOjS7DuX4CpmNRum3UuXGlHBKJrIEX3xor3jMa6x6XanbVFMtKWOzU\n/ZG279ZYJb77SG9UBSc6dY/WlO7yEt3p5aA2r/3kKknVnlTdUGHthwL/Fe8Bmqtz88X7BljlxNSz\n5Gnxvp06N0u8rw/shtUy/0ydWwYg3ncK+56mzs0EPq0B7Vknqbohp7Wfh5UzPTm8Ph2rCbII4H3e\nn4/QA1vPPh+bVX+LFVx5GhiDdaicXLOyS6es1zwa8UgkUlZap/0+LzQV6Q5chc2GbsQKWTwo3k8H\nNsAqVgHcDZwZDPj/gCHBgEciePG9gElO3bxyHNMKq7R3J/AS8KFT97UX/wPWs2JYPer9H+bxSedz\np+7MKpKedaI7PRKJlIp43xirbvY8lhe7M1bD/CesgEUDYH/geApnRQCXYbOiW7Ga0A9gkcDbhUC2\nSB0gVDbbBSuZ+y/gWaCfUzc7GPCxwACn7pq0YzYF5hSVsuXFH4rNogF2dereyXhfnDr14jfBCvs8\nAQzDqql9UVwed64S3emRSKTChGIs/wb2xNyQswDBirJsjlVOvFSdezm40LuF/S5R564Oa+mDsLSc\nrkC/aMDrHCdj0d0pDgEO8eK/xWqN/4F1t0zne8w1fr0X3wgbKO4B7IOlf4EVVpmT+WEpw+/UzfHi\nNwYWOXW1sglVomunVwexRnDNk1TtSdUNZdceemx/BOyOPUBvwnJpPwy7XIjNcHYBUOfGqnPbqXP9\nCZMEdW6JOtecwhrQj9eE9lwjqbqh4tq9+I29BVFchOX/b+/UCZBqr7k55gofBjQOx7QKhVcArvPi\nd8CM/CLsHvoHtsb9OOYJKlF3qF2eOANe1mseZ+KRasWL74uNlocW8d5B2PpoJMcQ7ztiObBfYN2+\ndlfnlof37sSeHRepW1XdalLmOdS5FRmvD6xW0bWA6qr4lUXSZ8nOqZsL4NRN9+J7ABOdumVe/CnA\nYC9+JJDuGv8JeDXt9anYoPJ9pzGjAeKaeKSa8eJfx2ZwLZ26n8K2epg7LZWK1M6pm5UdhZFMxK9a\nR0zRMBVZHqkevPgjsJnoI1gXxnWAPlh5zwHAHU7XTO0rx/lTz8yG1VVhrIjP7Ir1dG8DLCvK7Z22\nb18s7SvFO8B6WJnTZ7EZ/AfVKDeniXnikazgxR+FteT7BotsHoOlgKRcYHdiuZ1tgWFO3aVZkFmn\nEO/rYcbhYKw++U7q3L8y9vk3sD22jvmjOsuzjVQ9XrwDrsECBQFGYZ2xdsnYdRlwLXB7ajYbju+O\neUwaYV3emjt1P4b3WmKu5zzgn1iTmXrAyU5dtVXEC0FshwC3YbXI25fhmDxgU2ChU7cobEs957dw\n6r6sLr1JIBrx8p0/V/MhSyQXdXvx52Dur6+wutjpDMJSktafytRvutIVrPThsGL67OYcuXjNxfuu\nmOGdLd4fjOV236zOfRTeH9R4CQP/+HQqdO2aOmyEOtdPvN8Am/m9Bxylzr2Sfu6Q0lPfafV1FCsL\nuXjdy0K6bi9+LWAEViN+OlY/fmqaAWuDBRCCrf+2C/vPxAzkLKxk7YcUMgIrIdoP65d+eYaEu4GJ\nwP2Yi/omrKXzQuzv9Ban7vfStJeGF7878EZ42dGp+7wsx1UHSb1XINZOj+QG6wDjsRziq7CI5quB\nF526m8X7fsAmHfe598i7lt/eBbgSONeLb+TULS3pxF58M6C7Uze+er9C4ngB2ES8PxB4FgWEU8X7\nvs3m8/Nld9Jv7wkwBV3euTG/TNqZ5oMHcZZ4/y32fwQwPGXAw9KHYobhjrANzC0bXezlJFzPVKzA\n11jU/42ZA9eQ77wR5oZeEI59HFiArQmn8zI2my8Ir4eHf7cGPs5cY/fi18H+r5/DipxMxiqd/Rn0\nlPYdUulb22Cz+6OxFpydsOI+W6V9j6wZ8LpCnInXIrz4f2DrSC8B05yWLY3Hi98LaI9FjH6OueZu\nBZo6dT+HfRoDS4AjnJZeVjOs8T01sx2XnfoflgC3qnMrxPuG2MNiBlY3W4HBBfncjc3WnwBalTYb\n9+InAHs5dXL0Ob73dtN4819D+RHYSF3dc72J992w2dypqW3D+vP4LpM4NnPf5Xn8o/4K+gEdAW4+\nH545DOovY0zDpczoOYEnLriJxsBQLJ3nI8wgnI/N5N7FZn1X1