{ "cells": [ { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Demonstrating Mixture Models\n", "Liberally adapted from **Antonino Ingargiola**'s [github page](https://github.com/tritemio)." ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "### Need for mixture models\n", "We first demonstrate the need for a mixture model over a single model using a simple one dimensional example. Note that fitting a single Gaussian works well if the observed data \"follows\" that assumption. However, if the data has two (or more modes), using a single Gaussian does not work. " ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "import numpy as np\n", "import scipy.stats as st\n", "from scipy.stats import norm,bernoulli\n", "from scipy.optimize import minimize, show_options\n", "from mpl_toolkits.mplot3d import Axes3D\n", "#from sklearn import mixture\n", "import matplotlib.pyplot as plt\n", "import csv\n", "import math\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "#### Sampling from a mixture model" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "# generate data again\n", "N = 1000\n", "pi = 0.5\n", "mu1 = 0\n", "sigma1 = 0.05\n", "mu2 = 0.6\n", "sigma2 = 0.08\n", "samples = []\n", "for i in range(N):\n", " s = bernoulli.rvs(pi,size=1)\n", " if s == 1:\n", " v = norm(mu1, sigma1).rvs(1)\n", " else:\n", " v = norm(mu2, sigma2).rvs(1)\n", " samples.append(v[0])\n", " " ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6499: MatplotlibDeprecationWarning: \n", "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n", " alternative=\"'density'\", removal=\"3.1\")\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "h1 = plt.hist(np.array(samples), bins=20,normed=True,histtype='stepfilled',alpha=0.8);" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "#### Learning parameters for a distribution using MLE" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6499: MatplotlibDeprecationWarning: \n", "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n", " alternative=\"'density'\", removal=\"3.1\")\n" ] }, { "data": { "text/plain": [ "[]" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# first load two data sets\n", "single = []\n", "with open('../data/single.dat') as f:\n", " for line in f:\n", " single.append(float(line.strip()))\n", "s = np.array(single)\n", "double = []\n", "with open('../data/double.dat') as f:\n", " for line in f:\n", " double.append(float(line.strip()))\n", "d = np.array(double)\n", "\n", "# plot the empirical distribution and the fitted single Gaussians\n", "fig = plt.figure(num=None, figsize=(12, 6), dpi=96, facecolor='w', edgecolor='k')\n", "ax = fig.add_subplot(1,2,1)\n", "cnt,bins,ignored = ax.hist(s,30,normed=True,histtype='stepfilled',alpha=0.5)\n", "mu, sigma = norm.fit(single)\n", "ax.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) * np.exp( - (bins - mu)**2 / (2 * sigma**2) ), linewidth=2, color='r')\n", "\n", "ax = fig.add_subplot(1,2,2)\n", "cnt,bins,ignored = ax.hist(d,30,normed=True, histtype='stepfilled',alpha=0.5)\n", "mu, sigma = norm.fit(double)\n", "ax.plot(bins, 1/(sigma * np.sqrt(2 * np.pi)) * np.exp( - (bins - mu)**2 / (2 * sigma**2) ), linewidth=2, color='r')\n" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "The model for this sample is the linear combination of two Gaussian PDF:\n", "\n", "$$p(x|\\theta) = \\frac{\\pi_1}{\\sigma_1\\sqrt{2\\pi}} {\\rm exp} \\left\\{ -\\frac{(x-\\mu_1)^2}{2\\sigma_1^2} \\right\\} +\n", "\\frac{\\pi_2}{\\sigma_2\\sqrt{2\\pi}} {\\rm exp} \\left\\{ -\\frac{(x-\\mu_2)^2}{2\\sigma_2^2} \\right\\}$$\n", "\n", "where $\\theta = [\\mu_1, \\sigma_1, \\mu_2, \\sigma_2, \\pi_1]$. \n", "Note that $\\pi_2$ is not included in $\\theta$ since $\\pi_2 = 1-\\pi_1$.\n", "\n", "\n", "\n", "In python we can define $f(x|\\theta)$ using `normpdf()` implemented by *Numpy*: " ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "def pdf_model(x, theta):\n", " mu1, sig1, mu2, sig2, pi_1 = theta\n", " return pi_1*norm.pdf(x, mu1, sig1) + (1-pi_1)*norm.pdf(x, mu2, sig2)" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "##Maximum Likelihood: direct maximization\n", ">We first see how to estimate parameters for the mixture using a direct maxmization of the log likelihood.\n", "\n", "Given a sample $X = \\{x_i\\}$ of size $N$ extracted from the mixture distribution, the likelihood function is\n", "\n", "$$\\mathcal{L(\\theta,X)} = \\prod_i p(x_i|\\theta)$$\n", "\n", "and the log-likelihood function is:\n", "\n", "$$\\ln \\mathcal{L(\\theta,X)} = \\sum_i \\ln p(x_i|\\theta)$$\n", "\n", "Now, since $p(\\cdot)$ is the sum of two terms, the term $\\log p(x_i|\\theta)$ can't be simplified (it's the log of a sum). \n", "So for each $x_i$ we must compute the log of the sum of two exponetial. \n", "It's clear that not only the computation will be slow but also the numerical errors will be amplified.\n", "Moreover, often the likelihood function has local maxima other than the global one\n", "(in other terms the function is not convex).\n", "\n", "In python the log-likelihood function can be defined as:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "def log_likelihood_two_1d_gauss(theta, sample):\n", " return -np.log(pdf_model(sample, theta)).sum()" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "We now try to minimize using several options in the numpy.scipy.optimize function." ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6499: MatplotlibDeprecationWarning: \n", "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n", " alternative=\"'density'\", removal=\"3.1\")\n" ] }, { "data": { "image/png": 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SGmUASFKjPAeg49I4x2glDRgAkjRBx9MJZA8BSVKjDABJapQBIEmN8hyApsKTuNL0uQcgSY0yACSpUb0CIMnmJA8k2Zvk6gX6vz/JR7r+LyXZONT3jq79gSSvn1zpkqRxjAyAJGuAG4A3AGcDlyU5e96wK4BHq+qfAr8J/Hq37dkMniH8z4DNwG917ydJmrI+ewDnA3ural9VPQncCmyZN2YL8MFu+aPAT2bwcOAtwK1V9URVfR3Y272fJGnK+gTA6cDDQ+v7u7YFx1TVEeAx4AU9t5UkTcGquQw0yTZgW7f67SQPLDJ0HfA3K1PVinJex5cTdV5w4s5t1c8rv7ykzZ6e15nHumGfADgArB9aP6NrW2jM/iTPAZ4HfKvntgBU1XZg+6hiksxV1WyPuo8rzuv4cqLOC07cuTmvZ+tzCGgPsCnJWUlOZnBSd+e8MTuBy7vlnwY+XVXVtW/trhI6C9gE/PlSCpUkTdbIPYCqOpLkSuB2YA2wo6ruS3IdMFdVO4HfAX43yV7gMIOQoBv3+8D9wBHg7VX11DLNRZJ0DHqdA6iqXcCueW3XDC3/A/CvFtn214BfG6PG+UYeJjpOOa/jy4k6Lzhx5+a85sngSI0kqTXeCkKSGrXqAyDJqUnuSPJQ9+/aBcack+SLSe5Lck+Sn51GrX2Mc1uN1azHvH4lyf3d7+dTSY75krVpGDWvoXE/laSSHBdXmfSZV5Kf6X5n9yX58ErXuBQ9/g43JPlMki93f4uXTKPOY5VkR5KDSb6ySH+SvLeb9z1Jzuv1xlW1ql/Au4Gru+WrgV9fYMxLgE3d8j8BHgGeP+3aF6hzDfA14MXAycBfAmfPG/NvgRu75a3AR6Zd94Tm9RrgB7rlt50o8+rGnQLcCewGZqdd94R+X5uALwNru/UfmXbdE5rXduBt3fLZwDemXXfPuf0EcB7wlUX6LwE+DgR4FfClPu+76vcAeOZtJj4IvGn+gKp6sKoe6pa/CRwEZlaswv7Gua3GajZyXlX1map6vFvdzeA7Iatdn98XwPUM7n/1DytZ3Bj6zOvfADdU1aMAVXVwhWtcij7zKuCHu+XnAd9cwfqWrKruZHCF5WK2AB+qgd3A85OcNup9j4cAeGFVPdIt/1/ghUcbnOR8Bun/teUubAnGua3Ganast/y4gsH/Vla7kfPqdrXXV9WfrmRhY+rz+3oJ8JIkn0+yO8nmFatu6frM61eBNyfZz+DKxqtWprRlt6Tb7qyKW0Ek+STwogW63jm8UlWVZNHLlrrE+13g8qr63mSr1CQkeTMwC1w47VrGleT7gN8A3jrlUpbDcxgcBrqIwd7anUleXlV/O9WqxncZcHNV/fckP87g+0sva/XzYlUEQFW9drG+JH+d5LSqeqT7gF9wVzTJDwN/Cryz2wVajca5rcZq1uuWH0leyyDUL6yqJ1aotnGMmtcpwMuAz3ZH6V4E7ExyaVXNrViVx67P72s/g+PI3wW+nuRBBoGwZ2VKXJI+87qCwa3pqaovJnkug3vpHA+HuI6m9213hh0Ph4CGbzNxOfAn8wd0t6i4jcExsI+uYG3HapzbaqxmI+eV5FzgA8Clx8nxZBgxr6p6rKrWVdXGqtrI4NzGav/wh35/h3/M4H//JFnH4JDQvpUscgn6zOuvgJ8ESPJS4LnAoRWtcnnsBN7SXQ30KuCxoUPni5v22e0eZ79fAHwKeAj4JHBq1z4L3NQtvxn4LnD30Oucade+yHwuAR5kcI7inV3bdQw+OGDwB/kHDJ6d8OfAi6dd84Tm9Ungr4d+PzunXfMk5jVv7Gc5Dq4C6vn7CoPDW/cD9wJbp13zhOZ1NvB5BlcI3Q1cPO2ae87rFgZXN36Xwd7ZFcAvAb809Pu6oZv3vX3/Dv0msCQ16ng4BCRJWgYGgCQ1ygCQpEYZAJLUKANAkhplAEhSowwASWqUASBJjfr/WypnkcosD08AAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# generate data again\n", "N = 1000\n", "a = 0.3\n", "s1 = np.random.normal(0, 0.08, size=int(N*a))\n", "s2 = np.random.normal(0.6,0.12, size=int(N*(1-a)))\n", "d = np.concatenate([s1,s2])\n", "plt.hist(d, bins=20,normed=True,histtype='stepfilled',alpha=0.8);" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "# Initial guess\n", "theta0 = np.array([-0.2,0.2,0.8,0.2,0.5])" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ " fun: nan\n", " hess_inv: array([[ 0.97116987, -0.0475352 , 0.17865417, -0.16488305, -0.02788207],\n", " [-0.0475352 , 0.96867415, 0.14407314, -0.08872766, 0.00647282],\n", " [ 0.17865417, 0.14407314, 0.37427407, 0.43599009, 0.00503225],\n", " [-0.16488305, -0.08872766, 0.43599009, 0.76981043, 0.04466792],\n", " [-0.02788207, 0.00647282, 0.00503225, 0.04466792, 1.03149272]])\n", " jac: array([ nan, nan, nan, nan, nan])\n", " message: 'Desired error not necessarily achieved due to precision loss.'\n", " nfev: 798\n", " nit: 2\n", " njev: 114\n", " status: 2\n", " success: False\n", " x: array([ 267.92654208, -34.94438498, -134.27660849, -323.86197569,\n", " -272.13967672])" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Minimization 1\n", "res = minimize(log_likelihood_two_1d_gauss, x0=theta0, args=(d,), method='BFGS')\n", "#res # NOT CONVERGED\n", "res" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/chandola/anaconda/envs/previous/lib/python2.7/site-packages/ipykernel/__main__.py:2: RuntimeWarning: invalid value encountered in log\n", " from ipykernel import kernelapp as app\n", "/Users/chandola/anaconda/envs/previous/lib/python2.7/site-packages/scipy/optimize/optimize.py:2210: RuntimeWarning: overflow encountered in double_scalars\n", " elif (w - wlim)*(wlim - xc) >= 0.0:\n", "/Users/chandola/anaconda/envs/previous/lib/python2.7/site-packages/scipy/optimize/optimize.py:2189: RuntimeWarning: overflow encountered in double_scalars\n", " w = xb - ((xb - xc) * tmp2 - (xb - xa) * tmp1) / denom\n", "/Users/chandola/anaconda/envs/previous/lib/python2.7/site-packages/scipy/optimize/optimize.py:2183: RuntimeWarning: overflow encountered in double_scalars\n", " tmp2 = (xb - xc) * (fb - fa)\n", "/Users/chandola/anaconda/envs/previous/lib/python2.7/site-packages/scipy/optimize/optimize.py:2189: RuntimeWarning: invalid value encountered in double_scalars\n", " w = xb - ((xb - xc) * tmp2 - (xb - xa) * tmp1) / denom\n", "/Users/chandola/anaconda/envs/previous/lib/python2.7/site-packages/scipy/optimize/optimize.py:2182: RuntimeWarning: overflow encountered in double_scalars\n", " tmp1 = (xb - xa) * (fb - fc)\n", "/Users/chandola/anaconda/envs/previous/lib/python2.7/site-packages/scipy/optimize/optimize.py:2184: RuntimeWarning: invalid value encountered in double_scalars\n", " val = tmp2 - tmp1\n", "/Users/chandola/anaconda/envs/previous/lib/python2.7/site-packages/scipy/optimize/optimize.py:2190: RuntimeWarning: overflow encountered in double_scalars\n", " wlim = xb + grow_limit * (xc - xb)\n", "/Users/chandola/anaconda/envs/previous/lib/python2.7/site-packages/scipy/optimize/optimize.py:2226: RuntimeWarning: overflow encountered in double_scalars\n", " w = xc + _gold * (xc - xb)\n", "/Users/chandola/anaconda/envs/previous/lib/python2.7/site-packages/scipy/optimize/optimize.py:2245: RuntimeWarning: invalid value encountered in multiply\n", " return func(p + alpha*xi)\n", "/Users/chandola/anaconda/envs/previous/lib/python2.7/site-packages/scipy/stats/_distn_infrastructure.py:876: RuntimeWarning: invalid value encountered in greater_equal\n", " return (self.a <= x) & (x <= self.b)\n", "/Users/chandola/anaconda/envs/previous/lib/python2.7/site-packages/scipy/stats/_distn_infrastructure.py:876: RuntimeWarning: invalid value encountered in less_equal\n", " return (self.a <= x) & (x <= self.b)\n", "/Users/chandola/anaconda/envs/previous/lib/python2.7/site-packages/scipy/optimize/optimize.py:1837: RuntimeWarning: invalid value encountered in double_scalars\n", " if numpy.abs(x - xmid) < (tol2 - 0.5 * (b - a)):\n", "/Users/chandola/anaconda/envs/previous/lib/python2.7/site-packages/scipy/optimize/optimize.py:1881: RuntimeWarning: invalid value encountered in double_scalars\n", " u = x + rat\n" ] }, { "data": { "text/plain": [ " direc: array([[ 1., 0., 0., 0., 0.],\n", " [ 0., 1., 0., 0., 0.],\n", " [ 0., 0., 1., 0., 0.],\n", " [ 0., 0., 0., 1., 0.],\n", " [ 0., 0., 0., 0., 1.]])\n", " fun: nan\n", " message: 'Maximum number of function evaluations has been exceeded.'\n", " nfev: 20021\n", " nit: 303\n", " status: 1\n", " success: False\n", " x: array([ nan, nan, nan, nan, nan])" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Minimization 2\n", "res = minimize(log_likelihood_two_1d_gauss, x0=theta0, args=(d,), method='powell',\n", " options=dict(maxiter=10e3, maxfev=2e4))\n", "res # NOT CONVERGED" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "text/plain": [ " final_simplex: (array([[-0.00097222, 0.07819188, 0.60587216, 0.12474692, 0.29939166],\n", " [-0.00101552, 0.07822155, 0.60586571, 0.12476202, 0.2994433 ],\n", " [-0.0009647 , 0.07823022, 0.60587264, 0.12477544, 0.29938094],\n", " [-0.00098153, 0.07822998, 0.60587564, 0.12473607, 0.29948377],\n", " [-0.00096584, 0.07820587, 0.60583354, 0.12474542, 0.29944311],\n", " [-0.00101589, 0.0782172 , 0.60585488, 0.12474532, 0.29932456]]), array([-196.59947302, -196.59946993, -196.59946514, -196.59946409,\n", " -196.59945434, -196.59945 ]))\n", " fun: -196.59947301735491\n", " message: 'Optimization terminated successfully.'\n", " nfev: 547\n", " nit: 342\n", " status: 0\n", " success: True\n", " x: array([-0.00097222, 0.07819188, 0.60587216, 0.12474692, 0.29939166])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Minimization 3\n", "res = minimize(log_likelihood_two_1d_gauss, x0=theta0, args=(d,), method='Nelder-Mead',\n", " options=dict(maxiter=10e3, maxfev=2e4))\n", "res" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/chandola/anaconda/envs/previous/lib/python2.7/site-packages/ipykernel/__main__.py:2: RuntimeWarning: divide by zero encountered in log\n", " from ipykernel import kernelapp as app\n", "/Users/chandola/anaconda/envs/previous/lib/python2.7/site-packages/scipy/optimize/optimize.py:628: RuntimeWarning: invalid value encountered in double_scalars\n", " grad[k] = (f(*((xk + d,) + args)) - f0) / d[k]\n" ] }, { "data": { "text/plain": [ " fun: -108.44513835405974\n", " hess_inv: <5x5 LbfgsInvHessProduct with dtype=float64>\n", " jac: array([ 178.56037005, 1301.10202576, -836.06477403, 984.66398271,\n", " 734.90177499])\n", " message: 'CONVERGENCE: REL_REDUCTION_OF_F_<=_FACTR*EPSMCH'\n", " nfev: 300\n", " nit: 21\n", " status: 0\n", " success: True\n", " x: array([ 0.609071 , 0.15263442, -0.03097671, 0.09893651, 0.81543655])" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Minimization 4\n", "res = minimize(log_likelihood_two_1d_gauss, x0=theta0, args=(d,), method='L-BFGS-B',\n", " bounds=[(-0.5,2),(0.01,0.5),(-0.5,2),(0.01,0.5),(0.01,0.99)])\n", "res" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "### Why is the mixture model log likelihood difficult to optimize\n", "To answer this let us take the above data set with two modes. Let us assume that we know the true value for $\\pi$, $\\sigma_1$ and $\\sigma_2$. Now, we will compute the negative log likelihood (the quantity that we want to *minimize*) for various values of $\\mu_1$ and $\\mu_2$. Remember that the true parameter values are:\n", "0.3, 0.0, 0.08, 0.6, 0.12 for $\\pi,\\mu_1,\\sigma_1,\\mu_2,\\sigma_2$, respectively." ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6499: MatplotlibDeprecationWarning: \n", "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n", " alternative=\"'density'\", removal=\"3.1\")\n" ] }, { "data": { "image/png": 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lwD1VdSLJHcBkVU0A+4GDSaaA5+mFBgBJngReD6xIcjNwU1U9DnwA+BTwGuDB9pEkLZBO9xCq6ghwZKBsb9/2OeCWC5y74QLlk8B1XTsqSbq0/KayJAlYBE8ZLXY+fSJpsXCGIEkCDARJUmMgSJIAA0GS1BgIkiTAQJAkNQaCJAkwECRJjYEgSQIMBElSYyBIkgADQZLUGAiSJMBAkCQ1BoIkCegYCEm2JzmZZCrJniHHVya5tx0/lmRD37EPt/KTSd7WV/5kkkeTPJJkcj4GI0mavRlfkJNkGXA3cCNwGjieZKK9F/m824EXqmpTkp3AncCtSbbQe7/ytcBfA76Q5G9U1ffbeT9VVc/O43gkSbPUZYawFZiqqlNV9TJwCBgfqDMOHGjbh4FtSdLKD1XV96rqG8BUa0+SdJnpEghrgKf69k+3sqF1qmoaeBFYNcO5BXwuycNJdl3oD0+yK8lkksmzZ8926K4kaTYW8p3KN1TVmSRvBD6f5GtV9cXBSlW1D9gHMDY2VqPupCSdN5d3pD/woRvmsSeXRpcZwhlgXd/+2lY2tE6S5cBVwHM/7NyqOv/zGeB+vJQkSQuqSyAcBzYn2ZhkBb2bxBMDdSaA29r2DuChqqpWvrM9hbQR2Az8UZLXJnkdQJLXAjcBj819OJKk2ZrxklFVTSfZDRwFlgH3VNWJJHcAk1U1AewHDiaZAp6nFxq0evcBjwPTwAer6vtJ3gTc37vvzHLgM1X1u5dgfJKkjjrdQ6iqI8CRgbK9fdvngFsucO4ngE8MlJ0CfvxiOytJunT8prIkCTAQJEmNgSBJAhb2ewiLxlyePZakxcIZgiQJMBAkSY2BIEkCDARJUmMgSJIAA0GS1PjYqSSNwGJYOtsZgiQJMBAkSY2BIEkCrqB7CC4/IUk/nDMESRLQMRCSbE9yMslUkj1Djq9Mcm87fizJhr5jH27lJ5O8rWubkqTRmjEQkiwD7gbeDmwB3pNky0C124EXqmoTcBdwZzt3C73XaV4LbAf+U5JlHduUJI1QlxnCVmCqqk5V1cvAIWB8oM44cKBtHwa2pffC5HHgUFV9r6q+AUy19rq0KUkaoS6BsAZ4qm//dCsbWqeqpoEXgVU/5NwubUqSRuiyf8ooyS5gV9t9KcnJhezPHF0NPLvQnRgxx3zluBLHPZIx55/MuYk3d6nUJRDOAOv69te2smF1TidZDlwFPDfDuTO1CUBV7QP2dejnZS/JZFWNLXQ/RskxXzmuxHEvtTF3uWR0HNicZGOSFfRuEk8M1JkAbmvbO4CHqqpa+c72FNJGYDPwRx3blCSN0IwzhKqaTrIbOAosA+6pqhNJ7gAmq2oC2A8cTDIFPE/vFzyt3n3A48A08MGq+j7AsDbnf3iSpK7S+4+8RiHJrnYJ7IrhmK8cV+K4l9qYDQRJEuDSFZKkxkAYgST/PsnXkvxJkvuTvKHv2NClPRa7JLckOZHklSRjA8eW5JjhylmSJck9SZ5J8lhf2V9J8vkk/7P9/MsL2cf5lGRdkt9P8nj7d/1PW/mSGrOBMBqfB66rqr8F/A/gw3DhpT0WrJfz6zHgZ4Av9hcu5TFfYUuyfIre31+/PcDvVdVm4Pfa/lIxDfzzqtoCvBX4YPu7XVJjNhBGoKo+177BDfBlet+7gAsv7bHoVdUTVTXsS4RLdsxcQUuyVNUX6T1R2K9/CZsDwM0j7dQlVFVPV9VX2vZ3gCfora6wpMZsIIzePwYebNtX4hIeS3nMS3lsXbypqp5u2/8LeNNCduZSaas5/x3gGEtszJf90hWLRZIvAH91yKGPVNVnW52P0Jt6/uYo+3apdBmzrkxVVUmW3COMSX4E+C3gn1XVt3trePYshTEbCPOkqv7eDzue5B8B7wC21V8869tlWZDL1kxjvoBFPeYZLOWxdfGnSa6pqqeTXAM8s9Admk9JXkUvDH6zqn67FS+pMXvJaASSbAf+BfCuqvpu36ELLe2xlC3lMV/pS7L0L2FzG7BkZoltOf/9wBNV9Ut9h5bUmP1i2gi0JT1W0lvwD+DLVfX+duwj9O4rTNObhj44vJXFJcm7gU8Cq4H/DTxSVW9rx5bkmAGS/H3gP/AXS7J8YoG7dEkk+S/A36W32uefAv8a+K/AfcB64JvAP6iqwRvPi1KSG4D/BjwKvNKK/xW9+whLZswGgiQJ8JKRJKkxECRJgIEgSWoMBEkSYCBIkhoDQZIEGAiSpMZAkCQB8H8BOo39iLj2ecQAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# generate data again\n", "N = 1000\n", "pi = 0.5\n", "mu1 = -10\n", "sigma1 = 5\n", "mu2 = 10\n", "sigma2 = 5\n", "samples = []\n", "for i in range(N):\n", " s = bernoulli.rvs(pi,size=1)\n", " if s == 1:\n", " v = norm(mu1, sigma1).rvs(1)\n", " else:\n", " v = norm(mu2, sigma2).rvs(1)\n", " samples.append(v[0])\n", "plt.hist(samples, bins=20,normed=True,histtype='stepfilled',alpha=0.8); " ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "mm1, mm2 = np.meshgrid(np.arange(-25,25, 0.1),\n", " np.arange(-25,25, 0.1))\n", "m1 = np.ravel(mm1)\n", "m2 = np.ravel(mm2)\n", "\n", "ll = []\n", "for i in range(len(m1)):\n", " theta = (m1[i], sigma1, m2[i], sigma2, pi)\n", " ll.append(-log_likelihood_two_1d_gauss(theta,samples))\n", "ll = np.array(ll)" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "data": { "image/png": 