rTXxItfH2tX+itWTGZGeQqElONz\n6lV1rWwvfl+swthBmBG9xqn7rZznaISVC/0v5jE526n7Lrx3G+bN+gtQkDL+xZwnDzO6H2HduC4C\nBmPr0u2BC8LrbsBIYBrmpRmCXf9MpmBu+1HYuv5cYEktC9LLGtGdXovw4nti+ZLjgb8Be2NlBOdi\n7rE/MSM8A2tYL9i6VJH/0V78iUCqWcAn2B92Oj9jI/VUG77PsdH6bKfuubTz5AHrYu68wUEjhz8N\nC5sBNjr/AnOhnx8OGw+8BYg6NzCcZyww2am7Iu3c3QCHuQD3x3KQpwF80R46fAnzm8GRT9v+7WYy\ntdcLHHr7KPdNcdexNhBKnt4GpKpP/bneQr697CrqfbQ16/QZyTKB5xW2eP4g1lvUlNfzVjBu+OOF\nbnIvXgG+aM+j7b+kg1juN1glrBuAHzGjc6dTNzYckwpWXAysX90zci++OTZo2AU06HAAABpiSURB\nVAm7v7fM2OUboEtxruAKfN5xmJGcCOyW/rcT1mkPA15z6uZ78XsCf8dc4sOxv5/3M42zF98AWBr0\nn+rUPVIVWitLWDdf6dT97MV/j61Ll8RTWOOadtjfeTvg++J6cEeqhmjEy3f+nFlDCX/47bFlj57Y\nw6Jtxm7TgUkTmbjnruz6OuYWaw5MoDAX80WnrpcX3wTojD2YT8CqJ/XEHtDnhM9sCrQM55mLBcS8\njc2SuwAfp3327cC5GXp+Bh4FXuk5nudW5nFr+JyzsIjnz4BnsKCq+UAnpk69h65d/1Dnmnjxh4T3\nf8NchJ9TdF7xG5ghYdw+TNn3Fbb/ZV2WfroVP+30Hq0AnjuIh2+8kCOA29W5SwDu2dKfMOYwbvt5\nQ74+cCxXXPG6e96Lb1ARQ5Tte0W83xHw2EDtJ6BtQT4DKHSLb+nUfVHksUF7MEovYIOjBcApWBDV\nR06LHgR58X8BmmDtQk8E1sZSzFZUZvYaBoJfYC7ag526j734IViFrw+x3s7NhjK00eVc/jLmuj0G\nK0KzIWZchjp1r6edc0PgF2xQeSFwtVNXZPvI8L0yXdXHOnVPhDXqV8PPaUHLDOxezWRi0LQ5cCAW\nl9DtLd769jK9rFs5L0uN4cW3wwZmLbG/99QS2NYjGXlIH/rc5dT9kE2N5SXbf6OVoaxr4ok34l78\nuuUtoefFHwDsBXwZfl5N/WGnPdy2xEbcNzm1/NhwbGNsBvwgZkRerUqXUVqUZn+sPCXAPGz2OR5b\nx/oNc3NOTz1oM2/WsGbcF3uQnI89ZFtQ2L8ZzDg/iUW8LqcMhIFFC6xF3x5h8+fYjHBzYGB+ARuH\n93fCBhT3YTOUJWHfPqmKXeJ9faZOXUbXrqhzEtylH2MGv3vaR48I33sSsNUbu/Pb9f/k5rUWc/MP\nx7l/jGzrH9j8W3bKW2mehNmbwKZz4MwRcMwToMKbQ8e7PV5p4Jc2WG5eAoAljXm4yR/8DbgFC8Lp\nVZbrADX7gBDv18Ierp0wA1IP2K3BUoaM24/HMON3ERZzcBHwtlM3sdjzrXm/1C/rPZB2zJUUBk99\nAXQA2ob13HWAo7AqXZOBA1NLM6nPw+oHfBNe98UaqRyPBW9tReFAra9Td38J2gUb7I7EDDvYfb0F\ndg8txJpcpDgLC/LqQlgz9uJTHp67sLSo+7EB7FDWjBgfixlnCFkVwci/gLmS/4ndq5ulfeazAxjw\nxESdmBMz8PKSVGOYVN1QB4x46iGABYeAjZCXYLOJW5y69zOPDYbtTuwPcCxmjFpiI/WHsKpAh2G1\noNtjo/uJ2Oh8J2x9qDhmO3Wtyvt9vPiGwFpO3cKMiNSpwOvAQKduYXnPm/EZu2DfA2BHrLzh+Mrk\ni4YHZ73MWU0o0ZmajR2tzo0S70dh9bYBGqtb/XPF+02xEott1RVGPnvx62JlF69KX9/P+Ix66mwQ\nFTS1WVaftvu+wvQLb+DnA15kWd7KQqMNcNhouo3sw9Knj2BC3/vZOOOrXQiMKm4WWtN48V1/bs5d\nR49a5eZm/QXME6X5ebdxVb7nKNICibDKV0NS7RerWVtmPvkH2CBrSNr2SVj61EzMcP4b+9v6JLx/\nI+ZiHhBeH+3UjfLiz8QGbmOxWXmZHlQh5eq/mMt9FPZ33RGLFTgVixkZi80wwQaY3bFysAOduiFp\n5+qCzbZTbAH8gA1MB2CD7M2cuu8zNJyLDWr3AnxcF45UllpnxAsoSKVSzMVK8a3AgjymYxHRp4fX\n87GHxkeY+28MNkI+L/WHF2aWfTCX157YOs962DrgMZh7cSds3XkSNntdjBnCd7B82m0wl3ST8n4f\nL/5NbPaQyp1+CrjXqavS1nhhht+kvIE05UG8b4q5PdsCPdSZW1P8qhnbhuqKDkIS72cCs9S5vUr5\njMPDubYHTlZXfL6rF98BGwhtktr2QVe44CYz/Htf7jus8xsf//2W1Y18YC+nrqCI7dVKGHCthRm6\nUdg9zPCzuP29HZm4zysMO/6xVd3EXsHaKX6AuXVPcrp6WlgN6N0CCzLrhi2VfIj1cf4WOMip+ywM\nxsZRmAsN1n70TuxvtROQD7xVFQYv3Ot5xWU4hDX2YzAXe19gO8xF/nDmwNaLPzl8lw2culEZ7xVb\nXa0ino1IpDhqoxEHc7XNwkbPX6XvE9Z178ByMH/H3NGtMZfftsVFbXvxkk9+j/K6X8JD6hfsIfU+\nVnlpZfpsKESVLsPcoPdhI/9PsfSMfbER/7pO3SdUgJpwG4n3ecC26lavnCTe54XI837Yg7mbOjc1\n7f0NgWPUuTuLPK+Io6DgI+DTUGO7uM/ficLyns+oc4eVpjnMzhvnmznuD8xR50aknXPsDu/R5fqL\n2RMLCEylxCzEAsa+K65SVlVec/E+b9SRnNh8Pg+ktin8IaGedAY7Y4OYuyu6Bl1d94sXfyvmyTox\nM84geM/6YfEa3zl1v6b+f8qaSQHJdZEmVTckV3tSdUPtzxNfr6R18FAwobcX3wdzobXEZmSTS3pY\nOHVKxULmFmHuw0nY+l8XoElYV5+DBYD1yTjm86Dpn2nFM3K2yIl4vzGhDrJ4nz7L3hqYLt4fihnw\nvdINOIA693N4ryTmA03F+0aZ7vbwORtg13c5Nmt6I3OfoggzpSVhqDqwiF1Oen9H5uUX0CukuaVY\nHwuoW4ClMlUrR47i2WYL6DXmUG4ceyCdmy1gh+suocW1F/PBJddxGjbgawcsdupmYmleucj5xc1O\nw8z0toxtii2DRSKRCpDImXguppiF9fatMLf8DpgH4FDMC9AciyxvjeVfXuTUlVpUIVcQ74/HAnbS\nr/tJWO7wJWnbRgJ9U2vUFficP7C88e6Y0RJsoPkn5un4BehY1W0sxfuU3uYF+czDarofnrbLtcA9\nWOT9cU7dXWAdmgB1aWUwy4IXf3iBY9GQgbQc24sZ7+3I0Tu+x6VPH8Gj953KieEqv4RFjHeoi3nv\nkUikkFrnTs9FI14U3mqH7wlc4NQtD67DGmtAUFHE+/UwA709tpb5CbZWfwIWrPNixiFXAC+oq9w6\nvng/HIt1SDEOW2pI0V6dm1mZzyjmc1N/BE8W5HMKNjPcBouNeK2IQz7B4hhS6/tnYSlzrYG1nboP\nMw/w4lsAOy1twPkNl7FP5vufdmT8mZ+6fcKSxebq3CzxvkFsPBKJRKIRL9/5E7mGUlW6xfseWO7x\naqhzkrbP2liAIFjazbsVnX1DxtqP99thkfmZ7KeueloPhvSt/kBrda5P+nvB+P5Y1HGTmfxrd7qv\nG16+hMU77Atc6tQNSzvHYGygs4o7zualEx6l6wu92PjVvfhpZns2TbX6rAmSep9DcrUnVTckV3tS\ndUPtXxOPVDHifWesJGQ/zIhfA3yHzUpnpe+rzv0eCo20VOfW6CNdGdS5aaHTlmDV6CYB66ennlU1\n6txi8f4NYJx4fwWW3zsNuJkCRhTkswiLuD4dW1ZYB1j7eq7v+hiPjcNqDewfTncacK8X/yuF+fFX\nAPz7Avh8S0b+60reevIOd68c7RsCrdStHpgZiUQiZSXOxOs4wX37V2wm+SswRJ0bXvJRtQ/xflvM\ncKeKlvTCind8U5BPPta96zPxvn7mjNmL3w+4/8+GPLT/yzxXkM9czOU+BjjinZ1hZB/4fEsOX9HT\njanJ7xWJRJJPdKfXAcT7lljt5gfUuWeL2acBlh8LFg0+ASvA0Qs4S517uia05iri/QxWb+7wE1YQ\nqDdm4M/G0s6uUucuF+/bAQvVuQUhen8gtj5+fUE+6wFnzOjC4iuG8M785lwEfKiu6JKfkUgkUhzR\niJfn/Hl5jgkT3lZXcivMbCHen4ZFSoOlPx2szr0lZ511A8cddyHmAt8PK4SzFDM8TbAc6HOApphx\naogFbn0M7KauclXhKkOurFuJ93tjBVS+BtpghX+KSksDOJGpUx8JPbl3wOoDgNWcvxuFnSfBFx34\nc96GdFLnZlWv+vKRK9e8IiRVe1J1Q3K1J1U3xDXxinPxxecCBeJ9a3Xu22xIEO8lFSgm3m+PGeLP\nsVne5lhp0F+wutRvivfQqRPAP7Ca6tNY8/92BpYqdVNYA14HMz5T1JWv9nwtZgLwf5h3QrHiPCMI\n+fHAIcDzWM77I/z22xSsC9v7WMT+uercTPF+IcL/TdqF3YF/55oBj0QitYc6PRMX7/Oxbj1LsLrp\n22K53e9hNcZHA8dhZV1bY2VBNe34xuqsKlswittikdrljjIOEd+9sRzpU7H0pa8wQ/s6Fkz1EDAi\n9ZnhuG7AwcA96tyctO0bAaLO/SDer6XOLS6vpogh3ncHmqhzbxbxXmOs/O4/1K1epjVUqluirmpa\nZEYikbpJdKdnnsP7Lpir9CjMQLbEqqWlKkp5rIhJf1af0f6CFTR5SJ2bHPKLJ2KFXfYO+0zDXLDj\niitKIt53AAqwpi0CtMLyr8Eimn/Agsw2xdzd91QmhSsSiUQiySUacUC8b4u1NeyDGczUrHa1utgZ\nOcstsbXlc7FiJ8OxLme/AHnY7HgY1ixlEBbhXQCrOk59h6VIzcDKeN6INU6ZhBn/TbD16dGYu/yp\nClc7qyVrP0kiqbohas8GSdUNydWeVN1Qh9fEQy3vQ7GuSPlYjeld0nbpA5yjrvRGI+rcj6xeavTw\n8BmdsFn8f9S52Vh/5xQ7h1aZJ2Cz+SOxwUNLbL0VYJg6l35MJBKJRCLlJpEzcQoKGmLGsQm2dnwX\nVlXre2wteyrWlnQplvO7P7bWPFudW5QN3QDifRssSG1oNnVEIpFIJDnUOnc6BQXfYOvX/wOaYc0y\nXsVSrmbEaOBIJBKJ1BYS5U4Xkf2Bm7E153tV9doidvs71k+6Qr2US/n8RK6hJFU3JFd7UnVD1J4N\nkqobkqs9qbqh7Nrr1YCWMiMieVjv7f2xylnHi0jnzP3UudHVYcADXavpvNVNUnVDcrUnVTdE7dkg\nqbohudqTqhvKqD2njDgW1f2Fqs5S1WXAY1iQWk2yfg1/XlWRVN2QXO1J1Q1RezZIqm5Irvak6oYy\nas81I94KSK+S9l3YFolEIpFIJINcM+K5EGXXNtsCKkjbbAuoBG2zLaCCtM22gErQNtsCKkHbbAuo\nIG2zLaAStM22gArSNtsCKkHbsuyUU9HpIrILMEhV9w+vBwAr04PbRCR3BEcikUgkUgMkIsVMROpj\n6WI9sTKo7wLHq+r/siosEolEIpEcJKdSzFR1uYicC7yMpZjdFw14JBKJRCJFk1Mz8UgkEolEImUn\n1wLbagQR2UFEWmZbR3kRkb1FpHu2dVQEEUlsqoeINMy2hoqQVN0pQt2IxBGWBROHiDTOtoaKICIt\nwr+Ju+4i0q6y56hTRlxE/iIiE7GOY82yLKfMiMj2IvISMAarBZ8YRGRnEXkGuEdETk3Sg0JEdhWR\nR4BBItIxKUYl6H4SuEFEuiRFN4CI/FVErgRQ1RXZ1lMewr3+MDBMRLYRkUq1TK4pRGRHEXkauFlE\neibhfhFjbRF5DHgGVi3HJuWaby8i44EhlR181CkjjpVrHa2qB6nqp2A3Q5Y1FYuI1BORe4B7sCYv\njwKdU+9lU1tZCF6D4cCo8JNPQgYhIrINcCvwPNZc53Sgd1ZFlYHgYbodeAFrDnQ+0DerosqIiJwM\nPABcJiLHhm05P7sKBmUQcC/wIhZrdA7QLZu6SiPovgYYgRnCb7Aujy2yqassqPF7eNlcRM4Ovyfh\nuXg5VsjscVU9SVWXV+Z8Of+Fq4rgclkJ3BZeHyEim2Od0HLSmKvqSmAcsIeqjsZ6mueLSOPwXq6z\nC/Clqj6EfY8m2IMiCewGfKKq/8UezkuAv1WF+6ua2Qb4TFXvB24AngYOFZGO2ZVVJr4F9sLKLt8A\nyZhdqQUWfQ2crKqPAEOBNlhwbs4SdL8G7KOqDwAjgYbAL9nUVRpSyCbAXOA0oJ+INFPVFQnwJNQH\n3lTVe2DVrLxBRU9Wa424iJwgIkNE5JCw6XdgT6BncJGeCVwJ3AKrbuisk6b7UABVfVJVF4eZ90rg\nc2DtrIoshkzt2KCjZ3CPzsCq790iIv2zJrIYitA+CWgtIh1U9TdgBfZwOz1rIotARFyor5BiGrCD\niLQPM5X3gcnAWVkRWAJFaPfAD6o6Dvg65VYnx7JooEjt/wWmiUgjVZ0HLAI2yY664snUraovqup8\nEdkDmAi0A4aLyPFZE1kEGbolzMTnYAVRvsLunf7h7zWnlmGKuFduAFqJyI0i8j4wBHhARI6u0Aeo\naq36AQToB3yAuRE/A84I7/0dmwmeHF63wm7cXjmq+xSgado+m2E3bKvwul62dZfhmm8MXA/8Lbzu\nATwH7Jpt3SVo7xN0DwXexFyNzwPHA9cCTXJAd1Nslr0AuB/YIO29q4BbUvcIsAfmMt0k27pL0h60\n1gu/bw38CmyUbb1l1Z62T4PwXOmYbb1l1R2u917h91Mw71PW9Zdyn3cEbgq/HxLulw+ARkCDHNd+\nIjAB6BFenxmu+Vbl/ZxaNxNXuyK7ANeq6n+AswEn1uL0fmxU3yLs+z32kM76yK0Y3XsDe6bciar6\nHfAOcGR4nRMu9RKueS9V/QH7Hj+H3adga8xLsyI2gyK0nwPsA3RV1cuxP66RqnoQ5gXZVlWXZE1w\nIUuBAuxhMBs4GlYtCz0JdBKRvcM9Mg8bsOaKm7RI7aq6UlVXikieqn6EfY9rAETkgGyJzaBY7Wn7\ndAbmqupnIrKuiOxU8zLXoEjdhFLXqvqRqr4atr0BbIB5E7JNcboJrzuIyLPY7PY1YJaq/qnWQCvb\nFKtdbdnlGFV9LWwaj9mlcl/zWmHERaS3iPQQkQ3Cpv9h7or6qjoe+BBba1sKnAf0FpGuItIPMzCz\nclT3dGB3YPOwfwPgC2BxNvSmU8Zr7kRkYyww7+KwJHAsNuqflxXhlKr9Fey654vI5qo6Qy0eAewe\nmpStoMKg24W1vz+x6zoe8x50F5FOYVAyHXPv3iwiHYJuwdY7s0IZtHcM+626tqp6KnCyiCwAtsvW\n2ng5tKfWNZsDi0XkFOBtLE4hJ3WrqhZxXXtiS3e/kwXKoHursGtT4AfMO9ldVQ/GlsCyloZbnvtc\nbdklxb7YgKrc1zyxRjwENmwqIh5zf54I3C4i62Hdz1pQGAn9OLAV0FlVn8JcosdgATQnaYhUz0Hd\nj2Gj+uYAYXS5NhY0U+NU4Jp3BDZW1TvD+2MwI36Kqs7KYe2PYffLhuHYnUSkANgPeLgmPSBF6D4B\nuENEWqjqH6q6FHPd/kThrHCFqo4EHgQGAMcBF6vqwprSXQHtxwbtK4GVItJGREZjs8I9VPWaMEDJ\nZe2p2d++2DXfEzhRVe/Lcd0qIo3F6lBMAQ4ELlfVX3NU9zFB9xzgn6p6vqqmZrA9VXVyTemugPZV\n97mI5InIniLyAXAAMEBVy+8tq6n1gar8AeqHf7cCHkltA+7EHlwNgfuwlKD1wvsPAFelnaPG15Mr\noXtINnVXUvvQ8HsDoEXCtF8Zfm8BuBzSfTvwdMa+h4fv0wFYB8gL2xvl2DUvTXsTLKp7PWDnhGlf\nO2z7K3BsgnQ3Dn+f2wAHJ0T3luFeaYR5mXLtuViW+1zC74dURkPORX2WhFjqwFCgnoi8iLlTlsOq\nVJTzgDlAF8ydeDgWDHY1tu49MXUurdnZVGV1v5sN3VWk/Z2w7zJsJJok7ZPCvj9h0a+5ovt8YLaI\n9NCwpqaqo0WkM9Z3YB3AAf9Tc+nVGFWkPV9VPyZc/yRpF5F8VX07abqxaz4dW4pJgu6Xgm6n1l+j\nRrOLquia76WqM7Al0gqTGHe6iPTAUmXWx770lcAybO1yJ1hV4WkwFqQ0HiuQspuITMIqtPmou+xE\n7Tl9vwwK2lPHHQNchgXSbKNZaBxUhdo/rlnlydUedSf6Pp9RJYKy4YKooNtiT2z9OvV6OJYadAow\nOWzLw1KDRgHtwrZmhJSsqDtqz3Xt5dT9ZJruPYE9E3TNo/aoO3G6c1F7YmbiwHvAk1JYjedNoLVa\nZao8Efk/tdHPZsAyVf0KQFUXqKWSZYuk6oaoPRuUR/fyNN2vq+rr2ZG8iqi95om6a56c0p4YI66q\nS9Qi/VI53ftQmHvcF+gsImOxtc0p2dBYFEnVDVF7Nkiqbojas0HUXfPknPbqdj1U9Q8W+ZeHNRro\nELZ1wNyguwObZVtjbdIdtUfdUXvua4+66672xMzEU6h1fGmAjXy2DSOefwErVPVNtapmOUdSdUPU\nng2Sqhui9mwQddc8OaM926OZCo6AdsUqCr0JnJptPbVdd9QedUftuf8TdddN7RKEJAoR2QwrzHGD\nWjWcRJBU3RC1Z4Ok6oaoPRtE3TVPLmhPpBGPRCKRSCSSoOj0SCQSiUQiqxONeCQSiUQiCSUa8Ugk\nEolEEko04pFIJBKJJJRoxCORSCQSSSjRiEcikUgkklCiEY9E6jAiskJEPhCRj0RkqohcICJSyjFt\nROT4mtIYiUSKJxrxSKRus1hVu6nq1lgjhwOAgaUc0w44odqVRSKRUolGPBKJAKCqPwFnAOcCiEhb\nEXldRCaHn13DrtcAe4QZ/PkiUk9ErheRd0Vkmoicka3vEInUNWLFtkikDiMii1S1aca2BUBH4Ddg\npar+KSJbAo+q6o4i0gO4SFUPDvufAbRQ1atEpBFWR/poVZ1Vo18mEqmD1M+2gEgkkrM0BG4Xke2A\nFcCWYXvmmvm+wDYiclR4vS7WknFWTYiMROoy0YhHIpFViMgWWCvFn0RkEDBHVU8SkTzgjxIOPVdV\nX6kRkZFIZBVxTTwSiQAgIi2AEcBtYdO6wA/h995AXvh9EZDugn8ZOFtE6ofzdBSRtapfcSQSiTPx\nSKRu00REPgAaAMuBB4Gbwnt3Ak+JSG/gJWyNHGAasEJEpgL3A7cCbYEpIT3tR+DwGvsGkUgdJga2\nRSKRSCSSUKI7PRKJRCKRhBKNeCQSiUQiCSUa8UgkEolEEko04pFIJBKJJJRoxCORSCQSSSjRiEci\nkUgkklCiEY9EIpFIJKFEIx6JRCKRSEL5fy5ChMJR3iXRAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data.loc[:, :, 'price'].plot(figsize=(8,5))\n", "plt.ylabel('price in $')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we'll create a `zipline` algorithm by defining two functions -- `initialize()` which is called once before the simulation starts, and `handle_data()` which is called for every trading bar. We then instantiate the algorithm object.\n", "\n", "If you are confused about the syntax of `zipline`, check out the [tutorial](http://nbviewer.ipython.org/github/quantopian/zipline/blob/master/docs/tutorial.ipynb)." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "[2015-01-28 14:35:58.352355] INFO: Performance: Simulated 2411 trading days out of 2411.\n", "[2015-01-28 14:35:58.352976] INFO: Performance: first open: 2005-06-29 13:31:00+00:00\n", "[2015-01-28 14:35:58.353412] INFO: Performance: last close: 2015-01-27 21:00:00+00:00\n" ] }, { "data": { "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAD1CAYAAABUQVI+AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nQ6A9AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import zipline\n", "from zipline.api import (add_history, \n", " history, \n", " set_slippage, \n", " slippage,\n", " set_commission, \n", " commission, \n", " order_target_percent)\n", "\n", "from zipline import TradingAlgorithm\n", "\n", "\n", "def initialize(context):\n", " '''\n", " Called once at the very beginning of a backtest (and live trading). \n", " Use this method to set up any bookkeeping variables.