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lk+SMODkjhsk7vWQUMYBbacOttONRpuNVZ6JJdU65uATUaTPYOvwEWSONPOKqXkk8I8Oox+NEoiaqGKZB1syiCIX1vPwlVEm25CZuBUWUimqQL8b6Ib9eLEjsFZLZyjfIW49Tk/NSIWm16X1EbFlpeoe8M/xQdGzvLIDWlnyP8IGOfktiSxAELr5yCf/zH0/w/DObOfv8+Zbu8154/S6WnT+fZefPJ5fN8cM/fN7SumNCbBmmwd37H+Ktoa1c3HRuxX20DNNgVc9K3hh8iVm+xZzX+CEkYeK81L3Jnbzc92vi2X5mBz7I3OClEyr+iYhpmqRyPcTS24lmdhDL7CKe2UPWOHLEWRED6HITAW0RmlSHJtehSmEUMYgiBZEFj62so2kaZIyhkexYD8nsIRLZDhLZfXTFHscwHwJAlWoIaAsJaIsJ6ouRxepo8J5ohLXpvG0+Rn96N/W6/XJGqXGPiK1YbhzE1sgw6mQuhSKWTmxpokyqRGXEYvu/ii0jKmJhmS1VkkgXkNmyI+y00Z4ti0alhzNbKWulyoBXp6vXWoa1qTGIIovs2dvLyUunWlqzYPEk5s5v5cE/rWfuglYaLIg0K0hjlEiPZsI/QQ3T4L6Ox3h9cBPnN67gjLqTKxpP1sjw+KE/siO6iSWh5Zwe/iDiBCm7GWaOLUOPsGXoEdxSDSsavk5Yn17psI5JTDNHLLObSHoLkdQWIumtZIwhAERBwa1MptZ1Om6lHbc8CZfSVnKRIwgiqhRClULAtD+LL57ZRyT9NpH0ZgaTr9ATfw5BkPCr86h1LaPGdapTdrRBrZZ/MPSldlaF2JIEGZfkGZ8y4lHDqH2U7uc4fxqxeFNTKF1mq9ATjYVYOBS6TpMly/1XAKrdzNaIUWnc4oDpUMDN1t3dlq6VJJFJk2rZtduaMzzks1sf+eRZfP+f/sQv/+spvvrNS/F4xi5vlpIJLbZM0+ThzqfY0P86Z9cv4+wKj+BJ55I8ePA2DiR2cVbdJZwQOrOi8dghmunh5d5f05faxWTvKZxQ82EUceKUPasd0zRJZPczlHqD4dSbDKc3kzPyaXNdbiCoL8arzsSrzMSltCFWOJMoCBIedQoedQqNXIhpGkQzOxhIrqc/8RK7Bv+bPUO3UuM6jQb3+XjVWU6pcQxUyYNfacr3bVWJ969H9o/LyB79qMxWKVFFmXSuhGXEEjjIF9r3pUoS6YJOI0pEUvZeV7s+W7rNni3PqNhKWstshQJu4ok0yVTm8KzE92PGtAaeePotkskMukUrhlCNh5u/dC4//eGj/PSHj/K5r1yAPzB+z7gJLbae6FrFmt4NLAufzHkNZ1U0lng2wv0dv6YvfYgLGq9ntr+yPWN22Btdx6v9v0dA4JS6m6vK5XoikzPiDKY2Mph8laHUxsN9Vi65ibDrDPzqfHzaHFSppsKRjo0giPjUmfjUmbT5PkIss4Oe+HP0Jp6nN/48XmUqTd7LqXGd5hygeB9q9ekciL2CaRpV8Tp5ZT+xcRjZMyq2Sn0icXRcTyka7zWpuAZ5pcCh0KMUmtlSCmisV0cyW1Zft9ERPUmbrvDRhLXvd20wn+3sG4zR0jB2iW/2rCYee3ITW7cfYtEC6/5ZM2c3c/OXzuVXP32aH373AW767NlMndFgeX0xTFixtapnLc91r2FpzWIubvpART9VD2cGuL/jViKZIS5tvol2T+VLBFbIGEle6/89e6PrqNWncUr4U3jk2kqHNaFJZbsZSK5nILmB4fRmTDOHLLoP9zwFtEVo8sSbgXk0giDgVWfgVWcwyX8jvYkXOBR9kO0Dt+CK/JEW33XUuk6vCjFRbYS1aeyOvMBwppOAWnkLGLfkozfVWfb7HF1GLCWqqGCSn2moFpkNVgSJaBHxCYKAXGCTO4xk1mz2XsFoz5bdMqKMiUkmZxy2dXjf2CQJURBIWG6QVxEEiFoYwQMQDuXbEXoHopbE1ozpDei6wusb99kSWwALFk/mK39/Cb/66dPc8v0HOfPsOXzwshPLnuWakGJrXd9rPNb5DAuDc7my5YMVFVoD6R7uPfBLMkaaK1tvptnVXrFY7NCf2su63luJZXuZG7yEOYGLJtzYoGohkemgP7mW/sQ6YpldALjkFpo8lxDUl+BTZyEco6+tJLpo8JxPvftcBpIvcyByFzsGfkxn9H4mBT5OQFtQ6RCritG+rd7UzqoQWx7ZTzwbwTCNsvaWamUqI2ojzfZpI4MqFim2ijQ1hVE390LLiCLDWfv9Z4pkX+Ad7QhvRWwJgoCuKpZd4UVRwK2rljNb9bX5zJbVJnlZlli0oI3XNu7lI9edannu4SjtU+v55veuZuXd63nh2S2seX4rp545k2XLZ9M6qbYsmmLCia2Ng5u5v+MxZvmmcW3bpRVtPu9JHeT+A7cCAle3fYY6rfqtEUzTZHvkad4cuBdN8rO84avU6TMrHdaEI5ntpC+xhr7Ei8Qz+wDwqTOZ5L+RkOtkXHL1/yyUEkEQqXGdSkg/mb7Ei+wf/j1ber9NretUJgc+gSo5GVMAr1yPJnnpT+1mmq+yrQ+Qt38wMEnmYodPJ5YDl6QDZejZkkZ6iXLZop9m+TmLxYkttQixVajYs2vjAEfEViqbs3xcwaUqJCyKLQCfWyNq0ajU59Fx6YplsQVw2inTWLd+F6+8todTT5429oJ34XKpXPexZZx9/nwef+h11r6wjRee2UJjc5CFJ0xmzvxW2qfV23Kdfz8mlNjaGtnJXftX0u5p5SOTr0KqYLagM7GXBzp+gyqqXNn6aUJq9ZeG0rkY6/t+y8H4GzS7F7K09uNVM6dtIpDJDdKbeJG+xPNE0zsB8KmzmBz4BLWuUx1BQV50hd1nUuM6hYPRBzgYuZfB5OtMCnyMevd5x30TvSAI1GhT6UvtqnQowBFj02h2uKxiSxvxFUsY1kayWN83n9lKleBEoipJRbvRFyu2Cikj5nvN7MU96puVstjwDuBSZVtiy+/WGbI4gkcQBJrqA3R2D1nef9bMJhob/Dz59FucvHQqoljYe0t9Y4CP3rycqz58Kq+s28lr63fz1KNv8MTDG5EkkdbJtUxqD9PSWktTS5D6xiA+v277vWzCiK29sQPcufdPNOh1fLz9Q6gl9Gqxy4H4Lh48+FvckpcrWz+NX6n+Qcx9qd2s7fkFydwQi2uuZbrvnOP+wWcFw0wzkFhPT+I5hpIbMTHwKFOY5P8ote5laJIztugvIQoqrb4PEXadwe7B/2H34C8YSK5navALI1YTxy+12lQ6429UxVDqIyN7hoHylTVFQUQV1bKcRoTSiC2lFJmtAvqn3rnWvtgrpIyoHxZb1te5VMWylQOA36NzsNe6eGppCPLqW/stN+2LosCFFyzkN7evZsOruy17br0XHo/GWefM5axz5pKIp9mxrZMdWw+xZ1cPL6/ZQSq55fC1mq5QG/ZRE7b+73dCiK2uZA+37bmbgOzjk+3Xo4+kpCvBvvh2Huy4Db8S4srWm8s+U6xYTNNkR+QZNg7cg1uq4ezGv6FGa690WFWNaZrEMrvoiT9DX2I1WSOGJtXS7LucWtdZuBV7DZnHM7rcxOzab9EVe4x9w3fwZvfXmRb6K4J6dcwHrASjfVv9qd00uSvb0+YdFVvjYGyqS1oZxNZIZitXgsyWKBVtkFpM35ddo9FRVEkiZ5jkDANJtNZWMzp+x05my62pRJLWv38Br87mPYcsXz+pKcQL63fQPxSnNmjNv+/kpVN56pnN3H3veubNaSmZd5bLrbJg8WQWjMw+NE2T/t4ohzoH6T40RE/3MP29EQb6Y2PsdISqF1sD6SF+vfuPyILEJ6d+GK9SORPFPbGtPHzwdoJqmCtbbi5r2r0UZIwEG/pu50DsVZrdCzmp9iZUyTGhfC+yRoy+xAt0x54iltmDKCjUuE6lzn02fnW+c7quQARBoNF7IX5tPjsGfsTWvn+hxfchWnzXHJevaUidjCCI9KUrL7YOu8iPg7GpS9JLbv2gjWS2inF+H2W0Z6uYwwLFGKNqklTQqB/tcN9aDpdFsTXqm2WnLOjWFLqHopavD/ncxJMZ0pksqjK21JjSlm/D2L2/17LYEkWBj91wOt//94e57c4X+dynzy64nPh+CIJAbZ2P2jof8xa+88P2N79rbY+qFluxbJxf7f4DaSPDZ6feSI1auSHOu6NbeLjzDmrVRq5o/RSuKhctQ+mDrOn5ObFsDwtCVzHLf75TNnwPoumddMUeoy/xIoaZxqNMYUrwZmpdZzoO6SXErbQxL/wDdg/9DwcidxHP7mVa8MtIYuUy1ZVAEXUCSjP9VdC3NeoiPy7GpqJW8p4tVTpyGrHovQ47wBuoUmFiq9gyYqqAMuKRZvcsLsVae00hPVseTSVmcfwOQMibt1LojyRorBk7MTGpKYSiSGzb08PSBZMt32dSWy3XXLmUu/60nrv+9DLXXXNyVT7rqlZspXNpfrvnLobSw3xq6odpdNVXLJZd0c080nknYa2JK1o+hS65KxaLFfbF1rOh73ZkQXdOG74HhpmmL7GGrthjRNM7kASNsOtM6j3n4VWdEUXlQhI1pgW/jEeZyr6h29mS+xazav4eRarcB6lKUKNNYX9sQ1WYm3pk3zi5yOsMlziDVsoG+cMZIiN7+JSjXRRRIlmAfcPoWsM0MUwT0YZYOCycbIg8l2Jv/A7kxVY0mbbcU1Xjzz8nB4bjlsSWLEtMn1zHlh32fd/OWTGHgYEYTz6zmUQizY0fPt22HUS5qUqxlTNz/G7ffXTEO7lx8tW0eyrXI/NOoXUzulS9I2wMM8ebA/exbfhJarWpnFb3WVzy8fUQG4t0rp+u2ON0x54kYwzjkptpD3ySsHu5k8UaJwRBoMl7CbrUwPaBW3ir9/8wu/af0OXxcXKuBmq0KeyKvEAk04VfbapoLB5pfFzkXZJOT6q3pHtqUil7tkab7bMFT2/URInhArN3qmQ/QwX58uPoOqvoI/snMtZfN4+uYhgGyUwWlzp2fOERV/iewShzsPZve/6MJu5+9DX6B2PUWCwlQv495eorl6LrCg8+spEDHQN87IbTmTypeg4wVV3DhGma3HvgUbZFdnJFyweZG6hcVmZ3dMuEEVqpXJQXun/CtuEnmeZbwfLGrztC6yhi6d3sGPgJr3d9noORe/GqM5lT+48srP8PGr0XOUKrAoRcJzE3/M9kjRibe/+BeGZ/pUMaN2rUKQD0pStfShzP+YiJMpmaluY04ohoKWLWYjEjf0bFlt0Ge62Qk4UFZLZ8rnzzecSiUWnY70YQoHvQep/X4jmtAGzYtM/ymlEEQeCSixbzpc99gEgkyQ/+/RF+c/sLHOqyfiKynFRdZuuJrlW8OvAGH2g4k5NrKzdfcG9sKw933kFYaxwpHVav0BpKd/Bi989I5AZZGv4YU7zLKh1SVWCaJkOp1zkYfYDh1CYkQafecwGNnovQ5cZKh+cAeNWZzA1/l7f7vs2W3m8xJ/zt4+K0p19pRBF1+lN7Kv7vdbxc5POnEZMlmWM4ilrCBvmjy4iFkj+NWNj6w5kt26N37ItEVbY3fgfApx8RW/WBsXN/sixRG/DQ1W89a9pUH6CtKcRLr+3m/DPmWF53NAvmt/Ltf7yChx/dyHPPv83al3cxZ3YTp548jUUL23CNDMkeb6pKbMWycZ7rXsNJNYv5QP0ZFYtjf3wHDx28nRq1fiSjVb09Wh3x13i59zcooosVjd+gVptS6ZAqjmFm6UuspjP6APHMflSphkn+G6n3nOdksKoQt9LGnPB32NL7Lbb0/jNzw9/BpVR+lE05EQSRkNpOf2pPpUM57CKfyEUP+26VA13SMTFJGxk0qTQPvLx/l0yyhGXEYoZR55vcC8xsjWTWbBuUjopEG5ktQRBwqypxGw3vfre9zBZAU62fQ332sqZnnTSd361cz+4DfUxpLcwo2uVSueaqkzj/3Pk8v3ora9bu4De3r0aSBKZPbWDWrEamT2tgclstuj4+np1VJbYGM8PM8k3nigrOOzyY2M2DHb8loNRyZeunq1ZomabJ28OPsmngAWq0dk6v+/xxXzY0zDTdsafpjD5AKteLW2ljWuhL1LrOQCxySK1DeXHJzcyp/WdU5b0fAAAgAElEQVQ29/4jW/q+zbzwv0z4gd1jUaO1s3X4CXJGGkmszKdtOOIiH8tGyiu2Dg+jTpZMbEG+b6sUpxFLkdlSRblgn63RcmAhQ6XBXs8W5EuJdnq2/O78qeGhuPWetOZwgGf2dmMYpmVLhtNPnMq9T7zOw89u4ksfXW75Xn8Jv9/FJRct5qIPLmL3nh5ef2Mfm7ccZOVDrwMgCFBf56elOURTY4D6ej91YR/hWi8+n6ukNhJV9QSqVUN8ZNIVFZt32JXczwMdv8GrBLmq9dNVa++QMzO80ncHe6PrmOQ5maXhjyEJlXPUrzQ5I0FX7HE6ow+SMYbwqbNoD36aoHZiVR4BdvjLuJQWZof/kS293+Ltvu8xr+5fkMVjd5xUjdaOaRoMZg4cNjqtBOPlIu86ahh1oIRvV6qolLRBvphh1FqB9g35tfZPFcIRz6ykXbGlKsRt+GwFChBbbfVBMtkc3QMRGmutCXmXrnDeGXNY+dQbbN/TzYz24p0IRFFg2tR6pk2t5+orIBZLsWt3D3v29bJ/fz8HOvp5feM+DNM8vEaSBEJBD36/i0DAhc+r4/PqeL0aHo+G263hdln/0FBVYkuXNNQSfuKxQ0+qk/s7foUuubmq5dNVa1iazEVY0/0z+lK7mB+6nNn+C49bQZEzEhyKPcKh6ENkjAgBbSEtvqvxa/MqHZpDgXiUKcys+Vve7vsu2/r+jdnhf0QUKpf1KSchtR2A/tSeioqtIy7y5T2RODr5oxxN8qW0fiimJKlKMqZpkjUMZIsGo0fub/9UIRwZvZOwuc6t2vPN0hUZTZEZjCUsr5ncmB/NtedQv2WxBfDBM+fwwvod3HbvOr71VxehyKW1cfB4NBbMb2XB/NbDf5fJ5Ojri9LTG6GvP0r/QIzBwRhDQwkOHRpie6SLWDzFUXrMFlUltirFQLqH+w/ciiyoXNX6GbxKdY7giWQO8UL3f5LIDnFq3Wdo8yypdEgVIS+yHqUzupKsESWon0ir7xq8quMndizg1+YxLfhltg/cwq7BnzMt+OVj8gOFSwqiSwEG0nsqGscRF/nynkjURzJbiZz1h7W1fRWSOeui4b0ohRu9etSJRtlmafjwvEKbmbHD62w0uwN4NIW+aNzy9YIgUON1MxC1/v1rrQuiyCI7Ovo4dV675XW6pnDTVadwy2+e5c4H1nPTVaeU/T1AUSQaGwM0Nr73898wTGKxFLF4ing8TTye4hc/tbb/cS+2IplB7jtwKyYmV7beTECpqXRIf5Ge5DbW9PwcAZEVjV8/LhvhDTNNV+wxDkbuJ2MMj4isax0T0mOQWvcyEtkODkTuwqO00+S9rNIhlRxBEKjRJtOf2lvROI64yJc3s+UeOdFd6vmImqiU9jRiEQ3yR/d9ebAntrQCTyPqsowgQMKmmapHVdmXGrS1JuRx0W9DoMmSyJSmWrbt77Z1H4AFs1q4+Oz5PPzsJoI+F1ect7DiH7pEUcDn0/H57E+9OK7FVjwb5b6OW0kZCa5u/Sw1auVc6t+PfbH1rO/9LR65ljPqv4xXObYbh9+NYWbpiT9DR+Qe0rl+AtpC2vzXO5msY5wW34eIZ/eyb+hO3MoUAlpl5wiWg5A6mYOJN8kYSZQKji3Ku8iX14/ocIN8rrQjezRJYThjXQC8F0ebmhYeS2GCKb+2sN4rQRDQZdmWjQPkrRwiNsqIALU+N1s67AmnOe0NrFy9iVgyjcem7cJV5y9iKJLgwWfeJBJL8pFLlyKXuKQ4XlSdqel4kc4leaDj10QyA1zW/Anq9eo8ar5t+CnW9dxKjdbOOY1/e1wJLdM06Eu8yBvdX2H34C/QpDrmhr/NnPA/OULrOEAQBKYFv4QuN7Oj/8ekc/2VDqnkhNTJYJoMpu2bOJaS8XCRHy0jJo3SZrZ0USVZwp6tYprtj+xhX7BpBZYRgRGxZTOzpakkMxmyOevDr2v9HvojcXI2BmYvmNqEacKmXfbH8AiCwE1XncqFy+fy3LrtfO9nj7Pv4MR8HzguxVbWyPBg5+30pju5uPmjtLirryRnmgYb++9hY//dtLhP4KyGr6BW6enIcjCU2sRbvX/P9v5bEAWVWbV/x9zw95zm9+MMSXQxo+brGGaSHQM/xjStv8lPBEJafuDuQLqypcS8i3x5xZYsysiCTKIMma1SWD9IgogkiEVlttQixNZo75XdzBaAW1FslxF9I1mmqI3sVkPAi2Ga9A5bzyTOaK3D59bY8HZhEyJEUeBDF57IF288i4HhON/+z0e59a41HOot/9SDUnLclREN0+DxQ3/kQHwnFzReT7tndqVD+jMMM8eGvtvYG13HdN8KFtdcV/FhteNFInOAfcN3MJB8BU2qZVroi4Rdy4+br9/hz3ErbbQHb2bnwE/piP6JVt+HKh1SydAlPy45xECqwpkt2U88OzwOLvJ6WU4jlqJBPr+XXNy4niJG/qiihEBhYsulKLYzW349X7aOJJME3dZK2A0jzvFdQxEagtZsWURR4KQ5k1j9xi4SqQwurTDfjyXzJzF7agMPPrOJZ9ZuZc1ru5g7rZFlS6ZxwtxW9AL3HS+OK7FlmibPdd/Pjugmzqq7hNn+yo0Dei+yRpqXev6HQ4lNzAtexpzARRVvChwPMrlhDkT+l+7Yk4iixiT/jTR6Lzpmj/072CPsWsFQciMdw3cT1E44pg5FhNRJVZDZyrvIJ3OxstreuEZG9pQSTVLIGLmSCEVNUooSW7o8Ohjbfs9WvveqsPu7FXueWXBk/M5w0rr4bQzlfzY6B4ZZONn6APUzF03lmVe28+Kbuzl3aeEtIB63xvWXLOGiFXN5Zu12Vm/YyS//90UkSWTmlHrmTGtk5pR62ltqUJXqkjfVFU2ZWdf/FG8OrWNpzQpOCJ1Z6XD+jLQR58Xun9Kb2smJtTcwzXdWpUMqO4aZpSv2OB2Ru8gZCeo959HquxZFqk77DYfKIAgC7cFPM5zezM6Bn7Cg/ofHjBAPqZM4mHijok3yh13kc5Eyiy1XycuI+sgw6mQug1vWitpLk+QSNcgXaGwqy4WVEVWFgWF7r2vAlf9ZG7RhUhryuHCpCh02R/BMa65lSnMNj67dwtknTkey6UH2bvxeF1ecu5DLzlnAjn09vLb5AJu2dnDv46PO8ALN9X5am0K01AdorA9QX+OlrsaHa5zG87yb40ZsbRpax7q+p5jrX8rptR+sdDh/RjIX4YWu/2A4c5BTwzfT5lla6ZDKzlByI3uGfk0i20FQW8SkwE3HxRBih8KQRQ/TQl9iS+93ODD8RyYFPlbpkEpCUJ0EpslQ+gBhvTIZuyMu8hHqitMr74suacSyxZ8cPJrR0T8pI4Ob4oLXJbmoBnldOiL8CsEly7Z7rwDcimq7jDgqtoaT1sWWIAi0hYPs77NnGSEIApefMZ8f3/U8q17byTlLZtha/16IosDM9npmttdz3UUnMhxNsnNfD7v297HvYD/bdnez7vU971jjdqmE/C5CATcBnwu/Vyfgc+F1a/g8Gp4RZ3iPS8XtUosWhqMcF2Jrd3QLz3bdR7tnFuc0XFV1Zbl4doDnu35MLNvH6fVfoMk1v9IhlZVUtpu9w7fRn1iHLjcyq+ZvCepLq+774lB9BLSFNHjOozP6EDWu0/CqpXnTriQhdRIAA+l9FRNb42Vs6pI0elOlPU02KnBKNbKnmMyWXuDInaPXF5LZ8qgqsbS9vjW/riEKAgM2MlsAk+uCrN6yx9a8Q4ATZ7Yya1Iddz37OktmtRLwumzd1wp+r84Jc9s4Ye6RD+3JVIauvgjdvRF6B6L0DcboG4wzFEnQ0TXEUCSBYby3LbyqSLh0FV2T0TUFTT3yu6Zal1DHvNg6lNjHI52/o05v4cKmG5CE6vLoiGX7WNX1I1K5KGc1/BV1+rFraWCYGTqjD9IRuQeANv+HafJeesyUgxzGhzb/jQwkX2HX4M+ZX/dvE37IuC4F0CQ/g+nCTmuVgtEyYrzMJxJ1SS99z5Z4JLNVLHk3+uKtHwrPbCkFii2FRCZLzjAsZ2JEUSDocjFgY/wOwNSGWp7cuJ1DgxGaa6yP4BEEgZsuOpl/uvVRfrHyJb5+/dklHfT8XuiawuTmGiY3/2XDctM0iSfSDI84w0fjKeKJNLFEmngiTSKZIZHKkEqN/J7OMjicIJ3O2nLtn9jvUmMwmO5l5cHf4pF9XNZ8E6pYxvx4AUQzPazq+hEZI8lZDV85pl3hh1NvsXvwlySyB6hxncJk/01o8vHjGeZQOmTRQ3vgU2zr/3cORR+m2Xd5pUMqCkEQCKltDFTQa0sWFXTJVXavLZekk8glMU2zZJls7XDprgQjeySZoXTh44SOiK3CsmMuRWY4Zf+0pkfNC854JoNPs/6cC3lcDMTtfb0zmmoB2NbZY0tsQX58z43nL+U3j7zMnU9s4KMXVL6iIQgCHne+fFgIP/qmteuO2fP0iVyMlQd/A5hc3vLJqhssHcl08VzX/yNrplje+NVjVmhljAg7B37K5t5vYZBmdu03mVnz/zlCy6EoQvrJhPQldETuJp3rq3Q4RRNQW4lkOsmZxY+dKRS35BuH+Yg6JmZJfLEO7ymWTmzpYnGZLVEQUCWp4AZ5XbbvlwXg0/JiK2JTqNV63PRFY7bWNIcCeHSNLQfsj+ABOGfJDD54ymyeXL+N2x5db8sgdSJzTIqtrJHhwY7biGQGubT5JkJqdT3YI5kuVnX9CMPMsqLh64d7No4lTNOkL/4ib3T9Nb2J52n2XsHCulsI6idWOjSHYwBBEJgc+CQmOfYN3VHpcIomqLZhmDkiGfsu26UiP7KnzJktcXQYdelKiUc3yBe/l1yU2IKRUmQBpUAAt6wQt9noDuBV869r1GbfVtjrpicaxzTfu2fp3YiiwPy2Bt7ce8jWuqP5yHkncvFpc3j6le384M6n6R2yJ/gmIkWLLUEQ2gRBeFYQhM2CILwlCMJfj/x9jSAITwqCsH3k91Dx4Y6NYRo82XUXncm9nN94HU2uyeNxW8scEVo5ljd8lYBanWOCiiGd62Nb/w/YPnALmlzH/Lp/Y1LgRqQqK+M6TGx0uYEm76X0JlYTSW+tdDhFEVTzDb2V7dvyE8uVP7MFpZ2P6BoRW6UqIxbTIA/5JvdEgYIt7wRv//5e1b4bPEC930syk7G9bvGUZvqjcfZ0D9haN4ogCFx/7ol89vLT2N3Zz9/9/CEeWL2JpE2vsIlEKTJbWeDrpmnOBU4FvigIwlzg74CnTdOcATw98t9lZ23fE2yLvMEZ4YuY4Vs4Hre0TCTTfZTQ+toxJ7RM06Q79gwbu7/CUOpNJgduYl74+3iU9kqH5nCM0uy9ElWqYe/Qbwv+lF0N+OR6JEFhMH2gYjF4ZB/xbKSsr6NrRGwljBJmtkYGSJdiPqI+YmpazGugFXiiEPIN8olsBsPm/f2jBqUpe69rvW/EEX44amvdkmktiILAS9uKM+M9Y+FUvv/Zi5nX3sg9z27ka//5APc8u/GYzHQV3SBvmmYn0Dny54ggCFuAFuByYMXIZbcBzwF/W+z93o+3htazvv9ZFgRO4cRQdRmCxrK9rOr6ETkzw4qGrxNQmysdUklJ5/rYNfhzBpOv4dfmMjX4eXTZusOwg0MhSKKLVt/17Br8Gf3JNdS6llU6pIIQBBG/2lxRseWW/WTNLCkjiS6V/lg+5K0fgJKO7NFKmNnSJQUTk5SRPWwpYRe3rBSc2fIo+Xsmshk8ivVT2qNN8Xbc4AEaR8bvHBqKML2+1vI6v0tnYXsTq7fs4fpli4s6VVgX9PLV65azfX8PD655i5UvbuKB1ZuY0RbmpNmTWDCtiZZwoOKN9MVS0tOIgiC0AycA64CGESEGcAhoKOW93s2B+E6e7b6PSe4ZLK+/vKq+MfHsAKsO3ULOTB+TpcO++IvsHvolhpmmPfAJGjwXOrMMHcaNOvcKDsUeYv/wHwjpp0xYK4ig2kZH/LWSntSzg0fKP3jj2eGyia1ylBElQUQRpaJ7reCd1g2Fii1dLny+omtEbMUy9sSWR1WRRIEhu2LL70NA4OCQ/fLxOfOn86MHn2f9zv2cMqP4vuMZbXV87boV9AxGefHN3azbvI/fP/kqPAl+j87MtjBTm8O0N4Zoqw8R8OpV9Zwfi5K9KwmC4AX+BHzFNM3ho18E0zRNQRD+Yl5UEITPAJ8BmDSpsG/YQLqHhzvvIKDUVJ2XVjI3zKquW0gbUc5q+Orh3oxjgawRZc/grfQmVuNTZzI19CVc8rGVsXOofgRBpM3/Ebb2/YCe+DM0eM6vdEgFEVBa2J1bTTI3hEsOjvv93aMu8rkINWX6bHy4jFjqkT2SSsooPrPlKtIBPh+LwqDNct4oowLLrhu8KAj4NY0hG27wAKos0eD3sr9/yNY6gKXTWmkI+njg5bc4eXpbyYRPXdDLFWcu4IozF9A7GGXT7kO8vbeL7Qd62fD2kcyvW1dorPHTUOOjLughHPBQ4/dQ63cT9Lnw6GpVibGSiC1BEBTyQut3pmneO/LXXYIgNJmm2SkIQhPwF8+Jmqb5C+AXAEuXLrVdKE/m4jx48LcICFzW8omyfSIrhHQuxvNdPyaRG+Cs+r+mRmuvdEglYzj1FjsHfkLaGKTNfz3N3isRqkjkOhxfBLUl+NRZdETuoc69YkIa5Y5mvAczByoito5ktsp3IlEfKSOW3ti0OMuGUY6M2ym8Sd5VoH0DHBFb0Yx94Rh06QzaFFsAbTUB9vXbG78D+VOJV54yj58/vpY1W/eybHa77T3GIhz0suKE6aw4IT9ZIZpIsa9rgP3dg3T2DnOoP8L2Az2sfWsP725zkyQBv1vH59bwe3S8Lg2PS8Wj53+5dRWXpuDWFHRVwaUp6KqMrubd4WVJLKlYK1psCflofgVsMU3zR0f9r5XAx4EfjPz+QLH3ejeGmePRzt8xnBngypZPE1Cs15zLTcZI8kL3fxLJdHFG/ZcqNoaj1JhmjgORuzkYuRdNrmde+HvHxMgUh4mNIAi0+q9jS+936I49TaP3wkqHZJuAkhdbQ+mOiozsOjyyJ2evWdoOkiChimpJe7YgfyIxVaKeLSgus+WSCu/Z8o6WEW1aOACEXC4GE/YNWaeEQ7yyt4NkJouu2JMEZ82ZyhMbt3P7c6+wYHIjfld5B6l7XRpz2xuZ2974jr/PGQYDkQR9QzEGInEGowkGo0ki8STDsSSReIqewSixRJpYMv1nwuwvIQigKTKqIqMqEpoio8gSiiyiykf+bJVSZLaWAR8F3hQE4fWRv/smeZF1lyAInwL2AteW4F7v4Pmeh9gX38G5DdfQ4q4eU9CcmWFNz38zkN7LaXWfpcE1p9IhlYRUrpcd/T8mkn6bOvfZtAc+iSRWTybR4fjGry7Ar87hYPQ+6j0fmHDZLU3y4pKDDGc6KnN/0YUkSMTLbmyqlaWMmKgWsVVEZss9ktmKFZDZCrlc7Bmwn6GaEq7BME129fYzt6ne1lpRFPjMuafwD394nJ89+hJ/c8WKcRnB824kUSQcyJcSx8IwTJLpDPFUhkQyTSKdJZHKkExnSKazJNP5kTypTJZUJkc6k83/yubIZHOkMzlSmSyxRIp01voMzFKcRlwNvNer+4Fi938v3hxcx8bBNZwYOot5gZPKdRvbmKbBup5f0Z14m5PCN9HiXlzpkErCYPJVdgz8BNPMMj30V4Td1XXa08FBEARafNewpe+79MSfm5C9WwGlhaH0wYrcWxCEvIv8OIzsKcd8xEg2XvQ+epGzDSF/GjFrGKRzOVTJXmvFqF9WpIDMVo3LzWAiYWs+IsCM+jAA27p6bYstgPb6EDedvYRbn3qZXz2znk+dc1JFBJdVRFHAPVJGxII4G4v/+wWL9y36ThXgQHwXz/XcT7tnFsvC1VMuME2TV/p/T0f8NRbXXEu797RKh1Q0pmmwf/j3vN33r2hSmPn1/9cRWg5Vi19biFedRmf0AUzT+qfOasGvNDOcOYRRodjzXlvlKyPCyDBqo/RlxFJktkYNUgs9TQj5zBYUJti8h3u27L8+YY8bw4TBhD0hG3TrNAf9bD7YZfueo5y7cAZXnDyPp9/Yzn8//hIZGxmf44UJJ7aGMv080nknAaWWDzZ+GLGKLAbeGlzJ7sgLzAlcyAx/2ZJ640YmN8Tbfd+lI3Iv9e5zmFf3r85pQ4eqRhAEmr1Xksx20Z9YW+lwbONXmzDMDLFsb0Xu75a8xMuc2XJLOolsiTNbklKSnq1R64d4EXuNiq14AaVESRRxyYrtGYcAYbcbgJ6YfUPQBc0NbD7Ybass9m6uW7aIa09fxAtbdvNPf3yCA332S5rHMtWjVCyQMVI8fPB2DDPHpc0fR6uik4c7I6vYMvQIU7zLmBe8vNLhFE00vYNNPX9DJP02U4NfYGroCxOuB8bh+CSkn4xLbqIztnLCucoHlPyHmeFMZUqJHtlf/syWqJXUQR5G5hGWwEF+1PqhmMyWR86/T8azhQk2v6oVdBqxzpsviXUXILYWT2ommc2yubOw4dKQ/6Bz1anz+cbly+mJxPibOx7ljlWvMmwz03asMmHElmmaPNV1D32pQ3yw6SNVNVy6I/4ar/b/gWb3Qk6svaGqvD0KoSe+is29/wgIzAv/C/WecyodkoODZQRBpNF7KdH0TiLpLZUOxxY+JT91YbhCA6ldkpdELlbWMqZehp4tl6SRymUwTKOofVRRRkQgUaBQgqMyWwUMlAbwaxrDBWS26j15sdUVtS+WF7U2ossyL+3cZ3vtu1k6rZX/97FLOGvOFB559W2+fOsD/Prp9eztKWyO4rHChLFafmXgucMzD9s9syodzmF6kztZ2/MratR2Tgl/GnECe02ZpsG+4dvpjD6EX5vPjNDXUCR/pcNycLBN2LWc/cO/51DsYfza3EqHYxlF1HHLtRVrkvfIPkxMErk4nhEriFKTb5BPY5hGydpAdPFIn5RbLnzgvSAI6JJCvIgG+dHMVqzQzJamMVSA2NIVhaBLp3PYfhlYlWVOmtLG2l37+NQZS1Dl4qRBwKPzuQtO5ZKlc3howxae2bSTJzZuo7U2wEnT2zhhSjPTGmttNfJPdCaE2NoT28qa3seZ6VtUVTMPI5kuXuz5KW45xLL6LyKLE7fMljPibB/4MYPJV2n0fJBJgZsm7NgTBwdJ1Kh3n0tndCWpbDeabP+UVaXwK41EKpTZco8am+YiZRNbeWNTk5SRPuwoXyyj8xFTRgY3hYstAF0uziDVrYz2bBVeRtw/bN/RHaDZ7+NgpDDrjnPnTOOF7btZvWMv58yeVtAe76a1NsDnLjiVG846gTVb97B22z4eePkt7lu3CV1VmNEUZnpjLVMbaphcFyLs81T1ScZiqPqn6WC6l8c6/0BYa+TchmuqpkSXykVZ3f1fCAicUf9ldKk8b0zjQTLbzbb+75PIdDAl+JkJeWTeweHdNHguoDO6ku74k7T5b6h0OJbxK010J7dhmsa4zxh1y0e5yBenWd6To0f2lEpsjZ4iTOTShEqwVzFlxCOZrcIEW0BzMZhKFjQjs9Uf4KV9+wpaO7epnsm1IR7cuIUVM6eWVPT4XBoXLJ7FBYtnEUmk2LTvEJsPdLHtYC8PvPwWxkhvpabINAZ9NIf81Ae81AU8hH0ewn43QY8Lj1ZdI3jsUNViK22keOjg7QgCXNz8MZQqyRzlzAwv9vyMeHaA5Q1fxadMnE/N7yaa3sHWvu9jkmF2+B8IaAsrHZKDQ0nQ5DqC+ol0x56mxfehCXPAw6eMnkjsw6uMb2+q63Bmq3xN8uUY2TMqtpIlOJHolorMbI02yBfQ5A4Q1HXSuRzJbPbwYGqrtAUDPLE9zWAySchl7wCZIAhcdcI8bnlqNau27+bsWVNtrbeKz6Vx2qzJnDZrMgCpTJa9PYPs7x3kQP8Qnf3D7O7uZ92O/RjGO3vwFFki4NYJuHX8Lh2/W8Ora3h1Fa+u5UfxaAouVcWtKbjU/DgeTZYrnjGrWrFlmiZPd/2JgXQ3l7d8ioBSU+mQgHxc63t/S19yJ6fWfYawXpp0ayUYSKxn+8AtKFKQ2TXfxqW0VjokB4eS0uC5gIHkBgYS66l1L6t0OJbwK/lRJJHMoXEXW56RDH05TyTqI9msZAlH9mglFFsuWS2qZ0uVJBRRKrhnK6TnX5+BVMK22GoP5Wdq7hkYsC22AE6bOomH6sP8bu3rnDS5Ba9epvTmUWiKzMzmMDObw+/4e8MwGYjF6R2O0xeN0x+JMxhPMBRLMhhP0h+Ns7dngGjSmpO7psjoysjsw5E/q3J+DI8qS0f9yo/iUSUJWRJR5fzviiShyBKyKB7+b0myLuCqVmy9OvA82yIbWRa+kEme6pm9t3noQfbHNrAgdCVtniWVDqdgumJPsGfwVjzqFGbV/D2KNP6Dbx0cyk1AW4Qm19Mdf2rCiC3fiNgazhyiiQXjem9F1JAFmUQZM1tHlxFLt+eRMmLxeyn0p+zbJxyNV1GJpAsTk0EtL5L6EwmavfYOKLWH8kXUXf0DnNBs3xNRFAU+c9ZJ/N2fHue/V63jG+efWbGynSgK1Po81PrGdnnPZHNEk2liqRSxZIZ4Op0fx5M+8iuVyZHMjIzjyWRJjozgiYyM3UllsmRyucNjeYwS28ZUpdjaH9/Jmt5Hme6dz5LQ8kqHc5h9sZfZPPgw7d7TmeW/oNLhFIRpmnRE7uZA5C5C+olMD30NSSzv8FAHh0ohCCJ1rhUciNxFMtuNPgEa5TXJiyZ5iWQLd/QuFEEQcMvlHdnjEkfLiKXLbOniaIN8aTJbhQ6SHsWraAVntmpdeXPS/qT9odI+TaPJ52VbT+GmuFPCNXz4lEXcufY17n7lTa5dWv2tJYosEfK6CHlL572ZzRlkcrn8r6wx8t9ZsjmTTC5HzjDIZA3+9+vW9qs6sRXNDPFY5+8IqnWc13ht1TTD9WqxVvUAACAASURBVKV2s773dur0GRPWS8s0DfYM/Yqu2OPUuc9mavBzCBPYqsLBwQp1nnPoiNxNb/xZWv3XVTocS3iVBqKZQxW5t0vykMgWl9l5P/QyZLb0Eme2immQB/AoakHDpAFqXKOZrcJmPc6qC/Pawc6CmuRHuXzRHDoGhrhrw5tIoshVJ8ybkM+8YpClfLnQhb1S7ntRVSYXJiYPd95B1sxycfNHUcXy14utEM8OsKb7Z7ikAKfVfQ5pAloiGGaWnQM/oSv2OM3ey5ka/IIjtByOCzQpjF9bQE9iFWaRppfjhU9uYDgz/pktGB3ZMw4N8iWcj1jSBvmRzFYx0wd8ikakgPmGkC9BqpJEb4Fia15DA0PJFPuHCrOPgHyG83PLT+HMGVP4w8sb+dlza0lmCnfVd6gysRXNDHEouZ/zGj5EjVod6f6ckWZNz3+TNdMsq/8C2shpnYmEYabZ3v/v9CZWM8l/I5MCHz3uPqU4HN+E3ctJZbsnjKO8T2kglRsmY9gvJRVL3kW+fGJLFERUUS1pGVEWJWRBLE2DvKRgYhZ1ItGnaAX3bAmCQJ3LQ0+8sOzioqZ8z9/rB4vzapNEkS+ffRrXLJnPc1t38427H2Hj/sr4vx0LVJXYSuRiLAktZ7pvfJtC3wvTNFnfdzsD6X2cEv4kAbWl0iHZJmck2dr3fQaTrzIl+BmafVdUOiQHh3GnRj8FSdDpTbxQ6VAs4Tt8InH8s1vukZE95ZwrqUtaScuI+T3VkpQRD1s3FLGXt4jMFuRH7xQqtuq9XtqCAV7ef6Dg+48iigLXn7SIf77sAwB89+Fn+PaDT/PWwa4JN3e00lSV2AppdZwerp7G863DT7A/tp75wctodi+qdDi2yRkJtvb/K8Opt5ga+qJjVupw3CKJOiHXyfQn1mKYxQ8sLjfekUb+aLbwwcCF4pI95MwcqRIPi37HPcowH1GX1JKVEaFwB3jIu8CnclnSucJmTDa4vRyKFZ5dPG1SG5u7uxlIlCYzOq+5gR9dezEfP+1E9vYN8q2VT/G1ux5m5cYt9ETK1993LFFVYksR1KqZLXgosZlNg/fT6lnCbP+FlQ7HNjkjwdt93yOSepvpob+mzr2i0iE5OFSUWtcyskaUoeTrlQ5lTLxKHQhCRTJbo8am5Swl6pJOooRlRMj3bZXG1LQUYit/CGA4U5igbPT6iKRTBTfZn9nejmHCql27C1r/l1BliUsXzeHnN17O55efiq4o3P7Sq3z+d/fzjbsf4Y61r/HavoPEUsV/D45FJl6n9zgQzfSwrvdW/EoTJ9V+fML1N40KrWh6O9NrvkKt6/RKh+TgUHEC2kJk0Utfcg0h10mVDud9kQQFlxQklu0Z93u7pLyvUTJXWIO2FXRRYzhTWnuJkpcRi8xsAQynk4T1sX2i3k2TN28uezAyzIya8BhX/zltwQCz68M8tm07l82dg1jCZ5gqy3xgzjQ+MGcanUMR1u3ez6t7O3jojbd54PXNADQH/UwN1zCpJkhbTYDmoJ96nwdFqo5kSiVwxNa7yBppXur5OaZpcnrd55Gr5ESkVfI9Wv86IrS+Sq3rtEqH5OBQFYiCQo1+Mn3JlzDMdNWP7/HK9UQzlRNb5TyR6JJ0ulOFe0H9JXRJZTBdfEmrFD1bgZHM1lCqsMxWmy9vZnqgQLEFcNmcOfzfVS/w0t59LGufXNAeY9EU8HHF4rlcsXguyUyWbV29bOvqZWdPH28f6mH1jj3/P3tvHifHWd17f5/ae++eRTPaN0uWZFte5B2DMYtxjAMJYLYAISRwb7hk4b2QhJd7c5NAICuB8JL7hrDmBpKwGwPGNja28b4bS7YlWZK1S7P3XnvdP6pnNJJle5buru6Z+n4+/amqp2rqOR6Nu351znnOmbpWEoK+dIr+TIr+dIqedJLeVIJCMkkhZZBLGOQTBpqyMGXJwvyvmiNBEPDo2L8x4RzmiiUfanurjPniBza7xv6asr2TMwp/EAutmJhT6ElcxlDtdorWLykYF0ZtzouSVpdwpNb+kGeyIbbqXitrbelNXY0IkJB1jnnj875PSglfsOcawgPIaWGtrAl7bjlTS9NZJCE4UJqYsw2XrlrJilyWbz7+BBevXNFyr5KhKmxdMcjWFYNTYzXb4dB4kSMTJY4WyxwvVRguV/nl4WNM1OqnrdKuKwpZQydjNPoe6hqpRq/DpKaS0rSw56GmklAVDDXsgWgojXY8qoIsdVSGFBCLrZPYU7mT/ZUHOCv/qyxNnB21ObPCDxx2j/0dJWs76wof6prWJDEx7SSrn4UsJRirP9D5Ykvpw/LKOL6J2sYuDydytlottsx5Fd48lYSsYTahgnyq4dmqunMXg5OerYk5erYUSWJFJse+4tzFliQE7912AZ+8/Q5++PQzvPnss+Z8r7mS1FQ2DvSxceD53jnP9ynWTcZrdcardYp1i2LdpFQ3KVsWZdOiYtmMVKpULZuq5eD6M1twIEsShqKgqwq6oqBP9j2Uw60qN3ogylKjB2I4rkgSmiyhyOG+2uiPGO5LyFL4URtjsxF1sdhqMGrt44mxbzGYOJvNuWujNmdWBIHPnvHPM94o79Cf7JwWRzExnYQkNAr6NibMhwkCHyE67w14kpQSetar7jB5bWXb5lUkFVXSWp4gHxBg+85UE+n531OjPg+BNIkmKchCmnO7HQgLkyqSNGfPFsC6fIFfDs2vi8CFK5Zz2aqV/Pvjv+TcpYOc0ds7r/s1E1mS6Ekl6UklYYZBJNt1qTZ6HdZsB9NxqDf6HNadRs9D153qfWi5HrYbrgoN9z1qdRPH9bAbbXhsz8P1wuNm90OcTiy2AMurcN/wP5OQC1zS976O/gI+lSAIeK74L4zW72VV9t1xeYeYmJegkLiIkfrdVOydZPTNUZvzgqSU0BtQcdortqDRsqeVnq3J/oi+2TSxlZA13MDH8V1Uae6PNiEEaUWfl2dLCEFBTzJuzV1snZHv5Y4D+xit16b6Jc6F3730Ynb/+Cb++o67+KtrXkdvau73ihpNUdAUhUKyeT0Qp+P5/omeiI191/dxPS/c+j6eHzSOw+13Z3jvRS+2gsDnwZGvYHllrhr8IzR59itHouRQ+d85Xr2V5ZlfZ1nmjVGbExPT8eT08xBCZtx8uKPFVrohtqruaNvnTsjJ1q5GlE80o841p/XcVH9E07PnJbYgTJKfj2cLoNdIMmbO/Xd4Zm/4779zdITLV6ya832yhsHHXnkl/+OWW/nTn93GX7zm1V0tuFrJZJhQV5svjbrHhdMinin9lGP1HZzX81Z69Nas2GgVxyo/4XD5eyxJvYYVmXdGbU5MTFegSCmy2mYmrEejNuVF0eQUqpSg5jZ31d5MMKRU28RWs0g27tmM8g/z9WwB9OhJRq25/w7X53tQJZkdI/Ovtba+t4f/8aqrGKvV+KObfsqu4fb/TS12FrXYGjZ3sWPiRlamLmJd+hVRmzMrRuv3sr/4VXqMi1mb+0DX1QKLiYmSvLGNmnMQK4IK7bMhpfRS9drv2TLkZJvCiM1vRt0MsZVSdSrzaLcD0GekGKnPve2RKsts6evn8XnmbU1y1sASPn3N1ciSxMduvoVvPv4Elhs3l24Xi1ZsmV6J+4e/RErpZ1vvu7pKrJSsp9gz/o+ktY2c0fOHXZVjFhPTCeT08wCYsDq7mnxS6aUahWer1WKrBZ4tY0pszf+eGcWg4s6vnVBfIonluVTmUULi/IFlHChNzLlP4qmsKRT4zHXXcsWa1Xzrl9v50A03cuvuZ3Hm2FYoZuYsyqd0mKf1VWy/xmX9H2jrsur5UncOs2vsb9DlJWzs/ZOOL8wYE9OJJJQV6HIvReuJqE15UVJKHzV3rO1NfxNyCtu38ILWPIRbIbYSU/dsQhhxno2kAZYkwhIaQ/W5r+q8eOkKAO4/cnBetkwnrWl8+IqX8cmrX0POMPjCfQ/w/u/9gG889gRHSqWmzRNzMosyQX5n6RaO15/igt53ktdWRG3OjHG8IjvHPoVA4szej6NKmahNionpSoQQ5PRzGTPvJwg8RIf0ZD2VpNKD61vYfhW9Uf+qHRhymEBteTWSSvO/Z4zGC26nhhHTqk7ds/ECH3mOkYNJsXW8XmZ9bm4lF1Zmc6zK5rnr4HP86hmb5nSPF+LswQH+9tpreOzIUX78zE6+s307335yO2t78ly4fAXnLVvKhr5etEXcYqeZLDqxNWLuYfvEDaxIbeuqPK2wOvzfYntjbO77cwxlIGqTYmK6mpx+LkO126k6e0hrG6M257Qk5R4Aau5Ye8WWFIots0ViS5NUBALTm1+objqTnq1aE2ptZdRQDJYdk7w2t5V7g8nw93asNr8ekK9avY6vPfkoB0sTrMzm53WvUxFCcMHyZVywfBmj1Rr37N/P/QcP8t2G8FJliQ19vWzo7WNdT4HVhTzLs9lF3eNwriwqsWX7NR4Y+TJJuYcLe9/dNXlaQRCwb+KLlO1n2NDzYTId+mBYDASBhesdwXWP4vnH8LwRPH8c3y/iB2WCoE4QWASBCwSAhBAqQugIkUKWskhSAVnqQ5EHkeVlqMpqJKm7So4sBLJ6WFG7aG3vXLGlNMSWN0aBuS//ny2Tni3Tb82KRCEEepNb9kx5tppQRT7bBLGVVnUyms7ReYqt16xZz7/teJwbn93JBy+4ZF73ejF6U0nesGUzb9iymbJlseP4EDuOD7FrZISf7NyJ4/kASAIGMxmWZTMMZjIMpNP0p1L0pZL0JZNkDaOpja8XCotGbAVBwCOj36DujXPV4EdRpdYURWsFRys3MFy7gxWZt9KbiNvwtAvfr2A7O7HdXTjOszjuXjzvKAEn8meE0JClHiQphySyCHkQgYYQCiAAnyBwCQITP6jiekP4zjN4/sltOBR5AFXZgKZuQte2oipndGxoa6GgynmS6kpK1naWZ94UtTmnZUpsuWNtndeQw+9H05t7Uc6XnkPHaqLYUiQZVZKbUkV+umdrPixP5ThcKc7rHjnd4FWr1/Gz5/bwts3nzKvA6UzJ6DqXrlrJpavCYrqu73OoWGT/+AQHi0WOlEocKZXZfmwI85QVjbIkyBsGhUSCfMIgZxhkdZ2sbpAxdDK6RlrTSWsaaU0j2ehr2C3Oj7myaMTWc5V7OFR9mLMLv0avvi5qc2bMuPkIB0vfoDdxOcsz10dtzoLG92tYzuNY9uNY9i9x3eemhJUiL0NV1pE0XoWirESRlyLLg6HAmsOXRBDYuN5xXO8QrnsAx92D7eykbt0NgCRS6NoFJPTLMPRLkKT2hZAWE1ntLIZrP8cPHCTRpOqaTUSXMkhCpd6EBsuzwWgUd25lrS1d0puaswVhKLHWBAGXVUOxWZyn2FqRyvHQ8PyT268/82xue24v/7bjcf7gwsvnfb/ZokgSawoF1hQKJ40HQUDZshiqVhmuVhmr1Rmt1Riv1ymaJmO1OvvGximaFq7vv+D9JQFJTSOpqiRVlYTaaDKthNuEomI0+hwaioIuy+jq5L6CJsvoijLV+1CXG/0PGz0OO0HILQqxVXaO8dj4f7LE2MSm7OuiNmfG1J3DPDv+WZLqGtbl/1tH/MEsNFzvOKZ1D3XrAWz7SQI8hNDR1S0k0u9GU7egKRubHuYTQkNVVqIqK0G/bGrc88awnCex7EcwrYeoW79ACBVDu4ik8VoM/ZLY49VEMvpZHKv+lKqzl4x2ZtTmPA8hBAklR81tr9jSG55/02+tZ6sZKwenk5C1piTI57WG2JpHb0OAVZk8Pzu0m6JVJ6fPPZoymM7wxg2b+d6uHbx69XrO7u+MnF0hBFnDIGsYL9p3MQgCTNelZFmULYuqbVOxbKq2TdV2qDo2Nduh5oTHputSMi2OOxVM16XmOFiuiz+HRblCgCo1GlA3mktPbiebTYf7AlUKG0+r0rSm05KEIsnIkphqPj11fhbP5AUvtrzA5f7hLyMLlYv63ts1Nak8v8ausb9BQmFjz0eRG0UAY+aP541Rt+6gZt6B7ewEQFVWk069GUO7EE3djIiopIYs95CUryRpXEkQ+DjuTmrmndTNn1O37kWWekklryOduA5JykZi40Iiq4XtesrW0x0ptgAScoG6N/HSFzYRTdKREFitrCIv6ZTd5ja7Tio6tXnWx4IwjCgQ8xZbazJhGHhveYzz9eXzutfbN5/DvYcP8JmH7uGzr349Wb17nglCiIa3SmUgPTcvfRAEOL6P5bpYbqPhtOuFx960ZtONptK2605d7/o+thv2N7S9cHzyODznUvVP9EF0fD/skzitH6Lje3hzUXsNFrzY2jFxAxP2AS5f8rsklcJL/0AHEAQBeya+gOkeZVPfn6IrS6I2qesJAhfTeoCqeROW9QgBPpp6Brn0b5PQX4aizO+LsBUIIaGpm9HUzeTS78e0H6Ra+xGlytcpV/+DVOJaMsm3IjdWrMXMHlXOYyiDlO2dUZvygiTkPGP2vrbOKQkJTTZa7NnSGLaaG0ZMygZVd/42y0IirepM2PMTm+uzobdnT3GU8/vm9x2TUFX+6JIr+KM7bubT993Jn7/81YuqLIMQIgwTyjKZiIRmEAT4QTAlwLzAJ/ub75rRzy5osTVk7mRn6VbWZV7O8uR5UZszY45WbmCs/gCrc79JTj87anO6Gs8fp1r7EdX6T/D8MWSpl3TqrSSN14QhvC5BCJmEfhkJ/TIcdz/l6reo1m6gWv8JmeSbSSevR5Li5rJzIaNtYsJ8lCAIOjJUn1Dy1GvFtttnSMmWerZ0ScduwsrB6SRlnWFrfgnpk+S15LzFVkbTGUxm2DXRnC4AG3r6+MMLL+fvHrybv7z3Dj522SswlM7LNVyoCCGQhUCWZh8hW7Biy/aqPDjyVdLKEs4tdE9iecnawcHSN+lNXMZg6rqozelaHPcAldp3qJm3EwQOhn4R+cTvY2gXd33Ok6qspif3UdzUOyhV/5VS9ZtU6z8ll/kvJPQrO1IwdDJpbSPDtTuwvGMYytKozXkeCTmPHzg4fg1Nbl+JEF1OYPnNq4N1KkaTSz8AJBStKe16AHq0JBPzDCMCbCos4bGRw00Ty1euWovleXzh0fv5kztu4WOXXclAKl5A0+l0RwLTLAmCgEfHvonpFbmk730oXZLvZHvj7B77DIYyyLr8B+OH5hywnT2MTnyCodEPUDPvIGVcw2Dvl+nLf5KEflnXC63pKMoKenL/L/2Ff0CWexkrfprR4v/E89rfS6+bSWsbAKjYuyO25PQYcg6g7XlbumRgtbj0gxu4uH7zmiEnZZ2aazWlvVFBTzFmz78n4dk9gxQtk8PV5njcAK5eewYfv+yVHKmU+b1bf8RP9+7Cb3NLp5jZsSDF1sHaQxysPsyW3HX06GuiNmdGBIHPs+OfwwvqbOj5CHIX1QHrBBz3IKMTn2Ro7INY9mOkU29nsO9fyWc/hKJ0T0umuaBrW+gv/CP5zH/Fsn/J8YbQjJkZSWUVstCpOM9GbcppSTTEluk172E9E3QpgdXCnC298RLczPIPScXAC3zsJgi4Hi3JhFXDC164ZMFMOLc39JY+NnJk3jZN5+JlK/j8a69jfaGHLzz6AB++7Sc8eORQLLo6lAUntmruGI+OfpNefR2bctdEbc6MOVz+DiVrO2vz7yeptq9SdLfjeWOMlz7H0OgHsOyHyabeyWDfv5JLvxdZam5ri05GCIl08tcZ6PnfKMoqxoqfZrz0OYKguTkxCxEhZJLqWqr2nqhNOS0nPFttFltyoqVFTfVGxXerieUfkpMte5oQSuwz0vgE887bGkhmWJ7K8eBQ85pJT907leZTr3gtH7n4Cqq2zSfu/TkfuuVGbtj9NEWrdSHgmNmzoHK2gsDnoZGvE+Bzcd/7kLokZFSydnC4/G36kq+gP3lV1OZ0BUHgUKl9n3L1mwSBTSr5BjKpdywqgXU6FGU5/YW/o1T5GuXat3HcvfTm/hRZnlsj3MVCSlvPUPXWjmxKbUx5tkptnVeXDOxW5mw1PFtWEz1bKSW8Z9U1KWjzy2Pq1cOfHzErU/tz5ZKBVfxg33ZKtklWM+Z1r1MRQnDlqrW8bMVqfnHwOW589hm+9MTDfOWXj3BO/wAXL13JBYNLWZ6eWwHmmOawoMTW7vLtDJnPsK333aTV/qjNmRGOX+bZ8c9hKIOszb0/anO6Ast+nPHy53HdQxj6JeTTH1jwocLZIIRCLvM7aOomxkt/y9D479OX/ySqsjZq0zqWlLoOP7Cpu4c7zrOsCB1Z0rDaLLY0ycANXLzARRbNf1ToDS9UMwubJuVQyFSbUGur3wgF1pBZ5szc4Lzu9fKla/ne3ie5++hzXLt607xtOx2KJHHV6nVctXodzxXHuevgc9x3+AD/8sRD8ATkjQRbevs5s6eP9YUe1uZ6uqpWV7ezYMRWyT7Kk+M/YFlyK2vT3dE/MAgC9o3/b1y/yJl9n47ztF4C3y9TrHyRav0WFHkpfflPYOgXR21Wx5IwrkCWlzI68T8ZHvvv9OY/ga6dFbVZHUlKDYVo1dnXcWJLCIEhZTH9+TU0ni16oz+i5ZkkleavdjOkMIzYzJyttNI8sbXEyAAwVJ//731dtoc1mQI3H9zJr6w6s+UepjW5AmtyBd5z9vkcq5R5fOgoT40M8dTIMPcePjB1Xd5IsDKTY3kmy7J0hoFUmsFUmv5kirSqxZ6wJrIgxJYfeDw4+lUUSWNb77u65g9kqHYrY+aDrM69h5TWPf0ao6Bu3ctE6XP4folM6u1kU+9EiPit7KXQ1PX09/wDI+MfY2TiY/Tl/wJd656ac+0ioSxHEio15zngyqjNeR66nInEswVg+yZJmi+2Jj1bzWxGnZwUW978xZYuqxS0JMfN+f/ehRBcu3oz/7T9XraPHeOc3vaVGBlMZ7gmneGadRsBKFome8bHeK44zoFSkYPlIncffI6Kc7KHUZcVehNJehIJeowEBSNBXjfINT5ZXSej6WR1nZSqIXXJczcqFoTYeqZ4E+PWfi7r/8BUfkOnU3ePcKD4dXL6OXE9rRfB92sUK/8/1frNqMp6evOfQlPXR21WV6HIA/T3/D0j43/MyMSf0pf/JLq2NWqzOgohZJLKSmrO/qhNOS2GnKHmjrV1Tm0qp6o1eVt6C3K2munZAliayHG03pyFCVctX883dj/Kv+9+nLN7BiNzCuR0gwsGl3HB4LKTxsu2xfFqhaFqlaFahZF6jZF6jbF6jZ1jIxRNE9M7/SpPSQiSikpK08hoOilVJaWGjaUnt0ml0WBaCfcNpdFgWlFINBpMG4q6YEVb14utcesATxV/zKrUxaxIbYvanBkRBB57xj+PECrrCx/qmn6N7cZ2djJW/DSed5xM6h1kU7+BEHG15LkgSwX6Cn/NyPhHGZ34U/oKfx+L1lNIqKsoWo9HbcZp0aQ04/6Bl76wiehTnq3mFh6dZDKM2MzViLqkogiJSrPEVjLHQyPNEeC6rPC2M87jizvu58Ghg1wy0Fnh6owWeqrOKLzwYhrTdShaFkXLpGRZlGyTsmVTsi2qjk3Ftqk4FlXHYaxepOrY1F2XuuvM2A5VkjEUBV2W0eVQhGmNfV2R0aTGVg73w3PhsSrLaNL0rYQ6dRw2lJ4cU6TGuWnNpVspgLtabHmBw4OjX0WXMpzf8/aozZkxRyrfp2LvZkPhw2jxKrHnEQQB1foPKFa+hCQV6Cv8LboWty2aL7JUoC//VwyN/yGjEx+nv+cfUeS47+YkCWUlw7U7cPwyqpSJ2pyTCMOI5ba27JkeRmwFqqQiEE3N2RJCkFYTVJzmlKxYnixwm/MMRbtOTpt/Tu01K8/kpv3P8M877uesngHSanelQhiKiqGos65Y7wcBddeh5jjUXYe641B3XUzPpe44mJP7rhM2l/bcqTHb8zBdl5rrMGGZYcPpxnj4cWlWZTFZSCiS1BBioQhTRGPb+MhChNvGuZnS1WLrqYkfUbKPcMWSD7W1jcV8qNr7OFT+Nr2Jl9Gb7I5E/nbi+zUmyv9AzbyLhH4phexHkDrswdfNyHIfffm/ZHjsw4xO/C/6C38f91RsMJkYX3cOoupbIrbmZDQphR94uIGJKtqzkEZteJ5a5dkSQqDLWlM9WwBpJUGlCc2oAValCgAcqI5xjjb/ZvWKJPH7W6/gj+77Mf/fk/fyx+e/smtyjOeDJAQpVSOlak2/dxAEOL6P44fiy/E87Gn74Tkfx/NwfR/bD7eu72F74dZtXBPuB1NjbuDj+f6JsSBoHPuhgPRm7rHrWrE1au1jZ+kW1qQvZ2nynKjNmRF+4LBn4vOoUpa1+bjMw6m43lFGJ/4M1z1ALv3bpJPXL4ovonYT9lb8OKMT/4Px0mfoyX08/j0TJskD1N1DZDtMbOly6Emw/Spqm1YtT4YRnRaJrXAOvak5WxDmbTUrjLg6HUYe9ldGOacwf7EFcGa+n/ecuY2vP/Mw39j9GO/aeEFT7rtYEUKEIUVZJhVBlsnfz/C6rkwW8nybh0a+iiHnOK/nrVGbM2MOl79LzTnA2vx/QZHixqHTsewnGRr7fTx/lN78X5JJvTUWAC3E0LeRTf8WdesXVOs/iNqcjkCT+5CFjuk2t61KM9Ab3xeWV2nbnGojgb1Vni2gJZ6tjJKk5Myv6vskeS1Jj55ib7m5/UbftPZsXrNiA9969gm+ufuxpvRyjOlsutKztb34Q8rOcV4x8Adte8ubL1V7H0fK36Mv+QoKxoVRm9NR1MzbGS99BlkeoC/353GB0jaRTl6P7eygWPkymnoOmnpG1CZFihAShrKUegeKLU0K0yRsvzkiYiYoQkVCtFRsGZLR1JwtgIyaoOQ27/e0PtPPrtLxpt0PQm/Mh855GQEB/7H7cY7VynzwrMswlHgB0EKl6zxbI+YedpV+xrrMyxlIdJar/4UIAo+9E/+EImVYk3tf1OZ0DEEQUK5+i7HiX6OpbK+9PAAAIABJREFUm1hS+GwstNqIEIJC9r8jiSzjpb+J+ygChrK0Iz1baiOvzvarbZtTCIEq6a0NI8oalt/cv7usmsTyHJwmNKMGODM7wHGzNO8eiaciCcHvn3MFv7HxAu48vIc/vOeH7Bg71tQ5YjqHrhJbnm/z8OjXScoFthbeHLU5M+Zo5Uaqzj7W5t8fhw8bBEFAqfIlipUvkzSupC//qTgRPgIkKUsh+2Ecdz+l6jeiNidyDGUQyxsmCLyoTTmJSc+W00bPFoShxNZ6tvSmFjUFyKnh76roNEeYbsmH9ah2TDRfhAsheNsZ5/LJS67B8X0+dv9NfPrR2zlQHm/6XDHR0lVia0fxRsrOcS7sfU/XhA/r7hEOlf+TnsQl9CQujdqcjiAIfCbK/0i59h3SyTdQyP4JQjR/lUrMzDD0i0glXkel+i0cZ2/U5kSKLg8SBB6WNxq1KSehyZOerXaLLa3lni2zVWLLbo7YWpfpIylrPDF2qCn3Ox3n9C7ln17x67x9w3k8NnKED/3iB/zZQ7dw//EDuL7fsnlj2kfX5GyNWvvYVfoZazMvZyCxOWpzZkQQBDw38UWEUFiT++2ozekIgsBnvPQZauatjUKlvxknwncAufTvYFr3M1H+An2Fv1u0/ya6MgCA5R3HUDqnBpksVCShtt2zpUkaTgvDy+FqxObeP6+FYmuiSZ4tWUic27OSx8YO4gc+UouKUOuywjs3nM91qzfz4/3PcPPBnXzqkdvIaDqXLFnFxUtWsrVvKUklfjHtRrpCbHmBw8MjX8eQc5zbReHDkfpdFK3trM2/H03uidqcyJkutLKpd5NNvytqk2IaSFKWbPq3GC99lrp1B0njqqhNigS9UeTVcoegw+pNqlICx29O/aiZoggNp8liaDqGrGP7dlNFTF4NUzXG7eat3Ly4bw33De/hmeJxtuRb29cwqxm8Y8N5XL9+K4+OHOYXR/Zyz7Hn+Nmh3Qgh2JDrY3NhCRvz/WzI9TGQSC/al6NuoivE1lMTP6LkHOWKgd/rmvCh61c4UPwaGe1MliRfG7U5kRMEARPlz8dCq4NJGq+jWruRUuWrJPSXLcrQrib3IJCwvKGoTXkeUYgtVdKoua0rN2FM9Ue0SchGU+6ZVgwUSW6q2NrWuwpdUvjF8d0tF1uTKJLExUtWcvGSlTi+x9PjQzwxcoTtY8f5yf5nuGHfDgASisrqTIGV6TzLU1mWpXIsTWZYkkiTiFc3dgwdL7bGrQMnipcmuqdly4HSv+H6Vdbk3x/3PgRKlS9Trf+ETOrtsdDqUISQyGbez8j4n1Ct/5h08tejNqntSEJBlfPYHZazBaBKRvvFltBwWxlGlENBb3pW08SWEIIeLcOoXW7K/QASisYl/eu4e+hZ3rP+UhJtDuWpkszW3qVs7Q2FnuN7PFcaZ09plOfKY+wvT/DA8QOU7JOLuWY0nX4jRZ+RosdIUtCT9OgJCkaSvGaQa3zikhOtp6PFlhe4PDT6dXQpw7k910dtzoyp2LsYqv6MpenrSKlrojYncsrV71CufZt04lfJpt4btTkxL4KhnY+ubaVc/Q9SiWsRosNiaW1Al/uxveYWsWwGitBxg9Ylq5+OsPRDK8OIocAyPRPINe2+vVqGUavUtPsBXLN8C3cd38Xtx3by+hXRdi1RJZkN+T425PtOGi/bFsdqZY7WSgzVKxyvVxipVxk2qzw9MUTZPv3fjybLZFUjbEathg2p06pOStHIqBopVSepqKRUjaSikVJUkqpGStHQZQUpDmO+JB0ttnYWf0rRPsTLlnwQrUv6twWBz76JL6HJPazIvC1qcyKnZt5BsfIvJIxXkMt8MM4t6AKyqXczPP5RqvWbSSffELU5bUeTC9ScA1Gb8TxUyaDmjrV1TkVScYOZ93+bLZNhxGYXNu3Tczw2/mxT77khO8Dm3FJ+ePAJXrtsM5rUeY/PjBYKpVNF2CS251G064xb4adkW5TsOkXbpGRblJ3w81x5nIpjUXFsvJdYDSkAXVFJKioJWSWhND6ygt7YGrJKQlEwGmO6pGA0jg1ZQT/pI4dbSUGWFk5UqPP+WhoU7cM8XfwJK1MXsSx5btTmzJih2s+oOnvZUPgwcpfkl7UKy97OeOnv0LWz6cl+NA6ndglhNfktVGrfIZV4PULIUZvUVlS5F9t8PGoznocijPZ7toSG47dObCXkhthqcvmHfiNHxTWpezYJuXkhv7etvZA/e/xGfnTwSd60+vym3bddaLJMfyJNf2Jm9R6DIMDyXCquTc2xqboONdem6tjUGvt116HmOtRdh7rX2Louw051asx0XWzPZbZNiSQh0GUFTZbRJQVNVtAkGb3RC1GVZDRJmdpXG+cUIaHJCqokoUknzimTx7KMLE6ckyVx0jWKkE7al4SYt6OgI8VWEPg8NPp1VCnBeT3d4x1y/DIHS98kq2+hJ3F51OZEiusdY6z4F8jSEnpzf7Yok627FSEEmeT1jBb/HNO6l4Tx8qhNaiuaVMALTDzfRJaak0fUDGRJx21hzavTMenZalXJg5PDiM1jiZ4H4Lg5zprUQNPue1Z+GRf3reW7+x/l8iXrGEw0L/TZiQghMBQ1zOkyUvO616RwMz0Xq/ExT3M8uW97HrbvYXselj99zMXxPSzPo2zbjWvCMdv3cHwPx/NmLexeDAEokozcEF+yJFCEhCLN/EW0I8XWrtLPGLf2c0n/72DI3VNV/FDpP/D8Gmtyv72ow2W+X2N04s8I8OjP/0VcGb4LMfRLUeRBKvUfLjqxpcrhA9TxJ5ClwYitOYHS4mT1088ZJk57gYvUghemqTBikz1bSxMFoPliC+B9Gy7n/3nw23z2qdv4xPlvRJ3FA3cxc5JwazFBEOAFQSjAPBcn8HG8hhDzfdzpx4GPOznue7i+PzXm+n74CXwc38PzA9zAxwt8PD8cmykdJ7bKzhDbJ37IsuRWVia7p2FzzdnPUPVWBlJXk1RXR21OZIQlHj6L6+6nN/+JuNdhlyKERCpxLcXKV3Dcg6jKyqhNahuqFHpFHL+IQWeJLS+wCYKgbS9zk2LLDRxUWiC2Jj1bTfbY9es5hBAcqTc/x61XT/O7m67k73fcyj/vvIv/tumVi/rluhMRQqAIgSJJLS9/8ZEZXtdxSTSPjP4rslA4v+edXfMHHAQB+4tfQ5aSLM92T9izFVTrP6Bm3kk2/V4MvXvEcszzSSauRiBRq98ctSltRWl4Yh2vGLElJyNLGkHg49O+vo2K1BBbLcrbUiQZRVKoNTmMqEoKS40Ch2utWVV6af86rl+zjTuP7+Irz96DH8QtdWJenI4SW5ZfYdjczdbCW0gqhajNmTET5sMUrSdZkXkr6iIOmdnOToqVL5HQLyWdfGvU5sTME1kqoOsXUbN+TrCIHiaKlAXA9ZtXp6kZyA0vk9/C1YGnMt2z1SqScoK621yxBbAi2ceB2nDT7zvJ9au3cd2Krfz08A4++9TtWF77/l1iuo+OElt1d5wlxibWpl8WtSkzxg9cDpT+DwllGUtSV0dtTmT4fpWx4qeQpR4K2Y90jVcy5sVJGq/C80awnSejNqVtTL4wdZ7YCsN4XhvzthQRZpq0UmwlZIO61/xirauSSxi3K5Sc1vSTFELwnvWX8q51l3D/8F7++JHvs7fcOnEX0910lNhSpQTbet/VVQ/qoeqt1N0jrMq9B0l0XApc25gofwHPG6KQ/VicEL+AMPRLEEKnbt0dtSltQxIGQsi4QXMaGTeLye8XL3DbNudkGNHzWzdnUk5Qb3IYEWBtOsy321s51vR7TyKE4I2rzuPjW6+l5tp87JHv86VddzNht7dheEzn01FiK6X0kVb7ozZjxrh+lcPlb5HVzyavb4vanMiomXdRM28jk3onurYlanNimogkEhjaNurWvQRBMxdTdy5hcm0Sz+8ssXUijNg+sSW3KYxY9ZovTtakBpCFxLOVI02/96mc27OCz1z0Fl67bAu3HnmKD93/73xl9z0cqU20fO6Y7mDxumKawNHKDTh+mTOz7+4qb1wz8fxxJsqfR1M3kkm9M2pzYlqAoV9K3boXx92Lpq6P2py2IEspPL+zvBMSYYmBdoqtE2HE1s2ZUBLUas33bGmSwtr0IDtLB5t+79ORVg1+Z+MV/MqKs/ne/se4+chT3HR4O1tyS7li4Awu6ltDXuuOTigxzScWW3PE9sY4WvkRfYkrSGuL4wF0OiZKXyAITArZjy66SuOLBUO7CADLfnjxiC2RwAs6TGxFGUZs4ZxpJUnNq7WkpMWW7CpuPHw/ZadGRm2P0FmezPN7m6/iXesu5vajO7nz+C6+uOsX/Muuu1mX6WNrYQVb8kvZmB0g2eaG1jHREYutOXK4/G3AY0X2HVGbEhl1817q1i/IpX8LVVkVtTkxLUKWe1CVtVj2Y2RSi6O0iSwl8ILme1vmw+TLTNDG0g9yw5vWSrGVlBP4gU/dM0kqzW1xdk5+DT88fD+/nHiOl/W3N8WhoKd485oLeNPq89lfHeXhkf08NnaQGw4+wfcPPIZAsCyZZ126j9XpHlaleliezNNnpFtSrT8mWmKxNQfq7hGGqrcxkLoaQ2ludeJuwfdrTFS+gKqsI518S9TmxLQYXdtKtf5TgsBBiNZXgI4aSei4HVZn60QYsY1iq8V1tiD0bAHUvHrTxdbq5BIKWppHxne3XWxNIoRgTbqPNek+3rJmG3XXZldpiF2l4+wpD7OjeIRfDO2eul6VZAaMLIOJLP1Ghn4jQ5+RpldL0aOnyGuJWbWJiekMYrE1Bw6V/hNJaCzPLF6RUa5+A88boafwccQiXoW5WNDUs6nUbmjkbZ0ZtTktR2pUa+8kpCnPVvtqniltCF2mlbApcsmp0Kf3NPXeQggu7j2TW489SsmpkW1TKPHFSCga5/as4NyeE901Ko7Jgeo4h2vjHKkVOVYvcdwssX3iCOYp9bsEgoxqkNcS5LQEOTVBVk2Q1QyyqkFaNcgoerhVdVKKji4pizavuFOIn5KzpOo8x2j9HpZn3oQq56M2JxIc9yCV2vdJJV4Xrz5cJOhq+O9sO08tErGl49NZYks0Fo+3s8Cs3IY6WxklbHBccSstuf/lfVu4+egj3D28g2uXXdSSOeZLWjXYkl/KlvzSk8aDIKDqWoxYFUbMKuN2lXG7xrhVY8KuU3TqDNWHKDr154my6chCIq2EwiulaCQVnaSikVS08FjWSCgqSUUj0dhPyBpJWSWhaCRkFV1W4vDmPIjF1iw5VPoPFCnJ0vQbojYlMoqVf0YIg2z6t6I2JaZNyHIfstSL7ex+6YsXABIKQRsrtc+M0DPRznY98pRnq3VzZtTQs1V2W1NqY1mih83Zlfx86Je8dvB8VKl7HntCCNINb9WadN+LXmv7LmXHpOxYVByTshtuq65NxbGoupMfm4prMmSWqLk2Nc+ecUNlQ1YxZLUhvlSSjW04rpx0bvJYlxV0KTzWJ8ckBa2xr0nyohBx3fNX1wFU7GcZNx9mRfZtKFI6anMiwbQewbQeIpd+P7LUPS2VYuaPqq7HcfdEbUZbEEIlaOOqv5kgJh9Ibax3JrchjJiUEyhCoeS0rmL/65Zu47M7f8Ddwzu4auDcls0TJZqk0Kun6dVn/2xyfI+6a1P3HOqeHYowN9w3PYe660ydM71w33QdTM+haNc55hWxfHdqzGd2f6OapKBJSkOYhUJMbxxrkoImyycdq5Lc+Bn5lDEZTVZQRbjVGtdNnlMbnyjEXSy2ZsGh8rdQpDRLU6+P2pRICAKfYuXLKPIg6eTi9ewtVlRlHZb1CEHgLvg8PSEUfDpMbEUwpyQkJERLxZYQgqyaZsIptWyOLdlVbMgs48YjD3BJ7yaSit6yuboRVZJRtQRZ5r9AIQgCnMDD8lxMLxRflueGYmxy33MxfQfbczE9F9t3p66xpl1f9xxKTn3q2PZcbN/DnmdHA1lIU8JLlWRUEW6VqWMJVVJQJSkcEzLKKfuqJKPMQrQt7G/MJlKxdzNhPsrK7DuRpeiTLKOgbt2F4+6hJ/tHCBHXh1lsqPIqAjxc78iCL/UhkKDjmm+HciuYpddgvsiS2tKipgA5NceE3TqxJYTgratewaee+k++c/Bu3rP21S2ba7EjhEATobcpoxotmSMIApyG6ApFmIcTeA0x5uL4Ho7vYU3bt30PtzHm+v5J101+3CAcd32fqmvhBh6O7zfONa7xfdwg3M7m/8VYbM2QQ+Vvo0hpBlO/ErUpkRAEPqXq/0FVVpMwroranJgIUJRw9ZTrHVoUYqudq/46GVnILS83UdByPFvZ19I51qQGuHrwAm4++ghn51ZzQc8ZLZ0vpnUIIcIwoawQZUKPF/go/NcZXbvws9KaQMXew4T5KEvTb0CWmlsHpluomz/HdQ+RTb3nRO5IzKJCkcOVUp7Xusa+MZ2HLJSWrkYE6NFylJwyTgvreQG8cfmlrEkN8JV9t3CwNtzSuWIWPvIsnoXxU3MGHCl/F0VKMZi6JmpTIiEIfMq1/0RV1mDol0dtTkxECJFBEglcbyhqUxYpYchCtDl7SxZKy1sE9Wphfa1Ru7WNm1VJ4YMbriMh6/zDzu9zuDbS0vliYiaJxdZLUHMOMGY+yGDq9Ys2V8u0H8Bx95NJvS32ai1ihBDIch+eFz+gomAqP6TNxSkVoeLNMyH5pejTw5XNI9ZoS+cBKGhpPrLpTchC4m+e/g5PFQ+0fM6YmPjJ+RIcKX8PWRgMpBdnrhZApfYdFHmAhH5l1KbERIwkFfD98ajNaDkBHoLOaokSBFF5tuSWJ8j362ENqSGz9WILYMAo8Mebryevpfjsrh9ww6H7cGdYayomZi7EYutFMN3jjNbvZUnqtahSJmpzIsF2dmHZ20knf22qEW7M4kUSObygtaGeTiDA7zgv7mTCfrvFliLUlocRdVmjoOU5ZrYvRN2n5/jYlrdxae+Z/OjIg3xixzfZXnxuStTGxDSTzvo26TCOVn6IEBJL078atSmRUan9EEkYJI3XRW1KTAcgSRkCvzVtVTqJIOhAz9ak2GrzS09Y+qH11fSXGks4Yh5v+TzTMWSN9617Hb+38Q3Yvsvndt7AXz/9bR4f34vfcaU/YrqZuPTDC+B4EwzXbqcvcSWa3NzmqN2C75epW3eSMq5GklJRmxPTAUgiiR/Uojaj5QSBgxBq1GacxGRPRNHmd2RFKNR9q+XzLE8s5anSLuqeSUJuTX2mF2Jrfi2bsyu5e3gHNx19mC/svpEeLcOlfZu4qGcjyxO9cSPnmHkRi60X4Fj1JoLAXdQ9EGvmzwgCm2Ti2qhNiekQhDAIApsg6LwwWzPxcZA6TGxN9kSU2u3ZEgpui0syAKxKLgPgYO0IGzPrWj7fqaiSwlUD5/Ly/rN5YmIvdw1v56ajD/OTIw/Rp2c5J7+GzdlVnJFeRkZdnCWAYuZOLLZOg+ebHK/eTN64kIS6PGpzIiEIAqr1W9DUjWjq+qjNiekQTnh7XGDhdhHwAxupw7okBI3Cou0ObyqiPWHElcnlCAT7qgciEVuTKJLMtp4NbOvZQNGp8tj4Hp4Y38fdwzv4+fFfArDEyLM2NcCq1BJWJPpYlughp6Zi71fMCxKLrdMwUr8D16+wbBF7tRx3L467l3zmQ1GbEtNRhN6ssD9iZ4mRZuIHFpLorP55k1Xc5Tb3pVQlrS1iS5c1ViSXsqeyv+VzzZScmuKVS7byyiVbcXyX56rH2V0+wt7KUXaWD/PA6M6paw1ZY9DI06/n6dOz9OpZevUMPVqGvJoiIeuxGFvExGLrFILA51jlx6S1M0hrm6I2JzLq5m0IoZA04nIPMdNZHA8Lz68jifbmDb0Uk42x2x1GVITaljAiwIbMOn5+/B6qbo2U0ll1DVVJYUNmORsyJ6IdZafGofooR+qjHDfHOVYf57nqcR4Z341/yqpGTVLIqSmyapKcmiSjJskoCTJqkrRikFYSpBWDVOOjS2oszhYQsdg6hQnzEeruUTYUPrxo/9CDIKBm3YWubUOSslGbE9NRTBbWXLj5WgBeYKJ3WLkXr+Fdktrs2VIkFSew2zLX5swZ3H78bp4pPcu2nq1tmXM+ZNQkm9Ukm7MrTxr3A59xu8KYXWbcrjBuV5hwKhTtGkWnylFznJ3lw9Rc8wVbGctCIqnoJGSdlKKTkg0Ssk5C0UjK4XhC1k5slcnjcMyQtVm1k4lpLbHYOoVj1R+jyT0UEpdEbUpkOO5OPG+YXOq3ojYlpsMICB/4YoF/dXhBveM6RviNWlcS7U3c14SOH/h4gdvyEObyxFIKWp4nik91hdh6ISQhNcKIL/6y6gU+Vdek4tYpO3WqrknVM8Ota1HzTGquNXXNkFWk7lnUXQt3BqUpVEnGmCbIDFnDkNRw2/gkZA1D0tBltSHS1Klr9MZ5XVJRpM4qhdJtLOxvzFlScw5QtLazKvsbbX977CTq1j0IZAz94qhNiekwgsBGICEW+P8fnl9BEZ0ltiY9W+3O2VKkUNw5vo0st3ZuIQTn5rdw59B9TNgl8trC9qzLQiKrJsmqSZjlAkfbdxvCyw63nt34WJhT+zaWbzeusTF9m1G7HO57NpZnz0i0QbhwwJDUkwSYIWvoktIQZuqUaDMa5xOyhiapoYBr7E/+rCrJSIvI87awvzFnyfHqTUhCpT/1mqhNiRTTuh9d24rUYWGUmOgJghqiwzw+zSYIfFy/hiylozblJKbEltTehQmaFOau2b6FIbf+3/6invO4Y+g+Hhh7lNcNvrLl83UrmqRM5YHNB8d3MT0nFGWejeU5U2LM9O3wnGdj+k5DoDnUfRvbc6i6dcZ8l7oXHtd9e1YV+HVJRZMVDEnDkFU0SUWXVXSp8Zkck5QT442tJqlojfHp12iSiirkjksDisVWA9evMlK7i97EFYu2NQ+A6x3DcQ+QyizeXpAxL4zvV5FEZ4mQZuMGVQCUDvse8AIHhEBq89e2JoWrMp02FDYF6NHynJXbyP2jj3Jl/6UYbS5wuthQJQVVUsjM1rV2GoIgwA28KfF2slBzsCcFm+9geU64bZyzfCcUbJ7FhF0NjxvX2bNshC4gFGOy0hCloRhTG/uTQlWVlNPsh143TVJQxfOvCc+F16iz8DLHYqvBcO3neIHFYGpxF/C07EcA0LULI7YkphPxg9KC93i6fhmg4166PN9GRmn7G/uk2LLbJLYArlryMnYUd3LX8ANcPRiviO4WhBBTAqUZ4m0SP/CxfbchyNwpkTYpxGzfmXa+Idx8NxzzHOzAxfbC66quyXjjZ5zGNbbv4rW4PVMstgjV+FD1ZjLaRlLa2qjNiRTLfgJZ6kWRV770xTGLDt+fQJLyUZvRUlyvBIDSYStxvcBGkdpf+0uXwoem5dfbNufyxCBb81v4xfADbCtspVcvtG3umM5DEtJUQn+r1odMCrrJj+O7uIGH7TnYgYfTGJs85zTGvjTD+8diCyjZ26m7R1lfeEvUpkRKEARY9hPo2vkdF++O6Qw8bxRVia66dztw/AkAVDkXsSUn4wY2cgSFZHU5FFum1z6xBXDt0lexs7SH7x76Mb+z7p2LKpk6pv2cJOhacf9m3EQI8RUhxJAQYvu0sR4hxK1CiN2Nbce+mgxVb0GR0vQmLovalEjxvCN4/gS6dk7UpsR0IEHg4PvjyFJ/1Ka0lCmx1WEePC+wUCKoaj/p2TK99jYgz6lZ3rD8avZVD3DLsTvbOndMTLNp1qvC14BrThn7E+C2IAg2ALc1jjsOx5tgzHyQ/uQrO64XWruxnWcA0NQtEVsS04l43hABAbK8JGpTWortjSOQUKUO82z5VttXIgIYchKBwPTbK7YALiicw0U953Hn8H08OPpY2+ePiWkWTRFbQRDcBYydMvxG4OuN/a8Dv9aMuZrNcO0OgsBjSXJxl3sAsN2dCKGjyKujNiWmA3G9IwAo8rKILWkttjeGKucRHRa2ciPybIXhlSQ1t9L2uQHesOx1bMys5/uHf8p9o49EYkNMzHxp5bfJQBAERxv7x4CBFs41J4IgYLh2GxltEwl1RdTmRI7j7EFV1nfcQyamM3C9QwAoysL+f8X2RtHkzst6cH0TVYqmDEJSTlPzypHMrUgy7179ZjZl1/PDwzdzw+GbcWdZCiAmJmra8lQNwipnp610JoT4gBDiYSHEw8PDw+0wZ4qy/TR19yhLUq9u67ydSBAEOO5etAWe/Bwzdxx3P5KURRKdlcvUbEKx1Re1Gc8j9GxFI7ZSSoaaG43YAlAkhXevfgsv67uY+0cf4Z+e/TqHakdf+gdjYjqEVoqt40KIpQCN7dDpLgqC4ItBEFwYBMGF/f3tTbwdrv0cWRj0GIs7MR7A90fxgxqKEocQY06P4+5DVdYs6JWqQRBgeyPocuctAnB8K5LSDwApJUvFLUYy9ySSkLhu2Wt495rrKbtVvvDs1/jOwR8zZk9EaldMzExoZemHHwK/CfxVY3tDC+eaNZ5vMla/j97E5cgRueY7CWcqRBTX14p5PkHg4bj7SCUWdtFf1y/iBRZaR4qtOkpE31UZJU/VLeEHHpKItiHxluwG1p65ktuP3839o4/y2MSTnJPbxCW9F7AmuXJBvwzEdC9NEVtCiH8HXgn0CSEOAf+LUGR9Swjx28B+4K3NmKtZjJkP4AUmfclXRm1KR+AtkuTnmLnhuvsJAgtN3Ri1KS3F8kIHvNFhKy79wMMPHFTRvKrcsyGr9uATUHaL5NSeSGyYTkI2eP2y13BF/8X8YvhBHh57gicmnqJHK3BObhNbshtZkVwa1+aK6RiaIraCIHjHC5zq2GSokdodGMoAGW1z1KZ0BK43hEBCljovVyUmemz3aQA05cyILWktpnscAF0ZjNiSk3Ea1dtVKRqxNSmwivZoR4itSXJqluuWvYarB17Bk6VneGx8O3cN38+dw/eRkBOsS61iTWrBDnx4AAAgAElEQVQlK5PLWJYYQJVaVH48JuYlWJQV5G1vlJK1neWZt8Qu5waeN4Ik9yAiDhHEdCaWvR1ZyiMvcM+n6YZJ14bSWYun3cAEiGw1Yl4LX8LG7CFWpTZEYsOLocka2wpb2VbYSs2ts6uyl93lfeyrHmBHaScAAkGf3sug0c8So48+vYc+rUCPViAhG/GzIKalLEqxNVK7m4CA3uTLozalY/D9MWSpc95YYzqHIAiwnCfRtK0L/oFkekfR5b6OK3ActWcrJWfRpQRj9mnXOXUUSSXBefmzOC9/FgAlp8zB2hGO1I9z1DzO4fpRniw+w/QF8pqkkVOz5NQMWTVDVk2TVlKklRQpJUlaTpJSkiSVBHL8QhozBxal2Bqt30NaW09CWdhv6bPBD4pIUufVFoqJHs87jOcNoyffHrUpLcd0j2AoS6M243lMii0lopwtIQR9+iAjVveVW8iqGc7KnclZuRMhcMd3GLUnGLPGGbMnGHeKFO0SRbfMUGWEilvFD/zT3k+TNJJygoRsYMgGCVlvbA10WcOQdAxZR5/aalPHuqyhS1qcS7YIWXRiq+4cpursZXXuvVGb0lH4fhVFXhW1GTEdiGmHVbsN7YKILWktQRBQdw7Tn7wqalOeh91olROVZwtgibGcJycewAu8rvfuqJLKoNHPoHH6Vad+4FPz6lTcGlW3RtWtUvPqVN06dc+k5tUxPZOaZzJqj1P3TEzPwvbtGc+vS6Hw0hoCTZPCJsi6pKM1RNmkUNNO2Z8Ucbqko0jd/W+xWFh0Ymu0fg8CseibTp9KENQREb01x3Q2pvUgirwcZYF7gm1vBC8wO7KbRNRhRIBBYxWPBXczYh1lwOi831EzkYQ0FUacDX7gY/k2lmdhehamb2P5FpZnNcZtTN+ausbybezGeMktM2LZ4TnfxvGdGc0pCxld1jEa4uuEINPQZQOjIc4MSUefFGmNY2PaVpEWnRxoK4vutztm3kdG24Qm90ZtSkcRBBaiw/JUYqLH92tYzhOkEr8atSktp+6GteYSHdiOqBPE1jJjDQCH6/sWvNiaK5KQSDRCivPFD3xs38b0JgXbpBA7ed+cJuQmj0tumWHrxLVu8NLtjRShhGFQ2TghxBrhzzBkqp80fmJ/8pwRe9lehEUlturOYWrOQdbk3he1KR1HgIdYXH8OMTPAtB8kCBwS+uVRm9Jyas5+AJJq53VRmBRbmpSMzIa0mqOg9XGwtpsLCvHiolYTNgAP88Lmi+u7oUdtmiALRdqkB+7E2PT9sluZ2p9JiFSRFAwpFF+JKUFmTAm0xDQhpzf2T+S8hR65hZrPtqiermPmfQD0JC6N2JKYmO6gbt6FLBXQ1LOiNqXl1Jzn0OQeFCkdtSnPw/HryJIWefX2NalNPDlxP7ZvoUXUOihm9iiSQlpSZh0Wnc5kiNT0rKkctVDAmdSnhJo5Jc7qnkndtxh3SpiN61/awyamctOmvGaneNMmvWynC4UaHSzYFpfYqj9ARjsTTY5LHDwfAZx+9U3M4sT3K5j2Q6QS1yI68Mur2dTc/aTUNVGbcVocvxZZ9fjprEudxWPjd7Ov8jRnZs+L2pyYNjI9RFogN6d7uL47zXsWCrD6tP3J8SnxNhUSHWmMmQTTSna8ENp0wSadWCU6lds2lcOmTa0SnX5+8uebKdoWjdiy3CGqzj5WZd8VtSkdiRAaATNLyIxZHNStuwgCm6TxqqhNaTmeb1F3DlMwLo7alNPiBPVIQ4iTLEusIa3keKb8aCy2YmbNlIeNuXnYgiDACRqCzTNPCnmeGhINFyOEIq7m1hn3i+HCBd+a8eKDMCx66mpQFX3aCtEZ/7fP6b+4Cxk3HwKgkOjML9OoEcIgaFSpjokBqNZvQVVWoyoLux8ihF6tAJ+Uuj5qU06L7dciTY6fRBISZ+Uu4sHR2yg6o+TUeKFRTPsQQqAJFU1SyapzD/f7gX9iYUEjNGpNy2mb2k5beDC5X3arjNjj2I1FCjNlEYmth0koy+NCpi+AJNL4fjlqM2I6BMfdh+08TS7zgQVfNR6gaj8LQFrrTLHl+HX0DsklOzt3MQ+P/ZxHxu7iVQO/HrU5MTGzRhISSSVBkvm/wPwFH53ZnPOeqQvw/Bpl+ykKxoVRm9KxSFIWzy9GbUZMh1Cp3YgQGinjtVGb0hYqzrNoch61Q1tWOb7ZEZ4tgLSSY0v2Qp4qPUTRGY3anJiYrmBRiK2i9Uv8wCNvLOwK2PNBlnrw/fGozYjpAHy/TM38GUnjKiQpG7U5baFq7yalbuhYL57j11E6RGwBXNzzaiQk7hq6kSB46YTlmJjFzqIQWxPmoyhSkoy2KWpTOhZZ7sfzhwleoB9YzOKhWr+JILBIJd4YtSltwfFK1N2jZLTOzU1z/DpaB4mttJrjkt7Xsrf6NM+UH4vanJiYjmfBi60gCJiwHiern4Po8n5erUSRBwkCF88fjtqUmAgJAptK7XsY2vloHZos3mwq9k4A/i979x0n11XY/f9zbr/TZ7tWvdhyxQXTDARsMDZgSoDQ0iAkgVACKQSeXyA8JiQYSAJ5wg+ekPwoIRBCJwSC6WBs3LDBVbJ6WUnbZnf67ef3x4zWki1bki3tnZ09b7/GszN7d/XdMrPfOffcc3M9WrYSGZPIEEM89sUtT6WLyk9n3F3Hj6a+tiRPUK0oi6nvy1Y72k8QVyjaF6QdpacZ+moAomhfykmUNDXb1xEnc+Syr0w7yqKpB1vQhE7OOiPtKMfUC6fqORZNaDx3xauxNJtvTHyKalhJO5Ki9Ky+L1s1/04AirZaE+aRmMY6oHMUmrI8SRlQb30ByzwH21w+L07qwRay5ia0Hj03aNRdksXowRXbc0aRF618HWES8JV9/5eKP5l2JEXpSX1ftqr+XTjGKI4xknaUnqZpBXR9mDDalnYUJSXN9reI4xkKud/p2Ynip1qceDTC7RTsc9KO8rCixAfoud2Ihw3bK3jJqj8gljH/ue//ZXv9rrQjKUrP6euyJWVCPbiPgnVe2lGWBMvYTBBuTTuGkoIkaVJv/ge2dSGOdVHacRZNPdiClDF5q3fLVpj07sjWYSPOSl6x5s0MWCN86+C/c93BL9CM1Lp9inJYX5etVriHKGmS7+FXrb3Ess4hig8RxzNpR1EWWb31BeKkSjH3urSjLKqafxea0MlbZ6cd5WHFsrNKtSF6t2wBFMwyL1v9Bp40+Gy2Ne7k33Z/iJ/PXEc7bqYdTVFS19cryNeDewEo9PCr1l5yeJ6OH/yKjPuslNMoiyWKDtBofY2M82wsszePyDtdqv5d5KzN6Fpv7qKDB8qW3qNzyo6kC4MnD17B5vyF/HzmOm6p/JDb537KmfkLObvweMbddaf05L6KslT0ednagq0PYRvDaUdZEkxjA7pWwgtuUWVrmZBSMt/4OAKDYu61acdZVGFcoxXuYlXhFWlHeUTRQtkyU05y4srWMM8b/y1m/Ul+NX8DW+u/5N7abeSMAuuzZ7MmcwYrMxtw9Ud3QmJFWWr6vGxt7endA71GCA3HfiJt7wakjBCir389FMDzb8Dzb6GY/0N0fSjtOIuq6t+JRFK0H5d2lEeUyAhYWmXrsEF7lMtHX8LTh5/PzsZ9bG/cxdb6L7mrejMAA9YwI84qhu2VDFqjDFgjZI2CGv1S+k7f/jUN4lmCuNLTq0L3Ise+lGb7u/jBHTj2E9KOo5xGSVJnvv5RTGMjOffFacdZdPP+7Zhanqy5Ke0oj+hw2dKW8IsfU7PZXLiQzYULiWXMpLeXidYuDnp72dfazpbaA6vQG8KgYA5QMMvkjCJZo0BWz+PqWVw9h6NncHQXW3PRhbFsjpxVlral++g9jkbQWcKgVxcq7FWO9Xg0LUfL+5EqW31uvv5xkqTKYOmvl93ZFaRMqHp3UHQuRPT4KMoDZas/fka60Bl31zPurl+4rxU1qASTzAXTzIezVMNZGtE8U94E7biJ5NjnX9SFjqXZmJrduRY2pmZiCBNDszrXwkDv3qcLA0MYaELv3tbRhfHAtdZ5vy4MtKO2Nbofa6IJXY28KSetb8tWM9yJEDoZc13aUZYUISxc+9doeT8gSd6Epqk5Ff2o7d1Ay/sBheyrsczl94KkEW4jTOqU7MenHeW4JJ3zlWr0R9k6loyRI2PkWJV56CmiYhnTjhq0kybtqImXtPDjNl7Sxo/bBIlPmPiEMuhcJyFt2SSSIWESEsuQKAmJZUTyMKXtZB0uZ51S1y10olPoHlz2zAddW5qNoVmYmtUtiBaW5izctjS7b4q18oA+Llu7yBire3ZV6F6Wda+i2f42Le/75DLL42TEy0kczzBX/zCWuYl89tVpx0nFnHcbAo2S0/tnllgY1Vmmu8t0oZMzi+QowmNc/SKRMZGMiBcu8VFvR0lIctR90YO2795ODt8fEslOkYuScKHgHVn2Ihl03xedcM7DpczWnW4Bc7A0B1tzu/c52Au33YVrp3ttCkvtXu0xfVu2WuEudYqeR8kyN2OZm2m0vkHWfUHP72ZRTpyUMZXatUgZUC68E7EEJ12fCnPtWyjY52BoubSjKItIEzqW0HnMre1RSGRClAQE0idMggcuMiBIPMKkcx0k/sJonZ94BImHH3u0opmF20H3rAIPRxc6tuYuzG9ztAyOnsXWXVw9i6NlcPXOfZ25cBkcPaNG1E6jvixbYVwliOfJmGvSjrJk5TIvpVL9Wzz/RlznaWnHUU6RWvPf8IO7GCi8HdNYnXacVLTDCdrRBKPZq9KOckIE3REKeWp2gSnp0ISGpTtYPPY13RIZEyQ+ftLGj73urlUPv3vtxS28pNW9blOP5pnyD+DHLUIZPuzntTWXjJHF0ToFzDVyuHqWjJ7D0bNkugcpZPQcrpFFX8IHbSy2vvxOtaP9ALjL9I/JqeDaT8fQx6k1P49jX6pGt/pA27uBevMLZN2ryLjPTjtOaireTQAMuE9MOcmJOXzwQkKcchKlV2hC745aZeAkB6ejJMSLW505cHGz83Z89Nte3KQWzTPp76cdN0lkcszP1Sln3fKlZ8kYnaNGs3oe18h1jyLtzMezevh0U4uhT8vWBACuqcrWoyWERiH7W1RqH6TtX0/GeUbakZTHIAx3Mlf7IJa5mVL+TWnHSdVs+0by1mYsfTDtKCdE7z5NJycx50dRHo6hmeS07hy4EyClxE882nGDdtygFXcOVGgdvh3VacUNKsEU+9s78OL2MT+PqVlk9BwZPU/mcBEzcmT1wsLtjJEno+cwtP6b3tCXZcuLDqAJC0sbSDvKkuY6l2G2vkSt8Ulc+ykIdbDBkhTHs8xW34MQWQaLf7Wsf47tcIJWuIe1xdekHeWE6Vrn53X4tD2KspiEEJ15X7pLmeOfjSWWcbeENWgdUcZacb17X535YIYD8S7aceuYn8PWXLLG4WKWJ2vkyegPXGeMPNnurs2lsgxHn5atgzjGmNr19RgJoVHMv56ZuXdSb32ZwjI9cm0pS5IWs9W/IklqDJX/btmtEv9gs+0bEAgG3UvTjnLCDNGZ4xMmXspJFOX4dKGTM4rkjOOPnB1e1qMZ144qZ824vnA95e2nFTeOeVCAhuiOhnWLmJFfGCF7YKSs8z5TS/dFZl+WLT+ewtbH0o7RFxzrIlz76dSb/0HG/jUMY1XakZQTJGVApfpewnAng6VrluV6WkeSUjLbvp68fQ6WvnRGvS0tA0CQHHsUQFGWqoVlPczjF7Mg8WlGtYXRsWZ3xKwZ1WjFdRpRrbsIbuOY66lZmv2QEbKs0ZlTljUKZPRc93b2tByV2XdlS0qJH01TsM9PO0rfKOX/iMnKHczVPsxQ+UNqxHAJkDKiUn0/XnAHA4W349hLYzL46dQMt9OODrIit7ROTWTpneUp/LiechJFSY+l2VjWMGXrkXdlJjLBi5s0DxeyI0bKDpe0af8Azah+zNEygcDVMwujYkfOJ3O7hSzTPSLTOYkTqfdd2Upkm1h6WNrSmPy6FOj6IKXcH1GpfYhG64vks69MO5LyCKSMqNQ+QNu/kVL+Tcv6yMMjTbd+jCZMBtwnpx3lpLh651W/F1dTTqIovU8TWqcoGXmGj3MAZJgEC3PJFnZdRnXaCyNmDebbM7Si+jEXpdU48YVj+65sBfEcAJZeTjlJf3GdZ5EJbqHW+AyWeR62dV7akZRjkDKkUr2Wtv8zirk/IJd5YdqRekIiA2bbNzDgPAljiZ2CyhAOhubQiitpR1GUvmJqFkVtkKL5yIMzUkqCxOvutqx3j8rsvA0fOKF/q+/KVpjMA2DqpZST9BchBKX8WwnCbVSq72Nk4KPLfrJ1r0mkR6X6Pjz/Vkr515PLvCTtSD1jrn0rUdJgOHt52lFOmhCCnDFEI5xKO4qiLEtCiM5pkXT3uLsxH07fTb6JkgYAhsinnKT/aFqWwdJ7kLLNbPUaEqmOjuoVSVJjZu6d+P5tlAtvVUXrQaZa38fWhyks0RHZvDlGLTyYdgxFUR6lPixbTQD0JbarYKkwjXWUi+8kDLdRqf4tUqpVrdMWRRNMVd5GGO1goPgusu7z0o7UU7zoIFX/Lkayz1qyB3eUrNW0ogp+3Eg7iqIoj8LSfOZ5BInsrF6ra27KSfqXaz+FYv7NeP7NzNX+Dvkwp3JQTj8/+CVTc28lkXWGSteq81gew1Tzewg0hjNLbxfiYQP2egAq/q6UkyiK8mj03ZytpLvKsi6W93mYTrdc5moSWafW+DSgUy786ZIdNViKpJQ021+jWv8XDGMVg8VrMIzxtGP1nEQGTLV+yID7xCW1ttaDDVrr0YTBlLeFFRm1rI2iLDV9WLY6ZzQX/fel9ZxC9lUgY2rNzwI+5cLbl/WpYBZLkrSYq3+YtvdTXPtSyoW3o3UXvlSONtO6nihpMJp9btpRHhNdsxh2zuBA+y4eJ1+GECd+yLmiKOnrw6GIzsqxapRlcRRyv0Ux9/u0vJ8yM/9ukkTNKTmdgnALU5U34nk/o5h7HQPFd6ui9TCklBxqfouMuZa8dU7acR6zVZnH0wgnmQv2pB1FUZST1LeNRMqHLtevnB757G8wUHg7QXg303NvI4r2px2p70gZUWt8lunKnwAxQ+W/I599uXpR8QhqwV20wr2MZZ/fFyNBq7KPRxcmOxvXpx1FUZST1HfP1KJ7TiOJOkpuMWXcZzNU+lvipMpU5Y9pezemHalvBOF2pit/TK3577jOZYwMfBzbOjftWD3vYOObmFqRoUx/HDRgaRnW5p7MnsZNtKK5tOMoinIS+q9sdedqye7cLWXx2NYFjAz8E4axktnqNczXP4aUDz33lHJikqRFtf4JpitvIU4qDBb/ioHiX6BpubSj9bxWuId57w7Gcs9D66N5hGcVrwLg7vmvp5xEUZST0XdlS+/OX4nVgpupMPQxhst/Ty7z6zRa32Cq8haCcGvasZYUKSUt74dMzv4+9dZXyLhXMjr4L7jOU9OOtmQcqH8NXTiMZq9MO8oplTWGOLPwbPY0buJg++604yiKcoL6rmwZorOYadxd3FRZfEJYlPJvYKj0NySyyXTlbczX/y9J0ko7Ws/zg7uYnnsbleoH0PUyIwMfoVx4G5qmzohworzoILPtGxnNXonRh6OA5xSfT8Fawa0zn6IZzaQdR1GUE9B/ZUvv/FEKk2rKSRTHvoTRgU+Qca+i0foak7O/R6v9fbUI6jEE4VZm5t/F9NyfE8fTlAt/ynD5n7DMs9OOtuRM1L+KEDpjuavTjnJa6JrFpcNvQCL56eRHaEXqBNWK0uv6rmyZWucE1GE8n3ISBTrnUywX3srIwD+i68NUah9iuvJmPP9WdcQo4Af3MDP/LqYqf0wQbqGYex2jQ58k616pjjR8FLzoEDOtnzCSfQ6WXk47zmmTN8d42shb8OM6Pzz0QSr+7rQjKYryCPru2dzSBwHw4+mUkyhHssyzGC7/IwPFd5DIZncU509o+zctu5EuKSNa3k+ZqvwJ03N/ShBupZB7DWOD/0Y++3I04aQdccmaqH8JIXTGcy9OO8ppN2iv57Kxv0Ag+OGhD3DP/DeJkyDtWIqiHEPfLbNuaFkMLYcfT6UdRXkQITQyzuW49tNped+l3vxPZuffg2msJZd5Ea5zOZro33NaRvEkrfZ1NNvfIU5mMfQVlPJvIuM+RxWsU6AV7mOmdT1juef39ajWkYrWSq5Y8S7uqHyBe+f/m12NGzircCVrc0/B1NTvlKL0ir4rWwCuMU47OpB2DOVhCGGSdZ9PxrmStvcT6q2vMFf7P1Tr/0rGeRYZ9wpM48y+WIgySZq0/RtoeT8gCH4FgG1fQsl9C471JLWr8BTaX/sPNGExnvv1tKMsKkvP8qTh17E+/zTunvs6d1S+wF3zX2dl5iJWZS5i2Nm85IqXlAmh9IgSjzDxiKVPJAOixCOSAbEMiJPggbdlSCIjYhmQyHjhtiQmkTEJMVLGJCQgJZIEybGnMQhE9/8CIXQEGprQOxeMB94WFjo6umahi87FENbCbVM4GJqNoTmYwsXUXAzNQRd9+WdXOY6+/Km7xirmvM6coH74g92vhDDIuM/CdS4nCO+h2f4WTe86Gu1vYhiryNjPxHWehqGvW1I/xziZw/Nvoe3/DD+4AylDDH0F+exvknGvwNDH0o7Yd+r+FireLawqvAJTL6QdJxUjzmYuG/sLZv2d7Gr8jInWHexp/BwhNErWagat9RSslRTMMbLGEI5eROsuAn2qPLgkhUmbULa7t9sPXOQDt6PEI5Tthe0j6Z307lBNGOjCQBMWmtDRhdktRzqie60JHR0ToQlEdwbNg1/sHJ7SIOkWMpmQEBEnQbe0RSSyU9w6JS/qFrsTX9dREyaW5mJpWUzNxdJzWFoGS8ti6zksLYet5bD1HLaWx9bzWFpGvTBb4vqybGXMdUy1fkiYVBbmcCm9SwiBbZ2HbZ1HkryJtv8TWt6PqDc/R6357xj6GI79RGzrYmzzcWhaNu3IR0mkRxBuwQ9+iR/8giC8HwBDHyHrXk3GeQamcdaSKoxLiZSSPbXPYOkDrMi+IO04qRJCMORsZMjZyMXyN5nxtjHlbWHW38Hu5k1Ede+IbbXOH3Y9uzDyonfLiiZ0BIfPxtEZBUpkTCIjEhl2S0ZnVCmSPlESnHhJEqI76uNgai6mcLC1HDljuDP6IxxMrfN+Q9hHXNud6+7bmjDRhYkhrNSLiJTJwvckkl73++F3R+KOKJ4LZbNNEDcJkzbtqEI12U+QNImSYy8CLYSGreVx9EL3UsTVi51ro4Sjl3D1Eo5eOOUFWjk1+rJsZa1NADSCbQy4qmwtJZqWI+s+n6z7fOK4ghf8nLZ/M832dTRa/4VAwzQ3YJnnYhmbMc0zMfSVi/ZkK2VMFO8nDLcTRPcThFsIo+1IGSHQsMyzKeR+F8d6IqaxURWsRTDb/hmNYBsbSm9EX2K7y04nXRiMumcz6naWD5EyoRVXqIdTNKMZ2vE8XlwjiBuESRs/aXRHaQ7vcosf2KUmRHd0yOiOIlmYmosjit0SZB1RjB4oS50y1SlynUunOKVdjk41IbTO9wALm0e/tlssQ/y4QZA08OMGflLHj+t4ce2oSzWcwItrDzm4SAgNRy/g6iUyxgCuXiZjDJDRB8gYg2SNQSwtq56XUtCfZctcjyZM6sEWBtwnpx1HeZR0fWCheEkZEIT34ge/wg/vodn+Dg35DaCziKqpr8YwVmHoK9H1MXR9BF0bQNfKCJE74Sd3KWMSWSOJ54iTWeJkiiieJIoOEMUTRPF+pAy6/66NZZ5BLvMSbPM8LPN8tO4ZDJTFESdt9tY+S87cwHDmmWnH6WlCaGSNIbLGUNpRlIehC5OMUSbD8Q/wkDLBT+q04yrtaJ52PE87mqMdz9OKK1SDCQ7Gdz9ktNHQbDLGwMLvwuFLzhgmawxhaPbp+vKWtb4sW5owyVmbqfp3pR1FOUWEsLCtC7GtC4HDI0x7CcLthNEOomgfQbiVtnc9kge92kNDaBmEcBFYCGECOiCBGClDpPSRskUi2w/9t9HR9TEMYyWOdTGmsR7T3Iihr1k48bmSjon6VwjiCmcM/FnfjZYoyiPpjGJ1diWWrTXH3EZKSZA0acUVWtEszWiWVlShGc3QimaZ8bYRJkef2s7RC+TMEXLGCDlzmJwxQt4cJWsML7kDLXpJX5YtgJJ9AXtrnyOIK1j6QNpxlFNMCL1Teoz1wBUL90sZEsfTxMk0cVIhSeZJkhqJbCJlu1uqIiAGBKAjhIEQNkJk0EQWTSuiaSV0bRBdH0bXBlWp6kHtcD+Hmt9kOPNM8tbmtOMoSs8RQnQm2uu5Yxayw2WsGc3QiKZpRtM0ws71ofY9eI2jz8TiGiVyxih5c5SCOUa+e8noZfVi5zj6t2w5F7O39jnmvNsYzT4n7TjKIhHCxDDGMRhPO4pyGkmZsKv6CTThsqbwW2nHUZQl6cgyNmCve8j7w8SjGU1TD6doRJPUw85lX/M2wiPOdatrFnljlII1TsEco2COUzBXkDOGVQnr6tuy5RprcIwxKu2bVNlSlD4z3fohNf9eNpTegKmX0o6jKH3J1BxK1mpK1uqj7pdS4id16uEhauEh6t3LtHc/exs3L2ynCZOCOUrBWknRHKdorqRorcTVy8tukn7fli0hBIPupRyof50gnls2K0orSr8L4ln21D5DwT6X4cyz0o6jKMuOEGJhGYph58yj3hcmHvXwILXwINXwALXgwENKmKm5FK2VFM1VFK3x7vXKvp4T1rdlC2DIfQYT9a8y0/oJ4/n+P1eaovQ7KSU75/8ZKWM2lN6w7F4dK0qvMzWHAXs9A/b6o+4Pkha14ADVcIJqMMF8uJ+9zZsID6/9JgQ5Y5iStaozmmZ2RtQcvdgXj/O+LluuuZK8dRZTre+zIvdCte9YUZa46dYPmfduZ13xtTjGirTjKIpygiwtw5CziXnbb8AAACAASURBVCFn08J9UsruMhX7mQ/2MR/sZy7Yy/7m7Qvb2HqBcndXZtlaQ8laQ9YYWnIFrK/LFsBY9rlsm/sw8/7tlJ1L0o6jKMqj5EUH2VP9FEX7PEazz007jqIoj5EQgmx3sdXxzAUL94dJm/luAZsL9jIf7GOydt/CIq6Wnu2Wr7WUrbUM2GvJ6IM9XcD6vmyV3Sdh1wY5WP+GKluKskQlMmT73EcQQmdD+c1qlFpR+pipuQw7ZzDsnLFwXyxDqsEEc8HezsXfw7ba90lkDHQK2IC1rlu+1jFgr8PRi2l9CQ/R92VLEwZjuReyp/opav49FOxz046kKMpJ2l/7Ao1gB2cM/Bm2rlZAV5TlRhfmQok67IECtoc5fw+VYA+Tte8sjIC5RpkBax0D9noG7fWUrbWprZDf92ULYDR7BQcbX2df7fOcM/S+nh5qVBTlaHPeLzjQ+Aaj2SsYdJ+SdhxFUXrEUQUs37kvSgLmg71Ugt1U/F1U/N1MtO4AOqvuF83xbvnawIC9gbwxsigj5cuibGnCYmX+N9g1/wnmvFsYcJ+UdiRFUU6AF02yY+6fyJrrWFt8bdpxFEXpcYZmPWQivhfXmfN3MxvsouLvYl/zNnbWrwce2P04aG/sFrD1p2UJimVRtgBGMs9isvk/7Kl9hpJzEZqw0o6kKMojiBOfbZUPAZIzBt6uHrOKojwqjp5nReZ8VmTOBzpnoKiFh6gEu5j1dzLr7+BQ9V6QcmH0a9DexJCzkUF7Ixl94DHvEVs2ZUsInbXF3+O+mWuYqH+Z1YVXpx1JUZSH0VlP62O0wj1sHvx/cIzRtCMpitInhNA6i6la46zPPRXorANW8Xcx6+9gxt/BnuZN7Kj/GOjM/RqyNzJkd0bMiubKk971uGzKFkDRPp/hzDM40PgGA+5TyJrrj/9BiqIsuon6l5ht38Cawm9Rci5KO46iKH3O0jKMuecy5nYOopMyYT7cz6y3gxl/OzP+DvY1bwM6C7cO2hsZOuJoyeNZVmULYE3xNVT9X7Fj7v9w3vAH1K4JRekxM63r2V//IsOZZ7Ai96K04yiKsgwJoVG21lC21rCJy7oLsM4y423vlC9vO3fPff2EP9+yK1umlmdD6Y1smf1b9lY/y7rS69KOpChKV9W/i53zH6Vgn8P60uvVkcOKovSEzgKsQ2RzQ6zNPRnoTLyHT5zQxy/LlQFLzsWsyF3Noeb/MNu+Me04iqIAzWAX989+AMcY58yBv1Cjzoqi9DRHz5/wtsuybAGsLvwmeetMds59jFa4N+04irKstcMJtsz+NYaW5azBd2FoubQjKYqinDLLtmxpwuSMgT9H11y2Vq4ljOfTjqQoy5IXTXLf7DWA4Kyh92Dpg2lHUhRFOaWWbdkCsPQBzhx4B2E8z9bK+4kTL+1IirKseNEU9828h0QGnD30V7jGeNqRFEVRTrllXbYActYmzij/SWe+SOWDJDJIO5KiLAtedJD7Zt5NLD3OHnwPGXNt2pEURVFOi2VftgDK7hPYUP4jqv6dbKv8A4kM046kKH2tFe7j3pm/6o5ovYespda8UxSlf6my1TWcuYx1xdcx593GtsrfqxEuRTlN6sH93DvzbgDOHnqvWlxYUZS+p8rWEcZyz2V96feZ825j6+y1xEk77UiK0lfmvNvYMnMNhpbjnKH3kTFXpx1JURTltFNl60FGs1exsfwmav7d3Dd7jTpKUVFOkcnmddw/+0FcYyXnDr1Pne9QUZRlQ5WtYxjOXMYZA39OK9zDPTN/STucSDuSoixZUsbsrn6KXfP/Qsm5iLOHrsHUS2nHUhRFWTSqbD2MAfeJnD10DXHicc/M/2LeuyPtSIqy5IRJnS2zf8OhxrdYkbuaMwfega65acdSFEVZVKpsPYK8dSbnDb8fWx9h6+zfMlH/KlImacdSlCWhGezk7ul3UA/uZUPpjawtvgYh1FOOoijLj3rmOw7bGOGcofcx4F7Kvtrnub9yLWFSTzuWovQsKSWTze9yz8xfImXEOUN/zUj28rRjKYqipEaVrROgaw6bym9jXfF1VP07uWvqz6j6d6cdS1F6TpQ02T73EXbNf4KCfS7nD/8dOeuMtGMpiqKkykg7wFIhhGAs91zy1ma2z32YLTPXMJa7mtWFV6EJK+14ipK6mn8PO+Y+ShDPsqbwm6zIvUjtNlQWTSID4qRFLNvEiUcs2yTSJ5EBiQyRhEgZIUmQMkYiFz5WAKAhhI7AQAgdTZhomGiajSYc9MMXLYMuMup3WzkpqmydpKy1gfOGP8Te2mc42Pgm894dbCy/kZx1ZtrRFCUViQzYX/sCBxvfxDZGOXf4ferxoJwScdLCj2cJ4lnCZI4gniNM5gnjKmFSJUpqREmDKGks+kLUuuZiaHlMkcPQCxhaAVMrYGolTL2MpZextAEsfVAdFKKosvVo6JrD+tLrKTtPZOf8x7ln+i8ZzT2P1flXqgeVsqzUg63snPsY7WiC0ewVrCn8jnoMKCdMyoQgnsWLD+JFB/GiQ/jxFH40iR9PEyXNh3yMrrlYWglDK2Dro2TNjRhaDkPLoYtMd+TJQddcNGGjYaEJEyFMNGEAGgL9qJEpiQSZdEe9QiQxiQy7o2Kd0bFYesRJm1i2iJMWkWx0i16dKKnRjg4QxVVi6T8ks6FlsfQhbH0Y2xjB1kdxjFEcfQW2MYImzNP5bVZ6gCpbj0HJuYgLRj7C3trnmGx8m0r756wtvpYB58kIIdKOpyinTZy02Vf7PJPN72DpA5w1+C5KzoVpx1J6lJSSIJ6hFe2hFe6lHe2jHe6jHR04akRKEya2PoptjJCzNmPrw1j6EJY+sHDp9WkbcdImSOYI4zmCeJYgrhDEM/jxNH48Sc2/m1h6C9sLNGxjGMdYiWusxDVWkzFX4Rqr1QuXPiKklMffapFccskl8rbbbks7xqNSD7aye/5faIa7Kdrns7b4WjLmmrRjKcopJaWk4t3EnuqnCOM5RrNXsrrwm+qPgrJASokfT9IIttMMd9AMd9EKdxMljYVtbH0Q11yDa6zEMcZxjHFcYwWmVu77uVBSSqKkhhcfwosOdUf0DtCOJvCiAyQyXNjWNkbImuvJGGvJmuvJWhswtQH1Yr6HCCF+IaW85LjbqbJ16kgZM9m8jv31/yRO2oxkn82q/MvVatlKX2iF+9hT/SRV/y6y5jrWl/5Qzc1SiBOPRridRrCFerCVZrB9YXkcTZhkzDVkzQ1kzHVkjLVkzDXoWibl1L1JygQ/nqQV7qMd7aUV7qUV7sKLDi1M6Lf0EllzEzlrEznrzO5u1GzKyZcvVbZSFMY1JupfZLL1PTRMVuReyIrc1eoJRlmSFn6fm99F11xW5V/JaPbKvh+BUI4tTtrUgy3U/LupBffSDHciZQxAxlxNzjyDrLWJnHUGrrG6O09KeSzipE0r3E0z3Ekj3EEz2EE76pxGTiBwzVXkrbM7F/tsbH0o5cTLhypbPaAdHWBf7XNU2jdjanlW5F7MaPZKdM1JO5qiHFec+Ew2/4cDja8SJ153pPaVmHoh7WjKIpIyoRFup+r9kqp/J41wG1LGaEIna26iYJ9D3jqbnHUmhpZLO+6yESVNmsF26sFWGsFW6sHWhblgtjFCwTqXgn0eRftxWHo55bT9S5WtHtIItrGv9h9U/TsxtSIrci9kNPscNc9F6UmJDJlu/YiJ+pcJ4gpl52JWF36bjLk67WjKIomSBvPe7Z2L/0uipIFAkLU2ULDOp2ifT846C12z046qdEmZ0Ar3UAvupR7cS82/Z2GeXMZcTdG+gKJ9AQX73J4/yGApUWWrB9X9Leyvf5GqfyeGlmMs+zxGs1epkQKlJyQyYqb1EyYaX8GPpshbm1ldeDUF+9y0oymLwI+mqXi3MOfdQt2/D0mCqRUpORdRsi+iYJ+vnquWkE752k3Vv5Oqfyf14D4SGaIJi6J9HiXnEsrO47H0wbSjLmk9U7aEEFcB/wjowL9KKa99uG37vWwd1gjuZ6L+Vea829CExXDmMsZyz8c1xtOOpixDiQyYbv2QA/Vv4MfT5KyNrMq/gqJ9kTrqqc/50RSz7RupeD+nEewAOqMgZecJlJ1LyJqb1Ny8PhEnPvXg3u5o5e140SQAWXMDZfcJDDhPxjVWqcf8SeqJsiWE0IH7gSuA/cCtwKuklPcea/vlUrYOa4X7ONT4JjPtn5LIiJJzMWPZ51K0L1BPcMppFyUNJpvXcajxbcKkSt46k5X5l6mS1efCuEbFu5GZ1vXUg60A5MwNDLiXUnafqF70LQNSSrxogjnvNua8W2kE9yORuMZKBtwnM+g+VS1ddIJ6pWw9BfjfUsoru7f/F4CU8v3H2n65la3DwnieyeZ3mWxeR5hUcYwxRjJXMJy5TA3bK6dcOzrAZOPbTLd+RCx9Ss5FjOdeTN46R5WsPpXIkHnvdqZbP2bevx0pYzLmagbdpzHoPg3HGE07opKiIJ5jzruZ2fZN1P17kSRH/H48HccYSTtiz+qVsvUy4Cop5e93b/828CQp5ZuP2OYPgT8EWLNmzeP37Nlz2vL0ukQGVNo3M9X8LrXgPjShU3aexHDmcor249Rol/KoSZkw79/OZPM65r070ITBoPs0xnJXkzXXpR1POU3a0QGmm99nuvVjwqSGpZcYcn+NwcyvqZ+7ckxhPE/Fu+mokc+CdTZDmWcy6F6qDux6kCVTto60XEe2jqUV7mWq9X1mWj8lShpY+gDDmWcw5D4D11yVdjxliQjiWaZbP2Kq+X38eAZLLzOSuYKR7BXqcPA+lciIOe9WJpvXUfPvRgidsnMJw5nLKNkX0ZndoSjH50dTzLSvZ6b1E9rRAXRhM+Beykj22eTMM9VIOL1TttRuxMcokQFz3q1Mt35C1fslkoSsuYGhzNMYcC9Vi9cpD9H5nfkF060fLfzOFO3zGcleQdl5olpksk+FSZ2p5veYbH6HIK5g60OMZK9gOHO5KtbKYyKlpBFuY7r5A2bbNxBLj4y5mpHMcxjOPGNZL9jdK2XLoDNB/lnABJ0J8q+WUt5zrO1V2XpkQTzHbPsGZtvXLxw5lLc2M+A+hQHnidhqv/qyJWVCPbiP2fbPmG3fSJQ0u6Ohz2Q4czmOMZZ2ROU0aUcHONT4b6ZbPyaRAUX7fMayz6PkPF5NPVBOuThpM9u+ganmd2mEO9GFw3DmmYzmnrcsD67oibLVDfI84CN0ln74pJTybx5uW1W2TpwXHewcst3+Oc1wN9A5oqjkPoGy8wQyxlo1xNvnOit7b6PS/jmz7RsJ4gq6sCm7T2TIfYaa59fnmsFODjS+RqV9E0LoDLpPZ0XuhWrxWWXRNIJtHGr+D5X2jSQyouw8nhW5Fy6rg216pmydDFW2Hp12dIC59i1UvJtpBNsAsPVhSs7FlJyLKFjnqVME9YlERtSDe7s/71sI4gqaMCjaFzLoPpWy8wT1s+5zjeB+9te/xLx3B4aWYTR7JaPZ56ldhUpqHjii/juESY2ctZHx3EsoO0/o+xd8qmwtU0E8x7z3C+a826j5dxFLH00Y5K2zu6dreBwZc13fPwD6SRjPM+//knnvdqr+L4mSFpqwKNkXUnafRNm5BEPLph1TOc0awQ7217/AvHcHppZnLHc1o9mr1M9e6RmdBZJ/zMHGf+FFh8iYqxnPvZRB99K+/ZujypZCIgPqwZbuH+lf0Qr3AWBoOQr2uRSsc8jb53R3OfbnA2EpOvxzq/p3UfV+RTPcCYCllyjaF1F2nkDRvkCdl26ZaIcT7Kt/nkr7Zgwtx3juRYxmr1KH4Cs9S8qY2faNHGh8lVa4D9dYyarCyxlwntJ3f2tU2VIeIojnqPp3UvPvpubfjR9PA2BoWXLWZvLWZvLWWWTNDeqJfBHFiU