\n", " \n", " The context object is passed to all the other methods in your algorithm.\n", "\n", " Parameters\n", "\n", " context: An initialized and empty Python dictionary that has been \n", " augmented so that properties can be accessed using dot \n", " notation as well as the traditional bracket notation.\n", " \n", " Returns None\n", " '''\n", " # Register history container to keep a window of the last 100 prices.\n", " add_history(100, '1d', 'price')\n", " # Turn off the slippage model\n", " set_slippage(slippage.FixedSlippage(spread=0.0))\n", " # Set the commission model (Interactive Brokers Commission)\n", " set_commission(commission.PerShare(cost=0.01, min_trade_cost=1.0))\n", " context.tick = 0\n", " \n", "def handle_data(context, data):\n", " '''\n", " Called when a market event occurs for any of the algorithm's \n", " securities. \n", "\n", " Parameters\n", "\n", " data: A dictionary keyed by security id containing the current \n", " state of the securities in the algo's universe.\n", "\n", " context: The same context object from the initialize function.\n", " Stores the up to date portfolio as well as any state \n", " variables defined.\n", "\n", " Returns None\n", " '''\n", " # Allow history to accumulate 100 days of prices before trading\n", " # and rebalance every day thereafter.\n", " context.tick += 1\n", " if context.tick < 100:\n", " return\n", " # Get rolling window of past prices and compute returns\n", " prices = history(100, '1d', 'price').dropna()\n", " returns = prices.pct_change().dropna()\n", " try:\n", " # Perform Markowitz-style portfolio optimization\n", " weights, _, _ = optimal_portfolio(returns.T)\n", " # Rebalance portfolio accordingly\n", " for stock, weight in zip(prices.columns, weights):\n", " order_target_percent(stock, weight)\n", " except ValueError as e:\n", " # Sometimes this error is thrown\n", " # ValueError: Rank(A) < p or Rank([P; A; G]) < n\n", " pass\n", " \n", "# Instantinate algorithm \n", "algo = TradingAlgorithm(initialize=initialize, \n", " handle_data=handle_data)\n", "# Run algorithm\n", "results = algo.run(data)\n", "results.portfolio_value.plot()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the performance here is pretty good, even through the 2008 financial crisis. This is most likey due to our universe selection and shouldn't always be expected. Increasing the number of stocks in the universe might reduce the volatility as well. Please let us know in the comments section if you had any success with this strategy and how many stocks you used." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Conclusions\n", "\n", "In this blog, co-written by Quantopian friend [Dr. Thomas Starke](http://drtomstarke.com/), we wanted to provide an intuitive and gentle introduction to Markowitz portfolio optimization which still remains relevant today. By using simulation of various random portfolios we have seen that certain portfolios perform better than others. Convex optimization using `cvxopt` allowed us to then numerically determine the portfolios that live on the *efficient frontier*. The zipline backtest serves as an example but also shows compelling performance.\n", "\n", "## Next steps\n", "\n", "* Clone this notebook in the [Quantopian Research Platform](http://blog.quantopian.com/quantopian-research-your-backtesting-data-meets-ipython-notebook/) and run it on your own to see if you can enhance the performance. See [here]() for a forum thread containing this Notebook on Quantopian.\n", "* You can also download just the notebook for use in your own environment [here](https://raw.githubusercontent.com/quantopian/research_public/master/Markowitz-blog.ipynb).\n", "* Read a recent interview with Harry Markowitz: [What Does Harry Markowitz Think?](http://www.brunodefinetti.it/Spigolature/whatdoesharrymarkowitzthink.pdf)\n", "* In a future blog post we will outline the connections to Kelly optimization which also tells us the amount of leverage to use.\n", "* We are currently in the process of adding `cvxopt` to the Quantopian backtester -- stay tuned!" ] } ], "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": "2.7.6" } }, "nbformat": 4, "nbformat_minor": 0 }