8z3E7Nv4dacA+N4H4SGSKETt48k6JzIUX7QrLm+r57olIeXhjPs7/+Jaaa30MTFityL2BF7gXL+sgvZWmRMqHi3cRE/Uu0wn1kzfWsLryaon1h38zpUmVLOS4/mqIW3Ec9uI+6v4V2tB8AgYZrriZnbiJrbSRrbiBjrlFnij8FpJT48TTNYBv18H4awRaa4W6kjBEIMua6zqijfT4F6xxVepehRIYcanyLicZXSGTAaOYKVuZfhqmX0o6mKI+KlAkz7evZX/9P/GiKon0+a4q/Q9Zcn3a0x0yVLeWkRUmDRrCNRnA/jXAbjWA7UdIAQAgd11hFxlxL1lyHa6whY67B1Mp98wrlVJMywYsP0Qp30wp30Qx20gx3EiZ1ADRhkbM2dUcVzyJvnaXm3yxz894d7Kl+knZ0kLJzMWsKv4trrkw7lqKcEokMmGx+j4n6l4iTJiPZZ7Mq/0pMvZh2tEdNlS3lMeuMwkzRDHd0ykK4m1a4myCeW9jG0LK4xiocYxzXWIljjOMYK3CM0WUzEpbIED+awosO0I4maEf7aIf7aEX7SWQAdMpqxlhNxlxPzjqDnLkJ11yjFhhVAAjiCnuqn2K2/XNcYwVri79Hybko7ViKclpESYOJ+pc51PwfdOGwuvAqRjLPWZLTJFTZUk6bMK7RivbQDvfRjvZ3LuEEYVI9ajtLH8DWR7CNEWx9CEsfwtaHsfQBTH0AQ+SWxKhYIgOCeJ4wnsWPZ/DjaYJ4Gi86hBdPEkQzSJKF7S29vDAK6BprOiOB5qplUz6VEydlwlTr++ytfRYpI8bzL2E89yL1u6IsC61wH3uq/x9V/25y1kbWl96w5HYtqrKlLLooaeJFB/Cig3jRIfx4qnOJJgniuaMKCYAmDEythKkXMbQiplbA0HIYWh5Dy6KLHIaWQRMOuuaiCRtd2GjCRmB2R4W0RyxsUkokMVKGJERIGRBLnyTxiGWbOGkRyRZx0iRKGkRJnTCpESU1wmSeMJ5f2O13JFPLYxuj2PoojjHWHc3rjO6pXYHKifCiSXbOf4yafw8F+zw2lF6PY6xIO5aiLCopJbPtn7Gn+mmipM54/sWszL9sybzgUGVL6SlSxgRxhSCeJUhmCeI5wniuU2iSKmFcJUpqREmDWPon9bmF0BFogEAgkEhAIkmQMj6pz2VoGQytgKkVOxe9hKmVsPTB7kjdMJY+pBYOVR41KSVTre+xt/pvIARrC7/LcOZZS2KUV1FOlyhpsKf6aaZbPyZjrmZj6Y/JWr0/ynWiZUtNGFEWhRA6tjGMbQwfd9tEBkRJkzhpEcsmsfSIkzax9EikTyLD7khV2C1TMVImdAqWRCAA0d3/ryOEjoaJJkw0YaEJe2G0TBdudxQti6FlEUI/zd8JZTkL4yo75z/OnHcbRft8NpTeeEKPCUXpd4aWY2P5zQy6T2Xn/Me5e+adrM6/khW5Fy3JuVwPpsqW0nM0YWHpFqjTjyh9pOrfxY65fyRKGqwtvoax7PP64o+IopxKJeciHjfyD+ya/2f21j5H1f8VG8tvXfKno1KPdEVRlNNIyoT9tS+yZea96CLLucPXsiJ3tSpaivIwDC3HpvKfsqH0RurB/dw19efU/HvSjvWYqEe7oijKaRIlDbZW3s/++hcZzDyd84Y/QNZcl3YsRel5QghGspdz3vAHMLQc981cw8HGf9NL88xPhipbiqIop0Er3Mvd0++g5t/J+tIfsrH0FnVghaKcpIy5mvOGr6XsPoE91U+zc/5jC+sXLiVqzpaiKMopNufdxvbKR9A1h7OH3kve2px2JEVZsnTN5YzynzFhfJn99S/ix5OcOfAXGFou7WgnTI1sKYqinEKHGt/m/tkP4BjjnDf8AVW0FOUUEEJjVeHlbCq/lUZwP/fOvBs/nkk71glTZUtRFOUUkDJhT/Uz7K5+kpJzCecMvRdLH0w7lqL0laHM09k8+C78eIZ7p99FOzqQdqQTosqWoijKY5TIiB3zH+Vg45uMZa/izIG3q/lZinKaFO3zOGfwGhLpc9/Me2iHE2lHOi5VthRFUR6DRAZsq/wdM62fsrrwKtYWX6eWdVCU0yxrbeDsofciZcJ9s+/p+REu9YygKIryKMWJz9bZa5nzbmN96Q9YmX+pOu2OoiySjLmas4f+N1ImbJm5Bj+aTjvSw1JlS1EU5VGIE5/7K9dS8+9iY/lNjGavTDuSoiw7GXM1Zw29m0i22DL7PqKkkXakY1JlS1EU5SQlMuD+ygeo+XezofxmhjOXpR1JUZatrLmezQPvxI8nub/yQRIZph3pIVTZUhRFOQmJjNhW+Qeq/p2sL/0Rw5lnpB1JUZa9gn0uG0tvoebfy675T/TcSvOqbCmKopwgKRN2zX+cOe821hVfx0j28rQjKYrSNZh5KivzL2W69SOmWt9NO85RVNlSFEU5Qftqn2O69RNW5V/OWO65acdRFOVBVuVfQcm5iD3VT9EIdqQdZ0FPla1EhkSJn3YMRVGUh5hsfpcDjW8wmn0OK/O/kXYcRVGOQQiNjeU/xtAK7Jj7CHHSTjsS0GNlqxHN8PV9b+MHB9/PrypfZqL1S/y4N48sUBRl+Zj37mD3/L9Sdi5mXfF1ankHRelhppZnU/mteNEh9tY+m3YcoMdORO3qZc4qXMm0v43t9R9xf+17AOTNMYacTQzZGxm0N5IzRtSTnaIoi6IdTrB97sNkzDVsKv8JQuhpR1IU5TgK9rmM5a7mYOObDLhPoWifn2qenipbpuZwXvnFAMQyZM7fw4y/nRl/O/ubt7Or/jMAbD3PoL2BQXsjg/YGBqy16JqVZnRFUfpQlDS5v3ItAoMzB96BrrlpR1IU5QStLryKOe9Wds3/M48b+Qc0kV5P6KmydSRdmJ3RLGcT0DkKqBYeYtbfwYy/g1l/BwdavwI6+2hL1upuAdvAgLWerDGkRr8URXnUpEzYMfdRvHiKswf/CtsYTjuSoignQRMW64t/wH2zf83Bxn+xMv+y1LL0bNl6MCE0itY4RWucDfmnA+DFdSr+Tma7l92NG9le+xEAtp5jwF7PgLWeAXsdA9Y6LD2b5pegKMoScrDxX8x5t7K2+FoK9rlpx1EU5VEoOhcw4D6JA/WvMZy5HEsfSCXHkilbx+LoecYzFzCeuQCARMbUwgPM+ruo+LuoBLs42L4buoub5cwRytbahfJVslZjaHaaX4KiKD2oHmxlX+3zDLpPZiz7vLTjKIryGKwp/DZ3ercxUf8S60uvTyXDki5bD6YJnZK1mpK1mo35XwMgTNpU/N1Ugt0Lc8D2NW8FOqNleXOMsrWWsrWGsrW2W8DU/C9FWa6ipMH2yoexjWHWl/5ITUdQlCXOMcYYyVzBZOt7rMj9Oo4xsugZ+qpsHYupuYy6ZzPqnr1wnxdXqfh7mAt2U/H3cKh9D3saPwcOF7BRytYaStaahfJmaZm0vgRFURaJlJJd8/9CkMxx7tD7MDQ19UBR+sF4/teZan2fg42vpTK61fdl61gcvch45nGMZx4HdJ5g2/E8c8Ee5oO9zAX7mPK2sqdx88LHZI0hStZqitbKbgFbRUYfVK96FaWPzLZ/xmz7BlYXXkXOOiPtOIqinCKWPshw5jKmWz9mVf4VmHppUf/9ZVm2HkwIQcYokzHKrMxcuHC/F9eYD/YxF+xlPtjPfLCPifYvF+aAmZpL0VpFyVxJwVpJ0VxJ0RrHVIeHK8qSE8QVdlf/lby1mfHcr6cdR1GUU2wsezWTze8x2foeqxb5LBCqbD0CRy8w5p7LmPvAkUhh4lELDzAf7GM+2E81nGBP8ybCurewTdYYomCNUzTHKZgrKFjjFIwxtRaYovSozu7DfyaRIRvKb0KInjq5hqIop4BrrqRkX8BU83uszL10UR/nqmydJFNzFtbzOkxKSSuepRpMUA0nFq4Pte9GygTozAXLGkMUzDHy5opOCTNXkDdH1UiYoqRstn0Dc94vWFt8Da4xnnYc5TGSUgISEGqqh3KU4eyz2Vb5e6r+ryg5Fy3av6vK1ikghCBrDJE1hhjngoX7ExlTDyephQephQe6l4Mcat9DIuOF7VyjTN4cJW+MkTdHyZkjFMwxMvqAeoWtKKdZmNTZU/0kOWuTWuahRyVJkyjeTxQfIo6niJNZ4mSWJJknSepI2SSRbaT0QYZI5MLHCnSEsBDCQYgMmlZA0wroWhldG0LXRzD0FRj6OJqm5uH2u7LzeAwtx0z7p6ps9QtN6AsLscLjF+5PZEwzmqYWHqIWHqQeHqIeHmJv82bCI85QrgmTnDlEzhjpXMwRcsYwOXNYFTFFOUX2Vf+dKGlwVund6jGVMikToniCMLyfINpOFO0ijHYTJ3NHbacJF00bQNfKGPoYQuTQNBeBjRAmoAECkEgipPSR0uuUsqROHM8QhltJkupRxUwTLoaxDtNYj2VuwjQ2Yxrr1fkw+4gmLAacJzHbvoGkFCzaKXxU2UqBJnTy5hh5c4yVPDAhX0qJn9S75WuKRjRJPZykEU1xqH0viQyP+hwZY4icMUTWGCZrDC6MrmWNQUwto16hKcpx1IP7mWr9gBW5F5A116cdZ9mRMiGMtuEHv8IP7yQI7yNJGgAIYWEa63DsJ2DoqzH0lej6GIY+hnaKluSQMiSOp4niQ0TxBFG8lzDaTdu/nmb72wBowsEyz8ayLsCxLsY0zlClfIkbcJ/MVOsHVP27KDuPP/4HnAKqbPUQIQSOXsDRCww7Zx71PikT2vE8jWiaRjhNI5qiGU3TCGeY9XcRJq2jtjc0h4wxQEYfIGsMdt42BnD1zlGXjl5CF+rHryxfUibsmf9XLH2AVfmXpx1n2UiSOp5/C15wM15wO0lSB8A01uDaT+sUG3Mzhr7mtI8oCWFiGOMYxjhw8cL9Ukri+CBBtJUgvBc/uJta49PU+DSaVsCxnoBrX4ptX4ImnNOaUTn1Cva56MJh3vuFKlvK0YTQFgrTiLP5Ie8PkhbNaIZmOEMrnqUZVWhFs7SiWSrBLoK4+ZCPsfUCrl7ENcqda72Eo5dw9SJ2t/Q5egFNDaErAhft3QAAIABJREFUfWi69SMa4U42ld+Krg5SOa2SpE7b/xlt76f4wS+RJOhaCdd+CrZ1MbZ1IbpWTjvmAiHEQgnLOJcBECfz+MEdeP6teMEttLwfoAkHx34KGedZ2NbFanfjEqEJi4J9HlX/zkX7N1XZ6hOWlsGy1lC21hzz/WHi0Y7maMVztKNK5zqu0o46tyv+Tvy4cezPrWextTyOnsfW89haHlvPYWm57nX2iEsGU3OX5TB7ImOixCOSPmHiESZtIul37/MIu9dR4nfv94llQCwDIhkQy5BERsQyRMoYSYKUcmFOiUAghI4uDHRhYggHU3Ox9CyOlscxSmT1QXLmMFljWJXkRxAnbfbVPk/e2syg+7S04/QlKWO84FZa7e/iBTcjZYShj5PL/gau/dQltztO10pknMvIOJchZYwf3knb+ylt/3pa3o/Q9SGyznPIus9H14fSjqscR8E+jznvNvx4BnsRfl6qbC0TpuZgWisosOJht4llhB/XaMdVvIVLDT9u4MVV/KRBNZjATxoESWthcdeHEAJTuJ0ioLkYWudtQ9iYmoMhHAzNRhcWhmZjCBtdmN2LhS5MtG6h0ISOJgwEOprQEWjdEiEQaEfMSzt83c3ULSmd/xKkTEhkjCQmkTGJjEiIFsrN4esHLt0SlARE0idOfCIZHFGeAqJumQoTnyhpEx8xp+6RCKEd/T1Y+LotTM1FFyZCHP56oTPZt3Moeyd7TCwDQunhRVUCv4Wf1BeWGYHOwRVFa5xBewPD9pmMumerJUaOcKDxDcKkyubiO9TcxlMsjmdptr9N0/sOcTyDrpXIui8g41zeLVhL//sthI5jXYRjXURJvhHPv5mm9x3qzf+g3vwCrvN0cpmXYpkP3Quh9Ia81TmFX8Pfip1RZUtZRLowFnZVHo+UCX7SJIgbBEmze2ktXIcLlzZh0qYdzS2M+ETSI06CRfiKTg1N6OjC7hZDC0NzMISNaww8pEB2SuUDb5vCwdCco7bRME75HxwpE7y4TjOa+f/Ze+9wya7yTvdda+fKJ3VOUrdyBAVQMMEiCIQB44EBWxgcABsM944Z4xmPzcU2xjYeX/Bg7ngwGDwDNibayAKERFBCCZRz6Far88mVd173j6pzultq0ae7q2rvc2q/z1PPDlVnr99JtX/1rW99H41wkqq/hzl/Jzsat/Jk7YdIobHaOYst+UtYlztvqKNefjTH/sY1jDmXUjBPPfoXZCyJINxBvfk12t6PUCrENi+kUngvtvUixArODxXCwLEvx7EvJ4z202x9i2b7O7TcG7HNF1LMX41lnnX0C2UMlJyxGSkMGsETjHFZ38dbuf8BGX1FCImtdaYWjwel4u7UmX/IdFononR4tCk8LBrViVRFxCoGFqbYnh1hEwgEh0a/FiJiCxEyKXQk2mIUbSGSthBZ60TdOtGm5WBMhJA4ehlHLzPO1sXzkQqZ9Xawt3Ufu1p3cVvrfnL6GGeWX8uWwqXLahqnV+ypf42YkI2ltyUtZUXgB49Sa/4TrncHUtjknasoOK9H1zckLW3g6NoaysV3U8xfTbP97zRaX2dq7nexrYsoF34DQ89WvKYFKXRyxmaawY6BjJeZrYxEEEJiCBsDG9LvZZYtmtCZsE9hwj6Fc0fexN72/Txa/Q4/mfk/PFn/EReP/xplc33SMgeGG04y1bqBVbkrsPXnn1LPODp+8CS15hdwvbuQskSp8KsUnNcj5fF9AFtJSJmjmH8L+dwv0GxdQ731FSZn3kvOuZJS4Z1ospy0xAwgZ2xhrn3HQMbKzFZGxpAghGR97nzWOeexu/VT7pn9F27Y9+dcOHY1mwsvTlreQNhT/yogWV/8paSlLFvCaJJa4/O03B8gZZFy4dfJO7+AlLmkpaUOKZyO6XJeQ635JZqtb9H2bqZc+E1y9qtXRP7acsbR1zMZ1wmiGoZW6utYmdnKyBgyhBBszF/IhH0qd0x9jjunP48X1zm19MqkpfUVN5xkunUjqwtXYmpjSctZdijlUW9+hXrrKwAU82+lmHszUhYSVpZ+pCxSKf4Weec1zNc/xVztE7TdH1Ep/S66tippeUOLra0BwIv2991sDV/CRkZGBgC2VuLy1e9nQ/4C7pv9Gk83bktaUl/Z2/gGQmisK7wxaSnLDte7iwMz76bW/CKOdQmrxz5HufBrmdE6Rgx9M+OVjzNS+gB+8CiTM++h5f4gaVlDi6V3jK4XTfV9rCyylZExxGhC5+LxX8ePm/x05ktUzA1UzI1Jy+o5fjTDdOuHTORegakdfbVtRocorlKt/09a7g8x9I1MjPwllnn+0b8w43kRQpJ3rsIyL2Cu+nFmq3+J599HpfhehLCSljdULES4/WjuKK88cbLIVkbGkKMJnReN/wamdLhr+gvEKkpaUs/Z1/h3lFKsLbwhaSnLhrZ3G5Mz76bt3UwpfzWrRv+/zGj1EF1bw/jIX1HMv41m+7tMzf1nomg6aVlDhSbySKERRPN9HyszWxkZGdhaifNH38q8v5udK2w6MYybTDavZ8y5FFvP8mOORqxc5mp/w8z8R5ByjFUjn6JUeDtCmElLW3EIoVEuvJOxykcIw11Mzr4fP3g8aVlDgxACXRYJ1ZG7p/SSzGxlZGQAsCH3Qsask3m4eu2Kim5NNq8nUi5ri1lU62gE4TNMzX6AVvs7FHNvZtXo32AYJycta8XjWJcwMfpJhNCZnvs9XO/upCUNDZrIEcWtvo+Tma2MjAyg8ynv9PKVtMJZ9rbuS1pOT1Aq4kDzO5Sss8kbWUHJn0XLvZGp2fcTx1XGKh+jXPxNhDCSljU0GPoWJkY+gaatY6b6YdreyoowpxUpbGLl9n+cvo+QkZGxbFjrnIOjj/B088dJS+kJs+4deNEMa/NXJS0ltSgVU218ntnqx9D1k1k1+mls64VJyxpKNG2ciZGPY+gnMzv/p5nhGgBSGMRL7Gt7QuP0fYSMjIxlgxCSjbkLOdB+mCBuJy3nhDnQ/C6WvoqKfUHSUlJJrNrMVv+UevPL5J3XMjHycTSt/015M54fKYuMV/4cw9jKbPXP8Px7k5a0whHdtm/9JTNbGRkZh7Eudy6xiph0H0taygnRCnZR8x5mde5VQ9kD8mhE8TzTcx/C9W6nUvxtKsUPZNOGKUHKPOOVj6Fr65iZ/whBOJj+fRn9I3sHysjIOIxR6yQ0YTDlLu9VUZPN65BCZyL380lLSR1htJ+p2d8lCJ9mtPJhCrk3Zq1jUkYnwvUxhMgxPf9HRHH/a0ENJwoxACuUma2MjIzD0ITBiLWFWW/5fpqOlc90+2ZG7Rf3vQ3HciMMdzM190FiVWW88hc41iVJS8p4HjRtnLHKHxPHNWarH0WpMGlJK45Y+cgBRHQzs5WRkfEcRsxNzAe7USpOWspxMdO+jTBuMpF/RdJSUkUQ7mJq7j+DChmvfBzLPCtpSRlHwTROYaT4f+H5D1Jr/mPSclYcsfKQwu77OJnZysjIeA5FYw1R7NOKZpOWclxMt36Ira+mZJ6ZtJTUEIa7mZ77EKAYH/k4prE1aUkZSyTnXEHeeS315ldws4T5nhKpNtqwma1WWOeWqW9z99zNPFa7h12tJ5nxDtCOmijV/9UCGRkZHQrdSuuNYPm1D/HCSareg4w7L80S47uE0RTT8/8VRcj4yMcx9M1JS8o4RsrF96Br65mv/TXxAIpwDgth3ECX+b6Pk6pG1H7scu/8LURHqF6tCQ1HK5DXi+S0Anm9RE4rkNOL5LUiOb1ITiuS1wsYMmvmmZFxIuT1ToPW9jKMbE23bwZgPPeyZIWkhDiuMzP/B8RxIzNayxgpbEbLv8fU7H+i1vw8leL7kpa07Ilil1gF6LL/eZ2pMlsVc4L3bfszvLhNK2rQCuu0ogbNsE4rqtMKGzTDGo2wygF3N27UJD5CfQxTWl1TVlzcLpiyvH5w39byyOyTb0bGc3C0MgDtATRo7SVKKaZbN1M0T8/6IAJK+cxUP0IY7WO88meYxilJS8o4AUzjDPK5X6DZuoac/ars93mCBHHn/c3ovt/1k1SZLei0DLG1HLaWY9T82W+WsYppR01aUZ1mWKcZ1mgfYs6aYZ0pby/NsI4fe8/5eonA0Qrk9IVIWfEIJq3znCHMbGl0xtCgSRNd2nhR/xu09pJW+DTtcDcnVd6VtJTEUUoxV/sEnv8go+X/imWel7SkjB5Qyr+DtnsT1cb/YrzyV9l96QQIok45DUNW+j5W6szWsSCFJK93jNHEUWYOg9ijGTa6EbKFiFmN5uJxnWlvH62oQXyEFViGMBanKnN64bCpy8OPC+gyKwyYsfwxpIO/zHJDZto/RiAZtbNyBo3WV2m5P6BUeAc5+2VJy8noEVIWKObfznz9U7j+7VnpjhPAi2YAMAfQNWFZm61jwZAWFdOiwtjPfF2sYtyoRTOq0w4bNKNaZ/ryEFM270+zJ9qOGx25ncnCNKajFRbzynJaYdGY5bTCYkQti5hlpBVD2oRx/xu09gqlFLPtH1O2zhn62lqudze1xj+Qs19CMfe2pOVk9Ji8cyWN1tepNf4Ptvni7B5ynHjRJABWZrYGjxSyY4j0AhwlWhapkHbYPMSIHcwzW4iczfoH2N1+6nmNmS4McnoBR8vjaHlyWvHgvt4xZY6W627zGNLsw3edkfFcdGERKT9pGUumFTyNGx5gXeEXk5aSKFE0zVztL9D1zVRKv5vdiFcgQugU87/MXO2/4/l3YlsvSlrSssQL92PIMpp0+j5WZrZOAE3oFIwyBePoyXULxmzBiLXCejffrDO12Q6bNMM6095+2lHjiCsyoTOdaWt5cnoeW3ZMmK3lsbUcTjfXrbPfed7WcplByzgupDCWldmadW9HIBmxL0paSmIoFTNb+3OU8hkt/yFS9P8mkpEMOfvl1Jr/SL311cxsHSdutB9bXzOQsTKzNSCOxZgppfBjl3bUoh01aEfNRWPWjpq43eN21GQumMaNWkdcALCALnRsLYclnc5Wc7DlwtY5bGtJB0vaWJqDKW10YWSfjIcUKTSiePmYrTn3TorW6QNZWZRW6q0vdxLiSx/C0DcmLSejjwihU3BeT7XxOYLwaQx9S9KSlh3tYA8V+4UDGSszWylECNExPppz1ByzBSIV4kYt3KjVNWQt3Lh1yLkWXtzGjVrUglkmoz14UYtABT/zulLIRQNmSAtTWljSxtRsTGFhShtTWhjSwpAmprS7W7NzTpgY3X1dGFmpjWWEQKKOUFoljbjhJK1gF5vL70xaSmL4wePUG18kZ7+MnHNF0nIyBkDeuZJa83/TbH+bSvG9SctZVgRxnSCukjMG86EkM1srBE3o5PUSef3YEoPDOMCPXbzYxY1aeLGLF7W759p4sYsfdfb92MOLXWrhPL7vEsQefuw975TnkdCFji4N9K4J04WBIQ100X1IA21xX0cXJprQF79OEzqa0DFEZ1/vfu3C+c6x3r1G51wWmVv5zLt3ATBiX5CwkmRQymeu9t+RskKl+DtJy8kYEFKWcKxLabk/oFx4F2IADZVXCu3gGQCcAUWAM7M15OiyY3ByFI/7GmEcECgfP/YIYo8gPmRfBYvnAuUTxgGhCghin1D5BHGwuG2rJqEKCOOQSAWEKiSM/SMWrl0qEoHeNXW6NBYjbQvROFN2onOdKVZncap1YYFCTisOcc6bQrA8jOq8ezeOvg5bX5u0lESoN/+FINzJeOVPkPL4/5czlh+O/XJa7o14/j3Y1sVJy1k2NIOnAcgZWwYyXma2Mk4YXRroGDhaf/pLRSoiUiFhHBw0YSp8zrmF43DhOA4IVMfMLRjCID74WCh223m4zztlZkmHgl6iaFQoG2OUjVFGzFWMmqso6pUVGzlTSsEy+N6i2KPmP8zq/KuTlpIIYbibeutfyNkvyxKlhxDbvAApcrS9WzKzdQy0gh0YsjyQgqaQma2MZYAmNDShYfax52Ws4u40aSe/rR02DivhUQ/nqQdz7G0/fdhiBEvaTNjrWWNvZL1zEuuck/qqc5DEREi0pGUclbr/MLEKKFvnJy1l4CilmK9/GoFJufCepOVkJIAQJrZ1Ea53B0rFWfP1JdIMniJvbh3Yh+XMbGVk0FkIYGudqcSy8fyLEpRStKMm88EUM94Bprx9THq7uHvuJn4y+yOkkKxzTmJr/ixOKZ5zzDl0aUKpCE3aScs4KlXvPqQwKFlnJi1l4Lj+bbj+3VSKv42mjSYtJyMhbPNiWu6NBOEOTGNr0nJSTxS3aQd7BtppIjNbGRnHgBBisejtOuekxfNB7LPP3cmu5pPsaD7CjVPf4uapa9iSP51zK5ewKXfqsptujFSAJQpJyzgqVe8+iubpSDFcuXVKhVTrn8XQN5F3Xpe0nIwEscxOVNcP7svM1hJoBE+hiCmYg2vknZmtjIweYEiTTblT2JQ7hcsmXsOsd4BH6nfzcPUnbN/zCKvtDVwy9mo2509NWuqSiVSAFOl+iwiieVrBLjaVXpK0lIHTbH+XMNrDWOWPESn/PWX0F00bR9fW4PkPUci9KWk5qafhPwqQma2MjOXOqLWay6zX8KLRV/BY/V7unP0+/7rnc2wrnM3LVr1hWUwvRipAS3m0qOY/BEDJOjthJYNFKY9680tY5tnYZpYUnwGmcTpe8FDSMpYFdf9RcsZGdDm4yH2WSZeR0Ud0aXBW+SLevvmDXDp+JU83H+VLOz/JM80nkpZ2VCLlo6W8bk/NexhN2OSNk5OWMlCa7WuJ4llK+Xcsu+npjP5g6NuIoimiuJq0lFSjVETde5SiOdgcz8xsZWQMAF0aXDT6ct626QPktAL/tudzPFi9I2lZP5NQeegi3Ssr6/7DFM3TECL9qyZ7hVI+9eZXsczzsMxzk5aTkRIMvZNDGoY7E1aSbprBdiLlUsrMVkbGymXUWs1bNr2PTflT+f6Bb3D//G1JSzoiSsVEsY+e4jIWYdygFeyiaJ2RtJSB0nJvIIpnKebflrSUjBSh6xsACKPdCStJN1XvAQBK1lkDHTczWxkZA8aUFq9b96uclD+DH03+G9sbDyct6TmEqtOAWktxZKvhPw5AwTw9YSWDQ6mYRusbmPpWLGP46oplPD+aXIVAI4z2Jy0l1dS8+8kZmzG0wRQzXSAzWxkZCaAJndes/WUmrHVct//LVIPZpCUdRtgt3GqkuM5W3X8cgaQwREvdPf9ugnAXhdwvZblaGYchhETTxomi6aSlpJYodqn7j1K2Bj/9npmtjIyEMKTJa9ddDcANB77WaY+TEkLlAqCL9Jqtpv8EjrERTTpJSxkYzfY1aLKCYw9fqYuMoyPlCHGcrg9uaaLmP0SsQioJdJvIzFZGRoKUjVEuH7+K3a2neLx+b9JyFgnijtlKa2RLKUUjeIqCsS1pKQMjiqZxvTvJOVciUr5KNCMZpCwRq3rSMlJL1b0HTViJ5HlmZisjI2HOKl/EKms9P565jkiFScsBDolspdRsedEBwrhB3hyeKcSmez2KmLw9nA23M46OFHniuJm0jFSilGLOu5uSdU4i3SYys5WRkTBSSC4ZfxW1YI5Ha/ckLQeAIG4DYIh0TtE1g+0AQxPZUkrRcm/AMs9B19clLScjpQhhoZSXtIxU0g6fwQsnqdgvTGT8VFWQn/Rm+PCDf4UlTSxpYmomtrSwNLN7bmHfwpImtmZhad39Q56zNQtTGsis+3nGMmFz7jTGzNXcN38rZ5YuTDz5OYwXIlvpXI3YCnYghIZjbEhaykAIwicJw90US7+UtJSMFCMwUKQjOp425tyfADBiX5TI+KkyW3nN4UWjL8CL/c4j8vFjn2pQX9x3I49wiVMtZteQ2ZrVMWHSxNZsrK6J6zxnLxq3zjn7sH1dDk+xxIzkEEJwbuUSfjj5r0x6e1htJ2siFiNbKU0+bwZP4+jrh6b5dNu7CYGGY12etJSMNCMEkJ6FNmlirn0HBfMUTG0kkfHTZbb0HFete8VRXxerGDfycGMPL/IWzZkbeYuGrPPcwr6LF/m0Y4+5oIbXfT6Ig6OOpQt9MYJ20KBZOJp9mGE71KA5zzJuWYQtYymcWjyPm6au4bH6vcmbLbWQIJ9Os9UKdg5NP0SlFG33FizzfKRMf0/NjORQKkKQBQiejRdO0gi2s6l0dWIaUmW2looUkpzukOPEbgSHmjY38g4xae4Rz7uRRztyqQUNvO6xH/tHHWchwmbJrknrGrYjm7WumZMHX2dKMzNsQ4Ct5diY28ZTjQf5ufGrEp1KDGMXKbRU9kYM4wZ+NEtO35S0lIEQRrsIo70UctkUYsbRCEAsy9t6X5l17wRg1EmuaftQ/1Z6YdoWDVvk0j7EkHmLBu2gcWt395thixl/Dq/72khFRxlFYEkTR7M7ETZtYUrUwjoswtY5/9xznXw2bYj6xy1XTs6fydPNx5gLphg1VyWmI4jbqV2J2A467UhyxnCYLdfr3Chs6+KElWSknThuI1O6qCVJZtu3kTe2YOtrE9Mw1GarFywaNv34/8DDODzMkC2YMu+wyJp7WJStHjaZ8mYXI27xUQ0b6FLvGq9DomhdI3Ywv83Gkga2tA9bcGBJczHXTZfZn02/2JQ/BYBdrScTNVuhclO7ErEd7gLA1ocjOd7z78bQN6Fryf09ZCwPlGogRD5pGanCC6eo+4+xsZRsL9HsrpkCdKlTkDoFju+fRClFqMJOjtqzommHnevmsy3kubmRRyNsLUbhvMhDLSG5UhPa86wCPdScdbeLixEOLkRwNBtHs7Op0SNQNsYo6GX2tp/mvMqliekI4nZqC5q2wz1IYWBp40lL6TtK+XjBg+Sd1yQtJWMZEMU1NG0saRmpYqZ9KwBjzmWJ6sjM1gpACIEhDAxpHLdhg45pC+IAN/bxuubLPWQBwsGp0YXn/W70zaceNpj2Dhq8pawYNRfNl0Oua8AczSGvO+T0HHnNIa/nKOh5Cnqeop4fiqjaWnsT+91nEtUQxC56SpPj3XAvtr4OMQRm3Q8eRykPyxh8L7eM5Uccz2IapyQtI1XMtG+hYG7D1tckqmPl37kylowQAlPr1DeDwgldK4yjg9OgXePWjtxDFh24tKNDp01dZvw52tE+mmHrefPYHM2hZBQoGyUqRomKWWLUHGHMrDBujWJr6YzGHAur7Y080XiAdtTE0ZKZEghiF0cvJzL20XDDfThDkq/lBw8DYJpnJawkI+0oFRDH82hy5Ud8l0or2EUzeJot5V9LWkpmtjL6gy41dJkjr+eO+WuVUvhxQDNq0QxbNMImjbBJPWhSDxtUgxrVoM6edseYHUpBL7DaHmetvYp1zho25tYxZo4kXiT0WJiwOhXCp739bMwl044mVB66SF9BU6VivGiSEXs4ksX94BF0bR2arCQtJSPlRNEkCoWmrU5aSmqYbt+EQCY+hQgnaLaEEG8GPgKcAVyslPrJIc/9V+A3gAj4gFLquhMZK2N4EEJ08sA0k1HzZ99kvMhnzp9n2p9jxptl0pvmgDvN7TN3L05l5vQcJ+U3sq2whdOK2xgx0xmxWWDU6iRCz/oHkjNbcTuV04h+NE2sIix9OG4ofvg4lnFO0jIylgFhtBcAXUtuxV2aUCpmunUjZft8DC35DysnGtl6EHgT8L8OPSmEOBN4K3AWsA64QQhxqlJLWDKXkXEMWJrJGmcVa5zDV2rFKmbSnWZXey9PN3exvfEMD1UfA65jrbOa8ypn8YLKWZSMYjLCfwZ5rYQpLeb8qcQ0hMrDSGFky4s6P5Ok8y8GQRTPE0XTGM5w9H/MODHCqLNKVx+SVbpHo+Y9gB/Nsrn8jqSlACdotpRSjwBHmqJ5A/Bl1emIuUMI8SRwMXDbiYyXkbFUpJCLJuyi0fNRSjHtz/JI7QkerD7Kd/f9gOv2/ZCzy6fzkokXsSGXnua+QgjKxhjVYCaR8ZWKCWMPLYV9Eb1oEgBzCFYiBuHTABj6yckKyVgWBOHTaLKCJpNpR5M2plo/RJeFxHohPpt+5WytB24/5Hh399xzEEK8G3g3wKZNw5H0mjF4hBBMWGNMTIzxkokXM+3NcufsPdw1ey8PVB/hjNIpvGbtzzNhpWPZdNkYZcY/kMjYoep0RUhjzpYXTQMMRdmHMOysSDWGpFJ+xokRBE9i6CclLSMVhHGDWfcOVuWuSE3/1KOunRZC3CCEePAIjzf0QoBS6jNKqQuVUhdOTEz04pIZGUdl3BrltWuv4L+c/n5etealPNXYyd88/ll+cOBWYhUnLY+iMUI9mEepwTeVjZQHgJ7CyFYQzWLIUmreQPtJGO1BCgcp0/EBICO9KOUTRDsxsrIPAEy3biJWARO5K5KWsshRI1tKqaN3hn4ue4CNhxxv6J7LyEgVlmby8lWXcdHI+Vyz73quP3AjTzS28yub3kTBSK4Sc1EvE6oAL25ja8e+ovNECOKu2UplZGsGc0iKNobRXjRt3bJaSZuRDH7wJEqFmPrpSUtJHKUUk63rKRgnkzfTE+nrV1XAbwFvFUJYQoiTgFOAO/s0VkbGCVMw8rxt0xt5y8bXs7u9j08/9QWmvdnE9OT1EgDNsDbwsRcjWyk0W0E0h6kNR05KFE1mLXoyloQfPAiAaZ6ZsJLkaQSP0wp2sSr/yqSlHMYJmS0hxC8KIXYDlwDXCiGuA1BKPQR8BXgY+C7wvmwlYsZy4AUjZ/Oek6/Gj3z+fvuXmPXnE9GR0zqrJJtRfeBjh3EnZ0uT6ZuqC+J5jCGpORXF02hallqRcXS84H4MfWOWHA8caF6HJmzGnMuTlnIYJ2S2lFLfVEptUEpZSqnVSqlXH/LcnymltiqlTlNKfefEpWZkDIYNuXW86+RfIYhDvrDjK7iRO3ANOb1Twb8dNgY+drSYIJ8us6VUTBBVU1Ezp98o5RPHDaQcTVpKRspRKsD3H8AyX5C0lMQJohqz7dsYz70ULWV1Ald+c7GMjONgjbPtkiu3AAAgAElEQVSKqze/iWlvhm/s/s7AE9UX2vS0ouZAx4WDZktLmdkKVRNFjC7TXZS2F0RxFQBtCL7XjBPDDx4iVm5mtoCp1g+IVcDq/KuP/uIBk5mtjIzn4eTCZl655qU8UH2E+6uPDHRsSzoIBG7UOvqLe0ykAiCFZivq5K8ZspSwkv4Tx53vVYqV/71mnBht7w6EMLCM85OWkihKxRxoXkfJOpNcCnunpqo3YiN0+d7+uzGFji41TKljSB1DahhCx5JGZ1/qmN2HIXV0oWUrdjL6wksnXsxD1ce4du8NnF7chqUNxoBIITGljRe3BzLeoRw0W8bAx/5ZhKozparLE2uSvhxQqmOyhRjsStSM5YVSCte7Dcs4DymH+29lzr0LL5pKTcX4Z5Mqs1UPWnz1mZuP+euEEAfNl+gaMa1jzsyuQTOl0T3WsTSj+/rusTQWzz1338SSOlJkQcBhRArJ69e9iv/51D9yy/SdXLF6cEmXlmbjRZnZWiCMO4sFhsNsdfIEhbATVpKRZoJwO2G0j2L+zUlLSZz9zWuxtPHUVIx/NqkyW2ucUf7mhb9FoEKCOMSPI4J4Yb+z7TwX4cUBQRzhx8Hic3734cUBftR5bSty8fxw8XULzx9rDs5CpM2WJvaCGdNM7K6hszQDWzMOMWgLxyaW1vk6SzMWv97STIwsIrcs2JRfzxmlU7l1+i4uH794YNEtSzp48eCT8+PUmq1O/pomk6t/NigUnd+BSNnvICNdtL0bEUhs67KkpSRK099BzXuYTaW3I4SWtJwjkiqzJYCcbgH9r+8Tdg1bx4B1tl4U4MY+XnToOR9vwcDFAW4UdM1cgBsHzPoNvDjAi3zc7tcs1cgJIbC75szumjNbMw85Ng8+useO1jFtjjQPf14z0bLoW9946cSLeaT2OHfPP8AlYxcMZExL2vgJmK1IhQBIkaq3B6K4M7WmD8PUWreLgSCdN46M5FEqpu3+CMu6AG1IyqE8H/ua16AJm1X546nBPhjS9W46QHSpoUuNXn9GVkotRs8OmreOQesYNb+z7ZozN+o83459/CigHfk0whrtyF98TRgvrUSZIbWuIbNwDjFhue524fyh25xm4uhWd9/ClHoWbTsCm3LrWe+s5c6ZewZmtkxpUQ8HX+crTqnZirtTa9qQ56ZkZECntlYYHaBUeGfSUhLFj2aYad/K6vyV6CmOeqfr3XQFIITA0jrTivRoBmAhCteOvEWj1op8vNinHXXMmxt19r3Ypx129tuRx0xYY3fkdc7F/lGjblIIcppFTre6W5u8ZpPTLQq6TV53ulubou5Q0B2KhoMljRVt0oQQXDB6Lt/acx372gdY66zu+5iGtAi6BUYHSaxCEAKRssXKkWojkIhe/WOlms7PXpF8n86MdNJqX4cUeZwhn0Lc37gWlGJN/qqkpfxMMrO1DFiMwuknliyrlOqato4Ra4ce7dinFXqL51qhR+uQbTN0mfZqNMI27ej5zZouNcpGjqKeo2zmqRjdh1lg1Cx2HlYRUy7fP7lzSqdzzZ7v8WD1sYGYLVNa+N0+hYMkJkSSvnzCWPlIYaZOVz8Qi1HFMFEdGekkiqu0vVvIO1ciUthWa1CEcZMDze8x6lyCrae7tdXyvfNlHDNCiMWpxRGOfUVXrOLuNKdLI2zTDF3qQZt62KIetKkFLapBk2m3ypP1vTTD5+YblY0cq+wKq6wKa5wR1tqjrM+NM2YWU38TLRh5tuQ38kjtCV655iV9H0+XJoEafGRLqRiZwiTTWHnIIbmxLNxAF1YlZmQcSqt9HUr55J3XJS0lUQ40ryNSLusKb0xaylHJzFbGkpFCku9OIa7m6AmZQRwy7zeZ9evM+nVmvBpTXpUpr8r91R3cOv3w4mtzmsXm/CpOKqxhW2EtWwvruosl0sVpxa18d/8PqQUNSkZ/SxAYwiSIfWIVD7T0SEyUysTshcjWMCBEp9VIrAZf1DYj3SgV0mh/C8s8H0PfnLScxIiVz/7GtVTs88mbJyUt56hkZiujbxhSZ8IuM2EfueVIK3TZ255ld3uaXa0pnm4e4Dv7foJSCiEEJ+fXcE5lCy8c2cZaJx094rYWOm9u25s7Ob9yVl/HMrqNoCMVDtRkKBWnMsoYqzB1Sfv9QspOI/I4HnxvzIx00/ZuIoqmqBR/J2kpiTLZ/D5BXGVd4ReTlrIkhuOdKyOV5HSbbcV1bCuuWzznRQHbm/t5rLaLh6o7+dfdt/Gvu29jY26cy8bP4pLxMxKNeK1z1mBKk53N3X03W3q3xlIQ+4vGaxAo4lRGthThIblMKxspOh9Q4njwq1Ez0otSinrzqxj6Zmzz4qTlJEasAvY1/pWieRpF88yk5SyJ4Xjnylg2WJrBGaWNnFHayBs3XMqc3+DuuSe5ffoRvvzMjXxzz495ycQ5XLn2AkrG4EsASCHZmFvHM609fR9rwWCF3SKjg0INeNpyqSiVzunNfiCEgxAWUTybtJSMFOH6txGE2xkt/R4ihf+jg2K6dSNeNMNJld9KZRT+SGRmKyPVjJgFrlh9PlesPp+dzUmu3383Nxy4h5umHuB16y7mlWteOPBirhuctdw8fSdhHKL3cXWl3o3iDNxsoeiUGE4XnTIIw3GDEUKgyXGieCZpKRkpQSlFvfFFdG0tjv3ypOUkRqxC9jS+QcHcStlaPs23h+OdK2NFsDm/it/ceiV/cvbbOb24ga/vupWPPfxl9rfnBqpjnbOaWEVMev29EeoLka14sGYrvahl8ym2F+jaaqJof9IyMlKC692CHz5FKX91alvSDILp1k144STri29eVu8HmdnKWHascUb4nVNfz29tu4oZr85HH/5nHpjfMbjx7U49lwPuZF/HWYhsLbTPGRQKhUhhZGvY0LS1hNG+pGVkpAClQqqNz2Pom3Hsn09aTmJ0olpfo2BupWINppNHr8jMVsay5YLRbXz4rF9mlVXhU09cw50zjw1k3DFrBCk0DrjTfR1noRF0ErW20jiNCAKOsYH8csbQNxDHdaIsSX7oaba/TRjtoVT4taHO1Zpq/QAvnGRD8T8uq6gWZGYrY5kzahX50Bn/gVMK6/js9uu4fwARLk1ojJkVpr3+Ji8bsmO2kplGTJ+pEYhuPtlwoGubAAjDnQkryUiSOK5Ta/5vLPN8bPPFSctJjFj57Kl/jaJ5KmXrBUnLOWYys5Wx7LE1k/ef+no25Sb4zFPfYV+7/yu4xq1Rpv3+5ootlH4Y9DRiWk2NQEOxtKbsKwFD7xRqDMLtCSvJSJJa4wuouEml8J5lF83pJQea1+NHs2wovXVZ/hwys5WxIrA1k/ed8guYUufvn/oOYdzfm/KoOcKsP3fUxt4ngpbQasS0IoREqeFpzKxpY2hyBD94ImkpGQnhB4/RbF9LPvd6DOPkpOUkRhS32Vv/OmXrbMrWuUnLOS5SVfphd2ue//ijz2B0Gy/rQqJLrXN8yL4hZGd7yEMXGqamYYjOsSn1znOHntN0jO7rTKljykO2mr64r8vhXemxnBkxC/zqliv49BP/znX7f8pV6/pX9G/ELBPEAc2wRcHI92WMhchWGA84spVSUyPQUUPWmNk0TsMPHk1aRkYCKBUyV/sbpByhlH9H0nISZV/jGoK4xsbSLyct5bhJldkqGTZv2HQ+YRwRqJgwjghVTBBHz9lvhT6BigjiIz/iE5gGkYhF82VJHVPrbC3toDFbOLak0d12jzUdSzOwpI6tGdjdc519Y/F1aSwauRI4f2QrLxzZyrf33sVl42dRMftjhEaMToXv+aDaP7O1kLM14MhWaqcRhUGcyGKB5DCNs2h7txPFc2hyJGk5GQOk0foaQfgUY+U/QsrBF3BOC0FUZV/jW4w6L6Jgnpq0nOMmdWbrl0/uTTQi7Jouf3EbLhqxzrkQv3veiw7uB1H33OL5znNe1DnXDH1m/dbic14U4kXBMZs7SzOwu4bM0Q0s2dnamoHTNWY53cTRDBzNxNYNct1znfOd53K6mUXinsUvbbyce+e38519d/G2zS/ryxhlswTAfFBnQ19GSDJnSwPSF9mSwkQN2ZSqaZwNgO8/iGP/XMJqMgZFED5NrflFHOvncOzLk5aTKHvqXyNWPhuLyzeqBSkzW71E704HOgMaL4gjvChYNGleFOJ2j90oWDx2o4D2s44XztUDlym3TjsKcMPO+aWYOEvqXRNmke+asYJuUTAs8rpFQbcoGjZ53aJodPZL3ePlmGh4NFbZFS4ZO4Obpx7kdeteRNHo/V9BWe80Cq4H9Z5fewHZLVw48MiWkMQpnEbUhEWkvKRlDBTTOBUpHFz/nsxsDQlK+cxWP44UeSql4W427Yb7OND6HqvyV+AY65OWc0KsWLM1aBZyxwo9vKZSCi8OaYc+rSjobn3cMKAV+bTCzqO5uPVoRT4132Vfq0oz9GiG/vNOCUkhKRs2ZdOhbDiUzRwjZo5RK8eIlWfMzDNuF6iYzrKb9nzlmhdw6/TD3Dr9EFeuvbDn18/pnZ9Jta9mS6IJbeClHyQylav+pLCJlY9S8dDUGhJCxzLPw/N/ilLDVUF/WKk1/rEzfVj5CJqsJC0nUZ6pfRGJwfriW5KWcsJkZivFCCEWc72ON1sjVjGt0KceeDRCj0bgUgtc6oFLNWhT811qQZs5v8We1jxzfovoWVENXWiM2wVW20XWOGXW5sqsz1XYmB9h1Myn8gawPjfOtuI6bpl6iFevuaDnGqWQFPQ89bDZ0+s+G12YA59GlEInVmk0WxYAsfLQxKBi1sljWxfT9m4njHZi6FuSlpPRR1zvLuqtr1FwXodjXZK0nESpeQ8z276DDcW3YGrLP18xM1srHCkkBcOmYNhLer1SilrgMuc3mXabzHgNJt06U26DA+0aT9SeoBUdTFIu6BabC2NsLU5wamk1p5VXUzHTkcz54rHT+eLTP2BXa4pN+VU9v35RL9Dot9mSegLTiBqxClMXSdFkx2BFqsXgEgSSxzZfjOBTtL1bM7O1ggmjKWZrH8fQT6JcfHfSchJFqZhnav+IqY2ytvCGpOX0hMxsZRyGEKIzrWg6bCmMP+d5pRTVoM3e1jw7m7M805hlR2Oaa3c/wLfUfQBsyI1w3ugGLhzbzBmVtWgJTfm8cGQbX9r5Q+6Ze6ovZqug56iFjZ5f91A0MXizJenkisVEaCl6i9BFZ9VnGLcwtbGE1QwOTRvDNM6k7d5MKf8rScvJ6AOdPK2PggoYK/8hohvFHVam2zfS8J9i68j70eTK+Fmk5500Y1kghKBi5qiYOc6srFs878chO+rTPFLdz/1zu/ne3oe5dvcDlAyHS1dt5Yq1p7OlMNgbZNFw2FpYy33zO3jDht6H5At6gX19bkZtCHPgOVsLPRljFS4WVk0DmuyYrSjubzQxjTj2y5ivf5og3LFYWT5jZaCUYr7+t/jBo4yV/whd79f65uVBFLfZVfsnCuY2xp2VsygkPe+kGcsaU+qcVl7DaeU1vHHT+bRDn/vmdnPr5FPcsPcRvrvnQc6qrOMXN72Ac0fWD2x66qzyZv5t923UgxZFo7fTm3ndoRm2+jrdpktj4JEtbbHkRIDB0qafB4HeNVuh6m80MY049kuo1v+OVvv6oZ9iWmk029+k2b6OUv6Xh77MA8Ce+tfxozlOHf29FbUQZuV8JxmpwtFNXjxxMh8865X8/aVX8/aTX8y+dpWP3n8tf3r/texq9r9/IcAZxc6nxMfre3t+7ZyeI1IRfh8jT7owBr8acTGyla6aVrrs1DYL4/6tAE0rmqxgW5fQcm9ADVlh15VM27uNav3vcazLKObfnrScxGmHe9nfvIaJ3MuWdQHTI5GZrYy+UzBsXr/pPD71orfyzm2Xsr0+zYd+8g3+7Zl7+17PaXN+NbrUeLKxp+fXzmudJO1m1Or5tRfQhUEw4JvroZGtNGHITm2zYTRbAHnntURxlbZ7c9JSMnqAHzzGbPXPMYytjJRXVhTneFBKsbP6DwhhsrG08nITh/u3mzFQTKlz1YZz+OTFb+GCsU18cfsd/NWD36Md9s9M6FJjc24VOxoHen7tnN6ZlmyF7Z5fewFdDj6yddBspSuCIoWDFDpBVE1aSiJY5gvQtfU02v/W1wboGf0nCHcxM/9HaHKEsfKfIIeolMnzMefewbx7LxuKb10RpR6eTWa2MgZOxczxwbNeya9vu4y7Z57hT++7lmbYv8rgW/KreaY12fMoWk7r5DO1ov6ZLUOYg49sSROAME6X2RJCoMsSQTycZksISSH3JvzgMfzggaTlZBwnYTTJzPwfAILxyp+haaNJS0qcKG6zs/p5csZm1uSvTFpOX8jMVkYiCCF4zYaz+eBZr2R7Y5q/fOA6/Lg/xTs35iYI4ogD7nxPr+t0zVY7cnt63UNJIrKld5edpy2yBWBqI0NrtgDyzivRZIV688tJS8k4DqJomum53yeOm4xV/mzoVx4usKf+VbxohpPK70KIldnrNzNbGYly8cRJvP+Ml/NIdR+fffyWvoyxIdepF7anPd3T6+a6OVvtPka2dGEOfDWi3q1rE6awD6EhR/CjwSyuSCNCWBRyv4Tr/xTPfyhpORnHQBTNMDX/+8TxHGOVj2Ia25KWlAqawQ72Nf6dVbkrKFqnJy3nmLhv9mtLfm2qSj/Mei0+/eCP0YREFxJNCgypoQuJLhceB48NKTGkhiYkZrc3od49Z3Rfu7BvatritdJUFTsDLlu1jWcas3zjmXs4f3Qjl67a2tPrr3VGEcDedm9v0oOIbBnSJIz9gVZzX4hshXH/vq/jxdRGaPiPJS0jUfK5X6DR+jq15ucZN/4qez9bBkTRNFNzHyKOZxmrfBTLPDNpSalAqZgd8/8LXRbYVF5eqzGfad7F47Xrl/z6VJktNwy5/cBOolgRqpgojgnj6HnaKB8fgk7S9IL5MqWGqemYUna3B5+zuseWpi/um5qGrRlY2sHz9hG2tm5gSi17I1wib95yAffN7eYfnriVc0fWL7m90FIwpc6oVeKAO9eza0KnlY4u9P6aLWEQo4hUiN5NXO83i2YrjZEtbZQgrhMrHynMpOUkghQOxfzVzNf/Fte/Dce6NGlJGT+DMNzD9PwfEMc1xiofy4zWIRxofpeG/yTbRj6ALgtJy1ky7bDKPbP/zKi1ZclfkyqztS5f4v9c8bbnnI+VIoxjgjgijCOCrhELFs/FBCoiiCJCdej5CD/qvD6IIoK48/AXzj9nP8SPIhqB3z0f4nXPeVFIfIwrgIQQWJqOo+k4eqehtKMbOLqOoxnkDJNc93xON8jpJnmjsy0YJnndJG+YFAwLucJNmy41fuu0l/Chn3yDb+y8h1/d1tuK76vtSs9ztqAT3epvzlY3WV0F6AzIbMmO0Q3SGNmSnS4EfjSLra9JWE1y5J3X0Gx/i2r9M9jmhYghNZ5pxw+eZGb+vwGK8ZG/xDRWVu2oE8ELJ9lV+ycq9vmMLaNK8Uopfjr7RcLY56LxXwP+YElflyqz9XxIITC1TlQpSaI4xotDvCjE6xowLwpxD9m6YceguWFAOwzwoohW6ONFIa0wwI1CZt0W7SikFfq0wwA/io46tqMbFA2LgmFRNE1Khk3RtCmZFmXTpmI6VCybiuUwauVw9MHcmHvJlsI4L1l9Ct/d+xCv33ReTxtar7Iq3NF4tGfXW8Dus9kyu/lTQexha4Np8K0LCyEkYdy/XLTjxdI7+XdeND3UZksInXLxvUzP/RfqzX+hVFheUzDDgOvdzWz1TxCywHjlzzH0jUlLSg1KKXZUPwPAlvK7l9UM0NPNH7OvdT/nj76FkrH096BlYbbSgiYlOWmS03v7KTKM40Xj1Qx9WkFn2wg8moFPI/RpBJ3juu/RCDwm2zPUfJdmcOQVY7ZuMGblGHdyjNt5JpwCq50Ca3JF1uZKjFhOKv/A37T5Bdx04Am+s/tB3nbyxT277oRVoh35NEOXvN67KUpHs3Gj/k23Gd3Ilj/AMgxCCHRhEaj0RbYsrdNQ3AsnYWX0pz1ubPMF5OyXU299Gcd+CYa+OWlJGV2a7e8yX/sf6PomxisfRdPGk5aUKqZaP2TevZct5d/A1lclLWfJNMNp7p39ChP2qWwrvvyYvjYzWylAl5KSaVMyj90EhHFMPXCZ89pUfZd5r82s12bWbTHjtphxm9wzvZc5t3VY7putG2zIl9lcrLClOMrW0hhby2OJR8TW5SpcMLaJG/Y9yn/YcgGG7E00c8wqAzDr13tqtmzNohn2r4K80Z0eGnStLUM6BCmMbJnaGAKJF/W3AfhyoVx8D55/N3O1/87EyCcQKWocPowoFVNt/D2N1jewzQsYLf8hUg4mIr1c8KMZnql9gZJ5Bqvzr05azpJRKuau6S8AcNH4O4654n/2n7nM0aVkxMoxYv3sf2g/iph2m+xr1djXqrO7UWVPc56fTO3m+7ufBDoRjS3FEc4YWc35Y2s5d3xtz6N4S+EV687gJzM7uXd2FxeNb+nJNcfMTquXGa/GxtxET64JHbM14/WvFMFCZCuIB5usbshcKs2WFAamNooX9b4jwHJEkyNUih9gpvqn1JpfpFx4Z9KShpY4rjFb/Qtc/6cUcm+gXHjPiq0Zdbwopdg+/3fEKuTkkfcuqxZFj9e+z5T7BBeO/yp5/dgjlZnZGhJMTWNdvsS6fOk5z815LZ6qzvJ4dYpH5g7w/d1P8O2dj6BJyblja7l8zUlctnbzwIzXeSMbKBo2t0w+2TOzNWp1zNas3+jJ9RawpYXbRyN00GwNNrJlSocg7l/E7kSw9DV4YWa2FnDsy8n7r6bR/DKWeR62+YKkJQ0dfvA4s9WPEsWzjJT+E3lnZVZBP1GmWjcw797DlvKvY+trk5azZKr+Hh6c/zfW5c5jS/74Vv9mZiuDESvHhatyXLiqU804iCMem5virqld/Hj/Tj71wC185uHbedn6rbxhy5lsKFT6qkeXGhePb+HWyacI4qgnU4kF3UYTkjm/t02Mbc3qc87WwQT5QWJIh2aYzuKhtr6GufYdSctIFeXib+MHjzJX/XMmRj+Frq1OWtJQoJSi2b6GauMzaHKEiZG/xjROS1pWKnHDA+ys/iNl62xWL6OWPJEKuXP6HzCkzQVjVx93rvPyieFlDAxDapw9toZfO/0iPvPSX+Ljl1zFz609iR/sfpL33fRN/vreG5lq9zZC9GwuHNuMGwU8Wt3fk+tJISkbeeb9Zk+ut4Ct2UQqIuxTqyGzW/NqkAnyAIbM48e9/Vn1CltbQxDXCeP+/g0uJ6RwGCt/GKUCZub/mDilUcmVRBRXma3+MfP1T2OZL2DV6Kczo/U8KBXx1Nz/QAjJyZX3Lavpw4fnr2He382FY2/H1p47M7RUls93nJEIQghOH1nFB869nM+9/M384snn8OP9O/ntm77Bt3Y8dMy1x5bKWZV1SCF5YG5Pz65ZMfNUg16brY4Z6ld0a6H0gz/gmlemzKV2GtHR1wPghnsTVpIudH0Do+X/RhjuYLb2MZTqzweADHC9O5mceQ+u/xMqxfcwVv4TpDz+G/FKZ2/jm9T9x9hS/k0svXc5s/1myn2CR2vXcVLhMtblzjuha2VmK2PJVCyHd55+If/zJW/inNG1fPaRO/noT2943vITJ4Kjm2wtTvDQfO9uqGWjD2arm1PVr7ythaKmg16NaGkFwtgjGnBfxqVgGx2z1Q57Z8RXCrZ1IZXS7+B6dzFX+wRKxUlLWlHEcZO52v/L9PwfIWWZiZG/oZB7UyrL6KSFuv84u2tfYdy5nPHcS5KWs2SCuM1d018gr49x3uhbTvh6mdnKOGZW5Qp8+MJX8O6zXszdU3v4/du/zZzX+yjIGeU1bK9P4/doiq5k5KgGvdVpdfsjun0qbCqFxJRWApGtPAB+lL7olq2tRgqNdrA7aSmpJO9cRanwDlruDczXP5UZrh7Rdn/MgZl30WpfTzH/FlaNfgrT6G0f15VGGDd5cu6TmNoYWyrvSlrOMXHP7JdpRbNcPPbrGPLEywVlZivjuBBC8LrNZ/CRi17FgVadP7zjOup+b6M7p5RWEaqIZxq9SdQuGTmaoUsYH71i/1KxZX+nEYGu2RpsgrzZ7VPmpzAvSggNW19PO9yVtJTUUsy9jWL+rTTb32a+/kmU6t3f/LARRgeYmf8IM9U/7kSzRj9JufAbWYuko6CUYsf8Z/DDabaN/t/o3Q9wy4Fnmnexs3E7Z5Rfy7jdG0Odma2ME+L88XV8+MJXsK9V4y/v+WFPc7hOLnRqmWyvT/fkeiW9U4usEfYuSrSYs9XHBHZTWvh9bAl05DE7b4xeCs0WQE7fRCvIzNbzIYSglH8npfzVNNvXMVv9KCqFjcXTjFIeteaXODDzLlz/bsqF3+hGs7Ik+KUw2bqemfatbCi9laK5fH5mrXCWu2f+iTHrZM4ov7Zn101V6YfJVpM/uukGNCnQpUQTcnFraJ19XUh0qaFLgS41DCkxpNb9Gg1TW3heYi5su30VDalhaJ3zhqZhys55TWae80Q4Z2wt7z37Uv7H/bfwlSfv462nnN+T607YRfK6xdPNmZ5cr2h0zFY9bFExe/Mp62CCfD/7I9oDn0a0tU5dMi9Kp9lyjI1Mt28hjJvL6hPzIBFCUCq8HSmLVOt/x9Tchxgr/z9o2mjS0lKNUjFt70fUGp8njCZxrJ+jXHw3urZ82sokTTPYwc7q56lY57Gu8Mak5SwZpWLunP4HFDEXj/86sodFaVNltkDhRiFhEBPGMVEcE6ruNo4JutswjolU3LMoihQCS9Oxuqas8+gcW5qOpWvYmtHd6ti6jqXp2LqBo3eOHd1Y3DqGTk43yBkmhpRDkTz5ig2ncM/0Xv7lqfu4dM1mNhVHTviaQgg25Ud7No1Y6LbpqQe9q4y+MI3o9TWyZQ98GtFaNFu1gY67VHJGpw9gO3iGonVGwmrSTSH3RjS3EXsAACAASURBVDS5itnaXzA5+zuMlv8QyzwzaVmpQymF5/+EWuPz+OFTmPpWJkZ+D8s8N2lpy4owbvLE7F+jyyJbRz6wrMo8PFr7LlPuE1w0/g4KRm9XTabKbK3KFfirly+92Fl0mAGLCLoGLejuB1Fn60fRYef8OMKPOo9Dj70owgtD/Li7jSJaYcCc18YLI7woxA1DvChcstHTpVw0XgXTJG8Y5A2TomlRMDvbomlRsixK3W3ZsikY5rIzae8+42LumdrDZx+5kz+5uDc9r9bnKtw+tR2l1An/PIqGA0Aj7KHZGkhky6IRVvt2/SOPmQch8OLeFoHtFXnjJACawdOZ2VoCjn0pE9onmK3+KdNz/5lS4Z0Ucv9hWd0I+4VSCi+4l3rji3jBg+jaGkZLH8KxX579fI4RpRRPzf0tXjTFmWN/jKGVk5a0ZGa9HTw0fw0b8xeyOX9Jz6+fKrN1rGhSJjIFqJQiiGPcMMSNQtwwoB0EtMOQVhjghgGtIKDV3TaDzvONwKMZBMy2q9R9j7rvEz3PSiFNSEZsmxHbYczJLT4mcnlW5wuszuUZsZ1UGbKy5fDmrefy+Ufv4uHZA5w5euJVrNfnKjRCj1rgUjadE7pWQV8wW70zRlJIdKn3OWdr8NOIUmhYMo8bpdNsGXIUQ5ZoBtuTlrJsMI2trBr9W+Zqn6Da+ByufycjpQ+ia8unbUovUSrG9e+g3vwX/OARNG2cSvF3yDtXIoSRtLxlyd7GN5lz72Jz+Z0UrdOTlrNkgrjN7dOfxdEqvHDsV/pyX13WZisphBCL040lrOO+jlIKNwypBz41z6Xqed2ty5zrMu+1mW232duo8cDUgefUs7I1nbWFIhuKZTaVymypjHByZZQJJ5eYCXvt5tP5+vYH+Pr2B3pittblOq2B9rerJ2y28t1pxF5GtgBsafd1NaKlOXgDNludcYt4KTVbQgjy5smZ2TpGpCwwWv5DWu73qNb/jgMz76GUv5pC7heHxmDEyqXtfp9G65sE4S50bQ2V4vvJO6/KVhieAPPuPeyu/TPjzuWsyV+VtJwlo5Ti7tl/phXO8rLVH8SUub6Mk5mtBBFC4BgGjmGwKnf0JN92EDDVbjLZbLK/WWdfo86eRo3HZ6e5effTi6+rWDanjo5z1vgqzlu1lpMqI8gBmS9L03nNptP4ypP3caBVZ3WueELXW+N0qjLvb9c4rbzmhK6lCYmjmTR7GNkCsDQTr59mS9oEsU+kIrQeJmweDVuWcaPBTl8eC3njZKruvxIrH5ndJJeMEIK882ps8wLm639LtfE5mu3vUi78JrZ1Saqi5b0kCHfRbF9Ly72eOG5gGtsYLf8+jvVSxAD/r1Yi7XAvT859kpyxmZMqv7Ws/oZ2/v/svWeYG4d5rn1Pn0EHthdy2XuRRIqUSPVuFUuWZLkmsa1i+9hx7MTOiU/i5OTLlzjlHMeJYydWYiu2ZVuu6r13ihLF3ju5jduwi14GM+cHFiQlqyyAwQJL4r6uvXa1i5l5qcViHrzleePrOBJ7jcWB62jU51TsOnWxNYUwFIXpSoDpvt9dBJ3MZjkcGWX/6Ah7RobYNTzE+r686WNA01ndPo3zOrtY1txaceF1xbR5/HLfZp7p2c/HypxMbNQ9CAgcSznTqO2WdUfLiJBvkq+UgzyAJuYzehkrhSFN3uSdLvkYztRu5sitzMHGIp49OKVGy2sFSWqkIfC/SaXXMxr7PsNjf42qLMTn/gSaunJK3TDfDctKkEy/SCL1BOnMNgQkDH0tbuODqMqSU+LfWG1MK86e4X9EQGRu6E+RHDAAnSyi2WNsHPk5TfpcR20e3om62DpFMBSFBQ1NLGho4prZ+RvPcDLBloF+1vd188LRQzx+cC9NLjdXzZrLB2bNw6uWXgJ9L5oMD4tCrbzYd7BssaWKMgHVxWDKGQsCj6yTcFpsSRrpXOV6tgou9elcctLFVsocc2Q4oRJ41Py70Fhmb11slYGuraJFXUEi9RiR+M8ZGv0LVHk2HteNGPoFU660Ztkp0unXSaRfIJVeh21nkKUO/J7P4DKuQBLLn5Suk8e2LfaFv00q18fChr9El6eOPUbOzrJu8D8RBZlVjbdWfBiiLrZOYRoMFxd3zeLirlmkcyav9XbzxMG9/GTbJn69azs3zFvIjfMWo8vOPw3Wts3gzu3r6I6N0ekpbyKlSfcw5JDYclUisyVpRM3K+VEVMltpy9les/dDl/zk7CymnUIRyuuXqwSqFEKVQsQye6sdypRHECTcxjW49CtIpJ4mlvgNI5F/QordiaFfgku/HEWeVZOiGyCXGyKVeYNUeh2pzJvYdhpJDOA2rsKlX4IiL6jZ2KcyhyM/YjS1kZmBO/Bpi6sdTlFsGfk1o5mjrG3+H7jkygvwutg6TdAkmQumzeCCaTM4OBrmnp1b+PmOLTx1aD9fWnEuZ7Q4O5F0dlMndwIbBrvLFluNuscxF3m3pDOUdtY7quIN8gWxNcku8vr42HYyN4Yi1p7YAvCqC4hldlc7jFMGQVDGBcqVpDMbiScfJp58kFjiXmS5E0M7D11djarMr2qfk2VFSGe3kc5sIZ3ZRNY8CORLo279CnT9PDRlab0Xq4Iciz9Gf+xh2jzX0uK+otrhFEVPYiP7os8x13cp7a7lk3LNutg6DZkZCPL1cy9k2+AxvvvmOr7x4lPcsmApn1i83LF+rhaXl3a3j83DvVw/s7x3PCHVzRvpw46Us1yyVpEyYiXFli5VJ7NlyPnewKQ5ik8pbzihUnjU+QwnXyGTG0aVGqodzimDIAjo2lno2llYVmS87+kFYvFfEo3fgyi40dSlqMpiVGU+ijwHsUJO/jlrFNM8RNY8QCa7j0x2F2auZzxOFVVZhN9zK7q6ElmeWc9gTQLh1BscGv0hQX0F032/X+1wiiJuDvH60I8Ial0sDd44adeti63TmCVNLXz7smv4j43r+eWurQwkYnx55RrHvMuWNrTxYu9BLNsuS8SFNDcZyyRhZnAr5fWZuSSNeC7taB+SLmlkrAyWbSFWoO5fyGylcpMstqTA+HVHJ/W6xVDo1Yqmd9HgWlvlaE5NRNGH27gGt3ENlhUllXmTdOZN0pmtJNPrjj9OllqQpWnIUhuS1IwkNiBKIUTBgyi4EAR93F5CAGxs28Qmg2XFse04lhUhZ42Qs4bJ5QYwc/2YuW4s60QmWhJDqMo83MaV40Jv3pTrKZvqxDL72Dfyz7iVGcwJfnlKGb/mbJNXB+8E4NymO5CEyZNAdbF1mqNJMl9acS5tbi8/2b4JURD48so1jgiRhYFmHj+ym6OxUbrKWN8T0vK+JyOZePliS9byjtFWFl1y5kVaE/PnSVsZDMn5SRzteGYr4fi534uC2ErWsNhyKzORBJ1IZkddbE0CoujFpV+IS78QgJw1Rja7h6y5n6x5CDN3lER6N1YZmwcERCSpCUlqwdDOQ5Y7UaQuFHlWfa9jlUmZ/ewe/jtkyc+8hq8j1Wh7wbuxJfwbwunDrGn+HG65cVKvXVNiywZMy0IShHoqeBIRBIFbFi7FtC1+vmMLnV4/H16wpOzzzgvkd0vtHh0sS2wF1bzYCmcSTHOX92JbMDaNmynHxNaJlT3piogtWVCQBXnSM1uyqKGIBkkzPKnXLQZBkPCq84lmdlQ7lNMSSfQjaWeja2e/5fuWlSBnDWNZYSwrhm0nsUlh21nAAkRARhDUfNZLdCMKPiQxiCgGplS25HQhkwuza/hvAJsFDX+BKk2tqc6j8Q3sizzDXN+ldLjOnPTr15TY6hkb4+a7fw6AJApIgogsiciFz+JbPxRJesvXSuGzVPjvvMu7Iolokowq5x+jyoUF03LeCV6W8sul5fzyaV2WUWV50oxAa4WPLVzG0cgYd2/fxLKmFuY3lLeIs93tQ5cVDkTKWyTtH99pOJopX2y4xoVRIpfGqQ4ffVxg5fcjOr8LTBAENNGY9J4tyPdtJXK1K7YAvNpijkZ+RjY3iiL9rgddnclHFF2IoguYVu1Q6jiAacXZPfy3ZHOjLGz8Kwy5vdohFUU0e4w3hn9MSJs5qX1aJ1NTYsun63z8jGXkLBvTssjZFmbOwrTHF0znTiydNk/675RpEk2nTyyfzuXI5vILqTO5HDlrYkuj305BgBlK4UPBpSjosoJLVXArCi5Vxa2quFXl+HJpj6bh1fLfn0qCTRAEvrjiHHYND/KdN9fxL5deU1b/ligIzPQGOViu2Bpf0zPmgNgyCmLLdK6hXRfHM1sVNDbVJRep3OSWEQFcUqimy4gAPi2fhY1kttNg1EuJdeo4Sc5Ks3v470iaR5kX+joedV61QyoK00rz6uD3EQVp0vu0Tqa2xJamccuypY6f17JtMqZJJpd7y0faNEmbOdK58c+mSco0yZg5UqZJ0szml01nzfyi6WyWkUSSZDZCImuSyGbI5t55kTSAKIBX0/HrGgFdJ2AYBA2DkMugweWi0eWiyeMmaBg1I8rcisrty8/mm+ue58lD+7hqVnl/WF3eIC/2HSyrId0ta8iCxGimfLFRyGwlHTQhLZQRK2tsalRFbBlyiHDi6KRftxg8yux831Z6W11s1anjIJadYe/IPxLL7GVO6MsE9PJMqieb/N7DnzKW7eX85j/EJVev56+mxFalEAUBXVHQFecXrWZyORKZDLFMhlg6/zmaThNNp4mk00RSaUZTKSKpFLsGBwknk78j0BRJpNnjoc3rpcPno9PvoysYoCsQQKuA4ej7cW7HNBY0NHHPzq1cNmMOchnZremeAPFshtFMkqBW2oJPQRDwKjrRbPmWDYZcEFsOZrZO6tmqFLpoEDEnP8PkkoKkcxFydhapRhcVC4KET1vCWHpLtUOpU+eUwbJN9o58i9H0ZmYF/gcNxppqh1Q0+2PPc3h872GrUV3T1dNCbFUSVZJQDYOAMbGpDNu2iWUyDCcSDMUTDMTjDMZi9EWj9EaibO7rOy7GRAGmBQLMb2xkYXMTy1pbaXBXZiP5yQiCwEcWLOWvX36GF48e4uKuWSWfq8Od72HqiUVKFlsAflUn4oDYco03xTtZRtSOlxErZzqqS24G0r0VO/+7UXgnmDDDeJXaXcXh15YTTr1ByuxDl5016K1T53TDtnPsD/8L4dQbzPDfSrP7kmqHVDRDqf1sHvklba6lFd97OBHqYmuSEQQBr6bh1TRmBH93msOybfqjMQ6HwxwYCbNveJiXDx/mib37AJgW8LN6Wifnzeh6x+Od4qzWdto9Ph47sLcssdXu9gHQm4iwpKF0Y0yvohNxsGfLycyWMQmZLUNykcrFK3b+d+OE2BqubbGlL4cxGE1totVTF1t16pSKbefYF/5XhpOv0uX/FK2eD1Q7pKJJ5cZ4dfD7uOQQqxo+XRPTrXWxVWOIgkC7z0u7z8u5XdOBvAA7HB5lc18fG3p6+e227fx663ZmhYJ8YP48Lpw1E1Vydi2FKAhcNmM2P962kf5YlFaPt6TzNOpuREGgL1HeihyvojuyjFoW81OqCQf7q2RBRhQkRwXc29ElF6ZtkrUyKOLkmTi6xn2NErnyhhwqjS61ocstjKU3TsmbQ506tYBlm+wPf4fh5MtM932SNs+11Q6paHK2ySuD3ydrJ7mg6Y9QpcpsNiiW6su9Ou+LKAjMDAW5YfEi/uaKy7jrwzdx+6qV5Gyb7776Gp+7934e37MXyy5t6vLduGDaDABe7jlS8jkkUaTZ8DCQKE8o+RSdmANlRMhnopwURoIg5Ff2VHgaEZj0JnlDDiIIInFzeFKvWyyCIBDQzmQsvQ3LrtygQp06pyqWnWVf+J/Hhdbv0e69odohlcSmkXsYTu3n7IY/wK92VDuc49TF1hTEr+tcs2A+3772av768kto9rj593Xr+dojj3E47FwTdYvbw+xAiNd6y5tGazY8DCTLE1seWSdu5lfilItL0hydRgQwRK2ii6J1MS+2kpNcSpQEGV3ykzCdWQReSQL6Ciw7QyS9rdqh1KkzpchPHf5fRpKv0eX/FO3e66sdUknsj77AgeiLzPdfyTT3ymqH8xbqYmsKIwgCy9va+OaVV/An569lKJ7gq488ynMHDjh2jRWt7eweGSKeLV2cNBluhlLliQSvomFjEzfLF0mGrDpe8tMlvcLLqPOp8NQkr+wBcMuNxM3aLiMC+LTFSIJOOPV6tUOpU2fKkLNS7B7+e8KpN5gZuG1Klg4BBlN72Djyc1qNxSwN1F5Wri62TgEEQeD8mTP49nVXs6CpiW+/9Cq/2bbdkXMvb27Dsm22Dw6UfI5G3c1IOknOKj0r5R63bHDC/kEXKyG2nC1Nvh2jILaq4LXllhuIT4HMliio+PX8VKLtQAa0Tp1THdOKsWv4b4iktzE7+AVa3FdVO6SSiJtDvDL4H3jkJs5pur0mGuLfTu1FVKdkgobBX156MefP7OInb27i4V27yz7n/IZGJEFk+1DpYqtBd2PbNiPp0qcJPeMLqGPZ8gWNIWskHciQnUy+Z6tyZURDqk4ZEfKZrWRulJydnfRrF0tQX0UmFyaW3VftUOrUqWkyuTA7hv6KeHY/c0N/TJPr4mqHVBJZK8lLA/+Gbdusbf4CSo0ux66pacS0abKzb2B8D6KELApIhR2Ikogiisjjuw7LWSNzKqNIEl9eu4a0meMHr7/BNL+fZW2lWy5oksysQJA9I6VnNkJ6XiiMpBM0GaVNhnjGM1txB/yxXFIFMltipcuILgSEqoktbJuEOYJXaZn06xdDUF+JKEiEk6/hnWJrRerUmSySZi+7hv9/zFyE+Q3/C7+2rNohlYRtW6wb/C+i2WOc3/ylmn59qimxNRiN8437n5zQY0VBQBZFVFk+vnhalQuLp/Nfa7KMJo9/X5bRlfx/a+Nf64qCUfisyrgUBUPN7zvUZKnk9TLVRhJFvnLeGr72yGN866WX+c4Hr8WraSWfb16okWcOH8Cy7ZLWCoW0/DuNcDmZrXGxFXNAbBkVaJDXJa2iYksUJDRJr4rY8sj5heQxc7CmX8wAZNGNT1vGcOpVpvk+OWX/huvUqRSxzF52D/8dAAsb/zcedU6VIyqdTeFf0Z/cxlkNH6fFWFjtcN6TmhJbTV4337jmkvyy6eNLp/Nf5yyLTC6HmcuNL5y2yJonLZ0e33eYzeXImPmPaCqd34GYzZEZ33uYzeUmFIsoCPkF07qKR8svl/ZoKj5dw2fo+AyNgKETcBkEXDpBl4HisNdVORiKwh+fv5avPvwod2/czOfPWVXyuWYFQjy8fzf98SjtHl/RxweOi63S+43cSiGzVb5I0iWVjGVi2RaiQ7V9XdLIWBlHz/l2DMlN0izfa6xY3ONiK54dhNrM0L+FkH4uB0a/Rzy7f0rfSOrUcZpw8nX2hb+NLPlZ0PAXGHJ7tUMqmb2RZ9gXeYa5vkuZ7b2w2uG8LzUltjRZZvm0yro/W5adXzg9vlz6+JLpTP7rRDZLIpP/iKfSxNIZ4pks0VSavrEIkWSaZPade1f8hk6jx02z102zz0Orz0t7wEtn0I/f0Cv673onZoVCfGD+PB7dvYfrFs6n0+8v6Twz/AEADo2Nlia21PIzWy45b+TpRBnROGkZtVt25vdiSPnzpHJpXHJlFIkhuUlWYRpRl3xIokrMHJz0a5dCyFjFobHvM5x8uS626tQZpz/2KIfH7sKtzmR+6OsoUqDaIZVMb2Izm8O/ot21nOXBm6sdzoSoKbE1GYiigKHmy4XBEt+mF7Jmo8kko4kUo4kUw/E4w7EkQ7E4h4ZHef1QD6Z1IovmN3S6GoLMbgoxt7mRBa2N+CZBgN2ybClP7dvPr7du58vnlbZIdJo3L9K6I2NQgkecLIp4FI1IpvQGclWU887vTlg/jO9HTObSjoktvbAfMZeqoNjyMJqZ/KlAQRDwyE1TRmzJoge/dsZxc8ZanEyqU2eysG2LI5Ef0xd7iKC+kjnBLyOJk//m3ylG0odYN/RfBNRprG68dcr8fZ92YssJVFmiweOiwfPui5Uty2YoFqdnNELPaITDw6McHBrhgU07yY2Ppc9oCHLm9HbOntHJ3OaGivSX+HWdy+fM4dE9e/iDFWcSnODC7JMxFIUGw0V3dKz0OFSd0XR503ouSXUos1UQW871bemFbFkFXeQNyU1f7nDFzv9eeORmItm+qly7FBqM8wmnNhDN7MSnLa52OHXqVIWclWBf+F8IpzbQ6rmGLt8fTBlx8k7EsoO8NPBddNHHec1fQBZL70WebOpiq0KIokCzz0Ozz8OZ00/UxTOmyf7BEXb0DbD5aB8PbNrJvRu30+z1cPGCWVy2cA5Bl7OZkasXzOOhXbt5bv9BPrRkUUnn6PD46IlFS47Bp+qMlZHZgrzXljOZrUIWyjmxVSgjJivoIm9IHlK5eEX7wt4Nj9JEX3Irtm1NiRfroH42kqAzmHiuLrbqnJakzAH2jHyTZLaHmYHbpqyHVoFULsqLA9/BJsd5LX+ILpXWFlMt6mJrklFlmYVtzSxsa+ams5YQS6V5/XAPL+w5yC9e38JvNmzn0gWzuHnlUsdEV7vPx/ymRl44VLrYavd4eaWMHYl+VacnXnpmDPJ9W06ILU1SAGfFli6dKCNWCkNyYWGTtpLHTU4nC4/cjGWbJHIjeSuIGkcSNULGuYwkX2WG/zakKfQOuE6dcomkt7N35P9gY7Gg8S+mrLVDgayV4qWB75AwR7iw5Sv4lNLtjKpF7b9FPcXx6BoXz5/FX113Kf/60eu4eP4sntq5nz/8+YM8snU3luXMcum1XdM5ODJKX7S07FSL20Mk8+7DAe+HT9WIlOn+7pTYqkwZ8USDfKVwSR6gOsamBcuHaLZ0c9vJpsl1ETk7xUhqXbVDqVNnUrBtm/7Yo+wc+mtk0cfipm9OeaGVs03WDd7JaOYo5zbdTqM+u9ohlURdbNUQ7QEfn71wFf/8kWtY0NrED19+g28++hyxVPk38FXTOgHY0N1T0vHN7vyNfiBR2o3eq2rEshlsu3Tx6JJVErnyXcxPnkZ0CmMSxJYh538HiSrYP3jkZgBi2WOTfu1S8aoL0eUWBhPPVDuUOnUqjmVnODD6bxwa+wEB/SwWN/3dlLZ2gHxz/+tDd9Gf3M6Khk/S7lpe7ZDewubRVyb82LrYqkHaAz7+/OqLuP38s9nS08837n+S4Vh5I/+tXi+tXg+b+/pLOr7JlS9bDSVLE1seRSNnWaRyZknHQ75B3snMlpNlRE0cz5ZVdGVP9TJbuuRHFnWi5tQRW4Ig0uS6hEh6O0mzt9rh1KlTMVLmANsH/xeDiefp9N7CvNCfIouT22rgNLZts3HkHo7G32Bp8EZmetZWO6S3sG1sPc8N3D/hx9fFVo0iCAJXLp7HN665mMFYgr95+BmiZWa4lra2sGNgAKuE7FKjkZ+8HCw1szVuShrNlP5vMGSFhAMCSRXzrYpOii1RENFEraI9WyfKiJOf2crbPzQTnUKZLYAm18UIiAzGn652KHXqVIRw8nW2DX6NdG6Q+Q1fp9N3y5QYYnk/to3ex/7o88z3X8EC/5XVDuctdCcO8OzAvXS5Jr4SrKZ+Ixkzx6GBMN3DYxwbjTEcTRBJpkhmspg5q6wS1FRlSUcrX//AhRyLxPjWky+V1cO1sLmZeCZL91jxjeoh3UAAhpKlZdgKYqucdTsuWSWdy2KNW2eUiiiIaJJCynJ2ZY8h6Y7vXHzr+fP7ERNVEFuQ79uaamJLlUIEjbMZTDyDZTv7+65Tp5pYtsmRsZ+we+Qf0KRmljT9E0F9RbXDcoSdY4+ya+wxZnnPZ2ngxmqH8xZGM0M83PdjAkoDH2j7+ISPq6lpxMFIjD+7+5F3/bkoCCiyhDK+A1FT5PwOxJM+a0ph76GMrhb2Ho5/aDJuTcWtqbg0FY+uok6BHYiL21u47byz+ffn1/HAlp3ccEZpE4XzGhsA2DM0zPRAce7Bkiji13TCqdJc4D1KvswWy5Z+w3MVGtvN7PH1PaViSBpJB0qSJ5Pfj1i5zJYoSOiSqyo9WwA+pZWj8dcxrQzyeNl0KtDivpKR5GsMJ1+lyVX7az3q1Hk/0rkh9o38M9HMblrcl9Pl/zSiMHX+Jt+LvZGn2Ra+j+me1ZwV+nhN3Z9TuQQP9P43AgLXtX8aTZq4Y0BNia0Gj4uvXHc+Ocs+vvfQHN97aOYs0mYu//3x3Ydp08x/zuY/R5Np0tn8Kp5U1iSdNd83G6bIEh5dw2to+AwNn0sn4NIJuA2CboMGr4sGr5uQt7q7Dy9ZMIs3j/Twi9e3sGb2dJq9nqLP0e7zocsyB0dGgOInOoK6wUiyNLHlPi62yikj5s+RyGUcEFsqyQpktirZIA/5UmIiV7rfWTl4x8etY+YxAuq0qsRQCj51CYbczrH4I3WxVWfKM5Jcz4HR72HbJnODX6HBVVu9TOWwP/o8m0Z+SYfrTM5uqC0D1pxt8kjf3USyI9zQcRsBtaGo42tKbOmqwuq50x07n23bpLM5kpn87sN4OpP/nMoQT2eIpzLEUhmiyTTRVJpoMs3+/mFG40nS2bc2couCQMjroiXgpS3gpbPBz/TGANObAnj0ynv4CILAp9euYOORXu5Zv4UvXVr86h1REOgKBjgUHi0phpBhMFaiC7xHHi8jlpHZMsb9sZIOTCRqouJozxbkM1vhTHleYu+HIXuq0rMFJ8RWJNs/pcSWIIi0uD/AobEfEM3sxqvOr3ZIdeoUjWVnODz2I47FH8ejzGJO6CvocmV3CU8mB6Mv8ebwz2hzLWN1022IQvWSG2/Htm2eHbiPo4n9XNF6C52uWUWfo6bEltMIgpAvJapy0XsQk5ks4ViS4WiCoWicwUiMgbE4/aNRXtl9mET6xI26NeBlblsjCzubWdrVSpOv+KzTRGj0uLlqyTwe2rKLj5y9jJYSrjM94Oe1I90lXd+v6RweK02oFTJbiwXFAwAAIABJREFU5UwTHhdbDk0kph0QbSejSzqpXGV9qFySh4FUab+/cvEqLQiCSHQKre0p0OS6iO7oPfTHHsQbqoutOlOLePYg+8P/SiJ7lDbPdUzzfeyUKRsCHIq9whsjd9NqLObcpjuQhNqSJhvCz7F97HVWhS5hoa+0vrja+hfVEIaqYIQU2kO+3/mZbduE40mODo1ycCDMvv5hthzu48WdBwHobPBzzrzpnLdgJq1Br6NxXbtsAQ9v3c2jW3fzqbXF/9I7/X6eTO8nmk7j1YrLyPk1nbF0Gtu2i66jG7KCAMTLyWzJBcuG8kWSLqmMZZ21UDAkraLregBckrdqDfKSoOCWG4hkS7MPqSaSaNDsupy+2AOkzGPocku1Q6pT532xbYu+2AN0R+9BFj0saPgLAvoZ1Q7LUQ7FXuH14R/Toi9kTdPnkASl2iG9hT3Rzbw89Bjzvcs5p+GKks9TF1slIAgCIY+LkMfF8hl50zjbtukZGWPzoT7e2N/Nb9Zt49evbmXJ9FauW7mIZV2tjjT6hdwuVs3o5Pk9B/nEOWcU3UfW5s2Lv56xCAuam4o61q/pZK0cKdPEUIr7gxAFAV1WiJulCyV9PLPlhLGpLqmOiLa3nlMnbaUrurvQJXvIWGmyVgalCk3qPqWNSHZqela1eq6mP/4g/bEHmRG4rdrh1KnznqTMAQ6Ev0Mks5OQsZqZ/s+iSL/75n8qczD6Em+M3E2LvpC1TZ9HqrHBm97kQZ7o/wUdxkwua/lwWffwuthyCEEQ6GwI0NkQ4JoVCxmOJnhhxwGe3LyXb/72GeZ3NPOpi1cwszlU9rUunDeTVw8cYWt3P2d1dRR1bEFs9ceiRYstn5rPhI2lU0WLLQC3rJIoaxrRuTKiLjnfs2WIJ1zkXbKzy8QLFLy2ErkYfrH851KxeJU2+pPbsexcTfVUTARVCtFgXMBA4mk6vDejSMVN5NapMxnYts1A4kmOjP0YBIHZwS/QaFxUU1N5TrA/+jxvDv+MVmMxa5o/X3MZrXBmkAd7f4RPCXJN++8hi+XFVzut/qcYDV4XH1q9hH/5zAe59dJV9IUj/PlPH+NXr2wpe9/h8mlt6IrCaweL791pGZ9iPBYrvoTm08ozJnUpKgkHMlvpMlzoj59LzE8jOunddnxlj1X5/YgJszoTiT6lDcvOEZtCOxJPpt37IWw7R1/swWqHUqfO75AyB9g1/P9xcPROPOpcljV9K2/Me4oJrT2Rp443w9ei0IqbUe7r+QEiEtd3fAZDKt+Nv57ZqjCKLHH58rmcO386P3puA79Zt5X9/cP80bXnYailPcEUSeKMaW1sPNpbdP+UKkkEDJ2BWPF9Pz4tLyYimdIyQi5ZKatBXpcLZUQnMlsqtm1j2jkUh5ox9fGdixV1kZfzmclq9W35lHzZPJLtxadOvUkoQ24nZJzLsfjjtHmuP+XKMnWmJrZtMZB4giNjdwMwM3AHza7LTzmRBbBz7BG2he+nw3Umq5tuq7lm+IyV5oGeu0iaMW6a9ln8SnEWD+9GWZktQRD+SRCEXYIgbBEE4V5BEAIn/ezrgiDsEwRhtyAIteW1XwU8usYXrlrDbZetYsvhPv7+3udIZUrP0CzrbGUknqB3rPgMR5PbzVC8eCf4gjFpyZktWSkrs6UIEqIgOpPZKhikVmAZdSVd5N3SuNiqmrFpGwgCY1O0bwugw3szlp2mL/ZAtUOpU4dktoedQ3/FwdH/wqPOY1nzt2hxX3HKCS3bttkS/i3bwvcz3bOac5purzmhlbNNHun9CUPpXq5u/yQtunMWN+WWEZ8Elti2vQzYA3wdQBCERcBHgcXAVcD3BGGKNXhUiMuWzeUPr17L3t5BvvvYKyWXFBe356epdvYVX85pdLkYShQvtrzquDFpyWKrvEXSgiBgSIojAqkSy6j142KrNOPXiWDI+XR2PBep2DXeC1lU8ciNU7ZJHsClTKPBWMux+KNkc6VZmdSpUy6WnaU7+iu2Dv4JCfMos4NfYEHDN9Dk5mqH5ji2bfHmyM/YPfY4s7zns6rhUzXX82nZFk/2/4rDib1c0nITM9wLHD1/WbLStu0nTvrPdcDN419fD9xj23YaOCgIwj5gFfDqe51vaCzO39/9NIosIksSmiKhKjKqIqMp4+t4VBldVdAUGUNT0NX8Z5emYOgqhqogirX9juDc+V2MxJL85PkNPLpxF9esWFj0Odr9Xryaxu7+IS5bOKeoYxtcLjb1Fe+V5BlvkI+VWEbUJZlkGZmt/DmUss8BeVNTgLTl3ETiiTJi5TJbkiBjVHFlD+RLiWOZqSu2ADp8tzCcfIWe6G+YEbi12uHUOc2IpLdzcPROkmYPDcZaZvg/fcoObORsk9eH7uJo/A3m+69kaeBDNZe1s22bl4YeZnd0E2sar2Kx/2zHr+FkDu8zwC/Gv+4gL74KdI9/73cQBOEO4A6AxrZpZEyTeDK/jidj5shkc2SOr955/yAEAVy6iltX8RgaHkPF59bxu3X8HoOAxyDoNQh6XYR8LhS5Our66rPms7P7GPe8vJkVsztpDRTnxyUIArObGzgwNFL0tYMug2TWJJXNohcxVSiLIrokl+wC75JVkmWWAPNThM5YPwAkyliM/XZOlBEnw2urOg3yAH6lg77kVnJ2tuYaWyeKIbfT5L6EgcQTtHquQz8Fswl1ao9sbowjkZ8wmHgOTW5mQcOfE9DPrHZYFcO00rw6+H36k9tZGryRBf7a7Ch6Y+RZNoZf4ozAeawMXlSRa7yv2BIE4Smg9R1+9Oe2bd8//pg/B0zgp8UGYNv2ncCdACtXrrT/8lPv/MuwbRszZ5HKZEln8rsPk6ksqUyWZMYkkcrkP9JZ4skMsWSaWDJNJJ6iZ2iMSDxF1rTe9m+DgMegOeihNeSjrdFHZ1OA6S0BAh6joupbEAQ+fcnZ/MmPHuLnL27iK9edX/Q5ZjYG2bqpn2wuV5TfVtDI2xKMJFO0F2nh4FbVko1JXbJCysxi2TZiif9vDUkh5WDPlpOZLU1UAaHi+xHdsrdq04gAfrUD27aITrG1PW+n03sLQ4kXOBr5KXNDX6l2OHVOYfIN8E9yNPIzcnaKdu+H6PDcjCRWftVbtUjnYrw08B3CmSOsbPg9ZnrPq3ZI78jW0dd4ZfhxFnjP5Pymayp2339fsWXb9mXv9XNBED4FXAtcap+Yo+8BTn4V7hz/XskIgoAiSyiyhNdV/PG2bZNIZwlHE4xGk4xEEgyNxRkcjTEQjrFxbw/Pb9p//PEBj86czkbmT29mYVcr01sCjv8SGrwurj5rPr9dt40jg6NMbyoujdwVCpCzLXpHo3Q1TPzYgJ7PwIylUrT7isuouRWFeIllRE3OP93SORNDLi0j4lxmK399J3u2REFEnwwXedlLb/JQRa/xXviVfJJ6NNM9pcWWKoVo83yQnuivac1cXd+ZWKciRDO7OTT6X8SzB/FrS5jhvw1D6ax2WBUlbg7xwrF/JWGOcG7TZ+lw1abr/Z7oZp4duJeZ7gVc1vrhiplRQ5llREEQrgL+FLjQtu2TO64fAH4mCMK3gHZgLrC+nGuViyAIuMfLi53vImpiyTTdA6McPhbmYO8we7qHeGNX3ssq6DU4e+F01i6dycy2kGPC6+qzFvDwhl088uYuPnflOUUd2xH0A9AdHitObBl5sTWaKr6R26WoxLOliR2XXDAlzZYhtmRiZvliphI9W5AvJVbS+gHyE4kJM1rS2iQn8CjNiILCWKas9081QbvnegYTz3B47IcsbvwmQgVfbOucXmRywxyJ/JShxAuoUoi5wa8QMtbUXL+S04TTR3hx4DvY5Liw5cs06sX1FE8WB2M7ebz/HtqNGXyg7RNIFW7YL7dn698ADXhy/Am0zrbtz9m2vV0QhF8CO8iXF79g23auzGtVHI+hsaCrhQVdJ/amjUQSbD3Qx5u7u3n2zb08sX43Xa1Brjl3EasXdZXdjO/RNdYumMFLOw/y+xetwKVNXIS0+/NZqd6x4ibT/AW/rFTx5S63ojKWLk1M6FL+6ZYsIzOlOVxGdHxlj6iRtCqf2TJtk7SVQpcq41T/XoiChE9pYyxbnYXYTiKJBtN8n2B/+DsMJp6l2X1ptUOqM8Wx7Ay9sfvpi96HTY4O7420ez6EJE7+3+pk05fcxrrBO1FFN+c3/3HNevF1J/bzSN/dNKptXNf+B5Oy+qzcacR3lay2bf8t8LflnL8WCPlcXHjGbC48YzbxVIZ12w/xxPrdfO/el7n/pW38/lUrWTTjnVraJs5Fi2fxzNZ9vLH/KBcsmjXh4zRFJuR20V+k15ZXz/cJRNLFiy2XrNAbK8124PgiabN0seR0g3za4ZU9uqRX1GcLTvLaykWrIrYAAmonfcltVbm20zQaFzAQf5KjkbsJGqtQRGeXx9c5PbBti+HkyxyN3E06N0zIWM103++fNkvPD0Rf5M2Rn+FXOjiv+YsYcm1OV/YlD/NA73/jVxq4ofNWtEl6Da3nzIvAratcumIe3/zstXzxpvNIZ02++ZOn+dGjr2OapSfu5rY10uB1s37v0aKPbfV5OBYpbvWOKknoslxiZkshWWIZ8Xhmq6yVPbIjYksSRGRRIuV4GVGreBmx4CIfr3KTfDoXIVUlvy8nEQSBmYHbMa14fh9dnTpFEklvZ/vQ19kX/hdk0c+ixr9mXuhrp4XQsm2LLeHfsmE4v1D6otav1qzQGkj1cH/PD3FLXj7UeZsja3gmSm3Zt04RRFFg9aIuzpjbwa+e2cTj63dzdCDMH3/kIlx68elIQRA4a1Y7L+w4SNbMFWVH0eR1s7XnWNHX9Goq0RIyW4ailNyzVRBbaav0zJYmymRypiP9Srro/DLqfGar8tYPUL39iMDxxvjRzFFajcVVi8MpXEoXbd7r6Y3eS6PrAvza0mqHVGcKkMge5Wjkp4RTb6BKIWYHv0ijccFp0/tnWhnWD/2QnsRGZnkv4MzQR2vOrLTAYLqPe3v+E00yuLHzdtzy5K7qOj2eERVCU2Q+eeVKPv+hNeztHuIffvoMqXRpQmRZVxvprMm+/uGijmvyuhlNJMlZ1vs/+CS8mlaSE7whK2StXNHXKxwL5ZcRLWyyDrQAapJK2uGerXyDfOWtH4Cqem0FxqepRjPFZ2NrlU7vh9HlVg6M/js5q3JbAOpMfdLmIPvD32XrwJ8QyWxnuu8TnNHybzS5LjpthFbSHOO5Y/+HnuQmlodu5qzQx2tWaA2nj3Fv938iCyo3dt6OVwlOegynx7OiwqxZMpMv3Xw+B/uG+ff7SlvBs7Azb6q4q6e49TsNbjeWbRNOFHdz8KgqsXTxWZ0TE4XFC6ZCZqucMmDBssGR/YiiQspyNrNlSBoZK4NlFy9GJ4omGsiCXNUyoiq5ccmhU0psiYLKrMD/IGMOciRyd7XDqVODZHNjHB77bzYPfInh5Iu0eq7mjObv0u79EKJQ+SbrWiGcPsLT/d8kmu1nbdPnmeer3aXZw+lj/Lb7TkRB5MbO2x1bLF0sNVVGHArH+PvvP4E2voJH0xQMTcHQ8x9uQ8VlaHhcKh63jtet4dLVmljPs2L+ND5++Qp++sQGnt6wh8vPLs6zx6NrtId87O0bKuq4Bne+uW84lqDRM/H6s1tVGRkbK+paALpyou/Koxb34qIdF1tllBFPEmxeRS/5PJBvknc6s6Wf5CLvlkswhJsAgiDgkr3Ezer2SwXUTkYzU38i8WR82iJaPdfQF3uIoL7ylHb3rjNxTCtGX+wB+mOPYNkZGl0X0um9BU1uqnZok053fAPrh+5ClTxc3Pq1mvbaGxkXWgICN3V+lqBavd9XTYmtgjKOxFIMDEdJprOkUlky2XcvGQmCgNejEfAaBHwugj4XDQEXjSEPTSEvrY1e3K7Jcem9ctV8tu7v5ZfPbGLF/GmEfMXdbGe3NLD1SH9RxwTHxVbRmS1NLcmc1DjJK6tYdAfFlhOZLU1SHJ8cNCZBbAG4JV/VllEXCKjT6U1uxbTSyKeQE/Y038cZS29mf/jfWNb8f0/ZnXV13h/TitMfe5i++IPkrCQNxlo6vbdgKO+4fe6UxrYtdow9xI7Rh2nQZrGm+fPo0uT2PRVDIaMFcOO0O6oqtKDGxFZDwM2fffaK3/l+zrJIprIkkpn8Kp5Emlg8TTSeIhpPE4kmGY0mCY8lOHB0iFj8rTdQr0ensyVAZ1uAmZ2NzJ7eSGPQ7XjaUxAEPnX1Kv70ew9y7wtbufXa1UUdP6M5yIs7DzIWT+F3TyxrE3DlxdZoorimbJeiEs8UL5iMcRf4UvquVAeEkiaWX4osoIsKoxlnFzoXMlsVNzaVvYxkiis5O01AnQa2zWimm0Z9dlVjcRJRUJkT/DLbBv+M/aP/xvzQ/zpt+nDq5CmIrP74w5hWnJCxmg7vh3ErM6odWlXIWinWD91Fb2ITMzxrOKvh4zW9F3U43T+e0RK5cdodhNTq7z6tKbH1bkiiiMel4ZlghiqdyTIUjjMwHKN/KELfwBjd/aM8u24PT5q7AAgF3Cye28YZCztZMq/NsYXUTQEPF505h2fe3MuHLlhaVHZremO+ae/o8Ch+98S8u3y6hoDAWLK4m7tbVcjkckXvVSwnsyUKAqoklSe2xnu2MmVMNJ44l1oRU1NgEprkfRxN7H//B1aQoDodgNHMkVNKbEF+OrHL/2kOjt5Jb+xeOrw3VTukOpNA1orSH3uQ/vij5KwkIX1VXmSpM6sdWtWIZo/xyuC/E80e44zQLczxXlKz/VkAg+le7u3+TyRB5sbO6me0CkwJsVUsmqrQ0RKgo+Wt6f+cZdHTP8reQ4PsOtDP61sO8+Lr+9A1hdXLZ3Dpmnl0tpY/pXD1uQt5esMent6whw9fPPGdUO2hfEq2Z2SMJdMnJrYkUcSjq0SKFlv5fqtkNluU2NLGH1vqRKEmyWVNI57IbDnhIu98g7yrUEa0Km9smraSmFYWWazOO0xDCqJJHsKZI1W5fqVpdl1ONL2D7sg9uJVZ9f6tU5hMboS+2IMMxJ8kZ6fGM1k341ZOX5EF0JfYymtDP0AQRM5v/iNajAXVDuk9OZY6yr3dP0AVVW7svIOA2ljtkI5zSoqtd0MSRaa3h5jeHuLSNfMxcxa79vfz6saDvLLxAM+v38uZizq56aozaW/2l3ydpoCHZbPbeXHzAW66cPmEG/hDHgNNkekLFzdl5jd0RosUW4aSv0HHs1l8+sQbzXW5MA1YmvWCLsllZrbK9+o6fi5RIeN4g3whszVJxqa5KH4xVNFrvRuCIBBQpzN6ioqtvNnp50iYR9kX/hcWN/0dhtxe7bDqOEjS7KUv9gBDieewbYsG13m0ez6ES6ndpu/JIN+f9TA7xh4moHSypvlzuOXaES7vRG/yIPf33IUuubix8w78SnVeF9+N07oRQZZElsxr5/aPrOVbX7+R6y9bxs79x/jLbz/EfU9tKclLqsDapTMJR5Ps7R6c8DGCINAa8HJstLg+Iq+uES3SDf5471W2ONGil9GzBfm+rbJMTcfFVsaRBnkV07YwLefWdhrjqx8qbWxaMOSrprEp5EuJY9lecrazorVWkESdeaH/iYDAnuG/x7Sc7fGrUx1imT3sGfknthz7I4YSz9PkuoTlLd9hTvBLp73QyuTivDTwXXaMPkSXexWXtP5pzQutI4m93Nf9A9yylw93fr7mhBacZpmt98Lt0rj+smVcfM48fvHwBh54agu7Dxzji5+8oKRpxjPmdiBJAm/u6Wb+9Ik35zX5PfSFi5sy82oafZHibrouNZ+hShTpBl+u2NLE8jJbBZ8tJ3qttPHyW9rKIovO9OypooKAMAliq7Cyp7oTiUG1C9u2GMt0E9JOzZKLLjczN/Q1dg3/NXtG/pEFDX9xWnkqnSrYtkU49QZ9sQeIZnYhi27avTfQ4r4aVZp8k8taJJw+wquD3yeZC3Nmw8eY7bmwpvuzAPbHtvNo308Jqk18qOO241n/WuO0zmy9Ez6Pzu0fWcutt6xh3+FB/v77TxBLlOC0rinMn9bM1gN9RR3X7HMzFIlj2xM3RnVrKvFUcb1Hx93cixRbWpnGpJokl1yCBFBF58qIJwxSncvKCIKAPhku8tKJMmI1CWpdAKds31YBn7aIWYEvEknvYH/4X7EraFpbx1lyVpL+2CNsHvgSe0b+kUxumC7/pziz5T+Y5vtEXWgBtm2zP/oCz/T/IxY5Lmr9KnO8F9W80NoZeZNHen9Ck9bOTZ2frVmhBfXM1ruy9qxZBH0G3/7vZ/n2fz/L/7zj8qInFhfNbOXXz24mlkhPeJKywesinTWJpzN49Ikd49VVYkXuOSyYkxab2VJEEVEQSJdcRpRIlbGIuiD2smUItuPnGs9sOb2MWpe0iostXXIjIlQ9s+WSQmiSh5H0IWZ7L6xqLJWm0XU+WWuUw2M/QhL+g5mBz9UtIWqYlNnPsfhjDCSeJmcl8arzmBb6GCH9HIQaXStTDbJWijdHfsaR2Gu0GItY3XgrmuSpdljvy6bwyzw/+ADTXLO5tv0PUGvc66+mxFYuZxGNpnC7tZpwhV80p407Pnoe37v7BX71yJt8/INnF3X8/Gn5kdO93YOcOa9zQseEPHmriJFocsJiy62pZHI5MmYOdYKCsNQ9hYIglJWd0kSJiFV6iU0SRERBdCSzpY6LrUo0yVe6jCgKIi7ZV9WVPZB/PgTVLsKZw1WNY7Jo81yHacXpif4aQVCY4b+1LrhqCNu2GEtvoj/+GGOpjSCINOjn0uq5Go86r9rh1RxjmR5eHbyTmDnA4sAHWej/QM0/n23bZt3wk6wfeZrZnsVc1fqxqk1kF0NNia2BwShf/fovEARwGSper47PZ+D3uQj4DYJBNw0NHpoavDQ1eVHVyoe/csl0Llszn6de2c3KZV3MmzHx/qsZbSEEAfb3Dk9YbAU9447w8QTTmybmXF2wcUhkshMWW4XMVim9V5oklZzZ0sqcRoTy+74KHC8jOpzZMiSdVIWtHyDft1XtzBbk+7aORXZiWhlk8dTvZer0fgTbztIbux+wmOG/veZvUKc62dwYg4lnOZZ4grQ5gCL66fDeTLP7clSp9pqlq41t2xyMvcTGkV+gigYXtHyZZr24FXPVwLItnhu4n61j61jkW8mlLTfW7PLrt1NTYivgN/jIzauIxdPEYyki0RSRaJKDhwYZG0uQNd/aJxEMumhvC9LZEaRrWgOzZjURDEx8P+BEuemqM9iw/Sj3PLSBb3zhqgnXsXVVob3Rz5Fj4QlfK1BYvxOf+Podt5a/wcUzGQKuidk4lNPoXo4xqSNiq8yJxuPnESsktkSdocyIo+d8J9ySl4g58edWpQhpM7Bta9zcdE61w6k4giAwzfdJBEGiJ/pbTCvB7OAXEWvYUftUxLZtIpntDMSfJJx6Dcs28WmLmO77BEF9Vf338S5krSQbhu/maPwNmo0FrG68tabX7hQwrSyP99/Dvtg2VgYvYk3jxO/FlcC2bV4aWj/hx9eU2DIMlUsuWviOP7Ntm1gszfBIjMGhKINDUfr7R+npHWXX7l5yuXxDeWODh4Xz21i6dBqLFrSjKOWrXk1VuOHyZdz163Vs3d3LsgUT34s1rTnAvp6JL5f2j4ulsSLW7xyfLCxi16EiSUiiULT1A5TX5K5KEpkyrRZUUXbI+qEw2eissak2CWVEALfspy9V/fJdUJ0BwEjm0GkhtqAguD6OJLg4Erkb04owN/RVZNH5N3t13komF2Yo8RwDiadJmf3Ioptm9xU0uy4/7W0b3o/h9EFeG/wvErkRlgRvYIHvyimRlU3lkjzU+yN6kge5oOlazgyeX9V4bNvm0f5neHHwtQkfU1Ni670QBAGvV8fr1ZnR9VbPD9PM0d0TZv+BAfbs7ef1Nw/x4it70XWFs1fM5OILF9DRXt7EyblnzuK+J7fw5Mu7ihJbHY1+1m0/TCqTRVff/52WoSqoskSkiAlIoyC20sVlaNQSy4GaXIbYEiUyZTa3q6LkyLqe4z1bDpzrZIxJmEaEvNdWMpcgZ5tIQvX+lA3ZjyEHGUkfrFoM1aLdewOK5OfA6H+wffDPmd/wP9HltmqHdcph2RnCqQ0MJZ5lNLUJGwuftogO74dpMM6tW3G8D7ZtsSvyONtHH8CQglzU8tUps2Irlh3jvp4fMJod4qrWjzHfN/GtLJXAtm0e73+OFwdf45yGFRM+bsqIrfdCliVmdDUyo6uRSy9ehGnm2L2nn9deP8C61/bx4st7OHP5dG647ixaW0tzhpclkQvOnsP9T21hKByjMTixaY22xnx69thIjK4JrgLyuXQiRWS2Cm7wyRI8s0oqI5YhmFQpn5WybbvkFLDjZcQKNMhnrAyWbSFW8F3jCa+tKD6luuPrIXUGI5lDVY2hWjS5LkaVmtg78n/YNvh15gT/qL7axwFs2yaW3cNQ4gWGky9jWjFUKUSb93qaXBfX3fwnSMIMs37oLgZTu+l0r2RFwydQxYnv7K0mw+l+7uv5IRkrxQc7Ps1019yqxmPbNk8ce57nB19lVehMrmu/fMLHnhJi6+3IssTiRR0sXtTBLTev4tnnd/LUMzvYsu1+rr36DK66fGlJ045rzprF/U9t4fUth/nAhYsndExLKH9DHAhHJy62DI1ocuKZkUIZMZkp0jNLLq1/SpWkkhZRQ16o2UDWslCL2Mn41nM4W0Z0umfr5GXULtlw9Nwn4xl3kY+bkeqLLW0GPYmNpHOxKTE27jR+bQlLmv6BvSP/xK7hv6XdcwOdvo8iVjHjOFVJZrsZSr7EcPIlUmY/oqAQ1FfR5LoIv7Z8SpS9aoXu+AY2jPwUyzZZ2fj7zHCvqXnvrAJHE/t4qPfHqKLGzdM+R5NWXXFt2zZPHnuB5wZe4ezQGVzfcWVRb6ZP+VcCj1vjuqvP4MLz5vOLX6/n/gc3sm/fMe7DFW+YAAAcl0lEQVS49SJ0vbgGyqaQh+ntQTbt7J6w2GoO5G88x8ITX/PhKXL9TmGyMFlk/5Umy6TN4jNUqiQxli6tJ6kgsLJWrgyxJRE3y++zUgQJQRAqMo0IkLLSuKic2HJJteEiDxx3jx9JH6TNtbTK0VQHXW5hcdPfcXjsLnpj9xFJb2FW8A/rfUQTIGX2M5J8leHky8SzhxAQ8WmL6fDeREhfjTRFMjG1QtZKsnHkFxyOvUpIm8Gqxs/gVVqqHdaE2RnZwNPHfkNAaeT6jk/jrfKbyUJG67mBV1gZOoMbOq4qumpxyoutAj6fwW2fvoD581r5+S9e45+/8wRf+cMrihZcS+d38Mhz20mkMrj09+8TcOkqhqYwPBaf8DXcuspgZOKPL5QRS9lzWErPliqVUUYcd4DPWCZuSuuzUESZjJUo6diTEQQhnyVzWGxpk7SMurAfsdou8pC3fxAEkZHM6Su2AERBZWbgs/i15Rwc/T7bBr9Gh/dm2jwfrPcVvY1ktoeR1DpGkq8Rzx4AwKvOo8v/aRqMNXVn9xIZSu1j/dBdJHIjLPRfzaLAtVPGHsG2bV4beYrXhp9imms2V7f9HrpUuTesE43psf7neGG8dFhsRqvAaSO2IH9zveC8+fi8Bt//r+e484fP88XPXVpUSXHRnFYefnYbew8NsHzBxLyzGvxuhosQTx5dLSqzpUh5V/di+69KFU3lTBQq4zsIy2mS1yS57InGAqpDnl0nczyzVeEmeeO4i3z1xZYi6viUdoZPwyb5dyJknINXXcChsR9yNHIPQ4nn6fJ/5rTu5bJti3h2H+HU64wkXydpdgPgUecy3fd7NBjnoskT9zGs81ZydpYdow+xO/IELjk0pZrgIW/t8PTAb9gV2chC3woubbmxqoM/kBdaD/c9zctD61ndcBYfbL+i5D7c00psFThj+XQ+estqfvaLdTzx1DauumLi78RnTWtEFAX2HRqcsNgKeQ3CkYlnYtyaSiKVmXATuSAIaLJMquieLYlEsvisjipKJa/LObmMWCpOTSNCvkne8Z6t8czW5LnIV7+MCNCgzeRofAO2bdX7agBFCjA39Mc0pS7m8NgP2TX8t/i1pUzzfQKPenpYZOSsBGPpLYRTGxhNvUnWGkNAxKstosV9BSFjNarUUO0wpzyjmW7WD93FWKabmd7zWR68GUWcmOdiLZDMxXm49yf0JA9ybsMVnB26pOq9ZZZt8WDvk6wb3sC5DSu5rv3ysmKqKbEVjSR56tEtNLf4aG0P0tjsq9jangvOm8eu3X08+MgmVpzZRVPTxEzdNFWmszXAge7hCV8r6HUVZWzq0lQs2yaVNY/bOrwfhqJMamarHOsHoKzMlCY50yAPFRJbhQb5SXORH6v4dSZCSJvJgeiLRLPH8Kl1+4MCAf1MfNq3OBZ/nN7ob9g2+GcE9LNo91yPV11U9ZuKk+SzVwcYS29mLL2ZaGY3tp1DFl34tTMJ6GcR1Fcgi6ffEEUlsOwcuyNPsGP0QRTRzdrmL9DuWlbtsIoinBnkgZ67iJljNWHtAHmhdW/Po7wxspnzm1bzgdbyxV9Nia14LM29vzhhEqYoEu2dIWbMamLW3BbmLmjHH3CmUVIQBD764VVs39HDfQ9u5PbPTHyJbld7iI07uyeceQp4DMbiKSzLnpB4dGknfLMmKrY0RSZdZM9WqT5biiSVnJkqZLbKKSMqQvnGqAU0SXF8N+JklRGhdlzkARq0fMliOHOgLrbehigotHmupdl1Kf3xR+iPPcSOob/Co8yi2X0VDcYapCmUiShg2xYJ8zDR9A4i6e1EMtsxrXzLhFuZSZvngwS0M/Co8+uTmQ4Tzfazfui/GUkfpNN9FmeFPjHlJoGPJPbySO9PkQSRGzvvoM3oqnZI5Owcvzr6EJtHt3Nx81oub7nAkTdENfXsb20P8I/f/X0G+sfo7w3T2x3m6OEh1r28l+ef3gFA5/QGlp81g7PXzKGpubwVA36/i0suXshjT2zlumNn0NoyMQ+ujtYAL76xn0gshd/7/s17fo+ObUMsmcbnfv8XVNf4+p1irBw0WSp6sjDveVVaZsu0LCzbRizySVjo2SqrjCjJZK1cWV5dBTRRcdzUVJPyv7/JMTb105c6UvHrTASv3IwquRlOH2CmZ221w6lJJNGgw3sTre5rGUo+x7H4YxwY/R6Hx35IyDiHBmMNPm1JzTbT56wEsex+Ypk9RDO7iWV2YY4Pq2hyM0F9FX5tOX5tCYo0sd2udYrDti32Rp9ha/g+ZFFlddOtTHOdPeUypFtGX+X5gfsJqs1c1/Ep/Er1d1ialsnPj9zHjsgermy9iIua1zh27poSWwBut8bM2c3MnH2iUdKybLoPD7FrRy/bNh3hkfvf5OH7NrBgcQeXX72c+YvaS36iXXLhQp54ahsvvLibW25eNaFjOlryLyJ9g5EJiS2vK19WiiRSExJbxviC7eLEVvGThYokliS2CoLJLMErywmxpYgSNjZZO4da5rtlVZSJmRPfQzkRJEFCEZWKTyNCwUU+XnUXeQBBEAmpMxhO769qHFMBSdRocV9Js+sKYpldDCaeZSS1jsHEc0iCjl9fjl9bjk9bgi61VeVGms2NkjCPkMgeJp49SDyzn//X3rlHSV2ed/zz/i5z2dmdvcMuLMsusIiIEJCLIlWxShCNgihegjGxSTTJadM25+QkTZv2nJ42Pc05aZs0bU/T2KAYjBdi1IBVxAaIEVEwXAWW+2Xvy9537m//mJlltMj+5v6b5f38wzDz+73zwsMw332e5/0+vtB5JNHRaEXmJCrdN1LsmIHXcbVqbs8B/cE23ut6ik5fM7VFs7muYi1uIzWj7nwRlmG2dbzC3p7f0eiZwfKah3Do+c/qBsIBnj71Is0DJ/jMhGUsrpqf0fVtJ7YuhaYJ6hurqW+sZtmdc7jQPcg7O46wfetBfvT9TVw1cyIPPLKY8bXJ/yTl9br51Ox6du46zupV89H10Rt7a2L9Xa0dfcyYMrp3SbE7Krb6B/1QPfqe3CmYlDoMnUDSma3UGt0dCScKkxVbF3u2IqNcebk1ov9sg5HwyOPU18p8zxZE+7Z8kczOXLwUdnKRh2gpsbXnAIHwIA5dzQkcDSEEJc6rKXFeTYP8In3+/XT73qXHt5vu4WhLhal58Tim4TEbKDIm4zIn4NJr0LX0jsRLGSEU6cMf7sQf7sAfasMXasEXbmE4eJZg5OLBC4degcecQmXREorNaRQ7mlTfVQ6JZ7P2X3gJTZgsqPo8kz3XF1w2azg8yOaWZzgzdIzrym9icdUdWZ2yYZWh0DDrTj7PmaFz3Fd3F9dVZL7vrSDE1scpr/Bwx91zue2O2ex46xCbfrWb7313I/c9fANLll56kPXlWLhgCu/vOcXhIy3MvHr0uYfl3iIMQ6O9y9qR+5LYcOkBi67wrrhvVsB6psppGEnZRUCsHBeOJF2OM2KCNJRCdsrUovemm9lKd404UZ+tzJYRIXoi0Z+DMqKdXOQhsW/rBLXuWXneTWGhCQdlrnmUueYhpcQXOk9/4CD9gSMMBpvp9f8eKS/+mzc0Dw69AkMrxdA86KIIXTgRwkQQ/ZxJIkgZJCz9RKSPUGSQUGSAYKSHUKSXiPzoZ8jUvLiMWspdC3Cbkygy6yky6lVJMI/0B1vZ1bmOLv9xaouujWWzCi8eXf5WXjm/joFQL7fXrGGm1/pcwWzSHxzgyRPP0u7v4uHJq5hVOiMr71OQYiuOaeosXTaLeQun8PR//YYN63bQ0d7HyjULkxIPM2dMwDQ09u0/a0lsaZqgssxDR7c1V/h4GdGy2IqVEX1JzDp0pNCzZepx4ZNcOdBMIzt1sQSZnvUDkLGRPZk62fjRdZ1Zt36ABGNTm9g/VDgbEEKjy3dMia00EELgNifiNicyzhOdvxaRAYZD5/GFWvCH2vCHOwiGLxCM9DIcPEdYDhGRfqQMI4l+vgQaQphowoEu3OhaEaZeRpE5GVMrxaFX4NCrcBrVOPVxGJrKRtqFiAxzpG8LB3pewdAcLKz6AvWeRQWXzQJoHtjPG63PYQoHq+set0UjPEB3oIefHt9Af2iAzzesoamkMWvvVdBiK05pWRFf/fPlvPDM22zZvBfD0PnMauv1VofDoGlaDYcOt1i+p7LMQ3ePNaPSophL/eCwtbJSfPxOMpkth558GdHUUysHjmSnUihBGhkwNU0sI6aLQzMz7iAP0TKiPxfWD/GRPTZwkYeouWmpWUen6tvKOJpw4DEb8JgN+d6KIsv0BM7yXtdTXPCfYmLRXOZVPoRLL6zeLIhaKLzb/SY7u7ZQ45rEnbWPUGza48/ROtzOkyeeJSTDfLHxYeo9oyda0mFMiC2IZpvuX7uYYDDMa6/soW5yJXPnW1ep05vG89IrexgY8FFcPHqzXkWZh32Hz1ta22ka6Lpg0G9NbDnjYisJKweHoSedoYmLrVCSwicdY1JHXKjJ1Hu2RsqIMn2x5dQMQjJCWEbQM9g74NKd9Aazn21y2chFPk6VayonBn5LRIYLZkyIQmEHwjLIoZ5NfNj3Gg6tmOurv8wkjz3KbcniDw/zeusvOD54iJne+SwdtxJDS248XrY4OXiGdSefx6GZPD5lLeNdFpqp02TMiC2Ipt4f+NyNnDvTzc//ezvTptdQ4rXWRDp1SvQkzYmTnVw7a3Rn+DKvm74BH+FIBF27/Je0EIIip8NyZstpxOYHJnG6MNrsnpyAuZihSu4+I43MVlzgpepAD5kZ+RMncVajW8/ccXuX7syJ9YPdXOQBqpzTaO57i57AGSqcDfnejkJREHT6jvF+19P0BVuYXLyIOeVrCs43K06Xv41ftzxFb7CbW8bdw+zSG2xT/jzYd5QNp35JqcPLHzU+RLkjN5m2/B8DyDCGofPIl27GNxzg1Y3vWb6vflIlQsCp052Wri8rcSOlpH/AWl9Okctk2G+tXKVpAtPQk8psmYaelDiDxJ6t5ERLvBQYkjKp+wAMkRnrB8hMZssR+0kr48OoNSf+HJxGhLiLvL3EFkCn/2ied6JQ2J9gxMeerg281fZ9QtLPkvF/zMKqxwpWaB3t38dzZ36MP+xj1cQvMadssW2E1q7uD1h/8gVq3ON4YuojORNaYLPMlm84QEdLD9UpWDgkUjuhnD+4dSbbtx5k2Z2forK6ZNR7XC6T6qoSzp635sbtjflr9Q34KPOO7mrvdlgXWxAtJQaC1sWEw9CJSGnZpR4SREuKGbFUmtzjWbFQGmVERyZPI+qxzFY4BBnMcLt0J4FIgIiMZP1oc9RFvier75EMbqMMj1lFp+8Y072353s7CoVtOT+0l93dP2c43MO0kluYVbayoGYaJhKRYd7u/B/ev/Abal31rKhda5v+LCklW9t3sKVtO9NLpvJw/aoR8+lcYSux1d3ex99+7Skarqrl5jvn8KkbplnyvboUt6+Yw/atB/nfLQdY/dD1lu6ZUFtGS4u1Ly1vrK+rz2Jmy+U0kxoUnewoncRmd5dF7ykzxd6ri++VvGDShEDXtIxkttI50TiyloiXEbM0HzHsp8hIzw9pNDyG1zYu8nGqnFNpHT6QEZd/hWKs4Qv3sqf7Oc4OvofXUcsN1d+k0jkl39tKmaFQP5tbN3B26BizS6/nD6rvsk1/VkRGeOnca+zq/oB55ddyb90K9Dz0ktqqjDhuYjl3P3Ijg33DrPvBa/z9n6xn367jKa1VXuFhzrwGdv72CCGLp/RqxpfS3tFP2IKIKIk5wfcPWuvLcTtTyGwlcbowlROCI1mmZHu2Yl+eqYodU0u+v+zj90N6w6zjZPJkYyIuPZfDqC+6yNuFKud0/OEB+oOt+d6KQmEbpIxwvH87r537G84P/Z5ryu7mttq/LGihdX74JBtO/5DW4dMsq1nD0vGrbCO0AuEAT518gV3dH3DLuMXcV3dXXoQW2CyzZRg6t626jlvvmcu+d0/w6w2/4yffe5V5N07ngSeW4vY4k1pv0ZIm9rx3gsMHznHNnPpRr6+u9hKJSLovDFJddfnSY3FRNAU5MGTVO8tMzsohSUd400i+8Tzes5VsSS/esxWOJN+zBWAILa0yYiZNTc2Y2Mq0i7wzJrYC4dy5yA+FBigx7WF2WO2K9m11+I+qodQKBdAXaOH97mfo9B2l2jWd6yrXUmKOPoHErkgp+aBnBzs6N+E1yllT/wWqnRPyva0R+oMDrDv5POeHW1k5cTmLKufldT+2EltxNE1jzvVTmTW/gS0v7WbThnc4d6qTr373HspHEUGJzLimDqfLZO+eU9bEVlW0IbGzs39UseWJjeCx7J3lMLIrtlLIUhlaaicDjTRd4A1NS6sEmEmx5Uw4jZhJRsqIOfHaumhsahexVWyMx6l76fI3M7XkpnxvR6HIG2EZ5FDvZg73voahuZhf9TkaPPZpGk8Ff3iYLW0v0Dywn6nF13D7+Ptx6tltl0iGdl8nPzv5HAOhQdY23MdMb1O+t2RPsRVHN3Q+fd8CGq+q5Sf/8Co/+quN/Nn37qekbPSGdIg6zE+fUcuHB85Zur6yMiq2ui+MblaqaQK3y2TQYmbLYRr4k/TNCiYjtlKwVBgpIybpBG+meF/i/aneCwknGjNxGlGPn0bMrNiKN1/mwv6hyLCXsSlE7U6qXdNo9x3J91YUirzRNvwhu7t/zkCwjfriRcwpvw9X7IejQqXDf55N59fTF+xmSdUK5pXfZCvheHzgNOtPvYguNL485bPUFdkj22arnq1PYvq1dXz1u/fQe2GQn/7jJks9VXGumjmRzo5+LnSNPlqnrDQq4qyILQCP28FQEq7wgWAIadEuwdT1pHyk4vMKk2laT7lnS7s45icVTE231WxEyF6DfC7sHy4Oo7aP/QNAtXM6w6ELDIas2akoFGMFX7iPdzufZFvbPwERbhr/dRZVPVbQQktKyb6enTx3+seEZIjVkx7nuoqbbSW09lzYz5MnNlBsFPGVaY/aRmiBzTNbiTReVcuDX7mVp//ldbb+aje332ttHM/UpmhN/FhzG/MrL+9bYhg63hIXvT1DltZ2uxwM+ax9STsdBlJCMBTGYY7+124mmdmKC6BwEgIo1cyWkYb1A4CeZs9WumXMROKnEYOFnNnSixE2c5EHqHZNB6DDdwRPcVWed6NQZB8pI5wYeJt9PRsJRXxcXXoHV5euQNdyazOQaQIRP1vbNnK4/wMmFzWxrOZBigz7+IAlWjs0eiazdvK9WT8FniwFI7YAFtw8g707j7P5FztZcPMMykYRTwATJlVgGBpnTnYyf9HUUa/3et309g1b2o/bZTLss5a5cJixE3RBa2LL0LWslxH1FMWWPiLsUmyQT7OMaGbAGHVkrWydRox55eSiZ0sTOkV6MUM2KiMCeM1aHLqHDt9RGooX53s7CkVW6Q2c5/3u9XT5jlHtamJuxcOUOuyTWUmVDn8Lm1vW0xvo4obKZcyvWJp178BkCEVCbDy7iT09+5lbfi33Tlwx0o9sJwpKbAGsfHQJ+3Yd5/UXdrHm8aWjXm8YOjUTyjl3ptvS+qXJiC2nSXevtSxYfN6hPxiimNFPVTqM5OwR4mXEZERMqr1XZprGpIaWXmZLCIEh9LQEW5yRMmKGbROiIk7k5DQiRPu27FZGFEKj2jmdDtW3pRjDhCIBDva+ypG+NzA195hogIdotmh/77ts63gZp+5mVd2XqSuyl0XFYGiI9ade5OTgGW4bfxO3jrvRtn/vBSe2Ksd7WXjLDN7ZepA7P3sDHgtDoyfUlXPkUIul9YuLXbS29Vq61uUy8bVbKyOOWDNYzFYZup7UgOhU+q9SEWjAyMDmZEqWH3lfoac1GxHigi0Tma14liyzYksTGg7NzElmC+Ije+yV2YJoKfHc0B4GQ514DFVKVIwtWob2saf7WQZDnTQUL2Z2+eqCHbOTSCDs4832jRzp/32sbPjAyEEcu9Du62TdyefpC/bzYP1K5pTNzPeWLot9coFJcNOKOYSCYd7fdtjS9eNry+i5MIjPQn9VSYnL8rzDZLyzHDGx5bc4gsfUtaxntlLp80q8L9XslKlphNPIbEXXSK/JPo4mNAyhZVxsQdTY1J+rzJZewmDYXpktgHGuqwBUdksxphgKdfN2+3+wo/1f0TWTW2q+wYKqR8eE0GrznWHD6R/S3L+XxVXLuXviY7YTWs39J/j3Y+sIRAJ8ccrDeRNaey4cs3xtwWW2AOoaq2mYXsNgvzVRNKGugsmN1QwN+nG5Lu9sO67ay4TacsLhyKijgsZVlVBbbe10SYnHRUNtBbpuLcVZ7S1mUpV1zyS3aTKlqgK3hX6wOKamMaWinBJncmaxQgiayispc6Y2w6uuuBRfkkOzP05jcRUVTk9aa8RpKK7Ba2ZmrUQmumsoycK6l6LSWUNPsNN243G8Zi1exwRCMjeiU6HIBft7XqZ1eD/Xlq+iyXsbuijIr9JL8tvOzYRliNWTnmCCuyHf2/l/RGSE19u2UWp6+VzD/VQ48uMt6AsH+MXpbZavF1atCHKBEKIDOJXvfWSRKkCdgy9cVPwKGxW/wkbFr3AZy7GbLKWsHu0iW4mtsY4Q4j0ppTXPCoXtUPErbFT8ChsVv8JFxa5Ae7YUCoVCoVAoCgUlthQKhUKhUCiyiBJbueU/870BRVqo+BU2Kn6FjYpf4XLFx071bCkUCoVCoVBkEZXZUigUCoVCocgiSmzlACHE94UQHwoh9gohfimEKEt47dtCiGYhxGEhxKfzuU/FpRFC3C+EOCCEiAgh5n/sNRU/myOEWB6LT7MQ4lv53o/i8gghnhRCtAsh9ic8VyGEeEMIcTT2a3k+96j4ZIQQk4QQbwkhDsb+3/x67PkrOoZKbOWGN4BZUsrZwBHg2wBCiJnAg8A1wHLg34QQ9pugqdgP3At8xMFOxc/+xOLxY+AOYCbwUCxuCvvyM6Kfp0S+BbwppWwC3oz9XmFPQsA3pJQzgeuBr8U+c1d0DJXYygFSytelHJl0/A5QF3t8D/CslNIvpTwBNAML87FHxScjpTwkpbzUbCgVP/uzEGiWUh6XUgaAZ4nGTWFTpJTbgO6PPX0PsC72eB2wMqebUlhGStkipdwde9wPHAImcoXHUImt3PMYsDn2eCJwJuG1s7HnFIWBip/9UTEaG4yXUrbEHrcC4/O5GYU1hBANwFxgJ1d4DMfOQKc8I4TYAtRc4qXvSCl/FbvmO0RTrM/kcm+K0bESP4VCkX+klFIIoY7R2xwhRDHwIvCnUsq+xJmtV2IMldjKEFLK2y73uhDi88BdwB/Ki34b54BJCZfVxZ5T5JjR4vcJqPjZHxWjsUGbEKJWStkihKgF2vO9IcUnI4QwiQqtZ6SUG2NPX9ExVGXEHCCEWA58E7hbSjmU8NLLwINCCKcQohFoAt7Nxx4VKaHiZ392AU1CiEYhhIPogYaX87wnRfK8DDwae/wooLLNNkVEU1g/BQ5JKX+Q8NIVHUNlapoDhBDNgBPoij31jpTyidhr3yHaxxUimm7dfOlVFPlCCLEK+BFQDfQAH0gpPx17TcXP5gghVgD/DOjAk1LKv8vzlhSXQQixAbgFqALagL8GXgKeA+qBU8AaKeXHm+gVNkAIsQTYDuwDIrGn/4Jo39YVG0MlthQKhUKhUCiyiCojKhQKhUKhUGQRJbYUCoVCoVAosogSWwqFQqFQKBRZRIkthUKhUCgUiiyixJZCoVAoFApFFlFiS6FQKBQKhSKLKLGlUCgUCoVCkUWU2FIoFAqFQqHIIv8H5yVnfDFvIvoAAAAASUVORK5CYII=\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig = plt.figure(figsize=[10,10])\n", "cm = plt.cm.coolwarm\n", "\n", "ax = fig.gca(projection='3d')\n", "\n", "ll = np.array(ll)\n", "llz = ll.reshape(mm1.shape)\n", "surf = ax.plot_surface(mm1, mm2, llz, cmap=cm,\n", " linewidth=0, antialiased=False)\n", "plt.show()\n", "\n", "fig = plt.figure(figsize=[10,10])\n", "plt.contour(mm1, mm2, llz, 20,alpha=.8)\n" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "## Expectation Maximization\n", "Now we will learn the parameters using the EM procedure for learning Gaussian mixtures.\n", "\n", "Starting from the PDF $p_1()$ and $p_2()$ of the single components:\n", "\n", "$$p_1(x|\\theta) = \\frac{1}{\\sigma_1\\sqrt{2\\pi}} {\\rm exp} \\left\\{ -\\frac{(x-\\mu_1)^2}{2\\sigma_1^2} \\right\\}\n", "\\qquad\n", "p_2(x|\\theta) = \\frac{1}{\\sigma_2\\sqrt{2\\pi}} {\\rm exp} \\left\\{ -\\frac{(x-\\mu_2)^2}{2\\sigma_2^2} \\right\\}\n", "$$\n", "\n", "the mixture PDF is:\n", "\n", "$$ p(x|\\theta) = \\pi_1 p(x|\\theta_1) + \\pi_2 p(x|\\theta_2) $$\n", "\n", "If we know (or guess initially) the parameters $\\theta$, we can compute for each sample \n", "and each component the **responsibility function** defined as:\n", " \n", "$$\\gamma(i, k) = \\frac{\\pi_kp(x_i|\\theta_k)}{p(x_i|\\theta)}$$\n", "\n", "and starting from the \"effective\" number of samples for each category ($N_k$) we can compute the \n", "\"new\" estimation of parameters:\n", " \n", "$$N_k = \\sum_{i=1}^N \\gamma(i, k)\n", "\\qquad\\qquad\n", "k=1,2\n", "\\quad\n", "({\\rm note\\;that} \\quad N_1 + N_2 = N)\n", "$$\n", "\n", "$$\\mu_k^{new} = \\frac{1}{N_k}\\sum_{i=1}^N \\gamma(i, k) \\cdot s_i$$\n", "\n", "$$\\sigma_k^{2\\,new} = \\frac{1}{N_k}\\sum_{i=1}^N \\gamma(i, k) \\cdot (s_i - \\mu_k^{new})^2$$\n", "\n", "$$\\pi_k^{new} = \\frac{N_k}{N}$$\n", "\n", "Now we just loop \n", "\n", " 1. recompute $\\gamma(i, k)$\n", " 2. estimate updated parameters\n", "\n", "until convergence." ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [], "source": [ "d = np.array([2.3,3.2,3.1,1.6,1.9,11.5,10.2,12.3,8.6,10.9])" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[6.56 6.56]\n", "[18.1324 18.1324]\n", "0.5\n", "[6.56 6.56]\n", "[18.1324 18.1324]\n", "0.5\n", "[6.56 6.56]\n", "[18.1324 18.1324]\n", "0.5\n" ] } ], "source": [ "s = d\n", "N = len(s)\n", "max_iter = 3\n", "\n", "# Initial guess of parameters and initializations\n", "theta0 = np.array([0,1,0,1,0.5])\n", "mu1, sig1, mu2, sig2, pi_1 = theta0\n", "mu = np.array([mu1, mu2])\n", "sig = np.array([sig1, sig2])\n", "pi_ = np.array([pi_1, 1-pi_1])\n", "\n", "gamma = np.zeros((2, s.size))\n", "N_ = np.zeros(2)\n", "theta_new = theta0\n", "\n", "# EM loop\n", "counter = 0\n", "converged = False\n", "while not converged:\n", " # Compute the responsibility func. and new parameters\n", " for k in [0,1]:\n", " # E Step\n", " gamma[k,:] = pi_[k]*norm.pdf(s, mu[k], sig[k])/pdf_model(s, theta_new)\n", " # M Step\n", " N_[k] = 1.*gamma[k].sum()\n", " mu[k] = sum(gamma[k]*s)/N_[k]\n", " #sig[k] = np.sqrt( sum(gamma[k]*(s-mu[k])**2)/N_[k] )\n", " sig[k] = np.sqrt((sum(gamma[k]*(s**2))/N_[k]) - mu[k]*mu[k])\n", " pi_[k] = N_[k]/s.size\n", " print(mu)\n", " print(sig**2)\n", " print(pi)\n", " #print('________')\n", " theta_new = [mu[0], sig[0], mu[1], sig[1], pi_[0]]\n", " assert abs(N_.sum() - N)/float(N) < 1e-6 \n", " assert abs(pi_.sum() - 1) < 1e-6\n", " \n", " # Convergence check\n", " counter += 1\n", " converged = counter >= max_iter" ] }, { "cell_type": "code", "execution_count": 14, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Means: 6.56 6.56\n", "Std dev: 4.26 4.26\n", "Mix (1): 0.50 \n" ] } ], "source": [ "# print learnt parameters\n", "print(\"Means: %6.2f %6.2f\" % (theta_new[0], theta_new[2]))\n", "print(\"Std dev: %6.2f %6.2f\" % (theta_new[1], theta_new[3]))\n", "print(\"Mix (1): %6.2f \" % theta_new[4])" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "def sim_two_gauss_mix(theta, N=1000): \n", " x1 = np.random.normal(theta[0], theta[1], size=int(N*theta[4]))\n", " x2 = np.random.normal(theta[2], theta[3], size=int(N*(1-theta[4])))\n", " x = np.concatenate([x1,x2])\n", " return x" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/anaconda3/lib/python3.6/site-packages/matplotlib/axes/_axes.py:6499: MatplotlibDeprecationWarning: \n", "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n", " alternative=\"'density'\", removal=\"3.1\")\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# draw samples from the learnt model and compare with the actual data\n", "samples = sim_two_gauss_mix(theta_new)\n", "fig = plt.figure(num=None, figsize=(12, 6), dpi=96, facecolor='w', edgecolor='k')\n", "ax = fig.add_subplot(1,2,1)\n", "ax.set_xlim((-.3,1.2))\n", "ax.set_ylim((0,3))\n", "\n", "ax.hist(samples, bins=20,normed=True,histtype='stepfilled',alpha=0.5,color='r')\n", "t1 = plt.title('Samples generated using EM')\n", "ax = fig.add_subplot(1,2,2)\n", "ax.set_xlim((-.3,1.2))\n", "ax.set_ylim((0,3))\n", "ax.hist(d, bins=20,normed=True,histtype='stepfilled',alpha=0.5)\n", "t2 = plt.title('Observed samples')" ] }, { "cell_type": "markdown", "metadata": { "deletable": true, "editable": true }, "source": [ "### Animated view of 2d mixture learning" ] }, { "cell_type": "code", "execution_count": 17, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "def pltcontour(mu,sigma,ax,c):\n", " x1,x2 = np.mgrid[-3:3:.1, -3:3:.1]\n", " pos = np.dstack((x1, x2))\n", " rv = st.multivariate_normal(mu,sigma)\n", " levels = np.arange(-1.2, 1.6, 0.2)\n", " cn = ax.contour(x1, x2, rv.pdf(pos),1,colors=c,linewidth=16)\n", " return cn\n", " " ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "# load old faithful data\n", "data = []\n", "with open ('../data/oldfaithful.csv','r') as f:\n", " fr = csv.reader(f)\n", " for row in fr:\n", " data.append((float(row[1]),float(row[2])))\n", "data = np.array(data)\n", "data = st.zscore(data)\n" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/anaconda3/lib/python3.6/site-packages/matplotlib/contour.py:1000: UserWarning: The following kwargs were not used by contour: 'linewidth'\n", " s)\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# initialize\n", "mu1 = np.array([-1.5,1.5])\n", "mu2 = np.array([1.5,-1.5])\n", "sig1 = np.eye(2)\n", "sig2 = np.eye(2)\n", "pi = np.array([0.5,0.5])\n", "mu = [mu1, mu2]\n", "sig = [sig1, sig2]\n", "\n", "# plot initial\n", "fig = plt.figure(figsize=[12,24])\n", "#ax = fig.gca()\n", "cnt = 1\n", "ax = plt.subplot(6,2,cnt)\n", "colors = -1*np.ones([data.shape[0],])\n", "\n", "ax.scatter(data[:,0],data[:,1],c=colors,s=48,cmap=plt.colormaps()[29])\n", "# plot contours\n", "pltcontour(mu[0],sig[0],ax,'r')\n", "pltcontour(mu[1],sig[1],ax,'b')\n", "# RUN EM\n", "\n", "max_iter = 50\n", "N_ = np.zeros(2)\n", "\n", "## save data for animations\n", "gammas = []\n", "mus = []\n", "sigs = []\n", "# EM loop\n", "for iters in range(max_iter):\n", " \n", " # E Step\n", " gamma = np.zeros([data.shape[0],2])\n", " rv0 = st.multivariate_normal(mu[0],sig[0])\n", " rv1 = st.multivariate_normal(mu[1],sig[1])\n", "\n", " pdfs1 = rv0.pdf(data)\n", " pdfs2 = rv1.pdf(data)\n", " den = pdfs1*pi[0] + pdfs2*pi[1]\n", " gamma[:,0] = (pdfs1*pi[0])/den\n", " gamma[:,1] = (pdfs2*pi[1])/den\n", " \n", " # M Step\n", " mu = []\n", " pi = np.sum(gamma,axis=0)/data.shape[0]\n", " N_ = 1.*np.sum(gamma,axis=0)\n", " mu.append(sum(np.tile(gamma[:,0:1],[1,2])*data)/N_[0])\n", " mu.append(sum(np.tile(gamma[:,1:2],[1,2])*data)/N_[1])\n", "\n", " s0 = np.zeros(sig[0].shape)\n", " s1 = np.zeros(sig[1].shape)\n", " \n", " for i in range(data.shape[0]):\n", " dm0 = (data[i,:] - mu[0])\n", " dm0 = dm0[:,np.newaxis]\n", " s0 = s0 + gamma[i,0]*np.dot(dm0,np.transpose(dm0))\n", " dm1 = (data[i,:] - mu[1])\n", " dm1 = dm1[:,np.newaxis]\n", " s1 = s1 + gamma[i,1]*np.dot(dm1,np.transpose(dm1))\n", " sig = []\n", " sig.append(s0/N_[0])\n", " sig.append(s1/N_[1])\n", " \n", " # plot every 10th iteration\n", " \n", " if iters%10 == 0:\n", " colors = -1*gamma[:,0] + 1*gamma[:,1]\n", " cnt = cnt + 1\n", " ax = plt.subplot(6,2,cnt)\n", " scat = ax.scatter(data[:,0],data[:,1],c=colors,s=48,cmap=plt.colormaps()[1])\n", " # plot contours\n", " pltcontour(mu[0],sig[0],ax,'r')\n", " pltcontour(mu[1],sig[1],ax,'b')\n", "\n", " ## save data for animations\n", " gammas.append(gamma)\n", " sigs.append(sig)\n", " mus.append(mu)\n", "\n" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "def floatRgb(v, cmin, cmax):\n", " \"\"\"\n", " Return a tuple of floats between 0 and 1 for the red, green and\n", " blue amplitudes.\n", " \"\"\"\n", "\n", " try:\n", " # normalize to [0,1]\n", " x = float(v-cmin)/float(cmax-cmin)\n", " except:\n", " # cmax = cmin\n", " x = 0.5\n", " \n", " blue = min((max((4*(0.75-x), 0.)), 1.))\n", " red = min((max((4*(x-0.25), 0.)), 1.))\n", " green= min((max((4*math.fabs(x-0.5)-1., 0.)), 1.))\n", " return (red, green, blue)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true, "deletable": true, "editable": true }, "outputs": [], "source": [ "from tempfile import NamedTemporaryFile\n", "from matplotlib import animation\n", "from IPython.display import HTML\n", "\n", "VIDEO_TAG = \"\"\"\"\"\"\n", "\n", "def anim_to_html(anim):\n", " if not hasattr(anim, '_encoded_video'):\n", " with NamedTemporaryFile(suffix='.mp4') as f:\n", " anim.save(f.name, fps=20, extra_args=['-vcodec', 'libx264'])\n", " video = open(f.name, \"rb\").read()\n", " anim._encoded_video = video.encode(\"base64\")\n", " \n", " return VIDEO_TAG.format(anim._encoded_video)\n", "\n", "\n", "def display_animation(anim):\n", " plt.close(anim._fig)\n", " return HTML(anim_to_html(anim))" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": false, "deletable": true, "editable": true, "scrolled": false }, "outputs": [ { "ename": "AttributeError", "evalue": "'bytes' object has no attribute 'encode'", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mAttributeError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m()\u001b[0m\n\u001b[1;32m 22\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 23\u001b[0m \u001b[0;31m# call our new function to display the animation\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 24\u001b[0;31m \u001b[0mdisplay_animation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0manim\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m\u001b[0m in \u001b[0;36mdisplay_animation\u001b[0;34m(anim)\u001b[0m\n\u001b[1;32m 20\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mdisplay_animation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0manim\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 21\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclose\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0manim\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_fig\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 22\u001b[0;31m \u001b[0;32mreturn\u001b[0m \u001b[0mHTML\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0manim_to_html\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0manim\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m", "\u001b[0;32m\u001b[0m in \u001b[0;36manim_to_html\u001b[0;34m(anim)\u001b[0m\n\u001b[1;32m 13\u001b[0m \u001b[0manim\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msave\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfps\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m20\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextra_args\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'-vcodec'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'libx264'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 14\u001b[0m \u001b[0mvideo\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mopen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mf\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"rb\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mread\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 15\u001b[0;31m \u001b[0manim\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_encoded_video\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mvideo\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mencode\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"base64\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 16\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 17\u001b[0m \u001b[0;32mreturn\u001b[0m \u001b[0mVIDEO_TAG\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0manim\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_encoded_video\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mAttributeError\u001b[0m: 'bytes' object has no attribute 'encode'" ] } ], "source": [ "# First set up the figure, the axis, and the plot element we want to animate\n", "fig = plt.figure(figsize=[10,8])\n", "ax = plt.axes(xlim=(-4, 4), ylim=(-4, 4))\n", "scat = ax.scatter(data[:,0],data[:,1],s=48,alpha=0.6)\n", "# animation function. This is called sequentially\n", "def init():\n", " return scat\n", "\n", "def animate(i,gammas,mus,sigs):\n", " gamma = gammas[i]\n", " mu = mus[i]\n", " sig = sigs[i]\n", " cvals = -1*gamma[:,0] + 1*gamma[:,1]\n", " colors = [floatRgb(c,-1,1) for c in cvals]\n", " scat.set_facecolors(colors)\n", " scat.set_cmap(plt.colormaps()[29])\n", " #ax = scat.get_axes()\n", " return scat\n", "\n", "# call the animator. blit=True means only re-draw the parts that have changed.\n", "anim = animation.FuncAnimation(fig, animate,init_func=init,fargs=[gammas,mus,sigs],frames=len(gammas), interval=100, blit=False,repeat=True)\n", "\n", "# call our new function to display the animation\n", "display_animation(anim)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 27, "metadata": {}, "output_type": "execute_result" } ], "source": [ "axs = scat.axes\n", "axs." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "import numpy as np\n", "s = np.array([2.3,3.2,3.1,1.6,\n", "1.9,\n", "11.5,\n", "10.2,\n", "12.3,\n", "8.6,\n", "10.9])" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "# sample\n", "max_iter = 2\n", "N = 10\n", "\n", "# Initial guess of parameters and initializations\n", "theta0 = np.array([4,1,6,np.sqrt(2.0),0.5])\n", "mu1, sig1, mu2, sig2, pi_1 = theta0\n", "mu = np.array([mu1, mu2])\n", "sig = np.array([sig1, sig2])\n", "pi_ = np.array([pi_1, 1-pi_1])\n", "\n", "gamma = np.zeros((2, s.size))\n", "N_ = np.zeros(2)\n", "theta_new = theta0\n", "\n", "# EM loop\n", "counter = 0\n", "converged = False\n", "while not converged:\n", " # Compute the responsibility func. and new parameters\n", " for k in [0,1]:\n", " # E Step\n", " gamma[k,:] = pi_[k]*norm.pdf(s, mu[k], sig[k])/pdf_model(s, theta_new)\n", " # M Step\n", " N_[k] = 1.*gamma[k].sum()\n", " mu[k] = sum(gamma[k]*s)/N_[k]\n", " sig[k] = np.sqrt( sum(gamma[k]*(s-mu[k])**2)/N_[k] )\n", " pi_[k] = N_[k]/s.size\n", " theta_new = [mu[0], sig[0], mu[1], sig[1], pi_[0]]\n", " assert abs(N_.sum() - N)/float(N) < 1e-6 \n", " assert abs(pi_.sum() - 1) < 1e-6\n", " print \"iter\"\n", " # Convergence check\n", " counter += 1\n", " converged = counter >= max_iter" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false, "deletable": true, "editable": true }, "outputs": [], "source": [ "#\n", "X = np.array([[7,4,3],[4,1,8],[6,3,5],[8,6,1],[8,5,7],[7,2,9],[5,3,3],[9,5,8],[7,4,5],[8,2,2]])\n", "X1 = X - np.mean(X,axis=0)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "w = np.array([-0.14,-0.25,0.96])\n", "w = w[:,np.newaxis]" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[-2.155],\n", " [ 3.815],\n", " [ 0.155],\n", " [-4.715],\n", " [ 1.295],\n", " [ 4.105],\n", " [-1.625],\n", " [ 2.115],\n", " [-0.235],\n", " [-2.755]])" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "np.dot(X1,w)" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.4" } }, "nbformat": 4, "nbformat_minor": 2 }